LMFDB - Embedded newform 390.2.bb.a.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(121,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("390.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bb (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:	$3.11416567883$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	390.361
Dual form			390.2.bb.a.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-2.59808 - 1.50000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-2.59808 - 1.50000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-3.23205 + 1.86603i) q^{11} +1.00000 q^{12} +(-0.866025 + 3.50000i) q^{13} +3.00000 q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} -1.00000i q^{18} +(-1.96410 - 1.13397i) q^{19} +(0.866025 + 0.500000i) q^{20} -3.00000i q^{21} +(1.86603 - 3.23205i) q^{22} +(1.73205 + 3.00000i) q^{23} +(-0.866025 + 0.500000i) q^{24} -1.00000 q^{25} +(-1.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(-2.59808 + 1.50000i) q^{28} +(2.73205 + 4.73205i) q^{29} +(0.500000 - 0.866025i) q^{30} -8.92820i q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.23205 - 1.86603i) q^{33} -4.00000i q^{34} +(1.50000 - 2.59808i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-6.86603 + 3.96410i) q^{37} +2.26795 q^{38} +(-3.46410 + 1.00000i) q^{39} -1.00000 q^{40} +(3.46410 - 2.00000i) q^{41} +(1.50000 + 2.59808i) q^{42} +(-3.00000 + 5.19615i) q^{43} +3.73205i q^{44} +(-0.866025 - 0.500000i) q^{45} +(-3.00000 - 1.73205i) q^{46} +0.464102i q^{47} +(0.500000 - 0.866025i) q^{48} +(1.00000 + 1.73205i) q^{49} +(0.866025 - 0.500000i) q^{50} -4.00000 q^{51} +(2.59808 + 2.50000i) q^{52} -3.73205 q^{53} +(0.866025 - 0.500000i) q^{54} +(-1.86603 - 3.23205i) q^{55} +(1.50000 - 2.59808i) q^{56} -2.26795i q^{57} +(-4.73205 - 2.73205i) q^{58} +(3.92820 + 2.26795i) q^{59} +1.00000i q^{60} +(3.73205 - 6.46410i) q^{61} +(4.46410 + 7.73205i) q^{62} +(2.59808 - 1.50000i) q^{63} -1.00000 q^{64} +(-3.50000 - 0.866025i) q^{65} +3.73205 q^{66} +(4.73205 - 2.73205i) q^{67} +(2.00000 + 3.46410i) q^{68} +(-1.73205 + 3.00000i) q^{69} +3.00000i q^{70} +(-0.803848 - 0.464102i) q^{71} +(-0.866025 - 0.500000i) q^{72} +6.92820i q^{73} +(3.96410 - 6.86603i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-1.96410 + 1.13397i) q^{76} +11.1962 q^{77} +(2.50000 - 2.59808i) q^{78} +16.9282 q^{79} +(0.866025 - 0.500000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.00000 + 3.46410i) q^{82} +2.53590i q^{83} +(-2.59808 - 1.50000i) q^{84} +(-3.46410 - 2.00000i) q^{85} -6.00000i q^{86} +(-2.73205 + 4.73205i) q^{87} +(-1.86603 - 3.23205i) q^{88} +(-8.76795 + 5.06218i) q^{89} +1.00000 q^{90} +(7.50000 - 7.79423i) q^{91} +3.46410 q^{92} +(7.73205 - 4.46410i) q^{93} +(-0.232051 - 0.401924i) q^{94} +(1.13397 - 1.96410i) q^{95} +1.00000i q^{96} +(10.7321 + 6.19615i) q^{97} +(-1.73205 - 1.00000i) q^{98} -3.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9	$ 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{10} - 6 q^{11} + 4 q^{12} + 12 q^{14} - 2 q^{16} - 8 q^{17} + 6 q^{19} + 4 q^{22} - 4 q^{25} - 4 q^{26} - 4 q^{27} + 4 q^{29} + 2 q^{30} - 6 q^{33} + 6 q^{35} + 2 q^{36} - 24 q^{37} + 16 q^{38} - 4 q^{40} + 6 q^{42} - 12 q^{43} - 12 q^{46} + 2 q^{48} + 4 q^{49} - 16 q^{51} - 8 q^{53} - 4 q^{55} + 6 q^{56} - 12 q^{58} - 12 q^{59} + 8 q^{61} + 4 q^{62} - 4 q^{64} - 14 q^{65} + 8 q^{66} + 12 q^{67} + 8 q^{68} - 24 q^{71} + 2 q^{74} - 2 q^{75} + 6 q^{76} + 24 q^{77} + 10 q^{78} + 40 q^{79} - 2 q^{81} - 8 q^{82} - 4 q^{87} - 4 q^{88} - 42 q^{89} + 4 q^{90} + 30 q^{91} + 24 q^{93} + 6 q^{94} + 8 q^{95} + 36 q^{97}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^10 - 6 * q^11 + 4 * q^12 + 12 * q^14 - 2 * q^16 - 8 * q^17 + 6 * q^19 + 4 * q^22 - 4 * q^25 - 4 * q^26 - 4 * q^27 + 4 * q^29 + 2 * q^30 - 6 * q^33 + 6 * q^35 + 2 * q^36 - 24 * q^37 + 16 * q^38 - 4 * q^40 + 6 * q^42 - 12 * q^43 - 12 * q^46 + 2 * q^48 + 4 * q^49 - 16 * q^51 - 8 * q^53 - 4 * q^55 + 6 * q^56 - 12 * q^58 - 12 * q^59 + 8 * q^61 + 4 * q^62 - 4 * q^64 - 14 * q^65 + 8 * q^66 + 12 * q^67 + 8 * q^68 - 24 * q^71 + 2 * q^74 - 2 * q^75 + 6 * q^76 + 24 * q^77 + 10 * q^78 + 40 * q^79 - 2 * q^81 - 8 * q^82 - 4 * q^87 - 4 * q^88 - 42 * q^89 + 4 * q^90 + 30 * q^91 + 24 * q^93 + 6 * q^94 + 8 * q^95 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	−2.59808	−	1.50000i	−0.981981	−	0.566947i	−0.0791130	−	0.996866i	$-0.525209\pi$
$7$	−2.59808	−	1.50000i	−0.981981	−	0.566947i	−0.902867	+	0.429919i	$0.858542\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−3.23205	+	1.86603i	−0.974500	+	0.562628i	−0.900605	−	0.434638i	$-0.856876\pi$
$11$	−3.23205	+	1.86603i	−0.974500	+	0.562628i	−0.0738948	+	0.997266i	$0.523543\pi$
$12$	1.00000			0.288675
$13$	−0.866025	+	3.50000i	−0.240192	+	0.970725i
$13$	−0.866025	+	3.50000i	−0.240192	+	0.970725i
$14$	3.00000			0.801784
$15$	−0.866025	+	0.500000i	−0.223607	+	0.129099i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−1.96410	−	1.13397i	−0.450596	−	0.260152i	0.257486	−	0.966282i	$-0.417106\pi$
$19$	−1.96410	−	1.13397i	−0.450596	−	0.260152i	−0.708082	+	0.706130i	$0.750439\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$		−	3.00000i		−	0.654654i
$22$	1.86603	−	3.23205i	0.397838	−	0.689076i
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	0.988152	−	0.153481i	$-0.0490483\pi$
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	−0.626994	+	0.779024i	$0.715715\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	−1.00000			−0.200000
$26$	−1.00000	−	3.46410i	−0.196116	−	0.679366i
$27$	−1.00000			−0.192450
$28$	−2.59808	+	1.50000i	−0.490990	+	0.283473i
$29$	2.73205	+	4.73205i	0.507329	+	0.878720i	0.999964	+	0.00848369i	$0.00270048\pi$
$29$	2.73205	+	4.73205i	0.507329	+	0.878720i	−0.492635	+	0.870236i	$0.663966\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$		−	8.92820i		−	1.60355i	−0.597624	−	0.801776i	$-0.703889\pi$
$31$		−	8.92820i		−	1.60355i	0.597624	−	0.801776i	$-0.296111\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−3.23205	−	1.86603i	−0.562628	−	0.324833i
$34$		−	4.00000i		−	0.685994i
$35$	1.50000	−	2.59808i	0.253546	−	0.439155i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−6.86603	+	3.96410i	−1.12877	+	0.651694i	−0.943625	−	0.331017i	$-0.892608\pi$
$37$	−6.86603	+	3.96410i	−1.12877	+	0.651694i	−0.185143	+	0.982712i	$0.559275\pi$
$38$	2.26795			0.367910
$39$	−3.46410	+	1.00000i	−0.554700	+	0.160128i
$40$	−1.00000			−0.158114
$41$	3.46410	−	2.00000i	0.541002	−	0.312348i	−0.204483	−	0.978870i	$-0.565551\pi$
$41$	3.46410	−	2.00000i	0.541002	−	0.312348i	0.745485	+	0.666523i	$0.232218\pi$
$42$	1.50000	+	2.59808i	0.231455	+	0.400892i
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	−0.998828	−	0.0484030i	$-0.984587\pi$
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	0.541332	+	0.840809i	$0.317920\pi$
$44$			3.73205i			0.562628i
$45$	−0.866025	−	0.500000i	−0.129099	−	0.0745356i
$46$	−3.00000	−	1.73205i	−0.442326	−	0.255377i
$47$			0.464102i			0.0676962i	0.999427	+	0.0338481i	$0.0107762\pi$
$47$			0.464102i			0.0676962i	−0.999427	+	0.0338481i	$0.989224\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	1.00000	+	1.73205i	0.142857	+	0.247436i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	−4.00000			−0.560112
$52$	2.59808	+	2.50000i	0.360288	+	0.346688i
$53$	−3.73205			−0.512637			−0.256318	−	0.966592i	$-0.582510\pi$
$53$	−3.73205			−0.512637			−0.256318	+	0.966592i	$0.582510\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−1.86603	−	3.23205i	−0.251615	−	0.435810i
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$		−	2.26795i		−	0.300397i
$58$	−4.73205	−	2.73205i	−0.621349	−	0.358736i
$59$	3.92820	+	2.26795i	0.511409	+	0.295262i	0.733412	−	0.679784i	$-0.237926\pi$
$59$	3.92820	+	2.26795i	0.511409	+	0.295262i	−0.222004	+	0.975046i	$0.571260\pi$
$60$			1.00000i			0.129099i
$61$	3.73205	−	6.46410i	0.477840	−	0.827643i	−0.521837	−	0.853045i	$-0.674753\pi$
$61$	3.73205	−	6.46410i	0.477840	−	0.827643i	0.999677	+	0.0254017i	$0.00808648\pi$
$62$	4.46410	+	7.73205i	0.566941	+	0.981971i
$63$	2.59808	−	1.50000i	0.327327	−	0.188982i
$64$	−1.00000			−0.125000
$65$	−3.50000	−	0.866025i	−0.434122	−	0.107417i
$66$	3.73205			0.459384
$67$	4.73205	−	2.73205i	0.578112	−	0.333773i	−0.182271	−	0.983248i	$-0.558345\pi$
$67$	4.73205	−	2.73205i	0.578112	−	0.333773i	0.760383	+	0.649475i	$0.225011\pi$
$68$	2.00000	+	3.46410i	0.242536	+	0.420084i
$69$	−1.73205	+	3.00000i	−0.208514	+	0.361158i
$70$			3.00000i			0.358569i
$71$	−0.803848	−	0.464102i	−0.0953992	−	0.0550787i	0.451541	−	0.892250i	$-0.350874\pi$
$71$	−0.803848	−	0.464102i	−0.0953992	−	0.0550787i	−0.546941	+	0.837171i	$0.684208\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$			6.92820i			0.810885i	0.914121	+	0.405442i	$0.132883\pi$
$73$			6.92820i			0.810885i	−0.914121	+	0.405442i	$0.867117\pi$
$74$	3.96410	−	6.86603i	0.460817	−	0.798159i
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$	−1.96410	+	1.13397i	−0.225298	+	0.130076i
$77$	11.1962			1.27592
$78$	2.50000	−	2.59808i	0.283069	−	0.294174i
$79$	16.9282			1.90457			0.952286	−	0.305208i	$-0.0987259\pi$
$79$	16.9282			1.90457			0.952286	+	0.305208i	$0.0987259\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.00000	+	3.46410i	−0.220863	+	0.382546i
$83$			2.53590i			0.278351i	0.990268	+	0.139176i	$0.0444452\pi$
$83$			2.53590i			0.278351i	−0.990268	+	0.139176i	$0.955555\pi$
$84$	−2.59808	−	1.50000i	−0.283473	−	0.163663i
$85$	−3.46410	−	2.00000i	−0.375735	−	0.216930i
$86$		−	6.00000i		−	0.646997i
$87$	−2.73205	+	4.73205i	−0.292907	+	0.507329i
$88$	−1.86603	−	3.23205i	−0.198919	−	0.344538i
$89$	−8.76795	+	5.06218i	−0.929401	+	0.536590i	−0.886622	−	0.462495i	$-0.846954\pi$
$89$	−8.76795	+	5.06218i	−0.929401	+	0.536590i	−0.0427788	+	0.999085i	$0.513621\pi$
$90$	1.00000			0.105409
$91$	7.50000	−	7.79423i	0.786214	−	0.817057i
$92$	3.46410			0.361158
$93$	7.73205	−	4.46410i	0.801776	−	0.462906i
$94$	−0.232051	−	0.401924i	−0.0239342	−	0.0414553i
$95$	1.13397	−	1.96410i	0.116343	−	0.201513i
$96$			1.00000i			0.102062i
$97$	10.7321	+	6.19615i	1.08967	+	0.629124i	0.933490	−	0.358604i	$-0.116747\pi$
$97$	10.7321	+	6.19615i	1.08967	+	0.629124i	0.156185	+	0.987728i	$0.450080\pi$
$98$	−1.73205	−	1.00000i	−0.174964	−	0.101015i
$99$		−	3.73205i		−	0.375085i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	4.19615	+	7.26795i	0.417533	+	0.723188i	0.995691	−	0.0927369i	$-0.0295616\pi$
$101$	4.19615	+	7.26795i	0.417533	+	0.723188i	−0.578158	+	0.815925i	$0.696228\pi$
$102$	3.46410	−	2.00000i	0.342997	−	0.198030i
$103$	19.5885			1.93011			0.965054	−	0.262051i	$-0.0843989\pi$
$103$	19.5885			1.93011			0.965054	+	0.262051i	$0.0843989\pi$
$104$	−3.50000	−	0.866025i	−0.343203	−	0.0849208i
$105$	3.00000			0.292770
$106$	3.23205	−	1.86603i	0.313925	−	0.181244i
$107$	−0.464102	−	0.803848i	−0.0448664	−	0.0777109i	0.842720	−	0.538352i	$-0.180953\pi$
$107$	−0.464102	−	0.803848i	−0.0448664	−	0.0777109i	−0.887587	+	0.460641i	$0.847620\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$			10.3923i			0.995402i	0.867349	+	0.497701i	$0.165822\pi$
$109$			10.3923i			0.995402i	−0.867349	+	0.497701i	$0.834178\pi$
$110$	3.23205	+	1.86603i	0.308164	+	0.177919i
$111$	−6.86603	−	3.96410i	−0.651694	−	0.376256i
$112$			3.00000i			0.283473i
$113$	6.00000	−	10.3923i	0.564433	−	0.977626i	−0.432670	−	0.901553i	$-0.642428\pi$
$113$	6.00000	−	10.3923i	0.564433	−	0.977626i	0.997102	−	0.0760733i	$-0.0242383\pi$
$114$	1.13397	+	1.96410i	0.106206	+	0.183955i
$115$	−3.00000	+	1.73205i	−0.279751	+	0.161515i
$116$	5.46410			0.507329
$117$	−2.59808	−	2.50000i	−0.240192	−	0.231125i
$118$	−4.53590			−0.417563
$119$	10.3923	−	6.00000i	0.952661	−	0.550019i
$120$	−0.500000	−	0.866025i	−0.0456435	−	0.0790569i
$121$	1.46410	−	2.53590i	0.133100	−	0.230536i
$122$			7.46410i			0.675768i
$123$	3.46410	+	2.00000i	0.312348	+	0.180334i
$124$	−7.73205	−	4.46410i	−0.694359	−	0.400888i
$125$		−	1.00000i		−	0.0894427i
$126$	−1.50000	+	2.59808i	−0.133631	+	0.231455i
$127$	−2.33013	−	4.03590i	−0.206765	−	0.358128i	0.743928	−	0.668259i	$-0.232960\pi$
$127$	−2.33013	−	4.03590i	−0.206765	−	0.358128i	−0.950694	+	0.310131i	$0.899627\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−6.00000			−0.528271
$130$	3.46410	−	1.00000i	0.303822	−	0.0877058i
$131$	−20.3205			−1.77541			−0.887706	−	0.460412i	$-0.847702\pi$
$131$	−20.3205			−1.77541			−0.887706	+	0.460412i	$0.847702\pi$
$132$	−3.23205	+	1.86603i	−0.281314	+	0.162417i
$133$	3.40192	+	5.89230i	0.294984	+	0.510928i
$134$	−2.73205	+	4.73205i	−0.236013	+	0.408787i
$135$		−	1.00000i		−	0.0860663i
$136$	−3.46410	−	2.00000i	−0.297044	−	0.171499i
$137$	−5.66025	−	3.26795i	−0.483588	−	0.279200i	0.238322	−	0.971186i	$-0.423402\pi$
$137$	−5.66025	−	3.26795i	−0.483588	−	0.279200i	−0.721911	+	0.691986i	$0.756736\pi$
$138$		−	3.46410i		−	0.294884i
$139$	−10.8923	+	18.8660i	−0.923873	+	1.60020i	−0.130510	+	0.991447i	$0.541661\pi$
$139$	−10.8923	+	18.8660i	−0.923873	+	1.60020i	−0.793363	+	0.608748i	$0.791672\pi$
$140$	−1.50000	−	2.59808i	−0.126773	−	0.219578i
$141$	−0.401924	+	0.232051i	−0.0338481	+	0.0195422i
$142$	0.928203			0.0778931
$143$	−3.73205	−	12.9282i	−0.312090	−	1.08111i
$144$	1.00000			0.0833333
$145$	−4.73205	+	2.73205i	−0.392975	+	0.226884i
$146$	−3.46410	−	6.00000i	−0.286691	−	0.496564i
$147$	−1.00000	+	1.73205i	−0.0824786	+	0.142857i
$148$			7.92820i			0.651694i
$149$	19.7321	+	11.3923i	1.61651	+	0.933294i	0.987813	+	0.155646i	$0.0497458\pi$
$149$	19.7321	+	11.3923i	1.61651	+	0.933294i	0.628700	+	0.777648i	$0.283587\pi$
$150$	0.866025	+	0.500000i	0.0707107	+	0.0408248i
$151$		−	18.7846i		−	1.52867i	−0.644819	−	0.764335i	$-0.723067\pi$
$151$		−	18.7846i		−	1.52867i	0.644819	−	0.764335i	$-0.276933\pi$
$152$	1.13397	−	1.96410i	0.0919775	−	0.159310i
$153$	−2.00000	−	3.46410i	−0.161690	−	0.280056i
$154$	−9.69615	+	5.59808i	−0.781338	+	0.451106i
$155$	8.92820			0.717131
$156$	−0.866025	+	3.50000i	−0.0693375	+	0.280224i
$157$	10.8038			0.862241			0.431120	−	0.902294i	$-0.358118\pi$
$157$	10.8038			0.862241			0.431120	+	0.902294i	$0.358118\pi$
$158$	−14.6603	+	8.46410i	−1.16631	+	0.673368i
$159$	−1.86603	−	3.23205i	−0.147985	−	0.256318i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$		−	10.3923i		−	0.819028i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	−9.46410	−	5.46410i	−0.741286	−	0.427981i	0.0812509	−	0.996694i	$-0.474108\pi$
$163$	−9.46410	−	5.46410i	−0.741286	−	0.427981i	−0.822537	+	0.568712i	$0.807442\pi$
$164$		−	4.00000i		−	0.312348i
$165$	1.86603	−	3.23205i	0.145270	−	0.251615i
$166$	−1.26795	−	2.19615i	−0.0984119	−	0.170454i
$167$	−5.59808	+	3.23205i	−0.433192	+	0.250104i	−0.700706	−	0.713451i	$-0.747131\pi$
$167$	−5.59808	+	3.23205i	−0.433192	+	0.250104i	0.267513	+	0.963554i	$0.413798\pi$
$168$	3.00000			0.231455
$169$	−11.5000	−	6.06218i	−0.884615	−	0.466321i
$170$	4.00000			0.306786
$171$	1.96410	−	1.13397i	0.150199	−	0.0867172i
$172$	3.00000	+	5.19615i	0.228748	+	0.396203i
$173$	−11.0622	+	19.1603i	−0.841042	+	1.45673i	0.0479730	+	0.998849i	$0.484724\pi$
$173$	−11.0622	+	19.1603i	−0.841042	+	1.45673i	−0.889015	+	0.457879i	$0.848609\pi$
$174$		−	5.46410i		−	0.414232i
$175$	2.59808	+	1.50000i	0.196396	+	0.113389i
$176$	3.23205	+	1.86603i	0.243625	+	0.140657i
$177$			4.53590i			0.340939i
$178$	5.06218	−	8.76795i	0.379426	−	0.657186i
$179$	−11.4641	−	19.8564i	−0.856867	−	1.48414i	−0.874902	−	0.484300i	$-0.839074\pi$
$179$	−11.4641	−	19.8564i	−0.856867	−	1.48414i	0.0180347	−	0.999837i	$-0.494259\pi$
$180$	−0.866025	+	0.500000i	−0.0645497	+	0.0372678i
$181$	3.07180			0.228325			0.114162	−	0.993462i	$-0.463582\pi$
$181$	3.07180			0.228325			0.114162	+	0.993462i	$0.463582\pi$
$182$	−2.59808	+	10.5000i	−0.192582	+	0.778312i
$183$	7.46410			0.551762
$184$	−3.00000	+	1.73205i	−0.221163	+	0.127688i
$185$	−3.96410	−	6.86603i	−0.291447	−	0.504800i
$186$	−4.46410	+	7.73205i	−0.327324	+	0.566941i
$187$		−	14.9282i		−	1.09166i
$188$	0.401924	+	0.232051i	0.0293133	+	0.0169240i
$189$	2.59808	+	1.50000i	0.188982	+	0.109109i
$190$			2.26795i			0.164534i
$191$	−8.66025	+	15.0000i	−0.626634	+	1.08536i	0.361588	+	0.932338i	$0.382235\pi$
$191$	−8.66025	+	15.0000i	−0.626634	+	1.08536i	−0.988222	+	0.153024i	$0.951099\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−15.4641	+	8.92820i	−1.11313	+	0.642666i	−0.939638	−	0.342169i	$-0.888838\pi$
$193$	−15.4641	+	8.92820i	−1.11313	+	0.642666i	−0.173492	+	0.984835i	$0.555505\pi$
$194$	−12.3923			−0.889716
$195$	−1.00000	−	3.46410i	−0.0716115	−	0.248069i
$196$	2.00000			0.142857
$197$	−8.13397	+	4.69615i	−0.579522	+	0.334587i	−0.760943	−	0.648818i	$-0.775263\pi$
$197$	−8.13397	+	4.69615i	−0.579522	+	0.334587i	0.181422	+	0.983405i	$0.441930\pi$
$198$	1.86603	+	3.23205i	0.132613	+	0.229692i
$199$	5.53590	−	9.58846i	0.392429	−	0.679708i	−0.600340	−	0.799745i	$-0.704968\pi$
$199$	5.53590	−	9.58846i	0.392429	−	0.679708i	0.992769	+	0.120037i	$0.0383014\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	4.73205	+	2.73205i	0.333773	+	0.192704i
$202$	−7.26795	−	4.19615i	−0.511371	−	0.295240i
$203$		−	16.3923i		−	1.15051i
$204$	−2.00000	+	3.46410i	−0.140028	+	0.242536i
$205$	2.00000	+	3.46410i	0.139686	+	0.241943i
$206$	−16.9641	+	9.79423i	−1.18194	+	0.682396i
$207$	−3.46410			−0.240772
$208$	3.46410	−	1.00000i	0.240192	−	0.0693375i
$209$	8.46410			0.585474
$210$	−2.59808	+	1.50000i	−0.179284	+	0.103510i
$211$	10.9641	+	18.9904i	0.754800	+	1.30735i	0.945474	+	0.325698i	$0.105599\pi$
$211$	10.9641	+	18.9904i	0.754800	+	1.30735i	−0.190674	+	0.981653i	$0.561067\pi$
$212$	−1.86603	+	3.23205i	−0.128159	+	0.221978i
$213$		−	0.928203i		−	0.0635994i
$214$	0.803848	+	0.464102i	0.0549499	+	0.0317253i
$215$	−5.19615	−	3.00000i	−0.354375	−	0.204598i
$216$		−	1.00000i		−	0.0680414i
$217$	−13.3923	+	23.1962i	−0.909129	+	1.57466i
$218$	−5.19615	−	9.00000i	−0.351928	−	0.609557i
$219$	−6.00000	+	3.46410i	−0.405442	+	0.234082i
$220$	−3.73205			−0.251615
$221$	−10.3923	−	10.0000i	−0.699062	−	0.672673i
$222$	7.92820			0.532106
$223$	−7.66987	+	4.42820i	−0.513613	+	0.296534i	−0.734317	−	0.678806i	$-0.762498\pi$
$223$	−7.66987	+	4.42820i	−0.513613	+	0.296534i	0.220705	+	0.975341i	$0.429164\pi$
$224$	−1.50000	−	2.59808i	−0.100223	−	0.173591i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$			12.0000i			0.798228i
$227$	−11.6603	−	6.73205i	−0.773918	−	0.446822i	0.0603523	−	0.998177i	$-0.480778\pi$
$227$	−11.6603	−	6.73205i	−0.773918	−	0.446822i	−0.834271	+	0.551355i	$0.814111\pi$
$228$	−1.96410	−	1.13397i	−0.130076	−	0.0750993i
$229$			11.4641i			0.757569i	0.925485	+	0.378785i	$0.123658\pi$
$229$			11.4641i			0.757569i	−0.925485	+	0.378785i	$0.876342\pi$
$230$	1.73205	−	3.00000i	0.114208	−	0.197814i
$231$	5.59808	+	9.69615i	0.368326	+	0.637960i
$232$	−4.73205	+	2.73205i	−0.310674	+	0.179368i
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$	3.50000	+	0.866025i	0.228802	+	0.0566139i
$235$	−0.464102			−0.0302747
$236$	3.92820	−	2.26795i	0.255704	−	0.147631i
$237$	8.46410	+	14.6603i	0.549802	+	0.952286i
$238$	−6.00000	+	10.3923i	−0.388922	+	0.673633i
$239$			3.46410i			0.224074i	0.993704	+	0.112037i	$0.0357375\pi$
$239$			3.46410i			0.224074i	−0.993704	+	0.112037i	$0.964262\pi$
$240$	0.866025	+	0.500000i	0.0559017	+	0.0322749i
$241$	12.8205	+	7.40192i	0.825842	+	0.476800i	0.852427	−	0.522847i	$-0.175130\pi$
$241$	12.8205	+	7.40192i	0.825842	+	0.476800i	−0.0265852	+	0.999647i	$0.508463\pi$
$242$			2.92820i			0.188232i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−3.73205	−	6.46410i	−0.238920	−	0.413822i
$245$	−1.73205	+	1.00000i	−0.110657	+	0.0638877i
$246$	−4.00000			−0.255031
$247$	5.66987	−	5.89230i	0.360765	−	0.374918i
$248$	8.92820			0.566941
$249$	−2.19615	+	1.26795i	−0.139176	+	0.0803530i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−13.2321	+	22.9186i	−0.835200	+	1.44661i	0.0586681	+	0.998278i	$0.481315\pi$
$251$	−13.2321	+	22.9186i	−0.835200	+	1.44661i	−0.893868	+	0.448331i	$0.852019\pi$
$252$		−	3.00000i		−	0.188982i
$253$	−11.1962	−	6.46410i	−0.703896	−	0.406395i
$254$	4.03590	+	2.33013i	0.253235	+	0.146205i
$255$		−	4.00000i		−	0.250490i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.7321	−	18.5885i	−0.669447	−	1.15952i	−0.978059	−	0.208328i	$-0.933198\pi$
$257$	−10.7321	−	18.5885i	−0.669447	−	1.15952i	0.308612	−	0.951188i	$-0.400136\pi$
$258$	5.19615	−	3.00000i	0.323498	−	0.186772i
$259$	23.7846			1.47790
$260$	−2.50000	+	2.59808i	−0.155043	+	0.161126i
$261$	−5.46410			−0.338219
$262$	17.5981	−	10.1603i	1.08721	−	0.627703i
$263$	−10.2583	−	17.7679i	−0.632556	−	1.09562i	−0.987027	−	0.160552i	$-0.948673\pi$
$263$	−10.2583	−	17.7679i	−0.632556	−	1.09562i	0.354472	−	0.935067i	$-0.384661\pi$
$264$	1.86603	−	3.23205i	0.114846	−	0.198919i
$265$		−	3.73205i		−	0.229258i
$266$	−5.89230	−	3.40192i	−0.361280	−	0.208585i
$267$	−8.76795	−	5.06218i	−0.536590	−	0.309800i
$268$		−	5.46410i		−	0.333773i
$269$	15.4641	−	26.7846i	0.942863	−	1.63309i	0.182888	−	0.983134i	$-0.441455\pi$
$269$	15.4641	−	26.7846i	0.942863	−	1.63309i	0.759975	−	0.649953i	$-0.225211\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	−3.12436	+	1.80385i	−0.189791	+	0.109576i	−0.591885	−	0.806023i	$-0.701616\pi$
$271$	−3.12436	+	1.80385i	−0.189791	+	0.109576i	0.402094	+	0.915599i	$0.368283\pi$
$272$	4.00000			0.242536
$273$	10.5000	+	2.59808i	0.635489	+	0.157243i
$274$	6.53590			0.394848
$275$	3.23205	−	1.86603i	0.194900	−	0.112526i
$276$	1.73205	+	3.00000i	0.104257	+	0.180579i
$277$	9.79423	−	16.9641i	0.588478	−	1.01927i	−0.405954	−	0.913894i	$-0.633061\pi$
$277$	9.79423	−	16.9641i	0.588478	−	1.01927i	0.994432	−	0.105380i	$-0.0336060\pi$
$278$		−	21.7846i		−	1.30655i
$279$	7.73205	+	4.46410i	0.462906	+	0.267259i
$280$	2.59808	+	1.50000i	0.155265	+	0.0896421i
$281$			6.92820i			0.413302i	0.978415	+	0.206651i	$0.0662565\pi$
$281$			6.92820i			0.413302i	−0.978415	+	0.206651i	$0.933744\pi$
$282$	0.232051	−	0.401924i	0.0138184	−	0.0239342i
$283$	−7.19615	−	12.4641i	−0.427767	−	0.740914i	0.568907	−	0.822402i	$-0.307366\pi$
$283$	−7.19615	−	12.4641i	−0.427767	−	0.740914i	−0.996674	+	0.0814876i	$0.974033\pi$
$284$	−0.803848	+	0.464102i	−0.0476996	+	0.0275394i
$285$	2.26795			0.134342
$286$	9.69615	+	9.33013i	0.573346	+	0.551702i
$287$	−12.0000			−0.708338
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	2.73205	−	4.73205i	0.160432	−	0.277876i
$291$			12.3923i			0.726450i
$292$	6.00000	+	3.46410i	0.351123	+	0.202721i
$293$	16.6699	+	9.62436i	0.973864	+	0.562261i	0.900412	−	0.435038i	$-0.143265\pi$
$293$	16.6699	+	9.62436i	0.973864	+	0.562261i	0.0734522	+	0.997299i	$0.476598\pi$
$294$		−	2.00000i		−	0.116642i
$295$	−2.26795	+	3.92820i	−0.132045	+	0.228709i
$296$	−3.96410	−	6.86603i	−0.230409	−	0.399080i
$297$	3.23205	−	1.86603i	0.187543	−	0.108278i
$298$	−22.7846			−1.31988
$299$	−12.0000	+	3.46410i	−0.693978	+	0.200334i
$300$	−1.00000			−0.0577350
$301$	15.5885	−	9.00000i	0.898504	−	0.518751i
$302$	9.39230	+	16.2679i	0.540466	+	0.936115i
$303$	−4.19615	+	7.26795i	−0.241063	+	0.417533i
$304$			2.26795i			0.130076i
$305$	6.46410	+	3.73205i	0.370133	+	0.213697i
$306$	3.46410	+	2.00000i	0.198030	+	0.114332i
$307$		−	20.2487i		−	1.15565i	−0.816159	−	0.577827i	$-0.803901\pi$
$307$		−	20.2487i		−	1.15565i	0.816159	−	0.577827i	$-0.196099\pi$
$308$	5.59808	−	9.69615i	0.318980	−	0.552490i
$309$	9.79423	+	16.9641i	0.557174	+	0.965054i
$310$	−7.73205	+	4.46410i	−0.439151	+	0.253544i
$311$	5.07180			0.287595			0.143798	−	0.989607i	$-0.454069\pi$
$311$	5.07180			0.287595			0.143798	+	0.989607i	$0.454069\pi$
$312$	−1.00000	−	3.46410i	−0.0566139	−	0.196116i
$313$	1.32051			0.0746395			0.0373198	−	0.999303i	$-0.488118\pi$
$313$	1.32051			0.0746395			0.0373198	+	0.999303i	$0.488118\pi$
$314$	−9.35641	+	5.40192i	−0.528013	+	0.304848i
$315$	1.50000	+	2.59808i	0.0845154	+	0.146385i
$316$	8.46410	−	14.6603i	0.476143	−	0.824704i
$317$		−	23.5359i		−	1.32191i	−0.750427	−	0.660954i	$-0.770152\pi$
$317$		−	23.5359i		−	1.32191i	0.750427	−	0.660954i	$-0.229848\pi$
$318$	3.23205	+	1.86603i	0.181244	+	0.104642i
$319$	−17.6603	−	10.1962i	−0.988784	−	0.570875i
$320$		−	1.00000i		−	0.0559017i
$321$	0.464102	−	0.803848i	0.0259036	−	0.0448664i
$322$	5.19615	+	9.00000i	0.289570	+	0.501550i
$323$	7.85641	−	4.53590i	0.437142	−	0.252384i
$324$	−1.00000			−0.0555556
$325$	0.866025	−	3.50000i	0.0480384	−	0.194145i
$326$	10.9282			0.605257
$327$	−9.00000	+	5.19615i	−0.497701	+	0.287348i
$328$	2.00000	+	3.46410i	0.110432	+	0.191273i
$329$	0.696152	−	1.20577i	0.0383801	−	0.0664763i
$330$			3.73205i			0.205443i
$331$	5.53590	+	3.19615i	0.304280	+	0.175676i	0.644364	−	0.764719i	$-0.277122\pi$
$331$	5.53590	+	3.19615i	0.304280	+	0.175676i	−0.340084	+	0.940395i	$0.610455\pi$
$332$	2.19615	+	1.26795i	0.120530	+	0.0695878i
$333$		−	7.92820i		−	0.434463i
$334$	3.23205	−	5.59808i	0.176850	−	0.306313i
$335$	2.73205	+	4.73205i	0.149268	+	0.258540i
$336$	−2.59808	+	1.50000i	−0.141737	+	0.0818317i
$337$	−5.60770			−0.305471			−0.152735	−	0.988267i	$-0.548808\pi$
$337$	−5.60770			−0.305471			−0.152735	+	0.988267i	$0.548808\pi$
$338$	12.9904	−	0.500000i	0.706584	−	0.0271964i
$339$	12.0000			0.651751
$340$	−3.46410	+	2.00000i	−0.187867	+	0.108465i
$341$	16.6603	+	28.8564i	0.902203	+	1.56266i
$342$	−1.13397	+	1.96410i	−0.0613183	+	0.106206i
$343$			15.0000i			0.809924i
$344$	−5.19615	−	3.00000i	−0.280158	−	0.161749i
$345$	−3.00000	−	1.73205i	−0.161515	−	0.0932505i
$346$		−	22.1244i		−	1.18941i
$347$	8.19615	−	14.1962i	0.439993	−	0.762089i	−0.557696	−	0.830045i	$-0.688314\pi$
$347$	8.19615	−	14.1962i	0.439993	−	0.762089i	0.997688	+	0.0679560i	$0.0216478\pi$
$348$	2.73205	+	4.73205i	0.146453	+	0.253665i
$349$	15.1244	−	8.73205i	0.809588	−	0.467416i	−0.0372247	−	0.999307i	$-0.511852\pi$
$349$	15.1244	−	8.73205i	0.809588	−	0.467416i	0.846813	+	0.531891i	$0.178518\pi$
$350$	−3.00000			−0.160357
$351$	0.866025	−	3.50000i	0.0462250	−	0.186816i
$352$	−3.73205			−0.198919
$353$	−24.5885	+	14.1962i	−1.30871	+	0.755585i	−0.981881	−	0.189498i	$-0.939314\pi$
$353$	−24.5885	+	14.1962i	−1.30871	+	0.755585i	−0.326830	+	0.945083i	$0.605981\pi$
$354$	−2.26795	−	3.92820i	−0.120540	−	0.208782i
$355$	0.464102	−	0.803848i	0.0246320	−	0.0426638i
$356$			10.1244i			0.536590i
$357$	10.3923	+	6.00000i	0.550019	+	0.317554i
$358$	19.8564	+	11.4641i	1.04944	+	0.605897i
$359$			12.9282i			0.682324i	0.940004	+	0.341162i	$0.110821\pi$
$359$			12.9282i			0.682324i	−0.940004	+	0.341162i	$0.889179\pi$
$360$	0.500000	−	0.866025i	0.0263523	−	0.0456435i
$361$	−6.92820	−	12.0000i	−0.364642	−	0.631579i
$362$	−2.66025	+	1.53590i	−0.139820	+	0.0807250i
$363$	2.92820			0.153691
$364$	−3.00000	−	10.3923i	−0.157243	−	0.544705i
$365$	−6.92820			−0.362639
$366$	−6.46410	+	3.73205i	−0.337884	+	0.195077i
$367$	6.66025	+	11.5359i	0.347662	+	0.602169i	0.985834	−	0.167725i	$-0.0536422\pi$
$367$	6.66025	+	11.5359i	0.347662	+	0.602169i	−0.638171	+	0.769894i	$0.720309\pi$
$368$	1.73205	−	3.00000i	0.0902894	−	0.156386i
$369$			4.00000i			0.208232i
$370$	6.86603	+	3.96410i	0.356948	+	0.206084i
$371$	9.69615	+	5.59808i	0.503399	+	0.290638i
$372$		−	8.92820i		−	0.462906i
$373$	−11.4641	+	19.8564i	−0.593589	+	1.02813i	0.400156	+	0.916447i	$0.368956\pi$
$373$	−11.4641	+	19.8564i	−0.593589	+	1.02813i	−0.993744	+	0.111679i	$0.964377\pi$
$374$	7.46410	+	12.9282i	0.385960	+	0.668501i
$375$	0.866025	−	0.500000i	0.0447214	−	0.0258199i
$376$	−0.464102			−0.0239342
$377$	−18.9282	+	5.46410i	−0.974852	+	0.281416i
$378$	−3.00000			−0.154303
$379$	5.42820	−	3.13397i	0.278828	−	0.160981i	−0.354065	−	0.935221i	$-0.615201\pi$
$379$	5.42820	−	3.13397i	0.278828	−	0.160981i	0.632893	+	0.774239i	$0.281867\pi$
$380$	−1.13397	−	1.96410i	−0.0581717	−	0.100756i
$381$	2.33013	−	4.03590i	0.119376	−	0.206765i
$382$		−	17.3205i		−	0.886194i
$383$	31.8564	+	18.3923i	1.62779	+	0.939803i	0.984752	+	0.173966i	$0.0556582\pi$
$383$	31.8564	+	18.3923i	1.62779	+	0.939803i	0.643035	+	0.765837i	$0.277675\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$			11.1962i			0.570609i
$386$	8.92820	−	15.4641i	0.454434	−	0.787102i
$387$	−3.00000	−	5.19615i	−0.152499	−	0.264135i
$388$	10.7321	−	6.19615i	0.544837	−	0.314562i
$389$	−9.85641			−0.499740			−0.249870	−	0.968279i	$-0.580388\pi$
$389$	−9.85641			−0.499740			−0.249870	+	0.968279i	$0.580388\pi$
$390$	2.59808	+	2.50000i	0.131559	+	0.126592i
$391$	−13.8564			−0.700749
$392$	−1.73205	+	1.00000i	−0.0874818	+	0.0505076i
$393$	−10.1603	−	17.5981i	−0.512517	−	0.887706i
$394$	4.69615	−	8.13397i	0.236589	−	0.409784i
$395$			16.9282i			0.851750i
$396$	−3.23205	−	1.86603i	−0.162417	−	0.0937713i
$397$	−6.86603	−	3.96410i	−0.344596	−	0.198953i	0.317707	−	0.948189i	$-0.397087\pi$
$397$	−6.86603	−	3.96410i	−0.344596	−	0.198953i	−0.662303	+	0.749237i	$0.730421\pi$
$398$			11.0718i			0.554979i
$399$	−3.40192	+	5.89230i	−0.170309	+	0.294984i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−1.83975	+	1.06218i	−0.0918725	+	0.0530426i	−0.545232	−	0.838285i	$-0.683559\pi$
$401$	−1.83975	+	1.06218i	−0.0918725	+	0.0530426i	0.453360	+	0.891328i	$0.350225\pi$
$402$	−5.46410			−0.272525
$403$	31.2487	+	7.73205i	1.55661	+	0.385161i
$404$	8.39230			0.417533
$405$	0.866025	−	0.500000i	0.0430331	−	0.0248452i
$406$	8.19615	+	14.1962i	0.406768	+	0.704543i
$407$	14.7942	−	25.6244i	0.733323	−	1.27015i
$408$		−	4.00000i		−	0.198030i
$409$	0.820508	+	0.473721i	0.0405715	+	0.0234240i	0.520149	−	0.854076i	$-0.325877\pi$
$409$	0.820508	+	0.473721i	0.0405715	+	0.0234240i	−0.479577	+	0.877500i	$0.659210\pi$
$410$	−3.46410	−	2.00000i	−0.171080	−	0.0987730i
$411$		−	6.53590i		−	0.322392i
$412$	9.79423	−	16.9641i	0.482527	−	0.835761i
$413$	−6.80385	−	11.7846i	−0.334795	−	0.579883i
$414$	3.00000	−	1.73205i	0.147442	−	0.0851257i
$415$	−2.53590			−0.124482
$416$	−2.50000	+	2.59808i	−0.122573	+	0.127381i
$417$	−21.7846			−1.06680
$418$	−7.33013	+	4.23205i	−0.358528	+	0.206996i
$419$	8.92820	+	15.4641i	0.436171	+	0.755471i	0.997390	−	0.0721964i	$-0.0230008\pi$
$419$	8.92820	+	15.4641i	0.436171	+	0.755471i	−0.561219	+	0.827667i	$0.689668\pi$
$420$	1.50000	−	2.59808i	0.0731925	−	0.126773i
$421$			5.85641i			0.285424i	0.989764	+	0.142712i	$0.0455822\pi$
$421$			5.85641i			0.285424i	−0.989764	+	0.142712i	$0.954418\pi$
$422$	−18.9904	−	10.9641i	−0.924437	−	0.533724i
$423$	−0.401924	−	0.232051i	−0.0195422	−	0.0112827i
$424$		−	3.73205i		−	0.181244i
$425$	2.00000	−	3.46410i	0.0970143	−	0.168034i
$426$	0.464102	+	0.803848i	0.0224858	+	0.0389465i
$427$	−19.3923	+	11.1962i	−0.938459	+	0.541820i
$428$	−0.928203			−0.0448664
$429$	9.33013	−	9.69615i	0.450463	−	0.468135i
$430$	6.00000			0.289346
$431$	−12.0000	+	6.92820i	−0.578020	+	0.333720i	−0.760346	−	0.649518i	$-0.774971\pi$
$431$	−12.0000	+	6.92820i	−0.578020	+	0.333720i	0.182326	+	0.983238i	$0.441637\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−16.3923	+	28.3923i	−0.787764	+	1.36445i	0.139570	+	0.990212i	$0.455428\pi$
$433$	−16.3923	+	28.3923i	−0.787764	+	1.36445i	−0.927334	+	0.374235i	$0.877905\pi$
$434$		−	26.7846i		−	1.28570i
$435$	−4.73205	−	2.73205i	−0.226884	−	0.130992i
$436$	9.00000	+	5.19615i	0.431022	+	0.248851i
$437$		−	7.85641i		−	0.375823i
$438$	3.46410	−	6.00000i	0.165521	−	0.286691i
$439$	−10.6603	−	18.4641i	−0.508786	−	0.881243i	−0.999948	−	0.0101753i	$-0.996761\pi$
$439$	−10.6603	−	18.4641i	−0.508786	−	0.881243i	0.491162	−	0.871068i	$-0.336572\pi$
$440$	3.23205	−	1.86603i	0.154082	−	0.0889593i
$441$	−2.00000			−0.0952381
$442$	14.0000	+	3.46410i	0.665912	+	0.164771i
$443$	7.85641			0.373269			0.186635	−	0.982429i	$-0.440242\pi$
$443$	7.85641			0.373269			0.186635	+	0.982429i	$0.440242\pi$
$444$	−6.86603	+	3.96410i	−0.325847	+	0.188128i
$445$	−5.06218	−	8.76795i	−0.239970	−	0.415641i
$446$	4.42820	−	7.66987i	0.209682	−	0.363179i
$447$			22.7846i			1.07768i
$448$	2.59808	+	1.50000i	0.122748	+	0.0708683i
$449$	−15.6962	−	9.06218i	−0.740747	−	0.427671i	0.0815937	−	0.996666i	$-0.473999\pi$
$449$	−15.6962	−	9.06218i	−0.740747	−	0.427671i	−0.822341	+	0.568995i	$0.807332\pi$
$450$			1.00000i			0.0471405i
$451$	−7.46410	+	12.9282i	−0.351471	+	0.608765i
$452$	−6.00000	−	10.3923i	−0.282216	−	0.488813i
$453$	16.2679	−	9.39230i	0.764335	−	0.441289i
$454$	13.4641			0.631902
$455$	7.79423	+	7.50000i	0.365399	+	0.351605i
$456$	2.26795			0.106206
$457$	0.464102	−	0.267949i	0.0217098	−	0.0125341i	−0.489106	−	0.872224i	$-0.662677\pi$
$457$	0.464102	−	0.267949i	0.0217098	−	0.0125341i	0.510816	+	0.859690i	$0.329343\pi$
$458$	−5.73205	−	9.92820i	−0.267841	−	0.463914i
$459$	2.00000	−	3.46410i	0.0933520	−	0.161690i
$460$			3.46410i			0.161515i
$461$	28.0526	+	16.1962i	1.30654	+	0.754330i	0.981517	−	0.191377i	$-0.0612952\pi$
$461$	28.0526	+	16.1962i	1.30654	+	0.754330i	0.325021	+	0.945707i	$0.394629\pi$
$462$	−9.69615	−	5.59808i	−0.451106	−	0.260446i
$463$		−	0.784610i		−	0.0364639i	−0.999834	−	0.0182320i	$-0.994196\pi$
$463$		−	0.784610i		−	0.0364639i	0.999834	−	0.0182320i	$-0.00580373\pi$
$464$	2.73205	−	4.73205i	0.126832	−	0.219680i
$465$	4.46410	+	7.73205i	0.207018	+	0.358565i
$466$	−15.5885	+	9.00000i	−0.722121	+	0.416917i
$467$	3.60770			0.166944			0.0834721	−	0.996510i	$-0.473399\pi$
$467$	3.60770			0.166944			0.0834721	+	0.996510i	$0.473399\pi$
$468$	−3.46410	+	1.00000i	−0.160128	+	0.0462250i
$469$	−16.3923			−0.756926
$470$	0.401924	−	0.232051i	0.0185394	−	0.0107037i
$471$	5.40192	+	9.35641i	0.248908	+	0.431120i
$472$	−2.26795	+	3.92820i	−0.104391	+	0.180810i
$473$		−	22.3923i		−	1.02960i
$474$	−14.6603	−	8.46410i	−0.673368	−	0.388769i
$475$	1.96410	+	1.13397i	0.0901192	+	0.0520303i
$476$		−	12.0000i		−	0.550019i
$477$	1.86603	−	3.23205i	0.0854394	−	0.147985i
$478$	−1.73205	−	3.00000i	−0.0792222	−	0.137217i
$479$	−22.7321	+	13.1244i	−1.03865	+	0.599667i	−0.919452	−	0.393203i	$-0.871367\pi$
$479$	−22.7321	+	13.1244i	−1.03865	+	0.599667i	−0.119202	+	0.992870i	$0.538034\pi$
$480$	−1.00000			−0.0456435
$481$	−7.92820	−	27.4641i	−0.361495	−	1.25226i
$482$	−14.8038			−0.674297
$483$	9.00000	−	5.19615i	0.409514	−	0.236433i
$484$	−1.46410	−	2.53590i	−0.0665501	−	0.115268i
$485$	−6.19615	+	10.7321i	−0.281353	+	0.487317i
$486$			1.00000i			0.0453609i
$487$	−18.1865	−	10.5000i	−0.824110	−	0.475800i	0.0277214	−	0.999616i	$-0.491175\pi$
$487$	−18.1865	−	10.5000i	−0.824110	−	0.475800i	−0.851832	+	0.523815i	$0.824508\pi$
$488$	6.46410	+	3.73205i	0.292616	+	0.168942i
$489$		−	10.9282i		−	0.494190i
$490$	1.00000	−	1.73205i	0.0451754	−	0.0782461i
$491$	7.69615	+	13.3301i	0.347322	+	0.601580i	0.985773	−	0.168083i	$-0.0537576\pi$
$491$	7.69615	+	13.3301i	0.347322	+	0.601580i	−0.638450	+	0.769663i	$0.720424\pi$
$492$	3.46410	−	2.00000i	0.156174	−	0.0901670i
$493$	−21.8564			−0.984363
$494$	−1.96410	+	7.93782i	−0.0883691	+	0.357140i
$495$	3.73205			0.167743
$496$	−7.73205	+	4.46410i	−0.347179	+	0.200444i
$497$	1.39230	+	2.41154i	0.0624534	+	0.108172i
$498$	1.26795	−	2.19615i	0.0568182	−	0.0984119i
$499$			1.32051i			0.0591141i	0.999563	+	0.0295570i	$0.00940967\pi$
$499$			1.32051i			0.0591141i	−0.999563	+	0.0295570i	$0.990590\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$	−5.59808	−	3.23205i	−0.250104	−	0.144397i
$502$		−	26.4641i		−	1.18115i
$503$	−0.133975	+	0.232051i	−0.00597363	+	0.0103466i	−0.868997	−	0.494818i	$-0.835235\pi$
$503$	−0.133975	+	0.232051i	−0.00597363	+	0.0103466i	0.863023	+	0.505164i	$0.168568\pi$
$504$	1.50000	+	2.59808i	0.0668153	+	0.115728i
$505$	−7.26795	+	4.19615i	−0.323419	+	0.186726i
$506$	12.9282			0.574729
$507$	−0.500000	−	12.9904i	−0.0222058	−	0.576923i
$508$	−4.66025			−0.206765
$509$	4.60770	−	2.66025i	0.204232	−	0.117914i	−0.394396	−	0.918941i	$-0.629046\pi$
$509$	4.60770	−	2.66025i	0.204232	−	0.117914i	0.598628	+	0.801027i	$0.295713\pi$
$510$	2.00000	+	3.46410i	0.0885615	+	0.153393i
$511$	10.3923	−	18.0000i	0.459728	−	0.796273i
$512$		−	1.00000i		−	0.0441942i
$513$	1.96410	+	1.13397i	0.0867172	+	0.0500662i
$514$	18.5885	+	10.7321i	0.819902	+	0.473370i
$515$			19.5885i			0.863171i
$516$	−3.00000	+	5.19615i	−0.132068	+	0.228748i
$517$	−0.866025	−	1.50000i	−0.0380878	−	0.0659699i
$518$	−20.5981	+	11.8923i	−0.905028	+	0.522518i
$519$	−22.1244			−0.971151
$520$	0.866025	−	3.50000i	0.0379777	−	0.153485i
$521$	−27.3923			−1.20008			−0.600039	−	0.799970i	$-0.704848\pi$
$521$	−27.3923			−1.20008			−0.600039	+	0.799970i	$0.704848\pi$
$522$	4.73205	−	2.73205i	0.207116	−	0.119579i
$523$	−6.85641	−	11.8756i	−0.299810	−	0.519286i	0.676283	−	0.736642i	$-0.263590\pi$
$523$	−6.85641	−	11.8756i	−0.299810	−	0.519286i	−0.976092	+	0.217357i	$0.930257\pi$
$524$	−10.1603	+	17.5981i	−0.443853	+	0.768776i
$525$			3.00000i			0.130931i
$526$	17.7679	+	10.2583i	0.774719	+	0.447284i
$527$	30.9282	+	17.8564i	1.34725	+	0.777837i
$528$			3.73205i			0.162417i
$529$	5.50000	−	9.52628i	0.239130	−	0.414186i
$530$	1.86603	+	3.23205i	0.0810550	+	0.140391i
$531$	−3.92820	+	2.26795i	−0.170470	+	0.0984206i
$532$	6.80385			0.294984
$533$	4.00000	+	13.8564i	0.173259	+	0.600188i
$534$	10.1244			0.438124
$535$	0.803848	−	0.464102i	0.0347534	−	0.0200649i
$536$	2.73205	+	4.73205i	0.118007	+	0.204393i
$537$	11.4641	−	19.8564i	0.494713	−	0.856867i
$538$			30.9282i			1.33341i
$539$	−6.46410	−	3.73205i	−0.278429	−	0.160751i
$540$	−0.866025	−	0.500000i	−0.0372678	−	0.0215166i
$541$			26.7846i			1.15156i	0.817605	+	0.575780i	$0.195302\pi$
$541$			26.7846i			1.15156i	−0.817605	+	0.575780i	$0.804698\pi$
$542$	1.80385	−	3.12436i	0.0774819	−	0.134203i
$543$	1.53590	+	2.66025i	0.0659117	+	0.114162i
$544$	−3.46410	+	2.00000i	−0.148522	+	0.0857493i
$545$	−10.3923			−0.445157
$546$	−10.3923	+	3.00000i	−0.444750	+	0.128388i
$547$	29.3205			1.25365			0.626827	−	0.779158i	$-0.284353\pi$
$547$	29.3205			1.25365			0.626827	+	0.779158i	$0.284353\pi$
$548$	−5.66025	+	3.26795i	−0.241794	+	0.139600i
$549$	3.73205	+	6.46410i	0.159280	+	0.275881i
$550$	−1.86603	+	3.23205i	−0.0795676	+	0.137815i
$551$		−	12.3923i		−	0.527930i
$552$	−3.00000	−	1.73205i	−0.127688	−	0.0737210i
$553$	−43.9808	−	25.3923i	−1.87025	−	1.07979i
$554$			19.5885i			0.832234i
$555$	3.96410	−	6.86603i	0.168267	−	0.291447i
$556$	10.8923	+	18.8660i	0.461937	+	0.800098i
$557$	37.5788	−	21.6962i	1.59227	−	0.919295i	0.599349	−	0.800488i	$-0.295426\pi$
$557$	37.5788	−	21.6962i	1.59227	−	0.919295i	0.992917	−	0.118808i	$-0.0379072\pi$
$558$	−8.92820			−0.377961
$559$	−15.5885	−	15.0000i	−0.659321	−	0.634432i
$560$	−3.00000			−0.126773
$561$	12.9282	−	7.46410i	0.545829	−	0.315135i
$562$	−3.46410	−	6.00000i	−0.146124	−	0.253095i
$563$	−9.66025	+	16.7321i	−0.407131	+	0.705172i	−0.994567	−	0.104099i	$-0.966804\pi$
$563$	−9.66025	+	16.7321i	−0.407131	+	0.705172i	0.587436	+	0.809271i	$0.300137\pi$
$564$			0.464102i			0.0195422i
$565$	10.3923	+	6.00000i	0.437208	+	0.252422i
$566$	12.4641	+	7.19615i	0.523905	+	0.302477i
$567$			3.00000i			0.125988i
$568$	0.464102	−	0.803848i	0.0194733	−	0.0337287i
$569$	−9.16025	−	15.8660i	−0.384018	−	0.665138i	0.607615	−	0.794232i	$-0.292127\pi$
$569$	−9.16025	−	15.8660i	−0.384018	−	0.665138i	−0.991632	+	0.129094i	$0.958793\pi$
$570$	−1.96410	+	1.13397i	−0.0822672	+	0.0474970i
$571$	−16.8564			−0.705419			−0.352709	−	0.935733i	$-0.614740\pi$
$571$	−16.8564			−0.705419			−0.352709	+	0.935733i	$0.614740\pi$
$572$	−13.0622	−	3.23205i	−0.546157	−	0.135139i
$573$	−17.3205			−0.723575
$574$	10.3923	−	6.00000i	0.433766	−	0.250435i
$575$	−1.73205	−	3.00000i	−0.0722315	−	0.125109i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	25.3205i		−	1.05411i	−0.849832	−	0.527053i	$-0.823297\pi$
$577$		−	25.3205i		−	1.05411i	0.849832	−	0.527053i	$-0.176703\pi$
$578$	−0.866025	−	0.500000i	−0.0360219	−	0.0207973i
$579$	−15.4641	−	8.92820i	−0.642666	−	0.371043i
$580$			5.46410i			0.226884i
$581$	3.80385	−	6.58846i	0.157810	−	0.273335i
$582$	−6.19615	−	10.7321i	−0.256839	−	0.444858i
$583$	12.0622	−	6.96410i	0.499564	−	0.288424i
$584$	−6.92820			−0.286691
$585$	2.50000	−	2.59808i	0.103362	−	0.107417i
$586$	−19.2487			−0.795157
$587$	−4.26795	+	2.46410i	−0.176157	+	0.101704i	−0.585486	−	0.810683i	$-0.699096\pi$
$587$	−4.26795	+	2.46410i	−0.176157	+	0.101704i	0.409329	+	0.912387i	$0.365763\pi$
$588$	1.00000	+	1.73205i	0.0412393	+	0.0714286i
$589$	−10.1244	+	17.5359i	−0.417167	+	0.722554i
$590$		−	4.53590i		−	0.186740i
$591$	−8.13397	−	4.69615i	−0.334587	−	0.193174i
$592$	6.86603	+	3.96410i	0.282192	+	0.162924i
$593$			3.21539i			0.132040i	0.997818	+	0.0660201i	$0.0210302\pi$
$593$			3.21539i			0.132040i	−0.997818	+	0.0660201i	$0.978970\pi$
$594$	−1.86603	+	3.23205i	−0.0765639	+	0.132613i
$595$	6.00000	+	10.3923i	0.245976	+	0.426043i
$596$	19.7321	−	11.3923i	0.808256	−	0.466647i
$597$	11.0718			0.453138
$598$	8.66025	−	9.00000i	0.354144	−	0.368037i
$599$	15.0718			0.615817			0.307908	−	0.951416i	$-0.400371\pi$
$599$	15.0718			0.615817			0.307908	+	0.951416i	$0.400371\pi$
$600$	0.866025	−	0.500000i	0.0353553	−	0.0204124i
$601$	12.3564	+	21.4019i	0.504028	+	0.873003i	0.999989	+	0.00465778i	$0.00148262\pi$
$601$	12.3564	+	21.4019i	0.504028	+	0.873003i	−0.495961	+	0.868345i	$0.665184\pi$
$602$	−9.00000	+	15.5885i	−0.366813	+	0.635338i
$603$			5.46410i			0.222515i
$604$	−16.2679	−	9.39230i	−0.661933	−	0.382167i
$605$	2.53590	+	1.46410i	0.103099	+	0.0595242i
$606$		−	8.39230i		−	0.340914i
$607$	−18.7224	+	32.4282i	−0.759920	+	1.31622i	0.182971	+	0.983118i	$0.441429\pi$
$607$	−18.7224	+	32.4282i	−0.759920	+	1.31622i	−0.942891	+	0.333102i	$0.891905\pi$
$608$	−1.13397	−	1.96410i	−0.0459887	−	0.0796548i
$609$	14.1962	−	8.19615i	0.575257	−	0.332125i
$610$	−7.46410			−0.302213
$611$	−1.62436	−	0.401924i	−0.0657144	−	0.0162601i
$612$	−4.00000			−0.161690
$613$	−38.9711	+	22.5000i	−1.57403	+	0.908766i	−0.578362	+	0.815780i	$0.696308\pi$
$613$	−38.9711	+	22.5000i	−1.57403	+	0.908766i	−0.995667	+	0.0929864i	$0.970359\pi$
$614$	10.1244	+	17.5359i	0.408586	+	0.707691i
$615$	−2.00000	+	3.46410i	−0.0806478	+	0.139686i
$616$			11.1962i			0.451106i
$617$	24.7128	+	14.2679i	0.994900	+	0.574406i	0.906735	−	0.421700i	$-0.138566\pi$
$617$	24.7128	+	14.2679i	0.994900	+	0.574406i	0.0881649	+	0.996106i	$0.471900\pi$
$618$	−16.9641	−	9.79423i	−0.682396	−	0.393982i
$619$			42.5167i			1.70889i	0.519543	+	0.854444i	$0.326102\pi$
$619$			42.5167i			1.70889i	−0.519543	+	0.854444i	$0.673898\pi$
$620$	4.46410	−	7.73205i	0.179283	−	0.310527i
$621$	−1.73205	−	3.00000i	−0.0695048	−	0.120386i
$622$	−4.39230	+	2.53590i	−0.176115	+	0.101680i
$623$	30.3731			1.21687
$624$	2.59808	+	2.50000i	0.104006	+	0.100080i
$625$	1.00000			0.0400000
$626$	−1.14359	+	0.660254i	−0.0457072	+	0.0263891i
$627$	4.23205	+	7.33013i	0.169012	+	0.292737i
$628$	5.40192	−	9.35641i	0.215560	−	0.373361i
$629$		−	31.7128i		−	1.26447i
$630$	−2.59808	−	1.50000i	−0.103510	−	0.0597614i
$631$	6.92820	+	4.00000i	0.275807	+	0.159237i	0.631524	−	0.775356i	$-0.282430\pi$
$631$	6.92820	+	4.00000i	0.275807	+	0.159237i	−0.355716	+	0.934594i	$0.615763\pi$
$632$			16.9282i			0.673368i
$633$	−10.9641	+	18.9904i	−0.435784	+	0.754800i
$634$	11.7679	+	20.3827i	0.467365	+	0.809500i
$635$	4.03590	−	2.33013i	0.160160	−	0.0924683i
$636$	−3.73205			−0.147985
$637$	−6.92820	+	2.00000i	−0.274505	+	0.0792429i
$638$	20.3923			0.807339
$639$	0.803848	−	0.464102i	0.0317997	−	0.0183596i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−3.76795	+	6.52628i	−0.148825	+	0.257773i	−0.930793	−	0.365546i	$-0.880882\pi$
$641$	−3.76795	+	6.52628i	−0.148825	+	0.257773i	0.781968	+	0.623318i	$0.214216\pi$
$642$			0.928203i			0.0366333i
$643$	24.9282	+	14.3923i	0.983072	+	0.567577i	0.903196	−	0.429228i	$-0.141214\pi$
$643$	24.9282	+	14.3923i	0.983072	+	0.567577i	0.0798761	+	0.996805i	$0.474548\pi$
$644$	−9.00000	−	5.19615i	−0.354650	−	0.204757i
$645$		−	6.00000i		−	0.236250i
$646$	−4.53590	+	7.85641i	−0.178463	+	0.309106i
$647$	16.1340	+	27.9449i	0.634292	+	1.09863i	0.986665	+	0.162766i	$0.0520416\pi$
$647$	16.1340	+	27.9449i	0.634292	+	1.09863i	−0.352373	+	0.935860i	$0.614625\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−16.9282			−0.664490
$650$	1.00000	+	3.46410i	0.0392232	+	0.135873i
$651$	−26.7846			−1.04977
$652$	−9.46410	+	5.46410i	−0.370643	+	0.213991i
$653$	−14.7942	−	25.6244i	−0.578943	−	1.00276i	−0.995601	−	0.0936952i	$-0.970132\pi$
$653$	−14.7942	−	25.6244i	−0.578943	−	1.00276i	0.416658	−	0.909063i	$-0.363201\pi$
$654$	5.19615	−	9.00000i	0.203186	−	0.351928i
$655$		−	20.3205i		−	0.793988i
$656$	−3.46410	−	2.00000i	−0.135250	−	0.0780869i
$657$	−6.00000	−	3.46410i	−0.234082	−	0.135147i
$658$			1.39230i			0.0542777i
$659$	−7.85641	+	13.6077i	−0.306042	+	0.530081i	−0.977493	−	0.210969i	$-0.932338\pi$
$659$	−7.85641	+	13.6077i	−0.306042	+	0.530081i	0.671451	+	0.741049i	$0.265672\pi$
$660$	−1.86603	−	3.23205i	−0.0726349	−	0.125807i
$661$	36.7128	−	21.1962i	1.42796	−	0.824435i	0.431003	−	0.902351i	$-0.358160\pi$
$661$	36.7128	−	21.1962i	1.42796	−	0.824435i	0.996960	+	0.0779157i	$0.0248265\pi$
$662$	−6.39230			−0.248444
$663$	3.46410	−	14.0000i	0.134535	−	0.543715i
$664$	−2.53590			−0.0984119
$665$	−5.89230	+	3.40192i	−0.228494	+	0.131921i
$666$	3.96410	+	6.86603i	0.153606	+	0.266053i
$667$	−9.46410	+	16.3923i	−0.366451	+	0.634713i
$668$			6.46410i			0.250104i
$669$	−7.66987	−	4.42820i	−0.296534	−	0.171204i
$670$	−4.73205	−	2.73205i	−0.182815	−	0.105548i
$671$			27.8564i			1.07538i
$672$	1.50000	−	2.59808i	0.0578638	−	0.100223i
$673$	−12.3923	−	21.4641i	−0.477688	−	0.827380i	0.521985	−	0.852955i	$-0.325192\pi$
$673$	−12.3923	−	21.4641i	−0.477688	−	0.827380i	−0.999673	+	0.0255746i	$0.991858\pi$
$674$	4.85641	−	2.80385i	0.187062	−	0.108000i
$675$	1.00000			0.0384900
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$	−2.92820			−0.112540			−0.0562700	−	0.998416i	$-0.517921\pi$
$677$	−2.92820			−0.112540			−0.0562700	+	0.998416i	$0.517921\pi$
$678$	−10.3923	+	6.00000i	−0.399114	+	0.230429i
$679$	−18.5885	−	32.1962i	−0.713360	−	1.23557i
$680$	2.00000	−	3.46410i	0.0766965	−	0.132842i
$681$		−	13.4641i		−	0.515945i
$682$	−28.8564	−	16.6603i	−1.10497	−	0.637954i
$683$	−5.78461	−	3.33975i	−0.221342	−	0.127792i	0.385230	−	0.922821i	$-0.374122\pi$
$683$	−5.78461	−	3.33975i	−0.221342	−	0.127792i	−0.606571	+	0.795029i	$0.707456\pi$
$684$		−	2.26795i		−	0.0867172i
$685$	3.26795	−	5.66025i	0.124862	−	0.216267i
$686$	−7.50000	−	12.9904i	−0.286351	−	0.495975i
$687$	−9.92820	+	5.73205i	−0.378785	+	0.218691i
$688$	6.00000			0.228748
$689$	3.23205	−	13.0622i	0.123131	−	0.497629i
$690$	3.46410			0.131876
$691$	19.9641	−	11.5263i	0.759470	−	0.438480i	−0.0696353	−	0.997573i	$-0.522184\pi$
$691$	19.9641	−	11.5263i	0.759470	−	0.438480i	0.829106	+	0.559092i	$0.188850\pi$
$692$	11.0622	+	19.1603i	0.420521	+	0.728364i
$693$	−5.59808	+	9.69615i	−0.212653	+	0.368326i
$694$			16.3923i			0.622243i
$695$	−18.8660	−	10.8923i	−0.715629	−	0.413169i
$696$	−4.73205	−	2.73205i	−0.179368	−	0.103558i
$697$			16.0000i			0.606043i
$698$	−8.73205	+	15.1244i	−0.330513	+	0.572465i
$699$	9.00000	+	15.5885i	0.340411	+	0.589610i
$700$	2.59808	−	1.50000i	0.0981981	−	0.0566947i
$701$	16.3923			0.619129			0.309564	−	0.950878i	$-0.399817\pi$
$701$	16.3923			0.619129			0.309564	+	0.950878i	$0.399817\pi$
$702$	1.00000	+	3.46410i	0.0377426	+	0.130744i
$703$	17.9808			0.678157
$704$	3.23205	−	1.86603i	0.121812	−	0.0703285i
$705$	−0.232051	−	0.401924i	−0.00873954	−	0.0151373i
$706$	14.1962	−	24.5885i	0.534279	−	0.925399i
$707$		−	25.1769i		−	0.946875i
$708$	3.92820	+	2.26795i	0.147631	+	0.0852348i
$709$	−6.33975	−	3.66025i	−0.238094	−	0.137464i	0.376206	−	0.926536i	$-0.377228\pi$
$709$	−6.33975	−	3.66025i	−0.238094	−	0.137464i	−0.614300	+	0.789072i	$0.710562\pi$
$710$			0.928203i			0.0348348i
$711$	−8.46410	+	14.6603i	−0.317429	+	0.549802i
$712$	−5.06218	−	8.76795i	−0.189713	−	0.328593i
$713$	26.7846	−	15.4641i	1.00309	−	0.579135i
$714$	−12.0000			−0.449089
$715$	12.9282	−	3.73205i	0.483487	−	0.139571i
$716$	−22.9282			−0.856867
$717$	−3.00000	+	1.73205i	−0.112037	+	0.0646846i
$718$	−6.46410	−	11.1962i	−0.241238	−	0.417837i
$719$	−8.00000	+	13.8564i	−0.298350	+	0.516757i	−0.975759	−	0.218850i	$-0.929769\pi$
$719$	−8.00000	+	13.8564i	−0.298350	+	0.516757i	0.677409	+	0.735607i	$0.263103\pi$
$720$			1.00000i			0.0372678i
$721$	−50.8923	−	29.3827i	−1.89533	−	1.09427i
$722$	12.0000	+	6.92820i	0.446594	+	0.257841i
$723$			14.8038i			0.550561i
$724$	1.53590	−	2.66025i	0.0570812	−	0.0988676i
$725$	−2.73205	−	4.73205i	−0.101466	−	0.175744i
$726$	−2.53590	+	1.46410i	−0.0941160	+	0.0543379i
$727$	12.6603			0.469543			0.234771	−	0.972051i	$-0.424566\pi$
$727$	12.6603			0.469543			0.234771	+	0.972051i	$0.424566\pi$
$728$	7.79423	+	7.50000i	0.288873	+	0.277968i
$729$	1.00000			0.0370370
$730$	6.00000	−	3.46410i	0.222070	−	0.128212i
$731$	−12.0000	−	20.7846i	−0.443836	−	0.768747i
$732$	3.73205	−	6.46410i	0.137941	−	0.238920i
$733$			6.85641i			0.253247i	0.991951	+	0.126624i	$0.0404140\pi$
$733$			6.85641i			0.253247i	−0.991951	+	0.126624i	$0.959586\pi$
$734$	−11.5359	−	6.66025i	−0.425798	−	0.245834i
$735$	−1.73205	−	1.00000i	−0.0638877	−	0.0368856i
$736$			3.46410i			0.127688i
$737$	−10.1962	+	17.6603i	−0.375580	+	0.650524i
$738$	−2.00000	−	3.46410i	−0.0736210	−	0.127515i
$739$	37.9641	−	21.9186i	1.39653	−	0.806288i	0.402505	−	0.915418i	$-0.368140\pi$
$739$	37.9641	−	21.9186i	1.39653	−	0.806288i	0.994028	+	0.109130i	$0.0348064\pi$
$740$	−7.92820			−0.291447
$741$	7.93782	+	1.96410i	0.291603	+	0.0721531i
$742$	−11.1962			−0.411024
$743$	−2.53590	+	1.46410i	−0.0930331	+	0.0537127i	−0.545795	−	0.837919i	$-0.683772\pi$
$743$	−2.53590	+	1.46410i	−0.0930331	+	0.0537127i	0.452762	+	0.891632i	$0.350439\pi$
$744$	4.46410	+	7.73205i	0.163662	+	0.283471i
$745$	−11.3923	+	19.7321i	−0.417382	+	0.722926i
$746$		−	22.9282i		−	0.839461i
$747$	−2.19615	−	1.26795i	−0.0803530	−	0.0463918i
$748$	−12.9282	−	7.46410i	−0.472702	−	0.272915i
$749$			2.78461i			0.101747i
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	−20.5885	−	35.6603i	−0.751283	−	1.30126i	−0.947201	−	0.320641i	$-0.896102\pi$
$751$	−20.5885	−	35.6603i	−0.751283	−	1.30126i	0.195917	−	0.980620i	$-0.437232\pi$
$752$	0.401924	−	0.232051i	0.0146567	−	0.00846202i
$753$	−26.4641			−0.964405
$754$	13.6603	−	14.1962i	0.497477	−	0.516993i
$755$	18.7846			0.683642
$756$	2.59808	−	1.50000i	0.0944911	−	0.0545545i
$757$	−9.13397	−	15.8205i	−0.331980	−	0.575006i	0.650920	−	0.759146i	$-0.274383\pi$
$757$	−9.13397	−	15.8205i	−0.331980	−	0.575006i	−0.982900	+	0.184140i	$0.941050\pi$
$758$	−3.13397	+	5.42820i	−0.113831	+	0.197161i
$759$		−	12.9282i		−	0.469264i
$760$	1.96410	+	1.13397i	0.0712455	+	0.0411336i
$761$	38.0885	+	21.9904i	1.38071	+	0.797151i	0.992243	−	0.124314i	$-0.0396730\pi$
$761$	38.0885	+	21.9904i	1.38071	+	0.797151i	0.388463	+	0.921465i	$0.373006\pi$
$762$			4.66025i			0.168823i
$763$	15.5885	−	27.0000i	0.564340	−	0.977466i
$764$	8.66025	+	15.0000i	0.313317	+	0.542681i
$765$	3.46410	−	2.00000i	0.125245	−	0.0723102i
$766$	−36.7846			−1.32908
$767$	−11.3397	+	11.7846i	−0.409454	+	0.425518i
$768$	−1.00000			−0.0360844
$769$	34.3923	−	19.8564i	1.24022	−	0.716040i	0.271080	−	0.962557i	$-0.412619\pi$
$769$	34.3923	−	19.8564i	1.24022	−	0.716040i	0.969139	+	0.246517i	$0.0792860\pi$
$770$	−5.59808	−	9.69615i	−0.201741	−	0.349425i
$771$	10.7321	−	18.5885i	0.386505	−	0.669447i
$772$			17.8564i			0.642666i
$773$	46.2391	+	26.6962i	1.66310	+	0.960194i	0.971220	+	0.238186i	$0.0765528\pi$
$773$	46.2391	+	26.6962i	1.66310	+	0.960194i	0.691885	+	0.722008i	$0.256780\pi$
$774$	5.19615	+	3.00000i	0.186772	+	0.107833i
$775$			8.92820i			0.320711i
$776$	−6.19615	+	10.7321i	−0.222429	+	0.385258i
$777$	11.8923	+	20.5981i	0.426634	+	0.738952i
$778$	8.53590	−	4.92820i	0.306027	−	0.176685i
$779$	−9.07180			−0.325031
$780$	−3.50000	−	0.866025i	−0.125320	−	0.0310087i
$781$	3.46410			0.123955
$782$	12.0000	−	6.92820i	0.429119	−	0.247752i
$783$	−2.73205	−	4.73205i	−0.0976355	−	0.169110i
$784$	1.00000	−	1.73205i	0.0357143	−	0.0618590i
$785$			10.8038i			0.385606i
$786$	17.5981	+	10.1603i	0.627703	+	0.362404i
$787$	4.73205	+	2.73205i	0.168679	+	0.0973871i	0.581963	−	0.813215i	$-0.302285\pi$
$787$	4.73205	+	2.73205i	0.168679	+	0.0973871i	−0.413284	+	0.910602i	$0.635618\pi$
$788$			9.39230i			0.334587i
$789$	10.2583	−	17.7679i	0.365206	−	0.632556i
$790$	−8.46410	−	14.6603i	−0.301139	−	0.521588i
$791$	−31.1769	+	18.0000i	−1.10852	+	0.640006i
$792$	3.73205			0.132613
$793$	19.3923	+	18.6603i	0.688641	+	0.662645i
$794$	7.92820			0.281361
$795$	3.23205	−	1.86603i	0.114629	−	0.0661811i
$796$	−5.53590	−	9.58846i	−0.196215	−	0.339854i
$797$	18.9282	−	32.7846i	0.670471	−	1.16129i	−0.307299	−	0.951613i	$-0.599425\pi$
$797$	18.9282	−	32.7846i	0.670471	−	1.16129i	0.977771	−	0.209678i	$-0.0672414\pi$
$798$		−	6.80385i		−	0.240854i
$799$	−1.60770	−	0.928203i	−0.0568762	−	0.0328375i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$		−	10.1244i		−	0.357727i
$802$	1.06218	−	1.83975i	0.0375068	−	0.0649637i
$803$	−12.9282	−	22.3923i	−0.456226	−	0.790207i
$804$	4.73205	−	2.73205i	0.166887	−	0.0963520i
$805$	10.3923			0.366281
$806$	−30.9282	+	8.92820i	−1.08940	+	0.314483i
$807$	30.9282			1.08872
$808$	−7.26795	+	4.19615i	−0.255686	+	0.147620i
$809$	−17.3923	−	30.1244i	−0.611481	−	1.05912i	−0.990991	−	0.133928i	$-0.957241\pi$
$809$	−17.3923	−	30.1244i	−0.611481	−	1.05912i	0.379510	−	0.925188i	$-0.376093\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$			7.58846i			0.266467i	0.991085	+	0.133233i	$0.0425360\pi$
$811$			7.58846i			0.266467i	−0.991085	+	0.133233i	$0.957464\pi$
$812$	−14.1962	−	8.19615i	−0.498187	−	0.287629i
$813$	−3.12436	−	1.80385i	−0.109576	−	0.0632637i
$814$			29.5885i			1.03707i
$815$	5.46410	−	9.46410i	0.191399	−	0.331513i
$816$	2.00000	+	3.46410i	0.0700140	+	0.121268i
$817$	11.7846	−	6.80385i	0.412291	−	0.238036i
$818$	−0.947441			−0.0331265
$819$	3.00000	+	10.3923i	0.104828	+	0.363137i
$820$	4.00000			0.139686
$821$	42.7128	−	24.6603i	1.49069	−	0.860649i	0.490744	−	0.871304i	$-0.336725\pi$
$821$	42.7128	−	24.6603i	1.49069	−	0.860649i	0.999943	+	0.0106549i	$0.00339162\pi$
$822$	3.26795	+	5.66025i	0.113983	+	0.197424i
$823$	19.7942	−	34.2846i	0.689983	−	1.19509i	−0.281859	−	0.959456i	$-0.590951\pi$
$823$	19.7942	−	34.2846i	0.689983	−	1.19509i	0.971843	−	0.235631i	$-0.0757155\pi$
$824$			19.5885i			0.682396i
$825$	3.23205	+	1.86603i	0.112526	+	0.0649667i
$826$	11.7846	+	6.80385i	0.410039	+	0.236736i
$827$			50.4974i			1.75597i	0.478690	+	0.877984i	$0.341112\pi$
$827$			50.4974i			1.75597i	−0.478690	+	0.877984i	$0.658888\pi$
$828$	−1.73205	+	3.00000i	−0.0601929	+	0.104257i
$829$	19.6603	+	34.0526i	0.682829	+	1.18269i	0.974114	+	0.226058i	$0.0725839\pi$
$829$	19.6603	+	34.0526i	0.682829	+	1.18269i	−0.291285	+	0.956636i	$0.594083\pi$
$830$	2.19615	−	1.26795i	0.0762296	−	0.0440112i
$831$	19.5885			0.679516
$832$	0.866025	−	3.50000i	0.0300240	−	0.121341i
$833$	−8.00000			−0.277184
$834$	18.8660	−	10.8923i	0.653277	−	0.377170i
$835$	−3.23205	−	5.59808i	−0.111850	−	0.193729i
$836$	4.23205	−	7.33013i	0.146369	−	0.253518i
$837$			8.92820i			0.308604i
$838$	−15.4641	−	8.92820i	−0.534199	−	0.308420i
$839$	37.3923	+	21.5885i	1.29093	+	0.745316i	0.978818	−	0.204731i	$-0.0656318\pi$
$839$	37.3923	+	21.5885i	1.29093	+	0.745316i	0.312107	+	0.950047i	$0.398965\pi$
$840$			3.00000i			0.103510i
$841$	−0.428203	+	0.741670i	−0.0147656	+	0.0255748i
$842$	−2.92820	−	5.07180i	−0.100913	−	0.174786i
$843$	−6.00000	+	3.46410i	−0.206651	+	0.119310i
$844$	21.9282			0.754800
$845$	6.06218	−	11.5000i	0.208545	−	0.395612i
$846$	0.464102			0.0159561
$847$	−7.60770	+	4.39230i	−0.261403	+	0.150921i
$848$	1.86603	+	3.23205i	0.0640796	+	0.110989i
$849$	7.19615	−	12.4641i	0.246971	−	0.427767i
$850$			4.00000i			0.137199i
$851$	−23.7846	−	13.7321i	−0.815326	−	0.470729i
$852$	−0.803848	−	0.464102i	−0.0275394	−	0.0158999i
$853$		−	44.6410i		−	1.52848i	−0.644932	−	0.764240i	$-0.723114\pi$
$853$		−	44.6410i		−	1.52848i	0.644932	−	0.764240i	$-0.276886\pi$
$854$	11.1962	−	19.3923i	0.383124	−	0.663591i
$855$	1.13397	+	1.96410i	0.0387811	+	0.0671709i
$856$	0.803848	−	0.464102i	0.0274749	−	0.0158627i
$857$	−15.0718			−0.514843			−0.257421	−	0.966299i	$-0.582873\pi$
$857$	−15.0718			−0.514843			−0.257421	+	0.966299i	$0.582873\pi$
$858$	−3.23205	+	13.0622i	−0.110340	+	0.445935i
$859$	−19.9282			−0.679942			−0.339971	−	0.940436i	$-0.610417\pi$
$859$	−19.9282			−0.679942			−0.339971	+	0.940436i	$0.610417\pi$
$860$	−5.19615	+	3.00000i	−0.177187	+	0.102299i
$861$	−6.00000	−	10.3923i	−0.204479	−	0.354169i
$862$	6.92820	−	12.0000i	0.235976	−	0.408722i
$863$			10.9282i			0.372000i	0.982550	+	0.186000i	$0.0595525\pi$
$863$			10.9282i			0.372000i	−0.982550	+	0.186000i	$0.940447\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	−19.1603	−	11.0622i	−0.651468	−	0.376125i
$866$		−	32.7846i		−	1.11407i
$867$	−0.500000	+	0.866025i	−0.0169809	+	0.0294118i
$868$	13.3923	+	23.1962i	0.454564	+	0.787329i
$869$	−54.7128	+	31.5885i	−1.85601	+	1.07157i
$870$	5.46410			0.185250
$871$	5.46410	+	18.9282i	0.185144	+	0.641358i
$872$	−10.3923			−0.351928
$873$	−10.7321	+	6.19615i	−0.363225	+	0.209708i
$874$	3.92820	+	6.80385i	0.132873	+	0.230144i
$875$	−1.50000	+	2.59808i	−0.0507093	+	0.0878310i
$876$			6.92820i			0.234082i
$877$	29.1962	+	16.8564i	0.985884	+	0.569200i	0.904041	−	0.427445i	$-0.140586\pi$
$877$	29.1962	+	16.8564i	0.985884	+	0.569200i	0.0818426	+	0.996645i	$0.473920\pi$
$878$	18.4641	+	10.6603i	0.623133	+	0.359766i
$879$			19.2487i			0.649243i
$880$	−1.86603	+	3.23205i	−0.0629037	+	0.108952i
$881$	18.5526	+	32.1340i	0.625052	+	1.08262i	0.988531	+	0.151019i	$0.0482554\pi$
$881$	18.5526	+	32.1340i	0.625052	+	1.08262i	−0.363479	+	0.931602i	$0.618411\pi$
$882$	1.73205	−	1.00000i	0.0583212	−	0.0336718i
$883$	21.3205			0.717492			0.358746	−	0.933435i	$-0.383204\pi$
$883$	21.3205			0.717492			0.358746	+	0.933435i	$0.383204\pi$
$884$	−13.8564	+	4.00000i	−0.466041	+	0.134535i
$885$	−4.53590			−0.152473
$886$	−6.80385	+	3.92820i	−0.228580	+	0.131971i
$887$	−26.1340	−	45.2654i	−0.877493	−	1.51986i	−0.854083	−	0.520136i	$-0.825881\pi$
$887$	−26.1340	−	45.2654i	−0.877493	−	1.51986i	−0.0234098	−	0.999726i	$-0.507452\pi$
$888$	3.96410	−	6.86603i	0.133027	−	0.230409i
$889$			13.9808i			0.468900i
$890$	8.76795	+	5.06218i	0.293902	+	0.169685i
$891$	3.23205	+	1.86603i	0.108278	+	0.0625142i
$892$			8.85641i			0.296534i
$893$	0.526279	−	0.911543i	0.0176113	−	0.0305036i
$894$	−11.3923	−	19.7321i	−0.381016	−	0.659939i
$895$	19.8564	−	11.4641i	0.663726	−	0.383203i
$896$	−3.00000			−0.100223
$897$	−9.00000	−	8.66025i	−0.300501	−	0.289157i
$898$	18.1244			0.604818
$899$	42.2487	−	24.3923i	1.40907	−	0.813529i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	7.46410	−	12.9282i	0.248665	−	0.430701i
$902$		−	14.9282i		−	0.497055i
$903$	15.5885	+	9.00000i	0.518751	+	0.299501i
$904$	10.3923	+	6.00000i	0.345643	+	0.199557i
$905$			3.07180i			0.102110i
$906$	−9.39230	+	16.2679i	−0.312038	+	0.540466i
$907$	−3.53590	−	6.12436i	−0.117408	−	0.203356i	0.801332	−	0.598220i	$-0.204125\pi$
$907$	−3.53590	−	6.12436i	−0.117408	−	0.203356i	−0.918740	+	0.394864i	$0.870792\pi$
$908$	−11.6603	+	6.73205i	−0.386959	+	0.223411i
$909$	−8.39230			−0.278355
$910$	−10.5000	−	2.59808i	−0.348072	−	0.0861254i
$911$	−28.7846			−0.953677			−0.476838	−	0.878991i	$-0.658217\pi$
$911$	−28.7846			−0.953677			−0.476838	+	0.878991i	$0.658217\pi$
$912$	−1.96410	+	1.13397i	−0.0650379	+	0.0375497i
$913$	−4.73205	−	8.19615i	−0.156608	−	0.271253i
$914$	−0.267949	+	0.464102i	−0.00886297	+	0.0153511i
$915$			7.46410i			0.246756i
$916$	9.92820	+	5.73205i	0.328037	+	0.189392i
$917$	52.7942	+	30.4808i	1.74342	+	1.00656i
$918$			4.00000i			0.132020i
$919$	−27.9808	+	48.4641i	−0.923000	+	1.59868i	−0.128254	+	0.991741i	$0.540937\pi$
$919$	−27.9808	+	48.4641i	−0.923000	+	1.59868i	−0.794746	+	0.606942i	$0.792396\pi$
$920$	−1.73205	−	3.00000i	−0.0571040	−	0.0989071i
$921$	17.5359	−	10.1244i	0.577827	−	0.333609i
$922$	−32.3923			−1.06678
$923$	2.32051	−	2.41154i	0.0763805	−	0.0793769i
$924$	11.1962			0.368326
$925$	6.86603	−	3.96410i	0.225754	−	0.130339i
$926$	0.392305	+	0.679492i	0.0128919	+	0.0223295i
$927$	−9.79423	+	16.9641i	−0.321685	+	0.557174i
$928$			5.46410i			0.179368i
$929$	−26.1051	−	15.0718i	−0.856481	−	0.494490i	0.00635120	−	0.999980i	$-0.497978\pi$
$929$	−26.1051	−	15.0718i	−0.856481	−	0.494490i	−0.862832	+	0.505490i	$0.831312\pi$
$930$	−7.73205	−	4.46410i	−0.253544	−	0.146384i
$931$		−	4.53590i		−	0.148658i
$932$	9.00000	−	15.5885i	0.294805	−	0.510617i
$933$	2.53590	+	4.39230i	0.0830216	+	0.143798i
$934$	−3.12436	+	1.80385i	−0.102232	+	0.0590237i
$935$	14.9282			0.488204
$936$	2.50000	−	2.59808i	0.0817151	−	0.0849208i
$937$	33.7128			1.10135			0.550675	−	0.834720i	$-0.314370\pi$
$937$	33.7128			1.10135			0.550675	+	0.834720i	$0.314370\pi$
$938$	14.1962	−	8.19615i	0.463521	−	0.267614i
$939$	0.660254	+	1.14359i	0.0215466	+	0.0373198i
$940$	−0.232051	+	0.401924i	−0.00756866	+	0.0131093i
$941$		−	36.4974i		−	1.18978i	−0.803806	−	0.594891i	$-0.797195\pi$
$941$		−	36.4974i		−	1.18978i	0.803806	−	0.594891i	$-0.202805\pi$
$942$	−9.35641	−	5.40192i	−0.304848	−	0.176004i
$943$	12.0000	+	6.92820i	0.390774	+	0.225613i
$944$		−	4.53590i		−	0.147631i
$945$	−1.50000	+	2.59808i	−0.0487950	+	0.0845154i
$946$	11.1962	+	19.3923i	0.364018	+	0.630498i
$947$	−11.7846	+	6.80385i	−0.382948	+	0.221095i	−0.679100	−	0.734046i	$-0.737630\pi$
$947$	−11.7846	+	6.80385i	−0.382948	+	0.221095i	0.296152	+	0.955141i	$0.404297\pi$
$948$	16.9282			0.549802
$949$	−24.2487	−	6.00000i	−0.787146	−	0.194768i
$950$	−2.26795			−0.0735820
$951$	20.3827	−	11.7679i	0.660954	−	0.381602i
$952$	6.00000	+	10.3923i	0.194461	+	0.336817i
$953$	9.33975	−	16.1769i	0.302544	−	0.524022i	−0.674167	−	0.738579i	$-0.735497\pi$
$953$	9.33975	−	16.1769i	0.302544	−	0.524022i	0.976711	+	0.214557i	$0.0688307\pi$
$954$			3.73205i			0.120830i
$955$	−15.0000	−	8.66025i	−0.485389	−	0.280239i
$956$	3.00000	+	1.73205i	0.0970269	+	0.0560185i
$957$		−	20.3923i		−	0.659190i
$958$	13.1244	−	22.7321i	0.424029	−	0.734439i
$959$	9.80385	+	16.9808i	0.316583	+	0.548337i
$960$	0.866025	−	0.500000i	0.0279508	−	0.0161374i
$961$	−48.7128			−1.57138
$962$	20.5981	+	19.8205i	0.664109	+	0.639039i
$963$	0.928203			0.0299109
$964$	12.8205	−	7.40192i	0.412921	−	0.238400i
$965$	−8.92820	−	15.4641i	−0.287409	−	0.497807i
$966$	−5.19615	+	9.00000i	−0.167183	+	0.289570i
$967$			28.8564i			0.927959i	0.885846	+	0.463980i	$0.153579\pi$
$967$			28.8564i			0.927959i	−0.885846	+	0.463980i	$0.846421\pi$
$968$	2.53590	+	1.46410i	0.0815069	+	0.0470580i
$969$	7.85641	+	4.53590i	0.252384	+	0.145714i
$970$		−	12.3923i		−	0.397893i
$971$	10.3038	−	17.8468i	0.330666	−	0.572731i	−0.651976	−	0.758239i	$-0.726060\pi$
$971$	10.3038	−	17.8468i	0.330666	−	0.572731i	0.982643	+	0.185509i	$0.0593932\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	56.5981	−	32.6769i	1.81445	−	1.04757i
$974$	21.0000			0.672883
$975$	3.46410	−	1.00000i	0.110940	−	0.0320256i
$976$	−7.46410			−0.238920
$977$	−1.26795	+	0.732051i	−0.0405653	+	0.0234204i	−0.520145	−	0.854078i	$-0.674122\pi$
$977$	−1.26795	+	0.732051i	−0.0405653	+	0.0234204i	0.479580	+	0.877498i	$0.340789\pi$
$978$	5.46410	+	9.46410i	0.174723	+	0.302629i
$979$	18.8923	−	32.7224i	0.603801	−	1.04581i
$980$			2.00000i			0.0638877i
$981$	−9.00000	−	5.19615i	−0.287348	−	0.165900i
$982$	−13.3301	−	7.69615i	−0.425381	−	0.245594i
$983$			16.1769i			0.515963i	0.966150	+	0.257982i	$0.0830574\pi$
$983$			16.1769i			0.515963i	−0.966150	+	0.257982i	$0.916943\pi$
$984$	−2.00000	+	3.46410i	−0.0637577	+	0.110432i
$985$	−4.69615	−	8.13397i	−0.149632	−	0.259170i
$986$	18.9282	−	10.9282i	0.602797	−	0.348025i
$987$	1.39230			0.0443176
$988$	−2.26795	−	7.85641i	−0.0721531	−	0.249946i
$989$	−20.7846			−0.660912
$990$	−3.23205	+	1.86603i	−0.102721	+	0.0593062i
$991$	11.5885	+	20.0718i	0.368119	+	0.637602i	0.989272	−	0.146088i	$-0.0466684\pi$
$991$	11.5885	+	20.0718i	0.368119	+	0.637602i	−0.621152	+	0.783690i	$0.713335\pi$
$992$	4.46410	−	7.73205i	0.141735	−	0.245493i
$993$			6.39230i			0.202854i
$994$	−2.41154	−	1.39230i	−0.0764895	−	0.0441612i
$995$	9.58846	+	5.53590i	0.303975	+	0.175500i
$996$			2.53590i			0.0803530i
$997$	−5.00962	+	8.67691i	−0.158656	+	0.274801i	−0.934384	−	0.356267i	$-0.884049\pi$
$997$	−5.00962	+	8.67691i	−0.158656	+	0.274801i	0.775728	+	0.631067i	$0.217383\pi$
$998$	−0.660254	−	1.14359i	−0.0209000	−	0.0361998i
$999$	6.86603	−	3.96410i	0.217231	−	0.125419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bb.a.361.1	yes	4
3.2	odd	2		1170.2.bs.d.361.2		4
5.2	odd	4		1950.2.y.d.49.2		4
5.3	odd	4		1950.2.y.e.49.1		4
5.4	even	2		1950.2.bc.a.751.2		4
13.2	odd	12		5070.2.a.ba.1.2		2
13.3	even	3		5070.2.b.p.1351.1		4
13.4	even	6	inner	390.2.bb.a.121.1	✓	4
13.10	even	6		5070.2.b.p.1351.4		4
13.11	odd	12		5070.2.a.be.1.1		2
39.17	odd	6		1170.2.bs.d.901.2		4
65.4	even	6		1950.2.bc.a.901.2		4
65.17	odd	12		1950.2.y.e.199.1		4
65.43	odd	12		1950.2.y.d.199.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.a.121.1	✓	4	13.4	even	6	inner
390.2.bb.a.361.1	yes	4	1.1	even	1	trivial
1170.2.bs.d.361.2		4	3.2	odd	2
1170.2.bs.d.901.2		4	39.17	odd	6
1950.2.y.d.49.2		4	5.2	odd	4
1950.2.y.d.199.2		4	65.43	odd	12
1950.2.y.e.49.1		4	5.3	odd	4
1950.2.y.e.199.1		4	65.17	odd	12
1950.2.bc.a.751.2		4	5.4	even	2
1950.2.bc.a.901.2		4	65.4	even	6
5070.2.a.ba.1.2		2	13.2	odd	12
5070.2.a.be.1.1		2	13.11	odd	12
5070.2.b.p.1351.1		4	13.3	even	3
5070.2.b.p.1351.4		4	13.10	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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-2.59808 - 1.50000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-2.59808 - 1.50000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-3.23205 + 1.86603i) q^{11} +1.00000 q^{12} +(-0.866025 + 3.50000i) q^{13} +3.00000 q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} -1.00000i q^{18} +(-1.96410 - 1.13397i) q^{19} +(0.866025 + 0.500000i) q^{20} -3.00000i q^{21} +(1.86603 - 3.23205i) q^{22} +(1.73205 + 3.00000i) q^{23} +(-0.866025 + 0.500000i) q^{24} -1.00000 q^{25} +(-1.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(-2.59808 + 1.50000i) q^{28} +(2.73205 + 4.73205i) q^{29} +(0.500000 - 0.866025i) q^{30} -8.92820i q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.23205 - 1.86603i) q^{33} -4.00000i q^{34} +(1.50000 - 2.59808i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-6.86603 + 3.96410i) q^{37} +2.26795 q^{38} +(-3.46410 + 1.00000i) q^{39} -1.00000 q^{40} +(3.46410 - 2.00000i) q^{41} +(1.50000 + 2.59808i) q^{42} +(-3.00000 + 5.19615i) q^{43} +3.73205i q^{44} +(-0.866025 - 0.500000i) q^{45} +(-3.00000 - 1.73205i) q^{46} +0.464102i q^{47} +(0.500000 - 0.866025i) q^{48} +(1.00000 + 1.73205i) q^{49} +(0.866025 - 0.500000i) q^{50} -4.00000 q^{51} +(2.59808 + 2.50000i) q^{52} -3.73205 q^{53} +(0.866025 - 0.500000i) q^{54} +(-1.86603 - 3.23205i) q^{55} +(1.50000 - 2.59808i) q^{56} -2.26795i q^{57} +(-4.73205 - 2.73205i) q^{58} +(3.92820 + 2.26795i) q^{59} +1.00000i q^{60} +(3.73205 - 6.46410i) q^{61} +(4.46410 + 7.73205i) q^{62} +(2.59808 - 1.50000i) q^{63} -1.00000 q^{64} +(-3.50000 - 0.866025i) q^{65} +3.73205 q^{66} +(4.73205 - 2.73205i) q^{67} +(2.00000 + 3.46410i) q^{68} +(-1.73205 + 3.00000i) q^{69} +3.00000i q^{70} +(-0.803848 - 0.464102i) q^{71} +(-0.866025 - 0.500000i) q^{72} +6.92820i q^{73} +(3.96410 - 6.86603i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-1.96410 + 1.13397i) q^{76} +11.1962 q^{77} +(2.50000 - 2.59808i) q^{78} +16.9282 q^{79} +(0.866025 - 0.500000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.00000 + 3.46410i) q^{82} +2.53590i q^{83} +(-2.59808 - 1.50000i) q^{84} +(-3.46410 - 2.00000i) q^{85} -6.00000i q^{86} +(-2.73205 + 4.73205i) q^{87} +(-1.86603 - 3.23205i) q^{88} +(-8.76795 + 5.06218i) q^{89} +1.00000 q^{90} +(7.50000 - 7.79423i) q^{91} +3.46410 q^{92} +(7.73205 - 4.46410i) q^{93} +(-0.232051 - 0.401924i) q^{94} +(1.13397 - 1.96410i) q^{95} +1.00000i q^{96} +(10.7321 + 6.19615i) q^{97} +(-1.73205 - 1.00000i) q^{98} -3.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9	\( 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{10} - 6 q^{11} + 4 q^{12} + 12 q^{14} - 2 q^{16} - 8 q^{17} + 6 q^{19} + 4 q^{22} - 4 q^{25} - 4 q^{26} - 4 q^{27} + 4 q^{29} + 2 q^{30} - 6 q^{33} + 6 q^{35} + 2 q^{36} - 24 q^{37} + 16 q^{38} - 4 q^{40} + 6 q^{42} - 12 q^{43} - 12 q^{46} + 2 q^{48} + 4 q^{49} - 16 q^{51} - 8 q^{53} - 4 q^{55} + 6 q^{56} - 12 q^{58} - 12 q^{59} + 8 q^{61} + 4 q^{62} - 4 q^{64} - 14 q^{65} + 8 q^{66} + 12 q^{67} + 8 q^{68} - 24 q^{71} + 2 q^{74} - 2 q^{75} + 6 q^{76} + 24 q^{77} + 10 q^{78} + 40 q^{79} - 2 q^{81} - 8 q^{82} - 4 q^{87} - 4 q^{88} - 42 q^{89} + 4 q^{90} + 30 q^{91} + 24 q^{93} + 6 q^{94} + 8 q^{95} + 36 q^{97}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^10 - 6 * q^11 + 4 * q^12 + 12 * q^14 - 2 * q^16 - 8 * q^17 + 6 * q^19 + 4 * q^22 - 4 * q^25 - 4 * q^26 - 4 * q^27 + 4 * q^29 + 2 * q^30 - 6 * q^33 + 6 * q^35 + 2 * q^36 - 24 * q^37 + 16 * q^38 - 4 * q^40 + 6 * q^42 - 12 * q^43 - 12 * q^46 + 2 * q^48 + 4 * q^49 - 16 * q^51 - 8 * q^53 - 4 * q^55 + 6 * q^56 - 12 * q^58 - 12 * q^59 + 8 * q^61 + 4 * q^62 - 4 * q^64 - 14 * q^65 + 8 * q^66 + 12 * q^67 + 8 * q^68 - 24 * q^71 + 2 * q^74 - 2 * q^75 + 6 * q^76 + 24 * q^77 + 10 * q^78 + 40 * q^79 - 2 * q^81 - 8 * q^82 - 4 * q^87 - 4 * q^88 - 42 * q^89 + 4 * q^90 + 30 * q^91 + 24 * q^93 + 6 * q^94 + 8 * q^95 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

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