LMFDB - Embedded newform 390.2.bb.b.121.1

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			121.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	390.121
Dual form			390.2.bb.b.361.1

$q$-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} +(-1.73205 + 1.00000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(5.59808 + 3.23205i) q^{11} +1.00000 q^{12} +(1.00000 - 3.46410i) q^{13} +2.00000 q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +1.00000i q^{18} +(6.46410 - 3.73205i) q^{19} +(-0.866025 + 0.500000i) q^{20} +2.00000i q^{21} +(-3.23205 - 5.59808i) q^{22} +(-1.86603 + 3.23205i) q^{23} +(-0.866025 - 0.500000i) q^{24} -1.00000 q^{25} +(-2.59808 + 2.50000i) q^{26} -1.00000 q^{27} +(-1.73205 - 1.00000i) q^{28} +(-0.133975 + 0.232051i) q^{29} +(-0.500000 - 0.866025i) q^{30} -1.73205i q^{31} +(0.866025 - 0.500000i) q^{32} +(5.59808 - 3.23205i) q^{33} -4.00000i q^{34} +(-1.00000 - 1.73205i) q^{35} +(0.500000 - 0.866025i) q^{36} +(7.96410 + 4.59808i) q^{37} -7.46410 q^{38} +(-2.50000 - 2.59808i) q^{39} +1.00000 q^{40} +(1.73205 + 1.00000i) q^{41} +(1.00000 - 1.73205i) q^{42} +(-5.96410 - 10.3301i) q^{43} +6.46410i q^{44} +(0.866025 - 0.500000i) q^{45} +(3.23205 - 1.86603i) q^{46} -3.53590i q^{47} +(0.500000 + 0.866025i) q^{48} +(-1.50000 + 2.59808i) q^{49} +(0.866025 + 0.500000i) q^{50} +4.00000 q^{51} +(3.50000 - 0.866025i) q^{52} +0.928203 q^{53} +(0.866025 + 0.500000i) q^{54} +(-3.23205 + 5.59808i) q^{55} +(1.00000 + 1.73205i) q^{56} -7.46410i q^{57} +(0.232051 - 0.133975i) q^{58} +(7.33013 - 4.23205i) q^{59} +1.00000i q^{60} +(5.19615 + 9.00000i) q^{61} +(-0.866025 + 1.50000i) q^{62} +(1.73205 + 1.00000i) q^{63} -1.00000 q^{64} +(3.46410 + 1.00000i) q^{65} -6.46410 q^{66} +(-9.92820 - 5.73205i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(1.86603 + 3.23205i) q^{69} +2.00000i q^{70} +(-10.7321 + 6.19615i) q^{71} +(-0.866025 + 0.500000i) q^{72} +2.00000i q^{73} +(-4.59808 - 7.96410i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(6.46410 + 3.73205i) q^{76} -12.9282 q^{77} +(0.866025 + 3.50000i) q^{78} -13.9282 q^{79} +(-0.866025 - 0.500000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.00000 - 1.73205i) q^{82} +8.92820i q^{83} +(-1.73205 + 1.00000i) q^{84} +(-3.46410 + 2.00000i) q^{85} +11.9282i q^{86} +(0.133975 + 0.232051i) q^{87} +(3.23205 - 5.59808i) q^{88} +(-0.464102 - 0.267949i) q^{89} -1.00000 q^{90} +(1.73205 + 7.00000i) q^{91} -3.73205 q^{92} +(-1.50000 - 0.866025i) q^{93} +(-1.76795 + 3.06218i) q^{94} +(3.73205 + 6.46410i) q^{95} -1.00000i q^{96} +(0.464102 - 0.267949i) q^{97} +(2.59808 - 1.50000i) q^{98} -6.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9} + 2 q^{10} + 12 q^{11} + 4 q^{12} + 4 q^{13} + 8 q^{14} - 2 q^{16} + 8 q^{17} + 12 q^{19} - 6 q^{22} - 4 q^{23} - 4 q^{25} - 4 q^{27} - 4 q^{29} - 2 q^{30} + 12 q^{33}+ \cdots - 12 q^{97}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9 + 2 * q^10 + 12 * q^11 + 4 * q^12 + 4 * q^13 + 8 * q^14 - 2 * q^16 + 8 * q^17 + 12 * q^19 - 6 * q^22 - 4 * q^23 - 4 * q^25 - 4 * q^27 - 4 * q^29 - 2 * q^30 + 12 * q^33 - 4 * q^35 + 2 * q^36 + 18 * q^37 - 16 * q^38 - 10 * q^39 + 4 * q^40 + 4 * q^42 - 10 * q^43 + 6 * q^46 + 2 * q^48 - 6 * q^49 + 16 * q^51 + 14 * q^52 - 24 * q^53 - 6 * q^55 + 4 * q^56 - 6 * q^58 + 12 * q^59 - 4 * q^64 - 12 * q^66 - 12 * q^67 - 8 * q^68 + 4 * q^69 - 36 * q^71 - 8 * q^74 - 2 * q^75 + 12 * q^76 - 24 * q^77 - 28 * q^79 - 2 * q^81 - 4 * q^82 + 4 * q^87 + 6 * q^88 + 12 * q^89 - 4 * q^90 - 8 * q^92 - 6 * q^93 - 14 * q^94 + 8 * q^95 - 12 * q^97

Character values

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

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

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
$7$	−1.73205	+	1.00000i	−0.654654	+	0.377964i	−0.790237	−	0.612801i	$-0.790043\pi$
$7$	−1.73205	+	1.00000i	−0.654654	+	0.377964i	0.135583	+	0.990766i	$0.456709\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	5.59808	+	3.23205i	1.68788	+	0.974500i	0.956136	+	0.292925i	$0.0946285\pi$
$11$	5.59808	+	3.23205i	1.68788	+	0.974500i	0.731748	+	0.681575i	$0.238705\pi$
$12$	1.00000			0.288675
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$14$	2.00000			0.534522
$15$	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	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$			1.00000i			0.235702i
$19$	6.46410	−	3.73205i	1.48297	−	0.856191i	0.483154	−	0.875536i	$-0.339491\pi$
$19$	6.46410	−	3.73205i	1.48297	−	0.856191i	0.999813	+	0.0193444i	$0.00615788\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$			2.00000i			0.436436i
$22$	−3.23205	−	5.59808i	−0.689076	−	1.19351i
$23$	−1.86603	+	3.23205i	−0.389093	+	0.673929i	−0.992328	−	0.123635i	$-0.960545\pi$
$23$	−1.86603	+	3.23205i	−0.389093	+	0.673929i	0.603235	+	0.797564i	$0.293878\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	−1.00000			−0.200000
$26$	−2.59808	+	2.50000i	−0.509525	+	0.490290i
$27$	−1.00000			−0.192450
$28$	−1.73205	−	1.00000i	−0.327327	−	0.188982i
$29$	−0.133975	+	0.232051i	−0.0248785	+	0.0430908i	−0.878197	−	0.478300i	$-0.841253\pi$
$29$	−0.133975	+	0.232051i	−0.0248785	+	0.0430908i	0.853318	+	0.521391i	$0.174587\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$		−	1.73205i		−	0.311086i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$		−	1.73205i		−	0.311086i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	5.59808	−	3.23205i	0.974500	−	0.562628i
$34$		−	4.00000i		−	0.685994i
$35$	−1.00000	−	1.73205i	−0.169031	−	0.292770i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	7.96410	+	4.59808i	1.30929	+	0.755919i	0.981978	−	0.188997i	$-0.0605237\pi$
$37$	7.96410	+	4.59808i	1.30929	+	0.755919i	0.327313	+	0.944916i	$0.393857\pi$
$38$	−7.46410			−1.21084
$39$	−2.50000	−	2.59808i	−0.400320	−	0.416025i
$40$	1.00000			0.158114
$41$	1.73205	+	1.00000i	0.270501	+	0.156174i	0.629115	−	0.777312i	$-0.283417\pi$
$41$	1.73205	+	1.00000i	0.270501	+	0.156174i	−0.358614	+	0.933486i	$0.616751\pi$
$42$	1.00000	−	1.73205i	0.154303	−	0.267261i
$43$	−5.96410	−	10.3301i	−0.909517	−	1.57533i	−0.814736	−	0.579831i	$-0.803118\pi$
$43$	−5.96410	−	10.3301i	−0.909517	−	1.57533i	−0.0947805	−	0.995498i	$-0.530215\pi$
$44$			6.46410i			0.974500i
$45$	0.866025	−	0.500000i	0.129099	−	0.0745356i
$46$	3.23205	−	1.86603i	0.476540	−	0.275130i
$47$		−	3.53590i		−	0.515764i	−0.966176	−	0.257882i	$-0.916975\pi$
$47$		−	3.53590i		−	0.515764i	0.966176	−	0.257882i	$-0.0830245\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−1.50000	+	2.59808i	−0.214286	+	0.371154i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$	4.00000			0.560112
$52$	3.50000	−	0.866025i	0.485363	−	0.120096i
$53$	0.928203			0.127499			0.0637493	−	0.997966i	$-0.479694\pi$
$53$	0.928203			0.127499			0.0637493	+	0.997966i	$0.479694\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−3.23205	+	5.59808i	−0.435810	+	0.754844i
$56$	1.00000	+	1.73205i	0.133631	+	0.231455i
$57$		−	7.46410i		−	0.988644i
$58$	0.232051	−	0.133975i	0.0304698	−	0.0175917i
$59$	7.33013	−	4.23205i	0.954301	−	0.550966i	0.0598868	−	0.998205i	$-0.480926\pi$
$59$	7.33013	−	4.23205i	0.954301	−	0.550966i	0.894414	+	0.447239i	$0.147593\pi$
$60$			1.00000i			0.129099i
$61$	5.19615	+	9.00000i	0.665299	+	1.15233i	0.979204	+	0.202878i	$0.0650293\pi$
$61$	5.19615	+	9.00000i	0.665299	+	1.15233i	−0.313905	+	0.949454i	$0.601637\pi$
$62$	−0.866025	+	1.50000i	−0.109985	+	0.190500i
$63$	1.73205	+	1.00000i	0.218218	+	0.125988i
$64$	−1.00000			−0.125000
$65$	3.46410	+	1.00000i	0.429669	+	0.124035i
$66$	−6.46410			−0.795676
$67$	−9.92820	−	5.73205i	−1.21292	−	0.700281i	−0.249528	−	0.968368i	$-0.580276\pi$
$67$	−9.92820	−	5.73205i	−1.21292	−	0.700281i	−0.963395	+	0.268086i	$0.913609\pi$
$68$	−2.00000	+	3.46410i	−0.242536	+	0.420084i
$69$	1.86603	+	3.23205i	0.224643	+	0.389093i
$70$			2.00000i			0.239046i
$71$	−10.7321	+	6.19615i	−1.27366	+	0.735348i	−0.975675	−	0.219222i	$-0.929648\pi$
$71$	−10.7321	+	6.19615i	−1.27366	+	0.735348i	−0.297985	+	0.954570i	$0.596315\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$			2.00000i			0.234082i	0.993127	+	0.117041i	$0.0373409\pi$
$73$			2.00000i			0.234082i	−0.993127	+	0.117041i	$0.962659\pi$
$74$	−4.59808	−	7.96410i	−0.534516	−	0.925808i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	6.46410	+	3.73205i	0.741483	+	0.428096i
$77$	−12.9282			−1.47331
$78$	0.866025	+	3.50000i	0.0980581	+	0.396297i
$79$	−13.9282			−1.56705			−0.783523	−	0.621363i	$-0.786579\pi$
$79$	−13.9282			−1.56705			−0.783523	+	0.621363i	$0.786579\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.00000	−	1.73205i	−0.110432	−	0.191273i
$83$			8.92820i			0.979998i	0.871723	+	0.489999i	$0.163003\pi$
$83$			8.92820i			0.979998i	−0.871723	+	0.489999i	$0.836997\pi$
$84$	−1.73205	+	1.00000i	−0.188982	+	0.109109i
$85$	−3.46410	+	2.00000i	−0.375735	+	0.216930i
$86$			11.9282i			1.28625i
$87$	0.133975	+	0.232051i	0.0143636	+	0.0248785i
$88$	3.23205	−	5.59808i	0.344538	−	0.596757i
$89$	−0.464102	−	0.267949i	−0.0491947	−	0.0284026i	0.475201	−	0.879877i	$-0.342375\pi$
$89$	−0.464102	−	0.267949i	−0.0491947	−	0.0284026i	−0.524396	+	0.851475i	$0.675709\pi$
$90$	−1.00000			−0.105409
$91$	1.73205	+	7.00000i	0.181568	+	0.733799i
$92$	−3.73205			−0.389093
$93$	−1.50000	−	0.866025i	−0.155543	−	0.0898027i
$94$	−1.76795	+	3.06218i	−0.182350	+	0.315840i
$95$	3.73205	+	6.46410i	0.382900	+	0.663203i
$96$		−	1.00000i		−	0.102062i
$97$	0.464102	−	0.267949i	0.0471224	−	0.0272061i	−0.476254	−	0.879308i	$-0.658006\pi$
$97$	0.464102	−	0.267949i	0.0471224	−	0.0272061i	0.523376	+	0.852102i	$0.324672\pi$
$98$	2.59808	−	1.50000i	0.262445	−	0.151523i
$99$		−	6.46410i		−	0.649667i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−1.46410	+	2.53590i	−0.145684	+	0.252331i	−0.929628	−	0.368500i	$-0.879871\pi$
$101$	−1.46410	+	2.53590i	−0.145684	+	0.252331i	0.783944	+	0.620831i	$0.213205\pi$
$102$	−3.46410	−	2.00000i	−0.342997	−	0.198030i
$103$	−11.8564			−1.16825			−0.584123	−	0.811665i	$-0.698562\pi$
$103$	−11.8564			−1.16825			−0.584123	+	0.811665i	$0.698562\pi$
$104$	−3.46410	−	1.00000i	−0.339683	−	0.0980581i
$105$	−2.00000			−0.195180
$106$	−0.803848	−	0.464102i	−0.0780766	−	0.0450775i
$107$	3.92820	−	6.80385i	0.379754	−	0.657753i	−0.611273	−	0.791420i	$-0.709342\pi$
$107$	3.92820	−	6.80385i	0.379754	−	0.657753i	0.991026	+	0.133667i	$0.0426754\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$		−	15.8564i		−	1.51877i	−0.650643	−	0.759384i	$-0.725500\pi$
$109$		−	15.8564i		−	1.51877i	0.650643	−	0.759384i	$-0.274500\pi$
$110$	5.59808	−	3.23205i	0.533756	−	0.308164i
$111$	7.96410	−	4.59808i	0.755919	−	0.436430i
$112$		−	2.00000i		−	0.188982i
$113$	−0.401924	−	0.696152i	−0.0378098	−	0.0654885i	0.846501	−	0.532387i	$-0.178705\pi$
$113$	−0.401924	−	0.696152i	−0.0378098	−	0.0654885i	−0.884311	+	0.466898i	$0.845371\pi$
$114$	−3.73205	+	6.46410i	−0.349539	+	0.605419i
$115$	−3.23205	−	1.86603i	−0.301390	−	0.174008i
$116$	−0.267949			−0.0248785
$117$	−3.50000	+	0.866025i	−0.323575	+	0.0800641i
$118$	−8.46410			−0.779184
$119$	−6.92820	−	4.00000i	−0.635107	−	0.366679i
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	15.3923	+	26.6603i	1.39930	+	2.42366i
$122$		−	10.3923i		−	0.940875i
$123$	1.73205	−	1.00000i	0.156174	−	0.0901670i
$124$	1.50000	−	0.866025i	0.134704	−	0.0777714i
$125$		−	1.00000i		−	0.0894427i
$126$	−1.00000	−	1.73205i	−0.0890871	−	0.154303i
$127$	2.46410	−	4.26795i	0.218654	−	0.378719i	−0.735743	−	0.677261i	$-0.763167\pi$
$127$	2.46410	−	4.26795i	0.218654	−	0.378719i	0.954397	+	0.298542i	$0.0965002\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−11.9282			−1.05022
$130$	−2.50000	−	2.59808i	−0.219265	−	0.227866i
$131$	−18.6603			−1.63035			−0.815177	−	0.579212i	$-0.803360\pi$
$131$	−18.6603			−1.63035			−0.815177	+	0.579212i	$0.803360\pi$
$132$	5.59808	+	3.23205i	0.487250	+	0.281314i
$133$	−7.46410	+	12.9282i	−0.647220	+	1.12102i
$134$	5.73205	+	9.92820i	0.495174	+	0.857666i
$135$		−	1.00000i		−	0.0860663i
$136$	3.46410	−	2.00000i	0.297044	−	0.171499i
$137$	−2.13397	+	1.23205i	−0.182318	+	0.105261i	−0.588381	−	0.808584i	$-0.700235\pi$
$137$	−2.13397	+	1.23205i	−0.182318	+	0.105261i	0.406063	+	0.913845i	$0.366901\pi$
$138$		−	3.73205i		−	0.317693i
$139$	6.46410	+	11.1962i	0.548278	+	0.949645i	0.998393	+	0.0566745i	$0.0180497\pi$
$139$	6.46410	+	11.1962i	0.548278	+	0.949645i	−0.450115	+	0.892971i	$0.648617\pi$
$140$	1.00000	−	1.73205i	0.0845154	−	0.146385i
$141$	−3.06218	−	1.76795i	−0.257882	−	0.148888i
$142$	12.3923			1.03994
$143$	16.7942	−	16.1603i	1.40440	−	1.35139i
$144$	1.00000			0.0833333
$145$	−0.232051	−	0.133975i	−0.0192708	−	0.0111260i
$146$	1.00000	−	1.73205i	0.0827606	−	0.143346i
$147$	1.50000	+	2.59808i	0.123718	+	0.214286i
$148$			9.19615i			0.755919i
$149$	−11.7224	+	6.76795i	−0.960339	+	0.554452i	−0.896277	−	0.443494i	$-0.853739\pi$
$149$	−11.7224	+	6.76795i	−0.960339	+	0.554452i	−0.0640617	+	0.997946i	$0.520405\pi$
$150$	0.866025	−	0.500000i	0.0707107	−	0.0408248i
$151$		−	10.3923i		−	0.845714i	−0.906196	−	0.422857i	$-0.861027\pi$
$151$		−	10.3923i		−	0.845714i	0.906196	−	0.422857i	$-0.138973\pi$
$152$	−3.73205	−	6.46410i	−0.302709	−	0.524308i
$153$	2.00000	−	3.46410i	0.161690	−	0.280056i
$154$	11.1962	+	6.46410i	0.902212	+	0.520892i
$155$	1.73205			0.139122
$156$	1.00000	−	3.46410i	0.0800641	−	0.277350i
$157$	−5.00000			−0.399043			−0.199522	−	0.979893i	$-0.563939\pi$
$157$	−5.00000			−0.399043			−0.199522	+	0.979893i	$0.563939\pi$
$158$	12.0622	+	6.96410i	0.959615	+	0.554034i
$159$	0.464102	−	0.803848i	0.0368057	−	0.0637493i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$		−	7.46410i		−	0.588254i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	13.0359	−	7.52628i	1.02105	−	0.589504i	0.106642	−	0.994297i	$-0.465990\pi$
$163$	13.0359	−	7.52628i	1.02105	−	0.589504i	0.914408	+	0.404794i	$0.132657\pi$
$164$			2.00000i			0.156174i
$165$	3.23205	+	5.59808i	0.251615	+	0.435810i
$166$	4.46410	−	7.73205i	0.346481	−	0.600124i
$167$	14.1340	+	8.16025i	1.09372	+	0.631459i	0.934564	−	0.355794i	$-0.115790\pi$
$167$	14.1340	+	8.16025i	1.09372	+	0.631459i	0.159155	+	0.987254i	$0.449123\pi$
$168$	2.00000			0.154303
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$	4.00000			0.306786
$171$	−6.46410	−	3.73205i	−0.494322	−	0.285397i
$172$	5.96410	−	10.3301i	0.454758	−	0.787665i
$173$	−5.46410	−	9.46410i	−0.415428	−	0.719542i	0.580045	−	0.814584i	$-0.303035\pi$
$173$	−5.46410	−	9.46410i	−0.415428	−	0.719542i	−0.995473	+	0.0950419i	$0.969701\pi$
$174$		−	0.267949i		−	0.0203132i
$175$	1.73205	−	1.00000i	0.130931	−	0.0755929i
$176$	−5.59808	+	3.23205i	−0.421971	+	0.243625i
$177$		−	8.46410i		−	0.636201i
$178$	0.267949	+	0.464102i	0.0200836	+	0.0347859i
$179$	9.86603	−	17.0885i	0.737421	−	1.27725i	−0.216231	−	0.976342i	$-0.569377\pi$
$179$	9.86603	−	17.0885i	0.737421	−	1.27725i	0.953653	−	0.300909i	$-0.0972901\pi$
$180$	0.866025	+	0.500000i	0.0645497	+	0.0372678i
$181$	−2.92820			−0.217652			−0.108826	−	0.994061i	$-0.534709\pi$
$181$	−2.92820			−0.217652			−0.108826	+	0.994061i	$0.534709\pi$
$182$	2.00000	−	6.92820i	0.148250	−	0.513553i
$183$	10.3923			0.768221
$184$	3.23205	+	1.86603i	0.238270	+	0.137565i
$185$	−4.59808	+	7.96410i	−0.338057	+	0.585532i
$186$	0.866025	+	1.50000i	0.0635001	+	0.109985i
$187$			25.8564i			1.89081i
$188$	3.06218	−	1.76795i	0.223332	−	0.128941i
$189$	1.73205	−	1.00000i	0.125988	−	0.0727393i
$190$		−	7.46410i		−	0.541503i
$191$	−10.7321	−	18.5885i	−0.776544	−	1.34501i	−0.933923	−	0.357475i	$-0.883638\pi$
$191$	−10.7321	−	18.5885i	−0.776544	−	1.34501i	0.157379	−	0.987538i	$-0.449696\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	9.80385	+	5.66025i	0.705696	+	0.407434i	0.809466	−	0.587167i	$-0.199757\pi$
$193$	9.80385	+	5.66025i	0.705696	+	0.407434i	−0.103769	+	0.994601i	$0.533090\pi$
$194$	−0.535898			−0.0384753
$195$	2.59808	−	2.50000i	0.186052	−	0.179029i
$196$	−3.00000			−0.214286
$197$	3.80385	+	2.19615i	0.271013	+	0.156469i	0.629348	−	0.777124i	$-0.283322\pi$
$197$	3.80385	+	2.19615i	0.271013	+	0.156469i	−0.358335	+	0.933593i	$0.616655\pi$
$198$	−3.23205	+	5.59808i	−0.229692	+	0.397838i
$199$	2.53590	+	4.39230i	0.179765	+	0.311362i	0.941800	−	0.336174i	$-0.109133\pi$
$199$	2.53590	+	4.39230i	0.179765	+	0.311362i	−0.762035	+	0.647536i	$0.775800\pi$
$200$			1.00000i			0.0707107i
$201$	−9.92820	+	5.73205i	−0.700281	+	0.404308i
$202$	2.53590	−	1.46410i	0.178425	−	0.103014i
$203$		−	0.535898i		−	0.0376127i
$204$	2.00000	+	3.46410i	0.140028	+	0.242536i
$205$	−1.00000	+	1.73205i	−0.0698430	+	0.120972i
$206$	10.2679	+	5.92820i	0.715402	+	0.413037i
$207$	3.73205			0.259395
$208$	2.50000	+	2.59808i	0.173344	+	0.180144i
$209$	48.2487			3.33743
$210$	1.73205	+	1.00000i	0.119523	+	0.0690066i
$211$	5.66025	−	9.80385i	0.389668	−	0.674925i	−0.602737	−	0.797940i	$-0.705923\pi$
$211$	5.66025	−	9.80385i	0.389668	−	0.674925i	0.992405	+	0.123015i	$0.0392564\pi$
$212$	0.464102	+	0.803848i	0.0318746	+	0.0552085i
$213$			12.3923i			0.849107i
$214$	−6.80385	+	3.92820i	−0.465101	+	0.268526i
$215$	10.3301	−	5.96410i	0.704509	−	0.406748i
$216$			1.00000i			0.0680414i
$217$	1.73205	+	3.00000i	0.117579	+	0.203653i
$218$	−7.92820	+	13.7321i	−0.536966	+	0.930052i
$219$	1.73205	+	1.00000i	0.117041	+	0.0675737i
$220$	−6.46410			−0.435810
$221$	14.0000	−	3.46410i	0.941742	−	0.233021i
$222$	−9.19615			−0.617205
$223$	−17.7846	−	10.2679i	−1.19095	−	0.687593i	−0.232424	−	0.972614i	$-0.574666\pi$
$223$	−17.7846	−	10.2679i	−1.19095	−	0.687593i	−0.958521	+	0.285022i	$0.907999\pi$
$224$	−1.00000	+	1.73205i	−0.0668153	+	0.115728i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$			0.803848i			0.0534711i
$227$	−14.1962	+	8.19615i	−0.942232	+	0.543998i	−0.890659	−	0.454672i	$-0.849757\pi$
$227$	−14.1962	+	8.19615i	−0.942232	+	0.543998i	−0.0515725	+	0.998669i	$0.516423\pi$
$228$	6.46410	−	3.73205i	0.428096	−	0.247161i
$229$		−	7.85641i		−	0.519166i	−0.965721	−	0.259583i	$-0.916415\pi$
$229$		−	7.85641i		−	0.519166i	0.965721	−	0.259583i	$-0.0835851\pi$
$230$	1.86603	+	3.23205i	0.123042	+	0.213115i
$231$	−6.46410	+	11.1962i	−0.425307	+	0.736653i
$232$	0.232051	+	0.133975i	0.0152349	+	0.00879586i
$233$	6.12436			0.401220			0.200610	−	0.979671i	$-0.435708\pi$
$233$	6.12436			0.401220			0.200610	+	0.979671i	$0.435708\pi$
$234$	3.46410	+	1.00000i	0.226455	+	0.0653720i
$235$	3.53590			0.230657
$236$	7.33013	+	4.23205i	0.477151	+	0.275483i
$237$	−6.96410	+	12.0622i	−0.452367	+	0.783523i
$238$	4.00000	+	6.92820i	0.259281	+	0.449089i
$239$		−	16.3923i		−	1.06033i	−0.847894	−	0.530165i	$-0.822130\pi$
$239$		−	16.3923i		−	1.06033i	0.847894	−	0.530165i	$-0.177870\pi$
$240$	−0.866025	+	0.500000i	−0.0559017	+	0.0322749i
$241$	15.3564	−	8.86603i	0.989193	−	0.571111i	0.0841601	−	0.996452i	$-0.473179\pi$
$241$	15.3564	−	8.86603i	0.989193	−	0.571111i	0.905033	+	0.425341i	$0.139846\pi$
$242$		−	30.7846i		−	1.97891i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−5.19615	+	9.00000i	−0.332650	+	0.576166i
$245$	−2.59808	−	1.50000i	−0.165985	−	0.0958315i
$246$	−2.00000			−0.127515
$247$	−6.46410	−	26.1244i	−0.411301	−	1.66225i
$248$	−1.73205			−0.109985
$249$	7.73205	+	4.46410i	0.489999	+	0.282901i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−7.86603	−	13.6244i	−0.496499	−	0.859962i	0.503493	−	0.863999i	$-0.332048\pi$
$251$	−7.86603	−	13.6244i	−0.496499	−	0.859962i	−0.999992	+	0.00403776i	$0.998715\pi$
$252$			2.00000i			0.125988i
$253$	−20.8923	+	12.0622i	−1.31349	+	0.758343i
$254$	−4.26795	+	2.46410i	−0.267795	+	0.154611i
$255$			4.00000i			0.250490i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.66987	−	4.62436i	0.166542	−	0.288459i	−0.770660	−	0.637247i	$-0.780073\pi$
$257$	2.66987	−	4.62436i	0.166542	−	0.288459i	0.937202	+	0.348787i	$0.113407\pi$
$258$	10.3301	+	5.96410i	0.643126	+	0.371309i
$259$	−18.3923			−1.14284
$260$	0.866025	+	3.50000i	0.0537086	+	0.217061i
$261$	0.267949			0.0165856
$262$	16.1603	+	9.33013i	0.998384	+	0.576417i
$263$	−3.06218	+	5.30385i	−0.188822	+	0.327049i	−0.944858	−	0.327481i	$-0.893800\pi$
$263$	−3.06218	+	5.30385i	−0.188822	+	0.327049i	0.756036	+	0.654530i	$0.227134\pi$
$264$	−3.23205	−	5.59808i	−0.198919	−	0.344538i
$265$			0.928203i			0.0570191i
$266$	12.9282	−	7.46410i	0.792679	−	0.457653i
$267$	−0.464102	+	0.267949i	−0.0284026	+	0.0163982i
$268$		−	11.4641i		−	0.700281i
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	0.623082	−	0.782157i	$-0.285880\pi$
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	−0.988908	+	0.148527i	$0.952547\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	1.03590	+	0.598076i	0.0629263	+	0.0363305i	0.531133	−	0.847288i	$-0.321766\pi$
$271$	1.03590	+	0.598076i	0.0629263	+	0.0363305i	−0.468207	+	0.883619i	$0.655100\pi$
$272$	−4.00000			−0.242536
$273$	6.92820	+	2.00000i	0.419314	+	0.121046i
$274$	2.46410			0.148862
$275$	−5.59808	−	3.23205i	−0.337577	−	0.194900i
$276$	−1.86603	+	3.23205i	−0.112322	+	0.194547i
$277$	1.96410	+	3.40192i	0.118011	+	0.204402i	0.918980	−	0.394305i	$-0.129015\pi$
$277$	1.96410	+	3.40192i	0.118011	+	0.204402i	−0.800968	+	0.598707i	$0.795681\pi$
$278$		−	12.9282i		−	0.775382i
$279$	−1.50000	+	0.866025i	−0.0898027	+	0.0518476i
$280$	−1.73205	+	1.00000i	−0.103510	+	0.0597614i
$281$		−	8.92820i		−	0.532612i	−0.963889	−	0.266306i	$-0.914197\pi$
$281$		−	8.92820i		−	0.532612i	0.963889	−	0.266306i	$-0.0858032\pi$
$282$	1.76795	+	3.06218i	0.105280	+	0.182350i
$283$	4.96410	−	8.59808i	0.295085	−	0.511103i	−0.679920	−	0.733287i	$-0.737985\pi$
$283$	4.96410	−	8.59808i	0.295085	−	0.511103i	0.975005	+	0.222184i	$0.0713186\pi$
$284$	−10.7321	−	6.19615i	−0.636830	−	0.367674i
$285$	7.46410			0.442135
$286$	−22.6244	+	5.59808i	−1.33781	+	0.331021i
$287$	−4.00000			−0.236113
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	0.133975	+	0.232051i	0.00786726	+	0.0136265i
$291$		−	0.535898i		−	0.0314149i
$292$	−1.73205	+	1.00000i	−0.101361	+	0.0585206i
$293$	−27.5885	+	15.9282i	−1.61173	+	0.930536i	−0.622767	+	0.782408i	$0.713991\pi$
$293$	−27.5885	+	15.9282i	−1.61173	+	0.930536i	−0.988968	+	0.148128i	$0.952675\pi$
$294$		−	3.00000i		−	0.174964i
$295$	4.23205	+	7.33013i	0.246400	+	0.426776i
$296$	4.59808	−	7.96410i	0.267258	−	0.462904i
$297$	−5.59808	−	3.23205i	−0.324833	−	0.187543i
$298$	13.5359			0.784114
$299$	9.33013	+	9.69615i	0.539575	+	0.560743i
$300$	−1.00000			−0.0577350
$301$	20.6603	+	11.9282i	1.19084	+	0.687530i
$302$	−5.19615	+	9.00000i	−0.299005	+	0.517892i
$303$	1.46410	+	2.53590i	0.0841104	+	0.145684i
$304$			7.46410i			0.428096i
$305$	−9.00000	+	5.19615i	−0.515339	+	0.297531i
$306$	−3.46410	+	2.00000i	−0.198030	+	0.114332i
$307$			19.4641i			1.11087i	0.831558	+	0.555437i	$0.187449\pi$
$307$			19.4641i			1.11087i	−0.831558	+	0.555437i	$0.812551\pi$
$308$	−6.46410	−	11.1962i	−0.368326	−	0.637960i
$309$	−5.92820	+	10.2679i	−0.337244	+	0.584123i
$310$	−1.50000	−	0.866025i	−0.0851943	−	0.0491869i
$311$	−28.3923			−1.60998			−0.804990	−	0.593288i	$-0.797829\pi$
$311$	−28.3923			−1.60998			−0.804990	+	0.593288i	$0.797829\pi$
$312$	−2.59808	+	2.50000i	−0.147087	+	0.141535i
$313$	−28.0000			−1.58265			−0.791327	−	0.611393i	$-0.790609\pi$
$313$	−28.0000			−1.58265			−0.791327	+	0.611393i	$0.790609\pi$
$314$	4.33013	+	2.50000i	0.244363	+	0.141083i
$315$	−1.00000	+	1.73205i	−0.0563436	+	0.0975900i
$316$	−6.96410	−	12.0622i	−0.391761	−	0.678551i
$317$			14.5359i			0.816417i	0.912889	+	0.408209i	$0.133846\pi$
$317$			14.5359i			0.816417i	−0.912889	+	0.408209i	$0.866154\pi$
$318$	−0.803848	+	0.464102i	−0.0450775	+	0.0260255i
$319$	−1.50000	+	0.866025i	−0.0839839	+	0.0484881i
$320$		−	1.00000i		−	0.0559017i
$321$	−3.92820	−	6.80385i	−0.219251	−	0.379754i
$322$	−3.73205	+	6.46410i	−0.207979	+	0.360230i
$323$	25.8564	+	14.9282i	1.43869	+	0.830627i
$324$	−1.00000			−0.0555556
$325$	−1.00000	+	3.46410i	−0.0554700	+	0.192154i
$326$	−15.0526			−0.833684
$327$	−13.7321	−	7.92820i	−0.759384	−	0.438431i
$328$	1.00000	−	1.73205i	0.0552158	−	0.0956365i
$329$	3.53590	+	6.12436i	0.194940	+	0.337647i
$330$		−	6.46410i		−	0.355837i
$331$	−14.5359	+	8.39230i	−0.798965	+	0.461283i	−0.843109	−	0.537742i	$-0.819277\pi$
$331$	−14.5359	+	8.39230i	−0.798965	+	0.461283i	0.0441440	+	0.999025i	$0.485944\pi$
$332$	−7.73205	+	4.46410i	−0.424351	+	0.244999i
$333$		−	9.19615i		−	0.503946i
$334$	−8.16025	−	14.1340i	−0.446509	−	0.773377i
$335$	5.73205	−	9.92820i	0.313175	−	0.542436i
$336$	−1.73205	−	1.00000i	−0.0944911	−	0.0545545i
$337$	9.32051			0.507720			0.253860	−	0.967241i	$-0.418300\pi$
$337$	9.32051			0.507720			0.253860	+	0.967241i	$0.418300\pi$
$338$	6.06218	+	11.5000i	0.329739	+	0.625518i
$339$	−0.803848			−0.0436590
$340$	−3.46410	−	2.00000i	−0.187867	−	0.108465i
$341$	5.59808	−	9.69615i	0.303153	−	0.525076i
$342$	3.73205	+	6.46410i	0.201806	+	0.349539i
$343$		−	20.0000i		−	1.07990i
$344$	−10.3301	+	5.96410i	−0.556963	+	0.321563i
$345$	−3.23205	+	1.86603i	−0.174008	+	0.100463i
$346$			10.9282i			0.587504i
$347$	−0.803848	−	1.39230i	−0.0431528	−	0.0747428i	0.843642	−	0.536906i	$-0.180407\pi$
$347$	−0.803848	−	1.39230i	−0.0431528	−	0.0747428i	−0.886795	+	0.462163i	$0.847074\pi$
$348$	−0.133975	+	0.232051i	−0.00718179	+	0.0124392i
$349$	18.5885	+	10.7321i	0.995017	+	0.574474i	0.906770	−	0.421625i	$-0.138540\pi$
$349$	18.5885	+	10.7321i	0.995017	+	0.574474i	0.0882471	+	0.996099i	$0.471873\pi$
$350$	−2.00000			−0.106904
$351$	−1.00000	+	3.46410i	−0.0533761	+	0.184900i
$352$	6.46410			0.344538
$353$	1.73205	+	1.00000i	0.0921878	+	0.0532246i	0.545385	−	0.838186i	$-0.316383\pi$
$353$	1.73205	+	1.00000i	0.0921878	+	0.0532246i	−0.453197	+	0.891410i	$0.649717\pi$
$354$	−4.23205	+	7.33013i	−0.224931	+	0.389592i
$355$	−6.19615	−	10.7321i	−0.328858	−	0.569598i
$356$		−	0.535898i		−	0.0284026i
$357$	−6.92820	+	4.00000i	−0.366679	+	0.211702i
$358$	−17.0885	+	9.86603i	−0.903153	+	0.521436i
$359$			5.07180i			0.267679i	0.991003	+	0.133840i	$0.0427307\pi$
$359$			5.07180i			0.267679i	−0.991003	+	0.133840i	$0.957269\pi$
$360$	−0.500000	−	0.866025i	−0.0263523	−	0.0456435i
$361$	18.3564	−	31.7942i	0.966127	−	1.67338i
$362$	2.53590	+	1.46410i	0.133284	+	0.0769515i
$363$	30.7846			1.61577
$364$	−5.19615	+	5.00000i	−0.272352	+	0.262071i
$365$	−2.00000			−0.104685
$366$	−9.00000	−	5.19615i	−0.470438	−	0.271607i
$367$	−7.80385	+	13.5167i	−0.407358	+	0.705564i	−0.994593	−	0.103852i	$-0.966883\pi$
$367$	−7.80385	+	13.5167i	−0.407358	+	0.705564i	0.587235	+	0.809416i	$0.300216\pi$
$368$	−1.86603	−	3.23205i	−0.0972733	−	0.168482i
$369$		−	2.00000i		−	0.104116i
$370$	7.96410	−	4.59808i	0.414034	−	0.239043i
$371$	−1.60770	+	0.928203i	−0.0834674	+	0.0481899i
$372$		−	1.73205i		−	0.0898027i
$373$	7.89230	+	13.6699i	0.408648	+	0.707799i	0.994739	−	0.102446i	$-0.0326670\pi$
$373$	7.89230	+	13.6699i	0.408648	+	0.707799i	−0.586090	+	0.810246i	$0.699334\pi$
$374$	12.9282	−	22.3923i	0.668501	−	1.15788i
$375$	−0.866025	−	0.500000i	−0.0447214	−	0.0258199i
$376$	−3.53590			−0.182350
$377$	0.669873	+	0.696152i	0.0345002	+	0.0358537i
$378$	−2.00000			−0.102869
$379$	24.1244	+	13.9282i	1.23918	+	0.715444i	0.968928	−	0.247344i	$-0.0795579\pi$
$379$	24.1244	+	13.9282i	1.23918	+	0.715444i	0.270257	+	0.962788i	$0.412891\pi$
$380$	−3.73205	+	6.46410i	−0.191450	+	0.331601i
$381$	−2.46410	−	4.26795i	−0.126240	−	0.218654i
$382$			21.4641i			1.09820i
$383$	21.9904	−	12.6962i	1.12366	−	0.648743i	0.181324	−	0.983423i	$-0.441962\pi$
$383$	21.9904	−	12.6962i	1.12366	−	0.648743i	0.942332	+	0.334680i	$0.108628\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$		−	12.9282i		−	0.658882i
$386$	−5.66025	−	9.80385i	−0.288099	−	0.499003i
$387$	−5.96410	+	10.3301i	−0.303172	+	0.525110i
$388$	0.464102	+	0.267949i	0.0235612	+	0.0136031i
$389$	−23.7321			−1.20326			−0.601631	−	0.798774i	$-0.705482\pi$
$389$	−23.7321			−1.20326			−0.601631	+	0.798774i	$0.705482\pi$
$390$	−3.50000	+	0.866025i	−0.177229	+	0.0438529i
$391$	−14.9282			−0.754952
$392$	2.59808	+	1.50000i	0.131223	+	0.0757614i
$393$	−9.33013	+	16.1603i	−0.470643	+	0.815177i
$394$	−2.19615	−	3.80385i	−0.110641	−	0.191635i
$395$		−	13.9282i		−	0.700804i
$396$	5.59808	−	3.23205i	0.281314	−	0.162417i
$397$	10.5000	−	6.06218i	0.526980	−	0.304252i	−0.212806	−	0.977095i	$-0.568260\pi$
$397$	10.5000	−	6.06218i	0.526980	−	0.304252i	0.739786	+	0.672843i	$0.234927\pi$
$398$		−	5.07180i		−	0.254226i
$399$	7.46410	+	12.9282i	0.373672	+	0.647220i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	−27.7128	−	16.0000i	−1.38391	−	0.799002i	−0.391292	−	0.920267i	$-0.627972\pi$
$401$	−27.7128	−	16.0000i	−1.38391	−	0.799002i	−0.992620	+	0.121265i	$0.961305\pi$
$402$	11.4641			0.571777
$403$	−6.00000	−	1.73205i	−0.298881	−	0.0862796i
$404$	−2.92820			−0.145684
$405$	−0.866025	−	0.500000i	−0.0430331	−	0.0248452i
$406$	−0.267949	+	0.464102i	−0.0132981	+	0.0230330i
$407$	29.7224	+	51.4808i	1.47329	+	2.55181i
$408$		−	4.00000i		−	0.198030i
$409$	3.46410	−	2.00000i	0.171289	−	0.0988936i	−0.411905	−	0.911227i	$-0.635136\pi$
$409$	3.46410	−	2.00000i	0.171289	−	0.0988936i	0.583193	+	0.812333i	$0.301803\pi$
$410$	1.73205	−	1.00000i	0.0855399	−	0.0493865i
$411$			2.46410i			0.121545i
$412$	−5.92820	−	10.2679i	−0.292062	−	0.505866i
$413$	−8.46410	+	14.6603i	−0.416491	+	0.721384i
$414$	−3.23205	−	1.86603i	−0.158847	−	0.0917101i
$415$	−8.92820			−0.438268
$416$	−0.866025	−	3.50000i	−0.0424604	−	0.171602i
$417$	12.9282			0.633097
$418$	−41.7846	−	24.1244i	−2.04375	−	1.17996i
$419$	−11.1962	+	19.3923i	−0.546968	+	0.947376i	0.451512	+	0.892265i	$0.350885\pi$
$419$	−11.1962	+	19.3923i	−0.546968	+	0.947376i	−0.998480	+	0.0551112i	$0.982449\pi$
$420$	−1.00000	−	1.73205i	−0.0487950	−	0.0845154i
$421$			4.39230i			0.214068i	0.994255	+	0.107034i	$0.0341353\pi$
$421$			4.39230i			0.214068i	−0.994255	+	0.107034i	$0.965865\pi$
$422$	−9.80385	+	5.66025i	−0.477244	+	0.275537i
$423$	−3.06218	+	1.76795i	−0.148888	+	0.0859606i
$424$		−	0.928203i		−	0.0450775i
$425$	−2.00000	−	3.46410i	−0.0970143	−	0.168034i
$426$	6.19615	−	10.7321i	0.300205	−	0.519970i
$427$	−18.0000	−	10.3923i	−0.871081	−	0.502919i
$428$	7.85641			0.379754
$429$	−5.59808	−	22.6244i	−0.270278	−	1.09231i
$430$	−11.9282			−0.575229
$431$	24.5885	+	14.1962i	1.18438	+	0.683805i	0.957025	−	0.290006i	$-0.0936574\pi$
$431$	24.5885	+	14.1962i	1.18438	+	0.683805i	0.227360	+	0.973811i	$0.426991\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−9.66025	−	16.7321i	−0.464242	−	0.804091i	0.534925	−	0.844900i	$-0.320340\pi$
$433$	−9.66025	−	16.7321i	−0.464242	−	0.804091i	−0.999167	+	0.0408086i	$0.987007\pi$
$434$		−	3.46410i		−	0.166282i
$435$	−0.232051	+	0.133975i	−0.0111260	+	0.00642359i
$436$	13.7321	−	7.92820i	0.657646	−	0.379692i
$437$			27.8564i			1.33255i
$438$	−1.00000	−	1.73205i	−0.0477818	−	0.0827606i
$439$	8.92820	−	15.4641i	0.426120	−	0.738061i	−0.570404	−	0.821364i	$-0.693214\pi$
$439$	8.92820	−	15.4641i	0.426120	−	0.738061i	0.996524	+	0.0833027i	$0.0265468\pi$
$440$	5.59808	+	3.23205i	0.266878	+	0.154082i
$441$	3.00000			0.142857
$442$	−13.8564	−	4.00000i	−0.659082	−	0.190261i
$443$	16.3923			0.778822			0.389411	−	0.921064i	$-0.372679\pi$
$443$	16.3923			0.778822			0.389411	+	0.921064i	$0.372679\pi$
$444$	7.96410	+	4.59808i	0.377960	+	0.218215i
$445$	0.267949	−	0.464102i	0.0127020	−	0.0220005i
$446$	10.2679	+	17.7846i	0.486201	+	0.842126i
$447$			13.5359i			0.640226i
$448$	1.73205	−	1.00000i	0.0818317	−	0.0472456i
$449$	−13.6077	+	7.85641i	−0.642187	+	0.370767i	−0.785456	−	0.618917i	$-0.787572\pi$
$449$	−13.6077	+	7.85641i	−0.642187	+	0.370767i	0.143270	+	0.989684i	$0.454238\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	6.46410	+	11.1962i	0.304383	+	0.527206i
$452$	0.401924	−	0.696152i	0.0189049	−	0.0327443i
$453$	−9.00000	−	5.19615i	−0.422857	−	0.244137i
$454$	16.3923			0.769329
$455$	−7.00000	+	1.73205i	−0.328165	+	0.0811998i
$456$	−7.46410			−0.349539
$457$	21.2487	+	12.2679i	0.993973	+	0.573870i	0.906459	−	0.422293i	$-0.138775\pi$
$457$	21.2487	+	12.2679i	0.993973	+	0.573870i	0.0875134	+	0.996163i	$0.472108\pi$
$458$	−3.92820	+	6.80385i	−0.183553	+	0.317923i
$459$	−2.00000	−	3.46410i	−0.0933520	−	0.161690i
$460$		−	3.73205i		−	0.174008i
$461$	0.401924	−	0.232051i	0.0187195	−	0.0108077i	−0.490611	−	0.871379i	$-0.663226\pi$
$461$	0.401924	−	0.232051i	0.0187195	−	0.0108077i	0.509331	+	0.860571i	$0.329893\pi$
$462$	11.1962	−	6.46410i	0.520892	−	0.300737i
$463$			7.07180i			0.328654i	0.986406	+	0.164327i	$0.0525453\pi$
$463$			7.07180i			0.328654i	−0.986406	+	0.164327i	$0.947455\pi$
$464$	−0.133975	−	0.232051i	−0.00621961	−	0.0107727i
$465$	0.866025	−	1.50000i	0.0401610	−	0.0695608i
$466$	−5.30385	−	3.06218i	−0.245696	−	0.141853i
$467$	−15.8564			−0.733747			−0.366873	−	0.930271i	$-0.619572\pi$
$467$	−15.8564			−0.733747			−0.366873	+	0.930271i	$0.619572\pi$
$468$	−2.50000	−	2.59808i	−0.115563	−	0.120096i
$469$	22.9282			1.05873
$470$	−3.06218	−	1.76795i	−0.141248	−	0.0815494i
$471$	−2.50000	+	4.33013i	−0.115194	+	0.199522i
$472$	−4.23205	−	7.33013i	−0.194796	−	0.337396i
$473$		−	77.1051i		−	3.54530i
$474$	12.0622	−	6.96410i	0.554034	−	0.319872i
$475$	−6.46410	+	3.73205i	−0.296593	+	0.171238i
$476$		−	8.00000i		−	0.366679i
$477$	−0.464102	−	0.803848i	−0.0212498	−	0.0368057i
$478$	−8.19615	+	14.1962i	−0.374883	+	0.649317i
$479$	4.73205	+	2.73205i	0.216213	+	0.124831i	0.604195	−	0.796836i	$-0.293495\pi$
$479$	4.73205	+	2.73205i	0.216213	+	0.124831i	−0.387983	+	0.921667i	$0.626828\pi$
$480$	1.00000			0.0456435
$481$	23.8923	−	22.9904i	1.08940	−	1.04827i
$482$	−17.7321			−0.807673
$483$	−6.46410	−	3.73205i	−0.294127	−	0.169814i
$484$	−15.3923	+	26.6603i	−0.699650	+	1.21183i
$485$	0.267949	+	0.464102i	0.0121669	+	0.0210738i
$486$		−	1.00000i		−	0.0453609i
$487$	20.0718	−	11.5885i	0.909540	−	0.525123i	0.0292568	−	0.999572i	$-0.490686\pi$
$487$	20.0718	−	11.5885i	0.909540	−	0.525123i	0.880283	+	0.474449i	$0.157353\pi$
$488$	9.00000	−	5.19615i	0.407411	−	0.235219i
$489$		−	15.0526i		−	0.680700i
$490$	1.50000	+	2.59808i	0.0677631	+	0.117369i
$491$	8.66025	−	15.0000i	0.390832	−	0.676941i	−0.601728	−	0.798701i	$-0.705521\pi$
$491$	8.66025	−	15.0000i	0.390832	−	0.676941i	0.992559	+	0.121761i	$0.0388541\pi$
$492$	1.73205	+	1.00000i	0.0780869	+	0.0450835i
$493$	−1.07180			−0.0482713
$494$	−7.46410	+	25.8564i	−0.335826	+	1.16333i
$495$	6.46410			0.290540
$496$	1.50000	+	0.866025i	0.0673520	+	0.0388857i
$497$	12.3923	−	21.4641i	0.555871	−	0.962797i
$498$	−4.46410	−	7.73205i	−0.200041	−	0.346481i
$499$			6.53590i			0.292587i	0.989241	+	0.146293i	$0.0467344\pi$
$499$			6.53590i			0.292587i	−0.989241	+	0.146293i	$0.953266\pi$
$500$	0.866025	−	0.500000i	0.0387298	−	0.0223607i
$501$	14.1340	−	8.16025i	0.631459	−	0.364573i
$502$			15.7321i			0.702156i
$503$	15.5885	+	27.0000i	0.695055	+	1.20387i	0.970162	+	0.242457i	$0.0779533\pi$
$503$	15.5885	+	27.0000i	0.695055	+	1.20387i	−0.275107	+	0.961414i	$0.588713\pi$
$504$	1.00000	−	1.73205i	0.0445435	−	0.0771517i
$505$	−2.53590	−	1.46410i	−0.112846	−	0.0651517i
$506$	24.1244			1.07246
$507$	−11.5000	+	6.06218i	−0.510733	+	0.269231i
$508$	4.92820			0.218654
$509$	1.20577	+	0.696152i	0.0534449	+	0.0308564i	0.526484	−	0.850185i	$-0.323510\pi$
$509$	1.20577	+	0.696152i	0.0534449	+	0.0308564i	−0.473039	+	0.881041i	$0.656843\pi$
$510$	2.00000	−	3.46410i	0.0885615	−	0.153393i
$511$	−2.00000	−	3.46410i	−0.0884748	−	0.153243i
$512$			1.00000i			0.0441942i
$513$	−6.46410	+	3.73205i	−0.285397	+	0.164774i
$514$	−4.62436	+	2.66987i	−0.203972	+	0.117763i
$515$		−	11.8564i		−	0.522456i
$516$	−5.96410	−	10.3301i	−0.262555	−	0.454758i
$517$	11.4282	−	19.7942i	0.502612	−	0.870549i
$518$	15.9282	+	9.19615i	0.699845	+	0.404056i
$519$	−10.9282			−0.479695
$520$	1.00000	−	3.46410i	0.0438529	−	0.151911i
$521$	−17.3205			−0.758825			−0.379413	−	0.925228i	$-0.623874\pi$
$521$	−17.3205			−0.758825			−0.379413	+	0.925228i	$0.623874\pi$
$522$	−0.232051	−	0.133975i	−0.0101566	−	0.00586391i
$523$	−5.89230	+	10.2058i	−0.257653	+	0.446267i	−0.965613	−	0.259985i	$-0.916282\pi$
$523$	−5.89230	+	10.2058i	−0.257653	+	0.446267i	0.707960	+	0.706252i	$0.249616\pi$
$524$	−9.33013	−	16.1603i	−0.407588	−	0.705964i
$525$		−	2.00000i		−	0.0872872i
$526$	5.30385	−	3.06218i	0.231259	−	0.133517i
$527$	6.00000	−	3.46410i	0.261364	−	0.150899i
$528$			6.46410i			0.281314i
$529$	4.53590	+	7.85641i	0.197213	+	0.341583i
$530$	0.464102	−	0.803848i	0.0201593	−	0.0349169i
$531$	−7.33013	−	4.23205i	−0.318100	−	0.183655i
$532$	−14.9282			−0.647220
$533$	5.19615	−	5.00000i	0.225070	−	0.216574i
$534$	0.535898			0.0231906
$535$	6.80385	+	3.92820i	0.294156	+	0.169831i
$536$	−5.73205	+	9.92820i	−0.247587	+	0.428833i
$537$	−9.86603	−	17.0885i	−0.425750	−	0.737421i
$538$			12.0000i			0.517357i
$539$	−16.7942	+	9.69615i	−0.723379	+	0.417643i
$540$	0.866025	−	0.500000i	0.0372678	−	0.0215166i
$541$			26.9282i			1.15773i	0.815422	+	0.578867i	$0.196505\pi$
$541$			26.9282i			1.15773i	−0.815422	+	0.578867i	$0.803495\pi$
$542$	−0.598076	−	1.03590i	−0.0256896	−	0.0444956i
$543$	−1.46410	+	2.53590i	−0.0628306	+	0.108826i
$544$	3.46410	+	2.00000i	0.148522	+	0.0857493i
$545$	15.8564			0.679214
$546$	−5.00000	−	5.19615i	−0.213980	−	0.222375i
$547$	22.9282			0.980339			0.490170	−	0.871627i	$-0.336935\pi$
$547$	22.9282			0.980339			0.490170	+	0.871627i	$0.336935\pi$
$548$	−2.13397	−	1.23205i	−0.0911589	−	0.0526306i
$549$	5.19615	−	9.00000i	0.221766	−	0.384111i
$550$	3.23205	+	5.59808i	0.137815	+	0.238703i
$551$			2.00000i			0.0852029i
$552$	3.23205	−	1.86603i	0.137565	−	0.0794233i
$553$	24.1244	−	13.9282i	1.02587	−	0.592287i
$554$		−	3.92820i		−	0.166893i
$555$	4.59808	+	7.96410i	0.195177	+	0.338057i
$556$	−6.46410	+	11.1962i	−0.274139	+	0.474823i
$557$	15.3397	+	8.85641i	0.649966	+	0.375258i	0.788443	−	0.615108i	$-0.210887\pi$
$557$	15.3397	+	8.85641i	0.649966	+	0.375258i	−0.138477	+	0.990366i	$0.544221\pi$
$558$	1.73205			0.0733236
$559$	−41.7487	+	10.3301i	−1.76578	+	0.436918i
$560$	2.00000			0.0845154
$561$	22.3923	+	12.9282i	0.945404	+	0.545829i
$562$	−4.46410	+	7.73205i	−0.188307	+	0.326157i
$563$	2.33975	+	4.05256i	0.0986085	+	0.170795i	0.911109	−	0.412166i	$-0.135228\pi$
$563$	2.33975	+	4.05256i	0.0986085	+	0.170795i	−0.812500	+	0.582961i	$0.801894\pi$
$564$		−	3.53590i		−	0.148888i
$565$	0.696152	−	0.401924i	0.0292874	−	0.0169091i
$566$	−8.59808	+	4.96410i	−0.361404	+	0.208657i
$567$		−	2.00000i		−	0.0839921i
$568$	6.19615	+	10.7321i	0.259985	+	0.450307i
$569$	−14.6603	+	25.3923i	−0.614590	+	1.06450i	0.375867	+	0.926674i	$0.377345\pi$
$569$	−14.6603	+	25.3923i	−0.614590	+	1.06450i	−0.990456	+	0.137827i	$0.955988\pi$
$570$	−6.46410	−	3.73205i	−0.270751	−	0.156318i
$571$	−17.1769			−0.718832			−0.359416	−	0.933178i	$-0.617024\pi$
$571$	−17.1769			−0.718832			−0.359416	+	0.933178i	$0.617024\pi$
$572$	22.3923	+	6.46410i	0.936269	+	0.270278i
$573$	−21.4641			−0.896676
$574$	3.46410	+	2.00000i	0.144589	+	0.0834784i
$575$	1.86603	−	3.23205i	0.0778186	−	0.134786i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$		−	10.0000i		−	0.416305i	−0.978096	−	0.208153i	$-0.933255\pi$
$577$		−	10.0000i		−	0.416305i	0.978096	−	0.208153i	$-0.0667451\pi$
$578$	−0.866025	+	0.500000i	−0.0360219	+	0.0207973i
$579$	9.80385	−	5.66025i	0.407434	−	0.235232i
$580$		−	0.267949i		−	0.0111260i
$581$	−8.92820	−	15.4641i	−0.370404	−	0.641559i
$582$	−0.267949	+	0.464102i	−0.0111069	+	0.0192376i
$583$	5.19615	+	3.00000i	0.215203	+	0.124247i
$584$	2.00000			0.0827606
$585$	−0.866025	−	3.50000i	−0.0358057	−	0.144707i
$586$	31.8564			1.31598
$587$	−2.07180	−	1.19615i	−0.0855122	−	0.0493705i	0.456634	−	0.889655i	$-0.349055\pi$
$587$	−2.07180	−	1.19615i	−0.0855122	−	0.0493705i	−0.542146	+	0.840284i	$0.682388\pi$
$588$	−1.50000	+	2.59808i	−0.0618590	+	0.107143i
$589$	−6.46410	−	11.1962i	−0.266349	−	0.461329i
$590$		−	8.46410i		−	0.348462i
$591$	3.80385	−	2.19615i	0.156469	−	0.0903376i
$592$	−7.96410	+	4.59808i	−0.327323	+	0.188980i
$593$			45.1051i			1.85225i	0.377223	+	0.926123i	$0.376879\pi$
$593$			45.1051i			1.85225i	−0.377223	+	0.926123i	$0.623121\pi$
$594$	3.23205	+	5.59808i	0.132613	+	0.229692i
$595$	4.00000	−	6.92820i	0.163984	−	0.284029i
$596$	−11.7224	−	6.76795i	−0.480170	−	0.277226i
$597$	5.07180			0.207575
$598$	−3.23205	−	13.0622i	−0.132168	−	0.534152i
$599$	−10.3923			−0.424618			−0.212309	−	0.977203i	$-0.568098\pi$
$599$	−10.3923			−0.424618			−0.212309	+	0.977203i	$0.568098\pi$
$600$	0.866025	+	0.500000i	0.0353553	+	0.0204124i
$601$	9.89230	−	17.1340i	0.403516	−	0.698909i	−0.590632	−	0.806941i	$-0.701121\pi$
$601$	9.89230	−	17.1340i	0.403516	−	0.698909i	0.994147	+	0.108032i	$0.0344548\pi$
$602$	−11.9282	−	20.6603i	−0.486157	−	0.842049i
$603$			11.4641i			0.466854i
$604$	9.00000	−	5.19615i	0.366205	−	0.211428i
$605$	−26.6603	+	15.3923i	−1.08389	+	0.625786i
$606$		−	2.92820i		−	0.118950i
$607$	9.58846	+	16.6077i	0.389183	+	0.674086i	0.992340	−	0.123537i	$-0.0394239\pi$
$607$	9.58846	+	16.6077i	0.389183	+	0.674086i	−0.603156	+	0.797623i	$0.706091\pi$
$608$	3.73205	−	6.46410i	0.151355	−	0.262154i
$609$	−0.464102	−	0.267949i	−0.0188063	−	0.0108578i
$610$	10.3923			0.420772
$611$	−12.2487	−	3.53590i	−0.495530	−	0.143047i
$612$	4.00000			0.161690
$613$	−33.8205	−	19.5263i	−1.36600	−	0.788659i	−0.375583	−	0.926789i	$-0.622558\pi$
$613$	−33.8205	−	19.5263i	−1.36600	−	0.788659i	−0.990414	+	0.138130i	$0.955891\pi$
$614$	9.73205	−	16.8564i	0.392754	−	0.680269i
$615$	1.00000	+	1.73205i	0.0403239	+	0.0698430i
$616$			12.9282i			0.520892i
$617$	−19.4545	+	11.2321i	−0.783208	+	0.452185i	−0.837566	−	0.546336i	$-0.816022\pi$
$617$	−19.4545	+	11.2321i	−0.783208	+	0.452185i	0.0543580	+	0.998522i	$0.482689\pi$
$618$	10.2679	−	5.92820i	0.413037	−	0.238467i
$619$		−	24.2487i		−	0.974638i	−0.873224	−	0.487319i	$-0.837975\pi$
$619$		−	24.2487i		−	0.974638i	0.873224	−	0.487319i	$-0.162025\pi$
$620$	0.866025	+	1.50000i	0.0347804	+	0.0602414i
$621$	1.86603	−	3.23205i	0.0748810	−	0.129698i
$622$	24.5885	+	14.1962i	0.985907	+	0.569214i
$623$	1.07180			0.0429406
$624$	3.50000	−	0.866025i	0.140112	−	0.0346688i
$625$	1.00000			0.0400000
$626$	24.2487	+	14.0000i	0.969173	+	0.559553i
$627$	24.1244	−	41.7846i	0.963434	−	1.66872i
$628$	−2.50000	−	4.33013i	−0.0997609	−	0.172791i
$629$			36.7846i			1.46670i
$630$	1.73205	−	1.00000i	0.0690066	−	0.0398410i
$631$	27.2487	−	15.7321i	1.08475	−	0.626283i	0.152579	−	0.988291i	$-0.451242\pi$
$631$	27.2487	−	15.7321i	1.08475	−	0.626283i	0.932175	+	0.362008i	$0.117909\pi$
$632$			13.9282i			0.554034i
$633$	−5.66025	−	9.80385i	−0.224975	−	0.389668i
$634$	7.26795	−	12.5885i	0.288647	−	0.499952i
$635$	4.26795	+	2.46410i	0.169368	+	0.0977849i
$636$	0.928203			0.0368057
$637$	7.50000	+	7.79423i	0.297161	+	0.308819i
$638$	1.73205			0.0685725
$639$	10.7321	+	6.19615i	0.424553	+	0.245116i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−0.0717968	−	0.124356i	−0.00283580	−	0.00491175i	0.864604	−	0.502454i	$-0.167569\pi$
$641$	−0.0717968	−	0.124356i	−0.00283580	−	0.00491175i	−0.867440	+	0.497542i	$0.834236\pi$
$642$			7.85641i			0.310068i
$643$	−17.7846	+	10.2679i	−0.701357	+	0.404928i	−0.807852	−	0.589385i	$-0.799370\pi$
$643$	−17.7846	+	10.2679i	−0.701357	+	0.404928i	0.106496	+	0.994313i	$0.466037\pi$
$644$	6.46410	−	3.73205i	0.254721	−	0.147063i
$645$		−	11.9282i		−	0.469673i
$646$	−14.9282	−	25.8564i	−0.587342	−	1.01731i
$647$	6.66025	−	11.5359i	0.261842	−	0.453523i	−0.704890	−	0.709317i	$-0.749004\pi$
$647$	6.66025	−	11.5359i	0.261842	−	0.453523i	0.966731	+	0.255794i	$0.0823369\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	54.7128			2.14767
$650$	2.59808	−	2.50000i	0.101905	−	0.0980581i
$651$	3.46410			0.135769
$652$	13.0359	+	7.52628i	0.510525	+	0.294752i
$653$	−2.12436	+	3.67949i	−0.0831325	+	0.143990i	−0.904594	−	0.426274i	$-0.859826\pi$
$653$	−2.12436	+	3.67949i	−0.0831325	+	0.143990i	0.821461	+	0.570264i	$0.193159\pi$
$654$	7.92820	+	13.7321i	0.310017	+	0.536966i
$655$		−	18.6603i		−	0.729116i
$656$	−1.73205	+	1.00000i	−0.0676252	+	0.0390434i
$657$	1.73205	−	1.00000i	0.0675737	−	0.0390137i
$658$		−	7.07180i		−	0.275687i
$659$	0.133975	+	0.232051i	0.00521891	+	0.00903942i	0.868623	−	0.495473i	$-0.165005\pi$
$659$	0.133975	+	0.232051i	0.00521891	+	0.00903942i	−0.863404	+	0.504513i	$0.831672\pi$
$660$	−3.23205	+	5.59808i	−0.125807	+	0.217905i
$661$	−7.51666	−	4.33975i	−0.292364	−	0.168797i	0.346643	−	0.937997i	$-0.387321\pi$
$661$	−7.51666	−	4.33975i	−0.292364	−	0.168797i	−0.639008	+	0.769200i	$0.720655\pi$
$662$	16.7846			0.652352
$663$	4.00000	−	13.8564i	0.155347	−	0.538138i
$664$	8.92820			0.346481
$665$	−12.9282	−	7.46410i	−0.501334	−	0.289445i
$666$	−4.59808	+	7.96410i	−0.178172	+	0.308603i
$667$	−0.500000	−	0.866025i	−0.0193601	−	0.0335326i
$668$			16.3205i			0.631459i
$669$	−17.7846	+	10.2679i	−0.687593	+	0.396982i
$670$	−9.92820	+	5.73205i	−0.383560	+	0.221448i
$671$			67.1769i			2.59334i
$672$	1.00000	+	1.73205i	0.0385758	+	0.0668153i
$673$	−16.0000	+	27.7128i	−0.616755	+	1.06825i	0.373319	+	0.927703i	$0.378220\pi$
$673$	−16.0000	+	27.7128i	−0.616755	+	1.06825i	−0.990074	+	0.140548i	$0.955114\pi$
$674$	−8.07180	−	4.66025i	−0.310914	−	0.179506i
$675$	1.00000			0.0384900
$676$	0.500000	−	12.9904i	0.0192308	−	0.499630i
$677$	32.3923			1.24494			0.622469	−	0.782645i	$-0.286130\pi$
$677$	32.3923			1.24494			0.622469	+	0.782645i	$0.286130\pi$
$678$	0.696152	+	0.401924i	0.0267356	+	0.0154358i
$679$	−0.535898	+	0.928203i	−0.0205659	+	0.0356212i
$680$	2.00000	+	3.46410i	0.0766965	+	0.132842i
$681$			16.3923i			0.628154i
$682$	−9.69615	+	5.59808i	−0.371285	+	0.214361i
$683$	−35.3205	+	20.3923i	−1.35150	+	0.780290i	−0.988460	−	0.151483i	$-0.951595\pi$
$683$	−35.3205	+	20.3923i	−1.35150	+	0.780290i	−0.363042	+	0.931773i	$0.618262\pi$
$684$		−	7.46410i		−	0.285397i
$685$	−1.23205	−	2.13397i	−0.0470742	−	0.0815350i
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$	−6.80385	−	3.92820i	−0.259583	−	0.149870i
$688$	11.9282			0.454758
$689$	0.928203	−	3.21539i	0.0353617	−	0.122497i
$690$	3.73205			0.142077
$691$	−23.5359	−	13.5885i	−0.895348	−	0.516929i	−0.0196598	−	0.999807i	$-0.506258\pi$
$691$	−23.5359	−	13.5885i	−0.895348	−	0.516929i	−0.875688	+	0.482877i	$0.839592\pi$
$692$	5.46410	−	9.46410i	0.207714	−	0.359771i
$693$	6.46410	+	11.1962i	0.245551	+	0.425307i
$694$			1.60770i			0.0610273i
$695$	−11.1962	+	6.46410i	−0.424694	+	0.245197i
$696$	0.232051	−	0.133975i	0.00879586	−	0.00507829i
$697$			8.00000i			0.303022i
$698$	−10.7321	−	18.5885i	−0.406214	−	0.703583i
$699$	3.06218	−	5.30385i	0.115822	−	0.200610i
$700$	1.73205	+	1.00000i	0.0654654	+	0.0377964i
$701$	−0.267949			−0.0101203			−0.00506015	−	0.999987i	$-0.501611\pi$
$701$	−0.267949			−0.0101203			−0.00506015	+	0.999987i	$0.501611\pi$
$702$	2.59808	−	2.50000i	0.0980581	−	0.0943564i
$703$	68.6410			2.58884
$704$	−5.59808	−	3.23205i	−0.210985	−	0.121812i
$705$	1.76795	−	3.06218i	0.0665848	−	0.115328i
$706$	−1.00000	−	1.73205i	−0.0376355	−	0.0651866i
$707$		−	5.85641i		−	0.220253i
$708$	7.33013	−	4.23205i	0.275483	−	0.159050i
$709$	−19.8564	+	11.4641i	−0.745723	+	0.430543i	−0.824146	−	0.566377i	$-0.808345\pi$
$709$	−19.8564	+	11.4641i	−0.745723	+	0.430543i	0.0784234	+	0.996920i	$0.475011\pi$
$710$			12.3923i			0.465075i
$711$	6.96410	+	12.0622i	0.261174	+	0.452367i
$712$	−0.267949	+	0.464102i	−0.0100418	+	0.0173929i
$713$	5.59808	+	3.23205i	0.209650	+	0.121041i
$714$	8.00000			0.299392
$715$	16.1603	+	16.7942i	0.604359	+	0.628069i
$716$	19.7321			0.737421
$717$	−14.1962	−	8.19615i	−0.530165	−	0.306091i
$718$	2.53590	−	4.39230i	0.0946389	−	0.163919i
$719$	17.3205	+	30.0000i	0.645946	+	1.11881i	0.984082	+	0.177714i	$0.0568702\pi$
$719$	17.3205	+	30.0000i	0.645946	+	1.11881i	−0.338136	+	0.941097i	$0.609796\pi$
$720$			1.00000i			0.0372678i
$721$	20.5359	−	11.8564i	0.764797	−	0.441556i
$722$	−31.7942	+	18.3564i	−1.18326	+	0.683155i
$723$		−	17.7321i		−	0.659462i
$724$	−1.46410	−	2.53590i	−0.0544129	−	0.0942459i
$725$	0.133975	−	0.232051i	0.00497569	−	0.00861815i
$726$	−26.6603	−	15.3923i	−0.989455	−	0.571262i
$727$	−31.7128			−1.17616			−0.588082	−	0.808802i	$-0.700117\pi$
$727$	−31.7128			−1.17616			−0.588082	+	0.808802i	$0.700117\pi$
$728$	7.00000	−	1.73205i	0.259437	−	0.0641941i
$729$	1.00000			0.0370370
$730$	1.73205	+	1.00000i	0.0641061	+	0.0370117i
$731$	23.8564	−	41.3205i	0.882361	−	1.52829i
$732$	5.19615	+	9.00000i	0.192055	+	0.332650i
$733$		−	50.9282i		−	1.88108i	−0.339688	−	0.940538i	$-0.610322\pi$
$733$		−	50.9282i		−	1.88108i	0.339688	−	0.940538i	$-0.389678\pi$
$734$	13.5167	−	7.80385i	0.498909	−	0.288045i
$735$	−2.59808	+	1.50000i	−0.0958315	+	0.0553283i
$736$			3.73205i			0.137565i
$737$	−37.0526	−	64.1769i	−1.36485	−	2.36399i
$738$	−1.00000	+	1.73205i	−0.0368105	+	0.0637577i
$739$	−16.7321	−	9.66025i	−0.615498	−	0.355358i	0.159616	−	0.987179i	$-0.448974\pi$
$739$	−16.7321	−	9.66025i	−0.615498	−	0.355358i	−0.775114	+	0.631821i	$0.782308\pi$
$740$	−9.19615			−0.338057
$741$	−25.8564	−	7.46410i	−0.949859	−	0.274201i
$742$	1.85641			0.0681508
$743$	−35.0429	−	20.2321i	−1.28560	−	0.742242i	−0.307734	−	0.951472i	$-0.599571\pi$
$743$	−35.0429	−	20.2321i	−1.28560	−	0.742242i	−0.977866	+	0.209230i	$0.932904\pi$
$744$	−0.866025	+	1.50000i	−0.0317500	+	0.0549927i
$745$	−6.76795	−	11.7224i	−0.247958	−	0.429477i
$746$		−	15.7846i		−	0.577916i
$747$	7.73205	−	4.46410i	0.282901	−	0.163333i
$748$	−22.3923	+	12.9282i	−0.818744	+	0.472702i
$749$			15.7128i			0.574134i
$750$	0.500000	+	0.866025i	0.0182574	+	0.0316228i
$751$	−7.03590	+	12.1865i	−0.256744	+	0.444693i	−0.965368	−	0.260893i	$-0.915983\pi$
$751$	−7.03590	+	12.1865i	−0.256744	+	0.444693i	0.708624	+	0.705586i	$0.249316\pi$
$752$	3.06218	+	1.76795i	0.111666	+	0.0644705i
$753$	−15.7321			−0.573308
$754$	−0.232051	−	0.937822i	−0.00845079	−	0.0341535i
$755$	10.3923			0.378215
$756$	1.73205	+	1.00000i	0.0629941	+	0.0363696i
$757$	9.00000	−	15.5885i	0.327111	−	0.566572i	−0.654827	−	0.755779i	$-0.727258\pi$
$757$	9.00000	−	15.5885i	0.327111	−	0.566572i	0.981937	+	0.189207i	$0.0605917\pi$
$758$	−13.9282	−	24.1244i	−0.505895	−	0.876236i
$759$			24.1244i			0.875659i
$760$	6.46410	−	3.73205i	0.234478	−	0.135376i
$761$	4.39230	−	2.53590i	0.159221	−	0.0919262i	−0.418272	−	0.908322i	$-0.637364\pi$
$761$	4.39230	−	2.53590i	0.159221	−	0.0919262i	0.577493	+	0.816395i	$0.304031\pi$
$762$			4.92820i			0.178530i
$763$	15.8564	+	27.4641i	0.574040	+	0.994267i
$764$	10.7321	−	18.5885i	0.388272	−	0.672507i
$765$	3.46410	+	2.00000i	0.125245	+	0.0723102i
$766$	−25.3923			−0.917461
$767$	−7.33013	−	29.6244i	−0.264676	−	1.06967i
$768$	−1.00000			−0.0360844
$769$	−10.0359	−	5.79423i	−0.361904	−	0.208945i	0.308012	−	0.951383i	$-0.400336\pi$
$769$	−10.0359	−	5.79423i	−0.361904	−	0.208945i	−0.669916	+	0.742437i	$0.733670\pi$
$770$	−6.46410	+	11.1962i	−0.232950	+	0.403481i
$771$	−2.66987	−	4.62436i	−0.0961531	−	0.166542i
$772$			11.3205i			0.407434i
$773$	24.0000	−	13.8564i	0.863220	−	0.498380i	−0.00186926	−	0.999998i	$-0.500595\pi$
$773$	24.0000	−	13.8564i	0.863220	−	0.498380i	0.865089	+	0.501618i	$0.167262\pi$
$774$	10.3301	−	5.96410i	0.371309	−	0.214375i
$775$			1.73205i			0.0622171i
$776$	−0.267949	−	0.464102i	−0.00961882	−	0.0166603i
$777$	−9.19615	+	15.9282i	−0.329910	+	0.571421i
$778$	20.5526	+	11.8660i	0.736845	+	0.425418i
$779$	14.9282			0.534858
$780$	3.46410	+	1.00000i	0.124035	+	0.0358057i
$781$	−80.1051			−2.86639
$782$	12.9282	+	7.46410i	0.462312	+	0.266916i
$783$	0.133975	−	0.232051i	0.00478786	−	0.00829282i
$784$	−1.50000	−	2.59808i	−0.0535714	−	0.0927884i
$785$		−	5.00000i		−	0.178458i
$786$	16.1603	−	9.33013i	0.576417	−	0.332795i
$787$	1.50000	−	0.866025i	0.0534692	−	0.0308705i	−0.473027	−	0.881048i	$-0.656839\pi$
$787$	1.50000	−	0.866025i	0.0534692	−	0.0308705i	0.526496	+	0.850177i	$0.323505\pi$
$788$			4.39230i			0.156469i
$789$	3.06218	+	5.30385i	0.109016	+	0.188822i
$790$	−6.96410	+	12.0622i	−0.247772	+	0.429153i
$791$	1.39230	+	0.803848i	0.0495047	+	0.0285815i
$792$	−6.46410			−0.229692
$793$	36.3731	−	9.00000i	1.29165	−	0.319599i
$794$	−12.1244			−0.430277
$795$	0.803848	+	0.464102i	0.0285095	+	0.0164600i
$796$	−2.53590	+	4.39230i	−0.0898825	+	0.155681i
$797$	5.07180	+	8.78461i	0.179652	+	0.311167i	0.941761	−	0.336282i	$-0.109169\pi$
$797$	5.07180	+	8.78461i	0.179652	+	0.311167i	−0.762109	+	0.647449i	$0.775836\pi$
$798$		−	14.9282i		−	0.528453i
$799$	12.2487	−	7.07180i	0.433328	−	0.250182i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$			0.535898i			0.0189350i
$802$	16.0000	+	27.7128i	0.564980	+	0.978573i
$803$	−6.46410	+	11.1962i	−0.228113	+	0.395104i
$804$	−9.92820	−	5.73205i	−0.350141	−	0.202154i
$805$	7.46410			0.263075
$806$	4.33013	+	4.50000i	0.152522	+	0.158506i
$807$	−12.0000			−0.422420
$808$	2.53590	+	1.46410i	0.0892126	+	0.0515069i
$809$	21.3923	−	37.0526i	0.752113	−	1.30270i	−0.194683	−	0.980866i	$-0.562368\pi$
$809$	21.3923	−	37.0526i	0.752113	−	1.30270i	0.946797	−	0.321832i	$-0.104299\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$			40.7846i			1.43214i	0.698028	+	0.716071i	$0.254061\pi$
$811$			40.7846i			1.43214i	−0.698028	+	0.716071i	$0.745939\pi$
$812$	0.464102	−	0.267949i	0.0162868	−	0.00940317i
$813$	1.03590	−	0.598076i	0.0363305	−	0.0209754i
$814$		−	59.4449i		−	2.08354i
$815$	7.52628	+	13.0359i	0.263634	+	0.456628i
$816$	−2.00000	+	3.46410i	−0.0700140	+	0.121268i
$817$	−77.1051	−	44.5167i	−2.69757	−	1.55744i
$818$	−4.00000			−0.139857
$819$	5.19615	−	5.00000i	0.181568	−	0.174714i
$820$	−2.00000			−0.0698430
$821$	12.6506	+	7.30385i	0.441510	+	0.254906i	0.704238	−	0.709964i	$-0.251289\pi$
$821$	12.6506	+	7.30385i	0.441510	+	0.254906i	−0.262728	+	0.964870i	$0.584622\pi$
$822$	1.23205	−	2.13397i	0.0429727	−	0.0744309i
$823$	−19.5885	−	33.9282i	−0.682811	−	1.18266i	−0.974119	−	0.226034i	$-0.927424\pi$
$823$	−19.5885	−	33.9282i	−0.682811	−	1.18266i	0.291309	−	0.956629i	$-0.405909\pi$
$824$			11.8564i			0.413037i
$825$	−5.59808	+	3.23205i	−0.194900	+	0.112526i
$826$	14.6603	−	8.46410i	0.510095	−	0.294504i
$827$			17.3205i			0.602293i	0.953578	+	0.301147i	$0.0973693\pi$
$827$			17.3205i			0.602293i	−0.953578	+	0.301147i	$0.902631\pi$
$828$	1.86603	+	3.23205i	0.0648489	+	0.112322i
$829$	−8.26795	+	14.3205i	−0.287158	+	0.497372i	−0.973130	−	0.230256i	$-0.926044\pi$
$829$	−8.26795	+	14.3205i	−0.287158	+	0.497372i	0.685972	+	0.727628i	$0.259377\pi$
$830$	7.73205	+	4.46410i	0.268383	+	0.154951i
$831$	3.92820			0.136268
$832$	−1.00000	+	3.46410i	−0.0346688	+	0.120096i
$833$	−12.0000			−0.415775
$834$	−11.1962	−	6.46410i	−0.387691	−	0.223834i
$835$	−8.16025	+	14.1340i	−0.282397	+	0.489126i
$836$	24.1244	+	41.7846i	0.834358	+	1.44515i
$837$			1.73205i			0.0598684i
$838$	19.3923	−	11.1962i	0.669896	−	0.386765i
$839$	−37.7321	+	21.7846i	−1.30266	+	0.752088i	−0.980859	−	0.194721i	$-0.937620\pi$
$839$	−37.7321	+	21.7846i	−1.30266	+	0.752088i	−0.321796	+	0.946809i	$0.604287\pi$
$840$			2.00000i			0.0690066i
$841$	14.4641	+	25.0526i	0.498762	+	0.863881i
$842$	2.19615	−	3.80385i	0.0756844	−	0.131089i
$843$	−7.73205	−	4.46410i	−0.266306	−	0.153752i
$844$	11.3205			0.389668
$845$	6.92820	−	11.0000i	0.238337	−	0.378412i
$846$	3.53590			0.121567
$847$	−53.3205	−	30.7846i	−1.83211	−	1.05777i
$848$	−0.464102	+	0.803848i	−0.0159373	+	0.0276042i
$849$	−4.96410	−	8.59808i	−0.170368	−	0.295085i
$850$			4.00000i			0.137199i
$851$	−29.7224	+	17.1603i	−1.01887	+	0.588246i
$852$	−10.7321	+	6.19615i	−0.367674	+	0.212277i
$853$			43.8372i			1.50096i	0.660895	+	0.750478i	$0.270177\pi$
$853$			43.8372i			1.50096i	−0.660895	+	0.750478i	$0.729823\pi$
$854$	10.3923	+	18.0000i	0.355617	+	0.615947i
$855$	3.73205	−	6.46410i	0.127633	−	0.221068i
$856$	−6.80385	−	3.92820i	−0.232551	−	0.134263i
$857$	24.5167			0.837473			0.418737	−	0.908108i	$-0.362473\pi$
$857$	24.5167			0.837473			0.418737	+	0.908108i	$0.362473\pi$
$858$	−6.46410	+	22.3923i	−0.220681	+	0.764461i
$859$	−35.1769			−1.20022			−0.600110	−	0.799917i	$-0.704877\pi$
$859$	−35.1769			−1.20022			−0.600110	+	0.799917i	$0.704877\pi$
$860$	10.3301	+	5.96410i	0.352254	+	0.203374i
$861$	−2.00000	+	3.46410i	−0.0681598	+	0.118056i
$862$	−14.1962	−	24.5885i	−0.483523	−	0.837486i
$863$			35.5359i			1.20966i	0.796356	+	0.604828i	$0.206758\pi$
$863$			35.5359i			1.20966i	−0.796356	+	0.604828i	$0.793242\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	9.46410	−	5.46410i	0.321789	−	0.185785i
$866$			19.3205i			0.656538i
$867$	−0.500000	−	0.866025i	−0.0169809	−	0.0294118i
$868$	−1.73205	+	3.00000i	−0.0587896	+	0.101827i
$869$	−77.9711	−	45.0167i	−2.64499	−	1.52709i
$870$	0.267949			0.00908433
$871$	−29.7846	+	28.6603i	−1.00921	+	0.971116i
$872$	−15.8564			−0.536966
$873$	−0.464102	−	0.267949i	−0.0157075	−	0.00906871i
$874$	13.9282	−	24.1244i	0.471129	−	0.816019i
$875$	1.00000	+	1.73205i	0.0338062	+	0.0585540i
$876$			2.00000i			0.0675737i
$877$	−3.35641	+	1.93782i	−0.113338	+	0.0654356i	−0.555597	−	0.831452i	$-0.687510\pi$
$877$	−3.35641	+	1.93782i	−0.113338	+	0.0654356i	0.442260	+	0.896887i	$0.354177\pi$
$878$	−15.4641	+	8.92820i	−0.521888	+	0.301312i
$879$			31.8564i			1.07449i
$880$	−3.23205	−	5.59808i	−0.108952	−	0.188711i
$881$	7.00000	−	12.1244i	0.235836	−	0.408480i	−0.723679	−	0.690136i	$-0.757551\pi$
$881$	7.00000	−	12.1244i	0.235836	−	0.408480i	0.959515	+	0.281656i	$0.0908839\pi$
$882$	−2.59808	−	1.50000i	−0.0874818	−	0.0505076i
$883$	29.9282			1.00716			0.503582	−	0.863947i	$-0.332015\pi$
$883$	29.9282			1.00716			0.503582	+	0.863947i	$0.332015\pi$
$884$	10.0000	+	10.3923i	0.336336	+	0.349531i
$885$	8.46410			0.284518
$886$	−14.1962	−	8.19615i	−0.476929	−	0.275355i
$887$	−7.06218	+	12.2321i	−0.237125	+	0.410712i	−0.959888	−	0.280384i	$-0.909538\pi$
$887$	−7.06218	+	12.2321i	−0.237125	+	0.410712i	0.722763	+	0.691096i	$0.242872\pi$
$888$	−4.59808	−	7.96410i	−0.154301	−	0.267258i
$889$			9.85641i			0.330573i
$890$	−0.464102	+	0.267949i	−0.0155567	+	0.00898168i
$891$	−5.59808	+	3.23205i	−0.187543	+	0.108278i
$892$		−	20.5359i		−	0.687593i
$893$	−13.1962	−	22.8564i	−0.441592	−	0.764860i
$894$	6.76795	−	11.7224i	0.226354	−	0.392057i
$895$	17.0885	+	9.86603i	0.571204	+	0.329785i
$896$	−2.00000			−0.0668153
$897$	13.0622	−	3.23205i	0.436133	−	0.107915i
$898$	15.7128			0.524343
$899$	0.401924	+	0.232051i	0.0134049	+	0.00773933i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	1.85641	+	3.21539i	0.0618459	+	0.107120i
$902$		−	12.9282i		−	0.430462i
$903$	20.6603	−	11.9282i	0.687530	−	0.396946i
$904$	−0.696152	+	0.401924i	−0.0231537	+	0.0133678i
$905$		−	2.92820i		−	0.0973368i
$906$	5.19615	+	9.00000i	0.172631	+	0.299005i
$907$	10.4282	−	18.0622i	0.346263	−	0.599745i	−0.639320	−	0.768941i	$-0.720784\pi$
$907$	10.4282	−	18.0622i	0.346263	−	0.599745i	0.985582	+	0.169196i	$0.0541172\pi$
$908$	−14.1962	−	8.19615i	−0.471116	−	0.271999i
$909$	2.92820			0.0971224
$910$	6.92820	+	2.00000i	0.229668	+	0.0662994i
$911$	24.2487			0.803396			0.401698	−	0.915772i	$-0.368420\pi$
$911$	24.2487			0.803396			0.401698	+	0.915772i	$0.368420\pi$
$912$	6.46410	+	3.73205i	0.214048	+	0.123581i
$913$	−28.8564	+	49.9808i	−0.955008	+	1.65412i
$914$	−12.2679	−	21.2487i	−0.405788	−	0.702845i
$915$			10.3923i			0.343559i
$916$	6.80385	−	3.92820i	0.224805	−	0.129791i
$917$	32.3205	−	18.6603i	1.06732	−	0.616216i
$918$			4.00000i			0.132020i
$919$	−7.32051	−	12.6795i	−0.241481	−	0.418258i	0.719655	−	0.694332i	$-0.244300\pi$
$919$	−7.32051	−	12.6795i	−0.241481	−	0.418258i	−0.961136	+	0.276074i	$0.910967\pi$
$920$	−1.86603	+	3.23205i	−0.0615210	+	0.106558i
$921$	16.8564	+	9.73205i	0.555437	+	0.320682i
$922$	−0.464102			−0.0152844
$923$	10.7321	+	43.3731i	0.353250	+	1.42764i
$924$	−12.9282			−0.425307
$925$	−7.96410	−	4.59808i	−0.261858	−	0.151184i
$926$	3.53590	−	6.12436i	0.116197	−	0.201259i
$927$	5.92820	+	10.2679i	0.194708	+	0.337244i
$928$			0.267949i			0.00879586i
$929$	−5.32051	+	3.07180i	−0.174560	+	0.100782i	−0.584734	−	0.811225i	$-0.698801\pi$
$929$	−5.32051	+	3.07180i	−0.174560	+	0.100782i	0.410174	+	0.912007i	$0.365468\pi$
$930$	−1.50000	+	0.866025i	−0.0491869	+	0.0283981i
$931$			22.3923i			0.733878i
$932$	3.06218	+	5.30385i	0.100305	+	0.173733i
$933$	−14.1962	+	24.5885i	−0.464761	+	0.804990i
$934$	13.7321	+	7.92820i	0.449326	+	0.259419i
$935$	−25.8564			−0.845595
$936$	0.866025	+	3.50000i	0.0283069	+	0.114401i
$937$	−24.6410			−0.804987			−0.402493	−	0.915423i	$-0.631856\pi$
$937$	−24.6410			−0.804987			−0.402493	+	0.915423i	$0.631856\pi$
$938$	−19.8564	−	11.4641i	−0.648335	−	0.374316i
$939$	−14.0000	+	24.2487i	−0.456873	+	0.791327i
$940$	1.76795	+	3.06218i	0.0576641	+	0.0998772i
$941$		−	14.7846i		−	0.481965i	−0.970530	−	0.240982i	$-0.922530\pi$
$941$		−	14.7846i		−	0.481965i	0.970530	−	0.240982i	$-0.0774696\pi$
$942$	4.33013	−	2.50000i	0.141083	−	0.0814544i
$943$	−6.46410	+	3.73205i	−0.210500	+	0.121532i
$944$			8.46410i			0.275483i
$945$	1.00000	+	1.73205i	0.0325300	+	0.0563436i
$946$	−38.5526	+	66.7750i	−1.25345	+	2.17104i
$947$	8.19615	+	4.73205i	0.266339	+	0.153771i	0.627223	−	0.778840i	$-0.284192\pi$
$947$	8.19615	+	4.73205i	0.266339	+	0.153771i	−0.360884	+	0.932611i	$0.617525\pi$
$948$	−13.9282			−0.452367
$949$	6.92820	+	2.00000i	0.224899	+	0.0649227i
$950$	7.46410			0.242167
$951$	12.5885	+	7.26795i	0.408209	+	0.235679i
$952$	−4.00000	+	6.92820i	−0.129641	+	0.224544i
$953$	6.13397	+	10.6244i	0.198699	+	0.344157i	0.948107	−	0.317952i	$-0.102995\pi$
$953$	6.13397	+	10.6244i	0.198699	+	0.344157i	−0.749408	+	0.662109i	$0.769662\pi$
$954$			0.928203i			0.0300517i
$955$	18.5885	−	10.7321i	0.601508	−	0.347281i
$956$	14.1962	−	8.19615i	0.459136	−	0.265083i
$957$			1.73205i			0.0559893i
$958$	−2.73205	−	4.73205i	−0.0882686	−	0.152886i
$959$	2.46410	−	4.26795i	0.0795700	−	0.137819i
$960$	−0.866025	−	0.500000i	−0.0279508	−	0.0161374i
$961$	28.0000			0.903226
$962$	−32.1865	+	7.96410i	−1.03774	+	0.256773i
$963$	−7.85641			−0.253169
$964$	15.3564	+	8.86603i	0.494597	+	0.285555i
$965$	−5.66025	+	9.80385i	−0.182210	+	0.315597i
$966$	3.73205	+	6.46410i	0.120077	+	0.207979i
$967$		−	41.4641i		−	1.33340i	−0.745328	−	0.666698i	$-0.767707\pi$
$967$		−	41.4641i		−	1.33340i	0.745328	−	0.666698i	$-0.232293\pi$
$968$	26.6603	−	15.3923i	0.856893	−	0.494727i
$969$	25.8564	−	14.9282i	0.830627	−	0.479563i
$970$		−	0.535898i		−	0.0172067i
$971$	−2.26795	−	3.92820i	−0.0727820	−	0.126062i	0.827338	−	0.561705i	$-0.189854\pi$
$971$	−2.26795	−	3.92820i	−0.0727820	−	0.126062i	−0.900120	+	0.435643i	$0.856521\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−22.3923	−	12.9282i	−0.717864	−	0.414459i
$974$	−23.1769			−0.742636
$975$	2.50000	+	2.59808i	0.0800641	+	0.0832050i
$976$	−10.3923			−0.332650
$977$	10.9186	+	6.30385i	0.349316	+	0.201678i	0.664384	−	0.747391i	$-0.268694\pi$
$977$	10.9186	+	6.30385i	0.349316	+	0.201678i	−0.315068	+	0.949069i	$0.602027\pi$
$978$	−7.52628	+	13.0359i	−0.240664	+	0.416842i
$979$	−1.73205	−	3.00000i	−0.0553566	−	0.0958804i
$980$		−	3.00000i		−	0.0958315i
$981$	−13.7321	+	7.92820i	−0.438431	+	0.253128i
$982$	−15.0000	+	8.66025i	−0.478669	+	0.276360i
$983$		−	36.6077i		−	1.16760i	−0.811896	−	0.583802i	$-0.801564\pi$
$983$		−	36.6077i		−	1.16760i	0.811896	−	0.583802i	$-0.198436\pi$
$984$	−1.00000	−	1.73205i	−0.0318788	−	0.0552158i
$985$	−2.19615	+	3.80385i	−0.0699752	+	0.121201i
$986$	0.928203	+	0.535898i	0.0295600	+	0.0170665i
$987$	7.07180			0.225098
$988$	19.3923	−	18.6603i	0.616951	−	0.593662i
$989$	44.5167			1.41555
$990$	−5.59808	−	3.23205i	−0.177919	−	0.102721i
$991$	26.4282	−	45.7750i	0.839520	−	1.45409i	−0.0507774	−	0.998710i	$-0.516170\pi$
$991$	26.4282	−	45.7750i	0.839520	−	1.45409i	0.890297	−	0.455381i	$-0.150497\pi$
$992$	−0.866025	−	1.50000i	−0.0274963	−	0.0476250i
$993$			16.7846i			0.532643i
$994$	−21.4641	+	12.3923i	−0.680800	+	0.393060i
$995$	−4.39230	+	2.53590i	−0.139245	+	0.0803934i
$996$			8.92820i			0.282901i
$997$	−17.7846	−	30.8038i	−0.563244	−	0.975568i	−0.997211	−	0.0746386i	$-0.976220\pi$
$997$	−17.7846	−	30.8038i	−0.563244	−	0.975568i	0.433966	−	0.900929i	$-0.357114\pi$
$998$	3.26795	−	5.66025i	0.103445	−	0.179172i
$999$	−7.96410	−	4.59808i	−0.251973	−	0.145477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bb.b.121.1	✓	4
3.2	odd	2		1170.2.bs.e.901.2		4
5.2	odd	4		1950.2.y.f.199.1		4
5.3	odd	4		1950.2.y.c.199.2		4
5.4	even	2		1950.2.bc.b.901.2		4
13.4	even	6		5070.2.b.o.1351.2		4
13.6	odd	12		5070.2.a.bg.1.2		2
13.7	odd	12		5070.2.a.y.1.1		2
13.9	even	3		5070.2.b.o.1351.3		4
13.10	even	6	inner	390.2.bb.b.361.1	yes	4
39.23	odd	6		1170.2.bs.e.361.2		4
65.23	odd	12		1950.2.y.f.49.1		4
65.49	even	6		1950.2.bc.b.751.2		4
65.62	odd	12		1950.2.y.c.49.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.b.121.1	✓	4	1.1	even	1	trivial
390.2.bb.b.361.1	yes	4	13.10	even	6	inner
1170.2.bs.e.361.2		4	39.23	odd	6
1170.2.bs.e.901.2		4	3.2	odd	2
1950.2.y.c.49.2		4	65.62	odd	12
1950.2.y.c.199.2		4	5.3	odd	4
1950.2.y.f.49.1		4	65.23	odd	12
1950.2.y.f.199.1		4	5.2	odd	4
1950.2.bc.b.751.2		4	65.49	even	6
1950.2.bc.b.901.2		4	5.4	even	2
5070.2.a.y.1.1		2	13.7	odd	12
5070.2.a.bg.1.2		2	13.6	odd	12
5070.2.b.o.1351.2		4	13.4	even	6
5070.2.b.o.1351.3		4	13.9	even	3

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} +(-1.73205 + 1.00000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(5.59808 + 3.23205i) q^{11} +1.00000 q^{12} +(1.00000 - 3.46410i) q^{13} +2.00000 q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +1.00000i q^{18} +(6.46410 - 3.73205i) q^{19} +(-0.866025 + 0.500000i) q^{20} +2.00000i q^{21} +(-3.23205 - 5.59808i) q^{22} +(-1.86603 + 3.23205i) q^{23} +(-0.866025 - 0.500000i) q^{24} -1.00000 q^{25} +(-2.59808 + 2.50000i) q^{26} -1.00000 q^{27} +(-1.73205 - 1.00000i) q^{28} +(-0.133975 + 0.232051i) q^{29} +(-0.500000 - 0.866025i) q^{30} -1.73205i q^{31} +(0.866025 - 0.500000i) q^{32} +(5.59808 - 3.23205i) q^{33} -4.00000i q^{34} +(-1.00000 - 1.73205i) q^{35} +(0.500000 - 0.866025i) q^{36} +(7.96410 + 4.59808i) q^{37} -7.46410 q^{38} +(-2.50000 - 2.59808i) q^{39} +1.00000 q^{40} +(1.73205 + 1.00000i) q^{41} +(1.00000 - 1.73205i) q^{42} +(-5.96410 - 10.3301i) q^{43} +6.46410i q^{44} +(0.866025 - 0.500000i) q^{45} +(3.23205 - 1.86603i) q^{46} -3.53590i q^{47} +(0.500000 + 0.866025i) q^{48} +(-1.50000 + 2.59808i) q^{49} +(0.866025 + 0.500000i) q^{50} +4.00000 q^{51} +(3.50000 - 0.866025i) q^{52} +0.928203 q^{53} +(0.866025 + 0.500000i) q^{54} +(-3.23205 + 5.59808i) q^{55} +(1.00000 + 1.73205i) q^{56} -7.46410i q^{57} +(0.232051 - 0.133975i) q^{58} +(7.33013 - 4.23205i) q^{59} +1.00000i q^{60} +(5.19615 + 9.00000i) q^{61} +(-0.866025 + 1.50000i) q^{62} +(1.73205 + 1.00000i) q^{63} -1.00000 q^{64} +(3.46410 + 1.00000i) q^{65} -6.46410 q^{66} +(-9.92820 - 5.73205i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(1.86603 + 3.23205i) q^{69} +2.00000i q^{70} +(-10.7321 + 6.19615i) q^{71} +(-0.866025 + 0.500000i) q^{72} +2.00000i q^{73} +(-4.59808 - 7.96410i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(6.46410 + 3.73205i) q^{76} -12.9282 q^{77} +(0.866025 + 3.50000i) q^{78} -13.9282 q^{79} +(-0.866025 - 0.500000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.00000 - 1.73205i) q^{82} +8.92820i q^{83} +(-1.73205 + 1.00000i) q^{84} +(-3.46410 + 2.00000i) q^{85} +11.9282i q^{86} +(0.133975 + 0.232051i) q^{87} +(3.23205 - 5.59808i) q^{88} +(-0.464102 - 0.267949i) q^{89} -1.00000 q^{90} +(1.73205 + 7.00000i) q^{91} -3.73205 q^{92} +(-1.50000 - 0.866025i) q^{93} +(-1.76795 + 3.06218i) q^{94} +(3.73205 + 6.46410i) q^{95} -1.00000i q^{96} +(0.464102 - 0.267949i) q^{97} +(2.59808 - 1.50000i) q^{98} -6.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9} + 2 q^{10} + 12 q^{11} + 4 q^{12} + 4 q^{13} + 8 q^{14} - 2 q^{16} + 8 q^{17} + 12 q^{19} - 6 q^{22} - 4 q^{23} - 4 q^{25} - 4 q^{27} - 4 q^{29} - 2 q^{30} + 12 q^{33}+ \cdots - 12 q^{97}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9 + 2 * q^10 + 12 * q^11 + 4 * q^12 + 4 * q^13 + 8 * q^14 - 2 * q^16 + 8 * q^17 + 12 * q^19 - 6 * q^22 - 4 * q^23 - 4 * q^25 - 4 * q^27 - 4 * q^29 - 2 * q^30 + 12 * q^33 - 4 * q^35 + 2 * q^36 + 18 * q^37 - 16 * q^38 - 10 * q^39 + 4 * q^40 + 4 * q^42 - 10 * q^43 + 6 * q^46 + 2 * q^48 - 6 * q^49 + 16 * q^51 + 14 * q^52 - 24 * q^53 - 6 * q^55 + 4 * q^56 - 6 * q^58 + 12 * q^59 - 4 * q^64 - 12 * q^66 - 12 * q^67 - 8 * q^68 + 4 * q^69 - 36 * q^71 - 8 * q^74 - 2 * q^75 + 12 * q^76 - 24 * q^77 - 28 * q^79 - 2 * q^81 - 4 * q^82 + 4 * q^87 + 6 * q^88 + 12 * q^89 - 4 * q^90 - 8 * q^92 - 6 * q^93 - 14 * q^94 + 8 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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