LMFDB - Embedded newform 1170.2.bs.e.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(361,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1170.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bs (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:	$9.34249703649$
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:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1170.361
Dual form			1170.2.bs.e.901.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-1.73205 - 1.00000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-1.73205 - 1.00000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{10} +(-5.59808 + 3.23205i) q^{11} +(1.00000 + 3.46410i) q^{13} -2.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(6.46410 + 3.73205i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-3.23205 + 5.59808i) q^{22} +(1.86603 + 3.23205i) q^{23} -1.00000 q^{25} +(2.59808 + 2.50000i) q^{26} +(-1.73205 + 1.00000i) q^{28} +(0.133975 + 0.232051i) q^{29} +1.73205i q^{31} +(-0.866025 - 0.500000i) q^{32} +4.00000i q^{34} +(1.00000 - 1.73205i) q^{35} +(7.96410 - 4.59808i) q^{37} +7.46410 q^{38} +1.00000 q^{40} +(-1.73205 + 1.00000i) q^{41} +(-5.96410 + 10.3301i) q^{43} +6.46410i q^{44} +(3.23205 + 1.86603i) q^{46} -3.53590i q^{47} +(-1.50000 - 2.59808i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(3.50000 + 0.866025i) q^{52} -0.928203 q^{53} +(-3.23205 - 5.59808i) q^{55} +(-1.00000 + 1.73205i) q^{56} +(0.232051 + 0.133975i) q^{58} +(-7.33013 - 4.23205i) q^{59} +(5.19615 - 9.00000i) q^{61} +(0.866025 + 1.50000i) q^{62} -1.00000 q^{64} +(-3.46410 + 1.00000i) q^{65} +(-9.92820 + 5.73205i) q^{67} +(2.00000 + 3.46410i) q^{68} -2.00000i q^{70} +(10.7321 + 6.19615i) q^{71} -2.00000i q^{73} +(4.59808 - 7.96410i) q^{74} +(6.46410 - 3.73205i) q^{76} +12.9282 q^{77} -13.9282 q^{79} +(0.866025 - 0.500000i) q^{80} +(-1.00000 + 1.73205i) q^{82} +8.92820i q^{83} +(-3.46410 - 2.00000i) q^{85} +11.9282i q^{86} +(3.23205 + 5.59808i) q^{88} +(0.464102 - 0.267949i) q^{89} +(1.73205 - 7.00000i) q^{91} +3.73205 q^{92} +(-1.76795 - 3.06218i) q^{94} +(-3.73205 + 6.46410i) q^{95} +(0.464102 + 0.267949i) q^{97} +(-2.59808 - 1.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4}+O(q^{10}) $ 4 * q + 2 * q^4	$ 4 q + 2 q^{4} + 2 q^{10} - 12 q^{11} + 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^{29} + 4 q^{35} + 18 q^{37} + 16 q^{38} + 4 q^{40} - 10 q^{43} + 6 q^{46} - 6 q^{49} + 14 q^{52} + 24 q^{53} - 6 q^{55} - 4 q^{56} - 6 q^{58} - 12 q^{59} - 4 q^{64} - 12 q^{67} + 8 q^{68} + 36 q^{71} + 8 q^{74} + 12 q^{76} + 24 q^{77} - 28 q^{79} - 4 q^{82} + 6 q^{88} - 12 q^{89} + 8 q^{92} - 14 q^{94} - 8 q^{95} - 12 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 + 2 * q^10 - 12 * q^11 + 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^29 + 4 * q^35 + 18 * q^37 + 16 * q^38 + 4 * q^40 - 10 * q^43 + 6 * q^46 - 6 * q^49 + 14 * q^52 + 24 * q^53 - 6 * q^55 - 4 * q^56 - 6 * q^58 - 12 * q^59 - 4 * q^64 - 12 * q^67 + 8 * q^68 + 36 * q^71 + 8 * q^74 + 12 * q^76 + 24 * q^77 - 28 * q^79 - 4 * q^82 + 6 * q^88 - 12 * q^89 + 8 * q^92 - 14 * q^94 - 8 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	−1.73205	−	1.00000i	−0.654654	−	0.377964i	0.135583	−	0.990766i	$-0.456709\pi$
$7$	−1.73205	−	1.00000i	−0.654654	−	0.377964i	−0.790237	+	0.612801i	$0.790043\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−5.59808	+	3.23205i	−1.68788	+	0.974500i	−0.731748	+	0.681575i	$0.761295\pi$
$11$	−5.59808	+	3.23205i	−1.68788	+	0.974500i	−0.956136	+	0.292925i	$0.905371\pi$
$12$		0			0
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$14$	−2.00000			−0.534522
$15$		0			0
$16$	−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	$0.327873\pi$
$18$		0			0
$19$	6.46410	+	3.73205i	1.48297	+	0.856191i	0.999813	−	0.0193444i	$-0.00615788\pi$
$19$	6.46410	+	3.73205i	1.48297	+	0.856191i	0.483154	+	0.875536i	$0.339491\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$		0			0
$22$	−3.23205	+	5.59808i	−0.689076	+	1.19351i
$23$	1.86603	+	3.23205i	0.389093	+	0.673929i	0.992328	−	0.123635i	$-0.0394551\pi$
$23$	1.86603	+	3.23205i	0.389093	+	0.673929i	−0.603235	+	0.797564i	$0.706122\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	2.59808	+	2.50000i	0.509525	+	0.490290i
$27$		0			0
$28$	−1.73205	+	1.00000i	−0.327327	+	0.188982i
$29$	0.133975	+	0.232051i	0.0248785	+	0.0430908i	0.878197	−	0.478300i	$-0.158747\pi$
$29$	0.133975	+	0.232051i	0.0248785	+	0.0430908i	−0.853318	+	0.521391i	$0.825413\pi$
$30$		0			0
$31$			1.73205i			0.311086i	0.987829	+	0.155543i	$0.0497126\pi$
$31$			1.73205i			0.311086i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			4.00000i			0.685994i
$35$	1.00000	−	1.73205i	0.169031	−	0.292770i
$36$		0			0
$37$	7.96410	−	4.59808i	1.30929	−	0.755919i	0.327313	−	0.944916i	$-0.393857\pi$
$37$	7.96410	−	4.59808i	1.30929	−	0.755919i	0.981978	+	0.188997i	$0.0605237\pi$
$38$	7.46410			1.21084
$39$		0			0
$40$	1.00000			0.158114
$41$	−1.73205	+	1.00000i	−0.270501	+	0.156174i	−0.629115	−	0.777312i	$-0.716583\pi$
$41$	−1.73205	+	1.00000i	−0.270501	+	0.156174i	0.358614	+	0.933486i	$0.383249\pi$
$42$		0			0
$43$	−5.96410	+	10.3301i	−0.909517	+	1.57533i	−0.0947805	+	0.995498i	$0.530215\pi$
$43$	−5.96410	+	10.3301i	−0.909517	+	1.57533i	−0.814736	+	0.579831i	$0.803118\pi$
$44$			6.46410i			0.974500i
$45$		0			0
$46$	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			0
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		0			0
$52$	3.50000	+	0.866025i	0.485363	+	0.120096i
$53$	−0.928203			−0.127499			−0.0637493	−	0.997966i	$-0.520306\pi$
$53$	−0.928203			−0.127499			−0.0637493	+	0.997966i	$0.520306\pi$
$54$		0			0
$55$	−3.23205	−	5.59808i	−0.435810	−	0.754844i
$56$	−1.00000	+	1.73205i	−0.133631	+	0.231455i
$57$		0			0
$58$	0.232051	+	0.133975i	0.0304698	+	0.0175917i
$59$	−7.33013	−	4.23205i	−0.954301	−	0.550966i	−0.0598868	−	0.998205i	$-0.519074\pi$
$59$	−7.33013	−	4.23205i	−0.954301	−	0.550966i	−0.894414	+	0.447239i	$0.852407\pi$
$60$		0			0
$61$	5.19615	−	9.00000i	0.665299	−	1.15233i	−0.313905	−	0.949454i	$-0.601637\pi$
$61$	5.19615	−	9.00000i	0.665299	−	1.15233i	0.979204	−	0.202878i	$-0.0650293\pi$
$62$	0.866025	+	1.50000i	0.109985	+	0.190500i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−3.46410	+	1.00000i	−0.429669	+	0.124035i
$66$		0			0
$67$	−9.92820	+	5.73205i	−1.21292	+	0.700281i	−0.963395	−	0.268086i	$-0.913609\pi$
$67$	−9.92820	+	5.73205i	−1.21292	+	0.700281i	−0.249528	+	0.968368i	$0.580276\pi$
$68$	2.00000	+	3.46410i	0.242536	+	0.420084i
$69$		0			0
$70$		−	2.00000i		−	0.239046i
$71$	10.7321	+	6.19615i	1.27366	+	0.735348i	0.975675	−	0.219222i	$-0.0703521\pi$
$71$	10.7321	+	6.19615i	1.27366	+	0.735348i	0.297985	+	0.954570i	$0.403685\pi$
$72$		0			0
$73$		−	2.00000i		−	0.234082i	−0.993127	−	0.117041i	$-0.962659\pi$
$73$		−	2.00000i		−	0.234082i	0.993127	−	0.117041i	$-0.0373409\pi$
$74$	4.59808	−	7.96410i	0.534516	−	0.925808i
$75$		0			0
$76$	6.46410	−	3.73205i	0.741483	−	0.428096i
$77$	12.9282			1.47331
$78$		0			0
$79$	−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			0
$82$	−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	$0.836997\pi$
$84$		0			0
$85$	−3.46410	−	2.00000i	−0.375735	−	0.216930i
$86$			11.9282i			1.28625i
$87$		0			0
$88$	3.23205	+	5.59808i	0.344538	+	0.596757i
$89$	0.464102	−	0.267949i	0.0491947	−	0.0284026i	−0.475201	−	0.879877i	$-0.657625\pi$
$89$	0.464102	−	0.267949i	0.0491947	−	0.0284026i	0.524396	+	0.851475i	$0.324291\pi$
$90$		0			0
$91$	1.73205	−	7.00000i	0.181568	−	0.733799i
$92$	3.73205			0.389093
$93$		0			0
$94$	−1.76795	−	3.06218i	−0.182350	−	0.315840i
$95$	−3.73205	+	6.46410i	−0.382900	+	0.663203i
$96$		0			0
$97$	0.464102	+	0.267949i	0.0471224	+	0.0272061i	0.523376	−	0.852102i	$-0.324672\pi$
$97$	0.464102	+	0.267949i	0.0471224	+	0.0272061i	−0.476254	+	0.879308i	$0.658006\pi$
$98$	−2.59808	−	1.50000i	−0.262445	−	0.151523i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	1.46410	+	2.53590i	0.145684	+	0.252331i	0.929628	−	0.368500i	$-0.120129\pi$
$101$	1.46410	+	2.53590i	0.145684	+	0.252331i	−0.783944	+	0.620831i	$0.786795\pi$
$102$		0			0
$103$	−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
$105$		0			0
$106$	−0.803848	+	0.464102i	−0.0780766	+	0.0450775i
$107$	−3.92820	−	6.80385i	−0.379754	−	0.657753i	0.611273	−	0.791420i	$-0.290658\pi$
$107$	−3.92820	−	6.80385i	−0.379754	−	0.657753i	−0.991026	+	0.133667i	$0.957325\pi$
$108$		0			0
$109$			15.8564i			1.51877i	0.650643	+	0.759384i	$0.274500\pi$
$109$			15.8564i			1.51877i	−0.650643	+	0.759384i	$0.725500\pi$
$110$	−5.59808	−	3.23205i	−0.533756	−	0.308164i
$111$		0			0
$112$			2.00000i			0.188982i
$113$	0.401924	−	0.696152i	0.0378098	−	0.0654885i	−0.846501	−	0.532387i	$-0.821295\pi$
$113$	0.401924	−	0.696152i	0.0378098	−	0.0654885i	0.884311	+	0.466898i	$0.154629\pi$
$114$		0			0
$115$	−3.23205	+	1.86603i	−0.301390	+	0.174008i
$116$	0.267949			0.0248785
$117$		0			0
$118$	−8.46410			−0.779184
$119$	6.92820	−	4.00000i	0.635107	−	0.366679i
$120$		0			0
$121$	15.3923	−	26.6603i	1.39930	−	2.42366i
$122$		−	10.3923i		−	0.940875i
$123$		0			0
$124$	1.50000	+	0.866025i	0.134704	+	0.0777714i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	2.46410	+	4.26795i	0.218654	+	0.378719i	0.954397	−	0.298542i	$-0.0965002\pi$
$127$	2.46410	+	4.26795i	0.218654	+	0.378719i	−0.735743	+	0.677261i	$0.763167\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−2.50000	+	2.59808i	−0.219265	+	0.227866i
$131$	18.6603			1.63035			0.815177	−	0.579212i	$-0.196640\pi$
$131$	18.6603			1.63035			0.815177	+	0.579212i	$0.196640\pi$
$132$		0			0
$133$	−7.46410	−	12.9282i	−0.647220	−	1.12102i
$134$	−5.73205	+	9.92820i	−0.495174	+	0.857666i
$135$		0			0
$136$	3.46410	+	2.00000i	0.297044	+	0.171499i
$137$	2.13397	+	1.23205i	0.182318	+	0.105261i	0.588381	−	0.808584i	$-0.299765\pi$
$137$	2.13397	+	1.23205i	0.182318	+	0.105261i	−0.406063	+	0.913845i	$0.633099\pi$
$138$		0			0
$139$	6.46410	−	11.1962i	0.548278	−	0.949645i	−0.450115	−	0.892971i	$-0.648617\pi$
$139$	6.46410	−	11.1962i	0.548278	−	0.949645i	0.998393	−	0.0566745i	$-0.0180497\pi$
$140$	−1.00000	−	1.73205i	−0.0845154	−	0.146385i
$141$		0			0
$142$	12.3923			1.03994
$143$	−16.7942	−	16.1603i	−1.40440	−	1.35139i
$144$		0			0
$145$	−0.232051	+	0.133975i	−0.0192708	+	0.0111260i
$146$	−1.00000	−	1.73205i	−0.0827606	−	0.143346i
$147$		0			0
$148$		−	9.19615i		−	0.755919i
$149$	11.7224	+	6.76795i	0.960339	+	0.554452i	0.896277	−	0.443494i	$-0.146261\pi$
$149$	11.7224	+	6.76795i	0.960339	+	0.554452i	0.0640617	+	0.997946i	$0.479595\pi$
$150$		0			0
$151$			10.3923i			0.845714i	0.906196	+	0.422857i	$0.138973\pi$
$151$			10.3923i			0.845714i	−0.906196	+	0.422857i	$0.861027\pi$
$152$	3.73205	−	6.46410i	0.302709	−	0.524308i
$153$		0			0
$154$	11.1962	−	6.46410i	0.902212	−	0.520892i
$155$	−1.73205			−0.139122
$156$		0			0
$157$	−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			0
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$		−	7.46410i		−	0.588254i
$162$		0			0
$163$	13.0359	+	7.52628i	1.02105	+	0.589504i	0.914408	−	0.404794i	$-0.132657\pi$
$163$	13.0359	+	7.52628i	1.02105	+	0.589504i	0.106642	+	0.994297i	$0.465990\pi$
$164$			2.00000i			0.156174i
$165$		0			0
$166$	4.46410	+	7.73205i	0.346481	+	0.600124i
$167$	−14.1340	+	8.16025i	−1.09372	+	0.631459i	−0.934564	−	0.355794i	$-0.884210\pi$
$167$	−14.1340	+	8.16025i	−1.09372	+	0.631459i	−0.159155	+	0.987254i	$0.550877\pi$
$168$		0			0
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$	−4.00000			−0.306786
$171$		0			0
$172$	5.96410	+	10.3301i	0.454758	+	0.787665i
$173$	5.46410	−	9.46410i	0.415428	−	0.719542i	−0.580045	−	0.814584i	$-0.696965\pi$
$173$	5.46410	−	9.46410i	0.415428	−	0.719542i	0.995473	+	0.0950419i	$0.0302985\pi$
$174$		0			0
$175$	1.73205	+	1.00000i	0.130931	+	0.0755929i
$176$	5.59808	+	3.23205i	0.421971	+	0.243625i
$177$		0			0
$178$	0.267949	−	0.464102i	0.0200836	−	0.0347859i
$179$	−9.86603	−	17.0885i	−0.737421	−	1.27725i	−0.953653	−	0.300909i	$-0.902710\pi$
$179$	−9.86603	−	17.0885i	−0.737421	−	1.27725i	0.216231	−	0.976342i	$-0.430623\pi$
$180$		0			0
$181$	−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
$183$		0			0
$184$	3.23205	−	1.86603i	0.238270	−	0.137565i
$185$	4.59808	+	7.96410i	0.338057	+	0.585532i
$186$		0			0
$187$		−	25.8564i		−	1.89081i
$188$	−3.06218	−	1.76795i	−0.223332	−	0.128941i
$189$		0			0
$190$			7.46410i			0.541503i
$191$	10.7321	−	18.5885i	0.776544	−	1.34501i	−0.157379	−	0.987538i	$-0.550304\pi$
$191$	10.7321	−	18.5885i	0.776544	−	1.34501i	0.933923	−	0.357475i	$-0.116362\pi$
$192$		0			0
$193$	9.80385	−	5.66025i	0.705696	−	0.407434i	−0.103769	−	0.994601i	$-0.533090\pi$
$193$	9.80385	−	5.66025i	0.705696	−	0.407434i	0.809466	+	0.587167i	$0.199757\pi$
$194$	0.535898			0.0384753
$195$		0			0
$196$	−3.00000			−0.214286
$197$	−3.80385	+	2.19615i	−0.271013	+	0.156469i	−0.629348	−	0.777124i	$-0.716678\pi$
$197$	−3.80385	+	2.19615i	−0.271013	+	0.156469i	0.358335	+	0.933593i	$0.383345\pi$
$198$		0			0
$199$	2.53590	−	4.39230i	0.179765	−	0.311362i	−0.762035	−	0.647536i	$-0.775800\pi$
$199$	2.53590	−	4.39230i	0.179765	−	0.311362i	0.941800	+	0.336174i	$0.109133\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	2.53590	+	1.46410i	0.178425	+	0.103014i
$203$		−	0.535898i		−	0.0376127i
$204$		0			0
$205$	−1.00000	−	1.73205i	−0.0698430	−	0.120972i
$206$	−10.2679	+	5.92820i	−0.715402	+	0.413037i
$207$		0			0
$208$	2.50000	−	2.59808i	0.173344	−	0.180144i
$209$	−48.2487			−3.33743
$210$		0			0
$211$	5.66025	+	9.80385i	0.389668	+	0.674925i	0.992405	−	0.123015i	$-0.0392564\pi$
$211$	5.66025	+	9.80385i	0.389668	+	0.674925i	−0.602737	+	0.797940i	$0.705923\pi$
$212$	−0.464102	+	0.803848i	−0.0318746	+	0.0552085i
$213$		0			0
$214$	−6.80385	−	3.92820i	−0.465101	−	0.268526i
$215$	−10.3301	−	5.96410i	−0.704509	−	0.406748i
$216$		0			0
$217$	1.73205	−	3.00000i	0.117579	−	0.203653i
$218$	7.92820	+	13.7321i	0.536966	+	0.930052i
$219$		0			0
$220$	−6.46410			−0.435810
$221$	−14.0000	−	3.46410i	−0.941742	−	0.233021i
$222$		0			0
$223$	−17.7846	+	10.2679i	−1.19095	+	0.687593i	−0.958521	−	0.285022i	$-0.907999\pi$
$223$	−17.7846	+	10.2679i	−1.19095	+	0.687593i	−0.232424	+	0.972614i	$0.574666\pi$
$224$	1.00000	+	1.73205i	0.0668153	+	0.115728i
$225$		0			0
$226$		−	0.803848i		−	0.0534711i
$227$	14.1962	+	8.19615i	0.942232	+	0.543998i	0.890659	−	0.454672i	$-0.150243\pi$
$227$	14.1962	+	8.19615i	0.942232	+	0.543998i	0.0515725	+	0.998669i	$0.483577\pi$
$228$		0			0
$229$			7.85641i			0.519166i	0.965721	+	0.259583i	$0.0835851\pi$
$229$			7.85641i			0.519166i	−0.965721	+	0.259583i	$0.916415\pi$
$230$	−1.86603	+	3.23205i	−0.123042	+	0.213115i
$231$		0			0
$232$	0.232051	−	0.133975i	0.0152349	−	0.00879586i
$233$	−6.12436			−0.401220			−0.200610	−	0.979671i	$-0.564292\pi$
$233$	−6.12436			−0.401220			−0.200610	+	0.979671i	$0.564292\pi$
$234$		0			0
$235$	3.53590			0.230657
$236$	−7.33013	+	4.23205i	−0.477151	+	0.275483i
$237$		0			0
$238$	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			0
$241$	15.3564	+	8.86603i	0.989193	+	0.571111i	0.905033	−	0.425341i	$-0.139846\pi$
$241$	15.3564	+	8.86603i	0.989193	+	0.571111i	0.0841601	+	0.996452i	$0.473179\pi$
$242$		−	30.7846i		−	1.97891i
$243$		0			0
$244$	−5.19615	−	9.00000i	−0.332650	−	0.576166i
$245$	2.59808	−	1.50000i	0.165985	−	0.0958315i
$246$		0			0
$247$	−6.46410	+	26.1244i	−0.411301	+	1.66225i
$248$	1.73205			0.109985
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	7.86603	−	13.6244i	0.496499	−	0.859962i	−0.503493	−	0.863999i	$-0.667952\pi$
$251$	7.86603	−	13.6244i	0.496499	−	0.859962i	0.999992	+	0.00403776i	$0.00128526\pi$
$252$		0			0
$253$	−20.8923	−	12.0622i	−1.31349	−	0.758343i
$254$	4.26795	+	2.46410i	0.267795	+	0.154611i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.66987	−	4.62436i	−0.166542	−	0.288459i	0.770660	−	0.637247i	$-0.219927\pi$
$257$	−2.66987	−	4.62436i	−0.166542	−	0.288459i	−0.937202	+	0.348787i	$0.886593\pi$
$258$		0			0
$259$	−18.3923			−1.14284
$260$	−0.866025	+	3.50000i	−0.0537086	+	0.217061i
$261$		0			0
$262$	16.1603	−	9.33013i	0.998384	−	0.576417i
$263$	3.06218	+	5.30385i	0.188822	+	0.327049i	0.944858	−	0.327481i	$-0.106200\pi$
$263$	3.06218	+	5.30385i	0.188822	+	0.327049i	−0.756036	+	0.654530i	$0.772866\pi$
$264$		0			0
$265$		−	0.928203i		−	0.0570191i
$266$	−12.9282	−	7.46410i	−0.792679	−	0.457653i
$267$		0			0
$268$			11.4641i			0.700281i
$269$	6.00000	−	10.3923i	0.365826	−	0.633630i	−0.623082	−	0.782157i	$-0.714120\pi$
$269$	6.00000	−	10.3923i	0.365826	−	0.633630i	0.988908	+	0.148527i	$0.0474530\pi$
$270$		0			0
$271$	1.03590	−	0.598076i	0.0629263	−	0.0363305i	−0.468207	−	0.883619i	$-0.655100\pi$
$271$	1.03590	−	0.598076i	0.0629263	−	0.0363305i	0.531133	+	0.847288i	$0.321766\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	2.46410			0.148862
$275$	5.59808	−	3.23205i	0.337577	−	0.194900i
$276$		0			0
$277$	1.96410	−	3.40192i	0.118011	−	0.204402i	−0.800968	−	0.598707i	$-0.795681\pi$
$277$	1.96410	−	3.40192i	0.118011	−	0.204402i	0.918980	+	0.394305i	$0.129015\pi$
$278$		−	12.9282i		−	0.775382i
$279$		0			0
$280$	−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	$-0.0858032\pi$
$282$		0			0
$283$	4.96410	+	8.59808i	0.295085	+	0.511103i	0.975005	−	0.222184i	$-0.0713186\pi$
$283$	4.96410	+	8.59808i	0.295085	+	0.511103i	−0.679920	+	0.733287i	$0.737985\pi$
$284$	10.7321	−	6.19615i	0.636830	−	0.367674i
$285$		0			0
$286$	−22.6244	−	5.59808i	−1.33781	−	0.331021i
$287$	4.00000			0.236113
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	−0.133975	+	0.232051i	−0.00786726	+	0.0136265i
$291$		0			0
$292$	−1.73205	−	1.00000i	−0.101361	−	0.0585206i
$293$	27.5885	+	15.9282i	1.61173	+	0.930536i	0.988968	+	0.148128i	$0.0473247\pi$
$293$	27.5885	+	15.9282i	1.61173	+	0.930536i	0.622767	+	0.782408i	$0.286009\pi$
$294$		0			0
$295$	4.23205	−	7.33013i	0.246400	−	0.426776i
$296$	−4.59808	−	7.96410i	−0.267258	−	0.462904i
$297$		0			0
$298$	13.5359			0.784114
$299$	−9.33013	+	9.69615i	−0.539575	+	0.560743i
$300$		0			0
$301$	20.6603	−	11.9282i	1.19084	−	0.687530i
$302$	5.19615	+	9.00000i	0.299005	+	0.517892i
$303$		0			0
$304$		−	7.46410i		−	0.428096i
$305$	9.00000	+	5.19615i	0.515339	+	0.297531i
$306$		0			0
$307$		−	19.4641i		−	1.11087i	−0.831558	−	0.555437i	$-0.812551\pi$
$307$		−	19.4641i		−	1.11087i	0.831558	−	0.555437i	$-0.187449\pi$
$308$	6.46410	−	11.1962i	0.368326	−	0.637960i
$309$		0			0
$310$	−1.50000	+	0.866025i	−0.0851943	+	0.0491869i
$311$	28.3923			1.60998			0.804990	−	0.593288i	$-0.202171\pi$
$311$	28.3923			1.60998			0.804990	+	0.593288i	$0.202171\pi$
$312$		0			0
$313$	−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
$315$		0			0
$316$	−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			0
$319$	−1.50000	−	0.866025i	−0.0839839	−	0.0484881i
$320$		−	1.00000i		−	0.0559017i
$321$		0			0
$322$	−3.73205	−	6.46410i	−0.207979	−	0.360230i
$323$	−25.8564	+	14.9282i	−1.43869	+	0.830627i
$324$		0			0
$325$	−1.00000	−	3.46410i	−0.0554700	−	0.192154i
$326$	15.0526			0.833684
$327$		0			0
$328$	1.00000	+	1.73205i	0.0552158	+	0.0956365i
$329$	−3.53590	+	6.12436i	−0.194940	+	0.337647i
$330$		0			0
$331$	−14.5359	−	8.39230i	−0.798965	−	0.461283i	0.0441440	−	0.999025i	$-0.485944\pi$
$331$	−14.5359	−	8.39230i	−0.798965	−	0.461283i	−0.843109	+	0.537742i	$0.819277\pi$
$332$	7.73205	+	4.46410i	0.424351	+	0.244999i
$333$		0			0
$334$	−8.16025	+	14.1340i	−0.446509	+	0.773377i
$335$	−5.73205	−	9.92820i	−0.313175	−	0.542436i
$336$		0			0
$337$	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			0
$340$	−3.46410	+	2.00000i	−0.187867	+	0.108465i
$341$	−5.59808	−	9.69615i	−0.303153	−	0.525076i
$342$		0			0
$343$			20.0000i			1.07990i
$344$	10.3301	+	5.96410i	0.556963	+	0.321563i
$345$		0			0
$346$		−	10.9282i		−	0.587504i
$347$	0.803848	−	1.39230i	0.0431528	−	0.0747428i	−0.843642	−	0.536906i	$-0.819593\pi$
$347$	0.803848	−	1.39230i	0.0431528	−	0.0747428i	0.886795	+	0.462163i	$0.152926\pi$
$348$		0			0
$349$	18.5885	−	10.7321i	0.995017	−	0.574474i	0.0882471	−	0.996099i	$-0.471873\pi$
$349$	18.5885	−	10.7321i	0.995017	−	0.574474i	0.906770	+	0.421625i	$0.138540\pi$
$350$	2.00000			0.106904
$351$		0			0
$352$	6.46410			0.344538
$353$	−1.73205	+	1.00000i	−0.0921878	+	0.0532246i	−0.545385	−	0.838186i	$-0.683617\pi$
$353$	−1.73205	+	1.00000i	−0.0921878	+	0.0532246i	0.453197	+	0.891410i	$0.350283\pi$
$354$		0			0
$355$	−6.19615	+	10.7321i	−0.328858	+	0.569598i
$356$		−	0.535898i		−	0.0284026i
$357$		0			0
$358$	−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			0
$361$	18.3564	+	31.7942i	0.966127	+	1.67338i
$362$	−2.53590	+	1.46410i	−0.133284	+	0.0769515i
$363$		0			0
$364$	−5.19615	−	5.00000i	−0.272352	−	0.262071i
$365$	2.00000			0.104685
$366$		0			0
$367$	−7.80385	−	13.5167i	−0.407358	−	0.705564i	0.587235	−	0.809416i	$-0.300216\pi$
$367$	−7.80385	−	13.5167i	−0.407358	−	0.705564i	−0.994593	+	0.103852i	$0.966883\pi$
$368$	1.86603	−	3.23205i	0.0972733	−	0.168482i
$369$		0			0
$370$	7.96410	+	4.59808i	0.414034	+	0.239043i
$371$	1.60770	+	0.928203i	0.0834674	+	0.0481899i
$372$		0			0
$373$	7.89230	−	13.6699i	0.408648	−	0.707799i	−0.586090	−	0.810246i	$-0.699334\pi$
$373$	7.89230	−	13.6699i	0.408648	−	0.707799i	0.994739	+	0.102446i	$0.0326670\pi$
$374$	−12.9282	−	22.3923i	−0.668501	−	1.15788i
$375$		0			0
$376$	−3.53590			−0.182350
$377$	−0.669873	+	0.696152i	−0.0345002	+	0.0358537i
$378$		0			0
$379$	24.1244	−	13.9282i	1.23918	−	0.715444i	0.270257	−	0.962788i	$-0.412891\pi$
$379$	24.1244	−	13.9282i	1.23918	−	0.715444i	0.968928	+	0.247344i	$0.0795579\pi$
$380$	3.73205	+	6.46410i	0.191450	+	0.331601i
$381$		0			0
$382$		−	21.4641i		−	1.09820i
$383$	−21.9904	−	12.6962i	−1.12366	−	0.648743i	−0.181324	−	0.983423i	$-0.558038\pi$
$383$	−21.9904	−	12.6962i	−1.12366	−	0.648743i	−0.942332	+	0.334680i	$0.891372\pi$
$384$		0			0
$385$			12.9282i			0.658882i
$386$	5.66025	−	9.80385i	0.288099	−	0.499003i
$387$		0			0
$388$	0.464102	−	0.267949i	0.0235612	−	0.0136031i
$389$	23.7321			1.20326			0.601631	−	0.798774i	$-0.294518\pi$
$389$	23.7321			1.20326			0.601631	+	0.798774i	$0.294518\pi$
$390$		0			0
$391$	−14.9282			−0.754952
$392$	−2.59808	+	1.50000i	−0.131223	+	0.0757614i
$393$		0			0
$394$	−2.19615	+	3.80385i	−0.110641	+	0.191635i
$395$		−	13.9282i		−	0.700804i
$396$		0			0
$397$	10.5000	+	6.06218i	0.526980	+	0.304252i	0.739786	−	0.672843i	$-0.234927\pi$
$397$	10.5000	+	6.06218i	0.526980	+	0.304252i	−0.212806	+	0.977095i	$0.568260\pi$
$398$		−	5.07180i		−	0.254226i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	27.7128	−	16.0000i	1.38391	−	0.799002i	0.391292	−	0.920267i	$-0.372028\pi$
$401$	27.7128	−	16.0000i	1.38391	−	0.799002i	0.992620	+	0.121265i	$0.0386950\pi$
$402$		0			0
$403$	−6.00000	+	1.73205i	−0.298881	+	0.0862796i
$404$	2.92820			0.145684
$405$		0			0
$406$	−0.267949	−	0.464102i	−0.0132981	−	0.0230330i
$407$	−29.7224	+	51.4808i	−1.47329	+	2.55181i
$408$		0			0
$409$	3.46410	+	2.00000i	0.171289	+	0.0988936i	0.583193	−	0.812333i	$-0.301803\pi$
$409$	3.46410	+	2.00000i	0.171289	+	0.0988936i	−0.411905	+	0.911227i	$0.635136\pi$
$410$	−1.73205	−	1.00000i	−0.0855399	−	0.0493865i
$411$		0			0
$412$	−5.92820	+	10.2679i	−0.292062	+	0.505866i
$413$	8.46410	+	14.6603i	0.416491	+	0.721384i
$414$		0			0
$415$	−8.92820			−0.438268
$416$	0.866025	−	3.50000i	0.0424604	−	0.171602i
$417$		0			0
$418$	−41.7846	+	24.1244i	−2.04375	+	1.17996i
$419$	11.1962	+	19.3923i	0.546968	+	0.947376i	0.998480	+	0.0551112i	$0.0175513\pi$
$419$	11.1962	+	19.3923i	0.546968	+	0.947376i	−0.451512	+	0.892265i	$0.649115\pi$
$420$		0			0
$421$		−	4.39230i		−	0.214068i	−0.994255	−	0.107034i	$-0.965865\pi$
$421$		−	4.39230i		−	0.214068i	0.994255	−	0.107034i	$-0.0341353\pi$
$422$	9.80385	+	5.66025i	0.477244	+	0.275537i
$423$		0			0
$424$			0.928203i			0.0450775i
$425$	2.00000	−	3.46410i	0.0970143	−	0.168034i
$426$		0			0
$427$	−18.0000	+	10.3923i	−0.871081	+	0.502919i
$428$	−7.85641			−0.379754
$429$		0			0
$430$	−11.9282			−0.575229
$431$	−24.5885	+	14.1962i	−1.18438	+	0.683805i	−0.957025	−	0.290006i	$-0.906343\pi$
$431$	−24.5885	+	14.1962i	−1.18438	+	0.683805i	−0.227360	+	0.973811i	$0.573009\pi$
$432$		0			0
$433$	−9.66025	+	16.7321i	−0.464242	+	0.804091i	−0.999167	−	0.0408086i	$-0.987007\pi$
$433$	−9.66025	+	16.7321i	−0.464242	+	0.804091i	0.534925	+	0.844900i	$0.320340\pi$
$434$		−	3.46410i		−	0.166282i
$435$		0			0
$436$	13.7321	+	7.92820i	0.657646	+	0.379692i
$437$			27.8564i			1.33255i
$438$		0			0
$439$	8.92820	+	15.4641i	0.426120	+	0.738061i	0.996524	−	0.0833027i	$-0.0265468\pi$
$439$	8.92820	+	15.4641i	0.426120	+	0.738061i	−0.570404	+	0.821364i	$0.693214\pi$
$440$	−5.59808	+	3.23205i	−0.266878	+	0.154082i
$441$		0			0
$442$	−13.8564	+	4.00000i	−0.659082	+	0.190261i
$443$	−16.3923			−0.778822			−0.389411	−	0.921064i	$-0.627321\pi$
$443$	−16.3923			−0.778822			−0.389411	+	0.921064i	$0.627321\pi$
$444$		0			0
$445$	0.267949	+	0.464102i	0.0127020	+	0.0220005i
$446$	−10.2679	+	17.7846i	−0.486201	+	0.842126i
$447$		0			0
$448$	1.73205	+	1.00000i	0.0818317	+	0.0472456i
$449$	13.6077	+	7.85641i	0.642187	+	0.370767i	0.785456	−	0.618917i	$-0.212428\pi$
$449$	13.6077	+	7.85641i	0.642187	+	0.370767i	−0.143270	+	0.989684i	$0.545762\pi$
$450$		0			0
$451$	6.46410	−	11.1962i	0.304383	−	0.527206i
$452$	−0.401924	−	0.696152i	−0.0189049	−	0.0327443i
$453$		0			0
$454$	16.3923			0.769329
$455$	7.00000	+	1.73205i	0.328165	+	0.0811998i
$456$		0			0
$457$	21.2487	−	12.2679i	0.993973	−	0.573870i	0.0875134	−	0.996163i	$-0.472108\pi$
$457$	21.2487	−	12.2679i	0.993973	−	0.573870i	0.906459	+	0.422293i	$0.138775\pi$
$458$	3.92820	+	6.80385i	0.183553	+	0.317923i
$459$		0			0
$460$			3.73205i			0.174008i
$461$	−0.401924	−	0.232051i	−0.0187195	−	0.0108077i	0.490611	−	0.871379i	$-0.336774\pi$
$461$	−0.401924	−	0.232051i	−0.0187195	−	0.0108077i	−0.509331	+	0.860571i	$0.670107\pi$
$462$		0			0
$463$		−	7.07180i		−	0.328654i	−0.986406	−	0.164327i	$-0.947455\pi$
$463$		−	7.07180i		−	0.328654i	0.986406	−	0.164327i	$-0.0525453\pi$
$464$	0.133975	−	0.232051i	0.00621961	−	0.0107727i
$465$		0			0
$466$	−5.30385	+	3.06218i	−0.245696	+	0.141853i
$467$	15.8564			0.733747			0.366873	−	0.930271i	$-0.380428\pi$
$467$	15.8564			0.733747			0.366873	+	0.930271i	$0.380428\pi$
$468$		0			0
$469$	22.9282			1.05873
$470$	3.06218	−	1.76795i	0.141248	−	0.0815494i
$471$		0			0
$472$	−4.23205	+	7.33013i	−0.194796	+	0.337396i
$473$		−	77.1051i		−	3.54530i
$474$		0			0
$475$	−6.46410	−	3.73205i	−0.296593	−	0.171238i
$476$		−	8.00000i		−	0.366679i
$477$		0			0
$478$	−8.19615	−	14.1962i	−0.374883	−	0.649317i
$479$	−4.73205	+	2.73205i	−0.216213	+	0.124831i	−0.604195	−	0.796836i	$-0.706505\pi$
$479$	−4.73205	+	2.73205i	−0.216213	+	0.124831i	0.387983	+	0.921667i	$0.373172\pi$
$480$		0			0
$481$	23.8923	+	22.9904i	1.08940	+	1.04827i
$482$	17.7321			0.807673
$483$		0			0
$484$	−15.3923	−	26.6603i	−0.699650	−	1.21183i
$485$	−0.267949	+	0.464102i	−0.0121669	+	0.0210738i
$486$		0			0
$487$	20.0718	+	11.5885i	0.909540	+	0.525123i	0.880283	−	0.474449i	$-0.157353\pi$
$487$	20.0718	+	11.5885i	0.909540	+	0.525123i	0.0292568	+	0.999572i	$0.490686\pi$
$488$	−9.00000	−	5.19615i	−0.407411	−	0.235219i
$489$		0			0
$490$	1.50000	−	2.59808i	0.0677631	−	0.117369i
$491$	−8.66025	−	15.0000i	−0.390832	−	0.676941i	0.601728	−	0.798701i	$-0.294479\pi$
$491$	−8.66025	−	15.0000i	−0.390832	−	0.676941i	−0.992559	+	0.121761i	$0.961146\pi$
$492$		0			0
$493$	−1.07180			−0.0482713
$494$	7.46410	+	25.8564i	0.335826	+	1.16333i
$495$		0			0
$496$	1.50000	−	0.866025i	0.0673520	−	0.0388857i
$497$	−12.3923	−	21.4641i	−0.555871	−	0.962797i
$498$		0			0
$499$		−	6.53590i		−	0.292587i	−0.989241	−	0.146293i	$-0.953266\pi$
$499$		−	6.53590i		−	0.292587i	0.989241	−	0.146293i	$-0.0467344\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$		0			0
$502$		−	15.7321i		−	0.702156i
$503$	−15.5885	+	27.0000i	−0.695055	+	1.20387i	0.275107	+	0.961414i	$0.411287\pi$
$503$	−15.5885	+	27.0000i	−0.695055	+	1.20387i	−0.970162	+	0.242457i	$0.922047\pi$
$504$		0			0
$505$	−2.53590	+	1.46410i	−0.112846	+	0.0651517i
$506$	−24.1244			−1.07246
$507$		0			0
$508$	4.92820			0.218654
$509$	−1.20577	+	0.696152i	−0.0534449	+	0.0308564i	−0.526484	−	0.850185i	$-0.676490\pi$
$509$	−1.20577	+	0.696152i	−0.0534449	+	0.0308564i	0.473039	+	0.881041i	$0.343157\pi$
$510$		0			0
$511$	−2.00000	+	3.46410i	−0.0884748	+	0.153243i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−4.62436	−	2.66987i	−0.203972	−	0.117763i
$515$		−	11.8564i		−	0.522456i
$516$		0			0
$517$	11.4282	+	19.7942i	0.502612	+	0.870549i
$518$	−15.9282	+	9.19615i	−0.699845	+	0.404056i
$519$		0			0
$520$	1.00000	+	3.46410i	0.0438529	+	0.151911i
$521$	17.3205			0.758825			0.379413	−	0.925228i	$-0.376126\pi$
$521$	17.3205			0.758825			0.379413	+	0.925228i	$0.376126\pi$
$522$		0			0
$523$	−5.89230	−	10.2058i	−0.257653	−	0.446267i	0.707960	−	0.706252i	$-0.249616\pi$
$523$	−5.89230	−	10.2058i	−0.257653	−	0.446267i	−0.965613	+	0.259985i	$0.916282\pi$
$524$	9.33013	−	16.1603i	0.407588	−	0.705964i
$525$		0			0
$526$	5.30385	+	3.06218i	0.231259	+	0.133517i
$527$	−6.00000	−	3.46410i	−0.261364	−	0.150899i
$528$		0			0
$529$	4.53590	−	7.85641i	0.197213	−	0.341583i
$530$	−0.464102	−	0.803848i	−0.0201593	−	0.0349169i
$531$		0			0
$532$	−14.9282			−0.647220
$533$	−5.19615	−	5.00000i	−0.225070	−	0.216574i
$534$		0			0
$535$	6.80385	−	3.92820i	0.294156	−	0.169831i
$536$	5.73205	+	9.92820i	0.247587	+	0.428833i
$537$		0			0
$538$		−	12.0000i		−	0.517357i
$539$	16.7942	+	9.69615i	0.723379	+	0.417643i
$540$		0			0
$541$		−	26.9282i		−	1.15773i	−0.815422	−	0.578867i	$-0.803495\pi$
$541$		−	26.9282i		−	1.15773i	0.815422	−	0.578867i	$-0.196505\pi$
$542$	0.598076	−	1.03590i	0.0256896	−	0.0444956i
$543$		0			0
$544$	3.46410	−	2.00000i	0.148522	−	0.0857493i
$545$	−15.8564			−0.679214
$546$		0			0
$547$	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
$549$		0			0
$550$	3.23205	−	5.59808i	0.137815	−	0.238703i
$551$			2.00000i			0.0852029i
$552$		0			0
$553$	24.1244	+	13.9282i	1.02587	+	0.592287i
$554$		−	3.92820i		−	0.166893i
$555$		0			0
$556$	−6.46410	−	11.1962i	−0.274139	−	0.474823i
$557$	−15.3397	+	8.85641i	−0.649966	+	0.375258i	−0.788443	−	0.615108i	$-0.789113\pi$
$557$	−15.3397	+	8.85641i	−0.649966	+	0.375258i	0.138477	+	0.990366i	$0.455779\pi$
$558$		0			0
$559$	−41.7487	−	10.3301i	−1.76578	−	0.436918i
$560$	−2.00000			−0.0845154
$561$		0			0
$562$	−4.46410	−	7.73205i	−0.188307	−	0.326157i
$563$	−2.33975	+	4.05256i	−0.0986085	+	0.170795i	−0.911109	−	0.412166i	$-0.864772\pi$
$563$	−2.33975	+	4.05256i	−0.0986085	+	0.170795i	0.812500	+	0.582961i	$0.198106\pi$
$564$		0			0
$565$	0.696152	+	0.401924i	0.0292874	+	0.0169091i
$566$	8.59808	+	4.96410i	0.361404	+	0.208657i
$567$		0			0
$568$	6.19615	−	10.7321i	0.259985	−	0.450307i
$569$	14.6603	+	25.3923i	0.614590	+	1.06450i	0.990456	+	0.137827i	$0.0440118\pi$
$569$	14.6603	+	25.3923i	0.614590	+	1.06450i	−0.375867	+	0.926674i	$0.622655\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$	3.46410	−	2.00000i	0.144589	−	0.0834784i
$575$	−1.86603	−	3.23205i	−0.0778186	−	0.134786i
$576$		0			0
$577$			10.0000i			0.416305i	0.978096	+	0.208153i	$0.0667451\pi$
$577$			10.0000i			0.416305i	−0.978096	+	0.208153i	$0.933255\pi$
$578$	0.866025	+	0.500000i	0.0360219	+	0.0207973i
$579$		0			0
$580$			0.267949i			0.0111260i
$581$	8.92820	−	15.4641i	0.370404	−	0.641559i
$582$		0			0
$583$	5.19615	−	3.00000i	0.215203	−	0.124247i
$584$	−2.00000			−0.0827606
$585$		0			0
$586$	31.8564			1.31598
$587$	2.07180	−	1.19615i	0.0855122	−	0.0493705i	−0.456634	−	0.889655i	$-0.650945\pi$
$587$	2.07180	−	1.19615i	0.0855122	−	0.0493705i	0.542146	+	0.840284i	$0.317612\pi$
$588$		0			0
$589$	−6.46410	+	11.1962i	−0.266349	+	0.461329i
$590$		−	8.46410i		−	0.348462i
$591$		0			0
$592$	−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	$0.623121\pi$
$594$		0			0
$595$	4.00000	+	6.92820i	0.163984	+	0.284029i
$596$	11.7224	−	6.76795i	0.480170	−	0.277226i
$597$		0			0
$598$	−3.23205	+	13.0622i	−0.132168	+	0.534152i
$599$	10.3923			0.424618			0.212309	−	0.977203i	$-0.431902\pi$
$599$	10.3923			0.424618			0.212309	+	0.977203i	$0.431902\pi$
$600$		0			0
$601$	9.89230	+	17.1340i	0.403516	+	0.698909i	0.994147	−	0.108032i	$-0.0344548\pi$
$601$	9.89230	+	17.1340i	0.403516	+	0.698909i	−0.590632	+	0.806941i	$0.701121\pi$
$602$	11.9282	−	20.6603i	0.486157	−	0.842049i
$603$		0			0
$604$	9.00000	+	5.19615i	0.366205	+	0.211428i
$605$	26.6603	+	15.3923i	1.08389	+	0.625786i
$606$		0			0
$607$	9.58846	−	16.6077i	0.389183	−	0.674086i	−0.603156	−	0.797623i	$-0.706091\pi$
$607$	9.58846	−	16.6077i	0.389183	−	0.674086i	0.992340	+	0.123537i	$0.0394239\pi$
$608$	−3.73205	−	6.46410i	−0.151355	−	0.262154i
$609$		0			0
$610$	10.3923			0.420772
$611$	12.2487	−	3.53590i	0.495530	−	0.143047i
$612$		0			0
$613$	−33.8205	+	19.5263i	−1.36600	+	0.788659i	−0.990414	−	0.138130i	$-0.955891\pi$
$613$	−33.8205	+	19.5263i	−1.36600	+	0.788659i	−0.375583	+	0.926789i	$0.622558\pi$
$614$	−9.73205	−	16.8564i	−0.392754	−	0.680269i
$615$		0			0
$616$		−	12.9282i		−	0.520892i
$617$	19.4545	+	11.2321i	0.783208	+	0.452185i	0.837566	−	0.546336i	$-0.183978\pi$
$617$	19.4545	+	11.2321i	0.783208	+	0.452185i	−0.0543580	+	0.998522i	$0.517311\pi$
$618$		0			0
$619$			24.2487i			0.974638i	0.873224	+	0.487319i	$0.162025\pi$
$619$			24.2487i			0.974638i	−0.873224	+	0.487319i	$0.837975\pi$
$620$	−0.866025	+	1.50000i	−0.0347804	+	0.0602414i
$621$		0			0
$622$	24.5885	−	14.1962i	0.985907	−	0.569214i
$623$	−1.07180			−0.0429406
$624$		0			0
$625$	1.00000			0.0400000
$626$	−24.2487	+	14.0000i	−0.969173	+	0.559553i
$627$		0			0
$628$	−2.50000	+	4.33013i	−0.0997609	+	0.172791i
$629$			36.7846i			1.46670i
$630$		0			0
$631$	27.2487	+	15.7321i	1.08475	+	0.626283i	0.932175	−	0.362008i	$-0.117909\pi$
$631$	27.2487	+	15.7321i	1.08475	+	0.626283i	0.152579	+	0.988291i	$0.451242\pi$
$632$			13.9282i			0.554034i
$633$		0			0
$634$	7.26795	+	12.5885i	0.288647	+	0.499952i
$635$	−4.26795	+	2.46410i	−0.169368	+	0.0977849i
$636$		0			0
$637$	7.50000	−	7.79423i	0.297161	−	0.308819i
$638$	−1.73205			−0.0685725
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	0.0717968	−	0.124356i	0.00283580	−	0.00491175i	−0.864604	−	0.502454i	$-0.832431\pi$
$641$	0.0717968	−	0.124356i	0.00283580	−	0.00491175i	0.867440	+	0.497542i	$0.165764\pi$
$642$		0			0
$643$	−17.7846	−	10.2679i	−0.701357	−	0.404928i	0.106496	−	0.994313i	$-0.466037\pi$
$643$	−17.7846	−	10.2679i	−0.701357	−	0.404928i	−0.807852	+	0.589385i	$0.799370\pi$
$644$	−6.46410	−	3.73205i	−0.254721	−	0.147063i
$645$		0			0
$646$	−14.9282	+	25.8564i	−0.587342	+	1.01731i
$647$	−6.66025	−	11.5359i	−0.261842	−	0.453523i	0.704890	−	0.709317i	$-0.250996\pi$
$647$	−6.66025	−	11.5359i	−0.261842	−	0.453523i	−0.966731	+	0.255794i	$0.917663\pi$
$648$		0			0
$649$	54.7128			2.14767
$650$	−2.59808	−	2.50000i	−0.101905	−	0.0980581i
$651$		0			0
$652$	13.0359	−	7.52628i	0.510525	−	0.294752i
$653$	2.12436	+	3.67949i	0.0831325	+	0.143990i	0.904594	−	0.426274i	$-0.140174\pi$
$653$	2.12436	+	3.67949i	0.0831325	+	0.143990i	−0.821461	+	0.570264i	$0.806841\pi$
$654$		0			0
$655$			18.6603i			0.729116i
$656$	1.73205	+	1.00000i	0.0676252	+	0.0390434i
$657$		0			0
$658$			7.07180i			0.275687i
$659$	−0.133975	+	0.232051i	−0.00521891	+	0.00903942i	−0.868623	−	0.495473i	$-0.834995\pi$
$659$	−0.133975	+	0.232051i	−0.00521891	+	0.00903942i	0.863404	+	0.504513i	$0.168328\pi$
$660$		0			0
$661$	−7.51666	+	4.33975i	−0.292364	+	0.168797i	−0.639008	−	0.769200i	$-0.720655\pi$
$661$	−7.51666	+	4.33975i	−0.292364	+	0.168797i	0.346643	+	0.937997i	$0.387321\pi$
$662$	−16.7846			−0.652352
$663$		0			0
$664$	8.92820			0.346481
$665$	12.9282	−	7.46410i	0.501334	−	0.289445i
$666$		0			0
$667$	−0.500000	+	0.866025i	−0.0193601	+	0.0335326i
$668$			16.3205i			0.631459i
$669$		0			0
$670$	−9.92820	−	5.73205i	−0.383560	−	0.221448i
$671$			67.1769i			2.59334i
$672$		0			0
$673$	−16.0000	−	27.7128i	−0.616755	−	1.06825i	−0.990074	−	0.140548i	$-0.955114\pi$
$673$	−16.0000	−	27.7128i	−0.616755	−	1.06825i	0.373319	−	0.927703i	$-0.378220\pi$
$674$	8.07180	−	4.66025i	0.310914	−	0.179506i
$675$		0			0
$676$	0.500000	+	12.9904i	0.0192308	+	0.499630i
$677$	−32.3923			−1.24494			−0.622469	−	0.782645i	$-0.713870\pi$
$677$	−32.3923			−1.24494			−0.622469	+	0.782645i	$0.713870\pi$
$678$		0			0
$679$	−0.535898	−	0.928203i	−0.0205659	−	0.0356212i
$680$	−2.00000	+	3.46410i	−0.0766965	+	0.132842i
$681$		0			0
$682$	−9.69615	−	5.59808i	−0.371285	−	0.214361i
$683$	35.3205	+	20.3923i	1.35150	+	0.780290i	0.988460	−	0.151483i	$-0.0484049\pi$
$683$	35.3205	+	20.3923i	1.35150	+	0.780290i	0.363042	+	0.931773i	$0.381738\pi$
$684$		0			0
$685$	−1.23205	+	2.13397i	−0.0470742	+	0.0815350i
$686$	10.0000	+	17.3205i	0.381802	+	0.661300i
$687$		0			0
$688$	11.9282			0.454758
$689$	−0.928203	−	3.21539i	−0.0353617	−	0.122497i
$690$		0			0
$691$	−23.5359	+	13.5885i	−0.895348	+	0.516929i	−0.875688	−	0.482877i	$-0.839592\pi$
$691$	−23.5359	+	13.5885i	−0.895348	+	0.516929i	−0.0196598	+	0.999807i	$0.506258\pi$
$692$	−5.46410	−	9.46410i	−0.207714	−	0.359771i
$693$		0			0
$694$		−	1.60770i		−	0.0610273i
$695$	11.1962	+	6.46410i	0.424694	+	0.245197i
$696$		0			0
$697$		−	8.00000i		−	0.303022i
$698$	10.7321	−	18.5885i	0.406214	−	0.703583i
$699$		0			0
$700$	1.73205	−	1.00000i	0.0654654	−	0.0377964i
$701$	0.267949			0.0101203			0.00506015	−	0.999987i	$-0.498389\pi$
$701$	0.267949			0.0101203			0.00506015	+	0.999987i	$0.498389\pi$
$702$		0			0
$703$	68.6410			2.58884
$704$	5.59808	−	3.23205i	0.210985	−	0.121812i
$705$		0			0
$706$	−1.00000	+	1.73205i	−0.0376355	+	0.0651866i
$707$		−	5.85641i		−	0.220253i
$708$		0			0
$709$	−19.8564	−	11.4641i	−0.745723	−	0.430543i	0.0784234	−	0.996920i	$-0.475011\pi$
$709$	−19.8564	−	11.4641i	−0.745723	−	0.430543i	−0.824146	+	0.566377i	$0.808345\pi$
$710$			12.3923i			0.465075i
$711$		0			0
$712$	−0.267949	−	0.464102i	−0.0100418	−	0.0173929i
$713$	−5.59808	+	3.23205i	−0.209650	+	0.121041i
$714$		0			0
$715$	16.1603	−	16.7942i	0.604359	−	0.628069i
$716$	−19.7321			−0.737421
$717$		0			0
$718$	2.53590	+	4.39230i	0.0946389	+	0.163919i
$719$	−17.3205	+	30.0000i	−0.645946	+	1.11881i	0.338136	+	0.941097i	$0.390204\pi$
$719$	−17.3205	+	30.0000i	−0.645946	+	1.11881i	−0.984082	+	0.177714i	$0.943130\pi$
$720$		0			0
$721$	20.5359	+	11.8564i	0.764797	+	0.441556i
$722$	31.7942	+	18.3564i	1.18326	+	0.683155i
$723$		0			0
$724$	−1.46410	+	2.53590i	−0.0544129	+	0.0942459i
$725$	−0.133975	−	0.232051i	−0.00497569	−	0.00861815i
$726$		0			0
$727$	−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
$729$		0			0
$730$	1.73205	−	1.00000i	0.0641061	−	0.0370117i
$731$	−23.8564	−	41.3205i	−0.882361	−	1.52829i
$732$		0			0
$733$			50.9282i			1.88108i	0.339688	+	0.940538i	$0.389678\pi$
$733$			50.9282i			1.88108i	−0.339688	+	0.940538i	$0.610322\pi$
$734$	−13.5167	−	7.80385i	−0.498909	−	0.288045i
$735$		0			0
$736$		−	3.73205i		−	0.137565i
$737$	37.0526	−	64.1769i	1.36485	−	2.36399i
$738$		0			0
$739$	−16.7321	+	9.66025i	−0.615498	+	0.355358i	−0.775114	−	0.631821i	$-0.782308\pi$
$739$	−16.7321	+	9.66025i	−0.615498	+	0.355358i	0.159616	+	0.987179i	$0.448974\pi$
$740$	9.19615			0.338057
$741$		0			0
$742$	1.85641			0.0681508
$743$	35.0429	−	20.2321i	1.28560	−	0.742242i	0.307734	−	0.951472i	$-0.400429\pi$
$743$	35.0429	−	20.2321i	1.28560	−	0.742242i	0.977866	+	0.209230i	$0.0670958\pi$
$744$		0			0
$745$	−6.76795	+	11.7224i	−0.247958	+	0.429477i
$746$		−	15.7846i		−	0.577916i
$747$		0			0
$748$	−22.3923	−	12.9282i	−0.818744	−	0.472702i
$749$			15.7128i			0.574134i
$750$		0			0
$751$	−7.03590	−	12.1865i	−0.256744	−	0.444693i	0.708624	−	0.705586i	$-0.249316\pi$
$751$	−7.03590	−	12.1865i	−0.256744	−	0.444693i	−0.965368	+	0.260893i	$0.915983\pi$
$752$	−3.06218	+	1.76795i	−0.111666	+	0.0644705i
$753$		0			0
$754$	−0.232051	+	0.937822i	−0.00845079	+	0.0341535i
$755$	−10.3923			−0.378215
$756$		0			0
$757$	9.00000	+	15.5885i	0.327111	+	0.566572i	0.981937	−	0.189207i	$-0.0605917\pi$
$757$	9.00000	+	15.5885i	0.327111	+	0.566572i	−0.654827	+	0.755779i	$0.727258\pi$
$758$	13.9282	−	24.1244i	0.505895	−	0.876236i
$759$		0			0
$760$	6.46410	+	3.73205i	0.234478	+	0.135376i
$761$	−4.39230	−	2.53590i	−0.159221	−	0.0919262i	0.418272	−	0.908322i	$-0.362636\pi$
$761$	−4.39230	−	2.53590i	−0.159221	−	0.0919262i	−0.577493	+	0.816395i	$0.695969\pi$
$762$		0			0
$763$	15.8564	−	27.4641i	0.574040	−	0.994267i
$764$	−10.7321	−	18.5885i	−0.388272	−	0.672507i
$765$		0			0
$766$	−25.3923			−0.917461
$767$	7.33013	−	29.6244i	0.264676	−	1.06967i
$768$		0			0
$769$	−10.0359	+	5.79423i	−0.361904	+	0.208945i	−0.669916	−	0.742437i	$-0.733670\pi$
$769$	−10.0359	+	5.79423i	−0.361904	+	0.208945i	0.308012	+	0.951383i	$0.400336\pi$
$770$	6.46410	+	11.1962i	0.232950	+	0.403481i
$771$		0			0
$772$		−	11.3205i		−	0.407434i
$773$	−24.0000	−	13.8564i	−0.863220	−	0.498380i	0.00186926	−	0.999998i	$-0.499405\pi$
$773$	−24.0000	−	13.8564i	−0.863220	−	0.498380i	−0.865089	+	0.501618i	$0.832738\pi$
$774$		0			0
$775$		−	1.73205i		−	0.0622171i
$776$	0.267949	−	0.464102i	0.00961882	−	0.0166603i
$777$		0			0
$778$	20.5526	−	11.8660i	0.736845	−	0.425418i
$779$	−14.9282			−0.534858
$780$		0			0
$781$	−80.1051			−2.86639
$782$	−12.9282	+	7.46410i	−0.462312	+	0.266916i
$783$		0			0
$784$	−1.50000	+	2.59808i	−0.0535714	+	0.0927884i
$785$		−	5.00000i		−	0.178458i
$786$		0			0
$787$	1.50000	+	0.866025i	0.0534692	+	0.0308705i	0.526496	−	0.850177i	$-0.323505\pi$
$787$	1.50000	+	0.866025i	0.0534692	+	0.0308705i	−0.473027	+	0.881048i	$0.656839\pi$
$788$			4.39230i			0.156469i
$789$		0			0
$790$	−6.96410	−	12.0622i	−0.247772	−	0.429153i
$791$	−1.39230	+	0.803848i	−0.0495047	+	0.0285815i
$792$		0			0
$793$	36.3731	+	9.00000i	1.29165	+	0.319599i
$794$	12.1244			0.430277
$795$		0			0
$796$	−2.53590	−	4.39230i	−0.0898825	−	0.155681i
$797$	−5.07180	+	8.78461i	−0.179652	+	0.311167i	−0.941761	−	0.336282i	$-0.890831\pi$
$797$	−5.07180	+	8.78461i	−0.179652	+	0.311167i	0.762109	+	0.647449i	$0.224164\pi$
$798$		0			0
$799$	12.2487	+	7.07180i	0.433328	+	0.250182i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$		0			0
$802$	16.0000	−	27.7128i	0.564980	−	0.978573i
$803$	6.46410	+	11.1962i	0.228113	+	0.395104i
$804$		0			0
$805$	7.46410			0.263075
$806$	−4.33013	+	4.50000i	−0.152522	+	0.158506i
$807$		0			0
$808$	2.53590	−	1.46410i	0.0892126	−	0.0515069i
$809$	−21.3923	−	37.0526i	−0.752113	−	1.30270i	−0.946797	−	0.321832i	$-0.895701\pi$
$809$	−21.3923	−	37.0526i	−0.752113	−	1.30270i	0.194683	−	0.980866i	$-0.437632\pi$
$810$		0			0
$811$		−	40.7846i		−	1.43214i	−0.698028	−	0.716071i	$-0.745939\pi$
$811$		−	40.7846i		−	1.43214i	0.698028	−	0.716071i	$-0.254061\pi$
$812$	−0.464102	−	0.267949i	−0.0162868	−	0.00940317i
$813$		0			0
$814$			59.4449i			2.08354i
$815$	−7.52628	+	13.0359i	−0.263634	+	0.456628i
$816$		0			0
$817$	−77.1051	+	44.5167i	−2.69757	+	1.55744i
$818$	4.00000			0.139857
$819$		0			0
$820$	−2.00000			−0.0698430
$821$	−12.6506	+	7.30385i	−0.441510	+	0.254906i	−0.704238	−	0.709964i	$-0.748711\pi$
$821$	−12.6506	+	7.30385i	−0.441510	+	0.254906i	0.262728	+	0.964870i	$0.415378\pi$
$822$		0			0
$823$	−19.5885	+	33.9282i	−0.682811	+	1.18266i	0.291309	+	0.956629i	$0.405909\pi$
$823$	−19.5885	+	33.9282i	−0.682811	+	1.18266i	−0.974119	+	0.226034i	$0.927424\pi$
$824$			11.8564i			0.413037i
$825$		0			0
$826$	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	$0.902631\pi$
$828$		0			0
$829$	−8.26795	−	14.3205i	−0.287158	−	0.497372i	0.685972	−	0.727628i	$-0.259377\pi$
$829$	−8.26795	−	14.3205i	−0.287158	−	0.497372i	−0.973130	+	0.230256i	$0.926044\pi$
$830$	−7.73205	+	4.46410i	−0.268383	+	0.154951i
$831$		0			0
$832$	−1.00000	−	3.46410i	−0.0346688	−	0.120096i
$833$	12.0000			0.415775
$834$		0			0
$835$	−8.16025	−	14.1340i	−0.282397	−	0.489126i
$836$	−24.1244	+	41.7846i	−0.834358	+	1.44515i
$837$		0			0
$838$	19.3923	+	11.1962i	0.669896	+	0.386765i
$839$	37.7321	+	21.7846i	1.30266	+	0.752088i	0.980859	−	0.194721i	$-0.0623800\pi$
$839$	37.7321	+	21.7846i	1.30266	+	0.752088i	0.321796	+	0.946809i	$0.395713\pi$
$840$		0			0
$841$	14.4641	−	25.0526i	0.498762	−	0.863881i
$842$	−2.19615	−	3.80385i	−0.0756844	−	0.131089i
$843$		0			0
$844$	11.3205			0.389668
$845$	−6.92820	−	11.0000i	−0.238337	−	0.378412i
$846$		0			0
$847$	−53.3205	+	30.7846i	−1.83211	+	1.05777i
$848$	0.464102	+	0.803848i	0.0159373	+	0.0276042i
$849$		0			0
$850$		−	4.00000i		−	0.137199i
$851$	29.7224	+	17.1603i	1.01887	+	0.588246i
$852$		0			0
$853$		−	43.8372i		−	1.50096i	−0.660895	−	0.750478i	$-0.729823\pi$
$853$		−	43.8372i		−	1.50096i	0.660895	−	0.750478i	$-0.270177\pi$
$854$	−10.3923	+	18.0000i	−0.355617	+	0.615947i
$855$		0			0
$856$	−6.80385	+	3.92820i	−0.232551	+	0.134263i
$857$	−24.5167			−0.837473			−0.418737	−	0.908108i	$-0.637527\pi$
$857$	−24.5167			−0.837473			−0.418737	+	0.908108i	$0.637527\pi$
$858$		0			0
$859$	−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
$861$		0			0
$862$	−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			0
$865$	9.46410	+	5.46410i	0.321789	+	0.185785i
$866$			19.3205i			0.656538i
$867$		0			0
$868$	−1.73205	−	3.00000i	−0.0587896	−	0.101827i
$869$	77.9711	−	45.0167i	2.64499	−	1.52709i
$870$		0			0
$871$	−29.7846	−	28.6603i	−1.00921	−	0.971116i
$872$	15.8564			0.536966
$873$		0			0
$874$	13.9282	+	24.1244i	0.471129	+	0.816019i
$875$	−1.00000	+	1.73205i	−0.0338062	+	0.0585540i
$876$		0			0
$877$	−3.35641	−	1.93782i	−0.113338	−	0.0654356i	0.442260	−	0.896887i	$-0.354177\pi$
$877$	−3.35641	−	1.93782i	−0.113338	−	0.0654356i	−0.555597	+	0.831452i	$0.687510\pi$
$878$	15.4641	+	8.92820i	0.521888	+	0.301312i
$879$		0			0
$880$	−3.23205	+	5.59808i	−0.108952	+	0.188711i
$881$	−7.00000	−	12.1244i	−0.235836	−	0.408480i	0.723679	−	0.690136i	$-0.242449\pi$
$881$	−7.00000	−	12.1244i	−0.235836	−	0.408480i	−0.959515	+	0.281656i	$0.909116\pi$
$882$		0			0
$883$	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
$885$		0			0
$886$	−14.1962	+	8.19615i	−0.476929	+	0.275355i
$887$	7.06218	+	12.2321i	0.237125	+	0.410712i	0.959888	−	0.280384i	$-0.0904617\pi$
$887$	7.06218	+	12.2321i	0.237125	+	0.410712i	−0.722763	+	0.691096i	$0.757128\pi$
$888$		0			0
$889$		−	9.85641i		−	0.330573i
$890$	0.464102	+	0.267949i	0.0155567	+	0.00898168i
$891$		0			0
$892$			20.5359i			0.687593i
$893$	13.1962	−	22.8564i	0.441592	−	0.764860i
$894$		0			0
$895$	17.0885	−	9.86603i	0.571204	−	0.329785i
$896$	2.00000			0.0668153
$897$		0			0
$898$	15.7128			0.524343
$899$	−0.401924	+	0.232051i	−0.0134049	+	0.00773933i
$900$		0			0
$901$	1.85641	−	3.21539i	0.0618459	−	0.107120i
$902$		−	12.9282i		−	0.430462i
$903$		0			0
$904$	−0.696152	−	0.401924i	−0.0231537	−	0.0133678i
$905$		−	2.92820i		−	0.0973368i
$906$		0			0
$907$	10.4282	+	18.0622i	0.346263	+	0.599745i	0.985582	−	0.169196i	$-0.0541172\pi$
$907$	10.4282	+	18.0622i	0.346263	+	0.599745i	−0.639320	+	0.768941i	$0.720784\pi$
$908$	14.1962	−	8.19615i	0.471116	−	0.271999i
$909$		0			0
$910$	6.92820	−	2.00000i	0.229668	−	0.0662994i
$911$	−24.2487			−0.803396			−0.401698	−	0.915772i	$-0.631580\pi$
$911$	−24.2487			−0.803396			−0.401698	+	0.915772i	$0.631580\pi$
$912$		0			0
$913$	−28.8564	−	49.9808i	−0.955008	−	1.65412i
$914$	12.2679	−	21.2487i	0.405788	−	0.702845i
$915$		0			0
$916$	6.80385	+	3.92820i	0.224805	+	0.129791i
$917$	−32.3205	−	18.6603i	−1.06732	−	0.616216i
$918$		0			0
$919$	−7.32051	+	12.6795i	−0.241481	+	0.418258i	−0.961136	−	0.276074i	$-0.910967\pi$
$919$	−7.32051	+	12.6795i	−0.241481	+	0.418258i	0.719655	+	0.694332i	$0.244300\pi$
$920$	1.86603	+	3.23205i	0.0615210	+	0.106558i
$921$		0			0
$922$	−0.464102			−0.0152844
$923$	−10.7321	+	43.3731i	−0.353250	+	1.42764i
$924$		0			0
$925$	−7.96410	+	4.59808i	−0.261858	+	0.151184i
$926$	−3.53590	−	6.12436i	−0.116197	−	0.201259i
$927$		0			0
$928$		−	0.267949i		−	0.00879586i
$929$	5.32051	+	3.07180i	0.174560	+	0.100782i	0.584734	−	0.811225i	$-0.301199\pi$
$929$	5.32051	+	3.07180i	0.174560	+	0.100782i	−0.410174	+	0.912007i	$0.634532\pi$
$930$		0			0
$931$		−	22.3923i		−	0.733878i
$932$	−3.06218	+	5.30385i	−0.100305	+	0.173733i
$933$		0			0
$934$	13.7321	−	7.92820i	0.449326	−	0.259419i
$935$	25.8564			0.845595
$936$		0			0
$937$	−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
$939$		0			0
$940$	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	$-0.0774696\pi$
$942$		0			0
$943$	−6.46410	−	3.73205i	−0.210500	−	0.121532i
$944$			8.46410i			0.275483i
$945$		0			0
$946$	−38.5526	−	66.7750i	−1.25345	−	2.17104i
$947$	−8.19615	+	4.73205i	−0.266339	+	0.153771i	−0.627223	−	0.778840i	$-0.715808\pi$
$947$	−8.19615	+	4.73205i	−0.266339	+	0.153771i	0.360884	+	0.932611i	$0.382475\pi$
$948$		0			0
$949$	6.92820	−	2.00000i	0.224899	−	0.0649227i
$950$	−7.46410			−0.242167
$951$		0			0
$952$	−4.00000	−	6.92820i	−0.129641	−	0.224544i
$953$	−6.13397	+	10.6244i	−0.198699	+	0.344157i	−0.948107	−	0.317952i	$-0.897005\pi$
$953$	−6.13397	+	10.6244i	−0.198699	+	0.344157i	0.749408	+	0.662109i	$0.230338\pi$
$954$		0			0
$955$	18.5885	+	10.7321i	0.601508	+	0.347281i
$956$	−14.1962	−	8.19615i	−0.459136	−	0.265083i
$957$		0			0
$958$	−2.73205	+	4.73205i	−0.0882686	+	0.152886i
$959$	−2.46410	−	4.26795i	−0.0795700	−	0.137819i
$960$		0			0
$961$	28.0000			0.903226
$962$	32.1865	+	7.96410i	1.03774	+	0.256773i
$963$		0			0
$964$	15.3564	−	8.86603i	0.494597	−	0.285555i
$965$	5.66025	+	9.80385i	0.182210	+	0.315597i
$966$		0			0
$967$			41.4641i			1.33340i	0.745328	+	0.666698i	$0.232293\pi$
$967$			41.4641i			1.33340i	−0.745328	+	0.666698i	$0.767707\pi$
$968$	−26.6603	−	15.3923i	−0.856893	−	0.494727i
$969$		0			0
$970$			0.535898i			0.0172067i
$971$	2.26795	−	3.92820i	0.0727820	−	0.126062i	−0.827338	−	0.561705i	$-0.810146\pi$
$971$	2.26795	−	3.92820i	0.0727820	−	0.126062i	0.900120	+	0.435643i	$0.143479\pi$
$972$		0			0
$973$	−22.3923	+	12.9282i	−0.717864	+	0.414459i
$974$	23.1769			0.742636
$975$		0			0
$976$	−10.3923			−0.332650
$977$	−10.9186	+	6.30385i	−0.349316	+	0.201678i	−0.664384	−	0.747391i	$-0.731306\pi$
$977$	−10.9186	+	6.30385i	−0.349316	+	0.201678i	0.315068	+	0.949069i	$0.397973\pi$
$978$		0			0
$979$	−1.73205	+	3.00000i	−0.0553566	+	0.0958804i
$980$		−	3.00000i		−	0.0958315i
$981$		0			0
$982$	−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	$-0.198436\pi$
$984$		0			0
$985$	−2.19615	−	3.80385i	−0.0699752	−	0.121201i
$986$	−0.928203	+	0.535898i	−0.0295600	+	0.0170665i
$987$		0			0
$988$	19.3923	+	18.6603i	0.616951	+	0.593662i
$989$	−44.5167			−1.41555
$990$		0			0
$991$	26.4282	+	45.7750i	0.839520	+	1.45409i	0.890297	+	0.455381i	$0.150497\pi$
$991$	26.4282	+	45.7750i	0.839520	+	1.45409i	−0.0507774	+	0.998710i	$0.516170\pi$
$992$	0.866025	−	1.50000i	0.0274963	−	0.0476250i
$993$		0			0
$994$	−21.4641	−	12.3923i	−0.680800	−	0.393060i
$995$	4.39230	+	2.53590i	0.139245	+	0.0803934i
$996$		0			0
$997$	−17.7846	+	30.8038i	−0.563244	+	0.975568i	0.433966	+	0.900929i	$0.357114\pi$
$997$	−17.7846	+	30.8038i	−0.563244	+	0.975568i	−0.997211	+	0.0746386i	$0.976220\pi$
$998$	−3.26795	−	5.66025i	−0.103445	−	0.179172i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bs.e.361.2		4
3.2	odd	2		390.2.bb.b.361.1	yes	4
13.4	even	6	inner	1170.2.bs.e.901.2		4
15.2	even	4		1950.2.y.c.49.2		4
15.8	even	4		1950.2.y.f.49.1		4
15.14	odd	2		1950.2.bc.b.751.2		4
39.2	even	12		5070.2.a.y.1.1		2
39.11	even	12		5070.2.a.bg.1.2		2
39.17	odd	6		390.2.bb.b.121.1	✓	4
39.23	odd	6		5070.2.b.o.1351.3		4
39.29	odd	6		5070.2.b.o.1351.2		4
195.17	even	12		1950.2.y.f.199.1		4
195.134	odd	6		1950.2.bc.b.901.2		4
195.173	even	12		1950.2.y.c.199.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.b.121.1	✓	4	39.17	odd	6
390.2.bb.b.361.1	yes	4	3.2	odd	2
1170.2.bs.e.361.2		4	1.1	even	1	trivial
1170.2.bs.e.901.2		4	13.4	even	6	inner
1950.2.y.c.49.2		4	15.2	even	4
1950.2.y.c.199.2		4	195.173	even	12
1950.2.y.f.49.1		4	15.8	even	4
1950.2.y.f.199.1		4	195.17	even	12
1950.2.bc.b.751.2		4	15.14	odd	2
1950.2.bc.b.901.2		4	195.134	odd	6
5070.2.a.y.1.1		2	39.2	even	12
5070.2.a.bg.1.2		2	39.11	even	12
5070.2.b.o.1351.2		4	39.29	odd	6
5070.2.b.o.1351.3		4	39.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-1.73205 - 1.00000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-1.73205 - 1.00000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{10} +(-5.59808 + 3.23205i) q^{11} +(1.00000 + 3.46410i) q^{13} -2.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(6.46410 + 3.73205i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-3.23205 + 5.59808i) q^{22} +(1.86603 + 3.23205i) q^{23} -1.00000 q^{25} +(2.59808 + 2.50000i) q^{26} +(-1.73205 + 1.00000i) q^{28} +(0.133975 + 0.232051i) q^{29} +1.73205i q^{31} +(-0.866025 - 0.500000i) q^{32} +4.00000i q^{34} +(1.00000 - 1.73205i) q^{35} +(7.96410 - 4.59808i) q^{37} +7.46410 q^{38} +1.00000 q^{40} +(-1.73205 + 1.00000i) q^{41} +(-5.96410 + 10.3301i) q^{43} +6.46410i q^{44} +(3.23205 + 1.86603i) q^{46} -3.53590i q^{47} +(-1.50000 - 2.59808i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(3.50000 + 0.866025i) q^{52} -0.928203 q^{53} +(-3.23205 - 5.59808i) q^{55} +(-1.00000 + 1.73205i) q^{56} +(0.232051 + 0.133975i) q^{58} +(-7.33013 - 4.23205i) q^{59} +(5.19615 - 9.00000i) q^{61} +(0.866025 + 1.50000i) q^{62} -1.00000 q^{64} +(-3.46410 + 1.00000i) q^{65} +(-9.92820 + 5.73205i) q^{67} +(2.00000 + 3.46410i) q^{68} -2.00000i q^{70} +(10.7321 + 6.19615i) q^{71} -2.00000i q^{73} +(4.59808 - 7.96410i) q^{74} +(6.46410 - 3.73205i) q^{76} +12.9282 q^{77} -13.9282 q^{79} +(0.866025 - 0.500000i) q^{80} +(-1.00000 + 1.73205i) q^{82} +8.92820i q^{83} +(-3.46410 - 2.00000i) q^{85} +11.9282i q^{86} +(3.23205 + 5.59808i) q^{88} +(0.464102 - 0.267949i) q^{89} +(1.73205 - 7.00000i) q^{91} +3.73205 q^{92} +(-1.76795 - 3.06218i) q^{94} +(-3.73205 + 6.46410i) q^{95} +(0.464102 + 0.267949i) q^{97} +(-2.59808 - 1.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4}+O(q^{10}) \) 4 * q + 2 * q^4	\( 4 q + 2 q^{4} + 2 q^{10} - 12 q^{11} + 4 q^{13} - 8 q^{14} - 2 q^{16} - 8 q^{17} + 12 q^{19} - 6 q^{22} + 4 q^{23} - 4 q^{25} + 4 q^{29} + 4 q^{35} + 18 q^{37} + 16 q^{38} + 4 q^{40} - 10 q^{43} + 6 q^{46} - 6 q^{49} + 14 q^{52} + 24 q^{53} - 6 q^{55} - 4 q^{56} - 6 q^{58} - 12 q^{59} - 4 q^{64} - 12 q^{67} + 8 q^{68} + 36 q^{71} + 8 q^{74} + 12 q^{76} + 24 q^{77} - 28 q^{79} - 4 q^{82} + 6 q^{88} - 12 q^{89} + 8 q^{92} - 14 q^{94} - 8 q^{95} - 12 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 + 2 * q^10 - 12 * q^11 + 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^29 + 4 * q^35 + 18 * q^37 + 16 * q^38 + 4 * q^40 - 10 * q^43 + 6 * q^46 - 6 * q^49 + 14 * q^52 + 24 * q^53 - 6 * q^55 - 4 * q^56 - 6 * q^58 - 12 * q^59 - 4 * q^64 - 12 * q^67 + 8 * q^68 + 36 * q^71 + 8 * q^74 + 12 * q^76 + 24 * q^77 - 28 * q^79 - 4 * q^82 + 6 * q^88 - 12 * q^89 + 8 * q^92 - 14 * q^94 - 8 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more