LMFDB - Embedded newform 1134.2.h.c.541.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(109,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("1134.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.h (of order $3$, degree $2$, not 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:	$9.05503558921$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.541
Dual form			1134.2.h.c.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(2.00000 + 3.46410i) q^{13} +(-0.500000 + 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{19} -3.00000 q^{23} -5.00000 q^{25} +(2.00000 - 3.46410i) q^{26} +(2.50000 - 0.866025i) q^{28} +(3.00000 - 5.19615i) q^{29} +(-2.50000 + 4.33013i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{34} +(-4.00000 + 6.92820i) q^{37} +2.00000 q^{38} +(-1.50000 - 2.59808i) q^{41} +(-1.00000 + 1.73205i) q^{43} +(1.50000 + 2.59808i) q^{46} +(1.50000 + 2.59808i) q^{47} +(1.00000 + 6.92820i) q^{49} +(2.50000 + 4.33013i) q^{50} -4.00000 q^{52} +(-3.00000 - 5.19615i) q^{53} +(-2.00000 - 1.73205i) q^{56} -6.00000 q^{58} +(-6.00000 + 10.3923i) q^{59} +(-4.00000 - 6.92820i) q^{61} +5.00000 q^{62} +1.00000 q^{64} +(-4.00000 + 6.92820i) q^{67} +6.00000 q^{68} -15.0000 q^{71} +(-5.50000 - 9.52628i) q^{73} +8.00000 q^{74} +(-1.00000 - 1.73205i) q^{76} +(0.500000 + 0.866025i) q^{79} +(-1.50000 + 2.59808i) q^{82} +2.00000 q^{86} +(-4.50000 + 7.79423i) q^{89} +(2.00000 - 10.3923i) q^{91} +(1.50000 - 2.59808i) q^{92} +(1.50000 - 2.59808i) q^{94} +(-1.00000 + 1.73205i) q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - 4 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 - 4 * q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} - 4 q^{7} + 2 q^{8} + 4 q^{13} - q^{14} - q^{16} - 6 q^{17} - 2 q^{19} - 6 q^{23} - 10 q^{25} + 4 q^{26} + 5 q^{28} + 6 q^{29} - 5 q^{31} - q^{32} - 6 q^{34} - 8 q^{37} + 4 q^{38} - 3 q^{41} - 2 q^{43} + 3 q^{46} + 3 q^{47} + 2 q^{49} + 5 q^{50} - 8 q^{52} - 6 q^{53} - 4 q^{56} - 12 q^{58} - 12 q^{59} - 8 q^{61} + 10 q^{62} + 2 q^{64} - 8 q^{67} + 12 q^{68} - 30 q^{71} - 11 q^{73} + 16 q^{74} - 2 q^{76} + q^{79} - 3 q^{82} + 4 q^{86} - 9 q^{89} + 4 q^{91} + 3 q^{92} + 3 q^{94} - 2 q^{97} + 11 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 - 4 * q^7 + 2 * q^8 + 4 * q^13 - q^14 - q^16 - 6 * q^17 - 2 * q^19 - 6 * q^23 - 10 * q^25 + 4 * q^26 + 5 * q^28 + 6 * q^29 - 5 * q^31 - q^32 - 6 * q^34 - 8 * q^37 + 4 * q^38 - 3 * q^41 - 2 * q^43 + 3 * q^46 + 3 * q^47 + 2 * q^49 + 5 * q^50 - 8 * q^52 - 6 * q^53 - 4 * q^56 - 12 * q^58 - 12 * q^59 - 8 * q^61 + 10 * q^62 + 2 * q^64 - 8 * q^67 + 12 * q^68 - 30 * q^71 - 11 * q^73 + 16 * q^74 - 2 * q^76 + q^79 - 3 * q^82 + 4 * q^86 - 9 * q^89 + 4 * q^91 + 3 * q^92 + 3 * q^94 - 2 * q^97 + 11 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0			−	1.00000i	$-0.5\pi$
$5$		0			0				1.00000i	$0.5\pi$
$6$		0			0
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$	1.00000			0.353553
$9$		0			0
$10$		0			0
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$		0			0
$13$	2.00000	+	3.46410i	0.554700	+	0.960769i	0.997927	+	0.0643593i	$0.0205004\pi$
$13$	2.00000	+	3.46410i	0.554700	+	0.960769i	−0.443227	+	0.896410i	$0.646166\pi$
$14$	−0.500000	+	2.59808i	−0.133631	+	0.694365i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$		0			0
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.00000			−0.625543			−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000			−0.625543			−0.312772	+	0.949828i	$0.601257\pi$
$24$		0			0
$25$	−5.00000			−1.00000
$26$	2.00000	−	3.46410i	0.392232	−	0.679366i
$27$		0			0
$28$	2.50000	−	0.866025i	0.472456	−	0.163663i
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$		0			0
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	−0.998322	−	0.0579057i	$-0.981558\pi$
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	0.549309	+	0.835619i	$0.314891\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−3.00000	+	5.19615i	−0.514496	+	0.891133i
$35$		0			0
$36$		0			0
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	0.323640	+	0.946180i	$0.395093\pi$
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	−0.981236	+	0.192809i	$0.938240\pi$
$38$	2.00000			0.324443
$39$		0			0
$40$		0			0
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$		0			0
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	−0.932145	−	0.362084i	$-0.882065\pi$
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	0.779647	+	0.626219i	$0.215399\pi$
$44$		0			0
$45$		0			0
$46$	1.50000	+	2.59808i	0.221163	+	0.383065i
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	0.954441	−	0.298401i	$-0.0964533\pi$
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	−0.735643	+	0.677369i	$0.763120\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	2.50000	+	4.33013i	0.353553	+	0.612372i
$51$		0			0
$52$	−4.00000			−0.554700
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$		0			0
$55$		0			0
$56$	−2.00000	−	1.73205i	−0.267261	−	0.231455i
$57$		0			0
$58$	−6.00000			−0.787839
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	0.150148	+	0.988663i	$0.452025\pi$
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	−0.931282	+	0.364299i	$0.881308\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$	5.00000			0.635001
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$	6.00000			0.727607
$69$		0			0
$70$		0			0
$71$	−15.0000			−1.78017			−0.890086	−	0.455792i	$-0.849356\pi$
$71$	−15.0000			−1.78017			−0.890086	+	0.455792i	$0.849356\pi$
$72$		0			0
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	−0.984594	−	0.174855i	$-0.944054\pi$
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	0.340868	−	0.940111i	$-0.389279\pi$
$74$	8.00000			0.929981
$75$		0			0
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$		0			0
$78$		0			0
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$		0			0
$81$		0			0
$82$	−1.50000	+	2.59808i	−0.165647	+	0.286910i
$83$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$83$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$84$		0			0
$85$		0			0
$86$	2.00000			0.215666
$87$		0			0
$88$		0			0
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	−0.999653	−	0.0263586i	$-0.991609\pi$
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	0.522654	+	0.852545i	$0.324942\pi$
$90$		0			0
$91$	2.00000	−	10.3923i	0.209657	−	1.08941i
$92$	1.50000	−	2.59808i	0.156386	−	0.270868i
$93$		0			0
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$		0			0
$96$		0			0
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$	5.50000	−	4.33013i	0.555584	−	0.437409i
$99$		0			0
$100$	2.50000	−	4.33013i	0.250000	−	0.433013i
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$		0			0
$103$	−1.00000			−0.0985329			−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000			−0.0985329			−0.0492665	+	0.998786i	$0.515688\pi$
$104$	2.00000	+	3.46410i	0.196116	+	0.339683i
$105$		0			0
$106$	−3.00000	+	5.19615i	−0.291386	+	0.504695i
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	−0.973814	−	0.227345i	$-0.926996\pi$
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	0.683793	+	0.729676i	$0.260329\pi$
$108$		0			0
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	0.939577	+	0.342337i	$0.111218\pi$
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	−0.173316	+	0.984866i	$0.555448\pi$
$110$		0			0
$111$		0			0
$112$	−0.500000	+	2.59808i	−0.0472456	+	0.245495i
$113$	−9.00000	−	15.5885i	−0.846649	−	1.46644i	−0.884182	−	0.467143i	$-0.845283\pi$
$113$	−9.00000	−	15.5885i	−0.846649	−	1.46644i	0.0375328	−	0.999295i	$-0.488050\pi$
$114$		0			0
$115$		0			0
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$		0			0
$118$	12.0000			1.10469
$119$	−3.00000	+	15.5885i	−0.275010	+	1.42899i
$120$		0			0
$121$	−11.0000			−1.00000
$122$	−4.00000	+	6.92820i	−0.362143	+	0.627250i
$123$		0			0
$124$	−2.50000	−	4.33013i	−0.224507	−	0.388857i
$125$		0			0
$126$		0			0
$127$	−7.00000			−0.621150			−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000			−0.621150			−0.310575	+	0.950549i	$0.600522\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$	5.00000	−	1.73205i	0.433555	−	0.150188i
$134$	8.00000			0.691095
$135$		0			0
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	3.00000			0.256307			0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000			0.256307			0.128154	+	0.991754i	$0.459095\pi$
$138$		0			0
$139$	8.00000	+	13.8564i	0.678551	+	1.17529i	0.975417	+	0.220366i	$0.0707252\pi$
$139$	8.00000	+	13.8564i	0.678551	+	1.17529i	−0.296866	+	0.954919i	$0.595942\pi$
$140$		0			0
$141$		0			0
$142$	7.50000	+	12.9904i	0.629386	+	1.09013i
$143$		0			0
$144$		0			0
$145$		0			0
$146$	−5.50000	+	9.52628i	−0.455183	+	0.788400i
$147$		0			0
$148$	−4.00000	−	6.92820i	−0.328798	−	0.569495i
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$		0			0
$151$	17.0000			1.38344			0.691720	−	0.722166i	$-0.256853\pi$
$151$	17.0000			1.38344			0.691720	+	0.722166i	$0.256853\pi$
$152$	−1.00000	+	1.73205i	−0.0811107	+	0.140488i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	11.0000	−	19.0526i	0.877896	−	1.52056i	0.0242497	−	0.999706i	$-0.492280\pi$
$157$	11.0000	−	19.0526i	0.877896	−	1.52056i	0.853646	−	0.520854i	$-0.174386\pi$
$158$	0.500000	−	0.866025i	0.0397779	−	0.0688973i
$159$		0			0
$160$		0			0
$161$	6.00000	+	5.19615i	0.472866	+	0.409514i
$162$		0			0
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	−0.979076	−	0.203497i	$-0.934769\pi$
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	0.665771	+	0.746156i	$0.268103\pi$
$164$	3.00000			0.234261
$165$		0			0
$166$		0			0
$167$	−10.5000	−	18.1865i	−0.812514	−	1.40732i	−0.911099	−	0.412188i	$-0.864765\pi$
$167$	−10.5000	−	18.1865i	−0.812514	−	1.40732i	0.0985846	−	0.995129i	$-0.468568\pi$
$168$		0			0
$169$	−1.50000	+	2.59808i	−0.115385	+	0.199852i
$170$		0			0
$171$		0			0
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	0.973670	+	0.227964i	$0.0732068\pi$
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	−0.289412	+	0.957205i	$0.593460\pi$
$174$		0			0
$175$	10.0000	+	8.66025i	0.755929	+	0.654654i
$176$		0			0
$177$		0			0
$178$	9.00000			0.674579
$179$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$179$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−10.0000	+	3.46410i	−0.741249	+	0.256776i
$183$		0			0
$184$	−3.00000			−0.221163
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−3.00000			−0.218797
$189$		0			0
$190$		0			0
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.863743	−	0.503932i	$-0.831886\pi$
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.00454614	−	0.999990i	$-0.501447\pi$
$192$		0			0
$193$	9.50000	−	16.4545i	0.683825	−	1.18442i	−0.289980	−	0.957033i	$-0.593649\pi$
$193$	9.50000	−	16.4545i	0.683825	−	1.18442i	0.973805	−	0.227387i	$-0.0730182\pi$
$194$	2.00000			0.143592
$195$		0			0
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$	−11.5000	−	19.9186i	−0.815213	−	1.41199i	−0.909175	−	0.416415i	$-0.863286\pi$
$199$	−11.5000	−	19.9186i	−0.815213	−	1.41199i	0.0939612	−	0.995576i	$-0.470047\pi$
$200$	−5.00000			−0.353553
$201$		0			0
$202$	−3.00000	−	5.19615i	−0.211079	−	0.365600i
$203$	−15.0000	+	5.19615i	−1.05279	+	0.364698i
$204$		0			0
$205$		0			0
$206$	0.500000	+	0.866025i	0.0348367	+	0.0603388i
$207$		0			0
$208$	2.00000	−	3.46410i	0.138675	−	0.240192i
$209$		0			0
$210$		0			0
$211$	−13.0000	−	22.5167i	−0.894957	−	1.55011i	−0.833858	−	0.551979i	$-0.813873\pi$
$211$	−13.0000	−	22.5167i	−0.894957	−	1.55011i	−0.0610990	−	0.998132i	$-0.519461\pi$
$212$	6.00000			0.412082
$213$		0			0
$214$	6.00000			0.410152
$215$		0			0
$216$		0			0
$217$	12.5000	−	4.33013i	0.848555	−	0.293948i
$218$	8.00000	−	13.8564i	0.541828	−	0.938474i
$219$		0			0
$220$		0			0
$221$	12.0000	−	20.7846i	0.807207	−	1.39812i
$222$		0			0
$223$	9.50000	−	16.4545i	0.636167	−	1.10187i	−0.350100	−	0.936713i	$-0.613852\pi$
$223$	9.50000	−	16.4545i	0.636167	−	1.10187i	0.986267	−	0.165161i	$-0.0528144\pi$
$224$	2.50000	−	0.866025i	0.167038	−	0.0578638i
$225$		0			0
$226$	−9.00000	+	15.5885i	−0.598671	+	1.03693i
$227$	−18.0000			−1.19470			−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000			−1.19470			−0.597351	+	0.801980i	$0.703780\pi$
$228$		0			0
$229$	8.00000			0.528655			0.264327	−	0.964433i	$-0.414850\pi$
$229$	8.00000			0.528655			0.264327	+	0.964433i	$0.414850\pi$
$230$		0			0
$231$		0			0
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$	−9.00000	+	15.5885i	−0.589610	+	1.02123i	0.404674	+	0.914461i	$0.367385\pi$
$233$	−9.00000	+	15.5885i	−0.589610	+	1.02123i	−0.994283	+	0.106773i	$0.965948\pi$
$234$		0			0
$235$		0			0
$236$	−6.00000	−	10.3923i	−0.390567	−	0.676481i
$237$		0			0
$238$	15.0000	−	5.19615i	0.972306	−	0.336817i
$239$	10.5000	+	18.1865i	0.679189	+	1.17639i	0.975226	+	0.221213i	$0.0710015\pi$
$239$	10.5000	+	18.1865i	0.679189	+	1.17639i	−0.296037	+	0.955176i	$0.595665\pi$
$240$		0			0
$241$	5.00000			0.322078			0.161039	−	0.986948i	$-0.448515\pi$
$241$	5.00000			0.322078			0.161039	+	0.986948i	$0.448515\pi$
$242$	5.50000	+	9.52628i	0.353553	+	0.612372i
$243$		0			0
$244$	8.00000			0.512148
$245$		0			0
$246$		0			0
$247$	−8.00000			−0.509028
$248$	−2.50000	+	4.33013i	−0.158750	+	0.274963i
$249$		0			0
$250$		0			0
$251$	30.0000			1.89358			0.946792	−	0.321847i	$-0.104304\pi$
$251$	30.0000			1.89358			0.946792	+	0.321847i	$0.104304\pi$
$252$		0			0
$253$		0			0
$254$	3.50000	+	6.06218i	0.219610	+	0.380375i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	21.0000			1.30994			0.654972	−	0.755653i	$-0.272680\pi$
$257$	21.0000			1.30994			0.654972	+	0.755653i	$0.272680\pi$
$258$		0			0
$259$	20.0000	−	6.92820i	1.24274	−	0.430498i
$260$		0			0
$261$		0			0
$262$	−6.00000	−	10.3923i	−0.370681	−	0.642039i
$263$	−24.0000			−1.47990			−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000			−1.47990			−0.739952	+	0.672660i	$0.765152\pi$
$264$		0			0
$265$		0			0
$266$	−4.00000	−	3.46410i	−0.245256	−	0.212398i
$267$		0			0
$268$	−4.00000	−	6.92820i	−0.244339	−	0.423207i
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	−0.998361	−	0.0572259i	$-0.981774\pi$
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$270$		0			0
$271$	−10.0000	+	17.3205i	−0.607457	+	1.05215i	0.384201	+	0.923249i	$0.374477\pi$
$271$	−10.0000	+	17.3205i	−0.607457	+	1.05215i	−0.991658	+	0.128897i	$0.958856\pi$
$272$	−3.00000	+	5.19615i	−0.181902	+	0.315063i
$273$		0			0
$274$	−1.50000	−	2.59808i	−0.0906183	−	0.156956i
$275$		0			0
$276$		0			0
$277$	−16.0000			−0.961347			−0.480673	−	0.876900i	$-0.659608\pi$
$277$	−16.0000			−0.961347			−0.480673	+	0.876900i	$0.659608\pi$
$278$	8.00000	−	13.8564i	0.479808	−	0.831052i
$279$		0			0
$280$		0			0
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	−0.817810	−	0.575488i	$-0.804812\pi$
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	0.907293	+	0.420500i	$0.138145\pi$
$282$		0			0
$283$	14.0000	−	24.2487i	0.832214	−	1.44144i	−0.0640654	−	0.997946i	$-0.520407\pi$
$283$	14.0000	−	24.2487i	0.832214	−	1.44144i	0.896279	−	0.443491i	$-0.146260\pi$
$284$	7.50000	−	12.9904i	0.445043	−	0.770837i
$285$		0			0
$286$		0			0
$287$	−1.50000	+	7.79423i	−0.0885422	+	0.460079i
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$		0			0
$292$	11.0000			0.643726
$293$	−9.00000	−	15.5885i	−0.525786	−	0.910687i	−0.999549	−	0.0300351i	$-0.990438\pi$
$293$	−9.00000	−	15.5885i	−0.525786	−	0.910687i	0.473763	−	0.880652i	$-0.342895\pi$
$294$		0			0
$295$		0			0
$296$	−4.00000	+	6.92820i	−0.232495	+	0.402694i
$297$		0			0
$298$	−3.00000	−	5.19615i	−0.173785	−	0.301005i
$299$	−6.00000	−	10.3923i	−0.346989	−	0.601003i
$300$		0			0
$301$	5.00000	−	1.73205i	0.288195	−	0.0998337i
$302$	−8.50000	−	14.7224i	−0.489120	−	0.847181i
$303$		0			0
$304$	2.00000			0.114708
$305$		0			0
$306$		0			0
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	0.294384	+	0.955687i	$0.404886\pi$
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	−0.974841	+	0.222900i	$0.928448\pi$
$312$		0			0
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	0.999065	+	0.0432311i	$0.0137652\pi$
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	−0.462093	+	0.886831i	$0.652902\pi$
$314$	−22.0000			−1.24153
$315$		0			0
$316$	−1.00000			−0.0562544
$317$	−12.0000	−	20.7846i	−0.673987	−	1.16738i	−0.976764	−	0.214318i	$-0.931247\pi$
$317$	−12.0000	−	20.7846i	−0.673987	−	1.16738i	0.302777	−	0.953062i	$-0.402086\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$	1.50000	−	7.79423i	0.0835917	−	0.434355i
$323$	12.0000			0.667698
$324$		0			0
$325$	−10.0000	−	17.3205i	−0.554700	−	0.960769i
$326$	8.00000			0.443079
$327$		0			0
$328$	−1.50000	−	2.59808i	−0.0828236	−	0.143455i
$329$	1.50000	−	7.79423i	0.0826977	−	0.429710i
$330$		0			0
$331$	5.00000	+	8.66025i	0.274825	+	0.476011i	0.970091	−	0.242742i	$-0.0780468\pi$
$331$	5.00000	+	8.66025i	0.274825	+	0.476011i	−0.695266	+	0.718752i	$0.744713\pi$
$332$		0			0
$333$		0			0
$334$	−10.5000	+	18.1865i	−0.574534	+	0.995123i
$335$		0			0
$336$		0			0
$337$	−7.00000	−	12.1244i	−0.381314	−	0.660456i	0.609936	−	0.792451i	$-0.291195\pi$
$337$	−7.00000	−	12.1244i	−0.381314	−	0.660456i	−0.991250	+	0.131995i	$0.957862\pi$
$338$	3.00000			0.163178
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−1.00000	+	1.73205i	−0.0539164	+	0.0933859i
$345$		0			0
$346$	9.00000	−	15.5885i	0.483843	−	0.838041i
$347$	−3.00000	+	5.19615i	−0.161048	+	0.278944i	−0.935245	−	0.354001i	$-0.884821\pi$
$347$	−3.00000	+	5.19615i	−0.161048	+	0.278944i	0.774197	+	0.632945i	$0.218154\pi$
$348$		0			0
$349$	2.00000	−	3.46410i	0.107058	−	0.185429i	−0.807519	−	0.589841i	$-0.799190\pi$
$349$	2.00000	−	3.46410i	0.107058	−	0.185429i	0.914577	+	0.404412i	$0.132524\pi$
$350$	2.50000	−	12.9904i	0.133631	−	0.694365i
$351$		0			0
$352$		0			0
$353$	33.0000			1.75641			0.878206	−	0.478282i	$-0.158740\pi$
$353$	33.0000			1.75641			0.878206	+	0.478282i	$0.158740\pi$
$354$		0			0
$355$		0			0
$356$	−4.50000	−	7.79423i	−0.238500	−	0.413093i
$357$		0			0
$358$		0			0
$359$	10.5000	−	18.1865i	0.554169	−	0.959849i	−0.443799	−	0.896126i	$-0.646370\pi$
$359$	10.5000	−	18.1865i	0.554169	−	0.959849i	0.997968	−	0.0637221i	$-0.0202971\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−1.00000	−	1.73205i	−0.0525588	−	0.0910346i
$363$		0			0
$364$	8.00000	+	6.92820i	0.419314	+	0.363137i
$365$		0			0
$366$		0			0
$367$	−1.00000			−0.0521996			−0.0260998	−	0.999659i	$-0.508309\pi$
$367$	−1.00000			−0.0521996			−0.0260998	+	0.999659i	$0.508309\pi$
$368$	1.50000	+	2.59808i	0.0781929	+	0.135434i
$369$		0			0
$370$		0			0
$371$	−3.00000	+	15.5885i	−0.155752	+	0.809312i
$372$		0			0
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$		0			0
$375$		0			0
$376$	1.50000	+	2.59808i	0.0773566	+	0.133986i
$377$	24.0000			1.23606
$378$		0			0
$379$	−10.0000			−0.513665			−0.256833	−	0.966456i	$-0.582679\pi$
$379$	−10.0000			−0.513665			−0.256833	+	0.966456i	$0.582679\pi$
$380$		0			0
$381$		0			0
$382$	−12.0000	+	20.7846i	−0.613973	+	1.06343i
$383$	−15.0000			−0.766464			−0.383232	−	0.923652i	$-0.625189\pi$
$383$	−15.0000			−0.766464			−0.383232	+	0.923652i	$0.625189\pi$
$384$		0			0
$385$		0			0
$386$	−19.0000			−0.967075
$387$		0			0
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	−24.0000			−1.21685			−0.608424	−	0.793612i	$-0.708198\pi$
$389$	−24.0000			−1.21685			−0.608424	+	0.793612i	$0.708198\pi$
$390$		0			0
$391$	9.00000	+	15.5885i	0.455150	+	0.788342i
$392$	1.00000	+	6.92820i	0.0505076	+	0.349927i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−1.00000	+	1.73205i	−0.0501886	+	0.0869291i	−0.890028	−	0.455905i	$-0.849316\pi$
$397$	−1.00000	+	1.73205i	−0.0501886	+	0.0869291i	0.839840	+	0.542834i	$0.182649\pi$
$398$	−11.5000	+	19.9186i	−0.576443	+	0.998428i
$399$		0			0
$400$	2.50000	+	4.33013i	0.125000	+	0.216506i
$401$	15.0000			0.749064			0.374532	−	0.927214i	$-0.377803\pi$
$401$	15.0000			0.749064			0.374532	+	0.927214i	$0.377803\pi$
$402$		0			0
$403$	−20.0000			−0.996271
$404$	−3.00000	+	5.19615i	−0.149256	+	0.258518i
$405$		0			0
$406$	12.0000	+	10.3923i	0.595550	+	0.515761i
$407$		0			0
$408$		0			0
$409$	3.50000	−	6.06218i	0.173064	−	0.299755i	−0.766426	−	0.642333i	$-0.777967\pi$
$409$	3.50000	−	6.06218i	0.173064	−	0.299755i	0.939490	+	0.342578i	$0.111300\pi$
$410$		0			0
$411$		0			0
$412$	0.500000	−	0.866025i	0.0246332	−	0.0426660i
$413$	30.0000	−	10.3923i	1.47620	−	0.511372i
$414$		0			0
$415$		0			0
$416$	−4.00000			−0.196116
$417$		0			0
$418$		0			0
$419$	18.0000	+	31.1769i	0.879358	+	1.52309i	0.852047	+	0.523465i	$0.175361\pi$
$419$	18.0000	+	31.1769i	0.879358	+	1.52309i	0.0273103	+	0.999627i	$0.491306\pi$
$420$		0			0
$421$	−4.00000	+	6.92820i	−0.194948	+	0.337660i	−0.946883	−	0.321577i	$-0.895787\pi$
$421$	−4.00000	+	6.92820i	−0.194948	+	0.337660i	0.751935	+	0.659237i	$0.229121\pi$
$422$	−13.0000	+	22.5167i	−0.632830	+	1.09609i
$423$		0			0
$424$	−3.00000	−	5.19615i	−0.145693	−	0.252347i
$425$	15.0000	+	25.9808i	0.727607	+	1.26025i
$426$		0			0
$427$	−4.00000	+	20.7846i	−0.193574	+	1.00584i
$428$	−3.00000	−	5.19615i	−0.145010	−	0.251166i
$429$		0			0
$430$		0			0
$431$	7.50000	+	12.9904i	0.361262	+	0.625725i	0.988169	−	0.153370i	$-0.0490126\pi$
$431$	7.50000	+	12.9904i	0.361262	+	0.625725i	−0.626907	+	0.779094i	$0.715679\pi$
$432$		0			0
$433$	41.0000			1.97033			0.985167	−	0.171598i	$-0.0548929\pi$
$433$	41.0000			1.97033			0.985167	+	0.171598i	$0.0548929\pi$
$434$	−10.0000	−	8.66025i	−0.480015	−	0.415705i
$435$		0			0
$436$	−16.0000			−0.766261
$437$	3.00000	−	5.19615i	0.143509	−	0.248566i
$438$		0			0
$439$	0.500000	+	0.866025i	0.0238637	+	0.0413331i	0.877711	−	0.479191i	$-0.159070\pi$
$439$	0.500000	+	0.866025i	0.0238637	+	0.0413331i	−0.853847	+	0.520524i	$0.825737\pi$
$440$		0			0
$441$		0			0
$442$	−24.0000			−1.14156
$443$	−3.00000	−	5.19615i	−0.142534	−	0.246877i	0.785916	−	0.618333i	$-0.212192\pi$
$443$	−3.00000	−	5.19615i	−0.142534	−	0.246877i	−0.928450	+	0.371457i	$0.878858\pi$
$444$		0			0
$445$		0			0
$446$	−19.0000			−0.899676
$447$		0			0
$448$	−2.00000	−	1.73205i	−0.0944911	−	0.0818317i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$		0			0
$452$	18.0000			0.846649
$453$		0			0
$454$	9.00000	+	15.5885i	0.422391	+	0.731603i
$455$		0			0
$456$		0			0
$457$	−1.00000	−	1.73205i	−0.0467780	−	0.0810219i	0.841688	−	0.539964i	$-0.181562\pi$
$457$	−1.00000	−	1.73205i	−0.0467780	−	0.0810219i	−0.888466	+	0.458942i	$0.848229\pi$
$458$	−4.00000	−	6.92820i	−0.186908	−	0.323734i
$459$		0			0
$460$		0			0
$461$	18.0000	−	31.1769i	0.838344	−	1.45205i	−0.0529352	−	0.998598i	$-0.516858\pi$
$461$	18.0000	−	31.1769i	0.838344	−	1.45205i	0.891279	−	0.453456i	$-0.149809\pi$
$462$		0			0
$463$	6.50000	+	11.2583i	0.302081	+	0.523219i	0.976607	−	0.215032i	$-0.0689855\pi$
$463$	6.50000	+	11.2583i	0.302081	+	0.523219i	−0.674526	+	0.738251i	$0.735652\pi$
$464$	−6.00000			−0.278543
$465$		0			0
$466$	18.0000			0.833834
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	−0.970799	−	0.239892i	$-0.922888\pi$
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	0.693153	+	0.720791i	$0.256221\pi$
$468$		0			0
$469$	20.0000	−	6.92820i	0.923514	−	0.319915i
$470$		0			0
$471$		0			0
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$		0			0
$474$		0			0
$475$	5.00000	−	8.66025i	0.229416	−	0.397360i
$476$	−12.0000	−	10.3923i	−0.550019	−	0.476331i
$477$		0			0
$478$	10.5000	−	18.1865i	0.480259	−	0.831833i
$479$	9.00000			0.411220			0.205610	−	0.978634i	$-0.434082\pi$
$479$	9.00000			0.411220			0.205610	+	0.978634i	$0.434082\pi$
$480$		0			0
$481$	−32.0000			−1.45907
$482$	−2.50000	−	4.33013i	−0.113872	−	0.197232i
$483$		0			0
$484$	5.50000	−	9.52628i	0.250000	−	0.433013i
$485$		0			0
$486$		0			0
$487$	3.50000	+	6.06218i	0.158600	+	0.274703i	0.934364	−	0.356320i	$-0.115969\pi$
$487$	3.50000	+	6.06218i	0.158600	+	0.274703i	−0.775764	+	0.631023i	$0.782635\pi$
$488$	−4.00000	−	6.92820i	−0.181071	−	0.313625i
$489$		0			0
$490$		0			0
$491$	3.00000	+	5.19615i	0.135388	+	0.234499i	0.925746	−	0.378147i	$-0.123439\pi$
$491$	3.00000	+	5.19615i	0.135388	+	0.234499i	−0.790358	+	0.612646i	$0.790105\pi$
$492$		0			0
$493$	−36.0000			−1.62136
$494$	4.00000	+	6.92820i	0.179969	+	0.311715i
$495$		0			0
$496$	5.00000			0.224507
$497$	30.0000	+	25.9808i	1.34568	+	1.16540i
$498$		0			0
$499$	−34.0000			−1.52205			−0.761025	−	0.648723i	$-0.775303\pi$
$499$	−34.0000			−1.52205			−0.761025	+	0.648723i	$0.775303\pi$
$500$		0			0
$501$		0			0
$502$	−15.0000	−	25.9808i	−0.669483	−	1.15958i
$503$	−15.0000			−0.668817			−0.334408	−	0.942428i	$-0.608537\pi$
$503$	−15.0000			−0.668817			−0.334408	+	0.942428i	$0.608537\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$	3.50000	−	6.06218i	0.155287	−	0.268966i
$509$	6.00000			0.265945			0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000			0.265945			0.132973	+	0.991120i	$0.457548\pi$
$510$		0			0
$511$	−5.50000	+	28.5788i	−0.243306	+	1.26425i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−10.5000	−	18.1865i	−0.463135	−	0.802174i
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−16.0000	−	13.8564i	−0.703000	−	0.608816i
$519$		0			0
$520$		0			0
$521$	−7.50000	−	12.9904i	−0.328581	−	0.569119i	0.653650	−	0.756797i	$-0.273237\pi$
$521$	−7.50000	−	12.9904i	−0.328581	−	0.569119i	−0.982231	+	0.187678i	$0.939904\pi$
$522$		0			0
$523$	20.0000	−	34.6410i	0.874539	−	1.51475i	0.0172859	−	0.999851i	$-0.494497\pi$
$523$	20.0000	−	34.6410i	0.874539	−	1.51475i	0.857253	−	0.514895i	$-0.172169\pi$
$524$	−6.00000	+	10.3923i	−0.262111	+	0.453990i
$525$		0			0
$526$	12.0000	+	20.7846i	0.523225	+	0.906252i
$527$	30.0000			1.30682
$528$		0			0
$529$	−14.0000			−0.608696
$530$		0			0
$531$		0			0
$532$	−1.00000	+	5.19615i	−0.0433555	+	0.225282i
$533$	6.00000	−	10.3923i	0.259889	−	0.450141i
$534$		0			0
$535$		0			0
$536$	−4.00000	+	6.92820i	−0.172774	+	0.299253i
$537$		0			0
$538$	−9.00000	+	15.5885i	−0.388018	+	0.672066i
$539$		0			0
$540$		0			0
$541$	−19.0000	+	32.9090i	−0.816874	+	1.41487i	0.0911008	+	0.995842i	$0.470961\pi$
$541$	−19.0000	+	32.9090i	−0.816874	+	1.41487i	−0.907975	+	0.419025i	$0.862372\pi$
$542$	20.0000			0.859074
$543$		0			0
$544$	6.00000			0.257248
$545$		0			0
$546$		0			0
$547$	−13.0000	+	22.5167i	−0.555840	+	0.962743i	0.441998	+	0.897016i	$0.354270\pi$
$547$	−13.0000	+	22.5167i	−0.555840	+	0.962743i	−0.997838	+	0.0657267i	$0.979063\pi$
$548$	−1.50000	+	2.59808i	−0.0640768	+	0.110984i
$549$		0			0
$550$		0			0
$551$	6.00000	+	10.3923i	0.255609	+	0.442727i
$552$		0			0
$553$	0.500000	−	2.59808i	0.0212622	−	0.110481i
$554$	8.00000	+	13.8564i	0.339887	+	0.588702i
$555$		0			0
$556$	−16.0000			−0.678551
$557$	−6.00000	−	10.3923i	−0.254228	−	0.440336i	0.710457	−	0.703740i	$-0.248488\pi$
$557$	−6.00000	−	10.3923i	−0.254228	−	0.440336i	−0.964686	+	0.263404i	$0.915155\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$		0			0
$561$		0			0
$562$	−3.00000			−0.126547
$563$	−21.0000	+	36.3731i	−0.885044	+	1.53294i	−0.0393818	+	0.999224i	$0.512539\pi$
$563$	−21.0000	+	36.3731i	−0.885044	+	1.53294i	−0.845663	+	0.533718i	$0.820794\pi$
$564$		0			0
$565$		0			0
$566$	−28.0000			−1.17693
$567$		0			0
$568$	−15.0000			−0.629386
$569$	10.5000	+	18.1865i	0.440183	+	0.762419i	0.997703	−	0.0677445i	$-0.0215803\pi$
$569$	10.5000	+	18.1865i	0.440183	+	0.762419i	−0.557520	+	0.830164i	$0.688247\pi$
$570$		0			0
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$		0			0
$573$		0			0
$574$	7.50000	−	2.59808i	0.313044	−	0.108442i
$575$	15.0000			0.625543
$576$		0			0
$577$	−7.00000	−	12.1244i	−0.291414	−	0.504744i	0.682730	−	0.730670i	$-0.260792\pi$
$577$	−7.00000	−	12.1244i	−0.291414	−	0.504744i	−0.974144	+	0.225927i	$0.927459\pi$
$578$	19.0000			0.790296
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−5.50000	−	9.52628i	−0.227592	−	0.394200i
$585$		0			0
$586$	−9.00000	+	15.5885i	−0.371787	+	0.643953i
$587$	3.00000	−	5.19615i	0.123823	−	0.214468i	−0.797449	−	0.603386i	$-0.793818\pi$
$587$	3.00000	−	5.19615i	0.123823	−	0.214468i	0.921272	+	0.388918i	$0.127151\pi$
$588$		0			0
$589$	−5.00000	−	8.66025i	−0.206021	−	0.356840i
$590$		0			0
$591$		0			0
$592$	8.00000			0.328798
$593$	−4.50000	+	7.79423i	−0.184793	+	0.320071i	−0.943507	−	0.331353i	$-0.892495\pi$
$593$	−4.50000	+	7.79423i	−0.184793	+	0.320071i	0.758714	+	0.651424i	$0.225828\pi$
$594$		0			0
$595$		0			0
$596$	−3.00000	+	5.19615i	−0.122885	+	0.212843i
$597$		0			0
$598$	−6.00000	+	10.3923i	−0.245358	+	0.424973i
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	−0.999938	−	0.0111569i	$-0.996449\pi$
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	0.509631	+	0.860393i	$0.329782\pi$
$600$		0			0
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	−0.855648	−	0.517559i	$-0.826841\pi$
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	0.876043	+	0.482233i	$0.160174\pi$
$602$	−4.00000	−	3.46410i	−0.163028	−	0.141186i
$603$		0			0
$604$	−8.50000	+	14.7224i	−0.345860	+	0.599047i
$605$		0			0
$606$		0			0
$607$	−40.0000			−1.62355			−0.811775	−	0.583970i	$-0.801498\pi$
$607$	−40.0000			−1.62355			−0.811775	+	0.583970i	$0.801498\pi$
$608$	−1.00000	−	1.73205i	−0.0405554	−	0.0702439i
$609$		0			0
$610$		0			0
$611$	−6.00000	+	10.3923i	−0.242734	+	0.420428i
$612$		0			0
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$	−4.00000	−	6.92820i	−0.161427	−	0.279600i
$615$		0			0
$616$		0			0
$617$	13.5000	+	23.3827i	0.543490	+	0.941351i	0.998700	+	0.0509678i	$0.0162306\pi$
$617$	13.5000	+	23.3827i	0.543490	+	0.941351i	−0.455211	+	0.890384i	$0.650436\pi$
$618$		0			0
$619$	2.00000			0.0803868			0.0401934	−	0.999192i	$-0.487203\pi$
$619$	2.00000			0.0803868			0.0401934	+	0.999192i	$0.487203\pi$
$620$		0			0
$621$		0			0
$622$	24.0000			0.962312
$623$	22.5000	−	7.79423i	0.901443	−	0.312269i
$624$		0			0
$625$	25.0000			1.00000
$626$	9.50000	−	16.4545i	0.379696	−	0.657653i
$627$		0			0
$628$	11.0000	+	19.0526i	0.438948	+	0.760280i
$629$	48.0000			1.91389
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	0.500000	+	0.866025i	0.0198889	+	0.0344486i
$633$		0			0
$634$	−12.0000	+	20.7846i	−0.476581	+	0.825462i
$635$		0			0
$636$		0			0
$637$	−22.0000	+	17.3205i	−0.871672	+	0.686264i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	15.0000			0.592464			0.296232	−	0.955116i	$-0.404270\pi$
$641$	15.0000			0.592464			0.296232	+	0.955116i	$0.404270\pi$
$642$		0			0
$643$	17.0000	+	29.4449i	0.670415	+	1.16119i	0.977787	+	0.209603i	$0.0672170\pi$
$643$	17.0000	+	29.4449i	0.670415	+	1.16119i	−0.307372	+	0.951589i	$0.599450\pi$
$644$	−7.50000	+	2.59808i	−0.295541	+	0.102379i
$645$		0			0
$646$	−6.00000	−	10.3923i	−0.236067	−	0.408880i
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	0.763908	−	0.645325i	$-0.223278\pi$
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	−0.940822	+	0.338902i	$0.889945\pi$
$648$		0			0
$649$		0			0
$650$	−10.0000	+	17.3205i	−0.392232	+	0.679366i
$651$		0			0
$652$	−4.00000	−	6.92820i	−0.156652	−	0.271329i
$653$	−24.0000			−0.939193			−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000			−0.939193			−0.469596	+	0.882881i	$0.655601\pi$
$654$		0			0
$655$		0			0
$656$	−1.50000	+	2.59808i	−0.0585652	+	0.101438i
$657$		0			0
$658$	−7.50000	+	2.59808i	−0.292380	+	0.101284i
$659$	−15.0000	+	25.9808i	−0.584317	+	1.01207i	0.410643	+	0.911796i	$0.365304\pi$
$659$	−15.0000	+	25.9808i	−0.584317	+	1.01207i	−0.994960	+	0.100271i	$0.968029\pi$
$660$		0			0
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$	5.00000	−	8.66025i	0.194331	−	0.336590i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−9.00000	+	15.5885i	−0.348481	+	0.603587i
$668$	21.0000			0.812514
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−8.50000	+	14.7224i	−0.327651	+	0.567508i	−0.982045	−	0.188645i	$-0.939590\pi$
$673$	−8.50000	+	14.7224i	−0.327651	+	0.567508i	0.654394	+	0.756153i	$0.272924\pi$
$674$	−7.00000	+	12.1244i	−0.269630	+	0.467013i
$675$		0			0
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	−24.0000	−	41.5692i	−0.922395	−	1.59763i	−0.795698	−	0.605693i	$-0.792896\pi$
$677$	−24.0000	−	41.5692i	−0.922395	−	1.59763i	−0.126697	−	0.991941i	$-0.540438\pi$
$678$		0			0
$679$	5.00000	−	1.73205i	0.191882	−	0.0664700i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−24.0000	−	41.5692i	−0.918334	−	1.59060i	−0.801945	−	0.597398i	$-0.796201\pi$
$683$	−24.0000	−	41.5692i	−0.918334	−	1.59060i	−0.116390	−	0.993204i	$-0.537132\pi$
$684$		0			0
$685$		0			0
$686$	−18.5000	−	0.866025i	−0.706333	−	0.0330650i
$687$		0			0
$688$	2.00000			0.0762493
$689$	12.0000	−	20.7846i	0.457164	−	0.791831i
$690$		0			0
$691$	17.0000	+	29.4449i	0.646710	+	1.12014i	0.983904	+	0.178700i	$0.0571891\pi$
$691$	17.0000	+	29.4449i	0.646710	+	1.12014i	−0.337193	+	0.941435i	$0.609478\pi$
$692$	−18.0000			−0.684257
$693$		0			0
$694$	6.00000			0.227757
$695$		0			0
$696$		0			0
$697$	−9.00000	+	15.5885i	−0.340899	+	0.590455i
$698$	−4.00000			−0.151402
$699$		0			0
$700$	−12.5000	+	4.33013i	−0.472456	+	0.163663i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	−8.00000	−	13.8564i	−0.301726	−	0.522604i
$704$		0			0
$705$		0			0
$706$	−16.5000	−	28.5788i	−0.620986	−	1.07558i
$707$	−12.0000	−	10.3923i	−0.451306	−	0.390843i
$708$		0			0
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	−0.963512	−	0.267664i	$-0.913748\pi$
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	0.249952	−	0.968258i	$-0.419585\pi$
$710$		0			0
$711$		0			0
$712$	−4.50000	+	7.79423i	−0.168645	+	0.292101i
$713$	7.50000	−	12.9904i	0.280877	−	0.486494i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	−21.0000			−0.783713
$719$	4.50000	−	7.79423i	0.167822	−	0.290676i	−0.769832	−	0.638247i	$-0.779660\pi$
$719$	4.50000	−	7.79423i	0.167822	−	0.290676i	0.937654	+	0.347571i	$0.112993\pi$
$720$		0			0
$721$	2.00000	+	1.73205i	0.0744839	+	0.0645049i
$722$	7.50000	−	12.9904i	0.279121	−	0.483452i
$723$		0			0
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$	−15.0000	+	25.9808i	−0.557086	+	0.964901i
$726$		0			0
$727$	6.50000	−	11.2583i	0.241072	−	0.417548i	−0.719948	−	0.694028i	$-0.755834\pi$
$727$	6.50000	−	11.2583i	0.241072	−	0.417548i	0.961020	+	0.276479i	$0.0891678\pi$
$728$	2.00000	−	10.3923i	0.0741249	−	0.385164i
$729$		0			0
$730$		0			0
$731$	12.0000			0.443836
$732$		0			0
$733$	14.0000			0.517102			0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000			0.517102			0.258551	+	0.965998i	$0.416755\pi$
$734$	0.500000	+	0.866025i	0.0184553	+	0.0319656i
$735$		0			0
$736$	1.50000	−	2.59808i	0.0552907	−	0.0957664i
$737$		0			0
$738$		0			0
$739$	−1.00000	−	1.73205i	−0.0367856	−	0.0637145i	0.847046	−	0.531519i	$-0.178379\pi$
$739$	−1.00000	−	1.73205i	−0.0367856	−	0.0637145i	−0.883832	+	0.467804i	$0.845045\pi$
$740$		0			0
$741$		0			0
$742$	15.0000	−	5.19615i	0.550667	−	0.190757i
$743$	7.50000	+	12.9904i	0.275148	+	0.476571i	0.970173	−	0.242415i	$-0.0779397\pi$
$743$	7.50000	+	12.9904i	0.275148	+	0.476571i	−0.695024	+	0.718986i	$0.744606\pi$
$744$		0			0
$745$		0			0
$746$	2.00000	+	3.46410i	0.0732252	+	0.126830i
$747$		0			0
$748$		0			0
$749$	15.0000	−	5.19615i	0.548088	−	0.189863i
$750$		0			0
$751$	−31.0000			−1.13121			−0.565603	−	0.824678i	$-0.691357\pi$
$751$	−31.0000			−1.13121			−0.565603	+	0.824678i	$0.691357\pi$
$752$	1.50000	−	2.59808i	0.0546994	−	0.0947421i
$753$		0			0
$754$	−12.0000	−	20.7846i	−0.437014	−	0.756931i
$755$		0			0
$756$		0			0
$757$	−16.0000			−0.581530			−0.290765	−	0.956795i	$-0.593910\pi$
$757$	−16.0000			−0.581530			−0.290765	+	0.956795i	$0.593910\pi$
$758$	5.00000	+	8.66025i	0.181608	+	0.314555i
$759$		0			0
$760$		0			0
$761$	−21.0000			−0.761249			−0.380625	−	0.924730i	$-0.624291\pi$
$761$	−21.0000			−0.761249			−0.380625	+	0.924730i	$0.624291\pi$
$762$		0			0
$763$	8.00000	−	41.5692i	0.289619	−	1.50491i
$764$	24.0000			0.868290
$765$		0			0
$766$	7.50000	+	12.9904i	0.270986	+	0.469362i
$767$	−48.0000			−1.73318
$768$		0			0
$769$	11.0000	+	19.0526i	0.396670	+	0.687053i	0.993313	−	0.115454i	$-0.0368323\pi$
$769$	11.0000	+	19.0526i	0.396670	+	0.687053i	−0.596643	+	0.802507i	$0.703499\pi$
$770$		0			0
$771$		0			0
$772$	9.50000	+	16.4545i	0.341912	+	0.592210i
$773$	−15.0000	−	25.9808i	−0.539513	−	0.934463i	−0.998930	−	0.0462427i	$-0.985275\pi$
$773$	−15.0000	−	25.9808i	−0.539513	−	0.934463i	0.459418	−	0.888220i	$-0.348058\pi$
$774$		0			0
$775$	12.5000	−	21.6506i	0.449013	−	0.777714i
$776$	−1.00000	+	1.73205i	−0.0358979	+	0.0621770i
$777$		0			0
$778$	12.0000	+	20.7846i	0.430221	+	0.745164i
$779$	6.00000			0.214972
$780$		0			0
$781$		0			0
$782$	9.00000	−	15.5885i	0.321839	−	0.557442i
$783$		0			0
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$		0			0
$786$		0			0
$787$	11.0000	−	19.0526i	0.392108	−	0.679150i	−0.600620	−	0.799535i	$-0.705079\pi$
$787$	11.0000	−	19.0526i	0.392108	−	0.679150i	0.992727	+	0.120384i	$0.0384127\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−9.00000	+	46.7654i	−0.320003	+	1.66279i
$792$		0			0
$793$	16.0000	−	27.7128i	0.568177	−	0.984111i
$794$	2.00000			0.0709773
$795$		0			0
$796$	23.0000			0.815213
$797$	6.00000	+	10.3923i	0.212531	+	0.368114i	0.952506	−	0.304520i	$-0.0984960\pi$
$797$	6.00000	+	10.3923i	0.212531	+	0.368114i	−0.739975	+	0.672634i	$0.765163\pi$
$798$		0			0
$799$	9.00000	−	15.5885i	0.318397	−	0.551480i
$800$	2.50000	−	4.33013i	0.0883883	−	0.153093i
$801$		0			0
$802$	−7.50000	−	12.9904i	−0.264834	−	0.458706i
$803$		0			0
$804$		0			0
$805$		0			0
$806$	10.0000	+	17.3205i	0.352235	+	0.610089i
$807$		0			0
$808$	6.00000			0.211079
$809$	10.5000	+	18.1865i	0.369160	+	0.639404i	0.989434	−	0.144981i	$-0.0463120\pi$
$809$	10.5000	+	18.1865i	0.369160	+	0.639404i	−0.620274	+	0.784385i	$0.712979\pi$
$810$		0			0
$811$	−34.0000			−1.19390			−0.596951	−	0.802278i	$-0.703621\pi$
$811$	−34.0000			−1.19390			−0.596951	+	0.802278i	$0.703621\pi$
$812$	3.00000	−	15.5885i	0.105279	−	0.547048i
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−2.00000	−	3.46410i	−0.0699711	−	0.121194i
$818$	−7.00000			−0.244749
$819$		0			0
$820$		0			0
$821$	−18.0000	−	31.1769i	−0.628204	−	1.08808i	−0.987912	−	0.155017i	$-0.950457\pi$
$821$	−18.0000	−	31.1769i	−0.628204	−	1.08808i	0.359708	−	0.933065i	$-0.382876\pi$
$822$		0			0
$823$	18.5000	−	32.0429i	0.644869	−	1.11695i	−0.339462	−	0.940620i	$-0.610245\pi$
$823$	18.5000	−	32.0429i	0.644869	−	1.11695i	0.984332	−	0.176327i	$-0.0564216\pi$
$824$	−1.00000			−0.0348367
$825$		0			0
$826$	−24.0000	−	20.7846i	−0.835067	−	0.723189i
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$		0			0
$829$	26.0000	+	45.0333i	0.903017	+	1.56407i	0.823557	+	0.567234i	$0.191986\pi$
$829$	26.0000	+	45.0333i	0.903017	+	1.56407i	0.0794606	+	0.996838i	$0.474680\pi$
$830$		0			0
$831$		0			0
$832$	2.00000	+	3.46410i	0.0693375	+	0.120096i
$833$	33.0000	−	25.9808i	1.14338	−	0.900180i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	18.0000	−	31.1769i	0.621800	−	1.07699i
$839$	−12.0000	+	20.7846i	−0.414286	+	0.717564i	−0.995353	−	0.0962912i	$-0.969302\pi$
$839$	−12.0000	+	20.7846i	−0.414286	+	0.717564i	0.581067	+	0.813856i	$0.302635\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	8.00000			0.275698
$843$		0			0
$844$	26.0000			0.894957
$845$		0			0
$846$		0			0
$847$	22.0000	+	19.0526i	0.755929	+	0.654654i
$848$	−3.00000	+	5.19615i	−0.103020	+	0.178437i
$849$		0			0
$850$	15.0000	−	25.9808i	0.514496	−	0.891133i
$851$	12.0000	−	20.7846i	0.411355	−	0.712487i
$852$		0			0
$853$	−4.00000	+	6.92820i	−0.136957	+	0.237217i	−0.926343	−	0.376680i	$-0.877066\pi$
$853$	−4.00000	+	6.92820i	−0.136957	+	0.237217i	0.789386	+	0.613897i	$0.210399\pi$
$854$	20.0000	−	6.92820i	0.684386	−	0.237078i
$855$		0			0
$856$	−3.00000	+	5.19615i	−0.102538	+	0.177601i
$857$	−21.0000			−0.717346			−0.358673	−	0.933463i	$-0.616771\pi$
$857$	−21.0000			−0.717346			−0.358673	+	0.933463i	$0.616771\pi$
$858$		0			0
$859$	2.00000			0.0682391			0.0341196	−	0.999418i	$-0.489137\pi$
$859$	2.00000			0.0682391			0.0341196	+	0.999418i	$0.489137\pi$
$860$		0			0
$861$		0			0
$862$	7.50000	−	12.9904i	0.255451	−	0.442454i
$863$	22.5000	−	38.9711i	0.765909	−	1.32659i	−0.173856	−	0.984771i	$-0.555623\pi$
$863$	22.5000	−	38.9711i	0.765909	−	1.32659i	0.939765	−	0.341822i	$-0.111044\pi$
$864$		0			0
$865$		0			0
$866$	−20.5000	−	35.5070i	−0.696618	−	1.20658i
$867$		0			0
$868$	−2.50000	+	12.9904i	−0.0848555	+	0.440922i
$869$		0			0
$870$		0			0
$871$	−32.0000			−1.08428
$872$	8.00000	+	13.8564i	0.270914	+	0.469237i
$873$		0			0
$874$	−6.00000			−0.202953
$875$		0			0
$876$		0			0
$877$	38.0000			1.28317			0.641584	−	0.767052i	$-0.278277\pi$
$877$	38.0000			1.28317			0.641584	+	0.767052i	$0.278277\pi$
$878$	0.500000	−	0.866025i	0.0168742	−	0.0292269i
$879$		0			0
$880$		0			0
$881$	9.00000			0.303218			0.151609	−	0.988441i	$-0.451555\pi$
$881$	9.00000			0.303218			0.151609	+	0.988441i	$0.451555\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	12.0000	+	20.7846i	0.403604	+	0.699062i
$885$		0			0
$886$	−3.00000	+	5.19615i	−0.100787	+	0.174568i
$887$	−27.0000			−0.906571			−0.453286	−	0.891365i	$-0.649748\pi$
$887$	−27.0000			−0.906571			−0.453286	+	0.891365i	$0.649748\pi$
$888$		0			0
$889$	14.0000	+	12.1244i	0.469545	+	0.406638i
$890$		0			0
$891$		0			0
$892$	9.50000	+	16.4545i	0.318084	+	0.550937i
$893$	−6.00000			−0.200782
$894$		0			0
$895$		0			0
$896$	−0.500000	+	2.59808i	−0.0167038	+	0.0867956i
$897$		0			0
$898$	15.0000	+	25.9808i	0.500556	+	0.866989i
$899$	15.0000	+	25.9808i	0.500278	+	0.866507i
$900$		0			0
$901$	−18.0000	+	31.1769i	−0.599667	+	1.03865i
$902$		0			0
$903$		0			0
$904$	−9.00000	−	15.5885i	−0.299336	−	0.518464i
$905$		0			0
$906$		0			0
$907$	8.00000			0.265636			0.132818	−	0.991140i	$-0.457597\pi$
$907$	8.00000			0.265636			0.132818	+	0.991140i	$0.457597\pi$
$908$	9.00000	−	15.5885i	0.298675	−	0.517321i
$909$		0			0
$910$		0			0
$911$	−1.50000	+	2.59808i	−0.0496972	+	0.0860781i	−0.889804	−	0.456343i	$-0.849159\pi$
$911$	−1.50000	+	2.59808i	−0.0496972	+	0.0860781i	0.840107	+	0.542421i	$0.182492\pi$
$912$		0			0
$913$		0			0
$914$	−1.00000	+	1.73205i	−0.0330771	+	0.0572911i
$915$		0			0
$916$	−4.00000	+	6.92820i	−0.132164	+	0.228914i
$917$	−24.0000	−	20.7846i	−0.792550	−	0.686368i
$918$		0			0
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	−0.924427	−	0.381358i	$-0.875456\pi$
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	0.792480	+	0.609898i	$0.208790\pi$
$920$		0			0
$921$		0			0
$922$	−36.0000			−1.18560
$923$	−30.0000	−	51.9615i	−0.987462	−	1.71033i
$924$		0			0
$925$	20.0000	−	34.6410i	0.657596	−	1.13899i
$926$	6.50000	−	11.2583i	0.213603	−	0.369972i
$927$		0			0
$928$	3.00000	+	5.19615i	0.0984798	+	0.170572i
$929$	10.5000	+	18.1865i	0.344494	+	0.596681i	0.985262	−	0.171054i	$-0.0547172\pi$
$929$	10.5000	+	18.1865i	0.344494	+	0.596681i	−0.640768	+	0.767735i	$0.721384\pi$
$930$		0			0
$931$	−13.0000	−	5.19615i	−0.426058	−	0.170297i
$932$	−9.00000	−	15.5885i	−0.294805	−	0.510617i
$933$		0			0
$934$	12.0000			0.392652
$935$		0			0
$936$		0			0
$937$	−37.0000			−1.20874			−0.604369	−	0.796705i	$-0.706575\pi$
$937$	−37.0000			−1.20874			−0.604369	+	0.796705i	$0.706575\pi$
$938$	−16.0000	−	13.8564i	−0.522419	−	0.452428i
$939$		0			0
$940$		0			0
$941$	24.0000	−	41.5692i	0.782378	−	1.35512i	−0.148176	−	0.988961i	$-0.547340\pi$
$941$	24.0000	−	41.5692i	0.782378	−	1.35512i	0.930553	−	0.366157i	$-0.119327\pi$
$942$		0			0
$943$	4.50000	+	7.79423i	0.146540	+	0.253815i
$944$	12.0000			0.390567
$945$		0			0
$946$		0			0
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	0.681930	−	0.731417i	$-0.261141\pi$
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	−0.974391	+	0.224860i	$0.927807\pi$
$948$		0			0
$949$	22.0000	−	38.1051i	0.714150	−	1.23694i
$950$	−10.0000			−0.324443
$951$		0			0
$952$	−3.00000	+	15.5885i	−0.0972306	+	0.505225i
$953$	−21.0000			−0.680257			−0.340128	−	0.940379i	$-0.610471\pi$
$953$	−21.0000			−0.680257			−0.340128	+	0.940379i	$0.610471\pi$
$954$		0			0
$955$		0			0
$956$	−21.0000			−0.679189
$957$		0			0
$958$	−4.50000	−	7.79423i	−0.145388	−	0.251820i
$959$	−6.00000	−	5.19615i	−0.193750	−	0.167793i
$960$		0			0
$961$	3.00000	+	5.19615i	0.0967742	+	0.167618i
$962$	16.0000	+	27.7128i	0.515861	+	0.893497i
$963$		0			0
$964$	−2.50000	+	4.33013i	−0.0805196	+	0.139464i
$965$		0			0
$966$		0			0
$967$	9.50000	+	16.4545i	0.305499	+	0.529140i	0.977372	−	0.211526i	$-0.0678433\pi$
$967$	9.50000	+	16.4545i	0.305499	+	0.529140i	−0.671873	+	0.740666i	$0.734510\pi$
$968$	−11.0000			−0.353553
$969$		0			0
$970$		0			0
$971$	−15.0000	+	25.9808i	−0.481373	+	0.833762i	−0.999771	−	0.0213768i	$-0.993195\pi$
$971$	−15.0000	+	25.9808i	−0.481373	+	0.833762i	0.518399	+	0.855139i	$0.326528\pi$
$972$		0			0
$973$	8.00000	−	41.5692i	0.256468	−	1.33265i
$974$	3.50000	−	6.06218i	0.112147	−	0.194245i
$975$		0			0
$976$	−4.00000	+	6.92820i	−0.128037	+	0.221766i
$977$	4.50000	−	7.79423i	0.143968	−	0.249359i	−0.785020	−	0.619471i	$-0.787347\pi$
$977$	4.50000	−	7.79423i	0.143968	−	0.249359i	0.928987	+	0.370111i	$0.120681\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	3.00000	−	5.19615i	0.0957338	−	0.165816i
$983$	24.0000			0.765481			0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000			0.765481			0.382741	+	0.923856i	$0.374980\pi$
$984$		0			0
$985$		0			0
$986$	18.0000	+	31.1769i	0.573237	+	0.992875i
$987$		0			0
$988$	4.00000	−	6.92820i	0.127257	−	0.220416i
$989$	3.00000	−	5.19615i	0.0953945	−	0.165228i
$990$		0			0
$991$	−2.50000	−	4.33013i	−0.0794151	−	0.137551i	0.823583	−	0.567196i	$-0.191972\pi$
$991$	−2.50000	−	4.33013i	−0.0794151	−	0.137551i	−0.902998	+	0.429645i	$0.858639\pi$
$992$	−2.50000	−	4.33013i	−0.0793751	−	0.137482i
$993$		0			0
$994$	7.50000	−	38.9711i	0.237886	−	1.23609i
$995$		0			0
$996$		0			0
$997$	50.0000			1.58352			0.791758	−	0.610835i	$-0.209166\pi$
$997$	50.0000			1.58352			0.791758	+	0.610835i	$0.209166\pi$
$998$	17.0000	+	29.4449i	0.538126	+	0.932061i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.h.c.541.1		2
3.2	odd	2		1134.2.h.m.541.1		2
7.4	even	3		1134.2.e.n.865.1		2
9.2	odd	6		1134.2.g.g.163.1	yes	2
9.4	even	3		1134.2.e.n.919.1		2
9.5	odd	6		1134.2.e.d.919.1		2
9.7	even	3		1134.2.g.b.163.1	✓	2
21.11	odd	6		1134.2.e.d.865.1		2
63.2	odd	6		7938.2.a.g.1.1		1
63.4	even	3	inner	1134.2.h.c.109.1		2
63.11	odd	6		1134.2.g.g.487.1	yes	2
63.16	even	3		7938.2.a.y.1.1		1
63.25	even	3		1134.2.g.b.487.1	yes	2
63.32	odd	6		1134.2.h.m.109.1		2
63.47	even	6		7938.2.a.h.1.1		1
63.61	odd	6		7938.2.a.z.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.e.d.865.1		2	21.11	odd	6
1134.2.e.d.919.1		2	9.5	odd	6
1134.2.e.n.865.1		2	7.4	even	3
1134.2.e.n.919.1		2	9.4	even	3
1134.2.g.b.163.1	✓	2	9.7	even	3
1134.2.g.b.487.1	yes	2	63.25	even	3
1134.2.g.g.163.1	yes	2	9.2	odd	6
1134.2.g.g.487.1	yes	2	63.11	odd	6
1134.2.h.c.109.1		2	63.4	even	3	inner
1134.2.h.c.541.1		2	1.1	even	1	trivial
1134.2.h.m.109.1		2	63.32	odd	6
1134.2.h.m.541.1		2	3.2	odd	2
7938.2.a.g.1.1		1	63.2	odd	6
7938.2.a.h.1.1		1	63.47	even	6
7938.2.a.y.1.1		1	63.16	even	3
7938.2.a.z.1.1		1	63.61	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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(2.00000 + 3.46410i) q^{13} +(-0.500000 + 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{19} -3.00000 q^{23} -5.00000 q^{25} +(2.00000 - 3.46410i) q^{26} +(2.50000 - 0.866025i) q^{28} +(3.00000 - 5.19615i) q^{29} +(-2.50000 + 4.33013i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{34} +(-4.00000 + 6.92820i) q^{37} +2.00000 q^{38} +(-1.50000 - 2.59808i) q^{41} +(-1.00000 + 1.73205i) q^{43} +(1.50000 + 2.59808i) q^{46} +(1.50000 + 2.59808i) q^{47} +(1.00000 + 6.92820i) q^{49} +(2.50000 + 4.33013i) q^{50} -4.00000 q^{52} +(-3.00000 - 5.19615i) q^{53} +(-2.00000 - 1.73205i) q^{56} -6.00000 q^{58} +(-6.00000 + 10.3923i) q^{59} +(-4.00000 - 6.92820i) q^{61} +5.00000 q^{62} +1.00000 q^{64} +(-4.00000 + 6.92820i) q^{67} +6.00000 q^{68} -15.0000 q^{71} +(-5.50000 - 9.52628i) q^{73} +8.00000 q^{74} +(-1.00000 - 1.73205i) q^{76} +(0.500000 + 0.866025i) q^{79} +(-1.50000 + 2.59808i) q^{82} +2.00000 q^{86} +(-4.50000 + 7.79423i) q^{89} +(2.00000 - 10.3923i) q^{91} +(1.50000 - 2.59808i) q^{92} +(1.50000 - 2.59808i) q^{94} +(-1.00000 + 1.73205i) q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - 4 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 - 4 * q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} - 4 q^{7} + 2 q^{8} + 4 q^{13} - q^{14} - q^{16} - 6 q^{17} - 2 q^{19} - 6 q^{23} - 10 q^{25} + 4 q^{26} + 5 q^{28} + 6 q^{29} - 5 q^{31} - q^{32} - 6 q^{34} - 8 q^{37} + 4 q^{38} - 3 q^{41} - 2 q^{43} + 3 q^{46} + 3 q^{47} + 2 q^{49} + 5 q^{50} - 8 q^{52} - 6 q^{53} - 4 q^{56} - 12 q^{58} - 12 q^{59} - 8 q^{61} + 10 q^{62} + 2 q^{64} - 8 q^{67} + 12 q^{68} - 30 q^{71} - 11 q^{73} + 16 q^{74} - 2 q^{76} + q^{79} - 3 q^{82} + 4 q^{86} - 9 q^{89} + 4 q^{91} + 3 q^{92} + 3 q^{94} - 2 q^{97} + 11 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 - 4 * q^7 + 2 * q^8 + 4 * q^13 - q^14 - q^16 - 6 * q^17 - 2 * q^19 - 6 * q^23 - 10 * q^25 + 4 * q^26 + 5 * q^28 + 6 * q^29 - 5 * q^31 - q^32 - 6 * q^34 - 8 * q^37 + 4 * q^38 - 3 * q^41 - 2 * q^43 + 3 * q^46 + 3 * q^47 + 2 * q^49 + 5 * q^50 - 8 * q^52 - 6 * q^53 - 4 * q^56 - 12 * q^58 - 12 * q^59 - 8 * q^61 + 10 * q^62 + 2 * q^64 - 8 * q^67 + 12 * q^68 - 30 * q^71 - 11 * q^73 + 16 * q^74 - 2 * q^76 + q^79 - 3 * q^82 + 4 * q^86 - 9 * q^89 + 4 * q^91 + 3 * q^92 + 3 * q^94 - 2 * q^97 + 11 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more