LMFDB - Embedded newform 1134.2.h.e.109.1

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:	$0$
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:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.109
Dual form			1134.2.h.e.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +5.00000 q^{11} +(0.500000 + 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(-4.00000 - 6.92820i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-2.50000 + 4.33013i) q^{22} -4.00000 q^{23} -4.00000 q^{25} +(-2.50000 - 0.866025i) q^{28} +(2.50000 + 4.33013i) q^{29} +(-1.50000 - 2.59808i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.00000 + 3.46410i) q^{34} +(2.00000 - 1.73205i) q^{35} +(2.00000 + 3.46410i) q^{37} +8.00000 q^{38} +1.00000 q^{40} +(-1.00000 - 1.73205i) q^{43} +(-2.50000 - 4.33013i) q^{44} +(2.00000 - 3.46410i) q^{46} +(3.00000 - 5.19615i) q^{47} +(1.00000 - 6.92820i) q^{49} +(2.00000 - 3.46410i) q^{50} +(4.50000 - 7.79423i) q^{53} +5.00000 q^{55} +(2.00000 - 1.73205i) q^{56} -5.00000 q^{58} +(5.50000 + 9.52628i) q^{59} +(3.00000 - 5.19615i) q^{61} +3.00000 q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{67} -4.00000 q^{68} +(0.500000 + 2.59808i) q^{70} +2.00000 q^{71} +(-5.00000 + 8.66025i) q^{73} -4.00000 q^{74} +(-4.00000 + 6.92820i) q^{76} +(10.0000 - 8.66025i) q^{77} +(-1.50000 + 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(3.50000 + 6.06218i) q^{83} +(2.00000 - 3.46410i) q^{85} +2.00000 q^{86} +5.00000 q^{88} +(3.00000 + 5.19615i) q^{89} +(2.00000 + 3.46410i) q^{92} +(3.00000 + 5.19615i) q^{94} +(-4.00000 - 6.92820i) q^{95} +(-3.50000 - 6.06218i) q^{97} +(5.50000 + 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 2 q^{5} + 4 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 + 2 * q^5 + 4 * q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} + 2 q^{5} + 4 q^{7} + 2 q^{8} - q^{10} + 10 q^{11} + q^{14} - q^{16} + 4 q^{17} - 8 q^{19} - q^{20} - 5 q^{22} - 8 q^{23} - 8 q^{25} - 5 q^{28} + 5 q^{29} - 3 q^{31} - q^{32} + 4 q^{34} + 4 q^{35} + 4 q^{37} + 16 q^{38} + 2 q^{40} - 2 q^{43} - 5 q^{44} + 4 q^{46} + 6 q^{47} + 2 q^{49} + 4 q^{50} + 9 q^{53} + 10 q^{55} + 4 q^{56} - 10 q^{58} + 11 q^{59} + 6 q^{61} + 6 q^{62} + 2 q^{64} + 2 q^{67} - 8 q^{68} + q^{70} + 4 q^{71} - 10 q^{73} - 8 q^{74} - 8 q^{76} + 20 q^{77} - 3 q^{79} - q^{80} + 7 q^{83} + 4 q^{85} + 4 q^{86} + 10 q^{88} + 6 q^{89} + 4 q^{92} + 6 q^{94} - 8 q^{95} - 7 q^{97} + 11 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + 2 * q^5 + 4 * q^7 + 2 * q^8 - q^10 + 10 * q^11 + q^14 - q^16 + 4 * q^17 - 8 * q^19 - q^20 - 5 * q^22 - 8 * q^23 - 8 * q^25 - 5 * q^28 + 5 * q^29 - 3 * q^31 - q^32 + 4 * q^34 + 4 * q^35 + 4 * q^37 + 16 * q^38 + 2 * q^40 - 2 * q^43 - 5 * q^44 + 4 * q^46 + 6 * q^47 + 2 * q^49 + 4 * q^50 + 9 * q^53 + 10 * q^55 + 4 * q^56 - 10 * q^58 + 11 * q^59 + 6 * q^61 + 6 * q^62 + 2 * q^64 + 2 * q^67 - 8 * q^68 + q^70 + 4 * q^71 - 10 * q^73 - 8 * q^74 - 8 * q^76 + 20 * q^77 - 3 * q^79 - q^80 + 7 * q^83 + 4 * q^85 + 4 * q^86 + 10 * q^88 + 6 * q^89 + 4 * q^92 + 6 * q^94 - 8 * q^95 - 7 * q^97 + 11 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	1.00000			0.447214			0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000			0.447214			0.223607	+	0.974679i	$0.428217\pi$
$6$		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
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	5.00000			1.50756			0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000			1.50756			0.753778	+	0.657129i	$0.228229\pi$
$12$		0			0
$13$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$13$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$14$	0.500000	+	2.59808i	0.133631	+	0.694365i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$		0			0
$19$	−4.00000	−	6.92820i	−0.917663	−	1.58944i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−4.00000	−	6.92820i	−0.917663	−	1.58944i	−0.114708	−	0.993399i	$-0.536593\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		0			0
$22$	−2.50000	+	4.33013i	−0.533002	+	0.923186i
$23$	−4.00000			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$		0			0
$25$	−4.00000			−0.800000
$26$		0			0
$27$		0			0
$28$	−2.50000	−	0.866025i	−0.472456	−	0.163663i
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	0.999167	−	0.0408130i	$-0.0129948\pi$
$29$	2.50000	+	4.33013i	0.464238	+	0.804084i	−0.534928	+	0.844897i	$0.679661\pi$
$30$		0			0
$31$	−1.50000	−	2.59808i	−0.269408	−	0.466628i	0.699301	−	0.714827i	$-0.253495\pi$
$31$	−1.50000	−	2.59808i	−0.269408	−	0.466628i	−0.968709	+	0.248199i	$0.920161\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	2.00000	+	3.46410i	0.342997	+	0.594089i
$35$	2.00000	−	1.73205i	0.338062	−	0.292770i
$36$		0			0
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$	8.00000			1.29777
$39$		0			0
$40$	1.00000			0.158114
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$		0			0
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	0.779647	−	0.626219i	$-0.215399\pi$
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	−0.932145	+	0.362084i	$0.882065\pi$
$44$	−2.50000	−	4.33013i	−0.376889	−	0.652791i
$45$		0			0
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$		0			0
$52$		0			0
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	−0.371706	−	0.928351i	$-0.621227\pi$
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	0.989828	−	0.142269i	$-0.0454398\pi$
$54$		0			0
$55$	5.00000			0.674200
$56$	2.00000	−	1.73205i	0.267261	−	0.231455i
$57$		0			0
$58$	−5.00000			−0.656532
$59$	5.50000	+	9.52628i	0.716039	+	1.24022i	0.962557	+	0.271078i	$0.0873801\pi$
$59$	5.50000	+	9.52628i	0.716039	+	1.24022i	−0.246518	+	0.969138i	$0.579287\pi$
$60$		0			0
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	−0.607535	−	0.794293i	$-0.707841\pi$
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	0.991645	+	0.128994i	$0.0411748\pi$
$62$	3.00000			0.381000
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$	−4.00000			−0.485071
$69$		0			0
$70$	0.500000	+	2.59808i	0.0597614	+	0.310530i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$		0			0
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	0.409644	+	0.912245i	$0.365653\pi$
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	−0.994850	+	0.101361i	$0.967680\pi$
$74$	−4.00000			−0.464991
$75$		0			0
$76$	−4.00000	+	6.92820i	−0.458831	+	0.794719i
$77$	10.0000	−	8.66025i	1.13961	−	0.986928i
$78$		0			0
$79$	−1.50000	+	2.59808i	−0.168763	+	0.292306i	−0.937985	−	0.346675i	$-0.887311\pi$
$79$	−1.50000	+	2.59808i	−0.168763	+	0.292306i	0.769222	+	0.638982i	$0.220644\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$		0			0
$83$	3.50000	+	6.06218i	0.384175	+	0.665410i	0.991654	−	0.128925i	$-0.0411526\pi$
$83$	3.50000	+	6.06218i	0.384175	+	0.665410i	−0.607479	+	0.794335i	$0.707819\pi$
$84$		0			0
$85$	2.00000	−	3.46410i	0.216930	−	0.375735i
$86$	2.00000			0.215666
$87$		0			0
$88$	5.00000			0.533002
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$		0			0
$92$	2.00000	+	3.46410i	0.208514	+	0.361158i
$93$		0			0
$94$	3.00000	+	5.19615i	0.309426	+	0.535942i
$95$	−4.00000	−	6.92820i	−0.410391	−	0.710819i
$96$		0			0
$97$	−3.50000	−	6.06218i	−0.355371	−	0.615521i	0.631810	−	0.775123i	$-0.282312\pi$
$97$	−3.50000	−	6.06218i	−0.355371	−	0.615521i	−0.987181	+	0.159602i	$0.948979\pi$
$98$	5.50000	+	4.33013i	0.555584	+	0.437409i
$99$		0			0
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	10.0000			0.995037			0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000			0.995037			0.497519	+	0.867453i	$0.334245\pi$
$102$		0			0
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$		0			0
$105$		0			0
$106$	4.50000	+	7.79423i	0.437079	+	0.757042i
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	0.784366	−	0.620298i	$-0.212988\pi$
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	−0.929377	+	0.369132i	$0.879655\pi$
$108$		0			0
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$	−2.50000	+	4.33013i	−0.238366	+	0.412861i
$111$		0			0
$112$	0.500000	+	2.59808i	0.0472456	+	0.245495i
$113$	−8.00000	+	13.8564i	−0.752577	+	1.30350i	0.193993	+	0.981003i	$0.437856\pi$
$113$	−8.00000	+	13.8564i	−0.752577	+	1.30350i	−0.946570	+	0.322498i	$0.895477\pi$
$114$		0			0
$115$	−4.00000			−0.373002
$116$	2.50000	−	4.33013i	0.232119	−	0.402042i
$117$		0			0
$118$	−11.0000			−1.01263
$119$	−2.00000	−	10.3923i	−0.183340	−	0.952661i
$120$		0			0
$121$	14.0000			1.27273
$122$	3.00000	+	5.19615i	0.271607	+	0.470438i
$123$		0			0
$124$	−1.50000	+	2.59808i	−0.134704	+	0.233314i
$125$	−9.00000			−0.804984
$126$		0			0
$127$	9.00000			0.798621			0.399310	−	0.916816i	$-0.369250\pi$
$127$	9.00000			0.798621			0.399310	+	0.916816i	$0.369250\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	1.00000			0.0873704			0.0436852	−	0.999045i	$-0.486090\pi$
$131$	1.00000			0.0873704			0.0436852	+	0.999045i	$0.486090\pi$
$132$		0			0
$133$	−20.0000	−	6.92820i	−1.73422	−	0.600751i
$134$	−2.00000			−0.172774
$135$		0			0
$136$	2.00000	−	3.46410i	0.171499	−	0.297044i
$137$	−2.00000			−0.170872			−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000			−0.170872			−0.0854358	+	0.996344i	$0.527228\pi$
$138$		0			0
$139$	7.00000	−	12.1244i	0.593732	−	1.02837i	−0.399992	−	0.916519i	$-0.630987\pi$
$139$	7.00000	−	12.1244i	0.593732	−	1.02837i	0.993724	−	0.111856i	$-0.0356795\pi$
$140$	−2.50000	−	0.866025i	−0.211289	−	0.0731925i
$141$		0			0
$142$	−1.00000	+	1.73205i	−0.0839181	+	0.145350i
$143$		0			0
$144$		0			0
$145$	2.50000	+	4.33013i	0.207614	+	0.359597i
$146$	−5.00000	−	8.66025i	−0.413803	−	0.716728i
$147$		0			0
$148$	2.00000	−	3.46410i	0.164399	−	0.284747i
$149$	−18.0000			−1.47462			−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000			−1.47462			−0.737309	+	0.675556i	$0.763904\pi$
$150$		0			0
$151$	19.0000			1.54620			0.773099	−	0.634285i	$-0.218706\pi$
$151$	19.0000			1.54620			0.773099	+	0.634285i	$0.218706\pi$
$152$	−4.00000	−	6.92820i	−0.324443	−	0.561951i
$153$		0			0
$154$	2.50000	+	12.9904i	0.201456	+	1.04679i
$155$	−1.50000	−	2.59808i	−0.120483	−	0.208683i
$156$		0			0
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	0.934731	−	0.355357i	$-0.115641\pi$
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	−0.775113	+	0.631822i	$0.782307\pi$
$158$	−1.50000	−	2.59808i	−0.119334	−	0.206692i
$159$		0			0
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−8.00000	+	6.92820i	−0.630488	+	0.546019i
$162$		0			0
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$		0			0
$165$		0			0
$166$	−7.00000			−0.543305
$167$	7.00000	−	12.1244i	0.541676	−	0.938211i	−0.457132	−	0.889399i	$-0.651123\pi$
$167$	7.00000	−	12.1244i	0.541676	−	0.938211i	0.998808	−	0.0488118i	$-0.0155435\pi$
$168$		0			0
$169$	6.50000	+	11.2583i	0.500000	+	0.866025i
$170$	2.00000	+	3.46410i	0.153393	+	0.265684i
$171$		0			0
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−11.0000	+	19.0526i	−0.836315	+	1.44854i	0.0566411	+	0.998395i	$0.481961\pi$
$173$	−11.0000	+	19.0526i	−0.836315	+	1.44854i	−0.892956	+	0.450145i	$0.851372\pi$
$174$		0			0
$175$	−8.00000	+	6.92820i	−0.604743	+	0.523723i
$176$	−2.50000	+	4.33013i	−0.188445	+	0.326396i
$177$		0			0
$178$	−6.00000			−0.449719
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$		0			0
$184$	−4.00000			−0.294884
$185$	2.00000	+	3.46410i	0.147043	+	0.254686i
$186$		0			0
$187$	10.0000	−	17.3205i	0.731272	−	1.26660i
$188$	−6.00000			−0.437595
$189$		0			0
$190$	8.00000			0.580381
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.00454614	+	0.999990i	$0.501447\pi$
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.863743	+	0.503932i	$0.831886\pi$
$192$		0			0
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	0.761911	−	0.647682i	$-0.224262\pi$
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	−0.941865	+	0.335993i	$0.890928\pi$
$194$	7.00000			0.502571
$195$		0			0
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$		0			0
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	−0.786389	−	0.617731i	$-0.788052\pi$
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	0.928166	+	0.372168i	$0.121385\pi$
$200$	−4.00000			−0.282843
$201$		0			0
$202$	−5.00000	+	8.66025i	−0.351799	+	0.609333i
$203$	12.5000	+	4.33013i	0.877328	+	0.303915i
$204$		0			0
$205$		0			0
$206$	−4.00000	+	6.92820i	−0.278693	+	0.482711i
$207$		0			0
$208$		0			0
$209$	−20.0000	−	34.6410i	−1.38343	−	2.39617i
$210$		0			0
$211$	−1.00000	+	1.73205i	−0.0688428	+	0.119239i	−0.898392	−	0.439194i	$-0.855264\pi$
$211$	−1.00000	+	1.73205i	−0.0688428	+	0.119239i	0.829549	+	0.558433i	$0.188597\pi$
$212$	−9.00000			−0.618123
$213$		0			0
$214$	3.00000			0.205076
$215$	−1.00000	−	1.73205i	−0.0681994	−	0.118125i
$216$		0			0
$217$	−7.50000	−	2.59808i	−0.509133	−	0.176369i
$218$	1.00000	+	1.73205i	0.0677285	+	0.117309i
$219$		0			0
$220$	−2.50000	−	4.33013i	−0.168550	−	0.291937i
$221$		0			0
$222$		0			0
$223$	3.50000	+	6.06218i	0.234377	+	0.405953i	0.959092	−	0.283096i	$-0.0913615\pi$
$223$	3.50000	+	6.06218i	0.234377	+	0.405953i	−0.724714	+	0.689050i	$0.758028\pi$
$224$	−2.50000	−	0.866025i	−0.167038	−	0.0578638i
$225$		0			0
$226$	−8.00000	−	13.8564i	−0.532152	−	0.921714i
$227$	3.00000			0.199117			0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000			0.199117			0.0995585	+	0.995032i	$0.468257\pi$
$228$		0			0
$229$	−20.0000			−1.32164			−0.660819	−	0.750546i	$-0.729791\pi$
$229$	−20.0000			−1.32164			−0.660819	+	0.750546i	$0.729791\pi$
$230$	2.00000	−	3.46410i	0.131876	−	0.228416i
$231$		0			0
$232$	2.50000	+	4.33013i	0.164133	+	0.284287i
$233$	2.00000	+	3.46410i	0.131024	+	0.226941i	0.924072	−	0.382219i	$-0.124840\pi$
$233$	2.00000	+	3.46410i	0.131024	+	0.226941i	−0.793047	+	0.609160i	$0.791507\pi$
$234$		0			0
$235$	3.00000	−	5.19615i	0.195698	−	0.338960i
$236$	5.50000	−	9.52628i	0.358020	−	0.620108i
$237$		0			0
$238$	10.0000	+	3.46410i	0.648204	+	0.224544i
$239$	6.00000	−	10.3923i	0.388108	−	0.672222i	−0.604087	−	0.796918i	$-0.706462\pi$
$239$	6.00000	−	10.3923i	0.388108	−	0.672222i	0.992195	+	0.124696i	$0.0397955\pi$
$240$		0			0
$241$	−25.0000			−1.61039			−0.805196	−	0.593009i	$-0.797940\pi$
$241$	−25.0000			−1.61039			−0.805196	+	0.593009i	$0.797940\pi$
$242$	−7.00000	+	12.1244i	−0.449977	+	0.779383i
$243$		0			0
$244$	−6.00000			−0.384111
$245$	1.00000	−	6.92820i	0.0638877	−	0.442627i
$246$		0			0
$247$		0			0
$248$	−1.50000	−	2.59808i	−0.0952501	−	0.164978i
$249$		0			0
$250$	4.50000	−	7.79423i	0.284605	−	0.492950i
$251$	21.0000			1.32551			0.662754	−	0.748837i	$-0.269387\pi$
$251$	21.0000			1.32551			0.662754	+	0.748837i	$0.269387\pi$
$252$		0			0
$253$	−20.0000			−1.25739
$254$	−4.50000	+	7.79423i	−0.282355	+	0.489053i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.00000			−0.374270			−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000			−0.374270			−0.187135	+	0.982334i	$0.559920\pi$
$258$		0			0
$259$	10.0000	+	3.46410i	0.621370	+	0.215249i
$260$		0			0
$261$		0			0
$262$	−0.500000	+	0.866025i	−0.0308901	+	0.0535032i
$263$	−30.0000			−1.84988			−0.924940	−	0.380114i	$-0.875885\pi$
$263$	−30.0000			−1.84988			−0.924940	+	0.380114i	$0.875885\pi$
$264$		0			0
$265$	4.50000	−	7.79423i	0.276433	−	0.478796i
$266$	16.0000	−	13.8564i	0.981023	−	0.849591i
$267$		0			0
$268$	1.00000	−	1.73205i	0.0610847	−	0.105802i
$269$	−15.5000	+	26.8468i	−0.945052	+	1.63688i	−0.189404	+	0.981899i	$0.560656\pi$
$269$	−15.5000	+	26.8468i	−0.945052	+	1.63688i	−0.755648	+	0.654978i	$0.772678\pi$
$270$		0			0
$271$	−7.50000	−	12.9904i	−0.455593	−	0.789109i	0.543130	−	0.839649i	$-0.317239\pi$
$271$	−7.50000	−	12.9904i	−0.455593	−	0.789109i	−0.998722	+	0.0505395i	$0.983906\pi$
$272$	2.00000	+	3.46410i	0.121268	+	0.210042i
$273$		0			0
$274$	1.00000	−	1.73205i	0.0604122	−	0.104637i
$275$	−20.0000			−1.20605
$276$		0			0
$277$	−16.0000			−0.961347			−0.480673	−	0.876900i	$-0.659608\pi$
$277$	−16.0000			−0.961347			−0.480673	+	0.876900i	$0.659608\pi$
$278$	7.00000	+	12.1244i	0.419832	+	0.727171i
$279$		0			0
$280$	2.00000	−	1.73205i	0.119523	−	0.103510i
$281$	−1.00000	−	1.73205i	−0.0596550	−	0.103325i	0.834656	−	0.550772i	$-0.185667\pi$
$281$	−1.00000	−	1.73205i	−0.0596550	−	0.103325i	−0.894311	+	0.447447i	$0.852333\pi$
$282$		0			0
$283$	−5.00000	−	8.66025i	−0.297219	−	0.514799i	0.678280	−	0.734804i	$-0.262726\pi$
$283$	−5.00000	−	8.66025i	−0.297219	−	0.514799i	−0.975499	+	0.220005i	$0.929393\pi$
$284$	−1.00000	−	1.73205i	−0.0593391	−	0.102778i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	−5.00000			−0.293610
$291$		0			0
$292$	10.0000			0.585206
$293$	10.5000	−	18.1865i	0.613417	−	1.06247i	−0.377244	−	0.926114i	$-0.623128\pi$
$293$	10.5000	−	18.1865i	0.613417	−	1.06247i	0.990660	−	0.136355i	$-0.0435386\pi$
$294$		0			0
$295$	5.50000	+	9.52628i	0.320222	+	0.554641i
$296$	2.00000	+	3.46410i	0.116248	+	0.201347i
$297$		0			0
$298$	9.00000	−	15.5885i	0.521356	−	0.903015i
$299$		0			0
$300$		0			0
$301$	−5.00000	−	1.73205i	−0.288195	−	0.0998337i
$302$	−9.50000	+	16.4545i	−0.546664	+	0.946849i
$303$		0			0
$304$	8.00000			0.458831
$305$	3.00000	−	5.19615i	0.171780	−	0.297531i
$306$		0			0
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$	−12.5000	−	4.33013i	−0.712254	−	0.246732i
$309$		0			0
$310$	3.00000			0.170389
$311$	16.0000	+	27.7128i	0.907277	+	1.57145i	0.817832	+	0.575458i	$0.195176\pi$
$311$	16.0000	+	27.7128i	0.907277	+	1.57145i	0.0894452	+	0.995992i	$0.471491\pi$
$312$		0			0
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	−0.879810	−	0.475325i	$-0.842331\pi$
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	0.851549	+	0.524276i	$0.175664\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	3.00000			0.168763
$317$	−1.50000	+	2.59808i	−0.0842484	+	0.145922i	−0.905071	−	0.425261i	$-0.860182\pi$
$317$	−1.50000	+	2.59808i	−0.0842484	+	0.145922i	0.820822	+	0.571184i	$0.193516\pi$
$318$		0			0
$319$	12.5000	+	21.6506i	0.699866	+	1.21220i
$320$	1.00000			0.0559017
$321$		0			0
$322$	−2.00000	−	10.3923i	−0.111456	−	0.579141i
$323$	−32.0000			−1.78053
$324$		0			0
$325$		0			0
$326$	−4.00000			−0.221540
$327$		0			0
$328$		0			0
$329$	−3.00000	−	15.5885i	−0.165395	−	0.859419i
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	3.50000	−	6.06218i	0.192087	−	0.332705i
$333$		0			0
$334$	7.00000	+	12.1244i	0.383023	+	0.663415i
$335$	1.00000	+	1.73205i	0.0546358	+	0.0946320i
$336$		0			0
$337$	−4.50000	+	7.79423i	−0.245131	+	0.424579i	−0.962168	−	0.272456i	$-0.912164\pi$
$337$	−4.50000	+	7.79423i	−0.245131	+	0.424579i	0.717038	+	0.697034i	$0.245498\pi$
$338$	−13.0000			−0.707107
$339$		0			0
$340$	−4.00000			−0.216930
$341$	−7.50000	−	12.9904i	−0.406148	−	0.703469i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	−1.00000	−	1.73205i	−0.0539164	−	0.0933859i
$345$		0			0
$346$	−11.0000	−	19.0526i	−0.591364	−	1.02427i
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$		0			0
$349$	7.00000	+	12.1244i	0.374701	+	0.649002i	0.990282	−	0.139072i	$-0.0444119\pi$
$349$	7.00000	+	12.1244i	0.374701	+	0.649002i	−0.615581	+	0.788074i	$0.711079\pi$
$350$	−2.00000	−	10.3923i	−0.106904	−	0.555492i
$351$		0			0
$352$	−2.50000	−	4.33013i	−0.133250	−	0.230797i
$353$	24.0000			1.27739			0.638696	−	0.769460i	$-0.279474\pi$
$353$	24.0000			1.27739			0.638696	+	0.769460i	$0.279474\pi$
$354$		0			0
$355$	2.00000			0.106149
$356$	3.00000	−	5.19615i	0.159000	−	0.275396i
$357$		0			0
$358$	−6.00000	−	10.3923i	−0.317110	−	0.549250i
$359$	−5.00000	−	8.66025i	−0.263890	−	0.457071i	0.703382	−	0.710812i	$-0.251672\pi$
$359$	−5.00000	−	8.66025i	−0.263890	−	0.457071i	−0.967272	+	0.253741i	$0.918339\pi$
$360$		0			0
$361$	−22.5000	+	38.9711i	−1.18421	+	2.05111i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−5.00000	+	8.66025i	−0.261712	+	0.453298i
$366$		0			0
$367$	17.0000			0.887393			0.443696	−	0.896177i	$-0.353667\pi$
$367$	17.0000			0.887393			0.443696	+	0.896177i	$0.353667\pi$
$368$	2.00000	−	3.46410i	0.104257	−	0.180579i
$369$		0			0
$370$	−4.00000			−0.207950
$371$	−4.50000	−	23.3827i	−0.233628	−	1.21397i
$372$		0			0
$373$	−32.0000			−1.65690			−0.828449	−	0.560065i	$-0.810776\pi$
$373$	−32.0000			−1.65690			−0.828449	+	0.560065i	$0.810776\pi$
$374$	10.0000	+	17.3205i	0.517088	+	0.895622i
$375$		0			0
$376$	3.00000	−	5.19615i	0.154713	−	0.267971i
$377$		0			0
$378$		0			0
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$	−4.00000	+	6.92820i	−0.205196	+	0.355409i
$381$		0			0
$382$	−12.0000	−	20.7846i	−0.613973	−	1.06343i
$383$	−34.0000			−1.73732			−0.868659	−	0.495410i	$-0.835018\pi$
$383$	−34.0000			−1.73732			−0.868659	+	0.495410i	$0.835018\pi$
$384$		0			0
$385$	10.0000	−	8.66025i	0.509647	−	0.441367i
$386$	5.00000			0.254493
$387$		0			0
$388$	−3.50000	+	6.06218i	−0.177686	+	0.307760i
$389$	−2.00000			−0.101404			−0.0507020	−	0.998714i	$-0.516146\pi$
$389$	−2.00000			−0.101404			−0.0507020	+	0.998714i	$0.516146\pi$
$390$		0			0
$391$	−8.00000	+	13.8564i	−0.404577	+	0.700749i
$392$	1.00000	−	6.92820i	0.0505076	−	0.349927i
$393$		0			0
$394$	−1.00000	+	1.73205i	−0.0503793	+	0.0872595i
$395$	−1.50000	+	2.59808i	−0.0754732	+	0.130723i
$396$		0			0
$397$	−18.0000	−	31.1769i	−0.903394	−	1.56472i	−0.823058	−	0.567957i	$-0.807734\pi$
$397$	−18.0000	−	31.1769i	−0.903394	−	1.56472i	−0.0803356	−	0.996768i	$-0.525599\pi$
$398$	2.00000	+	3.46410i	0.100251	+	0.173640i
$399$		0			0
$400$	2.00000	−	3.46410i	0.100000	−	0.173205i
$401$	24.0000			1.19850			0.599251	−	0.800561i	$-0.295465\pi$
$401$	24.0000			1.19850			0.599251	+	0.800561i	$0.295465\pi$
$402$		0			0
$403$		0			0
$404$	−5.00000	−	8.66025i	−0.248759	−	0.430864i
$405$		0			0
$406$	−10.0000	+	8.66025i	−0.496292	+	0.429801i
$407$	10.0000	+	17.3205i	0.495682	+	0.858546i
$408$		0			0
$409$	12.5000	+	21.6506i	0.618085	+	1.07056i	0.989835	+	0.142222i	$0.0454247\pi$
$409$	12.5000	+	21.6506i	0.618085	+	1.07056i	−0.371750	+	0.928333i	$0.621242\pi$
$410$		0			0
$411$		0			0
$412$	−4.00000	−	6.92820i	−0.197066	−	0.341328i
$413$	27.5000	+	9.52628i	1.35319	+	0.468758i
$414$		0			0
$415$	3.50000	+	6.06218i	0.171808	+	0.297581i
$416$		0			0
$417$		0			0
$418$	40.0000			1.95646
$419$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$419$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$420$		0			0
$421$	−15.0000	−	25.9808i	−0.731055	−	1.26622i	−0.956433	−	0.291953i	$-0.905695\pi$
$421$	−15.0000	−	25.9808i	−0.731055	−	1.26622i	0.225377	−	0.974272i	$-0.427639\pi$
$422$	−1.00000	−	1.73205i	−0.0486792	−	0.0843149i
$423$		0			0
$424$	4.50000	−	7.79423i	0.218539	−	0.378521i
$425$	−8.00000	+	13.8564i	−0.388057	+	0.672134i
$426$		0			0
$427$	−3.00000	−	15.5885i	−0.145180	−	0.754378i
$428$	−1.50000	+	2.59808i	−0.0725052	+	0.125583i
$429$		0			0
$430$	2.00000			0.0964486
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$	6.00000	−	5.19615i	0.288009	−	0.249423i
$435$		0			0
$436$	−2.00000			−0.0957826
$437$	16.0000	+	27.7128i	0.765384	+	1.32568i
$438$		0			0
$439$	−7.50000	+	12.9904i	−0.357955	+	0.619997i	−0.987619	−	0.156871i	$-0.949859\pi$
$439$	−7.50000	+	12.9904i	−0.357955	+	0.619997i	0.629664	+	0.776868i	$0.283193\pi$
$440$	5.00000			0.238366
$441$		0			0
$442$		0			0
$443$	−8.50000	+	14.7224i	−0.403847	+	0.699484i	−0.994187	−	0.107671i	$-0.965661\pi$
$443$	−8.50000	+	14.7224i	−0.403847	+	0.699484i	0.590339	+	0.807155i	$0.298994\pi$
$444$		0			0
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$	−7.00000			−0.331460
$447$		0			0
$448$	2.00000	−	1.73205i	0.0944911	−	0.0818317i
$449$	16.0000			0.755087			0.377543	−	0.925992i	$-0.376769\pi$
$449$	16.0000			0.755087			0.377543	+	0.925992i	$0.376769\pi$
$450$		0			0
$451$		0			0
$452$	16.0000			0.752577
$453$		0			0
$454$	−1.50000	+	2.59808i	−0.0703985	+	0.121934i
$455$		0			0
$456$		0			0
$457$	−15.5000	+	26.8468i	−0.725059	+	1.25584i	0.233890	+	0.972263i	$0.424854\pi$
$457$	−15.5000	+	26.8468i	−0.725059	+	1.25584i	−0.958950	+	0.283577i	$0.908479\pi$
$458$	10.0000	−	17.3205i	0.467269	−	0.809334i
$459$		0			0
$460$	2.00000	+	3.46410i	0.0932505	+	0.161515i
$461$	7.00000	+	12.1244i	0.326023	+	0.564688i	0.981719	−	0.190337i	$-0.0609581\pi$
$461$	7.00000	+	12.1244i	0.326023	+	0.564688i	−0.655696	+	0.755025i	$0.727625\pi$
$462$		0			0
$463$	−8.00000	+	13.8564i	−0.371792	+	0.643962i	−0.989841	−	0.142177i	$-0.954590\pi$
$463$	−8.00000	+	13.8564i	−0.371792	+	0.643962i	0.618050	+	0.786139i	$0.287923\pi$
$464$	−5.00000			−0.232119
$465$		0			0
$466$	−4.00000			−0.185296
$467$	10.0000	+	17.3205i	0.462745	+	0.801498i	0.999097	−	0.0424970i	$-0.0135313\pi$
$467$	10.0000	+	17.3205i	0.462745	+	0.801498i	−0.536352	+	0.843995i	$0.680198\pi$
$468$		0			0
$469$	5.00000	+	1.73205i	0.230879	+	0.0799787i
$470$	3.00000	+	5.19615i	0.138380	+	0.239681i
$471$		0			0
$472$	5.50000	+	9.52628i	0.253158	+	0.438483i
$473$	−5.00000	−	8.66025i	−0.229900	−	0.398199i
$474$		0			0
$475$	16.0000	+	27.7128i	0.734130	+	1.27155i
$476$	−8.00000	+	6.92820i	−0.366679	+	0.317554i
$477$		0			0
$478$	6.00000	+	10.3923i	0.274434	+	0.475333i
$479$	38.0000			1.73626			0.868132	−	0.496333i	$-0.165321\pi$
$479$	38.0000			1.73626			0.868132	+	0.496333i	$0.165321\pi$
$480$		0			0
$481$		0			0
$482$	12.5000	−	21.6506i	0.569359	−	0.986159i
$483$		0			0
$484$	−7.00000	−	12.1244i	−0.318182	−	0.551107i
$485$	−3.50000	−	6.06218i	−0.158927	−	0.275269i
$486$		0			0
$487$	−2.50000	+	4.33013i	−0.113286	+	0.196217i	−0.917093	−	0.398673i	$-0.869471\pi$
$487$	−2.50000	+	4.33013i	−0.113286	+	0.196217i	0.803807	+	0.594890i	$0.202804\pi$
$488$	3.00000	−	5.19615i	0.135804	−	0.235219i
$489$		0			0
$490$	5.50000	+	4.33013i	0.248465	+	0.195615i
$491$	−4.50000	+	7.79423i	−0.203082	+	0.351749i	−0.949520	−	0.313707i	$-0.898429\pi$
$491$	−4.50000	+	7.79423i	−0.203082	+	0.351749i	0.746438	+	0.665455i	$0.231763\pi$
$492$		0			0
$493$	20.0000			0.900755
$494$		0			0
$495$		0			0
$496$	3.00000			0.134704
$497$	4.00000	−	3.46410i	0.179425	−	0.155386i
$498$		0			0
$499$	10.0000			0.447661			0.223831	−	0.974628i	$-0.428144\pi$
$499$	10.0000			0.447661			0.223831	+	0.974628i	$0.428144\pi$
$500$	4.50000	+	7.79423i	0.201246	+	0.348569i
$501$		0			0
$502$	−10.5000	+	18.1865i	−0.468638	+	0.811705i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	10.0000			0.444994
$506$	10.0000	−	17.3205i	0.444554	−	0.769991i
$507$		0			0
$508$	−4.50000	−	7.79423i	−0.199655	−	0.345813i
$509$	15.0000			0.664863			0.332432	−	0.943127i	$-0.392131\pi$
$509$	15.0000			0.664863			0.332432	+	0.943127i	$0.392131\pi$
$510$		0			0
$511$	5.00000	+	25.9808i	0.221187	+	1.14932i
$512$	1.00000			0.0441942
$513$		0			0
$514$	3.00000	−	5.19615i	0.132324	−	0.229192i
$515$	8.00000			0.352522
$516$		0			0
$517$	15.0000	−	25.9808i	0.659699	−	1.14263i
$518$	−8.00000	+	6.92820i	−0.351500	+	0.304408i
$519$		0			0
$520$		0			0
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	−0.598714	−	0.800963i	$-0.704321\pi$
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	0.993011	+	0.118020i	$0.0376547\pi$
$522$		0			0
$523$	−4.00000	−	6.92820i	−0.174908	−	0.302949i	0.765222	−	0.643767i	$-0.222629\pi$
$523$	−4.00000	−	6.92820i	−0.174908	−	0.302949i	−0.940129	+	0.340818i	$0.889296\pi$
$524$	−0.500000	−	0.866025i	−0.0218426	−	0.0378325i
$525$		0			0
$526$	15.0000	−	25.9808i	0.654031	−	1.13282i
$527$	−12.0000			−0.522728
$528$		0			0
$529$	−7.00000			−0.304348
$530$	4.50000	+	7.79423i	0.195468	+	0.338560i
$531$		0			0
$532$	4.00000	+	20.7846i	0.173422	+	0.901127i
$533$		0			0
$534$		0			0
$535$	−1.50000	−	2.59808i	−0.0648507	−	0.112325i
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$		0			0
$538$	−15.5000	−	26.8468i	−0.668252	−	1.15745i
$539$	5.00000	−	34.6410i	0.215365	−	1.49209i
$540$		0			0
$541$	9.00000	+	15.5885i	0.386940	+	0.670200i	0.992036	−	0.125952i	$-0.0401986\pi$
$541$	9.00000	+	15.5885i	0.386940	+	0.670200i	−0.605096	+	0.796152i	$0.706865\pi$
$542$	15.0000			0.644305
$543$		0			0
$544$	−4.00000			−0.171499
$545$	1.00000	−	1.73205i	0.0428353	−	0.0741929i
$546$		0			0
$547$	6.00000	+	10.3923i	0.256541	+	0.444343i	0.965313	−	0.261095i	$-0.0840836\pi$
$547$	6.00000	+	10.3923i	0.256541	+	0.444343i	−0.708772	+	0.705438i	$0.750750\pi$
$548$	1.00000	+	1.73205i	0.0427179	+	0.0739895i
$549$		0			0
$550$	10.0000	−	17.3205i	0.426401	−	0.738549i
$551$	20.0000	−	34.6410i	0.852029	−	1.47576i
$552$		0			0
$553$	1.50000	+	7.79423i	0.0637865	+	0.331444i
$554$	8.00000	−	13.8564i	0.339887	−	0.588702i
$555$		0			0
$556$	−14.0000			−0.593732
$557$	11.5000	−	19.9186i	0.487271	−	0.843978i	−0.512622	−	0.858614i	$-0.671326\pi$
$557$	11.5000	−	19.9186i	0.487271	−	0.843978i	0.999893	+	0.0146368i	$0.00465919\pi$
$558$		0			0
$559$		0			0
$560$	0.500000	+	2.59808i	0.0211289	+	0.109789i
$561$		0			0
$562$	2.00000			0.0843649
$563$	−8.50000	−	14.7224i	−0.358232	−	0.620477i	0.629433	−	0.777055i	$-0.283287\pi$
$563$	−8.50000	−	14.7224i	−0.358232	−	0.620477i	−0.987666	+	0.156578i	$0.949954\pi$
$564$		0			0
$565$	−8.00000	+	13.8564i	−0.336563	+	0.582943i
$566$	10.0000			0.420331
$567$		0			0
$568$	2.00000			0.0839181
$569$	−12.0000	+	20.7846i	−0.503066	+	0.871336i	0.496928	+	0.867792i	$0.334461\pi$
$569$	−12.0000	+	20.7846i	−0.503066	+	0.871336i	−0.999994	+	0.00354413i	$0.998872\pi$
$570$		0			0
$571$	15.0000	+	25.9808i	0.627730	+	1.08726i	0.988006	+	0.154415i	$0.0493493\pi$
$571$	15.0000	+	25.9808i	0.627730	+	1.08726i	−0.360276	+	0.932846i	$0.617317\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	16.0000			0.667246
$576$		0			0
$577$	−15.5000	+	26.8468i	−0.645273	+	1.11765i	0.338965	+	0.940799i	$0.389923\pi$
$577$	−15.5000	+	26.8468i	−0.645273	+	1.11765i	−0.984238	+	0.176847i	$0.943410\pi$
$578$	−1.00000			−0.0415945
$579$		0			0
$580$	2.50000	−	4.33013i	0.103807	−	0.179799i
$581$	17.5000	+	6.06218i	0.726022	+	0.251502i
$582$		0			0
$583$	22.5000	−	38.9711i	0.931855	−	1.61402i
$584$	−5.00000	+	8.66025i	−0.206901	+	0.358364i
$585$		0			0
$586$	10.5000	+	18.1865i	0.433751	+	0.751279i
$587$	−17.5000	−	30.3109i	−0.722302	−	1.25106i	−0.960075	−	0.279743i	$-0.909751\pi$
$587$	−17.5000	−	30.3109i	−0.722302	−	1.25106i	0.237773	−	0.971321i	$-0.423583\pi$
$588$		0			0
$589$	−12.0000	+	20.7846i	−0.494451	+	0.856415i
$590$	−11.0000			−0.452863
$591$		0			0
$592$	−4.00000			−0.164399
$593$	−18.0000	−	31.1769i	−0.739171	−	1.28028i	−0.952869	−	0.303383i	$-0.901884\pi$
$593$	−18.0000	−	31.1769i	−0.739171	−	1.28028i	0.213697	−	0.976900i	$-0.431449\pi$
$594$		0			0
$595$	−2.00000	−	10.3923i	−0.0819920	−	0.426043i
$596$	9.00000	+	15.5885i	0.368654	+	0.638528i
$597$		0			0
$598$		0			0
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	0.990752	+	0.135686i	$0.0433238\pi$
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	−0.377869	+	0.925859i	$0.623343\pi$
$600$		0			0
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	−0.963405	−	0.268049i	$-0.913621\pi$
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	0.249565	−	0.968358i	$-0.419712\pi$
$602$	4.00000	−	3.46410i	0.163028	−	0.141186i
$603$		0			0
$604$	−9.50000	−	16.4545i	−0.386550	−	0.669523i
$605$	14.0000			0.569181
$606$		0			0
$607$	−27.0000			−1.09590			−0.547948	−	0.836512i	$-0.684591\pi$
$607$	−27.0000			−1.09590			−0.547948	+	0.836512i	$0.684591\pi$
$608$	−4.00000	+	6.92820i	−0.162221	+	0.280976i
$609$		0			0
$610$	3.00000	+	5.19615i	0.121466	+	0.210386i
$611$		0			0
$612$		0			0
$613$	−6.00000	+	10.3923i	−0.242338	+	0.419741i	−0.961380	−	0.275225i	$-0.911248\pi$
$613$	−6.00000	+	10.3923i	−0.242338	+	0.419741i	0.719042	+	0.694967i	$0.244581\pi$
$614$	−14.0000	+	24.2487i	−0.564994	+	0.978598i
$615$		0			0
$616$	10.0000	−	8.66025i	0.402911	−	0.348932i
$617$	−1.00000	+	1.73205i	−0.0402585	+	0.0697297i	−0.885453	−	0.464730i	$-0.846151\pi$
$617$	−1.00000	+	1.73205i	−0.0402585	+	0.0697297i	0.845194	+	0.534460i	$0.179485\pi$
$618$		0			0
$619$	10.0000			0.401934			0.200967	−	0.979598i	$-0.435592\pi$
$619$	10.0000			0.401934			0.200967	+	0.979598i	$0.435592\pi$
$620$	−1.50000	+	2.59808i	−0.0602414	+	0.104341i
$621$		0			0
$622$	−32.0000			−1.28308
$623$	15.0000	+	5.19615i	0.600962	+	0.208179i
$624$		0			0
$625$	11.0000			0.440000
$626$	−0.500000	−	0.866025i	−0.0199840	−	0.0346133i
$627$		0			0
$628$	2.00000	−	3.46410i	0.0798087	−	0.138233i
$629$	16.0000			0.637962
$630$		0			0
$631$	−19.0000			−0.756378			−0.378189	−	0.925728i	$-0.623453\pi$
$631$	−19.0000			−0.756378			−0.378189	+	0.925728i	$0.623453\pi$
$632$	−1.50000	+	2.59808i	−0.0596668	+	0.103346i
$633$		0			0
$634$	−1.50000	−	2.59808i	−0.0595726	−	0.103183i
$635$	9.00000			0.357154
$636$		0			0
$637$		0			0
$638$	−25.0000			−0.989759
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	26.0000			1.02694			0.513469	−	0.858108i	$-0.328360\pi$
$641$	26.0000			1.02694			0.513469	+	0.858108i	$0.328360\pi$
$642$		0			0
$643$	−7.00000	+	12.1244i	−0.276053	+	0.478138i	−0.970400	−	0.241502i	$-0.922360\pi$
$643$	−7.00000	+	12.1244i	−0.276053	+	0.478138i	0.694347	+	0.719640i	$0.255693\pi$
$644$	10.0000	+	3.46410i	0.394055	+	0.136505i
$645$		0			0
$646$	16.0000	−	27.7128i	0.629512	−	1.09035i
$647$	9.00000	−	15.5885i	0.353827	−	0.612845i	−0.633090	−	0.774078i	$-0.718214\pi$
$647$	9.00000	−	15.5885i	0.353827	−	0.612845i	0.986916	+	0.161233i	$0.0515470\pi$
$648$		0			0
$649$	27.5000	+	47.6314i	1.07947	+	1.86970i
$650$		0			0
$651$		0			0
$652$	2.00000	−	3.46410i	0.0783260	−	0.135665i
$653$	−39.0000			−1.52619			−0.763094	−	0.646288i	$-0.776321\pi$
$653$	−39.0000			−1.52619			−0.763094	+	0.646288i	$0.776321\pi$
$654$		0			0
$655$	1.00000			0.0390732
$656$		0			0
$657$		0			0
$658$	15.0000	+	5.19615i	0.584761	+	0.202567i
$659$	20.0000	+	34.6410i	0.779089	+	1.34942i	0.932467	+	0.361255i	$0.117652\pi$
$659$	20.0000	+	34.6410i	0.779089	+	1.34942i	−0.153378	+	0.988168i	$0.549015\pi$
$660$		0			0
$661$	−5.00000	−	8.66025i	−0.194477	−	0.336845i	0.752252	−	0.658876i	$-0.228968\pi$
$661$	−5.00000	−	8.66025i	−0.194477	−	0.336845i	−0.946729	+	0.322031i	$0.895634\pi$
$662$	2.00000	+	3.46410i	0.0777322	+	0.134636i
$663$		0			0
$664$	3.50000	+	6.06218i	0.135826	+	0.235258i
$665$	−20.0000	−	6.92820i	−0.775567	−	0.268664i
$666$		0			0
$667$	−10.0000	−	17.3205i	−0.387202	−	0.670653i
$668$	−14.0000			−0.541676
$669$		0			0
$670$	−2.00000			−0.0772667
$671$	15.0000	−	25.9808i	0.579069	−	1.00298i
$672$		0			0
$673$	9.50000	+	16.4545i	0.366198	+	0.634274i	0.988968	−	0.148132i	$-0.0473259\pi$
$673$	9.50000	+	16.4545i	0.366198	+	0.634274i	−0.622770	+	0.782405i	$0.713993\pi$
$674$	−4.50000	−	7.79423i	−0.173334	−	0.300222i
$675$		0			0
$676$	6.50000	−	11.2583i	0.250000	−	0.433013i
$677$	13.5000	−	23.3827i	0.518847	−	0.898670i	−0.480913	−	0.876768i	$-0.659695\pi$
$677$	13.5000	−	23.3827i	0.518847	−	0.898670i	0.999760	−	0.0219013i	$-0.00697196\pi$
$678$		0			0
$679$	−17.5000	−	6.06218i	−0.671588	−	0.232645i
$680$	2.00000	−	3.46410i	0.0766965	−	0.132842i
$681$		0			0
$682$	15.0000			0.574380
$683$	4.50000	−	7.79423i	0.172188	−	0.298238i	−0.766997	−	0.641651i	$-0.778250\pi$
$683$	4.50000	−	7.79423i	0.172188	−	0.298238i	0.939184	+	0.343413i	$0.111583\pi$
$684$		0			0
$685$	−2.00000			−0.0764161
$686$	18.5000	−	0.866025i	0.706333	−	0.0330650i
$687$		0			0
$688$	2.00000			0.0762493
$689$		0			0
$690$		0			0
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	0.779857	+	0.625958i	$0.215292\pi$
$692$	22.0000			0.836315
$693$		0			0
$694$	12.0000			0.455514
$695$	7.00000	−	12.1244i	0.265525	−	0.459903i
$696$		0			0
$697$		0			0
$698$	−14.0000			−0.529908
$699$		0			0
$700$	10.0000	+	3.46410i	0.377964	+	0.130931i
$701$	−5.00000			−0.188847			−0.0944237	−	0.995532i	$-0.530101\pi$
$701$	−5.00000			−0.188847			−0.0944237	+	0.995532i	$0.530101\pi$
$702$		0			0
$703$	16.0000	−	27.7128i	0.603451	−	1.04521i
$704$	5.00000			0.188445
$705$		0			0
$706$	−12.0000	+	20.7846i	−0.451626	+	0.782239i
$707$	20.0000	−	17.3205i	0.752177	−	0.651405i
$708$		0			0
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	0.249952	+	0.968258i	$0.419585\pi$
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	−0.963512	+	0.267664i	$0.913748\pi$
$710$	−1.00000	+	1.73205i	−0.0375293	+	0.0650027i
$711$		0			0
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$	6.00000	+	10.3923i	0.224702	+	0.389195i
$714$		0			0
$715$		0			0
$716$	12.0000			0.448461
$717$		0			0
$718$	10.0000			0.373197
$719$	3.00000	+	5.19615i	0.111881	+	0.193784i	0.916529	−	0.399969i	$-0.130979\pi$
$719$	3.00000	+	5.19615i	0.111881	+	0.193784i	−0.804648	+	0.593753i	$0.797646\pi$
$720$		0			0
$721$	16.0000	−	13.8564i	0.595871	−	0.516040i
$722$	−22.5000	−	38.9711i	−0.837363	−	1.45036i
$723$		0			0
$724$		0			0
$725$	−10.0000	−	17.3205i	−0.371391	−	0.643268i
$726$		0			0
$727$	−3.50000	−	6.06218i	−0.129808	−	0.224834i	0.793794	−	0.608186i	$-0.208103\pi$
$727$	−3.50000	−	6.06218i	−0.129808	−	0.224834i	−0.923602	+	0.383353i	$0.874769\pi$
$728$		0			0
$729$		0			0
$730$	−5.00000	−	8.66025i	−0.185058	−	0.320530i
$731$	−8.00000			−0.295891
$732$		0			0
$733$	−6.00000			−0.221615			−0.110808	−	0.993842i	$-0.535344\pi$
$733$	−6.00000			−0.221615			−0.110808	+	0.993842i	$0.535344\pi$
$734$	−8.50000	+	14.7224i	−0.313741	+	0.543415i
$735$		0			0
$736$	2.00000	+	3.46410i	0.0737210	+	0.127688i
$737$	5.00000	+	8.66025i	0.184177	+	0.319005i
$738$		0			0
$739$	15.0000	−	25.9808i	0.551784	−	0.955718i	−0.446362	−	0.894852i	$-0.647281\pi$
$739$	15.0000	−	25.9808i	0.551784	−	0.955718i	0.998146	−	0.0608653i	$-0.0193860\pi$
$740$	2.00000	−	3.46410i	0.0735215	−	0.127343i
$741$		0			0
$742$	22.5000	+	7.79423i	0.826001	+	0.286135i
$743$	−15.0000	+	25.9808i	−0.550297	+	0.953142i	0.447956	+	0.894055i	$0.352152\pi$
$743$	−15.0000	+	25.9808i	−0.550297	+	0.953142i	−0.998253	+	0.0590862i	$0.981181\pi$
$744$		0			0
$745$	−18.0000			−0.659469
$746$	16.0000	−	27.7128i	0.585802	−	1.01464i
$747$		0			0
$748$	−20.0000			−0.731272
$749$	−7.50000	−	2.59808i	−0.274044	−	0.0949316i
$750$		0			0
$751$	45.0000			1.64207			0.821037	−	0.570875i	$-0.193396\pi$
$751$	45.0000			1.64207			0.821037	+	0.570875i	$0.193396\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$		0			0
$754$		0			0
$755$	19.0000			0.691481
$756$		0			0
$757$	−54.0000			−1.96266			−0.981332	−	0.192323i	$-0.938398\pi$
$757$	−54.0000			−1.96266			−0.981332	+	0.192323i	$0.938398\pi$
$758$	−8.00000	+	13.8564i	−0.290573	+	0.503287i
$759$		0			0
$760$	−4.00000	−	6.92820i	−0.145095	−	0.251312i
$761$	8.00000			0.290000			0.145000	−	0.989432i	$-0.453682\pi$
$761$	8.00000			0.290000			0.145000	+	0.989432i	$0.453682\pi$
$762$		0			0
$763$	−1.00000	−	5.19615i	−0.0362024	−	0.188113i
$764$	24.0000			0.868290
$765$		0			0
$766$	17.0000	−	29.4449i	0.614235	−	1.06389i
$767$		0			0
$768$		0			0
$769$	17.5000	−	30.3109i	0.631066	−	1.09304i	−0.356268	−	0.934384i	$-0.615951\pi$
$769$	17.5000	−	30.3109i	0.631066	−	1.09304i	0.987334	−	0.158655i	$-0.0507157\pi$
$770$	2.50000	+	12.9904i	0.0900937	+	0.468141i
$771$		0			0
$772$	−2.50000	+	4.33013i	−0.0899770	+	0.155845i
$773$	−5.00000	+	8.66025i	−0.179838	+	0.311488i	−0.941825	−	0.336104i	$-0.890891\pi$
$773$	−5.00000	+	8.66025i	−0.179838	+	0.311488i	0.761987	+	0.647592i	$0.224224\pi$
$774$		0			0
$775$	6.00000	+	10.3923i	0.215526	+	0.373303i
$776$	−3.50000	−	6.06218i	−0.125643	−	0.217620i
$777$		0			0
$778$	1.00000	−	1.73205i	0.0358517	−	0.0620970i
$779$		0			0
$780$		0			0
$781$	10.0000			0.357828
$782$	−8.00000	−	13.8564i	−0.286079	−	0.495504i
$783$		0			0
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$	2.00000	+	3.46410i	0.0713831	+	0.123639i
$786$		0			0
$787$	9.00000	+	15.5885i	0.320815	+	0.555668i	0.980656	−	0.195737i	$-0.0627098\pi$
$787$	9.00000	+	15.5885i	0.320815	+	0.555668i	−0.659841	+	0.751405i	$0.729376\pi$
$788$	−1.00000	−	1.73205i	−0.0356235	−	0.0617018i
$789$		0			0
$790$	−1.50000	−	2.59808i	−0.0533676	−	0.0924354i
$791$	8.00000	+	41.5692i	0.284447	+	1.47803i
$792$		0			0
$793$		0			0
$794$	36.0000			1.27759
$795$		0			0
$796$	−4.00000			−0.141776
$797$	−10.5000	+	18.1865i	−0.371929	+	0.644200i	−0.989862	−	0.142031i	$-0.954637\pi$
$797$	−10.5000	+	18.1865i	−0.371929	+	0.644200i	0.617933	+	0.786231i	$0.287970\pi$
$798$		0			0
$799$	−12.0000	−	20.7846i	−0.424529	−	0.735307i
$800$	2.00000	+	3.46410i	0.0707107	+	0.122474i
$801$		0			0
$802$	−12.0000	+	20.7846i	−0.423735	+	0.733930i
$803$	−25.0000	+	43.3013i	−0.882231	+	1.52807i
$804$		0			0
$805$	−8.00000	+	6.92820i	−0.281963	+	0.244187i
$806$		0			0
$807$		0			0
$808$	10.0000			0.351799
$809$	−20.0000	+	34.6410i	−0.703163	+	1.21791i	0.264188	+	0.964471i	$0.414896\pi$
$809$	−20.0000	+	34.6410i	−0.703163	+	1.21791i	−0.967351	+	0.253442i	$0.918437\pi$
$810$		0			0
$811$	−14.0000			−0.491606			−0.245803	−	0.969320i	$-0.579052\pi$
$811$	−14.0000			−0.491606			−0.245803	+	0.969320i	$0.579052\pi$
$812$	−2.50000	−	12.9904i	−0.0877328	−	0.455873i
$813$		0			0
$814$	−20.0000			−0.701000
$815$	2.00000	+	3.46410i	0.0700569	+	0.121342i
$816$		0			0
$817$	−8.00000	+	13.8564i	−0.279885	+	0.484774i
$818$	−25.0000			−0.874105
$819$		0			0
$820$		0			0
$821$	12.5000	−	21.6506i	0.436253	−	0.755612i	−0.561144	−	0.827718i	$-0.689639\pi$
$821$	12.5000	−	21.6506i	0.436253	−	0.755612i	0.997397	+	0.0721058i	$0.0229719\pi$
$822$		0			0
$823$	−20.0000	−	34.6410i	−0.697156	−	1.20751i	−0.969448	−	0.245295i	$-0.921115\pi$
$823$	−20.0000	−	34.6410i	−0.697156	−	1.20751i	0.272292	−	0.962215i	$-0.412218\pi$
$824$	8.00000			0.278693
$825$		0			0
$826$	−22.0000	+	19.0526i	−0.765478	+	0.662923i
$827$	9.00000			0.312961			0.156480	−	0.987681i	$-0.449985\pi$
$827$	9.00000			0.312961			0.156480	+	0.987681i	$0.449985\pi$
$828$		0			0
$829$	16.0000	−	27.7128i	0.555703	−	0.962506i	−0.442145	−	0.896943i	$-0.645783\pi$
$829$	16.0000	−	27.7128i	0.555703	−	0.962506i	0.997848	−	0.0655624i	$-0.0208842\pi$
$830$	−7.00000			−0.242974
$831$		0			0
$832$		0			0
$833$	−22.0000	−	17.3205i	−0.762255	−	0.600120i
$834$		0			0
$835$	7.00000	−	12.1244i	0.242245	−	0.419581i
$836$	−20.0000	+	34.6410i	−0.691714	+	1.19808i
$837$		0			0
$838$		0			0
$839$	14.0000	+	24.2487i	0.483334	+	0.837158i	0.999817	−	0.0191389i	$-0.00609246\pi$
$839$	14.0000	+	24.2487i	0.483334	+	0.837158i	−0.516483	+	0.856297i	$0.672759\pi$
$840$		0			0
$841$	2.00000	−	3.46410i	0.0689655	−	0.119452i
$842$	30.0000			1.03387
$843$		0			0
$844$	2.00000			0.0688428
$845$	6.50000	+	11.2583i	0.223607	+	0.387298i
$846$		0			0
$847$	28.0000	−	24.2487i	0.962091	−	0.833196i
$848$	4.50000	+	7.79423i	0.154531	+	0.267655i
$849$		0			0
$850$	−8.00000	−	13.8564i	−0.274398	−	0.475271i
$851$	−8.00000	−	13.8564i	−0.274236	−	0.474991i
$852$		0			0
$853$	−7.00000	−	12.1244i	−0.239675	−	0.415130i	0.720946	−	0.692992i	$-0.243708\pi$
$853$	−7.00000	−	12.1244i	−0.239675	−	0.415130i	−0.960621	+	0.277862i	$0.910374\pi$
$854$	15.0000	+	5.19615i	0.513289	+	0.177809i
$855$		0			0
$856$	−1.50000	−	2.59808i	−0.0512689	−	0.0888004i
$857$	−18.0000			−0.614868			−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000			−0.614868			−0.307434	+	0.951569i	$0.599470\pi$
$858$		0			0
$859$	−34.0000			−1.16007			−0.580033	−	0.814593i	$-0.696960\pi$
$859$	−34.0000			−1.16007			−0.580033	+	0.814593i	$0.696960\pi$
$860$	−1.00000	+	1.73205i	−0.0340997	+	0.0590624i
$861$		0			0
$862$	−6.00000	−	10.3923i	−0.204361	−	0.353963i
$863$	−5.00000	−	8.66025i	−0.170202	−	0.294798i	0.768288	−	0.640104i	$-0.221109\pi$
$863$	−5.00000	−	8.66025i	−0.170202	−	0.294798i	−0.938490	+	0.345305i	$0.887775\pi$
$864$		0			0
$865$	−11.0000	+	19.0526i	−0.374011	+	0.647806i
$866$	−7.00000	+	12.1244i	−0.237870	+	0.412002i
$867$		0			0
$868$	1.50000	+	7.79423i	0.0509133	+	0.264553i
$869$	−7.50000	+	12.9904i	−0.254420	+	0.440668i
$870$		0			0
$871$		0			0
$872$	1.00000	−	1.73205i	0.0338643	−	0.0586546i
$873$		0			0
$874$	−32.0000			−1.08242
$875$	−18.0000	+	15.5885i	−0.608511	+	0.526986i
$876$		0			0
$877$	−32.0000			−1.08056			−0.540282	−	0.841484i	$-0.681682\pi$
$877$	−32.0000			−1.08056			−0.540282	+	0.841484i	$0.681682\pi$
$878$	−7.50000	−	12.9904i	−0.253113	−	0.438404i
$879$		0			0
$880$	−2.50000	+	4.33013i	−0.0842750	+	0.145969i
$881$	−42.0000			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$		0			0
$883$	−40.0000			−1.34611			−0.673054	−	0.739594i	$-0.735018\pi$
$883$	−40.0000			−1.34611			−0.673054	+	0.739594i	$0.735018\pi$
$884$		0			0
$885$		0			0
$886$	−8.50000	−	14.7224i	−0.285563	−	0.494610i
$887$	36.0000			1.20876			0.604381	−	0.796696i	$-0.293421\pi$
$887$	36.0000			1.20876			0.604381	+	0.796696i	$0.293421\pi$
$888$		0			0
$889$	18.0000	−	15.5885i	0.603701	−	0.522820i
$890$	−6.00000			−0.201120
$891$		0			0
$892$	3.50000	−	6.06218i	0.117189	−	0.202977i
$893$	−48.0000			−1.60626
$894$		0			0
$895$	−6.00000	+	10.3923i	−0.200558	+	0.347376i
$896$	0.500000	+	2.59808i	0.0167038	+	0.0867956i
$897$		0			0
$898$	−8.00000	+	13.8564i	−0.266963	+	0.462394i
$899$	7.50000	−	12.9904i	0.250139	−	0.433253i
$900$		0			0
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$		0			0
$903$		0			0
$904$	−8.00000	+	13.8564i	−0.266076	+	0.460857i
$905$		0			0
$906$		0			0
$907$	12.0000			0.398453			0.199227	−	0.979953i	$-0.436157\pi$
$907$	12.0000			0.398453			0.199227	+	0.979953i	$0.436157\pi$
$908$	−1.50000	−	2.59808i	−0.0497792	−	0.0862202i
$909$		0			0
$910$		0			0
$911$	−15.0000	−	25.9808i	−0.496972	−	0.860781i	0.503022	−	0.864274i	$-0.332222\pi$
$911$	−15.0000	−	25.9808i	−0.496972	−	0.860781i	−0.999994	+	0.00349271i	$0.998888\pi$
$912$		0			0
$913$	17.5000	+	30.3109i	0.579165	+	1.00314i
$914$	−15.5000	−	26.8468i	−0.512694	−	0.888013i
$915$		0			0
$916$	10.0000	+	17.3205i	0.330409	+	0.572286i
$917$	2.00000	−	1.73205i	0.0660458	−	0.0571974i
$918$		0			0
$919$	16.0000	+	27.7128i	0.527791	+	0.914161i	0.999475	+	0.0323936i	$0.0103130\pi$
$919$	16.0000	+	27.7128i	0.527791	+	0.914161i	−0.471684	+	0.881768i	$0.656354\pi$
$920$	−4.00000			−0.131876
$921$		0			0
$922$	−14.0000			−0.461065
$923$		0			0
$924$		0			0
$925$	−8.00000	−	13.8564i	−0.263038	−	0.455596i
$926$	−8.00000	−	13.8564i	−0.262896	−	0.455350i
$927$		0			0
$928$	2.50000	−	4.33013i	0.0820665	−	0.142143i
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	−0.812607	−	0.582812i	$-0.801952\pi$
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	0.911034	+	0.412332i	$0.135286\pi$
$930$		0			0
$931$	−52.0000	+	20.7846i	−1.70423	+	0.681188i
$932$	2.00000	−	3.46410i	0.0655122	−	0.113470i
$933$		0			0
$934$	−20.0000			−0.654420
$935$	10.0000	−	17.3205i	0.327035	−	0.566441i
$936$		0			0
$937$	35.0000			1.14340			0.571700	−	0.820463i	$-0.306284\pi$
$937$	35.0000			1.14340			0.571700	+	0.820463i	$0.306284\pi$
$938$	−4.00000	+	3.46410i	−0.130605	+	0.113107i
$939$		0			0
$940$	−6.00000			−0.195698
$941$	5.50000	+	9.52628i	0.179295	+	0.310548i	0.941639	−	0.336624i	$-0.109285\pi$
$941$	5.50000	+	9.52628i	0.179295	+	0.310548i	−0.762344	+	0.647172i	$0.775952\pi$
$942$		0			0
$943$		0			0
$944$	−11.0000			−0.358020
$945$		0			0
$946$	10.0000			0.325128
$947$	16.0000	−	27.7128i	0.519930	−	0.900545i	−0.479801	−	0.877377i	$-0.659291\pi$
$947$	16.0000	−	27.7128i	0.519930	−	0.900545i	0.999732	−	0.0231683i	$-0.00737536\pi$
$948$		0			0
$949$		0			0
$950$	−32.0000			−1.03822
$951$		0			0
$952$	−2.00000	−	10.3923i	−0.0648204	−	0.336817i
$953$	2.00000			0.0647864			0.0323932	−	0.999475i	$-0.489687\pi$
$953$	2.00000			0.0647864			0.0323932	+	0.999475i	$0.489687\pi$
$954$		0			0
$955$	−12.0000	+	20.7846i	−0.388311	+	0.672574i
$956$	−12.0000			−0.388108
$957$		0			0
$958$	−19.0000	+	32.9090i	−0.613862	+	1.06324i
$959$	−4.00000	+	3.46410i	−0.129167	+	0.111862i
$960$		0			0
$961$	11.0000	−	19.0526i	0.354839	−	0.614599i
$962$		0			0
$963$		0			0
$964$	12.5000	+	21.6506i	0.402598	+	0.697320i
$965$	−2.50000	−	4.33013i	−0.0804778	−	0.139392i
$966$		0			0
$967$	30.5000	−	52.8275i	0.980814	−	1.69882i	0.321578	−	0.946883i	$-0.395787\pi$
$967$	30.5000	−	52.8275i	0.980814	−	1.69882i	0.659236	−	0.751936i	$-0.270880\pi$
$968$	14.0000			0.449977
$969$		0			0
$970$	7.00000			0.224756
$971$	−7.50000	−	12.9904i	−0.240686	−	0.416881i	0.720224	−	0.693742i	$-0.244039\pi$
$971$	−7.50000	−	12.9904i	−0.240686	−	0.416881i	−0.960910	+	0.276861i	$0.910706\pi$
$972$		0			0
$973$	−7.00000	−	36.3731i	−0.224410	−	1.16607i
$974$	−2.50000	−	4.33013i	−0.0801052	−	0.138746i
$975$		0			0
$976$	3.00000	+	5.19615i	0.0960277	+	0.166325i
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	0.999734	−	0.0230645i	$-0.00734232\pi$
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	−0.519841	+	0.854263i	$0.674009\pi$
$978$		0			0
$979$	15.0000	+	25.9808i	0.479402	+	0.830349i
$980$	−6.50000	+	2.59808i	−0.207635	+	0.0829925i
$981$		0			0
$982$	−4.50000	−	7.79423i	−0.143601	−	0.248724i
$983$	−60.0000			−1.91370			−0.956851	−	0.290578i	$-0.906153\pi$
$983$	−60.0000			−1.91370			−0.956851	+	0.290578i	$0.906153\pi$
$984$		0			0
$985$	2.00000			0.0637253
$986$	−10.0000	+	17.3205i	−0.318465	+	0.551597i
$987$		0			0
$988$		0			0
$989$	4.00000	+	6.92820i	0.127193	+	0.220304i
$990$		0			0
$991$	−23.5000	+	40.7032i	−0.746502	+	1.29298i	0.202988	+	0.979181i	$0.434935\pi$
$991$	−23.5000	+	40.7032i	−0.746502	+	1.29298i	−0.949490	+	0.313798i	$0.898398\pi$
$992$	−1.50000	+	2.59808i	−0.0476250	+	0.0824890i
$993$		0			0
$994$	1.00000	+	5.19615i	0.0317181	+	0.164812i
$995$	2.00000	−	3.46410i	0.0634043	−	0.109819i
$996$		0			0
$997$	38.0000			1.20347			0.601736	−	0.798695i	$-0.294476\pi$
$997$	38.0000			1.20347			0.601736	+	0.798695i	$0.294476\pi$
$998$	−5.00000	+	8.66025i	−0.158272	+	0.274136i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.h.e.109.1		2
3.2	odd	2		1134.2.h.l.109.1		2
7.2	even	3		1134.2.e.l.919.1		2
9.2	odd	6		1134.2.e.e.865.1		2
9.4	even	3		42.2.e.a.25.1	✓	2
9.5	odd	6		126.2.g.c.109.1		2
9.7	even	3		1134.2.e.l.865.1		2
21.2	odd	6		1134.2.e.e.919.1		2
36.23	even	6		1008.2.s.k.865.1		2
36.31	odd	6		336.2.q.b.193.1		2
45.4	even	6		1050.2.i.l.151.1		2
45.13	odd	12		1050.2.o.a.949.1		4
45.22	odd	12		1050.2.o.a.949.2		4
63.2	odd	6		1134.2.h.l.541.1		2
63.4	even	3		294.2.a.e.1.1		1
63.5	even	6		882.2.g.i.667.1		2
63.13	odd	6		294.2.e.b.67.1		2
63.16	even	3	inner	1134.2.h.e.541.1		2
63.23	odd	6		126.2.g.c.37.1		2
63.31	odd	6		294.2.a.f.1.1		1
63.32	odd	6		882.2.a.c.1.1		1
63.40	odd	6		294.2.e.b.79.1		2
63.41	even	6		882.2.g.i.361.1		2
63.58	even	3		42.2.e.a.37.1	yes	2
63.59	even	6		882.2.a.d.1.1		1
72.13	even	6		1344.2.q.g.193.1		2
72.67	odd	6		1344.2.q.s.193.1		2
252.23	even	6		1008.2.s.k.289.1		2
252.31	even	6		2352.2.a.f.1.1		1
252.59	odd	6		7056.2.a.bl.1.1		1
252.67	odd	6		2352.2.a.t.1.1		1
252.95	even	6		7056.2.a.w.1.1		1
252.103	even	6		2352.2.q.u.961.1		2
252.139	even	6		2352.2.q.u.1537.1		2
252.247	odd	6		336.2.q.b.289.1		2
315.4	even	6		7350.2.a.bl.1.1		1
315.58	odd	12		1050.2.o.a.499.2		4
315.94	odd	6		7350.2.a.q.1.1		1
315.184	even	6		1050.2.i.l.751.1		2
315.247	odd	12		1050.2.o.a.499.1		4
504.67	odd	6		9408.2.a.q.1.1		1
504.157	odd	6		9408.2.a.z.1.1		1
504.283	even	6		9408.2.a.cr.1.1		1
504.373	even	6		1344.2.q.g.961.1		2
504.445	even	6		9408.2.a.ce.1.1		1
504.499	odd	6		1344.2.q.s.961.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.e.a.25.1	✓	2	9.4	even	3
42.2.e.a.37.1	yes	2	63.58	even	3
126.2.g.c.37.1		2	63.23	odd	6
126.2.g.c.109.1		2	9.5	odd	6
294.2.a.e.1.1		1	63.4	even	3
294.2.a.f.1.1		1	63.31	odd	6
294.2.e.b.67.1		2	63.13	odd	6
294.2.e.b.79.1		2	63.40	odd	6
336.2.q.b.193.1		2	36.31	odd	6
336.2.q.b.289.1		2	252.247	odd	6
882.2.a.c.1.1		1	63.32	odd	6
882.2.a.d.1.1		1	63.59	even	6
882.2.g.i.361.1		2	63.41	even	6
882.2.g.i.667.1		2	63.5	even	6
1008.2.s.k.289.1		2	252.23	even	6
1008.2.s.k.865.1		2	36.23	even	6
1050.2.i.l.151.1		2	45.4	even	6
1050.2.i.l.751.1		2	315.184	even	6
1050.2.o.a.499.1		4	315.247	odd	12
1050.2.o.a.499.2		4	315.58	odd	12
1050.2.o.a.949.1		4	45.13	odd	12
1050.2.o.a.949.2		4	45.22	odd	12
1134.2.e.e.865.1		2	9.2	odd	6
1134.2.e.e.919.1		2	21.2	odd	6
1134.2.e.l.865.1		2	9.7	even	3
1134.2.e.l.919.1		2	7.2	even	3
1134.2.h.e.109.1		2	1.1	even	1	trivial
1134.2.h.e.541.1		2	63.16	even	3	inner
1134.2.h.l.109.1		2	3.2	odd	2
1134.2.h.l.541.1		2	63.2	odd	6
1344.2.q.g.193.1		2	72.13	even	6
1344.2.q.g.961.1		2	504.373	even	6
1344.2.q.s.193.1		2	72.67	odd	6
1344.2.q.s.961.1		2	504.499	odd	6
2352.2.a.f.1.1		1	252.31	even	6
2352.2.a.t.1.1		1	252.67	odd	6
2352.2.q.u.961.1		2	252.103	even	6
2352.2.q.u.1537.1		2	252.139	even	6
7056.2.a.w.1.1		1	252.95	even	6
7056.2.a.bl.1.1		1	252.59	odd	6
7350.2.a.q.1.1		1	315.94	odd	6
7350.2.a.bl.1.1		1	315.4	even	6
9408.2.a.q.1.1		1	504.67	odd	6
9408.2.a.z.1.1		1	504.157	odd	6
9408.2.a.ce.1.1		1	504.445	even	6
9408.2.a.cr.1.1		1	504.283	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +5.00000 q^{11} +(0.500000 + 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(-4.00000 - 6.92820i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-2.50000 + 4.33013i) q^{22} -4.00000 q^{23} -4.00000 q^{25} +(-2.50000 - 0.866025i) q^{28} +(2.50000 + 4.33013i) q^{29} +(-1.50000 - 2.59808i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.00000 + 3.46410i) q^{34} +(2.00000 - 1.73205i) q^{35} +(2.00000 + 3.46410i) q^{37} +8.00000 q^{38} +1.00000 q^{40} +(-1.00000 - 1.73205i) q^{43} +(-2.50000 - 4.33013i) q^{44} +(2.00000 - 3.46410i) q^{46} +(3.00000 - 5.19615i) q^{47} +(1.00000 - 6.92820i) q^{49} +(2.00000 - 3.46410i) q^{50} +(4.50000 - 7.79423i) q^{53} +5.00000 q^{55} +(2.00000 - 1.73205i) q^{56} -5.00000 q^{58} +(5.50000 + 9.52628i) q^{59} +(3.00000 - 5.19615i) q^{61} +3.00000 q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{67} -4.00000 q^{68} +(0.500000 + 2.59808i) q^{70} +2.00000 q^{71} +(-5.00000 + 8.66025i) q^{73} -4.00000 q^{74} +(-4.00000 + 6.92820i) q^{76} +(10.0000 - 8.66025i) q^{77} +(-1.50000 + 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(3.50000 + 6.06218i) q^{83} +(2.00000 - 3.46410i) q^{85} +2.00000 q^{86} +5.00000 q^{88} +(3.00000 + 5.19615i) q^{89} +(2.00000 + 3.46410i) q^{92} +(3.00000 + 5.19615i) q^{94} +(-4.00000 - 6.92820i) q^{95} +(-3.50000 - 6.06218i) q^{97} +(5.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 2 q^{5} + 4 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 + 2 * q^5 + 4 * q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} + 2 q^{5} + 4 q^{7} + 2 q^{8} - q^{10} + 10 q^{11} + q^{14} - q^{16} + 4 q^{17} - 8 q^{19} - q^{20} - 5 q^{22} - 8 q^{23} - 8 q^{25} - 5 q^{28} + 5 q^{29} - 3 q^{31} - q^{32} + 4 q^{34} + 4 q^{35} + 4 q^{37} + 16 q^{38} + 2 q^{40} - 2 q^{43} - 5 q^{44} + 4 q^{46} + 6 q^{47} + 2 q^{49} + 4 q^{50} + 9 q^{53} + 10 q^{55} + 4 q^{56} - 10 q^{58} + 11 q^{59} + 6 q^{61} + 6 q^{62} + 2 q^{64} + 2 q^{67} - 8 q^{68} + q^{70} + 4 q^{71} - 10 q^{73} - 8 q^{74} - 8 q^{76} + 20 q^{77} - 3 q^{79} - q^{80} + 7 q^{83} + 4 q^{85} + 4 q^{86} + 10 q^{88} + 6 q^{89} + 4 q^{92} + 6 q^{94} - 8 q^{95} - 7 q^{97} + 11 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + 2 * q^5 + 4 * q^7 + 2 * q^8 - q^10 + 10 * q^11 + q^14 - q^16 + 4 * q^17 - 8 * q^19 - q^20 - 5 * q^22 - 8 * q^23 - 8 * q^25 - 5 * q^28 + 5 * q^29 - 3 * q^31 - q^32 + 4 * q^34 + 4 * q^35 + 4 * q^37 + 16 * q^38 + 2 * q^40 - 2 * q^43 - 5 * q^44 + 4 * q^46 + 6 * q^47 + 2 * q^49 + 4 * q^50 + 9 * q^53 + 10 * q^55 + 4 * q^56 - 10 * q^58 + 11 * q^59 + 6 * q^61 + 6 * q^62 + 2 * q^64 + 2 * q^67 - 8 * q^68 + q^70 + 4 * q^71 - 10 * q^73 - 8 * q^74 - 8 * q^76 + 20 * q^77 - 3 * q^79 - q^80 + 7 * q^83 + 4 * q^85 + 4 * q^86 + 10 * q^88 + 6 * q^89 + 4 * q^92 + 6 * q^94 - 8 * q^95 - 7 * q^97 + 11 * q^98

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