LMFDB - Embedded newform 1134.2.h.b.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:	$0$
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 378)
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.b.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +(-2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +(-2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{10} +5.00000 q^{11} +(-3.00000 - 5.19615i) q^{13} +(0.500000 + 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(2.00000 - 3.46410i) q^{19} +(1.00000 - 1.73205i) q^{20} +(-2.50000 - 4.33013i) q^{22} -4.00000 q^{23} -1.00000 q^{25} +(-3.00000 + 5.19615i) q^{26} +(2.00000 - 1.73205i) q^{28} +(-3.50000 + 6.06218i) q^{29} +(-1.50000 + 2.59808i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{34} +(5.00000 + 1.73205i) q^{35} +(-4.00000 + 6.92820i) q^{37} -4.00000 q^{38} -2.00000 q^{40} +(3.00000 + 5.19615i) q^{41} +(-4.00000 + 6.92820i) q^{43} +(-2.50000 + 4.33013i) q^{44} +(2.00000 + 3.46410i) q^{46} +(-3.00000 - 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +(0.500000 + 0.866025i) q^{50} +6.00000 q^{52} +(3.00000 + 5.19615i) q^{53} -10.0000 q^{55} +(-2.50000 - 0.866025i) q^{56} +7.00000 q^{58} +(-3.50000 + 6.06218i) q^{59} +3.00000 q^{62} +1.00000 q^{64} +(6.00000 + 10.3923i) q^{65} +(-5.00000 + 8.66025i) q^{67} -4.00000 q^{68} +(-1.00000 - 5.19615i) q^{70} -4.00000 q^{71} +(-6.50000 - 11.2583i) q^{73} +8.00000 q^{74} +(2.00000 + 3.46410i) q^{76} +(-12.5000 - 4.33013i) q^{77} +(1.50000 + 2.59808i) q^{79} +(1.00000 + 1.73205i) q^{80} +(3.00000 - 5.19615i) q^{82} +(3.50000 - 6.06218i) q^{83} +(-4.00000 - 6.92820i) q^{85} +8.00000 q^{86} +5.00000 q^{88} +(-3.00000 + 5.19615i) q^{89} +(3.00000 + 15.5885i) q^{91} +(2.00000 - 3.46410i) q^{92} +(-3.00000 + 5.19615i) q^{94} +(-4.00000 + 6.92820i) q^{95} +(2.50000 - 4.33013i) q^{97} +(1.00000 - 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - 4 q^{5} - 5 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 - 4 * q^5 - 5 * q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} - 4 q^{5} - 5 q^{7} + 2 q^{8} + 2 q^{10} + 10 q^{11} - 6 q^{13} + q^{14} - q^{16} + 4 q^{17} + 4 q^{19} + 2 q^{20} - 5 q^{22} - 8 q^{23} - 2 q^{25} - 6 q^{26} + 4 q^{28} - 7 q^{29} - 3 q^{31} - q^{32} + 4 q^{34} + 10 q^{35} - 8 q^{37} - 8 q^{38} - 4 q^{40} + 6 q^{41} - 8 q^{43} - 5 q^{44} + 4 q^{46} - 6 q^{47} + 11 q^{49} + q^{50} + 12 q^{52} + 6 q^{53} - 20 q^{55} - 5 q^{56} + 14 q^{58} - 7 q^{59} + 6 q^{62} + 2 q^{64} + 12 q^{65} - 10 q^{67} - 8 q^{68} - 2 q^{70} - 8 q^{71} - 13 q^{73} + 16 q^{74} + 4 q^{76} - 25 q^{77} + 3 q^{79} + 2 q^{80} + 6 q^{82} + 7 q^{83} - 8 q^{85} + 16 q^{86} + 10 q^{88} - 6 q^{89} + 6 q^{91} + 4 q^{92} - 6 q^{94} - 8 q^{95} + 5 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 - 4 * q^5 - 5 * q^7 + 2 * q^8 + 2 * q^10 + 10 * q^11 - 6 * q^13 + q^14 - q^16 + 4 * q^17 + 4 * q^19 + 2 * q^20 - 5 * q^22 - 8 * q^23 - 2 * q^25 - 6 * q^26 + 4 * q^28 - 7 * q^29 - 3 * q^31 - q^32 + 4 * q^34 + 10 * q^35 - 8 * q^37 - 8 * q^38 - 4 * q^40 + 6 * q^41 - 8 * q^43 - 5 * q^44 + 4 * q^46 - 6 * q^47 + 11 * q^49 + q^50 + 12 * q^52 + 6 * q^53 - 20 * q^55 - 5 * q^56 + 14 * q^58 - 7 * q^59 + 6 * q^62 + 2 * q^64 + 12 * q^65 - 10 * q^67 - 8 * q^68 - 2 * q^70 - 8 * q^71 - 13 * q^73 + 16 * q^74 + 4 * q^76 - 25 * q^77 + 3 * q^79 + 2 * q^80 + 6 * q^82 + 7 * q^83 - 8 * q^85 + 16 * q^86 + 10 * q^88 - 6 * q^89 + 6 * q^91 + 4 * q^92 - 6 * q^94 - 8 * q^95 + 5 * q^97 + 2 * 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
$5$	−2.00000			−0.894427			−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000			−0.894427			−0.447214	+	0.894427i	$0.647584\pi$
$6$		0			0
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$	1.00000			0.353553
$9$		0			0
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	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
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	−0.896410	−	0.443227i	$-0.853834\pi$
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	0.0643593	−	0.997927i	$-0.479500\pi$
$14$	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	0.999853	−	0.0171533i	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$		0			0
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$	1.00000	−	1.73205i	0.223607	−	0.387298i
$21$		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
$25$	−1.00000			−0.200000
$26$	−3.00000	+	5.19615i	−0.588348	+	1.01905i
$27$		0			0
$28$	2.00000	−	1.73205i	0.377964	−	0.327327i
$29$	−3.50000	+	6.06218i	−0.649934	+	1.12572i	0.333205	+	0.942855i	$0.391870\pi$
$29$	−3.50000	+	6.06218i	−0.649934	+	1.12572i	−0.983138	+	0.182864i	$0.941463\pi$
$30$		0			0
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	−0.968709	−	0.248199i	$-0.920161\pi$
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	0.699301	+	0.714827i	$0.253495\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	2.00000	−	3.46410i	0.342997	−	0.594089i
$35$	5.00000	+	1.73205i	0.845154	+	0.292770i
$36$		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	$0.938240\pi$
$38$	−4.00000			−0.648886
$39$		0			0
$40$	−2.00000			−0.316228
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	0.999353	−	0.0359748i	$-0.0114536\pi$
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	−0.530831	+	0.847477i	$0.678120\pi$
$42$		0			0
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$	−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	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$		0			0
$52$	6.00000			0.832050
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$		0			0
$55$	−10.0000			−1.34840
$56$	−2.50000	−	0.866025i	−0.334077	−	0.115728i
$57$		0			0
$58$	7.00000			0.919145
$59$	−3.50000	+	6.06218i	−0.455661	+	0.789228i	−0.998726	−	0.0504625i	$-0.983930\pi$
$59$	−3.50000	+	6.06218i	−0.455661	+	0.789228i	0.543065	+	0.839691i	$0.317264\pi$
$60$		0			0
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$	3.00000			0.381000
$63$		0			0
$64$	1.00000			0.125000
$65$	6.00000	+	10.3923i	0.744208	+	1.28901i
$66$		0			0
$67$	−5.00000	+	8.66025i	−0.610847	+	1.05802i	0.380251	+	0.924883i	$0.375838\pi$
$67$	−5.00000	+	8.66025i	−0.610847	+	1.05802i	−0.991098	+	0.133135i	$0.957496\pi$
$68$	−4.00000			−0.485071
$69$		0			0
$70$	−1.00000	−	5.19615i	−0.119523	−	0.621059i
$71$	−4.00000			−0.474713			−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000			−0.474713			−0.237356	+	0.971423i	$0.576281\pi$
$72$		0			0
$73$	−6.50000	−	11.2583i	−0.760767	−	1.31769i	−0.942455	−	0.334332i	$-0.891489\pi$
$73$	−6.50000	−	11.2583i	−0.760767	−	1.31769i	0.181688	−	0.983356i	$-0.441844\pi$
$74$	8.00000			0.929981
$75$		0			0
$76$	2.00000	+	3.46410i	0.229416	+	0.397360i
$77$	−12.5000	−	4.33013i	−1.42451	−	0.493464i
$78$		0			0
$79$	1.50000	+	2.59808i	0.168763	+	0.292306i	0.937985	−	0.346675i	$-0.112689\pi$
$79$	1.50000	+	2.59808i	0.168763	+	0.292306i	−0.769222	+	0.638982i	$0.779356\pi$
$80$	1.00000	+	1.73205i	0.111803	+	0.193649i
$81$		0			0
$82$	3.00000	−	5.19615i	0.331295	−	0.573819i
$83$	3.50000	−	6.06218i	0.384175	−	0.665410i	−0.607479	−	0.794335i	$-0.707819\pi$
$83$	3.50000	−	6.06218i	0.384175	−	0.665410i	0.991654	+	0.128925i	$0.0411526\pi$
$84$		0			0
$85$	−4.00000	−	6.92820i	−0.433861	−	0.751469i
$86$	8.00000			0.862662
$87$		0			0
$88$	5.00000			0.533002
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$		0			0
$91$	3.00000	+	15.5885i	0.314485	+	1.63411i
$92$	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
$97$	2.50000	−	4.33013i	0.253837	−	0.439658i	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	2.50000	−	4.33013i	0.253837	−	0.439658i	0.964579	+	0.263795i	$0.0849741\pi$
$98$	1.00000	−	6.92820i	0.101015	−	0.699854i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−5.00000			−0.497519			−0.248759	−	0.968565i	$-0.580023\pi$
$101$	−5.00000			−0.497519			−0.248759	+	0.968565i	$0.580023\pi$
$102$		0			0
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$		0			0
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$		0			0
$109$	−8.00000	−	13.8564i	−0.766261	−	1.32720i	−0.939577	−	0.342337i	$-0.888782\pi$
$109$	−8.00000	−	13.8564i	−0.766261	−	1.32720i	0.173316	−	0.984866i	$-0.444552\pi$
$110$	5.00000	+	8.66025i	0.476731	+	0.825723i
$111$		0			0
$112$	0.500000	+	2.59808i	0.0472456	+	0.245495i
$113$	−2.00000	−	3.46410i	−0.188144	−	0.325875i	0.756487	−	0.654008i	$-0.226914\pi$
$113$	−2.00000	−	3.46410i	−0.188144	−	0.325875i	−0.944632	+	0.328133i	$0.893581\pi$
$114$		0			0
$115$	8.00000			0.746004
$116$	−3.50000	−	6.06218i	−0.324967	−	0.562859i
$117$		0			0
$118$	7.00000			0.644402
$119$	−2.00000	−	10.3923i	−0.183340	−	0.952661i
$120$		0			0
$121$	14.0000			1.27273
$122$		0			0
$123$		0			0
$124$	−1.50000	−	2.59808i	−0.134704	−	0.233314i
$125$	12.0000			1.07331
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	6.00000	−	10.3923i	0.526235	−	0.911465i
$131$	13.0000			1.13582			0.567908	−	0.823092i	$-0.307753\pi$
$131$	13.0000			1.13582			0.567908	+	0.823092i	$0.307753\pi$
$132$		0			0
$133$	−8.00000	+	6.92820i	−0.693688	+	0.600751i
$134$	10.0000			0.863868
$135$		0			0
$136$	2.00000	+	3.46410i	0.171499	+	0.297044i
$137$	−8.00000			−0.683486			−0.341743	−	0.939793i	$-0.611017\pi$
$137$	−8.00000			−0.683486			−0.341743	+	0.939793i	$0.611017\pi$
$138$		0			0
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	0.984297	−	0.176522i	$-0.0564848\pi$
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	−0.645021	+	0.764165i	$0.723151\pi$
$140$	−4.00000	+	3.46410i	−0.338062	+	0.292770i
$141$		0			0
$142$	2.00000	+	3.46410i	0.167836	+	0.290701i
$143$	−15.0000	−	25.9808i	−1.25436	−	2.17262i
$144$		0			0
$145$	7.00000	−	12.1244i	0.581318	−	1.00687i
$146$	−6.50000	+	11.2583i	−0.537944	+	0.931746i
$147$		0			0
$148$	−4.00000	−	6.92820i	−0.328798	−	0.569495i
$149$	9.00000			0.737309			0.368654	−	0.929567i	$-0.379819\pi$
$149$	9.00000			0.737309			0.368654	+	0.929567i	$0.379819\pi$
$150$		0			0
$151$	−17.0000			−1.38344			−0.691720	−	0.722166i	$-0.743147\pi$
$151$	−17.0000			−1.38344			−0.691720	+	0.722166i	$0.743147\pi$
$152$	2.00000	−	3.46410i	0.162221	−	0.280976i
$153$		0			0
$154$	2.50000	+	12.9904i	0.201456	+	1.04679i
$155$	3.00000	−	5.19615i	0.240966	−	0.417365i
$156$		0			0
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	1.50000	−	2.59808i	0.119334	−	0.206692i
$159$		0			0
$160$	1.00000	−	1.73205i	0.0790569	−	0.136931i
$161$	10.0000	+	3.46410i	0.788110	+	0.273009i
$162$		0			0
$163$	−1.00000	+	1.73205i	−0.0783260	+	0.135665i	−0.902528	−	0.430632i	$-0.858291\pi$
$163$	−1.00000	+	1.73205i	−0.0783260	+	0.135665i	0.824202	+	0.566296i	$0.191624\pi$
$164$	−6.00000			−0.468521
$165$		0			0
$166$	−7.00000			−0.543305
$167$	7.00000	+	12.1244i	0.541676	+	0.938211i	0.998808	+	0.0488118i	$0.0155435\pi$
$167$	7.00000	+	12.1244i	0.541676	+	0.938211i	−0.457132	+	0.889399i	$0.651123\pi$
$168$		0			0
$169$	−11.5000	+	19.9186i	−0.884615	+	1.53220i
$170$	−4.00000	+	6.92820i	−0.306786	+	0.531369i
$171$		0			0
$172$	−4.00000	−	6.92820i	−0.304997	−	0.528271i
$173$	−0.500000	−	0.866025i	−0.0380143	−	0.0658427i	0.846392	−	0.532560i	$-0.178770\pi$
$173$	−0.500000	−	0.866025i	−0.0380143	−	0.0658427i	−0.884407	+	0.466717i	$0.845437\pi$
$174$		0			0
$175$	2.50000	+	0.866025i	0.188982	+	0.0654654i
$176$	−2.50000	−	4.33013i	−0.188445	−	0.326396i
$177$		0			0
$178$	6.00000			0.449719
$179$	7.50000	+	12.9904i	0.560576	+	0.970947i	0.997446	+	0.0714220i	$0.0227537\pi$
$179$	7.50000	+	12.9904i	0.560576	+	0.970947i	−0.436870	+	0.899525i	$0.643913\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$	12.0000	−	10.3923i	0.889499	−	0.770329i
$183$		0			0
$184$	−4.00000			−0.294884
$185$	8.00000	−	13.8564i	0.588172	−	1.01874i
$186$		0			0
$187$	10.0000	+	17.3205i	0.731272	+	1.26660i
$188$	6.00000			0.437595
$189$		0			0
$190$	8.00000			0.580381
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	0.982828	+	0.184525i	$0.0590746\pi$
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	−0.331611	+	0.943416i	$0.607592\pi$
$192$		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	$-0.0730182\pi$
$194$	−5.00000			−0.358979
$195$		0			0
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$	−25.0000			−1.78118			−0.890588	−	0.454811i	$-0.849707\pi$
$197$	−25.0000			−1.78118			−0.890588	+	0.454811i	$0.849707\pi$
$198$		0			0
$199$	9.50000	+	16.4545i	0.673437	+	1.16643i	0.976923	+	0.213591i	$0.0685161\pi$
$199$	9.50000	+	16.4545i	0.673437	+	1.16643i	−0.303486	+	0.952836i	$0.598151\pi$
$200$	−1.00000			−0.0707107
$201$		0			0
$202$	2.50000	+	4.33013i	0.175899	+	0.304667i
$203$	14.0000	−	12.1244i	0.982607	−	0.850963i
$204$		0			0
$205$	−6.00000	−	10.3923i	−0.419058	−	0.725830i
$206$	−4.00000	−	6.92820i	−0.278693	−	0.482711i
$207$		0			0
$208$	−3.00000	+	5.19615i	−0.208013	+	0.360288i
$209$	10.0000	−	17.3205i	0.691714	−	1.19808i
$210$		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
$214$	12.0000			0.820303
$215$	8.00000	−	13.8564i	0.545595	−	0.944999i
$216$		0			0
$217$	6.00000	−	5.19615i	0.407307	−	0.352738i
$218$	−8.00000	+	13.8564i	−0.541828	+	0.938474i
$219$		0			0
$220$	5.00000	−	8.66025i	0.337100	−	0.583874i
$221$	12.0000	−	20.7846i	0.807207	−	1.39812i
$222$		0			0
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	−0.848799	−	0.528716i	$-0.822674\pi$
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	0.882281	+	0.470723i	$0.156007\pi$
$224$	2.00000	−	1.73205i	0.133631	−	0.115728i
$225$		0			0
$226$	−2.00000	+	3.46410i	−0.133038	+	0.230429i
$227$	−27.0000			−1.79205			−0.896026	−	0.444001i	$-0.853559\pi$
$227$	−27.0000			−1.79205			−0.896026	+	0.444001i	$0.853559\pi$
$228$		0			0
$229$	4.00000			0.264327			0.132164	−	0.991228i	$-0.457808\pi$
$229$	4.00000			0.264327			0.132164	+	0.991228i	$0.457808\pi$
$230$	−4.00000	−	6.92820i	−0.263752	−	0.456832i
$231$		0			0
$232$	−3.50000	+	6.06218i	−0.229786	+	0.398001i
$233$	11.0000	−	19.0526i	0.720634	−	1.24817i	−0.240112	−	0.970745i	$-0.577184\pi$
$233$	11.0000	−	19.0526i	0.720634	−	1.24817i	0.960746	−	0.277429i	$-0.0894825\pi$
$234$		0			0
$235$	6.00000	+	10.3923i	0.391397	+	0.677919i
$236$	−3.50000	−	6.06218i	−0.227831	−	0.394614i
$237$		0			0
$238$	−8.00000	+	6.92820i	−0.518563	+	0.449089i
$239$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$239$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$240$		0			0
$241$	−1.00000			−0.0644157			−0.0322078	−	0.999481i	$-0.510254\pi$
$241$	−1.00000			−0.0644157			−0.0322078	+	0.999481i	$0.510254\pi$
$242$	−7.00000	−	12.1244i	−0.449977	−	0.779383i
$243$		0			0
$244$		0			0
$245$	−11.0000	−	8.66025i	−0.702764	−	0.553283i
$246$		0			0
$247$	−24.0000			−1.52708
$248$	−1.50000	+	2.59808i	−0.0952501	+	0.164978i
$249$		0			0
$250$	−6.00000	−	10.3923i	−0.379473	−	0.657267i
$251$	−21.0000			−1.32551			−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000			−1.32551			−0.662754	+	0.748837i	$0.730613\pi$
$252$		0			0
$253$	−20.0000			−1.25739
$254$		0			0
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		0			0			−	1.00000i	$-0.5\pi$
$257$		0			0				1.00000i	$0.5\pi$
$258$		0			0
$259$	16.0000	−	13.8564i	0.994192	−	0.860995i
$260$	−12.0000			−0.744208
$261$		0			0
$262$	−6.50000	−	11.2583i	−0.401571	−	0.695542i
$263$	12.0000			0.739952			0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000			0.739952			0.369976	+	0.929041i	$0.379366\pi$
$264$		0			0
$265$	−6.00000	−	10.3923i	−0.368577	−	0.638394i
$266$	10.0000	+	3.46410i	0.613139	+	0.212398i
$267$		0			0
$268$	−5.00000	−	8.66025i	−0.305424	−	0.529009i
$269$	−15.5000	−	26.8468i	−0.945052	−	1.63688i	−0.755648	−	0.654978i	$-0.772678\pi$
$269$	−15.5000	−	26.8468i	−0.945052	−	1.63688i	−0.189404	−	0.981899i	$-0.560656\pi$
$270$		0			0
$271$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$271$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$272$	2.00000	−	3.46410i	0.121268	−	0.210042i
$273$		0			0
$274$	4.00000	+	6.92820i	0.241649	+	0.418548i
$275$	−5.00000			−0.301511
$276$		0			0
$277$	2.00000			0.120168			0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000			0.120168			0.0600842	+	0.998193i	$0.480863\pi$
$278$	4.00000	−	6.92820i	0.239904	−	0.415526i
$279$		0			0
$280$	5.00000	+	1.73205i	0.298807	+	0.103510i
$281$	−1.00000	+	1.73205i	−0.0596550	+	0.103325i	−0.894311	−	0.447447i	$-0.852333\pi$
$281$	−1.00000	+	1.73205i	−0.0596550	+	0.103325i	0.834656	+	0.550772i	$0.185667\pi$
$282$		0			0
$283$	−8.00000	+	13.8564i	−0.475551	+	0.823678i	−0.999608	−	0.0280052i	$-0.991084\pi$
$283$	−8.00000	+	13.8564i	−0.475551	+	0.823678i	0.524057	+	0.851683i	$0.324418\pi$
$284$	2.00000	−	3.46410i	0.118678	−	0.205557i
$285$		0			0
$286$	−15.0000	+	25.9808i	−0.886969	+	1.53627i
$287$	−3.00000	−	15.5885i	−0.177084	−	0.920158i
$288$		0			0
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	−14.0000			−0.822108
$291$		0			0
$292$	13.0000			0.760767
$293$	−13.5000	−	23.3827i	−0.788678	−	1.36603i	−0.926777	−	0.375613i	$-0.877432\pi$
$293$	−13.5000	−	23.3827i	−0.788678	−	1.36603i	0.138098	−	0.990419i	$-0.455901\pi$
$294$		0			0
$295$	7.00000	−	12.1244i	0.407556	−	0.705907i
$296$	−4.00000	+	6.92820i	−0.232495	+	0.402694i
$297$		0			0
$298$	−4.50000	−	7.79423i	−0.260678	−	0.451508i
$299$	12.0000	+	20.7846i	0.693978	+	1.20201i
$300$		0			0
$301$	16.0000	−	13.8564i	0.922225	−	0.798670i
$302$	8.50000	+	14.7224i	0.489120	+	0.847181i
$303$		0			0
$304$	−4.00000			−0.229416
$305$		0			0
$306$		0			0
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$	10.0000	−	8.66025i	0.569803	−	0.493464i
$309$		0			0
$310$	−6.00000			−0.340777
$311$	−11.0000	+	19.0526i	−0.623753	+	1.08037i	0.365028	+	0.930997i	$0.381059\pi$
$311$	−11.0000	+	19.0526i	−0.623753	+	1.08037i	−0.988781	+	0.149375i	$0.952274\pi$
$312$		0			0
$313$	−5.00000	−	8.66025i	−0.282617	−	0.489506i	0.689412	−	0.724370i	$-0.257869\pi$
$313$	−5.00000	−	8.66025i	−0.282617	−	0.489506i	−0.972028	+	0.234863i	$0.924536\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	−3.00000			−0.168763
$317$	16.5000	+	28.5788i	0.926732	+	1.60515i	0.788751	+	0.614713i	$0.210728\pi$
$317$	16.5000	+	28.5788i	0.926732	+	1.60515i	0.137981	+	0.990435i	$0.455939\pi$
$318$		0			0
$319$	−17.5000	+	30.3109i	−0.979812	+	1.69708i
$320$	−2.00000			−0.111803
$321$		0			0
$322$	−2.00000	−	10.3923i	−0.111456	−	0.579141i
$323$	16.0000			0.890264
$324$		0			0
$325$	3.00000	+	5.19615i	0.166410	+	0.288231i
$326$	2.00000			0.110770
$327$		0			0
$328$	3.00000	+	5.19615i	0.165647	+	0.286910i
$329$	3.00000	+	15.5885i	0.165395	+	0.859419i
$330$		0			0
$331$	−16.0000	−	27.7128i	−0.879440	−	1.52323i	−0.851957	−	0.523612i	$-0.824584\pi$
$331$	−16.0000	−	27.7128i	−0.879440	−	1.52323i	−0.0274825	−	0.999622i	$-0.508749\pi$
$332$	3.50000	+	6.06218i	0.192087	+	0.332705i
$333$		0			0
$334$	7.00000	−	12.1244i	0.383023	−	0.663415i
$335$	10.0000	−	17.3205i	0.546358	−	0.946320i
$336$		0			0
$337$	13.5000	+	23.3827i	0.735392	+	1.27374i	0.954551	+	0.298047i	$0.0963352\pi$
$337$	13.5000	+	23.3827i	0.735392	+	1.27374i	−0.219159	+	0.975689i	$0.570331\pi$
$338$	23.0000			1.25104
$339$		0			0
$340$	8.00000			0.433861
$341$	−7.50000	+	12.9904i	−0.406148	+	0.703469i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	−4.00000	+	6.92820i	−0.215666	+	0.373544i
$345$		0			0
$346$	−0.500000	+	0.866025i	−0.0268802	+	0.0465578i
$347$	13.5000	−	23.3827i	0.724718	−	1.25525i	−0.234372	−	0.972147i	$-0.575303\pi$
$347$	13.5000	−	23.3827i	0.724718	−	1.25525i	0.959090	−	0.283101i	$-0.0913633\pi$
$348$		0			0
$349$	10.0000	−	17.3205i	0.535288	−	0.927146i	−0.463862	−	0.885908i	$-0.653537\pi$
$349$	10.0000	−	17.3205i	0.535288	−	0.927146i	0.999149	−	0.0412379i	$-0.0131301\pi$
$350$	−0.500000	−	2.59808i	−0.0267261	−	0.138873i
$351$		0			0
$352$	−2.50000	+	4.33013i	−0.133250	+	0.230797i
$353$	−30.0000			−1.59674			−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000			−1.59674			−0.798369	+	0.602168i	$0.794304\pi$
$354$		0			0
$355$	8.00000			0.424596
$356$	−3.00000	−	5.19615i	−0.159000	−	0.275396i
$357$		0			0
$358$	7.50000	−	12.9904i	0.396387	−	0.686563i
$359$	−8.00000	+	13.8564i	−0.422224	+	0.731313i	−0.996157	−	0.0875892i	$-0.972084\pi$
$359$	−8.00000	+	13.8564i	−0.422224	+	0.731313i	0.573933	+	0.818902i	$0.305417\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$		0			0
$363$		0			0
$364$	−15.0000	−	5.19615i	−0.786214	−	0.272352i
$365$	13.0000	+	22.5167i	0.680451	+	1.17858i
$366$		0			0
$367$	−4.00000			−0.208798			−0.104399	−	0.994535i	$-0.533292\pi$
$367$	−4.00000			−0.208798			−0.104399	+	0.994535i	$0.533292\pi$
$368$	2.00000	+	3.46410i	0.104257	+	0.180579i
$369$		0			0
$370$	−16.0000			−0.831800
$371$	−3.00000	−	15.5885i	−0.155752	−	0.809312i
$372$		0			0
$373$	−20.0000			−1.03556			−0.517780	−	0.855514i	$-0.673242\pi$
$373$	−20.0000			−1.03556			−0.517780	+	0.855514i	$0.673242\pi$
$374$	10.0000	−	17.3205i	0.517088	−	0.895622i
$375$		0			0
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$	42.0000			2.16311
$378$		0			0
$379$	10.0000			0.513665			0.256833	−	0.966456i	$-0.417321\pi$
$379$	10.0000			0.513665			0.256833	+	0.966456i	$0.417321\pi$
$380$	−4.00000	−	6.92820i	−0.205196	−	0.355409i
$381$		0			0
$382$	9.00000	−	15.5885i	0.460480	−	0.797575i
$383$	−4.00000			−0.204390			−0.102195	−	0.994764i	$-0.532587\pi$
$383$	−4.00000			−0.204390			−0.102195	+	0.994764i	$0.532587\pi$
$384$		0			0
$385$	25.0000	+	8.66025i	1.27412	+	0.441367i
$386$	−19.0000			−0.967075
$387$		0			0
$388$	2.50000	+	4.33013i	0.126918	+	0.219829i
$389$	1.00000			0.0507020			0.0253510	−	0.999679i	$-0.491930\pi$
$389$	1.00000			0.0507020			0.0253510	+	0.999679i	$0.491930\pi$
$390$		0			0
$391$	−8.00000	−	13.8564i	−0.404577	−	0.700749i
$392$	5.50000	+	4.33013i	0.277792	+	0.218704i
$393$		0			0
$394$	12.5000	+	21.6506i	0.629741	+	1.09074i
$395$	−3.00000	−	5.19615i	−0.150946	−	0.261447i
$396$		0			0
$397$	9.00000	−	15.5885i	0.451697	−	0.782362i	−0.546795	−	0.837267i	$-0.684152\pi$
$397$	9.00000	−	15.5885i	0.451697	−	0.782362i	0.998492	+	0.0549046i	$0.0174855\pi$
$398$	9.50000	−	16.4545i	0.476192	−	0.824789i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−18.0000			−0.898877			−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000			−0.898877			−0.449439	+	0.893311i	$0.648376\pi$
$402$		0			0
$403$	18.0000			0.896644
$404$	2.50000	−	4.33013i	0.124380	−	0.215432i
$405$		0			0
$406$	−17.5000	−	6.06218i	−0.868510	−	0.300861i
$407$	−20.0000	+	34.6410i	−0.991363	+	1.71709i
$408$		0			0
$409$	5.00000	−	8.66025i	0.247234	−	0.428222i	−0.715523	−	0.698589i	$-0.753812\pi$
$409$	5.00000	−	8.66025i	0.247234	−	0.428222i	0.962757	+	0.270367i	$0.0871450\pi$
$410$	−6.00000	+	10.3923i	−0.296319	+	0.513239i
$411$		0			0
$412$	−4.00000	+	6.92820i	−0.197066	+	0.341328i
$413$	14.0000	−	12.1244i	0.688895	−	0.596601i
$414$		0			0
$415$	−7.00000	+	12.1244i	−0.343616	+	0.595161i
$416$	6.00000			0.294174
$417$		0			0
$418$	−20.0000			−0.978232
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	0.681426	−	0.731887i	$-0.261360\pi$
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	−0.974546	+	0.224189i	$0.928027\pi$
$420$		0			0
$421$	9.00000	−	15.5885i	0.438633	−	0.759735i	−0.558951	−	0.829201i	$-0.688796\pi$
$421$	9.00000	−	15.5885i	0.438633	−	0.759735i	0.997584	+	0.0694656i	$0.0221294\pi$
$422$	−13.0000	+	22.5167i	−0.632830	+	1.09609i
$423$		0			0
$424$	3.00000	+	5.19615i	0.145693	+	0.252347i
$425$	−2.00000	−	3.46410i	−0.0970143	−	0.168034i
$426$		0			0
$427$		0			0
$428$	−6.00000	−	10.3923i	−0.290021	−	0.502331i
$429$		0			0
$430$	−16.0000			−0.771589
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	0.997173	−	0.0751385i	$-0.0239399\pi$
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	−0.563658	+	0.826008i	$0.690607\pi$
$432$		0			0
$433$	−7.00000			−0.336399			−0.168199	−	0.985753i	$-0.553795\pi$
$433$	−7.00000			−0.336399			−0.168199	+	0.985753i	$0.553795\pi$
$434$	−7.50000	−	2.59808i	−0.360012	−	0.124712i
$435$		0			0
$436$	16.0000			0.766261
$437$	−8.00000	+	13.8564i	−0.382692	+	0.662842i
$438$		0			0
$439$	−1.50000	−	2.59808i	−0.0715911	−	0.123999i	0.828008	−	0.560717i	$-0.189474\pi$
$439$	−1.50000	−	2.59808i	−0.0715911	−	0.123999i	−0.899599	+	0.436717i	$0.856141\pi$
$440$	−10.0000			−0.476731
$441$		0			0
$442$	−24.0000			−1.14156
$443$	−5.50000	−	9.52628i	−0.261313	−	0.452607i	0.705278	−	0.708931i	$-0.250822\pi$
$443$	−5.50000	−	9.52628i	−0.261313	−	0.452607i	−0.966591	+	0.256323i	$0.917489\pi$
$444$		0			0
$445$	6.00000	−	10.3923i	0.284427	−	0.492642i
$446$	−1.00000			−0.0473514
$447$		0			0
$448$	−2.50000	−	0.866025i	−0.118114	−	0.0409159i
$449$	−14.0000			−0.660701			−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−14.0000			−0.660701			−0.330350	+	0.943858i	$0.607167\pi$
$450$		0			0
$451$	15.0000	+	25.9808i	0.706322	+	1.22339i
$452$	4.00000			0.188144
$453$		0			0
$454$	13.5000	+	23.3827i	0.633586	+	1.09740i
$455$	−6.00000	−	31.1769i	−0.281284	−	1.46160i
$456$		0			0
$457$	13.0000	+	22.5167i	0.608114	+	1.05328i	0.991551	+	0.129718i	$0.0414071\pi$
$457$	13.0000	+	22.5167i	0.608114	+	1.05328i	−0.383437	+	0.923567i	$0.625260\pi$
$458$	−2.00000	−	3.46410i	−0.0934539	−	0.161867i
$459$		0			0
$460$	−4.00000	+	6.92820i	−0.186501	+	0.323029i
$461$	11.5000	−	19.9186i	0.535608	−	0.927701i	−0.463525	−	0.886084i	$-0.653416\pi$
$461$	11.5000	−	19.9186i	0.535608	−	0.927701i	0.999134	−	0.0416172i	$-0.0132510\pi$
$462$		0			0
$463$	14.5000	+	25.1147i	0.673872	+	1.16718i	0.976797	+	0.214166i	$0.0687035\pi$
$463$	14.5000	+	25.1147i	0.673872	+	1.16718i	−0.302925	+	0.953014i	$0.597963\pi$
$464$	7.00000			0.324967
$465$		0			0
$466$	−22.0000			−1.01913
$467$	−3.50000	+	6.06218i	−0.161961	+	0.280524i	−0.935572	−	0.353137i	$-0.885115\pi$
$467$	−3.50000	+	6.06218i	−0.161961	+	0.280524i	0.773611	+	0.633661i	$0.218448\pi$
$468$		0			0
$469$	20.0000	−	17.3205i	0.923514	−	0.799787i
$470$	6.00000	−	10.3923i	0.276759	−	0.479361i
$471$		0			0
$472$	−3.50000	+	6.06218i	−0.161101	+	0.279034i
$473$	−20.0000	+	34.6410i	−0.919601	+	1.59280i
$474$		0			0
$475$	−2.00000	+	3.46410i	−0.0917663	+	0.158944i
$476$	10.0000	+	3.46410i	0.458349	+	0.158777i
$477$		0			0
$478$		0			0
$479$	26.0000			1.18797			0.593985	−	0.804476i	$-0.297554\pi$
$479$	26.0000			1.18797			0.593985	+	0.804476i	$0.297554\pi$
$480$		0			0
$481$	48.0000			2.18861
$482$	0.500000	+	0.866025i	0.0227744	+	0.0394464i
$483$		0			0
$484$	−7.00000	+	12.1244i	−0.318182	+	0.551107i
$485$	−5.00000	+	8.66025i	−0.227038	+	0.393242i
$486$		0			0
$487$	6.50000	+	11.2583i	0.294543	+	0.510164i	0.974879	−	0.222737i	$-0.0714992\pi$
$487$	6.50000	+	11.2583i	0.294543	+	0.510164i	−0.680335	+	0.732901i	$0.738166\pi$
$488$		0			0
$489$		0			0
$490$	−2.00000	+	13.8564i	−0.0903508	+	0.625969i
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	0.698285	−	0.715820i	$-0.253947\pi$
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	−0.969061	+	0.246822i	$0.920614\pi$
$492$		0			0
$493$	−28.0000			−1.26106
$494$	12.0000	+	20.7846i	0.539906	+	0.935144i
$495$		0			0
$496$	3.00000			0.134704
$497$	10.0000	+	3.46410i	0.448561	+	0.155386i
$498$		0			0
$499$	−8.00000			−0.358129			−0.179065	−	0.983837i	$-0.557307\pi$
$499$	−8.00000			−0.358129			−0.179065	+	0.983837i	$0.557307\pi$
$500$	−6.00000	+	10.3923i	−0.268328	+	0.464758i
$501$		0			0
$502$	10.5000	+	18.1865i	0.468638	+	0.811705i
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$		0			0
$505$	10.0000			0.444994
$506$	10.0000	+	17.3205i	0.444554	+	0.769991i
$507$		0			0
$508$		0			0
$509$	3.00000			0.132973			0.0664863	−	0.997787i	$-0.478821\pi$
$509$	3.00000			0.132973			0.0664863	+	0.997787i	$0.478821\pi$
$510$		0			0
$511$	6.50000	+	33.7750i	0.287543	+	1.49412i
$512$	1.00000			0.0441942
$513$		0			0
$514$		0			0
$515$	−16.0000			−0.705044
$516$		0			0
$517$	−15.0000	−	25.9808i	−0.659699	−	1.14263i
$518$	−20.0000	−	6.92820i	−0.878750	−	0.304408i
$519$		0			0
$520$	6.00000	+	10.3923i	0.263117	+	0.455733i
$521$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$521$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$522$		0			0
$523$	−13.0000	+	22.5167i	−0.568450	+	0.984585i	0.428269	+	0.903651i	$0.359124\pi$
$523$	−13.0000	+	22.5167i	−0.568450	+	0.984585i	−0.996719	+	0.0809336i	$0.974210\pi$
$524$	−6.50000	+	11.2583i	−0.283954	+	0.491822i
$525$		0			0
$526$	−6.00000	−	10.3923i	−0.261612	−	0.453126i
$527$	−12.0000			−0.522728
$528$		0			0
$529$	−7.00000			−0.304348
$530$	−6.00000	+	10.3923i	−0.260623	+	0.451413i
$531$		0			0
$532$	−2.00000	−	10.3923i	−0.0867110	−	0.450564i
$533$	18.0000	−	31.1769i	0.779667	−	1.35042i
$534$		0			0
$535$	12.0000	−	20.7846i	0.518805	−	0.898597i
$536$	−5.00000	+	8.66025i	−0.215967	+	0.374066i
$537$		0			0
$538$	−15.5000	+	26.8468i	−0.668252	+	1.15745i
$539$	27.5000	+	21.6506i	1.18451	+	0.932559i
$540$		0			0
$541$	15.0000	−	25.9808i	0.644900	−	1.11700i	−0.339424	−	0.940633i	$-0.610232\pi$
$541$	15.0000	−	25.9808i	0.644900	−	1.11700i	0.984325	−	0.176367i	$-0.0564345\pi$
$542$		0			0
$543$		0			0
$544$	−4.00000			−0.171499
$545$	16.0000	+	27.7128i	0.685365	+	1.18709i
$546$		0			0
$547$	9.00000	−	15.5885i	0.384812	−	0.666514i	−0.606931	−	0.794755i	$-0.707600\pi$
$547$	9.00000	−	15.5885i	0.384812	−	0.666514i	0.991743	+	0.128240i	$0.0409329\pi$
$548$	4.00000	−	6.92820i	0.170872	−	0.295958i
$549$		0			0
$550$	2.50000	+	4.33013i	0.106600	+	0.184637i
$551$	14.0000	+	24.2487i	0.596420	+	1.03303i
$552$		0			0
$553$	−1.50000	−	7.79423i	−0.0637865	−	0.331444i
$554$	−1.00000	−	1.73205i	−0.0424859	−	0.0735878i
$555$		0			0
$556$	−8.00000			−0.339276
$557$	5.50000	+	9.52628i	0.233042	+	0.403641i	0.958702	−	0.284413i	$-0.0917985\pi$
$557$	5.50000	+	9.52628i	0.233042	+	0.403641i	−0.725660	+	0.688054i	$0.758465\pi$
$558$		0			0
$559$	48.0000			2.03018
$560$	−1.00000	−	5.19615i	−0.0422577	−	0.219578i
$561$		0			0
$562$	2.00000			0.0843649
$563$	−10.0000	+	17.3205i	−0.421450	+	0.729972i	−0.996082	−	0.0884397i	$-0.971812\pi$
$563$	−10.0000	+	17.3205i	−0.421450	+	0.729972i	0.574632	+	0.818412i	$0.305145\pi$
$564$		0			0
$565$	4.00000	+	6.92820i	0.168281	+	0.291472i
$566$	16.0000			0.672530
$567$		0			0
$568$	−4.00000			−0.167836
$569$	6.00000	+	10.3923i	0.251533	+	0.435668i	0.963948	−	0.266090i	$-0.0857319\pi$
$569$	6.00000	+	10.3923i	0.251533	+	0.435668i	−0.712415	+	0.701758i	$0.752399\pi$
$570$		0			0
$571$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$571$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$572$	30.0000			1.25436
$573$		0			0
$574$	−12.0000	+	10.3923i	−0.500870	+	0.433766i
$575$	4.00000			0.166812
$576$		0			0
$577$	−21.5000	−	37.2391i	−0.895057	−	1.55028i	−0.833734	−	0.552166i	$-0.813802\pi$
$577$	−21.5000	−	37.2391i	−0.895057	−	1.55028i	−0.0613223	−	0.998118i	$-0.519532\pi$
$578$	−1.00000			−0.0415945
$579$		0			0
$580$	7.00000	+	12.1244i	0.290659	+	0.503436i
$581$	−14.0000	+	12.1244i	−0.580818	+	0.503003i
$582$		0			0
$583$	15.0000	+	25.9808i	0.621237	+	1.07601i
$584$	−6.50000	−	11.2583i	−0.268972	−	0.465873i
$585$		0			0
$586$	−13.5000	+	23.3827i	−0.557680	+	0.965930i
$587$	−10.0000	+	17.3205i	−0.412744	+	0.714894i	−0.995189	−	0.0979766i	$-0.968763\pi$
$587$	−10.0000	+	17.3205i	−0.412744	+	0.714894i	0.582445	+	0.812870i	$0.302096\pi$
$588$		0			0
$589$	6.00000	+	10.3923i	0.247226	+	0.428207i
$590$	−14.0000			−0.576371
$591$		0			0
$592$	8.00000			0.328798
$593$	−18.0000	+	31.1769i	−0.739171	+	1.28028i	0.213697	+	0.976900i	$0.431449\pi$
$593$	−18.0000	+	31.1769i	−0.739171	+	1.28028i	−0.952869	+	0.303383i	$0.901884\pi$
$594$		0			0
$595$	4.00000	+	20.7846i	0.163984	+	0.852086i
$596$	−4.50000	+	7.79423i	−0.184327	+	0.319264i
$597$		0			0
$598$	12.0000	−	20.7846i	0.490716	−	0.849946i
$599$	−15.0000	+	25.9808i	−0.612883	+	1.06155i	0.377869	+	0.925859i	$0.376657\pi$
$599$	−15.0000	+	25.9808i	−0.612883	+	1.06155i	−0.990752	+	0.135686i	$0.956676\pi$
$600$		0			0
$601$	5.00000	−	8.66025i	0.203954	−	0.353259i	−0.745845	−	0.666120i	$-0.767954\pi$
$601$	5.00000	−	8.66025i	0.203954	−	0.353259i	0.949799	+	0.312861i	$0.101287\pi$
$602$	−20.0000	−	6.92820i	−0.815139	−	0.282372i
$603$		0			0
$604$	8.50000	−	14.7224i	0.345860	−	0.599047i
$605$	−28.0000			−1.13836
$606$		0			0
$607$	−9.00000			−0.365299			−0.182649	−	0.983178i	$-0.558467\pi$
$607$	−9.00000			−0.365299			−0.182649	+	0.983178i	$0.558467\pi$
$608$	2.00000	+	3.46410i	0.0811107	+	0.140488i
$609$		0			0
$610$		0			0
$611$	−18.0000	+	31.1769i	−0.728202	+	1.26128i
$612$		0			0
$613$	3.00000	+	5.19615i	0.121169	+	0.209871i	0.920229	−	0.391381i	$-0.128002\pi$
$613$	3.00000	+	5.19615i	0.121169	+	0.209871i	−0.799060	+	0.601251i	$0.794669\pi$
$614$	1.00000	+	1.73205i	0.0403567	+	0.0698999i
$615$		0			0
$616$	−12.5000	−	4.33013i	−0.503639	−	0.174466i
$617$	−1.00000	−	1.73205i	−0.0402585	−	0.0697297i	0.845194	−	0.534460i	$-0.179485\pi$
$617$	−1.00000	−	1.73205i	−0.0402585	−	0.0697297i	−0.885453	+	0.464730i	$0.846151\pi$
$618$		0			0
$619$	4.00000			0.160774			0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000			0.160774			0.0803868	+	0.996764i	$0.474384\pi$
$620$	3.00000	+	5.19615i	0.120483	+	0.208683i
$621$		0			0
$622$	22.0000			0.882120
$623$	12.0000	−	10.3923i	0.480770	−	0.416359i
$624$		0			0
$625$	−19.0000			−0.760000
$626$	−5.00000	+	8.66025i	−0.199840	+	0.346133i
$627$		0			0
$628$	−7.00000	−	12.1244i	−0.279330	−	0.483814i
$629$	−32.0000			−1.27592
$630$		0			0
$631$	5.00000			0.199047			0.0995234	−	0.995035i	$-0.468268\pi$
$631$	5.00000			0.199047			0.0995234	+	0.995035i	$0.468268\pi$
$632$	1.50000	+	2.59808i	0.0596668	+	0.103346i
$633$		0			0
$634$	16.5000	−	28.5788i	0.655299	−	1.13501i
$635$		0			0
$636$		0			0
$637$	6.00000	−	41.5692i	0.237729	−	1.64703i
$638$	35.0000			1.38566
$639$		0			0
$640$	1.00000	+	1.73205i	0.0395285	+	0.0684653i
$641$	14.0000			0.552967			0.276483	−	0.961019i	$-0.410831\pi$
$641$	14.0000			0.552967			0.276483	+	0.961019i	$0.410831\pi$
$642$		0			0
$643$	−7.00000	−	12.1244i	−0.276053	−	0.478138i	0.694347	−	0.719640i	$-0.255693\pi$
$643$	−7.00000	−	12.1244i	−0.276053	−	0.478138i	−0.970400	+	0.241502i	$0.922360\pi$
$644$	−8.00000	+	6.92820i	−0.315244	+	0.273009i
$645$		0			0
$646$	−8.00000	−	13.8564i	−0.314756	−	0.545173i
$647$	9.00000	+	15.5885i	0.353827	+	0.612845i	0.986916	−	0.161233i	$-0.0515470\pi$
$647$	9.00000	+	15.5885i	0.353827	+	0.612845i	−0.633090	+	0.774078i	$0.718214\pi$
$648$		0			0
$649$	−17.5000	+	30.3109i	−0.686935	+	1.18981i
$650$	3.00000	−	5.19615i	0.117670	−	0.203810i
$651$		0			0
$652$	−1.00000	−	1.73205i	−0.0391630	−	0.0678323i
$653$	18.0000			0.704394			0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000			0.704394			0.352197	+	0.935926i	$0.385435\pi$
$654$		0			0
$655$	−26.0000			−1.01590
$656$	3.00000	−	5.19615i	0.117130	−	0.202876i
$657$		0			0
$658$	12.0000	−	10.3923i	0.467809	−	0.405134i
$659$	−20.5000	+	35.5070i	−0.798567	+	1.38316i	0.121983	+	0.992532i	$0.461075\pi$
$659$	−20.5000	+	35.5070i	−0.798567	+	1.38316i	−0.920550	+	0.390626i	$0.872259\pi$
$660$		0			0
$661$	19.0000	−	32.9090i	0.739014	−	1.28001i	−0.213925	−	0.976850i	$-0.568625\pi$
$661$	19.0000	−	32.9090i	0.739014	−	1.28001i	0.952940	−	0.303160i	$-0.0980418\pi$
$662$	−16.0000	+	27.7128i	−0.621858	+	1.07709i
$663$		0			0
$664$	3.50000	−	6.06218i	0.135826	−	0.235258i
$665$	16.0000	−	13.8564i	0.620453	−	0.537328i
$666$		0			0
$667$	14.0000	−	24.2487i	0.542082	−	0.938914i
$668$	−14.0000			−0.541676
$669$		0			0
$670$	−20.0000			−0.772667
$671$		0			0
$672$		0			0
$673$	−1.00000	+	1.73205i	−0.0385472	+	0.0667657i	−0.884655	−	0.466246i	$-0.845606\pi$
$673$	−1.00000	+	1.73205i	−0.0385472	+	0.0667657i	0.846108	+	0.533011i	$0.178940\pi$
$674$	13.5000	−	23.3827i	0.520001	−	0.900667i
$675$		0			0
$676$	−11.5000	−	19.9186i	−0.442308	−	0.766099i
$677$	−4.50000	−	7.79423i	−0.172949	−	0.299557i	0.766501	−	0.642244i	$-0.221996\pi$
$677$	−4.50000	−	7.79423i	−0.172949	−	0.299557i	−0.939450	+	0.342687i	$0.888663\pi$
$678$		0			0
$679$	−10.0000	+	8.66025i	−0.383765	+	0.332350i
$680$	−4.00000	−	6.92820i	−0.153393	−	0.265684i
$681$		0			0
$682$	15.0000			0.574380
$683$	−10.5000	−	18.1865i	−0.401771	−	0.695888i	0.592168	−	0.805814i	$-0.298272\pi$
$683$	−10.5000	−	18.1865i	−0.401771	−	0.695888i	−0.993940	+	0.109926i	$0.964939\pi$
$684$		0			0
$685$	16.0000			0.611329
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$		0			0
$688$	8.00000			0.304997
$689$	18.0000	−	31.1769i	0.685745	−	1.18775i
$690$		0			0
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	1.00000			0.0380143
$693$		0			0
$694$	−27.0000			−1.02491
$695$	−8.00000	−	13.8564i	−0.303457	−	0.525603i
$696$		0			0
$697$	−12.0000	+	20.7846i	−0.454532	+	0.787273i
$698$	−20.0000			−0.757011
$699$		0			0
$700$	−2.00000	+	1.73205i	−0.0755929	+	0.0654654i
$701$	−14.0000			−0.528773			−0.264386	−	0.964417i	$-0.585169\pi$
$701$	−14.0000			−0.528773			−0.264386	+	0.964417i	$0.585169\pi$
$702$		0			0
$703$	16.0000	+	27.7128i	0.603451	+	1.04521i
$704$	5.00000			0.188445
$705$		0			0
$706$	15.0000	+	25.9808i	0.564532	+	0.977799i
$707$	12.5000	+	4.33013i	0.470111	+	0.162851i
$708$		0			0
$709$	−4.00000	−	6.92820i	−0.150223	−	0.260194i	0.781086	−	0.624423i	$-0.214666\pi$
$709$	−4.00000	−	6.92820i	−0.150223	−	0.260194i	−0.931309	+	0.364229i	$0.881333\pi$
$710$	−4.00000	−	6.92820i	−0.150117	−	0.260011i
$711$		0			0
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$	6.00000	−	10.3923i	0.224702	−	0.389195i
$714$		0			0
$715$	30.0000	+	51.9615i	1.12194	+	1.94325i
$716$	−15.0000			−0.560576
$717$		0			0
$718$	16.0000			0.597115
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	−0.916529	−	0.399969i	$-0.869021\pi$
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	0.804648	+	0.593753i	$0.202354\pi$
$720$		0			0
$721$	−20.0000	−	6.92820i	−0.744839	−	0.258020i
$722$	1.50000	−	2.59808i	0.0558242	−	0.0966904i
$723$		0			0
$724$		0			0
$725$	3.50000	−	6.06218i	0.129987	−	0.225144i
$726$		0			0
$727$	16.0000	−	27.7128i	0.593407	−	1.02781i	−0.400362	−	0.916357i	$-0.631116\pi$
$727$	16.0000	−	27.7128i	0.593407	−	1.02781i	0.993770	−	0.111454i	$-0.0355509\pi$
$728$	3.00000	+	15.5885i	0.111187	+	0.577747i
$729$		0			0
$730$	13.0000	−	22.5167i	0.481152	−	0.833379i
$731$	−32.0000			−1.18356
$732$		0			0
$733$	−36.0000			−1.32969			−0.664845	−	0.746981i	$-0.731502\pi$
$733$	−36.0000			−1.32969			−0.664845	+	0.746981i	$0.731502\pi$
$734$	2.00000	+	3.46410i	0.0738213	+	0.127862i
$735$		0			0
$736$	2.00000	−	3.46410i	0.0737210	−	0.127688i
$737$	−25.0000	+	43.3013i	−0.920887	+	1.59502i
$738$		0			0
$739$	3.00000	+	5.19615i	0.110357	+	0.191144i	0.915914	−	0.401374i	$-0.131467\pi$
$739$	3.00000	+	5.19615i	0.110357	+	0.191144i	−0.805557	+	0.592518i	$0.798134\pi$
$740$	8.00000	+	13.8564i	0.294086	+	0.509372i
$741$		0			0
$742$	−12.0000	+	10.3923i	−0.440534	+	0.381514i
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	0.915794	−	0.401648i	$-0.131563\pi$
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	−0.805735	+	0.592277i	$0.798229\pi$
$744$		0			0
$745$	−18.0000			−0.659469
$746$	10.0000	+	17.3205i	0.366126	+	0.634149i
$747$		0			0
$748$	−20.0000			−0.731272
$749$	24.0000	−	20.7846i	0.876941	−	0.759453i
$750$		0			0
$751$	12.0000			0.437886			0.218943	−	0.975738i	$-0.429739\pi$
$751$	12.0000			0.437886			0.218943	+	0.975738i	$0.429739\pi$
$752$	−3.00000	+	5.19615i	−0.109399	+	0.189484i
$753$		0			0
$754$	−21.0000	−	36.3731i	−0.764775	−	1.32463i
$755$	34.0000			1.23739
$756$		0			0
$757$	−18.0000			−0.654221			−0.327111	−	0.944986i	$-0.606075\pi$
$757$	−18.0000			−0.654221			−0.327111	+	0.944986i	$0.606075\pi$
$758$	−5.00000	−	8.66025i	−0.181608	−	0.314555i
$759$		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
$763$	8.00000	+	41.5692i	0.289619	+	1.50491i
$764$	−18.0000			−0.651217
$765$		0			0
$766$	2.00000	+	3.46410i	0.0722629	+	0.125163i
$767$	42.0000			1.51653
$768$		0			0
$769$	−0.500000	−	0.866025i	−0.0180305	−	0.0312297i	0.856869	−	0.515534i	$-0.172406\pi$
$769$	−0.500000	−	0.866025i	−0.0180305	−	0.0312297i	−0.874900	+	0.484304i	$0.839073\pi$
$770$	−5.00000	−	25.9808i	−0.180187	−	0.936282i
$771$		0			0
$772$	9.50000	+	16.4545i	0.341912	+	0.592210i
$773$	19.0000	+	32.9090i	0.683383	+	1.18365i	0.973942	+	0.226796i	$0.0728252\pi$
$773$	19.0000	+	32.9090i	0.683383	+	1.18365i	−0.290560	+	0.956857i	$0.593841\pi$
$774$		0			0
$775$	1.50000	−	2.59808i	0.0538816	−	0.0933257i
$776$	2.50000	−	4.33013i	0.0897448	−	0.155443i
$777$		0			0
$778$	−0.500000	−	0.866025i	−0.0179259	−	0.0310485i
$779$	24.0000			0.859889
$780$		0			0
$781$	−20.0000			−0.715656
$782$	−8.00000	+	13.8564i	−0.286079	+	0.495504i
$783$		0			0
$784$	1.00000	−	6.92820i	0.0357143	−	0.247436i
$785$	14.0000	−	24.2487i	0.499681	−	0.865474i
$786$		0			0
$787$	−9.00000	+	15.5885i	−0.320815	+	0.555668i	−0.980656	−	0.195737i	$-0.937290\pi$
$787$	−9.00000	+	15.5885i	−0.320815	+	0.555668i	0.659841	+	0.751405i	$0.270624\pi$
$788$	12.5000	−	21.6506i	0.445294	−	0.771272i
$789$		0			0
$790$	−3.00000	+	5.19615i	−0.106735	+	0.184871i
$791$	2.00000	+	10.3923i	0.0711118	+	0.369508i
$792$		0			0
$793$		0			0
$794$	−18.0000			−0.638796
$795$		0			0
$796$	−19.0000			−0.673437
$797$	−16.5000	−	28.5788i	−0.584460	−	1.01231i	−0.994943	−	0.100446i	$-0.967973\pi$
$797$	−16.5000	−	28.5788i	−0.584460	−	1.01231i	0.410483	−	0.911868i	$-0.365360\pi$
$798$		0			0
$799$	12.0000	−	20.7846i	0.424529	−	0.735307i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$		0			0
$802$	9.00000	+	15.5885i	0.317801	+	0.550448i
$803$	−32.5000	−	56.2917i	−1.14690	−	1.98649i
$804$		0			0
$805$	−20.0000	−	6.92820i	−0.704907	−	0.244187i
$806$	−9.00000	−	15.5885i	−0.317011	−	0.549080i
$807$		0			0
$808$	−5.00000			−0.175899
$809$	−17.0000	−	29.4449i	−0.597688	−	1.03523i	−0.993161	−	0.116749i	$-0.962753\pi$
$809$	−17.0000	−	29.4449i	−0.597688	−	1.03523i	0.395473	−	0.918477i	$-0.370581\pi$
$810$		0			0
$811$	−50.0000			−1.75574			−0.877869	−	0.478901i	$-0.841035\pi$
$811$	−50.0000			−1.75574			−0.877869	+	0.478901i	$0.841035\pi$
$812$	3.50000	+	18.1865i	0.122826	+	0.638222i
$813$		0			0
$814$	40.0000			1.40200
$815$	2.00000	−	3.46410i	0.0700569	−	0.121342i
$816$		0			0
$817$	16.0000	+	27.7128i	0.559769	+	0.969549i
$818$	−10.0000			−0.349642
$819$		0			0
$820$	12.0000			0.419058
$821$	24.5000	+	42.4352i	0.855056	+	1.48100i	0.876593	+	0.481232i	$0.159811\pi$
$821$	24.5000	+	42.4352i	0.855056	+	1.48100i	−0.0215373	+	0.999768i	$0.506856\pi$
$822$		0			0
$823$	−6.50000	+	11.2583i	−0.226576	+	0.392441i	−0.956791	−	0.290776i	$-0.906086\pi$
$823$	−6.50000	+	11.2583i	−0.226576	+	0.392441i	0.730215	+	0.683217i	$0.239420\pi$
$824$	8.00000			0.278693
$825$		0			0
$826$	−17.5000	−	6.06218i	−0.608903	−	0.210930i
$827$	51.0000			1.77344			0.886722	−	0.462303i	$-0.152977\pi$
$827$	51.0000			1.77344			0.886722	+	0.462303i	$0.152977\pi$
$828$		0			0
$829$	−11.0000	−	19.0526i	−0.382046	−	0.661723i	0.609309	−	0.792933i	$-0.291447\pi$
$829$	−11.0000	−	19.0526i	−0.382046	−	0.661723i	−0.991355	+	0.131210i	$0.958114\pi$
$830$	14.0000			0.485947
$831$		0			0
$832$	−3.00000	−	5.19615i	−0.104006	−	0.180144i
$833$	−4.00000	+	27.7128i	−0.138592	+	0.960192i
$834$		0			0
$835$	−14.0000	−	24.2487i	−0.484490	−	0.839161i
$836$	10.0000	+	17.3205i	0.345857	+	0.599042i
$837$		0			0
$838$	−6.00000	+	10.3923i	−0.207267	+	0.358996i
$839$	2.00000	−	3.46410i	0.0690477	−	0.119594i	−0.829435	−	0.558604i	$-0.811337\pi$
$839$	2.00000	−	3.46410i	0.0690477	−	0.119594i	0.898482	+	0.439010i	$0.144671\pi$
$840$		0			0
$841$	−10.0000	−	17.3205i	−0.344828	−	0.597259i
$842$	−18.0000			−0.620321
$843$		0			0
$844$	26.0000			0.894957
$845$	23.0000	−	39.8372i	0.791224	−	1.37044i
$846$		0			0
$847$	−35.0000	−	12.1244i	−1.20261	−	0.416598i
$848$	3.00000	−	5.19615i	0.103020	−	0.178437i
$849$		0			0
$850$	−2.00000	+	3.46410i	−0.0685994	+	0.118818i
$851$	16.0000	−	27.7128i	0.548473	−	0.949983i
$852$		0			0
$853$	23.0000	−	39.8372i	0.787505	−	1.36400i	−0.139986	−	0.990153i	$-0.544706\pi$
$853$	23.0000	−	39.8372i	0.787505	−	1.36400i	0.927491	−	0.373845i	$-0.121961\pi$
$854$		0			0
$855$		0			0
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$	30.0000			1.02478			0.512390	−	0.858753i	$-0.328760\pi$
$857$	30.0000			1.02478			0.512390	+	0.858753i	$0.328760\pi$
$858$		0			0
$859$	−16.0000			−0.545913			−0.272956	−	0.962026i	$-0.588002\pi$
$859$	−16.0000			−0.545913			−0.272956	+	0.962026i	$0.588002\pi$
$860$	8.00000	+	13.8564i	0.272798	+	0.472500i
$861$		0			0
$862$	9.00000	−	15.5885i	0.306541	−	0.530945i
$863$	19.0000	−	32.9090i	0.646768	−	1.12023i	−0.337123	−	0.941461i	$-0.609454\pi$
$863$	19.0000	−	32.9090i	0.646768	−	1.12023i	0.983890	−	0.178774i	$-0.0572129\pi$
$864$		0			0
$865$	1.00000	+	1.73205i	0.0340010	+	0.0588915i
$866$	3.50000	+	6.06218i	0.118935	+	0.206001i
$867$		0			0
$868$	1.50000	+	7.79423i	0.0509133	+	0.264553i
$869$	7.50000	+	12.9904i	0.254420	+	0.440668i
$870$		0			0
$871$	60.0000			2.03302
$872$	−8.00000	−	13.8564i	−0.270914	−	0.469237i
$873$		0			0
$874$	16.0000			0.541208
$875$	−30.0000	−	10.3923i	−1.01419	−	0.351324i
$876$		0			0
$877$	34.0000			1.14810			0.574049	−	0.818821i	$-0.305372\pi$
$877$	34.0000			1.14810			0.574049	+	0.818821i	$0.305372\pi$
$878$	−1.50000	+	2.59808i	−0.0506225	+	0.0876808i
$879$		0			0
$880$	5.00000	+	8.66025i	0.168550	+	0.291937i
$881$	−54.0000			−1.81931			−0.909653	−	0.415369i	$-0.863653\pi$
$881$	−54.0000			−1.81931			−0.909653	+	0.415369i	$0.863653\pi$
$882$		0			0
$883$	2.00000			0.0673054			0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000			0.0673054			0.0336527	+	0.999434i	$0.489286\pi$
$884$	12.0000	+	20.7846i	0.403604	+	0.699062i
$885$		0			0
$886$	−5.50000	+	9.52628i	−0.184776	+	0.320042i
$887$	−42.0000			−1.41022			−0.705111	−	0.709097i	$-0.749103\pi$
$887$	−42.0000			−1.41022			−0.705111	+	0.709097i	$0.749103\pi$
$888$		0			0
$889$		0			0
$890$	−12.0000			−0.402241
$891$		0			0
$892$	0.500000	+	0.866025i	0.0167412	+	0.0289967i
$893$	−24.0000			−0.803129
$894$		0			0
$895$	−15.0000	−	25.9808i	−0.501395	−	0.868441i
$896$	0.500000	+	2.59808i	0.0167038	+	0.0867956i
$897$		0			0
$898$	7.00000	+	12.1244i	0.233593	+	0.404595i
$899$	−10.5000	−	18.1865i	−0.350195	−	0.606555i
$900$		0			0
$901$	−12.0000	+	20.7846i	−0.399778	+	0.692436i
$902$	15.0000	−	25.9808i	0.499445	−	0.865065i
$903$		0			0
$904$	−2.00000	−	3.46410i	−0.0665190	−	0.115214i
$905$		0			0
$906$		0			0
$907$	−42.0000			−1.39459			−0.697294	−	0.716786i	$-0.745613\pi$
$907$	−42.0000			−1.39459			−0.697294	+	0.716786i	$0.745613\pi$
$908$	13.5000	−	23.3827i	0.448013	−	0.775982i
$909$		0			0
$910$	−24.0000	+	20.7846i	−0.795592	+	0.689003i
$911$	−18.0000	+	31.1769i	−0.596367	+	1.03294i	0.396986	+	0.917825i	$0.370056\pi$
$911$	−18.0000	+	31.1769i	−0.596367	+	1.03294i	−0.993352	+	0.115113i	$0.963277\pi$
$912$		0			0
$913$	17.5000	−	30.3109i	0.579165	−	1.00314i
$914$	13.0000	−	22.5167i	0.430002	−	0.744785i
$915$		0			0
$916$	−2.00000	+	3.46410i	−0.0660819	+	0.114457i
$917$	−32.5000	−	11.2583i	−1.07324	−	0.371783i
$918$		0			0
$919$	−6.50000	+	11.2583i	−0.214415	+	0.371378i	−0.953092	−	0.302682i	$-0.902118\pi$
$919$	−6.50000	+	11.2583i	−0.214415	+	0.371378i	0.738676	+	0.674060i	$0.235451\pi$
$920$	8.00000			0.263752
$921$		0			0
$922$	−23.0000			−0.757465
$923$	12.0000	+	20.7846i	0.394985	+	0.684134i
$924$		0			0
$925$	4.00000	−	6.92820i	0.131519	−	0.227798i
$926$	14.5000	−	25.1147i	0.476500	−	0.825321i
$927$		0			0
$928$	−3.50000	−	6.06218i	−0.114893	−	0.199001i
$929$	−18.0000	−	31.1769i	−0.590561	−	1.02288i	−0.994157	−	0.107944i	$-0.965573\pi$
$929$	−18.0000	−	31.1769i	−0.590561	−	1.02288i	0.403596	−	0.914937i	$-0.367760\pi$
$930$		0			0
$931$	26.0000	−	10.3923i	0.852116	−	0.340594i
$932$	11.0000	+	19.0526i	0.360317	+	0.624087i
$933$		0			0
$934$	7.00000			0.229047
$935$	−20.0000	−	34.6410i	−0.654070	−	1.13288i
$936$		0			0
$937$	14.0000			0.457360			0.228680	−	0.973502i	$-0.426559\pi$
$937$	14.0000			0.457360			0.228680	+	0.973502i	$0.426559\pi$
$938$	−25.0000	−	8.66025i	−0.816279	−	0.282767i
$939$		0			0
$940$	−12.0000			−0.391397
$941$	−6.50000	+	11.2583i	−0.211894	+	0.367011i	−0.952307	−	0.305141i	$-0.901296\pi$
$941$	−6.50000	+	11.2583i	−0.211894	+	0.367011i	0.740413	+	0.672152i	$0.234630\pi$
$942$		0			0
$943$	−12.0000	−	20.7846i	−0.390774	−	0.676840i
$944$	7.00000			0.227831
$945$		0			0
$946$	40.0000			1.30051
$947$	−12.5000	−	21.6506i	−0.406195	−	0.703551i	0.588264	−	0.808669i	$-0.299811\pi$
$947$	−12.5000	−	21.6506i	−0.406195	−	0.703551i	−0.994460	+	0.105118i	$0.966478\pi$
$948$		0			0
$949$	−39.0000	+	67.5500i	−1.26599	+	2.19277i
$950$	4.00000			0.129777
$951$		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
$955$	−18.0000	−	31.1769i	−0.582466	−	1.00886i
$956$		0			0
$957$		0			0
$958$	−13.0000	−	22.5167i	−0.420011	−	0.727480i
$959$	20.0000	+	6.92820i	0.645834	+	0.223723i
$960$		0			0
$961$	11.0000	+	19.0526i	0.354839	+	0.614599i
$962$	−24.0000	−	41.5692i	−0.773791	−	1.34025i
$963$		0			0
$964$	0.500000	−	0.866025i	0.0161039	−	0.0278928i
$965$	−19.0000	+	32.9090i	−0.611632	+	1.05938i
$966$		0			0
$967$	−4.00000	−	6.92820i	−0.128631	−	0.222796i	0.794515	−	0.607244i	$-0.207725\pi$
$967$	−4.00000	−	6.92820i	−0.128631	−	0.222796i	−0.923147	+	0.384448i	$0.874392\pi$
$968$	14.0000			0.449977
$969$		0			0
$970$	10.0000			0.321081
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	−0.946094	−	0.323891i	$-0.895009\pi$
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	0.753545	+	0.657396i	$0.228342\pi$
$972$		0			0
$973$	−4.00000	−	20.7846i	−0.128234	−	0.666324i
$974$	6.50000	−	11.2583i	0.208273	−	0.360740i
$975$		0			0
$976$		0			0
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	−0.685381	−	0.728184i	$-0.740364\pi$
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	0.973317	+	0.229465i	$0.0736978\pi$
$978$		0			0
$979$	−15.0000	+	25.9808i	−0.479402	+	0.830349i
$980$	13.0000	−	5.19615i	0.415270	−	0.165985i
$981$		0			0
$982$	−6.00000	+	10.3923i	−0.191468	+	0.331632i
$983$	36.0000			1.14822			0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000			1.14822			0.574111	+	0.818778i	$0.305348\pi$
$984$		0			0
$985$	50.0000			1.59313
$986$	14.0000	+	24.2487i	0.445851	+	0.772236i
$987$		0			0
$988$	12.0000	−	20.7846i	0.381771	−	0.661247i
$989$	16.0000	−	27.7128i	0.508770	−	0.881216i
$990$		0			0
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	0.795474	−	0.605988i	$-0.207222\pi$
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	−0.922538	+	0.385906i	$0.873889\pi$
$992$	−1.50000	−	2.59808i	−0.0476250	−	0.0824890i
$993$		0			0
$994$	−2.00000	−	10.3923i	−0.0634361	−	0.329624i
$995$	−19.0000	−	32.9090i	−0.602340	−	1.04328i
$996$		0			0
$997$	−58.0000			−1.83688			−0.918439	−	0.395562i	$-0.870550\pi$
$997$	−58.0000			−1.83688			−0.918439	+	0.395562i	$0.870550\pi$
$998$	4.00000	+	6.92820i	0.126618	+	0.219308i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.h.b.541.1		2
3.2	odd	2		1134.2.h.o.541.1		2
7.4	even	3		1134.2.e.o.865.1		2
9.2	odd	6		378.2.g.d.163.1	yes	2
9.4	even	3		1134.2.e.o.919.1		2
9.5	odd	6		1134.2.e.b.919.1		2
9.7	even	3		378.2.g.c.163.1	yes	2
21.11	odd	6		1134.2.e.b.865.1		2
63.2	odd	6		2646.2.a.k.1.1		1
63.4	even	3	inner	1134.2.h.b.109.1		2
63.11	odd	6		378.2.g.d.109.1	yes	2
63.16	even	3		2646.2.a.t.1.1		1
63.25	even	3		378.2.g.c.109.1	✓	2
63.32	odd	6		1134.2.h.o.109.1		2
63.47	even	6		2646.2.a.c.1.1		1
63.61	odd	6		2646.2.a.bb.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.g.c.109.1	✓	2	63.25	even	3
378.2.g.c.163.1	yes	2	9.7	even	3
378.2.g.d.109.1	yes	2	63.11	odd	6
378.2.g.d.163.1	yes	2	9.2	odd	6
1134.2.e.b.865.1		2	21.11	odd	6
1134.2.e.b.919.1		2	9.5	odd	6
1134.2.e.o.865.1		2	7.4	even	3
1134.2.e.o.919.1		2	9.4	even	3
1134.2.h.b.109.1		2	63.4	even	3	inner
1134.2.h.b.541.1		2	1.1	even	1	trivial
1134.2.h.o.109.1		2	63.32	odd	6
1134.2.h.o.541.1		2	3.2	odd	2
2646.2.a.c.1.1		1	63.47	even	6
2646.2.a.k.1.1		1	63.2	odd	6
2646.2.a.t.1.1		1	63.16	even	3
2646.2.a.bb.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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +(-2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +(-2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{10} +5.00000 q^{11} +(-3.00000 - 5.19615i) q^{13} +(0.500000 + 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(2.00000 - 3.46410i) q^{19} +(1.00000 - 1.73205i) q^{20} +(-2.50000 - 4.33013i) q^{22} -4.00000 q^{23} -1.00000 q^{25} +(-3.00000 + 5.19615i) q^{26} +(2.00000 - 1.73205i) q^{28} +(-3.50000 + 6.06218i) q^{29} +(-1.50000 + 2.59808i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{34} +(5.00000 + 1.73205i) q^{35} +(-4.00000 + 6.92820i) q^{37} -4.00000 q^{38} -2.00000 q^{40} +(3.00000 + 5.19615i) q^{41} +(-4.00000 + 6.92820i) q^{43} +(-2.50000 + 4.33013i) q^{44} +(2.00000 + 3.46410i) q^{46} +(-3.00000 - 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +(0.500000 + 0.866025i) q^{50} +6.00000 q^{52} +(3.00000 + 5.19615i) q^{53} -10.0000 q^{55} +(-2.50000 - 0.866025i) q^{56} +7.00000 q^{58} +(-3.50000 + 6.06218i) q^{59} +3.00000 q^{62} +1.00000 q^{64} +(6.00000 + 10.3923i) q^{65} +(-5.00000 + 8.66025i) q^{67} -4.00000 q^{68} +(-1.00000 - 5.19615i) q^{70} -4.00000 q^{71} +(-6.50000 - 11.2583i) q^{73} +8.00000 q^{74} +(2.00000 + 3.46410i) q^{76} +(-12.5000 - 4.33013i) q^{77} +(1.50000 + 2.59808i) q^{79} +(1.00000 + 1.73205i) q^{80} +(3.00000 - 5.19615i) q^{82} +(3.50000 - 6.06218i) q^{83} +(-4.00000 - 6.92820i) q^{85} +8.00000 q^{86} +5.00000 q^{88} +(-3.00000 + 5.19615i) q^{89} +(3.00000 + 15.5885i) q^{91} +(2.00000 - 3.46410i) q^{92} +(-3.00000 + 5.19615i) q^{94} +(-4.00000 + 6.92820i) q^{95} +(2.50000 - 4.33013i) q^{97} +(1.00000 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - 4 q^{5} - 5 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 - 4 * q^5 - 5 * q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} - 4 q^{5} - 5 q^{7} + 2 q^{8} + 2 q^{10} + 10 q^{11} - 6 q^{13} + q^{14} - q^{16} + 4 q^{17} + 4 q^{19} + 2 q^{20} - 5 q^{22} - 8 q^{23} - 2 q^{25} - 6 q^{26} + 4 q^{28} - 7 q^{29} - 3 q^{31} - q^{32} + 4 q^{34} + 10 q^{35} - 8 q^{37} - 8 q^{38} - 4 q^{40} + 6 q^{41} - 8 q^{43} - 5 q^{44} + 4 q^{46} - 6 q^{47} + 11 q^{49} + q^{50} + 12 q^{52} + 6 q^{53} - 20 q^{55} - 5 q^{56} + 14 q^{58} - 7 q^{59} + 6 q^{62} + 2 q^{64} + 12 q^{65} - 10 q^{67} - 8 q^{68} - 2 q^{70} - 8 q^{71} - 13 q^{73} + 16 q^{74} + 4 q^{76} - 25 q^{77} + 3 q^{79} + 2 q^{80} + 6 q^{82} + 7 q^{83} - 8 q^{85} + 16 q^{86} + 10 q^{88} - 6 q^{89} + 6 q^{91} + 4 q^{92} - 6 q^{94} - 8 q^{95} + 5 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 - 4 * q^5 - 5 * q^7 + 2 * q^8 + 2 * q^10 + 10 * q^11 - 6 * q^13 + q^14 - q^16 + 4 * q^17 + 4 * q^19 + 2 * q^20 - 5 * q^22 - 8 * q^23 - 2 * q^25 - 6 * q^26 + 4 * q^28 - 7 * q^29 - 3 * q^31 - q^32 + 4 * q^34 + 10 * q^35 - 8 * q^37 - 8 * q^38 - 4 * q^40 + 6 * q^41 - 8 * q^43 - 5 * q^44 + 4 * q^46 - 6 * q^47 + 11 * q^49 + q^50 + 12 * q^52 + 6 * q^53 - 20 * q^55 - 5 * q^56 + 14 * q^58 - 7 * q^59 + 6 * q^62 + 2 * q^64 + 12 * q^65 - 10 * q^67 - 8 * q^68 - 2 * q^70 - 8 * q^71 - 13 * q^73 + 16 * q^74 + 4 * q^76 - 25 * q^77 + 3 * q^79 + 2 * q^80 + 6 * q^82 + 7 * q^83 - 8 * q^85 + 16 * q^86 + 10 * q^88 - 6 * q^89 + 6 * q^91 + 4 * q^92 - 6 * q^94 - 8 * q^95 + 5 * q^97 + 2 * q^98

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