LMFDB - Embedded newform 1134.2.e.e.919.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(865,1134)]

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([4, 4]))

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

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

chi := DirichletCharacter("1134.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.e (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			919.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.919
Dual form			1134.2.e.e.865.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} +(2.50000 - 4.33013i) q^{11} +(2.50000 - 0.866025i) q^{14} +1.00000 q^{16} +(-2.00000 - 3.46410i) q^{17} +(-4.00000 + 6.92820i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-2.50000 + 4.33013i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(2.00000 - 3.46410i) q^{25} +(-2.50000 + 0.866025i) q^{28} +(-2.50000 - 4.33013i) q^{29} +3.00000 q^{31} -1.00000 q^{32} +(2.00000 + 3.46410i) q^{34} +(-2.00000 - 1.73205i) q^{35} +(2.00000 - 3.46410i) q^{37} +(4.00000 - 6.92820i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-1.00000 - 1.73205i) q^{43} +(2.50000 - 4.33013i) q^{44} +(2.00000 + 3.46410i) q^{46} +6.00000 q^{47} +(5.50000 - 4.33013i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(-4.50000 - 7.79423i) q^{53} +5.00000 q^{55} +(2.50000 - 0.866025i) q^{56} +(2.50000 + 4.33013i) q^{58} +11.0000 q^{59} -6.00000 q^{61} -3.00000 q^{62} +1.00000 q^{64} -2.00000 q^{67} +(-2.00000 - 3.46410i) q^{68} +(2.00000 + 1.73205i) q^{70} -2.00000 q^{71} +(-5.00000 - 8.66025i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(-4.00000 + 6.92820i) q^{76} +(-2.50000 + 12.9904i) q^{77} +3.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +(-3.50000 - 6.06218i) q^{83} +(2.00000 - 3.46410i) q^{85} +(1.00000 + 1.73205i) q^{86} +(-2.50000 + 4.33013i) q^{88} +(-3.00000 + 5.19615i) q^{89} +(-2.00000 - 3.46410i) q^{92} -6.00000 q^{94} -8.00000 q^{95} +(-3.50000 - 6.06218i) q^{97} +(-5.50000 + 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} + q^{5} - 5 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 + q^5 - 5 * q^7 - 2 * q^8	$ 2 q - 2 q^{2} + 2 q^{4} + q^{5} - 5 q^{7} - 2 q^{8} - q^{10} + 5 q^{11} + 5 q^{14} + 2 q^{16} - 4 q^{17} - 8 q^{19} + q^{20} - 5 q^{22} - 4 q^{23} + 4 q^{25} - 5 q^{28} - 5 q^{29} + 6 q^{31} - 2 q^{32} + 4 q^{34} - 4 q^{35} + 4 q^{37} + 8 q^{38} - q^{40} - 2 q^{43} + 5 q^{44} + 4 q^{46} + 12 q^{47} + 11 q^{49} - 4 q^{50} - 9 q^{53} + 10 q^{55} + 5 q^{56} + 5 q^{58} + 22 q^{59} - 12 q^{61} - 6 q^{62} + 2 q^{64} - 4 q^{67} - 4 q^{68} + 4 q^{70} - 4 q^{71} - 10 q^{73} - 4 q^{74} - 8 q^{76} - 5 q^{77} + 6 q^{79} + q^{80} - 7 q^{83} + 4 q^{85} + 2 q^{86} - 5 q^{88} - 6 q^{89} - 4 q^{92} - 12 q^{94} - 16 q^{95} - 7 q^{97} - 11 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 + q^5 - 5 * q^7 - 2 * q^8 - q^10 + 5 * q^11 + 5 * q^14 + 2 * q^16 - 4 * q^17 - 8 * q^19 + q^20 - 5 * q^22 - 4 * q^23 + 4 * q^25 - 5 * q^28 - 5 * q^29 + 6 * q^31 - 2 * q^32 + 4 * q^34 - 4 * q^35 + 4 * q^37 + 8 * q^38 - q^40 - 2 * q^43 + 5 * q^44 + 4 * q^46 + 12 * q^47 + 11 * q^49 - 4 * q^50 - 9 * q^53 + 10 * q^55 + 5 * q^56 + 5 * q^58 + 22 * q^59 - 12 * q^61 - 6 * q^62 + 2 * q^64 - 4 * q^67 - 4 * q^68 + 4 * q^70 - 4 * q^71 - 10 * q^73 - 4 * q^74 - 8 * q^76 - 5 * q^77 + 6 * q^79 + q^80 - 7 * q^83 + 4 * q^85 + 2 * q^86 - 5 * q^88 - 6 * q^89 - 4 * q^92 - 12 * q^94 - 16 * q^95 - 7 * q^97 - 11 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	0.955901	−	0.293691i	$-0.0948835\pi$
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	−0.732294	+	0.680989i	$0.761550\pi$
$6$		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
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	−0.192201	−	0.981356i	$-0.561563\pi$
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	0.945979	−	0.324227i	$-0.105104\pi$
$12$		0			0
$13$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$13$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$14$	2.50000	−	0.866025i	0.668153	−	0.231455i
$15$		0			0
$16$	1.00000			0.250000
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$		0			0
$19$	−4.00000	+	6.92820i	−0.917663	+	1.58944i	−0.114708	+	0.993399i	$0.536593\pi$
$19$	−4.00000	+	6.92820i	−0.917663	+	1.58944i	−0.802955	+	0.596040i	$0.796740\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	−2.50000	+	4.33013i	−0.533002	+	0.923186i
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$		0			0
$27$		0			0
$28$	−2.50000	+	0.866025i	−0.472456	+	0.163663i
$29$	−2.50000	−	4.33013i	−0.464238	−	0.804084i	0.534928	−	0.844897i	$-0.320339\pi$
$29$	−2.50000	−	4.33013i	−0.464238	−	0.804084i	−0.999167	+	0.0408130i	$0.987005\pi$
$30$		0			0
$31$	3.00000			0.538816			0.269408	−	0.963026i	$-0.413172\pi$
$31$	3.00000			0.538816			0.269408	+	0.963026i	$0.413172\pi$
$32$	−1.00000			−0.176777
$33$		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	−0.653476	−	0.756948i	$-0.726690\pi$
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	0.982274	+	0.187453i	$0.0600231\pi$
$38$	4.00000	−	6.92820i	0.648886	−	1.12390i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$		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
$47$	6.00000			0.875190			0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000			0.875190			0.437595	+	0.899172i	$0.355830\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	−2.00000	+	3.46410i	−0.282843	+	0.489898i
$51$		0			0
$52$		0			0
$53$	−4.50000	−	7.79423i	−0.618123	−	1.07062i	−0.989828	−	0.142269i	$-0.954560\pi$
$53$	−4.50000	−	7.79423i	−0.618123	−	1.07062i	0.371706	−	0.928351i	$-0.378773\pi$
$54$		0			0
$55$	5.00000			0.674200
$56$	2.50000	−	0.866025i	0.334077	−	0.115728i
$57$		0			0
$58$	2.50000	+	4.33013i	0.328266	+	0.568574i
$59$	11.0000			1.43208			0.716039	−	0.698060i	$-0.245953\pi$
$59$	11.0000			1.43208			0.716039	+	0.698060i	$0.245953\pi$
$60$		0			0
$61$	−6.00000			−0.768221			−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000			−0.768221			−0.384111	+	0.923287i	$0.625492\pi$
$62$	−3.00000			−0.381000
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−2.00000			−0.244339			−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000			−0.244339			−0.122169	+	0.992509i	$0.538985\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$		0			0
$70$	2.00000	+	1.73205i	0.239046	+	0.207020i
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$		0			0
$73$	−5.00000	−	8.66025i	−0.585206	−	1.01361i	−0.994850	−	0.101361i	$-0.967680\pi$
$73$	−5.00000	−	8.66025i	−0.585206	−	1.01361i	0.409644	−	0.912245i	$-0.365653\pi$
$74$	−2.00000	+	3.46410i	−0.232495	+	0.402694i
$75$		0			0
$76$	−4.00000	+	6.92820i	−0.458831	+	0.794719i
$77$	−2.50000	+	12.9904i	−0.284901	+	1.48039i
$78$		0			0
$79$	3.00000			0.337526			0.168763	−	0.985657i	$-0.446023\pi$
$79$	3.00000			0.337526			0.168763	+	0.985657i	$0.446023\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$		0			0
$82$		0			0
$83$	−3.50000	−	6.06218i	−0.384175	−	0.665410i	0.607479	−	0.794335i	$-0.292181\pi$
$83$	−3.50000	−	6.06218i	−0.384175	−	0.665410i	−0.991654	+	0.128925i	$0.958847\pi$
$84$		0			0
$85$	2.00000	−	3.46410i	0.216930	−	0.375735i
$86$	1.00000	+	1.73205i	0.107833	+	0.186772i
$87$		0			0
$88$	−2.50000	+	4.33013i	−0.266501	+	0.461593i
$89$	−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
$91$		0			0
$92$	−2.00000	−	3.46410i	−0.208514	−	0.361158i
$93$		0			0
$94$	−6.00000			−0.618853
$95$	−8.00000			−0.820783
$96$		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
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	−0.502477	−	0.864590i	$-0.667578\pi$
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	0.999996	+	0.00286291i	$0.000911295\pi$
$102$		0			0
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$		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	$-0.787012\pi$
$107$	1.50000	−	2.59808i	0.145010	−	0.251166i	0.929377	+	0.369132i	$0.120345\pi$
$108$		0			0
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$	−5.00000			−0.476731
$111$		0			0
$112$	−2.50000	+	0.866025i	−0.236228	+	0.0818317i
$113$	8.00000	−	13.8564i	0.752577	−	1.30350i	−0.193993	−	0.981003i	$-0.562144\pi$
$113$	8.00000	−	13.8564i	0.752577	−	1.30350i	0.946570	−	0.322498i	$-0.104523\pi$
$114$		0			0
$115$	2.00000	−	3.46410i	0.186501	−	0.323029i
$116$	−2.50000	−	4.33013i	−0.232119	−	0.402042i
$117$		0			0
$118$	−11.0000			−1.01263
$119$	8.00000	+	6.92820i	0.733359	+	0.635107i
$120$		0			0
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	6.00000			0.543214
$123$		0			0
$124$	3.00000			0.269408
$125$	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	$0.369250\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$		0			0
$131$	0.500000	+	0.866025i	0.0436852	+	0.0756650i	0.887041	−	0.461690i	$-0.152757\pi$
$131$	0.500000	+	0.866025i	0.0436852	+	0.0756650i	−0.843356	+	0.537355i	$0.819423\pi$
$132$		0			0
$133$	4.00000	−	20.7846i	0.346844	−	1.80225i
$134$	2.00000			0.172774
$135$		0			0
$136$	2.00000	+	3.46410i	0.171499	+	0.297044i
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	−0.905577	−	0.424182i	$-0.860562\pi$
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	0.820141	+	0.572161i	$0.193895\pi$
$138$		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	$-0.0356795\pi$
$140$	−2.00000	−	1.73205i	−0.169031	−	0.146385i
$141$		0			0
$142$	2.00000			0.167836
$143$		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
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$		0			0
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	0.162758	+	0.986666i	$0.447961\pi$
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$	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
$157$	−4.00000			−0.319235			−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000			−0.319235			−0.159617	+	0.987179i	$0.551026\pi$
$158$	−3.00000			−0.238667
$159$		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	−0.777007	−	0.629492i	$-0.783263\pi$
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	0.933659	+	0.358162i	$0.116597\pi$
$164$		0			0
$165$		0			0
$166$	3.50000	+	6.06218i	0.271653	+	0.470516i
$167$	−7.00000	+	12.1244i	−0.541676	+	0.938211i	0.457132	+	0.889399i	$0.348877\pi$
$167$	−7.00000	+	12.1244i	−0.541676	+	0.938211i	−0.998808	+	0.0488118i	$0.984457\pi$
$168$		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
$173$	−22.0000			−1.67263			−0.836315	−	0.548250i	$-0.815294\pi$
$173$	−22.0000			−1.67263			−0.836315	+	0.548250i	$0.815294\pi$
$174$		0			0
$175$	−2.00000	+	10.3923i	−0.151186	+	0.785584i
$176$	2.50000	−	4.33013i	0.188445	−	0.326396i
$177$		0			0
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$		0			0
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$	4.00000			0.294086
$186$		0			0
$187$	−20.0000			−1.46254
$188$	6.00000			0.437595
$189$		0			0
$190$	8.00000			0.580381
$191$	−24.0000			−1.73658			−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000			−1.73658			−0.868290	+	0.496058i	$0.834780\pi$
$192$		0			0
$193$	5.00000			0.359908			0.179954	−	0.983675i	$-0.442405\pi$
$193$	5.00000			0.359908			0.179954	+	0.983675i	$0.442405\pi$
$194$	3.50000	+	6.06218i	0.251285	+	0.435239i
$195$		0			0
$196$	5.50000	−	4.33013i	0.392857	−	0.309295i
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	0.928166	−	0.372168i	$-0.121385\pi$
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	−0.786389	+	0.617731i	$0.788052\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$		0			0
$202$	−5.00000	+	8.66025i	−0.351799	+	0.609333i
$203$	10.0000	+	8.66025i	0.701862	+	0.607831i
$204$		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	$0.188597\pi$
$212$	−4.50000	−	7.79423i	−0.309061	−	0.535310i
$213$		0			0
$214$	−1.50000	+	2.59808i	−0.102538	+	0.177601i
$215$	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
$220$	5.00000			0.337100
$221$		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
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	−0.811943	−	0.583736i	$-0.801590\pi$
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	0.911502	+	0.411296i	$0.134924\pi$
$228$		0			0
$229$	10.0000	+	17.3205i	0.660819	+	1.14457i	0.980401	+	0.197013i	$0.0631241\pi$
$229$	10.0000	+	17.3205i	0.660819	+	1.14457i	−0.319582	+	0.947559i	$0.603543\pi$
$230$	−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	$-0.875160\pi$
$233$	−2.00000	+	3.46410i	−0.131024	+	0.226941i	0.793047	+	0.609160i	$0.208493\pi$
$234$		0			0
$235$	3.00000	+	5.19615i	0.195698	+	0.338960i
$236$	11.0000			0.716039
$237$		0			0
$238$	−8.00000	−	6.92820i	−0.518563	−	0.449089i
$239$	−6.00000	+	10.3923i	−0.388108	+	0.672222i	−0.992195	−	0.124696i	$-0.960204\pi$
$239$	−6.00000	+	10.3923i	−0.388108	+	0.672222i	0.604087	+	0.796918i	$0.293538\pi$
$240$		0			0
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	−0.110963	−	0.993825i	$-0.535394\pi$
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	0.916159	−	0.400815i	$-0.131273\pi$
$242$	7.00000	+	12.1244i	0.449977	+	0.779383i
$243$		0			0
$244$	−6.00000			−0.384111
$245$	6.50000	+	2.59808i	0.415270	+	0.165985i
$246$		0			0
$247$		0			0
$248$	−3.00000			−0.190500
$249$		0			0
$250$	−9.00000			−0.569210
$251$	−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
$254$	−9.00000			−0.564710
$255$		0			0
$256$	1.00000			0.0625000
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	0.757159	−	0.653231i	$-0.226587\pi$
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	−0.944294	+	0.329104i	$0.893253\pi$
$258$		0			0
$259$	−2.00000	+	10.3923i	−0.124274	+	0.645746i
$260$		0			0
$261$		0			0
$262$	−0.500000	−	0.866025i	−0.0308901	−	0.0535032i
$263$	−15.0000	+	25.9808i	−0.924940	+	1.60204i	−0.133281	+	0.991078i	$0.542551\pi$
$263$	−15.0000	+	25.9808i	−0.924940	+	1.60204i	−0.791658	+	0.610964i	$0.790782\pi$
$264$		0			0
$265$	4.50000	−	7.79423i	0.276433	−	0.478796i
$266$	−4.00000	+	20.7846i	−0.245256	+	1.27439i
$267$		0			0
$268$	−2.00000			−0.122169
$269$	15.5000	+	26.8468i	0.945052	+	1.63688i	0.755648	+	0.654978i	$0.227322\pi$
$269$	15.5000	+	26.8468i	0.945052	+	1.63688i	0.189404	+	0.981899i	$0.439344\pi$
$270$		0			0
$271$	−7.50000	+	12.9904i	−0.455593	+	0.789109i	−0.998722	−	0.0505395i	$-0.983906\pi$
$271$	−7.50000	+	12.9904i	−0.455593	+	0.789109i	0.543130	+	0.839649i	$0.317239\pi$
$272$	−2.00000	−	3.46410i	−0.121268	−	0.210042i
$273$		0			0
$274$	1.00000	−	1.73205i	0.0604122	−	0.104637i
$275$	−10.0000	−	17.3205i	−0.603023	−	1.04447i
$276$		0			0
$277$	8.00000	−	13.8564i	0.480673	−	0.832551i	−0.519081	−	0.854725i	$-0.673726\pi$
$277$	8.00000	−	13.8564i	0.480673	−	0.832551i	0.999754	+	0.0221745i	$0.00705893\pi$
$278$	−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	0.894311	−	0.447447i	$-0.147667\pi$
$281$	1.00000	+	1.73205i	0.0596550	+	0.103325i	−0.834656	+	0.550772i	$0.814333\pi$
$282$		0			0
$283$	10.0000			0.594438			0.297219	−	0.954809i	$-0.403941\pi$
$283$	10.0000			0.594438			0.297219	+	0.954809i	$0.403941\pi$
$284$	−2.00000			−0.118678
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	−2.50000	+	4.33013i	−0.146805	+	0.254274i
$291$		0			0
$292$	−5.00000	−	8.66025i	−0.292603	−	0.506803i
$293$	−10.5000	+	18.1865i	−0.613417	+	1.06247i	0.377244	+	0.926114i	$0.376872\pi$
$293$	−10.5000	+	18.1865i	−0.613417	+	1.06247i	−0.990660	+	0.136355i	$0.956461\pi$
$294$		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
$301$	4.00000	+	3.46410i	0.230556	+	0.199667i
$302$	9.50000	−	16.4545i	0.546664	−	0.946849i
$303$		0			0
$304$	−4.00000	+	6.92820i	−0.229416	+	0.397360i
$305$	−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	$0.205351\pi$
$308$	−2.50000	+	12.9904i	−0.142451	+	0.740196i
$309$		0			0
$310$	−1.50000	−	2.59808i	−0.0851943	−	0.147561i
$311$	32.0000			1.81455			0.907277	−	0.420534i	$-0.138157\pi$
$311$	32.0000			1.81455			0.907277	+	0.420534i	$0.138157\pi$
$312$		0			0
$313$	1.00000			0.0565233			0.0282617	−	0.999601i	$-0.491003\pi$
$313$	1.00000			0.0565233			0.0282617	+	0.999601i	$0.491003\pi$
$314$	4.00000			0.225733
$315$		0			0
$316$	3.00000			0.168763
$317$	−3.00000			−0.168497			−0.0842484	−	0.996445i	$-0.526849\pi$
$317$	−3.00000			−0.168497			−0.0842484	+	0.996445i	$0.526849\pi$
$318$		0			0
$319$	−25.0000			−1.39973
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$		0			0
$322$	−8.00000	−	6.92820i	−0.445823	−	0.386094i
$323$	32.0000			1.78053
$324$		0			0
$325$		0			0
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$		0			0
$328$		0			0
$329$	−15.0000	+	5.19615i	−0.826977	+	0.286473i
$330$		0			0
$331$	−4.00000			−0.219860			−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000			−0.219860			−0.109930	+	0.993939i	$0.535063\pi$
$332$	−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	$0.245498\pi$
$338$	−6.50000	−	11.2583i	−0.353553	−	0.612372i
$339$		0			0
$340$	2.00000	−	3.46410i	0.108465	−	0.187867i
$341$	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
$346$	22.0000			1.18273
$347$	−12.0000			−0.644194			−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000			−0.644194			−0.322097	+	0.946707i	$0.604388\pi$
$348$		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
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	−0.347024	−	0.937856i	$-0.612808\pi$
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	0.985719	−	0.168397i	$-0.0538590\pi$
$354$		0			0
$355$	−1.00000	−	1.73205i	−0.0530745	−	0.0919277i
$356$	−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	$-0.748328\pi$
$359$	5.00000	−	8.66025i	0.263890	−	0.457071i	0.967272	+	0.253741i	$0.0816611\pi$
$360$		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
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	−0.997960	−	0.0638362i	$-0.979666\pi$
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	0.554264	+	0.832341i	$0.313000\pi$
$368$	−2.00000	−	3.46410i	−0.104257	−	0.180579i
$369$		0			0
$370$	−4.00000			−0.207950
$371$	18.0000	+	15.5885i	0.934513	+	0.809312i
$372$		0			0
$373$	16.0000	+	27.7128i	0.828449	+	1.43492i	0.899255	+	0.437425i	$0.144109\pi$
$373$	16.0000	+	27.7128i	0.828449	+	1.43492i	−0.0708063	+	0.997490i	$0.522557\pi$
$374$	20.0000			1.03418
$375$		0			0
$376$	−6.00000			−0.309426
$377$		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	$0.365203\pi$
$380$	−8.00000			−0.410391
$381$		0			0
$382$	24.0000			1.22795
$383$	−17.0000	−	29.4449i	−0.868659	−	1.50456i	−0.863367	−	0.504576i	$-0.831649\pi$
$383$	−17.0000	−	29.4449i	−0.868659	−	1.50456i	−0.00529229	−	0.999986i	$-0.501685\pi$
$384$		0			0
$385$	−12.5000	+	4.33013i	−0.637059	+	0.220684i
$386$	−5.00000			−0.254493
$387$		0			0
$388$	−3.50000	−	6.06218i	−0.177686	−	0.307760i
$389$	−1.00000	+	1.73205i	−0.0507020	+	0.0878185i	−0.890263	−	0.455448i	$-0.849479\pi$
$389$	−1.00000	+	1.73205i	−0.0507020	+	0.0878185i	0.839561	+	0.543266i	$0.182813\pi$
$390$		0			0
$391$	−8.00000	+	13.8564i	−0.404577	+	0.700749i
$392$	−5.50000	+	4.33013i	−0.277792	+	0.218704i
$393$		0			0
$394$	2.00000			0.100759
$395$	1.50000	+	2.59808i	0.0754732	+	0.130723i
$396$		0			0
$397$	−18.0000	+	31.1769i	−0.903394	+	1.56472i	−0.0803356	+	0.996768i	$0.525599\pi$
$397$	−18.0000	+	31.1769i	−0.903394	+	1.56472i	−0.823058	+	0.567957i	$0.807734\pi$
$398$	−2.00000	−	3.46410i	−0.100251	−	0.173640i
$399$		0			0
$400$	2.00000	−	3.46410i	0.100000	−	0.173205i
$401$	12.0000	+	20.7846i	0.599251	+	1.03793i	0.992932	+	0.118686i	$0.0378683\pi$
$401$	12.0000	+	20.7846i	0.599251	+	1.03793i	−0.393680	+	0.919247i	$0.628798\pi$
$402$		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
$409$	−25.0000			−1.23617			−0.618085	−	0.786111i	$-0.712091\pi$
$409$	−25.0000			−1.23617			−0.618085	+	0.786111i	$0.712091\pi$
$410$		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
$418$	−20.0000	−	34.6410i	−0.978232	−	1.69435i
$419$		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
$425$	−16.0000			−0.776114
$426$		0			0
$427$	15.0000	−	5.19615i	0.725901	−	0.251459i
$428$	1.50000	−	2.59808i	0.0725052	−	0.125583i
$429$		0			0
$430$	−1.00000	+	1.73205i	−0.0482243	+	0.0835269i
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	0.973574	−	0.228373i	$-0.0733406\pi$
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	−0.684564	+	0.728953i	$0.740007\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$	7.50000	−	2.59808i	0.360012	−	0.124712i
$435$		0			0
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	32.0000			1.53077
$438$		0			0
$439$	15.0000			0.715911			0.357955	−	0.933739i	$-0.383474\pi$
$439$	15.0000			0.715911			0.357955	+	0.933739i	$0.383474\pi$
$440$	−5.00000			−0.238366
$441$		0			0
$442$		0			0
$443$	−17.0000			−0.807694			−0.403847	−	0.914826i	$-0.632327\pi$
$443$	−17.0000			−0.807694			−0.403847	+	0.914826i	$0.632327\pi$
$444$		0			0
$445$	−6.00000			−0.284427
$446$	−3.50000	−	6.06218i	−0.165730	−	0.287052i
$447$		0			0
$448$	−2.50000	+	0.866025i	−0.118114	+	0.0409159i
$449$	−16.0000			−0.755087			−0.377543	−	0.925992i	$-0.623231\pi$
$449$	−16.0000			−0.755087			−0.377543	+	0.925992i	$0.623231\pi$
$450$		0			0
$451$		0			0
$452$	8.00000	−	13.8564i	0.376288	−	0.651751i
$453$		0			0
$454$	−1.50000	+	2.59808i	−0.0703985	+	0.121934i
$455$		0			0
$456$		0			0
$457$	31.0000			1.45012			0.725059	−	0.688686i	$-0.241812\pi$
$457$	31.0000			1.45012			0.725059	+	0.688686i	$0.241812\pi$
$458$	−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	0.655696	−	0.755025i	$-0.272375\pi$
$461$	−7.00000	−	12.1244i	−0.326023	−	0.564688i	−0.981719	+	0.190337i	$0.939042\pi$
$462$		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	$0.287923\pi$
$464$	−2.50000	−	4.33013i	−0.116060	−	0.201021i
$465$		0			0
$466$	2.00000	−	3.46410i	0.0926482	−	0.160471i
$467$	−10.0000	+	17.3205i	−0.462745	+	0.801498i	−0.999097	−	0.0424970i	$-0.986469\pi$
$467$	−10.0000	+	17.3205i	−0.462745	+	0.801498i	0.536352	+	0.843995i	$0.319802\pi$
$468$		0			0
$469$	5.00000	−	1.73205i	0.230879	−	0.0799787i
$470$	−3.00000	−	5.19615i	−0.138380	−	0.239681i
$471$		0			0
$472$	−11.0000			−0.506316
$473$	−10.0000			−0.459800
$474$		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
$479$	19.0000	−	32.9090i	0.868132	−	1.50365i	0.00422900	−	0.999991i	$-0.498654\pi$
$479$	19.0000	−	32.9090i	0.868132	−	1.50365i	0.863903	−	0.503658i	$-0.168013\pi$
$480$		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	0.803807	−	0.594890i	$-0.202804\pi$
$487$	−2.50000	−	4.33013i	−0.113286	−	0.196217i	−0.917093	+	0.398673i	$0.869471\pi$
$488$	6.00000			0.271607
$489$		0			0
$490$	−6.50000	−	2.59808i	−0.293640	−	0.117369i
$491$	4.50000	−	7.79423i	0.203082	−	0.351749i	−0.746438	−	0.665455i	$-0.768237\pi$
$491$	4.50000	−	7.79423i	0.203082	−	0.351749i	0.949520	+	0.313707i	$0.101571\pi$
$492$		0			0
$493$	−10.0000	+	17.3205i	−0.450377	+	0.780076i
$494$		0			0
$495$		0			0
$496$	3.00000			0.134704
$497$	5.00000	−	1.73205i	0.224281	−	0.0776931i
$498$		0			0
$499$	−5.00000	−	8.66025i	−0.223831	−	0.387686i	0.732137	−	0.681157i	$-0.238523\pi$
$499$	−5.00000	−	8.66025i	−0.223831	−	0.387686i	−0.955968	+	0.293471i	$0.905190\pi$
$500$	9.00000			0.402492
$501$		0			0
$502$	21.0000			0.937276
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	10.0000			0.444994
$506$	20.0000			0.889108
$507$		0			0
$508$	9.00000			0.399310
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	0.982988	−	0.183669i	$-0.0587976\pi$
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	−0.650556	+	0.759458i	$0.725464\pi$
$510$		0			0
$511$	20.0000	+	17.3205i	0.884748	+	0.766214i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	3.00000	+	5.19615i	0.132324	+	0.229192i
$515$	4.00000	−	6.92820i	0.176261	−	0.305293i
$516$		0			0
$517$	15.0000	−	25.9808i	0.659699	−	1.14263i
$518$	2.00000	−	10.3923i	0.0878750	−	0.456612i
$519$		0			0
$520$		0			0
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	0.598714	−	0.800963i	$-0.295679\pi$
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	−0.993011	+	0.118020i	$0.962345\pi$
$522$		0			0
$523$	−4.00000	+	6.92820i	−0.174908	+	0.302949i	−0.940129	−	0.340818i	$-0.889296\pi$
$523$	−4.00000	+	6.92820i	−0.174908	+	0.302949i	0.765222	+	0.643767i	$0.222629\pi$
$524$	0.500000	+	0.866025i	0.0218426	+	0.0378325i
$525$		0			0
$526$	15.0000	−	25.9808i	0.654031	−	1.13282i
$527$	−6.00000	−	10.3923i	−0.261364	−	0.452696i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	−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
$535$	3.00000			0.129701
$536$	2.00000			0.0863868
$537$		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	−0.605096	−	0.796152i	$-0.706865\pi$
$541$	9.00000	−	15.5885i	0.386940	−	0.670200i	0.992036	+	0.125952i	$0.0401986\pi$
$542$	7.50000	−	12.9904i	0.322153	−	0.557985i
$543$		0			0
$544$	2.00000	+	3.46410i	0.0857493	+	0.148522i
$545$	−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
$551$	40.0000			1.70406
$552$		0			0
$553$	−7.50000	+	2.59808i	−0.318932	+	0.110481i
$554$	−8.00000	+	13.8564i	−0.339887	+	0.588702i
$555$		0			0
$556$	7.00000	−	12.1244i	0.296866	−	0.514187i
$557$	−11.5000	−	19.9186i	−0.487271	−	0.843978i	0.512622	−	0.858614i	$-0.328674\pi$
$557$	−11.5000	−	19.9186i	−0.487271	−	0.843978i	−0.999893	+	0.0146368i	$0.995341\pi$
$558$		0			0
$559$		0			0
$560$	−2.00000	−	1.73205i	−0.0845154	−	0.0731925i
$561$		0			0
$562$	−1.00000	−	1.73205i	−0.0421825	−	0.0730622i
$563$	−17.0000			−0.716465			−0.358232	−	0.933632i	$-0.616620\pi$
$563$	−17.0000			−0.716465			−0.358232	+	0.933632i	$0.616620\pi$
$564$		0			0
$565$	16.0000			0.673125
$566$	−10.0000			−0.420331
$567$		0			0
$568$	2.00000			0.0839181
$569$	−24.0000			−1.00613			−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000			−1.00613			−0.503066	+	0.864248i	$0.667795\pi$
$570$		0			0
$571$	−30.0000			−1.25546			−0.627730	−	0.778431i	$-0.716016\pi$
$571$	−30.0000			−1.25546			−0.627730	+	0.778431i	$0.716016\pi$
$572$		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	−0.984238	−	0.176847i	$-0.943410\pi$
$577$	−15.5000	−	26.8468i	−0.645273	−	1.11765i	0.338965	−	0.940799i	$-0.389923\pi$
$578$	−0.500000	+	0.866025i	−0.0207973	+	0.0360219i
$579$		0			0
$580$	2.50000	−	4.33013i	0.103807	−	0.179799i
$581$	14.0000	+	12.1244i	0.580818	+	0.503003i
$582$		0			0
$583$	−45.0000			−1.86371
$584$	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	$0.0902494\pi$
$587$	17.5000	+	30.3109i	0.722302	+	1.25106i	−0.237773	+	0.971321i	$0.576417\pi$
$588$		0			0
$589$	−12.0000	+	20.7846i	−0.494451	+	0.856415i
$590$	−5.50000	−	9.52628i	−0.226431	−	0.392191i
$591$		0			0
$592$	2.00000	−	3.46410i	0.0821995	−	0.142374i
$593$	18.0000	−	31.1769i	0.739171	−	1.28028i	−0.213697	−	0.976900i	$-0.568551\pi$
$593$	18.0000	−	31.1769i	0.739171	−	1.28028i	0.952869	−	0.303383i	$-0.0981160\pi$
$594$		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
$599$	30.0000			1.22577			0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000			1.22577			0.612883	+	0.790173i	$0.290010\pi$
$600$		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
$605$	7.00000	−	12.1244i	0.284590	−	0.492925i
$606$		0			0
$607$	13.5000	+	23.3827i	0.547948	+	0.949074i	0.998415	+	0.0562808i	$0.0179242\pi$
$607$	13.5000	+	23.3827i	0.547948	+	0.949074i	−0.450467	+	0.892793i	$0.648742\pi$
$608$	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	0.719042	−	0.694967i	$-0.244581\pi$
$613$	−6.00000	−	10.3923i	−0.242338	−	0.419741i	−0.961380	+	0.275225i	$0.911248\pi$
$614$	−28.0000			−1.12999
$615$		0			0
$616$	2.50000	−	12.9904i	0.100728	−	0.523397i
$617$	1.00000	−	1.73205i	0.0402585	−	0.0697297i	−0.845194	−	0.534460i	$-0.820515\pi$
$617$	1.00000	−	1.73205i	0.0402585	−	0.0697297i	0.885453	+	0.464730i	$0.153849\pi$
$618$		0			0
$619$	−5.00000	+	8.66025i	−0.200967	+	0.348085i	−0.948840	−	0.315757i	$-0.897742\pi$
$619$	−5.00000	+	8.66025i	−0.200967	+	0.348085i	0.747873	+	0.663842i	$0.231075\pi$
$620$	1.50000	+	2.59808i	0.0602414	+	0.104341i
$621$		0			0
$622$	−32.0000			−1.28308
$623$	3.00000	−	15.5885i	0.120192	−	0.624538i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	−1.00000			−0.0399680
$627$		0			0
$628$	−4.00000			−0.159617
$629$	−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	$0.623453\pi$
$632$	−3.00000			−0.119334
$633$		0			0
$634$	3.00000			0.119145
$635$	4.50000	+	7.79423i	0.178577	+	0.309305i
$636$		0			0
$637$		0			0
$638$	25.0000			0.989759
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	13.0000	−	22.5167i	0.513469	−	0.889355i	−0.486409	−	0.873731i	$-0.661693\pi$
$641$	13.0000	−	22.5167i	0.513469	−	0.889355i	0.999878	−	0.0156233i	$-0.00497325\pi$
$642$		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	$0.255693\pi$
$644$	8.00000	+	6.92820i	0.315244	+	0.273009i
$645$		0			0
$646$	−32.0000			−1.25902
$647$	−9.00000	−	15.5885i	−0.353827	−	0.612845i	0.633090	−	0.774078i	$-0.281786\pi$
$647$	−9.00000	−	15.5885i	−0.353827	−	0.612845i	−0.986916	+	0.161233i	$0.948453\pi$
$648$		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
$653$	−19.5000	−	33.7750i	−0.763094	−	1.32172i	−0.941248	−	0.337715i	$-0.890346\pi$
$653$	−19.5000	−	33.7750i	−0.763094	−	1.32172i	0.178154	−	0.984003i	$-0.442987\pi$
$654$		0			0
$655$	−0.500000	+	0.866025i	−0.0195366	+	0.0338384i
$656$		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	$-0.882348\pi$
$659$	−20.0000	−	34.6410i	−0.779089	−	1.34942i	0.153378	−	0.988168i	$-0.450985\pi$
$660$		0			0
$661$	10.0000			0.388955			0.194477	−	0.980907i	$-0.437699\pi$
$661$	10.0000			0.388955			0.194477	+	0.980907i	$0.437699\pi$
$662$	4.00000			0.155464
$663$		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
$668$	−7.00000	+	12.1244i	−0.270838	+	0.469105i
$669$		0			0
$670$	1.00000	+	1.73205i	0.0386334	+	0.0669150i
$671$	−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
$677$	27.0000			1.03769			0.518847	−	0.854867i	$-0.326361\pi$
$677$	27.0000			1.03769			0.518847	+	0.854867i	$0.326361\pi$
$678$		0			0
$679$	14.0000	+	12.1244i	0.537271	+	0.465290i
$680$	−2.00000	+	3.46410i	−0.0766965	+	0.132842i
$681$		0			0
$682$	−7.50000	+	12.9904i	−0.287190	+	0.497427i
$683$	−4.50000	−	7.79423i	−0.172188	−	0.298238i	0.766997	−	0.641651i	$-0.221750\pi$
$683$	−4.50000	−	7.79423i	−0.172188	−	0.298238i	−0.939184	+	0.343413i	$0.888417\pi$
$684$		0			0
$685$	−2.00000			−0.0764161
$686$	10.0000	−	15.5885i	0.381802	−	0.595170i
$687$		0			0
$688$	−1.00000	−	1.73205i	−0.0381246	−	0.0660338i
$689$		0			0
$690$		0			0
$691$	8.00000			0.304334			0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000			0.304334			0.152167	+	0.988355i	$0.451375\pi$
$692$	−22.0000			−0.836315
$693$		0			0
$694$	12.0000			0.455514
$695$	14.0000			0.531050
$696$		0			0
$697$		0			0
$698$	−7.00000	−	12.1244i	−0.264954	−	0.458914i
$699$		0			0
$700$	−2.00000	+	10.3923i	−0.0755929	+	0.392792i
$701$	5.00000			0.188847			0.0944237	−	0.995532i	$-0.469899\pi$
$701$	5.00000			0.188847			0.0944237	+	0.995532i	$0.469899\pi$
$702$		0			0
$703$	16.0000	+	27.7128i	0.603451	+	1.04521i
$704$	2.50000	−	4.33013i	0.0942223	−	0.163198i
$705$		0			0
$706$	−12.0000	+	20.7846i	−0.451626	+	0.782239i
$707$	−5.00000	+	25.9808i	−0.188044	+	0.977107i
$708$		0			0
$709$	38.0000			1.42712			0.713560	−	0.700594i	$-0.247082\pi$
$709$	38.0000			1.42712			0.713560	+	0.700594i	$0.247082\pi$
$710$	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
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$		0			0
$718$	−5.00000	+	8.66025i	−0.186598	+	0.323198i
$719$	−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
$721$	16.0000	+	13.8564i	0.595871	+	0.516040i
$722$	22.5000	+	38.9711i	0.837363	+	1.45036i
$723$		0			0
$724$		0			0
$725$	−20.0000			−0.742781
$726$		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
$731$	−4.00000	+	6.92820i	−0.147945	+	0.256249i
$732$		0			0
$733$	3.00000	+	5.19615i	0.110808	+	0.191924i	0.916096	−	0.400959i	$-0.131323\pi$
$733$	3.00000	+	5.19615i	0.110808	+	0.191924i	−0.805289	+	0.592883i	$0.797990\pi$
$734$	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	0.998146	+	0.0608653i	$0.0193860\pi$
$739$	15.0000	+	25.9808i	0.551784	+	0.955718i	−0.446362	+	0.894852i	$0.647281\pi$
$740$	4.00000			0.147043
$741$		0			0
$742$	−18.0000	−	15.5885i	−0.660801	−	0.572270i
$743$	15.0000	−	25.9808i	0.550297	−	0.953142i	−0.447956	−	0.894055i	$-0.647848\pi$
$743$	15.0000	−	25.9808i	0.550297	−	0.953142i	0.998253	−	0.0590862i	$-0.0188187\pi$
$744$		0			0
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$	−16.0000	−	27.7128i	−0.585802	−	1.01464i
$747$		0			0
$748$	−20.0000			−0.731272
$749$	−1.50000	+	7.79423i	−0.0548088	+	0.284795i
$750$		0			0
$751$	−22.5000	−	38.9711i	−0.821037	−	1.42208i	−0.904911	−	0.425601i	$-0.860063\pi$
$751$	−22.5000	−	38.9711i	−0.821037	−	1.42208i	0.0838743	−	0.996476i	$-0.473271\pi$
$752$	6.00000			0.218797
$753$		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	$0.938398\pi$
$758$	−16.0000			−0.581146
$759$		0			0
$760$	8.00000			0.290191
$761$	4.00000	+	6.92820i	0.145000	+	0.251147i	0.929373	−	0.369142i	$-0.120348\pi$
$761$	4.00000	+	6.92820i	0.145000	+	0.251147i	−0.784373	+	0.620289i	$0.787015\pi$
$762$		0			0
$763$	−4.00000	−	3.46410i	−0.144810	−	0.125409i
$764$	−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	$-0.0507157\pi$
$770$	12.5000	−	4.33013i	0.450469	−	0.156047i
$771$		0			0
$772$	5.00000			0.179954
$773$	5.00000	+	8.66025i	0.179838	+	0.311488i	0.941825	−	0.336104i	$-0.109109\pi$
$773$	5.00000	+	8.66025i	0.179838	+	0.311488i	−0.761987	+	0.647592i	$0.775776\pi$
$774$		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
$781$	−5.00000	+	8.66025i	−0.178914	+	0.309888i
$782$	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
$787$	−18.0000			−0.641631			−0.320815	−	0.947142i	$-0.603957\pi$
$787$	−18.0000			−0.641631			−0.320815	+	0.947142i	$0.603957\pi$
$788$	−2.00000			−0.0712470
$789$		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
$794$	18.0000	−	31.1769i	0.638796	−	1.10643i
$795$		0			0
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$	10.5000	−	18.1865i	0.371929	−	0.644200i	−0.617933	−	0.786231i	$-0.712030\pi$
$797$	10.5000	−	18.1865i	0.371929	−	0.644200i	0.989862	+	0.142031i	$0.0453631\pi$
$798$		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
$803$	−50.0000			−1.76446
$804$		0			0
$805$	−2.00000	+	10.3923i	−0.0704907	+	0.366281i
$806$		0			0
$807$		0			0
$808$	−5.00000	+	8.66025i	−0.175899	+	0.304667i
$809$	20.0000	+	34.6410i	0.703163	+	1.21791i	0.967351	+	0.253442i	$0.0815627\pi$
$809$	20.0000	+	34.6410i	0.703163	+	1.21791i	−0.264188	+	0.964471i	$0.585104\pi$
$810$		0			0
$811$	−14.0000			−0.491606			−0.245803	−	0.969320i	$-0.579052\pi$
$811$	−14.0000			−0.491606			−0.245803	+	0.969320i	$0.579052\pi$
$812$	10.0000	+	8.66025i	0.350931	+	0.303915i
$813$		0			0
$814$	10.0000	+	17.3205i	0.350500	+	0.607083i
$815$	4.00000			0.140114
$816$		0			0
$817$	16.0000			0.559769
$818$	25.0000			0.874105
$819$		0			0
$820$		0			0
$821$	25.0000			0.872506			0.436253	−	0.899824i	$-0.356305\pi$
$821$	25.0000			0.872506			0.436253	+	0.899824i	$0.356305\pi$
$822$		0			0
$823$	40.0000			1.39431			0.697156	−	0.716919i	$-0.254448\pi$
$823$	40.0000			1.39431			0.697156	+	0.716919i	$0.254448\pi$
$824$	4.00000	+	6.92820i	0.139347	+	0.241355i
$825$		0			0
$826$	27.5000	−	9.52628i	0.956847	−	0.331462i
$827$	−9.00000			−0.312961			−0.156480	−	0.987681i	$-0.550015\pi$
$827$	−9.00000			−0.312961			−0.156480	+	0.987681i	$0.550015\pi$
$828$		0			0
$829$	16.0000	+	27.7128i	0.555703	+	0.962506i	0.997848	+	0.0655624i	$0.0208842\pi$
$829$	16.0000	+	27.7128i	0.555703	+	0.962506i	−0.442145	+	0.896943i	$0.645783\pi$
$830$	−3.50000	+	6.06218i	−0.121487	+	0.210421i
$831$		0			0
$832$		0			0
$833$	−26.0000	−	10.3923i	−0.900847	−	0.360072i
$834$		0			0
$835$	−14.0000			−0.484490
$836$	20.0000	+	34.6410i	0.691714	+	1.19808i
$837$		0			0
$838$		0			0
$839$	−14.0000	−	24.2487i	−0.483334	−	0.837158i	0.516483	−	0.856297i	$-0.327241\pi$
$839$	−14.0000	−	24.2487i	−0.483334	−	0.837158i	−0.999817	+	0.0191389i	$0.993908\pi$
$840$		0			0
$841$	2.00000	−	3.46410i	0.0689655	−	0.119452i
$842$	15.0000	+	25.9808i	0.516934	+	0.895356i
$843$		0			0
$844$	−1.00000	+	1.73205i	−0.0344214	+	0.0596196i
$845$	−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
$850$	16.0000			0.548795
$851$	−16.0000			−0.548473
$852$		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
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	−0.977800	−	0.209539i	$-0.932804\pi$
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	0.670366	+	0.742030i	$0.266137\pi$
$858$		0			0
$859$	17.0000	+	29.4449i	0.580033	+	1.00465i	0.995475	+	0.0950262i	$0.0302935\pi$
$859$	17.0000	+	29.4449i	0.580033	+	1.00465i	−0.415442	+	0.909620i	$0.636373\pi$
$860$	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	$-0.778891\pi$
$863$	5.00000	−	8.66025i	0.170202	−	0.294798i	0.938490	+	0.345305i	$0.112225\pi$
$864$		0			0
$865$	−11.0000	−	19.0526i	−0.374011	−	0.647806i
$866$	−14.0000			−0.475739
$867$		0			0
$868$	−7.50000	+	2.59808i	−0.254567	+	0.0881845i
$869$	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
$875$	−22.5000	+	7.79423i	−0.760639	+	0.263493i
$876$		0			0
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	0.998888	+	0.0471555i	$0.0150156\pi$
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	−0.458606	+	0.888640i	$0.651651\pi$
$878$	−15.0000			−0.506225
$879$		0			0
$880$	5.00000			0.168550
$881$	42.0000			1.41502			0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000			1.41502			0.707508	+	0.706705i	$0.249819\pi$
$882$		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
$886$	17.0000			0.571126
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	0.992149	+	0.125061i	$0.0399128\pi$
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	−0.387768	+	0.921757i	$0.626754\pi$
$888$		0			0
$889$	−22.5000	+	7.79423i	−0.754626	+	0.261410i
$890$	6.00000			0.201120
$891$		0			0
$892$	3.50000	+	6.06218i	0.117189	+	0.202977i
$893$	−24.0000	+	41.5692i	−0.803129	+	1.39106i
$894$		0			0
$895$	−6.00000	+	10.3923i	−0.200558	+	0.347376i
$896$	2.50000	−	0.866025i	0.0835191	−	0.0289319i
$897$		0			0
$898$	16.0000			0.533927
$899$	−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
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	−0.948278	−	0.317441i	$-0.897176\pi$
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	0.749051	+	0.662512i	$0.230510\pi$
$908$	1.50000	−	2.59808i	0.0497792	−	0.0862202i
$909$		0			0
$910$		0			0
$911$	15.0000	+	25.9808i	0.496972	+	0.860781i	0.999994	−	0.00349271i	$-0.00111177\pi$
$911$	15.0000	+	25.9808i	0.496972	+	0.860781i	−0.503022	+	0.864274i	$0.667778\pi$
$912$		0			0
$913$	−35.0000			−1.15833
$914$	−31.0000			−1.02539
$915$		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	−0.471684	−	0.881768i	$-0.656354\pi$
$919$	16.0000	−	27.7128i	0.527791	−	0.914161i	0.999475	−	0.0323936i	$-0.0103130\pi$
$920$	−2.00000	+	3.46410i	−0.0659380	+	0.114208i
$921$		0			0
$922$	7.00000	+	12.1244i	0.230533	+	0.399294i
$923$		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
$929$	6.00000			0.196854			0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000			0.196854			0.0984268	+	0.995144i	$0.468619\pi$
$930$		0			0
$931$	8.00000	+	55.4256i	0.262189	+	1.81650i
$932$	−2.00000	+	3.46410i	−0.0655122	+	0.113470i
$933$		0			0
$934$	10.0000	−	17.3205i	0.327210	−	0.566744i
$935$	−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	$0.306284\pi$
$938$	−5.00000	+	1.73205i	−0.163256	+	0.0565535i
$939$		0			0
$940$	3.00000	+	5.19615i	0.0978492	+	0.169480i
$941$	11.0000			0.358590			0.179295	−	0.983795i	$-0.442618\pi$
$941$	11.0000			0.358590			0.179295	+	0.983795i	$0.442618\pi$
$942$		0			0
$943$		0			0
$944$	11.0000			0.358020
$945$		0			0
$946$	10.0000			0.325128
$947$	32.0000			1.03986			0.519930	−	0.854209i	$-0.325958\pi$
$947$	32.0000			1.03986			0.519930	+	0.854209i	$0.325958\pi$
$948$		0			0
$949$		0			0
$950$	−16.0000	−	27.7128i	−0.519109	−	0.899122i
$951$		0			0
$952$	−8.00000	−	6.92820i	−0.259281	−	0.224544i
$953$	−2.00000			−0.0647864			−0.0323932	−	0.999475i	$-0.510313\pi$
$953$	−2.00000			−0.0647864			−0.0323932	+	0.999475i	$0.510313\pi$
$954$		0			0
$955$	−12.0000	−	20.7846i	−0.388311	−	0.672574i
$956$	−6.00000	+	10.3923i	−0.194054	+	0.336111i
$957$		0			0
$958$	−19.0000	+	32.9090i	−0.613862	+	1.06324i
$959$	1.00000	−	5.19615i	0.0322917	−	0.167793i
$960$		0			0
$961$	−22.0000			−0.709677
$962$		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	$-0.270880\pi$
$968$	7.00000	+	12.1244i	0.224989	+	0.389692i
$969$		0			0
$970$	−3.50000	+	6.06218i	−0.112378	+	0.194645i
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	−0.720224	−	0.693742i	$-0.755961\pi$
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	0.960910	+	0.276861i	$0.0892941\pi$
$972$		0			0
$973$	−7.00000	+	36.3731i	−0.224410	+	1.16607i
$974$	2.50000	+	4.33013i	0.0801052	+	0.138746i
$975$		0			0
$976$	−6.00000			−0.192055
$977$	30.0000			0.959785			0.479893	−	0.877327i	$-0.340676\pi$
$977$	30.0000			0.959785			0.479893	+	0.877327i	$0.340676\pi$
$978$		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
$983$	−30.0000	+	51.9615i	−0.956851	+	1.65732i	−0.226778	+	0.973946i	$0.572819\pi$
$983$	−30.0000	+	51.9615i	−0.956851	+	1.65732i	−0.730073	+	0.683369i	$0.760514\pi$
$984$		0			0
$985$	−1.00000	−	1.73205i	−0.0318626	−	0.0551877i
$986$	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	−0.949490	−	0.313798i	$-0.898398\pi$
$991$	−23.5000	−	40.7032i	−0.746502	−	1.29298i	0.202988	−	0.979181i	$-0.434935\pi$
$992$	−3.00000			−0.0952501
$993$		0			0
$994$	−5.00000	+	1.73205i	−0.158590	+	0.0549373i
$995$	−2.00000	+	3.46410i	−0.0634043	+	0.109819i
$996$		0			0
$997$	−19.0000	+	32.9090i	−0.601736	+	1.04224i	0.390822	+	0.920466i	$0.372191\pi$
$997$	−19.0000	+	32.9090i	−0.601736	+	1.04224i	−0.992558	+	0.121771i	$0.961143\pi$
$998$	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.e.e.919.1		2
3.2	odd	2		1134.2.e.l.919.1		2
7.4	even	3		1134.2.h.l.109.1		2
9.2	odd	6		1134.2.h.e.541.1		2
9.4	even	3		126.2.g.c.37.1		2
9.5	odd	6		42.2.e.a.37.1	yes	2
9.7	even	3		1134.2.h.l.541.1		2
21.11	odd	6		1134.2.h.e.109.1		2
36.23	even	6		336.2.q.b.289.1		2
36.31	odd	6		1008.2.s.k.289.1		2
45.14	odd	6		1050.2.i.l.751.1		2
45.23	even	12		1050.2.o.a.499.2		4
45.32	even	12		1050.2.o.a.499.1		4
63.4	even	3		126.2.g.c.109.1		2
63.5	even	6		294.2.a.f.1.1		1
63.11	odd	6		1134.2.e.l.865.1		2
63.13	odd	6		882.2.g.i.667.1		2
63.23	odd	6		294.2.a.e.1.1		1
63.25	even	3	inner	1134.2.e.e.865.1		2
63.31	odd	6		882.2.g.i.361.1		2
63.32	odd	6		42.2.e.a.25.1	✓	2
63.40	odd	6		882.2.a.d.1.1		1
63.41	even	6		294.2.e.b.79.1		2
63.58	even	3		882.2.a.c.1.1		1
63.59	even	6		294.2.e.b.67.1		2
72.5	odd	6		1344.2.q.g.961.1		2
72.59	even	6		1344.2.q.s.961.1		2
252.23	even	6		2352.2.a.t.1.1		1
252.59	odd	6		2352.2.q.u.1537.1		2
252.67	odd	6		1008.2.s.k.865.1		2
252.95	even	6		336.2.q.b.193.1		2
252.103	even	6		7056.2.a.bl.1.1		1
252.131	odd	6		2352.2.a.f.1.1		1
252.167	odd	6		2352.2.q.u.961.1		2
252.247	odd	6		7056.2.a.w.1.1		1
315.32	even	12		1050.2.o.a.949.2		4
315.149	odd	6		7350.2.a.bl.1.1		1
315.158	even	12		1050.2.o.a.949.1		4
315.194	even	6		7350.2.a.q.1.1		1
315.284	odd	6		1050.2.i.l.151.1		2
504.5	even	6		9408.2.a.z.1.1		1
504.131	odd	6		9408.2.a.cr.1.1		1
504.149	odd	6		9408.2.a.ce.1.1		1
504.221	odd	6		1344.2.q.g.193.1		2
504.275	even	6		9408.2.a.q.1.1		1
504.347	even	6		1344.2.q.s.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.e.a.25.1	✓	2	63.32	odd	6
42.2.e.a.37.1	yes	2	9.5	odd	6
126.2.g.c.37.1		2	9.4	even	3
126.2.g.c.109.1		2	63.4	even	3
294.2.a.e.1.1		1	63.23	odd	6
294.2.a.f.1.1		1	63.5	even	6
294.2.e.b.67.1		2	63.59	even	6
294.2.e.b.79.1		2	63.41	even	6
336.2.q.b.193.1		2	252.95	even	6
336.2.q.b.289.1		2	36.23	even	6
882.2.a.c.1.1		1	63.58	even	3
882.2.a.d.1.1		1	63.40	odd	6
882.2.g.i.361.1		2	63.31	odd	6
882.2.g.i.667.1		2	63.13	odd	6
1008.2.s.k.289.1		2	36.31	odd	6
1008.2.s.k.865.1		2	252.67	odd	6
1050.2.i.l.151.1		2	315.284	odd	6
1050.2.i.l.751.1		2	45.14	odd	6
1050.2.o.a.499.1		4	45.32	even	12
1050.2.o.a.499.2		4	45.23	even	12
1050.2.o.a.949.1		4	315.158	even	12
1050.2.o.a.949.2		4	315.32	even	12
1134.2.e.e.865.1		2	63.25	even	3	inner
1134.2.e.e.919.1		2	1.1	even	1	trivial
1134.2.e.l.865.1		2	63.11	odd	6
1134.2.e.l.919.1		2	3.2	odd	2
1134.2.h.e.109.1		2	21.11	odd	6
1134.2.h.e.541.1		2	9.2	odd	6
1134.2.h.l.109.1		2	7.4	even	3
1134.2.h.l.541.1		2	9.7	even	3
1344.2.q.g.193.1		2	504.221	odd	6
1344.2.q.g.961.1		2	72.5	odd	6
1344.2.q.s.193.1		2	504.347	even	6
1344.2.q.s.961.1		2	72.59	even	6
2352.2.a.f.1.1		1	252.131	odd	6
2352.2.a.t.1.1		1	252.23	even	6
2352.2.q.u.961.1		2	252.167	odd	6
2352.2.q.u.1537.1		2	252.59	odd	6
7056.2.a.w.1.1		1	252.247	odd	6
7056.2.a.bl.1.1		1	252.103	even	6
7350.2.a.q.1.1		1	315.194	even	6
7350.2.a.bl.1.1		1	315.149	odd	6
9408.2.a.q.1.1		1	504.275	even	6
9408.2.a.z.1.1		1	504.5	even	6
9408.2.a.ce.1.1		1	504.149	odd	6
9408.2.a.cr.1.1		1	504.131	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} +(2.50000 - 4.33013i) q^{11} +(2.50000 - 0.866025i) q^{14} +1.00000 q^{16} +(-2.00000 - 3.46410i) q^{17} +(-4.00000 + 6.92820i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-2.50000 + 4.33013i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(2.00000 - 3.46410i) q^{25} +(-2.50000 + 0.866025i) q^{28} +(-2.50000 - 4.33013i) q^{29} +3.00000 q^{31} -1.00000 q^{32} +(2.00000 + 3.46410i) q^{34} +(-2.00000 - 1.73205i) q^{35} +(2.00000 - 3.46410i) q^{37} +(4.00000 - 6.92820i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-1.00000 - 1.73205i) q^{43} +(2.50000 - 4.33013i) q^{44} +(2.00000 + 3.46410i) q^{46} +6.00000 q^{47} +(5.50000 - 4.33013i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(-4.50000 - 7.79423i) q^{53} +5.00000 q^{55} +(2.50000 - 0.866025i) q^{56} +(2.50000 + 4.33013i) q^{58} +11.0000 q^{59} -6.00000 q^{61} -3.00000 q^{62} +1.00000 q^{64} -2.00000 q^{67} +(-2.00000 - 3.46410i) q^{68} +(2.00000 + 1.73205i) q^{70} -2.00000 q^{71} +(-5.00000 - 8.66025i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(-4.00000 + 6.92820i) q^{76} +(-2.50000 + 12.9904i) q^{77} +3.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +(-3.50000 - 6.06218i) q^{83} +(2.00000 - 3.46410i) q^{85} +(1.00000 + 1.73205i) q^{86} +(-2.50000 + 4.33013i) q^{88} +(-3.00000 + 5.19615i) q^{89} +(-2.00000 - 3.46410i) q^{92} -6.00000 q^{94} -8.00000 q^{95} +(-3.50000 - 6.06218i) q^{97} +(-5.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} + q^{5} - 5 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 + q^5 - 5 * q^7 - 2 * q^8	\( 2 q - 2 q^{2} + 2 q^{4} + q^{5} - 5 q^{7} - 2 q^{8} - q^{10} + 5 q^{11} + 5 q^{14} + 2 q^{16} - 4 q^{17} - 8 q^{19} + q^{20} - 5 q^{22} - 4 q^{23} + 4 q^{25} - 5 q^{28} - 5 q^{29} + 6 q^{31} - 2 q^{32} + 4 q^{34} - 4 q^{35} + 4 q^{37} + 8 q^{38} - q^{40} - 2 q^{43} + 5 q^{44} + 4 q^{46} + 12 q^{47} + 11 q^{49} - 4 q^{50} - 9 q^{53} + 10 q^{55} + 5 q^{56} + 5 q^{58} + 22 q^{59} - 12 q^{61} - 6 q^{62} + 2 q^{64} - 4 q^{67} - 4 q^{68} + 4 q^{70} - 4 q^{71} - 10 q^{73} - 4 q^{74} - 8 q^{76} - 5 q^{77} + 6 q^{79} + q^{80} - 7 q^{83} + 4 q^{85} + 2 q^{86} - 5 q^{88} - 6 q^{89} - 4 q^{92} - 12 q^{94} - 16 q^{95} - 7 q^{97} - 11 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 + q^5 - 5 * q^7 - 2 * q^8 - q^10 + 5 * q^11 + 5 * q^14 + 2 * q^16 - 4 * q^17 - 8 * q^19 + q^20 - 5 * q^22 - 4 * q^23 + 4 * q^25 - 5 * q^28 - 5 * q^29 + 6 * q^31 - 2 * q^32 + 4 * q^34 - 4 * q^35 + 4 * q^37 + 8 * q^38 - q^40 - 2 * q^43 + 5 * q^44 + 4 * q^46 + 12 * q^47 + 11 * q^49 - 4 * q^50 - 9 * q^53 + 10 * q^55 + 5 * q^56 + 5 * q^58 + 22 * q^59 - 12 * q^61 - 6 * q^62 + 2 * q^64 - 4 * q^67 - 4 * q^68 + 4 * q^70 - 4 * q^71 - 10 * q^73 - 4 * q^74 - 8 * q^76 - 5 * q^77 + 6 * q^79 + q^80 - 7 * q^83 + 4 * q^85 + 2 * q^86 - 5 * q^88 - 6 * q^89 - 4 * q^92 - 12 * q^94 - 16 * q^95 - 7 * q^97 - 11 * q^98

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