LMFDB - Embedded newform 1134.2.e.t.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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 378)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			919.1
Root			$-1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	1134.919
Dual form			1134.2.e.t.865.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-0.822876 - 1.42526i) q^{5} +(-1.32288 - 2.29129i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.822876 - 1.42526i) q^{5} +(-1.32288 - 2.29129i) q^{7} +1.00000 q^{8} +(-0.822876 - 1.42526i) q^{10} +(0.822876 - 1.42526i) q^{11} +(-0.322876 + 0.559237i) q^{13} +(-1.32288 - 2.29129i) q^{14} +1.00000 q^{16} +(0.822876 + 1.42526i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(-0.822876 - 1.42526i) q^{20} +(0.822876 - 1.42526i) q^{22} +(-4.64575 - 8.04668i) q^{23} +(1.14575 - 1.98450i) q^{25} +(-0.322876 + 0.559237i) q^{26} +(-1.32288 - 2.29129i) q^{28} +(-3.82288 - 6.62141i) q^{29} +0.645751 q^{31} +1.00000 q^{32} +(0.822876 + 1.42526i) q^{34} +(-2.17712 + 3.77089i) q^{35} +(-1.96863 + 3.40976i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(-0.822876 - 1.42526i) q^{40} +(2.46863 - 4.27579i) q^{41} +(-2.50000 - 4.33013i) q^{43} +(0.822876 - 1.42526i) q^{44} +(-4.64575 - 8.04668i) q^{46} -10.9373 q^{47} +(-3.50000 + 6.06218i) q^{49} +(1.14575 - 1.98450i) q^{50} +(-0.322876 + 0.559237i) q^{52} +(-3.00000 - 5.19615i) q^{53} -2.70850 q^{55} +(-1.32288 - 2.29129i) q^{56} +(-3.82288 - 6.62141i) q^{58} +13.6458 q^{59} +12.6458 q^{61} +0.645751 q^{62} +1.00000 q^{64} +1.06275 q^{65} +8.29150 q^{67} +(0.822876 + 1.42526i) q^{68} +(-2.17712 + 3.77089i) q^{70} +10.3542 q^{71} +(5.29150 + 9.16515i) q^{73} +(-1.96863 + 3.40976i) q^{74} +(-1.00000 + 1.73205i) q^{76} -4.35425 q^{77} -15.2288 q^{79} +(-0.822876 - 1.42526i) q^{80} +(2.46863 - 4.27579i) q^{82} +(1.35425 + 2.34563i) q^{83} +(1.35425 - 2.34563i) q^{85} +(-2.50000 - 4.33013i) q^{86} +(0.822876 - 1.42526i) q^{88} +(5.46863 - 9.47194i) q^{89} +1.70850 q^{91} +(-4.64575 - 8.04668i) q^{92} -10.9373 q^{94} +3.29150 q^{95} +(3.79150 + 6.56708i) q^{97} +(-3.50000 + 6.06218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{4} + 2 q^{5} + 4 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^4 + 2 * q^5 + 4 * q^8	$ 4 q + 4 q^{2} + 4 q^{4} + 2 q^{5} + 4 q^{8} + 2 q^{10} - 2 q^{11} + 4 q^{13} + 4 q^{16} - 2 q^{17} - 4 q^{19} + 2 q^{20} - 2 q^{22} - 8 q^{23} - 6 q^{25} + 4 q^{26} - 10 q^{29} - 8 q^{31} + 4 q^{32} - 2 q^{34} - 14 q^{35} + 8 q^{37} - 4 q^{38} + 2 q^{40} - 6 q^{41} - 10 q^{43} - 2 q^{44} - 8 q^{46} - 12 q^{47} - 14 q^{49} - 6 q^{50} + 4 q^{52} - 12 q^{53} - 32 q^{55} - 10 q^{58} + 44 q^{59} + 40 q^{61} - 8 q^{62} + 4 q^{64} + 36 q^{65} + 12 q^{67} - 2 q^{68} - 14 q^{70} + 52 q^{71} + 8 q^{74} - 4 q^{76} - 28 q^{77} - 8 q^{79} + 2 q^{80} - 6 q^{82} + 16 q^{83} + 16 q^{85} - 10 q^{86} - 2 q^{88} + 6 q^{89} + 28 q^{91} - 8 q^{92} - 12 q^{94} - 8 q^{95} - 6 q^{97} - 14 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^4 + 2 * q^5 + 4 * q^8 + 2 * q^10 - 2 * q^11 + 4 * q^13 + 4 * q^16 - 2 * q^17 - 4 * q^19 + 2 * q^20 - 2 * q^22 - 8 * q^23 - 6 * q^25 + 4 * q^26 - 10 * q^29 - 8 * q^31 + 4 * q^32 - 2 * q^34 - 14 * q^35 + 8 * q^37 - 4 * q^38 + 2 * q^40 - 6 * q^41 - 10 * q^43 - 2 * q^44 - 8 * q^46 - 12 * q^47 - 14 * q^49 - 6 * q^50 + 4 * q^52 - 12 * q^53 - 32 * q^55 - 10 * q^58 + 44 * q^59 + 40 * q^61 - 8 * q^62 + 4 * q^64 + 36 * q^65 + 12 * q^67 - 2 * q^68 - 14 * q^70 + 52 * q^71 + 8 * q^74 - 4 * q^76 - 28 * q^77 - 8 * q^79 + 2 * q^80 - 6 * q^82 + 16 * q^83 + 16 * q^85 - 10 * q^86 - 2 * q^88 + 6 * q^89 + 28 * q^91 - 8 * q^92 - 12 * q^94 - 8 * q^95 - 6 * q^97 - 14 * 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
$5$	−0.822876	−	1.42526i	−0.368001	−	0.637397i	0.621252	−	0.783611i	$-0.286624\pi$
$5$	−0.822876	−	1.42526i	−0.368001	−	0.637397i	−0.989253	+	0.146214i	$0.953291\pi$
$6$		0			0
$7$	−1.32288	−	2.29129i	−0.500000	−	0.866025i
$7$	−1.32288	−	2.29129i	−0.500000	−	0.866025i
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.822876	−	1.42526i	−0.260216	−	0.450708i
$11$	0.822876	−	1.42526i	0.248106	−	0.429733i	−0.714894	−	0.699233i	$-0.753525\pi$
$11$	0.822876	−	1.42526i	0.248106	−	0.429733i	0.963000	+	0.269500i	$0.0868584\pi$
$12$		0			0
$13$	−0.322876	+	0.559237i	−0.0895496	+	0.155104i	−0.907321	−	0.420439i	$-0.861876\pi$
$13$	−0.322876	+	0.559237i	−0.0895496	+	0.155104i	0.817771	+	0.575543i	$0.195209\pi$
$14$	−1.32288	−	2.29129i	−0.353553	−	0.612372i
$15$		0			0
$16$	1.00000			0.250000
$17$	0.822876	+	1.42526i	0.199577	+	0.345677i	0.948391	−	0.317103i	$-0.102710\pi$
$17$	0.822876	+	1.42526i	0.199577	+	0.345677i	−0.748815	+	0.662780i	$0.769377\pi$
$18$		0			0
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	−0.822876	−	1.42526i	−0.184001	−	0.318698i
$21$		0			0
$22$	0.822876	−	1.42526i	0.175438	−	0.303867i
$23$	−4.64575	−	8.04668i	−0.968706	−	1.67785i	−0.699310	−	0.714819i	$-0.746509\pi$
$23$	−4.64575	−	8.04668i	−0.968706	−	1.67785i	−0.269396	−	0.963029i	$-0.586824\pi$
$24$		0			0
$25$	1.14575	−	1.98450i	0.229150	−	0.396900i
$26$	−0.322876	+	0.559237i	−0.0633211	+	0.109675i
$27$		0			0
$28$	−1.32288	−	2.29129i	−0.250000	−	0.433013i
$29$	−3.82288	−	6.62141i	−0.709890	−	1.22957i	−0.964898	−	0.262627i	$-0.915411\pi$
$29$	−3.82288	−	6.62141i	−0.709890	−	1.22957i	0.255007	−	0.966939i	$-0.417922\pi$
$30$		0			0
$31$	0.645751			0.115980			0.0579902	−	0.998317i	$-0.481531\pi$
$31$	0.645751			0.115980			0.0579902	+	0.998317i	$0.481531\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	0.822876	+	1.42526i	0.141122	+	0.244430i
$35$	−2.17712	+	3.77089i	−0.368001	+	0.637397i
$36$		0			0
$37$	−1.96863	+	3.40976i	−0.323640	+	0.560561i	−0.981236	−	0.192809i	$-0.938240\pi$
$37$	−1.96863	+	3.40976i	−0.323640	+	0.560561i	0.657596	+	0.753371i	$0.271573\pi$
$38$	−1.00000	+	1.73205i	−0.162221	+	0.280976i
$39$		0			0
$40$	−0.822876	−	1.42526i	−0.130108	−	0.225354i
$41$	2.46863	−	4.27579i	0.385535	−	0.667766i	−0.606308	−	0.795230i	$-0.707350\pi$
$41$	2.46863	−	4.27579i	0.385535	−	0.667766i	0.991843	+	0.127464i	$0.0406837\pi$
$42$		0			0
$43$	−2.50000	−	4.33013i	−0.381246	−	0.660338i	0.609994	−	0.792406i	$-0.291172\pi$
$43$	−2.50000	−	4.33013i	−0.381246	−	0.660338i	−0.991241	+	0.132068i	$0.957838\pi$
$44$	0.822876	−	1.42526i	0.124053	−	0.214866i
$45$		0			0
$46$	−4.64575	−	8.04668i	−0.684979	−	1.18642i
$47$	−10.9373			−1.59536			−0.797681	−	0.603079i	$-0.793940\pi$
$47$	−10.9373			−1.59536			−0.797681	+	0.603079i	$0.793940\pi$
$48$		0			0
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$	1.14575	−	1.98450i	0.162034	−	0.280651i
$51$		0			0
$52$	−0.322876	+	0.559237i	−0.0447748	+	0.0775522i
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$		0			0
$55$	−2.70850			−0.365214
$56$	−1.32288	−	2.29129i	−0.176777	−	0.306186i
$57$		0			0
$58$	−3.82288	−	6.62141i	−0.501968	−	0.869434i
$59$	13.6458			1.77653			0.888263	−	0.459336i	$-0.151912\pi$
$59$	13.6458			1.77653			0.888263	+	0.459336i	$0.151912\pi$
$60$		0			0
$61$	12.6458			1.61912			0.809561	−	0.587035i	$-0.199705\pi$
$61$	12.6458			1.61912			0.809561	+	0.587035i	$0.199705\pi$
$62$	0.645751			0.0820105
$63$		0			0
$64$	1.00000			0.125000
$65$	1.06275			0.131817
$66$		0			0
$67$	8.29150			1.01297			0.506484	−	0.862249i	$-0.330945\pi$
$67$	8.29150			1.01297			0.506484	+	0.862249i	$0.330945\pi$
$68$	0.822876	+	1.42526i	0.0997883	+	0.172838i
$69$		0			0
$70$	−2.17712	+	3.77089i	−0.260216	+	0.450708i
$71$	10.3542			1.22882			0.614412	−	0.788986i	$-0.289393\pi$
$71$	10.3542			1.22882			0.614412	+	0.788986i	$0.289393\pi$
$72$		0			0
$73$	5.29150	+	9.16515i	0.619324	+	1.07270i	0.989609	+	0.143782i	$0.0459264\pi$
$73$	5.29150	+	9.16515i	0.619324	+	1.07270i	−0.370286	+	0.928918i	$0.620740\pi$
$74$	−1.96863	+	3.40976i	−0.228848	+	0.396377i
$75$		0			0
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$	−4.35425			−0.496213
$78$		0			0
$79$	−15.2288			−1.71337			−0.856684	−	0.515841i	$-0.827480\pi$
$79$	−15.2288			−1.71337			−0.856684	+	0.515841i	$0.827480\pi$
$80$	−0.822876	−	1.42526i	−0.0920003	−	0.159349i
$81$		0			0
$82$	2.46863	−	4.27579i	0.272614	−	0.472182i
$83$	1.35425	+	2.34563i	0.148648	+	0.257466i	0.930728	−	0.365712i	$-0.119174\pi$
$83$	1.35425	+	2.34563i	0.148648	+	0.257466i	−0.782080	+	0.623178i	$0.785841\pi$
$84$		0			0
$85$	1.35425	−	2.34563i	0.146889	−	0.254419i
$86$	−2.50000	−	4.33013i	−0.269582	−	0.466930i
$87$		0			0
$88$	0.822876	−	1.42526i	0.0877188	−	0.151933i
$89$	5.46863	−	9.47194i	0.579673	−	1.00402i	−0.415843	−	0.909436i	$-0.636514\pi$
$89$	5.46863	−	9.47194i	0.579673	−	1.00402i	0.995517	−	0.0945873i	$-0.0301532\pi$
$90$		0			0
$91$	1.70850			0.179099
$92$	−4.64575	−	8.04668i	−0.484353	−	0.838924i
$93$		0			0
$94$	−10.9373			−1.12809
$95$	3.29150			0.337701
$96$		0			0
$97$	3.79150	+	6.56708i	0.384969	+	0.666785i	0.991765	−	0.128072i	$-0.0408789\pi$
$97$	3.79150	+	6.56708i	0.384969	+	0.666785i	−0.606796	+	0.794858i	$0.707546\pi$
$98$	−3.50000	+	6.06218i	−0.353553	+	0.612372i
$99$		0			0
$100$	1.14575	−	1.98450i	0.114575	−	0.198450i
$101$	−6.82288	+	11.8176i	−0.678902	+	1.17589i	0.296411	+	0.955061i	$0.404210\pi$
$101$	−6.82288	+	11.8176i	−0.678902	+	1.17589i	−0.975312	+	0.220831i	$0.929123\pi$
$102$		0			0
$103$	5.96863	+	10.3380i	0.588106	+	1.01863i	0.994480	+	0.104923i	$0.0334597\pi$
$103$	5.96863	+	10.3380i	0.588106	+	1.01863i	−0.406374	+	0.913707i	$0.633207\pi$
$104$	−0.322876	+	0.559237i	−0.0316606	+	0.0548377i
$105$		0			0
$106$	−3.00000	−	5.19615i	−0.291386	−	0.504695i
$107$	3.00000	−	5.19615i	0.290021	−	0.502331i	−0.683793	−	0.729676i	$-0.739671\pi$
$107$	3.00000	−	5.19615i	0.290021	−	0.502331i	0.973814	+	0.227345i	$0.0730044\pi$
$108$		0			0
$109$	4.32288	+	7.48744i	0.414056	+	0.717167i	0.995329	−	0.0965423i	$-0.0307783\pi$
$109$	4.32288	+	7.48744i	0.414056	+	0.717167i	−0.581272	+	0.813709i	$0.697445\pi$
$110$	−2.70850			−0.258245
$111$		0			0
$112$	−1.32288	−	2.29129i	−0.125000	−	0.216506i
$113$	−3.82288	+	6.62141i	−0.359626	+	0.622890i	−0.987898	−	0.155103i	$-0.950429\pi$
$113$	−3.82288	+	6.62141i	−0.359626	+	0.622890i	0.628272	+	0.777993i	$0.283762\pi$
$114$		0			0
$115$	−7.64575	+	13.2428i	−0.712970	+	1.23490i
$116$	−3.82288	−	6.62141i	−0.354945	−	0.614783i
$117$		0			0
$118$	13.6458			1.25619
$119$	2.17712	−	3.77089i	0.199577	−	0.345677i
$120$		0			0
$121$	4.14575	+	7.18065i	0.376886	+	0.652787i
$122$	12.6458			1.14489
$123$		0			0
$124$	0.645751			0.0579902
$125$	−12.0000			−1.07331
$126$		0			0
$127$	6.64575			0.589715			0.294858	−	0.955541i	$-0.404728\pi$
$127$	6.64575			0.589715			0.294858	+	0.955541i	$0.404728\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	1.06275			0.0932090
$131$	−3.29150	−	5.70105i	−0.287580	−	0.498103i	0.685652	−	0.727930i	$-0.259517\pi$
$131$	−3.29150	−	5.70105i	−0.287580	−	0.498103i	−0.973232	+	0.229827i	$0.926184\pi$
$132$		0			0
$133$	5.29150			0.458831
$134$	8.29150			0.716277
$135$		0			0
$136$	0.822876	+	1.42526i	0.0705610	+	0.122215i
$137$	4.64575	−	8.04668i	0.396913	−	0.687474i	−0.596430	−	0.802665i	$-0.703415\pi$
$137$	4.64575	−	8.04668i	0.396913	−	0.687474i	0.993343	+	0.115191i	$0.0367480\pi$
$138$		0			0
$139$	9.79150	−	16.9594i	0.830504	−	1.43848i	−0.0671344	−	0.997744i	$-0.521386\pi$
$139$	9.79150	−	16.9594i	0.830504	−	1.43848i	0.897639	−	0.440732i	$-0.145281\pi$
$140$	−2.17712	+	3.77089i	−0.184001	+	0.318698i
$141$		0			0
$142$	10.3542			0.868909
$143$	0.531373	+	0.920365i	0.0444356	+	0.0769648i
$144$		0			0
$145$	−6.29150	+	10.8972i	−0.522481	+	0.904963i
$146$	5.29150	+	9.16515i	0.437928	+	0.758513i
$147$		0			0
$148$	−1.96863	+	3.40976i	−0.161820	+	0.280281i
$149$	−3.53137	−	6.11652i	−0.289301	−	0.501085i	0.684342	−	0.729161i	$-0.260090\pi$
$149$	−3.53137	−	6.11652i	−0.289301	−	0.501085i	−0.973643	+	0.228077i	$0.926756\pi$
$150$		0			0
$151$	−3.61438	+	6.26029i	−0.294134	+	0.509455i	−0.974783	−	0.223155i	$-0.928365\pi$
$151$	−3.61438	+	6.26029i	−0.294134	+	0.509455i	0.680649	+	0.732610i	$0.261698\pi$
$152$	−1.00000	+	1.73205i	−0.0811107	+	0.140488i
$153$		0			0
$154$	−4.35425			−0.350875
$155$	−0.531373	−	0.920365i	−0.0426809	−	0.0739255i
$156$		0			0
$157$	−4.00000			−0.319235			−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000			−0.319235			−0.159617	+	0.987179i	$0.551026\pi$
$158$	−15.2288			−1.21153
$159$		0			0
$160$	−0.822876	−	1.42526i	−0.0650540	−	0.112677i
$161$	−12.2915	+	21.2895i	−0.968706	+	1.67785i
$162$		0			0
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	−0.845780	−	0.533533i	$-0.820864\pi$
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	0.884943	+	0.465700i	$0.154198\pi$
$164$	2.46863	−	4.27579i	0.192767	−	0.333883i
$165$		0			0
$166$	1.35425	+	2.34563i	0.105110	+	0.182056i
$167$	−6.29150	+	10.8972i	−0.486851	+	0.843251i	−0.999886	−	0.0151171i	$-0.995188\pi$
$167$	−6.29150	+	10.8972i	−0.486851	+	0.843251i	0.513035	+	0.858368i	$0.328521\pi$
$168$		0			0
$169$	6.29150	+	10.8972i	0.483962	+	0.838246i
$170$	1.35425	−	2.34563i	0.103866	−	0.179901i
$171$		0			0
$172$	−2.50000	−	4.33013i	−0.190623	−	0.330169i
$173$	6.58301			0.500497			0.250248	−	0.968182i	$-0.419488\pi$
$173$	6.58301			0.500497			0.250248	+	0.968182i	$0.419488\pi$
$174$		0			0
$175$	−6.06275			−0.458301
$176$	0.822876	−	1.42526i	0.0620266	−	0.107433i
$177$		0			0
$178$	5.46863	−	9.47194i	0.409891	−	0.709952i
$179$	−0.531373	−	0.920365i	−0.0397167	−	0.0687913i	0.845484	−	0.534001i	$-0.179312\pi$
$179$	−0.531373	−	0.920365i	−0.0397167	−	0.0687913i	−0.885200	+	0.465210i	$0.845979\pi$
$180$		0			0
$181$	−13.2915			−0.987950			−0.493975	−	0.869476i	$-0.664457\pi$
$181$	−13.2915			−0.987950			−0.493975	+	0.869476i	$0.664457\pi$
$182$	1.70850			0.126642
$183$		0			0
$184$	−4.64575	−	8.04668i	−0.342489	−	0.593209i
$185$	6.47974			0.476400
$186$		0			0
$187$	2.70850			0.198065
$188$	−10.9373			−0.797681
$189$		0			0
$190$	3.29150			0.238791
$191$	26.8118			1.94003			0.970015	−	0.243043i	$-0.0781456\pi$
$191$	26.8118			1.94003			0.970015	+	0.243043i	$0.0781456\pi$
$192$		0			0
$193$	−7.00000			−0.503871			−0.251936	−	0.967744i	$-0.581067\pi$
$193$	−7.00000			−0.503871			−0.251936	+	0.967744i	$0.581067\pi$
$194$	3.79150	+	6.56708i	0.272214	+	0.471489i
$195$		0			0
$196$	−3.50000	+	6.06218i	−0.250000	+	0.433013i
$197$	15.2915			1.08947			0.544737	−	0.838607i	$-0.316629\pi$
$197$	15.2915			1.08947			0.544737	+	0.838607i	$0.316629\pi$
$198$		0			0
$199$	−10.9686	−	18.9982i	−0.777545	−	1.34675i	−0.933353	−	0.358961i	$-0.883131\pi$
$199$	−10.9686	−	18.9982i	−0.777545	−	1.34675i	0.155807	−	0.987787i	$-0.450202\pi$
$200$	1.14575	−	1.98450i	0.0810169	−	0.140325i
$201$		0			0
$202$	−6.82288	+	11.8176i	−0.480056	+	0.831481i
$203$	−10.1144	+	17.5186i	−0.709890	+	1.22957i
$204$		0			0
$205$	−8.12549			−0.567509
$206$	5.96863	+	10.3380i	0.415854	+	0.720280i
$207$		0			0
$208$	−0.322876	+	0.559237i	−0.0223874	+	0.0387761i
$209$	1.64575	+	2.85052i	0.113839	+	0.197175i
$210$		0			0
$211$	8.43725	−	14.6138i	0.580845	−	1.00605i	−0.414535	−	0.910033i	$-0.636056\pi$
$211$	8.43725	−	14.6138i	0.580845	−	1.00605i	0.995380	−	0.0960188i	$-0.0306109\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$		0			0
$214$	3.00000	−	5.19615i	0.205076	−	0.355202i
$215$	−4.11438	+	7.12631i	−0.280598	+	0.486010i
$216$		0			0
$217$	−0.854249	−	1.47960i	−0.0579902	−	0.100442i
$218$	4.32288	+	7.48744i	0.292782	+	0.507113i
$219$		0			0
$220$	−2.70850			−0.182607
$221$	−1.06275			−0.0714880
$222$		0			0
$223$	−8.93725	−	15.4798i	−0.598483	−	1.03660i	−0.993045	−	0.117733i	$-0.962437\pi$
$223$	−8.93725	−	15.4798i	−0.598483	−	1.03660i	0.394562	−	0.918869i	$-0.370896\pi$
$224$	−1.32288	−	2.29129i	−0.0883883	−	0.153093i
$225$		0			0
$226$	−3.82288	+	6.62141i	−0.254294	+	0.440450i
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	−0.948242	−	0.317547i	$-0.897141\pi$
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	0.749125	+	0.662428i	$0.230474\pi$
$228$		0			0
$229$	7.32288	+	12.6836i	0.483909	+	0.838155i	0.999829	−	0.0184814i	$-0.00588315\pi$
$229$	7.32288	+	12.6836i	0.483909	+	0.838155i	−0.515920	+	0.856637i	$0.672550\pi$
$230$	−7.64575	+	13.2428i	−0.504146	+	0.873206i
$231$		0			0
$232$	−3.82288	−	6.62141i	−0.250984	−	0.434717i
$233$	4.35425	−	7.54178i	0.285256	−	0.494078i	−0.687415	−	0.726265i	$-0.741255\pi$
$233$	4.35425	−	7.54178i	0.285256	−	0.494078i	0.972671	+	0.232186i	$0.0745879\pi$
$234$		0			0
$235$	9.00000	+	15.5885i	0.587095	+	1.01688i
$236$	13.6458			0.888263
$237$		0			0
$238$	2.17712	−	3.77089i	0.141122	−	0.244430i
$239$	−2.46863	+	4.27579i	−0.159682	+	0.276578i	−0.934754	−	0.355295i	$-0.884380\pi$
$239$	−2.46863	+	4.27579i	−0.159682	+	0.276578i	0.775072	+	0.631873i	$0.217714\pi$
$240$		0			0
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	−0.935242	−	0.354010i	$-0.884818\pi$
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	0.774202	+	0.632938i	$0.218151\pi$
$242$	4.14575	+	7.18065i	0.266499	+	0.461590i
$243$		0			0
$244$	12.6458			0.809561
$245$	11.5203			0.736002
$246$		0			0
$247$	−0.645751	−	1.11847i	−0.0410882	−	0.0711668i
$248$	0.645751			0.0410052
$249$		0			0
$250$	−12.0000			−0.758947
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$		0			0
$253$	−15.2915			−0.961369
$254$	6.64575			0.416992
$255$		0			0
$256$	1.00000			0.0625000
$257$	7.93725	+	13.7477i	0.495112	+	0.857560i	0.999984	−	0.00563467i	$-0.00179358\pi$
$257$	7.93725	+	13.7477i	0.495112	+	0.857560i	−0.504872	+	0.863194i	$0.668460\pi$
$258$		0			0
$259$	10.4170			0.647281
$260$	1.06275			0.0659087
$261$		0			0
$262$	−3.29150	−	5.70105i	−0.203350	−	0.352212i
$263$	−5.46863	+	9.47194i	−0.337210	+	0.584065i	−0.983907	−	0.178682i	$-0.942817\pi$
$263$	−5.46863	+	9.47194i	−0.337210	+	0.584065i	0.646697	+	0.762747i	$0.276150\pi$
$264$		0			0
$265$	−4.93725	+	8.55157i	−0.303293	+	0.525319i
$266$	5.29150			0.324443
$267$		0			0
$268$	8.29150			0.506484
$269$	13.6458	+	23.6351i	0.831996	+	1.44106i	0.896453	+	0.443139i	$0.146135\pi$
$269$	13.6458	+	23.6351i	0.831996	+	1.44106i	−0.0644567	+	0.997921i	$0.520531\pi$
$270$		0			0
$271$	10.6144	−	18.3846i	0.644778	−	1.11679i	−0.339575	−	0.940579i	$-0.610283\pi$
$271$	10.6144	−	18.3846i	0.644778	−	1.11679i	0.984353	−	0.176209i	$-0.0563833\pi$
$272$	0.822876	+	1.42526i	0.0498942	+	0.0864192i
$273$		0			0
$274$	4.64575	−	8.04668i	0.280660	−	0.486118i
$275$	−1.88562	−	3.26599i	−0.113707	−	0.196947i
$276$		0			0
$277$	8.96863	−	15.5341i	0.538873	−	0.933355i	−0.460093	−	0.887871i	$-0.652184\pi$
$277$	8.96863	−	15.5341i	0.538873	−	0.933355i	0.998965	−	0.0454837i	$-0.0144829\pi$
$278$	9.79150	−	16.9594i	0.587255	−	1.01716i
$279$		0			0
$280$	−2.17712	+	3.77089i	−0.130108	+	0.225354i
$281$	8.76013	+	15.1730i	0.522586	+	0.905145i	0.999655	+	0.0262789i	$0.00836580\pi$
$281$	8.76013	+	15.1730i	0.522586	+	0.905145i	−0.477069	+	0.878866i	$0.658301\pi$
$282$		0			0
$283$	8.29150			0.492879			0.246439	−	0.969158i	$-0.420739\pi$
$283$	8.29150			0.492879			0.246439	+	0.969158i	$0.420739\pi$
$284$	10.3542			0.614412
$285$		0			0
$286$	0.531373	+	0.920365i	0.0314207	+	0.0544223i
$287$	−13.0627			−0.771070
$288$		0			0
$289$	7.14575	−	12.3768i	0.420338	−	0.728047i
$290$	−6.29150	+	10.8972i	−0.369450	+	0.639906i
$291$		0			0
$292$	5.29150	+	9.16515i	0.309662	+	0.536350i
$293$	−11.4686	+	19.8642i	−0.670004	+	1.16048i	0.307898	+	0.951419i	$0.400374\pi$
$293$	−11.4686	+	19.8642i	−0.670004	+	1.16048i	−0.977902	+	0.209062i	$0.932959\pi$
$294$		0			0
$295$	−11.2288	−	19.4488i	−0.653763	−	1.13235i
$296$	−1.96863	+	3.40976i	−0.114424	+	0.198188i
$297$		0			0
$298$	−3.53137	−	6.11652i	−0.204567	−	0.354320i
$299$	6.00000			0.346989
$300$		0			0
$301$	−6.61438	+	11.4564i	−0.381246	+	0.660338i
$302$	−3.61438	+	6.26029i	−0.207984	+	0.360239i
$303$		0			0
$304$	−1.00000	+	1.73205i	−0.0573539	+	0.0993399i
$305$	−10.4059	−	18.0235i	−0.595839	−	1.03202i
$306$		0			0
$307$	−13.5830			−0.775223			−0.387612	−	0.921823i	$-0.626700\pi$
$307$	−13.5830			−0.775223			−0.387612	+	0.921823i	$0.626700\pi$
$308$	−4.35425			−0.248106
$309$		0			0
$310$	−0.531373	−	0.920365i	−0.0301800	−	0.0522732i
$311$	23.5203			1.33371			0.666856	−	0.745187i	$-0.267640\pi$
$311$	23.5203			1.33371			0.666856	+	0.745187i	$0.267640\pi$
$312$		0			0
$313$	23.2915			1.31651			0.658257	−	0.752793i	$-0.271294\pi$
$313$	23.2915			1.31651			0.658257	+	0.752793i	$0.271294\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	−15.2288			−0.856684
$317$	−20.8118			−1.16890			−0.584452	−	0.811428i	$-0.698691\pi$
$317$	−20.8118			−1.16890			−0.584452	+	0.811428i	$0.698691\pi$
$318$		0			0
$319$	−12.5830			−0.704513
$320$	−0.822876	−	1.42526i	−0.0460001	−	0.0796746i
$321$		0			0
$322$	−12.2915	+	21.2895i	−0.684979	+	1.18642i
$323$	−3.29150			−0.183144
$324$		0			0
$325$	0.739870	+	1.28149i	0.0410406	+	0.0710844i
$326$	0.500000	−	0.866025i	0.0276924	−	0.0479647i
$327$		0			0
$328$	2.46863	−	4.27579i	0.136307	−	0.236091i
$329$	14.4686	+	25.0604i	0.797681	+	1.38162i
$330$		0			0
$331$	−0.125492			−0.00689767			−0.00344884	−	0.999994i	$-0.501098\pi$
$331$	−0.125492			−0.00689767			−0.00344884	+	0.999994i	$0.501098\pi$
$332$	1.35425	+	2.34563i	0.0743241	+	0.128733i
$333$		0			0
$334$	−6.29150	+	10.8972i	−0.344256	+	0.596268i
$335$	−6.82288	−	11.8176i	−0.372774	−	0.645663i
$336$		0			0
$337$	4.70850	−	8.15536i	0.256488	−	0.444251i	−0.708810	−	0.705399i	$-0.750768\pi$
$337$	4.70850	−	8.15536i	0.256488	−	0.444251i	0.965299	+	0.261148i	$0.0841012\pi$
$338$	6.29150	+	10.8972i	0.342213	+	0.592730i
$339$		0			0
$340$	1.35425	−	2.34563i	0.0734444	−	0.127210i
$341$	0.531373	−	0.920365i	0.0287755	−	0.0498406i
$342$		0			0
$343$	18.5203			1.00000
$344$	−2.50000	−	4.33013i	−0.134791	−	0.233465i
$345$		0			0
$346$	6.58301			0.353905
$347$	−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
$349$	−12.6144	−	21.8487i	−0.675232	−	1.16954i	−0.976401	−	0.215966i	$-0.930710\pi$
$349$	−12.6144	−	21.8487i	−0.675232	−	1.16954i	0.301169	−	0.953571i	$-0.402623\pi$
$350$	−6.06275			−0.324067
$351$		0			0
$352$	0.822876	−	1.42526i	0.0438594	−	0.0759667i
$353$	6.00000	−	10.3923i	0.319348	−	0.553127i	−0.661004	−	0.750382i	$-0.729870\pi$
$353$	6.00000	−	10.3923i	0.319348	−	0.553127i	0.980352	+	0.197256i	$0.0632029\pi$
$354$		0			0
$355$	−8.52026	−	14.7575i	−0.452208	−	0.783248i
$356$	5.46863	−	9.47194i	0.289837	−	0.502012i
$357$		0			0
$358$	−0.531373	−	0.920365i	−0.0280839	−	0.0486428i
$359$	15.5830	−	26.9906i	0.822440	−	1.42451i	−0.0814209	−	0.996680i	$-0.525946\pi$
$359$	15.5830	−	26.9906i	0.822440	−	1.42451i	0.903860	−	0.427827i	$-0.140721\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−13.2915			−0.698586
$363$		0			0
$364$	1.70850			0.0895496
$365$	8.70850	−	15.0836i	0.455824	−	0.789510i
$366$		0			0
$367$	0.937254	−	1.62337i	0.0489243	−	0.0847393i	−0.840526	−	0.541771i	$-0.817754\pi$
$367$	0.937254	−	1.62337i	0.0489243	−	0.0847393i	0.889450	+	0.457032i	$0.151087\pi$
$368$	−4.64575	−	8.04668i	−0.242177	−	0.419462i
$369$		0			0
$370$	6.47974			0.336866
$371$	−7.93725	+	13.7477i	−0.412082	+	0.713746i
$372$		0			0
$373$	8.29150	+	14.3613i	0.429318	+	0.743600i	0.996813	−	0.0797767i	$-0.0254207\pi$
$373$	8.29150	+	14.3613i	0.429318	+	0.743600i	−0.567495	+	0.823377i	$0.692087\pi$
$374$	2.70850			0.140053
$375$		0			0
$376$	−10.9373			−0.564046
$377$	4.93725			0.254282
$378$		0			0
$379$	4.41699			0.226886			0.113443	−	0.993545i	$-0.463812\pi$
$379$	4.41699			0.226886			0.113443	+	0.993545i	$0.463812\pi$
$380$	3.29150			0.168851
$381$		0			0
$382$	26.8118			1.37181
$383$	0.291503	+	0.504897i	0.0148951	+	0.0257990i	0.873377	−	0.487045i	$-0.161925\pi$
$383$	0.291503	+	0.504897i	0.0148951	+	0.0257990i	−0.858482	+	0.512844i	$0.828592\pi$
$384$		0			0
$385$	3.58301	+	6.20595i	0.182607	+	0.316284i
$386$	−7.00000			−0.356291
$387$		0			0
$388$	3.79150	+	6.56708i	0.192484	+	0.333393i
$389$	−4.35425	+	7.54178i	−0.220769	+	0.382383i	−0.955042	−	0.296471i	$-0.904190\pi$
$389$	−4.35425	+	7.54178i	−0.220769	+	0.382383i	0.734273	+	0.678855i	$0.237523\pi$
$390$		0			0
$391$	7.64575	−	13.2428i	0.386662	−	0.669719i
$392$	−3.50000	+	6.06218i	−0.176777	+	0.306186i
$393$		0			0
$394$	15.2915			0.770375
$395$	12.5314	+	21.7050i	0.630522	+	1.09210i
$396$		0			0
$397$	5.67712	−	9.83307i	0.284927	−	0.493508i	−0.687665	−	0.726028i	$-0.741364\pi$
$397$	5.67712	−	9.83307i	0.284927	−	0.493508i	0.972591	+	0.232521i	$0.0746974\pi$
$398$	−10.9686	−	18.9982i	−0.549808	−	0.952295i
$399$		0			0
$400$	1.14575	−	1.98450i	0.0572876	−	0.0992250i
$401$	−13.4059	−	23.2197i	−0.669458	−	1.15953i	−0.978056	−	0.208342i	$-0.933193\pi$
$401$	−13.4059	−	23.2197i	−0.669458	−	1.15953i	0.308598	−	0.951192i	$-0.400140\pi$
$402$		0			0
$403$	−0.208497	+	0.361128i	−0.0103860	+	0.0179891i
$404$	−6.82288	+	11.8176i	−0.339451	+	0.587946i
$405$		0			0
$406$	−10.1144	+	17.5186i	−0.501968	+	0.869434i
$407$	3.23987	+	5.61162i	0.160594	+	0.278158i
$408$		0			0
$409$	−16.8745			−0.834391			−0.417195	−	0.908817i	$-0.636987\pi$
$409$	−16.8745			−0.834391			−0.417195	+	0.908817i	$0.636987\pi$
$410$	−8.12549			−0.401289
$411$		0			0
$412$	5.96863	+	10.3380i	0.294053	+	0.509315i
$413$	−18.0516	−	31.2663i	−0.888263	−	1.53852i
$414$		0			0
$415$	2.22876	−	3.86032i	0.109405	−	0.189496i
$416$	−0.322876	+	0.559237i	−0.0158303	+	0.0274189i
$417$		0			0
$418$	1.64575	+	2.85052i	0.0804963	+	0.139424i
$419$	−6.53137	+	11.3127i	−0.319078	+	0.552660i	−0.980296	−	0.197534i	$-0.936707\pi$
$419$	−6.53137	+	11.3127i	−0.319078	+	0.552660i	0.661218	+	0.750194i	$0.270040\pi$
$420$		0			0
$421$	12.6458	+	21.9031i	0.616316	+	1.06749i	0.990152	+	0.139996i	$0.0447090\pi$
$421$	12.6458	+	21.9031i	0.616316	+	1.06749i	−0.373836	+	0.927495i	$0.621958\pi$
$422$	8.43725	−	14.6138i	0.410719	−	0.711386i
$423$		0			0
$424$	−3.00000	−	5.19615i	−0.145693	−	0.252347i
$425$	3.77124			0.182932
$426$		0			0
$427$	−16.7288	−	28.9751i	−0.809561	−	1.40220i
$428$	3.00000	−	5.19615i	0.145010	−	0.251166i
$429$		0			0
$430$	−4.11438	+	7.12631i	−0.198413	+	0.343661i
$431$	4.40588	+	7.63121i	0.212224	+	0.367582i	0.952410	−	0.304819i	$-0.0985961\pi$
$431$	4.40588	+	7.63121i	0.212224	+	0.367582i	−0.740186	+	0.672402i	$0.765263\pi$
$432$		0			0
$433$	−19.0000			−0.913082			−0.456541	−	0.889702i	$-0.650912\pi$
$433$	−19.0000			−0.913082			−0.456541	+	0.889702i	$0.650912\pi$
$434$	−0.854249	−	1.47960i	−0.0410052	−	0.0710232i
$435$		0			0
$436$	4.32288	+	7.48744i	0.207028	+	0.358583i
$437$	18.5830			0.888946
$438$		0			0
$439$	−17.1660			−0.819289			−0.409644	−	0.912245i	$-0.634347\pi$
$439$	−17.1660			−0.819289			−0.409644	+	0.912245i	$0.634347\pi$
$440$	−2.70850			−0.129123
$441$		0			0
$442$	−1.06275			−0.0505497
$443$	−8.70850			−0.413753			−0.206877	−	0.978367i	$-0.566330\pi$
$443$	−8.70850			−0.413753			−0.206877	+	0.978367i	$0.566330\pi$
$444$		0			0
$445$	−18.0000			−0.853282
$446$	−8.93725	−	15.4798i	−0.423191	−	0.732989i
$447$		0			0
$448$	−1.32288	−	2.29129i	−0.0625000	−	0.108253i
$449$	7.64575			0.360825			0.180413	−	0.983591i	$-0.442257\pi$
$449$	7.64575			0.360825			0.180413	+	0.983591i	$0.442257\pi$
$450$		0			0
$451$	−4.06275	−	7.03688i	−0.191307	−	0.331354i
$452$	−3.82288	+	6.62141i	−0.179813	+	0.311445i
$453$		0			0
$454$	−3.00000	+	5.19615i	−0.140797	+	0.243868i
$455$	−1.40588	−	2.43506i	−0.0659087	−	0.114157i
$456$		0			0
$457$	2.29150			0.107192			0.0535960	−	0.998563i	$-0.482932\pi$
$457$	2.29150			0.107192			0.0535960	+	0.998563i	$0.482932\pi$
$458$	7.32288	+	12.6836i	0.342176	+	0.592665i
$459$		0			0
$460$	−7.64575	+	13.2428i	−0.356485	+	0.617450i
$461$	1.11438	+	1.93016i	0.0519018	+	0.0898965i	0.890809	−	0.454378i	$-0.150138\pi$
$461$	1.11438	+	1.93016i	0.0519018	+	0.0898965i	−0.838907	+	0.544274i	$0.816805\pi$
$462$		0			0
$463$	−14.6458	+	25.3672i	−0.680646	+	1.17891i	0.294138	+	0.955763i	$0.404967\pi$
$463$	−14.6458	+	25.3672i	−0.680646	+	1.17891i	−0.974784	+	0.223150i	$0.928366\pi$
$464$	−3.82288	−	6.62141i	−0.177473	−	0.307391i
$465$		0			0
$466$	4.35425	−	7.54178i	0.201707	−	0.349366i
$467$	13.1144	−	22.7148i	0.606861	−	1.05111i	−0.384893	−	0.922961i	$-0.625762\pi$
$467$	13.1144	−	22.7148i	0.606861	−	1.05111i	0.991754	−	0.128153i	$-0.0409049\pi$
$468$		0			0
$469$	−10.9686	−	18.9982i	−0.506484	−	0.877256i
$470$	9.00000	+	15.5885i	0.415139	+	0.719042i
$471$		0			0
$472$	13.6458			0.628097
$473$	−8.22876			−0.378359
$474$		0			0
$475$	2.29150	+	3.96900i	0.105141	+	0.182110i
$476$	2.17712	−	3.77089i	0.0997883	−	0.172838i
$477$		0			0
$478$	−2.46863	+	4.27579i	−0.112912	+	0.195570i
$479$	0.822876	−	1.42526i	0.0375981	−	0.0651219i	−0.846614	−	0.532207i	$-0.821363\pi$
$479$	0.822876	−	1.42526i	0.0375981	−	0.0651219i	0.884212	+	0.467086i	$0.154696\pi$
$480$		0			0
$481$	−1.27124	−	2.20186i	−0.0579637	−	0.100396i
$482$	−2.50000	+	4.33013i	−0.113872	+	0.197232i
$483$		0			0
$484$	4.14575	+	7.18065i	0.188443	+	0.326393i
$485$	6.23987	−	10.8078i	0.283338	−	0.490756i
$486$		0			0
$487$	3.93725	+	6.81952i	0.178414	+	0.309022i	0.941337	−	0.337467i	$-0.109570\pi$
$487$	3.93725	+	6.81952i	0.178414	+	0.309022i	−0.762923	+	0.646489i	$0.776237\pi$
$488$	12.6458			0.572446
$489$		0			0
$490$	11.5203			0.520432
$491$	18.8745	−	32.6916i	0.851795	−	1.47535i	−0.0277925	−	0.999614i	$-0.508848\pi$
$491$	18.8745	−	32.6916i	0.851795	−	1.47535i	0.879587	−	0.475738i	$-0.157819\pi$
$492$		0			0
$493$	6.29150	−	10.8972i	0.283355	−	0.490785i
$494$	−0.645751	−	1.11847i	−0.0290537	−	0.0503225i
$495$		0			0
$496$	0.645751			0.0289951
$497$	−13.6974	−	23.7246i	−0.614412	−	1.06419i
$498$		0			0
$499$	−18.0830	−	31.3207i	−0.809506	−	1.40211i	−0.913206	−	0.407498i	$-0.866401\pi$
$499$	−18.0830	−	31.3207i	−0.809506	−	1.40211i	0.103700	−	0.994609i	$-0.466932\pi$
$500$	−12.0000			−0.536656
$501$		0			0
$502$	−18.0000			−0.803379
$503$	−27.8745			−1.24286			−0.621431	−	0.783469i	$-0.713449\pi$
$503$	−27.8745			−1.24286			−0.621431	+	0.783469i	$0.713449\pi$
$504$		0			0
$505$	22.4575			0.999346
$506$	−15.2915			−0.679790
$507$		0			0
$508$	6.64575			0.294858
$509$	−19.9373	−	34.5323i	−0.883703	−	1.53062i	−0.847193	−	0.531286i	$-0.821709\pi$
$509$	−19.9373	−	34.5323i	−0.883703	−	1.53062i	−0.0365105	−	0.999333i	$-0.511624\pi$
$510$		0			0
$511$	14.0000	−	24.2487i	0.619324	−	1.07270i
$512$	1.00000			0.0441942
$513$		0			0
$514$	7.93725	+	13.7477i	0.350097	+	0.606386i
$515$	9.82288	−	17.0137i	0.432848	−	0.749714i
$516$		0			0
$517$	−9.00000	+	15.5885i	−0.395820	+	0.685580i
$518$	10.4170			0.457696
$519$		0			0
$520$	1.06275			0.0466045
$521$	19.9373	+	34.5323i	0.873467	+	1.51289i	0.858387	+	0.513003i	$0.171467\pi$
$521$	19.9373	+	34.5323i	0.873467	+	1.51289i	0.0150801	+	0.999886i	$0.495200\pi$
$522$		0			0
$523$	0.500000	−	0.866025i	0.0218635	−	0.0378686i	−0.854887	−	0.518815i	$-0.826373\pi$
$523$	0.500000	−	0.866025i	0.0218635	−	0.0378686i	0.876750	+	0.480946i	$0.159707\pi$
$524$	−3.29150	−	5.70105i	−0.143790	−	0.249052i
$525$		0			0
$526$	−5.46863	+	9.47194i	−0.238443	+	0.412996i
$527$	0.531373	+	0.920365i	0.0231470	+	0.0400917i
$528$		0			0
$529$	−31.6660	+	54.8471i	−1.37678	+	2.38466i
$530$	−4.93725	+	8.55157i	−0.214461	+	0.371457i
$531$		0			0
$532$	5.29150			0.229416
$533$	1.59412	+	2.76110i	0.0690490	+	0.119596i
$534$		0			0
$535$	−9.87451			−0.426912
$536$	8.29150			0.358138
$537$		0			0
$538$	13.6458	+	23.6351i	0.588310	+	1.01898i
$539$	5.76013	+	9.97684i	0.248106	+	0.429733i
$540$		0			0
$541$	20.5830	−	35.6508i	0.884933	−	1.53275i	0.0391415	−	0.999234i	$-0.487538\pi$
$541$	20.5830	−	35.6508i	0.884933	−	1.53275i	0.845791	−	0.533514i	$-0.179129\pi$
$542$	10.6144	−	18.3846i	0.455927	−	0.789688i
$543$		0			0
$544$	0.822876	+	1.42526i	0.0352805	+	0.0611076i
$545$	7.11438	−	12.3225i	0.304746	−	0.527836i
$546$		0			0
$547$	−3.85425	−	6.67575i	−0.164796	−	0.285435i	0.771787	−	0.635881i	$-0.219363\pi$
$547$	−3.85425	−	6.67575i	−0.164796	−	0.285435i	−0.936583	+	0.350447i	$0.886030\pi$
$548$	4.64575	−	8.04668i	0.198457	−	0.343737i
$549$		0			0
$550$	−1.88562	−	3.26599i	−0.0804032	−	0.139262i
$551$	15.2915			0.651440
$552$		0			0
$553$	20.1458	+	34.8935i	0.856684	+	1.48382i
$554$	8.96863	−	15.5341i	0.381040	−	0.659981i
$555$		0			0
$556$	9.79150	−	16.9594i	0.415252	−	0.719238i
$557$	16.1144	+	27.9109i	0.682788	+	1.18262i	0.974126	+	0.226004i	$0.0725661\pi$
$557$	16.1144	+	27.9109i	0.682788	+	1.18262i	−0.291338	+	0.956620i	$0.594101\pi$
$558$		0			0
$559$	3.22876			0.136562
$560$	−2.17712	+	3.77089i	−0.0920003	+	0.159349i
$561$		0			0
$562$	8.76013	+	15.1730i	0.369524	+	0.640034i
$563$	−34.4575			−1.45221			−0.726106	−	0.687583i	$-0.758672\pi$
$563$	−34.4575			−1.45221			−0.726106	+	0.687583i	$0.758672\pi$
$564$		0			0
$565$	12.5830			0.529371
$566$	8.29150			0.348518
$567$		0			0
$568$	10.3542			0.434455
$569$	−1.06275			−0.0445526			−0.0222763	−	0.999752i	$-0.507091\pi$
$569$	−1.06275			−0.0445526			−0.0222763	+	0.999752i	$0.507091\pi$
$570$		0			0
$571$	−1.29150			−0.0540477			−0.0270239	−	0.999635i	$-0.508603\pi$
$571$	−1.29150			−0.0540477			−0.0270239	+	0.999635i	$0.508603\pi$
$572$	0.531373	+	0.920365i	0.0222178	+	0.0384824i
$573$		0			0
$574$	−13.0627			−0.545228
$575$	−21.2915			−0.887917
$576$		0			0
$577$	10.8542	+	18.8001i	0.451868	+	0.782659i	0.998502	−	0.0547129i	$-0.0174244\pi$
$577$	10.8542	+	18.8001i	0.451868	+	0.782659i	−0.546634	+	0.837372i	$0.684091\pi$
$578$	7.14575	−	12.3768i	0.297224	−	0.514807i
$579$		0			0
$580$	−6.29150	+	10.8972i	−0.261240	+	0.452482i
$581$	3.58301	−	6.20595i	0.148648	−	0.257466i
$582$		0			0
$583$	−9.87451			−0.408960
$584$	5.29150	+	9.16515i	0.218964	+	0.379257i
$585$		0			0
$586$	−11.4686	+	19.8642i	−0.473765	+	0.820584i
$587$	−19.1144	−	33.1071i	−0.788935	−	1.36648i	−0.926620	−	0.375999i	$-0.877300\pi$
$587$	−19.1144	−	33.1071i	−0.788935	−	1.36648i	0.137685	−	0.990476i	$-0.456034\pi$
$588$		0			0
$589$	−0.645751	+	1.11847i	−0.0266077	+	0.0460859i
$590$	−11.2288	−	19.4488i	−0.462281	−	0.800693i
$591$		0			0
$592$	−1.96863	+	3.40976i	−0.0809101	+	0.140140i
$593$	−12.5314	+	21.7050i	−0.514602	+	0.891316i	0.485255	+	0.874373i	$0.338727\pi$
$593$	−12.5314	+	21.7050i	−0.514602	+	0.891316i	−0.999856	+	0.0169436i	$0.994606\pi$
$594$		0			0
$595$	−7.16601			−0.293778
$596$	−3.53137	−	6.11652i	−0.144651	−	0.250542i
$597$		0			0
$598$	6.00000			0.245358
$599$	−21.8745			−0.893768			−0.446884	−	0.894592i	$-0.647466\pi$
$599$	−21.8745			−0.893768			−0.446884	+	0.894592i	$0.647466\pi$
$600$		0			0
$601$	2.43725	+	4.22145i	0.0994177	+	0.172196i	0.911444	−	0.411425i	$-0.134969\pi$
$601$	2.43725	+	4.22145i	0.0994177	+	0.172196i	−0.812026	+	0.583621i	$0.801635\pi$
$602$	−6.61438	+	11.4564i	−0.269582	+	0.466930i
$603$		0			0
$604$	−3.61438	+	6.26029i	−0.147067	+	0.254727i
$605$	6.82288	−	11.8176i	0.277389	−	0.480452i
$606$		0			0
$607$	−13.2915	−	23.0216i	−0.539485	−	0.934416i	−0.998932	−	0.0462106i	$-0.985285\pi$
$607$	−13.2915	−	23.0216i	−0.539485	−	0.934416i	0.459446	−	0.888206i	$-0.348048\pi$
$608$	−1.00000	+	1.73205i	−0.0405554	+	0.0702439i
$609$		0			0
$610$	−10.4059	−	18.0235i	−0.421322	−	0.729751i
$611$	3.53137	−	6.11652i	0.142864	−	0.247448i
$612$		0			0
$613$	−13.1974	−	22.8585i	−0.533037	−	0.923248i	−0.999256	−	0.0385780i	$-0.987717\pi$
$613$	−13.1974	−	22.8585i	−0.533037	−	0.923248i	0.466218	−	0.884670i	$-0.345616\pi$
$614$	−13.5830			−0.548165
$615$		0			0
$616$	−4.35425			−0.175438
$617$	17.7601	−	30.7614i	0.714996	−	1.23841i	−0.247965	−	0.968769i	$-0.579762\pi$
$617$	17.7601	−	30.7614i	0.714996	−	1.23841i	0.962961	−	0.269640i	$-0.0869048\pi$
$618$		0			0
$619$	−1.14575	+	1.98450i	−0.0460516	+	0.0797638i	−0.888132	−	0.459588i	$-0.847997\pi$
$619$	−1.14575	+	1.98450i	−0.0460516	+	0.0797638i	0.842081	+	0.539351i	$0.181331\pi$
$620$	−0.531373	−	0.920365i	−0.0213405	−	0.0369628i
$621$		0			0
$622$	23.5203			0.943076
$623$	−28.9373			−1.15935
$624$		0			0
$625$	4.14575	+	7.18065i	0.165830	+	0.287226i
$626$	23.2915			0.930916
$627$		0			0
$628$	−4.00000			−0.159617
$629$	−6.47974			−0.258364
$630$		0			0
$631$	21.9373			0.873308			0.436654	−	0.899629i	$-0.356163\pi$
$631$	21.9373			0.873308			0.436654	+	0.899629i	$0.356163\pi$
$632$	−15.2288			−0.605767
$633$		0			0
$634$	−20.8118			−0.826541
$635$	−5.46863	−	9.47194i	−0.217016	−	0.375882i
$636$		0			0
$637$	−2.26013	−	3.91466i	−0.0895496	−	0.155104i
$638$	−12.5830			−0.498166
$639$		0			0
$640$	−0.822876	−	1.42526i	−0.0325270	−	0.0563384i
$641$	−4.11438	+	7.12631i	−0.162508	+	0.281472i	−0.935768	−	0.352617i	$-0.885292\pi$
$641$	−4.11438	+	7.12631i	−0.162508	+	0.281472i	0.773259	+	0.634090i	$0.218625\pi$
$642$		0			0
$643$	17.4373	−	30.2022i	0.687658	−	1.19106i	−0.284935	−	0.958547i	$-0.591972\pi$
$643$	17.4373	−	30.2022i	0.687658	−	1.19106i	0.972593	−	0.232512i	$-0.0746945\pi$
$644$	−12.2915	+	21.2895i	−0.484353	+	0.838924i
$645$		0			0
$646$	−3.29150			−0.129502
$647$	10.9373	+	18.9439i	0.429988	+	0.744761i	0.996872	−	0.0790370i	$-0.0251845\pi$
$647$	10.9373	+	18.9439i	0.429988	+	0.744761i	−0.566884	+	0.823798i	$0.691851\pi$
$648$		0			0
$649$	11.2288	−	19.4488i	0.440767	−	0.763431i
$650$	0.739870	+	1.28149i	0.0290201	+	0.0502643i
$651$		0			0
$652$	0.500000	−	0.866025i	0.0195815	−	0.0339162i
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	0.918736	−	0.394872i	$-0.129211\pi$
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	−0.801337	+	0.598213i	$0.795878\pi$
$654$		0			0
$655$	−5.41699	+	9.38251i	−0.211659	+	0.366605i
$656$	2.46863	−	4.27579i	0.0963837	−	0.166941i
$657$		0			0
$658$	14.4686	+	25.0604i	0.564046	+	0.976956i
$659$	−1.11438	−	1.93016i	−0.0434100	−	0.0751884i	0.843504	−	0.537123i	$-0.180489\pi$
$659$	−1.11438	−	1.93016i	−0.0434100	−	0.0751884i	−0.886914	+	0.461934i	$0.847156\pi$
$660$		0			0
$661$	39.1660			1.52338			0.761691	−	0.647941i	$-0.224370\pi$
$661$	39.1660			1.52338			0.761691	+	0.647941i	$0.224370\pi$
$662$	−0.125492			−0.00487739
$663$		0			0
$664$	1.35425	+	2.34563i	0.0525550	+	0.0910280i
$665$	−4.35425	−	7.54178i	−0.168851	−	0.292458i
$666$		0			0
$667$	−35.5203	+	61.5229i	−1.37535	+	2.38218i
$668$	−6.29150	+	10.8972i	−0.243426	+	0.421625i
$669$		0			0
$670$	−6.82288	−	11.8176i	−0.263591	−	0.456552i
$671$	10.4059	−	18.0235i	0.401715	−	0.695790i
$672$		0			0
$673$	23.8745	+	41.3519i	0.920295	+	1.59400i	0.798959	+	0.601386i	$0.205384\pi$
$673$	23.8745	+	41.3519i	0.920295	+	1.59400i	0.121336	+	0.992612i	$0.461282\pi$
$674$	4.70850	−	8.15536i	0.181365	−	0.314133i
$675$		0			0
$676$	6.29150	+	10.8972i	0.241981	+	0.419123i
$677$	−14.1255			−0.542887			−0.271443	−	0.962454i	$-0.587501\pi$
$677$	−14.1255			−0.542887			−0.271443	+	0.962454i	$0.587501\pi$
$678$		0			0
$679$	10.0314	−	17.3748i	0.384969	−	0.666785i
$680$	1.35425	−	2.34563i	0.0519331	−	0.0899507i
$681$		0			0
$682$	0.531373	−	0.920365i	0.0203473	−	0.0352426i
$683$	−10.4059	−	18.0235i	−0.398170	−	0.689651i	0.595330	−	0.803481i	$-0.297021\pi$
$683$	−10.4059	−	18.0235i	−0.398170	−	0.689651i	−0.993500	+	0.113831i	$0.963688\pi$
$684$		0			0
$685$	−15.2915			−0.584258
$686$	18.5203			0.707107
$687$		0			0
$688$	−2.50000	−	4.33013i	−0.0953116	−	0.165085i
$689$	3.87451			0.147607
$690$		0			0
$691$	24.7490			0.941497			0.470748	−	0.882267i	$-0.343984\pi$
$691$	24.7490			0.941497			0.470748	+	0.882267i	$0.343984\pi$
$692$	6.58301			0.250248
$693$		0			0
$694$	−12.0000			−0.455514
$695$	−32.2288			−1.22251
$696$		0			0
$697$	8.12549			0.307775
$698$	−12.6144	−	21.8487i	−0.477461	−	0.826987i
$699$		0			0
$700$	−6.06275			−0.229150
$701$	−5.41699			−0.204597			−0.102299	−	0.994754i	$-0.532620\pi$
$701$	−5.41699			−0.204597			−0.102299	+	0.994754i	$0.532620\pi$
$702$		0			0
$703$	−3.93725	−	6.81952i	−0.148496	−	0.257203i
$704$	0.822876	−	1.42526i	0.0310133	−	0.0537166i
$705$		0			0
$706$	6.00000	−	10.3923i	0.225813	−	0.391120i
$707$	36.1033			1.35780
$708$		0			0
$709$	−9.81176			−0.368488			−0.184244	−	0.982880i	$-0.558984\pi$
$709$	−9.81176			−0.368488			−0.184244	+	0.982880i	$0.558984\pi$
$710$	−8.52026	−	14.7575i	−0.319760	−	0.553840i
$711$		0			0
$712$	5.46863	−	9.47194i	0.204945	−	0.354976i
$713$	−3.00000	−	5.19615i	−0.112351	−	0.194597i
$714$		0			0
$715$	0.874508	−	1.51469i	0.0327047	−	0.0566463i
$716$	−0.531373	−	0.920365i	−0.0198583	−	0.0343957i
$717$		0			0
$718$	15.5830	−	26.9906i	0.581553	−	1.00728i
$719$	−3.53137	+	6.11652i	−0.131698	+	0.228108i	−0.924331	−	0.381591i	$-0.875376\pi$
$719$	−3.53137	+	6.11652i	−0.131698	+	0.228108i	0.792633	+	0.609699i	$0.208710\pi$
$720$		0			0
$721$	15.7915	−	27.3517i	0.588106	−	1.01863i
$722$	7.50000	+	12.9904i	0.279121	+	0.483452i
$723$		0			0
$724$	−13.2915			−0.493975
$725$	−17.5203			−0.650686
$726$		0			0
$727$	−12.6144	−	21.8487i	−0.467841	−	0.810325i	0.531483	−	0.847069i	$-0.321635\pi$
$727$	−12.6144	−	21.8487i	−0.467841	−	0.810325i	−0.999325	+	0.0367437i	$0.988301\pi$
$728$	1.70850			0.0633211
$729$		0			0
$730$	8.70850	−	15.0836i	0.322316	−	0.558268i
$731$	4.11438	−	7.12631i	0.152176	−	0.263576i
$732$		0			0
$733$	−4.38562	−	7.59612i	−0.161987	−	0.280569i	0.773594	−	0.633681i	$-0.218457\pi$
$733$	−4.38562	−	7.59612i	−0.161987	−	0.280569i	−0.935581	+	0.353112i	$0.885123\pi$
$734$	0.937254	−	1.62337i	0.0345947	−	0.0599197i
$735$		0			0
$736$	−4.64575	−	8.04668i	−0.171245	−	0.296604i
$737$	6.82288	−	11.8176i	0.251324	−	0.435306i
$738$		0			0
$739$	−10.7288	−	18.5828i	−0.394664	−	0.683578i	0.598395	−	0.801202i	$-0.295806\pi$
$739$	−10.7288	−	18.5828i	−0.394664	−	0.683578i	−0.993058	+	0.117624i	$0.962472\pi$
$740$	6.47974			0.238200
$741$		0			0
$742$	−7.93725	+	13.7477i	−0.291386	+	0.504695i
$743$	6.53137	−	11.3127i	0.239613	−	0.415022i	−0.720990	−	0.692945i	$-0.756313\pi$
$743$	6.53137	−	11.3127i	0.239613	−	0.415022i	0.960603	+	0.277923i	$0.0896462\pi$
$744$		0			0
$745$	−5.81176	+	10.0663i	−0.212926	+	0.368799i
$746$	8.29150	+	14.3613i	0.303573	+	0.525805i
$747$		0			0
$748$	2.70850			0.0990325
$749$	−15.8745			−0.580042
$750$		0			0
$751$	−0.228757	−	0.396218i	−0.00834745	−	0.0144582i	0.861822	−	0.507212i	$-0.169324\pi$
$751$	−0.228757	−	0.396218i	−0.00834745	−	0.0144582i	−0.870169	+	0.492753i	$0.835990\pi$
$752$	−10.9373			−0.398841
$753$		0			0
$754$	4.93725			0.179804
$755$	11.8967			0.432967
$756$		0			0
$757$	−40.9778			−1.48936			−0.744681	−	0.667420i	$-0.767398\pi$
$757$	−40.9778			−1.48936			−0.744681	+	0.667420i	$0.767398\pi$
$758$	4.41699			0.160432
$759$		0			0
$760$	3.29150			0.119395
$761$	9.29150	+	16.0934i	0.336817	+	0.583384i	0.983832	−	0.179093i	$-0.0573164\pi$
$761$	9.29150	+	16.0934i	0.336817	+	0.583384i	−0.647015	+	0.762477i	$0.723983\pi$
$762$		0			0
$763$	11.4373	−	19.8099i	0.414056	−	0.717167i
$764$	26.8118			0.970015
$765$		0			0
$766$	0.291503	+	0.504897i	0.0105324	+	0.0182427i
$767$	−4.40588	+	7.63121i	−0.159087	+	0.275547i
$768$		0			0
$769$	−9.70850	+	16.8156i	−0.350097	+	0.606386i	−0.986266	−	0.165163i	$-0.947185\pi$
$769$	−9.70850	+	16.8156i	−0.350097	+	0.606386i	0.636169	+	0.771550i	$0.280518\pi$
$770$	3.58301	+	6.20595i	0.129123	+	0.223647i
$771$		0			0
$772$	−7.00000			−0.251936
$773$	−19.1660	−	33.1965i	−0.689353	−	1.19400i	−0.972047	−	0.234785i	$-0.924561\pi$
$773$	−19.1660	−	33.1965i	−0.689353	−	1.19400i	0.282694	−	0.959210i	$-0.408772\pi$
$774$		0			0
$775$	0.739870	−	1.28149i	0.0265769	−	0.0460326i
$776$	3.79150	+	6.56708i	0.136107	+	0.235744i
$777$		0			0
$778$	−4.35425	+	7.54178i	−0.156107	+	0.270386i
$779$	4.93725	+	8.55157i	0.176895	+	0.306392i
$780$		0			0
$781$	8.52026	−	14.7575i	0.304879	−	0.528066i
$782$	7.64575	−	13.2428i	0.273412	−	0.473563i
$783$		0			0
$784$	−3.50000	+	6.06218i	−0.125000	+	0.216506i
$785$	3.29150	+	5.70105i	0.117479	+	0.203479i
$786$		0			0
$787$	−22.2915			−0.794606			−0.397303	−	0.917687i	$-0.630054\pi$
$787$	−22.2915			−0.794606			−0.397303	+	0.917687i	$0.630054\pi$
$788$	15.2915			0.544737
$789$		0			0
$790$	12.5314	+	21.7050i	0.445846	+	0.772228i
$791$	20.2288			0.719252
$792$		0			0
$793$	−4.08301	+	7.07197i	−0.144992	+	0.251133i
$794$	5.67712	−	9.83307i	0.201474	−	0.348963i
$795$		0			0
$796$	−10.9686	−	18.9982i	−0.388773	−	0.673374i
$797$	−16.4059	+	28.4158i	−0.581126	+	1.00654i	0.414220	+	0.910177i	$0.364054\pi$
$797$	−16.4059	+	28.4158i	−0.581126	+	1.00654i	−0.995346	+	0.0963632i	$0.969279\pi$
$798$		0			0
$799$	−9.00000	−	15.5885i	−0.318397	−	0.551480i
$800$	1.14575	−	1.98450i	0.0405084	−	0.0701627i
$801$		0			0
$802$	−13.4059	−	23.2197i	−0.473378	−	0.819915i
$803$	17.4170			0.614632
$804$		0			0
$805$	40.4575			1.42594
$806$	−0.208497	+	0.361128i	−0.00734401	+	0.0127202i
$807$		0			0
$808$	−6.82288	+	11.8176i	−0.240028	+	0.415741i
$809$	−18.2915	−	31.6818i	−0.643095	−	1.11387i	−0.984738	−	0.174043i	$-0.944317\pi$
$809$	−18.2915	−	31.6818i	−0.643095	−	1.11387i	0.341643	−	0.939830i	$-0.389017\pi$
$810$		0			0
$811$	−18.7085			−0.656944			−0.328472	−	0.944514i	$-0.606534\pi$
$811$	−18.7085			−0.656944			−0.328472	+	0.944514i	$0.606534\pi$
$812$	−10.1144	+	17.5186i	−0.354945	+	0.614783i
$813$		0			0
$814$	3.23987	+	5.61162i	0.113557	+	0.196687i
$815$	−1.64575			−0.0576482
$816$		0			0
$817$	10.0000			0.349856
$818$	−16.8745			−0.590003
$819$		0			0
$820$	−8.12549			−0.283754
$821$	−0.583005			−0.0203470			−0.0101735	−	0.999948i	$-0.503238\pi$
$821$	−0.583005			−0.0203470			−0.0101735	+	0.999948i	$0.503238\pi$
$822$		0			0
$823$	23.1033			0.805329			0.402665	−	0.915348i	$-0.368084\pi$
$823$	23.1033			0.805329			0.402665	+	0.915348i	$0.368084\pi$
$824$	5.96863	+	10.3380i	0.207927	+	0.360140i
$825$		0			0
$826$	−18.0516	−	31.2663i	−0.628097	−	1.08790i
$827$	19.7490			0.686741			0.343370	−	0.939200i	$-0.388431\pi$
$827$	19.7490			0.686741			0.343370	+	0.939200i	$0.388431\pi$
$828$		0			0
$829$	9.35425	+	16.2020i	0.324886	+	0.562720i	0.981489	−	0.191517i	$-0.0613406\pi$
$829$	9.35425	+	16.2020i	0.324886	+	0.562720i	−0.656603	+	0.754236i	$0.728007\pi$
$830$	2.22876	−	3.86032i	0.0773613	−	0.133994i
$831$		0			0
$832$	−0.322876	+	0.559237i	−0.0111937	+	0.0193881i
$833$	−11.5203			−0.399153
$834$		0			0
$835$	20.7085			0.716647
$836$	1.64575	+	2.85052i	0.0569195	+	0.0985875i
$837$		0			0
$838$	−6.53137	+	11.3127i	−0.225623	+	0.390790i
$839$	19.3542	+	33.5225i	0.668183	+	1.15733i	0.978412	+	0.206665i	$0.0662610\pi$
$839$	19.3542	+	33.5225i	0.668183	+	1.15733i	−0.310229	+	0.950662i	$0.600406\pi$
$840$		0			0
$841$	−14.7288	+	25.5110i	−0.507888	+	0.879688i
$842$	12.6458	+	21.9031i	0.435801	+	0.754830i
$843$		0			0
$844$	8.43725	−	14.6138i	0.290422	−	0.503026i
$845$	10.3542	−	17.9341i	0.356197	−	0.616951i
$846$		0			0
$847$	10.9686	−	18.9982i	0.376886	−	0.652787i
$848$	−3.00000	−	5.19615i	−0.103020	−	0.178437i
$849$		0			0
$850$	3.77124			0.129353
$851$	36.5830			1.25405
$852$		0			0
$853$	−8.06275	−	13.9651i	−0.276063	−	0.478155i	0.694340	−	0.719647i	$-0.255697\pi$
$853$	−8.06275	−	13.9651i	−0.276063	−	0.478155i	−0.970403	+	0.241492i	$0.922363\pi$
$854$	−16.7288	−	28.9751i	−0.572446	−	0.991506i
$855$		0			0
$856$	3.00000	−	5.19615i	0.102538	−	0.177601i
$857$	−10.4059	+	18.0235i	−0.355458	+	0.615672i	−0.987196	−	0.159510i	$-0.949008\pi$
$857$	−10.4059	+	18.0235i	−0.355458	+	0.615672i	0.631738	+	0.775182i	$0.282342\pi$
$858$		0			0
$859$	3.50000	+	6.06218i	0.119418	+	0.206839i	0.919537	−	0.393003i	$-0.128564\pi$
$859$	3.50000	+	6.06218i	0.119418	+	0.206839i	−0.800119	+	0.599841i	$0.795230\pi$
$860$	−4.11438	+	7.12631i	−0.140299	+	0.243005i
$861$		0			0
$862$	4.40588	+	7.63121i	0.150065	+	0.259920i
$863$	6.58301	−	11.4021i	0.224088	−	0.388132i	−0.731957	−	0.681350i	$-0.761393\pi$
$863$	6.58301	−	11.4021i	0.224088	−	0.388132i	0.956045	+	0.293218i	$0.0947263\pi$
$864$		0			0
$865$	−5.41699	−	9.38251i	−0.184183	−	0.319015i
$866$	−19.0000			−0.645646
$867$		0			0
$868$	−0.854249	−	1.47960i	−0.0289951	−	0.0502210i
$869$	−12.5314	+	21.7050i	−0.425098	+	0.736291i
$870$		0			0
$871$	−2.67712	+	4.63692i	−0.0907109	+	0.157116i
$872$	4.32288	+	7.48744i	0.146391	+	0.253557i
$873$		0			0
$874$	18.5830			0.628580
$875$	15.8745	+	27.4955i	0.536656	+	0.929516i
$876$		0			0
$877$	−10.6771	−	18.4933i	−0.360541	−	0.624475i	0.627509	−	0.778609i	$-0.284075\pi$
$877$	−10.6771	−	18.4933i	−0.360541	−	0.624475i	−0.988050	+	0.154134i	$0.950741\pi$
$878$	−17.1660			−0.579325
$879$		0			0
$880$	−2.70850			−0.0913034
$881$	27.8745			0.939116			0.469558	−	0.882902i	$-0.344413\pi$
$881$	27.8745			0.939116			0.469558	+	0.882902i	$0.344413\pi$
$882$		0			0
$883$	11.8745			0.399609			0.199805	−	0.979836i	$-0.435969\pi$
$883$	11.8745			0.399609			0.199805	+	0.979836i	$0.435969\pi$
$884$	−1.06275			−0.0357440
$885$		0			0
$886$	−8.70850			−0.292568
$887$	7.93725	+	13.7477i	0.266507	+	0.461603i	0.967957	−	0.251115i	$-0.0807972\pi$
$887$	7.93725	+	13.7477i	0.266507	+	0.461603i	−0.701450	+	0.712718i	$0.747464\pi$
$888$		0			0
$889$	−8.79150	−	15.2273i	−0.294858	−	0.510708i
$890$	−18.0000			−0.603361
$891$		0			0
$892$	−8.93725	−	15.4798i	−0.299241	−	0.518301i
$893$	10.9373	−	18.9439i	0.366001	−	0.633933i
$894$		0			0
$895$	−0.874508	+	1.51469i	−0.0292316	+	0.0506306i
$896$	−1.32288	−	2.29129i	−0.0441942	−	0.0765466i
$897$		0			0
$898$	7.64575			0.255142
$899$	−2.46863	−	4.27579i	−0.0823333	−	0.142605i
$900$		0			0
$901$	4.93725	−	8.55157i	0.164484	−	0.284894i
$902$	−4.06275	−	7.03688i	−0.135275	−	0.234303i
$903$		0			0
$904$	−3.82288	+	6.62141i	−0.127147	+	0.220225i
$905$	10.9373	+	18.9439i	0.363567	+	0.629716i
$906$		0			0
$907$	−12.8542	+	22.2642i	−0.426818	+	0.739271i	−0.996588	−	0.0825332i	$-0.973699\pi$
$907$	−12.8542	+	22.2642i	−0.426818	+	0.739271i	0.569770	+	0.821804i	$0.307032\pi$
$908$	−3.00000	+	5.19615i	−0.0995585	+	0.172440i
$909$		0			0
$910$	−1.40588	−	2.43506i	−0.0466045	−	0.0807214i
$911$	−6.53137	−	11.3127i	−0.216394	−	0.374805i	0.737309	−	0.675556i	$-0.236096\pi$
$911$	−6.53137	−	11.3127i	−0.216394	−	0.374805i	−0.953703	+	0.300750i	$0.902763\pi$
$912$		0			0
$913$	4.45751			0.147522
$914$	2.29150			0.0757962
$915$		0			0
$916$	7.32288	+	12.6836i	0.241955	+	0.419078i
$917$	−8.70850	+	15.0836i	−0.287580	+	0.498103i
$918$		0			0
$919$	−27.6144	+	47.8295i	−0.910914	+	1.57775i	−0.0981388	+	0.995173i	$0.531289\pi$
$919$	−27.6144	+	47.8295i	−0.910914	+	1.57775i	−0.812775	+	0.582577i	$0.802044\pi$
$920$	−7.64575	+	13.2428i	−0.252073	+	0.436603i
$921$		0			0
$922$	1.11438	+	1.93016i	0.0367001	+	0.0635664i
$923$	−3.34313	+	5.79048i	−0.110041	+	0.190596i
$924$		0			0
$925$	4.51111	+	7.81348i	0.148325	+	0.256906i
$926$	−14.6458	+	25.3672i	−0.481289	+	0.833617i
$927$		0			0
$928$	−3.82288	−	6.62141i	−0.125492	−	0.217359i
$929$	−1.06275			−0.0348676			−0.0174338	−	0.999848i	$-0.505550\pi$
$929$	−1.06275			−0.0348676			−0.0174338	+	0.999848i	$0.505550\pi$
$930$		0			0
$931$	−7.00000	−	12.1244i	−0.229416	−	0.397360i
$932$	4.35425	−	7.54178i	0.142628	−	0.247039i
$933$		0			0
$934$	13.1144	−	22.7148i	0.429116	−	0.743250i
$935$	−2.22876	−	3.86032i	−0.0728881	−	0.126246i
$936$		0			0
$937$	18.7490			0.612504			0.306252	−	0.951951i	$-0.400925\pi$
$937$	18.7490			0.612504			0.306252	+	0.951951i	$0.400925\pi$
$938$	−10.9686	−	18.9982i	−0.358138	−	0.620314i
$939$		0			0
$940$	9.00000	+	15.5885i	0.293548	+	0.508439i
$941$	15.3948			0.501855			0.250928	−	0.968006i	$-0.419264\pi$
$941$	15.3948			0.501855			0.250928	+	0.968006i	$0.419264\pi$
$942$		0			0
$943$	−45.8745			−1.49388
$944$	13.6458			0.444131
$945$		0			0
$946$	−8.22876			−0.267540
$947$	47.5203			1.54420			0.772100	−	0.635500i	$-0.219206\pi$
$947$	47.5203			1.54420			0.772100	+	0.635500i	$0.219206\pi$
$948$		0			0
$949$	−6.83399			−0.221841
$950$	2.29150	+	3.96900i	0.0743462	+	0.128771i
$951$		0			0
$952$	2.17712	−	3.77089i	0.0705610	−	0.122215i
$953$	−32.3320			−1.04734			−0.523668	−	0.851922i	$-0.675437\pi$
$953$	−32.3320			−1.04734			−0.523668	+	0.851922i	$0.675437\pi$
$954$		0			0
$955$	−22.0627	−	38.2138i	−0.713934	−	1.23657i
$956$	−2.46863	+	4.27579i	−0.0798411	+	0.138289i
$957$		0			0
$958$	0.822876	−	1.42526i	0.0265859	−	0.0460481i
$959$	−24.5830			−0.793827
$960$		0			0
$961$	−30.5830			−0.986549
$962$	−1.27124	−	2.20186i	−0.0409865	−	0.0709908i
$963$		0			0
$964$	−2.50000	+	4.33013i	−0.0805196	+	0.139464i
$965$	5.76013	+	9.97684i	0.185425	+	0.321166i
$966$		0			0
$967$	−25.9686	+	44.9790i	−0.835095	+	1.44643i	0.0588585	+	0.998266i	$0.481254\pi$
$967$	−25.9686	+	44.9790i	−0.835095	+	1.44643i	−0.893953	+	0.448160i	$0.852079\pi$
$968$	4.14575	+	7.18065i	0.133249	+	0.230795i
$969$		0			0
$970$	6.23987	−	10.8078i	0.200350	−	0.347017i
$971$	−10.9373	+	18.9439i	−0.350993	+	0.607938i	−0.986424	−	0.164220i	$-0.947489\pi$
$971$	−10.9373	+	18.9439i	−0.350993	+	0.607938i	0.635431	+	0.772158i	$0.280823\pi$
$972$		0			0
$973$	−51.8118			−1.66101
$974$	3.93725	+	6.81952i	0.126158	+	0.218512i
$975$		0			0
$976$	12.6458			0.404781
$977$	−20.1255			−0.643872			−0.321936	−	0.946762i	$-0.604334\pi$
$977$	−20.1255			−0.643872			−0.321936	+	0.946762i	$0.604334\pi$
$978$		0			0
$979$	−9.00000	−	15.5885i	−0.287641	−	0.498209i
$980$	11.5203			0.368001
$981$		0			0
$982$	18.8745	−	32.6916i	0.602310	−	1.04323i
$983$	13.4059	−	23.2197i	0.427581	−	0.740592i	−0.569076	−	0.822285i	$-0.692699\pi$
$983$	13.4059	−	23.2197i	0.427581	−	0.740592i	0.996658	+	0.0816923i	$0.0260325\pi$
$984$		0			0
$985$	−12.5830	−	21.7944i	−0.400928	−	0.694427i
$986$	6.29150	−	10.8972i	0.200362	−	0.347038i
$987$		0			0
$988$	−0.645751	−	1.11847i	−0.0205441	−	0.0355834i
$989$	−23.2288	+	40.2334i	−0.738631	+	1.27935i
$990$		0			0
$991$	20.9686	+	36.3187i	0.666090	+	1.15370i	0.978988	+	0.203916i	$0.0653668\pi$
$991$	20.9686	+	36.3187i	0.666090	+	1.15370i	−0.312898	+	0.949787i	$0.601300\pi$
$992$	0.645751			0.0205026
$993$		0			0
$994$	−13.6974	−	23.7246i	−0.434455	−	0.752497i
$995$	−18.0516	+	31.2663i	−0.572275	+	0.991210i
$996$		0			0
$997$	27.8431	−	48.2257i	0.881801	−	1.52732i	0.0324640	−	0.999473i	$-0.489665\pi$
$997$	27.8431	−	48.2257i	0.881801	−	1.52732i	0.849337	−	0.527851i	$-0.177002\pi$
$998$	−18.0830	−	31.3207i	−0.572408	−	0.991439i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.e.t.919.1		4
3.2	odd	2		1134.2.e.q.919.2		4
7.4	even	3		1134.2.h.q.109.2		4
9.2	odd	6		1134.2.h.t.541.1		4
9.4	even	3		378.2.g.g.163.1	yes	4
9.5	odd	6		378.2.g.h.163.2	yes	4
9.7	even	3		1134.2.h.q.541.2		4
21.11	odd	6		1134.2.h.t.109.1		4
63.4	even	3		378.2.g.g.109.1	✓	4
63.5	even	6		2646.2.a.bf.1.2		2
63.11	odd	6		1134.2.e.q.865.2		4
63.23	odd	6		2646.2.a.bi.1.1		2
63.25	even	3	inner	1134.2.e.t.865.1		4
63.32	odd	6		378.2.g.h.109.2	yes	4
63.40	odd	6		2646.2.a.bo.1.1		2
63.58	even	3		2646.2.a.bl.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.g.g.109.1	✓	4	63.4	even	3
378.2.g.g.163.1	yes	4	9.4	even	3
378.2.g.h.109.2	yes	4	63.32	odd	6
378.2.g.h.163.2	yes	4	9.5	odd	6
1134.2.e.q.865.2		4	63.11	odd	6
1134.2.e.q.919.2		4	3.2	odd	2
1134.2.e.t.865.1		4	63.25	even	3	inner
1134.2.e.t.919.1		4	1.1	even	1	trivial
1134.2.h.q.109.2		4	7.4	even	3
1134.2.h.q.541.2		4	9.7	even	3
1134.2.h.t.109.1		4	21.11	odd	6
1134.2.h.t.541.1		4	9.2	odd	6
2646.2.a.bf.1.2		2	63.5	even	6
2646.2.a.bi.1.1		2	63.23	odd	6
2646.2.a.bl.1.2		2	63.58	even	3
2646.2.a.bo.1.1		2	63.40	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.822876 - 1.42526i) q^{5} +(-1.32288 - 2.29129i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.822876 - 1.42526i) q^{5} +(-1.32288 - 2.29129i) q^{7} +1.00000 q^{8} +(-0.822876 - 1.42526i) q^{10} +(0.822876 - 1.42526i) q^{11} +(-0.322876 + 0.559237i) q^{13} +(-1.32288 - 2.29129i) q^{14} +1.00000 q^{16} +(0.822876 + 1.42526i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(-0.822876 - 1.42526i) q^{20} +(0.822876 - 1.42526i) q^{22} +(-4.64575 - 8.04668i) q^{23} +(1.14575 - 1.98450i) q^{25} +(-0.322876 + 0.559237i) q^{26} +(-1.32288 - 2.29129i) q^{28} +(-3.82288 - 6.62141i) q^{29} +0.645751 q^{31} +1.00000 q^{32} +(0.822876 + 1.42526i) q^{34} +(-2.17712 + 3.77089i) q^{35} +(-1.96863 + 3.40976i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(-0.822876 - 1.42526i) q^{40} +(2.46863 - 4.27579i) q^{41} +(-2.50000 - 4.33013i) q^{43} +(0.822876 - 1.42526i) q^{44} +(-4.64575 - 8.04668i) q^{46} -10.9373 q^{47} +(-3.50000 + 6.06218i) q^{49} +(1.14575 - 1.98450i) q^{50} +(-0.322876 + 0.559237i) q^{52} +(-3.00000 - 5.19615i) q^{53} -2.70850 q^{55} +(-1.32288 - 2.29129i) q^{56} +(-3.82288 - 6.62141i) q^{58} +13.6458 q^{59} +12.6458 q^{61} +0.645751 q^{62} +1.00000 q^{64} +1.06275 q^{65} +8.29150 q^{67} +(0.822876 + 1.42526i) q^{68} +(-2.17712 + 3.77089i) q^{70} +10.3542 q^{71} +(5.29150 + 9.16515i) q^{73} +(-1.96863 + 3.40976i) q^{74} +(-1.00000 + 1.73205i) q^{76} -4.35425 q^{77} -15.2288 q^{79} +(-0.822876 - 1.42526i) q^{80} +(2.46863 - 4.27579i) q^{82} +(1.35425 + 2.34563i) q^{83} +(1.35425 - 2.34563i) q^{85} +(-2.50000 - 4.33013i) q^{86} +(0.822876 - 1.42526i) q^{88} +(5.46863 - 9.47194i) q^{89} +1.70850 q^{91} +(-4.64575 - 8.04668i) q^{92} -10.9373 q^{94} +3.29150 q^{95} +(3.79150 + 6.56708i) q^{97} +(-3.50000 + 6.06218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{4} + 2 q^{5} + 4 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^4 + 2 * q^5 + 4 * q^8	\( 4 q + 4 q^{2} + 4 q^{4} + 2 q^{5} + 4 q^{8} + 2 q^{10} - 2 q^{11} + 4 q^{13} + 4 q^{16} - 2 q^{17} - 4 q^{19} + 2 q^{20} - 2 q^{22} - 8 q^{23} - 6 q^{25} + 4 q^{26} - 10 q^{29} - 8 q^{31} + 4 q^{32} - 2 q^{34} - 14 q^{35} + 8 q^{37} - 4 q^{38} + 2 q^{40} - 6 q^{41} - 10 q^{43} - 2 q^{44} - 8 q^{46} - 12 q^{47} - 14 q^{49} - 6 q^{50} + 4 q^{52} - 12 q^{53} - 32 q^{55} - 10 q^{58} + 44 q^{59} + 40 q^{61} - 8 q^{62} + 4 q^{64} + 36 q^{65} + 12 q^{67} - 2 q^{68} - 14 q^{70} + 52 q^{71} + 8 q^{74} - 4 q^{76} - 28 q^{77} - 8 q^{79} + 2 q^{80} - 6 q^{82} + 16 q^{83} + 16 q^{85} - 10 q^{86} - 2 q^{88} + 6 q^{89} + 28 q^{91} - 8 q^{92} - 12 q^{94} - 8 q^{95} - 6 q^{97} - 14 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^4 + 2 * q^5 + 4 * q^8 + 2 * q^10 - 2 * q^11 + 4 * q^13 + 4 * q^16 - 2 * q^17 - 4 * q^19 + 2 * q^20 - 2 * q^22 - 8 * q^23 - 6 * q^25 + 4 * q^26 - 10 * q^29 - 8 * q^31 + 4 * q^32 - 2 * q^34 - 14 * q^35 + 8 * q^37 - 4 * q^38 + 2 * q^40 - 6 * q^41 - 10 * q^43 - 2 * q^44 - 8 * q^46 - 12 * q^47 - 14 * q^49 - 6 * q^50 + 4 * q^52 - 12 * q^53 - 32 * q^55 - 10 * q^58 + 44 * q^59 + 40 * q^61 - 8 * q^62 + 4 * q^64 + 36 * q^65 + 12 * q^67 - 2 * q^68 - 14 * q^70 + 52 * q^71 + 8 * q^74 - 4 * q^76 - 28 * q^77 - 8 * q^79 + 2 * q^80 - 6 * q^82 + 16 * q^83 + 16 * q^85 - 10 * q^86 - 2 * q^88 + 6 * q^89 + 28 * q^91 - 8 * q^92 - 12 * q^94 - 8 * q^95 - 6 * q^97 - 14 * q^98

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