LMFDB - Embedded newform 81.2.e.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,2,Mod(10,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("81.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$81 = 3^{4}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	81.e (of order $9$ , degree $6$ , 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:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3$ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$3$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			19.1
Root			$0.500000 + 0.0126039i$ of defining polynomial
Character	$\chi$	$=$	81.19
Dual form			81.2.e.a.64.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.753189 + 0.274138i) q^{2} +(-1.03995 + 0.872619i) q^{4} +(0.477505 + 2.70806i) q^{5} +(1.82076 + 1.52780i) q^{7} +(1.34559 - 2.33062i) q^{8} +(-1.10204 - 1.90878i) q^{10} +(0.0434396 - 0.246358i) q^{11} +(-2.45446 - 0.893351i) q^{13} +(-1.79020 - 0.651581i) q^{14} +(0.0969067 - 0.549585i) q^{16} +(-0.146688 - 0.254072i) q^{17} +(1.39237 - 2.41166i) q^{19} +(-2.85969 - 2.39956i) q^{20} +(0.0348180 + 0.197463i) q^{22} +(5.12472 - 4.30015i) q^{23} +(-2.40714 + 0.876128i) q^{25} +2.09357 q^{26} -3.22668 q^{28} +(-0.333645 + 0.121437i) q^{29} +(2.11847 - 1.77761i) q^{31} +(1.01231 + 5.74108i) q^{32} +(0.180135 + 0.151151i) q^{34} +(-3.26796 + 5.66027i) q^{35} +(3.49619 + 6.05558i) q^{37} +(-0.387591 + 2.19814i) q^{38} +(6.95400 + 2.53105i) q^{40} +(-9.13156 - 3.32362i) q^{41} +(0.0452712 - 0.256746i) q^{43} +(0.169802 + 0.294106i) q^{44} +(-2.68104 + 4.64370i) q^{46} +(8.75249 + 7.34421i) q^{47} +(-0.234540 - 1.33014i) q^{49} +(1.57285 - 1.31978i) q^{50} +(3.33207 - 1.21277i) q^{52} -5.43137 q^{53} +0.687897 q^{55} +(6.01071 - 2.18772i) q^{56} +(0.218007 - 0.182930i) q^{58} +(-1.03788 - 5.88612i) q^{59} +(-9.07515 - 7.61495i) q^{61} +(-1.10830 + 1.91963i) q^{62} +(-1.77824 - 3.08001i) q^{64} +(1.24723 - 7.07342i) q^{65} +(-1.70113 - 0.619160i) q^{67} +(0.374256 + 0.136218i) q^{68} +(0.909693 - 5.15912i) q^{70} +(-0.185255 - 0.320871i) q^{71} +(-2.51339 + 4.35333i) q^{73} +(-4.29336 - 3.60255i) q^{74} +(0.656467 + 3.72301i) q^{76} +(0.455479 - 0.382193i) q^{77} +(-0.754406 + 0.274581i) q^{79} +1.53459 q^{80} +7.78892 q^{82} +(-2.58947 + 0.942488i) q^{83} +(0.617998 - 0.518562i) q^{85} +(0.0362861 + 0.205789i) q^{86} +(-0.515717 - 0.432738i) q^{88} +(5.22533 - 9.05054i) q^{89} +(-3.10412 - 5.37650i) q^{91} +(-1.57704 + 8.94385i) q^{92} +(-8.60560 - 3.13218i) q^{94} +(7.19580 + 2.61906i) q^{95} +(-2.57600 + 14.6092i) q^{97} +(0.541296 + 0.937552i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} - 6 q^{13} - 15 q^{14} - 9 q^{17} - 3 q^{19} + 3 q^{20} + 3 q^{22} + 12 q^{23} + 3 q^{25} + 30 q^{26} - 12 q^{28} + 6 q^{29}+ \cdots + 45 q^{98}+O(q^{100})$ 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 - 6 * q^13 - 15 * q^14 - 9 * q^17 - 3 * q^19 + 3 * q^20 + 3 * q^22 + 12 * q^23 + 3 * q^25 + 30 * q^26 - 12 * q^28 + 6 * q^29 + 3 * q^31 + 9 * q^34 - 12 * q^35 - 3 * q^37 - 42 * q^38 + 21 * q^40 - 15 * q^41 + 3 * q^43 - 3 * q^44 - 3 * q^46 + 15 * q^47 + 12 * q^49 + 33 * q^50 + 9 * q^52 + 18 * q^53 - 12 * q^55 + 33 * q^56 + 21 * q^58 + 12 * q^59 + 12 * q^61 + 12 * q^62 + 12 * q^64 - 3 * q^65 - 15 * q^67 - 9 * q^68 - 15 * q^70 - 27 * q^71 + 6 * q^73 - 33 * q^74 - 48 * q^76 - 15 * q^77 - 42 * q^79 - 42 * q^80 - 12 * q^82 - 39 * q^83 - 27 * q^85 - 51 * q^86 - 30 * q^88 - 9 * q^89 + 6 * q^91 + 39 * q^92 - 15 * q^94 + 33 * q^95 + 3 * q^97 + 45 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$ .

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.753189	+	0.274138i	−0.532585	+	0.193845i	−0.594292	−	0.804249i	$-0.702568\pi$
$2$	−0.753189	+	0.274138i	−0.532585	+	0.193845i	0.0617072	+	0.998094i	$0.480346\pi$
$3$		0			0
$3$		0			0
$4$	−1.03995	+	0.872619i	−0.519974	+	0.436310i
$5$	0.477505	+	2.70806i	0.213547	+	1.21108i	0.883411	+	0.468600i	$0.155241\pi$
$5$	0.477505	+	2.70806i	0.213547	+	1.21108i	−0.669864	+	0.742484i	$0.733648\pi$
$6$		0			0
$7$	1.82076	+	1.52780i	0.688183	+	0.577454i	0.918385	−	0.395689i	$-0.129494\pi$
$7$	1.82076	+	1.52780i	0.688183	+	0.577454i	−0.230202	+	0.973143i	$0.573939\pi$
$8$	1.34559	−	2.33062i	0.475736	−	0.823999i
$9$		0			0
$10$	−1.10204	−	1.90878i	−0.348494	−	0.603610i
$11$	0.0434396	−	0.246358i	0.0130975	−	0.0742798i	−0.977558	−	0.210665i	$-0.932437\pi$
$11$	0.0434396	−	0.246358i	0.0130975	−	0.0742798i	0.990656	+	0.136385i	$0.0435483\pi$
$12$		0			0
$13$	−2.45446	−	0.893351i	−0.680745	−	0.247771i	−0.0215777	−	0.999767i	$-0.506869\pi$
$13$	−2.45446	−	0.893351i	−0.680745	−	0.247771i	−0.659167	+	0.751996i	$0.729091\pi$
$14$	−1.79020	−	0.651581i	−0.478452	−	0.174142i
$15$		0			0
$16$	0.0969067	−	0.549585i	0.0242267	−	0.137396i
$17$	−0.146688	−	0.254072i	−0.0355772	−	0.0616215i	0.847689	−	0.530494i	$-0.177994\pi$
$17$	−0.146688	−	0.254072i	−0.0355772	−	0.0616215i	−0.883266	+	0.468873i	$0.844660\pi$
$18$		0			0
$19$	1.39237	−	2.41166i	0.319432	−	0.553273i	−0.660937	−	0.750441i	$-0.729841\pi$
$19$	1.39237	−	2.41166i	0.319432	−	0.553273i	0.980370	+	0.197168i	$0.0631745\pi$
$20$	−2.85969	−	2.39956i	−0.639446	−	0.536559i
$21$		0			0
$22$	0.0348180	+	0.197463i	0.00742323	+	0.0420992i
$23$	5.12472	−	4.30015i	1.06858	−	0.896643i	0.0736543	−	0.997284i	$-0.476534\pi$
$23$	5.12472	−	4.30015i	1.06858	−	0.896643i	0.994923	+	0.100641i	$0.0320894\pi$
$24$		0			0
$25$	−2.40714	+	0.876128i	−0.481428	+	0.175226i
$26$	2.09357			0.410584
$27$		0			0
$28$	−3.22668			−0.609786
$29$	−0.333645	+	0.121437i	−0.0619562	+	0.0225502i	−0.372812	−	0.927907i	$-0.621606\pi$
$29$	−0.333645	+	0.121437i	−0.0619562	+	0.0225502i	0.310856	+	0.950457i	$0.399384\pi$
$30$		0			0
$31$	2.11847	−	1.77761i	0.380488	−	0.319268i	−0.432406	−	0.901679i	$-0.642335\pi$
$31$	2.11847	−	1.77761i	0.380488	−	0.319268i	0.812894	+	0.582411i	$0.197891\pi$
$32$	1.01231	+	5.74108i	0.178952	+	1.01489i
$33$		0			0
$34$	0.180135	+	0.151151i	0.0308929	+	0.0259222i
$35$	−3.26796	+	5.66027i	−0.552386	+	0.956760i
$36$		0			0
$37$	3.49619	+	6.05558i	0.574770	+	0.995531i	0.996067	+	0.0886080i	$0.0282418\pi$
$37$	3.49619	+	6.05558i	0.574770	+	0.995531i	−0.421297	+	0.906923i	$0.638425\pi$
$38$	−0.387591	+	2.19814i	−0.0628756	+	0.356585i
$39$		0			0
$40$	6.95400	+	2.53105i	1.09952	+	0.400194i
$41$	−9.13156	−	3.32362i	−1.42611	−	0.519062i	−0.490296	−	0.871556i	$-0.663112\pi$
$41$	−9.13156	−	3.32362i	−1.42611	−	0.519062i	−0.935814	+	0.352494i	$0.885334\pi$
$42$		0			0
$43$	0.0452712	−	0.256746i	0.00690379	−	0.0391534i	−0.981161	−	0.193191i	$-0.938116\pi$
$43$	0.0452712	−	0.256746i	0.00690379	−	0.0391534i	0.988065	+	0.154037i	$0.0492276\pi$
$44$	0.169802	+	0.294106i	0.0255986	+	0.0443381i
$45$		0			0
$46$	−2.68104	+	4.64370i	−0.395298	+	0.684677i
$47$	8.75249	+	7.34421i	1.27668	+	1.07126i	0.993692	+	0.112140i	$0.0357704\pi$
$47$	8.75249	+	7.34421i	1.27668	+	1.07126i	0.282989	+	0.959123i	$0.408674\pi$
$48$		0			0
$49$	−0.234540	−	1.33014i	−0.0335057	−	0.190020i
$50$	1.57285	−	1.31978i	0.222435	−	0.186645i
$51$		0			0
$52$	3.33207	−	1.21277i	0.462074	−	0.168181i
$53$	−5.43137			−0.746056			−0.373028	−	0.927820i	$-0.621680\pi$
$53$	−5.43137			−0.746056			−0.373028	+	0.927820i	$0.621680\pi$
$54$		0			0
$55$	0.687897			0.0927560
$56$	6.01071	−	2.18772i	0.803215	−	0.292346i
$57$		0			0
$58$	0.218007	−	0.182930i	0.0286257	−	0.0240198i
$59$	−1.03788	−	5.88612i	−0.135121	−	0.766308i	−0.974776	−	0.223188i	$-0.928354\pi$
$59$	−1.03788	−	5.88612i	−0.135121	−	0.766308i	0.839655	−	0.543121i	$-0.182757\pi$
$60$		0			0
$61$	−9.07515	−	7.61495i	−1.16195	−	0.974995i	−0.162023	−	0.986787i	$-0.551802\pi$
$61$	−9.07515	−	7.61495i	−1.16195	−	0.974995i	−0.999930	+	0.0117924i	$0.996246\pi$
$62$	−1.10830	+	1.91963i	−0.140754	+	0.243793i
$63$		0			0
$64$	−1.77824	−	3.08001i	−0.222281	−	0.385001i
$65$	1.24723	−	7.07342i	0.154700	−	0.877350i
$66$		0			0
$67$	−1.70113	−	0.619160i	−0.207826	−	0.0756424i	0.236010	−	0.971751i	$-0.424160\pi$
$67$	−1.70113	−	0.619160i	−0.207826	−	0.0756424i	−0.443835	+	0.896108i	$0.646383\pi$
$68$	0.374256	+	0.136218i	0.0453852	+	0.0165189i
$69$		0			0
$70$	0.909693	−	5.15912i	0.108729	−	0.616633i
$71$	−0.185255	−	0.320871i	−0.0219857	−	0.0380804i	0.854823	−	0.518919i	$-0.173666\pi$
$71$	−0.185255	−	0.320871i	−0.0219857	−	0.0380804i	−0.876809	+	0.480839i	$0.840332\pi$
$72$		0			0
$73$	−2.51339	+	4.35333i	−0.294171	+	0.509518i	−0.974792	−	0.223117i	$-0.928377\pi$
$73$	−2.51339	+	4.35333i	−0.294171	+	0.509518i	0.680621	+	0.732636i	$0.261710\pi$
$74$	−4.29336	−	3.60255i	−0.499093	−	0.418789i
$75$		0			0
$76$	0.656467	+	3.72301i	0.0753019	+	0.427059i
$77$	0.455479	−	0.382193i	0.0519067	−	0.0435549i
$78$		0			0
$79$	−0.754406	+	0.274581i	−0.0848773	+	0.0308928i	−0.384110	−	0.923287i	$-0.625492\pi$
$79$	−0.754406	+	0.274581i	−0.0848773	+	0.0308928i	0.299233	+	0.954180i	$0.403269\pi$
$80$	1.53459			0.171572
$81$		0			0
$82$	7.78892			0.860143
$83$	−2.58947	+	0.942488i	−0.284231	+	0.103452i	−0.480201	−	0.877158i	$-0.659436\pi$
$83$	−2.58947	+	0.942488i	−0.284231	+	0.103452i	0.195971	+	0.980610i	$0.437214\pi$
$84$		0			0
$85$	0.617998	−	0.518562i	0.0670313	−	0.0562460i
$86$	0.0362861	+	0.205789i	0.00391283	+	0.0221908i
$87$		0			0
$88$	−0.515717	−	0.432738i	−0.0549756	−	0.0461300i
$89$	5.22533	−	9.05054i	0.553884	−	0.959356i	−0.444105	−	0.895975i	$-0.646478\pi$
$89$	5.22533	−	9.05054i	0.553884	−	0.959356i	0.997989	−	0.0633809i	$-0.0201883\pi$
$90$		0			0
$91$	−3.10412	−	5.37650i	−0.325401	−	0.563611i
$92$	−1.57704	+	8.94385i	−0.164418	+	0.932461i
$93$		0			0
$94$	−8.60560	−	3.13218i	−0.887600	−	0.323060i
$95$	7.19580	+	2.61906i	0.738273	+	0.268709i
$96$		0			0
$97$	−2.57600	+	14.6092i	−0.261553	+	1.48334i	0.517120	+	0.855913i	$0.327004\pi$
$97$	−2.57600	+	14.6092i	−0.261553	+	1.48334i	−0.778673	+	0.627430i	$0.784107\pi$
$98$	0.541296	+	0.937552i	0.0546791	+	0.0947070i
$99$		0			0
$100$	1.73877	−	3.01164i	0.173877	−	0.301164i
$101$	−3.06826	−	2.57457i	−0.305303	−	0.256180i	0.477244	−	0.878771i	$-0.341636\pi$
$101$	−3.06826	−	2.57457i	−0.305303	−	0.256180i	−0.782548	+	0.622591i	$0.786080\pi$
$102$		0			0
$103$	−1.02789	−	5.82943i	−0.101281	−	0.574391i	−0.992641	−	0.121095i	$-0.961359\pi$
$103$	−1.02789	−	5.82943i	−0.101281	−	0.574391i	0.891360	−	0.453296i	$-0.149752\pi$
$104$	−5.38475	+	4.51834i	−0.528018	+	0.443060i
$105$		0			0
$106$	4.09085	−	1.48895i	0.397338	−	0.144619i
$107$	0.258978			0.0250364			0.0125182	−	0.999922i	$-0.496015\pi$
$107$	0.258978			0.0250364			0.0125182	+	0.999922i	$0.496015\pi$
$108$		0			0
$109$	−8.55787			−0.819695			−0.409848	−	0.912154i	$-0.634418\pi$
$109$	−8.55787			−0.819695			−0.409848	+	0.912154i	$0.634418\pi$
$110$	−0.518117	+	0.188579i	−0.0494005	+	0.0179803i
$111$		0			0
$112$	1.01610	−	0.852609i	0.0960124	−	0.0805640i
$113$	0.541640	+	3.07179i	0.0509532	+	0.288970i	0.999628	−	0.0272843i	$-0.00868592\pi$
$113$	0.541640	+	3.07179i	0.0509532	+	0.288970i	−0.948675	+	0.316254i	$0.897575\pi$
$114$		0			0
$115$	14.0922	+	11.8247i	1.31410	+	1.10266i
$116$	0.241005	−	0.417432i	0.0223767	−	0.0387576i
$117$		0			0
$118$	2.39533	+	4.14884i	0.220508	+	0.381932i
$119$	0.121086	−	0.686714i	0.0111000	−	0.0629510i
$120$		0			0
$121$	10.2778	+	3.74082i	0.934347	+	0.340074i
$122$	8.92285	+	3.24765i	0.807837	+	0.294029i
$123$		0			0
$124$	−0.651922	+	3.69724i	−0.0585444	+	0.332022i
$125$	3.35257	+	5.80682i	0.299863	+	0.519378i
$126$		0			0
$127$	9.22726	−	15.9821i	0.818787	−	1.41818i	−0.0877893	−	0.996139i	$-0.527980\pi$
$127$	9.22726	−	15.9821i	0.818787	−	1.41818i	0.906576	−	0.422042i	$-0.138686\pi$
$128$	−6.74783	−	5.66210i	−0.596430	−	0.500464i
$129$		0			0
$130$	0.999692	+	5.66954i	0.0876788	+	0.497251i
$131$	−10.8973	+	9.14396i	−0.952105	+	0.798911i	−0.979651	−	0.200709i	$-0.935675\pi$
$131$	−10.8973	+	9.14396i	−0.952105	+	0.798911i	0.0275454	+	0.999621i	$0.491231\pi$
$132$		0			0
$133$	6.21971	−	2.26379i	0.539317	−	0.196295i
$134$	1.45101			0.125348
$135$		0			0
$136$	−0.789527			−0.0677014
$137$	−18.4984	+	6.73287i	−1.58042	+	0.575228i	−0.975296	−	0.220900i	$-0.929100\pi$
$137$	−18.4984	+	6.73287i	−1.58042	+	0.575228i	−0.605128	+	0.796128i	$0.706878\pi$
$138$		0			0
$139$	−13.7206	+	11.5129i	−1.16377	+	0.976515i	−0.999950	−	0.00997617i	$-0.996824\pi$
$139$	−13.7206	+	11.5129i	−1.16377	+	0.976515i	−0.163815	+	0.986491i	$0.552380\pi$
$140$	−1.54076	−	8.73806i	−0.130218	−	0.738501i
$141$		0			0
$142$	0.227495	+	0.190891i	0.0190910	+	0.0160192i
$143$	−0.326705	+	0.565870i	−0.0273205	+	0.0473205i
$144$		0			0
$145$	−0.488175	−	0.845544i	−0.0405408	−	0.0702186i
$146$	0.699647	−	3.96789i	0.0579032	−	0.328385i
$147$		0			0
$148$	−8.92007	−	3.24664i	−0.733225	−	0.266872i
$149$	15.3071	+	5.57132i	1.25401	+	0.456421i	0.881753	−	0.471711i	$-0.156363\pi$
$149$	15.3071	+	5.57132i	1.25401	+	0.456421i	0.372252	+	0.928132i	$0.378586\pi$
$150$		0			0
$151$	2.47880	−	14.0580i	0.201722	−	1.14402i	−0.700793	−	0.713365i	$-0.747170\pi$
$151$	2.47880	−	14.0580i	0.201722	−	1.14402i	0.902515	−	0.430659i	$-0.141719\pi$
$152$	−3.74711	−	6.49019i	−0.303931	−	0.526424i
$153$		0			0
$154$	−0.238288	+	0.412728i	−0.0192018	+	0.0332585i
$155$	5.82546	+	4.88814i	0.467912	+	0.392625i
$156$		0			0
$157$	0.132555	+	0.751757i	0.0105790	+	0.0599968i	0.989640	−	0.143569i	$-0.0458580\pi$
$157$	0.132555	+	0.751757i	0.0105790	+	0.0599968i	−0.979061	+	0.203566i	$0.934747\pi$
$158$	0.492937	−	0.413623i	0.0392159	−	0.0329061i
$159$		0			0
$160$	−15.0638	+	5.48279i	−1.19090	+	0.433452i
$161$	15.9006			1.25315
$162$		0			0
$163$	5.12834			0.401682			0.200841	−	0.979624i	$-0.435632\pi$
$163$	5.12834			0.401682			0.200841	+	0.979624i	$0.435632\pi$
$164$	12.3966	−	4.51199i	0.968011	−	0.352327i
$165$		0			0
$166$	1.69198	−	1.41974i	0.131323	−	0.110193i
$167$	−1.54566	−	8.76590i	−0.119607	−	0.678325i	−0.984366	−	0.176137i	$-0.943640\pi$
$167$	−1.54566	−	8.76590i	−0.119607	−	0.678325i	0.864759	−	0.502188i	$-0.167471\pi$
$168$		0			0
$169$	−4.73227	−	3.97085i	−0.364021	−	0.305450i
$170$	−0.323312	+	0.559992i	−0.0247969	+	0.0429495i
$171$		0			0
$172$	0.176962	+	0.306507i	0.0134932	+	0.0233709i
$173$	1.18276	−	6.70776i	0.0899235	−	0.509982i	−0.906262	−	0.422717i	$-0.861076\pi$
$173$	1.18276	−	6.70776i	0.0899235	−	0.509982i	0.996185	−	0.0872644i	$-0.0278125\pi$
$174$		0			0
$175$	−5.72137	−	2.08241i	−0.432495	−	0.157415i
$176$	−0.131185	−	0.0477476i	−0.00988847	−	0.00359911i
$177$		0			0
$178$	−1.45456	+	8.24923i	−0.109024	+	0.618306i
$179$	−9.17382	−	15.8895i	−0.685684	−	1.18764i	−0.973221	−	0.229870i	$-0.926170\pi$
$179$	−9.17382	−	15.8895i	−0.685684	−	1.18764i	0.287538	−	0.957769i	$-0.407163\pi$
$180$		0			0
$181$	−5.66282	+	9.80830i	−0.420914	+	0.729045i	−0.996029	−	0.0890276i	$-0.971624\pi$
$181$	−5.66282	+	9.80830i	−0.420914	+	0.729045i	0.575115	+	0.818073i	$0.304957\pi$
$182$	3.81190	+	3.19856i	0.282557	+	0.237093i
$183$		0			0
$184$	−3.12628	−	17.7300i	−0.230472	−	1.30707i
$185$	−14.7295	+	12.3595i	−1.08293	+	0.908687i
$186$		0			0
$187$	−0.0689648	+	0.0251011i	−0.00504321	+	0.00183558i
$188$	−15.5108			−1.13124
$189$		0			0
$190$	−6.13778			−0.445281
$191$	6.44480	−	2.34571i	0.466329	−	0.169730i	−0.0981596	−	0.995171i	$-0.531296\pi$
$191$	6.44480	−	2.34571i	0.466329	−	0.169730i	0.564489	+	0.825441i	$0.309073\pi$
$192$		0			0
$193$	15.6371	−	13.1211i	1.12558	−	0.944477i	0.126711	−	0.991940i	$-0.459558\pi$
$193$	15.6371	−	13.1211i	1.12558	−	0.944477i	0.998873	+	0.0474627i	$0.0151135\pi$
$194$	−2.06474	−	11.7097i	−0.148239	−	0.840707i
$195$		0			0
$196$	1.40462	+	1.17861i	0.100330	+	0.0841866i
$197$	1.51786	−	2.62902i	0.108143	−	0.187310i	−0.806875	−	0.590723i	$-0.798843\pi$
$197$	1.51786	−	2.62902i	0.108143	−	0.187310i	0.915018	+	0.403413i	$0.132176\pi$
$198$		0			0
$199$	1.13124	+	1.95936i	0.0801912	+	0.138895i	0.903332	−	0.428942i	$-0.141114\pi$
$199$	1.13124	+	1.95936i	0.0801912	+	0.138895i	−0.823141	+	0.567837i	$0.807780\pi$
$200$	−1.19709	+	6.78904i	−0.0846471	+	0.480058i
$201$		0			0
$202$	3.01677	+	1.09801i	0.212259	+	0.0772560i
$203$	−0.793018	−	0.288635i	−0.0556589	−	0.0202582i
$204$		0			0
$205$	4.64020	−	26.3159i	0.324086	−	1.83798i
$206$	2.37226	+	4.10888i	0.165283	+	0.286279i
$207$		0			0
$208$	−0.728826	+	1.26236i	−0.0505350	+	0.0875292i
$209$	−0.533649	−	0.447784i	−0.0369132	−	0.0309739i
$210$		0			0
$211$	4.41601	+	25.0445i	0.304011	+	1.72413i	0.628124	+	0.778113i	$0.283823\pi$
$211$	4.41601	+	25.0445i	0.304011	+	1.72413i	−0.324113	+	0.946018i	$0.605066\pi$
$212$	5.64834	−	4.73952i	0.387929	−	0.325511i
$213$		0			0
$214$	−0.195060	+	0.0709959i	−0.0133340	+	0.00485318i
$215$	0.716901			0.0488923
$216$		0			0
$217$	6.57305			0.446208
$218$	6.44569	−	2.34604i	0.436557	−	0.158894i
$219$		0			0
$220$	−0.715377	+	0.600272i	−0.0482307	+	0.0404703i
$221$	0.133066	+	0.754654i	0.00895097	+	0.0507635i
$222$		0			0
$223$	−2.93497	−	2.46274i	−0.196540	−	0.164917i	0.539206	−	0.842174i	$-0.318724\pi$
$223$	−2.93497	−	2.46274i	−0.196540	−	0.164917i	−0.735747	+	0.677257i	$0.763169\pi$
$224$	−6.92805	+	11.9997i	−0.462900	+	0.801766i
$225$		0			0
$226$	−1.25005	−	2.16515i	−0.0831523	−	0.144024i
$227$	−0.436897	+	2.47777i	−0.0289979	+	0.164455i	−0.995868	−	0.0908142i	$-0.971053\pi$
$227$	−0.436897	+	2.47777i	−0.0289979	+	0.164455i	0.966870	+	0.255269i	$0.0821642\pi$
$228$		0			0
$229$	14.9783	+	5.45167i	0.989797	+	0.360257i	0.785642	−	0.618682i	$-0.212333\pi$
$229$	14.9783	+	5.45167i	0.989797	+	0.360257i	0.204155	+	0.978939i	$0.434555\pi$
$230$	−13.8557	−	5.04305i	−0.913615	−	0.332529i
$231$		0			0
$232$	−0.165924	+	0.941003i	−0.0108935	+	0.0617799i
$233$	14.0641	+	24.3598i	0.921372	+	1.59586i	0.797295	+	0.603590i	$0.206264\pi$
$233$	14.0641	+	24.3598i	0.921372	+	1.59586i	0.124077	+	0.992273i	$0.460403\pi$
$234$		0			0
$235$	−15.7092	+	27.2092i	−1.02476	+	1.77493i
$236$	6.21569	+	5.21558i	0.404607	+	0.339505i
$237$		0			0
$238$	0.0970539	+	0.550420i	0.00629107	+	0.0356784i
$239$	11.2653	−	9.45270i	0.728691	−	0.611444i	−0.201083	−	0.979574i	$-0.564446\pi$
$239$	11.2653	−	9.45270i	0.728691	−	0.611444i	0.929774	+	0.368130i	$0.120002\pi$
$240$		0			0
$241$	−7.93378	+	2.88766i	−0.511059	+	0.186010i	−0.584662	−	0.811277i	$-0.698773\pi$
$241$	−7.93378	+	2.88766i	−0.511059	+	0.186010i	0.0736022	+	0.997288i	$0.476550\pi$
$242$	−8.76664			−0.563541
$243$		0			0
$244$	16.0826			1.02958
$245$	3.49012	−	1.27030i	0.222975	−	0.0811564i
$246$		0			0
$247$	−5.57198	+	4.67545i	−0.354537	+	0.297492i
$248$	−1.29235	−	7.32927i	−0.0820642	−	0.465409i
$249$		0			0
$250$	−4.11699	−	3.45457i	−0.260381	−	0.218486i
$251$	−11.6102	+	20.1095i	−0.732832	+	1.26930i	0.222835	+	0.974856i	$0.428469\pi$
$251$	−11.6102	+	20.1095i	−0.732832	+	1.26930i	−0.955668	+	0.294447i	$0.904865\pi$
$252$		0			0
$253$	−0.836762	−	1.44931i	−0.0526067	−	0.0911176i
$254$	−2.56857	+	14.5671i	−0.161166	+	0.914020i
$255$		0			0
$256$	13.3186	+	4.84758i	0.832413	+	0.302973i
$257$	6.45118	+	2.34804i	0.402413	+	0.146466i	0.535294	−	0.844666i	$-0.320201\pi$
$257$	6.45118	+	2.34804i	0.402413	+	0.146466i	−0.132881	+	0.991132i	$0.542423\pi$
$258$		0			0
$259$	−2.88598	+	16.3672i	−0.179326	+	1.01701i
$260$	4.87534	+	8.44434i	0.302356	+	0.523696i
$261$		0			0
$262$	5.70105	−	9.87451i	0.352212	−	0.610049i
$263$	−2.56850	−	2.15523i	−0.158381	−	0.132897i	0.560154	−	0.828389i	$-0.310742\pi$
$263$	−2.56850	−	2.15523i	−0.158381	−	0.132897i	−0.718534	+	0.695492i	$0.755187\pi$
$264$		0			0
$265$	−2.59351	−	14.7085i	−0.159318	−	0.903536i
$266$	−4.06402	+	3.41012i	−0.249181	+	0.209088i
$267$		0			0
$268$	2.30937	−	0.840543i	0.141067	−	0.0513444i
$269$	−12.7416			−0.776869			−0.388434	−	0.921476i	$-0.626984\pi$
$269$	−12.7416			−0.776869			−0.388434	+	0.921476i	$0.626984\pi$
$270$		0			0
$271$	−23.5566			−1.43096			−0.715481	−	0.698632i	$-0.753792\pi$
$271$	−23.5566			−1.43096			−0.715481	+	0.698632i	$0.753792\pi$
$272$	−0.153849	+	0.0559965i	−0.00932848	+	0.00339529i
$273$		0			0
$274$	12.0871	−	10.1422i	0.730206	−	0.612715i
$275$	0.111276	+	0.631078i	0.00671020	+	0.0380554i
$276$		0			0
$277$	3.20300	+	2.68763i	0.192450	+	0.161484i	0.733921	−	0.679235i	$-0.237688\pi$
$277$	3.20300	+	2.68763i	0.192450	+	0.161484i	−0.541472	+	0.840719i	$0.682133\pi$
$278$	7.17806	−	12.4328i	0.430511	−	0.745667i
$279$		0			0
$280$	8.79463	+	15.2327i	0.525580	+	0.910331i
$281$	3.75705	−	21.3073i	0.224127	−	1.27109i	−0.640220	−	0.768192i	$-0.721157\pi$
$281$	3.75705	−	21.3073i	0.224127	−	1.27109i	0.864347	−	0.502896i	$-0.167732\pi$
$282$		0			0
$283$	−4.91209	−	1.78785i	−0.291993	−	0.106277i	0.191870	−	0.981420i	$-0.438545\pi$
$283$	−4.91209	−	1.78785i	−0.291993	−	0.106277i	−0.483864	+	0.875143i	$0.660767\pi$
$284$	0.472654	+	0.172032i	0.0280468	+	0.0102082i
$285$		0			0
$286$	0.0909441	−	0.515770i	0.00537764	−	0.0304981i
$287$	−11.5486	−	20.0027i	−0.681690	−	1.18072i
$288$		0			0
$289$	8.45697	−	14.6479i	0.497469	−	0.861641i
$290$	0.599484	+	0.503027i	0.0352029	+	0.0295388i
$291$		0			0
$292$	−1.18500	−	6.72047i	−0.0693468	−	0.393285i
$293$	4.70517	−	3.94811i	0.274879	−	0.230651i	−0.494918	−	0.868940i	$-0.664802\pi$
$293$	4.70517	−	3.94811i	0.274879	−	0.230651i	0.769797	+	0.638289i	$0.220357\pi$
$294$		0			0
$295$	15.4444	−	5.62131i	0.899208	−	0.327285i
$296$	18.8177			1.09376
$297$		0			0
$298$	−13.0564			−0.756339
$299$	−16.4200	+	5.97638i	−0.949591	+	0.345623i
$300$		0			0
$301$	0.474684	−	0.398307i	0.0273603	−	0.0229580i
$302$	1.98683	+	11.2679i	0.114329	+	0.648393i
$303$		0			0
$304$	−1.19048	−	0.998934i	−0.0682789	−	0.0572928i
$305$	16.2884	−	28.2123i	0.932669	−	1.61543i
$306$		0			0
$307$	−9.50194	−	16.4578i	−0.542304	−	0.939298i	−0.998771	−	0.0495580i	$-0.984219\pi$
$307$	−9.50194	−	16.4578i	−0.542304	−	0.939298i	0.456467	−	0.889740i	$-0.349115\pi$
$308$	−0.140166	+	0.794920i	−0.00798669	+	0.0452948i
$309$		0			0
$310$	−5.72769	−	2.08471i	−0.325311	−	0.118404i
$311$	−20.2475	−	7.36948i	−1.14813	−	0.417885i	−0.303286	−	0.952900i	$-0.598084\pi$
$311$	−20.2475	−	7.36948i	−1.14813	−	0.417885i	−0.844843	+	0.535015i	$0.820306\pi$
$312$		0			0
$313$	−0.662228	+	3.75568i	−0.0374313	+	0.212284i	−0.997787	−	0.0664949i	$-0.978818\pi$
$313$	−0.662228	+	3.75568i	−0.0374313	+	0.212284i	0.960355	+	0.278778i	$0.0899295\pi$
$314$	−0.305925	−	0.529877i	−0.0172643	−	0.0299027i
$315$		0			0
$316$	0.544937	−	0.943859i	0.0306551	−	0.0530962i
$317$	−3.25913	−	2.73473i	−0.183051	−	0.153598i	0.546658	−	0.837356i	$-0.315900\pi$
$317$	−3.25913	−	2.73473i	−0.183051	−	0.153598i	−0.729709	+	0.683758i	$0.760344\pi$
$318$		0			0
$319$	0.0154235	+	0.0874713i	0.000863553	+	0.00489745i
$320$	7.49175	−	6.28632i	0.418801	−	0.351416i
$321$		0			0
$322$	−11.9762	+	4.35898i	−0.667407	+	0.242916i
$323$	−0.816980			−0.0454580
$324$		0			0
$325$	6.69092			0.371146
$326$	−3.86261	+	1.40587i	−0.213930	+	0.0778642i
$327$		0			0
$328$	−20.0334	+	16.8100i	−1.10616	+	0.928178i
$329$	4.71570	+	26.7441i	0.259985	+	1.47445i
$330$		0			0
$331$	−10.9497	−	9.18787i	−0.601849	−	0.505011i	0.290191	−	0.956969i	$-0.406281\pi$
$331$	−10.9497	−	9.18787i	−0.601849	−	0.505011i	−0.892039	+	0.451958i	$0.850726\pi$
$332$	1.87047	−	3.23976i	0.102656	−	0.177805i
$333$		0			0
$334$	3.56725	+	6.17865i	0.195191	+	0.338081i
$335$	0.864428	−	4.90242i	0.0472288	−	0.267848i
$336$		0			0
$337$	−33.5644	−	12.2164i	−1.82837	−	0.665472i	−0.993333	−	0.115278i	$-0.963224\pi$
$337$	−33.5644	−	12.2164i	−1.82837	−	0.665472i	−0.835037	−	0.550194i	$-0.814554\pi$
$338$	4.65286	+	1.69350i	0.253082	+	0.0921143i
$339$		0			0
$340$	−0.190178	+	1.07855i	−0.0103139	+	0.0584928i
$341$	−0.345903	−	0.599121i	−0.0187317	−	0.0324442i
$342$		0			0
$343$	9.92407	−	17.1890i	0.535849	−	0.928118i
$344$	−0.537461	−	0.450983i	−0.0289780	−	0.0243154i
$345$		0			0
$346$	0.948013	+	5.37645i	0.0509655	+	0.289040i
$347$	14.8931	−	12.4968i	0.799502	−	0.670862i	−0.148575	−	0.988901i	$-0.547469\pi$
$347$	14.8931	−	12.4968i	0.799502	−	0.670862i	0.948078	+	0.318039i	$0.103024\pi$
$348$		0			0
$349$	7.53700	−	2.74324i	0.403446	−	0.146842i	−0.132323	−	0.991207i	$-0.542244\pi$
$349$	7.53700	−	2.74324i	0.403446	−	0.146842i	0.535770	+	0.844364i	$0.320022\pi$
$350$	4.88014			0.260855
$351$		0			0
$352$	1.45834			0.0777296
$353$	8.22589	−	2.99398i	0.437820	−	0.159354i	−0.113700	−	0.993515i	$-0.536270\pi$
$353$	8.22589	−	2.99398i	0.437820	−	0.159354i	0.551520	+	0.834162i	$0.314048\pi$
$354$		0			0
$355$	0.780479	−	0.654900i	0.0414235	−	0.0347585i
$356$	2.46361	+	13.9718i	0.130571	+	0.740505i
$357$		0			0
$358$	11.2656	+	9.45292i	0.595403	+	0.499602i
$359$	−4.13896	+	7.16888i	−0.218446	+	0.378359i	−0.954333	−	0.298745i	$-0.903432\pi$
$359$	−4.13896	+	7.16888i	−0.218446	+	0.378359i	0.735887	+	0.677104i	$0.236765\pi$
$360$		0			0
$361$	5.62260	+	9.73862i	0.295926	+	0.512559i
$362$	1.57635	−	8.93990i	0.0828509	−	0.469871i
$363$		0			0
$364$	7.91977	+	2.88256i	0.415108	+	0.151087i
$365$	−12.9892	−	4.72770i	−0.679888	−	0.247459i
$366$		0			0
$367$	−2.56997	+	14.5750i	−0.134151	+	0.760809i	0.841296	+	0.540575i	$0.181793\pi$
$367$	−2.56997	+	14.5750i	−0.134151	+	0.760809i	−0.975447	+	0.220234i	$0.929318\pi$
$368$	−1.86668	−	3.23318i	−0.0973074	−	0.168541i
$369$		0			0
$370$	7.70585	−	13.3469i	0.400608	−	0.693874i
$371$	−9.88922	−	8.29804i	−0.513423	−	0.430813i
$372$		0			0
$373$	4.43383	+	25.1455i	0.229575	+	1.30198i	0.853743	+	0.520694i	$0.174327\pi$
$373$	4.43383	+	25.1455i	0.229575	+	1.30198i	−0.624168	+	0.781290i	$0.714562\pi$
$374$	0.0450623	−	0.0378118i	0.00233012	−	0.00195520i
$375$		0			0
$376$	28.8938	−	10.5165i	1.49008	−	0.542346i
$377$	0.927403			0.0477637
$378$		0			0
$379$	20.1244			1.03372			0.516861	−	0.856070i	$-0.327101\pi$
$379$	20.1244			1.03372			0.516861	+	0.856070i	$0.327101\pi$
$380$	−9.76869	+	3.55551i	−0.501123	+	0.182394i
$381$		0			0
$382$	−4.21110	+	3.53353i	−0.215459	+	0.180791i
$383$	4.14346	+	23.4987i	0.211721	+	1.20073i	0.886507	+	0.462716i	$0.153125\pi$
$383$	4.14346	+	23.4987i	0.211721	+	1.20073i	−0.674785	+	0.738014i	$0.735764\pi$
$384$		0			0
$385$	1.25250	+	1.05097i	0.0638331	+	0.0535623i
$386$	−8.18070	+	14.1694i	−0.416387	+	0.721203i
$387$		0			0
$388$	−10.0694	−	17.4407i	−0.511196	−	0.885418i
$389$	−6.59400	+	37.3964i	−0.334329	+	1.89607i	0.0994307	+	0.995044i	$0.468298\pi$
$389$	−6.59400	+	37.3964i	−0.334329	+	1.89607i	−0.433760	+	0.901029i	$0.642813\pi$
$390$		0			0
$391$	−1.84428	−	0.671264i	−0.0932694	−	0.0339473i
$392$	−3.41565	−	1.24320i	−0.172516	−	0.0627908i
$393$		0			0
$394$	−0.422524	+	2.39625i	−0.0212864	+	0.120721i
$395$	−1.10382	−	1.91187i	−0.0555390	−	0.0961964i
$396$		0			0
$397$	−10.1747	+	17.6230i	−0.510651	+	0.884474i	0.489272	+	0.872131i	$0.337262\pi$
$397$	−10.1747	+	17.6230i	−0.510651	+	0.884474i	−0.999924	+	0.0123433i	$0.996071\pi$
$398$	−1.38917	−	1.16565i	−0.0696328	−	0.0584289i
$399$		0			0
$400$	0.248239	+	1.40783i	0.0124119	+	0.0703916i
$401$	−5.32015	+	4.46414i	−0.265676	+	0.222928i	−0.765887	−	0.642975i	$-0.777700\pi$
$401$	−5.32015	+	4.46414i	−0.265676	+	0.222928i	0.500212	+	0.865903i	$0.333256\pi$
$402$		0			0
$403$	−6.78773	+	2.47053i	−0.338121	+	0.123066i
$404$	5.43745			0.270523
$405$		0			0
$406$	0.676418			0.0335701
$407$	1.64372	−	0.598264i	0.0814760	−	0.0296548i
$408$		0			0
$409$	−8.35444	+	7.01021i	−0.413101	+	0.346633i	−0.825531	−	0.564356i	$-0.809124\pi$
$409$	−8.35444	+	7.01021i	−0.413101	+	0.346633i	0.412431	+	0.910989i	$0.364680\pi$
$410$	3.71925	+	21.0929i	0.183681	+	1.04170i
$411$		0			0
$412$	6.15582	+	5.16535i	0.303276	+	0.254478i
$413$	7.10308	−	12.3029i	0.349520	−	0.605386i
$414$		0			0
$415$	−3.78880	−	6.56240i	−0.185985	−	0.322135i
$416$	2.64413	−	14.9956i	0.129639	−	0.735220i
$417$		0			0
$418$	0.524693	+	0.190973i	0.0256636	+	0.00934078i
$419$	−9.46194	−	3.44386i	−0.462246	−	0.168244i	0.100391	−	0.994948i	$-0.467991\pi$
$419$	−9.46194	−	3.44386i	−0.462246	−	0.168244i	−0.562637	+	0.826704i	$0.690213\pi$
$420$		0			0
$421$	−0.539623	+	3.06035i	−0.0262996	+	0.149152i	−0.995130	−	0.0985733i	$-0.968572\pi$
$421$	−0.539623	+	3.06035i	−0.0262996	+	0.149152i	0.968830	+	0.247726i	$0.0796832\pi$
$422$	−10.1917	−	17.6526i	−0.496126	−	0.859315i
$423$		0			0
$424$	−7.30837	+	12.6585i	−0.354926	+	0.614750i
$425$	0.575699	+	0.483069i	0.0279255	+	0.0234323i
$426$		0			0
$427$	−4.88955	−	27.7300i	−0.236622	−	1.34195i
$428$	−0.269324	+	0.225990i	−0.0130183	+	0.0109236i
$429$		0			0
$430$	−0.539962	+	0.196530i	−0.0260393	+	0.00947753i
$431$	28.0701			1.35209			0.676044	−	0.736862i	$-0.263693\pi$
$431$	28.0701			1.35209			0.676044	+	0.736862i	$0.263693\pi$
$432$		0			0
$433$	19.5251			0.938317			0.469158	−	0.883114i	$-0.344557\pi$
$433$	19.5251			0.938317			0.469158	+	0.883114i	$0.344557\pi$
$434$	−4.95075	+	1.80193i	−0.237644	+	0.0864952i
$435$		0			0
$436$	8.89973	−	7.46776i	0.426220	−	0.357641i
$437$	−3.23498	−	18.3465i	−0.154750	−	0.877631i
$438$		0			0
$439$	11.2069	+	9.40371i	0.534876	+	0.448815i	0.869781	−	0.493437i	$-0.164260\pi$
$439$	11.2069	+	9.40371i	0.534876	+	0.448815i	−0.334905	+	0.942252i	$0.608704\pi$
$440$	0.925624	−	1.60323i	0.0441274	−	0.0764309i
$441$		0			0
$442$	−0.307103	−	0.531918i	−0.0146074	−	0.0253008i
$443$	−3.18748	+	18.0771i	−0.151442	+	0.858868i	0.810526	+	0.585703i	$0.199182\pi$
$443$	−3.18748	+	18.0771i	−0.151442	+	0.858868i	−0.961967	+	0.273165i	$0.911930\pi$
$444$		0			0
$445$	27.0046	+	9.82886i	1.28014	+	0.465933i
$446$	2.88572	+	1.05032i	0.136643	+	0.0497339i
$447$		0			0
$448$	1.46788	−	8.32476i	0.0693508	−	0.393308i
$449$	6.92969	+	12.0026i	0.327032	+	0.566437i	0.981922	−	0.189288i	$-0.0606180\pi$
$449$	6.92969	+	12.0026i	0.327032	+	0.566437i	−0.654889	+	0.755725i	$0.727285\pi$
$450$		0			0
$451$	−1.21547	+	2.10526i	−0.0572344	+	0.0991328i
$452$	−3.24378	−	2.72185i	−0.152575	−	0.128025i
$453$		0			0
$454$	−0.350185	−	1.98600i	−0.0164350	−	0.0932075i
$455$	13.0777	−	10.9735i	0.613091	−	0.514445i
$456$		0			0
$457$	−16.5838	+	6.03602i	−0.775758	+	0.282353i	−0.699403	−	0.714728i	$-0.746551\pi$
$457$	−16.5838	+	6.03602i	−0.775758	+	0.282353i	−0.0763555	+	0.997081i	$0.524328\pi$
$458$	−12.7760			−0.596985
$459$		0			0
$460$	−24.9736			−1.16440
$461$	24.0919	−	8.76872i	1.12207	−	0.408400i	0.286663	−	0.958032i	$-0.407454\pi$
$461$	24.0919	−	8.76872i	1.12207	−	0.408400i	0.835407	+	0.549631i	$0.185232\pi$
$462$		0			0
$463$	14.0549	−	11.7935i	0.653189	−	0.548090i	−0.254848	−	0.966981i	$-0.582025\pi$
$463$	14.0549	−	11.7935i	0.653189	−	0.548090i	0.908037	+	0.418891i	$0.137581\pi$
$464$	0.0344074	+	0.195134i	0.00159732	+	0.00905888i
$465$		0			0
$466$	−17.2709	−	14.4920i	−0.800059	−	0.671329i
$467$	−8.13092	+	14.0832i	−0.376254	+	0.651692i	−0.990514	−	0.137412i	$-0.956121\pi$
$467$	−8.13092	+	14.0832i	−0.376254	+	0.651692i	0.614260	+	0.789104i	$0.289455\pi$
$468$		0			0
$469$	−2.15139	−	3.72632i	−0.0993421	−	0.172066i
$470$	4.37294	−	24.8002i	0.201709	−	1.14395i
$471$		0			0
$472$	−15.1149	−	5.50137i	−0.695719	−	0.253221i
$473$	−0.0612849	−	0.0223059i	−0.00281788	−	0.00102563i
$474$		0			0
$475$	−1.23872	+	7.02510i	−0.0568362	+	0.322334i
$476$	0.473317	+	0.819809i	0.0216944	+	0.0375759i
$477$		0			0
$478$	−5.89354	+	10.2079i	−0.269564	+	0.466899i
$479$	7.25575	+	6.08830i	0.331524	+	0.278181i	0.793320	−	0.608804i	$-0.208351\pi$
$479$	7.25575	+	6.08830i	0.331524	+	0.278181i	−0.461797	+	0.886986i	$0.652795\pi$
$480$		0			0
$481$	−3.17151	−	17.9865i	−0.144608	−	0.820114i
$482$	5.18401	−	4.34990i	0.236125	−	0.198133i
$483$		0			0
$484$	−13.9527	+	5.07836i	−0.634213	+	0.230835i
$485$	−40.7928			−1.85231
$486$		0			0
$487$	−0.467564			−0.0211874			−0.0105937	−	0.999944i	$-0.503372\pi$
$487$	−0.467564			−0.0211874			−0.0105937	+	0.999944i	$0.503372\pi$
$488$	−29.9590	+	10.9042i	−1.35618	+	0.493608i
$489$		0			0
$490$	−2.28048	+	1.91355i	−0.103022	+	0.0864453i
$491$	−4.34936	−	24.6665i	−0.196284	−	1.11318i	−0.910578	−	0.413337i	$-0.864363\pi$
$491$	−4.34936	−	24.6665i	−0.196284	−	1.11318i	0.714294	−	0.699846i	$-0.246748\pi$
$492$		0			0
$493$	0.0797954	+	0.0669563i	0.00359380	+	0.00301556i
$494$	2.91504	−	5.04899i	0.131154	−	0.227165i
$495$		0			0
$496$	−0.771653	−	1.33654i	−0.0346482	−	0.0600125i
$497$	0.152922	−	0.867261i	0.00685947	−	0.0389020i
$498$		0			0
$499$	13.1878	+	4.79996i	0.590367	+	0.214876i	0.619891	−	0.784688i	$-0.287177\pi$
$499$	13.1878	+	4.79996i	0.590367	+	0.214876i	−0.0295240	+	0.999564i	$0.509399\pi$
$500$	−8.55364	−	3.11327i	−0.382530	−	0.139230i
$501$		0			0
$502$	3.23191	−	18.3291i	0.144247	−	0.818068i
$503$	14.1558	+	24.5186i	0.631176	+	1.09323i	0.987312	+	0.158794i	$0.0507607\pi$
$503$	14.1558	+	24.5186i	0.631176	+	1.09323i	−0.356136	+	0.934434i	$0.615906\pi$
$504$		0			0
$505$	5.50701	−	9.53842i	0.245059	−	0.424454i
$506$	1.02755	+	0.862218i	0.0456803	+	0.0383303i
$507$		0			0
$508$	4.35041	+	24.6724i	0.193018	+	1.09466i
$509$	21.9759	−	18.4399i	0.974063	−	0.817336i	−0.00912008	−	0.999958i	$-0.502903\pi$
$509$	21.9759	−	18.4399i	0.974063	−	0.817336i	0.983183	+	0.182622i	$0.0584586\pi$
$510$		0			0
$511$	−11.2273	+	4.08640i	−0.496666	+	0.180772i
$512$	6.25700			0.276523
$513$		0			0
$514$	−5.50264			−0.242711
$515$	15.2957	−	5.56716i	0.674007	−	0.245319i
$516$		0			0
$517$	2.18951	−	1.83722i	0.0962946	−	0.0808008i
$518$	−2.31319	−	13.1188i	−0.101636	−	0.576406i
$519$		0			0
$520$	−14.8072	−	12.4247i	−0.649339	−	0.544860i
$521$	−12.4548	+	21.5724i	−0.545655	+	0.945102i	0.452910	+	0.891556i	$0.350386\pi$
$521$	−12.4548	+	21.5724i	−0.545655	+	0.945102i	−0.998565	+	0.0535462i	$0.982948\pi$
$522$		0			0
$523$	12.9324	+	22.3995i	0.565494	+	0.979464i	0.997004	+	0.0773554i	$0.0246476\pi$
$523$	12.9324	+	22.3995i	0.565494	+	0.979464i	−0.431510	+	0.902108i	$0.642019\pi$
$524$	3.35347	−	19.0185i	0.146497	−	0.830826i
$525$		0			0
$526$	2.52540	+	0.919169i	0.110113	+	0.0400777i
$527$	−0.762395	−	0.277489i	−0.0332104	−	0.0120876i
$528$		0			0
$529$	3.77754	−	21.4235i	0.164241	−	0.931456i
$530$	5.98556	+	10.3673i	0.259996	+	0.450327i
$531$		0			0
$532$	−4.49274	+	7.78166i	−0.194785	+	0.337378i
$533$	19.4439	+	16.3154i	0.842209	+	0.706698i
$534$		0			0
$535$	0.123663	+	0.701330i	0.00534644	+	0.0303212i
$536$	−3.73204	+	3.13155i	−0.161200	+	0.135262i
$537$		0			0
$538$	9.59683	−	3.49296i	0.413749	−	0.150592i
$539$	−0.337880			−0.0145535
$540$		0			0
$541$	−21.9158			−0.942232			−0.471116	−	0.882071i	$-0.656149\pi$
$541$	−21.9158			−0.942232			−0.471116	+	0.882071i	$0.656149\pi$
$542$	17.7426	−	6.45777i	0.762109	−	0.277385i
$543$		0			0
$544$	1.31015	−	1.09935i	0.0561723	−	0.0471342i
$545$	−4.08643	−	23.1753i	−0.175043	−	0.992720i
$546$		0			0
$547$	−7.64210	−	6.41248i	−0.326752	−	0.274178i	0.464623	−	0.885509i	$-0.346190\pi$
$547$	−7.64210	−	6.41248i	−0.326752	−	0.274178i	−0.791375	+	0.611331i	$0.790634\pi$
$548$	13.3621	−	23.1439i	0.570802	−	0.988658i
$549$		0			0
$550$	−0.256815	−	0.444816i	−0.0109506	−	0.0189670i
$551$	−0.171694	+	0.973722i	−0.00731439	+	0.0414820i
$552$		0			0
$553$	−1.79310	−	0.652634i	−0.0762502	−	0.0277528i
$554$	−3.14925	−	1.14623i	−0.133799	−	0.0486987i
$555$		0			0
$556$	4.22227	−	23.9457i	0.179064	−	1.01552i
$557$	−9.26650	−	16.0500i	−0.392634	−	0.680062i	0.600162	−	0.799879i	$-0.295103\pi$
$557$	−9.26650	−	16.0500i	−0.392634	−	0.680062i	−0.992796	+	0.119816i	$0.961769\pi$
$558$		0			0
$559$	−0.340480	+	0.589729i	−0.0144008	+	0.0249429i
$560$	2.79411	+	2.34454i	0.118073	+	0.0990749i
$561$		0			0
$562$	3.01138	+	17.0784i	0.127027	+	0.720408i
$563$	−33.4632	+	28.0789i	−1.41031	+	1.18339i	−0.454005	+	0.890999i	$0.650005\pi$
$563$	−33.4632	+	28.0789i	−1.41031	+	1.18339i	−0.956300	+	0.292388i	$0.905550\pi$
$564$		0			0
$565$	−8.05997	+	2.93359i	−0.339086	+	0.123417i
$566$	4.18985			0.176113
$567$		0			0
$568$	−0.997105			−0.0418376
$569$	12.7485	−	4.64008i	0.534446	−	0.194522i	−0.0606766	−	0.998157i	$-0.519326\pi$
$569$	12.7485	−	4.64008i	0.534446	−	0.194522i	0.595122	+	0.803635i	$0.297104\pi$
$570$		0			0
$571$	18.1926	−	15.2654i	0.761335	−	0.638836i	−0.177139	−	0.984186i	$-0.556684\pi$
$571$	18.1926	−	15.2654i	0.761335	−	0.638836i	0.938474	+	0.345350i	$0.112240\pi$
$572$	−0.154033	−	0.873565i	−0.00644044	−	0.0365256i
$573$		0			0
$574$	14.1818	+	11.8999i	0.591935	+	0.496693i
$575$	−8.56844	+	14.8410i	−0.357329	+	0.618911i
$576$		0			0
$577$	4.05951	+	7.03128i	0.169000	+	0.292716i	0.938068	−	0.346450i	$-0.112613\pi$
$577$	4.05951	+	7.03128i	0.169000	+	0.292716i	−0.769069	+	0.639166i	$0.779280\pi$
$578$	−2.35414	+	13.3510i	−0.0979194	+	0.555329i
$579$		0			0
$580$	1.24551	+	0.453330i	0.0517172	+	0.0188235i
$581$	−6.15473	−	2.24014i	−0.255341	−	0.0929366i
$582$		0			0
$583$	−0.235937	+	1.33806i	−0.00977150	+	0.0554169i
$584$	6.76397	+	11.7155i	0.279895	+	0.484793i
$585$		0			0
$586$	−2.46156	+	4.26354i	−0.101686	+	0.176125i
$587$	2.82823	+	2.37317i	0.116734	+	0.0979511i	0.699286	−	0.714842i	$-0.253501\pi$
$587$	2.82823	+	2.37317i	0.116734	+	0.0979511i	−0.582552	+	0.812793i	$0.697946\pi$
$588$		0			0
$589$	−1.33729	−	7.58412i	−0.0551019	−	0.312498i
$590$	−10.0915	+	8.46781i	−0.415462	+	0.348614i
$591$		0			0
$592$	3.66686	−	1.33463i	0.150707	−	0.0548529i
$593$	−29.4590			−1.20974			−0.604869	−	0.796325i	$-0.706774\pi$
$593$	−29.4590			−1.20974			−0.604869	+	0.796325i	$0.706774\pi$
$594$		0			0
$595$	1.91749			0.0786093
$596$	−20.7802	+	7.56338i	−0.851190	+	0.309808i
$597$		0			0
$598$	10.7290	−	9.00268i	0.438740	−	0.368147i
$599$	3.79862	+	21.5431i	0.155207	+	0.880225i	0.958596	+	0.284770i	$0.0919172\pi$
$599$	3.79862	+	21.5431i	0.155207	+	0.880225i	−0.803388	+	0.595455i	$0.796972\pi$
$600$		0			0
$601$	27.9764	+	23.4750i	1.14118	+	0.957566i	0.999477	−	0.0323424i	$-0.0102967\pi$
$601$	27.9764	+	23.4750i	1.14118	+	0.957566i	0.141706	+	0.989909i	$0.454741\pi$
$602$	−0.248335	+	0.430130i	−0.0101214	+	0.0175308i
$603$		0			0
$604$	9.68946	+	16.7826i	0.394258	+	0.682876i
$605$	−5.22267	+	29.6192i	−0.212332	+	1.20419i
$606$		0			0
$607$	6.18395	+	2.25077i	0.250999	+	0.0913561i	0.464456	−	0.885596i	$-0.346250\pi$
$607$	6.18395	+	2.25077i	0.250999	+	0.0913561i	−0.213457	+	0.976953i	$0.568472\pi$
$608$	15.2550	+	5.55238i	0.618674	+	0.225179i
$609$		0			0
$610$	−4.53415	+	25.7144i	−0.183582	+	1.04115i
$611$	−14.9217	−	25.8451i	−0.603667	−	1.04558i
$612$		0			0
$613$	3.57434	−	6.19093i	0.144366	−	0.250049i	−0.784770	−	0.619787i	$-0.787219\pi$
$613$	3.57434	−	6.19093i	0.144366	−	0.250049i	0.929136	+	0.369737i	$0.120552\pi$
$614$	11.6685	+	9.79101i	0.470901	+	0.395133i
$615$		0			0
$616$	−0.277860	−	1.57582i	−0.0111953	−	0.0634917i
$617$	−12.6684	+	10.6301i	−0.510012	+	0.427951i	−0.861133	−	0.508379i	$-0.830245\pi$
$617$	−12.6684	+	10.6301i	−0.510012	+	0.427951i	0.351121	+	0.936330i	$0.385800\pi$
$618$		0			0
$619$	1.40893	−	0.512808i	0.0566296	−	0.0206115i	−0.313550	−	0.949572i	$-0.601518\pi$
$619$	1.40893	−	0.512808i	0.0566296	−	0.0206115i	0.370180	+	0.928960i	$0.379296\pi$
$620$	−10.3236			−0.414608
$621$		0			0
$622$	17.2704			0.692481
$623$	23.3415	−	8.49561i	0.935157	−	0.340369i
$624$		0			0
$625$	−23.9360	+	20.0847i	−0.957439	+	0.803387i
$626$	−0.530793	−	3.01028i	−0.0212148	−	0.120315i
$627$		0			0
$628$	−0.793848	−	0.666118i	−0.0316780	−	0.0265810i
$629$	1.02570	−	1.77657i	0.0408974	−	0.0708363i
$630$		0			0
$631$	17.9456	+	31.0827i	0.714404	+	1.23738i	0.963189	+	0.268826i	$0.0866356\pi$
$631$	17.9456	+	31.0827i	0.714404	+	1.23738i	−0.248785	+	0.968559i	$0.580031\pi$
$632$	−0.375172	+	2.12771i	−0.0149235	+	0.0846356i
$633$		0			0
$634$	3.20443	+	1.16632i	0.127264	+	0.0463204i
$635$	47.6866	+	17.3565i	1.89238	+	0.688772i
$636$		0			0
$637$	−0.612614	+	3.47431i	−0.0242727	+	0.137657i
$638$	−0.0355961	−	0.0616542i	−0.00140926	−	0.00244091i
$639$		0			0
$640$	12.1112	−	20.9772i	0.478738	−	0.829198i
$641$	−30.0504	−	25.2152i	−1.18692	−	0.995942i	−0.999908	−	0.0135840i	$-0.995676\pi$
$641$	−30.0504	−	25.2152i	−1.18692	−	0.995942i	−0.187010	−	0.982358i	$-0.559880\pi$
$642$		0			0
$643$	−1.80915	−	10.2602i	−0.0713461	−	0.404624i	−0.999476	−	0.0323674i	$-0.989695\pi$
$643$	−1.80915	−	10.2602i	−0.0713461	−	0.404624i	0.928130	−	0.372256i	$-0.121416\pi$
$644$	−16.5358	+	13.8752i	−0.651603	+	0.546760i
$645$		0			0
$646$	0.615340	−	0.223965i	0.0242102	−	0.00881180i
$647$	39.1517			1.53921			0.769606	−	0.638519i	$-0.220453\pi$
$647$	39.1517			1.53921			0.769606	+	0.638519i	$0.220453\pi$
$648$		0			0
$649$	−1.49518			−0.0586910
$650$	−5.03953	+	1.83424i	−0.197667	+	0.0719448i
$651$		0			0
$652$	−5.33320	+	4.47509i	−0.208864	+	0.175258i
$653$	−5.71474	−	32.4099i	−0.223635	−	1.26830i	−0.865277	−	0.501294i	$-0.832858\pi$
$653$	−5.71474	−	32.4099i	−0.223635	−	1.26830i	0.641642	−	0.767004i	$-0.278253\pi$
$654$		0			0
$655$	−29.9660	−	25.1444i	−1.17087	−	0.982474i
$656$	−2.71152	+	4.69649i	−0.105867	+	0.183367i
$657$		0			0
$658$	−10.8834	−	18.8506i	−0.424279	−	0.734873i
$659$	3.74532	−	21.2407i	0.145897	−	0.827422i	−0.820746	−	0.571293i	$-0.806442\pi$
$659$	3.74532	−	21.2407i	0.145897	−	0.827422i	0.966643	−	0.256128i	$-0.0824470\pi$
$660$		0			0
$661$	−24.7105	−	8.99389i	−0.961127	−	0.349822i	−0.186652	−	0.982426i	$-0.559764\pi$
$661$	−24.7105	−	8.99389i	−0.961127	−	0.349822i	−0.774475	+	0.632604i	$0.781986\pi$
$662$	10.7659	+	3.91848i	0.418430	+	0.152296i
$663$		0			0
$664$	−1.28776	+	7.30326i	−0.0499749	+	0.283422i
$665$	9.10043	+	15.7624i	0.352900	+	0.611240i
$666$		0			0
$667$	−1.18764	+	2.05705i	−0.0459855	+	0.0796493i
$668$	9.25670	+	7.76729i	0.358152	+	0.300526i
$669$		0			0
$670$	0.692862	+	3.92942i	0.0267676	+	0.151807i
$671$	−2.27023	+	1.90495i	−0.0876412	+	0.0735397i
$672$		0			0
$673$	−10.8272	+	3.94080i	−0.417360	+	0.151907i	−0.542160	−	0.840275i	$-0.682393\pi$
$673$	−10.8272	+	3.94080i	−0.417360	+	0.151907i	0.124800	+	0.992182i	$0.460171\pi$
$674$	28.6293			1.10276
$675$		0			0
$676$	8.38635			0.322552
$677$	−31.8791	+	11.6030i	−1.22521	+	0.445941i	−0.871955	−	0.489585i	$-0.837148\pi$
$677$	−31.8791	+	11.6030i	−1.22521	+	0.445941i	−0.353257	+	0.935526i	$0.614926\pi$
$678$		0			0
$679$	−27.0103	+	22.6643i	−1.03656	+	0.869776i
$680$	−0.377003	−	2.13809i	−0.0144574	−	0.0819920i
$681$		0			0
$682$	0.424772	+	0.356426i	0.0162654	+	0.0136483i
$683$	18.3777	−	31.8310i	0.703201	−	1.21798i	−0.264135	−	0.964486i	$-0.585087\pi$
$683$	18.3777	−	31.8310i	0.703201	−	1.21798i	0.967337	−	0.253495i	$-0.0815801\pi$
$684$		0			0
$685$	−27.0661	−	46.8799i	−1.03414	−	1.79119i
$686$	−2.76254	+	15.6671i	−0.105474	+	0.598174i
$687$		0			0
$688$	−0.136717	−	0.0497608i	−0.00521227	−	0.00189711i
$689$	13.3311	+	4.85212i	0.507874	+	0.184851i
$690$		0			0
$691$	2.32309	−	13.1749i	0.0883744	−	0.501196i	−0.908203	−	0.418530i	$-0.862545\pi$
$691$	2.32309	−	13.1749i	0.0883744	−	0.501196i	0.996577	−	0.0826660i	$-0.0263435\pi$
$692$	4.62331	+	8.00781i	0.175752	+	0.304411i
$693$		0			0
$694$	−7.79146	+	13.4952i	−0.295760	+	0.512271i
$695$	−37.7294	−	31.6588i	−1.43116	−	1.20089i
$696$		0			0
$697$	0.495057	+	2.80761i	0.0187516	+	0.106346i
$698$	−4.92475	+	4.13236i	−0.186405	+	0.156412i
$699$		0			0
$700$	7.76708	−	2.82699i	0.293568	−	0.106850i
$701$	−5.00452			−0.189018			−0.0945091	−	0.995524i	$-0.530128\pi$
$701$	−5.00452			−0.189018			−0.0945091	+	0.995524i	$0.530128\pi$
$702$		0			0
$703$	19.4720			0.734400
$704$	−0.836033	+	0.304291i	−0.0315092	+	0.0114684i
$705$		0			0
$706$	−5.37489	+	4.51007i	−0.202287	+	0.169739i
$707$	−1.65313	−	9.37537i	−0.0621724	−	0.352597i
$708$		0			0
$709$	13.1330	+	11.0199i	0.493218	+	0.413859i	0.855178	−	0.518334i	$-0.173448\pi$
$709$	13.1330	+	11.0199i	0.493218	+	0.413859i	−0.361960	+	0.932194i	$0.617892\pi$
$710$	−0.408315	+	0.707223i	−0.0153238	+	0.0265416i
$711$		0			0
$712$	−14.0623	−	24.3566i	−0.527006	−	0.912800i
$713$	3.21258	−	18.2195i	0.120312	−	0.682324i
$714$		0			0
$715$	−1.68842	−	0.614533i	−0.0631432	−	0.0229822i
$716$	23.4058	+	8.51902i	0.874716	+	0.318371i
$717$		0			0
$718$	1.15215	−	6.53417i	0.0429979	−	0.243853i
$719$	−21.6760	−	37.5439i	−0.808377	−	1.40015i	−0.913987	−	0.405742i	$-0.867013\pi$
$719$	−21.6760	−	37.5439i	−0.808377	−	1.40015i	0.105610	−	0.994408i	$-0.466320\pi$
$720$		0			0
$721$	7.03467	−	12.1844i	0.261985	−	0.453771i
$722$	−6.90461	−	5.79365i	−0.256963	−	0.215617i
$723$		0			0
$724$	−2.66987	−	15.1416i	−0.0992251	−	0.562733i
$725$	0.696735	−	0.584630i	0.0258761	−	0.0217126i
$726$		0			0
$727$	34.1521	−	12.4303i	1.26663	−	0.461016i	0.380642	−	0.924722i	$-0.375703\pi$
$727$	34.1521	−	12.4303i	1.26663	−	0.461016i	0.885989	+	0.463706i	$0.153481\pi$
$728$	−16.7075			−0.619220
$729$		0			0
$730$	11.0794			0.410067
$731$	−0.0718726	+	0.0261595i	−0.00265830	+	0.000967544i
$732$		0			0
$733$	2.96889	−	2.49119i	0.109658	−	0.0920143i	−0.586310	−	0.810087i	$-0.699420\pi$
$733$	2.96889	−	2.49119i	0.109658	−	0.0920143i	0.695968	+	0.718073i	$0.254975\pi$
$734$	−2.05990	−	11.6823i	−0.0760322	−	0.431200i
$735$		0			0
$736$	29.8753	+	25.0683i	1.10122	+	0.924031i
$737$	−0.226432	+	0.392191i	−0.00834071	+	0.0144465i
$738$		0			0
$739$	−13.2241	−	22.9048i	−0.486456	−	0.842567i	0.513422	−	0.858136i	$-0.328377\pi$
$739$	−13.2241	−	22.9048i	−0.486456	−	0.842567i	−0.999879	+	0.0155689i	$0.995044\pi$
$740$	4.53273	−	25.7064i	0.166627	−	0.944986i
$741$		0			0
$742$	9.72326	+	3.53898i	0.356952	+	0.129920i
$743$	−12.6514	−	4.60474i	−0.464136	−	0.168932i	0.0993584	−	0.995052i	$-0.468321\pi$
$743$	−12.6514	−	4.60474i	−0.464136	−	0.168932i	−0.563494	+	0.826120i	$0.690543\pi$
$744$		0			0
$745$	−7.77830	+	44.1129i	−0.284975	+	1.61617i
$746$	−10.2329	−	17.7238i	−0.374651	−	0.648915i
$747$		0			0
$748$	0.0498160	−	0.0862839i	0.00182145	−	0.00315485i
$749$	0.471538	+	0.395667i	0.0172296	+	0.0144574i
$750$		0			0
$751$	0.654359	+	3.71106i	0.0238779	+	0.135418i	0.994416	−	0.105528i	$-0.0336533\pi$
$751$	0.654359	+	3.71106i	0.0238779	+	0.135418i	−0.970538	+	0.240946i	$0.922542\pi$
$752$	4.88444	−	4.09854i	0.178117	−	0.149458i
$753$		0			0
$754$	−0.698510	+	0.254237i	−0.0254382	+	0.00925876i
$755$	39.2536			1.42859
$756$		0			0
$757$	−33.7073			−1.22511			−0.612556	−	0.790427i	$-0.709859\pi$
$757$	−33.7073			−1.22511			−0.612556	+	0.790427i	$0.709859\pi$
$758$	−15.1575	+	5.51687i	−0.550544	+	0.200382i
$759$		0			0
$760$	15.7866	−	13.2465i	0.572640	−	0.480502i
$761$	1.67665	+	9.50874i	0.0607784	+	0.344692i	0.999999	+	0.00137744i	$0.000438452\pi$
$761$	1.67665	+	9.50874i	0.0607784	+	0.344692i	−0.939221	+	0.343314i	$0.888450\pi$
$762$		0			0
$763$	−15.5818	−	13.0747i	−0.564100	−	0.473336i
$764$	−4.65533	+	8.06327i	−0.168424	+	0.291719i
$765$		0			0
$766$	−9.56272	−	16.5631i	−0.345515	−	0.598450i
$767$	−2.71093	+	15.3745i	−0.0978861	+	0.555139i
$768$		0			0
$769$	−36.3764	−	13.2399i	−1.31177	−	0.477445i	−0.410957	−	0.911655i	$-0.634805\pi$
$769$	−36.3764	−	13.2399i	−1.31177	−	0.477445i	−0.900812	+	0.434210i	$0.857027\pi$
$770$	−1.23148	−	0.448221i	−0.0443793	−	0.0161528i
$771$		0			0
$772$	−4.81205	+	27.2905i	−0.173189	+	0.982206i
$773$	12.1519	+	21.0478i	0.437075	+	0.757036i	0.997462	−	0.0711944i	$-0.0226811\pi$
$773$	12.1519	+	21.0478i	0.437075	+	0.757036i	−0.560387	+	0.828231i	$0.689348\pi$
$774$		0			0
$775$	−3.54205	+	6.13500i	−0.127234	+	0.220376i
$776$	30.5824	+	25.6617i	1.09784	+	0.921200i
$777$		0			0
$778$	−5.28527	−	29.9742i	−0.189486	−	1.07463i
$779$	−20.7300	+	17.3945i	−0.742728	+	0.623223i
$780$		0			0
$781$	−0.0870967	+	0.0317006i	−0.00311656	+	0.00113434i
$782$	1.57311			0.0562544
$783$		0			0
$784$	−0.753755			−0.0269198
$785$	−1.97251	+	0.717936i	−0.0704020	+	0.0256242i
$786$		0			0
$787$	16.0414	−	13.4604i	0.571816	−	0.479810i	−0.310432	−	0.950596i	$-0.600474\pi$
$787$	16.0414	−	13.4604i	0.571816	−	0.479810i	0.882248	+	0.470785i	$0.156029\pi$
$788$	0.715633	+	4.05856i	0.0254934	+	0.144580i
$789$		0			0
$790$	1.35550	+	1.13740i	0.0482264	+	0.0404668i
$791$	−3.70688	+	6.42051i	−0.131802	+	0.228287i
$792$		0			0
$793$	15.4718	+	26.7979i	0.549419	+	0.951621i
$794$	2.83229	−	16.0627i	0.100514	−	0.570045i
$795$		0			0
$796$	−2.88620	−	1.05049i	−0.102299	−	0.0372337i
$797$	11.2169	+	4.08261i	0.397322	+	0.144614i	0.532951	−	0.846146i	$-0.321083\pi$
$797$	11.2169	+	4.08261i	0.397322	+	0.144614i	−0.135628	+	0.990760i	$0.543305\pi$
$798$		0			0
$799$	0.582068	−	3.30107i	0.0205921	−	0.116783i
$800$	−7.46668	−	12.9327i	−0.263987	−	0.457239i
$801$		0			0
$802$	2.78329	−	4.82080i	0.0982814	−	0.170228i
$803$	0.963297	+	0.808303i	0.0339940	+	0.0285244i
$804$		0			0
$805$	7.59263	+	43.0600i	0.267605	+	1.51766i
$806$	4.43518	−	3.72155i	0.156222	−	0.131086i
$807$		0			0
$808$	−10.1290	+	3.68664i	−0.356336	+	0.129696i
$809$	−8.60808			−0.302644			−0.151322	−	0.988485i	$-0.548353\pi$
$809$	−8.60808			−0.302644			−0.151322	+	0.988485i	$0.548353\pi$
$810$		0			0
$811$	1.53770			0.0539958			0.0269979	−	0.999635i	$-0.491405\pi$
$811$	1.53770			0.0539958			0.0269979	+	0.999635i	$0.491405\pi$
$812$	1.07656	−	0.391837i	0.0377800	−	0.0137508i
$813$		0			0
$814$	−1.07402	+	0.901211i	−0.0376444	+	0.0315874i
$815$	2.44881	+	13.8879i	0.0857779	+	0.486471i
$816$		0			0
$817$	−0.556149	−	0.466665i	−0.0194572	−	0.0163265i
$818$	4.37071	−	7.57029i	0.152818	−	0.264689i
$819$		0			0
$820$	18.1382	+	31.4163i	0.633413	+	1.09710i
$821$	−5.03168	+	28.5361i	−0.175607	+	0.995915i	0.761835	+	0.647772i	$0.224299\pi$
$821$	−5.03168	+	28.5361i	−0.175607	+	0.995915i	−0.937441	+	0.348144i	$0.886812\pi$
$822$		0			0
$823$	10.5779	+	3.85004i	0.368722	+	0.134204i	0.519734	−	0.854328i	$-0.326031\pi$
$823$	10.5779	+	3.85004i	0.368722	+	0.134204i	−0.151012	+	0.988532i	$0.548253\pi$
$824$	−14.9693	−	5.44838i	−0.521481	−	0.189803i
$825$		0			0
$826$	−1.97727	+	11.2136i	−0.0687979	+	0.390172i
$827$	15.4640	+	26.7844i	0.537734	+	0.931383i	0.999026	+	0.0441346i	$0.0140530\pi$
$827$	15.4640	+	26.7844i	0.537734	+	0.931383i	−0.461291	+	0.887249i	$0.652614\pi$
$828$		0			0
$829$	4.91762	−	8.51757i	0.170796	−	0.295827i	−0.767902	−	0.640567i	$-0.778699\pi$
$829$	4.91762	−	8.51757i	0.170796	−	0.295827i	0.938698	+	0.344739i	$0.112033\pi$
$830$	4.65269	+	3.90407i	0.161497	+	0.135512i
$831$		0			0
$832$	1.61310	+	9.14836i	0.0559243	+	0.317162i
$833$	−0.303547	+	0.254706i	−0.0105173	+	0.00882505i
$834$		0			0
$835$	23.0006	−	8.37152i	0.795967	−	0.289708i
$836$	0.945711			0.0327081
$837$		0			0
$838$	8.07072			0.278798
$839$	−12.3506	+	4.49524i	−0.426389	+	0.155193i	−0.546296	−	0.837592i	$-0.683963\pi$
$839$	−12.3506	+	4.49524i	−0.426389	+	0.155193i	0.119907	+	0.992785i	$0.461740\pi$
$840$		0			0
$841$	−22.1187	+	18.5598i	−0.762714	+	0.639993i
$842$	−0.432522	−	2.45296i	−0.0149057	−	0.0845344i
$843$		0			0
$844$	−26.4467	−	22.1914i	−0.910333	−	0.763860i
$845$	8.49363	−	14.7114i	0.292190	−	0.506088i
$846$		0			0
$847$	12.9982	+	22.5136i	0.446624	+	0.773575i
$848$	−0.526336	+	2.98500i	−0.0180745	+	0.102505i
$849$		0			0
$850$	−0.566038	−	0.206021i	−0.0194149	−	0.00706646i
$851$	43.9569	+	15.9990i	1.50682	+	0.548438i
$852$		0			0
$853$	2.68153	−	15.2077i	0.0918139	−	0.520703i	−0.903863	−	0.427821i	$-0.859281\pi$
$853$	2.68153	−	15.2077i	0.0918139	−	0.520703i	0.995677	−	0.0928812i	$-0.0296077\pi$
$854$	11.2846	+	19.5455i	0.386151	+	0.668834i
$855$		0			0
$856$	0.348478	−	0.603581i	0.0119107	−	0.0206300i
$857$	−16.8398	−	14.1302i	−0.575235	−	0.482680i	0.308143	−	0.951340i	$-0.400292\pi$
$857$	−16.8398	−	14.1302i	−0.575235	−	0.482680i	−0.883378	+	0.468660i	$0.844737\pi$
$858$		0			0
$859$	3.39772	+	19.2694i	0.115929	+	0.657464i	0.986286	+	0.165044i	$0.0527765\pi$
$859$	3.39772	+	19.2694i	0.115929	+	0.657464i	−0.870358	+	0.492420i	$0.836112\pi$
$860$	−0.745540	+	0.625582i	−0.0254227	+	0.0213322i
$861$		0			0
$862$	−21.1421	+	7.69508i	−0.720101	+	0.262095i
$863$	−21.8676			−0.744383			−0.372191	−	0.928156i	$-0.621393\pi$
$863$	−21.8676			−0.744383			−0.372191	+	0.928156i	$0.621393\pi$
$864$		0			0
$865$	18.7298			0.636833
$866$	−14.7061	+	5.35258i	−0.499733	+	0.181888i
$867$		0			0
$868$	−6.83563	+	5.73577i	−0.232016	+	0.194685i
$869$	0.0348743	+	0.197782i	0.00118303	+	0.00670929i
$870$		0			0
$871$	3.62223	+	3.03941i	0.122734	+	0.102986i
$872$	−11.5153	+	19.9452i	−0.389959	+	0.675428i
$873$		0			0
$874$	7.46602	+	12.9315i	0.252542	+	0.437416i
$875$	−2.76743	+	15.6949i	−0.0935563	+	0.530584i
$876$		0			0
$877$	36.7419	+	13.3729i	1.24068	+	0.451572i	0.877244	−	0.480045i	$-0.159380\pi$
$877$	36.7419	+	13.3729i	1.24068	+	0.451572i	0.363441	+	0.931617i	$0.381602\pi$
$878$	−11.0188	−	4.01053i	−0.371868	−	0.135349i
$879$		0			0
$880$	0.0666619	−	0.378058i	0.00224717	−	0.0127443i
$881$	−3.65254	−	6.32639i	−0.123057	−	0.213141i	0.797915	−	0.602771i	$-0.205937\pi$
$881$	−3.65254	−	6.32639i	−0.123057	−	0.213141i	−0.920972	+	0.389629i	$0.872603\pi$
$882$		0			0
$883$	1.74646	−	3.02496i	0.0587732	−	0.101798i	−0.835142	−	0.550035i	$-0.814614\pi$
$883$	1.74646	−	3.02496i	0.0587732	−	0.101798i	0.893915	+	0.448237i	$0.147948\pi$
$884$	−0.796907	−	0.668684i	−0.0268029	−	0.0224903i
$885$		0			0
$886$	−2.55485	−	14.4893i	−0.0858318	−	0.486776i
$887$	−21.7720	+	18.2688i	−0.731031	+	0.613408i	−0.930413	−	0.366514i	$-0.880551\pi$
$887$	−21.7720	+	18.2688i	−0.731031	+	0.613408i	0.199381	+	0.979922i	$0.436107\pi$
$888$		0			0
$889$	41.2181	−	15.0021i	1.38241	−	0.503156i
$890$	−23.0340			−0.772102
$891$		0			0
$892$	5.20125			0.174151
$893$	29.8985	−	10.8821i	1.00051	−	0.364157i
$894$		0			0
$895$	38.6493	−	32.4306i	1.29190	−	1.08404i
$896$	−3.63563	−	20.6187i	−0.121458	−	0.688821i
$897$		0			0
$898$	−8.50974	−	7.14052i	−0.283974	−	0.238282i
$899$	−0.490949	+	0.850349i	−0.0163741	+	0.0283607i
$900$		0			0
$901$	0.796719	+	1.37996i	0.0265426	+	0.0459731i
$902$	0.338348	−	1.91887i	0.0112658	−	0.0638913i
$903$		0			0
$904$	7.88800	+	2.87100i	0.262351	+	0.0954880i
$905$	−29.2655	−	10.6518i	−0.972819	−	0.354077i
$906$		0			0
$907$	9.22362	−	52.3097i	0.306265	−	1.73692i	−0.311224	−	0.950337i	$-0.600739\pi$
$907$	9.22362	−	52.3097i	0.306265	−	1.73692i	0.617489	−	0.786579i	$-0.288150\pi$
$908$	−1.70780	−	2.95799i	−0.0566753	−	0.0981644i
$909$		0			0
$910$	−6.84171	+	11.8502i	−0.226801	+	0.392830i
$911$	6.18649	+	5.19108i	0.204968	+	0.171988i	0.739493	−	0.673164i	$-0.235065\pi$
$911$	6.18649	+	5.19108i	0.204968	+	0.171988i	−0.534526	+	0.845152i	$0.679510\pi$
$912$		0			0
$913$	0.119704	+	0.678878i	0.00396164	+	0.0224676i
$914$	10.8360	−	9.09252i	0.358424	−	0.300754i
$915$		0			0
$916$	−20.3339	+	7.40094i	−0.671852	+	0.244534i
$917$	−33.8116			−1.11656
$918$		0			0
$919$	−47.9961			−1.58325			−0.791623	−	0.611009i	$-0.790764\pi$
$919$	−47.9961			−1.58325			−0.791623	+	0.611009i	$0.790764\pi$
$920$	46.5212	−	16.9323i	1.53376	−	0.558242i
$921$		0			0
$922$	−15.7419	+	13.2090i	−0.518431	+	0.435016i
$923$	0.168051	+	0.953063i	0.00553146	+	0.0313705i
$924$		0			0
$925$	−13.7213	−	11.5135i	−0.451153	−	0.378562i
$926$	−7.35298	+	12.7357i	−0.241634	+	0.418522i
$927$		0			0
$928$	−1.03493	−	1.79255i	−0.0339732	−	0.0588433i
$929$	5.03474	−	28.5534i	0.165185	−	0.936808i	−0.783689	−	0.621153i	$-0.786665\pi$
$929$	5.03474	−	28.5534i	0.165185	−	0.936808i	0.948874	−	0.315655i	$-0.102224\pi$
$930$		0			0
$931$	−3.53442	−	1.28642i	−0.115836	−	0.0421608i
$932$	−35.8828	−	13.0603i	−1.17538	−	0.427803i
$933$		0			0
$934$	2.26338	−	12.8363i	0.0740602	−	0.420016i
$935$	−0.100907	−	0.174775i	−0.00330000	−	0.00571576i
$936$		0			0
$937$	−2.51425	+	4.35481i	−0.0821369	+	0.142265i	−0.904168	−	0.427178i	$-0.859508\pi$
$937$	−2.51425	+	4.35481i	−0.0821369	+	0.142265i	0.822031	+	0.569443i	$0.192841\pi$
$938$	2.64193	+	2.21685i	0.0862622	+	0.0723826i
$939$		0			0
$940$	−7.40649	−	42.0043i	−0.241573	−	1.37003i
$941$	42.7767	−	35.8939i	1.39448	−	1.17011i	0.430995	−	0.902354i	$-0.358163\pi$
$941$	42.7767	−	35.8939i	1.39448	−	1.17011i	0.963487	−	0.267755i	$-0.0862817\pi$
$942$		0			0
$943$	−61.0887	+	22.2345i	−1.98932	+	0.724054i
$944$	−3.33551			−0.108561
$945$		0			0
$946$	0.0522740			0.00169957
$947$	39.9645	−	14.5459i	1.29867	−	0.472678i	0.402109	−	0.915592i	$-0.368277\pi$
$947$	39.9645	−	14.5459i	1.29867	−	0.472678i	0.896564	+	0.442914i	$0.146055\pi$
$948$		0			0
$949$	10.0581	−	8.43973i	0.326499	−	0.273965i
$950$	−0.992864	−	5.63081i	−0.0322127	−	0.182688i
$951$		0			0
$952$	−1.43754	−	1.20624i	−0.0465909	−	0.0390944i
$953$	10.9074	−	18.8922i	0.353325	−	0.611977i	−0.633505	−	0.773739i	$-0.718384\pi$
$953$	10.9074	−	18.8922i	0.353325	−	0.611977i	0.986830	+	0.161762i	$0.0517175\pi$
$954$		0			0
$955$	9.42977	+	16.3328i	0.305140	+	0.528518i
$956$	−3.46670	+	19.6606i	−0.112121	+	0.635870i
$957$		0			0
$958$	−7.13399	−	2.59656i	−0.230489	−	0.0838910i
$959$	−43.9676	−	16.0029i	−1.41979	−	0.516761i
$960$		0			0
$961$	−4.05507	+	22.9974i	−0.130809	+	0.741852i
$962$	7.31954	+	12.6778i	0.235991	+	0.408749i
$963$		0			0
$964$	5.73088	−	9.92618i	0.184579	−	0.319701i
$965$	42.9996	+	36.0809i	1.38421	+	1.16149i
$966$		0			0
$967$	0.803746	+	4.55827i	0.0258467	+	0.146584i	0.995000	−	0.0998746i	$-0.0318442\pi$
$967$	0.803746	+	4.55827i	0.0258467	+	0.146584i	−0.969153	+	0.246459i	$0.920733\pi$
$968$	22.5481	−	18.9201i	0.724724	−	0.608115i
$969$		0			0
$970$	30.7247	−	11.1829i	0.986511	−	0.359060i
$971$	21.6509			0.694809			0.347405	−	0.937715i	$-0.387063\pi$
$971$	21.6509			0.694809			0.347405	+	0.937715i	$0.387063\pi$
$972$		0			0
$973$	−42.5714			−1.36478
$974$	0.352164	−	0.128177i	0.0112841	−	0.00410707i
$975$		0			0
$976$	−5.06451	+	4.24963i	−0.162111	+	0.136027i
$977$	3.83499	+	21.7493i	0.122692	+	0.695822i	0.982652	+	0.185460i	$0.0593774\pi$
$977$	3.83499	+	21.7493i	0.122692	+	0.695822i	−0.859960	+	0.510362i	$0.829511\pi$
$978$		0			0
$979$	−2.00269	−	1.68046i	−0.0640063	−	0.0537076i
$980$	−2.52105	+	4.36659i	−0.0805320	+	0.139485i
$981$		0			0
$982$	10.0379	+	17.3862i	0.320323	+	0.554815i
$983$	2.40729	−	13.6524i	0.0767807	−	0.435445i	−0.922049	−	0.387074i	$-0.873486\pi$
$983$	2.40729	−	13.6524i	0.0767807	−	0.435445i	0.998829	−	0.0483713i	$-0.0154031\pi$
$984$		0			0
$985$	7.84434	+	2.85511i	0.249941	+	0.0909712i
$986$	−0.0784563	−	0.0285558i	−0.00249856	−	0.000909401i
$987$		0			0
$988$	1.71468	−	9.72444i	0.0545513	−	0.309376i
$989$	−0.872042	−	1.51042i	−0.0277293	−	0.0480286i
$990$		0			0
$991$	−17.4112	+	30.1570i	−0.553084	+	0.957970i	0.444966	+	0.895548i	$0.353216\pi$
$991$	−17.4112	+	30.1570i	−0.553084	+	0.957970i	−0.998050	+	0.0624224i	$0.980117\pi$
$992$	12.3499	+	10.3628i	0.392111	+	0.329020i
$993$		0			0
$994$	0.122571	+	0.695133i	0.00388771	+	0.0220483i
$995$	−4.76590	+	3.99906i	−0.151089	+	0.126779i
$996$		0			0
$997$	23.2572	−	8.46492i	0.736562	−	0.268087i	0.0536221	−	0.998561i	$-0.482923\pi$
$997$	23.2572	−	8.46492i	0.736562	−	0.268087i	0.682940	+	0.730475i	$0.260701\pi$
$998$	−11.2488			−0.356073
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.e.a.19.1		12
3.2	odd	2		27.2.e.a.7.2	yes	12
9.2	odd	6		243.2.e.d.136.1		12
9.4	even	3		243.2.e.b.217.2		12
9.5	odd	6		243.2.e.c.217.1		12
9.7	even	3		243.2.e.a.136.2		12
12.11	even	2		432.2.u.c.385.2		12
15.2	even	4		675.2.u.b.574.3		24
15.8	even	4		675.2.u.b.574.2		24
15.14	odd	2		675.2.l.c.601.1		12
27.2	odd	18		729.2.a.a.1.3		6
27.4	even	9	inner	81.2.e.a.64.1		12
27.5	odd	18		243.2.e.c.28.1		12
27.7	even	9		729.2.c.b.487.3		12
27.11	odd	18		729.2.c.e.244.4		12
27.13	even	9		243.2.e.a.109.2		12
27.14	odd	18		243.2.e.d.109.1		12
27.16	even	9		729.2.c.b.244.3		12
27.20	odd	18		729.2.c.e.487.4		12
27.22	even	9		243.2.e.b.28.2		12
27.23	odd	18		27.2.e.a.4.2	✓	12
27.25	even	9		729.2.a.d.1.4		6
108.23	even	18		432.2.u.c.193.2		12
135.23	even	36		675.2.u.b.274.3		24
135.77	even	36		675.2.u.b.274.2		24
135.104	odd	18		675.2.l.c.301.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.4.2	✓	12	27.23	odd	18
27.2.e.a.7.2	yes	12	3.2	odd	2
81.2.e.a.19.1		12	1.1	even	1	trivial
81.2.e.a.64.1		12	27.4	even	9	inner
243.2.e.a.109.2		12	27.13	even	9
243.2.e.a.136.2		12	9.7	even	3
243.2.e.b.28.2		12	27.22	even	9
243.2.e.b.217.2		12	9.4	even	3
243.2.e.c.28.1		12	27.5	odd	18
243.2.e.c.217.1		12	9.5	odd	6
243.2.e.d.109.1		12	27.14	odd	18
243.2.e.d.136.1		12	9.2	odd	6
432.2.u.c.193.2		12	108.23	even	18
432.2.u.c.385.2		12	12.11	even	2
675.2.l.c.301.1		12	135.104	odd	18
675.2.l.c.601.1		12	15.14	odd	2
675.2.u.b.274.2		24	135.77	even	36
675.2.u.b.274.3		24	135.23	even	36
675.2.u.b.574.2		24	15.8	even	4
675.2.u.b.574.3		24	15.2	even	4
729.2.a.a.1.3		6	27.2	odd	18
729.2.a.d.1.4		6	27.25	even	9
729.2.c.b.244.3		12	27.16	even	9
729.2.c.b.487.3		12	27.7	even	9
729.2.c.e.244.4		12	27.11	odd	18
729.2.c.e.487.4		12	27.20	odd	18

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	81.2.e.a.19.1

Level	$81$
Weight	$2$
Character	81.19
Analytic conductor	$0.647$
Analytic rank	$0$
Dimension	$12$
Inner twists	$2$