LMFDB - Embedded newform 2646.2.m.b.881.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(881,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("2646.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.m (of order $6$, 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:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.4
Root			$1.71298 + 0.256290i$ of defining polynomial
Character	$\chi$	$=$	2646.881
Dual form			2646.2.m.b.1763.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.80966 - 3.13442i) q^{5} +1.00000i q^{8} +3.61932i q^{10} +(-1.73534 + 1.00190i) q^{11} +(2.95206 + 1.70437i) q^{13} +(-0.500000 - 0.866025i) q^{16} -6.17418 q^{17} -1.01308i q^{19} +(-1.80966 - 3.13442i) q^{20} +(1.00190 - 1.73534i) q^{22} +(-2.62232 - 1.51400i) q^{23} +(-4.04972 - 7.01433i) q^{25} -3.40874 q^{26} +(-5.04560 + 2.91308i) q^{29} +(0.787812 + 0.454844i) q^{31} +(0.866025 + 0.500000i) q^{32} +(5.34700 - 3.08709i) q^{34} -7.33650 q^{37} +(0.506540 + 0.877353i) q^{38} +(3.13442 + 1.80966i) q^{40} +(2.85045 - 4.93712i) q^{41} +(-2.39949 - 4.15605i) q^{43} +2.00379i q^{44} +3.02799 q^{46} +(-1.11511 - 1.93143i) q^{47} +(7.01433 + 4.04972i) q^{50} +(2.95206 - 1.70437i) q^{52} -8.75365i q^{53} +7.25237i q^{55} +(2.91308 - 5.04560i) q^{58} +(4.49313 - 7.78233i) q^{59} +(-12.7410 + 7.35603i) q^{61} -0.909687 q^{62} -1.00000 q^{64} +(10.6844 - 6.16866i) q^{65} +(4.15821 - 7.20222i) q^{67} +(-3.08709 + 5.34700i) q^{68} -0.466287i q^{71} -4.21492i q^{73} +(6.35359 - 3.66825i) q^{74} +(-0.877353 - 0.506540i) q^{76} +(-1.91267 - 3.31284i) q^{79} -3.61932 q^{80} +5.70089i q^{82} +(4.00481 + 6.93654i) q^{83} +(-11.1732 + 19.3525i) q^{85} +(4.15605 + 2.39949i) q^{86} +(-1.00190 - 1.73534i) q^{88} -4.78647 q^{89} +(-2.62232 + 1.51400i) q^{92} +(1.93143 + 1.11511i) q^{94} +(-3.17542 - 1.83333i) q^{95} +(-10.1835 + 5.87944i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 12 q^{11} + 6 q^{13} - 8 q^{16} - 36 q^{17} - 6 q^{23} - 8 q^{25} + 24 q^{26} - 6 q^{29} + 6 q^{31} + 4 q^{37} + 6 q^{41} - 2 q^{43} - 12 q^{46} - 18 q^{47} + 12 q^{50} + 6 q^{52} + 6 q^{58}+ \cdots + 6 q^{97}+O(q^{100}) $ 16 * q + 8 * q^4 + 12 * q^11 + 6 * q^13 - 8 * q^16 - 36 * q^17 - 6 * q^23 - 8 * q^25 + 24 * q^26 - 6 * q^29 + 6 * q^31 + 4 * q^37 + 6 * q^41 - 2 * q^43 - 12 * q^46 - 18 * q^47 + 12 * q^50 + 6 * q^52 + 6 * q^58 + 30 * q^59 - 60 * q^61 - 36 * q^62 - 16 * q^64 + 42 * q^65 + 14 * q^67 - 18 * q^68 + 18 * q^74 - 16 * q^79 - 12 * q^85 + 24 * q^86 - 48 * q^89 - 6 * q^92 - 66 * q^95 + 6 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.80966	−	3.13442i	0.809304	−	1.40175i	−0.104043	−	0.994573i	$-0.533178\pi$
$5$	1.80966	−	3.13442i	0.809304	−	1.40175i	0.913347	−	0.407182i	$-0.133489\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$		0			0
$10$			3.61932i			1.14453i
$11$	−1.73534	+	1.00190i	−0.523224	+	0.302083i	−0.738253	−	0.674524i	$-0.764349\pi$
$11$	−1.73534	+	1.00190i	−0.523224	+	0.302083i	0.215029	+	0.976608i	$0.431015\pi$
$12$		0			0
$13$	2.95206	+	1.70437i	0.818754	+	0.472708i	0.849987	−	0.526804i	$-0.176610\pi$
$13$	2.95206	+	1.70437i	0.818754	+	0.472708i	−0.0312328	+	0.999512i	$0.509943\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−6.17418			−1.49746			−0.748730	−	0.662876i	$-0.769336\pi$
$17$	−6.17418			−1.49746			−0.748730	+	0.662876i	$0.769336\pi$
$18$		0			0
$19$		−	1.01308i		−	0.232417i	−0.993225	−	0.116208i	$-0.962926\pi$
$19$		−	1.01308i		−	0.232417i	0.993225	−	0.116208i	$-0.0370740\pi$
$20$	−1.80966	−	3.13442i	−0.404652	−	0.700877i
$21$		0			0
$22$	1.00190	−	1.73534i	0.213605	−	0.369975i
$23$	−2.62232	−	1.51400i	−0.546791	−	0.315690i	0.201035	−	0.979584i	$-0.435569\pi$
$23$	−2.62232	−	1.51400i	−0.546791	−	0.315690i	−0.747827	+	0.663894i	$0.768903\pi$
$24$		0			0
$25$	−4.04972	−	7.01433i	−0.809945	−	1.40287i
$26$	−3.40874			−0.668510
$27$		0			0
$28$		0			0
$29$	−5.04560	+	2.91308i	−0.936945	+	0.540945i	−0.889001	−	0.457905i	$-0.848600\pi$
$29$	−5.04560	+	2.91308i	−0.936945	+	0.540945i	−0.0479434	+	0.998850i	$0.515267\pi$
$30$		0			0
$31$	0.787812	+	0.454844i	0.141495	+	0.0816923i	0.569076	−	0.822285i	$-0.307301\pi$
$31$	0.787812	+	0.454844i	0.141495	+	0.0816923i	−0.427581	+	0.903977i	$0.640634\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	5.34700	−	3.08709i	0.917003	−	0.529432i
$35$		0			0
$36$		0			0
$37$	−7.33650			−1.20611			−0.603056	−	0.797699i	$-0.706051\pi$
$37$	−7.33650			−1.20611			−0.603056	+	0.797699i	$0.706051\pi$
$38$	0.506540	+	0.877353i	0.0821717	+	0.142325i
$39$		0			0
$40$	3.13442	+	1.80966i	0.495595	+	0.286132i
$41$	2.85045	−	4.93712i	0.445165	−	0.771048i	−0.552899	−	0.833248i	$-0.686478\pi$
$41$	2.85045	−	4.93712i	0.445165	−	0.771048i	0.998064	+	0.0622002i	$0.0198117\pi$
$42$		0			0
$43$	−2.39949	−	4.15605i	−0.365919	−	0.633791i	0.623004	−	0.782219i	$-0.285912\pi$
$43$	−2.39949	−	4.15605i	−0.365919	−	0.633791i	−0.988923	+	0.148428i	$0.952579\pi$
$44$			2.00379i			0.302083i
$45$		0			0
$46$	3.02799			0.446453
$47$	−1.11511	−	1.93143i	−0.162655	−	0.281727i	0.773165	−	0.634205i	$-0.218673\pi$
$47$	−1.11511	−	1.93143i	−0.162655	−	0.281727i	−0.935820	+	0.352478i	$0.885339\pi$
$48$		0			0
$49$		0			0
$50$	7.01433	+	4.04972i	0.991975	+	0.572717i
$51$		0			0
$52$	2.95206	−	1.70437i	0.409377	−	0.236354i
$53$		−	8.75365i		−	1.20241i	−0.799096	−	0.601203i	$-0.794688\pi$
$53$		−	8.75365i		−	1.20241i	0.799096	−	0.601203i	$-0.205312\pi$
$54$		0			0
$55$			7.25237i			0.977909i
$56$		0			0
$57$		0			0
$58$	2.91308	−	5.04560i	0.382506	−	0.662520i
$59$	4.49313	−	7.78233i	0.584956	−	1.01317i	−0.409925	−	0.912119i	$-0.634445\pi$
$59$	4.49313	−	7.78233i	0.584956	−	1.01317i	0.994881	−	0.101054i	$-0.0322216\pi$
$60$		0			0
$61$	−12.7410	+	7.35603i	−1.63132	+	0.941843i	−0.647634	+	0.761952i	$0.724241\pi$
$61$	−12.7410	+	7.35603i	−1.63132	+	0.941843i	−0.983686	+	0.179892i	$0.942425\pi$
$62$	−0.909687			−0.115530
$63$		0			0
$64$	−1.00000			−0.125000
$65$	10.6844	−	6.16866i	1.32524	−	0.765128i
$66$		0			0
$67$	4.15821	−	7.20222i	0.508006	−	0.879892i	−0.491951	−	0.870623i	$-0.663716\pi$
$67$	4.15821	−	7.20222i	0.508006	−	0.879892i	0.999957	−	0.00926908i	$-0.00295048\pi$
$68$	−3.08709	+	5.34700i	−0.374365	+	0.648419i
$69$		0			0
$70$		0			0
$71$		−	0.466287i		−	0.0553381i	−0.999617	−	0.0276691i	$-0.991192\pi$
$71$		−	0.466287i		−	0.0553381i	0.999617	−	0.0276691i	$-0.00880846\pi$
$72$		0			0
$73$		−	4.21492i		−	0.493319i	−0.969102	−	0.246659i	$-0.920667\pi$
$73$		−	4.21492i		−	0.493319i	0.969102	−	0.246659i	$-0.0793329\pi$
$74$	6.35359	−	3.66825i	0.738590	−	0.426425i
$75$		0			0
$76$	−0.877353	−	0.506540i	−0.100639	−	0.0581041i
$77$		0			0
$78$		0			0
$79$	−1.91267	−	3.31284i	−0.215192	−	0.372723i	0.738140	−	0.674648i	$-0.235704\pi$
$79$	−1.91267	−	3.31284i	−0.215192	−	0.372723i	−0.953332	+	0.301924i	$0.902371\pi$
$80$	−3.61932			−0.404652
$81$		0			0
$82$			5.70089i			0.629558i
$83$	4.00481	+	6.93654i	0.439585	+	0.761384i	0.997657	−	0.0684084i	$-0.0217921\pi$
$83$	4.00481	+	6.93654i	0.439585	+	0.761384i	−0.558072	+	0.829792i	$0.688459\pi$
$84$		0			0
$85$	−11.1732	+	19.3525i	−1.21190	+	2.09907i
$86$	4.15605	+	2.39949i	0.448158	+	0.258744i
$87$		0			0
$88$	−1.00190	−	1.73534i	−0.106803	−	0.184988i
$89$	−4.78647			−0.507365			−0.253683	−	0.967288i	$-0.581642\pi$
$89$	−4.78647			−0.507365			−0.253683	+	0.967288i	$0.581642\pi$
$90$		0			0
$91$		0			0
$92$	−2.62232	+	1.51400i	−0.273396	+	0.157845i
$93$		0			0
$94$	1.93143	+	1.11511i	0.199211	+	0.115015i
$95$	−3.17542	−	1.83333i	−0.325791	−	0.188096i
$96$		0			0
$97$	−10.1835	+	5.87944i	−1.03398	+	0.596967i	−0.918121	−	0.396299i	$-0.870294\pi$
$97$	−10.1835	+	5.87944i	−1.03398	+	0.596967i	−0.115856	+	0.993266i	$0.536961\pi$
$98$		0			0
$99$		0			0
$100$	−8.09945			−0.809945
$101$	6.44610	+	11.1650i	0.641411	+	1.11096i	0.985118	+	0.171879i	$0.0549840\pi$
$101$	6.44610	+	11.1650i	0.641411	+	1.11096i	−0.343707	+	0.939077i	$0.611683\pi$
$102$		0			0
$103$	−9.31740	−	5.37940i	−0.918070	−	0.530048i	−0.0350515	−	0.999386i	$-0.511160\pi$
$103$	−9.31740	−	5.37940i	−0.918070	−	0.530048i	−0.883019	+	0.469337i	$0.844493\pi$
$104$	−1.70437	+	2.95206i	−0.167127	+	0.289473i
$105$		0			0
$106$	4.37683	+	7.58088i	0.425115	+	0.736321i
$107$		−	2.63967i		−	0.255186i	−0.991827	−	0.127593i	$-0.959275\pi$
$107$		−	2.63967i		−	0.255186i	0.991827	−	0.127593i	$-0.0407251\pi$
$108$		0			0
$109$	−9.03535			−0.865430			−0.432715	−	0.901531i	$-0.642444\pi$
$109$	−9.03535			−0.865430			−0.432715	+	0.901531i	$0.642444\pi$
$110$	−3.62618	−	6.28073i	−0.345743	−	0.598844i
$111$		0			0
$112$		0			0
$113$	1.46411	+	0.845306i	0.137732	+	0.0795197i	0.567283	−	0.823523i	$-0.307995\pi$
$113$	1.46411	+	0.845306i	0.137732	+	0.0795197i	−0.429551	+	0.903043i	$0.641328\pi$
$114$		0			0
$115$	−9.49100	+	5.47963i	−0.885041	+	0.510978i
$116$			5.82616i			0.540945i
$117$		0			0
$118$			8.98627i			0.827253i
$119$		0			0
$120$		0			0
$121$	−3.49240	+	6.04902i	−0.317491	+	0.549911i
$122$	7.35603	−	12.7410i	0.665984	−	1.15352i
$123$		0			0
$124$	0.787812	−	0.454844i	0.0707476	−	0.0408462i
$125$	−11.2179			−1.00336
$126$		0			0
$127$	17.9292			1.59096			0.795478	−	0.605983i	$-0.207220\pi$
$127$	17.9292			1.59096			0.795478	+	0.605983i	$0.207220\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−6.16866	+	10.6844i	−0.541027	+	0.937087i
$131$	−8.66567	+	15.0094i	−0.757123	+	1.31138i	0.187188	+	0.982324i	$0.440062\pi$
$131$	−8.66567	+	15.0094i	−0.757123	+	1.31138i	−0.944312	+	0.329052i	$0.893271\pi$
$132$		0			0
$133$		0			0
$134$			8.31641i			0.718429i
$135$		0			0
$136$		−	6.17418i		−	0.529432i
$137$	0.000558693	0	0.000322562i	4.77324e−5	0	2.75583e-5i	−0.499976	−	0.866039i	$-0.666658\pi$
$137$	0.000558693	0	0.000322562i	4.77324e−5	0	2.75583e-5i	0.500024	+	0.866012i	$0.333325\pi$
$138$		0			0
$139$	−8.73273	−	5.04185i	−0.740701	−	0.427644i	0.0816233	−	0.996663i	$-0.473990\pi$
$139$	−8.73273	−	5.04185i	−0.740701	−	0.427644i	−0.822324	+	0.569019i	$0.807323\pi$
$140$		0			0
$141$		0			0
$142$	0.233144	+	0.403817i	0.0195650	+	0.0338875i
$143$	−6.83042			−0.571189
$144$		0			0
$145$			21.0867i			1.75116i
$146$	2.10746	+	3.65022i	0.174414	+	0.302095i
$147$		0			0
$148$	−3.66825	+	6.35359i	−0.301528	+	0.522262i
$149$	−9.74064	−	5.62376i	−0.797984	−	0.460716i	0.0447816	−	0.998997i	$-0.485741\pi$
$149$	−9.74064	−	5.62376i	−0.797984	−	0.460716i	−0.842766	+	0.538280i	$0.819074\pi$
$150$		0			0
$151$	2.36189	+	4.09092i	0.192208	+	0.332914i	0.945982	−	0.324220i	$-0.105102\pi$
$151$	2.36189	+	4.09092i	0.192208	+	0.332914i	−0.753774	+	0.657134i	$0.771768\pi$
$152$	1.01308			0.0821717
$153$		0			0
$154$		0			0
$155$	2.85134	−	1.64622i	0.229025	−	0.132228i
$156$		0			0
$157$	2.65845	+	1.53486i	0.212168	+	0.122495i	0.602318	−	0.798256i	$-0.294244\pi$
$157$	2.65845	+	1.53486i	0.212168	+	0.122495i	−0.390151	+	0.920751i	$0.627577\pi$
$158$	3.31284	+	1.91267i	0.263555	+	0.152164i
$159$		0			0
$160$	3.13442	−	1.80966i	0.247798	−	0.143066i
$161$		0			0
$162$		0			0
$163$	2.87373			0.225088			0.112544	−	0.993647i	$-0.464100\pi$
$163$	2.87373			0.225088			0.112544	+	0.993647i	$0.464100\pi$
$164$	−2.85045	−	4.93712i	−0.222582	−	0.385524i
$165$		0			0
$166$	−6.93654	−	4.00481i	−0.538380	−	0.310834i
$167$	−0.730517	+	1.26529i	−0.0565291	+	0.0979113i	−0.892905	−	0.450245i	$-0.851337\pi$
$167$	−0.730517	+	1.26529i	−0.0565291	+	0.0979113i	0.836376	+	0.548156i	$0.184670\pi$
$168$		0			0
$169$	−0.690233	−	1.19552i	−0.0530948	−	0.0919630i
$170$		−	22.3463i		−	1.71388i
$171$		0			0
$172$	−4.79899			−0.365919
$173$	−1.53541	−	2.65940i	−0.116735	−	0.202191i	0.801737	−	0.597677i	$-0.203909\pi$
$173$	−1.53541	−	2.65940i	−0.116735	−	0.202191i	−0.918472	+	0.395486i	$0.870576\pi$
$174$		0			0
$175$		0			0
$176$	1.73534	+	1.00190i	0.130806	+	0.0755209i
$177$		0			0
$178$	4.14521	−	2.39324i	0.310696	−	0.179381i
$179$		−	19.3193i		−	1.44399i	−0.691896	−	0.721997i	$-0.743224\pi$
$179$		−	19.3193i		−	1.44399i	0.691896	−	0.721997i	$-0.256776\pi$
$180$		0			0
$181$		−	7.89318i		−	0.586695i	−0.956006	−	0.293348i	$-0.905231\pi$
$181$		−	7.89318i		−	0.586695i	0.956006	−	0.293348i	$-0.0947693\pi$
$182$		0			0
$183$		0			0
$184$	1.51400	−	2.62232i	0.111613	−	0.193320i
$185$	−13.2765	+	22.9957i	−0.976111	+	1.69067i
$186$		0			0
$187$	10.7143	−	6.18590i	0.783506	−	0.452358i
$188$	−2.23022			−0.162655
$189$		0			0
$190$	3.66666			0.266007
$191$	11.5218	−	6.65211i	0.833688	−	0.481330i	−0.0214259	−	0.999770i	$-0.506821\pi$
$191$	11.5218	−	6.65211i	0.833688	−	0.481330i	0.855114	+	0.518441i	$0.173487\pi$
$192$		0			0
$193$	−3.26786	+	5.66011i	−0.235226	+	0.407423i	−0.959338	−	0.282259i	$-0.908916\pi$
$193$	−3.26786	+	5.66011i	−0.235226	+	0.407423i	0.724112	+	0.689682i	$0.242250\pi$
$194$	5.87944	−	10.1835i	0.422119	−	0.731132i
$195$		0			0
$196$		0			0
$197$			4.44250i			0.316515i	0.987398	+	0.158258i	$0.0505876\pi$
$197$			4.44250i			0.316515i	−0.987398	+	0.158258i	$0.949412\pi$
$198$		0			0
$199$			11.5108i			0.815982i	0.912986	+	0.407991i	$0.133770\pi$
$199$			11.5108i			0.815982i	−0.912986	+	0.407991i	$0.866230\pi$
$200$	7.01433	−	4.04972i	0.495988	−	0.286359i
$201$		0			0
$202$	−11.1650	−	6.44610i	−0.785565	−	0.453546i
$203$		0			0
$204$		0			0
$205$	−10.3167	−	17.8690i	−0.720547	−	1.24802i
$206$	10.7588			0.749601
$207$		0			0
$208$		−	3.40874i		−	0.236354i
$209$	1.01500	+	1.75804i	0.0702092	+	0.121606i
$210$		0			0
$211$	11.3005	−	19.5731i	0.777961	−	1.34747i	−0.155155	−	0.987890i	$-0.549588\pi$
$211$	11.3005	−	19.5731i	0.777961	−	1.34747i	0.933115	−	0.359577i	$-0.117079\pi$
$212$	−7.58088	−	4.37683i	−0.520657	−	0.300602i
$213$		0			0
$214$	1.31983	+	2.28602i	0.0902219	+	0.156269i
$215$	−17.3691			−1.18456
$216$		0			0
$217$		0			0
$218$	7.82484	−	4.51768i	0.529965	−	0.305976i
$219$		0			0
$220$	6.28073	+	3.62618i	0.423447	+	0.244477i
$221$	−18.2265	−	10.5231i	−1.22605	−	0.707860i
$222$		0			0
$223$	16.2994	−	9.41045i	1.09149	−	0.630170i	0.157515	−	0.987517i	$-0.449652\pi$
$223$	16.2994	−	9.41045i	1.09149	−	0.630170i	0.933972	+	0.357346i	$0.116318\pi$
$224$		0			0
$225$		0			0
$226$	−1.69061			−0.112458
$227$	7.30665	+	12.6555i	0.484960	+	0.839975i	0.999851	−	0.0172809i	$-0.00550095\pi$
$227$	7.30665	+	12.6555i	0.484960	+	0.839975i	−0.514891	+	0.857256i	$0.672168\pi$
$228$		0			0
$229$	−2.06044	−	1.18959i	−0.136158	−	0.0786106i	0.430374	−	0.902651i	$-0.358382\pi$
$229$	−2.06044	−	1.18959i	−0.136158	−	0.0786106i	−0.566531	+	0.824040i	$0.691715\pi$
$230$	5.47963	−	9.49100i	0.361316	−	0.625818i
$231$		0			0
$232$	−2.91308	−	5.04560i	−0.191253	−	0.331260i
$233$			10.4324i			0.683448i	0.939800	+	0.341724i	$0.111011\pi$
$233$			10.4324i			0.683448i	−0.939800	+	0.341724i	$0.888989\pi$
$234$		0			0
$235$	−8.07186			−0.526550
$236$	−4.49313	−	7.78233i	−0.292478	−	0.506587i
$237$		0			0
$238$		0			0
$239$	−20.5971	−	11.8917i	−1.33232	−	0.769213i	−0.346662	−	0.937990i	$-0.612685\pi$
$239$	−20.5971	−	11.8917i	−1.33232	−	0.769213i	−0.985654	+	0.168777i	$0.946018\pi$
$240$		0			0
$241$	−24.8105	+	14.3243i	−1.59818	+	0.922712i	−0.606348	+	0.795200i	$0.707366\pi$
$241$	−24.8105	+	14.3243i	−1.59818	+	0.922712i	−0.991837	+	0.127513i	$0.959301\pi$
$242$		−	6.98481i		−	0.449000i
$243$		0			0
$244$			14.7121i			0.941843i
$245$		0			0
$246$		0			0
$247$	1.72667	−	2.99067i	0.109865	−	0.190292i
$248$	−0.454844	+	0.787812i	−0.0288826	+	0.0500261i
$249$		0			0
$250$	9.71496	−	5.60894i	0.614428	−	0.354740i
$251$	11.0301			0.696216			0.348108	−	0.937454i	$-0.386824\pi$
$251$	11.0301			0.696216			0.348108	+	0.937454i	$0.386824\pi$
$252$		0			0
$253$	6.06748			0.381459
$254$	−15.5271	+	8.96458i	−0.974257	+	0.562488i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.54890	−	13.0751i	0.470888	−	0.815601i	−0.528558	−	0.848897i	$-0.677267\pi$
$257$	7.54890	−	13.0751i	0.470888	−	0.815601i	0.999446	+	0.0332960i	$0.0106004\pi$
$258$		0			0
$259$		0			0
$260$		−	12.3373i		−	0.765128i
$261$		0			0
$262$		−	17.3313i		−	1.07073i
$263$	17.0075	−	9.81926i	1.04873	−	0.605482i	0.126433	−	0.991975i	$-0.459647\pi$
$263$	17.0075	−	9.81926i	1.04873	−	0.605482i	0.922292	+	0.386493i	$0.126314\pi$
$264$		0			0
$265$	−27.4376	−	15.8411i	−1.68548	−	0.973112i
$266$		0			0
$267$		0			0
$268$	−4.15821	−	7.20222i	−0.254003	−	0.439946i
$269$	0.491005			0.0299371			0.0149686	−	0.999888i	$-0.495235\pi$
$269$	0.491005			0.0299371			0.0149686	+	0.999888i	$0.495235\pi$
$270$		0			0
$271$			14.0789i			0.855232i	0.903960	+	0.427616i	$0.140647\pi$
$271$			14.0789i			0.855232i	−0.903960	+	0.427616i	$0.859353\pi$
$272$	3.08709	+	5.34700i	0.187182	+	0.324209i
$273$		0			0
$274$	−0.000322562	0	0.000558693i	−1.94867e−5	0	3.37519e-5i
$275$	14.0553	+	8.11481i	0.847565	+	0.489342i
$276$		0			0
$277$	−15.3600	−	26.6043i	−0.922894	−	1.59850i	−0.794913	−	0.606723i	$-0.792484\pi$
$277$	−15.3600	−	26.6043i	−0.922894	−	1.59850i	−0.127981	−	0.991777i	$-0.540850\pi$
$278$	10.0837			0.604780
$279$		0			0
$280$		0			0
$281$	−6.86286	+	3.96227i	−0.409404	+	0.236369i	−0.690534	−	0.723300i	$-0.742624\pi$
$281$	−6.86286	+	3.96227i	−0.409404	+	0.236369i	0.281130	+	0.959670i	$0.409291\pi$
$282$		0			0
$283$	−9.97303	−	5.75793i	−0.592835	−	0.342273i	0.173383	−	0.984855i	$-0.444530\pi$
$283$	−9.97303	−	5.75793i	−0.592835	−	0.342273i	−0.766218	+	0.642581i	$0.777864\pi$
$284$	−0.403817	−	0.233144i	−0.0239621	−	0.0138345i
$285$		0			0
$286$	5.91532	−	3.41521i	0.349780	−	0.201946i
$287$		0			0
$288$		0			0
$289$	21.1205			1.24238
$290$	−10.5434	−	18.2616i	−0.619127	−	1.07236i
$291$		0			0
$292$	−3.65022	−	2.10746i	−0.213613	−	0.123330i
$293$	2.50937	−	4.34636i	0.146599	−	0.253917i	−0.783369	−	0.621557i	$-0.786501\pi$
$293$	2.50937	−	4.34636i	0.146599	−	0.253917i	0.929968	+	0.367639i	$0.119834\pi$
$294$		0			0
$295$	−16.2621	−	28.1667i	−0.946814	−	1.63993i
$296$		−	7.33650i		−	0.426425i
$297$		0			0
$298$	11.2475			0.651551
$299$	−5.16083	−	8.93882i	−0.298458	−	0.516945i
$300$		0			0
$301$		0			0
$302$	−4.09092	−	2.36189i	−0.235406	−	0.135912i
$303$		0			0
$304$	−0.877353	+	0.506540i	−0.0503197	+	0.0290521i
$305$			53.2476i			3.04895i
$306$		0			0
$307$			17.5309i			1.00054i	0.865869	+	0.500271i	$0.166766\pi$
$307$			17.5309i			1.00054i	−0.865869	+	0.500271i	$0.833234\pi$
$308$		0			0
$309$		0			0
$310$	−1.64622	+	2.85134i	−0.0934992	+	0.161945i
$311$	8.64759	−	14.9781i	0.490360	−	0.849328i	−0.509579	−	0.860424i	$-0.670199\pi$
$311$	8.64759	−	14.9781i	0.490360	−	0.849328i	0.999938	+	0.0110959i	$0.00353200\pi$
$312$		0			0
$313$	7.78988	−	4.49749i	0.440310	−	0.254213i	−0.263419	−	0.964681i	$-0.584850\pi$
$313$	7.78988	−	4.49749i	0.440310	−	0.254213i	0.703729	+	0.710468i	$0.251517\pi$
$314$	−3.06972			−0.173234
$315$		0			0
$316$	−3.82533			−0.215192
$317$	−5.82002	+	3.36019i	−0.326885	+	0.188727i	−0.654457	−	0.756099i	$-0.727103\pi$
$317$	−5.82002	+	3.36019i	−0.326885	+	0.188727i	0.327572	+	0.944826i	$0.393770\pi$
$318$		0			0
$319$	5.83721	−	10.1103i	0.326821	−	0.566071i
$320$	−1.80966	+	3.13442i	−0.101163	+	0.175219i
$321$		0			0
$322$		0			0
$323$			6.25494i			0.348034i
$324$		0			0
$325$		−	27.6089i		−	1.53147i
$326$	−2.48873	+	1.43687i	−0.137838	+	0.0795807i
$327$		0			0
$328$	4.93712	+	2.85045i	0.272607	+	0.157390i
$329$		0			0
$330$		0			0
$331$	9.38725	+	16.2592i	0.515970	+	0.893686i	0.999828	+	0.0185396i	$0.00590167\pi$
$331$	9.38725	+	16.2592i	0.515970	+	0.893686i	−0.483858	+	0.875146i	$0.660765\pi$
$332$	8.00963			0.439585
$333$		0			0
$334$		−	1.46103i		−	0.0799443i
$335$	−15.0499	−	26.0671i	−0.822262	−	1.42420i
$336$		0			0
$337$	2.42287	−	4.19654i	0.131982	−	0.228600i	−0.792458	−	0.609926i	$-0.791199\pi$
$337$	2.42287	−	4.19654i	0.131982	−	0.228600i	0.924441	+	0.381326i	$0.124532\pi$
$338$	1.19552	+	0.690233i	0.0650276	+	0.0375437i
$339$		0			0
$340$	11.1732	+	19.3525i	0.605949	+	1.04954i
$341$	−1.82283			−0.0987116
$342$		0			0
$343$		0			0
$344$	4.15605	−	2.39949i	0.224079	−	0.129372i
$345$		0			0
$346$	2.65940	+	1.53541i	0.142970	+	0.0825440i
$347$	−15.1305	−	8.73559i	−0.812247	−	0.468951i	0.0354887	−	0.999370i	$-0.488701\pi$
$347$	−15.1305	−	8.73559i	−0.812247	−	0.468951i	−0.847736	+	0.530419i	$0.822035\pi$
$348$		0			0
$349$	20.6338	−	11.9129i	1.10450	−	0.637683i	0.167101	−	0.985940i	$-0.446560\pi$
$349$	20.6338	−	11.9129i	1.10450	−	0.637683i	0.937399	+	0.348257i	$0.113226\pi$
$350$		0			0
$351$		0			0
$352$	−2.00379			−0.106803
$353$	−5.02061	−	8.69596i	−0.267220	−	0.462839i	0.700923	−	0.713237i	$-0.252772\pi$
$353$	−5.02061	−	8.69596i	−0.267220	−	0.462839i	−0.968143	+	0.250398i	$0.919438\pi$
$354$		0			0
$355$	−1.46154	−	0.843820i	−0.0775705	−	0.0447853i
$356$	−2.39324	+	4.14521i	−0.126841	+	0.219696i
$357$		0			0
$358$	9.65966	+	16.7310i	0.510529	+	0.884262i
$359$		−	12.1651i		−	0.642048i	−0.947071	−	0.321024i	$-0.895973\pi$
$359$		−	12.1651i		−	0.642048i	0.947071	−	0.321024i	$-0.104027\pi$
$360$		0			0
$361$	17.9737			0.945983
$362$	3.94659	+	6.83569i	0.207428	+	0.359276i
$363$		0			0
$364$		0			0
$365$	−13.2113	−	7.62756i	−0.691512	−	0.399245i
$366$		0			0
$367$	−3.14420	+	1.81531i	−0.164126	+	0.0947582i	−0.579813	−	0.814749i	$-0.696874\pi$
$367$	−3.14420	+	1.81531i	−0.164126	+	0.0947582i	0.415687	+	0.909508i	$0.363541\pi$
$368$			3.02799i			0.157845i
$369$		0			0
$370$		−	26.5531i		−	1.38043i
$371$		0			0
$372$		0			0
$373$	−2.74616	+	4.75648i	−0.142191	+	0.246281i	−0.928321	−	0.371779i	$-0.878748\pi$
$373$	−2.74616	+	4.75648i	−0.142191	+	0.246281i	0.786131	+	0.618060i	$0.212081\pi$
$374$	−6.18590	+	10.7143i	−0.319865	+	0.554023i
$375$		0			0
$376$	1.93143	−	1.11511i	0.0996057	−	0.0575074i
$377$	−19.8599			−1.02284
$378$		0			0
$379$	−15.5960			−0.801112			−0.400556	−	0.916272i	$-0.631183\pi$
$379$	−15.5960			−0.801112			−0.400556	+	0.916272i	$0.631183\pi$
$380$	−3.17542	+	1.83333i	−0.162896	+	0.0940478i
$381$		0			0
$382$	−6.65211	+	11.5218i	−0.340352	+	0.589506i
$383$	−4.71534	+	8.16720i	−0.240942	+	0.417324i	−0.960983	−	0.276607i	$-0.910790\pi$
$383$	−4.71534	+	8.16720i	−0.240942	+	0.417324i	0.720041	+	0.693932i	$0.244123\pi$
$384$		0			0
$385$		0			0
$386$		−	6.53573i		−	0.332660i
$387$		0			0
$388$			11.7589i			0.596967i
$389$	5.56142	−	3.21089i	0.281975	−	0.162798i	−0.352342	−	0.935871i	$-0.614615\pi$
$389$	5.56142	−	3.21089i	0.281975	−	0.162798i	0.634317	+	0.773073i	$0.281281\pi$
$390$		0			0
$391$	16.1907	+	9.34769i	0.818798	+	0.472733i
$392$		0			0
$393$		0			0
$394$	−2.22125	−	3.84732i	−0.111905	−	0.193825i
$395$	−13.8451			−0.696622
$396$		0			0
$397$		−	6.92531i		−	0.347572i	−0.984783	−	0.173786i	$-0.944400\pi$
$397$		−	6.92531i		−	0.347572i	0.984783	−	0.173786i	$-0.0556000\pi$
$398$	−5.75542	−	9.96868i	−0.288493	−	0.499685i
$399$		0			0
$400$	−4.04972	+	7.01433i	−0.202486	+	0.350716i
$401$	−9.16848	−	5.29343i	−0.457852	−	0.264341i	0.253289	−	0.967391i	$-0.418488\pi$
$401$	−9.16848	−	5.29343i	−0.457852	−	0.264341i	−0.711141	+	0.703050i	$0.751821\pi$
$402$		0			0
$403$	1.55045	+	2.68545i	0.0772332	+	0.133772i
$404$	12.8922			0.641411
$405$		0			0
$406$		0			0
$407$	12.7313	−	7.35042i	0.631067	−	0.364347i
$408$		0			0
$409$	7.72792	+	4.46172i	0.382121	+	0.220618i	0.678741	−	0.734378i	$-0.262526\pi$
$409$	7.72792	+	4.46172i	0.382121	+	0.220618i	−0.296620	+	0.954996i	$0.595859\pi$
$410$	17.8690	+	10.3167i	0.882486	+	0.509504i
$411$		0			0
$412$	−9.31740	+	5.37940i	−0.459035	+	0.265024i
$413$		0			0
$414$		0			0
$415$	28.9894			1.42303
$416$	1.70437	+	2.95206i	0.0835637	+	0.144737i
$417$		0			0
$418$	−1.75804	−	1.01500i	−0.0859883	−	0.0496454i
$419$	−17.1924	+	29.7781i	−0.839903	+	1.45475i	0.0500724	+	0.998746i	$0.484055\pi$
$419$	−17.1924	+	29.7781i	−0.839903	+	1.45475i	−0.889975	+	0.456009i	$0.849279\pi$
$420$		0			0
$421$	−17.7840	−	30.8028i	−0.866739	−	1.50124i	−0.865310	−	0.501237i	$-0.832879\pi$
$421$	−17.7840	−	30.8028i	−0.866739	−	1.50124i	−0.00142877	−	0.999999i	$-0.500455\pi$
$422$			22.6011i			1.10020i
$423$		0			0
$424$	8.75365			0.425115
$425$	25.0037	+	43.3077i	1.21286	+	2.10073i
$426$		0			0
$427$		0			0
$428$	−2.28602	−	1.31983i	−0.110499	−	0.0637965i
$429$		0			0
$430$	15.0420	−	8.68453i	0.725392	−	0.418805i
$431$			30.8695i			1.48693i	0.668774	+	0.743466i	$0.266820\pi$
$431$			30.8695i			1.48693i	−0.668774	+	0.743466i	$0.733180\pi$
$432$		0			0
$433$			23.2463i			1.11715i	0.829455	+	0.558574i	$0.188651\pi$
$433$			23.2463i			1.11715i	−0.829455	+	0.558574i	$0.811349\pi$
$434$		0			0
$435$		0			0
$436$	−4.51768	+	7.82484i	−0.216357	+	0.374742i
$437$	−1.53380	+	2.65662i	−0.0733716	+	0.127083i
$438$		0			0
$439$	19.2887	−	11.1364i	0.920601	−	0.531509i	0.0367744	−	0.999324i	$-0.488292\pi$
$439$	19.2887	−	11.1364i	0.920601	−	0.531509i	0.883827	+	0.467814i	$0.154958\pi$
$440$	−7.25237			−0.345743
$441$		0			0
$442$	21.0462			1.00107
$443$	15.5756	−	8.99259i	0.740020	−	0.427251i	−0.0820566	−	0.996628i	$-0.526149\pi$
$443$	15.5756	−	8.99259i	0.740020	−	0.427251i	0.822077	+	0.569377i	$0.192815\pi$
$444$		0			0
$445$	−8.66188	+	15.0028i	−0.410612	+	0.711202i
$446$	−9.41045	+	16.2994i	−0.445598	+	0.771798i
$447$		0			0
$448$		0			0
$449$		−	9.44363i		−	0.445673i	−0.974856	−	0.222836i	$-0.928468\pi$
$449$		−	9.44363i		−	0.445673i	0.974856	−	0.222836i	$-0.0715315\pi$
$450$		0			0
$451$			11.4234i			0.537908i
$452$	1.46411	−	0.845306i	0.0688661	−	0.0397599i
$453$		0			0
$454$	−12.6555	−	7.30665i	−0.593952	−	0.342918i
$455$		0			0
$456$		0			0
$457$	0.922251	+	1.59739i	0.0431411	+	0.0747225i	0.886790	−	0.462173i	$-0.152930\pi$
$457$	0.922251	+	1.59739i	0.0431411	+	0.0747225i	−0.843649	+	0.536896i	$0.819597\pi$
$458$	2.37919			0.111172
$459$		0			0
$460$			10.9593i			0.510978i
$461$	18.1869	+	31.5007i	0.847050	+	1.46713i	0.883829	+	0.467810i	$0.154957\pi$
$461$	18.1869	+	31.5007i	0.847050	+	1.46713i	−0.0367790	+	0.999323i	$0.511710\pi$
$462$		0			0
$463$	−15.9830	+	27.6834i	−0.742794	+	1.28656i	0.208425	+	0.978038i	$0.433166\pi$
$463$	−15.9830	+	27.6834i	−0.742794	+	1.28656i	−0.951219	+	0.308518i	$0.900167\pi$
$464$	5.04560	+	2.91308i	0.234236	+	0.135236i
$465$		0			0
$466$	−5.21619	−	9.03470i	−0.241635	−	0.418525i
$467$	24.4411			1.13100			0.565500	−	0.824748i	$-0.308683\pi$
$467$	24.4411			1.13100			0.565500	+	0.824748i	$0.308683\pi$
$468$		0			0
$469$		0			0
$470$	6.99044	−	4.03593i	0.322445	−	0.186164i
$471$		0			0
$472$	7.78233	+	4.49313i	0.358211	+	0.206813i
$473$	8.32786	+	4.80809i	0.382916	+	0.221076i
$474$		0			0
$475$	−7.10607	+	4.10269i	−0.326049	+	0.188245i
$476$		0			0
$477$		0			0
$478$	23.7835			1.08783
$479$	−5.48032	−	9.49220i	−0.250402	−	0.433710i	0.713234	−	0.700926i	$-0.247230\pi$
$479$	−5.48032	−	9.49220i	−0.250402	−	0.433710i	−0.963637	+	0.267216i	$0.913896\pi$
$480$		0			0
$481$	−21.6578	−	12.5041i	−0.987509	−	0.570139i
$482$	14.3243	−	24.8105i	0.652456	−	1.13009i
$483$		0			0
$484$	3.49240	+	6.04902i	0.158746	+	0.274955i
$485$			42.5591i			1.93251i
$486$		0			0
$487$	33.6175			1.52335			0.761677	−	0.647957i	$-0.224376\pi$
$487$	33.6175			1.52335			0.761677	+	0.647957i	$0.224376\pi$
$488$	−7.35603	−	12.7410i	−0.332992	−	0.576759i
$489$		0			0
$490$		0			0
$491$	19.6893	+	11.3676i	0.888568	+	0.513015i	0.873474	−	0.486871i	$-0.161862\pi$
$491$	19.6893	+	11.3676i	0.888568	+	0.513015i	0.0150939	+	0.999886i	$0.495195\pi$
$492$		0			0
$493$	31.1525	−	17.9859i	1.40304	−	0.810043i
$494$			3.45333i			0.155373i
$495$		0			0
$496$		−	0.909687i		−	0.0408462i
$497$		0			0
$498$		0			0
$499$	−9.76175	+	16.9079i	−0.436996	+	0.756899i	−0.997456	−	0.0712820i	$-0.977291\pi$
$499$	−9.76175	+	16.9079i	−0.436996	+	0.756899i	0.560460	+	0.828181i	$0.310624\pi$
$500$	−5.60894	+	9.71496i	−0.250839	+	0.434466i
$501$		0			0
$502$	−9.55238	+	5.51507i	−0.426343	+	0.246149i
$503$	13.6867			0.610262			0.305131	−	0.952310i	$-0.401300\pi$
$503$	13.6867			0.610262			0.305131	+	0.952310i	$0.401300\pi$
$504$		0			0
$505$	46.6609			2.07638
$506$	−5.25459	+	3.03374i	−0.233595	+	0.134866i
$507$		0			0
$508$	8.96458	−	15.5271i	0.397739	−	0.688904i
$509$	1.14583	−	1.98464i	0.0507881	−	0.0879675i	−0.839514	−	0.543338i	$-0.817160\pi$
$509$	1.14583	−	1.98464i	0.0507881	−	0.0879675i	0.890302	+	0.455371i	$0.150493\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$			15.0978i			0.665936i
$515$	−33.7226	+	19.4698i	−1.48600	+	0.857940i
$516$		0			0
$517$	3.87018	+	2.23445i	0.170210	+	0.0982710i
$518$		0			0
$519$		0			0
$520$	6.16866	+	10.6844i	0.270514	+	0.468543i
$521$	17.0820			0.748377			0.374189	−	0.927353i	$-0.377921\pi$
$521$	17.0820			0.748377			0.374189	+	0.927353i	$0.377921\pi$
$522$		0			0
$523$		−	41.2762i		−	1.80488i	−0.430815	−	0.902440i	$-0.641774\pi$
$523$		−	41.2762i		−	1.80488i	0.430815	−	0.902440i	$-0.358226\pi$
$524$	8.66567	+	15.0094i	0.378562	+	0.655688i
$525$		0			0
$526$	−9.81926	+	17.0075i	−0.428140	+	0.741561i
$527$	−4.86410	−	2.80829i	−0.211883	−	0.122331i
$528$		0			0
$529$	−6.91563	−	11.9782i	−0.300679	−	0.520792i
$530$	31.6822			1.37619
$531$		0			0
$532$		0			0
$533$	16.8294	−	9.71644i	0.728961	−	0.420866i
$534$		0			0
$535$	−8.27382	−	4.77689i	−0.357708	−	0.206523i
$536$	7.20222	+	4.15821i	0.311089	+	0.179607i
$537$		0			0
$538$	−0.425223	+	0.245503i	−0.0183327	+	0.0105844i
$539$		0			0
$540$		0			0
$541$	−45.4393			−1.95359			−0.976795	−	0.214177i	$-0.931293\pi$
$541$	−45.4393			−1.95359			−0.976795	+	0.214177i	$0.931293\pi$
$542$	−7.03945	−	12.1927i	−0.302370	−	0.523721i
$543$		0			0
$544$	−5.34700	−	3.08709i	−0.229251	−	0.132358i
$545$	−16.3509	+	28.3206i	−0.700395	+	1.21312i
$546$		0			0
$547$	15.1095	+	26.1705i	0.646037	+	1.11897i	0.984061	+	0.177832i	$0.0569082\pi$
$547$	15.1095	+	26.1705i	0.646037	+	1.11897i	−0.338024	+	0.941138i	$0.609758\pi$
$548$		0	0.000645123i		0	2.75583e-5i
$549$		0			0
$550$	−16.2296			−0.692034
$551$	2.95118	+	5.11160i	0.125725	+	0.217761i
$552$		0			0
$553$		0			0
$554$	26.6043	+	15.3600i	1.13031	+	0.652585i
$555$		0			0
$556$	−8.73273	+	5.04185i	−0.370350	+	0.213822i
$557$		−	25.4212i		−	1.07713i	−0.842584	−	0.538565i	$-0.818967\pi$
$557$		−	25.4212i		−	1.07713i	0.842584	−	0.538565i	$-0.181033\pi$
$558$		0			0
$559$		−	16.3585i		−	0.691892i
$560$		0			0
$561$		0			0
$562$	3.96227	−	6.86286i	0.167138	−	0.289492i
$563$	1.44346	−	2.50015i	0.0608346	−	0.105369i	−0.834004	−	0.551758i	$-0.813957\pi$
$563$	1.44346	−	2.50015i	0.0608346	−	0.105369i	0.894839	+	0.446390i	$0.147290\pi$
$564$		0			0
$565$	5.29909	−	3.05943i	0.222934	−	0.128711i
$566$	11.5159			0.484048
$567$		0			0
$568$	0.466287			0.0195650
$569$	−38.5945	+	22.2826i	−1.61797	+	0.934134i	−0.630523	+	0.776171i	$0.717159\pi$
$569$	−38.5945	+	22.2826i	−1.61797	+	0.934134i	−0.987445	+	0.157963i	$0.949507\pi$
$570$		0			0
$571$	3.26470	−	5.65462i	0.136623	−	0.236638i	−0.789593	−	0.613631i	$-0.789708\pi$
$571$	3.26470	−	5.65462i	0.136623	−	0.236638i	0.926216	+	0.376992i	$0.123042\pi$
$572$	−3.41521	+	5.91532i	−0.142797	+	0.247332i
$573$		0			0
$574$		0			0
$575$			24.5251i			1.02277i
$576$		0			0
$577$			1.35932i			0.0565891i	0.999600	+	0.0282945i	$0.00900764\pi$
$577$			1.35932i			0.0565891i	−0.999600	+	0.0282945i	$0.990992\pi$
$578$	−18.2909	+	10.5603i	−0.760802	+	0.439249i
$579$		0			0
$580$	18.2616	+	10.5434i	0.758273	+	0.437789i
$581$		0			0
$582$		0			0
$583$	8.77026	+	15.1905i	0.363227	+	0.629128i
$584$	4.21492			0.174414
$585$		0			0
$586$			5.01875i			0.207323i
$587$	−22.2025	−	38.4559i	−0.916397	−	1.58725i	−0.804843	−	0.593488i	$-0.797750\pi$
$587$	−22.2025	−	38.4559i	−0.916397	−	1.58725i	−0.111555	−	0.993758i	$-0.535583\pi$
$588$		0			0
$589$	0.460793	−	0.798117i	0.0189866	−	0.0328858i
$590$	28.1667	+	16.2621i	1.15961	+	0.669499i
$591$		0			0
$592$	3.66825	+	6.35359i	0.150764	+	0.261131i
$593$	14.3513			0.589336			0.294668	−	0.955600i	$-0.404791\pi$
$593$	14.3513			0.589336			0.294668	+	0.955600i	$0.404791\pi$
$594$		0			0
$595$		0			0
$596$	−9.74064	+	5.62376i	−0.398992	+	0.230358i
$597$		0			0
$598$	8.93882	+	5.16083i	0.365535	+	0.211042i
$599$	−3.03349	−	1.75139i	−0.123945	−	0.0715597i	0.436746	−	0.899585i	$-0.356131\pi$
$599$	−3.03349	−	1.75139i	−0.123945	−	0.0715597i	−0.560691	+	0.828025i	$0.689464\pi$
$600$		0			0
$601$	15.1846	−	8.76685i	0.619394	−	0.357607i	−0.157239	−	0.987561i	$-0.550259\pi$
$601$	15.1846	−	8.76685i	0.619394	−	0.357607i	0.776633	+	0.629953i	$0.216926\pi$
$602$		0			0
$603$		0			0
$604$	4.72379			0.192208
$605$	12.6401	+	21.8933i	0.513894	+	0.890090i
$606$		0			0
$607$	−0.0755923	−	0.0436432i	−0.00306820	−	0.00177142i	0.498465	−	0.866910i	$-0.333897\pi$
$607$	−0.0755923	−	0.0436432i	−0.00306820	−	0.00177142i	−0.501533	+	0.865138i	$0.667231\pi$
$608$	0.506540	−	0.877353i	0.0205429	−	0.0355814i
$609$		0			0
$610$	−26.6238	−	46.1138i	−1.07797	−	1.86709i
$611$		−	7.60224i		−	0.307554i
$612$		0			0
$613$	−25.0704			−1.01258			−0.506292	−	0.862362i	$-0.668984\pi$
$613$	−25.0704			−1.01258			−0.506292	+	0.862362i	$0.668984\pi$
$614$	−8.76545	−	15.1822i	−0.353745	−	0.612704i
$615$		0			0
$616$		0			0
$617$	10.6365	+	6.14101i	0.428211	+	0.247228i	0.698584	−	0.715528i	$-0.253814\pi$
$617$	10.6365	+	6.14101i	0.428211	+	0.247228i	−0.270373	+	0.962756i	$0.587147\pi$
$618$		0			0
$619$	17.5869	−	10.1538i	0.706875	−	0.408115i	−0.103028	−	0.994678i	$-0.532853\pi$
$619$	17.5869	−	10.1538i	0.706875	−	0.408115i	0.809903	+	0.586564i	$0.199520\pi$
$620$		−	3.29245i		−	0.132228i
$621$		0			0
$622$			17.2952i			0.693474i
$623$		0			0
$624$		0			0
$625$	−0.0518970	+	0.0898882i	−0.00207588	+	0.00359553i
$626$	−4.49749	+	7.78988i	−0.179756	+	0.311346i
$627$		0			0
$628$	2.65845	−	1.53486i	0.106084	−	0.0612475i
$629$	45.2969			1.80610
$630$		0			0
$631$	−45.9665			−1.82990			−0.914950	−	0.403568i	$-0.867770\pi$
$631$	−45.9665			−1.82990			−0.914950	+	0.403568i	$0.867770\pi$
$632$	3.31284	−	1.91267i	0.131778	−	0.0760818i
$633$		0			0
$634$	3.36019	−	5.82002i	0.133450	−	0.231143i
$635$	32.4456	−	56.1975i	1.28757	−	2.23013i
$636$		0			0
$637$		0			0
$638$			11.6744i			0.462195i
$639$		0			0
$640$		−	3.61932i		−	0.143066i
$641$	−27.4104	+	15.8254i	−1.08265	+	0.625067i	−0.931609	−	0.363461i	$-0.881595\pi$
$641$	−27.4104	+	15.8254i	−1.08265	+	0.625067i	−0.151038	+	0.988528i	$0.548262\pi$
$642$		0			0
$643$	−10.0106	−	5.77960i	−0.394778	−	0.227925i	0.289450	−	0.957193i	$-0.406528\pi$
$643$	−10.0106	−	5.77960i	−0.394778	−	0.227925i	−0.684228	+	0.729268i	$0.739861\pi$
$644$		0			0
$645$		0			0
$646$	−3.12747	−	5.41694i	−0.123049	−	0.213127i
$647$	−26.0730			−1.02504			−0.512519	−	0.858676i	$-0.671287\pi$
$647$	−26.0730			−1.02504			−0.512519	+	0.858676i	$0.671287\pi$
$648$		0			0
$649$			18.0066i			0.706822i
$650$	13.8045	+	23.9100i	0.541456	+	0.937829i
$651$		0			0
$652$	1.43687	−	2.48873i	0.0562720	−	0.0974660i
$653$	16.3952	+	9.46576i	0.641593	+	0.370424i	0.785228	−	0.619207i	$-0.212546\pi$
$653$	16.3952	+	9.46576i	0.641593	+	0.370424i	−0.143635	+	0.989631i	$0.545879\pi$
$654$		0			0
$655$	31.3638	+	54.3237i	1.22549	+	2.12260i
$656$	−5.70089			−0.222582
$657$		0			0
$658$		0			0
$659$	−23.3508	+	13.4816i	−0.909618	+	0.525168i	−0.880308	−	0.474402i	$-0.842664\pi$
$659$	−23.3508	+	13.4816i	−0.909618	+	0.525168i	−0.0293098	+	0.999570i	$0.509331\pi$
$660$		0			0
$661$	22.3201	+	12.8865i	0.868151	+	0.501227i	0.866733	−	0.498772i	$-0.166215\pi$
$661$	22.3201	+	12.8865i	0.868151	+	0.501227i	0.00141768	+	0.999999i	$0.499549\pi$
$662$	−16.2592	−	9.38725i	−0.631931	−	0.364846i
$663$		0			0
$664$	−6.93654	+	4.00481i	−0.269190	+	0.155417i
$665$		0			0
$666$		0			0
$667$	17.6416			0.683084
$668$	0.730517	+	1.26529i	0.0282646	+	0.0489557i
$669$		0			0
$670$	26.0671	+	15.0499i	1.00706	+	0.581427i
$671$	14.7400	−	25.5304i	0.569030	−	0.985590i
$672$		0			0
$673$	−12.9608	−	22.4487i	−0.499601	−	0.865335i	0.500398	−	0.865795i	$-0.333187\pi$
$673$	−12.9608	−	22.4487i	−0.499601	−	0.865335i	−1.00000		0.000460130i	$0.999854\pi$
$674$			4.84575i			0.186651i
$675$		0			0
$676$	−1.38047			−0.0530948
$677$	6.55382	+	11.3515i	0.251884	+	0.436275i	0.964044	−	0.265741i	$-0.0856166\pi$
$677$	6.55382	+	11.3515i	0.251884	+	0.436275i	−0.712161	+	0.702016i	$0.752283\pi$
$678$		0			0
$679$		0			0
$680$	−19.3525	−	11.1732i	−0.742134	−	0.428471i
$681$		0			0
$682$	1.57861	−	0.911413i	0.0604483	−	0.0348998i
$683$		−	29.6654i		−	1.13511i	−0.823334	−	0.567557i	$-0.807888\pi$
$683$		−	29.6654i		−	1.13511i	0.823334	−	0.567557i	$-0.192112\pi$
$684$		0			0
$685$		−	0.00233490i		−	8.92121e-5i
$686$		0			0
$687$		0			0
$688$	−2.39949	+	4.15605i	−0.0914799	+	0.158448i
$689$	14.9195	−	25.8413i	0.568387	−	0.984475i
$690$		0			0
$691$	40.9767	−	23.6579i	1.55883	−	0.899990i	0.561459	−	0.827504i	$-0.310240\pi$
$691$	40.9767	−	23.6579i	1.55883	−	0.899990i	0.997369	−	0.0724857i	$-0.0230932\pi$
$692$	−3.07081			−0.116735
$693$		0			0
$694$	17.4712			0.663197
$695$	−31.6065	+	18.2480i	−1.19890	+	0.692187i
$696$		0			0
$697$	−17.5992	+	30.4827i	−0.666616	+	1.15461i
$698$	−11.9129	+	20.6338i	−0.450910	+	0.780999i
$699$		0			0
$700$		0			0
$701$		−	13.7742i		−	0.520244i	−0.965576	−	0.260122i	$-0.916237\pi$
$701$		−	13.7742i		−	0.520244i	0.965576	−	0.260122i	$-0.0837627\pi$
$702$		0			0
$703$			7.43246i			0.280320i
$704$	1.73534	−	1.00190i	0.0654030	−	0.0377604i
$705$		0			0
$706$	8.69596	+	5.02061i	0.327277	+	0.188953i
$707$		0			0
$708$		0			0
$709$	21.9691	+	38.0517i	0.825069	+	1.42906i	0.901867	+	0.432014i	$0.142197\pi$
$709$	21.9691	+	38.0517i	0.825069	+	1.42906i	−0.0767981	+	0.997047i	$0.524470\pi$
$710$	1.68764			0.0633360
$711$		0			0
$712$		−	4.78647i		−	0.179381i
$713$	−1.37726	−	2.38549i	−0.0515789	−	0.0893373i
$714$		0			0
$715$	−12.3607	+	21.4094i	−0.462265	+	0.800667i
$716$	−16.7310	−	9.65966i	−0.625268	−	0.360998i
$717$		0			0
$718$	6.08254	+	10.5353i	0.226998	+	0.393173i
$719$	−29.5860			−1.10337			−0.551687	−	0.834051i	$-0.686016\pi$
$719$	−29.5860			−1.10337			−0.551687	+	0.834051i	$0.686016\pi$
$720$		0			0
$721$		0			0
$722$	−15.5657	+	8.98683i	−0.579294	+	0.334455i
$723$		0			0
$724$	−6.83569	−	3.94659i	−0.254046	−	0.146674i
$725$	40.8666	+	23.5943i	1.51775	+	0.876271i
$726$		0			0
$727$	10.1244	−	5.84534i	0.375494	−	0.216792i	−0.300362	−	0.953825i	$-0.597107\pi$
$727$	10.1244	−	5.84534i	0.375494	−	0.216792i	0.675856	+	0.737034i	$0.263774\pi$
$728$		0			0
$729$		0			0
$730$	15.2551			0.564617
$731$	14.8149	+	25.6602i	0.547949	+	0.949076i
$732$		0			0
$733$	28.6423	+	16.5366i	1.05793	+	0.610795i	0.924858	−	0.380312i	$-0.124183\pi$
$733$	28.6423	+	16.5366i	1.05793	+	0.610795i	0.133070	+	0.991107i	$0.457517\pi$
$734$	1.81531	−	3.14420i	0.0670042	−	0.116055i
$735$		0			0
$736$	−1.51400	−	2.62232i	−0.0558067	−	0.0966600i
$737$			16.6644i			0.613841i
$738$		0			0
$739$	43.5056			1.60038			0.800190	−	0.599747i	$-0.204732\pi$
$739$	43.5056			1.60038			0.800190	+	0.599747i	$0.204732\pi$
$740$	13.2765	+	22.9957i	0.488056	+	0.845337i
$741$		0			0
$742$		0			0
$743$	−18.0206	−	10.4042i	−0.661112	−	0.381693i	0.131589	−	0.991304i	$-0.457992\pi$
$743$	−18.0206	−	10.4042i	−0.661112	−	0.381693i	−0.792701	+	0.609611i	$0.791326\pi$
$744$		0			0
$745$	−35.2544	+	20.3542i	−1.29162	+	0.745719i
$746$		−	5.49231i		−	0.201088i
$747$		0			0
$748$		−	12.3718i		−	0.452358i
$749$		0			0
$750$		0			0
$751$	19.9492	−	34.5531i	0.727957	−	1.26086i	−0.229788	−	0.973241i	$-0.573803\pi$
$751$	19.9492	−	34.5531i	0.727957	−	1.26086i	0.957745	−	0.287618i	$-0.0928634\pi$
$752$	−1.11511	+	1.93143i	−0.0406638	+	0.0704318i
$753$		0			0
$754$	17.1992	−	9.92994i	0.626357	−	0.361627i
$755$	17.0969			0.622219
$756$		0			0
$757$	7.45545			0.270973			0.135486	−	0.990779i	$-0.456740\pi$
$757$	7.45545			0.270973			0.135486	+	0.990779i	$0.456740\pi$
$758$	13.5065	−	7.79800i	0.490579	−	0.283236i
$759$		0			0
$760$	1.83333	−	3.17542i	0.0665018	−	0.115185i
$761$	4.32462	−	7.49046i	0.156767	−	0.271529i	−0.776934	−	0.629582i	$-0.783226\pi$
$761$	4.32462	−	7.49046i	0.156767	−	0.271529i	0.933701	+	0.358053i	$0.116559\pi$
$762$		0			0
$763$		0			0
$764$		−	13.3042i		−	0.481330i
$765$		0			0
$766$		−	9.43067i		−	0.340744i
$767$	26.5280	−	15.3159i	0.957870	−	0.553026i
$768$		0			0
$769$	20.4818	+	11.8252i	0.738592	+	0.426426i	0.821557	−	0.570126i	$-0.193106\pi$
$769$	20.4818	+	11.8252i	0.738592	+	0.426426i	−0.0829652	+	0.996552i	$0.526439\pi$
$770$		0			0
$771$		0			0
$772$	3.26786	+	5.66011i	0.117613	+	0.203712i
$773$	46.5699			1.67500			0.837501	−	0.546436i	$-0.184016\pi$
$773$	46.5699			1.67500			0.837501	+	0.546436i	$0.184016\pi$
$774$		0			0
$775$		−	7.36796i		−	0.264665i
$776$	−5.87944	−	10.1835i	−0.211060	−	0.365566i
$777$		0			0
$778$	−3.21089	+	5.56142i	−0.115116	+	0.199387i
$779$	−5.00170	−	2.88773i	−0.179204	−	0.103464i
$780$		0			0
$781$	0.467172	+	0.809166i	0.0167167	+	0.0289542i
$782$	−18.6954			−0.668546
$783$		0			0
$784$		0			0
$785$	9.62178	−	5.55513i	0.343416	−	0.198271i
$786$		0			0
$787$	−21.1657	−	12.2200i	−0.754474	−	0.435596i	0.0728341	−	0.997344i	$-0.476796\pi$
$787$	−21.1657	−	12.2200i	−0.754474	−	0.435596i	−0.827308	+	0.561748i	$0.810129\pi$
$788$	3.84732	+	2.22125i	0.137055	+	0.0791288i
$789$		0			0
$790$	11.9902	−	6.92255i	0.426592	−	0.246293i
$791$		0			0
$792$		0			0
$793$	−50.1496			−1.78087
$794$	3.46266	+	5.99750i	0.122885	+	0.212843i
$795$		0			0
$796$	9.96868	+	5.75542i	0.353330	+	0.203995i
$797$	24.9202	−	43.1631i	0.882719	−	1.52891i	0.0344128	−	0.999408i	$-0.489044\pi$
$797$	24.9202	−	43.1631i	0.882719	−	1.52891i	0.848306	−	0.529506i	$-0.177623\pi$
$798$		0			0
$799$	6.88489	+	11.9250i	0.243570	+	0.421875i
$800$		−	8.09945i		−	0.286359i
$801$		0			0
$802$	10.5869			0.373835
$803$	4.22291	+	7.31430i	0.149023	+	0.258116i
$804$		0			0
$805$		0			0
$806$	−2.68545	−	1.55045i	−0.0945910	−	0.0546121i
$807$		0			0
$808$	−11.1650	+	6.44610i	−0.392782	+	0.226773i
$809$			12.3247i			0.433315i	0.976248	+	0.216657i	$0.0695154\pi$
$809$			12.3247i			0.433315i	−0.976248	+	0.216657i	$0.930485\pi$
$810$		0			0
$811$			24.8017i			0.870906i	0.900212	+	0.435453i	$0.143412\pi$
$811$			24.8017i			0.870906i	−0.900212	+	0.435453i	$0.856588\pi$
$812$		0			0
$813$		0			0
$814$	−7.35042	+	12.7313i	−0.257632	+	0.446232i
$815$	5.20047	−	9.00748i	0.182165	−	0.315518i
$816$		0			0
$817$	−4.21041	+	2.43088i	−0.147304	+	0.0850457i
$818$	−8.92343			−0.312000
$819$		0			0
$820$	−20.6333			−0.720547
$821$	31.3573	−	18.1041i	1.09438	−	0.631839i	0.159639	−	0.987175i	$-0.448967\pi$
$821$	31.3573	−	18.1041i	1.09438	−	0.631839i	0.934738	+	0.355336i	$0.115634\pi$
$822$		0			0
$823$	9.54093	−	16.5254i	0.332576	−	0.576038i	−0.650440	−	0.759557i	$-0.725416\pi$
$823$	9.54093	−	16.5254i	0.332576	−	0.576038i	0.983016	+	0.183519i	$0.0587489\pi$
$824$	5.37940	−	9.31740i	0.187400	−	0.324587i
$825$		0			0
$826$		0			0
$827$		−	31.9013i		−	1.10932i	−0.832079	−	0.554658i	$-0.812849\pi$
$827$		−	31.9013i		−	1.10932i	0.832079	−	0.554658i	$-0.187151\pi$
$828$		0			0
$829$			15.0856i			0.523943i	0.965076	+	0.261971i	$0.0843726\pi$
$829$			15.0856i			0.523943i	−0.965076	+	0.261971i	$0.915627\pi$
$830$	−25.1055	+	14.4947i	−0.871425	+	0.503118i
$831$		0			0
$832$	−2.95206	−	1.70437i	−0.102344	−	0.0590885i
$833$		0			0
$834$		0			0
$835$	2.64397	+	4.57950i	0.0914985	+	0.158480i
$836$	2.03000			0.0702092
$837$		0			0
$838$		−	34.3848i		−	1.18780i
$839$	8.19860	+	14.2004i	0.283047	+	0.490252i	0.972134	−	0.234427i	$-0.0753214\pi$
$839$	8.19860	+	14.2004i	0.283047	+	0.490252i	−0.689087	+	0.724679i	$0.741988\pi$
$840$		0			0
$841$	2.47206	−	4.28173i	0.0852434	−	0.147646i
$842$	30.8028	+	17.7840i	1.06153	+	0.612877i
$843$		0			0
$844$	−11.3005	−	19.5731i	−0.388980	−	0.673734i
$845$	−4.99634			−0.171879
$846$		0			0
$847$		0			0
$848$	−7.58088	+	4.37683i	−0.260329	+	0.150301i
$849$		0			0
$850$	−43.3077	−	25.0037i	−1.48544	−	0.857621i
$851$	19.2386	+	11.1074i	0.659492	+	0.380758i
$852$		0			0
$853$	16.5936	−	9.58030i	0.568153	−	0.328023i	−0.188258	−	0.982120i	$-0.560284\pi$
$853$	16.5936	−	9.58030i	0.568153	−	0.328023i	0.756411	+	0.654096i	$0.226951\pi$
$854$		0			0
$855$		0			0
$856$	2.63967			0.0902219
$857$	−8.05723	−	13.9555i	−0.275230	−	0.476712i	0.694963	−	0.719045i	$-0.255421\pi$
$857$	−8.05723	−	13.9555i	−0.275230	−	0.476712i	−0.970193	+	0.242333i	$0.922087\pi$
$858$		0			0
$859$	−10.4830	−	6.05238i	−0.357677	−	0.206505i	0.310384	−	0.950611i	$-0.399542\pi$
$859$	−10.4830	−	6.05238i	−0.357677	−	0.206505i	−0.668061	+	0.744106i	$0.732876\pi$
$860$	−8.68453	+	15.0420i	−0.296140	+	0.512929i
$861$		0			0
$862$	−15.4348	−	26.7338i	−0.525710	−	0.910556i
$863$			37.2655i			1.26853i	0.773115	+	0.634265i	$0.218697\pi$
$863$			37.2655i			1.26853i	−0.773115	+	0.634265i	$0.781303\pi$
$864$		0			0
$865$	−11.1142			−0.377896
$866$	−11.6232	−	20.1319i	−0.394971	−	0.684110i
$867$		0			0
$868$		0			0
$869$	6.63824	+	3.83259i	0.225187	+	0.130012i
$870$		0			0
$871$	24.5505	−	14.1743i	0.831863	−	0.480276i
$872$		−	9.03535i		−	0.305976i
$873$		0			0
$874$		−	3.06760i		−	0.103763i
$875$		0			0
$876$		0			0
$877$	4.85474	−	8.40866i	0.163933	−	0.283940i	−0.772343	−	0.635206i	$-0.780915\pi$
$877$	4.85474	−	8.40866i	0.163933	−	0.283940i	0.936276	+	0.351266i	$0.114249\pi$
$878$	−11.1364	+	19.2887i	−0.375834	+	0.650963i
$879$		0			0
$880$	6.28073	−	3.62618i	0.211723	−	0.122239i
$881$	2.63241			0.0886881			0.0443440	−	0.999016i	$-0.485880\pi$
$881$	2.63241			0.0886881			0.0443440	+	0.999016i	$0.485880\pi$
$882$		0			0
$883$	−36.3181			−1.22220			−0.611101	−	0.791553i	$-0.709273\pi$
$883$	−36.3181			−1.22220			−0.611101	+	0.791553i	$0.709273\pi$
$884$	−18.2265	+	10.5231i	−0.613025	+	0.353930i
$885$		0			0
$886$	−8.99259	+	15.5756i	−0.302112	+	0.523273i
$887$	8.18209	−	14.1718i	0.274728	−	0.475842i	−0.695339	−	0.718682i	$-0.744746\pi$
$887$	8.18209	−	14.1718i	0.274728	−	0.475842i	0.970066	+	0.242840i	$0.0780790\pi$
$888$		0			0
$889$		0			0
$890$		−	17.3238i		−	0.580694i
$891$		0			0
$892$		−	18.8209i		−	0.630170i
$893$	−1.95669	+	1.12969i	−0.0654781	+	0.0378038i
$894$		0			0
$895$	−60.5549	−	34.9614i	−2.02413	−	1.16863i
$896$		0			0
$897$		0			0
$898$	4.72182	+	8.17843i	0.157569	+	0.272918i
$899$	−5.29998			−0.176764
$900$		0			0
$901$			54.0466i			1.80055i
$902$	−5.71171	−	9.89297i	−0.190179	−	0.329400i
$903$		0			0
$904$	−0.845306	+	1.46411i	−0.0281145	+	0.0486957i
$905$	−24.7405	−	14.2839i	−0.822403	−	0.474814i
$906$		0			0
$907$	−5.41666	−	9.38192i	−0.179857	−	0.311522i	0.761974	−	0.647607i	$-0.224230\pi$
$907$	−5.41666	−	9.38192i	−0.179857	−	0.311522i	−0.941831	+	0.336086i	$0.890897\pi$
$908$	14.6133			0.484960
$909$		0			0
$910$		0			0
$911$	−36.8512	+	21.2760i	−1.22093	+	0.704907i	−0.965117	−	0.261818i	$-0.915678\pi$
$911$	−36.8512	+	21.2760i	−1.22093	+	0.704907i	−0.255817	+	0.966725i	$0.582345\pi$
$912$		0			0
$913$	−13.8994	−	8.02482i	−0.460003	−	0.265583i
$914$	−1.59739	−	0.922251i	−0.0528368	−	0.0305053i
$915$		0			0
$916$	−2.06044	+	1.18959i	−0.0680788	+	0.0393053i
$917$		0			0
$918$		0			0
$919$	25.9393			0.855659			0.427829	−	0.903860i	$-0.359278\pi$
$919$	25.9393			0.855659			0.427829	+	0.903860i	$0.359278\pi$
$920$	−5.47963	−	9.49100i	−0.180658	−	0.312909i
$921$		0			0
$922$	−31.5007	−	18.1869i	−1.03742	−	0.598955i
$923$	0.794727	−	1.37651i	0.0261588	−	0.0453083i
$924$		0			0
$925$	29.7108	+	51.4606i	0.976884	+	1.69201i
$926$		−	31.9660i		−	1.05047i
$927$		0			0
$928$	−5.82616			−0.191253
$929$	23.4456	+	40.6089i	0.769224	+	1.33234i	0.937984	+	0.346678i	$0.112690\pi$
$929$	23.4456	+	40.6089i	0.769224	+	1.33234i	−0.168760	+	0.985657i	$0.553976\pi$
$930$		0			0
$931$		0			0
$932$	9.03470	+	5.21619i	0.295942	+	0.170862i
$933$		0			0
$934$	−21.1666	+	12.2206i	−0.692593	+	0.399869i
$935$		−	44.7774i		−	1.46438i
$936$		0			0
$937$			0.209357i			0.00683939i	0.999994	+	0.00341969i	$0.00108852\pi$
$937$			0.209357i			0.00683939i	−0.999994	+	0.00341969i	$0.998911\pi$
$938$		0			0
$939$		0			0
$940$	−4.03593	+	6.99044i	−0.131638	+	0.228003i
$941$	−0.388565	+	0.673014i	−0.0126669	+	0.0219396i	−0.872289	−	0.488990i	$-0.837365\pi$
$941$	−0.388565	+	0.673014i	−0.0126669	+	0.0219396i	0.859622	+	0.510930i	$0.170699\pi$
$942$		0			0
$943$	−14.9496	+	8.63113i	−0.486825	+	0.281068i
$944$	−8.98627			−0.292478
$945$		0			0
$946$	−9.61619			−0.312649
$947$	43.1233	−	24.8972i	1.40132	−	0.809052i	0.406791	−	0.913521i	$-0.366648\pi$
$947$	43.1233	−	24.8972i	1.40132	−	0.809052i	0.994528	+	0.104470i	$0.0333145\pi$
$948$		0			0
$949$	7.18378	−	12.4427i	0.233196	−	0.403906i
$950$	4.10269	−	7.10607i	0.133109	−	0.230552i
$951$		0			0
$952$		0			0
$953$		−	41.4104i		−	1.34141i	−0.741722	−	0.670707i	$-0.765991\pi$
$953$		−	41.4104i		−	1.34141i	0.741722	−	0.670707i	$-0.234009\pi$
$954$		0			0
$955$		−	48.1522i		−	1.55817i
$956$	−20.5971	+	11.8917i	−0.666158	+	0.384607i
$957$		0			0
$958$	9.49220	+	5.48032i	0.306679	+	0.177061i
$959$		0			0
$960$		0			0
$961$	−15.0862	−	26.1301i	−0.486653	−	0.842907i
$962$	25.0082			0.806298
$963$		0			0
$964$			28.6487i			0.922712i
$965$	11.8274	+	20.4857i	0.380739	+	0.659459i
$966$		0			0
$967$	22.8028	−	39.4956i	0.733289	−	1.27009i	−0.222181	−	0.975005i	$-0.571318\pi$
$967$	22.8028	−	39.4956i	0.733289	−	1.27009i	0.955470	−	0.295088i	$-0.0953491\pi$
$968$	−6.04902	−	3.49240i	−0.194423	−	0.112250i
$969$		0			0
$970$	−21.2796	−	36.8573i	−0.683245	−	1.18342i
$971$	−8.73466			−0.280309			−0.140154	−	0.990130i	$-0.544760\pi$
$971$	−8.73466			−0.280309			−0.140154	+	0.990130i	$0.544760\pi$
$972$		0			0
$973$		0			0
$974$	−29.1136	+	16.8087i	−0.932860	+	0.538587i
$975$		0			0
$976$	12.7410	+	7.35603i	0.407830	+	0.235461i
$977$	−12.9058	−	7.45114i	−0.412892	−	0.238383i	0.279140	−	0.960250i	$-0.409951\pi$
$977$	−12.9058	−	7.45114i	−0.412892	−	0.238383i	−0.692031	+	0.721867i	$0.743284\pi$
$978$		0			0
$979$	8.30615	−	4.79556i	0.265466	−	0.153267i
$980$		0			0
$981$		0			0
$982$	−22.7353			−0.725512
$983$	1.53458	+	2.65798i	0.0489456	+	0.0847763i	0.889460	−	0.457013i	$-0.151081\pi$
$983$	1.53458	+	2.65798i	0.0489456	+	0.0847763i	−0.840515	+	0.541789i	$0.817747\pi$
$984$		0			0
$985$	13.9247	+	8.03941i	0.443677	+	0.256157i
$986$	−17.9859	+	31.1525i	−0.572787	+	0.992096i
$987$		0			0
$988$	−1.72667	−	2.99067i	−0.0549325	−	0.0951460i
$989$			14.5313i			0.462069i
$990$		0			0
$991$	−55.8150			−1.77302			−0.886510	−	0.462709i	$-0.846878\pi$
$991$	−55.8150			−1.77302			−0.886510	+	0.462709i	$0.846878\pi$
$992$	0.454844	+	0.787812i	0.0144413	+	0.0250131i
$993$		0			0
$994$		0			0
$995$	36.0798	+	20.8307i	1.14381	+	0.660377i
$996$		0			0
$997$	−5.30607	+	3.06346i	−0.168045	+	0.0970208i	−0.581664	−	0.813429i	$-0.697598\pi$
$997$	−5.30607	+	3.06346i	−0.168045	+	0.0970208i	0.413619	+	0.910450i	$0.364265\pi$
$998$		−	19.5235i		−	0.618006i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.m.b.881.4		16
3.2	odd	2		882.2.m.b.293.7		16
7.2	even	3		2646.2.t.b.2285.5		16
7.3	odd	6		2646.2.l.a.1097.1		16
7.4	even	3		378.2.l.a.341.4		16
7.5	odd	6		378.2.t.a.17.8		16
7.6	odd	2		2646.2.m.a.881.1		16
9.2	odd	6		2646.2.m.a.1763.1		16
9.7	even	3		882.2.m.a.587.6		16
21.2	odd	6		882.2.t.a.815.3		16
21.5	even	6		126.2.t.a.59.2	yes	16
21.11	odd	6		126.2.l.a.5.5	✓	16
21.17	even	6		882.2.l.b.509.8		16
21.20	even	2		882.2.m.a.293.6		16
28.11	odd	6		3024.2.ca.c.2609.7		16
28.19	even	6		3024.2.df.c.17.7		16
63.2	odd	6		2646.2.l.a.521.5		16
63.4	even	3		1134.2.k.b.971.8		16
63.5	even	6		1134.2.k.b.647.8		16
63.11	odd	6		378.2.t.a.89.8		16
63.16	even	3		882.2.l.b.227.4		16
63.20	even	6	inner	2646.2.m.b.1763.4		16
63.25	even	3		126.2.t.a.47.2	yes	16
63.32	odd	6		1134.2.k.a.971.1		16
63.34	odd	6		882.2.m.b.587.7		16
63.38	even	6		2646.2.t.b.1979.5		16
63.40	odd	6		1134.2.k.a.647.1		16
63.47	even	6		378.2.l.a.143.8		16
63.52	odd	6		882.2.t.a.803.3		16
63.61	odd	6		126.2.l.a.101.1	yes	16
84.11	even	6		1008.2.ca.c.257.8		16
84.47	odd	6		1008.2.df.c.689.5		16
252.11	even	6		3024.2.df.c.1601.7		16
252.47	odd	6		3024.2.ca.c.2033.7		16
252.151	odd	6		1008.2.df.c.929.5		16
252.187	even	6		1008.2.ca.c.353.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.5	✓	16	21.11	odd	6
126.2.l.a.101.1	yes	16	63.61	odd	6
126.2.t.a.47.2	yes	16	63.25	even	3
126.2.t.a.59.2	yes	16	21.5	even	6
378.2.l.a.143.8		16	63.47	even	6
378.2.l.a.341.4		16	7.4	even	3
378.2.t.a.17.8		16	7.5	odd	6
378.2.t.a.89.8		16	63.11	odd	6
882.2.l.b.227.4		16	63.16	even	3
882.2.l.b.509.8		16	21.17	even	6
882.2.m.a.293.6		16	21.20	even	2
882.2.m.a.587.6		16	9.7	even	3
882.2.m.b.293.7		16	3.2	odd	2
882.2.m.b.587.7		16	63.34	odd	6
882.2.t.a.803.3		16	63.52	odd	6
882.2.t.a.815.3		16	21.2	odd	6
1008.2.ca.c.257.8		16	84.11	even	6
1008.2.ca.c.353.8		16	252.187	even	6
1008.2.df.c.689.5		16	84.47	odd	6
1008.2.df.c.929.5		16	252.151	odd	6
1134.2.k.a.647.1		16	63.40	odd	6
1134.2.k.a.971.1		16	63.32	odd	6
1134.2.k.b.647.8		16	63.5	even	6
1134.2.k.b.971.8		16	63.4	even	3
2646.2.l.a.521.5		16	63.2	odd	6
2646.2.l.a.1097.1		16	7.3	odd	6
2646.2.m.a.881.1		16	7.6	odd	2
2646.2.m.a.1763.1		16	9.2	odd	6
2646.2.m.b.881.4		16	1.1	even	1	trivial
2646.2.m.b.1763.4		16	63.20	even	6	inner
2646.2.t.b.1979.5		16	63.38	even	6
2646.2.t.b.2285.5		16	7.2	even	3
3024.2.ca.c.2033.7		16	252.47	odd	6
3024.2.ca.c.2609.7		16	28.11	odd	6
3024.2.df.c.17.7		16	28.19	even	6
3024.2.df.c.1601.7		16	252.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.80966 - 3.13442i) q^{5} +1.00000i q^{8} +3.61932i q^{10} +(-1.73534 + 1.00190i) q^{11} +(2.95206 + 1.70437i) q^{13} +(-0.500000 - 0.866025i) q^{16} -6.17418 q^{17} -1.01308i q^{19} +(-1.80966 - 3.13442i) q^{20} +(1.00190 - 1.73534i) q^{22} +(-2.62232 - 1.51400i) q^{23} +(-4.04972 - 7.01433i) q^{25} -3.40874 q^{26} +(-5.04560 + 2.91308i) q^{29} +(0.787812 + 0.454844i) q^{31} +(0.866025 + 0.500000i) q^{32} +(5.34700 - 3.08709i) q^{34} -7.33650 q^{37} +(0.506540 + 0.877353i) q^{38} +(3.13442 + 1.80966i) q^{40} +(2.85045 - 4.93712i) q^{41} +(-2.39949 - 4.15605i) q^{43} +2.00379i q^{44} +3.02799 q^{46} +(-1.11511 - 1.93143i) q^{47} +(7.01433 + 4.04972i) q^{50} +(2.95206 - 1.70437i) q^{52} -8.75365i q^{53} +7.25237i q^{55} +(2.91308 - 5.04560i) q^{58} +(4.49313 - 7.78233i) q^{59} +(-12.7410 + 7.35603i) q^{61} -0.909687 q^{62} -1.00000 q^{64} +(10.6844 - 6.16866i) q^{65} +(4.15821 - 7.20222i) q^{67} +(-3.08709 + 5.34700i) q^{68} -0.466287i q^{71} -4.21492i q^{73} +(6.35359 - 3.66825i) q^{74} +(-0.877353 - 0.506540i) q^{76} +(-1.91267 - 3.31284i) q^{79} -3.61932 q^{80} +5.70089i q^{82} +(4.00481 + 6.93654i) q^{83} +(-11.1732 + 19.3525i) q^{85} +(4.15605 + 2.39949i) q^{86} +(-1.00190 - 1.73534i) q^{88} -4.78647 q^{89} +(-2.62232 + 1.51400i) q^{92} +(1.93143 + 1.11511i) q^{94} +(-3.17542 - 1.83333i) q^{95} +(-10.1835 + 5.87944i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 12 q^{11} + 6 q^{13} - 8 q^{16} - 36 q^{17} - 6 q^{23} - 8 q^{25} + 24 q^{26} - 6 q^{29} + 6 q^{31} + 4 q^{37} + 6 q^{41} - 2 q^{43} - 12 q^{46} - 18 q^{47} + 12 q^{50} + 6 q^{52} + 6 q^{58}+ \cdots + 6 q^{97}+O(q^{100}) \) 16 * q + 8 * q^4 + 12 * q^11 + 6 * q^13 - 8 * q^16 - 36 * q^17 - 6 * q^23 - 8 * q^25 + 24 * q^26 - 6 * q^29 + 6 * q^31 + 4 * q^37 + 6 * q^41 - 2 * q^43 - 12 * q^46 - 18 * q^47 + 12 * q^50 + 6 * q^52 + 6 * q^58 + 30 * q^59 - 60 * q^61 - 36 * q^62 - 16 * q^64 + 42 * q^65 + 14 * q^67 - 18 * q^68 + 18 * q^74 - 16 * q^79 - 12 * q^85 + 24 * q^86 - 48 * q^89 - 6 * q^92 - 66 * q^95 + 6 * q^97

Introduction

L-functions

Modular forms

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Database

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