LMFDB - Embedded newform 2646.2.m.a.1763.1

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			1763.1
Root			$1.71298 - 0.256290i$ of defining polynomial
Character	$\chi$	$=$	2646.1763
Dual form			2646.2.m.a.881.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.80966 - 3.13442i) q^{5} -1.00000i q^{8} +3.61932i q^{10} +(-1.73534 - 1.00190i) q^{11} +(-2.95206 + 1.70437i) q^{13} +(-0.500000 + 0.866025i) q^{16} +6.17418 q^{17} -1.01308i q^{19} +(1.80966 - 3.13442i) q^{20} +(1.00190 + 1.73534i) q^{22} +(-2.62232 + 1.51400i) q^{23} +(-4.04972 + 7.01433i) q^{25} +3.40874 q^{26} +(-5.04560 - 2.91308i) q^{29} +(-0.787812 + 0.454844i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-5.34700 - 3.08709i) q^{34} -7.33650 q^{37} +(-0.506540 + 0.877353i) q^{38} +(-3.13442 + 1.80966i) q^{40} +(-2.85045 - 4.93712i) q^{41} +(-2.39949 + 4.15605i) q^{43} -2.00379i q^{44} +3.02799 q^{46} +(1.11511 - 1.93143i) q^{47} +(7.01433 - 4.04972i) q^{50} +(-2.95206 - 1.70437i) q^{52} +8.75365i q^{53} +7.25237i q^{55} +(2.91308 + 5.04560i) q^{58} +(-4.49313 - 7.78233i) q^{59} +(12.7410 + 7.35603i) q^{61} +0.909687 q^{62} -1.00000 q^{64} +(10.6844 + 6.16866i) q^{65} +(4.15821 + 7.20222i) q^{67} +(3.08709 + 5.34700i) q^{68} +0.466287i q^{71} -4.21492i q^{73} +(6.35359 + 3.66825i) q^{74} +(0.877353 - 0.506540i) q^{76} +(-1.91267 + 3.31284i) q^{79} +3.61932 q^{80} +5.70089i q^{82} +(-4.00481 + 6.93654i) q^{83} +(-11.1732 - 19.3525i) q^{85} +(4.15605 - 2.39949i) q^{86} +(-1.00190 + 1.73534i) q^{88} +4.78647 q^{89} +(-2.62232 - 1.51400i) q^{92} +(-1.93143 + 1.11511i) q^{94} +(-3.17542 + 1.83333i) q^{95} +(10.1835 + 5.87944i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

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

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	−0.913347	−	0.407182i	$-0.866511\pi$
$5$	−1.80966	−	3.13442i	−0.809304	−	1.40175i	0.104043	−	0.994573i	$-0.466822\pi$
$6$		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	0.215029	−	0.976608i	$-0.431015\pi$
$11$	−1.73534	−	1.00190i	−0.523224	−	0.302083i	−0.738253	+	0.674524i	$0.764349\pi$
$12$		0			0
$13$	−2.95206	+	1.70437i	−0.818754	+	0.472708i	−0.849987	−	0.526804i	$-0.823390\pi$
$13$	−2.95206	+	1.70437i	−0.818754	+	0.472708i	0.0312328	+	0.999512i	$0.490057\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.17418			1.49746			0.748730	−	0.662876i	$-0.230664\pi$
$17$	6.17418			1.49746			0.748730	+	0.662876i	$0.230664\pi$
$18$		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	−0.747827	−	0.663894i	$-0.768903\pi$
$23$	−2.62232	+	1.51400i	−0.546791	+	0.315690i	0.201035	+	0.979584i	$0.435569\pi$
$24$		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	−0.0479434	−	0.998850i	$-0.515267\pi$
$29$	−5.04560	−	2.91308i	−0.936945	−	0.540945i	−0.889001	+	0.457905i	$0.848600\pi$
$30$		0			0
$31$	−0.787812	+	0.454844i	−0.141495	+	0.0816923i	−0.569076	−	0.822285i	$-0.692699\pi$
$31$	−0.787812	+	0.454844i	−0.141495	+	0.0816923i	0.427581	+	0.903977i	$0.359366\pi$
$32$	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	$-0.313522\pi$
$41$	−2.85045	−	4.93712i	−0.445165	−	0.771048i	−0.998064	+	0.0622002i	$0.980188\pi$
$42$		0			0
$43$	−2.39949	+	4.15605i	−0.365919	+	0.633791i	−0.988923	−	0.148428i	$-0.952579\pi$
$43$	−2.39949	+	4.15605i	−0.365919	+	0.633791i	0.623004	+	0.782219i	$0.285912\pi$
$44$		−	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	$-0.781327\pi$
$47$	1.11511	−	1.93143i	0.162655	−	0.281727i	0.935820	+	0.352478i	$0.114661\pi$
$48$		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	$0.205312\pi$
$53$			8.75365i			1.20241i	−0.799096	+	0.601203i	$0.794688\pi$
$54$		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	−0.994881	−	0.101054i	$-0.967778\pi$
$59$	−4.49313	−	7.78233i	−0.584956	−	1.01317i	0.409925	−	0.912119i	$-0.365555\pi$
$60$		0			0
$61$	12.7410	+	7.35603i	1.63132	+	0.941843i	0.983686	+	0.179892i	$0.0575747\pi$
$61$	12.7410	+	7.35603i	1.63132	+	0.941843i	0.647634	+	0.761952i	$0.275759\pi$
$62$	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	0.999957	+	0.00926908i	$0.00295048\pi$
$67$	4.15821	+	7.20222i	0.508006	+	0.879892i	−0.491951	+	0.870623i	$0.663716\pi$
$68$	3.08709	+	5.34700i	0.374365	+	0.648419i
$69$		0			0
$70$		0			0
$71$			0.466287i			0.0553381i	0.999617	+	0.0276691i	$0.00880846\pi$
$71$			0.466287i			0.0553381i	−0.999617	+	0.0276691i	$0.991192\pi$
$72$		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	−0.953332	−	0.301924i	$-0.902371\pi$
$79$	−1.91267	+	3.31284i	−0.215192	+	0.372723i	0.738140	+	0.674648i	$0.235704\pi$
$80$	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	$-0.978208\pi$
$83$	−4.00481	+	6.93654i	−0.439585	+	0.761384i	0.558072	+	0.829792i	$0.311541\pi$
$84$		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	$-0.418358\pi$
$89$	4.78647			0.507365			0.253683	+	0.967288i	$0.418358\pi$
$90$		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	$-0.129706\pi$
$97$	10.1835	+	5.87944i	1.03398	+	0.596967i	0.115856	+	0.993266i	$0.463039\pi$
$98$		0			0
$99$		0			0
$100$	−8.09945			−0.809945
$101$	−6.44610	+	11.1650i	−0.641411	+	1.11096i	0.343707	+	0.939077i	$0.388317\pi$
$101$	−6.44610	+	11.1650i	−0.641411	+	1.11096i	−0.985118	+	0.171879i	$0.945016\pi$
$102$		0			0
$103$	9.31740	−	5.37940i	0.918070	−	0.530048i	0.0350515	−	0.999386i	$-0.488840\pi$
$103$	9.31740	−	5.37940i	0.918070	−	0.530048i	0.883019	+	0.469337i	$0.155507\pi$
$104$	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	$0.0407251\pi$
$107$			2.63967i			0.255186i	−0.991827	+	0.127593i	$0.959275\pi$
$108$		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	−0.429551	−	0.903043i	$-0.641328\pi$
$113$	1.46411	−	0.845306i	0.137732	−	0.0795197i	0.567283	+	0.823523i	$0.307995\pi$
$114$		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	0.944312	+	0.329052i	$0.106729\pi$
$131$	8.66567	+	15.0094i	0.757123	+	1.31138i	−0.187188	+	0.982324i	$0.559938\pi$
$132$		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	0.500024	−	0.866012i	$-0.333325\pi$
$137$	0.000558693	0	0.000322562i	4.77324e−5	0	2.75583e-5i	−0.499976	+	0.866039i	$0.666658\pi$
$138$		0			0
$139$	8.73273	−	5.04185i	0.740701	−	0.427644i	−0.0816233	−	0.996663i	$-0.526010\pi$
$139$	8.73273	−	5.04185i	0.740701	−	0.427644i	0.822324	+	0.569019i	$0.192677\pi$
$140$		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	−0.842766	−	0.538280i	$-0.819074\pi$
$149$	−9.74064	+	5.62376i	−0.797984	+	0.460716i	0.0447816	+	0.998997i	$0.485741\pi$
$150$		0			0
$151$	2.36189	−	4.09092i	0.192208	−	0.332914i	−0.753774	−	0.657134i	$-0.771768\pi$
$151$	2.36189	−	4.09092i	0.192208	−	0.332914i	0.945982	+	0.324220i	$0.105102\pi$
$152$	−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	$-0.705756\pi$
$157$	−2.65845	+	1.53486i	−0.212168	+	0.122495i	0.390151	+	0.920751i	$0.372423\pi$
$158$	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	$-0.148663\pi$
$167$	0.730517	+	1.26529i	0.0565291	+	0.0979113i	−0.836376	+	0.548156i	$0.815330\pi$
$168$		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	$-0.796091\pi$
$173$	1.53541	−	2.65940i	0.116735	−	0.202191i	0.918472	+	0.395486i	$0.129424\pi$
$174$		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	$0.256776\pi$
$179$			19.3193i			1.44399i	−0.691896	+	0.721997i	$0.743224\pi$
$180$		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	0.855114	−	0.518441i	$-0.173487\pi$
$191$	11.5218	+	6.65211i	0.833688	+	0.481330i	−0.0214259	+	0.999770i	$0.506821\pi$
$192$		0			0
$193$	−3.26786	−	5.66011i	−0.235226	−	0.407423i	0.724112	−	0.689682i	$-0.242250\pi$
$193$	−3.26786	−	5.66011i	−0.235226	−	0.407423i	−0.959338	+	0.282259i	$0.908916\pi$
$194$	−5.87944	−	10.1835i	−0.422119	−	0.731132i
$195$		0			0
$196$		0			0
$197$		−	4.44250i		−	0.316515i	−0.987398	−	0.158258i	$-0.949412\pi$
$197$		−	4.44250i		−	0.316515i	0.987398	−	0.158258i	$-0.0505876\pi$
$198$		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	0.933115	+	0.359577i	$0.117079\pi$
$211$	11.3005	+	19.5731i	0.777961	+	1.34747i	−0.155155	+	0.987890i	$0.549588\pi$
$212$	−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	$-0.550348\pi$
$223$	−16.2994	−	9.41045i	−1.09149	−	0.630170i	−0.933972	+	0.357346i	$0.883682\pi$
$224$		0			0
$225$		0			0
$226$	−1.69061			−0.112458
$227$	−7.30665	+	12.6555i	−0.484960	+	0.839975i	−0.999851	−	0.0172809i	$-0.994499\pi$
$227$	−7.30665	+	12.6555i	−0.484960	+	0.839975i	0.514891	+	0.857256i	$0.327832\pi$
$228$		0			0
$229$	2.06044	−	1.18959i	0.136158	−	0.0786106i	−0.430374	−	0.902651i	$-0.641618\pi$
$229$	2.06044	−	1.18959i	0.136158	−	0.0786106i	0.566531	+	0.824040i	$0.308285\pi$
$230$	−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	$-0.888989\pi$
$233$		−	10.4324i		−	0.683448i	0.939800	−	0.341724i	$-0.111011\pi$
$234$		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	−0.985654	−	0.168777i	$-0.946018\pi$
$239$	−20.5971	+	11.8917i	−1.33232	+	0.769213i	−0.346662	+	0.937990i	$0.612685\pi$
$240$		0			0
$241$	24.8105	+	14.3243i	1.59818	+	0.922712i	0.991837	+	0.127513i	$0.0406994\pi$
$241$	24.8105	+	14.3243i	1.59818	+	0.922712i	0.606348	+	0.795200i	$0.292634\pi$
$242$			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	$-0.613176\pi$
$251$	−11.0301			−0.696216			−0.348108	+	0.937454i	$0.613176\pi$
$252$		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	$-0.322733\pi$
$257$	−7.54890	−	13.0751i	−0.470888	−	0.815601i	−0.999446	+	0.0332960i	$0.989400\pi$
$258$		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	0.922292	−	0.386493i	$-0.126314\pi$
$263$	17.0075	+	9.81926i	1.04873	+	0.605482i	0.126433	+	0.991975i	$0.459647\pi$
$264$		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	$-0.504765\pi$
$269$	−0.491005			−0.0299371			−0.0149686	+	0.999888i	$0.504765\pi$
$270$		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	−0.127981	+	0.991777i	$0.540850\pi$
$277$	−15.3600	+	26.6043i	−0.922894	+	1.59850i	−0.794913	+	0.606723i	$0.792484\pi$
$278$	−10.0837			−0.604780
$279$		0			0
$280$		0			0
$281$	−6.86286	−	3.96227i	−0.409404	−	0.236369i	0.281130	−	0.959670i	$-0.409291\pi$
$281$	−6.86286	−	3.96227i	−0.409404	−	0.236369i	−0.690534	+	0.723300i	$0.742624\pi$
$282$		0			0
$283$	9.97303	−	5.75793i	0.592835	−	0.342273i	−0.173383	−	0.984855i	$-0.555470\pi$
$283$	9.97303	−	5.75793i	0.592835	−	0.342273i	0.766218	+	0.642581i	$0.222136\pi$
$284$	−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	$-0.213499\pi$
$293$	−2.50937	−	4.34636i	−0.146599	−	0.253917i	−0.929968	+	0.367639i	$0.880166\pi$
$294$		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	$-0.329801\pi$
$311$	−8.64759	−	14.9781i	−0.490360	−	0.849328i	−0.999938	+	0.0110959i	$0.996468\pi$
$312$		0			0
$313$	−7.78988	−	4.49749i	−0.440310	−	0.254213i	0.263419	−	0.964681i	$-0.415150\pi$
$313$	−7.78988	−	4.49749i	−0.440310	−	0.254213i	−0.703729	+	0.710468i	$0.748483\pi$
$314$	3.06972			0.173234
$315$		0			0
$316$	−3.82533			−0.215192
$317$	−5.82002	−	3.36019i	−0.326885	−	0.188727i	0.327572	−	0.944826i	$-0.393770\pi$
$317$	−5.82002	−	3.36019i	−0.326885	−	0.188727i	−0.654457	+	0.756099i	$0.727103\pi$
$318$		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	−0.483858	−	0.875146i	$-0.660765\pi$
$331$	9.38725	−	16.2592i	0.515970	−	0.893686i	0.999828	−	0.0185396i	$-0.00590167\pi$
$332$	−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	0.924441	−	0.381326i	$-0.124532\pi$
$337$	2.42287	+	4.19654i	0.131982	+	0.228600i	−0.792458	+	0.609926i	$0.791199\pi$
$338$	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	−0.847736	−	0.530419i	$-0.822035\pi$
$347$	−15.1305	+	8.73559i	−0.812247	+	0.468951i	0.0354887	+	0.999370i	$0.488701\pi$
$348$		0			0
$349$	−20.6338	−	11.9129i	−1.10450	−	0.637683i	−0.167101	−	0.985940i	$-0.553440\pi$
$349$	−20.6338	−	11.9129i	−1.10450	−	0.637683i	−0.937399	+	0.348257i	$0.886774\pi$
$350$		0			0
$351$		0			0
$352$	−2.00379			−0.106803
$353$	5.02061	−	8.69596i	0.267220	−	0.462839i	−0.700923	−	0.713237i	$-0.747228\pi$
$353$	5.02061	−	8.69596i	0.267220	−	0.462839i	0.968143	+	0.250398i	$0.0805615\pi$
$354$		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	$0.104027\pi$
$359$			12.1651i			0.642048i	−0.947071	+	0.321024i	$0.895973\pi$
$360$		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	$-0.303126\pi$
$367$	3.14420	+	1.81531i	0.164126	+	0.0947582i	−0.415687	+	0.909508i	$0.636459\pi$
$368$		−	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	0.786131	−	0.618060i	$-0.212081\pi$
$373$	−2.74616	−	4.75648i	−0.142191	−	0.246281i	−0.928321	+	0.371779i	$0.878748\pi$
$374$	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	$-0.0892102\pi$
$383$	4.71534	+	8.16720i	0.240942	+	0.417324i	−0.720041	+	0.693932i	$0.755877\pi$
$384$		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	0.634317	−	0.773073i	$-0.281281\pi$
$389$	5.56142	+	3.21089i	0.281975	+	0.162798i	−0.352342	+	0.935871i	$0.614615\pi$
$390$		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	−0.711141	−	0.703050i	$-0.751821\pi$
$401$	−9.16848	+	5.29343i	−0.457852	+	0.264341i	0.253289	+	0.967391i	$0.418488\pi$
$402$		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	$-0.737474\pi$
$409$	−7.72792	+	4.46172i	−0.382121	+	0.220618i	0.296620	+	0.954996i	$0.404141\pi$
$410$	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	0.889975	+	0.456009i	$0.150721\pi$
$419$	17.1924	+	29.7781i	0.839903	+	1.45475i	−0.0500724	+	0.998746i	$0.515945\pi$
$420$		0			0
$421$	−17.7840	+	30.8028i	−0.866739	+	1.50124i	−0.00142877	+	0.999999i	$0.500455\pi$
$421$	−17.7840	+	30.8028i	−0.866739	+	1.50124i	−0.865310	+	0.501237i	$0.832879\pi$
$422$		−	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	$-0.733180\pi$
$431$		−	30.8695i		−	1.48693i	0.668774	−	0.743466i	$-0.266820\pi$
$432$		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	$-0.511708\pi$
$439$	−19.2887	−	11.1364i	−0.920601	−	0.531509i	−0.883827	+	0.467814i	$0.845042\pi$
$440$	7.25237			0.345743
$441$		0			0
$442$	21.0462			1.00107
$443$	15.5756	+	8.99259i	0.740020	+	0.427251i	0.822077	−	0.569377i	$-0.192815\pi$
$443$	15.5756	+	8.99259i	0.740020	+	0.427251i	−0.0820566	+	0.996628i	$0.526149\pi$
$444$		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	$0.0715315\pi$
$449$			9.44363i			0.445673i	−0.974856	+	0.222836i	$0.928468\pi$
$450$		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	−0.843649	−	0.536896i	$-0.819597\pi$
$457$	0.922251	−	1.59739i	0.0431411	−	0.0747225i	0.886790	+	0.462173i	$0.152930\pi$
$458$	−2.37919			−0.111172
$459$		0			0
$460$			10.9593i			0.510978i
$461$	−18.1869	+	31.5007i	−0.847050	+	1.46713i	0.0367790	+	0.999323i	$0.488290\pi$
$461$	−18.1869	+	31.5007i	−0.847050	+	1.46713i	−0.883829	+	0.467810i	$0.845043\pi$
$462$		0			0
$463$	−15.9830	−	27.6834i	−0.742794	−	1.28656i	−0.951219	−	0.308518i	$-0.900167\pi$
$463$	−15.9830	−	27.6834i	−0.742794	−	1.28656i	0.208425	−	0.978038i	$-0.433166\pi$
$464$	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	$-0.691317\pi$
$467$	−24.4411			−1.13100			−0.565500	+	0.824748i	$0.691317\pi$
$468$		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	$-0.752770\pi$
$479$	5.48032	−	9.49220i	0.250402	−	0.433710i	0.963637	+	0.267216i	$0.0861037\pi$
$480$		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	0.0150939	−	0.999886i	$-0.495195\pi$
$491$	19.6893	−	11.3676i	0.888568	−	0.513015i	0.873474	+	0.486871i	$0.161862\pi$
$492$		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	0.560460	−	0.828181i	$-0.310624\pi$
$499$	−9.76175	−	16.9079i	−0.436996	−	0.756899i	−0.997456	+	0.0712820i	$0.977291\pi$
$500$	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	$-0.598700\pi$
$503$	−13.6867			−0.610262			−0.305131	+	0.952310i	$0.598700\pi$
$504$		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	$-0.182840\pi$
$509$	−1.14583	−	1.98464i	−0.0507881	−	0.0879675i	−0.890302	+	0.455371i	$0.849507\pi$
$510$		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	$-0.622079\pi$
$521$	−17.0820			−0.748377			−0.374189	+	0.927353i	$0.622079\pi$
$522$		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	−0.338024	−	0.941138i	$-0.609758\pi$
$547$	15.1095	−	26.1705i	0.646037	−	1.11897i	0.984061	−	0.177832i	$-0.0569082\pi$
$548$		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	$0.181033\pi$
$557$			25.4212i			1.07713i	−0.842584	+	0.538565i	$0.818967\pi$
$558$		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	$-0.186043\pi$
$563$	−1.44346	−	2.50015i	−0.0608346	−	0.105369i	−0.894839	+	0.446390i	$0.852710\pi$
$564$		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	−0.987445	−	0.157963i	$-0.949507\pi$
$569$	−38.5945	−	22.2826i	−1.61797	−	0.934134i	−0.630523	−	0.776171i	$-0.717159\pi$
$570$		0			0
$571$	3.26470	+	5.65462i	0.136623	+	0.236638i	0.926216	−	0.376992i	$-0.123042\pi$
$571$	3.26470	+	5.65462i	0.136623	+	0.236638i	−0.789593	+	0.613631i	$0.789708\pi$
$572$	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	0.111555	−	0.993758i	$-0.464417\pi$
$587$	22.2025	−	38.4559i	0.916397	−	1.58725i	0.804843	−	0.593488i	$-0.202250\pi$
$588$		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	$-0.595209\pi$
$593$	−14.3513			−0.589336			−0.294668	+	0.955600i	$0.595209\pi$
$594$		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	−0.560691	−	0.828025i	$-0.689464\pi$
$599$	−3.03349	+	1.75139i	−0.123945	+	0.0715597i	0.436746	+	0.899585i	$0.356131\pi$
$600$		0			0
$601$	−15.1846	−	8.76685i	−0.619394	−	0.357607i	0.157239	−	0.987561i	$-0.449741\pi$
$601$	−15.1846	−	8.76685i	−0.619394	−	0.357607i	−0.776633	+	0.629953i	$0.783074\pi$
$602$		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	$-0.666103\pi$
$607$	0.0755923	−	0.0436432i	0.00306820	−	0.00177142i	0.501533	+	0.865138i	$0.332769\pi$
$608$	−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	−0.270373	−	0.962756i	$-0.587147\pi$
$617$	10.6365	−	6.14101i	0.428211	−	0.247228i	0.698584	+	0.715528i	$0.253814\pi$
$618$		0			0
$619$	−17.5869	−	10.1538i	−0.706875	−	0.408115i	0.103028	−	0.994678i	$-0.467147\pi$
$619$	−17.5869	−	10.1538i	−0.706875	−	0.408115i	−0.809903	+	0.586564i	$0.800480\pi$
$620$			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	−0.151038	−	0.988528i	$-0.548262\pi$
$641$	−27.4104	−	15.8254i	−1.08265	−	0.625067i	−0.931609	+	0.363461i	$0.881595\pi$
$642$		0			0
$643$	10.0106	−	5.77960i	0.394778	−	0.227925i	−0.289450	−	0.957193i	$-0.593472\pi$
$643$	10.0106	−	5.77960i	0.394778	−	0.227925i	0.684228	+	0.729268i	$0.260139\pi$
$644$		0			0
$645$		0			0
$646$	−3.12747	+	5.41694i	−0.123049	+	0.213127i
$647$	26.0730			1.02504			0.512519	−	0.858676i	$-0.328713\pi$
$647$	26.0730			1.02504			0.512519	+	0.858676i	$0.328713\pi$
$648$		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	−0.143635	−	0.989631i	$-0.545879\pi$
$653$	16.3952	−	9.46576i	0.641593	−	0.370424i	0.785228	+	0.619207i	$0.212546\pi$
$654$		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	−0.0293098	−	0.999570i	$-0.509331\pi$
$659$	−23.3508	−	13.4816i	−0.909618	−	0.525168i	−0.880308	+	0.474402i	$0.842664\pi$
$660$		0			0
$661$	−22.3201	+	12.8865i	−0.868151	+	0.501227i	−0.866733	−	0.498772i	$-0.833785\pi$
$661$	−22.3201	+	12.8865i	−0.868151	+	0.501227i	−0.00141768	+	0.999999i	$0.500451\pi$
$662$	−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	−1.00000		0.000460130i	$-0.999854\pi$
$673$	−12.9608	+	22.4487i	−0.499601	+	0.865335i	0.500398	+	0.865795i	$0.333187\pi$
$674$		−	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	$-0.914383\pi$
$677$	−6.55382	+	11.3515i	−0.251884	+	0.436275i	0.712161	+	0.702016i	$0.247717\pi$
$678$		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	$0.192112\pi$
$683$			29.6654i			1.13511i	−0.823334	+	0.567557i	$0.807888\pi$
$684$		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	−0.997369	−	0.0724857i	$-0.976907\pi$
$691$	−40.9767	−	23.6579i	−1.55883	−	0.899990i	−0.561459	−	0.827504i	$-0.689760\pi$
$692$	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	$0.0837627\pi$
$701$			13.7742i			0.520244i	−0.965576	+	0.260122i	$0.916237\pi$
$702$		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	−0.0767981	−	0.997047i	$-0.524470\pi$
$709$	21.9691	−	38.0517i	0.825069	−	1.42906i	0.901867	−	0.432014i	$-0.142197\pi$
$710$	−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	$-0.313984\pi$
$719$	29.5860			1.10337			0.551687	+	0.834051i	$0.313984\pi$
$720$		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	$-0.402893\pi$
$727$	−10.1244	−	5.84534i	−0.375494	−	0.216792i	−0.675856	+	0.737034i	$0.736226\pi$
$728$		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	$-0.875817\pi$
$733$	−28.6423	+	16.5366i	−1.05793	+	0.610795i	−0.133070	+	0.991107i	$0.542483\pi$
$734$	−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	−0.792701	−	0.609611i	$-0.791326\pi$
$743$	−18.0206	+	10.4042i	−0.661112	+	0.381693i	0.131589	+	0.991304i	$0.457992\pi$
$744$		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	0.957745	+	0.287618i	$0.0928634\pi$
$751$	19.9492	+	34.5531i	0.727957	+	1.26086i	−0.229788	+	0.973241i	$0.573803\pi$
$752$	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	$-0.216774\pi$
$761$	−4.32462	−	7.49046i	−0.156767	−	0.271529i	−0.933701	+	0.358053i	$0.883441\pi$
$762$		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	$-0.806894\pi$
$769$	−20.4818	+	11.8252i	−0.738592	+	0.426426i	0.0829652	+	0.996552i	$0.473561\pi$
$770$		0			0
$771$		0			0
$772$	3.26786	−	5.66011i	0.117613	−	0.203712i
$773$	−46.5699			−1.67500			−0.837501	−	0.546436i	$-0.815984\pi$
$773$	−46.5699			−1.67500			−0.837501	+	0.546436i	$0.815984\pi$
$774$		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	$-0.523204\pi$
$787$	21.1657	−	12.2200i	0.754474	−	0.435596i	0.827308	+	0.561748i	$0.189871\pi$
$788$	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	−0.848306	−	0.529506i	$-0.822377\pi$
$797$	−24.9202	−	43.1631i	−0.882719	−	1.52891i	−0.0344128	−	0.999408i	$-0.510956\pi$
$798$		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	$-0.930485\pi$
$809$		−	12.3247i		−	0.433315i	0.976248	−	0.216657i	$-0.0695154\pi$
$810$		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	0.934738	−	0.355336i	$-0.115634\pi$
$821$	31.3573	+	18.1041i	1.09438	+	0.631839i	0.159639	+	0.987175i	$0.448967\pi$
$822$		0			0
$823$	9.54093	+	16.5254i	0.332576	+	0.576038i	0.983016	−	0.183519i	$-0.0587489\pi$
$823$	9.54093	+	16.5254i	0.332576	+	0.576038i	−0.650440	+	0.759557i	$0.725416\pi$
$824$	−5.37940	−	9.31740i	−0.187400	−	0.324587i
$825$		0			0
$826$		0			0
$827$			31.9013i			1.10932i	0.832079	+	0.554658i	$0.187151\pi$
$827$			31.9013i			1.10932i	−0.832079	+	0.554658i	$0.812849\pi$
$828$		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	$-0.924679\pi$
$839$	−8.19860	+	14.2004i	−0.283047	+	0.490252i	0.689087	+	0.724679i	$0.258012\pi$
$840$		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	$-0.439716\pi$
$853$	−16.5936	−	9.58030i	−0.568153	−	0.328023i	−0.756411	+	0.654096i	$0.773049\pi$
$854$		0			0
$855$		0			0
$856$	2.63967			0.0902219
$857$	8.05723	−	13.9555i	0.275230	−	0.476712i	−0.694963	−	0.719045i	$-0.744579\pi$
$857$	8.05723	−	13.9555i	0.275230	−	0.476712i	0.970193	+	0.242333i	$0.0779127\pi$
$858$		0			0
$859$	10.4830	−	6.05238i	0.357677	−	0.206505i	−0.310384	−	0.950611i	$-0.600458\pi$
$859$	10.4830	−	6.05238i	0.357677	−	0.206505i	0.668061	+	0.744106i	$0.267124\pi$
$860$	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	$-0.781303\pi$
$863$		−	37.2655i		−	1.26853i	0.773115	−	0.634265i	$-0.218697\pi$
$864$		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	0.936276	−	0.351266i	$-0.114249\pi$
$877$	4.85474	+	8.40866i	0.163933	+	0.283940i	−0.772343	+	0.635206i	$0.780915\pi$
$878$	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	$-0.514120\pi$
$881$	−2.63241			−0.0886881			−0.0443440	+	0.999016i	$0.514120\pi$
$882$		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	$-0.255254\pi$
$887$	−8.18209	−	14.1718i	−0.274728	−	0.475842i	−0.970066	+	0.242840i	$0.921921\pi$
$888$		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	−0.941831	−	0.336086i	$-0.890897\pi$
$907$	−5.41666	+	9.38192i	−0.179857	+	0.311522i	0.761974	+	0.647607i	$0.224230\pi$
$908$	−14.6133			−0.484960
$909$		0			0
$910$		0			0
$911$	−36.8512	−	21.2760i	−1.22093	−	0.704907i	−0.255817	−	0.966725i	$-0.582345\pi$
$911$	−36.8512	−	21.2760i	−1.22093	−	0.704907i	−0.965117	+	0.261818i	$0.915678\pi$
$912$		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	0.168760	+	0.985657i	$0.446024\pi$
$929$	−23.4456	+	40.6089i	−0.769224	+	1.33234i	−0.937984	+	0.346678i	$0.887310\pi$
$930$		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	$-0.162635\pi$
$941$	0.388565	+	0.673014i	0.0126669	+	0.0219396i	−0.859622	+	0.510930i	$0.829301\pi$
$942$		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	0.994528	−	0.104470i	$-0.0333145\pi$
$947$	43.1233	+	24.8972i	1.40132	+	0.809052i	0.406791	+	0.913521i	$0.366648\pi$
$948$		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	$0.234009\pi$
$953$			41.4104i			1.34141i	−0.741722	+	0.670707i	$0.765991\pi$
$954$		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	0.955470	+	0.295088i	$0.0953491\pi$
$967$	22.8028	+	39.4956i	0.733289	+	1.27009i	−0.222181	+	0.975005i	$0.571318\pi$
$968$	−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	$-0.455240\pi$
$971$	8.73466			0.280309			0.140154	+	0.990130i	$0.455240\pi$
$972$		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	−0.692031	−	0.721867i	$-0.743284\pi$
$977$	−12.9058	+	7.45114i	−0.412892	+	0.238383i	0.279140	+	0.960250i	$0.409951\pi$
$978$		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	$-0.848919\pi$
$983$	−1.53458	+	2.65798i	−0.0489456	+	0.0847763i	0.840515	+	0.541789i	$0.182253\pi$
$984$		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	$-0.302402\pi$
$997$	5.30607	+	3.06346i	0.168045	+	0.0970208i	−0.413619	+	0.910450i	$0.635735\pi$
$998$			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.a.1763.1		16
3.2	odd	2		882.2.m.a.587.6		16
7.2	even	3		2646.2.l.a.521.5		16
7.3	odd	6		2646.2.t.b.1979.5		16
7.4	even	3		378.2.t.a.89.8		16
7.5	odd	6		378.2.l.a.143.8		16
7.6	odd	2		2646.2.m.b.1763.4		16
9.4	even	3		882.2.m.b.293.7		16
9.5	odd	6		2646.2.m.b.881.4		16
21.2	odd	6		882.2.l.b.227.4		16
21.5	even	6		126.2.l.a.101.1	yes	16
21.11	odd	6		126.2.t.a.47.2	yes	16
21.17	even	6		882.2.t.a.803.3		16
21.20	even	2		882.2.m.b.587.7		16
28.11	odd	6		3024.2.df.c.1601.7		16
28.19	even	6		3024.2.ca.c.2033.7		16
63.4	even	3		126.2.l.a.5.5	✓	16
63.5	even	6		378.2.t.a.17.8		16
63.11	odd	6		1134.2.k.b.971.8		16
63.13	odd	6		882.2.m.a.293.6		16
63.23	odd	6		2646.2.t.b.2285.5		16
63.25	even	3		1134.2.k.a.971.1		16
63.31	odd	6		882.2.l.b.509.8		16
63.32	odd	6		378.2.l.a.341.4		16
63.40	odd	6		126.2.t.a.59.2	yes	16
63.41	even	6	inner	2646.2.m.a.881.1		16
63.47	even	6		1134.2.k.a.647.1		16
63.58	even	3		882.2.t.a.815.3		16
63.59	even	6		2646.2.l.a.1097.1		16
63.61	odd	6		1134.2.k.b.647.8		16
84.11	even	6		1008.2.df.c.929.5		16
84.47	odd	6		1008.2.ca.c.353.8		16
252.67	odd	6		1008.2.ca.c.257.8		16
252.95	even	6		3024.2.ca.c.2609.7		16
252.103	even	6		1008.2.df.c.689.5		16
252.131	odd	6		3024.2.df.c.17.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.5	✓	16	63.4	even	3
126.2.l.a.101.1	yes	16	21.5	even	6
126.2.t.a.47.2	yes	16	21.11	odd	6
126.2.t.a.59.2	yes	16	63.40	odd	6
378.2.l.a.143.8		16	7.5	odd	6
378.2.l.a.341.4		16	63.32	odd	6
378.2.t.a.17.8		16	63.5	even	6
378.2.t.a.89.8		16	7.4	even	3
882.2.l.b.227.4		16	21.2	odd	6
882.2.l.b.509.8		16	63.31	odd	6
882.2.m.a.293.6		16	63.13	odd	6
882.2.m.a.587.6		16	3.2	odd	2
882.2.m.b.293.7		16	9.4	even	3
882.2.m.b.587.7		16	21.20	even	2
882.2.t.a.803.3		16	21.17	even	6
882.2.t.a.815.3		16	63.58	even	3
1008.2.ca.c.257.8		16	252.67	odd	6
1008.2.ca.c.353.8		16	84.47	odd	6
1008.2.df.c.689.5		16	252.103	even	6
1008.2.df.c.929.5		16	84.11	even	6
1134.2.k.a.647.1		16	63.47	even	6
1134.2.k.a.971.1		16	63.25	even	3
1134.2.k.b.647.8		16	63.61	odd	6
1134.2.k.b.971.8		16	63.11	odd	6
2646.2.l.a.521.5		16	7.2	even	3
2646.2.l.a.1097.1		16	63.59	even	6
2646.2.m.a.881.1		16	63.41	even	6	inner
2646.2.m.a.1763.1		16	1.1	even	1	trivial
2646.2.m.b.881.4		16	9.5	odd	6
2646.2.m.b.1763.4		16	7.6	odd	2
2646.2.t.b.1979.5		16	7.3	odd	6
2646.2.t.b.2285.5		16	63.23	odd	6
3024.2.ca.c.2033.7		16	28.19	even	6
3024.2.ca.c.2609.7		16	252.95	even	6
3024.2.df.c.17.7		16	252.131	odd	6
3024.2.df.c.1601.7		16	28.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
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

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Database

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