LMFDB - Embedded newform 88.2.i.a.9.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [88,2,Mod(9,88)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("88.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(88, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 88 = 2^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	88.i (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.702683537787$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			9.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	88.9
Dual form			88.2.i.a.49.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.30902 - 0.951057i) q^{3} +(0.190983 + 0.587785i) q^{5} +(-1.30902 - 0.951057i) q^{7} +(-0.118034 + 0.363271i) q^{9} +(1.23607 - 3.07768i) q^{11} +(-1.80902 + 5.56758i) q^{13} +(0.809017 + 0.587785i) q^{15} +(-0.572949 - 1.76336i) q^{17} +(-3.92705 + 2.85317i) q^{19} -2.61803 q^{21} -4.00000 q^{23} +(3.73607 - 2.71441i) q^{25} +(1.69098 + 5.20431i) q^{27} +(-5.92705 - 4.30625i) q^{29} +(0.336881 - 1.03681i) q^{31} +(-1.30902 - 5.20431i) q^{33} +(0.309017 - 0.951057i) q^{35} +(7.78115 + 5.65334i) q^{37} +(2.92705 + 9.00854i) q^{39} +(7.78115 - 5.65334i) q^{41} +1.52786 q^{43} -0.236068 q^{45} +(8.54508 - 6.20837i) q^{47} +(-1.35410 - 4.16750i) q^{49} +(-2.42705 - 1.76336i) q^{51} +(0.190983 - 0.587785i) q^{53} +(2.04508 + 0.138757i) q^{55} +(-2.42705 + 7.46969i) q^{57} +(1.92705 + 1.40008i) q^{59} +(-0.572949 - 1.76336i) q^{61} +(0.500000 - 0.363271i) q^{63} -3.61803 q^{65} -14.4721 q^{67} +(-5.23607 + 3.80423i) q^{69} +(-1.57295 - 4.84104i) q^{71} +(2.54508 + 1.84911i) q^{73} +(2.30902 - 7.10642i) q^{75} +(-4.54508 + 2.85317i) q^{77} +(-1.19098 + 3.66547i) q^{79} +(6.23607 + 4.53077i) q^{81} +(2.89919 + 8.92278i) q^{83} +(0.927051 - 0.673542i) q^{85} -11.8541 q^{87} -4.47214 q^{89} +(7.66312 - 5.56758i) q^{91} +(-0.545085 - 1.67760i) q^{93} +(-2.42705 - 1.76336i) q^{95} +(-3.80902 + 11.7229i) q^{97} +(0.972136 + 0.812299i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{3} + 3 q^{5} - 3 q^{7} + 4 q^{9} - 4 q^{11} - 5 q^{13} + q^{15} - 9 q^{17} - 9 q^{19} - 6 q^{21} - 16 q^{23} + 6 q^{25} + 9 q^{27} - 17 q^{29} + 17 q^{31} - 3 q^{33} - q^{35} + 11 q^{37} + 5 q^{39}+ \cdots - 14 q^{99}+O(q^{100}) $ 4 * q + 3 * q^3 + 3 * q^5 - 3 * q^7 + 4 * q^9 - 4 * q^11 - 5 * q^13 + q^15 - 9 * q^17 - 9 * q^19 - 6 * q^21 - 16 * q^23 + 6 * q^25 + 9 * q^27 - 17 * q^29 + 17 * q^31 - 3 * q^33 - q^35 + 11 * q^37 + 5 * q^39 + 11 * q^41 + 24 * q^43 + 8 * q^45 + 23 * q^47 + 8 * q^49 - 3 * q^51 + 3 * q^53 - 3 * q^55 - 3 * q^57 + q^59 - 9 * q^61 + 2 * q^63 - 10 * q^65 - 40 * q^67 - 12 * q^69 - 13 * q^71 - q^73 + 7 * q^75 - 7 * q^77 - 7 * q^79 + 16 * q^81 - 13 * q^83 - 3 * q^85 - 34 * q^87 + 15 * q^91 + 9 * q^93 - 3 * q^95 - 13 * q^97 - 14 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/88\mathbb{Z}\right)^\times$.

$n$	$23$	$45$	$57$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		0			0
$2$		0			0
$3$	1.30902	−	0.951057i	0.755761	−	0.549093i	−0.141846	−	0.989889i	$-0.545304\pi$
$3$	1.30902	−	0.951057i	0.755761	−	0.549093i	0.897607	+	0.440796i	$0.145304\pi$
$4$		0			0
$5$	0.190983	+	0.587785i	0.0854102	+	0.262866i	0.984636	−	0.174619i	$-0.0558694\pi$
$5$	0.190983	+	0.587785i	0.0854102	+	0.262866i	−0.899226	+	0.437485i	$0.855869\pi$
$6$		0			0
$7$	−1.30902	−	0.951057i	−0.494762	−	0.359466i	0.312251	−	0.950000i	$-0.398917\pi$
$7$	−1.30902	−	0.951057i	−0.494762	−	0.359466i	−0.807013	+	0.590534i	$0.798917\pi$
$8$		0			0
$9$	−0.118034	+	0.363271i	−0.0393447	+	0.121090i
$10$		0			0
$11$	1.23607	−	3.07768i	0.372689	−	0.927957i
$11$	1.23607	−	3.07768i	0.372689	−	0.927957i
$12$		0			0
$13$	−1.80902	+	5.56758i	−0.501731	+	1.54417i	0.304467	+	0.952523i	$0.401522\pi$
$13$	−1.80902	+	5.56758i	−0.501731	+	1.54417i	−0.806198	+	0.591646i	$0.798478\pi$
$14$		0			0
$15$	0.809017	+	0.587785i	0.208887	+	0.151765i
$16$		0			0
$17$	−0.572949	−	1.76336i	−0.138961	−	0.427677i	0.857224	−	0.514943i	$-0.172187\pi$
$17$	−0.572949	−	1.76336i	−0.138961	−	0.427677i	−0.996185	+	0.0872663i	$0.972187\pi$
$18$		0			0
$19$	−3.92705	+	2.85317i	−0.900927	+	0.654562i	−0.938704	−	0.344724i	$-0.887972\pi$
$19$	−3.92705	+	2.85317i	−0.900927	+	0.654562i	0.0377767	+	0.999286i	$0.487972\pi$
$20$		0			0
$21$	−2.61803			−0.571302
$22$		0			0
$23$	−4.00000			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$		0			0
$25$	3.73607	−	2.71441i	0.747214	−	0.542882i
$26$		0			0
$27$	1.69098	+	5.20431i	0.325430	+	1.00157i
$28$		0			0
$29$	−5.92705	−	4.30625i	−1.10063	−	0.799651i	−0.119464	−	0.992839i	$-0.538118\pi$
$29$	−5.92705	−	4.30625i	−1.10063	−	0.799651i	−0.981162	+	0.193187i	$0.938118\pi$
$30$		0			0
$31$	0.336881	−	1.03681i	0.0605056	−	0.186217i	−0.916235	−	0.400641i	$-0.868787\pi$
$31$	0.336881	−	1.03681i	0.0605056	−	0.186217i	0.976741	+	0.214424i	$0.0687874\pi$
$32$		0			0
$33$	−1.30902	−	5.20431i	−0.227871	−	0.905954i
$34$		0			0
$35$	0.309017	−	0.951057i	0.0522334	−	0.160758i
$36$		0			0
$37$	7.78115	+	5.65334i	1.27921	+	0.929403i	0.999529	−	0.0306888i	$-0.00977008\pi$
$37$	7.78115	+	5.65334i	1.27921	+	0.929403i	0.279685	+	0.960092i	$0.409770\pi$
$38$		0			0
$39$	2.92705	+	9.00854i	0.468703	+	1.44252i
$40$		0			0
$41$	7.78115	−	5.65334i	1.21521	−	0.882903i	0.219518	−	0.975608i	$-0.429551\pi$
$41$	7.78115	−	5.65334i	1.21521	−	0.882903i	0.995694	+	0.0927052i	$0.0295514\pi$
$42$		0			0
$43$	1.52786			0.232997			0.116499	−	0.993191i	$-0.462833\pi$
$43$	1.52786			0.232997			0.116499	+	0.993191i	$0.462833\pi$
$44$		0			0
$45$	−0.236068			−0.0351909
$46$		0			0
$47$	8.54508	−	6.20837i	1.24643	−	0.905583i	0.248420	−	0.968653i	$-0.420089\pi$
$47$	8.54508	−	6.20837i	1.24643	−	0.905583i	0.998009	+	0.0630690i	$0.0200888\pi$
$48$		0			0
$49$	−1.35410	−	4.16750i	−0.193443	−	0.595357i
$50$		0			0
$51$	−2.42705	−	1.76336i	−0.339855	−	0.246919i
$52$		0			0
$53$	0.190983	−	0.587785i	0.0262335	−	0.0807385i	−0.937083	−	0.349108i	$-0.886485\pi$
$53$	0.190983	−	0.587785i	0.0262335	−	0.0807385i	0.963316	+	0.268369i	$0.0864847\pi$
$54$		0			0
$55$	2.04508	+	0.138757i	0.275759	+	0.0187100i
$56$		0			0
$57$	−2.42705	+	7.46969i	−0.321471	+	0.989385i
$58$		0			0
$59$	1.92705	+	1.40008i	0.250881	+	0.182275i	0.706117	−	0.708095i	$-0.250445\pi$
$59$	1.92705	+	1.40008i	0.250881	+	0.182275i	−0.455236	+	0.890371i	$0.650445\pi$
$60$		0			0
$61$	−0.572949	−	1.76336i	−0.0733586	−	0.225775i	0.907654	−	0.419720i	$-0.137872\pi$
$61$	−0.572949	−	1.76336i	−0.0733586	−	0.225775i	−0.981012	+	0.193945i	$0.937872\pi$
$62$		0			0
$63$	0.500000	−	0.363271i	0.0629941	−	0.0457679i
$64$		0			0
$65$	−3.61803			−0.448762
$66$		0			0
$67$	−14.4721			−1.76805			−0.884026	−	0.467437i	$-0.845177\pi$
$67$	−14.4721			−1.76805			−0.884026	+	0.467437i	$0.845177\pi$
$68$		0			0
$69$	−5.23607	+	3.80423i	−0.630349	+	0.457975i
$70$		0			0
$71$	−1.57295	−	4.84104i	−0.186675	−	0.574526i	0.813298	−	0.581847i	$-0.197670\pi$
$71$	−1.57295	−	4.84104i	−0.186675	−	0.574526i	−0.999973	+	0.00732101i	$0.997670\pi$
$72$		0			0
$73$	2.54508	+	1.84911i	0.297880	+	0.216422i	0.726678	−	0.686978i	$-0.241063\pi$
$73$	2.54508	+	1.84911i	0.297880	+	0.216422i	−0.428799	+	0.903400i	$0.641063\pi$
$74$		0			0
$75$	2.30902	−	7.10642i	0.266622	−	0.820579i
$76$		0			0
$77$	−4.54508	+	2.85317i	−0.517961	+	0.325149i
$78$		0			0
$79$	−1.19098	+	3.66547i	−0.133996	+	0.412397i	−0.995433	−	0.0954679i	$-0.969565\pi$
$79$	−1.19098	+	3.66547i	−0.133996	+	0.412397i	0.861436	+	0.507865i	$0.169565\pi$
$80$		0			0
$81$	6.23607	+	4.53077i	0.692896	+	0.503419i
$82$		0			0
$83$	2.89919	+	8.92278i	0.318227	+	0.979402i	0.974406	+	0.224797i	$0.0721718\pi$
$83$	2.89919	+	8.92278i	0.318227	+	0.979402i	−0.656179	+	0.754606i	$0.727828\pi$
$84$		0			0
$85$	0.927051	−	0.673542i	0.100553	−	0.0730559i
$86$		0			0
$87$	−11.8541			−1.27089
$88$		0			0
$89$	−4.47214			−0.474045			−0.237023	−	0.971504i	$-0.576172\pi$
$89$	−4.47214			−0.474045			−0.237023	+	0.971504i	$0.576172\pi$
$90$		0			0
$91$	7.66312	−	5.56758i	0.803313	−	0.583641i
$92$		0			0
$93$	−0.545085	−	1.67760i	−0.0565227	−	0.173959i
$94$		0			0
$95$	−2.42705	−	1.76336i	−0.249010	−	0.180916i
$96$		0			0
$97$	−3.80902	+	11.7229i	−0.386747	+	1.19029i	0.548458	+	0.836178i	$0.315215\pi$
$97$	−3.80902	+	11.7229i	−0.386747	+	1.19029i	−0.935205	+	0.354107i	$0.884785\pi$
$98$		0			0
$99$	0.972136	+	0.812299i	0.0977033	+	0.0816391i
$100$		0			0
$101$	0.954915	−	2.93893i	0.0950176	−	0.292434i	−0.892241	−	0.451560i	$-0.850868\pi$
$101$	0.954915	−	2.93893i	0.0950176	−	0.292434i	0.987258	+	0.159126i	$0.0508676\pi$
$102$		0			0
$103$	−9.78115	−	7.10642i	−0.963766	−	0.700217i	−0.00974339	−	0.999953i	$-0.503101\pi$
$103$	−9.78115	−	7.10642i	−0.963766	−	0.700217i	−0.954022	+	0.299736i	$0.903101\pi$
$104$		0			0
$105$	−0.500000	−	1.53884i	−0.0487950	−	0.150176i
$106$		0			0
$107$	−3.16312	+	2.29814i	−0.305790	+	0.222170i	−0.730088	−	0.683353i	$-0.760521\pi$
$107$	−3.16312	+	2.29814i	−0.305790	+	0.222170i	0.424298	+	0.905523i	$0.360521\pi$
$108$		0			0
$109$	14.9443			1.43140			0.715701	−	0.698407i	$-0.246107\pi$
$109$	14.9443			1.43140			0.715701	+	0.698407i	$0.246107\pi$
$110$		0			0
$111$	15.5623			1.47711
$112$		0			0
$113$	−7.16312	+	5.20431i	−0.673850	+	0.489580i	−0.871312	−	0.490730i	$-0.836730\pi$
$113$	−7.16312	+	5.20431i	−0.673850	+	0.489580i	0.197462	+	0.980311i	$0.436730\pi$
$114$		0			0
$115$	−0.763932	−	2.35114i	−0.0712370	−	0.219245i
$116$		0			0
$117$	−1.80902	−	1.31433i	−0.167244	−	0.121510i
$118$		0			0
$119$	−0.927051	+	2.85317i	−0.0849826	+	0.261550i
$120$		0			0
$121$	−7.94427	−	7.60845i	−0.722207	−	0.691677i
$122$		0			0
$123$	4.80902	−	14.8006i	0.433614	−	1.33453i
$124$		0			0
$125$	4.80902	+	3.49396i	0.430132	+	0.312509i
$126$		0			0
$127$	−1.75329	−	5.39607i	−0.155579	−	0.478824i	0.842640	−	0.538477i	$-0.181000\pi$
$127$	−1.75329	−	5.39607i	−0.155579	−	0.478824i	−0.998219	+	0.0596539i	$0.981000\pi$
$128$		0			0
$129$	2.00000	−	1.45309i	0.176090	−	0.127937i
$130$		0			0
$131$	8.00000			0.698963			0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000			0.698963			0.349482	+	0.936943i	$0.386358\pi$
$132$		0			0
$133$	7.85410			0.681037
$134$		0			0
$135$	−2.73607	+	1.98787i	−0.235483	+	0.171089i
$136$		0			0
$137$	5.42705	+	16.7027i	0.463664	+	1.42701i	0.860655	+	0.509189i	$0.170055\pi$
$137$	5.42705	+	16.7027i	0.463664	+	1.42701i	−0.396990	+	0.917823i	$0.629945\pi$
$138$		0			0
$139$	13.1631	+	9.56357i	1.11648	+	0.811171i	0.983672	−	0.179971i	$-0.0576003\pi$
$139$	13.1631	+	9.56357i	1.11648	+	0.811171i	0.132809	+	0.991142i	$0.457600\pi$
$140$		0			0
$141$	5.28115	−	16.2537i	0.444753	−	1.36881i
$142$		0			0
$143$	14.8992	+	12.4495i	1.24593	+	1.04108i
$144$		0			0
$145$	1.39919	−	4.30625i	0.116196	−	0.357615i
$146$		0			0
$147$	−5.73607	−	4.16750i	−0.473103	−	0.343729i
$148$		0			0
$149$	−5.51722	−	16.9803i	−0.451988	−	1.39108i	−0.874635	−	0.484782i	$-0.838899\pi$
$149$	−5.51722	−	16.9803i	−0.451988	−	1.39108i	0.422646	−	0.906295i	$-0.361101\pi$
$150$		0			0
$151$	−5.92705	+	4.30625i	−0.482337	+	0.350438i	−0.802230	−	0.597016i	$-0.796353\pi$
$151$	−5.92705	+	4.30625i	−0.482337	+	0.350438i	0.319893	+	0.947454i	$0.396353\pi$
$152$		0			0
$153$	0.708204			0.0572549
$154$		0			0
$155$	0.673762			0.0541179
$156$		0			0
$157$	0.545085	−	0.396027i	0.0435025	−	0.0316064i	−0.565822	−	0.824528i	$-0.691441\pi$
$157$	0.545085	−	0.396027i	0.0435025	−	0.0316064i	0.609324	+	0.792921i	$0.291441\pi$
$158$		0			0
$159$	−0.309017	−	0.951057i	−0.0245066	−	0.0754237i
$160$		0			0
$161$	5.23607	+	3.80423i	0.412660	+	0.299815i
$162$		0			0
$163$	−2.71885	+	8.36775i	−0.212957	+	0.655413i	0.786336	+	0.617799i	$0.211976\pi$
$163$	−2.71885	+	8.36775i	−0.212957	+	0.655413i	−0.999292	+	0.0376135i	$0.988024\pi$
$164$		0			0
$165$	2.80902	−	1.76336i	0.218682	−	0.137277i
$166$		0			0
$167$	−4.42705	+	13.6251i	−0.342575	+	1.05434i	0.620293	+	0.784370i	$0.287014\pi$
$167$	−4.42705	+	13.6251i	−0.342575	+	1.05434i	−0.962869	+	0.269969i	$0.912986\pi$
$168$		0			0
$169$	−17.2082	−	12.5025i	−1.32371	−	0.961730i
$170$		0			0
$171$	−0.572949	−	1.76336i	−0.0438145	−	0.134847i
$172$		0			0
$173$	−7.16312	+	5.20431i	−0.544602	+	0.395676i	−0.825791	−	0.563976i	$-0.809271\pi$
$173$	−7.16312	+	5.20431i	−0.544602	+	0.395676i	0.281189	+	0.959652i	$0.409271\pi$
$174$		0			0
$175$	−7.47214			−0.564840
$176$		0			0
$177$	3.85410			0.289692
$178$		0			0
$179$	−19.6353	+	14.2658i	−1.46761	+	1.06628i	−0.486309	+	0.873787i	$0.661657\pi$
$179$	−19.6353	+	14.2658i	−1.46761	+	1.06628i	−0.981298	+	0.192493i	$0.938343\pi$
$180$		0			0
$181$	−2.86475	−	8.81678i	−0.212935	−	0.655346i	−0.999294	−	0.0375761i	$-0.988036\pi$
$181$	−2.86475	−	8.81678i	−0.212935	−	0.655346i	0.786359	−	0.617770i	$-0.211964\pi$
$182$		0			0
$183$	−2.42705	−	1.76336i	−0.179413	−	0.130351i
$184$		0			0
$185$	−1.83688	+	5.65334i	−0.135050	+	0.415642i
$186$		0			0
$187$	−6.13525	−	0.416272i	−0.448654	−	0.0304408i
$188$		0			0
$189$	2.73607	−	8.42075i	0.199020	−	0.612520i
$190$		0			0
$191$	−12.2533	−	8.90254i	−0.886617	−	0.644165i	0.0483768	−	0.998829i	$-0.484595\pi$
$191$	−12.2533	−	8.90254i	−0.886617	−	0.644165i	−0.934994	+	0.354664i	$0.884595\pi$
$192$		0			0
$193$	−2.28115	−	7.02067i	−0.164201	−	0.505359i	0.834776	−	0.550590i	$-0.185597\pi$
$193$	−2.28115	−	7.02067i	−0.164201	−	0.505359i	−0.998977	+	0.0452318i	$0.985597\pi$
$194$		0			0
$195$	−4.73607	+	3.44095i	−0.339157	+	0.246412i
$196$		0			0
$197$	0.472136			0.0336383			0.0168191	−	0.999859i	$-0.494646\pi$
$197$	0.472136			0.0336383			0.0168191	+	0.999859i	$0.494646\pi$
$198$		0			0
$199$	20.3607			1.44333			0.721665	−	0.692242i	$-0.243377\pi$
$199$	20.3607			1.44333			0.721665	+	0.692242i	$0.243377\pi$
$200$		0			0
$201$	−18.9443	+	13.7638i	−1.33623	+	0.970825i
$202$		0			0
$203$	3.66312	+	11.2739i	0.257101	+	0.791274i
$204$		0			0
$205$	4.80902	+	3.49396i	0.335876	+	0.244028i
$206$		0			0
$207$	0.472136	−	1.45309i	0.0328157	−	0.100996i
$208$		0			0
$209$	3.92705	+	15.6129i	0.271640	+	1.07997i
$210$		0			0
$211$	4.04508	−	12.4495i	0.278475	−	0.857058i	−0.709804	−	0.704399i	$-0.751216\pi$
$211$	4.04508	−	12.4495i	0.278475	−	0.857058i	0.988279	−	0.152659i	$-0.0487836\pi$
$212$		0			0
$213$	−6.66312	−	4.84104i	−0.456549	−	0.331703i
$214$		0			0
$215$	0.291796	+	0.898056i	0.0199003	+	0.0612469i
$216$		0			0
$217$	−1.42705	+	1.03681i	−0.0968745	+	0.0703835i
$218$		0			0
$219$	5.09017			0.343962
$220$		0			0
$221$	10.8541			0.730126
$222$		0			0
$223$	7.78115	−	5.65334i	0.521065	−	0.378576i	−0.295940	−	0.955206i	$-0.595633\pi$
$223$	7.78115	−	5.65334i	0.521065	−	0.378576i	0.817005	+	0.576631i	$0.195633\pi$
$224$		0			0
$225$	0.545085	+	1.67760i	0.0363390	+	0.111840i
$226$		0			0
$227$	−5.78115	−	4.20025i	−0.383709	−	0.278781i	0.379164	−	0.925330i	$-0.376212\pi$
$227$	−5.78115	−	4.20025i	−0.383709	−	0.278781i	−0.762873	+	0.646549i	$0.776212\pi$
$228$		0			0
$229$	−5.04508	+	15.5272i	−0.333389	+	1.02606i	0.634122	+	0.773233i	$0.281362\pi$
$229$	−5.04508	+	15.5272i	−0.333389	+	1.02606i	−0.967510	+	0.252831i	$0.918638\pi$
$230$		0			0
$231$	−3.23607	+	8.05748i	−0.212918	+	0.530143i
$232$		0			0
$233$	4.95492	−	15.2497i	0.324607	−	0.999038i	−0.647010	−	0.762481i	$-0.723981\pi$
$233$	4.95492	−	15.2497i	0.324607	−	0.999038i	0.971618	−	0.236557i	$-0.0760191\pi$
$234$		0			0
$235$	5.28115	+	3.83698i	0.344504	+	0.250297i
$236$		0			0
$237$	1.92705	+	5.93085i	0.125175	+	0.385250i
$238$		0			0
$239$	19.0172	−	13.8168i	1.23012	−	0.893736i	0.233222	−	0.972423i	$-0.425073\pi$
$239$	19.0172	−	13.8168i	1.23012	−	0.893736i	0.996899	+	0.0786876i	$0.0250730\pi$
$240$		0			0
$241$	1.05573			0.0680054			0.0340027	−	0.999422i	$-0.489175\pi$
$241$	1.05573			0.0680054			0.0340027	+	0.999422i	$0.489175\pi$
$242$		0			0
$243$	−3.94427			−0.253025
$244$		0			0
$245$	2.19098	−	1.59184i	0.139977	−	0.101699i
$246$		0			0
$247$	−8.78115	−	27.0256i	−0.558731	−	1.71960i
$248$		0			0
$249$	12.2812	+	8.92278i	0.778286	+	0.565458i
$250$		0			0
$251$	3.28115	−	10.0984i	0.207105	−	0.637402i	−0.792516	−	0.609851i	$-0.791229\pi$
$251$	3.28115	−	10.0984i	0.207105	−	0.637402i	0.999620	−	0.0275509i	$-0.00877084\pi$
$252$		0			0
$253$	−4.94427	+	12.3107i	−0.310844	+	0.773969i
$254$		0			0
$255$	0.572949	−	1.76336i	0.0358795	−	0.110426i
$256$		0			0
$257$	2.07295	+	1.50609i	0.129307	+	0.0939470i	0.650559	−	0.759456i	$-0.274535\pi$
$257$	2.07295	+	1.50609i	0.129307	+	0.0939470i	−0.521252	+	0.853403i	$0.674535\pi$
$258$		0			0
$259$	−4.80902	−	14.8006i	−0.298818	−	0.919667i
$260$		0			0
$261$	2.26393	−	1.64484i	0.140134	−	0.101813i
$262$		0			0
$263$	7.41641			0.457315			0.228658	−	0.973507i	$-0.426566\pi$
$263$	7.41641			0.457315			0.228658	+	0.973507i	$0.426566\pi$
$264$		0			0
$265$	0.381966			0.0234640
$266$		0			0
$267$	−5.85410	+	4.25325i	−0.358265	+	0.260295i
$268$		0			0
$269$	−0.281153	−	0.865300i	−0.0171422	−	0.0527583i	0.942120	−	0.335277i	$-0.108830\pi$
$269$	−0.281153	−	0.865300i	−0.0171422	−	0.0527583i	−0.959262	+	0.282519i	$0.908830\pi$
$270$		0			0
$271$	21.3435	+	15.5069i	1.29652	+	0.941979i	0.999915	−	0.0130205i	$-0.00414467\pi$
$271$	21.3435	+	15.5069i	1.29652	+	0.941979i	0.296608	+	0.954999i	$0.404145\pi$
$272$		0			0
$273$	4.73607	−	14.5761i	0.286640	−	0.882187i
$274$		0			0
$275$	−3.73607	−	14.8536i	−0.225293	−	0.895708i
$276$		0			0
$277$	−1.04508	+	3.21644i	−0.0627931	+	0.193257i	−0.977532	−	0.210789i	$-0.932397\pi$
$277$	−1.04508	+	3.21644i	−0.0627931	+	0.193257i	0.914738	+	0.404046i	$0.132397\pi$
$278$		0			0
$279$	0.336881	+	0.244758i	0.0201685	+	0.0146533i
$280$		0			0
$281$	4.19098	+	12.8985i	0.250013	+	0.769461i	0.994771	+	0.102127i	$0.0325648\pi$
$281$	4.19098	+	12.8985i	0.250013	+	0.769461i	−0.744758	+	0.667334i	$0.767435\pi$
$282$		0			0
$283$	−11.1631	+	8.11048i	−0.663579	+	0.482118i	−0.867870	−	0.496792i	$-0.834511\pi$
$283$	−11.1631	+	8.11048i	−0.663579	+	0.482118i	0.204291	+	0.978910i	$0.434511\pi$
$284$		0			0
$285$	−4.85410			−0.287532
$286$		0			0
$287$	−15.5623			−0.918614
$288$		0			0
$289$	10.9721	−	7.97172i	0.645420	−	0.468925i
$290$		0			0
$291$	6.16312	+	18.9681i	0.361288	+	1.11193i
$292$		0			0
$293$	8.54508	+	6.20837i	0.499209	+	0.362697i	0.808715	−	0.588201i	$-0.200164\pi$
$293$	8.54508	+	6.20837i	0.499209	+	0.362697i	−0.309506	+	0.950898i	$0.600164\pi$
$294$		0			0
$295$	−0.454915	+	1.40008i	−0.0264862	+	0.0815161i
$296$		0			0
$297$	18.1074	+	1.22857i	1.05070	+	0.0712889i
$298$		0			0
$299$	7.23607	−	22.2703i	0.418473	−	1.28793i
$300$		0			0
$301$	−2.00000	−	1.45309i	−0.115278	−	0.0837544i
$302$		0			0
$303$	−1.54508	−	4.75528i	−0.0887628	−	0.273184i
$304$		0			0
$305$	0.927051	−	0.673542i	0.0530828	−	0.0385669i
$306$		0			0
$307$	33.8885			1.93412			0.967061	−	0.254546i	$-0.0819260\pi$
$307$	33.8885			1.93412			0.967061	+	0.254546i	$0.0819260\pi$
$308$		0			0
$309$	−19.5623			−1.11286
$310$		0			0
$311$	−26.1074	+	18.9681i	−1.48041	+	1.07558i	−0.502991	+	0.864291i	$0.667767\pi$
$311$	−26.1074	+	18.9681i	−1.48041	+	1.07558i	−0.977423	+	0.211293i	$0.932233\pi$
$312$		0			0
$313$	−8.57295	−	26.3848i	−0.484572	−	1.49136i	−0.832600	−	0.553874i	$-0.813149\pi$
$313$	−8.57295	−	26.3848i	−0.484572	−	1.49136i	0.348028	−	0.937484i	$-0.386851\pi$
$314$		0			0
$315$	0.309017	+	0.224514i	0.0174111	+	0.0126499i
$316$		0			0
$317$	−0.100813	+	0.310271i	−0.00566223	+	0.0174265i	−0.953848	−	0.300291i	$-0.902916\pi$
$317$	−0.100813	+	0.310271i	−0.00566223	+	0.0174265i	0.948185	+	0.317717i	$0.102916\pi$
$318$		0			0
$319$	−20.5795	+	12.9188i	−1.15223	+	0.723312i
$320$		0			0
$321$	−1.95492	+	6.01661i	−0.109113	+	0.335814i
$322$		0			0
$323$	7.28115	+	5.29007i	0.405134	+	0.294347i
$324$		0			0
$325$	8.35410	+	25.7113i	0.463402	+	1.42621i
$326$		0			0
$327$	19.5623	−	14.2128i	1.08180	−	0.785972i
$328$		0			0
$329$	−17.0902			−0.942212
$330$		0			0
$331$	−8.94427			−0.491622			−0.245811	−	0.969318i	$-0.579054\pi$
$331$	−8.94427			−0.491622			−0.245811	+	0.969318i	$0.579054\pi$
$332$		0			0
$333$	−2.97214	+	2.15938i	−0.162872	+	0.118333i
$334$		0			0
$335$	−2.76393	−	8.50651i	−0.151010	−	0.464760i
$336$		0			0
$337$	−21.3435	−	15.5069i	−1.16265	−	0.844716i	−0.172541	−	0.985002i	$-0.555198\pi$
$337$	−21.3435	−	15.5069i	−1.16265	−	0.844716i	−0.990111	+	0.140286i	$0.955198\pi$
$338$		0			0
$339$	−4.42705	+	13.6251i	−0.240444	+	0.740012i
$340$		0			0
$341$	−2.77458	−	2.31838i	−0.150252	−	0.125548i
$342$		0			0
$343$	−5.69098	+	17.5150i	−0.307284	+	0.945724i
$344$		0			0
$345$	−3.23607	−	2.35114i	−0.174224	−	0.126581i
$346$		0			0
$347$	−2.62868	−	8.09024i	−0.141115	−	0.434307i	0.855376	−	0.518007i	$-0.173326\pi$
$347$	−2.62868	−	8.09024i	−0.141115	−	0.434307i	−0.996491	+	0.0837007i	$0.973326\pi$
$348$		0			0
$349$	−16.3992	+	11.9147i	−0.877828	+	0.637780i	−0.932676	−	0.360715i	$-0.882533\pi$
$349$	−16.3992	+	11.9147i	−0.877828	+	0.637780i	0.0548477	+	0.998495i	$0.482533\pi$
$350$		0			0
$351$	−32.0344			−1.70987
$352$		0			0
$353$	1.41641			0.0753878			0.0376939	−	0.999289i	$-0.487999\pi$
$353$	1.41641			0.0753878			0.0376939	+	0.999289i	$0.487999\pi$
$354$		0			0
$355$	2.54508	−	1.84911i	0.135079	−	0.0981407i
$356$		0			0
$357$	1.50000	+	4.61653i	0.0793884	+	0.244332i
$358$		0			0
$359$	−12.5451	−	9.11454i	−0.662104	−	0.481047i	0.205269	−	0.978706i	$-0.434193\pi$
$359$	−12.5451	−	9.11454i	−0.662104	−	0.481047i	−0.867373	+	0.497659i	$0.834193\pi$
$360$		0			0
$361$	1.40983	−	4.33901i	0.0742016	−	0.228369i
$362$		0			0
$363$	−17.6353	−	2.40414i	−0.925611	−	0.126185i
$364$		0			0
$365$	−0.600813	+	1.84911i	−0.0314480	+	0.0967870i
$366$		0			0
$367$	22.1074	+	16.0620i	1.15400	+	0.838427i	0.989007	−	0.147868i	$-0.0472410\pi$
$367$	22.1074	+	16.0620i	1.15400	+	0.838427i	0.164989	+	0.986295i	$0.447241\pi$
$368$		0			0
$369$	1.13525	+	3.49396i	0.0590990	+	0.181888i
$370$		0			0
$371$	−0.809017	+	0.587785i	−0.0420021	+	0.0305163i
$372$		0			0
$373$	−5.41641			−0.280451			−0.140225	−	0.990120i	$-0.544783\pi$
$373$	−5.41641			−0.280451			−0.140225	+	0.990120i	$0.544783\pi$
$374$		0			0
$375$	9.61803			0.496673
$376$		0			0
$377$	34.6976	−	25.2093i	1.78702	−	1.29834i
$378$		0			0
$379$	5.95492	+	18.3273i	0.305883	+	0.941412i	0.979346	+	0.202191i	$0.0648062\pi$
$379$	5.95492	+	18.3273i	0.305883	+	0.941412i	−0.673463	+	0.739221i	$0.735194\pi$
$380$		0			0
$381$	−7.42705	−	5.39607i	−0.380499	−	0.276449i
$382$		0			0
$383$	−0.607391	+	1.86936i	−0.0310362	+	0.0955197i	−0.965375	−	0.260867i	$-0.915992\pi$
$383$	−0.607391	+	1.86936i	−0.0310362	+	0.0955197i	0.934338	+	0.356387i	$0.115992\pi$
$384$		0			0
$385$	−2.54508	−	2.12663i	−0.129710	−	0.108383i
$386$		0			0
$387$	−0.180340	+	0.555029i	−0.00916719	+	0.0282137i
$388$		0			0
$389$	−21.6353	−	15.7189i	−1.09695	−	0.796982i	−0.116391	−	0.993203i	$-0.537133\pi$
$389$	−21.6353	−	15.7189i	−1.09695	−	0.796982i	−0.980560	+	0.196222i	$0.937133\pi$
$390$		0			0
$391$	2.29180	+	7.05342i	0.115901	+	0.356707i
$392$		0			0
$393$	10.4721	−	7.60845i	0.528249	−	0.383796i
$394$		0			0
$395$	−2.38197			−0.119850
$396$		0			0
$397$	−2.58359			−0.129667			−0.0648334	−	0.997896i	$-0.520652\pi$
$397$	−2.58359			−0.129667			−0.0648334	+	0.997896i	$0.520652\pi$
$398$		0			0
$399$	10.2812	−	7.46969i	0.514701	−	0.373952i
$400$		0			0
$401$	2.19098	+	6.74315i	0.109412	+	0.336737i	0.990741	−	0.135768i	$-0.0433500\pi$
$401$	2.19098	+	6.74315i	0.109412	+	0.336737i	−0.881328	+	0.472505i	$0.843350\pi$
$402$		0			0
$403$	5.16312	+	3.75123i	0.257193	+	0.186862i
$404$		0			0
$405$	−1.47214	+	4.53077i	−0.0731510	+	0.225136i
$406$		0			0
$407$	27.0172	−	16.9600i	1.33919	−	0.840677i
$408$		0			0
$409$	0.482779	−	1.48584i	0.0238719	−	0.0734701i	−0.938411	−	0.345521i	$-0.887702\pi$
$409$	0.482779	−	1.48584i	0.0238719	−	0.0734701i	0.962283	+	0.272051i	$0.0877021\pi$
$410$		0			0
$411$	22.9894	+	16.7027i	1.13398	+	0.823886i
$412$		0			0
$413$	−1.19098	−	3.66547i	−0.0586044	−	0.180366i
$414$		0			0
$415$	−4.69098	+	3.40820i	−0.230271	+	0.167302i
$416$		0			0
$417$	26.3262			1.28920
$418$		0			0
$419$	3.05573			0.149282			0.0746410	−	0.997210i	$-0.476219\pi$
$419$	3.05573			0.149282			0.0746410	+	0.997210i	$0.476219\pi$
$420$		0			0
$421$	6.54508	−	4.75528i	0.318988	−	0.231758i	−0.416756	−	0.909019i	$-0.636833\pi$
$421$	6.54508	−	4.75528i	0.318988	−	0.231758i	0.735743	+	0.677260i	$0.236833\pi$
$422$		0			0
$423$	1.24671	+	3.83698i	0.0606172	+	0.186560i
$424$		0			0
$425$	−6.92705	−	5.03280i	−0.336011	−	0.244127i
$426$		0			0
$427$	−0.927051	+	2.85317i	−0.0448631	+	0.138075i
$428$		0			0
$429$	31.3435	+	2.12663i	1.51328	+	0.102675i
$430$		0			0
$431$	−10.2467	+	31.5361i	−0.493567	+	1.51904i	0.325612	+	0.945504i	$0.394430\pi$
$431$	−10.2467	+	31.5361i	−0.493567	+	1.51904i	−0.819179	+	0.573539i	$0.805570\pi$
$432$		0			0
$433$	1.78115	+	1.29408i	0.0855967	+	0.0621897i	0.629761	−	0.776789i	$-0.283153\pi$
$433$	1.78115	+	1.29408i	0.0855967	+	0.0621897i	−0.544164	+	0.838979i	$0.683153\pi$
$434$		0			0
$435$	−2.26393	−	6.96767i	−0.108547	−	0.334074i
$436$		0			0
$437$	15.7082	−	11.4127i	0.751425	−	0.545942i
$438$		0			0
$439$	−0.944272			−0.0450676			−0.0225338	−	0.999746i	$-0.507173\pi$
$439$	−0.944272			−0.0450676			−0.0225338	+	0.999746i	$0.507173\pi$
$440$		0			0
$441$	1.67376			0.0797030
$442$		0			0
$443$	−4.69098	+	3.40820i	−0.222875	+	0.161928i	−0.693620	−	0.720341i	$-0.743985\pi$
$443$	−4.69098	+	3.40820i	−0.222875	+	0.161928i	0.470745	+	0.882269i	$0.343985\pi$
$444$		0			0
$445$	−0.854102	−	2.62866i	−0.0404883	−	0.124610i
$446$		0			0
$447$	−23.3713	−	16.9803i	−1.10543	−	0.803139i
$448$		0			0
$449$	12.1910	−	37.5200i	0.575328	−	1.77068i	−0.0597315	−	0.998214i	$-0.519024\pi$
$449$	12.1910	−	37.5200i	0.575328	−	1.77068i	0.635060	−	0.772463i	$-0.280976\pi$
$450$		0			0
$451$	−7.78115	−	30.9358i	−0.366400	−	1.45671i
$452$		0			0
$453$	−3.66312	+	11.2739i	−0.172108	+	0.529695i
$454$		0			0
$455$	4.73607	+	3.44095i	0.222030	+	0.161314i
$456$		0			0
$457$	2.95492	+	9.09429i	0.138225	+	0.425413i	0.996078	−	0.0884827i	$-0.0282018\pi$
$457$	2.95492	+	9.09429i	0.138225	+	0.425413i	−0.857853	+	0.513896i	$0.828202\pi$
$458$		0			0
$459$	8.20820	−	5.96361i	0.383126	−	0.278357i
$460$		0			0
$461$	−30.3607			−1.41404			−0.707019	−	0.707195i	$-0.749960\pi$
$461$	−30.3607			−1.41404			−0.707019	+	0.707195i	$0.749960\pi$
$462$		0			0
$463$	15.4164			0.716461			0.358231	−	0.933633i	$-0.383380\pi$
$463$	15.4164			0.716461			0.358231	+	0.933633i	$0.383380\pi$
$464$		0			0
$465$	0.881966	−	0.640786i	0.0409002	−	0.0297157i
$466$		0			0
$467$	−0.989357	−	3.04493i	−0.0457820	−	0.140902i	0.925553	−	0.378619i	$-0.123601\pi$
$467$	−0.989357	−	3.04493i	−0.0457820	−	0.140902i	−0.971335	+	0.237717i	$0.923601\pi$
$468$		0			0
$469$	18.9443	+	13.7638i	0.874765	+	0.635554i
$470$		0			0
$471$	0.336881	−	1.03681i	0.0155227	−	0.0477738i
$472$		0			0
$473$	1.88854	−	4.70228i	0.0868353	−	0.216211i
$474$		0			0
$475$	−6.92705	+	21.3193i	−0.317835	+	0.978195i
$476$		0			0
$477$	0.190983	+	0.138757i	0.00874451	+	0.00635326i
$478$		0			0
$479$	−7.10081	−	21.8541i	−0.324444	−	0.998537i	−0.971691	−	0.236256i	$-0.924079\pi$
$479$	−7.10081	−	21.8541i	−0.324444	−	0.998537i	0.647246	−	0.762281i	$-0.275921\pi$
$480$		0			0
$481$	−45.5517	+	33.0952i	−2.07698	+	1.50901i
$482$		0			0
$483$	10.4721			0.476499
$484$		0			0
$485$	−7.61803			−0.345917
$486$		0			0
$487$	26.7254	−	19.4172i	1.21104	−	0.879875i	0.215719	−	0.976455i	$-0.430790\pi$
$487$	26.7254	−	19.4172i	1.21104	−	0.879875i	0.995325	+	0.0965800i	$0.0307904\pi$
$488$		0			0
$489$	4.39919	+	13.5393i	0.198938	+	0.612269i
$490$		0			0
$491$	−15.7812	−	11.4657i	−0.712193	−	0.517439i	0.171687	−	0.985152i	$-0.445078\pi$
$491$	−15.7812	−	11.4657i	−0.712193	−	0.517439i	−0.883881	+	0.467713i	$0.845078\pi$
$492$		0			0
$493$	−4.19756	+	12.9188i	−0.189049	+	0.581832i
$494$		0			0
$495$	−0.291796	+	0.726543i	−0.0131153	+	0.0326557i
$496$		0			0
$497$	−2.54508	+	7.83297i	−0.114163	+	0.351357i
$498$		0			0
$499$	9.63525	+	7.00042i	0.431333	+	0.313382i	0.782182	−	0.623050i	$-0.214107\pi$
$499$	9.63525	+	7.00042i	0.431333	+	0.313382i	−0.350849	+	0.936432i	$0.614107\pi$
$500$		0			0
$501$	7.16312	+	22.0458i	0.320025	+	0.984934i
$502$		0			0
$503$	6.54508	−	4.75528i	0.291831	−	0.212028i	−0.432230	−	0.901763i	$-0.642273\pi$
$503$	6.54508	−	4.75528i	0.291831	−	0.212028i	0.724061	+	0.689736i	$0.242273\pi$
$504$		0			0
$505$	1.90983			0.0849863
$506$		0			0
$507$	−34.4164			−1.52849
$508$		0			0
$509$	15.7812	−	11.4657i	0.699487	−	0.508207i	−0.180278	−	0.983616i	$-0.557700\pi$
$509$	15.7812	−	11.4657i	0.699487	−	0.508207i	0.879765	+	0.475408i	$0.157700\pi$
$510$		0			0
$511$	−1.57295	−	4.84104i	−0.0695832	−	0.214155i
$512$		0			0
$513$	−21.4894	−	15.6129i	−0.948778	−	0.689328i
$514$		0			0
$515$	2.30902	−	7.10642i	0.101747	−	0.313146i
$516$		0			0
$517$	−8.54508	−	33.9730i	−0.375812	−	1.49413i
$518$		0			0
$519$	−4.42705	+	13.6251i	−0.194326	+	0.598074i
$520$		0			0
$521$	20.2533	+	14.7149i	0.887313	+	0.644670i	0.935176	−	0.354183i	$-0.115241\pi$
$521$	20.2533	+	14.7149i	0.887313	+	0.644670i	−0.0478633	+	0.998854i	$0.515241\pi$
$522$		0			0
$523$	−3.86475	−	11.8945i	−0.168994	−	0.520109i	0.830315	−	0.557295i	$-0.188161\pi$
$523$	−3.86475	−	11.8945i	−0.168994	−	0.520109i	−0.999308	+	0.0371860i	$0.988161\pi$
$524$		0			0
$525$	−9.78115	+	7.10642i	−0.426885	+	0.310150i
$526$		0			0
$527$	−2.02129			−0.0880486
$528$		0			0
$529$	−7.00000			−0.304348
$530$		0			0
$531$	−0.736068	+	0.534785i	−0.0319426	+	0.0232077i
$532$		0			0
$533$	17.3992	+	53.5492i	0.753642	+	2.31947i
$534$		0			0
$535$	−1.95492	−	1.42033i	−0.0845183	−	0.0614062i
$536$		0			0
$537$	−12.1353	+	37.3485i	−0.523675	+	1.61171i
$538$		0			0
$539$	−14.5000	−	0.983813i	−0.624559	−	0.0423758i
$540$		0			0
$541$	0.843459	−	2.59590i	0.0362631	−	0.111606i	−0.931286	−	0.364288i	$-0.881312\pi$
$541$	0.843459	−	2.59590i	0.0362631	−	0.111606i	0.967550	+	0.252681i	$0.0813124\pi$
$542$		0			0
$543$	−12.1353	−	8.81678i	−0.520774	−	0.378364i
$544$		0			0
$545$	2.85410	+	8.78402i	0.122256	+	0.376266i
$546$		0			0
$547$	8.25329	−	5.99637i	0.352885	−	0.256386i	−0.397193	−	0.917735i	$-0.630016\pi$
$547$	8.25329	−	5.99637i	0.352885	−	0.256386i	0.750078	+	0.661349i	$0.230016\pi$
$548$		0			0
$549$	0.708204			0.0302254
$550$		0			0
$551$	35.5623			1.51501
$552$		0			0
$553$	5.04508	−	3.66547i	0.214539	−	0.155872i
$554$		0			0
$555$	2.97214	+	9.14729i	0.126160	+	0.388281i
$556$		0			0
$557$	−26.5795	−	19.3112i	−1.12621	−	0.818240i	−0.141072	−	0.989999i	$-0.545055\pi$
$557$	−26.5795	−	19.3112i	−1.12621	−	0.818240i	−0.985139	+	0.171759i	$0.945055\pi$
$558$		0			0
$559$	−2.76393	+	8.50651i	−0.116902	+	0.359787i
$560$		0			0
$561$	−8.42705	+	5.29007i	−0.355790	+	0.223347i
$562$		0			0
$563$	4.80902	−	14.8006i	0.202676	−	0.623772i	−0.797125	−	0.603814i	$-0.793647\pi$
$563$	4.80902	−	14.8006i	0.202676	−	0.623772i	0.999801	−	0.0199579i	$-0.00635321\pi$
$564$		0			0
$565$	−4.42705	−	3.21644i	−0.186247	−	0.135317i
$566$		0			0
$567$	−3.85410	−	11.8617i	−0.161857	−	0.498145i
$568$		0			0
$569$	−20.8713	+	15.1639i	−0.874971	+	0.635704i	−0.931916	−	0.362673i	$-0.881864\pi$
$569$	−20.8713	+	15.1639i	−0.874971	+	0.635704i	0.0569449	+	0.998377i	$0.481864\pi$
$570$		0			0
$571$	−30.8328			−1.29031			−0.645157	−	0.764050i	$-0.723208\pi$
$571$	−30.8328			−1.29031			−0.645157	+	0.764050i	$0.723208\pi$
$572$		0			0
$573$	−24.5066			−1.02378
$574$		0			0
$575$	−14.9443	+	10.8576i	−0.623219	+	0.452795i
$576$		0			0
$577$	−5.98936	−	18.4333i	−0.249340	−	0.767390i	−0.994892	−	0.100943i	$-0.967814\pi$
$577$	−5.98936	−	18.4333i	−0.249340	−	0.767390i	0.745552	−	0.666447i	$-0.232186\pi$
$578$		0			0
$579$	−9.66312	−	7.02067i	−0.401586	−	0.291769i
$580$		0			0
$581$	4.69098	−	14.4374i	0.194615	−	0.598963i
$582$		0			0
$583$	−1.57295	−	1.31433i	−0.0651449	−	0.0544339i
$584$		0			0
$585$	0.427051	−	1.31433i	0.0176564	−	0.0543408i
$586$		0			0
$587$	−0.0729490	−	0.0530006i	−0.00301093	−	0.00218757i	0.586279	−	0.810109i	$-0.300592\pi$
$587$	−0.0729490	−	0.0530006i	−0.00301093	−	0.00218757i	−0.589290	+	0.807922i	$0.700592\pi$
$588$		0			0
$589$	1.63525	+	5.03280i	0.0673795	+	0.207373i
$590$		0			0
$591$	0.618034	−	0.449028i	0.0254225	−	0.0184705i
$592$		0			0
$593$	0.472136			0.0193883			0.00969415	−	0.999953i	$-0.496914\pi$
$593$	0.472136			0.0193883			0.00969415	+	0.999953i	$0.496914\pi$
$594$		0			0
$595$	−1.85410			−0.0760108
$596$		0			0
$597$	26.6525	−	19.3642i	1.09081	−	0.792522i
$598$		0			0
$599$	−7.75329	−	23.8622i	−0.316791	−	0.974982i	−0.975011	−	0.222156i	$-0.928690\pi$
$599$	−7.75329	−	23.8622i	−0.316791	−	0.974982i	0.658220	−	0.752825i	$-0.271310\pi$
$600$		0			0
$601$	25.1976	+	18.3071i	1.02783	+	0.746762i	0.967873	−	0.251439i	$-0.0809037\pi$
$601$	25.1976	+	18.3071i	1.02783	+	0.746762i	0.0599567	+	0.998201i	$0.480904\pi$
$602$		0			0
$603$	1.70820	−	5.25731i	0.0695634	−	0.214094i
$604$		0			0
$605$	2.95492	−	6.12261i	0.120134	−	0.248920i
$606$		0			0
$607$	−9.07953	+	27.9439i	−0.368527	+	1.13421i	0.579216	+	0.815174i	$0.303359\pi$
$607$	−9.07953	+	27.9439i	−0.368527	+	1.13421i	−0.947743	+	0.319035i	$0.896641\pi$
$608$		0			0
$609$	15.5172	+	11.2739i	0.628790	+	0.456842i
$610$		0			0
$611$	19.1074	+	58.8065i	0.773002	+	2.37906i
$612$		0			0
$613$	33.9615	−	24.6745i	1.37169	−	0.996592i	0.374089	−	0.927393i	$-0.377955\pi$
$613$	33.9615	−	24.6745i	1.37169	−	0.996592i	0.997603	−	0.0691996i	$-0.0220445\pi$
$614$		0			0
$615$	9.61803			0.387837
$616$		0			0
$617$	−25.4164			−1.02323			−0.511613	−	0.859216i	$-0.670952\pi$
$617$	−25.4164			−1.02323			−0.511613	+	0.859216i	$0.670952\pi$
$618$		0			0
$619$	5.78115	−	4.20025i	0.232364	−	0.168822i	−0.465510	−	0.885042i	$-0.654129\pi$
$619$	5.78115	−	4.20025i	0.232364	−	0.168822i	0.697875	+	0.716220i	$0.254129\pi$
$620$		0			0
$621$	−6.76393	−	20.8172i	−0.271427	−	0.835367i
$622$		0			0
$623$	5.85410	+	4.25325i	0.234540	+	0.170403i
$624$		0			0
$625$	6.00000	−	18.4661i	0.240000	−	0.738644i
$626$		0			0
$627$	19.9894	+	16.7027i	0.798298	+	0.667043i
$628$		0			0
$629$	5.51064	−	16.9600i	0.219724	−	0.676240i
$630$		0			0
$631$	−9.78115	−	7.10642i	−0.389382	−	0.282902i	0.375820	−	0.926692i	$-0.377361\pi$
$631$	−9.78115	−	7.10642i	−0.389382	−	0.282902i	−0.765202	+	0.643790i	$0.777361\pi$
$632$		0			0
$633$	−6.54508	−	20.1437i	−0.260144	−	0.800640i
$634$		0			0
$635$	2.83688	−	2.06111i	0.112578	−	0.0817928i
$636$		0			0
$637$	25.6525			1.01639
$638$		0			0
$639$	1.94427			0.0769142
$640$		0			0
$641$	−10.8713	+	7.89848i	−0.429391	+	0.311971i	−0.781406	−	0.624024i	$-0.785497\pi$
$641$	−10.8713	+	7.89848i	−0.429391	+	0.311971i	0.352014	+	0.935995i	$0.385497\pi$
$642$		0			0
$643$	−8.22542	−	25.3153i	−0.324379	−	0.998336i	−0.971720	−	0.236136i	$-0.924119\pi$
$643$	−8.22542	−	25.3153i	−0.324379	−	0.998336i	0.647341	−	0.762201i	$-0.275881\pi$
$644$		0			0
$645$	1.23607	+	0.898056i	0.0486701	+	0.0353609i
$646$		0			0
$647$	−3.84346	+	11.8290i	−0.151102	+	0.465044i	−0.997745	−	0.0671170i	$-0.978620\pi$
$647$	−3.84346	+	11.8290i	−0.151102	+	0.465044i	0.846643	+	0.532161i	$0.178620\pi$
$648$		0			0
$649$	6.69098	−	4.20025i	0.262644	−	0.164874i
$650$		0			0
$651$	−0.881966	+	2.71441i	−0.0345670	+	0.106386i
$652$		0			0
$653$	31.4894	+	22.8784i	1.23227	+	0.895299i	0.997059	−	0.0766440i	$-0.0244205\pi$
$653$	31.4894	+	22.8784i	1.23227	+	0.895299i	0.235215	+	0.971943i	$0.424420\pi$
$654$		0			0
$655$	1.52786	+	4.70228i	0.0596986	+	0.183733i
$656$		0			0
$657$	−0.972136	+	0.706298i	−0.0379266	+	0.0275553i
$658$		0			0
$659$	32.0000			1.24654			0.623272	−	0.782006i	$-0.285803\pi$
$659$	32.0000			1.24654			0.623272	+	0.782006i	$0.285803\pi$
$660$		0			0
$661$	6.94427			0.270101			0.135050	−	0.990839i	$-0.456880\pi$
$661$	6.94427			0.270101			0.135050	+	0.990839i	$0.456880\pi$
$662$		0			0
$663$	14.2082	−	10.3229i	0.551801	−	0.400907i
$664$		0			0
$665$	1.50000	+	4.61653i	0.0581675	+	0.179021i
$666$		0			0
$667$	23.7082	+	17.2250i	0.917985	+	0.666955i
$668$		0			0
$669$	4.80902	−	14.8006i	0.185927	−	0.572226i
$670$		0			0
$671$	−6.13525	−	0.416272i	−0.236849	−	0.0160700i
$672$		0			0
$673$	−2.39261	+	7.36369i	−0.0922283	+	0.283850i	−0.986521	−	0.163632i	$-0.947679\pi$
$673$	−2.39261	+	7.36369i	−0.0922283	+	0.283850i	0.894293	+	0.447482i	$0.147679\pi$
$674$		0			0
$675$	20.4443	+	14.8536i	0.786900	+	0.571717i
$676$		0			0
$677$	−6.28115	−	19.3314i	−0.241404	−	0.742966i	−0.996207	−	0.0870143i	$-0.972267\pi$
$677$	−6.28115	−	19.3314i	−0.241404	−	0.742966i	0.754803	−	0.655952i	$-0.227733\pi$
$678$		0			0
$679$	16.1353	−	11.7229i	0.619214	−	0.449885i
$680$		0			0
$681$	−11.5623			−0.443069
$682$		0			0
$683$	−0.944272			−0.0361316			−0.0180658	−	0.999837i	$-0.505751\pi$
$683$	−0.944272			−0.0361316			−0.0180658	+	0.999837i	$0.505751\pi$
$684$		0			0
$685$	−8.78115	+	6.37988i	−0.335511	+	0.243763i
$686$		0			0
$687$	8.16312	+	25.1235i	0.311442	+	0.958521i
$688$		0			0
$689$	2.92705	+	2.12663i	0.111512	+	0.0810180i
$690$		0			0
$691$	7.28115	−	22.4091i	0.276988	−	0.852482i	−0.711698	−	0.702485i	$-0.752074\pi$
$691$	7.28115	−	22.4091i	0.276988	−	0.852482i	0.988687	−	0.149997i	$-0.0479263\pi$
$692$		0			0
$693$	−0.500000	−	1.98787i	−0.0189934	−	0.0755129i
$694$		0			0
$695$	−3.10739	+	9.56357i	−0.117870	+	0.362767i
$696$		0			0
$697$	−14.4271	−	10.4819i	−0.546464	−	0.397029i
$698$		0			0
$699$	−8.01722	−	24.6745i	−0.303239	−	0.933274i
$700$		0			0
$701$	12.7254	−	9.24556i	0.480633	−	0.349200i	−0.320938	−	0.947100i	$-0.603998\pi$
$701$	12.7254	−	9.24556i	0.480633	−	0.349200i	0.801571	+	0.597900i	$0.203998\pi$
$702$		0			0
$703$	−46.6869			−1.76083
$704$		0			0
$705$	10.5623			0.397799
$706$		0			0
$707$	−4.04508	+	2.93893i	−0.152131	+	0.110530i
$708$		0			0
$709$	−6.10081	−	18.7764i	−0.229121	−	0.705161i	−0.997847	−	0.0655835i	$-0.979109\pi$
$709$	−6.10081	−	18.7764i	−0.229121	−	0.705161i	0.768726	−	0.639578i	$-0.220891\pi$
$710$		0			0
$711$	−1.19098	−	0.865300i	−0.0446654	−	0.0324513i
$712$		0			0
$713$	−1.34752	+	4.14725i	−0.0504652	+	0.155316i
$714$		0			0
$715$	−4.47214	+	11.1352i	−0.167248	+	0.416432i
$716$		0			0
$717$	11.7533	−	36.1729i	0.438935	−	1.35090i
$718$		0			0
$719$	−0.0729490	−	0.0530006i	−0.00272054	−	0.00197659i	0.586424	−	0.810004i	$-0.300535\pi$
$719$	−0.0729490	−	0.0530006i	−0.00272054	−	0.00197659i	−0.589145	+	0.808028i	$0.700535\pi$
$720$		0			0
$721$	6.04508	+	18.6049i	0.225131	+	0.692881i
$722$		0			0
$723$	1.38197	−	1.00406i	0.0513959	−	0.0373413i
$724$		0			0
$725$	−33.8328			−1.25652
$726$		0			0
$727$	−28.9443			−1.07348			−0.536742	−	0.843747i	$-0.680345\pi$
$727$	−28.9443			−1.07348			−0.536742	+	0.843747i	$0.680345\pi$
$728$		0			0
$729$	−23.8713	+	17.3435i	−0.884123	+	0.642353i
$730$		0			0
$731$	−0.875388	−	2.69417i	−0.0323774	−	0.0996474i
$732$		0			0
$733$	10.5451	+	7.66145i	0.389492	+	0.282982i	0.765247	−	0.643737i	$-0.222617\pi$
$733$	10.5451	+	7.66145i	0.389492	+	0.282982i	−0.375756	+	0.926719i	$0.622617\pi$
$734$		0			0
$735$	1.35410	−	4.16750i	0.0499468	−	0.153720i
$736$		0			0
$737$	−17.8885	+	44.5407i	−0.658933	+	1.64068i
$738$		0			0
$739$	2.51722	−	7.74721i	0.0925975	−	0.284986i	−0.894023	−	0.448022i	$-0.852129\pi$
$739$	2.51722	−	7.74721i	0.0925975	−	0.284986i	0.986620	+	0.163036i	$0.0521287\pi$
$740$		0			0
$741$	−37.1976	−	27.0256i	−1.36649	−	0.992811i
$742$		0			0
$743$	14.4271	+	44.4019i	0.529277	+	1.62895i	0.755700	+	0.654918i	$0.227297\pi$
$743$	14.4271	+	44.4019i	0.529277	+	1.62895i	−0.226422	+	0.974029i	$0.572703\pi$
$744$		0			0
$745$	8.92705	−	6.48588i	0.327062	−	0.237624i
$746$		0			0
$747$	−3.58359			−0.131117
$748$		0			0
$749$	6.32624			0.231156
$750$		0			0
$751$	−2.69098	+	1.95511i	−0.0981954	+	0.0713431i	−0.635800	−	0.771854i	$-0.719329\pi$
$751$	−2.69098	+	1.95511i	−0.0981954	+	0.0713431i	0.537604	+	0.843197i	$0.319329\pi$
$752$		0			0
$753$	−5.30902	−	16.3395i	−0.193471	−	0.595444i
$754$		0			0
$755$	−3.66312	−	2.66141i	−0.133315	−	0.0968587i
$756$		0			0
$757$	−8.39261	+	25.8298i	−0.305035	+	0.938800i	0.674630	+	0.738156i	$0.264303\pi$
$757$	−8.39261	+	25.8298i	−0.305035	+	0.938800i	−0.979664	+	0.200644i	$0.935697\pi$
$758$		0			0
$759$	5.23607	+	20.8172i	0.190057	+	0.755618i
$760$		0			0
$761$	2.01064	−	6.18812i	0.0728858	−	0.224319i	−0.907977	−	0.419020i	$-0.862374\pi$
$761$	2.01064	−	6.18812i	0.0728858	−	0.224319i	0.980863	+	0.194701i	$0.0623736\pi$
$762$		0			0
$763$	−19.5623	−	14.2128i	−0.708203	−	0.514540i
$764$		0			0
$765$	0.135255	+	0.416272i	0.00489015	+	0.0150503i
$766$		0			0
$767$	−11.2812	+	8.19624i	−0.407339	+	0.295949i
$768$		0			0
$769$	36.2492			1.30718			0.653590	−	0.756849i	$-0.273262\pi$
$769$	36.2492			1.30718			0.653590	+	0.756849i	$0.273262\pi$
$770$		0			0
$771$	4.14590			0.149311
$772$		0			0
$773$	−32.8713	+	23.8824i	−1.18230	+	0.858991i	−0.992429	−	0.122818i	$-0.960807\pi$
$773$	−32.8713	+	23.8824i	−1.18230	+	0.858991i	−0.189870	+	0.981809i	$0.560807\pi$
$774$		0			0
$775$	−1.55573	−	4.78804i	−0.0558834	−	0.171991i
$776$		0			0
$777$	−20.3713	−	14.8006i	−0.730817	−	0.530970i
$778$		0			0
$779$	−14.4271	+	44.4019i	−0.516903	+	1.59086i
$780$		0			0
$781$	−16.8435	−	1.14281i	−0.602706	−	0.0408931i
$782$		0			0
$783$	12.3885	−	38.1280i	0.442730	−	1.36258i
$784$		0			0
$785$	0.336881	+	0.244758i	0.0120238	+	0.00873580i
$786$		0			0
$787$	−7.28115	−	22.4091i	−0.259545	−	0.798798i	−0.992900	−	0.118952i	$-0.962047\pi$
$787$	−7.28115	−	22.4091i	−0.259545	−	0.798798i	0.733355	−	0.679846i	$-0.237953\pi$
$788$		0			0
$789$	9.70820	−	7.05342i	0.345621	−	0.251109i
$790$		0			0
$791$	14.3262			0.509382
$792$		0			0
$793$	10.8541			0.385440
$794$		0			0
$795$	0.500000	−	0.363271i	0.0177332	−	0.0128839i
$796$		0			0
$797$	3.53851	+	10.8904i	0.125340	+	0.385758i	0.993963	−	0.109716i	$-0.0349943\pi$
$797$	3.53851	+	10.8904i	0.125340	+	0.385758i	−0.868623	+	0.495474i	$0.834994\pi$
$798$		0			0
$799$	−15.8435	−	11.5109i	−0.560501	−	0.407228i
$800$		0			0
$801$	0.527864	−	1.62460i	0.0186512	−	0.0574024i
$802$		0			0
$803$	8.83688	−	5.54734i	0.311847	−	0.195761i
$804$		0			0
$805$	−1.23607	+	3.80423i	−0.0435657	+	0.134081i
$806$		0			0
$807$	−1.19098	−	0.865300i	−0.0419246	−	0.0304600i
$808$		0			0
$809$	−0.461493	−	1.42033i	−0.0162252	−	0.0499361i	0.942616	−	0.333879i	$-0.108358\pi$
$809$	−0.461493	−	1.42033i	−0.0162252	−	0.0499361i	−0.958841	+	0.283942i	$0.908358\pi$
$810$		0			0
$811$	−34.5795	+	25.1235i	−1.21425	+	0.882205i	−0.995610	−	0.0936000i	$-0.970163\pi$
$811$	−34.5795	+	25.1235i	−1.21425	+	0.882205i	−0.218642	+	0.975805i	$0.570163\pi$
$812$		0			0
$813$	42.6869			1.49710
$814$		0			0
$815$	−5.43769			−0.190474
$816$		0			0
$817$	−6.00000	+	4.35926i	−0.209913	+	0.152511i
$818$		0			0
$819$	1.11803	+	3.44095i	0.0390673	+	0.120237i
$820$		0			0
$821$	37.6697	+	27.3686i	1.31468	+	0.955172i	0.999982	+	0.00598061i	$0.00190370\pi$
$821$	37.6697	+	27.3686i	1.31468	+	0.955172i	0.314699	+	0.949191i	$0.398096\pi$
$822$		0			0
$823$	4.22542	−	13.0045i	0.147289	−	0.453309i	−0.850009	−	0.526768i	$-0.823404\pi$
$823$	4.22542	−	13.0045i	0.147289	−	0.453309i	0.997298	+	0.0734587i	$0.0234037\pi$
$824$		0			0
$825$	−19.0172	−	15.8904i	−0.662095	−	0.553234i
$826$		0			0
$827$	4.22542	−	13.0045i	0.146932	−	0.452211i	−0.850322	−	0.526263i	$-0.823593\pi$
$827$	4.22542	−	13.0045i	0.146932	−	0.452211i	0.997254	+	0.0740512i	$0.0235928\pi$
$828$		0			0
$829$	13.7812	+	10.0126i	0.478639	+	0.347752i	0.800799	−	0.598934i	$-0.204409\pi$
$829$	13.7812	+	10.0126i	0.478639	+	0.347752i	−0.322159	+	0.946685i	$0.604409\pi$
$830$		0			0
$831$	1.69098	+	5.20431i	0.0586596	+	0.180536i
$832$		0			0
$833$	−6.57295	+	4.77553i	−0.227739	+	0.165462i
$834$		0			0
$835$	−8.85410			−0.306409
$836$		0			0
$837$	5.96556			0.206200
$838$		0			0
$839$	−15.3435	+	11.1477i	−0.529715	+	0.384860i	−0.820251	−	0.572004i	$-0.806166\pi$
$839$	−15.3435	+	11.1477i	−0.529715	+	0.384860i	0.290536	+	0.956864i	$0.406166\pi$
$840$		0			0
$841$	7.62461	+	23.4661i	0.262918	+	0.809177i
$842$		0			0
$843$	17.7533	+	12.8985i	0.611456	+	0.444249i
$844$		0			0
$845$	4.06231	−	12.5025i	0.139748	−	0.430099i
$846$		0			0
$847$	3.16312	+	17.5150i	0.108686	+	0.601824i
$848$		0			0
$849$	−6.89919	+	21.2335i	−0.236779	+	0.728732i
$850$		0			0
$851$	−31.1246	−	22.6134i	−1.06694	−	0.775176i
$852$		0			0
$853$	−10.1697	−	31.2991i	−0.348204	−	1.07166i	−0.959846	−	0.280527i	$-0.909491\pi$
$853$	−10.1697	−	31.2991i	−0.348204	−	1.07166i	0.611642	−	0.791134i	$-0.290509\pi$
$854$		0			0
$855$	0.927051	−	0.673542i	0.0317045	−	0.0230346i
$856$		0			0
$857$	−26.3607			−0.900464			−0.450232	−	0.892912i	$-0.648659\pi$
$857$	−26.3607			−0.900464			−0.450232	+	0.892912i	$0.648659\pi$
$858$		0			0
$859$	13.8885			0.473871			0.236935	−	0.971525i	$-0.423857\pi$
$859$	13.8885			0.473871			0.236935	+	0.971525i	$0.423857\pi$
$860$		0			0
$861$	−20.3713	+	14.8006i	−0.694253	+	0.504404i
$862$		0			0
$863$	−3.86475	−	11.8945i	−0.131557	−	0.404892i	0.863481	−	0.504381i	$-0.168279\pi$
$863$	−3.86475	−	11.8945i	−0.131557	−	0.404892i	−0.995039	+	0.0994888i	$0.968279\pi$
$864$		0			0
$865$	−4.42705	−	3.21644i	−0.150524	−	0.109362i
$866$		0			0
$867$	6.78115	−	20.8702i	0.230300	−	0.708791i
$868$		0			0
$869$	9.80902	+	8.19624i	0.332748	+	0.278038i
$870$		0			0
$871$	26.1803	−	80.5748i	0.887087	−	2.73017i
$872$		0			0
$873$	−3.80902	−	2.76741i	−0.128916	−	0.0936627i
$874$		0			0
$875$	−2.97214	−	9.14729i	−0.100477	−	0.309235i
$876$		0			0
$877$	−15.3435	+	11.1477i	−0.518112	+	0.376430i	−0.815892	−	0.578204i	$-0.803754\pi$
$877$	−15.3435	+	11.1477i	−0.518112	+	0.376430i	0.297780	+	0.954634i	$0.403754\pi$
$878$		0			0
$879$	17.0902			0.576437
$880$		0			0
$881$	31.5279			1.06220			0.531100	−	0.847309i	$-0.321779\pi$
$881$	31.5279			1.06220			0.531100	+	0.847309i	$0.321779\pi$
$882$		0			0
$883$	−10.3992	+	7.55545i	−0.349961	+	0.254261i	−0.748852	−	0.662737i	$-0.769395\pi$
$883$	−10.3992	+	7.55545i	−0.349961	+	0.254261i	0.398892	+	0.916998i	$0.369395\pi$
$884$		0			0
$885$	0.736068	+	2.26538i	0.0247427	+	0.0761501i
$886$		0			0
$887$	40.1074	+	29.1397i	1.34667	+	0.978416i	0.999170	+	0.0407379i	$0.0129709\pi$
$887$	40.1074	+	29.1397i	1.34667	+	0.978416i	0.347505	+	0.937678i	$0.387029\pi$
$888$		0			0
$889$	−2.83688	+	8.73102i	−0.0951459	+	0.292829i
$890$		0			0
$891$	21.6525	−	13.5923i	0.725385	−	0.455359i
$892$		0			0
$893$	−15.8435	+	48.7612i	−0.530181	+	1.63173i
$894$		0			0
$895$	−12.1353	−	8.81678i	−0.405637	−	0.294712i
$896$		0			0
$897$	−11.7082	−	36.0341i	−0.390926	−	1.20315i
$898$		0			0
$899$	−6.46149	+	4.69455i	−0.215503	+	0.156572i
$900$		0			0
$901$	−1.14590			−0.0381754
$902$		0			0
$903$	−4.00000			−0.133112
$904$		0			0
$905$	4.63525	−	3.36771i	0.154081	−	0.111946i
$906$		0			0
$907$	8.42705	+	25.9358i	0.279816	+	0.861184i	0.987905	+	0.155061i	$0.0495574\pi$
$907$	8.42705	+	25.9358i	0.279816	+	0.861184i	−0.708089	+	0.706123i	$0.750443\pi$
$908$		0			0
$909$	0.954915	+	0.693786i	0.0316725	+	0.0230114i
$910$		0			0
$911$	14.5172	−	44.6794i	0.480977	−	1.48029i	−0.356747	−	0.934201i	$-0.616114\pi$
$911$	14.5172	−	44.6794i	0.480977	−	1.48029i	0.837724	−	0.546094i	$-0.183886\pi$
$912$		0			0
$913$	31.0451	+	2.10638i	1.02744	+	0.0697111i
$914$		0			0
$915$	0.572949	−	1.76336i	0.0189411	−	0.0582947i
$916$		0			0
$917$	−10.4721	−	7.60845i	−0.345820	−	0.251253i
$918$		0			0
$919$	−5.75329	−	17.7068i	−0.189783	−	0.584094i	0.810214	−	0.586134i	$-0.199351\pi$
$919$	−5.75329	−	17.7068i	−0.189783	−	0.584094i	−0.999998	+	0.00204006i	$0.999351\pi$
$920$		0			0
$921$	44.3607	−	32.2299i	1.46173	−	1.06201i
$922$		0			0
$923$	29.7984			0.980825
$924$		0			0
$925$	44.4164			1.46040
$926$		0			0
$927$	3.73607	−	2.71441i	0.122709	−	0.0891530i
$928$		0			0
$929$	−4.46149	−	13.7311i	−0.146377	−	0.450502i	0.850809	−	0.525476i	$-0.176113\pi$
$929$	−4.46149	−	13.7311i	−0.146377	−	0.450502i	−0.997185	+	0.0749741i	$0.976113\pi$
$930$		0			0
$931$	17.2082	+	12.5025i	0.563976	+	0.409753i
$932$		0			0
$933$	−16.1353	+	49.6592i	−0.528245	+	1.62577i
$934$		0			0
$935$	−0.927051	−	3.68571i	−0.0303178	−	0.120536i
$936$		0			0
$937$	0.482779	−	1.48584i	0.0157717	−	0.0485403i	−0.942861	−	0.333187i	$-0.891876\pi$
$937$	0.482779	−	1.48584i	0.0157717	−	0.0485403i	0.958633	+	0.284646i	$0.0918761\pi$
$938$		0			0
$939$	−36.3156	−	26.3848i	−1.18511	−	0.861036i
$940$		0			0
$941$	−9.04508	−	27.8379i	−0.294861	−	0.907490i	−0.983268	−	0.182165i	$-0.941690\pi$
$941$	−9.04508	−	27.8379i	−0.294861	−	0.907490i	0.688407	−	0.725325i	$-0.258310\pi$
$942$		0			0
$943$	−31.1246	+	22.6134i	−1.01356	+	0.736392i
$944$		0			0
$945$	5.47214			0.178009
$946$		0			0
$947$	18.8328			0.611984			0.305992	−	0.952034i	$-0.401012\pi$
$947$	18.8328			0.611984			0.305992	+	0.952034i	$0.401012\pi$
$948$		0			0
$949$	−14.8992	+	10.8249i	−0.483648	+	0.351391i
$950$		0			0
$951$	0.163119	+	0.502029i	0.00528949	+	0.0162794i
$952$		0			0
$953$	24.2533	+	17.6210i	0.785641	+	0.570802i	0.906667	−	0.421848i	$-0.138618\pi$
$953$	24.2533	+	17.6210i	0.785641	+	0.570802i	−0.121026	+	0.992649i	$0.538618\pi$
$954$		0			0
$955$	2.89261	−	8.90254i	0.0936026	−	0.288079i
$956$		0			0
$957$	−14.6525	+	36.4832i	−0.473647	+	1.17933i
$958$		0			0
$959$	8.78115	−	27.0256i	0.283558	−	0.872702i
$960$		0			0
$961$	24.1180	+	17.5228i	0.778001	+	0.565251i
$962$		0			0
$963$	−0.461493	−	1.42033i	−0.0148714	−	0.0457695i
$964$		0			0
$965$	3.69098	−	2.68166i	0.118817	−	0.0863256i
$966$		0			0
$967$	33.3050			1.07102			0.535508	−	0.844530i	$-0.320120\pi$
$967$	33.3050			1.07102			0.535508	+	0.844530i	$0.320120\pi$
$968$		0			0
$969$	14.5623			0.467809
$970$		0			0
$971$	9.01722	−	6.55139i	0.289376	−	0.210244i	−0.433620	−	0.901096i	$-0.642764\pi$
$971$	9.01722	−	6.55139i	0.289376	−	0.210244i	0.722997	+	0.690851i	$0.242764\pi$
$972$		0			0
$973$	−8.13525	−	25.0377i	−0.260804	−	0.802673i
$974$		0			0
$975$	35.3885	+	25.7113i	1.13334	+	0.823420i
$976$		0			0
$977$	−2.68441	+	8.26175i	−0.0858817	+	0.264317i	−0.984770	−	0.173861i	$-0.944376\pi$
$977$	−2.68441	+	8.26175i	−0.0858817	+	0.264317i	0.898889	+	0.438177i	$0.144376\pi$
$978$		0			0
$979$	−5.52786	+	13.7638i	−0.176671	+	0.439894i
$980$		0			0
$981$	−1.76393	+	5.42882i	−0.0563180	+	0.173329i
$982$		0			0
$983$	−6.54508	−	4.75528i	−0.208756	−	0.151670i	0.478495	−	0.878090i	$-0.341183\pi$
$983$	−6.54508	−	4.75528i	−0.208756	−	0.151670i	−0.687251	+	0.726420i	$0.741183\pi$
$984$		0			0
$985$	0.0901699	+	0.277515i	0.00287305	+	0.00884235i
$986$		0			0
$987$	−22.3713	+	16.2537i	−0.712087	+	0.517362i
$988$		0			0
$989$	−6.11146			−0.194333
$990$		0			0
$991$	27.0557			0.859454			0.429727	−	0.902959i	$-0.358610\pi$
$991$	27.0557			0.859454			0.429727	+	0.902959i	$0.358610\pi$
$992$		0			0
$993$	−11.7082	+	8.50651i	−0.371549	+	0.269946i
$994$		0			0
$995$	3.88854	+	11.9677i	0.123275	+	0.379402i
$996$		0			0
$997$	−23.1631	−	16.8290i	−0.733583	−	0.532979i	0.157112	−	0.987581i	$-0.449782\pi$
$997$	−23.1631	−	16.8290i	−0.733583	−	0.532979i	−0.890695	+	0.454601i	$0.849782\pi$
$998$		0			0
$999$	−16.2639	+	50.0552i	−0.514568	+	1.58368i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	88.2.i.a.9.1	✓	4
3.2	odd	2		792.2.r.b.361.1		4
4.3	odd	2		176.2.m.a.97.1		4
8.3	odd	2		704.2.m.g.449.1		4
8.5	even	2		704.2.m.b.449.1		4
11.2	odd	10		968.2.i.c.729.1		4
11.3	even	5		968.2.i.d.81.1		4
11.4	even	5		968.2.a.i.1.1		2
11.5	even	5	inner	88.2.i.a.49.1	yes	4
11.6	odd	10		968.2.i.k.753.1		4
11.7	odd	10		968.2.a.h.1.1		2
11.8	odd	10		968.2.i.c.81.1		4
11.9	even	5		968.2.i.d.729.1		4
11.10	odd	2		968.2.i.k.9.1		4
33.5	odd	10		792.2.r.b.577.1		4
33.26	odd	10		8712.2.a.bp.1.1		2
33.29	even	10		8712.2.a.bm.1.1		2
44.7	even	10		1936.2.a.u.1.2		2
44.15	odd	10		1936.2.a.t.1.2		2
44.27	odd	10		176.2.m.a.49.1		4
88.5	even	10		704.2.m.b.577.1		4
88.27	odd	10		704.2.m.g.577.1		4
88.29	odd	10		7744.2.a.cq.1.2		2
88.37	even	10		7744.2.a.cr.1.2		2
88.51	even	10		7744.2.a.cc.1.1		2
88.59	odd	10		7744.2.a.cb.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.i.a.9.1	✓	4	1.1	even	1	trivial
88.2.i.a.49.1	yes	4	11.5	even	5	inner
176.2.m.a.49.1		4	44.27	odd	10
176.2.m.a.97.1		4	4.3	odd	2
704.2.m.b.449.1		4	8.5	even	2
704.2.m.b.577.1		4	88.5	even	10
704.2.m.g.449.1		4	8.3	odd	2
704.2.m.g.577.1		4	88.27	odd	10
792.2.r.b.361.1		4	3.2	odd	2
792.2.r.b.577.1		4	33.5	odd	10
968.2.a.h.1.1		2	11.7	odd	10
968.2.a.i.1.1		2	11.4	even	5
968.2.i.c.81.1		4	11.8	odd	10
968.2.i.c.729.1		4	11.2	odd	10
968.2.i.d.81.1		4	11.3	even	5
968.2.i.d.729.1		4	11.9	even	5
968.2.i.k.9.1		4	11.10	odd	2
968.2.i.k.753.1		4	11.6	odd	10
1936.2.a.t.1.2		2	44.15	odd	10
1936.2.a.u.1.2		2	44.7	even	10
7744.2.a.cb.1.1		2	88.59	odd	10
7744.2.a.cc.1.1		2	88.51	even	10
7744.2.a.cq.1.2		2	88.29	odd	10
7744.2.a.cr.1.2		2	88.37	even	10
8712.2.a.bm.1.1		2	33.29	even	10
8712.2.a.bp.1.1		2	33.26	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 88 = 2^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	88.i (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30902 - 0.951057i) q^{3} +(0.190983 + 0.587785i) q^{5} +(-1.30902 - 0.951057i) q^{7} +(-0.118034 + 0.363271i) q^{9} +(1.23607 - 3.07768i) q^{11} +(-1.80902 + 5.56758i) q^{13} +(0.809017 + 0.587785i) q^{15} +(-0.572949 - 1.76336i) q^{17} +(-3.92705 + 2.85317i) q^{19} -2.61803 q^{21} -4.00000 q^{23} +(3.73607 - 2.71441i) q^{25} +(1.69098 + 5.20431i) q^{27} +(-5.92705 - 4.30625i) q^{29} +(0.336881 - 1.03681i) q^{31} +(-1.30902 - 5.20431i) q^{33} +(0.309017 - 0.951057i) q^{35} +(7.78115 + 5.65334i) q^{37} +(2.92705 + 9.00854i) q^{39} +(7.78115 - 5.65334i) q^{41} +1.52786 q^{43} -0.236068 q^{45} +(8.54508 - 6.20837i) q^{47} +(-1.35410 - 4.16750i) q^{49} +(-2.42705 - 1.76336i) q^{51} +(0.190983 - 0.587785i) q^{53} +(2.04508 + 0.138757i) q^{55} +(-2.42705 + 7.46969i) q^{57} +(1.92705 + 1.40008i) q^{59} +(-0.572949 - 1.76336i) q^{61} +(0.500000 - 0.363271i) q^{63} -3.61803 q^{65} -14.4721 q^{67} +(-5.23607 + 3.80423i) q^{69} +(-1.57295 - 4.84104i) q^{71} +(2.54508 + 1.84911i) q^{73} +(2.30902 - 7.10642i) q^{75} +(-4.54508 + 2.85317i) q^{77} +(-1.19098 + 3.66547i) q^{79} +(6.23607 + 4.53077i) q^{81} +(2.89919 + 8.92278i) q^{83} +(0.927051 - 0.673542i) q^{85} -11.8541 q^{87} -4.47214 q^{89} +(7.66312 - 5.56758i) q^{91} +(-0.545085 - 1.67760i) q^{93} +(-2.42705 - 1.76336i) q^{95} +(-3.80902 + 11.7229i) q^{97} +(0.972136 + 0.812299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{3} + 3 q^{5} - 3 q^{7} + 4 q^{9} - 4 q^{11} - 5 q^{13} + q^{15} - 9 q^{17} - 9 q^{19} - 6 q^{21} - 16 q^{23} + 6 q^{25} + 9 q^{27} - 17 q^{29} + 17 q^{31} - 3 q^{33} - q^{35} + 11 q^{37} + 5 q^{39}+ \cdots - 14 q^{99}+O(q^{100}) \) 4 * q + 3 * q^3 + 3 * q^5 - 3 * q^7 + 4 * q^9 - 4 * q^11 - 5 * q^13 + q^15 - 9 * q^17 - 9 * q^19 - 6 * q^21 - 16 * q^23 + 6 * q^25 + 9 * q^27 - 17 * q^29 + 17 * q^31 - 3 * q^33 - q^35 + 11 * q^37 + 5 * q^39 + 11 * q^41 + 24 * q^43 + 8 * q^45 + 23 * q^47 + 8 * q^49 - 3 * q^51 + 3 * q^53 - 3 * q^55 - 3 * q^57 + q^59 - 9 * q^61 + 2 * q^63 - 10 * q^65 - 40 * q^67 - 12 * q^69 - 13 * q^71 - q^73 + 7 * q^75 - 7 * q^77 - 7 * q^79 + 16 * q^81 - 13 * q^83 - 3 * q^85 - 34 * q^87 + 15 * q^91 + 9 * q^93 - 3 * q^95 - 13 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

Properties

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