LMFDB - Embedded newform 864.2.y.c.193.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.4
Character	$\chi$	$=$	864.193
Dual form			864.2.y.c.385.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.527750 + 1.64969i) q^{3} +(-0.220114 + 1.24833i) q^{5} +(2.06659 - 1.73408i) q^{7} +(-2.44296 - 1.74125i) q^{9} +O(q^{10})$	\(q+(-0.527750 + 1.64969i) q^{3} +(-0.220114 + 1.24833i) q^{5} +(2.06659 - 1.73408i) q^{7} +(-2.44296 - 1.74125i) q^{9} +(-0.816598 - 4.63116i) q^{11} +(5.12114 - 1.86394i) q^{13} +(-1.94319 - 1.02192i) q^{15} +(2.58790 - 4.48237i) q^{17} +(1.60795 + 2.78505i) q^{19} +(1.77005 + 4.32440i) q^{21} +(-5.70640 - 4.78823i) q^{23} +(3.18859 + 1.16055i) q^{25} +(4.16179 - 3.11119i) q^{27} +(4.64667 + 1.69125i) q^{29} +(-5.45581 - 4.57797i) q^{31} +(8.07094 + 1.09696i) q^{33} +(1.70981 + 2.96148i) q^{35} +(-4.05878 + 7.03001i) q^{37} +(0.372250 + 9.43200i) q^{39} +(5.89007 - 2.14381i) q^{41} +(1.35464 + 7.68253i) q^{43} +(2.71138 - 2.66634i) q^{45} +(-3.37956 + 2.83579i) q^{47} +(0.0482428 - 0.273599i) q^{49} +(6.02876 + 6.63480i) q^{51} -5.40231 q^{53} +5.96094 q^{55} +(-5.44307 + 1.18281i) q^{57} +(0.563127 - 3.19365i) q^{59} +(2.83148 - 2.37590i) q^{61} +(-8.06806 + 0.637833i) q^{63} +(1.19958 + 6.80314i) q^{65} +(12.7036 - 4.62375i) q^{67} +(10.9107 - 6.88680i) q^{69} +(1.66453 - 2.88306i) q^{71} +(-4.27984 - 7.41290i) q^{73} +(-3.59733 + 4.64771i) q^{75} +(-9.71835 - 8.15466i) q^{77} +(7.44075 + 2.70821i) q^{79} +(2.93611 + 8.50760i) q^{81} +(-3.51149 - 1.27808i) q^{83} +(5.02583 + 4.21717i) q^{85} +(-5.24232 + 6.77301i) q^{87} +(8.80137 + 15.2444i) q^{89} +(7.35109 - 12.7325i) q^{91} +(10.4315 - 6.58438i) q^{93} +(-3.83059 + 1.39422i) q^{95} +(-2.21046 - 12.5361i) q^{97} +(-6.06907 + 12.7356i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q+O(q^{10}) $ 54 * q	$ 54 q + 9 q^{11} + 12 q^{17} - 18 q^{19} + 12 q^{21} + 21 q^{27} + 6 q^{29} - 36 q^{31} - 9 q^{33} - 24 q^{39} + 3 q^{41} + 21 q^{43} + 42 q^{45} - 18 q^{49} - 24 q^{51} + 36 q^{53} + 72 q^{55} + 39 q^{57} - 18 q^{59} - 18 q^{61} + 30 q^{63} + 48 q^{65} + 27 q^{67} + 24 q^{69} + 84 q^{75} + 36 q^{77} - 72 q^{79} + 36 q^{81} - 6 q^{87} + 33 q^{89} - 36 q^{91} + 72 q^{93} - 36 q^{95} + 9 q^{97} - 120 q^{99}+O(q^{100}) $ 54 * q + 9 * q^11 + 12 * q^17 - 18 * q^19 + 12 * q^21 + 21 * q^27 + 6 * q^29 - 36 * q^31 - 9 * q^33 - 24 * q^39 + 3 * q^41 + 21 * q^43 + 42 * q^45 - 18 * q^49 - 24 * q^51 + 36 * q^53 + 72 * q^55 + 39 * q^57 - 18 * q^59 - 18 * q^61 + 30 * q^63 + 48 * q^65 + 27 * q^67 + 24 * q^69 + 84 * q^75 + 36 * q^77 - 72 * q^79 + 36 * q^81 - 6 * q^87 + 33 * q^89 - 36 * q^91 + 72 * q^93 - 36 * q^95 + 9 * q^97 - 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$	$1$

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			0
$2$		0			0
$3$	−0.527750	+	1.64969i	−0.304696	+	0.952450i
$3$	−0.527750	+	1.64969i	−0.304696	+	0.952450i
$4$		0			0
$5$	−0.220114	+	1.24833i	−0.0984379	+	0.558269i	0.895202	+	0.445661i	$0.147031\pi$
$5$	−0.220114	+	1.24833i	−0.0984379	+	0.558269i	−0.993640	+	0.112608i	$0.964080\pi$
$6$		0			0
$7$	2.06659	−	1.73408i	0.781098	−	0.655419i	−0.162427	−	0.986721i	$-0.551932\pi$
$7$	2.06659	−	1.73408i	0.781098	−	0.655419i	0.943525	+	0.331301i	$0.107488\pi$
$8$		0			0
$9$	−2.44296	−	1.74125i	−0.814320	−	0.580416i
$10$		0			0
$11$	−0.816598	−	4.63116i	−0.246213	−	1.39635i	−0.817657	−	0.575705i	$-0.804728\pi$
$11$	−0.816598	−	4.63116i	−0.246213	−	1.39635i	0.571444	−	0.820641i	$-0.306383\pi$
$12$		0			0
$13$	5.12114	−	1.86394i	1.42035	−	0.516965i	0.486201	−	0.873847i	$-0.338382\pi$
$13$	5.12114	−	1.86394i	1.42035	−	0.516965i	0.934149	+	0.356882i	$0.116160\pi$
$14$		0			0
$15$	−1.94319	−	1.02192i	−0.501729	−	0.263860i
$16$		0			0
$17$	2.58790	−	4.48237i	0.627657	−	1.08713i	−0.360363	−	0.932812i	$-0.617347\pi$
$17$	2.58790	−	4.48237i	0.627657	−	1.08713i	0.988021	−	0.154322i	$-0.0493195\pi$
$18$		0			0
$19$	1.60795	+	2.78505i	0.368889	+	0.638935i	0.989392	−	0.145269i	$-0.0464048\pi$
$19$	1.60795	+	2.78505i	0.368889	+	0.638935i	−0.620503	+	0.784204i	$0.713071\pi$
$20$		0			0
$21$	1.77005	+	4.32440i	0.386256	+	0.943660i
$22$		0			0
$23$	−5.70640	−	4.78823i	−1.18987	−	0.998416i	−0.999862	−	0.0166326i	$-0.994705\pi$
$23$	−5.70640	−	4.78823i	−1.18987	−	0.998416i	−0.190004	−	0.981783i	$-0.560850\pi$
$24$		0			0
$25$	3.18859	+	1.16055i	0.637718	+	0.232111i
$26$		0			0
$27$	4.16179	−	3.11119i	0.800937	−	0.598748i
$28$		0			0
$29$	4.64667	+	1.69125i	0.862865	+	0.314057i	0.735274	−	0.677770i	$-0.237053\pi$
$29$	4.64667	+	1.69125i	0.862865	+	0.314057i	0.127591	+	0.991827i	$0.459276\pi$
$30$		0			0
$31$	−5.45581	−	4.57797i	−0.979893	−	0.822228i	0.00418016	−	0.999991i	$-0.498669\pi$
$31$	−5.45581	−	4.57797i	−0.979893	−	0.822228i	−0.984073	+	0.177763i	$0.943114\pi$
$32$		0			0
$33$	8.07094	+	1.09696i	1.40497	+	0.190956i
$34$		0			0
$35$	1.70981	+	2.96148i	0.289010	+	0.500581i
$36$		0			0
$37$	−4.05878	+	7.03001i	−0.667259	+	1.15573i	0.311408	+	0.950276i	$0.399199\pi$
$37$	−4.05878	+	7.03001i	−0.667259	+	1.15573i	−0.978667	+	0.205451i	$0.934134\pi$
$38$		0			0
$39$	0.372250	+	9.43200i	0.0596077	+	1.51033i
$40$		0			0
$41$	5.89007	−	2.14381i	0.919875	−	0.334807i	0.161686	−	0.986842i	$-0.448307\pi$
$41$	5.89007	−	2.14381i	0.919875	−	0.334807i	0.758189	+	0.652035i	$0.226085\pi$
$42$		0			0
$43$	1.35464	+	7.68253i	0.206580	+	1.17158i	0.894933	+	0.446200i	$0.147223\pi$
$43$	1.35464	+	7.68253i	0.206580	+	1.17158i	−0.688353	+	0.725376i	$0.741666\pi$
$44$		0			0
$45$	2.71138	−	2.66634i	0.404188	−	0.397475i
$46$		0			0
$47$	−3.37956	+	2.83579i	−0.492960	+	0.413642i	−0.855086	−	0.518487i	$-0.826495\pi$
$47$	−3.37956	+	2.83579i	−0.492960	+	0.413642i	0.362126	+	0.932129i	$0.382051\pi$
$48$		0			0
$49$	0.0482428	−	0.273599i	0.00689184	−	0.0390855i
$50$		0			0
$51$	6.02876	+	6.63480i	0.844196	+	0.929058i
$52$		0			0
$53$	−5.40231			−0.742064			−0.371032	−	0.928620i	$-0.620996\pi$
$53$	−5.40231			−0.742064			−0.371032	+	0.928620i	$0.620996\pi$
$54$		0			0
$55$	5.96094			0.803773
$56$		0			0
$57$	−5.44307	+	1.18281i	−0.720953	+	0.156667i
$58$		0			0
$59$	0.563127	−	3.19365i	0.0733129	−	0.415778i	−0.925959	−	0.377624i	$-0.876741\pi$
$59$	0.563127	−	3.19365i	0.0733129	−	0.415778i	0.999272	−	0.0381540i	$-0.0121477\pi$
$60$		0			0
$61$	2.83148	−	2.37590i	0.362534	−	0.304202i	−0.443266	−	0.896390i	$-0.646180\pi$
$61$	2.83148	−	2.37590i	0.362534	−	0.304202i	0.805800	+	0.592188i	$0.201736\pi$
$62$		0			0
$63$	−8.06806	+	0.637833i	−1.01648	+	0.0803594i
$64$		0			0
$65$	1.19958	+	6.80314i	0.148789	+	0.843826i
$66$		0			0
$67$	12.7036	−	4.62375i	1.55200	−	0.564881i	0.583112	−	0.812392i	$-0.301835\pi$
$67$	12.7036	−	4.62375i	1.55200	−	0.564881i	0.968885	+	0.247511i	$0.0796127\pi$
$68$		0			0
$69$	10.9107	−	6.88680i	1.31349	−	0.829073i
$70$		0			0
$71$	1.66453	−	2.88306i	0.197544	−	0.342156i	−0.750188	−	0.661225i	$-0.770037\pi$
$71$	1.66453	−	2.88306i	0.197544	−	0.342156i	0.947731	+	0.319069i	$0.103370\pi$
$72$		0			0
$73$	−4.27984	−	7.41290i	−0.500918	−	0.867615i	−0.999999	−	0.00105997i	$-0.999663\pi$
$73$	−4.27984	−	7.41290i	−0.500918	−	0.867615i	0.499082	−	0.866555i	$-0.333671\pi$
$74$		0			0
$75$	−3.59733	+	4.64771i	−0.415384	+	0.536671i
$76$		0			0
$77$	−9.71835	−	8.15466i	−1.10751	−	0.929310i
$78$		0			0
$79$	7.44075	+	2.70821i	0.837150	+	0.304698i	0.724790	−	0.688970i	$-0.241937\pi$
$79$	7.44075	+	2.70821i	0.837150	+	0.304698i	0.112360	+	0.993668i	$0.464159\pi$
$80$		0			0
$81$	2.93611	+	8.50760i	0.326235	+	0.945289i
$82$		0			0
$83$	−3.51149	−	1.27808i	−0.385436	−	0.140287i	0.142032	−	0.989862i	$-0.454636\pi$
$83$	−3.51149	−	1.27808i	−0.385436	−	0.140287i	−0.527468	+	0.849575i	$0.676859\pi$
$84$		0			0
$85$	5.02583	+	4.21717i	0.545128	+	0.457417i
$86$		0			0
$87$	−5.24232	+	6.77301i	−0.562035	+	0.726143i
$88$		0			0
$89$	8.80137	+	15.2444i	0.932943	+	1.61590i	0.778262	+	0.627940i	$0.216102\pi$
$89$	8.80137	+	15.2444i	0.932943	+	1.61590i	0.154681	+	0.987964i	$0.450565\pi$
$90$		0			0
$91$	7.35109	−	12.7325i	0.770604	−	1.33473i
$92$		0			0
$93$	10.4315	−	6.58438i	1.08170	−	0.682769i
$94$		0			0
$95$	−3.83059	+	1.39422i	−0.393010	+	0.143044i
$96$		0			0
$97$	−2.21046	−	12.5361i	−0.224438	−	1.27285i	−0.863757	−	0.503909i	$-0.831895\pi$
$97$	−2.21046	−	12.5361i	−0.224438	−	1.27285i	0.639319	−	0.768942i	$-0.279217\pi$
$98$		0			0
$99$	−6.06907	+	12.7356i	−0.609965	+	1.27998i
$100$		0			0
$101$	3.68844	−	3.09497i	0.367013	−	0.307961i	−0.440566	−	0.897720i	$-0.645222\pi$
$101$	3.68844	−	3.09497i	0.367013	−	0.307961i	0.807579	+	0.589760i	$0.200778\pi$
$102$		0			0
$103$	−0.898013	+	5.09289i	−0.0884839	+	0.501817i	0.908066	+	0.418826i	$0.137558\pi$
$103$	−0.898013	+	5.09289i	−0.0884839	+	0.501817i	−0.996550	+	0.0829908i	$0.973553\pi$
$104$		0			0
$105$	−5.78787	+	1.25774i	−0.564838	+	0.122743i
$106$		0			0
$107$	−5.82640			−0.563259			−0.281630	−	0.959523i	$-0.590875\pi$
$107$	−5.82640			−0.563259			−0.281630	+	0.959523i	$0.590875\pi$
$108$		0			0
$109$	−5.14353			−0.492661			−0.246330	−	0.969186i	$-0.579225\pi$
$109$	−5.14353			−0.492661			−0.246330	+	0.969186i	$0.579225\pi$
$110$		0			0
$111$	−9.45533	−	10.4058i	−0.897460	−	0.987676i
$112$		0			0
$113$	1.98557	−	11.2607i	0.186787	−	1.05932i	−0.736851	−	0.676055i	$-0.763688\pi$
$113$	1.98557	−	11.2607i	0.186787	−	1.05932i	0.923638	−	0.383266i	$-0.125201\pi$
$114$		0			0
$115$	7.23334	−	6.06949i	0.674512	−	0.565983i
$116$		0			0
$117$	−15.7563	−	4.36364i	−1.45667	−	0.403418i
$118$		0			0
$119$	−2.42464	−	13.7508i	−0.222267	−	1.26054i
$120$		0			0
$121$	−10.4442	+	3.80136i	−0.949469	+	0.345578i
$122$		0			0
$123$	0.428143	+	10.8482i	0.0386043	+	0.978149i
$124$		0			0
$125$	−5.31956	+	9.21376i	−0.475796	+	0.824103i
$126$		0			0
$127$	−1.25691	−	2.17703i	−0.111533	−	0.193180i	0.804856	−	0.593471i	$-0.202243\pi$
$127$	−1.25691	−	2.17703i	−0.111533	−	0.193180i	−0.916388	+	0.400290i	$0.868909\pi$
$128$		0			0
$129$	−13.3887	−	1.81972i	−1.17881	−	0.160217i
$130$		0			0
$131$	−5.80475	−	4.87076i	−0.507163	−	0.425561i	0.352966	−	0.935636i	$-0.385173\pi$
$131$	−5.80475	−	4.87076i	−0.507163	−	0.425561i	−0.860130	+	0.510075i	$0.829617\pi$
$132$		0			0
$133$	8.15247	+	2.96726i	0.706909	+	0.257294i
$134$		0			0
$135$	2.96771	+	5.88009i	0.255420	+	0.506078i
$136$		0			0
$137$	11.1601	+	4.06194i	0.953470	+	0.347035i	0.771471	−	0.636264i	$-0.219521\pi$
$137$	11.1601	+	4.06194i	0.953470	+	0.347035i	0.181999	+	0.983299i	$0.441743\pi$
$138$		0			0
$139$	6.40951	+	5.37821i	0.543647	+	0.456174i	0.872783	−	0.488108i	$-0.162313\pi$
$139$	6.40951	+	5.37821i	0.543647	+	0.456174i	−0.329136	+	0.944283i	$0.606757\pi$
$140$		0			0
$141$	−2.89461	−	7.07182i	−0.243770	−	0.595554i
$142$		0			0
$143$	−12.8141	−	22.1947i	−1.07157	−	1.85602i
$144$		0			0
$145$	−3.13403	+	5.42830i	−0.260267	+	0.450795i
$146$		0			0
$147$	0.425893	+	0.223977i	0.0351271	+	0.0184733i
$148$		0			0
$149$	−17.8097	+	6.48222i	−1.45903	+	0.531044i	−0.945098	−	0.326787i	$-0.894034\pi$
$149$	−17.8097	+	6.48222i	−1.45903	+	0.531044i	−0.513933	+	0.857830i	$0.671812\pi$
$150$		0			0
$151$	−1.56863	−	8.89614i	−0.127653	−	0.723958i	−0.979697	−	0.200486i	$-0.935748\pi$
$151$	−1.56863	−	8.89614i	−0.127653	−	0.723958i	0.852043	−	0.523471i	$-0.175363\pi$
$152$		0			0
$153$	−14.1270	+	6.44408i	−1.14210	+	0.520973i
$154$		0			0
$155$	6.91571	−	5.80297i	0.555483	−	0.466105i
$156$		0			0
$157$	−2.98000	+	16.9004i	−0.237830	+	1.34880i	0.598741	+	0.800943i	$0.295668\pi$
$157$	−2.98000	+	16.9004i	−0.237830	+	1.34880i	−0.836571	+	0.547859i	$0.815443\pi$
$158$		0			0
$159$	2.85107	−	8.91214i	0.226104	−	0.706779i
$160$		0			0
$161$	−20.0960			−1.58378
$162$		0			0
$163$	13.4899			1.05661			0.528304	−	0.849056i	$-0.322828\pi$
$163$	13.4899			1.05661			0.528304	+	0.849056i	$0.322828\pi$
$164$		0			0
$165$	−3.14588	+	9.83371i	−0.244907	+	0.765554i
$166$		0			0
$167$	−2.74280	+	15.5552i	−0.212245	+	1.20370i	0.673380	+	0.739297i	$0.264842\pi$
$167$	−2.74280	+	15.5552i	−0.212245	+	1.20370i	−0.885624	+	0.464402i	$0.846269\pi$
$168$		0			0
$169$	12.7933	−	10.7348i	0.984097	−	0.825755i
$170$		0			0
$171$	0.921305	−	9.60362i	0.0704540	−	0.734407i
$172$		0			0
$173$	0.206065	+	1.16865i	0.0156668	+	0.0888510i	0.991639	−	0.129046i	$-0.0411915\pi$
$173$	0.206065	+	1.16865i	0.0156668	+	0.0888510i	−0.975972	+	0.217897i	$0.930080\pi$
$174$		0			0
$175$	8.60200	−	3.13087i	0.650250	−	0.236672i
$176$		0			0
$177$	4.97135	+	2.61443i	0.373669	+	0.196513i
$178$		0			0
$179$	−3.69819	+	6.40545i	−0.276416	+	0.478766i	−0.970491	−	0.241136i	$-0.922480\pi$
$179$	−3.69819	+	6.40545i	−0.276416	+	0.478766i	0.694076	+	0.719902i	$0.255813\pi$
$180$		0			0
$181$	−9.87045	−	17.0961i	−0.733665	−	1.27074i	−0.955307	−	0.295616i	$-0.904475\pi$
$181$	−9.87045	−	17.0961i	−0.733665	−	1.27074i	0.221642	−	0.975128i	$-0.428858\pi$
$182$		0			0
$183$	2.42518	+	5.92495i	0.179274	+	0.437985i
$184$		0			0
$185$	−7.88236	−	6.61409i	−0.579523	−	0.486277i
$186$		0			0
$187$	−22.8718	−	8.32467i	−1.67255	−	0.608760i
$188$		0			0
$189$	3.20569	−	13.6464i	0.233179	−	0.992631i
$190$		0			0
$191$	4.84225	+	1.76244i	0.350373	+	0.127525i	0.511211	−	0.859455i	$-0.329197\pi$
$191$	4.84225	+	1.76244i	0.350373	+	0.127525i	−0.160837	+	0.986981i	$0.551419\pi$
$192$		0			0
$193$	10.4522	+	8.77044i	0.752366	+	0.631310i	0.936128	−	0.351661i	$-0.114383\pi$
$193$	10.4522	+	8.77044i	0.752366	+	0.631310i	−0.183761	+	0.982971i	$0.558827\pi$
$194$		0			0
$195$	−11.8562	−	1.61142i	−0.849037	−	0.115396i
$196$		0			0
$197$	−5.85638	−	10.1435i	−0.417250	−	0.722698i	0.578412	−	0.815745i	$-0.303673\pi$
$197$	−5.85638	−	10.1435i	−0.417250	−	0.722698i	−0.995662	+	0.0930469i	$0.970339\pi$
$198$		0			0
$199$	−6.43862	+	11.1520i	−0.456422	+	0.790546i	−0.998769	−	0.0496087i	$-0.984203\pi$
$199$	−6.43862	+	11.1520i	−0.456422	+	0.790546i	0.542347	+	0.840155i	$0.317536\pi$
$200$		0			0
$201$	0.923413	+	23.3973i	0.0651325	+	1.65032i
$202$		0			0
$203$	12.5355	−	4.56256i	0.879821	−	0.320229i
$204$		0			0
$205$	1.37969	+	7.82462i	0.0963618	+	0.546495i
$206$		0			0
$207$	5.60300	+	21.6337i	0.389435	+	1.50365i
$208$		0			0
$209$	11.5850	−	9.72094i	0.801349	−	0.672412i
$210$		0			0
$211$	−0.729719	+	4.13844i	−0.0502359	+	0.284902i	−0.999569	−	0.0293709i	$-0.990650\pi$
$211$	−0.729719	+	4.13844i	−0.0502359	+	0.284902i	0.949333	+	0.314273i	$0.101761\pi$
$212$		0			0
$213$	3.87770	+	4.26750i	0.265695	+	0.292404i
$214$		0			0
$215$	−9.88849			−0.674389
$216$		0			0
$217$	−19.2135			−1.30430
$218$		0			0
$219$	14.4877	−	3.14826i	0.978987	−	0.212740i
$220$		0			0
$221$	4.89811	−	27.7786i	0.329483	−	1.86859i
$222$		0			0
$223$	12.7882	−	10.7306i	0.856360	−	0.718572i	−0.104820	−	0.994491i	$-0.533427\pi$
$223$	12.7882	−	10.7306i	0.856360	−	0.718572i	0.961181	+	0.275920i	$0.0889824\pi$
$224$		0			0
$225$	−5.76880	−	8.38731i	−0.384586	−	0.559154i
$226$		0			0
$227$	3.30400	+	18.7379i	0.219294	+	1.24368i	0.873297	+	0.487188i	$0.161977\pi$
$227$	3.30400	+	18.7379i	0.219294	+	1.24368i	−0.654003	+	0.756492i	$0.726912\pi$
$228$		0			0
$229$	5.59040	−	2.03474i	0.369424	−	0.134459i	−0.150636	−	0.988589i	$-0.548132\pi$
$229$	5.59040	−	2.03474i	0.369424	−	0.134459i	0.520059	+	0.854130i	$0.325910\pi$
$230$		0			0
$231$	18.5815	−	11.7287i	1.22258	−	0.771689i
$232$		0			0
$233$	−4.49876	+	7.79208i	−0.294724	+	0.510476i	−0.974921	−	0.222553i	$-0.928561\pi$
$233$	−4.49876	+	7.79208i	−0.294724	+	0.510476i	0.680197	+	0.733029i	$0.261894\pi$
$234$		0			0
$235$	−2.79610	−	4.84299i	−0.182398	−	0.315922i
$236$		0			0
$237$	−8.39456	+	10.8457i	−0.545285	+	0.704503i
$238$		0			0
$239$	0.116156	+	0.0974665i	0.00751351	+	0.00630458i	0.646537	−	0.762883i	$-0.276217\pi$
$239$	0.116156	+	0.0974665i	0.00751351	+	0.00630458i	−0.639023	+	0.769188i	$0.720661\pi$
$240$		0			0
$241$	−25.2581	−	9.19320i	−1.62702	−	0.592186i	−0.642317	−	0.766439i	$-0.722027\pi$
$241$	−25.2581	−	9.19320i	−1.62702	−	0.592186i	−0.984701	+	0.174253i	$0.944249\pi$
$242$		0			0
$243$	−15.5844	+	0.353800i	−0.999742	+	0.0226963i
$244$		0			0
$245$	0.330922	+	0.120446i	0.0211418	+	0.00769499i
$246$		0			0
$247$	13.4257	+	11.2655i	0.854259	+	0.716808i
$248$		0			0
$249$	3.96162	−	5.11837i	0.251057	−	0.324363i
$250$		0			0
$251$	−1.76741	−	3.06124i	−0.111558	−	0.193224i	0.804841	−	0.593491i	$-0.202251\pi$
$251$	−1.76741	−	3.06124i	−0.111558	−	0.193224i	−0.916399	+	0.400267i	$0.868917\pi$
$252$		0			0
$253$	−17.5152	+	30.3373i	−1.10117	+	1.90729i
$254$		0			0
$255$	−9.60942	+	6.06546i	−0.601765	+	0.379834i
$256$		0			0
$257$	6.67482	−	2.42944i	0.416364	−	0.151544i	−0.125339	−	0.992114i	$-0.540002\pi$
$257$	6.67482	−	2.42944i	0.416364	−	0.151544i	0.541703	+	0.840570i	$0.317780\pi$
$258$		0			0
$259$	3.80274	+	21.5664i	0.236291	+	1.34007i
$260$		0			0
$261$	−8.40675	−	12.2227i	−0.520365	−	0.756563i
$262$		0			0
$263$	−2.36713	+	1.98626i	−0.145963	+	0.122478i	−0.712846	−	0.701321i	$-0.752594\pi$
$263$	−2.36713	+	1.98626i	−0.145963	+	0.122478i	0.566882	+	0.823799i	$0.308149\pi$
$264$		0			0
$265$	1.18912	−	6.74385i	0.0730472	−	0.414271i
$266$		0			0
$267$	−29.7935	+	6.47430i	−1.82333	+	0.396221i
$268$		0			0
$269$	−19.4091			−1.18340			−0.591698	−	0.806160i	$-0.701542\pi$
$269$	−19.4091			−1.18340			−0.591698	+	0.806160i	$0.701542\pi$
$270$		0			0
$271$	−15.3654			−0.933380			−0.466690	−	0.884421i	$-0.654554\pi$
$271$	−15.3654			−0.933380			−0.466690	+	0.884421i	$0.654554\pi$
$272$		0			0
$273$	17.1251	+	18.8466i	1.03646	+	1.14065i
$274$		0			0
$275$	2.77090	−	15.7146i	0.167092	−	0.947624i
$276$		0			0
$277$	4.46848	−	3.74950i	0.268485	−	0.225285i	−0.498599	−	0.866833i	$-0.666152\pi$
$277$	4.46848	−	3.74950i	0.268485	−	0.225285i	0.767083	+	0.641548i	$0.221707\pi$
$278$		0			0
$279$	5.35696	+	20.6837i	0.320713	+	1.23830i
$280$		0			0
$281$	0.0948868	+	0.538130i	0.00566047	+	0.0321021i	0.987507	−	0.157574i	$-0.0503673\pi$
$281$	0.0948868	+	0.538130i	0.00566047	+	0.0321021i	−0.981847	+	0.189676i	$0.939256\pi$
$282$		0			0
$283$	−8.73569	+	3.17953i	−0.519283	+	0.189004i	−0.588347	−	0.808609i	$-0.700221\pi$
$283$	−8.73569	+	3.17953i	−0.519283	+	0.189004i	0.0690638	+	0.997612i	$0.477999\pi$
$284$		0			0
$285$	−0.278441	−	7.05509i	−0.0164934	−	0.417907i
$286$		0			0
$287$	8.45484	−	14.6442i	0.499073	−	0.864421i
$288$		0			0
$289$	−4.89443	−	8.47740i	−0.287908	−	0.498671i
$290$		0			0
$291$	21.8473	+	2.96937i	1.28071	+	0.174067i
$292$		0			0
$293$	14.9099	+	12.5109i	0.871044	+	0.730893i	0.964318	−	0.264748i	$-0.0852886\pi$
$293$	14.9099	+	12.5109i	0.871044	+	0.730893i	−0.0932735	+	0.995641i	$0.529733\pi$
$294$		0			0
$295$	3.86277	+	1.40593i	0.224899	+	0.0818566i
$296$		0			0
$297$	−17.8069	−	16.7333i	−1.03326	−	0.970966i
$298$		0			0
$299$	−38.1483	−	13.8848i	−2.20617	−	0.802981i
$300$		0			0
$301$	16.1216	+	13.5276i	0.929232	+	0.779719i
$302$		0			0
$303$	3.15917	+	7.71815i	0.181489	+	0.443396i
$304$		0			0
$305$	2.34265	+	4.05758i	0.134140	+	0.232337i
$306$		0			0
$307$	−7.10010	+	12.2977i	−0.405224	+	0.701869i	−0.994348	−	0.106174i	$-0.966140\pi$
$307$	−7.10010	+	12.2977i	−0.405224	+	0.701869i	0.589123	+	0.808043i	$0.299473\pi$
$308$		0			0
$309$	−7.92776	−	4.16921i	−0.450995	−	0.237178i
$310$		0			0
$311$	11.3415	−	4.12799i	0.643120	−	0.234077i	0.000188266	−	1.00000i	$-0.499940\pi$
$311$	11.3415	−	4.12799i	0.643120	−	0.234077i	0.642932	+	0.765923i	$0.277718\pi$
$312$		0			0
$313$	−4.80051	−	27.2251i	−0.271341	−	1.53885i	−0.750349	−	0.661042i	$-0.770115\pi$
$313$	−4.80051	−	27.2251i	−0.271341	−	1.53885i	0.479008	−	0.877810i	$-0.340996\pi$
$314$		0			0
$315$	0.979666	−	10.2120i	0.0551979	−	0.575379i
$316$		0			0
$317$	−9.63253	+	8.08265i	−0.541017	+	0.453967i	−0.871886	−	0.489710i	$-0.837103\pi$
$317$	−9.63253	+	8.08265i	−0.541017	+	0.453967i	0.330869	+	0.943677i	$0.392658\pi$
$318$		0			0
$319$	4.03798	−	22.9005i	0.226083	−	1.28218i
$320$		0			0
$321$	3.07488	−	9.61176i	0.171623	−	0.536476i
$322$		0			0
$323$	16.6449			0.926144
$324$		0			0
$325$	18.4924			1.02578
$326$		0			0
$327$	2.71450	−	8.48524i	0.150112	−	0.469235i
$328$		0			0
$329$	−2.06670	+	11.7208i	−0.113941	+	0.646190i
$330$		0			0
$331$	12.7463	−	10.6954i	0.700598	−	0.587872i	−0.221345	−	0.975195i	$-0.571045\pi$
$331$	12.7463	−	10.6954i	0.700598	−	0.587872i	0.921944	+	0.387324i	$0.126600\pi$
$332$		0			0
$333$	22.1564	−	10.1067i	1.21416	−	0.553844i
$334$		0			0
$335$	2.97570	+	16.8761i	0.162580	+	0.922037i
$336$		0			0
$337$	25.2065	−	9.17443i	1.37309	−	0.499763i	0.453012	−	0.891504i	$-0.350349\pi$
$337$	25.2065	−	9.17443i	1.37309	−	0.499763i	0.920075	+	0.391741i	$0.128127\pi$
$338$		0			0
$339$	17.5289	+	9.21844i	0.952037	+	0.500677i
$340$		0			0
$341$	−16.7461	+	29.0051i	−0.906852	+	1.57071i
$342$		0			0
$343$	9.06736	+	15.7051i	0.489591	+	0.847997i
$344$		0			0
$345$	6.19540	+	15.1359i	0.333549	+	0.814892i
$346$		0			0
$347$	−11.0406	−	9.26420i	−0.592693	−	0.497328i	0.296395	−	0.955066i	$-0.404216\pi$
$347$	−11.0406	−	9.26420i	−0.592693	−	0.497328i	−0.889088	+	0.457737i	$0.848660\pi$
$348$		0			0
$349$	−4.04973	−	1.47398i	−0.216777	−	0.0789003i	0.231349	−	0.972871i	$-0.425686\pi$
$349$	−4.04973	−	1.47398i	−0.216777	−	0.0789003i	−0.448126	+	0.893971i	$0.647908\pi$
$350$		0			0
$351$	15.5141	−	23.6902i	0.828079	−	1.26449i
$352$		0			0
$353$	29.2380	+	10.6418i	1.55618	+	0.566404i	0.969858	−	0.243671i	$-0.0783518\pi$
$353$	29.2380	+	10.6418i	1.55618	+	0.566404i	0.586325	+	0.810076i	$0.300574\pi$
$354$		0			0
$355$	3.23261	+	2.71248i	0.171569	+	0.143964i
$356$		0			0
$357$	23.9642	+	3.25709i	1.26832	+	0.172383i
$358$		0			0
$359$	15.7551	+	27.2887i	0.831524	+	1.44024i	0.896829	+	0.442377i	$0.145865\pi$
$359$	15.7551	+	27.2887i	0.831524	+	1.44024i	−0.0653054	+	0.997865i	$0.520802\pi$
$360$		0			0
$361$	4.32899	−	7.49802i	0.227841	−	0.394633i
$362$		0			0
$363$	−0.759174	−	19.2358i	−0.0398463	−	1.00962i
$364$		0			0
$365$	10.1958	−	3.71096i	0.533672	−	0.194241i
$366$		0			0
$367$	4.28801	+	24.3185i	0.223832	+	1.26941i	0.864905	+	0.501935i	$0.167378\pi$
$367$	4.28801	+	24.3185i	0.223832	+	1.26941i	−0.641073	+	0.767480i	$0.721511\pi$
$368$		0			0
$369$	−18.1221	−	5.01883i	−0.943400	−	0.261270i
$370$		0			0
$371$	−11.1644	+	9.36802i	−0.579625	+	0.486363i
$372$		0			0
$373$	−4.51846	+	25.6255i	−0.233957	+	1.32684i	0.610842	+	0.791753i	$0.290831\pi$
$373$	−4.51846	+	25.6255i	−0.233957	+	1.32684i	−0.844799	+	0.535084i	$0.820280\pi$
$374$		0			0
$375$	−12.3925	−	13.6382i	−0.639943	−	0.704273i
$376$		0			0
$377$	26.9487			1.38793
$378$		0			0
$379$	−24.8139			−1.27460			−0.637301	−	0.770615i	$-0.719949\pi$
$379$	−24.8139			−1.27460			−0.637301	+	0.770615i	$0.719949\pi$
$380$		0			0
$381$	4.25476	−	0.924586i	0.217978	−	0.0473680i
$382$		0			0
$383$	−1.49968	+	8.50513i	−0.0766303	+	0.434592i	0.922221	+	0.386664i	$0.126373\pi$
$383$	−1.49968	+	8.50513i	−0.0766303	+	0.434592i	−0.998851	+	0.0479277i	$0.984738\pi$
$384$		0			0
$385$	12.3188	−	10.3367i	0.627826	−	0.526808i
$386$		0			0
$387$	10.0679	−	21.1269i	0.511778	−	1.07394i
$388$		0			0
$389$	2.49620	+	14.1566i	0.126562	+	0.717770i	0.980368	+	0.197178i	$0.0631777\pi$
$389$	2.49620	+	14.1566i	0.126562	+	0.717770i	−0.853806	+	0.520592i	$0.825711\pi$
$390$		0			0
$391$	−36.2302	+	13.1867i	−1.83224	+	0.666881i
$392$		0			0
$393$	11.0987	−	7.00550i	0.559856	−	0.353381i
$394$		0			0
$395$	−5.01854	+	8.69237i	−0.252510	+	0.437361i
$396$		0			0
$397$	10.6310	+	18.4134i	0.533554	+	0.924142i	0.999232	+	0.0391881i	$0.0124772\pi$
$397$	10.6310	+	18.4134i	0.533554	+	0.924142i	−0.465678	+	0.884954i	$0.654189\pi$
$398$		0			0
$399$	−9.19752	+	11.8831i	−0.460452	+	0.594899i
$400$		0			0
$401$	−14.6342	−	12.2796i	−0.730797	−	0.613212i	0.199551	−	0.979887i	$-0.436051\pi$
$401$	−14.6342	−	12.2796i	−0.730797	−	0.613212i	−0.930349	+	0.366675i	$0.880496\pi$
$402$		0			0
$403$	−36.4731	−	13.2751i	−1.81685	−	0.661281i
$404$		0			0
$405$	−11.2665	+	1.79259i	−0.559839	+	0.0890746i
$406$		0			0
$407$	35.8715	+	13.0561i	1.77808	+	0.647169i
$408$		0			0
$409$	1.14783	+	0.963146i	0.0567567	+	0.0476245i	0.670725	−	0.741706i	$-0.265983\pi$
$409$	1.14783	+	0.963146i	0.0567567	+	0.0476245i	−0.613968	+	0.789331i	$0.710428\pi$
$410$		0			0
$411$	−12.5907	+	16.2670i	−0.621052	+	0.802392i
$412$		0			0
$413$	−4.37428	−	7.57648i	−0.215244	−	0.372814i
$414$		0			0
$415$	2.36839	−	4.10216i	0.116259	−	0.201367i
$416$		0			0
$417$	−12.2550	+	7.73535i	−0.600130	+	0.378802i
$418$		0			0
$419$	14.0890	−	5.12799i	0.688294	−	0.250519i	0.0258894	−	0.999665i	$-0.491758\pi$
$419$	14.0890	−	5.12799i	0.688294	−	0.250519i	0.662405	+	0.749146i	$0.269536\pi$
$420$		0			0
$421$	−6.32688	−	35.8815i	−0.308353	−	1.74876i	−0.607286	−	0.794483i	$-0.707742\pi$
$421$	−6.32688	−	35.8815i	−0.308353	−	1.74876i	0.298933	−	0.954274i	$-0.403369\pi$
$422$		0			0
$423$	13.1939	−	1.04307i	0.641512	−	0.0507157i
$424$		0			0
$425$	13.4538	−	11.2891i	0.652604	−	0.547600i
$426$		0			0
$427$	1.73153	−	9.82001i	0.0837948	−	0.475224i
$428$		0			0
$429$	43.3771	−	9.42610i	2.09427	−	0.455096i
$430$		0			0
$431$	3.36144			0.161915			0.0809574	−	0.996718i	$-0.474202\pi$
$431$	3.36144			0.161915			0.0809574	+	0.996718i	$0.474202\pi$
$432$		0			0
$433$	−28.8661			−1.38722			−0.693609	−	0.720351i	$-0.743981\pi$
$433$	−28.8661			−1.38722			−0.693609	+	0.720351i	$0.743981\pi$
$434$		0			0
$435$	−7.30103	−	8.03496i	−0.350058	−	0.385247i
$436$		0			0
$437$	4.15988	−	23.5919i	0.198994	−	1.12855i
$438$		0			0
$439$	23.4484	−	19.6756i	1.11913	−	0.939064i	0.120573	−	0.992705i	$-0.461527\pi$
$439$	23.4484	−	19.6756i	1.11913	−	0.939064i	0.998560	+	0.0536405i	$0.0170825\pi$
$440$		0			0
$441$	−0.594259	+	0.584388i	−0.0282980	+	0.0278280i
$442$		0			0
$443$	−0.575529	−	3.26399i	−0.0273442	−	0.155077i	0.968078	−	0.250647i	$-0.0806435\pi$
$443$	−0.575529	−	3.26399i	−0.0273442	−	0.155077i	−0.995423	+	0.0955708i	$0.969532\pi$
$444$		0			0
$445$	−20.9673	+	7.63148i	−0.993946	+	0.361767i
$446$		0			0
$447$	−1.29457	−	32.8016i	−0.0612310	−	1.55146i
$448$		0			0
$449$	−16.7574	+	29.0247i	−0.790830	+	1.36976i	0.134623	+	0.990897i	$0.457018\pi$
$449$	−16.7574	+	29.0247i	−0.790830	+	1.36976i	−0.925453	+	0.378861i	$0.876316\pi$
$450$		0			0
$451$	−14.7381	−	25.5272i	−0.693992	−	1.20203i
$452$		0			0
$453$	15.5037	+	2.10718i	0.728429	+	0.0990040i
$454$		0			0
$455$	14.2762	+	11.9792i	0.669279	+	0.561592i
$456$		0			0
$457$	25.6967	+	9.35282i	1.20204	+	0.437506i	0.863935	−	0.503603i	$-0.167992\pi$
$457$	25.6967	+	9.35282i	1.20204	+	0.437506i	0.338103	+	0.941109i	$0.390215\pi$
$458$		0			0
$459$	−3.17520	−	26.7061i	−0.148206	−	1.24654i
$460$		0			0
$461$	1.64642	+	0.599249i	0.0766816	+	0.0279098i	0.380076	−	0.924955i	$-0.375898\pi$
$461$	1.64642	+	0.599249i	0.0766816	+	0.0279098i	−0.303395	+	0.952865i	$0.598120\pi$
$462$		0			0
$463$	−30.9320	−	25.9550i	−1.43753	−	1.20623i	−0.941087	−	0.338164i	$-0.890194\pi$
$463$	−30.9320	−	25.9550i	−1.43753	−	1.20623i	−0.496445	−	0.868068i	$-0.665362\pi$
$464$		0			0
$465$	5.92334	+	14.4713i	0.274688	+	0.671090i
$466$		0			0
$467$	14.0139	+	24.2728i	0.648486	+	1.12321i	0.983485	+	0.180992i	$0.0579308\pi$
$467$	14.0139	+	24.2728i	0.648486	+	1.12321i	−0.334999	+	0.942219i	$0.608736\pi$
$468$		0			0
$469$	18.2353	−	31.5845i	0.842028	−	1.45844i
$470$		0			0
$471$	−26.3078	−	13.8353i	−1.21220	−	0.637496i
$472$		0			0
$473$	34.4728	−	12.5471i	1.58506	−	0.576915i
$474$		0			0
$475$	1.89490	+	10.7465i	0.0869440	+	0.493084i
$476$		0			0
$477$	13.1976	+	9.40676i	0.604278	+	0.430706i
$478$		0			0
$479$	19.2328	−	16.1383i	0.878771	−	0.737376i	−0.0871552	−	0.996195i	$-0.527778\pi$
$479$	19.2328	−	16.1383i	0.878771	−	0.737376i	0.965926	+	0.258819i	$0.0833332\pi$
$480$		0			0
$481$	−7.68205	+	43.5670i	−0.350271	+	1.98649i
$482$		0			0
$483$	10.6056	−	33.1521i	0.482573	−	1.50847i
$484$		0			0
$485$	16.1357			0.732687
$486$		0			0
$487$	8.94330			0.405260			0.202630	−	0.979255i	$-0.435051\pi$
$487$	8.94330			0.405260			0.202630	+	0.979255i	$0.435051\pi$
$488$		0			0
$489$	−7.11927	+	22.2541i	−0.321944	+	1.00636i
$490$		0			0
$491$	−3.62742	+	20.5721i	−0.163703	+	0.928407i	0.786688	+	0.617351i	$0.211794\pi$
$491$	−3.62742	+	20.5721i	−0.163703	+	0.928407i	−0.950391	+	0.311057i	$0.899317\pi$
$492$		0			0
$493$	19.6059	−	16.4513i	0.883006	−	0.740930i
$494$		0			0
$495$	−14.5623	−	10.3795i	−0.654529	−	0.466523i
$496$		0			0
$497$	−1.55953	−	8.84453i	−0.0699545	−	0.396731i
$498$		0			0
$499$	−14.6919	+	5.34742i	−0.657701	+	0.239384i	−0.649243	−	0.760581i	$-0.724914\pi$
$499$	−14.6919	+	5.34742i	−0.657701	+	0.239384i	−0.00845752	+	0.999964i	$0.502692\pi$
$500$		0			0
$501$	−24.2138	−	12.7340i	−1.08179	−	0.568915i
$502$		0			0
$503$	0.920598	−	1.59452i	0.0410475	−	0.0710963i	−0.844772	−	0.535127i	$-0.820264\pi$
$503$	0.920598	−	1.59452i	0.0410475	−	0.0710963i	0.885819	+	0.464030i	$0.153597\pi$
$504$		0			0
$505$	3.05165	+	5.28562i	0.135797	+	0.235207i
$506$		0			0
$507$	10.9575	+	26.7702i	0.486640	+	1.18891i
$508$		0			0
$509$	−27.7624	−	23.2954i	−1.23055	−	1.03255i	−0.998203	−	0.0599166i	$-0.980917\pi$
$509$	−27.7624	−	23.2954i	−1.23055	−	1.03255i	−0.232343	−	0.972634i	$-0.574639\pi$
$510$		0			0
$511$	−21.6992	−	7.89787i	−0.959917	−	0.349381i
$512$		0			0
$513$	15.3568	+	6.58817i	0.678018	+	0.290875i
$514$		0			0
$515$	−6.15992	−	2.24203i	−0.271439	−	0.0987956i
$516$		0			0
$517$	15.8927	+	13.3356i	0.698961	+	0.586498i
$518$		0			0
$519$	−2.03667	−	0.276812i	−0.0893997	−	0.0121507i
$520$		0			0
$521$	−7.74293	−	13.4111i	−0.339224	−	0.587553i	0.645063	−	0.764129i	$-0.276831\pi$
$521$	−7.74293	−	13.4111i	−0.339224	−	0.587553i	−0.984287	+	0.176576i	$0.943498\pi$
$522$		0			0
$523$	8.36424	−	14.4873i	0.365743	−	0.633485i	−0.623152	−	0.782101i	$-0.714148\pi$
$523$	8.36424	−	14.4873i	0.365743	−	0.633485i	0.988895	+	0.148615i	$0.0474816\pi$
$524$		0			0
$525$	0.625270	+	15.8430i	0.0272890	+	0.691444i
$526$		0			0
$527$	−34.6393	+	12.6077i	−1.50891	+	0.549198i
$528$		0			0
$529$	5.64185	+	31.9965i	0.245298	+	1.39115i
$530$		0			0
$531$	−6.93664	+	6.82142i	−0.301024	+	0.296025i
$532$		0			0
$533$	26.1680	−	21.9575i	1.13346	−	0.951086i
$534$		0			0
$535$	1.28247	−	7.27325i	0.0554460	−	0.314450i
$536$		0			0
$537$	−8.61530	−	9.48135i	−0.371778	−	0.409150i
$538$		0			0
$539$	−1.30647			−0.0562738
$540$		0			0
$541$	−24.8710			−1.06929			−0.534645	−	0.845077i	$-0.679555\pi$
$541$	−24.8710			−1.06929			−0.534645	+	0.845077i	$0.679555\pi$
$542$		0			0
$543$	33.4124	−	7.26072i	1.43386	−	0.311587i
$544$		0			0
$545$	1.13216	−	6.42081i	0.0484965	−	0.275037i
$546$		0			0
$547$	−30.1997	+	25.3406i	−1.29125	+	1.08348i	−0.299659	+	0.954046i	$0.596873\pi$
$547$	−30.1997	+	25.3406i	−1.29125	+	1.08348i	−0.991587	+	0.129438i	$0.958683\pi$
$548$		0			0
$549$	−11.0542	+	0.873909i	−0.471783	+	0.0372975i
$550$		0			0
$551$	2.76140	+	15.6607i	0.117640	+	0.667167i
$552$		0			0
$553$	20.0732	−	7.30606i	0.853601	−	0.310685i
$554$		0			0
$555$	15.0711	−	9.51288i	0.639733	−	0.403799i
$556$		0			0
$557$	−3.89805	+	6.75162i	−0.165166	+	0.286075i	−0.936714	−	0.350095i	$-0.886149\pi$
$557$	−3.89805	+	6.75162i	−0.165166	+	0.286075i	0.771548	+	0.636171i	$0.219483\pi$
$558$		0			0
$559$	21.2571	+	36.8184i	0.899080	+	1.55725i
$560$		0			0
$561$	25.8037	−	33.3381i	1.08943	−	1.40754i
$562$		0			0
$563$	30.8157	+	25.8574i	1.29873	+	1.08976i	0.990364	+	0.138491i	$0.0442252\pi$
$563$	30.8157	+	25.8574i	1.29873	+	1.08976i	0.308362	+	0.951269i	$0.400219\pi$
$564$		0			0
$565$	13.6200	+	4.95729i	0.572999	+	0.208555i
$566$		0			0
$567$	20.8206	+	12.4903i	0.874382	+	0.524543i
$568$		0			0
$569$	14.3499	+	5.22293i	0.601579	+	0.218957i	0.624814	−	0.780773i	$-0.285175\pi$
$569$	14.3499	+	5.22293i	0.601579	+	0.218957i	−0.0232358	+	0.999730i	$0.507397\pi$
$570$		0			0
$571$	28.3126	+	23.7571i	1.18485	+	0.994204i	0.999934	+	0.0114486i	$0.00364427\pi$
$571$	28.3126	+	23.7571i	1.18485	+	0.994204i	0.184911	+	0.982755i	$0.440800\pi$
$572$		0			0
$573$	−5.46297	+	7.05810i	−0.228219	+	0.294856i
$574$		0			0
$575$	−12.6384	−	21.8903i	−0.527057	−	0.912889i
$576$		0			0
$577$	−2.93194	+	5.07826i	−0.122058	+	0.211411i	−0.920579	−	0.390556i	$-0.872283\pi$
$577$	−2.93194	+	5.07826i	−0.122058	+	0.211411i	0.798521	+	0.601967i	$0.205616\pi$
$578$		0			0
$579$	−19.9847	+	12.6143i	−0.830535	+	0.524233i
$580$		0			0
$581$	−9.47310	+	3.44792i	−0.393010	+	0.143044i
$582$		0			0
$583$	4.41151	+	25.0189i	0.182706	+	1.03618i
$584$		0			0
$585$	8.91544	−	18.7086i	0.368608	−	0.773504i
$586$		0			0
$587$	9.35554	−	7.85023i	0.386144	−	0.324014i	−0.428965	−	0.903321i	$-0.641121\pi$
$587$	9.35554	−	7.85023i	0.386144	−	0.324014i	0.815109	+	0.579308i	$0.196677\pi$
$588$		0			0
$589$	3.97721	−	22.5559i	0.163878	−	0.929399i
$590$		0			0
$591$	19.8244	−	4.30797i	0.815468	−	0.177206i
$592$		0			0
$593$	−15.7207			−0.645572			−0.322786	−	0.946472i	$-0.604619\pi$
$593$	−15.7207			−0.645572			−0.322786	+	0.946472i	$0.604619\pi$
$594$		0			0
$595$	17.6992			0.725598
$596$		0			0
$597$	−14.9994	−	16.5072i	−0.613885	−	0.675595i
$598$		0			0
$599$	−0.585192	+	3.31879i	−0.0239103	+	0.135602i	−0.994426	−	0.105435i	$-0.966376\pi$
$599$	−0.585192	+	3.31879i	−0.0239103	+	0.135602i	0.970516	+	0.241037i	$0.0774876\pi$
$600$		0			0
$601$	−3.78693	+	3.17761i	−0.154472	+	0.129617i	−0.716748	−	0.697332i	$-0.754370\pi$
$601$	−3.78693	+	3.17761i	−0.154472	+	0.129617i	0.562276	+	0.826950i	$0.309926\pi$
$602$		0			0
$603$	−39.0856	−	10.8245i	−1.59169	−	0.440810i
$604$		0			0
$605$	−2.44644	−	13.8745i	−0.0994620	−	0.564077i
$606$		0			0
$607$	−13.3985	+	4.87665i	−0.543828	+	0.197937i	−0.599302	−	0.800523i	$-0.704555\pi$
$607$	−13.3985	+	4.87665i	−0.543828	+	0.197937i	0.0554741	+	0.998460i	$0.482333\pi$
$608$		0			0
$609$	0.911192	+	23.0876i	0.0369234	+	0.935558i
$610$		0			0
$611$	−12.0215	+	20.8218i	−0.486337	+	0.842360i
$612$		0			0
$613$	−7.51217	−	13.0115i	−0.303414	−	0.525528i	0.673493	−	0.739194i	$-0.264793\pi$
$613$	−7.51217	−	13.0115i	−0.303414	−	0.525528i	−0.976907	+	0.213665i	$0.931460\pi$
$614$		0			0
$615$	−13.6363	−	1.85337i	−0.549870	−	0.0747353i
$616$		0			0
$617$	−16.7540	−	14.0583i	−0.674492	−	0.565966i	0.239899	−	0.970798i	$-0.422886\pi$
$617$	−16.7540	−	14.0583i	−0.674492	−	0.565966i	−0.914391	+	0.404832i	$0.867330\pi$
$618$		0			0
$619$	−18.6994	−	6.80603i	−0.751593	−	0.273558i	−0.0623171	−	0.998056i	$-0.519849\pi$
$619$	−18.6994	−	6.80603i	−0.751593	−	0.273558i	−0.689276	+	0.724499i	$0.742071\pi$
$620$		0			0
$621$	−38.6459	−	2.17397i	−1.55081	−	0.0872383i
$622$		0			0
$623$	44.6238	+	16.2417i	1.78781	+	0.650711i
$624$		0			0
$625$	2.66595	+	2.23700i	0.106638	+	0.0894799i
$626$		0			0
$627$	9.92259	+	24.2418i	0.396270	+	0.968126i
$628$		0			0
$629$	21.0074	+	36.3859i	0.837620	+	1.45080i
$630$		0			0
$631$	−12.0073	+	20.7973i	−0.478004	+	0.827927i	−0.999682	−	0.0252154i	$-0.991973\pi$
$631$	−12.0073	+	20.7973i	−0.478004	+	0.827927i	0.521678	+	0.853142i	$0.325306\pi$
$632$		0			0
$633$	−6.44204	−	3.38787i	−0.256048	−	0.134656i
$634$		0			0
$635$	2.99431	−	1.08984i	0.118826	−	0.0432490i
$636$		0			0
$637$	−0.262914	−	1.49106i	−0.0104170	−	0.0590780i
$638$		0			0
$639$	−9.08651	+	4.14483i	−0.359457	+	0.163967i
$640$		0			0
$641$	−0.320698	+	0.269098i	−0.0126668	+	0.0106287i	−0.649099	−	0.760704i	$-0.724854\pi$
$641$	−0.320698	+	0.269098i	−0.0126668	+	0.0106287i	0.636432	+	0.771333i	$0.280409\pi$
$642$		0			0
$643$	−6.11471	+	34.6782i	−0.241141	+	1.36758i	0.588147	+	0.808754i	$0.299858\pi$
$643$	−6.11471	+	34.6782i	−0.241141	+	1.36758i	−0.829288	+	0.558822i	$0.811254\pi$
$644$		0			0
$645$	5.21865	−	16.3130i	0.205484	−	0.642322i
$646$		0			0
$647$	23.3707			0.918797			0.459398	−	0.888230i	$-0.348065\pi$
$647$	23.3707			0.918797			0.459398	+	0.888230i	$0.348065\pi$
$648$		0			0
$649$	−15.2501			−0.598621
$650$		0			0
$651$	10.1399	−	31.6963i	0.397414	−	1.24228i
$652$		0			0
$653$	−1.00702	+	5.71110i	−0.0394078	+	0.223493i	−0.998151	−	0.0607803i	$-0.980641\pi$
$653$	−1.00702	+	5.71110i	−0.0394078	+	0.223493i	0.958743	+	0.284273i	$0.0917522\pi$
$654$		0			0
$655$	7.35801	−	6.17411i	0.287501	−	0.241242i
$656$		0			0
$657$	−2.45221	+	25.5617i	−0.0956700	+	0.997257i
$658$		0			0
$659$	−7.11895	−	40.3736i	−0.277315	−	1.57273i	−0.731511	−	0.681830i	$-0.761185\pi$
$659$	−7.11895	−	40.3736i	−0.277315	−	1.57273i	0.454196	−	0.890902i	$-0.349927\pi$
$660$		0			0
$661$	3.45991	−	1.25931i	0.134575	−	0.0489813i	−0.273855	−	0.961771i	$-0.588299\pi$
$661$	3.45991	−	1.25931i	0.134575	−	0.0489813i	0.408430	+	0.912790i	$0.366077\pi$
$662$		0			0
$663$	43.2411	+	22.7405i	1.67934	+	0.883168i
$664$		0			0
$665$	−5.49858	+	9.52382i	−0.213226	+	0.369318i
$666$		0			0
$667$	−18.4176	−	31.9003i	−0.713134	−	1.23518i
$668$		0			0
$669$	10.9532	+	26.7596i	0.423473	+	1.03459i
$670$		0			0
$671$	−13.3153	−	11.1729i	−0.514033	−	0.431324i
$672$		0			0
$673$	9.44815	+	3.43884i	0.364199	+	0.132558i	0.517636	−	0.855601i	$-0.326812\pi$
$673$	9.44815	+	3.43884i	0.364199	+	0.132558i	−0.153437	+	0.988158i	$0.549034\pi$
$674$		0			0
$675$	16.8810	−	5.09033i	0.649748	−	0.195927i
$676$		0			0
$677$	18.8873	+	6.87440i	0.725896	+	0.264205i	0.678427	−	0.734668i	$-0.262662\pi$
$677$	18.8873	+	6.87440i	0.725896	+	0.264205i	0.0474695	+	0.998873i	$0.484884\pi$
$678$		0			0
$679$	−26.3067	−	22.0740i	−1.00956	−	0.847121i
$680$		0			0
$681$	−32.6555	−	4.43835i	−1.25136	−	0.170078i
$682$		0			0
$683$	25.0966	+	43.4686i	0.960295	+	1.66328i	0.721757	+	0.692147i	$0.243335\pi$
$683$	25.0966	+	43.4686i	0.960295	+	1.66328i	0.238538	+	0.971133i	$0.423332\pi$
$684$		0			0
$685$	−7.52712	+	13.0373i	−0.287596	+	0.498131i
$686$		0			0
$687$	0.406359	+	10.2963i	0.0155036	+	0.392827i
$688$		0			0
$689$	−27.6660	+	10.0696i	−1.05399	+	0.383621i
$690$		0			0
$691$	3.63405	+	20.6097i	0.138246	+	0.784031i	0.972544	+	0.232718i	$0.0747619\pi$
$691$	3.63405	+	20.6097i	0.138246	+	0.784031i	−0.834299	+	0.551313i	$0.814127\pi$
$692$		0			0
$693$	9.54226	+	36.8436i	0.362481	+	1.39957i
$694$		0			0
$695$	−8.12459	+	6.81734i	−0.308183	+	0.258596i
$696$		0			0
$697$	5.63355	−	31.9495i	0.213386	−	1.21017i
$698$		0			0
$699$	−10.4803	−	11.5338i	−0.396402	−	0.436250i
$700$		0			0
$701$	−13.1584			−0.496986			−0.248493	−	0.968634i	$-0.579935\pi$
$701$	−13.1584			−0.496986			−0.248493	+	0.968634i	$0.579935\pi$
$702$		0			0
$703$	−26.1053			−0.984579
$704$		0			0
$705$	9.46509	−	2.05682i	0.356476	−	0.0774643i
$706$		0			0
$707$	2.25559	−	12.7921i	0.0848300	−	0.481095i
$708$		0			0
$709$	−4.44673	+	3.73125i	−0.167000	+	0.140130i	−0.722458	−	0.691415i	$-0.756988\pi$
$709$	−4.44673	+	3.73125i	−0.167000	+	0.140130i	0.555457	+	0.831545i	$0.312543\pi$
$710$		0			0
$711$	−13.4618	−	19.5722i	−0.504857	−	0.734016i
$712$		0			0
$713$	9.21263	+	52.2474i	0.345016	+	1.95668i
$714$		0			0
$715$	30.5268	−	11.1109i	1.14164	−	0.415523i
$716$		0			0
$717$	−0.222091	+	0.140184i	−0.00829414	+	0.00523526i
$718$		0			0
$719$	−9.49214	+	16.4409i	−0.353997	+	0.613141i	−0.986946	−	0.161053i	$-0.948511\pi$
$719$	−9.49214	+	16.4409i	−0.353997	+	0.613141i	0.632949	+	0.774194i	$0.281844\pi$
$720$		0			0
$721$	6.97562	+	12.0821i	0.259786	+	0.449962i
$722$		0			0
$723$	28.4959	−	36.8164i	1.05977	−	1.36922i
$724$		0			0
$725$	12.8535	+	10.7854i	0.477369	+	0.400560i
$726$		0			0
$727$	−41.0617	−	14.9453i	−1.52290	−	0.554289i	−0.561026	−	0.827798i	$-0.689593\pi$
$727$	−41.0617	−	14.9453i	−1.52290	−	0.554289i	−0.961869	+	0.273509i	$0.911816\pi$
$728$		0			0
$729$	7.64102	−	25.8962i	0.283001	−	0.959120i
$730$		0			0
$731$	37.9416	+	13.8096i	1.40332	+	0.510767i
$732$		0			0
$733$	3.21786	+	2.70011i	0.118854	+	0.0997307i	0.700278	−	0.713871i	$-0.253059\pi$
$733$	3.21786	+	2.70011i	0.118854	+	0.0997307i	−0.581423	+	0.813601i	$0.697504\pi$
$734$		0			0
$735$	−0.373342	+	0.482354i	−0.0137709	+	0.0177919i
$736$		0			0
$737$	−31.7871	−	55.0568i	−1.17089	−	2.02804i
$738$		0			0
$739$	16.2996	−	28.2318i	0.599592	−	1.03852i	−0.393289	−	0.919415i	$-0.628663\pi$
$739$	16.2996	−	28.2318i	0.599592	−	1.03852i	0.992881	−	0.119109i	$-0.0380038\pi$
$740$		0			0
$741$	−25.6701	+	16.2029i	−0.943013	+	0.595230i
$742$		0			0
$743$	−45.3903	+	16.5207i	−1.66521	+	0.606087i	−0.991169	−	0.132606i	$-0.957665\pi$
$743$	−45.3903	+	16.5207i	−1.66521	+	0.606087i	−0.674042	+	0.738693i	$0.735443\pi$
$744$		0			0
$745$	−4.17176	−	23.6592i	−0.152841	−	0.866806i
$746$		0			0
$747$	6.35298	+	9.23666i	0.232443	+	0.337952i
$748$		0			0
$749$	−12.0408	+	10.1034i	−0.439961	+	0.369171i
$750$		0			0
$751$	−3.08738	+	17.5094i	−0.112660	+	0.638928i	0.875222	+	0.483722i	$0.160715\pi$
$751$	−3.08738	+	17.5094i	−0.112660	+	0.638928i	−0.987882	+	0.155206i	$0.950396\pi$
$752$		0			0
$753$	5.98285	−	1.30011i	0.218027	−	0.0473786i
$754$		0			0
$755$	11.4506			0.416729
$756$		0			0
$757$	−44.4417			−1.61526			−0.807631	−	0.589689i	$-0.799250\pi$
$757$	−44.4417			−1.61526			−0.807631	+	0.589689i	$0.799250\pi$
$758$		0			0
$759$	−40.8035	−	44.9052i	−1.48107	−	1.62996i
$760$		0			0
$761$	−5.15176	+	29.2171i	−0.186751	+	1.05912i	0.736934	+	0.675965i	$0.236273\pi$
$761$	−5.15176	+	29.2171i	−0.186751	+	1.05912i	−0.923685	+	0.383153i	$0.874838\pi$
$762$		0			0
$763$	−10.6296	+	8.91927i	−0.384817	+	0.322899i
$764$		0			0
$765$	−4.93477	−	19.0536i	−0.178417	−	0.688885i
$766$		0			0
$767$	−3.06893	−	17.4048i	−0.110813	−	0.628451i
$768$		0			0
$769$	−44.7462	+	16.2863i	−1.61359	+	0.587299i	−0.982146	−	0.188122i	$-0.939760\pi$
$769$	−44.7462	+	16.2863i	−1.61359	+	0.587299i	−0.631445	+	0.775421i	$0.717538\pi$
$770$		0			0
$771$	0.485185	+	12.2935i	0.0174735	+	0.442741i
$772$		0			0
$773$	13.5498	−	23.4690i	0.487353	−	0.844121i	−0.512541	−	0.858663i	$-0.671296\pi$
$773$	13.5498	−	23.4690i	0.487353	−	0.844121i	0.999894	+	0.0145421i	$0.00462906\pi$
$774$		0			0
$775$	−12.0834	−	20.9290i	−0.434048	−	0.751793i
$776$		0			0
$777$	−37.5848	−	5.10831i	−1.34835	−	0.183260i
$778$		0			0
$779$	15.4416	+	12.9570i	0.553252	+	0.464233i
$780$		0			0
$781$	−14.7111	−	5.35442i	−0.526406	−	0.191596i
$782$		0			0
$783$	24.6003	−	7.41803i	0.879142	−	0.265099i
$784$		0			0
$785$	−20.4413	−	7.44004i	−0.729583	−	0.265546i
$786$		0			0
$787$	−3.52412	−	2.95709i	−0.125621	−	0.105409i	0.577813	−	0.816169i	$-0.303906\pi$
$787$	−3.52412	−	2.95709i	−0.125621	−	0.105409i	−0.703434	+	0.710761i	$0.748351\pi$
$788$		0			0
$789$	−2.02746	−	4.95328i	−0.0721794	−	0.176341i
$790$		0			0
$791$	−15.4236	−	26.7145i	−0.548401	−	0.949858i
$792$		0			0
$793$	10.0719	−	17.4450i	0.357663	−	0.619491i
$794$		0			0
$795$	10.4977	+	5.52075i	0.372315	+	0.195801i
$796$		0			0
$797$	−28.5078	+	10.3760i	−1.00980	+	0.367536i	−0.793355	−	0.608759i	$-0.791668\pi$
$797$	−28.5078	+	10.3760i	−1.00980	+	0.367536i	−0.216442	+	0.976295i	$0.569445\pi$
$798$		0			0
$799$	3.96510	+	22.4872i	0.140275	+	0.795539i
$800$		0			0
$801$	5.04290	−	52.5669i	0.178182	−	1.85736i
$802$		0			0
$803$	−30.8354	+	25.8740i	−1.08816	+	0.913073i
$804$		0			0
$805$	4.42340	−	25.0863i	0.155904	−	0.884177i
$806$		0			0
$807$	10.2432	−	32.0191i	0.360576	−	1.12712i
$808$		0			0
$809$	−4.11576			−0.144702			−0.0723512	−	0.997379i	$-0.523050\pi$
$809$	−4.11576			−0.144702			−0.0723512	+	0.997379i	$0.523050\pi$
$810$		0			0
$811$	−27.8627			−0.978393			−0.489197	−	0.872173i	$-0.662710\pi$
$811$	−27.8627			−0.978393			−0.489197	+	0.872173i	$0.662710\pi$
$812$		0			0
$813$	8.10907	−	25.3481i	0.284397	−	0.888997i
$814$		0			0
$815$	−2.96930	+	16.8398i	−0.104010	+	0.589871i
$816$		0			0
$817$	−19.2181	+	16.1259i	−0.672355	+	0.564173i
$818$		0			0
$819$	−40.1288	+	18.3048i	−1.40221	+	0.639623i
$820$		0			0
$821$	3.48880	+	19.7860i	0.121760	+	0.690535i	0.983180	+	0.182641i	$0.0584646\pi$
$821$	3.48880	+	19.7860i	0.121760	+	0.690535i	−0.861420	+	0.507894i	$0.830424\pi$
$822$		0			0
$823$	3.68270	−	1.34039i	0.128371	−	0.0467232i	−0.277036	−	0.960860i	$-0.589352\pi$
$823$	3.68270	−	1.34039i	0.128371	−	0.0467232i	0.405407	+	0.914136i	$0.367130\pi$
$824$		0			0
$825$	24.4618	+	12.8645i	0.851652	+	0.447884i
$826$		0			0
$827$	17.0746	−	29.5742i	0.593744	−	1.02839i	−0.399979	−	0.916524i	$-0.630983\pi$
$827$	17.0746	−	29.5742i	0.593744	−	1.02839i	0.993723	−	0.111870i	$-0.0356840\pi$
$828$		0			0
$829$	1.60103	+	2.77306i	0.0556059	+	0.0963123i	0.892488	−	0.451070i	$-0.148958\pi$
$829$	1.60103	+	2.77306i	0.0556059	+	0.0963123i	−0.836883	+	0.547383i	$0.815624\pi$
$830$		0			0
$831$	3.82727	+	9.35040i	0.132767	+	0.324362i
$832$		0			0
$833$	−1.10152	−	0.924288i	−0.0381655	−	0.0320247i
$834$		0			0
$835$	−18.8143	−	6.84784i	−0.651095	−	0.236979i
$836$		0			0
$837$	−36.9489	−	2.07850i	−1.27714	−	0.0718435i
$838$		0			0
$839$	−23.4076	−	8.51967i	−0.808120	−	0.294132i	−0.0952729	−	0.995451i	$-0.530372\pi$
$839$	−23.4076	−	8.51967i	−0.808120	−	0.294132i	−0.712847	+	0.701320i	$0.752595\pi$
$840$		0			0
$841$	−3.48408	−	2.92349i	−0.120141	−	0.100810i
$842$		0			0
$843$	−0.937824	−	0.127464i	−0.0323004	−	0.00439009i
$844$		0			0
$845$	10.5846	+	18.3331i	0.364121	+	0.630676i
$846$		0			0
$847$	−14.9920	+	25.9668i	−0.515130	+	0.892231i
$848$		0			0
$849$	−0.634987	−	16.0892i	−0.0217927	−	0.552180i
$850$		0			0
$851$	56.8223	−	20.6816i	1.94784	−	0.708958i
$852$		0			0
$853$	−0.487715	−	2.76597i	−0.0166990	−	0.0947050i	0.975319	−	0.220800i	$-0.0708667\pi$
$853$	−0.487715	−	2.76597i	−0.0166990	−	0.0947050i	−0.992018	+	0.126095i	$0.959756\pi$
$854$		0			0
$855$	11.7857	+	3.26398i	0.403061	+	0.111626i
$856$		0			0
$857$	−27.1943	+	22.8187i	−0.928939	+	0.779473i	−0.975627	−	0.219437i	$-0.929578\pi$
$857$	−27.1943	+	22.8187i	−0.928939	+	0.779473i	0.0466874	+	0.998910i	$0.485134\pi$
$858$		0			0
$859$	−0.576658	+	3.27039i	−0.0196753	+	0.111584i	−0.993064	−	0.117577i	$-0.962487\pi$
$859$	−0.576658	+	3.27039i	−0.0196753	+	0.111584i	0.973388	+	0.229161i	$0.0735984\pi$
$860$		0			0
$861$	19.6964	+	21.6764i	0.671251	+	0.738728i
$862$		0			0
$863$	−20.4644			−0.696616			−0.348308	−	0.937380i	$-0.613244\pi$
$863$	−20.4644			−0.696616			−0.348308	+	0.937380i	$0.613244\pi$
$864$		0			0
$865$	−1.50422			−0.0511450
$866$		0			0
$867$	16.5681	−	3.60035i	0.562683	−	0.122274i
$868$		0			0
$869$	6.46605	−	36.6708i	0.219346	−	1.24397i
$870$		0			0
$871$	56.4388	−	47.3578i	1.91236	−	1.60466i
$872$		0			0
$873$	−16.4284	+	34.4742i	−0.556019	+	1.16678i
$874$		0			0
$875$	4.98399	+	28.2656i	0.168490	+	0.955552i
$876$		0			0
$877$	5.07461	−	1.84701i	0.171357	−	0.0623690i	−0.254917	−	0.966963i	$-0.582048\pi$
$877$	5.07461	−	1.84701i	0.171357	−	0.0623690i	0.426274	+	0.904594i	$0.359826\pi$
$878$		0			0
$879$	−28.5078	+	17.9941i	−0.961543	+	0.606925i
$880$		0			0
$881$	16.0782	−	27.8483i	0.541690	−	0.938234i	−0.457117	−	0.889406i	$-0.651118\pi$
$881$	16.0782	−	27.8483i	0.541690	−	0.938234i	0.998807	−	0.0488280i	$-0.0155486\pi$
$882$		0			0
$883$	7.09571	+	12.2901i	0.238790	+	0.413596i	0.960367	−	0.278738i	$-0.0899160\pi$
$883$	7.09571	+	12.2901i	0.238790	+	0.413596i	−0.721578	+	0.692334i	$0.756583\pi$
$884$		0			0
$885$	−4.35793	+	5.63040i	−0.146490	+	0.189264i
$886$		0			0
$887$	−5.76774	−	4.83971i	−0.193662	−	0.162501i	0.540801	−	0.841151i	$-0.318121\pi$
$887$	−5.76774	−	4.83971i	−0.193662	−	0.162501i	−0.734463	+	0.678649i	$0.762566\pi$
$888$		0			0
$889$	−6.37266	−	2.31946i	−0.213732	−	0.0777921i
$890$		0			0
$891$	37.0024	−	20.5449i	1.23963	−	0.688280i
$892$		0			0
$893$	−13.3320	−	4.85245i	−0.446138	−	0.162381i
$894$		0			0
$895$	−7.18208	−	6.02648i	−0.240070	−	0.201443i
$896$		0			0
$897$	43.0384	−	55.6052i	1.43701	−	1.85660i
$898$		0			0
$899$	−17.6089	−	30.4995i	−0.587289	−	1.01721i
$900$		0			0
$901$	−13.9806	+	24.2152i	−0.465762	+	0.806724i
$902$		0			0
$903$	−30.8245	+	19.4564i	−1.02578	+	0.647470i
$904$		0			0
$905$	23.5142	−	8.55846i	0.781637	−	0.284493i
$906$		0			0
$907$	8.15380	+	46.2425i	0.270743	+	1.53546i	0.752168	+	0.658971i	$0.229008\pi$
$907$	8.15380	+	46.2425i	0.270743	+	1.53546i	−0.481426	+	0.876487i	$0.659881\pi$
$908$		0			0
$909$	−14.3998	+	1.13840i	−0.477611	+	0.0377583i
$910$		0			0
$911$	10.9000	−	9.14621i	0.361134	−	0.303027i	−0.444109	−	0.895973i	$-0.646480\pi$
$911$	10.9000	−	9.14621i	0.361134	−	0.303027i	0.805243	+	0.592946i	$0.202035\pi$
$912$		0			0
$913$	−3.05150	+	17.3059i	−0.100990	+	0.572743i
$914$		0			0
$915$	−7.93009	+	1.72326i	−0.262161	+	0.0569691i
$916$		0			0
$917$	−20.4423			−0.675065
$918$		0			0
$919$	31.4523			1.03752			0.518758	−	0.854921i	$-0.326394\pi$
$919$	31.4523			1.03752			0.518758	+	0.854921i	$0.326394\pi$
$920$		0			0
$921$	−16.5404	−	18.2031i	−0.545024	−	0.599812i
$922$		0			0
$923$	3.15046	−	17.8672i	0.103699	−	0.588105i
$924$		0			0
$925$	−21.1005	+	17.7054i	−0.693780	+	0.582150i
$926$		0			0
$927$	11.0618	−	10.8781i	0.363317	−	0.357282i
$928$		0			0
$929$	−10.1698	−	57.6756i	−0.333659	−	1.89228i	−0.440088	−	0.897955i	$-0.645053\pi$
$929$	−10.1698	−	57.6756i	−0.333659	−	1.89228i	0.106428	−	0.994320i	$-0.466059\pi$
$930$		0			0
$931$	0.839559	−	0.305575i	0.0275154	−	0.0100148i
$932$		0			0
$933$	0.824404	+	20.8886i	0.0269898	+	0.683862i
$934$		0			0
$935$	15.4263	−	26.7192i	0.504494	−	0.873810i
$936$		0			0
$937$	9.59150	+	16.6130i	0.313341	+	0.542722i	0.979083	−	0.203459i	$-0.0652185\pi$
$937$	9.59150	+	16.6130i	0.313341	+	0.542722i	−0.665743	+	0.746181i	$0.731885\pi$
$938$		0			0
$939$	47.4464	+	6.44865i	1.54836	+	0.210444i
$940$		0			0
$941$	39.2192	+	32.9088i	1.27851	+	1.07280i	0.993448	+	0.114288i	$0.0364586\pi$
$941$	39.2192	+	32.9088i	1.27851	+	1.07280i	0.285062	+	0.958509i	$0.407986\pi$
$942$		0			0
$943$	−43.8762	−	15.9696i	−1.42880	−	0.520042i
$944$		0			0
$945$	16.3296	+	7.00551i	0.531201	+	0.227889i
$946$		0			0
$947$	−50.8361	−	18.5028i	−1.65195	−	0.601261i	−0.662884	−	0.748722i	$-0.730668\pi$
$947$	−50.8361	−	18.5028i	−1.65195	−	0.601261i	−0.989068	+	0.147461i	$0.952890\pi$
$948$		0			0
$949$	−35.7349	−	29.9852i	−1.16001	−	0.973360i
$950$		0			0
$951$	−8.25032	−	20.1563i	−0.267535	−	0.653613i
$952$		0			0
$953$	17.1783	+	29.7537i	0.556460	+	0.963817i	0.997788	+	0.0664715i	$0.0211742\pi$
$953$	17.1783	+	29.7537i	0.556460	+	0.963817i	−0.441328	+	0.897346i	$0.645493\pi$
$954$		0			0
$955$	−3.26594	+	5.65678i	−0.105683	+	0.183049i
$956$		0			0
$957$	35.6477	+	18.7472i	1.15233	+	0.606010i
$958$		0			0
$959$	30.1070	−	10.9581i	0.972207	−	0.353854i
$960$		0			0
$961$	3.42499	+	19.4241i	0.110484	+	0.626583i
$962$		0			0
$963$	14.2337	+	10.1452i	0.458673	+	0.326925i
$964$		0			0
$965$	−13.2491	+	11.1173i	−0.426502	+	0.357878i
$966$		0			0
$967$	−1.59297	+	9.03420i	−0.0512266	+	0.290520i	−0.999649	−	0.0264886i	$-0.991567\pi$
$967$	−1.59297	+	9.03420i	−0.0512266	+	0.290520i	0.948423	+	0.317009i	$0.102679\pi$
$968$		0			0
$969$	−8.78431	+	27.4589i	−0.282193	+	0.882106i
$970$		0			0
$971$	−10.9454			−0.351255			−0.175628	−	0.984457i	$-0.556195\pi$
$971$	−10.9454			−0.351255			−0.175628	+	0.984457i	$0.556195\pi$
$972$		0			0
$973$	22.5721			0.723627
$974$		0			0
$975$	−9.75938	+	30.5068i	−0.312550	+	0.977000i
$976$		0			0
$977$	−1.91033	+	10.8340i	−0.0611168	+	0.346610i	0.938880	+	0.344243i	$0.111865\pi$
$977$	−1.91033	+	10.8340i	−0.0611168	+	0.346610i	−0.999997	+	0.00236698i	$0.999247\pi$
$978$		0			0
$979$	63.4121	−	53.2090i	2.02666	−	1.70057i
$980$		0			0
$981$	12.5654	+	8.95616i	0.401184	+	0.285948i
$982$		0			0
$983$	2.79728	+	15.8642i	0.0892195	+	0.505989i	0.996366	+	0.0851742i	$0.0271447\pi$
$983$	2.79728	+	15.8642i	0.0892195	+	0.505989i	−0.907147	+	0.420815i	$0.861744\pi$
$984$		0			0
$985$	13.9515	−	5.07794i	0.444533	−	0.161797i
$986$		0			0
$987$	−18.2451	−	9.59508i	−0.580746	−	0.305415i
$988$		0			0
$989$	29.0557	−	50.3259i	0.923917	−	1.60027i
$990$		0			0
$991$	2.16585	+	3.75136i	0.0688005	+	0.119166i	0.898374	−	0.439232i	$-0.144749\pi$
$991$	2.16585	+	3.75136i	0.0688005	+	0.119166i	−0.829573	+	0.558398i	$0.811416\pi$
$992$		0			0
$993$	10.9173	+	26.6719i	0.346449	+	0.846407i
$994$		0			0
$995$	−12.5041	−	10.4922i	−0.396408	−	0.332626i
$996$		0			0
$997$	−51.1262	−	18.6084i	−1.61918	−	0.589335i	−0.635957	−	0.771724i	$-0.719395\pi$
$997$	−51.1262	−	18.6084i	−1.61918	−	0.589335i	−0.983226	+	0.182390i	$0.941617\pi$
$998$		0			0
$999$	4.97989	+	41.8851i	0.157557	+	1.32518i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.c.193.4	yes	54
4.3	odd	2		864.2.y.b.193.6	✓	54
27.7	even	9	inner	864.2.y.c.385.4	yes	54
108.7	odd	18		864.2.y.b.385.6	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.b.193.6	✓	54	4.3	odd	2
864.2.y.b.385.6	yes	54	108.7	odd	18
864.2.y.c.193.4	yes	54	1.1	even	1	trivial
864.2.y.c.385.4	yes	54	27.7	even	9	inner

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.527750 + 1.64969i) q^{3} +(-0.220114 + 1.24833i) q^{5} +(2.06659 - 1.73408i) q^{7} +(-2.44296 - 1.74125i) q^{9} +O(q^{10})\)	\(q+(-0.527750 + 1.64969i) q^{3} +(-0.220114 + 1.24833i) q^{5} +(2.06659 - 1.73408i) q^{7} +(-2.44296 - 1.74125i) q^{9} +(-0.816598 - 4.63116i) q^{11} +(5.12114 - 1.86394i) q^{13} +(-1.94319 - 1.02192i) q^{15} +(2.58790 - 4.48237i) q^{17} +(1.60795 + 2.78505i) q^{19} +(1.77005 + 4.32440i) q^{21} +(-5.70640 - 4.78823i) q^{23} +(3.18859 + 1.16055i) q^{25} +(4.16179 - 3.11119i) q^{27} +(4.64667 + 1.69125i) q^{29} +(-5.45581 - 4.57797i) q^{31} +(8.07094 + 1.09696i) q^{33} +(1.70981 + 2.96148i) q^{35} +(-4.05878 + 7.03001i) q^{37} +(0.372250 + 9.43200i) q^{39} +(5.89007 - 2.14381i) q^{41} +(1.35464 + 7.68253i) q^{43} +(2.71138 - 2.66634i) q^{45} +(-3.37956 + 2.83579i) q^{47} +(0.0482428 - 0.273599i) q^{49} +(6.02876 + 6.63480i) q^{51} -5.40231 q^{53} +5.96094 q^{55} +(-5.44307 + 1.18281i) q^{57} +(0.563127 - 3.19365i) q^{59} +(2.83148 - 2.37590i) q^{61} +(-8.06806 + 0.637833i) q^{63} +(1.19958 + 6.80314i) q^{65} +(12.7036 - 4.62375i) q^{67} +(10.9107 - 6.88680i) q^{69} +(1.66453 - 2.88306i) q^{71} +(-4.27984 - 7.41290i) q^{73} +(-3.59733 + 4.64771i) q^{75} +(-9.71835 - 8.15466i) q^{77} +(7.44075 + 2.70821i) q^{79} +(2.93611 + 8.50760i) q^{81} +(-3.51149 - 1.27808i) q^{83} +(5.02583 + 4.21717i) q^{85} +(-5.24232 + 6.77301i) q^{87} +(8.80137 + 15.2444i) q^{89} +(7.35109 - 12.7325i) q^{91} +(10.4315 - 6.58438i) q^{93} +(-3.83059 + 1.39422i) q^{95} +(-2.21046 - 12.5361i) q^{97} +(-6.06907 + 12.7356i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q+O(q^{10}) \) 54 * q	\( 54 q + 9 q^{11} + 12 q^{17} - 18 q^{19} + 12 q^{21} + 21 q^{27} + 6 q^{29} - 36 q^{31} - 9 q^{33} - 24 q^{39} + 3 q^{41} + 21 q^{43} + 42 q^{45} - 18 q^{49} - 24 q^{51} + 36 q^{53} + 72 q^{55} + 39 q^{57} - 18 q^{59} - 18 q^{61} + 30 q^{63} + 48 q^{65} + 27 q^{67} + 24 q^{69} + 84 q^{75} + 36 q^{77} - 72 q^{79} + 36 q^{81} - 6 q^{87} + 33 q^{89} - 36 q^{91} + 72 q^{93} - 36 q^{95} + 9 q^{97} - 120 q^{99}+O(q^{100}) \) 54 * q + 9 * q^11 + 12 * q^17 - 18 * q^19 + 12 * q^21 + 21 * q^27 + 6 * q^29 - 36 * q^31 - 9 * q^33 - 24 * q^39 + 3 * q^41 + 21 * q^43 + 42 * q^45 - 18 * q^49 - 24 * q^51 + 36 * q^53 + 72 * q^55 + 39 * q^57 - 18 * q^59 - 18 * q^61 + 30 * q^63 + 48 * q^65 + 27 * q^67 + 24 * q^69 + 84 * q^75 + 36 * q^77 - 72 * q^79 + 36 * q^81 - 6 * q^87 + 33 * q^89 - 36 * q^91 + 72 * q^93 - 36 * q^95 + 9 * q^97 - 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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