LMFDB - Embedded newform 702.2.bb.a.89.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(71,702)] 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("702.71"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bb (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			89.13
Character	$\chi$	$=$	702.89
Dual form			702.2.bb.a.71.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(3.62177 + 0.970449i) q^{5} +(-3.13748 - 0.840685i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(3.24719 - 1.87476i) q^{10} +(1.54706 + 1.54706i) q^{11} +(0.305736 - 3.59257i) q^{13} +(-2.81299 + 1.62408i) q^{14} -1.00000 q^{16} +(3.50770 - 6.07551i) q^{17} +(4.70354 - 1.26031i) q^{19} +(0.970449 - 3.62177i) q^{20} +2.18787 q^{22} +(-0.415879 + 0.720323i) q^{23} +(7.84529 + 4.52948i) q^{25} +(-2.32414 - 2.75652i) q^{26} +(-0.840685 + 3.13748i) q^{28} +9.26729i q^{29} +(-0.141470 + 0.527973i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.81572 - 6.77635i) q^{34} +(-10.5474 - 6.08953i) q^{35} +(1.90093 + 0.509353i) q^{37} +(2.43473 - 4.21708i) q^{38} +(-1.87476 - 3.24719i) q^{40} +(-0.455940 - 1.70159i) q^{41} +(0.0503260 - 0.0290558i) q^{43} +(1.54706 - 1.54706i) q^{44} +(0.215275 + 0.803416i) q^{46} +(-5.83570 + 1.56367i) q^{47} +(3.07486 + 1.77527i) q^{49} +(8.75029 - 2.34463i) q^{50} +(-3.59257 - 0.305736i) q^{52} +1.62324i q^{53} +(4.10174 + 7.10443i) q^{55} +(1.62408 + 2.81299i) q^{56} +(6.55297 + 6.55297i) q^{58} +(-2.06291 - 2.06291i) q^{59} +(-1.78999 - 3.10035i) q^{61} +(0.273299 + 0.473367i) q^{62} +1.00000i q^{64} +(4.59371 - 12.7147i) q^{65} +(-12.5547 + 3.36401i) q^{67} +(-6.07551 - 3.50770i) q^{68} +(-11.7641 + 3.15217i) q^{70} +(2.31786 + 8.65035i) q^{71} +(3.38343 - 3.38343i) q^{73} +(1.70433 - 0.983995i) q^{74} +(-1.26031 - 4.70354i) q^{76} +(-3.55328 - 6.15446i) q^{77} +(-5.86001 + 10.1498i) q^{79} +(-3.62177 - 0.970449i) q^{80} +(-1.52561 - 0.880809i) q^{82} +(-3.75798 - 14.0250i) q^{83} +(18.6000 - 18.6000i) q^{85} +(0.0150404 - 0.0561314i) q^{86} -2.18787i q^{88} +(-3.50606 + 13.0848i) q^{89} +(-3.97946 + 11.0146i) q^{91} +(0.720323 + 0.415879i) q^{92} +(-3.02078 + 5.23214i) q^{94} +18.2582 q^{95} +(2.55453 - 9.53363i) q^{97} +(3.42956 - 0.918947i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) $ 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	3.62177	+	0.970449i	1.61970	+	0.433998i	0.950914	−	0.309454i	$-0.100146\pi$
$5$	3.62177	+	0.970449i	1.61970	+	0.433998i	0.668789	+	0.743452i	$0.266813\pi$
$6$		0			0
$7$	−3.13748	−	0.840685i	−1.18586	−	0.317749i	−0.388609	−	0.921403i	$-0.627044\pi$
$7$	−3.13748	−	0.840685i	−1.18586	−	0.317749i	−0.797247	+	0.603653i	$0.793711\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	3.24719	−	1.87476i	1.02685	−	0.592852i
$11$	1.54706	+	1.54706i	0.466456	+	0.466456i	0.900764	−	0.434308i	$-0.143007\pi$
$11$	1.54706	+	1.54706i	0.466456	+	0.466456i	−0.434308	+	0.900764i	$0.643007\pi$
$12$		0			0
$13$	0.305736	−	3.59257i	0.0847958	−	0.996398i
$13$	0.305736	−	3.59257i	0.0847958	−	0.996398i
$14$	−2.81299	+	1.62408i	−0.751803	+	0.434054i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	3.50770	−	6.07551i	0.850742	−	1.47353i	−0.0297983	−	0.999556i	$-0.509487\pi$
$17$	3.50770	−	6.07551i	0.850742	−	1.47353i	0.880540	−	0.473972i	$-0.157180\pi$
$18$		0			0
$19$	4.70354	−	1.26031i	1.07907	−	0.289135i	0.324853	−	0.945765i	$-0.394685\pi$
$19$	4.70354	−	1.26031i	1.07907	−	0.289135i	0.754213	+	0.656630i	$0.228019\pi$
$20$	0.970449	−	3.62177i	0.216999	−	0.809852i
$21$		0			0
$22$	2.18787			0.466456
$23$	−0.415879	+	0.720323i	−0.0867167	+	0.150198i	−0.906121	−	0.423018i	$-0.860971\pi$
$23$	−0.415879	+	0.720323i	−0.0867167	+	0.150198i	0.819405	+	0.573215i	$0.194304\pi$
$24$		0			0
$25$	7.84529	+	4.52948i	1.56906	+	0.905896i
$26$	−2.32414	−	2.75652i	−0.455801	−	0.540597i
$27$		0			0
$28$	−0.840685	+	3.13748i	−0.158875	+	0.592928i
$29$			9.26729i			1.72089i	0.509541	+	0.860447i	$0.329815\pi$
$29$			9.26729i			1.72089i	−0.509541	+	0.860447i	$0.670185\pi$
$30$		0			0
$31$	−0.141470	+	0.527973i	−0.0254087	+	0.0948267i	−0.977466	−	0.211094i	$-0.932297\pi$
$31$	−0.141470	+	0.527973i	−0.0254087	+	0.0948267i	0.952057	+	0.305920i	$0.0989641\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$	−1.81572	−	6.77635i	−0.311393	−	1.16213i
$35$	−10.5474	−	6.08953i	−1.78283	−	1.02932i
$36$		0			0
$37$	1.90093	+	0.509353i	0.312511	+	0.0837372i	0.411666	−	0.911335i	$-0.364947\pi$
$37$	1.90093	+	0.509353i	0.312511	+	0.0837372i	−0.0991544	+	0.995072i	$0.531614\pi$
$38$	2.43473	−	4.21708i	0.394966	−	0.684100i
$39$		0			0
$40$	−1.87476	−	3.24719i	−0.296426	−	0.513425i
$41$	−0.455940	−	1.70159i	−0.0712059	−	0.265744i	0.921140	−	0.389231i	$-0.127259\pi$
$41$	−0.455940	−	1.70159i	−0.0712059	−	0.265744i	−0.992346	+	0.123487i	$0.960592\pi$
$42$		0			0
$43$	0.0503260	−	0.0290558i	0.00767465	−	0.00443096i	−0.496158	−	0.868232i	$-0.665256\pi$
$43$	0.0503260	−	0.0290558i	0.00767465	−	0.00443096i	0.503832	+	0.863801i	$0.331923\pi$
$44$	1.54706	−	1.54706i	0.233228	−	0.233228i
$45$		0			0
$46$	0.215275	+	0.803416i	0.0317405	+	0.118457i
$47$	−5.83570	+	1.56367i	−0.851224	+	0.228085i	−0.657951	−	0.753060i	$-0.728577\pi$
$47$	−5.83570	+	1.56367i	−0.851224	+	0.228085i	−0.193272	+	0.981145i	$0.561910\pi$
$48$		0			0
$49$	3.07486	+	1.77527i	0.439265	+	0.253610i
$50$	8.75029	−	2.34463i	1.23748	−	0.331581i
$51$		0			0
$52$	−3.59257	−	0.305736i	−0.498199	−	0.0423979i
$53$			1.62324i			0.222969i	0.993766	+	0.111484i	$0.0355605\pi$
$53$			1.62324i			0.222969i	−0.993766	+	0.111484i	$0.964440\pi$
$54$		0			0
$55$	4.10174	+	7.10443i	0.553079	+	0.957961i
$56$	1.62408	+	2.81299i	0.217027	+	0.375901i
$57$		0			0
$58$	6.55297	+	6.55297i	0.860447	+	0.860447i
$59$	−2.06291	−	2.06291i	−0.268568	−	0.268568i	0.559955	−	0.828523i	$-0.310818\pi$
$59$	−2.06291	−	2.06291i	−0.268568	−	0.268568i	−0.828523	+	0.559955i	$0.810818\pi$
$60$		0			0
$61$	−1.78999	−	3.10035i	−0.229185	−	0.396959i	0.728382	−	0.685171i	$-0.240273\pi$
$61$	−1.78999	−	3.10035i	−0.229185	−	0.396959i	−0.957567	+	0.288212i	$0.906939\pi$
$62$	0.273299	+	0.473367i	0.0347090	+	0.0601177i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	4.59371	−	12.7147i	0.569779	−	1.57707i
$66$		0			0
$67$	−12.5547	+	3.36401i	−1.53380	+	0.410979i	−0.924255	−	0.381775i	$-0.875313\pi$
$67$	−12.5547	+	3.36401i	−1.53380	+	0.410979i	−0.609541	+	0.792755i	$0.708646\pi$
$68$	−6.07551	−	3.50770i	−0.736764	−	0.425371i
$69$		0			0
$70$	−11.7641	+	3.15217i	−1.40608	+	0.376757i
$71$	2.31786	+	8.65035i	0.275079	+	1.02661i	0.955789	+	0.294055i	$0.0950048\pi$
$71$	2.31786	+	8.65035i	0.275079	+	1.02661i	−0.680710	+	0.732553i	$0.738329\pi$
$72$		0			0
$73$	3.38343	−	3.38343i	0.396001	−	0.396001i	−0.480819	−	0.876820i	$-0.659661\pi$
$73$	3.38343	−	3.38343i	0.396001	−	0.396001i	0.876820	+	0.480819i	$0.159661\pi$
$74$	1.70433	−	0.983995i	0.198124	−	0.114387i
$75$		0			0
$76$	−1.26031	−	4.70354i	−0.144567	−	0.539533i
$77$	−3.55328	−	6.15446i	−0.404934	−	0.701366i
$78$		0			0
$79$	−5.86001	+	10.1498i	−0.659302	+	1.14194i	0.321494	+	0.946911i	$0.395815\pi$
$79$	−5.86001	+	10.1498i	−0.659302	+	1.14194i	−0.980797	+	0.195033i	$0.937518\pi$
$80$	−3.62177	−	0.970449i	−0.404926	−	0.108500i
$81$		0			0
$82$	−1.52561	−	0.880809i	−0.168475	−	0.0972691i
$83$	−3.75798	−	14.0250i	−0.412492	−	1.53944i	−0.789807	−	0.613356i	$-0.789819\pi$
$83$	−3.75798	−	14.0250i	−0.412492	−	1.53944i	0.377315	−	0.926085i	$-0.376848\pi$
$84$		0			0
$85$	18.6000	−	18.6000i	2.01746	−	2.01746i
$86$	0.0150404	−	0.0561314i	0.00162184	−	0.00605280i
$87$		0			0
$88$		−	2.18787i		−	0.233228i
$89$	−3.50606	+	13.0848i	−0.371642	+	1.38699i	0.486548	+	0.873654i	$0.338256\pi$
$89$	−3.50606	+	13.0848i	−0.371642	+	1.38699i	−0.858190	+	0.513332i	$0.828411\pi$
$90$		0			0
$91$	−3.97946	+	11.0146i	−0.417160	+	1.15464i
$92$	0.720323	+	0.415879i	0.0750989	+	0.0433583i
$93$		0			0
$94$	−3.02078	+	5.23214i	−0.311570	+	0.539654i
$95$	18.2582			1.87325
$96$		0			0
$97$	2.55453	−	9.53363i	0.259373	−	0.967993i	−0.706232	−	0.707980i	$-0.749607\pi$
$97$	2.55453	−	9.53363i	0.259373	−	0.967993i	0.965605	−	0.260013i	$-0.0837268\pi$
$98$	3.42956	−	0.918947i	0.346438	−	0.0928277i
$99$		0			0
$100$	4.52948	−	7.84529i	0.452948	−	0.784529i
$101$	−4.39893			−0.437710			−0.218855	−	0.975757i	$-0.570232\pi$
$101$	−4.39893			−0.437710			−0.218855	+	0.975757i	$0.570232\pi$
$102$		0			0
$103$	−8.09876	+	4.67582i	−0.797994	+	0.460722i	−0.842769	−	0.538275i	$-0.819076\pi$
$103$	−8.09876	+	4.67582i	−0.797994	+	0.460722i	0.0447750	+	0.998997i	$0.485743\pi$
$104$	−2.75652	+	2.32414i	−0.270299	+	0.227901i
$105$		0			0
$106$	1.14780	+	1.14780i	0.111484	+	0.111484i
$107$	−4.41803	+	2.55075i	−0.427107	+	0.246590i	−0.698113	−	0.715987i	$-0.745977\pi$
$107$	−4.41803	+	2.55075i	−0.427107	+	0.246590i	0.271007	+	0.962577i	$0.412643\pi$
$108$		0			0
$109$	−0.923072	−	0.923072i	−0.0884142	−	0.0884142i	0.661516	−	0.749931i	$-0.269913\pi$
$109$	−0.923072	−	0.923072i	−0.0884142	−	0.0884142i	−0.749931	+	0.661516i	$0.769913\pi$
$110$	7.92396	+	2.12322i	0.755520	+	0.202441i
$111$		0			0
$112$	3.13748	+	0.840685i	0.296464	+	0.0794373i
$113$			11.5693i			1.08835i	0.838971	+	0.544176i	$0.183158\pi$
$113$			11.5693i			1.08835i	−0.838971	+	0.544176i	$0.816842\pi$
$114$		0			0
$115$	−2.20525	+	2.20525i	−0.205641	+	0.205641i
$116$	9.26729			0.860447
$117$		0			0
$118$	−2.91739			−0.268568
$119$	−16.1129	+	16.1129i	−1.47707	+	1.47707i
$120$		0			0
$121$		−	6.21322i		−	0.564838i
$122$	−3.45799	−	0.926566i	−0.313072	−	0.0838874i
$123$		0			0
$124$	0.527973	+	0.141470i	0.0474133	+	0.0127044i
$125$	10.7616	+	10.7616i	0.962547	+	0.962547i
$126$		0			0
$127$	2.86070	−	1.65163i	0.253846	−	0.146558i	−0.367678	−	0.929953i	$-0.619847\pi$
$127$	2.86070	−	1.65163i	0.253846	−	0.146558i	0.621524	+	0.783395i	$0.286514\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	−5.74243	−	12.2389i	−0.503645	−	1.07342i
$131$	−9.54763	+	5.51233i	−0.834181	+	0.481614i	−0.855282	−	0.518163i	$-0.826616\pi$
$131$	−9.54763	+	5.51233i	−0.834181	+	0.481614i	0.0211014	+	0.999777i	$0.493283\pi$
$132$		0			0
$133$	−15.8168			−1.37149
$134$	−6.49877	+	11.2562i	−0.561408	+	0.972388i
$135$		0			0
$136$	−6.77635	+	1.81572i	−0.581067	+	0.155697i
$137$	−2.94490	+	10.9905i	−0.251600	+	0.938984i	0.718350	+	0.695682i	$0.244898\pi$
$137$	−2.94490	+	10.9905i	−0.251600	+	0.938984i	−0.969950	+	0.243303i	$0.921769\pi$
$138$		0			0
$139$	3.67668			0.311852			0.155926	−	0.987769i	$-0.450164\pi$
$139$	3.67668			0.311852			0.155926	+	0.987769i	$0.450164\pi$
$140$	−6.08953	+	10.5474i	−0.514659	+	0.891416i
$141$		0			0
$142$	7.75569	+	4.47775i	0.650843	+	0.375765i
$143$	6.03090	−	5.08492i	0.504329	−	0.425222i
$144$		0			0
$145$	−8.99344	+	33.5640i	−0.746864	+	2.78734i
$146$		−	4.78490i		−	0.396001i
$147$		0			0
$148$	0.509353	−	1.90093i	0.0418686	−	0.156256i
$149$	−6.41670	+	6.41670i	−0.525676	+	0.525676i	−0.919280	−	0.393604i	$-0.871228\pi$
$149$	−6.41670	+	6.41670i	−0.525676	+	0.525676i	0.393604	+	0.919280i	$0.371228\pi$
$150$		0			0
$151$	4.88320	+	18.2244i	0.397389	+	1.48308i	0.817672	+	0.575684i	$0.195264\pi$
$151$	4.88320	+	18.2244i	0.397389	+	1.48308i	−0.420283	+	0.907393i	$0.638069\pi$
$152$	−4.21708	−	2.43473i	−0.342050	−	0.197483i
$153$		0			0
$154$	−6.86441	−	1.83931i	−0.553150	−	0.148216i
$155$	−1.02474	+	1.77490i	−0.0823092	+	0.142564i
$156$		0			0
$157$	11.0256	+	19.0969i	0.879939	+	1.52410i	0.851407	+	0.524506i	$0.175750\pi$
$157$	11.0256	+	19.0969i	0.879939	+	1.52410i	0.0285320	+	0.999593i	$0.490917\pi$
$158$	3.03336	+	11.3207i	0.241321	+	0.900623i
$159$		0			0
$160$	−3.24719	+	1.87476i	−0.256713	+	0.148213i
$161$	1.91038	−	1.91038i	0.150559	−	0.150559i
$162$		0			0
$163$	−1.64426	−	6.13647i	−0.128789	−	0.480646i	0.871158	−	0.491003i	$-0.163370\pi$
$163$	−1.64426	−	6.13647i	−0.128789	−	0.480646i	−0.999946	+	0.0103577i	$0.996703\pi$
$164$	−1.70159	+	0.455940i	−0.132872	+	0.0356030i
$165$		0			0
$166$	−12.5744	−	7.25986i	−0.975967	−	0.563475i
$167$	8.50863	−	2.27988i	0.658417	−	0.176422i	0.0858858	−	0.996305i	$-0.472628\pi$
$167$	8.50863	−	2.27988i	0.658417	−	0.176422i	0.572532	+	0.819883i	$0.305961\pi$
$168$		0			0
$169$	−12.8131	−	2.19675i	−0.985619	−	0.168981i
$170$		−	26.3044i		−	2.01746i
$171$		0			0
$172$	−0.0290558	−	0.0503260i	−0.00221548	−	0.00383732i
$173$	0.0252410	+	0.0437187i	0.00191904	+	0.00332387i	0.866983	−	0.498337i	$-0.166056\pi$
$173$	0.0252410	+	0.0437187i	0.00191904	+	0.00332387i	−0.865064	+	0.501661i	$0.832722\pi$
$174$		0			0
$175$	−20.8066	−	20.8066i	−1.57283	−	1.57283i
$176$	−1.54706	−	1.54706i	−0.116614	−	0.116614i
$177$		0			0
$178$	6.77319	+	11.7315i	0.507672	+	0.879314i
$179$	3.55609	+	6.15933i	0.265795	+	0.460370i	0.967772	−	0.251830i	$-0.0810323\pi$
$179$	3.55609	+	6.15933i	0.265795	+	0.460370i	−0.701977	+	0.712200i	$0.747699\pi$
$180$		0			0
$181$		−	20.6330i		−	1.53364i	−0.641863	−	0.766820i	$-0.721838\pi$
$181$		−	20.6330i		−	1.53364i	0.641863	−	0.766820i	$-0.278162\pi$
$182$	4.97458	+	10.6024i	0.368741	+	0.785901i
$183$		0			0
$184$	0.803416	−	0.215275i	0.0592286	−	0.0158703i
$185$	6.39043	+	3.68952i	0.469834	+	0.271259i
$186$		0			0
$187$	14.8258	−	3.97256i	1.08417	−	0.290502i
$188$	1.56367	+	5.83570i	0.114042	+	0.425612i
$189$		0			0
$190$	12.9105	−	12.9105i	0.936625	−	0.936625i
$191$	19.4788	−	11.2461i	1.40944	−	0.813738i	0.414102	−	0.910231i	$-0.364096\pi$
$191$	19.4788	−	11.2461i	1.40944	−	0.813738i	0.995334	+	0.0964927i	$0.0307624\pi$
$192$		0			0
$193$	1.74990	+	6.53071i	0.125961	+	0.470091i	0.999872	−	0.0159939i	$-0.00509122\pi$
$193$	1.74990	+	6.53071i	0.125961	+	0.470091i	−0.873912	+	0.486085i	$0.838425\pi$
$194$	−4.93497	−	8.54762i	−0.354310	−	0.613683i
$195$		0			0
$196$	1.77527	−	3.07486i	0.126805	−	0.219633i
$197$	5.95380	+	1.59532i	0.424191	+	0.113662i	0.464598	−	0.885522i	$-0.346199\pi$
$197$	5.95380	+	1.59532i	0.424191	+	0.113662i	−0.0404072	+	0.999183i	$0.512866\pi$
$198$		0			0
$199$	3.29772	+	1.90394i	0.233769	+	0.134967i	0.612310	−	0.790618i	$-0.290241\pi$
$199$	3.29772	+	1.90394i	0.233769	+	0.134967i	−0.378541	+	0.925585i	$0.623574\pi$
$200$	−2.34463	−	8.75029i	−0.165791	−	0.618739i
$201$		0			0
$202$	−3.11051	+	3.11051i	−0.218855	+	0.218855i
$203$	7.79088	−	29.0760i	0.546813	−	2.04073i
$204$		0			0
$205$		−	6.60524i		−	0.461330i
$206$	−2.42038	+	9.03299i	−0.168636	+	0.629358i
$207$		0			0
$208$	−0.305736	+	3.59257i	−0.0211989	+	0.249100i
$209$	9.22643	+	5.32688i	0.638205	+	0.368468i
$210$		0			0
$211$	9.59387	−	16.6171i	0.660469	−	1.14397i	−0.320024	−	0.947410i	$-0.603691\pi$
$211$	9.59387	−	16.6171i	0.660469	−	1.14397i	0.980493	−	0.196556i	$-0.0629758\pi$
$212$	1.62324			0.111484
$213$		0			0
$214$	−1.32036	+	4.92767i	−0.0902582	+	0.336848i
$215$	0.210466	−	0.0563943i	0.0143537	−	0.00384606i
$216$		0			0
$217$	0.887718	−	1.53757i	0.0602622	−	0.104377i
$218$	−1.30542			−0.0884142
$219$		0			0
$220$	7.10443	−	4.10174i	0.478980	−	0.276539i
$221$	−20.7542	−	14.4591i	−1.39608	−	0.972627i
$222$		0			0
$223$	0.198374	+	0.198374i	0.0132841	+	0.0132841i	0.713718	−	0.700434i	$-0.247010\pi$
$223$	0.198374	+	0.198374i	0.0132841	+	0.0132841i	−0.700434	+	0.713718i	$0.747010\pi$
$224$	2.81299	−	1.62408i	0.187951	−	0.108513i
$225$		0			0
$226$	8.18076	+	8.18076i	0.544176	+	0.544176i
$227$	−12.3064	−	3.29749i	−0.816804	−	0.218862i	−0.173856	−	0.984771i	$-0.555623\pi$
$227$	−12.3064	−	3.29749i	−0.816804	−	0.218862i	−0.642949	+	0.765909i	$0.722289\pi$
$228$		0			0
$229$	4.16011	+	1.11470i	0.274908	+	0.0736613i	0.393639	−	0.919265i	$-0.371216\pi$
$229$	4.16011	+	1.11470i	0.274908	+	0.0736613i	−0.118731	+	0.992926i	$0.537883\pi$
$230$			3.11870i			0.205641i
$231$		0			0
$232$	6.55297	−	6.55297i	0.430223	−	0.430223i
$233$	21.0744			1.38063			0.690313	−	0.723511i	$-0.257473\pi$
$233$	21.0744			1.38063			0.690313	+	0.723511i	$0.257473\pi$
$234$		0			0
$235$	−22.6530			−1.47772
$236$	−2.06291	+	2.06291i	−0.134284	+	0.134284i
$237$		0			0
$238$			22.7871i			1.47707i
$239$	−12.5730	−	3.36892i	−0.813278	−	0.217917i	−0.171873	−	0.985119i	$-0.554982\pi$
$239$	−12.5730	−	3.36892i	−0.813278	−	0.217917i	−0.641406	+	0.767202i	$0.721648\pi$
$240$		0			0
$241$	−1.20385	−	0.322572i	−0.0775471	−	0.0207787i	0.219837	−	0.975537i	$-0.429447\pi$
$241$	−1.20385	−	0.322572i	−0.0775471	−	0.0207787i	−0.297384	+	0.954758i	$0.596114\pi$
$242$	−4.39341	−	4.39341i	−0.282419	−	0.282419i
$243$		0			0
$244$	−3.10035	+	1.78999i	−0.198480	+	0.114592i
$245$	9.41360	+	9.41360i	0.601413	+	0.601413i
$246$		0			0
$247$	−3.08971	−	17.2831i	−0.196593	−	1.09970i
$248$	0.473367	−	0.273299i	0.0300588	−	0.0173545i
$249$		0			0
$250$	15.2192			0.962547
$251$	−5.64794	+	9.78252i	−0.356495	+	0.617467i	−0.987373	−	0.158415i	$-0.949362\pi$
$251$	−5.64794	+	9.78252i	−0.356495	+	0.617467i	0.630878	+	0.775882i	$0.282695\pi$
$252$		0			0
$253$	−1.75777	+	0.470993i	−0.110510	+	0.0296111i
$254$	0.854944	−	3.19070i	0.0536440	−	0.200202i
$255$		0			0
$256$	1.00000			0.0625000
$257$	0.813117	−	1.40836i	0.0507209	−	0.0878511i	−0.839550	−	0.543282i	$-0.817181\pi$
$257$	0.813117	−	1.40836i	0.0507209	−	0.0878511i	0.890271	+	0.455431i	$0.150515\pi$
$258$		0			0
$259$	−5.53593	−	3.19617i	−0.343986	−	0.198601i
$260$	−12.7147	−	4.59371i	−0.788534	−	0.284890i
$261$		0			0
$262$	−2.85339	+	10.6490i	−0.176283	+	0.657897i
$263$		−	11.3766i		−	0.701511i	−0.936467	−	0.350755i	$-0.885925\pi$
$263$		−	11.3766i		−	0.701511i	0.936467	−	0.350755i	$-0.114075\pi$
$264$		0			0
$265$	−1.57527	+	5.87898i	−0.0967680	+	0.361143i
$266$	−11.1842	+	11.1842i	−0.685745	+	0.685745i
$267$		0			0
$268$	3.36401	+	12.5547i	0.205490	+	0.766898i
$269$	−10.3721	−	5.98835i	−0.632400	−	0.365116i	0.149281	−	0.988795i	$-0.452304\pi$
$269$	−10.3721	−	5.98835i	−0.632400	−	0.365116i	−0.781681	+	0.623678i	$0.785637\pi$
$270$		0			0
$271$	23.9876	+	6.42745i	1.45714	+	0.390440i	0.898502	−	0.438970i	$-0.144657\pi$
$271$	23.9876	+	6.42745i	1.45714	+	0.390440i	0.558640	+	0.829410i	$0.311323\pi$
$272$	−3.50770	+	6.07551i	−0.212685	+	0.368382i
$273$		0			0
$274$	5.68912	+	9.85384i	0.343692	+	0.595292i
$275$	5.12975	+	19.1445i	0.309336	+	1.15446i
$276$		0			0
$277$	−13.5548	+	7.82589i	−0.814432	+	0.470212i	−0.848493	−	0.529207i	$-0.822489\pi$
$277$	−13.5548	+	7.82589i	−0.814432	+	0.470212i	0.0340608	+	0.999420i	$0.489156\pi$
$278$	2.59981	−	2.59981i	0.155926	−	0.155926i
$279$		0			0
$280$	3.15217	+	11.7641i	0.188378	+	0.703038i
$281$	−4.25406	+	1.13987i	−0.253776	+	0.0679991i	−0.383464	−	0.923556i	$-0.625269\pi$
$281$	−4.25406	+	1.13987i	−0.253776	+	0.0679991i	0.129688	+	0.991555i	$0.458602\pi$
$282$		0			0
$283$	15.8083	+	9.12694i	0.939707	+	0.542540i	0.889868	−	0.456217i	$-0.150796\pi$
$283$	15.8083	+	9.12694i	0.939707	+	0.542540i	0.0498385	+	0.998757i	$0.484129\pi$
$284$	8.65035	−	2.31786i	0.513304	−	0.137539i
$285$		0			0
$286$	0.668910	−	7.86007i	0.0395535	−	0.464776i
$287$			5.72202i			0.337760i
$288$		0			0
$289$	−16.1079	−	27.8997i	−0.947523	−	1.64116i
$290$	17.3740	+	30.0926i	1.02024	+	1.76710i
$291$		0			0
$292$	−3.38343	−	3.38343i	−0.198000	−	0.198000i
$293$	−7.90296	−	7.90296i	−0.461696	−	0.461696i	0.437515	−	0.899211i	$-0.355859\pi$
$293$	−7.90296	−	7.90296i	−0.461696	−	0.461696i	−0.899211	+	0.437515i	$0.855859\pi$
$294$		0			0
$295$	−5.46942	−	9.47332i	−0.318442	−	0.551558i
$296$	−0.983995	−	1.70433i	−0.0571936	−	0.0990622i
$297$		0			0
$298$			9.07458i			0.525676i
$299$	2.46066	+	1.71430i	0.142304	+	0.0991405i
$300$		0			0
$301$	−0.182324	+	0.0488535i	−0.0105090	+	0.00281587i
$302$	16.3395	+	9.43362i	0.940234	+	0.542844i
$303$		0			0
$304$	−4.70354	+	1.26031i	−0.269767	+	0.0722837i
$305$	−3.47419	−	12.9658i	−0.198931	−	0.742422i
$306$		0			0
$307$	−14.9777	+	14.9777i	−0.854823	+	0.854823i	−0.990723	−	0.135900i	$-0.956608\pi$
$307$	−14.9777	+	14.9777i	−0.854823	+	0.854823i	0.135900	+	0.990723i	$0.456608\pi$
$308$	−6.15446	+	3.55328i	−0.350683	+	0.202467i
$309$		0			0
$310$	0.530445	+	1.97965i	0.0301273	+	0.112436i
$311$	−6.94304	−	12.0257i	−0.393704	−	0.681915i	0.599231	−	0.800576i	$-0.295473\pi$
$311$	−6.94304	−	12.0257i	−0.393704	−	0.681915i	−0.992935	+	0.118661i	$0.962140\pi$
$312$		0			0
$313$	4.79094	−	8.29816i	0.270800	−	0.469040i	−0.698267	−	0.715838i	$-0.746045\pi$
$313$	4.79094	−	8.29816i	0.270800	−	0.469040i	0.969067	+	0.246798i	$0.0793784\pi$
$314$	21.2998	+	5.70727i	1.20202	+	0.322080i
$315$		0			0
$316$	10.1498	+	5.86001i	0.570972	+	0.329651i
$317$	−4.16793	−	15.5549i	−0.234095	−	0.873653i	−0.978555	−	0.205986i	$-0.933960\pi$
$317$	−4.16793	−	15.5549i	−0.234095	−	0.873653i	0.744460	−	0.667667i	$-0.232707\pi$
$318$		0			0
$319$	−14.3370	+	14.3370i	−0.802721	+	0.802721i
$320$	−0.970449	+	3.62177i	−0.0542498	+	0.202463i
$321$		0			0
$322$		−	2.70168i		−	0.150559i
$323$	8.84157	−	32.9972i	0.491958	−	1.83601i
$324$		0			0
$325$	18.6710	−	26.7999i	1.03568	−	1.48659i
$326$	−5.50181	−	3.17647i	−0.304717	−	0.175928i
$327$		0			0
$328$	−0.880809	+	1.52561i	−0.0486345	+	0.0842375i
$329$	19.6239			1.08190
$330$		0			0
$331$	1.91411	−	7.14356i	0.105209	−	0.392646i	−0.893160	−	0.449740i	$-0.851517\pi$
$331$	1.91411	−	7.14356i	0.105209	−	0.392646i	0.998369	+	0.0570939i	$0.0181834\pi$
$332$	−14.0250	+	3.75798i	−0.769721	+	0.206246i
$333$		0			0
$334$	4.40439	−	7.62863i	0.240998	−	0.417420i
$335$	−48.7346			−2.66266
$336$		0			0
$337$	−16.2869	+	9.40326i	−0.887205	+	0.512228i	−0.873027	−	0.487671i	$-0.837846\pi$
$337$	−16.2869	+	9.40326i	−0.887205	+	0.512228i	−0.0141778	+	0.999899i	$0.504513\pi$
$338$	−10.6135	+	7.50686i	−0.577300	+	0.408319i
$339$		0			0
$340$	−18.6000	−	18.6000i	−1.00873	−	1.00873i
$341$	−1.03567	+	0.597942i	−0.0560845	+	0.0323804i
$342$		0			0
$343$	7.92271	+	7.92271i	0.427786	+	0.427786i
$344$	−0.0561314	−	0.0150404i	−0.00302640	−	0.000810922i
$345$		0			0
$346$	0.0487619	+	0.0130657i	0.00262145	+	0.000702417i
$347$		−	24.7596i		−	1.32916i	−0.747215	−	0.664582i	$-0.768610\pi$
$347$		−	24.7596i		−	1.32916i	0.747215	−	0.664582i	$-0.231390\pi$
$348$		0			0
$349$	2.41492	−	2.41492i	0.129267	−	0.129267i	−0.639513	−	0.768780i	$-0.720864\pi$
$349$	2.41492	−	2.41492i	0.129267	−	0.129267i	0.768780	+	0.639513i	$0.220864\pi$
$350$	−29.4250			−1.57283
$351$		0			0
$352$	−2.18787			−0.116614
$353$	−3.14228	+	3.14228i	−0.167247	+	0.167247i	−0.785768	−	0.618521i	$-0.787732\pi$
$353$	−3.14228	+	3.14228i	−0.167247	+	0.167247i	0.618521	+	0.785768i	$0.287732\pi$
$354$		0			0
$355$			33.5789i			1.78218i
$356$	13.0848	+	3.50606i	0.693493	+	0.185821i
$357$		0			0
$358$	6.86984	+	1.84077i	0.363082	+	0.0972876i
$359$	1.76025	+	1.76025i	0.0929022	+	0.0929022i	0.752031	−	0.659128i	$-0.229075\pi$
$359$	1.76025	+	1.76025i	0.0929022	+	0.0929022i	−0.659128	+	0.752031i	$0.729075\pi$
$360$		0			0
$361$	4.08043	−	2.35584i	0.214759	−	0.123991i
$362$	−14.5897	−	14.5897i	−0.766820	−	0.766820i
$363$		0			0
$364$	11.0146	+	3.97946i	0.577321	+	0.208580i
$365$	15.5375	−	8.97055i	0.813268	−	0.469540i
$366$		0			0
$367$	8.15098			0.425478			0.212739	−	0.977109i	$-0.431762\pi$
$367$	8.15098			0.425478			0.212739	+	0.977109i	$0.431762\pi$
$368$	0.415879	−	0.720323i	0.0216792	−	0.0375494i
$369$		0			0
$370$	7.12760	−	1.90984i	0.370546	−	0.0992876i
$371$	1.36463	−	5.09287i	0.0708481	−	0.264409i
$372$		0			0
$373$	23.6763			1.22591			0.612956	−	0.790117i	$-0.289980\pi$
$373$	23.6763			1.22591			0.612956	+	0.790117i	$0.289980\pi$
$374$	7.67439	−	13.2924i	0.396833	−	0.687336i
$375$		0			0
$376$	5.23214	+	3.02078i	0.269827	+	0.155785i
$377$	33.2934	+	2.83334i	1.71470	+	0.145925i
$378$		0			0
$379$	2.92796	−	10.9273i	0.150399	−	0.561297i	−0.849057	−	0.528302i	$-0.822829\pi$
$379$	2.92796	−	10.9273i	0.150399	−	0.561297i	0.999456	−	0.0329946i	$-0.0105044\pi$
$380$		−	18.2582i		−	0.936625i
$381$		0			0
$382$	5.82140	−	21.7258i	0.297849	−	1.11159i
$383$	21.2432	−	21.2432i	1.08548	−	1.08548i	0.0894896	−	0.995988i	$-0.471476\pi$
$383$	21.2432	−	21.2432i	1.08548	−	1.08548i	0.995988	−	0.0894896i	$-0.0285236\pi$
$384$		0			0
$385$	−6.89655	−	25.7383i	−0.351481	−	1.31174i
$386$	5.85528	+	3.38055i	0.298026	+	0.172065i
$387$		0			0
$388$	−9.53363	−	2.55453i	−0.483997	−	0.129687i
$389$	−4.55590	+	7.89104i	−0.230993	+	0.400092i	−0.958101	−	0.286432i	$-0.907531\pi$
$389$	−4.55590	+	7.89104i	−0.230993	+	0.400092i	0.727108	+	0.686524i	$0.240864\pi$
$390$		0			0
$391$	2.91755	+	5.05335i	0.147547	+	0.255559i
$392$	−0.918947	−	3.42956i	−0.0464138	−	0.173219i
$393$		0			0
$394$	5.33803	−	3.08191i	0.268926	−	0.155265i
$395$	−31.0735	+	31.0735i	−1.56348	+	1.56348i
$396$		0			0
$397$	−2.78992	−	10.4121i	−0.140022	−	0.522570i	−0.999927	−	0.0121147i	$-0.996144\pi$
$397$	−2.78992	−	10.4121i	−0.140022	−	0.522570i	0.859904	−	0.510455i	$-0.170523\pi$
$398$	3.67812	−	0.985551i	0.184368	−	0.0494012i
$399$		0			0
$400$	−7.84529	−	4.52948i	−0.392265	−	0.226474i
$401$	−11.4714	+	3.07374i	−0.572852	+	0.153495i	−0.533604	−	0.845734i	$-0.679163\pi$
$401$	−11.4714	+	3.07374i	−0.572852	+	0.153495i	−0.0392478	+	0.999230i	$0.512496\pi$
$402$		0			0
$403$	1.85352	+	0.669660i	0.0923306	+	0.0333581i
$404$			4.39893i			0.218855i
$405$		0			0
$406$	−15.0508	−	26.0688i	−0.746960	−	1.29377i
$407$	2.15286	+	3.72885i	0.106713	+	0.184832i
$408$		0			0
$409$	−15.1835	−	15.1835i	−0.750777	−	0.750777i	0.223847	−	0.974624i	$-0.428138\pi$
$409$	−15.1835	−	15.1835i	−0.750777	−	0.750777i	−0.974624	+	0.223847i	$0.928138\pi$
$410$	−4.67061	−	4.67061i	−0.230665	−	0.230665i
$411$		0			0
$412$	4.67582	+	8.09876i	0.230361	+	0.398997i
$413$	4.73808	+	8.20659i	0.233146	+	0.403820i
$414$		0			0
$415$		−	54.4421i		−	2.67246i
$416$	2.32414	+	2.75652i	0.113950	+	0.135149i
$417$		0			0
$418$	10.2907	−	2.75740i	0.503337	−	0.134869i
$419$	9.35158	+	5.39914i	0.456855	+	0.263765i	0.710721	−	0.703474i	$-0.248369\pi$
$419$	9.35158	+	5.39914i	0.456855	+	0.263765i	−0.253866	+	0.967239i	$0.581702\pi$
$420$		0			0
$421$	6.34283	−	1.69956i	0.309131	−	0.0828313i	−0.100919	−	0.994895i	$-0.532178\pi$
$421$	6.34283	−	1.69956i	0.309131	−	0.0828313i	0.410049	+	0.912063i	$0.365512\pi$
$422$	−4.96615	−	18.5339i	−0.241748	−	0.902217i
$423$		0			0
$424$	1.14780	−	1.14780i	0.0557422	−	0.0557422i
$425$	55.0378	−	31.7761i	2.66973	−	1.54137i
$426$		0			0
$427$	3.00963	+	11.2321i	0.145646	+	0.543560i
$428$	2.55075	+	4.41803i	0.123295	+	0.213553i
$429$		0			0
$430$	0.108945	−	0.188699i	0.00525381	−	0.00909987i
$431$	−5.36331	−	1.43709i	−0.258341	−	0.0692224i	0.127324	−	0.991861i	$-0.459361\pi$
$431$	−5.36331	−	1.43709i	−0.258341	−	0.0692224i	−0.385665	+	0.922639i	$0.626028\pi$
$432$		0			0
$433$	31.1666	+	17.9940i	1.49777	+	0.864737i	0.999997	−	0.00257012i	$-0.000818096\pi$
$433$	31.1666	+	17.9940i	1.49777	+	0.864737i	0.497773	+	0.867308i	$0.334151\pi$
$434$	−0.459516	−	1.71494i	−0.0220575	−	0.0823197i
$435$		0			0
$436$	−0.923072	+	0.923072i	−0.0442071	+	0.0442071i
$437$	−1.04827	+	3.91220i	−0.0501456	+	0.187146i
$438$		0			0
$439$		−	20.3140i		−	0.969533i	−0.874644	−	0.484767i	$-0.838905\pi$
$439$		−	20.3140i		−	0.969533i	0.874644	−	0.484767i	$-0.161095\pi$
$440$	2.12322	−	7.92396i	0.101220	−	0.377760i
$441$		0			0
$442$	−24.8996	+	4.45131i	−1.18435	+	0.211727i
$443$	16.2468	+	9.38011i	0.771910	+	0.445662i	0.833556	−	0.552436i	$-0.186302\pi$
$443$	16.2468	+	9.38011i	0.771910	+	0.445662i	−0.0616456	+	0.998098i	$0.519635\pi$
$444$		0			0
$445$	−25.3963	+	43.9876i	−1.20390	+	2.08521i
$446$	0.280543			0.0132841
$447$		0			0
$448$	0.840685	−	3.13748i	0.0397187	−	0.148232i
$449$	−15.3460	+	4.11194i	−0.724221	+	0.194055i	−0.602054	−	0.798455i	$-0.705651\pi$
$449$	−15.3460	+	4.11194i	−0.724221	+	0.194055i	−0.122167	+	0.992510i	$0.538984\pi$
$450$		0			0
$451$	1.92710	−	3.33783i	0.0907435	−	0.157172i
$452$	11.5693			0.544176
$453$		0			0
$454$	−11.0336	+	6.37026i	−0.517833	+	0.298971i
$455$	−25.1018	+	36.0304i	−1.17679	+	1.68913i
$456$		0			0
$457$	−0.620379	−	0.620379i	−0.0290201	−	0.0290201i	0.692448	−	0.721468i	$-0.256532\pi$
$457$	−0.620379	−	0.620379i	−0.0290201	−	0.0290201i	−0.721468	+	0.692448i	$0.756532\pi$
$458$	3.72985	−	2.15343i	0.174285	−	0.100623i
$459$		0			0
$460$	2.20525	+	2.20525i	0.102820	+	0.102820i
$461$	−22.4997	−	6.02877i	−1.04792	−	0.280788i	−0.306525	−	0.951863i	$-0.599166\pi$
$461$	−22.4997	−	6.02877i	−1.04792	−	0.280788i	−0.741390	+	0.671074i	$0.765833\pi$
$462$		0			0
$463$	−17.4167	−	4.66680i	−0.809424	−	0.216885i	−0.169707	−	0.985495i	$-0.554282\pi$
$463$	−17.4167	−	4.66680i	−0.809424	−	0.216885i	−0.639718	+	0.768610i	$0.720949\pi$
$464$		−	9.26729i		−	0.430223i
$465$		0			0
$466$	14.9018	−	14.9018i	0.690313	−	0.690313i
$467$	−24.8989			−1.15218			−0.576091	−	0.817386i	$-0.695423\pi$
$467$	−24.8989			−1.15218			−0.576091	+	0.817386i	$0.695423\pi$
$468$		0			0
$469$	42.2181			1.94945
$470$	−16.0181	+	16.0181i	−0.738859	+	0.738859i
$471$		0			0
$472$			2.91739i			0.134284i
$473$	0.122808	+	0.0329064i	0.00564673	+	0.00151304i
$474$		0			0
$475$	42.6092	+	11.4171i	1.95504	+	0.523852i
$476$	16.1129	+	16.1129i	0.738535	+	0.738535i
$477$		0			0
$478$	−11.2726	+	6.50825i	−0.515598	+	0.297681i
$479$	5.37507	+	5.37507i	0.245593	+	0.245593i	0.819159	−	0.573566i	$-0.194440\pi$
$479$	5.37507	+	5.37507i	0.245593	+	0.245593i	−0.573566	+	0.819159i	$0.694440\pi$
$480$		0			0
$481$	2.41107	−	6.67350i	0.109935	−	0.304285i
$482$	−1.07935	+	0.623161i	−0.0491629	+	0.0283842i
$483$		0			0
$484$	−6.21322			−0.282419
$485$	18.5038	−	32.0495i	0.840215	−	1.45529i
$486$		0			0
$487$	−32.0391	+	8.58485i	−1.45183	+	0.389017i	−0.896660	−	0.442720i	$-0.854014\pi$
$487$	−32.0391	+	8.58485i	−1.45183	+	0.389017i	−0.555171	+	0.831736i	$0.687347\pi$
$488$	−0.926566	+	3.45799i	−0.0419437	+	0.156536i
$489$		0			0
$490$	13.3128			0.601413
$491$	12.9239	−	22.3849i	0.583248	−	1.01022i	−0.411843	−	0.911255i	$-0.635115\pi$
$491$	12.9239	−	22.3849i	0.583248	−	1.01022i	0.995091	−	0.0989607i	$-0.0315518\pi$
$492$		0			0
$493$	56.3035	+	32.5069i	2.53578	+	1.46404i
$494$	−14.4057	−	10.0362i	−0.648145	−	0.451552i
$495$		0			0
$496$	0.141470	−	0.527973i	0.00635218	−	0.0237067i
$497$		−	29.0889i		−	1.30482i
$498$		0			0
$499$	−4.22357	+	15.7626i	−0.189073	+	0.705629i	0.804649	+	0.593751i	$0.202353\pi$
$499$	−4.22357	+	15.7626i	−0.189073	+	0.705629i	−0.993722	+	0.111879i	$0.964313\pi$
$500$	10.7616	−	10.7616i	0.481273	−	0.481273i
$501$		0			0
$502$	2.92359	+	10.9110i	0.130486	+	0.486981i
$503$	6.80210	+	3.92720i	0.303291	+	0.175105i	0.643920	−	0.765093i	$-0.277307\pi$
$503$	6.80210	+	3.92720i	0.303291	+	0.175105i	−0.340630	+	0.940198i	$0.610640\pi$
$504$		0			0
$505$	−15.9319	−	4.26894i	−0.708960	−	0.189965i
$506$	−0.909889	+	1.57597i	−0.0404495	+	0.0700606i
$507$		0			0
$508$	−1.65163	−	2.86070i	−0.0732790	−	0.126923i
$509$	6.70498	+	25.0233i	0.297193	+	1.10914i	0.939460	+	0.342659i	$0.111328\pi$
$509$	6.70498	+	25.0233i	0.297193	+	1.10914i	−0.642267	+	0.766481i	$0.722006\pi$
$510$		0			0
$511$	−13.4599	+	7.77105i	−0.595429	+	0.343771i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	−0.420900	−	1.57082i	−0.0185651	−	0.0692860i
$515$	−33.8695	+	9.07529i	−1.49247	+	0.399905i
$516$		0			0
$517$	−11.4473	−	6.60908i	−0.503450	−	0.290667i
$518$	−6.17453	+	1.65446i	−0.271293	+	0.0726928i
$519$		0			0
$520$	−12.2389	+	5.74243i	−0.536712	+	0.251822i
$521$		−	44.6910i		−	1.95795i	−0.203981	−	0.978975i	$-0.565388\pi$
$521$		−	44.6910i		−	1.95795i	0.203981	−	0.978975i	$-0.434612\pi$
$522$		0			0
$523$	2.38397	+	4.12916i	0.104244	+	0.180556i	0.913429	−	0.406998i	$-0.133424\pi$
$523$	2.38397	+	4.12916i	0.104244	+	0.180556i	−0.809185	+	0.587554i	$0.800091\pi$
$524$	5.51233	+	9.54763i	0.240807	+	0.417090i
$525$		0			0
$526$	−8.04447	−	8.04447i	−0.350755	−	0.350755i
$527$	2.71147	+	2.71147i	0.118113	+	0.118113i
$528$		0			0
$529$	11.1541	+	19.3195i	0.484960	+	0.839976i
$530$	3.04319	+	5.27095i	0.132188	+	0.228956i
$531$		0			0
$532$			15.8168i			0.685745i
$533$	−6.25248	+	1.11776i	−0.270825	+	0.0484155i
$534$		0			0
$535$	−18.4764	+	4.95074i	−0.798806	+	0.214039i
$536$	11.2562	+	6.49877i	0.486194	+	0.280704i
$537$		0			0
$538$	−11.5686	+	3.09980i	−0.498758	+	0.133642i
$539$	2.01054	+	7.50343i	0.0866000	+	0.323196i
$540$		0			0
$541$	−31.0921	+	31.0921i	−1.33675	+	1.33675i	−0.437565	+	0.899187i	$0.644159\pi$
$541$	−31.0921	+	31.0921i	−1.33675	+	1.33675i	−0.899187	+	0.437565i	$0.855841\pi$
$542$	21.5067	−	12.4169i	0.923791	−	0.533351i
$543$		0			0
$544$	1.81572	+	6.77635i	0.0778483	+	0.290534i
$545$	−2.44736	−	4.23894i	−0.104833	−	0.181576i
$546$		0			0
$547$	7.14869	−	12.3819i	0.305656	−	0.529412i	−0.671751	−	0.740777i	$-0.734458\pi$
$547$	7.14869	−	12.3819i	0.305656	−	0.529412i	0.977407	+	0.211365i	$0.0677910\pi$
$548$	10.9905	+	2.94490i	0.469492	+	0.125800i
$549$		0			0
$550$	17.1645	+	9.90992i	0.731896	+	0.422561i
$551$	11.6797	+	43.5891i	0.497570	+	1.85696i
$552$		0			0
$553$	26.9185	−	26.9185i	1.14469	−	1.14469i
$554$	−4.05098	+	15.1185i	−0.172110	+	0.642322i
$555$		0			0
$556$		−	3.67668i		−	0.155926i
$557$	−11.2642	+	42.0386i	−0.477280	+	1.78123i	0.135277	+	0.990808i	$0.456807\pi$
$557$	−11.2642	+	42.0386i	−0.477280	+	1.78123i	−0.612557	+	0.790426i	$0.709859\pi$
$558$		0			0
$559$	−0.0889982	−	0.189683i	−0.00376422	−	0.00802273i
$560$	10.5474	+	6.08953i	0.445708	+	0.257330i
$561$		0			0
$562$	−2.20206	+	3.81409i	−0.0928885	+	0.160888i
$563$	−7.46962			−0.314807			−0.157403	−	0.987534i	$-0.550312\pi$
$563$	−7.46962			−0.314807			−0.157403	+	0.987534i	$0.550312\pi$
$564$		0			0
$565$	−11.2275	+	41.9015i	−0.472343	+	1.76281i
$566$	17.6319	−	4.72445i	0.741124	−	0.198583i
$567$		0			0
$568$	4.47775	−	7.75569i	0.187882	−	0.325422i
$569$	41.3056			1.73162			0.865810	−	0.500373i	$-0.166804\pi$
$569$	41.3056			1.73162			0.865810	+	0.500373i	$0.166804\pi$
$570$		0			0
$571$	38.0908	−	21.9917i	1.59405	−	0.920326i	0.601449	−	0.798911i	$-0.294590\pi$
$571$	38.0908	−	21.9917i	1.59405	−	0.920326i	0.992602	−	0.121415i	$-0.0387432\pi$
$572$	−5.08492	−	6.03090i	−0.212611	−	0.252165i
$573$		0			0
$574$	4.04608	+	4.04608i	0.168880	+	0.168880i
$575$	−6.52538	+	3.76743i	−0.272127	+	0.157113i
$576$		0			0
$577$	−27.8109	−	27.8109i	−1.15778	−	1.15778i	−0.984952	−	0.172831i	$-0.944709\pi$
$577$	−27.8109	−	27.8109i	−1.15778	−	1.15778i	−0.172831	−	0.984952i	$-0.555291\pi$
$578$	−31.1180	−	8.33806i	−1.29434	−	0.346817i
$579$		0			0
$580$	33.5640	+	8.99344i	1.39367	+	0.373432i
$581$			47.1624i			1.95663i
$582$		0			0
$583$	−2.51124	+	2.51124i	−0.104005	+	0.104005i
$584$	−4.78490			−0.198000
$585$		0			0
$586$	−11.1765			−0.461696
$587$	−7.42299	+	7.42299i	−0.306380	+	0.306380i	−0.843503	−	0.537124i	$-0.819511\pi$
$587$	−7.42299	+	7.42299i	−0.306380	+	0.306380i	0.537124	+	0.843503i	$0.319511\pi$
$588$		0			0
$589$			2.66164i			0.109671i
$590$	−10.5661	−	2.83118i	−0.435000	−	0.116558i
$591$		0			0
$592$	−1.90093	−	0.509353i	−0.0781279	−	0.0209343i
$593$	−24.8672	−	24.8672i	−1.02117	−	1.02117i	−0.999771	−	0.0214039i	$-0.993186\pi$
$593$	−24.8672	−	24.8672i	−1.02117	−	1.02117i	−0.0214039	−	0.999771i	$-0.506814\pi$
$594$		0			0
$595$	−73.9940	+	42.7205i	−3.03346	+	1.75137i
$596$	6.41670	+	6.41670i	0.262838	+	0.262838i
$597$		0			0
$598$	2.95214	−	0.527755i	0.120722	−	0.0215815i
$599$	−5.46701	+	3.15638i	−0.223376	+	0.128966i	−0.607512	−	0.794310i	$-0.707833\pi$
$599$	−5.46701	+	3.15638i	−0.223376	+	0.128966i	0.384137	+	0.923276i	$0.374499\pi$
$600$		0			0
$601$	33.7487			1.37664			0.688318	−	0.725409i	$-0.258349\pi$
$601$	33.7487			1.37664			0.688318	+	0.725409i	$0.258349\pi$
$602$	−0.0943777	+	0.163467i	−0.00384655	+	0.00666242i
$603$		0			0
$604$	18.2244	−	4.88320i	0.741539	−	0.198695i
$605$	6.02961	−	22.5028i	0.245139	−	0.914870i
$606$		0			0
$607$	25.8145			1.04778			0.523888	−	0.851787i	$-0.324481\pi$
$607$	25.8145			1.04778			0.523888	+	0.851787i	$0.324481\pi$
$608$	−2.43473	+	4.21708i	−0.0987414	+	0.171025i
$609$		0			0
$610$	−11.6249	−	6.71161i	−0.470677	−	0.271745i
$611$	3.83341	+	21.4432i	0.155083	+	0.867499i
$612$		0			0
$613$	4.39253	−	16.3932i	0.177413	−	0.662113i	−0.818715	−	0.574200i	$-0.805313\pi$
$613$	4.39253	−	16.3932i	0.177413	−	0.662113i	0.996128	−	0.0879138i	$-0.0280200\pi$
$614$			21.1817i			0.854823i
$615$		0			0
$616$	−1.83931	+	6.86441i	−0.0741080	+	0.276575i
$617$	−32.7229	+	32.7229i	−1.31737	+	1.31737i	−0.401528	+	0.915847i	$0.631521\pi$
$617$	−32.7229	+	32.7229i	−1.31737	+	1.31737i	−0.915847	+	0.401528i	$0.868479\pi$
$618$		0			0
$619$	−8.87599	−	33.1257i	−0.356756	−	1.33143i	−0.878260	−	0.478183i	$-0.841295\pi$
$619$	−8.87599	−	33.1257i	−0.356756	−	1.33143i	0.521504	−	0.853249i	$-0.325371\pi$
$620$	1.77490	+	1.02474i	0.0712819	+	0.0411546i
$621$		0			0
$622$	−13.4129	−	3.59398i	−0.537809	−	0.144106i
$623$	22.0004	−	38.1058i	0.881428	−	1.52668i
$624$		0			0
$625$	5.88500	+	10.1931i	0.235400	+	0.407725i
$626$	−2.47997	−	9.25539i	−0.0991197	−	0.369920i
$627$		0			0
$628$	19.0969	−	11.0256i	0.762049	−	0.439969i
$629$	9.76248	−	9.76248i	0.389256	−	0.389256i
$630$		0			0
$631$	−2.50134	−	9.33512i	−0.0995767	−	0.371625i	0.898097	−	0.439798i	$-0.144950\pi$
$631$	−2.50134	−	9.33512i	−0.0995767	−	0.371625i	−0.997674	+	0.0681724i	$0.978283\pi$
$632$	11.3207	−	3.03336i	0.450312	−	0.120661i
$633$		0			0
$634$	−13.9462	−	8.05183i	−0.553874	−	0.319779i
$635$	11.9636	−	3.20564i	0.474761	−	0.127212i
$636$		0			0
$637$	7.31786	−	10.5039i	0.289944	−	0.416178i
$638$			20.2756i			0.802721i
$639$		0			0
$640$	1.87476	+	3.24719i	0.0741066	+	0.128356i
$641$	11.1614	+	19.3321i	0.440848	+	0.763570i	0.997753	−	0.0670058i	$-0.0213446\pi$
$641$	11.1614	+	19.3321i	0.440848	+	0.763570i	−0.556905	+	0.830576i	$0.688011\pi$
$642$		0			0
$643$	−26.4365	−	26.4365i	−1.04255	−	1.04255i	−0.999053	−	0.0434999i	$-0.986149\pi$
$643$	−26.4365	−	26.4365i	−1.04255	−	1.04255i	−0.0434999	−	0.999053i	$-0.513851\pi$
$644$	−1.91038	−	1.91038i	−0.0752794	−	0.0752794i
$645$		0			0
$646$	−17.0806	−	29.5845i	−0.672027	−	1.16399i
$647$	1.97324	+	3.41775i	0.0775760	+	0.134366i	0.902204	−	0.431310i	$-0.141949\pi$
$647$	1.97324	+	3.41775i	0.0775760	+	0.134366i	−0.824628	+	0.565676i	$0.808615\pi$
$648$		0			0
$649$		−	6.38288i		−	0.250550i
$650$	−5.74797	−	32.1528i	−0.225454	−	1.26114i
$651$		0			0
$652$	−6.13647	+	1.64426i	−0.240323	+	0.0643943i
$653$	−12.8636	−	7.42680i	−0.503391	−	0.290633i	0.226722	−	0.973960i	$-0.427199\pi$
$653$	−12.8636	−	7.42680i	−0.503391	−	0.290633i	−0.730113	+	0.683326i	$0.760533\pi$
$654$		0			0
$655$	−39.9287	+	10.6989i	−1.56014	+	0.418039i
$656$	0.455940	+	1.70159i	0.0178015	+	0.0664360i
$657$		0			0
$658$	13.8762	−	13.8762i	0.540951	−	0.540951i
$659$	−34.6644	+	20.0135i	−1.35033	+	0.779615i	−0.988296	−	0.152548i	$-0.951252\pi$
$659$	−34.6644	+	20.0135i	−1.35033	+	0.779615i	−0.362037	+	0.932164i	$0.617919\pi$
$660$		0			0
$661$	1.32797	+	4.95604i	0.0516519	+	0.192768i	0.986931	−	0.161144i	$-0.0515182\pi$
$661$	1.32797	+	4.95604i	0.0516519	+	0.192768i	−0.935279	+	0.353911i	$0.884852\pi$
$662$	−3.69778	−	6.40474i	−0.143718	−	0.248927i
$663$		0			0
$664$	−7.25986	+	12.5744i	−0.281737	+	0.487983i
$665$	−57.2847	−	15.3494i	−2.22141	−	0.595224i
$666$		0			0
$667$	−6.67544	−	3.85407i	−0.258474	−	0.149230i
$668$	−2.27988	−	8.50863i	−0.0882112	−	0.329209i
$669$		0			0
$670$	−34.4606	+	34.4606i	−1.33133	+	1.33133i
$671$	2.02721	−	7.56564i	0.0782595	−	0.292068i
$672$		0			0
$673$		−	40.5684i		−	1.56380i	−0.623405	−	0.781899i	$-0.714251\pi$
$673$		−	40.5684i		−	1.56380i	0.623405	−	0.781899i	$-0.285749\pi$
$674$	−4.86748	+	18.1657i	−0.187489	+	0.699717i
$675$		0			0
$676$	−2.19675	+	12.8131i	−0.0844904	+	0.492810i
$677$	11.0747	+	6.39397i	0.425635	+	0.245740i	0.697485	−	0.716599i	$-0.254302\pi$
$677$	11.0747	+	6.39397i	0.425635	+	0.245740i	−0.271851	+	0.962339i	$0.587636\pi$
$678$		0			0
$679$	−16.0296	+	27.7640i	−0.615158	+	1.06549i
$680$	−26.3044			−1.00873
$681$		0			0
$682$	−0.309518	+	1.15514i	−0.0118520	+	0.0442324i
$683$	31.3371	−	8.39675i	1.19908	−	0.321293i	0.396612	−	0.917986i	$-0.370186\pi$
$683$	31.3371	−	8.39675i	1.19908	−	0.321293i	0.802469	+	0.596693i	$0.203519\pi$
$684$		0			0
$685$	−21.3315	+	36.9473i	−0.815035	+	1.41168i
$686$	11.2044			0.427786
$687$		0			0
$688$	−0.0503260	+	0.0290558i	−0.00191866	+	0.00110774i
$689$	5.83158	+	0.496281i	0.222166	+	0.0189068i
$690$		0			0
$691$	−6.81892	−	6.81892i	−0.259404	−	0.259404i	0.565408	−	0.824812i	$-0.308719\pi$
$691$	−6.81892	−	6.81892i	−0.259404	−	0.259404i	−0.824812	+	0.565408i	$0.808719\pi$
$692$	0.0437187	−	0.0252410i	0.00166194	−	0.000959519i
$693$		0			0
$694$	−17.5077	−	17.5077i	−0.664582	−	0.664582i
$695$	13.3161	+	3.56803i	0.505108	+	0.135343i
$696$		0			0
$697$	−11.9373	−	3.19860i	−0.452159	−	0.121156i
$698$		−	3.41521i		−	0.129267i
$699$		0			0
$700$	−20.8066	+	20.8066i	−0.786415	+	0.786415i
$701$	45.7174			1.72672			0.863360	−	0.504588i	$-0.168355\pi$
$701$	45.7174			1.72672			0.863360	+	0.504588i	$0.168355\pi$
$702$		0			0
$703$	9.58306			0.361432
$704$	−1.54706	+	1.54706i	−0.0583070	+	0.0583070i
$705$		0			0
$706$			4.44385i			0.167247i
$707$	13.8016	+	3.69811i	0.519061	+	0.139082i
$708$		0			0
$709$	−15.4828	−	4.14860i	−0.581468	−	0.155804i	−0.0439170	−	0.999035i	$-0.513984\pi$
$709$	−15.4828	−	4.14860i	−0.581468	−	0.155804i	−0.537551	+	0.843231i	$0.680650\pi$
$710$	23.7439	+	23.7439i	0.891092	+	0.891092i
$711$		0			0
$712$	11.7315	−	6.77319i	0.439657	−	0.253836i
$713$	−0.321476	−	0.321476i	−0.0120394	−	0.0120394i
$714$		0			0
$715$	26.7772	−	12.5637i	1.00141	−	0.469856i
$716$	6.15933	−	3.55609i	0.230185	−	0.132897i
$717$		0			0
$718$	2.48936			0.0929022
$719$	10.0799	−	17.4589i	0.375917	−	0.651107i	−0.614547	−	0.788880i	$-0.710661\pi$
$719$	10.0799	−	17.4589i	0.375917	−	0.651107i	0.990464	+	0.137773i	$0.0439944\pi$
$720$		0			0
$721$	29.3406	−	7.86179i	1.09270	−	0.292788i
$722$	1.21947	−	4.55112i	0.0453840	−	0.169375i
$723$		0			0
$724$	−20.6330			−0.766820
$725$	−41.9760	+	72.7046i	−1.55895	+	2.70018i
$726$		0			0
$727$	−19.8457	−	11.4579i	−0.736036	−	0.424950i	0.0845905	−	0.996416i	$-0.473042\pi$
$727$	−19.8457	−	11.4579i	−0.736036	−	0.424950i	−0.820626	+	0.571465i	$0.806375\pi$
$728$	10.6024	−	4.97458i	0.392950	−	0.184370i
$729$		0			0
$730$	4.64350	−	17.3298i	0.171864	−	0.641404i
$731$		−	0.407675i		−	0.0150784i
$732$		0			0
$733$	7.04796	−	26.3034i	0.260322	−	0.971536i	−0.704729	−	0.709476i	$-0.748931\pi$
$733$	7.04796	−	26.3034i	0.260322	−	0.971536i	0.965052	−	0.262060i	$-0.0844018\pi$
$734$	5.76362	−	5.76362i	0.212739	−	0.212739i
$735$		0			0
$736$	−0.215275	−	0.803416i	−0.00793513	−	0.0296143i
$737$	−24.6271	−	14.2185i	−0.907152	−	0.523744i
$738$		0			0
$739$	23.3006	+	6.24337i	0.857126	+	0.229666i	0.660513	−	0.750815i	$-0.270339\pi$
$739$	23.3006	+	6.24337i	0.857126	+	0.229666i	0.196613	+	0.980481i	$0.437006\pi$
$740$	3.68952	−	6.39043i	0.135629	−	0.234917i
$741$		0			0
$742$	−2.63627	−	4.56615i	−0.0967804	−	0.167628i
$743$	11.8113	+	44.0805i	0.433316	+	1.61716i	0.745064	+	0.666993i	$0.232419\pi$
$743$	11.8113	+	44.0805i	0.433316	+	1.61716i	−0.311747	+	0.950165i	$0.600914\pi$
$744$		0			0
$745$	−29.4669	+	17.0127i	−1.07958	+	0.623297i
$746$	16.7417	−	16.7417i	0.612956	−	0.612956i
$747$		0			0
$748$	−3.97256	−	14.8258i	−0.145251	−	0.542084i
$749$	16.0058	−	4.28875i	0.584841	−	0.156708i
$750$		0			0
$751$	27.0510	+	15.6179i	0.987104	+	0.569905i	0.904407	−	0.426670i	$-0.140313\pi$
$751$	27.0510	+	15.6179i	0.987104	+	0.569905i	0.0826964	+	0.996575i	$0.473647\pi$
$752$	5.83570	−	1.56367i	0.212806	−	0.0570212i
$753$		0			0
$754$	25.5454	−	21.5385i	0.930310	−	0.784385i
$755$			70.7433i			2.57461i
$756$		0			0
$757$	11.2648	+	19.5112i	0.409426	+	0.709147i	0.994826	−	0.101598i	$-0.0323956\pi$
$757$	11.2648	+	19.5112i	0.409426	+	0.709147i	−0.585399	+	0.810745i	$0.699062\pi$
$758$	−5.65638	−	9.79713i	−0.205449	−	0.355848i
$759$		0			0
$760$	−12.9105	−	12.9105i	−0.468313	−	0.468313i
$761$	−23.2943	−	23.2943i	−0.844417	−	0.844417i	0.145013	−	0.989430i	$-0.453678\pi$
$761$	−23.2943	−	23.2943i	−0.844417	−	0.844417i	−0.989430	+	0.145013i	$0.953678\pi$
$762$		0			0
$763$	2.12011	+	3.67213i	0.0767530	+	0.132940i
$764$	−11.2461	−	19.4788i	−0.406869	−	0.704718i
$765$		0			0
$766$		−	30.0424i		−	1.08548i
$767$	−8.04183	+	6.78043i	−0.290374	+	0.244827i
$768$		0			0
$769$	−50.4684	+	13.5230i	−1.81994	+	0.487651i	−0.996782	−	0.0801629i	$-0.974456\pi$
$769$	−50.4684	+	13.5230i	−1.81994	+	0.487651i	−0.823157	+	0.567814i	$0.807789\pi$
$770$	−23.0763	−	13.3231i	−0.831613	−	0.480132i
$771$		0			0
$772$	6.53071	−	1.74990i	0.235046	−	0.0629803i
$773$	10.2286	+	38.1735i	0.367896	+	1.37301i	0.863452	+	0.504431i	$0.168298\pi$
$773$	10.2286	+	38.1735i	0.367896	+	1.37301i	−0.495556	+	0.868576i	$0.665036\pi$
$774$		0			0
$775$	−3.50131	+	3.50131i	−0.125771	+	0.125771i
$776$	−8.54762	+	4.93497i	−0.306842	+	0.177155i
$777$		0			0
$778$	2.35831	+	8.80132i	0.0845494	+	0.315543i
$779$	−4.28907	−	7.42888i	−0.153672	−	0.266167i
$780$		0			0
$781$	−9.79675	+	16.9685i	−0.350555	+	0.607179i
$782$	5.63628	+	1.51024i	0.201553	+	0.0540060i
$783$		0			0
$784$	−3.07486	−	1.77527i	−0.109816	−	0.0634025i
$785$	21.3996	+	79.8643i	0.763784	+	2.85048i
$786$		0			0
$787$	0.606911	−	0.606911i	0.0216341	−	0.0216341i	−0.696207	−	0.717841i	$-0.745130\pi$
$787$	0.606911	−	0.606911i	0.0216341	−	0.0216341i	0.717841	+	0.696207i	$0.245130\pi$
$788$	1.59532	−	5.95380i	0.0568308	−	0.212095i
$789$		0			0
$790$			43.9445i			1.56348i
$791$	9.72618	−	36.2986i	0.345823	−	1.29063i
$792$		0			0
$793$	−11.6855	+	5.48276i	−0.414963	+	0.194699i
$794$	−9.33526	−	5.38971i	−0.331296	−	0.191274i
$795$		0			0
$796$	1.90394	−	3.29772i	0.0674833	−	0.116884i
$797$	22.1446			0.784401			0.392201	−	0.919880i	$-0.371714\pi$
$797$	22.1446			0.784401			0.392201	+	0.919880i	$0.371714\pi$
$798$		0			0
$799$	−10.9698	+	40.9397i	−0.388082	+	1.44834i
$800$	−8.75029	+	2.34463i	−0.309369	+	0.0828953i
$801$		0			0
$802$	−5.93801	+	10.2849i	−0.209678	+	0.363174i
$803$	10.4687			0.369434
$804$		0			0
$805$	8.77286	−	5.06501i	0.309203	−	0.178518i
$806$	1.78416	−	0.837118i	0.0628443	−	0.0294862i
$807$		0			0
$808$	3.11051	+	3.11051i	0.109427	+	0.109427i
$809$	−43.7042	+	25.2326i	−1.53656	+	0.887132i	−0.537521	+	0.843251i	$0.680639\pi$
$809$	−43.7042	+	25.2326i	−1.53656	+	0.887132i	−0.999037	+	0.0438813i	$0.986028\pi$
$810$		0			0
$811$	28.9155	+	28.9155i	1.01536	+	1.01536i	0.999880	+	0.0154811i	$0.00492798\pi$
$811$	28.9155	+	28.9155i	1.01536	+	1.01536i	0.0154811	+	0.999880i	$0.495072\pi$
$812$	−29.0760	−	7.79088i	−1.02037	−	0.273406i
$813$		0			0
$814$	4.15900	+	1.11440i	0.145773	+	0.0390597i
$815$		−	23.8205i		−	0.834397i
$816$		0			0
$817$	0.200091	−	0.200091i	0.00700031	−	0.00700031i
$818$	−21.4728			−0.750777
$819$		0			0
$820$	−6.60524			−0.230665
$821$	2.48343	−	2.48343i	0.0866725	−	0.0866725i	−0.662441	−	0.749114i	$-0.730480\pi$
$821$	2.48343	−	2.48343i	0.0866725	−	0.0866725i	0.749114	+	0.662441i	$0.230480\pi$
$822$		0			0
$823$		−	50.7370i		−	1.76858i	−0.466936	−	0.884291i	$-0.654642\pi$
$823$		−	50.7370i		−	1.76858i	0.466936	−	0.884291i	$-0.345358\pi$
$824$	9.03299	+	2.42038i	0.314679	+	0.0843180i
$825$		0			0
$826$	9.15326	+	2.45261i	0.318483	+	0.0853372i
$827$	−3.62799	−	3.62799i	−0.126158	−	0.126158i	0.641209	−	0.767366i	$-0.278433\pi$
$827$	−3.62799	−	3.62799i	−0.126158	−	0.126158i	−0.767366	+	0.641209i	$0.778433\pi$
$828$		0			0
$829$	−18.3968	+	10.6214i	−0.638949	+	0.368897i	−0.784209	−	0.620496i	$-0.786931\pi$
$829$	−18.3968	+	10.6214i	−0.638949	+	0.368897i	0.145261	+	0.989393i	$0.453598\pi$
$830$	−38.4964	−	38.4964i	−1.33623	−	1.33623i
$831$		0			0
$832$	3.59257	+	0.305736i	0.124550	+	0.0105995i
$833$	21.5713	−	12.4542i	0.747402	−	0.431513i
$834$		0			0
$835$	33.0288			1.14301
$836$	5.32688	−	9.22643i	0.184234	−	0.319103i
$837$		0			0
$838$	10.4303	−	2.79480i	0.360310	−	0.0965447i
$839$	5.32156	−	19.8603i	0.183721	−	0.685655i	−0.811180	−	0.584796i	$-0.801174\pi$
$839$	5.32156	−	19.8603i	0.183721	−	0.685655i	0.994901	−	0.100858i	$-0.0321589\pi$
$840$		0			0
$841$	−56.8827			−1.96147
$842$	3.28329	−	5.68683i	0.113150	−	0.195981i
$843$		0			0
$844$	−16.6171	−	9.59387i	−0.571983	−	0.330234i
$845$	−44.2740	−	20.3905i	−1.52307	−	0.701456i
$846$		0			0
$847$	−5.22336	+	19.4939i	−0.179477	+	0.669817i
$848$		−	1.62324i		−	0.0557422i
$849$		0			0
$850$	16.4485	−	61.3867i	0.564180	−	2.10555i
$851$	−1.15746	+	1.15746i	−0.0396771	+	0.0396771i
$852$		0			0
$853$	4.71414	+	17.5934i	0.161409	+	0.602387i	0.998471	+	0.0552788i	$0.0176048\pi$
$853$	4.71414	+	17.5934i	0.161409	+	0.602387i	−0.837062	+	0.547108i	$0.815729\pi$
$854$	10.0704	+	5.81417i	0.344603	+	0.198957i
$855$		0			0
$856$	4.92767	+	1.32036i	0.168424	+	0.0451291i
$857$	−8.45527	+	14.6450i	−0.288826	+	0.500262i	−0.973530	−	0.228560i	$-0.926598\pi$
$857$	−8.45527	+	14.6450i	−0.288826	+	0.500262i	0.684703	+	0.728822i	$0.259932\pi$
$858$		0			0
$859$	14.3028	+	24.7732i	0.488007	+	0.845252i	0.999905	−	0.0137939i	$-0.00439089\pi$
$859$	14.3028	+	24.7732i	0.488007	+	0.845252i	−0.511898	+	0.859046i	$0.671058\pi$
$860$	−0.0563943	−	0.210466i	−0.00192303	−	0.00717684i
$861$		0			0
$862$	−4.80861	+	2.77625i	−0.163782	+	0.0945595i
$863$	−7.73986	+	7.73986i	−0.263468	+	0.263468i	−0.826461	−	0.562993i	$-0.809650\pi$
$863$	−7.73986	+	7.73986i	−0.263468	+	0.263468i	0.562993	+	0.826461i	$0.309650\pi$
$864$		0			0
$865$	0.0489902	+	0.182834i	0.00166572	+	0.00621654i
$866$	34.7618	−	9.31439i	1.18125	−	0.316516i
$867$		0			0
$868$	−1.53757	−	0.887718i	−0.0521886	−	0.0301311i
$869$	−24.7682	+	6.63661i	−0.840202	+	0.225131i
$870$		0			0
$871$	8.24702	+	46.1319i	0.279440	+	1.56312i
$872$			1.30542i			0.0442071i
$873$		0			0
$874$	2.02511	+	3.50759i	0.0685002	+	0.118646i
$875$	−24.7172	−	42.8114i	−0.835593	−	1.44729i
$876$		0			0
$877$	33.2806	+	33.2806i	1.12381	+	1.12381i	0.991164	+	0.132643i	$0.0423464\pi$
$877$	33.2806	+	33.2806i	1.12381	+	1.12381i	0.132643	+	0.991164i	$0.457654\pi$
$878$	−14.3642	−	14.3642i	−0.484767	−	0.484767i
$879$		0			0
$880$	−4.10174	−	7.10443i	−0.138270	−	0.239490i
$881$	−9.67727	−	16.7615i	−0.326036	−	0.564710i	0.655686	−	0.755034i	$-0.272380\pi$
$881$	−9.67727	−	16.7615i	−0.326036	−	0.564710i	−0.981721	+	0.190324i	$0.939046\pi$
$882$		0			0
$883$			20.5335i			0.691007i	0.938417	+	0.345504i	$0.112292\pi$
$883$			20.5335i			0.691007i	−0.938417	+	0.345504i	$0.887708\pi$
$884$	−14.4591	+	20.7542i	−0.486313	+	0.698041i
$885$		0			0
$886$	18.1210	−	4.85550i	0.608786	−	0.163124i
$887$	18.9228	+	10.9251i	0.635364	+	0.366828i	0.782826	−	0.622240i	$-0.213777\pi$
$887$	18.9228	+	10.9251i	0.635364	+	0.366828i	−0.147463	+	0.989068i	$0.547111\pi$
$888$		0			0
$889$	−10.3639	+	2.77700i	−0.347594	+	0.0931374i
$890$	13.1461	+	49.0618i	0.440658	+	1.64456i
$891$		0			0
$892$	0.198374	−	0.198374i	0.00664204	−	0.00664204i
$893$	−25.4777	+	14.7096i	−0.852579	+	0.492237i
$894$		0			0
$895$	6.90201	+	25.7587i	0.230709	+	0.861017i
$896$	−1.62408	−	2.81299i	−0.0542567	−	0.0939753i
$897$		0			0
$898$	−7.94366	+	13.7588i	−0.265083	+	0.459138i
$899$	−4.89288	−	1.31104i	−0.163187	−	0.0437257i
$900$		0			0
$901$	9.86199	+	5.69382i	0.328551	+	0.189689i
$902$	−0.997539	−	3.72287i	−0.0332144	−	0.123958i
$903$		0			0
$904$	8.18076	−	8.18076i	0.272088	−	0.272088i
$905$	20.0233	−	74.7279i	0.665597	−	2.48404i
$906$		0			0
$907$		−	26.4955i		−	0.879769i	−0.898054	−	0.439885i	$-0.855019\pi$
$907$		−	26.4955i		−	0.879769i	0.898054	−	0.439885i	$-0.144981\pi$
$908$	−3.29749	+	12.3064i	−0.109431	+	0.408402i
$909$		0			0
$910$	7.72770	+	43.2269i	0.256171	+	1.43296i
$911$	−15.5279	−	8.96501i	−0.514461	−	0.297024i	0.220205	−	0.975454i	$-0.429327\pi$
$911$	−15.5279	−	8.96501i	−0.514461	−	0.297024i	−0.734665	+	0.678430i	$0.762661\pi$
$912$		0			0
$913$	15.8836	−	27.5113i	0.525672	−	0.910491i
$914$	−0.877349			−0.0290201
$915$		0			0
$916$	1.11470	−	4.16011i	0.0368307	−	0.137454i
$917$	34.5896	−	9.26827i	1.14225	−	0.306065i
$918$		0			0
$919$	20.4782	−	35.4692i	0.675512	−	1.17002i	−0.300806	−	0.953685i	$-0.597256\pi$
$919$	20.4782	−	35.4692i	0.675512	−	1.17002i	0.976319	−	0.216337i	$-0.0694108\pi$
$920$	3.11870			0.102820
$921$		0			0
$922$	−20.1727	+	11.6467i	−0.664352	+	0.383564i
$923$	31.7856	−	5.68232i	1.04624	−	0.187036i
$924$		0			0
$925$	12.6063	+	12.6063i	0.414492	+	0.414492i
$926$	−15.6154	+	9.01556i	−0.513154	+	0.296270i
$927$		0			0
$928$	−6.55297	−	6.55297i	−0.215112	−	0.215112i
$929$	−21.8150	−	5.84531i	−0.715727	−	0.191778i	−0.117463	−	0.993077i	$-0.537476\pi$
$929$	−21.8150	−	5.84531i	−0.715727	−	0.191778i	−0.598264	+	0.801299i	$0.704143\pi$
$930$		0			0
$931$	16.7001	+	4.47478i	0.547324	+	0.146655i
$932$		−	21.0744i		−	0.690313i
$933$		0			0
$934$	−17.6061	+	17.6061i	−0.576091	+	0.576091i
$935$	57.5507			1.88211
$936$		0			0
$937$	−6.24073			−0.203876			−0.101938	−	0.994791i	$-0.532504\pi$
$937$	−6.24073			−0.203876			−0.101938	+	0.994791i	$0.532504\pi$
$938$	29.8527	−	29.8527i	0.974725	−	0.974725i
$939$		0			0
$940$			22.6530i			0.738859i
$941$	−20.1901	−	5.40991i	−0.658177	−	0.176358i	−0.0857538	−	0.996316i	$-0.527330\pi$
$941$	−20.1901	−	5.40991i	−0.658177	−	0.176358i	−0.572423	+	0.819958i	$0.693997\pi$
$942$		0			0
$943$	1.41531	+	0.379232i	0.0460889	+	0.0123495i
$944$	2.06291	+	2.06291i	0.0671419	+	0.0671419i
$945$		0			0
$946$	0.110107	−	0.0635703i	0.00357988	−	0.00206685i
$947$	−6.94516	−	6.94516i	−0.225687	−	0.225687i	0.585201	−	0.810888i	$-0.301016\pi$
$947$	−6.94516	−	6.94516i	−0.225687	−	0.225687i	−0.810888	+	0.585201i	$0.801016\pi$
$948$		0			0
$949$	−11.1208	−	13.1896i	−0.360995	−	0.428154i
$950$	38.2024	−	22.0561i	1.23945	−	0.715596i
$951$		0			0
$952$	22.7871			0.738535
$953$	16.8681	−	29.2164i	0.546410	−	0.946410i	−0.452106	−	0.891964i	$-0.649327\pi$
$953$	16.8681	−	29.2164i	0.546410	−	0.946410i	0.998517	−	0.0544464i	$-0.0173394\pi$
$954$		0			0
$955$	81.4614	−	21.8275i	2.63603	−	0.706322i
$956$	−3.36892	+	12.5730i	−0.108959	+	0.406639i
$957$		0			0
$958$	7.60150			0.245593
$959$	18.4792	−	32.0068i	0.596723	−	1.03355i
$960$		0			0
$961$	26.5880	+	15.3506i	0.857679	+	0.495181i
$962$	−3.01399	−	6.42376i	−0.0971750	−	0.207110i
$963$		0			0
$964$	−0.322572	+	1.20385i	−0.0103893	+	0.0387735i
$965$			25.3509i			0.816075i
$966$		0			0
$967$	14.8707	−	55.4982i	0.478209	−	1.78470i	−0.130658	−	0.991428i	$-0.541709\pi$
$967$	14.8707	−	55.4982i	0.478209	−	1.78470i	0.608867	−	0.793273i	$-0.291624\pi$
$968$	−4.39341	+	4.39341i	−0.141209	+	0.141209i
$969$		0			0
$970$	−9.57827	−	35.7466i	−0.307540	−	1.14775i
$971$	−1.03496	−	0.597536i	−0.0332135	−	0.0191758i	0.483301	−	0.875454i	$-0.339438\pi$
$971$	−1.03496	−	0.597536i	−0.0332135	−	0.0191758i	−0.516515	+	0.856278i	$0.672771\pi$
$972$		0			0
$973$	−11.5355	−	3.09093i	−0.369812	−	0.0990907i
$974$	−16.5847	+	28.7255i	−0.531407	+	0.920424i
$975$		0			0
$976$	1.78999	+	3.10035i	0.0572961	+	0.0992398i
$977$	−3.14247	−	11.7278i	−0.100536	−	0.375207i	0.897264	−	0.441494i	$-0.145551\pi$
$977$	−3.14247	−	11.7278i	−0.100536	−	0.375207i	−0.997801	+	0.0662870i	$0.978885\pi$
$978$		0			0
$979$	−25.6670	+	14.8189i	−0.820322	+	0.473613i
$980$	9.41360	−	9.41360i	0.300706	−	0.300706i
$981$		0			0
$982$	−6.68991	−	24.9671i	−0.213484	−	0.796732i
$983$	−0.751256	+	0.201299i	−0.0239614	+	0.00642043i	−0.270780	−	0.962641i	$-0.587282\pi$
$983$	−0.751256	+	0.201299i	−0.0239614	+	0.00642043i	0.246818	+	0.969062i	$0.420615\pi$
$984$		0			0
$985$	20.0151	+	11.5557i	0.637734	+	0.368196i
$986$	62.7984	−	16.8268i	1.99991	−	0.535874i
$987$		0			0
$988$	−17.2831	+	3.08971i	−0.549849	+	0.0982966i
$989$			0.0483347i			0.00153695i
$990$		0			0
$991$	12.0018	+	20.7877i	0.381250	+	0.660344i	0.991241	−	0.132064i	$-0.0421604\pi$
$991$	12.0018	+	20.7877i	0.381250	+	0.660344i	−0.609991	+	0.792408i	$0.708827\pi$
$992$	−0.273299	−	0.473367i	−0.00867724	−	0.0150294i
$993$		0			0
$994$	−20.5690	−	20.5690i	−0.652408	−	0.652408i
$995$	10.0959	+	10.0959i	0.320061	+	0.320061i
$996$		0			0
$997$	−3.71583	−	6.43600i	−0.117681	−	0.203830i	0.801167	−	0.598441i	$-0.204213\pi$
$997$	−3.71583	−	6.43600i	−0.117681	−	0.203830i	−0.918848	+	0.394611i	$0.870880\pi$
$998$	8.15931	+	14.1323i	0.258278	+	0.447351i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bb.a.89.13		56
3.2	odd	2		234.2.y.a.11.6	✓	56
9.4	even	3		234.2.z.a.167.9	yes	56
9.5	odd	6		702.2.bc.a.557.6		56
13.6	odd	12		702.2.bc.a.305.6		56
39.32	even	12		234.2.z.a.227.9	yes	56
117.32	even	12	inner	702.2.bb.a.71.13		56
117.58	odd	12		234.2.y.a.149.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.6	✓	56	3.2	odd	2
234.2.y.a.149.6	yes	56	117.58	odd	12
234.2.z.a.167.9	yes	56	9.4	even	3
234.2.z.a.227.9	yes	56	39.32	even	12
702.2.bb.a.71.13		56	117.32	even	12	inner
702.2.bb.a.89.13		56	1.1	even	1	trivial
702.2.bc.a.305.6		56	13.6	odd	12
702.2.bc.a.557.6		56	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(3.62177 + 0.970449i) q^{5} +(-3.13748 - 0.840685i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(3.24719 - 1.87476i) q^{10} +(1.54706 + 1.54706i) q^{11} +(0.305736 - 3.59257i) q^{13} +(-2.81299 + 1.62408i) q^{14} -1.00000 q^{16} +(3.50770 - 6.07551i) q^{17} +(4.70354 - 1.26031i) q^{19} +(0.970449 - 3.62177i) q^{20} +2.18787 q^{22} +(-0.415879 + 0.720323i) q^{23} +(7.84529 + 4.52948i) q^{25} +(-2.32414 - 2.75652i) q^{26} +(-0.840685 + 3.13748i) q^{28} +9.26729i q^{29} +(-0.141470 + 0.527973i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.81572 - 6.77635i) q^{34} +(-10.5474 - 6.08953i) q^{35} +(1.90093 + 0.509353i) q^{37} +(2.43473 - 4.21708i) q^{38} +(-1.87476 - 3.24719i) q^{40} +(-0.455940 - 1.70159i) q^{41} +(0.0503260 - 0.0290558i) q^{43} +(1.54706 - 1.54706i) q^{44} +(0.215275 + 0.803416i) q^{46} +(-5.83570 + 1.56367i) q^{47} +(3.07486 + 1.77527i) q^{49} +(8.75029 - 2.34463i) q^{50} +(-3.59257 - 0.305736i) q^{52} +1.62324i q^{53} +(4.10174 + 7.10443i) q^{55} +(1.62408 + 2.81299i) q^{56} +(6.55297 + 6.55297i) q^{58} +(-2.06291 - 2.06291i) q^{59} +(-1.78999 - 3.10035i) q^{61} +(0.273299 + 0.473367i) q^{62} +1.00000i q^{64} +(4.59371 - 12.7147i) q^{65} +(-12.5547 + 3.36401i) q^{67} +(-6.07551 - 3.50770i) q^{68} +(-11.7641 + 3.15217i) q^{70} +(2.31786 + 8.65035i) q^{71} +(3.38343 - 3.38343i) q^{73} +(1.70433 - 0.983995i) q^{74} +(-1.26031 - 4.70354i) q^{76} +(-3.55328 - 6.15446i) q^{77} +(-5.86001 + 10.1498i) q^{79} +(-3.62177 - 0.970449i) q^{80} +(-1.52561 - 0.880809i) q^{82} +(-3.75798 - 14.0250i) q^{83} +(18.6000 - 18.6000i) q^{85} +(0.0150404 - 0.0561314i) q^{86} -2.18787i q^{88} +(-3.50606 + 13.0848i) q^{89} +(-3.97946 + 11.0146i) q^{91} +(0.720323 + 0.415879i) q^{92} +(-3.02078 + 5.23214i) q^{94} +18.2582 q^{95} +(2.55453 - 9.53363i) q^{97} +(3.42956 - 0.918947i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) \) 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

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