LMFDB - Embedded newform 702.2.bb.a.71.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(71,702)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			71.13
Character	$\chi$	$=$	702.71
Dual form			702.2.bb.a.89.13

$q$-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 $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

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	0.668789	−	0.743452i	$-0.266813\pi$
$5$	3.62177	−	0.970449i	1.61970	−	0.433998i	0.950914	+	0.309454i	$0.100146\pi$
$6$		0			0
$7$	−3.13748	+	0.840685i	−1.18586	+	0.317749i	−0.797247	−	0.603653i	$-0.793711\pi$
$7$	−3.13748	+	0.840685i	−1.18586	+	0.317749i	−0.388609	+	0.921403i	$0.627044\pi$
$8$	−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	−0.434308	−	0.900764i	$-0.643007\pi$
$11$	1.54706	−	1.54706i	0.466456	−	0.466456i	0.900764	+	0.434308i	$0.143007\pi$
$12$		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	0.880540	+	0.473972i	$0.157180\pi$
$17$	3.50770	+	6.07551i	0.850742	+	1.47353i	−0.0297983	+	0.999556i	$0.509487\pi$
$18$		0			0
$19$	4.70354	+	1.26031i	1.07907	+	0.289135i	0.754213	−	0.656630i	$-0.228019\pi$
$19$	4.70354	+	1.26031i	1.07907	+	0.289135i	0.324853	+	0.945765i	$0.394685\pi$
$20$	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	0.819405	−	0.573215i	$-0.194304\pi$
$23$	−0.415879	−	0.720323i	−0.0867167	−	0.150198i	−0.906121	+	0.423018i	$0.860971\pi$
$24$		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	$-0.670185\pi$
$29$		−	9.26729i		−	1.72089i	0.509541	−	0.860447i	$-0.329815\pi$
$30$		0			0
$31$	−0.141470	−	0.527973i	−0.0254087	−	0.0948267i	0.952057	−	0.305920i	$-0.0989641\pi$
$31$	−0.141470	−	0.527973i	−0.0254087	−	0.0948267i	−0.977466	+	0.211094i	$0.932297\pi$
$32$	−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	−0.0991544	−	0.995072i	$-0.531614\pi$
$37$	1.90093	−	0.509353i	0.312511	−	0.0837372i	0.411666	+	0.911335i	$0.364947\pi$
$38$	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	−0.992346	−	0.123487i	$-0.960592\pi$
$41$	−0.455940	+	1.70159i	−0.0712059	+	0.265744i	0.921140	+	0.389231i	$0.127259\pi$
$42$		0			0
$43$	0.0503260	+	0.0290558i	0.00767465	+	0.00443096i	0.503832	−	0.863801i	$-0.331923\pi$
$43$	0.0503260	+	0.0290558i	0.00767465	+	0.00443096i	−0.496158	+	0.868232i	$0.665256\pi$
$44$	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	−0.193272	−	0.981145i	$-0.561910\pi$
$47$	−5.83570	−	1.56367i	−0.851224	−	0.228085i	−0.657951	+	0.753060i	$0.728577\pi$
$48$		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	$-0.964440\pi$
$53$		−	1.62324i		−	0.222969i	0.993766	−	0.111484i	$-0.0355605\pi$
$54$		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	−0.828523	−	0.559955i	$-0.810818\pi$
$59$	−2.06291	+	2.06291i	−0.268568	+	0.268568i	0.559955	+	0.828523i	$0.310818\pi$
$60$		0			0
$61$	−1.78999	+	3.10035i	−0.229185	+	0.396959i	−0.957567	−	0.288212i	$-0.906939\pi$
$61$	−1.78999	+	3.10035i	−0.229185	+	0.396959i	0.728382	+	0.685171i	$0.240273\pi$
$62$	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	−0.609541	−	0.792755i	$-0.708646\pi$
$67$	−12.5547	−	3.36401i	−1.53380	−	0.410979i	−0.924255	+	0.381775i	$0.875313\pi$
$68$	−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	−0.680710	−	0.732553i	$-0.738329\pi$
$71$	2.31786	−	8.65035i	0.275079	−	1.02661i	0.955789	−	0.294055i	$-0.0950048\pi$
$72$		0			0
$73$	3.38343	+	3.38343i	0.396001	+	0.396001i	0.876820	−	0.480819i	$-0.159661\pi$
$73$	3.38343	+	3.38343i	0.396001	+	0.396001i	−0.480819	+	0.876820i	$0.659661\pi$
$74$	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	−0.980797	−	0.195033i	$-0.937518\pi$
$79$	−5.86001	−	10.1498i	−0.659302	−	1.14194i	0.321494	−	0.946911i	$-0.395815\pi$
$80$	−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	0.377315	+	0.926085i	$0.376848\pi$
$83$	−3.75798	+	14.0250i	−0.412492	+	1.53944i	−0.789807	+	0.613356i	$0.789819\pi$
$84$		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	−0.858190	−	0.513332i	$-0.828411\pi$
$89$	−3.50606	−	13.0848i	−0.371642	−	1.38699i	0.486548	−	0.873654i	$-0.338256\pi$
$90$		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	0.965605	+	0.260013i	$0.0837268\pi$
$97$	2.55453	+	9.53363i	0.259373	+	0.967993i	−0.706232	+	0.707980i	$0.749607\pi$
$98$	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	0.0447750	−	0.998997i	$-0.485743\pi$
$103$	−8.09876	−	4.67582i	−0.797994	−	0.460722i	−0.842769	+	0.538275i	$0.819076\pi$
$104$	−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	0.271007	−	0.962577i	$-0.412643\pi$
$107$	−4.41803	−	2.55075i	−0.427107	−	0.246590i	−0.698113	+	0.715987i	$0.745977\pi$
$108$		0			0
$109$	−0.923072	+	0.923072i	−0.0884142	+	0.0884142i	−0.749931	−	0.661516i	$-0.769913\pi$
$109$	−0.923072	+	0.923072i	−0.0884142	+	0.0884142i	0.661516	+	0.749931i	$0.269913\pi$
$110$	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	$-0.816842\pi$
$113$		−	11.5693i		−	1.08835i	0.838971	−	0.544176i	$-0.183158\pi$
$114$		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	0.621524	−	0.783395i	$-0.286514\pi$
$127$	2.86070	+	1.65163i	0.253846	+	0.146558i	−0.367678	+	0.929953i	$0.619847\pi$
$128$	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	0.0211014	−	0.999777i	$-0.493283\pi$
$131$	−9.54763	−	5.51233i	−0.834181	−	0.481614i	−0.855282	+	0.518163i	$0.826616\pi$
$132$		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	−0.969950	−	0.243303i	$-0.921769\pi$
$137$	−2.94490	−	10.9905i	−0.251600	−	0.938984i	0.718350	−	0.695682i	$-0.244898\pi$
$138$		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	0.393604	−	0.919280i	$-0.371228\pi$
$149$	−6.41670	−	6.41670i	−0.525676	−	0.525676i	−0.919280	+	0.393604i	$0.871228\pi$
$150$		0			0
$151$	4.88320	−	18.2244i	0.397389	−	1.48308i	−0.420283	−	0.907393i	$-0.638069\pi$
$151$	4.88320	−	18.2244i	0.397389	−	1.48308i	0.817672	−	0.575684i	$-0.195264\pi$
$152$	−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	0.0285320	−	0.999593i	$-0.490917\pi$
$157$	11.0256	−	19.0969i	0.879939	−	1.52410i	0.851407	−	0.524506i	$-0.175750\pi$
$158$	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	−0.999946	−	0.0103577i	$-0.996703\pi$
$163$	−1.64426	+	6.13647i	−0.128789	+	0.480646i	0.871158	+	0.491003i	$0.163370\pi$
$164$	−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	0.572532	−	0.819883i	$-0.305961\pi$
$167$	8.50863	+	2.27988i	0.658417	+	0.176422i	0.0858858	+	0.996305i	$0.472628\pi$
$168$		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	−0.865064	−	0.501661i	$-0.832722\pi$
$173$	0.0252410	−	0.0437187i	0.00191904	−	0.00332387i	0.866983	+	0.498337i	$0.166056\pi$
$174$		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	−0.701977	−	0.712200i	$-0.747699\pi$
$179$	3.55609	−	6.15933i	0.265795	−	0.460370i	0.967772	+	0.251830i	$0.0810323\pi$
$180$		0			0
$181$			20.6330i			1.53364i	0.641863	+	0.766820i	$0.278162\pi$
$181$			20.6330i			1.53364i	−0.641863	+	0.766820i	$0.721838\pi$
$182$	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	0.995334	−	0.0964927i	$-0.0307624\pi$
$191$	19.4788	+	11.2461i	1.40944	+	0.813738i	0.414102	+	0.910231i	$0.364096\pi$
$192$		0			0
$193$	1.74990	−	6.53071i	0.125961	−	0.470091i	−0.873912	−	0.486085i	$-0.838425\pi$
$193$	1.74990	−	6.53071i	0.125961	−	0.470091i	0.999872	+	0.0159939i	$0.00509122\pi$
$194$	−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	−0.0404072	−	0.999183i	$-0.512866\pi$
$197$	5.95380	−	1.59532i	0.424191	−	0.113662i	0.464598	+	0.885522i	$0.346199\pi$
$198$		0			0
$199$	3.29772	−	1.90394i	0.233769	−	0.134967i	−0.378541	−	0.925585i	$-0.623574\pi$
$199$	3.29772	−	1.90394i	0.233769	−	0.134967i	0.612310	+	0.790618i	$0.290241\pi$
$200$	−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	0.980493	+	0.196556i	$0.0629758\pi$
$211$	9.59387	+	16.6171i	0.660469	+	1.14397i	−0.320024	+	0.947410i	$0.603691\pi$
$212$	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	−0.700434	−	0.713718i	$-0.747010\pi$
$223$	0.198374	−	0.198374i	0.0132841	−	0.0132841i	0.713718	+	0.700434i	$0.247010\pi$
$224$	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	−0.642949	−	0.765909i	$-0.722289\pi$
$227$	−12.3064	+	3.29749i	−0.816804	+	0.218862i	−0.173856	+	0.984771i	$0.555623\pi$
$228$		0			0
$229$	4.16011	−	1.11470i	0.274908	−	0.0736613i	−0.118731	−	0.992926i	$-0.537883\pi$
$229$	4.16011	−	1.11470i	0.274908	−	0.0736613i	0.393639	+	0.919265i	$0.371216\pi$
$230$		−	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	−0.641406	−	0.767202i	$-0.721648\pi$
$239$	−12.5730	+	3.36892i	−0.813278	+	0.217917i	−0.171873	+	0.985119i	$0.554982\pi$
$240$		0			0
$241$	−1.20385	+	0.322572i	−0.0775471	+	0.0207787i	−0.297384	−	0.954758i	$-0.596114\pi$
$241$	−1.20385	+	0.322572i	−0.0775471	+	0.0207787i	0.219837	+	0.975537i	$0.429447\pi$
$242$	−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	0.630878	−	0.775882i	$-0.282695\pi$
$251$	−5.64794	−	9.78252i	−0.356495	−	0.617467i	−0.987373	+	0.158415i	$0.949362\pi$
$252$		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	0.890271	−	0.455431i	$-0.150515\pi$
$257$	0.813117	+	1.40836i	0.0507209	+	0.0878511i	−0.839550	+	0.543282i	$0.817181\pi$
$258$		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	$0.114075\pi$
$263$			11.3766i			0.701511i	−0.936467	+	0.350755i	$0.885925\pi$
$264$		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	−0.781681	−	0.623678i	$-0.785637\pi$
$269$	−10.3721	+	5.98835i	−0.632400	+	0.365116i	0.149281	+	0.988795i	$0.452304\pi$
$270$		0			0
$271$	23.9876	−	6.42745i	1.45714	−	0.390440i	0.558640	−	0.829410i	$-0.311323\pi$
$271$	23.9876	−	6.42745i	1.45714	−	0.390440i	0.898502	+	0.438970i	$0.144657\pi$
$272$	−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	0.0340608	−	0.999420i	$-0.489156\pi$
$277$	−13.5548	−	7.82589i	−0.814432	−	0.470212i	−0.848493	+	0.529207i	$0.822489\pi$
$278$	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	0.129688	−	0.991555i	$-0.458602\pi$
$281$	−4.25406	−	1.13987i	−0.253776	−	0.0679991i	−0.383464	+	0.923556i	$0.625269\pi$
$282$		0			0
$283$	15.8083	−	9.12694i	0.939707	−	0.542540i	0.0498385	−	0.998757i	$-0.484129\pi$
$283$	15.8083	−	9.12694i	0.939707	−	0.542540i	0.889868	+	0.456217i	$0.150796\pi$
$284$	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	−0.899211	−	0.437515i	$-0.855859\pi$
$293$	−7.90296	+	7.90296i	−0.461696	+	0.461696i	0.437515	+	0.899211i	$0.355859\pi$
$294$		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	0.135900	−	0.990723i	$-0.456608\pi$
$307$	−14.9777	−	14.9777i	−0.854823	−	0.854823i	−0.990723	+	0.135900i	$0.956608\pi$
$308$	−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	−0.992935	−	0.118661i	$-0.962140\pi$
$311$	−6.94304	+	12.0257i	−0.393704	+	0.681915i	0.599231	+	0.800576i	$0.295473\pi$
$312$		0			0
$313$	4.79094	+	8.29816i	0.270800	+	0.469040i	0.969067	−	0.246798i	$-0.0793784\pi$
$313$	4.79094	+	8.29816i	0.270800	+	0.469040i	−0.698267	+	0.715838i	$0.746045\pi$
$314$	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	0.744460	+	0.667667i	$0.232707\pi$
$317$	−4.16793	+	15.5549i	−0.234095	+	0.873653i	−0.978555	+	0.205986i	$0.933960\pi$
$318$		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	0.998369	−	0.0570939i	$-0.0181834\pi$
$331$	1.91411	+	7.14356i	0.105209	+	0.392646i	−0.893160	+	0.449740i	$0.851517\pi$
$332$	−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	−0.0141778	−	0.999899i	$-0.504513\pi$
$337$	−16.2869	−	9.40326i	−0.887205	−	0.512228i	−0.873027	+	0.487671i	$0.837846\pi$
$338$	−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	$0.231390\pi$
$347$			24.7596i			1.32916i	−0.747215	+	0.664582i	$0.768610\pi$
$348$		0			0
$349$	2.41492	+	2.41492i	0.129267	+	0.129267i	0.768780	−	0.639513i	$-0.220864\pi$
$349$	2.41492	+	2.41492i	0.129267	+	0.129267i	−0.639513	+	0.768780i	$0.720864\pi$
$350$	−29.4250			−1.57283
$351$		0			0
$352$	−2.18787			−0.116614
$353$	−3.14228	−	3.14228i	−0.167247	−	0.167247i	0.618521	−	0.785768i	$-0.287732\pi$
$353$	−3.14228	−	3.14228i	−0.167247	−	0.167247i	−0.785768	+	0.618521i	$0.787732\pi$
$354$		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	−0.659128	−	0.752031i	$-0.729075\pi$
$359$	1.76025	−	1.76025i	0.0929022	−	0.0929022i	0.752031	+	0.659128i	$0.229075\pi$
$360$		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	0.999456	+	0.0329946i	$0.0105044\pi$
$379$	2.92796	+	10.9273i	0.150399	+	0.561297i	−0.849057	+	0.528302i	$0.822829\pi$
$380$			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	0.995988	+	0.0894896i	$0.0285236\pi$
$383$	21.2432	+	21.2432i	1.08548	+	1.08548i	0.0894896	+	0.995988i	$0.471476\pi$
$384$		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	0.727108	−	0.686524i	$-0.240864\pi$
$389$	−4.55590	−	7.89104i	−0.230993	−	0.400092i	−0.958101	+	0.286432i	$0.907531\pi$
$390$		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	0.859904	+	0.510455i	$0.170523\pi$
$397$	−2.78992	+	10.4121i	−0.140022	+	0.522570i	−0.999927	+	0.0121147i	$0.996144\pi$
$398$	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	−0.0392478	−	0.999230i	$-0.512496\pi$
$401$	−11.4714	−	3.07374i	−0.572852	−	0.153495i	−0.533604	+	0.845734i	$0.679163\pi$
$402$		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	−0.974624	−	0.223847i	$-0.928138\pi$
$409$	−15.1835	+	15.1835i	−0.750777	+	0.750777i	0.223847	+	0.974624i	$0.428138\pi$
$410$	−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	−0.253866	−	0.967239i	$-0.581702\pi$
$419$	9.35158	−	5.39914i	0.456855	−	0.263765i	0.710721	+	0.703474i	$0.248369\pi$
$420$		0			0
$421$	6.34283	+	1.69956i	0.309131	+	0.0828313i	0.410049	−	0.912063i	$-0.365512\pi$
$421$	6.34283	+	1.69956i	0.309131	+	0.0828313i	−0.100919	+	0.994895i	$0.532178\pi$
$422$	−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	−0.385665	−	0.922639i	$-0.626028\pi$
$431$	−5.36331	+	1.43709i	−0.258341	+	0.0692224i	0.127324	+	0.991861i	$0.459361\pi$
$432$		0			0
$433$	31.1666	−	17.9940i	1.49777	−	0.864737i	0.497773	−	0.867308i	$-0.334151\pi$
$433$	31.1666	−	17.9940i	1.49777	−	0.864737i	0.999997	+	0.00257012i	$0.000818096\pi$
$434$	−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	$0.161095\pi$
$439$			20.3140i			0.969533i	−0.874644	+	0.484767i	$0.838905\pi$
$440$	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	−0.0616456	−	0.998098i	$-0.519635\pi$
$443$	16.2468	−	9.38011i	0.771910	−	0.445662i	0.833556	+	0.552436i	$0.186302\pi$
$444$		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	−0.122167	−	0.992510i	$-0.538984\pi$
$449$	−15.3460	−	4.11194i	−0.724221	−	0.194055i	−0.602054	+	0.798455i	$0.705651\pi$
$450$		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	−0.721468	−	0.692448i	$-0.756532\pi$
$457$	−0.620379	+	0.620379i	−0.0290201	+	0.0290201i	0.692448	+	0.721468i	$0.256532\pi$
$458$	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	−0.741390	−	0.671074i	$-0.765833\pi$
$461$	−22.4997	+	6.02877i	−1.04792	+	0.280788i	−0.306525	+	0.951863i	$0.599166\pi$
$462$		0			0
$463$	−17.4167	+	4.66680i	−0.809424	+	0.216885i	−0.639718	−	0.768610i	$-0.720949\pi$
$463$	−17.4167	+	4.66680i	−0.809424	+	0.216885i	−0.169707	+	0.985495i	$0.554282\pi$
$464$			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	−0.573566	−	0.819159i	$-0.694440\pi$
$479$	5.37507	−	5.37507i	0.245593	−	0.245593i	0.819159	+	0.573566i	$0.194440\pi$
$480$		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	−0.555171	−	0.831736i	$-0.687347\pi$
$487$	−32.0391	−	8.58485i	−1.45183	−	0.389017i	−0.896660	+	0.442720i	$0.854014\pi$
$488$	−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	0.995091	+	0.0989607i	$0.0315518\pi$
$491$	12.9239	+	22.3849i	0.583248	+	1.01022i	−0.411843	+	0.911255i	$0.635115\pi$
$492$		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	−0.993722	−	0.111879i	$-0.964313\pi$
$499$	−4.22357	−	15.7626i	−0.189073	−	0.705629i	0.804649	−	0.593751i	$-0.202353\pi$
$500$	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	−0.340630	−	0.940198i	$-0.610640\pi$
$503$	6.80210	−	3.92720i	0.303291	−	0.175105i	0.643920	+	0.765093i	$0.277307\pi$
$504$		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	−0.642267	−	0.766481i	$-0.722006\pi$
$509$	6.70498	−	25.0233i	0.297193	−	1.10914i	0.939460	−	0.342659i	$-0.111328\pi$
$510$		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	$0.434612\pi$
$521$			44.6910i			1.95795i	−0.203981	+	0.978975i	$0.565388\pi$
$522$		0			0
$523$	2.38397	−	4.12916i	0.104244	−	0.180556i	−0.809185	−	0.587554i	$-0.800091\pi$
$523$	2.38397	−	4.12916i	0.104244	−	0.180556i	0.913429	+	0.406998i	$0.133424\pi$
$524$	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	−0.899187	−	0.437565i	$-0.855841\pi$
$541$	−31.0921	−	31.0921i	−1.33675	−	1.33675i	−0.437565	−	0.899187i	$-0.644159\pi$
$542$	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	0.977407	−	0.211365i	$-0.0677910\pi$
$547$	7.14869	+	12.3819i	0.305656	+	0.529412i	−0.671751	+	0.740777i	$0.734458\pi$
$548$	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	−0.612557	−	0.790426i	$-0.709859\pi$
$557$	−11.2642	−	42.0386i	−0.477280	−	1.78123i	0.135277	−	0.990808i	$-0.456807\pi$
$558$		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	0.992602	+	0.121415i	$0.0387432\pi$
$571$	38.0908	+	21.9917i	1.59405	+	0.920326i	0.601449	+	0.798911i	$0.294590\pi$
$572$	−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	−0.172831	+	0.984952i	$0.555291\pi$
$577$	−27.8109	+	27.8109i	−1.15778	+	1.15778i	−0.984952	+	0.172831i	$0.944709\pi$
$578$	−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	0.537124	−	0.843503i	$-0.319511\pi$
$587$	−7.42299	−	7.42299i	−0.306380	−	0.306380i	−0.843503	+	0.537124i	$0.819511\pi$
$588$		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	−0.0214039	+	0.999771i	$0.506814\pi$
$593$	−24.8672	+	24.8672i	−1.02117	+	1.02117i	−0.999771	+	0.0214039i	$0.993186\pi$
$594$		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	0.384137	−	0.923276i	$-0.374499\pi$
$599$	−5.46701	−	3.15638i	−0.223376	−	0.128966i	−0.607512	+	0.794310i	$0.707833\pi$
$600$		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	0.996128	+	0.0879138i	$0.0280200\pi$
$613$	4.39253	+	16.3932i	0.177413	+	0.662113i	−0.818715	+	0.574200i	$0.805313\pi$
$614$		−	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	−0.915847	−	0.401528i	$-0.868479\pi$
$617$	−32.7229	−	32.7229i	−1.31737	−	1.31737i	−0.401528	−	0.915847i	$-0.631521\pi$
$618$		0			0
$619$	−8.87599	+	33.1257i	−0.356756	+	1.33143i	0.521504	+	0.853249i	$0.325371\pi$
$619$	−8.87599	+	33.1257i	−0.356756	+	1.33143i	−0.878260	+	0.478183i	$0.841295\pi$
$620$	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	−0.997674	−	0.0681724i	$-0.978283\pi$
$631$	−2.50134	+	9.33512i	−0.0995767	+	0.371625i	0.898097	+	0.439798i	$0.144950\pi$
$632$	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	−0.556905	−	0.830576i	$-0.688011\pi$
$641$	11.1614	−	19.3321i	0.440848	−	0.763570i	0.997753	+	0.0670058i	$0.0213446\pi$
$642$		0			0
$643$	−26.4365	+	26.4365i	−1.04255	+	1.04255i	−0.0434999	+	0.999053i	$0.513851\pi$
$643$	−26.4365	+	26.4365i	−1.04255	+	1.04255i	−0.999053	+	0.0434999i	$0.986149\pi$
$644$	−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	−0.824628	−	0.565676i	$-0.808615\pi$
$647$	1.97324	−	3.41775i	0.0775760	−	0.134366i	0.902204	+	0.431310i	$0.141949\pi$
$648$		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	−0.730113	−	0.683326i	$-0.760533\pi$
$653$	−12.8636	+	7.42680i	−0.503391	+	0.290633i	0.226722	+	0.973960i	$0.427199\pi$
$654$		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	−0.362037	−	0.932164i	$-0.617919\pi$
$659$	−34.6644	−	20.0135i	−1.35033	−	0.779615i	−0.988296	+	0.152548i	$0.951252\pi$
$660$		0			0
$661$	1.32797	−	4.95604i	0.0516519	−	0.192768i	−0.935279	−	0.353911i	$-0.884852\pi$
$661$	1.32797	−	4.95604i	0.0516519	−	0.192768i	0.986931	+	0.161144i	$0.0515182\pi$
$662$	−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	$0.285749\pi$
$673$			40.5684i			1.56380i	−0.623405	+	0.781899i	$0.714251\pi$
$674$	−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	−0.271851	−	0.962339i	$-0.587636\pi$
$677$	11.0747	−	6.39397i	0.425635	−	0.245740i	0.697485	+	0.716599i	$0.254302\pi$
$678$		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	0.802469	−	0.596693i	$-0.203519\pi$
$683$	31.3371	+	8.39675i	1.19908	+	0.321293i	0.396612	+	0.917986i	$0.370186\pi$
$684$		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	−0.824812	−	0.565408i	$-0.808719\pi$
$691$	−6.81892	+	6.81892i	−0.259404	+	0.259404i	0.565408	+	0.824812i	$0.308719\pi$
$692$	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	−0.537551	−	0.843231i	$-0.680650\pi$
$709$	−15.4828	+	4.14860i	−0.581468	+	0.155804i	−0.0439170	+	0.999035i	$0.513984\pi$
$710$	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	0.990464	−	0.137773i	$-0.0439944\pi$
$719$	10.0799	+	17.4589i	0.375917	+	0.651107i	−0.614547	+	0.788880i	$0.710661\pi$
$720$		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	−0.820626	−	0.571465i	$-0.806375\pi$
$727$	−19.8457	+	11.4579i	−0.736036	+	0.424950i	0.0845905	+	0.996416i	$0.473042\pi$
$728$	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	0.965052	+	0.262060i	$0.0844018\pi$
$733$	7.04796	+	26.3034i	0.260322	+	0.971536i	−0.704729	+	0.709476i	$0.748931\pi$
$734$	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	0.196613	−	0.980481i	$-0.437006\pi$
$739$	23.3006	−	6.24337i	0.857126	−	0.229666i	0.660513	+	0.750815i	$0.270339\pi$
$740$	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	−0.311747	−	0.950165i	$-0.600914\pi$
$743$	11.8113	−	44.0805i	0.433316	−	1.61716i	0.745064	−	0.666993i	$-0.232419\pi$
$744$		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	0.0826964	−	0.996575i	$-0.473647\pi$
$751$	27.0510	−	15.6179i	0.987104	−	0.569905i	0.904407	+	0.426670i	$0.140313\pi$
$752$	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	−0.585399	−	0.810745i	$-0.699062\pi$
$757$	11.2648	−	19.5112i	0.409426	−	0.709147i	0.994826	+	0.101598i	$0.0323956\pi$
$758$	−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	−0.989430	−	0.145013i	$-0.953678\pi$
$761$	−23.2943	+	23.2943i	−0.844417	+	0.844417i	0.145013	+	0.989430i	$0.453678\pi$
$762$		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	−0.823157	−	0.567814i	$-0.807789\pi$
$769$	−50.4684	−	13.5230i	−1.81994	−	0.487651i	−0.996782	+	0.0801629i	$0.974456\pi$
$770$	−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	−0.495556	−	0.868576i	$-0.665036\pi$
$773$	10.2286	−	38.1735i	0.367896	−	1.37301i	0.863452	−	0.504431i	$-0.168298\pi$
$774$		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	0.717841	−	0.696207i	$-0.245130\pi$
$787$	0.606911	+	0.606911i	0.0216341	+	0.0216341i	−0.696207	+	0.717841i	$0.745130\pi$
$788$	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	−0.999037	−	0.0438813i	$-0.986028\pi$
$809$	−43.7042	−	25.2326i	−1.53656	−	0.887132i	−0.537521	−	0.843251i	$-0.680639\pi$
$810$		0			0
$811$	28.9155	−	28.9155i	1.01536	−	1.01536i	0.0154811	−	0.999880i	$-0.495072\pi$
$811$	28.9155	−	28.9155i	1.01536	−	1.01536i	0.999880	−	0.0154811i	$-0.00492798\pi$
$812$	−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	0.749114	−	0.662441i	$-0.230480\pi$
$821$	2.48343	+	2.48343i	0.0866725	+	0.0866725i	−0.662441	+	0.749114i	$0.730480\pi$
$822$		0			0
$823$			50.7370i			1.76858i	0.466936	+	0.884291i	$0.345358\pi$
$823$			50.7370i			1.76858i	−0.466936	+	0.884291i	$0.654642\pi$
$824$	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	−0.767366	−	0.641209i	$-0.778433\pi$
$827$	−3.62799	+	3.62799i	−0.126158	+	0.126158i	0.641209	+	0.767366i	$0.278433\pi$
$828$		0			0
$829$	−18.3968	−	10.6214i	−0.638949	−	0.368897i	0.145261	−	0.989393i	$-0.453598\pi$
$829$	−18.3968	−	10.6214i	−0.638949	−	0.368897i	−0.784209	+	0.620496i	$0.786931\pi$
$830$	−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	0.994901	+	0.100858i	$0.0321589\pi$
$839$	5.32156	+	19.8603i	0.183721	+	0.685655i	−0.811180	+	0.584796i	$0.801174\pi$
$840$		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	−0.837062	−	0.547108i	$-0.815729\pi$
$853$	4.71414	−	17.5934i	0.161409	−	0.602387i	0.998471	−	0.0552788i	$-0.0176048\pi$
$854$	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	0.684703	−	0.728822i	$-0.259932\pi$
$857$	−8.45527	−	14.6450i	−0.288826	−	0.500262i	−0.973530	+	0.228560i	$0.926598\pi$
$858$		0			0
$859$	14.3028	−	24.7732i	0.488007	−	0.845252i	−0.511898	−	0.859046i	$-0.671058\pi$
$859$	14.3028	−	24.7732i	0.488007	−	0.845252i	0.999905	+	0.0137939i	$0.00439089\pi$
$860$	−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	0.562993	−	0.826461i	$-0.309650\pi$
$863$	−7.73986	−	7.73986i	−0.263468	−	0.263468i	−0.826461	+	0.562993i	$0.809650\pi$
$864$		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	0.132643	−	0.991164i	$-0.457654\pi$
$877$	33.2806	−	33.2806i	1.12381	−	1.12381i	0.991164	−	0.132643i	$-0.0423464\pi$
$878$	−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	−0.981721	−	0.190324i	$-0.939046\pi$
$881$	−9.67727	+	16.7615i	−0.326036	+	0.564710i	0.655686	+	0.755034i	$0.272380\pi$
$882$		0			0
$883$		−	20.5335i		−	0.691007i	−0.938417	−	0.345504i	$-0.887708\pi$
$883$		−	20.5335i		−	0.691007i	0.938417	−	0.345504i	$-0.112292\pi$
$884$	−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	−0.147463	−	0.989068i	$-0.547111\pi$
$887$	18.9228	−	10.9251i	0.635364	−	0.366828i	0.782826	+	0.622240i	$0.213777\pi$
$888$		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	$0.144981\pi$
$907$			26.4955i			0.879769i	−0.898054	+	0.439885i	$0.855019\pi$
$908$	−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	−0.734665	−	0.678430i	$-0.762661\pi$
$911$	−15.5279	+	8.96501i	−0.514461	+	0.297024i	0.220205	+	0.975454i	$0.429327\pi$
$912$		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	0.976319	+	0.216337i	$0.0694108\pi$
$919$	20.4782	+	35.4692i	0.675512	+	1.17002i	−0.300806	+	0.953685i	$0.597256\pi$
$920$	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	−0.598264	−	0.801299i	$-0.704143\pi$
$929$	−21.8150	+	5.84531i	−0.715727	+	0.191778i	−0.117463	+	0.993077i	$0.537476\pi$
$930$		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	−0.572423	−	0.819958i	$-0.693997\pi$
$941$	−20.1901	+	5.40991i	−0.658177	+	0.176358i	−0.0857538	+	0.996316i	$0.527330\pi$
$942$		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	−0.810888	−	0.585201i	$-0.801016\pi$
$947$	−6.94516	+	6.94516i	−0.225687	+	0.225687i	0.585201	+	0.810888i	$0.301016\pi$
$948$		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	0.998517	+	0.0544464i	$0.0173394\pi$
$953$	16.8681	+	29.2164i	0.546410	+	0.946410i	−0.452106	+	0.891964i	$0.649327\pi$
$954$		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	0.608867	+	0.793273i	$0.291624\pi$
$967$	14.8707	+	55.4982i	0.478209	+	1.78470i	−0.130658	+	0.991428i	$0.541709\pi$
$968$	−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	−0.516515	−	0.856278i	$-0.672771\pi$
$971$	−1.03496	+	0.597536i	−0.0332135	+	0.0191758i	0.483301	+	0.875454i	$0.339438\pi$
$972$		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	−0.997801	−	0.0662870i	$-0.978885\pi$
$977$	−3.14247	+	11.7278i	−0.100536	+	0.375207i	0.897264	+	0.441494i	$0.145551\pi$
$978$		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	0.246818	−	0.969062i	$-0.420615\pi$
$983$	−0.751256	−	0.201299i	−0.0239614	−	0.00642043i	−0.270780	+	0.962641i	$0.587282\pi$
$984$		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	−0.609991	−	0.792408i	$-0.708827\pi$
$991$	12.0018	−	20.7877i	0.381250	−	0.660344i	0.991241	+	0.132064i	$0.0421604\pi$
$992$	−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	−0.918848	−	0.394611i	$-0.870880\pi$
$997$	−3.71583	+	6.43600i	−0.117681	+	0.203830i	0.801167	+	0.598441i	$0.204213\pi$
$998$	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.71.13		56
3.2	odd	2		234.2.y.a.149.6	yes	56
9.2	odd	6		702.2.bc.a.305.6		56
9.7	even	3		234.2.z.a.227.9	yes	56
13.11	odd	12		702.2.bc.a.557.6		56
39.11	even	12		234.2.z.a.167.9	yes	56
117.11	even	12	inner	702.2.bb.a.89.13		56
117.115	odd	12		234.2.y.a.11.6	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.6	✓	56	117.115	odd	12
234.2.y.a.149.6	yes	56	3.2	odd	2
234.2.z.a.167.9	yes	56	39.11	even	12
234.2.z.a.227.9	yes	56	9.7	even	3
702.2.bb.a.71.13		56	1.1	even	1	trivial
702.2.bb.a.89.13		56	117.11	even	12	inner
702.2.bc.a.305.6		56	9.2	odd	6
702.2.bc.a.557.6		56	13.11	odd	12

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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
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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