LMFDB - Embedded newform 656.2.bs.d.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [656,2,Mod(33,656)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(656, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 9]))

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

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

chi := DirichletCharacter("656.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.bs (of order $20$, degree $8$, 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:	$5.23818637260$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 41)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			33.1
Character	$\chi$	$=$	656.33
Dual form			656.2.bs.d.497.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.22848 + 2.22848i) q^{3} +(-2.57687 + 0.837277i) q^{5} +(0.252316 - 1.59306i) q^{7} -6.93221i q^{9} +O(q^{10})$	\(q+(-2.22848 + 2.22848i) q^{3} +(-2.57687 + 0.837277i) q^{5} +(0.252316 - 1.59306i) q^{7} -6.93221i q^{9} +(-0.314590 - 0.617417i) q^{11} +(-1.50733 + 0.238738i) q^{13} +(3.87665 - 7.60835i) q^{15} +(0.942631 - 0.480295i) q^{17} +(0.126968 + 0.0201098i) q^{19} +(2.98781 + 4.11237i) q^{21} +(-1.52374 - 1.10707i) q^{23} +(1.89416 - 1.37619i) q^{25} +(8.76282 + 8.76282i) q^{27} +(7.39222 + 3.76652i) q^{29} +(-0.373094 + 1.14827i) q^{31} +(2.07696 + 0.674844i) q^{33} +(0.683646 + 4.31637i) q^{35} +(-1.86889 - 5.75186i) q^{37} +(2.82703 - 3.89107i) q^{39} +(5.96866 + 2.31844i) q^{41} +(6.21829 - 8.55874i) q^{43} +(5.80417 + 17.8634i) q^{45} +(0.991818 + 6.26210i) q^{47} +(4.18322 + 1.35921i) q^{49} +(-1.03031 + 3.17095i) q^{51} +(-11.1289 - 5.67046i) q^{53} +(1.32761 + 1.32761i) q^{55} +(-0.327760 + 0.238131i) q^{57} +(6.61738 + 4.80781i) q^{59} +(-1.54768 - 2.13021i) q^{61} +(-11.0434 - 1.74911i) q^{63} +(3.68431 - 1.87725i) q^{65} +(3.85439 - 7.56467i) q^{67} +(5.86269 - 0.928560i) q^{69} +(-1.94789 - 3.82296i) q^{71} -12.1957i q^{73} +(-1.15429 + 7.28788i) q^{75} +(-1.06296 + 0.345376i) q^{77} +(8.14191 - 8.14191i) q^{79} -18.2589 q^{81} -6.49090 q^{83} +(-2.02690 + 2.02690i) q^{85} +(-24.8670 + 8.07977i) q^{87} +(0.451128 - 2.84831i) q^{89} +2.46150i q^{91} +(-1.72745 - 3.39031i) q^{93} +(-0.344018 + 0.0544871i) q^{95} +(0.548878 - 1.07723i) q^{97} +(-4.28006 + 2.18080i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7}+O(q^{10}) $ 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7	$ 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{17} - 16 q^{19} - 10 q^{21} - 12 q^{23} - 8 q^{25} + 6 q^{27} + 40 q^{29} + 12 q^{31} + 10 q^{33} + 36 q^{35} + 50 q^{39} - 4 q^{41} + 16 q^{45} + 12 q^{47} - 30 q^{49} + 24 q^{51} - 26 q^{53} - 20 q^{55} + 10 q^{57} - 6 q^{59} + 30 q^{61} - 92 q^{63} + 68 q^{65} + 22 q^{67} - 38 q^{69} - 4 q^{71} - 4 q^{75} - 20 q^{77} + 2 q^{79} + 28 q^{81} - 80 q^{83} - 56 q^{85} + 10 q^{87} - 72 q^{89} - 6 q^{93} + 40 q^{95} - 22 q^{97} - 14 q^{99}+O(q^{100}) $ 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^17 - 16 * q^19 - 10 * q^21 - 12 * q^23 - 8 * q^25 + 6 * q^27 + 40 * q^29 + 12 * q^31 + 10 * q^33 + 36 * q^35 + 50 * q^39 - 4 * q^41 + 16 * q^45 + 12 * q^47 - 30 * q^49 + 24 * q^51 - 26 * q^53 - 20 * q^55 + 10 * q^57 - 6 * q^59 + 30 * q^61 - 92 * q^63 + 68 * q^65 + 22 * q^67 - 38 * q^69 - 4 * q^71 - 4 * q^75 - 20 * q^77 + 2 * q^79 + 28 * q^81 - 80 * q^83 - 56 * q^85 + 10 * q^87 - 72 * q^89 - 6 * q^93 + 40 * q^95 - 22 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.22848	+	2.22848i	−1.28661	+	1.28661i	−0.349778	+	0.936832i	$0.613743\pi$
$3$	−2.22848	+	2.22848i	−1.28661	+	1.28661i	−0.936832	+	0.349778i	$0.886257\pi$
$4$		0			0
$5$	−2.57687	+	0.837277i	−1.15241	+	0.374442i	−0.822052	−	0.569413i	$-0.807171\pi$
$5$	−2.57687	+	0.837277i	−1.15241	+	0.374442i	−0.330361	+	0.943855i	$0.607171\pi$
$6$		0			0
$7$	0.252316	−	1.59306i	0.0953664	−	0.602120i	−0.893003	−	0.450050i	$-0.851406\pi$
$7$	0.252316	−	1.59306i	0.0953664	−	0.602120i	0.988370	−	0.152070i	$-0.0485939\pi$
$8$		0			0
$9$		−	6.93221i		−	2.31074i
$10$		0			0
$11$	−0.314590	−	0.617417i	−0.0948524	−	0.186158i	0.838705	−	0.544586i	$-0.183313\pi$
$11$	−0.314590	−	0.617417i	−0.0948524	−	0.186158i	−0.933558	+	0.358427i	$0.883313\pi$
$12$		0			0
$13$	−1.50733	+	0.238738i	−0.418058	+	0.0662139i	−0.361920	−	0.932209i	$-0.617879\pi$
$13$	−1.50733	+	0.238738i	−0.418058	+	0.0662139i	−0.0561381	+	0.998423i	$0.517879\pi$
$14$		0			0
$15$	3.87665	−	7.60835i	1.00095	−	1.96447i
$16$		0			0
$17$	0.942631	−	0.480295i	0.228622	−	0.116489i	−0.335928	−	0.941888i	$-0.609050\pi$
$17$	0.942631	−	0.480295i	0.228622	−	0.116489i	0.564550	+	0.825399i	$0.309050\pi$
$18$		0			0
$19$	0.126968	+	0.0201098i	0.0291285	+	0.00461350i	0.170982	−	0.985274i	$-0.445306\pi$
$19$	0.126968	+	0.0201098i	0.0291285	+	0.00461350i	−0.141853	+	0.989888i	$0.545306\pi$
$20$		0			0
$21$	2.98781	+	4.11237i	0.651995	+	0.897394i
$22$		0			0
$23$	−1.52374	−	1.10707i	−0.317723	−	0.230839i	0.417480	−	0.908686i	$-0.362913\pi$
$23$	−1.52374	−	1.10707i	−0.317723	−	0.230839i	−0.735203	+	0.677847i	$0.762913\pi$
$24$		0			0
$25$	1.89416	−	1.37619i	0.378831	−	0.275237i
$26$		0			0
$27$	8.76282	+	8.76282i	1.68641	+	1.68641i
$28$		0			0
$29$	7.39222	+	3.76652i	1.37270	+	0.699426i	0.975847	−	0.218456i	$-0.0701022\pi$
$29$	7.39222	+	3.76652i	1.37270	+	0.699426i	0.396853	+	0.917882i	$0.370102\pi$
$30$		0			0
$31$	−0.373094	+	1.14827i	−0.0670097	+	0.206235i	−0.978955	−	0.204078i	$-0.934580\pi$
$31$	−0.373094	+	1.14827i	−0.0670097	+	0.206235i	0.911945	+	0.410313i	$0.134580\pi$
$32$		0			0
$33$	2.07696	+	0.674844i	0.361551	+	0.117475i
$34$		0			0
$35$	0.683646	+	4.31637i	0.115557	+	0.729600i
$36$		0			0
$37$	−1.86889	−	5.75186i	−0.307244	−	0.945600i	−0.978830	−	0.204673i	$-0.934387\pi$
$37$	−1.86889	−	5.75186i	−0.307244	−	0.945600i	0.671586	−	0.740926i	$-0.265613\pi$
$38$		0			0
$39$	2.82703	−	3.89107i	0.452687	−	0.623070i
$40$		0			0
$41$	5.96866	+	2.31844i	0.932147	+	0.362079i
$41$	5.96866	+	2.31844i	0.932147	+	0.362079i
$42$		0			0
$43$	6.21829	−	8.55874i	0.948280	−	1.30520i	−0.00400713	−	0.999992i	$-0.501276\pi$
$43$	6.21829	−	8.55874i	0.948280	−	1.30520i	0.952287	−	0.305204i	$-0.0987245\pi$
$44$		0			0
$45$	5.80417	+	17.8634i	0.865235	+	2.66292i
$46$		0			0
$47$	0.991818	+	6.26210i	0.144672	+	0.913421i	0.948089	+	0.318005i	$0.103013\pi$
$47$	0.991818	+	6.26210i	0.144672	+	0.913421i	−0.803418	+	0.595416i	$0.796987\pi$
$48$		0			0
$49$	4.18322	+	1.35921i	0.597603	+	0.194173i
$50$		0			0
$51$	−1.03031	+	3.17095i	−0.144272	+	0.444022i
$52$		0			0
$53$	−11.1289	−	5.67046i	−1.52867	−	0.778898i	−0.531020	−	0.847359i	$-0.678191\pi$
$53$	−11.1289	−	5.67046i	−1.52867	−	0.778898i	−0.997654	+	0.0684612i	$0.978191\pi$
$54$		0			0
$55$	1.32761	+	1.32761i	0.179015	+	0.179015i
$56$		0			0
$57$	−0.327760	+	0.238131i	−0.0434128	+	0.0315413i
$58$		0			0
$59$	6.61738	+	4.80781i	0.861509	+	0.625923i	0.928295	−	0.371844i	$-0.121274\pi$
$59$	6.61738	+	4.80781i	0.861509	+	0.625923i	−0.0667860	+	0.997767i	$0.521274\pi$
$60$		0			0
$61$	−1.54768	−	2.13021i	−0.198161	−	0.272745i	0.698360	−	0.715747i	$-0.253913\pi$
$61$	−1.54768	−	2.13021i	−0.198161	−	0.272745i	−0.896521	+	0.443002i	$0.853913\pi$
$62$		0			0
$63$	−11.0434	−	1.74911i	−1.39134	−	0.220367i
$64$		0			0
$65$	3.68431	−	1.87725i	0.456982	−	0.232844i
$66$		0			0
$67$	3.85439	−	7.56467i	0.470889	−	0.924172i	−0.526375	−	0.850252i	$-0.676449\pi$
$67$	3.85439	−	7.56467i	0.470889	−	0.924172i	0.997264	−	0.0739193i	$-0.0235507\pi$
$68$		0			0
$69$	5.86269	−	0.928560i	0.705786	−	0.111785i
$70$		0			0
$71$	−1.94789	−	3.82296i	−0.231172	−	0.453701i	0.746058	−	0.665881i	$-0.231944\pi$
$71$	−1.94789	−	3.82296i	−0.231172	−	0.453701i	−0.977231	+	0.212179i	$0.931944\pi$
$72$		0			0
$73$		−	12.1957i		−	1.42739i	−0.700455	−	0.713697i	$-0.747019\pi$
$73$		−	12.1957i		−	1.42739i	0.700455	−	0.713697i	$-0.252981\pi$
$74$		0			0
$75$	−1.15429	+	7.28788i	−0.133286	+	0.841532i
$76$		0			0
$77$	−1.06296	+	0.345376i	−0.121135	+	0.0393593i
$78$		0			0
$79$	8.14191	−	8.14191i	0.916037	−	0.916037i	−0.0807015	−	0.996738i	$-0.525716\pi$
$79$	8.14191	−	8.14191i	0.916037	−	0.916037i	0.996738	+	0.0807015i	$0.0257160\pi$
$80$		0			0
$81$	−18.2589			−2.02876
$82$		0			0
$83$	−6.49090			−0.712469			−0.356235	−	0.934397i	$-0.615940\pi$
$83$	−6.49090			−0.712469			−0.356235	+	0.934397i	$0.615940\pi$
$84$		0			0
$85$	−2.02690	+	2.02690i	−0.219848	+	0.219848i
$86$		0			0
$87$	−24.8670	+	8.07977i	−2.66602	+	0.866242i
$88$		0			0
$89$	0.451128	−	2.84831i	0.0478195	−	0.301920i	−0.952174	−	0.305557i	$-0.901157\pi$
$89$	0.451128	−	2.84831i	0.0478195	−	0.301920i	0.999993	+	0.00363635i	$0.00115749\pi$
$90$		0			0
$91$			2.46150i			0.258036i
$92$		0			0
$93$	−1.72745	−	3.39031i	−0.179128	−	0.351559i
$94$		0			0
$95$	−0.344018	+	0.0544871i	−0.0352955	+	0.00559026i
$96$		0			0
$97$	0.548878	−	1.07723i	0.0557301	−	0.109377i	−0.861462	−	0.507823i	$-0.830450\pi$
$97$	0.548878	−	1.07723i	0.0557301	−	0.109377i	0.917192	+	0.398446i	$0.130450\pi$
$98$		0			0
$99$	−4.28006	+	2.18080i	−0.430163	+	0.219179i
$100$		0			0
$101$	−5.23645	−	0.829373i	−0.521047	−	0.0825257i	−0.109629	−	0.993973i	$-0.534966\pi$
$101$	−5.23645	−	0.829373i	−0.521047	−	0.0825257i	−0.411418	+	0.911447i	$0.634966\pi$
$102$		0			0
$103$	−8.15642	−	11.2264i	−0.803676	−	1.10617i	−0.992268	−	0.124110i	$-0.960392\pi$
$103$	−8.15642	−	11.2264i	−0.803676	−	1.10617i	0.188592	−	0.982055i	$-0.439608\pi$
$104$		0			0
$105$	−11.1424	−	8.09544i	−1.08739	−	0.790034i
$106$		0			0
$107$	7.71269	−	5.60360i	0.745614	−	0.541720i	−0.148850	−	0.988860i	$-0.547557\pi$
$107$	7.71269	−	5.60360i	0.745614	−	0.541720i	0.894464	+	0.447139i	$0.147557\pi$
$108$		0			0
$109$	−1.66630	−	1.66630i	−0.159603	−	0.159603i	0.622788	−	0.782391i	$-0.286000\pi$
$109$	−1.66630	−	1.66630i	−0.159603	−	0.159603i	−0.782391	+	0.622788i	$0.786000\pi$
$110$		0			0
$111$	16.9827	+	8.65309i	1.61192	+	0.821315i
$112$		0			0
$113$	−2.37239	+	7.30147i	−0.223176	+	0.686865i	0.775296	+	0.631598i	$0.217601\pi$
$113$	−2.37239	+	7.30147i	−0.223176	+	0.686865i	−0.998472	+	0.0552663i	$0.982399\pi$
$114$		0			0
$115$	4.85342	+	1.57697i	0.452583	+	0.147053i
$116$		0			0
$117$	1.65498	+	10.4491i	0.153003	+	0.966022i
$118$		0			0
$119$	−0.527297	−	1.62285i	−0.0483372	−	0.148767i
$120$		0			0
$121$	6.18340	−	8.51072i	0.562127	−	0.773702i
$122$		0			0
$123$	−18.4676	+	8.13442i	−1.66517	+	0.733456i
$124$		0			0
$125$	4.23422	−	5.82791i	0.378720	−	0.521264i
$126$		0			0
$127$	1.92578	+	5.92695i	0.170886	+	0.525932i	0.999422	−	0.0340038i	$-0.0108258\pi$
$127$	1.92578	+	5.92695i	0.170886	+	0.525932i	−0.828536	+	0.559936i	$0.810826\pi$
$128$		0			0
$129$	5.21564	+	32.9302i	0.459211	+	2.89935i
$130$		0			0
$131$	−0.689839	−	0.224142i	−0.0602715	−	0.0195834i	0.278726	−	0.960371i	$-0.410088\pi$
$131$	−0.689839	−	0.224142i	−0.0602715	−	0.0195834i	−0.338998	+	0.940787i	$0.610088\pi$
$132$		0			0
$133$	0.0640721	−	0.197194i	0.00555576	−	0.0170989i
$134$		0			0
$135$	−29.9176	−	15.2438i	−2.57490	−	1.31198i
$136$		0			0
$137$	13.1949	+	13.1949i	1.12731	+	1.12731i	0.990612	+	0.136700i	$0.0436498\pi$
$137$	13.1949	+	13.1949i	1.12731	+	1.12731i	0.136700	+	0.990612i	$0.456350\pi$
$138$		0			0
$139$	5.13170	−	3.72840i	0.435265	−	0.316239i	−0.348486	−	0.937314i	$-0.613304\pi$
$139$	5.13170	−	3.72840i	0.435265	−	0.316239i	0.783751	+	0.621075i	$0.213304\pi$
$140$		0			0
$141$	−16.1652	−	11.7447i	−1.36135	−	0.989081i
$142$		0			0
$143$	0.621592	+	0.855548i	0.0519801	+	0.0715445i
$144$		0			0
$145$	−22.2024	−	3.51652i	−1.84381	−	0.292031i
$146$		0			0
$147$	−12.3512	+	6.29324i	−1.01871	+	0.519057i
$148$		0			0
$149$	5.86949	−	11.5195i	0.480848	−	0.943717i	−0.515382	−	0.856961i	$-0.672350\pi$
$149$	5.86949	−	11.5195i	0.480848	−	0.943717i	0.996230	−	0.0867562i	$-0.0276501\pi$
$150$		0			0
$151$	1.37899	−	0.218411i	0.112221	−	0.0177740i	−0.100071	−	0.994980i	$-0.531907\pi$
$151$	1.37899	−	0.218411i	0.112221	−	0.0177740i	0.212292	+	0.977206i	$0.431907\pi$
$152$		0			0
$153$	−3.32950	−	6.53451i	−0.269174	−	0.528284i
$154$		0			0
$155$		−	3.27132i		−	0.262759i
$156$		0			0
$157$	2.74716	−	17.3449i	0.219247	−	1.38427i	−0.594987	−	0.803735i	$-0.702843\pi$
$157$	2.74716	−	17.3449i	0.219247	−	1.38427i	0.814234	−	0.580537i	$-0.197157\pi$
$158$		0			0
$159$	37.4370	−	12.1640i	2.96895	−	0.964669i
$160$		0			0
$161$	−2.14809	+	2.14809i	−0.169293	+	0.169293i
$162$		0			0
$163$	−17.6081			−1.37918			−0.689588	−	0.724202i	$-0.742208\pi$
$163$	−17.6081			−1.37918			−0.689588	+	0.724202i	$0.742208\pi$
$164$		0			0
$165$	−5.91708			−0.460644
$166$		0			0
$167$	1.96297	−	1.96297i	0.151899	−	0.151899i	−0.627066	−	0.778966i	$-0.715745\pi$
$167$	1.96297	−	1.96297i	0.151899	−	0.151899i	0.778966	+	0.627066i	$0.215745\pi$
$168$		0			0
$169$	−10.1487	+	3.29751i	−0.780668	+	0.253654i
$170$		0			0
$171$	0.139405	−	0.880169i	0.0106606	−	0.0673082i
$172$		0			0
$173$			11.7096i			0.890265i	0.895465	+	0.445132i	$0.146843\pi$
$173$			11.7096i			0.890265i	−0.895465	+	0.445132i	$0.853157\pi$
$174$		0			0
$175$	−1.71442	−	3.36474i	−0.129598	−	0.254350i
$176$		0			0
$177$	−25.4607	+	4.03258i	−1.91375	+	0.303108i
$178$		0			0
$179$	−1.93111	+	3.79002i	−0.144338	+	0.283279i	−0.951846	−	0.306578i	$-0.900816\pi$
$179$	−1.93111	+	3.79002i	−0.144338	+	0.283279i	0.807508	+	0.589857i	$0.200816\pi$
$180$		0			0
$181$	4.13089	−	2.10479i	0.307047	−	0.156448i	−0.293677	−	0.955905i	$-0.594879\pi$
$181$	4.13089	−	2.10479i	0.307047	−	0.156448i	0.600724	+	0.799457i	$0.294879\pi$
$182$		0			0
$183$	8.19609	+	1.29813i	0.605872	+	0.0959607i
$184$		0			0
$185$	9.63179	+	13.2570i	0.708144	+	0.974676i
$186$		0			0
$187$	−0.593084	−	0.430901i	−0.0433706	−	0.0315106i
$188$		0			0
$189$	16.1707	−	11.7487i	1.17625	−	0.854592i
$190$		0			0
$191$	−15.8171	−	15.8171i	−1.14449	−	1.14449i	−0.987619	−	0.156869i	$-0.949860\pi$
$191$	−15.8171	−	15.8171i	−1.14449	−	1.14449i	−0.156869	−	0.987619i	$-0.550140\pi$
$192$		0			0
$193$	12.9855	+	6.61647i	0.934720	+	0.476264i	0.853884	−	0.520464i	$-0.174241\pi$
$193$	12.9855	+	6.61647i	0.934720	+	0.476264i	0.0808362	+	0.996727i	$0.474241\pi$
$194$		0			0
$195$	−4.02699	+	12.3938i	−0.288379	+	0.887538i
$196$		0			0
$197$	0.885009	+	0.287557i	0.0630543	+	0.0204876i	0.340374	−	0.940290i	$-0.389446\pi$
$197$	0.885009	+	0.287557i	0.0630543	+	0.0204876i	−0.277320	+	0.960778i	$0.589446\pi$
$198$		0			0
$199$	−0.0644895	−	0.407171i	−0.00457154	−	0.0288636i	0.985297	−	0.170850i	$-0.0546512\pi$
$199$	−0.0644895	−	0.407171i	−0.00457154	−	0.0288636i	−0.989869	+	0.141986i	$0.954651\pi$
$200$		0			0
$201$	8.26826	+	25.4471i	0.583198	+	1.79490i
$202$		0			0
$203$	7.86547	−	10.8259i	0.552048	−	0.759828i
$204$		0			0
$205$	−17.3216	−	0.976904i	−1.20980	−	0.0682299i
$206$		0			0
$207$	−7.67440	+	10.5629i	−0.533408	+	0.734173i
$208$		0			0
$209$	−0.0275268	−	0.0847187i	−0.00190407	−	0.00586011i
$210$		0			0
$211$	3.50778	+	22.1473i	0.241486	+	1.52468i	0.748728	+	0.662877i	$0.230665\pi$
$211$	3.50778	+	22.1473i	0.241486	+	1.52468i	−0.507243	+	0.861803i	$0.669335\pi$
$212$		0			0
$213$	12.8602	+	4.17853i	0.881166	+	0.286308i
$214$		0			0
$215$	−8.85770	+	27.2612i	−0.604090	+	1.85920i
$216$		0			0
$217$	1.73512	+	0.884087i	0.117788	+	0.0600157i
$218$		0			0
$219$	27.1777	+	27.1777i	1.83650	+	1.83650i
$220$		0			0
$221$	−1.30619	+	0.949004i	−0.0878640	+	0.0638369i
$222$		0			0
$223$	−3.29767	−	2.39590i	−0.220829	−	0.160441i	0.471871	−	0.881668i	$-0.343579\pi$
$223$	−3.29767	−	2.39590i	−0.220829	−	0.160441i	−0.692700	+	0.721226i	$0.743579\pi$
$224$		0			0
$225$	−9.54000	−	13.1307i	−0.636000	−	0.875379i
$226$		0			0
$227$	21.3270	+	3.37787i	1.41552	+	0.224197i	0.816875	−	0.576815i	$-0.195705\pi$
$227$	21.3270	+	3.37787i	1.41552	+	0.224197i	0.598649	+	0.801012i	$0.295705\pi$
$228$		0			0
$229$	8.82761	−	4.49789i	0.583345	−	0.297229i	−0.137304	−	0.990529i	$-0.543844\pi$
$229$	8.82761	−	4.49789i	0.583345	−	0.297229i	0.720649	+	0.693300i	$0.243844\pi$
$230$		0			0
$231$	1.59911	−	3.13844i	0.105214	−	0.206494i
$232$		0			0
$233$	−1.27079	+	0.201273i	−0.0832521	+	0.0131858i	−0.197922	−	0.980218i	$-0.563419\pi$
$233$	−1.27079	+	0.201273i	−0.0832521	+	0.0131858i	0.114669	+	0.993404i	$0.463419\pi$
$234$		0			0
$235$	−7.79890	−	15.3062i	−0.508744	−	0.998466i
$236$		0			0
$237$			36.2881i			2.35717i
$238$		0			0
$239$	1.11016	−	7.00929i	0.0718104	−	0.453393i	−0.925415	−	0.378955i	$-0.876284\pi$
$239$	1.11016	−	7.00929i	0.0718104	−	0.453393i	0.997226	−	0.0744383i	$-0.0237164\pi$
$240$		0			0
$241$	10.2597	−	3.33359i	0.660888	−	0.214735i	0.0406791	−	0.999172i	$-0.487048\pi$
$241$	10.2597	−	3.33359i	0.660888	−	0.214735i	0.620209	+	0.784437i	$0.287048\pi$
$242$		0			0
$243$	14.4009	−	14.4009i	0.923821	−	0.923821i
$244$		0			0
$245$	−11.9177			−0.761391
$246$		0			0
$247$	−0.196184			−0.0124829
$248$		0			0
$249$	14.4648	−	14.4648i	0.916670	−	0.916670i
$250$		0			0
$251$	−5.35009	+	1.73835i	−0.337695	+	0.109724i	−0.472955	−	0.881086i	$-0.656813\pi$
$251$	−5.35009	+	1.73835i	−0.337695	+	0.109724i	0.135261	+	0.990810i	$0.456813\pi$
$252$		0			0
$253$	−0.204167	+	1.28906i	−0.0128359	+	0.0810424i
$254$		0			0
$255$		−	9.03380i		−	0.565718i
$256$		0			0
$257$	−9.98071	−	19.5882i	−0.622580	−	1.22188i	−0.959861	−	0.280477i	$-0.909507\pi$
$257$	−9.98071	−	19.5882i	−0.622580	−	1.22188i	0.337281	−	0.941404i	$-0.390493\pi$
$258$		0			0
$259$	−9.63460	+	1.52597i	−0.598665	+	0.0948192i
$260$		0			0
$261$	26.1103	−	51.2444i	1.61619	−	3.17195i
$262$		0			0
$263$	−5.22227	+	2.66088i	−0.322019	+	0.164077i	−0.607526	−	0.794300i	$-0.707838\pi$
$263$	−5.22227	+	2.66088i	−0.322019	+	0.164077i	0.285507	+	0.958377i	$0.407838\pi$
$264$		0			0
$265$	33.4255	+	5.29409i	2.05331	+	0.325213i
$266$		0			0
$267$	5.34206	+	7.35272i	0.326929	+	0.449979i
$268$		0			0
$269$	−11.1080	−	8.07042i	−0.677265	−	0.492062i	0.195184	−	0.980767i	$-0.437470\pi$
$269$	−11.1080	−	8.07042i	−0.677265	−	0.492062i	−0.872449	+	0.488705i	$0.837470\pi$
$270$		0			0
$271$	−12.8738	+	9.35335i	−0.782026	+	0.568175i	−0.905586	−	0.424162i	$-0.860569\pi$
$271$	−12.8738	+	9.35335i	−0.782026	+	0.568175i	0.123560	+	0.992337i	$0.460569\pi$
$272$		0			0
$273$	−5.48540	−	5.48540i	−0.331992	−	0.331992i
$274$		0			0
$275$	−1.44556	−	0.736551i	−0.0871708	−	0.0444157i
$276$		0			0
$277$	−5.93200	+	18.2568i	−0.356420	+	1.09695i	0.598762	+	0.800927i	$0.295659\pi$
$277$	−5.93200	+	18.2568i	−0.356420	+	1.09695i	−0.955182	+	0.296020i	$0.904341\pi$
$278$		0			0
$279$	7.96002	+	2.58637i	0.476554	+	0.154842i
$280$		0			0
$281$	−0.226991	−	1.43316i	−0.0135411	−	0.0854954i	0.979992	−	0.199036i	$-0.0637809\pi$
$281$	−0.226991	−	1.43316i	−0.0135411	−	0.0854954i	−0.993533	+	0.113540i	$0.963781\pi$
$282$		0			0
$283$	2.91195	+	8.96207i	0.173098	+	0.532740i	0.999541	−	0.0302793i	$-0.00963967\pi$
$283$	2.91195	+	8.96207i	0.173098	+	0.532740i	−0.826444	+	0.563019i	$0.809640\pi$
$284$		0			0
$285$	0.645213	−	0.888059i	0.0382191	−	0.0526041i
$286$		0			0
$287$	5.19940	−	8.92345i	0.306911	−	0.526734i
$288$		0			0
$289$	−9.33448	+	12.8478i	−0.549087	+	0.755753i
$290$		0			0
$291$	1.17743	+	3.62375i	0.0690221	+	0.212428i
$292$		0			0
$293$	0.169720	+	1.07157i	0.00991512	+	0.0626016i	0.992150	−	0.125055i	$-0.0399108\pi$
$293$	0.169720	+	1.07157i	0.00991512	+	0.0626016i	−0.982235	+	0.187657i	$0.939911\pi$
$294$		0			0
$295$	−21.0776	−	6.84853i	−1.22719	−	0.398737i
$296$		0			0
$297$	2.65362	−	8.16701i	0.153979	−	0.473898i
$298$		0			0
$299$	2.56108	+	1.30494i	0.148111	+	0.0754665i
$300$		0			0
$301$	−12.0656	−	12.0656i	−0.695450	−	0.695450i
$302$		0			0
$303$	13.5175	−	9.82107i	0.776563	−	0.564206i
$304$		0			0
$305$	5.77176	+	4.19343i	0.330490	+	0.240115i
$306$		0			0
$307$	−17.4258	−	23.9845i	−0.994542	−	1.36887i	−0.928615	−	0.371045i	$-0.879000\pi$
$307$	−17.4258	−	23.9845i	−0.994542	−	1.36887i	−0.0659270	−	0.997824i	$-0.521000\pi$
$308$		0			0
$309$	43.1940	+	6.84126i	2.45722	+	0.389186i
$310$		0			0
$311$	15.3673	−	7.83002i	0.871399	−	0.444000i	0.0396900	−	0.999212i	$-0.487363\pi$
$311$	15.3673	−	7.83002i	0.871399	−	0.444000i	0.831709	+	0.555212i	$0.187363\pi$
$312$		0			0
$313$	−0.736533	+	1.44553i	−0.0416313	+	0.0817060i	−0.910885	−	0.412660i	$-0.864600\pi$
$313$	−0.736533	+	1.44553i	−0.0416313	+	0.0817060i	0.869254	+	0.494366i	$0.164600\pi$
$314$		0			0
$315$	29.9220	−	4.73917i	1.68591	−	0.267022i
$316$		0			0
$317$	−7.39686	−	14.5172i	−0.415449	−	0.815364i	−0.999992	−	0.00400175i	$-0.998726\pi$
$317$	−7.39686	−	14.5172i	−0.415449	−	0.815364i	0.584543	−	0.811363i	$-0.301274\pi$
$318$		0			0
$319$		−	5.74899i		−	0.321882i
$320$		0			0
$321$	−4.70006	+	29.6750i	−0.262332	+	1.65630i
$322$		0			0
$323$	0.129343	−	0.0420260i	0.00719682	−	0.00233839i
$324$		0			0
$325$	−2.52657	+	2.52657i	−0.140149	+	0.140149i
$326$		0			0
$327$	7.42662			0.410693
$328$		0			0
$329$	10.2261			0.563786
$330$		0			0
$331$	17.9285	−	17.9285i	0.985441	−	0.985441i	−0.0144544	−	0.999896i	$-0.504601\pi$
$331$	17.9285	−	17.9285i	0.985441	−	0.985441i	0.999896	+	0.0144544i	$0.00460115\pi$
$332$		0			0
$333$	−39.8731	+	12.9555i	−2.18503	+	0.709959i
$334$		0			0
$335$	−3.59856	+	22.7204i	−0.196610	+	1.24135i
$336$		0			0
$337$		−	26.2434i		−	1.42957i	−0.699344	−	0.714785i	$-0.746525\pi$
$337$		−	26.2434i		−	1.42957i	0.699344	−	0.714785i	$-0.253475\pi$
$338$		0			0
$339$	−10.9843	−	21.5580i	−0.596587	−	1.17087i
$340$		0			0
$341$	0.826331	−	0.130878i	0.0447483	−	0.00708744i
$342$		0			0
$343$	8.34654	−	16.3810i	0.450671	−	0.884491i
$344$		0			0
$345$	−14.3300	+	7.30148i	−0.771499	+	0.393098i
$346$		0			0
$347$	16.4622	+	2.60735i	0.883735	+	0.139970i	0.581774	−	0.813351i	$-0.302359\pi$
$347$	16.4622	+	2.60735i	0.883735	+	0.139970i	0.301961	+	0.953320i	$0.402359\pi$
$348$		0			0
$349$	5.08471	+	6.99851i	0.272178	+	0.374622i	0.923124	−	0.384503i	$-0.125627\pi$
$349$	5.08471	+	6.99851i	0.272178	+	0.374622i	−0.650945	+	0.759125i	$0.725627\pi$
$350$		0			0
$351$	−15.3005	−	11.1165i	−0.816680	−	0.593352i
$352$		0			0
$353$	−11.1586	+	8.10719i	−0.593912	+	0.431502i	−0.843713	−	0.536795i	$-0.819635\pi$
$353$	−11.1586	+	8.10719i	−0.593912	+	0.431502i	0.249801	+	0.968297i	$0.419635\pi$
$354$		0			0
$355$	8.22035	+	8.22035i	0.436291	+	0.436291i
$356$		0			0
$357$	4.79156	+	2.44142i	0.253596	+	0.129214i
$358$		0			0
$359$	5.59785	−	17.2284i	0.295443	−	0.909281i	−0.687629	−	0.726062i	$-0.741348\pi$
$359$	5.59785	−	17.2284i	0.295443	−	0.909281i	0.983072	−	0.183219i	$-0.0586517\pi$
$360$		0			0
$361$	−18.0544	−	5.86622i	−0.950229	−	0.308748i
$362$		0			0
$363$	5.18638	+	32.7455i	0.272214	+	1.71869i
$364$		0			0
$365$	10.2111	+	31.4267i	0.534476	+	1.64495i
$366$		0			0
$367$	−13.5735	+	18.6823i	−0.708531	+	0.975210i	0.291296	+	0.956633i	$0.405913\pi$
$367$	−13.5735	+	18.6823i	−0.708531	+	0.975210i	−0.999827	+	0.0185766i	$0.994087\pi$
$368$		0			0
$369$	16.0719	−	41.3759i	0.836669	−	2.15395i
$370$		0			0
$371$	−11.8414	+	16.2983i	−0.614774	+	0.846164i
$372$		0			0
$373$	4.36956	+	13.4481i	0.226247	+	0.696317i	0.998163	+	0.0605920i	$0.0192989\pi$
$373$	4.36956	+	13.4481i	0.226247	+	0.696317i	−0.771915	+	0.635725i	$0.780701\pi$
$374$		0			0
$375$	3.55149	+	22.4232i	0.183398	+	1.15793i
$376$		0			0
$377$	−12.0417	−	3.91259i	−0.620180	−	0.201509i
$378$		0			0
$379$	11.4876	−	35.3552i	0.590079	−	1.81608i	0.0122385	−	0.999925i	$-0.496104\pi$
$379$	11.4876	−	35.3552i	0.590079	−	1.81608i	0.577840	−	0.816150i	$-0.303896\pi$
$380$		0			0
$381$	−17.4996	−	8.91651i	−0.896533	−	0.456806i
$382$		0			0
$383$	4.89444	+	4.89444i	0.250094	+	0.250094i	0.821009	−	0.570915i	$-0.193411\pi$
$383$	4.89444	+	4.89444i	0.250094	+	0.250094i	−0.570915	+	0.821009i	$0.693411\pi$
$384$		0			0
$385$	2.44993	−	1.77998i	0.124860	−	0.0907162i
$386$		0			0
$387$	−59.3309	−	43.1065i	−3.01596	−	2.19122i
$388$		0			0
$389$	1.39142	+	1.91513i	0.0705480	+	0.0971010i	0.842833	−	0.538175i	$-0.180886\pi$
$389$	1.39142	+	1.91513i	0.0705480	+	0.0971010i	−0.772285	+	0.635276i	$0.780886\pi$
$390$		0			0
$391$	−1.96805	−	0.311708i	−0.0995284	−	0.0157637i
$392$		0			0
$393$	2.03678	−	1.03779i	0.102742	−	0.0523498i
$394$		0			0
$395$	−14.1636	+	27.7977i	−0.712650	+	1.39865i
$396$		0			0
$397$	15.9514	−	2.52646i	0.800580	−	0.126799i	0.257278	−	0.966337i	$-0.417174\pi$
$397$	15.9514	−	2.52646i	0.800580	−	0.126799i	0.543301	+	0.839538i	$0.317174\pi$
$398$		0			0
$399$	0.296658	+	0.582225i	0.0148515	+	0.0291477i
$400$		0			0
$401$			4.77242i			0.238323i	0.992875	+	0.119162i	$0.0380207\pi$
$401$			4.77242i			0.238323i	−0.992875	+	0.119162i	$0.961979\pi$
$402$		0			0
$403$	0.288242	−	1.81989i	0.0143584	−	0.0906551i
$404$		0			0
$405$	47.0508	−	15.2877i	2.33797	−	0.759653i
$406$		0			0
$407$	−2.96336	+	2.96336i	−0.146888	+	0.146888i
$408$		0			0
$409$	−9.57331			−0.473370			−0.236685	−	0.971586i	$-0.576061\pi$
$409$	−9.57331			−0.473370			−0.236685	+	0.971586i	$0.576061\pi$
$410$		0			0
$411$	−58.8088			−2.90083
$412$		0			0
$413$	9.32879	−	9.32879i	0.459040	−	0.459040i
$414$		0			0
$415$	16.7262	−	5.43468i	0.821058	−	0.266778i
$416$		0			0
$417$	−3.12722	+	19.7445i	−0.153141	+	0.966893i
$418$		0			0
$419$			8.06247i			0.393878i	0.980416	+	0.196939i	$0.0631000\pi$
$419$			8.06247i			0.393878i	−0.980416	+	0.196939i	$0.936900\pi$
$420$		0			0
$421$	−8.01644	−	15.7331i	−0.390697	−	0.766787i	0.608954	−	0.793206i	$-0.291590\pi$
$421$	−8.01644	−	15.7331i	−0.390697	−	0.766787i	−0.999651	+	0.0264191i	$0.991590\pi$
$422$		0			0
$423$	43.4101	−	6.87549i	2.11067	−	0.334298i
$424$		0			0
$425$	1.12452	−	2.20699i	0.0545471	−	0.107055i
$426$		0			0
$427$	−3.78405	+	1.92807i	−0.183123	+	0.0933058i
$428$		0			0
$429$	−3.29177	−	0.521365i	−0.158928	−	0.0251717i
$430$		0			0
$431$	5.96805	+	8.21431i	0.287471	+	0.395670i	0.928191	−	0.372105i	$-0.121364\pi$
$431$	5.96805	+	8.21431i	0.287471	+	0.395670i	−0.640720	+	0.767775i	$0.721364\pi$
$432$		0			0
$433$	26.8766	+	19.5270i	1.29161	+	0.938406i	0.999837	−	0.0180823i	$-0.00575610\pi$
$433$	26.8766	+	19.5270i	1.29161	+	0.938406i	0.291769	+	0.956489i	$0.405756\pi$
$434$		0			0
$435$	57.3140	−	41.6411i	2.74800	−	1.99654i
$436$		0			0
$437$	−0.171204	−	0.171204i	−0.00818981	−	0.00818981i
$438$		0			0
$439$	32.8349	+	16.7302i	1.56713	+	0.798490i	0.999689	−	0.0249274i	$-0.00793546\pi$
$439$	32.8349	+	16.7302i	1.56713	+	0.798490i	0.567436	+	0.823418i	$0.307935\pi$
$440$		0			0
$441$	9.42233	−	28.9989i	0.448682	−	1.38090i
$442$		0			0
$443$	−29.3333	−	9.53097i	−1.39367	−	0.452830i	−0.486530	−	0.873664i	$-0.661738\pi$
$443$	−29.3333	−	9.53097i	−1.39367	−	0.452830i	−0.907138	+	0.420834i	$0.861738\pi$
$444$		0			0
$445$	1.22232	+	7.71745i	0.0579437	+	0.365842i
$446$		0			0
$447$	12.5910	+	38.7510i	0.595532	+	1.83286i
$448$		0			0
$449$	17.4190	−	23.9753i	0.822055	−	1.13146i	−0.167295	−	0.985907i	$-0.553503\pi$
$449$	17.4190	−	23.9753i	0.822055	−	1.13146i	0.989350	−	0.145555i	$-0.0464969\pi$
$450$		0			0
$451$	−0.446235	−	4.41451i	−0.0210124	−	0.207871i
$452$		0			0
$453$	−2.58633	+	3.55977i	−0.121516	+	0.167253i
$454$		0			0
$455$	−2.06096	−	6.34298i	−0.0966193	−	0.297364i
$456$		0			0
$457$	−1.18792	−	7.50026i	−0.0555688	−	0.350847i	−0.999769	−	0.0214764i	$-0.993163\pi$
$457$	−1.18792	−	7.50026i	−0.0555688	−	0.350847i	0.944201	−	0.329371i	$-0.106837\pi$
$458$		0			0
$459$	12.4688	+	4.05137i	0.581996	+	0.189102i
$460$		0			0
$461$	−7.81323	+	24.0467i	−0.363898	+	1.11996i	0.586770	+	0.809754i	$0.300399\pi$
$461$	−7.81323	+	24.0467i	−0.363898	+	1.11996i	−0.950668	+	0.310210i	$0.899601\pi$
$462$		0			0
$463$	−13.1377	−	6.69397i	−0.610559	−	0.311095i	0.121233	−	0.992624i	$-0.461315\pi$
$463$	−13.1377	−	6.69397i	−0.610559	−	0.311095i	−0.731791	+	0.681529i	$0.761315\pi$
$464$		0			0
$465$	7.29005	+	7.29005i	0.338068	+	0.338068i
$466$		0			0
$467$	−17.8981	+	13.0037i	−0.828226	+	0.601742i	−0.919057	−	0.394125i	$-0.871048\pi$
$467$	−17.8981	+	13.0037i	−0.828226	+	0.601742i	0.0908306	+	0.995866i	$0.471048\pi$
$468$		0			0
$469$	−11.0784	−	8.04896i	−0.511555	−	0.371667i
$470$		0			0
$471$	32.5307	+	44.7746i	1.49893	+	2.06310i
$472$		0			0
$473$	−7.24052	−	1.14679i	−0.332920	−	0.0527293i
$474$		0			0
$475$	0.268172	−	0.136641i	0.0123046	−	0.00626950i
$476$		0			0
$477$	−39.3088	+	77.1479i	−1.79983	+	3.53236i
$478$		0			0
$479$	15.6892	−	2.48493i	0.716859	−	0.113539i	0.212660	−	0.977126i	$-0.431787\pi$
$479$	15.6892	−	2.48493i	0.716859	−	0.113539i	0.504200	+	0.863587i	$0.331787\pi$
$480$		0			0
$481$	4.19022	+	8.22377i	0.191058	+	0.374972i
$482$		0			0
$483$		−	9.57391i		−	0.435628i
$484$		0			0
$485$	−0.512446	+	3.23546i	−0.0232690	+	0.146915i
$486$		0			0
$487$	−20.0083	+	6.50110i	−0.906664	+	0.294593i	−0.724985	−	0.688765i	$-0.758153\pi$
$487$	−20.0083	+	6.50110i	−0.906664	+	0.294593i	−0.181679	+	0.983358i	$0.558153\pi$
$488$		0			0
$489$	39.2393	−	39.2393i	1.77446	−	1.77446i
$490$		0			0
$491$	0.0541126			0.00244207			0.00122103	−	0.999999i	$-0.499611\pi$
$491$	0.0541126			0.00244207			0.00122103	+	0.999999i	$0.499611\pi$
$492$		0			0
$493$	8.77717			0.395304
$494$		0			0
$495$	9.20325	−	9.20325i	0.413655	−	0.413655i
$496$		0			0
$497$	−6.58168	+	2.13852i	−0.295229	+	0.0959256i
$498$		0			0
$499$	−5.08470	+	32.1035i	−0.227623	+	1.43715i	0.563815	+	0.825901i	$0.309333\pi$
$499$	−5.08470	+	32.1035i	−0.227623	+	1.43715i	−0.791437	+	0.611251i	$0.790667\pi$
$500$		0			0
$501$			8.74887i			0.390871i
$502$		0			0
$503$	14.6571	+	28.7662i	0.653529	+	1.28262i	0.945321	+	0.326140i	$0.105748\pi$
$503$	14.6571	+	28.7662i	0.653529	+	1.28262i	−0.291793	+	0.956482i	$0.594252\pi$
$504$		0			0
$505$	14.1881	−	2.24717i	0.631362	−	0.0999979i
$506$		0			0
$507$	15.2677	−	29.9645i	0.678062	−	1.33077i
$508$		0			0
$509$	−25.7195	+	13.1047i	−1.14000	+	0.580857i	−0.918938	−	0.394403i	$-0.870951\pi$
$509$	−25.7195	+	13.1047i	−1.14000	+	0.580857i	−0.221059	+	0.975260i	$0.570951\pi$
$510$		0			0
$511$	−19.4284	−	3.07716i	−0.859462	−	0.136125i
$512$		0			0
$513$	0.936381	+	1.28882i	0.0413422	+	0.0569027i
$514$		0			0
$515$	30.4176	+	22.0997i	1.34036	+	0.973829i
$516$		0			0
$517$	3.55431	−	2.58236i	0.156318	−	0.113572i
$518$		0			0
$519$	−26.0946	−	26.0946i	−1.14542	−	1.14542i
$520$		0			0
$521$	15.6014	+	7.94931i	0.683509	+	0.348265i	0.761022	−	0.648726i	$-0.224698\pi$
$521$	15.6014	+	7.94931i	0.683509	+	0.348265i	−0.0775127	+	0.996991i	$0.524698\pi$
$522$		0			0
$523$	−2.25075	+	6.92710i	−0.0984185	+	0.302901i	−0.988130	−	0.153623i	$-0.950906\pi$
$523$	−2.25075	+	6.92710i	−0.0984185	+	0.302901i	0.889711	+	0.456524i	$0.150906\pi$
$524$		0			0
$525$	11.3188	+	3.67769i	0.493992	+	0.160508i
$526$		0			0
$527$	0.199816	+	1.26159i	0.00870411	+	0.0549556i
$528$		0			0
$529$	−6.01119	−	18.5005i	−0.261356	−	0.804371i
$530$		0			0
$531$	33.3287	−	45.8730i	1.44634	−	1.99072i
$532$		0			0
$533$	−9.55023	−	2.06971i	−0.413667	−	0.0896491i
$534$		0			0
$535$	−15.1829	+	20.8974i	−0.656413	+	0.903474i
$536$		0			0
$537$	−4.14253	−	12.7494i	−0.178763	−	0.550177i
$538$		0			0
$539$	−0.476798	−	3.01039i	−0.0205372	−	0.129667i
$540$		0			0
$541$	−28.9790	−	9.41585i	−1.24590	−	0.404819i	−0.389453	−	0.921046i	$-0.627336\pi$
$541$	−28.9790	−	9.41585i	−1.24590	−	0.404819i	−0.856451	+	0.516228i	$0.827336\pi$
$542$		0			0
$543$	−4.51511	+	13.8961i	−0.193762	+	0.596337i
$544$		0			0
$545$	5.68900	+	2.89869i	0.243690	+	0.124166i
$546$		0			0
$547$	22.9755	+	22.9755i	0.982360	+	0.982360i	0.999847	−	0.0174867i	$-0.00556648\pi$
$547$	22.9755	+	22.9755i	0.982360	+	0.982360i	−0.0174867	+	0.999847i	$0.505566\pi$
$548$		0			0
$549$	−14.7670	+	10.7289i	−0.630241	+	0.457897i
$550$		0			0
$551$	0.862832	+	0.626884i	0.0367579	+	0.0267062i
$552$		0			0
$553$	−10.9162	−	15.0249i	−0.464205	−	0.638923i
$554$		0			0
$555$	−51.0072	−	8.07874i	−2.16513	−	0.342924i
$556$		0			0
$557$	−22.1309	+	11.2762i	−0.937716	+	0.477790i	−0.854910	−	0.518776i	$-0.826388\pi$
$557$	−22.1309	+	11.2762i	−0.937716	+	0.477790i	−0.0828053	+	0.996566i	$0.526388\pi$
$558$		0			0
$559$	−7.32972	+	14.3854i	−0.310014	+	0.608437i
$560$		0			0
$561$	2.28193	−	0.361422i	0.0963430	−	0.0152592i
$562$		0			0
$563$	−11.3113	−	22.1997i	−0.476716	−	0.935608i	−0.996680	−	0.0814196i	$-0.974055\pi$
$563$	−11.3113	−	22.1997i	−0.476716	−	0.935608i	0.519964	−	0.854188i	$-0.325945\pi$
$564$		0			0
$565$		−	20.8013i		−	0.875118i
$566$		0			0
$567$	−4.60700	+	29.0875i	−0.193476	+	1.22156i
$568$		0			0
$569$	−13.3652	+	4.34260i	−0.560297	+	0.182051i	−0.575455	−	0.817834i	$-0.695175\pi$
$569$	−13.3652	+	4.34260i	−0.560297	+	0.182051i	0.0151580	+	0.999885i	$0.495175\pi$
$570$		0			0
$571$	21.7176	−	21.7176i	0.908854	−	0.908854i	−0.0873260	−	0.996180i	$-0.527832\pi$
$571$	21.7176	−	21.7176i	0.908854	−	0.908854i	0.996180	+	0.0873260i	$0.0278322\pi$
$572$		0			0
$573$	70.4962			2.94502
$574$		0			0
$575$	−4.40974			−0.183899
$576$		0			0
$577$	0.105596	−	0.105596i	0.00439603	−	0.00439603i	−0.704905	−	0.709301i	$-0.749011\pi$
$577$	0.105596	−	0.105596i	0.00439603	−	0.00439603i	0.709301	+	0.704905i	$0.249011\pi$
$578$		0			0
$579$	−43.6826	+	14.1933i	−1.81539	+	0.589855i
$580$		0			0
$581$	−1.63776	+	10.3404i	−0.0679456	+	0.428992i
$582$		0			0
$583$			8.65505i			0.358456i
$584$		0			0
$585$	−13.0135	−	25.5404i	−0.538041	−	1.05597i
$586$		0			0
$587$	−15.8079	+	2.50372i	−0.652460	+	0.103339i	−0.473885	−	0.880587i	$-0.657149\pi$
$587$	−15.8079	+	2.50372i	−0.652460	+	0.103339i	−0.178575	+	0.983926i	$0.557149\pi$
$588$		0			0
$589$	−0.0704625	+	0.138290i	−0.00290335	+	0.00569815i
$590$		0			0
$591$	−2.61304	+	1.33141i	−0.107486	+	0.0547668i
$592$		0			0
$593$	1.94396	+	0.307893i	0.0798289	+	0.0126436i	0.196221	−	0.980560i	$-0.437133\pi$
$593$	1.94396	+	0.307893i	0.0798289	+	0.0126436i	−0.116392	+	0.993203i	$0.537133\pi$
$594$		0			0
$595$	2.71756	+	3.74039i	0.111409	+	0.153341i
$596$		0			0
$597$	1.05108	+	0.763656i	0.0430180	+	0.0312544i
$598$		0			0
$599$	−15.0623	+	10.9434i	−0.615429	+	0.447136i	−0.851322	−	0.524644i	$-0.824199\pi$
$599$	−15.0623	+	10.9434i	−0.615429	+	0.447136i	0.235893	+	0.971779i	$0.424199\pi$
$600$		0			0
$601$	7.07160	+	7.07160i	0.288456	+	0.288456i	0.836470	−	0.548013i	$-0.184616\pi$
$601$	7.07160	+	7.07160i	0.288456	+	0.288456i	−0.548013	+	0.836470i	$0.684616\pi$
$602$		0			0
$603$	−52.4399	−	26.7194i	−2.13552	−	1.08810i
$604$		0			0
$605$	−8.80801	+	27.1083i	−0.358096	+	1.10211i
$606$		0			0
$607$	−36.0725	−	11.7207i	−1.46414	−	0.475727i	−0.534806	−	0.844975i	$-0.679615\pi$
$607$	−36.0725	−	11.7207i	−1.46414	−	0.475727i	−0.929331	+	0.369248i	$0.879615\pi$
$608$		0			0
$609$	6.59722	+	41.6532i	0.267333	+	1.68787i
$610$		0			0
$611$	−2.99000	−	9.20226i	−0.120962	−	0.372284i
$612$		0			0
$613$	−15.8786	+	21.8550i	−0.641331	+	0.882717i	−0.998686	−	0.0512520i	$-0.983679\pi$
$613$	−15.8786	+	21.8550i	−0.641331	+	0.882717i	0.357354	+	0.933969i	$0.383679\pi$
$614$		0			0
$615$	40.7779	−	36.4238i	1.64432	−	1.46875i
$616$		0			0
$617$	−5.89230	+	8.11005i	−0.237215	+	0.326498i	−0.910983	−	0.412445i	$-0.864675\pi$
$617$	−5.89230	+	8.11005i	−0.237215	+	0.326498i	0.673768	+	0.738943i	$0.264675\pi$
$618$		0			0
$619$	−10.2987	−	31.6960i	−0.413938	−	1.27397i	−0.913197	−	0.407518i	$-0.866394\pi$
$619$	−10.2987	−	31.6960i	−0.413938	−	1.27397i	0.499259	−	0.866453i	$-0.333606\pi$
$620$		0			0
$621$	−3.65129	−	23.0533i	−0.146521	−	0.925098i
$622$		0			0
$623$	−4.42370	−	1.43735i	−0.177232	−	0.0575861i
$624$		0			0
$625$	−9.64900	+	29.6966i	−0.385960	+	1.18786i
$626$		0			0
$627$	0.250136	+	0.127451i	0.00998948	+	0.00508989i
$628$		0			0
$629$	−4.52426	−	4.52426i	−0.180394	−	0.180394i
$630$		0			0
$631$	−8.52090	+	6.19080i	−0.339212	+	0.246452i	−0.744329	−	0.667813i	$-0.767231\pi$
$631$	−8.52090	+	6.19080i	−0.339212	+	0.246452i	0.405117	+	0.914265i	$0.367231\pi$
$632$		0			0
$633$	−57.1716	−	41.5376i	−2.27237	−	1.65097i
$634$		0			0
$635$	−9.92500	−	13.6606i	−0.393862	−	0.542104i
$636$		0			0
$637$	−6.62999	−	1.05009i	−0.262690	−	0.0416060i
$638$		0			0
$639$	−26.5015	+	13.5032i	−1.04838	+	0.534178i
$640$		0			0
$641$	−2.10778	+	4.13674i	−0.0832521	+	0.163391i	−0.928879	−	0.370382i	$-0.879227\pi$
$641$	−2.10778	+	4.13674i	−0.0832521	+	0.163391i	0.845627	+	0.533774i	$0.179227\pi$
$642$		0			0
$643$	29.6739	−	4.69989i	1.17023	−	0.185346i	0.459083	−	0.888393i	$-0.348178\pi$
$643$	29.6739	−	4.69989i	1.17023	−	0.185346i	0.711143	+	0.703048i	$0.248178\pi$
$644$		0			0
$645$	−41.0118	−	80.4901i	−1.61484	−	3.16930i
$646$		0			0
$647$		−	16.4853i		−	0.648104i	−0.946039	−	0.324052i	$-0.894955\pi$
$647$		−	16.4853i		−	0.648104i	0.946039	−	0.324052i	$-0.105045\pi$
$648$		0			0
$649$	0.886663	−	5.59817i	0.0348046	−	0.219747i
$650$		0			0
$651$	−5.83684	+	1.89650i	−0.228764	+	0.0743298i
$652$		0			0
$653$	23.6145	−	23.6145i	0.924105	−	0.924105i	−0.0732110	−	0.997316i	$-0.523325\pi$
$653$	23.6145	−	23.6145i	0.924105	−	0.924105i	0.997316	+	0.0732110i	$0.0233247\pi$
$654$		0			0
$655$	1.96530			0.0767905
$656$		0			0
$657$	−84.5428			−3.29833
$658$		0			0
$659$	3.37421	−	3.37421i	0.131441	−	0.131441i	−0.638326	−	0.769766i	$-0.720373\pi$
$659$	3.37421	−	3.37421i	0.131441	−	0.131441i	0.769766	+	0.638326i	$0.220373\pi$
$660$		0			0
$661$	12.2982	−	3.99593i	0.478345	−	0.155424i	−0.0599133	−	0.998204i	$-0.519082\pi$
$661$	12.2982	−	3.99593i	0.478345	−	0.155424i	0.538258	+	0.842780i	$0.319082\pi$
$662$		0			0
$663$	0.795985	−	5.02565i	0.0309135	−	0.195180i
$664$		0			0
$665$			0.561789i			0.0217853i
$666$		0			0
$667$	−7.09406	−	13.9229i	−0.274683	−	0.539096i
$668$		0			0
$669$	12.6880	−	2.00958i	0.490546	−	0.0776949i
$670$		0			0
$671$	−0.828340	+	1.62571i	−0.0319777	+	0.0627598i
$672$		0			0
$673$	5.66568	−	2.88681i	0.218396	−	0.111278i	−0.341370	−	0.939929i	$-0.610891\pi$
$673$	5.66568	−	2.88681i	0.218396	−	0.111278i	0.559766	+	0.828651i	$0.310891\pi$
$674$		0			0
$675$	28.6574	+	4.53889i	1.10303	+	0.174702i
$676$		0			0
$677$	−20.5198	−	28.2431i	−0.788642	−	1.08547i	−0.994276	−	0.106843i	$-0.965926\pi$
$677$	−20.5198	−	28.2431i	−0.788642	−	1.08547i	0.205634	−	0.978629i	$-0.434074\pi$
$678$		0			0
$679$	−1.57761	−	1.14620i	−0.0605430	−	0.0439871i
$680$		0			0
$681$	−55.0542	+	39.9992i	−2.10968	+	1.53277i
$682$		0			0
$683$	−17.6969	−	17.6969i	−0.677154	−	0.677154i	0.282201	−	0.959355i	$-0.408935\pi$
$683$	−17.6969	−	17.6969i	−0.677154	−	0.677154i	−0.959355	+	0.282201i	$0.908935\pi$
$684$		0			0
$685$	−45.0492	−	22.9537i	−1.72124	−	0.877017i
$686$		0			0
$687$	−9.64867	+	29.6956i	−0.368120	+	1.13296i
$688$		0			0
$689$	18.1287	+	5.89037i	0.690649	+	0.224405i
$690$		0			0
$691$	−4.16500	−	26.2968i	−0.158444	−	1.00038i	−0.930891	−	0.365298i	$-0.880967\pi$
$691$	−4.16500	−	26.2968i	−0.158444	−	1.00038i	0.772446	−	0.635080i	$-0.219033\pi$
$692$		0			0
$693$	2.39422	+	7.36865i	0.0909489	+	0.279912i
$694$		0			0
$695$	−10.1020	+	13.9043i	−0.383192	+	0.527419i
$696$		0			0
$697$	6.73977	−	0.681281i	0.255287	−	0.0258053i
$698$		0			0
$699$	2.38339	−	3.28045i	0.0901480	−	0.124078i
$700$		0			0
$701$	6.42667	+	19.7793i	0.242732	+	0.747052i	0.996001	+	0.0893399i	$0.0284757\pi$
$701$	6.42667	+	19.7793i	0.242732	+	0.747052i	−0.753269	+	0.657712i	$0.771524\pi$
$702$		0			0
$703$	−0.121621	−	0.767886i	−0.00458703	−	0.0289614i
$704$		0			0
$705$	51.4891	+	16.7298i	1.93919	+	0.630082i
$706$		0			0
$707$	−2.64248	+	8.13272i	−0.0993807	+	0.305862i
$708$		0			0
$709$	7.83436	+	3.99181i	0.294226	+	0.149915i	0.594872	−	0.803820i	$-0.297203\pi$
$709$	7.83436	+	3.99181i	0.294226	+	0.149915i	−0.300647	+	0.953736i	$0.597203\pi$
$710$		0			0
$711$	−56.4414	−	56.4414i	−2.11672	−	2.11672i
$712$		0			0
$713$	1.83971	−	1.33662i	0.0688975	−	0.0500570i
$714$		0			0
$715$	−2.31809	−	1.68419i	−0.0866918	−	0.0629852i
$716$		0			0
$717$	13.1461	+	18.0940i	0.490948	+	0.675732i
$718$		0			0
$719$	−12.8945	−	2.04229i	−0.480885	−	0.0761647i	−0.0887143	−	0.996057i	$-0.528276\pi$
$719$	−12.8945	−	2.04229i	−0.480885	−	0.0761647i	−0.392171	+	0.919892i	$0.628276\pi$
$720$		0			0
$721$	−19.9422	+	10.1611i	−0.742688	+	0.378418i
$722$		0			0
$723$	−15.4347	+	30.2924i	−0.574024	+	1.12659i
$724$		0			0
$725$	19.1855	−	3.03868i	0.712530	−	0.112854i
$726$		0			0
$727$	12.5723	+	24.6746i	0.466282	+	0.915131i	0.997685	+	0.0680111i	$0.0216653\pi$
$727$	12.5723	+	24.6746i	0.466282	+	0.915131i	−0.531402	+	0.847120i	$0.678335\pi$
$728$		0			0
$729$			9.40774i			0.348435i
$730$		0			0
$731$	1.75084	−	11.0543i	0.0647570	−	0.408860i
$732$		0			0
$733$	−23.2536	+	7.55554i	−0.858890	+	0.279070i	−0.705165	−	0.709043i	$-0.749127\pi$
$733$	−23.2536	+	7.55554i	−0.858890	+	0.279070i	−0.153725	+	0.988114i	$0.549127\pi$
$734$		0			0
$735$	26.5582	−	26.5582i	0.979615	−	0.979615i
$736$		0			0
$737$	−5.88311			−0.216707
$738$		0			0
$739$	35.1342			1.29243			0.646215	−	0.763155i	$-0.276351\pi$
$739$	35.1342			1.29243			0.646215	+	0.763155i	$0.276351\pi$
$740$		0			0
$741$	0.437191	−	0.437191i	0.0160606	−	0.0160606i
$742$		0			0
$743$	−5.44093	+	1.76787i	−0.199608	+	0.0648567i	−0.407115	−	0.913377i	$-0.633465\pi$
$743$	−5.44093	+	1.76787i	−0.199608	+	0.0648567i	0.207507	+	0.978234i	$0.433465\pi$
$744$		0			0
$745$	−5.47991	+	34.5988i	−0.200768	+	1.26760i
$746$		0			0
$747$			44.9963i			1.64633i
$748$		0			0
$749$	−6.98083	−	13.7007i	−0.255074	−	0.500611i
$750$		0			0
$751$	11.5290	−	1.82601i	0.420699	−	0.0666322i	0.0575040	−	0.998345i	$-0.481686\pi$
$751$	11.5290	−	1.82601i	0.420699	−	0.0666322i	0.363195	+	0.931713i	$0.381686\pi$
$752$		0			0
$753$	8.04868	−	15.7964i	0.293310	−	0.575654i
$754$		0			0
$755$	−3.37062	+	1.71741i	−0.122669	+	0.0625031i
$756$		0			0
$757$	37.9100	+	6.00436i	1.37786	+	0.218232i	0.801027	−	0.598628i	$-0.204287\pi$
$757$	37.9100	+	6.00436i	1.37786	+	0.218232i	0.576836	+	0.816860i	$0.304287\pi$
$758$		0			0
$759$	−2.41765	−	3.32761i	−0.0877552	−	0.120785i
$760$		0			0
$761$	39.0623	+	28.3804i	1.41601	+	1.02879i	0.992415	+	0.122935i	$0.0392305\pi$
$761$	39.0623	+	28.3804i	1.41601	+	1.02879i	0.423591	+	0.905854i	$0.360769\pi$
$762$		0			0
$763$	−3.07495	+	2.23408i	−0.111321	+	0.0808792i
$764$		0			0
$765$	14.0509	+	14.0509i	0.508011	+	0.508011i
$766$		0			0
$767$	−11.1224	−	5.66713i	−0.401606	−	0.204628i
$768$		0			0
$769$	1.21277	−	3.73252i	0.0437336	−	0.134598i	−0.926806	−	0.375541i	$-0.877457\pi$
$769$	1.21277	−	3.73252i	0.0437336	−	0.134598i	0.970539	+	0.240943i	$0.0774568\pi$
$770$		0			0
$771$	65.8937	+	21.4102i	2.37310	+	0.771068i
$772$		0			0
$773$	−5.21943	−	32.9542i	−0.187730	−	1.18528i	−0.883995	−	0.467496i	$-0.845156\pi$
$773$	−5.21943	−	32.9542i	−0.187730	−	1.18528i	0.696265	−	0.717784i	$-0.254844\pi$
$774$		0			0
$775$	0.873528	+	2.68844i	0.0313781	+	0.0965717i
$776$		0			0
$777$	18.0699	−	24.8711i	0.648254	−	0.892244i
$778$		0			0
$779$	0.711206	+	0.414396i	0.0254816	+	0.0148473i
$780$		0			0
$781$	−1.74757	+	2.40533i	−0.0625330	+	0.0860693i
$782$		0			0
$783$	31.7713	+	97.7821i	1.13541	+	3.49445i
$784$		0			0
$785$	7.44338	+	46.9957i	0.265666	+	1.67735i
$786$		0			0
$787$	10.7260	+	3.48510i	0.382342	+	0.124230i	0.493881	−	0.869530i	$-0.335578\pi$
$787$	10.7260	+	3.48510i	0.382342	+	0.124230i	−0.111539	+	0.993760i	$0.535578\pi$
$788$		0			0
$789$	5.70800	−	17.5674i	0.203210	−	0.625416i
$790$		0			0
$791$	11.0331	+	5.62164i	0.392291	+	0.199882i
$792$		0			0
$793$	2.84143	+	2.84143i	0.100902	+	0.100902i
$794$		0			0
$795$	−86.2857	+	62.6903i	−3.06024	+	2.22339i
$796$		0			0
$797$	23.1041	+	16.7861i	0.818391	+	0.594596i	0.916251	−	0.400604i	$-0.131200\pi$
$797$	23.1041	+	16.7861i	0.818391	+	0.594596i	−0.0978602	+	0.995200i	$0.531200\pi$
$798$		0			0
$799$	3.94257	+	5.42648i	0.139478	+	0.191975i
$800$		0			0
$801$	−19.7451	−	3.12731i	−0.697658	−	0.110498i
$802$		0			0
$803$	−7.52981	+	3.83663i	−0.265721	+	0.135392i
$804$		0			0
$805$	3.73680	−	7.33389i	0.131705	−	0.258486i
$806$		0			0
$807$	42.7386	−	6.76913i	1.50447	−	0.238285i
$808$		0			0
$809$	4.83865	+	9.49639i	0.170118	+	0.333875i	0.960287	−	0.279013i	$-0.0900074\pi$
$809$	4.83865	+	9.49639i	0.170118	+	0.333875i	−0.790169	+	0.612889i	$0.790007\pi$
$810$		0			0
$811$			33.8780i			1.18962i	0.803867	+	0.594809i	$0.202772\pi$
$811$			33.8780i			1.18962i	−0.803867	+	0.594809i	$0.797228\pi$
$812$		0			0
$813$	7.84519	−	49.5326i	0.275143	−	1.73718i
$814$		0			0
$815$	45.3739	−	14.7429i	1.58938	−	0.516421i
$816$		0			0
$817$	0.961639	−	0.961639i	0.0336435	−	0.0336435i
$818$		0			0
$819$	17.0637			0.596252
$820$		0			0
$821$	50.1853			1.75148			0.875739	−	0.482785i	$-0.160375\pi$
$821$	50.1853			1.75148			0.875739	+	0.482785i	$0.160375\pi$
$822$		0			0
$823$	31.8583	−	31.8583i	1.11051	−	1.11051i	0.117431	−	0.993081i	$-0.462534\pi$
$823$	31.8583	−	31.8583i	1.11051	−	1.11051i	0.993081	−	0.117431i	$-0.0374659\pi$
$824$		0			0
$825$	4.86279	−	1.58002i	0.169301	−	0.0550091i
$826$		0			0
$827$	0.559901	−	3.53508i	0.0194697	−	0.122927i	−0.976039	−	0.217595i	$-0.930179\pi$
$827$	0.559901	−	3.53508i	0.0194697	−	0.122927i	0.995509	+	0.0946679i	$0.0301789\pi$
$828$		0			0
$829$		−	18.5904i		−	0.645672i	−0.946455	−	0.322836i	$-0.895364\pi$
$829$		−	18.5904i		−	0.645672i	0.946455	−	0.322836i	$-0.104636\pi$
$830$		0			0
$831$	−27.4656	−	53.9042i	−0.952770	−	1.86992i
$832$		0			0
$833$	4.59605	−	0.727944i	0.159244	−	0.0252217i
$834$		0			0
$835$	−3.41478	+	6.70188i	−0.118173	+	0.231928i
$836$		0			0
$837$	−13.3314	+	6.79269i	−0.460801	+	0.234790i
$838$		0			0
$839$	35.8357	+	5.67582i	1.23719	+	0.195951i	0.740546	−	0.672006i	$-0.234567\pi$
$839$	35.8357	+	5.67582i	1.23719	+	0.195951i	0.496640	+	0.867957i	$0.334567\pi$
$840$		0			0
$841$	23.4124	+	32.2244i	0.807324	+	1.11119i
$842$		0			0
$843$	3.69961	+	2.68793i	0.127421	+	0.0925771i
$844$		0			0
$845$	23.3909	−	16.9945i	0.804673	−	0.584629i
$846$		0			0
$847$	−11.9979	−	11.9979i	−0.412253	−	0.412253i
$848$		0			0
$849$	−26.4610	−	13.4825i	−0.908139	−	0.462720i
$850$		0			0
$851$	−3.51997	+	10.8333i	−0.120663	+	0.371362i
$852$		0			0
$853$	−15.2753	−	4.96325i	−0.523017	−	0.169939i	0.0355971	−	0.999366i	$-0.488667\pi$
$853$	−15.2753	−	4.96325i	−0.523017	−	0.169939i	−0.558614	+	0.829428i	$0.688667\pi$
$854$		0			0
$855$	0.377716	+	2.38480i	0.0129176	+	0.0815586i
$856$		0			0
$857$	−4.88329	−	15.0292i	−0.166810	−	0.513389i	0.832355	−	0.554243i	$-0.186992\pi$
$857$	−4.88329	−	15.0292i	−0.166810	−	0.513389i	−0.999165	+	0.0408542i	$0.986992\pi$
$858$		0			0
$859$	11.8857	−	16.3593i	0.405535	−	0.558171i	−0.556587	−	0.830789i	$-0.687890\pi$
$859$	11.8857	−	16.3593i	0.405535	−	0.558171i	0.962122	+	0.272618i	$0.0878895\pi$
$860$		0			0
$861$	8.29895	+	31.4724i	0.282828	+	1.07258i
$862$		0			0
$863$	6.30383	−	8.67648i	0.214585	−	0.295351i	−0.688132	−	0.725585i	$-0.741569\pi$
$863$	6.30383	−	8.67648i	0.214585	−	0.295351i	0.902717	+	0.430234i	$0.141569\pi$
$864$		0			0
$865$	−9.80418	−	30.1742i	−0.333352	−	1.02595i
$866$		0			0
$867$	−7.82937	−	49.4327i	−0.265899	−	1.67882i
$868$		0			0
$869$	−7.58832	−	2.46560i	−0.257416	−	0.0836396i
$870$		0			0
$871$	−4.00387	+	12.3226i	−0.135666	+	0.417537i
$872$		0			0
$873$	−7.46761	−	3.80494i	−0.252740	−	0.128778i
$874$		0			0
$875$	−8.21584	−	8.21584i	−0.277746	−	0.277746i
$876$		0			0
$877$	9.77788	−	7.10405i	0.330176	−	0.239887i	−0.410330	−	0.911937i	$-0.634586\pi$
$877$	9.77788	−	7.10405i	0.330176	−	0.239887i	0.740505	+	0.672051i	$0.234586\pi$
$878$		0			0
$879$	−2.76618	−	2.00975i	−0.0933008	−	0.0677870i
$880$		0			0
$881$	5.54253	+	7.62863i	0.186732	+	0.257015i	0.892112	−	0.451815i	$-0.149223\pi$
$881$	5.54253	+	7.62863i	0.186732	+	0.257015i	−0.705379	+	0.708830i	$0.749223\pi$
$882$		0			0
$883$	23.2136	+	3.67668i	0.781200	+	0.123730i	0.534282	−	0.845306i	$-0.320582\pi$
$883$	23.2136	+	3.67668i	0.781200	+	0.123730i	0.246918	+	0.969036i	$0.420582\pi$
$884$		0			0
$885$	62.2327	−	31.7091i	2.09193	−	1.06589i
$886$		0			0
$887$	22.0210	−	43.2187i	0.739394	−	1.45114i	−0.147448	−	0.989070i	$-0.547106\pi$
$887$	22.0210	−	43.2187i	0.739394	−	1.45114i	0.886842	−	0.462073i	$-0.152894\pi$
$888$		0			0
$889$	9.92789	−	1.57242i	0.332971	−	0.0527374i
$890$		0			0
$891$	5.74405	+	11.2733i	0.192433	+	0.377671i
$892$		0			0
$893$			0.815032i			0.0272740i
$894$		0			0
$895$	1.80293	−	11.3833i	0.0602654	−	0.380500i
$896$		0			0
$897$	−8.61534	+	2.79929i	−0.287658	+	0.0934657i
$898$		0			0
$899$	−7.08296	+	7.08296i	−0.236230	+	0.236230i
$900$		0			0
$901$	−13.2140			−0.440221
$902$		0			0
$903$	53.7758			1.78955
$904$		0			0
$905$	−8.88248	+	8.88248i	−0.295264	+	0.295264i
$906$		0			0
$907$	8.16520	−	2.65304i	0.271121	−	0.0880926i	−0.170301	−	0.985392i	$-0.554474\pi$
$907$	8.16520	−	2.65304i	0.271121	−	0.0880926i	0.441422	+	0.897299i	$0.354474\pi$
$908$		0			0
$909$	−5.74938	+	36.3002i	−0.190695	+	1.20400i
$910$		0			0
$911$		−	21.0427i		−	0.697176i	−0.937276	−	0.348588i	$-0.886661\pi$
$911$		−	21.0427i		−	0.697176i	0.937276	−	0.348588i	$-0.113339\pi$
$912$		0			0
$913$	2.04197	+	4.00760i	0.0675794	+	0.132632i
$914$		0			0
$915$	−22.2072	+	3.51727i	−0.734147	+	0.116277i
$916$		0			0
$917$	−0.531129	+	1.04240i	−0.0175394	+	0.0344231i
$918$		0			0
$919$	−42.6461	+	21.7293i	−1.40676	+	0.716782i	−0.982063	−	0.188552i	$-0.939621\pi$
$919$	−42.6461	+	21.7293i	−1.40676	+	0.716782i	−0.424700	+	0.905334i	$0.639621\pi$
$920$		0			0
$921$	92.2819	+	14.6160i	3.04079	+	0.481614i
$922$		0			0
$923$	3.84880	+	5.29742i	0.126685	+	0.174367i
$924$		0			0
$925$	−11.4556	−	8.32298i	−0.376658	−	0.273658i
$926$		0			0
$927$	−77.8234	+	56.5420i	−2.55606	+	1.85708i
$928$		0			0
$929$	−36.8866	−	36.8866i	−1.21021	−	1.21021i	−0.970957	−	0.239254i	$-0.923097\pi$
$929$	−36.8866	−	36.8866i	−1.21021	−	1.21021i	−0.239254	−	0.970957i	$-0.576903\pi$
$930$		0			0
$931$	0.503802	+	0.256700i	0.0165115	+	0.00841300i
$932$		0			0
$933$	−16.7966	+	51.6946i	−0.549896	+	1.69241i
$934$		0			0
$935$	1.88909	+	0.613801i	0.0617797	+	0.0200735i
$936$		0			0
$937$	2.38729	+	15.0727i	0.0779893	+	0.492405i	0.995505	+	0.0947061i	$0.0301911\pi$
$937$	2.38729	+	15.0727i	0.0779893	+	0.492405i	−0.917516	+	0.397699i	$0.869809\pi$
$938$		0			0
$939$	−1.57998	−	4.86267i	−0.0515606	−	0.158687i
$940$		0			0
$941$	32.5243	−	44.7658i	1.06026	−	1.45932i	0.180701	−	0.983538i	$-0.442163\pi$
$941$	32.5243	−	44.7658i	1.06026	−	1.45932i	0.879561	−	0.475787i	$-0.157837\pi$
$942$		0			0
$943$	−6.52804	−	10.1404i	−0.212582	−	0.330217i
$944$		0			0
$945$	−31.8329	+	43.8143i	−1.03553	+	1.42528i
$946$		0			0
$947$	0.485672	+	1.49474i	0.0157822	+	0.0485727i	0.958637	−	0.284630i	$-0.0918707\pi$
$947$	0.485672	+	1.49474i	0.0157822	+	0.0485727i	−0.942855	+	0.333203i	$0.891871\pi$
$948$		0			0
$949$	2.91156	+	18.3829i	0.0945133	+	0.596734i
$950$		0			0
$951$	48.8348	+	15.8674i	1.58358	+	0.514536i
$952$		0			0
$953$	13.1845	−	40.5778i	0.427089	−	1.31444i	−0.473891	−	0.880584i	$-0.657151\pi$
$953$	13.1845	−	40.5778i	0.427089	−	1.31444i	0.900980	−	0.433861i	$-0.142849\pi$
$954$		0			0
$955$	54.0021	+	27.5154i	1.74747	+	0.890379i
$956$		0			0
$957$	12.8115	+	12.8115i	0.414137	+	0.414137i
$958$		0			0
$959$	24.3495	−	17.6909i	0.786285	−	0.571270i
$960$		0			0
$961$	23.9002	+	17.3645i	0.770975	+	0.560146i
$962$		0			0
$963$	−38.8453	−	53.4660i	−1.25177	−	1.72292i
$964$		0			0
$965$	−39.0019	−	6.17730i	−1.25552	−	0.198854i
$966$		0			0
$967$	−3.68798	+	1.87912i	−0.118597	+	0.0604284i	−0.512283	−	0.858817i	$-0.671200\pi$
$967$	−3.68798	+	1.87912i	−0.118597	+	0.0604284i	0.393685	+	0.919245i	$0.371200\pi$
$968$		0			0
$969$	−0.194583	+	0.381891i	−0.00625091	+	0.0122681i
$970$		0			0
$971$	−15.8383	+	2.50854i	−0.508276	+	0.0805030i	−0.405305	−	0.914181i	$-0.632835\pi$
$971$	−15.8383	+	2.50854i	−0.508276	+	0.0805030i	−0.102971	+	0.994684i	$0.532835\pi$
$972$		0			0
$973$	−4.64475	−	9.11584i	−0.148904	−	0.292240i
$974$		0			0
$975$		−	11.2608i		−	0.360635i
$976$		0			0
$977$	6.69308	−	42.2584i	0.214131	−	1.35197i	−0.613056	−	0.790039i	$-0.710060\pi$
$977$	6.69308	−	42.2584i	0.214131	−	1.35197i	0.827187	−	0.561927i	$-0.189940\pi$
$978$		0			0
$979$	−1.90052	+	0.617515i	−0.0607408	+	0.0197359i
$980$		0			0
$981$	−11.5511	+	11.5511i	−0.368799	+	0.368799i
$982$		0			0
$983$	31.6046			1.00803			0.504015	−	0.863695i	$-0.331856\pi$
$983$	31.6046			1.00803			0.504015	+	0.863695i	$0.331856\pi$
$984$		0			0
$985$	−2.52132			−0.0803360
$986$		0			0
$987$	−22.7887	+	22.7887i	−0.725373	+	0.725373i
$988$		0			0
$989$	−18.9502	+	6.15728i	−0.602580	+	0.195790i
$990$		0			0
$991$	−4.28861	+	27.0772i	−0.136232	+	0.860137i	0.821024	+	0.570894i	$0.193403\pi$
$991$	−4.28861	+	27.0772i	−0.136232	+	0.860137i	−0.957256	+	0.289242i	$0.906597\pi$
$992$		0			0
$993$			79.9066i			2.53576i
$994$		0			0
$995$	0.507096	+	0.995231i	0.0160760	+	0.0315510i
$996$		0			0
$997$	24.5211	−	3.88375i	0.776590	−	0.123000i	0.244456	−	0.969660i	$-0.421391\pi$
$997$	24.5211	−	3.88375i	0.776590	−	0.123000i	0.532133	+	0.846661i	$0.321391\pi$
$998$		0			0
$999$	34.0257	−	66.7793i	1.07653	−	2.11280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.bs.d.33.1		24
4.3	odd	2		41.2.g.a.33.1	yes	24
12.11	even	2		369.2.u.a.361.3		24
41.5	even	20	inner	656.2.bs.d.497.1		24
164.87	odd	20		41.2.g.a.5.1	✓	24
164.95	even	40		1681.2.a.m.1.3		24
164.151	even	40		1681.2.a.m.1.4		24
492.251	even	20		369.2.u.a.46.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.5.1	✓	24	164.87	odd	20
41.2.g.a.33.1	yes	24	4.3	odd	2
369.2.u.a.46.3		24	492.251	even	20
369.2.u.a.361.3		24	12.11	even	2
656.2.bs.d.33.1		24	1.1	even	1	trivial
656.2.bs.d.497.1		24	41.5	even	20	inner
1681.2.a.m.1.3		24	164.95	even	40
1681.2.a.m.1.4		24	164.151	even	40

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:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.bs (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.22848 + 2.22848i) q^{3} +(-2.57687 + 0.837277i) q^{5} +(0.252316 - 1.59306i) q^{7} -6.93221i q^{9} +O(q^{10})\)	\(q+(-2.22848 + 2.22848i) q^{3} +(-2.57687 + 0.837277i) q^{5} +(0.252316 - 1.59306i) q^{7} -6.93221i q^{9} +(-0.314590 - 0.617417i) q^{11} +(-1.50733 + 0.238738i) q^{13} +(3.87665 - 7.60835i) q^{15} +(0.942631 - 0.480295i) q^{17} +(0.126968 + 0.0201098i) q^{19} +(2.98781 + 4.11237i) q^{21} +(-1.52374 - 1.10707i) q^{23} +(1.89416 - 1.37619i) q^{25} +(8.76282 + 8.76282i) q^{27} +(7.39222 + 3.76652i) q^{29} +(-0.373094 + 1.14827i) q^{31} +(2.07696 + 0.674844i) q^{33} +(0.683646 + 4.31637i) q^{35} +(-1.86889 - 5.75186i) q^{37} +(2.82703 - 3.89107i) q^{39} +(5.96866 + 2.31844i) q^{41} +(6.21829 - 8.55874i) q^{43} +(5.80417 + 17.8634i) q^{45} +(0.991818 + 6.26210i) q^{47} +(4.18322 + 1.35921i) q^{49} +(-1.03031 + 3.17095i) q^{51} +(-11.1289 - 5.67046i) q^{53} +(1.32761 + 1.32761i) q^{55} +(-0.327760 + 0.238131i) q^{57} +(6.61738 + 4.80781i) q^{59} +(-1.54768 - 2.13021i) q^{61} +(-11.0434 - 1.74911i) q^{63} +(3.68431 - 1.87725i) q^{65} +(3.85439 - 7.56467i) q^{67} +(5.86269 - 0.928560i) q^{69} +(-1.94789 - 3.82296i) q^{71} -12.1957i q^{73} +(-1.15429 + 7.28788i) q^{75} +(-1.06296 + 0.345376i) q^{77} +(8.14191 - 8.14191i) q^{79} -18.2589 q^{81} -6.49090 q^{83} +(-2.02690 + 2.02690i) q^{85} +(-24.8670 + 8.07977i) q^{87} +(0.451128 - 2.84831i) q^{89} +2.46150i q^{91} +(-1.72745 - 3.39031i) q^{93} +(-0.344018 + 0.0544871i) q^{95} +(0.548878 - 1.07723i) q^{97} +(-4.28006 + 2.18080i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7}+O(q^{10}) \) 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7	\( 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{17} - 16 q^{19} - 10 q^{21} - 12 q^{23} - 8 q^{25} + 6 q^{27} + 40 q^{29} + 12 q^{31} + 10 q^{33} + 36 q^{35} + 50 q^{39} - 4 q^{41} + 16 q^{45} + 12 q^{47} - 30 q^{49} + 24 q^{51} - 26 q^{53} - 20 q^{55} + 10 q^{57} - 6 q^{59} + 30 q^{61} - 92 q^{63} + 68 q^{65} + 22 q^{67} - 38 q^{69} - 4 q^{71} - 4 q^{75} - 20 q^{77} + 2 q^{79} + 28 q^{81} - 80 q^{83} - 56 q^{85} + 10 q^{87} - 72 q^{89} - 6 q^{93} + 40 q^{95} - 22 q^{97} - 14 q^{99}+O(q^{100}) \) 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^17 - 16 * q^19 - 10 * q^21 - 12 * q^23 - 8 * q^25 + 6 * q^27 + 40 * q^29 + 12 * q^31 + 10 * q^33 + 36 * q^35 + 50 * q^39 - 4 * q^41 + 16 * q^45 + 12 * q^47 - 30 * q^49 + 24 * q^51 - 26 * q^53 - 20 * q^55 + 10 * q^57 - 6 * q^59 + 30 * q^61 - 92 * q^63 + 68 * q^65 + 22 * q^67 - 38 * q^69 - 4 * q^71 - 4 * q^75 - 20 * q^77 + 2 * q^79 + 28 * q^81 - 80 * q^83 - 56 * q^85 + 10 * q^87 - 72 * q^89 - 6 * q^93 + 40 * q^95 - 22 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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