LMFDB - Embedded newform 1000.2.d.c.501.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(501,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1000.501");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.d (of order $2$, degree $1$, 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:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			501.10
Character	$\chi$	$=$	1000.501
Dual form			1000.2.d.c.501.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23486 + 0.689292i) q^{2} +2.52102i q^{3} +(1.04975 - 1.70236i) q^{4} +(-1.73772 - 3.11311i) q^{6} +0.987050 q^{7} +(-0.122873 + 2.82576i) q^{8} -3.35556 q^{9} +O(q^{10})$	\(q+(-1.23486 + 0.689292i) q^{2} +2.52102i q^{3} +(1.04975 - 1.70236i) q^{4} +(-1.73772 - 3.11311i) q^{6} +0.987050 q^{7} +(-0.122873 + 2.82576i) q^{8} -3.35556 q^{9} +2.58742i q^{11} +(4.29168 + 2.64645i) q^{12} +3.40597i q^{13} +(-1.21887 + 0.680366i) q^{14} +(-1.79604 - 3.57411i) q^{16} +6.42173 q^{17} +(4.14364 - 2.31296i) q^{18} -2.95990i q^{19} +2.48838i q^{21} +(-1.78349 - 3.19510i) q^{22} -3.90476 q^{23} +(-7.12380 - 0.309766i) q^{24} +(-2.34771 - 4.20590i) q^{26} -0.896380i q^{27} +(1.03616 - 1.68031i) q^{28} +5.52423i q^{29} -1.53121 q^{31} +(4.68146 + 3.17552i) q^{32} -6.52296 q^{33} +(-7.92993 + 4.42645i) q^{34} +(-3.52251 + 5.71237i) q^{36} +8.80977i q^{37} +(2.04024 + 3.65506i) q^{38} -8.58654 q^{39} +10.8421 q^{41} +(-1.71522 - 3.07279i) q^{42} -1.76479i q^{43} +(4.40472 + 2.71615i) q^{44} +(4.82183 - 2.69152i) q^{46} -13.3842 q^{47} +(9.01041 - 4.52787i) q^{48} -6.02573 q^{49} +16.1893i q^{51} +(5.79819 + 3.57543i) q^{52} +4.36357i q^{53} +(0.617868 + 1.10690i) q^{54} +(-0.121282 + 2.78916i) q^{56} +7.46198 q^{57} +(-3.80781 - 6.82164i) q^{58} +7.09201i q^{59} -6.56276i q^{61} +(1.89083 - 1.05545i) q^{62} -3.31211 q^{63} +(-7.96980 - 0.694419i) q^{64} +(8.05493 - 4.49622i) q^{66} -13.1309i q^{67} +(6.74123 - 10.9321i) q^{68} -9.84401i q^{69} +5.68370 q^{71} +(0.412308 - 9.48200i) q^{72} -12.9136 q^{73} +(-6.07251 - 10.8788i) q^{74} +(-5.03881 - 3.10716i) q^{76} +2.55392i q^{77} +(10.6032 - 5.91864i) q^{78} -0.0125371 q^{79} -7.80689 q^{81} +(-13.3884 + 7.47336i) q^{82} -1.90681i q^{83} +(4.23611 + 2.61218i) q^{84} +(1.21646 + 2.17927i) q^{86} -13.9267 q^{87} +(-7.31143 - 0.317925i) q^{88} +4.82356 q^{89} +3.36187i q^{91} +(-4.09903 + 6.64731i) q^{92} -3.86023i q^{93} +(16.5277 - 9.22566i) q^{94} +(-8.00556 + 11.8021i) q^{96} +7.44702 q^{97} +(7.44093 - 4.15349i) q^{98} -8.68226i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9}+O(q^{10}) $ 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9	$ 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9} + 12 q^{14} + 18 q^{16} - 6 q^{24} + 20 q^{26} + 48 q^{31} - 6 q^{34} - 40 q^{36} + 8 q^{39} + 44 q^{41} + 8 q^{44} - 30 q^{46} + 12 q^{49} - 2 q^{54} + 50 q^{56} + 72 q^{64} + 42 q^{66} + 96 q^{71} + 6 q^{74} - 2 q^{76} + 96 q^{79} - 56 q^{81} + 116 q^{84} + 46 q^{86} - 44 q^{89} - 14 q^{94} + 12 q^{96}+O(q^{100}) $ 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9 + 12 * q^14 + 18 * q^16 - 6 * q^24 + 20 * q^26 + 48 * q^31 - 6 * q^34 - 40 * q^36 + 8 * q^39 + 44 * q^41 + 8 * q^44 - 30 * q^46 + 12 * q^49 - 2 * q^54 + 50 * q^56 + 72 * q^64 + 42 * q^66 + 96 * q^71 + 6 * q^74 - 2 * q^76 + 96 * q^79 - 56 * q^81 + 116 * q^84 + 46 * q^86 - 44 * q^89 - 14 * q^94 + 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−1.23486	+	0.689292i	−0.873177	+	0.487403i
$2$	−1.23486	+	0.689292i	−0.873177	+	0.487403i
$3$			2.52102i			1.45551i	0.685835	+	0.727757i	$0.259437\pi$
$3$			2.52102i			1.45551i	−0.685835	+	0.727757i	$0.740563\pi$
$4$	1.04975	−	1.70236i	0.524876	−	0.851179i
$5$		0			0
$5$		0			0
$6$	−1.73772	−	3.11311i	−0.709422	−	1.27092i
$7$	0.987050			0.373070			0.186535	−	0.982448i	$-0.440274\pi$
$7$	0.987050			0.373070			0.186535	+	0.982448i	$0.440274\pi$
$8$	−0.122873	+	2.82576i	−0.0434422	+	0.999056i
$9$	−3.35556			−1.11852
$10$		0			0
$11$			2.58742i			0.780138i	0.920786	+	0.390069i	$0.127549\pi$
$11$			2.58742i			0.780138i	−0.920786	+	0.390069i	$0.872451\pi$
$12$	4.29168	+	2.64645i	1.23890	+	0.763964i
$13$			3.40597i			0.944647i	0.881425	+	0.472324i	$0.156585\pi$
$13$			3.40597i			0.944647i	−0.881425	+	0.472324i	$0.843415\pi$
$14$	−1.21887	+	0.680366i	−0.325756	+	0.181835i
$15$		0			0
$16$	−1.79604	−	3.57411i	−0.449011	−	0.893526i
$17$	6.42173			1.55750			0.778750	−	0.627335i	$-0.215854\pi$
$17$	6.42173			1.55750			0.778750	+	0.627335i	$0.215854\pi$
$18$	4.14364	−	2.31296i	0.976666	−	0.545171i
$19$		−	2.95990i		−	0.679048i	−0.940597	−	0.339524i	$-0.889734\pi$
$19$		−	2.95990i		−	0.679048i	0.940597	−	0.339524i	$-0.110266\pi$
$20$		0			0
$21$			2.48838i			0.543008i
$22$	−1.78349	−	3.19510i	−0.380242	−	0.681198i
$23$	−3.90476			−0.814200			−0.407100	−	0.913384i	$-0.633460\pi$
$23$	−3.90476			−0.814200			−0.407100	+	0.913384i	$0.633460\pi$
$24$	−7.12380	−	0.309766i	−1.45414	−	0.0632307i
$25$		0			0
$26$	−2.34771	−	4.20590i	−0.460424	−	0.824844i
$27$		−	0.896380i		−	0.172508i
$28$	1.03616	−	1.68031i	0.195815	−	0.317549i
$29$			5.52423i			1.02582i	0.858441	+	0.512912i	$0.171433\pi$
$29$			5.52423i			1.02582i	−0.858441	+	0.512912i	$0.828567\pi$
$30$		0			0
$31$	−1.53121			−0.275014			−0.137507	−	0.990501i	$-0.543909\pi$
$31$	−1.53121			−0.275014			−0.137507	+	0.990501i	$0.543909\pi$
$32$	4.68146	+	3.17552i	0.827573	+	0.561357i
$33$	−6.52296			−1.13550
$34$	−7.92993	+	4.42645i	−1.35997	+	0.759130i
$35$		0			0
$36$	−3.52251	+	5.71237i	−0.587085	+	0.952061i
$37$			8.80977i			1.44832i	0.689634	+	0.724158i	$0.257772\pi$
$37$			8.80977i			1.44832i	−0.689634	+	0.724158i	$0.742228\pi$
$38$	2.04024	+	3.65506i	0.330970	+	0.592929i
$39$	−8.58654			−1.37495
$40$		0			0
$41$	10.8421			1.69325			0.846624	−	0.532191i	$-0.178631\pi$
$41$	10.8421			1.69325			0.846624	+	0.532191i	$0.178631\pi$
$42$	−1.71522	−	3.07279i	−0.264664	−	0.474142i
$43$		−	1.76479i		−	0.269128i	−0.990905	−	0.134564i	$-0.957037\pi$
$43$		−	1.76479i		−	0.269128i	0.990905	−	0.134564i	$-0.0429634\pi$
$44$	4.40472	+	2.71615i	0.664036	+	0.409475i
$45$		0			0
$46$	4.82183	−	2.69152i	0.710940	−	0.396844i
$47$	−13.3842			−1.95229			−0.976146	−	0.217113i	$-0.930336\pi$
$47$	−13.3842			−1.95229			−0.976146	+	0.217113i	$0.930336\pi$
$48$	9.01041	−	4.52787i	1.30054	−	0.653541i
$49$	−6.02573			−0.860819
$50$		0			0
$51$			16.1893i			2.26696i
$52$	5.79819	+	3.57543i	0.804064	+	0.495823i
$53$			4.36357i			0.599383i	0.954036	+	0.299691i	$0.0968837\pi$
$53$			4.36357i			0.599383i	−0.954036	+	0.299691i	$0.903116\pi$
$54$	0.617868	+	1.10690i	0.0840812	+	0.150630i
$55$		0			0
$56$	−0.121282	+	2.78916i	−0.0162070	+	0.372718i
$57$	7.46198			0.988364
$58$	−3.80781	−	6.82164i	−0.499990	−	0.895725i
$59$			7.09201i			0.923301i	0.887062	+	0.461651i	$0.152743\pi$
$59$			7.09201i			0.923301i	−0.887062	+	0.461651i	$0.847257\pi$
$60$		0			0
$61$		−	6.56276i		−	0.840275i	−0.907460	−	0.420138i	$-0.861982\pi$
$61$		−	6.56276i		−	0.840275i	0.907460	−	0.420138i	$-0.138018\pi$
$62$	1.89083	−	1.05545i	0.240136	−	0.134043i
$63$	−3.31211			−0.417286
$64$	−7.96980	−	0.694419i	−0.996226	−	0.0868023i
$65$		0			0
$66$	8.05493	−	4.49622i	0.991493	−	0.553447i
$67$		−	13.1309i		−	1.60419i	−0.597195	−	0.802096i	$-0.703718\pi$
$67$		−	13.1309i		−	1.60419i	0.597195	−	0.802096i	$-0.296282\pi$
$68$	6.74123	−	10.9321i	0.817494	−	1.32571i
$69$		−	9.84401i		−	1.18508i
$70$		0			0
$71$	5.68370			0.674531			0.337265	−	0.941410i	$-0.390498\pi$
$71$	5.68370			0.674531			0.337265	+	0.941410i	$0.390498\pi$
$72$	0.412308	−	9.48200i	0.0485910	−	1.11746i
$73$	−12.9136			−1.51143			−0.755713	−	0.654903i	$-0.772710\pi$
$73$	−12.9136			−1.51143			−0.755713	+	0.654903i	$0.772710\pi$
$74$	−6.07251	−	10.8788i	−0.705914	−	1.26464i
$75$		0			0
$76$	−5.03881	−	3.10716i	−0.577991	−	0.356416i
$77$			2.55392i			0.291046i
$78$	10.6032	−	5.91864i	1.20057	−	0.670154i
$79$	−0.0125371			−0.00141054			−0.000705269	−	1.00000i	$-0.500224\pi$
$79$	−0.0125371			−0.00141054			−0.000705269		1.00000i	$0.500224\pi$
$80$		0			0
$81$	−7.80689			−0.867432
$82$	−13.3884	+	7.47336i	−1.47851	+	0.825295i
$83$		−	1.90681i		−	0.209300i	−0.994509	−	0.104650i	$-0.966628\pi$
$83$		−	1.90681i		−	0.209300i	0.994509	−	0.104650i	$-0.0333722\pi$
$84$	4.23611	+	2.61218i	0.462197	+	0.285012i
$85$		0			0
$86$	1.21646	+	2.17927i	0.131174	+	0.234997i
$87$	−13.9267			−1.49310
$88$	−7.31143	−	0.317925i	−0.779401	−	0.0338909i
$89$	4.82356			0.511296			0.255648	−	0.966770i	$-0.417711\pi$
$89$	4.82356			0.511296			0.255648	+	0.966770i	$0.417711\pi$
$90$		0			0
$91$			3.36187i			0.352419i
$92$	−4.09903	+	6.64731i	−0.427354	+	0.693029i
$93$		−	3.86023i		−	0.400287i
$94$	16.5277	−	9.22566i	1.70470	−	0.951554i
$95$		0			0
$96$	−8.00556	+	11.8021i	−0.817064	+	1.20454i
$97$	7.44702			0.756131			0.378065	−	0.925779i	$-0.376589\pi$
$97$	7.44702			0.756131			0.378065	+	0.925779i	$0.376589\pi$
$98$	7.44093	−	4.15349i	0.751647	−	0.419566i
$99$		−	8.68226i		−	0.872600i
$100$		0			0
$101$		−	16.8836i		−	1.67998i	−0.542603	−	0.839989i	$-0.682561\pi$
$101$		−	16.8836i		−	1.67998i	0.542603	−	0.839989i	$-0.317439\pi$
$102$	−11.1592	−	19.9916i	−1.10492	−	1.97946i
$103$	−14.7696			−1.45529			−0.727645	−	0.685954i	$-0.759385\pi$
$103$	−14.7696			−1.45529			−0.727645	+	0.685954i	$0.759385\pi$
$104$	−9.62446	−	0.418502i	−0.943756	−	0.0410375i
$105$		0			0
$106$	−3.00778	−	5.38839i	−0.292141	−	0.523367i
$107$			8.58598i			0.830038i	0.909813	+	0.415019i	$0.136225\pi$
$107$			8.58598i			0.830038i	−0.909813	+	0.415019i	$0.863775\pi$
$108$	−1.52596	−	0.940977i	−0.146836	−	0.0905455i
$109$		−	7.49133i		−	0.717539i	−0.933426	−	0.358769i	$-0.883196\pi$
$109$		−	7.49133i		−	0.717539i	0.933426	−	0.358769i	$-0.116804\pi$
$110$		0			0
$111$	−22.2096			−2.10805
$112$	−1.77278	−	3.52782i	−0.167512	−	0.333348i
$113$	14.3254			1.34762			0.673810	−	0.738905i	$-0.264657\pi$
$113$	14.3254			1.34762			0.673810	+	0.738905i	$0.264657\pi$
$114$	−9.21450	+	5.14349i	−0.863017	+	0.481732i
$115$		0			0
$116$	9.40421	+	5.79907i	0.873159	+	0.538430i
$117$		−	11.4290i		−	1.05661i
$118$	−4.88847	−	8.75763i	−0.450020	−	0.806205i
$119$	6.33857			0.581056
$120$		0			0
$121$	4.30524			0.391385
$122$	4.52366	+	8.10408i	0.409553	+	0.733709i
$123$			27.3331i			2.46455i
$124$	−1.60740	+	2.60667i	−0.144348	+	0.234086i
$125$		0			0
$126$	4.08998	−	2.28301i	0.364365	−	0.203387i
$127$	7.49354			0.664944			0.332472	−	0.943113i	$-0.392117\pi$
$127$	7.49354			0.664944			0.332472	+	0.943113i	$0.392117\pi$
$128$	10.3202	−	4.63602i	0.912189	−	0.409770i
$129$	4.44908			0.391720
$130$		0			0
$131$		−	9.24629i		−	0.807852i	−0.914792	−	0.403926i	$-0.867645\pi$
$131$		−	9.24629i		−	0.807852i	0.914792	−	0.403926i	$-0.132355\pi$
$132$	−6.84749	+	11.1044i	−0.595997	+	0.966514i
$133$		−	2.92157i		−	0.253332i
$134$	9.05101	+	16.2148i	0.781888	+	1.40074i
$135$		0			0
$136$	−0.789058	+	18.1463i	−0.0676611	+	1.55603i
$137$	−11.4199			−0.975669			−0.487835	−	0.872936i	$-0.662213\pi$
$137$	−11.4199			−0.975669			−0.487835	+	0.872936i	$0.662213\pi$
$138$	6.78540	+	12.1560i	0.577611	+	1.03478i
$139$			20.7292i			1.75823i	0.476614	+	0.879113i	$0.341864\pi$
$139$			20.7292i			1.75823i	−0.476614	+	0.879113i	$0.658136\pi$
$140$		0			0
$141$		−	33.7420i		−	2.84159i
$142$	−7.01856	+	3.91773i	−0.588985	+	0.328769i
$143$	−8.81270			−0.736955
$144$	6.02673	+	11.9931i	0.502228	+	0.999428i
$145$		0			0
$146$	15.9465	−	8.90127i	1.31974	−	0.736674i
$147$		−	15.1910i		−	1.25293i
$148$	14.9974	+	9.24807i	1.23278	+	0.760187i
$149$			16.0809i			1.31740i	0.752405	+	0.658701i	$0.228894\pi$
$149$			16.0809i			1.31740i	−0.752405	+	0.658701i	$0.771106\pi$
$150$		0			0
$151$	−11.3444			−0.923193			−0.461597	−	0.887090i	$-0.652723\pi$
$151$	−11.3444			−0.923193			−0.461597	+	0.887090i	$0.652723\pi$
$152$	8.36396	+	0.363692i	0.678407	+	0.0294993i
$153$	−21.5485			−1.74209
$154$	−1.76039	−	3.15372i	−0.141857	−	0.254134i
$155$		0			0
$156$	−9.01374	+	14.6174i	−0.721677	+	1.17033i
$157$			3.42796i			0.273581i	0.990600	+	0.136790i	$0.0436787\pi$
$157$			3.42796i			0.273581i	−0.990600	+	0.136790i	$0.956321\pi$
$158$	0.0154816	−	0.00864175i	0.00123165	−	0.000687501i
$159$	−11.0007			−0.872410
$160$		0			0
$161$	−3.85420			−0.303753
$162$	9.64041	−	5.38123i	0.757422	−	0.422789i
$163$		−	5.39025i		−	0.422197i	−0.977465	−	0.211098i	$-0.932296\pi$
$163$		−	5.39025i		−	0.422197i	0.977465	−	0.211098i	$-0.0677040\pi$
$164$	11.3815	−	18.4571i	0.888745	−	1.44126i
$165$		0			0
$166$	1.31435	+	2.35465i	0.102014	+	0.182756i
$167$	10.1776			0.787565			0.393783	−	0.919204i	$-0.371166\pi$
$167$	10.1776			0.787565			0.393783	+	0.919204i	$0.371166\pi$
$168$	−7.03155	−	0.305754i	−0.542496	−	0.0235895i
$169$	1.39934			0.107641
$170$		0			0
$171$			9.93213i			0.759529i
$172$	−3.00431	−	1.85259i	−0.229076	−	0.141259i
$173$			16.4630i			1.25166i	0.779960	+	0.625829i	$0.215239\pi$
$173$			16.4630i			1.25166i	−0.779960	+	0.625829i	$0.784761\pi$
$174$	17.1975	−	9.59957i	1.30374	−	0.727742i
$175$		0			0
$176$	9.24773	−	4.64712i	0.697074	−	0.350290i
$177$	−17.8791			−1.34388
$178$	−5.95642	+	3.32484i	−0.446452	+	0.249208i
$179$		−	5.76554i		−	0.430937i	−0.976511	−	0.215468i	$-0.930872\pi$
$179$		−	5.76554i		−	0.430937i	0.976511	−	0.215468i	$-0.0691278\pi$
$180$		0			0
$181$		−	7.40362i		−	0.550307i	−0.961400	−	0.275153i	$-0.911271\pi$
$181$		−	7.40362i		−	0.550307i	0.961400	−	0.275153i	$-0.0887286\pi$
$182$	−2.31731	−	4.15143i	−0.171770	−	0.307724i
$183$	16.5449			1.22303
$184$	0.479790	−	11.0339i	0.0353706	−	0.813431i
$185$		0			0
$186$	2.66083	+	4.76684i	0.195101	+	0.349521i
$187$			16.6157i			1.21506i
$188$	−14.0501	+	22.7848i	−1.02471	+	1.66175i
$189$		−	0.884772i		−	0.0643577i
$190$		0			0
$191$	−9.94899			−0.719884			−0.359942	−	0.932975i	$-0.617203\pi$
$191$	−9.94899			−0.719884			−0.359942	+	0.932975i	$0.617203\pi$
$192$	1.75065	−	20.0921i	0.126342	−	1.45002i
$193$	1.49517			0.107625			0.0538124	−	0.998551i	$-0.482863\pi$
$193$	1.49517			0.107625			0.0538124	+	0.998551i	$0.482863\pi$
$194$	−9.19602	+	5.13318i	−0.660236	+	0.368541i
$195$		0			0
$196$	−6.32552	+	10.2580i	−0.451823	+	0.732711i
$197$		−	0.630014i		−	0.0448867i	−0.999748	−	0.0224433i	$-0.992855\pi$
$197$		−	0.630014i		−	0.0448867i	0.999748	−	0.0224433i	$-0.00714454\pi$
$198$	5.98462	+	10.7214i	0.425308	+	0.761934i
$199$	22.1737			1.57185			0.785927	−	0.618319i	$-0.212186\pi$
$199$	22.1737			1.57185			0.785927	+	0.618319i	$0.212186\pi$
$200$		0			0
$201$	33.1032			2.33492
$202$	11.6377	+	20.8488i	0.818827	+	1.46692i
$203$			5.45269i			0.382704i
$204$	27.5601	+	16.9948i	1.92959	+	1.18987i
$205$		0			0
$206$	18.2383	−	10.1806i	1.27073	−	0.709313i
$207$	13.1027			0.910699
$208$	12.1733	−	6.11727i	0.844067	−	0.424157i
$209$	7.65852			0.529751
$210$		0			0
$211$			4.10000i			0.282256i	0.989991	+	0.141128i	$0.0450728\pi$
$211$			4.10000i			0.282256i	−0.989991	+	0.141128i	$0.954927\pi$
$212$	7.42836	+	4.58067i	0.510182	+	0.314601i
$213$			14.3287i			0.981789i
$214$	−5.91825	−	10.6025i	−0.404563	−	0.724770i
$215$		0			0
$216$	2.53295	+	0.110141i	0.172346	+	0.00749414i
$217$	−1.51138			−0.102599
$218$	5.16371	+	9.25073i	0.349731	+	0.626538i
$219$		−	32.5556i		−	2.19990i
$220$		0			0
$221$			21.8723i			1.47129i
$222$	27.4258	−	15.3089i	1.84070	−	1.02747i
$223$	−6.67042			−0.446684			−0.223342	−	0.974740i	$-0.571697\pi$
$223$	−6.67042			−0.446684			−0.223342	+	0.974740i	$0.571697\pi$
$224$	4.62084	+	3.13439i	0.308743	+	0.209425i
$225$		0			0
$226$	−17.6898	+	9.87438i	−1.17671	+	0.656834i
$227$			19.0966i			1.26749i	0.773544	+	0.633743i	$0.218482\pi$
$227$			19.0966i			1.26749i	−0.773544	+	0.633743i	$0.781518\pi$
$228$	7.83323	−	12.7030i	0.518768	−	0.841274i
$229$			0.468986i			0.0309914i	0.999880	+	0.0154957i	$0.00493264\pi$
$229$			0.468986i			0.0309914i	−0.999880	+	0.0154957i	$0.995067\pi$
$230$		0			0
$231$	−6.43848			−0.423621
$232$	−15.6101	−	0.678778i	−1.02485	−	0.0445640i
$233$	13.5809			0.889711			0.444856	−	0.895602i	$-0.353255\pi$
$233$	13.5809			0.889711			0.444856	+	0.895602i	$0.353255\pi$
$234$	7.87789	+	14.1131i	0.514994	+	0.922605i
$235$		0			0
$236$	12.0731	+	7.44485i	0.785894	+	0.484619i
$237$		−	0.0316064i		−	0.00205306i
$238$	−7.82724	+	4.36913i	−0.507365	+	0.283209i
$239$	26.5090			1.71473			0.857363	−	0.514712i	$-0.172101\pi$
$239$	26.5090			1.71473			0.857363	+	0.514712i	$0.172101\pi$
$240$		0			0
$241$	−16.9199			−1.08991			−0.544953	−	0.838466i	$-0.683453\pi$
$241$	−16.9199			−1.08991			−0.544953	+	0.838466i	$0.683453\pi$
$242$	−5.31636	+	2.96757i	−0.341749	+	0.190763i
$243$		−	22.3705i		−	1.43507i
$244$	−11.1722	−	6.88927i	−0.715225	−	0.441040i
$245$		0			0
$246$	−18.8405	−	33.7526i	−1.20123	−	2.15199i
$247$	10.0814			0.641461
$248$	0.188145	−	4.32684i	0.0119472	−	0.274755i
$249$	4.80712			0.304639
$250$		0			0
$251$			29.8442i			1.88375i	0.335963	+	0.941875i	$0.390938\pi$
$251$			29.8442i			1.88375i	−0.335963	+	0.941875i	$0.609062\pi$
$252$	−3.47689	+	5.63839i	−0.219023	+	0.355185i
$253$		−	10.1033i		−	0.635188i
$254$	−9.25346	+	5.16524i	−0.580614	+	0.324096i
$255$		0			0
$256$	−9.54847	+	12.8385i	−0.596779	+	0.802406i
$257$	−3.16940			−0.197702			−0.0988508	−	0.995102i	$-0.531517\pi$
$257$	−3.16940			−0.197702			−0.0988508	+	0.995102i	$0.531517\pi$
$258$	−5.49399	+	3.06672i	−0.342041	+	0.190926i
$259$			8.69568i			0.540323i
$260$		0			0
$261$		−	18.5369i		−	1.14740i
$262$	6.37340	+	11.4179i	0.393750	+	0.705398i
$263$	1.43272			0.0883452			0.0441726	−	0.999024i	$-0.485935\pi$
$263$	1.43272			0.0883452			0.0441726	+	0.999024i	$0.485935\pi$
$264$	0.801495	−	18.4323i	0.0493286	−	1.13443i
$265$		0			0
$266$	2.01382	+	3.60773i	0.123475	+	0.221204i
$267$			12.1603i			0.744199i
$268$	−22.3534	−	13.7842i	−1.36545	−	0.842002i
$269$			13.8639i			0.845295i	0.906294	+	0.422648i	$0.138899\pi$
$269$			13.8639i			0.845295i	−0.906294	+	0.422648i	$0.861101\pi$
$270$		0			0
$271$	13.5926			0.825689			0.412845	−	0.910802i	$-0.364535\pi$
$271$	13.5926			0.825689			0.412845	+	0.910802i	$0.364535\pi$
$272$	−11.5337	−	22.9520i	−0.699334	−	1.39167i
$273$	−8.47535			−0.512951
$274$	14.1020	−	7.87166i	0.851932	−	0.475544i
$275$		0			0
$276$	−16.7580	−	10.3338i	−1.00871	−	0.622019i
$277$		−	15.3660i		−	0.923252i	−0.887075	−	0.461626i	$-0.847266\pi$
$277$		−	15.3660i		−	0.923252i	0.887075	−	0.461626i	$-0.152734\pi$
$278$	−14.2885	−	25.5976i	−0.856965	−	1.53524i
$279$	5.13809			0.307609
$280$		0			0
$281$	29.9045			1.78395			0.891976	−	0.452082i	$-0.149319\pi$
$281$	29.9045			1.78395			0.891976	+	0.452082i	$0.149319\pi$
$282$	23.2581	+	41.6666i	1.38500	+	2.48121i
$283$		−	8.39203i		−	0.498855i	−0.968394	−	0.249427i	$-0.919758\pi$
$283$		−	8.39203i		−	0.498855i	0.968394	−	0.249427i	$-0.0802424\pi$
$284$	5.96647	−	9.67568i	0.354045	−	0.574146i
$285$		0			0
$286$	10.8824	−	6.07453i	0.643492	−	0.359194i
$287$	10.7017			0.631700
$288$	−15.7089	−	10.6556i	−0.925658	−	0.627890i
$289$	24.2387			1.42580
$290$		0			0
$291$			18.7741i			1.10056i
$292$	−13.5561	+	21.9836i	−0.793311	+	1.28649i
$293$		−	17.3090i		−	1.01120i	−0.862767	−	0.505602i	$-0.831271\pi$
$293$		−	17.3090i		−	1.01120i	0.862767	−	0.505602i	$-0.168729\pi$
$294$	10.4711	+	18.7588i	0.610684	+	1.09403i
$295$		0			0
$296$	−24.8943	−	1.08248i	−1.44695	−	0.0629180i
$297$	2.31931			0.134580
$298$	−11.0845	−	19.8577i	−0.642106	−	1.15033i
$299$		−	13.2995i		−	0.769132i
$300$		0			0
$301$		−	1.74194i		−	0.100404i
$302$	14.0087	−	7.81960i	0.806111	−	0.449967i
$303$	42.5639			2.44523
$304$	−10.5790	+	5.31611i	−0.606747	+	0.304900i
$305$		0			0
$306$	26.6094	−	14.8532i	1.52116	−	0.849103i
$307$		−	6.86621i		−	0.391875i	−0.980616	−	0.195938i	$-0.937225\pi$
$307$		−	6.86621i		−	0.391875i	0.980616	−	0.195938i	$-0.0627750\pi$
$308$	4.34768	+	2.68098i	0.247732	+	0.152763i
$309$		−	37.2345i		−	2.11819i
$310$		0			0
$311$	16.2362			0.920669			0.460335	−	0.887745i	$-0.347729\pi$
$311$	16.2362			0.920669			0.460335	+	0.887745i	$0.347729\pi$
$312$	1.05505	−	24.2635i	0.0597307	−	1.37365i
$313$	23.2770			1.31570			0.657848	−	0.753151i	$-0.271467\pi$
$313$	23.2770			1.31570			0.657848	+	0.753151i	$0.271467\pi$
$314$	−2.36286	−	4.23304i	−0.133344	−	0.238884i
$315$		0			0
$316$	−0.0131609	+	0.0213427i	−0.000740357	+	0.00120062i
$317$		−	10.9755i		−	0.616444i	−0.951314	−	0.308222i	$-0.900266\pi$
$317$		−	10.9755i		−	0.616444i	0.951314	−	0.308222i	$-0.0997340\pi$
$318$	13.5843	−	7.58268i	0.761768	−	0.425215i
$319$	−14.2935			−0.800283
$320$		0			0
$321$	−21.6455			−1.20813
$322$	4.75939	−	2.65667i	0.265230	−	0.148050i
$323$		−	19.0077i		−	1.05762i
$324$	−8.19530	+	13.2901i	−0.455294	+	0.738340i
$325$		0			0
$326$	3.71546	+	6.65619i	0.205780	+	0.368652i
$327$	18.8858			1.04439
$328$	−1.33220	+	30.6371i	−0.0735584	+	1.69165i
$329$	−13.2109			−0.728341
$330$		0			0
$331$			8.51210i			0.467867i	0.972253	+	0.233934i	$0.0751599\pi$
$331$			8.51210i			0.467867i	−0.972253	+	0.233934i	$0.924840\pi$
$332$	−3.24608	−	2.00168i	−0.178152	−	0.109857i
$333$		−	29.5617i		−	1.61997i
$334$	−12.5679	+	7.01533i	−0.687684	+	0.383862i
$335$		0			0
$336$	8.89372	−	4.46923i	0.485192	−	0.243816i
$337$	7.85182			0.427716			0.213858	−	0.976865i	$-0.431397\pi$
$337$	7.85182			0.427716			0.213858	+	0.976865i	$0.431397\pi$
$338$	−1.72798	+	0.964552i	−0.0939899	+	0.0524647i
$339$			36.1147i			1.96148i
$340$		0			0
$341$		−	3.96190i		−	0.214549i
$342$	−6.84615	−	12.2648i	−0.370197	−	0.663203i
$343$	−12.8570			−0.694215
$344$	4.98687	+	0.216845i	0.268874	+	0.0116915i
$345$		0			0
$346$	−11.3478	−	20.3295i	−0.610063	−	1.09292i
$347$		−	8.69959i		−	0.467019i	−0.972355	−	0.233509i	$-0.924979\pi$
$347$		−	8.69959i		−	0.467019i	0.972355	−	0.233509i	$-0.0750209\pi$
$348$	−14.6196	+	23.7082i	−0.783692	+	1.27089i
$349$			28.3837i			1.51934i	0.650307	+	0.759671i	$0.274640\pi$
$349$			28.3837i			1.51934i	−0.650307	+	0.759671i	$0.725360\pi$
$350$		0			0
$351$	3.05305			0.162960
$352$	−8.21641	+	12.1129i	−0.437936	+	0.645621i
$353$	−0.481597			−0.0256328			−0.0128164	−	0.999918i	$-0.504080\pi$
$353$	−0.481597			−0.0256328			−0.0128164	+	0.999918i	$0.504080\pi$
$354$	22.0782	−	12.3239i	1.17344	−	0.655010i
$355$		0			0
$356$	5.06354	−	8.21143i	0.268367	−	0.435205i
$357$			15.9797i			0.845735i
$358$	3.97414	+	7.11963i	0.210040	+	0.376284i
$359$	−25.7634			−1.35974			−0.679871	−	0.733332i	$-0.737964\pi$
$359$	−25.7634			−1.35974			−0.679871	+	0.733332i	$0.737964\pi$
$360$		0			0
$361$	10.2390			0.538894
$362$	5.10326	+	9.14242i	0.268221	+	0.480515i
$363$			10.8536i			0.569667i
$364$	5.72310	+	3.52913i	0.299972	+	0.184976i
$365$		0			0
$366$	−20.4306	+	11.4043i	−1.06792	+	0.596110i
$367$	33.5522			1.75141			0.875705	−	0.482846i	$-0.160397\pi$
$367$	33.5522			1.75141			0.875705	+	0.482846i	$0.160397\pi$
$368$	7.01312	+	13.9560i	0.365584	+	0.727509i
$369$	−36.3813			−1.89393
$370$		0			0
$371$			4.30706i			0.223611i
$372$	−6.57149	−	4.05228i	−0.340716	−	0.210101i
$373$		−	1.98369i		−	0.102712i	−0.998680	−	0.0513558i	$-0.983646\pi$
$373$		−	1.98369i		−	0.102712i	0.998680	−	0.0513558i	$-0.0163542\pi$
$374$	−11.4531	−	20.5181i	−0.592226	−	1.06097i
$375$		0			0
$376$	1.64456	−	37.8206i	0.0848118	−	1.95045i
$377$	−18.8154			−0.969041
$378$	0.609866	+	1.09257i	0.0313681	+	0.0561956i
$379$			7.87441i			0.404481i	0.979336	+	0.202241i	$0.0648223\pi$
$379$			7.87441i			0.404481i	−0.979336	+	0.202241i	$0.935178\pi$
$380$		0			0
$381$			18.8914i			0.967836i
$382$	12.2856	−	6.85776i	0.628586	−	0.350874i
$383$	−18.3989			−0.940140			−0.470070	−	0.882629i	$-0.655771\pi$
$383$	−18.3989			−0.940140			−0.470070	+	0.882629i	$0.655771\pi$
$384$	11.6875	+	26.0176i	0.596426	+	1.32770i
$385$		0			0
$386$	−1.84633	+	1.03061i	−0.0939756	+	0.0524567i
$387$			5.92187i			0.301025i
$388$	7.81753	−	12.6775i	0.396875	−	0.643602i
$389$			6.68208i			0.338795i	0.985548	+	0.169397i	$0.0541821\pi$
$389$			6.68208i			0.338795i	−0.985548	+	0.169397i	$0.945818\pi$
$390$		0			0
$391$	−25.0754			−1.26812
$392$	0.740400	−	17.0273i	0.0373958	−	0.860006i
$393$	23.3101			1.17584
$394$	0.434264	+	0.777979i	0.0218779	+	0.0391940i
$395$		0			0
$396$	−14.7803	−	9.11422i	−0.742739	−	0.458007i
$397$		−	16.4470i		−	0.825454i	−0.910855	−	0.412727i	$-0.864576\pi$
$397$		−	16.4470i		−	0.825454i	0.910855	−	0.412727i	$-0.135424\pi$
$398$	−27.3814	+	15.2842i	−1.37251	+	0.766127i
$399$	7.36535			0.368729
$400$		0			0
$401$	−4.50865			−0.225151			−0.112576	−	0.993643i	$-0.535910\pi$
$401$	−4.50865			−0.225151			−0.112576	+	0.993643i	$0.535910\pi$
$402$	−40.8778	+	22.8178i	−2.03880	+	1.13805i
$403$		−	5.21528i		−	0.259792i
$404$	−28.7419	−	17.7236i	−1.42996	−	0.881780i
$405$		0			0
$406$	−3.75850	−	6.73330i	−0.186531	−	0.334168i
$407$	−22.7946			−1.12989
$408$	−45.7472	−	1.98923i	−2.26482	−	0.0984817i
$409$	10.3945			0.513974			0.256987	−	0.966415i	$-0.417270\pi$
$409$	10.3945			0.513974			0.256987	+	0.966415i	$0.417270\pi$
$410$		0			0
$411$		−	28.7899i		−	1.42010i
$412$	−15.5044	+	25.1431i	−0.763847	+	1.23871i
$413$			7.00017i			0.344456i
$414$	−16.1800	+	9.03158i	−0.795202	+	0.443878i
$415$		0			0
$416$	−10.8157	+	15.9449i	−0.530285	+	0.781765i
$417$	−52.2587			−2.55912
$418$	−9.45719	+	5.27896i	−0.462566	+	0.258202i
$419$		−	2.14309i		−	0.104697i	−0.998629	−	0.0523484i	$-0.983329\pi$
$419$		−	2.14309i		−	0.104697i	0.998629	−	0.0523484i	$-0.0166706\pi$
$420$		0			0
$421$			16.1241i			0.785840i	0.919573	+	0.392920i	$0.128535\pi$
$421$			16.1241i			0.785840i	−0.919573	+	0.392920i	$0.871465\pi$
$422$	−2.82610	−	5.06292i	−0.137572	−	0.246459i
$423$	44.9117			2.18368
$424$	−12.3304	−	0.536165i	−0.598817	−	0.0260385i
$425$		0			0
$426$	−9.87669	−	17.6940i	−0.478527	−	0.857275i
$427$		−	6.47777i		−	0.313481i
$428$	14.6164	+	9.01314i	0.706510	+	0.435667i
$429$		−	22.2170i		−	1.07265i
$430$		0			0
$431$	30.9580			1.49119			0.745597	−	0.666397i	$-0.232164\pi$
$431$	30.9580			1.49119			0.745597	+	0.666397i	$0.232164\pi$
$432$	−3.20376	+	1.60994i	−0.154141	+	0.0774581i
$433$	13.6048			0.653807			0.326903	−	0.945058i	$-0.393995\pi$
$433$	13.6048			0.653807			0.326903	+	0.945058i	$0.393995\pi$
$434$	1.86635	−	1.04179i	0.0895875	−	0.0500073i
$435$		0			0
$436$	−12.7529	−	7.86403i	−0.610754	−	0.376619i
$437$			11.5577i			0.552881i
$438$	22.4403	+	40.2015i	1.07224	+	1.92090i
$439$	−10.5245			−0.502308			−0.251154	−	0.967947i	$-0.580810\pi$
$439$	−10.5245			−0.502308			−0.251154	+	0.967947i	$0.580810\pi$
$440$		0			0
$441$	20.2197			0.962844
$442$	−15.0764	−	27.0092i	−0.717110	−	1.28469i
$443$		−	3.73431i		−	0.177422i	−0.996057	−	0.0887112i	$-0.971725\pi$
$443$		−	3.73431i		−	0.177422i	0.996057	−	0.0887112i	$-0.0282748\pi$
$444$	−23.3146	+	37.8087i	−1.10646	+	1.79432i
$445$		0			0
$446$	8.23703	−	4.59787i	0.390035	−	0.217715i
$447$	−40.5405			−1.91750
$448$	−7.86659	−	0.685426i	−0.371662	−	0.0323833i
$449$	0.546483			0.0257901			0.0128951	−	0.999917i	$-0.495895\pi$
$449$	0.546483			0.0257901			0.0128951	+	0.999917i	$0.495895\pi$
$450$		0			0
$451$			28.0531i			1.32097i
$452$	15.0381	−	24.3869i	0.707333	−	1.14707i
$453$		−	28.5995i		−	1.34372i
$454$	−13.1631	−	23.5816i	−0.617777	−	1.10674i
$455$		0			0
$456$	−0.916876	+	21.0858i	−0.0429367	+	0.987431i
$457$	10.5326			0.492694			0.246347	−	0.969182i	$-0.420770\pi$
$457$	10.5326			0.492694			0.246347	+	0.969182i	$0.420770\pi$
$458$	−0.323268	−	0.579131i	−0.0151053	−	0.0270610i
$459$		−	5.75631i		−	0.268682i
$460$		0			0
$461$		−	22.9918i		−	1.07083i	−0.844588	−	0.535417i	$-0.820154\pi$
$461$		−	22.9918i		−	1.07083i	0.844588	−	0.535417i	$-0.179846\pi$
$462$	7.95062	−	4.43800i	0.369896	−	0.206474i
$463$	−11.8921			−0.552674			−0.276337	−	0.961061i	$-0.589121\pi$
$463$	−11.8921			−0.552674			−0.276337	+	0.961061i	$0.589121\pi$
$464$	19.7442	−	9.92174i	0.916600	−	0.460605i
$465$		0			0
$466$	−16.7704	+	9.36118i	−0.776875	+	0.433648i
$467$			22.8888i			1.05917i	0.848258	+	0.529583i	$0.177652\pi$
$467$			22.8888i			1.05917i	−0.848258	+	0.529583i	$0.822348\pi$
$468$	−19.4562	−	11.9976i	−0.899362	−	0.554588i
$469$		−	12.9608i		−	0.598475i
$470$		0			0
$471$	−8.64196			−0.398200
$472$	−20.0403	−	0.871417i	−0.922429	−	0.0401102i
$473$	4.56626			0.209957
$474$	0.0217861	+	0.0390294i	0.00100067	+	0.00179268i
$475$		0			0
$476$	6.65393	−	10.7905i	0.304982	−	0.494582i
$477$		−	14.6422i		−	0.670422i
$478$	−32.7349	+	18.2725i	−1.49726	+	0.835763i
$479$	−13.7929			−0.630212			−0.315106	−	0.949056i	$-0.602040\pi$
$479$	−13.7929			−0.630212			−0.315106	+	0.949056i	$0.602040\pi$
$480$		0			0
$481$	−30.0058			−1.36815
$482$	20.8937	−	11.6628i	0.951681	−	0.531224i
$483$		−	9.71652i		−	0.442117i
$484$	4.51943	−	7.32906i	0.205429	−	0.333139i
$485$		0			0
$486$	15.4198	+	27.6244i	0.699457	+	1.25307i
$487$	3.39709			0.153937			0.0769685	−	0.997034i	$-0.475476\pi$
$487$	3.39709			0.153937			0.0769685	+	0.997034i	$0.475476\pi$
$488$	18.5448	+	0.806386i	0.839482	+	0.0365034i
$489$	13.5889			0.614513
$490$		0			0
$491$		−	0.924686i		−	0.0417305i	−0.999782	−	0.0208652i	$-0.993358\pi$
$491$		−	0.924686i		−	0.0417305i	0.999782	−	0.0208652i	$-0.00664209\pi$
$492$	46.5308	+	28.6930i	2.09777	+	1.29358i
$493$			35.4751i			1.59772i
$494$	−12.4490	+	6.94900i	−0.560109	+	0.312650i
$495$		0			0
$496$	2.75013	+	5.47272i	0.123484	+	0.245733i
$497$	5.61009			0.251647
$498$	−5.93612	+	3.31351i	−0.266004	+	0.148482i
$499$			6.18797i			0.277012i	0.990362	+	0.138506i	$0.0442300\pi$
$499$			6.18797i			0.277012i	−0.990362	+	0.138506i	$0.955770\pi$
$500$		0			0
$501$			25.6579i			1.14631i
$502$	−20.5714	−	36.8534i	−0.918146	−	1.64485i
$503$	32.4360			1.44625			0.723126	−	0.690716i	$-0.242705\pi$
$503$	32.4360			1.44625			0.723126	+	0.690716i	$0.242705\pi$
$504$	0.406969	−	9.35921i	0.0181278	−	0.416892i
$505$		0			0
$506$	6.96411	+	12.4761i	0.309593	+	0.554631i
$507$			3.52776i			0.156673i
$508$	7.86636	−	12.7567i	0.349013	−	0.565986i
$509$		−	17.6619i		−	0.782848i	−0.920210	−	0.391424i	$-0.871983\pi$
$509$		−	17.6619i		−	0.782848i	0.920210	−	0.391424i	$-0.128017\pi$
$510$		0			0
$511$	−12.7464			−0.563867
$512$	2.94153	−	22.4354i	0.129999	−	0.991514i
$513$	−2.65320			−0.117142
$514$	3.91376	−	2.18464i	0.172629	−	0.0963605i
$515$		0			0
$516$	4.67043	−	7.57393i	0.205604	−	0.333424i
$517$		−	34.6307i		−	1.52306i
$518$	−5.99386	−	10.7379i	−0.263355	−	0.471798i
$519$	−41.5036			−1.82181
$520$		0			0
$521$	32.0921			1.40598			0.702989	−	0.711200i	$-0.251848\pi$
$521$	32.0921			1.40598			0.702989	+	0.711200i	$0.251848\pi$
$522$	12.7773	+	22.8904i	0.559249	+	1.00189i
$523$			15.8864i			0.694666i	0.937742	+	0.347333i	$0.112913\pi$
$523$			15.8864i			0.694666i	−0.937742	+	0.347333i	$0.887087\pi$
$524$	−15.7405	−	9.70631i	−0.687627	−	0.424022i
$525$		0			0
$526$	−1.76920	+	0.987561i	−0.0771410	+	0.0430597i
$527$	−9.83305			−0.428334
$528$	11.7155	+	23.3137i	0.509852	+	1.01460i
$529$	−7.75281			−0.337079
$530$		0			0
$531$		−	23.7977i		−	1.03273i
$532$	−4.97356	−	3.06692i	−0.215631	−	0.132968i
$533$			36.9279i			1.59952i
$534$	−8.38201	−	15.0163i	−0.362725	−	0.649817i
$535$		0			0
$536$	37.1047	+	1.61343i	1.60268	+	0.0696896i
$537$	14.5351			0.627234
$538$	−9.55626	−	17.1199i	−0.412000	−	0.738092i
$539$		−	15.5911i		−	0.671557i
$540$		0			0
$541$			12.3537i			0.531128i	0.964093	+	0.265564i	$0.0855582\pi$
$541$			12.3537i			0.531128i	−0.964093	+	0.265564i	$0.914442\pi$
$542$	−16.7849	+	9.36925i	−0.720973	+	0.402444i
$543$	18.6647			0.800979
$544$	30.0631	+	20.3923i	1.28894	+	0.874314i
$545$		0			0
$546$	10.4659	−	5.84199i	0.447897	−	0.250014i
$547$		−	24.2942i		−	1.03875i	−0.854548	−	0.519373i	$-0.826166\pi$
$547$		−	24.2942i		−	1.03875i	0.854548	−	0.519373i	$-0.173834\pi$
$548$	−11.9881	+	19.4408i	−0.512105	+	0.830469i
$549$			22.0218i			0.939865i
$550$		0			0
$551$	16.3512			0.696583
$552$	27.8168	+	1.20956i	1.18396	+	0.0514824i
$553$	−0.0123748			−0.000526229
$554$	10.5917	+	18.9748i	0.449996	+	0.806163i
$555$		0			0
$556$	35.2885	+	21.7605i	1.49656	+	0.922850i
$557$			36.4662i			1.54512i	0.634941	+	0.772561i	$0.281024\pi$
$557$			36.4662i			1.54512i	−0.634941	+	0.772561i	$0.718976\pi$
$558$	−6.34481	+	3.54164i	−0.268597	+	0.149930i
$559$	6.01084			0.254231
$560$		0			0
$561$	−41.8887			−1.76854
$562$	−36.9278	+	20.6129i	−1.55771	+	0.869504i
$563$		−	15.3735i		−	0.647916i	−0.946072	−	0.323958i	$-0.894986\pi$
$563$		−	15.3735i		−	0.647916i	0.946072	−	0.323958i	$-0.105014\pi$
$564$	−57.4410	−	35.4207i	−2.41870	−	1.49148i
$565$		0			0
$566$	5.78457	+	10.3630i	0.243143	+	0.435588i
$567$	−7.70579			−0.323613
$568$	−0.698373	+	16.0607i	−0.0293031	+	0.673894i
$569$	−38.5969			−1.61807			−0.809034	−	0.587762i	$-0.800009\pi$
$569$	−38.5969			−1.61807			−0.809034	+	0.587762i	$0.800009\pi$
$570$		0			0
$571$		−	47.4014i		−	1.98369i	−0.127468	−	0.991843i	$-0.540685\pi$
$571$		−	47.4014i		−	1.98369i	0.127468	−	0.991843i	$-0.459315\pi$
$572$	−9.25115	+	15.0024i	−0.386810	+	0.627280i
$573$		−	25.0816i		−	1.04780i
$574$	−13.2151	+	7.37658i	−0.551586	+	0.307893i
$575$		0			0
$576$	26.7432	+	2.33016i	1.11430	+	0.0970902i
$577$	26.2255			1.09178			0.545890	−	0.837857i	$-0.316192\pi$
$577$	26.2255			1.09178			0.545890	+	0.837857i	$0.316192\pi$
$578$	−29.9313	+	16.7075i	−1.24498	+	0.694941i
$579$			3.76937i			0.156650i
$580$		0			0
$581$		−	1.88212i		−	0.0780835i
$582$	−12.9409	−	23.1834i	−0.536416	−	0.960983i
$583$	−11.2904			−0.467601
$584$	1.58674	−	36.4908i	0.0656596	−	1.51000i
$585$		0			0
$586$	11.9310	+	21.3742i	0.492864	+	0.882959i
$587$		−	43.4873i		−	1.79491i	−0.441104	−	0.897456i	$-0.645413\pi$
$587$		−	43.4873i		−	1.79491i	0.441104	−	0.897456i	$-0.354587\pi$
$588$	−25.8605	−	15.9468i	−1.06647	−	0.657635i
$589$			4.53225i			0.186748i
$590$		0			0
$591$	1.58828			0.0653332
$592$	31.4870	−	15.8227i	1.29411	−	0.650309i
$593$	17.1599			0.704673			0.352336	−	0.935873i	$-0.385387\pi$
$593$	17.1599			0.704673			0.352336	+	0.935873i	$0.385387\pi$
$594$	−2.86403	+	1.59869i	−0.117512	+	0.0655949i
$595$		0			0
$596$	27.3755	+	16.8810i	1.12135	+	0.691473i
$597$			55.9005i			2.28786i
$598$	9.16726	+	16.4230i	0.374877	+	0.671588i
$599$	30.0179			1.22650			0.613248	−	0.789890i	$-0.289863\pi$
$599$	30.0179			1.22650			0.613248	+	0.789890i	$0.289863\pi$
$600$		0			0
$601$	13.2518			0.540553			0.270277	−	0.962783i	$-0.412885\pi$
$601$	13.2518			0.540553			0.270277	+	0.962783i	$0.412885\pi$
$602$	1.20070	+	2.15105i	0.0489370	+	0.0876701i
$603$			44.0615i			1.79432i
$604$	−11.9088	+	19.3122i	−0.484562	+	0.785802i
$605$		0			0
$606$	−52.5604	+	29.3390i	−2.13512	+	1.19181i
$607$	−37.4734			−1.52100			−0.760499	−	0.649339i	$-0.775046\pi$
$607$	−37.4734			−1.52100			−0.760499	+	0.649339i	$0.775046\pi$
$608$	9.39922	−	13.8567i	0.381189	−	0.561962i
$609$	−13.7464			−0.557030
$610$		0			0
$611$		−	45.5864i		−	1.84423i
$612$	−22.6206	+	36.6833i	−0.914384	+	1.48283i
$613$		−	12.7689i		−	0.515731i	−0.966181	−	0.257866i	$-0.916981\pi$
$613$		−	12.7689i		−	0.515731i	0.966181	−	0.257866i	$-0.0830192\pi$
$614$	4.73283	+	8.47880i	0.191001	+	0.342177i
$615$		0			0
$616$	−7.21674	−	0.313807i	−0.290771	−	0.0126437i
$617$	−0.516811			−0.0208060			−0.0104030	−	0.999946i	$-0.503311\pi$
$617$	−0.516811			−0.0208060			−0.0104030	+	0.999946i	$0.503311\pi$
$618$	25.6654	+	45.9793i	1.03242	+	1.84956i
$619$		−	0.00333486i		−	0.000134040i	−1.00000		6.70198e-5i	$-0.999979\pi$
$619$		−	0.00333486i		−	0.000134040i	1.00000		6.70198e-5i	$-2.13330e-5\pi$
$620$		0			0
$621$			3.50015i			0.140456i
$622$	−20.0494	+	11.1915i	−0.803907	+	0.448737i
$623$	4.76109			0.190749
$624$	15.4218	+	30.6892i	0.617366	+	1.22855i
$625$		0			0
$626$	−28.7438	+	16.0447i	−1.14883	+	0.641274i
$627$			19.3073i			0.771060i
$628$	5.83561	+	3.59850i	0.232866	+	0.143596i
$629$			56.5740i			2.25575i
$630$		0			0
$631$	−25.5020			−1.01522			−0.507608	−	0.861588i	$-0.669470\pi$
$631$	−25.5020			−1.01522			−0.507608	+	0.861588i	$0.669470\pi$
$632$	0.00154048	−	0.0354269i	6.12768e−5	−	0.00140921i
$633$	−10.3362			−0.410827
$634$	7.56531	+	13.5532i	0.300457	+	0.538265i
$635$		0			0
$636$	−11.5480	+	18.7271i	−0.457907	+	0.742576i
$637$		−	20.5235i		−	0.813170i
$638$	17.6505	−	9.85241i	0.698789	−	0.390061i
$639$	−19.0720			−0.754476
$640$		0			0
$641$	−26.0346			−1.02831			−0.514153	−	0.857698i	$-0.671894\pi$
$641$	−26.0346			−1.02831			−0.514153	+	0.857698i	$0.671894\pi$
$642$	26.7291	−	14.9200i	1.05491	−	0.588847i
$643$		−	43.3445i		−	1.70934i	−0.519172	−	0.854670i	$-0.673760\pi$
$643$		−	43.3445i		−	1.70934i	0.519172	−	0.854670i	$-0.326240\pi$
$644$	−4.04595	+	6.56122i	−0.159433	+	0.258548i
$645$		0			0
$646$	13.1019	+	23.4718i	0.515486	+	0.923487i
$647$	−8.45686			−0.332474			−0.166237	−	0.986086i	$-0.553162\pi$
$647$	−8.45686			−0.332474			−0.166237	+	0.986086i	$0.553162\pi$
$648$	0.959256	−	22.0604i	0.0376831	−	0.866613i
$649$	−18.3500			−0.720302
$650$		0			0
$651$		−	3.81024i		−	0.149335i
$652$	−9.17613	−	5.65842i	−0.359365	−	0.221601i
$653$		−	33.3643i		−	1.30565i	−0.757511	−	0.652823i	$-0.773585\pi$
$653$		−	33.3643i		−	1.30565i	0.757511	−	0.652823i	$-0.226415\pi$
$654$	−23.3213	+	13.0178i	−0.911935	+	0.509038i
$655$		0			0
$656$	−19.4728	−	38.7507i	−0.760286	−	1.51296i
$657$	43.3325			1.69056
$658$	16.3136	−	9.10618i	0.635971	−	0.354996i
$659$		−	32.6141i		−	1.27046i	−0.772321	−	0.635232i	$-0.780904\pi$
$659$		−	32.6141i		−	1.27046i	0.772321	−	0.635232i	$-0.219096\pi$
$660$		0			0
$661$		−	18.8002i		−	0.731242i	−0.930764	−	0.365621i	$-0.880857\pi$
$661$		−	18.8002i		−	0.731242i	0.930764	−	0.365621i	$-0.119143\pi$
$662$	−5.86733	−	10.5112i	−0.228040	−	0.408531i
$663$	−55.1405			−2.14148
$664$	5.38819	+	0.234296i	0.209102	+	0.00909245i
$665$		0			0
$666$	20.3767	+	36.5045i	0.789580	+	1.41452i
$667$		−	21.5708i		−	0.835225i
$668$	10.6839	−	17.3259i	0.413374	−	0.670359i
$669$		−	16.8163i		−	0.650155i
$670$		0			0
$671$	16.9806			0.655530
$672$	−7.90188	+	11.6492i	−0.304822	+	0.449379i
$673$	33.1539			1.27799			0.638995	−	0.769211i	$-0.279350\pi$
$673$	33.1539			1.27799			0.638995	+	0.769211i	$0.279350\pi$
$674$	−9.69589	+	5.41220i	−0.373472	+	0.208470i
$675$		0			0
$676$	1.46896	−	2.38217i	0.0564983	−	0.0916220i
$677$		−	2.35046i		−	0.0903354i	−0.998979	−	0.0451677i	$-0.985618\pi$
$677$		−	2.35046i		−	0.0903354i	0.998979	−	0.0451677i	$-0.0143822\pi$
$678$	−24.8936	−	44.5965i	−0.956031	−	1.71272i
$679$	7.35058			0.282089
$680$		0			0
$681$	−48.1430			−1.84484
$682$	2.73091	+	4.89239i	0.104572	+	0.187339i
$683$			32.6775i			1.25037i	0.780477	+	0.625185i	$0.214976\pi$
$683$			32.6775i			1.25037i	−0.780477	+	0.625185i	$0.785024\pi$
$684$	16.9080	+	10.4263i	0.646495	+	0.398659i
$685$		0			0
$686$	15.8766	−	8.86226i	0.606173	−	0.338363i
$687$	−1.18232			−0.0451085
$688$	−6.30755	+	3.16964i	−0.240473	+	0.120841i
$689$	−14.8622			−0.566205
$690$		0			0
$691$		−	26.6872i		−	1.01523i	−0.861585	−	0.507614i	$-0.830528\pi$
$691$		−	26.6872i		−	1.01523i	0.861585	−	0.507614i	$-0.169472\pi$
$692$	28.0259	+	17.2821i	1.06539	+	0.656966i
$693$		−	8.56982i		−	0.325541i
$694$	5.99656	+	10.7428i	0.227626	+	0.407790i
$695$		0			0
$696$	1.71122	−	39.3535i	0.0648635	−	1.49169i
$697$	69.6250			2.63723
$698$	−19.5646	−	35.0498i	−0.740533	−	1.32666i
$699$			34.2377i			1.29499i
$700$		0			0
$701$		−	7.22199i		−	0.272771i	−0.990656	−	0.136385i	$-0.956451\pi$
$701$		−	7.22199i		−	0.272771i	0.990656	−	0.136385i	$-0.0435485\pi$
$702$	−3.77008	+	2.10444i	−0.142293	+	0.0794271i
$703$	26.0760			0.983477
$704$	1.79675	−	20.6213i	0.0677177	−	0.777193i
$705$		0			0
$706$	0.594704	−	0.331961i	0.0223820	−	0.0124935i
$707$		−	16.6649i		−	0.626749i
$708$	−18.7686	+	30.4367i	−0.705369	+	1.14388i
$709$		−	18.4855i		−	0.694239i	−0.937821	−	0.347120i	$-0.887160\pi$
$709$		−	18.4855i		−	0.694239i	0.937821	−	0.347120i	$-0.112840\pi$
$710$		0			0
$711$	0.0420691			0.00157772
$712$	−0.592685	+	13.6302i	−0.0222118	+	0.510814i
$713$	5.97903			0.223917
$714$	−11.0147	−	19.7327i	−0.412214	−	0.738476i
$715$		0			0
$716$	−9.81501	−	6.05239i	−0.366804	−	0.226188i
$717$			66.8299i			2.49581i
$718$	31.8142	−	17.7585i	1.18729	−	0.662743i
$719$	49.0942			1.83091			0.915453	−	0.402425i	$-0.131833\pi$
$719$	49.0942			1.83091			0.915453	+	0.402425i	$0.131833\pi$
$720$		0			0
$721$	−14.5783			−0.542925
$722$	−12.6437	+	7.05765i	−0.470550	+	0.262659i
$723$		−	42.6555i		−	1.58637i
$724$	−12.6036	−	7.77196i	−0.468409	−	0.288843i
$725$		0			0
$726$	−7.48131	−	13.4027i	−0.277658	−	0.497420i
$727$	28.2967			1.04947			0.524734	−	0.851266i	$-0.324165\pi$
$727$	28.2967			1.04947			0.524734	+	0.851266i	$0.324165\pi$
$728$	−9.49982	−	0.413083i	−0.352087	−	0.0153099i
$729$	32.9759			1.22133
$730$		0			0
$731$		−	11.3330i		−	0.419167i
$732$	17.3680	−	28.1653i	0.641940	−	1.04102i
$733$			0.896942i			0.0331293i	0.999863	+	0.0165646i	$0.00527293\pi$
$733$			0.896942i			0.0331293i	−0.999863	+	0.0165646i	$0.994727\pi$
$734$	−41.4322	+	23.1273i	−1.52929	+	0.853643i
$735$		0			0
$736$	−18.2800	−	12.3996i	−0.673810	−	0.457057i
$737$	33.9751			1.25149
$738$	44.9257	−	25.0773i	1.65374	−	0.923110i
$739$			4.13752i			0.152201i	0.997100	+	0.0761006i	$0.0242470\pi$
$739$			4.13752i			0.152201i	−0.997100	+	0.0761006i	$0.975753\pi$
$740$		0			0
$741$			25.4153i			0.933655i
$742$	−2.96882	−	5.31861i	−0.108989	−	0.195252i
$743$	−30.8313			−1.13109			−0.565545	−	0.824717i	$-0.691334\pi$
$743$	−30.8313			−1.13109			−0.565545	+	0.824717i	$0.691334\pi$
$744$	10.9081	+	0.474318i	0.399909	+	0.0173893i
$745$		0			0
$746$	1.36734	+	2.44958i	0.0500620	+	0.0896854i
$747$			6.39843i			0.234106i
$748$	28.2859	+	17.4424i	1.03424	+	0.637758i
$749$			8.47479i			0.309662i
$750$		0			0
$751$	1.39394			0.0508655			0.0254327	−	0.999677i	$-0.491904\pi$
$751$	1.39394			0.0508655			0.0254327	+	0.999677i	$0.491904\pi$
$752$	24.0387	+	47.8367i	0.876600	+	1.74443i
$753$	−75.2380			−2.74182
$754$	23.2343	−	12.9693i	0.846144	−	0.472314i
$755$		0			0
$756$	−1.50620	−	0.928791i	−0.0547799	−	0.0337798i
$757$		−	28.5258i		−	1.03679i	−0.855142	−	0.518393i	$-0.826530\pi$
$757$		−	28.5258i		−	1.03679i	0.855142	−	0.518393i	$-0.173470\pi$
$758$	−5.42777	−	9.72378i	−0.197145	−	0.353184i
$759$	25.4706			0.924525
$760$		0			0
$761$	14.1092			0.511458			0.255729	−	0.966748i	$-0.417684\pi$
$761$	14.1092			0.511458			0.255729	+	0.966748i	$0.417684\pi$
$762$	−13.0217	−	23.3282i	−0.471726	−	0.845092i
$763$		−	7.39431i		−	0.267692i
$764$	−10.4440	+	16.9367i	−0.377850	+	0.612750i
$765$		0			0
$766$	22.7201	−	12.6822i	0.820909	−	0.458228i
$767$	−24.1552			−0.872194
$768$	−32.3661	−	24.0719i	−1.16791	−	0.868620i
$769$	50.3144			1.81438			0.907192	−	0.420716i	$-0.138221\pi$
$769$	50.3144			1.81438			0.907192	+	0.420716i	$0.138221\pi$
$770$		0			0
$771$		−	7.99013i		−	0.287758i
$772$	1.56956	−	2.54532i	0.0564897	−	0.0916080i
$773$		−	48.4710i		−	1.74338i	−0.490056	−	0.871691i	$-0.663024\pi$
$773$		−	48.4710i		−	1.74338i	0.490056	−	0.871691i	$-0.336976\pi$
$774$	−4.08190	−	7.31267i	−0.146721	−	0.262848i
$775$		0			0
$776$	−0.915038	+	21.0435i	−0.0328480	+	0.755417i
$777$	−21.9220			−0.786448
$778$	−4.60591	−	8.25142i	−0.165130	−	0.295828i
$779$		−	32.0915i		−	1.14980i
$780$		0			0
$781$			14.7061i			0.526227i
$782$	30.9645	−	17.2843i	1.10729	−	0.618084i
$783$	4.95181			0.176963
$784$	10.8225	+	21.5366i	0.386517	+	0.769165i
$785$		0			0
$786$	−28.7847	+	16.0675i	−1.02672	+	0.573108i
$787$		−	1.32396i		−	0.0471941i	−0.999722	−	0.0235971i	$-0.992488\pi$
$787$		−	1.32396i		−	0.0471941i	0.999722	−	0.0235971i	$-0.00751187\pi$
$788$	−1.07251	−	0.661359i	−0.0382066	−	0.0235599i
$789$			3.61192i			0.128588i
$790$		0			0
$791$	14.1399			0.502756
$792$	24.5340	+	1.06682i	0.871776	+	0.0379076i
$793$	22.3526			0.793764
$794$	11.3368	+	20.3098i	0.402329	+	0.720767i
$795$		0			0
$796$	23.2769	−	37.7476i	0.825028	−	1.33793i
$797$		−	8.06593i		−	0.285710i	−0.989744	−	0.142855i	$-0.954372\pi$
$797$		−	8.06593i		−	0.285710i	0.989744	−	0.142855i	$-0.0456282\pi$
$798$	−9.09517	+	5.07688i	−0.321965	+	0.179720i
$799$	−85.9501			−3.04069
$800$		0			0
$801$	−16.1858			−0.571896
$802$	5.56755	−	3.10778i	0.196597	−	0.109739i
$803$		−	33.4130i		−	1.17912i
$804$	34.7502	−	56.3536i	1.22554	−	1.98744i
$805$		0			0
$806$	3.59485	+	6.44013i	0.126623	+	0.226844i
$807$	−34.9512			−1.23034
$808$	47.7089	+	2.07454i	1.67839	+	0.0729819i
$809$	−11.0404			−0.388159			−0.194080	−	0.980986i	$-0.562172\pi$
$809$	−11.0404			−0.388159			−0.194080	+	0.980986i	$0.562172\pi$
$810$		0			0
$811$		−	0.410182i		−	0.0144034i	−0.999974	−	0.00720172i	$-0.997708\pi$
$811$		−	0.410182i		−	0.0144034i	0.999974	−	0.00720172i	$-0.00229240\pi$
$812$	9.28242	+	5.72397i	0.325749	+	0.200872i
$813$			34.2672i			1.20180i
$814$	28.1481	−	15.7121i	0.986591	−	0.550710i
$815$		0			0
$816$	57.8624	−	29.0767i	2.02559	−	1.01789i
$817$	−5.22361			−0.182751
$818$	−12.8357	+	7.16484i	−0.448790	+	0.250513i
$819$		−	11.2810i		−	0.394188i
$820$		0			0
$821$			41.6835i			1.45476i	0.686233	+	0.727382i	$0.259263\pi$
$821$			41.6835i			1.45476i	−0.686233	+	0.727382i	$0.740737\pi$
$822$	19.8446	+	35.5514i	0.692161	+	1.24000i
$823$	29.3227			1.02213			0.511063	−	0.859543i	$-0.329252\pi$
$823$	29.3227			1.02213			0.511063	+	0.859543i	$0.329252\pi$
$824$	1.81478	−	41.7352i	0.0632210	−	1.45392i
$825$		0			0
$826$	−4.82516	−	8.64422i	−0.167889	−	0.300771i
$827$		−	5.80461i		−	0.201846i	−0.994894	−	0.100923i	$-0.967820\pi$
$827$		−	5.80461i		−	0.201846i	0.994894	−	0.100923i	$-0.0321796\pi$
$828$	13.7546	−	22.3054i	0.478004	−	0.775168i
$829$		−	38.6044i		−	1.34079i	−0.742006	−	0.670393i	$-0.766125\pi$
$829$		−	38.6044i		−	1.34079i	0.742006	−	0.670393i	$-0.233875\pi$
$830$		0			0
$831$	38.7380			1.34381
$832$	2.36517	−	27.1450i	0.0819976	−	0.941082i
$833$	−38.6957			−1.34072
$834$	64.5322	−	36.0216i	2.23457	−	1.24732i
$835$		0			0
$836$	8.03955	−	13.0375i	0.278053	−	0.450913i
$837$			1.37255i			0.0474423i
$838$	1.47722	+	2.64641i	0.0510296	+	0.0914188i
$839$	20.9360			0.722791			0.361395	−	0.932413i	$-0.382300\pi$
$839$	20.9360			0.722791			0.361395	+	0.932413i	$0.382300\pi$
$840$		0			0
$841$	−1.51708			−0.0523131
$842$	−11.1142	−	19.9110i	−0.383021	−	0.686177i
$843$			75.3899i			2.59657i
$844$	6.97966	+	4.30398i	0.240250	+	0.148149i
$845$		0			0
$846$	−55.4596	+	30.9573i	−1.90674	+	1.06433i
$847$	4.24949			0.146014
$848$	15.5959	−	7.83716i	0.535564	−	0.269129i
$849$	21.1565			0.726090
$850$		0			0
$851$		−	34.4001i		−	1.17922i
$852$	24.3926	+	15.0416i	0.835678	+	0.515317i
$853$			48.1468i			1.64851i	0.566215	+	0.824257i	$0.308407\pi$
$853$			48.1468i			1.64851i	−0.566215	+	0.824257i	$0.691593\pi$
$854$	4.46508	+	7.99913i	0.152792	+	0.273725i
$855$		0			0
$856$	−24.2619	−	1.05498i	−0.829254	−	0.0360586i
$857$	−45.8270			−1.56542			−0.782710	−	0.622386i	$-0.786163\pi$
$857$	−45.8270			−1.56542			−0.782710	+	0.622386i	$0.786163\pi$
$858$	15.3140	+	27.4349i	0.522812	+	0.936612i
$859$		−	0.681686i		−	0.0232588i	−0.999932	−	0.0116294i	$-0.996298\pi$
$859$		−	0.681686i		−	0.0232588i	0.999932	−	0.0116294i	$-0.00370184\pi$
$860$		0			0
$861$			26.9792i			0.919448i
$862$	−38.2288	+	21.3391i	−1.30208	+	0.726813i
$863$	−31.6018			−1.07574			−0.537869	−	0.843029i	$-0.680770\pi$
$863$	−31.6018			−1.07574			−0.537869	+	0.843029i	$0.680770\pi$
$864$	2.84647	−	4.19637i	0.0968389	−	0.142763i
$865$		0			0
$866$	−16.8001	+	9.37771i	−0.570889	+	0.318668i
$867$			61.1062i			2.07528i
$868$	−1.58658	+	2.57292i	−0.0538520	+	0.0873305i
$869$		−	0.0324389i		−	0.00110041i
$870$		0			0
$871$	44.7234			1.51540
$872$	21.1687	+	0.920482i	0.716862	+	0.0311714i
$873$	−24.9890			−0.845748
$874$	−7.96665	−	14.2722i	−0.269476	−	0.482763i
$875$		0			0
$876$	−55.4212	−	34.1753i	−1.87251	−	1.15468i
$877$			31.3435i			1.05840i	0.848499	+	0.529198i	$0.177507\pi$
$877$			31.3435i			1.05840i	−0.848499	+	0.529198i	$0.822493\pi$
$878$	12.9963	−	7.25447i	0.438604	−	0.244827i
$879$	43.6364			1.47182
$880$		0			0
$881$	−5.59365			−0.188455			−0.0942274	−	0.995551i	$-0.530038\pi$
$881$	−5.59365			−0.188455			−0.0942274	+	0.995551i	$0.530038\pi$
$882$	−24.9685	+	13.9373i	−0.840733	+	0.469293i
$883$		−	3.97695i		−	0.133835i	−0.997759	−	0.0669175i	$-0.978684\pi$
$883$		−	3.97695i		−	0.133835i	0.997759	−	0.0669175i	$-0.0213164\pi$
$884$	37.2344	+	22.9604i	1.25233	+	0.772243i
$885$		0			0
$886$	2.57403	+	4.61134i	0.0864763	+	0.154921i
$887$	−24.7381			−0.830624			−0.415312	−	0.909679i	$-0.636328\pi$
$887$	−24.7381			−0.830624			−0.415312	+	0.909679i	$0.636328\pi$
$888$	2.72896	−	62.7590i	0.0915781	−	2.10605i
$889$	7.39650			0.248071
$890$		0			0
$891$		−	20.1997i		−	0.676716i
$892$	−7.00229	+	11.3554i	−0.234454	+	0.380208i
$893$			39.6161i			1.32570i
$894$	50.0617	−	27.9442i	1.67431	−	0.934595i
$895$		0			0
$896$	10.1866	−	4.57598i	0.340310	−	0.152873i
$897$	33.5284			1.11948
$898$	−0.674830	+	0.376687i	−0.0225194	+	0.0125702i
$899$		−	8.45878i		−	0.282116i
$900$		0			0
$901$			28.0217i			0.933538i
$902$	−19.3368	−	34.6416i	−0.643844	−	1.15344i
$903$	4.39147			0.146139
$904$	−1.76020	+	40.4801i	−0.0585435	+	1.34635i
$905$		0			0
$906$	19.7134	+	35.3163i	0.654934	+	1.17331i
$907$		−	24.6646i		−	0.818976i	−0.912316	−	0.409488i	$-0.865707\pi$
$907$		−	24.6646i		−	0.818976i	0.912316	−	0.409488i	$-0.134293\pi$
$908$	32.5092	+	20.0467i	1.07886	+	0.665273i
$909$			56.6539i			1.87909i
$910$		0			0
$911$	−11.4372			−0.378930			−0.189465	−	0.981887i	$-0.560675\pi$
$911$	−11.4372			−0.378930			−0.189465	+	0.981887i	$0.560675\pi$
$912$	−13.4020	−	26.6699i	−0.443786	−	0.883129i
$913$	4.93374			0.163283
$914$	−13.0063	+	7.26003i	−0.430209	+	0.240140i
$915$		0			0
$916$	0.798381	+	0.492318i	0.0263793	+	0.0162667i
$917$		−	9.12655i		−	0.301385i
$918$	3.96778	+	7.10823i	0.130956	+	0.234607i
$919$	−2.39236			−0.0789167			−0.0394583	−	0.999221i	$-0.512563\pi$
$919$	−2.39236			−0.0789167			−0.0394583	+	0.999221i	$0.512563\pi$
$920$		0			0
$921$	17.3099			0.570380
$922$	15.8481	+	28.3916i	0.521928	+	0.935028i
$923$			19.3585i			0.637194i
$924$	−6.75881	+	10.9606i	−0.222348	+	0.360577i
$925$		0			0
$926$	14.6851	−	8.19716i	0.482582	−	0.269375i
$927$	49.5602			1.62777
$928$	−17.5423	+	25.8615i	−0.575853	+	0.848944i
$929$	−7.84705			−0.257453			−0.128727	−	0.991680i	$-0.541089\pi$
$929$	−7.84705			−0.257453			−0.128727	+	0.991680i	$0.541089\pi$
$930$		0			0
$931$			17.8356i			0.584537i
$932$	14.2565	−	23.1195i	0.466988	−	0.757303i
$933$			40.9318i			1.34005i
$934$	−15.7771	−	28.2644i	−0.516241	−	0.924839i
$935$		0			0
$936$	32.2955	+	1.40431i	1.05561	+	0.0459013i
$937$	9.82605			0.321003			0.160502	−	0.987036i	$-0.448689\pi$
$937$	9.82605			0.321003			0.160502	+	0.987036i	$0.448689\pi$
$938$	8.93380	+	16.0048i	0.291699	+	0.522575i
$939$			58.6819i			1.91501i
$940$		0			0
$941$			21.9950i			0.717015i	0.933527	+	0.358508i	$0.116714\pi$
$941$			21.9950i			0.717015i	−0.933527	+	0.358508i	$0.883286\pi$
$942$	10.6716	−	5.95684i	0.347699	−	0.194084i
$943$	−42.3358			−1.37864
$944$	25.3476	−	12.7375i	0.824994	−	0.414572i
$945$		0			0
$946$	−5.63869	+	3.14749i	−0.183330	+	0.102334i
$947$			17.0055i			0.552605i	0.961071	+	0.276302i	$0.0891092\pi$
$947$			17.0055i			0.552605i	−0.961071	+	0.276302i	$0.910891\pi$
$948$	−0.0538054	−	0.0331789i	−0.00174752	−	0.00107760i
$949$		−	43.9835i		−	1.42776i
$950$		0			0
$951$	27.6694			0.897243
$952$	−0.778839	+	17.9113i	−0.0252423	+	0.580507i
$953$	23.5659			0.763374			0.381687	−	0.924292i	$-0.375343\pi$
$953$	23.5659			0.763374			0.381687	+	0.924292i	$0.375343\pi$
$954$	10.0928	+	18.0811i	0.326766	+	0.585397i
$955$		0			0
$956$	27.8279	−	45.1278i	0.900018	−	1.45954i
$957$		−	36.0343i		−	1.16482i
$958$	17.0322	−	9.50732i	0.550287	−	0.307168i
$959$	−11.2720			−0.363993
$960$		0			0
$961$	−28.6554			−0.924367
$962$	37.0530	−	20.6828i	1.19464	−	0.666840i
$963$		−	28.8108i		−	0.928414i
$964$	−17.7617	+	28.8037i	−0.572066	+	0.927705i
$965$		0			0
$966$	6.69753	+	11.9985i	0.215489	+	0.386046i
$967$	38.1868			1.22801			0.614003	−	0.789304i	$-0.289558\pi$
$967$	38.1868			1.22801			0.614003	+	0.789304i	$0.289558\pi$
$968$	−0.528998	+	12.1656i	−0.0170026	+	0.391016i
$969$	47.9189			1.53938
$970$		0			0
$971$			52.4070i			1.68182i	0.541175	+	0.840910i	$0.317980\pi$
$971$			52.4070i			1.68182i	−0.541175	+	0.840910i	$0.682020\pi$
$972$	−38.0826	−	23.4835i	−1.22150	−	0.753233i
$973$			20.4607i			0.655941i
$974$	−4.19493	+	2.34159i	−0.134414	+	0.0750294i
$975$		0			0
$976$	−23.4560	+	11.7870i	−0.750808	+	0.377293i
$977$	−55.0981			−1.76274			−0.881372	−	0.472422i	$-0.843380\pi$
$977$	−55.0981			−1.76274			−0.881372	+	0.472422i	$0.843380\pi$
$978$	−16.7804	+	9.36675i	−0.536579	+	0.299516i
$979$			12.4806i			0.398882i
$980$		0			0
$981$			25.1376i			0.802582i
$982$	0.637379	+	1.14186i	0.0203396	+	0.0364381i
$983$	−7.53753			−0.240410			−0.120205	−	0.992749i	$-0.538355\pi$
$983$	−7.53753			−0.240410			−0.120205	+	0.992749i	$0.538355\pi$
$984$	−77.2368	−	3.35851i	−2.46222	−	0.107065i
$985$		0			0
$986$	−24.4527	−	43.8067i	−0.778733	−	1.39509i
$987$		−	33.3050i		−	1.06011i
$988$	10.5829	−	17.1621i	0.336687	−	0.545998i
$989$			6.89110i			0.219124i
$990$		0			0
$991$	36.7106			1.16615			0.583076	−	0.812418i	$-0.301849\pi$
$991$	36.7106			1.16615			0.583076	+	0.812418i	$0.301849\pi$
$992$	−7.16832	−	4.86240i	−0.227594	−	0.154381i
$993$	−21.4592			−0.680987
$994$	−6.92767	+	3.86699i	−0.219732	+	0.122654i
$995$		0			0
$996$	5.04629	−	8.18345i	0.159898	−	0.259302i
$997$			41.3341i			1.30906i	0.756035	+	0.654531i	$0.227134\pi$
$997$			41.3341i			1.30906i	−0.756035	+	0.654531i	$0.772866\pi$
$998$	−4.26532	−	7.64127i	−0.135016	−	0.241880i
$999$	7.89690			0.249847

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.d.c.501.10	yes	40
4.3	odd	2		4000.2.d.c.2001.9		40
5.2	odd	4		1000.2.f.d.749.5		20
5.3	odd	4		1000.2.f.c.749.16		20
5.4	even	2	inner	1000.2.d.c.501.31	yes	40
8.3	odd	2		4000.2.d.c.2001.10		40
8.5	even	2	inner	1000.2.d.c.501.9	✓	40
20.3	even	4		4000.2.f.c.3249.18		20
20.7	even	4		4000.2.f.d.3249.3		20
20.19	odd	2		4000.2.d.c.2001.32		40
40.3	even	4		4000.2.f.d.3249.4		20
40.13	odd	4		1000.2.f.d.749.6		20
40.19	odd	2		4000.2.d.c.2001.31		40
40.27	even	4		4000.2.f.c.3249.17		20
40.29	even	2	inner	1000.2.d.c.501.32	yes	40
40.37	odd	4		1000.2.f.c.749.15		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1000.2.d.c.501.9	✓	40	8.5	even	2	inner
1000.2.d.c.501.10	yes	40	1.1	even	1	trivial
1000.2.d.c.501.31	yes	40	5.4	even	2	inner
1000.2.d.c.501.32	yes	40	40.29	even	2	inner
1000.2.f.c.749.15		20	40.37	odd	4
1000.2.f.c.749.16		20	5.3	odd	4
1000.2.f.d.749.5		20	5.2	odd	4
1000.2.f.d.749.6		20	40.13	odd	4
4000.2.d.c.2001.9		40	4.3	odd	2
4000.2.d.c.2001.10		40	8.3	odd	2
4000.2.d.c.2001.31		40	40.19	odd	2
4000.2.d.c.2001.32		40	20.19	odd	2
4000.2.f.c.3249.17		20	40.27	even	4
4000.2.f.c.3249.18		20	20.3	even	4
4000.2.f.d.3249.3		20	20.7	even	4
4000.2.f.d.3249.4		20	40.3	even	4

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:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23486 + 0.689292i) q^{2} +2.52102i q^{3} +(1.04975 - 1.70236i) q^{4} +(-1.73772 - 3.11311i) q^{6} +0.987050 q^{7} +(-0.122873 + 2.82576i) q^{8} -3.35556 q^{9} +O(q^{10})\)	\(q+(-1.23486 + 0.689292i) q^{2} +2.52102i q^{3} +(1.04975 - 1.70236i) q^{4} +(-1.73772 - 3.11311i) q^{6} +0.987050 q^{7} +(-0.122873 + 2.82576i) q^{8} -3.35556 q^{9} +2.58742i q^{11} +(4.29168 + 2.64645i) q^{12} +3.40597i q^{13} +(-1.21887 + 0.680366i) q^{14} +(-1.79604 - 3.57411i) q^{16} +6.42173 q^{17} +(4.14364 - 2.31296i) q^{18} -2.95990i q^{19} +2.48838i q^{21} +(-1.78349 - 3.19510i) q^{22} -3.90476 q^{23} +(-7.12380 - 0.309766i) q^{24} +(-2.34771 - 4.20590i) q^{26} -0.896380i q^{27} +(1.03616 - 1.68031i) q^{28} +5.52423i q^{29} -1.53121 q^{31} +(4.68146 + 3.17552i) q^{32} -6.52296 q^{33} +(-7.92993 + 4.42645i) q^{34} +(-3.52251 + 5.71237i) q^{36} +8.80977i q^{37} +(2.04024 + 3.65506i) q^{38} -8.58654 q^{39} +10.8421 q^{41} +(-1.71522 - 3.07279i) q^{42} -1.76479i q^{43} +(4.40472 + 2.71615i) q^{44} +(4.82183 - 2.69152i) q^{46} -13.3842 q^{47} +(9.01041 - 4.52787i) q^{48} -6.02573 q^{49} +16.1893i q^{51} +(5.79819 + 3.57543i) q^{52} +4.36357i q^{53} +(0.617868 + 1.10690i) q^{54} +(-0.121282 + 2.78916i) q^{56} +7.46198 q^{57} +(-3.80781 - 6.82164i) q^{58} +7.09201i q^{59} -6.56276i q^{61} +(1.89083 - 1.05545i) q^{62} -3.31211 q^{63} +(-7.96980 - 0.694419i) q^{64} +(8.05493 - 4.49622i) q^{66} -13.1309i q^{67} +(6.74123 - 10.9321i) q^{68} -9.84401i q^{69} +5.68370 q^{71} +(0.412308 - 9.48200i) q^{72} -12.9136 q^{73} +(-6.07251 - 10.8788i) q^{74} +(-5.03881 - 3.10716i) q^{76} +2.55392i q^{77} +(10.6032 - 5.91864i) q^{78} -0.0125371 q^{79} -7.80689 q^{81} +(-13.3884 + 7.47336i) q^{82} -1.90681i q^{83} +(4.23611 + 2.61218i) q^{84} +(1.21646 + 2.17927i) q^{86} -13.9267 q^{87} +(-7.31143 - 0.317925i) q^{88} +4.82356 q^{89} +3.36187i q^{91} +(-4.09903 + 6.64731i) q^{92} -3.86023i q^{93} +(16.5277 - 9.22566i) q^{94} +(-8.00556 + 11.8021i) q^{96} +7.44702 q^{97} +(7.44093 - 4.15349i) q^{98} -8.68226i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9}+O(q^{10}) \) 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9	\( 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9} + 12 q^{14} + 18 q^{16} - 6 q^{24} + 20 q^{26} + 48 q^{31} - 6 q^{34} - 40 q^{36} + 8 q^{39} + 44 q^{41} + 8 q^{44} - 30 q^{46} + 12 q^{49} - 2 q^{54} + 50 q^{56} + 72 q^{64} + 42 q^{66} + 96 q^{71} + 6 q^{74} - 2 q^{76} + 96 q^{79} - 56 q^{81} + 116 q^{84} + 46 q^{86} - 44 q^{89} - 14 q^{94} + 12 q^{96}+O(q^{100}) \) 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9 + 12 * q^14 + 18 * q^16 - 6 * q^24 + 20 * q^26 + 48 * q^31 - 6 * q^34 - 40 * q^36 + 8 * q^39 + 44 * q^41 + 8 * q^44 - 30 * q^46 + 12 * q^49 - 2 * q^54 + 50 * q^56 + 72 * q^64 + 42 * q^66 + 96 * q^71 + 6 * q^74 - 2 * q^76 + 96 * q^79 - 56 * q^81 + 116 * q^84 + 46 * q^86 - 44 * q^89 - 14 * q^94 + 12 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more