LMFDB - Embedded newform 1000.2.m.d.601.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(201,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1000.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.m (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			601.5
Character	$\chi$	$=$	1000.601
Dual form			1000.2.m.d.401.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0481856 + 0.0350089i) q^{3} +1.71675 q^{7} +(-0.925955 - 2.84980i) q^{9} +(0.573356 - 1.76461i) q^{11} +(0.173457 + 0.533844i) q^{13} +(3.15952 - 2.29552i) q^{17} +(-4.69249 + 3.40929i) q^{19} +(0.0827227 + 0.0601016i) q^{21} +(2.25969 - 6.95461i) q^{23} +(0.110366 - 0.339673i) q^{27} +(-2.13709 - 1.55269i) q^{29} +(1.56235 - 1.13511i) q^{31} +(0.0894045 - 0.0649561i) q^{33} +(-0.235731 - 0.725506i) q^{37} +(-0.0103312 + 0.0317961i) q^{39} +(-3.00636 - 9.25262i) q^{41} +9.68774 q^{43} +(8.42338 + 6.11994i) q^{47} -4.05276 q^{49} +0.232607 q^{51} +(0.900166 + 0.654009i) q^{53} -0.345466 q^{57} +(1.56343 + 4.81174i) q^{59} +(4.18521 - 12.8808i) q^{61} +(-1.58963 - 4.89239i) q^{63} +(1.01005 - 0.733847i) q^{67} +(0.352358 - 0.256003i) q^{69} +(10.8951 + 7.91578i) q^{71} +(1.26382 - 3.88964i) q^{73} +(0.984309 - 3.02939i) q^{77} +(-5.25455 - 3.81765i) q^{79} +(-7.25533 + 5.27131i) q^{81} +(-0.738788 + 0.536761i) q^{83} +(-0.0486192 - 0.149634i) q^{87} +(1.61785 - 4.97923i) q^{89} +(0.297782 + 0.916478i) q^{91} +0.115022 q^{93} +(-11.7557 - 8.54098i) q^{97} -5.55967 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{3} + 16 q^{7} - 10 q^{9} + 6 q^{11} - 10 q^{13} - 4 q^{17} + 6 q^{19} - 4 q^{21} + 4 q^{23} - 26 q^{27} + 2 q^{29} + 6 q^{31} - 32 q^{33} - 16 q^{37} + 12 q^{39} + 52 q^{43} + 8 q^{47} + 60 q^{49}+ \cdots - 92 q^{99}+O(q^{100}) $ 32 * q - 2 * q^3 + 16 * q^7 - 10 * q^9 + 6 * q^11 - 10 * q^13 - 4 * q^17 + 6 * q^19 - 4 * q^21 + 4 * q^23 - 26 * q^27 + 2 * q^29 + 6 * q^31 - 32 * q^33 - 16 * q^37 + 12 * q^39 + 52 * q^43 + 8 * q^47 + 60 * q^49 - 60 * q^51 - 28 * q^53 + 48 * q^57 + 30 * q^59 + 14 * q^61 + 24 * q^63 + 4 * q^69 + 12 * q^71 + 4 * q^73 - 90 * q^77 - 16 * q^79 - 52 * q^81 - 80 * q^83 - 84 * q^87 - 24 * q^89 - 4 * q^91 + 80 * q^93 + 12 * q^97 - 92 * q^99

Character values

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

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

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
$3$	0.0481856	+	0.0350089i	0.0278200	+	0.0202124i	0.601608	−	0.798791i	$-0.294527\pi$
$3$	0.0481856	+	0.0350089i	0.0278200	+	0.0202124i	−0.573788	+	0.819004i	$0.694527\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.71675			0.648871			0.324436	−	0.945908i	$-0.394826\pi$
$7$	1.71675			0.648871			0.324436	+	0.945908i	$0.394826\pi$
$8$		0			0
$9$	−0.925955	−	2.84980i	−0.308652	−	0.949932i
$10$		0			0
$11$	0.573356	−	1.76461i	0.172873	−	0.532049i	−0.826657	−	0.562707i	$-0.809760\pi$
$11$	0.573356	−	1.76461i	0.172873	−	0.532049i	0.999530	+	0.0306574i	$0.00976008\pi$
$12$		0			0
$13$	0.173457	+	0.533844i	0.0481082	+	0.148062i	0.972225	−	0.234048i	$-0.0751974\pi$
$13$	0.173457	+	0.533844i	0.0481082	+	0.148062i	−0.924117	+	0.382110i	$0.875197\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.15952	−	2.29552i	0.766295	−	0.556746i	−0.134539	−	0.990908i	$-0.542955\pi$
$17$	3.15952	−	2.29552i	0.766295	−	0.556746i	0.900835	+	0.434162i	$0.142955\pi$
$18$		0			0
$19$	−4.69249	+	3.40929i	−1.07653	+	0.782145i	−0.977075	−	0.212897i	$-0.931710\pi$
$19$	−4.69249	+	3.40929i	−1.07653	+	0.782145i	−0.0994556	+	0.995042i	$0.531710\pi$
$20$		0			0
$21$	0.0827227	+	0.0601016i	0.0180516	+	0.0131152i
$22$		0			0
$23$	2.25969	−	6.95461i	0.471178	−	1.45014i	−0.379866	−	0.925041i	$-0.624030\pi$
$23$	2.25969	−	6.95461i	0.471178	−	1.45014i	0.851044	−	0.525094i	$-0.175970\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.110366	−	0.339673i	0.0212400	−	0.0653700i
$28$		0			0
$29$	−2.13709	−	1.55269i	−0.396848	−	0.288327i	0.371408	−	0.928470i	$-0.378875\pi$
$29$	−2.13709	−	1.55269i	−0.396848	−	0.288327i	−0.768256	+	0.640143i	$0.778875\pi$
$30$		0			0
$31$	1.56235	−	1.13511i	0.280607	−	0.203873i	−0.438575	−	0.898694i	$-0.644517\pi$
$31$	1.56235	−	1.13511i	0.280607	−	0.203873i	0.719182	+	0.694822i	$0.244517\pi$
$32$		0			0
$33$	0.0894045	−	0.0649561i	0.0155633	−	0.0113074i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.235731	−	0.725506i	−0.0387539	−	0.119272i	0.929808	−	0.368045i	$-0.119973\pi$
$37$	−0.235731	−	0.725506i	−0.0387539	−	0.119272i	−0.968562	+	0.248773i	$0.919973\pi$
$38$		0			0
$39$	−0.0103312	+	0.0317961i	−0.00165431	+	0.00509146i
$40$		0			0
$41$	−3.00636	−	9.25262i	−0.469514	−	1.44502i	−0.853215	−	0.521559i	$-0.825351\pi$
$41$	−3.00636	−	9.25262i	−0.469514	−	1.44502i	0.383701	−	0.923457i	$-0.374649\pi$
$42$		0			0
$43$	9.68774			1.47737			0.738683	−	0.674053i	$-0.235448\pi$
$43$	9.68774			1.47737			0.738683	+	0.674053i	$0.235448\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	8.42338	+	6.11994i	1.22868	+	0.892685i	0.996790	−	0.0800577i	$-0.0255104\pi$
$47$	8.42338	+	6.11994i	1.22868	+	0.892685i	0.231886	+	0.972743i	$0.425510\pi$
$48$		0			0
$49$	−4.05276			−0.578966
$50$		0			0
$51$	0.232607			0.0325715
$52$		0			0
$53$	0.900166	+	0.654009i	0.123647	+	0.0898351i	0.647890	−	0.761734i	$-0.275652\pi$
$53$	0.900166	+	0.654009i	0.123647	+	0.0898351i	−0.524243	+	0.851569i	$0.675652\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.345466			−0.0457581
$58$		0			0
$59$	1.56343	+	4.81174i	0.203541	+	0.626435i	0.999770	+	0.0214397i	$0.00682500\pi$
$59$	1.56343	+	4.81174i	0.203541	+	0.626435i	−0.796229	+	0.604995i	$0.793175\pi$
$60$		0			0
$61$	4.18521	−	12.8808i	0.535862	−	1.64921i	−0.205918	−	0.978569i	$-0.566018\pi$
$61$	4.18521	−	12.8808i	0.535862	−	1.64921i	0.741780	−	0.670643i	$-0.233982\pi$
$62$		0			0
$63$	−1.58963	−	4.89239i	−0.200275	−	0.616383i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.01005	−	0.733847i	0.123398	−	0.0896537i	−0.524375	−	0.851488i	$-0.675701\pi$
$67$	1.01005	−	0.733847i	0.123398	−	0.0896537i	0.647772	+	0.761834i	$0.275701\pi$
$68$		0			0
$69$	0.352358	−	0.256003i	0.0424189	−	0.0308191i
$70$		0			0
$71$	10.8951	+	7.91578i	1.29302	+	0.939430i	0.999862	−	0.0166349i	$-0.00529530\pi$
$71$	10.8951	+	7.91578i	1.29302	+	0.939430i	0.293154	+	0.956065i	$0.405295\pi$
$72$		0			0
$73$	1.26382	−	3.88964i	0.147919	−	0.455248i	−0.849456	−	0.527660i	$-0.823070\pi$
$73$	1.26382	−	3.88964i	0.147919	−	0.455248i	0.997375	+	0.0724119i	$0.0230696\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.984309	−	3.02939i	0.112172	−	0.345231i
$78$		0			0
$79$	−5.25455	−	3.81765i	−0.591183	−	0.429520i	0.251555	−	0.967843i	$-0.419058\pi$
$79$	−5.25455	−	3.81765i	−0.591183	−	0.429520i	−0.842738	+	0.538323i	$0.819058\pi$
$80$		0			0
$81$	−7.25533	+	5.27131i	−0.806148	+	0.585701i
$82$		0			0
$83$	−0.738788	+	0.536761i	−0.0810925	+	0.0589172i	−0.627593	−	0.778542i	$-0.715960\pi$
$83$	−0.738788	+	0.536761i	−0.0810925	+	0.0589172i	0.546500	+	0.837459i	$0.315960\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.0486192	−	0.149634i	−0.00521252	−	0.0160425i
$88$		0			0
$89$	1.61785	−	4.97923i	0.171492	−	0.527797i	−0.827964	−	0.560781i	$-0.810501\pi$
$89$	1.61785	−	4.97923i	0.171492	−	0.527797i	0.999456	+	0.0329839i	$0.0105010\pi$
$90$		0			0
$91$	0.297782	+	0.916478i	0.0312160	+	0.0960730i
$92$		0			0
$93$	0.115022			0.0119272
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−11.7557	−	8.54098i	−1.19361	−	0.867205i	−0.199965	−	0.979803i	$-0.564083\pi$
$97$	−11.7557	−	8.54098i	−1.19361	−	0.867205i	−0.993641	+	0.112598i	$0.964083\pi$
$98$		0			0
$99$	−5.55967			−0.558768
$100$		0			0
$101$	−1.84989			−0.184071			−0.0920354	−	0.995756i	$-0.529337\pi$
$101$	−1.84989			−0.184071			−0.0920354	+	0.995756i	$0.529337\pi$
$102$		0			0
$103$	−8.34571	−	6.06351i	−0.822327	−	0.597456i	0.0950510	−	0.995472i	$-0.469699\pi$
$103$	−8.34571	−	6.06351i	−0.822327	−	0.597456i	−0.917378	+	0.398017i	$0.869699\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	15.1159			1.46131			0.730656	−	0.682746i	$-0.239214\pi$
$107$	15.1159			1.46131			0.730656	+	0.682746i	$0.239214\pi$
$108$		0			0
$109$	−1.40146	−	4.31325i	−0.134235	−	0.413134i	0.861235	−	0.508207i	$-0.169692\pi$
$109$	−1.40146	−	4.31325i	−0.134235	−	0.413134i	−0.995470	+	0.0950729i	$0.969692\pi$
$110$		0			0
$111$	0.0140403	−	0.0432116i	0.00133265	−	0.00410146i
$112$		0			0
$113$	4.82952	+	14.8637i	0.454323	+	1.39826i	0.871929	+	0.489633i	$0.162869\pi$
$113$	4.82952	+	14.8637i	0.454323	+	1.39826i	−0.417606	+	0.908628i	$0.637131\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.36073	−	0.988632i	0.125800	−	0.0913990i
$118$		0			0
$119$	5.42411	−	3.94084i	0.497227	−	0.361257i
$120$		0			0
$121$	6.11408	+	4.44214i	0.555826	+	0.403831i
$122$		0			0
$123$	0.179061	−	0.551092i	0.0161454	−	0.0496903i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−0.414665	+	1.27621i	−0.0367956	+	0.113245i	−0.967767	−	0.251846i	$-0.918962\pi$
$127$	−0.414665	+	1.27621i	−0.0367956	+	0.113245i	0.930972	+	0.365091i	$0.118962\pi$
$128$		0			0
$129$	0.466810	+	0.339157i	0.0411003	+	0.0298611i
$130$		0			0
$131$	−11.2000	+	8.13727i	−0.978548	+	0.710957i	−0.957384	−	0.288819i	$-0.906737\pi$
$131$	−11.2000	+	8.13727i	−0.978548	+	0.710957i	−0.0211645	+	0.999776i	$0.506737\pi$
$132$		0			0
$133$	−8.05583	+	5.85291i	−0.698529	+	0.507511i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.60633	+	8.02147i	0.222674	+	0.685320i	0.998519	+	0.0543972i	$0.0173237\pi$
$137$	2.60633	+	8.02147i	0.222674	+	0.685320i	−0.775845	+	0.630923i	$0.782676\pi$
$138$		0			0
$139$	−4.91470	+	15.1259i	−0.416860	+	1.28296i	0.493717	+	0.869622i	$0.335638\pi$
$139$	−4.91470	+	15.1259i	−0.416860	+	1.28296i	−0.910577	+	0.413340i	$0.864362\pi$
$140$		0			0
$141$	0.191633	+	0.589786i	0.0161384	+	0.0496690i
$142$		0			0
$143$	1.04148			0.0870928
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.195285	−	0.141883i	−0.0161068	−	0.0117023i
$148$		0			0
$149$	8.35969			0.684852			0.342426	−	0.939545i	$-0.388751\pi$
$149$	8.35969			0.684852			0.342426	+	0.939545i	$0.388751\pi$
$150$		0			0
$151$	−5.35624			−0.435885			−0.217942	−	0.975962i	$-0.569934\pi$
$151$	−5.35624			−0.435885			−0.217942	+	0.975962i	$0.569934\pi$
$152$		0			0
$153$	−9.46734	−	6.87843i	−0.765389	−	0.556088i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−13.3180			−1.06289			−0.531446	−	0.847092i	$-0.678351\pi$
$157$	−13.3180			−1.06289			−0.531446	+	0.847092i	$0.678351\pi$
$158$		0			0
$159$	0.0204789	+	0.0630277i	0.00162408	+	0.00499842i
$160$		0			0
$161$	3.87932	−	11.9393i	0.305734	−	0.940951i
$162$		0			0
$163$	4.38148	+	13.4848i	0.343184	+	1.05621i	0.962549	+	0.271109i	$0.0873903\pi$
$163$	4.38148	+	13.4848i	0.343184	+	1.05621i	−0.619364	+	0.785104i	$0.712610\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−18.3470	+	13.3299i	−1.41973	+	1.03150i	−0.427916	+	0.903818i	$0.640752\pi$
$167$	−18.3470	+	13.3299i	−1.41973	+	1.03150i	−0.991816	+	0.127677i	$0.959248\pi$
$168$		0			0
$169$	10.2623	−	7.45601i	0.789409	−	0.573539i
$170$		0			0
$171$	14.0608	+	10.2158i	1.07526	+	0.781220i
$172$		0			0
$173$	−2.09238	+	6.43969i	−0.159081	+	0.489601i	−0.998551	−	0.0538045i	$-0.982865\pi$
$173$	−2.09238	+	6.43969i	−0.159081	+	0.489601i	0.839471	+	0.543405i	$0.182865\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−0.0931189	+	0.286590i	−0.00699924	+	0.0215415i
$178$		0			0
$179$	20.3012	+	14.7497i	1.51739	+	1.10245i	0.962764	+	0.270342i	$0.0871368\pi$
$179$	20.3012	+	14.7497i	1.51739	+	1.10245i	0.554621	+	0.832103i	$0.312863\pi$
$180$		0			0
$181$	−20.3908	+	14.8148i	−1.51564	+	1.10117i	−0.552039	+	0.833818i	$0.686150\pi$
$181$	−20.3908	+	14.8148i	−1.51564	+	1.10117i	−0.963598	+	0.267356i	$0.913850\pi$
$182$		0			0
$183$	0.652608	−	0.474148i	0.0482422	−	0.0350500i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−2.23917	−	6.89146i	−0.163744	−	0.503953i
$188$		0			0
$189$	0.189472	−	0.583133i	0.0137820	−	0.0424167i
$190$		0			0
$191$	−6.14957	−	18.9264i	−0.444967	−	1.36947i	−0.882520	−	0.470275i	$-0.844155\pi$
$191$	−6.14957	−	18.9264i	−0.444967	−	1.36947i	0.437552	−	0.899193i	$-0.355845\pi$
$192$		0			0
$193$	4.79198			0.344934			0.172467	−	0.985015i	$-0.444826\pi$
$193$	4.79198			0.344934			0.172467	+	0.985015i	$0.444826\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−0.542119	−	0.393872i	−0.0386244	−	0.0280622i	0.568306	−	0.822818i	$-0.307599\pi$
$197$	−0.542119	−	0.393872i	−0.0386244	−	0.0280622i	−0.606930	+	0.794755i	$0.707599\pi$
$198$		0			0
$199$	9.41311			0.667278			0.333639	−	0.942701i	$-0.391723\pi$
$199$	9.41311			0.667278			0.333639	+	0.942701i	$0.391723\pi$
$200$		0			0
$201$	0.0743612			0.00524504
$202$		0			0
$203$	−3.66886	−	2.66558i	−0.257503	−	0.187087i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−21.9116			−1.52296
$208$		0			0
$209$	3.32560	+	10.2351i	0.230036	+	0.707979i
$210$		0			0
$211$	−3.80217	+	11.7019i	−0.261752	+	0.805589i	0.730672	+	0.682729i	$0.239207\pi$
$211$	−3.80217	+	11.7019i	−0.261752	+	0.805589i	−0.992424	+	0.122861i	$0.960793\pi$
$212$		0			0
$213$	0.247866	+	0.762854i	0.0169835	+	0.0522699i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	2.68217	−	1.94871i	0.182078	−	0.132287i
$218$		0			0
$219$	0.197070	−	0.143180i	0.0133168	−	0.00967519i
$220$		0			0
$221$	1.77349	+	1.28852i	0.119298	+	0.0866750i
$222$		0			0
$223$	4.36656	−	13.4389i	0.292406	−	0.899934i	−0.691674	−	0.722210i	$-0.743127\pi$
$223$	4.36656	−	13.4389i	0.292406	−	0.899934i	0.984080	−	0.177724i	$-0.0568735\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.21158	+	3.72885i	−0.0804151	+	0.247492i	−0.983179	−	0.182644i	$-0.941534\pi$
$227$	−1.21158	+	3.72885i	−0.0804151	+	0.247492i	0.902764	+	0.430136i	$0.141534\pi$
$228$		0			0
$229$	−2.16082	−	1.56993i	−0.142791	−	0.103744i	0.514096	−	0.857732i	$-0.328127\pi$
$229$	−2.16082	−	1.56993i	−0.142791	−	0.103744i	−0.656887	+	0.753989i	$0.728127\pi$
$230$		0			0
$231$	0.153485	−	0.111514i	0.0100986	−	0.00733705i
$232$		0			0
$233$	−18.1188	+	13.1641i	−1.18700	+	0.862409i	−0.992944	−	0.118581i	$-0.962165\pi$
$233$	−18.1188	+	13.1641i	−1.18700	+	0.862409i	−0.194059	+	0.980990i	$0.562165\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.119542	−	0.367912i	−0.00776508	−	0.0238985i
$238$		0			0
$239$	6.69719	−	20.6118i	0.433205	−	1.33327i	−0.461710	−	0.887031i	$-0.652764\pi$
$239$	6.69719	−	20.6118i	0.433205	−	1.33327i	0.894915	−	0.446237i	$-0.147236\pi$
$240$		0			0
$241$	5.45316	+	16.7831i	0.351269	+	1.08109i	0.958141	+	0.286296i	$0.0924239\pi$
$241$	5.45316	+	16.7831i	0.351269	+	1.08109i	−0.606872	+	0.794799i	$0.707576\pi$
$242$		0			0
$243$	−1.60560			−0.103000
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2.63397	−	1.91369i	−0.167596	−	0.121765i
$248$		0			0
$249$	−0.0543904			−0.00344685
$250$		0			0
$251$	−16.2475			−1.02553			−0.512766	−	0.858528i	$-0.671379\pi$
$251$	−16.2475			−1.02553			−0.512766	+	0.858528i	$0.671379\pi$
$252$		0			0
$253$	−10.9765	−	7.97493i	−0.690090	−	0.501379i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.12754			−0.569361			−0.284680	−	0.958623i	$-0.591887\pi$
$257$	−9.12754			−0.569361			−0.284680	+	0.958623i	$0.591887\pi$
$258$		0			0
$259$	−0.404692	−	1.24551i	−0.0251463	−	0.0773924i
$260$		0			0
$261$	−2.44599	+	7.52800i	−0.151403	+	0.465971i
$262$		0			0
$263$	5.93742	+	18.2735i	0.366117	+	1.12679i	0.949279	+	0.314436i	$0.101816\pi$
$263$	5.93742	+	18.2735i	0.366117	+	1.12679i	−0.583161	+	0.812356i	$0.698184\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.252274	−	0.183288i	0.0154389	−	0.0112170i
$268$		0			0
$269$	−4.36357	+	3.17032i	−0.266052	+	0.193298i	−0.712811	−	0.701356i	$-0.752578\pi$
$269$	−4.36357	+	3.17032i	−0.266052	+	0.193298i	0.446759	+	0.894654i	$0.352578\pi$
$270$		0			0
$271$	17.3290	+	12.5902i	1.05266	+	0.764803i	0.972717	−	0.231996i	$-0.0745258\pi$
$271$	17.3290	+	12.5902i	1.05266	+	0.764803i	0.0799442	+	0.996799i	$0.474526\pi$
$272$		0			0
$273$	−0.0177361	+	0.0545861i	−0.00107344	+	0.00330370i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−4.45635	+	13.7152i	−0.267756	+	0.824068i	0.723290	+	0.690545i	$0.242629\pi$
$277$	−4.45635	+	13.7152i	−0.267756	+	0.824068i	−0.991046	+	0.133524i	$0.957371\pi$
$278$		0			0
$279$	−4.68151	−	3.40132i	−0.280275	−	0.203632i
$280$		0			0
$281$	−10.6166	+	7.71340i	−0.633332	+	0.460143i	−0.857553	−	0.514395i	$-0.828016\pi$
$281$	−10.6166	+	7.71340i	−0.633332	+	0.460143i	0.224221	+	0.974538i	$0.428016\pi$
$282$		0			0
$283$	−21.4630	+	15.5938i	−1.27584	+	0.926953i	−0.999419	−	0.0340827i	$-0.989149\pi$
$283$	−21.4630	+	15.5938i	−1.27584	+	0.926953i	−0.276423	+	0.961036i	$0.589149\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5.16117	−	15.8844i	−0.304654	−	0.937629i
$288$		0			0
$289$	−0.540169	+	1.66247i	−0.0317747	+	0.0977923i
$290$		0			0
$291$	−0.267443	−	0.823105i	−0.0156778	−	0.0482513i
$292$		0			0
$293$	24.1828			1.41277			0.706386	−	0.707827i	$-0.250324\pi$
$293$	24.1828			1.41277			0.706386	+	0.707827i	$0.250324\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.536110	−	0.389506i	−0.0311082	−	0.0226015i
$298$		0			0
$299$	4.10464			0.237377
$300$		0			0
$301$	16.6314			0.958621
$302$		0			0
$303$	−0.0891380	−	0.0647625i	−0.00512084	−	0.00372051i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	19.1169			1.09106			0.545530	−	0.838091i	$-0.316328\pi$
$307$	19.1169			1.09106			0.545530	+	0.838091i	$0.316328\pi$
$308$		0			0
$309$	−0.189866	−	0.584348i	−0.0108011	−	0.0332424i
$310$		0			0
$311$	7.01668	−	21.5951i	0.397879	−	1.22455i	−0.528817	−	0.848736i	$-0.677364\pi$
$311$	7.01668	−	21.5951i	0.397879	−	1.22455i	0.926696	−	0.375811i	$-0.122636\pi$
$312$		0			0
$313$	−4.14797	−	12.7661i	−0.234457	−	0.721585i	−0.997193	−	0.0748747i	$-0.976144\pi$
$313$	−4.14797	−	12.7661i	−0.234457	−	0.721585i	0.762736	−	0.646710i	$-0.223856\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	22.0105	−	15.9915i	1.23623	−	0.898174i	0.238889	−	0.971047i	$-0.423217\pi$
$317$	22.0105	−	15.9915i	1.23623	−	0.898174i	0.997341	+	0.0728730i	$0.0232168\pi$
$318$		0			0
$319$	−3.96520	+	2.88089i	−0.222009	+	0.161299i
$320$		0			0
$321$	0.728370	+	0.529192i	0.0406537	+	0.0295366i
$322$		0			0
$323$	−6.99988	+	21.5434i	−0.389484	+	1.19871i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	0.0834719	−	0.256900i	0.00461601	−	0.0142066i
$328$		0			0
$329$	14.4608	+	10.5064i	0.797252	+	0.579238i
$330$		0			0
$331$	−23.3469	+	16.9625i	−1.28326	+	0.932344i	−0.999646	−	0.0265941i	$-0.991534\pi$
$331$	−23.3469	+	16.9625i	−1.28326	+	0.932344i	−0.283615	+	0.958938i	$0.591534\pi$
$332$		0			0
$333$	−1.84927	+	1.34357i	−0.101339	+	0.0736272i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	6.48418	+	19.9562i	0.353216	+	1.08709i	0.957037	+	0.289966i	$0.0936440\pi$
$337$	6.48418	+	19.9562i	0.353216	+	1.08709i	−0.603821	+	0.797120i	$0.706356\pi$
$338$		0			0
$339$	−0.287649	+	0.885294i	−0.0156230	+	0.0480825i
$340$		0			0
$341$	−1.10725	−	3.40776i	−0.0599609	−	0.184541i
$342$		0			0
$343$	−18.9748			−1.02455
$344$		0			0
$345$		0			0
$346$		0			0
$347$	14.2570	+	10.3583i	0.765355	+	0.556063i	0.900548	−	0.434756i	$-0.143165\pi$
$347$	14.2570	+	10.3583i	0.765355	+	0.556063i	−0.135193	+	0.990819i	$0.543165\pi$
$348$		0			0
$349$	13.6103			0.728544			0.364272	−	0.931293i	$-0.381318\pi$
$349$	13.6103			0.728544			0.364272	+	0.931293i	$0.381318\pi$
$350$		0			0
$351$	0.200476			0.0107006
$352$		0			0
$353$	10.5459	+	7.66202i	0.561299	+	0.407808i	0.831934	−	0.554874i	$-0.187234\pi$
$353$	10.5459	+	7.66202i	0.561299	+	0.407808i	−0.270635	+	0.962682i	$0.587234\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.399328			0.0211347
$358$		0			0
$359$	−4.59073	−	14.1288i	−0.242289	−	0.745690i	−0.996070	−	0.0885643i	$-0.971772\pi$
$359$	−4.59073	−	14.1288i	−0.242289	−	0.745690i	0.753781	−	0.657126i	$-0.228228\pi$
$360$		0			0
$361$	4.52484	−	13.9260i	0.238150	−	0.732949i
$362$		0			0
$363$	0.139096	+	0.428095i	0.00730067	+	0.0224691i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−21.4062	+	15.5525i	−1.11740	+	0.811836i	−0.983812	−	0.179202i	$-0.942649\pi$
$367$	−21.4062	+	15.5525i	−1.11740	+	0.811836i	−0.133584	+	0.991038i	$0.542649\pi$
$368$		0			0
$369$	−23.5843	+	17.1350i	−1.22775	+	0.892013i
$370$		0			0
$371$	1.54536	+	1.12277i	0.0802312	+	0.0582914i
$372$		0			0
$373$	10.3367	−	31.8132i	0.535215	−	1.64722i	−0.207968	−	0.978136i	$-0.566685\pi$
$373$	10.3367	−	31.8132i	0.535215	−	1.64722i	0.743183	−	0.669088i	$-0.233315\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.458201	−	1.41020i	0.0235986	−	0.0726289i
$378$		0			0
$379$	−19.6075	−	14.2457i	−1.00717	−	0.731753i	−0.0435574	−	0.999051i	$-0.513869\pi$
$379$	−19.6075	−	14.2457i	−1.00717	−	0.731753i	−0.963614	+	0.267298i	$0.913869\pi$
$380$		0			0
$381$	−0.0646596	+	0.0469779i	−0.00331261	+	0.00240675i
$382$		0			0
$383$	2.06777	−	1.50232i	0.105658	−	0.0767650i	−0.533702	−	0.845673i	$-0.679200\pi$
$383$	2.06777	−	1.50232i	0.105658	−	0.0767650i	0.639360	+	0.768908i	$0.279200\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−8.97041	−	27.6081i	−0.455992	−	1.40340i
$388$		0			0
$389$	−3.92452	+	12.0784i	−0.198981	+	0.612400i	0.800926	+	0.598763i	$0.204341\pi$
$389$	−3.92452	+	12.0784i	−0.198981	+	0.612400i	−0.999907	+	0.0136371i	$0.995659\pi$
$390$		0			0
$391$	−8.82494	−	27.1604i	−0.446296	−	1.37356i
$392$		0			0
$393$	−0.824556			−0.0415933
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−16.2097	−	11.7770i	−0.813541	−	0.591072i	0.101314	−	0.994855i	$-0.467695\pi$
$397$	−16.2097	−	11.7770i	−0.813541	−	0.591072i	−0.914855	+	0.403782i	$0.867695\pi$
$398$		0			0
$399$	−0.593079			−0.0296911
$400$		0			0
$401$	0.685119			0.0342132			0.0171066	−	0.999854i	$-0.494555\pi$
$401$	0.685119			0.0342132			0.0171066	+	0.999854i	$0.494555\pi$
$402$		0			0
$403$	0.876975	+	0.637160i	0.0436852	+	0.0317392i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.41539			−0.0701583
$408$		0			0
$409$	−0.120676	−	0.371402i	−0.00596704	−	0.0183647i	0.948029	−	0.318185i	$-0.103073\pi$
$409$	−0.120676	−	0.371402i	−0.00596704	−	0.0183647i	−0.953996	+	0.299820i	$0.903073\pi$
$410$		0			0
$411$	−0.155235	+	0.477764i	−0.00765718	+	0.0235664i
$412$		0			0
$413$	2.68402	+	8.26056i	0.132072	+	0.406476i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.766359	+	0.556792i	−0.0375288	+	0.0272662i
$418$		0			0
$419$	13.9723	−	10.1515i	0.682591	−	0.495931i	−0.191625	−	0.981468i	$-0.561376\pi$
$419$	13.9723	−	10.1515i	0.682591	−	0.495931i	0.874216	+	0.485537i	$0.161376\pi$
$420$		0			0
$421$	14.0506	+	10.2083i	0.684784	+	0.497524i	0.874941	−	0.484229i	$-0.160900\pi$
$421$	14.0506	+	10.2083i	0.684784	+	0.497524i	−0.190158	+	0.981754i	$0.560900\pi$
$422$		0			0
$423$	9.64092	−	29.6717i	0.468758	−	1.44269i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	7.18497	−	22.1131i	0.347705	−	1.07013i
$428$		0			0
$429$	0.0501843	+	0.0364610i	0.00242292	+	0.00176035i
$430$		0			0
$431$	27.9780	−	20.3272i	1.34765	−	0.979126i	0.348526	−	0.937299i	$-0.386682\pi$
$431$	27.9780	−	20.3272i	1.34765	−	0.979126i	0.999125	−	0.0418269i	$-0.0133178\pi$
$432$		0			0
$433$	30.7353	−	22.3305i	1.47704	−	1.07314i	0.498550	−	0.866861i	$-0.333866\pi$
$433$	30.7353	−	22.3305i	1.47704	−	1.07314i	0.978494	−	0.206275i	$-0.0661341\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	13.1067	+	40.3383i	0.626979	+	1.92964i
$438$		0			0
$439$	1.45680	−	4.48356i	0.0695291	−	0.213989i	−0.910254	−	0.414050i	$-0.864114\pi$
$439$	1.45680	−	4.48356i	0.0695291	−	0.213989i	0.979783	+	0.200061i	$0.0641140\pi$
$440$		0			0
$441$	3.75268	+	11.5495i	0.178699	+	0.549979i
$442$		0			0
$443$	30.4179			1.44520			0.722600	−	0.691267i	$-0.242947\pi$
$443$	30.4179			1.44520			0.722600	+	0.691267i	$0.242947\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.402817	+	0.292663i	0.0190526	+	0.0138425i
$448$		0			0
$449$	−13.7761			−0.650133			−0.325067	−	0.945691i	$-0.605387\pi$
$449$	−13.7761			−0.650133			−0.325067	+	0.945691i	$0.605387\pi$
$450$		0			0
$451$	−18.0510			−0.849986
$452$		0			0
$453$	−0.258094	−	0.187516i	−0.0121263	−	0.00881027i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	14.6462			0.685122			0.342561	−	0.939496i	$-0.388706\pi$
$457$	14.6462			0.685122			0.342561	+	0.939496i	$0.388706\pi$
$458$		0			0
$459$	−0.431022	−	1.32655i	−0.0201184	−	0.0619180i
$460$		0			0
$461$	6.89410	−	21.2179i	0.321090	−	0.988215i	−0.652084	−	0.758147i	$-0.726105\pi$
$461$	6.89410	−	21.2179i	0.321090	−	0.988215i	0.973175	−	0.230068i	$-0.0738949\pi$
$462$		0			0
$463$	−4.94346	−	15.2144i	−0.229742	−	0.707073i	−0.997776	−	0.0666636i	$-0.978765\pi$
$463$	−4.94346	−	15.2144i	−0.229742	−	0.707073i	0.768033	−	0.640410i	$-0.221235\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.94787	−	5.04792i	0.321509	−	0.233590i	−0.415310	−	0.909680i	$-0.636327\pi$
$467$	6.94787	−	5.04792i	0.321509	−	0.233590i	0.736819	+	0.676090i	$0.236327\pi$
$468$		0			0
$469$	1.73401	−	1.25983i	0.0800692	−	0.0581737i
$470$		0			0
$471$	−0.641736	−	0.466248i	−0.0295696	−	0.0214836i
$472$		0			0
$473$	5.55452	−	17.0951i	0.255397	−	0.786032i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.03028	−	3.17087i	0.0471732	−	0.145184i
$478$		0			0
$479$	−3.64835	−	2.65068i	−0.166697	−	0.121113i	0.501309	−	0.865268i	$-0.332852\pi$
$479$	−3.64835	−	2.65068i	−0.166697	−	0.121113i	−0.668006	+	0.744156i	$0.732852\pi$
$480$		0			0
$481$	0.346418	−	0.251687i	0.0157953	−	0.0114760i
$482$		0			0
$483$	0.604910	−	0.439493i	0.0275244	−	0.0199976i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−2.17503	−	6.69405i	−0.0985599	−	0.303336i	0.889605	−	0.456730i	$-0.150980\pi$
$487$	−2.17503	−	6.69405i	−0.0985599	−	0.303336i	−0.988165	+	0.153394i	$0.950980\pi$
$488$		0			0
$489$	−0.260964	+	0.803165i	−0.0118012	+	0.0363204i
$490$		0			0
$491$	−7.80243	−	24.0134i	−0.352119	−	1.08371i	−0.957661	−	0.287897i	$-0.907044\pi$
$491$	−7.80243	−	24.0134i	−0.352119	−	1.08371i	0.605543	−	0.795813i	$-0.292956\pi$
$492$		0			0
$493$	−10.3164			−0.464628
$494$		0			0
$495$		0			0
$496$		0			0
$497$	18.7042	+	13.5894i	0.839000	+	0.609569i
$498$		0			0
$499$	−22.8665			−1.02364			−0.511822	−	0.859092i	$-0.671029\pi$
$499$	−22.8665			−1.02364			−0.511822	+	0.859092i	$0.671029\pi$
$500$		0			0
$501$	−1.35072			−0.0603459
$502$		0			0
$503$	7.13284	+	5.18231i	0.318038	+	0.231068i	0.735338	−	0.677701i	$-0.237024\pi$
$503$	7.13284	+	5.18231i	0.318038	+	0.231068i	−0.417300	+	0.908769i	$0.637024\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.755523			0.0335539
$508$		0			0
$509$	6.02799	+	18.5522i	0.267186	+	0.822314i	0.991182	+	0.132509i	$0.0423035\pi$
$509$	6.02799	+	18.5522i	0.267186	+	0.822314i	−0.723996	+	0.689804i	$0.757697\pi$
$510$		0			0
$511$	2.16967	−	6.67755i	0.0959804	−	0.295397i
$512$		0			0
$513$	0.640150	+	1.97018i	0.0282633	+	0.0869856i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	15.6289	−	11.3551i	0.687358	−	0.499395i
$518$		0			0
$519$	−0.326269	+	0.237048i	−0.0143216	+	0.0104053i
$520$		0			0
$521$	−10.7036	−	7.77662i	−0.468933	−	0.340700i	0.328092	−	0.944646i	$-0.393594\pi$
$521$	−10.7036	−	7.77662i	−0.468933	−	0.340700i	−0.797025	+	0.603946i	$0.793594\pi$
$522$		0			0
$523$	−13.1941	+	40.6072i	−0.576937	+	1.77563i	0.0525482	+	0.998618i	$0.483266\pi$
$523$	−13.1941	+	40.6072i	−0.576937	+	1.77563i	−0.629486	+	0.777012i	$0.716734\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.33059	−	7.17283i	0.101522	−	0.312453i
$528$		0			0
$529$	−24.6530	−	17.9114i	−1.07187	−	0.778758i
$530$		0			0
$531$	12.2648	−	8.91090i	0.532247	−	0.386700i
$532$		0			0
$533$	4.41799	−	3.20985i	0.191364	−	0.139034i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.461856	+	1.42145i	0.0199306	+	0.0613400i
$538$		0			0
$539$	−2.32368	+	7.15154i	−0.100088	+	0.308039i
$540$		0			0
$541$	2.59118	+	7.97483i	0.111404	+	0.342865i	0.991180	−	0.132523i	$-0.0423078\pi$
$541$	2.59118	+	7.97483i	0.111404	+	0.342865i	−0.879776	+	0.475388i	$0.842308\pi$
$542$		0			0
$543$	−1.50119			−0.0644224
$544$		0			0
$545$		0			0
$546$		0			0
$547$	11.6881	+	8.49189i	0.499747	+	0.363087i	0.808920	−	0.587918i	$-0.200052\pi$
$547$	11.6881	+	8.49189i	0.499747	+	0.363087i	−0.309174	+	0.951006i	$0.600052\pi$
$548$		0			0
$549$	−40.5829			−1.73203
$550$		0			0
$551$	15.3218			0.652732
$552$		0			0
$553$	−9.02076	−	6.55396i	−0.383602	−	0.278703i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	17.2330			0.730187			0.365093	−	0.930971i	$-0.381037\pi$
$557$	17.2330			0.730187			0.365093	+	0.930971i	$0.381037\pi$
$558$		0			0
$559$	1.68040	+	5.17175i	0.0710734	+	0.218742i
$560$		0			0
$561$	0.133367	−	0.410460i	0.00563074	−	0.0173296i
$562$		0			0
$563$	−2.20350	−	6.78168i	−0.0928665	−	0.285814i	0.893825	−	0.448415i	$-0.148011\pi$
$563$	−2.20350	−	6.78168i	−0.0928665	−	0.285814i	−0.986692	+	0.162602i	$0.948011\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−12.4556	+	9.04953i	−0.523086	+	0.380044i
$568$		0			0
$569$	11.5916	−	8.42179i	0.485945	−	0.353060i	−0.317678	−	0.948199i	$-0.602903\pi$
$569$	11.5916	−	8.42179i	0.485945	−	0.353060i	0.803623	+	0.595139i	$0.202903\pi$
$570$		0			0
$571$	−8.30283	−	6.03236i	−0.347462	−	0.252446i	0.400341	−	0.916366i	$-0.368892\pi$
$571$	−8.30283	−	6.03236i	−0.347462	−	0.252446i	−0.747804	+	0.663920i	$0.768892\pi$
$572$		0			0
$573$	0.366273	−	1.12727i	0.0153013	−	0.0470924i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	2.96534	−	9.12639i	0.123449	−	0.379937i	−0.870166	−	0.492758i	$-0.835989\pi$
$577$	2.96534	−	9.12639i	0.123449	−	0.379937i	0.993615	+	0.112821i	$0.0359888\pi$
$578$		0			0
$579$	0.230904	+	0.167762i	0.00959606	+	0.00697194i
$580$		0			0
$581$	−1.26832	+	0.921485i	−0.0526186	+	0.0382296i
$582$		0			0
$583$	1.67019	−	1.21346i	0.0691720	−	0.0502564i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.63478	−	5.03134i	−0.0674747	−	0.207666i	0.911634	−	0.411003i	$-0.134821\pi$
$587$	−1.63478	−	5.03134i	−0.0674747	−	0.207666i	−0.979109	+	0.203337i	$0.934821\pi$
$588$		0			0
$589$	−3.46138	+	10.6530i	−0.142624	+	0.438950i
$590$		0			0
$591$	−0.0123333	−	0.0379580i	−0.000507324	−	0.00156138i
$592$		0			0
$593$	2.21453			0.0909397			0.0454699	−	0.998966i	$-0.485522\pi$
$593$	2.21453			0.0909397			0.0454699	+	0.998966i	$0.485522\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.453577	+	0.329543i	0.0185637	+	0.0134873i
$598$		0			0
$599$	1.85018			0.0755964			0.0377982	−	0.999285i	$-0.487966\pi$
$599$	1.85018			0.0755964			0.0377982	+	0.999285i	$0.487966\pi$
$600$		0			0
$601$	32.8477			1.33988			0.669942	−	0.742413i	$-0.266319\pi$
$601$	32.8477			1.33988			0.669942	+	0.742413i	$0.266319\pi$
$602$		0			0
$603$	−3.02658	−	2.19894i	−0.123252	−	0.0895477i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	29.1371			1.18264			0.591319	−	0.806438i	$-0.298608\pi$
$607$	29.1371			1.18264			0.591319	+	0.806438i	$0.298608\pi$
$608$		0			0
$609$	−0.0834671	−	0.256885i	−0.00338226	−	0.0104095i
$610$		0			0
$611$	−1.80601	+	5.55832i	−0.0730632	+	0.224865i
$612$		0			0
$613$	−1.17501	−	3.61632i	−0.0474584	−	0.146062i	0.924519	−	0.381136i	$-0.124467\pi$
$613$	−1.17501	−	3.61632i	−0.0474584	−	0.146062i	−0.971978	+	0.235074i	$0.924467\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	39.8466	−	28.9502i	1.60416	−	1.16549i	0.725278	−	0.688456i	$-0.241711\pi$
$617$	39.8466	−	28.9502i	1.60416	−	1.16549i	0.878884	−	0.477035i	$-0.158289\pi$
$618$		0			0
$619$	−5.13396	+	3.73004i	−0.206351	+	0.149923i	−0.686161	−	0.727449i	$-0.740706\pi$
$619$	−5.13396	+	3.73004i	−0.206351	+	0.149923i	0.479810	+	0.877372i	$0.340706\pi$
$620$		0			0
$621$	−2.11290	−	1.53511i	−0.0847876	−	0.0616018i
$622$		0			0
$623$	2.77745	−	8.54810i	0.111276	−	0.342472i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.198075	+	0.609612i	−0.00791035	+	0.0243455i
$628$		0			0
$629$	−2.41021	−	1.75112i	−0.0961014	−	0.0698218i
$630$		0			0
$631$	4.48099	−	3.25563i	0.178385	−	0.129604i	−0.495010	−	0.868888i	$-0.664835\pi$
$631$	4.48099	−	3.25563i	0.178385	−	0.129604i	0.673395	+	0.739283i	$0.264835\pi$
$632$		0			0
$633$	−0.592879	+	0.430752i	−0.0235648	+	0.0171208i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−0.702979	−	2.16355i	−0.0278530	−	0.0857228i
$638$		0			0
$639$	12.4700	−	38.3786i	0.493304	−	1.51823i
$640$		0			0
$641$	3.16032	+	9.72646i	0.124825	+	0.384172i	0.993869	−	0.110563i	$-0.0352653\pi$
$641$	3.16032	+	9.72646i	0.124825	+	0.384172i	−0.869044	+	0.494735i	$0.835265\pi$
$642$		0			0
$643$	20.5779			0.811515			0.405757	−	0.913981i	$-0.367008\pi$
$643$	20.5779			0.811515			0.405757	+	0.913981i	$0.367008\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−5.59123	−	4.06226i	−0.219814	−	0.159704i	0.472429	−	0.881369i	$-0.343377\pi$
$647$	−5.59123	−	4.06226i	−0.219814	−	0.159704i	−0.692243	+	0.721665i	$0.743377\pi$
$648$		0			0
$649$	9.38723			0.368481
$650$		0			0
$651$	0.197464			0.00773923
$652$		0			0
$653$	1.34166	+	0.974775i	0.0525033	+	0.0381459i	0.613727	−	0.789518i	$-0.289669\pi$
$653$	1.34166	+	0.974775i	0.0525033	+	0.0381459i	−0.561224	+	0.827664i	$0.689669\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−12.2549			−0.478110
$658$		0			0
$659$	−0.956983	−	2.94529i	−0.0372788	−	0.114732i	0.930685	−	0.365820i	$-0.119212\pi$
$659$	−0.956983	−	2.94529i	−0.0372788	−	0.114732i	−0.967964	+	0.251088i	$0.919212\pi$
$660$		0			0
$661$	−4.38102	+	13.4834i	−0.170402	+	0.524443i	−0.999394	−	0.0348175i	$-0.988915\pi$
$661$	−4.38102	+	13.4834i	−0.170402	+	0.524443i	0.828992	+	0.559261i	$0.188915\pi$
$662$		0			0
$663$	0.0403472	+	0.124176i	0.00156696	+	0.00482259i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−15.6275	+	11.3540i	−0.605099	+	0.439630i
$668$		0			0
$669$	0.680886	−	0.494692i	0.0263246	−	0.0191259i
$670$		0			0
$671$	−20.3299	−	14.7705i	−0.784826	−	0.570210i
$672$		0			0
$673$	−1.58367	+	4.87403i	−0.0610460	+	0.187880i	−0.976929	−	0.213566i	$-0.931492\pi$
$673$	−1.58367	+	4.87403i	−0.0610460	+	0.187880i	0.915883	+	0.401446i	$0.131492\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−8.36884	+	25.7566i	−0.321641	+	0.989908i	0.651294	+	0.758826i	$0.274227\pi$
$677$	−8.36884	+	25.7566i	−0.321641	+	0.989908i	−0.972934	+	0.231082i	$0.925773\pi$
$678$		0			0
$679$	−20.1815	−	14.6627i	−0.774496	−	0.562704i
$680$		0			0
$681$	−0.188923	+	0.137261i	−0.00723956	+	0.00525985i
$682$		0			0
$683$	11.8925	−	8.64040i	0.455053	−	0.330616i	−0.336534	−	0.941671i	$-0.609255\pi$
$683$	11.8925	−	8.64040i	0.455053	−	0.330616i	0.791588	+	0.611056i	$0.209255\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−0.0491590	−	0.151296i	−0.00187553	−	0.00577229i
$688$		0			0
$689$	−0.192999	+	0.593991i	−0.00735269	+	0.0226293i
$690$		0			0
$691$	4.25630	+	13.0995i	0.161917	+	0.498330i	0.998796	−	0.0490586i	$-0.0156221\pi$
$691$	4.25630	+	13.0995i	0.161917	+	0.498330i	−0.836879	+	0.547388i	$0.815622\pi$
$692$		0			0
$693$	−9.54458			−0.362569
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−30.7382	−	22.3326i	−1.16429	−	0.845909i
$698$		0			0
$699$	−1.33393			−0.0504538
$700$		0			0
$701$	3.95616			0.149422			0.0747111	−	0.997205i	$-0.476197\pi$
$701$	3.95616			0.149422			0.0747111	+	0.997205i	$0.476197\pi$
$702$		0			0
$703$	3.57962	+	2.60075i	0.135008	+	0.0980891i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.17580			−0.119438
$708$		0			0
$709$	−10.5384	−	32.4338i	−0.395777	−	1.21808i	−0.928355	−	0.371696i	$-0.878776\pi$
$709$	−10.5384	−	32.4338i	−0.395777	−	1.21808i	0.532577	−	0.846381i	$-0.321224\pi$
$710$		0			0
$711$	−6.01406	+	18.5094i	−0.225545	+	0.694156i
$712$		0			0
$713$	−4.36385	−	13.4305i	−0.163427	−	0.502978i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.04431	−	0.758732i	0.0390003	−	0.0283354i
$718$		0			0
$719$	−18.8977	+	13.7300i	−0.704766	+	0.512043i	−0.881481	−	0.472220i	$-0.843453\pi$
$719$	−18.8977	+	13.7300i	−0.704766	+	0.512043i	0.176715	+	0.984262i	$0.443453\pi$
$720$		0			0
$721$	−14.3275	−	10.4095i	−0.533584	−	0.387672i
$722$		0			0
$723$	−0.324794	+	0.999614i	−0.0120792	+	0.0371760i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−3.95904	+	12.1847i	−0.146833	+	0.451904i	−0.997242	−	0.0742170i	$-0.976354\pi$
$727$	−3.95904	+	12.1847i	−0.146833	+	0.451904i	0.850409	+	0.526121i	$0.176354\pi$
$728$		0			0
$729$	21.6886	+	15.7577i	0.803283	+	0.583619i
$730$		0			0
$731$	30.6086	−	22.2384i	1.13210	−	0.822518i
$732$		0			0
$733$	21.6920	−	15.7602i	0.801213	−	0.582115i	−0.110057	−	0.993925i	$-0.535103\pi$
$733$	21.6920	−	15.7602i	0.801213	−	0.582115i	0.911270	+	0.411810i	$0.135103\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.715832	−	2.20310i	−0.0263680	−	0.0811524i
$738$		0			0
$739$	−15.7123	+	48.3574i	−0.577986	+	1.77886i	0.0477941	+	0.998857i	$0.484781\pi$
$739$	−15.7123	+	48.3574i	−0.577986	+	1.77886i	−0.625780	+	0.780000i	$0.715219\pi$
$740$		0			0
$741$	−0.0599233	−	0.184425i	−0.00220134	−	0.00677502i
$742$		0			0
$743$	−25.4540			−0.933816			−0.466908	−	0.884306i	$-0.654632\pi$
$743$	−25.4540			−0.933816			−0.466908	+	0.884306i	$0.654632\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.21374	+	1.60838i	0.0809966	+	0.0588475i
$748$		0			0
$749$	25.9503			0.948203
$750$		0			0
$751$	−21.1719			−0.772574			−0.386287	−	0.922379i	$-0.626243\pi$
$751$	−21.1719			−0.772574			−0.386287	+	0.922379i	$0.626243\pi$
$752$		0			0
$753$	−0.782895	−	0.568806i	−0.0285303	−	0.0207285i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−34.8326			−1.26601			−0.633006	−	0.774147i	$-0.718179\pi$
$757$	−34.8326			−1.26601			−0.633006	+	0.774147i	$0.718179\pi$
$758$		0			0
$759$	−0.249718	−	0.768554i	−0.00906420	−	0.0278967i
$760$		0			0
$761$	−2.49606	+	7.68209i	−0.0904822	+	0.278476i	−0.986050	−	0.166450i	$-0.946770\pi$
$761$	−2.49606	+	7.68209i	−0.0904822	+	0.278476i	0.895568	+	0.444925i	$0.146770\pi$
$762$		0			0
$763$	−2.40596	−	7.40478i	−0.0871015	−	0.268071i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.29753	+	1.66926i	−0.0829591	+	0.0602733i
$768$		0			0
$769$	10.2491	−	7.44644i	0.369593	−	0.268525i	−0.387449	−	0.921891i	$-0.626644\pi$
$769$	10.2491	−	7.44644i	0.369593	−	0.268525i	0.757042	+	0.653366i	$0.226644\pi$
$770$		0			0
$771$	−0.439816	−	0.319545i	−0.0158396	−	0.0115081i
$772$		0			0
$773$	−12.6446	+	38.9161i	−0.454795	+	1.39971i	0.416582	+	0.909098i	$0.363228\pi$
$773$	−12.6446	+	38.9161i	−0.454795	+	1.39971i	−0.871376	+	0.490615i	$0.836772\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.0241037	−	0.0741836i	0.000864716	−	0.00266132i
$778$		0			0
$779$	45.6522	+	33.1682i	1.63566	+	1.18838i
$780$		0			0
$781$	20.2150	−	14.6871i	0.723351	−	0.525545i
$782$		0			0
$783$	−0.763269	+	0.554547i	−0.0272770	+	0.0198179i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	0.801249	+	2.46599i	0.0285615	+	0.0879031i	0.964321	−	0.264735i	$-0.0852846\pi$
$787$	0.801249	+	2.46599i	0.0285615	+	0.0879031i	−0.935760	+	0.352638i	$0.885285\pi$
$788$		0			0
$789$	−0.353637	+	1.08838i	−0.0125898	+	0.0387474i
$790$		0			0
$791$	8.29108	+	25.5173i	0.294797	+	0.907291i
$792$		0			0
$793$	7.60228			0.269965
$794$		0			0
$795$		0			0
$796$		0			0
$797$	17.4095	+	12.6487i	0.616676	+	0.448041i	0.851759	−	0.523934i	$-0.175536\pi$
$797$	17.4095	+	12.6487i	0.616676	+	0.448041i	−0.235083	+	0.971975i	$0.575536\pi$
$798$		0			0
$799$	40.6623			1.43853
$800$		0			0
$801$	−15.6878			−0.554302
$802$		0			0
$803$	−6.13907	−	4.46029i	−0.216643	−	0.157400i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.321251			−0.0113086
$808$		0			0
$809$	−1.07271	−	3.30147i	−0.0377146	−	0.116074i	0.930427	−	0.366478i	$-0.119436\pi$
$809$	−1.07271	−	3.30147i	−0.0377146	−	0.116074i	−0.968141	+	0.250404i	$0.919436\pi$
$810$		0			0
$811$	−11.3665	+	34.9826i	−0.399133	+	1.22841i	0.526563	+	0.850136i	$0.323481\pi$
$811$	−11.3665	+	34.9826i	−0.399133	+	1.22841i	−0.925696	+	0.378269i	$0.876519\pi$
$812$		0			0
$813$	0.394237	+	1.21334i	0.0138265	+	0.0425536i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−45.4596	+	33.0283i	−1.59043	+	1.15552i
$818$		0			0
$819$	2.33604	−	1.69723i	0.0816280	−	0.0593062i
$820$		0			0
$821$	−38.2615	−	27.7986i	−1.33534	−	0.970179i	−0.999602	−	0.0282220i	$-0.991015\pi$
$821$	−38.2615	−	27.7986i	−1.33534	−	0.970179i	−0.335735	−	0.941957i	$-0.608985\pi$
$822$		0			0
$823$	3.23902	−	9.96867i	0.112905	−	0.347486i	−0.878599	−	0.477560i	$-0.841521\pi$
$823$	3.23902	−	9.96867i	0.112905	−	0.347486i	0.991504	+	0.130074i	$0.0415214\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.78324	−	5.48824i	0.0620093	−	0.190845i	−0.915253	−	0.402880i	$-0.868009\pi$
$827$	1.78324	−	5.48824i	0.0620093	−	0.190845i	0.977262	+	0.212035i	$0.0680091\pi$
$828$		0			0
$829$	23.6650	+	17.1936i	0.821919	+	0.597159i	0.917261	−	0.398286i	$-0.130395\pi$
$829$	23.6650	+	17.1936i	0.821919	+	0.597159i	−0.0953427	+	0.995445i	$0.530395\pi$
$830$		0			0
$831$	−0.694887	+	0.504865i	−0.0241054	+	0.0175136i
$832$		0			0
$833$	−12.8048	+	9.30322i	−0.443659	+	0.322337i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.213136	−	0.655966i	−0.00736707	−	0.0226735i
$838$		0			0
$839$	4.96033	−	15.2663i	0.171250	−	0.527052i	−0.828193	−	0.560444i	$-0.810631\pi$
$839$	4.96033	−	15.2663i	0.171250	−	0.527052i	0.999442	+	0.0333911i	$0.0106307\pi$
$840$		0			0
$841$	−6.80517	−	20.9442i	−0.234661	−	0.722212i
$842$		0			0
$843$	−0.781604			−0.0269199
$844$		0			0
$845$		0			0
$846$		0			0
$847$	10.4964	+	7.62605i	0.360659	+	0.262034i
$848$		0			0
$849$	−1.58013			−0.0542298
$850$		0			0
$851$	−5.57828			−0.191221
$852$		0			0
$853$	27.2433	+	19.7934i	0.932792	+	0.677713i	0.946675	−	0.322190i	$-0.104419\pi$
$853$	27.2433	+	19.7934i	0.932792	+	0.677713i	−0.0138826	+	0.999904i	$0.504419\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−18.5384			−0.633260			−0.316630	−	0.948549i	$-0.602551\pi$
$857$	−18.5384			−0.633260			−0.316630	+	0.948549i	$0.602551\pi$
$858$		0			0
$859$	−0.00514740	−	0.0158421i	−0.000175627	−	0.000540524i	0.950969	−	0.309287i	$-0.100090\pi$
$859$	−0.00514740	−	0.0158421i	−0.000175627	−	0.000540524i	−0.951144	+	0.308747i	$0.900090\pi$
$860$		0			0
$861$	0.307403	−	0.946089i	0.0104763	−	0.0322426i
$862$		0			0
$863$	10.2867	+	31.6593i	0.350164	+	1.07769i	0.958761	+	0.284214i	$0.0917328\pi$
$863$	10.2867	+	31.6593i	0.350164	+	1.07769i	−0.608597	+	0.793480i	$0.708267\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−0.0842296	+	0.0611964i	−0.00286059	+	0.00207834i
$868$		0			0
$869$	−9.74939	+	7.08335i	−0.330725	+	0.240286i
$870$		0			0
$871$	0.566961	+	0.411921i	0.0192107	+	0.0139574i
$872$		0			0
$873$	−13.4548	+	41.4098i	−0.455378	+	1.40151i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	12.5958	−	38.7660i	0.425331	−	1.30903i	−0.477346	−	0.878715i	$-0.658401\pi$
$877$	12.5958	−	38.7660i	0.425331	−	1.30903i	0.902677	−	0.430319i	$-0.141599\pi$
$878$		0			0
$879$	1.16526	+	0.846612i	0.0393033	+	0.0285555i
$880$		0			0
$881$	−20.0854	+	14.5929i	−0.676694	+	0.491647i	−0.872259	−	0.489044i	$-0.837346\pi$
$881$	−20.0854	+	14.5929i	−0.676694	+	0.491647i	0.195565	+	0.980691i	$0.437346\pi$
$882$		0			0
$883$	−1.37115	+	0.996201i	−0.0461430	+	0.0335248i	−0.610618	−	0.791926i	$-0.709079\pi$
$883$	−1.37115	+	0.996201i	−0.0461430	+	0.0335248i	0.564475	+	0.825450i	$0.309079\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3.74964	−	11.5402i	−0.125901	−	0.387482i	0.868164	−	0.496278i	$-0.165300\pi$
$887$	−3.74964	−	11.5402i	−0.125901	−	0.387482i	−0.994064	+	0.108796i	$0.965300\pi$
$888$		0			0
$889$	−0.711877	+	2.19093i	−0.0238756	+	0.0734816i
$890$		0			0
$891$	5.14190	+	15.8252i	0.172260	+	0.530163i
$892$		0			0
$893$	−60.3913			−2.02092
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.197784	+	0.143699i	0.00660383	+	0.00479796i
$898$		0			0
$899$	−5.10137			−0.170140
$900$		0			0
$901$	4.34538			0.144766
$902$		0			0
$903$	0.801396	+	0.582249i	0.0266688	+	0.0193760i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−14.9224			−0.495491			−0.247746	−	0.968825i	$-0.579690\pi$
$907$	−14.9224			−0.495491			−0.247746	+	0.968825i	$0.579690\pi$
$908$		0			0
$909$	1.71291	+	5.27180i	0.0568137	+	0.174855i
$910$		0			0
$911$	−14.2166	+	43.7543i	−0.471018	+	1.44964i	0.380236	+	0.924890i	$0.375843\pi$
$911$	−14.2166	+	43.7543i	−0.471018	+	1.44964i	−0.851254	+	0.524754i	$0.824157\pi$
$912$		0			0
$913$	0.523584	+	1.61143i	0.0173281	+	0.0533304i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−19.2276	+	13.9697i	−0.634952	+	0.461319i
$918$		0			0
$919$	4.67512	−	3.39667i	0.154218	−	0.112046i	−0.508000	−	0.861357i	$-0.669615\pi$
$919$	4.67512	−	3.39667i	0.154218	−	0.112046i	0.662218	+	0.749311i	$0.269615\pi$
$920$		0			0
$921$	0.921160	+	0.669262i	0.0303532	+	0.0220529i
$922$		0			0
$923$	−2.33596	+	7.18935i	−0.0768891	+	0.236640i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−9.55202	+	29.3981i	−0.313730	+	0.965560i
$928$		0			0
$929$	−11.1761	−	8.11994i	−0.366677	−	0.266406i	0.389155	−	0.921172i	$-0.372767\pi$
$929$	−11.1761	−	8.11994i	−0.366677	−	0.266406i	−0.755832	+	0.654766i	$0.772767\pi$
$930$		0			0
$931$	19.0175	−	13.8171i	0.623275	−	0.452836i
$932$		0			0
$933$	1.09412	−	0.794928i	0.0358200	−	0.0260248i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	0.746290	+	2.29684i	0.0243802	+	0.0750346i	0.962506	−	0.271259i	$-0.0874400\pi$
$937$	0.746290	+	2.29684i	0.0243802	+	0.0750346i	−0.938126	+	0.346294i	$0.887440\pi$
$938$		0			0
$939$	0.247056	−	0.760360i	0.00806237	−	0.0248134i
$940$		0			0
$941$	9.18367	+	28.2644i	0.299379	+	0.921394i	0.981715	+	0.190356i	$0.0609641\pi$
$941$	9.18367	+	28.2644i	0.299379	+	0.921394i	−0.682336	+	0.731039i	$0.739036\pi$
$942$		0			0
$943$	−71.1417			−2.31669
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.39633	+	5.37375i	0.240348	+	0.174623i	0.701438	−	0.712730i	$-0.252542\pi$
$947$	7.39633	+	5.37375i	0.240348	+	0.174623i	−0.461090	+	0.887353i	$0.652542\pi$
$948$		0			0
$949$	2.29568			0.0745209
$950$		0			0
$951$	1.62043			0.0525461
$952$		0			0
$953$	23.7118	+	17.2277i	0.768102	+	0.558059i	0.901385	−	0.433019i	$-0.142552\pi$
$953$	23.7118	+	17.2277i	0.768102	+	0.558059i	−0.133283	+	0.991078i	$0.542552\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−0.291922			−0.00943651
$958$		0			0
$959$	4.47443	+	13.7709i	0.144487	+	0.444685i
$960$		0			0
$961$	−8.42707	+	25.9359i	−0.271841	+	0.836640i
$962$		0			0
$963$	−13.9967	−	43.0773i	−0.451036	−	1.38815i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	28.0016	−	20.3443i	0.900470	−	0.654230i	−0.0381168	−	0.999273i	$-0.512136\pi$
$967$	28.0016	−	20.3443i	0.900470	−	0.654230i	0.938587	+	0.345044i	$0.112136\pi$
$968$		0			0
$969$	−1.09151	+	0.793025i	−0.0350642	+	0.0254756i
$970$		0			0
$971$	24.0628	+	17.4826i	0.772211	+	0.561044i	0.902631	−	0.430415i	$-0.141633\pi$
$971$	24.0628	+	17.4826i	0.772211	+	0.561044i	−0.130420	+	0.991459i	$0.541633\pi$
$972$		0			0
$973$	−8.43732	+	25.9674i	−0.270488	+	0.832477i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−13.0352	+	40.1184i	−0.417035	+	1.28350i	0.493384	+	0.869812i	$0.335760\pi$
$977$	−13.0352	+	40.1184i	−0.417035	+	1.28350i	−0.910418	+	0.413689i	$0.864240\pi$
$978$		0			0
$979$	−7.85878	−	5.70974i	−0.251168	−	0.182484i
$980$		0			0
$981$	−10.9942	+	7.98775i	−0.351017	+	0.255029i
$982$		0			0
$983$	18.8353	−	13.6846i	0.600752	−	0.436472i	−0.245394	−	0.969424i	$-0.578917\pi$
$983$	18.8353	−	13.6846i	0.600752	−	0.436472i	0.846146	+	0.532952i	$0.178917\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	0.328987	+	1.01252i	0.0104718	+	0.0322288i
$988$		0			0
$989$	21.8913	−	67.3744i	0.696102	−	2.14238i
$990$		0			0
$991$	16.3062	+	50.1854i	0.517984	+	1.59419i	0.777786	+	0.628529i	$0.216343\pi$
$991$	16.3062	+	50.1854i	0.517984	+	1.59419i	−0.259802	+	0.965662i	$0.583657\pi$
$992$		0			0
$993$	−1.71882			−0.0545452
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−47.8165	−	34.7408i	−1.51437	−	1.10025i	−0.964194	−	0.265199i	$-0.914562\pi$
$997$	−47.8165	−	34.7408i	−1.51437	−	1.10025i	−0.550171	−	0.835052i	$-0.685438\pi$
$998$		0			0
$999$	−0.272451			−0.00861997

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.m.d.601.5		32
5.2	odd	4		200.2.q.a.129.5	✓	32
5.3	odd	4		1000.2.q.c.649.4		32
5.4	even	2		1000.2.m.e.601.4		32
20.7	even	4		400.2.y.d.129.4		32
25.6	even	5	inner	1000.2.m.d.401.5		32
25.8	odd	20		200.2.q.a.169.5	yes	32
25.9	even	10		5000.2.a.q.1.9		16
25.16	even	5		5000.2.a.r.1.8		16
25.17	odd	20		1000.2.q.c.849.4		32
25.19	even	10		1000.2.m.e.401.4		32
100.59	odd	10		10000.2.a.br.1.8		16
100.83	even	20		400.2.y.d.369.4		32
100.91	odd	10		10000.2.a.bq.1.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.q.a.129.5	✓	32	5.2	odd	4
200.2.q.a.169.5	yes	32	25.8	odd	20
400.2.y.d.129.4		32	20.7	even	4
400.2.y.d.369.4		32	100.83	even	20
1000.2.m.d.401.5		32	25.6	even	5	inner
1000.2.m.d.601.5		32	1.1	even	1	trivial
1000.2.m.e.401.4		32	25.19	even	10
1000.2.m.e.601.4		32	5.4	even	2
1000.2.q.c.649.4		32	5.3	odd	4
1000.2.q.c.849.4		32	25.17	odd	20
5000.2.a.q.1.9		16	25.9	even	10
5000.2.a.r.1.8		16	25.16	even	5
10000.2.a.bq.1.9		16	100.91	odd	10
10000.2.a.br.1.8		16	100.59	odd	10

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.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0481856 + 0.0350089i) q^{3} +1.71675 q^{7} +(-0.925955 - 2.84980i) q^{9} +(0.573356 - 1.76461i) q^{11} +(0.173457 + 0.533844i) q^{13} +(3.15952 - 2.29552i) q^{17} +(-4.69249 + 3.40929i) q^{19} +(0.0827227 + 0.0601016i) q^{21} +(2.25969 - 6.95461i) q^{23} +(0.110366 - 0.339673i) q^{27} +(-2.13709 - 1.55269i) q^{29} +(1.56235 - 1.13511i) q^{31} +(0.0894045 - 0.0649561i) q^{33} +(-0.235731 - 0.725506i) q^{37} +(-0.0103312 + 0.0317961i) q^{39} +(-3.00636 - 9.25262i) q^{41} +9.68774 q^{43} +(8.42338 + 6.11994i) q^{47} -4.05276 q^{49} +0.232607 q^{51} +(0.900166 + 0.654009i) q^{53} -0.345466 q^{57} +(1.56343 + 4.81174i) q^{59} +(4.18521 - 12.8808i) q^{61} +(-1.58963 - 4.89239i) q^{63} +(1.01005 - 0.733847i) q^{67} +(0.352358 - 0.256003i) q^{69} +(10.8951 + 7.91578i) q^{71} +(1.26382 - 3.88964i) q^{73} +(0.984309 - 3.02939i) q^{77} +(-5.25455 - 3.81765i) q^{79} +(-7.25533 + 5.27131i) q^{81} +(-0.738788 + 0.536761i) q^{83} +(-0.0486192 - 0.149634i) q^{87} +(1.61785 - 4.97923i) q^{89} +(0.297782 + 0.916478i) q^{91} +0.115022 q^{93} +(-11.7557 - 8.54098i) q^{97} -5.55967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{3} + 16 q^{7} - 10 q^{9} + 6 q^{11} - 10 q^{13} - 4 q^{17} + 6 q^{19} - 4 q^{21} + 4 q^{23} - 26 q^{27} + 2 q^{29} + 6 q^{31} - 32 q^{33} - 16 q^{37} + 12 q^{39} + 52 q^{43} + 8 q^{47} + 60 q^{49}+ \cdots - 92 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 + 16 * q^7 - 10 * q^9 + 6 * q^11 - 10 * q^13 - 4 * q^17 + 6 * q^19 - 4 * q^21 + 4 * q^23 - 26 * q^27 + 2 * q^29 + 6 * q^31 - 32 * q^33 - 16 * q^37 + 12 * q^39 + 52 * q^43 + 8 * q^47 + 60 * q^49 - 60 * q^51 - 28 * q^53 + 48 * q^57 + 30 * q^59 + 14 * q^61 + 24 * q^63 + 4 * q^69 + 12 * q^71 + 4 * q^73 - 90 * q^77 - 16 * q^79 - 52 * q^81 - 80 * q^83 - 84 * q^87 - 24 * q^89 - 4 * q^91 + 80 * q^93 + 12 * q^97 - 92 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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