LMFDB - Embedded newform 20.5.f.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,5,Mod(13,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("20.13");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	20.f (of order $4$, degree $2$, 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:	$2.06739926168$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{241})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 121x^{2} + 3600 $ x^4 + 121*x^2 + 3600
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.1
Root			$7.26209i$ of defining polynomial
Character	$\chi$	$=$	20.17
Dual form			20.5.f.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.2621 + 10.2621i) q^{3} +(-24.7863 + 3.26209i) q^{5} +(50.7863 + 50.7863i) q^{7} -129.621i q^{9} +O(q^{10})$	\(q+(-10.2621 + 10.2621i) q^{3} +(-24.7863 + 3.26209i) q^{5} +(50.7863 + 50.7863i) q^{7} -129.621i q^{9} +2.62087 q^{11} +(-43.4275 + 43.4275i) q^{13} +(220.883 - 287.835i) q^{15} +(131.331 + 131.331i) q^{17} +403.725i q^{19} -1042.35 q^{21} +(-334.455 + 334.455i) q^{23} +(603.718 - 161.710i) q^{25} +(498.952 + 498.952i) q^{27} -1172.97i q^{29} +955.313 q^{31} +(-26.8956 + 26.8956i) q^{33} +(-1424.47 - 1093.13i) q^{35} +(673.305 + 673.305i) q^{37} -891.313i q^{39} +818.621 q^{41} +(2.48083 - 2.48083i) q^{43} +(422.835 + 3212.82i) q^{45} +(-1563.81 - 1563.81i) q^{47} +2757.49i q^{49} -2695.46 q^{51} +(277.662 - 277.662i) q^{53} +(-64.9617 + 8.54952i) q^{55} +(-4143.06 - 4143.06i) q^{57} +6333.66i q^{59} +6518.49 q^{61} +(6582.96 - 6582.96i) q^{63} +(934.741 - 1218.07i) q^{65} +(-713.488 - 713.488i) q^{67} -6864.42i q^{69} +288.280 q^{71} +(-5564.19 + 5564.19i) q^{73} +(-4535.92 + 7854.88i) q^{75} +(133.104 + 133.104i) q^{77} -4061.80i q^{79} +258.720 q^{81} +(1284.98 - 1284.98i) q^{83} +(-3683.61 - 2826.79i) q^{85} +(12037.1 + 12037.1i) q^{87} +4418.77i q^{89} -4411.04 q^{91} +(-9803.51 + 9803.51i) q^{93} +(-1316.99 - 10006.8i) q^{95} +(-8805.47 - 8805.47i) q^{97} -339.720i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 10 q^{3} - 6 q^{5} + 110 q^{7}+O(q^{10}) $ 4 * q - 10 * q^3 - 6 * q^5 + 110 * q^7	$ 4 q - 10 q^{3} - 6 q^{5} + 110 q^{7} - 300 q^{11} - 360 q^{13} + 542 q^{15} + 960 q^{17} - 1996 q^{21} - 810 q^{23} + 1856 q^{25} + 2120 q^{27} - 836 q^{31} - 1660 q^{33} - 2562 q^{35} - 660 q^{37} + 2964 q^{41} + 3270 q^{43} + 1474 q^{45} - 2250 q^{47} + 1948 q^{51} + 1980 q^{53} - 6780 q^{55} - 13840 q^{57} + 15828 q^{61} + 12950 q^{63} - 732 q^{65} - 4810 q^{67} - 5988 q^{71} - 14060 q^{73} - 11282 q^{75} - 1020 q^{77} + 8176 q^{81} + 19950 q^{83} + 16376 q^{85} + 24800 q^{87} - 11124 q^{91} - 34060 q^{93} - 15576 q^{95} - 3180 q^{97}+O(q^{100}) $ 4 * q - 10 * q^3 - 6 * q^5 + 110 * q^7 - 300 * q^11 - 360 * q^13 + 542 * q^15 + 960 * q^17 - 1996 * q^21 - 810 * q^23 + 1856 * q^25 + 2120 * q^27 - 836 * q^31 - 1660 * q^33 - 2562 * q^35 - 660 * q^37 + 2964 * q^41 + 3270 * q^43 + 1474 * q^45 - 2250 * q^47 + 1948 * q^51 + 1980 * q^53 - 6780 * q^55 - 13840 * q^57 + 15828 * q^61 + 12950 * q^63 - 732 * q^65 - 4810 * q^67 - 5988 * q^71 - 14060 * q^73 - 11282 * q^75 - 1020 * q^77 + 8176 * q^81 + 19950 * q^83 + 16376 * q^85 + 24800 * q^87 - 11124 * q^91 - 34060 * q^93 - 15576 * q^95 - 3180 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−10.2621	+	10.2621i	−1.14023	+	1.14023i	−0.151824	+	0.988407i	$0.548515\pi$
$3$	−10.2621	+	10.2621i	−1.14023	+	1.14023i	−0.988407	+	0.151824i	$0.951485\pi$
$4$		0			0
$5$	−24.7863	+	3.26209i	−0.991450	+	0.130483i
$5$	−24.7863	+	3.26209i	−0.991450	+	0.130483i
$6$		0			0
$7$	50.7863	+	50.7863i	1.03645	+	1.03645i	0.999310	+	0.0371444i	$0.0118262\pi$
$7$	50.7863	+	50.7863i	1.03645	+	1.03645i	0.0371444	+	0.999310i	$0.488174\pi$
$8$		0			0
$9$		−	129.621i		−	1.60026i
$10$		0			0
$11$	2.62087			0.0216601			0.0108301	−	0.999941i	$-0.496553\pi$
$11$	2.62087			0.0216601			0.0108301	+	0.999941i	$0.496553\pi$
$12$		0			0
$13$	−43.4275	+	43.4275i	−0.256967	+	0.256967i	−0.823820	−	0.566852i	$-0.808161\pi$
$13$	−43.4275	+	43.4275i	−0.256967	+	0.256967i	0.566852	+	0.823820i	$0.308161\pi$
$14$		0			0
$15$	220.883	−	287.835i	0.981702	−	1.27926i
$16$		0			0
$17$	131.331	+	131.331i	0.454432	+	0.454432i	0.896822	−	0.442391i	$-0.145870\pi$
$17$	131.331	+	131.331i	0.454432	+	0.454432i	−0.442391	+	0.896822i	$0.645870\pi$
$18$		0			0
$19$			403.725i			1.11835i	0.829049	+	0.559176i	$0.188882\pi$
$19$			403.725i			1.11835i	−0.829049	+	0.559176i	$0.811118\pi$
$20$		0			0
$21$	−1042.35			−2.36360
$22$		0			0
$23$	−334.455	+	334.455i	−0.632241	+	0.632241i	−0.948630	−	0.316389i	$-0.897530\pi$
$23$	−334.455	+	334.455i	−0.632241	+	0.632241i	0.316389	+	0.948630i	$0.397530\pi$
$24$		0			0
$25$	603.718	−	161.710i	0.965948	−	0.258736i
$26$		0			0
$27$	498.952	+	498.952i	0.684433	+	0.684433i
$28$		0			0
$29$		−	1172.97i		−	1.39473i	−0.716717	−	0.697364i	$-0.754356\pi$
$29$		−	1172.97i		−	1.39473i	0.716717	−	0.697364i	$-0.245644\pi$
$30$		0			0
$31$	955.313			0.994082			0.497041	−	0.867727i	$-0.334420\pi$
$31$	955.313			0.994082			0.497041	+	0.867727i	$0.334420\pi$
$32$		0			0
$33$	−26.8956	+	26.8956i	−0.0246976	+	0.0246976i
$34$		0			0
$35$	−1424.47	−	1093.13i	−1.16283	−	0.892353i
$36$		0			0
$37$	673.305	+	673.305i	0.491823	+	0.491823i	0.908880	−	0.417057i	$-0.136939\pi$
$37$	673.305	+	673.305i	0.491823	+	0.491823i	−0.417057	+	0.908880i	$0.636939\pi$
$38$		0			0
$39$		−	891.313i		−	0.586005i
$40$		0			0
$41$	818.621			0.486984			0.243492	−	0.969903i	$-0.421707\pi$
$41$	818.621			0.486984			0.243492	+	0.969903i	$0.421707\pi$
$42$		0			0
$43$	2.48083	−	2.48083i	0.00134171	−	0.00134171i	−0.706436	−	0.707777i	$-0.749698\pi$
$43$	2.48083	−	2.48083i	0.00134171	−	0.00134171i	0.707777	+	0.706436i	$0.249698\pi$
$44$		0			0
$45$	422.835	+	3212.82i	0.208807	+	1.58658i
$46$		0			0
$47$	−1563.81	−	1563.81i	−0.707926	−	0.707926i	0.258173	−	0.966099i	$-0.416880\pi$
$47$	−1563.81	−	1563.81i	−0.707926	−	0.707926i	−0.966099	+	0.258173i	$0.916880\pi$
$48$		0			0
$49$			2757.49i			1.14848i
$50$		0			0
$51$	−2695.46			−1.03632
$52$		0			0
$53$	277.662	−	277.662i	0.0988471	−	0.0988471i	−0.655954	−	0.754801i	$-0.727733\pi$
$53$	277.662	−	277.662i	0.0988471	−	0.0988471i	0.754801	+	0.655954i	$0.227733\pi$
$54$		0			0
$55$	−64.9617	+	8.54952i	−0.0214749	+	0.00282629i
$56$		0			0
$57$	−4143.06	−	4143.06i	−1.27518	−	1.27518i
$58$		0			0
$59$			6333.66i			1.81949i	0.415163	+	0.909747i	$0.363725\pi$
$59$			6333.66i			1.81949i	−0.415163	+	0.909747i	$0.636275\pi$
$60$		0			0
$61$	6518.49			1.75181			0.875906	−	0.482483i	$-0.160265\pi$
$61$	6518.49			1.75181			0.875906	+	0.482483i	$0.160265\pi$
$62$		0			0
$63$	6582.96	−	6582.96i	1.65859	−	1.65859i
$64$		0			0
$65$	934.741	−	1218.07i	0.221240	−	0.288300i
$66$		0			0
$67$	−713.488	−	713.488i	−0.158942	−	0.158942i	0.623156	−	0.782098i	$-0.285850\pi$
$67$	−713.488	−	713.488i	−0.158942	−	0.158942i	−0.782098	+	0.623156i	$0.785850\pi$
$68$		0			0
$69$		−	6864.42i		−	1.44180i
$70$		0			0
$71$	288.280			0.0571871			0.0285935	−	0.999591i	$-0.490897\pi$
$71$	288.280			0.0571871			0.0285935	+	0.999591i	$0.490897\pi$
$72$		0			0
$73$	−5564.19	+	5564.19i	−1.04413	+	1.04413i	−0.0451542	+	0.998980i	$0.514378\pi$
$73$	−5564.19	+	5564.19i	−1.04413	+	1.04413i	−0.998980	+	0.0451542i	$0.985622\pi$
$74$		0			0
$75$	−4535.92	+	7854.88i	−0.806386	+	1.39642i
$76$		0			0
$77$	133.104	+	133.104i	0.0224497	+	0.0224497i
$78$		0			0
$79$		−	4061.80i		−	0.650825i	−0.945572	−	0.325413i	$-0.894497\pi$
$79$		−	4061.80i		−	0.650825i	0.945572	−	0.325413i	$-0.105503\pi$
$80$		0			0
$81$	258.720			0.0394330
$82$		0			0
$83$	1284.98	−	1284.98i	0.186527	−	0.186527i	−0.607666	−	0.794193i	$-0.707894\pi$
$83$	1284.98	−	1284.98i	0.186527	−	0.186527i	0.794193	+	0.607666i	$0.207894\pi$
$84$		0			0
$85$	−3683.61	−	2826.79i	−0.509842	−	0.391251i
$86$		0			0
$87$	12037.1	+	12037.1i	1.59031	+	1.59031i
$88$		0			0
$89$			4418.77i			0.557855i	0.960312	+	0.278927i	$0.0899789\pi$
$89$			4418.77i			0.557855i	−0.960312	+	0.278927i	$0.910021\pi$
$90$		0			0
$91$	−4411.04			−0.532670
$92$		0			0
$93$	−9803.51	+	9803.51i	−1.13348	+	1.13348i
$94$		0			0
$95$	−1316.99	−	10006.8i	−0.145927	−	1.10879i
$96$		0			0
$97$	−8805.47	−	8805.47i	−0.935857	−	0.935857i	0.0622067	−	0.998063i	$-0.480186\pi$
$97$	−8805.47	−	8805.47i	−0.935857	−	0.935857i	−0.998063	+	0.0622067i	$0.980186\pi$
$98$		0			0
$99$		−	339.720i		−	0.0346618i
$100$		0			0
$101$	−1031.51			−0.101118			−0.0505591	−	0.998721i	$-0.516100\pi$
$101$	−1031.51			−0.101118			−0.0505591	+	0.998721i	$0.516100\pi$
$102$		0			0
$103$	3761.50	−	3761.50i	0.354558	−	0.354558i	−0.507244	−	0.861802i	$-0.669336\pi$
$103$	3761.50	−	3761.50i	0.354558	−	0.354558i	0.861802	+	0.507244i	$0.169336\pi$
$104$		0			0
$105$	25835.9	−	3400.22i	2.34339	−	0.308410i
$106$		0			0
$107$	7295.22	+	7295.22i	0.637193	+	0.637193i	0.949862	−	0.312669i	$-0.101223\pi$
$107$	7295.22	+	7295.22i	0.637193	+	0.637193i	−0.312669	+	0.949862i	$0.601223\pi$
$108$		0			0
$109$		−	11024.8i		−	0.927932i	−0.885853	−	0.463966i	$-0.846426\pi$
$109$		−	11024.8i		−	0.927932i	0.885853	−	0.463966i	$-0.153574\pi$
$110$		0			0
$111$	−13819.0			−1.12158
$112$		0			0
$113$	10618.6	−	10618.6i	0.831590	−	0.831590i	−0.156144	−	0.987734i	$-0.549906\pi$
$113$	10618.6	−	10618.6i	0.831590	−	0.831590i	0.987734	+	0.156144i	$0.0499063\pi$
$114$		0			0
$115$	7198.88	−	9380.92i	0.544339	−	0.709333i
$116$		0			0
$117$	5629.11	+	5629.11i	0.411214	+	0.411214i
$118$		0			0
$119$			13339.6i			0.941996i
$120$		0			0
$121$	−14634.1			−0.999531
$122$		0			0
$123$	−8400.76	+	8400.76i	−0.555275	+	0.555275i
$124$		0			0
$125$	−14436.4	+	5977.56i	−0.923929	+	0.382564i
$126$		0			0
$127$	−5392.27	−	5392.27i	−0.334321	−	0.334321i	0.519904	−	0.854225i	$-0.325968\pi$
$127$	−5392.27	−	5392.27i	−0.334321	−	0.334321i	−0.854225	+	0.519904i	$0.825968\pi$
$128$		0			0
$129$			50.9170i			0.00305973i
$130$		0			0
$131$	5496.97			0.320318			0.160159	−	0.987091i	$-0.448799\pi$
$131$	5496.97			0.320318			0.160159	+	0.987091i	$0.448799\pi$
$132$		0			0
$133$	−20503.7	+	20503.7i	−1.15912	+	1.15912i
$134$		0			0
$135$	−13994.8	−	10739.5i	−0.767889	−	0.589274i
$136$		0			0
$137$	22555.6	+	22555.6i	1.20175	+	1.20175i	0.973634	+	0.228115i	$0.0732561\pi$
$137$	22555.6	+	22555.6i	1.20175	+	1.20175i	0.228115	+	0.973634i	$0.426744\pi$
$138$		0			0
$139$		−	7013.68i		−	0.363008i	−0.983390	−	0.181504i	$-0.941903\pi$
$139$		−	7013.68i		−	0.363008i	0.983390	−	0.181504i	$-0.0580966\pi$
$140$		0			0
$141$	32095.9			1.61440
$142$		0			0
$143$	−113.818	+	113.818i	−0.00556594	+	0.00556594i
$144$		0			0
$145$	3826.32	+	29073.5i	0.181989	+	1.38280i
$146$		0			0
$147$	−28297.6	−	28297.6i	−1.30953	−	1.30953i
$148$		0			0
$149$		−	26156.6i		−	1.17817i	−0.808071	−	0.589085i	$-0.799488\pi$
$149$		−	26156.6i		−	1.17817i	0.808071	−	0.589085i	$-0.200512\pi$
$150$		0			0
$151$	15510.9			0.680274			0.340137	−	0.940376i	$-0.389527\pi$
$151$	15510.9			0.680274			0.340137	+	0.940376i	$0.389527\pi$
$152$		0			0
$153$	17023.2	−	17023.2i	0.727208	−	0.727208i
$154$		0			0
$155$	−23678.6	+	3116.31i	−0.985583	+	0.129711i
$156$		0			0
$157$	4476.39	+	4476.39i	0.181605	+	0.181605i	0.792055	−	0.610450i	$-0.209011\pi$
$157$	4476.39	+	4476.39i	0.181605	+	0.181605i	−0.610450	+	0.792055i	$0.709011\pi$
$158$		0			0
$159$			5698.77i			0.225417i
$160$		0			0
$161$	−33971.5			−1.31058
$162$		0			0
$163$	27868.7	−	27868.7i	1.04892	−	1.04892i	0.0501793	−	0.998740i	$-0.484021\pi$
$163$	27868.7	−	27868.7i	1.04892	−	1.04892i	0.998740	−	0.0501793i	$-0.0159793\pi$
$164$		0			0
$165$	578.906	−	754.378i	0.0212638	−	0.0277090i
$166$		0			0
$167$	−443.484	−	443.484i	−0.0159017	−	0.0159017i	0.699111	−	0.715013i	$-0.253579\pi$
$167$	−443.484	−	443.484i	−0.0159017	−	0.0159017i	−0.715013	+	0.699111i	$0.753579\pi$
$168$		0			0
$169$			24789.1i			0.867936i
$170$		0			0
$171$	52331.2			1.78965
$172$		0			0
$173$	40238.8	−	40238.8i	1.34447	−	1.34447i	0.452927	−	0.891548i	$-0.350380\pi$
$173$	40238.8	−	40238.8i	1.34447	−	1.34447i	0.891548	−	0.452927i	$-0.149620\pi$
$174$		0			0
$175$	38873.2	+	22447.9i	1.26933	+	0.732993i
$176$		0			0
$177$	−64996.6	−	64996.6i	−2.07465	−	2.07465i
$178$		0			0
$179$			46438.3i			1.44934i	0.689097	+	0.724669i	$0.258007\pi$
$179$			46438.3i			1.44934i	−0.689097	+	0.724669i	$0.741993\pi$
$180$		0			0
$181$	−2233.36			−0.0681713			−0.0340857	−	0.999419i	$-0.510852\pi$
$181$	−2233.36			−0.0681713			−0.0340857	+	0.999419i	$0.510852\pi$
$182$		0			0
$183$	−66893.3	+	66893.3i	−1.99747	+	1.99747i
$184$		0			0
$185$	−18885.1	−	14492.3i	−0.551793	−	0.423443i
$186$		0			0
$187$	344.201	+	344.201i	0.00984304	+	0.00984304i
$188$		0			0
$189$			50679.8i			1.41877i
$190$		0			0
$191$	−48918.4			−1.34093			−0.670465	−	0.741941i	$-0.733905\pi$
$191$	−48918.4			−1.34093			−0.670465	+	0.741941i	$0.733905\pi$
$192$		0			0
$193$	−13323.5	+	13323.5i	−0.357687	+	0.357687i	−0.862960	−	0.505273i	$-0.831392\pi$
$193$	−13323.5	+	13323.5i	−0.357687	+	0.357687i	0.505273	+	0.862960i	$0.331392\pi$
$194$		0			0
$195$	2907.54	+	22092.3i	0.0764639	+	0.580995i
$196$		0			0
$197$	−1938.12	−	1938.12i	−0.0499399	−	0.0499399i	0.681696	−	0.731636i	$-0.261243\pi$
$197$	−1938.12	−	1938.12i	−0.0499399	−	0.0499399i	−0.731636	+	0.681696i	$0.761243\pi$
$198$		0			0
$199$		−	50510.0i		−	1.27547i	−0.770254	−	0.637737i	$-0.779871\pi$
$199$		−	50510.0i		−	1.27547i	0.770254	−	0.637737i	$-0.220129\pi$
$200$		0			0
$201$	14643.8			0.362460
$202$		0			0
$203$	59570.6	−	59570.6i	1.44557	−	1.44557i
$204$		0			0
$205$	−20290.6	+	2670.41i	−0.482821	+	0.0635434i
$206$		0			0
$207$	43352.4	+	43352.4i	1.01175	+	1.01175i
$208$		0			0
$209$			1058.11i			0.0242236i
$210$		0			0
$211$	22185.3			0.498311			0.249155	−	0.968464i	$-0.419847\pi$
$211$	22185.3			0.498311			0.249155	+	0.968464i	$0.419847\pi$
$212$		0			0
$213$	−2958.36	+	2958.36i	−0.0652065	+	0.0652065i
$214$		0			0
$215$	−53.3978	+	69.5831i	−0.00115517	+	0.00150531i
$216$		0			0
$217$	48516.8	+	48516.8i	1.03032	+	1.03032i
$218$		0			0
$219$		−	114200.i		−	2.38111i
$220$		0			0
$221$	−11406.7			−0.233548
$222$		0			0
$223$	−34667.1	+	34667.1i	−0.697121	+	0.697121i	−0.963789	−	0.266667i	$-0.914077\pi$
$223$	−34667.1	+	34667.1i	−0.697121	+	0.697121i	0.266667	+	0.963789i	$0.414077\pi$
$224$		0			0
$225$	−20961.0	−	78254.4i	−0.414044	−	1.54577i
$226$		0			0
$227$	−17110.2	−	17110.2i	−0.332049	−	0.332049i	0.521315	−	0.853364i	$-0.325442\pi$
$227$	−17110.2	−	17110.2i	−0.332049	−	0.332049i	−0.853364	+	0.521315i	$0.825442\pi$
$228$		0			0
$229$		−	45065.4i		−	0.859354i	−0.902983	−	0.429677i	$-0.858627\pi$
$229$		−	45065.4i		−	0.859354i	0.902983	−	0.429677i	$-0.141373\pi$
$230$		0			0
$231$	−2731.86			−0.0511958
$232$		0			0
$233$	−25977.7	+	25977.7i	−0.478507	+	0.478507i	−0.904654	−	0.426147i	$-0.859871\pi$
$233$	−25977.7	+	25977.7i	−0.478507	+	0.478507i	0.426147	+	0.904654i	$0.359871\pi$
$234$		0			0
$235$	43862.3	+	33659.7i	0.794247	+	0.609501i
$236$		0			0
$237$	41682.6	+	41682.6i	0.742092	+	0.742092i
$238$		0			0
$239$			31171.1i			0.545702i	0.962056	+	0.272851i	$0.0879666\pi$
$239$			31171.1i			0.545702i	−0.962056	+	0.272851i	$0.912033\pi$
$240$		0			0
$241$	60259.8			1.03751			0.518757	−	0.854922i	$-0.326395\pi$
$241$	60259.8			1.03751			0.518757	+	0.854922i	$0.326395\pi$
$242$		0			0
$243$	−43070.1	+	43070.1i	−0.729396	+	0.729396i
$244$		0			0
$245$	−8995.17	−	68347.8i	−0.149857	−	1.13866i
$246$		0			0
$247$	−17532.8	−	17532.8i	−0.287380	−	0.287380i
$248$		0			0
$249$			26373.2i			0.425368i
$250$		0			0
$251$	−89398.1			−1.41899			−0.709497	−	0.704708i	$-0.751078\pi$
$251$	−89398.1			−1.41899			−0.709497	+	0.704708i	$0.751078\pi$
$252$		0			0
$253$	−876.566	+	876.566i	−0.0136944	+	0.0136944i
$254$		0			0
$255$	66810.3	−	8792.81i	1.02746	−	0.135222i
$256$		0			0
$257$	77033.7	+	77033.7i	1.16631	+	1.16631i	0.983067	+	0.183244i	$0.0586600\pi$
$257$	77033.7	+	77033.7i	1.16631	+	1.16631i	0.183244	+	0.983067i	$0.441340\pi$
$258$		0			0
$259$			68389.3i			1.01950i
$260$		0			0
$261$	−152041.			−2.23193
$262$		0			0
$263$	14579.0	−	14579.0i	0.210773	−	0.210773i	−0.593823	−	0.804596i	$-0.702382\pi$
$263$	14579.0	−	14579.0i	0.210773	−	0.210773i	0.804596	+	0.593823i	$0.202382\pi$
$264$		0			0
$265$	−5976.44	+	7787.95i	−0.0851041	+	0.110900i
$266$		0			0
$267$	−45345.8	−	45345.8i	−0.636084	−	0.636084i
$268$		0			0
$269$			113034.i			1.56209i	0.624475	+	0.781045i	$0.285313\pi$
$269$			113034.i			1.56209i	−0.624475	+	0.781045i	$0.714687\pi$
$270$		0			0
$271$	−112208.			−1.52786			−0.763930	−	0.645299i	$-0.776733\pi$
$271$	−112208.			−1.52786			−0.763930	+	0.645299i	$0.776733\pi$
$272$		0			0
$273$	45266.5	−	45266.5i	0.607367	−	0.607367i
$274$		0			0
$275$	1582.27	−	423.821i	0.0209225	−	0.00560425i
$276$		0			0
$277$	−66251.9	−	66251.9i	−0.863453	−	0.863453i	0.128284	−	0.991737i	$-0.459053\pi$
$277$	−66251.9	−	66251.9i	−0.863453	−	0.863453i	−0.991737	+	0.128284i	$0.959053\pi$
$278$		0			0
$279$		−	123829.i		−	1.59079i
$280$		0			0
$281$	128293.			1.62476			0.812382	−	0.583125i	$-0.198170\pi$
$281$	128293.			1.62476			0.812382	+	0.583125i	$0.198170\pi$
$282$		0			0
$283$	−39634.8	+	39634.8i	−0.494885	+	0.494885i	−0.909841	−	0.414956i	$-0.863797\pi$
$283$	−39634.8	+	39634.8i	−0.494885	+	0.494885i	0.414956	+	0.909841i	$0.363797\pi$
$284$		0			0
$285$	116206.	+	89176.0i	1.43067	+	1.09789i
$286$		0			0
$287$	41574.7	+	41574.7i	0.504737	+	0.504737i
$288$		0			0
$289$		−	49025.5i		−	0.586984i
$290$		0			0
$291$	180725.			2.13419
$292$		0			0
$293$	52917.7	−	52917.7i	0.616404	−	0.616404i	−0.328203	−	0.944607i	$-0.606443\pi$
$293$	52917.7	−	52917.7i	0.616404	−	0.616404i	0.944607	+	0.328203i	$0.106443\pi$
$294$		0			0
$295$	−20660.9	−	156988.i	−0.237414	−	1.80394i
$296$		0			0
$297$	1307.69	+	1307.69i	0.0148249	+	0.0148249i
$298$		0			0
$299$		−	29049.1i		−	0.324931i
$300$		0			0
$301$	251.984			0.00278125
$302$		0			0
$303$	10585.4	−	10585.4i	0.115298	−	0.115298i
$304$		0			0
$305$	−161569.	+	21263.9i	−1.73683	+	0.228582i
$306$		0			0
$307$	−89679.6	−	89679.6i	−0.951518	−	0.951518i	0.0473601	−	0.998878i	$-0.484919\pi$
$307$	−89679.6	−	89679.6i	−0.951518	−	0.951518i	−0.998878	+	0.0473601i	$0.984919\pi$
$308$		0			0
$309$			77201.8i			0.808556i
$310$		0			0
$311$	130542.			1.34967			0.674836	−	0.737968i	$-0.264214\pi$
$311$	130542.			1.34967			0.674836	+	0.737968i	$0.264214\pi$
$312$		0			0
$313$	6721.82	−	6721.82i	0.0686117	−	0.0686117i	−0.671968	−	0.740580i	$-0.734551\pi$
$313$	6721.82	−	6721.82i	0.0686117	−	0.0686117i	0.740580	+	0.671968i	$0.234551\pi$
$314$		0			0
$315$	−141693.	+	184641.i	−1.42799	+	1.86083i
$316$		0			0
$317$	−2963.12	−	2963.12i	−0.0294870	−	0.0294870i	0.692210	−	0.721697i	$-0.256637\pi$
$317$	−2963.12	−	2963.12i	−0.0294870	−	0.0294870i	−0.721697	+	0.692210i	$0.756637\pi$
$318$		0			0
$319$		−	3074.20i		−	0.0302100i
$320$		0			0
$321$	−149728.			−1.45310
$322$		0			0
$323$	−53021.5	+	53021.5i	−0.508215	+	0.508215i
$324$		0			0
$325$	−19195.3	+	33240.6i	−0.181730	+	0.314704i
$326$		0			0
$327$	113137.	+	113137.i	1.05806	+	1.05806i
$328$		0			0
$329$		−	158840.i		−	1.46747i
$330$		0			0
$331$	131934.			1.20420			0.602101	−	0.798420i	$-0.294330\pi$
$331$	131934.			1.20420			0.602101	+	0.798420i	$0.294330\pi$
$332$		0			0
$333$	87274.4	−	87274.4i	0.787043	−	0.787043i
$334$		0			0
$335$	20012.2	+	15357.3i	0.178322	+	0.136843i
$336$		0			0
$337$	−57168.8	−	57168.8i	−0.503384	−	0.503384i	0.409104	−	0.912488i	$-0.365841\pi$
$337$	−57168.8	−	57168.8i	−0.503384	−	0.503384i	−0.912488	+	0.409104i	$0.865841\pi$
$338$		0			0
$339$			217938.i			1.89641i
$340$		0			0
$341$	2503.75			0.0215319
$342$		0			0
$343$	−18104.7	+	18104.7i	−0.153888	+	0.153888i
$344$		0			0
$345$	22392.3	+	170143.i	0.188131	+	1.42948i
$346$		0			0
$347$	−111649.	−	111649.i	−0.927246	−	0.927246i	0.0702816	−	0.997527i	$-0.477610\pi$
$347$	−111649.	−	111649.i	−0.927246	−	0.927246i	−0.997527	+	0.0702816i	$0.977610\pi$
$348$		0			0
$349$		−	37725.2i		−	0.309728i	−0.987936	−	0.154864i	$-0.950506\pi$
$349$		−	37725.2i		−	0.309728i	0.987936	−	0.154864i	$-0.0494939\pi$
$350$		0			0
$351$	−43336.4			−0.351754
$352$		0			0
$353$	−98297.9	+	98297.9i	−0.788851	+	0.788851i	−0.981306	−	0.192455i	$-0.938355\pi$
$353$	−98297.9	+	98297.9i	−0.788851	+	0.788851i	0.192455	+	0.981306i	$0.438355\pi$
$354$		0			0
$355$	−7145.39	+	940.395i	−0.0566982	+	0.00746197i
$356$		0			0
$357$	−136892.	−	136892.i	−1.07409	−	1.07409i
$358$		0			0
$359$			175541.i			1.36204i	0.732267	+	0.681018i	$0.238463\pi$
$359$			175541.i			1.36204i	−0.732267	+	0.681018i	$0.761537\pi$
$360$		0			0
$361$	−32673.1			−0.250712
$362$		0			0
$363$	150177.	−	150177.i	1.13970	−	1.13970i
$364$		0			0
$365$	119765.	−	156066.i	0.898965	−	1.17145i
$366$		0			0
$367$	2090.35	+	2090.35i	0.0155199	+	0.0155199i	0.714824	−	0.699304i	$-0.246507\pi$
$367$	2090.35	+	2090.35i	0.0155199	+	0.0155199i	−0.699304	+	0.714824i	$0.746507\pi$
$368$		0			0
$369$		−	106110.i		−	0.779301i
$370$		0			0
$371$	28202.8			0.204901
$372$		0			0
$373$	26326.4	−	26326.4i	0.189223	−	0.189223i	−0.606137	−	0.795360i	$-0.707282\pi$
$373$	26326.4	−	26326.4i	0.189223	−	0.189223i	0.795360	+	0.606137i	$0.207282\pi$
$374$		0			0
$375$	86805.2	−	209490.i	0.617282	−	1.48971i
$376$		0			0
$377$	50939.0	+	50939.0i	0.358400	+	0.358400i
$378$		0			0
$379$			178086.i			1.23980i	0.784681	+	0.619899i	$0.212827\pi$
$379$			178086.i			1.23980i	−0.784681	+	0.619899i	$0.787173\pi$
$380$		0			0
$381$	110672.			0.762408
$382$		0			0
$383$	152109.	−	152109.i	1.03695	−	1.03695i	0.0376570	−	0.999291i	$-0.488011\pi$
$383$	152109.	−	152109.i	1.03695	−	1.03695i	0.999291	−	0.0376570i	$-0.0119894\pi$
$384$		0			0
$385$	−3733.36	−	2864.96i	−0.0251871	−	0.0193285i
$386$		0			0
$387$	−321.567	−	321.567i	−0.00214709	−	0.00214709i
$388$		0			0
$389$			105964.i			0.700260i	0.936701	+	0.350130i	$0.113863\pi$
$389$			105964.i			0.700260i	−0.936701	+	0.350130i	$0.886137\pi$
$390$		0			0
$391$	−87848.6			−0.574621
$392$		0			0
$393$	−56410.4	+	56410.4i	−0.365236	+	0.365236i
$394$		0			0
$395$	13250.0	+	100677.i	0.0849220	+	0.645261i
$396$		0			0
$397$	131873.	+	131873.i	0.836708	+	0.836708i	0.988424	−	0.151716i	$-0.0484800\pi$
$397$	131873.	+	131873.i	0.836708	+	0.836708i	−0.151716	+	0.988424i	$0.548480\pi$
$398$		0			0
$399$		−	420821.i		−	2.64333i
$400$		0			0
$401$	−47401.0			−0.294780			−0.147390	−	0.989078i	$-0.547087\pi$
$401$	−47401.0			−0.294780			−0.147390	+	0.989078i	$0.547087\pi$
$402$		0			0
$403$	−41486.8	+	41486.8i	−0.255447	+	0.255447i
$404$		0			0
$405$	−6412.70	+	843.967i	−0.0390959	+	0.00514536i
$406$		0			0
$407$	1764.65	+	1764.65i	0.0106529	+	0.0106529i
$408$		0			0
$409$			1189.53i			0.00711097i	0.999994	+	0.00355549i	$0.00113175\pi$
$409$			1189.53i			0.00711097i	−0.999994	+	0.00355549i	$0.998868\pi$
$410$		0			0
$411$	−462936.			−2.74055
$412$		0			0
$413$	−321663.	+	321663.i	−1.88582	+	1.88582i
$414$		0			0
$415$	−27658.2	+	36041.7i	−0.160594	+	0.209271i
$416$		0			0
$417$	71975.0	+	71975.0i	0.413913	+	0.413913i
$418$		0			0
$419$		−	145531.i		−	0.828948i	−0.910061	−	0.414474i	$-0.863966\pi$
$419$		−	145531.i		−	0.828948i	0.910061	−	0.414474i	$-0.136034\pi$
$420$		0			0
$421$	231931.			1.30856			0.654281	−	0.756251i	$-0.272971\pi$
$421$	231931.			1.30856			0.654281	+	0.756251i	$0.272971\pi$
$422$		0			0
$423$	−202702.	+	202702.i	−1.13286	+	1.13286i
$424$		0			0
$425$	100524.	+	58049.2i	0.556535	+	0.321380i
$426$		0			0
$427$	331050.	+	331050.i	1.81567	+	1.81567i
$428$		0			0
$429$		−	2336.02i		−	0.0126929i
$430$		0			0
$431$	−105563.			−0.568275			−0.284138	−	0.958784i	$-0.591707\pi$
$431$	−105563.			−0.568275			−0.284138	+	0.958784i	$0.591707\pi$
$432$		0			0
$433$	87734.1	−	87734.1i	0.467943	−	0.467943i	−0.433305	−	0.901248i	$-0.642653\pi$
$433$	87734.1	−	87734.1i	0.467943	−	0.467943i	0.901248	+	0.433305i	$0.142653\pi$
$434$		0			0
$435$	−337620.	−	259088.i	−1.78423	−	1.36921i
$436$		0			0
$437$	−135028.	−	135028.i	−0.707068	−	0.707068i
$438$		0			0
$439$			54525.1i			0.282922i	0.989944	+	0.141461i	$0.0451800\pi$
$439$			54525.1i			0.282922i	−0.989944	+	0.141461i	$0.954820\pi$
$440$		0			0
$441$	357428.			1.83786
$442$		0			0
$443$	155457.	−	155457.i	0.792143	−	0.792143i	−0.189699	−	0.981842i	$-0.560751\pi$
$443$	155457.	−	155457.i	0.792143	−	0.792143i	0.981842	+	0.189699i	$0.0607514\pi$
$444$		0			0
$445$	−14414.4	−	109525.i	−0.0727909	−	0.553086i
$446$		0			0
$447$	268421.	+	268421.i	1.34339	+	1.34339i
$448$		0			0
$449$		−	193346.i		−	0.959052i	−0.877528	−	0.479526i	$-0.840809\pi$
$449$		−	193346.i		−	0.959052i	0.877528	−	0.479526i	$-0.159191\pi$
$450$		0			0
$451$	2145.50			0.0105481
$452$		0			0
$453$	−159174.	+	159174.i	−0.775670	+	0.775670i
$454$		0			0
$455$	109333.	−	14389.2i	0.528116	−	0.0695046i
$456$		0			0
$457$	−32065.3	−	32065.3i	−0.153534	−	0.153534i	0.626161	−	0.779694i	$-0.284625\pi$
$457$	−32065.3	−	32065.3i	−0.153534	−	0.153534i	−0.779694	+	0.626161i	$0.784625\pi$
$458$		0			0
$459$			131055.i			0.622056i
$460$		0			0
$461$	−297478.			−1.39976			−0.699880	−	0.714260i	$-0.746763\pi$
$461$	−297478.			−1.39976			−0.699880	+	0.714260i	$0.746763\pi$
$462$		0			0
$463$	29795.1	−	29795.1i	0.138990	−	0.138990i	−0.634189	−	0.773178i	$-0.718666\pi$
$463$	29795.1	−	29795.1i	0.138990	−	0.138990i	0.773178	+	0.634189i	$0.218666\pi$
$464$		0			0
$465$	211012.	−	274972.i	0.975893	−	1.27169i
$466$		0			0
$467$	−259050.	−	259050.i	−1.18782	−	1.18782i	−0.977669	−	0.210150i	$-0.932605\pi$
$467$	−259050.	−	259050.i	−1.18782	−	1.18782i	−0.210150	−	0.977669i	$-0.567395\pi$
$468$		0			0
$469$		−	72470.8i		−	0.329471i
$470$		0			0
$471$	−91874.2			−0.414145
$472$		0			0
$473$	6.50194	−	6.50194i	2.90617e−5	−	2.90617e-5i
$474$		0			0
$475$	65286.4	+	243736.i	0.289358	+	1.08027i
$476$		0			0
$477$	−35990.7	−	35990.7i	−0.158181	−	0.158181i
$478$		0			0
$479$		−	237433.i		−	1.03483i	−0.855734	−	0.517417i	$-0.826894\pi$
$479$		−	237433.i		−	1.03483i	0.855734	−	0.517417i	$-0.173106\pi$
$480$		0			0
$481$	−58479.9			−0.252765
$482$		0			0
$483$	348618.	−	348618.i	1.49436	−	1.49436i
$484$		0			0
$485$	246979.	+	189531.i	1.04997	+	0.805742i
$486$		0			0
$487$	−55918.6	−	55918.6i	−0.235775	−	0.235775i	0.579323	−	0.815098i	$-0.303317\pi$
$487$	−55918.6	−	55918.6i	−0.235775	−	0.235775i	−0.815098	+	0.579323i	$0.803317\pi$
$488$		0			0
$489$			571983.i			2.39202i
$490$		0			0
$491$	337941.			1.40178			0.700888	−	0.713272i	$-0.252787\pi$
$491$	337941.			1.40178			0.700888	+	0.713272i	$0.252787\pi$
$492$		0			0
$493$	154047.	−	154047.i	0.633809	−	0.633809i
$494$		0			0
$495$	1108.20	+	8420.39i	0.00452279	+	0.0343654i
$496$		0			0
$497$	14640.7	+	14640.7i	0.0592718	+	0.0592718i
$498$		0			0
$499$			5945.12i			0.0238759i	0.999929	+	0.0119379i	$0.00380006\pi$
$499$			5945.12i			0.0238759i	−0.999929	+	0.0119379i	$0.996200\pi$
$500$		0			0
$501$	9102.14			0.0362634
$502$		0			0
$503$	−183548.	+	183548.i	−0.725460	+	0.725460i	−0.969712	−	0.244252i	$-0.921458\pi$
$503$	−183548.	+	183548.i	−0.725460	+	0.725460i	0.244252	+	0.969712i	$0.421458\pi$
$504$		0			0
$505$	25567.2	−	3364.86i	0.100254	−	0.0131942i
$506$		0			0
$507$	−254388.	−	254388.i	−0.989648	−	0.989648i
$508$		0			0
$509$		−	192463.i		−	0.742869i	−0.928459	−	0.371435i	$-0.878866\pi$
$509$		−	192463.i		−	0.742869i	0.928459	−	0.371435i	$-0.121134\pi$
$510$		0			0
$511$	−565169.			−2.16439
$512$		0			0
$513$	−201439.	+	201439.i	−0.765437	+	0.765437i
$514$		0			0
$515$	−80963.3	+	105504.i	−0.305263	+	0.397791i
$516$		0			0
$517$	−4098.55	−	4098.55i	−0.0153338	−	0.0153338i
$518$		0			0
$519$			825868.i			3.06603i
$520$		0			0
$521$	−164471.			−0.605917			−0.302959	−	0.953004i	$-0.597974\pi$
$521$	−164471.			−0.605917			−0.302959	+	0.953004i	$0.597974\pi$
$522$		0			0
$523$	140683.	−	140683.i	0.514327	−	0.514327i	−0.401522	−	0.915849i	$-0.631519\pi$
$523$	140683.	−	140683.i	0.514327	−	0.514327i	0.915849	+	0.401522i	$0.131519\pi$
$524$		0			0
$525$	−629283.	+	168558.i	−2.28311	+	0.611547i
$526$		0			0
$527$	125462.	+	125462.i	0.451743	+	0.451743i
$528$		0			0
$529$			56120.1i			0.200543i
$530$		0			0
$531$	820974.			2.91166
$532$		0			0
$533$	−35550.6	+	35550.6i	−0.125139	+	0.125139i
$534$		0			0
$535$	−204619.	−	157024.i	−0.714889	−	0.548602i
$536$		0			0
$537$	−476553.	−	476553.i	−1.65258	−	1.65258i
$538$		0			0
$539$			7227.03i			0.0248761i
$540$		0			0
$541$	266246.			0.909678			0.454839	−	0.890574i	$-0.349697\pi$
$541$	266246.			0.909678			0.454839	+	0.890574i	$0.349697\pi$
$542$		0			0
$543$	22918.9	−	22918.9i	0.0777311	−	0.0777311i
$544$		0			0
$545$	35963.7	+	273263.i	0.121080	+	0.919999i
$546$		0			0
$547$	109382.	+	109382.i	0.365569	+	0.365569i	0.865858	−	0.500289i	$-0.166773\pi$
$547$	109382.	+	109382.i	0.365569	+	0.365569i	−0.500289	+	0.865858i	$0.666773\pi$
$548$		0			0
$549$		−	844932.i		−	2.80335i
$550$		0			0
$551$	473556.			1.55980
$552$		0			0
$553$	206284.	−	206284.i	0.674551	−	0.674551i
$554$		0			0
$555$	342522.	−	45078.9i	1.11200	−	0.146348i
$556$		0			0
$557$	297316.	+	297316.i	0.958314	+	0.958314i	0.999165	−	0.0408511i	$-0.0130069\pi$
$557$	297316.	+	297316.i	0.958314	+	0.958314i	−0.0408511	+	0.999165i	$0.513007\pi$
$558$		0			0
$559$			215.472i			0.000689553i
$560$		0			0
$561$	−7064.45			−0.0224467
$562$		0			0
$563$	−351323.	+	351323.i	−1.10838	+	1.10838i	−0.115018	+	0.993363i	$0.536693\pi$
$563$	−351323.	+	351323.i	−1.10838	+	1.10838i	−0.993363	+	0.115018i	$0.963307\pi$
$564$		0			0
$565$	−228556.	+	297834.i	−0.715972	+	0.932990i
$566$		0			0
$567$	13139.4	+	13139.4i	0.0408705	+	0.0408705i
$568$		0			0
$569$		−	417127.i		−	1.28838i	−0.764866	−	0.644189i	$-0.777195\pi$
$569$		−	417127.i		−	1.28838i	0.764866	−	0.644189i	$-0.222805\pi$
$570$		0			0
$571$	−238761.			−0.732303			−0.366151	−	0.930555i	$-0.619325\pi$
$571$	−238761.			−0.732303			−0.366151	+	0.930555i	$0.619325\pi$
$572$		0			0
$573$	502005.	−	502005.i	1.52897	−	1.52897i
$574$		0			0
$575$	−147832.	+	256001.i	−0.447129	+	0.774295i
$576$		0			0
$577$	−253766.	−	253766.i	−0.762222	−	0.762222i	0.214502	−	0.976724i	$-0.431187\pi$
$577$	−253766.	−	253766.i	−0.762222	−	0.762222i	−0.976724	+	0.214502i	$0.931187\pi$
$578$		0			0
$579$		−	273454.i		−	0.815693i
$580$		0			0
$581$	130519.			0.386653
$582$		0			0
$583$	727.716	−	727.716i	0.00214104	−	0.00214104i
$584$		0			0
$585$	−157887.	−	121162.i	−0.461355	−	0.354042i
$586$		0			0
$587$	−240128.	−	240128.i	−0.696895	−	0.696895i	0.266845	−	0.963740i	$-0.414019\pi$
$587$	−240128.	−	240128.i	−0.696895	−	0.696895i	−0.963740	+	0.266845i	$0.914019\pi$
$588$		0			0
$589$			385684.i			1.11173i
$590$		0			0
$591$	39778.3			0.113886
$592$		0			0
$593$	174126.	−	174126.i	0.495171	−	0.495171i	−0.414760	−	0.909931i	$-0.636134\pi$
$593$	174126.	−	174126.i	0.495171	−	0.495171i	0.909931	+	0.414760i	$0.136134\pi$
$594$		0			0
$595$	−43514.9	−	330639.i	−0.122915	−	0.933942i
$596$		0			0
$597$	518338.	+	518338.i	1.45434	+	1.45434i
$598$		0			0
$599$			44274.6i			0.123396i	0.998095	+	0.0616980i	$0.0196516\pi$
$599$			44274.6i			0.123396i	−0.998095	+	0.0616980i	$0.980348\pi$
$600$		0			0
$601$	−555368.			−1.53756			−0.768780	−	0.639513i	$-0.779136\pi$
$601$	−555368.			−1.53756			−0.768780	+	0.639513i	$0.779136\pi$
$602$		0			0
$603$	−92483.0	+	92483.0i	−0.254347	+	0.254347i
$604$		0			0
$605$	362725.	−	47737.8i	0.990985	−	0.130422i
$606$		0			0
$607$	−167752.	−	167752.i	−0.455292	−	0.455292i	0.441815	−	0.897106i	$-0.354335\pi$
$607$	−167752.	−	167752.i	−0.455292	−	0.455292i	−0.897106	+	0.441815i	$0.854335\pi$
$608$		0			0
$609$			1.22264e6i			3.29658i
$610$		0			0
$611$	135825.			0.363828
$612$		0			0
$613$	−181095.	+	181095.i	−0.481932	+	0.481932i	−0.905748	−	0.423816i	$-0.860690\pi$
$613$	−181095.	+	181095.i	−0.481932	+	0.481932i	0.423816	+	0.905748i	$0.360690\pi$
$614$		0			0
$615$	180819.	−	235627.i	0.478074	−	0.622982i
$616$		0			0
$617$	46817.9	+	46817.9i	0.122982	+	0.122982i	0.765919	−	0.642937i	$-0.222284\pi$
$617$	46817.9	+	46817.9i	0.122982	+	0.122982i	−0.642937	+	0.765919i	$0.722284\pi$
$618$		0			0
$619$		−	366573.i		−	0.956706i	−0.878168	−	0.478353i	$-0.841234\pi$
$619$		−	366573.i		−	0.956706i	0.878168	−	0.478353i	$-0.158766\pi$
$620$		0			0
$621$	−333754.			−0.865453
$622$		0			0
$623$	−224413.	+	224413.i	−0.578191	+	0.578191i
$624$		0			0
$625$	338325.	−	195254.i	0.866112	−	0.499851i
$626$		0			0
$627$	−10858.4	−	10858.4i	−0.0276206	−	0.0276206i
$628$		0			0
$629$			176851.i			0.447000i
$630$		0			0
$631$	99400.6			0.249649			0.124825	−	0.992179i	$-0.460163\pi$
$631$	99400.6			0.249649			0.124825	+	0.992179i	$0.460163\pi$
$632$		0			0
$633$	−227667.	+	227667.i	−0.568190	+	0.568190i
$634$		0			0
$635$	151244.	+	116064.i	0.375086	+	0.287840i
$636$		0			0
$637$	−119751.	−	119751.i	−0.295121	−	0.295121i
$638$		0			0
$639$		−	37367.1i		−	0.0915141i
$640$		0			0
$641$	−147541.			−0.359083			−0.179542	−	0.983750i	$-0.557461\pi$
$641$	−147541.			−0.359083			−0.179542	+	0.983750i	$0.557461\pi$
$642$		0			0
$643$	−224429.	+	224429.i	−0.542821	+	0.542821i	−0.924355	−	0.381534i	$-0.875396\pi$
$643$	−224429.	+	224429.i	−0.542821	+	0.542821i	0.381534	+	0.924355i	$0.375396\pi$
$644$		0			0
$645$	−166.096	−	1262.04i	−0.000399244	−	0.00303357i
$646$		0			0
$647$	−403860.	−	403860.i	−0.964766	−	0.964766i	0.0346338	−	0.999400i	$-0.488974\pi$
$647$	−403860.	−	403860.i	−0.964766	−	0.964766i	−0.999400	+	0.0346338i	$0.988974\pi$
$648$		0			0
$649$			16599.7i			0.0394104i
$650$		0			0
$651$	−995767.			−2.34961
$652$		0			0
$653$	−109597.	+	109597.i	−0.257024	+	0.257024i	−0.823843	−	0.566818i	$-0.808174\pi$
$653$	−109597.	+	109597.i	−0.257024	+	0.257024i	0.566818	+	0.823843i	$0.308174\pi$
$654$		0			0
$655$	−136249.	+	17931.6i	−0.317579	+	0.0417962i
$656$		0			0
$657$	721235.	+	721235.i	1.67088	+	1.67088i
$658$		0			0
$659$			37101.9i			0.0854330i	0.999087	+	0.0427165i	$0.0136012\pi$
$659$			37101.9i			0.0854330i	−0.999087	+	0.0427165i	$0.986399\pi$
$660$		0			0
$661$	19393.8			0.0443873			0.0221937	−	0.999754i	$-0.492935\pi$
$661$	19393.8			0.0443873			0.0221937	+	0.999754i	$0.492935\pi$
$662$		0			0
$663$	117057.	−	117057.i	0.266299	−	0.266299i
$664$		0			0
$665$	441325.	−	575095.i	0.997965	−	1.30046i
$666$		0			0
$667$	392305.	+	392305.i	0.881805	+	0.881805i
$668$		0			0
$669$		−	711514.i		−	1.58976i
$670$		0			0
$671$	17084.1			0.0379444
$672$		0			0
$673$	528789.	−	528789.i	1.16749	−	1.16749i	0.184691	−	0.982797i	$-0.440872\pi$
$673$	528789.	−	528789.i	1.16749	−	1.16749i	0.982797	−	0.184691i	$-0.0591284\pi$
$674$		0			0
$675$	381911.	+	220540.i	0.838214	+	0.484039i
$676$		0			0
$677$	107241.	+	107241.i	0.233982	+	0.233982i	0.814353	−	0.580370i	$-0.197092\pi$
$677$	107241.	+	107241.i	0.233982	+	0.233982i	−0.580370	+	0.814353i	$0.697092\pi$
$678$		0			0
$679$		−	894394.i		−	1.93995i
$680$		0			0
$681$	351172.			0.757227
$682$		0			0
$683$	125089.	−	125089.i	0.268149	−	0.268149i	−0.560205	−	0.828354i	$-0.689278\pi$
$683$	125089.	−	125089.i	0.268149	−	0.268149i	0.828354	+	0.560205i	$0.189278\pi$
$684$		0			0
$685$	−632648.	−	485491.i	−1.34828	−	1.03467i
$686$		0			0
$687$	462465.	+	462465.i	0.979863	+	0.979863i
$688$		0			0
$689$			24116.3i			0.0508010i
$690$		0			0
$691$	628995.			1.31732			0.658660	−	0.752441i	$-0.271124\pi$
$691$	628995.			1.31732			0.658660	+	0.752441i	$0.271124\pi$
$692$		0			0
$693$	17253.1	−	17253.1i	0.0359253	−	0.0359253i
$694$		0			0
$695$	22879.2	+	173843.i	0.0473666	+	0.359905i
$696$		0			0
$697$	107510.	+	107510.i	0.221301	+	0.221301i
$698$		0			0
$699$		−	533170.i		−	1.09122i
$700$		0			0
$701$	24731.8			0.0503292			0.0251646	−	0.999683i	$-0.491989\pi$
$701$	24731.8			0.0503292			0.0251646	+	0.999683i	$0.491989\pi$
$702$		0			0
$703$	−271830.	+	271830.i	−0.550031	+	0.550031i
$704$		0			0
$705$	−795537.	+	104700.i	−1.60060	+	0.210653i
$706$		0			0
$707$	−52386.3	−	52386.3i	−0.104804	−	0.104804i
$708$		0			0
$709$			615630.i			1.22469i	0.790589	+	0.612347i	$0.209774\pi$
$709$			615630.i			1.22469i	−0.790589	+	0.612347i	$0.790226\pi$
$710$		0			0
$711$	−526494.			−1.04149
$712$		0			0
$713$	−319510.	+	319510.i	−0.628500	+	0.628500i
$714$		0			0
$715$	2449.84	−	3192.40i	0.00479209	−	0.00624462i
$716$		0			0
$717$	−319880.	−	319880.i	−0.622227	−	0.622227i
$718$		0			0
$719$			10946.7i			0.0211751i	0.999944	+	0.0105876i	$0.00337019\pi$
$719$			10946.7i			0.0211751i	−0.999944	+	0.0105876i	$0.996630\pi$
$720$		0			0
$721$	382066.			0.734966
$722$		0			0
$723$	−618391.	+	618391.i	−1.18301	+	1.18301i
$724$		0			0
$725$	−189680.	−	708141.i	−0.360866	−	1.34724i
$726$		0			0
$727$	16343.7	+	16343.7i	0.0309230	+	0.0309230i	0.722399	−	0.691476i	$-0.243039\pi$
$727$	16343.7	+	16343.7i	0.0309230	+	0.0309230i	−0.691476	+	0.722399i	$0.743039\pi$
$728$		0			0
$729$		−	863022.i		−	1.62393i
$730$		0			0
$731$	651.618			0.00121943
$732$		0			0
$733$	−686430.	+	686430.i	−1.27758	+	1.27758i	−0.335563	+	0.942018i	$0.608927\pi$
$733$	−686430.	+	686430.i	−1.27758	+	1.27758i	−0.942018	+	0.335563i	$0.891073\pi$
$734$		0			0
$735$	793701.	+	609082.i	1.46920	+	1.12746i
$736$		0			0
$737$	−1869.96	−	1869.96i	−0.00344269	−	0.00344269i
$738$		0			0
$739$			862613.i			1.57953i	0.613411	+	0.789764i	$0.289797\pi$
$739$			862613.i			1.57953i	−0.613411	+	0.789764i	$0.710203\pi$
$740$		0			0
$741$	359846.			0.655360
$742$		0			0
$743$	327982.	−	327982.i	0.594117	−	0.594117i	−0.344624	−	0.938741i	$-0.611993\pi$
$743$	327982.	−	327982.i	0.594117	−	0.594117i	0.938741	+	0.344624i	$0.111993\pi$
$744$		0			0
$745$	85325.0	+	648323.i	0.153732	+	1.16810i
$746$		0			0
$747$	−166561.	−	166561.i	−0.298491	−	0.298491i
$748$		0			0
$749$			740994.i			1.32084i
$750$		0			0
$751$	502393.			0.890766			0.445383	−	0.895340i	$-0.353068\pi$
$751$	502393.			0.890766			0.445383	+	0.895340i	$0.353068\pi$
$752$		0			0
$753$	917411.	−	917411.i	1.61798	−	1.61798i
$754$		0			0
$755$	−384458.	+	50598.0i	−0.674458	+	0.0887645i
$756$		0			0
$757$	−130437.	−	130437.i	−0.227619	−	0.227619i	0.584079	−	0.811697i	$-0.301456\pi$
$757$	−130437.	−	130437.i	−0.227619	−	0.227619i	−0.811697	+	0.584079i	$0.801456\pi$
$758$		0			0
$759$		−	17990.8i		−	0.0312296i
$760$		0			0
$761$	−743295.			−1.28349			−0.641744	−	0.766919i	$-0.721789\pi$
$761$	−743295.			−1.28349			−0.641744	+	0.766919i	$0.721789\pi$
$762$		0			0
$763$	559907.	−	559907.i	0.961759	−	0.961759i
$764$		0			0
$765$	−366411.	+	477473.i	−0.626102	+	0.815879i
$766$		0			0
$767$	−275055.	−	275055.i	−0.467551	−	0.467551i
$768$		0			0
$769$			735171.i			1.24319i	0.783341	+	0.621593i	$0.213514\pi$
$769$			735171.i			1.24319i	−0.783341	+	0.621593i	$0.786486\pi$
$770$		0			0
$771$	−1.58105e6			−2.65973
$772$		0			0
$773$	−26037.4	+	26037.4i	−0.0435751	+	0.0435751i	−0.728559	−	0.684983i	$-0.759809\pi$
$773$	−26037.4	+	26037.4i	−0.0435751	+	0.0435751i	0.684983	+	0.728559i	$0.259809\pi$
$774$		0			0
$775$	576739.	−	154484.i	0.960232	−	0.257205i
$776$		0			0
$777$	−701817.	−	701817.i	−1.16247	−	1.16247i
$778$		0			0
$779$			330498.i			0.544620i
$780$		0			0
$781$	755.546			0.00123868
$782$		0			0
$783$	585254.	−	585254.i	0.954598	−	0.954598i
$784$		0			0
$785$	−125555.	−	96350.6i	−0.203749	−	0.156356i
$786$		0			0
$787$	618339.	+	618339.i	0.998337	+	0.998337i	0.999999	−	0.00166175i	$-0.000528953\pi$
$787$	618339.	+	618339.i	0.998337	+	0.998337i	−0.00166175	+	0.999999i	$0.500529\pi$
$788$		0			0
$789$			299222.i			0.480661i
$790$		0			0
$791$	1.07856e6			1.72381
$792$		0			0
$793$	−283082.	+	283082.i	−0.450158	+	0.450158i
$794$		0			0
$795$	−18589.9	−	141251.i	−0.0294132	−	0.223490i
$796$		0			0
$797$	−629621.	−	629621.i	−0.991202	−	0.991202i	0.00875927	−	0.999962i	$-0.497212\pi$
$797$	−629621.	−	629621.i	−0.991202	−	0.991202i	−0.999962	+	0.00875927i	$0.997212\pi$
$798$		0			0
$799$		−	410753.i		−	0.643408i
$800$		0			0
$801$	572765.			0.892712
$802$		0			0
$803$	−14583.0	+	14583.0i	−0.0226161	+	0.0226161i
$804$		0			0
$805$	842026.	−	110818.i	1.29937	−	0.171009i
$806$		0			0
$807$	−1.15997e6	−	1.15997e6i	−1.78114	−	1.78114i
$808$		0			0
$809$		−	678155.i		−	1.03617i	−0.855329	−	0.518086i	$-0.826645\pi$
$809$		−	678155.i		−	1.03617i	0.855329	−	0.518086i	$-0.173355\pi$
$810$		0			0
$811$	717645.			1.09111			0.545554	−	0.838076i	$-0.316319\pi$
$811$	717645.			1.09111			0.545554	+	0.838076i	$0.316319\pi$
$812$		0			0
$813$	1.15148e6	−	1.15148e6i	1.74211	−	1.74211i
$814$		0			0
$815$	−599852.	+	781672.i	−0.903085	+	1.17682i
$816$		0			0
$817$	1001.57	+	1001.57i	0.00150051	+	0.00150051i
$818$		0			0
$819$			571763.i			0.852409i
$820$		0			0
$821$	442401.			0.656341			0.328171	−	0.944618i	$-0.393568\pi$
$821$	442401.			0.656341			0.328171	+	0.944618i	$0.393568\pi$
$822$		0			0
$823$	−99684.4	+	99684.4i	−0.147173	+	0.147173i	−0.776854	−	0.629681i	$-0.783186\pi$
$823$	−99684.4	+	99684.4i	−0.147173	+	0.147173i	0.629681	+	0.776854i	$0.283186\pi$
$824$		0			0
$825$	−11888.1	+	20586.7i	−0.0174664	+	0.0302467i
$826$		0			0
$827$	326428.	+	326428.i	0.477284	+	0.477284i	0.904262	−	0.426978i	$-0.140422\pi$
$827$	326428.	+	326428.i	0.477284	+	0.477284i	−0.426978	+	0.904262i	$0.640422\pi$
$828$		0			0
$829$			199488.i			0.290274i	0.989412	+	0.145137i	$0.0463622\pi$
$829$			199488.i			0.290274i	−0.989412	+	0.145137i	$0.953638\pi$
$830$		0			0
$831$	1.35977e6			1.96907
$832$		0			0
$833$	−362143.	+	362143.i	−0.521904	+	0.521904i
$834$		0			0
$835$	12439.0	+	9545.62i	0.0178407	+	0.0136909i
$836$		0			0
$837$	476655.	+	476655.i	0.680383	+	0.680383i
$838$		0			0
$839$			144155.i			0.204788i	0.994744	+	0.102394i	$0.0326503\pi$
$839$			144155.i			0.204788i	−0.994744	+	0.102394i	$0.967350\pi$
$840$		0			0
$841$	−668571.			−0.945269
$842$		0			0
$843$	−1.31655e6	+	1.31655e6i	−1.85261	+	1.85261i
$844$		0			0
$845$	−80864.2	−	614429.i	−0.113251	−	0.860515i
$846$		0			0
$847$	−743213.	−	743213.i	−1.03597	−	1.03597i
$848$		0			0
$849$		−	813472.i		−	1.12857i
$850$		0			0
$851$	−450381.			−0.621901
$852$		0			0
$853$	177183.	−	177183.i	0.243514	−	0.243514i	−0.574788	−	0.818302i	$-0.694915\pi$
$853$	177183.	−	177183.i	0.243514	−	0.243514i	0.818302	+	0.574788i	$0.194915\pi$
$854$		0			0
$855$	−1.29710e6	+	170709.i	−1.77435	+	0.233520i
$856$		0			0
$857$	913058.	+	913058.i	1.24319	+	1.24319i	0.958671	+	0.284517i	$0.0918333\pi$
$857$	913058.	+	913058.i	1.24319	+	1.24319i	0.284517	+	0.958671i	$0.408167\pi$
$858$		0			0
$859$		−	577486.i		−	0.782627i	−0.920257	−	0.391314i	$-0.872021\pi$
$859$		−	577486.i		−	0.782627i	0.920257	−	0.391314i	$-0.127979\pi$
$860$		0			0
$861$	−853286.			−1.15103
$862$		0			0
$863$	851198.	−	851198.i	1.14290	−	1.14290i	0.154985	−	0.987917i	$-0.450467\pi$
$863$	851198.	−	851198.i	1.14290	−	1.14290i	0.987917	−	0.154985i	$-0.0495329\pi$
$864$		0			0
$865$	−866107.	+	1.12863e6i	−1.15755	+	1.50841i
$866$		0			0
$867$	503103.	+	503103.i	0.669297	+	0.669297i
$868$		0			0
$869$		−	10645.5i		−	0.0140970i
$870$		0			0
$871$	61970.0			0.0816856
$872$		0			0
$873$	−1.14137e6	+	1.14137e6i	−1.49761	+	1.49761i
$874$		0			0
$875$	−1.03675e6	−	429592.i	−1.35412	−	0.561100i
$876$		0			0
$877$	−310416.	−	310416.i	−0.403594	−	0.403594i	0.475904	−	0.879497i	$-0.342121\pi$
$877$	−310416.	−	310416.i	−0.403594	−	0.403594i	−0.879497	+	0.475904i	$0.842121\pi$
$878$		0			0
$879$			1.08609e6i			1.40569i
$880$		0			0
$881$	−184629.			−0.237875			−0.118937	−	0.992902i	$-0.537949\pi$
$881$	−184629.			−0.237875			−0.118937	+	0.992902i	$0.537949\pi$
$882$		0			0
$883$	−128659.	+	128659.i	−0.165014	+	0.165014i	−0.784784	−	0.619770i	$-0.787226\pi$
$883$	−128659.	+	128659.i	−0.165014	+	0.165014i	0.619770	+	0.784784i	$0.287226\pi$
$884$		0			0
$885$	1.82305e6	+	1.39900e6i	2.32762	+	1.78620i
$886$		0			0
$887$	867482.	+	867482.i	1.10259	+	1.10259i	0.994098	+	0.108490i	$0.0346015\pi$
$887$	867482.	+	867482.i	1.10259	+	1.10259i	0.108490	+	0.994098i	$0.465399\pi$
$888$		0			0
$889$		−	547706.i		−	0.693017i
$890$		0			0
$891$	678.072			0.000854123
$892$		0			0
$893$	631349.	−	631349.i	0.791711	−	0.791711i
$894$		0			0
$895$	−151486.	−	1.15103e6i	−0.189115	−	1.43695i
$896$		0			0
$897$	298105.	+	298105.i	0.370496	+	0.370496i
$898$		0			0
$899$		−	1.12055e6i		−	1.38648i
$900$		0			0
$901$	72931.0			0.0898385
$902$		0			0
$903$	−2585.88	+	2585.88i	−0.00317127	+	0.00317127i
$904$		0			0
$905$	55356.7	−	7285.42i	0.0675885	−	0.00889523i
$906$		0			0
$907$	−202050.	−	202050.i	−0.245609	−	0.245609i	0.573557	−	0.819166i	$-0.305563\pi$
$907$	−202050.	−	202050.i	−0.245609	−	0.245609i	−0.819166	+	0.573557i	$0.805563\pi$
$908$		0			0
$909$			133705.i			0.161815i
$910$		0			0
$911$	−1.05464e6			−1.27077			−0.635385	−	0.772195i	$-0.719159\pi$
$911$	−1.05464e6			−1.27077			−0.635385	+	0.772195i	$0.719159\pi$
$912$		0			0
$913$	3367.78	−	3367.78i	0.00404020	−	0.00404020i
$914$		0			0
$915$	1.43982e6	−	1.87625e6i	1.71976	−	2.24103i
$916$		0			0
$917$	279171.	+	279171.i	0.331995	+	0.331995i
$918$		0			0
$919$		−	342880.i		−	0.405987i	−0.979180	−	0.202993i	$-0.934933\pi$
$919$		−	342880.i		−	0.405987i	0.979180	−	0.202993i	$-0.0650670\pi$
$920$		0			0
$921$	1.84060e6			2.16990
$922$		0			0
$923$	−12519.3	+	12519.3i	−0.0146952	+	0.0146952i
$924$		0			0
$925$	515366.	+	297606.i	0.602328	+	0.347823i
$926$		0			0
$927$	−487569.	−	487569.i	−0.567384	−	0.567384i
$928$		0			0
$929$			475075.i			0.550467i	0.961377	+	0.275233i	$0.0887551\pi$
$929$			475075.i			0.550467i	−0.961377	+	0.275233i	$0.911245\pi$
$930$		0			0
$931$	−1.11327e6			−1.28440
$932$		0			0
$933$	−1.33963e6	+	1.33963e6i	−1.53894	+	1.53894i
$934$		0			0
$935$	−9654.28	−	7408.65i	−0.0110432	−	0.00847453i
$936$		0			0
$937$	−253616.	−	253616.i	−0.288867	−	0.288867i	0.547765	−	0.836632i	$-0.315479\pi$
$937$	−253616.	−	253616.i	−0.288867	−	0.288867i	−0.836632	+	0.547765i	$0.815479\pi$
$938$		0			0
$939$			137960.i			0.156467i
$940$		0			0
$941$	−796405.			−0.899404			−0.449702	−	0.893179i	$-0.648470\pi$
$941$	−796405.			−0.899404			−0.449702	+	0.893179i	$0.648470\pi$
$942$		0			0
$943$	−273792.	+	273792.i	−0.307892	+	0.307892i
$944$		0			0
$945$	−165322.	−	1.25616e6i	−0.185126	−	1.40664i
$946$		0			0
$947$	−568270.	−	568270.i	−0.633658	−	0.633658i	0.315326	−	0.948984i	$-0.397886\pi$
$947$	−568270.	−	568270.i	−0.633658	−	0.633658i	−0.948984	+	0.315326i	$0.897886\pi$
$948$		0			0
$949$		−	483278.i		−	0.536617i
$950$		0			0
$951$	60815.6			0.0672441
$952$		0			0
$953$	1.01963e6	−	1.01963e6i	1.12269	−	1.12269i	0.131349	−	0.991336i	$-0.458069\pi$
$953$	1.01963e6	−	1.01963e6i	1.12269	−	1.12269i	0.991336	−	0.131349i	$-0.0419309\pi$
$954$		0			0
$955$	1.21251e6	−	159576.i	1.32947	−	0.174969i
$956$		0			0
$957$	31547.7	+	31547.7i	0.0344464	+	0.0344464i
$958$		0			0
$959$			2.29103e6i			2.49112i
$960$		0			0
$961$	−10897.9			−0.0118004
$962$		0			0
$963$	945613.	−	945613.i	1.01967	−	1.01967i
$964$		0			0
$965$	286777.	−	373702.i	0.307957	−	0.401301i
$966$		0			0
$967$	938620.	+	938620.i	1.00378	+	1.00378i	0.999993	+	0.00378276i	$0.00120409\pi$
$967$	938620.	+	938620.i	1.00378	+	1.00378i	0.00378276	+	0.999993i	$0.498796\pi$
$968$		0			0
$969$		−	1.08822e6i		−	1.15897i
$970$		0			0
$971$	−86589.8			−0.0918392			−0.0459196	−	0.998945i	$-0.514622\pi$
$971$	−86589.8			−0.0918392			−0.0459196	+	0.998945i	$0.514622\pi$
$972$		0			0
$973$	356199.	−	356199.i	0.376241	−	0.376241i
$974$		0			0
$975$	−144134.	−	538101.i	−0.151620	−	0.566050i
$976$		0			0
$977$	790687.	+	790687.i	0.828353	+	0.828353i	0.987289	−	0.158936i	$-0.0508063\pi$
$977$	790687.	+	790687.i	0.828353	+	0.828353i	−0.158936	+	0.987289i	$0.550806\pi$
$978$		0			0
$979$			11581.0i			0.0120832i
$980$		0			0
$981$	−1.42904e6			−1.48493
$982$		0			0
$983$	405794.	−	405794.i	0.419951	−	0.419951i	−0.465236	−	0.885187i	$-0.654030\pi$
$983$	405794.	−	405794.i	0.419951	−	0.419951i	0.885187	+	0.465236i	$0.154030\pi$
$984$		0			0
$985$	54361.0	+	41716.4i	0.0560293	+	0.0429966i
$986$		0			0
$987$	1.63003e6	+	1.63003e6i	1.67325	+	1.67325i
$988$		0			0
$989$			1659.45i			0.00169657i
$990$		0			0
$991$	−1.53857e6			−1.56664			−0.783321	−	0.621617i	$-0.786476\pi$
$991$	−1.53857e6			−1.56664			−0.783321	+	0.621617i	$0.786476\pi$
$992$		0			0
$993$	−1.35391e6	+	1.35391e6i	−1.37307	+	1.37307i
$994$		0			0
$995$	164768.	+	1.25196e6i	0.166428	+	1.26457i
$996$		0			0
$997$	−1.29030e6	−	1.29030e6i	−1.29808	−	1.29808i	−0.929661	−	0.368416i	$-0.879900\pi$
$997$	−1.29030e6	−	1.29030e6i	−1.29808	−	1.29808i	−0.368416	−	0.929661i	$-0.620100\pi$
$998$		0			0
$999$			671894.i			0.673240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.5.f.a.17.1	yes	4
3.2	odd	2		180.5.l.a.37.2		4
4.3	odd	2		80.5.p.e.17.2		4
5.2	odd	4		100.5.f.c.93.2		4
5.3	odd	4	inner	20.5.f.a.13.1	✓	4
5.4	even	2		100.5.f.c.57.2		4
8.3	odd	2		320.5.p.l.257.1		4
8.5	even	2		320.5.p.m.257.2		4
15.2	even	4		900.5.l.a.793.1		4
15.8	even	4		180.5.l.a.73.2		4
15.14	odd	2		900.5.l.a.757.1		4
20.3	even	4		80.5.p.e.33.2		4
20.7	even	4		400.5.p.h.193.1		4
20.19	odd	2		400.5.p.h.257.1		4
40.3	even	4		320.5.p.l.193.1		4
40.13	odd	4		320.5.p.m.193.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.5.f.a.13.1	✓	4	5.3	odd	4	inner
20.5.f.a.17.1	yes	4	1.1	even	1	trivial
80.5.p.e.17.2		4	4.3	odd	2
80.5.p.e.33.2		4	20.3	even	4
100.5.f.c.57.2		4	5.4	even	2
100.5.f.c.93.2		4	5.2	odd	4
180.5.l.a.37.2		4	3.2	odd	2
180.5.l.a.73.2		4	15.8	even	4
320.5.p.l.193.1		4	40.3	even	4
320.5.p.l.257.1		4	8.3	odd	2
320.5.p.m.193.2		4	40.13	odd	4
320.5.p.m.257.2		4	8.5	even	2
400.5.p.h.193.1		4	20.7	even	4
400.5.p.h.257.1		4	20.19	odd	2
900.5.l.a.757.1		4	15.14	odd	2
900.5.l.a.793.1		4	15.2	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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	20.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-10.2621 + 10.2621i) q^{3} +(-24.7863 + 3.26209i) q^{5} +(50.7863 + 50.7863i) q^{7} -129.621i q^{9} +O(q^{10})\)	\(q+(-10.2621 + 10.2621i) q^{3} +(-24.7863 + 3.26209i) q^{5} +(50.7863 + 50.7863i) q^{7} -129.621i q^{9} +2.62087 q^{11} +(-43.4275 + 43.4275i) q^{13} +(220.883 - 287.835i) q^{15} +(131.331 + 131.331i) q^{17} +403.725i q^{19} -1042.35 q^{21} +(-334.455 + 334.455i) q^{23} +(603.718 - 161.710i) q^{25} +(498.952 + 498.952i) q^{27} -1172.97i q^{29} +955.313 q^{31} +(-26.8956 + 26.8956i) q^{33} +(-1424.47 - 1093.13i) q^{35} +(673.305 + 673.305i) q^{37} -891.313i q^{39} +818.621 q^{41} +(2.48083 - 2.48083i) q^{43} +(422.835 + 3212.82i) q^{45} +(-1563.81 - 1563.81i) q^{47} +2757.49i q^{49} -2695.46 q^{51} +(277.662 - 277.662i) q^{53} +(-64.9617 + 8.54952i) q^{55} +(-4143.06 - 4143.06i) q^{57} +6333.66i q^{59} +6518.49 q^{61} +(6582.96 - 6582.96i) q^{63} +(934.741 - 1218.07i) q^{65} +(-713.488 - 713.488i) q^{67} -6864.42i q^{69} +288.280 q^{71} +(-5564.19 + 5564.19i) q^{73} +(-4535.92 + 7854.88i) q^{75} +(133.104 + 133.104i) q^{77} -4061.80i q^{79} +258.720 q^{81} +(1284.98 - 1284.98i) q^{83} +(-3683.61 - 2826.79i) q^{85} +(12037.1 + 12037.1i) q^{87} +4418.77i q^{89} -4411.04 q^{91} +(-9803.51 + 9803.51i) q^{93} +(-1316.99 - 10006.8i) q^{95} +(-8805.47 - 8805.47i) q^{97} -339.720i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 10 q^{3} - 6 q^{5} + 110 q^{7}+O(q^{10}) \) 4 * q - 10 * q^3 - 6 * q^5 + 110 * q^7	\( 4 q - 10 q^{3} - 6 q^{5} + 110 q^{7} - 300 q^{11} - 360 q^{13} + 542 q^{15} + 960 q^{17} - 1996 q^{21} - 810 q^{23} + 1856 q^{25} + 2120 q^{27} - 836 q^{31} - 1660 q^{33} - 2562 q^{35} - 660 q^{37} + 2964 q^{41} + 3270 q^{43} + 1474 q^{45} - 2250 q^{47} + 1948 q^{51} + 1980 q^{53} - 6780 q^{55} - 13840 q^{57} + 15828 q^{61} + 12950 q^{63} - 732 q^{65} - 4810 q^{67} - 5988 q^{71} - 14060 q^{73} - 11282 q^{75} - 1020 q^{77} + 8176 q^{81} + 19950 q^{83} + 16376 q^{85} + 24800 q^{87} - 11124 q^{91} - 34060 q^{93} - 15576 q^{95} - 3180 q^{97}+O(q^{100}) \) 4 * q - 10 * q^3 - 6 * q^5 + 110 * q^7 - 300 * q^11 - 360 * q^13 + 542 * q^15 + 960 * q^17 - 1996 * q^21 - 810 * q^23 + 1856 * q^25 + 2120 * q^27 - 836 * q^31 - 1660 * q^33 - 2562 * q^35 - 660 * q^37 + 2964 * q^41 + 3270 * q^43 + 1474 * q^45 - 2250 * q^47 + 1948 * q^51 + 1980 * q^53 - 6780 * q^55 - 13840 * q^57 + 15828 * q^61 + 12950 * q^63 - 732 * q^65 - 4810 * q^67 - 5988 * q^71 - 14060 * q^73 - 11282 * q^75 - 1020 * q^77 + 8176 * q^81 + 19950 * q^83 + 16376 * q^85 + 24800 * q^87 - 11124 * q^91 - 34060 * q^93 - 15576 * q^95 - 3180 * q^97

Introduction

L-functions

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