LMFDB - Embedded newform 81.7.d.c.53.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,7,Mod(26,81)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(81, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("81.26"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	81.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,52] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$18.6343807732$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 10x^{2} + 100 $ x^4 - 10*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.2
Root			$2.73861 - 1.58114i$ of defining polynomial
Character	$\chi$	$=$	81.53
Dual form			81.7.d.c.26.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(8.21584 - 4.74342i) q^{2} +(13.0000 - 22.5167i) q^{4} +(-115.022 - 66.4078i) q^{5} +(201.500 + 349.008i) q^{7} +360.500i q^{8} -1260.00 q^{10} +(-1298.10 + 749.460i) q^{11} +(480.500 - 832.250i) q^{13} +(3310.98 + 1911.60i) q^{14} +(2542.00 + 4402.87i) q^{16} +9619.65i q^{17} +8021.00 q^{19} +(-2990.57 + 1726.60i) q^{20} +(-7110.00 + 12314.9i) q^{22} +(-9185.31 - 5303.14i) q^{23} +(1007.50 + 1745.04i) q^{25} -9116.85i q^{26} +10478.0 q^{28} +(-2136.12 + 1233.29i) q^{29} +(-24427.0 + 42308.8i) q^{31} +(21788.4 + 12579.5i) q^{32} +(45630.0 + 79033.5i) q^{34} -53524.7i q^{35} +24167.0 q^{37} +(65899.2 - 38046.9i) q^{38} +(23940.0 - 41465.3i) q^{40} +(-61290.2 - 35385.9i) q^{41} +(30401.0 + 52656.1i) q^{43} +38971.9i q^{44} -100620. q^{46} +(-23382.3 + 13499.8i) q^{47} +(-22380.0 + 38763.3i) q^{49} +(16554.9 + 9557.98i) q^{50} +(-12493.0 - 21638.5i) q^{52} -137635. i q^{53} +199080. q^{55} +(-125817. + 72640.7i) q^{56} +(-11700.0 + 20265.0i) q^{58} +(84475.3 + 48771.8i) q^{59} +(-136500. - 236424. i) q^{61} +463470. i q^{62} -86696.0 q^{64} +(-110536. + 63817.9i) q^{65} +(42789.5 - 74113.6i) q^{67} +(216602. + 125055. i) q^{68} +(-253890. - 439750. i) q^{70} +341754. i q^{71} -152737. q^{73} +(198552. - 114634. i) q^{74} +(104273. - 180606. i) q^{76} +(-523135. - 302032. i) q^{77} +(37029.5 + 64137.0i) q^{79} -675235. i q^{80} -671400. q^{82} +(83637.2 - 48288.0i) q^{83} +(638820. - 1.10647e6i) q^{85} +(499539. + 288409. i) q^{86} +(-270180. - 467965. i) q^{88} -1.19369e6i q^{89} +387283. q^{91} +(-238818. + 137882. i) q^{92} +(-128070. + 221824. i) q^{94} +(-922589. - 532657. i) q^{95} +(598656. + 1.03690e6i) q^{97} +424631. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 52 q^{4} + 806 q^{7} - 5040 q^{10} + 1922 q^{13} + 10168 q^{16} + 32084 q^{19} - 28440 q^{22} + 4030 q^{25} + 41912 q^{28} - 97708 q^{31} + 182520 q^{34} + 96668 q^{37} + 95760 q^{40} + 121604 q^{43}+ \cdots + 2394626 q^{97}+O(q^{100}) $ 4 * q + 52 * q^4 + 806 * q^7 - 5040 * q^10 + 1922 * q^13 + 10168 * q^16 + 32084 * q^19 - 28440 * q^22 + 4030 * q^25 + 41912 * q^28 - 97708 * q^31 + 182520 * q^34 + 96668 * q^37 + 95760 * q^40 + 121604 * q^43 - 402480 * q^46 - 89520 * q^49 - 49972 * q^52 + 796320 * q^55 - 46800 * q^58 - 545998 * q^61 - 346784 * q^64 + 171158 * q^67 - 1015560 * q^70 - 610948 * q^73 + 417092 * q^76 + 148118 * q^79 - 2685600 * q^82 + 2555280 * q^85 - 1080720 * q^88 + 1549132 * q^91 - 512280 * q^94 + 2394626 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	8.21584	−	4.74342i	1.02698	−	0.592927i	0.110862	−	0.993836i	$-0.464639\pi$
$2$	8.21584	−	4.74342i	1.02698	−	0.592927i	0.916118	+	0.400909i	$0.131306\pi$
$3$		0			0
$3$		0			0
$4$	13.0000	−	22.5167i	0.203125	−	0.351823i
$5$	−115.022	−	66.4078i	−0.920174	−	0.531263i	−0.0364834	−	0.999334i	$-0.511616\pi$
$5$	−115.022	−	66.4078i	−0.920174	−	0.531263i	−0.883691	+	0.468072i	$0.844949\pi$
$6$		0			0
$7$	201.500	+	349.008i	0.587464	+	1.01752i	0.994563	+	0.104133i	$0.0332068\pi$
$7$	201.500	+	349.008i	0.587464	+	1.01752i	−0.407100	+	0.913384i	$0.633460\pi$
$8$			360.500i			0.704101i
$9$		0			0
$10$	−1260.00			−1.26000
$11$	−1298.10	+	749.460i	−0.975284	+	0.563080i	−0.900843	−	0.434145i	$-0.857050\pi$
$11$	−1298.10	+	749.460i	−0.975284	+	0.563080i	−0.0744407	+	0.997225i	$0.523717\pi$
$12$		0			0
$13$	480.500	−	832.250i	0.218707	−	0.378812i	−0.735706	−	0.677301i	$-0.763149\pi$
$13$	480.500	−	832.250i	0.218707	−	0.378812i	0.954413	+	0.298489i	$0.0964827\pi$
$14$	3310.98	+	1911.60i	1.20663	+	0.696646i
$15$		0			0
$16$	2542.00	+	4402.87i	0.620605	+	1.07492i
$17$			9619.65i			1.95800i	0.203863	+	0.978999i	$0.434650\pi$
$17$			9619.65i			1.95800i	−0.203863	+	0.978999i	$0.565350\pi$
$18$		0			0
$19$	8021.00			1.16941			0.584706	−	0.811245i	$-0.301210\pi$
$19$	8021.00			1.16941			0.584706	+	0.811245i	$0.301210\pi$
$20$	−2990.57	+	1726.60i	−0.373821	+	0.215825i
$21$		0			0
$22$	−7110.00	+	12314.9i	−0.667731	+	1.15654i
$23$	−9185.31	−	5303.14i	−0.754936	−	0.435863i	0.0725386	−	0.997366i	$-0.476890\pi$
$23$	−9185.31	−	5303.14i	−0.754936	−	0.435863i	−0.827475	+	0.561503i	$0.810223\pi$
$24$		0			0
$25$	1007.50	+	1745.04i	0.0644800	+	0.111683i
$26$		−	9116.85i		−	0.518710i
$27$		0			0
$28$	10478.0			0.477314
$29$	−2136.12	+	1233.29i	−0.0875853	+	0.0505674i	−0.543153	−	0.839634i	$-0.682770\pi$
$29$	−2136.12	+	1233.29i	−0.0875853	+	0.0505674i	0.455568	+	0.890201i	$0.349436\pi$
$30$		0			0
$31$	−24427.0	+	42308.8i	−0.819946	+	1.42019i	0.0857760	+	0.996314i	$0.472663\pi$
$31$	−24427.0	+	42308.8i	−0.819946	+	1.42019i	−0.905722	+	0.423873i	$0.860670\pi$
$32$	21788.4	+	12579.5i	0.664929	+	0.383897i
$33$		0			0
$34$	45630.0	+	79033.5i	1.16095	+	2.01083i
$35$		−	53524.7i		−	1.24839i
$36$		0			0
$37$	24167.0			0.477109			0.238554	−	0.971129i	$-0.423326\pi$
$37$	24167.0			0.477109			0.238554	+	0.971129i	$0.423326\pi$
$38$	65899.2	−	38046.9i	1.20096	−	0.693376i
$39$		0			0
$40$	23940.0	−	41465.3i	0.374063	−	0.647895i
$41$	−61290.2	−	35385.9i	−0.889281	−	0.513427i	−0.0155739	−	0.999879i	$-0.504958\pi$
$41$	−61290.2	−	35385.9i	−0.889281	−	0.513427i	−0.873707	+	0.486452i	$0.838291\pi$
$42$		0			0
$43$	30401.0	+	52656.1i	0.382369	+	0.662282i	0.991400	−	0.130864i	$-0.0417750\pi$
$43$	30401.0	+	52656.1i	0.382369	+	0.662282i	−0.609032	+	0.793146i	$0.708442\pi$
$44$			38971.9i			0.457503i
$45$		0			0
$46$	−100620.			−1.03374
$47$	−23382.3	+	13499.8i	−0.225213	+	0.130027i	−0.608362	−	0.793660i	$-0.708173\pi$
$47$	−23382.3	+	13499.8i	−0.225213	+	0.130027i	0.383149	+	0.923687i	$0.374840\pi$
$48$		0			0
$49$	−22380.0	+	38763.3i	−0.190227	+	0.329483i
$50$	16554.9	+	9557.98i	0.132439	+	0.0764639i
$51$		0			0
$52$	−12493.0	−	21638.5i	−0.0888499	−	0.153892i
$53$		−	137635.i		−	0.924488i	−0.886753	−	0.462244i	$-0.847044\pi$
$53$		−	137635.i		−	0.924488i	0.886753	−	0.462244i	$-0.152956\pi$
$54$		0			0
$55$	199080.			1.19657
$56$	−125817.	+	72640.7i	−0.716434	+	0.413634i
$57$		0			0
$58$	−11700.0	+	20265.0i	−0.0599656	+	0.103863i
$59$	84475.3	+	48771.8i	0.411314	+	0.237472i	0.691354	−	0.722516i	$-0.257014\pi$
$59$	84475.3	+	48771.8i	0.411314	+	0.237472i	−0.280040	+	0.959988i	$0.590348\pi$
$60$		0			0
$61$	−136500.	−	236424.i	−0.601370	−	1.04160i	−0.992614	−	0.121316i	$-0.961289\pi$
$61$	−136500.	−	236424.i	−0.601370	−	1.04160i	0.391244	−	0.920287i	$-0.372045\pi$
$62$			463470.i			1.94467i
$63$		0			0
$64$	−86696.0			−0.330719
$65$	−110536.	+	63817.9i	−0.402498	+	0.232382i
$66$		0			0
$67$	42789.5	−	74113.6i	0.142270	−	0.246419i	−0.786081	−	0.618123i	$-0.787893\pi$
$67$	42789.5	−	74113.6i	0.142270	−	0.246419i	0.928351	+	0.371705i	$0.121227\pi$
$68$	216602.	+	125055.i	0.688869	+	0.397719i
$69$		0			0
$70$	−253890.	−	439750.i	−0.740204	−	1.28207i
$71$			341754.i			0.954857i	0.878671	+	0.477428i	$0.158431\pi$
$71$			341754.i			0.954857i	−0.878671	+	0.477428i	$0.841569\pi$
$72$		0			0
$73$	−152737.			−0.392623			−0.196311	−	0.980542i	$-0.562896\pi$
$73$	−152737.			−0.392623			−0.196311	+	0.980542i	$0.562896\pi$
$74$	198552.	−	114634.i	0.489981	−	0.282891i
$75$		0			0
$76$	104273.	−	180606.i	0.237537	−	0.411426i
$77$	−523135.	−	302032.i	−1.14589	−	0.661578i
$78$		0			0
$79$	37029.5	+	64137.0i	0.0751046	+	0.130085i	0.901132	−	0.433545i	$-0.142738\pi$
$79$	37029.5	+	64137.0i	0.0751046	+	0.130085i	−0.826027	+	0.563630i	$0.809404\pi$
$80$		−	675235.i		−	1.31882i
$81$		0			0
$82$	−671400.			−1.21770
$83$	83637.2	−	48288.0i	0.146273	−	0.0844510i	−0.425077	−	0.905157i	$-0.639753\pi$
$83$	83637.2	−	48288.0i	0.146273	−	0.0844510i	0.571351	+	0.820706i	$0.306420\pi$
$84$		0			0
$85$	638820.	−	1.10647e6i	1.04021	−	1.80170i
$86$	499539.	+	288409.i	0.785370	+	0.453434i
$87$		0			0
$88$	−270180.	−	467965.i	−0.396465	−	0.686698i
$89$		−	1.19369e6i		−	1.69325i	−0.532188	−	0.846626i	$-0.678630\pi$
$89$		−	1.19369e6i		−	1.69325i	0.532188	−	0.846626i	$-0.321370\pi$
$90$		0			0
$91$	387283.			0.513930
$92$	−238818.	+	137882.i	−0.306693	+	0.177069i
$93$		0			0
$94$	−128070.	+	221824.i	−0.154193	+	0.267070i
$95$	−922589.	−	532657.i	−1.07606	−	0.621265i
$96$		0			0
$97$	598656.	+	1.03690e6i	0.655938	+	1.13612i	0.981658	+	0.190651i	$0.0610599\pi$
$97$	598656.	+	1.03690e6i	0.655938	+	1.13612i	−0.325720	+	0.945466i	$0.605607\pi$
$98$			424631.i			0.451163i
$99$		0			0
$100$	52390.0			0.0523900
$101$	765585.	−	442011.i	0.743069	−	0.429011i	−0.0801151	−	0.996786i	$-0.525529\pi$
$101$	765585.	−	442011.i	0.743069	−	0.429011i	0.823184	+	0.567775i	$0.192195\pi$
$102$		0			0
$103$	−587066.	+	1.01683e6i	−0.537249	+	0.930543i	0.461802	+	0.886983i	$0.347203\pi$
$103$	−587066.	+	1.01683e6i	−0.537249	+	0.930543i	−0.999051	+	0.0435595i	$0.986130\pi$
$104$	300026.	+	173220.i	0.266722	+	0.153992i
$105$		0			0
$106$	−652860.	−	1.13079e6i	−0.548154	−	0.949430i
$107$			583839.i			0.476586i	0.971193	+	0.238293i	$0.0765879\pi$
$107$			583839.i			0.476586i	−0.971193	+	0.238293i	$0.923412\pi$
$108$		0			0
$109$	188786.			0.145777			0.0728887	−	0.997340i	$-0.476778\pi$
$109$	188786.			0.145777			0.0728887	+	0.997340i	$0.476778\pi$
$110$	1.63561e6	−	944319.i	1.22886	−	0.709481i
$111$		0			0
$112$	−1.02443e6	+	1.77436e6i	−0.729166	+	1.26295i
$113$	1.42372e6	+	821987.i	0.986711	+	0.569678i	0.904290	−	0.426920i	$-0.140401\pi$
$113$	1.42372e6	+	821987.i	0.986711	+	0.569678i	0.0824216	+	0.996598i	$0.473735\pi$
$114$		0			0
$115$	704340.	+	1.21995e6i	0.463115	+	0.802139i
$116$			64131.0i			0.0410860i
$117$		0			0
$118$	925380.			0.563215
$119$	−3.35734e6	+	1.93836e6i	−1.99230	+	1.15025i
$120$		0			0
$121$	237600.	−	411534.i	0.134119	−	0.232300i
$122$	−2.24292e6	−	1.29495e6i	−1.23519	−	0.713137i
$123$		0			0
$124$	635102.	+	1.10003e6i	0.333103	+	0.576951i
$125$			1.80762e6i			0.925502i
$126$		0			0
$127$	3.10101e6			1.51388			0.756940	−	0.653484i	$-0.226693\pi$
$127$	3.10101e6			1.51388			0.756940	+	0.653484i	$0.226693\pi$
$128$	−2.10674e6	+	1.21633e6i	−1.00457	+	0.579989i
$129$		0			0
$130$	−605430.	+	1.04864e6i	−0.275571	+	0.477303i
$131$	2.78422e6	+	1.60747e6i	1.23848	+	0.715037i	0.968783	−	0.247908i	$-0.0797432\pi$
$131$	2.78422e6	+	1.60747e6i	1.23848	+	0.715037i	0.269697	+	0.962945i	$0.413077\pi$
$132$		0			0
$133$	1.61623e6	+	2.79940e6i	0.686987	+	1.18990i
$134$		−	811874.i		−	0.337423i
$135$		0			0
$136$	−3.46788e6			−1.37863
$137$	2.49283e6	−	1.43924e6i	0.969464	−	0.559720i	0.0703910	−	0.997519i	$-0.477575\pi$
$137$	2.49283e6	−	1.43924e6i	0.969464	−	0.559720i	0.899073	+	0.437799i	$0.144242\pi$
$138$		0			0
$139$	738310.	−	1.27879e6i	0.274912	−	0.476162i	−0.695201	−	0.718816i	$-0.744685\pi$
$139$	738310.	−	1.27879e6i	0.274912	−	0.476162i	0.970113	+	0.242654i	$0.0780179\pi$
$140$	−1.20520e6	−	695821.i	−0.439212	−	0.253579i
$141$		0			0
$142$	1.62108e6	+	2.80779e6i	0.566160	+	0.980618i
$143$			1.44046e6i			0.492599i
$144$		0			0
$145$	327600.			0.107458
$146$	−1.25486e6	+	724495.i	−0.403216	+	0.232797i
$147$		0			0
$148$	314171.	−	544160.i	0.0969128	−	0.167858i
$149$	−483946.	−	279406.i	−0.146298	−	0.0844651i	0.425064	−	0.905163i	$-0.360251\pi$
$149$	−483946.	−	279406.i	−0.146298	−	0.0844651i	−0.571362	+	0.820698i	$0.693585\pi$
$150$		0			0
$151$	−1.85869e6	−	3.21935e6i	−0.539855	−	0.935056i	−0.998911	−	0.0466492i	$-0.985146\pi$
$151$	−1.85869e6	−	3.21935e6i	−0.539855	−	0.935056i	0.459056	−	0.888407i	$-0.348188\pi$
$152$			2.89157e6i			0.823384i
$153$		0			0
$154$	−5.73066e6			−1.56907
$155$	5.61927e6	−	3.24429e6i	1.50899	−	0.871213i
$156$		0			0
$157$	−618481.	+	1.07124e6i	−0.159819	+	0.276814i	−0.934803	−	0.355166i	$-0.884424\pi$
$157$	−618481.	+	1.07124e6i	−0.159819	+	0.276814i	0.774985	+	0.631980i	$0.217758\pi$
$158$	608457.	+	351293.i	0.154262	+	0.0890631i
$159$		0			0
$160$	−1.67076e6	−	2.89384e6i	−0.407900	−	0.706504i
$161$		−	4.27433e6i		−	1.02421i
$162$		0			0
$163$	6.87639e6			1.58781			0.793903	−	0.608044i	$-0.208046\pi$
$163$	6.87639e6			1.58781			0.793903	+	0.608044i	$0.208046\pi$
$164$	−1.59354e6	+	920033.i	−0.361271	+	0.208580i
$165$		0			0
$166$	458100.	−	793452.i	0.100147	−	0.173459i
$167$	1.66093e6	+	958939.i	0.356617	+	0.205893i	0.667596	−	0.744524i	$-0.267323\pi$
$167$	1.66093e6	+	958939.i	0.356617	+	0.205893i	−0.310979	+	0.950417i	$0.600657\pi$
$168$		0			0
$169$	1.95164e6	+	3.38035e6i	0.404334	+	0.700327i
$170$		−	1.21208e7i		−	2.46708i
$171$		0			0
$172$	1.58085e6			0.310675
$173$	−3.31141e6	+	1.91184e6i	−0.639550	+	0.369244i	−0.784441	−	0.620203i	$-0.787050\pi$
$173$	−3.31141e6	+	1.91184e6i	−0.639550	+	0.369244i	0.144891	+	0.989448i	$0.453717\pi$
$174$		0			0
$175$	−406022.	+	703252.i	−0.0757593	+	0.131219i
$176$	−6.59955e6	−	3.81025e6i	−1.21053	−	0.698901i
$177$		0			0
$178$	−5.66217e6	−	9.80717e6i	−1.00397	−	1.73894i
$179$			1.60130e6i			0.279199i	0.990208	+	0.139600i	$0.0445815\pi$
$179$			1.60130e6i			0.279199i	−0.990208	+	0.139600i	$0.955418\pi$
$180$		0			0
$181$	570647.			0.0962347			0.0481174	−	0.998842i	$-0.484678\pi$
$181$	570647.			0.0962347			0.0481174	+	0.998842i	$0.484678\pi$
$182$	3.18185e6	−	1.83704e6i	0.527796	−	0.304723i
$183$		0			0
$184$	1.91178e6	−	3.31130e6i	0.306891	−	0.531551i
$185$	−2.77973e6	−	1.60488e6i	−0.439023	−	0.253470i
$186$		0			0
$187$	−7.20954e6	−	1.24873e7i	−1.10251	−	1.90960i
$188$			701988.i			0.105647i
$189$		0			0
$190$	−1.01065e7			−1.47346
$191$	3.59103e6	−	2.07328e6i	0.515369	−	0.297549i	−0.219669	−	0.975575i	$-0.570498\pi$
$191$	3.59103e6	−	2.07328e6i	0.515369	−	0.297549i	0.735038	+	0.678026i	$0.237164\pi$
$192$		0			0
$193$	2.23619e6	−	3.87319e6i	0.311054	−	0.538762i	−0.667536	−	0.744577i	$-0.732651\pi$
$193$	2.23619e6	−	3.87319e6i	0.311054	−	0.538762i	0.978591	+	0.205815i	$0.0659845\pi$
$194$	9.83693e6	+	5.67935e6i	1.34727	+	0.777846i
$195$		0			0
$196$	581880.	+	1.00785e6i	0.0772797	+	0.133852i
$197$			1.18772e7i			1.55351i	0.629801	+	0.776757i	$0.283137\pi$
$197$			1.18772e7i			1.55351i	−0.629801	+	0.776757i	$0.716863\pi$
$198$		0			0
$199$	902693.			0.114546			0.0572731	−	0.998359i	$-0.481759\pi$
$199$	902693.			0.114546			0.0572731	+	0.998359i	$0.481759\pi$
$200$	−629087.	+	363203.i	−0.0786358	+	0.0454004i
$201$		0			0
$202$	4.19328e6	−	7.26297e6i	0.508745	−	0.881171i
$203$	−860856.	−	497015.i	−0.102906	−	0.0594130i
$204$		0			0
$205$	4.69980e6	+	8.14029e6i	0.545529	+	0.944884i
$206$			1.11388e7i			1.27420i
$207$		0			0
$208$	4.88572e6			0.542924
$209$	−1.04121e7	+	6.01142e6i	−1.14051	+	0.658473i
$210$		0			0
$211$	−2.83768e6	+	4.91500e6i	−0.302076	+	0.523211i	−0.976606	−	0.215037i	$-0.931013\pi$
$211$	−2.83768e6	+	4.91500e6i	−0.302076	+	0.523211i	0.674530	+	0.738247i	$0.264346\pi$
$212$	−3.09908e6	−	1.78925e6i	−0.325256	−	0.187787i
$213$		0			0
$214$	2.76939e6	+	4.79672e6i	0.282581	+	0.489444i
$215$		−	8.07546e6i		−	0.812553i
$216$		0			0
$217$	−1.96882e7			−1.92675
$218$	1.55104e6	−	895491.i	0.149710	−	0.0864354i
$219$		0			0
$220$	2.58804e6	−	4.48262e6i	0.243054	−	0.420982i
$221$	8.00596e6	+	4.62224e6i	0.741714	+	0.428229i
$222$		0			0
$223$	2.82382e6	+	4.89100e6i	0.254638	+	0.441045i	0.964797	−	0.262996i	$-0.0847105\pi$
$223$	2.82382e6	+	4.89100e6i	0.254638	+	0.441045i	−0.710159	+	0.704041i	$0.751377\pi$
$224$			1.01391e7i			0.902102i
$225$		0			0
$226$	1.55961e7			1.35111
$227$	−1.08964e7	+	6.29106e6i	−0.931552	+	0.537832i	−0.887302	−	0.461189i	$-0.847423\pi$
$227$	−1.08964e7	+	6.29106e6i	−0.931552	+	0.537832i	−0.0442496	+	0.999021i	$0.514090\pi$
$228$		0			0
$229$	3.25883e6	−	5.64445e6i	0.271366	−	0.470019i	−0.697846	−	0.716248i	$-0.745858\pi$
$229$	3.25883e6	−	5.64445e6i	0.271366	−	0.470019i	0.969212	+	0.246229i	$0.0791914\pi$
$230$	1.15735e7	+	6.68196e6i	0.951219	+	0.549187i
$231$		0			0
$232$	−444600.	−	770070.i	−0.0356046	−	0.0616689i
$233$		−	8.32618e6i		−	0.658230i	−0.944290	−	0.329115i	$-0.893250\pi$
$233$		−	8.32618e6i		−	0.658230i	0.944290	−	0.329115i	$-0.106750\pi$
$234$		0			0
$235$	3.58596e6			0.276313
$236$	2.19636e6	−	1.26807e6i	0.167096	−	0.0964731i
$237$		0			0
$238$	−1.83889e7	+	3.18505e7i	−1.36403	+	2.36257i
$239$	−1.80342e7	−	1.04120e7i	−1.32100	−	0.762679i	−0.337110	−	0.941465i	$-0.609450\pi$
$239$	−1.80342e7	−	1.04120e7i	−1.32100	−	0.762679i	−0.983888	+	0.178787i	$0.942783\pi$
$240$		0			0
$241$	−2.31464e6	−	4.00908e6i	−0.165361	−	0.286414i	0.771422	−	0.636323i	$-0.219546\pi$
$241$	−2.31464e6	−	4.00908e6i	−0.165361	−	0.286414i	−0.936783	+	0.349910i	$0.886212\pi$
$242$		−	4.50813e6i		−	0.318090i
$243$		0			0
$244$	−7.09797e6			−0.488613
$245$	5.14837e6	−	2.97241e6i	0.350084	−	0.202121i
$246$		0			0
$247$	3.85409e6	−	6.67548e6i	0.255759	−	0.442988i
$248$	−1.52523e7	−	8.80593e6i	−0.999955	−	0.577324i
$249$		0			0
$250$	8.57430e6	+	1.48511e7i	0.548755	+	0.950472i
$251$		−	1.38242e7i		−	0.874215i	−0.899409	−	0.437107i	$-0.856003\pi$
$251$		−	1.38242e7i		−	0.874215i	0.899409	−	0.437107i	$-0.143997\pi$
$252$		0			0
$253$	1.58980e7			0.981702
$254$	2.54774e7	−	1.47094e7i	1.55472	−	0.897620i
$255$		0			0
$256$	−8.76481e6	+	1.51811e7i	−0.522423	+	0.904864i
$257$	−5.94653e6	−	3.43323e6i	−0.350319	−	0.202257i	0.314507	−	0.949255i	$-0.398161\pi$
$257$	−5.94653e6	−	3.43323e6i	−0.350319	−	0.202257i	−0.664826	+	0.746998i	$0.731494\pi$
$258$		0			0
$259$	4.86965e6	+	8.43448e6i	0.280284	+	0.485466i
$260$			3.31853e6i			0.188810i
$261$		0			0
$262$	3.04996e7			1.69586
$263$	1.21391e7	−	7.00853e6i	0.667299	−	0.385265i	−0.127754	−	0.991806i	$-0.540777\pi$
$263$	1.21391e7	−	7.00853e6i	0.667299	−	0.385265i	0.795052	+	0.606541i	$0.207443\pi$
$264$		0			0
$265$	−9.14004e6	+	1.58310e7i	−0.491146	+	0.850690i
$266$	2.65574e7	+	1.53329e7i	1.41104	+	0.814667i
$267$		0			0
$268$	−1.11253e6	−	1.92695e6i	−0.0577971	−	0.100108i
$269$			3.86044e6i			0.198326i	0.995071	+	0.0991630i	$0.0316165\pi$
$269$			3.86044e6i			0.198326i	−0.995071	+	0.0991630i	$0.968383\pi$
$270$		0			0
$271$	−9.15729e6			−0.460107			−0.230054	−	0.973178i	$-0.573890\pi$
$271$	−9.15729e6			−0.460107			−0.230054	+	0.973178i	$0.573890\pi$
$272$	−4.23541e7	+	2.44531e7i	−2.10469	+	1.21514i
$273$		0			0
$274$	1.36538e7	−	2.36491e7i	0.663746	−	1.14964i
$275$	−2.61568e6	−	1.51016e6i	−0.125773	−	0.0726148i
$276$		0			0
$277$	6.42492e6	+	1.11283e7i	0.302293	+	0.523587i	0.976655	−	0.214814i	$-0.0689145\pi$
$277$	6.42492e6	+	1.11283e7i	0.302293	+	0.523587i	−0.674362	+	0.738401i	$0.735581\pi$
$278$		−	1.40084e7i		−	0.652012i
$279$		0			0
$280$	1.92956e7			0.878992
$281$	2.81343e7	−	1.62433e7i	1.26799	−	0.732076i	0.293385	−	0.955994i	$-0.405218\pi$
$281$	2.81343e7	−	1.62433e7i	1.26799	−	0.732076i	0.974608	+	0.223918i	$0.0718848\pi$
$282$		0			0
$283$	1.43908e6	−	2.49256e6i	0.0634930	−	0.109973i	−0.832532	−	0.553978i	$-0.813109\pi$
$283$	1.43908e6	−	2.49256e6i	0.0634930	−	0.109973i	0.896025	+	0.444005i	$0.146443\pi$
$284$	7.69515e6	+	4.44280e6i	0.335940	+	0.193955i
$285$		0			0
$286$	6.83271e6	+	1.18346e7i	0.292075	+	0.505889i
$287$		−	2.85210e7i		−	1.20648i
$288$		0			0
$289$	−6.84001e7			−2.83376
$290$	2.69151e6	−	1.55394e6i	0.110357	−	0.0637149i
$291$		0			0
$292$	−1.98558e6	+	3.43913e6i	−0.0797515	+	0.138134i
$293$	−3.58268e6	−	2.06846e6i	−0.142431	−	0.0822327i	0.427091	−	0.904209i	$-0.359538\pi$
$293$	−3.58268e6	−	2.06846e6i	−0.142431	−	0.0822327i	−0.569522	+	0.821976i	$0.692872\pi$
$294$		0			0
$295$	−6.47766e6	−	1.12196e7i	−0.252320	−	0.437031i
$296$			8.71220e6i			0.335933i
$297$		0			0
$298$	−5.30136e6			−0.200327
$299$	−8.82708e6	+	5.09632e6i	−0.330220	+	0.190653i
$300$		0			0
$301$	−1.22516e7	+	2.12204e7i	−0.449256	+	0.778133i
$302$	−3.05415e7	−	1.76331e7i	−1.10884	−	0.640189i
$303$		0			0
$304$	2.03894e7	+	3.53154e7i	0.725744	+	1.25703i
$305$			3.62585e7i			1.27794i
$306$		0			0
$307$	4.41342e6			0.152532			0.0762659	−	0.997088i	$-0.475700\pi$
$307$	4.41342e6			0.152532			0.0762659	+	0.997088i	$0.475700\pi$
$308$	−1.36015e7	+	7.85284e6i	−0.465517	+	0.268766i
$309$		0			0
$310$	3.07780e7	−	5.33091e7i	1.03313	−	1.78944i
$311$	1.15733e7	+	6.68183e6i	0.384747	+	0.222134i	0.679882	−	0.733322i	$-0.262031\pi$
$311$	1.15733e7	+	6.68183e6i	0.384747	+	0.222134i	−0.295135	+	0.955456i	$0.595365\pi$
$312$		0			0
$313$	−3.00206e7	−	5.19973e7i	−0.979010	−	1.69569i	−0.666013	−	0.745940i	$-0.732001\pi$
$313$	−3.00206e7	−	5.19973e7i	−0.979010	−	1.69569i	−0.312996	−	0.949754i	$-0.601333\pi$
$314$			1.17349e7i			0.379043i
$315$		0			0
$316$	1.92553e6			0.0610225
$317$	−5.07484e7	+	2.92996e7i	−1.59311	+	0.919780i	−0.600336	+	0.799748i	$0.704966\pi$
$317$	−5.07484e7	+	2.92996e7i	−1.59311	+	0.919780i	−0.992770	+	0.120032i	$0.961700\pi$
$318$		0			0
$319$	1.84860e6	−	3.20187e6i	0.0569470	−	0.0986351i
$320$	9.97192e6	+	5.75729e6i	0.304319	+	0.175699i
$321$		0			0
$322$	−2.02749e7	−	3.51172e7i	−0.607284	−	1.05185i
$323$			7.71592e7i			2.28971i
$324$		0			0
$325$	1.93642e6			0.0564090
$326$	5.64953e7	−	3.26176e7i	1.63065	−	0.941454i
$327$		0			0
$328$	1.27566e7	−	2.20951e7i	0.361504	−	0.626144i
$329$	−9.42306e6	−	5.44040e6i	−0.264609	−	0.152772i
$330$		0			0
$331$	−5.48803e6	−	9.50555e6i	−0.151333	−	0.262116i	0.780385	−	0.625299i	$-0.215023\pi$
$331$	−5.48803e6	−	9.50555e6i	−0.151333	−	0.262116i	−0.931718	+	0.363183i	$0.881690\pi$
$332$		−	2.51097e6i		−	0.0686164i
$333$		0			0
$334$	1.81946e7			0.488318
$335$	−9.84345e6	+	5.68312e6i	−0.261826	+	0.151165i
$336$		0			0
$337$	−4.25818e6	+	7.37538e6i	−0.111259	+	0.192706i	−0.916278	−	0.400543i	$-0.868822\pi$
$337$	−4.25818e6	+	7.37538e6i	−0.111259	+	0.192706i	0.805019	+	0.593249i	$0.202155\pi$
$338$	3.20688e7	+	1.85149e7i	0.830486	+	0.479481i
$339$		0			0
$340$	−1.66093e7	−	2.87682e7i	−0.422586	−	0.731940i
$341$		−	7.32282e7i		−	1.84678i
$342$		0			0
$343$	2.93743e7			0.727922
$344$	−1.89825e7	+	1.09595e7i	−0.466314	+	0.269226i
$345$		0			0
$346$	−1.81373e7	+	3.14148e7i	−0.437870	+	0.758413i
$347$	4.57445e7	+	2.64106e7i	1.09484	+	0.632106i	0.934861	−	0.355014i	$-0.115524\pi$
$347$	4.57445e7	+	2.64106e7i	1.09484	+	0.632106i	0.159979	+	0.987120i	$0.448857\pi$
$348$		0			0
$349$	−2.49584e7	−	4.32291e7i	−0.587137	−	1.01695i	−0.994605	−	0.103732i	$-0.966922\pi$
$349$	−2.49584e7	−	4.32291e7i	−0.587137	−	1.01695i	0.407468	−	0.913220i	$-0.366412\pi$
$350$			7.70374e6i			0.179679i
$351$		0			0
$352$	−3.77114e7			−0.864660
$353$	225903.	−	130425.i	0.00513567	−	0.00296508i	−0.497430	−	0.867504i	$-0.665723\pi$
$353$	225903.	−	130425.i	0.00513567	−	0.00296508i	0.502566	+	0.864539i	$0.332390\pi$
$354$		0			0
$355$	2.26951e7	−	3.93091e7i	0.507280	−	0.878634i
$356$	−2.68779e7	−	1.55180e7i	−0.595725	−	0.343942i
$357$		0			0
$358$	7.59564e6	+	1.31560e7i	0.165545	+	0.286732i
$359$		−	256884.i		−	0.00555206i	−0.999996	−	0.00277603i	$-0.999116\pi$
$359$		−	256884.i		−	0.00555206i	0.999996	−	0.00277603i	$-0.000883640\pi$
$360$		0			0
$361$	1.72906e7			0.367525
$362$	4.68834e6	−	2.70682e6i	0.0988311	−	0.0570602i
$363$		0			0
$364$	5.03468e6	−	8.72032e6i	0.104392	−	0.180812i
$365$	1.75681e7	+	1.01429e7i	0.361281	+	0.208586i
$366$		0			0
$367$	−1.62845e7	−	2.82055e7i	−0.329439	−	0.570606i	0.652961	−	0.757391i	$-0.273526\pi$
$367$	−1.62845e7	−	2.82055e7i	−0.329439	−	0.570606i	−0.982401	+	0.186786i	$0.940193\pi$
$368$		−	5.39223e7i		−	1.08199i
$369$		0			0
$370$	−3.04504e7			−0.601157
$371$	4.80357e7	−	2.77334e7i	0.940682	−	0.543103i
$372$		0			0
$373$	−4.16734e7	+	7.21804e7i	−0.803031	+	1.39089i	0.114582	+	0.993414i	$0.463447\pi$
$373$	−4.16734e7	+	7.21804e7i	−0.803031	+	1.39089i	−0.917613	+	0.397476i	$0.869886\pi$
$374$	−1.18465e8	−	6.83957e7i	−2.26451	−	1.30742i
$375$		0			0
$376$	−4.86666e6	−	8.42930e6i	−0.0915519	−	0.158573i
$377$			2.37038e6i			0.0442378i
$378$		0			0
$379$	−7.31011e7			−1.34278			−0.671392	−	0.741103i	$-0.734303\pi$
$379$	−7.31011e7			−1.34278			−0.671392	+	0.741103i	$0.734303\pi$
$380$	−2.39873e7	+	1.38491e7i	−0.437151	+	0.252389i
$381$		0			0
$382$	1.96689e7	−	3.40675e7i	0.352849	−	0.611153i
$383$	−3.41653e7	−	1.97253e7i	−0.608119	−	0.351098i	0.164110	−	0.986442i	$-0.447525\pi$
$383$	−3.41653e7	−	1.97253e7i	−0.608119	−	0.351098i	−0.772229	+	0.635344i	$0.780858\pi$
$384$		0			0
$385$	4.01146e7	+	6.94806e7i	0.702944	+	1.21753i
$386$		−	4.24287e7i		−	0.737731i
$387$		0			0
$388$	3.11301e7			0.532949
$389$	6.50125e7	−	3.75350e7i	1.10446	−	0.637658i	0.167068	−	0.985945i	$-0.446570\pi$
$389$	6.50125e7	−	3.75350e7i	1.10446	−	0.637658i	0.937388	+	0.348288i	$0.113237\pi$
$390$		0			0
$391$	5.10143e7	−	8.83594e7i	0.853418	−	1.47816i
$392$	−1.39742e7	−	8.06798e6i	−0.231989	−	0.133939i
$393$		0			0
$394$	5.63385e7	+	9.75811e7i	0.921120	+	1.59543i
$395$		−	9.83620e6i		−	0.159601i
$396$		0			0
$397$	6.34586e7			1.01419			0.507095	−	0.861890i	$-0.330719\pi$
$397$	6.34586e7			1.01419			0.507095	+	0.861890i	$0.330719\pi$
$398$	7.41638e6	−	4.28185e6i	0.117637	−	0.0679176i
$399$		0			0
$400$	−5.12213e6	+	8.87179e6i	−0.0800333	+	0.138622i
$401$	6.61911e7	+	3.82155e7i	1.02652	+	0.592661i	0.915985	−	0.401212i	$-0.131411\pi$
$401$	6.61911e7	+	3.82155e7i	1.02652	+	0.592661i	0.110533	+	0.993872i	$0.464744\pi$
$402$		0			0
$403$	2.34743e7	+	4.06588e7i	0.358656	+	0.621211i
$404$		−	2.29845e7i		−	0.348571i
$405$		0			0
$406$	−9.43020e6			−0.140910
$407$	−3.13712e7	+	1.81122e7i	−0.465317	+	0.268651i
$408$		0			0
$409$	−5.31235e7	+	9.20127e7i	−0.776456	+	1.34486i	0.157516	+	0.987516i	$0.449651\pi$
$409$	−5.31235e7	+	9.20127e7i	−0.776456	+	1.34486i	−0.933972	+	0.357345i	$0.883682\pi$
$410$	7.72256e7	+	4.45862e7i	1.12049	+	0.646918i
$411$		0			0
$412$	1.52637e7	+	2.64376e7i	0.218257	+	0.378033i
$413$			3.93101e7i			0.558025i
$414$		0			0
$415$	−1.28268e7			−0.179463
$416$	2.09387e7	−	1.20889e7i	0.290850	−	0.167922i
$417$		0			0
$418$	−5.70293e7	+	9.87777e7i	−0.780853	+	1.35248i
$419$	3.27247e7	+	1.88936e7i	0.444870	+	0.256846i	0.705661	−	0.708549i	$-0.250650\pi$
$419$	3.27247e7	+	1.88936e7i	0.444870	+	0.256846i	−0.260791	+	0.965395i	$0.583983\pi$
$420$		0			0
$421$	7.87278e6	+	1.36361e7i	0.105507	+	0.182744i	0.913945	−	0.405837i	$-0.133020\pi$
$421$	7.87278e6	+	1.36361e7i	0.105507	+	0.182744i	−0.808438	+	0.588581i	$0.799687\pi$
$422$			5.38412e7i			0.716435i
$423$		0			0
$424$	4.96174e7			0.650933
$425$	−1.67867e7	+	9.69180e6i	−0.218674	+	0.126252i
$426$		0			0
$427$	5.50093e7	−	9.52789e7i	0.706566	−	1.22381i
$428$	1.31461e7	+	7.58990e6i	0.167674	+	0.0968066i
$429$		0			0
$430$	−3.83053e7	−	6.63467e7i	−0.481785	−	0.834476i
$431$			3.16419e7i			0.395212i	0.980282	+	0.197606i	$0.0633167\pi$
$431$			3.16419e7i			0.395212i	−0.980282	+	0.197606i	$0.936683\pi$
$432$		0			0
$433$	−6.50979e7			−0.801868			−0.400934	−	0.916107i	$-0.631314\pi$
$433$	−6.50979e7			−0.801868			−0.400934	+	0.916107i	$0.631314\pi$
$434$	−1.61755e8	+	9.33892e7i	−1.97874	+	1.14242i
$435$		0			0
$436$	2.45422e6	−	4.25083e6i	0.0296110	−	0.0512878i
$437$	−7.36753e7	−	4.25365e7i	−0.882832	−	0.509703i
$438$		0			0
$439$	1.57538e7	+	2.72864e7i	0.186205	+	0.322517i	0.943982	−	0.329997i	$-0.107048\pi$
$439$	1.57538e7	+	2.72864e7i	0.186205	+	0.322517i	−0.757777	+	0.652514i	$0.773714\pi$
$440$			7.17683e7i			0.842509i
$441$		0			0
$442$	8.77009e7			1.01563
$443$	−1.22241e7	+	7.05762e6i	−0.140607	+	0.0811796i	−0.568653	−	0.822577i	$-0.692535\pi$
$443$	−1.22241e7	+	7.05762e6i	−0.140607	+	0.0811796i	0.428046	+	0.903757i	$0.359202\pi$
$444$		0			0
$445$	−7.92704e7	+	1.37300e8i	−0.899562	+	1.55809i
$446$	4.64001e7	+	2.67891e7i	0.523015	+	0.301963i
$447$		0			0
$448$	−1.74692e7	−	3.02576e7i	−0.194285	−	0.336512i
$449$			4.88403e7i			0.539560i	0.962922	+	0.269780i	$0.0869509\pi$
$449$			4.88403e7i			0.539560i	−0.962922	+	0.269780i	$0.913049\pi$
$450$		0			0
$451$	1.06081e8			1.15640
$452$	3.70168e7	−	2.13717e7i	0.400851	−	0.231432i
$453$		0			0
$454$	−5.96822e7	+	1.03373e8i	−0.637790	+	1.10468i
$455$	−4.45460e7	−	2.57186e7i	−0.472905	−	0.273032i
$456$		0			0
$457$	8.14710e7	+	1.41112e8i	0.853600	+	1.47848i	0.877938	+	0.478775i	$0.158919\pi$
$457$	8.14710e7	+	1.41112e8i	0.853600	+	1.47848i	−0.0243379	+	0.999704i	$0.507748\pi$
$458$		−	6.18319e7i		−	0.643600i
$459$		0			0
$460$	3.66257e7			0.376281
$461$	1.04904e8	−	6.05666e7i	1.07076	−	0.618202i	0.142369	−	0.989814i	$-0.454528\pi$
$461$	1.04904e8	−	6.05666e7i	1.07076	−	0.618202i	0.928388	+	0.371612i	$0.121195\pi$
$462$		0			0
$463$	5.41193e7	−	9.37373e7i	0.545267	−	0.944429i	−0.453324	−	0.891346i	$-0.649762\pi$
$463$	5.41193e7	−	9.37373e7i	0.545267	−	0.944429i	0.998590	−	0.0530833i	$-0.0169049\pi$
$464$	−1.08600e7	−	6.27004e6i	−0.108712	−	0.0627648i
$465$		0			0
$466$	−3.94945e7	−	6.84065e7i	−0.390283	−	0.675989i
$467$			5.06445e7i			0.497258i	0.968599	+	0.248629i	$0.0799799\pi$
$467$			5.06445e7i			0.497258i	−0.968599	+	0.248629i	$0.920020\pi$
$468$		0			0
$469$	3.44883e7			0.334313
$470$	2.94617e7	−	1.70097e7i	0.283768	−	0.163834i
$471$		0			0
$472$	−1.75822e7	+	3.04533e7i	−0.167204	+	0.289607i
$473$	−7.89272e7	−	4.55687e7i	−0.745836	−	0.430609i
$474$		0			0
$475$	8.08116e6	+	1.39970e7i	0.0754037	+	0.130603i
$476$			1.00795e8i			0.934581i
$477$		0			0
$478$	−1.97554e8			−1.80885
$479$	−1.52392e8	+	8.79833e7i	−1.38661	+	0.800560i	−0.992932	−	0.118688i	$-0.962131\pi$
$479$	−1.52392e8	+	8.79833e7i	−1.38661	+	0.800560i	−0.393679	+	0.919248i	$0.628798\pi$
$480$		0			0
$481$	1.16122e7	−	2.01130e7i	0.104347	−	0.180735i
$482$	−3.80335e7	−	2.19586e7i	−0.339645	−	0.196094i
$483$		0			0
$484$	−6.17759e6	−	1.06999e7i	−0.0544857	−	0.0943721i
$485$		−	1.59022e8i		−	1.39390i
$486$		0			0
$487$	1.32967e8			1.15121			0.575607	−	0.817726i	$-0.304766\pi$
$487$	1.32967e8			1.15121			0.575607	+	0.817726i	$0.304766\pi$
$488$	8.52308e7	−	4.92080e7i	0.733394	−	0.423425i
$489$		0			0
$490$	2.81988e7	−	4.88418e7i	0.239686	−	0.415148i
$491$	1.85642e8	+	1.07181e8i	1.56831	+	0.905464i	0.996366	+	0.0851718i	$0.0271439\pi$
$491$	1.85642e8	+	1.07181e8i	1.56831	+	0.905464i	0.571944	+	0.820293i	$0.306189\pi$
$492$		0			0
$493$	−1.18638e7	−	2.05487e7i	−0.0990109	−	0.171492i
$494$		−	7.31262e7i		−	0.606586i
$495$		0			0
$496$	−2.48374e8			−2.03545
$497$	−1.19275e8	+	6.88634e7i	−0.971583	+	0.560943i
$498$		0			0
$499$	9.10615e7	−	1.57723e8i	0.732880	−	1.26939i	−0.222767	−	0.974872i	$-0.571509\pi$
$499$	9.10615e7	−	1.57723e8i	0.732880	−	1.26939i	0.955647	−	0.294514i	$-0.0951578\pi$
$500$	4.07016e7	+	2.34991e7i	0.325613	+	0.187993i
$501$		0			0
$502$	−6.55738e7	−	1.13577e8i	−0.518346	−	0.897801i
$503$		−	9.74226e7i		−	0.765519i	−0.923848	−	0.382759i	$-0.874974\pi$
$503$		−	9.74226e7i		−	0.765519i	0.923848	−	0.382759i	$-0.125026\pi$
$504$		0			0
$505$	−1.17412e8			−0.911670
$506$	1.30615e8	−	7.54106e7i	1.00819	−	0.582078i
$507$		0			0
$508$	4.03131e7	−	6.98243e7i	0.307507	−	0.532618i
$509$	2.23945e7	+	1.29295e7i	0.169820	+	0.0980455i	0.582501	−	0.812830i	$-0.302074\pi$
$509$	2.23945e7	+	1.29295e7i	0.169820	+	0.0980455i	−0.412681	+	0.910876i	$0.635408\pi$
$510$		0			0
$511$	−3.07765e7	−	5.33065e7i	−0.230652	−	0.399500i
$512$			1.06108e7i			0.0790569i
$513$		0			0
$514$	−6.51409e7			−0.479694
$515$	1.35051e8	−	7.79716e7i	0.988725	−	0.570841i
$516$		0			0
$517$	2.02351e7	−	3.50482e7i	0.146431	−	0.253626i
$518$	8.00165e7	+	4.61976e7i	0.575692	+	0.332376i
$519$		0			0
$520$	−2.30063e7	−	3.98481e7i	−0.163620	−	0.283399i
$521$		−	1.94679e8i		−	1.37659i	−0.725430	−	0.688296i	$-0.758359\pi$
$521$		−	1.94679e8i		−	1.37659i	0.725430	−	0.688296i	$-0.241641\pi$
$522$		0			0
$523$	6.83930e7			0.478086			0.239043	−	0.971009i	$-0.423166\pi$
$523$	6.83930e7			0.478086			0.239043	+	0.971009i	$0.423166\pi$
$524$	7.23896e7	−	4.17942e7i	0.503133	−	0.290484i
$525$		0			0
$526$	6.64888e7	−	1.15162e8i	0.456868	−	0.791319i
$527$	−4.06996e8	−	2.34979e8i	−2.78073	−	1.60545i
$528$		0			0
$529$	−1.77714e7	−	3.07809e7i	−0.120048	−	0.207929i
$530$			1.73420e8i			1.16485i
$531$		0			0
$532$	8.40440e7			0.558177
$533$	−5.88998e7	+	3.40058e7i	−0.388985	+	0.224580i
$534$		0			0
$535$	3.87715e7	−	6.71541e7i	0.253192	−	0.438542i
$536$	2.67179e7	+	1.54256e7i	0.173504	+	0.100172i
$537$		0			0
$538$	1.83117e7	+	3.17167e7i	0.117593	+	0.203677i
$539$		−	6.70916e7i		−	0.428452i
$540$		0			0
$541$	1.37627e8			0.869187			0.434593	−	0.900627i	$-0.356892\pi$
$541$	1.37627e8			0.869187			0.434593	+	0.900627i	$0.356892\pi$
$542$	−7.52348e7	+	4.34368e7i	−0.472521	+	0.272810i
$543$		0			0
$544$	−1.21011e8	+	2.09597e8i	−0.751670	+	1.30193i
$545$	−2.17145e7	−	1.25369e7i	−0.134141	−	0.0774461i
$546$		0			0
$547$	−6.91760e7	−	1.19816e8i	−0.422662	−	0.732072i	0.573537	−	0.819180i	$-0.305571\pi$
$547$	−6.91760e7	−	1.19816e8i	−0.422662	−	0.732072i	−0.996199	+	0.0871077i	$0.972238\pi$
$548$		−	7.48404e7i		−	0.454773i
$549$		0			0
$550$	−2.86533e7			−0.172221
$551$	−1.71338e7	+	9.89221e6i	−0.102423	+	0.0591341i
$552$		0			0
$553$	−1.49229e7	+	2.58472e7i	−0.0882424	+	0.152840i
$554$	1.05572e8	+	6.09521e7i	0.620898	+	0.358476i
$555$		0			0
$556$	−1.91960e7	−	3.32485e7i	−0.111683	−	0.193441i
$557$			2.31331e8i			1.33866i	0.742967	+	0.669328i	$0.233418\pi$
$557$			2.31331e8i			1.33866i	−0.742967	+	0.669328i	$0.766582\pi$
$558$		0			0
$559$	5.84307e7			0.334507
$560$	2.35663e8	−	1.36060e8i	1.34192	−	0.774758i
$561$		0			0
$562$	1.54098e8	−	2.66905e8i	0.868136	−	1.50365i
$563$	1.65417e7	+	9.55034e6i	0.0926945	+	0.0535172i	0.545631	−	0.838026i	$-0.316290\pi$
$563$	1.65417e7	+	9.55034e6i	0.0926945	+	0.0535172i	−0.452936	+	0.891543i	$0.649623\pi$
$564$		0			0
$565$	−1.09173e8	−	1.89093e8i	−0.605297	−	1.04841i
$566$		−	2.73046e7i		−	0.150587i
$567$		0			0
$568$	−1.23202e8			−0.672315
$569$	4.53306e6	−	2.61716e6i	0.0246068	−	0.0142067i	−0.487646	−	0.873041i	$-0.662144\pi$
$569$	4.53306e6	−	2.61716e6i	0.0246068	−	0.0142067i	0.512253	+	0.858835i	$0.328811\pi$
$570$		0			0
$571$	−1.47069e8	+	2.54731e8i	−0.789975	+	1.36828i	0.136006	+	0.990708i	$0.456573\pi$
$571$	−1.47069e8	+	2.54731e8i	−0.789975	+	1.36828i	−0.925981	+	0.377569i	$0.876760\pi$
$572$	3.24344e7	+	1.87260e7i	0.173308	+	0.100059i
$573$		0			0
$574$	−1.35287e8	−	2.34324e8i	−0.715354	−	1.23903i
$575$		−	2.13717e7i		−	0.112418i
$576$		0			0
$577$	−1.42033e8			−0.739368			−0.369684	−	0.929158i	$-0.620534\pi$
$577$	−1.42033e8			−0.739368			−0.369684	+	0.929158i	$0.620534\pi$
$578$	−5.61964e8	+	3.24450e8i	−2.91021	+	1.68021i
$579$		0			0
$580$	4.25880e6	−	7.37646e6i	0.0218275	−	0.0378063i
$581$	3.37058e7	+	1.94601e7i	0.171861	+	0.0992238i
$582$		0			0
$583$	1.03152e8	+	1.78664e8i	0.520561	+	0.901638i
$584$		−	5.50616e7i		−	0.276446i
$585$		0			0
$586$	−3.92463e7			−0.195032
$587$	9.13958e6	−	5.27674e6i	0.0451868	−	0.0260886i	−0.477236	−	0.878775i	$-0.658361\pi$
$587$	9.13958e6	−	5.27674e6i	0.0451868	−	0.0260886i	0.522423	+	0.852686i	$0.325028\pi$
$588$		0			0
$589$	−1.95929e8	+	3.39359e8i	−0.958855	+	1.66078i
$590$	−1.06439e8	−	6.14525e7i	−0.518256	−	0.299215i
$591$		0			0
$592$	6.14325e7	+	1.06404e8i	0.296096	+	0.512854i
$593$			3.33771e8i			1.60061i	0.599596	+	0.800303i	$0.295328\pi$
$593$			3.33771e8i			1.60061i	−0.599596	+	0.800303i	$0.704672\pi$
$594$		0			0
$595$	5.14889e8			2.44435
$596$	−1.25826e7	+	7.26456e6i	−0.0594335	+	0.0343139i
$597$		0			0
$598$	−4.83479e7	+	8.37410e7i	−0.226086	+	0.391593i
$599$	3.05735e8	+	1.76516e8i	1.42254	+	0.821305i	0.996516	−	0.0834057i	$-0.0265797\pi$
$599$	3.05735e8	+	1.76516e8i	1.42254	+	0.821305i	0.426026	+	0.904711i	$0.359913\pi$
$600$		0			0
$601$	1.70638e8	+	2.95554e8i	0.786055	+	1.36149i	0.928367	+	0.371665i	$0.121213\pi$
$601$	1.70638e8	+	2.95554e8i	0.786055	+	1.36149i	−0.142312	+	0.989822i	$0.545454\pi$
$602$			2.32458e8i			1.06550i
$603$		0			0
$604$	−9.66521e7			−0.438632
$605$	−5.46582e7	+	3.15569e7i	−0.246825	+	0.142505i
$606$		0			0
$607$	1.14781e8	−	1.98806e8i	0.513220	−	0.888922i	−0.486663	−	0.873590i	$-0.661786\pi$
$607$	1.14781e8	−	1.98806e8i	0.513220	−	0.888922i	0.999882	−	0.0153325i	$-0.00488067\pi$
$608$	1.74765e8	+	1.00900e8i	0.777577	+	0.448934i
$609$		0			0
$610$	1.71989e8	+	2.97894e8i	0.757726	+	1.31242i
$611$			2.59465e7i			0.113751i
$612$		0			0
$613$	−3.31047e8			−1.43717			−0.718586	−	0.695438i	$-0.755210\pi$
$613$	−3.31047e8			−1.43717			−0.718586	+	0.695438i	$0.755210\pi$
$614$	3.62600e7	−	2.09347e7i	0.156647	−	0.0904402i
$615$		0			0
$616$	1.08883e8	−	1.88590e8i	0.465818	−	0.806820i
$617$	3.10951e8	+	1.79528e8i	1.32384	+	0.764321i	0.984340	−	0.176283i	$-0.0564074\pi$
$617$	3.10951e8	+	1.79528e8i	1.32384	+	0.764321i	0.339504	+	0.940605i	$0.389741\pi$
$618$		0			0
$619$	7.55653e6	+	1.30883e7i	0.0318603	+	0.0551837i	0.881516	−	0.472154i	$-0.156523\pi$
$619$	7.55653e6	+	1.30883e7i	0.0318603	+	0.0551837i	−0.849656	+	0.527338i	$0.823190\pi$
$620$		−	1.68703e8i		−	0.707861i
$621$		0			0
$622$	1.26779e8			0.526836
$623$	4.16608e8	−	2.40529e8i	1.72291	−	0.994724i
$624$		0			0
$625$	1.35782e8	−	2.35182e8i	0.556165	−	0.963305i
$626$	−4.93289e8	−	2.84801e8i	−2.01085	−	1.16096i
$627$		0			0
$628$	1.60805e7	+	2.78523e7i	0.0649263	+	0.112456i
$629$			2.32478e8i			0.934179i
$630$		0			0
$631$	−1.91510e7			−0.0762259			−0.0381129	−	0.999273i	$-0.512135\pi$
$631$	−1.91510e7			−0.0762259			−0.0381129	+	0.999273i	$0.512135\pi$
$632$	−2.31214e7	+	1.33491e7i	−0.0915930	+	0.0528812i
$633$		0			0
$634$	−2.77960e8	+	4.81442e8i	−1.09073	+	1.88919i
$635$	−3.56683e8	−	2.05931e8i	−1.39303	−	0.804268i
$636$		0			0
$637$	2.15072e7	+	3.72515e7i	0.0832080	+	0.144121i
$638$		−	3.50747e7i		−	0.135062i
$639$		0			0
$640$	3.23094e8			1.23251
$641$	−6.51610e7	+	3.76207e7i	−0.247408	+	0.142841i	−0.618577	−	0.785724i	$-0.712290\pi$
$641$	−6.51610e7	+	3.76207e7i	−0.247408	+	0.142841i	0.371169	+	0.928565i	$0.378957\pi$
$642$		0			0
$643$	1.10786e8	−	1.91887e8i	0.416728	−	0.721795i	−0.578880	−	0.815413i	$-0.696510\pi$
$643$	1.10786e8	−	1.91887e8i	0.416728	−	0.721795i	0.995608	+	0.0936182i	$0.0298433\pi$
$644$	−9.62436e7	−	5.55663e7i	−0.360342	−	0.208043i
$645$		0			0
$646$	3.65998e8	+	6.33928e8i	1.35763	+	2.35148i
$647$		−	3.67765e8i		−	1.35787i	−0.734199	−	0.678934i	$-0.762442\pi$
$647$		−	3.67765e8i		−	1.35787i	0.734199	−	0.678934i	$-0.237558\pi$
$648$		0			0
$649$	−1.46210e8			−0.534864
$650$	1.59093e7	−	9.18522e6i	0.0579309	−	0.0334464i
$651$		0			0
$652$	8.93931e7	−	1.54833e8i	0.322523	−	0.558627i
$653$	−1.19246e8	−	6.88468e7i	−0.428258	−	0.247255i	0.270346	−	0.962763i	$-0.412862\pi$
$653$	−1.19246e8	−	6.88468e7i	−0.428258	−	0.247255i	−0.698604	+	0.715508i	$0.746195\pi$
$654$		0			0
$655$	−2.13497e8	−	3.69788e8i	−0.759745	−	1.31592i
$656$		−	3.59804e8i		−	1.27454i
$657$		0			0
$658$	−1.03224e8			−0.362330
$659$	−4.70292e7	+	2.71523e7i	−0.164328	+	0.0948748i	−0.579909	−	0.814682i	$-0.696912\pi$
$659$	−4.70292e7	+	2.71523e7i	−0.164328	+	0.0948748i	0.415581	+	0.909556i	$0.363578\pi$
$660$		0			0
$661$	−2.21501e8	+	3.83651e8i	−0.766958	+	1.32841i	0.172248	+	0.985054i	$0.444897\pi$
$661$	−2.21501e8	+	3.83651e8i	−0.766958	+	1.32841i	−0.939205	+	0.343356i	$0.888436\pi$
$662$	−9.01776e7	−	5.20641e7i	−0.310831	−	0.179459i
$663$		0			0
$664$	1.74078e7	+	3.01512e7i	0.0594620	+	0.102991i
$665$		−	4.29322e8i		−	1.45988i
$666$		0			0
$667$	2.61612e7			0.0881617
$668$	4.31842e7	−	2.49324e7i	0.144876	−	0.0836440i
$669$		0			0
$670$	−5.39148e7	+	9.33831e7i	−0.179260	+	0.310487i
$671$	3.54381e8	+	2.04602e8i	1.17301	+	0.677239i
$672$		0			0
$673$	2.62660e8	+	4.54940e8i	0.861685	+	1.49248i	0.870301	+	0.492520i	$0.163924\pi$
$673$	2.62660e8	+	4.54940e8i	0.861685	+	1.49248i	−0.00861562	+	0.999963i	$0.502742\pi$
$674$			8.07932e7i			0.263873i
$675$		0			0
$676$	1.01485e8			0.328522
$677$	−8.79164e7	+	5.07586e7i	−0.283337	+	0.163585i	−0.634933	−	0.772567i	$-0.718972\pi$
$677$	−8.79164e7	+	5.07586e7i	−0.283337	+	0.163585i	0.351596	+	0.936152i	$0.385639\pi$
$678$		0			0
$679$	−2.41259e8	+	4.17872e8i	−0.770679	+	1.33485i
$680$	3.98882e8	+	2.30294e8i	1.26858	+	0.732414i
$681$		0			0
$682$	−3.47352e8	−	6.01631e8i	−1.09501	−	1.89661i
$683$			5.87819e7i			0.184494i	0.995736	+	0.0922468i	$0.0294049\pi$
$683$			5.87819e7i			0.184494i	−0.995736	+	0.0922468i	$0.970595\pi$
$684$		0			0
$685$	−3.82307e8			−1.18943
$686$	2.41334e8	−	1.39334e8i	0.747561	−	0.431604i
$687$		0			0
$688$	−1.54559e8	+	2.67703e8i	−0.474600	+	0.822032i
$689$	−1.14547e8	−	6.61336e7i	−0.350207	−	0.202192i
$690$		0			0
$691$	−1.02888e8	−	1.78206e8i	−0.311838	−	0.540119i	0.666922	−	0.745127i	$-0.267611\pi$
$691$	−1.02888e8	−	1.78206e8i	−0.311838	−	0.540119i	−0.978760	+	0.205008i	$0.934278\pi$
$692$			9.94159e7i			0.300011i
$693$		0			0
$694$	5.01106e8			1.49917
$695$	−1.69843e8	+	9.80591e7i	−0.505934	+	0.292101i
$696$		0			0
$697$	3.40400e8	−	5.89590e8i	1.00529	−	1.74121i
$698$	−4.10108e8	−	2.36776e8i	−1.20596	−	0.696259i
$699$		0			0
$700$	1.05566e7	+	1.82845e7i	0.0307772	+	0.0533077i
$701$			1.77405e8i			0.515005i	0.966278	+	0.257502i	$0.0828995\pi$
$701$			1.77405e8i			0.515005i	−0.966278	+	0.257502i	$0.917100\pi$
$702$		0			0
$703$	1.93844e8			0.557937
$704$	1.12540e8	−	6.49752e7i	0.322545	−	0.186221i
$705$		0			0
$706$	1.23732e6	−	2.14310e6i	0.00351615	−	0.00609016i
$707$	3.08531e8	+	1.78130e8i	0.873052	+	0.504057i
$708$		0			0
$709$	−2.02058e7	−	3.49975e7i	−0.0566941	−	0.0981970i	0.836285	−	0.548294i	$-0.184723\pi$
$709$	−2.02058e7	−	3.49975e7i	−0.0566941	−	0.0981970i	−0.892980	+	0.450097i	$0.851389\pi$
$710$		−	4.30610e8i		−	1.20312i
$711$		0			0
$712$	4.30325e8			1.19222
$713$	4.48739e8	−	2.59080e8i	1.23801	−	0.714767i
$714$		0			0
$715$	9.56579e7	−	1.65684e8i	0.261700	−	0.453277i
$716$	3.60560e7	+	2.08169e7i	0.0982286	+	0.0567123i
$717$		0			0
$718$	−1.21851e6	−	2.11052e6i	−0.00329197	−	0.00570186i
$719$			3.24675e8i			0.873498i	0.899583	+	0.436749i	$0.143870\pi$
$719$			3.24675e8i			0.873498i	−0.899583	+	0.436749i	$0.856130\pi$
$720$		0			0
$721$	−4.73176e8			−1.26246
$722$	1.42056e8	−	8.20163e7i	0.377441	−	0.217916i
$723$		0			0
$724$	7.41841e6	−	1.28491e7i	0.0195477	−	0.0338576i
$725$	−4.30428e6	−	2.48508e6i	−0.0112950	−	0.00652117i
$726$		0			0
$727$	−2.71558e8	−	4.70353e8i	−0.706740	−	1.22411i	−0.966060	−	0.258318i	$-0.916832\pi$
$727$	−2.71558e8	−	4.70353e8i	−0.706740	−	1.22411i	0.259320	−	0.965791i	$-0.416502\pi$
$728$			1.39615e8i			0.361859i
$729$		0			0
$730$	1.92449e8			0.494705
$731$	−5.06533e8	+	2.92447e8i	−1.29675	+	0.748678i
$732$		0			0
$733$	−1.76244e8	+	3.05264e8i	−0.447510	+	0.775109i	−0.998223	−	0.0595849i	$-0.981022\pi$
$733$	−1.76244e8	+	3.05264e8i	−0.447510	+	0.775109i	0.550714	+	0.834694i	$0.314356\pi$
$734$	−2.67581e8	−	1.54488e8i	−0.676655	−	0.390667i
$735$		0			0
$736$	−1.33422e8	−	2.31094e8i	−0.334653	−	0.579636i
$737$			1.28276e8i			0.320437i
$738$		0			0
$739$	−6.08455e8			−1.50763			−0.753816	−	0.657086i	$-0.771789\pi$
$739$	−6.08455e8			−1.50763			−0.753816	+	0.657086i	$0.771789\pi$
$740$	−7.22730e7	+	4.17268e7i	−0.178353	+	0.102972i
$741$		0			0
$742$	2.63103e8	−	4.55707e8i	0.644041	−	1.11551i
$743$	2.09444e8	+	1.20923e8i	0.510625	+	0.294809i	0.733090	−	0.680131i	$-0.238077\pi$
$743$	2.09444e8	+	1.20923e8i	0.510625	+	0.294809i	−0.222466	+	0.974941i	$0.571411\pi$
$744$		0			0
$745$	3.71095e7	+	6.42756e7i	0.0897463	+	0.155445i
$746$			7.90697e8i			1.90455i
$747$		0			0
$748$	−3.74896e8			−0.895790
$749$	−2.03765e8	+	1.17643e8i	−0.484935	+	0.279977i
$750$		0			0
$751$	2.49236e8	−	4.31690e8i	0.588425	−	1.01918i	−0.406013	−	0.913867i	$-0.633081\pi$
$751$	2.49236e8	−	4.31690e8i	0.588425	−	1.01918i	0.994439	−	0.105316i	$-0.0335853\pi$
$752$	−1.18875e8	−	6.86328e7i	−0.279537	−	0.161391i
$753$		0			0
$754$	1.12437e7	+	1.94747e7i	0.0262298	+	0.0454314i
$755$			4.93727e8i			1.14722i
$756$		0			0
$757$	1.14551e8			0.264064			0.132032	−	0.991245i	$-0.457850\pi$
$757$	1.14551e8			0.264064			0.132032	+	0.991245i	$0.457850\pi$
$758$	−6.00587e8	+	3.46749e8i	−1.37901	+	0.796173i
$759$		0			0
$760$	1.92023e8	−	3.32593e8i	0.437433	−	0.757657i
$761$	−3.39399e8	−	1.95952e8i	−0.770118	−	0.444628i	0.0627990	−	0.998026i	$-0.479997\pi$
$761$	−3.39399e8	−	1.95952e8i	−0.770118	−	0.444628i	−0.832917	+	0.553399i	$0.813331\pi$
$762$		0			0
$763$	3.80404e7	+	6.58879e7i	0.0856389	+	0.148331i
$764$		−	1.07811e8i		−	0.241758i
$765$		0			0
$766$	−3.74262e8			−0.832701
$767$	8.11807e7	−	4.68697e7i	0.179915	−	0.103874i
$768$		0			0
$769$	−4.07192e7	+	7.05277e7i	−0.0895406	+	0.155089i	−0.907317	−	0.420447i	$-0.861873\pi$
$769$	−4.07192e7	+	7.05277e7i	−0.0895406	+	0.155089i	0.817776	+	0.575536i	$0.195207\pi$
$770$	6.59150e8	+	3.80561e8i	1.44382	+	0.833589i
$771$		0			0
$772$	−5.81409e7	−	1.00703e8i	−0.126366	−	0.218872i
$773$		−	7.23925e8i		−	1.56731i	−0.621196	−	0.783655i	$-0.713353\pi$
$773$		−	7.23925e8i		−	1.56731i	0.621196	−	0.783655i	$-0.286647\pi$
$774$		0			0
$775$	−9.84408e7			−0.211480
$776$	−3.73803e8	+	2.15815e8i	−0.799941	+	0.461846i
$777$		0			0
$778$	3.56088e8	−	6.16763e8i	0.756169	−	1.30972i
$779$	−4.91608e8	−	2.83830e8i	−1.03994	−	0.600408i
$780$		0			0
$781$	−2.56131e8	−	4.43631e8i	−0.537661	−	0.931256i
$782$		−	9.67929e8i		−	2.02406i
$783$		0			0
$784$	−2.27560e8			−0.472223
$785$	1.42278e8	−	8.21440e7i	0.294122	−	0.169811i
$786$		0			0
$787$	4.40642e6	−	7.63215e6i	0.00903986	−	0.0156575i	−0.861470	−	0.507808i	$-0.830456\pi$
$787$	4.40642e6	−	7.63215e6i	0.00903986	−	0.0156575i	0.870510	+	0.492151i	$0.163789\pi$
$788$	2.67435e8	+	1.54404e8i	0.546562	+	0.315557i
$789$		0			0
$790$	−4.66572e7	−	8.08126e7i	−0.0946318	−	0.163907i
$791$			6.62521e8i			1.33866i
$792$		0			0
$793$	−2.62352e8			−0.526096
$794$	5.21366e8	−	3.01011e8i	1.04155	−	0.601341i
$795$		0			0
$796$	1.17350e7	−	2.03256e7i	0.0232672	−	0.0403000i
$797$	7.85361e8	+	4.53428e8i	1.55129	+	0.895640i	0.998037	+	0.0626303i	$0.0199489\pi$
$797$	7.85361e8	+	4.53428e8i	1.55129	+	0.895640i	0.553258	+	0.833010i	$0.313384\pi$
$798$		0			0
$799$	−1.29863e8	−	2.24929e8i	−0.254592	−	0.440967i
$800$			5.06955e7i			0.0990147i
$801$		0			0
$802$	7.25088e8			1.40562
$803$	1.98268e8	−	1.14470e8i	0.382919	−	0.221078i
$804$		0			0
$805$	−2.83849e8	+	4.91641e8i	−0.544126	+	0.942454i
$806$	3.85723e8	+	2.22697e8i	0.736665	+	0.425314i
$807$		0			0
$808$	1.59345e8	+	2.75993e8i	0.302067	+	0.523196i
$809$			2.56667e8i			0.484757i	0.970182	+	0.242379i	$0.0779277\pi$
$809$			2.56667e8i			0.484757i	−0.970182	+	0.242379i	$0.922072\pi$
$810$		0			0
$811$	1.04558e8			0.196017			0.0980087	−	0.995186i	$-0.468753\pi$
$811$	1.04558e8			0.196017			0.0980087	+	0.995186i	$0.468753\pi$
$812$	−2.23822e7	+	1.29224e7i	−0.0418057	+	0.0241365i
$813$		0			0
$814$	−1.71827e8	+	2.97614e8i	−0.318580	+	0.551798i
$815$	−7.90934e8	−	4.56646e8i	−1.46106	−	0.843542i
$816$		0			0
$817$	2.43846e8	+	4.22354e8i	0.447147	+	0.774481i
$818$			1.00795e9i			1.84153i
$819$		0			0
$820$	2.44390e8			0.443242
$821$	1.71744e8	−	9.91564e7i	0.310350	−	0.179181i	−0.336733	−	0.941600i	$-0.609322\pi$
$821$	1.71744e8	−	9.91564e7i	0.310350	−	0.179181i	0.647083	+	0.762419i	$0.275989\pi$
$822$		0			0
$823$	−4.42543e7	+	7.66507e7i	−0.0793882	+	0.137504i	−0.902986	−	0.429670i	$-0.858630\pi$
$823$	−4.42543e7	+	7.66507e7i	−0.0793882	+	0.137504i	0.823598	+	0.567174i	$0.191963\pi$
$824$	−3.66567e8	−	2.11637e8i	−0.655196	−	0.378278i
$825$		0			0
$826$	1.86464e8	+	3.22965e8i	0.330868	+	0.573081i
$827$		−	9.40582e8i		−	1.66295i	−0.555560	−	0.831476i	$-0.687496\pi$
$827$		−	9.40582e8i		−	1.66295i	0.555560	−	0.831476i	$-0.312504\pi$
$828$		0			0
$829$	−4.25518e7			−0.0746886			−0.0373443	−	0.999302i	$-0.511890\pi$
$829$	−4.25518e7			−0.0746886			−0.0373443	+	0.999302i	$0.511890\pi$
$830$	−1.05383e8	+	6.08429e7i	−0.184304	+	0.106408i
$831$		0			0
$832$	−4.16574e7	+	7.21528e7i	−0.0723307	+	0.125280i
$833$	−3.72889e8	−	2.15288e8i	−0.645127	−	0.372464i
$834$		0			0
$835$	−1.27362e8	−	2.20598e8i	−0.218766	−	0.378915i
$836$			3.12594e8i			0.535009i
$837$		0			0
$838$	3.58481e8			0.609164
$839$	3.13806e8	−	1.81176e8i	0.531343	−	0.306771i	−0.210220	−	0.977654i	$-0.567418\pi$
$839$	3.13806e8	−	1.81176e8i	0.531343	−	0.306771i	0.741563	+	0.670883i	$0.234085\pi$
$840$		0			0
$841$	−2.94370e8	+	5.09863e8i	−0.494886	+	0.857167i
$842$	1.29363e8	+	7.46878e7i	0.216707	+	0.125116i
$843$		0			0
$844$	7.37796e7	+	1.27790e8i	0.122718	+	0.212554i
$845$		−	5.18418e8i		−	0.859231i
$846$		0			0
$847$	1.91505e8			0.315159
$848$	6.05989e8	−	3.49868e8i	0.993751	−	0.573742i
$849$		0			0
$850$	−9.19444e7	+	1.59252e8i	−0.149716	+	0.259316i
$851$	−2.21981e8	−	1.28161e8i	−0.360187	−	0.207954i
$852$		0			0
$853$	−5.71326e8	−	9.89566e8i	−0.920528	−	1.59440i	−0.798599	−	0.601863i	$-0.794425\pi$
$853$	−5.71326e8	−	9.89566e8i	−0.920528	−	1.59440i	−0.121929	−	0.992539i	$-0.538908\pi$
$854$		−	1.04373e9i		−	1.67577i
$855$		0			0
$856$	−2.10474e8			−0.335565
$857$	2.71854e8	−	1.56955e8i	0.431911	−	0.249364i	−0.268250	−	0.963349i	$-0.586445\pi$
$857$	2.71854e8	−	1.56955e8i	0.431911	−	0.249364i	0.700160	+	0.713986i	$0.253112\pi$
$858$		0			0
$859$	−2.06304e8	+	3.57329e8i	−0.325483	+	0.563753i	−0.981610	−	0.190897i	$-0.938860\pi$
$859$	−2.06304e8	+	3.57329e8i	−0.325483	+	0.563753i	0.656127	+	0.754651i	$0.272194\pi$
$860$	−1.81832e8	−	1.04981e8i	−0.285875	−	0.165050i
$861$		0			0
$862$	1.50091e8	+	2.59964e8i	0.234332	+	0.405875i
$863$		−	7.45960e8i		−	1.16060i	−0.814402	−	0.580301i	$-0.802935\pi$
$863$		−	7.45960e8i		−	1.16060i	0.814402	−	0.580301i	$-0.197065\pi$
$864$		0			0
$865$	5.07846e8			0.784663
$866$	−5.34834e8	+	3.08786e8i	−0.823503	+	0.475449i
$867$		0			0
$868$	−2.55946e8	+	4.43312e8i	−0.391372	+	0.677876i
$869$	−9.61362e7	−	5.55042e7i	−0.146497	−	0.0845798i
$870$		0			0
$871$	−4.11207e7	−	7.12232e7i	−0.0622309	−	0.107787i
$872$			6.80573e7i			0.102642i
$873$		0			0
$874$	−8.07073e8			−1.20887
$875$	−6.30875e8	+	3.64236e8i	−0.941714	+	0.543699i
$876$		0			0
$877$	4.09687e8	−	7.09598e8i	0.607370	−	1.05200i	−0.384302	−	0.923207i	$-0.625558\pi$
$877$	4.09687e8	−	7.09598e8i	0.607370	−	1.05200i	0.991672	−	0.128788i	$-0.0411087\pi$
$878$	2.58861e8	+	1.49454e8i	0.382458	+	0.220812i
$879$		0			0
$880$	5.06061e8	+	8.76524e8i	0.742600	+	1.28622i
$881$		−	1.15485e9i		−	1.68888i	−0.535653	−	0.844438i	$-0.679935\pi$
$881$		−	1.15485e9i		−	1.68888i	0.535653	−	0.844438i	$-0.320065\pi$
$882$		0			0
$883$	3.95346e8			0.574242			0.287121	−	0.957894i	$-0.407302\pi$
$883$	3.95346e8			0.574242			0.287121	+	0.957894i	$0.407302\pi$
$884$	2.08155e8	−	1.20178e8i	0.301321	−	0.173968i
$885$		0			0
$886$	−6.69544e7	+	1.15968e8i	−0.0962671	+	0.166740i
$887$	6.43033e8	+	3.71255e8i	0.921430	+	0.531988i	0.884091	−	0.467315i	$-0.154779\pi$
$887$	6.43033e8	+	3.71255e8i	0.921430	+	0.531988i	0.0373387	+	0.999303i	$0.488112\pi$
$888$		0			0
$889$	6.24853e8	+	1.08228e9i	0.889349	+	1.54040i
$890$			1.50405e9i			2.13350i
$891$		0			0
$892$	1.46839e8			0.206893
$893$	−1.87549e8	+	1.08282e8i	−0.263367	+	0.152055i
$894$		0			0
$895$	1.06339e8	−	1.84184e8i	0.148328	−	0.256912i
$896$	−8.49015e8	−	4.90179e8i	−1.18030	−	0.681445i
$897$		0			0
$898$	2.31670e8	+	4.01264e8i	0.319920	+	0.554117i
$899$		−	1.20502e8i		−	0.165850i
$900$		0			0
$901$	1.32400e9			1.81015
$902$	8.71546e8	−	5.03187e8i	1.18760	−	0.685662i
$903$		0			0
$904$	−2.96326e8	+	5.13252e8i	−0.401111	+	0.694744i
$905$	−6.56368e7	−	3.78954e7i	−0.0885527	−	0.0511259i
$906$		0			0
$907$	6.11885e8	+	1.05982e9i	0.820064	+	1.42039i	0.905634	+	0.424061i	$0.139396\pi$
$907$	6.11885e8	+	1.05982e9i	0.820064	+	1.42039i	−0.0855693	+	0.996332i	$0.527271\pi$
$908$			3.27135e8i			0.436988i
$909$		0			0
$910$	−4.87977e8			−0.647552
$911$	−6.80021e8	+	3.92610e8i	−0.899429	+	0.519286i	−0.877015	−	0.480463i	$-0.840469\pi$
$911$	−6.80021e8	+	3.92610e8i	−0.899429	+	0.519286i	−0.0224143	+	0.999749i	$0.507135\pi$
$912$		0			0
$913$	−7.23798e7	+	1.25365e8i	−0.0951054	+	0.164727i
$914$	1.33870e9	+	7.72902e8i	1.75326	+	1.01225i
$915$		0			0
$916$	−8.47295e7	−	1.46756e8i	−0.110242	−	0.190945i
$917$			1.29562e9i			1.68023i
$918$		0			0
$919$	−5.58148e8			−0.719122			−0.359561	−	0.933121i	$-0.617074\pi$
$919$	−5.58148e8			−0.719122			−0.359561	+	0.933121i	$0.617074\pi$
$920$	−4.39793e8	+	2.53914e8i	−0.564787	+	0.326080i
$921$		0			0
$922$	5.74585e8	−	9.95211e8i	0.733098	−	1.26976i
$923$	2.84425e8	+	1.64213e8i	0.361711	+	0.208834i
$924$		0			0
$925$	2.43483e7	+	4.21724e7i	0.0307640	+	0.0532848i
$926$		−	1.02684e9i		−	1.29321i
$927$		0			0
$928$	−6.20568e7			−0.0776507
$929$	−5.81254e8	+	3.35587e8i	−0.724968	+	0.418560i	−0.816578	−	0.577235i	$-0.804132\pi$
$929$	−5.81254e8	+	3.35587e8i	−0.724968	+	0.418560i	0.0916107	+	0.995795i	$0.470798\pi$
$930$		0			0
$931$	−1.79510e8	+	3.10920e8i	−0.222454	+	0.385301i
$932$	−1.87478e8	−	1.08240e8i	−0.231580	−	0.133703i
$933$		0			0
$934$	2.40228e8	+	4.16087e8i	0.294838	+	0.510674i
$935$			1.91508e9i			2.34289i
$936$		0			0
$937$	−4.07277e8			−0.495076			−0.247538	−	0.968878i	$-0.579621\pi$
$937$	−4.07277e8			−0.495076			−0.247538	+	0.968878i	$0.579621\pi$
$938$	2.83351e8	−	1.63593e8i	0.343333	−	0.198223i
$939$		0			0
$940$	4.66175e7	−	8.07438e7i	0.0561261	−	0.0972133i
$941$	−1.27501e9	−	7.36127e8i	−1.53019	−	0.883454i	−0.999353	−	0.0359779i	$-0.988545\pi$
$941$	−1.27501e9	−	7.36127e8i	−1.53019	−	0.883454i	−0.530834	−	0.847476i	$-0.678121\pi$
$942$		0			0
$943$	3.75313e8	+	6.50060e8i	0.447567	+	0.775209i
$944$			4.95912e8i			0.589506i
$945$		0			0
$946$	−8.64604e8			−1.02128
$947$	7.96395e8	−	4.59799e8i	0.937732	−	0.541400i	0.0484834	−	0.998824i	$-0.484561\pi$
$947$	7.96395e8	−	4.59799e8i	0.937732	−	0.541400i	0.889249	+	0.457424i	$0.151228\pi$
$948$		0			0
$949$	−7.33901e7	+	1.27115e8i	−0.0858695	+	0.148730i
$950$	1.32787e8	+	7.66646e7i	0.154876	+	0.0894178i
$951$		0			0
$952$	−6.98778e8	−	1.21032e9i	−0.809894	−	1.40278i
$953$			9.44943e8i			1.09176i	0.837863	+	0.545880i	$0.183804\pi$
$953$			9.44943e8i			1.09176i	−0.837863	+	0.545880i	$0.816196\pi$
$954$		0			0
$955$	−5.50728e8			−0.632306
$956$	−4.68888e8	+	2.70713e8i	−0.536655	+	0.309838i
$957$		0			0
$958$	−8.34683e8	+	1.44571e9i	−0.949347	+	1.64432i
$959$	1.00461e9	+	5.80013e8i	1.13905	+	0.657630i
$960$		0			0
$961$	−7.49605e8	−	1.29835e9i	−0.844622	−	1.46293i
$962$		−	2.20327e8i		−	0.247481i
$963$		0			0
$964$	−1.20361e8			−0.134356
$965$	−5.14421e8	+	2.97001e8i	−0.572448	+	0.330503i
$966$		0			0
$967$	4.47995e7	−	7.75950e7i	0.0495443	−	0.0858133i	−0.840190	−	0.542293i	$-0.817556\pi$
$967$	4.47995e7	−	7.75950e7i	0.0495443	−	0.0858133i	0.889734	+	0.456479i	$0.150890\pi$
$968$	1.48358e8	+	8.56545e7i	0.163563	+	0.0944331i
$969$		0			0
$970$	−7.54307e8	−	1.30650e9i	−0.826481	−	1.43151i
$971$		−	3.70582e8i		−	0.404787i	−0.979304	−	0.202394i	$-0.935128\pi$
$971$		−	3.70582e8i		−	0.404787i	0.979304	−	0.202394i	$-0.0648720\pi$
$972$		0			0
$973$	5.95077e8			0.646004
$974$	1.09243e9	−	6.30717e8i	1.18227	−	0.682586i
$975$		0			0
$976$	6.93963e8	−	1.20198e9i	0.746427	−	1.29285i
$977$	1.24942e8	+	7.21351e7i	0.133975	+	0.0773505i	0.565489	−	0.824756i	$-0.308687\pi$
$977$	1.24942e8	+	7.21351e7i	0.133975	+	0.0773505i	−0.431515	+	0.902106i	$0.642021\pi$
$978$		0			0
$979$	8.94623e8	+	1.54953e9i	0.953437	+	1.65140i
$980$		−	1.54566e8i		−	0.164223i
$981$		0			0
$982$	2.03361e9			2.14750
$983$	−3.79146e8	+	2.18900e8i	−0.399159	+	0.230455i	−0.686121	−	0.727487i	$-0.740688\pi$
$983$	−3.79146e8	+	2.18900e8i	−0.399159	+	0.230455i	0.286962	+	0.957942i	$0.407355\pi$
$984$		0			0
$985$	7.88739e8	−	1.36614e9i	0.825324	−	1.42950i
$986$	−1.94942e8	−	1.12550e8i	−0.203364	−	0.117412i
$987$		0			0
$988$	−1.00206e8	−	1.73562e8i	−0.103902	−	0.179964i
$989$		−	6.44883e8i		−	0.666641i
$990$		0			0
$991$	−4.48947e8			−0.461290			−0.230645	−	0.973038i	$-0.574084\pi$
$991$	−4.48947e8			−0.461290			−0.230645	+	0.973038i	$0.574084\pi$
$992$	−1.06445e9	+	6.14561e8i	−1.09041	+	0.629550i
$993$		0			0
$994$	−6.53295e8	+	1.13154e9i	−0.665197	+	1.15216i
$995$	−1.03829e8	−	5.99459e7i	−0.105402	−	0.0608541i
$996$		0			0
$997$	−5.22164e8	−	9.04415e8i	−0.526892	−	0.912604i	−0.999509	−	0.0313358i	$-0.990024\pi$
$997$	−5.22164e8	−	9.04415e8i	−0.526892	−	0.912604i	0.472617	−	0.881268i	$-0.343309\pi$
$998$		−	1.72777e9i		−	1.73818i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.7.d.c.53.2		4
3.2	odd	2	inner	81.7.d.c.53.1		4
9.2	odd	6	inner	81.7.d.c.26.2		4
9.4	even	3		27.7.b.a.26.2	yes	2
9.5	odd	6		27.7.b.a.26.1	✓	2
9.7	even	3	inner	81.7.d.c.26.1		4
36.23	even	6		432.7.e.g.161.1		2
36.31	odd	6		432.7.e.g.161.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.7.b.a.26.1	✓	2	9.5	odd	6
27.7.b.a.26.2	yes	2	9.4	even	3
81.7.d.c.26.1		4	9.7	even	3	inner
81.7.d.c.26.2		4	9.2	odd	6	inner
81.7.d.c.53.1		4	3.2	odd	2	inner
81.7.d.c.53.2		4	1.1	even	1	trivial
432.7.e.g.161.1		2	36.23	even	6
432.7.e.g.161.2		2	36.31	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	81.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(8.21584 - 4.74342i) q^{2} +(13.0000 - 22.5167i) q^{4} +(-115.022 - 66.4078i) q^{5} +(201.500 + 349.008i) q^{7} +360.500i q^{8} -1260.00 q^{10} +(-1298.10 + 749.460i) q^{11} +(480.500 - 832.250i) q^{13} +(3310.98 + 1911.60i) q^{14} +(2542.00 + 4402.87i) q^{16} +9619.65i q^{17} +8021.00 q^{19} +(-2990.57 + 1726.60i) q^{20} +(-7110.00 + 12314.9i) q^{22} +(-9185.31 - 5303.14i) q^{23} +(1007.50 + 1745.04i) q^{25} -9116.85i q^{26} +10478.0 q^{28} +(-2136.12 + 1233.29i) q^{29} +(-24427.0 + 42308.8i) q^{31} +(21788.4 + 12579.5i) q^{32} +(45630.0 + 79033.5i) q^{34} -53524.7i q^{35} +24167.0 q^{37} +(65899.2 - 38046.9i) q^{38} +(23940.0 - 41465.3i) q^{40} +(-61290.2 - 35385.9i) q^{41} +(30401.0 + 52656.1i) q^{43} +38971.9i q^{44} -100620. q^{46} +(-23382.3 + 13499.8i) q^{47} +(-22380.0 + 38763.3i) q^{49} +(16554.9 + 9557.98i) q^{50} +(-12493.0 - 21638.5i) q^{52} -137635. i q^{53} +199080. q^{55} +(-125817. + 72640.7i) q^{56} +(-11700.0 + 20265.0i) q^{58} +(84475.3 + 48771.8i) q^{59} +(-136500. - 236424. i) q^{61} +463470. i q^{62} -86696.0 q^{64} +(-110536. + 63817.9i) q^{65} +(42789.5 - 74113.6i) q^{67} +(216602. + 125055. i) q^{68} +(-253890. - 439750. i) q^{70} +341754. i q^{71} -152737. q^{73} +(198552. - 114634. i) q^{74} +(104273. - 180606. i) q^{76} +(-523135. - 302032. i) q^{77} +(37029.5 + 64137.0i) q^{79} -675235. i q^{80} -671400. q^{82} +(83637.2 - 48288.0i) q^{83} +(638820. - 1.10647e6i) q^{85} +(499539. + 288409. i) q^{86} +(-270180. - 467965. i) q^{88} -1.19369e6i q^{89} +387283. q^{91} +(-238818. + 137882. i) q^{92} +(-128070. + 221824. i) q^{94} +(-922589. - 532657. i) q^{95} +(598656. + 1.03690e6i) q^{97} +424631. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 52 q^{4} + 806 q^{7} - 5040 q^{10} + 1922 q^{13} + 10168 q^{16} + 32084 q^{19} - 28440 q^{22} + 4030 q^{25} + 41912 q^{28} - 97708 q^{31} + 182520 q^{34} + 96668 q^{37} + 95760 q^{40} + 121604 q^{43}+ \cdots + 2394626 q^{97}+O(q^{100}) \) 4 * q + 52 * q^4 + 806 * q^7 - 5040 * q^10 + 1922 * q^13 + 10168 * q^16 + 32084 * q^19 - 28440 * q^22 + 4030 * q^25 + 41912 * q^28 - 97708 * q^31 + 182520 * q^34 + 96668 * q^37 + 95760 * q^40 + 121604 * q^43 - 402480 * q^46 - 89520 * q^49 - 49972 * q^52 + 796320 * q^55 - 46800 * q^58 - 545998 * q^61 - 346784 * q^64 + 171158 * q^67 - 1015560 * q^70 - 610948 * q^73 + 417092 * q^76 + 148118 * q^79 - 2685600 * q^82 + 2555280 * q^85 - 1080720 * q^88 + 1549132 * q^91 - 512280 * q^94 + 2394626 * q^97

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