LMFDB - Embedded newform 76.7.j.a.29.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(13,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, degree $6$, 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:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			29.9
Character	$\chi$	$=$	76.29
Dual form			76.7.j.a.21.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(24.5774 + 29.2903i) q^{3} +(-71.7580 - 26.1178i) q^{5} +(38.3425 - 66.4112i) q^{7} +(-127.279 + 721.834i) q^{9} +O(q^{10})$	\(q+(24.5774 + 29.2903i) q^{3} +(-71.7580 - 26.1178i) q^{5} +(38.3425 - 66.4112i) q^{7} +(-127.279 + 721.834i) q^{9} +(1034.16 + 1791.22i) q^{11} +(-2344.42 + 2793.97i) q^{13} +(-998.632 - 2743.72i) q^{15} +(492.142 + 2791.08i) q^{17} +(-5789.95 - 3677.28i) q^{19} +(2887.56 - 509.155i) q^{21} +(-7825.94 + 2848.41i) q^{23} +(-7502.37 - 6295.24i) q^{25} +(-131.446 + 75.8905i) q^{27} +(-7791.13 - 1373.79i) q^{29} +(-7948.87 - 4589.28i) q^{31} +(-27048.2 + 74314.3i) q^{33} +(-4485.90 + 3764.12i) q^{35} +77258.1i q^{37} -139456. q^{39} +(38920.5 + 46383.7i) q^{41} +(77587.9 + 28239.7i) q^{43} +(27986.0 - 48473.2i) q^{45} +(16841.0 - 95510.3i) q^{47} +(55884.2 + 96794.3i) q^{49} +(-69655.8 + 83012.5i) q^{51} +(-52862.8 - 145239. i) q^{53} +(-27426.6 - 155544. i) q^{55} +(-34593.5 - 259967. i) q^{57} +(28598.9 - 5042.75i) q^{59} +(165056. - 60075.4i) q^{61} +(43057.7 + 36129.7i) q^{63} +(241203. - 139259. i) q^{65} +(439159. + 77435.6i) q^{67} +(-275772. - 159217. i) q^{69} +(-88568.2 + 243339. i) q^{71} +(66451.6 - 55759.5i) q^{73} -374467. i q^{75} +158609. q^{77} +(178707. + 212975. i) q^{79} +(496657. + 180768. i) q^{81} +(-376338. + 651836. i) q^{83} +(37581.6 - 213136. i) q^{85} +(-151247. - 261968. i) q^{87} +(514235. - 612841. i) q^{89} +(95660.0 + 262824. i) q^{91} +(-60941.6 - 345617. i) q^{93} +(319433. + 415095. i) q^{95} +(-787575. + 138871. i) q^{97} +(-1.42459e6 + 518508. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9 + 1680 * q^11 - 2940 * q^13 + 2496 * q^15 - 5112 * q^17 - 15792 * q^19 - 32076 * q^21 - 19272 * q^23 + 58896 * q^25 - 124830 * q^27 + 126840 * q^29 + 30780 * q^31 - 274470 * q^33 - 226284 * q^35 + 178968 * q^39 + 83394 * q^41 + 418848 * q^43 - 95472 * q^45 - 498696 * q^47 - 744330 * q^49 + 1334538 * q^51 + 458004 * q^53 - 260136 * q^55 - 981984 * q^57 - 523362 * q^59 - 644172 * q^61 + 926832 * q^63 + 1337220 * q^65 + 1719114 * q^67 + 1333800 * q^69 - 1895220 * q^71 - 1189704 * q^73 + 1337256 * q^77 + 147432 * q^79 + 272130 * q^81 + 442800 * q^83 + 1479096 * q^85 + 1300572 * q^87 - 301596 * q^89 + 661008 * q^91 + 3576 * q^93 - 5709984 * q^95 + 1386630 * q^97 + 3822798 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	24.5774	+	29.2903i	0.910276	+	1.08482i	0.996075	+	0.0885118i	$0.0282111\pi$
$3$	24.5774	+	29.2903i	0.910276	+	1.08482i	−0.0857995	+	0.996312i	$0.527344\pi$
$4$		0			0
$5$	−71.7580	−	26.1178i	−0.574064	−	0.208942i	0.0386419	−	0.999253i	$-0.487697\pi$
$5$	−71.7580	−	26.1178i	−0.574064	−	0.208942i	−0.612706	+	0.790311i	$0.709919\pi$
$6$		0			0
$7$	38.3425	−	66.4112i	0.111786	−	0.193619i	−0.804705	−	0.593676i	$-0.797676\pi$
$7$	38.3425	−	66.4112i	0.111786	−	0.193619i	0.916490	+	0.400057i	$0.131010\pi$
$8$		0			0
$9$	−127.279	+	721.834i	−0.174594	+	0.990170i
$10$		0			0
$11$	1034.16	+	1791.22i	0.776979	+	1.34577i	0.933675	+	0.358121i	$0.116582\pi$
$11$	1034.16	+	1791.22i	0.776979	+	1.34577i	−0.156696	+	0.987647i	$0.550084\pi$
$12$		0			0
$13$	−2344.42	+	2793.97i	−1.06710	+	1.27172i	−0.106343	+	0.994329i	$0.533914\pi$
$13$	−2344.42	+	2793.97i	−1.06710	+	1.27172i	−0.960757	+	0.277391i	$0.910530\pi$
$14$		0			0
$15$	−998.632	−	2743.72i	−0.295891	−	0.812954i
$16$		0			0
$17$	492.142	+	2791.08i	0.100171	+	0.568101i	0.993039	+	0.117782i	$0.0375784\pi$
$17$	492.142	+	2791.08i	0.100171	+	0.568101i	−0.892868	+	0.450318i	$0.851310\pi$
$18$		0			0
$19$	−5789.95	−	3677.28i	−0.844138	−	0.536125i
$19$	−5789.95	−	3677.28i	−0.844138	−	0.536125i
$20$		0			0
$21$	2887.56	−	509.155i	0.311798	−	0.0549784i
$22$		0			0
$23$	−7825.94	+	2848.41i	−0.643211	+	0.234110i	−0.642971	−	0.765890i	$-0.722298\pi$
$23$	−7825.94	+	2848.41i	−0.643211	+	0.234110i	−0.000239558		1.00000i	$0.500076\pi$
$24$		0			0
$25$	−7502.37	−	6295.24i	−0.480152	−	0.402895i
$26$		0			0
$27$	−131.446	+	75.8905i	−0.00667816	+	0.00385564i
$28$		0			0
$29$	−7791.13	−	1373.79i	−0.319452	−	0.0563281i	0.0116228	−	0.999932i	$-0.496300\pi$
$29$	−7791.13	−	1373.79i	−0.319452	−	0.0563281i	−0.331075	+	0.943604i	$0.607411\pi$
$30$		0			0
$31$	−7948.87	−	4589.28i	−0.266821	−	0.154049i	0.360621	−	0.932712i	$-0.382565\pi$
$31$	−7948.87	−	4589.28i	−0.266821	−	0.154049i	−0.627442	+	0.778663i	$0.715898\pi$
$32$		0			0
$33$	−27048.2	+	74314.3i	−0.752656	+	2.06791i
$34$		0			0
$35$	−4485.90	+	3764.12i	−0.104627	+	0.0877928i
$36$		0			0
$37$			77258.1i			1.52524i	0.646846	+	0.762621i	$0.276088\pi$
$37$			77258.1i			1.52524i	−0.646846	+	0.762621i	$0.723912\pi$
$38$		0			0
$39$	−139456.			−2.35095
$40$		0			0
$41$	38920.5	+	46383.7i	0.564712	+	0.672997i	0.970537	−	0.240953i	$-0.0774601\pi$
$41$	38920.5	+	46383.7i	0.564712	+	0.672997i	−0.405825	+	0.913951i	$0.633016\pi$
$42$		0			0
$43$	77587.9	+	28239.7i	0.975863	+	0.355185i	0.780230	−	0.625492i	$-0.215102\pi$
$43$	77587.9	+	28239.7i	0.975863	+	0.355185i	0.195632	+	0.980677i	$0.437324\pi$
$44$		0			0
$45$	27986.0	−	48473.2i	0.307116	−	0.531941i
$46$		0			0
$47$	16841.0	−	95510.3i	0.162209	−	0.919934i	−0.789686	−	0.613511i	$-0.789757\pi$
$47$	16841.0	−	95510.3i	0.162209	−	0.919934i	0.951895	−	0.306423i	$-0.0991322\pi$
$48$		0			0
$49$	55884.2	+	96794.3i	0.475008	+	0.822738i
$50$		0			0
$51$	−69655.8	+	83012.5i	−0.525106	+	0.625797i
$52$		0			0
$53$	−52862.8	−	145239.i	−0.355077	−	0.975567i	−0.980713	−	0.195452i	$-0.937383\pi$
$53$	−52862.8	−	145239.i	−0.355077	−	0.975567i	0.625636	−	0.780115i	$-0.284840\pi$
$54$		0			0
$55$	−27426.6	−	155544.i	−0.164848	−	0.934901i
$56$		0			0
$57$	−34593.5	−	259967.i	−0.186797	−	1.40376i
$58$		0			0
$59$	28598.9	−	5042.75i	0.139249	−	0.0245534i	−0.103589	−	0.994620i	$-0.533033\pi$
$59$	28598.9	−	5042.75i	0.139249	−	0.0245534i	0.242838	+	0.970067i	$0.421922\pi$
$60$		0			0
$61$	165056.	−	60075.4i	0.727179	−	0.264672i	0.0482090	−	0.998837i	$-0.484649\pi$
$61$	165056.	−	60075.4i	0.727179	−	0.264672i	0.678970	+	0.734166i	$0.262426\pi$
$62$		0			0
$63$	43057.7	+	36129.7i	0.172198	+	0.144492i
$64$		0			0
$65$	241203.	−	139259.i	0.878300	−	0.507087i
$66$		0			0
$67$	439159.	+	77435.6i	1.46015	+	0.257464i	0.846616	−	0.532204i	$-0.178636\pi$
$67$	439159.	+	77435.6i	1.46015	+	0.257464i	0.613534	+	0.789668i	$0.289747\pi$
$68$		0			0
$69$	−275772.	−	159217.i	−0.839467	−	0.484666i
$70$		0			0
$71$	−88568.2	+	243339.i	−0.247459	+	0.679887i	0.752319	+	0.658799i	$0.228935\pi$
$71$	−88568.2	+	243339.i	−0.247459	+	0.679887i	−0.999778	+	0.0210881i	$0.993287\pi$
$72$		0			0
$73$	66451.6	−	55759.5i	0.170819	−	0.143334i	−0.553370	−	0.832935i	$-0.686659\pi$
$73$	66451.6	−	55759.5i	0.170819	−	0.143334i	0.724190	+	0.689601i	$0.242214\pi$
$74$		0			0
$75$		−	374467.i		−	0.887626i
$76$		0			0
$77$	158609.			0.347421
$78$		0			0
$79$	178707.	+	212975.i	0.362460	+	0.431963i	0.916197	−	0.400729i	$-0.131243\pi$
$79$	178707.	+	212975.i	0.362460	+	0.431963i	−0.553737	+	0.832692i	$0.686799\pi$
$80$		0			0
$81$	496657.	+	180768.i	0.934548	+	0.340148i
$82$		0			0
$83$	−376338.	+	651836.i	−0.658178	+	1.14000i	0.322909	+	0.946430i	$0.395339\pi$
$83$	−376338.	+	651836.i	−0.658178	+	1.14000i	−0.981087	+	0.193568i	$0.937994\pi$
$84$		0			0
$85$	37581.6	−	213136.i	0.0611954	−	0.347056i
$86$		0			0
$87$	−151247.	−	261968.i	−0.229684	−	0.397824i
$88$		0			0
$89$	514235.	−	612841.i	0.729443	−	0.869317i	−0.266068	−	0.963954i	$-0.585725\pi$
$89$	514235.	−	612841.i	0.729443	−	0.869317i	0.995512	+	0.0946374i	$0.0301692\pi$
$90$		0			0
$91$	95660.0	+	262824.i	0.126942	+	0.348771i
$92$		0			0
$93$	−60941.6	−	345617.i	−0.0757644	−	0.429681i
$94$		0			0
$95$	319433.	+	415095.i	0.372570	+	0.484147i
$96$		0			0
$97$	−787575.	+	138871.i	−0.862933	+	0.152158i	−0.587561	−	0.809180i	$-0.699912\pi$
$97$	−787575.	+	138871.i	−0.862933	+	0.152158i	−0.275371	+	0.961338i	$0.588801\pi$
$98$		0			0
$99$	−1.42459e6	+	518508.i	−1.46819	+	0.534379i
$100$		0			0
$101$	−212170.	−	178032.i	−0.205930	−	0.172796i	0.533990	−	0.845491i	$-0.320692\pi$
$101$	−212170.	−	178032.i	−0.205930	−	0.172796i	−0.739920	+	0.672695i	$0.765137\pi$
$102$		0			0
$103$	442956.	−	255741.i	0.405368	−	0.234039i	−0.283430	−	0.958993i	$-0.591472\pi$
$103$	442956.	−	255741.i	0.405368	−	0.234039i	0.688797	+	0.724954i	$0.258139\pi$
$104$		0			0
$105$	−220504.	−	38880.8i	−0.190479	−	0.0335867i
$106$		0			0
$107$	996452.	+	575302.i	0.813402	+	0.469618i	0.848136	−	0.529779i	$-0.177725\pi$
$107$	996452.	+	575302.i	0.813402	+	0.469618i	−0.0347341	+	0.999397i	$0.511058\pi$
$108$		0			0
$109$	370168.	−	1.01703e6i	0.285837	−	0.785332i	−0.710800	−	0.703394i	$-0.751667\pi$
$109$	370168.	−	1.01703e6i	0.285837	−	0.785332i	0.996637	−	0.0819378i	$-0.0261109\pi$
$110$		0			0
$111$	−2.26291e6	+	1.89881e6i	−1.65462	+	1.38839i
$112$		0			0
$113$		−	2.65324e6i		−	1.83883i	−0.393290	−	0.919414i	$-0.628663\pi$
$113$		−	2.65324e6i		−	1.83883i	0.393290	−	0.919414i	$-0.371337\pi$
$114$		0			0
$115$	635968.			0.418160
$116$		0			0
$117$	−1.71839e6	−	2.04790e6i	−1.07291	−	1.27865i
$118$		0			0
$119$	204229.	+	74333.2i	0.121193	+	0.0441105i
$120$		0			0
$121$	−1.25319e6	+	2.17059e6i	−0.707394	+	1.22524i
$122$		0			0
$123$	−402023.	+	2.27998e6i	−0.216040	+	1.22523i
$124$		0			0
$125$	970526.	+	1.68100e6i	0.496909	+	0.860672i
$126$		0			0
$127$	−1.11029e6	+	1.32319e6i	−0.542034	+	0.645970i	−0.965642	−	0.259875i	$-0.916319\pi$
$127$	−1.11029e6	+	1.32319e6i	−0.542034	+	0.645970i	0.423609	+	0.905845i	$0.360763\pi$
$128$		0			0
$129$	1.07976e6	+	2.96663e6i	0.502991	+	1.38196i
$130$		0			0
$131$	26250.5	+	148874.i	0.0116768	+	0.0662225i	0.990089	−	0.140439i	$-0.0448513\pi$
$131$	26250.5	+	148874.i	0.0116768	+	0.0662225i	−0.978413	+	0.206661i	$0.933740\pi$
$132$		0			0
$133$	−466214.	+	243521.i	−0.198167	+	0.103510i
$134$		0			0
$135$	11414.4	−	2012.67i	0.00463930	−	0.000818033i
$136$		0			0
$137$	−200172.	+	72856.7i	−0.0778470	+	0.0283340i	−0.380650	−	0.924719i	$-0.624300\pi$
$137$	−200172.	+	72856.7i	−0.0778470	+	0.0283340i	0.302803	+	0.953053i	$0.402078\pi$
$138$		0			0
$139$	1.25182e6	+	1.05040e6i	0.466120	+	0.391121i	0.845377	−	0.534170i	$-0.179376\pi$
$139$	1.25182e6	+	1.05040e6i	0.466120	+	0.391121i	−0.379257	+	0.925291i	$0.623820\pi$
$140$		0			0
$141$	3.21143e6	−	1.85412e6i	1.14562	−	0.661425i
$142$		0			0
$143$	−7.42911e6	−	1.30995e6i	−2.54056	−	0.447968i
$144$		0			0
$145$	523196.	+	302067.i	0.171617	+	0.0990831i
$146$		0			0
$147$	−1.46164e6	+	4.01582e6i	−0.460138	+	1.26422i
$148$		0			0
$149$	2.27499e6	−	1.90895e6i	0.687736	−	0.577079i	−0.230520	−	0.973068i	$-0.574043\pi$
$149$	2.27499e6	−	1.90895e6i	0.687736	−	0.577079i	0.918255	+	0.395989i	$0.129598\pi$
$150$		0			0
$151$		−	5.75464e6i		−	1.67143i	−0.549165	−	0.835714i	$-0.685054\pi$
$151$		−	5.75464e6i		−	1.67143i	0.549165	−	0.835714i	$-0.314946\pi$
$152$		0			0
$153$	−2.07733e6			−0.580006
$154$		0			0
$155$	450533.	+	536924.i	0.120985	+	0.144184i
$156$		0			0
$157$	6.43140e6	+	2.34084e6i	1.66191	+	0.604885i	0.990661	−	0.136349i	$-0.0435368\pi$
$157$	6.43140e6	+	2.34084e6i	1.66191	+	0.604885i	0.671247	+	0.741234i	$0.265759\pi$
$158$		0			0
$159$	2.95487e6	−	5.11798e6i	0.735100	−	1.27323i
$160$		0			0
$161$	−110900.	+	628946.i	−0.0265738	+	0.150708i
$162$		0			0
$163$	2.26349e6	+	3.92049e6i	0.522657	+	0.905268i	0.999652	+	0.0263624i	$0.00839239\pi$
$163$	2.26349e6	+	3.92049e6i	0.522657	+	0.905268i	−0.476996	+	0.878906i	$0.658274\pi$
$164$		0			0
$165$	3.88185e6	−	4.62621e6i	0.864146	−	1.02985i
$166$		0			0
$167$	−2.05920e6	−	5.65761e6i	−0.442129	−	1.21474i	−0.938089	−	0.346394i	$-0.887406\pi$
$167$	−2.05920e6	−	5.65761e6i	−0.442129	−	1.21474i	0.495960	−	0.868345i	$-0.334816\pi$
$168$		0			0
$169$	−1.47180e6	−	8.34700e6i	−0.304922	−	1.72930i
$170$		0			0
$171$	3.39133e6	−	3.71134e6i	0.678237	−	0.742237i
$172$		0			0
$173$	−2.13835e6	+	377049.i	−0.412991	+	0.0728214i	−0.376283	−	0.926505i	$-0.622798\pi$
$173$	−2.13835e6	+	377049.i	−0.412991	+	0.0728214i	−0.0367075	+	0.999326i	$0.511687\pi$
$174$		0			0
$175$	−705734.	+	256866.i	−0.131682	+	0.0479284i
$176$		0			0
$177$	850590.	+	713730.i	0.153391	+	0.128711i
$178$		0			0
$179$	5.00916e6	−	2.89204e6i	0.873385	−	0.504249i	0.00491335	−	0.999988i	$-0.498436\pi$
$179$	5.00916e6	−	2.89204e6i	0.873385	−	0.504249i	0.868472	+	0.495739i	$0.165103\pi$
$180$		0			0
$181$	−6.17887e6	−	1.08950e6i	−1.04201	−	0.183735i	−0.373650	−	0.927570i	$-0.621894\pi$
$181$	−6.17887e6	−	1.08950e6i	−1.04201	−	0.183735i	−0.668364	+	0.743835i	$0.733005\pi$
$182$		0			0
$183$	5.81628e6	+	3.35803e6i	0.949056	+	0.547938i
$184$		0			0
$185$	2.01781e6	−	5.54389e6i	0.318688	−	0.875587i
$186$		0			0
$187$	−4.49047e6	+	3.76795e6i	−0.686700	+	0.576210i
$188$		0			0
$189$			11639.3i			0.00172402i
$190$		0			0
$191$	−5.25184e6			−0.753722			−0.376861	−	0.926270i	$-0.622997\pi$
$191$	−5.25184e6			−0.753722			−0.376861	+	0.926270i	$0.622997\pi$
$192$		0			0
$193$	6.91741e6	+	8.24384e6i	0.962213	+	1.14672i	0.989124	+	0.147083i	$0.0469885\pi$
$193$	6.91741e6	+	8.24384e6i	0.962213	+	1.14672i	−0.0269109	+	0.999638i	$0.508567\pi$
$194$		0			0
$195$	1.00071e7	+	3.64228e6i	1.34960	+	0.491213i
$196$		0			0
$197$	−5.74026e6	+	9.94243e6i	−0.750815	+	1.30045i	0.196613	+	0.980481i	$0.437006\pi$
$197$	−5.74026e6	+	9.94243e6i	−0.750815	+	1.30045i	−0.947428	+	0.319969i	$0.896328\pi$
$198$		0			0
$199$	−510864.	+	2.89726e6i	−0.0648256	+	0.367644i	0.935087	+	0.354418i	$0.115321\pi$
$199$	−510864.	+	2.89726e6i	−0.0648256	+	0.367644i	−0.999913	+	0.0132257i	$0.995790\pi$
$200$		0			0
$201$	8.52530e6	+	1.47663e7i	1.04984	+	1.81837i
$202$		0			0
$203$	−389966.	+	464744.i	−0.0466164	+	0.0555553i
$204$		0			0
$205$	−1.58142e6	−	4.34492e6i	−0.183563	−	0.504336i
$206$		0			0
$207$	−1.06000e6	−	6.01158e6i	−0.119508	−	0.677762i
$208$		0			0
$209$	599084.	−	1.41739e7i	0.0656219	−	1.55257i
$210$		0			0
$211$	−7.78947e6	+	1.37349e6i	−0.829203	+	0.146211i	−0.572111	−	0.820176i	$-0.693875\pi$
$211$	−7.78947e6	+	1.37349e6i	−0.829203	+	0.146211i	−0.257092	+	0.966387i	$0.582764\pi$
$212$		0			0
$213$	−9.30424e6	+	3.38647e6i	−0.962814	+	0.350436i
$214$		0			0
$215$	−4.83000e6	−	4.05285e6i	−0.485995	−	0.407798i
$216$		0			0
$217$	−609559.	+	351929.i	−0.0596536	+	0.0344410i
$218$		0			0
$219$	3.26642e6	+	575958.i	0.310985	+	0.0548351i
$220$		0			0
$221$	−8.95198e6	−	5.16843e6i	−0.829358	−	0.478830i
$222$		0			0
$223$	−6.01119e6	+	1.65156e7i	−0.542058	+	1.48929i	0.302142	+	0.953263i	$0.402298\pi$
$223$	−6.01119e6	+	1.65156e7i	−0.542058	+	1.48929i	−0.844200	+	0.536029i	$0.819924\pi$
$224$		0			0
$225$	5.49901e6	−	4.61422e6i	0.482766	−	0.405089i
$226$		0			0
$227$		−	1.39172e7i		−	1.18980i	−0.803799	−	0.594901i	$-0.797191\pi$
$227$		−	1.39172e7i		−	1.18980i	0.803799	−	0.594901i	$-0.202809\pi$
$228$		0			0
$229$	9.46672e6			0.788303			0.394151	−	0.919046i	$-0.371039\pi$
$229$	9.46672e6			0.788303			0.394151	+	0.919046i	$0.371039\pi$
$230$		0			0
$231$	3.89821e6	+	4.64570e6i	0.316249	+	0.376891i
$232$		0			0
$233$	−3.42874e6	−	1.24796e6i	−0.271061	−	0.0986581i	0.202914	−	0.979197i	$-0.434959\pi$
$233$	−3.42874e6	−	1.24796e6i	−0.271061	−	0.0986581i	−0.473975	+	0.880539i	$0.657181\pi$
$234$		0			0
$235$	−3.70300e6	+	6.41378e6i	−0.285331	+	0.494209i
$236$		0			0
$237$	−1.84592e6	+	1.04687e7i	−0.138666	+	0.786411i
$238$		0			0
$239$	−8.43139e6	−	1.46036e7i	−0.617597	−	1.06971i	−0.989923	−	0.141608i	$-0.954773\pi$
$239$	−8.43139e6	−	1.46036e7i	−0.617597	−	1.06971i	0.372325	−	0.928102i	$-0.378561\pi$
$240$		0			0
$241$	−4.24597e6	+	5.06015e6i	−0.303337	+	0.361503i	−0.896083	−	0.443886i	$-0.853599\pi$
$241$	−4.24597e6	+	5.06015e6i	−0.303337	+	0.361503i	0.592746	+	0.805389i	$0.298044\pi$
$242$		0			0
$243$	6.94965e6	+	1.90940e7i	0.484333	+	1.33069i
$244$		0			0
$245$	−1.48209e6	−	8.40534e6i	−0.100780	−	0.571553i
$246$		0			0
$247$	2.38483e7	−	7.55584e6i	1.58258	−	0.501409i
$248$		0			0
$249$	−2.83419e7	+	4.99744e6i	−1.83582	+	0.323705i
$250$		0			0
$251$	−1.85689e7	+	6.75854e6i	−1.17426	+	0.427397i	−0.854173	−	0.519989i	$-0.825936\pi$
$251$	−1.85689e7	+	6.75854e6i	−1.17426	+	0.427397i	−0.320092	+	0.947387i	$0.603714\pi$
$252$		0			0
$253$	−1.31954e7	−	1.10723e7i	−0.814818	−	0.683714i
$254$		0			0
$255$	7.16646e6	−	4.13756e6i	0.432200	−	0.249531i
$256$		0			0
$257$	−1.96703e7	−	3.46841e6i	−1.15881	−	0.204330i	−0.438992	−	0.898491i	$-0.644664\pi$
$257$	−1.96703e7	−	3.46841e6i	−1.15881	−	0.204330i	−0.719819	+	0.694162i	$0.755775\pi$
$258$		0			0
$259$	5.13080e6	+	2.96227e6i	0.295315	+	0.170500i
$260$		0			0
$261$	1.98329e6	−	5.44905e6i	0.111549	−	0.306478i
$262$		0			0
$263$	−2.58724e7	+	2.17095e7i	−1.42223	+	1.19339i	−0.472094	+	0.881548i	$0.656502\pi$
$263$	−2.58724e7	+	2.17095e7i	−1.42223	+	1.19339i	−0.950134	+	0.311842i	$0.899054\pi$
$264$		0			0
$265$			1.18028e7i			0.634229i
$266$		0			0
$267$	3.05889e7			1.60705
$268$		0			0
$269$	5.73293e6	+	6.83224e6i	0.294523	+	0.350999i	0.892932	−	0.450192i	$-0.148644\pi$
$269$	5.73293e6	+	6.83224e6i	0.294523	+	0.350999i	−0.598408	+	0.801191i	$0.704200\pi$
$270$		0			0
$271$	1.43509e7	+	5.22331e6i	0.721062	+	0.262445i	0.676376	−	0.736556i	$-0.263549\pi$
$271$	1.43509e7	+	5.22331e6i	0.721062	+	0.262445i	0.0446853	+	0.999001i	$0.485771\pi$
$272$		0			0
$273$	−5.34709e6	+	9.26144e6i	−0.262803	+	0.455188i
$274$		0			0
$275$	3.51748e6	−	1.99486e7i	0.169135	−	0.959214i
$276$		0			0
$277$	7.12708e6	+	1.23445e7i	0.335330	+	0.580808i	0.983548	−	0.180646i	$-0.0578189\pi$
$277$	7.12708e6	+	1.23445e7i	0.335330	+	0.580808i	−0.648218	+	0.761455i	$0.724486\pi$
$278$		0			0
$279$	4.32442e6	−	5.15364e6i	0.199120	−	0.237302i
$280$		0			0
$281$	1.05765e7	+	2.90586e7i	0.476674	+	1.30965i	0.912300	+	0.409523i	$0.134305\pi$
$281$	1.05765e7	+	2.90586e7i	0.476674	+	1.30965i	−0.435626	+	0.900128i	$0.643473\pi$
$282$		0			0
$283$	−285001.	−	1.61632e6i	−0.0125744	−	0.0713130i	0.977875	−	0.209191i	$-0.0670830\pi$
$283$	−285001.	−	1.61632e6i	−0.0125744	−	0.0713130i	−0.990449	+	0.137878i	$0.955972\pi$
$284$		0			0
$285$	−4.30741e6	+	1.95582e7i	−0.186072	+	0.844880i
$286$		0			0
$287$	4.57271e6	−	806292.i	0.193432	−	0.0341072i
$288$		0			0
$289$	1.51340e7	−	5.50832e6i	0.626989	−	0.228205i
$290$		0			0
$291$	−2.34241e7	−	1.96552e7i	−0.950571	−	0.797624i
$292$		0			0
$293$	2.26806e7	−	1.30947e7i	0.901679	−	0.520584i	0.0239343	−	0.999714i	$-0.492381\pi$
$293$	2.26806e7	−	1.30947e7i	0.901679	−	0.520584i	0.877744	+	0.479129i	$0.159047\pi$
$294$		0			0
$295$	−2.18390e6	−	385081.i	−0.0850682	−	0.0149998i
$296$		0			0
$297$	−271873.	−	156966.i	−0.0103776	−	0.00599150i
$298$		0			0
$299$	1.03889e7	−	2.85433e7i	0.388648	−	1.06780i
$300$		0			0
$301$	4.85035e6	−	4.06993e6i	0.177858	−	0.149241i
$302$		0			0
$303$		−	1.05901e7i		−	0.380690i
$304$		0			0
$305$	−1.34131e7			−0.472749
$306$		0			0
$307$	−2.55440e7	−	3.04421e7i	−0.882823	−	1.05211i	−0.998270	−	0.0587934i	$-0.981275\pi$
$307$	−2.55440e7	−	3.04421e7i	−0.882823	−	1.05211i	0.115448	−	0.993314i	$-0.463170\pi$
$308$		0			0
$309$	1.83774e7	+	6.68884e6i	0.622888	+	0.226713i
$310$		0			0
$311$	2.39785e7	−	4.15320e7i	0.797151	−	1.38071i	−0.124313	−	0.992243i	$-0.539673\pi$
$311$	2.39785e7	−	4.15320e7i	0.797151	−	1.38071i	0.921464	−	0.388464i	$-0.126994\pi$
$312$		0			0
$313$	−3.21524e6	+	1.82345e7i	−0.104853	+	0.594650i	0.886426	+	0.462870i	$0.153180\pi$
$313$	−3.21524e6	+	1.82345e7i	−0.104853	+	0.594650i	−0.991279	+	0.131780i	$0.957931\pi$
$314$		0			0
$315$	−2.14611e6	−	3.71717e6i	−0.0686625	−	0.118927i
$316$		0			0
$317$	2.83848e7	−	3.38277e7i	0.891062	−	1.06193i	−0.106648	−	0.994297i	$-0.534012\pi$
$317$	2.83848e7	−	3.38277e7i	0.891062	−	1.06193i	0.997710	−	0.0676298i	$-0.0215437\pi$
$318$		0			0
$319$	−5.59652e6	−	1.53763e7i	−0.172403	−	0.473674i
$320$		0			0
$321$	7.63950e6	+	4.33258e7i	0.230967	+	1.30988i
$322$		0			0
$323$	7.41411e6	−	1.79699e7i	0.220014	−	0.533260i
$324$		0			0
$325$	3.51774e7	−	6.20273e6i	1.02474	−	0.180689i
$326$		0			0
$327$	3.88868e7	−	1.41536e7i	1.11214	−	0.404785i
$328$		0			0
$329$	−5.69723e6	−	4.78054e6i	−0.159984	−	0.134242i
$330$		0			0
$331$	−2.64705e7	+	1.52828e7i	−0.729926	+	0.421423i	−0.818395	−	0.574656i	$-0.805136\pi$
$331$	−2.64705e7	+	1.52828e7i	−0.729926	+	0.421423i	0.0884693	+	0.996079i	$0.471802\pi$
$332$		0			0
$333$	−5.57675e7	−	9.83332e6i	−1.51025	−	0.266298i
$334$		0			0
$335$	−2.94907e7	−	1.70265e7i	−0.784425	−	0.452888i
$336$		0			0
$337$	−2.50396e7	+	6.87956e7i	−0.654240	+	1.79751i	−0.0527788	+	0.998606i	$0.516808\pi$
$337$	−2.50396e7	+	6.87956e7i	−0.654240	+	1.79751i	−0.601461	+	0.798902i	$0.705414\pi$
$338$		0			0
$339$	7.77141e7	−	6.52099e7i	1.99481	−	1.67384i
$340$		0			0
$341$		−	1.89842e7i		−	0.478772i
$342$		0			0
$343$	1.75929e7			0.435968
$344$		0			0
$345$	1.56305e7	+	1.86277e7i	0.380640	+	0.453630i
$346$		0			0
$347$	4.04005e6	+	1.47046e6i	0.0966937	+	0.0351936i	0.389914	−	0.920851i	$-0.372505\pi$
$347$	4.04005e6	+	1.47046e6i	0.0966937	+	0.0351936i	−0.293220	+	0.956045i	$0.594727\pi$
$348$		0			0
$349$	1.96553e7	−	3.40440e7i	0.462385	−	0.800874i	−0.536694	−	0.843777i	$-0.680327\pi$
$349$	1.96553e7	−	3.40440e7i	0.462385	−	0.800874i	0.999079	+	0.0429027i	$0.0136605\pi$
$350$		0			0
$351$	96129.2	−	545176.i	0.00222297	−	0.0126071i
$352$		0			0
$353$	−2.76949e7	−	4.79689e7i	−0.629615	−	1.09053i	−0.987629	−	0.156809i	$-0.949879\pi$
$353$	−2.76949e7	−	4.79689e7i	−0.629615	−	1.09053i	0.358014	−	0.933716i	$-0.383454\pi$
$354$		0			0
$355$	1.27110e7	−	1.51483e7i	0.284114	−	0.338594i
$356$		0			0
$357$	2.84218e6	+	7.80884e6i	0.0624666	+	0.171625i
$358$		0			0
$359$	1.48195e7	+	8.40454e7i	0.320294	+	1.81648i	0.540866	+	0.841109i	$0.318096\pi$
$359$	1.48195e7	+	8.40454e7i	0.320294	+	1.81648i	−0.220572	+	0.975371i	$0.570792\pi$
$360$		0			0
$361$	2.00011e7	+	4.25825e7i	0.425139	+	0.905128i
$362$		0			0
$363$	−9.43774e7	+	1.66413e7i	−1.97310	+	0.347910i
$364$		0			0
$365$	−6.22475e6	+	2.26562e6i	−0.128010	+	0.0465918i
$366$		0			0
$367$	4.94254e7	+	4.14728e7i	0.999889	+	0.839006i	0.986969	−	0.160910i	$-0.0514429\pi$
$367$	4.94254e7	+	4.14728e7i	0.999889	+	0.839006i	0.0129198	+	0.999917i	$0.495887\pi$
$368$		0			0
$369$	−3.84351e7	+	2.21905e7i	−0.764977	+	0.441660i
$370$		0			0
$371$	−1.16724e7	−	2.05816e6i	−0.228581	−	0.0403049i
$372$		0			0
$373$	−9.35341e6	−	5.40020e6i	−0.180237	−	0.104060i	0.407167	−	0.913354i	$-0.366517\pi$
$373$	−9.35341e6	−	5.40020e6i	−0.180237	−	0.104060i	−0.587404	+	0.809294i	$0.699850\pi$
$374$		0			0
$375$	−2.53839e7	+	6.97416e7i	−0.481354	+	1.32251i
$376$		0			0
$377$	2.21040e7	−	1.85474e7i	0.412521	−	0.346147i
$378$		0			0
$379$			6.39309e7i			1.17434i	0.809464	+	0.587169i	$0.199758\pi$
$379$			6.39309e7i			1.17434i	−0.809464	+	0.587169i	$0.800242\pi$
$380$		0			0
$381$	−6.60449e7			−1.19416
$382$		0			0
$383$	5.38058e6	+	6.41233e6i	0.0957708	+	0.114135i	0.811801	−	0.583934i	$-0.198487\pi$
$383$	5.38058e6	+	6.41233e6i	0.0957708	+	0.114135i	−0.716030	+	0.698069i	$0.754043\pi$
$384$		0			0
$385$	−1.13815e7	−	4.14252e6i	−0.199442	−	0.0725910i
$386$		0			0
$387$	−3.02597e7	+	5.24113e7i	−0.522073	+	0.904257i
$388$		0			0
$389$	−5.64759e6	+	3.20291e7i	−0.0959432	+	0.544121i	0.898511	+	0.438951i	$0.144650\pi$
$389$	−5.64759e6	+	3.20291e7i	−0.0959432	+	0.544121i	−0.994454	+	0.105170i	$0.966461\pi$
$390$		0			0
$391$	−1.18016e7	−	2.04410e7i	−0.197429	−	0.341957i
$392$		0			0
$393$	−3.71539e6	+	4.42783e6i	−0.0612106	+	0.0729480i
$394$		0			0
$395$	−7.26124e6	−	1.99501e7i	−0.117820	−	0.323708i
$396$		0			0
$397$	−1.04676e7	−	5.93648e7i	−0.167292	−	0.948763i	−0.946669	−	0.322207i	$-0.895575\pi$
$397$	−1.04676e7	−	5.93648e7i	−0.167292	−	0.948763i	0.779377	−	0.626556i	$-0.215536\pi$
$398$		0			0
$399$	−1.85911e7	−	7.67041e6i	−0.292676	−	0.120753i
$400$		0			0
$401$	9.52502e7	−	1.67952e7i	1.47718	−	0.260466i	0.623728	−	0.781642i	$-0.285617\pi$
$401$	9.52502e7	−	1.67952e7i	1.47718	−	0.260466i	0.853450	+	0.521175i	$0.174506\pi$
$402$		0			0
$403$	3.14578e7	−	1.14497e7i	0.480632	−	0.174936i
$404$		0			0
$405$	−3.09179e7	−	2.59432e7i	−0.465419	−	0.390533i
$406$		0			0
$407$	−1.38386e8	+	7.98972e7i	−2.05262	+	1.18508i
$408$		0			0
$409$	6.56591e7	+	1.15775e7i	0.959676	+	0.169217i	0.631479	−	0.775393i	$-0.282448\pi$
$409$	6.56591e7	+	1.15775e7i	0.959676	+	0.169217i	0.328197	+	0.944609i	$0.393559\pi$
$410$		0			0
$411$	−7.05371e6	−	4.07246e6i	−0.101600	−	0.0586586i
$412$		0			0
$413$	761657.	−	2.09264e6i	0.0108121	−	0.0297060i
$414$		0			0
$415$	4.40298e7	−	3.69454e7i	0.616030	−	0.516911i
$416$		0			0
$417$			6.24823e7i			0.861686i
$418$		0			0
$419$	−1.27794e8			−1.73728			−0.868640	−	0.495444i	$-0.835005\pi$
$419$	−1.27794e8			−1.73728			−0.868640	+	0.495444i	$0.835005\pi$
$420$		0			0
$421$	−1.63721e7	−	1.95115e7i	−0.219411	−	0.261484i	0.645100	−	0.764098i	$-0.276816\pi$
$421$	−1.63721e7	−	1.95115e7i	−0.219411	−	0.261484i	−0.864510	+	0.502615i	$0.832371\pi$
$422$		0			0
$423$	6.67991e7	+	2.43129e7i	0.882570	+	0.321229i
$424$		0			0
$425$	1.38783e7	−	2.40379e7i	0.180787	−	0.313133i
$426$		0			0
$427$	2.33898e6	−	1.32650e7i	0.0300430	−	0.170382i
$428$		0			0
$429$	−1.44220e8	−	2.49796e8i	−1.82664	−	3.16383i
$430$		0			0
$431$	1.45103e7	−	1.72927e7i	0.181236	−	0.215988i	−0.667776	−	0.744362i	$-0.732754\pi$
$431$	1.45103e7	−	1.72927e7i	0.181236	−	0.215988i	0.849012	+	0.528374i	$0.177198\pi$
$432$		0			0
$433$	1.14127e7	+	3.13561e7i	0.140580	+	0.386241i	0.989924	−	0.141599i	$-0.0452243\pi$
$433$	1.14127e7	+	3.13561e7i	0.140580	+	0.386241i	−0.849344	+	0.527840i	$0.823002\pi$
$434$		0			0
$435$	4.01119e6	+	2.27486e7i	0.0487310	+	0.276367i
$436$		0			0
$437$	5.57862e7	+	1.22861e7i	0.668471	+	0.147221i
$438$		0			0
$439$	1.04442e7	−	1.84159e6i	0.123447	−	0.0217670i	−0.111583	−	0.993755i	$-0.535592\pi$
$439$	1.04442e7	−	1.84159e6i	0.123447	−	0.0217670i	0.235030	+	0.971988i	$0.424481\pi$
$440$		0			0
$441$	−7.69823e7	+	2.80193e7i	−0.897584	+	0.326694i
$442$		0			0
$443$	5.77489e7	+	4.84571e7i	0.664252	+	0.557374i	0.911358	−	0.411615i	$-0.135035\pi$
$443$	5.77489e7	+	4.84571e7i	0.664252	+	0.557374i	−0.247106	+	0.968988i	$0.579480\pi$
$444$		0			0
$445$	−5.29065e7	+	3.05456e7i	−0.600384	+	0.346632i
$446$		0			0
$447$	1.11827e8	+	1.97181e7i	1.25206	+	0.220772i
$448$		0			0
$449$	−1.22766e8	−	7.08787e7i	−1.35624	−	0.783027i	−0.367128	−	0.930171i	$-0.619659\pi$
$449$	−1.22766e8	−	7.08787e7i	−1.35624	−	0.783027i	−0.989115	+	0.147143i	$0.952992\pi$
$450$		0			0
$451$	−4.28332e7	+	1.17683e8i	−0.466929	+	1.28288i
$452$		0			0
$453$	1.68555e8	−	1.41434e8i	1.81321	−	1.52146i
$454$		0			0
$455$		−	2.13581e7i		−	0.226741i
$456$		0			0
$457$	1.65338e8			1.73230			0.866150	−	0.499785i	$-0.166588\pi$
$457$	1.65338e8			1.73230			0.866150	+	0.499785i	$0.166588\pi$
$458$		0			0
$459$	−276507.	−	329528.i	−0.00285935	−	0.00340764i
$460$		0			0
$461$	5.29831e7	+	1.92843e7i	0.540798	+	0.196834i	0.597953	−	0.801531i	$-0.295981\pi$
$461$	5.29831e7	+	1.92843e7i	0.540798	+	0.196834i	−0.0571554	+	0.998365i	$0.518203\pi$
$462$		0			0
$463$	−5.79378e7	+	1.00351e8i	−0.583739	+	1.01107i	0.411292	+	0.911504i	$0.365078\pi$
$463$	−5.79378e7	+	1.00351e8i	−0.583739	+	1.01107i	−0.995031	+	0.0995622i	$0.968256\pi$
$464$		0			0
$465$	−4.65370e6	+	2.63925e7i	−0.0462849	+	0.262495i
$466$		0			0
$467$	−8.36534e7	−	1.44892e8i	−0.821359	−	1.42264i	−0.904671	−	0.426112i	$-0.859883\pi$
$467$	−8.36534e7	−	1.44892e8i	−0.821359	−	1.42264i	0.0833119	−	0.996524i	$-0.473450\pi$
$468$		0			0
$469$	2.19811e7	−	2.61960e7i	0.213074	−	0.253932i
$470$		0			0
$471$	8.95037e7	+	2.45909e8i	0.856600	+	2.35349i
$472$		0			0
$473$	2.96549e7	+	1.68181e8i	0.280229	+	1.58926i
$474$		0			0
$475$	2.02889e7	+	6.40374e7i	0.189312	+	0.597521i
$476$		0			0
$477$	1.11567e8	−	1.96723e7i	1.02797	−	0.181259i
$478$		0			0
$479$	1.93950e7	−	7.05919e6i	0.176475	−	0.0642315i	−0.252272	−	0.967656i	$-0.581178\pi$
$479$	1.93950e7	−	7.05919e6i	0.176475	−	0.0642315i	0.428746	+	0.903425i	$0.358955\pi$
$480$		0			0
$481$	−2.15857e8	−	1.81125e8i	−1.93968	−	1.62759i
$482$		0			0
$483$	−2.11476e7	+	1.22096e7i	−0.187681	+	0.108358i
$484$		0			0
$485$	6.01418e7	+	1.06046e7i	0.527171	+	0.0929545i
$486$		0			0
$487$	−1.28996e8	−	7.44760e7i	−1.11684	−	0.644807i	−0.176246	−	0.984346i	$-0.556395\pi$
$487$	−1.28996e8	−	7.44760e7i	−1.11684	−	0.644807i	−0.940592	+	0.339539i	$0.889729\pi$
$488$		0			0
$489$	−5.92012e7	+	1.62654e8i	−0.506295	+	1.39103i
$490$		0			0
$491$	1.16653e8	−	9.78838e7i	0.985491	−	0.826925i	0.000582330	−	1.00000i	$-0.499815\pi$
$491$	1.16653e8	−	9.78838e7i	0.985491	−	0.826925i	0.984909	+	0.173075i	$0.0553702\pi$
$492$		0			0
$493$		−	2.24217e7i		−	0.187124i
$494$		0			0
$495$	1.15768e8			0.954492
$496$		0			0
$497$	1.27645e7	+	1.52122e7i	0.103977	+	0.123914i
$498$		0			0
$499$	−1.30689e8	−	4.75668e7i	−1.05181	−	0.382827i	−0.242464	−	0.970160i	$-0.577956\pi$
$499$	−1.30689e8	−	4.75668e7i	−1.05181	−	0.382827i	−0.809345	+	0.587333i	$0.800178\pi$
$500$		0			0
$501$	1.15103e8	−	1.99364e8i	0.915320	−	1.58538i
$502$		0			0
$503$	1.49634e7	−	8.48616e7i	0.117578	−	0.666818i	−0.867863	−	0.496803i	$-0.834507\pi$
$503$	1.49634e7	−	8.48616e7i	0.117578	−	0.666818i	0.985441	−	0.170015i	$-0.0543817\pi$
$504$		0			0
$505$	1.05751e7	+	1.83166e7i	0.0821127	+	0.142223i
$506$		0			0
$507$	2.08313e8	−	2.48257e8i	1.59842	−	1.90493i
$508$		0			0
$509$	4.35275e7	+	1.19591e8i	0.330073	+	0.906869i	0.988092	+	0.153867i	$0.0491727\pi$
$509$	4.35275e7	+	1.19591e8i	0.330073	+	0.906869i	−0.658018	+	0.753002i	$0.728605\pi$
$510$		0			0
$511$	−1.15513e6	−	6.55109e6i	−0.00865705	−	0.0490966i
$512$		0			0
$513$	1.04014e6	+	43963.0i	0.00770439	+	0.000325638i
$514$		0			0
$515$	−3.84650e7	+	6.78242e6i	−0.281608	+	0.0496550i
$516$		0			0
$517$	1.88496e8	−	6.86069e7i	1.36405	−	0.496474i
$518$		0			0
$519$	−6.35990e7	−	5.33659e7i	−0.454934	−	0.381735i
$520$		0			0
$521$	2.00038e8	−	1.15492e8i	1.41449	−	0.816654i	0.418679	−	0.908134i	$-0.362493\pi$
$521$	2.00038e8	−	1.15492e8i	1.41449	−	0.816654i	0.995807	+	0.0914808i	$0.0291600\pi$
$522$		0			0
$523$	−9.01399e7	−	1.58941e7i	−0.630104	−	0.111104i	−0.150529	−	0.988606i	$-0.548098\pi$
$523$	−9.01399e7	−	1.58941e7i	−0.630104	−	0.111104i	−0.479574	+	0.877501i	$0.659209\pi$
$524$		0			0
$525$	−2.48688e7	−	1.43580e7i	−0.171861	−	0.0992240i
$526$		0			0
$527$	8.89706e6	−	2.44445e7i	0.0607876	−	0.167013i
$528$		0			0
$529$	−6.02701e7	+	5.05726e7i	−0.407132	+	0.341624i
$530$		0			0
$531$			2.12855e7i			0.142167i
$532$		0			0
$533$	−2.20841e8			−1.45847
$534$		0			0
$535$	−5.64778e7	−	6.73076e7i	−0.368822	−	0.439545i
$536$		0			0
$537$	2.07821e8	+	7.56406e7i	1.34204	+	0.488464i
$538$		0			0
$539$	−1.15586e8	+	2.00201e8i	−0.738143	+	1.27850i
$540$		0			0
$541$	4.27370e7	−	2.42374e8i	0.269906	−	1.53071i	−0.484786	−	0.874633i	$-0.661102\pi$
$541$	4.27370e7	−	2.42374e8i	0.269906	−	1.53071i	0.754692	−	0.656079i	$-0.227786\pi$
$542$		0			0
$543$	−1.19949e8	−	2.07758e8i	−0.749200	−	1.29765i
$544$		0			0
$545$	−5.31250e7	+	6.33119e7i	−0.328178	+	0.391107i
$546$		0			0
$547$	−6.14696e6	−	1.68886e7i	−0.0375576	−	0.103189i	0.919496	−	0.393099i	$-0.128597\pi$
$547$	−6.14696e6	−	1.68886e7i	−0.0375576	−	0.103189i	−0.957054	+	0.289910i	$0.906375\pi$
$548$		0			0
$549$	2.23564e7	+	1.26789e8i	0.135109	+	0.766242i
$550$		0			0
$551$	4.00584e7	+	3.66043e7i	0.239463	+	0.218815i
$552$		0			0
$553$	2.09960e7	−	3.70216e6i	0.124154	−	0.0218917i
$554$		0			0
$555$	2.11974e8	−	7.71524e7i	1.23995	−	0.451305i
$556$		0			0
$557$	−1.90990e7	−	1.60259e7i	−0.110521	−	0.0927380i	0.585853	−	0.810418i	$-0.300760\pi$
$557$	−1.90990e7	−	1.60259e7i	−0.110521	−	0.0927380i	−0.696373	+	0.717680i	$0.745204\pi$
$558$		0			0
$559$	−2.60799e8	+	1.50573e8i	−1.49304	+	0.862007i
$560$		0			0
$561$	−2.20729e8	−	3.89204e7i	−1.25017	−	0.220439i
$562$		0			0
$563$	3.09697e7	+	1.78804e7i	0.173545	+	0.100196i	0.584256	−	0.811569i	$-0.301386\pi$
$563$	3.09697e7	+	1.78804e7i	0.173545	+	0.100196i	−0.410711	+	0.911765i	$0.634720\pi$
$564$		0			0
$565$	−6.92968e7	+	1.90391e8i	−0.384209	+	1.05561i
$566$		0			0
$567$	3.10481e7	−	2.60525e7i	0.170328	−	0.142922i
$568$		0			0
$569$			2.41542e8i			1.31116i	0.755124	+	0.655581i	$0.227576\pi$
$569$			2.41542e8i			1.31116i	−0.755124	+	0.655581i	$0.772424\pi$
$570$		0			0
$571$	5.92661e7			0.318345			0.159172	−	0.987251i	$-0.449117\pi$
$571$	5.92661e7			0.318345			0.159172	+	0.987251i	$0.449117\pi$
$572$		0			0
$573$	−1.29077e8	−	1.53828e8i	−0.686095	−	0.817656i
$574$		0			0
$575$	7.66445e7	+	2.78963e7i	0.403160	+	0.146738i
$576$		0			0
$577$	1.78971e7	−	3.09987e7i	0.0931655	−	0.161367i	−0.815676	−	0.578509i	$-0.803635\pi$
$577$	1.78971e7	−	3.09987e7i	0.0931655	−	0.161367i	0.908841	+	0.417142i	$0.136968\pi$
$578$		0			0
$579$	−7.14521e7	+	4.05225e8i	−0.368112	+	2.08766i
$580$		0			0
$581$	2.88595e7	+	4.99861e7i	0.147150	+	0.254871i
$582$		0			0
$583$	2.05487e8	−	2.44890e8i	1.03700	−	1.23585i
$584$		0			0
$585$	6.98217e7	+	1.91833e8i	0.348757	+	0.958201i
$586$		0			0
$587$	6.80443e7	+	3.85899e8i	0.336417	+	1.90791i	0.412773	+	0.910834i	$0.364560\pi$
$587$	6.80443e7	+	3.85899e8i	0.336417	+	1.90791i	−0.0763561	+	0.997081i	$0.524329\pi$
$588$		0			0
$589$	2.91474e7	+	5.58019e7i	0.142644	+	0.273088i
$590$		0			0
$591$	−4.32297e8	+	7.62257e7i	−2.09421	+	0.369265i
$592$		0			0
$593$	−4.63053e7	+	1.68538e7i	−0.222058	+	0.0808226i	−0.450653	−	0.892699i	$-0.648809\pi$
$593$	−4.63053e7	+	1.68538e7i	−0.222058	+	0.0808226i	0.228595	+	0.973522i	$0.426587\pi$
$594$		0			0
$595$	−1.27136e7	−	1.06680e7i	−0.0603558	−	0.0506445i
$596$		0			0
$597$	−9.74171e7	+	5.62438e7i	−0.457838	+	0.264333i
$598$		0			0
$599$	−3.57259e8	−	6.29944e7i	−1.66228	−	0.293104i	−0.737991	−	0.674810i	$-0.764226\pi$
$599$	−3.57259e8	−	6.29944e7i	−1.66228	−	0.293104i	−0.924284	+	0.381706i	$0.875337\pi$
$600$		0			0
$601$	−2.48291e8	−	1.43351e8i	−1.14377	−	0.660354i	−0.196405	−	0.980523i	$-0.562927\pi$
$601$	−2.48291e8	−	1.43351e8i	−1.14377	−	0.660354i	−0.947360	+	0.320169i	$0.896260\pi$
$602$		0			0
$603$	−1.11791e8	+	3.07144e8i	−0.509866	+	1.40085i
$604$		0			0
$605$	1.46618e8	−	1.23027e8i	0.662094	−	0.555563i
$606$		0			0
$607$		−	6.67463e7i		−	0.298443i	−0.988804	−	0.149221i	$-0.952323\pi$
$607$		−	6.67463e7i		−	0.298443i	0.988804	−	0.149221i	$-0.0476767\pi$
$608$		0			0
$609$	−2.31968e7			−0.102702
$610$		0			0
$611$	2.27370e8	+	2.70970e8i	0.996805	+	1.18795i
$612$		0			0
$613$	3.29132e8	+	1.19794e8i	1.42886	+	0.520061i	0.936603	−	0.350392i	$-0.113951\pi$
$613$	3.29132e8	+	1.19794e8i	1.42886	+	0.520061i	0.492252	+	0.870453i	$0.336174\pi$
$614$		0			0
$615$	8.83965e7	−	1.53107e8i	0.380023	−	0.658219i
$616$		0			0
$617$	−3.64178e7	+	2.06535e8i	−0.155045	+	0.879304i	0.803700	+	0.595035i	$0.202862\pi$
$617$	−3.64178e7	+	2.06535e8i	−0.155045	+	0.879304i	−0.958745	+	0.284269i	$0.908249\pi$
$618$		0			0
$619$	−7.25585e7	−	1.25675e8i	−0.305926	−	0.529879i	0.671541	−	0.740967i	$-0.265633\pi$
$619$	−7.25585e7	−	1.25675e8i	−0.305926	−	0.529879i	−0.977467	+	0.211088i	$0.932299\pi$
$620$		0			0
$621$	812523.	−	968327.i	0.00339282	−	0.00404341i
$622$		0			0
$623$	−2.09825e7	−	5.76489e7i	−0.0867746	−	0.238411i
$624$		0			0
$625$	833624.	+	4.72772e6i	0.00341453	+	0.0193647i
$626$		0			0
$627$	4.29882e8	−	3.30812e8i	1.74400	−	1.34208i
$628$		0			0
$629$	−2.15633e8	+	3.80220e7i	−0.866491	+	0.152786i
$630$		0			0
$631$	−1.13854e8	+	4.14396e7i	−0.453171	+	0.164941i	−0.558514	−	0.829495i	$-0.688628\pi$
$631$	−1.13854e8	+	4.14396e7i	−0.453171	+	0.164941i	0.105343	+	0.994436i	$0.466406\pi$
$632$		0			0
$633$	−2.31675e8	−	1.94399e8i	−0.913416	−	0.766447i
$634$		0			0
$635$	1.14231e8	−	6.59515e7i	0.446133	−	0.257575i
$636$		0			0
$637$	−4.01456e8	−	7.07876e7i	−1.55317	−	0.273866i
$638$		0			0
$639$	−1.64378e8	−	9.49035e7i	−0.629999	−	0.363730i
$640$		0			0
$641$	−7.68424e7	+	2.11123e8i	−0.291761	+	0.801606i	0.704048	+	0.710152i	$0.251374\pi$
$641$	−7.68424e7	+	2.11123e8i	−0.291761	+	0.801606i	−0.995809	+	0.0914543i	$0.970848\pi$
$642$		0			0
$643$	6.02638e7	−	5.05673e7i	0.226685	−	0.190212i	−0.522370	−	0.852719i	$-0.674952\pi$
$643$	6.02638e7	−	5.05673e7i	0.226685	−	0.190212i	0.749056	+	0.662507i	$0.230508\pi$
$644$		0			0
$645$		−	2.41080e8i		−	0.898427i
$646$		0			0
$647$	3.06519e8			1.13174			0.565868	−	0.824496i	$-0.308541\pi$
$647$	3.06519e8			1.13174			0.565868	+	0.824496i	$0.308541\pi$
$648$		0			0
$649$	3.86084e7	+	4.60117e7i	0.141237	+	0.168320i
$650$		0			0
$651$	−2.52895e7	−	9.20463e6i	−0.0916637	−	0.0333629i
$652$		0			0
$653$	9.23118e7	−	1.59889e8i	0.331526	−	0.574220i	−0.651285	−	0.758833i	$-0.725770\pi$
$653$	9.23118e7	−	1.59889e8i	0.331526	−	0.574220i	0.982811	+	0.184613i	$0.0591032\pi$
$654$		0			0
$655$	2.00458e6	−	1.13685e7i	0.00713343	−	0.0404557i
$656$		0			0
$657$	3.17912e7	+	5.50640e7i	0.112101	+	0.194165i
$658$		0			0
$659$	7.42754e7	−	8.85180e7i	0.259531	−	0.309297i	−0.620507	−	0.784201i	$-0.713073\pi$
$659$	7.42754e7	−	8.85180e7i	0.259531	−	0.309297i	0.880037	+	0.474905i	$0.157517\pi$
$660$		0			0
$661$	−1.16644e7	−	3.20478e7i	−0.0403887	−	0.110967i	0.917859	−	0.396907i	$-0.129916\pi$
$661$	−1.16644e7	−	3.20478e7i	−0.0403887	−	0.110967i	−0.958248	+	0.285940i	$0.907694\pi$
$662$		0			0
$663$	−6.86322e7	−	3.89232e8i	−0.235498	−	1.33558i
$664$		0			0
$665$	3.98148e7	−	5.29811e6i	0.135388	−	0.0180159i
$666$		0			0
$667$	6.48860e7	−	1.14412e7i	0.218662	−	0.0385560i
$668$		0			0
$669$	−6.31486e8	+	2.29842e8i	−2.10904	+	0.767628i
$670$		0			0
$671$	2.78302e8	+	2.33523e8i	0.921190	+	0.772970i
$672$		0			0
$673$	−5.51790e7	+	3.18576e7i	−0.181021	+	0.104512i	−0.587772	−	0.809027i	$-0.699995\pi$
$673$	−5.51790e7	+	3.18576e7i	−0.181021	+	0.104512i	0.406751	+	0.913539i	$0.366662\pi$
$674$		0			0
$675$	1.46391e6	+	258126.i	0.00475995	+	0.000839307i
$676$		0			0
$677$	3.57135e8	+	2.06192e8i	1.15098	+	0.664516i	0.949125	−	0.314901i	$-0.101971\pi$
$677$	3.57135e8	+	2.06192e8i	1.15098	+	0.664516i	0.201850	+	0.979416i	$0.435304\pi$
$678$		0			0
$679$	−2.09751e7	+	5.76285e7i	−0.0670029	+	0.184089i
$680$		0			0
$681$	4.07639e8	−	3.42050e8i	1.29073	−	1.08305i
$682$		0			0
$683$		−	3.90211e8i		−	1.22472i	−0.790578	−	0.612362i	$-0.790220\pi$
$683$		−	3.90211e8i		−	1.22472i	0.790578	−	0.612362i	$-0.209780\pi$
$684$		0			0
$685$	1.62668e7			0.0506094
$686$		0			0
$687$	2.32668e8	+	2.77283e8i	0.717573	+	0.855170i
$688$		0			0
$689$	5.29727e8	+	1.92805e8i	1.61955	+	0.589469i
$690$		0			0
$691$	−1.40008e6	+	2.42502e6i	−0.00424346	+	0.00734989i	−0.868139	−	0.496321i	$-0.834684\pi$
$691$	−1.40008e6	+	2.42502e6i	−0.00424346	+	0.00734989i	0.863896	+	0.503670i	$0.168017\pi$
$692$		0			0
$693$	−2.01876e7	+	1.14490e8i	−0.0606575	+	0.344006i
$694$		0			0
$695$	−6.23940e7	−	1.08070e8i	−0.185861	−	0.321921i
$696$		0			0
$697$	−1.10306e8	+	1.31458e8i	−0.325762	+	0.388228i
$698$		0			0
$699$	−4.77166e7	−	1.31100e8i	−0.139713	−	0.383859i
$700$		0			0
$701$	−8.85538e7	−	5.02214e8i	−0.257071	−	1.45792i	−0.790700	−	0.612204i	$-0.790283\pi$
$701$	−8.85538e7	−	5.02214e8i	−0.257071	−	1.45792i	0.533629	−	0.845719i	$-0.320828\pi$
$702$		0			0
$703$	2.84100e8	−	4.47320e8i	0.817721	−	1.28752i
$704$		0			0
$705$	−2.78871e8	+	4.91725e7i	−0.795860	+	0.140332i
$706$		0			0
$707$	−1.99584e7	+	7.26427e6i	−0.0564765	+	0.0205558i
$708$		0			0
$709$	−3.69349e8	−	3.09921e8i	−1.03633	−	0.869584i	−0.0447394	−	0.998999i	$-0.514246\pi$
$709$	−3.69349e8	−	3.09921e8i	−1.03633	−	0.869584i	−0.991591	+	0.129415i	$0.958690\pi$
$710$		0			0
$711$	−1.76478e8	+	1.01890e8i	−0.491001	+	0.283479i
$712$		0			0
$713$	7.52795e7	+	1.32738e7i	0.207687	+	0.0366207i
$714$		0			0
$715$	4.98885e8	+	2.88031e8i	1.36484	+	0.787992i
$716$		0			0
$717$	2.20521e8	−	6.05877e8i	0.598264	−	1.64372i
$718$		0			0
$719$	−8.90497e7	+	7.47216e7i	−0.239577	+	0.201029i	−0.754669	−	0.656106i	$-0.772202\pi$
$719$	−8.90497e7	+	7.47216e7i	−0.239577	+	0.201029i	0.515091	+	0.857135i	$0.327758\pi$
$720$		0			0
$721$		−	3.92230e7i		−	0.104649i
$722$		0			0
$723$	−2.52568e8			−0.668287
$724$		0			0
$725$	4.98036e7	+	5.93536e7i	0.130691	+	0.155752i
$726$		0			0
$727$	6.01255e8	+	2.18839e8i	1.56479	+	0.569536i	0.971827	−	0.235696i	$-0.0757369\pi$
$727$	6.01255e8	+	2.18839e8i	1.56479	+	0.569536i	0.592960	+	0.805232i	$0.297959\pi$
$728$		0			0
$729$	−1.95814e8	+	3.39160e8i	−0.505430	+	0.875431i
$730$		0			0
$731$	−4.06349e7	+	2.30452e8i	−0.104027	+	0.589967i
$732$		0			0
$733$	2.57244e8	+	4.45560e8i	0.653182	+	1.13134i	0.982346	+	0.187071i	$0.0598996\pi$
$733$	2.57244e8	+	4.45560e8i	0.653182	+	1.13134i	−0.329165	+	0.944273i	$0.606767\pi$
$734$		0			0
$735$	2.09769e8	−	2.49992e8i	0.528297	−	0.629600i
$736$		0			0
$737$	3.15457e8	+	8.66710e8i	0.788020	+	2.16507i
$738$		0			0
$739$	−1.97887e7	−	1.12227e8i	−0.0490325	−	0.278077i	0.950427	−	0.310947i	$-0.100646\pi$
$739$	−1.97887e7	−	1.12227e8i	−0.0490325	−	0.278077i	−0.999460	+	0.0328704i	$0.989535\pi$
$740$		0			0
$741$	8.07442e8	+	5.12819e8i	1.98453	+	1.26040i
$742$		0			0
$743$	−5.96038e7	+	1.05098e7i	−0.145314	+	0.0256228i	−0.245832	−	0.969312i	$-0.579061\pi$
$743$	−5.96038e7	+	1.05098e7i	−0.145314	+	0.0256228i	0.100518	+	0.994935i	$0.467950\pi$
$744$		0			0
$745$	−2.13107e8	+	7.75644e7i	−0.515381	+	0.187583i
$746$		0			0
$747$	−4.22618e8	−	3.54618e8i	−1.01388	−	0.850745i
$748$		0			0
$749$	7.64130e7	−	4.41171e7i	0.181854	−	0.104993i
$750$		0			0
$751$	−1.37803e8	−	2.42983e7i	−0.325340	−	0.0573663i	0.00859277	−	0.999963i	$-0.497265\pi$
$751$	−1.37803e8	−	2.42983e7i	−0.325340	−	0.0573663i	−0.333933	+	0.942597i	$0.608376\pi$
$752$		0			0
$753$	−6.54336e8	−	3.77781e8i	−1.53256	−	0.884821i
$754$		0			0
$755$	−1.50299e8	+	4.12942e8i	−0.349232	+	0.959507i
$756$		0			0
$757$	3.67161e8	−	3.08085e8i	0.846388	−	0.710204i	−0.112603	−	0.993640i	$-0.535919\pi$
$757$	3.67161e8	−	3.08085e8i	0.846388	−	0.710204i	0.958991	+	0.283436i	$0.0914745\pi$
$758$		0			0
$759$		−	6.58624e8i		−	1.50630i
$760$		0			0
$761$	1.61619e8			0.366723			0.183361	−	0.983046i	$-0.441302\pi$
$761$	1.61619e8			0.366723			0.183361	+	0.983046i	$0.441302\pi$
$762$		0			0
$763$	−5.33489e7	−	6.35787e7i	−0.120102	−	0.143132i
$764$		0			0
$765$	1.49065e8	+	5.42554e7i	0.332960	+	0.121188i
$766$		0			0
$767$	−5.29584e7	+	9.17267e7i	−0.117368	+	0.203287i
$768$		0			0
$769$	7.22004e7	−	4.09469e8i	0.158767	−	0.900413i	−0.796493	−	0.604647i	$-0.793314\pi$
$769$	7.22004e7	−	4.09469e8i	0.158767	−	0.900413i	0.955260	−	0.295766i	$-0.0955749\pi$
$770$		0			0
$771$	−3.81856e8	−	6.61394e8i	−0.833175	−	1.44310i
$772$		0			0
$773$	3.11777e7	−	3.71561e7i	0.0675003	−	0.0804437i	−0.731238	−	0.682123i	$-0.761057\pi$
$773$	3.11777e7	−	3.71561e7i	0.0675003	−	0.0804437i	0.798738	+	0.601679i	$0.205501\pi$
$774$		0			0
$775$	3.07447e7	+	8.44704e7i	0.0660489	+	0.181468i
$776$		0			0
$777$	3.93364e7	+	2.23088e8i	0.0838554	+	0.475568i
$778$		0			0
$779$	−5.47818e7	−	4.11681e8i	−0.115884	−	0.870859i
$780$		0			0
$781$	−5.27467e8	+	9.30066e7i	−1.10724	+	0.195236i
$782$		0			0
$783$	1.12837e6	−	410693.i	0.00235053	−	0.000855525i
$784$		0			0
$785$	−4.00367e8	−	3.35948e8i	−0.827656	−	0.694486i
$786$		0			0
$787$	8.21823e8	−	4.74480e8i	1.68599	−	0.973405i	0.728448	−	0.685101i	$-0.240242\pi$
$787$	8.21823e8	−	4.74480e8i	1.68599	−	0.973405i	0.957539	−	0.288304i	$-0.0930912\pi$
$788$		0			0
$789$	−1.27175e9	−	2.24244e8i	−2.58924	−	0.456553i
$790$		0			0
$791$	−1.76205e8	−	1.01732e8i	−0.356032	−	0.205555i
$792$		0			0
$793$	−2.19111e8	+	6.02003e8i	−0.439385	+	1.20720i
$794$		0			0
$795$	−3.45706e8	+	2.90082e8i	−0.688027	+	0.577323i
$796$		0			0
$797$		−	4.19151e7i		−	0.0827934i	−0.999143	−	0.0413967i	$-0.986819\pi$
$797$		−	4.19151e7i		−	0.0827934i	0.999143	−	0.0413967i	$-0.0131807\pi$
$798$		0			0
$799$	2.74865e8			0.538864
$800$		0			0
$801$	3.76919e8	+	4.49194e8i	0.733415	+	0.874050i
$802$		0			0
$803$	1.68599e8	+	6.13650e7i	0.325618	+	0.118515i
$804$		0			0
$805$	2.43846e7	−	4.22354e7i	0.0467443	−	0.0809635i
$806$		0			0
$807$	−5.92173e7	+	3.35838e8i	−0.112675	+	0.639012i
$808$		0			0
$809$	5.20047e8	+	9.00748e8i	0.982193	+	1.70121i	0.653800	+	0.756667i	$0.273174\pi$
$809$	5.20047e8	+	9.00748e8i	0.982193	+	1.70121i	0.328393	+	0.944541i	$0.393493\pi$
$810$		0			0
$811$	1.64335e8	−	1.95847e8i	0.308083	−	0.367159i	−0.589681	−	0.807637i	$-0.700746\pi$
$811$	1.64335e8	−	1.95847e8i	0.308083	−	0.367159i	0.897764	+	0.440477i	$0.145191\pi$
$812$		0			0
$813$	1.99717e8	+	5.48718e8i	0.371658	+	1.02112i
$814$		0			0
$815$	−6.00294e7	−	3.40444e8i	−0.110890	−	0.628887i
$816$		0			0
$817$	−3.45384e8	−	4.48819e8i	−0.633339	−	0.823010i
$818$		0			0
$819$	−2.01891e8	+	3.55988e7i	−0.367506	+	0.0648012i
$820$		0			0
$821$	3.24078e8	−	1.17955e8i	0.585626	−	0.213150i	−0.0321787	−	0.999482i	$-0.510245\pi$
$821$	3.24078e8	−	1.17955e8i	0.585626	−	0.213150i	0.617804	+	0.786332i	$0.288022\pi$
$822$		0			0
$823$	4.13390e8	+	3.46876e8i	0.741585	+	0.622263i	0.933263	−	0.359194i	$-0.116949\pi$
$823$	4.13390e8	+	3.46876e8i	0.741585	+	0.622263i	−0.191678	+	0.981458i	$0.561393\pi$
$824$		0			0
$825$	6.70752e8	−	3.87259e8i	1.19454	−	0.689667i
$826$		0			0
$827$	−1.44003e8	−	2.53916e7i	−0.254598	−	0.0448925i	0.0448924	−	0.998992i	$-0.485706\pi$
$827$	−1.44003e8	−	2.53916e7i	−0.254598	−	0.0448925i	−0.299490	+	0.954099i	$0.596817\pi$
$828$		0			0
$829$	−5.96480e8	−	3.44378e8i	−1.04696	−	0.604465i	−0.125167	−	0.992136i	$-0.539947\pi$
$829$	−5.96480e8	−	3.44378e8i	−1.04696	−	0.604465i	−0.921798	+	0.387670i	$0.873280\pi$
$830$		0			0
$831$	−1.86407e8	+	5.12149e8i	−0.324832	+	0.892470i
$832$		0			0
$833$	−2.42657e8	+	2.03614e8i	−0.419816	+	0.352267i
$834$		0			0
$835$			4.59760e8i			0.789718i
$836$		0			0
$837$	1.39313e6			0.00237583
$838$		0			0
$839$	−6.83131e8	−	8.14124e8i	−1.15669	−	1.37849i	−0.912657	−	0.408726i	$-0.865973\pi$
$839$	−6.83131e8	−	8.14124e8i	−1.15669	−	1.37849i	−0.244036	−	0.969766i	$-0.578471\pi$
$840$		0			0
$841$	−5.00137e8	−	1.82035e8i	−0.840816	−	0.306032i
$842$		0			0
$843$	−5.91191e8	+	1.02397e9i	−0.986836	+	1.70925i
$844$		0			0
$845$	−1.12392e8	+	6.37404e8i	−0.186279	+	1.05644i
$846$		0			0
$847$	9.61010e7	+	1.66452e8i	0.158153	+	0.273929i
$848$		0			0
$849$	4.03379e7	−	4.80728e7i	0.0659159	−	0.0785555i
$850$		0			0
$851$	−2.20063e8	−	6.04617e8i	−0.357074	−	0.981052i
$852$		0			0
$853$	7.48681e7	+	4.24598e8i	0.120628	+	0.684118i	0.983809	+	0.179222i	$0.0573580\pi$
$853$	7.48681e7	+	4.24598e8i	0.120628	+	0.684118i	−0.863180	+	0.504896i	$0.831531\pi$
$854$		0			0
$855$	−3.40287e8	+	1.77745e8i	−0.544436	+	0.284379i
$856$		0			0
$857$	9.67713e7	−	1.70634e7i	0.153746	−	0.0271096i	−0.0962453	−	0.995358i	$-0.530683\pi$
$857$	9.67713e7	−	1.70634e7i	0.153746	−	0.0271096i	0.249991	+	0.968248i	$0.419572\pi$
$858$		0			0
$859$	−3.40981e8	+	1.24107e8i	−0.537962	+	0.195802i	−0.596690	−	0.802472i	$-0.703518\pi$
$859$	−3.40981e8	+	1.24107e8i	−0.537962	+	0.195802i	0.0587282	+	0.998274i	$0.481295\pi$
$860$		0			0
$861$	1.36002e8	+	1.14119e8i	0.213077	+	0.178792i
$862$		0			0
$863$	−6.14083e8	+	3.54541e8i	−0.955421	+	0.551612i	−0.894761	−	0.446546i	$-0.852654\pi$
$863$	−6.14083e8	+	3.54541e8i	−0.955421	+	0.551612i	−0.0606601	+	0.998158i	$0.519321\pi$
$864$		0			0
$865$	1.63291e8	+	2.87927e7i	0.252299	+	0.0444871i
$866$		0			0
$867$	5.33295e8	+	3.07898e8i	0.818295	+	0.472443i
$868$		0			0
$869$	−1.96672e8	+	5.40353e8i	−0.299698	+	0.823414i
$870$		0			0
$871$	−1.24593e9	+	1.04546e9i	−1.88555	+	1.58216i
$872$		0			0
$873$		−	5.86174e8i		−	0.881016i
$874$		0			0
$875$	1.48850e8			0.222190
$876$		0			0
$877$	1.31927e8	+	1.57224e8i	0.195584	+	0.233089i	0.854919	−	0.518761i	$-0.173606\pi$
$877$	1.31927e8	+	1.57224e8i	0.195584	+	0.233089i	−0.659335	+	0.751849i	$0.729162\pi$
$878$		0			0
$879$	9.40977e8	+	3.42488e8i	1.38552	+	0.504288i
$880$		0			0
$881$	2.37910e8	−	4.12073e8i	0.347925	−	0.602623i	−0.637956	−	0.770073i	$-0.720220\pi$
$881$	2.37910e8	−	4.12073e8i	0.347925	−	0.602623i	0.985881	+	0.167450i	$0.0535531\pi$
$882$		0			0
$883$	−2.09511e6	+	1.18820e7i	−0.00304316	+	0.0172586i	−0.986292	−	0.165012i	$-0.947234\pi$
$883$	−2.09511e6	+	1.18820e7i	−0.00304316	+	0.0172586i	0.983248	+	0.182271i	$0.0583448\pi$
$884$		0			0
$885$	−4.23956e7	−	7.34314e7i	−0.0611633	−	0.105938i
$886$		0			0
$887$	6.31283e8	−	7.52334e8i	0.904593	−	1.07805i	−0.0920147	−	0.995758i	$-0.529331\pi$
$887$	6.31283e8	−	7.52334e8i	0.904593	−	1.07805i	0.996608	−	0.0822947i	$-0.0262249\pi$
$888$		0			0
$889$	4.53036e7	+	1.24471e8i	0.0644803	+	0.177158i
$890$		0			0
$891$	1.89827e8	+	1.07656e9i	0.268365	+	1.52197i
$892$		0			0
$893$	−4.48727e8	+	4.91070e8i	−0.630127	+	0.689587i
$894$		0			0
$895$	−4.34981e8	+	7.66989e7i	−0.606738	+	0.106984i
$896$		0			0
$897$	1.09137e9	−	3.97228e8i	1.51216	−	0.550380i
$898$		0			0
$899$	5.56259e7	+	4.66757e7i	0.0765593	+	0.0642409i
$900$		0			0
$901$	3.79359e8	−	2.19023e8i	0.518651	−	0.299444i
$902$		0			0
$903$	2.38418e8	+	4.20396e7i	0.323800	+	0.0570946i
$904$		0			0
$905$	4.14928e8	+	2.39559e8i	0.559793	+	0.323197i
$906$		0			0
$907$	2.48164e8	−	6.81826e8i	0.332596	−	0.913801i	−0.654838	−	0.755770i	$-0.727263\pi$
$907$	2.48164e8	−	6.81826e8i	0.332596	−	0.913801i	0.987434	−	0.158032i	$-0.0505148\pi$
$908$		0			0
$909$	1.55514e8	−	1.30492e8i	0.207051	−	0.173737i
$910$		0			0
$911$			2.80074e8i			0.370440i	0.982697	+	0.185220i	$0.0592998\pi$
$911$			2.80074e8i			0.370440i	−0.982697	+	0.185220i	$0.940700\pi$
$912$		0			0
$913$	−1.55677e9			−2.04556
$914$		0			0
$915$	−3.29660e8	−	3.92874e8i	−0.430332	−	0.512849i
$916$		0			0
$917$	1.08934e7	+	3.96488e6i	0.0141272	+	0.00514188i
$918$		0			0
$919$	−2.18672e7	+	3.78751e7i	−0.0281738	+	0.0487985i	−0.879769	−	0.475402i	$-0.842303\pi$
$919$	−2.18672e7	+	3.78751e7i	−0.0281738	+	0.0487985i	0.851595	+	0.524201i	$0.175636\pi$
$920$		0			0
$921$	2.63852e8	−	1.49638e9i	0.337739	−	1.91541i
$922$		0			0
$923$	−4.72241e8	−	8.17946e8i	−0.600563	−	1.04021i
$924$		0			0
$925$	4.86358e8	−	5.79619e8i	0.614513	−	0.732347i
$926$		0			0
$927$	1.28224e8	+	3.52291e8i	0.160964	+	0.442245i
$928$		0			0
$929$	−2.11426e8	−	1.19906e9i	−0.263701	−	1.49552i	−0.772709	−	0.634761i	$-0.781099\pi$
$929$	−2.11426e8	−	1.19906e9i	−0.263701	−	1.49552i	0.509008	−	0.860762i	$-0.330012\pi$
$930$		0			0
$931$	3.23735e7	−	7.65936e8i	0.0401181	−	0.949168i
$932$		0			0
$933$	1.80581e9	−	3.18413e8i	2.22345	−	0.392055i
$934$		0			0
$935$	4.20638e8	−	1.53100e8i	0.514605	−	0.187301i
$936$		0			0
$937$	−6.34376e8	−	5.32305e8i	−0.771131	−	0.647056i	0.169867	−	0.985467i	$-0.445666\pi$
$937$	−6.34376e8	−	5.32305e8i	−0.771131	−	0.647056i	−0.940998	+	0.338411i	$0.890111\pi$
$938$		0			0
$939$	−6.13116e8	+	3.53983e8i	−0.740536	+	0.427548i
$940$		0			0
$941$	−7.15752e8	−	1.26206e8i	−0.859001	−	0.151465i	−0.273237	−	0.961947i	$-0.588094\pi$
$941$	−7.15752e8	−	1.26206e8i	−0.859001	−	0.151465i	−0.585764	+	0.810482i	$0.699206\pi$
$942$		0			0
$943$	−4.36709e8	−	2.52134e8i	−0.520784	−	0.300675i
$944$		0			0
$945$	303994.	−	835216.i	0.000360221	−	0.000989699i
$946$		0			0
$947$	1.10163e9	−	9.24379e8i	1.29714	−	1.08843i	0.306508	−	0.951868i	$-0.400839\pi$
$947$	1.10163e9	−	9.24379e8i	1.29714	−	1.08843i	0.990632	−	0.136561i	$-0.0436051\pi$
$948$		0			0
$949$			3.16388e8i			0.370187i
$950$		0			0
$951$	1.68845e9			1.96312
$952$		0			0
$953$	−3.53758e8	−	4.21593e8i	−0.408722	−	0.487096i	0.521937	−	0.852984i	$-0.325210\pi$
$953$	−3.53758e8	−	4.21593e8i	−0.408722	−	0.487096i	−0.930659	+	0.365888i	$0.880765\pi$
$954$		0			0
$955$	3.76861e8	+	1.37166e8i	0.432685	+	0.157484i
$956$		0			0
$957$	3.12828e8	−	5.41834e8i	0.356919	−	0.618202i
$958$		0			0
$959$	−2.83661e6	+	1.60872e7i	−0.00321620	+	0.0182400i
$960$		0			0
$961$	−4.01629e8	−	6.95642e8i	−0.452538	−	0.783818i
$962$		0			0
$963$	−5.42100e8	+	6.46049e8i	−0.607016	+	0.723414i
$964$		0			0
$965$	−2.81068e8	−	7.72229e8i	−0.312774	−	0.859339i
$966$		0			0
$967$	1.79436e8	+	1.01763e9i	0.198440	+	1.12541i	0.907434	+	0.420195i	$0.138038\pi$
$967$	1.79436e8	+	1.01763e9i	0.198440	+	1.12541i	−0.708994	+	0.705215i	$0.750850\pi$
$968$		0			0
$969$	7.08564e8	−	2.24494e8i	0.778767	−	0.246737i
$970$		0			0
$971$	−1.24464e9	+	2.19464e8i	−1.35952	+	0.239720i	−0.805408	−	0.592721i	$-0.798054\pi$
$971$	−1.24464e9	+	2.19464e8i	−1.35952	+	0.239720i	−0.554113	+	0.832441i	$0.686943\pi$
$972$		0			0
$973$	1.17756e8	−	4.28599e7i	0.127834	−	0.0465278i
$974$		0			0
$975$	1.04625e9	+	8.77908e8i	1.12881	+	0.947186i
$976$		0			0
$977$	−1.45507e7	+	8.40086e6i	−0.0156027	+	0.00900825i	−0.507781	−	0.861486i	$-0.669534\pi$
$977$	−1.45507e7	+	8.40086e6i	−0.0156027	+	0.00900825i	0.492178	+	0.870494i	$0.336201\pi$
$978$		0			0
$979$	1.62953e9	+	2.87331e8i	1.73666	+	0.306220i
$980$		0			0
$981$	6.87011e8	+	3.96646e8i	0.727707	+	0.420142i
$982$		0			0
$983$	−2.65993e8	+	7.30811e8i	−0.280034	+	0.769386i	0.717324	+	0.696740i	$0.245367\pi$
$983$	−2.65993e8	+	7.30811e8i	−0.280034	+	0.769386i	−0.997358	+	0.0726467i	$0.976855\pi$
$984$		0			0
$985$	6.71584e8	−	5.63526e8i	0.702735	−	0.589665i
$986$		0			0
$987$		−	2.84367e8i		−	0.295752i
$988$		0			0
$989$	−6.87637e8			−0.710837
$990$		0			0
$991$	7.36567e8	+	8.77806e8i	0.756818	+	0.901940i	0.997642	−	0.0686286i	$-0.0218623\pi$
$991$	7.36567e8	+	8.77806e8i	0.756818	+	0.901940i	−0.240825	+	0.970569i	$0.577418\pi$
$992$		0			0
$993$	−1.09821e9	−	3.99717e8i	−1.12160	−	0.408230i
$994$		0			0
$995$	1.12328e8	−	1.94559e8i	0.114030	−	0.197506i
$996$		0			0
$997$	−1.22047e8	+	6.92164e8i	−0.123152	+	0.698431i	0.859236	+	0.511580i	$0.170939\pi$
$997$	−1.22047e8	+	6.92164e8i	−0.123152	+	0.698431i	−0.982388	+	0.186852i	$0.940172\pi$
$998$		0			0
$999$	−5.86315e6	−	1.01553e7i	−0.00588078	−	0.0101858i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.29.9	yes	60
19.2	odd	18	inner	76.7.j.a.21.9	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.21.9	✓	60	19.2	odd	18	inner
76.7.j.a.29.9	yes	60	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(24.5774 + 29.2903i) q^{3} +(-71.7580 - 26.1178i) q^{5} +(38.3425 - 66.4112i) q^{7} +(-127.279 + 721.834i) q^{9} +O(q^{10})\)	\(q+(24.5774 + 29.2903i) q^{3} +(-71.7580 - 26.1178i) q^{5} +(38.3425 - 66.4112i) q^{7} +(-127.279 + 721.834i) q^{9} +(1034.16 + 1791.22i) q^{11} +(-2344.42 + 2793.97i) q^{13} +(-998.632 - 2743.72i) q^{15} +(492.142 + 2791.08i) q^{17} +(-5789.95 - 3677.28i) q^{19} +(2887.56 - 509.155i) q^{21} +(-7825.94 + 2848.41i) q^{23} +(-7502.37 - 6295.24i) q^{25} +(-131.446 + 75.8905i) q^{27} +(-7791.13 - 1373.79i) q^{29} +(-7948.87 - 4589.28i) q^{31} +(-27048.2 + 74314.3i) q^{33} +(-4485.90 + 3764.12i) q^{35} +77258.1i q^{37} -139456. q^{39} +(38920.5 + 46383.7i) q^{41} +(77587.9 + 28239.7i) q^{43} +(27986.0 - 48473.2i) q^{45} +(16841.0 - 95510.3i) q^{47} +(55884.2 + 96794.3i) q^{49} +(-69655.8 + 83012.5i) q^{51} +(-52862.8 - 145239. i) q^{53} +(-27426.6 - 155544. i) q^{55} +(-34593.5 - 259967. i) q^{57} +(28598.9 - 5042.75i) q^{59} +(165056. - 60075.4i) q^{61} +(43057.7 + 36129.7i) q^{63} +(241203. - 139259. i) q^{65} +(439159. + 77435.6i) q^{67} +(-275772. - 159217. i) q^{69} +(-88568.2 + 243339. i) q^{71} +(66451.6 - 55759.5i) q^{73} -374467. i q^{75} +158609. q^{77} +(178707. + 212975. i) q^{79} +(496657. + 180768. i) q^{81} +(-376338. + 651836. i) q^{83} +(37581.6 - 213136. i) q^{85} +(-151247. - 261968. i) q^{87} +(514235. - 612841. i) q^{89} +(95660.0 + 262824. i) q^{91} +(-60941.6 - 345617. i) q^{93} +(319433. + 415095. i) q^{95} +(-787575. + 138871. i) q^{97} +(-1.42459e6 + 518508. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) \) 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9 + 1680 * q^11 - 2940 * q^13 + 2496 * q^15 - 5112 * q^17 - 15792 * q^19 - 32076 * q^21 - 19272 * q^23 + 58896 * q^25 - 124830 * q^27 + 126840 * q^29 + 30780 * q^31 - 274470 * q^33 - 226284 * q^35 + 178968 * q^39 + 83394 * q^41 + 418848 * q^43 - 95472 * q^45 - 498696 * q^47 - 744330 * q^49 + 1334538 * q^51 + 458004 * q^53 - 260136 * q^55 - 981984 * q^57 - 523362 * q^59 - 644172 * q^61 + 926832 * q^63 + 1337220 * q^65 + 1719114 * q^67 + 1333800 * q^69 - 1895220 * q^71 - 1189704 * q^73 + 1337256 * q^77 + 147432 * q^79 + 272130 * q^81 + 442800 * q^83 + 1479096 * q^85 + 1300572 * q^87 - 301596 * q^89 + 661008 * q^91 + 3576 * q^93 - 5709984 * q^95 + 1386630 * q^97 + 3822798 * q^99

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