LMFDB - Embedded newform 76.7.j.a.29.7

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			29.7
Character	$\chi$	$=$	76.29
Dual form			76.7.j.a.21.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(15.2868 + 18.2181i) q^{3} +(-90.7408 - 33.0269i) q^{5} +(-57.6521 + 99.8564i) q^{7} +(28.3767 - 160.932i) q^{9} +O(q^{10})$	\(q+(15.2868 + 18.2181i) q^{3} +(-90.7408 - 33.0269i) q^{5} +(-57.6521 + 99.8564i) q^{7} +(28.3767 - 160.932i) q^{9} +(-847.329 - 1467.62i) q^{11} +(-294.417 + 350.872i) q^{13} +(-785.448 - 2158.00i) q^{15} +(-1213.76 - 6883.60i) q^{17} +(168.439 + 6856.93i) q^{19} +(-2700.51 + 476.172i) q^{21} +(22166.1 - 8067.82i) q^{23} +(-4826.34 - 4049.78i) q^{25} +(18380.0 - 10611.7i) q^{27} +(-28103.1 - 4955.34i) q^{29} +(-35500.7 - 20496.4i) q^{31} +(13784.2 - 37871.9i) q^{33} +(8529.35 - 7156.97i) q^{35} -46331.5i q^{37} -10892.9 q^{39} +(-41265.7 - 49178.5i) q^{41} +(-38251.3 - 13922.4i) q^{43} +(-7890.03 + 13665.9i) q^{45} +(1995.19 - 11315.3i) q^{47} +(52177.0 + 90373.2i) q^{49} +(106852. - 127341. i) q^{51} +(55354.8 + 152086. i) q^{53} +(28416.4 + 161157. i) q^{55} +(-122345. + 107889. i) q^{57} +(91587.5 - 16149.3i) q^{59} +(-40171.8 + 14621.3i) q^{61} +(14434.1 + 12111.7i) q^{63} +(38303.8 - 22114.7i) q^{65} +(-187695. - 33095.8i) q^{67} +(485829. + 280494. i) q^{69} +(-121287. + 333234. i) q^{71} +(-325378. + 273024. i) q^{73} -149835. i q^{75} +195401. q^{77} +(-149619. - 178309. i) q^{79} +(362352. + 131885. i) q^{81} +(-285527. + 494547. i) q^{83} +(-117206. + 664710. i) q^{85} +(-339330. - 587737. i) q^{87} +(-227531. + 271161. i) q^{89} +(-18063.1 - 49627.9i) q^{91} +(-169288. - 960079. i) q^{93} +(211179. - 627766. i) q^{95} +(507984. - 89571.2i) q^{97} +(-260231. + 94716.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	15.2868	+	18.2181i	0.566178	+	0.674744i	0.970842	−	0.239721i	$-0.0770560\pi$
$3$	15.2868	+	18.2181i	0.566178	+	0.674744i	−0.404664	+	0.914465i	$0.632612\pi$
$4$		0			0
$5$	−90.7408	−	33.0269i	−0.725926	−	0.264216i	−0.0474868	−	0.998872i	$-0.515121\pi$
$5$	−90.7408	−	33.0269i	−0.725926	−	0.264216i	−0.678439	+	0.734656i	$0.737343\pi$
$6$		0			0
$7$	−57.6521	+	99.8564i	−0.168082	+	0.291126i	−0.937745	−	0.347323i	$-0.887091\pi$
$7$	−57.6521	+	99.8564i	−0.168082	+	0.291126i	0.769664	+	0.638450i	$0.220424\pi$
$8$		0			0
$9$	28.3767	−	160.932i	0.0389255	−	0.220758i
$10$		0			0
$11$	−847.329	−	1467.62i	−0.636611	−	1.10264i	−0.986171	−	0.165729i	$-0.947002\pi$
$11$	−847.329	−	1467.62i	−0.636611	−	1.10264i	0.349561	−	0.936914i	$-0.386331\pi$
$12$		0			0
$13$	−294.417	+	350.872i	−0.134009	+	0.159705i	−0.828875	−	0.559433i	$-0.811019\pi$
$13$	−294.417	+	350.872i	−0.134009	+	0.159705i	0.694867	+	0.719138i	$0.255463\pi$
$14$		0			0
$15$	−785.448	−	2158.00i	−0.232725	−	0.639407i
$16$		0			0
$17$	−1213.76	−	6883.60i	−0.247052	−	1.40110i	−0.815679	−	0.578504i	$-0.803637\pi$
$17$	−1213.76	−	6883.60i	−0.247052	−	1.40110i	0.568628	−	0.822595i	$-0.307474\pi$
$18$		0			0
$19$	168.439	+	6856.93i	0.0245573	+	0.999698i
$19$	168.439	+	6856.93i	0.0245573	+	0.999698i
$20$		0			0
$21$	−2700.51	+	476.172i	−0.291600	+	0.0514170i
$22$		0			0
$23$	22166.1	−	8067.82i	1.82182	−	0.663090i	0.826914	−	0.562328i	$-0.190094\pi$
$23$	22166.1	−	8067.82i	1.82182	−	0.663090i	0.994911	−	0.100761i	$-0.0321279\pi$
$24$		0			0
$25$	−4826.34	−	4049.78i	−0.308885	−	0.259186i
$26$		0			0
$27$	18380.0	−	10611.7i	0.933803	−	0.539131i
$28$		0			0
$29$	−28103.1	−	4955.34i	−1.15229	−	0.203179i	−0.435313	−	0.900279i	$-0.643362\pi$
$29$	−28103.1	−	4955.34i	−1.15229	−	0.203179i	−0.716974	+	0.697100i	$0.754473\pi$
$30$		0			0
$31$	−35500.7	−	20496.4i	−1.19166	−	0.688005i	−0.232977	−	0.972482i	$-0.574847\pi$
$31$	−35500.7	−	20496.4i	−1.19166	−	0.688005i	−0.958683	+	0.284477i	$0.908180\pi$
$32$		0			0
$33$	13784.2	−	37871.9i	0.383567	−	1.05384i
$34$		0			0
$35$	8529.35	−	7156.97i	0.198935	−	0.166926i
$36$		0			0
$37$		−	46331.5i		−	0.914684i	−0.889291	−	0.457342i	$-0.848801\pi$
$37$		−	46331.5i		−	0.914684i	0.889291	−	0.457342i	$-0.151199\pi$
$38$		0			0
$39$	−10892.9			−0.183633
$40$		0			0
$41$	−41265.7	−	49178.5i	−0.598738	−	0.713549i	0.378522	−	0.925592i	$-0.376433\pi$
$41$	−41265.7	−	49178.5i	−0.598738	−	0.713549i	−0.977260	+	0.212044i	$0.931988\pi$
$42$		0			0
$43$	−38251.3	−	13922.4i	−0.481107	−	0.175109i	0.0900704	−	0.995935i	$-0.471291\pi$
$43$	−38251.3	−	13922.4i	−0.481107	−	0.175109i	−0.571177	+	0.820827i	$0.693513\pi$
$44$		0			0
$45$	−7890.03	+	13665.9i	−0.0865847	+	0.149969i
$46$		0			0
$47$	1995.19	−	11315.3i	0.0192172	−	0.108986i	−0.973690	−	0.227875i	$-0.926822\pi$
$47$	1995.19	−	11315.3i	0.0192172	−	0.108986i	0.992908	+	0.118889i	$0.0379332\pi$
$48$		0			0
$49$	52177.0	+	90373.2i	0.443497	+	0.768159i
$50$		0			0
$51$	106852.	−	127341.i	0.805508	−	0.959968i
$52$		0			0
$53$	55354.8	+	152086.i	0.371816	+	1.02156i	0.974659	+	0.223696i	$0.0718122\pi$
$53$	55354.8	+	152086.i	0.371816	+	1.02156i	−0.602843	+	0.797860i	$0.705966\pi$
$54$		0			0
$55$	28416.4	+	161157.i	0.170797	+	0.968639i
$56$		0			0
$57$	−122345.	+	107889.i	−0.660637	+	0.582577i
$58$		0			0
$59$	91587.5	−	16149.3i	0.445944	−	0.0786319i	0.0538331	−	0.998550i	$-0.482856\pi$
$59$	91587.5	−	16149.3i	0.445944	−	0.0786319i	0.392111	+	0.919918i	$0.371745\pi$
$60$		0			0
$61$	−40171.8	+	14621.3i	−0.176983	+	0.0644166i	−0.428992	−	0.903308i	$-0.641131\pi$
$61$	−40171.8	+	14621.3i	−0.176983	+	0.0644166i	0.252009	+	0.967725i	$0.418909\pi$
$62$		0			0
$63$	14434.1	+	12111.7i	0.0577257	+	0.0484376i
$64$		0			0
$65$	38303.8	−	22114.7i	0.139477	−	0.0805270i
$66$		0			0
$67$	−187695.	−	33095.8i	−0.624064	−	0.110039i	−0.147331	−	0.989087i	$-0.547068\pi$
$67$	−187695.	−	33095.8i	−0.624064	−	0.110039i	−0.476733	+	0.879048i	$0.658179\pi$
$68$		0			0
$69$	485829.	+	280494.i	1.47889	+	0.853839i
$70$		0			0
$71$	−121287.	+	333234.i	−0.338876	+	0.931053i	0.646839	+	0.762627i	$0.276091\pi$
$71$	−121287.	+	333234.i	−0.338876	+	0.931053i	−0.985714	+	0.168426i	$0.946132\pi$
$72$		0			0
$73$	−325378.	+	273024.i	−0.836410	+	0.701832i	−0.956753	−	0.290901i	$-0.906045\pi$
$73$	−325378.	+	273024.i	−0.836410	+	0.701832i	0.120343	+	0.992732i	$0.461601\pi$
$74$		0			0
$75$		−	149835.i		−	0.355164i
$76$		0			0
$77$	195401.			0.428011
$78$		0			0
$79$	−149619.	−	178309.i	−0.303463	−	0.361654i	0.592665	−	0.805449i	$-0.298076\pi$
$79$	−149619.	−	178309.i	−0.303463	−	0.361654i	−0.896128	+	0.443796i	$0.853632\pi$
$80$		0			0
$81$	362352.	+	131885.i	0.681829	+	0.248166i
$82$		0			0
$83$	−285527.	+	494547.i	−0.499358	+	0.864914i	−1.00000		0.000740745i	$-0.999764\pi$
$83$	−285527.	+	494547.i	−0.499358	+	0.864914i	0.500641	+	0.865655i	$0.333098\pi$
$84$		0			0
$85$	−117206.	+	664710.i	−0.190851	+	1.08237i
$86$		0			0
$87$	−339330.	−	587737.i	−0.515305	−	0.892535i
$88$		0			0
$89$	−227531.	+	271161.i	−0.322753	+	0.384642i	−0.902886	−	0.429880i	$-0.858556\pi$
$89$	−227531.	+	271161.i	−0.322753	+	0.384642i	0.580133	+	0.814522i	$0.303000\pi$
$90$		0			0
$91$	−18063.1	−	49627.9i	−0.0239700	−	0.0658570i
$92$		0			0
$93$	−169288.	−	960079.i	−0.210464	−	1.19360i
$94$		0			0
$95$	211179.	−	627766.i	0.246309	−	0.732196i
$96$		0			0
$97$	507984.	−	89571.2i	0.556589	−	0.0981417i	0.111724	−	0.993739i	$-0.464363\pi$
$97$	507984.	−	89571.2i	0.556589	−	0.0981417i	0.444865	+	0.895598i	$0.353252\pi$
$98$		0			0
$99$	−260231.	+	94716.5i	−0.268197	+	0.0976158i
$100$		0			0
$101$	1.15765e6	+	971380.i	1.12360	+	0.942812i	0.998781	−	0.0493674i	$-0.0157205\pi$
$101$	1.15765e6	+	971380.i	1.12360	+	0.942812i	0.124819	+	0.992180i	$0.460165\pi$
$102$		0			0
$103$	683342.	−	394528.i	0.625355	−	0.361049i	−0.153596	−	0.988134i	$-0.549085\pi$
$103$	683342.	−	394528.i	0.625355	−	0.361049i	0.778951	+	0.627085i	$0.215752\pi$
$104$		0			0
$105$	260773.	+	45981.3i	0.225265	+	0.0397204i
$106$		0			0
$107$	−1.43252e6	−	827064.i	−1.16936	−	0.675131i	−0.215831	−	0.976431i	$-0.569246\pi$
$107$	−1.43252e6	−	827064.i	−1.16936	−	0.675131i	−0.953529	+	0.301300i	$0.902579\pi$
$108$		0			0
$109$	22261.0	−	61161.7i	0.0171896	−	0.0472281i	−0.930801	−	0.365526i	$-0.880889\pi$
$109$	22261.0	−	61161.7i	0.0171896	−	0.0472281i	0.947991	+	0.318298i	$0.103111\pi$
$110$		0			0
$111$	844072.	−	708260.i	0.617178	−	0.517874i
$112$		0			0
$113$		−	1.58959e6i		−	1.10167i	−0.834615	−	0.550834i	$-0.814310\pi$
$113$		−	1.58959e6i		−	1.10167i	0.834615	−	0.550834i	$-0.185690\pi$
$114$		0			0
$115$	−2.27783e6			−1.49771
$116$		0			0
$117$	48112.1	+	57337.8i	0.0300398	+	0.0358000i
$118$		0			0
$119$	757347.	+	275652.i	0.449422	+	0.163576i
$120$		0			0
$121$	−550153.	+	952892.i	−0.310547	+	0.537883i
$122$		0			0
$123$	265119.	−	1.50356e6i	0.142471	−	0.807991i
$124$		0			0
$125$	1.05860e6	+	1.83355e6i	0.542004	+	0.938779i
$126$		0			0
$127$	1.49325e6	−	1.77958e6i	0.728988	−	0.868775i	−0.266483	−	0.963840i	$-0.585862\pi$
$127$	1.49325e6	−	1.77958e6i	0.728988	−	0.868775i	0.995471	+	0.0950652i	$0.0303060\pi$
$128$		0			0
$129$	−331102.	−	909695.i	−0.154238	−	0.423766i
$130$		0			0
$131$	−601568.	−	3.41166e6i	−0.267591	−	1.51758i	−0.761555	−	0.648100i	$-0.775564\pi$
$131$	−601568.	−	3.41166e6i	−0.267591	−	1.51758i	0.493964	−	0.869482i	$-0.335547\pi$
$132$		0			0
$133$	−694419.	−	378497.i	−0.295166	−	0.160882i
$134$		0			0
$135$	−2.01829e6	+	355879.i	−0.820319	+	0.144644i
$136$		0			0
$137$	−1.84327e6	+	670896.i	−0.716849	+	0.260912i	−0.674588	−	0.738195i	$-0.735678\pi$
$137$	−1.84327e6	+	670896.i	−0.716849	+	0.260912i	−0.0422615	+	0.999107i	$0.513456\pi$
$138$		0			0
$139$	−2.28329e6	−	1.91591e6i	−0.850193	−	0.713397i	0.109639	−	0.993971i	$-0.465030\pi$
$139$	−2.28329e6	−	1.91591e6i	−0.850193	−	0.713397i	−0.959832	+	0.280575i	$0.909475\pi$
$140$		0			0
$141$	236643.	−	136626.i	0.0844183	−	0.0487389i
$142$		0			0
$143$	764414.	+	134787.i	0.261409	+	0.0460935i
$144$		0			0
$145$	2.38644e6	+	1.37781e6i	0.782793	+	0.451945i
$146$		0			0
$147$	−848808.	+	2.33208e6i	−0.267213	+	0.734162i
$148$		0			0
$149$	−77742.0	+	65233.2i	−0.0235016	+	0.0197201i	−0.654463	−	0.756094i	$-0.727105\pi$
$149$	−77742.0	+	65233.2i	−0.0235016	+	0.0197201i	0.630961	+	0.775814i	$0.282661\pi$
$150$		0			0
$151$		−	5.14513e6i		−	1.49440i	−0.664601	−	0.747198i	$-0.731399\pi$
$151$		−	5.14513e6i		−	1.49440i	0.664601	−	0.747198i	$-0.268601\pi$
$152$		0			0
$153$	−1.14224e6			−0.318920
$154$		0			0
$155$	2.54443e6	+	3.03234e6i	0.683275	+	0.814296i
$156$		0			0
$157$	5.81262e6	+	2.11562e6i	1.50201	+	0.546687i	0.956580	−	0.291469i	$-0.0941439\pi$
$157$	5.81262e6	+	2.11562e6i	1.50201	+	0.546687i	0.545431	+	0.838156i	$0.316366\pi$
$158$		0			0
$159$	−1.92452e6	+	3.33337e6i	−0.478775	+	0.829262i
$160$		0			0
$161$	−472302.	+	2.67856e6i	−0.113173	+	0.641835i
$162$		0			0
$163$	2.08174e6	+	3.60569e6i	0.480689	+	0.832578i	0.999755	−	0.0221563i	$-0.00705313\pi$
$163$	2.08174e6	+	3.60569e6i	0.480689	+	0.832578i	−0.519065	+	0.854735i	$0.673720\pi$
$164$		0			0
$165$	−2.50158e6	+	2.98127e6i	−0.556882	+	0.663666i
$166$		0			0
$167$	883755.	+	2.42810e6i	0.189750	+	0.521335i	0.997690	−	0.0679303i	$-0.0216396\pi$
$167$	883755.	+	2.42810e6i	0.189750	+	0.521335i	−0.807940	+	0.589265i	$0.799417\pi$
$168$		0			0
$169$	801736.	+	4.54687e6i	0.166101	+	0.942004i
$170$		0			0
$171$	1.10828e6	+	167470.i	0.221647	+	0.0334926i
$172$		0			0
$173$	2.35854e6	−	415875.i	0.455518	−	0.0803201i	0.0588187	−	0.998269i	$-0.481267\pi$
$173$	2.35854e6	−	415875.i	0.455518	−	0.0803201i	0.396699	+	0.917949i	$0.370156\pi$
$174$		0			0
$175$	682644.	−	248462.i	0.127374	−	0.0463603i
$176$		0			0
$177$	1.69429e6	+	1.42168e6i	0.305540	+	0.256378i
$178$		0			0
$179$	7.63996e6	−	4.41093e6i	1.33209	−	0.769080i	0.346466	−	0.938062i	$-0.387381\pi$
$179$	7.63996e6	−	4.41093e6i	1.33209	−	0.769080i	0.985619	+	0.168982i	$0.0540481\pi$
$180$		0			0
$181$	−8.37586e6	−	1.47689e6i	−1.41252	−	0.249065i	−0.585241	−	0.810860i	$-0.699000\pi$
$181$	−8.37586e6	−	1.47689e6i	−1.41252	−	0.249065i	−0.827277	+	0.561795i	$0.810111\pi$
$182$		0			0
$183$	−880471.	−	508340.i	−0.143669	−	0.0829471i
$184$		0			0
$185$	−1.53019e6	+	4.20416e6i	−0.241674	+	0.663993i
$186$		0			0
$187$	−9.07403e6	+	7.61402e6i	−1.38764	+	1.16436i
$188$		0			0
$189$			2.44715e6i			0.362473i
$190$		0			0
$191$	6.55762e6			0.941123			0.470561	−	0.882367i	$-0.344051\pi$
$191$	6.55762e6			0.941123			0.470561	+	0.882367i	$0.344051\pi$
$192$		0			0
$193$	−7.56021e6	−	9.00991e6i	−1.05163	−	1.25328i	−0.966433	−	0.256917i	$-0.917293\pi$
$193$	−7.56021e6	−	9.00991e6i	−1.05163	−	1.25328i	−0.0851946	−	0.996364i	$-0.527151\pi$
$194$		0			0
$195$	988431.	+	359760.i	0.133304	+	0.0485186i
$196$		0			0
$197$	2.88732e6	−	5.00098e6i	0.377655	−	0.654118i	−0.613065	−	0.790032i	$-0.710064\pi$
$197$	2.88732e6	−	5.00098e6i	0.377655	−	0.654118i	0.990721	+	0.135914i	$0.0433971\pi$
$198$		0			0
$199$	−690779.	+	3.91760e6i	−0.0876556	+	0.497120i	0.909096	+	0.416586i	$0.136774\pi$
$199$	−690779.	+	3.91760e6i	−0.0876556	+	0.497120i	−0.996752	+	0.0805336i	$0.974338\pi$
$200$		0			0
$201$	−2.26632e6	−	3.92538e6i	−0.279083	−	0.483385i
$202$		0			0
$203$	2.11503e6	−	2.52059e6i	0.252830	−	0.301311i
$204$		0			0
$205$	2.12026e6	+	5.82537e6i	0.246109	+	0.676180i
$206$		0			0
$207$	−669370.	−	3.79619e6i	−0.0754667	−	0.427993i
$208$		0			0
$209$	9.92063e6	−	6.05728e6i	1.08668	−	0.663497i
$210$		0			0
$211$	−1.57725e7	+	2.78112e6i	−1.67901	+	0.296055i	−0.930289	−	0.366827i	$-0.880444\pi$
$211$	−1.57725e7	+	2.78112e6i	−1.67901	+	0.296055i	−0.748723	+	0.662883i	$0.769333\pi$
$212$		0			0
$213$	−7.92498e6	+	2.88446e6i	−0.820086	+	0.298487i
$214$		0			0
$215$	3.01114e6	+	2.52665e6i	0.302982	+	0.254232i
$216$		0			0
$217$	4.09338e6	−	2.36332e6i	0.400593	−	0.231282i
$218$		0			0
$219$	−9.94797e6	−	1.75410e6i	−0.947114	−	0.167002i
$220$		0			0
$221$	2.77262e6	+	1.60077e6i	0.256870	+	0.148304i
$222$		0			0
$223$	4.01317e6	−	1.10261e7i	0.361887	−	0.994277i	−0.616474	−	0.787375i	$-0.711440\pi$
$223$	4.01317e6	−	1.10261e7i	0.361887	−	0.994277i	0.978362	−	0.206902i	$-0.0663382\pi$
$224$		0			0
$225$	−788695.	+	661794.i	−0.0692407	+	0.0580999i
$226$		0			0
$227$		−	1.02426e7i		−	0.875657i	−0.899059	−	0.437828i	$-0.855748\pi$
$227$		−	1.02426e7i		−	0.875657i	0.899059	−	0.437828i	$-0.144252\pi$
$228$		0			0
$229$	1.05134e7			0.875462			0.437731	−	0.899106i	$-0.355782\pi$
$229$	1.05134e7			0.875462			0.437731	+	0.899106i	$0.355782\pi$
$230$		0			0
$231$	2.98706e6	+	3.55984e6i	0.242330	+	0.288798i
$232$		0			0
$233$	1.03076e7	+	3.75164e6i	0.814869	+	0.296588i	0.715634	−	0.698476i	$-0.246138\pi$
$233$	1.03076e7	+	3.75164e6i	0.814869	+	0.296588i	0.0992356	+	0.995064i	$0.468360\pi$
$234$		0			0
$235$	−554755.	+	960864.i	−0.0427462	+	0.0740386i
$236$		0			0
$237$	961256.	−	5.45156e6i	0.0722095	−	0.409520i
$238$		0			0
$239$	6.35095e6	+	1.10002e7i	0.465205	+	0.805759i	0.999211	−	0.0397218i	$-0.0126472\pi$
$239$	6.35095e6	+	1.10002e7i	0.465205	+	0.805759i	−0.534005	+	0.845481i	$0.679314\pi$
$240$		0			0
$241$	1.05230e7	−	1.25409e7i	0.751779	−	0.895935i	−0.245519	−	0.969392i	$-0.578959\pi$
$241$	1.05230e7	−	1.25409e7i	0.751779	−	0.895935i	0.997298	+	0.0734564i	$0.0234030\pi$
$242$		0			0
$243$	−2.15520e6	−	5.92135e6i	−0.150199	−	0.412669i
$244$		0			0
$245$	−1.74983e6	−	9.92378e6i	−0.118986	−	0.674806i
$246$		0			0
$247$	−2.45550e6	−	1.95970e6i	−0.162948	−	0.130046i
$248$		0			0
$249$	−1.33745e7	+	2.35828e6i	−0.866321	+	0.152756i
$250$		0			0
$251$	1.07248e7	−	3.90350e6i	0.678215	−	0.246850i	0.0201340	−	0.999797i	$-0.493591\pi$
$251$	1.07248e7	−	3.90350e6i	0.678215	−	0.246850i	0.658081	+	0.752947i	$0.271368\pi$
$252$		0			0
$253$	−3.06225e7	−	2.56953e7i	−1.89094	−	1.58669i
$254$		0			0
$255$	−1.39015e7	+	8.02601e6i	−0.838378	+	0.484038i
$256$		0			0
$257$	−1.03192e7	−	1.81955e6i	−0.607918	−	0.107192i	−0.138789	−	0.990322i	$-0.544321\pi$
$257$	−1.03192e7	−	1.81955e6i	−0.607918	−	0.107192i	−0.469129	+	0.883130i	$0.655432\pi$
$258$		0			0
$259$	4.62650e6	+	2.67111e6i	0.266289	+	0.153742i
$260$		0			0
$261$	−1.59495e6	+	4.38209e6i	−0.0897068	+	0.246467i
$262$		0			0
$263$	2.07497e7	−	1.74110e7i	1.14063	−	0.957100i	0.141168	−	0.989986i	$-0.454914\pi$
$263$	2.07497e7	−	1.74110e7i	1.14063	−	0.957100i	0.999459	+	0.0328860i	$0.0104698\pi$
$264$		0			0
$265$		−	1.56286e7i		−	0.839813i
$266$		0			0
$267$	−8.41825e6			−0.442270
$268$		0			0
$269$	1.87872e7	+	2.23898e7i	0.965176	+	1.15025i	0.988606	+	0.150526i	$0.0480967\pi$
$269$	1.87872e7	+	2.23898e7i	0.965176	+	1.15025i	−0.0234304	+	0.999725i	$0.507459\pi$
$270$		0			0
$271$	−7.37618e6	−	2.68471e6i	−0.370616	−	0.134893i	0.149996	−	0.988687i	$-0.452074\pi$
$271$	−7.37618e6	−	2.68471e6i	−0.370616	−	0.134893i	−0.520612	+	0.853794i	$0.674296\pi$
$272$		0			0
$273$	627999.	−	1.08773e6i	0.0308654	−	0.0534604i
$274$		0			0
$275$	−1.85403e6	+	1.05147e7i	−0.0891493	+	0.505591i
$276$		0			0
$277$	654860.	+	1.13425e6i	0.0308112	+	0.0533666i	0.881020	−	0.473079i	$-0.156858\pi$
$277$	654860.	+	1.13425e6i	0.0308112	+	0.0533666i	−0.850209	+	0.526446i	$0.823524\pi$
$278$		0			0
$279$	−4.30592e6	+	5.13160e6i	−0.198268	+	0.236287i
$280$		0			0
$281$	−2.25235e6	−	6.18829e6i	−0.101512	−	0.278902i	0.878532	−	0.477684i	$-0.158524\pi$
$281$	−2.25235e6	−	6.18829e6i	−0.101512	−	0.278902i	−0.980044	+	0.198782i	$0.936301\pi$
$282$		0			0
$283$	4.08221e6	+	2.31514e7i	0.180109	+	1.02145i	0.932080	+	0.362254i	$0.117993\pi$
$283$	4.08221e6	+	2.31514e7i	0.180109	+	1.02145i	−0.751970	+	0.659197i	$0.770896\pi$
$284$		0			0
$285$	1.46650e7	−	5.74925e6i	0.633499	−	0.248357i
$286$		0			0
$287$	7.28984e6	−	1.28539e6i	0.308370	−	0.0543740i
$288$		0			0
$289$	−2.32288e7	+	8.45460e6i	−0.962352	+	0.350267i
$290$		0			0
$291$	9.39726e6	+	7.88524e6i	0.381349	+	0.319990i
$292$		0			0
$293$	4.34000e6	−	2.50570e6i	0.172539	−	0.0996153i	−0.411244	−	0.911525i	$-0.634905\pi$
$293$	4.34000e6	−	2.50570e6i	0.172539	−	0.0996153i	0.583782	+	0.811910i	$0.301572\pi$
$294$		0			0
$295$	−8.84408e6	−	1.55945e6i	−0.344498	−	0.0607443i
$296$		0			0
$297$	−3.11479e7	−	1.79832e7i	−1.18894	−	0.686434i
$298$		0			0
$299$	−3.69531e6	+	1.01528e7i	−0.138241	+	0.379815i
$300$		0			0
$301$	3.59551e6	−	3.01699e6i	0.131844	−	0.110630i
$302$		0			0
$303$			3.59394e7i			1.29194i
$304$		0			0
$305$	4.12812e6			0.145497
$306$		0			0
$307$	2.45137e7	+	2.92143e7i	0.847217	+	1.00967i	0.999771	+	0.0213783i	$0.00680546\pi$
$307$	2.45137e7	+	2.92143e7i	0.847217	+	1.00967i	−0.152555	+	0.988295i	$0.548750\pi$
$308$		0			0
$309$	1.76337e7	+	6.41813e6i	0.597678	+	0.217537i
$310$		0			0
$311$	−3.07750e6	+	5.33039e6i	−0.102310	+	0.177206i	−0.912636	−	0.408773i	$-0.865957\pi$
$311$	−3.07750e6	+	5.33039e6i	−0.102310	+	0.177206i	0.810326	+	0.585979i	$0.199290\pi$
$312$		0			0
$313$	−2.83026e6	+	1.60512e7i	−0.0922982	+	0.523449i	0.903244	+	0.429128i	$0.141179\pi$
$313$	−2.83026e6	+	1.60512e7i	−0.0922982	+	0.523449i	−0.995542	+	0.0943209i	$0.969932\pi$
$314$		0			0
$315$	−909753.	−	1.57574e6i	−0.0291066	−	0.0504142i
$316$		0			0
$317$	−1.11651e7	+	1.33061e7i	−0.350498	+	0.417708i	−0.912273	−	0.409583i	$-0.865674\pi$
$317$	−1.11651e7	+	1.33061e7i	−0.350498	+	0.417708i	0.561775	+	0.827290i	$0.310119\pi$
$318$		0			0
$319$	1.65401e7	+	4.54434e7i	0.509525	+	1.39991i
$320$		0			0
$321$	−6.83106e6	−	3.87409e7i	−0.206525	−	1.17126i
$322$		0			0
$323$	4.69959e7	−	9.48216e6i	1.39461	−	0.281384i
$324$		0			0
$325$	2.84191e6	−	501105.i	0.0827866	−	0.0145975i
$326$		0			0
$327$	1.45455e6	−	529413.i	0.0415992	−	0.0151409i
$328$		0			0
$329$	1.01488e6	+	851583.i	0.0284988	+	0.0239133i
$330$		0			0
$331$	−1.41999e7	+	8.19833e6i	−0.391563	+	0.226069i	−0.682837	−	0.730571i	$-0.739254\pi$
$331$	−1.41999e7	+	8.19833e6i	−0.391563	+	0.226069i	0.291274	+	0.956640i	$0.405921\pi$
$332$		0			0
$333$	−7.45624e6	−	1.31474e6i	−0.201924	−	0.0356046i
$334$		0			0
$335$	1.59386e7	+	9.20214e6i	0.423950	+	0.244768i
$336$		0			0
$337$	−1.62486e7	+	4.46427e7i	−0.424548	+	1.16644i	0.524529	+	0.851392i	$0.324241\pi$
$337$	−1.62486e7	+	4.46427e7i	−0.424548	+	1.16644i	−0.949077	+	0.315043i	$0.897981\pi$
$338$		0			0
$339$	2.89594e7	−	2.42998e7i	0.743344	−	0.623740i
$340$		0			0
$341$			6.94686e7i			1.75197i
$342$		0			0
$343$	−2.55979e7			−0.634339
$344$		0			0
$345$	−3.48207e7	−	4.14977e7i	−0.847969	−	1.01057i
$346$		0			0
$347$	3.92224e7	+	1.42758e7i	0.938740	+	0.341673i	0.765668	−	0.643236i	$-0.222409\pi$
$347$	3.92224e7	+	1.42758e7i	0.938740	+	0.341673i	0.173072	+	0.984909i	$0.444631\pi$
$348$		0			0
$349$	1.50024e7	−	2.59850e7i	0.352927	−	0.611288i	−0.633834	−	0.773469i	$-0.718520\pi$
$349$	1.50024e7	−	2.59850e7i	0.352927	−	0.611288i	0.986761	+	0.162181i	$0.0518530\pi$
$350$		0			0
$351$	−1.68803e6	+	9.57331e6i	−0.0390355	+	0.221381i
$352$		0			0
$353$	−2.55658e7	−	4.42813e7i	−0.581214	−	1.00669i	−0.995336	−	0.0964702i	$-0.969245\pi$
$353$	−2.55658e7	−	4.42813e7i	−0.581214	−	1.00669i	0.414122	−	0.910221i	$-0.364089\pi$
$354$		0			0
$355$	2.20114e7	−	2.62322e7i	0.491997	−	0.586340i
$356$		0			0
$357$	6.55556e6	+	1.80113e7i	0.144081	+	0.395858i
$358$		0			0
$359$	3.38354e6	+	1.91890e7i	0.0731288	+	0.414734i	0.999292	+	0.0376120i	$0.0119751\pi$
$359$	3.38354e6	+	1.91890e7i	0.0731288	+	0.414734i	−0.926164	+	0.377122i	$0.876914\pi$
$360$		0			0
$361$	−4.69891e7	+	2.30994e6i	−0.998794	+	0.0490998i
$362$		0			0
$363$	−2.57699e7	+	4.54394e6i	−0.538758	+	0.0949976i
$364$		0			0
$365$	3.85422e7	−	1.40282e7i	0.792607	−	0.288485i
$366$		0			0
$367$	−2.73682e7	−	2.29646e7i	−0.553666	−	0.464581i	0.322514	−	0.946565i	$-0.395472\pi$
$367$	−2.73682e7	−	2.29646e7i	−0.553666	−	0.464581i	−0.876180	+	0.481984i	$0.839916\pi$
$368$		0			0
$369$	−9.08539e6	+	5.24545e6i	−0.180828	+	0.104401i
$370$		0			0
$371$	−1.83781e7	−	3.24055e6i	−0.359897	−	0.0634596i
$372$		0			0
$373$	−1.61645e7	−	9.33259e6i	−0.311484	−	0.179836i	0.336106	−	0.941824i	$-0.390890\pi$
$373$	−1.61645e7	−	9.33259e6i	−0.311484	−	0.179836i	−0.647591	+	0.761989i	$0.724223\pi$
$374$		0			0
$375$	−1.72212e7	+	4.73149e7i	−0.326565	+	0.897230i
$376$		0			0
$377$	1.00127e7	−	8.40168e6i	0.186865	−	0.156798i
$378$		0			0
$379$		−	7.97856e7i		−	1.46557i	−0.680460	−	0.732785i	$-0.738220\pi$
$379$		−	7.97856e7i		−	1.46557i	0.680460	−	0.732785i	$-0.261780\pi$
$380$		0			0
$381$	5.52476e7			0.998937
$382$		0			0
$383$	−4.09883e7	−	4.88479e7i	−0.729563	−	0.869460i	0.265959	−	0.963984i	$-0.414311\pi$
$383$	−4.09883e7	−	4.88479e7i	−0.729563	−	0.869460i	−0.995523	+	0.0945244i	$0.969867\pi$
$384$		0			0
$385$	−1.77309e7	−	6.45350e6i	−0.310704	−	0.113087i
$386$		0			0
$387$	−3.32600e6	+	5.76081e6i	−0.0573839	+	0.0993918i
$388$		0			0
$389$	9.32867e6	−	5.29055e7i	0.158479	−	0.898778i	−0.797057	−	0.603904i	$-0.793611\pi$
$389$	9.32867e6	−	5.29055e7i	0.158479	−	0.898778i	0.955536	−	0.294874i	$-0.0952777\pi$
$390$		0			0
$391$	−8.24401e7	−	1.42790e8i	−1.37914	−	2.38874i
$392$		0			0
$393$	5.29580e7	−	6.31128e7i	0.872476	−	1.03978i
$394$		0			0
$395$	7.68756e6	+	2.11214e7i	0.124738	+	0.342713i
$396$		0			0
$397$	2.09325e7	+	1.18714e8i	0.334542	+	1.89728i	0.431709	+	0.902013i	$0.357911\pi$
$397$	2.09325e7	+	1.18714e8i	0.334542	+	1.89728i	−0.0971669	+	0.995268i	$0.530978\pi$
$398$		0			0
$399$	−3.71995e6	−	1.84370e7i	−0.0585624	−	0.290249i
$400$		0			0
$401$	6.37463e7	−	1.12402e7i	0.988603	−	0.174317i	0.344111	−	0.938929i	$-0.388180\pi$
$401$	6.37463e7	−	1.12402e7i	0.988603	−	0.174317i	0.644492	+	0.764611i	$0.277069\pi$
$402$		0			0
$403$	1.76436e7	−	6.42175e6i	0.269571	−	0.0981157i
$404$		0			0
$405$	−2.85243e7	−	2.39348e7i	−0.429389	−	0.360300i
$406$		0			0
$407$	−6.79969e7	+	3.92580e7i	−1.00857	+	0.582298i
$408$		0			0
$409$	2.05426e7	+	3.62221e6i	0.300251	+	0.0529424i	0.321744	−	0.946827i	$-0.395731\pi$
$409$	2.05426e7	+	3.62221e6i	0.300251	+	0.0529424i	−0.0214932	+	0.999769i	$0.506842\pi$
$410$		0			0
$411$	−4.04002e7	−	2.33250e7i	−0.581912	−	0.335967i
$412$		0			0
$413$	−3.66760e6	+	1.00766e7i	−0.0520633	+	0.143043i
$414$		0			0
$415$	4.22423e7	−	3.54455e7i	0.591021	−	0.495926i
$416$		0			0
$417$		−	7.08854e7i		−	0.977572i
$418$		0			0
$419$	2.09917e7			0.285368			0.142684	−	0.989768i	$-0.454427\pi$
$419$	2.09917e7			0.285368			0.142684	+	0.989768i	$0.454427\pi$
$420$		0			0
$421$	6.26378e7	+	7.46488e7i	0.839441	+	1.00041i	0.999911	+	0.0133657i	$0.00425455\pi$
$421$	6.26378e7	+	7.46488e7i	0.839441	+	1.00041i	−0.160470	+	0.987041i	$0.551301\pi$
$422$		0			0
$423$	−1.76438e6	−	642182.i	−0.0233115	−	0.00848471i
$424$		0			0
$425$	−2.20190e7	+	3.81380e7i	−0.286834	+	0.496811i
$426$		0			0
$427$	855955.	−	4.85436e6i	0.0109943	−	0.0623517i
$428$		0			0
$429$	9.22988e6	+	1.59866e7i	0.116903	+	0.202481i
$430$		0			0
$431$	8.79044e7	−	1.04760e8i	1.09794	−	1.30847i	0.150476	−	0.988614i	$-0.451919\pi$
$431$	8.79044e7	−	1.04760e8i	1.09794	−	1.30847i	0.947465	−	0.319861i	$-0.103636\pi$
$432$		0			0
$433$	3.68775e6	+	1.01320e7i	0.0454253	+	0.124805i	0.960331	−	0.278863i	$-0.0899574\pi$
$433$	3.68775e6	+	1.01320e7i	0.0454253	+	0.124805i	−0.914906	+	0.403668i	$0.867735\pi$
$434$		0			0
$435$	1.13799e7	+	6.45387e7i	0.138252	+	0.784066i
$436$		0			0
$437$	5.90541e7	+	1.50633e8i	0.707629	+	1.80499i
$438$		0			0
$439$	−5.77786e7	+	1.01879e7i	−0.682926	+	0.120418i	−0.504339	−	0.863506i	$-0.668264\pi$
$439$	−5.77786e7	+	1.01879e7i	−0.682926	+	0.120418i	−0.178587	+	0.983924i	$0.557153\pi$
$440$		0			0
$441$	1.60246e7	−	5.83247e6i	0.186840	−	0.0680043i
$442$		0			0
$443$	−9.69378e6	−	8.13404e6i	−0.111502	−	0.0935611i	0.585332	−	0.810794i	$-0.300964\pi$
$443$	−9.69378e6	−	8.13404e6i	−0.111502	−	0.0935611i	−0.696834	+	0.717232i	$0.745409\pi$
$444$		0			0
$445$	2.96019e7	−	1.70907e7i	0.335923	−	0.193945i
$446$		0			0
$447$	−2.37685e6	−	419103.i	−0.0266121	−	0.00469243i
$448$		0			0
$449$	−1.45455e8	−	8.39786e7i	−1.60690	−	0.927747i	−0.990057	−	0.140664i	$-0.955076\pi$
$449$	−1.45455e8	−	8.39786e7i	−1.60690	−	0.927747i	−0.616847	−	0.787083i	$-0.711590\pi$
$450$		0			0
$451$	−3.72096e7	+	1.02233e8i	−0.405626	+	1.11445i
$452$		0			0
$453$	9.37345e7	−	7.86526e7i	1.00834	−	0.846094i
$454$		0			0
$455$			5.09984e6i			0.0541406i
$456$		0			0
$457$	−1.61713e8			−1.69432			−0.847161	−	0.531336i	$-0.821690\pi$
$457$	−1.61713e8			−1.69432			−0.847161	+	0.531336i	$0.821690\pi$
$458$		0			0
$459$	−9.53559e7	−	1.13641e8i	−0.986074	−	1.17516i
$460$		0			0
$461$	1.03740e8	+	3.77581e7i	1.05887	+	0.385396i	0.812003	−	0.583654i	$-0.198377\pi$
$461$	1.03740e8	+	3.77581e7i	1.05887	+	0.385396i	0.246865	+	0.969050i	$0.420600\pi$
$462$		0			0
$463$	−2.75922e6	+	4.77911e6i	−0.0277999	+	0.0481508i	−0.879591	−	0.475731i	$-0.842183\pi$
$463$	−2.75922e6	+	4.77911e6i	−0.0277999	+	0.0481508i	0.851791	+	0.523882i	$0.175517\pi$
$464$		0			0
$465$	−1.63472e7	+	9.27094e7i	−0.162586	+	0.922072i
$466$		0			0
$467$	−6.28931e7	−	1.08934e8i	−0.617522	−	1.06958i	−0.989936	−	0.141513i	$-0.954803\pi$
$467$	−6.28931e7	−	1.08934e8i	−0.617522	−	1.06958i	0.372415	−	0.928066i	$-0.378530\pi$
$468$		0			0
$469$	1.41259e7	−	1.68345e7i	0.136929	−	0.163186i
$470$		0			0
$471$	5.03138e7	+	1.38236e8i	0.481531	+	1.32300i
$472$		0			0
$473$	1.19788e7	+	6.79351e7i	0.113196	+	0.641965i
$474$		0			0
$475$	2.69561e7	−	3.37760e7i	0.251522	−	0.315157i
$476$		0			0
$477$	2.60464e7	−	4.59267e6i	0.239989	−	0.0423166i
$478$		0			0
$479$	7.34035e7	−	2.67167e7i	0.667898	−	0.243095i	0.0142552	−	0.999898i	$-0.495462\pi$
$479$	7.34035e7	−	2.67167e7i	0.667898	−	0.243095i	0.653642	+	0.756804i	$0.273240\pi$
$480$		0			0
$481$	1.62564e7	+	1.36408e7i	0.146080	+	0.122576i
$482$		0			0
$483$	−5.60182e7	+	3.23421e7i	−0.497150	+	0.287030i
$484$		0			0
$485$	−4.90531e7	−	8.64939e6i	−0.429973	−	0.0758159i
$486$		0			0
$487$	−2.75110e7	−	1.58835e7i	−0.238188	−	0.137518i	0.376156	−	0.926556i	$-0.377246\pi$
$487$	−2.75110e7	−	1.58835e7i	−0.238188	−	0.137518i	−0.614344	+	0.789039i	$0.710579\pi$
$488$		0			0
$489$	−3.38655e7	+	9.30448e7i	−0.289622	+	0.795730i
$490$		0			0
$491$	3.75811e7	−	3.15343e7i	0.317486	−	0.266403i	−0.470092	−	0.882618i	$-0.655779\pi$
$491$	3.75811e7	−	3.15343e7i	0.317486	−	0.266403i	0.787578	+	0.616215i	$0.211335\pi$
$492$		0			0
$493$			1.99465e8i			1.66466i
$494$		0			0
$495$	2.67418e7			0.220483
$496$		0			0
$497$	−2.62831e7	−	3.13230e7i	−0.214095	−	0.255149i
$498$		0			0
$499$	1.23803e8	+	4.50606e7i	0.996390	+	0.362656i	0.788191	−	0.615430i	$-0.211018\pi$
$499$	1.23803e8	+	4.50606e7i	0.996390	+	0.362656i	0.208198	+	0.978087i	$0.433240\pi$
$500$		0			0
$501$	−3.07255e7	+	5.32182e7i	−0.244335	+	0.423201i
$502$		0			0
$503$	4.07105e6	−	2.30881e7i	0.0319891	−	0.181419i	−0.964627	−	0.263620i	$-0.915084\pi$
$503$	4.07105e6	−	2.30881e7i	0.0319891	−	0.181419i	0.996616	+	0.0822003i	$0.0261947\pi$
$504$		0			0
$505$	−7.29640e7	−	1.26377e8i	−0.566545	−	0.981285i
$506$		0			0
$507$	−7.05794e7	+	8.41132e7i	−0.541569	+	0.645417i
$508$		0			0
$509$	4.34134e7	+	1.19277e8i	0.329208	+	0.904491i	0.988313	+	0.152440i	$0.0487131\pi$
$509$	4.34134e7	+	1.19277e8i	0.329208	+	0.904491i	−0.659105	+	0.752051i	$0.729065\pi$
$510$		0			0
$511$	−8.50451e6	−	4.82315e7i	−0.0637363	−	0.361466i
$512$		0			0
$513$	7.58597e7	+	1.24243e8i	0.561900	+	0.920281i
$514$		0			0
$515$	−7.50370e7	+	1.32311e7i	−0.549356	+	0.0968663i
$516$		0			0
$517$	−1.82971e7	+	6.65960e6i	−0.132407	+	0.0481922i
$518$		0			0
$519$	4.36310e7	+	3.66108e7i	0.312100	+	0.261883i
$520$		0			0
$521$	−1.63751e8	+	9.45414e7i	−1.15790	+	0.668511i	−0.950799	−	0.309809i	$-0.899735\pi$
$521$	−1.63751e8	+	9.45414e7i	−1.15790	+	0.668511i	−0.207097	+	0.978320i	$0.566402\pi$
$522$		0			0
$523$	1.62562e8	+	2.86641e7i	1.13636	+	0.200370i	0.710011	−	0.704191i	$-0.248690\pi$
$523$	1.62562e8	+	2.86641e7i	1.13636	+	0.200370i	0.426345	+	0.904561i	$0.359801\pi$
$524$		0			0
$525$	1.49620e7	+	8.63829e6i	0.103398	+	0.0596966i
$526$		0			0
$527$	−9.79992e7	+	2.69251e8i	−0.669562	+	1.83961i
$528$		0			0
$529$	3.12846e8	−	2.62509e8i	2.11331	−	1.77328i
$530$		0			0
$531$		−	1.51977e7i		−	0.101506i
$532$		0			0
$533$	2.94047e7			0.194193
$534$		0			0
$535$	1.02672e8	+	1.22360e8i	0.670489	+	0.799058i
$536$		0			0
$537$	1.97149e8	+	7.17565e7i	1.27313	+	0.463381i
$538$		0			0
$539$	8.84221e7	−	1.53152e8i	0.564670	−	0.978037i
$540$		0			0
$541$	−1.98707e7	+	1.12692e8i	−0.125493	+	0.711708i	0.855520	+	0.517769i	$0.173237\pi$
$541$	−1.98707e7	+	1.12692e8i	−0.125493	+	0.711708i	−0.981014	+	0.193939i	$0.937874\pi$
$542$		0			0
$543$	−1.01134e8	−	1.75169e8i	−0.631681	−	1.09410i
$544$		0			0
$545$	−4.03997e6	+	4.81465e6i	−0.0249568	+	0.0297423i
$546$		0			0
$547$	2.53910e6	+	6.97612e6i	0.0155138	+	0.0426238i	0.947208	−	0.320620i	$-0.103891\pi$
$547$	2.53910e6	+	6.97612e6i	0.0155138	+	0.0426238i	−0.931694	+	0.363244i	$0.881669\pi$
$548$		0			0
$549$	1.21310e6	+	6.87985e6i	0.00733129	+	0.0415778i
$550$		0			0
$551$	2.92448e7	−	1.93536e8i	0.174821	−	1.15693i
$552$		0			0
$553$	2.64312e7	−	4.66053e6i	0.156294	−	0.0275588i
$554$		0			0
$555$	−9.99834e7	+	3.63910e7i	−0.584856	+	0.212870i
$556$		0			0
$557$	−2.36145e8	−	1.98149e8i	−1.36651	−	1.14664i	−0.973912	−	0.226927i	$-0.927132\pi$
$557$	−2.36145e8	−	1.98149e8i	−1.36651	−	1.14664i	−0.392597	−	0.919711i	$-0.628423\pi$
$558$		0			0
$559$	1.61468e7	−	9.32236e6i	0.0924381	−	0.0533692i
$560$		0			0
$561$	−2.77426e8	−	4.89176e7i	−1.57130	−	0.277062i
$562$		0			0
$563$	−3.12163e7	−	1.80228e7i	−0.174927	−	0.100994i	0.409980	−	0.912094i	$-0.365536\pi$
$563$	−3.12163e7	−	1.80228e7i	−0.174927	−	0.100994i	−0.584907	+	0.811100i	$0.698869\pi$
$564$		0			0
$565$	−5.24994e7	+	1.44241e8i	−0.291078	+	0.799730i
$566$		0			0
$567$	−3.40600e7	+	2.85797e7i	−0.186851	+	0.156786i
$568$		0			0
$569$		−	2.33183e8i		−	1.26579i	−0.774239	−	0.632893i	$-0.781867\pi$
$569$		−	2.33183e8i		−	1.26579i	0.774239	−	0.632893i	$-0.218133\pi$
$570$		0			0
$571$	−8.79249e7			−0.472285			−0.236142	−	0.971718i	$-0.575883\pi$
$571$	−8.79249e7			−0.472285			−0.236142	+	0.971718i	$0.575883\pi$
$572$		0			0
$573$	1.00245e8	+	1.19467e8i	0.532843	+	0.635017i
$574$		0			0
$575$	−1.39654e8	−	5.08299e7i	−0.734599	−	0.267372i
$576$		0			0
$577$	7.83129e7	−	1.35642e8i	0.407667	−	0.706100i	−0.586961	−	0.809615i	$-0.699676\pi$
$577$	7.83129e7	−	1.35642e8i	0.407667	−	0.706100i	0.994628	+	0.103515i	$0.0330090\pi$
$578$		0			0
$579$	4.85720e7	−	2.75465e8i	0.250236	−	1.41916i
$580$		0			0
$581$	−3.29224e7	−	5.70233e7i	−0.167866	−	0.290753i
$582$		0			0
$583$	1.76300e8	−	2.10107e8i	0.889708	−	1.06031i
$584$		0			0
$585$	−2.47204e6	−	6.79187e6i	−0.0123477	−	0.0339252i
$586$		0			0
$587$	3.85452e7	+	2.18601e8i	0.190571	+	1.08078i	0.918587	+	0.395219i	$0.129331\pi$
$587$	3.85452e7	+	2.18601e8i	0.190571	+	1.08078i	−0.728016	+	0.685560i	$0.759557\pi$
$588$		0			0
$589$	1.34562e8	−	2.46878e8i	0.658534	−	1.20820i
$590$		0			0
$591$	1.35246e8	−	2.38475e7i	0.655183	−	0.115526i
$592$		0			0
$593$	−2.03523e8	+	7.40762e7i	−0.975998	+	0.355234i	−0.780283	−	0.625426i	$-0.784925\pi$
$593$	−2.03523e8	+	7.40762e7i	−0.975998	+	0.355234i	−0.195715	+	0.980661i	$0.562703\pi$
$594$		0			0
$595$	−5.96183e7	−	5.00257e7i	−0.283028	−	0.237488i
$596$		0			0
$597$	−8.19310e7	+	4.73029e7i	−0.385057	+	0.222313i
$598$		0			0
$599$	−2.72334e8	−	4.80199e7i	−1.26713	−	0.223430i	−0.500624	−	0.865665i	$-0.666896\pi$
$599$	−2.72334e8	−	4.80199e7i	−1.26713	−	0.223430i	−0.766508	+	0.642235i	$0.778007\pi$
$600$		0			0
$601$	−1.91895e8	−	1.10791e8i	−0.883975	−	0.510363i	−0.0120082	−	0.999928i	$-0.503822\pi$
$601$	−1.91895e8	−	1.10791e8i	−0.883975	−	0.510363i	−0.871967	+	0.489565i	$0.837156\pi$
$602$		0			0
$603$	−1.06524e7	+	2.92671e7i	−0.0485841	+	0.133484i
$604$		0			0
$605$	8.13924e7	−	6.82963e7i	0.367551	−	0.308412i
$606$		0			0
$607$			6.12539e7i			0.273885i	0.990579	+	0.136942i	$0.0437275\pi$
$607$			6.12539e7i			0.273885i	−0.990579	+	0.136942i	$0.956273\pi$
$608$		0			0
$609$	7.82524e7			0.346454
$610$		0			0
$611$	3.38281e6	+	4.03147e6i	0.0148304	+	0.0176742i
$612$		0			0
$613$	3.04083e8	+	1.10677e8i	1.32011	+	0.480481i	0.903494	−	0.428602i	$-0.140994\pi$
$613$	3.04083e8	+	1.10677e8i	1.32011	+	0.480481i	0.416617	+	0.909082i	$0.363216\pi$
$614$		0			0
$615$	−7.37152e7	+	1.27678e8i	−0.316907	+	0.548899i
$616$		0			0
$617$	−4.04446e7	+	2.29373e8i	−0.172189	+	0.976531i	0.769150	+	0.639068i	$0.220680\pi$
$617$	−4.04446e7	+	2.29373e8i	−0.172189	+	0.976531i	−0.941339	+	0.337463i	$0.890431\pi$
$618$		0			0
$619$	−8.95043e7	−	1.55026e8i	−0.377374	−	0.653631i	0.613305	−	0.789846i	$-0.289840\pi$
$619$	−8.95043e7	−	1.55026e8i	−0.377374	−	0.653631i	−0.990679	+	0.136215i	$0.956506\pi$
$620$		0			0
$621$	3.21801e8	−	3.83508e8i	1.34373	−	1.60140i
$622$		0			0
$623$	−1.39595e7	−	3.83534e7i	−0.0577305	−	0.158613i
$624$		0			0
$625$	−1.84074e7	−	1.04393e8i	−0.0753965	−	0.427595i
$626$		0			0
$627$	2.62007e8	+	8.81385e7i	1.06294	+	0.357572i
$628$		0			0
$629$	−3.18928e8	+	5.62355e7i	−1.28156	+	0.225974i
$630$		0			0
$631$	2.69856e8	−	9.82197e7i	1.07410	−	0.390940i	0.256391	−	0.966573i	$-0.417466\pi$
$631$	2.69856e8	−	9.82197e7i	1.07410	−	0.390940i	0.817708	+	0.575633i	$0.195244\pi$
$632$		0			0
$633$	−2.91778e8	−	2.44831e8i	−1.15038	−	0.965284i
$634$		0			0
$635$	−1.94273e8	+	1.12163e8i	−0.758735	+	0.438056i
$636$		0			0
$637$	−4.70712e7	−	8.29992e6i	−0.182111	−	0.0321111i
$638$		0			0
$639$	5.01864e7	+	2.89751e7i	0.192346	+	0.111051i
$640$		0			0
$641$	1.04249e7	−	2.86423e7i	0.0395821	−	0.108751i	−0.918327	−	0.395823i	$-0.870460\pi$
$641$	1.04249e7	−	2.86423e7i	0.0395821	−	0.108751i	0.957909	+	0.287072i	$0.0926818\pi$
$642$		0			0
$643$	3.89205e7	−	3.26582e7i	0.146402	−	0.122846i	−0.566645	−	0.823962i	$-0.691759\pi$
$643$	3.89205e7	−	3.26582e7i	0.146402	−	0.122846i	0.713047	+	0.701116i	$0.247315\pi$
$644$		0			0
$645$			9.34817e7i			0.348375i
$646$		0			0
$647$	2.21372e8			0.817355			0.408678	−	0.912679i	$-0.365990\pi$
$647$	2.21372e8			0.817355			0.408678	+	0.912679i	$0.365990\pi$
$648$		0			0
$649$	−1.01306e8	−	1.20732e8i	−0.370596	−	0.441659i
$650$		0			0
$651$	1.05630e8	+	3.84461e7i	0.382863	+	0.139351i
$652$		0			0
$653$	2.69577e6	−	4.66921e6i	0.00968152	−	0.0167689i	−0.861144	−	0.508361i	$-0.830252\pi$
$653$	2.69577e6	−	4.66921e6i	0.00968152	−	0.0167689i	0.870826	+	0.491592i	$0.163585\pi$
$654$		0			0
$655$	−5.80900e7	+	3.29445e8i	−0.206718	+	1.17235i
$656$		0			0
$657$	3.47053e7	+	6.01114e7i	0.122377	+	0.211963i
$658$		0			0
$659$	1.60674e8	−	1.91484e8i	0.561422	−	0.669077i	−0.408425	−	0.912792i	$-0.633922\pi$
$659$	1.60674e8	−	1.91484e8i	0.561422	−	0.669077i	0.969847	+	0.243715i	$0.0783661\pi$
$660$		0			0
$661$	1.93223e8	+	5.30875e8i	0.669042	+	1.83818i	0.530217	+	0.847862i	$0.322110\pi$
$661$	1.93223e8	+	5.30875e8i	0.669042	+	1.83818i	0.138825	+	0.990317i	$0.455667\pi$
$662$		0			0
$663$	1.32214e7	+	7.49825e7i	0.0453668	+	0.257288i
$664$		0			0
$665$	5.05115e7	+	5.72796e7i	0.171761	+	0.194776i
$666$		0			0
$667$	−6.62917e8	+	1.16890e8i	−2.23399	+	0.393913i
$668$		0			0
$669$	2.62223e8	−	9.54414e7i	0.875775	−	0.318756i
$670$		0			0
$671$	5.54973e7	+	4.65677e7i	0.183698	+	0.154141i
$672$		0			0
$673$	4.50243e8	−	2.59948e8i	1.47707	−	0.852788i	0.477407	−	0.878682i	$-0.341577\pi$
$673$	4.50243e8	−	2.59948e8i	1.47707	−	0.852788i	0.999665	+	0.0258943i	$0.00824332\pi$
$674$		0			0
$675$	−1.31683e8	−	2.32193e7i	−0.428173	−	0.0754985i
$676$		0			0
$677$	−2.65163e8	−	1.53092e8i	−0.854570	−	0.493386i	0.00762015	−	0.999971i	$-0.497574\pi$
$677$	−2.65163e8	−	1.53092e8i	−0.854570	−	0.493386i	−0.862190	+	0.506585i	$0.830908\pi$
$678$		0			0
$679$	−2.03421e7	+	5.58894e7i	−0.0649809	+	0.178534i
$680$		0			0
$681$	1.86601e8	−	1.56577e8i	0.590844	−	0.495777i
$682$		0			0
$683$			1.00148e8i			0.314326i	0.987573	+	0.157163i	$0.0502348\pi$
$683$			1.00148e8i			0.314326i	−0.987573	+	0.157163i	$0.949765\pi$
$684$		0			0
$685$	1.89418e8			0.589316
$686$		0			0
$687$	1.60716e8	+	1.91534e8i	0.495667	+	0.590713i
$688$		0			0
$689$	−6.96602e7	−	2.53542e7i	−0.212974	−	0.0775162i
$690$		0			0
$691$	−2.86469e8	+	4.96179e8i	−0.868247	+	1.50385i	−0.00446097	+	0.999990i	$0.501420\pi$
$691$	−2.86469e8	+	4.96179e8i	−0.868247	+	1.50385i	−0.863786	+	0.503858i	$0.831913\pi$
$692$		0			0
$693$	5.54484e6	−	3.14464e7i	0.0166606	−	0.0944867i
$694$		0			0
$695$	1.43911e8	+	2.49262e8i	0.428687	+	0.742508i
$696$		0			0
$697$	−2.88438e8	+	3.43747e8i	−0.851833	+	1.01518i
$698$		0			0
$699$	8.92217e7	+	2.45135e8i	0.261240	+	0.717750i
$700$		0			0
$701$	−1.06437e7	−	6.03631e7i	−0.0308984	−	0.175234i	0.965453	−	0.260576i	$-0.0839126\pi$
$701$	−1.06437e7	−	6.03631e7i	−0.0308984	−	0.175234i	−0.996352	+	0.0853427i	$0.972801\pi$
$702$		0			0
$703$	3.17692e8	−	7.80402e6i	0.914408	−	0.0224622i
$704$		0			0
$705$	−2.59855e7	+	4.58195e6i	−0.0741591	+	0.0130762i
$706$		0			0
$707$	−1.63739e8	+	5.95962e7i	−0.463334	+	0.168640i
$708$		0			0
$709$	−2.54526e8	−	2.13573e8i	−0.714158	−	0.599250i	0.211605	−	0.977355i	$-0.432131\pi$
$709$	−2.54526e8	−	2.13573e8i	−0.714158	−	0.599250i	−0.925762	+	0.378106i	$0.876576\pi$
$710$		0			0
$711$	−3.29414e7	+	1.90187e7i	−0.0916503	+	0.0529143i
$712$		0			0
$713$	−9.52275e8	−	1.67912e8i	−2.62720	−	0.463247i
$714$		0			0
$715$	−6.49119e7	−	3.74769e7i	−0.177585	−	0.102529i
$716$		0			0
$717$	−1.03316e8	+	2.83859e8i	−0.280293	+	0.770097i
$718$		0			0
$719$	1.36026e8	−	1.14139e8i	0.365961	−	0.307078i	−0.441200	−	0.897409i	$-0.645447\pi$
$719$	1.36026e8	−	1.14139e8i	0.365961	−	0.307078i	0.807161	+	0.590331i	$0.201003\pi$
$720$		0			0
$721$			9.09814e7i			0.242743i
$722$		0			0
$723$	3.89334e8			1.03017
$724$		0			0
$725$	1.15567e8	+	1.37728e8i	0.303264	+	0.361416i
$726$		0			0
$727$	5.61796e8	+	2.04477e8i	1.46209	+	0.532159i	0.945941	−	0.324338i	$-0.105142\pi$
$727$	5.61796e8	+	2.04477e8i	1.46209	+	0.532159i	0.516152	+	0.856497i	$0.327364\pi$
$728$		0			0
$729$	2.15483e8	−	3.73228e8i	0.556200	−	0.963367i
$730$		0			0
$731$	−4.94078e7	+	2.80205e8i	−0.126486	+	0.717339i
$732$		0			0
$733$	−2.76101e7	−	4.78221e7i	−0.0701061	−	0.121427i	0.828842	−	0.559483i	$-0.189000\pi$
$733$	−2.76101e7	−	4.78221e7i	−0.0701061	−	0.121427i	−0.898948	+	0.438056i	$0.855667\pi$
$734$		0			0
$735$	1.54043e8	−	1.83581e8i	0.387954	−	0.462345i
$736$		0			0
$737$	1.10468e8	+	3.03508e8i	0.275952	+	0.758172i
$738$		0			0
$739$	3.38780e7	+	1.92131e8i	0.0839429	+	0.476064i	0.997580	+	0.0695324i	$0.0221507\pi$
$739$	3.38780e7	+	1.92131e8i	0.0839429	+	0.476064i	−0.913637	+	0.406531i	$0.866738\pi$
$740$		0			0
$741$	−1.83479e6	−	7.46920e7i	−0.00450953	−	0.183577i
$742$		0			0
$743$	−2.17117e8	+	3.82836e7i	−0.529331	+	0.0933354i	−0.431925	−	0.901909i	$-0.642166\pi$
$743$	−2.17117e8	+	3.82836e7i	−0.529331	+	0.0933354i	−0.0974059	+	0.995245i	$0.531054\pi$
$744$		0			0
$745$	9.20882e6	−	3.35174e6i	0.0222708	−	0.00810590i
$746$		0			0
$747$	7.14862e7	+	5.99841e7i	0.171499	+	0.143904i
$748$		0			0
$749$	1.65175e8	−	9.53639e7i	0.393097	−	0.226954i
$750$		0			0
$751$	−4.78970e8	−	8.44554e7i	−1.13081	−	0.199392i	−0.423226	−	0.906024i	$-0.639103\pi$
$751$	−4.78970e8	−	8.44554e7i	−1.13081	−	0.199392i	−0.707581	+	0.706632i	$0.750214\pi$
$752$		0			0
$753$	2.35062e8	+	1.35713e8i	0.550551	+	0.317861i
$754$		0			0
$755$	−1.69928e8	+	4.66873e8i	−0.394843	+	1.08482i
$756$		0			0
$757$	−5.89281e8	+	4.94466e8i	−1.35842	+	1.13985i	−0.381957	+	0.924180i	$0.624750\pi$
$757$	−5.89281e8	+	4.94466e8i	−1.35842	+	1.13985i	−0.976466	+	0.215672i	$0.930806\pi$
$758$		0			0
$759$		−	9.50682e8i		−	2.17425i
$760$		0			0
$761$	−2.45772e8			−0.557672			−0.278836	−	0.960339i	$-0.589949\pi$
$761$	−2.45772e8			−0.557672			−0.278836	+	0.960339i	$0.589949\pi$
$762$		0			0
$763$	4.82399e6	+	5.74901e6i	0.0108601	+	0.0129425i
$764$		0			0
$765$	1.03647e8	+	3.77246e7i	0.231512	+	0.0842636i
$766$		0			0
$767$	−2.12985e7	+	3.68901e7i	−0.0472024	+	0.0817569i
$768$		0			0
$769$	9.14708e7	−	5.18757e8i	0.201142	−	1.14073i	−0.702253	−	0.711927i	$-0.747823\pi$
$769$	9.14708e7	−	5.18757e8i	0.201142	−	1.14073i	0.903396	−	0.428808i	$-0.141066\pi$
$770$		0			0
$771$	−1.24598e8	−	2.15810e8i	−0.271862	−	0.470879i
$772$		0			0
$773$	7.66904e7	−	9.13961e7i	0.166036	−	0.197874i	−0.676611	−	0.736341i	$-0.736552\pi$
$773$	7.66904e7	−	9.13961e7i	0.166036	−	0.197874i	0.842647	+	0.538467i	$0.180996\pi$
$774$		0			0
$775$	8.83328e7	+	2.42692e8i	0.189765	+	0.521376i
$776$		0			0
$777$	2.20618e7	+	1.25119e8i	0.0470303	+	0.266722i
$778$		0			0
$779$	3.30263e8	−	2.91239e8i	0.698630	−	0.616081i
$780$		0			0
$781$	5.91830e8	−	1.04356e8i	1.24235	−	0.219060i
$782$		0			0
$783$	−5.69121e8	+	2.07143e8i	−1.18555	+	0.431505i
$784$		0			0
$785$	−4.57569e8	−	3.83946e8i	−0.945906	−	0.793709i
$786$		0			0
$787$	−1.44638e8	+	8.35070e7i	−0.296729	+	0.171316i	−0.640972	−	0.767564i	$-0.721469\pi$
$787$	−1.44638e8	+	8.35070e7i	−0.296729	+	0.171316i	0.344244	+	0.938880i	$0.388135\pi$
$788$		0			0
$789$	6.34391e8	+	1.11860e8i	1.29159	+	0.227743i
$790$		0			0
$791$	1.58731e8	+	9.16434e7i	0.320725	+	0.185171i
$792$		0			0
$793$	6.69703e6	−	1.83999e7i	0.0134296	−	0.0368975i
$794$		0			0
$795$	2.84723e8	−	2.38911e8i	0.566659	−	0.475483i
$796$		0			0
$797$		−	2.86518e6i		−	0.00565949i	−0.999996	−	0.00282974i	$-0.999099\pi$
$797$		−	2.86518e6i		−	0.00565949i	0.999996	−	0.00282974i	$-0.000900737\pi$
$798$		0			0
$799$	−8.03117e7			−0.157448
$800$		0			0
$801$	3.71819e7	+	4.43117e7i	0.0723493	+	0.0862226i
$802$		0			0
$803$	6.76398e8	+	2.46189e8i	1.30634	+	0.475468i
$804$		0			0
$805$	1.31322e8	−	2.27456e8i	0.251738	−	0.436023i
$806$		0			0
$807$	−1.20702e8	+	6.84536e8i	−0.229665	+	1.30249i
$808$		0			0
$809$	798305.	+	1.38270e6i	0.00150773	+	0.00261146i	0.866778	−	0.498694i	$-0.166187\pi$
$809$	798305.	+	1.38270e6i	0.00150773	+	0.00261146i	−0.865271	+	0.501305i	$0.832853\pi$
$810$		0			0
$811$	4.63328e8	−	5.52173e8i	0.868613	−	1.03517i	−0.130431	−	0.991457i	$-0.541636\pi$
$811$	4.63328e8	−	5.52173e8i	0.868613	−	1.03517i	0.999044	−	0.0437149i	$-0.0139193\pi$
$812$		0			0
$813$	−6.38479e7	−	1.75421e8i	−0.118816	−	0.326444i
$814$		0			0
$815$	−6.98143e7	−	3.95936e8i	−0.128965	−	0.731396i
$816$		0			0
$817$	8.90216e7	−	2.64632e8i	0.163241	−	0.485262i
$818$		0			0
$819$	−8.49931e6	+	1.49866e6i	−0.0154715	+	0.00272804i
$820$		0			0
$821$	−7.50145e8	+	2.73031e8i	−1.35555	+	0.493380i	−0.914676	−	0.404188i	$-0.867554\pi$
$821$	−7.50145e8	+	2.73031e8i	−1.35555	+	0.493380i	−0.440875	+	0.897568i	$0.645332\pi$
$822$		0			0
$823$	−1.70445e8	−	1.43020e8i	−0.305763	−	0.256565i	0.476975	−	0.878917i	$-0.341733\pi$
$823$	−1.70445e8	−	1.43020e8i	−0.305763	−	0.256565i	−0.782738	+	0.622351i	$0.786178\pi$
$824$		0			0
$825$	−2.19900e8	+	1.26959e8i	−0.391619	+	0.226101i
$826$		0			0
$827$	9.83717e7	+	1.73456e7i	0.173922	+	0.0306671i	0.259931	−	0.965627i	$-0.416300\pi$
$827$	9.83717e7	+	1.73456e7i	0.173922	+	0.0306671i	−0.0860090	+	0.996294i	$0.527411\pi$
$828$		0			0
$829$	−1.31946e8	−	7.61793e7i	−0.231598	−	0.133713i	0.379711	−	0.925105i	$-0.376023\pi$
$829$	−1.31946e8	−	7.61793e7i	−0.231598	−	0.133713i	−0.611309	+	0.791392i	$0.709357\pi$
$830$		0			0
$831$	−1.06532e7	+	2.92694e7i	−0.0185642	+	0.0510047i
$832$		0			0
$833$	5.58762e8	−	4.68857e8i	0.966701	−	0.811158i
$834$		0			0
$835$		−	2.49515e8i		−	0.428586i
$836$		0			0
$837$	−8.70007e8			−1.48370
$838$		0			0
$839$	−1.16877e8	−	1.39289e8i	−0.197899	−	0.235847i	0.657964	−	0.753049i	$-0.271418\pi$
$839$	−1.16877e8	−	1.39289e8i	−0.197899	−	0.235847i	−0.855863	+	0.517203i	$0.826973\pi$
$840$		0			0
$841$	2.06280e8	+	7.50797e7i	0.346792	+	0.126222i
$842$		0			0
$843$	7.83075e7	−	1.35633e8i	0.130714	−	0.226403i
$844$		0			0
$845$	7.74191e7	−	4.39066e8i	0.128315	−	0.727712i
$846$		0			0
$847$	−6.34349e7	−	1.09872e8i	−0.104395	−	0.180817i
$848$		0			0
$849$	−3.59370e8	+	4.28280e8i	−0.587244	+	0.699850i
$850$		0			0
$851$	−3.73794e8	−	1.02699e9i	−0.606518	−	1.66639i
$852$		0			0
$853$	−7.10108e7	−	4.02722e8i	−0.114413	−	0.648871i	−0.987039	−	0.160481i	$-0.948695\pi$
$853$	−7.10108e7	−	4.02722e8i	−0.114413	−	0.648871i	0.872625	−	0.488390i	$-0.162416\pi$
$854$		0			0
$855$	−9.50353e7	−	5.17995e7i	−0.152050	−	0.0828757i
$856$		0			0
$857$	−4.00405e8	+	7.06023e7i	−0.636147	+	0.112170i	−0.482415	−	0.875943i	$-0.660240\pi$
$857$	−4.00405e8	+	7.06023e7i	−0.636147	+	0.112170i	−0.153732	+	0.988113i	$0.549129\pi$
$858$		0			0
$859$	6.38167e8	−	2.32274e8i	1.00683	−	0.366455i	0.214613	−	0.976699i	$-0.431151\pi$
$859$	6.38167e8	−	2.32274e8i	1.00683	−	0.366455i	0.792213	+	0.610244i	$0.208929\pi$
$860$		0			0
$861$	1.34856e8	+	1.13157e8i	0.211281	+	0.177286i
$862$		0			0
$863$	−6.33321e7	+	3.65648e7i	−0.0985353	+	0.0568894i	−0.548458	−	0.836178i	$-0.684785\pi$
$863$	−6.33321e7	+	3.65648e7i	−0.0985353	+	0.0568894i	0.449923	+	0.893068i	$0.351452\pi$
$864$		0			0
$865$	−2.27751e8	−	4.01587e7i	−0.351894	−	0.0620485i
$866$		0			0
$867$	−5.09121e8	−	2.93941e8i	−0.781203	−	0.451028i
$868$		0			0
$869$	−1.34913e8	+	3.70670e8i	−0.205586	+	0.564844i
$870$		0			0
$871$	6.68731e7	−	5.61132e7i	0.101204	−	0.0849201i
$872$		0			0
$873$		−	8.42927e7i		−	0.126691i
$874$		0			0
$875$	−2.44123e8			−0.364405
$876$		0			0
$877$	−2.98187e8	−	3.55366e8i	−0.442069	−	0.526838i	0.498295	−	0.867008i	$-0.333960\pi$
$877$	−2.98187e8	−	3.55366e8i	−0.442069	−	0.526838i	−0.940364	+	0.340170i	$0.889515\pi$
$878$		0			0
$879$	1.11994e8	+	4.07624e7i	0.164902	+	0.0600195i
$880$		0			0
$881$	1.39198e7	−	2.41097e7i	0.0203565	−	0.0352586i	−0.855668	−	0.517526i	$-0.826853\pi$
$881$	1.39198e7	−	2.41097e7i	0.0203565	−	0.0352586i	0.876024	+	0.482267i	$0.160187\pi$
$882$		0			0
$883$	3.10127e7	−	1.75882e8i	0.0450462	−	0.255470i	−0.953966	−	0.299916i	$-0.903041\pi$
$883$	3.10127e7	−	1.75882e8i	0.0450462	−	0.255470i	0.999012	+	0.0444465i	$0.0141524\pi$
$884$		0			0
$885$	−1.06787e8	−	1.84961e8i	−0.154060	−	0.266840i
$886$		0			0
$887$	1.54692e8	−	1.84355e8i	0.221665	−	0.264170i	−0.643739	−	0.765245i	$-0.722618\pi$
$887$	1.54692e8	−	1.84355e8i	0.221665	−	0.264170i	0.865404	+	0.501075i	$0.167062\pi$
$888$		0			0
$889$	9.16138e7	+	2.51707e8i	0.130393	+	0.358253i
$890$		0			0
$891$	−1.13474e8	−	6.43544e8i	−0.160422	−	0.909799i
$892$		0			0
$893$	7.79243e7	+	1.17750e7i	0.109425	+	0.0165350i
$894$		0			0
$895$	−8.38936e8	+	1.47927e8i	−1.17020	+	0.206338i
$896$		0			0
$897$	−2.41454e8	+	8.78820e7i	−0.334547	+	0.121765i
$898$		0			0
$899$	8.96116e8	+	7.51930e8i	1.23335	+	1.03490i
$900$		0			0
$901$	9.79712e8	−	5.65637e8i	1.33944	−	0.773327i
$902$		0			0
$903$	1.09928e8	+	1.93832e7i	0.149294	+	0.0263246i
$904$		0			0
$905$	7.11255e8	+	4.10643e8i	0.959577	+	0.554012i
$906$		0			0
$907$	−2.73479e8	+	7.51377e8i	−0.366524	+	1.00702i	0.610150	+	0.792286i	$0.291109\pi$
$907$	−2.73479e8	+	7.51377e8i	−0.366524	+	1.00702i	−0.976674	+	0.214729i	$0.931113\pi$
$908$		0			0
$909$	1.89177e8	−	1.58738e8i	0.251870	−	0.211344i
$910$		0			0
$911$			2.24537e7i			0.0296984i	0.999890	+	0.0148492i	$0.00472682\pi$
$911$			2.24537e7i			0.0296984i	−0.999890	+	0.0148492i	$0.995273\pi$
$912$		0			0
$913$	9.67740e8			1.27159
$914$		0			0
$915$	6.31057e7	+	7.52064e7i	0.0823769	+	0.0981729i
$916$		0			0
$917$	3.75358e8	+	1.36619e8i	0.486786	+	0.177175i
$918$		0			0
$919$	−6.66337e8	+	1.15413e9i	−0.858514	+	1.48699i	0.0148320	+	0.999890i	$0.495279\pi$
$919$	−6.66337e8	+	1.15413e9i	−0.858514	+	1.48699i	−0.873346	+	0.487100i	$0.838055\pi$
$920$		0			0
$921$	−1.57493e8	+	8.93187e8i	−0.201596	+	1.14331i
$922$		0			0
$923$	−8.12136e7	−	1.40666e8i	−0.103282	−	0.178889i
$924$		0			0
$925$	−1.87632e8	+	2.23611e8i	−0.237073	+	0.282533i
$926$		0			0
$927$	−4.41013e7	−	1.21167e8i	−0.0553620	−	0.152106i
$928$		0			0
$929$	8.66796e7	+	4.91585e8i	0.108111	+	0.613128i	0.989932	+	0.141544i	$0.0452066\pi$
$929$	8.66796e7	+	4.91585e8i	0.108111	+	0.613128i	−0.881821	+	0.471584i	$0.843682\pi$
$930$		0			0
$931$	−6.10894e8	+	3.72996e8i	−0.757036	+	0.462227i
$932$		0			0
$933$	−1.44155e8	+	2.54184e7i	−0.177494	+	0.0312970i
$934$		0			0
$935$	1.07485e9	−	3.91214e8i	1.31496	−	0.478608i
$936$		0			0
$937$	7.68059e8	+	6.44478e8i	0.933632	+	0.783410i	0.976466	−	0.215672i	$-0.0691941\pi$
$937$	7.68059e8	+	6.44478e8i	0.933632	+	0.783410i	−0.0428337	+	0.999082i	$0.513639\pi$
$938$		0			0
$939$	−3.35688e8	+	1.93809e8i	−0.405451	+	0.234087i
$940$		0			0
$941$	3.48682e8	+	6.14820e7i	0.418466	+	0.0737869i	0.378917	−	0.925431i	$-0.376297\pi$
$941$	3.48682e8	+	6.14820e7i	0.418466	+	0.0737869i	0.0395494	+	0.999218i	$0.487408\pi$
$942$		0			0
$943$	−1.31146e9	−	7.57174e8i	−1.56394	−	0.902943i
$944$		0			0
$945$	8.08219e7	−	2.22056e8i	0.0957710	−	0.263129i
$946$		0			0
$947$	−1.53489e7	+	1.28792e7i	−0.0180728	+	0.0151649i	−0.651779	−	0.758409i	$-0.725977\pi$
$947$	−1.53489e7	+	1.28792e7i	−0.0180728	+	0.0151649i	0.633706	+	0.773574i	$0.281533\pi$
$948$		0			0
$949$		−	1.94549e8i		−	0.227631i
$950$		0			0
$951$	−4.13090e8			−0.480290
$952$		0			0
$953$	7.82972e8	+	9.33110e8i	0.904623	+	1.07809i	0.996605	+	0.0823273i	$0.0262353\pi$
$953$	7.82972e8	+	9.33110e8i	0.904623	+	1.07809i	−0.0919821	+	0.995761i	$0.529320\pi$
$954$		0			0
$955$	−5.95044e8	−	2.16578e8i	−0.683186	−	0.248659i
$956$		0			0
$957$	−5.75048e8	+	9.96013e8i	−0.656098	+	1.13639i
$958$		0			0
$959$	3.92752e7	−	2.22741e8i	0.0445311	−	0.252548i
$960$		0			0
$961$	3.96450e8	+	6.86671e8i	0.446702	+	0.773711i
$962$		0			0
$963$	−1.73751e8	+	2.07069e8i	−0.194558	+	0.231865i
$964$		0			0
$965$	3.88450e8	+	1.06726e9i	0.432268	+	1.18765i
$966$		0			0
$967$	2.18280e8	+	1.23792e9i	0.241398	+	1.36904i	0.828711	+	0.559676i	$0.189075\pi$
$967$	2.18280e8	+	1.23792e9i	0.241398	+	1.36904i	−0.587313	+	0.809360i	$0.699814\pi$
$968$		0			0
$969$	8.91164e8	+	7.11224e8i	0.979459	+	0.781691i
$970$		0			0
$971$	1.37951e9	−	2.43244e8i	1.50684	−	0.265696i	0.641592	−	0.767046i	$-0.278274\pi$
$971$	1.37951e9	−	2.43244e8i	1.50684	−	0.265696i	0.865244	+	0.501350i	$0.167163\pi$
$972$		0			0
$973$	3.22953e8	−	1.17545e8i	0.350591	−	0.127605i
$974$		0			0
$975$	5.25728e7	+	4.41139e7i	0.0567215	+	0.0475950i
$976$		0			0
$977$	−7.24980e8	+	4.18567e8i	−0.777396	+	0.448830i	−0.835507	−	0.549480i	$-0.814826\pi$
$977$	−7.24980e8	+	4.18567e8i	−0.777396	+	0.448830i	0.0581106	+	0.998310i	$0.481492\pi$
$978$		0			0
$979$	5.90753e8	+	1.04166e8i	0.629590	+	0.111014i
$980$		0			0
$981$	−9.21120e6	−	5.31809e6i	−0.00975684	−	0.00563311i
$982$		0			0
$983$	5.85083e8	−	1.60750e9i	0.615966	−	1.69235i	−0.100681	−	0.994919i	$-0.532102\pi$
$983$	5.85083e8	−	1.60750e9i	0.615966	−	1.69235i	0.716648	−	0.697435i	$-0.245676\pi$
$984$		0			0
$985$	−4.27164e8	+	3.58433e8i	−0.446978	+	0.375059i
$986$		0			0
$987$			3.15071e7i			0.0327685i
$988$		0			0
$989$	−9.60208e8			−0.992605
$990$		0			0
$991$	−7.11008e8	−	8.47346e8i	−0.730556	−	0.870642i	0.265055	−	0.964233i	$-0.414610\pi$
$991$	−7.11008e8	−	8.47346e8i	−0.730556	−	0.870642i	−0.995611	+	0.0935909i	$0.970165\pi$
$992$		0			0
$993$	−3.66429e8	−	1.33369e8i	−0.374233	−	0.136210i
$994$		0			0
$995$	1.92068e8	−	3.32672e8i	0.194978	−	0.337712i
$996$		0			0
$997$	2.12678e8	−	1.20616e9i	0.214604	−	1.21708i	−0.666989	−	0.745068i	$-0.732417\pi$
$997$	2.12678e8	−	1.20616e9i	0.214604	−	1.21708i	0.881592	−	0.472011i	$-0.156472\pi$
$998$		0			0
$999$	−4.91657e8	−	8.51575e8i	−0.493135	−	0.854135i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.29.7	yes	60
19.2	odd	18	inner	76.7.j.a.21.7	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.21.7	✓	60	19.2	odd	18	inner
76.7.j.a.29.7	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)

\(f(q)\)	\(=\)	\(q+(15.2868 + 18.2181i) q^{3} +(-90.7408 - 33.0269i) q^{5} +(-57.6521 + 99.8564i) q^{7} +(28.3767 - 160.932i) q^{9} +O(q^{10})\)	\(q+(15.2868 + 18.2181i) q^{3} +(-90.7408 - 33.0269i) q^{5} +(-57.6521 + 99.8564i) q^{7} +(28.3767 - 160.932i) q^{9} +(-847.329 - 1467.62i) q^{11} +(-294.417 + 350.872i) q^{13} +(-785.448 - 2158.00i) q^{15} +(-1213.76 - 6883.60i) q^{17} +(168.439 + 6856.93i) q^{19} +(-2700.51 + 476.172i) q^{21} +(22166.1 - 8067.82i) q^{23} +(-4826.34 - 4049.78i) q^{25} +(18380.0 - 10611.7i) q^{27} +(-28103.1 - 4955.34i) q^{29} +(-35500.7 - 20496.4i) q^{31} +(13784.2 - 37871.9i) q^{33} +(8529.35 - 7156.97i) q^{35} -46331.5i q^{37} -10892.9 q^{39} +(-41265.7 - 49178.5i) q^{41} +(-38251.3 - 13922.4i) q^{43} +(-7890.03 + 13665.9i) q^{45} +(1995.19 - 11315.3i) q^{47} +(52177.0 + 90373.2i) q^{49} +(106852. - 127341. i) q^{51} +(55354.8 + 152086. i) q^{53} +(28416.4 + 161157. i) q^{55} +(-122345. + 107889. i) q^{57} +(91587.5 - 16149.3i) q^{59} +(-40171.8 + 14621.3i) q^{61} +(14434.1 + 12111.7i) q^{63} +(38303.8 - 22114.7i) q^{65} +(-187695. - 33095.8i) q^{67} +(485829. + 280494. i) q^{69} +(-121287. + 333234. i) q^{71} +(-325378. + 273024. i) q^{73} -149835. i q^{75} +195401. q^{77} +(-149619. - 178309. i) q^{79} +(362352. + 131885. i) q^{81} +(-285527. + 494547. i) q^{83} +(-117206. + 664710. i) q^{85} +(-339330. - 587737. i) q^{87} +(-227531. + 271161. i) q^{89} +(-18063.1 - 49627.9i) q^{91} +(-169288. - 960079. i) q^{93} +(211179. - 627766. i) q^{95} +(507984. - 89571.2i) q^{97} +(-260231. + 94716.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 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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