LMFDB - Embedded newform 147.6.c.c.146.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(146,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("147.146");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.c (of order $2$, degree $1$, 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:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 171 x^{14} + 21495 x^{12} - 1128902 x^{10} + 42970860 x^{8} - 655075344 x^{6} + \cdots + 90230547456 $ x^16 - 171x^14 + 21495x^12 - 1128902x^10 + 42970860x^8 - 655075344x^6 + 7244325760x^4 - 29387167488*x^2 + 90230547456
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{8}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.14
Root			$5.89199 - 3.40174i$ of defining polynomial
Character	$\chi$	$=$	147.146
Dual form			147.6.c.c.146.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.80349i q^{2} +(12.4320 + 9.40448i) q^{3} -14.2874 q^{4} +14.9141 q^{5} +(-63.9832 + 84.5813i) q^{6} +120.507i q^{8} +(66.1117 + 233.834i) q^{9} +O(q^{10})$	\(q+6.80349i q^{2} +(12.4320 + 9.40448i) q^{3} -14.2874 q^{4} +14.9141 q^{5} +(-63.9832 + 84.5813i) q^{6} +120.507i q^{8} +(66.1117 + 233.834i) q^{9} +101.468i q^{10} +96.0737i q^{11} +(-177.622 - 134.366i) q^{12} -416.854i q^{13} +(185.413 + 140.259i) q^{15} -1277.07 q^{16} +208.498 q^{17} +(-1590.89 + 449.790i) q^{18} +2651.38i q^{19} -213.085 q^{20} -653.636 q^{22} +2617.73i q^{23} +(-1133.31 + 1498.15i) q^{24} -2902.57 q^{25} +2836.06 q^{26} +(-1377.18 + 3528.78i) q^{27} -7220.50i q^{29} +(-954.253 + 1261.45i) q^{30} +4297.41i q^{31} -4832.28i q^{32} +(-903.523 + 1194.39i) q^{33} +1418.52i q^{34} +(-944.567 - 3340.89i) q^{36} +3679.00 q^{37} -18038.6 q^{38} +(3920.29 - 5182.35i) q^{39} +1797.26i q^{40} +15452.3 q^{41} -6011.11 q^{43} -1372.65i q^{44} +(985.997 + 3487.42i) q^{45} -17809.7 q^{46} -3907.44 q^{47} +(-15876.6 - 12010.1i) q^{48} -19747.6i q^{50} +(2592.06 + 1960.82i) q^{51} +5955.77i q^{52} -36297.2i q^{53} +(-24008.0 - 9369.63i) q^{54} +1432.85i q^{55} +(-24934.8 + 32962.1i) q^{57} +49124.6 q^{58} -7827.45 q^{59} +(-2649.08 - 2003.95i) q^{60} -20193.7i q^{61} -29237.3 q^{62} -7989.78 q^{64} -6217.00i q^{65} +(-8126.04 - 6147.10i) q^{66} +43937.9 q^{67} -2978.91 q^{68} +(-24618.3 + 32543.7i) q^{69} -26028.0i q^{71} +(-28178.6 + 7966.93i) q^{72} +50911.3i q^{73} +25030.0i q^{74} +(-36084.9 - 27297.1i) q^{75} -37881.4i q^{76} +(35258.0 + 26671.6i) q^{78} -50114.3 q^{79} -19046.3 q^{80} +(-50307.5 + 30918.3i) q^{81} +105129. i q^{82} +107835. q^{83} +3109.57 q^{85} -40896.5i q^{86} +(67905.0 - 89765.6i) q^{87} -11577.6 q^{88} +136779. q^{89} +(-23726.6 + 6708.22i) q^{90} -37400.6i q^{92} +(-40414.8 + 53425.6i) q^{93} -26584.2i q^{94} +39543.0i q^{95} +(45445.1 - 60075.2i) q^{96} +25183.4i q^{97} +(-22465.3 + 6351.59i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 172 q^{4} + 1212 q^{9}+O(q^{10}) $ 16 * q - 172 * q^4 + 1212 * q^9	$ 16 q - 172 q^{4} + 1212 q^{9} + 1188 q^{15} + 5716 q^{16} + 876 q^{18} - 21900 q^{22} + 13156 q^{25} - 900 q^{30} - 15132 q^{36} + 20932 q^{37} + 34836 q^{39} + 111052 q^{43} - 163392 q^{46} - 63192 q^{51} - 31368 q^{57} + 83412 q^{58} - 120132 q^{60} - 158884 q^{64} + 204404 q^{67} - 661728 q^{72} - 277512 q^{78} + 502616 q^{79} - 358524 q^{81} + 205152 q^{85} + 719028 q^{88} - 35352 q^{93} + 215472 q^{99}+O(q^{100}) $ 16 * q - 172 * q^4 + 1212 * q^9 + 1188 * q^15 + 5716 * q^16 + 876 * q^18 - 21900 * q^22 + 13156 * q^25 - 900 * q^30 - 15132 * q^36 + 20932 * q^37 + 34836 * q^39 + 111052 * q^43 - 163392 * q^46 - 63192 * q^51 - 31368 * q^57 + 83412 * q^58 - 120132 * q^60 - 158884 * q^64 + 204404 * q^67 - 661728 * q^72 - 277512 * q^78 + 502616 * q^79 - 358524 * q^81 + 205152 * q^85 + 719028 * q^88 - 35352 * q^93 + 215472 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$			6.80349i			1.20270i	0.798986	+	0.601349i	$0.205370\pi$
$2$			6.80349i			1.20270i	−0.798986	+	0.601349i	$0.794630\pi$
$3$	12.4320	+	9.40448i	0.797516	+	0.603297i
$3$	12.4320	+	9.40448i	0.797516	+	0.603297i
$4$	−14.2874			−0.446483
$5$	14.9141			0.266792			0.133396	−	0.991063i	$-0.457412\pi$
$5$	14.9141			0.266792			0.133396	+	0.991063i	$0.457412\pi$
$6$	−63.9832	+	84.5813i	−0.725585	+	0.959171i
$7$		0			0
$7$		0			0
$8$			120.507i			0.665714i
$9$	66.1117	+	233.834i	0.272065	+	0.962279i
$10$			101.468i			0.320870i
$11$			96.0737i			0.239399i	0.992810	+	0.119700i	$0.0381931\pi$
$11$			96.0737i			0.239399i	−0.992810	+	0.119700i	$0.961807\pi$
$12$	−177.622	−	134.366i	−0.356077	−	0.269362i
$13$		−	416.854i		−	0.684109i	−0.939680	−	0.342055i	$-0.888877\pi$
$13$		−	416.854i		−	0.684109i	0.939680	−	0.342055i	$-0.111123\pi$
$14$		0			0
$15$	185.413	+	140.259i	0.212771	+	0.160955i
$16$	−1277.07			−1.24714
$17$	208.498			0.174977			0.0874884	−	0.996166i	$-0.472116\pi$
$17$	208.498			0.174977			0.0874884	+	0.996166i	$0.472116\pi$
$18$	−1590.89	+	449.790i	−1.15733	+	0.327211i
$19$			2651.38i			1.68495i	0.538733	+	0.842476i	$0.318903\pi$
$19$			2651.38i			1.68495i	−0.538733	+	0.842476i	$0.681097\pi$
$20$	−213.085			−0.119118
$21$		0			0
$22$	−653.636			−0.287925
$23$			2617.73i			1.03182i	0.856642	+	0.515911i	$0.172546\pi$
$23$			2617.73i			1.03182i	−0.856642	+	0.515911i	$0.827454\pi$
$24$	−1133.31	+	1498.15i	−0.401624	+	0.530918i
$25$	−2902.57			−0.928822
$26$	2836.06			0.822777
$27$	−1377.18	+	3528.78i	−0.363564	+	0.931569i
$28$		0			0
$29$		−	7220.50i		−	1.59431i	−0.603776	−	0.797154i	$-0.706338\pi$
$29$		−	7220.50i		−	1.59431i	0.603776	−	0.797154i	$-0.293662\pi$
$30$	−954.253	+	1261.45i	−0.193580	+	0.255899i
$31$			4297.41i			0.803160i	0.915824	+	0.401580i	$0.131539\pi$
$31$			4297.41i			0.803160i	−0.915824	+	0.401580i	$0.868461\pi$
$32$		−	4832.28i		−	0.834214i
$33$	−903.523	+	1194.39i	−0.144429	+	0.190925i
$34$			1418.52i			0.210444i
$35$		0			0
$36$	−944.567	−	3340.89i	−0.121472	−	0.429641i
$37$	3679.00			0.441799			0.220900	−	0.975297i	$-0.429101\pi$
$37$	3679.00			0.441799			0.220900	+	0.975297i	$0.429101\pi$
$38$	−18038.6			−2.02649
$39$	3920.29	−	5182.35i	0.412721	−	0.545588i
$40$			1797.26i			0.177607i
$41$	15452.3			1.43560			0.717798	−	0.696251i	$-0.245150\pi$
$41$	15452.3			1.43560			0.717798	+	0.696251i	$0.245150\pi$
$42$		0			0
$43$	−6011.11			−0.495774			−0.247887	−	0.968789i	$-0.579736\pi$
$43$	−6011.11			−0.495774			−0.247887	+	0.968789i	$0.579736\pi$
$44$		−	1372.65i		−	0.106888i
$45$	985.997	+	3487.42i	0.0725846	+	0.256728i
$46$	−17809.7			−1.24097
$47$	−3907.44			−0.258016			−0.129008	−	0.991644i	$-0.541179\pi$
$47$	−3907.44			−0.258016			−0.129008	+	0.991644i	$0.541179\pi$
$48$	−15876.6	−	12010.1i	−0.994611	−	0.752394i
$49$		0			0
$50$		−	19747.6i		−	1.11709i
$51$	2592.06	+	1960.82i	0.139547	+	0.105563i
$52$			5955.77i			0.305443i
$53$		−	36297.2i		−	1.77494i	−0.460868	−	0.887469i	$-0.652462\pi$
$53$		−	36297.2i		−	1.77494i	0.460868	−	0.887469i	$-0.347538\pi$
$54$	−24008.0	−	9369.63i	−1.12040	−	0.437258i
$55$			1432.85i			0.0638697i
$56$		0			0
$57$	−24934.8	+	32962.1i	−1.01653	+	1.34378i
$58$	49124.6			1.91747
$59$	−7827.45			−0.292746			−0.146373	−	0.989230i	$-0.546760\pi$
$59$	−7827.45			−0.292746			−0.146373	+	0.989230i	$0.546760\pi$
$60$	−2649.08	−	2003.95i	−0.0949984	−	0.0718635i
$61$		−	20193.7i		−	0.694850i	−0.937708	−	0.347425i	$-0.887056\pi$
$61$		−	20193.7i		−	0.694850i	0.937708	−	0.347425i	$-0.112944\pi$
$62$	−29237.3			−0.965959
$63$		0			0
$64$	−7989.78			−0.243829
$65$		−	6217.00i		−	0.182515i
$66$	−8126.04	−	6147.10i	−0.229625	−	0.173704i
$67$	43937.9			1.19578			0.597892	−	0.801577i	$-0.296005\pi$
$67$	43937.9			1.19578			0.597892	+	0.801577i	$0.296005\pi$
$68$	−2978.91			−0.0781241
$69$	−24618.3	+	32543.7i	−0.622495	+	0.822894i
$70$		0			0
$71$		−	26028.0i		−	0.612765i	−0.951908	−	0.306383i	$-0.900881\pi$
$71$		−	26028.0i		−	0.612765i	0.951908	−	0.306383i	$-0.0991187\pi$
$72$	−28178.6	+	7966.93i	−0.640603	+	0.181117i
$73$			50911.3i			1.11817i	0.829111	+	0.559084i	$0.188847\pi$
$73$			50911.3i			1.11817i	−0.829111	+	0.559084i	$0.811153\pi$
$74$			25030.0i			0.531351i
$75$	−36084.9	−	27297.1i	−0.740751	−	0.560356i
$76$		−	37881.4i		−	0.752302i
$77$		0			0
$78$	35258.0	+	26671.6i	0.656178	+	0.496379i
$79$	−50114.3			−0.903429			−0.451715	−	0.892163i	$-0.649187\pi$
$79$	−50114.3			−0.903429			−0.451715	+	0.892163i	$0.649187\pi$
$80$	−19046.3			−0.332726
$81$	−50307.5	+	30918.3i	−0.851962	+	0.523604i
$82$			105129.i			1.72659i
$83$	107835.			1.71817			0.859086	−	0.511832i	$-0.171033\pi$
$83$	107835.			1.71817			0.859086	+	0.511832i	$0.171033\pi$
$84$		0			0
$85$	3109.57			0.0466824
$86$		−	40896.5i		−	0.596266i
$87$	67905.0	−	89765.6i	0.961842	−	1.27149i
$88$	−11577.6			−0.159371
$89$	136779.			1.83039			0.915194	−	0.403013i	$-0.132037\pi$
$89$	136779.			1.83039			0.915194	+	0.403013i	$0.132037\pi$
$90$	−23726.6	+	6708.22i	−0.308766	+	0.0872973i
$91$		0			0
$92$		−	37400.6i		−	0.460690i
$93$	−40414.8	+	53425.6i	−0.484544	+	0.640533i
$94$		−	26584.2i		−	0.310316i
$95$			39543.0i			0.449531i
$96$	45445.1	−	60075.2i	0.503279	−	0.665299i
$97$			25183.4i			0.271759i	0.990725	+	0.135880i	$0.0433861\pi$
$97$			25183.4i			0.271759i	−0.990725	+	0.135880i	$0.956614\pi$
$98$		0			0
$99$	−22465.3	+	6351.59i	−0.230369	+	0.0651320i
$100$	41470.3			0.414703
$101$	78062.7			0.761448			0.380724	−	0.924689i	$-0.375675\pi$
$101$	78062.7			0.761448			0.380724	+	0.924689i	$0.375675\pi$
$102$	−13340.4	+	17635.1i	−0.126960	+	0.167833i
$103$			97991.9i			0.910117i	0.890462	+	0.455059i	$0.150382\pi$
$103$			97991.9i			0.910117i	−0.890462	+	0.455059i	$0.849618\pi$
$104$	50233.9			0.455421
$105$		0			0
$106$	246947.			2.13471
$107$			135095.i			1.14072i	0.821395	+	0.570360i	$0.193196\pi$
$107$			135095.i			1.14072i	−0.821395	+	0.570360i	$0.806804\pi$
$108$	19676.4	−	50417.2i	0.162325	−	0.415929i
$109$	75132.0			0.605702			0.302851	−	0.953038i	$-0.402062\pi$
$109$	75132.0			0.605702			0.302851	+	0.953038i	$0.402062\pi$
$110$	−9748.40			−0.0768160
$111$	45737.5	+	34599.0i	0.352342	+	0.266536i
$112$		0			0
$113$			88078.7i			0.648895i	0.945904	+	0.324448i	$0.105178\pi$
$113$			88078.7i			0.648895i	−0.945904	+	0.324448i	$0.894822\pi$
$114$	−224257.	−	169644.i	−1.61616	−	1.22258i
$115$			39041.0i			0.275281i
$116$			103163.i			0.711831i
$117$	97474.5	−	27558.9i	0.658304	−	0.186122i
$118$		−	53254.0i		−	0.352085i
$119$		0			0
$120$	−16902.3	+	22343.6i	−0.107150	+	0.141645i
$121$	151821.			0.942688
$122$	137388.			0.835695
$123$	192103.	+	145320.i	1.14491	+	0.866091i
$124$		−	61398.9i		−	0.358597i
$125$	−89895.8			−0.514594
$126$		0			0
$127$	−141581.			−0.778923			−0.389462	−	0.921043i	$-0.627339\pi$
$127$	−141581.			−0.778923			−0.389462	+	0.921043i	$0.627339\pi$
$128$		−	208991.i		−	1.12747i
$129$	−74730.4	−	56531.3i	−0.395388	−	0.299099i
$130$	42297.3			0.219510
$131$	−153197.			−0.779959			−0.389979	−	0.920824i	$-0.627518\pi$
$131$	−153197.			−0.779959			−0.389979	+	0.920824i	$0.627518\pi$
$132$	12909.0	−	17064.8i	0.0644850	−	0.0852446i
$133$		0			0
$134$			298931.i			1.43817i
$135$	−20539.4	+	52628.6i	−0.0969960	+	0.248535i
$136$			25125.6i			0.116485i
$137$			90239.8i			0.410768i	0.978681	+	0.205384i	$0.0658444\pi$
$137$			90239.8i			0.410768i	−0.978681	+	0.205384i	$0.934156\pi$
$138$	−221411.	−	167491.i	−0.989694	−	0.748674i
$139$		−	133215.i		−	0.584814i	−0.956294	−	0.292407i	$-0.905544\pi$
$139$		−	133215.i		−	0.584814i	0.956294	−	0.292407i	$-0.0944562\pi$
$140$		0			0
$141$	−48577.5	−	36747.4i	−0.205772	−	0.155661i
$142$	177081.			0.736972
$143$	40048.7			0.163775
$144$	−84429.1	−	298621.i	−0.339301	−	1.20009i
$145$		−	107687.i		−	0.425348i
$146$	−346374.			−1.34482
$147$		0			0
$148$	−52563.5			−0.197256
$149$		−	28153.3i		−	0.103888i	−0.998650	−	0.0519439i	$-0.983458\pi$
$149$		−	28153.3i		−	0.103888i	0.998650	−	0.0519439i	$-0.0165417\pi$
$150$	185716.	−	245503.i	0.673939	−	0.890900i
$151$	−6546.74			−0.0233659			−0.0116830	−	0.999932i	$-0.503719\pi$
$151$	−6546.74			−0.0233659			−0.0116830	+	0.999932i	$0.503719\pi$
$152$	−319510.			−1.12170
$153$	13784.2	+	48754.0i	0.0476050	+	0.168377i
$154$		0			0
$155$			64092.0i			0.214276i
$156$	−56010.9	+	74042.5i	−0.184273	+	0.243596i
$157$		−	68166.3i		−	0.220709i	−0.993892	−	0.110355i	$-0.964801\pi$
$157$		−	68166.3i		−	0.220709i	0.993892	−	0.110355i	$-0.0351986\pi$
$158$		−	340952.i		−	1.08655i
$159$	341356.	−	451248.i	1.07081	−	1.41554i
$160$		−	72069.2i		−	0.222561i
$161$		0			0
$162$	−210352.	−	342266.i	−0.629738	−	1.02465i
$163$	423816.			1.24942			0.624709	−	0.780857i	$-0.285217\pi$
$163$	423816.			1.24942			0.624709	+	0.780857i	$0.285217\pi$
$164$	−220773.			−0.640969
$165$	−13475.2	+	17813.3i	−0.0385324	+	0.0509371i
$166$			733657.i			2.06644i
$167$	−30916.2			−0.0857818			−0.0428909	−	0.999080i	$-0.513657\pi$
$167$	−30916.2			−0.0857818			−0.0428909	+	0.999080i	$0.513657\pi$
$168$		0			0
$169$	197526.			0.531995
$170$			21155.9i			0.0561448i
$171$	−619982.	+	175287.i	−1.62139	+	0.458416i
$172$	85883.4			0.221354
$173$	179220.			0.455272			0.227636	−	0.973746i	$-0.426900\pi$
$173$	179220.			0.455272			0.227636	+	0.973746i	$0.426900\pi$
$174$	610719.	+	461991.i	1.52921	+	1.15681i
$175$		0			0
$176$		−	122693.i		−	0.298563i
$177$	−97311.3	−	73613.1i	−0.233469	−	0.176613i
$178$			930572.i			2.20140i
$179$			142179.i			0.331667i	0.986154	+	0.165834i	$0.0530315\pi$
$179$			142179.i			0.331667i	−0.986154	+	0.165834i	$0.946969\pi$
$180$	−14087.4	−	49826.4i	−0.0324077	−	0.114625i
$181$		−	321437.i		−	0.729288i	−0.931147	−	0.364644i	$-0.881191\pi$
$181$		−	321437.i		−	0.729288i	0.931147	−	0.364644i	$-0.118809\pi$
$182$		0			0
$183$	189911.	−	251049.i	0.419201	−	0.554154i
$184$	−315455.			−0.686898
$185$	54869.0			0.117868
$186$	−363480.	−	274962.i	−0.770368	−	0.582761i
$187$			20031.2i			0.0418893i
$188$	55827.3			0.115200
$189$		0			0
$190$	−269030.			−0.540651
$191$			528819.i			1.04887i	0.851449	+	0.524437i	$0.175724\pi$
$191$			528819.i			1.04887i	−0.851449	+	0.524437i	$0.824276\pi$
$192$	−99329.4	−	75139.7i	−0.194457	−	0.147101i
$193$	−95232.1			−0.184031			−0.0920153	−	0.995758i	$-0.529331\pi$
$193$	−95232.1			−0.184031			−0.0920153	+	0.995758i	$0.529331\pi$
$194$	−171335.			−0.326844
$195$	58467.6	−	77290.1i	0.110111	−	0.145558i
$196$		0			0
$197$		−	705756.i		−	1.29565i	−0.761787	−	0.647827i	$-0.775678\pi$
$197$		−	705756.i		−	1.29565i	0.761787	−	0.647827i	$-0.224322\pi$
$198$	−43213.0	−	152842.i	−0.0783342	−	0.277064i
$199$		−	87307.3i		−	0.156285i	−0.996942	−	0.0781426i	$-0.975101\pi$
$199$		−	87307.3i		−	0.156285i	0.996942	−	0.0781426i	$-0.0248990\pi$
$200$		−	349780.i		−	0.618330i
$201$	546239.	+	413213.i	0.953657	+	0.721413i
$202$			531099.i			0.915792i
$203$		0			0
$204$	−37034.0	−	28015.1i	−0.0623053	−	0.0471321i
$205$	230457.			0.383005
$206$	−666687.			−1.09460
$207$	−612113.	+	173062.i	−0.992900	+	0.280722i
$208$			532350.i			0.853177i
$209$	−254728.			−0.403376
$210$		0			0
$211$	−330657.			−0.511294			−0.255647	−	0.966770i	$-0.582289\pi$
$211$	−330657.			−0.511294			−0.255647	+	0.966770i	$0.582289\pi$
$212$			518594.i			0.792479i
$213$	244779.	−	323581.i	0.369680	−	0.488690i
$214$	−919115.			−1.37194
$215$	−89650.4			−0.132268
$216$	−425243.	−	165960.i	−0.620159	−	0.242030i
$217$		0			0
$218$			511160.i			0.728476i
$219$	−478794.	+	632931.i	−0.674587	+	0.891757i
$220$		−	20471.8i		−	0.0285167i
$221$		−	86913.4i		−	0.119703i
$222$	−235394.	+	311174.i	−0.320563	+	0.423761i
$223$			232532.i			0.313128i	0.987668	+	0.156564i	$0.0500417\pi$
$223$			232532.i			0.313128i	−0.987668	+	0.156564i	$0.949958\pi$
$224$		0			0
$225$	−191894.	−	678719.i	−0.252700	−	0.893786i
$226$	−599242.			−0.780425
$227$	448252.			0.577375			0.288687	−	0.957423i	$-0.406781\pi$
$227$	448252.			0.577375			0.288687	+	0.957423i	$0.406781\pi$
$228$	356255.	−	470944.i	0.453862	−	0.599973i
$229$		−	576156.i		−	0.726025i	−0.931784	−	0.363012i	$-0.881748\pi$
$229$		−	576156.i		−	0.726025i	0.931784	−	0.363012i	$-0.118252\pi$
$230$	−265615.			−0.331080
$231$		0			0
$232$	870122.			1.06135
$233$		−	406966.i		−	0.491098i	−0.969384	−	0.245549i	$-0.921032\pi$
$233$		−	406966.i		−	0.491098i	0.969384	−	0.245549i	$-0.0789682\pi$
$234$	187497.	+	663167.i	0.223848	+	0.791741i
$235$	−58276.0			−0.0688367
$236$	111834.			0.130706
$237$	−623024.	−	471299.i	−0.720499	−	0.545036i
$238$		0			0
$239$			266151.i			0.301393i	0.988580	+	0.150696i	$0.0481516\pi$
$239$			266151.i			0.301393i	−0.988580	+	0.150696i	$0.951848\pi$
$240$	−236785.	−	179121.i	−0.265354	−	0.200732i
$241$			388486.i			0.430857i	0.976520	+	0.215428i	$0.0691148\pi$
$241$			388486.i			0.430857i	−0.976520	+	0.215428i	$0.930885\pi$
$242$			1.03291e6i			1.13377i
$243$	−916196.	−	88737.8i	−0.995342	−	0.0964036i
$244$			288516.i			0.310238i
$245$		0			0
$246$	−988685.	+	1.30697e6i	−1.04165	+	1.37698i
$247$	1.10524e6			1.15269
$248$	−517868.			−0.534675
$249$	1.34062e6	+	1.01414e6i	1.37027	+	1.03657i
$250$		−	611605.i		−	0.618901i
$251$	1.09673e6			1.09879			0.549397	−	0.835561i	$-0.314857\pi$
$251$	1.09673e6			1.09879			0.549397	+	0.835561i	$0.314857\pi$
$252$		0			0
$253$	−251495.			−0.247017
$254$		−	963242.i		−	0.936810i
$255$	38658.3	+	29243.9i	0.0372300	+	0.0281634i
$256$	1.16620e6			1.11217
$257$	100324.			0.0947482			0.0473741	−	0.998877i	$-0.484915\pi$
$257$	100324.			0.0947482			0.0473741	+	0.998877i	$0.484915\pi$
$258$	384610.	−	508427.i	0.359726	−	0.475532i
$259$		0			0
$260$			88825.1i			0.0814896i
$261$	1.68840e6	−	477359.i	1.53417	−	0.433755i
$262$		−	1.04227e6i		−	0.938055i
$263$		−	1.30495e6i		−	1.16333i	−0.813427	−	0.581667i	$-0.802401\pi$
$263$		−	1.30495e6i		−	1.16333i	0.813427	−	0.581667i	$-0.197599\pi$
$264$	−143933.	−	108881.i	−0.127101	−	0.0961484i
$265$		−	541340.i		−	0.473539i
$266$		0			0
$267$	1.70044e6	+	1.28633e6i	1.45976	+	1.10427i
$268$	−627761.			−0.533897
$269$	1.26072e6			1.06228			0.531139	−	0.847285i	$-0.321764\pi$
$269$	1.26072e6			1.06228			0.531139	+	0.847285i	$0.321764\pi$
$270$	−358058.	−	139740.i	−0.298912	−	0.116657i
$271$		−	1.24738e6i		−	1.03176i	−0.856662	−	0.515878i	$-0.827466\pi$
$271$		−	1.24738e6i		−	1.03176i	0.856662	−	0.515878i	$-0.172534\pi$
$272$	−266267.			−0.218220
$273$		0			0
$274$	−613945.			−0.494030
$275$		−	278861.i		−	0.222359i
$276$	351733.	−	464966.i	0.277933	−	0.367408i
$277$	658899.			0.515964			0.257982	−	0.966150i	$-0.416942\pi$
$277$	658899.			0.515964			0.257982	+	0.966150i	$0.416942\pi$
$278$	906330.			0.703354
$279$	−1.00488e6	+	284109.i	−0.772864	+	0.218511i
$280$		0			0
$281$		−	1.28896e6i		−	0.973809i	−0.873455	−	0.486904i	$-0.838126\pi$
$281$		−	1.28896e6i		−	0.973809i	0.873455	−	0.486904i	$-0.161874\pi$
$282$	250011.	−	330496.i	0.187213	−	0.247482i
$283$		−	1.00909e6i		−	0.748966i	−0.927234	−	0.374483i	$-0.877820\pi$
$283$		−	1.00909e6i		−	0.748966i	0.927234	−	0.374483i	$-0.122180\pi$
$284$			371873.i			0.273589i
$285$	−371881.	+	491600.i	−0.271201	+	0.358509i
$286$			272471.i			0.196972i
$287$		0			0
$288$	1.12995e6	−	319470.i	0.802746	−	0.226960i
$289$	−1.37639e6			−0.969383
$290$	732650.			0.511566
$291$	−236836.	+	313081.i	−0.163952	+	0.216733i
$292$		−	727392.i		−	0.499242i
$293$	1.94711e6			1.32502			0.662508	−	0.749055i	$-0.269492\pi$
$293$	1.94711e6			1.32502			0.662508	+	0.749055i	$0.269492\pi$
$294$		0			0
$295$	−116739.			−0.0781021
$296$			443345.i			0.294112i
$297$	−339023.	−	132311.i	−0.223017	−	0.0870371i
$298$	191541.			0.124946
$299$	1.09121e6			0.705878
$300$	515561.	+	390006.i	0.330732	+	0.250189i
$301$		0			0
$302$		−	44540.7i		−	0.0281022i
$303$	970480.	+	734139.i	0.607267	+	0.459380i
$304$		−	3.38599e6i		−	2.10137i
$305$		−	301171.i		−	0.185380i
$306$	−331697.	+	93780.5i	−0.202506	+	0.0572544i
$307$		−	1.97804e6i		−	1.19782i	−0.800818	−	0.598908i	$-0.795602\pi$
$307$		−	1.97804e6i		−	1.19782i	0.800818	−	0.598908i	$-0.204398\pi$
$308$		0			0
$309$	−921563.	+	1.21824e6i	−0.549071	+	0.725833i
$310$	−436049.			−0.257710
$311$	−1.07146e6			−0.628169			−0.314084	−	0.949395i	$-0.601697\pi$
$311$	−1.07146e6			−0.628169			−0.314084	+	0.949395i	$0.601697\pi$
$312$	624510.	+	472423.i	0.363206	+	0.274754i
$313$			416279.i			0.240173i	0.992763	+	0.120086i	$0.0383172\pi$
$313$			416279.i			0.240173i	−0.992763	+	0.120086i	$0.961683\pi$
$314$	463768.			0.265446
$315$		0			0
$316$	716005.			0.403365
$317$		−	2.89214e6i		−	1.61648i	−0.588851	−	0.808242i	$-0.700420\pi$
$317$		−	2.89214e6i		−	1.61648i	0.588851	−	0.808242i	$-0.299580\pi$
$318$	3.07006e6	+	2.32241e6i	1.70247	+	1.28787i
$319$	693700.			0.381676
$320$	−119160.			−0.0650515
$321$	−1.27049e6	+	1.67950e6i	−0.688193	+	0.909743i
$322$		0			0
$323$			552808.i			0.294828i
$324$	718765.	−	441743.i	0.380386	−	0.233780i
$325$			1.20995e6i			0.635416i
$326$			2.88342e6i			1.50267i
$327$	934045.	+	706577.i	0.483057	+	0.365418i
$328$			1.86211e6i			0.955697i
$329$		0			0
$330$	−121193.	−	91678.6i	−0.0612620	−	0.0463429i
$331$	−3.47755e6			−1.74463			−0.872315	−	0.488944i	$-0.837382\pi$
$331$	−3.47755e6			−1.74463			−0.872315	+	0.488944i	$0.837382\pi$
$332$	−1.54069e6			−0.767134
$333$	243225.	+	860274.i	0.120198	+	0.425134i
$334$		−	210338.i		−	0.103170i
$335$	655295.			0.319025
$336$		0			0
$337$	916887.			0.439786			0.219893	−	0.975524i	$-0.429429\pi$
$337$	916887.			0.439786			0.219893	+	0.975524i	$0.429429\pi$
$338$			1.34387e6i			0.639829i
$339$	−828334.	+	1.09500e6i	−0.391477	+	0.517504i
$340$	−44427.8			−0.0208429
$341$	−412868.			−0.192276
$342$	−1.19256e6	−	4.21804e6i	−0.551336	−	1.95005i
$343$		0			0
$344$		−	724382.i		−	0.330044i
$345$	−367161.	+	485360.i	−0.166077	+	0.219541i
$346$			1.21932e6i			0.547555i
$347$			1.23792e6i			0.551912i	0.961170	+	0.275956i	$0.0889945\pi$
$347$			1.23792e6i			0.551912i	−0.961170	+	0.275956i	$0.911006\pi$
$348$	−970189.	+	1.28252e6i	−0.429446	+	0.567697i
$349$			2.19902e6i			0.966419i	0.875505	+	0.483210i	$0.160529\pi$
$349$			2.19902e6i			0.966419i	−0.875505	+	0.483210i	$0.839471\pi$
$350$		0			0
$351$	1.47098e6	+	574083.i	0.637295	+	0.248718i
$352$	464255.			0.199710
$353$	2.66911e6			1.14006			0.570032	−	0.821622i	$-0.306931\pi$
$353$	2.66911e6			1.14006			0.570032	+	0.821622i	$0.306931\pi$
$354$	500826.	−	662056.i	0.212412	−	0.280793i
$355$		−	388184.i		−	0.163481i
$356$	−1.95422e6			−0.817237
$357$		0			0
$358$	−967312.			−0.398896
$359$			4.54793e6i			1.86242i	0.364484	+	0.931210i	$0.381245\pi$
$359$			4.54793e6i			1.86242i	−0.364484	+	0.931210i	$0.618755\pi$
$360$	−420259.	+	118820.i	−0.170908	+	0.0483206i
$361$	−4.55371e6			−1.83907
$362$	2.18689e6			0.877113
$363$	1.88744e6	+	1.42780e6i	0.751809	+	0.568721i
$364$		0			0
$365$			759296.i			0.298318i
$366$	1.70801e6	+	1.29206e6i	0.666480	+	0.504173i
$367$		−	2.13509e6i		−	0.827469i	−0.910398	−	0.413735i	$-0.864224\pi$
$367$		−	2.13509e6i		−	0.827469i	0.910398	−	0.413735i	$-0.135776\pi$
$368$		−	3.34301e6i		−	1.28682i
$369$	1.02157e6	+	3.61326e6i	0.390575	+	1.38144i
$370$			373300.i			0.141760i
$371$		0			0
$372$	577425.	−	763315.i	0.216341	−	0.285987i
$373$	−3.25854e6			−1.21269			−0.606346	−	0.795201i	$-0.707365\pi$
$373$	−3.25854e6			−1.21269			−0.606346	+	0.795201i	$0.707365\pi$
$374$	−136282.			−0.0503802
$375$	−1.11759e6	−	845423.i	−0.410397	−	0.310453i
$376$		−	470874.i		−	0.171765i
$377$	−3.00989e6			−1.09068
$378$		0			0
$379$	−3.32017e6			−1.18730			−0.593652	−	0.804722i	$-0.702314\pi$
$379$	−3.32017e6			−1.18730			−0.593652	+	0.804722i	$0.702314\pi$
$380$		−	564968.i		−	0.200708i
$381$	−1.76014e6	−	1.33149e6i	−0.621204	−	0.469922i
$382$	−3.59781e6			−1.26148
$383$	−3.46201e6			−1.20596			−0.602978	−	0.797758i	$-0.706019\pi$
$383$	−3.46201e6			−1.20596			−0.602978	+	0.797758i	$0.706019\pi$
$384$	1.96545e6	−	2.59819e6i	0.680197	−	0.899173i
$385$		0			0
$386$		−	647910.i		−	0.221333i
$387$	−397405.	−	1.40560e6i	−0.134882	−	0.477073i
$388$		−	359806.i		−	0.121336i
$389$		−	2.49213e6i		−	0.835018i	−0.908673	−	0.417509i	$-0.862903\pi$
$389$		−	2.49213e6i		−	0.835018i	0.908673	−	0.417509i	$-0.137097\pi$
$390$	525842.	+	397784.i	0.175063	+	0.132430i
$391$			545792.i			0.180545i
$392$		0			0
$393$	−1.90455e6	−	1.44074e6i	−0.622030	−	0.470547i
$394$	4.80161e6			1.55828
$395$	−747410.			−0.241027
$396$	320971.	−	90748.0i	0.102856	−	0.0290803i
$397$		−	3.04840e6i		−	0.970722i	−0.874314	−	0.485361i	$-0.838688\pi$
$397$		−	3.04840e6i		−	0.970722i	0.874314	−	0.485361i	$-0.161312\pi$
$398$	593994.			0.187964
$399$		0			0
$400$	3.70678e6			1.15837
$401$		−	51572.9i		−	0.0160162i	−0.999968	−	0.00800812i	$-0.997451\pi$
$401$		−	51572.9i		−	0.0160162i	0.999968	−	0.00800812i	$-0.00254909\pi$
$402$	−2.81129e6	+	3.71633e6i	−0.867642	+	1.14696i
$403$	1.79139e6			0.549449
$404$	−1.11532e6			−0.339973
$405$	−750291.	+	461119.i	−0.227296	+	0.139693i
$406$		0			0
$407$			353455.i			0.105766i
$408$	−236293.	+	312362.i	−0.0702748	+	0.0928983i
$409$			4.53920e6i			1.34175i	0.741571	+	0.670875i	$0.234081\pi$
$409$			4.53920e6i			1.34175i	−0.741571	+	0.670875i	$0.765919\pi$
$410$			1.56791e6i			0.460639i
$411$	−848658.	+	1.12187e6i	−0.247815	+	0.327594i
$412$		−	1.40005e6i		−	0.406351i
$413$		0			0
$414$	−1.17743e6	−	4.16450e6i	−0.337624	−	1.19416i
$415$	1.60827e6			0.458394
$416$	−2.01435e6			−0.570693
$417$	1.25282e6	−	1.65614e6i	0.352817	−	0.466399i
$418$		−	1.73304e6i		−	0.485140i
$419$	1.89078e6			0.526145			0.263072	−	0.964776i	$-0.415264\pi$
$419$	1.89078e6			0.526145			0.263072	+	0.964776i	$0.415264\pi$
$420$		0			0
$421$	−5.04901e6			−1.38836			−0.694178	−	0.719803i	$-0.744232\pi$
$421$	−5.04901e6			−1.38836			−0.694178	+	0.719803i	$0.744232\pi$
$422$		−	2.24962e6i		−	0.614933i
$423$	−258327.	−	913691.i	−0.0701971	−	0.248284i
$424$	4.37407e6			1.18160
$425$	−605181.			−0.162522
$426$	2.20148e6	+	1.66535e6i	0.587747	+	0.444613i
$427$		0			0
$428$		−	1.93016e6i		−	0.509312i
$429$	497887.	+	376637.i	0.130613	+	0.0988051i
$430$		−	609935.i		−	0.159079i
$431$		−	3.26850e6i		−	0.847530i	−0.905772	−	0.423765i	$-0.860708\pi$
$431$		−	3.26850e6i		−	0.847530i	0.905772	−	0.423765i	$-0.139292\pi$
$432$	1.75875e6	−	4.50649e6i	0.453414	−	1.16179i
$433$			1.69788e6i			0.435198i	0.976038	+	0.217599i	$0.0698226\pi$
$433$			1.69788e6i			0.435198i	−0.976038	+	0.217599i	$0.930177\pi$
$434$		0			0
$435$	1.01274e6	−	1.33877e6i	0.256612	−	0.339222i
$436$	−1.07344e6			−0.270435
$437$	−6.94058e6			−1.73857
$438$	−4.30614e6	−	3.25747e6i	−1.07251	−	0.811325i
$439$			4.42320e6i			1.09541i	0.836673	+	0.547703i	$0.184498\pi$
$439$			4.42320e6i			1.09541i	−0.836673	+	0.547703i	$0.815502\pi$
$440$	−172669.			−0.0425190
$441$		0			0
$442$	591314.			0.143967
$443$		−	5.22017e6i		−	1.26379i	−0.775054	−	0.631895i	$-0.782277\pi$
$443$		−	5.22017e6i		−	1.26379i	0.775054	−	0.631895i	$-0.217723\pi$
$444$	−653471.	−	494332.i	−0.157315	−	0.119004i
$445$	2.03993e6			0.488332
$446$	−1.58203e6			−0.376598
$447$	264767.	−	350004.i	0.0626752	−	0.0828522i
$448$		0			0
$449$			3.80274e6i			0.890186i	0.895484	+	0.445093i	$0.146829\pi$
$449$			3.80274e6i			0.890186i	−0.895484	+	0.445093i	$0.853171\pi$
$450$	4.61765e6	−	1.30555e6i	1.07495	−	0.303921i
$451$			1.48456e6i			0.343681i
$452$		−	1.25842e6i		−	0.289720i
$453$	−81389.4	−	61568.7i	−0.0186347	−	0.0140966i
$454$			3.04968e6i			0.694407i
$455$		0			0
$456$	−3.97217e6	−	3.00482e6i	−0.894572	−	0.676717i
$457$	1.83749e6			0.411561			0.205781	−	0.978598i	$-0.434027\pi$
$457$	1.83749e6			0.411561			0.205781	+	0.978598i	$0.434027\pi$
$458$	3.91987e6			0.873188
$459$	−287140.	+	735745.i	−0.0636154	+	0.163003i
$460$		−	557797.i		−	0.122908i
$461$	−7.79775e6			−1.70890			−0.854450	−	0.519533i	$-0.826106\pi$
$461$	−7.79775e6			−1.70890			−0.854450	+	0.519533i	$0.826106\pi$
$462$		0			0
$463$	254809.			0.0552410			0.0276205	−	0.999618i	$-0.491207\pi$
$463$	254809.			0.0552410			0.0276205	+	0.999618i	$0.491207\pi$
$464$			9.22106e6i			1.98832i
$465$	−602751.	+	796795.i	−0.129272	+	0.170889i
$466$	2.76878e6			0.590642
$467$	−4.98525e6			−1.05778			−0.528889	−	0.848691i	$-0.677391\pi$
$467$	−4.98525e6			−1.05778			−0.528889	+	0.848691i	$0.677391\pi$
$468$	−1.39266e6	+	393746.i	−0.293921	+	0.0831002i
$469$		0			0
$470$		−	396480.i		−	0.0827897i
$471$	641068.	−	847446.i	0.133153	−	0.176019i
$472$		−	943264.i		−	0.194885i
$473$		−	577509.i		−	0.118688i
$474$	3.20648e6	−	4.23873e6i	0.655514	−	0.866543i
$475$		−	7.69581e6i		−	1.56502i
$476$		0			0
$477$	8.48750e6	−	2.39967e6i	1.70798	−	0.482897i
$478$	−1.81075e6			−0.362485
$479$	7.71216e6			1.53581			0.767904	−	0.640564i	$-0.221300\pi$
$479$	7.71216e6			1.53581			0.767904	+	0.640564i	$0.221300\pi$
$480$	677773.	−	895968.i	0.134271	−	0.177496i
$481$		−	1.53360e6i		−	0.302239i
$482$	−2.64306e6			−0.518191
$483$		0			0
$484$	−2.16913e6			−0.420894
$485$			375588.i			0.0725031i
$486$	603727.	−	6.23332e6i	0.115944	−	1.19710i
$487$	−8.12051e6			−1.55153			−0.775767	−	0.631020i	$-0.782637\pi$
$487$	−8.12051e6			−1.55153			−0.775767	+	0.631020i	$0.782637\pi$
$488$	2.43348e6			0.462572
$489$	5.26890e6	+	3.98576e6i	0.996432	+	0.753771i
$490$		0			0
$491$			7.72726e6i			1.44651i	0.690581	+	0.723255i	$0.257355\pi$
$491$			7.72726e6i			1.44651i	−0.690581	+	0.723255i	$0.742645\pi$
$492$	−2.74466e6	−	2.07626e6i	−0.511183	−	0.386695i
$493$		−	1.50546e6i		−	0.278967i
$494$			7.51947e6i			1.38634i
$495$	−335050.	+	94728.4i	−0.0614605	+	0.0173767i
$496$		−	5.48808e6i		−	1.00165i
$497$		0			0
$498$	−6.89966e6	+	9.12086e6i	−1.24668	+	1.64802i
$499$	2.33074e6			0.419028			0.209514	−	0.977806i	$-0.432812\pi$
$499$	2.33074e6			0.419028			0.209514	+	0.977806i	$0.432812\pi$
$500$	1.28438e6			0.229757
$501$	−384352.	−	290751.i	−0.0684124	−	0.0517519i
$502$			7.46161e6i			1.32152i
$503$	3.86914e6			0.681859			0.340930	−	0.940089i	$-0.389258\pi$
$503$	3.86914e6			0.681859			0.340930	+	0.940089i	$0.389258\pi$
$504$		0			0
$505$	1.16424e6			0.203148
$506$		−	1.71104e6i		−	0.297087i
$507$	2.45565e6	+	1.85763e6i	0.424275	+	0.320951i
$508$	2.02283e6			0.347776
$509$	−4.29903e6			−0.735489			−0.367744	−	0.929927i	$-0.619870\pi$
$509$	−4.29903e6			−0.735489			−0.367744	+	0.929927i	$0.619870\pi$
$510$	−198960.	+	263011.i	−0.0338720	+	0.0447764i
$511$		0			0
$512$			1.24648e6i			0.210142i
$513$	−9.35613e6	−	3.65143e6i	−1.56965	−	0.612589i
$514$			682552.i			0.113953i
$515$			1.46146e6i			0.242812i
$516$	1.06771e6	+	807688.i	0.176534	+	0.133543i
$517$		−	375402.i		−	0.0617689i
$518$		0			0
$519$	2.22807e6	+	1.68547e6i	0.363087	+	0.274664i
$520$	749193.			0.121503
$521$	−4.57032e6			−0.737653			−0.368827	−	0.929498i	$-0.620240\pi$
$521$	−4.57032e6			−0.737653			−0.368827	+	0.929498i	$0.620240\pi$
$522$	3.24771e6	+	1.14870e7i	0.521676	+	1.84514i
$523$			2.15375e6i			0.344304i	0.985070	+	0.172152i	$0.0550720\pi$
$523$			2.15375e6i			0.344304i	−0.985070	+	0.172152i	$0.944928\pi$
$524$	2.18879e6			0.348238
$525$		0			0
$526$	8.87821e6			1.39914
$527$			896002.i			0.140534i
$528$	1.15386e6	−	1.52532e6i	0.180122	−	0.238109i
$529$	−416145.			−0.0646555
$530$	3.68300e6			0.569524
$531$	−517486.	−	1.83032e6i	−0.0796457	−	0.281703i
$532$		0			0
$533$		−	6.44133e6i		−	0.982104i
$534$	−8.75154e6	+	1.15689e7i	−1.32810	+	1.75566i
$535$			2.01482e6i			0.304335i
$536$			5.29484e6i			0.796051i
$537$	−1.33712e6	+	1.76757e6i	−0.200094	+	0.264510i
$538$			8.57730e6i			1.27760i
$539$		0			0
$540$	293456.	−	751928.i	0.0433070	−	0.110967i
$541$	−5.46624e6			−0.802963			−0.401481	−	0.915867i	$-0.631505\pi$
$541$	−5.46624e6			−0.802963			−0.401481	+	0.915867i	$0.631505\pi$
$542$	8.48656e6			1.24089
$543$	3.02294e6	−	3.99612e6i	0.439978	−	0.581619i
$544$		−	1.00752e6i		−	0.145968i
$545$	1.12053e6			0.161596
$546$		0			0
$547$	7.32611e6			1.04690			0.523450	−	0.852056i	$-0.324645\pi$
$547$	7.32611e6			1.04690			0.523450	+	0.852056i	$0.324645\pi$
$548$		−	1.28930e6i		−	0.183401i
$549$	4.72197e6	−	1.33504e6i	0.668640	−	0.189044i
$550$	1.89722e6			0.267431
$551$	1.91443e7			2.68633
$552$	−3.92175e6	−	2.96669e6i	−0.547813	−	0.414404i
$553$		0			0
$554$			4.48281e6i			0.620549i
$555$	682134.	+	516014.i	0.0940020	+	0.0711097i
$556$			1.90331e6i			0.261109i
$557$			7.63525e6i			1.04276i	0.853324	+	0.521381i	$0.174583\pi$
$557$			7.63525e6i			1.04276i	−0.853324	+	0.521381i	$0.825417\pi$
$558$	−1.93293e6	−	6.83668e6i	−0.262803	−	0.929522i
$559$			2.50575e6i			0.339163i
$560$		0			0
$561$	−188383.	+	249029.i	−0.0252717	+	0.0334074i
$562$	8.76942e6			1.17120
$563$	2.17576e6			0.289295			0.144648	−	0.989483i	$-0.453795\pi$
$563$	2.17576e6			0.289295			0.144648	+	0.989483i	$0.453795\pi$
$564$	694048.	+	525026.i	0.0918738	+	0.0694998i
$565$			1.31361e6i			0.173120i
$566$	6.86531e6			0.900780
$567$		0			0
$568$	3.13656e6			0.407927
$569$		−	8.38705e6i		−	1.08600i	−0.839734	−	0.542998i	$-0.817289\pi$
$569$		−	8.38705e6i		−	1.08600i	0.839734	−	0.542998i	$-0.182711\pi$
$570$	−3.34459e6	−	2.53009e6i	−0.431178	−	0.326173i
$571$	2.54473e6			0.326626			0.163313	−	0.986574i	$-0.447782\pi$
$571$	2.54473e6			0.326626			0.163313	+	0.986574i	$0.447782\pi$
$572$	−572193.			−0.0731228
$573$	−4.97326e6	+	6.57430e6i	−0.632783	+	0.836494i
$574$		0			0
$575$		−	7.59813e6i		−	0.958379i
$576$	−528218.	−	1.86828e6i	−0.0663372	−	0.234631i
$577$		−	1.02039e7i		−	1.27592i	−0.770068	−	0.637962i	$-0.779778\pi$
$577$		−	1.02039e7i		−	1.27592i	0.770068	−	0.637962i	$-0.220222\pi$
$578$		−	9.36422e6i		−	1.16588i
$579$	−1.18393e6	−	895608.i	−0.146767	−	0.111025i
$580$			1.53858e6i			0.189911i
$581$		0			0
$582$	−2.13004e6	−	1.61131e6i	−0.260664	−	0.197184i
$583$	3.48720e6			0.424919
$584$	−6.13517e6			−0.744380
$585$	1.45375e6	−	411017.i	0.175630	−	0.0496558i
$586$			1.32471e7i			1.59359i
$587$	−1.90974e6			−0.228760			−0.114380	−	0.993437i	$-0.536488\pi$
$587$	−1.90974e6			−0.228760			−0.114380	+	0.993437i	$0.536488\pi$
$588$		0			0
$589$	−1.13940e7			−1.35329
$590$		−	794235.i		−	0.0939332i
$591$	6.63727e6	−	8.77400e6i	0.781665	−	1.03331i
$592$	−4.69833e6			−0.550984
$593$	−9.68502e6			−1.13100			−0.565502	−	0.824747i	$-0.691317\pi$
$593$	−9.68502e6			−1.13100			−0.565502	+	0.824747i	$0.691317\pi$
$594$	900175.	−	2.30654e6i	0.104679	−	0.268222i
$595$		0			0
$596$			402239.i			0.0463841i
$597$	821080.	−	1.08541e6i	0.0942865	−	0.124640i
$598$			7.42403e6i			0.848959i
$599$		−	4.03346e6i		−	0.459315i	−0.973271	−	0.229658i	$-0.926239\pi$
$599$		−	4.03346e6i		−	0.459315i	0.973271	−	0.229658i	$-0.0737606\pi$
$600$	3.28950e6	−	4.34849e6i	0.373037	−	0.493128i
$601$		−	1.16260e7i		−	1.31293i	−0.754356	−	0.656466i	$-0.772051\pi$
$601$		−	1.16260e7i		−	1.31293i	0.754356	−	0.656466i	$-0.227949\pi$
$602$		0			0
$603$	2.90481e6	+	1.02742e7i	0.325330	+	1.15068i
$604$	93536.2			0.0104325
$605$	2.26427e6			0.251501
$606$	−4.99471e6	+	6.60265e6i	−0.552495	+	0.730359i
$607$		−	7.51421e6i		−	0.827774i	−0.910328	−	0.413887i	$-0.864171\pi$
$607$		−	7.51421e6i		−	0.827774i	0.910328	−	0.413887i	$-0.135829\pi$
$608$	1.28122e7			1.40561
$609$		0			0
$610$	2.04901e6			0.222956
$611$			1.62883e6i			0.176511i
$612$	−196941.	−	696570.i	−0.0212548	−	0.0751772i
$613$	3.74103e6			0.402105			0.201053	−	0.979580i	$-0.435564\pi$
$613$	3.74103e6			0.402105			0.201053	+	0.979580i	$0.435564\pi$
$614$	1.34576e7			1.44061
$615$	2.86505e6	+	2.16732e6i	0.305453	+	0.231066i
$616$		0			0
$617$		−	1.48513e7i		−	1.57055i	−0.619146	−	0.785276i	$-0.712521\pi$
$617$		−	1.48513e7i		−	1.57055i	0.619146	−	0.785276i	$-0.287479\pi$
$618$	−8.28828e6	−	6.26984e6i	−0.872958	−	0.660367i
$619$			8.36596e6i			0.877585i	0.898588	+	0.438793i	$0.144594\pi$
$619$			8.36596e6i			0.877585i	−0.898588	+	0.438793i	$0.855406\pi$
$620$		−	915711.i		−	0.0956707i
$621$	−9.23738e6	−	3.60508e6i	−0.961213	−	0.375134i
$622$		−	7.28969e6i		−	0.755497i
$623$		0			0
$624$	−5.00647e6	+	6.61820e6i	−0.514719	+	0.680423i
$625$	7.72981e6			0.791533
$626$	−2.83215e6			−0.288855
$627$	−3.16679e6	−	2.39558e6i	−0.321699	−	0.243356i
$628$			973922.i			0.0985428i
$629$	767065.			0.0773047
$630$		0			0
$631$	8.21939e6			0.821800			0.410900	−	0.911680i	$-0.365215\pi$
$631$	8.21939e6			0.821800			0.410900	+	0.911680i	$0.365215\pi$
$632$		−	6.03913e6i		−	0.601426i
$633$	−4.11074e6	−	3.10965e6i	−0.407766	−	0.308463i
$634$	1.96766e7			1.94414
$635$	−2.11155e6			−0.207810
$636$	−4.87710e6	+	6.44718e6i	−0.478100	+	0.632015i
$637$		0			0
$638$			4.71958e6i			0.459041i
$639$	6.08622e6	−	1.72075e6i	0.589651	−	0.166712i
$640$		−	3.11692e6i		−	0.300799i
$641$			4.93371e6i			0.474273i	0.971476	+	0.237137i	$0.0762089\pi$
$641$			4.93371e6i			0.474273i	−0.971476	+	0.237137i	$0.923791\pi$
$642$	−1.14265e7	−	8.64380e6i	−1.09415	−	0.827689i
$643$		−	1.06965e7i		−	1.02027i	−0.860094	−	0.510135i	$-0.829595\pi$
$643$		−	1.06965e7i		−	1.02027i	0.860094	−	0.510135i	$-0.170405\pi$
$644$		0			0
$645$	−1.11454e6	−	843115.i	−0.105486	−	0.0797971i
$646$	−3.76102e6			−0.354589
$647$	−8.71767e6			−0.818728			−0.409364	−	0.912371i	$-0.634249\pi$
$647$	−8.71767e6			−0.818728			−0.409364	+	0.912371i	$0.634249\pi$
$648$	−3.72588e6	−	6.06241e6i	−0.348571	−	0.567163i
$649$		−	752012.i		−	0.0700831i
$650$	−8.23186e6			−0.764213
$651$		0			0
$652$	−6.05524e6			−0.557844
$653$			9.86209e6i			0.905078i	0.891745	+	0.452539i	$0.149482\pi$
$653$			9.86209e6i			0.905078i	−0.891745	+	0.452539i	$0.850518\pi$
$654$	−4.80719e6	+	6.35476e6i	−0.439488	+	0.580972i
$655$	−2.28479e6			−0.208087
$656$	−1.97336e7			−1.79038
$657$	−1.19048e7	+	3.36583e6i	−1.07599	+	0.304214i
$658$		0			0
$659$			7.63431e6i			0.684788i	0.939556	+	0.342394i	$0.111238\pi$
$659$			7.63431e6i			0.684788i	−0.939556	+	0.342394i	$0.888762\pi$
$660$	192527.	−	254507.i	0.0172041	−	0.0227426i
$661$			1.40247e7i			1.24850i	0.781223	+	0.624252i	$0.214596\pi$
$661$			1.40247e7i			1.24850i	−0.781223	+	0.624252i	$0.785404\pi$
$662$		−	2.36595e7i		−	2.09826i
$663$	817375.	−	1.08051e6i	0.0722166	−	0.0954653i
$664$			1.29949e7i			1.14381i
$665$		0			0
$666$	−5.85286e6	+	1.65478e6i	−0.511308	+	0.144562i
$667$	1.89013e7			1.64504
$668$	441714.			0.0383001
$669$	−2.18684e6	+	2.89085e6i	−0.188909	+	0.249724i
$670$			4.45829e6i			0.383691i
$671$	1.94008e6			0.166347
$672$		0			0
$673$	−1.03156e7			−0.877920			−0.438960	−	0.898507i	$-0.644653\pi$
$673$	−1.03156e7			−0.877920			−0.438960	+	0.898507i	$0.644653\pi$
$674$			6.23803e6i			0.528930i
$675$	3.99736e6	−	1.02425e7i	0.337687	−	0.865262i
$676$	−2.82214e6			−0.237526
$677$	4.53726e6			0.380472			0.190236	−	0.981738i	$-0.439075\pi$
$677$	4.53726e6			0.380472			0.190236	+	0.981738i	$0.439075\pi$
$678$	−7.44981e6	−	5.63556e6i	−0.622402	−	0.470828i
$679$		0			0
$680$			374725.i			0.0310771i
$681$	5.57269e6	+	4.21558e6i	0.460466	+	0.348329i
$682$		−	2.80894e6i		−	0.231250i
$683$		−	901559.i		−	0.0739507i	−0.999316	−	0.0369754i	$-0.988228\pi$
$683$		−	901559.i		−	0.0739507i	0.999316	−	0.0369754i	$-0.0117723\pi$
$684$	8.85796e6	−	2.50440e6i	0.723925	−	0.204675i
$685$			1.34585e6i			0.109590i
$686$		0			0
$687$	5.41844e6	−	7.16280e6i	0.438009	−	0.579016i
$688$	7.67659e6			0.618297
$689$	−1.51306e7			−1.21425
$690$	−3.30214e6	−	2.49797e6i	−0.264042	−	0.199740i
$691$		−	1.71097e7i		−	1.36316i	−0.731742	−	0.681582i	$-0.761292\pi$
$691$		−	1.71097e7i		−	1.36316i	0.731742	−	0.681582i	$-0.238708\pi$
$692$	−2.56059e6			−0.203271
$693$		0			0
$694$	−8.42220e6			−0.663784
$695$		−	1.98679e6i		−	0.156023i
$696$	1.08174e7	+	8.18304e6i	0.846447	+	0.640312i
$697$	3.22177e6			0.251196
$698$	−1.49610e7			−1.16231
$699$	3.82730e6	−	5.05942e6i	0.296278	−	0.391658i
$700$		0			0
$701$			2.02857e6i			0.155917i	0.996957	+	0.0779587i	$0.0248402\pi$
$701$			2.02857e6i			0.155917i	−0.996957	+	0.0779587i	$0.975160\pi$
$702$	−3.90577e6	+	1.00078e7i	−0.299132	+	0.766473i
$703$			9.75441e6i			0.744411i
$704$		−	767608.i		−	0.0583724i
$705$	−724490.	−	548055.i	−0.0548984	−	0.0415290i
$706$			1.81592e7i			1.37115i
$707$		0			0
$708$	1.39033e6	+	1.05174e6i	0.104240	+	0.0788545i
$709$	−1.67894e7			−1.25435			−0.627176	−	0.778878i	$-0.715789\pi$
$709$	−1.67894e7			−1.25435			−0.627176	+	0.778878i	$0.715789\pi$
$710$	2.64100e6			0.196618
$711$	−3.31314e6	−	1.17184e7i	−0.245791	−	0.869351i
$712$			1.64828e7i			1.21852i
$713$	−1.12494e7			−0.828718
$714$		0			0
$715$	597290.			0.0436939
$716$		−	2.03137e6i		−	0.148084i
$717$	−2.50301e6	+	3.30880e6i	−0.181829	+	0.240366i
$718$	−3.09418e7			−2.23993
$719$	2.63704e7			1.90237			0.951183	−	0.308627i	$-0.0998696\pi$
$719$	2.63704e7			1.90237			0.951183	+	0.308627i	$0.0998696\pi$
$720$	−1.25918e6	−	4.45367e6i	−0.0905228	−	0.320175i
$721$		0			0
$722$		−	3.09811e7i		−	2.21184i
$723$	−3.65351e6	+	4.82968e6i	−0.259935	+	0.343615i
$724$			4.59251e6i			0.325614i
$725$			2.09580e7i			1.48083i
$726$	−9.71399e6	+	1.28412e7i	−0.684000	+	0.904199i
$727$		−	1.63660e7i		−	1.14844i	−0.818702	−	0.574218i	$-0.805306\pi$
$727$		−	1.63660e7i		−	1.14844i	0.818702	−	0.574218i	$-0.194694\pi$
$728$		0			0
$729$	−1.05557e7	−	9.71953e6i	−0.735642	−	0.677371i
$730$	−5.16586e6			−0.358786
$731$	−1.25331e6			−0.0867489
$732$	−2.71334e6	+	3.58685e6i	−0.187166	+	0.247420i
$733$			2.65023e7i			1.82189i	0.412525	+	0.910946i	$0.364647\pi$
$733$			2.65023e7i			1.82189i	−0.412525	+	0.910946i	$0.635353\pi$
$734$	1.45261e7			0.995196
$735$		0			0
$736$	1.26496e7			0.860759
$737$			4.22128e6i			0.286270i
$738$	−2.45828e7	+	6.95027e6i	−1.66146	+	0.469743i
$739$	−1.36791e7			−0.921397			−0.460698	−	0.887557i	$-0.652401\pi$
$739$	−1.36791e7			−0.921397			−0.460698	+	0.887557i	$0.652401\pi$
$740$	−783937.			−0.0526262
$741$	1.37404e7	+	1.03942e7i	0.919290	+	0.695416i
$742$		0			0
$743$			9.39766e6i			0.624522i	0.949996	+	0.312261i	$0.101086\pi$
$743$			9.39766e6i			0.624522i	−0.949996	+	0.312261i	$0.898914\pi$
$744$	−6.43816e6	−	4.87028e6i	−0.426412	−	0.322568i
$745$		−	419882.i		−	0.0277164i
$746$		−	2.21694e7i		−	1.45850i
$747$	7.12918e6	+	2.52156e7i	0.467453	+	1.65336i
$748$		−	286195.i		−	0.0187029i
$749$		0			0
$750$	5.75183e6	−	7.60351e6i	0.373381	−	0.493584i
$751$	−1.35043e7			−0.873723			−0.436862	−	0.899529i	$-0.643910\pi$
$751$	−1.35043e7			−0.873723			−0.436862	+	0.899529i	$0.643910\pi$
$752$	4.99006e6			0.321782
$753$	1.36346e7	+	1.03142e7i	0.876307	+	0.662900i
$754$		−	2.04778e7i		−	1.31176i
$755$	−97638.9			−0.00623383
$756$		0			0
$757$	−7.36283e6			−0.466987			−0.233494	−	0.972358i	$-0.575016\pi$
$757$	−7.36283e6			−0.466987			−0.233494	+	0.972358i	$0.575016\pi$
$758$		−	2.25887e7i		−	1.42797i
$759$	−3.12659e6	−	2.36517e6i	−0.197000	−	0.149025i
$760$	−4.76521e6			−0.299259
$761$	2.48311e6			0.155430			0.0777150	−	0.996976i	$-0.475238\pi$
$761$	2.48311e6			0.155430			0.0777150	+	0.996976i	$0.475238\pi$
$762$	9.05879e6	−	1.19751e7i	0.565175	−	0.747121i
$763$		0			0
$764$		−	7.55547e6i		−	0.468304i
$765$	205579.	+	727122.i	0.0127006	+	0.0449215i
$766$		−	2.35538e7i		−	1.45040i
$767$			3.26290e6i			0.200270i
$768$	1.44982e7	+	1.09675e7i	0.886976	+	0.670971i
$769$			2.15050e7i			1.31136i	0.755038	+	0.655681i	$0.227618\pi$
$769$			2.15050e7i			1.31136i	−0.755038	+	0.655681i	$0.772382\pi$
$770$		0			0
$771$	1.24723e6	+	943492.i	0.0755632	+	0.0571614i
$772$	1.36062e6			0.0821664
$773$	−9.92550e6			−0.597453			−0.298726	−	0.954339i	$-0.596562\pi$
$773$	−9.92550e6			−0.597453			−0.298726	+	0.954339i	$0.596562\pi$
$774$	9.56299e6	−	2.70374e6i	0.573774	−	0.162223i
$775$		−	1.24735e7i		−	0.745993i
$776$	−3.03478e6			−0.180914
$777$		0			0
$778$	1.69551e7			1.00427
$779$			4.09698e7i			2.41891i
$780$	−835353.	+	1.10428e6i	−0.0491625	+	0.0649893i
$781$	2.50060e6			0.146696
$782$	−3.71329e6			−0.217141
$783$	2.54796e7	+	9.94393e6i	1.48521	+	0.579634i
$784$		0			0
$785$		−	1.01664e6i		−	0.0588834i
$786$	9.80203e6	−	1.29576e7i	0.565926	−	0.748114i
$787$		−	1.03681e6i		−	0.0596708i	−0.999555	−	0.0298354i	$-0.990502\pi$
$787$		−	1.03681e6i		−	0.0596708i	0.999555	−	0.0298354i	$-0.00949831\pi$
$788$			1.00835e7i			0.578487i
$789$	1.22724e7	−	1.62232e7i	0.701836	−	0.927778i
$790$		−	5.08500e6i		−	0.289883i
$791$		0			0
$792$	−765412.	−	2.70723e6i	−0.0433593	−	0.153360i
$793$	−8.41782e6			−0.475353
$794$	2.07397e7			1.16749
$795$	5.09102e6	−	6.72996e6i	0.285685	−	0.377655i
$796$			1.24740e6i			0.0697786i
$797$	−1.52399e7			−0.849838			−0.424919	−	0.905231i	$-0.639697\pi$
$797$	−1.52399e7			−0.849838			−0.424919	+	0.905231i	$0.639697\pi$
$798$		0			0
$799$	−814695.			−0.0451469
$800$			1.40260e7i			0.774836i
$801$	9.04267e6	+	3.19835e7i	0.497984	+	1.76134i
$802$	350875.			0.0192627
$803$	−4.89123e6			−0.267688
$804$	−7.80435e6	−	5.90376e6i	−0.425791	−	0.322099i
$805$		0			0
$806$			1.21877e7i			0.660821i
$807$	1.56733e7	+	1.18564e7i	0.847184	+	0.640869i
$808$			9.40712e6i			0.506907i
$809$			5.45336e6i			0.292949i	0.989214	+	0.146475i	$0.0467927\pi$
$809$			5.45336e6i			0.292949i	−0.989214	+	0.146475i	$0.953207\pi$
$810$	−3.13722e6	−	5.10460e6i	−0.168009	−	0.273369i
$811$			9.69507e6i			0.517605i	0.965930	+	0.258803i	$0.0833279\pi$
$811$			9.69507e6i			0.517605i	−0.965930	+	0.258803i	$0.916672\pi$
$812$		0			0
$813$	1.17310e7	−	1.55075e7i	0.622456	−	0.822842i
$814$	−2.40473e6			−0.127205
$815$	6.32083e6			0.333335
$816$	−3.31024e6	−	2.50410e6i	−0.174034	−	0.131651i
$817$		−	1.59377e7i		−	0.835355i
$818$	−3.08824e7			−1.61372
$819$		0			0
$820$	−3.29264e6			−0.171005
$821$		−	1.63719e7i		−	0.847699i	−0.905733	−	0.423849i	$-0.860679\pi$
$821$		−	1.63719e7i		−	0.847699i	0.905733	−	0.423849i	$-0.139321\pi$
$822$	−7.63260e6	−	5.77384e6i	−0.393997	−	0.298047i
$823$	2.37540e7			1.22247			0.611233	−	0.791451i	$-0.290674\pi$
$823$	2.37540e7			1.22247			0.611233	+	0.791451i	$0.290674\pi$
$824$	−1.18087e7			−0.605878
$825$	2.62254e6	−	3.46681e6i	0.134149	−	0.177335i
$826$		0			0
$827$			2.87632e7i			1.46242i	0.682151	+	0.731211i	$0.261045\pi$
$827$			2.87632e7i			1.46242i	−0.682151	+	0.731211i	$0.738955\pi$
$828$	8.74553e6	−	2.47262e6i	0.443313	−	0.125338i
$829$		−	3.69015e7i		−	1.86491i	−0.361286	−	0.932455i	$-0.617662\pi$
$829$		−	3.69015e7i		−	1.86491i	0.361286	−	0.932455i	$-0.382338\pi$
$830$			1.09418e7i			0.551309i
$831$	8.19146e6	+	6.19660e6i	0.411490	+	0.311280i
$832$			3.33057e6i			0.166805i
$833$		0			0
$834$	1.12675e7	+	8.52356e6i	0.560937	+	0.424332i
$835$	−461088.			−0.0228859
$836$	3.63941e6			0.180101
$837$	−1.51646e7	−	5.91830e6i	−0.748199	−	0.292000i
$838$			1.28639e7i			0.632793i
$839$	2.41096e7			1.18246			0.591229	−	0.806504i	$-0.298643\pi$
$839$	2.41096e7			1.18246			0.591229	+	0.806504i	$0.298643\pi$
$840$		0			0
$841$	−3.16245e7			−1.54182
$842$		−	3.43509e7i		−	1.66977i
$843$	1.21220e7	−	1.60244e7i	0.587496	−	0.776628i
$844$	4.72424e6			0.228284
$845$	2.94592e6			0.141932
$846$	6.21629e6	−	1.75753e6i	0.298611	−	0.0844260i
$847$		0			0
$848$			4.63539e7i			2.21359i
$849$	9.48993e6	−	1.25450e7i	0.451849	−	0.597313i
$850$		−	4.11734e6i		−	0.195465i
$851$			9.63060e6i			0.455858i
$852$	−3.49727e6	+	4.62314e6i	−0.165056	+	0.218192i
$853$		−	1.08498e7i		−	0.510561i	−0.966867	−	0.255281i	$-0.917832\pi$
$853$		−	1.08498e7i		−	0.510561i	0.966867	−	0.255281i	$-0.0821678\pi$
$854$		0			0
$855$	−9.24648e6	+	2.61425e6i	−0.432575	+	0.122302i
$856$	−1.62799e7			−0.759393
$857$	2.90805e7			1.35254			0.676270	−	0.736654i	$-0.263595\pi$
$857$	2.90805e7			1.35254			0.676270	+	0.736654i	$0.263595\pi$
$858$	−2.56244e6	+	3.38737e6i	−0.118833	+	0.157088i
$859$		−	3.67954e7i		−	1.70142i	−0.525636	−	0.850709i	$-0.676173\pi$
$859$		−	3.67954e7i		−	1.70142i	0.525636	−	0.850709i	$-0.323827\pi$
$860$	1.28087e6			0.0590555
$861$		0			0
$862$	2.22372e7			1.01932
$863$		−	2.85606e6i		−	0.130539i	−0.997868	−	0.0652695i	$-0.979209\pi$
$863$		−	2.85606e6i		−	0.130539i	0.997868	−	0.0652695i	$-0.0207907\pi$
$864$	1.70521e7	+	6.65492e6i	0.777128	+	0.303290i
$865$	2.67290e6			0.121463
$866$	−1.15515e7			−0.523412
$867$	−1.71113e7	−	1.29442e7i	−0.773099	−	0.584826i
$868$		0			0
$869$		−	4.81467e6i		−	0.216280i
$870$	9.10834e6	+	6.89018e6i	0.407982	+	0.308626i
$871$		−	1.83157e7i		−	0.818047i
$872$			9.05395e6i			0.403224i
$873$	−5.88872e6	+	1.66491e6i	−0.261508	+	0.0739361i
$874$		−	4.72202e7i		−	2.09098i
$875$		0			0
$876$	6.84074e6	−	9.04297e6i	0.301192	−	0.398154i
$877$	−5.35187e6			−0.234967			−0.117483	−	0.993075i	$-0.537483\pi$
$877$	−5.35187e6			−0.234967			−0.117483	+	0.993075i	$0.537483\pi$
$878$	−3.00932e7			−1.31744
$879$	2.42065e7	+	1.83115e7i	1.05672	+	0.799378i
$880$		−	1.82985e6i		−	0.0796542i
$881$	−2.78347e6			−0.120822			−0.0604111	−	0.998174i	$-0.519241\pi$
$881$	−2.78347e6			−0.120822			−0.0604111	+	0.998174i	$0.519241\pi$
$882$		0			0
$883$	−626626.			−0.0270462			−0.0135231	−	0.999909i	$-0.504305\pi$
$883$	−626626.			−0.0270462			−0.0135231	+	0.999909i	$0.504305\pi$
$884$			1.24177e6i			0.0534454i
$885$	−1.45131e6	−	1.09787e6i	−0.0622877	−	0.0471188i
$886$	3.55153e7			1.51996
$887$	−4.27454e7			−1.82423			−0.912117	−	0.409930i	$-0.865553\pi$
$887$	−4.27454e7			−1.82423			−0.912117	+	0.409930i	$0.865553\pi$
$888$	−4.16943e6	+	5.51169e6i	−0.177437	+	0.234559i
$889$		0			0
$890$			1.38786e7i			0.587316i
$891$	−2.97043e6	−	4.83323e6i	−0.125350	−	0.203959i
$892$		−	3.32229e6i		−	0.139806i
$893$		−	1.03601e7i		−	0.434746i
$894$	2.38125e6	+	1.80134e6i	0.0996461	+	0.0753793i
$895$			2.12047e6i			0.0884861i
$896$		0			0
$897$	1.35660e7	+	1.02622e7i	0.562950	+	0.425855i
$898$	−2.58719e7			−1.07062
$899$	3.10294e7			1.28048
$900$	2.74167e6	+	9.69716e6i	0.112826	+	0.399060i
$901$		−	7.56790e6i		−	0.310573i
$902$	−1.01002e7			−0.413344
$903$		0			0
$904$	−1.06141e7			−0.431979
$905$		−	4.79394e6i		−	0.194568i
$906$	418882.	−	553732.i	0.0169540	−	0.0224119i
$907$	7.04109e6			0.284198			0.142099	−	0.989852i	$-0.454615\pi$
$907$	7.04109e6			0.284198			0.142099	+	0.989852i	$0.454615\pi$
$908$	−6.40438e6			−0.257788
$909$	5.16086e6	+	1.82537e7i	0.207163	+	0.732726i
$910$		0			0
$911$		−	1.05335e6i		−	0.0420509i	−0.999779	−	0.0210255i	$-0.993307\pi$
$911$		−	1.05335e6i		−	0.0420509i	0.999779	−	0.0210255i	$-0.00669310\pi$
$912$	3.18434e7	−	4.20948e7i	1.26775	−	1.67587i
$913$			1.03602e7i			0.411329i
$914$			1.25013e7i			0.494984i
$915$	2.83235e6	−	3.74417e6i	0.111839	−	0.147844i
$916$			8.23180e6i			0.324157i
$917$		0			0
$918$	−5.00563e6	−	1.95355e6i	−0.196043	−	0.0765101i
$919$	1.81997e7			0.710844			0.355422	−	0.934706i	$-0.384337\pi$
$919$	1.81997e7			0.710844			0.355422	+	0.934706i	$0.384337\pi$
$920$	−4.70473e6			−0.183259
$921$	1.86025e7	−	2.45911e7i	0.722639	−	0.955278i
$922$		−	5.30519e7i		−	2.05529i
$923$	−1.08499e7			−0.419198
$924$		0			0
$925$	−1.06785e7			−0.410353
$926$			1.73359e6i			0.0664383i
$927$	−2.29138e7	+	6.47841e6i	−0.875787	+	0.247611i
$928$	−3.48915e7			−1.32999
$929$	3.36714e7			1.28004			0.640018	−	0.768360i	$-0.278927\pi$
$929$	3.36714e7			1.28004			0.640018	+	0.768360i	$0.278927\pi$
$930$	−5.42098e6	−	4.10081e6i	−0.205528	−	0.155476i
$931$		0			0
$932$			5.81450e6i			0.219267i
$933$	−1.33205e7	−	1.00765e7i	−0.500975	−	0.378973i
$934$		−	3.39171e7i		−	1.27219i
$935$			298748.i			0.0111757i
$936$	3.32105e6	+	1.17464e7i	0.123904	+	0.438242i
$937$			3.25239e7i			1.21019i	0.796153	+	0.605095i	$0.206865\pi$
$937$			3.25239e7i			1.21019i	−0.796153	+	0.605095i	$0.793135\pi$
$938$		0			0
$939$	−3.91489e6	+	5.17520e6i	−0.144896	+	0.191542i
$940$	832615.			0.0307344
$941$	1.62948e7			0.599895			0.299947	−	0.953956i	$-0.403031\pi$
$941$	1.62948e7			0.599895			0.299947	+	0.953956i	$0.403031\pi$
$942$	5.76559e6	+	4.36150e6i	0.211698	+	0.160143i
$943$			4.04498e7i			1.48128i
$944$	9.99618e6			0.365093
$945$		0			0
$946$	3.92908e6			0.142746
$947$			1.21518e7i			0.440317i	0.975464	+	0.220158i	$0.0706574\pi$
$947$			1.21518e7i			0.440317i	−0.975464	+	0.220158i	$0.929343\pi$
$948$	8.90142e6	+	6.73366e6i	0.321690	+	0.243349i
$949$	2.12226e7			0.764948
$950$	5.23583e7			1.88225
$951$	2.71991e7	−	3.59552e7i	0.975220	−	1.28917i
$952$		0			0
$953$		−	2.91378e7i		−	1.03926i	−0.854391	−	0.519630i	$-0.826070\pi$
$953$		−	2.91378e7i		−	1.03926i	0.854391	−	0.519630i	$-0.173930\pi$
$954$	1.63261e7	+	5.77446e7i	0.580780	+	2.05419i
$955$			7.88686e6i			0.279831i
$956$		−	3.80261e6i		−	0.134567i
$957$	8.62411e6	+	6.52389e6i	0.304393	+	0.230264i
$958$			5.24696e7i			1.84711i
$959$		0			0
$960$	−1.48141e6	−	1.12064e6i	−0.0518796	−	0.0392454i
$961$	1.01615e7			0.354934
$962$	1.04339e7			0.363502
$963$	−3.15897e7	+	8.93134e6i	−1.09769	+	0.310349i
$964$		−	5.55047e6i		−	0.192370i
$965$	−1.42030e6			−0.0490978
$966$		0			0
$967$	4.05970e7			1.39614			0.698068	−	0.716032i	$-0.254043\pi$
$967$	4.05970e7			1.39614			0.698068	+	0.716032i	$0.254043\pi$
$968$			1.82955e7i			0.627561i
$969$	−5.19887e6	+	6.87254e6i	−0.177869	+	0.235130i
$970$	−2.55531e6			−0.0871994
$971$	−1.12136e7			−0.381677			−0.190838	−	0.981621i	$-0.561121\pi$
$971$	−1.12136e7			−0.381677			−0.190838	+	0.981621i	$0.561121\pi$
$972$	1.30901e7	+	1.26784e6i	0.444403	+	0.0430425i
$973$		0			0
$974$		−	5.52478e7i		−	1.86603i
$975$	−1.13789e7	+	1.50421e7i	−0.383345	+	0.506754i
$976$			2.57887e7i			0.866572i
$977$		−	2.82925e7i		−	0.948276i	−0.880451	−	0.474138i	$-0.842760\pi$
$977$		−	2.82925e7i		−	0.948276i	0.880451	−	0.474138i	$-0.157240\pi$
$978$	−2.71171e7	+	3.58469e7i	−0.906559	+	1.19841i
$979$			1.31408e7i			0.438194i
$980$		0			0
$981$	4.96710e6	+	1.75684e7i	0.164790	+	0.582854i
$982$	−5.25723e7			−1.73972
$983$	−3.44078e7			−1.13573			−0.567863	−	0.823123i	$-0.692230\pi$
$983$	−3.44078e7			−1.13573			−0.567863	+	0.823123i	$0.692230\pi$
$984$	−1.75121e7	+	2.31498e7i	−0.576569	+	0.762184i
$985$		−	1.05257e7i		−	0.345670i
$986$	1.02424e7			0.335513
$987$		0			0
$988$	−1.57910e7			−0.514657
$989$		−	1.57354e7i		−	0.511550i
$990$	−644483.	−	2.27951e6i	−0.0208989	−	0.0739184i
$991$	−4.97942e7			−1.61063			−0.805313	−	0.592850i	$-0.798003\pi$
$991$	−4.97942e7			−1.61063			−0.805313	+	0.592850i	$0.798003\pi$
$992$	2.07663e7			0.670007
$993$	−4.32331e7	−	3.27045e7i	−1.39137	−	1.05253i
$994$		0			0
$995$		−	1.30211e6i		−	0.0416956i
$996$	−1.91540e7	−	1.44894e7i	−0.611802	−	0.462810i
$997$			1.01229e7i			0.322529i	0.986911	+	0.161265i	$0.0515572\pi$
$997$			1.01229e7i			0.322529i	−0.986911	+	0.161265i	$0.948443\pi$
$998$			1.58572e7i			0.503964i
$999$	−5.06664e6	+	1.29824e7i	−0.160623	+	0.411567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.c.c.146.14		16
3.2	odd	2	inner	147.6.c.c.146.3		16
7.4	even	3		21.6.g.c.5.2	✓	16
7.5	odd	6		21.6.g.c.17.7	yes	16
7.6	odd	2	inner	147.6.c.c.146.13		16
21.5	even	6		21.6.g.c.17.2	yes	16
21.11	odd	6		21.6.g.c.5.7	yes	16
21.20	even	2	inner	147.6.c.c.146.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.g.c.5.2	✓	16	7.4	even	3
21.6.g.c.5.7	yes	16	21.11	odd	6
21.6.g.c.17.2	yes	16	21.5	even	6
21.6.g.c.17.7	yes	16	7.5	odd	6
147.6.c.c.146.3		16	3.2	odd	2	inner
147.6.c.c.146.4		16	21.20	even	2	inner
147.6.c.c.146.13		16	7.6	odd	2	inner
147.6.c.c.146.14		16	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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+6.80349i q^{2} +(12.4320 + 9.40448i) q^{3} -14.2874 q^{4} +14.9141 q^{5} +(-63.9832 + 84.5813i) q^{6} +120.507i q^{8} +(66.1117 + 233.834i) q^{9} +O(q^{10})\)	\(q+6.80349i q^{2} +(12.4320 + 9.40448i) q^{3} -14.2874 q^{4} +14.9141 q^{5} +(-63.9832 + 84.5813i) q^{6} +120.507i q^{8} +(66.1117 + 233.834i) q^{9} +101.468i q^{10} +96.0737i q^{11} +(-177.622 - 134.366i) q^{12} -416.854i q^{13} +(185.413 + 140.259i) q^{15} -1277.07 q^{16} +208.498 q^{17} +(-1590.89 + 449.790i) q^{18} +2651.38i q^{19} -213.085 q^{20} -653.636 q^{22} +2617.73i q^{23} +(-1133.31 + 1498.15i) q^{24} -2902.57 q^{25} +2836.06 q^{26} +(-1377.18 + 3528.78i) q^{27} -7220.50i q^{29} +(-954.253 + 1261.45i) q^{30} +4297.41i q^{31} -4832.28i q^{32} +(-903.523 + 1194.39i) q^{33} +1418.52i q^{34} +(-944.567 - 3340.89i) q^{36} +3679.00 q^{37} -18038.6 q^{38} +(3920.29 - 5182.35i) q^{39} +1797.26i q^{40} +15452.3 q^{41} -6011.11 q^{43} -1372.65i q^{44} +(985.997 + 3487.42i) q^{45} -17809.7 q^{46} -3907.44 q^{47} +(-15876.6 - 12010.1i) q^{48} -19747.6i q^{50} +(2592.06 + 1960.82i) q^{51} +5955.77i q^{52} -36297.2i q^{53} +(-24008.0 - 9369.63i) q^{54} +1432.85i q^{55} +(-24934.8 + 32962.1i) q^{57} +49124.6 q^{58} -7827.45 q^{59} +(-2649.08 - 2003.95i) q^{60} -20193.7i q^{61} -29237.3 q^{62} -7989.78 q^{64} -6217.00i q^{65} +(-8126.04 - 6147.10i) q^{66} +43937.9 q^{67} -2978.91 q^{68} +(-24618.3 + 32543.7i) q^{69} -26028.0i q^{71} +(-28178.6 + 7966.93i) q^{72} +50911.3i q^{73} +25030.0i q^{74} +(-36084.9 - 27297.1i) q^{75} -37881.4i q^{76} +(35258.0 + 26671.6i) q^{78} -50114.3 q^{79} -19046.3 q^{80} +(-50307.5 + 30918.3i) q^{81} +105129. i q^{82} +107835. q^{83} +3109.57 q^{85} -40896.5i q^{86} +(67905.0 - 89765.6i) q^{87} -11577.6 q^{88} +136779. q^{89} +(-23726.6 + 6708.22i) q^{90} -37400.6i q^{92} +(-40414.8 + 53425.6i) q^{93} -26584.2i q^{94} +39543.0i q^{95} +(45445.1 - 60075.2i) q^{96} +25183.4i q^{97} +(-22465.3 + 6351.59i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 172 q^{4} + 1212 q^{9}+O(q^{10}) \) 16 * q - 172 * q^4 + 1212 * q^9	\( 16 q - 172 q^{4} + 1212 q^{9} + 1188 q^{15} + 5716 q^{16} + 876 q^{18} - 21900 q^{22} + 13156 q^{25} - 900 q^{30} - 15132 q^{36} + 20932 q^{37} + 34836 q^{39} + 111052 q^{43} - 163392 q^{46} - 63192 q^{51} - 31368 q^{57} + 83412 q^{58} - 120132 q^{60} - 158884 q^{64} + 204404 q^{67} - 661728 q^{72} - 277512 q^{78} + 502616 q^{79} - 358524 q^{81} + 205152 q^{85} + 719028 q^{88} - 35352 q^{93} + 215472 q^{99}+O(q^{100}) \) 16 * q - 172 * q^4 + 1212 * q^9 + 1188 * q^15 + 5716 * q^16 + 876 * q^18 - 21900 * q^22 + 13156 * q^25 - 900 * q^30 - 15132 * q^36 + 20932 * q^37 + 34836 * q^39 + 111052 * q^43 - 163392 * q^46 - 63192 * q^51 - 31368 * q^57 + 83412 * q^58 - 120132 * q^60 - 158884 * q^64 + 204404 * q^67 - 661728 * q^72 - 277512 * q^78 + 502616 * q^79 - 358524 * q^81 + 205152 * q^85 + 719028 * q^88 - 35352 * q^93 + 215472 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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