LMFDB - Embedded newform 147.6.c.c.146.3

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			146.3
Root			$-5.89199 + 3.40174i$ of defining polynomial
Character	$\chi$	$=$	147.146
Dual form			147.6.c.c.146.13

$q$-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	$-0.794630\pi$
$2$		−	6.80349i		−	1.20270i	0.798986	−	0.601349i	$-0.205370\pi$
$3$	−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	$-0.542588\pi$
$5$	−14.9141			−0.266792			−0.133396	+	0.991063i	$0.542588\pi$
$6$	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	$-0.961807\pi$
$11$		−	96.0737i		−	0.239399i	0.992810	−	0.119700i	$-0.0381931\pi$
$12$	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	$-0.527884\pi$
$17$	−208.498			−0.174977			−0.0874884	+	0.996166i	$0.527884\pi$
$18$	−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	$-0.827454\pi$
$23$		−	2617.73i		−	1.03182i	0.856642	−	0.515911i	$-0.172546\pi$
$24$	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	$0.293662\pi$
$29$			7220.50i			1.59431i	−0.603776	+	0.797154i	$0.706338\pi$
$30$	−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	$-0.754850\pi$
$41$	−15452.3			−1.43560			−0.717798	+	0.696251i	$0.754850\pi$
$42$		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	$-0.458821\pi$
$47$	3907.44			0.258016			0.129008	+	0.991644i	$0.458821\pi$
$48$	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	$0.347538\pi$
$53$			36297.2i			1.77494i	−0.460868	+	0.887469i	$0.652462\pi$
$54$	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	$-0.453240\pi$
$59$	7827.45			0.292746			0.146373	+	0.989230i	$0.453240\pi$
$60$	−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	$0.0991187\pi$
$71$			26028.0i			0.612765i	−0.951908	+	0.306383i	$0.900881\pi$
$72$	−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	$-0.828967\pi$
$83$	−107835.			−1.71817			−0.859086	+	0.511832i	$0.828967\pi$
$84$		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	$-0.867963\pi$
$89$	−136779.			−1.83039			−0.915194	+	0.403013i	$0.867963\pi$
$90$	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	$-0.624325\pi$
$101$	−78062.7			−0.761448			−0.380724	+	0.924689i	$0.624325\pi$
$102$	−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	$-0.806804\pi$
$107$		−	135095.i		−	1.14072i	0.821395	−	0.570360i	$-0.193196\pi$
$108$	−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	$-0.894822\pi$
$113$		−	88078.7i		−	0.648895i	0.945904	−	0.324448i	$-0.105178\pi$
$114$	−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	$-0.372482\pi$
$131$	153197.			0.779959			0.389979	+	0.920824i	$0.372482\pi$
$132$	−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	$-0.934156\pi$
$137$		−	90239.8i		−	0.410768i	0.978681	−	0.205384i	$-0.0658444\pi$
$138$	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	$0.0165417\pi$
$149$			28153.3i			0.103888i	−0.998650	+	0.0519439i	$0.983458\pi$
$150$	−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	$-0.486343\pi$
$167$	30916.2			0.0857818			0.0428909	+	0.999080i	$0.486343\pi$
$168$		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	$-0.573100\pi$
$173$	−179220.			−0.455272			−0.227636	+	0.973746i	$0.573100\pi$
$174$	−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	$-0.946969\pi$
$179$		−	142179.i		−	0.331667i	0.986154	−	0.165834i	$-0.0530315\pi$
$180$	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	$-0.824276\pi$
$191$		−	528819.i		−	1.04887i	0.851449	−	0.524437i	$-0.175724\pi$
$192$	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	$0.224322\pi$
$197$			705756.i			1.29565i	−0.761787	+	0.647827i	$0.775678\pi$
$198$	−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	$-0.593219\pi$
$227$	−448252.			−0.577375			−0.288687	+	0.957423i	$0.593219\pi$
$228$	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	$0.0789682\pi$
$233$			406966.i			0.491098i	−0.969384	+	0.245549i	$0.921032\pi$
$234$	−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	$-0.951848\pi$
$239$		−	266151.i		−	0.301393i	0.988580	−	0.150696i	$-0.0481516\pi$
$240$	−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	$-0.685143\pi$
$251$	−1.09673e6			−1.09879			−0.549397	+	0.835561i	$0.685143\pi$
$252$		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	$-0.515085\pi$
$257$	−100324.			−0.0947482			−0.0473741	+	0.998877i	$0.515085\pi$
$258$	−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	$0.197599\pi$
$263$			1.30495e6i			1.16333i	−0.813427	+	0.581667i	$0.802401\pi$
$264$	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	$-0.678236\pi$
$269$	−1.26072e6			−1.06228			−0.531139	+	0.847285i	$0.678236\pi$
$270$	−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	$0.161874\pi$
$281$			1.28896e6i			0.973809i	−0.873455	+	0.486904i	$0.838126\pi$
$282$	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	$-0.730508\pi$
$293$	−1.94711e6			−1.32502			−0.662508	+	0.749055i	$0.730508\pi$
$294$		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	$-0.398303\pi$
$311$	1.07146e6			0.628169			0.314084	+	0.949395i	$0.398303\pi$
$312$	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	$0.299580\pi$
$317$			2.89214e6i			1.61648i	−0.588851	+	0.808242i	$0.700420\pi$
$318$	−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	$-0.911006\pi$
$347$		−	1.23792e6i		−	0.551912i	0.961170	−	0.275956i	$-0.0889945\pi$
$348$	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	$-0.693069\pi$
$353$	−2.66911e6			−1.14006			−0.570032	+	0.821622i	$0.693069\pi$
$354$	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	$-0.618755\pi$
$359$		−	4.54793e6i		−	1.86242i	0.364484	−	0.931210i	$-0.381245\pi$
$360$	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	$-0.293981\pi$
$383$	3.46201e6			1.20596			0.602978	+	0.797758i	$0.293981\pi$
$384$	−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	$0.137097\pi$
$389$			2.49213e6i			0.835018i	−0.908673	+	0.417509i	$0.862903\pi$
$390$	−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	$0.00254909\pi$
$401$			51572.9i			0.0160162i	−0.999968	+	0.00800812i	$0.997451\pi$
$402$	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	$-0.584736\pi$
$419$	−1.89078e6			−0.526145			−0.263072	+	0.964776i	$0.584736\pi$
$420$		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	$0.139292\pi$
$431$			3.26850e6i			0.847530i	−0.905772	+	0.423765i	$0.860708\pi$
$432$	−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	$0.217723\pi$
$443$			5.22017e6i			1.26379i	−0.775054	+	0.631895i	$0.782277\pi$
$444$	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	$-0.853171\pi$
$449$		−	3.80274e6i		−	0.890186i	0.895484	−	0.445093i	$-0.146829\pi$
$450$	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	$-0.173894\pi$
$461$	7.79775e6			1.70890			0.854450	+	0.519533i	$0.173894\pi$
$462$		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	$-0.322609\pi$
$467$	4.98525e6			1.05778			0.528889	+	0.848691i	$0.322609\pi$
$468$	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	$-0.778700\pi$
$479$	−7.71216e6			−1.53581			−0.767904	+	0.640564i	$0.778700\pi$
$480$	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	$-0.742645\pi$
$491$		−	7.72726e6i		−	1.44651i	0.690581	−	0.723255i	$-0.257355\pi$
$492$	−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	$-0.610742\pi$
$503$	−3.86914e6			−0.681859			−0.340930	+	0.940089i	$0.610742\pi$
$504$		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	$-0.380130\pi$
$509$	4.29903e6			0.735489			0.367744	+	0.929927i	$0.380130\pi$
$510$	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	$-0.379760\pi$
$521$	4.57032e6			0.737653			0.368827	+	0.929498i	$0.379760\pi$
$522$	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	$-0.825417\pi$
$557$		−	7.63525e6i		−	1.04276i	0.853324	−	0.521381i	$-0.174583\pi$
$558$	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	$-0.546205\pi$
$563$	−2.17576e6			−0.289295			−0.144648	+	0.989483i	$0.546205\pi$
$564$	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	$0.182711\pi$
$569$			8.38705e6i			1.08600i	−0.839734	+	0.542998i	$0.817289\pi$
$570$	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	$-0.463512\pi$
$587$	1.90974e6			0.228760			0.114380	+	0.993437i	$0.463512\pi$
$588$		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	$-0.308683\pi$
$593$	9.68502e6			1.13100			0.565502	+	0.824747i	$0.308683\pi$
$594$	−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	$0.0737606\pi$
$599$			4.03346e6i			0.459315i	−0.973271	+	0.229658i	$0.926239\pi$
$600$	−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	$0.287479\pi$
$617$			1.48513e7i			1.57055i	−0.619146	+	0.785276i	$0.712521\pi$
$618$	−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	$-0.923791\pi$
$641$		−	4.93371e6i		−	0.474273i	0.971476	−	0.237137i	$-0.0762089\pi$
$642$	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	$-0.365751\pi$
$647$	8.71767e6			0.818728			0.409364	+	0.912371i	$0.365751\pi$
$648$	−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	$-0.850518\pi$
$653$		−	9.86209e6i		−	0.905078i	0.891745	−	0.452539i	$-0.149482\pi$
$654$	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	$-0.888762\pi$
$659$		−	7.63431e6i		−	0.684788i	0.939556	−	0.342394i	$-0.111238\pi$
$660$	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	$-0.560925\pi$
$677$	−4.53726e6			−0.380472			−0.190236	+	0.981738i	$0.560925\pi$
$678$	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	$0.0117723\pi$
$683$			901559.i			0.0739507i	−0.999316	+	0.0369754i	$0.988228\pi$
$684$	−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	$-0.975160\pi$
$701$		−	2.02857e6i		−	0.155917i	0.996957	−	0.0779587i	$-0.0248402\pi$
$702$	−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	$-0.900130\pi$
$719$	−2.63704e7			−1.90237			−0.951183	+	0.308627i	$0.900130\pi$
$720$	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	$-0.898914\pi$
$743$		−	9.39766e6i		−	0.624522i	0.949996	−	0.312261i	$-0.101086\pi$
$744$	−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	$-0.524762\pi$
$761$	−2.48311e6			−0.155430			−0.0777150	+	0.996976i	$0.524762\pi$
$762$	−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	$-0.403438\pi$
$773$	9.92550e6			0.597453			0.298726	+	0.954339i	$0.403438\pi$
$774$	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	$-0.360303\pi$
$797$	1.52399e7			0.849838			0.424919	+	0.905231i	$0.360303\pi$
$798$		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	$-0.953207\pi$
$809$		−	5.45336e6i		−	0.292949i	0.989214	−	0.146475i	$-0.0467927\pi$
$810$	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	$0.139321\pi$
$821$			1.63719e7i			0.847699i	−0.905733	+	0.423849i	$0.860679\pi$
$822$	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	$-0.738955\pi$
$827$		−	2.87632e7i		−	1.46242i	0.682151	−	0.731211i	$-0.261045\pi$
$828$	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	$-0.701357\pi$
$839$	−2.41096e7			−1.18246			−0.591229	+	0.806504i	$0.701357\pi$
$840$		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	$-0.736405\pi$
$857$	−2.90805e7			−1.35254			−0.676270	+	0.736654i	$0.736405\pi$
$858$	−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	$0.0207907\pi$
$863$			2.85606e6i			0.130539i	−0.997868	+	0.0652695i	$0.979209\pi$
$864$	−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	$-0.480759\pi$
$881$	2.78347e6			0.120822			0.0604111	+	0.998174i	$0.480759\pi$
$882$		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	$-0.134447\pi$
$887$	4.27454e7			1.82423			0.912117	+	0.409930i	$0.134447\pi$
$888$	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	$0.00669310\pi$
$911$			1.05335e6i			0.0420509i	−0.999779	+	0.0210255i	$0.993307\pi$
$912$	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	$-0.721073\pi$
$929$	−3.36714e7			−1.28004			−0.640018	+	0.768360i	$0.721073\pi$
$930$	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	$-0.596969\pi$
$941$	−1.62948e7			−0.599895			−0.299947	+	0.953956i	$0.596969\pi$
$942$	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	$-0.929343\pi$
$947$		−	1.21518e7i		−	0.440317i	0.975464	−	0.220158i	$-0.0706574\pi$
$948$	−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	$0.173930\pi$
$953$			2.91378e7i			1.03926i	−0.854391	+	0.519630i	$0.826070\pi$
$954$	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	$-0.438879\pi$
$971$	1.12136e7			0.381677			0.190838	+	0.981621i	$0.438879\pi$
$972$	−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	$0.157240\pi$
$977$			2.82925e7i			0.948276i	−0.880451	+	0.474138i	$0.842760\pi$
$978$	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	$-0.307770\pi$
$983$	3.44078e7			1.13573			0.567863	+	0.823123i	$0.307770\pi$
$984$	−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.146.3		16
3.2	odd	2	inner	147.6.c.c.146.14		16
7.4	even	3		21.6.g.c.5.7	yes	16
7.5	odd	6		21.6.g.c.17.2	yes	16
7.6	odd	2	inner	147.6.c.c.146.4		16
21.5	even	6		21.6.g.c.17.7	yes	16
21.11	odd	6		21.6.g.c.5.2	✓	16
21.20	even	2	inner	147.6.c.c.146.13		16

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

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

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Representations

Groups

Database

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