LMFDB - Embedded newform 69.5.d.a.22.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,5,Mod(22,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("69.22");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	69.d (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:	$7.13252745279$
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} + 5598 x^{14} + 11369517 x^{12} + 11272666128 x^{10} + 5958872960073 x^{8} + \cdots + 13\!\cdots\!52 $ x^16 + 5598x^14 + 11369517x^12 + 11272666128x^10 + 5958872960073x^8 + 1661250441139200x^6 + 215215956313867368x^4 + 8236967436040727664*x^2 + 13861812915684254052
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			22.2
Root			$32.2151i$ of defining polynomial
Character	$\chi$	$=$	69.22
Dual form			69.5.d.a.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.46704 q^{2} +5.19615 q^{3} +25.8226 q^{4} +30.6703i q^{5} -33.6037 q^{6} -37.9803i q^{7} -63.5230 q^{8} +27.0000 q^{9} +O(q^{10})$	\(q-6.46704 q^{2} +5.19615 q^{3} +25.8226 q^{4} +30.6703i q^{5} -33.6037 q^{6} -37.9803i q^{7} -63.5230 q^{8} +27.0000 q^{9} -198.346i q^{10} +2.87351i q^{11} +134.178 q^{12} -18.8732 q^{13} +245.620i q^{14} +159.368i q^{15} -2.35578 q^{16} +445.446i q^{17} -174.610 q^{18} +401.904i q^{19} +791.987i q^{20} -197.351i q^{21} -18.5831i q^{22} +(60.7534 + 525.500i) q^{23} -330.075 q^{24} -315.668 q^{25} +122.054 q^{26} +140.296 q^{27} -980.749i q^{28} -922.372 q^{29} -1030.64i q^{30} +767.928 q^{31} +1031.60 q^{32} +14.9312i q^{33} -2880.72i q^{34} +1164.87 q^{35} +697.210 q^{36} +1758.86i q^{37} -2599.13i q^{38} -98.0681 q^{39} -1948.27i q^{40} -2565.91 q^{41} +1276.28i q^{42} -17.6066i q^{43} +74.2014i q^{44} +828.099i q^{45} +(-392.894 - 3398.43i) q^{46} -2034.86 q^{47} -12.2410 q^{48} +958.496 q^{49} +2041.44 q^{50} +2314.61i q^{51} -487.355 q^{52} -1304.09i q^{53} -907.300 q^{54} -88.1315 q^{55} +2412.62i q^{56} +2088.35i q^{57} +5965.01 q^{58} +4380.32 q^{59} +4115.28i q^{60} -735.665i q^{61} -4966.22 q^{62} -1025.47i q^{63} -6633.72 q^{64} -578.847i q^{65} -96.5606i q^{66} +3483.41i q^{67} +11502.6i q^{68} +(315.684 + 2730.58i) q^{69} -7533.25 q^{70} +5667.75 q^{71} -1715.12 q^{72} +2214.08 q^{73} -11374.6i q^{74} -1640.26 q^{75} +10378.2i q^{76} +109.137 q^{77} +634.210 q^{78} -3995.75i q^{79} -72.2526i q^{80} +729.000 q^{81} +16593.8 q^{82} -9286.49i q^{83} -5096.12i q^{84} -13662.0 q^{85} +113.862i q^{86} -4792.79 q^{87} -182.534i q^{88} -10926.4i q^{89} -5355.34i q^{90} +716.811i q^{91} +(1568.81 + 13569.8i) q^{92} +3990.27 q^{93} +13159.5 q^{94} -12326.5 q^{95} +5360.36 q^{96} +10200.5i q^{97} -6198.63 q^{98} +77.5848i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{2} + 144 q^{4} - 36 q^{6} + 372 q^{8} + 432 q^{9}+O(q^{10}) $ 16 * q + 12 * q^2 + 144 * q^4 - 36 * q^6 + 372 * q^8 + 432 * q^9	$ 16 q + 12 q^{2} + 144 q^{4} - 36 q^{6} + 372 q^{8} + 432 q^{9} + 104 q^{13} + 680 q^{16} + 324 q^{18} - 732 q^{23} - 1764 q^{24} - 2984 q^{25} + 1800 q^{26} - 3528 q^{29} - 400 q^{31} + 5244 q^{32} + 912 q^{35} + 3888 q^{36} + 2016 q^{39} + 1008 q^{41} - 1168 q^{46} - 8664 q^{47} - 2016 q^{48} + 7240 q^{49} - 18852 q^{50} - 20952 q^{52} - 972 q^{54} + 6816 q^{55} - 13352 q^{58} + 20112 q^{59} + 4248 q^{62} - 896 q^{64} - 10044 q^{69} - 10680 q^{70} + 40368 q^{71} + 10044 q^{72} - 9568 q^{73} + 7560 q^{75} + 2952 q^{77} - 6912 q^{78} + 11664 q^{81} + 71800 q^{82} + 42744 q^{85} + 8352 q^{87} - 9876 q^{92} - 10008 q^{93} + 73720 q^{94} + 33312 q^{95} - 24948 q^{96} - 59052 q^{98}+O(q^{100}) $ 16 * q + 12 * q^2 + 144 * q^4 - 36 * q^6 + 372 * q^8 + 432 * q^9 + 104 * q^13 + 680 * q^16 + 324 * q^18 - 732 * q^23 - 1764 * q^24 - 2984 * q^25 + 1800 * q^26 - 3528 * q^29 - 400 * q^31 + 5244 * q^32 + 912 * q^35 + 3888 * q^36 + 2016 * q^39 + 1008 * q^41 - 1168 * q^46 - 8664 * q^47 - 2016 * q^48 + 7240 * q^49 - 18852 * q^50 - 20952 * q^52 - 972 * q^54 + 6816 * q^55 - 13352 * q^58 + 20112 * q^59 + 4248 * q^62 - 896 * q^64 - 10044 * q^69 - 10680 * q^70 + 40368 * q^71 + 10044 * q^72 - 9568 * q^73 + 7560 * q^75 + 2952 * q^77 - 6912 * q^78 + 11664 * q^81 + 71800 * q^82 + 42744 * q^85 + 8352 * q^87 - 9876 * q^92 - 10008 * q^93 + 73720 * q^94 + 33312 * q^95 - 24948 * q^96 - 59052 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$-1$	$1$

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 $

$2$	−6.46704			−1.61676			−0.808380	−	0.588661i	$-0.799655\pi$
$2$	−6.46704			−1.61676			−0.808380	+	0.588661i	$0.799655\pi$
$3$	5.19615			0.577350
$3$	5.19615			0.577350
$4$	25.8226			1.61391
$5$			30.6703i			1.22681i	0.789767	+	0.613406i	$0.210201\pi$
$5$			30.6703i			1.22681i	−0.789767	+	0.613406i	$0.789799\pi$
$6$	−33.6037			−0.933436
$7$		−	37.9803i		−	0.775108i	−0.921847	−	0.387554i	$-0.873320\pi$
$7$		−	37.9803i		−	0.775108i	0.921847	−	0.387554i	$-0.126680\pi$
$8$	−63.5230			−0.992546
$9$	27.0000			0.333333
$10$		−	198.346i		−	1.98346i
$11$			2.87351i			0.0237480i	0.999930	+	0.0118740i	$0.00377970\pi$
$11$			2.87351i			0.0237480i	−0.999930	+	0.0118740i	$0.996220\pi$
$12$	134.178			0.931792
$13$	−18.8732			−0.111676			−0.0558379	−	0.998440i	$-0.517783\pi$
$13$	−18.8732			−0.111676			−0.0558379	+	0.998440i	$0.517783\pi$
$14$			245.620i			1.25316i
$15$			159.368i			0.708301i
$16$	−2.35578			−0.00920227
$17$			445.446i			1.54134i	0.637237	+	0.770668i	$0.280077\pi$
$17$			445.446i			1.54134i	−0.637237	+	0.770668i	$0.719923\pi$
$18$	−174.610			−0.538920
$19$			401.904i			1.11331i	0.830745	+	0.556654i	$0.187915\pi$
$19$			401.904i			1.11331i	−0.830745	+	0.556654i	$0.812085\pi$
$20$			791.987i			1.97997i
$21$		−	197.351i		−	0.447509i
$22$		−	18.5831i		−	0.0383948i
$23$	60.7534	+	525.500i	0.114846	+	0.993383i
$23$	60.7534	+	525.500i	0.114846	+	0.993383i
$24$	−330.075			−0.573047
$25$	−315.668			−0.505069
$26$	122.054			0.180553
$27$	140.296			0.192450
$28$		−	980.749i		−	1.25096i
$29$	−922.372			−1.09676			−0.548378	−	0.836230i	$-0.684755\pi$
$29$	−922.372			−1.09676			−0.548378	+	0.836230i	$0.684755\pi$
$30$		−	1030.64i		−	1.14515i
$31$	767.928			0.799093			0.399546	−	0.916713i	$-0.369168\pi$
$31$	767.928			0.799093			0.399546	+	0.916713i	$0.369168\pi$
$32$	1031.60			1.00742
$33$			14.9312i			0.0137109i
$34$		−	2880.72i		−	2.49197i
$35$	1164.87			0.950913
$36$	697.210			0.537970
$37$			1758.86i			1.28477i	0.766380	+	0.642387i	$0.222056\pi$
$37$			1758.86i			1.28477i	−0.766380	+	0.642387i	$0.777944\pi$
$38$		−	2599.13i		−	1.79995i
$39$	−98.0681			−0.0644761
$40$		−	1948.27i		−	1.21767i
$41$	−2565.91			−1.52642			−0.763208	−	0.646153i	$-0.776377\pi$
$41$	−2565.91			−1.52642			−0.763208	+	0.646153i	$0.776377\pi$
$42$			1276.28i			0.723514i
$43$		−	17.6066i		−	0.00952221i	−0.999989	−	0.00476110i	$-0.998484\pi$
$43$		−	17.6066i		−	0.00952221i	0.999989	−	0.00476110i	$-0.00151551\pi$
$44$			74.2014i			0.0383272i
$45$			828.099i			0.408938i
$46$	−392.894	−	3398.43i	−0.185678	−	1.60606i
$47$	−2034.86			−0.921166			−0.460583	−	0.887617i	$-0.652360\pi$
$47$	−2034.86			−0.921166			−0.460583	+	0.887617i	$0.652360\pi$
$48$	−12.2410			−0.00531294
$49$	958.496			0.399207
$50$	2041.44			0.816576
$51$			2314.61i			0.889891i
$52$	−487.355			−0.180235
$53$		−	1304.09i		−	0.464252i	−0.972686	−	0.232126i	$-0.925432\pi$
$53$		−	1304.09i		−	0.464252i	0.972686	−	0.232126i	$-0.0745682\pi$
$54$	−907.300			−0.311145
$55$	−88.1315			−0.0291344
$56$			2412.62i			0.769331i
$57$			2088.35i			0.642768i
$58$	5965.01			1.77319
$59$	4380.32			1.25835			0.629175	−	0.777264i	$-0.283393\pi$
$59$	4380.32			1.25835			0.629175	+	0.777264i	$0.283393\pi$
$60$			4115.28i			1.14313i
$61$		−	735.665i		−	0.197706i	−0.995102	−	0.0988532i	$-0.968483\pi$
$61$		−	735.665i		−	0.197706i	0.995102	−	0.0988532i	$-0.0315174\pi$
$62$	−4966.22			−1.29194
$63$		−	1025.47i		−	0.258369i
$64$	−6633.72			−1.61956
$65$		−	578.847i		−	0.137005i
$66$		−	96.5606i		−	0.0221673i
$67$			3483.41i			0.775988i	0.921662	+	0.387994i	$0.126832\pi$
$67$			3483.41i			0.775988i	−0.921662	+	0.387994i	$0.873168\pi$
$68$			11502.6i			2.48758i
$69$	315.684	+	2730.58i	0.0663062	+	0.573530i
$70$	−7533.25			−1.53740
$71$	5667.75			1.12433			0.562165	−	0.827025i	$-0.309968\pi$
$71$	5667.75			1.12433			0.562165	+	0.827025i	$0.309968\pi$
$72$	−1715.12			−0.330849
$73$	2214.08			0.415477			0.207739	−	0.978184i	$-0.433390\pi$
$73$	2214.08			0.415477			0.207739	+	0.978184i	$0.433390\pi$
$74$		−	11374.6i		−	2.07717i
$75$	−1640.26			−0.291602
$76$			10378.2i			1.79678i
$77$	109.137			0.0184073
$78$	634.210			0.104242
$79$		−	3995.75i		−	0.640243i	−0.947377	−	0.320121i	$-0.896276\pi$
$79$		−	3995.75i		−	0.640243i	0.947377	−	0.320121i	$-0.103724\pi$
$80$		−	72.2526i		−	0.0112895i
$81$	729.000			0.111111
$82$	16593.8			2.46785
$83$		−	9286.49i		−	1.34802i	−0.738723	−	0.674009i	$-0.764571\pi$
$83$		−	9286.49i		−	1.34802i	0.738723	−	0.674009i	$-0.235429\pi$
$84$		−	5096.12i		−	0.722240i
$85$	−13662.0			−1.89093
$86$			113.862i			0.0153951i
$87$	−4792.79			−0.633213
$88$		−	182.534i		−	0.0235710i
$89$		−	10926.4i		−	1.37942i	−0.724084	−	0.689712i	$-0.757737\pi$
$89$		−	10926.4i		−	1.37942i	0.724084	−	0.689712i	$-0.242263\pi$
$90$		−	5355.34i		−	0.661154i
$91$			716.811i			0.0865609i
$92$	1568.81	+	13569.8i	0.185351	+	1.60323i
$93$	3990.27			0.461356
$94$	13159.5			1.48930
$95$	−12326.5			−1.36582
$96$	5360.36			0.581637
$97$			10200.5i			1.08412i	0.840338	+	0.542062i	$0.182356\pi$
$97$			10200.5i			1.08412i	−0.840338	+	0.542062i	$0.817644\pi$
$98$	−6198.63			−0.645422
$99$			77.5848i			0.00791601i
$100$	−8151.37			−0.815137
$101$	9869.64			0.967517			0.483758	−	0.875202i	$-0.339271\pi$
$101$	9869.64			0.967517			0.483758	+	0.875202i	$0.339271\pi$
$102$		−	14968.6i		−	1.43874i
$103$			998.879i			0.0941539i	0.998891	+	0.0470769i	$0.0149906\pi$
$103$			998.879i			0.0941539i	−0.998891	+	0.0470769i	$0.985009\pi$
$104$	1198.88			0.110843
$105$	6052.83			0.549010
$106$			8433.57i			0.750585i
$107$			5796.64i			0.506301i	0.967427	+	0.253150i	$0.0814667\pi$
$107$			5796.64i			0.506301i	−0.967427	+	0.253150i	$0.918533\pi$
$108$	3622.81			0.310597
$109$		−	20927.9i		−	1.76146i	−0.473615	−	0.880732i	$-0.657051\pi$
$109$		−	20927.9i		−	1.76146i	0.473615	−	0.880732i	$-0.342949\pi$
$110$	569.949			0.0471033
$111$			9139.28i			0.741765i
$112$			89.4733i			0.00713276i
$113$			24530.2i			1.92107i	0.278156	+	0.960536i	$0.410277\pi$
$113$			24530.2i			1.92107i	−0.278156	+	0.960536i	$0.589723\pi$
$114$		−	13505.5i		−	1.03920i
$115$	−16117.2	+	1863.32i	−1.21870	+	0.140894i
$116$	−23818.0			−1.77007
$117$	−509.577			−0.0372253
$118$	−28327.7			−2.03445
$119$	16918.2			1.19470
$120$		−	10123.5i		−	0.703021i
$121$	14632.7			0.999436
$122$			4757.58i			0.319644i
$123$	−13332.8			−0.881277
$124$	19829.9			1.28966
$125$			9487.30i			0.607187i
$126$			6631.74i			0.417721i
$127$	27149.7			1.68329			0.841643	−	0.540034i	$-0.181589\pi$
$127$	27149.7			1.68329			0.841643	+	0.540034i	$0.181589\pi$
$128$	26394.9			1.61102
$129$		−	91.4864i		−	0.00549765i
$130$			3743.43i			0.221505i
$131$	−23768.2			−1.38501			−0.692505	−	0.721413i	$-0.743493\pi$
$131$	−23768.2			−1.38501			−0.692505	+	0.721413i	$0.743493\pi$
$132$			385.562i			0.0221282i
$133$	15264.4			0.862934
$134$		−	22527.3i		−	1.25459i
$135$			4302.93i			0.236100i
$136$		−	28296.1i		−	1.52985i
$137$		−	33951.5i		−	1.80891i	−0.426566	−	0.904456i	$-0.640277\pi$
$137$		−	33951.5i		−	1.80891i	0.426566	−	0.904456i	$-0.359723\pi$
$138$	−2041.54	−	17658.7i	−0.107201	−	0.927260i
$139$	−12417.8			−0.642708			−0.321354	−	0.946959i	$-0.604138\pi$
$139$	−12417.8			−0.642708			−0.321354	+	0.946959i	$0.604138\pi$
$140$	30079.9			1.53469
$141$	−10573.4			−0.531836
$142$	−36653.6			−1.81777
$143$		−	54.2324i		−	0.00265208i
$144$	−63.6061			−0.00306742
$145$		−	28289.4i		−	1.34551i
$146$	−14318.5			−0.671726
$147$	4980.49			0.230482
$148$			45418.2i			2.07351i
$149$		−	27210.8i		−	1.22566i	−0.790216	−	0.612828i	$-0.790032\pi$
$149$		−	27210.8i		−	1.22566i	0.790216	−	0.612828i	$-0.209968\pi$
$150$	10607.6			0.471450
$151$	19847.0			0.870445			0.435223	−	0.900323i	$-0.356670\pi$
$151$	19847.0			0.870445			0.435223	+	0.900323i	$0.356670\pi$
$152$		−	25530.1i		−	1.10501i
$153$			12027.0i			0.513779i
$154$	−705.792			−0.0297602
$155$			23552.6i			0.980337i
$156$	−2532.37			−0.104059
$157$			19686.5i			0.798673i	0.916805	+	0.399336i	$0.130759\pi$
$157$			19686.5i			0.798673i	−0.916805	+	0.399336i	$0.869241\pi$
$158$			25840.7i			1.03512i
$159$		−	6776.23i		−	0.268036i
$160$			31639.6i			1.23592i
$161$	19958.6	−	2307.43i	0.769980	−	0.0890178i
$162$	−4714.47			−0.179640
$163$	−27266.0			−1.02623			−0.513117	−	0.858318i	$-0.671509\pi$
$163$	−27266.0			−1.02623			−0.513117	+	0.858318i	$0.671509\pi$
$164$	−66258.3			−2.46350
$165$	−457.945			−0.0168207
$166$			60056.1i			2.17942i
$167$	2373.33			0.0850992			0.0425496	−	0.999094i	$-0.486452\pi$
$167$	2373.33			0.0850992			0.0425496	+	0.999094i	$0.486452\pi$
$168$			12536.4i			0.444173i
$169$	−28204.8			−0.987529
$170$	88352.5			3.05718
$171$			10851.4i			0.371102i
$172$		−	454.647i		−	0.0153680i
$173$	−41114.3			−1.37373			−0.686865	−	0.726785i	$-0.741013\pi$
$173$	−41114.3			−1.37373			−0.686865	+	0.726785i	$0.741013\pi$
$174$	30995.1			1.02375
$175$			11989.2i			0.391484i
$176$		−	6.76936i		−	0.000218536i
$177$	22760.8			0.726509
$178$			70661.5i			2.23020i
$179$	42221.7			1.31774			0.658870	−	0.752256i	$-0.271035\pi$
$179$	42221.7			1.31774			0.658870	+	0.752256i	$0.271035\pi$
$180$			21383.6i			0.659989i
$181$		−	38216.7i		−	1.16653i	−0.812282	−	0.583264i	$-0.801775\pi$
$181$		−	38216.7i		−	1.16653i	0.812282	−	0.583264i	$-0.198225\pi$
$182$		−	4635.64i		−	0.139948i
$183$		−	3822.63i		−	0.114146i
$184$	−3859.23	−	33381.3i	−0.113990	−	0.985979i
$185$	−53944.7			−1.57618
$186$	−25805.2			−0.745902
$187$	−1279.99			−0.0366037
$188$	−52545.2			−1.48668
$189$		−	5328.49i		−	0.149170i
$190$	79716.1			2.20820
$191$			7251.62i			0.198778i	0.995049	+	0.0993889i	$0.0316888\pi$
$191$			7251.62i			0.198778i	−0.995049	+	0.0993889i	$0.968311\pi$
$192$	−34469.8			−0.935054
$193$	56100.9			1.50611			0.753053	−	0.657960i	$-0.228580\pi$
$193$	56100.9			1.50611			0.753053	+	0.657960i	$0.228580\pi$
$194$		−	65967.2i		−	1.75277i
$195$		−	3007.78i		−	0.0791001i
$196$	24750.8			0.644285
$197$	611.120			0.0157469			0.00787343	−	0.999969i	$-0.497494\pi$
$197$	611.120			0.0157469			0.00787343	+	0.999969i	$0.497494\pi$
$198$		−	501.744i		−	0.0127983i
$199$			16019.0i			0.404511i	0.979333	+	0.202255i	$0.0648271\pi$
$199$			16019.0i			0.404511i	−0.979333	+	0.202255i	$0.935173\pi$
$200$	20052.2			0.501305
$201$			18100.3i			0.448017i
$202$	−63827.3			−1.56424
$203$			35032.0i			0.850105i
$204$			59769.1i			1.43620i
$205$		−	78697.1i		−	1.87263i
$206$		−	6459.79i		−	0.152224i
$207$	1640.34	+	14188.5i	0.0382819	+	0.331128i
$208$	44.4612			0.00102767
$209$	−1154.88			−0.0264388
$210$	−39143.9			−0.887617
$211$	−71443.1			−1.60470			−0.802352	−	0.596851i	$-0.796419\pi$
$211$	−71443.1			−1.60470			−0.802352	+	0.596851i	$0.796419\pi$
$212$		−	33674.8i		−	0.749262i
$213$	29450.5			0.649133
$214$		−	37487.1i		−	0.818566i
$215$	539.999			0.0116820
$216$	−8912.03			−0.191016
$217$		−	29166.1i		−	0.619383i
$218$			135342.i			2.84786i
$219$	11504.7			0.239876
$220$	−2275.78			−0.0470203
$221$		−	8407.00i		−	0.172130i
$222$		−	59104.1i		−	1.19925i
$223$	33361.2			0.670861			0.335430	−	0.942065i	$-0.391118\pi$
$223$	33361.2			0.670861			0.335430	+	0.942065i	$0.391118\pi$
$224$		−	39180.6i		−	0.780863i
$225$	−8523.05			−0.168356
$226$		−	158637.i		−	3.10591i
$227$			38396.9i			0.745151i	0.928002	+	0.372576i	$0.121525\pi$
$227$			38396.9i			0.745151i	−0.928002	+	0.372576i	$0.878475\pi$
$228$			53926.7i			1.03737i
$229$		−	36981.1i		−	0.705195i	−0.935775	−	0.352598i	$-0.885298\pi$
$229$		−	36981.1i		−	0.705195i	0.935775	−	0.352598i	$-0.114702\pi$
$230$	104231.	−	12050.2i	1.97034	−	0.227792i
$231$	567.091			0.0106275
$232$	58591.8			1.08858
$233$	1258.03			0.0231729			0.0115864	−	0.999933i	$-0.496312\pi$
$233$	1258.03			0.0231729			0.0115864	+	0.999933i	$0.496312\pi$
$234$	3295.45			0.0601843
$235$		−	62409.7i		−	1.13010i
$236$	113111.			2.03087
$237$		−	20762.5i		−	0.369644i
$238$	−109411.			−1.93155
$239$	64284.0			1.12540			0.562700	−	0.826661i	$-0.309762\pi$
$239$	64284.0			1.12540			0.562700	+	0.826661i	$0.309762\pi$
$240$		−	375.435i		−	0.00651798i
$241$		−	75781.7i		−	1.30476i	−0.757893	−	0.652379i	$-0.773771\pi$
$241$		−	75781.7i		−	1.30476i	0.757893	−	0.652379i	$-0.226229\pi$
$242$	−94630.5			−1.61585
$243$	3788.00			0.0641500
$244$		−	18996.8i		−	0.319081i
$245$			29397.4i			0.489752i
$246$	86223.9			1.42481
$247$		−	7585.22i		−	0.124330i
$248$	−48781.1			−0.793137
$249$		−	48254.0i		−	0.778278i
$250$		−	61354.7i		−	0.981676i
$251$			41556.8i			0.659622i	0.944047	+	0.329811i	$0.106985\pi$
$251$			41556.8i			0.659622i	−0.944047	+	0.329811i	$0.893015\pi$
$252$		−	26480.2i		−	0.416985i
$253$	−1510.03	+	174.575i	−0.0235909	+	0.00272736i
$254$	−175578.			−2.72147
$255$	−70989.7			−1.09173
$256$	−64557.1			−0.985064
$257$	−1221.34			−0.0184914			−0.00924571	−	0.999957i	$-0.502943\pi$
$257$	−1221.34			−0.0184914			−0.00924571	+	0.999957i	$0.502943\pi$
$258$			591.646i			0.00888838i
$259$	66801.9			0.995839
$260$		−	14947.3i		−	0.221114i
$261$	−24904.0			−0.365585
$262$	153710.			2.23923
$263$			76995.0i			1.11314i	0.830800	+	0.556571i	$0.187883\pi$
$263$			76995.0i			1.11314i	−0.830800	+	0.556571i	$0.812117\pi$
$264$		−	948.474i		−	0.0136087i
$265$	39996.7			0.569551
$266$	−98715.7			−1.39516
$267$		−	56775.3i		−	0.796410i
$268$			89950.6i			1.25238i
$269$	−42071.1			−0.581405			−0.290703	−	0.956813i	$-0.593889\pi$
$269$	−42071.1			−0.581405			−0.290703	+	0.956813i	$0.593889\pi$
$270$		−	27827.2i		−	0.381717i
$271$	−20682.6			−0.281623			−0.140811	−	0.990036i	$-0.544971\pi$
$271$	−20682.6			−0.281623			−0.140811	+	0.990036i	$0.544971\pi$
$272$		−	1049.37i		−	0.0141838i
$273$			3724.66i			0.0499759i
$274$			219566.i			2.92458i
$275$		−	907.076i		−	0.0119944i
$276$	8151.77	+	70510.5i	0.107012	+	0.925627i
$277$	49755.5			0.648457			0.324229	−	0.945979i	$-0.394895\pi$
$277$	49755.5			0.648457			0.324229	+	0.945979i	$0.394895\pi$
$278$	80306.1			1.03910
$279$	20734.1			0.266364
$280$	−73995.9			−0.943825
$281$			124430.i			1.57584i	0.615777	+	0.787920i	$0.288842\pi$
$281$			124430.i			1.57584i	−0.615777	+	0.787920i	$0.711158\pi$
$282$	68378.7			0.859850
$283$			127805.i			1.59579i	0.602799	+	0.797893i	$0.294052\pi$
$283$			127805.i			1.59579i	−0.602799	+	0.797893i	$0.705948\pi$
$284$	146356.			1.81457
$285$	−64050.5			−0.788556
$286$			350.723i			0.00428777i
$287$			97453.9i			1.18314i
$288$	27853.3			0.335808
$289$	−114901.			−1.37572
$290$			182949.i			2.17537i
$291$			53003.5i			0.625920i
$292$	57173.2			0.670543
$293$		−	154004.i		−	1.79389i	−0.442138	−	0.896947i	$-0.645780\pi$
$293$		−	154004.i		−	1.79389i	0.442138	−	0.896947i	$-0.354220\pi$
$294$	−32209.0			−0.372634
$295$			134346.i			1.54376i
$296$		−	111728.i		−	1.27520i
$297$			403.142i			0.00457031i
$298$			175973.i			1.98159i
$299$	−1146.61	−	9917.87i	−0.0128255	−	0.110937i
$300$	−42355.8			−0.470620
$301$	−668.703			−0.00738074
$302$	−128351.			−1.40730
$303$	51284.1			0.558596
$304$		−	946.798i		−	0.0102450i
$305$	22563.1			0.242549
$306$		−	77779.3i		−	0.830656i
$307$	−97973.3			−1.03952			−0.519758	−	0.854314i	$-0.673978\pi$
$307$	−97973.3			−1.03952			−0.519758	+	0.854314i	$0.673978\pi$
$308$	2818.19			0.0297077
$309$			5190.33i			0.0543598i
$310$		−	152316.i		−	1.58497i
$311$	−24925.3			−0.257704			−0.128852	−	0.991664i	$-0.541129\pi$
$311$	−24925.3			−0.257704			−0.128852	+	0.991664i	$0.541129\pi$
$312$	6229.58			0.0639955
$313$			1190.84i			0.0121553i	0.999982	+	0.00607764i	$0.00193459\pi$
$313$			1190.84i			0.0121553i	−0.999982	+	0.00607764i	$0.998065\pi$
$314$		−	127313.i		−	1.29126i
$315$	31451.4			0.316971
$316$		−	103181.i		−	1.03329i
$317$	129908.			1.29275			0.646377	−	0.763018i	$-0.276283\pi$
$317$	129908.			1.29275			0.646377	+	0.763018i	$0.276283\pi$
$318$			43822.1i			0.433350i
$319$		−	2650.45i		−	0.0260458i
$320$		−	203458.i		−	1.98690i
$321$			30120.2i			0.292313i
$322$	−129073.	+	14922.2i	−1.24487	+	0.143920i
$323$	−179027.			−1.71598
$324$	18824.7			0.179323
$325$	5957.68			0.0564040
$326$	176330.			1.65917
$327$		−	108745.i		−	1.01698i
$328$	162994.			1.51504
$329$			77284.5i			0.714004i
$330$	2961.54			0.0271951
$331$	89871.7			0.820290			0.410145	−	0.912020i	$-0.365478\pi$
$331$	89871.7			0.820290			0.410145	+	0.912020i	$0.365478\pi$
$332$		−	239801.i		−	2.17558i
$333$			47489.1i			0.428258i
$334$	−15348.4			−0.137585
$335$	−106837.			−0.951992
$336$			464.917i			0.00411810i
$337$		−	28151.1i		−	0.247877i	−0.992290	−	0.123938i	$-0.960448\pi$
$337$		−	28151.1i		−	0.247877i	0.992290	−	0.123938i	$-0.0395525\pi$
$338$	182402.			1.59660
$339$			127462.i			1.10913i
$340$	−352787.			−3.05179
$341$			2206.65i			0.0189769i
$342$		−	70176.5i		−	0.599983i
$343$		−	127595.i		−	1.08454i
$344$			1118.42i			0.00945123i
$345$	−83747.7	+	9682.12i	−0.703614	+	0.0813453i
$346$	265888.			2.22099
$347$	17305.7			0.143725			0.0718623	−	0.997415i	$-0.477106\pi$
$347$	17305.7			0.143725			0.0718623	+	0.997415i	$0.477106\pi$
$348$	−123762.			−1.02195
$349$	92761.0			0.761578			0.380789	−	0.924662i	$-0.375652\pi$
$349$	92761.0			0.761578			0.380789	+	0.924662i	$0.375652\pi$
$350$		−	77534.5i		−	0.632935i
$351$	−2647.84			−0.0214920
$352$			2964.32i			0.0239243i
$353$	203342.			1.63184			0.815920	−	0.578165i	$-0.196231\pi$
$353$	203342.			1.63184			0.815920	+	0.578165i	$0.196231\pi$
$354$	−147195.			−1.17459
$355$			173832.i			1.37934i
$356$		−	282148.i		−	2.22627i
$357$	87909.4			0.689762
$358$	−273050.			−2.13047
$359$		−	91489.8i		−	0.709878i	−0.934889	−	0.354939i	$-0.884502\pi$
$359$		−	91489.8i		−	0.709878i	0.934889	−	0.354939i	$-0.115498\pi$
$360$		−	52603.3i		−	0.405890i
$361$	−31205.8			−0.239453
$362$			247149.i			1.88600i
$363$	76034.0			0.577025
$364$			18509.9i			0.139702i
$365$			67906.5i			0.509713i
$366$			24721.1i			0.184546i
$367$			80073.3i			0.594505i	0.954799	+	0.297253i	$0.0960704\pi$
$367$			80073.3i			0.594505i	−0.954799	+	0.297253i	$0.903930\pi$
$368$	−143.122	−	1237.96i	−0.00105684	−	0.00914139i
$369$	−69279.4			−0.508805
$370$	348862.			2.54830
$371$	−49529.6			−0.359846
$372$	103039.			0.744588
$373$			76100.2i			0.546976i	0.961875	+	0.273488i	$0.0881773\pi$
$373$			76100.2i			0.546976i	−0.961875	+	0.273488i	$0.911823\pi$
$374$	8277.77			0.0591793
$375$			49297.5i			0.350560i
$376$	129260.			0.914300
$377$	17408.1			0.122481
$378$			34459.5i			0.241171i
$379$			162209.i			1.12927i	0.825342	+	0.564634i	$0.190983\pi$
$379$			162209.i			1.12927i	−0.825342	+	0.564634i	$0.809017\pi$
$380$	−318303.			−2.20431
$381$	141074.			0.971846
$382$		−	46896.5i		−	0.321376i
$383$		−	209744.i		−	1.42986i	−0.699197	−	0.714929i	$-0.746459\pi$
$383$		−	209744.i		−	1.42986i	0.699197	−	0.714929i	$-0.253541\pi$
$384$	137152.			0.930120
$385$			3347.26i			0.0225823i
$386$	−362807.			−2.43501
$387$		−	475.377i		−	0.00317407i
$388$			263404.i			1.74968i
$389$		−	43194.3i		−	0.285448i	−0.989763	−	0.142724i	$-0.954414\pi$
$389$		−	43194.3i		−	0.285448i	0.989763	−	0.142724i	$-0.0455861\pi$
$390$			19451.4i			0.127886i
$391$	−234082.	+	27062.3i	−1.53114	+	0.177016i
$392$	−60886.5			−0.396231
$393$	−123503.			−0.799636
$394$	−3952.14			−0.0254589
$395$	122551.			0.785458
$396$			2003.44i			0.0127757i
$397$	−167885.			−1.06520			−0.532599	−	0.846367i	$-0.678785\pi$
$397$	−167885.			−1.06520			−0.532599	+	0.846367i	$0.678785\pi$
$398$		−	103596.i		−	0.653996i
$399$	79316.3			0.498215
$400$	743.646			0.00464779
$401$			81170.0i			0.504785i	0.967625	+	0.252393i	$0.0812175\pi$
$401$			81170.0i			0.504785i	−0.967625	+	0.252393i	$0.918783\pi$
$402$		−	117055.i		−	0.724335i
$403$	−14493.3			−0.0892393
$404$	254860.			1.56149
$405$			22358.7i			0.136313i
$406$		−	226553.i		−	1.37442i
$407$	−5054.09			−0.0305108
$408$		−	147031.i		−	0.883258i
$409$	−149090.			−0.891254			−0.445627	−	0.895219i	$-0.647019\pi$
$409$	−149090.			−0.891254			−0.445627	+	0.895219i	$0.647019\pi$
$410$			508937.i			3.02759i
$411$		−	176417.i		−	1.04438i
$412$			25793.6i			0.151956i
$413$		−	166366.i		−	0.975358i
$414$	−10608.1	−	91757.5i	−0.0618926	−	0.535354i
$415$	284820.			1.65376
$416$	−19469.7			−0.112505
$417$	−64524.6			−0.371068
$418$	7468.62			0.0427452
$419$		−	142909.i		−	0.814013i	−0.913425	−	0.407006i	$-0.866573\pi$
$419$		−	142909.i		−	0.814013i	0.913425	−	0.407006i	$-0.133427\pi$
$420$	156300.			0.886053
$421$		−	20088.3i		−	0.113339i	−0.998393	−	0.0566693i	$-0.981952\pi$
$421$		−	20088.3i		−	0.113339i	0.998393	−	0.0566693i	$-0.0180481\pi$
$422$	462025.			2.59442
$423$	−54941.1			−0.307055
$424$			82839.4i			0.460792i
$425$		−	140613.i		−	0.778482i
$426$	−190458.			−1.04949
$427$	−27940.8			−0.153244
$428$			149684.i			0.817124i
$429$		−	281.800i		−	0.00153118i
$430$	−3492.19			−0.0188869
$431$		−	52245.2i		−	0.281249i	−0.990063	−	0.140625i	$-0.955089\pi$
$431$		−	52245.2i		−	0.281249i	0.990063	−	0.140625i	$-0.0449111\pi$
$432$	−330.507			−0.00177098
$433$		−	10421.5i		−	0.0555848i	−0.999614	−	0.0277924i	$-0.991152\pi$
$433$		−	10421.5i		−	0.0555848i	0.999614	−	0.0277924i	$-0.00884773\pi$
$434$			188619.i			1.00139i
$435$		−	146996.i		−	0.776833i
$436$		−	540414.i		−	2.84285i
$437$	−211200.	+	24417.0i	−1.10594	+	0.127859i
$438$	−74401.2			−0.387821
$439$	66984.2			0.347571			0.173785	−	0.984784i	$-0.444400\pi$
$439$	66984.2			0.347571			0.173785	+	0.984784i	$0.444400\pi$
$440$	5598.37			0.0289172
$441$	25879.4			0.133069
$442$			54368.4i			0.278293i
$443$	−222081.			−1.13163			−0.565814	−	0.824533i	$-0.691438\pi$
$443$	−222081.			−1.13163			−0.565814	+	0.824533i	$0.691438\pi$
$444$			236000.i			1.19714i
$445$	335117.			1.69229
$446$	−215748.			−1.08462
$447$		−	141391.i		−	0.707633i
$448$			251951.i			1.25533i
$449$	97092.3			0.481606			0.240803	−	0.970574i	$-0.422589\pi$
$449$	97092.3			0.481606			0.240803	+	0.970574i	$0.422589\pi$
$450$	55118.9			0.272192
$451$		−	7373.15i		−	0.0362493i
$452$			633432.i			3.10044i
$453$	103128.			0.502552
$454$		−	248314.i		−	1.20473i
$455$	−21984.8			−0.106194
$456$		−	132658.i		−	0.637977i
$457$		−	80986.2i		−	0.387774i	−0.981024	−	0.193887i	$-0.937890\pi$
$457$		−	80986.2i		−	0.387774i	0.981024	−	0.193887i	$-0.0621095\pi$
$458$			239158.i			1.14013i
$459$			62494.4i			0.296630i
$460$	−416189.	+	48115.8i	−1.96687	+	0.227391i
$461$	−7531.74			−0.0354400			−0.0177200	−	0.999843i	$-0.505641\pi$
$461$	−7531.74			−0.0354400			−0.0177200	+	0.999843i	$0.505641\pi$
$462$	−3667.40			−0.0171820
$463$	147202.			0.686674			0.343337	−	0.939212i	$-0.388443\pi$
$463$	147202.			0.686674			0.343337	+	0.939212i	$0.388443\pi$
$464$	2172.91			0.0100927
$465$			122383.i			0.565998i
$466$	−8135.75			−0.0374650
$467$		−	91391.0i		−	0.419054i	−0.977803	−	0.209527i	$-0.932808\pi$
$467$		−	91391.0i		−	0.419054i	0.977803	−	0.209527i	$-0.0671924\pi$
$468$	−13158.6			−0.0600783
$469$	132301.			0.601475
$470$			403606.i			1.82710i
$471$			102294.i			0.461114i
$472$	−278251.			−1.24897
$473$	50.5926			0.000226134
$474$			134272.i			0.597626i
$475$		−	126868.i		−	0.562298i
$476$	436871.			1.92814
$477$		−	35210.3i		−	0.154751i
$478$	−415727.			−1.81950
$479$		−	416999.i		−	1.81745i	−0.417390	−	0.908727i	$-0.637055\pi$
$479$		−	416999.i		−	1.81745i	0.417390	−	0.908727i	$-0.362945\pi$
$480$			164404.i			0.713559i
$481$		−	33195.3i		−	0.143478i
$482$			490083.i			2.10948i
$483$	103708.	−	11989.8i	0.444548	−	0.0513945i
$484$	377855.			1.61300
$485$	−312854.			−1.33002
$486$	−24497.1			−0.103715
$487$	−252578.			−1.06497			−0.532485	−	0.846440i	$-0.678742\pi$
$487$	−252578.			−1.06497			−0.532485	+	0.846440i	$0.678742\pi$
$488$			46731.7i			0.196233i
$489$	−141678.			−0.592497
$490$		−	190114.i		−	0.791812i
$491$	458417.			1.90151			0.950753	−	0.309951i	$-0.100313\pi$
$491$	458417.			1.90151			0.950753	+	0.309951i	$0.100313\pi$
$492$	−344288.			−1.42230
$493$		−	410867.i		−	1.69047i
$494$			49053.9i			0.201011i
$495$	−2379.55			−0.00971146
$496$	−1809.07			−0.00735347
$497$		−	215263.i		−	0.871478i
$498$			312061.i			1.25829i
$499$	−57901.6			−0.232536			−0.116268	−	0.993218i	$-0.537093\pi$
$499$	−57901.6			−0.232536			−0.116268	+	0.993218i	$0.537093\pi$
$500$			244987.i			0.979946i
$501$	12332.2			0.0491320
$502$		−	268750.i		−	1.06645i
$503$		−	244716.i		−	0.967223i	−0.875283	−	0.483611i	$-0.839325\pi$
$503$		−	244716.i		−	0.967223i	0.875283	−	0.483611i	$-0.160675\pi$
$504$			65140.8i			0.256444i
$505$			302705.i			1.18696i
$506$	9765.41	−	1128.99i	0.0381408	−	0.00440948i
$507$	−146556.			−0.570150
$508$	701076.			2.71667
$509$	65168.6			0.251537			0.125769	−	0.992060i	$-0.459860\pi$
$509$	65168.6			0.251537			0.125769	+	0.992060i	$0.459860\pi$
$510$	459093.			1.76506
$511$		−	84091.3i		−	0.322040i
$512$	−4824.57			−0.0184043
$513$			56385.6i			0.214256i
$514$	7898.45			0.0298962
$515$	−30635.9			−0.115509
$516$		−	2362.41i		−	0.00887272i
$517$		−	5847.18i		−	0.0218759i
$518$	−432010.			−1.61003
$519$	−213636.			−0.793123
$520$			36770.1i			0.135984i
$521$			73665.5i			0.271387i	0.990751	+	0.135693i	$0.0433262\pi$
$521$			73665.5i			0.271387i	−0.990751	+	0.135693i	$0.956674\pi$
$522$	161055.			0.591064
$523$			443396.i			1.62102i	0.585726	+	0.810509i	$0.300810\pi$
$523$			443396.i			1.62102i	−0.585726	+	0.810509i	$0.699190\pi$
$524$	−613755.			−2.23528
$525$			62297.6i			0.226023i
$526$		−	497929.i		−	1.79968i
$527$			342071.i			1.23167i
$528$		−	35.1746i		−	0.000126172i
$529$	−272459.	+	63851.8i	−0.973621	+	0.228172i
$530$	−258660.			−0.920827
$531$	118269.			0.419450
$532$	394167.			1.39270
$533$	48426.9			0.170464
$534$			367168.i			1.28760i
$535$	−177785.			−0.621136
$536$		−	221276.i		−	0.770204i
$537$	219391.			0.760798
$538$	272075.			0.939992
$539$			2754.25i			0.00948037i
$540$			111113.i			0.381045i
$541$	217747.			0.743974			0.371987	−	0.928238i	$-0.378677\pi$
$541$	217747.			0.743974			0.371987	+	0.928238i	$0.378677\pi$
$542$	133755.			0.455316
$543$		−	198580.i		−	0.673496i
$544$			459523.i			1.55278i
$545$	641867.			2.16099
$546$		−	24087.5i		−	0.0807991i
$547$	400661.			1.33907			0.669533	−	0.742782i	$-0.266494\pi$
$547$	400661.			1.33907			0.669533	+	0.742782i	$0.266494\pi$
$548$		−	876715.i		−	2.91942i
$549$		−	19863.0i		−	0.0659021i
$550$			5866.10i			0.0193921i
$551$		−	370705.i		−	1.22103i
$552$	−20053.2	−	173454.i	−0.0658120	−	0.569255i
$553$	−151760.			−0.496257
$554$	−321770.			−1.04840
$555$	−280305.			−0.910006
$556$	−320659.			−1.03727
$557$			344709.i			1.11107i	0.831492	+	0.555536i	$0.187487\pi$
$557$			344709.i			1.11107i	−0.831492	+	0.555536i	$0.812513\pi$
$558$	−134088.			−0.430647
$559$			332.292i			0.00106340i
$560$	−2744.18			−0.00875056
$561$	−6651.04			−0.0211331
$562$		−	804693.i		−	2.54776i
$563$		−	301392.i		−	0.950857i	−0.879754	−	0.475429i	$-0.842293\pi$
$563$		−	301392.i		−	0.950857i	0.879754	−	0.475429i	$-0.157707\pi$
$564$	−273033.			−0.858335
$565$	−752348.			−2.35680
$566$		−	826519.i		−	2.58000i
$567$		−	27687.6i		−	0.0861232i
$568$	−360032.			−1.11595
$569$			21821.5i			0.0674000i	0.999432	+	0.0337000i	$0.0107291\pi$
$569$			21821.5i			0.0674000i	−0.999432	+	0.0337000i	$0.989271\pi$
$570$	414217.			1.27491
$571$			324837.i			0.996307i	0.867089	+	0.498153i	$0.165988\pi$
$571$			324837.i			0.996307i	−0.867089	+	0.498153i	$0.834012\pi$
$572$		−	1400.42i		−	0.00428022i
$573$			37680.5i			0.114764i
$574$		−	630238.i		−	1.91285i
$575$	−19177.9	−	165884.i	−0.0580050	−	0.501728i
$576$	−179110.			−0.539853
$577$	30900.0			0.0928127			0.0464063	−	0.998923i	$-0.485223\pi$
$577$	30900.0			0.0928127			0.0464063	+	0.998923i	$0.485223\pi$
$578$	743070.			2.22420
$579$	291509.			0.869550
$580$		−	730506.i		−	2.17154i
$581$	−352704.			−1.04486
$582$		−	342776.i		−	1.01196i
$583$	3747.30			0.0110251
$584$	−140645.			−0.412380
$585$		−	15628.9i		−	0.0456684i
$586$			995950.i			2.90029i
$587$	360981.			1.04763			0.523816	−	0.851831i	$-0.324508\pi$
$587$	360981.			1.04763			0.523816	+	0.851831i	$0.324508\pi$
$588$	128609.			0.371978
$589$			308633.i			0.889636i
$590$		−	868819.i		−	2.49589i
$591$	3175.47			0.00909146
$592$		−	4143.48i		−	0.0118228i
$593$	376995.			1.07208			0.536038	−	0.844194i	$-0.319920\pi$
$593$	376995.			1.07208			0.536038	+	0.844194i	$0.319920\pi$
$594$		−	2607.14i		−	0.00738909i
$595$			518886.i			1.46568i
$596$		−	702653.i		−	1.97810i
$597$			83237.3i			0.233544i
$598$	7415.18	+	64139.2i	0.0207357	+	0.179358i
$599$	44444.7			0.123870			0.0619350	−	0.998080i	$-0.480273\pi$
$599$	44444.7			0.123870			0.0619350	+	0.998080i	$0.480273\pi$
$600$	104194.			0.289428
$601$	132070.			0.365643			0.182821	−	0.983146i	$-0.441477\pi$
$601$	132070.			0.365643			0.182821	+	0.983146i	$0.441477\pi$
$602$	4324.53			0.0119329
$603$			94052.0i			0.258663i
$604$	512501.			1.40482
$605$			448791.i			1.22612i
$606$	−331657.			−0.903115
$607$	300182.			0.814719			0.407360	−	0.913268i	$-0.366450\pi$
$607$	300182.			0.814719			0.407360	+	0.913268i	$0.366450\pi$
$608$			414605.i			1.12157i
$609$			182031.i			0.490808i
$610$	−145916.			−0.392143
$611$	38404.3			0.102872
$612$			310569.i			0.829193i
$613$		−	236992.i		−	0.630686i	−0.948978	−	0.315343i	$-0.897881\pi$
$613$		−	236992.i		−	0.630686i	0.948978	−	0.315343i	$-0.102119\pi$
$614$	633597.			1.68065
$615$		−	408922.i		−	1.08116i
$616$	−6932.69			−0.0182701
$617$		−	109059.i		−	0.286479i	−0.989688	−	0.143239i	$-0.954248\pi$
$617$		−	109059.i		−	0.286479i	0.989688	−	0.143239i	$-0.0457519\pi$
$618$		−	33566.0i		−	0.0878867i
$619$			316224.i			0.825304i	0.910889	+	0.412652i	$0.135397\pi$
$619$			316224.i			0.825304i	−0.910889	+	0.412652i	$0.864603\pi$
$620$			608189.i			1.58218i
$621$	8523.46	+	73725.6i	0.0221021	+	0.191177i
$622$	161193.			0.416645
$623$	−414989.			−1.06920
$624$	231.027			0.000593326
$625$	−488271.			−1.24997
$626$		−	7701.22i		−	0.0196522i
$627$	−6000.91			−0.0152645
$628$			508356.i			1.28899i
$629$	−783475.			−1.98027
$630$	−203398.			−0.512466
$631$			383989.i			0.964407i	0.876059	+	0.482203i	$0.160163\pi$
$631$			383989.i			0.964407i	−0.876059	+	0.482203i	$0.839837\pi$
$632$			253822.i			0.635470i
$633$	−371229.			−0.926477
$634$	−840117.			−2.09007
$635$			832691.i			2.06508i
$636$		−	174980.i		−	0.432587i
$637$	−18089.9			−0.0445818
$638$			17140.5i			0.0421098i
$639$	153029.			0.374777
$640$			809539.i			1.97641i
$641$			676424.i			1.64628i	0.567841	+	0.823138i	$0.307779\pi$
$641$			676424.i			1.64628i	−0.567841	+	0.823138i	$0.692221\pi$
$642$		−	194789.i		−	0.472600i
$643$		−	143739.i		−	0.347659i	−0.984776	−	0.173830i	$-0.944386\pi$
$643$		−	143739.i		−	0.347659i	0.984776	−	0.173830i	$-0.0556142\pi$
$644$	515384.	−	59583.8i	1.24268	−	0.143667i
$645$	2805.92			0.00674459
$646$	1.15777e6			2.77433
$647$	−590807.			−1.41136			−0.705679	−	0.708532i	$-0.749358\pi$
$647$	−590807.			−1.41136			−0.705679	+	0.708532i	$0.749358\pi$
$648$	−46308.2			−0.110283
$649$			12586.9i			0.0298833i
$650$	−38528.5			−0.0911918
$651$		−	151552.i		−	0.357601i
$652$	−704079.			−1.65625
$653$	−231344.			−0.542541			−0.271270	−	0.962503i	$-0.587444\pi$
$653$	−231344.			−0.542541			−0.271270	+	0.962503i	$0.587444\pi$
$654$			703257.i			1.64421i
$655$		−	728977.i		−	1.69915i
$656$	6044.71			0.0140465
$657$	59780.1			0.138492
$658$		−	499802.i		−	1.15437i
$659$			564690.i			1.30029i	0.759812	+	0.650143i	$0.225291\pi$
$659$			564690.i			1.30029i	−0.759812	+	0.650143i	$0.774709\pi$
$660$	−11825.3			−0.0271472
$661$			640670.i			1.46633i	0.680051	+	0.733165i	$0.261958\pi$
$661$			640670.i			1.46633i	−0.680051	+	0.733165i	$0.738042\pi$
$662$	−581204.			−1.32621
$663$		−	43684.0i		−	0.0993793i
$664$			589905.i			1.33797i
$665$			468165.i			1.05866i
$666$		−	307114.i		−	0.692390i
$667$	−56037.2	−	484706.i	−0.125958	−	1.08950i
$668$	61285.5			0.137342
$669$	173350.			0.387322
$670$	690921.			1.53914
$671$	2113.94			0.00469513
$672$		−	203588.i		−	0.450831i
$673$	460196.			1.01604			0.508022	−	0.861344i	$-0.330377\pi$
$673$	460196.			1.01604			0.508022	+	0.861344i	$0.330377\pi$
$674$			182054.i			0.400757i
$675$	−44287.0			−0.0972007
$676$	−728321.			−1.59378
$677$		−	156681.i		−	0.341852i	−0.985284	−	0.170926i	$-0.945324\pi$
$677$		−	156681.i		−	0.341852i	0.985284	−	0.170926i	$-0.0546759\pi$
$678$		−	824305.i		−	1.79320i
$679$	387419.			0.840314
$680$	867849.			1.87684
$681$			199516.i			0.430213i
$682$		−	14270.5i		−	0.0306810i
$683$	448126.			0.960635			0.480318	−	0.877095i	$-0.340521\pi$
$683$	448126.			0.960635			0.480318	+	0.877095i	$0.340521\pi$
$684$			280211.i			0.598926i
$685$	1.04130e6			2.21920
$686$			825160.i			1.75344i
$687$		−	192160.i		−	0.407145i
$688$			41.4772i			8.76260e-5i
$689$			24612.3i			0.0518458i
$690$	541599.	−	62614.6i	1.13757	−	0.131516i
$691$	−274108.			−0.574070			−0.287035	−	0.957920i	$-0.592670\pi$
$691$	−274108.			−0.574070			−0.287035	+	0.957920i	$0.592670\pi$
$692$	−1.06168e6			−2.21708
$693$	2946.69			0.00613576
$694$	−111917.			−0.232368
$695$		−	380857.i		−	0.788482i
$696$	304452.			0.628493
$697$		−	1.14297e6i		−	2.35272i
$698$	−599889.			−1.23129
$699$	6536.93			0.0133789
$700$			309592.i			0.631820i
$701$			247781.i			0.504234i	0.967697	+	0.252117i	$0.0811267\pi$
$701$			247781.i			0.504234i	−0.967697	+	0.252117i	$0.918873\pi$
$702$	17123.7			0.0347474
$703$	−706891.			−1.43035
$704$		−	19062.1i		−	0.0384613i
$705$		−	324290.i		−	0.652463i
$706$	−1.31502e6			−2.63829
$707$		−	374852.i		−	0.749930i
$708$	587742.			1.17252
$709$		−	360175.i		−	0.716508i	−0.933624	−	0.358254i	$-0.883372\pi$
$709$		−	360175.i		−	0.716508i	0.933624	−	0.358254i	$-0.116628\pi$
$710$		−	1.12418e6i		−	2.23007i
$711$		−	107885.i		−	0.213414i
$712$			694078.i			1.36914i
$713$	46654.2	+	403546.i	0.0917723	+	0.793805i
$714$	−568514.			−1.11518
$715$	1663.32			0.00325360
$716$	1.09027e6			2.12672
$717$	334030.			0.649750
$718$			591668.i			1.14770i
$719$	380773.			0.736559			0.368280	−	0.929715i	$-0.379947\pi$
$719$	380773.			0.736559			0.368280	+	0.929715i	$0.379947\pi$
$720$		−	1950.82i		−	0.00376316i
$721$	37937.7			0.0729795
$722$	201809.			0.387139
$723$		−	393773.i		−	0.753303i
$724$		−	986853.i		−	1.88267i
$725$	291164.			0.553938
$726$	−491714.			−0.932910
$727$		−	115974.i		−	0.219428i	−0.993963	−	0.109714i	$-0.965007\pi$
$727$		−	115974.i		−	0.219428i	0.993963	−	0.109714i	$-0.0349934\pi$
$728$		−	45533.9i		−	0.0859157i
$729$	19683.0			0.0370370
$730$		−	439154.i		−	0.824083i
$731$	7842.77			0.0146769
$732$		−	98710.2i		−	0.184221i
$733$			564579.i			1.05079i	0.850858	+	0.525396i	$0.176083\pi$
$733$			564579.i			1.05079i	−0.850858	+	0.525396i	$0.823917\pi$
$734$		−	517837.i		−	0.961172i
$735$			152753.i			0.282759i
$736$	62673.3	+	542107.i	0.115698	+	1.00076i
$737$	−10009.6			−0.0184282
$738$	448033.			0.822616
$739$	−181881.			−0.333042			−0.166521	−	0.986038i	$-0.553253\pi$
$739$	−181881.			−0.333042			−0.166521	+	0.986038i	$0.553253\pi$
$740$	−1.39299e6			−2.54381
$741$		−	39414.0i		−	0.0717817i
$742$	320310.			0.581784
$743$		−	750026.i		−	1.35862i	−0.733850	−	0.679311i	$-0.762279\pi$
$743$		−	750026.i		−	1.35862i	0.733850	−	0.679311i	$-0.237721\pi$
$744$	−253474.			−0.457918
$745$	834564.			1.50365
$746$		−	492143.i		−	0.884328i
$747$		−	250735.i		−	0.449339i
$748$	−33052.7			−0.0590751
$749$	220158.			0.392438
$750$		−	318808.i		−	0.566771i
$751$			764417.i			1.35535i	0.735363	+	0.677674i	$0.237012\pi$
$751$			764417.i			1.35535i	−0.735363	+	0.677674i	$0.762988\pi$
$752$	4793.68			0.00847683
$753$			215936.i			0.380833i
$754$	−112579.			−0.198023
$755$			608715.i			1.06787i
$756$		−	137595.i		−	0.240747i
$757$		−	1.05333e6i		−	1.83811i	−0.394130	−	0.919055i	$-0.628954\pi$
$757$		−	1.05333e6i		−	1.83811i	0.394130	−	0.919055i	$-0.371046\pi$
$758$		−	1.04901e6i		−	1.82575i
$759$	−7846.34	+	907.120i	−0.0136202	+	0.00157464i
$760$	783017.			1.35564
$761$	−869147.			−1.50080			−0.750402	−	0.660982i	$-0.770140\pi$
$761$	−869147.			−1.50080			−0.750402	+	0.660982i	$0.770140\pi$
$762$	−912332.			−1.57124
$763$	−794850.			−1.36533
$764$			187255.i			0.320810i
$765$	−368873.			−0.630310
$766$			1.35643e6i			2.31174i
$767$	−82670.7			−0.140527
$768$	−335449.			−0.568727
$769$		−	213097.i		−	0.360350i	−0.983635	−	0.180175i	$-0.942334\pi$
$769$		−	213097.i		−	0.360350i	0.983635	−	0.180175i	$-0.0576665\pi$
$770$		−	21646.9i		−	0.0365101i
$771$	−6346.27			−0.0106760
$772$	1.44867e6			2.43072
$773$			679272.i			1.13680i	0.822752	+	0.568401i	$0.192438\pi$
$773$			679272.i			1.13680i	−0.822752	+	0.568401i	$0.807562\pi$
$774$			3074.28i			0.00513171i
$775$	−242411.			−0.403597
$776$		−	647968.i		−	1.07604i
$777$	347113.			0.574948
$778$			279339.i			0.461501i
$779$		−	1.03125e6i		−	1.69937i
$780$		−	77668.6i		−	0.127660i
$781$			16286.3i			0.0267006i
$782$	1.51382e6	−	175013.i	2.47548	−	0.286192i
$783$	−129405.			−0.211071
$784$	−2258.01			−0.00367361
$785$	−603791.			−0.979822
$786$	798698.			1.29282
$787$			57080.5i			0.0921591i	0.998938	+	0.0460795i	$0.0146728\pi$
$787$			57080.5i			0.0921591i	−0.998938	+	0.0460795i	$0.985327\pi$
$788$	15780.7			0.0254140
$789$			400078.i			0.642673i
$790$	−792542.			−1.26990
$791$	931663.			1.48904
$792$		−	4928.41i		−	0.00785700i
$793$			13884.4i			0.0220790i
$794$	1.08572e6			1.72217
$795$	207829.			0.328830
$796$			413652.i			0.652844i
$797$			166613.i			0.262297i	0.991363	+	0.131148i	$0.0418664\pi$
$797$			166613.i			0.262297i	−0.991363	+	0.131148i	$0.958134\pi$
$798$	−512942.			−0.805494
$799$		−	906419.i		−	1.41983i
$800$	−325644.			−0.508819
$801$		−	295013.i		−	0.459808i
$802$		−	524929.i		−	0.816116i
$803$			6362.17i			0.00986676i
$804$			467397.i			0.723059i
$805$	70769.7	+	612138.i	0.109208	+	0.944621i
$806$	93728.5			0.144279
$807$	−218608.			−0.335674
$808$	−626949.			−0.960305
$809$	−92633.7			−0.141538			−0.0707688	−	0.997493i	$-0.522545\pi$
$809$	−92633.7			−0.141538			−0.0707688	+	0.997493i	$0.522545\pi$
$810$		−	144594.i		−	0.220385i
$811$	−1.07406e6			−1.63300			−0.816501	−	0.577345i	$-0.804089\pi$
$811$	−1.07406e6			−1.63300			−0.816501	+	0.577345i	$0.804089\pi$
$812$			904616.i			1.37199i
$813$	−107470.			−0.162595
$814$	32685.0			0.0493287
$815$		−	836258.i		−	1.25900i
$816$		−	5452.71i		−	0.00818902i
$817$	7076.15			0.0106011
$818$	964170.			1.44094
$819$			19353.9i			0.0288536i
$820$		−	2.03216e6i		−	3.02225i
$821$	−90301.1			−0.133970			−0.0669849	−	0.997754i	$-0.521338\pi$
$821$	−90301.1			−0.133970			−0.0669849	+	0.997754i	$0.521338\pi$
$822$			1.14090e6i			1.68851i
$823$	1.01440e6			1.49765			0.748827	−	0.662765i	$-0.230617\pi$
$823$	1.01440e6			1.49765			0.748827	+	0.662765i	$0.230617\pi$
$824$		−	63451.7i		−	0.0934521i
$825$		−	4713.31i		−	0.00692497i
$826$			1.07589e6i			1.57692i
$827$			633034.i			0.925584i	0.886467	+	0.462792i	$0.153152\pi$
$827$			633034.i			0.925584i	−0.886467	+	0.462792i	$0.846848\pi$
$828$	42357.8	+	366383.i	0.0617836	+	0.534411i
$829$	431150.			0.627364			0.313682	−	0.949528i	$-0.398437\pi$
$829$	431150.			0.627364			0.313682	+	0.949528i	$0.398437\pi$
$830$	−1.84194e6			−2.67374
$831$	258537.			0.374387
$832$	125200.			0.180866
$833$			426958.i			0.615312i
$834$	417283.			0.599927
$835$			72790.8i			0.104401i
$836$	−29821.9			−0.0426699
$837$	107737.			0.153785
$838$			924197.i			1.31606i
$839$			363057.i			0.515764i	0.966176	+	0.257882i	$0.0830246\pi$
$839$			363057.i			0.515764i	−0.966176	+	0.257882i	$0.916975\pi$
$840$	−384494.			−0.544918
$841$	143489.			0.202874
$842$			129911.i			0.183241i
$843$			646557.i			0.909812i
$844$	−1.84484e6			−2.58985
$845$		−	865050.i		−	1.21151i
$846$	355306.			0.496435
$847$		−	555756.i		−	0.774671i
$848$			3072.14i			0.00427218i
$849$			664094.i			0.921327i
$850$			909351.i			1.25862i
$851$	−924278.	+	106856.i	−1.27627	+	0.147551i
$852$	760488.			1.04764
$853$	−249641.			−0.343097			−0.171549	−	0.985176i	$-0.554877\pi$
$853$	−249641.			−0.343097			−0.171549	+	0.985176i	$0.554877\pi$
$854$	180694.			0.247758
$855$	−332816.			−0.455273
$856$		−	368220.i		−	0.502527i
$857$	−995475.			−1.35540			−0.677702	−	0.735337i	$-0.737024\pi$
$857$	−995475.			−1.35540			−0.677702	+	0.735337i	$0.737024\pi$
$858$			1822.41i			0.00247555i
$859$	−265730.			−0.360125			−0.180063	−	0.983655i	$-0.557630\pi$
$859$	−265730.			−0.360125			−0.180063	+	0.983655i	$0.557630\pi$
$860$	13944.2			0.0188537
$861$			506385.i			0.683085i
$862$			337871.i			0.454713i
$863$	1.24867e6			1.67658			0.838292	−	0.545222i	$-0.183555\pi$
$863$	1.24867e6			1.67658			0.838292	+	0.545222i	$0.183555\pi$
$864$	144730.			0.193879
$865$		−	1.26099e6i		−	1.68531i
$866$			67396.5i			0.0898672i
$867$	−597044.			−0.794270
$868$		−	753145.i		−	0.999630i
$869$	11481.8			0.0152045
$870$			950630.i			1.25595i
$871$		−	65743.1i		−	0.0866591i
$872$			1.32941e6i			1.74833i
$873$			275414.i			0.361375i
$874$	1.36584e6	−	157906.i	1.78804	−	0.206716i
$875$	360331.			0.470636
$876$	297081.			0.387138
$877$	−1.11188e6			−1.44563			−0.722816	−	0.691040i	$-0.757153\pi$
$877$	−1.11188e6			−1.44563			−0.722816	+	0.691040i	$0.757153\pi$
$878$	−433189.			−0.561938
$879$		−	800228.i		−	1.03571i
$880$	207.619			0.000268102
$881$			494568.i			0.637198i	0.947890	+	0.318599i	$0.103212\pi$
$881$			494568.i			0.637198i	−0.947890	+	0.318599i	$0.896788\pi$
$882$	−167363.			−0.215141
$883$	1.25154e6			1.60518			0.802588	−	0.596533i	$-0.203456\pi$
$883$	1.25154e6			1.60518			0.802588	+	0.596533i	$0.203456\pi$
$884$		−	217090.i		−	0.277802i
$885$			698081.i			0.891290i
$886$	1.43621e6			1.82957
$887$	954894.			1.21369			0.606845	−	0.794820i	$-0.292435\pi$
$887$	954894.			1.21369			0.606845	+	0.794820i	$0.292435\pi$
$888$		−	580554.i		−	0.736236i
$889$		−	1.03116e6i		−	1.30473i
$890$	−2.16721e6			−2.73603
$891$			2094.79i			0.00263867i
$892$	861473.			1.08271
$893$		−	817817.i		−	1.02554i
$894$			914384.i			1.14407i
$895$			1.29495e6i			1.61662i
$896$		−	1.00249e6i		−	1.24871i
$897$	−5957.97	−	51534.8i	−0.00740480	−	0.0640495i
$898$	−627899.			−0.778641
$899$	−708315.			−0.876410
$900$	−220087.			−0.271712
$901$	580900.			0.715569
$902$			47682.5i			0.0586065i
$903$	−3474.68			−0.00426127
$904$		−	1.55823e6i		−	1.90675i
$905$	1.17212e6			1.43111
$906$	−666934.			−0.812505
$907$			901053.i			1.09531i	0.836705	+	0.547653i	$0.184479\pi$
$907$			901053.i			1.09531i	−0.836705	+	0.547653i	$0.815521\pi$
$908$			991507.i			1.20261i
$909$	266480.			0.322506
$910$	142177.			0.171690
$911$		−	433818.i		−	0.522722i	−0.965241	−	0.261361i	$-0.915829\pi$
$911$		−	433818.i		−	0.522722i	0.965241	−	0.261361i	$-0.0841713\pi$
$912$		−	4919.71i		−	0.00591493i
$913$	26684.8			0.0320127
$914$			523741.i			0.626937i
$915$	117241.			0.140036
$916$		−	954949.i		−	1.13812i
$917$			902722.i			1.07353i
$918$		−	404153.i		−	0.479580i
$919$		−	885622.i		−	1.04862i	−0.851528	−	0.524309i	$-0.824324\pi$
$919$		−	885622.i		−	1.04862i	0.851528	−	0.524309i	$-0.175676\pi$
$920$	1.02382e6	−	118364.i	1.20961	−	0.139844i
$921$	−509084.			−0.600165
$922$	48708.1			0.0572980
$923$	−106969.			−0.125561
$924$	14643.8			0.0171518
$925$		−	555215.i		−	0.648900i
$926$	−951959.			−1.11019
$927$			26969.7i			0.0313846i
$928$	−951521.			−1.10490
$929$	873695.			1.01234			0.506172	−	0.862432i	$-0.331060\pi$
$929$	873695.			1.01234			0.506172	+	0.862432i	$0.331060\pi$
$930$		−	791455.i		−	0.915082i
$931$			385223.i			0.444440i
$932$	32485.7			0.0373990
$933$	−129516.			−0.148785
$934$			591029.i			0.677509i
$935$		−	39257.8i		−	0.0449058i
$936$	32369.8			0.0369478
$937$			1.14527e6i			1.30445i	0.758026	+	0.652224i	$0.226164\pi$
$937$			1.14527e6i			1.30445i	−0.758026	+	0.652224i	$0.773836\pi$
$938$	−855595.			−0.972440
$939$			6187.79i			0.00701786i
$940$		−	1.61158e6i		−	1.82388i
$941$		−	436365.i		−	0.492800i	−0.969168	−	0.246400i	$-0.920752\pi$
$941$		−	436365.i		−	0.492800i	0.969168	−	0.246400i	$-0.0792477\pi$
$942$		−	661539.i		−	0.745510i
$943$	−155887.	−	1.34838e6i	−0.175302	−	1.51632i
$944$	−10319.1			−0.0115797
$945$	163426.			0.183003
$946$	−327.184			−0.000365604
$947$	185120.			0.206421			0.103211	−	0.994660i	$-0.467088\pi$
$947$	185120.			0.206421			0.103211	+	0.994660i	$0.467088\pi$
$948$		−	536142.i		−	0.596573i
$949$	−41786.8			−0.0463987
$950$			820463.i			0.909100i
$951$	675020.			0.746372
$952$	−1.07469e6			−1.18580
$953$		−	874426.i		−	0.962803i	−0.876500	−	0.481401i	$-0.840128\pi$
$953$		−	874426.i		−	0.962803i	0.876500	−	0.481401i	$-0.159872\pi$
$954$			227706.i			0.250195i
$955$	−222409.			−0.243863
$956$	1.65998e6			1.81630
$957$		−	13772.1i		−	0.0150375i
$958$			2.69675e6i			2.93839i
$959$	−1.28949e6			−1.40210
$960$		−	1.05720e6i		−	1.14714i
$961$	−333807.			−0.361451
$962$			214675.i			0.231970i
$963$			156509.i			0.168767i
$964$		−	1.95688e6i		−	2.10576i
$965$			1.72063e6i			1.84771i
$966$	−670685.	+	77538.3i	−0.718727	+	0.0830925i
$967$	642170.			0.686748			0.343374	−	0.939199i	$-0.388430\pi$
$967$	642170.			0.686748			0.343374	+	0.939199i	$0.388430\pi$
$968$	−929515.			−0.991987
$969$	−930249.			−0.990722
$970$	2.02324e6			2.15032
$971$			129817.i			0.137687i	0.997627	+	0.0688433i	$0.0219309\pi$
$971$			129817.i			0.137687i	−0.997627	+	0.0688433i	$0.978069\pi$
$972$	97815.8			0.103532
$973$			471630.i			0.498168i
$974$	1.63343e6			1.72180
$975$	30957.0			0.0325649
$976$			1733.07i			0.00181935i
$977$			386284.i			0.404685i	0.979315	+	0.202343i	$0.0648554\pi$
$977$			386284.i			0.404685i	−0.979315	+	0.202343i	$0.935145\pi$
$978$	916240.			0.957925
$979$	31397.2			0.0327586
$980$			759116.i			0.790417i
$981$		−	565055.i		−	0.587155i
$982$	−2.96460e6			−3.07428
$983$			270499.i			0.279936i	0.990156	+	0.139968i	$0.0446999\pi$
$983$			270499.i			0.279936i	−0.990156	+	0.139968i	$0.955300\pi$
$984$	846941.			0.874708
$985$			18743.2i			0.0193185i
$986$			2.65709e6i			2.73308i
$987$			401582.i			0.412230i
$988$		−	195870.i		−	0.200657i
$989$	9252.25	−	1069.66i	0.00945920	−	0.00109358i
$990$	15388.6			0.0157011
$991$	−217838.			−0.221813			−0.110906	−	0.993831i	$-0.535375\pi$
$991$	−217838.			−0.221813			−0.110906	+	0.993831i	$0.535375\pi$
$992$	792197.			0.805025
$993$	466987.			0.473594
$994$			1.39211e6i			1.40897i
$995$	−491308.			−0.496259
$996$		−	1.24604e6i		−	1.25607i
$997$	−446564.			−0.449256			−0.224628	−	0.974445i	$-0.572117\pi$
$997$	−446564.			−0.449256			−0.224628	+	0.974445i	$0.572117\pi$
$998$	374452.			0.375954
$999$			246761.i			0.247255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.5.d.a.22.2	yes	16
3.2	odd	2		207.5.d.c.91.15		16
4.3	odd	2		1104.5.c.c.1057.7		16
23.22	odd	2	inner	69.5.d.a.22.1	✓	16
69.68	even	2		207.5.d.c.91.16		16
92.91	even	2		1104.5.c.c.1057.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.5.d.a.22.1	✓	16	23.22	odd	2	inner
69.5.d.a.22.2	yes	16	1.1	even	1	trivial
207.5.d.c.91.15		16	3.2	odd	2
207.5.d.c.91.16		16	69.68	even	2
1104.5.c.c.1057.2		16	92.91	even	2
1104.5.c.c.1057.7		16	4.3	odd	2

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	69.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-6.46704 q^{2} +5.19615 q^{3} +25.8226 q^{4} +30.6703i q^{5} -33.6037 q^{6} -37.9803i q^{7} -63.5230 q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q-6.46704 q^{2} +5.19615 q^{3} +25.8226 q^{4} +30.6703i q^{5} -33.6037 q^{6} -37.9803i q^{7} -63.5230 q^{8} +27.0000 q^{9} -198.346i q^{10} +2.87351i q^{11} +134.178 q^{12} -18.8732 q^{13} +245.620i q^{14} +159.368i q^{15} -2.35578 q^{16} +445.446i q^{17} -174.610 q^{18} +401.904i q^{19} +791.987i q^{20} -197.351i q^{21} -18.5831i q^{22} +(60.7534 + 525.500i) q^{23} -330.075 q^{24} -315.668 q^{25} +122.054 q^{26} +140.296 q^{27} -980.749i q^{28} -922.372 q^{29} -1030.64i q^{30} +767.928 q^{31} +1031.60 q^{32} +14.9312i q^{33} -2880.72i q^{34} +1164.87 q^{35} +697.210 q^{36} +1758.86i q^{37} -2599.13i q^{38} -98.0681 q^{39} -1948.27i q^{40} -2565.91 q^{41} +1276.28i q^{42} -17.6066i q^{43} +74.2014i q^{44} +828.099i q^{45} +(-392.894 - 3398.43i) q^{46} -2034.86 q^{47} -12.2410 q^{48} +958.496 q^{49} +2041.44 q^{50} +2314.61i q^{51} -487.355 q^{52} -1304.09i q^{53} -907.300 q^{54} -88.1315 q^{55} +2412.62i q^{56} +2088.35i q^{57} +5965.01 q^{58} +4380.32 q^{59} +4115.28i q^{60} -735.665i q^{61} -4966.22 q^{62} -1025.47i q^{63} -6633.72 q^{64} -578.847i q^{65} -96.5606i q^{66} +3483.41i q^{67} +11502.6i q^{68} +(315.684 + 2730.58i) q^{69} -7533.25 q^{70} +5667.75 q^{71} -1715.12 q^{72} +2214.08 q^{73} -11374.6i q^{74} -1640.26 q^{75} +10378.2i q^{76} +109.137 q^{77} +634.210 q^{78} -3995.75i q^{79} -72.2526i q^{80} +729.000 q^{81} +16593.8 q^{82} -9286.49i q^{83} -5096.12i q^{84} -13662.0 q^{85} +113.862i q^{86} -4792.79 q^{87} -182.534i q^{88} -10926.4i q^{89} -5355.34i q^{90} +716.811i q^{91} +(1568.81 + 13569.8i) q^{92} +3990.27 q^{93} +13159.5 q^{94} -12326.5 q^{95} +5360.36 q^{96} +10200.5i q^{97} -6198.63 q^{98} +77.5848i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{2} + 144 q^{4} - 36 q^{6} + 372 q^{8} + 432 q^{9}+O(q^{10}) \) 16 * q + 12 * q^2 + 144 * q^4 - 36 * q^6 + 372 * q^8 + 432 * q^9	\( 16 q + 12 q^{2} + 144 q^{4} - 36 q^{6} + 372 q^{8} + 432 q^{9} + 104 q^{13} + 680 q^{16} + 324 q^{18} - 732 q^{23} - 1764 q^{24} - 2984 q^{25} + 1800 q^{26} - 3528 q^{29} - 400 q^{31} + 5244 q^{32} + 912 q^{35} + 3888 q^{36} + 2016 q^{39} + 1008 q^{41} - 1168 q^{46} - 8664 q^{47} - 2016 q^{48} + 7240 q^{49} - 18852 q^{50} - 20952 q^{52} - 972 q^{54} + 6816 q^{55} - 13352 q^{58} + 20112 q^{59} + 4248 q^{62} - 896 q^{64} - 10044 q^{69} - 10680 q^{70} + 40368 q^{71} + 10044 q^{72} - 9568 q^{73} + 7560 q^{75} + 2952 q^{77} - 6912 q^{78} + 11664 q^{81} + 71800 q^{82} + 42744 q^{85} + 8352 q^{87} - 9876 q^{92} - 10008 q^{93} + 73720 q^{94} + 33312 q^{95} - 24948 q^{96} - 59052 q^{98}+O(q^{100}) \) 16 * q + 12 * q^2 + 144 * q^4 - 36 * q^6 + 372 * q^8 + 432 * q^9 + 104 * q^13 + 680 * q^16 + 324 * q^18 - 732 * q^23 - 1764 * q^24 - 2984 * q^25 + 1800 * q^26 - 3528 * q^29 - 400 * q^31 + 5244 * q^32 + 912 * q^35 + 3888 * q^36 + 2016 * q^39 + 1008 * q^41 - 1168 * q^46 - 8664 * q^47 - 2016 * q^48 + 7240 * q^49 - 18852 * q^50 - 20952 * q^52 - 972 * q^54 + 6816 * q^55 - 13352 * q^58 + 20112 * q^59 + 4248 * q^62 - 896 * q^64 - 10044 * q^69 - 10680 * q^70 + 40368 * q^71 + 10044 * q^72 - 9568 * q^73 + 7560 * q^75 + 2952 * q^77 - 6912 * q^78 + 11664 * q^81 + 71800 * q^82 + 42744 * q^85 + 8352 * q^87 - 9876 * q^92 - 10008 * q^93 + 73720 * q^94 + 33312 * q^95 - 24948 * q^96 - 59052 * q^98

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