LMFDB - Embedded newform 57.5.c.a.37.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,5,Mod(37,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, 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("57.37");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	57.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:	$5.89208789578$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 190x^{12} + 14073x^{10} + 516256x^{8} + 9846472x^{6} + 92351712x^{4} + 334182672x^{2} + 45349632 $ x^14 + 190x^12 + 14073x^10 + 516256x^8 + 9846472x^6 + 92351712x^4 + 334182672x^2 + 45349632
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{11}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			37.14
Root			$7.66280i$ of defining polynomial
Character	$\chi$	$=$	57.37
Dual form			57.5.c.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+7.66280i q^{2} -5.19615i q^{3} -42.7185 q^{4} -31.0118 q^{5} +39.8171 q^{6} +66.5198 q^{7} -204.739i q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+7.66280i q^{2} -5.19615i q^{3} -42.7185 q^{4} -31.0118 q^{5} +39.8171 q^{6} +66.5198 q^{7} -204.739i q^{8} -27.0000 q^{9} -237.637i q^{10} -96.7107 q^{11} +221.972i q^{12} -223.343i q^{13} +509.728i q^{14} +161.142i q^{15} +885.376 q^{16} -376.331 q^{17} -206.896i q^{18} +(-324.930 + 157.295i) q^{19} +1324.78 q^{20} -345.647i q^{21} -741.075i q^{22} -390.497 q^{23} -1063.85 q^{24} +336.729 q^{25} +1711.43 q^{26} +140.296i q^{27} -2841.63 q^{28} +124.246i q^{29} -1234.80 q^{30} +850.411i q^{31} +3508.64i q^{32} +502.523i q^{33} -2883.75i q^{34} -2062.89 q^{35} +1153.40 q^{36} -997.110i q^{37} +(-1205.32 - 2489.87i) q^{38} -1160.52 q^{39} +6349.31i q^{40} -204.703i q^{41} +2648.62 q^{42} -914.829 q^{43} +4131.34 q^{44} +837.318 q^{45} -2992.30i q^{46} +2071.92 q^{47} -4600.55i q^{48} +2023.88 q^{49} +2580.29i q^{50} +1955.47i q^{51} +9540.87i q^{52} -459.580i q^{53} -1075.06 q^{54} +2999.17 q^{55} -13619.2i q^{56} +(817.327 + 1688.38i) q^{57} -952.071 q^{58} +1558.52i q^{59} -6883.74i q^{60} +2249.34 q^{61} -6516.53 q^{62} -1796.03 q^{63} -12720.0 q^{64} +6926.25i q^{65} -3850.74 q^{66} -1205.42i q^{67} +16076.3 q^{68} +2029.08i q^{69} -15807.6i q^{70} +3825.85i q^{71} +5527.95i q^{72} -8774.43 q^{73} +7640.65 q^{74} -1749.70i q^{75} +(13880.5 - 6719.40i) q^{76} -6433.17 q^{77} -8892.86i q^{78} -2063.59i q^{79} -27457.1 q^{80} +729.000 q^{81} +1568.60 q^{82} +2078.71 q^{83} +14765.5i q^{84} +11670.7 q^{85} -7010.15i q^{86} +645.600 q^{87} +19800.4i q^{88} +9032.69i q^{89} +6416.20i q^{90} -14856.7i q^{91} +16681.5 q^{92} +4418.87 q^{93} +15876.7i q^{94} +(10076.6 - 4877.99i) q^{95} +18231.4 q^{96} +17319.7i q^{97} +15508.6i q^{98} +2611.19 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 156 q^{4} + 18 q^{5} + 36 q^{6} - 54 q^{7} - 378 q^{9}+O(q^{10}) $ 14 * q - 156 * q^4 + 18 * q^5 + 36 * q^6 - 54 * q^7 - 378 * q^9	$ 14 q - 156 q^{4} + 18 q^{5} + 36 q^{6} - 54 q^{7} - 378 q^{9} - 318 q^{11} + 1252 q^{16} - 654 q^{17} - 694 q^{19} + 960 q^{20} - 492 q^{23} - 1764 q^{24} + 3736 q^{25} + 1296 q^{26} - 3536 q^{28} - 1152 q^{30} + 4566 q^{35} + 4212 q^{36} - 4440 q^{38} - 2952 q^{39} + 2304 q^{42} - 8422 q^{43} + 11232 q^{44} - 486 q^{45} + 12258 q^{47} + 2376 q^{49} - 972 q^{54} + 12782 q^{55} - 4860 q^{57} - 24856 q^{58} + 5378 q^{61} - 41088 q^{62} + 1458 q^{63} - 26012 q^{64} + 792 q^{66} + 26832 q^{68} + 12594 q^{73} + 23856 q^{74} - 12652 q^{76} - 20610 q^{77} - 64056 q^{80} + 10206 q^{81} + 59704 q^{82} - 29436 q^{83} + 26182 q^{85} - 12384 q^{87} + 103704 q^{92} + 38016 q^{93} + 22818 q^{95} - 4932 q^{96} + 8586 q^{99}+O(q^{100}) $ 14 * q - 156 * q^4 + 18 * q^5 + 36 * q^6 - 54 * q^7 - 378 * q^9 - 318 * q^11 + 1252 * q^16 - 654 * q^17 - 694 * q^19 + 960 * q^20 - 492 * q^23 - 1764 * q^24 + 3736 * q^25 + 1296 * q^26 - 3536 * q^28 - 1152 * q^30 + 4566 * q^35 + 4212 * q^36 - 4440 * q^38 - 2952 * q^39 + 2304 * q^42 - 8422 * q^43 + 11232 * q^44 - 486 * q^45 + 12258 * q^47 + 2376 * q^49 - 972 * q^54 + 12782 * q^55 - 4860 * q^57 - 24856 * q^58 + 5378 * q^61 - 41088 * q^62 + 1458 * q^63 - 26012 * q^64 + 792 * q^66 + 26832 * q^68 + 12594 * q^73 + 23856 * q^74 - 12652 * q^76 - 20610 * q^77 - 64056 * q^80 + 10206 * q^81 + 59704 * q^82 - 29436 * q^83 + 26182 * q^85 - 12384 * q^87 + 103704 * q^92 + 38016 * q^93 + 22818 * q^95 - 4932 * q^96 + 8586 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$1$	$-1$

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 $

$2$			7.66280i			1.91570i	0.287268	+	0.957850i	$0.407253\pi$
$2$			7.66280i			1.91570i	−0.287268	+	0.957850i	$0.592747\pi$
$3$		−	5.19615i		−	0.577350i
$3$		−	5.19615i		−	0.577350i
$4$	−42.7185			−2.66991
$5$	−31.0118			−1.24047			−0.620235	−	0.784416i	$-0.712963\pi$
$5$	−31.0118			−1.24047			−0.620235	+	0.784416i	$0.712963\pi$
$6$	39.8171			1.10603
$7$	66.5198			1.35755			0.678773	−	0.734348i	$-0.262512\pi$
$7$	66.5198			1.35755			0.678773	+	0.734348i	$0.262512\pi$
$8$		−	204.739i		−	3.19904i
$9$	−27.0000			−0.333333
$10$		−	237.637i		−	2.37637i
$11$	−96.7107			−0.799262			−0.399631	−	0.916676i	$-0.630862\pi$
$11$	−96.7107			−0.799262			−0.399631	+	0.916676i	$0.630862\pi$
$12$			221.972i			1.54147i
$13$		−	223.343i		−	1.32155i	−0.750582	−	0.660777i	$-0.770227\pi$
$13$		−	223.343i		−	1.32155i	0.750582	−	0.660777i	$-0.229773\pi$
$14$			509.728i			2.60065i
$15$			161.142i			0.716186i
$16$	885.376			3.45850
$17$	−376.331			−1.30218			−0.651091	−	0.759000i	$-0.725688\pi$
$17$	−376.331			−1.30218			−0.651091	+	0.759000i	$0.725688\pi$
$18$		−	206.896i		−	0.638567i
$19$	−324.930	+	157.295i	−0.900083	+	0.435720i
$19$	−324.930	+	157.295i	−0.900083	+	0.435720i
$20$	1324.78			3.31194
$21$		−	345.647i		−	0.783780i
$22$		−	741.075i		−	1.53115i
$23$	−390.497			−0.738180			−0.369090	−	0.929394i	$-0.620331\pi$
$23$	−390.497			−0.738180			−0.369090	+	0.929394i	$0.620331\pi$
$24$	−1063.85			−1.84697
$25$	336.729			0.538767
$26$	1711.43			2.53170
$27$			140.296i			0.192450i
$28$	−2841.63			−3.62452
$29$			124.246i			0.147736i	0.997268	+	0.0738679i	$0.0235343\pi$
$29$			124.246i			0.147736i	−0.997268	+	0.0738679i	$0.976466\pi$
$30$	−1234.80			−1.37200
$31$			850.411i			0.884923i	0.896787	+	0.442462i	$0.145895\pi$
$31$			850.411i			0.884923i	−0.896787	+	0.442462i	$0.854105\pi$
$32$			3508.64i			3.42641i
$33$			502.523i			0.461454i
$34$		−	2883.75i		−	2.49459i
$35$	−2062.89			−1.68400
$36$	1153.40			0.889969
$37$		−	997.110i		−	0.728349i	−0.931331	−	0.364174i	$-0.881351\pi$
$37$		−	997.110i		−	0.728349i	0.931331	−	0.364174i	$-0.118649\pi$
$38$	−1205.32	−	2489.87i	−0.834708	−	1.72429i
$39$	−1160.52			−0.763000
$40$			6349.31i			3.96832i
$41$		−	204.703i		−	0.121775i	−0.998145	−	0.0608873i	$-0.980607\pi$
$41$		−	204.703i		−	0.121775i	0.998145	−	0.0608873i	$-0.0193930\pi$
$42$	2648.62			1.50149
$43$	−914.829			−0.494770			−0.247385	−	0.968917i	$-0.579571\pi$
$43$	−914.829			−0.494770			−0.247385	+	0.968917i	$0.579571\pi$
$44$	4131.34			2.13396
$45$	837.318			0.413490
$46$		−	2992.30i		−	1.41413i
$47$	2071.92			0.937943			0.468972	−	0.883213i	$-0.344625\pi$
$47$	2071.92			0.937943			0.468972	+	0.883213i	$0.344625\pi$
$48$		−	4600.55i		−	1.99677i
$49$	2023.88			0.842931
$50$			2580.29i			1.03212i
$51$			1955.47i			0.751815i
$52$			9540.87i			3.52843i
$53$		−	459.580i		−	0.163610i	−0.996648	−	0.0818049i	$-0.973932\pi$
$53$		−	459.580i		−	0.163610i	0.996648	−	0.0818049i	$-0.0260684\pi$
$54$	−1075.06			−0.368677
$55$	2999.17			0.991461
$56$		−	13619.2i		−	4.34285i
$57$	817.327	+	1688.38i	0.251563	+	0.519663i
$58$	−952.071			−0.283018
$59$			1558.52i			0.447722i	0.974621	+	0.223861i	$0.0718661\pi$
$59$			1558.52i			0.447722i	−0.974621	+	0.223861i	$0.928134\pi$
$60$		−	6883.74i		−	1.91215i
$61$	2249.34			0.604500			0.302250	−	0.953229i	$-0.402262\pi$
$61$	2249.34			0.604500			0.302250	+	0.953229i	$0.402262\pi$
$62$	−6516.53			−1.69525
$63$	−1796.03			−0.452515
$64$	−12720.0			−3.10547
$65$			6926.25i			1.63935i
$66$	−3850.74			−0.884008
$67$		−	1205.42i		−	0.268526i	−0.990946	−	0.134263i	$-0.957133\pi$
$67$		−	1205.42i		−	0.268526i	0.990946	−	0.134263i	$-0.0428668\pi$
$68$	16076.3			3.47671
$69$			2029.08i			0.426189i
$70$		−	15807.6i		−	3.22603i
$71$			3825.85i			0.758946i	0.925203	+	0.379473i	$0.123895\pi$
$71$			3825.85i			0.758946i	−0.925203	+	0.379473i	$0.876105\pi$
$72$			5527.95i			1.06635i
$73$	−8774.43			−1.64654			−0.823271	−	0.567648i	$-0.807853\pi$
$73$	−8774.43			−1.64654			−0.823271	+	0.567648i	$0.807853\pi$
$74$	7640.65			1.39530
$75$		−	1749.70i		−	0.311057i
$76$	13880.5	−	6719.40i	2.40314	−	1.16333i
$77$	−6433.17			−1.08503
$78$		−	8892.86i		−	1.46168i
$79$		−	2063.59i		−	0.330650i	−0.986239	−	0.165325i	$-0.947133\pi$
$79$		−	2063.59i		−	0.330650i	0.986239	−	0.165325i	$-0.0528673\pi$
$80$	−27457.1			−4.29017
$81$	729.000			0.111111
$82$	1568.60			0.233284
$83$	2078.71			0.301744			0.150872	−	0.988553i	$-0.451792\pi$
$83$	2078.71			0.301744			0.150872	+	0.988553i	$0.451792\pi$
$84$			14765.5i			2.09262i
$85$	11670.7			1.61532
$86$		−	7010.15i		−	0.947830i
$87$	645.600			0.0852953
$88$			19800.4i			2.55687i
$89$			9032.69i			1.14035i	0.821524	+	0.570173i	$0.193124\pi$
$89$			9032.69i			1.14035i	−0.821524	+	0.570173i	$0.806876\pi$
$90$			6416.20i			0.792123i
$91$		−	14856.7i		−	1.79407i
$92$	16681.5			1.97087
$93$	4418.87			0.510911
$94$			15876.7i			1.79682i
$95$	10076.6	−	4877.99i	1.11653	−	0.540497i
$96$	18231.4			1.97824
$97$			17319.7i			1.84076i	0.391029	+	0.920378i	$0.372119\pi$
$97$			17319.7i			1.84076i	−0.391029	+	0.920378i	$0.627881\pi$
$98$			15508.6i			1.61480i
$99$	2611.19			0.266421
$100$	−14384.6			−1.43846
$101$	−15941.5			−1.56274			−0.781370	−	0.624068i	$-0.785479\pi$
$101$	−15941.5			−1.56274			−0.781370	+	0.624068i	$0.785479\pi$
$102$	−14984.4			−1.44025
$103$		−	10645.3i		−	1.00343i	−0.865034	−	0.501713i	$-0.832703\pi$
$103$		−	10645.3i		−	1.00343i	0.865034	−	0.501713i	$-0.167297\pi$
$104$	−45726.9			−4.22771
$105$			10719.1i			0.972255i
$106$	3521.67			0.313427
$107$		−	18781.0i		−	1.64041i	−0.572071	−	0.820204i	$-0.693860\pi$
$107$		−	18781.0i		−	1.64041i	0.572071	−	0.820204i	$-0.306140\pi$
$108$		−	5993.24i		−	0.513824i
$109$		−	21327.8i		−	1.79512i	−0.440892	−	0.897560i	$-0.645338\pi$
$109$		−	21327.8i		−	1.79512i	0.440892	−	0.897560i	$-0.354662\pi$
$110$			22982.0i			1.89934i
$111$	−5181.13			−0.420512
$112$	58895.0			4.69507
$113$		−	19874.4i		−	1.55646i	−0.627982	−	0.778228i	$-0.716119\pi$
$113$		−	19874.4i		−	1.55646i	0.627982	−	0.778228i	$-0.283881\pi$
$114$	−12937.8	+	6263.02i	−0.995518	+	0.481919i
$115$	12110.0			0.915691
$116$		−	5307.60i		−	0.394441i
$117$			6030.25i			0.440518i
$118$	−11942.6			−0.857701
$119$	−25033.4			−1.76777
$120$	32992.0			2.29111
$121$	−5288.05			−0.361181
$122$			17236.3i			1.15804i
$123$	−1063.67			−0.0703066
$124$		−	36328.3i		−	2.36266i
$125$	8939.78			0.572146
$126$		−	13762.6i		−	0.866884i
$127$			4351.55i			0.269797i	0.990859	+	0.134898i	$0.0430708\pi$
$127$			4351.55i			0.269797i	−0.990859	+	0.134898i	$0.956929\pi$
$128$		−	41332.5i		−	2.52274i
$129$			4753.59i			0.285655i
$130$	−53074.5			−3.14050
$131$	−13141.6			−0.765781			−0.382891	−	0.923794i	$-0.625071\pi$
$131$	−13141.6			−0.765781			−0.382891	+	0.923794i	$0.625071\pi$
$132$		−	21467.1i		−	1.23204i
$133$	−21614.2	+	10463.2i	−1.22190	+	0.591509i
$134$	9236.86			0.514416
$135$		−	4350.83i		−	0.238729i
$136$			77049.4i			4.16574i
$137$	9050.47			0.482203			0.241102	−	0.970500i	$-0.422491\pi$
$137$	9050.47			0.482203			0.241102	+	0.970500i	$0.422491\pi$
$138$	−15548.5			−0.816450
$139$	18613.0			0.963358			0.481679	−	0.876348i	$-0.340027\pi$
$139$	18613.0			0.963358			0.481679	+	0.876348i	$0.340027\pi$
$140$	88123.8			4.49611
$141$		−	10766.0i		−	0.541522i
$142$	−29316.7			−1.45391
$143$			21599.6i			1.05627i
$144$	−23905.1			−1.15283
$145$		−	3853.08i		−	0.183262i
$146$		−	67236.7i		−	3.15428i
$147$		−	10516.4i		−	0.486667i
$148$			42595.1i			1.94462i
$149$	13792.7			0.621265			0.310632	−	0.950530i	$-0.399459\pi$
$149$	13792.7			0.621265			0.310632	+	0.950530i	$0.399459\pi$
$150$	13407.6			0.595892
$151$			29335.3i			1.28658i	0.765623	+	0.643290i	$0.222431\pi$
$151$			29335.3i			1.28658i	−0.765623	+	0.643290i	$0.777569\pi$
$152$	32204.3	+	66525.7i	1.39389	+	2.87940i
$153$	10160.9			0.434061
$154$		−	49296.1i		−	2.07860i
$155$		−	26372.8i		−	1.09772i
$156$	49575.8			2.03714
$157$	−7196.50			−0.291959			−0.145980	−	0.989288i	$-0.546633\pi$
$157$	−7196.50			−0.291959			−0.145980	+	0.989288i	$0.546633\pi$
$158$	15812.9			0.633426
$159$	−2388.05			−0.0944602
$160$		−	108809.i		−	4.25035i
$161$	−25975.8			−1.00211
$162$			5586.18i			0.212856i
$163$	37224.5			1.40105			0.700525	−	0.713628i	$-0.252949\pi$
$163$	37224.5			1.40105			0.700525	+	0.713628i	$0.252949\pi$
$164$			8744.62i			0.325127i
$165$		−	15584.1i		−	0.572420i
$166$			15928.8i			0.578051i
$167$		−	14869.2i		−	0.533157i	−0.963813	−	0.266579i	$-0.914107\pi$
$167$		−	14869.2i		−	0.533157i	0.963813	−	0.266579i	$-0.0858932\pi$
$168$	−70767.3			−2.50734
$169$	−21321.0			−0.746507
$170$			89430.1i			3.09447i
$171$	8773.10	−	4246.96i	0.300028	−	0.145240i
$172$	39080.1			1.32099
$173$		−	114.377i		−	0.00382163i	−0.999998	−	0.00191081i	$-0.999392\pi$
$173$		−	114.377i		−	0.00382163i	0.999998	−	0.00191081i	$-0.000608231\pi$
$174$			4947.11i			0.163400i
$175$	22399.1			0.731401
$176$	−85625.3			−2.76425
$177$	8098.30			0.258492
$178$	−69215.7			−2.18456
$179$		−	43040.2i		−	1.34328i	−0.740876	−	0.671642i	$-0.765589\pi$
$179$		−	43040.2i		−	1.34328i	0.740876	−	0.671642i	$-0.234411\pi$
$180$	−35769.0			−1.10398
$181$			30164.6i			0.920748i	0.887725	+	0.460374i	$0.152285\pi$
$181$			30164.6i			0.920748i	−0.887725	+	0.460374i	$0.847715\pi$
$182$	113844.			3.43690
$183$		−	11687.9i		−	0.349008i
$184$			79950.0i			2.36147i
$185$			30922.1i			0.903495i
$186$			33860.9i			0.978752i
$187$	36395.2			1.04078
$188$	−88509.2			−2.50422
$189$			9332.46i			0.261260i
$190$	37379.0	+	77215.3i	1.03543	+	2.13893i
$191$	−11022.2			−0.302136			−0.151068	−	0.988523i	$-0.548271\pi$
$191$	−11022.2			−0.302136			−0.151068	+	0.988523i	$0.548271\pi$
$192$			66095.0i			1.79294i
$193$		−	21979.9i		−	0.590080i	−0.955485	−	0.295040i	$-0.904667\pi$
$193$		−	21979.9i		−	0.590080i	0.955485	−	0.295040i	$-0.0953330\pi$
$194$	−132717.			−3.52634
$195$	35989.9			0.946479
$196$	−86457.1			−2.25055
$197$	−21455.8			−0.552857			−0.276428	−	0.961035i	$-0.589151\pi$
$197$	−21455.8			−0.552857			−0.276428	+	0.961035i	$0.589151\pi$
$198$			20009.0i			0.510382i
$199$	−33117.8			−0.836288			−0.418144	−	0.908381i	$-0.637319\pi$
$199$	−33117.8			−0.836288			−0.418144	+	0.908381i	$0.637319\pi$
$200$		−	68941.5i		−	1.72354i
$201$	−6263.52			−0.155034
$202$		−	122157.i		−	2.99374i
$203$			8264.80i			0.200558i
$204$		−	83534.8i		−	2.00728i
$205$			6348.20i			0.151058i
$206$	81573.2			1.92226
$207$	10543.4			0.246060
$208$		−	197742.i		−	4.57060i
$209$	31424.2	−	15212.1i	0.719402	−	0.348254i
$210$	−82138.4			−1.86255
$211$			35557.7i			0.798672i	0.916805	+	0.399336i	$0.130759\pi$
$211$			35557.7i			0.798672i	−0.916805	+	0.399336i	$0.869241\pi$
$212$			19632.6i			0.436823i
$213$	19879.7			0.438178
$214$	143915.			3.14253
$215$	28370.5			0.613747
$216$	28724.0			0.615656
$217$			56569.2i			1.20132i
$218$	163431.			3.43891
$219$			45593.3i			0.950632i
$220$	−128120.			−2.64711
$221$			84050.7i			1.72090i
$222$		−	39702.0i		−	0.805576i
$223$		−	18777.3i		−	0.377593i	−0.982016	−	0.188796i	$-0.939541\pi$
$223$		−	18777.3i		−	0.377593i	0.982016	−	0.188796i	$-0.0604586\pi$
$224$			233394.i			4.65150i
$225$	−9091.69			−0.179589
$226$	152293.			2.98170
$227$		−	97464.6i		−	1.89145i	−0.324966	−	0.945726i	$-0.605353\pi$
$227$		−	97464.6i		−	1.89145i	0.324966	−	0.945726i	$-0.394647\pi$
$228$	−34915.0	−	72125.3i	−0.671649	−	1.38745i
$229$	−63879.5			−1.21812			−0.609061	−	0.793123i	$-0.708454\pi$
$229$	−63879.5			−1.21812			−0.609061	+	0.793123i	$0.708454\pi$
$230$			92796.6i			1.75419i
$231$			33427.7i			0.626445i
$232$	25437.9			0.472613
$233$	54786.7			1.00917			0.504584	−	0.863363i	$-0.331646\pi$
$233$	54786.7			1.00917			0.504584	+	0.863363i	$0.331646\pi$
$234$	−46208.6			−0.843901
$235$	−64253.8			−1.16349
$236$		−	66577.6i		−	1.19538i
$237$	−10722.7			−0.190901
$238$		−	191826.i		−	3.38652i
$239$	−5539.90			−0.0969853			−0.0484926	−	0.998824i	$-0.515442\pi$
$239$	−5539.90			−0.0969853			−0.0484926	+	0.998824i	$0.515442\pi$
$240$			142671.i			2.47693i
$241$			70958.5i			1.22172i	0.791740	+	0.610858i	$0.209175\pi$
$241$			70958.5i			1.22172i	−0.791740	+	0.610858i	$0.790825\pi$
$242$		−	40521.2i		−	0.691914i
$243$		−	3788.00i		−	0.0641500i
$244$	−96088.7			−1.61396
$245$	−62764.0			−1.04563
$246$		−	8150.68i		−	0.134686i
$247$	35130.6	+	72570.7i	0.575827	+	1.18951i
$248$	174112.			2.83091
$249$		−	10801.3i		−	0.174212i
$250$			68503.8i			1.09606i
$251$	−54385.8			−0.863254			−0.431627	−	0.902052i	$-0.642060\pi$
$251$	−54385.8			−0.863254			−0.431627	+	0.902052i	$0.642060\pi$
$252$	76723.9			1.20817
$253$	37765.3			0.589999
$254$	−33345.1			−0.516850
$255$		−	60642.6i		−	0.932604i
$256$	113203.			1.72734
$257$			24099.3i			0.364870i	0.983218	+	0.182435i	$0.0583979\pi$
$257$			24099.3i			0.364870i	−0.983218	+	0.182435i	$0.941602\pi$
$258$	−36425.8			−0.547230
$259$		−	66327.5i		−	0.988767i
$260$		−	295879.i		−	4.37691i
$261$		−	3354.64i		−	0.0492453i
$262$		−	100701.i		−	1.46701i
$263$	−6608.17			−0.0955366			−0.0477683	−	0.998858i	$-0.515211\pi$
$263$	−6608.17			−0.0955366			−0.0477683	+	0.998858i	$0.515211\pi$
$264$	102886.			1.47621
$265$			14252.4i			0.202953i
$266$	−80177.5	−	165626.i	−1.13315	−	2.34080i
$267$	46935.2			0.658379
$268$			51493.6i			0.716941i
$269$		−	54109.3i		−	0.747768i	−0.927475	−	0.373884i	$-0.878026\pi$
$269$		−	54109.3i		−	0.747768i	0.927475	−	0.373884i	$-0.121974\pi$
$270$	33339.5			0.457333
$271$	−10178.4			−0.138593			−0.0692966	−	0.997596i	$-0.522075\pi$
$271$	−10178.4			−0.138593			−0.0692966	+	0.997596i	$0.522075\pi$
$272$	−333194.			−4.50360
$273$	−77197.7			−1.03581
$274$			69352.0i			0.923757i
$275$	−32565.3			−0.430616
$276$		−	86679.5i		−	1.13788i
$277$	−83306.7			−1.08573			−0.542863	−	0.839821i	$-0.682660\pi$
$277$	−83306.7			−1.08573			−0.542863	+	0.839821i	$0.682660\pi$
$278$			142628.i			1.84550i
$279$		−	22961.1i		−	0.294974i
$280$			422354.i			5.38717i
$281$		−	41738.9i		−	0.528602i	−0.964440	−	0.264301i	$-0.914859\pi$
$281$		−	41738.9i		−	0.528602i	0.964440	−	0.264301i	$-0.0851412\pi$
$282$	82497.7			1.03739
$283$	−88422.3			−1.10405			−0.552025	−	0.833827i	$-0.686145\pi$
$283$	−88422.3			−1.10405			−0.552025	+	0.833827i	$0.686145\pi$
$284$		−	163434.i		−	2.02631i
$285$	−25346.8	−	52359.8i	−0.312056	−	0.644626i
$286$	−165514.			−2.02349
$287$		−	13616.8i		−	0.165315i
$288$		−	94733.3i		−	1.14214i
$289$	58103.7			0.695678
$290$	29525.4			0.351075
$291$	89995.7			1.06276
$292$	374830.			4.39612
$293$			166236.i			1.93638i	0.250222	+	0.968189i	$0.419497\pi$
$293$			166236.i			1.93638i	−0.250222	+	0.968189i	$0.580503\pi$
$294$	80584.9			0.932307
$295$		−	48332.4i		−	0.555386i
$296$	−204147.			−2.33002
$297$		−	13568.1i		−	0.153818i
$298$			105691.i			1.19016i
$299$			87214.8i			0.975546i
$300$			74744.5i			0.830494i
$301$	−60854.2			−0.671673
$302$	−224790.			−2.46470
$303$			82834.5i			0.902248i
$304$	−287685.	+	139265.i	−3.11293	+	1.50694i
$305$	−69756.1			−0.749864
$306$			77861.2i			0.831530i
$307$		−	87933.5i		−	0.932991i	−0.884524	−	0.466495i	$-0.845516\pi$
$307$		−	87933.5i		−	0.932991i	0.884524	−	0.466495i	$-0.154484\pi$
$308$	274816.			2.89694
$309$	−55314.8			−0.579328
$310$	202089.			2.10290
$311$	−5226.64			−0.0540383			−0.0270191	−	0.999635i	$-0.508602\pi$
$311$	−5226.64			−0.0540383			−0.0270191	+	0.999635i	$0.508602\pi$
$312$			237604.i			2.44087i
$313$	175685.			1.79327			0.896635	−	0.442770i	$-0.146004\pi$
$313$	175685.			1.79327			0.896635	+	0.442770i	$0.146004\pi$
$314$		−	55145.4i		−	0.559306i
$315$	55698.2			0.561332
$316$			88153.4i			0.882805i
$317$			71780.5i			0.714312i	0.934045	+	0.357156i	$0.116254\pi$
$317$			71780.5i			0.714312i	−0.934045	+	0.357156i	$0.883746\pi$
$318$		−	18299.1i		−	0.180957i
$319$		−	12015.9i		−	0.118080i
$320$	394469.			3.85224
$321$	−97589.1			−0.947090
$322$		−	199047.i		−	1.91975i
$323$	122281.	−	59194.8i	1.17207	−	0.567386i
$324$	−31141.8			−0.296656
$325$		−	75206.0i		−	0.712010i
$326$			285244.i			2.68399i
$327$	−110823.			−1.03641
$328$	−41910.7			−0.389562
$329$	137823.			1.27330
$330$	119418.			1.09659
$331$		−	167277.i		−	1.52679i	−0.645929	−	0.763397i	$-0.723530\pi$
$331$		−	167277.i		−	1.52679i	0.645929	−	0.763397i	$-0.276470\pi$
$332$	−88799.5			−0.805628
$333$			26922.0i			0.242783i
$334$	113940.			1.02137
$335$			37382.1i			0.333099i
$336$		−	306027.i		−	2.71070i
$337$			65743.6i			0.578887i	0.957195	+	0.289443i	$0.0934702\pi$
$337$			65743.6i			0.578887i	−0.957195	+	0.289443i	$0.906530\pi$
$338$		−	163379.i		−	1.43008i
$339$	−103270.			−0.898620
$340$	−498554.			−4.31275
$341$		−	82243.9i		−	0.707285i
$342$	32543.6	+	67226.6i	0.278236	+	0.574763i
$343$	−25086.1			−0.213228
$344$			187301.i			1.58279i
$345$		−	62925.5i		−	0.528674i
$346$	876.452			0.00732109
$347$	−72772.1			−0.604374			−0.302187	−	0.953249i	$-0.597717\pi$
$347$	−72772.1			−0.604374			−0.302187	+	0.953249i	$0.597717\pi$
$348$	−27579.1			−0.227731
$349$	−25274.7			−0.207508			−0.103754	−	0.994603i	$-0.533086\pi$
$349$	−25274.7			−0.207508			−0.103754	+	0.994603i	$0.533086\pi$
$350$			171640.i			1.40114i
$351$	31334.1			0.254333
$352$		−	339323.i		−	2.73859i
$353$	−24312.9			−0.195114			−0.0975569	−	0.995230i	$-0.531103\pi$
$353$	−24312.9			−0.195114			−0.0975569	+	0.995230i	$0.531103\pi$
$354$			62055.7i			0.495194i
$355$		−	118646.i		−	0.941450i
$356$		−	385863.i		−	3.04462i
$357$			130077.i			1.02062i
$358$	329808.			2.57333
$359$	42430.8			0.329224			0.164612	−	0.986358i	$-0.447363\pi$
$359$	42430.8			0.329224			0.164612	+	0.986358i	$0.447363\pi$
$360$		−	171431.i		−	1.32277i
$361$	80837.7	−	102219.i	0.620297	−	0.784367i
$362$	−231145.			−1.76388
$363$			27477.5i			0.208528i
$364$			634657.i			4.79001i
$365$	272110.			2.04249
$366$	89562.3			0.668595
$367$	20131.8			0.149469			0.0747343	−	0.997203i	$-0.476189\pi$
$367$	20131.8			0.149469			0.0747343	+	0.997203i	$0.476189\pi$
$368$	−345737.			−2.55300
$369$			5526.98i			0.0405915i
$370$	−236950.			−1.73083
$371$		−	30571.2i		−	0.222108i
$372$	−188767.			−1.36408
$373$			74524.4i			0.535650i	0.963468	+	0.267825i	$0.0863048\pi$
$373$			74524.4i			0.535650i	−0.963468	+	0.267825i	$0.913695\pi$
$374$			278889.i			1.99383i
$375$		−	46452.5i		−	0.330329i
$376$		−	424201.i		−	3.00052i
$377$	27749.4			0.195241
$378$	−71512.8			−0.500496
$379$			258162.i			1.79727i	0.438698	+	0.898635i	$0.355440\pi$
$379$			258162.i			1.79727i	−0.438698	+	0.898635i	$0.644560\pi$
$380$	−430459.	+	208380.i	−2.98102	+	1.44308i
$381$	22611.3			0.155767
$382$		−	84461.1i		−	0.578802i
$383$		−	11040.1i		−	0.0752617i	−0.999292	−	0.0376309i	$-0.988019\pi$
$383$		−	11040.1i		−	0.0752617i	0.999292	−	0.0376309i	$-0.0119811\pi$
$384$	−214770.			−1.45650
$385$	199504.			1.34595
$386$	168428.			1.13042
$387$	24700.4			0.164923
$388$		−	739871.i		−	4.91465i
$389$	78536.2			0.519004			0.259502	−	0.965743i	$-0.416442\pi$
$389$	78536.2			0.519004			0.259502	+	0.965743i	$0.416442\pi$
$390$			275783.i			1.81317i
$391$	146956.			0.961245
$392$		−	414366.i		−	2.69657i
$393$			68285.6i			0.442124i
$394$		−	164412.i		−	1.05911i
$395$			63995.4i			0.410161i
$396$	−111546.			−0.711318
$397$	−209309.			−1.32802			−0.664012	−	0.747722i	$-0.731148\pi$
$397$	−209309.			−1.32802			−0.664012	+	0.747722i	$0.731148\pi$
$398$		−	253775.i		−	1.60208i
$399$	54368.4	+	112311.i	0.341508	+	0.705466i
$400$	298132.			1.86332
$401$		−	11923.9i		−	0.0741533i	−0.999312	−	0.0370766i	$-0.988195\pi$
$401$		−	11923.9i		−	0.0741533i	0.999312	−	0.0370766i	$-0.0118046\pi$
$402$		−	47996.1i		−	0.296998i
$403$	189933.			1.16947
$404$	680998.			4.17237
$405$	−22607.6			−0.137830
$406$	−63331.5			−0.384209
$407$			96431.1i			0.582141i
$408$	400361.			2.40509
$409$		−	251129.i		−	1.50124i	−0.660735	−	0.750620i	$-0.729755\pi$
$409$		−	251129.i		−	1.50124i	0.660735	−	0.750620i	$-0.270245\pi$
$410$	−48645.0			−0.289381
$411$		−	47027.6i		−	0.278400i
$412$			454753.i			2.67905i
$413$			103672.i			0.607803i
$414$			80792.2i			0.471378i
$415$	−64464.6			−0.374304
$416$	783629.			4.52818
$417$		−	96716.2i		−	0.556195i
$418$	116567.	+	240797.i	0.667150	+	1.37816i
$419$	−269215.			−1.53346			−0.766729	−	0.641971i	$-0.778117\pi$
$419$	−269215.			−1.53346			−0.766729	+	0.641971i	$0.778117\pi$
$420$		−	457905.i		−	2.59583i
$421$		−	198288.i		−	1.11875i	−0.828916	−	0.559373i	$-0.811042\pi$
$421$		−	198288.i		−	1.11875i	0.828916	−	0.559373i	$-0.188958\pi$
$422$	−272472.			−1.53002
$423$	−55941.7			−0.312648
$424$	−94093.8			−0.523395
$425$	−126722.			−0.701572
$426$			152334.i			0.839417i
$427$	149626.			0.820637
$428$			802298.i			4.37974i
$429$	112235.			0.609837
$430$			217397.i			1.17576i
$431$		−	231203.i		−	1.24462i	−0.782769	−	0.622312i	$-0.786193\pi$
$431$		−	231203.i		−	1.24462i	0.782769	−	0.622312i	$-0.213807\pi$
$432$			124215.i			0.665588i
$433$			152306.i			0.812346i	0.913796	+	0.406173i	$0.133137\pi$
$433$			152306.i			0.812346i	−0.913796	+	0.406173i	$0.866863\pi$
$434$	−433478.			−2.30138
$435$	−20021.2			−0.105806
$436$			911093.i			4.79281i
$437$	126884.	−	61423.2i	0.664423	−	0.321640i
$438$	−349372.			−1.82113
$439$		−	51920.1i		−	0.269405i	−0.990886	−	0.134703i	$-0.956992\pi$
$439$		−	51920.1i		−	0.269405i	0.990886	−	0.134703i	$-0.0430079\pi$
$440$		−	614046.i		−	3.17172i
$441$	−54644.7			−0.280977
$442$	−644064.			−3.29674
$443$	−108874.			−0.554777			−0.277389	−	0.960758i	$-0.589469\pi$
$443$	−108874.			−0.554777			−0.277389	+	0.960758i	$0.589469\pi$
$444$	221330.			1.12273
$445$		−	280119.i		−	1.41457i
$446$	143887.			0.723355
$447$		−	71669.0i		−	0.358687i
$448$	−846131.			−4.21581
$449$			20420.5i			0.101292i	0.998717	+	0.0506458i	$0.0161280\pi$
$449$			20420.5i			0.101292i	−0.998717	+	0.0506458i	$0.983872\pi$
$450$		−	69667.8i		−	0.344039i
$451$			19797.0i			0.0973298i
$452$			849004.i			4.15559i
$453$	152431.			0.742807
$454$	746852.			3.62345
$455$			460733.i			2.22549i
$456$	345678.	−	167339.i	1.66242	−	0.804760i
$457$	−273160.			−1.30793			−0.653966	−	0.756524i	$-0.726896\pi$
$457$	−273160.			−1.30793			−0.653966	+	0.756524i	$0.726896\pi$
$458$		−	489496.i		−	2.33356i
$459$		−	52797.7i		−	0.250605i
$460$	−517322.			−2.44481
$461$	−9562.08			−0.0449936			−0.0224968	−	0.999747i	$-0.507162\pi$
$461$	−9562.08			−0.0449936			−0.0224968	+	0.999747i	$0.507162\pi$
$462$	−256150.			−1.20008
$463$	−207971.			−0.970157			−0.485078	−	0.874471i	$-0.661209\pi$
$463$	−207971.			−0.970157			−0.485078	+	0.874471i	$0.661209\pi$
$464$			110004.i			0.510944i
$465$	−137037.			−0.633770
$466$			419820.i			1.93326i
$467$	382668.			1.75464			0.877320	−	0.479906i	$-0.159329\pi$
$467$	382668.			1.75464			0.877320	+	0.479906i	$0.159329\pi$
$468$		−	257604.i		−	1.17614i
$469$		−	80183.9i		−	0.364537i
$470$		−	492364.i		−	2.22890i
$471$			37394.1i			0.168563i
$472$	319089.			1.43228
$473$	88473.7			0.395450
$474$		−	82166.0i		−	0.365709i
$475$	−109413.	+	52965.7i	−0.484935	+	0.234751i
$476$	1.06939e6			4.71979
$477$			12408.7i			0.0545366i
$478$		−	42451.1i		−	0.185795i
$479$	297347.			1.29596			0.647981	−	0.761657i	$-0.275614\pi$
$479$	297347.			1.29596			0.647981	+	0.761657i	$0.275614\pi$
$480$	−565389.			−2.45394
$481$	−222697.			−0.962553
$482$	−543741.			−2.34044
$483$			134974.i			0.578571i
$484$	225897.			0.964319
$485$		−	537114.i		−	2.28340i
$486$	29026.7			0.122892
$487$		−	144535.i		−	0.609418i	−0.952445	−	0.304709i	$-0.901441\pi$
$487$		−	144535.i		−	0.609418i	0.952445	−	0.304709i	$-0.0985593\pi$
$488$		−	460528.i		−	1.93382i
$489$		−	193424.i		−	0.808897i
$490$		−	480948.i		−	2.00312i
$491$	−355659.			−1.47527			−0.737634	−	0.675201i	$-0.764057\pi$
$491$	−355659.			−1.47527			−0.737634	+	0.675201i	$0.764057\pi$
$492$	45438.4			0.187712
$493$		−	46757.5i		−	0.192379i
$494$	−556095.	+	269199.i	−2.27874	+	1.10311i
$495$	−80977.5			−0.330487
$496$			752934.i			3.06051i
$497$			254494.i			1.03030i
$498$	82768.3			0.333738
$499$	−20809.3			−0.0835712			−0.0417856	−	0.999127i	$-0.513305\pi$
$499$	−20809.3			−0.0835712			−0.0417856	+	0.999127i	$0.513305\pi$
$500$	−381894.			−1.52758
$501$	−77262.7			−0.307818
$502$		−	416748.i		−	1.65374i
$503$	−206622.			−0.816658			−0.408329	−	0.912835i	$-0.633888\pi$
$503$	−206622.			−0.816658			−0.408329	+	0.912835i	$0.633888\pi$
$504$			367718.i			1.44762i
$505$	494374.			1.93853
$506$			289388.i			1.13026i
$507$			110787.i			0.430996i
$508$		−	185892.i		−	0.720332i
$509$		−	42466.7i		−	0.163913i	−0.996636	−	0.0819565i	$-0.973883\pi$
$509$		−	42466.7i		−	0.163913i	0.996636	−	0.0819565i	$-0.0261168\pi$
$510$	464692.			1.78659
$511$	−583673.			−2.23526
$512$			206133.i			0.786334i
$513$	−22067.8	−	45586.4i	−0.0838543	−	0.173221i
$514$	−184668.			−0.698981
$515$			330131.i			1.24472i
$516$		−	203066.i		−	0.762674i
$517$	−200376.			−0.749662
$518$	508254.			1.89418
$519$	−594.323			−0.00220642
$520$	1.41807e6			5.24435
$521$		−	182974.i		−	0.674084i	−0.941490	−	0.337042i	$-0.890574\pi$
$521$		−	182974.i		−	0.674084i	0.941490	−	0.337042i	$-0.109426\pi$
$522$	25705.9			0.0943392
$523$			415644.i			1.51956i	0.650180	+	0.759780i	$0.274693\pi$
$523$			415644.i			1.51956i	−0.650180	+	0.759780i	$0.725307\pi$
$524$	561389.			2.04457
$525$		−	116389.i		−	0.422274i
$526$		−	50637.1i		−	0.183020i
$527$		−	320036.i		−	1.15233i
$528$			444922.i			1.59594i
$529$	−127353.			−0.455090
$530$	−109213.			−0.388797
$531$		−	42080.0i		−	0.149241i
$532$	923329.	−	446973.i	3.26237	−	1.57928i
$533$	−45719.0			−0.160932
$534$			359655.i			1.26126i
$535$			582433.i			2.03488i
$536$	−246795.			−0.859028
$537$	−223643.			−0.775546
$538$	414629.			1.43250
$539$	−195731.			−0.673723
$540$			185861.i			0.637383i
$541$	−261668.			−0.894039			−0.447020	−	0.894524i	$-0.647515\pi$
$541$	−261668.			−0.894039			−0.447020	+	0.894524i	$0.647515\pi$
$542$		−	77995.2i		−	0.265503i
$543$	156740.			0.531594
$544$		−	1.32041e6i		−	4.46180i
$545$			661414.i			2.22679i
$546$		−	591551.i		−	1.98430i
$547$			329628.i			1.10166i	0.834616	+	0.550832i	$0.185689\pi$
$547$			329628.i			1.10166i	−0.834616	+	0.550832i	$0.814311\pi$
$548$	−386623.			−1.28744
$549$	−60732.3			−0.201500
$550$		−	249542.i		−	0.824931i
$551$	−19543.2	−	40371.2i	−0.0643714	−	0.132974i
$552$	415432.			1.36340
$553$		−	137269.i		−	0.448873i
$554$		−	638363.i		−	2.07993i
$555$	160676.			0.521633
$556$	−795121.			−2.57208
$557$	516273.			1.66406			0.832030	−	0.554731i	$-0.187179\pi$
$557$	516273.			1.66406			0.832030	+	0.554731i	$0.187179\pi$
$558$	175946.			0.565083
$559$			204320.i			0.653865i
$560$	−1.82644e6			−5.82410
$561$		−	189115.i		−	0.600897i
$562$	319837.			1.01264
$563$		−	598589.i		−	1.88848i	−0.329259	−	0.944240i	$-0.606799\pi$
$563$		−	598589.i		−	1.88848i	0.329259	−	0.944240i	$-0.393201\pi$
$564$			459907.i			1.44581i
$565$			616340.i			1.93074i
$566$		−	677562.i		−	2.11503i
$567$	48492.9			0.150838
$568$	783299.			2.42790
$569$		−	204518.i		−	0.631694i	−0.948810	−	0.315847i	$-0.897711\pi$
$569$		−	204518.i		−	0.631694i	0.948810	−	0.315847i	$-0.102289\pi$
$570$	401223.	−	194227.i	1.23491	−	0.597806i
$571$	381630.			1.17050			0.585249	−	0.810853i	$-0.300997\pi$
$571$	381630.			1.17050			0.585249	+	0.810853i	$0.300997\pi$
$572$		−	922704.i		−	2.82014i
$573$			57273.1i			0.174438i
$574$	104343.			0.316693
$575$	−131492.			−0.397707
$576$	343440.			1.03516
$577$	12294.8			0.0369291			0.0184645	−	0.999830i	$-0.494122\pi$
$577$	12294.8			0.0369291			0.0184645	+	0.999830i	$0.494122\pi$
$578$			445237.i			1.33271i
$579$	−114211.			−0.340683
$580$			164598.i			0.489292i
$581$	138275.			0.409631
$582$			689619.i			2.03593i
$583$			44446.3i			0.130767i
$584$			1.79646e6i			5.26736i
$585$		−	187009.i		−	0.546450i
$586$	−1.27383e6			−3.70952
$587$	−218105.			−0.632978			−0.316489	−	0.948596i	$-0.602504\pi$
$587$	−218105.			−0.632978			−0.316489	+	0.948596i	$0.602504\pi$
$588$			449244.i			1.29935i
$589$	−133765.	−	276324.i	−0.385578	−	0.796504i
$590$	370362.			1.06395
$591$			111488.i			0.319192i
$592$		−	882817.i		−	2.51899i
$593$	595532.			1.69354			0.846771	−	0.531958i	$-0.178544\pi$
$593$	595532.			1.69354			0.846771	+	0.531958i	$0.178544\pi$
$594$	103970.			0.294669
$595$	776330.			2.19287
$596$	−589204.			−1.65872
$597$			172085.i			0.482831i
$598$	−668310.			−1.86885
$599$			554111.i			1.54434i	0.635415	+	0.772171i	$0.280829\pi$
$599$			554111.i			1.54434i	−0.635415	+	0.772171i	$0.719171\pi$
$600$	−358231.			−0.995085
$601$			158275.i			0.438192i	0.975703	+	0.219096i	$0.0703108\pi$
$601$			158275.i			0.438192i	−0.975703	+	0.219096i	$0.929689\pi$
$602$		−	466314.i		−	1.28672i
$603$			32546.2i			0.0895088i
$604$		−	1.25316e6i		−	3.43505i
$605$	163992.			0.448034
$606$	−634744.			−1.72844
$607$		−	165273.i		−	0.448565i	−0.974524	−	0.224283i	$-0.927996\pi$
$607$		−	165273.i		−	0.448565i	0.974524	−	0.224283i	$-0.0720039\pi$
$608$	−551890.	−	1.14006e6i	−1.49295	−	3.08405i
$609$	42945.2			0.115792
$610$		−	534527.i		−	1.43652i
$611$		−	462747.i		−	1.23954i
$612$	−434060.			−1.15890
$613$	310690.			0.826810			0.413405	−	0.910547i	$-0.364339\pi$
$613$	310690.			0.826810			0.413405	+	0.910547i	$0.364339\pi$
$614$	673817.			1.78733
$615$	32986.2			0.0872133
$616$			1.31712e6i			3.47107i
$617$	−342236.			−0.898990			−0.449495	−	0.893283i	$-0.648396\pi$
$617$	−342236.			−0.898990			−0.449495	+	0.893283i	$0.648396\pi$
$618$		−	423867.i		−	1.10982i
$619$	−174299.			−0.454899			−0.227449	−	0.973790i	$-0.573039\pi$
$619$	−174299.			−0.454899			−0.227449	+	0.973790i	$0.573039\pi$
$620$			1.12660e6i			2.93081i
$621$		−	54785.3i		−	0.142063i
$622$		−	40050.7i		−	0.103521i
$623$			600852.i			1.54807i
$624$	−1.02750e6			−2.63883
$625$	−487694.			−1.24850
$626$			1.34624e6i			3.43537i
$627$	−79044.3	−	163285.i	−0.201065	−	0.415347i
$628$	307424.			0.779504
$629$			375243.i			0.948443i
$630$			426804.i			1.07534i
$631$	194539.			0.488594			0.244297	−	0.969700i	$-0.421443\pi$
$631$	194539.			0.488594			0.244297	+	0.969700i	$0.421443\pi$
$632$	−422496.			−1.05776
$633$	184763.			0.461114
$634$	−550040.			−1.36841
$635$		−	134949.i		−	0.334675i
$636$	102014.			0.252200
$637$		−	452018.i		−	1.11398i
$638$	92075.4			0.226205
$639$		−	103298.i		−	0.252982i
$640$			1.28179e6i			3.12938i
$641$			36618.5i			0.0891218i	0.999007	+	0.0445609i	$0.0141889\pi$
$641$			36618.5i			0.0891218i	−0.999007	+	0.0445609i	$0.985811\pi$
$642$		−	747806.i		−	1.81434i
$643$	425283.			1.02862			0.514311	−	0.857603i	$-0.328048\pi$
$643$	425283.			1.02862			0.514311	+	0.857603i	$0.328048\pi$
$644$	1.10965e6			2.67555
$645$		−	147417.i		−	0.354347i
$646$	453598.	+	937015.i	1.08694	+	2.24534i
$647$	−654404.			−1.56328			−0.781641	−	0.623729i	$-0.785617\pi$
$647$	−654404.			−1.56328			−0.781641	+	0.623729i	$0.785617\pi$
$648$		−	149255.i		−	0.355449i
$649$		−	150725.i		−	0.357847i
$650$	576289.			1.36400
$651$	293942.			0.693585
$652$	−1.59018e6			−3.74068
$653$	−70972.3			−0.166442			−0.0832210	−	0.996531i	$-0.526521\pi$
$653$	−70972.3			−0.166442			−0.0832210	+	0.996531i	$0.526521\pi$
$654$		−	849212.i		−	1.98546i
$655$	407543.			0.949929
$656$		−	181239.i		−	0.421157i
$657$	236909.			0.548848
$658$			1.05611e6i			2.43926i
$659$		−	612650.i		−	1.41072i	−0.708848	−	0.705361i	$-0.750785\pi$
$659$		−	612650.i		−	1.41072i	0.708848	−	0.705361i	$-0.249215\pi$
$660$			665731.i			1.52831i
$661$			115644.i			0.264679i	0.991204	+	0.132340i	$0.0422490\pi$
$661$			115644.i			0.264679i	−0.991204	+	0.132340i	$0.957751\pi$
$662$	1.28181e6			2.92488
$663$	436740.			0.993565
$664$		−	425593.i		−	0.965291i
$665$	670296.	−	324482.i	1.51574	−	0.733750i
$666$	−206298.			−0.465099
$667$		−	48517.7i		−	0.109056i
$668$			635191.i			1.42348i
$669$	−97569.8			−0.218003
$670$	−286451.			−0.638118
$671$	−217536.			−0.483154
$672$	1.21275e6			2.68555
$673$			378924.i			0.836609i	0.908307	+	0.418304i	$0.137375\pi$
$673$			378924.i			0.836609i	−0.908307	+	0.418304i	$0.862625\pi$
$674$	−503780.			−1.10897
$675$			47241.8i			0.103686i
$676$	910801.			1.99311
$677$			224567.i			0.489969i	0.969527	+	0.244985i	$0.0787829\pi$
$677$			224567.i			0.489969i	−0.969527	+	0.244985i	$0.921217\pi$
$678$		−	791340.i		−	1.72149i
$679$			1.15210e6i			2.49891i
$680$		−	2.38944e6i		−	5.16747i
$681$	−506441.			−1.09203
$682$	630218.			1.35495
$683$		−	437977.i		−	0.938881i	−0.882964	−	0.469440i	$-0.844456\pi$
$683$		−	437977.i		−	0.938881i	0.882964	−	0.469440i	$-0.155544\pi$
$684$	−374774.	+	181424.i	−0.801046	+	0.387777i
$685$	−280671.			−0.598159
$686$		−	192230.i		−	0.408481i
$687$			331928.i			0.703283i
$688$	−809968.			−1.71116
$689$	−102644.			−0.216219
$690$	482185.			1.01278
$691$	−480883.			−1.00712			−0.503562	−	0.863959i	$-0.667977\pi$
$691$	−480883.			−1.00712			−0.503562	+	0.863959i	$0.667977\pi$
$692$			4886.04i			0.0102034i
$693$	173696.			0.361678
$694$		−	557638.i		−	1.15780i
$695$	−577223.			−1.19502
$696$		−	132179.i		−	0.272863i
$697$			77036.0i			0.158573i
$698$		−	193675.i		−	0.397524i
$699$		−	284680.i		−	0.582643i
$700$	−956859.			−1.95277
$701$	688873.			1.40185			0.700927	−	0.713233i	$-0.252770\pi$
$701$	688873.			1.40185			0.700927	+	0.713233i	$0.252770\pi$
$702$			240107.i			0.487226i
$703$	156840.	+	323991.i	0.317356	+	0.655574i
$704$	1.23016e6			2.48208
$705$			333872.i			0.671742i
$706$		−	186305.i		−	0.373779i
$707$	−1.06043e6			−2.12149
$708$	−345948.			−0.690151
$709$	−70606.7			−0.140460			−0.0702301	−	0.997531i	$-0.522373\pi$
$709$	−70606.7			−0.140460			−0.0702301	+	0.997531i	$0.522373\pi$
$710$	909162.			1.80354
$711$			55716.8i			0.110217i
$712$	1.84934e6			3.64802
$713$		−	332083.i		−	0.653233i
$714$	−996758.			−1.95521
$715$		−	669843.i		−	1.31027i
$716$			1.83861e6i			3.58645i
$717$			28786.1i			0.0559945i
$718$			325138.i			0.630695i
$719$	−768931.			−1.48741			−0.743703	−	0.668510i	$-0.766933\pi$
$719$	−768931.			−1.48741			−0.743703	+	0.668510i	$0.766933\pi$
$720$	741341.			1.43006
$721$		−	708126.i		−	1.36220i
$722$	783288.	+	619443.i	1.50261	+	1.18830i
$723$	368711.			0.705358
$724$		−	1.28859e6i		−	2.45831i
$725$			41837.2i			0.0795952i
$726$	−210555.			−0.399477
$727$	148091.			0.280194			0.140097	−	0.990138i	$-0.455259\pi$
$727$	148091.			0.280194			0.140097	+	0.990138i	$0.455259\pi$
$728$	−3.04174e6			−5.73931
$729$	−19683.0			−0.0370370
$730$			2.08513e6i			3.91279i
$731$	344278.			0.644280
$732$			499291.i			0.931820i
$733$	−442880.			−0.824287			−0.412143	−	0.911119i	$-0.635220\pi$
$733$	−442880.			−0.824287			−0.412143	+	0.911119i	$0.635220\pi$
$734$			154266.i			0.286337i
$735$			326131.i			0.603695i
$736$		−	1.37011e6i		−	2.52931i
$737$			116577.i			0.214623i
$738$	−42352.2			−0.0777612
$739$	−25120.5			−0.0459981			−0.0229990	−	0.999735i	$-0.507321\pi$
$739$	−25120.5			−0.0459981			−0.0229990	+	0.999735i	$0.507321\pi$
$740$		−	1.32095e6i		−	2.41225i
$741$	377089.	−	182544.i	0.686763	−	0.332454i
$742$	234261.			0.425492
$743$			799665.i			1.44854i	0.689517	+	0.724270i	$0.257823\pi$
$743$			799665.i			1.44854i	−0.689517	+	0.724270i	$0.742177\pi$
$744$		−	904713.i		−	1.63443i
$745$	−427736.			−0.770661
$746$	−571066.			−1.02614
$747$	−56125.3			−0.100581
$748$	−1.55475e6			−2.77880
$749$		−	1.24931e6i		−	2.22693i
$750$	355956.			0.632811
$751$		−	81171.6i		−	0.143921i	−0.997407	−	0.0719605i	$-0.977074\pi$
$751$		−	81171.6i		−	0.143921i	0.997407	−	0.0719605i	$-0.0229255\pi$
$752$	1.83442e6			3.24388
$753$			282597.i			0.498400i
$754$			212638.i			0.374023i
$755$		−	909739.i		−	1.59596i
$756$		−	398669.i		−	0.697540i
$757$	613413.			1.07044			0.535219	−	0.844714i	$-0.320229\pi$
$757$	613413.			1.07044			0.535219	+	0.844714i	$0.320229\pi$
$758$	−1.97824e6			−3.44303
$759$		−	196234.i		−	0.340636i
$760$	−998713.	−	2.06308e6i	−1.72907	−	3.57181i
$761$	−280102.			−0.483667			−0.241833	−	0.970318i	$-0.577749\pi$
$761$	−280102.			−0.483667			−0.241833	+	0.970318i	$0.577749\pi$
$762$			173266.i			0.298403i
$763$		−	1.41872e6i		−	2.43696i
$764$	470853.			0.806675
$765$	−315108.			−0.538439
$766$	84597.9			0.144179
$767$	348084.			0.591689
$768$		−	588221.i		−	0.997282i
$769$	−409111.			−0.691812			−0.345906	−	0.938269i	$-0.612428\pi$
$769$	−409111.			−0.691812			−0.345906	+	0.938269i	$0.612428\pi$
$770$			1.52876e6i			2.57844i
$771$	125224.			0.210658
$772$			938949.i			1.57546i
$773$			338770.i			0.566952i	0.958979	+	0.283476i	$0.0914876\pi$
$773$			338770.i			0.566952i	−0.958979	+	0.283476i	$0.908512\pi$
$774$			189274.i			0.315943i
$775$			286358.i			0.476767i
$776$	3.54601e6			5.88866
$777$	−344648.			−0.570865
$778$			601807.i			0.994256i
$779$	32198.7	+	66514.1i	0.0530596	+	0.109607i
$780$	−1.53743e6			−2.52701
$781$		−	370000.i		−	0.606596i
$782$			1.12610e6i			1.84146i
$783$	−17431.2			−0.0284318
$784$	1.79189e6			2.91528
$785$	223176.			0.362167
$786$	−523259.			−0.846977
$787$		−	618561.i		−	0.998695i	−0.866402	−	0.499347i	$-0.833573\pi$
$787$		−	618561.i		−	0.998695i	0.866402	−	0.499347i	$-0.166427\pi$
$788$	916561.			1.47608
$789$			34337.1i			0.0551581i
$790$	−490384.			−0.785746
$791$		−	1.32204e6i		−	2.11296i
$792$		−	534611.i		−	0.852291i
$793$		−	502375.i		−	0.798880i
$794$		−	1.60389e6i		−	2.54410i
$795$	74057.6			0.117175
$796$	1.41475e6			2.23281
$797$			985905.i			1.55210i	0.630674	+	0.776048i	$0.282778\pi$
$797$			985905.i			1.55210i	−0.630674	+	0.776048i	$0.717222\pi$
$798$	−860616.	+	416614.i	−1.35146	+	0.654227i
$799$	−779725.			−1.22137
$800$			1.18146e6i			1.84603i
$801$		−	243882.i		−	0.380116i
$802$	91370.6			0.142055
$803$	848581.			1.31602
$804$	267568.			0.413926
$805$	805555.			1.24309
$806$			1.45542e6i			2.24036i
$807$	−281160.			−0.431724
$808$			3.26384e6i			4.99927i
$809$	459065.			0.701418			0.350709	−	0.936485i	$-0.385941\pi$
$809$	459065.			0.701418			0.350709	+	0.936485i	$0.385941\pi$
$810$		−	173237.i		−	0.264041i
$811$		−	1.02357e6i		−	1.55624i	−0.628116	−	0.778120i	$-0.716174\pi$
$811$		−	1.02357e6i		−	1.55624i	0.628116	−	0.778120i	$-0.283826\pi$
$812$		−	353060.i		−	0.535472i
$813$			52888.6i			0.0800168i
$814$	−738933.			−1.11521
$815$	−1.15440e6			−1.73796
$816$			1.73133e6i			2.60015i
$817$	297255.	−	143898.i	0.445334	−	0.215581i
$818$	1.92435e6			2.87592
$819$			401131.i			0.598024i
$820$		−	271186.i		−	0.403310i
$821$	−1.07226e6			−1.59079			−0.795397	−	0.606089i	$-0.792738\pi$
$821$	−1.07226e6			−1.59079			−0.795397	+	0.606089i	$0.792738\pi$
$822$	360363.			0.533331
$823$	923304.			1.36316			0.681578	−	0.731746i	$-0.261294\pi$
$823$	923304.			1.36316			0.681578	+	0.731746i	$0.261294\pi$
$824$	−2.17951e6			−3.21000
$825$			169214.i			0.248616i
$826$	−794420.			−1.16437
$827$			785245.i			1.14814i	0.818807	+	0.574069i	$0.194636\pi$
$827$			785245.i			1.14814i	−0.818807	+	0.574069i	$0.805364\pi$
$828$	−450400.			−0.656958
$829$			871166.i			1.26763i	0.773486	+	0.633814i	$0.218511\pi$
$829$			871166.i			1.26763i	−0.773486	+	0.633814i	$0.781489\pi$
$830$		−	493979.i		−	0.717055i
$831$			432874.i			0.626845i
$832$			2.84092e6i			4.10404i
$833$	−761647.			−1.09765
$834$	741117.			1.06550
$835$			461121.i			0.661366i
$836$	−1.34239e6	+	649838.i	−1.92074	+	0.929806i
$837$	−119309.			−0.170304
$838$		−	2.06294e6i		−	2.93765i
$839$			756483.i			1.07467i	0.843369	+	0.537335i	$0.180569\pi$
$839$			756483.i			1.07467i	−0.843369	+	0.537335i	$0.819431\pi$
$840$	2.19462e6			3.11029
$841$	691844.			0.978174
$842$	1.51944e6			2.14318
$843$	−216882.			−0.305188
$844$		−	1.51897e6i		−	2.13238i
$845$	661201.			0.926020
$846$		−	428670.i		−	0.598939i
$847$	−351759.			−0.490319
$848$		−	406901.i		−	0.565845i
$849$			459456.i			0.637424i
$850$		−	971042.i		−	1.34400i
$851$			389369.i			0.537653i
$852$	−849230.			−1.16989
$853$	1.07957e6			1.48372			0.741859	−	0.670556i	$-0.233944\pi$
$853$	1.07957e6			1.48372			0.741859	+	0.670556i	$0.233944\pi$
$854$			1.14655e6i			1.57209i
$855$	−272069.	+	131706.i	−0.372175	+	0.180166i
$856$	−3.84521e6			−5.24774
$857$			514381.i			0.700363i	0.936682	+	0.350181i	$0.113880\pi$
$857$			514381.i			0.700363i	−0.936682	+	0.350181i	$0.886120\pi$
$858$			860034.i			1.16826i
$859$	931603.			1.26254			0.631269	−	0.775564i	$-0.282534\pi$
$859$	931603.			1.26254			0.631269	+	0.775564i	$0.282534\pi$
$860$	−1.21194e6			−1.63865
$861$	−70755.0			−0.0954445
$862$	1.77166e6			2.38433
$863$		−	106157.i		−	0.142537i	−0.997457	−	0.0712684i	$-0.977295\pi$
$863$		−	106157.i		−	0.142537i	0.997457	−	0.0712684i	$-0.0227047\pi$
$864$	−492248.			−0.659412
$865$			3547.05i			0.00474061i
$866$	−1.16709e6			−1.55621
$867$		−	301916.i		−	0.401650i
$868$		−	2.41655e6i		−	3.20742i
$869$			199571.i			0.264276i
$870$		−	153418.i		−	0.202693i
$871$	−269221.			−0.354872
$872$	−4.36663e6			−5.74267
$873$		−	467631.i		−	0.613586i
$874$	470674.	+	972289.i	0.616165	+	1.27284i
$875$	594672.			0.776715
$876$		−	1.94768e6i		−	2.53810i
$877$		−	1.08342e6i		−	1.40864i	−0.709885	−	0.704318i	$-0.751253\pi$
$877$		−	1.08342e6i		−	1.40864i	0.709885	−	0.704318i	$-0.248747\pi$
$878$	397853.			0.516100
$879$	863788.			1.11797
$880$	2.65539e6			3.42897
$881$	222607.			0.286805			0.143403	−	0.989664i	$-0.454196\pi$
$881$	222607.			0.286805			0.143403	+	0.989664i	$0.454196\pi$
$882$		−	418731.i		−	0.538268i
$883$	141019.			0.180865			0.0904326	−	0.995903i	$-0.471175\pi$
$883$	141019.			0.180865			0.0904326	+	0.995903i	$0.471175\pi$
$884$		−	3.59052e6i		−	4.59466i
$885$	−251143.			−0.320652
$886$		−	834284.i		−	1.06279i
$887$			368002.i			0.467738i	0.972268	+	0.233869i	$0.0751387\pi$
$887$			368002.i			0.467738i	−0.972268	+	0.233869i	$0.924861\pi$
$888$			1.06078e6i			1.34524i
$889$			289464.i			0.366262i
$890$	2.14650e6			2.70988
$891$	−70502.1			−0.0888069
$892$			802139.i			1.00814i
$893$	−673227.	+	325902.i	−0.844226	+	0.408680i
$894$	549185.			0.687138
$895$			1.33475e6i			1.66630i
$896$		−	2.74943e6i		−	3.42473i
$897$	453181.			0.563232
$898$	−156478.			−0.194044
$899$	−105660.			−0.130735
$900$	388384.			0.479486
$901$			172954.i			0.213050i
$902$	−151700.			−0.186455
$903$			316208.i			0.387790i
$904$	−4.06906e6			−4.97917
$905$		−	935458.i		−	1.14216i
$906$			1.16805e6i			1.42300i
$907$			30630.6i			0.0372341i	0.999827	+	0.0186170i	$0.00592633\pi$
$907$			30630.6i			0.0372341i	−0.999827	+	0.0186170i	$0.994074\pi$
$908$			4.16354e6i			5.05000i
$909$	430421.			0.520913
$910$	−3.53050e6			−4.26338
$911$		−	983363.i		−	1.18489i	−0.805612	−	0.592443i	$-0.798163\pi$
$911$		−	983363.i		−	1.18489i	0.805612	−	0.592443i	$-0.201837\pi$
$912$	723642.	+	1.49485e6i	0.870030	+	1.79725i
$913$	−201034.			−0.241172
$914$		−	2.09317e6i		−	2.50561i
$915$			362464.i			0.432934i
$916$	2.72884e6			3.25227
$917$	−874174.			−1.03958
$918$	404578.			0.480084
$919$	−251425.			−0.297699			−0.148850	−	0.988860i	$-0.547557\pi$
$919$	−251425.			−0.297699			−0.148850	+	0.988860i	$0.547557\pi$
$920$		−	2.47939e6i		−	2.92933i
$921$	−456916.			−0.538663
$922$		−	73272.3i		−	0.0861942i
$923$	854475.			1.00299
$924$		−	1.42798e6i		−	1.67255i
$925$		−	335756.i		−	0.392410i
$926$		−	1.59364e6i		−	1.85853i
$927$			287424.i			0.334475i
$928$	−435934.			−0.506203
$929$	−72535.3			−0.0840461			−0.0420231	−	0.999117i	$-0.513380\pi$
$929$	−72535.3			−0.0840461			−0.0420231	+	0.999117i	$0.513380\pi$
$930$		−	1.05009e6i		−	1.21411i
$931$	−657618.	+	318345.i	−0.758708	+	0.367282i
$932$	−2.34041e6			−2.69439
$933$			27158.4i			0.0311990i
$934$			2.93231e6i			3.36136i
$935$	−1.12868e6			−1.29106
$936$	1.23463e6			1.40924
$937$	−1.08328e6			−1.23385			−0.616926	−	0.787021i	$-0.711622\pi$
$937$	−1.08328e6			−1.23385			−0.616926	+	0.787021i	$0.711622\pi$
$938$	614434.			0.698344
$939$		−	912886.i		−	1.03535i
$940$	2.74483e6			3.10641
$941$			1.24676e6i			1.40800i	0.710200	+	0.704000i	$0.248604\pi$
$941$			1.24676e6i			1.40800i	−0.710200	+	0.704000i	$0.751396\pi$
$942$	−286544.			−0.322916
$943$			79936.1i			0.0898916i
$944$			1.37988e6i			1.54845i
$945$		−	289416.i		−	0.324085i
$946$			677957.i			0.757565i
$947$	1.61908e6			1.80538			0.902688	−	0.430295i	$-0.141591\pi$
$947$	1.61908e6			1.80538			0.902688	+	0.430295i	$0.141591\pi$
$948$	458058.			0.509688
$949$			1.95970e6i			2.17600i
$950$	−405866.	−	838413.i	−0.449713	−	0.928989i
$951$	372982.			0.412408
$952$			5.12531e6i			5.65518i
$953$			15402.2i			0.0169589i	0.999964	+	0.00847943i	$0.00269912\pi$
$953$			15402.2i			0.0169589i	−0.999964	+	0.00847943i	$0.997301\pi$
$954$	−95085.1			−0.104476
$955$	341819.			0.374791
$956$	236656.			0.258942
$957$	−62436.4			−0.0681733
$958$			2.27851e6i			2.48267i
$959$	602035.			0.654613
$960$		−	2.04972e6i		−	2.22409i
$961$	200322.			0.216911
$962$		−	1.70648e6i		−	1.84396i
$963$			507088.i			0.546803i
$964$		−	3.03124e6i		−	3.26187i
$965$			681635.i			0.731977i
$966$	−1.03428e6			−1.10837
$967$	759485.			0.812207			0.406103	−	0.913827i	$-0.366887\pi$
$967$	759485.			0.812207			0.406103	+	0.913827i	$0.366887\pi$
$968$			1.08267e6i			1.15543i
$969$	−307585.	−	635391.i	−0.327581	−	0.676696i
$970$	4.11580e6			4.37432
$971$		−	1.34647e6i		−	1.42810i	−0.700094	−	0.714051i	$-0.746859\pi$
$971$		−	1.34647e6i		−	1.42810i	0.700094	−	0.714051i	$-0.253141\pi$
$972$			161818.i			0.171275i
$973$	1.23813e6			1.30780
$974$	1.10754e6			1.16746
$975$	−390782.			−0.411079
$976$	1.99152e6			2.09066
$977$			16560.0i			0.0173489i	0.999962	+	0.00867443i	$0.00276119\pi$
$977$			16560.0i			0.0173489i	−0.999962	+	0.00867443i	$0.997239\pi$
$978$	1.48217e6			1.54960
$979$		−	873557.i		−	0.911435i
$980$	2.68119e6			2.79174
$981$			575851.i			0.598374i
$982$		−	2.72534e6i		−	2.82617i
$983$			564322.i			0.584009i	0.956417	+	0.292005i	$0.0943222\pi$
$983$			564322.i			0.584009i	−0.956417	+	0.292005i	$0.905678\pi$
$984$			217774.i			0.224914i
$985$	665383.			0.685803
$986$	358293.			0.368540
$987$		−	716151.i		−	0.735141i
$988$	−1.50073e6	−	3.10011e6i	−1.53741	−	3.17588i
$989$	357238.			0.365229
$990$		−	620515.i		−	0.633114i
$991$		−	1.79483e6i		−	1.82758i	−0.406187	−	0.913790i	$-0.633142\pi$
$991$		−	1.79483e6i		−	1.82758i	0.406187	−	0.913790i	$-0.366858\pi$
$992$	−2.98379e6			−3.03211
$993$	−869198.			−0.881495
$994$	−1.95014e6			−1.97375
$995$	1.02704e6			1.03739
$996$			461416.i			0.465130i
$997$	−1.68225e6			−1.69239			−0.846193	−	0.532876i	$-0.821111\pi$
$997$	−1.68225e6			−1.69239			−0.846193	+	0.532876i	$0.821111\pi$
$998$		−	159458.i		−	0.160097i
$999$	139891.			0.140171

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.5.c.a.37.14	yes	14
3.2	odd	2		171.5.c.e.37.1		14
4.3	odd	2		912.5.o.b.721.9		14
19.18	odd	2	inner	57.5.c.a.37.1	✓	14
57.56	even	2		171.5.c.e.37.14		14
76.75	even	2		912.5.o.b.721.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.5.c.a.37.1	✓	14	19.18	odd	2	inner
57.5.c.a.37.14	yes	14	1.1	even	1	trivial
171.5.c.e.37.1		14	3.2	odd	2
171.5.c.e.37.14		14	57.56	even	2
912.5.o.b.721.2		14	76.75	even	2
912.5.o.b.721.9		14	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:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	57.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+7.66280i q^{2} -5.19615i q^{3} -42.7185 q^{4} -31.0118 q^{5} +39.8171 q^{6} +66.5198 q^{7} -204.739i q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+7.66280i q^{2} -5.19615i q^{3} -42.7185 q^{4} -31.0118 q^{5} +39.8171 q^{6} +66.5198 q^{7} -204.739i q^{8} -27.0000 q^{9} -237.637i q^{10} -96.7107 q^{11} +221.972i q^{12} -223.343i q^{13} +509.728i q^{14} +161.142i q^{15} +885.376 q^{16} -376.331 q^{17} -206.896i q^{18} +(-324.930 + 157.295i) q^{19} +1324.78 q^{20} -345.647i q^{21} -741.075i q^{22} -390.497 q^{23} -1063.85 q^{24} +336.729 q^{25} +1711.43 q^{26} +140.296i q^{27} -2841.63 q^{28} +124.246i q^{29} -1234.80 q^{30} +850.411i q^{31} +3508.64i q^{32} +502.523i q^{33} -2883.75i q^{34} -2062.89 q^{35} +1153.40 q^{36} -997.110i q^{37} +(-1205.32 - 2489.87i) q^{38} -1160.52 q^{39} +6349.31i q^{40} -204.703i q^{41} +2648.62 q^{42} -914.829 q^{43} +4131.34 q^{44} +837.318 q^{45} -2992.30i q^{46} +2071.92 q^{47} -4600.55i q^{48} +2023.88 q^{49} +2580.29i q^{50} +1955.47i q^{51} +9540.87i q^{52} -459.580i q^{53} -1075.06 q^{54} +2999.17 q^{55} -13619.2i q^{56} +(817.327 + 1688.38i) q^{57} -952.071 q^{58} +1558.52i q^{59} -6883.74i q^{60} +2249.34 q^{61} -6516.53 q^{62} -1796.03 q^{63} -12720.0 q^{64} +6926.25i q^{65} -3850.74 q^{66} -1205.42i q^{67} +16076.3 q^{68} +2029.08i q^{69} -15807.6i q^{70} +3825.85i q^{71} +5527.95i q^{72} -8774.43 q^{73} +7640.65 q^{74} -1749.70i q^{75} +(13880.5 - 6719.40i) q^{76} -6433.17 q^{77} -8892.86i q^{78} -2063.59i q^{79} -27457.1 q^{80} +729.000 q^{81} +1568.60 q^{82} +2078.71 q^{83} +14765.5i q^{84} +11670.7 q^{85} -7010.15i q^{86} +645.600 q^{87} +19800.4i q^{88} +9032.69i q^{89} +6416.20i q^{90} -14856.7i q^{91} +16681.5 q^{92} +4418.87 q^{93} +15876.7i q^{94} +(10076.6 - 4877.99i) q^{95} +18231.4 q^{96} +17319.7i q^{97} +15508.6i q^{98} +2611.19 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 156 q^{4} + 18 q^{5} + 36 q^{6} - 54 q^{7} - 378 q^{9}+O(q^{10}) \) 14 * q - 156 * q^4 + 18 * q^5 + 36 * q^6 - 54 * q^7 - 378 * q^9	\( 14 q - 156 q^{4} + 18 q^{5} + 36 q^{6} - 54 q^{7} - 378 q^{9} - 318 q^{11} + 1252 q^{16} - 654 q^{17} - 694 q^{19} + 960 q^{20} - 492 q^{23} - 1764 q^{24} + 3736 q^{25} + 1296 q^{26} - 3536 q^{28} - 1152 q^{30} + 4566 q^{35} + 4212 q^{36} - 4440 q^{38} - 2952 q^{39} + 2304 q^{42} - 8422 q^{43} + 11232 q^{44} - 486 q^{45} + 12258 q^{47} + 2376 q^{49} - 972 q^{54} + 12782 q^{55} - 4860 q^{57} - 24856 q^{58} + 5378 q^{61} - 41088 q^{62} + 1458 q^{63} - 26012 q^{64} + 792 q^{66} + 26832 q^{68} + 12594 q^{73} + 23856 q^{74} - 12652 q^{76} - 20610 q^{77} - 64056 q^{80} + 10206 q^{81} + 59704 q^{82} - 29436 q^{83} + 26182 q^{85} - 12384 q^{87} + 103704 q^{92} + 38016 q^{93} + 22818 q^{95} - 4932 q^{96} + 8586 q^{99}+O(q^{100}) \) 14 * q - 156 * q^4 + 18 * q^5 + 36 * q^6 - 54 * q^7 - 378 * q^9 - 318 * q^11 + 1252 * q^16 - 654 * q^17 - 694 * q^19 + 960 * q^20 - 492 * q^23 - 1764 * q^24 + 3736 * q^25 + 1296 * q^26 - 3536 * q^28 - 1152 * q^30 + 4566 * q^35 + 4212 * q^36 - 4440 * q^38 - 2952 * q^39 + 2304 * q^42 - 8422 * q^43 + 11232 * q^44 - 486 * q^45 + 12258 * q^47 + 2376 * q^49 - 972 * q^54 + 12782 * q^55 - 4860 * q^57 - 24856 * q^58 + 5378 * q^61 - 41088 * q^62 + 1458 * q^63 - 26012 * q^64 + 792 * q^66 + 26832 * q^68 + 12594 * q^73 + 23856 * q^74 - 12652 * q^76 - 20610 * q^77 - 64056 * q^80 + 10206 * q^81 + 59704 * q^82 - 29436 * q^83 + 26182 * q^85 - 12384 * q^87 + 103704 * q^92 + 38016 * q^93 + 22818 * q^95 - 4932 * q^96 + 8586 * q^99

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