LMFDB - Embedded newform 65.6.c.b.51.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,6,Mod(51,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("65.51");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	65.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:	$10.4249482878$
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} + 227x^{12} + 16583x^{10} + 514217x^{8} + 6872896x^{6} + 35265600x^{4} + 63141120x^{2} + 26873856 $ x^14 + 227x^12 + 16583x^10 + 514217x^8 + 6872896x^6 + 35265600x^4 + 63141120x^2 + 26873856
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.3
Root			$-4.25184i$ of defining polynomial
Character	$\chi$	$=$	65.51
Dual form			65.6.c.b.51.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-6.25184i q^{2} +1.69265 q^{3} -7.08552 q^{4} +25.0000i q^{5} -10.5822i q^{6} -79.8024i q^{7} -155.761i q^{8} -240.135 q^{9} +156.296 q^{10} -347.604i q^{11} -11.9933 q^{12} +(-101.369 - 600.847i) q^{13} -498.912 q^{14} +42.3163i q^{15} -1200.53 q^{16} -348.516 q^{17} +1501.29i q^{18} +596.069i q^{19} -177.138i q^{20} -135.078i q^{21} -2173.16 q^{22} +929.723 q^{23} -263.650i q^{24} -625.000 q^{25} +(-3756.40 + 633.742i) q^{26} -817.779 q^{27} +565.442i q^{28} -1010.52 q^{29} +264.555 q^{30} +326.900i q^{31} +2521.17i q^{32} -588.372i q^{33} +2178.86i q^{34} +1995.06 q^{35} +1701.48 q^{36} -3041.01i q^{37} +3726.53 q^{38} +(-171.582 - 1017.02i) q^{39} +3894.03 q^{40} -15442.4i q^{41} -844.484 q^{42} +15943.2 q^{43} +2462.95i q^{44} -6003.37i q^{45} -5812.48i q^{46} +5759.75i q^{47} -2032.08 q^{48} +10438.6 q^{49} +3907.40i q^{50} -589.915 q^{51} +(718.251 + 4257.32i) q^{52} +36879.5 q^{53} +5112.62i q^{54} +8690.09 q^{55} -12430.1 q^{56} +1008.94i q^{57} +6317.61i q^{58} +9442.94i q^{59} -299.833i q^{60} -30228.3 q^{61} +2043.73 q^{62} +19163.4i q^{63} -22655.1 q^{64} +(15021.2 - 2534.22i) q^{65} -3678.41 q^{66} +45470.8i q^{67} +2469.42 q^{68} +1573.70 q^{69} -12472.8i q^{70} -64611.3i q^{71} +37403.7i q^{72} +33697.5i q^{73} -19011.9 q^{74} -1057.91 q^{75} -4223.46i q^{76} -27739.6 q^{77} +(-6358.28 + 1072.70i) q^{78} +8422.21 q^{79} -30013.3i q^{80} +56968.6 q^{81} -96543.6 q^{82} -43575.0i q^{83} +957.096i q^{84} -8712.89i q^{85} -99674.7i q^{86} -1710.46 q^{87} -54143.2 q^{88} -20667.0i q^{89} -37532.1 q^{90} +(-47949.1 + 8089.48i) q^{91} -6587.58 q^{92} +553.328i q^{93} +36009.1 q^{94} -14901.7 q^{95} +4267.47i q^{96} +50661.4i q^{97} -65260.3i q^{98} +83471.8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 84 q^{3} - 38 q^{4} + 1118 q^{9} + 550 q^{10} + 168 q^{12} - 1132 q^{13} + 6440 q^{14} - 3434 q^{16} + 228 q^{17} + 2328 q^{22} + 8104 q^{23} - 8750 q^{25} - 142 q^{26} + 13680 q^{27} - 16700 q^{29}+ \cdots + 318800 q^{95}+O(q^{100}) $ 14 * q - 84 * q^3 - 38 * q^4 + 1118 * q^9 + 550 * q^10 + 168 * q^12 - 1132 * q^13 + 6440 * q^14 - 3434 * q^16 + 228 * q^17 + 2328 * q^22 + 8104 * q^23 - 8750 * q^25 - 142 * q^26 + 13680 * q^27 - 16700 * q^29 + 12700 * q^30 - 2000 * q^35 + 39970 * q^36 - 5652 * q^38 + 2416 * q^39 + 24750 * q^40 - 96836 * q^42 - 64948 * q^43 - 35932 * q^48 + 29010 * q^49 + 18632 * q^51 - 48972 * q^52 + 106232 * q^53 - 33400 * q^55 - 87808 * q^56 - 65252 * q^61 + 127744 * q^62 + 44754 * q^64 - 40550 * q^65 + 165768 * q^66 + 58536 * q^68 - 318208 * q^69 - 151892 * q^74 + 52500 * q^75 - 123736 * q^77 + 219028 * q^78 - 4336 * q^79 + 364406 * q^81 + 391092 * q^82 - 328560 * q^87 - 282548 * q^88 - 14750 * q^90 - 34376 * q^91 - 163604 * q^92 + 797896 * q^94 + 318800 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	6.25184i		−	1.10518i	−0.833453	−	0.552590i	$-0.813640\pi$
$2$		−	6.25184i		−	1.10518i	0.833453	−	0.552590i	$-0.186360\pi$
$3$	1.69265			0.108584			0.0542918	−	0.998525i	$-0.482710\pi$
$3$	1.69265			0.108584			0.0542918	+	0.998525i	$0.482710\pi$
$4$	−7.08552			−0.221423
$5$			25.0000i			0.447214i
$5$			25.0000i			0.447214i
$6$		−	10.5822i		−	0.120004i
$7$		−	79.8024i		−	0.615561i	−0.951457	−	0.307780i	$-0.900414\pi$
$7$		−	79.8024i		−	0.615561i	0.951457	−	0.307780i	$-0.0995862\pi$
$8$		−	155.761i		−	0.860468i
$9$	−240.135			−0.988210
$10$	156.296			0.494251
$11$		−	347.604i		−	0.866169i	−0.901353	−	0.433084i	$-0.857425\pi$
$11$		−	347.604i		−	0.866169i	0.901353	−	0.433084i	$-0.142575\pi$
$12$	−11.9933			−0.0240429
$13$	−101.369	−	600.847i	−0.166359	−	0.986065i
$13$	−101.369	−	600.847i	−0.166359	−	0.986065i
$14$	−498.912			−0.680306
$15$			42.3163i			0.0485601i
$16$	−1200.53			−1.17239
$17$	−348.516			−0.292482			−0.146241	−	0.989249i	$-0.546718\pi$
$17$	−348.516			−0.292482			−0.146241	+	0.989249i	$0.546718\pi$
$18$			1501.29i			1.09215i
$19$			596.069i			0.378802i	0.981900	+	0.189401i	$0.0606547\pi$
$19$			596.069i			0.378802i	−0.981900	+	0.189401i	$0.939345\pi$
$20$		−	177.138i		−	0.0990232i
$21$		−	135.078i		−	0.0668398i
$22$	−2173.16			−0.957272
$23$	929.723			0.366466			0.183233	−	0.983069i	$-0.441344\pi$
$23$	929.723			0.366466			0.183233	+	0.983069i	$0.441344\pi$
$24$		−	263.650i		−	0.0934327i
$25$	−625.000			−0.200000
$26$	−3756.40	+	633.742i	−1.08978	+	0.183856i
$27$	−817.779			−0.215887
$28$			565.442i			0.136299i
$29$	−1010.52			−0.223126			−0.111563	−	0.993757i	$-0.535586\pi$
$29$	−1010.52			−0.223126			−0.111563	+	0.993757i	$0.535586\pi$
$30$	264.555			0.0536676
$31$			326.900i			0.0610958i	0.999533	+	0.0305479i	$0.00972521\pi$
$31$			326.900i			0.0610958i	−0.999533	+	0.0305479i	$0.990275\pi$
$32$			2521.17i			0.435239i
$33$		−	588.372i		−	0.0940518i
$34$			2178.86i			0.323246i
$35$	1995.06			0.275287
$36$	1701.48			0.218812
$37$		−	3041.01i		−	0.365185i	−0.983189	−	0.182593i	$-0.941551\pi$
$37$		−	3041.01i		−	0.365185i	0.983189	−	0.182593i	$-0.0584489\pi$
$38$	3726.53			0.418645
$39$	−171.582	−	1017.02i	−0.0180638	−	0.107071i
$40$	3894.03			0.384813
$41$		−	15442.4i		−	1.43468i	−0.696722	−	0.717342i	$-0.745359\pi$
$41$		−	15442.4i		−	1.43468i	0.696722	−	0.717342i	$-0.254641\pi$
$42$	−844.484			−0.0738700
$43$	15943.2			1.31494			0.657470	−	0.753481i	$-0.271627\pi$
$43$	15943.2			1.31494			0.657470	+	0.753481i	$0.271627\pi$
$44$			2462.95i			0.191789i
$45$		−	6003.37i		−	0.441941i
$46$		−	5812.48i		−	0.405011i
$47$			5759.75i			0.380329i	0.981752	+	0.190164i	$0.0609021\pi$
$47$			5759.75i			0.380329i	−0.981752	+	0.190164i	$0.939098\pi$
$48$	−2032.08			−0.127303
$49$	10438.6			0.621085
$50$			3907.40i			0.221036i
$51$	−589.915			−0.0317588
$52$	718.251	+	4257.32i	0.0368356	+	0.218337i
$53$	36879.5			1.80341			0.901706	−	0.432350i	$-0.142315\pi$
$53$	36879.5			1.80341			0.901706	+	0.432350i	$0.142315\pi$
$54$			5112.62i			0.238594i
$55$	8690.09			0.387363
$56$	−12430.1			−0.529671
$57$			1008.94i			0.0411317i
$58$			6317.61i			0.246594i
$59$			9442.94i			0.353165i	0.984286	+	0.176582i	$0.0565042\pi$
$59$			9442.94i			0.353165i	−0.984286	+	0.176582i	$0.943496\pi$
$60$		−	299.833i		−	0.0107523i
$61$	−30228.3			−1.04013			−0.520067	−	0.854126i	$-0.674093\pi$
$61$	−30228.3			−1.04013			−0.520067	+	0.854126i	$0.674093\pi$
$62$	2043.73			0.0675218
$63$			19163.4i			0.608303i
$64$	−22655.1			−0.691377
$65$	15021.2	−	2534.22i	0.440982	−	0.0743979i
$66$	−3678.41			−0.103944
$67$			45470.8i			1.23750i	0.785587	+	0.618751i	$0.212361\pi$
$67$			45470.8i			1.23750i	−0.785587	+	0.618751i	$0.787639\pi$
$68$	2469.42			0.0647622
$69$	1573.70			0.0397922
$70$		−	12472.8i		−	0.304242i
$71$		−	64611.3i		−	1.52112i	−0.649269	−	0.760559i	$-0.724925\pi$
$71$		−	64611.3i		−	1.52112i	0.649269	−	0.760559i	$-0.275075\pi$
$72$			37403.7i			0.850323i
$73$			33697.5i			0.740100i	0.929012	+	0.370050i	$0.120660\pi$
$73$			33697.5i			0.740100i	−0.929012	+	0.370050i	$0.879340\pi$
$74$	−19011.9			−0.403595
$75$	−1057.91			−0.0217167
$76$		−	4223.46i		−	0.0838754i
$77$	−27739.6			−0.533180
$78$	−6358.28	+	1072.70i	−0.118332	+	0.0199638i
$79$	8422.21			0.151830			0.0759151	−	0.997114i	$-0.475812\pi$
$79$	8422.21			0.151830			0.0759151	+	0.997114i	$0.475812\pi$
$80$		−	30013.3i		−	0.524311i
$81$	56968.6			0.964768
$82$	−96543.6			−1.58558
$83$		−	43575.0i		−	0.694293i	−0.937811	−	0.347146i	$-0.887151\pi$
$83$		−	43575.0i		−	0.694293i	0.937811	−	0.347146i	$-0.112849\pi$
$84$			957.096i			0.0147999i
$85$		−	8712.89i		−	0.130802i
$86$		−	99674.7i		−	1.45324i
$87$	−1710.46			−0.0242278
$88$	−54143.2			−0.745311
$89$		−	20667.0i		−	0.276568i	−0.990393	−	0.138284i	$-0.955841\pi$
$89$		−	20667.0i		−	0.276568i	0.990393	−	0.138284i	$-0.0441586\pi$
$90$	−37532.1			−0.488424
$91$	−47949.1	+	8089.48i	−0.606983	+	0.102404i
$92$	−6587.58			−0.0811439
$93$			553.328i			0.00663400i
$94$	36009.1			0.420332
$95$	−14901.7			−0.169406
$96$			4267.47i			0.0472598i
$97$			50661.4i			0.546699i	0.961915	+	0.273349i	$0.0881315\pi$
$97$			50661.4i			0.546699i	−0.961915	+	0.273349i	$0.911868\pi$
$98$		−	65260.3i		−	0.686410i
$99$			83471.8i			0.855956i
$100$	4428.45			0.0442845
$101$	125153.			1.22078			0.610390	−	0.792101i	$-0.291013\pi$
$101$	125153.			1.22078			0.610390	+	0.792101i	$0.291013\pi$
$102$			3688.06i			0.0350992i
$103$	−137844.			−1.28025			−0.640127	−	0.768269i	$-0.721118\pi$
$103$	−137844.			−1.28025			−0.640127	+	0.768269i	$0.721118\pi$
$104$	−93588.8	+	15789.3i	−0.848478	+	0.143146i
$105$	3376.94			0.0298917
$106$		−	230565.i		−	1.99309i
$107$	216001.			1.82388			0.911941	−	0.410321i	$-0.134583\pi$
$107$	216001.			1.82388			0.911941	+	0.410321i	$0.134583\pi$
$108$	5794.39			0.0478023
$109$			128349.i			1.03473i	0.855765	+	0.517365i	$0.173087\pi$
$109$			128349.i			1.03473i	−0.855765	+	0.517365i	$0.826913\pi$
$110$		−	54329.1i		−	0.428105i
$111$		−	5147.37i		−	0.0396531i
$112$			95805.4i			0.721680i
$113$	−86731.4			−0.638970			−0.319485	−	0.947591i	$-0.603510\pi$
$113$	−86731.4			−0.638970			−0.319485	+	0.947591i	$0.603510\pi$
$114$	6307.72			0.0454580
$115$			23243.1i			0.163889i
$116$	7160.06			0.0494051
$117$	24342.2	+	144284.i	0.164397	+	0.974439i
$118$	59035.8			0.390311
$119$			27812.4i			0.180041i
$120$	6591.24			0.0417844
$121$	40222.7			0.249751
$122$			188983.i			1.14954i
$123$		−	26138.6i		−	0.155783i
$124$		−	2316.26i		−	0.0135280i
$125$		−	15625.0i		−	0.0894427i
$126$	119806.			0.672284
$127$	149618.			0.823143			0.411571	−	0.911378i	$-0.364980\pi$
$127$	149618.			0.823143			0.411571	+	0.911378i	$0.364980\pi$
$128$			222313.i			1.19934i
$129$	26986.4			0.142781
$130$	−15843.5	−	93910.0i	−0.0822231	−	0.487364i
$131$	172247.			0.876948			0.438474	−	0.898744i	$-0.355519\pi$
$131$	172247.			0.876948			0.438474	+	0.898744i	$0.355519\pi$
$132$			4168.92i			0.0208252i
$133$	47567.8			0.233176
$134$	284277.			1.36766
$135$		−	20444.5i		−	0.0965476i
$136$			54285.3i			0.251672i
$137$		−	139444.i		−	0.634742i	−0.948301	−	0.317371i	$-0.897200\pi$
$137$		−	139444.i		−	0.634742i	0.948301	−	0.317371i	$-0.102800\pi$
$138$		−	9838.51i		−	0.0439776i
$139$	−286164.			−1.25626			−0.628129	−	0.778109i	$-0.716179\pi$
$139$	−286164.			−1.25626			−0.628129	+	0.778109i	$0.716179\pi$
$140$	−14136.1			−0.0609548
$141$			9749.25i			0.0412975i
$142$	−403940.			−1.68111
$143$	−208857.	+	35236.2i	−0.854099	+	0.144095i
$144$	288290.			1.15857
$145$		−	25263.0i		−	0.0997849i
$146$	210671.			0.817944
$147$	17668.9			0.0674396
$148$			21547.1i			0.0808603i
$149$		−	338865.i		−	1.25044i	−0.780450	−	0.625218i	$-0.785010\pi$
$149$		−	338865.i		−	1.25044i	0.780450	−	0.625218i	$-0.214990\pi$
$150$			6613.87i			0.0240009i
$151$		−	250158.i		−	0.892838i	−0.894824	−	0.446419i	$-0.852699\pi$
$151$		−	250158.i		−	0.892838i	0.894824	−	0.446419i	$-0.147301\pi$
$152$	92844.6			0.325947
$153$	83690.8			0.289034
$154$			173424.i			0.589260i
$155$	−8172.51			−0.0273229
$156$	1215.75	+	7206.15i	0.00399974	+	0.0237078i
$157$	86667.0			0.280611			0.140306	−	0.990108i	$-0.455192\pi$
$157$	86667.0			0.280611			0.140306	+	0.990108i	$0.455192\pi$
$158$		−	52654.3i		−	0.167800i
$159$	62424.1			0.195821
$160$	−63029.3			−0.194645
$161$		−	74194.2i		−	0.225582i
$162$		−	356159.i		−	1.06624i
$163$		−	366645.i		−	1.08088i	−0.841383	−	0.540440i	$-0.818258\pi$
$163$		−	366645.i		−	1.08088i	0.841383	−	0.540440i	$-0.181742\pi$
$164$			109418.i			0.317671i
$165$	14709.3			0.0420612
$166$	−272424.			−0.767318
$167$			165848.i			0.460170i	0.973171	+	0.230085i	$0.0739004\pi$
$167$			165848.i			0.460170i	−0.973171	+	0.230085i	$0.926100\pi$
$168$	−21039.9			−0.0575135
$169$	−350742.	+	121814.i	−0.944649	+	0.328081i
$170$	−54471.6			−0.144560
$171$		−	143137.i		−	0.374336i
$172$	−112966.			−0.291157
$173$	−72933.7			−0.185273			−0.0926366	−	0.995700i	$-0.529529\pi$
$173$	−72933.7			−0.185273			−0.0926366	+	0.995700i	$0.529529\pi$
$174$			10693.5i			0.0267761i
$175$			49876.5i			0.123112i
$176$			417309.i			1.01549i
$177$			15983.6i			0.0383479i
$178$	−129207.			−0.305657
$179$	−294844.			−0.687796			−0.343898	−	0.939007i	$-0.611747\pi$
$179$	−294844.			−0.687796			−0.343898	+	0.939007i	$0.611747\pi$
$180$			42537.0i			0.0978557i
$181$	−320179.			−0.726434			−0.363217	−	0.931705i	$-0.618322\pi$
$181$	−320179.			−0.726434			−0.363217	+	0.931705i	$0.618322\pi$
$182$	50574.1	+	299770.i	0.113175	+	0.670826i
$183$	−51166.0			−0.112942
$184$		−	144815.i		−	0.315333i
$185$	76025.2			0.163316
$186$	3459.32			0.00733176
$187$			121145.i			0.253339i
$188$		−	40810.9i		−	0.0842134i
$189$			65260.7i			0.132892i
$190$			93163.3i			0.187224i
$191$	−645198.			−1.27970			−0.639852	−	0.768498i	$-0.721004\pi$
$191$	−645198.			−1.27970			−0.639852	+	0.768498i	$0.721004\pi$
$192$	−38347.1			−0.0750723
$193$			374762.i			0.724207i	0.932138	+	0.362103i	$0.117941\pi$
$193$			374762.i			0.724207i	−0.932138	+	0.362103i	$0.882059\pi$
$194$	316727.			0.604201
$195$	25425.6	−	4289.55i	0.0478834	−	0.00807840i
$196$	−73962.7			−0.137522
$197$		−	258051.i		−	0.473739i	−0.971541	−	0.236870i	$-0.923879\pi$
$197$		−	258051.i		−	0.473739i	0.971541	−	0.236870i	$-0.0761215\pi$
$198$	521852.			0.945986
$199$	−663577.			−1.18784			−0.593921	−	0.804523i	$-0.702421\pi$
$199$	−663577.			−1.18784			−0.593921	+	0.804523i	$0.702421\pi$
$200$			97350.8i			0.172094i
$201$			76966.3i			0.134372i
$202$		−	782437.i		−	1.34918i
$203$			80641.9i			0.137348i
$204$	4179.86			0.00703212
$205$	386061.			0.641610
$206$			861781.i			1.41491i
$207$	−223259.			−0.362146
$208$	121697.	+	721336.i	0.195038	+	1.15606i
$209$	207196.			0.328107
$210$		−	21112.1i		−	0.0330357i
$211$	−442397.			−0.684078			−0.342039	−	0.939686i	$-0.611118\pi$
$211$	−442397.			−0.684078			−0.342039	+	0.939686i	$0.611118\pi$
$212$	−261310.			−0.399316
$213$		−	109364.i		−	0.165168i
$214$		−	1.35041e6i		−	2.01572i
$215$			398581.i			0.588059i
$216$			127378.i			0.185764i
$217$	26087.4			0.0376082
$218$	802419.			1.14356
$219$			57038.1i			0.0803628i
$220$	−61573.8			−0.0857708
$221$	35328.6	+	209405.i	0.0486571	+	0.288407i
$222$	−32180.5			−0.0438239
$223$		−	1.01503e6i		−	1.36684i	−0.730024	−	0.683421i	$-0.760491\pi$
$223$		−	1.01503e6i		−	1.36684i	0.730024	−	0.683421i	$-0.239509\pi$
$224$	201196.			0.267916
$225$	150084.			0.197642
$226$			542231.i			0.706176i
$227$		−	1.08487e6i		−	1.39737i	−0.715429	−	0.698686i	$-0.753769\pi$
$227$		−	1.08487e6i		−	1.39737i	0.715429	−	0.698686i	$-0.246231\pi$
$228$		−	7148.85i		−	0.00910750i
$229$		−	145546.i		−	0.183405i	−0.995786	−	0.0917025i	$-0.970769\pi$
$229$		−	145546.i		−	0.183405i	0.995786	−	0.0917025i	$-0.0292309\pi$
$230$	145312.			0.181127
$231$	−46953.5			−0.0578946
$232$			157400.i			0.191993i
$233$	1.43704e6			1.73413			0.867063	−	0.498199i	$-0.166005\pi$
$233$	1.43704e6			1.73413			0.867063	+	0.498199i	$0.166005\pi$
$234$	902043.	−	152184.i	1.07693	−	0.181689i
$235$	−143994.			−0.170088
$236$		−	66908.2i		−	0.0781987i
$237$	14255.9			0.0164863
$238$	173879.			0.198977
$239$			1.40230e6i			1.58798i	0.607932	+	0.793989i	$0.291999\pi$
$239$			1.40230e6i			1.58798i	−0.607932	+	0.793989i	$0.708001\pi$
$240$		−	50802.1i		−	0.0569316i
$241$		−	154670.i		−	0.171539i	−0.996315	−	0.0857694i	$-0.972665\pi$
$241$		−	154670.i		−	0.171539i	0.996315	−	0.0857694i	$-0.0273348\pi$
$242$		−	251466.i		−	0.276020i
$243$	295148.			0.320645
$244$	214183.			0.230309
$245$			260964.i			0.277758i
$246$	−163415.			−0.172168
$247$	358147.	−	60422.8i	0.373524	−	0.0630171i
$248$	50918.4			0.0525710
$249$		−	73757.4i		−	0.0753888i
$250$	−97685.0			−0.0988503
$251$	−443511.			−0.444345			−0.222173	−	0.975007i	$-0.571315\pi$
$251$	−443511.			−0.444345			−0.222173	+	0.975007i	$0.571315\pi$
$252$		−	135782.i		−	0.134692i
$253$		−	323175.i		−	0.317422i
$254$		−	935389.i		−	0.909721i
$255$		−	14747.9i		−	0.0142030i
$256$	664906.			0.634104
$257$	74281.7			0.0701534			0.0350767	−	0.999385i	$-0.488832\pi$
$257$	74281.7			0.0701534			0.0350767	+	0.999385i	$0.488832\pi$
$258$		−	168714.i		−	0.157799i
$259$	−242680.			−0.224794
$260$	−106433.	+	17956.3i	−0.0976433	+	0.0164734i
$261$	242661.			0.220495
$262$		−	1.07686e6i		−	0.969186i
$263$	−1.05149e6			−0.937382			−0.468691	−	0.883362i	$-0.655274\pi$
$263$	−1.05149e6			−0.937382			−0.468691	+	0.883362i	$0.655274\pi$
$264$	−91645.6			−0.0809285
$265$			921987.i			0.806510i
$266$		−	297386.i		−	0.257701i
$267$		−	34982.0i		−	0.0300307i
$268$		−	322185.i		−	0.274011i
$269$	1.14160e6			0.961910			0.480955	−	0.876745i	$-0.340290\pi$
$269$	1.14160e6			0.961910			0.480955	+	0.876745i	$0.340290\pi$
$270$	−127816.			−0.106702
$271$			1.94328e6i			1.60736i	0.595062	+	0.803680i	$0.297127\pi$
$271$			1.94328e6i			1.60736i	−0.595062	+	0.803680i	$0.702873\pi$
$272$	418404.			0.342905
$273$	−81161.1	+	13692.7i	−0.0659084	+	0.0111194i
$274$	−871780.			−0.701504
$275$			217252.i			0.173234i
$276$	−11150.5			−0.00881090
$277$	2.21371e6			1.73349			0.866745	−	0.498751i	$-0.166208\pi$
$277$	2.21371e6			1.73349			0.866745	+	0.498751i	$0.166208\pi$
$278$			1.78906e6i			1.38839i
$279$		−	78500.2i		−	0.0603754i
$280$		−	310753.i		−	0.236876i
$281$			2.00377e6i			1.51385i	0.653503	+	0.756924i	$0.273299\pi$
$281$			2.00377e6i			1.51385i	−0.653503	+	0.756924i	$0.726701\pi$
$282$	60950.8			0.0456412
$283$	−1.76589e6			−1.31069			−0.655343	−	0.755332i	$-0.727476\pi$
$283$	−1.76589e6			−1.31069			−0.655343	+	0.755332i	$0.727476\pi$
$284$			457805.i			0.336810i
$285$	−25223.4			−0.0183947
$286$	220291.	+	1.30574e6i	0.159251	+	0.943933i
$287$	−1.23234e6			−0.883135
$288$		−	605422.i		−	0.430107i
$289$	−1.29839e6			−0.914454
$290$	−157940.			−0.110280
$291$			85752.2i			0.0593626i
$292$		−	238764.i		−	0.163875i
$293$		−	461695.i		−	0.314186i	−0.987584	−	0.157093i	$-0.949788\pi$
$293$		−	461695.i		−	0.314186i	0.987584	−	0.157093i	$-0.0502122\pi$
$294$		−	110463.i		−	0.0745329i
$295$	−236074.			−0.157940
$296$	−473672.			−0.314230
$297$			284263.i			0.186995i
$298$	−2.11853e6			−1.38196
$299$	−94244.9	−	558622.i	−0.0609649	−	0.361360i
$300$	7495.83			0.00480857
$301$		−	1.27231e6i		−	0.809425i
$302$	−1.56395e6			−0.986746
$303$	211840.			0.132557
$304$		−	715600.i		−	0.444106i
$305$		−	755708.i		−	0.465162i
$306$		−	523221.i		−	0.319435i
$307$			454420.i			0.275176i	0.990490	+	0.137588i	$0.0439350\pi$
$307$			454420.i			0.275176i	−0.990490	+	0.137588i	$0.956065\pi$
$308$	196550.			0.118058
$309$	−233322.			−0.139015
$310$			51093.2i			0.0301967i
$311$	2.92806e6			1.71664			0.858319	−	0.513117i	$-0.171509\pi$
$311$	2.92806e6			1.71664			0.858319	+	0.513117i	$0.171509\pi$
$312$	−158413.	+	26725.9i	−0.0921308	+	0.0155434i
$313$	−761062.			−0.439096			−0.219548	−	0.975602i	$-0.570458\pi$
$313$	−761062.			−0.439096			−0.219548	+	0.975602i	$0.570458\pi$
$314$		−	541828.i		−	0.310126i
$315$	−479084.			−0.272041
$316$	−59675.7			−0.0336186
$317$		−	1.69741e6i		−	0.948721i	−0.880331	−	0.474360i	$-0.842679\pi$
$317$		−	1.69741e6i		−	0.948721i	0.880331	−	0.474360i	$-0.157321\pi$
$318$		−	390265.i		−	0.216417i
$319$			351260.i			0.193265i
$320$		−	566376.i		−	0.309193i
$321$	365615.			0.198044
$322$	−463850.			−0.249309
$323$		−	207739.i		−	0.110793i
$324$	−403652.			−0.213621
$325$	63355.5	+	375530.i	0.0332718	+	0.197213i
$326$	−2.29221e6			−1.19457
$327$			217251.i			0.112355i
$328$	−2.40533e6			−1.23450
$329$	459642.			0.234116
$330$		−	91960.2i		−	0.0464852i
$331$		−	2.60365e6i		−	1.30621i	−0.757269	−	0.653103i	$-0.773467\pi$
$331$		−	2.60365e6i		−	1.30621i	0.757269	−	0.653103i	$-0.226533\pi$
$332$			308752.i			0.153732i
$333$			730252.i			0.360880i
$334$	1.03685e6			0.508571
$335$	−1.13677e6			−0.553428
$336$			162165.i			0.0783627i
$337$	3.80058e6			1.82295			0.911476	−	0.411354i	$-0.134944\pi$
$337$	3.80058e6			1.82295			0.911476	+	0.411354i	$0.134944\pi$
$338$	761564.	+	2.19278e6i	0.362589	+	1.04401i
$339$	−146806.			−0.0693816
$340$			61735.4i			0.0289626i
$341$	113632.			0.0529193
$342$	−894870.			−0.413709
$343$		−	2.17426e6i		−	0.997876i
$344$		−	2.48334e6i		−	1.13146i
$345$			39342.4i			0.0177956i
$346$			455970.i			0.204760i
$347$	−1.86081e6			−0.829620			−0.414810	−	0.909908i	$-0.636152\pi$
$347$	−1.86081e6			−0.829620			−0.414810	+	0.909908i	$0.636152\pi$
$348$	12119.5			0.00536459
$349$			3.17108e6i			1.39362i	0.717257	+	0.696809i	$0.245397\pi$
$349$			3.17108e6i			1.39362i	−0.717257	+	0.696809i	$0.754603\pi$
$350$	311820.			0.136061
$351$	82897.3	+	491360.i	0.0359147	+	0.212879i
$352$	876369.			0.376990
$353$		−	3.64751e6i		−	1.55797i	−0.627042	−	0.778986i	$-0.715734\pi$
$353$		−	3.64751e6i		−	1.55797i	0.627042	−	0.778986i	$-0.284266\pi$
$354$	99927.0			0.0423813
$355$	1.61528e6			0.680264
$356$			146436.i			0.0612384i
$357$			47076.7i			0.0195495i
$358$			1.84332e6i			0.760138i
$359$		−	2.47657e6i		−	1.01418i	−0.861894	−	0.507089i	$-0.830722\pi$
$359$		−	2.47657e6i		−	1.01418i	0.861894	−	0.507089i	$-0.169278\pi$
$360$	−935094.			−0.380276
$361$	2.12080e6			0.856509
$362$			2.00171e6i			0.802840i
$363$	68083.0			0.0271189
$364$	339744.	−	57318.2i	0.134400	−	0.0226746i
$365$	−842438.			−0.330983
$366$			319882.i			0.124821i
$367$	2.57928e6			0.999617			0.499809	−	0.866136i	$-0.333404\pi$
$367$	2.57928e6			0.999617			0.499809	+	0.866136i	$0.333404\pi$
$368$	−1.11616e6			−0.429643
$369$			3.70827e6i			1.41777i
$370$		−	475297.i		−	0.180493i
$371$		−	2.94307e6i		−	1.11011i
$372$		−	3920.62i		−	0.00146892i
$373$	3.08130e6			1.14673			0.573366	−	0.819299i	$-0.305637\pi$
$373$	3.08130e6			1.14673			0.573366	+	0.819299i	$0.305637\pi$
$374$	757381.			0.279985
$375$		−	26447.7i		−	0.00971201i
$376$	897147.			0.327261
$377$	102435.	+	607168.i	0.0371190	+	0.220017i
$378$	408000.			0.146869
$379$			4.13531e6i			1.47880i	0.673266	+	0.739401i	$0.264891\pi$
$379$			4.13531e6i			1.47880i	−0.673266	+	0.739401i	$0.735109\pi$
$380$	105587.			0.0375102
$381$	253251.			0.0893798
$382$			4.03368e6i			1.41430i
$383$			562543.i			0.195956i	0.995189	+	0.0979781i	$0.0312375\pi$
$383$			562543.i			0.195956i	−0.995189	+	0.0979781i	$0.968763\pi$
$384$			376299.i			0.130228i
$385$		−	693490.i		−	0.238445i
$386$	2.34295e6			0.800379
$387$	−3.82853e6			−1.29944
$388$		−	358963.i		−	0.121052i
$389$	3.07454e6			1.03016			0.515081	−	0.857141i	$-0.327762\pi$
$389$	3.07454e6			1.03016			0.515081	+	0.857141i	$0.327762\pi$
$390$	−26817.6	−	158957.i	−0.00892808	−	0.0529198i
$391$	−324023.			−0.107185
$392$		−	1.62593e6i		−	0.534424i
$393$	291555.			0.0952222
$394$	−1.61329e6			−0.523567
$395$			210555.i			0.0679005i
$396$		−	591441.i		−	0.189528i
$397$			2.98399e6i			0.950213i	0.879928	+	0.475106i	$0.157590\pi$
$397$			2.98399e6i			0.950213i	−0.879928	+	0.475106i	$0.842410\pi$
$398$			4.14858e6i			1.31278i
$399$	80515.7			0.0253191
$400$	750333.			0.234479
$401$		−	3.78267e6i		−	1.17473i	−0.809322	−	0.587365i	$-0.800165\pi$
$401$		−	3.78267e6i		−	1.17473i	0.809322	−	0.587365i	$-0.199835\pi$
$402$	481181.			0.148506
$403$	196417.	−	33137.5i	0.0602444	−	0.0101638i
$404$	−886774.			−0.270309
$405$			1.42421e6i			0.431457i
$406$	504161.			0.151794
$407$	−1.05707e6			−0.316312
$408$			91886.0i			0.0273274i
$409$			1.84043e6i			0.544014i	0.962295	+	0.272007i	$0.0876874\pi$
$409$			1.84043e6i			0.544014i	−0.962295	+	0.272007i	$0.912313\pi$
$410$		−	2.41359e6i		−	0.709094i
$411$		−	236029.i		−	0.0689226i
$412$	976699.			0.283477
$413$	753570.			0.217394
$414$			1.39578e6i			0.400236i
$415$	1.08938e6			0.310497
$416$	1.51484e6	−	255568.i	0.429174	−	0.0724059i
$417$	−484377.			−0.136409
$418$		−	1.29536e6i		−	0.362617i
$419$	−1.33969e6			−0.372795			−0.186398	−	0.982474i	$-0.559681\pi$
$419$	−1.33969e6			−0.372795			−0.186398	+	0.982474i	$0.559681\pi$
$420$	−23927.4			−0.00661870
$421$		−	3.34684e6i		−	0.920300i	−0.887841	−	0.460150i	$-0.847796\pi$
$421$		−	3.34684e6i		−	0.920300i	0.887841	−	0.460150i	$-0.152204\pi$
$422$			2.76579e6i			0.756030i
$423$		−	1.38312e6i		−	0.375845i
$424$		−	5.74440e6i		−	1.55178i
$425$	217822.			0.0584965
$426$	−683729.			−0.182541
$427$			2.41229e6i			0.640266i
$428$	−1.53048e6			−0.403849
$429$	−353521.	+	59642.5i	−0.0927412	+	0.0156463i
$430$	2.49187e6			0.649911
$431$		−	2.33057e6i		−	0.604322i	−0.953257	−	0.302161i	$-0.902292\pi$
$431$		−	2.33057e6i		−	0.604322i	0.953257	−	0.302161i	$-0.0977080\pi$
$432$	981770.			0.253105
$433$	4.42705e6			1.13474			0.567368	−	0.823464i	$-0.307962\pi$
$433$	4.42705e6			1.13474			0.567368	+	0.823464i	$0.307962\pi$
$434$		−	163095.i		−	0.0415638i
$435$		−	42761.4i		−	0.0108350i
$436$		−	909422.i		−	0.229113i
$437$			554179.i			0.138818i
$438$	356593.			0.0888153
$439$	−1.15753e6			−0.286663			−0.143331	−	0.989675i	$-0.545781\pi$
$439$	−1.15753e6			−0.286663			−0.143331	+	0.989675i	$0.545781\pi$
$440$		−	1.35358e6i		−	0.333313i
$441$	−2.50667e6			−0.613762
$442$	1.30916e6	−	220869.i	0.318741	−	0.0537748i
$443$	1.05603e6			0.255662			0.127831	−	0.991796i	$-0.459199\pi$
$443$	1.05603e6			0.255662			0.127831	+	0.991796i	$0.459199\pi$
$444$			36471.8i			0.00878010i
$445$	516674.			0.123685
$446$	−6.34583e6			−1.51061
$447$		−	573581.i		−	0.135777i
$448$			1.80793e6i			0.425585i
$449$		−	1.94396e6i		−	0.455063i	−0.973771	−	0.227532i	$-0.926934\pi$
$449$		−	1.94396e6i		−	0.455063i	0.973771	−	0.227532i	$-0.0730655\pi$
$450$		−	938303.i		−	0.218430i
$451$	−5.36784e6			−1.24268
$452$	614537.			0.141482
$453$		−	423431.i		−	0.0969475i
$454$	−6.78242e6			−1.54435
$455$	−202237.	−	1.19873e6i	−0.0457965	−	0.271451i
$456$	157153.			0.0353925
$457$		−	1.36746e6i		−	0.306285i	−0.988204	−	0.153142i	$-0.951061\pi$
$457$		−	1.36746e6i		−	0.306285i	0.988204	−	0.153142i	$-0.0489393\pi$
$458$	−909930.			−0.202696
$459$	285009.			0.0631432
$460$		−	164689.i		−	0.0362887i
$461$			2.24706e6i			0.492451i	0.969213	+	0.246225i	$0.0791904\pi$
$461$			2.24706e6i			0.492451i	−0.969213	+	0.246225i	$0.920810\pi$
$462$			293546.i			0.0639839i
$463$			5.51050e6i			1.19464i	0.802001	+	0.597322i	$0.203769\pi$
$463$			5.51050e6i			1.19464i	−0.802001	+	0.597322i	$0.796231\pi$
$464$	1.21316e6			0.261592
$465$	−13833.2			−0.00296682
$466$		−	8.98418e6i		−	1.91652i
$467$	−6.19075e6			−1.31356			−0.656782	−	0.754081i	$-0.728083\pi$
$467$	−6.19075e6			−1.31356			−0.656782	+	0.754081i	$0.728083\pi$
$468$	−172477.	−	1.02233e6i	−0.0364013	−	0.215763i
$469$	3.62868e6			0.761758
$470$			900227.i			0.187978i
$471$	146697.			0.0304698
$472$	1.47085e6			0.303887
$473$		−	5.54193e6i		−	1.13896i
$474$		−	89125.4i		−	0.0182203i
$475$		−	372543.i		−	0.0757605i
$476$		−	197065.i		−	0.0398651i
$477$	−8.85605e6			−1.78215
$478$	8.76693e6			1.75500
$479$			2.70933e6i			0.539540i	0.962925	+	0.269770i	$0.0869477\pi$
$479$			2.70933e6i			0.539540i	−0.962925	+	0.269770i	$0.913052\pi$
$480$	−106687.			−0.0211352
$481$	−1.82718e6	+	308263.i	−0.360097	+	0.0607518i
$482$	−966970.			−0.189581
$483$		−	125585.i		−	0.0244945i
$484$	−284999.			−0.0553006
$485$	−1.26654e6			−0.244491
$486$		−	1.84522e6i		−	0.354370i
$487$			860967.i			0.164499i	0.996612	+	0.0822497i	$0.0262105\pi$
$487$			860967.i			0.164499i	−0.996612	+	0.0822497i	$0.973790\pi$
$488$			4.70840e6i			0.895002i
$489$		−	620603.i		−	0.117366i
$490$	1.63151e6			0.306972
$491$	−5.39938e6			−1.01074			−0.505371	−	0.862902i	$-0.668644\pi$
$491$	−5.39938e6			−1.01074			−0.505371	+	0.862902i	$0.668644\pi$
$492$			185206.i			0.0344939i
$493$	352182.			0.0652604
$494$	−377754.	−	2.23908e6i	−0.0696453	−	0.412811i
$495$	−2.08679e6			−0.382795
$496$		−	392454.i		−	0.0716284i
$497$	−5.15614e6			−0.936341
$498$	−461119.			−0.0833182
$499$			6.64091e6i			1.19392i	0.802270	+	0.596961i	$0.203625\pi$
$499$			6.64091e6i			1.19392i	−0.802270	+	0.596961i	$0.796375\pi$
$500$			110711.i			0.0198046i
$501$			280722.i			0.0499669i
$502$			2.77276e6i			0.491081i
$503$	−902536.			−0.159054			−0.0795270	−	0.996833i	$-0.525341\pi$
$503$	−902536.			−0.159054			−0.0795270	+	0.996833i	$0.525341\pi$
$504$	2.98491e6			0.523425
$505$			3.12882e6i			0.545950i
$506$	−2.02044e6			−0.350808
$507$	−593683.	+	206189.i	−0.102573	+	0.0356243i
$508$	−1.06012e6			−0.182262
$509$			1.04133e7i			1.78153i	0.454463	+	0.890765i	$0.349831\pi$
$509$			1.04133e7i			1.78153i	−0.454463	+	0.890765i	$0.650169\pi$
$510$	−92201.4			−0.0156968
$511$	2.68914e6			0.455577
$512$			2.95714e6i			0.498536i
$513$		−	487453.i		−	0.0817785i
$514$		−	464397.i		−	0.0775321i
$515$		−	3.44611e6i		−	0.572547i
$516$	−191212.			−0.0316149
$517$	2.00211e6			0.329429
$518$			1.51720e6i			0.248438i
$519$	−123451.			−0.0201176
$520$	−394734.	−	2.33972e6i	−0.0640171	−	0.379451i
$521$	9.15829e6			1.47816			0.739078	−	0.673620i	$-0.235262\pi$
$521$	9.15829e6			1.47816			0.739078	+	0.673620i	$0.235262\pi$
$522$		−	1.51708e6i		−	0.243687i
$523$	2.69871e6			0.431422			0.215711	−	0.976457i	$-0.430793\pi$
$523$	2.69871e6			0.431422			0.215711	+	0.976457i	$0.430793\pi$
$524$	−1.22046e6			−0.194176
$525$			84423.6i			0.0133680i
$526$			6.57376e6i			1.03598i
$527$		−	113930.i		−	0.0178694i
$528$			706359.i			0.110266i
$529$	−5.57196e6			−0.865702
$530$	5.76411e6			0.891339
$531$		−	2.26758e6i		−	0.349001i
$532$	−337043.			−0.0516304
$533$	−9.27854e6	+	1.56538e6i	−1.41469	+	0.238672i
$534$	−218702.			−0.0331894
$535$			5.40003e6i			0.815665i
$536$	7.08260e6			1.06483
$537$	−499068.			−0.0746834
$538$		−	7.13712e6i		−	1.06308i
$539$		−	3.62849e6i		−	0.537964i
$540$			144860.i			0.0213778i
$541$			4.72656e6i			0.694308i	0.937808	+	0.347154i	$0.112852\pi$
$541$			4.72656e6i			0.694308i	−0.937808	+	0.347154i	$0.887148\pi$
$542$	1.21491e7			1.77642
$543$	−541951.			−0.0788788
$544$		−	878668.i		−	0.127300i
$545$	−3.20873e6			−0.462745
$546$	85604.4	+	507406.i	0.0122889	+	0.0728407i
$547$	6.86187e6			0.980560			0.490280	−	0.871565i	$-0.336895\pi$
$547$	6.86187e6			0.980560			0.490280	+	0.871565i	$0.336895\pi$
$548$			988031.i			0.140546i
$549$	7.25887e6			1.02787
$550$	1.35823e6			0.191454
$551$		−	602340.i		−	0.0845206i
$552$		−	245121.i		−	0.0342400i
$553$		−	672113.i		−	0.0934607i
$554$		−	1.38398e7i		−	1.91582i
$555$	128684.			0.0177334
$556$	2.02763e6			0.278164
$557$		−	7.61918e6i		−	1.04057i	−0.853994	−	0.520284i	$-0.825826\pi$
$557$		−	7.61918e6i		−	1.04057i	0.853994	−	0.520284i	$-0.174174\pi$
$558$	−490771.			−0.0667257
$559$	−1.61615e6	−	9.57946e6i	−0.218752	−	1.29662i
$560$	−2.39513e6			−0.322745
$561$			205057.i			0.0275085i
$562$	1.25273e7			1.67307
$563$	5.28508e6			0.702717			0.351359	−	0.936241i	$-0.385720\pi$
$563$	5.28508e6			0.702717			0.351359	+	0.936241i	$0.385720\pi$
$564$		−	69078.6i		−	0.00914420i
$565$		−	2.16828e6i		−	0.285756i
$566$			1.10401e7i			1.44854i
$567$		−	4.54623e6i		−	0.593873i
$568$	−1.00639e7			−1.30887
$569$	−2.01677e6			−0.261142			−0.130571	−	0.991439i	$-0.541681\pi$
$569$	−2.01677e6			−0.261142			−0.130571	+	0.991439i	$0.541681\pi$
$570$			157693.i			0.0203294i
$571$	3.23985e6			0.415847			0.207924	−	0.978145i	$-0.433329\pi$
$571$	3.23985e6			0.415847			0.207924	+	0.978145i	$0.433329\pi$
$572$	1.47986e6	−	249667.i	0.189117	−	0.0319059i
$573$	−1.09210e6			−0.138955
$574$			7.70442e6i			0.976023i
$575$	−581077.			−0.0732933
$576$	5.44027e6			0.683226
$577$		−	1.19043e7i		−	1.48855i	−0.667871	−	0.744277i	$-0.732794\pi$
$577$		−	1.19043e7i		−	1.48855i	0.667871	−	0.744277i	$-0.267206\pi$
$578$			8.11735e6i			1.01064i
$579$			634342.i			0.0786370i
$580$			179002.i			0.0220946i
$581$	−3.47739e6			−0.427379
$582$	536109.			0.0656063
$583$		−	1.28194e7i		−	1.56206i
$584$	5.24877e6			0.636833
$585$	−3.60711e6	+	608555.i	−0.435782	+	0.0735208i
$586$	−2.88645e6			−0.347232
$587$			9.46460e6i			1.13372i	0.823813	+	0.566862i	$0.191843\pi$
$587$			9.46460e6i			1.13372i	−0.823813	+	0.566862i	$0.808157\pi$
$588$	−125193.			−0.0149327
$589$	−194855.			−0.0231432
$590$			1.47589e6i			0.174552i
$591$		−	436790.i		−	0.0514403i
$592$			3.65083e6i			0.428141i
$593$			1.41613e7i			1.65374i	0.562396	+	0.826868i	$0.309880\pi$
$593$			1.41613e7i			1.65374i	−0.562396	+	0.826868i	$0.690120\pi$
$594$	1.77717e6			0.206663
$595$	−695310.			−0.0805167
$596$			2.40104e6i			0.276875i
$597$	−1.12321e6			−0.128980
$598$	−3.49241e6	+	589204.i	−0.399368	+	0.0673772i
$599$	1.01054e7			1.15077			0.575385	−	0.817883i	$-0.304852\pi$
$599$	1.01054e7			1.15077			0.575385	+	0.817883i	$0.304852\pi$
$600$			164781.i			0.0186865i
$601$	8.84176e6			0.998510			0.499255	−	0.866455i	$-0.333607\pi$
$601$	8.84176e6			0.998510			0.499255	+	0.866455i	$0.333607\pi$
$602$	−7.95428e6			−0.894560
$603$		−	1.09191e7i		−	1.22291i
$604$			1.77250e6i			0.197694i
$605$			1.00557e6i			0.111692i
$606$		−	1.32439e6i		−	0.146499i
$607$	−1.04036e6			−0.114607			−0.0573037	−	0.998357i	$-0.518250\pi$
$607$	−1.04036e6			−0.114607			−0.0573037	+	0.998357i	$0.518250\pi$
$608$	−1.50279e6			−0.164870
$609$			136499.i			0.0149137i
$610$	−4.72456e6			−0.514088
$611$	3.46073e6	−	583859.i	0.375029	−	0.0632711i
$612$	−592993.			−0.0639987
$613$		−	1.55993e7i		−	1.67670i	−0.545136	−	0.838348i	$-0.683522\pi$
$613$		−	1.55993e7i		−	1.67670i	0.545136	−	0.838348i	$-0.316478\pi$
$614$	2.84096e6			0.304119
$615$	653466.			0.0696683
$616$			4.32076e6i			0.458784i
$617$			6.22785e6i			0.658606i	0.944224	+	0.329303i	$0.106814\pi$
$617$			6.22785e6i			0.658606i	−0.944224	+	0.329303i	$0.893186\pi$
$618$			1.45869e6i			0.153636i
$619$		−	5.93914e6i		−	0.623013i	−0.950244	−	0.311506i	$-0.899166\pi$
$619$		−	5.93914e6i		−	0.623013i	0.950244	−	0.311506i	$-0.100834\pi$
$620$	57906.5			0.00604990
$621$	−760308.			−0.0791153
$622$		−	1.83058e7i		−	1.89719i
$623$	−1.64927e6			−0.170244
$624$	205990.	+	1.22097e6i	0.0211780	+	0.125529i
$625$	390625.			0.0400000
$626$			4.75804e6i			0.485280i
$627$	350710.			0.0356270
$628$	−614081.			−0.0621336
$629$			1.05984e6i			0.106810i
$630$			2.99516e6i			0.300655i
$631$			4.46331e6i			0.446256i	0.974789	+	0.223128i	$0.0716267\pi$
$631$			4.46331e6i			0.446256i	−0.974789	+	0.223128i	$0.928373\pi$
$632$		−	1.31185e6i		−	0.130645i
$633$	−748823.			−0.0742797
$634$	−1.06119e7			−1.04851
$635$			3.74046e6i			0.368121i
$636$	−442307.			−0.0433592
$637$	−1.05815e6	−	6.27199e6i	−0.103323	−	0.612430i
$638$	2.19602e6			0.213592
$639$			1.55154e7i			1.50318i
$640$	−5.55783e6			−0.536359
$641$	−1.24423e7			−1.19607			−0.598034	−	0.801471i	$-0.704051\pi$
$641$	−1.24423e7			−1.19607			−0.598034	+	0.801471i	$0.704051\pi$
$642$		−	2.28577e6i		−	0.218874i
$643$			1.66453e7i			1.58769i	0.608123	+	0.793843i	$0.291923\pi$
$643$			1.66453e7i			1.58769i	−0.608123	+	0.793843i	$0.708077\pi$
$644$			525705.i			0.0499490i
$645$			674659.i			0.0638535i
$646$	−1.29875e6			−0.122446
$647$	4.63858e6			0.435637			0.217818	−	0.975989i	$-0.430106\pi$
$647$	4.63858e6			0.435637			0.217818	+	0.975989i	$0.430106\pi$
$648$		−	8.87350e6i		−	0.830152i
$649$	3.28240e6			0.305900
$650$	2.34775e6	−	396089.i	0.217956	−	0.0367713i
$651$	44156.9			0.00408363
$652$			2.59788e6i			0.239331i
$653$	−9.29555e6			−0.853085			−0.426542	−	0.904468i	$-0.640268\pi$
$653$	−9.29555e6			−0.853085			−0.426542	+	0.904468i	$0.640268\pi$
$654$	1.35822e6			0.124172
$655$			4.30618e6i			0.392183i
$656$			1.85391e7i			1.68201i
$657$		−	8.09195e6i		−	0.731374i
$658$		−	2.87361e6i		−	0.258740i
$659$	−1.35509e7			−1.21550			−0.607750	−	0.794129i	$-0.707928\pi$
$659$	−1.35509e7			−1.21550			−0.607750	+	0.794129i	$0.707928\pi$
$660$	−104223.			−0.00931331
$661$			1.17407e7i			1.04517i	0.852586	+	0.522587i	$0.175033\pi$
$661$			1.17407e7i			1.04517i	−0.852586	+	0.522587i	$0.824967\pi$
$662$	−1.62776e7			−1.44359
$663$	59799.0	+	354449.i	0.00528336	+	0.0313163i
$664$	−6.78731e6			−0.597417
$665$			1.18919e6i			0.104279i
$666$	4.56542e6			0.398837
$667$	−939504.			−0.0817681
$668$		−	1.17512e6i		−	0.101892i
$669$		−	1.71810e6i		−	0.148417i
$670$			7.10691e6i			0.611637i
$671$			1.05075e7i			0.900932i
$672$	340554.			0.0290913
$673$	−5.06991e6			−0.431482			−0.215741	−	0.976451i	$-0.569217\pi$
$673$	−5.06991e6			−0.431482			−0.215741	+	0.976451i	$0.569217\pi$
$674$		−	2.37606e7i		−	2.01469i
$675$	511112.			0.0431774
$676$	2.48519e6	−	863118.i	0.209167	−	0.0726446i
$677$	5.82577e6			0.488519			0.244259	−	0.969710i	$-0.421455\pi$
$677$	5.82577e6			0.488519			0.244259	+	0.969710i	$0.421455\pi$
$678$			917808.i			0.0766792i
$679$	4.04291e6			0.336526
$680$	−1.35713e6			−0.112551
$681$		−	1.83630e6i		−	0.151732i
$682$		−	710408.i		−	0.0584853i
$683$			2.06645e6i			0.169501i	0.996402	+	0.0847505i	$0.0270093\pi$
$683$			2.06645e6i			0.169501i	−0.996402	+	0.0847505i	$0.972991\pi$
$684$			1.01420e6i			0.0828865i
$685$	3.48609e6			0.283865
$686$	−1.35931e7			−1.10283
$687$		−	246358.i		−	0.0199148i
$688$	−1.91404e7			−1.54163
$689$	−3.73843e6	−	2.21589e7i	−0.300014	−	1.77828i
$690$	245963.			0.0196674
$691$		−	1.57696e7i		−	1.25639i	−0.778055	−	0.628197i	$-0.783793\pi$
$691$		−	1.57696e7i		−	1.25639i	0.778055	−	0.628197i	$-0.216207\pi$
$692$	516773.			0.0410237
$693$	6.66125e6			0.526893
$694$			1.16335e7i			0.916880i
$695$		−	7.15411e6i		−	0.561816i
$696$			266423.i			0.0208473i
$697$			5.38193e6i			0.419620i
$698$	1.98251e7			1.54020
$699$	2.43242e6			0.188298
$700$		−	353401.i		−	0.0272598i
$701$	1.41323e7			1.08622			0.543112	−	0.839660i	$-0.317246\pi$
$701$	1.41323e7			1.08622			0.543112	+	0.839660i	$0.317246\pi$
$702$	3.07191e6	−	518261.i	0.235269	−	0.0396922i
$703$	1.81265e6			0.138333
$704$			7.87498e6i			0.598850i
$705$	−243731.			−0.0184688
$706$	−2.28036e7			−1.72184
$707$		−	9.98751e6i		−	0.751465i
$708$		−	113252.i		−	0.00849109i
$709$		−	1.41194e7i		−	1.05487i	−0.849594	−	0.527437i	$-0.823153\pi$
$709$		−	1.41194e7i		−	1.05487i	0.849594	−	0.527437i	$-0.176847\pi$
$710$		−	1.00985e7i		−	0.751815i
$711$	−2.02247e6			−0.150040
$712$	−3.21911e6			−0.237978
$713$			303927.i			0.0223895i
$714$	294316.			0.0216057
$715$	−880904.	−	5.22142e6i	−0.0644412	−	0.381965i
$716$	2.08912e6			0.152294
$717$			2.37360e6i			0.172428i
$718$	−1.54831e7			−1.12085
$719$	1.64679e7			1.18800			0.593998	−	0.804466i	$-0.297549\pi$
$719$	1.64679e7			1.18800			0.593998	+	0.804466i	$0.297549\pi$
$720$			7.20724e6i			0.518129i
$721$			1.10003e7i			0.788074i
$722$		−	1.32589e7i		−	0.946596i
$723$		−	261802.i		−	0.0186263i
$724$	2.26863e6			0.160849
$725$	631575.			0.0446252
$726$		−	425644.i		−	0.0299713i
$727$	1.62564e7			1.14074			0.570372	−	0.821386i	$-0.306799\pi$
$727$	1.62564e7			1.14074			0.570372	+	0.821386i	$0.306799\pi$
$728$	1.26003e6	+	7.46861e6i	0.0881154	+	0.522290i
$729$	−1.33438e7			−0.929951
$730$			5.26679e6i			0.365796i
$731$	−5.55647e6			−0.384597
$732$	362538.			0.0250078
$733$		−	9.29766e6i		−	0.639166i	−0.947558	−	0.319583i	$-0.896457\pi$
$733$		−	9.29766e6i		−	0.639166i	0.947558	−	0.319583i	$-0.103543\pi$
$734$		−	1.61253e7i		−	1.10476i
$735$			441722.i			0.0301599i
$736$			2.34399e6i			0.159500i
$737$	1.58058e7			1.07189
$738$	2.31835e7			1.56689
$739$			1.88424e7i			1.26919i	0.772846	+	0.634594i	$0.218833\pi$
$739$			1.88424e7i			1.26919i	−0.772846	+	0.634594i	$0.781167\pi$
$740$	−538678.			−0.0361618
$741$	606217.	−	102275.i	0.0405586	−	0.00684263i
$742$	−1.83996e7			−1.22687
$743$			5.69309e6i			0.378335i	0.981945	+	0.189167i	$0.0605789\pi$
$743$			5.69309e6i			0.378335i	−0.981945	+	0.189167i	$0.939421\pi$
$744$	86187.2			0.00570835
$745$	8.47163e6			0.559212
$746$		−	1.92638e7i		−	1.26735i
$747$			1.04639e7i			0.686107i
$748$		−	858378.i		−	0.0560950i
$749$		−	1.72374e7i		−	1.12271i
$750$	−165347.			−0.0107335
$751$	6.08780e6			0.393877			0.196938	−	0.980416i	$-0.436900\pi$
$751$	6.08780e6			0.393877			0.196938	+	0.980416i	$0.436900\pi$
$752$		−	6.91477e6i		−	0.445896i
$753$	−750710.			−0.0482486
$754$	3.79592e6	−	640409.i	0.243158	−	0.0410231i
$755$	6.25396e6			0.399289
$756$		−	462407.i		−	0.0294252i
$757$	−2.95463e6			−0.187397			−0.0936986	−	0.995601i	$-0.529869\pi$
$757$	−2.95463e6			−0.187397			−0.0936986	+	0.995601i	$0.529869\pi$
$758$	2.58533e7			1.63434
$759$		−	547023.i		−	0.0344668i
$760$			2.32111e6i			0.145768i
$761$			8.52748e6i			0.533776i	0.963728	+	0.266888i	$0.0859954\pi$
$761$			8.52748e6i			0.533776i	−0.963728	+	0.266888i	$0.914005\pi$
$762$		−	1.58329e6i		−	0.0987808i
$763$	1.02426e7			0.636940
$764$	4.57157e6			0.283356
$765$			2.09227e6i			0.129260i
$766$	3.51693e6			0.216567
$767$	5.67377e6	−	957220.i	0.348243	−	0.0587521i
$768$	1.12545e6			0.0688533
$769$			2.39512e7i			1.46054i	0.683161	+	0.730268i	$0.260605\pi$
$769$			2.39512e7i			1.46054i	−0.683161	+	0.730268i	$0.739395\pi$
$770$	−4.33559e6			−0.263525
$771$	125733.			0.00761751
$772$		−	2.65539e6i		−	0.160356i
$773$			2.01813e7i			1.21479i	0.794400	+	0.607395i	$0.207786\pi$
$773$			2.01813e7i			1.21479i	−0.794400	+	0.607395i	$0.792214\pi$
$774$			2.39354e7i			1.43611i
$775$		−	204313.i		−	0.0122192i
$776$	7.89110e6			0.470417
$777$	−410772.			−0.0244089
$778$		−	1.92215e7i		−	1.13851i
$779$	9.20476e6			0.543461
$780$	−180154.	+	30393.7i	−0.0106025	+	0.00178874i
$781$	−2.24591e7			−1.31754
$782$			2.02574e6i			0.118459i
$783$	826382.			0.0481700
$784$	−1.25318e7			−0.728156
$785$			2.16668e6i			0.125493i
$786$		−	1.82275e6i		−	0.105238i
$787$			1.40623e7i			0.809320i	0.914467	+	0.404660i	$0.132610\pi$
$787$			1.40623e7i			0.809320i	−0.914467	+	0.404660i	$0.867390\pi$
$788$			1.82842e6i			0.104897i
$789$	−1.77981e6			−0.101784
$790$	1.31636e6			0.0750423
$791$			6.92138e6i			0.393325i
$792$	1.30017e7			0.736523
$793$	3.06421e6	+	1.81626e7i	0.173035	+	1.02564i
$794$	1.86554e7			1.05016
$795$			1.56060e6i			0.0875738i
$796$	4.70179e6			0.263015
$797$	−2.70118e7			−1.50629			−0.753144	−	0.657856i	$-0.771464\pi$
$797$	−2.70118e7			−1.50629			−0.753144	+	0.657856i	$0.771464\pi$
$798$		−	503371.i		−	0.0279822i
$799$		−	2.00736e6i		−	0.111240i
$800$		−	1.57573e6i		−	0.0870478i
$801$			4.96286e6i			0.273307i
$802$	−2.36487e7			−1.29829
$803$	1.17134e7			0.641052
$804$		−	545346.i		−	0.0297531i
$805$	1.85485e6			0.100883
$806$	−207170.	−	1.22797e6i	−0.0112329	−	0.0665809i
$807$	1.93234e6			0.104448
$808$		−	1.94940e7i		−	1.05044i
$809$	−2.49077e7			−1.33802			−0.669011	−	0.743253i	$-0.733282\pi$
$809$	−2.49077e7			−1.33802			−0.669011	+	0.743253i	$0.733282\pi$
$810$	8.90396e6			0.476838
$811$		−	2.79023e7i		−	1.48966i	−0.667254	−	0.744830i	$-0.732530\pi$
$811$		−	2.79023e7i		−	1.48966i	0.667254	−	0.744830i	$-0.267470\pi$
$812$		−	571390.i		−	0.0304119i
$813$			3.28930e6i			0.174533i
$814$			6.60861e6i			0.349582i
$815$	9.16614e6			0.483384
$816$	708212.			0.0372339
$817$			9.50328e6i			0.498102i
$818$	1.15061e7			0.601233
$819$	1.15142e7	−	1.94257e6i	0.599827	−	0.101197i
$820$	−2.73544e6			−0.142067
$821$			3.05086e6i			0.157966i	0.996876	+	0.0789831i	$0.0251673\pi$
$821$			3.05086e6i			0.157966i	−0.996876	+	0.0789831i	$0.974833\pi$
$822$	−1.47562e6			−0.0761719
$823$	3.07364e7			1.58181			0.790904	−	0.611940i	$-0.209610\pi$
$823$	3.07364e7			1.58181			0.790904	+	0.611940i	$0.209610\pi$
$824$			2.14708e7i			1.10162i
$825$			367732.i			0.0188104i
$826$		−	4.71120e6i		−	0.240260i
$827$			1.24059e7i			0.630762i	0.948965	+	0.315381i	$0.102132\pi$
$827$			1.24059e7i			0.630762i	−0.948965	+	0.315381i	$0.897868\pi$
$828$	1.58191e6			0.0801872
$829$	3.70578e6			0.187281			0.0936405	−	0.995606i	$-0.470150\pi$
$829$	3.70578e6			0.187281			0.0936405	+	0.995606i	$0.470150\pi$
$830$		−	6.81061e6i		−	0.343155i
$831$	3.74704e6			0.188229
$832$	2.29652e6	+	1.36122e7i	0.115017	+	0.681743i
$833$	−3.63800e6			−0.181656
$834$			3.02825e6i			0.150757i
$835$	−4.14619e6			−0.205794
$836$	−1.46809e6			−0.0726503
$837$		−	267332.i		−	0.0131898i
$838$			8.37555e6i			0.412006i
$839$		−	1.14249e7i		−	0.560336i	−0.959951	−	0.280168i	$-0.909610\pi$
$839$		−	1.14249e7i		−	0.560336i	0.959951	−	0.280168i	$-0.0903902\pi$
$840$		−	525997.i		−	0.0257208i
$841$	−1.94900e7			−0.950215
$842$	−2.09239e7			−1.01710
$843$			3.39169e6i			0.164379i
$844$	3.13461e6			0.151470
$845$	−3.04536e6	−	8.76854e6i	−0.146722	−	0.422460i
$846$	−8.64704e6			−0.415376
$847$		−	3.20987e6i		−	0.153737i
$848$	−4.42750e7			−2.11431
$849$	−2.98904e6			−0.142319
$850$		−	1.36179e6i		−	0.0646492i
$851$		−	2.82730e6i		−	0.133828i
$852$			774904.i			0.0365720i
$853$			1.55707e6i			0.0732715i	0.999329	+	0.0366357i	$0.0116641\pi$
$853$			1.55707e6i			0.0732715i	−0.999329	+	0.0366357i	$0.988336\pi$
$854$	1.50813e7			0.707609
$855$	3.57843e6			0.167408
$856$		−	3.36447e7i		−	1.56939i
$857$	3.44187e7			1.60082			0.800411	−	0.599452i	$-0.204615\pi$
$857$	3.44187e7			1.60082			0.800411	+	0.599452i	$0.204615\pi$
$858$	372876.	+	2.21016e6i	0.0172920	+	0.102496i
$859$	−3.90745e7			−1.80680			−0.903402	−	0.428795i	$-0.858938\pi$
$859$	−3.90745e7			−1.80680			−0.903402	+	0.428795i	$0.858938\pi$
$860$		−	2.82416e6i		−	0.130209i
$861$	−2.08593e6			−0.0958940
$862$	−1.45703e7			−0.667884
$863$		−	6.51731e6i		−	0.297880i	−0.988846	−	0.148940i	$-0.952414\pi$
$863$		−	6.51731e6i		−	0.297880i	0.988846	−	0.148940i	$-0.0475861\pi$
$864$		−	2.06176e6i		−	0.0939624i
$865$		−	1.82334e6i		−	0.0828567i
$866$		−	2.76772e7i		−	1.25409i
$867$	−2.19773e6			−0.0992947
$868$	−184843.			−0.00832730
$869$		−	2.92759e6i		−	0.131511i
$870$	−267338.			−0.0119746
$871$	2.73210e7	−	4.60933e6i	1.22026	−	0.205869i
$872$	1.99919e7			0.890352
$873$		−	1.21656e7i		−	0.540253i
$874$	3.46464e6			0.153419
$875$	−1.24691e6			−0.0550574
$876$		−	404145.i		−	0.0177941i
$877$		−	8.12717e6i		−	0.356813i	−0.983957	−	0.178406i	$-0.942906\pi$
$877$		−	8.12717e6i		−	0.356813i	0.983957	−	0.178406i	$-0.0570942\pi$
$878$			7.23670e6i			0.316814i
$879$		−	781489.i		−	0.0341154i
$880$	−1.04327e7			−0.454142
$881$	−3.51008e7			−1.52362			−0.761811	−	0.647799i	$-0.775690\pi$
$881$	−3.51008e7			−1.52362			−0.761811	+	0.647799i	$0.775690\pi$
$882$			1.56713e7i			0.678317i
$883$	−1.82712e7			−0.788616			−0.394308	−	0.918978i	$-0.629016\pi$
$883$	−1.82712e7			−0.788616			−0.394308	+	0.918978i	$0.629016\pi$
$884$	−250322.	−	1.48374e6i	−0.0107738	−	0.0638598i
$885$	−399590.			−0.0171497
$886$		−	6.60211e6i		−	0.282552i
$887$	−2.42140e6			−0.103337			−0.0516686	−	0.998664i	$-0.516454\pi$
$887$	−2.42140e6			−0.103337			−0.0516686	+	0.998664i	$0.516454\pi$
$888$	−801761.			−0.0341203
$889$		−	1.19399e7i		−	0.506695i
$890$		−	3.23016e6i		−	0.136694i
$891$		−	1.98025e7i		−	0.835652i
$892$			7.19205e6i			0.302650i
$893$	−3.43321e6			−0.144069
$894$	−3.58594e6			−0.150058
$895$		−	7.37110e6i		−	0.307592i
$896$	1.77411e7			0.738264
$897$	−159524.	−	945552.i	−0.00661979	−	0.0392378i
$898$	−1.21533e7			−0.502927
$899$		−	330339.i		−	0.0136320i
$900$	−1.06343e6			−0.0437624
$901$	−1.28531e7			−0.527466
$902$			3.35589e7i			1.37338i
$903$		−	2.15358e6i		−	0.0878903i
$904$			1.35094e7i			0.549813i
$905$		−	8.00447e6i		−	0.324871i
$906$	−2.64722e6			−0.107144
$907$	−3.34288e7			−1.34928			−0.674641	−	0.738146i	$-0.735702\pi$
$907$	−3.34288e7			−1.34928			−0.674641	+	0.738146i	$0.735702\pi$
$908$			7.68685e6i			0.309410i
$909$	−3.00536e7			−1.20639
$910$	−7.49425e6	+	1.26435e6i	−0.300002	+	0.0506133i
$911$	2.70119e7			1.07835			0.539173	−	0.842195i	$-0.318737\pi$
$911$	2.70119e7			1.07835			0.539173	+	0.842195i	$0.318737\pi$
$912$		−	1.21126e6i		−	0.0482226i
$913$	−1.51468e7			−0.601375
$914$	−8.54917e6			−0.338500
$915$		−	1.27915e6i		−	0.0505090i
$916$			1.03127e6i			0.0406100i
$917$		−	1.37457e7i		−	0.539815i
$918$		−	1.78183e6i		−	0.0697846i
$919$	2.66405e7			1.04053			0.520264	−	0.854006i	$-0.325834\pi$
$919$	2.66405e7			1.04053			0.520264	+	0.854006i	$0.325834\pi$
$920$	3.62037e6			0.141021
$921$			769174.i			0.0298796i
$922$	1.40483e7			0.544247
$923$	−3.88215e7	+	6.54957e6i	−1.49992	+	0.253051i
$924$	332690.			0.0128192
$925$			1.90063e6i			0.0730371i
$926$	3.44508e7			1.32030
$927$	3.31012e7			1.26516
$928$		−	2.54770e6i		−	0.0971131i
$929$		−	4.83068e7i		−	1.83641i	−0.396111	−	0.918203i	$-0.629640\pi$
$929$		−	4.83068e7i		−	1.83641i	0.396111	−	0.918203i	$-0.370360\pi$
$930$			86483.0i			0.00327886i
$931$			6.22211e6i			0.235268i
$932$	−1.01822e7			−0.383975
$933$	4.95618e6			0.186399
$934$			3.87036e7i			1.45172i
$935$	−3.02863e6			−0.113297
$936$	2.24739e7	−	3.79157e6i	0.838474	−	0.141459i
$937$	−1.14184e7			−0.424871			−0.212435	−	0.977175i	$-0.568140\pi$
$937$	−1.14184e7			−0.424871			−0.212435	+	0.977175i	$0.568140\pi$
$938$		−	2.26860e7i		−	0.841880i
$939$	−1.28821e6			−0.0476786
$940$	1.02027e6			0.0376614
$941$			1.76576e7i			0.650065i	0.945703	+	0.325032i	$0.105375\pi$
$941$			1.76576e7i			0.650065i	−0.945703	+	0.325032i	$0.894625\pi$
$942$		−	917127.i		−	0.0336746i
$943$		−	1.43572e7i		−	0.525763i
$944$		−	1.13366e7i		−	0.414048i
$945$	−1.63152e6			−0.0594309
$946$	−3.46473e7			−1.25875
$947$			3.26209e7i			1.18201i	0.806668	+	0.591004i	$0.201268\pi$
$947$			3.26209e7i			1.18201i	−0.806668	+	0.591004i	$0.798732\pi$
$948$	−101010.			−0.00365043
$949$	2.02471e7	−	3.41588e6i	0.729787	−	0.123122i
$950$	−2.32908e6			−0.0837290
$951$		−	2.87312e6i		−	0.103016i
$952$	4.33210e6			0.154919
$953$	−1.42376e7			−0.507815			−0.253908	−	0.967229i	$-0.581716\pi$
$953$	−1.42376e7			−0.507815			−0.253908	+	0.967229i	$0.581716\pi$
$954$			5.53666e7i			1.96960i
$955$		−	1.61300e7i		−	0.572301i
$956$		−	9.93600e6i		−	0.351614i
$957$			594561.i			0.0209854i
$958$	1.69383e7			0.596289
$959$	−1.11279e7			−0.390722
$960$		−	958678.i		−	0.0335733i
$961$	2.85223e7			0.996267
$962$	1.92721e6	+	1.14232e7i	0.0671417	+	0.397971i
$963$	−5.18695e7			−1.80238
$964$			1.09591e6i			0.0379826i
$965$	−9.36906e6			−0.323875
$966$	−785137.			−0.0270709
$967$			8.95349e6i			0.307912i	0.988078	+	0.153956i	$0.0492013\pi$
$967$			8.95349e6i			0.307912i	−0.988078	+	0.153956i	$0.950799\pi$
$968$		−	6.26515e6i		−	0.214903i
$969$		−	351630.i		−	0.0120303i
$970$			7.91818e6i			0.270207i
$971$	1.34908e7			0.459188			0.229594	−	0.973287i	$-0.426260\pi$
$971$	1.34908e7			0.459188			0.229594	+	0.973287i	$0.426260\pi$
$972$	−2.09128e6			−0.0709981
$973$			2.28366e7i			0.773303i
$974$	5.38263e6			0.181801
$975$	107239.	+	635640.i	0.00361277	+	0.0214141i
$976$	3.62901e7			1.21945
$977$		−	460562.i		−	0.0154366i	−0.999970	−	0.00771831i	$-0.997543\pi$
$977$		−	460562.i		−	0.0154366i	0.999970	−	0.00771831i	$-0.00245684\pi$
$978$	−3.87991e6			−0.129710
$979$	−7.18391e6			−0.239554
$980$		−	1.84907e6i		−	0.0615018i
$981$		−	3.08211e7i		−	1.02253i
$982$			3.37561e7i			1.11705i
$983$			5.99559e7i			1.97901i	0.144492	+	0.989506i	$0.453845\pi$
$983$			5.99559e7i			1.97901i	−0.144492	+	0.989506i	$0.546155\pi$
$984$	−4.07139e6			−0.134046
$985$	6.45127e6			0.211863
$986$		−	2.20179e6i		−	0.0721245i
$987$	778014.			0.0254211
$988$	−2.53766e6	+	428127.i	−0.0827066	+	0.0139534i
$989$	1.48228e7			0.481881
$990$			1.30463e7i			0.423058i
$991$	3.36545e7			1.08858			0.544288	−	0.838898i	$-0.316800\pi$
$991$	3.36545e7			1.08858			0.544288	+	0.838898i	$0.316800\pi$
$992$	−824172.			−0.0265913
$993$		−	4.40706e6i		−	0.141833i
$994$			3.22354e7i			1.03482i
$995$		−	1.65894e7i		−	0.531219i
$996$			522610.i			0.0166928i
$997$	5.51854e6			0.175827			0.0879137	−	0.996128i	$-0.471980\pi$
$997$	5.51854e6			0.175827			0.0879137	+	0.996128i	$0.471980\pi$
$998$	4.15179e7			1.31950
$999$			2.48687e6i			0.0788388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.6.c.b.51.3	✓	14
13.5	odd	4		845.6.a.i.1.2		7
13.8	odd	4		845.6.a.j.1.6		7
13.12	even	2	inner	65.6.c.b.51.12	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.6.c.b.51.3	✓	14	1.1	even	1	trivial
65.6.c.b.51.12	yes	14	13.12	even	2	inner
845.6.a.i.1.2		7	13.5	odd	4
845.6.a.j.1.6		7	13.8	odd	4

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	65.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-6.25184i q^{2} +1.69265 q^{3} -7.08552 q^{4} +25.0000i q^{5} -10.5822i q^{6} -79.8024i q^{7} -155.761i q^{8} -240.135 q^{9} +156.296 q^{10} -347.604i q^{11} -11.9933 q^{12} +(-101.369 - 600.847i) q^{13} -498.912 q^{14} +42.3163i q^{15} -1200.53 q^{16} -348.516 q^{17} +1501.29i q^{18} +596.069i q^{19} -177.138i q^{20} -135.078i q^{21} -2173.16 q^{22} +929.723 q^{23} -263.650i q^{24} -625.000 q^{25} +(-3756.40 + 633.742i) q^{26} -817.779 q^{27} +565.442i q^{28} -1010.52 q^{29} +264.555 q^{30} +326.900i q^{31} +2521.17i q^{32} -588.372i q^{33} +2178.86i q^{34} +1995.06 q^{35} +1701.48 q^{36} -3041.01i q^{37} +3726.53 q^{38} +(-171.582 - 1017.02i) q^{39} +3894.03 q^{40} -15442.4i q^{41} -844.484 q^{42} +15943.2 q^{43} +2462.95i q^{44} -6003.37i q^{45} -5812.48i q^{46} +5759.75i q^{47} -2032.08 q^{48} +10438.6 q^{49} +3907.40i q^{50} -589.915 q^{51} +(718.251 + 4257.32i) q^{52} +36879.5 q^{53} +5112.62i q^{54} +8690.09 q^{55} -12430.1 q^{56} +1008.94i q^{57} +6317.61i q^{58} +9442.94i q^{59} -299.833i q^{60} -30228.3 q^{61} +2043.73 q^{62} +19163.4i q^{63} -22655.1 q^{64} +(15021.2 - 2534.22i) q^{65} -3678.41 q^{66} +45470.8i q^{67} +2469.42 q^{68} +1573.70 q^{69} -12472.8i q^{70} -64611.3i q^{71} +37403.7i q^{72} +33697.5i q^{73} -19011.9 q^{74} -1057.91 q^{75} -4223.46i q^{76} -27739.6 q^{77} +(-6358.28 + 1072.70i) q^{78} +8422.21 q^{79} -30013.3i q^{80} +56968.6 q^{81} -96543.6 q^{82} -43575.0i q^{83} +957.096i q^{84} -8712.89i q^{85} -99674.7i q^{86} -1710.46 q^{87} -54143.2 q^{88} -20667.0i q^{89} -37532.1 q^{90} +(-47949.1 + 8089.48i) q^{91} -6587.58 q^{92} +553.328i q^{93} +36009.1 q^{94} -14901.7 q^{95} +4267.47i q^{96} +50661.4i q^{97} -65260.3i q^{98} +83471.8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 84 q^{3} - 38 q^{4} + 1118 q^{9} + 550 q^{10} + 168 q^{12} - 1132 q^{13} + 6440 q^{14} - 3434 q^{16} + 228 q^{17} + 2328 q^{22} + 8104 q^{23} - 8750 q^{25} - 142 q^{26} + 13680 q^{27} - 16700 q^{29}+ \cdots + 318800 q^{95}+O(q^{100}) \) 14 * q - 84 * q^3 - 38 * q^4 + 1118 * q^9 + 550 * q^10 + 168 * q^12 - 1132 * q^13 + 6440 * q^14 - 3434 * q^16 + 228 * q^17 + 2328 * q^22 + 8104 * q^23 - 8750 * q^25 - 142 * q^26 + 13680 * q^27 - 16700 * q^29 + 12700 * q^30 - 2000 * q^35 + 39970 * q^36 - 5652 * q^38 + 2416 * q^39 + 24750 * q^40 - 96836 * q^42 - 64948 * q^43 - 35932 * q^48 + 29010 * q^49 + 18632 * q^51 - 48972 * q^52 + 106232 * q^53 - 33400 * q^55 - 87808 * q^56 - 65252 * q^61 + 127744 * q^62 + 44754 * q^64 - 40550 * q^65 + 165768 * q^66 + 58536 * q^68 - 318208 * q^69 - 151892 * q^74 + 52500 * q^75 - 123736 * q^77 + 219028 * q^78 - 4336 * q^79 + 364406 * q^81 + 391092 * q^82 - 328560 * q^87 - 282548 * q^88 - 14750 * q^90 - 34376 * q^91 - 163604 * q^92 + 797896 * q^94 + 318800 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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