LMFDB - Embedded newform 26.4.b.a.25.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [26,4,Mod(25,26)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(26, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("26.25"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	26.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.53404966015$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{217})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 109x^{2} + 2916 $ x^4 + 109*x^2 + 2916
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			25.1
Root			$-7.86546i$ of defining polynomial
Character	$\chi$	$=$	26.25
Dual form			26.4.b.a.25.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000i q^{2} -8.86546 q^{3} -4.00000 q^{4} -16.8655i q^{5} +17.7309i q^{6} +10.8655i q^{7} +8.00000i q^{8} +51.5964 q^{9} -33.7309 q^{10} -35.1928i q^{11} +35.4618 q^{12} +(-20.1345 - 42.3273i) q^{13} +21.7309 q^{14} +149.520i q^{15} +16.0000 q^{16} -30.3273 q^{17} -103.193i q^{18} +28.3855i q^{19} +67.4618i q^{20} -96.3273i q^{21} -70.3855 q^{22} +24.6546 q^{23} -70.9237i q^{24} -159.444 q^{25} +(-84.6546 + 40.2691i) q^{26} -218.058 q^{27} -43.4618i q^{28} +290.116 q^{29} +299.040 q^{30} -219.731i q^{31} -32.0000i q^{32} +312.000i q^{33} +60.6546i q^{34} +183.251 q^{35} -206.386 q^{36} +118.713i q^{37} +56.7710 q^{38} +(178.502 + 375.251i) q^{39} +134.924 q^{40} -83.6947i q^{41} -192.655 q^{42} -293.636 q^{43} +140.771i q^{44} -870.197i q^{45} -49.3092i q^{46} -166.211i q^{47} -141.847 q^{48} +224.942 q^{49} +318.887i q^{50} +268.865 q^{51} +(80.5382 + 169.309i) q^{52} -76.3855 q^{53} +436.116i q^{54} -593.542 q^{55} -86.9237 q^{56} -251.651i q^{57} -580.233i q^{58} +184.691i q^{59} -598.080i q^{60} +197.811 q^{61} -439.462 q^{62} +560.618i q^{63} -64.0000 q^{64} +(-713.869 + 339.578i) q^{65} +624.000 q^{66} -321.273i q^{67} +121.309 q^{68} -218.574 q^{69} -366.502i q^{70} +368.946i q^{71} +412.771i q^{72} +843.273i q^{73} +237.426 q^{74} +1413.54 q^{75} -113.542i q^{76} +382.386 q^{77} +(750.502 - 357.004i) q^{78} +184.044 q^{79} -269.847i q^{80} +540.084 q^{81} -167.389 q^{82} -1274.16i q^{83} +385.309i q^{84} +511.484i q^{85} +587.273i q^{86} -2572.02 q^{87} +281.542 q^{88} -1367.43i q^{89} -1740.39 q^{90} +(459.906 - 218.771i) q^{91} -98.6184 q^{92} +1948.02i q^{93} -332.422 q^{94} +478.735 q^{95} +283.695i q^{96} +690.241i q^{97} -449.884i q^{98} -1815.82i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} - 16 q^{4} + 118 q^{9} - 76 q^{10} + 24 q^{12} - 110 q^{13} + 28 q^{14} + 64 q^{16} + 26 q^{17} + 72 q^{22} - 196 q^{23} - 78 q^{25} - 44 q^{26} - 666 q^{27} + 748 q^{29} + 548 q^{30} + 350 q^{35}+ \cdots + 324 q^{95}+O(q^{100}) $ 4 * q - 6 * q^3 - 16 * q^4 + 118 * q^9 - 76 * q^10 + 24 * q^12 - 110 * q^13 + 28 * q^14 + 64 * q^16 + 26 * q^17 + 72 * q^22 - 196 * q^23 - 78 * q^25 - 44 * q^26 - 666 * q^27 + 748 * q^29 + 548 * q^30 + 350 * q^35 - 472 * q^36 - 480 * q^38 - 52 * q^39 + 304 * q^40 - 476 * q^42 - 438 * q^43 - 96 * q^48 + 1106 * q^49 + 1046 * q^51 + 440 * q^52 + 48 * q^53 - 960 * q^55 - 112 * q^56 - 564 * q^61 - 1640 * q^62 - 256 * q^64 - 1294 * q^65 + 2496 * q^66 - 104 * q^68 - 1876 * q^69 - 52 * q^74 + 4240 * q^75 + 1176 * q^77 + 2236 * q^78 - 1444 * q^79 - 668 * q^81 + 1216 * q^82 - 4160 * q^87 - 288 * q^88 - 3544 * q^90 + 1162 * q^91 + 784 * q^92 - 1860 * q^94 + 324 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$-1$

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 $

$2$		−	2.00000i		−	0.707107i
$2$		−	2.00000i		−	0.707107i
$3$	−8.86546			−1.70616			−0.853079	−	0.521781i	$-0.825268\pi$
$3$	−8.86546			−1.70616			−0.853079	+	0.521781i	$0.825268\pi$
$4$	−4.00000			−0.500000
$5$		−	16.8655i		−	1.50849i	−0.656592	−	0.754246i	$-0.728002\pi$
$5$		−	16.8655i		−	1.50849i	0.656592	−	0.754246i	$-0.271998\pi$
$6$			17.7309i			1.20644i
$7$			10.8655i			0.586680i	0.956008	+	0.293340i	$0.0947667\pi$
$7$			10.8655i			0.586680i	−0.956008	+	0.293340i	$0.905233\pi$
$8$			8.00000i			0.353553i
$9$	51.5964			1.91098
$10$	−33.7309			−1.06667
$11$		−	35.1928i		−	0.964638i	−0.875996	−	0.482319i	$-0.839795\pi$
$11$		−	35.1928i		−	0.964638i	0.875996	−	0.482319i	$-0.160205\pi$
$12$	35.4618			0.853079
$13$	−20.1345	−	42.3273i	−0.429563	−	0.903037i
$13$	−20.1345	−	42.3273i	−0.429563	−	0.903037i
$14$	21.7309			0.414845
$15$			149.520i			2.57373i
$16$	16.0000			0.250000
$17$	−30.3273			−0.432674			−0.216337	−	0.976319i	$-0.569411\pi$
$17$	−30.3273			−0.432674			−0.216337	+	0.976319i	$0.569411\pi$
$18$		−	103.193i		−	1.35126i
$19$			28.3855i			0.342741i	0.985207	+	0.171371i	$0.0548196\pi$
$19$			28.3855i			0.342741i	−0.985207	+	0.171371i	$0.945180\pi$
$20$			67.4618i			0.754246i
$21$		−	96.3273i		−	1.00097i
$22$	−70.3855			−0.682102
$23$	24.6546			0.223515			0.111757	−	0.993736i	$-0.464352\pi$
$23$	24.6546			0.223515			0.111757	+	0.993736i	$0.464352\pi$
$24$		−	70.9237i		−	0.603218i
$25$	−159.444			−1.27555
$26$	−84.6546	+	40.2691i	−0.638544	+	0.303747i
$27$	−218.058			−1.55427
$28$		−	43.4618i		−	0.293340i
$29$	290.116			1.85770			0.928849	−	0.370457i	$-0.120799\pi$
$29$	290.116			1.85770			0.928849	+	0.370457i	$0.120799\pi$
$30$	299.040			1.81990
$31$		−	219.731i		−	1.27306i	−0.771252	−	0.636530i	$-0.780369\pi$
$31$		−	219.731i		−	1.27306i	0.771252	−	0.636530i	$-0.219631\pi$
$32$		−	32.0000i		−	0.176777i
$33$			312.000i			1.64583i
$34$			60.6546i			0.305946i
$35$	183.251			0.885002
$36$	−206.386			−0.955489
$37$			118.713i			0.527467i	0.964596	+	0.263733i	$0.0849539\pi$
$37$			118.713i			0.527467i	−0.964596	+	0.263733i	$0.915046\pi$
$38$	56.7710			0.242355
$39$	178.502	+	375.251i	0.732902	+	1.54072i
$40$	134.924			0.533333
$41$		−	83.6947i		−	0.318803i	−0.987214	−	0.159401i	$-0.949044\pi$
$41$		−	83.6947i		−	0.318803i	0.987214	−	0.159401i	$-0.0509564\pi$
$42$	−192.655			−0.707792
$43$	−293.636			−1.04138			−0.520688	−	0.853747i	$-0.674324\pi$
$43$	−293.636			−1.04138			−0.520688	+	0.853747i	$0.674324\pi$
$44$			140.771i			0.482319i
$45$		−	870.197i		−	2.88269i
$46$		−	49.3092i		−	0.158049i
$47$		−	166.211i		−	0.515837i	−0.966167	−	0.257919i	$-0.916963\pi$
$47$		−	166.211i		−	0.515837i	0.966167	−	0.257919i	$-0.0830366\pi$
$48$	−141.847			−0.426540
$49$	224.942			0.655807
$50$			318.887i			0.901950i
$51$	268.865			0.738210
$52$	80.5382	+	169.309i	0.214781	+	0.451518i
$53$	−76.3855			−0.197969			−0.0989845	−	0.995089i	$-0.531559\pi$
$53$	−76.3855			−0.197969			−0.0989845	+	0.995089i	$0.531559\pi$
$54$			436.116i			1.09904i
$55$	−593.542			−1.45515
$56$	−86.9237			−0.207423
$57$		−	251.651i		−	0.584771i
$58$		−	580.233i		−	1.31359i
$59$			184.691i			0.407537i	0.979019	+	0.203769i	$0.0653190\pi$
$59$			184.691i			0.407537i	−0.979019	+	0.203769i	$0.934681\pi$
$60$		−	598.080i		−	1.28686i
$61$	197.811			0.415199			0.207599	−	0.978214i	$-0.433435\pi$
$61$	197.811			0.415199			0.207599	+	0.978214i	$0.433435\pi$
$62$	−439.462			−0.900189
$63$			560.618i			1.12113i
$64$	−64.0000			−0.125000
$65$	−713.869	+	339.578i	−1.36222	+	0.647992i
$66$	624.000			1.16377
$67$		−	321.273i		−	0.585817i	−0.956140	−	0.292909i	$-0.905377\pi$
$67$		−	321.273i		−	0.585817i	0.956140	−	0.292909i	$-0.0946231\pi$
$68$	121.309			0.216337
$69$	−218.574			−0.381352
$70$		−	366.502i		−	0.625791i
$71$			368.946i			0.616701i	0.951273	+	0.308351i	$0.0997770\pi$
$71$			368.946i			0.616701i	−0.951273	+	0.308351i	$0.900223\pi$
$72$			412.771i			0.675632i
$73$			843.273i			1.35202i	0.736891	+	0.676011i	$0.236293\pi$
$73$			843.273i			1.35202i	−0.736891	+	0.676011i	$0.763707\pi$
$74$	237.426			0.372975
$75$	1413.54			2.17629
$76$		−	113.542i		−	0.171371i
$77$	382.386			0.565933
$78$	750.502	−	357.004i	1.08946	−	0.518240i
$79$	184.044			0.262109			0.131054	−	0.991375i	$-0.458164\pi$
$79$	184.044			0.262109			0.131054	+	0.991375i	$0.458164\pi$
$80$		−	269.847i		−	0.377123i
$81$	540.084			0.740856
$82$	−167.389			−0.225428
$83$		−	1274.16i		−	1.68503i	−0.538675	−	0.842514i	$-0.681075\pi$
$83$		−	1274.16i		−	1.68503i	0.538675	−	0.842514i	$-0.318925\pi$
$84$			385.309i			0.500484i
$85$			511.484i			0.652685i
$86$			587.273i			0.736364i
$87$	−2572.02			−3.16953
$88$	281.542			0.341051
$89$		−	1367.43i		−	1.62863i	−0.580426	−	0.814313i	$-0.697114\pi$
$89$		−	1367.43i		−	1.62863i	0.580426	−	0.814313i	$-0.302886\pi$
$90$	−1740.39			−2.03837
$91$	459.906	−	218.771i	0.529793	−	0.252016i
$92$	−98.6184			−0.111757
$93$			1948.02i			2.17204i
$94$	−332.422			−0.364752
$95$	478.735			0.517023
$96$			283.695i			0.301609i
$97$			690.241i			0.722509i	0.932467	+	0.361254i	$0.117651\pi$
$97$			690.241i			0.722509i	−0.932467	+	0.361254i	$0.882349\pi$
$98$		−	449.884i		−	0.463726i
$99$		−	1815.82i		−	1.84340i
$100$	637.775			0.637775
$101$	−1395.21			−1.37454			−0.687269	−	0.726403i	$-0.741191\pi$
$101$	−1395.21			−1.37454			−0.687269	+	0.726403i	$0.741191\pi$
$102$		−	537.731i		−	0.521993i
$103$	1416.28			1.35485			0.677427	−	0.735590i	$-0.263095\pi$
$103$	1416.28			1.35485			0.677427	+	0.735590i	$0.263095\pi$
$104$	338.618	−	161.076i	0.319272	−	0.151873i
$105$	−1624.60			−1.50995
$106$			152.771i			0.139985i
$107$	451.068			0.407537			0.203768	−	0.979019i	$-0.434681\pi$
$107$	451.068			0.407537			0.203768	+	0.979019i	$0.434681\pi$
$108$	872.233			0.777136
$109$			1386.13i			1.21805i	0.793152	+	0.609024i	$0.208439\pi$
$109$			1386.13i			1.21805i	−0.793152	+	0.609024i	$0.791561\pi$
$110$			1187.08i			1.02895i
$111$		−	1052.44i		−	0.899942i
$112$			173.847i			0.146670i
$113$	1528.78			1.27270			0.636351	−	0.771399i	$-0.280443\pi$
$113$	1528.78			1.27270			0.636351	+	0.771399i	$0.280443\pi$
$114$	−503.301			−0.413496
$115$		−	415.811i		−	0.337170i
$116$	−1160.47			−0.928849
$117$	−1038.87	−	2183.94i	−0.820885	−	1.72568i
$118$	369.382			0.288172
$119$		−	329.520i		−	0.253841i
$120$	−1196.16			−0.909950
$121$	92.4697			0.0694738
$122$		−	395.622i		−	0.293590i
$123$			741.992i			0.543928i
$124$			878.924i			0.636530i
$125$			580.909i			0.415665i
$126$	1121.24			0.792760
$127$	1447.67			1.01149			0.505747	−	0.862682i	$-0.331217\pi$
$127$	1447.67			1.01149			0.505747	+	0.862682i	$0.331217\pi$
$128$			128.000i			0.0883883i
$129$	2603.22			1.77675
$130$	679.157	+	1427.74i	0.458200	+	0.963238i
$131$	631.877			0.421430			0.210715	−	0.977548i	$-0.432421\pi$
$131$	631.877			0.421430			0.210715	+	0.977548i	$0.432421\pi$
$132$		−	1248.00i		−	0.822913i
$133$	−308.422			−0.201079
$134$	−642.546			−0.414235
$135$			3677.65i			2.34461i
$136$		−	242.618i		−	0.152973i
$137$		−	547.418i		−	0.341380i	−0.985325	−	0.170690i	$-0.945400\pi$
$137$		−	547.418i		−	0.341380i	0.985325	−	0.170690i	$-0.0545997\pi$
$138$			437.149i			0.269656i
$139$	−677.070			−0.413153			−0.206577	−	0.978430i	$-0.566232\pi$
$139$	−677.070			−0.413153			−0.206577	+	0.978430i	$0.566232\pi$
$140$	−733.004			−0.442501
$141$			1473.54i			0.880100i
$142$	737.891			0.436074
$143$	−1489.61	+	708.590i	−0.871104	+	0.414373i
$144$	825.542			0.477744
$145$		−	4892.95i		−	2.80233i
$146$	1686.55			0.956024
$147$	−1994.21			−1.11891
$148$		−	474.851i		−	0.263733i
$149$			284.334i			0.156332i	0.996940	+	0.0781662i	$0.0249065\pi$
$149$			284.334i			0.156332i	−0.996940	+	0.0781662i	$0.975094\pi$
$150$		−	2827.08i		−	1.53887i
$151$			2708.68i			1.45980i	0.683555	+	0.729899i	$0.260433\pi$
$151$			2708.68i			1.45980i	−0.683555	+	0.729899i	$0.739567\pi$
$152$	−227.084			−0.121177
$153$	−1564.78			−0.826829
$154$		−	764.771i		−	0.400175i
$155$	−3705.86			−1.92040
$156$	−714.008	−	1501.00i	−0.366451	−	0.770362i
$157$	−883.775			−0.449254			−0.224627	−	0.974445i	$-0.572116\pi$
$157$	−883.775			−0.449254			−0.224627	+	0.974445i	$0.572116\pi$
$158$		−	368.088i		−	0.185339i
$159$	677.193			0.337767
$160$	−539.695			−0.266666
$161$			267.884i			0.131132i
$162$		−	1080.17i		−	0.523864i
$163$		−	3340.78i		−	1.60534i	−0.596425	−	0.802669i	$-0.703413\pi$
$163$		−	3340.78i		−	1.60534i	0.596425	−	0.802669i	$-0.296587\pi$
$164$			334.779i			0.159401i
$165$	5262.02			2.48271
$166$	−2548.32			−1.19149
$167$			1816.52i			0.841715i	0.907127	+	0.420857i	$0.138271\pi$
$167$			1816.52i			0.841715i	−0.907127	+	0.420857i	$0.861729\pi$
$168$	770.618			0.353896
$169$	−1386.20	+	1704.48i	−0.630952	+	0.775822i
$170$	1022.97			0.461518
$171$			1464.59i			0.654971i
$172$	1174.55			0.520688
$173$	984.241			0.432546			0.216273	−	0.976333i	$-0.430610\pi$
$173$	984.241			0.432546			0.216273	+	0.976333i	$0.430610\pi$
$174$			5144.03i			2.24120i
$175$		−	1732.43i		−	0.748339i
$176$		−	563.084i		−	0.241159i
$177$		−	1637.37i		−	0.695323i
$178$	−2734.87			−1.15161
$179$	3777.32			1.57726			0.788631	−	0.614866i	$-0.210790\pi$
$179$	3777.32			1.57726			0.788631	+	0.614866i	$0.210790\pi$
$180$			3480.79i			1.44135i
$181$	−2329.80			−0.956754			−0.478377	−	0.878154i	$-0.658775\pi$
$181$	−2329.80			−0.956754			−0.478377	+	0.878154i	$0.658775\pi$
$182$	−437.542	−	919.811i	−0.178202	−	0.374621i
$183$	−1753.69			−0.708395
$184$			197.237i			0.0790244i
$185$	2002.15			0.795680
$186$	3896.03			1.53586
$187$			1067.30i			0.417373i
$188$			664.843i			0.257919i
$189$		−	2369.30i		−	0.911859i
$190$		−	957.470i		−	0.365590i
$191$	−4611.93			−1.74716			−0.873579	−	0.486681i	$-0.838207\pi$
$191$	−4611.93			−1.74716			−0.873579	+	0.486681i	$0.838207\pi$
$192$	567.389			0.213270
$193$			952.799i			0.355358i	0.984089	+	0.177679i	$0.0568588\pi$
$193$			952.799i			0.355358i	−0.984089	+	0.177679i	$0.943141\pi$
$194$	1380.48			0.510891
$195$	6328.78	−	3010.52i	2.32417	−	1.10558i
$196$	−899.767			−0.327903
$197$		−	2050.54i		−	0.741598i	−0.928713	−	0.370799i	$-0.879084\pi$
$197$		−	2050.54i		−	0.741598i	0.928713	−	0.370799i	$-0.120916\pi$
$198$	−3631.64			−1.30348
$199$	2585.31			0.920943			0.460472	−	0.887674i	$-0.347680\pi$
$199$	2585.31			0.920943			0.460472	+	0.887674i	$0.347680\pi$
$200$		−	1275.55i		−	0.450975i
$201$			2848.23i			0.999497i
$202$			2790.42i			0.971946i
$203$			3152.25i			1.08987i
$204$	−1075.46			−0.369105
$205$	−1411.55			−0.480912
$206$		−	2832.55i		−	0.958026i
$207$	1272.09			0.427132
$208$	−322.153	−	677.237i	−0.107391	−	0.225759i
$209$	998.965			0.330621
$210$			3249.21i			1.06770i
$211$	−1756.23			−0.573003			−0.286501	−	0.958080i	$-0.592492\pi$
$211$	−1756.23			−0.573003			−0.286501	+	0.958080i	$0.592492\pi$
$212$	305.542			0.0989845
$213$		−	3270.87i		−	1.05219i
$214$		−	902.137i		−	0.288172i
$215$			4952.31i			1.57091i
$216$		−	1744.47i		−	0.549518i
$217$	2387.48			0.746878
$218$	2772.26			0.861290
$219$		−	7476.00i		−	2.30676i
$220$	2374.17			0.727575
$221$	610.626	+	1283.67i	0.185860	+	0.390720i
$222$	−2104.89			−0.636355
$223$		−	2038.12i		−	0.612030i	−0.952027	−	0.306015i	$-0.901004\pi$
$223$		−	2038.12i		−	0.612030i	0.952027	−	0.306015i	$-0.0989959\pi$
$224$	347.695			0.103711
$225$	−8226.72			−2.43755
$226$		−	3057.56i		−	0.899937i
$227$			4691.85i			1.37185i	0.727674	+	0.685923i	$0.240601\pi$
$227$			4691.85i			1.37185i	−0.727674	+	0.685923i	$0.759399\pi$
$228$			1006.60i			0.292386i
$229$			576.154i			0.166259i	0.996539	+	0.0831296i	$0.0264915\pi$
$229$			576.154i			0.166259i	−0.996539	+	0.0831296i	$0.973508\pi$
$230$	−831.622			−0.238415
$231$	−3390.02			−0.965572
$232$			2320.93i			0.656796i
$233$	−724.319			−0.203656			−0.101828	−	0.994802i	$-0.532469\pi$
$233$	−724.319			−0.203656			−0.101828	+	0.994802i	$0.532469\pi$
$234$	−4367.87	+	2077.74i	−1.22024	+	0.580453i
$235$	−2803.22			−0.778137
$236$		−	738.763i		−	0.203769i
$237$	−1631.64			−0.447199
$238$	−659.040			−0.179493
$239$		−	3137.80i		−	0.849237i	−0.905372	−	0.424619i	$-0.860408\pi$
$239$		−	3137.80i		−	0.849237i	0.905372	−	0.424619i	$-0.139592\pi$
$240$			2392.32i			0.643432i
$241$		−	1763.74i		−	0.471421i	−0.971823	−	0.235710i	$-0.924258\pi$
$241$		−	1763.74i		−	0.471421i	0.971823	−	0.235710i	$-0.0757417\pi$
$242$		−	184.939i		−	0.0491254i
$243$	1099.48			0.290253
$244$	−791.245			−0.207599
$245$		−	3793.75i		−	0.989280i
$246$	1483.98			0.384615
$247$	1201.48	−	571.529i	0.309508	−	0.147229i
$248$	1757.85			0.450094
$249$			11296.0i			2.87492i
$250$	1161.82			0.293920
$251$	1646.01			0.413925			0.206962	−	0.978349i	$-0.433642\pi$
$251$	1646.01			0.413925			0.206962	+	0.978349i	$0.433642\pi$
$252$		−	2242.47i		−	0.560566i
$253$		−	867.663i		−	0.215611i
$254$		−	2895.33i		−	0.715234i
$255$		−	4534.54i		−	1.11358i
$256$	256.000			0.0625000
$257$	6415.73			1.55721			0.778603	−	0.627516i	$-0.215928\pi$
$257$	6415.73			1.55721			0.778603	+	0.627516i	$0.215928\pi$
$258$		−	5206.45i		−	1.25635i
$259$	−1289.87			−0.309454
$260$	2855.48	−	1358.31i	0.681112	−	0.323996i
$261$	14969.0			3.55002
$262$		−	1263.75i		−	0.297996i
$263$	−3660.48			−0.858232			−0.429116	−	0.903249i	$-0.641175\pi$
$263$	−3660.48			−0.858232			−0.429116	+	0.903249i	$0.641175\pi$
$264$	−2496.00			−0.581887
$265$			1288.28i			0.298635i
$266$			616.843i			0.142185i
$267$			12122.9i			2.77869i
$268$			1285.09i			0.292909i
$269$	−5645.30			−1.27955			−0.639777	−	0.768560i	$-0.720973\pi$
$269$	−5645.30			−1.27955			−0.639777	+	0.768560i	$0.720973\pi$
$270$	7355.30			1.65789
$271$			6671.87i			1.49552i	0.663966	+	0.747762i	$0.268872\pi$
$271$			6671.87i			1.49552i	−0.663966	+	0.747762i	$0.731128\pi$
$272$	−485.237			−0.108168
$273$	−4077.27	+	1939.51i	−0.903912	+	0.429979i
$274$	−1094.84			−0.241392
$275$			5611.27i			1.23044i
$276$	874.297			0.190676
$277$	2905.39			0.630210			0.315105	−	0.949057i	$-0.397960\pi$
$277$	2905.39			0.630210			0.315105	+	0.949057i	$0.397960\pi$
$278$			1354.14i			0.292144i
$279$		−	11337.3i		−	2.43279i
$280$			1466.01i			0.312895i
$281$		−	8009.76i		−	1.70044i	−0.526431	−	0.850218i	$-0.676470\pi$
$281$		−	8009.76i		−	1.70044i	0.526431	−	0.850218i	$-0.323530\pi$
$282$	2947.07			0.622325
$283$	−3707.71			−0.778800			−0.389400	−	0.921069i	$-0.627318\pi$
$283$	−3707.71			−0.778800			−0.389400	+	0.921069i	$0.627318\pi$
$284$		−	1475.78i		−	0.308351i
$285$	−4244.20			−0.882123
$286$	1417.18	+	2979.23i	0.293006	+	0.615963i
$287$	909.382			0.187035
$288$		−	1651.08i		−	0.337816i
$289$	−3993.25			−0.812794
$290$	−9785.89			−1.98154
$291$		−	6119.30i		−	1.23271i
$292$		−	3373.09i		−	0.676011i
$293$			1674.00i			0.333775i	0.985976	+	0.166887i	$0.0533717\pi$
$293$			1674.00i			0.333775i	−0.985976	+	0.166887i	$0.946628\pi$
$294$			3988.42i			0.791189i
$295$	3114.90			0.614767
$296$	−949.703			−0.186488
$297$			7674.07i			1.49931i
$298$	568.667			0.110544
$299$	−496.409	−	1043.56i	−0.0960136	−	0.201842i
$300$	−5654.17			−1.08815
$301$		−	3190.50i		−	0.610954i
$302$	5417.37			1.03223
$303$	12369.2			2.34518
$304$			454.168i			0.0856853i
$305$		−	3336.18i		−	0.626324i
$306$			3129.56i			0.584657i
$307$		−	299.935i		−	0.0557597i	−0.999611	−	0.0278798i	$-0.991124\pi$
$307$		−	299.935i		−	0.0557597i	0.999611	−	0.0278798i	$-0.00887558\pi$
$308$	−1529.54			−0.282967
$309$	−12555.9			−2.31159
$310$			7411.73i			1.35793i
$311$	890.140			0.162300			0.0811498	−	0.996702i	$-0.474141\pi$
$311$	890.140			0.162300			0.0811498	+	0.996702i	$0.474141\pi$
$312$	−3002.01	+	1428.02i	−0.544728	+	0.259120i
$313$	−1154.20			−0.208432			−0.104216	−	0.994555i	$-0.533233\pi$
$313$	−1154.20			−0.208432			−0.104216	+	0.994555i	$0.533233\pi$
$314$			1767.55i			0.317671i
$315$	9455.09			1.69122
$316$	−736.176			−0.131054
$317$		−	2708.86i		−	0.479951i	−0.970779	−	0.239976i	$-0.922861\pi$
$317$		−	2708.86i		−	0.479951i	0.970779	−	0.239976i	$-0.0771394\pi$
$318$		−	1354.39i		−	0.238837i
$319$		−	10210.0i		−	1.79201i
$320$			1079.39i			0.188562i
$321$	−3998.93			−0.695322
$322$	535.767			0.0927240
$323$		−	860.856i		−	0.148295i
$324$	−2160.34			−0.370428
$325$	3210.33	+	6748.82i	0.547929	+	1.15187i
$326$	−6681.56			−1.13514
$327$		−	12288.7i		−	2.07818i
$328$	669.558			0.112714
$329$	1805.96			0.302631
$330$		−	10524.0i		−	1.75554i
$331$		−	8187.12i		−	1.35953i	−0.733429	−	0.679766i	$-0.762081\pi$
$331$		−	8187.12i		−	1.35953i	0.733429	−	0.679766i	$-0.237919\pi$
$332$			5096.64i			0.842514i
$333$			6125.15i			1.00798i
$334$	3633.04			0.595182
$335$	−5418.42			−0.883701
$336$		−	1541.24i		−	0.250242i
$337$	8770.94			1.41776			0.708878	−	0.705331i	$-0.249202\pi$
$337$	8770.94			1.41776			0.708878	+	0.705331i	$0.249202\pi$
$338$	3408.96	+	2772.40i	0.548589	+	0.446150i
$339$	−13553.3			−2.17143
$340$		−	2045.94i		−	0.326342i
$341$	−7732.94			−1.22804
$342$	2929.18			0.463134
$343$			6170.95i			0.971428i
$344$		−	2349.09i		−	0.368182i
$345$			3686.36i			0.575266i
$346$		−	1968.48i		−	0.305856i
$347$	−4278.96			−0.661978			−0.330989	−	0.943635i	$-0.607382\pi$
$347$	−4278.96			−0.661978			−0.330989	+	0.943635i	$0.607382\pi$
$348$	10288.1			1.58476
$349$			6181.46i			0.948097i	0.880499	+	0.474049i	$0.157208\pi$
$349$			6181.46i			0.948097i	−0.880499	+	0.474049i	$0.842792\pi$
$350$	−3464.86			−0.529156
$351$	4390.50	+	9229.82i	0.667657	+	1.40356i
$352$	−1126.17			−0.170525
$353$			5471.61i			0.824998i	0.910958	+	0.412499i	$0.135344\pi$
$353$			5471.61i			0.824998i	−0.910958	+	0.412499i	$0.864656\pi$
$354$	−3274.74			−0.491668
$355$	6222.44			0.930289
$356$			5469.73i			0.814313i
$357$			2921.35i			0.433093i
$358$		−	7554.64i		−	1.11529i
$359$			6398.77i			0.940709i	0.882478	+	0.470354i	$0.155874\pi$
$359$			6398.77i			0.940709i	−0.882478	+	0.470354i	$0.844126\pi$
$360$	6961.57			1.01919
$361$	6053.26			0.882528
$362$			4659.60i			0.676528i
$363$	−819.786			−0.118533
$364$	−1839.62	+	875.084i	−0.264897	+	0.126008i
$365$	14222.2			2.03952
$366$			3507.37i			0.500911i
$367$	9636.19			1.37059			0.685293	−	0.728267i	$-0.259674\pi$
$367$	9636.19			1.37059			0.685293	+	0.728267i	$0.259674\pi$
$368$	394.474			0.0558787
$369$		−	4318.34i		−	0.609225i
$370$		−	4004.29i		−	0.562630i
$371$		−	829.964i		−	0.116144i
$372$		−	7792.06i		−	1.08602i
$373$	8807.88			1.22267			0.611333	−	0.791373i	$-0.290634\pi$
$373$	8807.88			1.22267			0.611333	+	0.791373i	$0.290634\pi$
$374$	2134.60			0.295127
$375$		−	5150.03i		−	0.709190i
$376$	1329.69			0.182376
$377$	−5841.36	−	12279.8i	−0.797998	−	1.67757i
$378$	−4738.61			−0.644782
$379$			8678.95i			1.17627i	0.808761	+	0.588137i	$0.200138\pi$
$379$			8678.95i			1.17627i	−0.808761	+	0.588137i	$0.799862\pi$
$380$	−1914.94			−0.258511
$381$	−12834.2			−1.72577
$382$			9223.86i			1.23543i
$383$			2712.30i			0.361860i	0.983496	+	0.180930i	$0.0579107\pi$
$383$			2712.30i			0.361860i	−0.983496	+	0.180930i	$0.942089\pi$
$384$		−	1134.78i		−	0.150805i
$385$		−	6449.11i		−	0.853706i
$386$	1905.60			0.251276
$387$	−15150.6			−1.99004
$388$		−	2760.96i		−	0.361254i
$389$	290.941			0.0379211			0.0189605	−	0.999820i	$-0.493964\pi$
$389$	290.941			0.0379211			0.0189605	+	0.999820i	$0.493964\pi$
$390$	−6021.04	−	12657.6i	−0.781761	−	1.64344i
$391$	−747.707			−0.0967089
$392$			1799.53i			0.231863i
$393$	−5601.88			−0.719027
$394$	−4101.08			−0.524389
$395$		−	3103.99i		−	0.395389i
$396$			7263.28i			0.921700i
$397$			14114.0i			1.78429i	0.451751	+	0.892144i	$0.350799\pi$
$397$			14114.0i			1.78429i	−0.451751	+	0.892144i	$0.649201\pi$
$398$		−	5170.62i		−	0.651205i
$399$	2734.30			0.343073
$400$	−2551.10			−0.318887
$401$		−	11342.0i		−	1.41245i	−0.707987	−	0.706226i	$-0.750396\pi$
$401$		−	11342.0i		−	1.41245i	0.707987	−	0.706226i	$-0.249604\pi$
$402$	5696.47			0.706751
$403$	−9300.62	+	4424.18i	−1.14962	+	0.546859i
$404$	5580.83			0.687269
$405$		−	9108.77i		−	1.11758i
$406$	6304.50			0.770657
$407$	4177.83			0.508814
$408$			2150.92i			0.260997i
$409$		−	4686.94i		−	0.566636i	−0.959026	−	0.283318i	$-0.908565\pi$
$409$		−	4686.94i		−	0.566636i	0.959026	−	0.283318i	$-0.0914352\pi$
$410$			2823.10i			0.340056i
$411$			4853.11i			0.582448i
$412$	−5665.11			−0.677427
$413$	−2006.75			−0.239094
$414$		−	2544.18i		−	0.302028i
$415$	−21489.3			−2.54185
$416$	−1354.47	+	644.305i	−0.159636	+	0.0759367i
$417$	6002.54			0.704905
$418$		−	1997.93i		−	0.233785i
$419$	11889.7			1.38627			0.693137	−	0.720806i	$-0.256228\pi$
$419$	11889.7			1.38627			0.693137	+	0.720806i	$0.256228\pi$
$420$	6498.42			0.754977
$421$			4755.64i			0.550536i	0.961367	+	0.275268i	$0.0887666\pi$
$421$			4755.64i			0.550536i	−0.961367	+	0.275268i	$0.911233\pi$
$422$			3512.45i			0.405174i
$423$		−	8575.88i		−	0.985753i
$424$		−	611.084i		−	0.0699926i
$425$	4835.50			0.551897
$426$	−6541.75			−0.744011
$427$			2149.31i			0.243589i
$428$	−1804.27			−0.203768
$429$	13206.1	−	6281.98i	1.48624	−	0.706985i
$430$	9904.63			1.11080
$431$			4378.13i			0.489297i	0.969612	+	0.244649i	$0.0786726\pi$
$431$			4378.13i			0.489297i	−0.969612	+	0.244649i	$0.921327\pi$
$432$	−3488.93			−0.388568
$433$	−15576.3			−1.72875			−0.864377	−	0.502844i	$-0.832287\pi$
$433$	−15576.3			−1.72875			−0.864377	+	0.502844i	$0.832287\pi$
$434$		−	4774.96i		−	0.528123i
$435$			43378.2i			4.78121i
$436$		−	5544.52i		−	0.609024i
$437$			699.834i			0.0766077i
$438$	−14952.0			−1.63113
$439$	13474.8			1.46495			0.732477	−	0.680792i	$-0.238364\pi$
$439$	13474.8			1.46495			0.732477	+	0.680792i	$0.238364\pi$
$440$		−	4748.34i		−	0.514473i
$441$	11606.2			1.25323
$442$	2567.35	−	1221.25i	0.276281	−	0.131423i
$443$	−24.4564			−0.00262294			−0.00131147	−	0.999999i	$-0.500417\pi$
$443$	−24.4564			−0.00262294			−0.00131147	+	0.999999i	$0.500417\pi$
$444$			4209.77i			0.449971i
$445$	−23062.4			−2.45677
$446$	−4076.25			−0.432771
$447$		−	2520.75i		−	0.266728i
$448$		−	695.389i		−	0.0733350i
$449$		−	13636.7i		−	1.43331i	−0.697427	−	0.716655i	$-0.745672\pi$
$449$		−	13636.7i		−	1.43331i	0.697427	−	0.716655i	$-0.254328\pi$
$450$			16453.4i			1.72361i
$451$	−2945.45			−0.307529
$452$	−6115.12			−0.636351
$453$		−	24013.7i		−	2.49065i
$454$	9383.70			0.970042
$455$	−3689.67	−	7756.52i	−0.380164	−	0.799190i
$456$	2013.21			0.206748
$457$		−	13380.5i		−	1.36962i	−0.728723	−	0.684808i	$-0.759886\pi$
$457$		−	13380.5i		−	1.36962i	0.728723	−	0.684808i	$-0.240114\pi$
$458$	1152.31			0.117563
$459$	6613.12			0.672492
$460$			1663.24i			0.168585i
$461$			6782.55i			0.685238i	0.939474	+	0.342619i	$0.111314\pi$
$461$			6782.55i			0.685238i	−0.939474	+	0.342619i	$0.888686\pi$
$462$			6780.05i			0.682763i
$463$		−	10966.2i		−	1.10074i	−0.834922	−	0.550368i	$-0.814488\pi$
$463$		−	10966.2i		−	1.10074i	0.834922	−	0.550368i	$-0.185512\pi$
$464$	4641.86			0.464425
$465$	32854.2			3.27651
$466$			1448.64i			0.144006i
$467$	609.640			0.0604085			0.0302043	−	0.999544i	$-0.490384\pi$
$467$	609.640			0.0604085			0.0302043	+	0.999544i	$0.490384\pi$
$468$	4155.48	+	8735.74i	0.410442	+	0.862841i
$469$	3490.78			0.343687
$470$			5606.45i			0.550226i
$471$	7835.07			0.766499
$472$	−1477.53			−0.144086
$473$			10333.9i			1.00455i
$474$			3263.27i			0.316217i
$475$		−	4525.89i		−	0.437184i
$476$			1318.08i			0.126920i
$477$	−3941.22			−0.378314
$478$	−6275.61			−0.600501
$479$			8405.28i			0.801769i	0.916129	+	0.400884i	$0.131297\pi$
$479$			8405.28i			0.801769i	−0.916129	+	0.400884i	$0.868703\pi$
$480$	4784.64			0.454975
$481$	5024.79	−	2390.23i	0.476322	−	0.226580i
$482$	−3527.48			−0.333345
$483$		−	2374.91i		−	0.223731i
$484$	−369.879			−0.0347369
$485$	11641.2			1.08990
$486$		−	2198.96i		−	0.205240i
$487$		−	16160.4i		−	1.50370i	−0.659337	−	0.751848i	$-0.729163\pi$
$487$		−	16160.4i		−	1.50370i	0.659337	−	0.751848i	$-0.270837\pi$
$488$			1582.49i			0.146795i
$489$			29617.5i			2.73896i
$490$	−7587.49			−0.699527
$491$	−6426.96			−0.590722			−0.295361	−	0.955386i	$-0.595440\pi$
$491$	−6426.96			−0.590722			−0.295361	+	0.955386i	$0.595440\pi$
$492$		−	2967.97i		−	0.271964i
$493$	−8798.45			−0.803777
$494$	−1143.06	−	2402.96i	−0.104107	−	0.218855i
$495$	−30624.6			−2.78076
$496$		−	3515.69i		−	0.318265i
$497$	−4008.76			−0.361806
$498$	22592.0			2.03288
$499$			15240.3i			1.36724i	0.729840	+	0.683618i	$0.239595\pi$
$499$			15240.3i			1.36724i	−0.729840	+	0.683618i	$0.760405\pi$
$500$		−	2323.64i		−	0.207832i
$501$		−	16104.3i		−	1.43610i
$502$		−	3292.02i		−	0.292689i
$503$	10404.0			0.922250			0.461125	−	0.887335i	$-0.347446\pi$
$503$	10404.0			0.922250			0.461125	+	0.887335i	$0.347446\pi$
$504$	−4484.95			−0.396380
$505$			23530.8i			2.07348i
$506$	−1735.33			−0.152460
$507$	12289.3	−	15111.0i	1.07650	−	1.32368i
$508$	−5790.67			−0.505747
$509$			14623.3i			1.27341i	0.771106	+	0.636707i	$0.219704\pi$
$509$			14623.3i			1.27341i	−0.771106	+	0.636707i	$0.780296\pi$
$510$	−9069.08			−0.787423
$511$	−9162.55			−0.793204
$512$		−	512.000i		−	0.0441942i
$513$		−	6189.70i		−	0.532713i
$514$		−	12831.5i		−	1.10111i
$515$		−	23886.2i		−	2.04379i
$516$	−10412.9			−0.888376
$517$	−5849.42			−0.497596
$518$			2579.74i			0.218817i
$519$	−8725.75			−0.737992
$520$	−2716.63	−	5710.96i	−0.229100	−	0.481619i
$521$	−19937.9			−1.67657			−0.838285	−	0.545232i	$-0.816442\pi$
$521$	−19937.9			−1.67657			−0.838285	+	0.545232i	$0.816442\pi$
$522$		−	29937.9i		−	2.51024i
$523$	4327.00			0.361771			0.180886	−	0.983504i	$-0.442104\pi$
$523$	4327.00			0.361771			0.180886	+	0.983504i	$0.442104\pi$
$524$	−2527.51			−0.210715
$525$			15358.8i			1.27679i
$526$			7320.96i			0.606862i
$527$			6663.85i			0.550819i
$528$			4992.00i			0.411456i
$529$	−11559.2			−0.950041
$530$	2576.55			0.211167
$531$			9529.38i			0.778794i
$532$	1233.69			0.100540
$533$	−3542.57	+	1685.15i	−0.287891	+	0.136946i
$534$	24245.9			1.96483
$535$		−	7607.48i		−	0.614766i
$536$	2570.18			0.207118
$537$	−33487.7			−2.69106
$538$			11290.6i			0.904782i
$539$		−	7916.32i		−	0.632616i
$540$		−	14710.6i		−	1.17230i
$541$		−	2602.93i		−	0.206855i	−0.994637	−	0.103428i	$-0.967019\pi$
$541$		−	2602.93i		−	0.206855i	0.994637	−	0.103428i	$-0.0329810\pi$
$542$	13343.7			1.05750
$543$	20654.7			1.63237
$544$			970.474i			0.0764866i
$545$	23377.7			1.83742
$546$	3879.01	+	8154.55i	0.304041	+	0.639162i
$547$	11225.3			0.877441			0.438720	−	0.898624i	$-0.355432\pi$
$547$	11225.3			0.877441			0.438720	+	0.898624i	$0.355432\pi$
$548$			2189.67i			0.170690i
$549$	10206.3			0.793435
$550$	11222.5			0.870055
$551$			8235.11i			0.636710i
$552$		−	1748.59i		−	0.134828i
$553$			1999.72i			0.153774i
$554$		−	5810.78i		−	0.445626i
$555$	−17749.9			−1.35756
$556$	2708.28			0.206577
$557$			8248.83i			0.627494i	0.949507	+	0.313747i	$0.101584\pi$
$557$			8248.83i			0.627494i	−0.949507	+	0.313747i	$0.898416\pi$
$558$	−22674.6			−1.72024
$559$	5912.24	+	12428.8i	0.447336	+	0.940401i
$560$	2932.02			0.221250
$561$		−	9462.12i		−	0.712105i
$562$	−16019.5			−1.20239
$563$	1693.06			0.126739			0.0633696	−	0.997990i	$-0.479815\pi$
$563$	1693.06			0.126739			0.0633696	+	0.997990i	$0.479815\pi$
$564$		−	5894.14i		−	0.440050i
$565$		−	25783.6i		−	1.91986i
$566$			7415.42i			0.550695i
$567$			5868.26i			0.434645i
$568$	−2951.57			−0.218037
$569$	−8251.55			−0.607949			−0.303974	−	0.952680i	$-0.598314\pi$
$569$	−8251.55			−0.607949			−0.303974	+	0.952680i	$0.598314\pi$
$570$			8488.41i			0.623755i
$571$	23153.2			1.69691			0.848453	−	0.529271i	$-0.177534\pi$
$571$	23153.2			1.69691			0.848453	+	0.529271i	$0.177534\pi$
$572$	5958.46	−	2834.36i	0.435552	−	0.207186i
$573$	40886.9			2.98093
$574$		−	1818.76i		−	0.132254i
$575$	−3931.02			−0.285104
$576$	−3302.17			−0.238872
$577$		−	2058.46i		−	0.148518i	−0.997239	−	0.0742590i	$-0.976341\pi$
$577$		−	2058.46i		−	0.148518i	0.997239	−	0.0742590i	$-0.0236591\pi$
$578$			7986.51i			0.574732i
$579$		−	8447.00i		−	0.606296i
$580$			19571.8i			1.40116i
$581$	13844.3			0.988571
$582$	−12238.6			−0.871660
$583$			2688.22i			0.190968i
$584$	−6746.18			−0.478012
$585$	−36833.1	+	17521.0i	−2.60318	+	1.23830i
$586$	3348.00			0.236014
$587$		−	12861.7i		−	0.904361i	−0.891926	−	0.452180i	$-0.850646\pi$
$587$		−	12861.7i		−	0.904361i	0.891926	−	0.452180i	$-0.149354\pi$
$588$	7976.85			0.559455
$589$	6237.18			0.436330
$590$		−	6229.79i		−	0.434706i
$591$			18179.0i			1.26528i
$592$			1899.41i			0.131867i
$593$			18098.4i			1.25331i	0.779298	+	0.626653i	$0.215576\pi$
$593$			18098.4i			1.25331i	−0.779298	+	0.626653i	$0.784424\pi$
$594$	15348.1			1.06017
$595$	−5557.51			−0.382917
$596$		−	1137.33i		−	0.0781662i
$597$	−22920.0			−1.57128
$598$	−2087.13	+	992.818i	−0.142724	+	0.0678919i
$599$	−15338.0			−1.04623			−0.523115	−	0.852262i	$-0.675230\pi$
$599$	−15338.0			−1.04623			−0.523115	+	0.852262i	$0.675230\pi$
$600$			11308.3i			0.769435i
$601$	22289.4			1.51282			0.756409	−	0.654099i	$-0.226952\pi$
$601$	22289.4			1.51282			0.756409	+	0.654099i	$0.226952\pi$
$602$	−6380.99			−0.432010
$603$		−	16576.5i		−	1.11948i
$604$		−	10834.7i		−	0.729899i
$605$		−	1559.54i		−	0.104801i
$606$		−	24738.3i		−	1.65829i
$607$	7191.81			0.480900			0.240450	−	0.970662i	$-0.422705\pi$
$607$	7191.81			0.480900			0.240450	+	0.970662i	$0.422705\pi$
$608$	908.337			0.0605887
$609$		−	27946.1i		−	1.85950i
$610$	−6672.35			−0.442878
$611$	−7035.26	+	3346.58i	−0.465820	+	0.221584i
$612$	6259.12			0.413415
$613$		−	797.058i		−	0.0525169i	−0.999655	−	0.0262584i	$-0.991641\pi$
$613$		−	797.058i		−	0.0525169i	0.999655	−	0.0262584i	$-0.00835928\pi$
$614$	−599.871			−0.0394280
$615$	12514.0			0.820512
$616$			3059.08i			0.200088i
$617$			20908.3i			1.36424i	0.731240	+	0.682120i	$0.238942\pi$
$617$			20908.3i			1.36424i	−0.731240	+	0.682120i	$0.761058\pi$
$618$			25111.9i			1.63454i
$619$			12309.9i			0.799315i	0.916665	+	0.399658i	$0.130871\pi$
$619$			12309.9i			0.799315i	−0.916665	+	0.399658i	$0.869129\pi$
$620$	14823.5			0.960200
$621$	−5376.14			−0.347403
$622$		−	1780.28i		−	0.114763i
$623$	14857.8			0.955481
$624$	2856.03	+	6004.02i	0.183226	+	0.385181i
$625$	−10133.2			−0.648522
$626$			2308.40i			0.147384i
$627$	−8856.28			−0.564092
$628$	3535.10			0.224627
$629$		−	3600.24i		−	0.228221i
$630$		−	18910.2i		−	1.19587i
$631$		−	10332.7i		−	0.651881i	−0.945390	−	0.325940i	$-0.894319\pi$
$631$		−	10332.7i		−	0.651881i	0.945390	−	0.325940i	$-0.105681\pi$
$632$			1472.35i			0.0926693i
$633$	15569.8			0.977634
$634$	−5417.71			−0.339377
$635$		−	24415.6i		−	1.52583i
$636$	−2708.77			−0.168883
$637$	−4529.10	−	9521.18i	−0.281710	−	0.592218i
$638$	−20420.0			−1.26714
$639$			19036.3i			1.17850i
$640$	2158.78			0.133333
$641$	−676.867			−0.0417077			−0.0208539	−	0.999783i	$-0.506638\pi$
$641$	−676.867			−0.0417077			−0.0208539	+	0.999783i	$0.506638\pi$
$642$			7997.86i			0.491667i
$643$		−	26312.7i		−	1.61379i	−0.590692	−	0.806897i	$-0.701145\pi$
$643$		−	26312.7i		−	1.61379i	0.590692	−	0.806897i	$-0.298855\pi$
$644$		−	1071.53i		−	0.0655658i
$645$		−	43904.5i		−	2.68022i
$646$	−1721.71			−0.104860
$647$	−169.876			−0.0103223			−0.00516113	−	0.999987i	$-0.501643\pi$
$647$	−169.876			−0.0103223			−0.00516113	+	0.999987i	$0.501643\pi$
$648$			4320.67i			0.261932i
$649$	6499.78			0.393126
$650$	13497.6	−	6420.65i	0.814494	−	0.387444i
$651$	−21166.1			−1.27429
$652$			13363.1i			0.802669i
$653$	−14426.6			−0.864558			−0.432279	−	0.901740i	$-0.642290\pi$
$653$	−14426.6			−0.864558			−0.432279	+	0.901740i	$0.642290\pi$
$654$	−24577.4			−1.46950
$655$		−	10656.9i		−	0.635724i
$656$		−	1339.12i		−	0.0797007i
$657$			43509.8i			2.58368i
$658$		−	3611.91i		−	0.213993i
$659$	−25211.8			−1.49031			−0.745155	−	0.666892i	$-0.767624\pi$
$659$	−25211.8			−1.49031			−0.745155	+	0.666892i	$0.767624\pi$
$660$	−21048.1			−1.24136
$661$			22839.0i			1.34393i	0.740585	+	0.671963i	$0.234548\pi$
$661$			22839.0i			1.34393i	−0.740585	+	0.671963i	$0.765452\pi$
$662$	−16374.2			−0.961334
$663$	−5413.48	−	11380.3i	−0.317107	−	0.666631i
$664$	10193.3			0.595747
$665$			5201.67i			0.303327i
$666$	12250.3			0.712747
$667$	7152.70			0.415223
$668$		−	7266.07i		−	0.420857i
$669$			18068.9i			1.04422i
$670$			10836.8i			0.624871i
$671$		−	6961.52i		−	0.400516i
$672$	−3082.47			−0.176948
$673$	16708.2			0.956989			0.478495	−	0.878090i	$-0.341183\pi$
$673$	16708.2			0.956989			0.478495	+	0.878090i	$0.341183\pi$
$674$		−	17541.9i		−	1.00250i
$675$	34768.0			1.98255
$676$	5544.80	−	6817.93i	0.315476	−	0.387911i
$677$	−15842.6			−0.899378			−0.449689	−	0.893185i	$-0.648465\pi$
$677$	−15842.6			−0.899378			−0.449689	+	0.893185i	$0.648465\pi$
$678$			27106.7i			1.53543i
$679$	−7499.78			−0.423881
$680$	−4091.87			−0.230759
$681$		−	41595.4i		−	2.34059i
$682$			15465.9i			0.868356i
$683$			16467.3i			0.922550i	0.887257	+	0.461275i	$0.152608\pi$
$683$			16467.3i			0.922550i	−0.887257	+	0.461275i	$0.847392\pi$
$684$		−	5858.36i		−	0.327485i
$685$	−9232.45			−0.514969
$686$	12341.9			0.686904
$687$		−	5107.87i		−	0.283664i
$688$	−4698.18			−0.260344
$689$	1537.99	+	3233.19i	0.0850401	+	0.178773i
$690$	7372.71			0.406775
$691$			16531.0i			0.910086i	0.890470	+	0.455043i	$0.150376\pi$
$691$			16531.0i			0.910086i	−0.890470	+	0.455043i	$0.849624\pi$
$692$	−3936.96			−0.216273
$693$	19729.7			1.08149
$694$			8557.92i			0.468089i
$695$			11419.1i			0.623239i
$696$		−	20576.1i		−	1.12060i
$697$			2538.23i			0.137938i
$698$	12362.9			0.670406
$699$	6421.43			0.347469
$700$			6929.72i			0.374170i
$701$	11032.2			0.594409			0.297205	−	0.954814i	$-0.403946\pi$
$701$	11032.2			0.594409			0.297205	+	0.954814i	$0.403946\pi$
$702$	18459.6	−	8781.00i	0.992470	−	0.472105i
$703$	−3369.72			−0.180785
$704$			2252.34i			0.120580i
$705$	24851.9			1.32762
$706$	10943.2			0.583362
$707$		−	15159.6i		−	0.806414i
$708$			6549.48i			0.347662i
$709$			20979.1i			1.11127i	0.831427	+	0.555633i	$0.187524\pi$
$709$			20979.1i			1.11127i	−0.831427	+	0.555633i	$0.812476\pi$
$710$		−	12444.9i		−	0.657814i
$711$	9496.01			0.500883
$712$	10939.5			0.575806
$713$		−	5417.38i		−	0.284548i
$714$	5842.69			0.306243
$715$	11950.7	+	25123.0i	0.625078	+	1.31405i
$716$	−15109.3			−0.788631
$717$			27818.1i			1.44893i
$718$	12797.5			0.665181
$719$	17699.8			0.918068			0.459034	−	0.888419i	$-0.348196\pi$
$719$	17699.8			0.918068			0.459034	+	0.888419i	$0.348196\pi$
$720$		−	13923.1i		−	0.720674i
$721$			15388.5i			0.794865i
$722$		−	12106.5i		−	0.624042i
$723$			15636.4i			0.804319i
$724$	9319.19			0.478377
$725$	−46257.2			−2.36959
$726$			1639.57i			0.0838158i
$727$	−33899.2			−1.72937			−0.864686	−	0.502313i	$-0.832482\pi$
$727$	−33899.2			−1.72937			−0.864686	+	0.502313i	$0.832482\pi$
$728$	1750.17	+	3679.24i	0.0891010	+	0.187310i
$729$	−24329.6			−1.23607
$730$		−	28444.4i		−	1.44216i
$731$	8905.20			0.450576
$732$	7014.75			0.354197
$733$		−	29937.3i		−	1.50854i	−0.656564	−	0.754270i	$-0.727991\pi$
$733$		−	29937.3i		−	1.50854i	0.656564	−	0.754270i	$-0.272009\pi$
$734$		−	19272.4i		−	0.969151i
$735$			33633.3i			1.68787i
$736$		−	788.947i		−	0.0395122i
$737$	−11306.5			−0.565101
$738$	−8636.69			−0.430787
$739$		−	16595.2i		−	0.826068i	−0.910716	−	0.413034i	$-0.864469\pi$
$739$		−	16595.2i		−	0.826068i	0.910716	−	0.413034i	$-0.135531\pi$
$740$	−8008.59			−0.397840
$741$	−10651.7	+	5066.87i	−0.528070	+	0.251196i
$742$	−1659.93			−0.0821265
$743$			4929.07i			0.243378i	0.992568	+	0.121689i	$0.0388311\pi$
$743$			4929.07i			0.243378i	−0.992568	+	0.121689i	$0.961169\pi$
$744$	−15584.1			−0.767932
$745$	4795.42			0.235826
$746$		−	17615.8i		−	0.864556i
$747$		−	65742.1i		−	3.22005i
$748$		−	4269.21i		−	0.208687i
$749$			4901.07i			0.239094i
$750$	−10300.1			−0.501473
$751$	10687.7			0.519305			0.259653	−	0.965702i	$-0.416392\pi$
$751$	10687.7			0.519305			0.259653	+	0.965702i	$0.416392\pi$
$752$		−	2659.37i		−	0.128959i
$753$	−14592.6			−0.706221
$754$	−24559.7	+	11682.7i	−1.18622	+	0.564270i
$755$	45683.2			2.20210
$756$			9477.21i			0.455930i
$757$	28909.2			1.38801			0.694004	−	0.719971i	$-0.255845\pi$
$757$	28909.2			1.38801			0.694004	+	0.719971i	$0.255845\pi$
$758$	17357.9			0.831751
$759$			7692.23i			0.367866i
$760$			3829.88i			0.182795i
$761$		−	25399.7i		−	1.20991i	−0.796261	−	0.604954i	$-0.793192\pi$
$761$		−	25399.7i		−	1.20991i	0.796261	−	0.604954i	$-0.206808\pi$
$762$			25668.5i			1.22030i
$763$	−15060.9			−0.714604
$764$	18447.7			0.873579
$765$			26390.7i			1.24727i
$766$	5424.61			0.255873
$767$	7817.46	−	3718.66i	0.368021	−	0.175063i
$768$	−2269.56			−0.106635
$769$		−	23740.3i		−	1.11326i	−0.830761	−	0.556630i	$-0.812094\pi$
$769$		−	23740.3i		−	1.11326i	0.830761	−	0.556630i	$-0.187906\pi$
$770$	−12898.2			−0.603662
$771$	−56878.4			−2.65684
$772$		−	3811.20i		−	0.177679i
$773$		−	37.2842i		−	0.00173483i	−1.00000		0.000867413i	$-0.999724\pi$
$773$		−	37.2842i		−	0.00173483i	1.00000		0.000867413i	$-0.000276106\pi$
$774$			30301.2i			1.40717i
$775$			35034.7i			1.62385i
$776$	−5521.93			−0.255445
$777$	11435.3			0.527978
$778$		−	581.883i		−	0.0268143i
$779$	2375.72			0.109267
$780$	−25315.1	+	12042.1i	−1.16209	+	0.552789i
$781$	12984.2			0.594893
$782$			1495.41i			0.0683835i
$783$	−63262.3			−2.88737
$784$	3599.07			0.163952
$785$			14905.3i			0.677697i
$786$			11203.8i			0.508429i
$787$		−	6972.34i		−	0.315803i	−0.987455	−	0.157902i	$-0.949527\pi$
$787$		−	6972.34i		−	0.315803i	0.987455	−	0.157902i	$-0.0504729\pi$
$788$			8202.16i			0.370799i
$789$	32451.9			1.46428
$790$	−6207.97			−0.279582
$791$			16610.9i			0.746669i
$792$	14526.6			0.651741
$793$	−3982.84	−	8372.81i	−0.178354	−	0.374940i
$794$	28228.0			1.26168
$795$		−	11421.2i		−	0.509518i
$796$	−10341.2			−0.460472
$797$	−13689.7			−0.608425			−0.304212	−	0.952604i	$-0.598393\pi$
$797$	−13689.7			−0.608425			−0.304212	+	0.952604i	$0.598393\pi$
$798$		−	5468.60i		−	0.242589i
$799$			5040.73i			0.223189i
$800$			5102.20i			0.225487i
$801$		−	70554.6i		−	3.11227i
$802$	−22684.0			−0.998754
$803$	29677.1			1.30421
$804$		−	11392.9i		−	0.499748i
$805$	4517.98			0.197811
$806$	8848.36	+	18601.2i	0.386688	+	0.812904i
$807$	50048.2			2.18312
$808$		−	11161.7i		−	0.485973i
$809$	−7098.88			−0.308509			−0.154254	−	0.988031i	$-0.549298\pi$
$809$	−7098.88			−0.308509			−0.154254	+	0.988031i	$0.549298\pi$
$810$	−18217.5			−0.790246
$811$			24631.2i			1.06649i	0.845962	+	0.533243i	$0.179027\pi$
$811$			24631.2i			1.06649i	−0.845962	+	0.533243i	$0.820973\pi$
$812$		−	12609.0i		−	0.544937i
$813$		−	59149.2i		−	2.55160i
$814$		−	8355.66i		−	0.359786i
$815$	−56343.8			−2.42164
$816$	4301.85			0.184552
$817$		−	8335.02i		−	0.356922i
$818$	−9373.87			−0.400672
$819$	23729.5	−	11287.8i	1.01242	−	0.481596i
$820$	5646.20			0.240456
$821$			2290.09i			0.0973506i	0.998815	+	0.0486753i	$0.0154999\pi$
$821$			2290.09i			0.0973506i	−0.998815	+	0.0486753i	$0.984500\pi$
$822$	9706.22			0.411853
$823$	−36484.9			−1.54530			−0.772651	−	0.634831i	$-0.781070\pi$
$823$	−36484.9			−1.54530			−0.772651	+	0.634831i	$0.781070\pi$
$824$			11330.2i			0.479013i
$825$		−	49746.4i		−	2.09933i
$826$			4013.50i			0.169065i
$827$		−	3929.01i		−	0.165206i	−0.996583	−	0.0826028i	$-0.973677\pi$
$827$		−	3929.01i		−	0.165206i	0.996583	−	0.0826028i	$-0.0263233\pi$
$828$	−5088.35			−0.213566
$829$	−17401.7			−0.729055			−0.364527	−	0.931193i	$-0.618769\pi$
$829$	−17401.7			−0.729055			−0.364527	+	0.931193i	$0.618769\pi$
$830$			42978.6i			1.79736i
$831$	−25757.6			−1.07524
$832$	1288.61	+	2708.95i	0.0536954	+	0.112880i
$833$	−6821.88			−0.283750
$834$		−	12005.1i		−	0.498443i
$835$	30636.4			1.26972
$836$	−3995.86			−0.165311
$837$			47914.1i			1.97868i
$838$		−	23779.3i		−	0.980243i
$839$			39966.0i			1.64455i	0.569089	+	0.822276i	$0.307296\pi$
$839$			39966.0i			1.64455i	−0.569089	+	0.822276i	$0.692704\pi$
$840$		−	12996.8i		−	0.533849i
$841$	59778.5			2.45105
$842$	9511.28			0.389288
$843$			71010.2i			2.90121i
$844$	7024.91			0.286501
$845$	28746.9	+	23378.9i	1.17032	+	0.951786i
$846$	−17151.8			−0.697033
$847$			1004.73i			0.0407589i
$848$	−1222.17			−0.0494923
$849$	32870.6			1.32876
$850$		−	9671.00i		−	0.390250i
$851$			2926.82i			0.117897i
$852$			13083.5i			0.526095i
$853$		−	7753.33i		−	0.311218i	−0.987819	−	0.155609i	$-0.950266\pi$
$853$		−	7753.33i		−	0.311218i	0.987819	−	0.155609i	$-0.0497340\pi$
$854$	4298.62			0.172243
$855$	24701.0			0.988019
$856$			3608.55i			0.144086i
$857$	34346.7			1.36903			0.684515	−	0.728998i	$-0.260014\pi$
$857$	34346.7			1.36903			0.684515	+	0.728998i	$0.260014\pi$
$858$	−12564.0	−	26412.2i	−0.499914	−	1.05093i
$859$	−23048.5			−0.915489			−0.457744	−	0.889084i	$-0.651342\pi$
$859$	−23048.5			−0.915489			−0.457744	+	0.889084i	$0.651342\pi$
$860$		−	19809.3i		−	0.785454i
$861$	−8062.09			−0.319112
$862$	8756.26			0.345985
$863$		−	8452.37i		−	0.333398i	−0.986008	−	0.166699i	$-0.946689\pi$
$863$		−	8452.37i		−	0.333398i	0.986008	−	0.166699i	$-0.0533107\pi$
$864$			6977.86i			0.274759i
$865$		−	16599.7i		−	0.652492i
$866$			31152.7i			1.22241i
$867$	35402.0			1.38675
$868$	−9549.91			−0.373439
$869$		−	6477.02i		−	0.252840i
$870$	86756.5			3.38083
$871$	−13598.6	+	6468.68i	−0.529014	+	0.251645i
$872$	−11089.0			−0.430645
$873$			35613.9i			1.38070i
$874$	1399.67			0.0541699
$875$	−6311.85			−0.243862
$876$			29904.0i			1.15338i
$877$		−	3371.07i		−	0.129798i	−0.997892	−	0.0648990i	$-0.979327\pi$
$877$		−	3371.07i		−	0.129798i	0.997892	−	0.0648990i	$-0.0206725\pi$
$878$		−	26949.5i		−	1.03588i
$879$		−	14840.8i		−	0.569473i
$880$	−9496.67			−0.363787
$881$	−9930.37			−0.379753			−0.189877	−	0.981808i	$-0.560809\pi$
$881$	−9930.37			−0.379753			−0.189877	+	0.981808i	$0.560809\pi$
$882$		−	23212.4i		−	0.886169i
$883$	−38422.6			−1.46435			−0.732176	−	0.681116i	$-0.761495\pi$
$883$	−38422.6			−1.46435			−0.732176	+	0.681116i	$0.761495\pi$
$884$	−2442.50	−	5134.69i	−0.0929302	−	0.195360i
$885$	−27615.0			−1.04889
$886$			48.9129i			0.00185470i
$887$	−26078.1			−0.987168			−0.493584	−	0.869698i	$-0.664314\pi$
$887$	−26078.1			−0.987168			−0.493584	+	0.869698i	$0.664314\pi$
$888$	8419.55			0.318177
$889$			15729.6i			0.593422i
$890$			46124.8i			1.73720i
$891$		−	19007.1i		−	0.714658i
$892$			8152.49i			0.306015i
$893$	4717.98			0.176799
$894$	−5041.50			−0.188605
$895$		−	63706.2i		−	2.37929i
$896$	−1390.78			−0.0518556
$897$	4400.89	+	9251.66i	0.163814	+	0.344375i
$898$	−27273.4			−1.01350
$899$		−	63747.6i		−	2.36496i
$900$	32906.9			1.21877
$901$	2316.57			0.0856560
$902$			5890.90i			0.217456i
$903$			28285.2i			1.04238i
$904$			12230.2i			0.449968i
$905$			39293.1i			1.44326i
$906$	−48027.5			−1.76115
$907$	−8988.90			−0.329076			−0.164538	−	0.986371i	$-0.552613\pi$
$907$	−8988.90			−0.329076			−0.164538	+	0.986371i	$0.552613\pi$
$908$		−	18767.4i		−	0.685923i
$909$	−71987.7			−2.62671
$910$	−15513.0	+	7379.35i	−0.565112	+	0.268817i
$911$	28318.0			1.02988			0.514938	−	0.857227i	$-0.327815\pi$
$911$	28318.0			1.02988			0.514938	+	0.857227i	$0.327815\pi$
$912$		−	4026.41i		−	0.146193i
$913$	−44841.2			−1.62544
$914$	−26761.1			−0.968465
$915$			29576.7i			1.06861i
$916$		−	2304.62i		−	0.0831296i
$917$			6865.64i			0.247245i
$918$		−	13226.2i		−	0.475524i
$919$	−12863.6			−0.461730			−0.230865	−	0.972986i	$-0.574155\pi$
$919$	−12863.6			−0.461730			−0.230865	+	0.972986i	$0.574155\pi$
$920$	3326.49			0.119208
$921$			2659.07i			0.0951348i
$922$	13565.1			0.484537
$923$	15616.5	−	7428.55i	0.556904	−	0.264912i
$924$	13560.1			0.482786
$925$		−	18928.0i		−	0.672810i
$926$	−21932.3			−0.778337
$927$	73074.8			2.58909
$928$		−	9283.73i		−	0.328398i
$929$			1899.49i			0.0670833i	0.999437	+	0.0335416i	$0.0106786\pi$
$929$			1899.49i			0.0670833i	−0.999437	+	0.0335416i	$0.989321\pi$
$930$		−	65708.4i		−	2.31684i
$931$			6385.09i			0.224772i
$932$	2897.28			0.101828
$933$	−7891.50			−0.276909
$934$		−	1219.28i		−	0.0427153i
$935$	18000.5			0.629605
$936$	17471.5	−	8310.96i	0.610121	−	0.290227i
$937$	−35209.9			−1.22760			−0.613798	−	0.789463i	$-0.710359\pi$
$937$	−35209.9			−1.22760			−0.613798	+	0.789463i	$0.710359\pi$
$938$		−	6981.56i		−	0.243023i
$939$	10232.5			0.355618
$940$	11212.9			0.389068
$941$		−	56666.1i		−	1.96308i	−0.191247	−	0.981542i	$-0.561253\pi$
$941$		−	56666.1i		−	1.96308i	0.191247	−	0.981542i	$-0.438747\pi$
$942$		−	15670.1i		−	0.541997i
$943$		−	2063.46i		−	0.0712572i
$944$			2955.05i			0.101884i
$945$	−39959.4			−1.37553
$946$	20667.8			0.710324
$947$		−	27336.3i		−	0.938026i	−0.883191	−	0.469013i	$-0.844610\pi$
$947$		−	27336.3i		−	0.938026i	0.883191	−	0.469013i	$-0.155390\pi$
$948$	6526.54			0.223599
$949$	35693.5	−	16978.9i	1.22093	−	0.580779i
$950$	−9051.79			−0.309136
$951$			24015.3i			0.818873i
$952$	2636.16			0.0897463
$953$	14435.1			0.490659			0.245329	−	0.969440i	$-0.421104\pi$
$953$	14435.1			0.490659			0.245329	+	0.969440i	$0.421104\pi$
$954$			7882.43i			0.267509i
$955$			77782.3i			2.63558i
$956$			12551.2i			0.424619i
$957$			90516.3i			3.05745i
$958$	16810.6			0.566936
$959$	5947.95			0.200281
$960$		−	9569.28i		−	0.321716i
$961$	−18490.7			−0.620680
$962$	−4780.46	−	10049.6i	−0.160216	−	0.336810i
$963$	23273.5			0.778793
$964$			7054.96i			0.235710i
$965$	16069.4			0.536054
$966$	−4749.82			−0.158202
$967$		−	21556.9i		−	0.716879i	−0.933553	−	0.358440i	$-0.883309\pi$
$967$		−	21556.9i		−	0.716879i	0.933553	−	0.358440i	$-0.116691\pi$
$968$			739.757i			0.0245627i
$969$			7631.89i			0.253015i
$970$		−	23282.5i		−	0.770675i
$971$	−3153.54			−0.104225			−0.0521123	−	0.998641i	$-0.516595\pi$
$971$	−3153.54			−0.104225			−0.0521123	+	0.998641i	$0.516595\pi$
$972$	−4397.91			−0.145127
$973$		−	7356.68i		−	0.242389i
$974$	−32320.9			−1.06327
$975$	−28461.0	−	59831.4i	−0.934853	−	1.96527i
$976$	3164.98			0.103800
$977$			4929.61i			0.161425i	0.996737	+	0.0807125i	$0.0257196\pi$
$977$			4929.61i			0.161425i	−0.996737	+	0.0807125i	$0.974280\pi$
$978$	59235.1			1.93674
$979$	−48123.8			−1.57103
$980$			15175.0i			0.494640i
$981$			71519.3i			2.32766i
$982$			12853.9i			0.417704i
$983$		−	15526.2i		−	0.503774i	−0.967757	−	0.251887i	$-0.918949\pi$
$983$		−	15526.2i		−	0.503774i	0.967757	−	0.251887i	$-0.0810511\pi$
$984$	−5935.94			−0.192308
$985$	−34583.3			−1.11870
$986$			17596.9i			0.568356i
$987$	−16010.6			−0.516337
$988$	−4805.93	+	2286.12i	−0.154754	+	0.0736145i
$989$	−7239.49			−0.232763
$990$			61249.2i			1.96629i
$991$	29876.8			0.957687			0.478844	−	0.877900i	$-0.341056\pi$
$991$	29876.8			0.957687			0.478844	+	0.877900i	$0.341056\pi$
$992$	−7031.39			−0.225047
$993$			72582.6i			2.31958i
$994$			8017.53i			0.255836i
$995$		−	43602.4i		−	1.38924i
$996$		−	45184.1i		−	1.43746i
$997$	2600.46			0.0826052			0.0413026	−	0.999147i	$-0.486849\pi$
$997$	2600.46			0.0826052			0.0413026	+	0.999147i	$0.486849\pi$
$998$	30480.7			0.966782
$999$		−	25886.3i		−	0.819826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.4.b.a.25.1	✓	4
3.2	odd	2		234.4.b.b.181.4		4
4.3	odd	2		208.4.f.d.129.3		4
5.2	odd	4		650.4.c.f.649.4		4
5.3	odd	4		650.4.c.e.649.1		4
5.4	even	2		650.4.d.d.51.4		4
8.3	odd	2		832.4.f.h.129.2		4
8.5	even	2		832.4.f.j.129.4		4
13.2	odd	12		338.4.c.i.191.2		4
13.3	even	3		338.4.e.g.147.4		8
13.4	even	6		338.4.e.g.23.4		8
13.5	odd	4		338.4.a.f.1.1		2
13.6	odd	12		338.4.c.i.315.2		4
13.7	odd	12		338.4.c.h.315.2		4
13.8	odd	4		338.4.a.i.1.1		2
13.9	even	3		338.4.e.g.23.2		8
13.10	even	6		338.4.e.g.147.2		8
13.11	odd	12		338.4.c.h.191.2		4
13.12	even	2	inner	26.4.b.a.25.3	yes	4
39.38	odd	2		234.4.b.b.181.1		4
52.51	odd	2		208.4.f.d.129.4		4
65.12	odd	4		650.4.c.e.649.4		4
65.38	odd	4		650.4.c.f.649.1		4
65.64	even	2		650.4.d.d.51.2		4
104.51	odd	2		832.4.f.h.129.1		4
104.77	even	2		832.4.f.j.129.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.b.a.25.1	✓	4	1.1	even	1	trivial
26.4.b.a.25.3	yes	4	13.12	even	2	inner
208.4.f.d.129.3		4	4.3	odd	2
208.4.f.d.129.4		4	52.51	odd	2
234.4.b.b.181.1		4	39.38	odd	2
234.4.b.b.181.4		4	3.2	odd	2
338.4.a.f.1.1		2	13.5	odd	4
338.4.a.i.1.1		2	13.8	odd	4
338.4.c.h.191.2		4	13.11	odd	12
338.4.c.h.315.2		4	13.7	odd	12
338.4.c.i.191.2		4	13.2	odd	12
338.4.c.i.315.2		4	13.6	odd	12
338.4.e.g.23.2		8	13.9	even	3
338.4.e.g.23.4		8	13.4	even	6
338.4.e.g.147.2		8	13.10	even	6
338.4.e.g.147.4		8	13.3	even	3
650.4.c.e.649.1		4	5.3	odd	4
650.4.c.e.649.4		4	65.12	odd	4
650.4.c.f.649.1		4	65.38	odd	4
650.4.c.f.649.4		4	5.2	odd	4
650.4.d.d.51.2		4	65.64	even	2
650.4.d.d.51.4		4	5.4	even	2
832.4.f.h.129.1		4	104.51	odd	2
832.4.f.h.129.2		4	8.3	odd	2
832.4.f.j.129.3		4	104.77	even	2
832.4.f.j.129.4		4	8.5	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	26.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} -8.86546 q^{3} -4.00000 q^{4} -16.8655i q^{5} +17.7309i q^{6} +10.8655i q^{7} +8.00000i q^{8} +51.5964 q^{9} -33.7309 q^{10} -35.1928i q^{11} +35.4618 q^{12} +(-20.1345 - 42.3273i) q^{13} +21.7309 q^{14} +149.520i q^{15} +16.0000 q^{16} -30.3273 q^{17} -103.193i q^{18} +28.3855i q^{19} +67.4618i q^{20} -96.3273i q^{21} -70.3855 q^{22} +24.6546 q^{23} -70.9237i q^{24} -159.444 q^{25} +(-84.6546 + 40.2691i) q^{26} -218.058 q^{27} -43.4618i q^{28} +290.116 q^{29} +299.040 q^{30} -219.731i q^{31} -32.0000i q^{32} +312.000i q^{33} +60.6546i q^{34} +183.251 q^{35} -206.386 q^{36} +118.713i q^{37} +56.7710 q^{38} +(178.502 + 375.251i) q^{39} +134.924 q^{40} -83.6947i q^{41} -192.655 q^{42} -293.636 q^{43} +140.771i q^{44} -870.197i q^{45} -49.3092i q^{46} -166.211i q^{47} -141.847 q^{48} +224.942 q^{49} +318.887i q^{50} +268.865 q^{51} +(80.5382 + 169.309i) q^{52} -76.3855 q^{53} +436.116i q^{54} -593.542 q^{55} -86.9237 q^{56} -251.651i q^{57} -580.233i q^{58} +184.691i q^{59} -598.080i q^{60} +197.811 q^{61} -439.462 q^{62} +560.618i q^{63} -64.0000 q^{64} +(-713.869 + 339.578i) q^{65} +624.000 q^{66} -321.273i q^{67} +121.309 q^{68} -218.574 q^{69} -366.502i q^{70} +368.946i q^{71} +412.771i q^{72} +843.273i q^{73} +237.426 q^{74} +1413.54 q^{75} -113.542i q^{76} +382.386 q^{77} +(750.502 - 357.004i) q^{78} +184.044 q^{79} -269.847i q^{80} +540.084 q^{81} -167.389 q^{82} -1274.16i q^{83} +385.309i q^{84} +511.484i q^{85} +587.273i q^{86} -2572.02 q^{87} +281.542 q^{88} -1367.43i q^{89} -1740.39 q^{90} +(459.906 - 218.771i) q^{91} -98.6184 q^{92} +1948.02i q^{93} -332.422 q^{94} +478.735 q^{95} +283.695i q^{96} +690.241i q^{97} -449.884i q^{98} -1815.82i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} - 16 q^{4} + 118 q^{9} - 76 q^{10} + 24 q^{12} - 110 q^{13} + 28 q^{14} + 64 q^{16} + 26 q^{17} + 72 q^{22} - 196 q^{23} - 78 q^{25} - 44 q^{26} - 666 q^{27} + 748 q^{29} + 548 q^{30} + 350 q^{35}+ \cdots + 324 q^{95}+O(q^{100}) \) 4 * q - 6 * q^3 - 16 * q^4 + 118 * q^9 - 76 * q^10 + 24 * q^12 - 110 * q^13 + 28 * q^14 + 64 * q^16 + 26 * q^17 + 72 * q^22 - 196 * q^23 - 78 * q^25 - 44 * q^26 - 666 * q^27 + 748 * q^29 + 548 * q^30 + 350 * q^35 - 472 * q^36 - 480 * q^38 - 52 * q^39 + 304 * q^40 - 476 * q^42 - 438 * q^43 - 96 * q^48 + 1106 * q^49 + 1046 * q^51 + 440 * q^52 + 48 * q^53 - 960 * q^55 - 112 * q^56 - 564 * q^61 - 1640 * q^62 - 256 * q^64 - 1294 * q^65 + 2496 * q^66 - 104 * q^68 - 1876 * q^69 - 52 * q^74 + 4240 * q^75 + 1176 * q^77 + 2236 * q^78 - 1444 * q^79 - 668 * q^81 + 1216 * q^82 - 4160 * q^87 - 288 * q^88 - 3544 * q^90 + 1162 * q^91 + 784 * q^92 - 1860 * q^94 + 324 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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