LMFDB - Embedded newform 209.4.d.b.208.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [209,4,Mod(208,209)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("209.208"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(209, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	209.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$12.3313991912$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			208.1
Character	$\chi$	$=$	209.208
Dual form			209.4.d.b.208.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.32196 q^{2} -6.45839i q^{3} +20.3232 q^{4} +7.08774 q^{5} +34.3713i q^{6} -10.5649i q^{7} -65.5837 q^{8} -14.7108 q^{9} -37.7207 q^{10} +(-33.6008 + 14.2122i) q^{11} -131.255i q^{12} +7.25119 q^{13} +56.2258i q^{14} -45.7754i q^{15} +186.448 q^{16} -134.173i q^{17} +78.2903 q^{18} +(72.6966 + 39.6762i) q^{19} +144.046 q^{20} -68.2320 q^{21} +(178.822 - 75.6368i) q^{22} -12.6377 q^{23} +423.565i q^{24} -74.7639 q^{25} -38.5905 q^{26} -79.3683i q^{27} -214.712i q^{28} -52.6291 q^{29} +243.615i q^{30} -83.1766i q^{31} -467.598 q^{32} +(91.7880 + 217.007i) q^{33} +714.063i q^{34} -74.8810i q^{35} -298.971 q^{36} -147.631i q^{37} +(-386.888 - 211.155i) q^{38} -46.8310i q^{39} -464.840 q^{40} -368.977 q^{41} +363.128 q^{42} -99.9229i q^{43} +(-682.877 + 288.838i) q^{44} -104.267 q^{45} +67.2571 q^{46} -426.641 q^{47} -1204.15i q^{48} +231.384 q^{49} +397.890 q^{50} -866.542 q^{51} +147.368 q^{52} +419.044i q^{53} +422.395i q^{54} +(-238.154 + 100.733i) q^{55} +692.883i q^{56} +(256.245 - 469.503i) q^{57} +280.090 q^{58} -82.1826i q^{59} -930.304i q^{60} -481.522i q^{61} +442.663i q^{62} +155.418i q^{63} +996.953 q^{64} +51.3946 q^{65} +(-488.492 - 1154.90i) q^{66} +747.489i q^{67} -2726.83i q^{68} +81.6190i q^{69} +398.514i q^{70} +800.169i q^{71} +964.790 q^{72} +413.710i q^{73} +785.683i q^{74} +482.854i q^{75} +(1477.43 + 806.349i) q^{76} +(150.150 + 354.988i) q^{77} +249.233i q^{78} -384.925 q^{79} +1321.49 q^{80} -909.784 q^{81} +1963.68 q^{82} +590.529i q^{83} -1386.70 q^{84} -950.984i q^{85} +531.785i q^{86} +339.900i q^{87} +(2203.66 - 932.089i) q^{88} -1225.16i q^{89} +554.902 q^{90} -76.6078i q^{91} -256.838 q^{92} -537.187 q^{93} +2270.57 q^{94} +(515.255 + 281.215i) q^{95} +3019.93i q^{96} -169.865i q^{97} -1231.41 q^{98} +(494.295 - 209.073i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 236 q^{4} + 16 q^{5} - 484 q^{9} + 74 q^{11} + 668 q^{16} - 264 q^{20} - 296 q^{23} + 1040 q^{25} - 672 q^{26} - 428 q^{36} + 700 q^{38} - 2472 q^{42} - 668 q^{44} + 248 q^{45} - 2284 q^{47} - 2880 q^{49}+ \cdots - 414 q^{99}+O(q^{100}) $ 56 * q + 236 * q^4 + 16 * q^5 - 484 * q^9 + 74 * q^11 + 668 * q^16 - 264 * q^20 - 296 * q^23 + 1040 * q^25 - 672 * q^26 - 428 * q^36 + 700 * q^38 - 2472 * q^42 - 668 * q^44 + 248 * q^45 - 2284 * q^47 - 2880 * q^49 - 614 * q^55 + 2112 * q^58 + 1460 * q^64 + 4964 * q^66 + 2154 * q^77 - 5680 * q^80 - 456 * q^81 + 7840 * q^82 + 10312 * q^92 - 728 * q^93 - 414 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−5.32196			−1.88160			−0.940798	−	0.338968i	$-0.889922\pi$
$2$	−5.32196			−1.88160			−0.940798	+	0.338968i	$0.889922\pi$
$3$		−	6.45839i		−	1.24292i	−0.783447	−	0.621459i	$-0.786540\pi$
$3$		−	6.45839i		−	1.24292i	0.783447	−	0.621459i	$-0.213460\pi$
$4$	20.3232			2.54040
$5$	7.08774			0.633947			0.316974	−	0.948434i	$-0.397333\pi$
$5$	7.08774			0.633947			0.316974	+	0.948434i	$0.397333\pi$
$6$			34.3713i			2.33867i
$7$		−	10.5649i		−	0.570449i	−0.958461	−	0.285225i	$-0.907932\pi$
$7$		−	10.5649i		−	0.570449i	0.958461	−	0.285225i	$-0.0920682\pi$
$8$	−65.5837			−2.89842
$9$	−14.7108			−0.544845
$10$	−37.7207			−1.19283
$11$	−33.6008	+	14.2122i	−0.921002	+	0.389558i
$11$	−33.6008	+	14.2122i	−0.921002	+	0.389558i
$12$		−	131.255i		−	3.15751i
$13$	7.25119			0.154701			0.0773507	−	0.997004i	$-0.475354\pi$
$13$	7.25119			0.154701			0.0773507	+	0.997004i	$0.475354\pi$
$14$			56.2258i			1.07335i
$15$		−	45.7754i		−	0.787944i
$16$	186.448			2.91325
$17$		−	134.173i		−	1.91422i	−0.289726	−	0.957110i	$-0.593564\pi$
$17$		−	134.173i		−	1.91422i	0.289726	−	0.957110i	$-0.406436\pi$
$18$	78.2903			1.02518
$19$	72.6966	+	39.6762i	0.877776	+	0.479071i
$19$	72.6966	+	39.6762i	0.877776	+	0.479071i
$20$	144.046			1.61048
$21$	−68.2320			−0.709021
$22$	178.822	−	75.6368i	1.73295	−	0.732992i
$23$	−12.6377			−0.114571			−0.0572856	−	0.998358i	$-0.518245\pi$
$23$	−12.6377			−0.114571			−0.0572856	+	0.998358i	$0.518245\pi$
$24$			423.565i			3.60250i
$25$	−74.7639			−0.598111
$26$	−38.5905			−0.291086
$27$		−	79.3683i		−	0.565720i
$28$		−	214.712i		−	1.44917i
$29$	−52.6291			−0.336999			−0.168500	−	0.985702i	$-0.553892\pi$
$29$	−52.6291			−0.336999			−0.168500	+	0.985702i	$0.553892\pi$
$30$			243.615i			1.48259i
$31$		−	83.1766i		−	0.481902i	−0.970537	−	0.240951i	$-0.922541\pi$
$31$		−	83.1766i		−	0.481902i	0.970537	−	0.240951i	$-0.0774593\pi$
$32$	−467.598			−2.58314
$33$	91.7880	+	217.007i	0.484189	+	1.14473i
$34$			714.063i			3.60179i
$35$		−	74.8810i		−	0.361634i
$36$	−298.971			−1.38413
$37$		−	147.631i		−	0.655954i	−0.944686	−	0.327977i	$-0.893633\pi$
$37$		−	147.631i		−	0.655954i	0.944686	−	0.327977i	$-0.106367\pi$
$38$	−386.888	−	211.155i	−1.65162	−	0.901418i
$39$		−	46.8310i		−	0.192281i
$40$	−464.840			−1.83744
$41$	−368.977			−1.40548			−0.702738	−	0.711448i	$-0.748039\pi$
$41$	−368.977			−1.40548			−0.702738	+	0.711448i	$0.748039\pi$
$42$	363.128			1.33409
$43$		−	99.9229i		−	0.354374i	−0.984177	−	0.177187i	$-0.943300\pi$
$43$		−	99.9229i		−	0.354374i	0.984177	−	0.177187i	$-0.0566998\pi$
$44$	−682.877	+	288.838i	−2.33972	+	0.989636i
$45$	−104.267			−0.345403
$46$	67.2571			0.215577
$47$	−426.641			−1.32409			−0.662043	−	0.749466i	$-0.730310\pi$
$47$	−426.641			−1.32409			−0.662043	+	0.749466i	$0.730310\pi$
$48$		−	1204.15i		−	3.62093i
$49$	231.384			0.674588
$50$	397.890			1.12540
$51$	−866.542			−2.37922
$52$	147.368			0.393004
$53$			419.044i			1.08604i	0.839719	+	0.543021i	$0.182719\pi$
$53$			419.044i			1.08604i	−0.839719	+	0.543021i	$0.817281\pi$
$54$			422.395i			1.06446i
$55$	−238.154	+	100.733i	−0.583866	+	0.246959i
$56$			692.883i			1.65340i
$57$	256.245	−	469.503i	0.595446	−	1.09100i
$58$	280.090			0.634097
$59$		−	82.1826i		−	0.181343i	−0.995881	−	0.0906717i	$-0.971099\pi$
$59$		−	82.1826i		−	0.181343i	0.995881	−	0.0906717i	$-0.0289014\pi$
$60$		−	930.304i		−	2.00170i
$61$		−	481.522i		−	1.01070i	−0.862915	−	0.505349i	$-0.831364\pi$
$61$		−	481.522i		−	1.01070i	0.862915	−	0.505349i	$-0.168636\pi$
$62$			442.663i			0.906745i
$63$			155.418i			0.310806i
$64$	996.953			1.94717
$65$	51.3946			0.0980725
$66$	−488.492	−	1154.90i	−0.911048	−	2.15392i
$67$			747.489i			1.36299i	0.731823	+	0.681495i	$0.238670\pi$
$67$			747.489i			1.36299i	−0.731823	+	0.681495i	$0.761330\pi$
$68$		−	2726.83i		−	4.86289i
$69$			81.6190i			0.142403i
$70$			398.514i			0.680450i
$71$			800.169i			1.33750i	0.743487	+	0.668751i	$0.233171\pi$
$71$			800.169i			1.33750i	−0.743487	+	0.668751i	$0.766829\pi$
$72$	964.790			1.57919
$73$			413.710i			0.663302i	0.943402	+	0.331651i	$0.107606\pi$
$73$			413.710i			0.663302i	−0.943402	+	0.331651i	$0.892394\pi$
$74$			785.683i			1.23424i
$75$			482.854i			0.743403i
$76$	1477.43	+	806.349i	2.22991	+	1.21703i
$77$	150.150	+	354.988i	0.222223	+	0.525385i
$78$			249.233i			0.361795i
$79$	−384.925			−0.548196			−0.274098	−	0.961702i	$-0.588379\pi$
$79$	−384.925			−0.548196			−0.274098	+	0.961702i	$0.588379\pi$
$80$	1321.49			1.84684
$81$	−909.784			−1.24799
$82$	1963.68			2.64454
$83$			590.529i			0.780952i	0.920613	+	0.390476i	$0.127689\pi$
$83$			590.529i			0.780952i	−0.920613	+	0.390476i	$0.872311\pi$
$84$	−1386.70			−1.80120
$85$		−	950.984i		−	1.21351i
$86$			531.785i			0.666789i
$87$			339.900i			0.418863i
$88$	2203.66	−	932.089i	2.66945	−	1.12910i
$89$		−	1225.16i		−	1.45918i	−0.683887	−	0.729588i	$-0.739712\pi$
$89$		−	1225.16i		−	1.45918i	0.683887	−	0.729588i	$-0.260288\pi$
$90$	554.902			0.649909
$91$		−	76.6078i		−	0.0882493i
$92$	−256.838			−0.291057
$93$	−537.187			−0.598965
$94$	2270.57			2.49140
$95$	515.255	+	281.215i	0.556464	+	0.303706i
$96$			3019.93i			3.21063i
$97$		−	169.865i		−	0.177806i	−0.996040	−	0.0889028i	$-0.971664\pi$
$97$		−	169.865i		−	0.177806i	0.996040	−	0.0889028i	$-0.0283361\pi$
$98$	−1231.41			−1.26930
$99$	494.295	−	209.073i	0.501803	−	0.212249i
$100$	−1519.44			−1.51944
$101$			700.136i			0.689764i	0.938646	+	0.344882i	$0.112081\pi$
$101$			700.136i			0.689764i	−0.938646	+	0.344882i	$0.887919\pi$
$102$	4611.70			4.47673
$103$		−	1520.22i		−	1.45429i	−0.686486	−	0.727143i	$-0.740848\pi$
$103$		−	1520.22i		−	1.45429i	0.686486	−	0.727143i	$-0.259152\pi$
$104$	−475.560			−0.448389
$105$	−483.611			−0.449482
$106$		−	2230.14i		−	2.04349i
$107$	−1677.53			−1.51563			−0.757815	−	0.652469i	$-0.773733\pi$
$107$	−1677.53			−1.51563			−0.757815	+	0.652469i	$0.773733\pi$
$108$		−	1613.02i		−	1.43716i
$109$	−113.616			−0.0998385			−0.0499192	−	0.998753i	$-0.515896\pi$
$109$	−113.616			−0.0998385			−0.0499192	+	0.998753i	$0.515896\pi$
$110$	1267.44	−	536.094i	1.09860	−	0.464678i
$111$	−953.456			−0.815297
$112$		−	1969.80i		−	1.66186i
$113$		−	1836.81i		−	1.52913i	−0.644544	−	0.764567i	$-0.722953\pi$
$113$		−	1836.81i		−	1.52913i	0.644544	−	0.764567i	$-0.277047\pi$
$114$	−1363.72	+	2498.68i	−1.12039	+	2.05283i
$115$	−89.5726			−0.0726320
$116$	−1069.59			−0.856115
$117$	−106.671			−0.0842883
$118$			437.372i			0.341215i
$119$	−1417.52			−1.09196
$120$			3002.12i			2.28379i
$121$	927.026	−	955.083i	0.696488	−	0.717568i
$122$			2562.64i			1.90173i
$123$			2383.00i			1.74689i
$124$		−	1690.42i		−	1.22423i
$125$	−1415.88			−1.01312
$126$		−	827.127i		−	0.584812i
$127$	1074.78			0.750958			0.375479	−	0.926831i	$-0.377478\pi$
$127$	1074.78			0.750958			0.375479	+	0.926831i	$0.377478\pi$
$128$	−1564.96			−1.08066
$129$	−645.341			−0.440458
$130$	−273.520			−0.184533
$131$		−	247.392i		−	0.164998i	−0.996591	−	0.0824989i	$-0.973710\pi$
$131$		−	247.392i		−	0.164998i	0.996591	−	0.0824989i	$-0.0262901\pi$
$132$	1865.43	+	4410.28i	1.23004	+	2.90808i
$133$	419.174	−	768.030i	0.273286	−	0.500727i
$134$		−	3978.10i		−	2.56460i
$135$		−	562.542i		−	0.358637i
$136$			8799.56i			5.54821i
$137$	1217.39			0.759190			0.379595	−	0.925153i	$-0.376063\pi$
$137$	1217.39			0.759190			0.379595	+	0.925153i	$0.376063\pi$
$138$		−	434.373i		−	0.267944i
$139$			2675.37i			1.63253i	0.577675	+	0.816267i	$0.303960\pi$
$139$			2675.37i			1.63253i	−0.577675	+	0.816267i	$0.696040\pi$
$140$		−	1521.82i		−	0.918698i
$141$			2755.42i			1.64573i
$142$		−	4258.47i		−	2.51664i
$143$	−243.646	+	103.055i	−0.142480	+	0.0602652i
$144$	−2742.80			−1.58727
$145$	−373.022			−0.213640
$146$		−	2201.75i		−	1.24807i
$147$		−	1494.37i		−	0.838457i
$148$		−	3000.33i		−	1.66639i
$149$		−	1696.77i		−	0.932918i	−0.884543	−	0.466459i	$-0.845530\pi$
$149$		−	1696.77i		−	0.932918i	0.884543	−	0.466459i	$-0.154470\pi$
$150$		−	2569.73i		−	1.39878i
$151$	−616.093			−0.332032			−0.166016	−	0.986123i	$-0.553090\pi$
$151$	−616.093			−0.332032			−0.166016	+	0.986123i	$0.553090\pi$
$152$	−4767.71	−	2602.11i	−2.54416	−	1.38855i
$153$			1973.79i			1.04295i
$154$	−799.092	−	1889.23i	−0.418134	−	0.988561i
$155$		−	589.535i		−	0.305500i
$156$		−	951.758i		−	0.488472i
$157$	2248.89			1.14319			0.571595	−	0.820536i	$-0.306325\pi$
$157$	2248.89			1.14319			0.571595	+	0.820536i	$0.306325\pi$
$158$	2048.56			1.03148
$159$	2706.35			1.34986
$160$	−3314.21			−1.63757
$161$			133.515i			0.0653570i
$162$	4841.83			2.34821
$163$	−1519.14			−0.729990			−0.364995	−	0.931010i	$-0.618929\pi$
$163$	−1519.14			−0.729990			−0.364995	+	0.931010i	$0.618929\pi$
$164$	−7498.81			−3.57048
$165$	650.570	+	1538.09i	0.306950	+	0.725698i
$166$		−	3142.77i		−	1.46944i
$167$	3360.15			1.55698			0.778492	−	0.627655i	$-0.215985\pi$
$167$	3360.15			1.55698			0.778492	+	0.627655i	$0.215985\pi$
$168$	4474.91			2.05504
$169$	−2144.42			−0.976067
$170$			5061.09i			2.28334i
$171$	−1069.43	−	583.670i	−0.478252	−	0.261020i
$172$		−	2030.76i		−	0.900254i
$173$	1670.01			0.733922			0.366961	−	0.930236i	$-0.380398\pi$
$173$	1670.01			0.733922			0.366961	+	0.930236i	$0.380398\pi$
$174$		−	1808.93i		−	0.788130i
$175$			789.870i			0.341192i
$176$	−6264.79	+	2649.84i	−2.68311	+	1.13488i
$177$	−530.767			−0.225395
$178$			6520.25i			2.74558i
$179$		−	639.111i		−	0.266868i	−0.991058	−	0.133434i	$-0.957400\pi$
$179$		−	639.111i		−	0.266868i	0.991058	−	0.133434i	$-0.0426005\pi$
$180$	−2119.03			−0.877463
$181$			1150.34i			0.472399i	0.971705	+	0.236200i	$0.0759019\pi$
$181$			1150.34i			0.472399i	−0.971705	+	0.236200i	$0.924098\pi$
$182$			407.704i			0.166049i
$183$	−3109.86			−1.25622
$184$	828.825			0.332075
$185$		−	1046.37i		−	0.415840i
$186$	2858.89			1.12701
$187$	1906.89	+	4508.32i	0.745700	+	1.76300i
$188$	−8670.73			−3.36371
$189$	−838.516			−0.322715
$190$	−2742.16	−	1496.61i	−1.04704	−	0.571452i
$191$	1956.51			0.741195			0.370597	−	0.928794i	$-0.379153\pi$
$191$	1956.51			0.741195			0.370597	+	0.928794i	$0.379153\pi$
$192$		−	6438.71i		−	2.42018i
$193$	111.119			0.0414433			0.0207216	−	0.999785i	$-0.493404\pi$
$193$	111.119			0.0414433			0.0207216	+	0.999785i	$0.493404\pi$
$194$			904.013i			0.334558i
$195$		−	331.926i		−	0.121896i
$196$	4702.46			1.71373
$197$		−	2995.97i		−	1.08352i	−0.840533	−	0.541761i	$-0.817758\pi$
$197$		−	2995.97i		−	1.08352i	0.840533	−	0.541761i	$-0.182242\pi$
$198$	−2630.62	+	1112.68i	−0.944191	+	0.399367i
$199$	−2942.16			−1.04806			−0.524030	−	0.851700i	$-0.675572\pi$
$199$	−2942.16			−1.04806			−0.524030	+	0.851700i	$0.675572\pi$
$200$	4903.29			1.73358
$201$	4827.58			1.69408
$202$		−	3726.09i		−	1.29786i
$203$			556.020i			0.192241i
$204$	−17610.9			−6.04417
$205$	−2615.21			−0.890998
$206$			8090.53i			2.73638i
$207$	185.910			0.0624235
$208$	1351.97			0.450683
$209$	−3006.55	−	299.973i	−0.995060	−	0.0992803i
$210$	2573.76			0.845744
$211$	−3097.40			−1.01059			−0.505293	−	0.862948i	$-0.668616\pi$
$211$	−3097.40			−1.01059			−0.505293	+	0.862948i	$0.668616\pi$
$212$			8516.34i			2.75898i
$213$	5167.81			1.66240
$214$	8927.72			2.85180
$215$		−	708.228i		−	0.224655i
$216$			5205.27i			1.63969i
$217$	−878.750			−0.274901
$218$	604.657			0.187856
$219$	2671.90			0.824430
$220$	−4840.05	+	2047.21i	−1.48326	+	0.627377i
$221$		−	972.914i		−	0.296132i
$222$	5074.25			1.53406
$223$		−	4601.63i		−	1.38183i	−0.722936	−	0.690915i	$-0.757208\pi$
$223$		−	4601.63i		−	1.38183i	0.722936	−	0.690915i	$-0.242792\pi$
$224$			4940.11i			1.47355i
$225$	1099.84			0.325878
$226$			9775.41i			2.87721i
$227$	2732.13			0.798845			0.399423	−	0.916767i	$-0.369211\pi$
$227$	2732.13			0.798845			0.399423	+	0.916767i	$0.369211\pi$
$228$	5207.72	−	9541.82i	1.51267	−	2.77159i
$229$	6061.86			1.74925			0.874627	−	0.484796i	$-0.161106\pi$
$229$	6061.86			1.74925			0.874627	+	0.484796i	$0.161106\pi$
$230$	476.701			0.136664
$231$	2292.65	−	969.728i	0.653010	−	0.276205i
$232$	3451.61			0.976765
$233$		−	5926.91i		−	1.66646i	−0.552928	−	0.833229i	$-0.686489\pi$
$233$		−	5926.91i		−	1.66646i	0.552928	−	0.833229i	$-0.313511\pi$
$234$	567.698			0.158597
$235$	−3023.93			−0.839401
$236$		−	1670.22i		−	0.460685i
$237$			2486.00i			0.681362i
$238$	7543.98			2.05464
$239$			3635.19i			0.983852i	0.870637	+	0.491926i	$0.163707\pi$
$239$			3635.19i			0.983852i	−0.870637	+	0.491926i	$0.836293\pi$
$240$		−	8534.73i		−	2.29548i
$241$	4513.56			1.20641			0.603204	−	0.797587i	$-0.293891\pi$
$241$	4513.56			1.20641			0.603204	+	0.797587i	$0.293891\pi$
$242$	−4933.59	+	5082.91i	−1.31051	+	1.35017i
$243$			3732.80i			0.985428i
$244$		−	9786.09i		−	2.56758i
$245$	1639.99			0.427653
$246$		−	12682.2i		−	3.28695i
$247$	527.137	+	287.700i	0.135793	+	0.0741130i
$248$			5455.03i			1.39675i
$249$	3813.87			0.970659
$250$	7535.23			1.90628
$251$	1656.69			0.416610			0.208305	−	0.978064i	$-0.433205\pi$
$251$	1656.69			0.416610			0.208305	+	0.978064i	$0.433205\pi$
$252$			3158.59i			0.789574i
$253$	424.636	−	179.609i	0.105520	−	0.0446322i
$254$	−5719.95			−1.41300
$255$	−6141.82			−1.50830
$256$	353.017			0.0861859
$257$		−	3291.80i		−	0.798977i	−0.916738	−	0.399488i	$-0.869188\pi$
$257$		−	3291.80i		−	0.798977i	0.916738	−	0.399488i	$-0.130812\pi$
$258$	3434.48			0.828765
$259$	−1559.70			−0.374189
$260$	1044.50			0.249144
$261$	774.218			0.183613
$262$			1316.61i			0.310459i
$263$			5107.76i			1.19756i	0.800914	+	0.598779i	$0.204347\pi$
$263$			5107.76i			1.19756i	−0.800914	+	0.598779i	$0.795653\pi$
$264$	−6019.80	−	14232.1i	−1.40338	−	3.31790i
$265$			2970.08i			0.688493i
$266$	−2230.83	+	4087.42i	−0.514213	+	0.942165i
$267$	−7912.56			−1.81364
$268$			15191.4i			3.46254i
$269$		−	7733.96i		−	1.75297i	−0.481433	−	0.876483i	$-0.659884\pi$
$269$		−	7733.96i		−	1.75297i	0.481433	−	0.876483i	$-0.340116\pi$
$270$			2993.83i			0.674809i
$271$		−	5766.99i		−	1.29269i	−0.763044	−	0.646347i	$-0.776296\pi$
$271$		−	5766.99i		−	1.29269i	0.763044	−	0.646347i	$-0.223704\pi$
$272$		−	25016.3i		−	5.57659i
$273$	−494.763			−0.109687
$274$	−6478.92			−1.42849
$275$	2512.13	−	1062.56i	0.550861	−	0.232999i
$276$			1658.76i			0.361760i
$277$		−	3188.68i		−	0.691657i	−0.938298	−	0.345829i	$-0.887598\pi$
$277$		−	3188.68i		−	0.691657i	0.938298	−	0.345829i	$-0.112402\pi$
$278$		−	14238.2i		−	3.07177i
$279$			1223.60i			0.262562i
$280$			4910.98i			1.04817i
$281$	472.238			0.100254			0.0501270	−	0.998743i	$-0.484037\pi$
$281$	472.238			0.100254			0.0501270	+	0.998743i	$0.484037\pi$
$282$		−	14664.2i		−	3.09660i
$283$		−	3934.48i		−	0.826434i	−0.910633	−	0.413217i	$-0.864405\pi$
$283$		−	3934.48i		−	0.826434i	0.910633	−	0.413217i	$-0.135595\pi$
$284$			16262.0i			3.39779i
$285$	1816.20	−	3327.72i	0.377481	−	0.691639i
$286$	1296.67	−	548.457i	0.268090	−	0.113395i
$287$			3898.19i			0.801753i
$288$	6878.75			1.40741
$289$	−13089.4			−2.66423
$290$	1985.21			0.401984
$291$	−1097.05			−0.220998
$292$			8407.92i			1.68506i
$293$	2974.58			0.593094			0.296547	−	0.955018i	$-0.404165\pi$
$293$	2974.58			0.593094			0.296547	+	0.955018i	$0.404165\pi$
$294$			7952.95i			1.57764i
$295$		−	582.489i		−	0.114962i
$296$			9682.16i			1.90123i
$297$	1128.00	+	2666.84i	0.220381	+	0.521029i
$298$			9030.13i			1.75537i
$299$	−91.6381			−0.0177243
$300$			9813.16i			1.88854i
$301$	−1055.67			−0.202153
$302$	3278.82			0.624751
$303$	4521.75			0.857319
$304$	13554.1	+	7397.55i	2.55718	+	1.39565i
$305$		−	3412.91i		−	0.640730i
$306$		−	10504.4i		−	1.96242i
$307$	−7163.74			−1.33178			−0.665890	−	0.746050i	$-0.731948\pi$
$307$	−7163.74			−1.33178			−0.665890	+	0.746050i	$0.731948\pi$
$308$	3051.53	+	7214.50i	0.564537	+	1.33469i
$309$	−9818.16			−1.80756
$310$			3137.48i			0.574828i
$311$	9382.39			1.71070			0.855348	−	0.518054i	$-0.173343\pi$
$311$	9382.39			1.71070			0.855348	+	0.518054i	$0.173343\pi$
$312$			3071.35i			0.557311i
$313$	468.917			0.0846798			0.0423399	−	0.999103i	$-0.486519\pi$
$313$	468.917			0.0846798			0.0423399	+	0.999103i	$0.486519\pi$
$314$	−11968.5			−2.15102
$315$			1101.56i			0.197035i
$316$	−7822.92			−1.39264
$317$			2593.50i			0.459513i	0.973248	+	0.229756i	$0.0737929\pi$
$317$			2593.50i			0.459513i	−0.973248	+	0.229756i	$0.926207\pi$
$318$	−14403.1			−2.53989
$319$	1768.38	−	747.976i	0.310377	−	0.131281i
$320$	7066.15			1.23440
$321$			10834.1i			1.88380i
$322$		−	710.563i		−	0.122975i
$323$	5323.48	−	9753.92i	0.917047	−	1.68026i
$324$	−18489.7			−3.17040
$325$	−542.127			−0.0925286
$326$	8084.81			1.37355
$327$			733.774i			0.124091i
$328$	24198.9			4.07366
$329$			4507.41i			0.755324i
$330$	−3462.31	−	8185.65i	−0.577556	−	1.36547i
$331$		−	7229.87i		−	1.20057i	−0.799785	−	0.600287i	$-0.795053\pi$
$331$		−	7229.87i		−	1.20057i	0.799785	−	0.600287i	$-0.204947\pi$
$332$			12001.5i			1.98393i
$333$			2171.77i			0.357394i
$334$	−17882.6			−2.92961
$335$			5298.01i			0.864063i
$336$	−12721.7			−2.06555
$337$	−2638.71			−0.426527			−0.213264	−	0.976995i	$-0.568409\pi$
$337$	−2638.71			−0.426527			−0.213264	+	0.976995i	$0.568409\pi$
$338$	11412.5			1.83656
$339$	−11862.8			−1.90059
$340$		−	19327.1i		−	3.08281i
$341$	1182.12	+	2794.80i	0.187729	+	0.443833i
$342$	5691.44	+	3106.27i	0.899877	+	0.491133i
$343$		−	6068.29i		−	0.955267i
$344$			6553.31i			1.02713i
$345$			578.495i			0.0902757i
$346$	−8887.72			−1.38094
$347$		−	7961.06i		−	1.23162i	−0.787895	−	0.615810i	$-0.788829\pi$
$347$		−	7961.06i		−	1.23162i	0.787895	−	0.615810i	$-0.211171\pi$
$348$			6907.86i			1.06408i
$349$		−	11950.3i		−	1.83290i	−0.400144	−	0.916452i	$-0.631040\pi$
$349$		−	11950.3i		−	1.83290i	0.400144	−	0.916452i	$-0.368960\pi$
$350$		−	4203.66i		−	0.641985i
$351$		−	575.515i		−	0.0875177i
$352$	15711.7	−	6645.60i	2.37907	−	1.00628i
$353$	−4101.23			−0.618375			−0.309187	−	0.951001i	$-0.600057\pi$
$353$	−4101.23			−0.618375			−0.309187	+	0.951001i	$0.600057\pi$
$354$	2824.72			0.424102
$355$			5671.39i			0.847905i
$356$		−	24899.2i		−	3.70690i
$357$			9154.89i			1.35722i
$358$			3401.32i			0.502138i
$359$			6629.41i			0.974616i	0.873230	+	0.487308i	$0.162021\pi$
$359$			6629.41i			0.974616i	−0.873230	+	0.487308i	$0.837979\pi$
$360$	6838.18			1.00112
$361$	3710.59	+	5768.65i	0.540982	+	0.841034i
$362$		−	6122.07i		−	0.888864i
$363$	−6168.30	−	5987.10i	−0.891878	−	0.865678i
$364$		−	1556.92i		−	0.224189i
$365$			2932.27i			0.420499i
$366$	16550.5			2.36369
$367$	−6578.26			−0.935646			−0.467823	−	0.883822i	$-0.654962\pi$
$367$	−6578.26			−0.935646			−0.467823	+	0.883822i	$0.654962\pi$
$368$	−2356.27			−0.333774
$369$	5427.95			0.765767
$370$			5568.72i			0.782444i
$371$	4427.15			0.619531
$372$	−10917.4			−1.52161
$373$	−787.959			−0.109381			−0.0546903	−	0.998503i	$-0.517417\pi$
$373$	−787.959			−0.109381			−0.0546903	+	0.998503i	$0.517417\pi$
$374$	−10148.4	−	23993.1i	−1.40311	−	3.31725i
$375$			9144.28i			1.25922i
$376$	27980.7			3.83775
$377$	−381.624			−0.0521343
$378$	4462.54			0.607218
$379$			7904.27i			1.07128i	0.844447	+	0.535640i	$0.179929\pi$
$379$			7904.27i			1.07128i	−0.844447	+	0.535640i	$0.820071\pi$
$380$	10471.6	+	5715.20i	1.41364	+	0.771535i
$381$		−	6941.38i		−	0.933379i
$382$	−10412.5			−1.39463
$383$			7868.63i			1.04979i	0.851168	+	0.524893i	$0.175895\pi$
$383$			7868.63i			1.04979i	−0.851168	+	0.524893i	$0.824105\pi$
$384$			10107.1i			1.34317i
$385$	1064.23	+	2516.06i	0.140878	+	0.333066i
$386$	−591.373			−0.0779795
$387$			1469.95i			0.193079i
$388$		−	3452.20i		−	0.451698i
$389$	11584.1			1.50986			0.754930	−	0.655806i	$-0.227671\pi$
$389$	11584.1			1.50986			0.754930	+	0.655806i	$0.227671\pi$
$390$			1766.50i			0.229359i
$391$			1695.63i			0.219314i
$392$	−15175.0			−1.95524
$393$	−1597.75			−0.205079
$394$			15944.4i			2.03875i
$395$	−2728.25			−0.347527
$396$	10045.7	−	4249.04i	1.27478	−	0.539198i
$397$	−389.561			−0.0492482			−0.0246241	−	0.999697i	$-0.507839\pi$
$397$	−389.561			−0.0492482			−0.0246241	+	0.999697i	$0.507839\pi$
$398$	15658.0			1.97202
$399$	−4960.24	−	2707.19i	−0.622362	−	0.339672i
$400$	−13939.6			−1.74245
$401$		−	6269.76i		−	0.780791i	−0.920647	−	0.390395i	$-0.872338\pi$
$401$		−	6269.76i		−	0.780791i	0.920647	−	0.390395i	$-0.127662\pi$
$402$	−25692.2			−3.18758
$403$		−	603.130i		−	0.0745509i
$404$			14229.0i			1.75228i
$405$	−6448.31			−0.791159
$406$		−	2959.11i		−	0.361720i
$407$	2098.16	+	4960.50i	0.255533	+	0.604135i
$408$	56831.0			6.89597
$409$	12366.2			1.49503			0.747517	−	0.664243i	$-0.231246\pi$
$409$	12366.2			1.49503			0.747517	+	0.664243i	$0.231246\pi$
$410$	13918.1			1.67650
$411$		−	7862.41i		−	0.943610i
$412$		−	30895.7i		−	3.69447i
$413$	−868.248			−0.103447
$414$	−989.408			−0.117456
$415$			4185.52i			0.495082i
$416$	−3390.64			−0.399615
$417$	17278.6			2.02911
$418$	16000.7	+	1596.44i	1.87230	+	0.186805i
$419$	14001.5			1.63250			0.816252	−	0.577696i	$-0.196048\pi$
$419$	14001.5			1.63250			0.816252	+	0.577696i	$0.196048\pi$
$420$	−9828.54			−1.14187
$421$			11154.9i			1.29135i	0.763612	+	0.645675i	$0.223424\pi$
$421$			11154.9i			1.29135i	−0.763612	+	0.645675i	$0.776576\pi$
$422$	16484.2			1.90151
$423$	6276.24			0.721422
$424$		−	27482.5i		−	3.14780i
$425$			10031.3i			1.14492i
$426$	−27502.8			−3.12797
$427$	−5087.22			−0.576552
$428$	−34092.7			−3.85031
$429$	665.572	+	1573.56i	0.0749047	+	0.177091i
$430$			3769.16i			0.422709i
$431$	−8806.34			−0.984191			−0.492096	−	0.870541i	$-0.663769\pi$
$431$	−8806.34			−0.984191			−0.492096	+	0.870541i	$0.663769\pi$
$432$		−	14798.1i		−	1.64808i
$433$			5358.11i			0.594675i	0.954772	+	0.297338i	$0.0960987\pi$
$433$			5358.11i			0.594675i	−0.954772	+	0.297338i	$0.903901\pi$
$434$	4676.67			0.517252
$435$			2409.12i			0.265537i
$436$	−2309.03			−0.253630
$437$	−918.716	−	501.415i	−0.100568	−	0.0548877i
$438$	−14219.7			−1.55125
$439$	11154.5			1.21270			0.606352	−	0.795197i	$-0.292632\pi$
$439$	11154.5			1.21270			0.606352	+	0.795197i	$0.292632\pi$
$440$	15619.0	−	6606.41i	1.69229	−	0.715792i
$441$	−3403.84			−0.367546
$442$			5177.81i			0.557202i
$443$	−7580.45			−0.812998			−0.406499	−	0.913651i	$-0.633251\pi$
$443$	−7580.45			−0.812998			−0.406499	+	0.913651i	$0.633251\pi$
$444$	−19377.3			−2.07118
$445$		−	8683.62i		−	0.925040i
$446$			24489.7i			2.60005i
$447$	−10958.4			−1.15954
$448$		−	10532.7i		−	1.11076i
$449$			10999.8i			1.15615i	0.815982	+	0.578077i	$0.196197\pi$
$449$			10999.8i			1.15615i	−0.815982	+	0.578077i	$0.803803\pi$
$450$	−5853.29			−0.613171
$451$	12397.9	−	5243.98i	1.29445	−	0.547515i
$452$		−	37329.8i		−	3.88462i
$453$			3978.97i			0.412689i
$454$	−14540.3			−1.50310
$455$		−	542.977i		−	0.0559454i
$456$	−16805.5	+	30791.8i	−1.72585	+	3.16218i
$457$		−	3371.63i		−	0.345117i	−0.984999	−	0.172558i	$-0.944797\pi$
$457$		−	3371.63i		−	0.345117i	0.984999	−	0.172558i	$-0.0552033\pi$
$458$	−32261.0			−3.29139
$459$	−10649.1			−1.08291
$460$	−1820.40			−0.184515
$461$		−	2070.32i		−	0.209164i	−0.994516	−	0.104582i	$-0.966650\pi$
$461$		−	2070.32i		−	0.209164i	0.994516	−	0.104582i	$-0.0333504\pi$
$462$	−12201.4	+	5160.85i	−1.22870	+	0.519707i
$463$	−16357.5			−1.64189			−0.820945	−	0.571007i	$-0.806553\pi$
$463$	−16357.5			−1.64189			−0.820945	+	0.571007i	$0.806553\pi$
$464$	−9812.59			−0.981763
$465$	−3807.45			−0.379712
$466$			31542.8i			3.13560i
$467$	7245.20			0.717919			0.358959	−	0.933353i	$-0.383132\pi$
$467$	7245.20			0.717919			0.358959	+	0.933353i	$0.383132\pi$
$468$	−2167.90			−0.214126
$469$	7897.12			0.777516
$470$	16093.2			1.57941
$471$		−	14524.2i		−	1.42089i
$472$			5389.84i			0.525609i
$473$	1420.13	+	3357.49i	0.138050	+	0.326379i
$474$		−	13230.4i		−	1.28205i
$475$	−5435.08	−	2966.35i	−0.525008	−	0.286538i
$476$	−28808.6			−2.77403
$477$		−	6164.49i		−	0.591724i
$478$		−	19346.3i		−	1.85121i
$479$		−	15693.2i		−	1.49696i	−0.663160	−	0.748478i	$-0.730785\pi$
$479$		−	15693.2i		−	1.49696i	0.663160	−	0.748478i	$-0.269215\pi$
$480$			21404.5i			2.03537i
$481$		−	1070.50i		−	0.101477i
$482$	−24021.0			−2.26997
$483$	862.294			0.0812334
$484$	18840.2	−	19410.4i	1.76936	−	1.82291i
$485$		−	1203.96i		−	0.112719i
$486$		−	19865.8i		−	1.85418i
$487$			5614.70i			0.522436i	0.965280	+	0.261218i	$0.0841242\pi$
$487$			5614.70i			0.522436i	−0.965280	+	0.261218i	$0.915876\pi$
$488$			31580.0i			2.92943i
$489$			9811.21i			0.907318i
$490$	−8727.95			−0.804670
$491$			14538.5i			1.33628i	0.744037	+	0.668139i	$0.232909\pi$
$491$			14538.5i			1.33628i	−0.744037	+	0.668139i	$0.767091\pi$
$492$			48430.2i			4.43781i
$493$			7061.41i			0.645091i
$494$	−2805.40	−	1531.13i	−0.255508	−	0.139451i
$495$	3503.44	−	1481.86i	0.318117	−	0.134555i
$496$		−	15508.1i		−	1.40390i
$497$	8453.68			0.762976
$498$	−20297.2			−1.82639
$499$	12231.5			1.09731			0.548656	−	0.836048i	$-0.315140\pi$
$499$	12231.5			1.09731			0.548656	+	0.836048i	$0.315140\pi$
$500$	−28775.2			−2.57373
$501$		−	21701.2i		−	1.93520i
$502$	−8816.81			−0.783891
$503$		−	6208.25i		−	0.550323i	−0.961398	−	0.275161i	$-0.911269\pi$
$503$		−	6208.25i		−	0.550323i	0.961398	−	0.275161i	$-0.0887313\pi$
$504$		−	10192.9i		−	0.900847i
$505$			4962.38i			0.437274i
$506$	−2259.89	+	955.873i	−0.198546	+	0.0839797i
$507$			13849.5i			1.21317i
$508$	21843.1			1.90774
$509$		−	19690.4i		−	1.71466i	−0.514771	−	0.857328i	$-0.672123\pi$
$509$		−	19690.4i		−	1.71466i	0.514771	−	0.857328i	$-0.327877\pi$
$510$	32686.5			2.83801
$511$	4370.79			0.378380
$512$	10640.9			0.918490
$513$	3149.04	−	5769.81i	0.271020	−	0.496576i
$514$			17518.8i			1.50335i
$515$		−	10774.9i		−	0.921940i
$516$	−13115.4			−1.11894
$517$	14335.5	−	6063.52i	1.21949	−	0.515809i
$518$	8300.64			0.704072
$519$		−	10785.6i		−	0.912205i
$520$	−3370.65			−0.284255
$521$			1929.89i			0.162284i	0.996703	+	0.0811422i	$0.0258568\pi$
$521$			1929.89i			0.162284i	−0.996703	+	0.0811422i	$0.974143\pi$
$522$	−4120.35			−0.345485
$523$	6363.47			0.532036			0.266018	−	0.963968i	$-0.414292\pi$
$523$	6363.47			0.532036			0.266018	+	0.963968i	$0.414292\pi$
$524$		−	5027.80i		−	0.419161i
$525$	5101.29			0.424074
$526$		−	27183.3i		−	2.25332i
$527$	−11160.1			−0.922466
$528$	17113.7	+	40460.5i	1.41056	+	3.33488i
$529$	−12007.3			−0.986873
$530$		−	15806.6i		−	1.29547i
$531$			1208.97i			0.0988041i
$532$	8518.97	−	15608.8i	0.694256	−	1.27205i
$533$	−2675.52			−0.217429
$534$	42110.3			3.41253
$535$	−11889.9			−0.960830
$536$		−	49023.1i		−	3.95051i
$537$	−4127.63			−0.331695
$538$			41159.8i			3.29837i
$539$	−7774.67	+	3288.47i	−0.621297	+	0.262791i
$540$		−	11432.7i		−	0.911082i
$541$			5120.71i			0.406944i	0.979081	+	0.203472i	$0.0652225\pi$
$541$			5120.71i			0.406944i	−0.979081	+	0.203472i	$0.934777\pi$
$542$			30691.7i			2.43233i
$543$	7429.36			0.587153
$544$			62739.0i			4.94469i
$545$	−805.278			−0.0632923
$546$	2633.11			0.206386
$547$	−12380.7			−0.967754			−0.483877	−	0.875136i	$-0.660772\pi$
$547$	−12380.7			−0.967754			−0.483877	+	0.875136i	$0.660772\pi$
$548$	24741.4			1.92865
$549$			7083.59i			0.550674i
$550$	−13369.4	+	5654.90i	−1.03650	+	0.438410i
$551$	−3825.96	−	2088.13i	−0.295810	−	0.161447i
$552$		−	5352.88i		−	0.412742i
$553$			4066.68i			0.312718i
$554$			16970.0i			1.30142i
$555$	−6757.85			−0.516855
$556$			54372.2i			4.14730i
$557$			5585.69i			0.424907i	0.977171	+	0.212454i	$0.0681454\pi$
$557$			5585.69i			0.424907i	−0.977171	+	0.212454i	$0.931855\pi$
$558$		−	6511.93i		−	0.494036i
$559$		−	724.560i		−	0.0548222i
$560$		−	13961.4i		−	1.05353i
$561$	29116.5	−	12315.5i	2.19126	−	0.926844i
$562$	−2513.23			−0.188637
$563$	−12385.5			−0.927150			−0.463575	−	0.886058i	$-0.653434\pi$
$563$	−12385.5			−0.927150			−0.463575	+	0.886058i	$0.653434\pi$
$564$			55999.0i			4.18082i
$565$		−	13018.8i		−	0.969390i
$566$			20939.2i			1.55501i
$567$			9611.74i			0.711914i
$568$		−	52478.1i		−	3.87664i
$569$	18212.1			1.34181			0.670906	−	0.741543i	$-0.265906\pi$
$569$	18212.1			1.34181			0.670906	+	0.741543i	$0.265906\pi$
$570$	−9665.72	+	17710.0i	−0.710267	+	1.30138i
$571$		−	7046.29i		−	0.516424i	−0.966088	−	0.258212i	$-0.916867\pi$
$571$		−	7046.29i		−	0.516424i	0.966088	−	0.258212i	$-0.0831333\pi$
$572$	−4951.67	+	2094.42i	−0.361957	+	0.153098i
$573$		−	12635.9i		−	0.921244i
$574$		−	20746.0i		−	1.50857i
$575$	944.841			0.0685263
$576$	−14666.0			−1.06091
$577$	17331.0			1.25043			0.625216	−	0.780452i	$-0.285011\pi$
$577$	17331.0			1.25043			0.625216	+	0.780452i	$0.285011\pi$
$578$	69661.2			5.01301
$579$		−	717.652i		−	0.0515106i
$580$	−7581.01			−0.542731
$581$	6238.86			0.445493
$582$	5838.47			0.415829
$583$	−5955.55	−	14080.2i	−0.423077	−	1.00025i
$584$		−	27132.6i		−	1.92253i
$585$	−756.056			−0.0534343
$586$	−15830.6			−1.11596
$587$	24401.8			1.71579			0.857896	−	0.513823i	$-0.171771\pi$
$587$	24401.8			1.71579			0.857896	+	0.513823i	$0.171771\pi$
$588$		−	30370.3i		−	2.13002i
$589$	3300.14	−	6046.66i	0.230865	−	0.423002i
$590$			3099.98i			0.216312i
$591$	−19349.1			−1.34673
$592$		−	27525.4i		−	1.91096i
$593$			19045.5i			1.31889i	0.751752	+	0.659446i	$0.229209\pi$
$593$			19045.5i			1.31889i	−0.751752	+	0.659446i	$0.770791\pi$
$594$	−6003.17	−	14192.8i	−0.414668	−	0.980367i
$595$	−10047.0			−0.692248
$596$		−	34483.8i		−	2.36999i
$597$			19001.6i			1.30265i
$598$	487.694			0.0333500
$599$		−	24866.5i		−	1.69619i	−0.529843	−	0.848096i	$-0.677749\pi$
$599$		−	24866.5i		−	1.69619i	0.529843	−	0.848096i	$-0.322251\pi$
$600$		−	31667.4i		−	2.15469i
$601$	14444.5			0.980375			0.490188	−	0.871617i	$-0.336928\pi$
$601$	14444.5			0.980375			0.490188	+	0.871617i	$0.336928\pi$
$602$	5618.24			0.380369
$603$		−	10996.2i		−	0.742618i
$604$	−12521.0			−0.843496
$605$	6570.52	−	6769.38i	0.441537	−	0.454900i
$606$	−24064.6			−1.61313
$607$	−19299.0			−1.29048			−0.645240	−	0.763980i	$-0.723243\pi$
$607$	−19299.0			−1.29048			−0.645240	+	0.763980i	$0.723243\pi$
$608$	−33992.8	−	18552.5i	−2.26742	−	1.23751i
$609$	3590.99			0.238940
$610$			18163.3i			1.20559i
$611$	−3093.66			−0.204838
$612$			40113.9i			2.64952i
$613$		−	6615.50i		−	0.435885i	−0.975962	−	0.217942i	$-0.930066\pi$
$613$		−	6615.50i		−	0.435885i	0.975962	−	0.217942i	$-0.0699345\pi$
$614$	38125.1			2.50587
$615$			16890.1i			1.10744i
$616$	−9847.40	−	23281.4i	−0.644096	−	1.52278i
$617$	11856.1			0.773593			0.386796	−	0.922165i	$-0.373582\pi$
$617$	11856.1			0.773593			0.386796	+	0.922165i	$0.373582\pi$
$618$	52251.8			3.40109
$619$	4273.23			0.277472			0.138736	−	0.990329i	$-0.455696\pi$
$619$	4273.23			0.277472			0.138736	+	0.990329i	$0.455696\pi$
$620$		−	11981.3i		−	0.776094i
$621$			1003.03i			0.0648152i
$622$	−49932.7			−3.21884
$623$	−12943.6			−0.832386
$624$		−	8731.54i		−	0.560163i
$625$	−689.874			−0.0441519
$626$	−2495.56			−0.159333
$627$	−1937.34	+	19417.5i	−0.123397	+	1.23678i
$628$	45704.7			2.90416
$629$	−19808.0			−1.25564
$630$		−	5862.46i		−	0.370740i
$631$	19914.7			1.25640			0.628201	−	0.778051i	$-0.283791\pi$
$631$	19914.7			1.25640			0.628201	+	0.778051i	$0.283791\pi$
$632$	25244.8			1.58890
$633$			20004.2i			1.25608i
$634$		−	13802.5i		−	0.864617i
$635$	7617.79			0.476068
$636$	55001.8			3.42919
$637$	1677.81			0.104360
$638$	−9411.24	+	3980.70i	−0.584004	+	0.247018i
$639$		−	11771.1i		−	0.728731i
$640$	−11092.0			−0.685079
$641$		−	5216.96i		−	0.321463i	−0.986998	−	0.160731i	$-0.948615\pi$
$641$		−	5216.96i		−	0.321463i	0.986998	−	0.160731i	$-0.0513853\pi$
$642$		−	57658.7i		−	3.54456i
$643$	−4100.83			−0.251510			−0.125755	−	0.992061i	$-0.540135\pi$
$643$	−4100.83			−0.251510			−0.125755	+	0.992061i	$0.540135\pi$
$644$			2713.46i			0.166033i
$645$	−4574.01			−0.279227
$646$	−28331.3	+	51909.9i	−1.72551	+	3.16156i
$647$	−12553.4			−0.762789			−0.381395	−	0.924412i	$-0.624556\pi$
$647$	−12553.4			−0.762789			−0.381395	+	0.924412i	$0.624556\pi$
$648$	59667.0			3.61719
$649$	1168.00	+	2761.40i	0.0706439	+	0.167018i
$650$	2885.18			0.174102
$651$			5675.31i			0.341679i
$652$	−30873.9			−1.85447
$653$	24950.6			1.49524			0.747620	−	0.664127i	$-0.231197\pi$
$653$	24950.6			1.49524			0.747620	+	0.664127i	$0.231197\pi$
$654$		−	3905.11i		−	0.233489i
$655$		−	1753.45i		−	0.104600i
$656$	−68795.0			−4.09450
$657$		−	6086.01i		−	0.361397i
$658$		−	23988.2i		−	1.42121i
$659$	9249.83			0.546771			0.273386	−	0.961905i	$-0.411857\pi$
$659$	9249.83			0.546771			0.273386	+	0.961905i	$0.411857\pi$
$660$	13221.7	+	31259.0i	0.779778	+	1.84357i
$661$			28272.5i			1.66365i	0.555037	+	0.831826i	$0.312704\pi$
$661$			28272.5i			1.66365i	−0.555037	+	0.831826i	$0.687296\pi$
$662$			38477.1i			2.25899i
$663$	−6283.46			−0.368068
$664$		−	38729.1i		−	2.26352i
$665$	2971.00	−	5443.60i	0.173249	−	0.317434i
$666$		−	11558.0i		−	0.672470i
$667$	665.110			0.0386104
$668$	68289.1			3.95537
$669$	−29719.2			−1.71750
$670$		−	28195.8i		−	1.62582i
$671$	6843.50	+	16179.5i	0.393726	+	0.930855i
$672$	31905.1			1.83150
$673$	−4388.41			−0.251353			−0.125677	−	0.992071i	$-0.540110\pi$
$673$	−4388.41			−0.251353			−0.125677	+	0.992071i	$0.540110\pi$
$674$	14043.1			0.802552
$675$			5933.89i			0.338364i
$676$	−43581.5			−2.47961
$677$	−22350.3			−1.26882			−0.634411	−	0.772996i	$-0.718757\pi$
$677$	−22350.3			−1.26882			−0.634411	+	0.772996i	$0.718757\pi$
$678$	63133.4			3.57614
$679$	−1794.60			−0.101429
$680$			62369.0i			3.51727i
$681$		−	17645.2i		−	0.992899i
$682$	−6291.21	−	14873.8i	−0.353230	−	0.835114i
$683$			14093.8i			0.789582i	0.918771	+	0.394791i	$0.129183\pi$
$683$			14093.8i			0.789582i	−0.918771	+	0.394791i	$0.870817\pi$
$684$	−21734.2	−	11862.1i	−1.21495	−	0.663095i
$685$	8628.58			0.481286
$686$			32295.2i			1.79743i
$687$		−	39149.9i		−	2.17418i
$688$		−	18630.4i		−	1.03238i
$689$			3038.57i			0.168012i
$690$		−	3078.72i		−	0.169862i
$691$	13053.2			0.718619			0.359309	−	0.933219i	$-0.383012\pi$
$691$	13053.2			0.718619			0.359309	+	0.933219i	$0.383012\pi$
$692$	33940.0			1.86446
$693$	−2208.83	−	5222.16i	−0.121077	−	0.286253i
$694$			42368.4i			2.31741i
$695$			18962.4i			1.03494i
$696$		−	22291.9i		−	1.21404i
$697$			49506.7i			2.69039i
$698$			63598.9i			3.44879i
$699$	−38278.3			−2.07127
$700$			16052.7i			0.866765i
$701$			2935.77i			0.158178i	0.996868	+	0.0790888i	$0.0252011\pi$
$701$			2935.77i			0.158178i	−0.996868	+	0.0790888i	$0.974799\pi$
$702$			3062.87i			0.164673i
$703$	5857.42	−	10732.2i	0.314249	−	0.575781i
$704$	−33498.4	+	14168.9i	−1.79335	+	0.758538i
$705$			19529.7i			1.04331i
$706$	21826.6			1.16353
$707$	7396.84			0.393475
$708$	−10786.9			−0.572594
$709$	−8070.55			−0.427498			−0.213749	−	0.976889i	$-0.568567\pi$
$709$	−8070.55			−0.427498			−0.213749	+	0.976889i	$0.568567\pi$
$710$		−	30182.9i		−	1.59541i
$711$	5662.57			0.298682
$712$			80350.5i			4.22930i
$713$			1051.16i			0.0552121i
$714$		−	48722.0i		−	2.55374i
$715$	−1726.90	+	730.431i	−0.0903249	+	0.0382050i
$716$		−	12988.8i		−	0.677953i
$717$	23477.5			1.22285
$718$		−	35281.5i		−	1.83383i
$719$	4007.06			0.207842			0.103921	−	0.994586i	$-0.466861\pi$
$719$	4007.06			0.207842			0.103921	+	0.994586i	$0.466861\pi$
$720$	−19440.3			−1.00624
$721$	−16060.9			−0.829596
$722$	−19747.6	−	30700.5i	−1.01791	−	1.58249i
$723$		−	29150.4i		−	1.49947i
$724$			23378.7i			1.20008i
$725$	3934.76			0.201563
$726$	32827.4	+	31863.1i	1.67815	+	1.62886i
$727$	−9809.90			−0.500453			−0.250226	−	0.968187i	$-0.580505\pi$
$727$	−9809.90			−0.500453			−0.250226	+	0.968187i	$0.580505\pi$
$728$			5024.23i			0.255783i
$729$	−456.313			−0.0231831
$730$		−	15605.4i		−	0.791208i
$731$	−13407.0			−0.678350
$732$	−63202.4			−3.19130
$733$		−	14745.6i		−	0.743031i	−0.928427	−	0.371516i	$-0.878838\pi$
$733$		−	14745.6i		−	0.743031i	0.928427	−	0.371516i	$-0.121162\pi$
$734$	35009.2			1.76051
$735$		−	10591.7i		−	0.531538i
$736$	5909.35			0.295953
$737$	−10623.5	−	25116.2i	−0.530964	−	1.25532i
$738$	−28887.3			−1.44086
$739$			2622.70i			0.130551i	0.997867	+	0.0652757i	$0.0207927\pi$
$739$			2622.70i			0.130551i	−0.997867	+	0.0652757i	$0.979207\pi$
$740$		−	21265.6i		−	1.05640i
$741$	1858.08	−	3404.46i	0.0921163	−	0.168780i
$742$	−23561.1			−1.16571
$743$	22266.2			1.09942			0.549709	−	0.835356i	$-0.314739\pi$
$743$	22266.2			1.09942			0.549709	+	0.835356i	$0.314739\pi$
$744$	35230.7			1.73605
$745$		−	12026.3i		−	0.591420i
$746$	4193.49			0.205810
$747$		−	8687.16i		−	0.425498i
$748$	38754.3	+	91623.6i	1.89438	+	4.47873i
$749$			17722.8i			0.864590i
$750$		−	48665.4i		−	2.36935i
$751$			6336.62i			0.307891i	0.988079	+	0.153946i	$0.0491981\pi$
$751$			6336.62i			0.307891i	−0.988079	+	0.153946i	$0.950802\pi$
$752$	−79546.4			−3.85739
$753$		−	10699.5i		−	0.517812i
$754$	2030.99			0.0980957
$755$	−4366.71			−0.210491
$756$	−17041.3			−0.819825
$757$	−23455.9			−1.12618			−0.563090	−	0.826395i	$-0.690388\pi$
$757$	−23455.9			−1.12618			−0.563090	+	0.826395i	$0.690388\pi$
$758$		−	42066.2i		−	2.01572i
$759$	−1159.99	−	2742.46i	−0.0554741	−	0.131153i
$760$	−33792.3	−	18443.1i	−1.61286	−	0.880266i
$761$			32752.7i			1.56016i	0.625677	+	0.780082i	$0.284823\pi$
$761$			32752.7i			1.56016i	−0.625677	+	0.780082i	$0.715177\pi$
$762$			36941.7i			1.75624i
$763$			1200.33i			0.0569528i
$764$	39762.6			1.88293
$765$			13989.7i			0.661177i
$766$		−	41876.5i		−	1.97527i
$767$		−	595.922i		−	0.0280541i
$768$		−	2279.92i		−	0.107122i
$769$			20005.5i			0.938125i	0.883165	+	0.469063i	$0.155408\pi$
$769$			20005.5i			0.938125i	−0.883165	+	0.469063i	$0.844592\pi$
$770$	−5663.76	−	13390.4i	−0.265075	−	0.626696i
$771$	−21259.8			−0.993063
$772$	2258.30			0.105283
$773$		−	1789.58i		−	0.0832687i	−0.999133	−	0.0416344i	$-0.986744\pi$
$773$		−	1789.58i		−	0.0832687i	0.999133	−	0.0416344i	$-0.0132565\pi$
$774$		−	7823.00i		−	0.363297i
$775$			6218.61i			0.288231i
$776$			11140.4i			0.515355i
$777$			10073.1i			0.465086i
$778$	−61649.9			−2.84095
$779$	−26823.4	−	14639.6i	−1.23369	−	0.673323i
$780$		−	6745.81i		−	0.309665i
$781$	−11372.2	−	26886.3i	−0.521035	−	1.23184i
$782$		−	9024.09i		−	0.412661i
$783$			4177.09i			0.190647i
$784$	43141.0			1.96524
$785$	15939.5			0.724722
$786$	8503.17			0.385875
$787$	20825.7			0.943271			0.471636	−	0.881794i	$-0.343664\pi$
$787$	20825.7			0.943271			0.471636	+	0.881794i	$0.343664\pi$
$788$		−	60887.7i		−	2.75258i
$789$	32987.9			1.48847
$790$	14519.6			0.653906
$791$	−19405.6			−0.872293
$792$	−32417.7	+	13711.8i	−1.45444	+	0.615186i
$793$		−	3491.61i		−	0.156357i
$794$	2073.23			0.0926652
$795$	19181.9			0.855740
$796$	−59794.1			−2.66249
$797$		−	151.188i		−	0.00671940i	−0.999994	−	0.00335970i	$-0.998931\pi$
$797$		−	151.188i		−	0.00671940i	0.999994	−	0.00335970i	$-0.00106943\pi$
$798$	26398.2	+	14407.5i	1.17103	+	0.639125i
$799$			57243.7i			2.53459i
$800$	34959.4			1.54500
$801$			18023.1i			0.795025i
$802$			33367.4i			1.46913i
$803$	−5879.73	−	13901.0i	−0.258395	−	0.610903i
$804$	98111.9			4.30366
$805$			946.322i			0.0414329i
$806$			3209.83i			0.140275i
$807$	−49948.9			−2.17879
$808$		−	45917.5i		−	1.99922i
$809$			4555.14i			0.197961i	0.995089	+	0.0989803i	$0.0315581\pi$
$809$			4555.14i			0.197961i	−0.995089	+	0.0989803i	$0.968442\pi$
$810$	34317.7			1.48864
$811$	35243.8			1.52599			0.762995	−	0.646405i	$-0.223728\pi$
$811$	35243.8			1.52599			0.762995	+	0.646405i	$0.223728\pi$
$812$			11300.1i			0.488370i
$813$	−37245.5			−1.60671
$814$	−11166.3	−	26399.6i	−0.480809	−	1.13674i
$815$	−10767.3			−0.462775
$816$	−161565.			−6.93125
$817$	3964.56	−	7264.06i	0.169771	−	0.311061i
$818$	−65812.3			−2.81305
$819$			1126.96i			0.0480822i
$820$	−53149.6			−2.26349
$821$		−	29213.0i		−	1.24183i	−0.783879	−	0.620914i	$-0.786762\pi$
$821$		−	29213.0i		−	1.24183i	0.783879	−	0.620914i	$-0.213238\pi$
$822$			41843.4i			1.77549i
$823$	−18653.1			−0.790044			−0.395022	−	0.918672i	$-0.629263\pi$
$823$	−18653.1			−0.790044			−0.395022	+	0.918672i	$0.629263\pi$
$824$			99701.5i			4.21513i
$825$	−6862.43	−	16224.3i	−0.289599	−	0.684676i
$826$	4620.78			0.194646
$827$	17460.7			0.734183			0.367091	−	0.930185i	$-0.380354\pi$
$827$	17460.7			0.734183			0.367091	+	0.930185i	$0.380354\pi$
$828$	3778.30			0.158581
$829$		−	10479.8i		−	0.439055i	−0.975606	−	0.219528i	$-0.929548\pi$
$829$		−	10479.8i		−	0.439055i	0.975606	−	0.219528i	$-0.0704516\pi$
$830$		−	22275.1i		−	0.931544i
$831$	−20593.7			−0.859673
$832$	7229.09			0.301230
$833$		−	31045.4i		−	1.29131i
$834$	−91956.0			−3.81796
$835$	23815.9			0.987045
$836$	−61102.8	−	6096.42i	−2.52785	−	0.252212i
$837$	−6601.59			−0.272622
$838$	−74515.5			−3.07171
$839$			26031.5i			1.07117i	0.844483	+	0.535583i	$0.179908\pi$
$839$			26031.5i			1.07117i	−0.844483	+	0.535583i	$0.820092\pi$
$840$	31717.0			1.30279
$841$	−21619.2			−0.886431
$842$		−	59366.1i		−	2.42980i
$843$		−	3049.90i		−	0.124607i
$844$	−62949.1			−2.56730
$845$	−15199.1			−0.618775
$846$	−33401.9			−1.35742
$847$	−10090.3	−	9793.90i	−0.409336	−	0.397311i
$848$			78129.9i			3.16391i
$849$	−25410.4			−1.02719
$850$		−	53386.1i		−	2.15427i
$851$			1865.71i			0.0751534i
$852$	105026.			4.22318
$853$			2728.81i			0.109534i	0.998499	+	0.0547671i	$0.0174416\pi$
$853$			2728.81i			0.109534i	−0.998499	+	0.0547671i	$0.982558\pi$
$854$	27074.0			1.08484
$855$	−7579.82	−	4136.90i	−0.303186	−	0.165473i
$856$	110018.			4.39293
$857$	−4265.06			−0.170002			−0.0850009	−	0.996381i	$-0.527089\pi$
$857$	−4265.06			−0.170002			−0.0850009	+	0.996381i	$0.527089\pi$
$858$	−3542.15	−	8374.42i	−0.140940	−	0.333214i
$859$	−14382.9			−0.571291			−0.285645	−	0.958335i	$-0.592208\pi$
$859$	−14382.9			−0.571291			−0.285645	+	0.958335i	$0.592208\pi$
$860$		−	14393.5i		−	0.570713i
$861$	25176.1			0.996513
$862$	46867.0			1.85185
$863$		−	21174.6i		−	0.835216i	−0.908627	−	0.417608i	$-0.862869\pi$
$863$		−	21174.6i		−	0.835216i	0.908627	−	0.417608i	$-0.137131\pi$
$864$			37112.5i			1.46133i
$865$	11836.6			0.465268
$866$		−	28515.6i		−	1.11894i
$867$			84536.4i			3.31143i
$868$	−17859.0			−0.698359
$869$	12933.8	−	5470.64i	0.504889	−	0.213554i
$870$		−	12821.2i		−	0.499633i
$871$			5420.18i			0.210856i
$872$	7451.33			0.289374
$873$			2498.85i			0.0968765i
$874$	4889.37	+	2668.51i	0.189228	+	0.103277i
$875$			14958.5i			0.577932i
$876$	54301.6			2.09439
$877$	−4200.02			−0.161716			−0.0808578	−	0.996726i	$-0.525766\pi$
$877$	−4200.02			−0.161716			−0.0808578	+	0.996726i	$0.525766\pi$
$878$	−59363.9			−2.28182
$879$		−	19211.0i		−	0.737167i
$880$	−44403.3	+	18781.4i	−1.70095	+	0.719454i
$881$	−12047.1			−0.460700			−0.230350	−	0.973108i	$-0.573987\pi$
$881$	−12047.1			−0.460700			−0.230350	+	0.973108i	$0.573987\pi$
$882$	18115.1			0.691573
$883$	13112.2			0.499729			0.249864	−	0.968281i	$-0.419614\pi$
$883$	13112.2			0.499729			0.249864	+	0.968281i	$0.419614\pi$
$884$		−	19772.7i		−	0.752296i
$885$	−3761.94			−0.142888
$886$	40342.8			1.52973
$887$	8520.56			0.322539			0.161270	−	0.986910i	$-0.448441\pi$
$887$	8520.56			0.322539			0.161270	+	0.986910i	$0.448441\pi$
$888$	62531.2			2.36307
$889$		−	11354.9i		−	0.428383i
$890$			46213.8i			1.74055i
$891$	30569.5	−	12930.0i	1.14940	−	0.486165i
$892$		−	93520.1i		−	3.51041i
$893$	−31015.4	−	16927.5i	−1.16225	−	0.634331i
$894$	58320.1			2.18179
$895$		−	4529.86i		−	0.169180i
$896$			16533.6i			0.616460i
$897$			591.835i			0.0220299i
$898$		−	58540.6i		−	2.17542i
$899$			4377.51i			0.162401i
$900$	22352.3			0.827862
$901$	56224.4			2.07892
$902$	−65981.2	+	27908.2i	−2.43563	+	1.03020i
$903$			6817.94i			0.251259i
$904$			120465.i			4.43207i
$905$			8153.33i			0.299476i
$906$		−	21175.9i		−	0.776514i
$907$			549.784i			0.0201271i	0.999949	+	0.0100636i	$0.00320338\pi$
$907$			549.784i			0.0201271i	−0.999949	+	0.0100636i	$0.996797\pi$
$908$	55525.7			2.02939
$909$		−	10299.6i		−	0.375814i
$910$			2889.70i			0.105267i
$911$			10258.5i			0.373082i	0.982447	+	0.186541i	$0.0597277\pi$
$911$			10258.5i			0.373082i	−0.982447	+	0.186541i	$0.940272\pi$
$912$	47776.3	−	87537.8i	1.73468	−	3.17836i
$913$	−8392.72	−	19842.2i	−0.304226	−	0.719258i
$914$			17943.7i			0.649370i
$915$	−22041.9			−0.796374
$916$	123197.			4.44381
$917$	−2613.66			−0.0941228
$918$	56674.0			2.03760
$919$			39102.2i			1.40355i	0.712399	+	0.701774i	$0.247608\pi$
$919$			39102.2i			1.40355i	−0.712399	+	0.701774i	$0.752392\pi$
$920$	5874.50			0.210518
$921$			46266.3i			1.65529i
$922$			11018.2i			0.393562i
$923$			5802.18i			0.206913i
$924$	46594.1	−	19708.0i	1.65891	−	0.701673i
$925$			11037.4i			0.392334i
$926$	87053.7			3.08937
$927$			22363.6i			0.792361i
$928$	24609.3			0.870516
$929$	5492.27			0.193967			0.0969836	−	0.995286i	$-0.469081\pi$
$929$	5492.27			0.193967			0.0969836	+	0.995286i	$0.469081\pi$
$930$	20263.1			0.714465
$931$	16820.8	+	9180.43i	0.592137	+	0.323176i
$932$		−	120454.i		−	4.23348i
$933$		−	60595.1i		−	2.12626i
$934$	−38558.7			−1.35083
$935$	13515.6	+	31953.8i	0.472734	+	1.11765i
$936$	6995.88			0.244303
$937$		−	33537.4i		−	1.16928i	−0.811291	−	0.584642i	$-0.801235\pi$
$937$		−	33537.4i		−	1.16928i	0.811291	−	0.584642i	$-0.198765\pi$
$938$	−42028.1			−1.46297
$939$		−	3028.45i		−	0.105250i
$940$	−61455.9			−2.13242
$941$	−42108.5			−1.45876			−0.729382	−	0.684107i	$-0.760192\pi$
$941$	−42108.5			−1.45876			−0.729382	+	0.684107i	$0.760192\pi$
$942$			77297.1i			2.67354i
$943$	4663.01			0.161027
$944$		−	15322.8i		−	0.528298i
$945$	−5943.18			−0.204584
$946$	−7557.85	−	17868.4i	−0.259753	−	0.614114i
$947$	−7922.05			−0.271840			−0.135920	−	0.990720i	$-0.543399\pi$
$947$	−7922.05			−0.271840			−0.135920	+	0.990720i	$0.543399\pi$
$948$			50523.5i			1.73094i
$949$			2999.89i			0.102614i
$950$	28925.3	+	15786.8i	0.987852	+	0.539148i
$951$	16749.8			0.571137
$952$	92966.2			3.16497
$953$	−49075.7			−1.66812			−0.834060	−	0.551673i	$-0.813990\pi$
$953$	−49075.7			−1.66812			−0.834060	+	0.551673i	$0.813990\pi$
$954$			32807.1i			1.11339i
$955$	13867.3			0.469878
$956$			73878.7i			2.49938i
$957$	−4830.72	−	11420.9i	−0.163171	−	0.385773i
$958$			83518.7i			2.81667i
$959$		−	12861.6i		−	0.433079i
$960$		−	45635.9i		−	1.53426i
$961$	22872.6			0.767770
$962$			5697.14i			0.190939i
$963$	24677.8			0.825784
$964$	91730.2			3.06476
$965$	787.586			0.0262728
$966$	−4589.09			−0.152848
$967$		−	54784.9i		−	1.82188i	−0.412534	−	0.910942i	$-0.635356\pi$
$967$		−	54784.9i		−	1.82188i	0.412534	−	0.910942i	$-0.364644\pi$
$968$	−60797.8	+	62637.9i	−2.01871	+	2.07981i
$969$	−62994.6	−	34381.1i	−2.08842	−	1.13981i
$970$			6407.41i			0.212092i
$971$		−	50465.7i		−	1.66789i	−0.551848	−	0.833945i	$-0.686077\pi$
$971$		−	50465.7i		−	1.66789i	0.551848	−	0.833945i	$-0.313923\pi$
$972$			75862.5i			2.50338i
$973$	28265.0			0.931277
$974$		−	29881.2i		−	0.983014i
$975$			3501.27i			0.115006i
$976$		−	89778.8i		−	2.94442i
$977$			28217.2i			0.923999i	0.886880	+	0.462000i	$0.152868\pi$
$977$			28217.2i			0.923999i	−0.886880	+	0.462000i	$0.847132\pi$
$978$		−	52214.8i		−	1.70721i
$979$	17412.2	+	41166.3i	0.568434	+	1.34390i
$980$	33329.9			1.08641
$981$	1671.38			0.0543965
$982$		−	77373.1i		−	2.51433i
$983$			12672.3i			0.411172i	0.978639	+	0.205586i	$0.0659101\pi$
$983$			12672.3i			0.411172i	−0.978639	+	0.205586i	$0.934090\pi$
$984$		−	156286.i		−	5.06322i
$985$		−	21234.6i		−	0.686895i
$986$		−	37580.5i		−	1.21380i
$987$	29110.6			0.938805
$988$	10713.1	+	5846.99i	0.344970	+	0.188277i
$989$			1262.79i			0.0406011i
$990$	−18645.1	+	7886.38i	−0.598567	+	0.253177i
$991$		−	840.805i		−	0.0269516i	−0.999909	−	0.0134758i	$-0.995710\pi$
$991$		−	840.805i		−	0.0269516i	0.999909	−	0.0134758i	$-0.00428961\pi$
$992$			38893.2i			1.24482i
$993$	−46693.4			−1.49221
$994$	−44990.1			−1.43561
$995$	−20853.2			−0.664414
$996$	77510.1			2.46587
$997$		−	54892.3i		−	1.74369i	−0.489783	−	0.871844i	$-0.662924\pi$
$997$		−	54892.3i		−	1.74369i	0.489783	−	0.871844i	$-0.337076\pi$
$998$	−65095.7			−2.06470
$999$	−11717.2			−0.371087

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.4.d.b.208.1	✓	56
11.10	odd	2	inner	209.4.d.b.208.55	yes	56
19.18	odd	2	inner	209.4.d.b.208.56	yes	56
209.208	even	2	inner	209.4.d.b.208.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.4.d.b.208.1	✓	56	1.1	even	1	trivial
209.4.d.b.208.2	yes	56	209.208	even	2	inner
209.4.d.b.208.55	yes	56	11.10	odd	2	inner
209.4.d.b.208.56	yes	56	19.18	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	209.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.32196 q^{2} -6.45839i q^{3} +20.3232 q^{4} +7.08774 q^{5} +34.3713i q^{6} -10.5649i q^{7} -65.5837 q^{8} -14.7108 q^{9} -37.7207 q^{10} +(-33.6008 + 14.2122i) q^{11} -131.255i q^{12} +7.25119 q^{13} +56.2258i q^{14} -45.7754i q^{15} +186.448 q^{16} -134.173i q^{17} +78.2903 q^{18} +(72.6966 + 39.6762i) q^{19} +144.046 q^{20} -68.2320 q^{21} +(178.822 - 75.6368i) q^{22} -12.6377 q^{23} +423.565i q^{24} -74.7639 q^{25} -38.5905 q^{26} -79.3683i q^{27} -214.712i q^{28} -52.6291 q^{29} +243.615i q^{30} -83.1766i q^{31} -467.598 q^{32} +(91.7880 + 217.007i) q^{33} +714.063i q^{34} -74.8810i q^{35} -298.971 q^{36} -147.631i q^{37} +(-386.888 - 211.155i) q^{38} -46.8310i q^{39} -464.840 q^{40} -368.977 q^{41} +363.128 q^{42} -99.9229i q^{43} +(-682.877 + 288.838i) q^{44} -104.267 q^{45} +67.2571 q^{46} -426.641 q^{47} -1204.15i q^{48} +231.384 q^{49} +397.890 q^{50} -866.542 q^{51} +147.368 q^{52} +419.044i q^{53} +422.395i q^{54} +(-238.154 + 100.733i) q^{55} +692.883i q^{56} +(256.245 - 469.503i) q^{57} +280.090 q^{58} -82.1826i q^{59} -930.304i q^{60} -481.522i q^{61} +442.663i q^{62} +155.418i q^{63} +996.953 q^{64} +51.3946 q^{65} +(-488.492 - 1154.90i) q^{66} +747.489i q^{67} -2726.83i q^{68} +81.6190i q^{69} +398.514i q^{70} +800.169i q^{71} +964.790 q^{72} +413.710i q^{73} +785.683i q^{74} +482.854i q^{75} +(1477.43 + 806.349i) q^{76} +(150.150 + 354.988i) q^{77} +249.233i q^{78} -384.925 q^{79} +1321.49 q^{80} -909.784 q^{81} +1963.68 q^{82} +590.529i q^{83} -1386.70 q^{84} -950.984i q^{85} +531.785i q^{86} +339.900i q^{87} +(2203.66 - 932.089i) q^{88} -1225.16i q^{89} +554.902 q^{90} -76.6078i q^{91} -256.838 q^{92} -537.187 q^{93} +2270.57 q^{94} +(515.255 + 281.215i) q^{95} +3019.93i q^{96} -169.865i q^{97} -1231.41 q^{98} +(494.295 - 209.073i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 236 q^{4} + 16 q^{5} - 484 q^{9} + 74 q^{11} + 668 q^{16} - 264 q^{20} - 296 q^{23} + 1040 q^{25} - 672 q^{26} - 428 q^{36} + 700 q^{38} - 2472 q^{42} - 668 q^{44} + 248 q^{45} - 2284 q^{47} - 2880 q^{49}+ \cdots - 414 q^{99}+O(q^{100}) \) 56 * q + 236 * q^4 + 16 * q^5 - 484 * q^9 + 74 * q^11 + 668 * q^16 - 264 * q^20 - 296 * q^23 + 1040 * q^25 - 672 * q^26 - 428 * q^36 + 700 * q^38 - 2472 * q^42 - 668 * q^44 + 248 * q^45 - 2284 * q^47 - 2880 * q^49 - 614 * q^55 + 2112 * q^58 + 1460 * q^64 + 4964 * q^66 + 2154 * q^77 - 5680 * q^80 - 456 * q^81 + 7840 * q^82 + 10312 * q^92 - 728 * q^93 - 414 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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