LMFDB - Embedded newform 230.5.c.a.229.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,5,Mod(229,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("230.229");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	230.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$23.7750915093$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.14
Character	$\chi$	$=$	230.229
Dual form			230.5.c.a.229.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.82843i q^{2} -10.7328i q^{3} -8.00000 q^{4} +(12.7779 + 21.4878i) q^{5} +30.3568 q^{6} -32.1609 q^{7} -22.6274i q^{8} -34.1923 q^{9} +O(q^{10})$	\(q+2.82843i q^{2} -10.7328i q^{3} -8.00000 q^{4} +(12.7779 + 21.4878i) q^{5} +30.3568 q^{6} -32.1609 q^{7} -22.6274i q^{8} -34.1923 q^{9} +(-60.7766 + 36.1415i) q^{10} +66.8245i q^{11} +85.8621i q^{12} -199.267i q^{13} -90.9648i q^{14} +(230.623 - 137.143i) q^{15} +64.0000 q^{16} -387.012 q^{17} -96.7104i q^{18} -79.4751i q^{19} +(-102.224 - 171.902i) q^{20} +345.175i q^{21} -189.008 q^{22} +(528.590 + 20.8329i) q^{23} -242.855 q^{24} +(-298.448 + 549.139i) q^{25} +563.611 q^{26} -502.376i q^{27} +257.287 q^{28} -355.063 q^{29} +(387.898 + 652.301i) q^{30} -1565.50 q^{31} +181.019i q^{32} +717.212 q^{33} -1094.64i q^{34} +(-410.950 - 691.066i) q^{35} +273.538 q^{36} -282.364 q^{37} +224.789 q^{38} -2138.68 q^{39} +(486.213 - 289.132i) q^{40} -3180.57 q^{41} -976.304 q^{42} -1927.07 q^{43} -534.596i q^{44} +(-436.907 - 734.716i) q^{45} +(-58.9244 + 1495.08i) q^{46} +410.094i q^{47} -686.897i q^{48} -1366.68 q^{49} +(-1553.20 - 844.139i) q^{50} +4153.71i q^{51} +1594.13i q^{52} +397.862 q^{53} +1420.93 q^{54} +(-1435.91 + 853.880i) q^{55} +727.718i q^{56} -852.987 q^{57} -1004.27i q^{58} +430.824 q^{59} +(-1844.99 + 1097.14i) q^{60} -3718.52i q^{61} -4427.89i q^{62} +1099.65 q^{63} -512.000 q^{64} +(4281.80 - 2546.22i) q^{65} +2028.58i q^{66} -6255.24 q^{67} +3096.10 q^{68} +(223.595 - 5673.23i) q^{69} +(1954.63 - 1162.34i) q^{70} +4737.99 q^{71} +773.683i q^{72} -7516.72i q^{73} -798.646i q^{74} +(5893.78 + 3203.18i) q^{75} +635.801i q^{76} -2149.14i q^{77} -6049.11i q^{78} +3317.09i q^{79} +(817.789 + 1375.22i) q^{80} -8161.46 q^{81} -8996.00i q^{82} +11643.0 q^{83} -2761.40i q^{84} +(-4945.22 - 8316.03i) q^{85} -5450.59i q^{86} +3810.81i q^{87} +1512.07 q^{88} +9235.38i q^{89} +(2078.09 - 1235.76i) q^{90} +6408.60i q^{91} +(-4228.72 - 166.663i) q^{92} +16802.1i q^{93} -1159.92 q^{94} +(1707.74 - 1015.53i) q^{95} +1942.84 q^{96} -11892.2 q^{97} -3865.55i q^{98} -2284.88i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9}+O(q^{10}) $ 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9	$ 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9} + 3072 q^{16} + 512 q^{24} + 1488 q^{25} - 384 q^{26} - 2940 q^{29} + 4732 q^{31} + 2556 q^{35} + 12864 q^{36} + 2736 q^{39} + 828 q^{41} - 64 q^{46} + 32572 q^{49} - 3264 q^{50} + 10112 q^{54} + 12824 q^{55} + 7092 q^{59} - 24576 q^{64} + 14000 q^{69} - 6592 q^{70} - 12708 q^{71} + 24728 q^{75} - 13040 q^{81} - 15700 q^{85} - 9728 q^{94} - 46608 q^{95} - 4096 q^{96}+O(q^{100}) $ 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9 + 3072 * q^16 + 512 * q^24 + 1488 * q^25 - 384 * q^26 - 2940 * q^29 + 4732 * q^31 + 2556 * q^35 + 12864 * q^36 + 2736 * q^39 + 828 * q^41 - 64 * q^46 + 32572 * q^49 - 3264 * q^50 + 10112 * q^54 + 12824 * q^55 + 7092 * q^59 - 24576 * q^64 + 14000 * q^69 - 6592 * q^70 - 12708 * q^71 + 24728 * q^75 - 13040 * q^81 - 15700 * q^85 - 9728 * q^94 - 46608 * q^95 - 4096 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$-1$

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 $

$2$			2.82843i			0.707107i
$2$			2.82843i			0.707107i
$3$		−	10.7328i		−	1.19253i	−0.802788	−	0.596265i	$-0.796651\pi$
$3$		−	10.7328i		−	1.19253i	0.802788	−	0.596265i	$-0.203349\pi$
$4$	−8.00000			−0.500000
$5$	12.7779	+	21.4878i	0.511118	+	0.859511i
$5$	12.7779	+	21.4878i	0.511118	+	0.859511i
$6$	30.3568			0.843246
$7$	−32.1609			−0.656345			−0.328172	−	0.944618i	$-0.606433\pi$
$7$	−32.1609			−0.656345			−0.328172	+	0.944618i	$0.606433\pi$
$8$		−	22.6274i		−	0.353553i
$9$	−34.1923			−0.422127
$10$	−60.7766	+	36.1415i	−0.607766	+	0.361415i
$11$			66.8245i			0.552269i	0.961119	+	0.276134i	$0.0890535\pi$
$11$			66.8245i			0.552269i	−0.961119	+	0.276134i	$0.910946\pi$
$12$			85.8621i			0.596265i
$13$		−	199.267i		−	1.17909i	−0.807734	−	0.589546i	$-0.799306\pi$
$13$		−	199.267i		−	1.17909i	0.807734	−	0.589546i	$-0.200694\pi$
$14$		−	90.9648i		−	0.464106i
$15$	230.623	−	137.143i	1.02499	−	0.609523i
$16$	64.0000			0.250000
$17$	−387.012			−1.33914			−0.669571	−	0.742748i	$-0.733522\pi$
$17$	−387.012			−1.33914			−0.669571	+	0.742748i	$0.733522\pi$
$18$		−	96.7104i		−	0.298489i
$19$		−	79.4751i		−	0.220153i	−0.993923	−	0.110076i	$-0.964890\pi$
$19$		−	79.4751i		−	0.220153i	0.993923	−	0.110076i	$-0.0351095\pi$
$20$	−102.224	−	171.902i	−0.255559	−	0.429755i
$21$			345.175i			0.782711i
$22$	−189.008			−0.390513
$23$	528.590	+	20.8329i	0.999224	+	0.0393817i
$23$	528.590	+	20.8329i	0.999224	+	0.0393817i
$24$	−242.855			−0.421623
$25$	−298.448	+	549.139i	−0.477517	+	0.878622i
$26$	563.611			0.833745
$27$		−	502.376i		−	0.689131i
$28$	257.287			0.328172
$29$	−355.063			−0.422191			−0.211096	−	0.977465i	$-0.567703\pi$
$29$	−355.063			−0.422191			−0.211096	+	0.977465i	$0.567703\pi$
$30$	387.898	+	652.301i	0.430998	+	0.724779i
$31$	−1565.50			−1.62903			−0.814514	−	0.580144i	$-0.802996\pi$
$31$	−1565.50			−1.62903			−0.814514	+	0.580144i	$0.802996\pi$
$32$			181.019i			0.176777i
$33$	717.212			0.658597
$34$		−	1094.64i		−	0.946917i
$35$	−410.950	−	691.066i	−0.335470	−	0.564135i
$36$	273.538			0.211063
$37$	−282.364			−0.206256			−0.103128	−	0.994668i	$-0.532885\pi$
$37$	−282.364			−0.206256			−0.103128	+	0.994668i	$0.532885\pi$
$38$	224.789			0.155671
$39$	−2138.68			−1.40610
$40$	486.213	−	289.132i	0.303883	−	0.180707i
$41$	−3180.57			−1.89207			−0.946034	−	0.324067i	$-0.894950\pi$
$41$	−3180.57			−1.89207			−0.946034	+	0.324067i	$0.894950\pi$
$42$	−976.304			−0.553460
$43$	−1927.07			−1.04222			−0.521112	−	0.853488i	$-0.674483\pi$
$43$	−1927.07			−1.04222			−0.521112	+	0.853488i	$0.674483\pi$
$44$		−	534.596i		−	0.276134i
$45$	−436.907	−	734.716i	−0.215757	−	0.362823i
$46$	−58.9244	+	1495.08i	−0.0278471	+	0.706558i
$47$			410.094i			0.185647i	0.995683	+	0.0928234i	$0.0295892\pi$
$47$			410.094i			0.185647i	−0.995683	+	0.0928234i	$0.970411\pi$
$48$		−	686.897i		−	0.298132i
$49$	−1366.68			−0.569211
$50$	−1553.20	−	844.139i	−0.621280	−	0.337656i
$51$			4153.71i			1.59697i
$52$			1594.13i			0.589546i
$53$	397.862			0.141638			0.0708192	−	0.997489i	$-0.477439\pi$
$53$	397.862			0.141638			0.0708192	+	0.997489i	$0.477439\pi$
$54$	1420.93			0.487289
$55$	−1435.91	+	853.880i	−0.474681	+	0.282274i
$56$			727.718i			0.232053i
$57$	−852.987			−0.262538
$58$		−	1004.27i		−	0.298534i
$59$	430.824			0.123764			0.0618822	−	0.998083i	$-0.480290\pi$
$59$	430.824			0.123764			0.0618822	+	0.998083i	$0.480290\pi$
$60$	−1844.99	+	1097.14i	−0.512496	+	0.304762i
$61$		−	3718.52i		−	0.999333i	−0.866218	−	0.499667i	$-0.833456\pi$
$61$		−	3718.52i		−	0.999333i	0.866218	−	0.499667i	$-0.166544\pi$
$62$		−	4427.89i		−	1.15190i
$63$	1099.65			0.277061
$64$	−512.000			−0.125000
$65$	4281.80	−	2546.22i	1.01344	−	0.602655i
$66$			2028.58i			0.465698i
$67$	−6255.24			−1.39346			−0.696730	−	0.717334i	$-0.745362\pi$
$67$	−6255.24			−1.39346			−0.696730	+	0.717334i	$0.745362\pi$
$68$	3096.10			0.669571
$69$	223.595	−	5673.23i	0.0469639	−	1.19160i
$70$	1954.63	−	1162.34i	0.398904	−	0.237213i
$71$	4737.99			0.939890			0.469945	−	0.882696i	$-0.344274\pi$
$71$	4737.99			0.939890			0.469945	+	0.882696i	$0.344274\pi$
$72$			773.683i			0.149244i
$73$		−	7516.72i		−	1.41053i	−0.708943	−	0.705266i	$-0.750828\pi$
$73$		−	7516.72i		−	1.41053i	0.708943	−	0.705266i	$-0.249172\pi$
$74$		−	798.646i		−	0.145845i
$75$	5893.78	+	3203.18i	1.04778	+	0.569453i
$76$			635.801i			0.110076i
$77$		−	2149.14i		−	0.362479i
$78$		−	6049.11i		−	0.994265i
$79$			3317.09i			0.531500i	0.964042	+	0.265750i	$0.0856195\pi$
$79$			3317.09i			0.531500i	−0.964042	+	0.265750i	$0.914380\pi$
$80$	817.789	+	1375.22i	0.127779	+	0.214878i
$81$	−8161.46			−1.24394
$82$		−	8996.00i		−	1.33789i
$83$	11643.0			1.69009			0.845045	−	0.534695i	$-0.179573\pi$
$83$	11643.0			1.69009			0.845045	+	0.534695i	$0.179573\pi$
$84$		−	2761.40i		−	0.391355i
$85$	−4945.22	−	8316.03i	−0.684460	−	1.15101i
$86$		−	5450.59i		−	0.736964i
$87$			3810.81i			0.503475i
$88$	1512.07			0.195257
$89$			9235.38i			1.16594i	0.812495	+	0.582968i	$0.198109\pi$
$89$			9235.38i			1.16594i	−0.812495	+	0.582968i	$0.801891\pi$
$90$	2078.09	−	1235.76i	0.256554	−	0.152563i
$91$			6408.60i			0.773892i
$92$	−4228.72	−	166.663i	−0.499612	−	0.0196909i
$93$			16802.1i			1.94266i
$94$	−1159.92			−0.131272
$95$	1707.74	−	1015.53i	0.189223	−	0.112524i
$96$	1942.84			0.210811
$97$	−11892.2			−1.26392			−0.631961	−	0.775000i	$-0.717750\pi$
$97$	−11892.2			−1.26392			−0.631961	+	0.775000i	$0.717750\pi$
$98$		−	3865.55i		−	0.402493i
$99$		−	2284.88i		−	0.233128i
$100$	2387.59	−	4393.11i	0.238759	−	0.439311i
$101$	6144.29			0.602323			0.301161	−	0.953573i	$-0.402626\pi$
$101$	6144.29			0.602323			0.301161	+	0.953573i	$0.402626\pi$
$102$	−11748.5			−1.12923
$103$	9397.26			0.885782			0.442891	−	0.896575i	$-0.353953\pi$
$103$	9397.26			0.885782			0.442891	+	0.896575i	$0.353953\pi$
$104$	−4508.89			−0.416872
$105$	−7417.05	+	4410.63i	−0.672748	+	0.400057i
$106$			1125.32i			0.100154i
$107$	−5309.23			−0.463729			−0.231864	−	0.972748i	$-0.574483\pi$
$107$	−5309.23			−0.463729			−0.231864	+	0.972748i	$0.574483\pi$
$108$			4019.01i			0.344565i
$109$		−	11469.7i		−	0.965385i	−0.875790	−	0.482693i	$-0.839659\pi$
$109$		−	11469.7i		−	0.965385i	0.875790	−	0.482693i	$-0.160341\pi$
$110$	−2415.14	−	4061.37i	−0.199598	−	0.335650i
$111$			3030.55i			0.245966i
$112$	−2058.30			−0.164086
$113$	2201.72			0.172427			0.0862137	−	0.996277i	$-0.472523\pi$
$113$	2201.72			0.172427			0.0862137	+	0.996277i	$0.472523\pi$
$114$		−	2412.61i		−	0.185643i
$115$	6306.64	+	11624.4i	0.476872	+	0.878973i
$116$	2840.50			0.211096
$117$			6813.38i			0.497727i
$118$			1218.55i			0.0875146i
$119$	12446.7			0.878939
$120$	−3103.19	−	5218.41i	−0.215499	−	0.362389i
$121$	10175.5			0.694999
$122$	10517.6			0.706635
$123$			34136.3i			2.25635i
$124$	12524.0			0.814514
$125$	−15613.3	+	603.883i	−0.999253	+	0.0386485i
$126$			3110.29i			0.195912i
$127$			28340.7i			1.75713i	0.477623	+	0.878565i	$0.341499\pi$
$127$			28340.7i			1.75713i	−0.477623	+	0.878565i	$0.658501\pi$
$128$		−	1448.15i		−	0.0883883i
$129$			20682.8i			1.24288i
$130$	7201.80	+	12110.7i	0.426142	+	0.716612i
$131$	−10267.8			−0.598319			−0.299159	−	0.954203i	$-0.596706\pi$
$131$	−10267.8			−0.598319			−0.299159	+	0.954203i	$0.596706\pi$
$132$	−5737.70			−0.329299
$133$			2555.99i			0.144496i
$134$		−	17692.5i		−	0.985325i
$135$	10794.9	−	6419.34i	0.592315	−	0.352227i
$136$			8757.09i			0.473458i
$137$	−6237.03			−0.332305			−0.166152	−	0.986100i	$-0.553134\pi$
$137$	−6237.03			−0.332305			−0.166152	+	0.986100i	$0.553134\pi$
$138$	16046.3	+	632.422i	0.842592	+	0.0332085i
$139$	−10865.3			−0.562358			−0.281179	−	0.959655i	$-0.590725\pi$
$139$	−10865.3			−0.562358			−0.281179	+	0.959655i	$0.590725\pi$
$140$	3287.60	+	5528.53i	0.167735	+	0.282068i
$141$	4401.44			0.221389
$142$			13401.1i			0.664603i
$143$	13315.9			0.651176
$144$	−2188.31			−0.105532
$145$	−4536.97	−	7629.50i	−0.215789	−	0.362878i
$146$	21260.5			0.997397
$147$			14668.2i			0.678801i
$148$	2258.91			0.103128
$149$			2930.78i			0.132011i	0.997819	+	0.0660055i	$0.0210255\pi$
$149$			2930.78i			0.132011i	−0.997819	+	0.0660055i	$0.978975\pi$
$150$	−9059.95	+	16670.1i	−0.402664	+	0.740895i
$151$	3431.01			0.150476			0.0752381	−	0.997166i	$-0.476028\pi$
$151$	3431.01			0.150476			0.0752381	+	0.997166i	$0.476028\pi$
$152$	−1798.32			−0.0778357
$153$	13232.8			0.565288
$154$	6078.68			0.256311
$155$	−20003.8	−	33639.0i	−0.832625	−	1.40017i
$156$	17109.5			0.703052
$157$	30931.7			1.25489			0.627443	−	0.778663i	$-0.284102\pi$
$157$	30931.7			1.25489			0.627443	+	0.778663i	$0.284102\pi$
$158$	−9382.14			−0.375827
$159$		−	4270.16i		−	0.168908i
$160$	−3889.70	+	2313.06i	−0.151941	+	0.0903537i
$161$	−16999.9	−	670.006i	−0.655836	−	0.0258480i
$162$		−	23084.1i		−	0.879595i
$163$		−	13070.8i		−	0.491958i	−0.969275	−	0.245979i	$-0.920891\pi$
$163$		−	13070.8i		−	0.491958i	0.969275	−	0.245979i	$-0.0791094\pi$
$164$	25444.5			0.946034
$165$	9164.50	+	15411.3i	0.336621	+	0.566071i
$166$			32931.5i			1.19507i
$167$		−	12664.8i		−	0.454116i	−0.973881	−	0.227058i	$-0.927089\pi$
$167$		−	12664.8i		−	0.454116i	0.973881	−	0.227058i	$-0.0729107\pi$
$168$	7810.43			0.276730
$169$	−11146.2			−0.390260
$170$	23521.3	−	13987.2i	0.813885	−	0.483986i
$171$			2717.43i			0.0929323i
$172$	15416.6			0.521112
$173$		−	57187.2i		−	1.91076i	−0.295376	−	0.955381i	$-0.595445\pi$
$173$		−	57187.2i		−	1.91076i	0.295376	−	0.955381i	$-0.404555\pi$
$174$	−10778.6			−0.356011
$175$	9598.36	−	17660.8i	0.313416	−	0.576679i
$176$			4276.77i			0.138067i
$177$		−	4623.93i		−	0.147593i
$178$	−26121.6			−0.824442
$179$	41221.8			1.28653			0.643266	−	0.765643i	$-0.277579\pi$
$179$	41221.8			1.28653			0.643266	+	0.765643i	$0.277579\pi$
$180$	3495.26	+	5877.73i	0.107878	+	0.181411i
$181$		−	13634.8i		−	0.416189i	−0.978109	−	0.208095i	$-0.933274\pi$
$181$		−	13634.8i		−	0.416189i	0.978109	−	0.208095i	$-0.0667262\pi$
$182$	−18126.2			−0.547224
$183$	−39910.0			−1.19173
$184$	471.395	−	11960.6i	0.0139235	−	0.353279i
$185$	−3608.03	−	6067.37i	−0.105421	−	0.177279i
$186$	−47523.5			−1.37367
$187$		−	25861.9i		−	0.739567i
$188$		−	3280.75i		−	0.0928234i
$189$			16156.9i			0.452307i
$190$	2872.35	+	4830.22i	0.0795664	+	0.133801i
$191$			56138.6i			1.53884i	0.638741	+	0.769422i	$0.279456\pi$
$191$			56138.6i			1.53884i	−0.638741	+	0.769422i	$0.720544\pi$
$192$			5495.18i			0.149066i
$193$		−	1337.90i		−	0.0359176i	−0.999839	−	0.0179588i	$-0.994283\pi$
$193$		−	1337.90i		−	0.0359176i	0.999839	−	0.0179588i	$-0.00571677\pi$
$194$		−	33636.4i		−	0.893728i
$195$	−27328.0	−	45955.5i	−0.718684	−	1.20856i
$196$	10933.4			0.284606
$197$		−	35546.2i		−	0.915927i	−0.888971	−	0.457964i	$-0.848579\pi$
$197$		−	35546.2i		−	0.915927i	0.888971	−	0.457964i	$-0.151421\pi$
$198$	6462.63			0.164846
$199$			21838.0i			0.551452i	0.961236	+	0.275726i	$0.0889182\pi$
$199$			21838.0i			0.551452i	−0.961236	+	0.275726i	$0.911082\pi$
$200$	12425.6	+	6753.11i	0.310640	+	0.168828i
$201$			67136.0i			1.66174i
$202$			17378.7i			0.425906i
$203$	11419.1			0.277103
$204$		−	33229.7i		−	0.798484i
$205$	−40641.1	−	68343.3i	−0.967070	−	1.62625i
$206$			26579.5i			0.626343i
$207$	−18073.7	−	712.325i	−0.421799	−	0.0166241i
$208$		−	12753.1i		−	0.294773i
$209$	5310.89			0.121583
$210$	−12475.2	−	20978.6i	−0.282883	−	0.475705i
$211$	78350.9			1.75986			0.879932	−	0.475100i	$-0.157588\pi$
$211$	78350.9			1.75986			0.879932	+	0.475100i	$0.157588\pi$
$212$	−3182.90			−0.0708192
$213$		−	50851.7i		−	1.12085i
$214$		−	15016.8i		−	0.327906i
$215$	−24624.0	−	41408.5i	−0.532700	−	0.895803i
$216$	−11367.5			−0.243645
$217$	50347.7			1.06920
$218$	32441.3			0.682630
$219$	−80675.2			−1.68210
$220$	11487.3	−	6831.04i	0.237341	−	0.141137i
$221$			77118.7i			1.57897i
$222$	−8571.68			−0.173924
$223$			44718.5i			0.899244i	0.893219	+	0.449622i	$0.148441\pi$
$223$			44718.5i			0.899244i	−0.893219	+	0.449622i	$0.851559\pi$
$224$		−	5821.74i		−	0.116026i
$225$	10204.6	−	18776.3i	0.201573	−	0.370890i
$226$			6227.42i			0.121925i
$227$	67756.9			1.31493			0.657464	−	0.753486i	$-0.271629\pi$
$227$	67756.9			1.31493			0.657464	+	0.753486i	$0.271629\pi$
$228$	6823.90			0.131269
$229$			68468.0i			1.30562i	0.757522	+	0.652810i	$0.226410\pi$
$229$			68468.0i			1.30562i	−0.757522	+	0.652810i	$0.773590\pi$
$230$	−32878.8	+	17837.9i	−0.621527	+	0.337200i
$231$	−23066.2			−0.432267
$232$			8034.15i			0.149267i
$233$		−	37854.7i		−	0.697282i	−0.937256	−	0.348641i	$-0.886643\pi$
$233$		−	37854.7i		−	0.697282i	0.937256	−	0.348641i	$-0.113357\pi$
$234$	−19271.2			−0.351946
$235$	−8812.00	+	5240.16i	−0.159565	+	0.0948874i
$236$	−3446.59			−0.0618822
$237$	35601.5			0.633829
$238$			35204.5i			0.621504i
$239$	7868.92			0.137759			0.0688794	−	0.997625i	$-0.478058\pi$
$239$	7868.92			0.137759			0.0688794	+	0.997625i	$0.478058\pi$
$240$	14759.9	−	8777.13i	0.256248	−	0.152381i
$241$		−	20959.3i		−	0.360863i	−0.983588	−	0.180432i	$-0.942251\pi$
$241$		−	20959.3i		−	0.360863i	0.983588	−	0.180432i	$-0.0577494\pi$
$242$			28780.6i			0.491439i
$243$			46902.6i			0.794300i
$244$			29748.1i			0.499667i
$245$	−17463.3	−	29366.8i	−0.290934	−	0.489243i
$246$	−96552.0			−1.59548
$247$	−15836.7			−0.259580
$248$			35423.1i			0.575948i
$249$		−	124962.i		−	2.01548i
$250$	−1708.04	−	44161.2i	−0.0273286	−	0.706578i
$251$		−	49396.0i		−	0.784051i	−0.919954	−	0.392025i	$-0.871775\pi$
$251$		−	49396.0i		−	0.784051i	0.919954	−	0.392025i	$-0.128225\pi$
$252$	−8797.24			−0.138530
$253$	−1392.15	+	35322.8i	−0.0217493	+	0.551840i
$254$	−80159.7			−1.24248
$255$	−89254.0	+	53075.9i	−1.37261	+	0.816238i
$256$	4096.00			0.0625000
$257$		−	44507.8i		−	0.673860i	−0.941530	−	0.336930i	$-0.890611\pi$
$257$		−	44507.8i		−	0.673860i	0.941530	−	0.336930i	$-0.109389\pi$
$258$	−58499.9			−0.878852
$259$	9081.08			0.135375
$260$	−34254.4	+	20369.8i	−0.506721	+	0.301328i
$261$	12140.4			0.178218
$262$		−	29041.6i		−	0.423075i
$263$	−118490.			−1.71305			−0.856525	−	0.516105i	$-0.827381\pi$
$263$	−118490.			−1.71305			−0.856525	+	0.516105i	$0.827381\pi$
$264$		−	16228.7i		−	0.232849i
$265$	5083.86	+	8549.17i	0.0723939	+	0.121740i
$266$	−7229.43			−0.102174
$267$	99121.2			1.39041
$268$	50041.9			0.696730
$269$	−73871.0			−1.02087			−0.510434	−	0.859917i	$-0.670515\pi$
$269$	−73871.0			−1.02087			−0.510434	+	0.859917i	$0.670515\pi$
$270$	18156.6	+	30532.7i	0.249062	+	0.418830i
$271$	−72423.6			−0.986147			−0.493073	−	0.869988i	$-0.664127\pi$
$271$	−72423.6			−0.986147			−0.493073	+	0.869988i	$0.664127\pi$
$272$	−24768.8			−0.334786
$273$	68782.0			0.922889
$274$		−	17641.0i		−	0.234975i
$275$	−36696.0	−	19943.7i	−0.485236	−	0.263718i
$276$	−1788.76	+	45385.8i	−0.0234819	+	0.595802i
$277$		−	7406.75i		−	0.0965313i	−0.998835	−	0.0482656i	$-0.984631\pi$
$277$		−	7406.75i		−	0.0965313i	0.998835	−	0.0482656i	$-0.0153694\pi$
$278$		−	30731.7i		−	0.397647i
$279$	53527.9			0.687656
$280$	−15637.0	+	9298.74i	−0.199452	+	0.118606i
$281$			120342.i			1.52406i	0.647539	+	0.762032i	$0.275798\pi$
$281$			120342.i			1.52406i	−0.647539	+	0.762032i	$0.724202\pi$
$282$			12449.2i			0.156546i
$283$	−15727.5			−0.196375			−0.0981874	−	0.995168i	$-0.531304\pi$
$283$	−15727.5			−0.196375			−0.0981874	+	0.995168i	$0.531304\pi$
$284$	−37903.9			−0.469945
$285$	−10899.4	−	18328.8i	−0.134188	−	0.225655i
$286$			37663.1i			0.460451i
$287$	102290.			1.24185
$288$		−	6189.46i		−	0.0746222i
$289$	66257.5			0.793303
$290$	21579.5	−	12832.5i	0.256593	−	0.152586i
$291$			127637.i			1.50727i
$292$			60133.8i			0.705266i
$293$	−148380.			−1.72838			−0.864190	−	0.503166i	$-0.832168\pi$
$293$	−148380.			−1.72838			−0.864190	+	0.503166i	$0.832168\pi$
$294$	−41488.0			−0.479985
$295$	5505.04	+	9257.44i	0.0632582	+	0.106377i
$296$			6389.17i			0.0729224i
$297$	33571.1			0.380586
$298$	−8289.49			−0.0933459
$299$	4151.31	−	105330.i	0.0464347	−	1.17818i
$300$	−47150.2	−	25625.4i	−0.523892	−	0.284727i
$301$	61976.4			0.684059
$302$			9704.35i			0.106403i
$303$		−	65945.3i		−	0.718288i
$304$		−	5086.40i		−	0.0550381i
$305$	79902.7	−	47515.0i	0.858937	−	0.510777i
$306$			37428.1i			0.399719i
$307$		−	17766.8i		−	0.188510i	−0.995548	−	0.0942548i	$-0.969953\pi$
$307$		−	17766.8i		−	0.188510i	0.995548	−	0.0942548i	$-0.0300468\pi$
$308$			17193.1i			0.181239i
$309$		−	100859.i		−	1.05632i
$310$	95145.5	−	56579.3i	0.990067	−	0.588755i
$311$	−79706.0			−0.824081			−0.412041	−	0.911165i	$-0.635184\pi$
$311$	−79706.0			−0.824081			−0.412041	+	0.911165i	$0.635184\pi$
$312$			48392.9i			0.497133i
$313$	−146146.			−1.49176			−0.745880	−	0.666081i	$-0.767971\pi$
$313$	−146146.			−1.49176			−0.745880	+	0.666081i	$0.767971\pi$
$314$			87488.0i			0.887338i
$315$	14051.3	+	23629.1i	0.141611	+	0.238137i
$316$		−	26536.7i		−	0.265750i
$317$		−	84900.4i		−	0.844872i	−0.906393	−	0.422436i	$-0.861175\pi$
$317$		−	84900.4i		−	0.844872i	0.906393	−	0.422436i	$-0.138825\pi$
$318$	12077.8			0.119436
$319$		−	23726.9i		−	0.233163i
$320$	−6542.31	−	11001.7i	−0.0638897	−	0.107439i
$321$			56982.8i			0.553011i
$322$	1895.06	−	48083.0i	0.0182773	−	0.463746i
$323$			30757.8i			0.294816i
$324$	65291.7			0.621968
$325$	109425.	+	59470.8i	1.03598	+	0.563037i
$326$	36969.9			0.347867
$327$	−123102.			−1.15125
$328$			71968.0i			0.668947i
$329$		−	13189.0i		−	0.121848i
$330$	−43589.7	+	25921.1i	−0.400273	+	0.238027i
$331$	5943.64			0.0542496			0.0271248	−	0.999632i	$-0.491365\pi$
$331$	5943.64			0.0542496			0.0271248	+	0.999632i	$0.491365\pi$
$332$	−93144.3			−0.845045
$333$	9654.67			0.0870661
$334$	35821.6			0.321108
$335$	−79929.1	−	134411.i	−0.712222	−	1.19769i
$336$			22091.2i			0.195678i
$337$	104486.			0.920018			0.460009	−	0.887914i	$-0.347846\pi$
$337$	104486.			0.920018			0.460009	+	0.887914i	$0.347846\pi$
$338$		−	31526.3i		−	0.275956i
$339$		−	23630.6i		−	0.205625i
$340$	39561.8	+	66528.2i	0.342230	+	0.575504i
$341$		−	104614.i		−	0.899661i
$342$	−7686.06			−0.0657131
$343$	121172.			1.02994
$344$			43604.7i			0.368482i
$345$	124762.	−	67687.7i	1.04820	−	0.568684i
$346$	161750.			1.35111
$347$			163303.i			1.35624i	0.734951	+	0.678120i	$0.237205\pi$
$347$			163303.i			1.35624i	−0.734951	+	0.678120i	$0.762795\pi$
$348$		−	30486.4i		−	0.251738i
$349$	−23761.4			−0.195084			−0.0975421	−	0.995231i	$-0.531098\pi$
$349$	−23761.4			−0.195084			−0.0975421	+	0.995231i	$0.531098\pi$
$350$	49952.3	+	27148.3i	0.407774	+	0.221619i
$351$	−100107.			−0.812549
$352$	−12096.5			−0.0976283
$353$		−	153040.i		−	1.22817i	−0.789242	−	0.614083i	$-0.789526\pi$
$353$		−	153040.i		−	1.22817i	0.789242	−	0.614083i	$-0.210474\pi$
$354$	13078.5			0.104364
$355$	60541.8	+	101809.i	0.480395	+	0.807846i
$356$		−	73883.1i		−	0.582968i
$357$		−	133587.i		−	1.04816i
$358$			116593.i			0.909715i
$359$			107729.i			0.835876i	0.908475	+	0.417938i	$0.137247\pi$
$359$			107729.i			0.835876i	−0.908475	+	0.417938i	$0.862753\pi$
$360$	−16624.7	+	9886.08i	−0.128277	+	0.0762815i
$361$	124005.			0.951533
$362$	38565.0			0.294290
$363$		−	109211.i		−	0.828807i
$364$		−	51268.8i		−	0.386946i
$365$	161518.	−	96048.3i	1.21237	−	0.720948i
$366$		−	112883.i		−	0.842683i
$367$	−170833.			−1.26835			−0.634176	−	0.773189i	$-0.718661\pi$
$367$	−170833.			−1.26835			−0.634176	+	0.773189i	$0.718661\pi$
$368$	33829.7	+	1333.31i	0.249806	+	0.00984543i
$369$	108751.			0.798693
$370$	17161.1	−	10205.1i	0.125355	−	0.0745439i
$371$	−12795.6			−0.0929637
$372$		−	134417.i		−	0.971332i
$373$	−126656.			−0.910351			−0.455176	−	0.890402i	$-0.650424\pi$
$373$	−126656.			−0.910351			−0.455176	+	0.890402i	$0.650424\pi$
$374$	73148.5			0.522953
$375$	6481.34	+	167574.i	0.0460895	+	1.19164i
$376$	9279.37			0.0656361
$377$			70752.2i			0.497803i
$378$	−45698.5			−0.319830
$379$		−	125461.i		−	0.873436i	−0.899599	−	0.436718i	$-0.856141\pi$
$379$		−	125461.i		−	0.873436i	0.899599	−	0.436718i	$-0.143859\pi$
$380$	−13661.9	+	8124.23i	−0.0946117	+	0.0562620i
$381$	304175.			2.09543
$382$	−158784.			−1.08813
$383$	85726.1			0.584407			0.292204	−	0.956356i	$-0.405611\pi$
$383$	85726.1			0.584407			0.292204	+	0.956356i	$0.405611\pi$
$384$	−15542.7			−0.105406
$385$	46180.2	−	27461.6i	0.311554	−	0.185269i
$386$	3784.14			0.0253976
$387$	65891.0			0.439951
$388$	95138.0			0.631961
$389$		−	107464.i		−	0.710175i	−0.934833	−	0.355088i	$-0.884451\pi$
$389$		−	107464.i		−	0.710175i	0.934833	−	0.355088i	$-0.115549\pi$
$390$	129982.	−	77295.2i	0.854582	−	0.508187i
$391$	−204571.	−	8062.60i	−1.33810	−	0.0527377i
$392$			30924.4i			0.201247i
$393$			110201.i			0.713513i
$394$	100540.			0.647658
$395$	−71276.8	+	42385.6i	−0.456830	+	0.271659i
$396$			18279.1i			0.116564i
$397$			78875.4i			0.500450i	0.968188	+	0.250225i	$0.0805046\pi$
$397$			78875.4i			0.500450i	−0.968188	+	0.250225i	$0.919495\pi$
$398$	−61767.3			−0.389935
$399$	27432.8			0.172316
$400$	−19100.7	+	35144.9i	−0.119379	+	0.219656i
$401$			317572.i			1.97494i	0.157810	+	0.987470i	$0.449557\pi$
$401$			317572.i			1.97494i	−0.157810	+	0.987470i	$0.550443\pi$
$402$	−189889.			−1.17503
$403$			311951.i			1.92078i
$404$	−49154.3			−0.301161
$405$	−104287.	−	175372.i	−0.635798	−	1.06918i
$406$			32298.2i			0.195941i
$407$		−	18868.8i		−	0.113909i
$408$	93987.8			0.564613
$409$	88147.1			0.526940			0.263470	−	0.964668i	$-0.415133\pi$
$409$	88147.1			0.526940			0.263470	+	0.964668i	$0.415133\pi$
$410$	193304.	−	114950.i	1.14993	−	0.683822i
$411$			66940.6i			0.396283i
$412$	−75178.1			−0.442891
$413$	−13855.7			−0.0812321
$414$	2014.76	−	51120.1i	0.0117550	−	0.298257i
$415$	148774.	+	250183.i	0.863836	+	1.45265i
$416$	36071.1			0.208436
$417$			116615.i			0.670628i
$418$			15021.5i			0.0859725i
$419$			296581.i			1.68933i	0.535294	+	0.844666i	$0.320201\pi$
$419$			296581.i			1.68933i	−0.535294	+	0.844666i	$0.679799\pi$
$420$	59336.4	−	35285.1i	0.336374	−	0.200029i
$421$			232746.i			1.31316i	0.754257	+	0.656580i	$0.227997\pi$
$421$			232746.i			1.31316i	−0.754257	+	0.656580i	$0.772003\pi$
$422$			221610.i			1.24441i
$423$		−	14022.0i		−	0.0783665i
$424$		−	9002.60i		−	0.0500768i
$425$	115503.	−	212524.i	0.639464	−	1.17660i
$426$	143830.			0.792559
$427$			119591.i			0.655907i
$428$	42473.9			0.231864
$429$		−	142917.i		−	0.776547i
$430$	117121.	−	69647.3i	0.633429	−	0.376676i
$431$		−	169053.i		−	0.910054i	−0.890478	−	0.455027i	$-0.849630\pi$
$431$		−	169053.i		−	0.910054i	0.890478	−	0.455027i	$-0.150370\pi$
$432$		−	32152.1i		−	0.172283i
$433$	−3297.51			−0.0175878			−0.00879389	−	0.999961i	$-0.502799\pi$
$433$	−3297.51			−0.0175878			−0.00879389	+	0.999961i	$0.502799\pi$
$434$			142405.i			0.756041i
$435$	−81885.7	+	48694.3i	−0.432742	+	0.257335i
$436$			91757.9i			0.482693i
$437$	1655.70	−	42009.7i	0.00866999	−	0.219982i
$438$		−	228184.i		−	1.18942i
$439$	−129179.			−0.670290			−0.335145	−	0.942167i	$-0.608785\pi$
$439$	−129179.			−0.670290			−0.335145	+	0.942167i	$0.608785\pi$
$440$	19321.1	+	32490.9i	0.0997991	+	0.167825i
$441$	46729.8			0.240279
$442$	−218124.			−1.11650
$443$		−	50576.7i		−	0.257717i	−0.991663	−	0.128859i	$-0.958869\pi$
$443$		−	50576.7i		−	0.257717i	0.991663	−	0.128859i	$-0.0411313\pi$
$444$		−	24244.4i		−	0.122983i
$445$	−198448.	+	118009.i	−1.00213	+	0.595931i
$446$	−126483.			−0.635861
$447$	31455.3			0.157427
$448$	16466.4			0.0820431
$449$	−26833.9			−0.133104			−0.0665521	−	0.997783i	$-0.521200\pi$
$449$	−26833.9			−0.133104			−0.0665521	+	0.997783i	$0.521200\pi$
$450$	53107.4	+	28863.0i	0.262259	+	0.142534i
$451$		−	212540.i		−	1.04493i
$452$	−17613.8			−0.0862137
$453$		−	36824.2i		−	0.179447i
$454$			191646.i			0.929795i
$455$	−137706.	+	81888.7i	−0.665168	+	0.395550i
$456$			19300.9i			0.0928214i
$457$	144882.			0.693719			0.346859	−	0.937917i	$-0.387248\pi$
$457$	144882.			0.693719			0.346859	+	0.937917i	$0.387248\pi$
$458$	−193657.			−0.923213
$459$			194426.i			0.922844i
$460$	−50453.1	−	92995.3i	−0.238436	−	0.439486i
$461$	−42260.4			−0.198853			−0.0994265	−	0.995045i	$-0.531701\pi$
$461$	−42260.4			−0.198853			−0.0994265	+	0.995045i	$0.531701\pi$
$462$		−	65241.0i		−	0.305659i
$463$		−	17285.6i		−	0.0806347i	−0.999187	−	0.0403173i	$-0.987163\pi$
$463$		−	17285.6i		−	0.0806347i	0.999187	−	0.0403173i	$-0.0128369\pi$
$464$	−22724.0			−0.105548
$465$	−361040.	+	214696.i	−1.66974	+	0.992930i
$466$	107069.			0.493053
$467$	56316.2			0.258226			0.129113	−	0.991630i	$-0.458787\pi$
$467$	56316.2			0.258226			0.129113	+	0.991630i	$0.458787\pi$
$468$		−	54507.1i		−	0.248863i
$469$	201174.			0.914590
$470$	−14821.4	−	24924.1i	−0.0670955	−	0.112830i
$471$		−	331982.i		−	1.49649i
$472$		−	9748.43i		−	0.0437573i
$473$		−	128776.i		−	0.575588i
$474$			100696.i			0.448185i
$475$	43642.9	+	23719.2i	0.193431	+	0.105127i
$476$	−99573.3			−0.439470
$477$	−13603.8			−0.0597894
$478$			22256.7i			0.0974102i
$479$		−	423961.i		−	1.84780i	−0.382632	−	0.923901i	$-0.624982\pi$
$479$		−	423961.i		−	1.84780i	0.382632	−	0.923901i	$-0.375018\pi$
$480$	24825.5	+	41747.3i	0.107749	+	0.181195i
$481$			56265.8i			0.243195i
$482$	59281.8			0.255169
$483$	−7191.02	+	182456.i	−0.0308245	+	0.782104i
$484$	−81403.8			−0.347500
$485$	−151959.	−	255538.i	−0.646013	−	1.08636i
$486$	−132661.			−0.561655
$487$			97535.5i			0.411249i	0.978631	+	0.205624i	$0.0659225\pi$
$487$			97535.5i			0.411249i	−0.978631	+	0.205624i	$0.934077\pi$
$488$	−84140.5			−0.353318
$489$	−140286.			−0.586674
$490$	83061.9	−	49393.7i	0.345947	−	0.205721i
$491$	53009.7			0.219884			0.109942	−	0.993938i	$-0.464934\pi$
$491$	53009.7			0.219884			0.109942	+	0.993938i	$0.464934\pi$
$492$		−	273090.i		−	1.12817i
$493$	137414.			0.565374
$494$		−	44793.1i		−	0.183551i
$495$	49097.0	−	29196.1i	0.200376	−	0.119156i
$496$	−100192.			−0.407257
$497$	−152378.			−0.616892
$498$	353446.			1.42516
$499$	288112.			1.15707			0.578536	−	0.815657i	$-0.303624\pi$
$499$	288112.			1.15707			0.578536	+	0.815657i	$0.303624\pi$
$500$	124907.	−	4831.06i	0.499626	−	0.0193243i
$501$	−135929.			−0.541547
$502$	139713.			0.554408
$503$	−93767.2			−0.370608			−0.185304	−	0.982681i	$-0.559327\pi$
$503$	−93767.2			−0.370608			−0.185304	+	0.982681i	$0.559327\pi$
$504$		−	24882.3i		−	0.0979558i
$505$	78511.4	+	132027.i	0.307858	+	0.517703i
$506$	−99907.8	−	3937.60i	−0.390210	−	0.0153791i
$507$			119630.i			0.465397i
$508$		−	226726.i		−	0.878565i
$509$	−416816.			−1.60883			−0.804413	−	0.594071i	$-0.797520\pi$
$509$	−416816.			−1.60883			−0.804413	+	0.594071i	$0.797520\pi$
$510$	−150121.	−	252448.i	−0.577168	−	0.970582i
$511$			241745.i			0.925795i
$512$			11585.2i			0.0441942i
$513$	−39926.4			−0.151714
$514$	125887.			0.476491
$515$	120078.	+	201926.i	0.452739	+	0.761339i
$516$		−	165463.i		−	0.621442i
$517$	−27404.3			−0.102527
$518$			25685.2i			0.0957245i
$519$	−613777.			−2.27864
$520$	−57614.4	−	96886.0i	−0.213071	−	0.358306i
$521$			5565.76i			0.0205045i	0.999947	+	0.0102522i	$0.00326345\pi$
$521$			5565.76i			0.0205045i	−0.999947	+	0.0102522i	$0.996737\pi$
$522$			34338.2i			0.126019i
$523$	−26677.0			−0.0975290			−0.0487645	−	0.998810i	$-0.515528\pi$
$523$	−26677.0			−0.0975290			−0.0487645	+	0.998810i	$0.515528\pi$
$524$	82142.0			0.299159
$525$	−189549.	−	103017.i	−0.687707	−	0.373758i
$526$		−	335140.i		−	1.21131i
$527$	605866.			2.18150
$528$	45901.6			0.164649
$529$	278973.	+	22024.1i	0.996898	+	0.0787023i
$530$	−24180.7	+	14379.3i	−0.0860830	+	0.0511902i
$531$	−14730.8			−0.0522443
$532$		−	20447.9i		−	0.0722480i
$533$			633781.i			2.23092i
$534$			280357.i			0.983171i
$535$	−67841.1	−	114084.i	−0.237020	−	0.398580i
$536$			141540.i			0.492662i
$537$		−	442424.i		−	1.53423i
$538$		−	208939.i		−	0.721862i
$539$		−	91327.5i		−	0.314358i
$540$	−86359.6	+	51354.7i	−0.296158	+	0.176114i
$541$	443860.			1.51653			0.758265	−	0.651946i	$-0.226047\pi$
$541$	443860.			1.51653			0.758265	+	0.651946i	$0.226047\pi$
$542$		−	204845.i		−	0.697311i
$543$	−146339.			−0.496318
$544$		−	70056.7i		−	0.236729i
$545$	246459.	−	146560.i	0.829759	−	0.493426i
$546$			194545.i			0.652581i
$547$			9608.54i			0.0321131i	0.999871	+	0.0160566i	$0.00511119\pi$
$547$			9608.54i			0.0321131i	−0.999871	+	0.0160566i	$0.994889\pi$
$548$	49896.2			0.166152
$549$			127145.i			0.421845i
$550$	56409.2	−	103792.i	0.186477	−	0.343114i
$551$			28218.6i			0.0929465i
$552$	−128371.	−	5059.38i	−0.421296	−	0.0166042i
$553$		−	106681.i		−	0.348847i
$554$	20949.4			0.0682579
$555$	−65119.7	+	38724.2i	−0.211410	+	0.125718i
$556$	86922.5			0.281179
$557$	−244474.			−0.787994			−0.393997	−	0.919112i	$-0.628908\pi$
$557$	−244474.			−0.787994			−0.393997	+	0.919112i	$0.628908\pi$
$558$			151400.i			0.486247i
$559$			384002.i			1.22888i
$560$	−26300.8	−	44228.2i	−0.0838674	−	0.141034i
$561$	−277570.			−0.881955
$562$	−340378.			−1.07768
$563$	−334688.			−1.05590			−0.527951	−	0.849275i	$-0.677040\pi$
$563$	−334688.			−1.05590			−0.527951	+	0.849275i	$0.677040\pi$
$564$	−35211.5			−0.110695
$565$	28133.5	+	47310.1i	0.0881307	+	0.148203i
$566$		−	44484.0i		−	0.138858i
$567$	262480.			0.816451
$568$		−	107208.i		−	0.332301i
$569$		−	395133.i		−	1.22045i	−0.792230	−	0.610223i	$-0.791080\pi$
$569$		−	395133.i		−	1.22045i	0.792230	−	0.610223i	$-0.208920\pi$
$570$	51841.7	−	30828.2i	0.159562	−	0.0948853i
$571$		−	596354.i		−	1.82908i	−0.404499	−	0.914539i	$-0.632554\pi$
$571$		−	596354.i		−	1.82908i	0.404499	−	0.914539i	$-0.367446\pi$
$572$	−106527.			−0.325588
$573$	602522.			1.83512
$574$			289320.i			0.878120i
$575$	−169197.	+	284052.i	−0.511748	+	0.859135i
$576$	17506.4			0.0527659
$577$		−	398331.i		−	1.19645i	−0.801330	−	0.598223i	$-0.795874\pi$
$577$		−	398331.i		−	1.19645i	0.801330	−	0.598223i	$-0.204126\pi$
$578$			187404.i			0.560950i
$579$	−14359.3			−0.0428328
$580$	36295.8	+	61036.0i	0.107895	+	0.181439i
$581$	−374450.			−1.10928
$582$	−361011.			−1.06580
$583$			26587.0i			0.0782225i
$584$	−170084.			−0.498698
$585$	−146404.	+	87061.0i	−0.427802	+	0.254397i
$586$		−	419681.i		−	1.22215i
$587$			29338.2i			0.0851445i	0.999093	+	0.0425723i	$0.0135553\pi$
$587$			29338.2i			0.0851445i	−0.999093	+	0.0425723i	$0.986445\pi$
$588$		−	117346.i		−	0.339401i
$589$			124418.i			0.358635i
$590$	−26184.0	+	15570.6i	−0.0752198	+	0.0447303i
$591$	−381509.			−1.09227
$592$	−18071.3			−0.0515639
$593$			225414.i			0.641019i	0.947245	+	0.320510i	$0.103854\pi$
$593$			225414.i			0.641019i	−0.947245	+	0.320510i	$0.896146\pi$
$594$			94953.3i			0.269115i
$595$	159043.	+	267451.i	0.449242	+	0.755458i
$596$		−	23446.2i		−	0.0660055i
$597$	234383.			0.657623
$598$	297919.	+	11741.7i	0.833098	+	0.0328343i
$599$	−379816.			−1.05857			−0.529285	−	0.848444i	$-0.677540\pi$
$599$	−379816.			−1.05857			−0.529285	+	0.848444i	$0.677540\pi$
$600$	72479.6	−	133361.i	0.201332	−	0.370447i
$601$	−485961.			−1.34540			−0.672701	−	0.739914i	$-0.734866\pi$
$601$	−485961.			−1.34540			−0.672701	+	0.739914i	$0.734866\pi$
$602$			175296.i			0.483703i
$603$	213881.			0.588217
$604$	−27448.1			−0.0752381
$605$	130022.	+	218648.i	0.355226	+	0.597359i
$606$	186521.			0.507906
$607$			634822.i			1.72296i	0.507794	+	0.861479i	$0.330461\pi$
$607$			634822.i			1.72296i	−0.507794	+	0.861479i	$0.669539\pi$
$608$	14386.5			0.0389178
$609$		−	122559.i		−	0.330453i
$610$	134393.	+	225999.i	0.361174	+	0.607360i
$611$	81718.1			0.218895
$612$	−105863.			−0.282644
$613$	−368112.			−0.979623			−0.489811	−	0.871828i	$-0.662934\pi$
$613$	−368112.			−0.979623			−0.489811	+	0.871828i	$0.662934\pi$
$614$	50252.2			0.133296
$615$	−733513.	+	436192.i	−1.93935	+	1.15326i
$616$	−48629.4			−0.128156
$617$	214378.			0.563131			0.281565	−	0.959542i	$-0.409146\pi$
$617$	214378.			0.563131			0.281565	+	0.959542i	$0.409146\pi$
$618$	285271.			0.746932
$619$			131041.i			0.342001i	0.985271	+	0.171000i	$0.0546999\pi$
$619$			131041.i			0.342001i	−0.985271	+	0.171000i	$0.945300\pi$
$620$	160031.	+	269112.i	0.416313	+	0.700083i
$621$	10466.0	−	265551.i	0.0271392	−	0.688596i
$622$		−	225443.i		−	0.582714i
$623$		−	297018.i		−	0.765256i
$624$	−136876.			−0.351526
$625$	−212482.	−	327779.i	−0.543955	−	0.839115i
$626$		−	413364.i		−	1.05483i
$627$		−	57000.5i		−	0.144992i
$628$	−247453.			−0.627443
$629$	109278.			0.276206
$630$	−66833.2	+	39743.2i	−0.168388	+	0.100134i
$631$		−	712608.i		−	1.78975i	−0.446319	−	0.894874i	$-0.647265\pi$
$631$		−	712608.i		−	1.78975i	0.446319	−	0.894874i	$-0.352735\pi$
$632$	75057.2			0.187913
$633$		−	840922.i		−	2.09869i
$634$	240135.			0.597415
$635$	−608979.	+	362137.i	−1.51027	+	0.898100i
$636$			34161.3i			0.0844540i
$637$			272333.i			0.671153i
$638$	67109.8			0.164871
$639$	−162003.			−0.396753
$640$	31117.6	−	18504.4i	0.0759707	−	0.0451769i
$641$			345839.i			0.841701i	0.907130	+	0.420850i	$0.138268\pi$
$641$			345839.i			0.841701i	−0.907130	+	0.420850i	$0.861732\pi$
$642$	−161172.			−0.391037
$643$	−123844.			−0.299538			−0.149769	−	0.988721i	$-0.547853\pi$
$643$	−123844.			−0.299538			−0.149769	+	0.988721i	$0.547853\pi$
$644$	135999.	+	5360.05i	0.327918	+	0.0129240i
$645$	−444428.	+	264284.i	−1.06827	+	0.635260i
$646$	−86996.3			−0.208466
$647$		−	662039.i		−	1.58152i	−0.612125	−	0.790761i	$-0.709685\pi$
$647$		−	662039.i		−	1.58152i	0.612125	−	0.790761i	$-0.290315\pi$
$648$			184673.i			0.439798i
$649$			28789.6i			0.0683512i
$650$	−168209.	+	309501.i	−0.398127	+	0.732547i
$651$		−	540371.i		−	1.27506i
$652$			104567.i			0.245979i
$653$		−	751409.i		−	1.76218i	−0.472949	−	0.881090i	$-0.656810\pi$
$653$		−	751409.i		−	1.76218i	0.472949	−	0.881090i	$-0.343190\pi$
$654$		−	348185.i		−	0.814057i
$655$	−131201.	−	220631.i	−0.305811	−	0.514261i
$656$	−203556.			−0.473017
$657$			257014.i			0.595423i
$658$	37304.1			0.0861598
$659$			404740.i			0.931977i	0.884791	+	0.465988i	$0.154301\pi$
$659$			404740.i			0.931977i	−0.884791	+	0.465988i	$0.845699\pi$
$660$	−73316.0	−	123290.i	−0.168310	−	0.283036i
$661$			234287.i			0.536223i	0.963388	+	0.268112i	$0.0863996\pi$
$661$			234287.i			0.536223i	−0.963388	+	0.268112i	$0.913600\pi$
$662$			16811.1i			0.0383602i
$663$	827697.			1.88297
$664$		−	263452.i		−	0.597537i
$665$	−54922.5	+	32660.3i	−0.124196	+	0.0738545i
$666$			27307.5i			0.0615650i
$667$	−187682.	−	7397.00i	−0.421864	−	0.0166266i
$668$			101319.i			0.227058i
$669$	479953.			1.07237
$670$	380172.	−	226074.i	0.846897	−	0.503617i
$671$	248488.			0.551901
$672$	−62483.4			−0.138365
$673$			36682.1i			0.0809887i	0.999180	+	0.0404944i	$0.0128933\pi$
$673$			36682.1i			0.0809887i	−0.999180	+	0.0404944i	$0.987107\pi$
$674$			295530.i			0.650551i
$675$	275874.	+	149933.i	0.605486	+	0.329072i
$676$	89169.8			0.195130
$677$	406291.			0.886462			0.443231	−	0.896407i	$-0.353832\pi$
$677$	406291.			0.886462			0.443231	+	0.896407i	$0.353832\pi$
$678$	66837.4			0.145399
$679$	382465.			0.829569
$680$	−188170.	+	111898.i	−0.406943	+	0.241993i
$681$		−	727219.i		−	1.56809i
$682$	295892.			0.636157
$683$			451959.i			0.968853i	0.874832	+	0.484427i	$0.160972\pi$
$683$			451959.i			0.968853i	−0.874832	+	0.484427i	$0.839028\pi$
$684$		−	21739.5i		−	0.0464662i
$685$	−79696.4	−	134020.i	−0.169847	−	0.285620i
$686$			342726.i			0.728280i
$687$	734851.			1.55699
$688$	−123333.			−0.260556
$689$		−	79280.7i		−	0.167005i
$690$	191450.	+	352881.i	0.402121	+	0.741190i
$691$	917669.			1.92190			0.960948	−	0.276729i	$-0.0892504\pi$
$691$	917669.			1.92190			0.960948	+	0.276729i	$0.0892504\pi$
$692$			457498.i			0.955381i
$693$			73483.9i			0.153012i
$694$	−461892.			−0.959006
$695$	−138836.	−	233471.i	−0.287431	−	0.483352i
$696$	86228.7			0.178005
$697$	1.23092e6			2.53375
$698$		−	67207.5i		−	0.137945i
$699$	−406286.			−0.831529
$700$	−76786.9	+	141286.i	−0.156708	+	0.288340i
$701$		−	258920.i		−	0.526902i	−0.964673	−	0.263451i	$-0.915139\pi$
$701$		−	258920.i		−	0.526902i	0.964673	−	0.263451i	$-0.0848608\pi$
$702$		−	283145.i		−	0.574559i
$703$			22440.9i			0.0454077i
$704$		−	34214.2i		−	0.0690336i
$705$	56241.4	+	94577.2i	0.113156	+	0.190287i
$706$	432864.			0.868444
$707$	−197606.			−0.395331
$708$			36991.4i			0.0737963i
$709$			835627.i			1.66234i	0.556017	+	0.831171i	$0.312329\pi$
$709$			835627.i			1.66234i	−0.556017	+	0.831171i	$0.687671\pi$
$710$	−287959.	+	171238.i	−0.571233	+	0.339690i
$711$		−	113419.i		−	0.224360i
$712$	208973.			0.412221
$713$	−827505.	−	32613.9i	−1.62776	−	0.0641539i
$714$	377841.			0.741162
$715$	170150.	+	286129.i	0.332828	+	0.559693i
$716$	−329774.			−0.643266
$717$		−	84455.3i		−	0.164282i
$718$	−304702.			−0.591054
$719$	223269.			0.431888			0.215944	−	0.976406i	$-0.430717\pi$
$719$	223269.			0.431888			0.215944	+	0.976406i	$0.430717\pi$
$720$	−27962.1	−	47021.8i	−0.0539391	−	0.0907056i
$721$	−302224.			−0.581379
$722$			350738.i			0.672835i
$723$	−224951.			−0.430340
$724$			109078.i			0.208095i
$725$	105968.	−	194979.i	0.201603	−	0.370947i
$726$	308896.			0.586055
$727$	−491038.			−0.929065			−0.464532	−	0.885556i	$-0.653778\pi$
$727$	−491038.			−0.929065			−0.464532	+	0.885556i	$0.653778\pi$
$728$	145010.			0.273612
$729$	−157684.			−0.296710
$730$	271666.	+	456841.i	0.509787	+	0.857273i
$731$	745801.			1.39569
$732$	319280.			0.595867
$733$	636651.			1.18493			0.592467	−	0.805595i	$-0.298154\pi$
$733$	636651.			1.18493			0.592467	+	0.805595i	$0.298154\pi$
$734$		−	483189.i		−	0.896861i
$735$	−315187.	+	187430.i	−0.583437	+	0.346948i
$736$	−3771.16	+	95684.9i	−0.00696177	+	0.176640i
$737$		−	418004.i		−	0.769565i
$738$			307594.i			0.564761i
$739$	531381.			0.973010			0.486505	−	0.873678i	$-0.338272\pi$
$739$	531381.			0.973010			0.486505	+	0.873678i	$0.338272\pi$
$740$	28864.3	+	48539.0i	0.0527105	+	0.0886395i
$741$			169972.i			0.309557i
$742$		−	36191.5i		−	0.0657352i
$743$	150462.			0.272551			0.136276	−	0.990671i	$-0.456487\pi$
$743$	150462.			0.272551			0.136276	+	0.990671i	$0.456487\pi$
$744$	380188.			0.686835
$745$	−62975.8	+	37449.3i	−0.113465	+	0.0674732i
$746$		−	358238.i		−	0.643716i
$747$	−398102.			−0.713433
$748$			206895.i			0.369783i
$749$	170750.			0.304366
$750$	−473971.	+	18332.0i	−0.842616	+	0.0325902i
$751$		−	830944.i		−	1.47330i	−0.676273	−	0.736651i	$-0.736406\pi$
$751$		−	830944.i		−	1.47330i	0.676273	−	0.736651i	$-0.263594\pi$
$752$			26246.0i			0.0464117i
$753$	−530156.			−0.935004
$754$	−200117.			−0.352000
$755$	43841.2	+	73724.7i	0.0769111	+	0.129336i
$756$		−	129255.i		−	0.226154i
$757$	−395848.			−0.690776			−0.345388	−	0.938460i	$-0.612253\pi$
$757$	−395848.			−0.690776			−0.345388	+	0.938460i	$0.612253\pi$
$758$	354858.			0.617612
$759$	379111.	+	14941.6i	0.658086	+	0.0259367i
$760$	−22978.8	−	38641.8i	−0.0397832	−	0.0669006i
$761$	961763.			1.66073			0.830365	−	0.557221i	$-0.188132\pi$
$761$	961763.			1.66073			0.830365	+	0.557221i	$0.188132\pi$
$762$			860336.i			1.48169i
$763$			368877.i			0.633626i
$764$		−	449108.i		−	0.769422i
$765$	169088.	+	284344.i	0.288929	+	0.485871i
$766$			242470.i			0.413238i
$767$		−	85848.8i		−	0.145930i
$768$		−	43961.4i		−	0.0745331i
$769$		−	675366.i		−	1.14205i	−0.820931	−	0.571027i	$-0.806545\pi$
$769$		−	675366.i		−	1.14205i	0.820931	−	0.571027i	$-0.193455\pi$
$770$	77673.0	+	130617.i	0.131005	+	0.220302i
$771$	−477692.			−0.803598
$772$			10703.2i			0.0179588i
$773$	−895069.			−1.49795			−0.748975	−	0.662598i	$-0.769454\pi$
$773$	−895069.			−1.49795			−0.748975	+	0.662598i	$0.769454\pi$
$774$			186368.i			0.311092i
$775$	467219.	−	859675.i	0.777889	−	1.43130i
$776$			269091.i			0.446864i
$777$		−	97465.1i		−	0.161439i
$778$	303955.			0.502170
$779$			252776.i			0.416544i
$780$	218624.	+	367644.i	0.359342	+	0.604280i
$781$			316614.i			0.519072i
$782$	22804.5	−	578613.i	0.0372912	−	0.946182i
$783$			178375.i			0.290945i
$784$	−87467.3			−0.142303
$785$	395243.	+	664653.i	0.641394	+	1.07859i
$786$	−311697.			−0.504530
$787$	216173.			0.349021			0.174510	−	0.984655i	$-0.444166\pi$
$787$	216173.			0.349021			0.174510	+	0.984655i	$0.444166\pi$
$788$			284370.i			0.457964i
$789$			1.27173e6i			2.04286i
$790$	−119885.	−	201601.i	−0.192092	−	0.323027i
$791$	−70809.4			−0.113172
$792$	−51701.0			−0.0824230
$793$	−740977.			−1.17831
$794$	−223093.			−0.353872
$795$	91756.3	−	54563.9i	0.145178	−	0.0863319i
$796$		−	174704.i		−	0.275726i
$797$	169900.			0.267472			0.133736	−	0.991017i	$-0.457303\pi$
$797$	169900.			0.267472			0.133736	+	0.991017i	$0.457303\pi$
$798$			77591.8i			0.121846i
$799$		−	158711.i		−	0.248608i
$800$	−99404.8	−	54024.9i	−0.155320	−	0.0844139i
$801$		−	315779.i		−	0.492173i
$802$	−898230.			−1.39649
$803$	502302.			0.778993
$804$		−	537088.i		−	0.830871i
$805$	−202827.	−	373852.i	−0.312993	−	0.576909i
$806$	−882331.			−1.35819
$807$			792840.i			1.21741i
$808$		−	139029.i		−	0.212953i
$809$	−86864.2			−0.132722			−0.0663612	−	0.997796i	$-0.521139\pi$
$809$	−86864.2			−0.132722			−0.0663612	+	0.997796i	$0.521139\pi$
$810$	496026.	−	294967.i	0.756022	−	0.449577i
$811$	301777.			0.458823			0.229411	−	0.973330i	$-0.426320\pi$
$811$	301777.			0.458823			0.229411	+	0.973330i	$0.426320\pi$
$812$	−91353.1			−0.138551
$813$			777306.i			1.17601i
$814$	53369.2			0.0805456
$815$	280863.	−	167018.i	0.422843	−	0.251448i
$816$			265838.i			0.399242i
$817$			153154.i			0.229448i
$818$			249318.i			0.372603i
$819$		−	219125.i		−	0.326681i
$820$	325129.	+	546746.i	0.483535	+	0.813127i
$821$	−274319.			−0.406977			−0.203488	−	0.979077i	$-0.565228\pi$
$821$	−274319.			−0.406977			−0.203488	+	0.979077i	$0.565228\pi$
$822$	−189337.			−0.280215
$823$			44819.1i			0.0661704i	0.999453	+	0.0330852i	$0.0105333\pi$
$823$			44819.1i			0.0661704i	−0.999453	+	0.0330852i	$0.989467\pi$
$824$		−	212636.i		−	0.313171i
$825$	−214051.	+	393849.i	−0.314491	+	0.578658i
$826$		−	39189.8i		−	0.0574398i
$827$	532530.			0.778633			0.389317	−	0.921104i	$-0.372711\pi$
$827$	532530.			0.778633			0.389317	+	0.921104i	$0.372711\pi$
$828$	144589.	+	5698.60i	0.210900	+	0.00831204i
$829$	253495.			0.368859			0.184429	−	0.982846i	$-0.440956\pi$
$829$	253495.			0.368859			0.184429	+	0.982846i	$0.440956\pi$
$830$	−707624.	+	420797.i	−1.02718	+	0.610824i
$831$	−79494.9			−0.115116
$832$			102025.i			0.147387i
$833$	528921.			0.762255
$834$	−329837.			−0.474206
$835$	272139.	−	161831.i	0.390317	−	0.232107i
$836$	−42487.1			−0.0607917
$837$			786468.i			1.12261i
$838$	−838857.			−1.19454
$839$			31149.2i			0.0442510i	0.999755	+	0.0221255i	$0.00704334\pi$
$839$			31149.2i			0.0442510i	−0.999755	+	0.0221255i	$0.992957\pi$
$840$	99801.2	+	167829.i	0.141442	+	0.237852i
$841$	−581211.			−0.821755
$842$	−658304.			−0.928544
$843$	1.29160e6			1.81749
$844$	−626807.			−0.879932
$845$	−142426.	−	239507.i	−0.199469	−	0.335433i
$846$	39660.3			0.0554135
$847$	−327253.			−0.456159
$848$	25463.2			0.0354096
$849$			168799.i			0.234183i
$850$	601107.	+	326692.i	0.831982	+	0.452169i
$851$	−149255.	−	5882.47i	−0.206096	−	0.00812270i
$852$			406814.i			0.560424i
$853$		−	637748.i		−	0.876499i	−0.898853	−	0.438249i	$-0.855599\pi$
$853$		−	637748.i		−	0.876499i	0.898853	−	0.438249i	$-0.144401\pi$
$854$	−338254.			−0.463796
$855$	−58391.6	+	34723.2i	−0.0798763	+	0.0474994i
$856$			120134.i			0.163953i
$857$		−	308606.i		−	0.420186i	−0.977681	−	0.210093i	$-0.932623\pi$
$857$		−	308606.i		−	0.420186i	0.977681	−	0.210093i	$-0.0673768\pi$
$858$	404229.			0.549102
$859$	353332.			0.478847			0.239423	−	0.970915i	$-0.423042\pi$
$859$	353332.			0.478847			0.239423	+	0.970915i	$0.423042\pi$
$860$	196992.	+	331268.i	0.266350	+	0.447902i
$861$		−	1.09785e6i		−	1.48094i
$862$	478153.			0.643505
$863$		−	386287.i		−	0.518667i	−0.965788	−	0.259334i	$-0.916497\pi$
$863$		−	386287.i		−	0.518667i	0.965788	−	0.259334i	$-0.0835029\pi$
$864$	90939.8			0.121822
$865$	1.22883e6	−	730735.i	1.64232	−	0.976625i
$866$		−	9326.78i		−	0.0124364i
$867$		−	711126.i		−	0.946037i
$868$	−402782.			−0.534602
$869$	−221663.			−0.293531
$870$	−137728.	−	231608.i	−0.181963	−	0.305995i
$871$			1.24646e6i			1.64302i
$872$	−259531.			−0.341315
$873$	406623.			0.533536
$874$	118821.	+	4683.02i	0.155551	+	0.00613061i
$875$	502139.	−	19421.4i	0.655855	−	0.0253668i
$876$	645402.			0.841050
$877$			383881.i			0.499111i	0.968361	+	0.249555i	$0.0802845\pi$
$877$			383881.i			0.499111i	−0.968361	+	0.249555i	$0.919716\pi$
$878$		−	365373.i		−	0.473966i
$879$			1.59252e6i			2.06114i
$880$	−91898.2	+	54648.3i	−0.118670	+	0.0705686i
$881$			317561.i			0.409143i	0.978852	+	0.204572i	$0.0655802\pi$
$881$			317561.i			0.409143i	−0.978852	+	0.204572i	$0.934420\pi$
$882$			132172.i			0.169903i
$883$		−	142062.i		−	0.182203i	−0.995842	−	0.0911016i	$-0.970961\pi$
$883$		−	142062.i		−	0.182203i	0.995842	−	0.0911016i	$-0.0290388\pi$
$884$		−	616949.i		−	0.789487i
$885$	99357.9	−	59084.3i	0.126857	−	0.0754372i
$886$	143053.			0.182234
$887$		−	309038.i		−	0.392794i	−0.980524	−	0.196397i	$-0.937076\pi$
$887$		−	309038.i		−	0.392794i	0.980524	−	0.196397i	$-0.0629241\pi$
$888$	68573.5			0.0869621
$889$		−	911464.i		−	1.15328i
$890$	−333780.	−	561295.i	−0.421387	−	0.708616i
$891$		−	545386.i		−	0.686987i
$892$		−	357748.i		−	0.449622i
$893$	32592.2			0.0408706
$894$			88969.1i			0.111318i
$895$	526729.	+	885764.i	0.657569	+	1.10579i
$896$			46574.0i			0.0580132i
$897$	−1.13049e6	−	44555.0i	−1.40501	−	0.0553748i
$898$		−	75897.8i		−	0.0941189i
$899$	555849.			0.687761
$900$	−81637.0	+	150211.i	−0.100786	+	0.185445i
$901$	−153978.			−0.189674
$902$	601154.			0.738878
$903$		−	665178.i		−	0.815760i
$904$		−	49819.3i		−	0.0609623i
$905$	292981.	−	174225.i	0.357719	−	0.212722i
$906$	104155.			0.126888
$907$	−1.01343e6			−1.23191			−0.615957	−	0.787780i	$-0.711230\pi$
$907$	−1.01343e6			−1.23191			−0.615957	+	0.787780i	$0.711230\pi$
$908$	−542055.			−0.657464
$909$	−210087.			−0.254257
$910$	−231616.	−	389493.i	−0.279696	−	0.470345i
$911$			72313.2i			0.0871327i	0.999051	+	0.0435663i	$0.0138720\pi$
$911$			72313.2i			0.0871327i	−0.999051	+	0.0435663i	$0.986128\pi$
$912$	−54591.2			−0.0656346
$913$			778040.i			0.933385i
$914$			409789.i			0.490533i
$915$	−509968.	−	857577.i	−0.609117	−	1.02431i
$916$		−	547744.i		−	0.652810i
$917$	330220.			0.392704
$918$	−549919.			−0.652550
$919$		−	1.24532e6i		−	1.47451i	−0.675612	−	0.737257i	$-0.736121\pi$
$919$		−	1.24532e6i		−	1.47451i	0.675612	−	0.737257i	$-0.263879\pi$
$920$	263030.	−	142703.i	0.310764	−	0.168600i
$921$	−190687.			−0.224803
$922$		−	119531.i		−	0.140610i
$923$		−	944123.i		−	1.10822i
$924$	184530.			0.216133
$925$	84271.0	−	155057.i	0.0984906	−	0.181221i
$926$	48891.0			0.0570173
$927$	−321314.			−0.373913
$928$		−	64273.2i		−	0.0746335i
$929$	1.03519e6			1.19946			0.599732	−	0.800201i	$-0.295274\pi$
$929$	1.03519e6			1.19946			0.599732	+	0.800201i	$0.295274\pi$
$930$	−607253.	−	1.02117e6i	−0.702108	−	1.18068i
$931$			108617.i			0.125313i
$932$			302838.i			0.348641i
$933$			855466.i			0.982742i
$934$			159286.i			0.182593i
$935$	555715.	−	330462.i	0.635666	−	0.378006i
$936$	154169.			0.175973
$937$	−1.05503e6			−1.20167			−0.600836	−	0.799372i	$-0.705166\pi$
$937$	−1.05503e6			−1.20167			−0.600836	+	0.799372i	$0.705166\pi$
$938$			569006.i			0.646713i
$939$			1.56855e6i			1.77897i
$940$	70496.0	−	41921.3i	0.0797827	−	0.0474437i
$941$			768131.i			0.867474i	0.901040	+	0.433737i	$0.142805\pi$
$941$			768131.i			0.867474i	−0.901040	+	0.433737i	$0.857195\pi$
$942$	938988.			1.05818
$943$	−1.68121e6	−	66260.5i	−1.89060	−	0.0745129i
$944$	27572.7			0.0309411
$945$	−347175.	+	206452.i	−0.388763	+	0.231182i
$946$	364233.			0.407002
$947$		−	1.52362e6i		−	1.69893i	−0.527643	−	0.849466i	$-0.676924\pi$
$947$		−	1.52362e6i		−	1.69893i	0.527643	−	0.849466i	$-0.323076\pi$
$948$	−284812.			−0.316915
$949$	−1.49783e6			−1.66315
$950$	−67088.0	+	123441.i	−0.0743357	+	0.136776i
$951$	−911216.			−1.00754
$952$		−	281636.i		−	0.310752i
$953$	−291650.			−0.321126			−0.160563	−	0.987026i	$-0.551331\pi$
$953$	−291650.			−0.321126			−0.160563	+	0.987026i	$0.551331\pi$
$954$		−	38477.4i		−	0.0422775i
$955$	−1.20629e6	+	717335.i	−1.32265	+	0.786531i
$956$	−62951.4			−0.0688794
$957$	−254655.			−0.278054
$958$	1.19914e6			1.30659
$959$	200588.			0.218107
$960$	−118079.	+	70217.1i	−0.128124	+	0.0761904i
$961$	1.52726e6			1.65373
$962$	−159144.			−0.171965
$963$	181535.			0.195752
$964$			167674.i			0.180432i
$965$	28748.4	−	17095.6i	0.0308716	−	0.0183581i
$966$	−516064.	−	20339.3i	−0.553031	−	0.0217962i
$967$		−	1.25256e6i		−	1.33950i	−0.742585	−	0.669752i	$-0.766400\pi$
$967$		−	1.25256e6i		−	1.33950i	0.742585	−	0.669752i	$-0.233600\pi$
$968$		−	230245.i		−	0.245719i
$969$	330117.			0.351576
$970$	722770.	−	429804.i	0.768169	−	0.456800i
$971$		−	1.12149e6i		−	1.18947i	−0.803920	−	0.594737i	$-0.797256\pi$
$971$		−	1.12149e6i		−	1.18947i	0.803920	−	0.594737i	$-0.202744\pi$
$972$		−	375221.i		−	0.397150i
$973$	349438.			0.369100
$974$	−275872.			−0.290797
$975$	638286.	−	1.17443e6i	0.671438	−	1.23543i
$976$		−	237985.i		−	0.249833i
$977$	−101445.			−0.106278			−0.0531388	−	0.998587i	$-0.516923\pi$
$977$	−101445.			−0.106278			−0.0531388	+	0.998587i	$0.516923\pi$
$978$		−	396789.i		−	0.414841i
$979$	−617150.			−0.643910
$980$	139707.	+	234935.i	0.145467	+	0.244622i
$981$			392177.i			0.407515i
$982$			149934.i			0.155481i
$983$	231278.			0.239347			0.119673	−	0.992813i	$-0.461815\pi$
$983$	231278.			0.239347			0.119673	+	0.992813i	$0.461815\pi$
$984$	772416.			0.797739
$985$	763809.	−	454208.i	0.787249	−	0.468147i
$986$			388664.i			0.399780i
$987$	−141554.			−0.145308
$988$	126694.			0.129790
$989$	−1.01863e6	−	40146.6i	−1.04142	−	0.0410446i
$990$	82579.1	+	138867.i	0.0842558	+	0.141687i
$991$	−1.03663e6			−1.05555			−0.527773	−	0.849385i	$-0.676973\pi$
$991$	−1.03663e6			−1.05555			−0.527773	+	0.849385i	$0.676973\pi$
$992$		−	283385.i		−	0.287974i
$993$		−	63791.7i		−	0.0646942i
$994$		−	430990.i		−	0.436209i
$995$	−469251.	+	279045.i	−0.473979	+	0.281857i
$996$			999696.i			1.00774i
$997$		−	483408.i		−	0.486322i	−0.969986	−	0.243161i	$-0.921816\pi$
$997$		−	483408.i		−	0.486322i	0.969986	−	0.243161i	$-0.0781843\pi$
$998$			814904.i			0.818173i
$999$			141853.i			0.142137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.c.a.229.14	yes	48
5.4	even	2	inner	230.5.c.a.229.35	yes	48
23.22	odd	2	inner	230.5.c.a.229.36	yes	48
115.114	odd	2	inner	230.5.c.a.229.13	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.c.a.229.13	✓	48	115.114	odd	2	inner
230.5.c.a.229.14	yes	48	1.1	even	1	trivial
230.5.c.a.229.35	yes	48	5.4	even	2	inner
230.5.c.a.229.36	yes	48	23.22	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.82843i q^{2} -10.7328i q^{3} -8.00000 q^{4} +(12.7779 + 21.4878i) q^{5} +30.3568 q^{6} -32.1609 q^{7} -22.6274i q^{8} -34.1923 q^{9} +O(q^{10})\)	\(q+2.82843i q^{2} -10.7328i q^{3} -8.00000 q^{4} +(12.7779 + 21.4878i) q^{5} +30.3568 q^{6} -32.1609 q^{7} -22.6274i q^{8} -34.1923 q^{9} +(-60.7766 + 36.1415i) q^{10} +66.8245i q^{11} +85.8621i q^{12} -199.267i q^{13} -90.9648i q^{14} +(230.623 - 137.143i) q^{15} +64.0000 q^{16} -387.012 q^{17} -96.7104i q^{18} -79.4751i q^{19} +(-102.224 - 171.902i) q^{20} +345.175i q^{21} -189.008 q^{22} +(528.590 + 20.8329i) q^{23} -242.855 q^{24} +(-298.448 + 549.139i) q^{25} +563.611 q^{26} -502.376i q^{27} +257.287 q^{28} -355.063 q^{29} +(387.898 + 652.301i) q^{30} -1565.50 q^{31} +181.019i q^{32} +717.212 q^{33} -1094.64i q^{34} +(-410.950 - 691.066i) q^{35} +273.538 q^{36} -282.364 q^{37} +224.789 q^{38} -2138.68 q^{39} +(486.213 - 289.132i) q^{40} -3180.57 q^{41} -976.304 q^{42} -1927.07 q^{43} -534.596i q^{44} +(-436.907 - 734.716i) q^{45} +(-58.9244 + 1495.08i) q^{46} +410.094i q^{47} -686.897i q^{48} -1366.68 q^{49} +(-1553.20 - 844.139i) q^{50} +4153.71i q^{51} +1594.13i q^{52} +397.862 q^{53} +1420.93 q^{54} +(-1435.91 + 853.880i) q^{55} +727.718i q^{56} -852.987 q^{57} -1004.27i q^{58} +430.824 q^{59} +(-1844.99 + 1097.14i) q^{60} -3718.52i q^{61} -4427.89i q^{62} +1099.65 q^{63} -512.000 q^{64} +(4281.80 - 2546.22i) q^{65} +2028.58i q^{66} -6255.24 q^{67} +3096.10 q^{68} +(223.595 - 5673.23i) q^{69} +(1954.63 - 1162.34i) q^{70} +4737.99 q^{71} +773.683i q^{72} -7516.72i q^{73} -798.646i q^{74} +(5893.78 + 3203.18i) q^{75} +635.801i q^{76} -2149.14i q^{77} -6049.11i q^{78} +3317.09i q^{79} +(817.789 + 1375.22i) q^{80} -8161.46 q^{81} -8996.00i q^{82} +11643.0 q^{83} -2761.40i q^{84} +(-4945.22 - 8316.03i) q^{85} -5450.59i q^{86} +3810.81i q^{87} +1512.07 q^{88} +9235.38i q^{89} +(2078.09 - 1235.76i) q^{90} +6408.60i q^{91} +(-4228.72 - 166.663i) q^{92} +16802.1i q^{93} -1159.92 q^{94} +(1707.74 - 1015.53i) q^{95} +1942.84 q^{96} -11892.2 q^{97} -3865.55i q^{98} -2284.88i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9}+O(q^{10}) \) 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9	\( 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9} + 3072 q^{16} + 512 q^{24} + 1488 q^{25} - 384 q^{26} - 2940 q^{29} + 4732 q^{31} + 2556 q^{35} + 12864 q^{36} + 2736 q^{39} + 828 q^{41} - 64 q^{46} + 32572 q^{49} - 3264 q^{50} + 10112 q^{54} + 12824 q^{55} + 7092 q^{59} - 24576 q^{64} + 14000 q^{69} - 6592 q^{70} - 12708 q^{71} + 24728 q^{75} - 13040 q^{81} - 15700 q^{85} - 9728 q^{94} - 46608 q^{95} - 4096 q^{96}+O(q^{100}) \) 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9 + 3072 * q^16 + 512 * q^24 + 1488 * q^25 - 384 * q^26 - 2940 * q^29 + 4732 * q^31 + 2556 * q^35 + 12864 * q^36 + 2736 * q^39 + 828 * q^41 - 64 * q^46 + 32572 * q^49 - 3264 * q^50 + 10112 * q^54 + 12824 * q^55 + 7092 * q^59 - 24576 * q^64 + 14000 * q^69 - 6592 * q^70 - 12708 * q^71 + 24728 * q^75 - 13040 * q^81 - 15700 * q^85 - 9728 * q^94 - 46608 * q^95 - 4096 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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