LMFDB - Embedded newform 201.4.d.b.200.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(200,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("201.200");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.d (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:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			200.16
Character	$\chi$	$=$	201.200
Dual form			201.4.d.b.200.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.40522 q^{2} +(-5.19596 + 0.0441335i) q^{3} +3.59552 q^{4} -14.7776 q^{5} +(17.6934 - 0.150284i) q^{6} -33.3251i q^{7} +14.9982 q^{8} +(26.9961 - 0.458632i) q^{9} +O(q^{10})$	\(q-3.40522 q^{2} +(-5.19596 + 0.0441335i) q^{3} +3.59552 q^{4} -14.7776 q^{5} +(17.6934 - 0.150284i) q^{6} -33.3251i q^{7} +14.9982 q^{8} +(26.9961 - 0.458632i) q^{9} +50.3210 q^{10} +23.6977 q^{11} +(-18.6822 + 0.158683i) q^{12} -8.04145i q^{13} +113.479i q^{14} +(76.7840 - 0.652187i) q^{15} -79.8364 q^{16} -109.764i q^{17} +(-91.9277 + 1.56174i) q^{18} +10.5190 q^{19} -53.1332 q^{20} +(1.47075 + 173.156i) q^{21} -80.6959 q^{22} -130.802i q^{23} +(-77.9302 + 0.661923i) q^{24} +93.3780 q^{25} +27.3829i q^{26} +(-140.251 + 3.57447i) q^{27} -119.821i q^{28} -175.183i q^{29} +(-261.466 + 2.22084i) q^{30} +99.0741i q^{31} +151.875 q^{32} +(-123.132 + 1.04586i) q^{33} +373.769i q^{34} +492.466i q^{35} +(97.0651 - 1.64902i) q^{36} +35.5694 q^{37} -35.8193 q^{38} +(0.354897 + 41.7831i) q^{39} -221.638 q^{40} -277.992 q^{41} +(-5.00823 - 589.634i) q^{42} -287.185i q^{43} +85.2056 q^{44} +(-398.938 + 6.77749i) q^{45} +445.408i q^{46} +302.077i q^{47} +(414.827 - 3.52346i) q^{48} -767.562 q^{49} -317.973 q^{50} +(4.84425 + 570.328i) q^{51} -28.9132i q^{52} +457.909 q^{53} +(477.584 - 12.1718i) q^{54} -350.196 q^{55} -499.817i q^{56} +(-54.6561 + 0.464238i) q^{57} +596.536i q^{58} -504.454i q^{59} +(276.079 - 2.34495i) q^{60} +64.0196i q^{61} -337.369i q^{62} +(-15.2839 - 899.648i) q^{63} +121.524 q^{64} +118.834i q^{65} +(419.293 - 3.56139i) q^{66} +(498.821 + 227.905i) q^{67} -394.658i q^{68} +(5.77272 + 679.640i) q^{69} -1676.95i q^{70} +1124.94i q^{71} +(404.893 - 6.87866i) q^{72} -469.363 q^{73} -121.122 q^{74} +(-485.189 + 4.12110i) q^{75} +37.8211 q^{76} -789.728i q^{77} +(-1.20850 - 142.281i) q^{78} -874.125i q^{79} +1179.79 q^{80} +(728.579 - 24.7625i) q^{81} +946.623 q^{82} +499.620i q^{83} +(5.28812 + 622.586i) q^{84} +1622.05i q^{85} +977.928i q^{86} +(7.73143 + 910.244i) q^{87} +355.423 q^{88} -774.410i q^{89} +(1358.47 - 23.0788i) q^{90} -267.982 q^{91} -470.300i q^{92} +(-4.37248 - 514.785i) q^{93} -1028.64i q^{94} -155.445 q^{95} +(-789.136 + 6.70276i) q^{96} -124.415i q^{97} +2613.72 q^{98} +(639.746 - 10.8685i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 268 q^{4} - 46 q^{6} + 22 q^{9}+O(q^{10}) $ 64 * q + 268 * q^4 - 46 * q^6 + 22 * q^9	$ 64 q + 268 q^{4} - 46 q^{6} + 22 q^{9} - 36 q^{10} + 20 q^{15} + 556 q^{16} + 128 q^{19} + 96 q^{22} - 904 q^{24} + 2080 q^{25} - 236 q^{33} - 1574 q^{36} + 1004 q^{37} - 176 q^{39} - 648 q^{40} - 1220 q^{49} + 2188 q^{54} - 1344 q^{55} + 550 q^{60} + 4336 q^{64} - 3512 q^{67} + 3968 q^{73} - 3316 q^{76} - 1170 q^{81} + 4020 q^{82} - 9270 q^{84} + 2436 q^{88} + 746 q^{90} - 3408 q^{91} - 1412 q^{93} - 7032 q^{96}+O(q^{100}) $ 64 * q + 268 * q^4 - 46 * q^6 + 22 * q^9 - 36 * q^10 + 20 * q^15 + 556 * q^16 + 128 * q^19 + 96 * q^22 - 904 * q^24 + 2080 * q^25 - 236 * q^33 - 1574 * q^36 + 1004 * q^37 - 176 * q^39 - 648 * q^40 - 1220 * q^49 + 2188 * q^54 - 1344 * q^55 + 550 * q^60 + 4336 * q^64 - 3512 * q^67 + 3968 * q^73 - 3316 * q^76 - 1170 * q^81 + 4020 * q^82 - 9270 * q^84 + 2436 * q^88 + 746 * q^90 - 3408 * q^91 - 1412 * q^93 - 7032 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−3.40522			−1.20393			−0.601963	−	0.798524i	$-0.705615\pi$
$2$	−3.40522			−1.20393			−0.601963	+	0.798524i	$0.705615\pi$
$3$	−5.19596	+	0.0441335i	−0.999964	+	0.00849349i
$3$	−5.19596	+	0.0441335i	−0.999964	+	0.00849349i
$4$	3.59552			0.449440
$5$	−14.7776			−1.32175			−0.660875	−	0.750496i	$-0.729815\pi$
$5$	−14.7776			−1.32175			−0.660875	+	0.750496i	$0.729815\pi$
$6$	17.6934	−	0.150284i	1.20388	−	0.0102255i
$7$		−	33.3251i		−	1.79939i	−0.436523	−	0.899693i	$-0.643790\pi$
$7$		−	33.3251i		−	1.79939i	0.436523	−	0.899693i	$-0.356210\pi$
$8$	14.9982			0.662834
$9$	26.9961	−	0.458632i	0.999856	−	0.0169864i
$10$	50.3210			1.59129
$11$	23.6977			0.649557			0.324779	−	0.945790i	$-0.394710\pi$
$11$	23.6977			0.649557			0.324779	+	0.945790i	$0.394710\pi$
$12$	−18.6822	+	0.158683i	−0.449424	+	0.00381731i
$13$		−	8.04145i		−	0.171561i	−0.996314	−	0.0857807i	$-0.972662\pi$
$13$		−	8.04145i		−	0.171561i	0.996314	−	0.0857807i	$-0.0273384\pi$
$14$			113.479i			2.16633i
$15$	76.7840	−	0.652187i	1.32170	−	0.0112263i
$16$	−79.8364			−1.24744
$17$		−	109.764i		−	1.56598i	−0.622037	−	0.782988i	$-0.713695\pi$
$17$		−	109.764i		−	1.56598i	0.622037	−	0.782988i	$-0.286305\pi$
$18$	−91.9277	+	1.56174i	−1.20375	+	0.0204503i
$19$	10.5190			0.127011			0.0635056	−	0.997981i	$-0.479772\pi$
$19$	10.5190			0.127011			0.0635056	+	0.997981i	$0.479772\pi$
$20$	−53.1332			−0.594048
$21$	1.47075	+	173.156i	0.0152831	+	1.79932i
$22$	−80.6959			−0.782019
$23$		−	130.802i		−	1.18583i	−0.805267	−	0.592913i	$-0.797978\pi$
$23$		−	130.802i		−	1.18583i	0.805267	−	0.592913i	$-0.202022\pi$
$24$	−77.9302	+	0.661923i	−0.662810	+	0.00562977i
$25$	93.3780			0.747024
$26$			27.3829i			0.206547i
$27$	−140.251	+	3.57447i	−0.999675	+	0.0254780i
$28$		−	119.821i		−	0.808717i
$29$		−	175.183i		−	1.12175i	−0.827902	−	0.560873i	$-0.810465\pi$
$29$		−	175.183i		−	1.12175i	0.827902	−	0.560873i	$-0.189535\pi$
$30$	−261.466	+	2.22084i	−1.59123	+	0.0135156i
$31$			99.0741i			0.574007i	0.957929	+	0.287004i	$0.0926592\pi$
$31$			99.0741i			0.574007i	−0.957929	+	0.287004i	$0.907341\pi$
$32$	151.875			0.838997
$33$	−123.132	+	1.04586i	−0.649534	+	0.00551700i
$34$			373.769i			1.88532i
$35$			492.466i			2.37834i
$36$	97.0651	−	1.64902i	0.449375	−	0.00763435i
$37$	35.5694			0.158043			0.0790213	−	0.996873i	$-0.474820\pi$
$37$	35.5694			0.158043			0.0790213	+	0.996873i	$0.474820\pi$
$38$	−35.8193			−0.152912
$39$	0.354897	+	41.7831i	0.00145715	+	0.171555i
$40$	−221.638			−0.876101
$41$	−277.992			−1.05890			−0.529452	−	0.848340i	$-0.677602\pi$
$41$	−277.992			−1.05890			−0.529452	+	0.848340i	$0.677602\pi$
$42$	−5.00823	−	589.634i	−0.0183997	−	2.16625i
$43$		−	287.185i		−	1.01850i	−0.860620	−	0.509248i	$-0.829924\pi$
$43$		−	287.185i		−	1.01850i	0.860620	−	0.509248i	$-0.170076\pi$
$44$	85.2056			0.291937
$45$	−398.938	+	6.77749i	−1.32156	+	0.0224517i
$46$			445.408i			1.42765i
$47$			302.077i			0.937498i	0.883331	+	0.468749i	$0.155295\pi$
$47$			302.077i			0.937498i	−0.883331	+	0.468749i	$0.844705\pi$
$48$	414.827	−	3.52346i	1.24740	−	0.0105951i
$49$	−767.562			−2.23779
$50$	−317.973			−0.899363
$51$	4.84425	+	570.328i	0.0133006	+	1.56592i
$52$		−	28.9132i		−	0.0771066i
$53$	457.909			1.18677			0.593383	−	0.804920i	$-0.297792\pi$
$53$	457.909			1.18677			0.593383	+	0.804920i	$0.297792\pi$
$54$	477.584	−	12.1718i	1.20354	−	0.0306737i
$55$	−350.196			−0.858552
$56$		−	499.817i		−	1.19269i
$57$	−54.6561	+	0.464238i	−0.127007	+	0.00107877i
$58$			596.536i			1.35050i
$59$		−	504.454i		−	1.11312i	−0.830806	−	0.556562i	$-0.812120\pi$
$59$		−	504.454i		−	1.11312i	0.830806	−	0.556562i	$-0.187880\pi$
$60$	276.079	−	2.34495i	0.594026	−	0.00504554i
$61$			64.0196i			0.134375i	0.997740	+	0.0671875i	$0.0214026\pi$
$61$			64.0196i			0.134375i	−0.997740	+	0.0671875i	$0.978597\pi$
$62$		−	337.369i		−	0.691063i
$63$	−15.2839	−	899.648i	−0.0305650	−	1.79913i
$64$	121.524			0.237352
$65$			118.834i			0.226761i
$66$	419.293	−	3.56139i	0.781991	−	0.00664207i
$67$	498.821	+	227.905i	0.909563	+	0.415567i
$67$	498.821	+	227.905i	0.909563	+	0.415567i
$68$		−	394.658i		−	0.703813i
$69$	5.77272	+	679.640i	0.0100718	+	1.18578i
$70$		−	1676.95i		−	2.86335i
$71$			1124.94i			1.88037i	0.340664	+	0.940185i	$0.389348\pi$
$71$			1124.94i			1.88037i	−0.340664	+	0.940185i	$0.610652\pi$
$72$	404.893	−	6.87866i	0.662738	−	0.0112591i
$73$	−469.363			−0.752531			−0.376265	−	0.926512i	$-0.622792\pi$
$73$	−469.363			−0.752531			−0.376265	+	0.926512i	$0.622792\pi$
$74$	−121.122			−0.190272
$75$	−485.189	+	4.12110i	−0.746997	+	0.00634484i
$76$	37.8211			0.0570839
$77$		−	789.728i		−	1.16880i
$78$	−1.20850	−	142.281i	−0.00175431	−	0.206540i
$79$		−	874.125i		−	1.24490i	−0.782662	−	0.622448i	$-0.786138\pi$
$79$		−	874.125i		−	1.24490i	0.782662	−	0.622448i	$-0.213862\pi$
$80$	1179.79			1.64881
$81$	728.579	−	24.7625i	0.999423	−	0.0339678i
$82$	946.623			1.27484
$83$			499.620i			0.660728i	0.943854	+	0.330364i	$0.107171\pi$
$83$			499.620i			0.660728i	−0.943854	+	0.330364i	$0.892829\pi$
$84$	5.28812	+	622.586i	0.00686882	+	0.808687i
$85$			1622.05i			2.06983i
$86$			977.928i			1.22619i
$87$	7.73143	+	910.244i	0.00952754	+	1.12171i
$88$	355.423			0.430548
$89$		−	774.410i		−	0.922329i	−0.887315	−	0.461164i	$-0.847432\pi$
$89$		−	774.410i		−	0.922329i	0.887315	−	0.461164i	$-0.152568\pi$
$90$	1358.47	−	23.0788i	1.59106	−	0.0270302i
$91$	−267.982			−0.308705
$92$		−	470.300i		−	0.532958i
$93$	−4.37248	−	514.785i	−0.00487532	−	0.573987i
$94$		−	1028.64i		−	1.12868i
$95$	−155.445			−0.167877
$96$	−789.136	+	6.70276i	−0.838967	+	0.00712601i
$97$		−	124.415i		−	0.130231i	−0.997878	−	0.0651157i	$-0.979258\pi$
$97$		−	124.415i		−	0.130231i	0.997878	−	0.0651157i	$-0.0207416\pi$
$98$	2613.72			2.69414
$99$	639.746	−	10.8685i	0.649463	−	0.0110336i
$100$	335.743			0.335743
$101$	838.960			0.826531			0.413266	−	0.910610i	$-0.364388\pi$
$101$	838.960			0.826531			0.413266	+	0.910610i	$0.364388\pi$
$102$	−16.4957	−	1942.09i	−0.0160129	−	1.88525i
$103$	−1469.95			−1.40620			−0.703102	−	0.711089i	$-0.748202\pi$
$103$	−1469.95			−1.40620			−0.703102	+	0.711089i	$0.748202\pi$
$104$		−	120.607i		−	0.113717i
$105$	−21.7342	−	2558.83i	−0.0202004	−	2.37825i
$106$	−1559.28			−1.42878
$107$		−	490.921i		−	0.443543i	−0.975099	−	0.221772i	$-0.928816\pi$
$107$		−	490.921i		−	0.443543i	0.975099	−	0.221772i	$-0.0711839\pi$
$108$	−504.274	+	12.8521i	−0.449294	+	0.0114508i
$109$		−	1257.76i		−	1.10525i	−0.833431	−	0.552624i	$-0.813627\pi$
$109$		−	1257.76i		−	1.10525i	0.833431	−	0.552624i	$-0.186373\pi$
$110$	1192.49			1.03363
$111$	−184.817	+	1.56980i	−0.158037	+	0.00134233i
$112$			2660.56i			2.24463i
$113$	−1380.09			−1.14892			−0.574462	−	0.818531i	$-0.694789\pi$
$113$	−1380.09			−1.14892			−0.574462	+	0.818531i	$0.694789\pi$
$114$	186.116	−	1.58083i	0.152907	−	0.00129876i
$115$			1932.93i			1.56737i
$116$		−	629.874i		−	0.504158i
$117$	−3.68807	−	217.088i	−0.00291420	−	0.171537i
$118$			1717.78i			1.34012i
$119$	−3657.88			−2.81780
$120$	1151.62	−	9.78165i	0.876069	−	0.00744115i
$121$	−769.419			−0.578076
$122$		−	218.001i		−	0.161778i
$123$	1444.44	−	12.2687i	1.05887	−	0.00899378i
$124$			356.223i			0.257982i
$125$	467.297			0.334371
$126$	52.0452	+	3063.50i	0.0367981	+	2.16602i
$127$	−1337.41			−0.934458			−0.467229	−	0.884136i	$-0.654748\pi$
$127$	−1337.41			−0.934458			−0.467229	+	0.884136i	$0.654748\pi$
$128$	−1628.81			−1.12475
$129$	12.6745	+	1492.20i	0.00865058	+	1.01846i
$130$		−	404.654i		−	0.273004i
$131$			984.130i			0.656365i	0.944614	+	0.328182i	$0.106436\pi$
$131$			984.130i			0.656365i	−0.944614	+	0.328182i	$0.893564\pi$
$132$	−442.725	+	3.76042i	−0.291927	+	0.00247956i
$133$		−	350.545i		−	0.228542i
$134$	−1698.60	−	776.065i	−1.09505	−	0.500312i
$135$	2072.57	−	52.8221i	1.32132	−	0.0336756i
$136$		−	1646.26i		−	1.03798i
$137$	860.234			0.536458			0.268229	−	0.963355i	$-0.413562\pi$
$137$	860.234			0.536458			0.268229	+	0.963355i	$0.413562\pi$
$138$	−19.6574	−	2314.32i	−0.0121257	−	1.42760i
$139$			1219.40i			0.744089i	0.928215	+	0.372044i	$0.121343\pi$
$139$			1219.40i			0.744089i	−0.928215	+	0.372044i	$0.878657\pi$
$140$			1770.67i			1.06892i
$141$	−13.3317	−	1569.58i	−0.00796263	−	0.937464i
$142$		−	3830.68i		−	2.26383i
$143$		−	190.564i		−	0.111439i
$144$	−2155.27	+	36.6155i	−1.24726	+	0.0211895i
$145$			2588.79i			1.48267i
$146$	1598.28			0.905992
$147$	3988.23	−	33.8752i	2.23771	−	0.0190066i
$148$	127.891			0.0710307
$149$			2256.59i			1.24072i	0.784317	+	0.620360i	$0.213014\pi$
$149$			2256.59i			1.24072i	−0.784317	+	0.620360i	$0.786986\pi$
$150$	1652.18	−	14.0332i	0.899330	−	0.00763873i
$151$	−787.744			−0.424541			−0.212271	−	0.977211i	$-0.568086\pi$
$151$	−787.744			−0.424541			−0.212271	+	0.977211i	$0.568086\pi$
$152$	157.766			0.0841873
$153$	−50.3411	−	2963.19i	−0.0266002	−	1.56575i
$154$			2689.20i			1.40715i
$155$		−	1464.08i		−	0.758694i
$156$	1.27604	+	150.232i	0.000654904	+	0.0771038i
$157$	2123.43			1.07942			0.539708	−	0.841852i	$-0.318535\pi$
$157$	2123.43			1.07942			0.539708	+	0.841852i	$0.318535\pi$
$158$			2976.59i			1.49876i
$159$	−2379.28	+	20.2091i	−1.18672	+	0.0100798i
$160$	−2244.35			−1.10895
$161$	−4358.97			−2.13376
$162$	−2480.97	+	84.3219i	−1.20323	+	0.0408948i
$163$	1535.05			0.737636			0.368818	−	0.929502i	$-0.379763\pi$
$163$	1535.05			0.737636			0.368818	+	0.929502i	$0.379763\pi$
$164$	−999.526			−0.475914
$165$	1819.60	−	15.4553i	0.858521	−	0.00729210i
$166$		−	1701.32i		−	0.795468i
$167$			1762.74i			0.816795i	0.912804	+	0.408398i	$0.133912\pi$
$167$			1762.74i			0.816795i	−0.912804	+	0.408398i	$0.866088\pi$
$168$	22.0587	+	2597.03i	0.0101301	+	1.19265i
$169$	2132.34			0.970567
$170$		−	5523.42i		−	2.49192i
$171$	283.971	−	4.82433i	0.126993	−	0.00215746i
$172$		−	1032.58i		−	0.457753i
$173$			3764.49i			1.65439i	0.561917	+	0.827194i	$0.310064\pi$
$173$			3764.49i			1.65439i	−0.561917	+	0.827194i	$0.689936\pi$
$174$	−26.3272	−	3099.58i	−0.0114705	−	1.35045i
$175$		−	3111.83i		−	1.34419i
$176$	−1891.94			−0.810286
$177$	22.2633	+	2621.12i	0.00945430	+	1.11308i
$178$			2637.04i			1.11042i
$179$	−3280.14			−1.36966			−0.684830	−	0.728703i	$-0.740124\pi$
$179$	−3280.14			−1.36966			−0.684830	+	0.728703i	$0.740124\pi$
$180$	−1434.39	+	24.3686i	−0.593962	+	0.0100907i
$181$	−4166.58			−1.71105			−0.855523	−	0.517765i	$-0.826764\pi$
$181$	−4166.58			−1.71105			−0.855523	+	0.517765i	$0.826764\pi$
$182$	912.539			0.371659
$183$	−2.82541	−	332.644i	−0.00114131	−	0.134370i
$184$		−	1961.79i		−	0.786006i
$185$	−525.631			−0.208893
$186$	14.8893	+	1752.96i	0.00586953	+	0.691038i
$187$		−	2601.15i		−	1.01719i
$188$			1086.12i			0.421349i
$189$	119.119	+	4673.86i	0.0458448	+	1.79880i
$190$	529.325			0.202112
$191$	−1321.60			−0.500670			−0.250335	−	0.968159i	$-0.580541\pi$
$191$	−1321.60			−0.500670			−0.250335	+	0.968159i	$0.580541\pi$
$192$	−631.436	+	5.36329i	−0.237344	+	0.00201595i
$193$	4215.77			1.57232			0.786161	−	0.618022i	$-0.212066\pi$
$193$	4215.77			1.57232			0.786161	+	0.618022i	$0.212066\pi$
$194$			423.661i			0.156789i
$195$	−5.24453	−	617.455i	−0.00192599	−	0.226753i
$196$	−2759.79			−1.00575
$197$	−1543.34			−0.558164			−0.279082	−	0.960267i	$-0.590030\pi$
$197$	−1543.34			−0.558164			−0.279082	+	0.960267i	$0.590030\pi$
$198$	−2178.47	+	37.0097i	−0.781906	+	0.0132837i
$199$	−30.7293			−0.0109464			−0.00547322	−	0.999985i	$-0.501742\pi$
$199$	−30.7293			−0.0109464			−0.00547322	+	0.999985i	$0.501742\pi$
$200$	1400.50			0.495153
$201$	−2601.92	−	1162.17i	−0.913059	−	0.407827i
$202$	−2856.84			−0.995083
$203$	−5837.99			−2.01846
$204$	17.4176	+	2050.63i	0.00597782	+	0.703787i
$205$	4108.06			1.39961
$206$	5005.52			1.69297
$207$	−59.9897	−	3531.13i	−0.0201429	−	1.18565i
$208$			642.001i			0.214013i
$209$	249.275			0.0825010
$210$	74.0098	+	8713.39i	0.0243198	+	2.86324i
$211$	−980.925			−0.320046			−0.160023	−	0.987113i	$-0.551157\pi$
$211$	−980.925			−0.320046			−0.160023	+	0.987113i	$0.551157\pi$
$212$	1646.42			0.533380
$213$	−49.6477	−	5845.17i	−0.0159709	−	1.88030i
$214$			1671.69i			0.533993i
$215$			4243.91i			1.34620i
$216$	−2103.51	+	53.6106i	−0.662619	+	0.0168877i
$217$	3301.65			1.03286
$218$			4282.96i			1.33064i
$219$	2438.79	−	20.7146i	0.752504	−	0.00639161i
$220$	−1259.14			−0.385868
$221$	−882.659			−0.268661
$222$	629.344	−	5.34552i	0.190265	−	0.00161607i
$223$	−2809.97			−0.843810			−0.421905	−	0.906640i	$-0.638638\pi$
$223$	−2809.97			−0.843810			−0.421905	+	0.906640i	$0.638638\pi$
$224$		−	5061.24i		−	1.50968i
$225$	2520.84	−	42.8261i	0.746917	−	0.0126892i
$226$	4699.52			1.38322
$227$		−	5043.52i		−	1.47467i	−0.675527	−	0.737336i	$-0.736084\pi$
$227$		−	5043.52i		−	1.47467i	0.675527	−	0.737336i	$-0.263916\pi$
$228$	−196.517	+	1.66918i	−0.0570819	+	0.000484842i
$229$			4829.94i			1.39376i	0.717187	+	0.696881i	$0.245429\pi$
$229$			4829.94i			1.39376i	−0.717187	+	0.696881i	$0.754571\pi$
$230$		−	6582.07i		−	1.88699i
$231$	34.8534	+	4103.40i	0.00992722	+	1.16876i
$232$		−	2627.43i		−	0.743532i
$233$	4374.65			1.23001			0.615007	−	0.788522i	$-0.289153\pi$
$233$	4374.65			1.23001			0.615007	+	0.788522i	$0.289153\pi$
$234$	12.5587	+	739.232i	0.00350849	+	0.206518i
$235$		−	4463.97i		−	1.23914i
$236$		−	1813.77i		−	0.500282i
$237$	38.5781	+	4541.92i	0.0105735	+	1.24485i
$238$	12455.9			3.39242
$239$	−2126.36			−0.575494			−0.287747	−	0.957706i	$-0.592906\pi$
$239$	−2126.36			−0.575494			−0.287747	+	0.957706i	$0.592906\pi$
$240$	−6130.16	+	52.0683i	−1.64875	+	0.0140041i
$241$	4457.08			1.19131			0.595655	−	0.803241i	$-0.296893\pi$
$241$	4457.08			1.19131			0.595655	+	0.803241i	$0.296893\pi$
$242$	2620.04			0.695961
$243$	−3784.58	+	160.820i	−0.999098	+	0.0424552i
$244$			230.184i			0.0603935i
$245$	11342.7			2.95780
$246$	−4918.62	+	41.7778i	−1.27480	+	0.0108279i
$247$		−	84.5877i		−	0.0217902i
$248$			1485.93i			0.380471i
$249$	−22.0499	−	2596.01i	−0.00561188	−	0.660704i
$250$	−1591.25			−0.402558
$251$	3123.74			0.785533			0.392766	−	0.919638i	$-0.371518\pi$
$251$	3123.74			0.785533			0.392766	+	0.919638i	$0.371518\pi$
$252$	−54.9538	−	3234.70i	−0.0137372	−	0.808600i
$253$		−	3099.70i		−	0.770262i
$254$	4554.18			1.12502
$255$	−71.5865	−	8428.09i	−0.0175801	−	2.06976i
$256$	4574.28			1.11677
$257$		−	6918.92i		−	1.67934i	−0.543096	−	0.839670i	$-0.682748\pi$
$257$		−	6918.92i		−	1.67934i	0.543096	−	0.839670i	$-0.317252\pi$
$258$	−43.1593	−	5081.28i	−0.0104147	−	1.22615i
$259$		−	1185.35i		−	0.284380i
$260$			427.269i			0.101916i
$261$	−80.3444	−	4729.26i	−0.0190544	−	1.12158i
$262$		−	3351.18i		−	0.790215i
$263$		−	924.339i		−	0.216719i	−0.994112	−	0.108360i	$-0.965440\pi$
$263$		−	924.339i		−	0.216719i	0.994112	−	0.108360i	$-0.0345598\pi$
$264$	−1846.77	+	15.6861i	−0.430533	+	0.00365686i
$265$	−6766.80			−1.56861
$266$			1193.68i			0.275148i
$267$	34.1774	+	4023.81i	0.00783379	+	0.922296i
$268$	1793.52	+	819.436i	0.408794	+	0.186772i
$269$			1285.26i			0.291315i	0.989335	+	0.145657i	$0.0465297\pi$
$269$			1285.26i			0.291315i	−0.989335	+	0.145657i	$0.953470\pi$
$270$	−7057.55	+	179.871i	−1.59077	+	0.0405429i
$271$			4669.50i			1.04669i	0.852122	+	0.523343i	$0.175315\pi$
$271$			4669.50i			1.04669i	−0.852122	+	0.523343i	$0.824685\pi$
$272$			8763.13i			1.95347i
$273$	1392.43	−	11.8270i	0.308694	−	0.00262198i
$274$	−2929.29			−0.645856
$275$	2212.85			0.485235
$276$	20.7559	+	2443.66i	0.00452667	+	0.532939i
$277$	5486.52			1.19008			0.595042	−	0.803695i	$-0.297135\pi$
$277$	5486.52			1.19008			0.595042	+	0.803695i	$0.297135\pi$
$278$		−	4152.33i		−	0.895828i
$279$	45.4385	+	2674.61i	0.00975029	+	0.573924i
$280$			7386.11i			1.57644i
$281$	8730.17			1.85338			0.926688	−	0.375832i	$-0.122643\pi$
$281$	8730.17			1.85338			0.926688	+	0.375832i	$0.122643\pi$
$282$	45.3973	+	5344.76i	0.00958642	+	1.12864i
$283$	1416.03			0.297435			0.148718	−	0.988880i	$-0.452485\pi$
$283$	1416.03			0.297435			0.148718	+	0.988880i	$0.452485\pi$
$284$			4044.76i			0.845114i
$285$	807.687	−	6.86033i	0.167871	−	0.00142586i
$286$			648.912i			0.134164i
$287$			9264.11i			1.90538i
$288$	4100.03	−	69.6546i	0.838876	−	0.0142515i
$289$	−7135.06			−1.45228
$290$		−	8815.39i		−	1.78503i
$291$	5.49087	+	646.457i	0.00110612	+	0.130227i
$292$	−1687.60			−0.338218
$293$		−	5225.50i		−	1.04190i	−0.853587	−	0.520951i	$-0.825578\pi$
$293$		−	5225.50i		−	1.04190i	0.853587	−	0.520951i	$-0.174422\pi$
$294$	−13580.8	+	115.352i	−2.69404	+	0.0228826i
$295$			7454.63i			1.47127i
$296$	533.478			0.104756
$297$	−3323.62	+	84.7066i	−0.649346	+	0.0165494i
$298$		−	7684.20i		−	1.49374i
$299$	−1051.83			−0.203442
$300$	−1744.51	+	14.8175i	−0.335731	+	0.00285163i
$301$	−9570.47			−1.83267
$302$	2682.44			0.511116
$303$	−4359.21	+	37.0262i	−0.826502	+	0.00702013i
$304$	−839.795			−0.158439
$305$		−	946.057i		−	0.177610i
$306$	171.422	+	10090.3i	0.0320247	+	1.88505i
$307$	−5573.37			−1.03612			−0.518061	−	0.855344i	$-0.673346\pi$
$307$	−5573.37			−1.03612			−0.518061	+	0.855344i	$0.673346\pi$
$308$		−	2839.49i		−	0.525308i
$309$	7637.83	−	64.8742i	1.40615	−	0.0119436i
$310$			4985.51i			0.913413i
$311$	−2933.41			−0.534850			−0.267425	−	0.963579i	$-0.586173\pi$
$311$	−2933.41			−0.534850			−0.267425	+	0.963579i	$0.586173\pi$
$312$	5.32282	+	626.672i	0.000965851	+	0.113713i
$313$		−	10040.3i		−	1.81314i	−0.422060	−	0.906568i	$-0.638693\pi$
$313$		−	10040.3i		−	1.81314i	0.422060	−	0.906568i	$-0.361307\pi$
$314$	−7230.75			−1.29954
$315$	225.860	+	13294.7i	0.0403993	+	2.37800i
$316$		−	3142.93i		−	0.559506i
$317$		−	6739.05i		−	1.19402i	−0.802235	−	0.597008i	$-0.796356\pi$
$317$		−	6739.05i		−	1.19402i	0.802235	−	0.597008i	$-0.203644\pi$
$318$	8101.96	−	68.8164i	1.42873	−	0.0121353i
$319$		−	4151.43i		−	0.728638i
$320$	−1795.84			−0.313720
$321$	21.6660	+	2550.81i	0.00376723	+	0.443527i
$322$	14843.3			2.56889
$323$		−	1154.60i		−	0.198897i
$324$	2619.62	−	89.0342i	0.449181	−	0.0152665i
$325$		−	750.895i		−	0.128161i
$326$	−5227.19			−0.888059
$327$	55.5095	+	6535.30i	0.00938741	+	1.10521i
$328$	−4169.38			−0.701877
$329$	10066.7			1.68692
$330$	−6196.15	+	52.6288i	−1.03360	+	0.00877916i
$331$			3474.78i			0.577013i	0.957478	+	0.288506i	$0.0931586\pi$
$331$			3474.78i			0.577013i	−0.957478	+	0.288506i	$0.906841\pi$
$332$			1796.39i			0.296958i
$333$	960.236	−	16.3133i	0.158020	−	0.00268457i
$334$		−	6002.51i		−	0.983362i
$335$	−7371.39	−	3367.89i	−1.20221	−	0.549276i
$336$	−117.420	−	13824.2i	−0.0190648	−	2.24455i
$337$			656.002i			0.106038i	0.998594	+	0.0530189i	$0.0168844\pi$
$337$			656.002i			0.106038i	−0.998594	+	0.0530189i	$0.983116\pi$
$338$	−7261.07			−1.16849
$339$	7170.92	−	60.9083i	1.14888	−	0.00975836i
$340$			5832.10i			0.930265i
$341$			2347.83i			0.372850i
$342$	−966.983	+	16.4279i	−0.152890	+	0.00259742i
$343$			14148.6i			2.22726i
$344$		−	4307.26i		−	0.675093i
$345$	−85.3071	−	10043.5i	−0.0133124	−	1.56731i
$346$		−	12818.9i		−	1.99176i
$347$	−128.861			−0.0199356			−0.00996778	−	0.999950i	$-0.503173\pi$
$347$	−128.861			−0.0199356			−0.00996778	+	0.999950i	$0.503173\pi$
$348$	27.7985	+	3272.80i	0.00428206	+	0.504140i
$349$	−36.2719			−0.00556329			−0.00278165	−	0.999996i	$-0.500885\pi$
$349$	−36.2719			−0.00556329			−0.00278165	+	0.999996i	$0.500885\pi$
$350$			10596.5i			1.61830i
$351$	28.7439	+	1127.82i	0.00437104	+	0.171506i
$352$	3599.08			0.544977
$353$	2018.24			0.304306			0.152153	−	0.988357i	$-0.451379\pi$
$353$	2018.24			0.304306			0.152153	+	0.988357i	$0.451379\pi$
$354$	−75.8114	−	8925.50i	−0.0113823	−	1.34007i
$355$		−	16624.0i		−	2.48538i
$356$		−	2784.41i		−	0.414532i
$357$	19006.2	−	161.435i	2.81769	−	0.0239329i
$358$	11169.6			1.64897
$359$			3457.43i			0.508290i	0.967166	+	0.254145i	$0.0817940\pi$
$359$			3457.43i			0.508290i	−0.967166	+	0.254145i	$0.918206\pi$
$360$	−5983.36	+	101.650i	−0.875974	+	0.0148818i
$361$	−6748.35			−0.983868
$362$	14188.1			2.05997
$363$	3997.87	−	33.9571i	0.578055	−	0.00490988i
$364$	−963.536			−0.138745
$365$	6936.06			0.994658
$366$	9.62113	+	1132.72i	0.00137406	+	0.161772i
$367$			6341.71i			0.902001i	0.892524	+	0.451001i	$0.148933\pi$
$367$			6341.71i			0.902001i	−0.892524	+	0.451001i	$0.851067\pi$
$368$			10442.7i			1.47925i
$369$	−7504.70	+	127.496i	−1.05875	+	0.0179869i
$370$	1789.89			0.251492
$371$		−	15259.9i		−	2.13545i
$372$	−15.7213	−	1850.92i	−0.00219117	−	0.257973i
$373$			6313.07i			0.876349i	0.898890	+	0.438174i	$0.144375\pi$
$373$			6313.07i			0.876349i	−0.898890	+	0.438174i	$0.855625\pi$
$374$			8857.48i			1.22462i
$375$	−2428.06	+	20.6234i	−0.334359	+	0.00283997i
$376$			4530.61i			0.621405i
$377$	−1408.73			−0.192448
$378$	−405.628	−	15915.5i	−0.0551938	−	2.16563i
$379$		−	12905.6i		−	1.74913i	−0.484912	−	0.874563i	$-0.661148\pi$
$379$		−	12905.6i		−	1.74913i	0.484912	−	0.874563i	$-0.338852\pi$
$380$	−558.906			−0.0754507
$381$	6949.15	−	59.0246i	0.934424	−	0.00793680i
$382$	4500.35			0.602770
$383$	−4621.47			−0.616569			−0.308284	−	0.951294i	$-0.599755\pi$
$383$	−4621.47			−0.616569			−0.308284	+	0.951294i	$0.599755\pi$
$384$	8463.27	−	71.8852i	1.12471	−	0.00955307i
$385$			11670.3i			1.54487i
$386$	−14355.6			−1.89296
$387$	−131.712	−	7752.88i	−0.0173005	−	1.01835i
$388$		−	447.337i		−	0.0585312i
$389$			12861.1i			1.67631i	0.545434	+	0.838154i	$0.316365\pi$
$389$			12861.1i			1.67631i	−0.545434	+	0.838154i	$0.683635\pi$
$390$	17.8588	+	2102.57i	0.00231876	+	0.272994i
$391$	−14357.3			−1.85698
$392$	−11512.1			−1.48328
$393$	−43.4330	−	5113.50i	−0.00557483	−	0.656341i
$394$	5255.41			0.671989
$395$			12917.5i			1.64544i
$396$	2300.22	−	39.0780i	0.291895	−	0.00495895i
$397$	8306.82			1.05014			0.525072	−	0.851058i	$-0.324038\pi$
$397$	8306.82			1.05014			0.525072	+	0.851058i	$0.324038\pi$
$398$	104.640			0.0131787
$399$	15.4708	+	1821.42i	0.00194112	+	0.228534i
$400$	−7454.97			−0.931871
$401$	172.978			0.0215415			0.0107707	−	0.999942i	$-0.496572\pi$
$401$	172.978			0.0215415			0.0107707	+	0.999942i	$0.496572\pi$
$402$	8860.09	+	3957.44i	1.09926	+	0.490993i
$403$	796.700			0.0984775
$404$	3016.50			0.371476
$405$	−10766.7	+	365.931i	−1.32099	+	0.0448970i
$406$	19879.6			2.43007
$407$	842.913			0.102658
$408$	72.6551	+	8553.90i	0.00881609	+	1.03794i
$409$			4471.47i			0.540587i	0.962778	+	0.270294i	$0.0871208\pi$
$409$			4471.47i			0.540587i	−0.962778	+	0.270294i	$0.912879\pi$
$410$	−13988.8			−1.68502
$411$	−4469.75	+	37.9651i	−0.536439	+	0.00455640i
$412$	−5285.25			−0.632004
$413$	−16811.0			−2.00294
$414$	204.278	+	12024.3i	0.0242505	+	1.42744i
$415$		−	7383.19i		−	0.873317i
$416$		−	1221.29i		−	0.143940i
$417$	−53.8164	−	6335.97i	−0.00631991	−	0.744062i
$418$	−848.836			−0.0993252
$419$			8801.18i			1.02617i	0.858337	+	0.513086i	$0.171498\pi$
$419$			8801.18i			1.02617i	−0.858337	+	0.513086i	$0.828502\pi$
$420$	−78.1458	−	9200.34i	−0.00907887	−	1.06888i
$421$	−8373.34			−0.969339			−0.484669	−	0.874697i	$-0.661060\pi$
$421$	−8373.34			−0.969339			−0.484669	+	0.874697i	$0.661060\pi$
$422$	3340.27			0.385312
$423$	138.542	+	8154.89i	0.0159247	+	0.937363i
$424$	6867.81			0.786628
$425$		−	10249.5i		−	1.16982i
$426$	169.061	+	19904.1i	0.0192278	+	2.26375i
$427$	2133.46			0.241792
$428$		−	1765.12i		−	0.199346i
$429$	8.41025	+	990.164i	0.000946505	+	0.111435i
$430$		−	14451.5i		−	1.62072i
$431$		−	5314.08i		−	0.593899i	−0.954893	−	0.296949i	$-0.904031\pi$
$431$		−	5314.08i		−	0.593899i	0.954893	−	0.296949i	$-0.0959692\pi$
$432$	11197.1	−	285.372i	1.24704	−	0.0317824i
$433$			11788.3i			1.30834i	0.756347	+	0.654170i	$0.226982\pi$
$433$			11788.3i			1.30834i	−0.756347	+	0.654170i	$0.773018\pi$
$434$	−11242.9			−1.24349
$435$	−114.252	−	13451.2i	−0.0125930	−	1.48262i
$436$		−	4522.32i		−	0.496743i
$437$		−	1375.89i		−	0.150613i
$438$	−8304.62	+	70.5377i	−0.905959	+	0.00769503i
$439$	13306.1			1.44661			0.723307	−	0.690527i	$-0.242621\pi$
$439$	13306.1			1.44661			0.723307	+	0.690527i	$0.242621\pi$
$440$	−5252.31			−0.569078
$441$	−20721.2	+	352.028i	−2.23747	+	0.0380119i
$442$	3005.65			0.323448
$443$	3712.24			0.398136			0.199068	−	0.979986i	$-0.436209\pi$
$443$	3712.24			0.398136			0.199068	+	0.979986i	$0.436209\pi$
$444$	−664.515	+	5.64425i	−0.0710281	+	0.000603298i
$445$			11443.9i			1.21909i
$446$	9568.57			1.01589
$447$	−99.5913	−	11725.2i	−0.0105380	−	1.24068i
$448$		−	4049.81i		−	0.427088i
$449$		−	17643.2i		−	1.85442i	−0.374544	−	0.927209i	$-0.622201\pi$
$449$		−	17643.2i		−	1.85442i	0.374544	−	0.927209i	$-0.377799\pi$
$450$	−8584.03	+	145.832i	−0.899233	+	0.0152769i
$451$	−6587.77			−0.687818
$452$	−4962.16			−0.516372
$453$	4093.09	−	34.7659i	0.424526	−	0.00360583i
$454$			17174.3i			1.77540i
$455$	3960.14			0.408031
$456$	−819.744	+	6.96274i	−0.0841843	+	0.000715044i
$457$	−4037.72			−0.413297			−0.206648	−	0.978415i	$-0.566256\pi$
$457$	−4037.72			−0.413297			−0.206648	+	0.978415i	$0.566256\pi$
$458$		−	16447.0i		−	1.67799i
$459$	392.346	+	15394.4i	0.0398980	+	1.56547i
$460$			6949.91i			0.704437i
$461$			34.1467i			0.00344982i	0.999999	+	0.00172491i	$0.000549057\pi$
$461$			34.1467i			0.00344982i	−0.999999	+	0.00172491i	$0.999451\pi$
$462$	−118.684	−	13973.0i	−0.0119516	−	1.40710i
$463$			14924.3i			1.49804i	0.662548	+	0.749020i	$0.269475\pi$
$463$			14924.3i			1.49804i	−0.662548	+	0.749020i	$0.730525\pi$
$464$			13986.0i			1.39932i
$465$	64.6148	+	7607.30i	0.00644396	+	0.758667i
$466$	−14896.7			−1.48085
$467$			9021.82i			0.893962i	0.894544	+	0.446981i	$0.147501\pi$
$467$			9021.82i			0.893962i	−0.894544	+	0.446981i	$0.852499\pi$
$468$	−13.2605	−	780.544i	−0.00130976	−	0.0770955i
$469$	7594.94	−	16623.3i	0.747765	−	1.63665i
$470$			15200.8i			1.49183i
$471$	−11033.3	+	93.7144i	−1.07938	+	0.00916800i
$472$		−	7565.91i		−	0.737816i
$473$		−	6805.63i		−	0.661571i
$474$	−131.367	−	15466.2i	−0.0127297	−	1.49871i
$475$	982.239			0.0948805
$476$	−13152.0			−1.26643
$477$	12361.7	−	210.011i	1.18659	−	0.0201588i
$478$	7240.73			0.692853
$479$			4215.55i			0.402116i	0.979579	+	0.201058i	$0.0644380\pi$
$479$			4215.55i			0.402116i	−0.979579	+	0.201058i	$0.935562\pi$
$480$	11661.5	−	99.0508i	1.10891	−	0.00941881i
$481$		−	286.030i		−	0.0271140i
$482$	−15177.3			−1.43425
$483$	22649.1	−	192.377i	2.13368	−	0.0181231i
$484$	−2766.46			−0.259810
$485$			1838.56i			0.172133i
$486$	12887.3	−	547.627i	1.20284	−	0.0511129i
$487$		−	18507.9i		−	1.72212i	−0.508503	−	0.861060i	$-0.669801\pi$
$487$		−	18507.9i		−	1.72212i	0.508503	−	0.861060i	$-0.330199\pi$
$488$			960.180i			0.0890682i
$489$	−7976.08	+	67.7472i	−0.737609	+	0.00626510i
$490$	−38624.5			−3.56098
$491$			9043.23i			0.831192i	0.909549	+	0.415596i	$0.136427\pi$
$491$			9043.23i			0.831192i	−0.909549	+	0.415596i	$0.863573\pi$
$492$	5193.50	−	44.1125i	0.475897	−	0.00404217i
$493$	−19228.7			−1.75663
$494$			288.040i			0.0262338i
$495$	−9453.92	+	160.611i	−0.858428	+	0.0145837i
$496$		−	7909.72i		−	0.716042i
$497$	37488.9			3.38351
$498$	75.0849	+	8839.97i	0.00675630	+	0.795439i
$499$			10411.5i			0.934029i	0.884250	+	0.467015i	$0.154670\pi$
$499$			10411.5i			0.934029i	−0.884250	+	0.467015i	$0.845330\pi$
$500$	1680.18			0.150280
$501$	−77.7957	−	9159.13i	−0.00693744	−	0.816766i
$502$	−10637.0			−0.945724
$503$	−16056.8			−1.42333			−0.711666	−	0.702518i	$-0.752059\pi$
$503$	−16056.8			−1.42333			−0.711666	+	0.702518i	$0.752059\pi$
$504$	−229.232	−	13493.1i	−0.0202595	−	1.19252i
$505$	−12397.8			−1.09247
$506$			10555.1i			0.927339i
$507$	−11079.5	+	94.1073i	−0.970532	+	0.00824349i
$508$	−4808.69			−0.419983
$509$		−	13404.6i		−	1.16728i	−0.812012	−	0.583641i	$-0.801628\pi$
$509$		−	13404.6i		−	1.16728i	0.812012	−	0.583641i	$-0.198372\pi$
$510$	243.768	+	28699.5i	0.0211651	+	2.49183i
$511$			15641.6i			1.35409i
$512$	−2545.90			−0.219754
$513$	−1475.29	+	37.5996i	−0.126970	+	0.00323599i
$514$			23560.5i			2.02180i
$515$	21722.4			1.85865
$516$	45.5713	+	5365.25i	0.00388792	+	0.457736i
$517$			7158.52i			0.608958i
$518$			4036.39i			0.342372i
$519$	−166.140	−	19560.2i	−0.0140515	−	1.65433i
$520$			1782.29i			0.150305i
$521$	−1061.18			−0.0892345			−0.0446173	−	0.999004i	$-0.514207\pi$
$521$	−1061.18			−0.0892345			−0.0446173	+	0.999004i	$0.514207\pi$
$522$	273.590	+	16104.2i	0.0229401	+	1.35031i
$523$	9913.71			0.828865			0.414432	−	0.910080i	$-0.363980\pi$
$523$	9913.71			0.828865			0.414432	+	0.910080i	$0.363980\pi$
$524$			3538.46i			0.294997i
$525$	137.336	+	16169.0i	0.0114168	+	1.34414i
$526$			3147.58i			0.260914i
$527$	10874.7			0.898882
$528$	9830.45	−	83.4978i	0.810257	−	0.00688215i
$529$	−4942.03			−0.406183
$530$	23042.4			1.88849
$531$	−231.358	−	13618.3i	−0.0189079	−	1.11296i
$532$		−	1260.39i		−	0.102716i
$533$			2235.46i			0.181667i
$534$	−116.381	−	13701.9i	−0.00943131	−	1.11038i
$535$			7254.64i			0.586253i
$536$	7481.43	+	3418.16i	0.602889	+	0.275452i
$537$	17043.5	−	144.764i	1.36961	−	0.0116332i
$538$		−	4376.59i		−	0.350722i
$539$	−18189.5			−1.45357
$540$	7451.97	−	189.923i	0.593855	−	0.0151352i
$541$		−	21322.4i		−	1.69449i	−0.531201	−	0.847246i	$-0.678259\pi$
$541$		−	21322.4i		−	1.69449i	0.531201	−	0.847246i	$-0.321741\pi$
$542$		−	15900.7i		−	1.26013i
$543$	21649.4	−	183.885i	1.71098	−	0.0145327i
$544$		−	16670.3i		−	1.31385i
$545$			18586.8i			1.46086i
$546$	−4741.52	+	40.2735i	−0.371645	+	0.00315668i
$547$		−	1687.69i		−	0.131920i	−0.997822	−	0.0659600i	$-0.978989\pi$
$547$		−	1687.69i		−	0.131920i	0.997822	−	0.0659600i	$-0.0210110\pi$
$548$	3092.99			0.241106
$549$	29.3614	+	1728.28i	0.00228254	+	0.134356i
$550$	−7535.22			−0.584187
$551$		−	1842.74i		−	0.142474i
$552$	86.5805	+	10193.4i	0.00667593	+	0.785977i
$553$	−29130.3			−2.24005
$554$	−18682.8			−1.43277
$555$	2731.16	−	23.1979i	0.208885	−	0.00177423i
$556$			4384.39i			0.334423i
$557$		−	19043.6i		−	1.44866i	−0.689452	−	0.724331i	$-0.742149\pi$
$557$		−	19043.6i		−	1.44866i	0.689452	−	0.724331i	$-0.257851\pi$
$558$	−154.728	−	9107.65i	−0.0117386	−	0.690963i
$559$	−2309.39			−0.174735
$560$		−	39316.7i		−	2.96684i
$561$	114.798	+	13515.5i	0.00863950	+	1.01715i
$562$	−29728.2			−2.23133
$563$	−11244.3			−0.841723			−0.420862	−	0.907125i	$-0.638272\pi$
$563$	−11244.3			−0.841723			−0.420862	+	0.907125i	$0.638272\pi$
$564$	−47.9344	−	5643.46i	−0.00357872	−	0.421334i
$565$	20394.5			1.51859
$566$	−4821.89			−0.358090
$567$	−825.214	−	24280.0i	−0.0611212	−	1.79835i
$568$			16872.2i			1.24637i
$569$			16049.7i			1.18249i	0.806491	+	0.591247i	$0.201364\pi$
$569$			16049.7i			1.18249i	−0.806491	+	0.591247i	$0.798636\pi$
$570$	−2750.35	+	23.3609i	−0.202105	+	0.00171663i
$571$	21220.6			1.55526			0.777631	−	0.628721i	$-0.216421\pi$
$571$	21220.6			1.55526			0.777631	+	0.628721i	$0.216421\pi$
$572$		−	685.177i		−	0.0500851i
$573$	6867.01	−	58.3269i	0.500652	−	0.00425243i
$574$		−	31546.3i		−	2.29393i
$575$		−	12214.0i		−	0.885841i
$576$	3280.68	−	55.7349i	0.237318	−	0.00403175i
$577$		−	6829.46i		−	0.492746i	−0.969175	−	0.246373i	$-0.920761\pi$
$577$		−	6829.46i		−	0.492746i	0.969175	−	0.246373i	$-0.0792388\pi$
$578$	24296.4			1.74844
$579$	−21905.0	+	186.057i	−1.57227	+	0.0133545i
$580$			9308.04i			0.666371i
$581$	16649.9			1.18890
$582$	−18.6976	−	2201.33i	−0.00133169	−	0.156783i
$583$	10851.4			0.770872
$584$	−7039.60			−0.498803
$585$	54.5008	+	3208.04i	0.00385185	+	0.226729i
$586$			17794.0i			1.25437i
$587$	12047.4			0.847104			0.423552	−	0.905872i	$-0.360783\pi$
$587$	12047.4			0.847104			0.423552	+	0.905872i	$0.360783\pi$
$588$	14339.8	−	121.799i	1.00572	−	0.00854235i
$589$			1042.16i			0.0729054i
$590$		−	25384.6i		−	1.77130i
$591$	8019.14	−	68.1129i	0.558144	−	0.00474076i
$592$	−2839.73			−0.197149
$593$	−20841.1			−1.44324			−0.721620	−	0.692290i	$-0.756602\pi$
$593$	−20841.1			−1.44324			−0.721620	+	0.692290i	$0.756602\pi$
$594$	11317.6	−	288.445i	0.781765	−	0.0199243i
$595$	54054.8			3.72442
$596$			8113.63i			0.557630i
$597$	159.668	−	1.35619i	0.0109460	−	9.29735e-5i
$598$	3581.73			0.244929
$599$	7366.51			0.502483			0.251242	−	0.967924i	$-0.419161\pi$
$599$	7366.51			0.502483			0.251242	+	0.967924i	$0.419161\pi$
$600$	−7276.97	+	61.8091i	−0.495135	+	0.00420558i
$601$	−13526.2			−0.918044			−0.459022	−	0.888425i	$-0.651800\pi$
$601$	−13526.2			−0.918044			−0.459022	+	0.888425i	$0.651800\pi$
$602$	32589.6			2.20640
$603$	13570.8	+	5923.76i	0.916490	+	0.400057i
$604$	−2832.35			−0.190806
$605$	11370.2			0.764072
$606$	14844.1	−	126.082i	0.995048	−	0.00845173i
$607$	13296.2			0.889090			0.444545	−	0.895756i	$-0.353365\pi$
$607$	13296.2			0.889090			0.444545	+	0.895756i	$0.353365\pi$
$608$	1597.56			0.106562
$609$	30334.0	−	257.651i	2.01838	−	0.0171437i
$610$			3221.53i			0.213830i
$611$	2429.14			0.160838
$612$	−181.002	−	10654.2i	−0.0119552	−	0.703711i
$613$	12936.6			0.852372			0.426186	−	0.904636i	$-0.359857\pi$
$613$	12936.6			0.852372			0.426186	+	0.904636i	$0.359857\pi$
$614$	18978.6			1.24741
$615$	−21345.3	+	181.303i	−1.39956	+	0.0118875i
$616$		−	11844.5i		−	0.774723i
$617$		−	3473.18i		−	0.226621i	−0.993560	−	0.113310i	$-0.963855\pi$
$617$		−	3473.18i		−	0.226621i	0.993560	−	0.113310i	$-0.0361454\pi$
$618$	−26008.5	+	220.911i	−1.69291	+	0.0143792i
$619$	22622.3			1.46893			0.734464	−	0.678647i	$-0.237433\pi$
$619$	22622.3			1.46893			0.734464	+	0.678647i	$0.237433\pi$
$620$		−	5264.13i		−	0.340988i
$621$	467.545	+	18345.0i	0.0302125	+	1.18544i
$622$	9988.90			0.643920
$623$	−25807.3			−1.65963
$624$	−28.3337	−	3335.81i	−0.00181772	−	0.214005i
$625$	−18577.8			−1.18898
$626$			34189.4i			2.18288i
$627$	−1295.22	+	11.0014i	−0.0824981	+	0.000700721i
$628$	7634.84			0.485133
$629$		−	3904.23i		−	0.247491i
$630$	−769.104	−	45271.2i	−0.0486379	−	2.86293i
$631$		−	6356.07i		−	0.401000i	−0.979694	−	0.200500i	$-0.935743\pi$
$631$		−	6356.07i		−	0.401000i	0.979694	−	0.200500i	$-0.0642567\pi$
$632$		−	13110.3i		−	0.825159i
$633$	5096.85	−	43.2916i	0.320034	−	0.00271831i
$634$			22948.0i			1.43751i
$635$	19763.8			1.23512
$636$	−8554.74	+	72.6622i	−0.533361	+	0.00453026i
$637$			6172.32i			0.383919i
$638$			14136.5i			0.877227i
$639$	515.935	+	30369.1i	0.0319406	+	1.88010i
$640$	24070.0			1.48664
$641$	19981.9			1.23126			0.615631	−	0.788035i	$-0.288901\pi$
$641$	19981.9			1.23126			0.615631	+	0.788035i	$0.288901\pi$
$642$	−73.7776	−	8686.06i	−0.00453547	−	0.533974i
$643$	−22039.6			−1.35172			−0.675861	−	0.737029i	$-0.736228\pi$
$643$	−22039.6			−1.35172			−0.675861	+	0.737029i	$0.736228\pi$
$644$	−15672.8			−0.958997
$645$	−187.298	−	22051.2i	−0.0114339	−	1.34615i
$646$			3931.66i			0.239457i
$647$	−19504.4			−1.18516			−0.592578	−	0.805513i	$-0.701890\pi$
$647$	−19504.4			−1.18516			−0.592578	+	0.805513i	$0.701890\pi$
$648$	10927.4	−	371.394i	0.662451	−	0.0225150i
$649$		−	11954.4i		−	0.723037i
$650$			2556.96i			0.154296i
$651$	−17155.3	+	145.713i	−1.03282	+	0.00877259i
$652$	5519.31			0.331523
$653$	−29205.6			−1.75023			−0.875117	−	0.483912i	$-0.839215\pi$
$653$	−29205.6			−1.75023			−0.875117	+	0.483912i	$0.839215\pi$
$654$	−189.022	−	22254.1i	−0.0113018	−	1.33059i
$655$		−	14543.1i		−	0.867551i
$656$	22193.9			1.32092
$657$	−12671.0	+	215.265i	−0.752422	+	0.0127828i
$658$	−34279.4			−2.03093
$659$			20041.8i			1.18470i	0.805681	+	0.592350i	$0.201800\pi$
$659$			20041.8i			1.18470i	−0.805681	+	0.592350i	$0.798200\pi$
$660$	6542.43	−	55.5700i	0.385854	−	0.00327736i
$661$		−	4013.65i		−	0.236177i	−0.993003	−	0.118088i	$-0.962323\pi$
$661$		−	4013.65i		−	0.236177i	0.993003	−	0.118088i	$-0.0376766\pi$
$662$		−	11832.4i		−	0.694681i
$663$	4586.27	−	38.9548i	0.268651	−	0.00228187i
$664$			7493.41i			0.437953i
$665$			5180.22i			0.302076i
$666$	−3269.81	+	55.5502i	−0.190244	+	0.00323202i
$667$	−22914.2			−1.33020
$668$			6337.96i			0.367101i
$669$	14600.5	−	124.014i	0.843779	−	0.00716688i
$670$	25101.2	+	11468.4i	1.44738	+	0.661288i
$671$			1517.12i			0.0872842i
$672$	223.370	+	26298.0i	0.0128224	+	1.50963i
$673$		−	10740.4i		−	0.615176i	−0.951520	−	0.307588i	$-0.900478\pi$
$673$		−	10740.4i		−	0.615176i	0.951520	−	0.307588i	$-0.0995219\pi$
$674$		−	2233.83i		−	0.127662i
$675$	−13096.3	+	333.777i	−0.746782	+	0.0190327i
$676$	7666.86			0.436212
$677$	1348.41			0.0765488			0.0382744	−	0.999267i	$-0.487814\pi$
$677$	1348.41			0.0765488			0.0382744	+	0.999267i	$0.487814\pi$
$678$	−24418.6	+	207.406i	−1.38317	+	0.0117484i
$679$	−4146.15			−0.234336
$680$			24327.8i			1.37195i
$681$	222.588	+	26206.0i	0.0125251	+	1.47462i
$682$		−	7994.87i		−	0.448885i
$683$	−12636.0			−0.707909			−0.353955	−	0.935263i	$-0.615163\pi$
$683$	−12636.0			−0.707909			−0.353955	+	0.935263i	$0.615163\pi$
$684$	1021.02	−	17.3460i	0.0570757	−	0.000969648i
$685$	−12712.2			−0.709064
$686$		−	48179.0i		−	2.68146i
$687$	−213.162	−	25096.2i	−0.0118379	−	1.39371i
$688$			22927.8i			1.27052i
$689$		−	3682.25i		−	0.203603i
$690$	290.489	+	34200.2i	0.0160272	+	1.88693i
$691$	−7610.67			−0.418992			−0.209496	−	0.977809i	$-0.567182\pi$
$691$	−7610.67			−0.418992			−0.209496	+	0.977809i	$0.567182\pi$
$692$			13535.3i			0.743548i
$693$	−362.195	−	21319.6i	−0.0198537	−	1.16864i
$694$	438.801			0.0240010
$695$		−	18019.9i		−	0.983499i
$696$	115.958	+	13652.0i	0.00631517	+	0.743505i
$697$			30513.4i			1.65822i
$698$	123.514			0.00669780
$699$	−22730.5	+	193.069i	−1.22997	+	0.0104471i
$700$		−	11188.7i		−	0.604131i
$701$	17693.6			0.953321			0.476660	−	0.879088i	$-0.341847\pi$
$701$	17693.6			0.953321			0.476660	+	0.879088i	$0.341847\pi$
$702$	−97.8793	−	3840.47i	−0.00526242	−	0.206480i
$703$	374.153			0.0200732
$704$	2879.85			0.154174
$705$	197.011	+	23194.6i	0.0105246	+	1.23909i
$706$	−6872.54			−0.366362
$707$		−	27958.4i		−	1.48725i
$708$	80.0481	+	9424.31i	0.00424914	+	0.500264i
$709$	−18498.7			−0.979877			−0.489939	−	0.871757i	$-0.662981\pi$
$709$	−18498.7			−0.979877			−0.489939	+	0.871757i	$0.662981\pi$
$710$			56608.3i			2.99222i
$711$	−400.901	−	23598.0i	−0.0211462	−	1.24472i
$712$		−	11614.8i		−	0.611351i
$713$	12959.0			0.680673
$714$	−64720.4	+	549.722i	−3.39230	+	0.0288135i
$715$			2816.08i			0.147294i
$716$	−11793.8			−0.615580
$717$	11048.5	−	93.8438i	0.575473	−	0.00488795i
$718$		−	11773.3i		−	0.611944i
$719$		−	8814.90i		−	0.457219i	−0.973518	−	0.228609i	$-0.926582\pi$
$719$		−	8814.90i		−	0.457219i	0.973518	−	0.228609i	$-0.0734178\pi$
$720$	31849.8	−	541.090i	1.64857	−	0.0280073i
$721$			48986.4i			2.53030i
$722$	22979.6			1.18451
$723$	−23158.8	+	196.706i	−1.19127	+	0.0101184i
$724$	−14981.0			−0.769013
$725$		−	16358.2i		−	0.837972i
$726$	−13613.6	+	115.631i	−0.695936	+	0.00591113i
$727$			1845.50i			0.0941485i	0.998891	+	0.0470742i	$0.0149897\pi$
$727$			1845.50i			0.0941485i	−0.998891	+	0.0470742i	$0.985010\pi$
$728$	−4019.26			−0.204620
$729$	19657.4	−	1002.64i	0.998702	−	0.0509395i
$730$	−23618.8			−1.19750
$731$	−31522.5			−1.59494
$732$	−10.1588	−	1196.03i	−0.000512951	−	0.0603913i
$733$		−	20657.5i		−	1.04093i	−0.853882	−	0.520466i	$-0.825758\pi$
$733$		−	20657.5i		−	1.04093i	0.853882	−	0.520466i	$-0.174242\pi$
$734$		−	21594.9i		−	1.08594i
$735$	−58936.5	+	500.594i	−2.95769	+	0.0251220i
$736$		−	19865.4i		−	0.994905i
$737$	11820.9	+	5400.82i	0.590813	+	0.269934i
$738$	25555.1	−	434.152i	1.27466	−	0.0216549i
$739$		−	11568.3i		−	0.575843i	−0.957654	−	0.287922i	$-0.907036\pi$
$739$		−	11568.3i		−	0.575843i	0.957654	−	0.287922i	$-0.0929642\pi$
$740$	−1889.92			−0.0938848
$741$	3.73315	+	439.515i	0.000185075	+	0.0217894i
$742$			51963.1i			2.57093i
$743$			499.940i			0.0246851i	0.999924	+	0.0123426i	$0.00392886\pi$
$743$			499.940i			0.0246851i	−0.999924	+	0.0123426i	$0.996071\pi$
$744$	−65.5794	−	7720.86i	−0.00323153	−	0.380458i
$745$		−	33347.1i		−	1.63992i
$746$		−	21497.4i		−	1.05506i
$747$	229.142	+	13487.8i	0.0112234	+	0.660632i
$748$		−	9352.48i		−	0.457166i
$749$	−16360.0			−0.798105
$750$	8268.08	−	70.2274i	0.402543	−	0.00341912i
$751$	−25895.8			−1.25826			−0.629129	−	0.777301i	$-0.716588\pi$
$751$	−25895.8			−1.25826			−0.629129	+	0.777301i	$0.716588\pi$
$752$		−	24116.7i		−	1.16948i
$753$	−16230.8	+	137.861i	−0.785505	+	0.00667191i
$754$	4797.02			0.231694
$755$	11641.0			0.561137
$756$	428.296	+	16805.0i	0.0206045	+	0.808454i
$757$		−	2542.94i		−	0.122094i	−0.998135	−	0.0610468i	$-0.980556\pi$
$757$		−	2542.94i		−	0.122094i	0.998135	−	0.0610468i	$-0.0194439\pi$
$758$			43946.6i			2.10582i
$759$	136.800	+	16105.9i	0.00654221	+	0.770234i
$760$	−2331.40			−0.111275
$761$			14696.3i			0.700051i	0.936740	+	0.350026i	$0.113827\pi$
$761$			14696.3i			0.700051i	−0.936740	+	0.350026i	$0.886173\pi$
$762$	−23663.4	+	200.992i	−1.12498	+	0.00955533i
$763$	−41915.1			−1.98877
$764$	−4751.86			−0.225021
$765$	743.922	+	43788.9i	0.0351589	+	2.06953i
$766$	15737.1			0.742304
$767$	−4056.54			−0.190969
$768$	−23767.8	+	201.879i	−1.11673	+	0.00948525i
$769$		−	19707.8i		−	0.924164i	−0.886837	−	0.462082i	$-0.847103\pi$
$769$		−	19707.8i		−	0.924164i	0.886837	−	0.462082i	$-0.152897\pi$
$770$		−	39740.0i		−	1.85991i
$771$	305.356	+	35950.5i	0.0142635	+	1.67928i
$772$	15157.9			0.706665
$773$			23401.9i			1.08888i	0.838799	+	0.544442i	$0.183258\pi$
$773$			23401.9i			1.08888i	−0.838799	+	0.544442i	$0.816742\pi$
$774$	448.509	+	26400.3i	0.0208286	+	1.22602i
$775$			9251.34i			0.428797i
$776$		−	1866.00i		−	0.0863217i
$777$	52.3138	+	6159.06i	0.00241537	+	0.284369i
$778$		−	43794.9i		−	2.01815i
$779$	−2924.18			−0.134493
$780$	−18.8568	−	2220.07i	−0.000865619	−	0.101912i
$781$			26658.6i			1.22141i
$782$	48889.6			2.23566
$783$	626.185	+	24569.5i	0.0285799	+	1.12138i
$784$	61279.4			2.79152
$785$	−31379.3			−1.42672
$786$	147.899	+	17412.6i	0.00671168	+	0.790187i
$787$		−	15525.4i		−	0.703202i	−0.936150	−	0.351601i	$-0.885637\pi$
$787$		−	15525.4i		−	0.703202i	0.936150	−	0.351601i	$-0.114363\pi$
$788$	−5549.11			−0.250861
$789$	40.7943	+	4802.83i	0.00184070	+	0.216711i
$790$		−	43986.9i		−	1.98099i
$791$			45991.8i			2.06736i
$792$	9595.05	−	163.008i	0.430486	−	0.00731345i
$793$	514.811			0.0230536
$794$	−28286.6			−1.26430
$795$	35160.1	−	298.642i	1.56855	−	0.0133230i
$796$	−110.488			−0.00491977
$797$		−	5392.99i		−	0.239686i	−0.992793	−	0.119843i	$-0.961761\pi$
$797$		−	5392.99i		−	0.239686i	0.992793	−	0.119843i	$-0.0382391\pi$
$798$	−52.6814	−	6202.34i	−0.00233697	−	0.275138i
$799$	33157.0			1.46810
$800$	14181.8			0.626751
$801$	−355.169	−	20906.0i	−0.0156670	−	0.922196i
$802$	−589.029			−0.0259344
$803$	−11122.8			−0.488812
$804$	−9355.24	−	4178.61i	−0.410366	−	0.183294i
$805$	64415.3			2.82030
$806$	−2712.94			−0.118560
$807$	−56.7230	−	6678.17i	−0.00247428	−	0.291304i
$808$	12582.9			0.547853
$809$	−20798.1			−0.903860			−0.451930	−	0.892053i	$-0.649264\pi$
$809$	−20798.1			−0.903860			−0.451930	+	0.892053i	$0.649264\pi$
$810$	36662.9	−	1246.08i	1.59037	−	0.0540527i
$811$			31020.6i			1.34313i	0.740945	+	0.671565i	$0.234378\pi$
$811$			31020.6i			1.34313i	−0.740945	+	0.671565i	$0.765622\pi$
$812$	−20990.6			−0.907175
$813$	−206.081	−	24262.5i	−0.00889001	−	1.04665i
$814$	−2870.31			−0.123592
$815$	−22684.4			−0.974970
$816$	−386.747	−	45532.9i	−0.0165917	−	1.95340i
$817$		−	3020.89i		−	0.129360i
$818$		−	15226.3i		−	0.650827i
$819$	−7234.48	+	122.905i	−0.308661	+	0.00524378i
$820$	14770.6			0.629039
$821$			5534.52i			0.235269i	0.993057	+	0.117635i	$0.0375312\pi$
$821$			5534.52i			0.235269i	−0.993057	+	0.117635i	$0.962469\pi$
$822$	15220.5	−	129.279i	0.645833	−	0.00548557i
$823$	−9525.88			−0.403465			−0.201732	−	0.979441i	$-0.564657\pi$
$823$	−9525.88			−0.403465			−0.201732	+	0.979441i	$0.564657\pi$
$824$	−22046.7			−0.932079
$825$	−11497.9	+	97.6605i	−0.485217	+	0.00412134i
$826$	57245.1			2.41139
$827$			15094.8i			0.634701i	0.948308	+	0.317350i	$0.102793\pi$
$827$			15094.8i			0.634701i	−0.948308	+	0.317350i	$0.897207\pi$
$828$	−215.694	−	12696.3i	−0.00905301	−	0.532881i
$829$	21586.7			0.904389			0.452195	−	0.891919i	$-0.350641\pi$
$829$	21586.7			0.904389			0.452195	+	0.891919i	$0.350641\pi$
$830$			25141.4i			1.05141i
$831$	−28507.8	+	242.139i	−1.19004	+	0.0101080i
$832$		−	977.232i		−	0.0407205i
$833$			84250.5i			3.50433i
$834$	183.257	+	21575.4i	0.00760871	+	0.895796i
$835$		−	26049.1i		−	1.07960i
$836$	896.274			0.0370793
$837$	−354.137	−	13895.2i	−0.0146246	−	0.573821i
$838$		−	29970.0i		−	1.23544i
$839$			5422.37i			0.223124i	0.993757	+	0.111562i	$0.0355854\pi$
$839$			5422.37i			0.223124i	−0.993757	+	0.111562i	$0.964415\pi$
$840$	−325.974	−	38378.0i	−0.0133895	−	1.57639i
$841$	−6300.05			−0.258315
$842$	28513.1			1.16701
$843$	−45361.7	+	385.293i	−1.85331	+	0.0157416i
$844$	−3526.94			−0.143841
$845$	−31510.8			−1.28285
$846$	−471.766	−	27769.2i	−0.0191721	−	1.12852i
$847$			25641.0i			1.04018i
$848$	−36557.8			−1.48042
$849$	−7357.64	+	62.4942i	−0.297425	+	0.00252626i
$850$			34901.9i			1.40838i
$851$		−	4652.53i		−	0.187411i
$852$	−178.509	−	21016.4i	−0.00717796	−	0.845083i
$853$	−41955.8			−1.68410			−0.842052	−	0.539397i	$-0.818652\pi$
$853$	−41955.8			−1.68410			−0.842052	+	0.539397i	$0.818652\pi$
$854$	−7264.90			−0.291100
$855$	−4196.41	+	71.2920i	−0.167853	+	0.00285162i
$856$		−	7362.94i		−	0.293995i
$857$	−11822.8			−0.471249			−0.235624	−	0.971844i	$-0.575713\pi$
$857$	−11822.8			−0.471249			−0.235624	+	0.971844i	$0.575713\pi$
$858$	−28.6387	−	3371.73i	−0.00113952	−	0.134159i
$859$	−2828.87			−0.112363			−0.0561815	−	0.998421i	$-0.517893\pi$
$859$	−2828.87			−0.112363			−0.0561815	+	0.998421i	$0.517893\pi$
$860$			15259.1i			0.605035i
$861$	−408.857	−	48136.0i	−0.0161833	−	1.90531i
$862$			18095.6i			0.715011i
$863$		−	20318.8i		−	0.801460i	−0.916196	−	0.400730i	$-0.868757\pi$
$863$		−	20318.8i		−	0.801460i	0.916196	−	0.400730i	$-0.131243\pi$
$864$	−21300.5	+	542.871i	−0.838725	+	0.0213760i
$865$		−	55630.2i		−	2.18669i
$866$		−	40141.9i		−	1.57515i
$867$	37073.5	−	314.895i	1.45223	−	0.0123349i
$868$	11871.2			0.464209
$869$		−	20714.7i		−	0.808630i
$870$	389.053	+	45804.4i	0.0151611	+	1.78496i
$871$	1832.68	−	4011.25i	0.0712952	−	0.156046i
$872$		−	18864.2i		−	0.732596i
$873$	−57.0607	−	3358.72i	−0.00221216	−	0.130213i
$874$			4685.22i			0.181327i
$875$		−	15572.7i		−	0.601662i
$876$	8768.73	−	74.4798i	0.338205	−	0.00287265i
$877$	−555.331			−0.0213822			−0.0106911	−	0.999943i	$-0.503403\pi$
$877$	−555.331			−0.0213822			−0.0106911	+	0.999943i	$0.503403\pi$
$878$	−45310.0			−1.74162
$879$	230.619	+	27151.5i	0.00884937	+	1.04186i
$880$	27958.4			1.07100
$881$		−	25260.0i		−	0.965984i	−0.875625	−	0.482992i	$-0.839550\pi$
$881$		−	25260.0i		−	0.965984i	0.875625	−	0.482992i	$-0.160450\pi$
$882$	70560.2	−	1198.73i	2.69375	−	0.0457636i
$883$		−	2717.38i		−	0.103564i	−0.998658	−	0.0517820i	$-0.983510\pi$
$883$		−	2717.38i		−	0.103564i	0.998658	−	0.0517820i	$-0.0164901\pi$
$884$	−3173.62			−0.120747
$885$	−328.998	−	38734.0i	−0.0124962	−	1.47122i
$886$	−12641.0			−0.479326
$887$			39882.8i			1.50973i	0.655878	+	0.754867i	$0.272299\pi$
$887$			39882.8i			1.50973i	−0.655878	+	0.754867i	$0.727701\pi$
$888$	−2771.93	+	23.5442i	−0.104752	+	0.000889743i
$889$			44569.4i			1.68145i
$890$		−	38969.1i		−	1.46769i
$891$	17265.7	−	586.815i	0.649182	−	0.0220640i
$892$	−10103.3			−0.379242
$893$			3177.53i			0.119073i
$894$	339.130	+	39926.8i	0.0126870	+	1.49368i
$895$	48472.7			1.81035
$896$			54280.4i			2.02386i
$897$	5465.29	−	46.4211i	0.203435	−	0.00172793i
$898$			60078.9i			2.23258i
$899$	17356.1			0.643891
$900$	9063.75	−	153.982i	0.335694	−	0.00570305i
$901$		−	50261.7i		−	1.85845i
$902$	22432.8			0.828083
$903$	49727.8	−	422.378i	1.83260	−	0.0155657i
$904$	−20699.0			−0.761545
$905$	61572.1			2.26158
$906$	−13937.9	+	118.385i	−0.511098	+	0.00434116i
$907$	−20095.0			−0.735658			−0.367829	−	0.929893i	$-0.619899\pi$
$907$	−20095.0			−0.735658			−0.367829	+	0.929893i	$0.619899\pi$
$908$		−	18134.1i		−	0.662777i
$909$	22648.7	−	384.774i	0.826412	−	0.0140398i
$910$	−13485.1			−0.491240
$911$		−	28989.3i		−	1.05429i	−0.849775	−	0.527145i	$-0.823262\pi$
$911$		−	28989.3i		−	1.05429i	0.849775	−	0.527145i	$-0.176738\pi$
$912$	4363.55	−	37.0631i	0.158434	−	0.00134570i
$913$			11839.8i			0.429180i
$914$	13749.3			0.497579
$915$	41.7528	+	4915.68i	0.00150853	+	0.177604i
$916$			17366.2i			0.626412i
$917$	32796.2			1.18105
$918$	−1336.03	−	52421.4i	−0.0480342	−	1.88471i
$919$			31414.6i			1.12761i	0.825908	+	0.563804i	$0.190663\pi$
$919$			31414.6i			1.12761i	−0.825908	+	0.563804i	$0.809337\pi$
$920$			28990.6i			1.03890i
$921$	28959.1	−	245.972i	1.03608	−	0.00880028i
$922$		−	116.277i		−	0.00415334i
$923$	9046.18			0.322599
$924$	125.316	+	14753.9i	0.00446169	+	0.525289i
$925$	3321.40			0.118062
$926$		−	50820.6i		−	1.80353i
$927$	−39683.1	+	674.168i	−1.40600	+	0.0238863i
$928$		−	26605.9i		−	0.941142i
$929$	−29247.0			−1.03290			−0.516450	−	0.856317i	$-0.672747\pi$
$929$	−29247.0			−1.03290			−0.516450	+	0.856317i	$0.672747\pi$
$930$	−220.028	−	25904.5i	−0.00775806	−	0.913380i
$931$	−8073.95			−0.284225
$932$	15729.2			0.552817
$933$	15241.9	−	129.461i	0.534831	−	0.00454274i
$934$		−	30721.3i		−	1.07626i
$935$			38438.8i			1.34447i
$936$	−55.3144	−	3255.93i	−0.00193163	−	0.113700i
$937$		−	9091.36i		−	0.316971i	−0.987361	−	0.158486i	$-0.949339\pi$
$937$		−	9091.36i		−	0.316971i	0.987361	−	0.158486i	$-0.0506611\pi$
$938$	−25862.5	+	56605.9i	−0.900255	+	1.97041i
$939$	443.113	+	52169.1i	0.0153998	+	1.81307i
$940$		−	16050.3i		−	0.556919i
$941$	7.72502			0.000267618			0.000133809	−	1.00000i	$-0.499957\pi$
$941$	7.72502			0.000267618			0.000133809		1.00000i	$0.499957\pi$
$942$	37570.7	−	319.118i	1.29949	−	0.0110376i
$943$			36361.8i			1.25568i
$944$			40273.8i			1.38856i
$945$	−1760.30	−	69068.6i	−0.0605954	−	2.37757i
$946$			23174.7i			0.796483i
$947$		−	27094.3i		−	0.929722i	−0.885384	−	0.464861i	$-0.846104\pi$
$947$		−	27094.3i		−	0.929722i	0.885384	−	0.464861i	$-0.153896\pi$
$948$	138.709	+	16330.6i	0.00475216	+	0.559486i
$949$			3774.36i			0.129105i
$950$	−3344.74			−0.114229
$951$	297.418	+	35015.9i	0.0101414	+	1.19397i
$952$	−54861.8			−1.86773
$953$		−	262.432i		−	0.00892025i	−0.999990	−	0.00446013i	$-0.998580\pi$
$953$		−	262.432i		−	0.00892025i	0.999990	−	0.00446013i	$-0.00141971\pi$
$954$	−42094.5	+	715.135i	−1.42857	+	0.0242698i
$955$	19530.2			0.661760
$956$	−7645.39			−0.258650
$957$	183.217	+	21570.7i	0.00618868	+	0.728612i
$958$		−	14354.9i		−	0.484118i
$959$		−	28667.4i		−	0.965295i
$960$	9331.12	−	79.2566i	0.313709	−	0.00266458i
$961$	19975.3			0.670516
$962$			973.994i			0.0326433i
$963$	−225.152	−	13252.9i	−0.00753418	−	0.443479i
$964$	16025.5			0.535422
$965$	−62299.1			−2.07822
$966$	−77125.1	+	655.084i	−2.56880	+	0.0218188i
$967$	21450.9			0.713355			0.356677	−	0.934228i	$-0.383910\pi$
$967$	21450.9			0.713355			0.356677	+	0.934228i	$0.383910\pi$
$968$	−11539.9			−0.383168
$969$	50.9564	+	5999.25i	0.00168933	+	0.198889i
$970$		−	6260.70i		−	0.207236i
$971$		−	29418.5i		−	0.972279i	−0.873881	−	0.486140i	$-0.838405\pi$
$971$		−	29418.5i		−	0.972279i	0.873881	−	0.486140i	$-0.161595\pi$
$972$	−13607.5	+	578.232i	−0.449035	+	0.0190811i
$973$	40636.7			1.33890
$974$			63023.4i			2.07331i
$975$	33.1396	+	3901.63i	0.00108853	+	0.128156i
$976$		−	5111.09i		−	0.167625i
$977$		−	44933.5i		−	1.47139i	−0.677311	−	0.735697i	$-0.736855\pi$
$977$		−	44933.5i		−	1.47139i	0.677311	−	0.735697i	$-0.263145\pi$
$978$	27160.3	−	230.694i	0.888027	−	0.00754272i
$979$		−	18351.7i		−	0.599105i
$980$	40783.1			1.32935
$981$	−576.851	−	33954.7i	−0.0187741	−	1.10509i
$982$		−	30794.2i		−	1.00069i
$983$	18222.1			0.591246			0.295623	−	0.955305i	$-0.404473\pi$
$983$	18222.1			0.591246			0.295623	+	0.955305i	$0.404473\pi$
$984$	21664.0	−	184.009i	0.701852	−	0.00596138i
$985$	22806.9			0.737754
$986$	65478.0			2.11485
$987$	−52306.4	+	444.280i	−1.68686	+	0.0143278i
$988$		−	304.137i		−	0.00979340i
$989$	−37564.2			−1.20776
$990$	32192.7	−	546.915i	1.03349	−	0.0175577i
$991$		−	19524.5i		−	0.625847i	−0.949778	−	0.312924i	$-0.898692\pi$
$991$		−	19524.5i		−	0.625847i	0.949778	−	0.312924i	$-0.101308\pi$
$992$			15046.8i			0.481591i
$993$	−153.354	−	18054.8i	−0.00490085	−	0.576992i
$994$	−127658.			−4.07350
$995$	454.106			0.0144685
$996$	−79.2811	−	9334.00i	−0.00252221	−	0.296947i
$997$	−1260.19			−0.0400306			−0.0200153	−	0.999800i	$-0.506371\pi$
$997$	−1260.19			−0.0400306			−0.0200153	+	0.999800i	$0.506371\pi$
$998$		−	35453.3i		−	1.12450i
$999$	−4988.63	+	127.142i	−0.157991	+	0.00402661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.d.b.200.16	yes	64
3.2	odd	2	inner	201.4.d.b.200.50	yes	64
67.66	odd	2	inner	201.4.d.b.200.49	yes	64
201.200	even	2	inner	201.4.d.b.200.15	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.d.b.200.15	✓	64	201.200	even	2	inner
201.4.d.b.200.16	yes	64	1.1	even	1	trivial
201.4.d.b.200.49	yes	64	67.66	odd	2	inner
201.4.d.b.200.50	yes	64	3.2	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.40522 q^{2} +(-5.19596 + 0.0441335i) q^{3} +3.59552 q^{4} -14.7776 q^{5} +(17.6934 - 0.150284i) q^{6} -33.3251i q^{7} +14.9982 q^{8} +(26.9961 - 0.458632i) q^{9} +O(q^{10})\)	\(q-3.40522 q^{2} +(-5.19596 + 0.0441335i) q^{3} +3.59552 q^{4} -14.7776 q^{5} +(17.6934 - 0.150284i) q^{6} -33.3251i q^{7} +14.9982 q^{8} +(26.9961 - 0.458632i) q^{9} +50.3210 q^{10} +23.6977 q^{11} +(-18.6822 + 0.158683i) q^{12} -8.04145i q^{13} +113.479i q^{14} +(76.7840 - 0.652187i) q^{15} -79.8364 q^{16} -109.764i q^{17} +(-91.9277 + 1.56174i) q^{18} +10.5190 q^{19} -53.1332 q^{20} +(1.47075 + 173.156i) q^{21} -80.6959 q^{22} -130.802i q^{23} +(-77.9302 + 0.661923i) q^{24} +93.3780 q^{25} +27.3829i q^{26} +(-140.251 + 3.57447i) q^{27} -119.821i q^{28} -175.183i q^{29} +(-261.466 + 2.22084i) q^{30} +99.0741i q^{31} +151.875 q^{32} +(-123.132 + 1.04586i) q^{33} +373.769i q^{34} +492.466i q^{35} +(97.0651 - 1.64902i) q^{36} +35.5694 q^{37} -35.8193 q^{38} +(0.354897 + 41.7831i) q^{39} -221.638 q^{40} -277.992 q^{41} +(-5.00823 - 589.634i) q^{42} -287.185i q^{43} +85.2056 q^{44} +(-398.938 + 6.77749i) q^{45} +445.408i q^{46} +302.077i q^{47} +(414.827 - 3.52346i) q^{48} -767.562 q^{49} -317.973 q^{50} +(4.84425 + 570.328i) q^{51} -28.9132i q^{52} +457.909 q^{53} +(477.584 - 12.1718i) q^{54} -350.196 q^{55} -499.817i q^{56} +(-54.6561 + 0.464238i) q^{57} +596.536i q^{58} -504.454i q^{59} +(276.079 - 2.34495i) q^{60} +64.0196i q^{61} -337.369i q^{62} +(-15.2839 - 899.648i) q^{63} +121.524 q^{64} +118.834i q^{65} +(419.293 - 3.56139i) q^{66} +(498.821 + 227.905i) q^{67} -394.658i q^{68} +(5.77272 + 679.640i) q^{69} -1676.95i q^{70} +1124.94i q^{71} +(404.893 - 6.87866i) q^{72} -469.363 q^{73} -121.122 q^{74} +(-485.189 + 4.12110i) q^{75} +37.8211 q^{76} -789.728i q^{77} +(-1.20850 - 142.281i) q^{78} -874.125i q^{79} +1179.79 q^{80} +(728.579 - 24.7625i) q^{81} +946.623 q^{82} +499.620i q^{83} +(5.28812 + 622.586i) q^{84} +1622.05i q^{85} +977.928i q^{86} +(7.73143 + 910.244i) q^{87} +355.423 q^{88} -774.410i q^{89} +(1358.47 - 23.0788i) q^{90} -267.982 q^{91} -470.300i q^{92} +(-4.37248 - 514.785i) q^{93} -1028.64i q^{94} -155.445 q^{95} +(-789.136 + 6.70276i) q^{96} -124.415i q^{97} +2613.72 q^{98} +(639.746 - 10.8685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 268 q^{4} - 46 q^{6} + 22 q^{9}+O(q^{10}) \) 64 * q + 268 * q^4 - 46 * q^6 + 22 * q^9	\( 64 q + 268 q^{4} - 46 q^{6} + 22 q^{9} - 36 q^{10} + 20 q^{15} + 556 q^{16} + 128 q^{19} + 96 q^{22} - 904 q^{24} + 2080 q^{25} - 236 q^{33} - 1574 q^{36} + 1004 q^{37} - 176 q^{39} - 648 q^{40} - 1220 q^{49} + 2188 q^{54} - 1344 q^{55} + 550 q^{60} + 4336 q^{64} - 3512 q^{67} + 3968 q^{73} - 3316 q^{76} - 1170 q^{81} + 4020 q^{82} - 9270 q^{84} + 2436 q^{88} + 746 q^{90} - 3408 q^{91} - 1412 q^{93} - 7032 q^{96}+O(q^{100}) \) 64 * q + 268 * q^4 - 46 * q^6 + 22 * q^9 - 36 * q^10 + 20 * q^15 + 556 * q^16 + 128 * q^19 + 96 * q^22 - 904 * q^24 + 2080 * q^25 - 236 * q^33 - 1574 * q^36 + 1004 * q^37 - 176 * q^39 - 648 * q^40 - 1220 * q^49 + 2188 * q^54 - 1344 * q^55 + 550 * q^60 + 4336 * q^64 - 3512 * q^67 + 3968 * q^73 - 3316 * q^76 - 1170 * q^81 + 4020 * q^82 - 9270 * q^84 + 2436 * q^88 + 746 * q^90 - 3408 * q^91 - 1412 * q^93 - 7032 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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