LMFDB - Embedded newform 201.4.d.b.200.6

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			200.6
Character	$\chi$	$=$	201.200
Dual form			201.4.d.b.200.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.99884 q^{2} +(-4.36958 + 2.81190i) q^{3} +16.9884 q^{4} +3.29226 q^{5} +(21.8428 - 14.0562i) q^{6} -9.19710i q^{7} -44.9316 q^{8} +(11.1865 - 24.5736i) q^{9} +O(q^{10})$	\(q-4.99884 q^{2} +(-4.36958 + 2.81190i) q^{3} +16.9884 q^{4} +3.29226 q^{5} +(21.8428 - 14.0562i) q^{6} -9.19710i q^{7} -44.9316 q^{8} +(11.1865 - 24.5736i) q^{9} -16.4575 q^{10} -0.534155 q^{11} +(-74.2322 + 47.7697i) q^{12} +25.8147i q^{13} +45.9748i q^{14} +(-14.3858 + 9.25751i) q^{15} +88.6985 q^{16} +72.5797i q^{17} +(-55.9193 + 122.840i) q^{18} -11.7485 q^{19} +55.9303 q^{20} +(25.8613 + 40.1875i) q^{21} +2.67016 q^{22} +45.6947i q^{23} +(196.332 - 126.343i) q^{24} -114.161 q^{25} -129.044i q^{26} +(20.2184 + 138.832i) q^{27} -156.244i q^{28} -143.975i q^{29} +(71.9123 - 46.2768i) q^{30} -183.749i q^{31} -83.9372 q^{32} +(2.33403 - 1.50199i) q^{33} -362.814i q^{34} -30.2793i q^{35} +(190.040 - 417.467i) q^{36} -193.400 q^{37} +58.7291 q^{38} +(-72.5883 - 112.799i) q^{39} -147.927 q^{40} +111.361 q^{41} +(-129.277 - 200.891i) q^{42} -293.174i q^{43} -9.07444 q^{44} +(36.8288 - 80.9028i) q^{45} -228.421i q^{46} -257.510i q^{47} +(-387.575 + 249.411i) q^{48} +258.413 q^{49} +570.673 q^{50} +(-204.087 - 317.143i) q^{51} +438.550i q^{52} -174.407 q^{53} +(-101.069 - 693.997i) q^{54} -1.75858 q^{55} +413.240i q^{56} +(51.3362 - 33.0357i) q^{57} +719.708i q^{58} +81.3265i q^{59} +(-244.392 + 157.270i) q^{60} +43.6450i q^{61} +918.532i q^{62} +(-226.006 - 102.883i) q^{63} -290.000 q^{64} +84.9888i q^{65} +(-11.6675 + 7.50821i) q^{66} +(306.951 - 454.471i) q^{67} +1233.01i q^{68} +(-128.489 - 199.667i) q^{69} +151.361i q^{70} -412.843i q^{71} +(-502.625 + 1104.13i) q^{72} +205.263 q^{73} +966.773 q^{74} +(498.836 - 321.009i) q^{75} -199.589 q^{76} +4.91268i q^{77} +(362.857 + 563.866i) q^{78} -521.312i q^{79} +292.019 q^{80} +(-478.726 - 549.784i) q^{81} -556.677 q^{82} +121.914i q^{83} +(439.342 + 682.721i) q^{84} +238.951i q^{85} +1465.53i q^{86} +(404.843 + 629.110i) q^{87} +24.0004 q^{88} -1335.98i q^{89} +(-184.101 + 404.420i) q^{90} +237.420 q^{91} +776.280i q^{92} +(516.684 + 802.906i) q^{93} +1287.25i q^{94} -38.6793 q^{95} +(366.770 - 236.023i) q^{96} +1196.90i q^{97} -1291.77 q^{98} +(-5.97530 + 13.1261i) 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 $

$2$	−4.99884			−1.76736			−0.883678	−	0.468095i	$-0.844941\pi$
$2$	−4.99884			−1.76736			−0.883678	+	0.468095i	$0.844941\pi$
$3$	−4.36958	+	2.81190i	−0.840926	+	0.541150i
$3$	−4.36958	+	2.81190i	−0.840926	+	0.541150i
$4$	16.9884			2.12355
$5$	3.29226			0.294469			0.147234	−	0.989102i	$-0.452963\pi$
$5$	3.29226			0.294469			0.147234	+	0.989102i	$0.452963\pi$
$6$	21.8428	−	14.0562i	1.48622	−	0.956405i
$7$		−	9.19710i		−	0.496597i	−0.968684	−	0.248298i	$-0.920129\pi$
$7$		−	9.19710i		−	0.496597i	0.968684	−	0.248298i	$-0.0798714\pi$
$8$	−44.9316			−1.98571
$9$	11.1865	−	24.5736i	0.414313	−	0.910134i
$10$	−16.4575			−0.520432
$11$	−0.534155			−0.0146413			−0.00732063	−	0.999973i	$-0.502330\pi$
$11$	−0.534155			−0.0146413			−0.00732063	+	0.999973i	$0.502330\pi$
$12$	−74.2322	+	47.7697i	−1.78575	+	1.14916i
$13$			25.8147i			0.550747i	0.961337	+	0.275373i	$0.0888015\pi$
$13$			25.8147i			0.550747i	−0.961337	+	0.275373i	$0.911199\pi$
$14$			45.9748i			0.877664i
$15$	−14.3858	+	9.25751i	−0.247627	+	0.159352i
$16$	88.6985			1.38591
$17$			72.5797i			1.03548i	0.855538	+	0.517740i	$0.173227\pi$
$17$			72.5797i			1.03548i	−0.855538	+	0.517740i	$0.826773\pi$
$18$	−55.9193	+	122.840i	−0.732239	+	1.60853i
$19$	−11.7485			−0.141858			−0.0709289	−	0.997481i	$-0.522596\pi$
$19$	−11.7485			−0.141858			−0.0709289	+	0.997481i	$0.522596\pi$
$20$	55.9303			0.625319
$21$	25.8613	+	40.1875i	0.268733	+	0.417601i
$22$	2.67016			0.0258763
$23$			45.6947i			0.414261i	0.978313	+	0.207131i	$0.0664125\pi$
$23$			45.6947i			0.414261i	−0.978313	+	0.207131i	$0.933587\pi$
$24$	196.332	−	126.343i	1.66984	−	1.07457i
$25$	−114.161			−0.913288
$26$		−	129.044i		−	0.973366i
$27$	20.2184	+	138.832i	0.144113	+	0.989561i
$28$		−	156.244i		−	1.05455i
$29$		−	143.975i		−	0.921913i	−0.887423	−	0.460957i	$-0.847506\pi$
$29$		−	143.975i		−	0.921913i	0.887423	−	0.460957i	$-0.152494\pi$
$30$	71.9123	−	46.2768i	0.437645	−	0.281632i
$31$		−	183.749i		−	1.06459i	−0.846559	−	0.532295i	$-0.821330\pi$
$31$		−	183.749i		−	1.06459i	0.846559	−	0.532295i	$-0.178670\pi$
$32$	−83.9372			−0.463692
$33$	2.33403	−	1.50199i	0.0123122	−	0.00792312i
$34$		−	362.814i		−	1.83006i
$35$		−	30.2793i		−	0.146232i
$36$	190.040	−	417.467i	0.879815	−	1.93272i
$37$	−193.400			−0.859316			−0.429658	−	0.902992i	$-0.641366\pi$
$37$	−193.400			−0.859316			−0.429658	+	0.902992i	$0.641366\pi$
$38$	58.7291			0.250713
$39$	−72.5883	−	112.799i	−0.298037	−	0.463137i
$40$	−147.927			−0.584731
$41$	111.361			0.424188			0.212094	−	0.977249i	$-0.431972\pi$
$41$	111.361			0.424188			0.212094	+	0.977249i	$0.431972\pi$
$42$	−129.277	−	200.891i	−0.474948	−	0.738050i
$43$		−	293.174i		−	1.03973i	−0.854247	−	0.519867i	$-0.825981\pi$
$43$		−	293.174i		−	1.03973i	0.854247	−	0.519867i	$-0.174019\pi$
$44$	−9.07444			−0.0310915
$45$	36.8288	−	80.9028i	0.122002	−	0.268006i
$46$		−	228.421i		−	0.732148i
$47$		−	257.510i		−	0.799185i	−0.916693	−	0.399592i	$-0.869152\pi$
$47$		−	257.510i		−	0.799185i	0.916693	−	0.399592i	$-0.130848\pi$
$48$	−387.575	+	249.411i	−1.16545	+	0.749988i
$49$	258.413			0.753392
$50$	570.673			1.61411
$51$	−204.087	−	317.143i	−0.560350	−	0.870762i
$52$			438.550i			1.16954i
$53$	−174.407			−0.452013			−0.226006	−	0.974126i	$-0.572567\pi$
$53$	−174.407			−0.452013			−0.226006	+	0.974126i	$0.572567\pi$
$54$	−101.069	−	693.997i	−0.254698	−	1.74891i
$55$	−1.75858			−0.00431140
$56$			413.240i			0.986099i
$57$	51.3362	−	33.0357i	0.119292	−	0.0767664i
$58$			719.708i			1.62935i
$59$			81.3265i			0.179454i	0.995966	+	0.0897272i	$0.0285995\pi$
$59$			81.3265i			0.179454i	−0.995966	+	0.0897272i	$0.971400\pi$
$60$	−244.392	+	157.270i	−0.525847	+	0.338392i
$61$			43.6450i			0.0916094i	0.998950	+	0.0458047i	$0.0145852\pi$
$61$			43.6450i			0.0916094i	−0.998950	+	0.0458047i	$0.985415\pi$
$62$			918.532i			1.88151i
$63$	−226.006	−	102.883i	−0.451970	−	0.205747i
$64$	−290.000			−0.566406
$65$			84.9888i			0.162178i
$66$	−11.6675	+	7.50821i	−0.0217601	+	0.0140030i
$67$	306.951	−	454.471i	0.559703	−	0.828694i
$67$	306.951	−	454.471i	0.559703	−	0.828694i
$68$			1233.01i			2.19889i
$69$	−128.489	−	199.667i	−0.224178	−	0.348363i
$70$			151.361i			0.258445i
$71$		−	412.843i		−	0.690076i	−0.938589	−	0.345038i	$-0.887866\pi$
$71$		−	412.843i		−	0.690076i	0.938589	−	0.345038i	$-0.112134\pi$
$72$	−502.625	+	1104.13i	−0.822707	+	1.80727i
$73$	205.263			0.329100			0.164550	−	0.986369i	$-0.447383\pi$
$73$	205.263			0.329100			0.164550	+	0.986369i	$0.447383\pi$
$74$	966.773			1.51872
$75$	498.836	−	321.009i	0.768008	−	0.494226i
$76$	−199.589			−0.301242
$77$			4.91268i			0.00727081i
$78$	362.857	+	563.866i	0.526737	+	0.818529i
$79$		−	521.312i		−	0.742432i	−0.928547	−	0.371216i	$-0.878941\pi$
$79$		−	521.312i		−	0.742432i	0.928547	−	0.371216i	$-0.121059\pi$
$80$	292.019			0.408109
$81$	−478.726	−	549.784i	−0.656689	−	0.754161i
$82$	−556.677			−0.749691
$83$			121.914i			0.161226i	0.996745	+	0.0806131i	$0.0256878\pi$
$83$			121.914i			0.161226i	−0.996745	+	0.0806131i	$0.974312\pi$
$84$	439.342	+	682.721i	0.570669	+	0.886797i
$85$			238.951i			0.304917i
$86$			1465.53i			1.83758i
$87$	404.843	+	629.110i	0.498894	+	0.775261i
$88$	24.0004			0.0290734
$89$		−	1335.98i		−	1.59116i	−0.605848	−	0.795581i	$-0.707166\pi$
$89$		−	1335.98i		−	1.59116i	0.605848	−	0.795581i	$-0.292834\pi$
$90$	−184.101	+	404.420i	−0.215622	+	0.473663i
$91$	237.420			0.273499
$92$			776.280i			0.879705i
$93$	516.684	+	802.906i	0.576103	+	0.895242i
$94$			1287.25i			1.41244i
$95$	−38.6793			−0.0417727
$96$	366.770	−	236.023i	0.389930	−	0.250927i
$97$			1196.90i			1.25285i	0.779482	+	0.626424i	$0.215482\pi$
$97$			1196.90i			1.25285i	−0.779482	+	0.626424i	$0.784518\pi$
$98$	−1291.77			−1.33151
$99$	−5.97530	+	13.1261i	−0.00606607	+	0.0133255i
$100$	−1939.41			−1.93941
$101$	−1753.61			−1.72763			−0.863814	−	0.503810i	$-0.831931\pi$
$101$	−1753.61			−1.72763			−0.863814	+	0.503810i	$0.831931\pi$
$102$	1020.20	+	1585.35i	0.990339	+	1.53895i
$103$	398.303			0.381029			0.190514	−	0.981684i	$-0.438984\pi$
$103$	398.303			0.381029			0.190514	+	0.981684i	$0.438984\pi$
$104$		−	1159.89i		−	1.09363i
$105$	85.1423	+	132.308i	0.0791337	+	0.122971i
$106$	871.834			0.798868
$107$		−	1647.37i		−	1.48839i	−0.667965	−	0.744193i	$-0.732834\pi$
$107$		−	1647.37i		−	1.48839i	0.667965	−	0.744193i	$-0.267166\pi$
$108$	343.479	+	2358.53i	0.306030	+	2.10138i
$109$		−	1767.60i		−	1.55326i	−0.629959	−	0.776628i	$-0.716928\pi$
$109$		−	1767.60i		−	1.55326i	0.629959	−	0.776628i	$-0.283072\pi$
$110$	8.79086			0.00761978
$111$	845.075	−	543.820i	0.722621	−	0.465019i
$112$		−	815.770i		−	0.688241i
$113$	614.185			0.511307			0.255654	−	0.966768i	$-0.417709\pi$
$113$	614.185			0.511307			0.255654	+	0.966768i	$0.417709\pi$
$114$	−256.621	+	165.140i	−0.210831	+	0.135674i
$115$			150.439i			0.121987i
$116$		−	2445.91i		−	1.95773i
$117$	634.361	+	288.775i	0.501254	+	0.228182i
$118$		−	406.538i		−	0.317160i
$119$	667.523			0.514216
$120$	646.377	−	415.954i	0.491715	−	0.316427i
$121$	−1330.71			−0.999786
$122$		−	218.174i		−	0.161906i
$123$	−486.602	+	313.136i	−0.356710	+	0.229549i
$124$		−	3121.60i		−	2.26071i
$125$	−787.381			−0.563404
$126$	1129.77	+	514.296i	0.798792	+	0.363628i
$127$	−1637.17			−1.14390			−0.571952	−	0.820287i	$-0.693814\pi$
$127$	−1637.17			−1.14390			−0.571952	+	0.820287i	$0.693814\pi$
$128$	2121.16			1.46473
$129$	824.375	+	1281.05i	0.562653	+	0.874340i
$130$		−	424.845i		−	0.286626i
$131$		−	1824.09i		−	1.21658i	−0.793715	−	0.608290i	$-0.791856\pi$
$131$		−	1824.09i		−	1.21658i	0.793715	−	0.608290i	$-0.208144\pi$
$132$	39.6515	−	25.5164i	0.0261456	−	0.0168251i
$133$			108.053i			0.0704462i
$134$	−1534.40	+	2271.83i	−0.989194	+	1.46460i
$135$	66.5644	+	457.070i	0.0424367	+	0.291395i
$136$		−	3261.12i		−	2.05617i
$137$	−1485.17			−0.926180			−0.463090	−	0.886311i	$-0.653259\pi$
$137$	−1485.17			−0.926180			−0.463090	+	0.886311i	$0.653259\pi$
$138$	642.296	+	998.102i	0.396202	+	0.615682i
$139$		−	614.065i		−	0.374707i	−0.982293	−	0.187354i	$-0.940009\pi$
$139$		−	614.065i		−	0.374707i	0.982293	−	0.187354i	$-0.0599910\pi$
$140$		−	514.397i		−	0.310532i
$141$	724.092	+	1125.21i	0.432479	+	0.672055i
$142$			2063.73i			1.21961i
$143$		−	13.7891i		−	0.00806363i
$144$	992.222	−	2179.64i	0.574203	−	1.26137i
$145$		−	474.004i		−	0.271475i
$146$	−1026.08			−0.581636
$147$	−1129.16	+	726.632i	−0.633547	+	0.407698i
$148$	−3285.55			−1.82480
$149$			1292.33i			0.710547i	0.934762	+	0.355274i	$0.115612\pi$
$149$			1292.33i			0.710547i	−0.934762	+	0.355274i	$0.884388\pi$
$150$	−2493.60	+	1604.67i	−1.35734	+	0.873473i
$151$	2039.62			1.09922			0.549608	−	0.835422i	$-0.314777\pi$
$151$	2039.62			1.09922			0.549608	+	0.835422i	$0.314777\pi$
$152$	527.880			0.281689
$153$	1783.55	+	811.910i	0.942426	+	0.429013i
$154$		−	24.5577i		−	0.0128501i
$155$		−	604.950i		−	0.313489i
$156$	−1233.16	−	1916.28i	−0.632896	−	0.983495i
$157$	−155.918			−0.0792588			−0.0396294	−	0.999214i	$-0.512618\pi$
$157$	−155.918			−0.0792588			−0.0396294	+	0.999214i	$0.512618\pi$
$158$			2605.95i			1.31214i
$159$	762.086	−	490.415i	0.380109	−	0.244607i
$160$	−276.343			−0.136543
$161$	420.259			0.205721
$162$	2393.08	+	2748.28i	1.16060	+	1.33287i
$163$	−2833.26			−1.36146			−0.680730	−	0.732534i	$-0.738337\pi$
$163$	−2833.26			−1.36146			−0.680730	+	0.732534i	$0.738337\pi$
$164$	1891.85			0.900784
$165$	7.68425	−	4.94495i	0.00362557	−	0.00233311i
$166$		−	609.428i		−	0.284944i
$167$		−	3883.55i		−	1.79951i	−0.436396	−	0.899755i	$-0.643745\pi$
$167$		−	3883.55i		−	1.79951i	0.436396	−	0.899755i	$-0.356255\pi$
$168$	−1161.99	−	1805.69i	−0.533628	−	0.829237i
$169$	1530.60			0.696678
$170$		−	1194.48i		−	0.538897i
$171$	−131.425	+	288.704i	−0.0587736	+	0.129110i
$172$		−	4980.55i		−	2.20793i
$173$			290.336i			0.127594i	0.997963	+	0.0637971i	$0.0203211\pi$
$173$			290.336i			0.127594i	−0.997963	+	0.0637971i	$0.979679\pi$
$174$	−2023.75	−	3144.82i	−0.881723	−	1.37016i
$175$			1049.95i			0.453536i
$176$	−47.3788			−0.0202915
$177$	−228.682	−	355.363i	−0.0971117	−	0.150908i
$178$			6678.34i			2.81215i
$179$	324.144			0.135350			0.0676750	−	0.997707i	$-0.478442\pi$
$179$	324.144			0.135350			0.0676750	+	0.997707i	$0.478442\pi$
$180$	625.662	−	1374.41i	0.259078	−	0.569125i
$181$	2243.54			0.921330			0.460665	−	0.887574i	$-0.347611\pi$
$181$	2243.54			0.921330			0.460665	+	0.887574i	$0.347611\pi$
$182$	−1186.83			−0.483371
$183$	−122.725	−	190.710i	−0.0495744	−	0.0770367i
$184$		−	2053.14i		−	0.822604i
$185$	−636.722			−0.253042
$186$	−2582.82	−	4013.60i	−1.01818	−	1.58221i
$187$		−	38.7688i		−	0.0151607i
$188$		−	4374.68i		−	1.69711i
$189$	1276.85	−	185.951i	0.491413	−	0.0715658i
$190$	193.351			0.0738273
$191$	−3246.43			−1.22986			−0.614931	−	0.788581i	$-0.710816\pi$
$191$	−3246.43			−1.22986			−0.614931	+	0.788581i	$0.710816\pi$
$192$	1267.18	−	815.450i	0.476305	−	0.306511i
$193$	504.647			0.188214			0.0941070	−	0.995562i	$-0.470000\pi$
$193$	504.647			0.188214			0.0941070	+	0.995562i	$0.470000\pi$
$194$		−	5983.09i		−	2.21423i
$195$	−238.980	−	371.365i	−0.0877625	−	0.136380i
$196$	4390.03			1.59986
$197$	−3208.46			−1.16037			−0.580186	−	0.814484i	$-0.697020\pi$
$197$	−3208.46			−1.16037			−0.580186	+	0.814484i	$0.697020\pi$
$198$	29.8696	−	65.6154i	0.0107209	−	0.0235509i
$199$	3083.43			1.09838			0.549192	−	0.835696i	$-0.314936\pi$
$199$	3083.43			1.09838			0.549192	+	0.835696i	$0.314936\pi$
$200$	5129.43			1.81353
$201$	−63.3224	+	2848.96i	−0.0222210	+	0.999753i
$202$	8766.01			3.05334
$203$	−1324.15			−0.457819
$204$	−3467.11	−	5387.75i	−1.18993	−	1.84911i
$205$	366.630			0.124910
$206$	−1991.05			−0.673414
$207$	1122.89	+	511.162i	0.377033	+	0.171634i
$208$			2289.73i			0.763288i
$209$	6.27554			0.00207698
$210$	−425.613	−	661.385i	−0.139857	−	0.217333i
$211$	2860.61			0.933329			0.466665	−	0.884434i	$-0.345455\pi$
$211$	2860.61			0.933329			0.466665	+	0.884434i	$0.345455\pi$
$212$	−2962.90			−0.959872
$213$	1160.87	+	1803.95i	0.373435	+	0.580303i
$214$			8234.94i			2.63051i
$215$		−	965.205i		−	0.306170i
$216$	−908.446	−	6237.92i	−0.286166	−	1.96499i
$217$	−1689.96			−0.528672
$218$			8835.93i			2.74516i
$219$	−896.915	+	577.180i	−0.276748	+	0.178092i
$220$	−29.8755			−0.00915547
$221$	−1873.62			−0.570288
$222$	−4224.39	+	2718.47i	−1.27713	+	0.821854i
$223$	1975.88			0.593339			0.296670	−	0.954980i	$-0.404124\pi$
$223$	1975.88			0.593339			0.296670	+	0.954980i	$0.404124\pi$
$224$			771.979i			0.230268i
$225$	−1277.06	+	2805.35i	−0.378387	+	0.831215i
$226$	−3070.21			−0.903662
$227$			3417.21i			0.999156i	0.866269	+	0.499578i	$0.166512\pi$
$227$			3417.21i			0.999156i	−0.866269	+	0.499578i	$0.833488\pi$
$228$	872.119	−	561.224i	0.253322	−	0.163017i
$229$			5689.32i			1.64175i	0.571108	+	0.820875i	$0.306514\pi$
$229$			5689.32i			1.64175i	−0.571108	+	0.820875i	$0.693486\pi$
$230$		−	752.021i		−	0.215595i
$231$	−13.8140	−	21.4664i	−0.00393460	−	0.00611421i
$232$			6469.02i			1.83066i
$233$	510.678			0.143586			0.0717932	−	0.997420i	$-0.477128\pi$
$233$	510.678			0.143586			0.0717932	+	0.997420i	$0.477128\pi$
$234$	−3171.07	−	1443.54i	−0.885894	−	0.403278i
$235$		−	847.791i		−	0.235335i
$236$			1381.61i			0.381080i
$237$	1465.87	+	2277.91i	0.401767	+	0.624330i
$238$	−3336.84			−0.908804
$239$	1047.88			0.283606			0.141803	−	0.989895i	$-0.454710\pi$
$239$	1047.88			0.283606			0.141803	+	0.989895i	$0.454710\pi$
$240$	−1276.00	+	821.127i	−0.343189	+	0.220848i
$241$	−5024.79			−1.34305			−0.671525	−	0.740982i	$-0.734360\pi$
$241$	−5024.79			−1.34305			−0.671525	+	0.740982i	$0.734360\pi$
$242$	6652.03			1.76698
$243$	3637.77	+	1056.19i	0.960341	+	0.278827i
$244$			741.459i			0.194537i
$245$	850.764			0.221850
$246$	2432.44	−	1565.32i	0.630435	−	0.405695i
$247$		−	303.285i		−	0.0781278i
$248$			8256.14i			2.11397i
$249$	−342.809	−	532.712i	−0.0872476	−	0.135579i
$250$	3935.99			0.995736
$251$	−1515.37			−0.381074			−0.190537	−	0.981680i	$-0.561023\pi$
$251$	−1515.37			−0.381074			−0.190537	+	0.981680i	$0.561023\pi$
$252$	−3839.48	−	1747.82i	−0.959781	−	0.436913i
$253$		−	24.4081i		−	0.00606531i
$254$	8183.97			2.02169
$255$	−671.907	−	1044.12i	−0.165006	−	0.256412i
$256$	−8283.34			−2.02230
$257$		−	1618.53i		−	0.392845i	−0.980519	−	0.196422i	$-0.937068\pi$
$257$		−	1618.53i		−	0.392845i	0.980519	−	0.196422i	$-0.0629324\pi$
$258$	−4120.92	−	6403.75i	−0.994408	−	1.54527i
$259$			1778.72i			0.426734i
$260$			1443.82i			0.344393i
$261$	−3537.99	−	1610.57i	−0.839065	−	0.381961i
$262$			9118.36i			2.15013i
$263$			2352.92i			0.551664i	0.961206	+	0.275832i	$0.0889533\pi$
$263$			2352.92i			0.551664i	−0.961206	+	0.275832i	$0.911047\pi$
$264$	−104.872	+	67.4868i	−0.0244485	+	0.0157330i
$265$	−574.194			−0.133104
$266$		−	540.137i		−	0.124504i
$267$	3756.63	+	5837.66i	0.861057	+	1.33805i
$268$	5214.61	−	7720.73i	1.18856	−	1.75977i
$269$			7856.87i			1.78083i	0.455154	+	0.890413i	$0.349584\pi$
$269$			7856.87i			1.78083i	−0.455154	+	0.890413i	$0.650416\pi$
$270$	−332.745	−	2284.82i	−0.0750007	−	0.514999i
$271$		−	7091.41i		−	1.58957i	−0.606893	−	0.794783i	$-0.707585\pi$
$271$		−	7091.41i		−	1.58957i	0.606893	−	0.794783i	$-0.292415\pi$
$272$			6437.71i			1.43509i
$273$	−1037.43	+	667.602i	−0.229993	+	0.148004i
$274$	7424.13			1.63689
$275$	60.9797			0.0133717
$276$	−2182.82	−	3392.02i	−0.476052	−	0.739766i
$277$	−6206.40			−1.34623			−0.673116	−	0.739537i	$-0.735044\pi$
$277$	−6206.40			−1.34623			−0.673116	+	0.739537i	$0.735044\pi$
$278$			3069.61i			0.662242i
$279$	−4515.38	−	2055.50i	−0.968921	−	0.441074i
$280$			1360.50i			0.290376i
$281$	7997.38			1.69781			0.848903	−	0.528549i	$-0.177264\pi$
$281$	7997.38			1.69781			0.848903	+	0.528549i	$0.177264\pi$
$282$	−3619.62	−	5624.75i	−0.764345	−	1.18776i
$283$	−5145.79			−1.08087			−0.540434	−	0.841387i	$-0.681740\pi$
$283$	−5145.79			−1.08087			−0.540434	+	0.841387i	$0.681740\pi$
$284$		−	7013.54i		−	1.46541i
$285$	169.012	−	108.762i	0.0351278	−	0.0226053i
$286$			68.9293i			0.0142513i
$287$		−	1024.20i		−	0.210650i
$288$	−938.959	+	2062.64i	−0.192114	+	0.422022i
$289$	−354.814			−0.0722195
$290$			2369.47i			0.479793i
$291$	−3365.55	−	5229.93i	−0.677979	−	1.05355i
$292$	3487.10			0.698860
$293$		−	6360.37i		−	1.26818i	−0.773259	−	0.634090i	$-0.781375\pi$
$293$		−	6360.37i		−	1.26818i	0.773259	−	0.634090i	$-0.218625\pi$
$294$	5644.48	−	3632.32i	1.11970	−	0.720548i
$295$			267.748i			0.0528437i
$296$	8689.74			1.70636
$297$	−10.7998	−	74.1576i	−0.00210999	−	0.0144884i
$298$		−	6460.13i		−	1.25579i
$299$	−1179.60			−0.228153
$300$	8474.42	−	5453.43i	1.63090	−	1.04951i
$301$	−2696.35			−0.516329
$302$	−10195.7			−1.94271
$303$	7662.53	−	4930.97i	1.45281	−	0.934907i
$304$	−1042.08			−0.196603
$305$			143.691i			0.0269761i
$306$	−8915.66	−	4058.61i	−1.66560	−	0.758219i
$307$	258.295			0.0480185			0.0240093	−	0.999712i	$-0.492357\pi$
$307$	258.295			0.0480185			0.0240093	+	0.999712i	$0.492357\pi$
$308$			83.4586i			0.0154399i
$309$	−1740.42	+	1119.99i	−0.320417	+	0.206194i
$310$			3024.05i			0.554047i
$311$	4934.80			0.899765			0.449882	−	0.893088i	$-0.351466\pi$
$311$	4934.80			0.899765			0.449882	+	0.893088i	$0.351466\pi$
$312$	3261.51	+	5068.25i	0.591816	+	0.919658i
$313$		−	6696.26i		−	1.20925i	−0.796510	−	0.604625i	$-0.793323\pi$
$313$		−	6696.26i		−	1.20925i	0.796510	−	0.604625i	$-0.206677\pi$
$314$	779.410			0.140079
$315$	−744.072	−	338.718i	−0.133091	−	0.0605860i
$316$		−	8856.25i		−	1.57659i
$317$			4272.51i			0.756997i	0.925602	+	0.378499i	$0.123560\pi$
$317$			4272.51i			0.756997i	−0.925602	+	0.378499i	$0.876440\pi$
$318$	−3809.55	+	2451.51i	−0.671789	+	0.432307i
$319$			76.9050i			0.0134980i
$320$	−954.755			−0.166789
$321$	4632.24	+	7198.32i	0.805440	+	1.25162i
$322$	−2100.81			−0.363582
$323$		−	852.705i		−	0.146891i
$324$	−8132.80	−	9339.94i	−1.39451	−	1.60150i
$325$		−	2947.03i		−	0.502991i
$326$	14163.0			2.40619
$327$	4970.30	+	7723.65i	0.840545	+	1.30617i
$328$	−5003.63			−0.842315
$329$	−2368.35			−0.396873
$330$	−38.4124	+	24.7190i	−0.00640767	+	0.00412344i
$331$		−	8717.58i		−	1.44762i	−0.690000	−	0.723809i	$-0.742390\pi$
$331$		−	8717.58i		−	1.44762i	0.690000	−	0.723809i	$-0.257610\pi$
$332$			2071.12i			0.342372i
$333$	−2163.46	+	4752.53i	−0.356026	+	0.782093i
$334$			19413.2i			3.18038i
$335$	1010.56	−	1496.24i	0.164815	−	0.244024i
$336$	2293.86	+	3564.57i	0.372442	+	0.578760i
$337$		−	3897.90i		−	0.630066i	−0.949081	−	0.315033i	$-0.897984\pi$
$337$		−	3897.90i		−	0.630066i	0.949081	−	0.315033i	$-0.102016\pi$
$338$	−7651.23			−1.23128
$339$	−2683.73	+	1727.03i	−0.429971	+	0.276694i
$340$			4059.40i			0.647506i
$341$			98.1506i			0.0155870i
$342$	656.970	−	1443.19i	0.103874	−	0.228183i
$343$		−	5531.26i		−	0.870729i
$344$			13172.8i			2.06462i
$345$	−423.019	−	657.355i	−0.0660133	−	0.102582i
$346$		−	1451.34i		−	0.225505i
$347$	−2565.10			−0.396836			−0.198418	−	0.980118i	$-0.563580\pi$
$347$	−2565.10			−0.396836			−0.198418	+	0.980118i	$0.563580\pi$
$348$	6877.64	+	10687.6i	1.05943	+	1.64631i
$349$	−1669.46			−0.256058			−0.128029	−	0.991770i	$-0.540865\pi$
$349$	−1669.46			−0.256058			−0.128029	+	0.991770i	$0.540865\pi$
$350$		−	5248.53i		−	0.801560i
$351$	−3583.90	+	521.933i	−0.544998	+	0.0793695i
$352$	44.8355			0.00678903
$353$	12901.4			1.94524			0.972620	−	0.232399i	$-0.0746577\pi$
$353$	12901.4			1.94524			0.972620	+	0.232399i	$0.0746577\pi$
$354$	1143.14	+	1776.40i	0.171631	+	0.266708i
$355$		−	1359.19i		−	0.203206i
$356$		−	22696.1i		−	3.37891i
$357$	−2916.80	+	1877.01i	−0.432418	+	0.278268i
$358$	−1620.34			−0.239212
$359$		−	4438.42i		−	0.652509i	−0.945282	−	0.326254i	$-0.894213\pi$
$359$		−	4438.42i		−	0.652509i	0.945282	−	0.326254i	$-0.105787\pi$
$360$	−1654.77	+	3635.09i	−0.242262	+	0.532184i
$361$	−6720.97			−0.979876
$362$	−11215.1			−1.62832
$363$	5814.66	−	3741.83i	0.840746	−	0.541034i
$364$	4033.39			0.580789
$365$	675.781			0.0969096
$366$	613.484	+	953.331i	0.0876157	+	0.136151i
$367$			8828.01i			1.25564i	0.778360	+	0.627818i	$0.216052\pi$
$367$			8828.01i			1.25564i	−0.778360	+	0.627818i	$0.783948\pi$
$368$			4053.06i			0.574131i
$369$	1245.74	−	2736.55i	0.175747	−	0.386068i
$370$	3182.87			0.447215
$371$			1604.04i			0.224468i
$372$	8777.63	+	13640.1i	1.22338	+	1.90109i
$373$		−	3688.86i		−	0.512070i	−0.966668	−	0.256035i	$-0.917584\pi$
$373$		−	3688.86i		−	0.512070i	0.966668	−	0.256035i	$-0.0824162\pi$
$374$			193.799i			0.0267944i
$375$	3440.52	−	2214.03i	0.473781	−	0.304886i
$376$			11570.3i			1.58695i
$377$	3716.67			0.507741
$378$	−6382.76	+	929.539i	−0.868502	+	0.126482i
$379$			1814.82i			0.245966i	0.992409	+	0.122983i	$0.0392461\pi$
$379$			1814.82i			0.245966i	−0.992409	+	0.122983i	$0.960754\pi$
$380$	−657.099			−0.0887065
$381$	7153.77	−	4603.57i	0.961938	−	0.619024i
$382$	16228.4			2.17360
$383$	−12813.6			−1.70951			−0.854755	−	0.519032i	$-0.826293\pi$
$383$	−12813.6			−1.70951			−0.854755	+	0.519032i	$0.826293\pi$
$384$	−9268.58	+	5964.49i	−1.23173	+	0.792640i
$385$			16.1738i			0.00214103i
$386$	−2522.65			−0.332641
$387$	−7204.34	−	3279.58i	−0.946298	−	0.430776i
$388$			20333.3i			2.66049i
$389$			9071.03i			1.18231i	0.806557	+	0.591156i	$0.201328\pi$
$389$			9071.03i			1.18231i	−0.806557	+	0.591156i	$0.798672\pi$
$390$	1194.62	+	1856.40i	0.155108	+	0.241031i
$391$	−3316.51			−0.428959
$392$	−11610.9			−1.49602
$393$	5129.17	+	7970.53i	0.658352	+	1.02305i
$394$	16038.6			2.05079
$395$		−	1716.29i		−	0.218623i
$396$	−101.511	+	222.992i	−0.0128816	+	0.0282974i
$397$	6457.70			0.816380			0.408190	−	0.912897i	$-0.366160\pi$
$397$	6457.70			0.816380			0.408190	+	0.912897i	$0.366160\pi$
$398$	−15413.6			−1.94124
$399$	−303.833	−	472.144i	−0.0381220	−	0.0592400i
$400$	−10125.9			−1.26574
$401$	12953.7			1.61316			0.806578	−	0.591128i	$-0.201317\pi$
$401$	12953.7			1.61316			0.806578	+	0.591128i	$0.201317\pi$
$402$	316.539	−	14241.5i	0.0392724	−	1.76692i
$403$	4743.43			0.586320
$404$	−29791.0			−3.66871
$405$	−1576.09	−	1810.03i	−0.193375	−	0.222077i
$406$	6619.23			0.809130
$407$	103.305			0.0125815
$408$	9169.94	+	14249.7i	1.11270	+	1.72908i
$409$			11030.7i			1.33357i	0.745250	+	0.666786i	$0.232330\pi$
$409$			11030.7i			1.33357i	−0.745250	+	0.666786i	$0.767670\pi$
$410$	−1832.73			−0.220761
$411$	6489.57	−	4176.15i	0.778849	−	0.501202i
$412$	6766.53			0.809133
$413$	747.968			0.0891165
$414$	−5613.12	−	2555.22i	−0.666353	−	0.303338i
$415$			401.372i			0.0474761i
$416$		−	2166.81i		−	0.255377i
$417$	1726.69	+	2683.21i	0.202773	+	0.315101i
$418$	−31.3704			−0.00367076
$419$		−	4762.74i		−	0.555311i	−0.960681	−	0.277655i	$-0.910443\pi$
$419$		−	4762.74i		−	0.555311i	0.960681	−	0.277655i	$-0.0895573\pi$
$420$	1446.43	+	2247.70i	0.168044	+	0.261134i
$421$	−11078.9			−1.28255			−0.641273	−	0.767313i	$-0.721593\pi$
$421$	−11078.9			−1.28255			−0.641273	+	0.767313i	$0.721593\pi$
$422$	−14299.7			−1.64953
$423$	−6327.95	−	2880.62i	−0.727366	−	0.331113i
$424$	7836.39			0.897568
$425$		−	8285.77i		−	0.945692i
$426$	−5803.01	−	9017.65i	−0.659993	−	1.02560i
$427$	401.408			0.0454929
$428$		−	27986.2i		−	3.16066i
$429$	38.7734	+	60.2524i	0.00436363	+	0.00678092i
$430$			4824.91i			0.541111i
$431$			2356.33i			0.263342i	0.991293	+	0.131671i	$0.0420342\pi$
$431$			2356.33i			0.263342i	−0.991293	+	0.131671i	$0.957966\pi$
$432$	1793.35	+	12314.2i	0.199728	+	1.37145i
$433$		−	4716.16i		−	0.523427i	−0.965146	−	0.261714i	$-0.915712\pi$
$433$		−	4716.16i		−	0.523427i	0.965146	−	0.261714i	$-0.0842876\pi$
$434$	8447.84			0.934353
$435$	1332.85	+	2071.20i	0.146909	+	0.228290i
$436$		−	30028.6i		−	3.29842i
$437$		−	536.846i		−	0.0587662i
$438$	4483.54	−	2885.23i	0.489113	−	0.314753i
$439$	−2017.37			−0.219325			−0.109663	−	0.993969i	$-0.534977\pi$
$439$	−2017.37			−0.219325			−0.109663	+	0.993969i	$0.534977\pi$
$440$	79.0157			0.00856120
$441$	2890.73	−	6350.15i	0.312140	−	0.685688i
$442$	9365.94			1.00790
$443$	9624.03			1.03217			0.516085	−	0.856537i	$-0.327389\pi$
$443$	9624.03			1.03217			0.516085	+	0.856537i	$0.327389\pi$
$444$	14356.5	−	9238.63i	1.53452	−	0.987491i
$445$		−	4398.39i		−	0.468548i
$446$	−9877.10			−1.04864
$447$	−3633.89	−	5646.93i	−0.384513	−	0.597518i
$448$			2667.16i			0.281275i
$449$			539.090i			0.0566620i	0.999599	+	0.0283310i	$0.00901924\pi$
$449$			539.090i			0.0566620i	−0.999599	+	0.0283310i	$0.990981\pi$
$450$	6383.80	−	14023.5i	0.668745	−	1.46905i
$451$	−59.4842			−0.00621064
$452$	10434.0			1.08579
$453$	−8912.27	+	5735.20i	−0.924360	+	0.594841i
$454$		−	17082.1i		−	1.76586i
$455$	781.650			0.0805370
$456$	−2306.61	+	1484.35i	−0.236880	+	0.152436i
$457$	−9908.41			−1.01421			−0.507107	−	0.861883i	$-0.669285\pi$
$457$	−9908.41			−1.01421			−0.507107	+	0.861883i	$0.669285\pi$
$458$		−	28440.0i		−	2.90156i
$459$	−10076.4	+	1467.45i	−1.02467	+	0.149226i
$460$			2555.72i			0.259046i
$461$			8353.86i			0.843987i	0.906599	+	0.421994i	$0.138670\pi$
$461$			8353.86i			0.843987i	−0.906599	+	0.421994i	$0.861330\pi$
$462$	69.0538	+	107.307i	0.00695384	+	0.0108060i
$463$		−	4396.16i		−	0.441267i	−0.975357	−	0.220634i	$-0.929187\pi$
$463$		−	4396.16i		−	0.441267i	0.975357	−	0.220634i	$-0.0708125\pi$
$464$		−	12770.4i		−	1.27769i
$465$	1701.06	+	2643.38i	0.169645	+	0.263621i
$466$	−2552.80			−0.253768
$467$		−	9008.50i		−	0.892641i	−0.894873	−	0.446321i	$-0.852734\pi$
$467$		−	9008.50i		−	0.892641i	0.894873	−	0.446321i	$-0.147266\pi$
$468$	10776.8	+	4905.82i	1.06444	+	0.484555i
$469$	−4179.82	−	2823.06i	−0.411527	−	0.277947i
$470$			4237.97i			0.415921i
$471$	681.297	−	438.426i	0.0666508	−	0.0428909i
$472$		−	3654.13i		−	0.356345i
$473$			156.600i			0.0152230i
$474$	−7327.67	−	11386.9i	−0.710066	−	1.10341i
$475$	1341.22			0.129557
$476$	11340.1			1.09196
$477$	−1951.00	+	4285.82i	−0.187275	+	0.411392i
$478$	−5238.20			−0.501233
$479$			9673.56i			0.922748i	0.887206	+	0.461374i	$0.152643\pi$
$479$			9673.56i			0.922748i	−0.887206	+	0.461374i	$0.847357\pi$
$480$	1207.50	−	777.049i	0.114822	−	0.0738901i
$481$		−	4992.55i		−	0.473265i
$482$	25118.1			2.37365
$483$	−1836.36	+	1181.73i	−0.172996	+	0.111326i
$484$	−22606.7			−2.12309
$485$			3940.49i			0.368925i
$486$	−18184.6	−	5279.74i	−1.69727	−	0.492786i
$487$			15787.3i			1.46898i	0.678621	+	0.734489i	$0.262578\pi$
$487$			15787.3i			1.46898i	−0.678621	+	0.734489i	$0.737422\pi$
$488$		−	1961.04i		−	0.181910i
$489$	12380.2	−	7966.84i	1.14489	−	0.736754i
$490$	−4252.84			−0.392089
$491$			10946.3i			1.00611i	0.864255	+	0.503054i	$0.167790\pi$
$491$			10946.3i			1.00611i	−0.864255	+	0.503054i	$0.832210\pi$
$492$	−8266.58	+	5319.68i	−0.757492	+	0.487459i
$493$	10449.7			0.954623
$494$			1516.07i			0.138080i
$495$	−19.6723	+	43.2147i	−0.00178627	+	0.00392395i
$496$		−	16298.3i		−	1.47543i
$497$	−3796.96			−0.342690
$498$	1713.65	+	2662.94i	0.154198	+	0.239617i
$499$			7533.92i			0.675881i	0.941167	+	0.337941i	$0.109730\pi$
$499$			7533.92i			0.675881i	−0.941167	+	0.337941i	$0.890270\pi$
$500$	−13376.3			−1.19642
$501$	10920.1	+	16969.5i	0.973805	+	1.51325i
$502$	7575.11			0.673493
$503$	−14596.0			−1.29385			−0.646924	−	0.762555i	$-0.723945\pi$
$503$	−14596.0			−1.29385			−0.646924	+	0.762555i	$0.723945\pi$
$504$	10154.8	+	4622.69i	0.897483	+	0.408554i
$505$	−5773.34			−0.508733
$506$			122.012i			0.0107196i
$507$	−6688.08	+	4303.90i	−0.585855	+	0.377007i
$508$	−27813.0			−2.42914
$509$			13035.5i			1.13514i	0.823325	+	0.567571i	$0.192117\pi$
$509$			13035.5i			1.13514i	−0.823325	+	0.567571i	$0.807883\pi$
$510$	3358.76	+	5219.38i	0.291624	+	0.453172i
$511$		−	1887.83i		−	0.163430i
$512$	24437.8			2.10939
$513$	−237.537	−	1631.07i	−0.0204435	−	0.140377i
$514$			8090.77i			0.694297i
$515$	1311.32			0.112201
$516$	14004.8	+	21762.9i	1.19482	+	1.85670i
$517$			137.550i			0.0117011i
$518$		−	8891.51i		−	0.754191i
$519$	−816.394	−	1268.64i	−0.0690476	−	0.107297i
$520$		−	3818.68i		−	0.322039i
$521$	−1147.31			−0.0964770			−0.0482385	−	0.998836i	$-0.515361\pi$
$521$	−1147.31			−0.0964770			−0.0482385	+	0.998836i	$0.515361\pi$
$522$	17685.8	+	8050.98i	1.48293	+	0.675061i
$523$	8026.36			0.671067			0.335534	−	0.942028i	$-0.391083\pi$
$523$	8026.36			0.671067			0.335534	+	0.942028i	$0.391083\pi$
$524$		−	30988.5i		−	2.58347i
$525$	−2952.35	−	4587.84i	−0.245431	−	0.381390i
$526$		−	11761.9i		−	0.974987i
$527$	13336.5			1.10236
$528$	207.025	−	133.224i	0.0170637	−	0.0109808i
$529$	10079.0			0.828388
$530$	2870.31			0.235242
$531$	1998.49	+	909.755i	0.163328	+	0.0743503i
$532$			1835.64i			0.149596i
$533$			2874.75i			0.233620i
$534$	−18778.8	−	29181.5i	−1.52180	−	2.36481i
$535$		−	5423.58i		−	0.438283i
$536$	−13791.8	+	20420.1i	−1.11141	+	1.64555i
$537$	−1416.37	+	911.459i	−0.113819	+	0.0732446i
$538$		−	39275.3i		−	3.14735i
$539$	−138.033			−0.0110306
$540$	1130.82	+	7764.89i	0.0901164	+	0.618792i
$541$			5233.92i			0.415940i	0.978135	+	0.207970i	$0.0666857\pi$
$541$			5233.92i			0.415940i	−0.978135	+	0.207970i	$0.933314\pi$
$542$			35448.8i			2.80933i
$543$	−9803.31	+	6308.59i	−0.774770	+	0.498578i
$544$		−	6092.13i		−	0.480144i
$545$		−	5819.39i		−	0.457386i
$546$	5185.93	−	3337.24i	0.406479	−	0.261576i
$547$		−	3958.43i		−	0.309416i	−0.987960	−	0.154708i	$-0.950556\pi$
$547$		−	3958.43i		−	0.309416i	0.987960	−	0.154708i	$-0.0494436\pi$
$548$	−25230.7			−1.96679
$549$	1072.52	+	488.233i	0.0833768	+	0.0379550i
$550$	−304.828			−0.0236325
$551$			1691.50i			0.130781i
$552$	5773.21	+	8971.34i	0.445152	+	0.691749i
$553$	−4794.56			−0.368689
$554$	31024.8			2.37927
$555$	2782.21	−	1790.40i	0.212789	−	0.136934i
$556$		−	10432.0i		−	0.795710i
$557$			10351.0i			0.787406i	0.919238	+	0.393703i	$0.128806\pi$
$557$			10351.0i			0.787406i	−0.919238	+	0.393703i	$0.871194\pi$
$558$	22571.7	+	10275.1i	1.71243	+	0.779535i
$559$	7568.19			0.572631
$560$		−	2685.73i		−	0.202666i
$561$	109.014	+	169.404i	0.00820424	+	0.0127491i
$562$	−39977.6			−3.00063
$563$	−8231.23			−0.616172			−0.308086	−	0.951358i	$-0.599688\pi$
$563$	−8231.23			−0.616172			−0.308086	+	0.951358i	$0.599688\pi$
$564$	12301.2	+	19115.5i	0.918391	+	1.42714i
$565$	2022.06			0.150564
$566$	25723.0			1.91028
$567$	−5056.42	+	4402.90i	−0.374514	+	0.326110i
$568$			18549.7i			1.37029i
$569$			9834.79i			0.724597i	0.932062	+	0.362299i	$0.118008\pi$
$569$			9834.79i			0.724597i	−0.932062	+	0.362299i	$0.881992\pi$
$570$	−844.865	+	543.685i	−0.0620833	+	0.0399517i
$571$	−15233.3			−1.11645			−0.558225	−	0.829689i	$-0.688518\pi$
$571$	−15233.3			−1.11645			−0.558225	+	0.829689i	$0.688518\pi$
$572$		−	234.254i		−	0.0171235i
$573$	14185.5	−	9128.63i	1.03422	−	0.665539i
$574$			5119.81i			0.372294i
$575$		−	5216.56i		−	0.378340i
$576$	−3244.07	+	7126.35i	−0.234669	+	0.515505i
$577$			3372.91i			0.243355i	0.992570	+	0.121678i	$0.0388274\pi$
$577$			3372.91i			0.243355i	−0.992570	+	0.121678i	$0.961173\pi$
$578$	1773.66			0.127638
$579$	−2205.10	+	1419.02i	−0.158274	+	0.101852i
$580$		−	8052.56i		−	0.576490i
$581$	1121.25			0.0800645
$582$	16823.8	+	26143.6i	1.19823	+	1.86200i
$583$	93.1605			0.00661804
$584$	−9222.81			−0.653498
$585$	2088.48	+	950.723i	0.147604	+	0.0671924i
$586$			31794.5i			2.24133i
$587$	−9780.03			−0.687675			−0.343838	−	0.939029i	$-0.611727\pi$
$587$	−9780.03			−0.687675			−0.343838	+	0.939029i	$0.611727\pi$
$588$	−19182.6	+	12344.3i	−1.34537	+	0.865767i
$589$			2158.78i			0.151021i
$590$		−	1338.43i		−	0.0933937i
$591$	14019.6	−	9021.86i	0.975787	−	0.627936i
$592$	−17154.3			−1.19094
$593$	−9387.18			−0.650060			−0.325030	−	0.945704i	$-0.605374\pi$
$593$	−9387.18			−0.650060			−0.325030	+	0.945704i	$0.605374\pi$
$594$	53.9864	+	370.702i	0.00372910	+	0.0256062i
$595$	2197.66			0.151421
$596$			21954.6i			1.50888i
$597$	−13473.3	+	8670.28i	−0.923660	+	0.594390i
$598$	5896.61			0.403228
$599$	−26517.1			−1.80878			−0.904389	−	0.426708i	$-0.859673\pi$
$599$	−26517.1			−1.80878			−0.904389	+	0.426708i	$0.859673\pi$
$600$	−22413.5	+	14423.4i	−1.52504	+	0.981391i
$601$	−24225.2			−1.64421			−0.822103	−	0.569338i	$-0.807199\pi$
$601$	−24225.2			−1.64421			−0.822103	+	0.569338i	$0.807199\pi$
$602$	13478.6			0.912538
$603$	−7734.30	−	12626.8i	−0.522330	−	0.852743i
$604$	34649.8			2.33424
$605$	−4381.06			−0.294406
$606$	−38303.8	+	24649.1i	−2.56763	+	1.65231i
$607$	9766.26			0.653049			0.326524	−	0.945189i	$-0.394123\pi$
$607$	9766.26			0.653049			0.326524	+	0.945189i	$0.394123\pi$
$608$	986.139			0.0657783
$609$	5785.99	−	3723.38i	0.384992	−	0.247749i
$610$		−	718.288i		−	0.0476764i
$611$	6647.54			0.440149
$612$	30299.6	+	13793.0i	2.00129	+	0.911031i
$613$	10898.7			0.718100			0.359050	−	0.933318i	$-0.383101\pi$
$613$	10898.7			0.718100			0.359050	+	0.933318i	$0.383101\pi$
$614$	−1291.18			−0.0848659
$615$	−1602.02	+	1030.93i	−0.105040	+	0.0675951i
$616$		−	220.735i		−	0.0144377i
$617$			24878.7i			1.62331i	0.584140	+	0.811653i	$0.301432\pi$
$617$			24878.7i			1.62331i	−0.584140	+	0.811653i	$0.698568\pi$
$618$	8700.06	−	5598.64i	0.566291	−	0.364418i
$619$	4262.84			0.276798			0.138399	−	0.990377i	$-0.455804\pi$
$619$	4262.84			0.276798			0.138399	+	0.990377i	$0.455804\pi$
$620$		−	10277.1i		−	0.665709i
$621$	−6343.87	+	923.876i	−0.409937	+	0.0597003i
$622$	−24668.3			−1.59021
$623$	−12287.1			−0.790166
$624$	−6438.48	−	10005.1i	−0.413053	−	0.641869i
$625$	11677.9			0.747383
$626$			33473.6i			2.13718i
$627$	−27.4215	+	17.6462i	−0.00174659	+	0.00112396i
$628$	−2648.80			−0.168310
$629$		−	14036.9i		−	0.889805i
$630$	3719.50	+	1693.20i	0.235219	+	0.107077i
$631$			12036.1i			0.759347i	0.925121	+	0.379674i	$0.123964\pi$
$631$			12036.1i			0.759347i	−0.925121	+	0.379674i	$0.876036\pi$
$632$			23423.3i			1.47426i
$633$	−12499.7	+	8043.74i	−0.784861	+	0.505071i
$634$		−	21357.6i		−	1.33788i
$635$	−5390.01			−0.336844
$636$	12946.6	−	8331.37i	0.807181	−	0.519435i
$637$			6670.86i			0.414928i
$638$		−	384.436i		−	0.0238557i
$639$	−10145.0	−	4618.25i	−0.628062	−	0.285908i
$640$	6983.42			0.431318
$641$	21561.9			1.32862			0.664310	−	0.747457i	$-0.268726\pi$
$641$	21561.9			1.32862			0.664310	+	0.747457i	$0.268726\pi$
$642$	−23155.8	−	35983.2i	−1.42350	−	2.21206i
$643$	23171.3			1.42113			0.710564	−	0.703633i	$-0.248440\pi$
$643$	23171.3			1.42113			0.710564	+	0.703633i	$0.248440\pi$
$644$	7139.53			0.436859
$645$	2714.06	+	4217.54i	0.165684	+	0.257466i
$646$			4262.54i			0.259609i
$647$	14959.7			0.909005			0.454502	−	0.890745i	$-0.349817\pi$
$647$	14959.7			0.909005			0.454502	+	0.890745i	$0.349817\pi$
$648$	21509.9	+	24702.6i	1.30400	+	1.49755i
$649$		−	43.4410i		−	0.00262744i
$650$			14731.7i			0.888964i
$651$	7384.41	−	4751.99i	0.444574	−	0.286091i
$652$	−48132.5			−2.89113
$653$	18549.7			1.11165			0.555825	−	0.831299i	$-0.312402\pi$
$653$	18549.7			1.11165			0.555825	+	0.831299i	$0.312402\pi$
$654$	−24845.7	−	38609.3i	−1.48554	−	2.30848i
$655$		−	6005.40i		−	0.358245i
$656$	9877.57			0.587888
$657$	2296.17	−	5044.07i	0.136350	−	0.299525i
$658$	11839.0			0.701416
$659$		−	1699.48i		−	0.100459i	−0.998738	−	0.0502295i	$-0.984005\pi$
$659$		−	1699.48i		−	0.100459i	0.998738	−	0.0502295i	$-0.0159953\pi$
$660$	130.543	−	84.0067i	0.00769907	−	0.00495448i
$661$			13425.9i			0.790024i	0.918676	+	0.395012i	$0.129260\pi$
$661$			13425.9i			0.790024i	−0.918676	+	0.395012i	$0.870740\pi$
$662$			43577.8i			2.55846i
$663$	8186.95	−	5268.44i	0.479570	−	0.308611i
$664$		−	5477.78i		−	0.320149i
$665$			355.737i			0.0207442i
$666$	10814.8	−	23757.1i	0.629225	−	1.38224i
$667$	6578.90			0.381913
$668$		−	65975.3i		−	3.82135i
$669$	−8633.76	+	5555.97i	−0.498954	+	0.321086i
$670$	−5051.65	+	7479.45i	−0.291287	+	0.431278i
$671$		−	23.3132i		−	0.00134128i
$672$	−2170.73	−	3373.22i	−0.124609	−	0.193638i
$673$		−	29978.8i		−	1.71709i	−0.512742	−	0.858543i	$-0.671370\pi$
$673$		−	29978.8i		−	1.71709i	0.512742	−	0.858543i	$-0.328630\pi$
$674$			19485.0i			1.11355i
$675$	−2308.16	−	15849.2i	−0.131616	−	0.903755i
$676$	26002.5			1.47943
$677$	23244.0			1.31955			0.659777	−	0.751461i	$-0.270651\pi$
$677$	23244.0			1.31955			0.659777	+	0.751461i	$0.270651\pi$
$678$	13415.5	−	8633.13i	0.759913	−	0.489017i
$679$	11008.0			0.622161
$680$		−	10736.5i		−	0.605477i
$681$	−9608.85	−	14931.8i	−0.540693	−	0.840216i
$682$		−	490.639i		−	0.0275477i
$683$	8786.35			0.492240			0.246120	−	0.969239i	$-0.420844\pi$
$683$	8786.35			0.492240			0.246120	+	0.969239i	$0.420844\pi$
$684$	−2232.69	+	4904.62i	−0.124809	+	0.274171i
$685$	−4889.57			−0.272731
$686$			27649.9i			1.53889i
$687$	−15997.8	−	24859.9i	−0.888433	−	1.38059i
$688$		−	26004.1i		−	1.44098i
$689$		−	4502.27i		−	0.248945i
$690$	2114.61	+	3286.01i	0.116669	+	0.181299i
$691$	12149.8			0.668884			0.334442	−	0.942416i	$-0.391452\pi$
$691$	12149.8			0.668884			0.334442	+	0.942416i	$0.391452\pi$
$692$			4932.34i			0.270953i
$693$	120.722	+	54.9555i	0.00661741	+	0.00301239i
$694$	12822.5			0.701350
$695$		−	2021.66i		−	0.110340i
$696$	−18190.2	−	28266.9i	−0.990660	−	1.53945i
$697$			8082.56i			0.439238i
$698$	8345.37			0.452545
$699$	−2231.45	+	1435.98i	−0.120746	+	0.0777018i
$700$			17837.0i			0.963106i
$701$	−31485.5			−1.69642			−0.848211	−	0.529659i	$-0.822320\pi$
$701$	−31485.5			−1.69642			−0.848211	+	0.529659i	$0.822320\pi$
$702$	17915.3	−	2609.06i	0.963205	−	0.140274i
$703$	2272.16			0.121901
$704$	154.905			0.00829290
$705$	2383.90	+	3704.49i	0.127352	+	0.197899i
$706$	−64491.8			−3.43793
$707$			16128.1i			0.857935i
$708$	−3884.94	−	6037.04i	−0.206222	−	0.320460i
$709$	−11297.2			−0.598412			−0.299206	−	0.954189i	$-0.596722\pi$
$709$	−11297.2			−0.598412			−0.299206	+	0.954189i	$0.596722\pi$
$710$			6794.36i			0.359138i
$711$	−12810.5	−	5831.63i	−0.675713	−	0.307599i
$712$			60027.6i			3.15959i
$713$	8396.37			0.441019
$714$	14580.6	−	9382.86i	0.764237	−	0.491799i
$715$		−	45.3972i		−	0.00237449i
$716$	5506.68			0.287422
$717$	−4578.81	+	2946.54i	−0.238492	+	0.153474i
$718$			22186.9i			1.15322i
$719$		−	30608.1i		−	1.58761i	−0.608174	−	0.793804i	$-0.708098\pi$
$719$		−	30608.1i		−	1.58761i	0.608174	−	0.793804i	$-0.291902\pi$
$720$	3266.66	−	7175.96i	0.169085	−	0.371434i
$721$		−	3663.23i		−	0.189218i
$722$	33597.1			1.73179
$723$	21956.2	−	14129.2i	1.12941	−	0.726791i
$724$	38114.1			1.95649
$725$			16436.3i			0.841973i
$726$	−29066.6	+	18704.8i	−1.48590	+	0.956200i
$727$		−	22003.7i		−	1.12252i	−0.827639	−	0.561261i	$-0.810316\pi$
$727$		−	22003.7i		−	1.12252i	0.827639	−	0.561261i	$-0.189684\pi$
$728$	−10667.7			−0.543091
$729$	−18865.4	+	5613.91i	−0.958463	+	0.285216i
$730$	−3378.12			−0.171274
$731$	21278.5			1.07662
$732$	−2084.91	−	3239.86i	−0.105274	−	0.163591i
$733$		−	38495.1i		−	1.93977i	−0.243568	−	0.969884i	$-0.578318\pi$
$733$		−	38495.1i		−	1.93977i	0.243568	−	0.969884i	$-0.421682\pi$
$734$		−	44129.8i		−	2.21916i
$735$	−3717.48	+	2392.26i	−0.186560	+	0.120054i
$736$		−	3835.49i		−	0.192090i
$737$	−163.960	+	242.758i	−0.00819475	+	0.0121331i
$738$	−6227.24	+	13679.6i	−0.310607	+	0.682319i
$739$			37795.3i			1.88136i	0.339298	+	0.940679i	$0.389811\pi$
$739$			37795.3i			1.88136i	−0.339298	+	0.940679i	$0.610189\pi$
$740$	−10816.9			−0.537347
$741$	852.806	+	1325.23i	0.0422789	+	0.0656997i
$742$		−	8018.35i		−	0.396715i
$743$		−	31869.7i		−	1.57360i	−0.617207	−	0.786801i	$-0.711736\pi$
$743$		−	31869.7i		−	1.57360i	0.617207	−	0.786801i	$-0.288264\pi$
$744$	−23215.4	−	36075.8i	−1.14398	−	1.77769i
$745$			4254.68i			0.209234i
$746$			18440.0i			0.905010i
$747$	2995.86	+	1363.78i	0.146738	+	0.0667982i
$748$		−	658.621i		−	0.0321946i
$749$	−15151.0			−0.739128
$750$	−17198.6	+	11067.6i	−0.837340	+	0.538842i
$751$	−4710.48			−0.228879			−0.114439	−	0.993430i	$-0.536507\pi$
$751$	−4710.48			−0.228879			−0.114439	+	0.993430i	$0.536507\pi$
$752$		−	22840.8i		−	1.10760i
$753$	6621.54	−	4261.08i	0.320455	−	0.206218i
$754$	−18579.0			−0.897359
$755$	6714.96			0.323685
$756$	21691.6	−	3159.01i	1.04354	−	0.151974i
$757$			4201.56i			0.201728i	0.994900	+	0.100864i	$0.0321607\pi$
$757$			4201.56i			0.201728i	−0.994900	+	0.100864i	$0.967839\pi$
$758$		−	9072.02i		−	0.434710i
$759$	68.6330	+	106.653i	0.00328224	+	0.00510048i
$760$	1737.92			0.0829487
$761$		−	19626.1i		−	0.934884i	−0.884024	−	0.467442i	$-0.845176\pi$
$761$		−	19626.1i		−	0.934884i	0.884024	−	0.467442i	$-0.154824\pi$
$762$	−35760.5	+	23012.5i	−1.70009	+	1.09404i
$763$	−16256.8			−0.771342
$764$	−55151.7			−2.61167
$765$	5871.90	+	2673.02i	0.277515	+	0.126331i
$766$	64052.9			3.02131
$767$	−2099.42			−0.0988339
$768$	36194.7	−	23291.9i	1.70060	−	1.09437i
$769$			1523.04i			0.0714205i	0.999362	+	0.0357103i	$0.0113693\pi$
$769$			1523.04i			0.0714205i	−0.999362	+	0.0357103i	$0.988631\pi$
$770$		−	80.8504i		−	0.00378396i
$771$	4551.14	+	7072.29i	0.212588	+	0.330353i
$772$	8573.15			0.399682
$773$		−	12696.1i		−	0.590748i	−0.955382	−	0.295374i	$-0.904556\pi$
$773$		−	12696.1i		−	0.590748i	0.955382	−	0.295374i	$-0.0954443\pi$
$774$	36013.4	+	16394.1i	1.67245	+	0.761335i
$775$			20977.0i			0.972278i
$776$		−	53778.4i		−	2.48780i
$777$	−5001.57	−	7772.24i	−0.230927	−	0.358851i
$778$		−	45344.6i		−	2.08957i
$779$	−1308.33			−0.0601744
$780$	−4059.88	−	6308.90i	−0.186368	−	0.289609i
$781$			220.522i			0.0101036i
$782$	16578.7			0.758124
$783$	19988.3	−	2910.95i	0.912290	−	0.132859i
$784$	22920.9			1.04414
$785$	−513.324			−0.0233392
$786$	−25639.9	−	39843.4i	−1.16354	−	1.80810i
$787$		−	9543.37i		−	0.432254i	−0.976365	−	0.216127i	$-0.930657\pi$
$787$		−	9543.37i		−	0.432254i	0.976365	−	0.216127i	$-0.0693426\pi$
$788$	−54506.6			−2.46411
$789$	−6616.18	−	10281.3i	−0.298533	−	0.463908i
$790$			8579.48i			0.386385i
$791$		−	5648.73i		−	0.253913i
$792$	268.480	−	589.778i	0.0120455	−	0.0264607i
$793$	−1126.68			−0.0504536
$794$	−32281.0			−1.44283
$795$	2508.99	−	1614.58i	0.111930	−	0.0720291i
$796$	52382.5			2.33247
$797$		−	7097.33i		−	0.315433i	−0.987484	−	0.157717i	$-0.949587\pi$
$797$		−	7097.33i		−	0.315433i	0.987484	−	0.157717i	$-0.0504133\pi$
$798$	1518.81	+	2360.17i	0.0673751	+	0.104698i
$799$	18690.0			0.827540
$800$	9582.35			0.423484
$801$	−32829.8	−	14944.9i	−1.44817	−	0.659239i
$802$	−64753.3			−2.85102
$803$	−109.643			−0.00481843
$804$	−1075.75	+	48399.3i	−0.0471874	+	2.12303i
$805$	1383.60			0.0605784
$806$	−23711.6			−1.03624
$807$	−22092.7	−	34331.2i	−0.963694	−	1.49754i
$808$	78792.4			3.43058
$809$	2597.42			0.112881			0.0564404	−	0.998406i	$-0.482025\pi$
$809$	2597.42			0.112881			0.0564404	+	0.998406i	$0.482025\pi$
$810$	7878.64	+	9048.06i	0.341762	+	0.392489i
$811$		−	32049.1i		−	1.38766i	−0.720137	−	0.693832i	$-0.755921\pi$
$811$		−	32049.1i		−	1.38766i	0.720137	−	0.693832i	$-0.244079\pi$
$812$	−22495.2			−0.972202
$813$	19940.3	+	30986.5i	0.860194	+	1.33671i
$814$	−516.407			−0.0222359
$815$	−9327.83			−0.400908
$816$	−18102.2	−	28130.1i	−0.776598	−	1.20680i
$817$			3444.36i			0.147495i
$818$		−	55140.5i		−	2.35690i
$819$	2655.89	−	5834.28i	0.113314	−	0.248921i
$820$	6228.46			0.265253
$821$		−	13864.5i		−	0.589372i	−0.955594	−	0.294686i	$-0.904785\pi$
$821$		−	13864.5i		−	0.589372i	0.955594	−	0.294686i	$-0.0952151\pi$
$822$	−32440.3	+	20875.9i	−1.37650	+	0.885803i
$823$	−26930.8			−1.14064			−0.570321	−	0.821422i	$-0.693181\pi$
$823$	−26930.8			−1.14064			−0.570321	+	0.821422i	$0.693181\pi$
$824$	−17896.4			−0.756614
$825$	−266.456	+	171.469i	−0.0112446	+	0.00723609i
$826$	−3738.97			−0.157501
$827$			2761.82i			0.116128i	0.998313	+	0.0580640i	$0.0184928\pi$
$827$			2761.82i			0.116128i	−0.998313	+	0.0580640i	$0.981507\pi$
$828$	19076.0	+	8683.83i	0.800649	+	0.364473i
$829$	394.321			0.0165203			0.00826016	−	0.999966i	$-0.497371\pi$
$829$	394.321			0.0165203			0.00826016	+	0.999966i	$0.497371\pi$
$830$		−	2006.40i		−	0.0839072i
$831$	27119.3	−	17451.8i	1.13208	−	0.728513i
$832$		−	7486.26i		−	0.311946i
$833$			18755.6i			0.780122i
$834$	−8631.44	−	13412.9i	−0.358372	−	0.556896i
$835$		−	12785.7i		−	0.529900i
$836$	106.611			0.00441057
$837$	25510.2	−	3715.12i	1.05348	−	0.153421i
$838$			23808.2i			0.981432i
$839$			19917.4i			0.819576i	0.912181	+	0.409788i	$0.134397\pi$
$839$			19917.4i			0.819576i	−0.912181	+	0.409788i	$0.865603\pi$
$840$	−3825.58	−	5944.79i	−0.157137	−	0.244184i
$841$	3660.19			0.150076
$842$	55381.6			2.26672
$843$	−34945.2	+	22487.8i	−1.42773	+	0.918768i
$844$	48597.2			1.98197
$845$	5039.14			0.205150
$846$	31632.4	+	14399.8i	1.28551	+	0.585195i
$847$			12238.7i			0.496490i
$848$	−15469.7			−0.626451
$849$	22484.9	−	14469.4i	0.908929	−	0.584911i
$850$			41419.3i			1.67137i
$851$		−	8837.34i		−	0.355981i
$852$	19721.4	+	30646.2i	0.793007	+	1.23230i
$853$	−40204.2			−1.61379			−0.806897	−	0.590692i	$-0.798855\pi$
$853$	−40204.2			−1.61379			−0.806897	+	0.590692i	$0.798855\pi$
$854$	−2006.57			−0.0804022
$855$	−432.684	+	950.490i	−0.0173070	+	0.0380188i
$856$			74018.9i			2.95551i
$857$	−14129.3			−0.563184			−0.281592	−	0.959534i	$-0.590862\pi$
$857$	−14129.3			−0.563184			−0.281592	+	0.959534i	$0.590862\pi$
$858$	−193.822	−	301.192i	−0.00771210	−	0.0119843i
$859$	26902.0			1.06855			0.534275	−	0.845311i	$-0.320585\pi$
$859$	26902.0			1.06855			0.534275	+	0.845311i	$0.320585\pi$
$860$		−	16397.3i		−	0.650166i
$861$	2879.95	+	4475.32i	0.113993	+	0.177141i
$862$		−	11778.9i		−	0.465419i
$863$		−	37677.5i		−	1.48616i	−0.669203	−	0.743080i	$-0.733364\pi$
$863$		−	37677.5i		−	1.48616i	0.669203	−	0.743080i	$-0.266636\pi$
$864$	−1697.08	−	11653.1i	−0.0668238	−	0.458851i
$865$			955.861i			0.0375725i
$866$			23575.3i			0.925083i
$867$	1550.39	−	997.702i	0.0607312	−	0.0390816i
$868$	−28709.7			−1.12266
$869$			278.461i			0.0108701i
$870$	−6662.70	−	10353.6i	−0.259640	−	0.403470i
$871$	11732.0	+	7923.86i	0.456400	+	0.308254i
$872$			79420.8i			3.08432i
$873$	29412.1	+	13389.0i	1.14026	+	0.519072i
$874$			2683.61i			0.103861i
$875$			7241.62i			0.279785i
$876$	−15237.2	+	9805.37i	−0.587689	+	0.378188i
$877$	−12381.6			−0.476737			−0.238369	−	0.971175i	$-0.576613\pi$
$877$	−12381.6			−0.476737			−0.238369	+	0.971175i	$0.576613\pi$
$878$	10084.5			0.387626
$879$	17884.7	+	27792.1i	0.686276	+	1.06645i
$880$	−155.983			−0.00597523
$881$			15436.8i			0.590330i	0.955446	+	0.295165i	$0.0953746\pi$
$881$			15436.8i			0.590330i	−0.955446	+	0.295165i	$0.904625\pi$
$882$	−14450.3	+	31743.4i	−0.551663	+	1.21185i
$883$		−	4383.35i		−	0.167057i	−0.996505	−	0.0835286i	$-0.973381\pi$
$883$		−	4383.35i		−	0.167057i	0.996505	−	0.0835286i	$-0.0266190\pi$
$884$	−31829.9			−1.21103
$885$	−752.881	−	1169.95i	−0.0285964	−	0.0444377i
$886$	−48109.0			−1.82421
$887$			12118.6i			0.458742i	0.973339	+	0.229371i	$0.0736669\pi$
$887$			12118.6i			0.458742i	−0.973339	+	0.229371i	$0.926333\pi$
$888$	−37970.5	+	24434.7i	−1.43492	+	0.923394i
$889$			15057.3i			0.568059i
$890$			21986.8i			0.828091i
$891$	255.714	+	293.670i	0.00961476	+	0.0110419i
$892$	33567.0			1.25999
$893$			3025.37i			0.113371i
$894$	18165.2	+	28228.1i	0.679571	+	1.05603i
$895$	1067.17			0.0398564
$896$		−	19508.5i		−	0.727382i
$897$	5154.34	−	3316.90i	0.191860	−	0.123465i
$898$		−	2694.82i		−	0.100142i
$899$	−26455.3			−0.981461
$900$	−21695.2	+	47658.4i	−0.803524	+	1.76513i
$901$		−	12658.4i		−	0.468050i
$902$	297.352			0.0109764
$903$	11781.9	−	7581.86i	0.434195	−	0.279412i
$904$	−27596.3			−1.01531
$905$	7386.31			0.271303
$906$	44551.0	−	28669.3i	1.63367	−	1.05130i
$907$	−28308.2			−1.03634			−0.518168	−	0.855279i	$-0.673386\pi$
$907$	−28308.2			−1.03634			−0.518168	+	0.855279i	$0.673386\pi$
$908$			58053.0i			2.12176i
$909$	−19616.7	+	43092.5i	−0.715779	+	1.57237i
$910$	−3907.35			−0.142338
$911$		−	21407.1i		−	0.778540i	−0.921124	−	0.389270i	$-0.872727\pi$
$911$		−	21407.1i		−	0.778540i	0.921124	−	0.389270i	$-0.127273\pi$
$912$	4553.44	−	2930.22i	0.165328	−	0.106392i
$913$		−	65.1209i		−	0.00236056i
$914$	49530.5			1.79248
$915$	−404.044	−	627.869i	−0.0145981	−	0.0226849i
$916$			96652.4i			3.48634i
$917$	−16776.4			−0.604150
$918$	50370.1	−	7335.54i	1.81096	−	0.263735i
$919$		−	11113.4i		−	0.398909i	−0.979907	−	0.199454i	$-0.936083\pi$
$919$		−	11113.4i		−	0.398909i	0.979907	−	0.199454i	$-0.0639170\pi$
$920$		−	6759.46i		−	0.242231i
$921$	−1128.64	+	726.300i	−0.0403800	+	0.0259852i
$922$		−	41759.6i		−	1.49163i
$923$	10657.4			0.380057
$924$	−234.677	−	364.679i	−0.00835531	−	0.0129838i
$925$	22078.7			0.784803
$926$			21975.7i			0.779877i
$927$	4455.60	−	9787.75i	0.157865	−	0.346787i
$928$			12084.9i			0.427484i
$929$	10332.9			0.364919			0.182460	−	0.983213i	$-0.441594\pi$
$929$	10332.9			0.364919			0.182460	+	0.983213i	$0.441594\pi$
$930$	−8503.32	−	13213.8i	−0.299822	−	0.465912i
$931$	−3035.98			−0.106875
$932$	8675.60			0.304913
$933$	−21563.0	+	13876.2i	−0.756636	+	0.486908i
$934$			45032.0i			1.57762i
$935$		−	127.637i		−	0.00446437i
$936$	−28502.8	−	12975.1i	−0.995346	−	0.453103i
$937$		−	17437.7i		−	0.607965i	−0.952678	−	0.303983i	$-0.901684\pi$
$937$		−	17437.7i		−	0.607965i	0.952678	−	0.303983i	$-0.0983165\pi$
$938$	20894.2	+	14112.0i	0.727314	+	0.491231i
$939$	18829.2	+	29259.9i	0.654386	+	1.01689i
$940$		−	14402.6i		−	0.499746i
$941$	1667.96			0.0577832			0.0288916	−	0.999583i	$-0.490802\pi$
$941$	1667.96			0.0577832			0.0288916	+	0.999583i	$0.490802\pi$
$942$	−3405.69	+	2191.62i	−0.117796	+	0.0758035i
$943$			5088.62i			0.175725i
$944$			7213.54i			0.248708i
$945$	4203.72	−	612.200i	0.144706	−	0.0210739i
$946$		−	782.820i		−	0.0269045i
$947$			18381.5i			0.630749i	0.948967	+	0.315375i	$0.102130\pi$
$947$			18381.5i			0.630749i	−0.948967	+	0.315375i	$0.897870\pi$
$948$	24902.9	+	38698.1i	0.853173	+	1.32580i
$949$			5298.81i			0.181251i
$950$	−6704.57			−0.228974
$951$	−12013.9	−	18669.1i	−0.409649	−	0.636579i
$952$	−29992.9			−1.02109
$953$		−	53990.8i		−	1.83519i	−0.397520	−	0.917594i	$-0.630129\pi$
$953$		−	53990.8i		−	1.83519i	0.397520	−	0.917594i	$-0.369871\pi$
$954$	9752.73	−	21424.1i	0.330981	−	0.727077i
$955$	−10688.1			−0.362156
$956$	17801.9			0.602252
$957$	−216.249	−	336.043i	−0.00730443	−	0.0113508i
$958$		−	48356.6i		−	1.63083i
$959$			13659.3i			0.459938i
$960$	4171.88	−	2684.68i	0.140257	−	0.0902578i
$961$	−3972.73			−0.133354
$962$			24957.0i			0.836429i
$963$	−40481.9	−	18428.2i	−1.35463	−	0.616658i
$964$	−85363.1			−2.85203
$965$	1661.43			0.0554232
$966$	9179.65	−	5907.26i	0.305746	−	0.196753i
$967$	9011.08			0.299666			0.149833	−	0.988711i	$-0.452126\pi$
$967$	9011.08			0.299666			0.149833	+	0.988711i	$0.452126\pi$
$968$	59791.1			1.98529
$969$	2397.72	+	3725.96i	0.0794901	+	0.123524i
$970$		−	19697.9i		−	0.652022i
$971$			11334.2i			0.374594i	0.982303	+	0.187297i	$0.0599726\pi$
$971$			11334.2i			0.374594i	−0.982303	+	0.187297i	$0.940027\pi$
$972$	61799.9	+	17943.0i	2.03933	+	0.592102i
$973$	−5647.62			−0.186079
$974$		−	78918.3i		−	2.59621i
$975$	8286.75	+	12877.3i	0.272193	+	0.422978i
$976$			3871.25i			0.126963i
$977$		−	43177.5i		−	1.41389i	−0.707268	−	0.706945i	$-0.750073\pi$
$977$		−	43177.5i		−	1.41389i	0.707268	−	0.706945i	$-0.249927\pi$
$978$	−61886.4	+	39824.9i	−2.02342	+	1.30211i
$979$			713.620i			0.0232966i
$980$	14453.1			0.471110
$981$	−43436.2	−	19773.1i	−1.41367	−	0.643535i
$982$		−	54718.7i		−	1.77815i
$983$	−30183.2			−0.979344			−0.489672	−	0.871907i	$-0.662883\pi$
$983$	−30183.2			−0.979344			−0.489672	+	0.871907i	$0.662883\pi$
$984$	21863.8	−	14069.7i	0.708325	−	0.455819i
$985$	−10563.1			−0.341694
$986$	−52236.2			−1.68716
$987$	10348.7	−	6659.55i	0.333741	−	0.214768i
$988$		−	5152.33i		−	0.165908i
$989$	13396.5			0.430722
$990$	98.3385	−	216.023i	0.00315697	−	0.00693502i
$991$		−	50681.9i		−	1.62458i	−0.583251	−	0.812292i	$-0.698219\pi$
$991$		−	50681.9i		−	1.62458i	0.583251	−	0.812292i	$-0.301781\pi$
$992$			15423.4i			0.493642i
$993$	24512.9	+	38092.2i	0.783378	+	1.21734i
$994$	18980.4			0.605655
$995$	10151.5			0.323440
$996$	−5823.78	−	9049.93i	−0.185275	−	0.287910i
$997$	50227.3			1.59550			0.797751	−	0.602987i	$-0.206023\pi$
$997$	50227.3			1.59550			0.797751	+	0.602987i	$0.206023\pi$
$998$		−	37660.9i		−	1.19452i
$999$	−3910.24	−	26850.0i	−0.123838	−	0.850346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.d.b.200.6	yes	64
3.2	odd	2	inner	201.4.d.b.200.60	yes	64
67.66	odd	2	inner	201.4.d.b.200.59	yes	64
201.200	even	2	inner	201.4.d.b.200.5	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.d.b.200.5	✓	64	201.200	even	2	inner
201.4.d.b.200.6	yes	64	1.1	even	1	trivial
201.4.d.b.200.59	yes	64	67.66	odd	2	inner
201.4.d.b.200.60	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)

\(f(q)\)	\(=\)	\(q-4.99884 q^{2} +(-4.36958 + 2.81190i) q^{3} +16.9884 q^{4} +3.29226 q^{5} +(21.8428 - 14.0562i) q^{6} -9.19710i q^{7} -44.9316 q^{8} +(11.1865 - 24.5736i) q^{9} +O(q^{10})\)	\(q-4.99884 q^{2} +(-4.36958 + 2.81190i) q^{3} +16.9884 q^{4} +3.29226 q^{5} +(21.8428 - 14.0562i) q^{6} -9.19710i q^{7} -44.9316 q^{8} +(11.1865 - 24.5736i) q^{9} -16.4575 q^{10} -0.534155 q^{11} +(-74.2322 + 47.7697i) q^{12} +25.8147i q^{13} +45.9748i q^{14} +(-14.3858 + 9.25751i) q^{15} +88.6985 q^{16} +72.5797i q^{17} +(-55.9193 + 122.840i) q^{18} -11.7485 q^{19} +55.9303 q^{20} +(25.8613 + 40.1875i) q^{21} +2.67016 q^{22} +45.6947i q^{23} +(196.332 - 126.343i) q^{24} -114.161 q^{25} -129.044i q^{26} +(20.2184 + 138.832i) q^{27} -156.244i q^{28} -143.975i q^{29} +(71.9123 - 46.2768i) q^{30} -183.749i q^{31} -83.9372 q^{32} +(2.33403 - 1.50199i) q^{33} -362.814i q^{34} -30.2793i q^{35} +(190.040 - 417.467i) q^{36} -193.400 q^{37} +58.7291 q^{38} +(-72.5883 - 112.799i) q^{39} -147.927 q^{40} +111.361 q^{41} +(-129.277 - 200.891i) q^{42} -293.174i q^{43} -9.07444 q^{44} +(36.8288 - 80.9028i) q^{45} -228.421i q^{46} -257.510i q^{47} +(-387.575 + 249.411i) q^{48} +258.413 q^{49} +570.673 q^{50} +(-204.087 - 317.143i) q^{51} +438.550i q^{52} -174.407 q^{53} +(-101.069 - 693.997i) q^{54} -1.75858 q^{55} +413.240i q^{56} +(51.3362 - 33.0357i) q^{57} +719.708i q^{58} +81.3265i q^{59} +(-244.392 + 157.270i) q^{60} +43.6450i q^{61} +918.532i q^{62} +(-226.006 - 102.883i) q^{63} -290.000 q^{64} +84.9888i q^{65} +(-11.6675 + 7.50821i) q^{66} +(306.951 - 454.471i) q^{67} +1233.01i q^{68} +(-128.489 - 199.667i) q^{69} +151.361i q^{70} -412.843i q^{71} +(-502.625 + 1104.13i) q^{72} +205.263 q^{73} +966.773 q^{74} +(498.836 - 321.009i) q^{75} -199.589 q^{76} +4.91268i q^{77} +(362.857 + 563.866i) q^{78} -521.312i q^{79} +292.019 q^{80} +(-478.726 - 549.784i) q^{81} -556.677 q^{82} +121.914i q^{83} +(439.342 + 682.721i) q^{84} +238.951i q^{85} +1465.53i q^{86} +(404.843 + 629.110i) q^{87} +24.0004 q^{88} -1335.98i q^{89} +(-184.101 + 404.420i) q^{90} +237.420 q^{91} +776.280i q^{92} +(516.684 + 802.906i) q^{93} +1287.25i q^{94} -38.6793 q^{95} +(366.770 - 236.023i) q^{96} +1196.90i q^{97} -1291.77 q^{98} +(-5.97530 + 13.1261i) 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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