LMFDB - Embedded newform 201.4.d.b.200.17

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			200.17
Character	$\chi$	$=$	201.200
Dual form			201.4.d.b.200.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.37562 q^{2} +(0.888938 - 5.11955i) q^{3} +3.39482 q^{4} +12.9769 q^{5} +(-3.00072 + 17.2817i) q^{6} +25.4642i q^{7} +15.5453 q^{8} +(-25.4196 - 9.10193i) q^{9} +O(q^{10})$	\(q-3.37562 q^{2} +(0.888938 - 5.11955i) q^{3} +3.39482 q^{4} +12.9769 q^{5} +(-3.00072 + 17.2817i) q^{6} +25.4642i q^{7} +15.5453 q^{8} +(-25.4196 - 9.10193i) q^{9} -43.8050 q^{10} -36.8082 q^{11} +(3.01779 - 17.3800i) q^{12} +23.7660i q^{13} -85.9574i q^{14} +(11.5356 - 66.4357i) q^{15} -79.6338 q^{16} -40.6902i q^{17} +(85.8069 + 30.7247i) q^{18} -127.774 q^{19} +44.0541 q^{20} +(130.365 + 22.6361i) q^{21} +124.251 q^{22} +160.041i q^{23} +(13.8189 - 79.5851i) q^{24} +43.3990 q^{25} -80.2249i q^{26} +(-69.1942 + 122.046i) q^{27} +86.4463i q^{28} -74.9835i q^{29} +(-38.9399 + 224.262i) q^{30} +76.1652i q^{31} +144.451 q^{32} +(-32.7202 + 188.442i) q^{33} +137.355i q^{34} +330.445i q^{35} +(-86.2949 - 30.8994i) q^{36} -321.560 q^{37} +431.315 q^{38} +(121.671 + 21.1265i) q^{39} +201.730 q^{40} -43.6176 q^{41} +(-440.063 - 76.4108i) q^{42} +131.767i q^{43} -124.957 q^{44} +(-329.866 - 118.114i) q^{45} -540.237i q^{46} +383.726i q^{47} +(-70.7895 + 407.689i) q^{48} -305.424 q^{49} -146.499 q^{50} +(-208.316 - 36.1711i) q^{51} +80.6812i q^{52} +402.760 q^{53} +(233.573 - 411.980i) q^{54} -477.655 q^{55} +395.849i q^{56} +(-113.583 + 654.143i) q^{57} +253.116i q^{58} +239.905i q^{59} +(39.1614 - 225.537i) q^{60} +324.150i q^{61} -257.105i q^{62} +(231.773 - 647.288i) q^{63} +149.459 q^{64} +308.408i q^{65} +(110.451 - 636.107i) q^{66} +(501.117 - 222.810i) q^{67} -138.136i q^{68} +(819.336 + 142.266i) q^{69} -1115.46i q^{70} -239.847i q^{71} +(-395.156 - 141.493i) q^{72} -277.231 q^{73} +1085.47 q^{74} +(38.5790 - 222.183i) q^{75} -433.768 q^{76} -937.291i q^{77} +(-410.715 - 71.3150i) q^{78} -303.458i q^{79} -1033.40 q^{80} +(563.310 + 462.734i) q^{81} +147.236 q^{82} +85.1158i q^{83} +(442.566 + 76.8454i) q^{84} -528.032i q^{85} -444.796i q^{86} +(-383.882 - 66.6557i) q^{87} -572.196 q^{88} -1134.79i q^{89} +(1113.50 + 398.710i) q^{90} -605.181 q^{91} +543.309i q^{92} +(389.931 + 67.7062i) q^{93} -1295.32i q^{94} -1658.10 q^{95} +(128.408 - 739.523i) q^{96} +1578.21i q^{97} +1031.00 q^{98} +(935.649 + 335.026i) 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 $

$2$	−3.37562			−1.19346			−0.596731	−	0.802441i	$-0.703534\pi$
$2$	−3.37562			−1.19346			−0.596731	+	0.802441i	$0.703534\pi$
$3$	0.888938	−	5.11955i	0.171076	−	0.985258i
$3$	0.888938	−	5.11955i	0.171076	−	0.985258i
$4$	3.39482			0.424353
$5$	12.9769			1.16069			0.580343	−	0.814372i	$-0.302919\pi$
$5$	12.9769			1.16069			0.580343	+	0.814372i	$0.302919\pi$
$6$	−3.00072	+	17.2817i	−0.204173	+	1.17587i
$7$			25.4642i			1.37494i	0.726215	+	0.687468i	$0.241278\pi$
$7$			25.4642i			1.37494i	−0.726215	+	0.687468i	$0.758722\pi$
$8$	15.5453			0.687013
$9$	−25.4196	−	9.10193i	−0.941466	−	0.337108i
$10$	−43.8050			−1.38524
$11$	−36.8082			−1.00892			−0.504459	−	0.863436i	$-0.668308\pi$
$11$	−36.8082			−1.00892			−0.504459	+	0.863436i	$0.668308\pi$
$12$	3.01779	−	17.3800i	0.0725967	−	0.418097i
$13$			23.7660i			0.507038i	0.967330	+	0.253519i	$0.0815880\pi$
$13$			23.7660i			0.507038i	−0.967330	+	0.253519i	$0.918412\pi$
$14$		−	85.9574i		−	1.64093i
$15$	11.5356	−	66.4357i	0.198566	−	1.14357i
$16$	−79.6338			−1.24428
$17$		−	40.6902i		−	0.580520i	−0.956948	−	0.290260i	$-0.906258\pi$
$17$		−	40.6902i		−	0.580520i	0.956948	−	0.290260i	$-0.0937417\pi$
$18$	85.8069	+	30.7247i	1.12360	+	0.402326i
$19$	−127.774			−1.54280			−0.771402	−	0.636348i	$-0.780444\pi$
$19$	−127.774			−1.54280			−0.771402	+	0.636348i	$0.780444\pi$
$20$	44.0541			0.492540
$21$	130.365	+	22.6361i	1.35467	+	0.235219i
$22$	124.251			1.20411
$23$			160.041i			1.45090i	0.688273	+	0.725452i	$0.258369\pi$
$23$			160.041i			1.45090i	−0.688273	+	0.725452i	$0.741631\pi$
$24$	13.8189	−	79.5851i	0.117532	−	0.676885i
$25$	43.3990			0.347192
$26$		−	80.2249i		−	0.605131i
$27$	−69.1942	+	122.046i	−0.493201	+	0.869915i
$28$			86.4463i			0.583458i
$29$		−	74.9835i		−	0.480141i	−0.970755	−	0.240070i	$-0.922829\pi$
$29$		−	74.9835i		−	0.480141i	0.970755	−	0.240070i	$-0.0771705\pi$
$30$	−38.9399	+	224.262i	−0.236981	+	1.36481i
$31$			76.1652i			0.441280i	0.975355	+	0.220640i	$0.0708145\pi$
$31$			76.1652i			0.441280i	−0.975355	+	0.220640i	$0.929185\pi$
$32$	144.451			0.797985
$33$	−32.7202	+	188.442i	−0.172602	+	0.994044i
$34$			137.355i			0.692828i
$35$			330.445i			1.59587i
$36$	−86.2949	−	30.8994i	−0.399514	−	0.143053i
$37$	−321.560			−1.42876			−0.714380	−	0.699757i	$-0.753291\pi$
$37$	−321.560			−1.42876			−0.714380	+	0.699757i	$0.753291\pi$
$38$	431.315			1.84128
$39$	121.671	+	21.1265i	0.499563	+	0.0867422i
$40$	201.730			0.797407
$41$	−43.6176			−0.166144			−0.0830722	−	0.996544i	$-0.526473\pi$
$41$	−43.6176			−0.166144			−0.0830722	+	0.996544i	$0.526473\pi$
$42$	−440.063	−	76.4108i	−1.61674	−	0.280725i
$43$			131.767i			0.467309i	0.972320	+	0.233655i	$0.0750685\pi$
$43$			131.767i			0.467309i	−0.972320	+	0.233655i	$0.924932\pi$
$44$	−124.957			−0.428137
$45$	−329.866	−	118.114i	−1.09275	−	0.391277i
$46$		−	540.237i		−	1.73160i
$47$			383.726i			1.19090i	0.803393	+	0.595450i	$0.203026\pi$
$47$			383.726i			1.19090i	−0.803393	+	0.595450i	$0.796974\pi$
$48$	−70.7895	+	407.689i	−0.212866	+	1.22593i
$49$	−305.424			−0.890448
$50$	−146.499			−0.414360
$51$	−208.316	−	36.1711i	−0.571962	−	0.0993131i
$52$			80.6812i			0.215163i
$53$	402.760			1.04384			0.521918	−	0.852996i	$-0.325217\pi$
$53$	402.760			1.04384			0.521918	+	0.852996i	$0.325217\pi$
$54$	233.573	−	411.980i	0.588617	−	1.03821i
$55$	−477.655			−1.17104
$56$			395.849i			0.944599i
$57$	−113.583	+	654.143i	−0.263937	+	1.52006i
$58$			253.116i			0.573030i
$59$			239.905i			0.529373i	0.964335	+	0.264686i	$0.0852685\pi$
$59$			239.905i			0.529373i	−0.964335	+	0.264686i	$0.914732\pi$
$60$	39.1614	−	225.537i	0.0842619	−	0.485279i
$61$			324.150i			0.680379i	0.940357	+	0.340189i	$0.110491\pi$
$61$			324.150i			0.680379i	−0.940357	+	0.340189i	$0.889509\pi$
$62$		−	257.105i		−	0.526651i
$63$	231.773	−	647.288i	0.463503	−	1.29446i
$64$	149.459			0.291912
$65$			308.408i			0.588512i
$66$	110.451	−	636.107i	0.205994	−	1.18635i
$67$	501.117	−	222.810i	0.913750	−	0.406277i
$67$	501.117	−	222.810i	0.913750	−	0.406277i
$68$		−	138.136i		−	0.246345i
$69$	819.336	+	142.266i	1.42951	+	0.248215i
$70$		−	1115.46i		−	1.90461i
$71$		−	239.847i		−	0.400909i	−0.979703	−	0.200455i	$-0.935758\pi$
$71$		−	239.847i		−	0.400909i	0.979703	−	0.200455i	$-0.0642419\pi$
$72$	−395.156	−	141.493i	−0.646800	−	0.231598i
$73$	−277.231			−0.444486			−0.222243	−	0.974991i	$-0.571338\pi$
$73$	−277.231			−0.444486			−0.222243	+	0.974991i	$0.571338\pi$
$74$	1085.47			1.70517
$75$	38.5790	−	222.183i	0.0593963	−	0.342073i
$76$	−433.768			−0.654693
$77$		−	937.291i		−	1.38720i
$78$	−410.715	−	71.3150i	−0.596210	−	0.103524i
$79$		−	303.458i		−	0.432174i	−0.976374	−	0.216087i	$-0.930671\pi$
$79$		−	303.458i		−	0.432174i	0.976374	−	0.216087i	$-0.0693294\pi$
$80$	−1033.40			−1.44422
$81$	563.310	+	462.734i	0.772716	+	0.634752i
$82$	147.236			0.198287
$83$			85.1158i			0.112562i	0.998415	+	0.0562812i	$0.0179243\pi$
$83$			85.1158i			0.112562i	−0.998415	+	0.0562812i	$0.982076\pi$
$84$	442.566	+	76.8454i	0.574856	+	0.0998158i
$85$		−	528.032i		−	0.673801i
$86$		−	444.796i		−	0.557716i
$87$	−383.882	−	66.6557i	−0.473062	−	0.0821407i
$88$	−572.196			−0.693140
$89$		−	1134.79i		−	1.35155i	−0.737110	−	0.675773i	$-0.763810\pi$
$89$		−	1134.79i		−	1.35155i	0.737110	−	0.675773i	$-0.236190\pi$
$90$	1113.50	+	398.710i	1.30415	+	0.466974i
$91$	−605.181			−0.697145
$92$			543.309i			0.615695i
$93$	389.931	+	67.7062i	0.434774	+	0.0754925i
$94$		−	1295.32i		−	1.42129i
$95$	−1658.10			−1.79071
$96$	128.408	−	739.523i	0.136516	−	0.786221i
$97$			1578.21i			1.65199i	0.563680	+	0.825993i	$0.309385\pi$
$97$			1578.21i			1.65199i	−0.563680	+	0.825993i	$0.690615\pi$
$98$	1031.00			1.06272
$99$	935.649	+	335.026i	0.949862	+	0.340115i
$100$	147.332			0.147332
$101$	−1013.22			−0.998210			−0.499105	−	0.866541i	$-0.666338\pi$
$101$	−1013.22			−0.998210			−0.499105	+	0.866541i	$0.666338\pi$
$102$	703.195	+	122.100i	0.682615	+	0.118527i
$103$	1267.80			1.21282			0.606408	−	0.795153i	$-0.292610\pi$
$103$	1267.80			1.21282			0.606408	+	0.795153i	$0.292610\pi$
$104$			369.450i			0.348342i
$105$	1691.73	+	293.745i	1.57234	+	0.273015i
$106$	−1359.56			−1.24578
$107$		−	975.746i		−	0.881578i	−0.897611	−	0.440789i	$-0.854699\pi$
$107$		−	975.746i		−	0.881578i	0.897611	−	0.440789i	$-0.145301\pi$
$108$	−234.902	+	414.323i	−0.209291	+	0.369151i
$109$		−	996.496i		−	0.875660i	−0.899058	−	0.437830i	$-0.855747\pi$
$109$		−	996.496i		−	0.875660i	0.899058	−	0.437830i	$-0.144253\pi$
$110$	1612.38			1.39759
$111$	−285.847	+	1646.24i	−0.244427	+	1.40770i
$112$		−	2027.81i		−	1.71080i
$113$	−1020.46			−0.849531			−0.424765	−	0.905304i	$-0.639643\pi$
$113$	−1020.46			−0.849531			−0.424765	+	0.905304i	$0.639643\pi$
$114$	383.413	−	2208.14i	0.314999	−	1.81413i
$115$			2076.83i			1.68404i
$116$		−	254.555i		−	0.203749i
$117$	216.316	−	604.121i	0.170927	−	0.477359i
$118$		−	809.829i		−	0.631787i
$119$	1036.14			0.798177
$120$	179.325	−	1032.77i	0.136417	−	0.785651i
$121$	23.8451			0.0179151
$122$		−	1094.21i		−	0.812006i
$123$	−38.7733	+	223.302i	−0.0284234	+	0.163695i
$124$			258.567i			0.187258i
$125$	−1058.93			−0.757705
$126$	−782.378	+	2185.00i	−0.553173	+	1.54488i
$127$	889.497			0.621497			0.310748	−	0.950492i	$-0.399420\pi$
$127$	889.497			0.621497			0.310748	+	0.950492i	$0.399420\pi$
$128$	−1660.12			−1.14637
$129$	674.588	+	117.133i	0.460420	+	0.0799455i
$130$		−	1041.07i		−	0.702367i
$131$			1602.94i			1.06908i	0.845142	+	0.534542i	$0.179516\pi$
$131$			1602.94i			1.06908i	−0.845142	+	0.534542i	$0.820484\pi$
$132$	−111.079	+	639.725i	−0.0732441	+	0.421825i
$133$		−	3253.65i		−	2.12126i
$134$	−1691.58	+	752.123i	−1.09053	+	0.484877i
$135$	−897.924	+	1583.77i	−0.572452	+	1.00970i
$136$		−	632.544i		−	0.398825i
$137$	833.738			0.519934			0.259967	−	0.965617i	$-0.416288\pi$
$137$	833.738			0.519934			0.259967	+	0.965617i	$0.416288\pi$
$138$	−2765.77	−	480.237i	−1.70607	−	0.296235i
$139$			3036.32i			1.85278i	0.376560	+	0.926392i	$0.377107\pi$
$139$			3036.32i			1.85278i	−0.376560	+	0.926392i	$0.622893\pi$
$140$			1121.80i			0.677211i
$141$	1964.51	+	341.109i	1.17334	+	0.203735i
$142$			809.632i			0.478470i
$143$		−	874.783i		−	0.511560i
$144$	2024.26	+	724.821i	1.17144	+	0.419456i
$145$		−	973.050i		−	0.557293i
$146$	935.827			0.530477
$147$	−271.503	+	1563.63i	−0.152335	+	0.877321i
$148$	−1091.64			−0.606299
$149$			3304.75i			1.81702i	0.417866	+	0.908509i	$0.362778\pi$
$149$			3304.75i			1.81702i	−0.417866	+	0.908509i	$0.637222\pi$
$150$	−130.228	+	750.007i	−0.0708872	+	0.408252i
$151$	−3625.31			−1.95380			−0.976900	−	0.213698i	$-0.931449\pi$
$151$	−3625.31			−1.95380			−0.976900	+	0.213698i	$0.931449\pi$
$152$	−1986.28			−1.05993
$153$	−370.360	+	1034.33i	−0.195698	+	0.546539i
$154$			3163.94i			1.65557i
$155$			988.385i			0.512187i
$156$	413.051	+	71.7206i	0.211991	+	0.0368093i
$157$	−2393.46			−1.21668			−0.608341	−	0.793676i	$-0.708165\pi$
$157$	−2393.46			−1.21668			−0.608341	+	0.793676i	$0.708165\pi$
$158$			1024.36i			0.515783i
$159$	358.028	−	2061.95i	0.178576	−	1.02845i
$160$	1874.52			0.926210
$161$	−4075.30			−1.99490
$162$	−1901.52	−	1562.02i	−0.922207	−	0.757553i
$163$	−202.020			−0.0970764			−0.0485382	−	0.998821i	$-0.515456\pi$
$163$	−202.020			−0.0970764			−0.0485382	+	0.998821i	$0.515456\pi$
$164$	−148.074			−0.0705038
$165$	−424.606	+	2445.38i	−0.200337	+	1.15377i
$166$		−	287.319i		−	0.134339i
$167$		−	3953.92i		−	1.83212i	−0.401042	−	0.916060i	$-0.631352\pi$
$167$		−	3953.92i		−	1.83212i	0.401042	−	0.916060i	$-0.368648\pi$
$168$	2026.57	+	351.886i	0.930674	+	0.161599i
$169$	1632.18			0.742912
$170$			1782.44i			0.804156i
$171$	3247.95	+	1162.99i	1.45250	+	0.520092i
$172$			447.326i			0.198304i
$173$		−	3674.45i		−	1.61482i	−0.589994	−	0.807408i	$-0.700870\pi$
$173$		−	3674.45i		−	1.61482i	0.589994	−	0.807408i	$-0.299130\pi$
$174$	1295.84	+	225.004i	0.564582	+	0.0980318i
$175$			1105.12i			0.477366i
$176$	2931.18			1.25537
$177$	1228.21	+	213.261i	0.521569	+	0.0905631i
$178$			3830.62i			1.61302i
$179$	1745.46			0.728836			0.364418	−	0.931235i	$-0.381268\pi$
$179$	1745.46			0.728836			0.364418	+	0.931235i	$0.381268\pi$
$180$	−1119.84	−	400.978i	−0.463710	−	0.166039i
$181$	−4446.80			−1.82612			−0.913060	−	0.407825i	$-0.866287\pi$
$181$	−4446.80			−1.82612			−0.913060	+	0.407825i	$0.866287\pi$
$182$	2042.86			0.832016
$183$	1659.50	+	288.149i	0.670348	+	0.116397i
$184$			2487.89i			0.996790i
$185$	−4172.84			−1.65834
$186$	−1316.26	−	228.550i	−0.518887	−	0.0900975i
$187$			1497.74i			0.585697i
$188$			1302.68i			0.505361i
$189$	−3107.79	−	1761.97i	−1.19608	−	0.678120i
$190$	5597.12			2.13715
$191$	4629.44			1.75379			0.876897	−	0.480679i	$-0.159610\pi$
$191$	4629.44			1.75379			0.876897	+	0.480679i	$0.159610\pi$
$192$	132.860	−	765.163i	0.0499393	−	0.287609i
$193$	−230.772			−0.0860690			−0.0430345	−	0.999074i	$-0.513703\pi$
$193$	−230.772			−0.0860690			−0.0430345	+	0.999074i	$0.513703\pi$
$194$		−	5327.43i		−	1.97158i
$195$	1578.91	+	274.155i	0.579836	+	0.100680i
$196$	−1036.86			−0.377864
$197$	3169.83			1.14640			0.573201	−	0.819415i	$-0.305702\pi$
$197$	3169.83			1.14640			0.573201	+	0.819415i	$0.305702\pi$
$198$	−3158.40	−	1130.92i	−1.13362	−	0.405914i
$199$	1010.58			0.359992			0.179996	−	0.983667i	$-0.442392\pi$
$199$	1010.58			0.359992			0.179996	+	0.983667i	$0.442392\pi$
$200$	674.652			0.238525
$201$	−695.225	−	2763.56i	−0.243967	−	0.969784i
$202$	3420.25			1.19133
$203$	1909.39			0.660163
$204$	−707.195	−	122.794i	−0.242713	−	0.0421438i
$205$	−566.019			−0.192842
$206$	−4279.62			−1.44745
$207$	1456.68	−	4068.16i	0.489112	−	1.36598i
$208$		−	1892.57i		−	0.630896i
$209$	4703.12			1.55656
$210$	−5710.64	−	991.573i	−1.87653	−	0.325833i
$211$	−1098.33			−0.358350			−0.179175	−	0.983817i	$-0.557343\pi$
$211$	−1098.33			−0.358350			−0.179175	+	0.983817i	$0.557343\pi$
$212$	1367.30			0.442954
$213$	−1227.91	−	213.209i	−0.394999	−	0.0685861i
$214$			3293.75i			1.05213i
$215$			1709.92i			0.542399i
$216$	−1075.65	+	1897.24i	−0.338836	+	0.597644i
$217$	−1939.48			−0.606731
$218$			3363.79i			1.04507i
$219$	−246.441	+	1419.30i	−0.0760409	+	0.437933i
$220$	−1621.55			−0.496933
$221$	967.043			0.294346
$222$	964.912	−	5557.09i	0.291715	−	1.68003i
$223$	3245.61			0.974628			0.487314	−	0.873227i	$-0.337977\pi$
$223$	3245.61			0.974628			0.487314	+	0.873227i	$0.337977\pi$
$224$			3678.32i			1.09718i
$225$	−1103.18	−	395.014i	−0.326869	−	0.117041i
$226$	3444.69			1.01388
$227$		−	652.739i		−	0.190854i	−0.995436	−	0.0954269i	$-0.969578\pi$
$227$		−	652.739i		−	0.190854i	0.995436	−	0.0954269i	$-0.0304216\pi$
$228$	−385.593	+	2220.70i	−0.112002	+	0.645041i
$229$		−	3296.25i		−	0.951189i	−0.879665	−	0.475595i	$-0.842233\pi$
$229$		−	3296.25i		−	0.951189i	0.879665	−	0.475595i	$-0.157767\pi$
$230$		−	7010.58i		−	2.00984i
$231$	−4798.51	−	833.194i	−1.36675	−	0.237317i
$232$		−	1165.64i		−	0.329863i
$233$	−2658.55			−0.747499			−0.373750	−	0.927530i	$-0.621928\pi$
$233$	−2658.55			−0.747499			−0.373750	+	0.927530i	$0.621928\pi$
$234$	−730.201	+	2039.28i	−0.203995	+	0.569710i
$235$			4979.57i			1.38226i
$236$			814.435i			0.224641i
$237$	−1553.57	−	269.756i	−0.425803	−	0.0739347i
$238$	−3497.63			−0.952595
$239$	694.669			0.188010			0.0940050	−	0.995572i	$-0.470033\pi$
$239$	694.669			0.188010			0.0940050	+	0.995572i	$0.470033\pi$
$240$	−918.626	+	5290.52i	−0.247071	+	1.42292i
$241$	6289.72			1.68115			0.840574	−	0.541697i	$-0.182218\pi$
$241$	6289.72			1.68115			0.840574	+	0.541697i	$0.182218\pi$
$242$	−80.4919			−0.0213811
$243$	2869.74	−	2472.55i	0.757588	−	0.652733i
$244$			1100.43i			0.288720i
$245$	−3963.44			−1.03353
$246$	130.884	−	753.784i	0.0339222	−	0.195364i
$247$		−	3036.66i		−	0.782260i
$248$			1184.01i			0.303165i
$249$	435.755	+	75.6627i	0.110903	+	0.0192568i
$250$	3574.53			0.904293
$251$	630.838			0.158638			0.0793190	−	0.996849i	$-0.474725\pi$
$251$	630.838			0.158638			0.0793190	+	0.996849i	$0.474725\pi$
$252$	786.828	−	2197.43i	0.196689	−	0.549305i
$253$		−	5890.81i		−	1.46384i
$254$	−3002.61			−0.741733
$255$	−2703.28	−	469.388i	−0.663868	−	0.115271i
$256$	4408.27			1.07624
$257$		−	433.650i		−	0.105254i	−0.998614	−	0.0526272i	$-0.983241\pi$
$257$		−	433.650i		−	0.105254i	0.998614	−	0.0526272i	$-0.0167595\pi$
$258$	−2277.15	−	395.396i	−0.549494	−	0.0954120i
$259$		−	8188.26i		−	1.96445i
$260$			1046.99i			0.249737i
$261$	−682.494	+	1906.05i	−0.161860	+	0.452036i
$262$		−	5410.94i		−	1.27591i
$263$		−	1214.52i		−	0.284754i	−0.989813	−	0.142377i	$-0.954525\pi$
$263$		−	1214.52i		−	0.284754i	0.989813	−	0.142377i	$-0.0454745\pi$
$264$	−508.647	+	2929.39i	−0.118580	+	0.682922i
$265$	5226.56			1.21157
$266$			10983.1i			2.53164i
$267$	−5809.61	−	1008.76i	−1.33162	−	0.231217i
$268$	1701.20	−	756.400i	0.387752	−	0.172405i
$269$		−	5775.47i		−	1.30906i	−0.756037	−	0.654529i	$-0.772867\pi$
$269$		−	5775.47i		−	1.30906i	0.756037	−	0.654529i	$-0.227133\pi$
$270$	3031.05	−	5346.21i	0.683200	−	1.20504i
$271$			7319.22i			1.64063i	0.571912	+	0.820315i	$0.306202\pi$
$271$			7319.22i			1.64063i	−0.571912	+	0.820315i	$0.693798\pi$
$272$			3240.32i			0.722328i
$273$	−537.968	+	3098.25i	−0.119265	+	0.686867i
$274$	−2814.38			−0.620522
$275$	−1597.44			−0.350288
$276$	2781.50	+	482.968i	0.606618	+	0.105331i
$277$	−5017.69			−1.08839			−0.544194	−	0.838959i	$-0.683165\pi$
$277$	−5017.69			−1.08839			−0.544194	+	0.838959i	$0.683165\pi$
$278$		−	10249.5i		−	2.21123i
$279$	693.250	−	1936.09i	0.148759	−	0.415450i
$280$			5136.88i			1.09638i
$281$	2699.79			0.573154			0.286577	−	0.958057i	$-0.407483\pi$
$281$	2699.79			0.573154			0.286577	+	0.958057i	$0.407483\pi$
$282$	−6631.43	−	1151.46i	−1.40034	−	0.243150i
$283$	−5660.68			−1.18902			−0.594509	−	0.804089i	$-0.702654\pi$
$283$	−5660.68			−1.18902			−0.594509	+	0.804089i	$0.702654\pi$
$284$		−	814.237i		−	0.170127i
$285$	−1473.95	+	8488.73i	−0.306348	+	1.76431i
$286$			2952.94i			0.610527i
$287$		−	1110.69i		−	0.228438i
$288$	−3671.88	−	1314.78i	−0.751276	−	0.269007i
$289$	3257.30			0.662997
$290$			3284.65i			0.665108i
$291$	8079.71	+	1402.93i	1.62763	+	0.282616i
$292$	−941.150			−0.188619
$293$			6345.62i			1.26524i	0.774462	+	0.632620i	$0.218020\pi$
$293$			6345.62i			1.26524i	−0.774462	+	0.632620i	$0.781980\pi$
$294$	916.491	−	5278.23i	0.181806	−	1.04705i
$295$			3113.22i			0.614436i
$296$	−4998.76			−0.981578
$297$	2546.92	−	4492.29i	0.497599	−	0.877673i
$298$		−	11155.6i		−	2.16854i
$299$	−3803.52			−0.735663
$300$	130.969	−	754.272i	0.0252050	−	0.145160i
$301$	−3355.34			−0.642520
$302$	12237.7			2.33179
$303$	−900.691	+	5187.23i	−0.170770	+	0.983494i
$304$	10175.1			1.91968
$305$			4206.44i			0.789706i
$306$	1250.19	−	3491.50i	0.233558	−	0.652274i
$307$	−3255.65			−0.605244			−0.302622	−	0.953111i	$-0.597862\pi$
$307$	−3255.65			−0.605244			−0.302622	+	0.953111i	$0.597862\pi$
$308$		−	3181.93i		−	0.588661i
$309$	1127.00	−	6490.57i	0.207484	−	1.19494i
$310$		−	3336.41i		−	0.611276i
$311$	−2302.81			−0.419873			−0.209936	−	0.977715i	$-0.567326\pi$
$311$	−2302.81			−0.419873			−0.209936	+	0.977715i	$0.567326\pi$
$312$	1891.42	+	328.418i	0.343207	+	0.0595930i
$313$		−	7364.70i		−	1.32996i	−0.746861	−	0.664980i	$-0.768440\pi$
$313$		−	7364.70i		−	1.32996i	0.746861	−	0.664980i	$-0.231560\pi$
$314$	8079.42			1.45206
$315$	3007.69	−	8399.77i	0.537981	−	1.50246i
$316$		−	1030.19i		−	0.183394i
$317$			9348.76i			1.65640i	0.560433	+	0.828200i	$0.310635\pi$
$317$			9348.76i			1.65640i	−0.560433	+	0.828200i	$0.689365\pi$
$318$	−1208.57	+	6960.36i	−0.213123	+	1.22741i
$319$			2760.01i			0.484423i
$320$	1939.51			0.338819
$321$	−4995.38	−	867.378i	−0.868582	−	0.150817i
$322$	13756.7			2.38084
$323$			5199.14i			0.895628i
$324$	1912.34	+	1570.90i	0.327904	+	0.269359i
$325$			1031.42i			0.176039i
$326$	681.944			0.115857
$327$	−5101.61	−	885.823i	−0.862751	−	0.149805i
$328$	−678.050			−0.114143
$329$	−9771.28			−1.63741
$330$	1433.31	−	8254.68i	0.239094	−	1.37698i
$331$			4695.72i			0.779759i	0.920866	+	0.389880i	$0.127483\pi$
$331$			4695.72i			0.779759i	−0.920866	+	0.389880i	$0.872517\pi$
$332$			288.953i			0.0477661i
$333$	8173.92	+	2926.82i	1.34513	+	0.481647i
$334$			13347.0i			2.18657i
$335$	6502.93	−	2891.38i	1.06058	−	0.471560i
$336$	−10381.5	−	1802.60i	−1.68558	−	0.292678i
$337$		−	2079.28i		−	0.336099i	−0.985779	−	0.168050i	$-0.946253\pi$
$337$		−	2079.28i		−	0.336099i	0.985779	−	0.168050i	$-0.0537469\pi$
$338$	−5509.62			−0.886638
$339$	−907.127	+	5224.30i	−0.145335	+	0.837007i
$340$		−	1792.57i		−	0.285929i
$341$		−	2803.50i		−	0.445215i
$342$	−10963.9	−	3925.80i	−1.73350	−	0.620711i
$343$			956.846i			0.150626i
$344$			2048.36i			0.321048i
$345$	10632.4	+	1846.17i	1.65922	+	0.288100i
$346$			12403.5i			1.92722i
$347$	−10156.7			−1.57129			−0.785645	−	0.618678i	$-0.787669\pi$
$347$	−10156.7			−1.57129			−0.785645	+	0.618678i	$0.787669\pi$
$348$	−1303.21	−	226.284i	−0.200745	−	0.0348566i
$349$	2024.53			0.310517			0.155259	−	0.987874i	$-0.450379\pi$
$349$	2024.53			0.310517			0.155259	+	0.987874i	$0.450379\pi$
$350$		−	3730.46i		−	0.569719i
$351$	−2900.53	−	1644.47i	−0.441080	−	0.250072i
$352$	−5316.97			−0.805101
$353$	9596.52			1.44694			0.723472	−	0.690354i	$-0.242545\pi$
$353$	9596.52			1.44694			0.723472	+	0.690354i	$0.242545\pi$
$354$	−4145.96	−	719.888i	−0.622473	−	0.108084i
$355$		−	3112.46i		−	0.465330i
$356$		−	3852.41i		−	0.573532i
$357$	921.068	−	5304.59i	0.136549	−	0.786410i
$358$	−5892.01			−0.869839
$359$		−	5290.57i		−	0.777787i	−0.921283	−	0.388894i	$-0.872857\pi$
$359$		−	5290.57i		−	0.777787i	0.921283	−	0.388894i	$-0.127143\pi$
$360$	−5127.89	−	1836.13i	−0.750731	−	0.268813i
$361$	9467.09			1.38024
$362$	15010.7			2.17941
$363$	21.1968	−	122.076i	0.00306486	−	0.0176510i
$364$	−2054.48			−0.295835
$365$	−3597.59			−0.515908
$366$	−5601.84	−	972.682i	−0.800036	−	0.138915i
$367$		−	4796.80i		−	0.682264i	−0.940015	−	0.341132i	$-0.889190\pi$
$367$		−	4796.80i		−	0.682264i	0.940015	−	0.341132i	$-0.110810\pi$
$368$		−	12744.6i		−	1.80533i
$369$	1108.74	+	397.004i	0.156419	+	0.0560087i
$370$	14085.9			1.97917
$371$			10255.9i			1.43521i
$372$	1323.75	+	229.850i	0.184498	+	0.0320354i
$373$		−	3699.98i		−	0.513613i	−0.966463	−	0.256807i	$-0.917330\pi$
$373$		−	3699.98i		−	0.513613i	0.966463	−	0.256807i	$-0.0826703\pi$
$374$		−	5055.79i		−	0.699007i
$375$	−941.319	+	5421.22i	−0.129625	+	0.746535i
$376$			5965.16i			0.818164i
$377$	1782.05			0.243450
$378$	10490.7	+	5947.75i	1.42747	+	0.809311i
$379$			1163.22i			0.157653i	0.996888	+	0.0788264i	$0.0251173\pi$
$379$			1163.22i			0.157653i	−0.996888	+	0.0788264i	$0.974883\pi$
$380$	−5628.95			−0.759893
$381$	790.708	−	4553.82i	0.106323	−	0.612335i
$382$	−15627.2			−2.09309
$383$	8797.38			1.17370			0.586848	−	0.809697i	$-0.300369\pi$
$383$	8797.38			1.17370			0.586848	+	0.809697i	$0.300369\pi$
$384$	−1475.75	+	8499.08i	−0.196117	+	1.12947i
$385$		−	12163.1i		−	1.61010i
$386$	778.998			0.102720
$387$	1199.33	−	3349.46i	0.157534	−	0.439956i
$388$			5357.73i			0.701025i
$389$		−	1326.77i		−	0.172931i	−0.996255	−	0.0864655i	$-0.972443\pi$
$389$		−	1326.77i		−	0.172931i	0.996255	−	0.0864655i	$-0.0275572\pi$
$390$	−5329.80	−	925.445i	−0.692012	−	0.120158i
$391$	6512.09			0.842278
$392$	−4747.92			−0.611750
$393$	8206.36	+	1424.92i	1.05332	+	0.182895i
$394$	−10700.1			−1.36819
$395$		−	3937.94i		−	0.501618i
$396$	3176.36	+	1137.35i	0.403076	+	0.144329i
$397$	774.595			0.0979240			0.0489620	−	0.998801i	$-0.484409\pi$
$397$	774.595			0.0979240			0.0489620	+	0.998801i	$0.484409\pi$
$398$	−3411.35			−0.429637
$399$	−16657.2	−	2892.29i	−2.08998	−	0.362897i
$400$	−3456.02			−0.432003
$401$	−11104.3			−1.38285			−0.691423	−	0.722450i	$-0.743016\pi$
$401$	−11104.3			−1.38285			−0.691423	+	0.722450i	$0.743016\pi$
$402$	2346.82	+	9328.73i	0.291166	+	1.15740i
$403$	−1810.14			−0.223746
$404$	−3439.70			−0.423593
$405$	7309.99	+	6004.84i	0.896880	+	0.736748i
$406$	−6445.38			−0.787879
$407$	11836.1			1.44150
$408$	−3238.34	−	562.292i	−0.392945	−	0.0682295i
$409$			5312.07i			0.642213i	0.947043	+	0.321107i	$0.104055\pi$
$409$			5312.07i			0.642213i	−0.947043	+	0.321107i	$0.895945\pi$
$410$	1910.67			0.230149
$411$	741.141	−	4268.36i	0.0889484	−	0.512269i
$412$	4303.96			0.514662
$413$	−6108.99			−0.727854
$414$	−4917.19	+	13732.6i	−0.583737	+	1.63024i
$415$			1104.54i			0.130650i
$416$			3433.01i			0.404609i
$417$	15544.6	+	2699.10i	1.82547	+	0.316967i
$418$	−15875.9			−1.85770
$419$			3027.01i			0.352934i	0.984307	+	0.176467i	$0.0564669\pi$
$419$			3027.01i			0.352934i	−0.984307	+	0.176467i	$0.943533\pi$
$420$	5743.12	+	997.213i	0.667228	+	0.115855i
$421$	−4328.94			−0.501140			−0.250570	−	0.968099i	$-0.580618\pi$
$421$	−4328.94			−0.501140			−0.250570	+	0.968099i	$0.580618\pi$
$422$	3707.53			0.427677
$423$	3492.65	−	9754.17i	0.401462	−	1.12119i
$424$	6261.04			0.717129
$425$		−	1765.92i		−	0.201552i
$426$	4144.95	+	719.713i	0.471417	+	0.0818549i
$427$	−8254.20			−0.935477
$428$		−	3312.48i		−	0.374100i
$429$	−4478.49	−	777.628i	−0.504018	−	0.0875157i
$430$		−	5772.06i		−	0.647333i
$431$			7244.58i			0.809650i	0.914394	+	0.404825i	$0.132668\pi$
$431$			7244.58i			0.809650i	−0.914394	+	0.404825i	$0.867332\pi$
$432$	5510.20	−	9718.96i	0.613679	−	1.08242i
$433$			11929.0i			1.32395i	0.749527	+	0.661974i	$0.230281\pi$
$433$			11929.0i			1.32395i	−0.749527	+	0.661974i	$0.769719\pi$
$434$	6546.96			0.724111
$435$	−4981.58	−	864.982i	−0.549077	−	0.0953395i
$436$		−	3382.93i		−	0.371589i
$437$		−	20449.0i		−	2.23846i
$438$	831.893	−	4791.01i	0.0907520	−	0.522656i
$439$	−11199.1			−1.21755			−0.608773	−	0.793345i	$-0.708338\pi$
$439$	−11199.1			−1.21755			−0.608773	+	0.793345i	$0.708338\pi$
$440$	−7425.31			−0.804518
$441$	7763.74	+	2779.95i	0.838327	+	0.300178i
$442$	−3264.37			−0.351290
$443$	−12710.0			−1.36314			−0.681569	−	0.731754i	$-0.738702\pi$
$443$	−12710.0			−1.36314			−0.681569	+	0.731754i	$0.738702\pi$
$444$	−970.400	+	5588.70i	−0.103723	+	0.597360i
$445$		−	14726.0i		−	1.56872i
$446$	−10956.0			−1.16318
$447$	16918.8	+	2937.72i	1.79023	+	0.310849i
$448$			3805.85i			0.401361i
$449$		−	10077.2i		−	1.05919i	−0.848252	−	0.529593i	$-0.822345\pi$
$449$		−	10077.2i		−	1.05919i	0.848252	−	0.529593i	$-0.177655\pi$
$450$	3723.93	+	1333.42i	0.390106	+	0.139684i
$451$	1605.49			0.167626
$452$	−3464.28			−0.360501
$453$	−3222.68	+	18560.0i	−0.334249	+	1.92500i
$454$			2203.40i			0.227777i
$455$	−7853.35			−0.809166
$456$	−1765.68	+	10168.9i	−0.181328	+	1.04430i
$457$	13150.3			1.34605			0.673024	−	0.739621i	$-0.264995\pi$
$457$	13150.3			1.34605			0.673024	+	0.739621i	$0.264995\pi$
$458$			11126.9i			1.13521i
$459$	4966.07	+	2815.53i	0.505003	+	0.286313i
$460$			7050.45i			0.714628i
$461$			12405.4i			1.25331i	0.779297	+	0.626654i	$0.215576\pi$
$461$			12405.4i			1.25331i	−0.779297	+	0.626654i	$0.784424\pi$
$462$	16197.9	+	2812.55i	1.63116	+	0.283228i
$463$			12252.1i			1.22981i	0.788600	+	0.614906i	$0.210806\pi$
$463$			12252.1i			1.22981i	−0.788600	+	0.614906i	$0.789194\pi$
$464$			5971.22i			0.597428i
$465$	5060.09	+	878.614i	0.504636	+	0.0876231i
$466$	8974.26			0.892112
$467$			8659.57i			0.858067i	0.903289	+	0.429034i	$0.141146\pi$
$467$			8659.57i			0.858067i	−0.903289	+	0.429034i	$0.858854\pi$
$468$	734.355	−	2050.88i	0.0725332	−	0.202569i
$469$	5673.67	+	12760.5i	0.558605	+	1.25635i
$470$		−	16809.1i		−	1.64968i
$471$	−2127.64	+	12253.4i	−0.208145	+	1.19875i
$472$			3729.41i			0.363686i
$473$		−	4850.11i		−	0.471477i
$474$	5244.26	+	910.593i	0.508179	+	0.0882383i
$475$	−5545.24			−0.535649
$476$	3517.52			0.338709
$477$	−10238.0	−	3665.89i	−0.982736	−	0.351886i
$478$	−2344.94			−0.224383
$479$		−	13164.2i		−	1.25572i	−0.778328	−	0.627858i	$-0.783932\pi$
$479$		−	13164.2i		−	1.25572i	0.778328	−	0.627858i	$-0.216068\pi$
$480$	1666.33	−	9596.68i	0.158453	−	0.912556i
$481$		−	7642.19i		−	0.724436i
$482$	−21231.7			−2.00639
$483$	−3622.69	+	20863.7i	−0.341280	+	1.96549i
$484$	80.9497			0.00760234
$485$			20480.2i			1.91744i
$486$	−9687.15	+	8346.39i	−0.904153	+	0.779013i
$487$		−	17068.2i		−	1.58816i	−0.607813	−	0.794081i	$-0.707953\pi$
$487$		−	17068.2i		−	1.58816i	0.607813	−	0.794081i	$-0.292047\pi$
$488$			5039.02i			0.467429i
$489$	−179.584	+	1034.25i	−0.0166075	+	0.0956452i
$490$	13379.1			1.23348
$491$		−	3594.26i		−	0.330360i	−0.986263	−	0.165180i	$-0.947180\pi$
$491$		−	3594.26i		−	0.330360i	0.986263	−	0.165180i	$-0.0528205\pi$
$492$	−131.629	+	758.072i	−0.0120615	+	0.0694645i
$493$	−3051.10			−0.278731
$494$			10250.6i			0.933598i
$495$	12141.8	+	4347.58i	1.10249	+	0.394766i
$496$		−	6065.32i		−	0.549074i
$497$	6107.50			0.551225
$498$	−1470.94	−	255.409i	−0.132359	−	0.0229822i
$499$			22046.3i			1.97781i	0.148549	+	0.988905i	$0.452540\pi$
$499$			22046.3i			1.97781i	−0.148549	+	0.988905i	$0.547460\pi$
$500$	−3594.86			−0.321534
$501$	−20242.3	−	3514.80i	−1.80511	−	0.313432i
$502$	−2129.47			−0.189328
$503$	−12183.4			−1.07998			−0.539989	−	0.841672i	$-0.681572\pi$
$503$	−12183.4			−1.07998			−0.539989	+	0.841672i	$0.681572\pi$
$504$	3602.99	−	10062.3i	0.318432	−	0.889308i
$505$	−13148.4			−1.15861
$506$			19885.1i			1.74704i
$507$	1450.91	−	8356.02i	0.127095	−	0.731960i
$508$	3019.68			0.263734
$509$		−	19575.0i		−	1.70461i	−0.523045	−	0.852305i	$-0.675204\pi$
$509$		−	19575.0i		−	1.70461i	0.523045	−	0.852305i	$-0.324796\pi$
$510$	9125.27	+	1584.48i	0.792301	+	0.137572i
$511$		−	7059.46i		−	0.611139i
$512$	−1599.68			−0.138079
$513$	8841.19	−	15594.2i	0.760913	−	1.34211i
$514$			1463.84i			0.125617i
$515$	16452.1			1.40770
$516$	2290.11	+	397.645i	0.195380	+	0.0339251i
$517$		−	14124.3i		−	1.20152i
$518$			27640.5i			2.34450i
$519$	−18811.5	−	3266.36i	−1.59101	−	0.276257i
$520$			4794.30i			0.404316i
$521$	19342.4			1.62650			0.813250	−	0.581915i	$-0.197696\pi$
$521$	19342.4			1.62650			0.813250	+	0.581915i	$0.197696\pi$
$522$	2303.84	−	6434.10i	0.193173	−	0.539488i
$523$	−1463.92			−0.122395			−0.0611977	−	0.998126i	$-0.519492\pi$
$523$	−1463.92			−0.122395			−0.0611977	+	0.998126i	$0.519492\pi$
$524$			5441.71i			0.453668i
$525$	5657.71	+	982.383i	0.470329	+	0.0816661i
$526$			4099.75i			0.339843i
$527$	3099.18			0.256172
$528$	2605.64	−	15006.3i	0.214765	−	1.23687i
$529$	−13446.0			−1.10512
$530$	−17642.9			−1.44596
$531$	2183.60	−	6098.29i	0.178456	−	0.498386i
$532$		−	11045.6i		−	0.900161i
$533$		−	1036.61i		−	0.0842415i
$534$	19611.1	+	3405.19i	1.58924	+	0.275949i
$535$		−	12662.1i		−	1.02324i
$536$	7790.04	−	3463.66i	0.627758	−	0.279118i
$537$	1551.61	−	8935.96i	0.124687	−	0.718092i
$538$			19495.8i			1.56231i
$539$	11242.1			0.898389
$540$	−3048.29	+	5376.62i	−0.242921	+	0.428468i
$541$		−	15789.3i		−	1.25478i	−0.778705	−	0.627390i	$-0.784123\pi$
$541$		−	15789.3i		−	1.25478i	0.778705	−	0.627390i	$-0.215877\pi$
$542$		−	24706.9i		−	1.95803i
$543$	−3952.93	+	22765.6i	−0.312406	+	1.79920i
$544$		−	5877.73i		−	0.463246i
$545$		−	12931.4i		−	1.01637i
$546$	1815.98	−	10458.5i	0.142338	−	0.819750i
$547$		−	12904.3i		−	1.00868i	−0.863505	−	0.504340i	$-0.831736\pi$
$547$		−	12904.3i		−	1.00868i	0.863505	−	0.504340i	$-0.168264\pi$
$548$	2830.39			0.220636
$549$	2950.39	−	8239.74i	0.229361	−	0.640553i
$550$	5392.35			0.418056
$551$			9580.91i			0.740763i
$552$	12736.9	+	2211.58i	0.982095	+	0.170527i
$553$	7727.31			0.594211
$554$	16937.8			1.29895
$555$	−3709.40	+	21363.1i	−0.283703	+	1.63390i
$556$			10307.8i			0.786234i
$557$			661.144i			0.0502936i	0.999684	+	0.0251468i	$0.00800533\pi$
$557$			661.144i			0.0502936i	−0.999684	+	0.0251468i	$0.991995\pi$
$558$	−2340.15	+	6535.50i	−0.177538	+	0.495824i
$559$	−3131.57			−0.236943
$560$		−	26314.6i		−	1.98570i
$561$	7667.73	+	1331.39i	0.577062	+	0.100199i
$562$	−9113.48			−0.684037
$563$	−7973.11			−0.596850			−0.298425	−	0.954433i	$-0.596461\pi$
$563$	−7973.11			−0.596850			−0.298425	+	0.954433i	$0.596461\pi$
$564$	6669.15	+	1158.00i	0.497911	+	0.0864553i
$565$	−13242.4			−0.986038
$566$	19108.3			1.41905
$567$	−11783.1	+	14344.2i	−0.872744	+	1.06243i
$568$		−	3728.50i		−	0.275430i
$569$		−	4744.28i		−	0.349544i	−0.984609	−	0.174772i	$-0.944081\pi$
$569$		−	4744.28i		−	0.349544i	0.984609	−	0.174772i	$-0.0559188\pi$
$570$	4975.49	−	28654.7i	0.365615	−	2.10564i
$571$	−17993.3			−1.31873			−0.659364	−	0.751823i	$-0.729175\pi$
$571$	−17993.3			−1.31873			−0.659364	+	0.751823i	$0.729175\pi$
$572$		−	2969.73i		−	0.217082i
$573$	4115.29	−	23700.6i	0.300032	−	1.72794i
$574$			3749.25i			0.272632i
$575$			6945.60i			0.503742i
$576$	−3799.19	−	1360.37i	−0.274825	−	0.0984061i
$577$			490.847i			0.0354146i	0.999843	+	0.0177073i	$0.00563670\pi$
$577$			490.847i			0.0354146i	−0.999843	+	0.0177073i	$0.994363\pi$
$578$	−10995.4			−0.791262
$579$	−205.142	+	1181.45i	−0.0147244	+	0.0848001i
$580$		−	3303.33i		−	0.236489i
$581$	−2167.40			−0.154766
$582$	−27274.0	−	4735.76i	−1.94252	−	0.337291i
$583$	−14824.9			−1.05314
$584$	−4309.65			−0.305368
$585$	2807.11	−	7839.59i	0.198392	−	0.554064i
$586$		−	21420.4i		−	1.51002i
$587$	−8620.77			−0.606163			−0.303081	−	0.952965i	$-0.598015\pi$
$587$	−8620.77			−0.606163			−0.303081	+	0.952965i	$0.598015\pi$
$588$	−921.704	+	5308.25i	−0.0646436	+	0.372294i
$589$		−	9731.90i		−	0.680808i
$590$		−	10509.0i		−	0.733306i
$591$	2817.78	−	16228.1i	0.196122	−	1.12950i
$592$	25607.0			1.77778
$593$	10223.6			0.707982			0.353991	−	0.935249i	$-0.384824\pi$
$593$	10223.6			0.707982			0.353991	+	0.935249i	$0.384824\pi$
$594$	−8597.42	+	15164.3i	−0.593866	+	1.04747i
$595$	13445.9			0.926433
$596$			11219.0i			0.771056i
$597$	898.347	−	5173.74i	0.0615861	−	0.354685i
$598$	12839.2			0.877986
$599$	5119.50			0.349210			0.174605	−	0.984639i	$-0.444135\pi$
$599$	5119.50			0.349210			0.174605	+	0.984639i	$0.444135\pi$
$600$	599.724	−	3453.91i	0.0408061	−	0.235009i
$601$	−5833.63			−0.395938			−0.197969	−	0.980208i	$-0.563435\pi$
$601$	−5833.63			−0.395938			−0.197969	+	0.980208i	$0.563435\pi$
$602$	11326.4			0.766824
$603$	−14766.2	+	1102.60i	−0.997224	+	0.0744635i
$604$	−12307.3			−0.829100
$605$	309.434			0.0207939
$606$	3040.39	−	17510.1i	0.203808	−	1.17376i
$607$	79.5204			0.00531735			0.00265868	−	0.999996i	$-0.499154\pi$
$607$	79.5204			0.00531735			0.00265868	+	0.999996i	$0.499154\pi$
$608$	−18457.0			−1.23113
$609$	1697.33	−	9775.23i	0.112938	−	0.650430i
$610$		−	14199.4i		−	0.942484i
$611$	−9119.63			−0.603831
$612$	−1257.31	+	3511.36i	−0.0830450	+	0.231925i
$613$	−4413.71			−0.290813			−0.145406	−	0.989372i	$-0.546449\pi$
$613$	−4413.71			−0.290813			−0.145406	+	0.989372i	$0.546449\pi$
$614$	10989.9			0.722336
$615$	−503.156	+	2897.76i	−0.0329906	+	0.189999i
$616$		−	14570.5i		−	0.953023i
$617$			25998.2i			1.69635i	0.529718	+	0.848174i	$0.322298\pi$
$617$			25998.2i			1.69635i	−0.529718	+	0.848174i	$0.677702\pi$
$618$	−3804.31	+	21909.7i	−0.247625	+	1.42611i
$619$	−4157.32			−0.269946			−0.134973	−	0.990849i	$-0.543095\pi$
$619$	−4157.32			−0.269946			−0.134973	+	0.990849i	$0.543095\pi$
$620$			3355.39i			0.217348i
$621$	−19532.3	−	11073.9i	−1.26216	−	0.715587i
$622$	7773.42			0.501103
$623$	28896.5			1.85829
$624$	−9689.12	−	1682.38i	−0.621595	−	0.107931i
$625$	−19166.4			−1.22665
$626$			24860.4i			1.58726i
$627$	4180.78	−	24077.8i	0.266291	−	1.53361i
$628$	−8125.38			−0.516302
$629$			13084.4i			0.829424i
$630$	−10152.8	+	28354.5i	−0.642060	+	1.79312i
$631$			29250.2i			1.84537i	0.385549	+	0.922687i	$0.374012\pi$
$631$			29250.2i			1.84537i	−0.385549	+	0.922687i	$0.625988\pi$
$632$		−	4717.36i		−	0.296909i
$633$	−976.343	+	5622.93i	−0.0613052	+	0.353067i
$634$		−	31557.9i		−	1.97685i
$635$	11542.9			0.721363
$636$	1215.44	−	6999.94i	0.0757790	−	0.436424i
$637$		−	7258.69i		−	0.451491i
$638$		−	9316.74i		−	0.578140i
$639$	−2183.07	+	6096.80i	−0.135150	+	0.377443i
$640$	−21543.2			−1.33058
$641$	105.873			0.00652379			0.00326190	−	0.999995i	$-0.498962\pi$
$641$	105.873			0.00652379			0.00326190	+	0.999995i	$0.498962\pi$
$642$	16862.5	+	2927.94i	1.03662	+	0.179995i
$643$	14084.2			0.863806			0.431903	−	0.901920i	$-0.357842\pi$
$643$	14084.2			0.863806			0.431903	+	0.901920i	$0.357842\pi$
$644$	−13834.9			−0.846541
$645$	8754.04	+	1520.02i	0.534403	+	0.0927916i
$646$		−	17550.3i		−	1.06890i
$647$	5252.23			0.319144			0.159572	−	0.987186i	$-0.448989\pi$
$647$	5252.23			0.319144			0.159572	+	0.987186i	$0.448989\pi$
$648$	8756.84	+	7193.36i	0.530866	+	0.436083i
$649$		−	8830.48i		−	0.534094i
$650$		−	3481.68i		−	0.210096i
$651$	−1724.08	+	9929.28i	−0.103797	+	0.597787i
$652$	−685.823			−0.0411946
$653$	5274.71			0.316103			0.158051	−	0.987431i	$-0.449479\pi$
$653$	5274.71			0.316103			0.158051	+	0.987431i	$0.449479\pi$
$654$	17221.1	+	2990.20i	1.02966	+	0.178786i
$655$			20801.2i			1.24087i
$656$	3473.43			0.206730
$657$	7047.10	+	2523.34i	0.418468	+	0.149840i
$658$	32984.1			1.95419
$659$			25936.9i			1.53317i	0.642142	+	0.766585i	$0.278046\pi$
$659$			25936.9i			1.53317i	−0.642142	+	0.766585i	$0.721954\pi$
$660$	−1441.46	+	8301.63i	−0.0850134	+	0.489607i
$661$			685.663i			0.0403468i	0.999796	+	0.0201734i	$0.00642182\pi$
$661$			685.663i			0.0403468i	−0.999796	+	0.0201734i	$0.993578\pi$
$662$		−	15851.0i		−	0.930614i
$663$	859.642	−	4950.83i	0.0503555	−	0.290006i
$664$			1323.15i			0.0773319i
$665$		−	42222.1i		−	2.46211i
$666$	−27592.1	−	9879.83i	−1.60536	−	0.574828i
$667$	12000.4			0.696638
$668$		−	13422.9i		−	0.777465i
$669$	2885.15	−	16616.1i	0.166736	−	0.960260i
$670$	−21951.4	+	9760.19i	−1.26576	+	0.562790i
$671$		−	11931.4i		−	0.686446i
$672$	18831.3	+	3269.80i	1.08100	+	0.187701i
$673$			2028.50i			0.116185i	0.998311	+	0.0580927i	$0.0185019\pi$
$673$			2028.50i			0.116185i	−0.998311	+	0.0580927i	$0.981498\pi$
$674$			7018.86i			0.401122i
$675$	−3002.96	+	5296.66i	−0.171235	+	0.302027i
$676$	5540.96			0.315257
$677$	15069.5			0.855493			0.427746	−	0.903899i	$-0.359308\pi$
$677$	15069.5			0.855493			0.427746	+	0.903899i	$0.359308\pi$
$678$	3062.12	−	17635.3i	0.173451	−	0.998936i
$679$	−40187.7			−2.27138
$680$		−	8208.43i		−	0.462910i
$681$	−3341.73	−	580.245i	−0.188040	−	0.0326505i
$682$			9463.57i			0.531347i
$683$	6490.61			0.363626			0.181813	−	0.983333i	$-0.441804\pi$
$683$	6490.61			0.363626			0.181813	+	0.983333i	$0.441804\pi$
$684$	11026.2	+	3948.13i	0.616371	+	0.220703i
$685$	10819.3			0.603481
$686$		−	3229.95i		−	0.179767i
$687$	−16875.3	−	2930.16i	−0.937167	−	0.162726i
$688$		−	10493.1i		−	0.581462i
$689$			9571.97i			0.529264i
$690$	−35891.0	−	6231.97i	−1.98021	−	0.343836i
$691$	26586.9			1.46369			0.731847	−	0.681469i	$-0.238658\pi$
$691$	26586.9			1.46369			0.731847	+	0.681469i	$0.238658\pi$
$692$		−	12474.1i		−	0.685251i
$693$	−8531.15	+	23825.5i	−0.467636	+	1.30600i
$694$	34285.0			1.87528
$695$			39401.9i			2.15050i
$696$	−5967.57	−	1036.19i	−0.325000	−	0.0564318i
$697$			1774.81i			0.0964501i
$698$	−6834.04			−0.370590
$699$	−2363.29	+	13610.6i	−0.127879	+	0.736479i
$700$			3751.68i			0.202572i
$701$	28289.6			1.52423			0.762114	−	0.647443i	$-0.224161\pi$
$701$	28289.6			1.52423			0.762114	+	0.647443i	$0.224161\pi$
$702$	9791.11	+	5551.10i	0.526413	+	0.298451i
$703$	41086.9			2.20430
$704$	−5501.32			−0.294516
$705$	25493.1	+	4426.53i	1.36188	+	0.236472i
$706$	−32394.2			−1.72687
$707$		−	25800.8i		−	1.37247i
$708$	4169.54	+	723.983i	0.221329	+	0.0384307i
$709$	13973.4			0.740172			0.370086	−	0.928998i	$-0.379328\pi$
$709$	13973.4			0.740172			0.370086	+	0.928998i	$0.379328\pi$
$710$			10506.5i			0.555354i
$711$	−2762.06	+	7713.78i	−0.145689	+	0.406877i
$712$		−	17640.7i		−	0.928530i
$713$	−12189.5			−0.640254
$714$	−3109.18	+	17906.3i	−0.162966	+	0.938551i
$715$		−	11351.9i		−	0.593760i
$716$	5925.52			0.309284
$717$	617.518	−	3556.39i	0.0321641	−	0.185238i
$718$			17859.0i			0.928260i
$719$			1439.96i			0.0746893i	0.999302	+	0.0373447i	$0.0118899\pi$
$719$			1439.96i			0.0746893i	−0.999302	+	0.0373447i	$0.988110\pi$
$720$	26268.5	+	9405.90i	1.35968	+	0.486857i
$721$			32283.5i			1.66755i
$722$	−31957.3			−1.64727
$723$	5591.18	−	32200.5i	0.287604	−	1.65636i
$724$	−15096.1			−0.774919
$725$		−	3254.21i		−	0.166701i
$726$	−71.5524	+	412.082i	−0.00365779	+	0.0210659i
$727$			22541.9i			1.14998i	0.818161	+	0.574989i	$0.194994\pi$
$727$			22541.9i			1.14998i	−0.818161	+	0.574989i	$0.805006\pi$
$728$	−9407.74			−0.478948
$729$	−10107.3	−	16889.7i	−0.513505	−	0.858087i
$730$	12144.1			0.615717
$731$	5361.64			0.271282
$732$	5633.70	+	978.214i	0.284464	+	0.0493932i
$733$			6321.54i			0.318542i	0.987235	+	0.159271i	$0.0509144\pi$
$733$			6321.54i			0.318542i	−0.987235	+	0.159271i	$0.949086\pi$
$734$			16192.2i			0.814257i
$735$	−3523.26	+	20291.0i	−0.176813	+	1.01829i
$736$			23118.0i			1.15780i
$737$	−18445.2	+	8201.24i	−0.921898	+	0.409900i
$738$	−3742.69	−	1340.14i	−0.186681	−	0.0668443i
$739$			34435.5i			1.71411i	0.515223	+	0.857056i	$0.327709\pi$
$739$			34435.5i			1.71411i	−0.515223	+	0.857056i	$0.672291\pi$
$740$	−14166.1			−0.703722
$741$	−15546.3	−	2699.41i	−0.770728	−	0.133826i
$742$		−	34620.2i		−	1.71287i
$743$			2422.86i			0.119631i	0.998209	+	0.0598157i	$0.0190513\pi$
$743$			2422.86i			0.119631i	−0.998209	+	0.0598157i	$0.980949\pi$
$744$	6061.62	+	1052.52i	0.298696	+	0.0518644i
$745$			42885.3i			2.10899i
$746$			12489.7i			0.612978i
$747$	774.718	−	2163.61i	0.0379457	−	0.105974i
$748$			5084.54i			0.248542i
$749$	24846.5			1.21211
$750$	3177.54	−	18300.0i	0.154703	−	0.890962i
$751$	18344.6			0.891350			0.445675	−	0.895195i	$-0.352964\pi$
$751$	18344.6			0.891350			0.445675	+	0.895195i	$0.352964\pi$
$752$		−	30557.6i		−	1.48181i
$753$	560.776	−	3229.61i	0.0271392	−	0.156299i
$754$	−6015.54			−0.290548
$755$	−47045.2			−2.26775
$756$	−10550.4	−	5981.58i	−0.507559	−	0.287762i
$757$			31835.1i			1.52849i	0.644925	+	0.764246i	$0.276888\pi$
$757$			31835.1i			1.52849i	−0.644925	+	0.764246i	$0.723112\pi$
$758$		−	3926.58i		−	0.188153i
$759$	−30158.3	−	5236.57i	−1.44226	−	0.250429i
$760$	−25775.7			−1.23024
$761$		−	9027.44i		−	0.430019i	−0.976612	−	0.215009i	$-0.931022\pi$
$761$		−	9027.44i		−	0.430019i	0.976612	−	0.215009i	$-0.0689782\pi$
$762$	−2669.13	+	15372.0i	−0.126893	+	0.730798i
$763$	25374.9			1.20398
$764$	15716.1			0.744227
$765$	−4806.11	+	13422.3i	−0.227144	+	0.634361i
$766$	−29696.6			−1.40076
$767$	−5701.58			−0.268412
$768$	3918.68	−	22568.4i	0.184119	−	1.06037i
$769$		−	2526.85i		−	0.118492i	−0.998243	−	0.0592462i	$-0.981130\pi$
$769$		−	2526.85i		−	0.118492i	0.998243	−	0.0592462i	$-0.0188697\pi$
$770$			41058.0i			1.92159i
$771$	−2220.10	−	385.489i	−0.103703	−	0.0180065i
$772$	−783.429			−0.0365236
$773$			18344.1i			0.853544i	0.904359	+	0.426772i	$0.140349\pi$
$773$			18344.1i			0.853544i	−0.904359	+	0.426772i	$0.859651\pi$
$774$	−4048.50	+	11306.5i	−0.188011	+	0.525070i
$775$			3305.49i			0.153209i
$776$			24533.8i			1.13494i
$777$	−41920.2	−	7278.86i	−1.93549	−	0.336072i
$778$			4478.69i			0.206387i
$779$	5573.18			0.256328
$780$	5360.11	+	930.709i	0.246055	+	0.0427240i
$781$			8828.33i			0.404485i
$782$	−21982.4			−1.00523
$783$	9151.41	+	5188.42i	0.417682	+	0.236806i
$784$	24322.0			1.10796
$785$	−31059.6			−1.41219
$786$	−27701.6	−	4809.99i	−1.25710	−	0.218278i
$787$		−	3805.97i		−	0.172386i	−0.996278	−	0.0861932i	$-0.972530\pi$
$787$		−	3805.97i		−	0.172386i	0.996278	−	0.0861932i	$-0.0274702\pi$
$788$	10761.0			0.486479
$789$	−6217.78	−	1079.63i	−0.280556	−	0.0487146i
$790$			13293.0i			0.598662i
$791$		−	25985.2i		−	1.16805i
$792$	14545.0	+	5208.09i	0.652568	+	0.233663i
$793$	−7703.73			−0.344978
$794$	−2614.74			−0.116869
$795$	4646.09	−	26757.6i	0.207270	−	1.19370i
$796$	3430.75			0.152764
$797$			38234.5i			1.69929i	0.527354	+	0.849646i	$0.323184\pi$
$797$			38234.5i			1.69929i	−0.527354	+	0.849646i	$0.676816\pi$
$798$	56228.4	+	9763.29i	2.49432	+	0.433103i
$799$	15613.9			0.691340
$800$	6269.01			0.277054
$801$	−10328.8	+	28845.9i	−0.455617	+	1.27243i
$802$	37483.9			1.65038
$803$	10204.4			0.448449
$804$	−2360.16	−	9381.79i	−0.103528	−	0.411530i
$805$	−52884.6			−2.31545
$806$	6110.35			0.267032
$807$	−29567.8	−	5134.04i	−1.28976	−	0.223949i
$808$	−15750.9			−0.685784
$809$	−33068.0			−1.43710			−0.718548	−	0.695478i	$-0.755193\pi$
$809$	−33068.0			−1.43710			−0.718548	+	0.695478i	$0.755193\pi$
$810$	−24675.8	−	20270.1i	−1.07039	−	0.879281i
$811$			9056.94i			0.392148i	0.980589	+	0.196074i	$0.0628193\pi$
$811$			9056.94i			0.392148i	−0.980589	+	0.196074i	$0.937181\pi$
$812$	6482.04			0.280142
$813$	37471.1	+	6506.33i	1.61644	+	0.280673i
$814$	−39954.0			−1.72038
$815$	−2621.59			−0.112675
$816$	16589.0	+	2880.44i	0.711679	+	0.123573i
$817$		−	16836.4i		−	0.720966i
$818$		−	17931.6i		−	0.766457i
$819$	15383.4	+	5508.31i	0.656338	+	0.235013i
$820$	−1921.53			−0.0818328
$821$			30840.3i			1.31100i	0.755194	+	0.655501i	$0.227543\pi$
$821$			30840.3i			1.31100i	−0.755194	+	0.655501i	$0.772457\pi$
$822$	−2501.81	+	14408.4i	−0.106157	+	0.611374i
$823$	−24984.1			−1.05819			−0.529096	−	0.848562i	$-0.677469\pi$
$823$	−24984.1			−1.05819			−0.529096	+	0.848562i	$0.677469\pi$
$824$	19708.4			0.833221
$825$	−1420.03	+	8178.17i	−0.0599260	+	0.345124i
$826$	20621.6			0.868666
$827$			6105.03i			0.256702i	0.991729	+	0.128351i	$0.0409684\pi$
$827$			6105.03i			0.256702i	−0.991729	+	0.128351i	$0.959032\pi$
$828$	4945.16	−	13810.7i	0.207556	−	0.579655i
$829$	3743.91			0.156853			0.0784267	−	0.996920i	$-0.475010\pi$
$829$	3743.91			0.156853			0.0784267	+	0.996920i	$0.475010\pi$
$830$		−	3728.50i		−	0.155925i
$831$	−4460.41	+	25688.3i	−0.186197	+	1.07234i
$832$			3552.04i			0.148011i
$833$			12427.8i			0.516923i
$834$	−52472.6	−	9111.14i	−2.17863	−	0.378289i
$835$		−	51309.5i		−	2.12651i
$836$	15966.2			0.660531
$837$	−9295.64	−	5270.19i	−0.383876	−	0.217640i
$838$		−	10218.1i		−	0.421213i
$839$		−	18925.5i		−	0.778762i	−0.921077	−	0.389381i	$-0.872689\pi$
$839$		−	18925.5i		−	0.778762i	0.921077	−	0.389381i	$-0.127311\pi$
$840$	26298.5	+	4566.37i	1.08022	+	0.187565i
$841$	18766.5			0.769465
$842$	14612.9			0.598091
$843$	2399.95	−	13821.7i	0.0980530	−	0.564704i
$844$	−3728.62			−0.152067
$845$	21180.6			0.862288
$846$	−11789.9	+	32926.4i	−0.479130	+	1.33810i
$847$			607.195i			0.0246322i
$848$	−32073.3			−1.29882
$849$	−5031.99	+	28980.1i	−0.203413	+	1.17149i
$850$			5961.06i			0.240544i
$851$		−	51462.7i		−	2.07299i
$852$	−4168.53	−	723.806i	−0.167619	−	0.0291047i
$853$	1548.09			0.0621400			0.0310700	−	0.999517i	$-0.490109\pi$
$853$	1548.09			0.0621400			0.0310700	+	0.999517i	$0.490109\pi$
$854$	27863.1			1.11646
$855$	42148.2	+	15091.9i	1.68589	+	0.603664i
$856$		−	15168.3i		−	0.605656i
$857$	30142.9			1.20147			0.600735	−	0.799448i	$-0.294875\pi$
$857$	30142.9			1.20147			0.600735	+	0.799448i	$0.294875\pi$
$858$	15117.7	+	2624.98i	0.601527	+	0.104447i
$859$	−26167.6			−1.03938			−0.519690	−	0.854355i	$-0.673953\pi$
$859$	−26167.6			−1.03938			−0.519690	+	0.854355i	$0.673953\pi$
$860$			5804.89i			0.230169i
$861$	−5686.21	−	987.331i	−0.225070	−	0.0390803i
$862$		−	24455.0i		−	0.966287i
$863$		−	43297.8i		−	1.70785i	−0.520397	−	0.853924i	$-0.674216\pi$
$863$		−	43297.8i		−	1.70785i	0.520397	−	0.853924i	$-0.325784\pi$
$864$	−9995.15	+	17629.6i	−0.393567	+	0.694179i
$865$		−	47682.8i		−	1.87429i
$866$		−	40267.7i		−	1.58008i
$867$	2895.54	−	16675.9i	0.113423	−	0.653223i
$868$	−6584.20			−0.257468
$869$			11169.8i			0.436028i
$870$	16815.9	+	2919.85i	0.655303	+	0.113784i
$871$	5295.30	+	11909.5i	0.205998	+	0.463306i
$872$		−	15490.9i		−	0.601591i
$873$	14364.7	−	40117.4i	0.556899	−	1.55529i
$874$			69028.0i			2.67152i
$875$		−	26964.7i		−	1.04180i
$876$	−836.624	+	4818.26i	−0.0322682	+	0.185838i
$877$	22876.4			0.880823			0.440412	−	0.897796i	$-0.354833\pi$
$877$	22876.4			0.880823			0.440412	+	0.897796i	$0.354833\pi$
$878$	37803.8			1.45309
$879$	32486.7	+	5640.87i	1.24659	+	0.216453i
$880$	38037.5			1.45709
$881$		−	41764.1i		−	1.59712i	−0.601912	−	0.798562i	$-0.705594\pi$
$881$		−	41764.1i		−	1.59712i	0.601912	−	0.798562i	$-0.294406\pi$
$882$	−26207.5	−	9384.05i	−1.00051	−	0.358251i
$883$			13722.4i			0.522983i	0.965206	+	0.261492i	$0.0842144\pi$
$883$			13722.4i			0.522983i	−0.965206	+	0.261492i	$0.915786\pi$
$884$	3282.94			0.124906
$885$	15938.3	+	2767.46i	0.605378	+	0.105115i
$886$	42904.1			1.62685
$887$			38575.2i			1.46023i	0.683323	+	0.730117i	$0.260534\pi$
$887$			38575.2i			1.46023i	−0.683323	+	0.730117i	$0.739466\pi$
$888$	−4443.59	+	25591.4i	−0.167925	+	0.967107i
$889$			22650.3i			0.854518i
$890$			49709.5i			1.87221i
$891$	−20734.4	−	17032.4i	−0.779607	−	0.640413i
$892$	11018.3			0.413586
$893$		−	49030.1i		−	1.83732i
$894$	−57111.6	−	9916.63i	−2.13657	−	0.370986i
$895$	22650.6			0.845950
$896$		−	42273.7i		−	1.57619i
$897$	−3381.10	+	19472.3i	−0.125854	+	0.724818i
$898$			34017.0i			1.26410i
$899$	5711.13			0.211876
$900$	−3745.11	−	1341.00i	−0.138708	−	0.0496668i
$901$		−	16388.4i		−	0.605967i
$902$	−5419.51			−0.200055
$903$	−2982.69	+	17177.8i	−0.109920	+	0.633048i
$904$	−15863.4			−0.583639
$905$	−57705.5			−2.11955
$906$	10878.5	−	62651.4i	0.398913	−	2.29741i
$907$	−14486.0			−0.530319			−0.265160	−	0.964205i	$-0.585425\pi$
$907$	−14486.0			−0.530319			−0.265160	+	0.964205i	$0.585425\pi$
$908$		−	2215.93i		−	0.0809893i
$909$	25755.6	+	9222.26i	0.939781	+	0.336505i
$910$	26509.9			0.965709
$911$			15051.5i			0.547395i	0.961816	+	0.273698i	$0.0882468\pi$
$911$			15051.5i			0.547395i	−0.961816	+	0.273698i	$0.911753\pi$
$912$	9045.03	−	52091.9i	0.328411	−	1.89138i
$913$		−	3132.96i		−	0.113566i
$914$	−44390.4			−1.60646
$915$	21535.1	+	3739.27i	0.778064	+	0.135100i
$916$		−	11190.2i		−	0.403640i
$917$	−40817.7			−1.46992
$918$	−16763.6	−	9504.16i	−0.602702	−	0.341704i
$919$		−	10792.8i		−	0.387401i	−0.981061	−	0.193701i	$-0.937951\pi$
$919$		−	10792.8i		−	0.387401i	0.981061	−	0.193701i	$-0.0620490\pi$
$920$			32285.0i			1.15696i
$921$	−2894.08	+	16667.5i	−0.103543	+	0.596322i
$922$		−	41875.8i		−	1.49578i
$923$	5700.19			0.203276
$924$	−16290.1	−	2828.54i	−0.579983	−	0.100706i
$925$	−13955.4			−0.496054
$926$		−	41358.4i		−	1.46773i
$927$	−32227.0	−	11539.4i	−1.14183	−	0.408851i
$928$		−	10831.4i		−	0.383145i
$929$	−35909.9			−1.26821			−0.634105	−	0.773247i	$-0.718631\pi$
$929$	−35909.9			−1.26821			−0.634105	+	0.773247i	$0.718631\pi$
$930$	−17080.9	−	2965.87i	−0.602265	−	0.104575i
$931$	39025.1			1.37379
$932$	−9025.30			−0.317203
$933$	−2047.06	+	11789.4i	−0.0718303	+	0.413683i
$934$		−	29231.4i		−	1.02407i
$935$			19435.9i			0.679810i
$936$	3362.71	−	9391.26i	0.117429	−	0.327952i
$937$		−	18838.8i		−	0.656816i	−0.944536	−	0.328408i	$-0.893488\pi$
$937$		−	18838.8i		−	0.656816i	0.944536	−	0.328408i	$-0.106512\pi$
$938$	−19152.2	−	43074.7i	−0.666674	−	1.49940i
$939$	−37704.0	−	6546.77i	−1.31035	−	0.227525i
$940$			16904.7i			0.586566i
$941$	53891.8			1.86697			0.933487	−	0.358611i	$-0.116749\pi$
$941$	53891.8			1.86697			0.933487	+	0.358611i	$0.116749\pi$
$942$	7182.11	−	41363.0i	0.248414	−	1.43066i
$943$		−	6980.59i		−	0.241060i
$944$		−	19104.6i		−	0.658687i
$945$	−40329.4	−	22864.9i	−1.38827	−	0.787084i
$946$			16372.1i			0.562690i
$947$			2477.15i			0.0850017i	0.999096	+	0.0425009i	$0.0135325\pi$
$947$			2477.15i			0.0850017i	−0.999096	+	0.0425009i	$0.986467\pi$
$948$	−5274.09	−	915.772i	−0.180690	−	0.0313744i
$949$		−	6588.67i		−	0.225371i
$950$	18718.6			0.639277
$951$	47861.4	+	8310.47i	1.63198	+	0.283371i
$952$	16107.2			0.548359
$953$			57162.1i			1.94298i	0.237078	+	0.971491i	$0.423810\pi$
$953$			57162.1i			1.94298i	−0.237078	+	0.971491i	$0.576190\pi$
$954$	34559.5	+	12374.7i	1.17286	+	0.419963i
$955$	60075.6			2.03560
$956$	2358.28			0.0797825
$957$	14130.0	+	2453.48i	0.477281	+	0.0828732i
$958$			44437.4i			1.49865i
$959$			21230.4i			0.714876i
$960$	1724.11	−	9929.42i	0.0579638	−	0.333824i
$961$	23989.9			0.805272
$962$			25797.1i			0.864587i
$963$	−8881.17	+	24803.0i	−0.297188	+	0.829976i
$964$	21352.5			0.713400
$965$	−2994.69			−0.0998990
$966$	12228.8	−	70428.0i	0.407305	−	2.34574i
$967$	−22084.0			−0.734410			−0.367205	−	0.930140i	$-0.619685\pi$
$967$	−22084.0			−0.734410			−0.367205	+	0.930140i	$0.619685\pi$
$968$	370.680			0.0123079
$969$	26617.2	+	4621.71i	0.882424	+	0.153221i
$970$		−	69133.3i		−	2.28839i
$971$		−	14976.2i		−	0.494962i	−0.968893	−	0.247481i	$-0.920397\pi$
$971$		−	14976.2i		−	0.494962i	0.968893	−	0.247481i	$-0.0796029\pi$
$972$	9742.25	−	8393.87i	0.321484	−	0.276989i
$973$	−77317.3			−2.54746
$974$			57615.8i			1.89541i
$975$	5280.40	+	916.868i	0.173444	+	0.0301162i
$976$		−	25813.2i		−	0.846580i
$977$			36298.5i			1.18863i	0.804232	+	0.594316i	$0.202577\pi$
$977$			36298.5i			1.18863i	−0.804232	+	0.594316i	$0.797423\pi$
$978$	606.206	−	3491.25i	0.0198204	−	0.114149i
$979$			41769.6i			1.36360i
$980$	−13455.2			−0.438582
$981$	−9070.03	+	25330.5i	−0.295193	+	0.824404i
$982$			12132.9i			0.394272i
$983$	−8448.46			−0.274124			−0.137062	−	0.990562i	$-0.543766\pi$
$983$	−8448.46			−0.274124			−0.137062	+	0.990562i	$0.543766\pi$
$984$	−602.745	+	3471.31i	−0.0195272	+	0.112461i
$985$	41134.5			1.33061
$986$	10299.3			0.332655
$987$	−8686.06	+	50024.5i	−0.280122	+	1.61327i
$988$		−	10308.9i		−	0.331954i
$989$	−21088.1			−0.678020
$990$	−40986.1	−	14675.8i	−1.31578	−	0.471139i
$991$		−	5350.79i		−	0.171517i	−0.996316	−	0.0857586i	$-0.972669\pi$
$991$		−	5350.79i		−	0.171517i	0.996316	−	0.0857586i	$-0.0273314\pi$
$992$			11002.1i			0.352135i
$993$	24040.0	+	4174.21i	0.768264	+	0.133398i
$994$	−20616.6			−0.657866
$995$	13114.2			0.417838
$996$	1479.31	+	256.862i	0.0470620	+	0.00817166i
$997$	22306.2			0.708569			0.354285	−	0.935138i	$-0.384724\pi$
$997$	22306.2			0.708569			0.354285	+	0.935138i	$0.384724\pi$
$998$		−	74419.9i		−	2.36044i
$999$	22250.1	−	39245.0i	0.704667	−	1.24290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.d.b.200.17	✓	64
3.2	odd	2	inner	201.4.d.b.200.47	yes	64
67.66	odd	2	inner	201.4.d.b.200.48	yes	64
201.200	even	2	inner	201.4.d.b.200.18	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.d.b.200.17	✓	64	1.1	even	1	trivial
201.4.d.b.200.18	yes	64	201.200	even	2	inner
201.4.d.b.200.47	yes	64	3.2	odd	2	inner
201.4.d.b.200.48	yes	64	67.66	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)

\(f(q)\)	\(=\)	\(q-3.37562 q^{2} +(0.888938 - 5.11955i) q^{3} +3.39482 q^{4} +12.9769 q^{5} +(-3.00072 + 17.2817i) q^{6} +25.4642i q^{7} +15.5453 q^{8} +(-25.4196 - 9.10193i) q^{9} +O(q^{10})\)	\(q-3.37562 q^{2} +(0.888938 - 5.11955i) q^{3} +3.39482 q^{4} +12.9769 q^{5} +(-3.00072 + 17.2817i) q^{6} +25.4642i q^{7} +15.5453 q^{8} +(-25.4196 - 9.10193i) q^{9} -43.8050 q^{10} -36.8082 q^{11} +(3.01779 - 17.3800i) q^{12} +23.7660i q^{13} -85.9574i q^{14} +(11.5356 - 66.4357i) q^{15} -79.6338 q^{16} -40.6902i q^{17} +(85.8069 + 30.7247i) q^{18} -127.774 q^{19} +44.0541 q^{20} +(130.365 + 22.6361i) q^{21} +124.251 q^{22} +160.041i q^{23} +(13.8189 - 79.5851i) q^{24} +43.3990 q^{25} -80.2249i q^{26} +(-69.1942 + 122.046i) q^{27} +86.4463i q^{28} -74.9835i q^{29} +(-38.9399 + 224.262i) q^{30} +76.1652i q^{31} +144.451 q^{32} +(-32.7202 + 188.442i) q^{33} +137.355i q^{34} +330.445i q^{35} +(-86.2949 - 30.8994i) q^{36} -321.560 q^{37} +431.315 q^{38} +(121.671 + 21.1265i) q^{39} +201.730 q^{40} -43.6176 q^{41} +(-440.063 - 76.4108i) q^{42} +131.767i q^{43} -124.957 q^{44} +(-329.866 - 118.114i) q^{45} -540.237i q^{46} +383.726i q^{47} +(-70.7895 + 407.689i) q^{48} -305.424 q^{49} -146.499 q^{50} +(-208.316 - 36.1711i) q^{51} +80.6812i q^{52} +402.760 q^{53} +(233.573 - 411.980i) q^{54} -477.655 q^{55} +395.849i q^{56} +(-113.583 + 654.143i) q^{57} +253.116i q^{58} +239.905i q^{59} +(39.1614 - 225.537i) q^{60} +324.150i q^{61} -257.105i q^{62} +(231.773 - 647.288i) q^{63} +149.459 q^{64} +308.408i q^{65} +(110.451 - 636.107i) q^{66} +(501.117 - 222.810i) q^{67} -138.136i q^{68} +(819.336 + 142.266i) q^{69} -1115.46i q^{70} -239.847i q^{71} +(-395.156 - 141.493i) q^{72} -277.231 q^{73} +1085.47 q^{74} +(38.5790 - 222.183i) q^{75} -433.768 q^{76} -937.291i q^{77} +(-410.715 - 71.3150i) q^{78} -303.458i q^{79} -1033.40 q^{80} +(563.310 + 462.734i) q^{81} +147.236 q^{82} +85.1158i q^{83} +(442.566 + 76.8454i) q^{84} -528.032i q^{85} -444.796i q^{86} +(-383.882 - 66.6557i) q^{87} -572.196 q^{88} -1134.79i q^{89} +(1113.50 + 398.710i) q^{90} -605.181 q^{91} +543.309i q^{92} +(389.931 + 67.7062i) q^{93} -1295.32i q^{94} -1658.10 q^{95} +(128.408 - 739.523i) q^{96} +1578.21i q^{97} +1031.00 q^{98} +(935.649 + 335.026i) 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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