LMFDB - Embedded newform 201.4.d.b.200.20

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			200.20
Character	$\chi$	$=$	201.200
Dual form			201.4.d.b.200.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.33139 q^{2} +(0.842682 + 5.12737i) q^{3} +3.09813 q^{4} +0.324421 q^{5} +(-2.80730 - 17.0812i) q^{6} +12.9394i q^{7} +16.3300 q^{8} +(-25.5798 + 8.64147i) q^{9} +O(q^{10})$	\(q-3.33139 q^{2} +(0.842682 + 5.12737i) q^{3} +3.09813 q^{4} +0.324421 q^{5} +(-2.80730 - 17.0812i) q^{6} +12.9394i q^{7} +16.3300 q^{8} +(-25.5798 + 8.64147i) q^{9} -1.08077 q^{10} +32.5456 q^{11} +(2.61074 + 15.8853i) q^{12} +60.3820i q^{13} -43.1060i q^{14} +(0.273383 + 1.66342i) q^{15} -79.1866 q^{16} +46.6474i q^{17} +(85.2161 - 28.7881i) q^{18} +119.758 q^{19} +1.00510 q^{20} +(-66.3448 + 10.9038i) q^{21} -108.422 q^{22} +30.7188i q^{23} +(13.7610 + 83.7299i) q^{24} -124.895 q^{25} -201.156i q^{26} +(-65.8636 - 123.875i) q^{27} +40.0878i q^{28} -301.867i q^{29} +(-0.910746 - 5.54151i) q^{30} +202.045i q^{31} +133.161 q^{32} +(27.4256 + 166.873i) q^{33} -155.401i q^{34} +4.19780i q^{35} +(-79.2496 + 26.7724i) q^{36} -336.952 q^{37} -398.959 q^{38} +(-309.600 + 50.8828i) q^{39} +5.29780 q^{40} -391.355 q^{41} +(221.020 - 36.3246i) q^{42} +79.4241i q^{43} +100.831 q^{44} +(-8.29861 + 2.80347i) q^{45} -102.336i q^{46} +405.749i q^{47} +(-66.7291 - 406.019i) q^{48} +175.573 q^{49} +416.073 q^{50} +(-239.178 + 39.3089i) q^{51} +187.071i q^{52} -695.253 q^{53} +(219.417 + 412.675i) q^{54} +10.5585 q^{55} +211.300i q^{56} +(100.917 + 614.041i) q^{57} +1005.64i q^{58} -642.905i q^{59} +(0.846979 + 5.15351i) q^{60} -234.830i q^{61} -673.089i q^{62} +(-111.815 - 330.986i) q^{63} +189.882 q^{64} +19.5892i q^{65} +(-91.3651 - 555.919i) q^{66} +(-164.961 + 523.021i) q^{67} +144.520i q^{68} +(-157.507 + 25.8862i) q^{69} -13.9845i q^{70} +360.554i q^{71} +(-417.718 + 141.115i) q^{72} +821.222 q^{73} +1122.52 q^{74} +(-105.247 - 640.381i) q^{75} +371.025 q^{76} +421.119i q^{77} +(1031.40 - 169.510i) q^{78} -768.991i q^{79} -25.6898 q^{80} +(579.650 - 442.094i) q^{81} +1303.75 q^{82} -877.176i q^{83} +(-205.545 + 33.7813i) q^{84} +15.1334i q^{85} -264.592i q^{86} +(1547.78 - 254.378i) q^{87} +531.470 q^{88} +280.125i q^{89} +(27.6459 - 9.33946i) q^{90} -781.303 q^{91} +95.1710i q^{92} +(-1035.96 + 170.259i) q^{93} -1351.71i q^{94} +38.8518 q^{95} +(112.212 + 682.766i) q^{96} +1203.97i q^{97} -584.902 q^{98} +(-832.509 + 281.242i) 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 $

$2$	−3.33139			−1.17782			−0.588911	−	0.808198i	$-0.700443\pi$
$2$	−3.33139			−1.17782			−0.588911	+	0.808198i	$0.700443\pi$
$3$	0.842682	+	5.12737i	0.162174	+	0.986762i
$3$	0.842682	+	5.12737i	0.162174	+	0.986762i
$4$	3.09813			0.387267
$5$	0.324421			0.0290171			0.0145085	−	0.999895i	$-0.495382\pi$
$5$	0.324421			0.0290171			0.0145085	+	0.999895i	$0.495382\pi$
$6$	−2.80730	−	17.0812i	−0.191012	−	1.16223i
$7$			12.9394i			0.698659i	0.937000	+	0.349330i	$0.113591\pi$
$7$			12.9394i			0.698659i	−0.937000	+	0.349330i	$0.886409\pi$
$8$	16.3300			0.721691
$9$	−25.5798	+	8.64147i	−0.947399	+	0.320055i
$10$	−1.08077			−0.0341770
$11$	32.5456			0.892078			0.446039	−	0.895013i	$-0.352834\pi$
$11$	32.5456			0.892078			0.446039	+	0.895013i	$0.352834\pi$
$12$	2.61074	+	15.8853i	0.0628047	+	0.382140i
$13$			60.3820i			1.28823i	0.764930	+	0.644113i	$0.222773\pi$
$13$			60.3820i			1.28823i	−0.764930	+	0.644113i	$0.777227\pi$
$14$		−	43.1060i		−	0.822897i
$15$	0.273383	+	1.66342i	0.00470582	+	0.0286330i
$16$	−79.1866			−1.23729
$17$			46.6474i			0.665510i	0.943013	+	0.332755i	$0.107978\pi$
$17$			46.6474i			0.665510i	−0.943013	+	0.332755i	$0.892022\pi$
$18$	85.2161	−	28.7881i	1.11587	−	0.376968i
$19$	119.758			1.44601			0.723007	−	0.690841i	$-0.242759\pi$
$19$	119.758			1.44601			0.723007	+	0.690841i	$0.242759\pi$
$20$	1.00510			0.0112374
$21$	−66.3448	+	10.9038i	−0.689411	+	0.113304i
$22$	−108.422			−1.05071
$23$			30.7188i			0.278492i	0.990258	+	0.139246i	$0.0444679\pi$
$23$			30.7188i			0.278492i	−0.990258	+	0.139246i	$0.955532\pi$
$24$	13.7610	+	83.7299i	0.117040	+	0.712138i
$25$	−124.895			−0.999158
$26$		−	201.156i		−	1.51730i
$27$	−65.8636	−	123.875i	−0.469461	−	0.882953i
$28$			40.0878i			0.270567i
$29$		−	301.867i		−	1.93294i	−0.256776	−	0.966471i	$-0.582660\pi$
$29$		−	301.867i		−	1.93294i	0.256776	−	0.966471i	$-0.417340\pi$
$30$	−0.910746	−	5.54151i	−0.00554262	−	0.0337246i
$31$			202.045i			1.17059i	0.810820	+	0.585295i	$0.199021\pi$
$31$			202.045i			1.17059i	−0.810820	+	0.585295i	$0.800979\pi$
$32$	133.161			0.735619
$33$	27.4256	+	166.873i	0.144672	+	0.880269i
$34$		−	155.401i		−	0.783852i
$35$			4.19780i			0.0202731i
$36$	−79.2496	+	26.7724i	−0.366896	+	0.123947i
$37$	−336.952			−1.49715			−0.748574	−	0.663051i	$-0.769261\pi$
$37$	−336.952			−1.49715			−0.748574	+	0.663051i	$0.769261\pi$
$38$	−398.959			−1.70315
$39$	−309.600	+	50.8828i	−1.27117	+	0.208917i
$40$	5.29780			0.0209414
$41$	−391.355			−1.49072			−0.745358	−	0.666664i	$-0.767722\pi$
$41$	−391.355			−1.49072			−0.745358	+	0.666664i	$0.767722\pi$
$42$	221.020	−	36.3246i	0.812003	−	0.133453i
$43$			79.4241i			0.281676i	0.990033	+	0.140838i	$0.0449797\pi$
$43$			79.4241i			0.281676i	−0.990033	+	0.140838i	$0.955020\pi$
$44$	100.831			0.345472
$45$	−8.29861	+	2.80347i	−0.0274908	+	0.00928705i
$46$		−	102.336i		−	0.328014i
$47$			405.749i			1.25925i	0.776900	+	0.629623i	$0.216791\pi$
$47$			405.749i			1.25925i	−0.776900	+	0.629623i	$0.783209\pi$
$48$	−66.7291	−	406.019i	−0.200657	−	1.22091i
$49$	175.573			0.511875
$50$	416.073			1.17683
$51$	−239.178	+	39.3089i	−0.656700	+	0.107928i
$52$			187.071i			0.498887i
$53$	−695.253			−1.80189			−0.900947	−	0.433930i	$-0.857127\pi$
$53$	−695.253			−1.80189			−0.900947	+	0.433930i	$0.857127\pi$
$54$	219.417	+	412.675i	0.552942	+	1.03996i
$55$	10.5585			0.0258855
$56$			211.300i			0.504216i
$57$	100.917	+	614.041i	0.234506	+	1.42687i
$58$			1005.64i			2.27666i
$59$		−	642.905i		−	1.41863i	−0.704892	−	0.709315i	$-0.749004\pi$
$59$		−	642.905i		−	1.41863i	0.704892	−	0.709315i	$-0.250996\pi$
$60$	0.846979	+	5.15351i	0.00182241	+	0.0110886i
$61$		−	234.830i		−	0.492901i	−0.969155	−	0.246450i	$-0.920736\pi$
$61$		−	234.830i		−	0.492901i	0.969155	−	0.246450i	$-0.0792643\pi$
$62$		−	673.089i		−	1.37875i
$63$	−111.815	−	330.986i	−0.223609	−	0.661909i
$64$	189.882			0.370863
$65$			19.5892i			0.0373806i
$66$	−91.3651	−	555.919i	−0.170398	−	1.03680i
$67$	−164.961	+	523.021i	−0.300793	+	0.953689i
$67$	−164.961	+	523.021i	−0.300793	+	0.953689i
$68$			144.520i			0.257730i
$69$	−157.507	+	25.8862i	−0.274805	+	0.0451642i
$70$		−	13.9845i		−	0.0238781i
$71$			360.554i			0.602674i	0.953518	+	0.301337i	$0.0974329\pi$
$71$			360.554i			0.602674i	−0.953518	+	0.301337i	$0.902567\pi$
$72$	−417.718	+	141.115i	−0.683730	+	0.230981i
$73$	821.222			1.31667			0.658334	−	0.752726i	$-0.271261\pi$
$73$	821.222			1.31667			0.658334	+	0.752726i	$0.271261\pi$
$74$	1122.52			1.76338
$75$	−105.247	−	640.381i	−0.162038	−	0.985931i
$76$	371.025			0.559993
$77$			421.119i			0.623259i
$78$	1031.40	−	169.510i	1.49722	−	0.246067i
$79$		−	768.991i		−	1.09517i	−0.836751	−	0.547584i	$-0.815548\pi$
$79$		−	768.991i		−	1.09517i	0.836751	−	0.547584i	$-0.184452\pi$
$80$	−25.6898			−0.0359026
$81$	579.650	−	442.094i	0.795130	−	0.606439i
$82$	1303.75			1.75580
$83$		−	877.176i		−	1.16003i	−0.814606	−	0.580015i	$-0.803047\pi$
$83$		−	877.176i		−	1.16003i	0.814606	−	0.580015i	$-0.196953\pi$
$84$	−205.545	+	33.7813i	−0.266986	+	0.0438791i
$85$			15.1334i			0.0193111i
$86$		−	264.592i		−	0.331764i
$87$	1547.78	−	254.378i	1.90735	−	0.313473i
$88$	531.470			0.643805
$89$			280.125i			0.333632i	0.985988	+	0.166816i	$0.0533485\pi$
$89$			280.125i			0.333632i	−0.985988	+	0.166816i	$0.946651\pi$
$90$	27.6459	−	9.33946i	0.0323792	−	0.0109385i
$91$	−781.303			−0.900031
$92$			95.1710i			0.107851i
$93$	−1035.96	+	170.259i	−1.15509	+	0.189840i
$94$		−	1351.71i		−	1.48317i
$95$	38.8518			0.0419591
$96$	112.212	+	682.766i	0.119298	+	0.725881i
$97$			1203.97i			1.26025i	0.776494	+	0.630125i	$0.216996\pi$
$97$			1203.97i			1.26025i	−0.776494	+	0.630125i	$0.783004\pi$
$98$	−584.902			−0.602898
$99$	−832.509	+	281.242i	−0.845154	+	0.285514i
$100$	−386.941			−0.386941
$101$	1682.66			1.65774			0.828868	−	0.559444i	$-0.188985\pi$
$101$	1682.66			1.65774			0.828868	+	0.559444i	$0.188985\pi$
$102$	796.796	−	130.953i	0.773476	−	0.127121i
$103$	−764.574			−0.731415			−0.365707	−	0.930730i	$-0.619173\pi$
$103$	−764.574			−0.731415			−0.365707	+	0.930730i	$0.619173\pi$
$104$			986.038i			0.929702i
$105$	−21.5236	+	3.53741i	−0.0200047	+	0.00328777i
$106$	2316.16			2.12231
$107$			1182.93i			1.06877i	0.845241	+	0.534385i	$0.179457\pi$
$107$			1182.93i			1.06877i	−0.845241	+	0.534385i	$0.820543\pi$
$108$	−204.054	−	383.781i	−0.181807	−	0.341938i
$109$			1406.50i			1.23595i	0.786198	+	0.617975i	$0.212047\pi$
$109$			1406.50i			1.23595i	−0.786198	+	0.617975i	$0.787953\pi$
$110$	−35.1743			−0.0304885
$111$	−283.943	−	1727.67i	−0.242799	−	1.47733i
$112$		−	1024.62i		−	0.864445i
$113$	976.309			0.812773			0.406387	−	0.913701i	$-0.366789\pi$
$113$	976.309			0.812773			0.406387	+	0.913701i	$0.366789\pi$
$114$	−336.195	−	2045.61i	−0.276207	−	1.68060i
$115$			9.96582i			0.00808102i
$116$		−	935.225i		−	0.748564i
$117$	−521.789	−	1544.56i	−0.412303	−	1.22046i
$118$			2141.77i			1.67089i
$119$	−603.587			−0.464964
$120$	4.46435	+	27.1637i	0.00339615	+	0.0206642i
$121$	−271.785			−0.204196
$122$			782.311i			0.580550i
$123$	−329.788	−	2006.62i	−0.241756	−	1.47098i
$124$			625.962i			0.453331i
$125$	−81.0711			−0.0580097
$126$	372.499	+	1102.64i	0.263372	+	0.779612i
$127$	151.881			0.106120			0.0530601	−	0.998591i	$-0.483103\pi$
$127$	151.881			0.106120			0.0530601	+	0.998591i	$0.483103\pi$
$128$	−1697.86			−1.17243
$129$	−407.237	+	66.9292i	−0.277947	+	0.0456806i
$130$		−	65.2591i		−	0.0440277i
$131$			885.794i			0.590780i	0.955377	+	0.295390i	$0.0954496\pi$
$131$			885.794i			0.590780i	−0.955377	+	0.295390i	$0.904550\pi$
$132$	84.9681	+	516.995i	0.0560267	+	0.340899i
$133$			1549.58i			1.01027i
$134$	549.548	−	1742.38i	0.354281	−	1.12328i
$135$	−21.3675	−	40.1876i	−0.0136224	−	0.0256207i
$136$			761.753i			0.480292i
$137$	−672.803			−0.419573			−0.209786	−	0.977747i	$-0.567277\pi$
$137$	−672.803			−0.419573			−0.209786	+	0.977747i	$0.567277\pi$
$138$	524.715	−	86.2368i	0.323672	−	0.0531954i
$139$		−	391.936i		−	0.239163i	−0.992824	−	0.119581i	$-0.961845\pi$
$139$		−	391.936i		−	0.239163i	0.992824	−	0.119581i	$-0.0381552\pi$
$140$			13.0053i			0.00785108i
$141$	−2080.42	+	341.917i	−1.24258	+	0.204217i
$142$		−	1201.14i		−	0.709843i
$143$			1965.17i			1.14920i
$144$	2025.58	−	684.289i	1.17221	−	0.396001i
$145$		−	97.9320i		−	0.0560883i
$146$	−2735.81			−1.55080
$147$	147.952	+	900.228i	0.0830129	+	0.505099i
$148$	−1043.92			−0.579796
$149$			1767.74i			0.971940i	0.873976	+	0.485970i	$0.161534\pi$
$149$			1767.74i			0.971940i	−0.873976	+	0.485970i	$0.838466\pi$
$150$	350.617	+	2133.36i	0.190852	+	1.16125i
$151$	−1541.44			−0.830733			−0.415367	−	0.909654i	$-0.636347\pi$
$151$	−1541.44			−0.830733			−0.415367	+	0.909654i	$0.636347\pi$
$152$	1955.64			1.04358
$153$	−403.103	−	1193.23i	−0.212999	−	0.630503i
$154$		−	1402.91i		−	0.734088i
$155$			65.5476i			0.0339671i
$156$	−959.184	+	157.642i	−0.492283	+	0.0809066i
$157$	640.262			0.325468			0.162734	−	0.986670i	$-0.447969\pi$
$157$	640.262			0.325468			0.162734	+	0.986670i	$0.447969\pi$
$158$			2561.80i			1.28991i
$159$	−585.877	−	3564.82i	−0.292221	−	1.77804i
$160$	43.2003			0.0213455
$161$	−397.481			−0.194571
$162$	−1931.04	+	1472.79i	−0.936522	+	0.714278i
$163$	−2203.53			−1.05886			−0.529430	−	0.848354i	$-0.677594\pi$
$163$	−2203.53			−1.05886			−0.529430	+	0.848354i	$0.677594\pi$
$164$	−1212.47			−0.577305
$165$	8.89742	+	54.1371i	0.00419796	+	0.0255428i
$166$			2922.21i			1.36631i
$167$		−	105.943i		−	0.0490904i	−0.999699	−	0.0245452i	$-0.992186\pi$
$167$		−	105.943i		−	0.0490904i	0.999699	−	0.0245452i	$-0.00781376\pi$
$168$	−1083.41	+	178.058i	−0.497542	+	0.0817708i
$169$	−1448.98			−0.659527
$170$		−	50.4152i		−	0.0227451i
$171$	−3063.37	+	1034.88i	−1.36995	+	0.462803i
$172$			246.067i			0.109084i
$173$		−	2591.44i		−	1.13887i	−0.822038	−	0.569433i	$-0.807163\pi$
$173$		−	2591.44i		−	1.13887i	0.822038	−	0.569433i	$-0.192837\pi$
$174$	−5156.26	+	847.431i	−2.24653	+	0.369216i
$175$		−	1616.06i		−	0.698071i
$176$	−2577.18			−1.10376
$177$	3296.41	−	541.765i	1.39985	−	0.230065i
$178$		−	933.206i		−	0.392959i
$179$	2667.94			1.11403			0.557015	−	0.830502i	$-0.311947\pi$
$179$	2667.94			1.11403			0.557015	+	0.830502i	$0.311947\pi$
$180$	−25.7102	+	8.68554i	−0.0106463	+	0.00359657i
$181$	347.984			0.142903			0.0714515	−	0.997444i	$-0.477237\pi$
$181$	347.984			0.142903			0.0714515	+	0.997444i	$0.477237\pi$
$182$	2602.82			1.06008
$183$	1204.06	−	197.887i	0.486376	−	0.0799358i
$184$			501.638i			0.200985i
$185$	−109.314			−0.0434429
$186$	3451.18	−	567.200i	1.36050	−	0.223597i
$187$			1518.17i			0.593687i
$188$			1257.07i			0.487664i
$189$	1602.86	−	852.232i	0.616883	−	0.327994i
$190$	−129.430			−0.0494204
$191$	−865.452			−0.327863			−0.163932	−	0.986472i	$-0.552418\pi$
$191$	−865.452			−0.327863			−0.163932	+	0.986472i	$0.552418\pi$
$192$	160.010	+	973.593i	0.0601443	+	0.365953i
$193$	4803.15			1.79139			0.895696	−	0.444667i	$-0.146678\pi$
$193$	4803.15			1.79139			0.895696	+	0.444667i	$0.146678\pi$
$194$		−	4010.88i		−	1.48435i
$195$	−100.441	+	16.5074i	−0.0368857	+	0.00606216i
$196$	543.949			0.198232
$197$	1382.16			0.499874			0.249937	−	0.968262i	$-0.419590\pi$
$197$	1382.16			0.499874			0.249937	+	0.968262i	$0.419590\pi$
$198$	2773.41	−	936.925i	0.995442	−	0.336285i
$199$	−1488.09			−0.530091			−0.265046	−	0.964236i	$-0.585387\pi$
$199$	−1488.09			−0.530091			−0.265046	+	0.964236i	$0.585387\pi$
$200$	−2039.53			−0.721084
$201$	−2820.73	−	405.074i	−0.989845	−	0.142148i
$202$	−5605.60			−1.95252
$203$	3905.96			1.35047
$204$	−741.007	+	121.784i	−0.254318	+	0.0417971i
$205$	−126.964			−0.0432563
$206$	2547.09			0.861477
$207$	−265.456	−	785.780i	−0.0891326	−	0.263843i
$208$		−	4781.44i		−	1.59391i
$209$	3897.58			1.28996
$210$	71.7035	−	11.7845i	0.0235620	−	0.00387241i
$211$	−2212.23			−0.721782			−0.360891	−	0.932608i	$-0.617527\pi$
$211$	−2212.23			−0.721782			−0.360891	+	0.932608i	$0.617527\pi$
$212$	−2153.99			−0.697813
$213$	−1848.69	+	303.832i	−0.594696	+	0.0977381i
$214$		−	3940.81i		−	1.25882i
$215$			25.7668i			0.00817341i
$216$	−1075.55	−	2022.88i	−0.338806	−	0.637219i
$217$	−2614.33			−0.817844
$218$		−	4685.60i		−	1.45573i
$219$	692.029	+	4210.71i	0.213530	+	1.29924i
$220$	32.7115			0.0100246
$221$	−2816.66			−0.857327
$222$	945.924	+	5755.55i	0.285974	+	1.74003i
$223$	1283.66			0.385470			0.192735	−	0.981251i	$-0.438264\pi$
$223$	1283.66			0.385470			0.192735	+	0.981251i	$0.438264\pi$
$224$			1723.02i			0.513947i
$225$	3194.78	−	1079.27i	0.946601	−	0.319785i
$226$	−3252.46			−0.957303
$227$		−	2661.54i		−	0.778206i	−0.921194	−	0.389103i	$-0.872785\pi$
$227$		−	2661.54i		−	0.778206i	0.921194	−	0.389103i	$-0.127215\pi$
$228$	312.656	+	1902.38i	0.0908164	+	0.552580i
$229$			821.342i			0.237012i	0.992953	+	0.118506i	$0.0378105\pi$
$229$			821.342i			0.237012i	−0.992953	+	0.118506i	$0.962189\pi$
$230$		−	33.2000i		−	0.00951801i
$231$	−2159.23	+	354.869i	−0.615008	+	0.101076i
$232$		−	4929.49i		−	1.39499i
$233$	−1145.43			−0.322059			−0.161030	−	0.986950i	$-0.551482\pi$
$233$	−1145.43			−0.322059			−0.161030	+	0.986950i	$0.551482\pi$
$234$	1738.28	+	5145.52i	0.485620	+	1.43749i
$235$			131.634i			0.0365397i
$236$		−	1991.81i		−	0.549388i
$237$	3942.90	−	648.014i	1.08067	−	0.177608i
$238$	2010.78			0.547646
$239$	4533.27			1.22692			0.613458	−	0.789727i	$-0.289778\pi$
$239$	4533.27			1.22692			0.613458	+	0.789727i	$0.289778\pi$
$240$	−21.6483	−	131.721i	−0.00582247	−	0.0354273i
$241$	2983.48			0.797439			0.398720	−	0.917073i	$-0.369455\pi$
$241$	2983.48			0.797439			0.398720	+	0.917073i	$0.369455\pi$
$242$	905.421			0.240507
$243$	2755.24	+	2599.53i	0.727361	+	0.686256i
$244$		−	727.536i		−	0.190884i
$245$	56.9596			0.0148531
$246$	1098.65	+	6684.83i	0.284745	+	1.73256i
$247$			7231.19i			1.86279i
$248$			3299.39i			0.844805i
$249$	4497.60	−	739.180i	1.14467	−	0.188127i
$250$	270.079			0.0683252
$251$	−7018.06			−1.76485			−0.882423	−	0.470457i	$-0.844089\pi$
$251$	−7018.06			−1.76485			−0.882423	+	0.470457i	$0.844089\pi$
$252$	−346.418	−	1025.44i	−0.0865964	−	0.256335i
$253$			999.761i			0.248437i
$254$	−505.974			−0.124991
$255$	−77.5945	+	12.7526i	−0.0190555	+	0.00313177i
$256$	4137.17			1.01005
$257$			4923.99i			1.19514i	0.801818	+	0.597568i	$0.203866\pi$
$257$			4923.99i			1.19514i	−0.801818	+	0.597568i	$0.796134\pi$
$258$	1356.66	−	222.967i	0.327372	−	0.0538036i
$259$		−	4359.94i		−	1.04600i
$260$			60.6899i			0.0144763i
$261$	2608.58	+	7721.69i	0.618647	+	1.83127i
$262$		−	2950.92i		−	0.695834i
$263$		−	1354.24i		−	0.317513i	−0.987318	−	0.158756i	$-0.949252\pi$
$263$		−	1354.24i		−	0.317513i	0.987318	−	0.158756i	$-0.0507484\pi$
$264$	447.860	+	2725.04i	0.104409	+	0.635283i
$265$	−225.555			−0.0522857
$266$		−	5162.27i		−	1.18992i
$267$	−1436.31	+	236.056i	−0.329215	+	0.0541064i
$268$	−511.070	+	1620.39i	−0.116487	+	0.369332i
$269$			1361.80i			0.308664i	0.988019	+	0.154332i	$0.0493226\pi$
$269$			1361.80i			0.308664i	−0.988019	+	0.154332i	$0.950677\pi$
$270$	71.1835	+	133.880i	0.0160448	+	0.0301767i
$271$			2096.96i			0.470041i	0.971990	+	0.235020i	$0.0755157\pi$
$271$			2096.96i			0.470041i	−0.971990	+	0.235020i	$0.924484\pi$
$272$		−	3693.85i		−	0.823429i
$273$	−658.390	−	4006.03i	−0.145962	−	0.888117i
$274$	2241.37			0.494182
$275$	−4064.77			−0.891327
$276$	−487.976	+	80.1988i	−0.106423	+	0.0174906i
$277$	608.373			0.131962			0.0659812	−	0.997821i	$-0.478982\pi$
$277$	608.373			0.131962			0.0659812	+	0.997821i	$0.478982\pi$
$278$			1305.69i			0.281691i
$279$	−1745.97	−	5168.26i	−0.374653	−	1.10902i
$280$			68.5500i			0.0146309i
$281$	−7772.73			−1.65011			−0.825057	−	0.565049i	$-0.808857\pi$
$281$	−7772.73			−1.65011			−0.825057	+	0.565049i	$0.808857\pi$
$282$	6930.70	−	1139.06i	1.46354	−	0.240532i
$283$	5371.20			1.12821			0.564107	−	0.825702i	$-0.309220\pi$
$283$	5371.20			1.12821			0.564107	+	0.825702i	$0.309220\pi$
$284$			1117.04i			0.233396i
$285$	32.7397	+	199.208i	0.00680468	+	0.0414037i
$286$		−	6546.73i		−	1.35355i
$287$		−	5063.88i		−	1.04150i
$288$	−3406.23	+	1150.71i	−0.696924	+	0.235438i
$289$	2737.02			0.557097
$290$			326.249i			0.0660621i
$291$	−6173.18	+	1014.56i	−1.24357	+	0.204380i
$292$	2544.26			0.509902
$293$			4783.08i			0.953688i	0.878988	+	0.476844i	$0.158219\pi$
$293$			4783.08i			0.953688i	−0.878988	+	0.476844i	$0.841781\pi$
$294$	−492.886	−	2999.01i	−0.0977745	−	0.594917i
$295$		−	208.572i		−	0.0411645i
$296$	−5502.42			−1.08048
$297$	−2143.57	−	4031.58i	−0.418796	−	0.787663i
$298$		−	5889.03i		−	1.14477i
$299$	−1854.86			−0.358761
$300$	−326.068	−	1983.99i	−0.0627518	−	0.381818i
$301$	−1027.70			−0.196795
$302$	5135.14			0.978457
$303$	1417.95	+	8627.63i	0.268842	+	1.63579i
$304$	−9483.20			−1.78914
$305$		−	76.1839i		−	0.0143025i
$306$	1342.89	+	3975.11i	0.250876	+	0.742621i
$307$	8199.11			1.52426			0.762131	−	0.647423i	$-0.224153\pi$
$307$	8199.11			1.52426			0.762131	+	0.647423i	$0.224153\pi$
$308$			1304.68i			0.241367i
$309$	−644.293	−	3920.25i	−0.118617	−	0.721732i
$310$		−	218.364i		−	0.0400073i
$311$	7001.27			1.27655			0.638273	−	0.769810i	$-0.279649\pi$
$311$	7001.27			1.27655			0.638273	+	0.769810i	$0.279649\pi$
$312$	−5055.78	+	830.916i	−0.917394	+	0.150774i
$313$			8012.38i			1.44692i	0.690366	+	0.723461i	$0.257450\pi$
$313$			8012.38i			1.44692i	−0.690366	+	0.723461i	$0.742550\pi$
$314$	−2132.96			−0.383344
$315$	−36.2751	−	107.379i	−0.00648849	−	0.0192067i
$316$		−	2382.44i		−	0.424122i
$317$		−	10364.6i		−	1.83638i	−0.396141	−	0.918190i	$-0.629651\pi$
$317$		−	10364.6i		−	1.83638i	0.396141	−	0.918190i	$-0.370349\pi$
$318$	1951.78	+	11875.8i	0.344184	+	2.09422i
$319$		−	9824.44i		−	1.72434i
$320$	61.6016			0.0107614
$321$	−6065.33	+	996.836i	−1.05462	+	0.173327i
$322$	1324.16			0.229170
$323$			5586.38i			0.962336i
$324$	1795.83	−	1369.67i	0.307927	−	0.234854i
$325$		−	7541.39i		−	1.28714i
$326$	7340.83			1.24715
$327$	−7211.66	+	1185.23i	−1.21959	+	0.200439i
$328$	−6390.83			−1.07584
$329$	−5250.13			−0.879784
$330$	−29.6408	−	180.352i	−0.00494445	−	0.0300849i
$331$		−	8403.76i		−	1.39551i	−0.716338	−	0.697753i	$-0.754183\pi$
$331$		−	8403.76i		−	1.39551i	0.716338	−	0.697753i	$-0.245817\pi$
$332$		−	2717.61i		−	0.449241i
$333$	8619.15	−	2911.76i	1.41840	−	0.479169i
$334$			352.936i			0.0578198i
$335$	−53.5167	+	169.679i	−0.00872815	+	0.0276733i
$336$	5253.62	−	863.432i	0.853002	−	0.140191i
$337$		−	5307.99i		−	0.857996i	−0.903305	−	0.428998i	$-0.858867\pi$
$337$		−	5307.99i		−	0.857996i	0.903305	−	0.428998i	$-0.141133\pi$
$338$	4827.11			0.776806
$339$	822.717	+	5005.89i	0.131811	+	0.802014i
$340$			46.8853i			0.00747857i
$341$			6575.67i			1.04426i
$342$	10205.3	−	3447.59i	1.61356	−	0.545100i
$343$			6710.00i			1.05629i
$344$			1297.00i			0.203283i
$345$	−51.0984	+	8.39802i	−0.00797405	+	0.00131053i
$346$			8633.10i			1.34138i
$347$	1804.05			0.279097			0.139548	−	0.990215i	$-0.455435\pi$
$347$	1804.05			0.279097			0.139548	+	0.990215i	$0.455435\pi$
$348$	4795.24	−	788.097i	0.738655	−	0.121398i
$349$	−3370.83			−0.517010			−0.258505	−	0.966010i	$-0.583230\pi$
$349$	−3370.83			−0.517010			−0.258505	+	0.966010i	$0.583230\pi$
$350$			5383.71i			0.822204i
$351$	7479.81	−	3976.97i	1.13744	−	0.604773i
$352$	4333.81			0.656229
$353$	−2545.66			−0.383830			−0.191915	−	0.981412i	$-0.561470\pi$
$353$	−2545.66			−0.383830			−0.191915	+	0.981412i	$0.561470\pi$
$354$	−10981.6	+	1804.83i	−1.64878	+	0.270976i
$355$			116.971i			0.0174878i
$356$			867.866i			0.129204i
$357$	−508.632	−	3094.81i	−0.0754052	−	0.458809i
$358$	−8887.95			−1.31213
$359$			7459.53i			1.09665i	0.836264	+	0.548327i	$0.184735\pi$
$359$			7459.53i			1.09665i	−0.836264	+	0.548327i	$0.815265\pi$
$360$	−135.516	+	45.7808i	−0.0198398	+	0.00670238i
$361$	7482.87			1.09096
$362$	−1159.27			−0.168314
$363$	−229.028	−	1393.54i	−0.0331154	−	0.201493i
$364$	−2420.58			−0.348552
$365$	266.422			0.0382059
$366$	−4011.19	+	659.239i	−0.572865	+	0.0941502i
$367$			389.983i			0.0554685i	0.999615	+	0.0277343i	$0.00882922\pi$
$367$			389.983i			0.0554685i	−0.999615	+	0.0277343i	$0.991171\pi$
$368$		−	2432.52i		−	0.344576i
$369$	10010.8	−	3381.88i	1.41230	−	0.477111i
$370$	364.168			0.0511680
$371$		−	8996.12i		−	1.25891i
$372$	−3209.54	+	527.487i	−0.447330	+	0.0735186i
$373$			3726.68i			0.517319i	0.965969	+	0.258659i	$0.0832807\pi$
$373$			3726.68i			0.517319i	−0.965969	+	0.258659i	$0.916719\pi$
$374$		−	5057.60i		−	0.699258i
$375$	−68.3171	−	415.681i	−0.00940768	−	0.0572418i
$376$			6625.89i			0.908787i
$377$	18227.3			2.49007
$378$	−5339.75	+	2839.12i	−0.726579	+	0.386318i
$379$			1843.28i			0.249823i	0.992168	+	0.124911i	$0.0398647\pi$
$379$			1843.28i			0.249823i	−0.992168	+	0.124911i	$0.960135\pi$
$380$	120.368			0.0162494
$381$	127.987	+	778.750i	0.0172099	+	0.104715i
$382$	2883.15			0.386165
$383$	919.170			0.122630			0.0613152	−	0.998118i	$-0.480471\pi$
$383$	919.170			0.122630			0.0613152	+	0.998118i	$0.480471\pi$
$384$	−1430.75	−	8705.55i	−0.190138	−	1.15691i
$385$			136.620i			0.0180852i
$386$	−16001.2			−2.10994
$387$	−686.341	−	2031.65i	−0.0901517	−	0.266860i
$388$			3730.05i			0.488053i
$389$		−	2319.58i		−	0.302333i	−0.988508	−	0.151166i	$-0.951697\pi$
$389$		−	2319.58i		−	0.302333i	0.988508	−	0.151166i	$-0.0483029\pi$
$390$	334.607	−	54.9926i	0.0434449	−	0.00714015i
$391$	−1432.95			−0.185339
$392$	2867.11			0.369416
$393$	−4541.79	+	746.442i	−0.582959	+	0.0958092i
$394$	−4604.52			−0.588763
$395$		−	249.477i		−	0.0317786i
$396$	−2579.22	+	871.325i	−0.327300	+	0.110570i
$397$	12491.7			1.57919			0.789596	−	0.613627i	$-0.210290\pi$
$397$	12491.7			1.57919			0.789596	+	0.613627i	$0.210290\pi$
$398$	4957.41			0.624353
$399$	−7945.29	+	1305.81i	−0.996897	+	0.163840i
$400$	9890.00			1.23625
$401$	−6074.90			−0.756524			−0.378262	−	0.925699i	$-0.623478\pi$
$401$	−6074.90			−0.756524			−0.378262	+	0.925699i	$0.623478\pi$
$402$	9396.94	+	1349.46i	1.16586	+	0.167425i
$403$	−12199.9			−1.50799
$404$	5213.12			0.641986
$405$	188.051	−	143.425i	0.0230724	−	0.0175971i
$406$	−13012.3			−1.59061
$407$	−10966.3			−1.33557
$408$	−3905.79	+	641.915i	−0.473934	+	0.0778910i
$409$			12938.4i			1.56422i	0.623143	+	0.782108i	$0.285856\pi$
$409$			12938.4i			1.56422i	−0.623143	+	0.782108i	$0.714144\pi$
$410$	422.965			0.0509482
$411$	−566.959	−	3449.71i	−0.0680439	−	0.414019i
$412$	−2368.75			−0.283253
$413$	8318.78			0.991139
$414$	884.336	+	2617.74i	0.104982	+	0.310760i
$415$		−	284.574i		−	0.0336607i
$416$			8040.53i			0.947643i
$417$	2009.60	−	330.277i	0.235997	−	0.0387860i
$418$	−12984.3			−1.51934
$419$		−	10344.4i		−	1.20610i	−0.797702	−	0.603052i	$-0.793951\pi$
$419$		−	10344.4i		−	1.20610i	0.797702	−	0.603052i	$-0.206049\pi$
$420$	−66.6831	+	10.9594i	−0.00774715	+	0.00127324i
$421$	5909.83			0.684151			0.342075	−	0.939673i	$-0.388870\pi$
$421$	5909.83			0.684151			0.342075	+	0.939673i	$0.388870\pi$
$422$	7369.79			0.850132
$423$	−3506.27	−	10379.0i	−0.403028	−	1.19301i
$424$	−11353.5			−1.30041
$425$		−	5826.02i		−	0.664949i
$426$	6158.70	−	1012.18i	0.700446	−	0.115118i
$427$	3038.55			0.344370
$428$			3664.89i			0.413899i
$429$	−10076.1	+	1656.01i	−1.13399	+	0.186370i
$430$		−	85.8393i		−	0.00962683i
$431$			9233.56i			1.03194i	0.856607	+	0.515969i	$0.172568\pi$
$431$			9233.56i			1.03194i	−0.856607	+	0.515969i	$0.827432\pi$
$432$	5215.52	+	9809.23i	0.580860	+	1.09247i
$433$		−	11070.5i		−	1.22867i	−0.789046	−	0.614335i	$-0.789425\pi$
$433$		−	11070.5i		−	1.22867i	0.789046	−	0.614335i	$-0.210575\pi$
$434$	8709.34			0.963276
$435$	502.133	−	82.5255i	0.0553459	−	0.00909608i
$436$			4357.53i			0.478642i
$437$			3678.81i			0.402703i
$438$	−2305.41	−	14027.5i	−0.251500	−	1.53027i
$439$	−1024.52			−0.111384			−0.0556922	−	0.998448i	$-0.517737\pi$
$439$	−1024.52			−0.111384			−0.0556922	+	0.998448i	$0.517737\pi$
$440$	172.420			0.0186813
$441$	−4491.12	+	1517.21i	−0.484950	+	0.163828i
$442$	9383.39			1.00978
$443$	−5739.26			−0.615532			−0.307766	−	0.951462i	$-0.599581\pi$
$443$	−5739.26			−0.615532			−0.307766	+	0.951462i	$0.599581\pi$
$444$	−879.693	−	5352.57i	−0.0940279	−	0.572121i
$445$			90.8785i			0.00968102i
$446$	−4276.35			−0.454016
$447$	−9063.86	+	1489.64i	−0.959073	+	0.157624i
$448$			2456.95i			0.259107i
$449$			3915.72i			0.411569i	0.978597	+	0.205784i	$0.0659746\pi$
$449$			3915.72i			0.411569i	−0.978597	+	0.205784i	$0.934025\pi$
$450$	−10643.0	+	3595.48i	−1.11493	+	0.376650i
$451$	−12736.9			−1.32984
$452$	3024.74			0.314760
$453$	−1298.94	−	7903.54i	−0.134723	−	0.819736i
$454$			8866.63i			0.916589i
$455$	−253.471			−0.0261163
$456$	1647.98	+	10027.3i	0.169241	+	1.02976i
$457$	5797.19			0.593394			0.296697	−	0.954972i	$-0.404115\pi$
$457$	5797.19			0.593394			0.296697	+	0.954972i	$0.404115\pi$
$458$		−	2736.21i		−	0.279158i
$459$	5778.44	−	3072.37i	0.587614	−	0.312431i
$460$			30.8755i			0.00312951i
$461$			12653.3i			1.27835i	0.769060	+	0.639177i	$0.220725\pi$
$461$			12653.3i			1.27835i	−0.769060	+	0.639177i	$0.779275\pi$
$462$	7193.23	−	1182.21i	0.724371	−	0.119050i
$463$			17587.0i			1.76531i	0.470020	+	0.882656i	$0.344247\pi$
$463$			17587.0i			1.76531i	−0.470020	+	0.882656i	$0.655753\pi$
$464$			23903.8i			2.39161i
$465$	−336.086	+	55.2357i	−0.0335175	+	0.00550859i
$466$	3815.88			0.379329
$467$		−	6528.32i		−	0.646883i	−0.946248	−	0.323442i	$-0.895160\pi$
$467$		−	6528.32i		−	0.646883i	0.946248	−	0.323442i	$-0.104840\pi$
$468$	−1616.57	−	4785.24i	−0.159671	−	0.472645i
$469$	−6767.55	−	2134.48i	−0.666304	−	0.210152i
$470$		−	438.522i		−	0.0430373i
$471$	539.537	+	3282.86i	0.0527825	+	0.321159i
$472$		−	10498.7i		−	1.02381i
$473$			2584.90i			0.251277i
$474$	−13135.3	+	2158.79i	−1.27284	+	0.209191i
$475$	−14957.1			−1.44480
$476$	−1869.99			−0.180065
$477$	17784.4	−	6008.01i	1.70711	−	0.576704i
$478$	−15102.1			−1.44509
$479$			9422.65i			0.898814i	0.893327	+	0.449407i	$0.148365\pi$
$479$			9422.65i			0.898814i	−0.893327	+	0.449407i	$0.851635\pi$
$480$	36.4041	+	221.504i	0.00346169	+	0.0210629i
$481$		−	20345.8i		−	1.92867i
$482$	−9939.13			−0.939242
$483$	−334.950	−	2038.03i	−0.0315544	−	0.191995i
$484$	−842.027			−0.0790784
$485$			390.592i			0.0365688i
$486$	−9178.76	−	8660.05i	−0.856702	−	0.808288i
$487$			12845.2i			1.19522i	0.801789	+	0.597608i	$0.203882\pi$
$487$			12845.2i			1.19522i	−0.801789	+	0.597608i	$0.796118\pi$
$488$		−	3834.78i		−	0.355722i
$489$	−1856.88	−	11298.3i	−0.171720	−	1.04484i
$490$	−189.754			−0.0174944
$491$			11383.6i			1.04630i	0.852241	+	0.523150i	$0.175243\pi$
$491$			11383.6i			1.04630i	−0.852241	+	0.523150i	$0.824757\pi$
$492$	−1021.73	−	6216.78i	−0.0936239	−	0.569663i
$493$	14081.3			1.28639
$494$		−	24089.9i		−	2.19404i
$495$	−270.083	+	91.2407i	−0.0245239	+	0.00828478i
$496$		−	15999.2i		−	1.44836i
$497$	−4665.33			−0.421064
$498$	−14983.2	+	2462.49i	−1.34822	+	0.221580i
$499$			15020.2i			1.34749i	0.738965	+	0.673744i	$0.235315\pi$
$499$			15020.2i			1.34749i	−0.738965	+	0.673744i	$0.764685\pi$
$500$	−251.169			−0.0224652
$501$	543.207	−	89.2760i	0.0484405	−	0.00796119i
$502$	23379.9			2.07868
$503$	−14106.1			−1.25041			−0.625207	−	0.780459i	$-0.714986\pi$
$503$	−14106.1			−1.25041			−0.625207	+	0.780459i	$0.714986\pi$
$504$	−1825.94	−	5405.00i	−0.161377	−	0.477694i
$505$	545.891			0.0481027
$506$		−	3330.59i		−	0.292614i
$507$	−1221.03	−	7429.45i	−0.106958	−	0.650796i
$508$	470.548			0.0410968
$509$			0.756070i			6.58393e-5i	1.00000		3.29197e-5i	$1.04787e-5\pi$
$509$			0.756070i			6.58393e-5i	−1.00000		3.29197e-5i	$0.999990\pi$
$510$	258.497	−	42.4840i	0.0224440	−	0.00368867i
$511$			10626.1i			0.919902i
$512$	−199.639			−0.0172322
$513$	−7887.66	−	14834.9i	−0.678848	−	1.27676i
$514$		−	16403.7i		−	1.40766i
$515$	−248.044			−0.0212235
$516$	−1261.67	+	207.356i	−0.107640	+	0.0176906i
$517$			13205.3i			1.12335i
$518$			14524.6i			1.23200i
$519$	13287.3	−	2183.76i	1.12379	−	0.184695i
$520$			319.891i			0.0269772i
$521$	10052.1			0.845282			0.422641	−	0.906297i	$-0.361103\pi$
$521$	10052.1			0.845282			0.422641	+	0.906297i	$0.361103\pi$
$522$	−8690.18	−	25723.9i	−0.728657	−	2.15691i
$523$	7510.08			0.627902			0.313951	−	0.949439i	$-0.398347\pi$
$523$	7510.08			0.627902			0.313951	+	0.949439i	$0.398347\pi$
$524$			2744.31i			0.228789i
$525$	8286.12	−	1361.82i	0.688830	−	0.113209i
$526$			4511.48i			0.373974i
$527$	−9424.87			−0.779039
$528$	−2171.74	−	13214.1i	−0.179001	−	1.08915i
$529$	11223.4			0.922442
$530$	751.409			0.0615833
$531$	5555.65	+	16445.4i	0.454039	+	1.34401i
$532$			4800.82i			0.391244i
$533$		−	23630.8i		−	1.92038i
$534$	4784.89	−	786.395i	0.387757	−	0.0637278i
$535$			383.768i			0.0310126i
$536$	−2693.81	+	8540.94i	−0.217080	+	0.688269i
$537$	2248.23	+	13679.5i	0.180667	+	1.09928i
$538$		−	4536.70i		−	0.363552i
$539$	5714.13			0.456633
$540$	−66.1995	−	124.507i	−0.00527550	−	0.00992205i
$541$		−	4241.43i		−	0.337067i	−0.985696	−	0.168534i	$-0.946097\pi$
$541$		−	4241.43i		−	0.337067i	0.985696	−	0.168534i	$-0.0539032\pi$
$542$		−	6985.77i		−	0.553625i
$543$	293.240	+	1784.24i	0.0231752	+	0.141011i
$544$			6211.63i			0.489561i
$545$			456.299i			0.0358637i
$546$	2193.35	+	13345.6i	0.171917	+	1.04604i
$547$			1250.68i			0.0977612i	0.998805	+	0.0488806i	$0.0155654\pi$
$547$			1250.68i			0.0977612i	−0.998805	+	0.0488806i	$0.984435\pi$
$548$	−2084.43			−0.162487
$549$	2029.28	+	6006.91i	0.157755	+	0.466974i
$550$	13541.3			1.04983
$551$		−	36150.9i		−	2.79506i
$552$	−2572.08	+	422.721i	−0.198325	+	0.0325946i
$553$	9950.24			0.765149
$554$	−2026.73			−0.155428
$555$	−92.1170	−	560.494i	−0.00704531	−	0.0428678i
$556$		−	1214.27i		−	0.0926197i
$557$			12554.4i			0.955024i	0.878625	+	0.477512i	$0.158461\pi$
$557$			12554.4i			0.955024i	−0.878625	+	0.477512i	$0.841539\pi$
$558$	5816.48	+	17217.5i	0.441275	+	1.30623i
$559$	−4795.78			−0.362862
$560$		−	332.409i		−	0.0250837i
$561$	−7784.20	+	1279.33i	−0.585828	+	0.0962806i
$562$	25894.0			1.94354
$563$	16238.4			1.21557			0.607785	−	0.794102i	$-0.292058\pi$
$563$	16238.4			1.21557			0.607785	+	0.794102i	$0.292058\pi$
$564$	−6445.43	+	1059.31i	−0.481209	+	0.0790866i
$565$	316.735			0.0235843
$566$	−17893.5			−1.32884
$567$	5720.41	+	7500.29i	0.423694	+	0.555525i
$568$			5887.85i			0.434945i
$569$			2932.55i			0.216061i	0.994148	+	0.108031i	$0.0344545\pi$
$569$			2932.55i			0.216061i	−0.994148	+	0.108031i	$0.965546\pi$
$570$	−109.069	−	663.638i	−0.00801471	−	0.0487662i
$571$	14922.6			1.09368			0.546841	−	0.837237i	$-0.315830\pi$
$571$	14922.6			1.09368			0.546841	+	0.837237i	$0.315830\pi$
$572$			6088.35i			0.445046i
$573$	−729.300	−	4437.49i	−0.0531709	−	0.323523i
$574$			16869.7i			1.22671i
$575$		−	3836.62i		−	0.278257i
$576$	−4857.13	+	1640.86i	−0.351355	+	0.118696i
$577$		−	5306.99i		−	0.382900i	−0.981502	−	0.191450i	$-0.938681\pi$
$577$		−	5306.99i		−	0.382900i	0.981502	−	0.191450i	$-0.0613189\pi$
$578$	−9118.06			−0.656162
$579$	4047.53	+	24627.5i	0.290517	+	1.76768i
$580$		−	303.406i		−	0.0217211i
$581$	11350.1			0.810466
$582$	20565.2	−	3379.89i	1.46470	−	0.240723i
$583$	−22627.4			−1.60743
$584$	13410.6			0.950228
$585$	−169.279	−	501.086i	−0.0119638	−	0.0354143i
$586$		−	15934.3i		−	1.12328i
$587$	14837.5			1.04328			0.521642	−	0.853165i	$-0.325320\pi$
$587$	14837.5			1.04328			0.521642	+	0.853165i	$0.325320\pi$
$588$	458.376	+	2789.03i	0.0321481	+	0.195608i
$589$			24196.4i			1.69269i
$590$			694.834i			0.0484845i
$591$	1164.72	+	7086.86i	0.0810666	+	0.493256i
$592$	26682.1			1.85241
$593$	9540.63			0.660686			0.330343	−	0.943861i	$-0.392836\pi$
$593$	9540.63			0.660686			0.330343	+	0.943861i	$0.392836\pi$
$594$	7141.06	+	13430.7i	0.493268	+	0.927728i
$595$	−195.816			−0.0134919
$596$			5476.70i			0.376400i
$597$	−1253.99	−	7630.00i	−0.0859671	−	0.523074i
$598$	6179.26			0.422556
$599$	15775.4			1.07607			0.538034	−	0.842923i	$-0.319167\pi$
$599$	15775.4			1.07607			0.538034	+	0.842923i	$0.319167\pi$
$600$	−1718.68	−	10457.4i	−0.116941	−	0.711538i
$601$	−3542.52			−0.240437			−0.120218	−	0.992747i	$-0.538360\pi$
$601$	−3542.52			−0.240437			−0.120218	+	0.992747i	$0.538360\pi$
$602$	3423.65			0.231790
$603$	−300.015	−	14804.3i	−0.0202613	−	0.999795i
$604$	−4775.59			−0.321715
$605$	−88.1728			−0.00592518
$606$	−4723.74	−	28742.0i	−0.316648	−	1.92667i
$607$	−15366.4			−1.02751			−0.513757	−	0.857936i	$-0.671747\pi$
$607$	−15366.4			−1.02751			−0.513757	+	0.857936i	$0.671747\pi$
$608$	15947.1			1.06371
$609$	3291.48	+	20027.3i	0.219011	+	1.33259i
$610$			253.798i			0.0168459i
$611$	−24499.9			−1.62219
$612$	−1248.87	−	3696.79i	−0.0824876	−	0.244173i
$613$	−2061.34			−0.135818			−0.0679092	−	0.997692i	$-0.521633\pi$
$613$	−2061.34			−0.135818			−0.0679092	+	0.997692i	$0.521633\pi$
$614$	−27314.4			−1.79531
$615$	−106.990	−	650.990i	−0.00701505	−	0.0426836i
$616$			6876.87i			0.449800i
$617$		−	21494.8i		−	1.40251i	−0.712910	−	0.701256i	$-0.752623\pi$
$617$		−	21494.8i		−	1.40251i	0.712910	−	0.701256i	$-0.247377\pi$
$618$	2146.39	+	13059.9i	0.139709	+	0.850073i
$619$	3833.23			0.248902			0.124451	−	0.992226i	$-0.460283\pi$
$619$	3833.23			0.248902			0.124451	+	0.992226i	$0.460283\pi$
$620$			203.075i			0.0131543i
$621$	3805.29	−	2023.25i	0.245895	−	0.130741i
$622$	−23323.9			−1.50354
$623$	−3624.64			−0.233095
$624$	24516.2	−	4029.23i	1.57281	−	0.258491i
$625$	15585.5			0.997475
$626$		−	26692.3i		−	1.70422i
$627$	3284.42	+	19984.3i	0.209198	+	1.27288i
$628$	1983.62			0.126043
$629$		−	15717.9i		−	0.996367i
$630$	120.847	+	357.720i	0.00764229	+	0.0226221i
$631$			2659.11i			0.167761i	0.996476	+	0.0838807i	$0.0267315\pi$
$631$			2659.11i			0.167761i	−0.996476	+	0.0838807i	$0.973269\pi$
$632$		−	12557.6i		−	0.790373i
$633$	−1864.20	−	11342.9i	−0.117054	−	0.712228i
$634$			34528.4i			2.16293i
$635$	49.2734			0.00307930
$636$	−1815.13	−	11044.3i	−0.113167	−	0.688576i
$637$			10601.5i			0.659411i
$638$			32729.0i			2.03096i
$639$	−3115.72	−	9222.88i	−0.192889	−	0.570973i
$640$	−550.821			−0.0340205
$641$	7902.03			0.486913			0.243457	−	0.969912i	$-0.421719\pi$
$641$	7902.03			0.486913			0.243457	+	0.969912i	$0.421719\pi$
$642$	20206.0	−	3320.85i	1.24216	−	0.204149i
$643$	−5540.28			−0.339794			−0.169897	−	0.985462i	$-0.554343\pi$
$643$	−5540.28			−0.339794			−0.169897	+	0.985462i	$0.554343\pi$
$644$	−1231.45			−0.0753509
$645$	−132.116	+	21.7132i	−0.00806522	+	0.00132552i
$646$		−	18610.4i		−	1.13346i
$647$	2620.75			0.159246			0.0796230	−	0.996825i	$-0.474628\pi$
$647$	2620.75			0.159246			0.0796230	+	0.996825i	$0.474628\pi$
$648$	9465.69	−	7219.40i	0.573838	−	0.437662i
$649$		−	20923.7i		−	1.26553i
$650$			25123.3i			1.51602i
$651$	−2203.05	−	13404.6i	−0.132633	−	0.807018i
$652$	−6826.85			−0.410061
$653$	−15994.7			−0.958531			−0.479265	−	0.877670i	$-0.659097\pi$
$653$	−15994.7			−0.958531			−0.479265	+	0.877670i	$0.659097\pi$
$654$	24024.8	−	3948.47i	1.43646	−	0.236082i
$655$			287.370i			0.0171427i
$656$	30990.1			1.84445
$657$	−21006.7	+	7096.57i	−1.24741	+	0.421406i
$658$	17490.2			1.03623
$659$		−	18108.2i		−	1.07040i	−0.844724	−	0.535202i	$-0.820235\pi$
$659$		−	18108.2i		−	1.07040i	0.844724	−	0.535202i	$-0.179765\pi$
$660$	27.5654	+	167.724i	0.00162573	+	0.00989189i
$661$			23057.1i			1.35676i	0.734712	+	0.678379i	$0.237317\pi$
$661$			23057.1i			1.35676i	−0.734712	+	0.678379i	$0.762683\pi$
$662$			27996.2i			1.64366i
$663$	−2373.55	−	14442.1i	−0.139036	−	0.845978i
$664$		−	14324.3i		−	0.837184i
$665$			502.718i			0.0293151i
$666$	−28713.7	+	9700.19i	−1.67062	+	0.564377i
$667$	9273.00			0.538309
$668$		−	328.225i		−	0.0190111i
$669$	1081.71	+	6581.77i	0.0625133	+	0.380368i
$670$	178.285	−	565.266i	0.0102802	−	0.0325942i
$671$		−	7642.69i		−	0.439706i
$672$	−8834.55	+	1451.96i	−0.507143	+	0.0833489i
$673$		−	6250.04i		−	0.357981i	−0.983851	−	0.178990i	$-0.942717\pi$
$673$		−	6250.04i		−	0.357981i	0.983851	−	0.178990i	$-0.0572831\pi$
$674$			17683.0i			1.01057i
$675$	8226.02	+	15471.3i	0.469066	+	0.882210i
$676$	−4489.14			−0.255413
$677$	−5834.49			−0.331223			−0.165611	−	0.986191i	$-0.552960\pi$
$677$	−5834.49			−0.331223			−0.165611	+	0.986191i	$0.552960\pi$
$678$	−2740.79	−	16676.6i	−0.155250	−	0.944631i
$679$	−15578.5			−0.880485
$680$			247.129i			0.0139367i
$681$	13646.7	−	2242.83i	0.767904	−	0.126205i
$682$		−	21906.1i		−	1.22995i
$683$	−1896.28			−0.106236			−0.0531181	−	0.998588i	$-0.516916\pi$
$683$	−1896.28			−0.106236			−0.0531181	+	0.998588i	$0.516916\pi$
$684$	−9490.73	+	3206.20i	−0.530537	+	0.179228i
$685$	−218.271			−0.0121748
$686$		−	22353.6i		−	1.24412i
$687$	−4211.32	+	692.129i	−0.233875	+	0.0384372i
$688$		−	6289.33i		−	0.348515i
$689$		−	41980.7i		−	2.32125i
$690$	170.229	−	27.9770i	0.00939202	−	0.00154358i
$691$	23878.7			1.31460			0.657299	−	0.753630i	$-0.271699\pi$
$691$	23878.7			1.31460			0.657299	+	0.753630i	$0.271699\pi$
$692$		−	8028.64i		−	0.441045i
$693$	−3639.09	−	10772.1i	−0.199477	−	0.590475i
$694$	−6009.99			−0.328727
$695$		−	127.152i		−	0.00693980i
$696$	25275.3	−	4153.99i	1.37652	−	0.226231i
$697$		−	18255.7i		−	0.992086i
$698$	11229.5			0.608946
$699$	−965.236	−	5873.06i	−0.0522297	−	0.317796i
$700$		−	5006.76i		−	0.270340i
$701$	−26262.2			−1.41499			−0.707496	−	0.706717i	$-0.750175\pi$
$701$	−26262.2			−1.41499			−0.707496	+	0.706717i	$0.750175\pi$
$702$	−24918.1	+	13248.8i	−1.33971	+	0.712315i
$703$	−40352.5			−2.16490
$704$	6179.81			0.330839
$705$	−674.933	+	110.925i	−0.0360560	+	0.00592579i
$706$	8480.59			0.452084
$707$			21772.6i			1.15819i
$708$	10212.7	−	1678.46i	0.542115	−	0.0890965i
$709$	510.704			0.0270520			0.0135260	−	0.999909i	$-0.495694\pi$
$709$	510.704			0.0270520			0.0135260	+	0.999909i	$0.495694\pi$
$710$		−	389.676i		−	0.0205976i
$711$	6645.21	+	19670.6i	0.350513	+	1.03756i
$712$			4574.45i			0.240779i
$713$	−6206.58			−0.326000
$714$	1694.45	+	10310.0i	0.0888140	+	0.540396i
$715$			637.541i			0.0333464i
$716$	8265.64			0.431427
$717$	3820.10	+	23243.7i	0.198974	+	1.21067i
$718$		−	24850.6i		−	1.29167i
$719$		−	28848.3i		−	1.49633i	−0.663514	−	0.748164i	$-0.730936\pi$
$719$		−	28848.3i		−	1.49633i	0.663514	−	0.748164i	$-0.269064\pi$
$720$	657.139	−	221.998i	0.0340141	−	0.0114908i
$721$		−	9893.09i		−	0.511010i
$722$	−24928.3			−1.28495
$723$	2514.12	+	15297.4i	0.129324	+	0.786883i
$724$	1078.10			0.0553416
$725$			37701.6i			1.93131i
$726$	762.982	+	4642.43i	0.0390040	+	0.237323i
$727$		−	24336.9i		−	1.24155i	−0.783989	−	0.620774i	$-0.786818\pi$
$727$		−	24336.9i		−	1.24155i	0.783989	−	0.620774i	$-0.213182\pi$
$728$	−12758.7			−0.649545
$729$	−11007.0	+	16317.7i	−0.559212	+	0.829025i
$730$	−887.553			−0.0449997
$731$	−3704.93			−0.187458
$732$	3730.34	−	613.081i	0.188357	−	0.0309565i
$733$			26132.3i			1.31680i	0.752667	+	0.658402i	$0.228767\pi$
$733$			26132.3i			1.31680i	−0.752667	+	0.658402i	$0.771233\pi$
$734$		−	1299.18i		−	0.0653321i
$735$	47.9988	+	292.053i	0.00240879	+	0.0146565i
$736$			4090.55i			0.204864i
$737$	−5368.74	+	17022.0i	−0.268331	+	0.850766i
$738$	−33349.8	+	11266.4i	−1.66344	+	0.561952i
$739$		−	18001.4i		−	0.896063i	−0.894018	−	0.448032i	$-0.852125\pi$
$739$		−	18001.4i		−	0.896063i	0.894018	−	0.448032i	$-0.147875\pi$
$740$	−338.670			−0.0168240
$741$	−37077.0	+	6093.59i	−1.83813	+	0.302097i
$742$			29969.6i			1.48277i
$743$			30893.0i			1.52538i	0.646766	+	0.762689i	$0.276121\pi$
$743$			30893.0i			1.52538i	−0.646766	+	0.762689i	$0.723879\pi$
$744$	−16917.2	+	2780.34i	−0.833622	+	0.137006i
$745$			573.492i			0.0282029i
$746$		−	12415.0i		−	0.609310i
$747$	7580.09	+	22438.0i	0.371273	+	1.09901i
$748$			4703.49i			0.229915i
$749$	−15306.4			−0.746707
$750$	227.591	+	1384.79i	0.0110806	+	0.0674207i
$751$	−9666.80			−0.469702			−0.234851	−	0.972031i	$-0.575460\pi$
$751$	−9666.80			−0.469702			−0.234851	+	0.972031i	$0.575460\pi$
$752$		−	32129.9i		−	1.55806i
$753$	−5913.99	−	35984.2i	−0.286212	−	1.74148i
$754$	−60722.3			−2.93286
$755$	−500.076			−0.0241055
$756$	4965.88	−	2640.33i	0.238898	−	0.127021i
$757$			8671.39i			0.416337i	0.978093	+	0.208169i	$0.0667502\pi$
$757$			8671.39i			0.416337i	−0.978093	+	0.208169i	$0.933250\pi$
$758$		−	6140.68i		−	0.294247i
$759$	−5126.14	+	842.481i	−0.245148	+	0.0402900i
$760$	634.451			0.0302815
$761$			13120.5i			0.624991i	0.949919	+	0.312495i	$0.101165\pi$
$761$			13120.5i			0.624991i	−0.949919	+	0.312495i	$0.898835\pi$
$762$	−426.375	−	2594.32i	−0.0202703	−	0.123336i
$763$	−18199.2			−0.863508
$764$	−2681.29			−0.126971
$765$	−130.775	−	387.109i	−0.00618062	−	0.0182954i
$766$	−3062.11			−0.144437
$767$	38819.9			1.82752
$768$	3486.32	+	21212.8i	0.163804	+	0.996680i
$769$		−	1755.44i		−	0.0823185i	−0.999153	−	0.0411592i	$-0.986895\pi$
$769$		−	1755.44i		−	0.0823185i	0.999153	−	0.0411592i	$-0.0131051\pi$
$770$		−	455.133i		−	0.0213011i
$771$	−25247.1	+	4149.35i	−1.17932	+	0.193820i
$772$	14880.8			0.693747
$773$		−	16169.5i		−	0.752363i	−0.926546	−	0.376181i	$-0.877237\pi$
$773$		−	16169.5i		−	0.752363i	0.926546	−	0.376181i	$-0.122763\pi$
$774$	2286.47	+	6768.21i	0.106183	+	0.314313i
$775$		−	25234.3i		−	1.16961i
$776$			19660.8i			0.909511i
$777$	22355.0	−	3674.04i	1.03215	−	0.169634i
$778$			7727.42i			0.356094i
$779$	−46867.7			−2.15560
$780$	−311.179	+	51.1422i	−0.0142846	+	0.00234767i
$781$			11734.4i			0.537632i
$782$	4773.72			0.218297
$783$	−37393.8	+	19882.1i	−1.70670	+	0.907442i
$784$	−13903.1			−0.633339
$785$	207.714			0.00944413
$786$	15130.5	−	2486.69i	0.686623	−	0.112846i
$787$		−	10742.3i		−	0.486560i	−0.969956	−	0.243280i	$-0.921777\pi$
$787$		−	10742.3i		−	0.486560i	0.969956	−	0.243280i	$-0.0782235\pi$
$788$	4282.13			0.193584
$789$	6943.67	−	1141.19i	0.313309	−	0.0514923i
$790$			831.103i			0.0374295i
$791$			12632.8i			0.567852i
$792$	−13594.9	+	4592.68i	−0.609940	+	0.206053i
$793$	14179.5			0.634968
$794$	−41614.6			−1.86001
$795$	−190.071	−	1156.50i	−0.00847939	−	0.0515935i
$796$	−4610.31			−0.205287
$797$			9997.14i			0.444312i	0.975011	+	0.222156i	$0.0713095\pi$
$797$			9997.14i			0.444312i	−0.975011	+	0.222156i	$0.928691\pi$
$798$	26468.8	−	4350.15i	1.17417	−	0.192974i
$799$	−18927.2			−0.838041
$800$	−16631.1			−0.734999
$801$	−2420.70	−	7165.54i	−0.106780	−	0.316082i
$802$	20237.9			0.891052
$803$	26727.1			1.17457
$804$	−8739.00	−	1254.97i	−0.383334	−	0.0550491i
$805$	−128.951			−0.00564588
$806$	40642.4			1.77614
$807$	−6982.47	+	1147.57i	−0.304578	+	0.0500574i
$808$	27477.9			1.19637
$809$	12998.8			0.564914			0.282457	−	0.959280i	$-0.408851\pi$
$809$	12998.8			0.564914			0.282457	+	0.959280i	$0.408851\pi$
$810$	−626.469	+	477.802i	−0.0271752	+	0.0207263i
$811$		−	33113.2i		−	1.43374i	−0.697207	−	0.716870i	$-0.745574\pi$
$811$		−	33113.2i		−	1.43374i	0.697207	−	0.716870i	$-0.254426\pi$
$812$	12101.2			0.522991
$813$	−10751.9	+	1767.07i	−0.463818	+	0.0762284i
$814$	36532.9			1.57307
$815$	−714.873			−0.0307250
$816$	18939.7	−	3112.74i	0.812529	−	0.133539i
$817$			9511.64i			0.407307i
$818$		−	43102.9i		−	1.84237i
$819$	19985.6	−	6751.61i	0.852689	−	0.288059i
$820$	−393.351			−0.0167517
$821$		−	31448.1i		−	1.33684i	−0.743784	−	0.668420i	$-0.766971\pi$
$821$		−	31448.1i		−	1.33684i	0.743784	−	0.668420i	$-0.233029\pi$
$822$	1888.76	+	11492.3i	0.0801436	+	0.487640i
$823$	−20449.3			−0.866120			−0.433060	−	0.901365i	$-0.642566\pi$
$823$	−20449.3			−0.866120			−0.433060	+	0.901365i	$0.642566\pi$
$824$	−12485.5			−0.527856
$825$	−3425.31	−	20841.6i	−0.144550	−	0.879528i
$826$	−27713.1			−1.16739
$827$			5325.68i			0.223932i	0.993712	+	0.111966i	$0.0357148\pi$
$827$			5325.68i			0.223932i	−0.993712	+	0.111966i	$0.964285\pi$
$828$	−822.418	−	2434.45i	−0.0345181	−	0.102178i
$829$	−9109.02			−0.381628			−0.190814	−	0.981626i	$-0.561113\pi$
$829$	−9109.02			−0.381628			−0.190814	+	0.981626i	$0.561113\pi$
$830$			948.026i			0.0396464i
$831$	512.665	+	3119.35i	0.0214009	+	0.130216i
$832$			11465.4i			0.477755i
$833$			8190.04i			0.340658i
$834$	−6694.76	+	1100.28i	−0.277962	+	0.0456830i
$835$		−	34.3700i		−	0.00142446i
$836$	12075.2			0.499558
$837$	25028.3	−	13307.4i	1.03358	−	0.549547i
$838$			34461.2i			1.42058i
$839$			39910.9i			1.64229i	0.570723	+	0.821143i	$0.306663\pi$
$839$			39910.9i			1.64229i	−0.570723	+	0.821143i	$0.693337\pi$
$840$	−351.481	+	57.7659i	−0.0144372	+	0.00237275i
$841$	−66734.8			−2.73626
$842$	−19687.9			−0.805808
$843$	−6549.94	−	39853.6i	−0.267606	−	1.62827i
$844$	−6853.78			−0.279522
$845$	−470.080			−0.0191375
$846$	11680.7	+	34576.4i	0.474695	+	1.40515i
$847$		−	3516.72i		−	0.142664i
$848$	55054.7			2.22947
$849$	4526.21	+	27540.1i	0.182967	+	1.11328i
$850$			19408.7i			0.783192i
$851$		−	10350.8i		−	0.416944i
$852$	−5727.49	+	941.312i	−0.230306	+	0.0378507i
$853$	30420.8			1.22109			0.610544	−	0.791982i	$-0.290951\pi$
$853$	30420.8			1.22109			0.610544	+	0.791982i	$0.290951\pi$
$854$	−10122.6			−0.405607
$855$	−993.821	+	335.737i	−0.0397520	+	0.0134292i
$856$			19317.3i			0.771323i
$857$	−6931.01			−0.276265			−0.138132	−	0.990414i	$-0.544110\pi$
$857$	−6931.01			−0.276265			−0.138132	+	0.990414i	$0.544110\pi$
$858$	33567.5	−	5516.81i	1.33563	−	0.219511i
$859$	4298.70			0.170745			0.0853725	−	0.996349i	$-0.472792\pi$
$859$	4298.70			0.170745			0.0853725	+	0.996349i	$0.472792\pi$
$860$			79.8291i			0.00316529i
$861$	25964.4	−	4267.24i	1.02772	−	0.168905i
$862$		−	30760.6i		−	1.21544i
$863$			15604.2i			0.615496i	0.951468	+	0.307748i	$0.0995753\pi$
$863$			15604.2i			0.615496i	−0.951468	+	0.307748i	$0.900425\pi$
$864$	−8770.48	−	16495.3i	−0.345345	−	0.649517i
$865$		−	840.718i		−	0.0330466i
$866$			36880.1i			1.44715i
$867$	2306.43	+	14033.7i	0.0903467	+	0.549722i
$868$	−8099.54			−0.316724
$869$		−	25027.2i		−	0.976975i
$870$	−1672.80	+	274.924i	−0.0651876	+	0.0107136i
$871$	−31581.0	−	9960.65i	−1.22857	−	0.387490i
$872$			22968.2i			0.891974i
$873$	−10404.0	−	30797.2i	−0.403349	−	1.19396i
$874$		−	12255.5i		−	0.474313i
$875$		−	1049.01i		−	0.0405290i
$876$	2144.00	+	13045.3i	0.0826929	+	0.503152i
$877$	12565.5			0.483815			0.241908	−	0.970299i	$-0.422227\pi$
$877$	12565.5			0.483815			0.241908	+	0.970299i	$0.422227\pi$
$878$	3413.08			0.131191
$879$	−24524.6	+	4030.62i	−0.941063	+	0.154664i
$880$	−836.089			−0.0320279
$881$			34681.7i			1.32629i	0.748493	+	0.663143i	$0.230778\pi$
$881$			34681.7i			1.32629i	−0.748493	+	0.663143i	$0.769222\pi$
$882$	14961.7	−	5054.42i	0.571185	−	0.192960i
$883$			3142.24i			0.119756i	0.998206	+	0.0598781i	$0.0190712\pi$
$883$			3142.24i			0.119756i	−0.998206	+	0.0598781i	$0.980929\pi$
$884$	−8726.40			−0.332014
$885$	1069.42	−	175.760i	0.0406196	−	0.00667582i
$886$	19119.7			0.724987
$887$			4890.90i			0.185141i	0.995706	+	0.0925707i	$0.0295084\pi$
$887$			4890.90i			0.185141i	−0.995706	+	0.0925707i	$0.970492\pi$
$888$	−4636.79	−	28212.9i	−0.175226	−	1.06618i
$889$			1965.24i			0.0741418i
$890$		−	302.751i		−	0.0114025i
$891$	18865.0	−	14388.2i	0.709318	−	0.540991i
$892$	3976.94			0.149280
$893$			48591.5i			1.82089i
$894$	30195.2	−	4962.58i	1.12962	−	0.185653i
$895$	865.536			0.0323259
$896$		−	21969.2i		−	0.819129i
$897$	−1563.06	−	9510.56i	−0.0581817	−	0.354011i
$898$		−	13044.8i		−	0.484755i
$899$	60990.7			2.26268
$900$	9897.86	−	3343.74i	0.366587	−	0.123842i
$901$		−	32431.8i		−	1.19918i
$902$	42431.5			1.56631
$903$	−866.021	−	5269.38i	−0.0319151	−	0.194190i
$904$	15943.1			0.586571
$905$	112.893			0.00414663
$906$	4327.29	+	26329.7i	0.158680	+	0.965504i
$907$	13504.6			0.494390			0.247195	−	0.968966i	$-0.420491\pi$
$907$	13504.6			0.494390			0.247195	+	0.968966i	$0.420491\pi$
$908$		−	8245.82i		−	0.301373i
$909$	−43042.2	+	14540.7i	−1.57054	+	0.530566i
$910$	844.410			0.0307604
$911$		−	4489.18i		−	0.163264i	−0.996663	−	0.0816318i	$-0.973987\pi$
$911$		−	4489.18i		−	0.163264i	0.996663	−	0.0816318i	$-0.0260132\pi$
$912$	−7991.31	−	48623.8i	−0.290152	−	1.76546i
$913$		−	28548.2i		−	1.03484i
$914$	−19312.7			−0.698914
$915$	390.623	−	64.1988i	0.0141132	−	0.00231950i
$916$			2544.63i			0.0917869i
$917$	−11461.6			−0.412754
$918$	−19250.2	+	10235.2i	−0.692105	+	0.367988i
$919$		−	42043.2i		−	1.50912i	−0.656234	−	0.754558i	$-0.727851\pi$
$919$		−	42043.2i		−	1.50912i	0.656234	−	0.754558i	$-0.272149\pi$
$920$			162.742i			0.00583200i
$921$	6909.24	+	42039.9i	0.247196	+	1.50408i
$922$		−	42152.9i		−	1.50567i
$923$	−21770.9			−0.776381
$924$	−6689.58	+	1099.43i	−0.238172	+	0.0391436i
$925$	42083.5			1.49589
$926$		−	58589.2i		−	2.07922i
$927$	19557.6	−	6607.05i	0.692942	−	0.234093i
$928$		−	40197.0i		−	1.42191i
$929$	14545.7			0.513702			0.256851	−	0.966451i	$-0.417315\pi$
$929$	14545.7			0.513702			0.256851	+	0.966451i	$0.417315\pi$
$930$	1119.63	−	184.012i	0.0394777	−	0.00648814i
$931$	21026.2			0.740179
$932$	−3548.71			−0.124723
$933$	5899.84	+	35898.1i	0.207023	+	1.25965i
$934$			21748.3i			0.761914i
$935$			492.525i			0.0172271i
$936$	−8520.82	−	25222.6i	−0.297555	−	0.880798i
$937$			42694.3i			1.48854i	0.667878	+	0.744271i	$0.267203\pi$
$937$			42694.3i			1.48854i	−0.667878	+	0.744271i	$0.732797\pi$
$938$	22545.3	+	7110.79i	0.784788	+	0.247522i
$939$	−41082.4	+	6751.88i	−1.42777	+	0.234653i
$940$			407.818i			0.0141506i
$941$	28165.3			0.975730			0.487865	−	0.872919i	$-0.337776\pi$
$941$	28165.3			0.975730			0.487865	+	0.872919i	$0.337776\pi$
$942$	−1797.41	−	10936.5i	−0.0621684	−	0.378269i
$943$		−	12022.0i		−	0.415153i
$944$			50909.5i			1.75526i
$945$	520.001	−	276.482i	0.0179002	−	0.00951742i
$946$		−	8611.31i		−	0.295960i
$947$		−	12131.3i		−	0.416278i	−0.978099	−	0.208139i	$-0.933259\pi$
$947$		−	12131.3i		−	0.416278i	0.978099	−	0.208139i	$-0.0667406\pi$
$948$	12215.6	−	2007.63i	0.418507	−	0.0687816i
$949$			49587.0i			1.69617i
$950$	49827.8			1.70171
$951$	53143.0	−	8734.03i	1.81207	−	0.297813i
$952$	−9856.59			−0.335561
$953$			43566.9i			1.48087i	0.672128	+	0.740435i	$0.265380\pi$
$953$			43566.9i			1.48087i	−0.672128	+	0.740435i	$0.734620\pi$
$954$	−59246.8	+	20015.0i	−2.01068	+	0.679255i
$955$	−280.771			−0.00951364
$956$	14044.7			0.475144
$957$	50373.5	−	8278.88i	1.70151	−	0.279643i
$958$		−	31390.5i		−	1.05864i
$959$		−	8705.64i		−	0.293138i
$960$	51.9105	+	315.854i	0.00174521	+	0.0106189i
$961$	−11031.1			−0.370283
$962$			67779.7i			2.27163i
$963$	−10222.3	−	30259.2i	−0.342065	−	1.01255i
$964$	9243.22			0.308822
$965$	1558.24			0.0519810
$966$	1115.85	+	6789.47i	0.0371655	+	0.226136i
$967$	15703.8			0.522234			0.261117	−	0.965307i	$-0.415909\pi$
$967$	15703.8			0.522234			0.261117	+	0.965307i	$0.415909\pi$
$968$	−4438.25			−0.147367
$969$	−28643.4	+	4707.54i	−0.949597	+	0.156066i
$970$		−	1301.21i		−	0.0430715i
$971$		−	3229.49i		−	0.106735i	−0.998575	−	0.0533673i	$-0.983005\pi$
$971$		−	3229.49i		−	0.106735i	0.998575	−	0.0533673i	$-0.0169954\pi$
$972$	8536.10	+	8053.70i	0.281683	+	0.265764i
$973$	5071.40			0.167093
$974$		−	42792.2i		−	1.40775i
$975$	38667.5	−	6354.99i	1.27010	−	0.208741i
$976$			18595.4i			0.609862i
$977$		−	53822.6i		−	1.76247i	−0.472676	−	0.881236i	$-0.656712\pi$
$977$		−	53822.6i		−	1.76247i	0.472676	−	0.881236i	$-0.343288\pi$
$978$	6185.98	+	37639.1i	0.202255	+	1.23064i
$979$			9116.84i			0.297626i
$980$	176.469			0.00575212
$981$	−12154.3	−	35978.0i	−0.395572	−	1.17094i
$982$		−	37923.0i		−	1.23236i
$983$	−44152.5			−1.43260			−0.716301	−	0.697792i	$-0.754166\pi$
$983$	−44152.5			−1.43260			−0.716301	+	0.697792i	$0.754166\pi$
$984$	−5385.44	−	32768.1i	−0.174473	−	1.06160i
$985$	448.403			0.0145049
$986$	−46910.3			−1.51514
$987$	−4424.19	−	26919.3i	−0.142678	−	0.868138i
$988$			22403.2i			0.721398i
$989$	−2439.81			−0.0784445
$990$	899.751	−	303.958i	0.0288848	−	0.00975800i
$991$		−	18835.8i		−	0.603773i	−0.953344	−	0.301886i	$-0.902384\pi$
$991$		−	18835.8i		−	0.603773i	0.953344	−	0.301886i	$-0.0976164\pi$
$992$			26904.5i			0.861109i
$993$	43089.2	−	7081.69i	1.37703	−	0.226315i
$994$	15542.0			0.495939
$995$	−482.769			−0.0153817
$996$	13934.2	−	2290.08i	0.443294	−	0.0728553i
$997$	−27234.5			−0.865121			−0.432561	−	0.901605i	$-0.642390\pi$
$997$	−27234.5			−0.865121			−0.432561	+	0.901605i	$0.642390\pi$
$998$		−	50038.1i		−	1.58710i
$999$	22192.9	+	41739.8i	0.702854	+	1.32191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.d.b.200.20	yes	64
3.2	odd	2	inner	201.4.d.b.200.46	yes	64
67.66	odd	2	inner	201.4.d.b.200.45	yes	64
201.200	even	2	inner	201.4.d.b.200.19	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.d.b.200.19	✓	64	201.200	even	2	inner
201.4.d.b.200.20	yes	64	1.1	even	1	trivial
201.4.d.b.200.45	yes	64	67.66	odd	2	inner
201.4.d.b.200.46	yes	64	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.33139 q^{2} +(0.842682 + 5.12737i) q^{3} +3.09813 q^{4} +0.324421 q^{5} +(-2.80730 - 17.0812i) q^{6} +12.9394i q^{7} +16.3300 q^{8} +(-25.5798 + 8.64147i) q^{9} +O(q^{10})\)	\(q-3.33139 q^{2} +(0.842682 + 5.12737i) q^{3} +3.09813 q^{4} +0.324421 q^{5} +(-2.80730 - 17.0812i) q^{6} +12.9394i q^{7} +16.3300 q^{8} +(-25.5798 + 8.64147i) q^{9} -1.08077 q^{10} +32.5456 q^{11} +(2.61074 + 15.8853i) q^{12} +60.3820i q^{13} -43.1060i q^{14} +(0.273383 + 1.66342i) q^{15} -79.1866 q^{16} +46.6474i q^{17} +(85.2161 - 28.7881i) q^{18} +119.758 q^{19} +1.00510 q^{20} +(-66.3448 + 10.9038i) q^{21} -108.422 q^{22} +30.7188i q^{23} +(13.7610 + 83.7299i) q^{24} -124.895 q^{25} -201.156i q^{26} +(-65.8636 - 123.875i) q^{27} +40.0878i q^{28} -301.867i q^{29} +(-0.910746 - 5.54151i) q^{30} +202.045i q^{31} +133.161 q^{32} +(27.4256 + 166.873i) q^{33} -155.401i q^{34} +4.19780i q^{35} +(-79.2496 + 26.7724i) q^{36} -336.952 q^{37} -398.959 q^{38} +(-309.600 + 50.8828i) q^{39} +5.29780 q^{40} -391.355 q^{41} +(221.020 - 36.3246i) q^{42} +79.4241i q^{43} +100.831 q^{44} +(-8.29861 + 2.80347i) q^{45} -102.336i q^{46} +405.749i q^{47} +(-66.7291 - 406.019i) q^{48} +175.573 q^{49} +416.073 q^{50} +(-239.178 + 39.3089i) q^{51} +187.071i q^{52} -695.253 q^{53} +(219.417 + 412.675i) q^{54} +10.5585 q^{55} +211.300i q^{56} +(100.917 + 614.041i) q^{57} +1005.64i q^{58} -642.905i q^{59} +(0.846979 + 5.15351i) q^{60} -234.830i q^{61} -673.089i q^{62} +(-111.815 - 330.986i) q^{63} +189.882 q^{64} +19.5892i q^{65} +(-91.3651 - 555.919i) q^{66} +(-164.961 + 523.021i) q^{67} +144.520i q^{68} +(-157.507 + 25.8862i) q^{69} -13.9845i q^{70} +360.554i q^{71} +(-417.718 + 141.115i) q^{72} +821.222 q^{73} +1122.52 q^{74} +(-105.247 - 640.381i) q^{75} +371.025 q^{76} +421.119i q^{77} +(1031.40 - 169.510i) q^{78} -768.991i q^{79} -25.6898 q^{80} +(579.650 - 442.094i) q^{81} +1303.75 q^{82} -877.176i q^{83} +(-205.545 + 33.7813i) q^{84} +15.1334i q^{85} -264.592i q^{86} +(1547.78 - 254.378i) q^{87} +531.470 q^{88} +280.125i q^{89} +(27.6459 - 9.33946i) q^{90} -781.303 q^{91} +95.1710i q^{92} +(-1035.96 + 170.259i) q^{93} -1351.71i q^{94} +38.8518 q^{95} +(112.212 + 682.766i) q^{96} +1203.97i q^{97} -584.902 q^{98} +(-832.509 + 281.242i) 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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