LMFDB - Embedded newform 200.4.f.b.149.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [200,4,Mod(149,200)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("200.149"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(200, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	200.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$11.8003820011$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{11} + 7x^{10} - 12x^{9} + 21x^{8} - 68x^{6} + 336x^{4} - 768x^{3} + 1792x^{2} - 4096x + 4096 $ x^12 - 4x^11 + 7x^10 - 12x^9 + 21x^8 - 68x^6 + 336x^4 - 768x^3 + 1792x^2 - 4096*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.8
Root			$1.71681 + 1.02595i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.4.f.b.149.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.690860 + 2.74276i) q^{2} +4.24443 q^{3} +(-7.04543 - 3.78972i) q^{4} +(-2.93231 + 11.6414i) q^{6} -14.6308i q^{7} +(15.2617 - 16.7057i) q^{8} -8.98481 q^{9} -14.9969i q^{11} +(-29.9038 - 16.0852i) q^{12} -85.6955 q^{13} +(40.1288 + 10.1078i) q^{14} +(35.2761 + 53.4004i) q^{16} -91.9247i q^{17} +(6.20724 - 24.6432i) q^{18} -60.3737i q^{19} -62.0995i q^{21} +(41.1330 + 10.3608i) q^{22} -1.33730i q^{23} +(64.7771 - 70.9063i) q^{24} +(59.2035 - 235.042i) q^{26} -152.735 q^{27} +(-55.4467 + 103.080i) q^{28} +25.5118i q^{29} +73.4354 q^{31} +(-170.835 + 59.8615i) q^{32} -63.6535i q^{33} +(252.127 + 63.5070i) q^{34} +(63.3018 + 34.0499i) q^{36} -211.259 q^{37} +(165.590 + 41.7098i) q^{38} -363.728 q^{39} +330.839 q^{41} +(170.324 + 42.9020i) q^{42} +388.500 q^{43} +(-56.8342 + 105.660i) q^{44} +(3.66788 + 0.923883i) q^{46} -550.348i q^{47} +(149.727 + 226.654i) q^{48} +128.939 q^{49} -390.168i q^{51} +(603.761 + 324.762i) q^{52} -187.705 q^{53} +(105.518 - 418.915i) q^{54} +(-244.419 - 223.291i) q^{56} -256.252i q^{57} +(-69.9727 - 17.6251i) q^{58} +779.090i q^{59} +358.850i q^{61} +(-50.7335 + 201.415i) q^{62} +131.455i q^{63} +(-46.1625 - 509.915i) q^{64} +(174.586 + 43.9756i) q^{66} +283.674 q^{67} +(-348.369 + 647.648i) q^{68} -5.67606i q^{69} -534.811 q^{71} +(-137.123 + 150.098i) q^{72} -1016.16i q^{73} +(145.950 - 579.431i) q^{74} +(-228.799 + 425.359i) q^{76} -219.418 q^{77} +(251.285 - 997.618i) q^{78} -1119.59 q^{79} -405.683 q^{81} +(-228.563 + 907.411i) q^{82} -1190.49 q^{83} +(-235.340 + 437.518i) q^{84} +(-268.399 + 1065.56i) q^{86} +108.283i q^{87} +(-250.535 - 228.879i) q^{88} +398.940 q^{89} +1253.80i q^{91} +(-5.06797 + 9.42182i) q^{92} +311.691 q^{93} +(1509.47 + 380.213i) q^{94} +(-725.097 + 254.078i) q^{96} +278.022i q^{97} +(-89.0787 + 353.648i) q^{98} +134.745i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 12 q^{3} - 16 q^{4} - 36 q^{6} + 24 q^{8} + 108 q^{9} + 164 q^{12} - 68 q^{14} - 56 q^{16} - 450 q^{18} - 492 q^{22} - 360 q^{24} - 308 q^{26} - 432 q^{27} - 628 q^{28} - 264 q^{31} - 856 q^{32}+ \cdots - 638 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 12 * q^3 - 16 * q^4 - 36 * q^6 + 24 * q^8 + 108 * q^9 + 164 * q^12 - 68 * q^14 - 56 * q^16 - 450 * q^18 - 492 * q^22 - 360 * q^24 - 308 * q^26 - 432 * q^27 - 628 * q^28 - 264 * q^31 - 856 * q^32 + 180 * q^34 + 440 * q^36 - 136 * q^37 + 1388 * q^38 - 600 * q^39 + 40 * q^41 + 2332 * q^42 + 1204 * q^43 + 472 * q^44 - 1268 * q^46 + 2536 * q^48 - 1308 * q^49 + 1272 * q^52 - 1056 * q^53 + 1512 * q^54 - 728 * q^56 - 1528 * q^58 - 2104 * q^62 + 2048 * q^64 + 2928 * q^66 + 2412 * q^67 - 960 * q^68 - 1592 * q^71 - 744 * q^72 + 420 * q^74 + 2256 * q^76 - 824 * q^77 + 160 * q^78 - 2016 * q^79 + 2508 * q^81 - 352 * q^82 - 3556 * q^83 - 1048 * q^84 - 244 * q^86 - 1008 * q^88 + 424 * q^89 - 1068 * q^92 - 2784 * q^93 - 292 * q^94 - 5920 * q^96 - 638 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−0.690860	+	2.74276i	−0.244256	+	0.969711i
$2$	−0.690860	+	2.74276i	−0.244256	+	0.969711i
$3$	4.24443			0.816841			0.408420	−	0.912794i	$-0.366080\pi$
$3$	4.24443			0.816841			0.408420	+	0.912794i	$0.366080\pi$
$4$	−7.04543	−	3.78972i	−0.880678	−	0.473715i
$5$		0			0
$5$		0			0
$6$	−2.93231	+	11.6414i	−0.199518	+	0.792100i
$7$		−	14.6308i		−	0.789990i	−0.918683	−	0.394995i	$-0.870746\pi$
$7$		−	14.6308i		−	0.789990i	0.918683	−	0.394995i	$-0.129254\pi$
$8$	15.2617	−	16.7057i	0.674477	−	0.738296i
$9$	−8.98481			−0.332771
$10$		0			0
$11$		−	14.9969i		−	0.411068i	−0.978650	−	0.205534i	$-0.934107\pi$
$11$		−	14.9969i		−	0.411068i	0.978650	−	0.205534i	$-0.0658931\pi$
$12$	−29.9038	−	16.0852i	−0.719374	−	0.386950i
$13$	−85.6955			−1.82828			−0.914140	−	0.405398i	$-0.867133\pi$
$13$	−85.6955			−1.82828			−0.914140	+	0.405398i	$0.867133\pi$
$14$	40.1288	+	10.1078i	0.766062	+	0.192960i
$15$		0			0
$16$	35.2761	+	53.4004i	0.551188	+	0.834381i
$17$		−	91.9247i		−	1.31147i	−0.754991	−	0.655735i	$-0.772359\pi$
$17$		−	91.9247i		−	1.31147i	0.754991	−	0.655735i	$-0.227641\pi$
$18$	6.20724	−	24.6432i	0.0812812	−	0.322691i
$19$		−	60.3737i		−	0.728983i	−0.931207	−	0.364492i	$-0.881243\pi$
$19$		−	60.3737i		−	0.728983i	0.931207	−	0.364492i	$-0.118757\pi$
$20$		0			0
$21$		−	62.0995i		−	0.645296i
$22$	41.1330	+	10.3608i	0.398617	+	0.100406i
$23$		−	1.33730i		−	0.0121237i	−0.999982	−	0.00606186i	$-0.998070\pi$
$23$		−	1.33730i		−	0.0121237i	0.999982	−	0.00606186i	$-0.00192956\pi$
$24$	64.7771	−	70.9063i	0.550941	−	0.603070i
$25$		0			0
$26$	59.2035	−	235.042i	0.446568	−	1.77290i
$27$	−152.735			−1.08866
$28$	−55.4467	+	103.080i	−0.374230	+	0.695727i
$29$			25.5118i			0.163360i	0.996659	+	0.0816798i	$0.0260285\pi$
$29$			25.5118i			0.163360i	−0.996659	+	0.0816798i	$0.973972\pi$
$30$		0			0
$31$	73.4354			0.425464			0.212732	−	0.977111i	$-0.431764\pi$
$31$	73.4354			0.425464			0.212732	+	0.977111i	$0.431764\pi$
$32$	−170.835	+	59.8615i	−0.943739	+	0.330691i
$33$		−	63.6535i		−	0.335777i
$34$	252.127	+	63.5070i	1.27175	+	0.320334i
$35$		0			0
$36$	63.3018	+	34.0499i	0.293064	+	0.157638i
$37$	−211.259			−0.938668			−0.469334	−	0.883021i	$-0.655506\pi$
$37$	−211.259			−0.938668			−0.469334	+	0.883021i	$0.655506\pi$
$38$	165.590	+	41.7098i	0.706903	+	0.178058i
$39$	−363.728			−1.49341
$40$		0			0
$41$	330.839			1.26020			0.630102	−	0.776512i	$-0.283013\pi$
$41$	330.839			1.26020			0.630102	+	0.776512i	$0.283013\pi$
$42$	170.324	+	42.9020i	0.625751	+	0.157617i
$43$	388.500			1.37781			0.688904	−	0.724853i	$-0.258092\pi$
$43$	388.500			1.37781			0.688904	+	0.724853i	$0.258092\pi$
$44$	−56.8342	+	105.660i	−0.194729	+	0.362019i
$45$		0			0
$46$	3.66788	+	0.923883i	0.0117565	+	0.00296129i
$47$		−	550.348i		−	1.70801i	−0.520265	−	0.854005i	$-0.674167\pi$
$47$		−	550.348i		−	1.70801i	0.520265	−	0.854005i	$-0.325833\pi$
$48$	149.727	+	226.654i	0.450233	+	0.681556i
$49$	128.939			0.375915
$50$		0			0
$51$		−	390.168i		−	1.07126i
$52$	603.761	+	324.762i	1.61013	+	0.866084i
$53$	−187.705			−0.486477			−0.243239	−	0.969966i	$-0.578210\pi$
$53$	−187.705			−0.486477			−0.243239	+	0.969966i	$0.578210\pi$
$54$	105.518	−	418.915i	0.265912	−	1.05569i
$55$		0			0
$56$	−244.419	−	223.291i	−0.583246	−	0.532830i
$57$		−	256.252i		−	0.595463i
$58$	−69.9727	−	17.6251i	−0.158412	−	0.0399015i
$59$			779.090i			1.71913i	0.511023	+	0.859567i	$0.329267\pi$
$59$			779.090i			1.71913i	−0.511023	+	0.859567i	$0.670733\pi$
$60$		0			0
$61$			358.850i			0.753215i	0.926373	+	0.376607i	$0.122909\pi$
$61$			358.850i			0.753215i	−0.926373	+	0.376607i	$0.877091\pi$
$62$	−50.7335	+	201.415i	−0.103922	+	0.412577i
$63$			131.455i			0.262886i
$64$	−46.1625	−	509.915i	−0.0901611	−	0.995927i
$65$		0			0
$66$	174.586	+	43.9756i	0.325607	+	0.0820155i
$67$	283.674			0.517258			0.258629	−	0.965977i	$-0.416729\pi$
$67$	283.674			0.517258			0.258629	+	0.965977i	$0.416729\pi$
$68$	−348.369	+	647.648i	−0.621263	+	1.15498i
$69$		−	5.67606i		−	0.00990315i
$70$		0			0
$71$	−534.811			−0.893949			−0.446975	−	0.894547i	$-0.647499\pi$
$71$	−534.811			−0.893949			−0.446975	+	0.894547i	$0.647499\pi$
$72$	−137.123	+	150.098i	−0.224446	+	0.245683i
$73$		−	1016.16i		−	1.62921i	−0.580014	−	0.814607i	$-0.696953\pi$
$73$		−	1016.16i		−	1.62921i	0.580014	−	0.814607i	$-0.303047\pi$
$74$	145.950	−	579.431i	0.229275	−	0.910237i
$75$		0			0
$76$	−228.799	+	425.359i	−0.345330	+	0.642000i
$77$	−219.418			−0.324740
$78$	251.285	−	997.618i	0.364775	−	1.44818i
$79$	−1119.59			−1.59447			−0.797237	−	0.603666i	$-0.793706\pi$
$79$	−1119.59			−1.59447			−0.797237	+	0.603666i	$0.793706\pi$
$80$		0			0
$81$	−405.683			−0.556493
$82$	−228.563	+	907.411i	−0.307812	+	1.22203i
$83$	−1190.49			−1.57437			−0.787186	−	0.616716i	$-0.788463\pi$
$83$	−1190.49			−1.57437			−0.787186	+	0.616716i	$0.788463\pi$
$84$	−235.340	+	437.518i	−0.305687	+	0.568299i
$85$		0			0
$86$	−268.399	+	1065.56i	−0.336537	+	1.33607i
$87$			108.283i			0.133439i
$88$	−250.535	−	228.879i	−0.303490	−	0.277256i
$89$	398.940			0.475141			0.237571	−	0.971370i	$-0.423649\pi$
$89$	398.940			0.475141			0.237571	+	0.971370i	$0.423649\pi$
$90$		0			0
$91$			1253.80i			1.44432i
$92$	−5.06797	+	9.42182i	−0.00574318	+	0.0106771i
$93$	311.691			0.347536
$94$	1509.47	+	380.213i	1.65628	+	0.417191i
$95$		0			0
$96$	−725.097	+	254.078i	−0.770885	+	0.270122i
$97$			278.022i			0.291019i	0.989357	+	0.145510i	$0.0464822\pi$
$97$			278.022i			0.291019i	−0.989357	+	0.145510i	$0.953518\pi$
$98$	−89.0787	+	353.648i	−0.0918195	+	0.364529i
$99$			134.745i			0.136791i
$100$		0			0
$101$		−	116.836i		−	0.115105i	−0.998342	−	0.0575523i	$-0.981670\pi$
$101$		−	116.836i		−	0.115105i	0.998342	−	0.0575523i	$-0.0183296\pi$
$102$	1070.14	+	269.551i	1.03882	+	0.261662i
$103$			1458.02i			1.39478i	0.716691	+	0.697391i	$0.245656\pi$
$103$			1458.02i			1.39478i	−0.716691	+	0.697391i	$0.754344\pi$
$104$	−1307.86	+	1431.60i	−1.23313	+	1.34981i
$105$		0			0
$106$	129.678	−	514.830i	0.118825	−	0.471742i
$107$	−695.124			−0.628039			−0.314020	−	0.949417i	$-0.601676\pi$
$107$	−695.124			−0.628039			−0.314020	+	0.949417i	$0.601676\pi$
$108$	1076.08	+	578.823i	0.958761	+	0.515715i
$109$		−	191.775i		−	0.168520i	−0.996444	−	0.0842602i	$-0.973147\pi$
$109$		−	191.775i		−	0.168520i	0.996444	−	0.0842602i	$-0.0268527\pi$
$110$		0			0
$111$	−896.673			−0.766743
$112$	781.292	−	516.118i	0.659153	−	0.435434i
$113$		−	1234.25i		−	1.02751i	−0.857938	−	0.513753i	$-0.828255\pi$
$113$		−	1234.25i		−	1.02751i	0.857938	−	0.513753i	$-0.171745\pi$
$114$	702.837	+	177.034i	0.577427	+	0.145445i
$115$		0			0
$116$	96.6827	−	179.742i	0.0773859	−	0.143867i
$117$	769.958			0.608398
$118$	−2136.85	−	538.242i	−1.66706	−	0.419908i
$119$	−1344.93			−1.03605
$120$		0			0
$121$	1106.09			0.831023
$122$	−984.239	−	247.915i	−0.730400	−	0.183977i
$123$	1404.22			1.02939
$124$	−517.384	−	278.299i	−0.374697	−	0.201549i
$125$		0			0
$126$	−360.550	−	90.8171i	−0.254923	−	0.0642114i
$127$			786.958i			0.549852i	0.961465	+	0.274926i	$0.0886534\pi$
$127$			786.958i			0.549852i	−0.961465	+	0.274926i	$0.911347\pi$
$128$	1430.46	+	225.667i	0.987784	+	0.155831i
$129$	1648.96			1.12545
$130$		0			0
$131$		−	28.0441i		−	0.0187040i	−0.999956	−	0.00935201i	$-0.997023\pi$
$131$		−	28.0441i		−	0.0187040i	0.999956	−	0.00935201i	$-0.00297688\pi$
$132$	−241.229	+	448.466i	−0.159063	+	0.295712i
$133$	−883.317			−0.575890
$134$	−195.979	+	778.048i	−0.126343	+	0.501590i
$135$		0			0
$136$	−1535.67	−	1402.92i	−0.968253	−	0.884557i
$137$		−	71.4326i		−	0.0445467i	−0.999752	−	0.0222733i	$-0.992910\pi$
$137$		−	71.4326i		−	0.0445467i	0.999752	−	0.0222733i	$-0.00709041\pi$
$138$	15.5680	+	3.92136i	0.00960319	+	0.00241890i
$139$		−	2343.99i		−	1.43032i	−0.698961	−	0.715160i	$-0.746354\pi$
$139$		−	2343.99i		−	1.43032i	0.698961	−	0.715160i	$-0.253646\pi$
$140$		0			0
$141$		−	2335.91i		−	1.39517i
$142$	369.479	−	1466.86i	0.218352	−	0.866872i
$143$			1285.17i			0.751548i
$144$	−316.949	−	479.792i	−0.183419	−	0.277658i
$145$		0			0
$146$	2787.08	+	702.024i	1.57987	+	0.397945i
$147$	547.272			0.307063
$148$	1488.41	+	800.611i	0.826665	+	0.444661i
$149$		−	1417.40i		−	0.779315i	−0.920960	−	0.389657i	$-0.872593\pi$
$149$		−	1417.40i		−	0.779315i	0.920960	−	0.389657i	$-0.127407\pi$
$150$		0			0
$151$	1296.61			0.698786			0.349393	−	0.936976i	$-0.386388\pi$
$151$	1296.61			0.698786			0.349393	+	0.936976i	$0.386388\pi$
$152$	−1008.59	−	921.404i	−0.538205	−	0.491683i
$153$			825.926i			0.436419i
$154$	151.587	−	601.809i	0.0793196	−	0.314904i
$155$		0			0
$156$	2562.62	+	1378.43i	1.31522	+	0.707453i
$157$	2002.41			1.01790			0.508948	−	0.860797i	$-0.330034\pi$
$157$	2002.41			1.01790			0.508948	+	0.860797i	$0.330034\pi$
$158$	773.478	−	3070.76i	0.389459	−	1.54618i
$159$	−796.702			−0.397375
$160$		0			0
$161$	−19.5657			−0.00957762
$162$	280.270	−	1112.69i	0.135927	−	0.539637i
$163$	163.315			0.0784774			0.0392387	−	0.999230i	$-0.487507\pi$
$163$	163.315			0.0784774			0.0392387	+	0.999230i	$0.487507\pi$
$164$	−2330.90	−	1253.79i	−1.10983	−	0.596977i
$165$		0			0
$166$	822.459	−	3265.21i	0.384549	−	1.52669i
$167$		−	243.412i		−	0.112789i	−0.998409	−	0.0563945i	$-0.982040\pi$
$167$		−	243.412i		−	0.112789i	0.998409	−	0.0563945i	$-0.0179604\pi$
$168$	−1037.42	−	947.743i	−0.476420	−	0.435238i
$169$	5146.71			2.34261
$170$		0			0
$171$			542.447i			0.242584i
$172$	−2737.15	−	1472.31i	−1.21341	−	0.652688i
$173$	1955.73			0.859490			0.429745	−	0.902950i	$-0.358604\pi$
$173$	1955.73			0.859490			0.429745	+	0.902950i	$0.358604\pi$
$174$	−296.994	−	74.8085i	−0.129397	−	0.0325932i
$175$		0			0
$176$	800.842	−	529.033i	0.342987	−	0.226576i
$177$			3306.79i			1.40426i
$178$	−275.611	+	1094.20i	−0.116056	+	0.460749i
$179$			3978.28i			1.66118i	0.556887	+	0.830588i	$0.311995\pi$
$179$			3978.28i			1.66118i	−0.556887	+	0.830588i	$0.688005\pi$
$180$		0			0
$181$		−	964.412i		−	0.396045i	−0.980197	−	0.198022i	$-0.936548\pi$
$181$		−	964.412i		−	0.396045i	0.980197	−	0.198022i	$-0.0634519\pi$
$182$	−3438.86	−	866.197i	−1.40058	−	0.352784i
$183$			1523.12i			0.615256i
$184$	−22.3405	−	20.4094i	−0.00895089	−	0.00817717i
$185$		0			0
$186$	−215.335	+	854.894i	−0.0848878	+	0.337010i
$187$	−1378.59			−0.539104
$188$	−2085.66	+	3877.43i	−0.809110	+	1.50421i
$189$			2234.64i			0.860032i
$190$		0			0
$191$	−908.237			−0.344072			−0.172036	−	0.985091i	$-0.555035\pi$
$191$	−908.237			−0.344072			−0.172036	+	0.985091i	$0.555035\pi$
$192$	−195.933	−	2164.30i	−0.0736473	−	0.813514i
$193$		−	1243.86i		−	0.463910i	−0.972727	−	0.231955i	$-0.925488\pi$
$193$		−	1243.86i		−	0.463910i	0.972727	−	0.231955i	$-0.0745122\pi$
$194$	−762.547	−	192.074i	−0.282205	−	0.0710831i
$195$		0			0
$196$	−908.430	−	488.642i	−0.331060	−	0.178077i
$197$	−1884.72			−0.681627			−0.340813	−	0.940131i	$-0.610702\pi$
$197$	−1884.72			−0.681627			−0.340813	+	0.940131i	$0.610702\pi$
$198$	−369.572	−	93.0897i	−0.132648	−	0.0334121i
$199$	3886.45			1.38444			0.692219	−	0.721688i	$-0.256633\pi$
$199$	3886.45			1.38444			0.692219	+	0.721688i	$0.256633\pi$
$200$		0			0
$201$	1204.03			0.422517
$202$	320.452	+	80.7170i	0.111618	+	0.0281150i
$203$	373.259			0.129052
$204$	−1478.63	+	2748.90i	−0.507473	+	0.943438i
$205$		0			0
$206$	−3998.98	−	1007.28i	−1.35254	−	0.340684i
$207$			12.0154i			0.00403442i
$208$	−3023.00	−	4576.17i	−1.00773	−	1.52548i
$209$	−905.421			−0.299662
$210$		0			0
$211$		−	3282.65i		−	1.07103i	−0.844527	−	0.535514i	$-0.820118\pi$
$211$		−	3282.65i		−	1.07103i	0.844527	−	0.535514i	$-0.179882\pi$
$212$	1322.46	+	711.350i	0.428430	+	0.230451i
$213$	−2269.97			−0.730214
$214$	480.233	−	1906.56i	0.153402	−	0.609016i
$215$		0			0
$216$	−2330.99	+	2551.55i	−0.734278	+	0.803754i
$217$		−	1074.42i		−	0.336112i
$218$	525.992	+	132.490i	0.163416	+	0.0411621i
$219$		−	4313.02i		−	1.33081i
$220$		0			0
$221$			7877.53i			2.39774i
$222$	619.475	−	2459.36i	0.187281	−	0.743519i
$223$		−	1453.07i		−	0.436343i	−0.975910	−	0.218171i	$-0.929991\pi$
$223$		−	1453.07i		−	0.436343i	0.975910	−	0.218171i	$-0.0700092\pi$
$224$	875.823	+	2499.46i	0.261243	+	0.745545i
$225$		0			0
$226$	3385.24	+	852.691i	0.996383	+	0.250974i
$227$	4750.20			1.38891			0.694454	−	0.719537i	$-0.255646\pi$
$227$	4750.20			1.38891			0.694454	+	0.719537i	$0.255646\pi$
$228$	−971.123	+	1805.40i	−0.282080	+	0.524412i
$229$		−	6475.51i		−	1.86862i	−0.356462	−	0.934310i	$-0.616017\pi$
$229$		−	6475.51i		−	1.86862i	0.356462	−	0.934310i	$-0.383983\pi$
$230$		0			0
$231$	−931.303			−0.265261
$232$	426.194	+	389.353i	0.120608	+	0.110182i
$233$		−	257.988i		−	0.0725379i	−0.999342	−	0.0362690i	$-0.988453\pi$
$233$		−	257.988i		−	0.0725379i	0.999342	−	0.0362690i	$-0.0115473\pi$
$234$	−531.933	+	2111.81i	−0.148605	+	0.589971i
$235$		0			0
$236$	2952.53	−	5489.02i	0.814379	−	1.51400i
$237$	−4752.01			−1.30243
$238$	929.160	−	3688.83i	0.253061	−	1.00467i
$239$	257.014			0.0695600			0.0347800	−	0.999395i	$-0.488927\pi$
$239$	257.014			0.0695600			0.0347800	+	0.999395i	$0.488927\pi$
$240$		0			0
$241$	1194.01			0.319140			0.159570	−	0.987187i	$-0.448989\pi$
$241$	1194.01			0.319140			0.159570	+	0.987187i	$0.448989\pi$
$242$	−764.154	+	3033.74i	−0.202982	+	0.805852i
$243$	2401.95			0.634096
$244$	1359.94	−	2528.25i	0.356809	−	0.663340i
$245$		0			0
$246$	−970.121	+	3851.44i	−0.251434	+	0.998207i
$247$			5173.75i			1.33279i
$248$	1120.75	−	1226.79i	0.286966	−	0.314118i
$249$	−5052.94			−1.28601
$250$		0			0
$251$		−	587.080i		−	0.147634i	−0.997272	−	0.0738171i	$-0.976482\pi$
$251$		−	587.080i		−	0.147634i	0.997272	−	0.0738171i	$-0.0235181\pi$
$252$	498.178	−	926.158i	0.124533	−	0.231518i
$253$	−20.0553			−0.00498367
$254$	−2158.43	−	543.677i	−0.533198	−	0.134305i
$255$		0			0
$256$	−1607.20	+	3767.51i	−0.392383	+	0.919802i
$257$		−	791.436i		−	0.192095i	−0.995377	−	0.0960475i	$-0.969380\pi$
$257$		−	791.436i		−	0.192095i	0.995377	−	0.0960475i	$-0.0306201\pi$
$258$	−1139.20	+	4522.70i	−0.274898	+	1.09136i
$259$			3090.89i			0.741539i
$260$		0			0
$261$		−	229.219i		−	0.0543613i
$262$	76.9182	+	19.3746i	0.0181375	+	0.00456856i
$263$		−	2705.80i		−	0.634398i	−0.948359	−	0.317199i	$-0.897258\pi$
$263$		−	2705.80i		−	0.634398i	0.948359	−	0.317199i	$-0.102742\pi$
$264$	−1063.38	−	971.459i	−0.247903	−	0.226474i
$265$		0			0
$266$	610.248	−	2422.72i	0.140664	−	0.558446i
$267$	1693.27			0.388115
$268$	−1998.60	−	1075.04i	−0.455538	−	0.245033i
$269$			2767.26i			0.627222i	0.949552	+	0.313611i	$0.101539\pi$
$269$			2767.26i			0.627222i	−0.949552	+	0.313611i	$0.898461\pi$
$270$		0			0
$271$	400.361			0.0897423			0.0448712	−	0.998993i	$-0.485712\pi$
$271$	400.361			0.0897423			0.0448712	+	0.998993i	$0.485712\pi$
$272$	4908.81	−	3242.74i	1.09427	−	0.722868i
$273$			5321.65i			1.17978i
$274$	195.922	+	49.3499i	0.0431974	+	0.0108808i
$275$		0			0
$276$	−21.5107	+	39.9902i	−0.00469127	+	0.00872149i
$277$	6743.86			1.46281			0.731407	−	0.681942i	$-0.238864\pi$
$277$	6743.86			1.46281			0.731407	+	0.681942i	$0.238864\pi$
$278$	6428.99	+	1619.37i	1.38700	+	0.349364i
$279$	−659.803			−0.141582
$280$		0			0
$281$	−6373.81			−1.35313			−0.676565	−	0.736382i	$-0.736532\pi$
$281$	−6373.81			−1.35313			−0.676565	+	0.736382i	$0.736532\pi$
$282$	6406.84	+	1613.79i	1.35291	+	0.340779i
$283$	−2383.90			−0.500736			−0.250368	−	0.968151i	$-0.580552\pi$
$283$	−2383.90			−0.500736			−0.250368	+	0.968151i	$0.580552\pi$
$284$	3767.97	+	2026.78i	0.787281	+	0.423477i
$285$		0			0
$286$	−3524.91	−	887.872i	−0.728784	−	0.183570i
$287$		−	4840.45i		−	0.995549i
$288$	1534.92	−	537.844i	0.314049	−	0.110044i
$289$	−3537.14			−0.719956
$290$		0			0
$291$			1180.05i			0.237717i
$292$	−3850.96	+	7159.28i	−0.771783	+	1.43481i
$293$	−748.528			−0.149247			−0.0746237	−	0.997212i	$-0.523776\pi$
$293$	−748.528			−0.149247			−0.0746237	+	0.997212i	$0.523776\pi$
$294$	−378.088	+	1501.03i	−0.0750019	+	0.297762i
$295$		0			0
$296$	−3224.16	+	3529.23i	−0.633110	+	0.693015i
$297$			2290.56i			0.447514i
$298$	3887.58	+	979.224i	0.755710	+	0.190352i
$299$			114.600i			0.0221655i
$300$		0			0
$301$		−	5684.08i		−	1.08845i
$302$	−895.776	+	3556.29i	−0.170683	+	0.677621i
$303$		−	495.900i		−	0.0940222i
$304$	3223.98	−	2129.75i	0.608250	−	0.401807i
$305$		0			0
$306$	−2265.31	−	570.599i	−0.423200	−	0.106598i
$307$	−2639.75			−0.490745			−0.245372	−	0.969429i	$-0.578910\pi$
$307$	−2639.75			−0.490745			−0.245372	+	0.969429i	$0.578910\pi$
$308$	1545.89	+	831.531i	0.285991	+	0.153834i
$309$			6188.45i			1.13932i
$310$		0			0
$311$	−2880.46			−0.525196			−0.262598	−	0.964905i	$-0.584579\pi$
$311$	−2880.46			−0.525196			−0.262598	+	0.964905i	$0.584579\pi$
$312$	−5551.11	+	6076.35i	−1.00727	+	1.10258i
$313$			3620.24i			0.653763i	0.945065	+	0.326882i	$0.105998\pi$
$313$			3620.24i			0.653763i	−0.945065	+	0.326882i	$0.894002\pi$
$314$	−1383.38	+	5492.12i	−0.248627	+	0.987065i
$315$		0			0
$316$	7887.97	+	4242.92i	1.40422	+	0.755326i
$317$	2066.64			0.366164			0.183082	−	0.983098i	$-0.441393\pi$
$317$	2066.64			0.366164			0.183082	+	0.983098i	$0.441393\pi$
$318$	550.409	−	2185.16i	0.0970610	−	0.385338i
$319$	382.599			0.0671519
$320$		0			0
$321$	−2950.41			−0.513008
$322$	13.5172	−	53.6641i	0.00233939	−	0.00928752i
$323$	−5549.83			−0.956040
$324$	2858.21	+	1537.43i	0.490091	+	0.263619i
$325$		0			0
$326$	−112.828	+	447.933i	−0.0191686	+	0.0761004i
$327$		−	813.976i		−	0.137654i
$328$	5049.16	−	5526.91i	0.849979	−	0.930403i
$329$	−8052.04			−1.34931
$330$		0			0
$331$			3193.53i			0.530309i	0.964206	+	0.265155i	$0.0854230\pi$
$331$			3193.53i			0.530309i	−0.964206	+	0.265155i	$0.914577\pi$
$332$	8387.48	+	4511.61i	1.38651	+	0.745803i
$333$	1898.12			0.312361
$334$	667.619	+	168.163i	0.109373	+	0.0275493i
$335$		0			0
$336$	3316.14	−	2190.63i	0.538423	−	0.355680i
$337$		−	7803.01i		−	1.26130i	−0.776068	−	0.630649i	$-0.782789\pi$
$337$		−	7803.01i		−	1.26130i	0.776068	−	0.630649i	$-0.217211\pi$
$338$	−3555.66	+	14116.2i	−0.572196	+	2.27165i
$339$		−	5238.67i		−	0.839309i
$340$		0			0
$341$		−	1101.31i		−	0.174895i
$342$	−1487.80	−	374.754i	−0.235237	−	0.0592526i
$343$		−	6904.86i		−	1.08696i
$344$	5929.16	−	6490.18i	0.929300	−	1.01723i
$345$		0			0
$346$	−1351.14	+	5364.10i	−0.209935	+	0.833456i
$347$	−9098.25			−1.40755			−0.703775	−	0.710423i	$-0.748504\pi$
$347$	−9098.25			−1.40755			−0.703775	+	0.710423i	$0.748504\pi$
$348$	410.363	−	762.901i	0.0632119	−	0.117517i
$349$			8700.89i			1.33452i	0.744824	+	0.667261i	$0.232533\pi$
$349$			8700.89i			1.33452i	−0.744824	+	0.667261i	$0.767467\pi$
$350$		0			0
$351$	13088.7			1.99038
$352$	897.739	+	2562.00i	0.135937	+	0.387941i
$353$		−	1182.38i		−	0.178276i	−0.996019	−	0.0891382i	$-0.971589\pi$
$353$		−	1182.38i		−	0.178276i	0.996019	−	0.0891382i	$-0.0284113\pi$
$354$	−9069.73	−	2284.53i	−1.36172	−	0.342998i
$355$		0			0
$356$	−2810.70	−	1511.87i	−0.418446	−	0.225081i
$357$	−5708.48			−0.846288
$358$	−10911.4	−	2748.43i	−1.61086	−	0.405752i
$359$	7514.20			1.10469			0.552346	−	0.833615i	$-0.313733\pi$
$359$	7514.20			1.10469			0.552346	+	0.833615i	$0.313733\pi$
$360$		0			0
$361$	3214.01			0.468584
$362$	2645.15	+	666.273i	0.384049	+	0.0967363i
$363$	4694.73			0.678814
$364$	4751.53	−	8833.52i	0.684198	−	1.27198i
$365$		0			0
$366$	−4177.53	−	1052.26i	−0.596621	−	0.150280i
$367$		−	7217.04i		−	1.02650i	−0.858238	−	0.513251i	$-0.828441\pi$
$367$		−	7217.04i		−	1.02650i	0.858238	−	0.513251i	$-0.171559\pi$
$368$	71.4121	−	47.1745i	0.0101158	−	0.00668245i
$369$	−2972.53			−0.419359
$370$		0			0
$371$			2746.28i			0.384312i
$372$	−2196.00	−	1181.22i	−0.306068	−	0.164633i
$373$	−2350.20			−0.326244			−0.163122	−	0.986606i	$-0.552156\pi$
$373$	−2350.20			−0.326244			−0.163122	+	0.986606i	$0.552156\pi$
$374$	952.411	−	3781.13i	0.131679	−	0.522775i
$375$		0			0
$376$	−9193.96	−	8399.23i	−1.26102	−	1.15201i
$377$		−	2186.25i		−	0.298667i
$378$	−6129.07	−	1543.82i	−0.833983	−	0.210068i
$379$			3493.78i			0.473518i	0.971568	+	0.236759i	$0.0760852\pi$
$379$			3493.78i			0.473518i	−0.971568	+	0.236759i	$0.923915\pi$
$380$		0			0
$381$			3340.19i			0.449142i
$382$	627.464	−	2491.07i	0.0840415	−	0.333650i
$383$		−	14241.7i		−	1.90004i	−0.312191	−	0.950019i	$-0.601063\pi$
$383$		−	14241.7i		−	1.90004i	0.312191	−	0.950019i	$-0.398937\pi$
$384$	6071.50	+	957.828i	0.806862	+	0.127289i
$385$		0			0
$386$	3411.59	+	859.329i	0.449859	+	0.113313i
$387$	−3490.60			−0.458494
$388$	1053.63	−	1958.78i	0.137860	−	0.256294i
$389$		−	7518.81i		−	0.979997i	−0.871723	−	0.489998i	$-0.836997\pi$
$389$		−	7518.81i		−	0.979997i	0.871723	−	0.489998i	$-0.163003\pi$
$390$		0			0
$391$	−122.930			−0.0158999
$392$	1967.82	−	2154.02i	0.253546	−	0.277537i
$393$		−	119.031i		−	0.0152782i
$394$	1302.07	−	5169.32i	0.166491	−	0.660981i
$395$		0			0
$396$	510.645	−	949.334i	0.0648002	−	0.120469i
$397$	−4665.28			−0.589782			−0.294891	−	0.955531i	$-0.595283\pi$
$397$	−4665.28			−0.589782			−0.294891	+	0.955531i	$0.595283\pi$
$398$	−2684.99	+	10659.6i	−0.338157	+	1.34250i
$399$	−3749.18			−0.470410
$400$		0			0
$401$	−3094.11			−0.385318			−0.192659	−	0.981266i	$-0.561711\pi$
$401$	−3094.11			−0.385318			−0.192659	+	0.981266i	$0.561711\pi$
$402$	−831.818	+	3302.37i	−0.103202	+	0.409720i
$403$	−6293.08			−0.777867
$404$	−442.774	+	823.156i	−0.0545268	+	0.101370i
$405$		0			0
$406$	−257.870	+	1023.76i	−0.0315218	+	0.125144i
$407$			3168.24i			0.385857i
$408$	−6518.04	−	5954.61i	−0.790909	−	0.722543i
$409$	−7341.17			−0.887525			−0.443762	−	0.896144i	$-0.646357\pi$
$409$	−7341.17			−0.887525			−0.443762	+	0.896144i	$0.646357\pi$
$410$		0			0
$411$		−	303.191i		−	0.0363876i
$412$	5525.47	−	10272.3i	0.660729	−	1.22835i
$413$	11398.7			1.35810
$414$	−32.9552	−	8.30092i	−0.00391222	−	0.000985430i
$415$		0			0
$416$	14639.8	−	5129.86i	1.72542	−	0.604596i
$417$		−	9948.90i		−	1.16834i
$418$	625.519	−	2483.35i	0.0731941	−	0.290585i
$419$		−	6193.33i		−	0.722110i	−0.932544	−	0.361055i	$-0.882417\pi$
$419$		−	6193.33i		−	0.722110i	0.932544	−	0.361055i	$-0.117583\pi$
$420$		0			0
$421$		−	4266.62i		−	0.493925i	−0.969025	−	0.246962i	$-0.920568\pi$
$421$		−	4266.62i		−	0.493925i	0.969025	−	0.246962i	$-0.0794324\pi$
$422$	9003.50	+	2267.85i	1.03859	+	0.261605i
$423$			4944.77i			0.568376i
$424$	−2864.70	+	3135.75i	−0.328118	+	0.359164i
$425$		0			0
$426$	1568.23	−	6225.97i	0.178359	−	0.708097i
$427$	5250.28			0.595032
$428$	4897.45	+	2634.33i	0.553100	+	0.297511i
$429$			5454.81i			0.613895i
$430$		0			0
$431$	−328.807			−0.0367473			−0.0183736	−	0.999831i	$-0.505849\pi$
$431$	−328.807			−0.0367473			−0.0183736	+	0.999831i	$0.505849\pi$
$432$	−5387.89	−	8156.11i	−0.600058	−	0.908359i
$433$			6914.22i			0.767382i	0.923462	+	0.383691i	$0.125347\pi$
$433$			6914.22i			0.767382i	−0.923462	+	0.383691i	$0.874653\pi$
$434$	2946.87	+	742.274i	0.325932	+	0.0820974i
$435$		0			0
$436$	−726.774	+	1351.14i	−0.0798306	+	0.148412i
$437$	−80.7375			−0.00883798
$438$	11829.6	+	2979.69i	1.29050	+	0.325058i
$439$	11922.4			1.29619			0.648093	−	0.761562i	$-0.275567\pi$
$439$	11922.4			1.29619			0.648093	+	0.761562i	$0.275567\pi$
$440$		0			0
$441$	−1158.49			−0.125094
$442$	−21606.1	−	5442.26i	−2.32511	−	0.585661i
$443$	−6687.54			−0.717234			−0.358617	−	0.933485i	$-0.616752\pi$
$443$	−6687.54			−0.717234			−0.358617	+	0.933485i	$0.616752\pi$
$444$	6317.44	+	3398.14i	0.675254	+	0.363217i
$445$		0			0
$446$	3985.41	+	1003.86i	0.423126	+	0.106579i
$447$		−	6016.05i		−	0.636576i
$448$	−7460.47	+	675.395i	−0.786773	+	0.0712264i
$449$	−3761.85			−0.395396			−0.197698	−	0.980263i	$-0.563347\pi$
$449$	−3761.85			−0.395396			−0.197698	+	0.980263i	$0.563347\pi$
$450$		0			0
$451$		−	4961.57i		−	0.518030i
$452$	−4677.45	+	8695.79i	−0.486745	+	0.904902i
$453$	5503.38			0.570797
$454$	−3281.72	+	13028.7i	−0.339249	+	1.34684i
$455$		0			0
$456$	−4280.88	−	3910.84i	−0.439628	−	0.401626i
$457$			957.270i			0.0979852i	0.998799	+	0.0489926i	$0.0156011\pi$
$457$			957.270i			0.0979852i	−0.998799	+	0.0489926i	$0.984399\pi$
$458$	17760.8	+	4473.67i	1.81202	+	0.456421i
$459$			14040.1i			1.42775i
$460$		0			0
$461$		−	2903.76i		−	0.293365i	−0.989184	−	0.146683i	$-0.953140\pi$
$461$		−	2903.76i		−	0.293365i	0.989184	−	0.146683i	$-0.0468596\pi$
$462$	643.400	−	2554.34i	0.0647915	−	0.257226i
$463$			6265.25i			0.628879i	0.949278	+	0.314440i	$0.101817\pi$
$463$			6265.25i			0.628879i	−0.949278	+	0.314440i	$0.898183\pi$
$464$	−1362.34	+	899.957i	−0.136304	+	0.0900419i
$465$		0			0
$466$	707.597	+	178.233i	0.0703408	+	0.0177178i
$467$	−4895.67			−0.485107			−0.242553	−	0.970138i	$-0.577985\pi$
$467$	−4895.67			−0.485107			−0.242553	+	0.970138i	$0.577985\pi$
$468$	−5424.68	−	2917.92i	−0.535803	−	0.288207i
$469$		−	4150.38i		−	0.408629i
$470$		0			0
$471$	8499.09			0.831460
$472$	13015.3	+	11890.2i	1.26923	+	1.15952i
$473$		−	5826.32i		−	0.566373i
$474$	3282.97	−	13033.6i	0.318126	−	1.26298i
$475$		0			0
$476$	9475.63	+	5096.92i	0.912426	+	0.490792i
$477$	1686.50			0.161885
$478$	−177.560	+	704.926i	−0.0169904	+	0.0674531i
$479$	5684.05			0.542194			0.271097	−	0.962552i	$-0.412614\pi$
$479$	5684.05			0.542194			0.271097	+	0.962552i	$0.412614\pi$
$480$		0			0
$481$	18103.9			1.71615
$482$	−824.892	+	3274.87i	−0.0779518	+	0.309474i
$483$	−83.0454			−0.00782339
$484$	−7792.89	−	4191.78i	−0.731864	−	0.393668i
$485$		0			0
$486$	−1659.41	+	6587.97i	−0.154882	+	0.614890i
$487$			16399.6i			1.52595i	0.646430	+	0.762973i	$0.276261\pi$
$487$			16399.6i			1.52595i	−0.646430	+	0.762973i	$0.723739\pi$
$488$	5994.86	+	5476.66i	0.556095	+	0.508026i
$489$	693.179			0.0641036
$490$		0			0
$491$		−	10721.8i		−	0.985472i	−0.870179	−	0.492736i	$-0.835997\pi$
$491$		−	10721.8i		−	0.985472i	0.870179	−	0.492736i	$-0.164003\pi$
$492$	−9893.35	−	5321.61i	−0.906558	−	0.487636i
$493$	2345.17			0.214241
$494$	−14190.3	−	3574.34i	−1.29242	−	0.325541i
$495$		0			0
$496$	2590.51	+	3921.48i	0.234511	+	0.354999i
$497$			7824.73i			0.706211i
$498$	3490.87	−	13859.0i	0.314116	−	1.24706i
$499$		−	11116.5i		−	0.997281i	−0.866809	−	0.498640i	$-0.833833\pi$
$499$		−	11116.5i		−	0.997281i	0.866809	−	0.498640i	$-0.166167\pi$
$500$		0			0
$501$		−	1033.14i		−	0.0921306i
$502$	1610.22	+	405.590i	0.143162	+	0.0360605i
$503$			6432.33i			0.570186i	0.958500	+	0.285093i	$0.0920245\pi$
$503$			6432.33i			0.570186i	−0.958500	+	0.285093i	$0.907976\pi$
$504$	2196.05	+	2006.23i	0.194087	+	0.177310i
$505$		0			0
$506$	13.8554	−	55.0069i	0.00121729	−	0.00483272i
$507$	21844.9			1.91354
$508$	2982.35	−	5544.45i	0.260473	−	0.484243i
$509$		−	9622.35i		−	0.837924i	−0.908004	−	0.418962i	$-0.862394\pi$
$509$		−	9622.35i		−	0.837924i	0.908004	−	0.418962i	$-0.137606\pi$
$510$		0			0
$511$	−14867.3			−1.28706
$512$	−9223.01	−	7010.98i	−0.796100	−	0.605165i
$513$			9221.18i			0.793616i
$514$	2170.72	+	546.771i	0.186277	+	0.0469203i
$515$		0			0
$516$	−11617.6	−	6249.10i	−0.991159	−	0.533142i
$517$	−8253.53			−0.702108
$518$	−8477.56	−	2135.37i	−0.719078	−	0.181125i
$519$	8300.98			0.702066
$520$		0			0
$521$	−19725.1			−1.65868			−0.829338	−	0.558747i	$-0.811282\pi$
$521$	−19725.1			−1.65868			−0.829338	+	0.558747i	$0.811282\pi$
$522$	628.692	+	158.358i	0.0527147	+	0.0132781i
$523$	4068.08			0.340123			0.170062	−	0.985433i	$-0.445603\pi$
$523$	4068.08			0.340123			0.170062	+	0.985433i	$0.445603\pi$
$524$	−106.279	+	197.583i	−0.00886037	+	0.0164722i
$525$		0			0
$526$	7421.35	+	1869.33i	0.615183	+	0.154955i
$527$		−	6750.52i		−	0.557984i
$528$	3399.12	−	2245.44i	0.280166	−	0.185077i
$529$	12165.2			0.999853
$530$		0			0
$531$		−	6999.98i		−	0.572078i
$532$	6223.35	+	3347.52i	0.507174	+	0.272808i
$533$	−28351.4			−2.30401
$534$	−1169.81	+	4644.23i	−0.0947992	+	0.376359i
$535$		0			0
$536$	4329.34	−	4738.98i	0.348878	−	0.381889i
$537$			16885.5i			1.35692i
$538$	−7589.92	−	1911.79i	−0.608224	−	0.153203i
$539$		−	1933.69i		−	0.154527i
$540$		0			0
$541$			13192.1i			1.04837i	0.851603	+	0.524187i	$0.175631\pi$
$541$			13192.1i			1.04837i	−0.851603	+	0.524187i	$0.824369\pi$
$542$	−276.593	+	1098.09i	−0.0219201	+	0.0870241i
$543$		−	4093.38i		−	0.323506i
$544$	5502.75	+	15704.0i	0.433692	+	1.23769i
$545$		0			0
$546$	−14596.0	−	3676.51i	−1.14405	−	0.288169i
$547$	2125.25			0.166123			0.0830614	−	0.996544i	$-0.473530\pi$
$547$	2125.25			0.166123			0.0830614	+	0.996544i	$0.473530\pi$
$548$	−270.709	+	503.273i	−0.0211024	+	0.0392313i
$549$		−	3224.20i		−	0.250648i
$550$		0			0
$551$	1540.24			0.119086
$552$	−94.8227	−	86.6262i	−0.00731145	−	0.00667945i
$553$			16380.5i			1.25962i
$554$	−4659.06	+	18496.8i	−0.357301	+	1.41851i
$555$		0			0
$556$	−8883.06	+	16514.4i	−0.677564	+	1.25965i
$557$	18387.1			1.39872			0.699360	−	0.714769i	$-0.253468\pi$
$557$	18387.1			1.39872			0.699360	+	0.714769i	$0.253468\pi$
$558$	455.831	−	1809.68i	0.0345822	−	0.137294i
$559$	−33292.7			−2.51902
$560$		0			0
$561$	−5851.32			−0.440362
$562$	4403.41	−	17481.8i	0.330510	−	1.31215i
$563$	22098.7			1.65426			0.827132	−	0.562008i	$-0.189971\pi$
$563$	22098.7			1.65426			0.827132	+	0.562008i	$0.189971\pi$
$564$	−8852.45	+	16457.5i	−0.660914	+	1.22870i
$565$		0			0
$566$	1646.94	−	6538.46i	0.122308	−	0.485569i
$567$			5935.48i			0.439624i
$568$	−8162.11	+	8934.40i	−0.602948	+	0.659999i
$569$	19489.2			1.43591			0.717954	−	0.696091i	$-0.245079\pi$
$569$	19489.2			1.43591			0.717954	+	0.696091i	$0.245079\pi$
$570$		0			0
$571$			1501.40i			0.110038i	0.998485	+	0.0550189i	$0.0175219\pi$
$571$			1501.40i			0.110038i	−0.998485	+	0.0550189i	$0.982478\pi$
$572$	4870.43	−	9054.57i	0.356019	−	0.661872i
$573$	−3854.95			−0.281052
$574$	13276.2	+	3344.07i	0.965395	+	0.243169i
$575$		0			0
$576$	414.761	+	4581.49i	0.0300030	+	0.331416i
$577$			15875.8i			1.14544i	0.819753	+	0.572718i	$0.194111\pi$
$577$			15875.8i			1.14544i	−0.819753	+	0.572718i	$0.805889\pi$
$578$	2443.67	−	9701.52i	0.175853	−	0.698149i
$579$		−	5279.46i		−	0.378941i
$580$		0			0
$581$			17417.8i			1.24374i
$582$	−3236.58	−	815.246i	−0.230516	−	0.0580636i
$583$			2815.00i			0.199975i
$584$	−16975.7	−	15508.3i	−1.20284	−	1.09887i
$585$		0			0
$586$	517.128	−	2053.03i	0.0364545	−	0.144727i
$587$	−5444.12			−0.382799			−0.191399	−	0.981512i	$-0.561303\pi$
$587$	−5444.12			−0.382799			−0.191399	+	0.981512i	$0.561303\pi$
$588$	−3855.77	−	2074.01i	−0.270424	−	0.145460i
$589$		−	4433.57i		−	0.310156i
$590$		0			0
$591$	−7999.55			−0.556781
$592$	−7452.38	−	11281.3i	−0.517383	−	0.783207i
$593$		−	28383.8i		−	1.96557i	−0.184744	−	0.982787i	$-0.559146\pi$
$593$		−	28383.8i		−	1.96557i	0.184744	−	0.982787i	$-0.440854\pi$
$594$	−6282.45	−	1582.45i	−0.433959	−	0.109308i
$595$		0			0
$596$	−5371.55	+	9986.18i	−0.369173	+	0.686326i
$597$	16495.8			1.13087
$598$	−314.320	−	79.1726i	−0.0214942	−	0.00541406i
$599$	2045.77			0.139546			0.0697729	−	0.997563i	$-0.477773\pi$
$599$	2045.77			0.139546			0.0697729	+	0.997563i	$0.477773\pi$
$600$		0			0
$601$	13847.5			0.939851			0.469926	−	0.882706i	$-0.344281\pi$
$601$	13847.5			0.939851			0.469926	+	0.882706i	$0.344281\pi$
$602$	15590.0	+	3926.90i	1.05549	+	0.265861i
$603$	−2548.76			−0.172128
$604$	−9135.18	−	4913.79i	−0.615406	−	0.331025i
$605$		0			0
$606$	1360.13	+	342.598i	0.0911744	+	0.0229655i
$607$			11611.0i			0.776405i	0.921574	+	0.388202i	$0.126904\pi$
$607$			11611.0i			0.776405i	−0.921574	+	0.388202i	$0.873096\pi$
$608$	3614.06	+	10313.9i	0.241068	+	0.687970i
$609$	1584.27			0.105415
$610$		0			0
$611$			47162.3i			3.12272i
$612$	3130.03	−	5819.00i	0.206738	−	0.384345i
$613$	21644.9			1.42615			0.713076	−	0.701087i	$-0.247301\pi$
$613$	21644.9			1.42615			0.713076	+	0.701087i	$0.247301\pi$
$614$	1823.70	−	7240.20i	0.119867	−	0.475881i
$615$		0			0
$616$	−3348.68	+	3665.53i	−0.219030	+	0.239754i
$617$		−	3432.62i		−	0.223974i	−0.993710	−	0.111987i	$-0.964278\pi$
$617$		−	3432.62i		−	0.223974i	0.993710	−	0.111987i	$-0.0357215\pi$
$618$	−16973.4	−	4275.35i	−1.10481	−	0.278284i
$619$			2936.25i			0.190659i	0.995446	+	0.0953295i	$0.0303905\pi$
$619$			2936.25i			0.190659i	−0.995446	+	0.0953295i	$0.969610\pi$
$620$		0			0
$621$			204.252i			0.0131986i
$622$	1989.99	−	7900.40i	0.128282	−	0.509288i
$623$		−	5836.82i		−	0.375357i
$624$	−12830.9	−	19423.2i	−0.823153	−	1.24608i
$625$		0			0
$626$	−9929.43	−	2501.08i	−0.633961	−	0.159685i
$627$	−3843.00			−0.244776
$628$	−14107.8	−	7588.57i	−0.896439	−	0.482193i
$629$			19419.9i			1.23104i
$630$		0			0
$631$	−18455.3			−1.16433			−0.582167	−	0.813069i	$-0.697795\pi$
$631$	−18455.3			−1.16433			−0.582167	+	0.813069i	$0.697795\pi$
$632$	−17086.8	+	18703.5i	−1.07544	+	1.17719i
$633$		−	13933.0i		−	0.874859i
$634$	−1427.76	+	5668.28i	−0.0894376	+	0.355073i
$635$		0			0
$636$	5613.10	+	3019.28i	0.349959	+	0.188242i
$637$	−11049.5			−0.687278
$638$	−264.323	+	1049.38i	−0.0164022	+	0.0651179i
$639$	4805.18			0.297480
$640$		0			0
$641$	−14764.4			−0.909761			−0.454880	−	0.890552i	$-0.650318\pi$
$641$	−14764.4			−0.909761			−0.454880	+	0.890552i	$0.650318\pi$
$642$	2038.32	−	8092.25i	0.125305	−	0.497470i
$643$	21285.4			1.30547			0.652733	−	0.757588i	$-0.273622\pi$
$643$	21285.4			1.30547			0.652733	+	0.757588i	$0.273622\pi$
$644$	137.849	+	74.1487i	0.00843480	+	0.00453706i
$645$		0			0
$646$	3834.16	−	15221.8i	0.233518	−	0.927083i
$647$			18831.7i			1.14428i	0.820156	+	0.572140i	$0.193887\pi$
$647$			18831.7i			1.14428i	−0.820156	+	0.572140i	$0.806113\pi$
$648$	−6191.41	+	6777.23i	−0.375342	+	0.410856i
$649$	11684.0			0.706681
$650$		0			0
$651$		−	4560.30i		−	0.274550i
$652$	−1150.62	−	618.918i	−0.0691134	−	0.0371759i
$653$	−26184.9			−1.56921			−0.784605	−	0.619996i	$-0.787134\pi$
$653$	−26184.9			−1.56921			−0.784605	+	0.619996i	$0.787134\pi$
$654$	2232.54	+	562.343i	0.133485	+	0.0336229i
$655$		0			0
$656$	11670.7	+	17666.9i	0.694610	+	1.05149i
$657$			9130.01i			0.542155i
$658$	5562.83	−	22084.8i	0.329577	−	1.30844i
$659$			5338.89i			0.315590i	0.987472	+	0.157795i	$0.0504385\pi$
$659$			5338.89i			0.315590i	−0.987472	+	0.157795i	$0.949561\pi$
$660$		0			0
$661$		−	23161.9i		−	1.36293i	−0.731852	−	0.681464i	$-0.761344\pi$
$661$		−	23161.9i		−	1.36293i	0.731852	−	0.681464i	$-0.238656\pi$
$662$	−8759.08	−	2206.28i	−0.514247	−	0.129531i
$663$			33435.6i			1.95857i
$664$	−18168.8	+	19887.9i	−1.06188	+	1.16235i
$665$		0			0
$666$	−1311.33	+	5206.08i	−0.0762961	+	0.302900i
$667$	34.1169			0.00198052
$668$	−922.461	+	1714.94i	−0.0534298	+	0.0993308i
$669$		−	6167.44i		−	0.356423i
$670$		0			0
$671$	5381.66			0.309622
$672$	3717.37	+	10608.8i	0.213394	+	0.608991i
$673$		−	3571.25i		−	0.204549i	−0.994756	−	0.102275i	$-0.967388\pi$
$673$		−	3571.25i		−	0.204549i	0.994756	−	0.102275i	$-0.0326121\pi$
$674$	21401.8	+	5390.79i	1.22309	+	0.308079i
$675$		0			0
$676$	−36260.8	−	19504.6i	−2.06308	−	1.10973i
$677$	−1010.61			−0.0573721			−0.0286861	−	0.999588i	$-0.509132\pi$
$677$	−1010.61			−0.0573721			−0.0286861	+	0.999588i	$0.509132\pi$
$678$	14368.4	+	3619.19i	0.813887	+	0.205006i
$679$	4067.69			0.229902
$680$		0			0
$681$	20161.9			1.13452
$682$	3020.62	+	760.848i	0.169597	+	0.0427190i
$683$	−24805.2			−1.38967			−0.694836	−	0.719168i	$-0.744523\pi$
$683$	−24805.2			−1.38967			−0.694836	+	0.719168i	$0.744523\pi$
$684$	2055.72	−	3821.77i	0.114916	−	0.213639i
$685$		0			0
$686$	18938.3	+	4770.29i	1.05404	+	0.265496i
$687$		−	27484.9i		−	1.52637i
$688$	13704.8	+	20746.1i	0.759431	+	1.14962i
$689$	16085.5			0.889417
$690$		0			0
$691$		−	12948.4i		−	0.712854i	−0.934323	−	0.356427i	$-0.883995\pi$
$691$		−	12948.4i		−	0.712854i	0.934323	−	0.356427i	$-0.116005\pi$
$692$	−13779.0	−	7411.68i	−0.756934	−	0.407153i
$693$	1971.43			0.108064
$694$	6285.61	−	24954.3i	0.343802	−	1.36492i
$695$		0			0
$696$	1808.95	+	1652.58i	0.0985173	+	0.0900014i
$697$		−	30412.3i		−	1.65272i
$698$	−23864.4	−	6011.09i	−1.29410	−	0.325965i
$699$		−	1095.01i		−	0.0592519i
$700$		0			0
$701$		−	27490.7i		−	1.48118i	−0.671954	−	0.740592i	$-0.734545\pi$
$701$		−	27490.7i		−	1.48118i	0.671954	−	0.740592i	$-0.265455\pi$
$702$	−9042.45	+	35899.1i	−0.486161	+	1.93009i
$703$			12754.5i			0.684273i
$704$	−7647.16	+	692.296i	−0.409394	+	0.0370623i
$705$		0			0
$706$	3242.97	+	816.856i	0.172877	+	0.0435450i
$707$	−1709.40			−0.0909316
$708$	12531.8	−	23297.8i	0.665218	−	1.23670i
$709$		−	11490.7i		−	0.608663i	−0.952566	−	0.304332i	$-0.901567\pi$
$709$		−	11490.7i		−	0.608663i	0.952566	−	0.304332i	$-0.0984331\pi$
$710$		0			0
$711$	10059.3			0.530595
$712$	6088.49	−	6664.58i	0.320472	−	0.350795i
$713$		−	98.2048i		−	0.00515820i
$714$	3943.76	−	15657.0i	0.206711	−	0.820654i
$715$		0			0
$716$	15076.6	−	28028.7i	0.786924	−	1.46296i
$717$	1090.88			0.0568195
$718$	−5191.26	+	20609.6i	−0.269827	+	1.07123i
$719$	−30178.1			−1.56530			−0.782652	−	0.622459i	$-0.786134\pi$
$719$	−30178.1			−1.56530			−0.782652	+	0.622459i	$0.786134\pi$
$720$		0			0
$721$	21332.0			1.10186
$722$	−2220.43	+	8815.26i	−0.114454	+	0.454391i
$723$	5067.88			0.260687
$724$	−3654.85	+	6794.69i	−0.187612	+	0.348788i
$725$		0			0
$726$	−3243.40	+	12876.5i	−0.165804	+	0.658253i
$727$			24019.3i			1.22535i	0.790336	+	0.612674i	$0.209906\pi$
$727$			24019.3i			1.22535i	−0.790336	+	0.612674i	$0.790094\pi$
$728$	20945.6	+	19135.0i	1.06634	+	0.974163i
$729$	21148.4			1.07445
$730$		0			0
$731$		−	35712.7i		−	1.80695i
$732$	5772.18	−	10731.0i	0.291456	−	0.541843i
$733$	14231.8			0.717142			0.358571	−	0.933502i	$-0.383264\pi$
$733$	14231.8			0.717142			0.358571	+	0.933502i	$0.383264\pi$
$734$	19794.6	+	4985.96i	0.995411	+	0.250729i
$735$		0			0
$736$	80.0525	+	228.457i	0.00400920	+	0.0114416i
$737$		−	4254.24i		−	0.212628i
$738$	2053.60	−	8152.92i	0.102431	−	0.406657i
$739$			34171.8i			1.70099i	0.525985	+	0.850494i	$0.323697\pi$
$739$			34171.8i			1.70099i	−0.525985	+	0.850494i	$0.676303\pi$
$740$		0			0
$741$			21959.6i			1.08867i
$742$	−7532.38	−	1897.30i	−0.372672	−	0.0938705i
$743$			1648.56i			0.0813994i	0.999171	+	0.0406997i	$0.0129587\pi$
$743$			1648.56i			0.0813994i	−0.999171	+	0.0406997i	$0.987041\pi$
$744$	4756.93	−	5207.03i	0.234405	−	0.256585i
$745$		0			0
$746$	1623.66	−	6446.04i	0.0796870	−	0.316362i
$747$	10696.3			0.523905
$748$	9712.75	+	5224.47i	0.474777	+	0.255382i
$749$			10170.2i			0.496145i
$750$		0			0
$751$	7622.18			0.370356			0.185178	−	0.982705i	$-0.440714\pi$
$751$	7622.18			0.370356			0.185178	+	0.982705i	$0.440714\pi$
$752$	29388.8	−	19414.1i	1.42513	−	0.941435i
$753$		−	2491.82i		−	0.120594i
$754$	5996.35	+	1510.39i	0.289621	+	0.0729512i
$755$		0			0
$756$	8468.66	−	15744.0i	0.407410	−	0.757412i
$757$	−1436.99			−0.0689939			−0.0344970	−	0.999405i	$-0.510983\pi$
$757$	−1436.99			−0.0689939			−0.0344970	+	0.999405i	$0.510983\pi$
$758$	−9582.59	−	2413.71i	−0.459176	−	0.115660i
$759$	−85.1235			−0.00407087
$760$		0			0
$761$	−4491.30			−0.213942			−0.106971	−	0.994262i	$-0.534115\pi$
$761$	−4491.30			−0.213942			−0.106971	+	0.994262i	$0.534115\pi$
$762$	−9161.32	−	2307.60i	−0.435538	−	0.109705i
$763$	−2805.83			−0.133129
$764$	6398.92	+	3441.96i	0.303017	+	0.162992i
$765$		0			0
$766$	39061.4	+	9838.99i	1.84249	+	0.464095i
$767$		−	66764.5i		−	3.14306i
$768$	−6821.64	+	15990.9i	−0.320514	+	0.751332i
$769$	−7977.22			−0.374078			−0.187039	−	0.982353i	$-0.559889\pi$
$769$	−7977.22			−0.374078			−0.187039	+	0.982353i	$0.559889\pi$
$770$		0			0
$771$		−	3359.19i		−	0.156911i
$772$	−4713.86	+	8763.49i	−0.219761	+	0.408556i
$773$	21972.3			1.02237			0.511183	−	0.859472i	$-0.329208\pi$
$773$	21972.3			1.02237			0.511183	+	0.859472i	$0.329208\pi$
$774$	2411.52	−	9573.87i	0.111990	−	0.444607i
$775$		0			0
$776$	4644.56	+	4243.08i	0.214858	+	0.196286i
$777$			13119.1i			0.605719i
$778$	20622.3	+	5194.44i	0.950314	+	0.239370i
$779$		−	19974.0i		−	0.918668i
$780$		0			0
$781$			8020.53i			0.367474i
$782$	84.9277	−	337.168i	0.00388364	−	0.0154183i
$783$		−	3896.55i		−	0.177843i
$784$	4548.46	+	6885.39i	0.207200	+	0.313656i
$785$		0			0
$786$	326.474	+	82.2339i	0.0148154	+	0.00373179i
$787$	−14770.5			−0.669010			−0.334505	−	0.942394i	$-0.608569\pi$
$787$	−14770.5			−0.669010			−0.334505	+	0.942394i	$0.608569\pi$
$788$	13278.6	+	7142.54i	0.600294	+	0.322897i
$789$		−	11484.6i		−	0.518203i
$790$		0			0
$791$	−18058.0			−0.811720
$792$	2251.01	+	2056.43i	0.100993	+	0.0922627i
$793$		−	30751.8i		−	1.37709i
$794$	3223.05	−	12795.7i	0.144058	−	0.571918i
$795$		0			0
$796$	−27381.7	−	14728.5i	−1.21924	−	0.655829i
$797$	−33342.5			−1.48187			−0.740936	−	0.671576i	$-0.765618\pi$
$797$	−33342.5			−1.48187			−0.740936	+	0.671576i	$0.765618\pi$
$798$	2590.16	−	10283.1i	0.114900	−	0.456162i
$799$	−50590.5			−2.24001
$800$		0			0
$801$	−3584.40			−0.158113
$802$	2137.60	−	8486.39i	0.0941161	−	0.373647i
$803$	−15239.3			−0.669718
$804$	−8482.93	−	4562.95i	−0.372102	−	0.200153i
$805$		0			0
$806$	4347.63	−	17260.4i	0.189999	−	0.754307i
$807$			11745.4i			0.512341i
$808$	−1951.82	−	1783.11i	−0.0849813	−	0.0776355i
$809$	−27061.3			−1.17605			−0.588026	−	0.808842i	$-0.700095\pi$
$809$	−27061.3			−1.17605			−0.588026	+	0.808842i	$0.700095\pi$
$810$		0			0
$811$			36672.2i			1.58784i	0.608025	+	0.793918i	$0.291962\pi$
$811$			36672.2i			1.58784i	−0.608025	+	0.793918i	$0.708038\pi$
$812$	−2629.77	−	1414.55i	−0.113654	−	0.0611341i
$813$	1699.30			0.0733052
$814$	−8689.70	−	2188.81i	−0.374169	−	0.0942477i
$815$		0			0
$816$	20835.1	−	13763.6i	0.893841	−	0.590468i
$817$		−	23455.2i		−	1.00440i
$818$	5071.72	−	20135.0i	0.216783	−	0.860642i
$819$		−	11265.1i		−	0.480629i
$820$		0			0
$821$		−	24984.9i		−	1.06209i	−0.847342	−	0.531047i	$-0.821799\pi$
$821$		−	24984.9i		−	1.06209i	0.847342	−	0.531047i	$-0.178201\pi$
$822$	831.578	+	209.462i	0.0352854	+	0.00888787i
$823$			30397.5i			1.28747i	0.765247	+	0.643737i	$0.222617\pi$
$823$			30397.5i			1.28747i	−0.765247	+	0.643737i	$0.777383\pi$
$824$	24357.2	+	22251.8i	1.02976	+	0.940749i
$825$		0			0
$826$	−7874.92	+	31263.9i	−0.331723	+	1.31696i
$827$	−21641.5			−0.909972			−0.454986	−	0.890498i	$-0.650356\pi$
$827$	−21641.5			−0.909972			−0.454986	+	0.890498i	$0.650356\pi$
$828$	45.5348	−	84.6533i	0.00191116	−	0.00355302i
$829$		−	36955.2i		−	1.54826i	−0.633028	−	0.774129i	$-0.718188\pi$
$829$		−	36955.2i		−	1.54826i	0.633028	−	0.774129i	$-0.281812\pi$
$830$		0			0
$831$	28623.8			1.19489
$832$	3955.91	+	43697.4i	0.164840	+	1.82083i
$833$		−	11852.7i		−	0.493002i
$834$	27287.4	+	6873.29i	1.13296	+	0.285375i
$835$		0			0
$836$	6379.08	+	3431.29i	0.263906	+	0.141954i
$837$	−11216.2			−0.463186
$838$	16986.8	+	4278.72i	0.700238	+	0.176380i
$839$	4786.98			0.196978			0.0984891	−	0.995138i	$-0.468599\pi$
$839$	4786.98			0.196978			0.0984891	+	0.995138i	$0.468599\pi$
$840$		0			0
$841$	23738.1			0.973314
$842$	11702.3	+	2947.63i	0.478964	+	0.120644i
$843$	−27053.2			−1.10529
$844$	−12440.3	+	23127.6i	−0.507362	+	0.943230i
$845$		0			0
$846$	−13562.3	−	3416.14i	−0.551160	−	0.138829i
$847$		−	16183.0i		−	0.656500i
$848$	−6621.50	−	10023.5i	−0.268141	−	0.405907i
$849$	−10118.3			−0.409021
$850$		0			0
$851$			282.515i			0.0113801i
$852$	15992.9	+	8602.54i	0.643084	+	0.345913i
$853$	4074.67			0.163557			0.0817785	−	0.996651i	$-0.473940\pi$
$853$	4074.67			0.163557			0.0817785	+	0.996651i	$0.473940\pi$
$854$	−3627.20	+	14400.2i	−0.145340	+	0.577009i
$855$		0			0
$856$	−10608.8	+	11612.6i	−0.423598	+	0.463679i
$857$		−	6011.57i		−	0.239616i	−0.992797	−	0.119808i	$-0.961772\pi$
$857$		−	6011.57i		−	0.239616i	0.992797	−	0.119808i	$-0.0382280\pi$
$858$	−14961.2	−	3768.51i	−0.595301	−	0.149947i
$859$			16761.1i			0.665752i	0.942971	+	0.332876i	$0.108019\pi$
$859$			16761.1i			0.665752i	−0.942971	+	0.332876i	$0.891981\pi$
$860$		0			0
$861$		−	20544.9i		−	0.813205i
$862$	227.159	−	901.837i	0.00897573	−	0.0356342i
$863$		−	25926.9i		−	1.02267i	−0.859382	−	0.511334i	$-0.829152\pi$
$863$		−	25926.9i		−	1.02267i	0.859382	−	0.511334i	$-0.170848\pi$
$864$	26092.5	−	9142.95i	1.02741	−	0.360011i
$865$		0			0
$866$	−18964.0	−	4776.76i	−0.744138	−	0.187437i
$867$	−15013.2			−0.588089
$868$	−4071.75	+	7569.75i	−0.159221	+	0.296007i
$869$			16790.4i			0.655438i
$870$		0			0
$871$	−24309.6			−0.945692
$872$	−3203.74	−	2926.81i	−0.124418	−	0.113663i
$873$		−	2497.98i		−	0.0968427i
$874$	55.7783	−	221.443i	0.00215873	−	0.00857029i
$875$		0			0
$876$	−16345.1	+	30387.1i	−0.630424	+	1.17201i
$877$	26838.9			1.03339			0.516697	−	0.856169i	$-0.327161\pi$
$877$	26838.9			1.03339			0.516697	+	0.856169i	$0.327161\pi$
$878$	−8236.71	+	32700.3i	−0.316601	+	1.25692i
$879$	−3177.08			−0.121911
$880$		0			0
$881$	−16191.5			−0.619190			−0.309595	−	0.950869i	$-0.600193\pi$
$881$	−16191.5			−0.619190			−0.309595	+	0.950869i	$0.600193\pi$
$882$	800.355	−	3177.46i	0.0305548	−	0.121305i
$883$	−22021.1			−0.839263			−0.419631	−	0.907695i	$-0.637841\pi$
$883$	−22021.1			−0.839263			−0.419631	+	0.907695i	$0.637841\pi$
$884$	29853.6	−	55500.5i	1.13584	−	2.11163i
$885$		0			0
$886$	4620.15	−	18342.3i	0.175189	−	0.695510i
$887$		−	8897.22i		−	0.336797i	−0.985719	−	0.168399i	$-0.946140\pi$
$887$		−	8897.22i		−	0.336797i	0.985719	−	0.168399i	$-0.0538596\pi$
$888$	−13684.7	+	14979.6i	−0.517151	+	0.566083i
$889$	11513.8			0.434378
$890$		0			0
$891$			6084.01i			0.228756i
$892$	−5506.71	+	10237.5i	−0.206702	+	0.384278i
$893$	−33226.5			−1.24511
$894$	16500.6	+	4156.25i	0.617295	+	0.155487i
$895$		0			0
$896$	3301.70	−	20928.9i	0.123105	−	0.780340i
$897$			486.412i			0.0181057i
$898$	2598.91	−	10317.8i	0.0965777	−	0.383420i
$899$			1873.47i			0.0695036i
$900$		0			0
$901$			17254.7i			0.638001i
$902$	13608.4	+	3427.75i	0.502339	+	0.126532i
$903$		−	24125.7i		−	0.889094i
$904$	−20619.0	−	18836.7i	−0.758603	−	0.693029i
$905$		0			0
$906$	−3802.06	+	15094.4i	−0.139420	+	0.553508i
$907$	15822.5			0.579246			0.289623	−	0.957141i	$-0.406470\pi$
$907$	15822.5			0.579246			0.289623	+	0.957141i	$0.406470\pi$
$908$	−33467.2	−	18001.9i	−1.22318	−	0.657946i
$909$			1049.75i			0.0383035i
$910$		0			0
$911$	4136.51			0.150438			0.0752188	−	0.997167i	$-0.476034\pi$
$911$	4136.51			0.150438			0.0752188	+	0.997167i	$0.476034\pi$
$912$	13684.0	−	9039.56i	0.496843	−	0.328212i
$913$			17853.7i			0.647174i
$914$	−2625.56	−	661.339i	−0.0950173	−	0.0239334i
$915$		0			0
$916$	−24540.4	+	45622.7i	−0.885193	+	1.64565i
$917$	−410.309			−0.0147760
$918$	−38508.6	−	9699.75i	−1.38450	−	0.348736i
$919$	8655.85			0.310697			0.155348	−	0.987860i	$-0.450350\pi$
$919$	8655.85			0.310697			0.155348	+	0.987860i	$0.450350\pi$
$920$		0			0
$921$	−11204.2			−0.400860
$922$	7964.30	+	2006.09i	0.284480	+	0.0716562i
$923$	45830.9			1.63439
$924$	6561.43	+	3529.38i	0.233609	+	0.125658i
$925$		0			0
$926$	−17184.1	−	4328.41i	−0.609831	−	0.153607i
$927$		−	13100.0i		−	0.464143i
$928$	−1527.18	−	4358.31i	−0.0540216	−	0.154169i
$929$	19787.3			0.698817			0.349409	−	0.936970i	$-0.386382\pi$
$929$	19787.3			0.698817			0.349409	+	0.936970i	$0.386382\pi$
$930$		0			0
$931$		−	7784.52i		−	0.274036i
$932$	−977.701	+	1817.63i	−0.0343623	+	0.0638826i
$933$	−12225.9			−0.429002
$934$	3382.22	−	13427.6i	0.118490	−	0.470413i
$935$		0			0
$936$	11750.8	−	12862.7i	0.410351	−	0.449178i
$937$		−	21427.2i		−	0.747061i	−0.927618	−	0.373531i	$-0.878147\pi$
$937$		−	21427.2i		−	0.747061i	0.927618	−	0.373531i	$-0.121853\pi$
$938$	11383.5	+	2867.33i	0.396252	+	0.0998099i
$939$			15365.8i			0.534021i
$940$		0			0
$941$			40905.9i			1.41710i	0.705659	+	0.708552i	$0.250651\pi$
$941$			40905.9i			1.41710i	−0.705659	+	0.708552i	$0.749349\pi$
$942$	−5871.68	+	23310.9i	−0.203089	+	0.806275i
$943$		−	442.430i		−	0.0152784i
$944$	−41603.7	+	27483.2i	−1.43441	+	0.947567i
$945$		0			0
$946$	15980.2	+	4025.17i	0.549218	+	0.138340i
$947$	4430.18			0.152019			0.0760093	−	0.997107i	$-0.475782\pi$
$947$	4430.18			0.152019			0.0760093	+	0.997107i	$0.475782\pi$
$948$	33480.0	+	18008.8i	1.14702	+	0.616981i
$949$			87080.3i			2.97866i
$950$		0			0
$951$	8771.69			0.299097
$952$	−20525.9	+	22468.1i	−0.698792	+	0.764911i
$953$			12381.1i			0.420844i	0.977611	+	0.210422i	$0.0674839\pi$
$953$			12381.1i			0.420844i	−0.977611	+	0.210422i	$0.932516\pi$
$954$	−1165.13	+	4625.65i	−0.0395414	+	0.156982i
$955$		0			0
$956$	−1810.77	−	974.010i	−0.0612600	−	0.0329516i
$957$	1623.92			0.0548524
$958$	−3926.88	+	15590.0i	−0.132434	+	0.525771i
$959$	−1045.12			−0.0351915
$960$		0			0
$961$	−24398.2			−0.818980
$962$	−12507.3	+	49654.6i	−0.419179	+	1.66417i
$963$	6245.56			0.208993
$964$	−8412.29	−	4524.95i	−0.281060	−	0.151181i
$965$		0			0
$966$	57.3727	−	227.773i	0.00191091	−	0.00758643i
$967$			51294.8i			1.70582i	0.522056	+	0.852911i	$0.325165\pi$
$967$			51294.8i			1.70582i	−0.522056	+	0.852911i	$0.674835\pi$
$968$	16880.8	−	18478.1i	0.560506	−	0.613541i
$969$	−23555.9			−0.780933
$970$		0			0
$971$			11036.3i			0.364750i	0.983229	+	0.182375i	$0.0583785\pi$
$971$			11036.3i			0.364750i	−0.983229	+	0.182375i	$0.941621\pi$
$972$	−16922.8	−	9102.72i	−0.558434	−	0.300381i
$973$	−34294.5			−1.12994
$974$	−44980.1	−	11329.8i	−1.47973	−	0.372721i
$975$		0			0
$976$	−19162.7	+	12658.8i	−0.628468	+	0.415163i
$977$			24788.2i			0.811713i	0.913937	+	0.405857i	$0.133027\pi$
$977$			24788.2i			0.811713i	−0.913937	+	0.405857i	$0.866973\pi$
$978$	−478.890	+	1901.22i	−0.0156577	+	0.0621619i
$979$		−	5982.88i		−	0.195315i
$980$		0			0
$981$			1723.06i			0.0560787i
$982$	29407.2	+	7407.24i	0.955623	+	0.240707i
$983$		−	28853.0i		−	0.936183i	−0.883680	−	0.468091i	$-0.844942\pi$
$983$		−	28853.0i		−	0.936183i	0.883680	−	0.468091i	$-0.155058\pi$
$984$	21430.8	−	23458.6i	0.694298	−	0.759992i
$985$		0			0
$986$	−1620.18	+	6432.22i	−0.0523297	+	0.207752i
$987$	−34176.3			−1.10217
$988$	19607.1	−	36451.3i	0.631360	−	1.17376i
$989$		−	519.540i		−	0.0167041i
$990$		0			0
$991$	−50061.0			−1.60468			−0.802342	−	0.596865i	$-0.796413\pi$
$991$	−50061.0			−1.60468			−0.802342	+	0.596865i	$0.796413\pi$
$992$	−12545.3	+	4395.95i	−0.401527	+	0.140697i
$993$			13554.7i			0.433178i
$994$	−21461.3	−	5405.79i	−0.684821	−	0.172496i
$995$		0			0
$996$	35600.1	+	19149.2i	1.13256	+	0.609203i
$997$	−7718.06			−0.245169			−0.122584	−	0.992458i	$-0.539118\pi$
$997$	−7718.06			−0.245169			−0.122584	+	0.992458i	$0.539118\pi$
$998$	30489.9	+	7679.94i	0.967074	+	0.243592i
$999$	32266.6			1.02189

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.4.f.b.149.8		12
4.3	odd	2		800.4.f.c.49.4		12
5.2	odd	4		200.4.d.b.101.1		12
5.3	odd	4		40.4.d.a.21.12	yes	12
5.4	even	2		200.4.f.c.149.5		12
8.3	odd	2		800.4.f.b.49.10		12
8.5	even	2		200.4.f.c.149.6		12
15.8	even	4		360.4.k.c.181.1		12
20.3	even	4		160.4.d.a.81.4		12
20.7	even	4		800.4.d.d.401.9		12
20.19	odd	2		800.4.f.b.49.9		12
40.3	even	4		160.4.d.a.81.9		12
40.13	odd	4		40.4.d.a.21.11	✓	12
40.19	odd	2		800.4.f.c.49.3		12
40.27	even	4		800.4.d.d.401.4		12
40.29	even	2	inner	200.4.f.b.149.7		12
40.37	odd	4		200.4.d.b.101.2		12
60.23	odd	4		1440.4.k.c.721.11		12
80.3	even	4		1280.4.a.ba.1.5		6
80.13	odd	4		1280.4.a.bc.1.2		6
80.43	even	4		1280.4.a.bd.1.2		6
80.53	odd	4		1280.4.a.bb.1.5		6
120.53	even	4		360.4.k.c.181.2		12
120.83	odd	4		1440.4.k.c.721.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.d.a.21.11	✓	12	40.13	odd	4
40.4.d.a.21.12	yes	12	5.3	odd	4
160.4.d.a.81.4		12	20.3	even	4
160.4.d.a.81.9		12	40.3	even	4
200.4.d.b.101.1		12	5.2	odd	4
200.4.d.b.101.2		12	40.37	odd	4
200.4.f.b.149.7		12	40.29	even	2	inner
200.4.f.b.149.8		12	1.1	even	1	trivial
200.4.f.c.149.5		12	5.4	even	2
200.4.f.c.149.6		12	8.5	even	2
360.4.k.c.181.1		12	15.8	even	4
360.4.k.c.181.2		12	120.53	even	4
800.4.d.d.401.4		12	40.27	even	4
800.4.d.d.401.9		12	20.7	even	4
800.4.f.b.49.9		12	20.19	odd	2
800.4.f.b.49.10		12	8.3	odd	2
800.4.f.c.49.3		12	40.19	odd	2
800.4.f.c.49.4		12	4.3	odd	2
1280.4.a.ba.1.5		6	80.3	even	4
1280.4.a.bb.1.5		6	80.53	odd	4
1280.4.a.bc.1.2		6	80.13	odd	4
1280.4.a.bd.1.2		6	80.43	even	4
1440.4.k.c.721.5		12	120.83	odd	4
1440.4.k.c.721.11		12	60.23	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.690860 + 2.74276i) q^{2} +4.24443 q^{3} +(-7.04543 - 3.78972i) q^{4} +(-2.93231 + 11.6414i) q^{6} -14.6308i q^{7} +(15.2617 - 16.7057i) q^{8} -8.98481 q^{9} -14.9969i q^{11} +(-29.9038 - 16.0852i) q^{12} -85.6955 q^{13} +(40.1288 + 10.1078i) q^{14} +(35.2761 + 53.4004i) q^{16} -91.9247i q^{17} +(6.20724 - 24.6432i) q^{18} -60.3737i q^{19} -62.0995i q^{21} +(41.1330 + 10.3608i) q^{22} -1.33730i q^{23} +(64.7771 - 70.9063i) q^{24} +(59.2035 - 235.042i) q^{26} -152.735 q^{27} +(-55.4467 + 103.080i) q^{28} +25.5118i q^{29} +73.4354 q^{31} +(-170.835 + 59.8615i) q^{32} -63.6535i q^{33} +(252.127 + 63.5070i) q^{34} +(63.3018 + 34.0499i) q^{36} -211.259 q^{37} +(165.590 + 41.7098i) q^{38} -363.728 q^{39} +330.839 q^{41} +(170.324 + 42.9020i) q^{42} +388.500 q^{43} +(-56.8342 + 105.660i) q^{44} +(3.66788 + 0.923883i) q^{46} -550.348i q^{47} +(149.727 + 226.654i) q^{48} +128.939 q^{49} -390.168i q^{51} +(603.761 + 324.762i) q^{52} -187.705 q^{53} +(105.518 - 418.915i) q^{54} +(-244.419 - 223.291i) q^{56} -256.252i q^{57} +(-69.9727 - 17.6251i) q^{58} +779.090i q^{59} +358.850i q^{61} +(-50.7335 + 201.415i) q^{62} +131.455i q^{63} +(-46.1625 - 509.915i) q^{64} +(174.586 + 43.9756i) q^{66} +283.674 q^{67} +(-348.369 + 647.648i) q^{68} -5.67606i q^{69} -534.811 q^{71} +(-137.123 + 150.098i) q^{72} -1016.16i q^{73} +(145.950 - 579.431i) q^{74} +(-228.799 + 425.359i) q^{76} -219.418 q^{77} +(251.285 - 997.618i) q^{78} -1119.59 q^{79} -405.683 q^{81} +(-228.563 + 907.411i) q^{82} -1190.49 q^{83} +(-235.340 + 437.518i) q^{84} +(-268.399 + 1065.56i) q^{86} +108.283i q^{87} +(-250.535 - 228.879i) q^{88} +398.940 q^{89} +1253.80i q^{91} +(-5.06797 + 9.42182i) q^{92} +311.691 q^{93} +(1509.47 + 380.213i) q^{94} +(-725.097 + 254.078i) q^{96} +278.022i q^{97} +(-89.0787 + 353.648i) q^{98} +134.745i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 12 q^{3} - 16 q^{4} - 36 q^{6} + 24 q^{8} + 108 q^{9} + 164 q^{12} - 68 q^{14} - 56 q^{16} - 450 q^{18} - 492 q^{22} - 360 q^{24} - 308 q^{26} - 432 q^{27} - 628 q^{28} - 264 q^{31} - 856 q^{32}+ \cdots - 638 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 12 * q^3 - 16 * q^4 - 36 * q^6 + 24 * q^8 + 108 * q^9 + 164 * q^12 - 68 * q^14 - 56 * q^16 - 450 * q^18 - 492 * q^22 - 360 * q^24 - 308 * q^26 - 432 * q^27 - 628 * q^28 - 264 * q^31 - 856 * q^32 + 180 * q^34 + 440 * q^36 - 136 * q^37 + 1388 * q^38 - 600 * q^39 + 40 * q^41 + 2332 * q^42 + 1204 * q^43 + 472 * q^44 - 1268 * q^46 + 2536 * q^48 - 1308 * q^49 + 1272 * q^52 - 1056 * q^53 + 1512 * q^54 - 728 * q^56 - 1528 * q^58 - 2104 * q^62 + 2048 * q^64 + 2928 * q^66 + 2412 * q^67 - 960 * q^68 - 1592 * q^71 - 744 * q^72 + 420 * q^74 + 2256 * q^76 - 824 * q^77 + 160 * q^78 - 2016 * q^79 + 2508 * q^81 - 352 * q^82 - 3556 * q^83 - 1048 * q^84 - 244 * q^86 - 1008 * q^88 + 424 * q^89 - 1068 * q^92 - 2784 * q^93 - 292 * q^94 - 5920 * q^96 - 638 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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