LMFDB - Embedded newform 200.6.f.d.149.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,6,Mod(149,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("200.149");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	200.f (of order $2$, degree $1$, not 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:	$32.0767639626$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.3
Character	$\chi$	$=$	200.149
Dual form			200.6.f.d.149.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.36768 - 1.78549i) q^{2} +29.6034 q^{3} +(25.6240 + 19.1679i) q^{4} +(-158.902 - 52.8566i) q^{6} -90.3364i q^{7} +(-103.318 - 148.639i) q^{8} +633.360 q^{9} -181.932i q^{11} +(758.558 + 567.435i) q^{12} -455.237 q^{13} +(-161.295 + 484.897i) q^{14} +(289.182 + 982.319i) q^{16} -615.967i q^{17} +(-3399.68 - 1130.86i) q^{18} -2493.63i q^{19} -2674.26i q^{21} +(-324.839 + 976.555i) q^{22} -4427.05i q^{23} +(-3058.55 - 4400.21i) q^{24} +(2443.57 + 812.823i) q^{26} +11556.0 q^{27} +(1731.56 - 2314.78i) q^{28} +7659.34i q^{29} -6767.72 q^{31} +(201.685 - 5789.11i) q^{32} -5385.81i q^{33} +(-1099.80 + 3306.31i) q^{34} +(16229.2 + 12140.2i) q^{36} +4808.64 q^{37} +(-4452.35 + 13385.0i) q^{38} -13476.6 q^{39} +1885.99 q^{41} +(-4774.88 + 14354.6i) q^{42} +8262.94 q^{43} +(3487.26 - 4661.84i) q^{44} +(-7904.46 + 23763.0i) q^{46} +5728.44i q^{47} +(8560.77 + 29080.0i) q^{48} +8646.33 q^{49} -18234.7i q^{51} +(-11665.0 - 8725.95i) q^{52} +32364.5 q^{53} +(-62028.9 - 20633.1i) q^{54} +(-13427.5 + 9333.33i) q^{56} -73819.8i q^{57} +(13675.7 - 41112.9i) q^{58} +20848.8i q^{59} -13265.1i q^{61} +(36327.0 + 12083.7i) q^{62} -57215.5i q^{63} +(-11419.0 + 30714.0i) q^{64} +(-9616.33 + 28909.3i) q^{66} +9642.36 q^{67} +(11806.8 - 15783.6i) q^{68} -131056. i q^{69} -33088.4 q^{71} +(-65437.2 - 94141.9i) q^{72} -18595.6i q^{73} +(-25811.2 - 8585.79i) q^{74} +(47797.6 - 63896.7i) q^{76} -16435.1 q^{77} +(72337.9 + 24062.3i) q^{78} -44201.2 q^{79} +188190. q^{81} +(-10123.4 - 3367.42i) q^{82} -80063.0 q^{83} +(51260.1 - 68525.4i) q^{84} +(-44352.8 - 14753.4i) q^{86} +226742. i q^{87} +(-27042.2 + 18796.8i) q^{88} +81639.3 q^{89} +41124.5i q^{91} +(84857.3 - 113439. i) q^{92} -200348. q^{93} +(10228.1 - 30748.4i) q^{94} +(5970.56 - 171377. i) q^{96} -22224.8i q^{97} +(-46410.7 - 15438.0i) q^{98} -115229. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9} + 848 q^{14} - 110 q^{16} - 18918 q^{24} + 18344 q^{26} + 14320 q^{31} + 19182 q^{34} + 29656 q^{36} - 44904 q^{39} - 11608 q^{41} + 23186 q^{44} - 75224 q^{46} - 125304 q^{49}+ \cdots + 115582 q^{96}+O(q^{100}) $ 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9 + 848 * q^14 - 110 * q^16 - 18918 * q^24 + 18344 * q^26 + 14320 * q^31 + 19182 * q^34 + 29656 * q^36 - 44904 * q^39 - 11608 * q^41 + 23186 * q^44 - 75224 * q^46 - 125304 * q^49 - 177894 * q^54 - 73816 * q^56 - 230354 * q^64 + 262878 * q^66 - 15448 * q^71 - 4224 * q^74 + 111902 * q^76 + 15560 * q^79 + 193968 * q^81 + 195112 * q^84 - 131972 * q^86 + 6320 * q^89 + 117080 * q^94 + 115582 * q^96

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 $

$2$	−5.36768	−	1.78549i	−0.948881	−	0.315633i
$2$	−5.36768	−	1.78549i	−0.948881	−	0.315633i
$3$	29.6034			1.89906			0.949529	−	0.313679i	$-0.101562\pi$
$3$	29.6034			1.89906			0.949529	+	0.313679i	$0.101562\pi$
$4$	25.6240	+	19.1679i	0.800751	+	0.598997i
$5$		0			0
$5$		0			0
$6$	−158.902	−	52.8566i	−1.80198	−	0.599406i
$7$		−	90.3364i		−	0.696816i	−0.937343	−	0.348408i	$-0.886722\pi$
$7$		−	90.3364i		−	0.696816i	0.937343	−	0.348408i	$-0.113278\pi$
$8$	−103.318	−	148.639i	−0.570754	−	0.821121i
$9$	633.360			2.60642
$10$		0			0
$11$		−	181.932i		−	0.453344i	−0.973971	−	0.226672i	$-0.927215\pi$
$11$		−	181.932i		−	0.453344i	0.973971	−	0.226672i	$-0.0727846\pi$
$12$	758.558	+	567.435i	1.52067	+	1.13753i
$13$	−455.237			−0.747101			−0.373551	−	0.927610i	$-0.621860\pi$
$13$	−455.237			−0.747101			−0.373551	+	0.927610i	$0.621860\pi$
$14$	−161.295	+	484.897i	−0.219938	+	0.661195i
$15$		0			0
$16$	289.182	+	982.319i	0.282404	+	0.959295i
$17$		−	615.967i		−	0.516934i	−0.966020	−	0.258467i	$-0.916783\pi$
$17$		−	615.967i		−	0.516934i	0.966020	−	0.258467i	$-0.0832173\pi$
$18$	−3399.68	−	1130.86i	−2.47318	−	0.822674i
$19$		−	2493.63i		−	1.58470i	−0.610067	−	0.792350i	$-0.708857\pi$
$19$		−	2493.63i		−	1.58470i	0.610067	−	0.792350i	$-0.291143\pi$
$20$		0			0
$21$		−	2674.26i		−	1.32329i
$22$	−324.839	+	976.555i	−0.143091	+	0.430170i
$23$		−	4427.05i		−	1.74500i	−0.488616	−	0.872499i	$-0.662498\pi$
$23$		−	4427.05i		−	1.74500i	0.488616	−	0.872499i	$-0.337502\pi$
$24$	−3058.55	−	4400.21i	−1.08389	−	1.55936i
$25$		0			0
$26$	2443.57	+	812.823i	0.708910	+	0.235810i
$27$	11556.0			3.05069
$28$	1731.56	−	2314.78i	0.417391	−	0.557976i
$29$			7659.34i			1.69121i	0.533813	+	0.845603i	$0.320759\pi$
$29$			7659.34i			1.69121i	−0.533813	+	0.845603i	$0.679241\pi$
$30$		0			0
$31$	−6767.72			−1.26485			−0.632424	−	0.774622i	$-0.717940\pi$
$31$	−6767.72			−1.26485			−0.632424	+	0.774622i	$0.717940\pi$
$32$	201.685	−	5789.11i	0.0348176	−	0.999394i
$33$		−	5385.81i		−	0.860927i
$34$	−1099.80	+	3306.31i	−0.163162	+	0.490509i
$35$		0			0
$36$	16229.2	+	12140.2i	2.08709	+	1.56124i
$37$	4808.64			0.577455			0.288727	−	0.957411i	$-0.406768\pi$
$37$	4808.64			0.577455			0.288727	+	0.957411i	$0.406768\pi$
$38$	−4452.35	+	13385.0i	−0.500185	+	1.50369i
$39$	−13476.6			−1.41879
$40$		0			0
$41$	1885.99			0.175218			0.0876092	−	0.996155i	$-0.472077\pi$
$41$	1885.99			0.175218			0.0876092	+	0.996155i	$0.472077\pi$
$42$	−4774.88	+	14354.6i	−0.417676	+	1.25565i
$43$	8262.94			0.681496			0.340748	−	0.940155i	$-0.389320\pi$
$43$	8262.94			0.681496			0.340748	+	0.940155i	$0.389320\pi$
$44$	3487.26	−	4661.84i	0.271552	−	0.363016i
$45$		0			0
$46$	−7904.46	+	23763.0i	−0.550780	+	1.65580i
$47$			5728.44i			0.378261i	0.981952	+	0.189130i	$0.0605669\pi$
$47$			5728.44i			0.378261i	−0.981952	+	0.189130i	$0.939433\pi$
$48$	8560.77	+	29080.0i	0.536302	+	1.82176i
$49$	8646.33			0.514448
$50$		0			0
$51$		−	18234.7i		−	0.981687i
$52$	−11665.0	−	8725.95i	−0.598242	−	0.447512i
$53$	32364.5			1.58263			0.791316	−	0.611408i	$-0.209396\pi$
$53$	32364.5			1.58263			0.791316	+	0.611408i	$0.209396\pi$
$54$	−62028.9	−	20633.1i	−2.89474	−	0.962899i
$55$		0			0
$56$	−13427.5	+	9333.33i	−0.572170	+	0.397710i
$57$		−	73819.8i		−	3.00944i
$58$	13675.7	−	41112.9i	0.533801	−	1.60475i
$59$			20848.8i			0.779740i	0.920870	+	0.389870i	$0.127480\pi$
$59$			20848.8i			0.779740i	−0.920870	+	0.389870i	$0.872520\pi$
$60$		0			0
$61$		−	13265.1i		−	0.456442i	−0.973609	−	0.228221i	$-0.926709\pi$
$61$		−	13265.1i		−	0.456442i	0.973609	−	0.228221i	$-0.0732909\pi$
$62$	36327.0	+	12083.7i	1.20019	+	0.399228i
$63$		−	57215.5i		−	1.81620i
$64$	−11419.0	+	30714.0i	−0.348480	+	0.937316i
$65$		0			0
$66$	−9616.33	+	28909.3i	−0.271737	+	0.816918i
$67$	9642.36			0.262420			0.131210	−	0.991355i	$-0.458114\pi$
$67$	9642.36			0.262420			0.131210	+	0.991355i	$0.458114\pi$
$68$	11806.8	−	15783.6i	0.309642	−	0.413935i
$69$		−	131056.i		−	3.31385i
$70$		0			0
$71$	−33088.4			−0.778986			−0.389493	−	0.921029i	$-0.627350\pi$
$71$	−33088.4			−0.778986			−0.389493	+	0.921029i	$0.627350\pi$
$72$	−65437.2	−	94141.9i	−1.48763	−	2.14019i
$73$		−	18595.6i		−	0.408417i	−0.978927	−	0.204208i	$-0.934538\pi$
$73$		−	18595.6i		−	0.408417i	0.978927	−	0.204208i	$-0.0654620\pi$
$74$	−25811.2	−	8585.79i	−0.547936	−	0.182264i
$75$		0			0
$76$	47797.6	−	63896.7i	0.949231	−	1.26895i
$77$	−16435.1			−0.315897
$78$	72337.9	+	24062.3i	1.34626	+	0.447817i
$79$	−44201.2			−0.796831			−0.398415	−	0.917205i	$-0.630440\pi$
$79$	−44201.2			−0.796831			−0.398415	+	0.917205i	$0.630440\pi$
$80$		0			0
$81$	188190.			3.18701
$82$	−10123.4	−	3367.42i	−0.166261	−	0.0553048i
$83$	−80063.0			−1.27567			−0.637833	−	0.770175i	$-0.720169\pi$
$83$	−80063.0			−1.27567			−0.637833	+	0.770175i	$0.720169\pi$
$84$	51260.1	−	68525.4i	0.792649	−	1.05963i
$85$		0			0
$86$	−44352.8	−	14753.4i	−0.646659	−	0.215103i
$87$			226742.i			3.21170i
$88$	−27042.2	+	18796.8i	−0.372251	+	0.258748i
$89$	81639.3			1.09251			0.546254	−	0.837620i	$-0.316053\pi$
$89$	81639.3			1.09251			0.546254	+	0.837620i	$0.316053\pi$
$90$		0			0
$91$			41124.5i			0.520592i
$92$	84857.3	−	113439.i	1.04525	−	1.39731i
$93$	−200348.			−2.40202
$94$	10228.1	−	30748.4i	0.119392	−	0.358925i
$95$		0			0
$96$	5970.56	−	171377.i	0.0661206	−	1.89791i
$97$		−	22224.8i		−	0.239833i	−0.992784	−	0.119917i	$-0.961737\pi$
$97$		−	22224.8i		−	0.239833i	0.992784	−	0.119917i	$-0.0382627\pi$
$98$	−46410.7	−	15438.0i	−0.488150	−	0.162377i
$99$		−	115229.i		−	1.18161i
$100$		0			0
$101$			38894.0i			0.379384i	0.981844	+	0.189692i	$0.0607489\pi$
$101$			38894.0i			0.379384i	−0.981844	+	0.189692i	$0.939251\pi$
$102$	−32557.9	+	97878.1i	−0.309853	+	0.931505i
$103$		−	175773.i		−	1.63253i	−0.577681	−	0.816263i	$-0.696042\pi$
$103$		−	175773.i		−	1.63253i	0.577681	−	0.816263i	$-0.303958\pi$
$104$	47034.0	+	67665.9i	0.426411	+	0.613461i
$105$		0			0
$106$	−173723.	−	57786.6i	−1.50173	−	0.499531i
$107$	128182.			1.08235			0.541175	−	0.840910i	$-0.317980\pi$
$107$	128182.			1.08235			0.541175	+	0.840910i	$0.317980\pi$
$108$	296111.	+	221504.i	2.44284	+	1.82735i
$109$			49566.1i			0.399594i	0.979837	+	0.199797i	$0.0640283\pi$
$109$			49566.1i			0.399594i	−0.979837	+	0.199797i	$0.935972\pi$
$110$		0			0
$111$	142352.			1.09662
$112$	88739.2	−	26123.7i	0.668452	−	0.196784i
$113$			92377.7i			0.680567i	0.940323	+	0.340283i	$0.110523\pi$
$113$			92377.7i			0.680567i	−0.940323	+	0.340283i	$0.889477\pi$
$114$	−131805.	+	396241.i	−0.949879	+	2.85560i
$115$		0			0
$116$	−146814.	+	196263.i	−1.01303	+	1.35423i
$117$	−288329.			−1.94726
$118$	37225.3	−	111909.i	0.246112	−	0.739881i
$119$	−55644.2			−0.360208
$120$		0			0
$121$	127952.			0.794479
$122$	−23684.7	+	71202.9i	−0.144069	+	0.433110i
$123$	55831.7			0.332750
$124$	−173416.	−	129723.i	−1.01283	−	0.757641i
$125$		0			0
$126$	−102158.	+	307115.i	−0.573252	+	1.72335i
$127$		−	137192.i		−	0.754778i	−0.926055	−	0.377389i	$-0.876822\pi$
$127$		−	137192.i		−	0.754778i	0.926055	−	0.377389i	$-0.123178\pi$
$128$	116133.	−	144474.i	0.626514	−	0.779410i
$129$	244611.			1.29420
$130$		0			0
$131$		−	91906.6i		−	0.467917i	−0.972247	−	0.233958i	$-0.924832\pi$
$131$		−	91906.6i		−	0.467917i	0.972247	−	0.233958i	$-0.0751679\pi$
$132$	103235.	−	138006.i	0.515693	−	0.689388i
$133$	−225265.			−1.10424
$134$	−51757.1	−	17216.4i	−0.249005	−	0.0828284i
$135$		0			0
$136$	−91556.6	+	63640.1i	−0.424465	+	0.295042i
$137$			220709.i			1.00466i	0.864676	+	0.502330i	$0.167524\pi$
$137$			220709.i			1.00466i	−0.864676	+	0.502330i	$0.832476\pi$
$138$	−233999.	+	703465.i	−1.04596	+	3.14445i
$139$			154375.i			0.677706i	0.940839	+	0.338853i	$0.110039\pi$
$139$			154375.i			0.677706i	−0.940839	+	0.338853i	$0.889961\pi$
$140$		0			0
$141$			169581.i			0.718339i
$142$	177608.	+	59079.1i	0.739165	+	0.245874i
$143$			82822.4i			0.338694i
$144$	183157.	+	622162.i	0.736065	+	2.50033i
$145$		0			0
$146$	−33202.4	+	99815.4i	−0.128910	+	0.387539i
$147$	255961.			0.976967
$148$	123217.	+	92171.6i	0.462397	+	0.345894i
$149$			152976.i			0.564492i	0.959342	+	0.282246i	$0.0910794\pi$
$149$			152976.i			0.564492i	−0.959342	+	0.282246i	$0.908921\pi$
$150$		0			0
$151$	−440485.			−1.57213			−0.786066	−	0.618143i	$-0.787885\pi$
$151$	−440485.			−1.57213			−0.786066	+	0.618143i	$0.787885\pi$
$152$	−370649.	+	257635.i	−1.30123	+	0.904474i
$153$		−	390129.i		−	1.34735i
$154$	88218.5	+	29344.8i	0.299749	+	0.0997078i
$155$		0			0
$156$	−345324.	−	258318.i	−1.13610	−	0.849851i
$157$	433381.			1.40320			0.701601	−	0.712570i	$-0.252469\pi$
$157$	433381.			1.40320			0.701601	+	0.712570i	$0.252469\pi$
$158$	237258.	+	78920.9i	0.756098	+	0.251507i
$159$	958100.			3.00551
$160$		0			0
$161$	−399924.			−1.21594
$162$	−1.01014e6	−	336012.i	−3.02410	−	1.00593i
$163$	−201943.			−0.595333			−0.297666	−	0.954670i	$-0.596208\pi$
$163$	−201943.			−0.595333			−0.297666	+	0.954670i	$0.596208\pi$
$164$	48326.6	+	36150.5i	0.140306	+	0.104955i
$165$		0			0
$166$	429753.	+	142952.i	1.21046	+	0.402643i
$167$			300699.i			0.834337i	0.908829	+	0.417168i	$0.136977\pi$
$167$			300699.i			0.834337i	−0.908829	+	0.417168i	$0.863023\pi$
$168$	−397499.	+	276298.i	−1.08658	+	0.755275i
$169$	−164052.			−0.441840
$170$		0			0
$171$		−	1.57936e6i		−	4.13040i
$172$	211730.	+	158383.i	0.545709	+	0.408214i
$173$	100504.			0.255311			0.127656	−	0.991819i	$-0.459255\pi$
$173$	100504.			0.255311			0.127656	+	0.991819i	$0.459255\pi$
$174$	404847.	−	1.21708e6i	1.01372	−	3.04752i
$175$		0			0
$176$	178715.	−	52611.6i	0.434891	−	0.128026i
$177$			617194.i			1.48077i
$178$	−438214.	−	145766.i	−1.03666	−	0.344832i
$179$			554078.i			1.29252i	0.763116	+	0.646262i	$0.223669\pi$
$179$			554078.i			1.29252i	−0.763116	+	0.646262i	$0.776331\pi$
$180$		0			0
$181$			227592.i			0.516368i	0.966096	+	0.258184i	$0.0831241\pi$
$181$			227592.i			0.516368i	−0.966096	+	0.258184i	$0.916876\pi$
$182$	73427.5	−	220743.i	0.164316	−	0.493980i
$183$		−	392692.i		−	0.866811i
$184$	−658031.	+	457392.i	−1.43285	+	0.995964i
$185$		0			0
$186$	1.07540e6	+	357719.i	2.27923	+	0.758158i
$187$	−112064.			−0.234349
$188$	−109802.	+	146786.i	−0.226577	+	0.302893i
$189$		−	1.04393e6i		−	2.12577i
$190$		0			0
$191$	796597.			1.57999			0.789997	−	0.613111i	$-0.210082\pi$
$191$	796597.			1.57999			0.789997	+	0.613111i	$0.210082\pi$
$192$	−338041.	+	909238.i	−0.661783	+	1.78002i
$193$		−	356611.i		−	0.689131i	−0.938762	−	0.344565i	$-0.888026\pi$
$193$		−	356611.i		−	0.689131i	0.938762	−	0.344565i	$-0.111974\pi$
$194$	−39682.3	+	119296.i	−0.0756994	+	0.227573i
$195$		0			0
$196$	221554.	+	165732.i	0.411945	+	0.308153i
$197$	−226534.			−0.415880			−0.207940	−	0.978142i	$-0.566676\pi$
$197$	−226534.			−0.415880			−0.207940	+	0.978142i	$0.566676\pi$
$198$	−205740.	+	618511.i	−0.372955	+	1.12120i
$199$	177886.			0.318427			0.159213	−	0.987244i	$-0.449104\pi$
$199$	177886.			0.318427			0.159213	+	0.987244i	$0.449104\pi$
$200$		0			0
$201$	285447.			0.498350
$202$	69444.9	−	208770.i	0.119746	−	0.359990i
$203$	691917.			1.17846
$204$	349521.	−	467247.i	0.588028	−	0.786087i
$205$		0			0
$206$	−313842.	+	943495.i	−0.515280	+	1.54907i
$207$		−	2.80392e6i		−	4.54820i
$208$	−131646.	−	447188.i	−0.210985	−	0.716691i
$209$	−453671.			−0.718415
$210$		0			0
$211$		−	525263.i		−	0.812215i	−0.913825	−	0.406107i	$-0.866886\pi$
$211$		−	525263.i		−	0.812215i	0.913825	−	0.406107i	$-0.133114\pi$
$212$	829310.	+	620361.i	1.26729	+	0.947992i
$213$	−979528.			−1.47934
$214$	−688041.	−	228868.i	−1.02702	−	0.341626i
$215$		0			0
$216$	−1.19394e6	−	1.71767e6i	−1.74119	−	2.50498i
$217$			611372.i			0.881366i
$218$	88500.0	−	266055.i	0.126125	−	0.379167i
$219$		−	550494.i		−	0.775607i
$220$		0			0
$221$			280411.i			0.386202i
$222$	−764100.	−	254168.i	−1.04056	−	0.346130i
$223$			711308.i			0.957846i	0.877857	+	0.478923i	$0.158973\pi$
$223$			711308.i			0.957846i	−0.877857	+	0.478923i	$0.841027\pi$
$224$	−522967.	−	18219.5i	−0.696393	−	0.0242614i
$225$		0			0
$226$	164940.	−	495854.i	0.214810	−	0.645777i
$227$	−216347.			−0.278668			−0.139334	−	0.990245i	$-0.544496\pi$
$227$	−216347.			−0.278668			−0.139334	+	0.990245i	$0.544496\pi$
$228$	1.41497e6	−	1.89156e6i	1.80265	−	2.40981i
$229$			759408.i			0.956944i	0.878103	+	0.478472i	$0.158809\pi$
$229$			759408.i			0.956944i	−0.878103	+	0.478472i	$0.841191\pi$
$230$		0			0
$231$	−486535.			−0.599907
$232$	1.13848e6	−	791344.i	1.38868	−	0.965262i
$233$			860736.i			1.03868i	0.854569	+	0.519338i	$0.173821\pi$
$233$			860736.i			1.03868i	−0.854569	+	0.519338i	$0.826179\pi$
$234$	1.54766e6	+	514810.i	1.84772	+	0.614621i
$235$		0			0
$236$	−399627.	+	534229.i	−0.467062	+	0.624378i
$237$	−1.30850e6			−1.51323
$238$	298681.	+	99352.4i	0.341794	+	0.113694i
$239$	348130.			0.394228			0.197114	−	0.980381i	$-0.436843\pi$
$239$	348130.			0.394228			0.197114	+	0.980381i	$0.436843\pi$
$240$		0			0
$241$	−844167.			−0.936237			−0.468119	−	0.883666i	$-0.655068\pi$
$241$	−844167.			−0.936237			−0.468119	+	0.883666i	$0.655068\pi$
$242$	−686804.	−	228457.i	−0.753866	−	0.250764i
$243$	2.76295e6			3.00163
$244$	254264.	−	339905.i	0.273408	−	0.365497i
$245$		0			0
$246$	−299687.	−	99687.0i	−0.315740	−	0.105027i
$247$			1.13519e6i			1.18393i
$248$	699224.	+	1.00595e6i	0.721917	+	1.03859i
$249$	−2.37014e6			−2.42256
$250$		0			0
$251$			1.52042e6i			1.52328i	0.648000	+	0.761640i	$0.275606\pi$
$251$			1.52042e6i			1.52328i	−0.648000	+	0.761640i	$0.724394\pi$
$252$	1.09670e6	−	1.46609e6i	1.08790	−	1.45432i
$253$	−805423.			−0.791085
$254$	−244955.	+	736403.i	−0.238233	+	0.716195i
$255$		0			0
$256$	−881323.	+	568138.i	−0.840496	+	0.541818i
$257$			682391.i			0.644466i	0.946660	+	0.322233i	$0.104434\pi$
$257$			682391.i			0.644466i	−0.946660	+	0.322233i	$0.895566\pi$
$258$	−1.31299e6	−	436751.i	−1.22804	−	0.408493i
$259$		−	434395.i		−	0.402379i
$260$		0			0
$261$			4.85112e6i			4.40799i
$262$	−164099.	+	493326.i	−0.147690	+	0.443997i
$263$		−	91394.4i		−	0.0814761i	−0.999170	−	0.0407381i	$-0.987029\pi$
$263$		−	91394.4i		−	0.0814761i	0.999170	−	0.0407381i	$-0.0129709\pi$
$264$	−800541.	+	556449.i	−0.706925	+	0.491378i
$265$		0			0
$266$	1.20915e6	+	402209.i	1.04780	+	0.348536i
$267$	2.41680e6			2.07474
$268$	247076.	+	184824.i	0.210133	+	0.157189i
$269$			935475.i			0.788227i	0.919062	+	0.394114i	$0.128948\pi$
$269$			935475.i			0.788227i	−0.919062	+	0.394114i	$0.871052\pi$
$270$		0			0
$271$	512294.			0.423737			0.211868	−	0.977298i	$-0.432045\pi$
$271$	512294.			0.423737			0.211868	+	0.977298i	$0.432045\pi$
$272$	605076.	−	178127.i	0.495892	−	0.145984i
$273$			1.21742e6i			0.988634i
$274$	394075.	−	1.18470e6i	0.317105	−	0.953304i
$275$		0			0
$276$	2.51206e6	−	3.35817e6i	1.98499	−	2.65357i
$277$	−615832.			−0.482239			−0.241120	−	0.970495i	$-0.577515\pi$
$277$	−615832.			−0.482239			−0.241120	+	0.970495i	$0.577515\pi$
$278$	275636.	−	828638.i	0.213907	−	0.643062i
$279$	−4.28641e6			−3.29673
$280$		0			0
$281$	1.22082e6			0.922330			0.461165	−	0.887314i	$-0.347432\pi$
$281$	1.22082e6			0.922330			0.461165	+	0.887314i	$0.347432\pi$
$282$	302786.	−	910258.i	0.226732	−	0.681619i
$283$	−696315.			−0.516820			−0.258410	−	0.966035i	$-0.583199\pi$
$283$	−696315.			−0.516820			−0.258410	+	0.966035i	$0.583199\pi$
$284$	−847858.	−	634235.i	−0.623774	−	0.466611i
$285$		0			0
$286$	147879.	−	444564.i	0.106903	−	0.321380i
$287$		−	170374.i		−	0.122095i
$288$	127739.	−	3.66659e6i	0.0907493	−	2.60484i
$289$	1.04044e6			0.732779
$290$		0			0
$291$		−	657931.i		−	0.455457i
$292$	356439.	−	476495.i	0.244641	−	0.327040i
$293$	134741.			0.0916922			0.0458461	−	0.998949i	$-0.485402\pi$
$293$	134741.			0.0916922			0.0458461	+	0.998949i	$0.485402\pi$
$294$	−1.37392e6	−	457016.i	−0.927025	−	0.308363i
$295$		0			0
$296$	−496817.	−	714750.i	−0.329584	−	0.474160i
$297$		−	2.10241e6i		−	1.38301i
$298$	273137.	−	821126.i	0.178172	−	0.535636i
$299$			2.01536e6i			1.30369i
$300$		0			0
$301$		−	746444.i		−	0.474877i
$302$	2.36438e6	+	786483.i	1.49177	+	0.496217i
$303$			1.15139e6i			0.720472i
$304$	2.44953e6	−	721112.i	1.52020	−	0.447526i
$305$		0			0
$306$	−696572.	+	2.09409e6i	−0.425268	+	1.27847i
$307$	280871.			0.170083			0.0850414	−	0.996377i	$-0.472898\pi$
$307$	280871.			0.170083			0.0850414	+	0.996377i	$0.472898\pi$
$308$	−421134.	−	315027.i	−0.252955	−	0.189222i
$309$		−	5.20348e6i		−	3.10026i
$310$		0			0
$311$	−2.40348e6			−1.40909			−0.704547	−	0.709657i	$-0.748850\pi$
$311$	−2.40348e6			−1.40909			−0.704547	+	0.709657i	$0.748850\pi$
$312$	1.39236e6	+	2.00314e6i	0.809779	+	1.16500i
$313$			619525.i			0.357436i	0.983900	+	0.178718i	$0.0571949\pi$
$313$			619525.i			0.357436i	−0.983900	+	0.178718i	$0.942805\pi$
$314$	−2.32625e6	−	773798.i	−1.33147	−	0.442898i
$315$		0			0
$316$	−1.13261e6	−	847245.i	−0.638063	−	0.477300i
$317$	−913021.			−0.510308			−0.255154	−	0.966900i	$-0.582126\pi$
$317$	−913021.			−0.510308			−0.255154	+	0.966900i	$0.582126\pi$
$318$	−5.14278e6	−	1.71068e6i	−2.85187	−	0.948639i
$319$	1.39348e6			0.766698
$320$		0			0
$321$	3.79462e6			2.05545
$322$	2.14666e6	+	714061.i	1.15378	+	0.383792i
$323$	−1.53599e6			−0.819185
$324$	4.82218e6	+	3.60721e6i	2.55200	+	1.90901i
$325$		0			0
$326$	1.08397e6	+	360568.i	0.564900	+	0.187907i
$327$			1.46733e6i			0.758852i
$328$	−194856.	−	280331.i	−0.100007	−	0.143875i
$329$	517487.			0.263578
$330$		0			0
$331$		−	3.37863e6i		−	1.69500i	−0.530793	−	0.847502i	$-0.678106\pi$
$331$		−	3.37863e6i		−	1.69500i	0.530793	−	0.847502i	$-0.321894\pi$
$332$	−2.05154e6	−	1.53464e6i	−1.02149	−	0.764120i
$333$	3.04560e6			1.50509
$334$	536896.	−	1.61406e6i	0.263345	−	0.791686i
$335$		0			0
$336$	2.62698e6	−	773349.i	1.26943	−	0.373704i
$337$		−	3.19536e6i		−	1.53266i	−0.642448	−	0.766329i	$-0.722081\pi$
$337$		−	3.19536e6i		−	1.53266i	0.642448	−	0.766329i	$-0.277919\pi$
$338$	880579.	+	292914.i	0.419254	+	0.139459i
$339$			2.73469e6i			1.29244i
$340$		0			0
$341$			1.23127e6i			0.573412i
$342$	−2.81994e6	+	8.47752e6i	−1.30369	+	3.91926i
$343$		−	2.29936e6i		−	1.05529i
$344$	−853706.	−	1.22819e6i	−0.388966	−	0.559591i
$345$		0			0
$346$	−539476.	−	179450.i	−0.242260	−	0.0805847i
$347$	−2.15234e6			−0.959592			−0.479796	−	0.877380i	$-0.659289\pi$
$347$	−2.15234e6			−0.959592			−0.479796	+	0.877380i	$0.659289\pi$
$348$	−4.34618e6	+	5.81006e6i	−1.92380	+	2.57177i
$349$			2.78827e6i			1.22538i	0.790322	+	0.612692i	$0.209913\pi$
$349$			2.78827e6i			1.22538i	−0.790322	+	0.612692i	$0.790087\pi$
$350$		0			0
$351$	−5.26072e6			−2.27917
$352$	−1.05323e6	−	36693.0i	−0.453069	−	0.0157843i
$353$			3.23259e6i			1.38075i	0.723453	+	0.690373i	$0.242554\pi$
$353$			3.23259e6i			1.38075i	−0.723453	+	0.690373i	$0.757446\pi$
$354$	1.10199e6	−	3.31290e6i	0.467381	−	1.40508i
$355$		0			0
$356$	2.09193e6	+	1.56486e6i	0.874826	+	0.654409i
$357$	−1.64726e6			−0.684055
$358$	989303.	−	2.97412e6i	0.407964	−	1.22645i
$359$	2.02100e6			0.827620			0.413810	−	0.910363i	$-0.364198\pi$
$359$	2.02100e6			0.827620			0.413810	+	0.910363i	$0.364198\pi$
$360$		0			0
$361$	−3.74207e6			−1.51128
$362$	406363.	−	1.22164e6i	0.162983	−	0.489972i
$363$	3.78780e6			1.50876
$364$	−788271.	+	1.05378e6i	−0.311833	+	0.416864i
$365$		0			0
$366$	−701149.	+	2.10785e6i	−0.273595	+	0.822500i
$367$			2.50488e6i			0.970781i	0.874297	+	0.485391i	$0.161323\pi$
$367$			2.50488e6i			0.970781i	−0.874297	+	0.485391i	$0.838677\pi$
$368$	4.34877e6	−	1.28022e6i	1.67397	−	0.492795i
$369$	1.19451e6			0.456693
$370$		0			0
$371$		−	2.92370e6i		−	1.10280i
$372$	−5.13371e6	−	3.84024e6i	−1.92342	−	1.43880i
$373$	−495172.			−0.184283			−0.0921413	−	0.995746i	$-0.529371\pi$
$373$	−495172.			−0.184283			−0.0921413	+	0.995746i	$0.529371\pi$
$374$	601525.	+	200090.i	0.222369	+	0.0739684i
$375$		0			0
$376$	851468.	−	591848.i	0.310598	−	0.215894i
$377$		−	3.48682e6i		−	1.26350i
$378$	−1.86392e6	+	5.60347e6i	−0.670963	+	2.01710i
$379$			2.19040e6i			0.783294i	0.920116	+	0.391647i	$0.128095\pi$
$379$			2.19040e6i			0.783294i	−0.920116	+	0.391647i	$0.871905\pi$
$380$		0			0
$381$		−	4.06135e6i		−	1.43337i
$382$	−4.27588e6	−	1.42232e6i	−1.49923	−	0.498699i
$383$			289759.i			0.100935i	0.998726	+	0.0504674i	$0.0160711\pi$
$383$			289759.i			0.100935i	−0.998726	+	0.0504674i	$0.983929\pi$
$384$	3.43793e6	−	4.27693e6i	1.18979	−	1.48014i
$385$		0			0
$386$	−636726.	+	1.91417e6i	−0.217513	+	0.653903i
$387$	5.23342e6			1.77627
$388$	426004.	−	569490.i	0.143659	−	0.192047i
$389$			2.11554e6i			0.708839i	0.935087	+	0.354420i	$0.115322\pi$
$389$			2.11554e6i			0.708839i	−0.935087	+	0.354420i	$0.884678\pi$
$390$		0			0
$391$	−2.72692e6			−0.902048
$392$	−893317.	−	1.28518e6i	−0.293623	−	0.422424i
$393$		−	2.72075e6i		−	0.888601i
$394$	1.21596e6	+	404475.i	0.394621	+	0.131266i
$395$		0			0
$396$	2.20869e6	−	2.95263e6i	0.707779	−	0.946173i
$397$	1.80742e6			0.575549			0.287774	−	0.957698i	$-0.407085\pi$
$397$	1.80742e6			0.575549			0.287774	+	0.957698i	$0.407085\pi$
$398$	−954837.	−	317615.i	−0.302149	−	0.100506i
$399$	−6.66861e6			−2.09702
$400$		0			0
$401$	−2.59111e6			−0.804683			−0.402342	−	0.915490i	$-0.631804\pi$
$401$	−2.59111e6			−0.804683			−0.402342	+	0.915490i	$0.631804\pi$
$402$	−1.53219e6	−	509663.i	−0.472875	−	0.157296i
$403$	3.08092e6			0.944969
$404$	−745516.	+	996620.i	−0.227250	+	0.303792i
$405$		0			0
$406$	−3.71399e6	−	1.23541e6i	−1.11822	−	0.371961i
$407$		−	874847.i		−	0.261786i
$408$	−2.71038e6	+	1.88396e6i	−0.806084	+	0.560302i
$409$	5.00884e6			1.48057			0.740285	−	0.672293i	$-0.234690\pi$
$409$	5.00884e6			1.48057			0.740285	+	0.672293i	$0.234690\pi$
$410$		0			0
$411$			6.53375e6i			1.90791i
$412$	3.36921e6	−	4.50402e6i	0.977878	−	1.30725i
$413$	1.88340e6			0.543335
$414$	−5.00638e6	+	1.50505e7i	−1.43556	+	4.31570i
$415$		0			0
$416$	−91814.5	+	2.63542e6i	−0.0260122	+	0.746648i
$417$			4.57003e6i			1.28700i
$418$	2.43516e6	+	810026.i	0.681690	+	0.226756i
$419$		−	2.27862e6i		−	0.634071i	−0.948414	−	0.317035i	$-0.897313\pi$
$419$		−	2.27862e6i		−	0.634071i	0.948414	−	0.317035i	$-0.102687\pi$
$420$		0			0
$421$		−	1.30407e6i		−	0.358587i	−0.983796	−	0.179293i	$-0.942619\pi$
$421$		−	1.30407e6i		−	0.358587i	0.983796	−	0.179293i	$-0.0573811\pi$
$422$	−937853.	+	2.81945e6i	−0.256362	+	0.770695i
$423$			3.62817e6i			0.985907i
$424$	−3.34382e6	−	4.81063e6i	−0.903293	−	1.29953i
$425$		0			0
$426$	5.25780e6	+	1.74894e6i	1.40372	+	0.466929i
$427$	−1.19832e6			−0.318056
$428$	3.28454e6	+	2.45698e6i	0.866693	+	0.648325i
$429$			2.45182e6i			0.643200i
$430$		0			0
$431$	3.93997e6			1.02164			0.510822	−	0.859687i	$-0.329341\pi$
$431$	3.93997e6			1.02164			0.510822	+	0.859687i	$0.329341\pi$
$432$	3.34179e6	+	1.13517e7i	0.861528	+	2.92651i
$433$			5.84454e6i			1.49806i	0.662534	+	0.749032i	$0.269481\pi$
$433$			5.84454e6i			1.49806i	−0.662534	+	0.749032i	$0.730519\pi$
$434$	1.09160e6	−	3.28165e6i	0.278189	−	0.836311i
$435$		0			0
$436$	−950080.	+	1.27008e6i	−0.239356	+	0.319975i
$437$	−1.10394e7			−2.76530
$438$	−982902.	+	2.95487e6i	−0.244808	+	0.735959i
$439$	7.63016e6			1.88961			0.944805	−	0.327634i	$-0.106251\pi$
$439$	7.63016e6			1.88961			0.944805	+	0.327634i	$0.106251\pi$
$440$		0			0
$441$	5.47624e6			1.34087
$442$	500672.	−	1.50516e6i	0.121898	−	0.366460i
$443$	−1.99010e6			−0.481798			−0.240899	−	0.970550i	$-0.577442\pi$
$443$	−1.99010e6			−0.481798			−0.240899	+	0.970550i	$0.577442\pi$
$444$	3.64763e6	+	2.72859e6i	0.878119	+	0.656872i
$445$		0			0
$446$	1.27004e6	−	3.81808e6i	0.302328	−	0.908882i
$447$			4.52861e6i			1.07200i
$448$	2.77459e6	+	1.03155e6i	0.653137	+	0.242826i
$449$	2.05507e6			0.481074			0.240537	−	0.970640i	$-0.422676\pi$
$449$	2.05507e6			0.481074			0.240537	+	0.970640i	$0.422676\pi$
$450$		0			0
$451$		−	343122.i		−	0.0794342i
$452$	−1.77069e6	+	2.36709e6i	−0.407658	+	0.544965i
$453$	−1.30398e7			−2.98557
$454$	1.16128e6	+	386287.i	0.264423	+	0.0879569i
$455$		0			0
$456$	−1.09725e7	+	7.62687e6i	−2.47111	+	1.71765i
$457$			2.74689e6i			0.615250i	0.951508	+	0.307625i	$0.0995342\pi$
$457$			2.74689e6i			0.615250i	−0.951508	+	0.307625i	$0.900466\pi$
$458$	1.35592e6	−	4.07626e6i	0.302044	−	0.908026i
$459$		−	7.11811e6i		−	1.57700i
$460$		0			0
$461$		−	4.01666e6i		−	0.880264i	−0.897933	−	0.440132i	$-0.854932\pi$
$461$		−	4.01666e6i		−	0.880264i	0.897933	−	0.440132i	$-0.145068\pi$
$462$	2.61157e6	+	868705.i	0.569241	+	0.189351i
$463$		−	7.77791e6i		−	1.68620i	−0.537753	−	0.843102i	$-0.680727\pi$
$463$		−	7.77791e6i		−	1.68620i	0.537753	−	0.843102i	$-0.319273\pi$
$464$	−7.52391e6	+	2.21494e6i	−1.62237	+	0.477604i
$465$		0			0
$466$	1.53684e6	−	4.62015e6i	0.327841	−	0.985580i
$467$	−3.81432e6			−0.809329			−0.404664	−	0.914465i	$-0.632612\pi$
$467$	−3.81432e6			−0.809329			−0.404664	+	0.914465i	$0.632612\pi$
$468$	−7.38816e6	−	5.52667e6i	−1.55927	−	1.16640i
$469$		−	871056.i		−	0.182858i
$470$		0			0
$471$	1.28295e7			2.66476
$472$	3.09893e6	−	2.15404e6i	0.640261	−	0.445040i
$473$		−	1.50330e6i		−	0.308952i
$474$	7.02364e6	+	2.33633e6i	1.43587	+	0.477625i
$475$		0			0
$476$	−1.42583e6	−	1.06658e6i	−0.288437	−	0.215763i
$477$	2.04984e7			4.12500
$478$	−1.86865e6	−	621584.i	−0.374075	−	0.124431i
$479$	2.44255e6			0.486413			0.243206	−	0.969975i	$-0.421801\pi$
$479$	2.44255e6			0.486413			0.243206	+	0.969975i	$0.421801\pi$
$480$		0			0
$481$	−2.18907e6			−0.431417
$482$	4.53122e6	+	1.50725e6i	0.888378	+	0.295508i
$483$	−1.18391e7			−2.30914
$484$	3.27864e6	+	2.45257e6i	0.636180	+	0.475891i
$485$		0			0
$486$	−1.48307e7	−	4.93323e6i	−2.84819	−	0.947416i
$487$		−	8.35163e6i		−	1.59569i	−0.602862	−	0.797846i	$-0.705973\pi$
$487$		−	8.35163e6i		−	1.59569i	0.602862	−	0.797846i	$-0.294027\pi$
$488$	−1.97171e6	+	1.37052e6i	−0.374795	+	0.260516i
$489$	−5.97820e6			−1.13057
$490$		0			0
$491$			340069.i			0.0636595i	0.999493	+	0.0318298i	$0.0101334\pi$
$491$			340069.i			0.0636595i	−0.999493	+	0.0318298i	$0.989867\pi$
$492$	1.43063e6	+	1.07018e6i	0.266450	+	0.199316i
$493$	4.71790e6			0.874241
$494$	2.02688e6	−	6.09335e6i	0.373688	−	1.12341i
$495$		0			0
$496$	−1.95710e6	−	6.64806e6i	−0.357199	−	1.21336i
$497$			2.98909e6i			0.542810i
$498$	1.27221e7	+	4.23186e6i	2.29872	+	0.764642i
$499$			648994.i			0.116678i	0.998297	+	0.0583391i	$0.0185805\pi$
$499$			648994.i			0.116678i	−0.998297	+	0.0583391i	$0.981420\pi$
$500$		0			0
$501$			8.90172e6i			1.58445i
$502$	2.71470e6	−	8.16114e6i	0.480798	−	1.44541i
$503$			3.13514e6i			0.552506i	0.961085	+	0.276253i	$0.0890928\pi$
$503$			3.13514e6i			0.552506i	−0.961085	+	0.276253i	$0.910907\pi$
$504$	−8.50445e6	+	5.91137e6i	−1.49132	+	1.03660i
$505$		0			0
$506$	4.32326e6	+	1.43808e6i	0.750645	+	0.249693i
$507$	−4.85650e6			−0.839080
$508$	2.62968e6	−	3.51541e6i	0.452110	−	0.604390i
$509$		−	5.04542e6i		−	0.863183i	−0.902069	−	0.431591i	$-0.857952\pi$
$509$		−	5.04542e6i		−	0.863183i	0.902069	−	0.431591i	$-0.142048\pi$
$510$		0			0
$511$	−1.67986e6			−0.284591
$512$	5.74507e6	−	1.47599e6i	0.968546	−	0.248833i
$513$		−	2.88163e7i		−	4.83443i
$514$	1.21840e6	−	3.66286e6i	0.203415	−	0.611522i
$515$		0			0
$516$	6.26792e6	+	4.68868e6i	1.03633	+	0.775223i
$517$	1.04219e6			0.171482
$518$	−775610.	+	2.33170e6i	−0.127004	+	0.381810i
$519$	2.97527e6			0.484851
$520$		0			0
$521$	598792.			0.0966456			0.0483228	−	0.998832i	$-0.484612\pi$
$521$	598792.			0.0966456			0.0483228	+	0.998832i	$0.484612\pi$
$522$	8.66165e6	−	2.60393e7i	1.39131	−	4.18266i
$523$	−1.12334e7			−1.79580			−0.897901	−	0.440197i	$-0.854909\pi$
$523$	−1.12334e7			−1.79580			−0.897901	+	0.440197i	$0.854909\pi$
$524$	1.76166e6	−	2.35502e6i	0.280281	−	0.374685i
$525$		0			0
$526$	−163184.	+	490576.i	−0.0257166	+	0.0773111i
$527$			4.16869e6i			0.653843i
$528$	5.29058e6	−	1.55748e6i	0.825884	−	0.243130i
$529$	−1.31624e7			−2.04502
$530$		0			0
$531$			1.32048e7i			2.03233i
$532$	−5.77220e6	−	4.31786e6i	−0.884224	−	0.661439i
$533$	−858572.			−0.130906
$534$	−1.29726e7	−	4.31518e6i	−1.96868	−	0.654856i
$535$		0			0
$536$	−996225.	−	1.43323e6i	−0.149777	−	0.215478i
$537$			1.64026e7i			2.45458i
$538$	1.67028e6	−	5.02133e6i	0.248791	−	0.747934i
$539$		−	1.57305e6i		−	0.233222i
$540$		0			0
$541$		−	8.05017e6i		−	1.18253i	−0.806478	−	0.591264i	$-0.798629\pi$
$541$		−	8.05017e6i		−	1.18253i	0.806478	−	0.591264i	$-0.201371\pi$
$542$	−2.74983e6	−	914697.i	−0.402076	−	0.133746i
$543$			6.73748e6i			0.980614i
$544$	−3.56590e6	−	124231.i	−0.516620	−	0.0179984i
$545$		0			0
$546$	2.17370e6	−	6.53475e6i	0.312046	−	0.938096i
$547$	−6.14990e6			−0.878819			−0.439410	−	0.898287i	$-0.644812\pi$
$547$	−6.14990e6			−0.878819			−0.439410	+	0.898287i	$0.644812\pi$
$548$	−4.23054e6	+	5.65547e6i	−0.601789	+	0.804483i
$549$		−	8.40159e6i		−	1.18968i
$550$		0			0
$551$	1.90995e7			2.68005
$552$	−1.94800e7	+	1.35403e7i	−2.72107	+	1.89139i
$553$			3.99298e6i			0.555244i
$554$	3.30559e6	+	1.09956e6i	0.457588	+	0.152211i
$555$		0			0
$556$	−2.95905e6	+	3.95572e6i	−0.405944	+	0.542673i
$557$	6.26714e6			0.855917			0.427959	−	0.903798i	$-0.359233\pi$
$557$	6.26714e6			0.855917			0.427959	+	0.903798i	$0.359233\pi$
$558$	2.30081e7	+	7.65335e6i	3.12820	+	1.04056i
$559$	−3.76160e6			−0.509146
$560$		0			0
$561$	−3.31748e6			−0.445042
$562$	−6.55298e6	−	2.17977e6i	−0.875182	−	0.291118i
$563$	149874.			0.0199276			0.00996378	−	0.999950i	$-0.496828\pi$
$563$	149874.			0.0199276			0.00996378	+	0.999950i	$0.496828\pi$
$564$	−3.25052e6	+	4.34535e6i	−0.430283	+	0.575211i
$565$		0			0
$566$	3.73760e6	+	1.24327e6i	0.490401	+	0.163126i
$567$		−	1.70004e7i		−	2.22076i
$568$	3.41861e6	+	4.91822e6i	0.444609	+	0.639642i
$569$	−2.10351e6			−0.272373			−0.136186	−	0.990683i	$-0.543485\pi$
$569$	−2.10351e6			−0.272373			−0.136186	+	0.990683i	$0.543485\pi$
$570$		0			0
$571$		−	8.72030e6i		−	1.11929i	−0.828734	−	0.559643i	$-0.810938\pi$
$571$		−	8.72030e6i		−	1.11929i	0.828734	−	0.559643i	$-0.189062\pi$
$572$	−1.58753e6	+	2.12224e6i	−0.202877	+	0.271210i
$573$	2.35820e7			3.00050
$574$	−304201.	+	914511.i	−0.0385372	+	0.115854i
$575$		0			0
$576$	−7.23234e6	+	1.94530e7i	−0.908285	+	2.44304i
$577$		−	5.44606e6i		−	0.680993i	−0.940246	−	0.340497i	$-0.889405\pi$
$577$		−	5.44606e6i		−	0.680993i	0.940246	−	0.340497i	$-0.110595\pi$
$578$	−5.58476e6	−	1.85770e6i	−0.695321	−	0.231290i
$579$		−	1.05569e7i		−	1.30870i
$580$		0			0
$581$			7.23261e6i			0.888904i
$582$	−1.17473e6	+	3.53156e6i	−0.143758	+	0.432175i
$583$		−	5.88816e6i		−	0.717477i
$584$	−2.76403e6	+	1.92125e6i	−0.335360	+	0.233106i
$585$		0			0
$586$	−723249.	−	240580.i	−0.0870050	−	0.0289411i
$587$	−1.53801e6			−0.184232			−0.0921158	−	0.995748i	$-0.529363\pi$
$587$	−1.53801e6			−0.184232			−0.0921158	+	0.995748i	$0.529363\pi$
$588$	6.55874e6	+	4.90623e6i	0.782307	+	0.585201i
$589$			1.68762e7i			2.00441i
$590$		0			0
$591$	−6.70618e6			−0.789781
$592$	1.39057e6	+	4.72361e6i	0.163076	+	0.553950i
$593$			1.23546e7i			1.44275i	0.692542	+	0.721377i	$0.256491\pi$
$593$			1.23546e7i			1.44275i	−0.692542	+	0.721377i	$0.743509\pi$
$594$	−3.75383e6	+	1.12851e7i	−0.436525	+	1.31231i
$595$		0			0
$596$	−2.93223e6	+	3.91986e6i	−0.338129	+	0.452017i
$597$	5.26604e6			0.604711
$598$	3.59841e6	−	1.08178e7i	0.411488	−	1.23705i
$599$	1.46319e7			1.66622			0.833112	−	0.553105i	$-0.186557\pi$
$599$	1.46319e7			1.66622			0.833112	+	0.553105i	$0.186557\pi$
$600$		0			0
$601$	−1.08262e7			−1.22261			−0.611306	−	0.791394i	$-0.709356\pi$
$601$	−1.08262e7			−1.22261			−0.611306	+	0.791394i	$0.709356\pi$
$602$	−1.33277e6	+	4.00668e6i	−0.149887	+	0.450602i
$603$	6.10709e6			0.683976
$604$	−1.12870e7	−	8.44318e6i	−1.25889	−	0.941702i
$605$		0			0
$606$	2.05580e6	−	6.18031e6i	0.227405	−	0.683642i
$607$			722652.i			0.0796082i	0.999208	+	0.0398041i	$0.0126734\pi$
$607$			722652.i			0.0796082i	−0.999208	+	0.0398041i	$0.987327\pi$
$608$	−1.44359e7	−	502927.i	−1.58374	−	0.0551754i
$609$	2.04831e7			2.23796
$610$		0			0
$611$		−	2.60780e6i		−	0.282599i
$612$	7.47796e6	−	9.99668e6i	0.807058	−	1.07889i
$613$	−1.19951e6			−0.128930			−0.0644648	−	0.997920i	$-0.520534\pi$
$613$	−1.19951e6			−0.128930			−0.0644648	+	0.997920i	$0.520534\pi$
$614$	−1.50762e6	−	501492.i	−0.161388	−	0.0536838i
$615$		0			0
$616$	1.69804e6	+	2.44290e6i	0.180300	+	0.259390i
$617$		−	1.26945e7i		−	1.34246i	−0.741249	−	0.671230i	$-0.765766\pi$
$617$		−	1.26945e7i		−	1.34246i	0.741249	−	0.671230i	$-0.234234\pi$
$618$	−9.29078e6	+	2.79307e7i	−0.978546	+	2.94178i
$619$		−	9.69565e6i		−	1.01707i	−0.861042	−	0.508534i	$-0.830187\pi$
$619$		−	9.69565e6i		−	1.01707i	0.861042	−	0.508534i	$-0.169813\pi$
$620$		0			0
$621$		−	5.11590e7i		−	5.32344i
$622$	1.29011e7	+	4.29140e6i	1.33706	+	0.444757i
$623$		−	7.37501e6i		−	0.761276i
$624$	−3.89718e6	−	1.32383e7i	−0.400672	−	1.36104i
$625$		0			0
$626$	1.10616e6	−	3.32541e6i	0.112819	−	0.339164i
$627$	−1.34302e7			−1.36431
$628$	1.11050e7	+	8.30700e6i	1.12362	+	0.840515i
$629$		−	2.96196e6i		−	0.298506i
$630$		0			0
$631$	2.38091e6			0.238051			0.119025	−	0.992891i	$-0.462023\pi$
$631$	2.38091e6			0.238051			0.119025	+	0.992891i	$0.462023\pi$
$632$	4.56676e6	+	6.57001e6i	0.454794	+	0.654295i
$633$		−	1.55496e7i		−	1.54244i
$634$	4.90081e6	+	1.63019e6i	0.484222	+	0.161070i
$635$		0			0
$636$	2.45504e7	+	1.83648e7i	2.40666	+	1.80029i
$637$	−3.93613e6			−0.384345
$638$	−7.47977e6	−	2.48805e6i	−0.727506	−	0.241996i
$639$	−2.09569e7			−2.03037
$640$		0			0
$641$	6.37112e6			0.612450			0.306225	−	0.951959i	$-0.400934\pi$
$641$	6.37112e6			0.612450			0.306225	+	0.951959i	$0.400934\pi$
$642$	−2.03683e7	−	6.77527e6i	−1.95037	−	0.648768i
$643$	1.64996e7			1.57379			0.786896	−	0.617086i	$-0.211687\pi$
$643$	1.64996e7			1.57379			0.786896	+	0.617086i	$0.211687\pi$
$644$	−1.02477e7	−	7.66571e6i	−0.973666	−	0.728346i
$645$		0			0
$646$	8.24471e6	+	2.74250e6i	0.777310	+	0.258562i
$647$			2.94843e6i			0.276905i	0.990369	+	0.138452i	$0.0442128\pi$
$647$			2.94843e6i			0.276905i	−0.990369	+	0.138452i	$0.955787\pi$
$648$	−1.94433e7	−	2.79723e7i	−1.81900	−	2.61692i
$649$	3.79306e6			0.353491
$650$		0			0
$651$			1.80987e7i			1.67376i
$652$	−5.17460e6	−	3.87083e6i	−0.476713	−	0.356603i
$653$	−1.02662e7			−0.942167			−0.471083	−	0.882089i	$-0.656137\pi$
$653$	−1.02662e7			−0.942167			−0.471083	+	0.882089i	$0.656137\pi$
$654$	2.61990e6	−	7.87614e6i	0.239519	−	0.720061i
$655$		0			0
$656$	545394.	+	1.85264e6i	0.0494824	+	0.168086i
$657$		−	1.17777e7i		−	1.06451i
$658$	−2.77770e6	−	923968.i	−0.250104	−	0.0831941i
$659$		−	7.94727e6i		−	0.712860i	−0.934322	−	0.356430i	$-0.883994\pi$
$659$		−	7.94727e6i		−	0.712860i	0.934322	−	0.356430i	$-0.116006\pi$
$660$		0			0
$661$			9.79140e6i			0.871648i	0.900032	+	0.435824i	$0.143543\pi$
$661$			9.79140e6i			0.871648i	−0.900032	+	0.435824i	$0.856457\pi$
$662$	−6.03252e6	+	1.81354e7i	−0.535000	+	1.60836i
$663$			8.30112e6i			0.733420i
$664$	8.27191e6	+	1.19005e7i	0.728091	+	1.04748i
$665$		0			0
$666$	−1.63478e7	−	5.43790e6i	−1.42815	−	0.475057i
$667$	3.39083e7			2.95115
$668$	−5.76378e6	+	7.70513e6i	−0.499765	+	0.668096i
$669$			2.10571e7i			1.81901i
$670$		0			0
$671$	−2.41335e6			−0.206926
$672$	−1.54816e7	−	539359.i	−1.32249	−	0.0460739i
$673$		−	1.64861e7i		−	1.40307i	−0.712635	−	0.701535i	$-0.752498\pi$
$673$		−	1.64861e7i		−	1.40307i	0.712635	−	0.701535i	$-0.247502\pi$
$674$	−5.70530e6	+	1.71517e7i	−0.483758	+	1.45431i
$675$		0			0
$676$	−4.20368e6	−	3.14454e6i	−0.353804	−	0.264661i
$677$	2.81251e6			0.235843			0.117922	−	0.993023i	$-0.462377\pi$
$677$	2.81251e6			0.235843			0.117922	+	0.993023i	$0.462377\pi$
$678$	4.88277e6	−	1.46790e7i	0.407936	−	1.22637i
$679$	−2.00771e6			−0.167120
$680$		0			0
$681$	−6.40461e6			−0.529206
$682$	2.19842e6	−	6.60905e6i	0.180988	−	0.544100i
$683$	−1.56071e7			−1.28018			−0.640090	−	0.768300i	$-0.721103\pi$
$683$	−1.56071e7			−1.28018			−0.640090	+	0.768300i	$0.721103\pi$
$684$	3.02731e7	−	4.04697e7i	2.47410	−	3.30742i
$685$		0			0
$686$	−4.10550e6	+	1.23423e7i	−0.333085	+	1.00135i
$687$			2.24811e7i			1.81729i
$688$	2.38949e6	+	8.11684e6i	0.192457	+	0.653756i
$689$	−1.47335e7			−1.18239
$690$		0			0
$691$			1.32611e7i			1.05654i	0.849077	+	0.528269i	$0.177159\pi$
$691$			1.32611e7i			1.05654i	−0.849077	+	0.528269i	$0.822841\pi$
$692$	2.57533e6	+	1.92646e6i	0.204441	+	0.152931i
$693$	−1.04094e7			−0.823362
$694$	1.15531e7	+	3.84298e6i	0.910539	+	0.302879i
$695$		0			0
$696$	3.37027e7	−	2.34265e7i	2.63719	−	1.83309i
$697$		−	1.16171e6i		−	0.0905763i
$698$	4.97844e6	−	1.49666e7i	0.386772	−	1.16274i
$699$			2.54807e7i			1.97251i
$700$		0			0
$701$		−	2.41803e7i		−	1.85852i	−0.369432	−	0.929258i	$-0.620448\pi$
$701$		−	2.41803e7i		−	1.85852i	0.369432	−	0.929258i	$-0.379552\pi$
$702$	2.82379e7	+	9.39297e6i	2.16266	+	0.719383i
$703$		−	1.19909e7i		−	0.915093i
$704$	5.58787e6	+	2.07748e6i	0.424927	+	0.157981i
$705$		0			0
$706$	5.77177e6	−	1.73515e7i	0.435810	−	1.31016i
$707$	3.51354e6			0.264361
$708$	−1.18303e7	+	1.58150e7i	−0.886979	+	1.18573i
$709$		−	3.10586e6i		−	0.232042i	−0.993247	−	0.116021i	$-0.962986\pi$
$709$		−	3.10586e6i		−	0.232042i	0.993247	−	0.116021i	$-0.0370140\pi$
$710$		0			0
$711$	−2.79953e7			−2.07688
$712$	−8.43477e6	−	1.21348e7i	−0.623553	−	0.897081i
$713$			2.99610e7i			2.20716i
$714$	8.84196e6	+	2.94117e6i	0.649087	+	0.215911i
$715$		0			0
$716$	−1.06205e7	+	1.41977e7i	−0.774219	+	1.03499i
$717$	1.03058e7			0.748661
$718$	−1.08481e7	−	3.60849e6i	−0.785313	−	0.261225i
$719$	7.95560e6			0.573919			0.286960	−	0.957943i	$-0.407355\pi$
$719$	7.95560e6			0.573919			0.286960	+	0.957943i	$0.407355\pi$
$720$		0			0
$721$	−1.58787e7			−1.13757
$722$	2.00862e7	+	6.68143e6i	1.43402	+	0.477009i
$723$	−2.49902e7			−1.77797
$724$	−4.36246e6	+	5.83181e6i	−0.309303	+	0.413483i
$725$		0			0
$726$	−2.03317e7	−	6.76309e6i	−1.43164	−	0.476216i
$727$			2.50891e7i			1.76055i	0.474463	+	0.880276i	$0.342642\pi$
$727$			2.50891e7i			1.76055i	−0.474463	+	0.880276i	$0.657358\pi$
$728$	6.11270e6	−	4.24888e6i	0.427469	−	0.297130i
$729$	3.60626e7			2.51327
$730$		0			0
$731$		−	5.08969e6i		−	0.352288i
$732$	7.52709e6	−	1.00624e7i	0.519217	−	0.694100i
$733$	2.58258e7			1.77539			0.887694	−	0.460434i	$-0.152306\pi$
$733$	2.58258e7			1.77539			0.887694	+	0.460434i	$0.152306\pi$
$734$	4.47244e6	−	1.34454e7i	0.306411	−	0.921156i
$735$		0			0
$736$	−2.56287e7	−	892869.i	−1.74394	−	0.0607566i
$737$		−	1.75426e6i		−	0.118966i
$738$	−6.41176e6	−	2.13279e6i	−0.433347	−	0.144148i
$739$			2.15950e7i			1.45459i	0.686323	+	0.727297i	$0.259224\pi$
$739$			2.15950e7i			1.45459i	−0.686323	+	0.727297i	$0.740776\pi$
$740$		0			0
$741$			3.36055e7i			2.24835i
$742$	−5.22024e6	+	1.56935e7i	−0.348081	+	1.04643i
$743$		−	1.25570e7i		−	0.834479i	−0.908797	−	0.417239i	$-0.862998\pi$
$743$		−	1.25570e7i		−	0.834479i	0.908797	−	0.417239i	$-0.137002\pi$
$744$	2.06994e7	+	2.97794e7i	1.37096	+	1.97235i
$745$		0			0
$746$	2.65793e6	+	884126.i	0.174862	+	0.0581657i
$747$	−5.07088e7			−3.32492
$748$	−2.87154e6	−	2.14804e6i	−0.187655	−	0.140374i
$749$		−	1.15795e7i		−	0.754199i
$750$		0			0
$751$	−5.43894e6			−0.351896			−0.175948	−	0.984399i	$-0.556299\pi$
$751$	−5.43894e6			−0.351896			−0.175948	+	0.984399i	$0.556299\pi$
$752$	−5.62715e6	+	1.65656e6i	−0.362864	+	0.106823i
$753$			4.50097e7i			2.89280i
$754$	−6.22569e6	+	1.87161e7i	−0.398803	+	1.19891i
$755$		0			0
$756$	2.00099e7	−	2.67496e7i	1.27333	−	1.70221i
$757$	−1.06247e7			−0.673873			−0.336937	−	0.941527i	$-0.609391\pi$
$757$	−1.06247e7			−0.673873			−0.336937	+	0.941527i	$0.609391\pi$
$758$	3.91094e6	−	1.17574e7i	0.247234	−	0.743253i
$759$	−2.38433e7			−1.50232
$760$		0			0
$761$	2.31511e7			1.44914			0.724570	−	0.689201i	$-0.242038\pi$
$761$	2.31511e7			1.44914			0.724570	+	0.689201i	$0.242038\pi$
$762$	−7.25151e6	+	2.18000e7i	−0.452419	+	1.36010i
$763$	4.47763e6			0.278443
$764$	2.04120e7	+	1.52691e7i	1.26518	+	0.946412i
$765$		0			0
$766$	517363.	−	1.55534e6i	0.0318584	−	0.0957751i
$767$		−	9.49113e6i		−	0.582545i
$768$	−2.60902e7	+	1.68188e7i	−1.59615	+	1.02894i
$769$	−9.09958e6			−0.554888			−0.277444	−	0.960742i	$-0.589487\pi$
$769$	−9.09958e6			−0.554888			−0.277444	+	0.960742i	$0.589487\pi$
$770$		0			0
$771$			2.02011e7i			1.22388i
$772$	6.83549e6	−	9.13781e6i	0.412787	−	0.551822i
$773$	1.82799e7			1.10034			0.550169	−	0.835053i	$-0.314563\pi$
$773$	1.82799e7			1.10034			0.550169	+	0.835053i	$0.314563\pi$
$774$	−2.80913e7	−	9.34423e6i	−1.68547	−	0.560649i
$775$		0			0
$776$	−3.30347e6	+	2.29622e6i	−0.196932	+	0.136886i
$777$		−	1.28596e7i		−	0.764142i
$778$	3.77728e6	−	1.13556e7i	0.223733	−	0.672604i
$779$		−	4.70295e6i		−	0.277669i
$780$		0			0
$781$			6.01985e6i			0.353149i
$782$	1.46372e7	+	4.86889e6i	0.855937	+	0.284717i
$783$			8.85113e7i			5.15934i
$784$	2.50036e6	+	8.49345e6i	0.145282	+	0.493508i
$785$		0			0
$786$	−4.85787e6	+	1.46041e7i	−0.280472	+	0.843177i
$787$	3.07594e6			0.177028			0.0885139	−	0.996075i	$-0.471788\pi$
$787$	3.07594e6			0.177028			0.0885139	+	0.996075i	$0.471788\pi$
$788$	−5.80472e6	−	4.34219e6i	−0.333017	−	0.249111i
$789$		−	2.70558e6i		−	0.154728i
$790$		0			0
$791$	8.34507e6			0.474230
$792$	−1.71275e7	+	1.19051e7i	−0.970242	+	0.674407i
$793$			6.03877e6i			0.341009i
$794$	−9.70164e6	−	3.22713e6i	−0.546127	−	0.181662i
$795$		0			0
$796$	4.55816e6	+	3.40971e6i	0.254981	+	0.190737i
$797$	2.64996e6			0.147772			0.0738861	−	0.997267i	$-0.476460\pi$
$797$	2.64996e6			0.147772			0.0738861	+	0.997267i	$0.476460\pi$
$798$	3.57950e7	+	1.19068e7i	1.98983	+	0.661891i
$799$	3.52853e6			0.195536
$800$		0			0
$801$	5.17071e7			2.84754
$802$	1.39083e7	+	4.62641e6i	0.763549	+	0.253985i
$803$	−3.38315e6			−0.185153
$804$	7.31429e6	+	5.47141e6i	0.399054	+	0.298510i
$805$		0			0
$806$	−1.65374e7	−	5.50096e6i	−0.896664	−	0.298264i
$807$			2.76932e7i			1.49689i
$808$	5.78115e6	−	4.01843e6i	0.311520	−	0.216535i
$809$	−4.52804e6			−0.243242			−0.121621	−	0.992577i	$-0.538809\pi$
$809$	−4.52804e6			−0.243242			−0.121621	+	0.992577i	$0.538809\pi$
$810$		0			0
$811$			2.45669e7i			1.31159i	0.754939	+	0.655795i	$0.227666\pi$
$811$			2.45669e7i			1.31159i	−0.754939	+	0.655795i	$0.772334\pi$
$812$	1.77297e7	+	1.32626e7i	0.943652	+	0.705893i
$813$	1.51656e7			0.804701
$814$	−1.56203e6	+	4.69590e6i	−0.0826283	+	0.248404i
$815$		0			0
$816$	1.79123e7	−	5.27315e6i	0.941728	−	0.277233i
$817$		−	2.06047e7i		−	1.07997i
$818$	−2.68859e7	−	8.94325e6i	−1.40489	−	0.467318i
$819$			2.60466e7i			1.35688i
$820$		0			0
$821$			3.38228e7i			1.75126i	0.482981	+	0.875631i	$0.339554\pi$
$821$			3.38228e7i			1.75126i	−0.482981	+	0.875631i	$0.660446\pi$
$822$	1.16660e7	−	3.50711e7i	0.602200	−	1.81038i
$823$		−	1.50699e7i		−	0.775554i	−0.921753	−	0.387777i	$-0.873243\pi$
$823$		−	1.50699e7i		−	0.775554i	0.921753	−	0.387777i	$-0.126757\pi$
$824$	−2.61267e7	+	1.81605e7i	−1.34050	+	0.931770i
$825$		0			0
$826$	−1.01095e7	−	3.36280e6i	−0.515561	−	0.171495i
$827$	−1.25312e7			−0.637132			−0.318566	−	0.947901i	$-0.603201\pi$
$827$	−1.25312e7			−0.637132			−0.318566	+	0.947901i	$0.603201\pi$
$828$	5.37453e7	−	7.18477e7i	2.72436	−	3.64198i
$829$		−	6.28073e6i		−	0.317412i	−0.987326	−	0.158706i	$-0.949268\pi$
$829$		−	6.28073e6i		−	0.317412i	0.987326	−	0.158706i	$-0.0507323\pi$
$830$		0			0
$831$	−1.82307e7			−0.915801
$832$	5.19835e6	−	1.39821e7i	0.260350	−	0.700270i
$833$		−	5.32585e6i		−	0.265936i
$834$	8.15976e6	−	2.45305e7i	0.406221	−	1.22121i
$835$		0			0
$836$	−1.16249e7	−	8.69593e6i	−0.575271	−	0.430329i
$837$	−7.82078e7			−3.85866
$838$	−4.06847e6	+	1.22309e7i	−0.200134	+	0.601658i
$839$	−2.04326e7			−1.00212			−0.501058	−	0.865414i	$-0.667056\pi$
$839$	−2.04326e7			−1.00212			−0.501058	+	0.865414i	$0.667056\pi$
$840$		0			0
$841$	−3.81543e7			−1.86018
$842$	−2.32840e6	+	6.99981e6i	−0.113182	+	0.340256i
$843$	3.61404e7			1.75156
$844$	1.00682e7	−	1.34594e7i	0.486514	−	0.650382i
$845$		0			0
$846$	6.47806e6	−	1.94748e7i	0.311185	−	0.935509i
$847$		−	1.15587e7i		−	0.553605i
$848$	9.35924e6	+	3.17923e7i	0.446942	+	1.51821i
$849$	−2.06133e7			−0.981472
$850$		0			0
$851$		−	2.12881e7i		−	1.00766i
$852$	−2.50995e7	−	1.87755e7i	−1.18458	−	0.886121i
$853$	−2.97962e7			−1.40213			−0.701066	−	0.713097i	$-0.747292\pi$
$853$	−2.97962e7			−1.40213			−0.701066	+	0.713097i	$0.747292\pi$
$854$	6.43221e6	+	2.13960e6i	0.301798	+	0.100389i
$855$		0			0
$856$	−1.32435e7	−	1.90528e7i	−0.617756	−	0.888741i
$857$		−	2.06770e7i		−	0.961690i	−0.876806	−	0.480845i	$-0.840330\pi$
$857$		−	2.06770e7i		−	0.961690i	0.876806	−	0.480845i	$-0.159670\pi$
$858$	4.37771e6	−	1.31606e7i	0.203015	−	0.610320i
$859$		−	2.17795e7i		−	1.00708i	−0.863971	−	0.503542i	$-0.832030\pi$
$859$		−	2.17795e7i		−	1.00708i	0.863971	−	0.503542i	$-0.167970\pi$
$860$		0			0
$861$		−	5.04363e6i		−	0.231865i
$862$	−2.11485e7	−	7.03478e6i	−0.969419	−	0.322465i
$863$		−	2.24327e7i		−	1.02531i	−0.858596	−	0.512654i	$-0.828663\pi$
$863$		−	2.24327e7i		−	1.02531i	0.858596	−	0.512654i	$-0.171337\pi$
$864$	2.33067e6	−	6.68989e7i	0.106218	−	3.04884i
$865$		0			0
$866$	1.04354e7	−	3.13716e7i	0.472839	−	1.42148i
$867$	3.08006e7			1.39159
$868$	−1.17187e7	+	1.56658e7i	−0.527936	+	0.705755i
$869$			8.04162e6i			0.361239i
$870$		0			0
$871$	−4.38956e6			−0.196054
$872$	7.36745e6	−	5.12105e6i	0.328115	−	0.228070i
$873$		−	1.40763e7i		−	0.625107i
$874$	5.92560e7	+	1.97108e7i	2.62394	+	0.872821i
$875$		0			0
$876$	1.05518e7	−	1.41059e7i	0.464587	−	0.621068i
$877$	3.66024e7			1.60698			0.803491	−	0.595317i	$-0.202973\pi$
$877$	3.66024e7			1.60698			0.803491	+	0.595317i	$0.202973\pi$
$878$	−4.09563e7	−	1.36236e7i	−1.79302	−	0.596424i
$879$	3.98880e6			0.174129
$880$		0			0
$881$	−4.27422e7			−1.85531			−0.927656	−	0.373436i	$-0.878179\pi$
$881$	−4.27422e7			−1.85531			−0.927656	+	0.373436i	$0.878179\pi$
$882$	−2.93947e7	−	9.77779e6i	−1.27233	−	0.423223i
$883$	−1.39684e7			−0.602901			−0.301451	−	0.953482i	$-0.597471\pi$
$883$	−1.39684e7			−0.602901			−0.301451	+	0.953482i	$0.597471\pi$
$884$	−5.37489e6	+	7.18526e6i	−0.231334	+	0.309252i
$885$		0			0
$886$	1.06822e7	+	3.55330e6i	0.457169	+	0.152071i
$887$			8.75249e6i			0.373528i	0.982405	+	0.186764i	$0.0597999\pi$
$887$			8.75249e6i			0.373528i	−0.982405	+	0.186764i	$0.940200\pi$
$888$	−1.47075e7	−	2.11590e7i	−0.625900	−	0.900458i
$889$	−1.23934e7			−0.525941
$890$		0			0
$891$		−	3.42378e7i		−	1.44481i
$892$	−1.36343e7	+	1.82266e7i	−0.573747	+	0.766996i
$893$	1.42846e7			0.599430
$894$	8.08579e6	−	2.43081e7i	0.338360	−	1.01720i
$895$		0			0
$896$	−1.30513e7	−	1.04910e7i	−0.543105	−	0.436565i
$897$			5.96614e7i			2.47578i
$898$	−1.10310e7	−	3.66932e6i	−0.456482	−	0.151843i
$899$		−	5.18363e7i		−	2.13912i
$900$		0			0
$901$		−	1.99355e7i		−	0.818116i
$902$	−612642.	+	1.84177e6i	−0.0250721	+	0.0753736i
$903$		−	2.20973e7i		−	0.901819i
$904$	1.37309e7	−	9.54423e6i	0.558828	−	0.388436i
$905$		0			0
$906$	6.99938e7	+	2.32826e7i	2.83295	+	0.942345i
$907$	4.22342e7			1.70469			0.852345	−	0.522979i	$-0.175180\pi$
$907$	4.22342e7			1.70469			0.852345	+	0.522979i	$0.175180\pi$
$908$	−5.54369e6	−	4.14693e6i	−0.223144	−	0.166921i
$909$			2.46339e7i			0.988834i
$910$		0			0
$911$	3.59551e7			1.43537			0.717686	−	0.696367i	$-0.245201\pi$
$911$	3.59551e7			1.43537			0.717686	+	0.696367i	$0.245201\pi$
$912$	7.25145e7	−	2.13473e7i	2.88694	−	0.849878i
$913$			1.45661e7i			0.578316i
$914$	4.90456e6	−	1.47445e7i	0.194193	−	0.583799i
$915$		0			0
$916$	−1.45563e7	+	1.94591e7i	−0.573207	+	0.766274i
$917$	−8.30252e6			−0.326052
$918$	−1.27093e7	+	3.82077e7i	−0.497755	+	1.49639i
$919$	−4.72565e6			−0.184575			−0.0922875	−	0.995732i	$-0.529418\pi$
$919$	−4.72565e6			−0.184575			−0.0922875	+	0.995732i	$0.529418\pi$
$920$		0			0
$921$	8.31472e6			0.322997
$922$	−7.17172e6	+	2.15602e7i	−0.277841	+	0.835266i
$923$	1.50631e7			0.581981
$924$	−1.24670e7	−	9.32586e6i	−0.480376	−	0.359343i
$925$		0			0
$926$	−1.38874e7	+	4.17493e7i	−0.532223	+	1.60001i
$927$		−	1.11328e8i		−	4.25505i
$928$	4.43407e7	+	1.54477e6i	1.69018	+	0.0588837i
$929$	3.52534e7			1.34018			0.670088	−	0.742282i	$-0.266256\pi$
$929$	3.52534e7			1.34018			0.670088	+	0.742282i	$0.266256\pi$
$930$		0			0
$931$		−	2.15607e7i		−	0.815246i
$932$	−1.64985e7	+	2.20555e7i	−0.622164	+	0.831721i
$933$	−7.11513e7			−2.67595
$934$	2.04741e7	+	6.81044e6i	0.767957	+	0.255451i
$935$		0			0
$936$	2.97895e7	+	4.28569e7i	1.11141	+	1.59894i
$937$			4.46076e7i			1.65982i	0.557899	+	0.829909i	$0.311607\pi$
$937$			4.46076e7i			1.65982i	−0.557899	+	0.829909i	$0.688393\pi$
$938$	−1.55526e6	+	4.67555e6i	−0.0577161	+	0.173511i
$939$			1.83400e7i			0.678791i
$940$		0			0
$941$			901496.i			0.0331886i	0.999862	+	0.0165943i	$0.00528238\pi$
$941$			901496.i			0.0331886i	−0.999862	+	0.0165943i	$0.994718\pi$
$942$	−6.88649e7	−	2.29070e7i	−2.52854	−	0.841089i
$943$		−	8.34937e6i		−	0.305756i
$944$	−2.04801e7	+	6.02909e6i	−0.748001	+	0.220202i
$945$		0			0
$946$	−2.68412e6	+	8.06921e6i	−0.0975157	+	0.293159i
$947$	−1.66417e7			−0.603006			−0.301503	−	0.953465i	$-0.597488\pi$
$947$	−1.66417e7			−0.603006			−0.301503	+	0.953465i	$0.597488\pi$
$948$	−3.35292e7	−	2.50813e7i	−1.21172	−	0.906420i
$949$			8.46542e6i			0.305129i
$950$		0			0
$951$	−2.70285e7			−0.969105
$952$	5.74902e6	+	8.27089e6i	0.205590	+	0.295774i
$953$		−	1.76926e7i		−	0.631043i	−0.948918	−	0.315522i	$-0.897821\pi$
$953$		−	1.76926e7i		−	0.631043i	0.948918	−	0.315522i	$-0.102179\pi$
$954$	−1.10029e8	−	3.65998e7i	−3.91414	−	1.30199i
$955$		0			0
$956$	8.92050e6	+	6.67293e6i	0.315678	+	0.236141i
$957$	4.12518e7			1.45600
$958$	−1.31108e7	−	4.36116e6i	−0.461548	−	0.153528i
$959$	1.99381e7			0.700063
$960$		0			0
$961$	1.71729e7			0.599841
$962$	1.17502e7	+	3.90857e6i	0.409363	+	0.136170i
$963$	8.11855e7			2.82106
$964$	−2.16310e7	−	1.61809e7i	−0.749693	−	0.560804i
$965$		0			0
$966$	6.35485e7	+	2.11386e7i	2.19110	+	0.728843i
$967$		−	1.08926e7i		−	0.374598i	−0.982303	−	0.187299i	$-0.940027\pi$
$967$		−	1.08926e7i		−	0.374598i	0.982303	−	0.187299i	$-0.0599733\pi$
$968$	−1.32196e7	−	1.90186e7i	−0.453452	−	0.652363i
$969$	−4.54705e7			−1.55568
$970$		0			0
$971$		−	1.33282e7i		−	0.453654i	−0.973935	−	0.226827i	$-0.927165\pi$
$971$		−	1.33282e7i		−	0.453654i	0.973935	−	0.226827i	$-0.0728351\pi$
$972$	7.07980e7	+	5.29600e7i	2.40356	+	1.79797i
$973$	1.39457e7			0.472236
$974$	−1.49118e7	+	4.48289e7i	−0.503654	+	1.51412i
$975$		0			0
$976$	1.30306e7	−	3.83603e6i	0.437863	−	0.128901i
$977$		−	5.24537e7i		−	1.75808i	−0.476745	−	0.879042i	$-0.658184\pi$
$977$		−	5.24537e7i		−	1.75808i	0.476745	−	0.879042i	$-0.341816\pi$
$978$	3.20891e7	+	1.06740e7i	1.07278	+	0.356846i
$979$		−	1.48528e7i		−	0.495282i
$980$		0			0
$981$			3.13932e7i			1.04151i
$982$	607191.	−	1.82538e6i	0.0200931	−	0.0604053i
$983$		−	9.86355e6i		−	0.325574i	−0.986661	−	0.162787i	$-0.947952\pi$
$983$		−	9.86355e6i		−	0.325574i	0.986661	−	0.162787i	$-0.0520483\pi$
$984$	−5.76839e6	−	8.29875e6i	−0.189918	−	0.273228i
$985$		0			0
$986$	−2.53242e7	−	8.42377e6i	−0.829551	−	0.275940i
$987$	1.53194e7			0.500550
$988$	−2.17592e7	+	2.90882e7i	−0.709172	+	0.948034i
$989$		−	3.65804e7i		−	1.18921i
$990$		0			0
$991$	2.89033e7			0.934897			0.467448	−	0.884020i	$-0.345173\pi$
$991$	2.89033e7			0.934897			0.467448	+	0.884020i	$0.345173\pi$
$992$	−1.36495e6	+	3.91791e7i	−0.0440389	+	1.26408i
$993$		−	1.00019e8i		−	3.21891i
$994$	5.33699e6	−	1.60445e7i	0.171329	−	0.515062i
$995$		0			0
$996$	−6.07325e7	−	4.54306e7i	−1.93987	−	1.45111i
$997$	4.81768e6			0.153497			0.0767485	−	0.997050i	$-0.475546\pi$
$997$	4.81768e6			0.153497			0.0767485	+	0.997050i	$0.475546\pi$
$998$	1.15877e6	−	3.48360e6i	0.0368275	−	0.110714i
$999$	5.55686e7			1.76163

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.f.d.149.3		40
4.3	odd	2		800.6.f.d.49.2		40
5.2	odd	4		200.6.d.c.101.11	✓	20
5.3	odd	4		200.6.d.d.101.10	yes	20
5.4	even	2	inner	200.6.f.d.149.38		40
8.3	odd	2		800.6.f.d.49.40		40
8.5	even	2	inner	200.6.f.d.149.37		40
20.3	even	4		800.6.d.b.401.1		20
20.7	even	4		800.6.d.d.401.20		20
20.19	odd	2		800.6.f.d.49.39		40
40.3	even	4		800.6.d.b.401.20		20
40.13	odd	4		200.6.d.d.101.9	yes	20
40.19	odd	2		800.6.f.d.49.1		40
40.27	even	4		800.6.d.d.401.1		20
40.29	even	2	inner	200.6.f.d.149.4		40
40.37	odd	4		200.6.d.c.101.12	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.6.d.c.101.11	✓	20	5.2	odd	4
200.6.d.c.101.12	yes	20	40.37	odd	4
200.6.d.d.101.9	yes	20	40.13	odd	4
200.6.d.d.101.10	yes	20	5.3	odd	4
200.6.f.d.149.3		40	1.1	even	1	trivial
200.6.f.d.149.4		40	40.29	even	2	inner
200.6.f.d.149.37		40	8.5	even	2	inner
200.6.f.d.149.38		40	5.4	even	2	inner
800.6.d.b.401.1		20	20.3	even	4
800.6.d.b.401.20		20	40.3	even	4
800.6.d.d.401.1		20	40.27	even	4
800.6.d.d.401.20		20	20.7	even	4
800.6.f.d.49.1		40	40.19	odd	2
800.6.f.d.49.2		40	4.3	odd	2
800.6.f.d.49.39		40	20.19	odd	2
800.6.f.d.49.40		40	8.3	odd	2

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-5.36768 - 1.78549i) q^{2} +29.6034 q^{3} +(25.6240 + 19.1679i) q^{4} +(-158.902 - 52.8566i) q^{6} -90.3364i q^{7} +(-103.318 - 148.639i) q^{8} +633.360 q^{9} -181.932i q^{11} +(758.558 + 567.435i) q^{12} -455.237 q^{13} +(-161.295 + 484.897i) q^{14} +(289.182 + 982.319i) q^{16} -615.967i q^{17} +(-3399.68 - 1130.86i) q^{18} -2493.63i q^{19} -2674.26i q^{21} +(-324.839 + 976.555i) q^{22} -4427.05i q^{23} +(-3058.55 - 4400.21i) q^{24} +(2443.57 + 812.823i) q^{26} +11556.0 q^{27} +(1731.56 - 2314.78i) q^{28} +7659.34i q^{29} -6767.72 q^{31} +(201.685 - 5789.11i) q^{32} -5385.81i q^{33} +(-1099.80 + 3306.31i) q^{34} +(16229.2 + 12140.2i) q^{36} +4808.64 q^{37} +(-4452.35 + 13385.0i) q^{38} -13476.6 q^{39} +1885.99 q^{41} +(-4774.88 + 14354.6i) q^{42} +8262.94 q^{43} +(3487.26 - 4661.84i) q^{44} +(-7904.46 + 23763.0i) q^{46} +5728.44i q^{47} +(8560.77 + 29080.0i) q^{48} +8646.33 q^{49} -18234.7i q^{51} +(-11665.0 - 8725.95i) q^{52} +32364.5 q^{53} +(-62028.9 - 20633.1i) q^{54} +(-13427.5 + 9333.33i) q^{56} -73819.8i q^{57} +(13675.7 - 41112.9i) q^{58} +20848.8i q^{59} -13265.1i q^{61} +(36327.0 + 12083.7i) q^{62} -57215.5i q^{63} +(-11419.0 + 30714.0i) q^{64} +(-9616.33 + 28909.3i) q^{66} +9642.36 q^{67} +(11806.8 - 15783.6i) q^{68} -131056. i q^{69} -33088.4 q^{71} +(-65437.2 - 94141.9i) q^{72} -18595.6i q^{73} +(-25811.2 - 8585.79i) q^{74} +(47797.6 - 63896.7i) q^{76} -16435.1 q^{77} +(72337.9 + 24062.3i) q^{78} -44201.2 q^{79} +188190. q^{81} +(-10123.4 - 3367.42i) q^{82} -80063.0 q^{83} +(51260.1 - 68525.4i) q^{84} +(-44352.8 - 14753.4i) q^{86} +226742. i q^{87} +(-27042.2 + 18796.8i) q^{88} +81639.3 q^{89} +41124.5i q^{91} +(84857.3 - 113439. i) q^{92} -200348. q^{93} +(10228.1 - 30748.4i) q^{94} +(5970.56 - 171377. i) q^{96} -22224.8i q^{97} +(-46410.7 - 15438.0i) q^{98} -115229. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9} + 848 q^{14} - 110 q^{16} - 18918 q^{24} + 18344 q^{26} + 14320 q^{31} + 19182 q^{34} + 29656 q^{36} - 44904 q^{39} - 11608 q^{41} + 23186 q^{44} - 75224 q^{46} - 125304 q^{49}+ \cdots + 115582 q^{96}+O(q^{100}) \) 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9 + 848 * q^14 - 110 * q^16 - 18918 * q^24 + 18344 * q^26 + 14320 * q^31 + 19182 * q^34 + 29656 * q^36 - 44904 * q^39 - 11608 * q^41 + 23186 * q^44 - 75224 * q^46 - 125304 * q^49 - 177894 * q^54 - 73816 * q^56 - 230354 * q^64 + 262878 * q^66 - 15448 * q^71 - 4224 * q^74 + 111902 * q^76 + 15560 * q^79 + 193968 * q^81 + 195112 * q^84 - 131972 * q^86 + 6320 * q^89 + 117080 * q^94 + 115582 * q^96

Introduction

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