LMFDB - Embedded newform 200.6.d.c.101.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,6,Mod(101,200)]

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, 0]))

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

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

chi := DirichletCharacter("200.101");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	200.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$32.0767639626$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} - 130 x^{17} + 144 x^{16} + 1560 x^{15} - 12320 x^{14} - 56128 x^{13} + \cdots + 11\!\cdots\!24 $ x^20 - x^19 - 130x^17 + 144x^16 + 1560x^15 - 12320x^14 - 56128x^13 + 672256x^12 - 4183040x^11 + 25763840x^10 - 133857280x^9 + 688390144x^8 - 1839202304x^7 - 12918456320x^6 + 52344913920x^5 + 154618822656x^4 - 4466765987840x^3 - 35184372088832x + 1125899906842624
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{49}\cdot 5^{4}\cdot 31 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.11
Root			$-1.78549 + 5.36768i$ of defining polynomial
Character	$\chi$	$=$	200.101
Dual form			200.6.d.c.101.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.78549 - 5.36768i) q^{2} -29.6034i q^{3} +(-25.6240 - 19.1679i) q^{4} +(-158.902 - 52.8566i) q^{6} +90.3364 q^{7} +(-148.639 + 103.318i) q^{8} -633.360 q^{9} +O(q^{10})$	\(q+(1.78549 - 5.36768i) q^{2} -29.6034i q^{3} +(-25.6240 - 19.1679i) q^{4} +(-158.902 - 52.8566i) q^{6} +90.3364 q^{7} +(-148.639 + 103.318i) q^{8} -633.360 q^{9} -181.932i q^{11} +(-567.435 + 758.558i) q^{12} +455.237i q^{13} +(161.295 - 484.897i) q^{14} +(289.182 + 982.319i) q^{16} +615.967 q^{17} +(-1130.86 + 3399.68i) q^{18} +2493.63i q^{19} -2674.26i q^{21} +(-976.555 - 324.839i) q^{22} -4427.05 q^{23} +(3058.55 + 4400.21i) q^{24} +(2443.57 + 812.823i) q^{26} +11556.0i q^{27} +(-2314.78 - 1731.56i) q^{28} -7659.34i q^{29} -6767.72 q^{31} +(5789.11 + 201.685i) q^{32} -5385.81 q^{33} +(1099.80 - 3306.31i) q^{34} +(16229.2 + 12140.2i) q^{36} +4808.64i q^{37} +(13385.0 + 4452.35i) q^{38} +13476.6 q^{39} +1885.99 q^{41} +(-14354.6 - 4774.88i) q^{42} -8262.94i q^{43} +(-3487.26 + 4661.84i) q^{44} +(-7904.46 + 23763.0i) q^{46} -5728.44 q^{47} +(29080.0 - 8560.77i) q^{48} -8646.33 q^{49} -18234.7i q^{51} +(8725.95 - 11665.0i) q^{52} -32364.5i q^{53} +(62028.9 + 20633.1i) q^{54} +(-13427.5 + 9333.33i) q^{56} +73819.8 q^{57} +(-41112.9 - 13675.7i) q^{58} -20848.8i q^{59} -13265.1i q^{61} +(-12083.7 + 36327.0i) q^{62} -57215.5 q^{63} +(11419.0 - 30714.0i) q^{64} +(-9616.33 + 28909.3i) q^{66} +9642.36i q^{67} +(-15783.6 - 11806.8i) q^{68} +131056. i q^{69} -33088.4 q^{71} +(94141.9 - 65437.2i) q^{72} -18595.6 q^{73} +(25811.2 + 8585.79i) q^{74} +(47797.6 - 63896.7i) q^{76} -16435.1i q^{77} +(24062.3 - 72337.9i) q^{78} +44201.2 q^{79} +188190. q^{81} +(3367.42 - 10123.4i) q^{82} +80063.0i q^{83} +(-51260.1 + 68525.4i) q^{84} +(-44352.8 - 14753.4i) q^{86} -226742. q^{87} +(18796.8 + 27042.2i) q^{88} -81639.3 q^{89} +41124.5i q^{91} +(113439. + 84857.3i) q^{92} +200348. i q^{93} +(-10228.1 + 30748.4i) q^{94} +(5970.56 - 171377. i) q^{96} +22224.8 q^{97} +(-15438.0 + 46410.7i) q^{98} +115229. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{2} + q^{4} + 33 q^{6} - 196 q^{7} - 391 q^{8} - 1620 q^{9}+O(q^{10}) $ 20 * q - q^2 + q^4 + 33 * q^6 - 196 * q^7 - 391 * q^8 - 1620 * q^9	$ 20 q - q^{2} + q^{4} + 33 q^{6} - 196 q^{7} - 391 q^{8} - 1620 q^{9} - 241 q^{12} - 424 q^{14} - 55 q^{16} - 3368 q^{18} + 1197 q^{22} - 7184 q^{23} + 9459 q^{24} + 9172 q^{26} - 13492 q^{28} + 7160 q^{31} + 7869 q^{32} - 2836 q^{33} - 9591 q^{34} + 14828 q^{36} + 21505 q^{38} + 22452 q^{39} - 5804 q^{41} - 14272 q^{42} - 11593 q^{44} - 37612 q^{46} + 44180 q^{47} + 66571 q^{48} + 62652 q^{49} + 6136 q^{52} + 88947 q^{54} - 36908 q^{56} + 43696 q^{57} - 84012 q^{58} + 87460 q^{62} - 1240 q^{63} + 115177 q^{64} + 131439 q^{66} - 143341 q^{68} - 7724 q^{71} - 25772 q^{72} - 105136 q^{73} + 2112 q^{74} + 55951 q^{76} - 10948 q^{78} - 7780 q^{79} + 96984 q^{81} + 117501 q^{82} - 97556 q^{84} - 65986 q^{86} - 106188 q^{87} - 122597 q^{88} - 3160 q^{89} + 88908 q^{92} - 58540 q^{94} + 57791 q^{96} - 73688 q^{97} + 164655 q^{98}+O(q^{100}) $ 20 * q - q^2 + q^4 + 33 * q^6 - 196 * q^7 - 391 * q^8 - 1620 * q^9 - 241 * q^12 - 424 * q^14 - 55 * q^16 - 3368 * q^18 + 1197 * q^22 - 7184 * q^23 + 9459 * q^24 + 9172 * q^26 - 13492 * q^28 + 7160 * q^31 + 7869 * q^32 - 2836 * q^33 - 9591 * q^34 + 14828 * q^36 + 21505 * q^38 + 22452 * q^39 - 5804 * q^41 - 14272 * q^42 - 11593 * q^44 - 37612 * q^46 + 44180 * q^47 + 66571 * q^48 + 62652 * q^49 + 6136 * q^52 + 88947 * q^54 - 36908 * q^56 + 43696 * q^57 - 84012 * q^58 + 87460 * q^62 - 1240 * q^63 + 115177 * q^64 + 131439 * q^66 - 143341 * q^68 - 7724 * q^71 - 25772 * q^72 - 105136 * q^73 + 2112 * q^74 + 55951 * q^76 - 10948 * q^78 - 7780 * q^79 + 96984 * q^81 + 117501 * q^82 - 97556 * q^84 - 65986 * q^86 - 106188 * q^87 - 122597 * q^88 - 3160 * q^89 + 88908 * q^92 - 58540 * q^94 + 57791 * q^96 - 73688 * q^97 + 164655 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	1.78549	−	5.36768i	0.315633	−	0.948881i
$2$	1.78549	−	5.36768i	0.315633	−	0.948881i
$3$		−	29.6034i		−	1.89906i	−0.313679	−	0.949529i	$-0.601562\pi$
$3$		−	29.6034i		−	1.89906i	0.313679	−	0.949529i	$-0.398438\pi$
$4$	−25.6240	−	19.1679i	−0.800751	−	0.598997i
$5$		0			0
$5$		0			0
$6$	−158.902	−	52.8566i	−1.80198	−	0.599406i
$7$	90.3364			0.696816			0.348408	−	0.937343i	$-0.386722\pi$
$7$	90.3364			0.696816			0.348408	+	0.937343i	$0.386722\pi$
$8$	−148.639	+	103.318i	−0.821121	+	0.570754i
$9$	−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	$-0.0727846\pi$
$12$	−567.435	+	758.558i	−1.13753	+	1.52067i
$13$			455.237i			0.747101i	0.927610	+	0.373551i	$0.121860\pi$
$13$			455.237i			0.747101i	−0.927610	+	0.373551i	$0.878140\pi$
$14$	161.295	−	484.897i	0.219938	−	0.661195i
$15$		0			0
$16$	289.182	+	982.319i	0.282404	+	0.959295i
$17$	615.967			0.516934			0.258467	−	0.966020i	$-0.416783\pi$
$17$	615.967			0.516934			0.258467	+	0.966020i	$0.416783\pi$
$18$	−1130.86	+	3399.68i	−0.822674	+	2.47318i
$19$			2493.63i			1.58470i	0.610067	+	0.792350i	$0.291143\pi$
$19$			2493.63i			1.58470i	−0.610067	+	0.792350i	$0.708857\pi$
$20$		0			0
$21$		−	2674.26i		−	1.32329i
$22$	−976.555	−	324.839i	−0.430170	−	0.143091i
$23$	−4427.05			−1.74500			−0.872499	−	0.488616i	$-0.837502\pi$
$23$	−4427.05			−1.74500			−0.872499	+	0.488616i	$0.837502\pi$
$24$	3058.55	+	4400.21i	1.08389	+	1.55936i
$25$		0			0
$26$	2443.57	+	812.823i	0.708910	+	0.235810i
$27$			11556.0i			3.05069i
$28$	−2314.78	−	1731.56i	−0.557976	−	0.417391i
$29$		−	7659.34i		−	1.69121i	−0.533813	−	0.845603i	$-0.679241\pi$
$29$		−	7659.34i		−	1.69121i	0.533813	−	0.845603i	$-0.320759\pi$
$30$		0			0
$31$	−6767.72			−1.26485			−0.632424	−	0.774622i	$-0.717940\pi$
$31$	−6767.72			−1.26485			−0.632424	+	0.774622i	$0.717940\pi$
$32$	5789.11	+	201.685i	0.999394	+	0.0348176i
$33$	−5385.81			−0.860927
$34$	1099.80	−	3306.31i	0.163162	−	0.490509i
$35$		0			0
$36$	16229.2	+	12140.2i	2.08709	+	1.56124i
$37$			4808.64i			0.577455i	0.957411	+	0.288727i	$0.0932321\pi$
$37$			4808.64i			0.577455i	−0.957411	+	0.288727i	$0.906768\pi$
$38$	13385.0	+	4452.35i	1.50369	+	0.500185i
$39$	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	$0.472077\pi$
$42$	−14354.6	−	4774.88i	−1.25565	−	0.417676i
$43$		−	8262.94i		−	0.681496i	−0.940155	−	0.340748i	$-0.889320\pi$
$43$		−	8262.94i		−	0.681496i	0.940155	−	0.340748i	$-0.110680\pi$
$44$	−3487.26	+	4661.84i	−0.271552	+	0.363016i
$45$		0			0
$46$	−7904.46	+	23763.0i	−0.550780	+	1.65580i
$47$	−5728.44			−0.378261			−0.189130	−	0.981952i	$-0.560567\pi$
$47$	−5728.44			−0.378261			−0.189130	+	0.981952i	$0.560567\pi$
$48$	29080.0	−	8560.77i	1.82176	−	0.536302i
$49$	−8646.33			−0.514448
$50$		0			0
$51$		−	18234.7i		−	0.981687i
$52$	8725.95	−	11665.0i	0.447512	−	0.598242i
$53$		−	32364.5i		−	1.58263i	−0.611408	−	0.791316i	$-0.709396\pi$
$53$		−	32364.5i		−	1.58263i	0.611408	−	0.791316i	$-0.290604\pi$
$54$	62028.9	+	20633.1i	2.89474	+	0.962899i
$55$		0			0
$56$	−13427.5	+	9333.33i	−0.572170	+	0.397710i
$57$	73819.8			3.00944
$58$	−41112.9	−	13675.7i	−1.60475	−	0.533801i
$59$		−	20848.8i		−	0.779740i	−0.920870	−	0.389870i	$-0.872520\pi$
$59$		−	20848.8i		−	0.779740i	0.920870	−	0.389870i	$-0.127480\pi$
$60$		0			0
$61$		−	13265.1i		−	0.456442i	−0.973609	−	0.228221i	$-0.926709\pi$
$61$		−	13265.1i		−	0.456442i	0.973609	−	0.228221i	$-0.0732909\pi$
$62$	−12083.7	+	36327.0i	−0.399228	+	1.20019i
$63$	−57215.5			−1.81620
$64$	11419.0	−	30714.0i	0.348480	−	0.937316i
$65$		0			0
$66$	−9616.33	+	28909.3i	−0.271737	+	0.816918i
$67$			9642.36i			0.262420i	0.991355	+	0.131210i	$0.0418862\pi$
$67$			9642.36i			0.262420i	−0.991355	+	0.131210i	$0.958114\pi$
$68$	−15783.6	−	11806.8i	−0.413935	−	0.309642i
$69$			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	$0.627350\pi$
$72$	94141.9	−	65437.2i	2.14019	−	1.48763i
$73$	−18595.6			−0.408417			−0.204208	−	0.978927i	$-0.565462\pi$
$73$	−18595.6			−0.408417			−0.204208	+	0.978927i	$0.565462\pi$
$74$	25811.2	+	8585.79i	0.547936	+	0.182264i
$75$		0			0
$76$	47797.6	−	63896.7i	0.949231	−	1.26895i
$77$		−	16435.1i		−	0.315897i
$78$	24062.3	−	72337.9i	0.447817	−	1.34626i
$79$	44201.2			0.796831			0.398415	−	0.917205i	$-0.369560\pi$
$79$	44201.2			0.796831			0.398415	+	0.917205i	$0.369560\pi$
$80$		0			0
$81$	188190.			3.18701
$82$	3367.42	−	10123.4i	0.0553048	−	0.166261i
$83$			80063.0i			1.27567i	0.770175	+	0.637833i	$0.220169\pi$
$83$			80063.0i			1.27567i	−0.770175	+	0.637833i	$0.779831\pi$
$84$	−51260.1	+	68525.4i	−0.792649	+	1.05963i
$85$		0			0
$86$	−44352.8	−	14753.4i	−0.646659	−	0.215103i
$87$	−226742.			−3.21170
$88$	18796.8	+	27042.2i	0.258748	+	0.372251i
$89$	−81639.3			−1.09251			−0.546254	−	0.837620i	$-0.683947\pi$
$89$	−81639.3			−1.09251			−0.546254	+	0.837620i	$0.683947\pi$
$90$		0			0
$91$			41124.5i			0.520592i
$92$	113439.	+	84857.3i	1.39731	+	1.04525i
$93$			200348.i			2.40202i
$94$	−10228.1	+	30748.4i	−0.119392	+	0.358925i
$95$		0			0
$96$	5970.56	−	171377.i	0.0661206	−	1.89791i
$97$	22224.8			0.239833			0.119917	−	0.992784i	$-0.461737\pi$
$97$	22224.8			0.239833			0.119917	+	0.992784i	$0.461737\pi$
$98$	−15438.0	+	46410.7i	−0.162377	+	0.488150i
$99$			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	$0.939251\pi$
$102$	−97878.1	−	32557.9i	−0.931505	−	0.309853i
$103$	−175773.			−1.63253			−0.816263	−	0.577681i	$-0.803958\pi$
$103$	−175773.			−1.63253			−0.816263	+	0.577681i	$0.803958\pi$
$104$	−47034.0	−	67665.9i	−0.426411	−	0.613461i
$105$		0			0
$106$	−173723.	−	57786.6i	−1.50173	−	0.499531i
$107$			128182.i			1.08235i	0.840910	+	0.541175i	$0.182020\pi$
$107$			128182.i			1.08235i	−0.840910	+	0.541175i	$0.817980\pi$
$108$	221504.	−	296111.i	1.82735	−	2.44284i
$109$		−	49566.1i		−	0.399594i	−0.979837	−	0.199797i	$-0.935972\pi$
$109$		−	49566.1i		−	0.399594i	0.979837	−	0.199797i	$-0.0640283\pi$
$110$		0			0
$111$	142352.			1.09662
$112$	26123.7	+	88739.2i	0.196784	+	0.668452i
$113$	92377.7			0.680567			0.340283	−	0.940323i	$-0.389477\pi$
$113$	92377.7			0.680567			0.340283	+	0.940323i	$0.389477\pi$
$114$	131805.	−	396241.i	0.949879	−	2.85560i
$115$		0			0
$116$	−146814.	+	196263.i	−1.01303	+	1.35423i
$117$		−	288329.i		−	1.94726i
$118$	−111909.	−	37225.3i	−0.739881	−	0.246112i
$119$	55644.2			0.360208
$120$		0			0
$121$	127952.			0.794479
$122$	−71202.9	−	23684.7i	−0.433110	−	0.144069i
$123$		−	55831.7i		−	0.332750i
$124$	173416.	+	129723.i	1.01283	+	0.757641i
$125$		0			0
$126$	−102158.	+	307115.i	−0.573252	+	1.72335i
$127$	137192.			0.754778			0.377389	−	0.926055i	$-0.376822\pi$
$127$	137192.			0.754778			0.377389	+	0.926055i	$0.376822\pi$
$128$	−144474.	−	116133.i	−0.779410	−	0.626514i
$129$	−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	$-0.0751679\pi$
$132$	138006.	+	103235.i	0.689388	+	0.515693i
$133$			225265.i			1.10424i
$134$	51757.1	+	17216.4i	0.249005	+	0.0828284i
$135$		0			0
$136$	−91556.6	+	63640.1i	−0.424465	+	0.295042i
$137$	−220709.			−1.00466			−0.502330	−	0.864676i	$-0.667524\pi$
$137$	−220709.			−1.00466			−0.502330	+	0.864676i	$0.667524\pi$
$138$	703465.	+	233999.i	3.14445	+	1.04596i
$139$		−	154375.i		−	0.677706i	−0.940839	−	0.338853i	$-0.889961\pi$
$139$		−	154375.i		−	0.677706i	0.940839	−	0.338853i	$-0.110039\pi$
$140$		0			0
$141$			169581.i			0.718339i
$142$	−59079.1	+	177608.i	−0.245874	+	0.739165i
$143$	82822.4			0.338694
$144$	−183157.	−	622162.i	−0.736065	−	2.50033i
$145$		0			0
$146$	−33202.4	+	99815.4i	−0.128910	+	0.387539i
$147$			255961.i			0.976967i
$148$	92171.6	−	123217.i	0.345894	−	0.462397i
$149$		−	152976.i		−	0.564492i	−0.959342	−	0.282246i	$-0.908921\pi$
$149$		−	152976.i		−	0.564492i	0.959342	−	0.282246i	$-0.0910794\pi$
$150$		0			0
$151$	−440485.			−1.57213			−0.786066	−	0.618143i	$-0.787885\pi$
$151$	−440485.			−1.57213			−0.786066	+	0.618143i	$0.787885\pi$
$152$	−257635.	−	370649.i	−0.904474	−	1.30123i
$153$	−390129.			−1.34735
$154$	−88218.5	−	29344.8i	−0.299749	−	0.0997078i
$155$		0			0
$156$	−345324.	−	258318.i	−1.13610	−	0.849851i
$157$			433381.i			1.40320i	0.712570	+	0.701601i	$0.247531\pi$
$157$			433381.i			1.40320i	−0.712570	+	0.701601i	$0.752469\pi$
$158$	78920.9	−	237258.i	0.251507	−	0.756098i
$159$	−958100.			−3.00551
$160$		0			0
$161$	−399924.			−1.21594
$162$	336012.	−	1.01014e6i	1.00593	−	3.02410i
$163$			201943.i			0.595333i	0.954670	+	0.297666i	$0.0962083\pi$
$163$			201943.i			0.595333i	−0.954670	+	0.297666i	$0.903792\pi$
$164$	−48326.6	−	36150.5i	−0.140306	−	0.104955i
$165$		0			0
$166$	429753.	+	142952.i	1.21046	+	0.402643i
$167$	−300699.			−0.834337			−0.417168	−	0.908829i	$-0.636977\pi$
$167$	−300699.			−0.834337			−0.417168	+	0.908829i	$0.636977\pi$
$168$	276298.	+	397499.i	0.755275	+	1.08658i
$169$	164052.			0.441840
$170$		0			0
$171$		−	1.57936e6i		−	4.13040i
$172$	−158383.	+	211730.i	−0.408214	+	0.545709i
$173$		−	100504.i		−	0.255311i	−0.991819	−	0.127656i	$-0.959255\pi$
$173$		−	100504.i		−	0.255311i	0.991819	−	0.127656i	$-0.0407452\pi$
$174$	−404847.	+	1.21708e6i	−1.01372	+	3.04752i
$175$		0			0
$176$	178715.	−	52611.6i	0.434891	−	0.128026i
$177$	−617194.			−1.48077
$178$	−145766.	+	438214.i	−0.344832	+	1.03666i
$179$		−	554078.i		−	1.29252i	−0.763116	−	0.646262i	$-0.776331\pi$
$179$		−	554078.i		−	1.29252i	0.763116	−	0.646262i	$-0.223669\pi$
$180$		0			0
$181$			227592.i			0.516368i	0.966096	+	0.258184i	$0.0831241\pi$
$181$			227592.i			0.516368i	−0.966096	+	0.258184i	$0.916876\pi$
$182$	220743.	+	73427.5i	0.493980	+	0.164316i
$183$	−392692.			−0.866811
$184$	658031.	−	457392.i	1.43285	−	0.995964i
$185$		0			0
$186$	1.07540e6	+	357719.i	2.27923	+	0.758158i
$187$		−	112064.i		−	0.234349i
$188$	146786.	+	109802.i	0.302893	+	0.226577i
$189$			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	$0.210082\pi$
$192$	−909238.	−	338041.i	−1.78002	−	0.661783i
$193$	−356611.			−0.689131			−0.344565	−	0.938762i	$-0.611974\pi$
$193$	−356611.			−0.689131			−0.344565	+	0.938762i	$0.611974\pi$
$194$	39682.3	−	119296.i	0.0756994	−	0.227573i
$195$		0			0
$196$	221554.	+	165732.i	0.411945	+	0.308153i
$197$		−	226534.i		−	0.415880i	−0.978142	−	0.207940i	$-0.933324\pi$
$197$		−	226534.i		−	0.415880i	0.978142	−	0.207940i	$-0.0666759\pi$
$198$	618511.	+	205740.i	1.12120	+	0.372955i
$199$	−177886.			−0.318427			−0.159213	−	0.987244i	$-0.550896\pi$
$199$	−177886.			−0.318427			−0.159213	+	0.987244i	$0.550896\pi$
$200$		0			0
$201$	285447.			0.498350
$202$	208770.	+	69444.9i	0.359990	+	0.119746i
$203$		−	691917.i		−	1.17846i
$204$	−349521.	+	467247.i	−0.588028	+	0.786087i
$205$		0			0
$206$	−313842.	+	943495.i	−0.515280	+	1.54907i
$207$	2.80392e6			4.54820
$208$	−447188.	+	131646.i	−0.716691	+	0.210985i
$209$	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	$-0.133114\pi$
$212$	−620361.	+	829310.i	−0.947992	+	1.26729i
$213$			979528.i			1.47934i
$214$	688041.	+	228868.i	1.02702	+	0.341626i
$215$		0			0
$216$	−1.19394e6	−	1.71767e6i	−1.74119	−	2.50498i
$217$	−611372.			−0.881366
$218$	−266055.	−	88500.0i	−0.379167	−	0.126125i
$219$			550494.i			0.775607i
$220$		0			0
$221$			280411.i			0.386202i
$222$	254168.	−	764100.i	0.346130	−	1.04056i
$223$	711308.			0.957846			0.478923	−	0.877857i	$-0.341027\pi$
$223$	711308.			0.957846			0.478923	+	0.877857i	$0.341027\pi$
$224$	522967.	+	18219.5i	0.696393	+	0.0242614i
$225$		0			0
$226$	164940.	−	495854.i	0.214810	−	0.645777i
$227$		−	216347.i		−	0.278668i	−0.990245	−	0.139334i	$-0.955504\pi$
$227$		−	216347.i		−	0.278668i	0.990245	−	0.139334i	$-0.0444961\pi$
$228$	−1.89156e6	−	1.41497e6i	−2.40981	−	1.80265i
$229$		−	759408.i		−	0.956944i	−0.878103	−	0.478472i	$-0.841191\pi$
$229$		−	759408.i		−	0.956944i	0.878103	−	0.478472i	$-0.158809\pi$
$230$		0			0
$231$	−486535.			−0.599907
$232$	791344.	+	1.13848e6i	0.965262	+	1.38868i
$233$	860736.			1.03868			0.519338	−	0.854569i	$-0.326179\pi$
$233$	860736.			1.03868			0.519338	+	0.854569i	$0.326179\pi$
$234$	−1.54766e6	−	514810.i	−1.84772	−	0.614621i
$235$		0			0
$236$	−399627.	+	534229.i	−0.467062	+	0.624378i
$237$		−	1.30850e6i		−	1.51323i
$238$	99352.4	−	298681.i	0.113694	−	0.341794i
$239$	−348130.			−0.394228			−0.197114	−	0.980381i	$-0.563157\pi$
$239$	−348130.			−0.394228			−0.197114	+	0.980381i	$0.563157\pi$
$240$		0			0
$241$	−844167.			−0.936237			−0.468119	−	0.883666i	$-0.655068\pi$
$241$	−844167.			−0.936237			−0.468119	+	0.883666i	$0.655068\pi$
$242$	228457.	−	686804.i	0.250764	−	0.753866i
$243$		−	2.76295e6i		−	3.00163i
$244$	−254264.	+	339905.i	−0.273408	+	0.365497i
$245$		0			0
$246$	−299687.	−	99687.0i	−0.315740	−	0.105027i
$247$	−1.13519e6			−1.18393
$248$	1.00595e6	−	699224.i	1.03859	−	0.721917i
$249$	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	$0.724394\pi$
$252$	1.46609e6	+	1.09670e6i	1.45432	+	1.08790i
$253$			805423.i			0.791085i
$254$	244955.	−	736403.i	0.238233	−	0.716195i
$255$		0			0
$256$	−881323.	+	568138.i	−0.840496	+	0.541818i
$257$	−682391.			−0.644466			−0.322233	−	0.946660i	$-0.604434\pi$
$257$	−682391.			−0.644466			−0.322233	+	0.946660i	$0.604434\pi$
$258$	−436751.	+	1.31299e6i	−0.408493	+	1.22804i
$259$			434395.i			0.402379i
$260$		0			0
$261$			4.85112e6i			4.40799i
$262$	−493326.	−	164099.i	−0.443997	−	0.147690i
$263$	−91394.4			−0.0814761			−0.0407381	−	0.999170i	$-0.512971\pi$
$263$	−91394.4			−0.0814761			−0.0407381	+	0.999170i	$0.512971\pi$
$264$	800541.	−	556449.i	0.706925	−	0.491378i
$265$		0			0
$266$	1.20915e6	+	402209.i	1.04780	+	0.348536i
$267$			2.41680e6i			2.07474i
$268$	184824.	−	247076.i	0.157189	−	0.210133i
$269$		−	935475.i		−	0.788227i	−0.919062	−	0.394114i	$-0.871052\pi$
$269$		−	935475.i		−	0.788227i	0.919062	−	0.394114i	$-0.128948\pi$
$270$		0			0
$271$	512294.			0.423737			0.211868	−	0.977298i	$-0.432045\pi$
$271$	512294.			0.423737			0.211868	+	0.977298i	$0.432045\pi$
$272$	178127.	+	605076.i	0.145984	+	0.495892i
$273$	1.21742e6			0.988634
$274$	−394075.	+	1.18470e6i	−0.317105	+	0.953304i
$275$		0			0
$276$	2.51206e6	−	3.35817e6i	1.98499	−	2.65357i
$277$		−	615832.i		−	0.482239i	−0.970495	−	0.241120i	$-0.922485\pi$
$277$		−	615832.i		−	0.482239i	0.970495	−	0.241120i	$-0.0775147\pi$
$278$	−828638.	−	275636.i	−0.643062	−	0.213907i
$279$	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	$0.347432\pi$
$282$	910258.	+	302786.i	0.681619	+	0.226732i
$283$			696315.i			0.516820i	0.966035	+	0.258410i	$0.0831986\pi$
$283$			696315.i			0.516820i	−0.966035	+	0.258410i	$0.916801\pi$
$284$	847858.	+	634235.i	0.623774	+	0.466611i
$285$		0			0
$286$	147879.	−	444564.i	0.106903	−	0.321380i
$287$	170374.			0.122095
$288$	−3.66659e6	−	127739.i	−2.60484	−	0.0907493i
$289$	−1.04044e6			−0.732779
$290$		0			0
$291$		−	657931.i		−	0.455457i
$292$	476495.	+	356439.i	0.327040	+	0.244641i
$293$		−	134741.i		−	0.0916922i	−0.998949	−	0.0458461i	$-0.985402\pi$
$293$		−	134741.i		−	0.0916922i	0.998949	−	0.0458461i	$-0.0145984\pi$
$294$	1.37392e6	+	457016.i	0.927025	+	0.308363i
$295$		0			0
$296$	−496817.	−	714750.i	−0.329584	−	0.474160i
$297$	2.10241e6			1.38301
$298$	−821126.	−	273137.i	−0.535636	−	0.178172i
$299$		−	2.01536e6i		−	1.30369i
$300$		0			0
$301$		−	746444.i		−	0.474877i
$302$	−786483.	+	2.36438e6i	−0.496217	+	1.49177i
$303$	1.15139e6			0.720472
$304$	−2.44953e6	+	721112.i	−1.52020	+	0.447526i
$305$		0			0
$306$	−696572.	+	2.09409e6i	−0.425268	+	1.27847i
$307$			280871.i			0.170083i	0.996377	+	0.0850414i	$0.0271023\pi$
$307$			280871.i			0.170083i	−0.996377	+	0.0850414i	$0.972898\pi$
$308$	−315027.	+	421134.i	−0.189222	+	0.252955i
$309$			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	$0.748850\pi$
$312$	−2.00314e6	+	1.39236e6i	−1.16500	+	0.809779i
$313$	619525.			0.357436			0.178718	−	0.983900i	$-0.442805\pi$
$313$	619525.			0.357436			0.178718	+	0.983900i	$0.442805\pi$
$314$	2.32625e6	+	773798.i	1.33147	+	0.442898i
$315$		0			0
$316$	−1.13261e6	−	847245.i	−0.638063	−	0.477300i
$317$		−	913021.i		−	0.510308i	−0.966900	−	0.255154i	$-0.917874\pi$
$317$		−	913021.i		−	0.510308i	0.966900	−	0.255154i	$-0.0821262\pi$
$318$	−1.71068e6	+	5.14278e6i	−0.948639	+	2.85187i
$319$	−1.39348e6			−0.766698
$320$		0			0
$321$	3.79462e6			2.05545
$322$	−714061.	+	2.14666e6i	−0.383792	+	1.15378i
$323$			1.53599e6i			0.819185i
$324$	−4.82218e6	−	3.60721e6i	−2.55200	−	1.90901i
$325$		0			0
$326$	1.08397e6	+	360568.i	0.564900	+	0.187907i
$327$	−1.46733e6			−0.758852
$328$	−280331.	+	194856.i	−0.143875	+	0.100007i
$329$	−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	$-0.321894\pi$
$332$	1.53464e6	−	2.05154e6i	0.764120	−	1.02149i
$333$		−	3.04560e6i		−	1.50509i
$334$	−536896.	+	1.61406e6i	−0.263345	+	0.791686i
$335$		0			0
$336$	2.62698e6	−	773349.i	1.26943	−	0.373704i
$337$	3.19536e6			1.53266			0.766329	−	0.642448i	$-0.222081\pi$
$337$	3.19536e6			1.53266			0.766329	+	0.642448i	$0.222081\pi$
$338$	292914.	−	880579.i	0.139459	−	0.419254i
$339$		−	2.73469e6i		−	1.29244i
$340$		0			0
$341$			1.23127e6i			0.573412i
$342$	−8.47752e6	−	2.81994e6i	−3.91926	−	1.30369i
$343$	−2.29936e6			−1.05529
$344$	853706.	+	1.22819e6i	0.388966	+	0.559591i
$345$		0			0
$346$	−539476.	−	179450.i	−0.242260	−	0.0805847i
$347$		−	2.15234e6i		−	0.959592i	−0.877380	−	0.479796i	$-0.840711\pi$
$347$		−	2.15234e6i		−	0.959592i	0.877380	−	0.479796i	$-0.159289\pi$
$348$	5.81006e6	+	4.34618e6i	2.57177	+	1.92380i
$349$		−	2.78827e6i		−	1.22538i	−0.790322	−	0.612692i	$-0.790087\pi$
$349$		−	2.78827e6i		−	1.22538i	0.790322	−	0.612692i	$-0.209913\pi$
$350$		0			0
$351$	−5.26072e6			−2.27917
$352$	36693.0	−	1.05323e6i	0.0157843	−	0.453069i
$353$	3.23259e6			1.38075			0.690373	−	0.723453i	$-0.257446\pi$
$353$	3.23259e6			1.38075			0.690373	+	0.723453i	$0.257446\pi$
$354$	−1.10199e6	+	3.31290e6i	−0.467381	+	1.40508i
$355$		0			0
$356$	2.09193e6	+	1.56486e6i	0.874826	+	0.654409i
$357$		−	1.64726e6i		−	0.684055i
$358$	−2.97412e6	−	989303.i	−1.22645	−	0.407964i
$359$	−2.02100e6			−0.827620			−0.413810	−	0.910363i	$-0.635802\pi$
$359$	−2.02100e6			−0.827620			−0.413810	+	0.910363i	$0.635802\pi$
$360$		0			0
$361$	−3.74207e6			−1.51128
$362$	1.22164e6	+	406363.i	0.489972	+	0.162983i
$363$		−	3.78780e6i		−	1.50876i
$364$	788271.	−	1.05378e6i	0.311833	−	0.416864i
$365$		0			0
$366$	−701149.	+	2.10785e6i	−0.273595	+	0.822500i
$367$	−2.50488e6			−0.970781			−0.485391	−	0.874297i	$-0.661323\pi$
$367$	−2.50488e6			−0.970781			−0.485391	+	0.874297i	$0.661323\pi$
$368$	−1.28022e6	−	4.34877e6i	−0.492795	−	1.67397i
$369$	−1.19451e6			−0.456693
$370$		0			0
$371$		−	2.92370e6i		−	1.10280i
$372$	3.84024e6	−	5.13371e6i	1.43880	−	1.92342i
$373$			495172.i			0.184283i	0.995746	+	0.0921413i	$0.0293711\pi$
$373$			495172.i			0.184283i	−0.995746	+	0.0921413i	$0.970629\pi$
$374$	−601525.	−	200090.i	−0.222369	−	0.0739684i
$375$		0			0
$376$	851468.	−	591848.i	0.310598	−	0.215894i
$377$	3.48682e6			1.26350
$378$	5.60347e6	+	1.86392e6i	2.01710	+	0.670963i
$379$		−	2.19040e6i		−	0.783294i	−0.920116	−	0.391647i	$-0.871905\pi$
$379$		−	2.19040e6i		−	0.783294i	0.920116	−	0.391647i	$-0.128095\pi$
$380$		0			0
$381$		−	4.06135e6i		−	1.43337i
$382$	1.42232e6	−	4.27588e6i	0.498699	−	1.49923i
$383$	289759.			0.100935			0.0504674	−	0.998726i	$-0.483929\pi$
$383$	289759.			0.100935			0.0504674	+	0.998726i	$0.483929\pi$
$384$	−3.43793e6	+	4.27693e6i	−1.18979	+	1.48014i
$385$		0			0
$386$	−636726.	+	1.91417e6i	−0.217513	+	0.653903i
$387$			5.23342e6i			1.77627i
$388$	−569490.	−	426004.i	−0.192047	−	0.143659i
$389$		−	2.11554e6i		−	0.708839i	−0.935087	−	0.354420i	$-0.884678\pi$
$389$		−	2.11554e6i		−	0.708839i	0.935087	−	0.354420i	$-0.115322\pi$
$390$		0			0
$391$	−2.72692e6			−0.902048
$392$	1.28518e6	−	893317.i	0.422424	−	0.293623i
$393$	−2.72075e6			−0.888601
$394$	−1.21596e6	−	404475.i	−0.394621	−	0.131266i
$395$		0			0
$396$	2.20869e6	−	2.95263e6i	0.707779	−	0.946173i
$397$			1.80742e6i			0.575549i	0.957698	+	0.287774i	$0.0929153\pi$
$397$			1.80742e6i			0.575549i	−0.957698	+	0.287774i	$0.907085\pi$
$398$	−317615.	+	954837.i	−0.100506	+	0.302149i
$399$	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	$0.631804\pi$
$402$	509663.	−	1.53219e6i	0.157296	−	0.472875i
$403$		−	3.08092e6i		−	0.944969i
$404$	745516.	−	996620.i	0.227250	−	0.303792i
$405$		0			0
$406$	−3.71399e6	−	1.23541e6i	−1.11822	−	0.371961i
$407$	874847.			0.261786
$408$	1.88396e6	+	2.71038e6i	0.560302	+	0.806084i
$409$	−5.00884e6			−1.48057			−0.740285	−	0.672293i	$-0.765310\pi$
$409$	−5.00884e6			−1.48057			−0.740285	+	0.672293i	$0.765310\pi$
$410$		0			0
$411$			6.53375e6i			1.90791i
$412$	4.50402e6	+	3.36921e6i	1.30725	+	0.977878i
$413$		−	1.88340e6i		−	0.543335i
$414$	5.00638e6	−	1.50505e7i	1.43556	−	4.31570i
$415$		0			0
$416$	−91814.5	+	2.63542e6i	−0.0260122	+	0.746648i
$417$	−4.57003e6			−1.28700
$418$	810026.	−	2.43516e6i	0.226756	−	0.681690i
$419$			2.27862e6i			0.634071i	0.948414	+	0.317035i	$0.102687\pi$
$419$			2.27862e6i			0.634071i	−0.948414	+	0.317035i	$0.897313\pi$
$420$		0			0
$421$		−	1.30407e6i		−	0.358587i	−0.983796	−	0.179293i	$-0.942619\pi$
$421$		−	1.30407e6i		−	0.358587i	0.983796	−	0.179293i	$-0.0573811\pi$
$422$	−2.81945e6	−	937853.i	−0.770695	−	0.256362i
$423$	3.62817e6			0.985907
$424$	3.34382e6	+	4.81063e6i	0.903293	+	1.29953i
$425$		0			0
$426$	5.25780e6	+	1.74894e6i	1.40372	+	0.466929i
$427$		−	1.19832e6i		−	0.318056i
$428$	2.45698e6	−	3.28454e6i	0.648325	−	0.866693i
$429$		−	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	$0.329341\pi$
$432$	−1.13517e7	+	3.34179e6i	−2.92651	+	0.861528i
$433$	5.84454e6			1.49806			0.749032	−	0.662534i	$-0.230519\pi$
$433$	5.84454e6			1.49806			0.749032	+	0.662534i	$0.230519\pi$
$434$	−1.09160e6	+	3.28165e6i	−0.278189	+	0.836311i
$435$		0			0
$436$	−950080.	+	1.27008e6i	−0.239356	+	0.319975i
$437$		−	1.10394e7i		−	2.76530i
$438$	2.95487e6	+	982902.i	0.735959	+	0.244808i
$439$	−7.63016e6			−1.88961			−0.944805	−	0.327634i	$-0.893749\pi$
$439$	−7.63016e6			−1.88961			−0.944805	+	0.327634i	$0.893749\pi$
$440$		0			0
$441$	5.47624e6			1.34087
$442$	1.50516e6	+	500672.i	0.366460	+	0.121898i
$443$			1.99010e6i			0.481798i	0.970550	+	0.240899i	$0.0774422\pi$
$443$			1.99010e6i			0.481798i	−0.970550	+	0.240899i	$0.922558\pi$
$444$	−3.64763e6	−	2.72859e6i	−0.878119	−	0.656872i
$445$		0			0
$446$	1.27004e6	−	3.81808e6i	0.302328	−	0.908882i
$447$	−4.52861e6			−1.07200
$448$	1.03155e6	−	2.77459e6i	0.242826	−	0.653137i
$449$	−2.05507e6			−0.481074			−0.240537	−	0.970640i	$-0.577324\pi$
$449$	−2.05507e6			−0.481074			−0.240537	+	0.970640i	$0.577324\pi$
$450$		0			0
$451$		−	343122.i		−	0.0794342i
$452$	−2.36709e6	−	1.77069e6i	−0.544965	−	0.407658i
$453$			1.30398e7i			2.98557i
$454$	−1.16128e6	−	386287.i	−0.264423	−	0.0879569i
$455$		0			0
$456$	−1.09725e7	+	7.62687e6i	−2.47111	+	1.71765i
$457$	−2.74689e6			−0.615250			−0.307625	−	0.951508i	$-0.599534\pi$
$457$	−2.74689e6			−0.615250			−0.307625	+	0.951508i	$0.599534\pi$
$458$	−4.07626e6	−	1.35592e6i	−0.908026	−	0.302044i
$459$			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	$-0.145068\pi$
$462$	−868705.	+	2.61157e6i	−0.189351	+	0.569241i
$463$	−7.77791e6			−1.68620			−0.843102	−	0.537753i	$-0.819273\pi$
$463$	−7.77791e6			−1.68620			−0.843102	+	0.537753i	$0.819273\pi$
$464$	7.52391e6	−	2.21494e6i	1.62237	−	0.477604i
$465$		0			0
$466$	1.53684e6	−	4.62015e6i	0.327841	−	0.985580i
$467$		−	3.81432e6i		−	0.809329i	−0.914465	−	0.404664i	$-0.867388\pi$
$467$		−	3.81432e6i		−	0.809329i	0.914465	−	0.404664i	$-0.132612\pi$
$468$	−5.52667e6	+	7.38816e6i	−1.16640	+	1.55927i
$469$			871056.i			0.182858i
$470$		0			0
$471$	1.28295e7			2.66476
$472$	2.15404e6	+	3.09893e6i	0.445040	+	0.640261i
$473$	−1.50330e6			−0.308952
$474$	−7.02364e6	−	2.33633e6i	−1.43587	−	0.477625i
$475$		0			0
$476$	−1.42583e6	−	1.06658e6i	−0.288437	−	0.215763i
$477$			2.04984e7i			4.12500i
$478$	−621584.	+	1.86865e6i	−0.124431	+	0.374075i
$479$	−2.44255e6			−0.486413			−0.243206	−	0.969975i	$-0.578199\pi$
$479$	−2.44255e6			−0.486413			−0.243206	+	0.969975i	$0.578199\pi$
$480$		0			0
$481$	−2.18907e6			−0.431417
$482$	−1.50725e6	+	4.53122e6i	−0.295508	+	0.888378i
$483$			1.18391e7i			2.30914i
$484$	−3.27864e6	−	2.45257e6i	−0.636180	−	0.475891i
$485$		0			0
$486$	−1.48307e7	−	4.93323e6i	−2.84819	−	0.947416i
$487$	8.35163e6			1.59569			0.797846	−	0.602862i	$-0.205973\pi$
$487$	8.35163e6			1.59569			0.797846	+	0.602862i	$0.205973\pi$
$488$	1.37052e6	+	1.97171e6i	0.260516	+	0.374795i
$489$	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	$0.989867\pi$
$492$	−1.07018e6	+	1.43063e6i	−0.199316	+	0.266450i
$493$		−	4.71790e6i		−	0.874241i
$494$	−2.02688e6	+	6.09335e6i	−0.373688	+	1.12341i
$495$		0			0
$496$	−1.95710e6	−	6.64806e6i	−0.357199	−	1.21336i
$497$	−2.98909e6			−0.542810
$498$	4.23186e6	−	1.27221e7i	0.764642	−	2.29872i
$499$		−	648994.i		−	0.116678i	−0.998297	−	0.0583391i	$-0.981420\pi$
$499$		−	648994.i		−	0.116678i	0.998297	−	0.0583391i	$-0.0185805\pi$
$500$		0			0
$501$			8.90172e6i			1.58445i
$502$	8.16114e6	+	2.71470e6i	1.44541	+	0.480798i
$503$	3.13514e6			0.552506			0.276253	−	0.961085i	$-0.410907\pi$
$503$	3.13514e6			0.552506			0.276253	+	0.961085i	$0.410907\pi$
$504$	8.50445e6	−	5.91137e6i	1.49132	−	1.03660i
$505$		0			0
$506$	4.32326e6	+	1.43808e6i	0.750645	+	0.249693i
$507$		−	4.85650e6i		−	0.839080i
$508$	−3.51541e6	−	2.62968e6i	−0.604390	−	0.452110i
$509$			5.04542e6i			0.863183i	0.902069	+	0.431591i	$0.142048\pi$
$509$			5.04542e6i			0.863183i	−0.902069	+	0.431591i	$0.857952\pi$
$510$		0			0
$511$	−1.67986e6			−0.284591
$512$	1.47599e6	+	5.74507e6i	0.248833	+	0.968546i
$513$	−2.88163e7			−4.83443
$514$	−1.21840e6	+	3.66286e6i	−0.203415	+	0.611522i
$515$		0			0
$516$	6.26792e6	+	4.68868e6i	1.03633	+	0.775223i
$517$			1.04219e6i			0.171482i
$518$	2.33170e6	+	775610.i	0.381810	+	0.127004i
$519$	−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	$0.484612\pi$
$522$	2.60393e7	+	8.66165e6i	4.18266	+	1.39131i
$523$			1.12334e7i			1.79580i	0.440197	+	0.897901i	$0.354909\pi$
$523$			1.12334e7i			1.79580i	−0.440197	+	0.897901i	$0.645091\pi$
$524$	−1.76166e6	+	2.35502e6i	−0.280281	+	0.374685i
$525$		0			0
$526$	−163184.	+	490576.i	−0.0257166	+	0.0773111i
$527$	−4.16869e6			−0.653843
$528$	−1.55748e6	−	5.29058e6i	−0.243130	−	0.825884i
$529$	1.31624e7			2.04502
$530$		0			0
$531$			1.32048e7i			2.03233i
$532$	4.31786e6	−	5.77220e6i	0.661439	−	0.884224i
$533$			858572.i			0.130906i
$534$	1.29726e7	+	4.31518e6i	1.96868	+	0.654856i
$535$		0			0
$536$	−996225.	−	1.43323e6i	−0.149777	−	0.215478i
$537$	−1.64026e7			−2.45458
$538$	−5.02133e6	−	1.67028e6i	−0.747934	−	0.248791i
$539$			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	$-0.201371\pi$
$542$	914697.	−	2.74983e6i	0.133746	−	0.402076i
$543$	6.73748e6			0.980614
$544$	3.56590e6	+	124231.i	0.516620	+	0.0179984i
$545$		0			0
$546$	2.17370e6	−	6.53475e6i	0.312046	−	0.938096i
$547$		−	6.14990e6i		−	0.878819i	−0.898287	−	0.439410i	$-0.855188\pi$
$547$		−	6.14990e6i		−	0.878819i	0.898287	−	0.439410i	$-0.144812\pi$
$548$	5.65547e6	+	4.23054e6i	0.804483	+	0.601789i
$549$			8.40159e6i			1.18968i
$550$		0			0
$551$	1.90995e7			2.68005
$552$	−1.35403e7	−	1.94800e7i	−1.89139	−	2.72107i
$553$	3.99298e6			0.555244
$554$	−3.30559e6	−	1.09956e6i	−0.457588	−	0.152211i
$555$		0			0
$556$	−2.95905e6	+	3.95572e6i	−0.405944	+	0.542673i
$557$			6.26714e6i			0.855917i	0.903798	+	0.427959i	$0.140767\pi$
$557$			6.26714e6i			0.855917i	−0.903798	+	0.427959i	$0.859233\pi$
$558$	7.65335e6	−	2.30081e7i	1.04056	−	3.12820i
$559$	3.76160e6			0.509146
$560$		0			0
$561$	−3.31748e6			−0.445042
$562$	2.17977e6	−	6.55298e6i	0.291118	−	0.875182i
$563$		−	149874.i		−	0.0199276i	−0.999950	−	0.00996378i	$-0.996828\pi$
$563$		−	149874.i		−	0.0199276i	0.999950	−	0.00996378i	$-0.00317162\pi$
$564$	3.25052e6	−	4.34535e6i	0.430283	−	0.575211i
$565$		0			0
$566$	3.73760e6	+	1.24327e6i	0.490401	+	0.163126i
$567$	1.70004e7			2.22076
$568$	4.91822e6	−	3.41861e6i	0.639642	−	0.444609i
$569$	2.10351e6			0.272373			0.136186	−	0.990683i	$-0.456515\pi$
$569$	2.10351e6			0.272373			0.136186	+	0.990683i	$0.456515\pi$
$570$		0			0
$571$		−	8.72030e6i		−	1.11929i	−0.828734	−	0.559643i	$-0.810938\pi$
$571$		−	8.72030e6i		−	1.11929i	0.828734	−	0.559643i	$-0.189062\pi$
$572$	−2.12224e6	−	1.58753e6i	−0.271210	−	0.202877i
$573$		−	2.35820e7i		−	3.00050i
$574$	304201.	−	914511.i	0.0385372	−	0.115854i
$575$		0			0
$576$	−7.23234e6	+	1.94530e7i	−0.908285	+	2.44304i
$577$	5.44606e6			0.680993			0.340497	−	0.940246i	$-0.389405\pi$
$577$	5.44606e6			0.680993			0.340497	+	0.940246i	$0.389405\pi$
$578$	−1.85770e6	+	5.58476e6i	−0.231290	+	0.695321i
$579$			1.05569e7i			1.30870i
$580$		0			0
$581$			7.23261e6i			0.888904i
$582$	−3.53156e6	−	1.17473e6i	−0.432175	−	0.143758i
$583$	−5.88816e6			−0.717477
$584$	2.76403e6	−	1.92125e6i	0.335360	−	0.233106i
$585$		0			0
$586$	−723249.	−	240580.i	−0.0870050	−	0.0289411i
$587$		−	1.53801e6i		−	0.184232i	−0.995748	−	0.0921158i	$-0.970637\pi$
$587$		−	1.53801e6i		−	0.184232i	0.995748	−	0.0921158i	$-0.0293630\pi$
$588$	4.90623e6	−	6.55874e6i	0.585201	−	0.782307i
$589$		−	1.68762e7i		−	2.00441i
$590$		0			0
$591$	−6.70618e6			−0.789781
$592$	−4.72361e6	+	1.39057e6i	−0.553950	+	0.163076i
$593$	1.23546e7			1.44275			0.721377	−	0.692542i	$-0.243509\pi$
$593$	1.23546e7			1.44275			0.721377	+	0.692542i	$0.243509\pi$
$594$	3.75383e6	−	1.12851e7i	0.436525	−	1.31231i
$595$		0			0
$596$	−2.93223e6	+	3.91986e6i	−0.338129	+	0.452017i
$597$			5.26604e6i			0.604711i
$598$	−1.08178e7	−	3.59841e6i	−1.23705	−	0.411488i
$599$	−1.46319e7			−1.66622			−0.833112	−	0.553105i	$-0.813443\pi$
$599$	−1.46319e7			−1.66622			−0.833112	+	0.553105i	$0.813443\pi$
$600$		0			0
$601$	−1.08262e7			−1.22261			−0.611306	−	0.791394i	$-0.709356\pi$
$601$	−1.08262e7			−1.22261			−0.611306	+	0.791394i	$0.709356\pi$
$602$	−4.00668e6	−	1.33277e6i	−0.450602	−	0.149887i
$603$		−	6.10709e6i		−	0.683976i
$604$	1.12870e7	+	8.44318e6i	1.25889	+	0.941702i
$605$		0			0
$606$	2.05580e6	−	6.18031e6i	0.227405	−	0.683642i
$607$	−722652.			−0.0796082			−0.0398041	−	0.999208i	$-0.512673\pi$
$607$	−722652.			−0.0796082			−0.0398041	+	0.999208i	$0.512673\pi$
$608$	−502927.	+	1.44359e7i	−0.0551754	+	1.58374i
$609$	−2.04831e7			−2.23796
$610$		0			0
$611$		−	2.60780e6i		−	0.282599i
$612$	9.99668e6	+	7.47796e6i	1.07889	+	0.807058i
$613$			1.19951e6i			0.128930i	0.997920	+	0.0644648i	$0.0205340\pi$
$613$			1.19951e6i			0.128930i	−0.997920	+	0.0644648i	$0.979466\pi$
$614$	1.50762e6	+	501492.i	0.161388	+	0.0536838i
$615$		0			0
$616$	1.69804e6	+	2.44290e6i	0.180300	+	0.259390i
$617$	1.26945e7			1.34246			0.671230	−	0.741249i	$-0.265766\pi$
$617$	1.26945e7			1.34246			0.671230	+	0.741249i	$0.265766\pi$
$618$	2.79307e7	+	9.29078e6i	2.94178	+	0.978546i
$619$			9.69565e6i			1.01707i	0.861042	+	0.508534i	$0.169813\pi$
$619$			9.69565e6i			1.01707i	−0.861042	+	0.508534i	$0.830187\pi$
$620$		0			0
$621$		−	5.11590e7i		−	5.32344i
$622$	−4.29140e6	+	1.29011e7i	−0.444757	+	1.33706i
$623$	−7.37501e6			−0.761276
$624$	3.89718e6	+	1.32383e7i	0.400672	+	1.36104i
$625$		0			0
$626$	1.10616e6	−	3.32541e6i	0.112819	−	0.339164i
$627$		−	1.34302e7i		−	1.36431i
$628$	8.30700e6	−	1.11050e7i	0.840515	−	1.12362i
$629$			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	$0.462023\pi$
$632$	−6.57001e6	+	4.56676e6i	−0.654295	+	0.454794i
$633$	−1.55496e7			−1.54244
$634$	−4.90081e6	−	1.63019e6i	−0.484222	−	0.161070i
$635$		0			0
$636$	2.45504e7	+	1.83648e7i	2.40666	+	1.80029i
$637$		−	3.93613e6i		−	0.384345i
$638$	−2.48805e6	+	7.47977e6i	−0.241996	+	0.727506i
$639$	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	$0.400934\pi$
$642$	6.77527e6	−	2.03683e7i	0.648768	−	1.95037i
$643$		−	1.64996e7i		−	1.57379i	−0.617086	−	0.786896i	$-0.711687\pi$
$643$		−	1.64996e7i		−	1.57379i	0.617086	−	0.786896i	$-0.288313\pi$
$644$	1.02477e7	+	7.66571e6i	0.973666	+	0.728346i
$645$		0			0
$646$	8.24471e6	+	2.74250e6i	0.777310	+	0.258562i
$647$	−2.94843e6			−0.276905			−0.138452	−	0.990369i	$-0.544213\pi$
$647$	−2.94843e6			−0.276905			−0.138452	+	0.990369i	$0.544213\pi$
$648$	−2.79723e7	+	1.94433e7i	−2.61692	+	1.81900i
$649$	−3.79306e6			−0.353491
$650$		0			0
$651$			1.80987e7i			1.67376i
$652$	3.87083e6	−	5.17460e6i	0.356603	−	0.476713i
$653$			1.02662e7i			0.942167i	0.882089	+	0.471083i	$0.156137\pi$
$653$			1.02662e7i			0.942167i	−0.882089	+	0.471083i	$0.843863\pi$
$654$	−2.61990e6	+	7.87614e6i	−0.239519	+	0.720061i
$655$		0			0
$656$	545394.	+	1.85264e6i	0.0494824	+	0.168086i
$657$	1.17777e7			1.06451
$658$	−923968.	+	2.77770e6i	−0.0831941	+	0.250104i
$659$			7.94727e6i			0.712860i	0.934322	+	0.356430i	$0.116006\pi$
$659$			7.94727e6i			0.712860i	−0.934322	+	0.356430i	$0.883994\pi$
$660$		0			0
$661$			9.79140e6i			0.871648i	0.900032	+	0.435824i	$0.143543\pi$
$661$			9.79140e6i			0.871648i	−0.900032	+	0.435824i	$0.856457\pi$
$662$	−1.81354e7	−	6.03252e6i	−1.60836	−	0.535000i
$663$	8.30112e6			0.733420
$664$	−8.27191e6	−	1.19005e7i	−0.728091	−	1.04748i
$665$		0			0
$666$	−1.63478e7	−	5.43790e6i	−1.42815	−	0.475057i
$667$			3.39083e7i			2.95115i
$668$	7.70513e6	+	5.76378e6i	0.668096	+	0.499765i
$669$		−	2.10571e7i		−	1.81901i
$670$		0			0
$671$	−2.41335e6			−0.206926
$672$	539359.	−	1.54816e7i	0.0460739	−	1.32249i
$673$	−1.64861e7			−1.40307			−0.701535	−	0.712635i	$-0.747502\pi$
$673$	−1.64861e7			−1.40307			−0.701535	+	0.712635i	$0.747502\pi$
$674$	5.70530e6	−	1.71517e7i	0.483758	−	1.45431i
$675$		0			0
$676$	−4.20368e6	−	3.14454e6i	−0.353804	−	0.264661i
$677$			2.81251e6i			0.235843i	0.993023	+	0.117922i	$0.0376231\pi$
$677$			2.81251e6i			0.235843i	−0.993023	+	0.117922i	$0.962377\pi$
$678$	−1.46790e7	−	4.88277e6i	−1.22637	−	0.407936i
$679$	2.00771e6			0.167120
$680$		0			0
$681$	−6.40461e6			−0.529206
$682$	6.60905e6	+	2.19842e6i	0.544100	+	0.180988i
$683$			1.56071e7i			1.28018i	0.768300	+	0.640090i	$0.221103\pi$
$683$			1.56071e7i			1.28018i	−0.768300	+	0.640090i	$0.778897\pi$
$684$	−3.02731e7	+	4.04697e7i	−2.47410	+	3.30742i
$685$		0			0
$686$	−4.10550e6	+	1.23423e7i	−0.333085	+	1.00135i
$687$	−2.24811e7			−1.81729
$688$	8.11684e6	−	2.38949e6i	0.653756	−	0.192457i
$689$	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	$0.822841\pi$
$692$	−1.92646e6	+	2.57533e6i	−0.152931	+	0.204441i
$693$			1.04094e7i			0.823362i
$694$	−1.15531e7	−	3.84298e6i	−0.910539	−	0.302879i
$695$		0			0
$696$	3.37027e7	−	2.34265e7i	2.63719	−	1.83309i
$697$	1.16171e6			0.0905763
$698$	−1.49666e7	−	4.97844e6i	−1.16274	−	0.386772i
$699$		−	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	$-0.379552\pi$
$702$	−9.39297e6	+	2.82379e7i	−0.719383	+	2.16266i
$703$	−1.19909e7			−0.915093
$704$	−5.58787e6	−	2.07748e6i	−0.424927	−	0.157981i
$705$		0			0
$706$	5.77177e6	−	1.73515e7i	0.435810	−	1.31016i
$707$			3.51354e6i			0.264361i
$708$	1.58150e7	+	1.18303e7i	1.18573	+	0.886979i
$709$			3.10586e6i			0.232042i	0.993247	+	0.116021i	$0.0370140\pi$
$709$			3.10586e6i			0.232042i	−0.993247	+	0.116021i	$0.962986\pi$
$710$		0			0
$711$	−2.79953e7			−2.07688
$712$	1.21348e7	−	8.43477e6i	0.897081	−	0.623553i
$713$	2.99610e7			2.20716
$714$	−8.84196e6	−	2.94117e6i	−0.649087	−	0.215911i
$715$		0			0
$716$	−1.06205e7	+	1.41977e7i	−0.774219	+	1.03499i
$717$			1.03058e7i			0.748661i
$718$	−3.60849e6	+	1.08481e7i	−0.261225	+	0.785313i
$719$	−7.95560e6			−0.573919			−0.286960	−	0.957943i	$-0.592645\pi$
$719$	−7.95560e6			−0.573919			−0.286960	+	0.957943i	$0.592645\pi$
$720$		0			0
$721$	−1.58787e7			−1.13757
$722$	−6.68143e6	+	2.00862e7i	−0.477009	+	1.43402i
$723$			2.49902e7i			1.77797i
$724$	4.36246e6	−	5.83181e6i	0.309303	−	0.413483i
$725$		0			0
$726$	−2.03317e7	−	6.76309e6i	−1.43164	−	0.476216i
$727$	−2.50891e7			−1.76055			−0.880276	−	0.474463i	$-0.842642\pi$
$727$	−2.50891e7			−1.76055			−0.880276	+	0.474463i	$0.842642\pi$
$728$	−4.24888e6	−	6.11270e6i	−0.297130	−	0.427469i
$729$	−3.60626e7			−2.51327
$730$		0			0
$731$		−	5.08969e6i		−	0.352288i
$732$	1.00624e7	+	7.52709e6i	0.694100	+	0.519217i
$733$		−	2.58258e7i		−	1.77539i	−0.460434	−	0.887694i	$-0.652306\pi$
$733$		−	2.58258e7i		−	1.77539i	0.460434	−	0.887694i	$-0.347694\pi$
$734$	−4.47244e6	+	1.34454e7i	−0.306411	+	0.921156i
$735$		0			0
$736$	−2.56287e7	−	892869.i	−1.74394	−	0.0607566i
$737$	1.75426e6			0.118966
$738$	−2.13279e6	+	6.41176e6i	−0.144148	+	0.433347i
$739$		−	2.15950e7i		−	1.45459i	−0.686323	−	0.727297i	$-0.740776\pi$
$739$		−	2.15950e7i		−	1.45459i	0.686323	−	0.727297i	$-0.259224\pi$
$740$		0			0
$741$			3.36055e7i			2.24835i
$742$	−1.56935e7	−	5.22024e6i	−1.04643	−	0.348081i
$743$	−1.25570e7			−0.834479			−0.417239	−	0.908797i	$-0.637002\pi$
$743$	−1.25570e7			−0.834479			−0.417239	+	0.908797i	$0.637002\pi$
$744$	−2.06994e7	−	2.97794e7i	−1.37096	−	1.97235i
$745$		0			0
$746$	2.65793e6	+	884126.i	0.174862	+	0.0581657i
$747$		−	5.07088e7i		−	3.32492i
$748$	−2.14804e6	+	2.87154e6i	−0.140374	+	0.187655i
$749$			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	$0.556299\pi$
$752$	−1.65656e6	−	5.62715e6i	−0.106823	−	0.362864i
$753$	4.50097e7			2.89280
$754$	6.22569e6	−	1.87161e7i	0.398803	−	1.19891i
$755$		0			0
$756$	2.00099e7	−	2.67496e7i	1.27333	−	1.70221i
$757$		−	1.06247e7i		−	0.673873i	−0.941527	−	0.336937i	$-0.890609\pi$
$757$		−	1.06247e7i		−	0.673873i	0.941527	−	0.336937i	$-0.109391\pi$
$758$	−1.17574e7	−	3.91094e6i	−0.743253	−	0.247234i
$759$	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	$0.242038\pi$
$762$	−2.18000e7	−	7.25151e6i	−1.36010	−	0.452419i
$763$		−	4.47763e6i		−	0.278443i
$764$	−2.04120e7	−	1.52691e7i	−1.26518	−	0.946412i
$765$		0			0
$766$	517363.	−	1.55534e6i	0.0318584	−	0.0957751i
$767$	9.49113e6			0.582545
$768$	1.68188e7	+	2.60902e7i	1.02894	+	1.59615i
$769$	9.09958e6			0.554888			0.277444	−	0.960742i	$-0.410513\pi$
$769$	9.09958e6			0.554888			0.277444	+	0.960742i	$0.410513\pi$
$770$		0			0
$771$			2.02011e7i			1.22388i
$772$	9.13781e6	+	6.83549e6i	0.551822	+	0.412787i
$773$		−	1.82799e7i		−	1.10034i	−0.835053	−	0.550169i	$-0.814563\pi$
$773$		−	1.82799e7i		−	1.10034i	0.835053	−	0.550169i	$-0.185437\pi$
$774$	2.80913e7	+	9.34423e6i	1.68547	+	0.560649i
$775$		0			0
$776$	−3.30347e6	+	2.29622e6i	−0.196932	+	0.136886i
$777$	1.28596e7			0.764142
$778$	−1.13556e7	−	3.77728e6i	−0.672604	−	0.223733i
$779$			4.70295e6i			0.277669i
$780$		0			0
$781$			6.01985e6i			0.353149i
$782$	−4.86889e6	+	1.46372e7i	−0.284717	+	0.855937i
$783$	8.85113e7			5.15934
$784$	−2.50036e6	−	8.49345e6i	−0.145282	−	0.493508i
$785$		0			0
$786$	−4.85787e6	+	1.46041e7i	−0.280472	+	0.843177i
$787$			3.07594e6i			0.177028i	0.996075	+	0.0885139i	$0.0282118\pi$
$787$			3.07594e6i			0.177028i	−0.996075	+	0.0885139i	$0.971788\pi$
$788$	−4.34219e6	+	5.80472e6i	−0.249111	+	0.333017i
$789$			2.70558e6i			0.154728i
$790$		0			0
$791$	8.34507e6			0.474230
$792$	−1.19051e7	−	1.71275e7i	−0.674407	−	0.970242i
$793$	6.03877e6			0.341009
$794$	9.70164e6	+	3.22713e6i	0.546127	+	0.181662i
$795$		0			0
$796$	4.55816e6	+	3.40971e6i	0.254981	+	0.190737i
$797$			2.64996e6i			0.147772i	0.997267	+	0.0738861i	$0.0235401\pi$
$797$			2.64996e6i			0.147772i	−0.997267	+	0.0738861i	$0.976460\pi$
$798$	1.19068e7	−	3.57950e7i	0.661891	−	1.98983i
$799$	−3.52853e6			−0.195536
$800$		0			0
$801$	5.17071e7			2.84754
$802$	−4.62641e6	+	1.39083e7i	−0.253985	+	0.763549i
$803$			3.38315e6i			0.185153i
$804$	−7.31429e6	−	5.47141e6i	−0.399054	−	0.298510i
$805$		0			0
$806$	−1.65374e7	−	5.50096e6i	−0.896664	−	0.298264i
$807$	−2.76932e7			−1.49689
$808$	−4.01843e6	−	5.78115e6i	−0.216535	−	0.311520i
$809$	4.52804e6			0.243242			0.121621	−	0.992577i	$-0.461191\pi$
$809$	4.52804e6			0.243242			0.121621	+	0.992577i	$0.461191\pi$
$810$		0			0
$811$			2.45669e7i			1.31159i	0.754939	+	0.655795i	$0.227666\pi$
$811$			2.45669e7i			1.31159i	−0.754939	+	0.655795i	$0.772334\pi$
$812$	−1.32626e7	+	1.77297e7i	−0.705893	+	0.943652i
$813$		−	1.51656e7i		−	0.804701i
$814$	1.56203e6	−	4.69590e6i	0.0826283	−	0.248404i
$815$		0			0
$816$	1.79123e7	−	5.27315e6i	0.941728	−	0.277233i
$817$	2.06047e7			1.07997
$818$	−8.94325e6	+	2.68859e7i	−0.467318	+	1.40489i
$819$		−	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	$0.660446\pi$
$822$	3.50711e7	+	1.16660e7i	1.81038	+	0.602200i
$823$	−1.50699e7			−0.775554			−0.387777	−	0.921753i	$-0.626757\pi$
$823$	−1.50699e7			−0.775554			−0.387777	+	0.921753i	$0.626757\pi$
$824$	2.61267e7	−	1.81605e7i	1.34050	−	0.931770i
$825$		0			0
$826$	−1.01095e7	−	3.36280e6i	−0.515561	−	0.171495i
$827$		−	1.25312e7i		−	0.637132i	−0.947901	−	0.318566i	$-0.896799\pi$
$827$		−	1.25312e7i		−	0.637132i	0.947901	−	0.318566i	$-0.103201\pi$
$828$	−7.18477e7	−	5.37453e7i	−3.64198	−	2.72436i
$829$			6.28073e6i			0.317412i	0.987326	+	0.158706i	$0.0507323\pi$
$829$			6.28073e6i			0.317412i	−0.987326	+	0.158706i	$0.949268\pi$
$830$		0			0
$831$	−1.82307e7			−0.915801
$832$	1.39821e7	+	5.19835e6i	0.700270	+	0.260350i
$833$	−5.32585e6			−0.265936
$834$	−8.15976e6	+	2.45305e7i	−0.406221	+	1.22121i
$835$		0			0
$836$	−1.16249e7	−	8.69593e6i	−0.575271	−	0.430329i
$837$		−	7.82078e7i		−	3.85866i
$838$	1.22309e7	+	4.06847e6i	0.601658	+	0.200134i
$839$	2.04326e7			1.00212			0.501058	−	0.865414i	$-0.332944\pi$
$839$	2.04326e7			1.00212			0.501058	+	0.865414i	$0.332944\pi$
$840$		0			0
$841$	−3.81543e7			−1.86018
$842$	−6.99981e6	−	2.32840e6i	−0.340256	−	0.113182i
$843$		−	3.61404e7i		−	1.75156i
$844$	−1.00682e7	+	1.34594e7i	−0.486514	+	0.650382i
$845$		0			0
$846$	6.47806e6	−	1.94748e7i	0.311185	−	0.935509i
$847$	1.15587e7			0.553605
$848$	3.17923e7	−	9.35924e6i	1.51821	−	0.446942i
$849$	2.06133e7			0.981472
$850$		0			0
$851$		−	2.12881e7i		−	1.00766i
$852$	1.87755e7	−	2.50995e7i	0.886121	−	1.18458i
$853$			2.97962e7i			1.40213i	0.713097	+	0.701066i	$0.247292\pi$
$853$			2.97962e7i			1.40213i	−0.713097	+	0.701066i	$0.752708\pi$
$854$	−6.43221e6	−	2.13960e6i	−0.301798	−	0.100389i
$855$		0			0
$856$	−1.32435e7	−	1.90528e7i	−0.617756	−	0.888741i
$857$	2.06770e7			0.961690			0.480845	−	0.876806i	$-0.340330\pi$
$857$	2.06770e7			0.961690			0.480845	+	0.876806i	$0.340330\pi$
$858$	−1.31606e7	−	4.37771e6i	−0.610320	−	0.203015i
$859$			2.17795e7i			1.00708i	0.863971	+	0.503542i	$0.167970\pi$
$859$			2.17795e7i			1.00708i	−0.863971	+	0.503542i	$0.832030\pi$
$860$		0			0
$861$		−	5.04363e6i		−	0.231865i
$862$	7.03478e6	−	2.11485e7i	0.322465	−	0.969419i
$863$	−2.24327e7			−1.02531			−0.512654	−	0.858596i	$-0.671337\pi$
$863$	−2.24327e7			−1.02531			−0.512654	+	0.858596i	$0.671337\pi$
$864$	−2.33067e6	+	6.68989e7i	−0.106218	+	3.04884i
$865$		0			0
$866$	1.04354e7	−	3.13716e7i	0.472839	−	1.42148i
$867$			3.08006e7i			1.39159i
$868$	1.56658e7	+	1.17187e7i	0.705755	+	0.527936i
$869$		−	8.04162e6i		−	0.361239i
$870$		0			0
$871$	−4.38956e6			−0.196054
$872$	5.12105e6	+	7.36745e6i	0.228070	+	0.328115i
$873$	−1.40763e7			−0.625107
$874$	−5.92560e7	−	1.97108e7i	−2.62394	−	0.872821i
$875$		0			0
$876$	1.05518e7	−	1.41059e7i	0.464587	−	0.621068i
$877$			3.66024e7i			1.60698i	0.595317	+	0.803491i	$0.297027\pi$
$877$			3.66024e7i			1.60698i	−0.595317	+	0.803491i	$0.702973\pi$
$878$	−1.36236e7	+	4.09563e7i	−0.596424	+	1.79302i
$879$	−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	$0.878179\pi$
$882$	9.77779e6	−	2.93947e7i	0.423223	−	1.27233i
$883$			1.39684e7i			0.602901i	0.953482	+	0.301451i	$0.0974708\pi$
$883$			1.39684e7i			0.602901i	−0.953482	+	0.301451i	$0.902529\pi$
$884$	5.37489e6	−	7.18526e6i	0.231334	−	0.309252i
$885$		0			0
$886$	1.06822e7	+	3.55330e6i	0.457169	+	0.152071i
$887$	−8.75249e6			−0.373528			−0.186764	−	0.982405i	$-0.559800\pi$
$887$	−8.75249e6			−0.373528			−0.186764	+	0.982405i	$0.559800\pi$
$888$	−2.11590e7	+	1.47075e7i	−0.900458	+	0.625900i
$889$	1.23934e7			0.525941
$890$		0			0
$891$		−	3.42378e7i		−	1.44481i
$892$	−1.82266e7	−	1.36343e7i	−0.766996	−	0.573747i
$893$		−	1.42846e7i		−	0.599430i
$894$	−8.08579e6	+	2.43081e7i	−0.338360	+	1.01720i
$895$		0			0
$896$	−1.30513e7	−	1.04910e7i	−0.543105	−	0.436565i
$897$	−5.96614e7			−2.47578
$898$	−3.66932e6	+	1.10310e7i	−0.151843	+	0.456482i
$899$			5.18363e7i			2.13912i
$900$		0			0
$901$		−	1.99355e7i		−	0.818116i
$902$	−1.84177e6	−	612642.i	−0.0753736	−	0.0250721i
$903$	−2.20973e7			−0.901819
$904$	−1.37309e7	+	9.54423e6i	−0.558828	+	0.388436i
$905$		0			0
$906$	6.99938e7	+	2.32826e7i	2.83295	+	0.942345i
$907$			4.22342e7i			1.70469i	0.522979	+	0.852345i	$0.324820\pi$
$907$			4.22342e7i			1.70469i	−0.522979	+	0.852345i	$0.675180\pi$
$908$	−4.14693e6	+	5.54369e6i	−0.166921	+	0.223144i
$909$		−	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	$0.245201\pi$
$912$	2.13473e7	+	7.25145e7i	0.849878	+	2.88694i
$913$	1.45661e7			0.578316
$914$	−4.90456e6	+	1.47445e7i	−0.194193	+	0.583799i
$915$		0			0
$916$	−1.45563e7	+	1.94591e7i	−0.573207	+	0.766274i
$917$		−	8.30252e6i		−	0.326052i
$918$	3.82077e7	+	1.27093e7i	1.49639	+	0.497755i
$919$	4.72565e6			0.184575			0.0922875	−	0.995732i	$-0.470582\pi$
$919$	4.72565e6			0.184575			0.0922875	+	0.995732i	$0.470582\pi$
$920$		0			0
$921$	8.31472e6			0.322997
$922$	−2.15602e7	−	7.17172e6i	−0.835266	−	0.277841i
$923$		−	1.50631e7i		−	0.581981i
$924$	1.24670e7	+	9.32586e6i	0.480376	+	0.359343i
$925$		0			0
$926$	−1.38874e7	+	4.17493e7i	−0.532223	+	1.60001i
$927$	1.11328e8			4.25505
$928$	1.54477e6	−	4.43407e7i	0.0588837	−	1.69018i
$929$	−3.52534e7			−1.34018			−0.670088	−	0.742282i	$-0.733744\pi$
$929$	−3.52534e7			−1.34018			−0.670088	+	0.742282i	$0.733744\pi$
$930$		0			0
$931$		−	2.15607e7i		−	0.815246i
$932$	−2.20555e7	−	1.64985e7i	−0.831721	−	0.622164i
$933$			7.11513e7i			2.67595i
$934$	−2.04741e7	−	6.81044e6i	−0.767957	−	0.255451i
$935$		0			0
$936$	2.97895e7	+	4.28569e7i	1.11141	+	1.59894i
$937$	−4.46076e7			−1.65982			−0.829909	−	0.557899i	$-0.811607\pi$
$937$	−4.46076e7			−1.65982			−0.829909	+	0.557899i	$0.811607\pi$
$938$	4.67555e6	+	1.55526e6i	0.173511	+	0.0577161i
$939$		−	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	$0.994718\pi$
$942$	2.29070e7	−	6.88649e7i	0.841089	−	2.52854i
$943$	−8.34937e6			−0.305756
$944$	2.04801e7	−	6.02909e6i	0.748001	−	0.220202i
$945$		0			0
$946$	−2.68412e6	+	8.06921e6i	−0.0975157	+	0.293159i
$947$		−	1.66417e7i		−	0.603006i	−0.953465	−	0.301503i	$-0.902512\pi$
$947$		−	1.66417e7i		−	0.603006i	0.953465	−	0.301503i	$-0.0974884\pi$
$948$	−2.50813e7	+	3.35292e7i	−0.906420	+	1.21172i
$949$		−	8.46542e6i		−	0.305129i
$950$		0			0
$951$	−2.70285e7			−0.969105
$952$	−8.27089e6	+	5.74902e6i	−0.295774	+	0.205590i
$953$	−1.76926e7			−0.631043			−0.315522	−	0.948918i	$-0.602179\pi$
$953$	−1.76926e7			−0.631043			−0.315522	+	0.948918i	$0.602179\pi$
$954$	1.10029e8	+	3.65998e7i	3.91414	+	1.30199i
$955$		0			0
$956$	8.92050e6	+	6.67293e6i	0.315678	+	0.236141i
$957$			4.12518e7i			1.45600i
$958$	−4.36116e6	+	1.31108e7i	−0.153528	+	0.461548i
$959$	−1.99381e7			−0.700063
$960$		0			0
$961$	1.71729e7			0.599841
$962$	−3.90857e6	+	1.17502e7i	−0.136170	+	0.409363i
$963$		−	8.11855e7i		−	2.82106i
$964$	2.16310e7	+	1.61809e7i	0.749693	+	0.560804i
$965$		0			0
$966$	6.35485e7	+	2.11386e7i	2.19110	+	0.728843i
$967$	1.08926e7			0.374598			0.187299	−	0.982303i	$-0.440027\pi$
$967$	1.08926e7			0.374598			0.187299	+	0.982303i	$0.440027\pi$
$968$	−1.90186e7	+	1.32196e7i	−0.652363	+	0.453452i
$969$	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	$-0.0728351\pi$
$972$	−5.29600e7	+	7.07980e7i	−1.79797	+	2.40356i
$973$		−	1.39457e7i		−	0.472236i
$974$	1.49118e7	−	4.48289e7i	0.503654	−	1.51412i
$975$		0			0
$976$	1.30306e7	−	3.83603e6i	0.437863	−	0.128901i
$977$	5.24537e7			1.75808			0.879042	−	0.476745i	$-0.158184\pi$
$977$	5.24537e7			1.75808			0.879042	+	0.476745i	$0.158184\pi$
$978$	1.06740e7	−	3.20891e7i	0.356846	−	1.07278i
$979$			1.48528e7i			0.495282i
$980$		0			0
$981$			3.13932e7i			1.04151i
$982$	1.82538e6	+	607191.i	0.0604053	+	0.0200931i
$983$	−9.86355e6			−0.325574			−0.162787	−	0.986661i	$-0.552048\pi$
$983$	−9.86355e6			−0.325574			−0.162787	+	0.986661i	$0.552048\pi$
$984$	5.76839e6	+	8.29875e6i	0.189918	+	0.273228i
$985$		0			0
$986$	−2.53242e7	−	8.42377e6i	−0.829551	−	0.275940i
$987$			1.53194e7i			0.500550i
$988$	2.90882e7	+	2.17592e7i	0.948034	+	0.709172i
$989$			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	$0.345173\pi$
$992$	−3.91791e7	−	1.36495e6i	−1.26408	−	0.0440389i
$993$	−1.00019e8			−3.21891
$994$	−5.33699e6	+	1.60445e7i	−0.171329	+	0.515062i
$995$		0			0
$996$	−6.07325e7	−	4.54306e7i	−1.93987	−	1.45111i
$997$			4.81768e6i			0.153497i	0.997050	+	0.0767485i	$0.0244539\pi$
$997$			4.81768e6i			0.153497i	−0.997050	+	0.0767485i	$0.975546\pi$
$998$	−3.48360e6	−	1.15877e6i	−0.110714	−	0.0368275i
$999$	−5.55686e7			−1.76163

Twists

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

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

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	200.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.78549 - 5.36768i) q^{2} -29.6034i q^{3} +(-25.6240 - 19.1679i) q^{4} +(-158.902 - 52.8566i) q^{6} +90.3364 q^{7} +(-148.639 + 103.318i) q^{8} -633.360 q^{9} +O(q^{10})\)	\(q+(1.78549 - 5.36768i) q^{2} -29.6034i q^{3} +(-25.6240 - 19.1679i) q^{4} +(-158.902 - 52.8566i) q^{6} +90.3364 q^{7} +(-148.639 + 103.318i) q^{8} -633.360 q^{9} -181.932i q^{11} +(-567.435 + 758.558i) q^{12} +455.237i q^{13} +(161.295 - 484.897i) q^{14} +(289.182 + 982.319i) q^{16} +615.967 q^{17} +(-1130.86 + 3399.68i) q^{18} +2493.63i q^{19} -2674.26i q^{21} +(-976.555 - 324.839i) q^{22} -4427.05 q^{23} +(3058.55 + 4400.21i) q^{24} +(2443.57 + 812.823i) q^{26} +11556.0i q^{27} +(-2314.78 - 1731.56i) q^{28} -7659.34i q^{29} -6767.72 q^{31} +(5789.11 + 201.685i) q^{32} -5385.81 q^{33} +(1099.80 - 3306.31i) q^{34} +(16229.2 + 12140.2i) q^{36} +4808.64i q^{37} +(13385.0 + 4452.35i) q^{38} +13476.6 q^{39} +1885.99 q^{41} +(-14354.6 - 4774.88i) q^{42} -8262.94i q^{43} +(-3487.26 + 4661.84i) q^{44} +(-7904.46 + 23763.0i) q^{46} -5728.44 q^{47} +(29080.0 - 8560.77i) q^{48} -8646.33 q^{49} -18234.7i q^{51} +(8725.95 - 11665.0i) q^{52} -32364.5i q^{53} +(62028.9 + 20633.1i) q^{54} +(-13427.5 + 9333.33i) q^{56} +73819.8 q^{57} +(-41112.9 - 13675.7i) q^{58} -20848.8i q^{59} -13265.1i q^{61} +(-12083.7 + 36327.0i) q^{62} -57215.5 q^{63} +(11419.0 - 30714.0i) q^{64} +(-9616.33 + 28909.3i) q^{66} +9642.36i q^{67} +(-15783.6 - 11806.8i) q^{68} +131056. i q^{69} -33088.4 q^{71} +(94141.9 - 65437.2i) q^{72} -18595.6 q^{73} +(25811.2 + 8585.79i) q^{74} +(47797.6 - 63896.7i) q^{76} -16435.1i q^{77} +(24062.3 - 72337.9i) q^{78} +44201.2 q^{79} +188190. q^{81} +(3367.42 - 10123.4i) q^{82} +80063.0i q^{83} +(-51260.1 + 68525.4i) q^{84} +(-44352.8 - 14753.4i) q^{86} -226742. q^{87} +(18796.8 + 27042.2i) q^{88} -81639.3 q^{89} +41124.5i q^{91} +(113439. + 84857.3i) q^{92} +200348. i q^{93} +(-10228.1 + 30748.4i) q^{94} +(5970.56 - 171377. i) q^{96} +22224.8 q^{97} +(-15438.0 + 46410.7i) q^{98} +115229. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} + q^{4} + 33 q^{6} - 196 q^{7} - 391 q^{8} - 1620 q^{9}+O(q^{10}) \) 20 * q - q^2 + q^4 + 33 * q^6 - 196 * q^7 - 391 * q^8 - 1620 * q^9	\( 20 q - q^{2} + q^{4} + 33 q^{6} - 196 q^{7} - 391 q^{8} - 1620 q^{9} - 241 q^{12} - 424 q^{14} - 55 q^{16} - 3368 q^{18} + 1197 q^{22} - 7184 q^{23} + 9459 q^{24} + 9172 q^{26} - 13492 q^{28} + 7160 q^{31} + 7869 q^{32} - 2836 q^{33} - 9591 q^{34} + 14828 q^{36} + 21505 q^{38} + 22452 q^{39} - 5804 q^{41} - 14272 q^{42} - 11593 q^{44} - 37612 q^{46} + 44180 q^{47} + 66571 q^{48} + 62652 q^{49} + 6136 q^{52} + 88947 q^{54} - 36908 q^{56} + 43696 q^{57} - 84012 q^{58} + 87460 q^{62} - 1240 q^{63} + 115177 q^{64} + 131439 q^{66} - 143341 q^{68} - 7724 q^{71} - 25772 q^{72} - 105136 q^{73} + 2112 q^{74} + 55951 q^{76} - 10948 q^{78} - 7780 q^{79} + 96984 q^{81} + 117501 q^{82} - 97556 q^{84} - 65986 q^{86} - 106188 q^{87} - 122597 q^{88} - 3160 q^{89} + 88908 q^{92} - 58540 q^{94} + 57791 q^{96} - 73688 q^{97} + 164655 q^{98}+O(q^{100}) \) 20 * q - q^2 + q^4 + 33 * q^6 - 196 * q^7 - 391 * q^8 - 1620 * q^9 - 241 * q^12 - 424 * q^14 - 55 * q^16 - 3368 * q^18 + 1197 * q^22 - 7184 * q^23 + 9459 * q^24 + 9172 * q^26 - 13492 * q^28 + 7160 * q^31 + 7869 * q^32 - 2836 * q^33 - 9591 * q^34 + 14828 * q^36 + 21505 * q^38 + 22452 * q^39 - 5804 * q^41 - 14272 * q^42 - 11593 * q^44 - 37612 * q^46 + 44180 * q^47 + 66571 * q^48 + 62652 * q^49 + 6136 * q^52 + 88947 * q^54 - 36908 * q^56 + 43696 * q^57 - 84012 * q^58 + 87460 * q^62 - 1240 * q^63 + 115177 * q^64 + 131439 * q^66 - 143341 * q^68 - 7724 * q^71 - 25772 * q^72 - 105136 * q^73 + 2112 * q^74 + 55951 * q^76 - 10948 * q^78 - 7780 * q^79 + 96984 * q^81 + 117501 * q^82 - 97556 * q^84 - 65986 * q^86 - 106188 * q^87 - 122597 * q^88 - 3160 * q^89 + 88908 * q^92 - 58540 * q^94 + 57791 * q^96 - 73688 * q^97 + 164655 * q^98

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