LMFDB - Embedded newform 76.6.e.a.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(45,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("76.45");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.e (of order $3$, degree $2$, 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:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} + 1540 x^{16} - 768 x^{15} + 1608492 x^{14} - 1027368 x^{13} + 897054160 x^{12} + \cdots + 80\!\cdots\!36 $ x^18 - 2x^17 + 1540x^16 - 768x^15 + 1608492x^14 - 1027368x^13 + 897054160x^12 - 1275481376x^11 + 361098181456x^10 - 863969476320x^9 + 79755165392064x^8 - 375077568148992x^7 + 12736924096193536x^6 - 57314532742553600x^5 + 977121800205220864x^4 - 4977732006498379776x^3 + 53672321824823513088x^2 - 185653809995679793152*x + 804303742853852430336
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{3}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.4
Root			$3.49628 + 6.05573i$ of defining polynomial
Character	$\chi$	$=$	76.49
Dual form			76.6.e.a.45.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.99628 + 6.92176i) q^{3} +(31.6056 - 54.7425i) q^{5} -80.2775 q^{7} +(89.5595 + 155.122i) q^{9} +O(q^{10})$	\(q+(-3.99628 + 6.92176i) q^{3} +(31.6056 - 54.7425i) q^{5} -80.2775 q^{7} +(89.5595 + 155.122i) q^{9} -475.169 q^{11} +(-337.473 - 584.520i) q^{13} +(252.609 + 437.532i) q^{15} +(866.499 - 1500.82i) q^{17} +(-574.366 - 1464.99i) q^{19} +(320.811 - 555.661i) q^{21} +(-2424.72 - 4199.73i) q^{23} +(-435.326 - 754.007i) q^{25} -3373.81 q^{27} +(2394.08 + 4146.67i) q^{29} -127.218 q^{31} +(1898.91 - 3289.01i) q^{33} +(-2537.22 + 4394.59i) q^{35} -13949.4 q^{37} +5394.54 q^{39} +(7883.24 - 13654.2i) q^{41} +(964.112 - 1669.89i) q^{43} +11322.3 q^{45} +(8099.51 + 14028.8i) q^{47} -10362.5 q^{49} +(6925.54 + 11995.4i) q^{51} +(8925.98 + 15460.3i) q^{53} +(-15018.0 + 26011.9i) q^{55} +(12435.6 + 1878.90i) q^{57} +(8424.75 - 14592.1i) q^{59} +(11641.7 + 20164.0i) q^{61} +(-7189.61 - 12452.8i) q^{63} -42664.1 q^{65} +(13618.4 + 23587.8i) q^{67} +38759.3 q^{69} +(-37449.3 + 64864.1i) q^{71} +(34900.9 - 60450.1i) q^{73} +6958.73 q^{75} +38145.4 q^{77} +(11408.5 - 19760.1i) q^{79} +(-8280.29 + 14341.9i) q^{81} -58008.8 q^{83} +(-54772.4 - 94868.6i) q^{85} -38269.6 q^{87} +(8203.84 + 14209.5i) q^{89} +(27091.5 + 46923.8i) q^{91} +(508.400 - 880.575i) q^{93} +(-98350.5 - 14859.7i) q^{95} +(65710.8 - 113814. i) q^{97} +(-42555.9 - 73709.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 11 q^{3} + 11 q^{5} + 336 q^{7} - 902 q^{9}+O(q^{10}) $ 18 * q - 11 * q^3 + 11 * q^5 + 336 * q^7 - 902 * q^9	$ 18 q - 11 q^{3} + 11 q^{5} + 336 q^{7} - 902 q^{9} - 320 q^{11} + 227 q^{13} - 101 q^{15} + 179 q^{17} - 868 q^{19} - 5700 q^{21} - 3425 q^{23} - 7054 q^{25} + 14722 q^{27} - 7349 q^{29} - 9960 q^{31} - 2998 q^{33} + 15888 q^{35} + 26444 q^{37} - 30246 q^{39} - 7311 q^{41} - 8283 q^{43} - 62164 q^{45} + 37603 q^{47} + 124738 q^{49} + 47227 q^{51} - 20337 q^{53} + 716 q^{55} - 57555 q^{57} - 74455 q^{59} - 7569 q^{61} - 52544 q^{63} + 188998 q^{65} - 26177 q^{67} + 116282 q^{69} - 53463 q^{71} - 14103 q^{73} + 120912 q^{75} - 31960 q^{77} + 31825 q^{79} - 21137 q^{81} + 82600 q^{83} - 50787 q^{85} - 339766 q^{87} - 155197 q^{89} - 2800 q^{91} - 46460 q^{93} + 49315 q^{95} + 111241 q^{97} - 193544 q^{99}+O(q^{100}) $ 18 * q - 11 * q^3 + 11 * q^5 + 336 * q^7 - 902 * q^9 - 320 * q^11 + 227 * q^13 - 101 * q^15 + 179 * q^17 - 868 * q^19 - 5700 * q^21 - 3425 * q^23 - 7054 * q^25 + 14722 * q^27 - 7349 * q^29 - 9960 * q^31 - 2998 * q^33 + 15888 * q^35 + 26444 * q^37 - 30246 * q^39 - 7311 * q^41 - 8283 * q^43 - 62164 * q^45 + 37603 * q^47 + 124738 * q^49 + 47227 * q^51 - 20337 * q^53 + 716 * q^55 - 57555 * q^57 - 74455 * q^59 - 7569 * q^61 - 52544 * q^63 + 188998 * q^65 - 26177 * q^67 + 116282 * q^69 - 53463 * q^71 - 14103 * q^73 + 120912 * q^75 - 31960 * q^77 + 31825 * q^79 - 21137 * q^81 + 82600 * q^83 - 50787 * q^85 - 339766 * q^87 - 155197 * q^89 - 2800 * q^91 - 46460 * q^93 + 49315 * q^95 + 111241 * q^97 - 193544 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−3.99628	+	6.92176i	−0.256361	+	0.444031i	−0.965264	−	0.261275i	$-0.915857\pi$
$3$	−3.99628	+	6.92176i	−0.256361	+	0.444031i	0.708903	+	0.705306i	$0.249190\pi$
$4$		0			0
$5$	31.6056	−	54.7425i	0.565378	−	0.979263i	−0.431637	−	0.902048i	$-0.642064\pi$
$5$	31.6056	−	54.7425i	0.565378	−	0.979263i	0.997014	−	0.0772156i	$-0.0246030\pi$
$6$		0			0
$7$	−80.2775			−0.619225			−0.309613	−	0.950863i	$-0.600199\pi$
$7$	−80.2775			−0.619225			−0.309613	+	0.950863i	$0.600199\pi$
$8$		0			0
$9$	89.5595	+	155.122i	0.368558	+	0.638361i
$10$		0			0
$11$	−475.169			−1.18404			−0.592020	−	0.805923i	$-0.701669\pi$
$11$	−475.169			−1.18404			−0.592020	+	0.805923i	$0.701669\pi$
$12$		0			0
$13$	−337.473	−	584.520i	−0.553835	−	0.959270i	−0.997993	−	0.0633218i	$-0.979831\pi$
$13$	−337.473	−	584.520i	−0.553835	−	0.959270i	0.444158	−	0.895948i	$-0.353503\pi$
$14$		0			0
$15$	252.609	+	437.532i	0.289882	+	0.502090i
$16$		0			0
$17$	866.499	−	1500.82i	0.727186	−	1.25952i	−0.230881	−	0.972982i	$-0.574161\pi$
$17$	866.499	−	1500.82i	0.727186	−	1.25952i	0.958068	−	0.286542i	$-0.0925058\pi$
$18$		0			0
$19$	−574.366	−	1464.99i	−0.365010	−	0.931004i
$19$	−574.366	−	1464.99i	−0.365010	−	0.931004i
$20$		0			0
$21$	320.811	−	555.661i	0.158745	−	0.274955i
$22$		0			0
$23$	−2424.72	−	4199.73i	−0.955743	−	1.65540i	−0.732658	−	0.680597i	$-0.761721\pi$
$23$	−2424.72	−	4199.73i	−0.955743	−	1.65540i	−0.223085	−	0.974799i	$-0.571613\pi$
$24$		0			0
$25$	−435.326	−	754.007i	−0.139304	−	0.241282i
$26$		0			0
$27$	−3373.81			−0.890658
$28$		0			0
$29$	2394.08	+	4146.67i	0.528620	+	0.915597i	0.999443	+	0.0333693i	$0.0106237\pi$
$29$	2394.08	+	4146.67i	0.528620	+	0.915597i	−0.470823	+	0.882228i	$0.656043\pi$
$30$		0			0
$31$	−127.218			−0.0237764			−0.0118882	−	0.999929i	$-0.503784\pi$
$31$	−127.218			−0.0237764			−0.0118882	+	0.999929i	$0.503784\pi$
$32$		0			0
$33$	1898.91	−	3289.01i	0.303542	−	0.525751i
$34$		0			0
$35$	−2537.22	+	4394.59i	−0.350096	+	0.606384i
$36$		0			0
$37$	−13949.4			−1.67514			−0.837570	−	0.546331i	$-0.816024\pi$
$37$	−13949.4			−1.67514			−0.837570	+	0.546331i	$0.816024\pi$
$38$		0			0
$39$	5394.54			0.567927
$40$		0			0
$41$	7883.24	−	13654.2i	0.732394	−	1.26854i	−0.223463	−	0.974712i	$-0.571736\pi$
$41$	7883.24	−	13654.2i	0.732394	−	1.26854i	0.955857	−	0.293831i	$-0.0949304\pi$
$42$		0			0
$43$	964.112	−	1669.89i	0.0795163	−	0.137726i	−0.823525	−	0.567280i	$-0.807996\pi$
$43$	964.112	−	1669.89i	0.0795163	−	0.137726i	0.903041	+	0.429554i	$0.141329\pi$
$44$		0			0
$45$	11322.3			0.833498
$46$		0			0
$47$	8099.51	+	14028.8i	0.534828	+	0.926349i	0.999172	+	0.0406941i	$0.0129569\pi$
$47$	8099.51	+	14028.8i	0.534828	+	0.926349i	−0.464344	+	0.885655i	$0.653710\pi$
$48$		0			0
$49$	−10362.5			−0.616560
$50$		0			0
$51$	6925.54	+	11995.4i	0.372845	+	0.645786i
$52$		0			0
$53$	8925.98	+	15460.3i	0.436482	+	0.756009i	0.997415	−	0.0718520i	$-0.0228909\pi$
$53$	8925.98	+	15460.3i	0.436482	+	0.756009i	−0.560933	+	0.827861i	$0.689558\pi$
$54$		0			0
$55$	−15018.0	+	26011.9i	−0.669430	+	1.15949i
$56$		0			0
$57$	12435.6	+	1878.90i	0.506969	+	0.0765978i
$58$		0			0
$59$	8424.75	−	14592.1i	0.315084	−	0.545742i	−0.664371	−	0.747403i	$-0.731301\pi$
$59$	8424.75	−	14592.1i	0.315084	−	0.545742i	0.979455	+	0.201661i	$0.0646339\pi$
$60$		0			0
$61$	11641.7	+	20164.0i	0.400583	+	0.693830i	0.993796	−	0.111215i	$-0.0354743\pi$
$61$	11641.7	+	20164.0i	0.400583	+	0.693830i	−0.593214	+	0.805045i	$0.702141\pi$
$62$		0			0
$63$	−7189.61	−	12452.8i	−0.228220	−	0.395289i
$64$		0			0
$65$	−42664.1			−1.25250
$66$		0			0
$67$	13618.4	+	23587.8i	0.370630	+	0.641950i	0.989663	−	0.143415i	$-0.0458085\pi$
$67$	13618.4	+	23587.8i	0.370630	+	0.641950i	−0.619033	+	0.785365i	$0.712475\pi$
$68$		0			0
$69$	38759.3			0.980062
$70$		0			0
$71$	−37449.3	+	64864.1i	−0.881654	+	1.52707i	−0.0321524	+	0.999483i	$0.510236\pi$
$71$	−37449.3	+	64864.1i	−0.881654	+	1.52707i	−0.849501	+	0.527586i	$0.823097\pi$
$72$		0			0
$73$	34900.9	−	60450.1i	0.766530	−	1.32767i	−0.172903	−	0.984939i	$-0.555315\pi$
$73$	34900.9	−	60450.1i	0.766530	−	1.32767i	0.939434	−	0.342731i	$-0.111352\pi$
$74$		0			0
$75$	6958.73			0.142849
$76$		0			0
$77$	38145.4			0.733188
$78$		0			0
$79$	11408.5	−	19760.1i	0.205665	−	0.356222i	−0.744680	−	0.667422i	$-0.767398\pi$
$79$	11408.5	−	19760.1i	0.205665	−	0.356222i	0.950344	+	0.311200i	$0.100731\pi$
$80$		0			0
$81$	−8280.29	+	14341.9i	−0.140227	+	0.242881i
$82$		0			0
$83$	−58008.8			−0.924270			−0.462135	−	0.886810i	$-0.652916\pi$
$83$	−58008.8			−0.924270			−0.462135	+	0.886810i	$0.652916\pi$
$84$		0			0
$85$	−54772.4	−	94868.6i	−0.822270	−	1.42421i
$86$		0			0
$87$	−38269.6			−0.542071
$88$		0			0
$89$	8203.84	+	14209.5i	0.109785	+	0.190153i	0.915683	−	0.401901i	$-0.131651\pi$
$89$	8203.84	+	14209.5i	0.109785	+	0.190153i	−0.805898	+	0.592054i	$0.798317\pi$
$90$		0			0
$91$	27091.5	+	46923.8i	0.342948	+	0.594004i
$92$		0			0
$93$	508.400	−	880.575i	0.00609535	−	0.0105575i
$94$		0			0
$95$	−98350.5	−	14859.7i	−1.11807	−	0.168928i
$96$		0			0
$97$	65710.8	−	113814.i	0.709100	−	1.22820i	−0.256092	−	0.966653i	$-0.582435\pi$
$97$	65710.8	−	113814.i	0.709100	−	1.22820i	0.965191	−	0.261544i	$-0.0842318\pi$
$98$		0			0
$99$	−42555.9	−	73709.0i	−0.436387	−	0.755845i
$100$		0			0
$101$	−46068.0	−	79792.2i	−0.449362	−	0.778318i	0.548983	−	0.835834i	$-0.315015\pi$
$101$	−46068.0	−	79792.2i	−0.449362	−	0.778318i	−0.998345	+	0.0575159i	$0.981682\pi$
$102$		0			0
$103$	149801.			1.39130			0.695651	−	0.718380i	$-0.255116\pi$
$103$	149801.			1.39130			0.695651	+	0.718380i	$0.255116\pi$
$104$		0			0
$105$	−20278.8	−	35124.0i	−0.179502	−	0.310907i
$106$		0			0
$107$	62370.7			0.526649			0.263324	−	0.964707i	$-0.415181\pi$
$107$	62370.7			0.526649			0.263324	+	0.964707i	$0.415181\pi$
$108$		0			0
$109$	−27370.0	+	47406.1i	−0.220652	+	0.382180i	−0.955006	−	0.296586i	$-0.904152\pi$
$109$	−27370.0	+	47406.1i	−0.220652	+	0.382180i	0.734354	+	0.678767i	$0.237485\pi$
$110$		0			0
$111$	55745.6	−	96554.3i	0.429441	−	0.743813i
$112$		0			0
$113$	−84395.3			−0.621759			−0.310879	−	0.950449i	$-0.600624\pi$
$113$	−84395.3			−0.621759			−0.310879	+	0.950449i	$0.600624\pi$
$114$		0			0
$115$	−306538.			−2.16142
$116$		0			0
$117$	60447.8	−	104699.i	0.408240	−	0.707093i
$118$		0			0
$119$	−69560.4	+	120482.i	−0.450292	+	0.779929i
$120$		0			0
$121$	64734.8			0.401952
$122$		0			0
$123$	63007.2	+	109132.i	0.375515	+	0.650411i
$124$		0			0
$125$	142500.			0.815717
$126$		0			0
$127$	59200.7	+	102539.i	0.325700	+	0.564128i	0.981654	−	0.190672i	$-0.0610668\pi$
$127$	59200.7	+	102539.i	0.325700	+	0.564128i	−0.655954	+	0.754801i	$0.727734\pi$
$128$		0			0
$129$	7705.72	+	13346.7i	0.0407698	+	0.0706154i
$130$		0			0
$131$	−37228.3	+	64481.4i	−0.189538	+	0.328289i	−0.945096	−	0.326792i	$-0.894032\pi$
$131$	−37228.3	+	64481.4i	−0.189538	+	0.328289i	0.755559	+	0.655081i	$0.227366\pi$
$132$		0			0
$133$	46108.6	+	117606.i	0.226023	+	0.576501i
$134$		0			0
$135$	−106631.	+	184691.i	−0.503559	+	0.872189i
$136$		0			0
$137$	−70227.1	−	121637.i	−0.319671	−	0.553686i	0.660748	−	0.750607i	$-0.270239\pi$
$137$	−70227.1	−	121637.i	−0.319671	−	0.553686i	−0.980419	+	0.196921i	$0.936906\pi$
$138$		0			0
$139$	−112322.	−	194548.i	−0.493093	−	0.854061i	0.506876	−	0.862019i	$-0.330800\pi$
$139$	−112322.	−	194548.i	−0.493093	−	0.854061i	−0.999968	+	0.00795774i	$0.997467\pi$
$140$		0			0
$141$	−129472.			−0.548437
$142$		0			0
$143$	160357.	+	277746.i	0.655763	+	1.13581i
$144$		0			0
$145$	302665.			1.19548
$146$		0			0
$147$	41411.5	−	71726.9i	0.158062	−	0.273772i
$148$		0			0
$149$	−146994.	+	254601.i	−0.542417	+	0.939494i	0.456347	+	0.889802i	$0.349157\pi$
$149$	−146994.	+	254601.i	−0.542417	+	0.939494i	−0.998765	+	0.0496923i	$0.984176\pi$
$150$		0			0
$151$	366703.			1.30880			0.654398	−	0.756150i	$-0.272922\pi$
$151$	366703.			1.30880			0.654398	+	0.756150i	$0.272922\pi$
$152$		0			0
$153$	310413.			1.07204
$154$		0			0
$155$	−4020.81	+	6964.26i	−0.0134426	+	0.0232833i
$156$		0			0
$157$	14338.2	−	24834.5i	0.0464243	−	0.0804093i	−0.841880	−	0.539666i	$-0.818551\pi$
$157$	14338.2	−	24834.5i	0.0464243	−	0.0804093i	0.888304	+	0.459256i	$0.151884\pi$
$158$		0			0
$159$	−142683.			−0.447588
$160$		0			0
$161$	194650.	+	337144.i	0.591820	+	1.02506i
$162$		0			0
$163$	12767.3			0.0376383			0.0188192	−	0.999823i	$-0.494009\pi$
$163$	12767.3			0.0376383			0.0188192	+	0.999823i	$0.494009\pi$
$164$		0			0
$165$	−120032.	−	207902.i	−0.343232	−	0.594495i
$166$		0			0
$167$	−121547.	−	210526.i	−0.337252	−	0.584138i	0.646663	−	0.762776i	$-0.276164\pi$
$167$	−121547.	−	210526.i	−0.337252	−	0.584138i	−0.983915	+	0.178638i	$0.942831\pi$
$168$		0			0
$169$	−42129.2	+	72969.8i	−0.113466	+	0.196529i
$170$		0			0
$171$	175812.	−	220301.i	0.459789	−	0.576137i
$172$		0			0
$173$	−213672.	+	370091.i	−0.542792	+	0.940143i	0.455951	+	0.890005i	$0.349299\pi$
$173$	−213672.	+	370091.i	−0.542792	+	0.940143i	−0.998742	+	0.0501376i	$0.984034\pi$
$174$		0			0
$175$	34946.9	+	60529.7i	0.0862607	+	0.149408i
$176$		0			0
$177$	67335.2	+	116628.i	0.161551	+	0.279814i
$178$		0			0
$179$	41174.1			0.0960488			0.0480244	−	0.998846i	$-0.484707\pi$
$179$	41174.1			0.0960488			0.0480244	+	0.998846i	$0.484707\pi$
$180$		0			0
$181$	−241411.	−	418136.i	−0.547723	−	0.948684i	−0.998430	−	0.0560122i	$-0.982161\pi$
$181$	−241411.	−	418136.i	−0.547723	−	0.948684i	0.450707	−	0.892672i	$-0.351172\pi$
$182$		0			0
$183$	−186094.			−0.410776
$184$		0			0
$185$	−440879.	+	763624.i	−0.947087	+	1.64040i
$186$		0			0
$187$	−411734.	+	713144.i	−0.861018	+	1.49133i
$188$		0			0
$189$	270841.			0.551518
$190$		0			0
$191$	218201.			0.432786			0.216393	−	0.976306i	$-0.430571\pi$
$191$	218201.			0.432786			0.216393	+	0.976306i	$0.430571\pi$
$192$		0			0
$193$	357570.	−	619329.i	0.690983	−	1.19682i	−0.280533	−	0.959844i	$-0.590511\pi$
$193$	357570.	−	619329.i	0.690983	−	1.19682i	0.971516	−	0.236973i	$-0.0761554\pi$
$194$		0			0
$195$	170498.	−	295310.i	0.321094	−	0.556150i
$196$		0			0
$197$	17740.5			0.0325686			0.0162843	−	0.999867i	$-0.494816\pi$
$197$	17740.5			0.0325686			0.0162843	+	0.999867i	$0.494816\pi$
$198$		0			0
$199$	−290101.	−	502469.i	−0.519297	−	0.899449i	−0.999748	−	0.0224275i	$-0.992861\pi$
$199$	−290101.	−	502469.i	−0.519297	−	0.899449i	0.480451	−	0.877021i	$-0.340473\pi$
$200$		0			0
$201$	−217692.			−0.380061
$202$		0			0
$203$	−192191.	−	332884.i	−0.327335	−	0.566961i
$204$		0			0
$205$	−498309.	−	863096.i	−0.828159	−	1.43441i
$206$		0			0
$207$	434313.	−	752252.i	0.704493	−	1.22022i
$208$		0			0
$209$	272921.	+	696119.i	0.432186	+	1.10235i
$210$		0			0
$211$	418159.	−	724272.i	0.646599	−	1.11994i	−0.337330	−	0.941386i	$-0.609524\pi$
$211$	418159.	−	724272.i	0.646599	−	1.11994i	0.983930	−	0.178556i	$-0.0571427\pi$
$212$		0			0
$213$	−299316.	−	518430.i	−0.452044	−	0.782963i
$214$		0			0
$215$	−60942.6	−	105556.i	−0.0899135	−	0.155735i
$216$		0			0
$217$	10212.8			0.0147229
$218$		0			0
$219$	278947.	+	483151.i	0.393017	+	0.680726i
$220$		0			0
$221$	−1.16968e6			−1.61096
$222$		0			0
$223$	349535.	−	605413.i	0.470684	−	0.815248i	−0.528754	−	0.848775i	$-0.677341\pi$
$223$	349535.	−	605413.i	0.470684	−	0.815248i	0.999438	+	0.0335271i	$0.0106740\pi$
$224$		0			0
$225$	77975.2	−	135057.i	0.102683	−	0.177853i
$226$		0			0
$227$	813403.			1.04771			0.523855	−	0.851808i	$-0.324493\pi$
$227$	813403.			1.04771			0.523855	+	0.851808i	$0.324493\pi$
$228$		0			0
$229$	−1.18902e6			−1.49830			−0.749151	−	0.662399i	$-0.769538\pi$
$229$	−1.18902e6			−1.49830			−0.749151	+	0.662399i	$0.769538\pi$
$230$		0			0
$231$	−152440.	+	264033.i	−0.187961	+	0.325558i
$232$		0			0
$233$	−106736.	+	184872.i	−0.128801	+	0.223091i	−0.923212	−	0.384290i	$-0.874446\pi$
$233$	−106736.	+	184872.i	−0.128801	+	0.223091i	0.794411	+	0.607381i	$0.207780\pi$
$234$		0			0
$235$	1.02396e6			1.20952
$236$		0			0
$237$	91182.9	+	157933.i	0.105449	+	0.182643i
$238$		0			0
$239$	−965775.			−1.09366			−0.546829	−	0.837245i	$-0.684165\pi$
$239$	−965775.			−1.09366			−0.546829	+	0.837245i	$0.684165\pi$
$240$		0			0
$241$	391235.	+	677639.i	0.433906	+	0.751547i	0.997206	−	0.0747059i	$-0.0238018\pi$
$241$	391235.	+	677639.i	0.433906	+	0.751547i	−0.563300	+	0.826252i	$0.690468\pi$
$242$		0			0
$243$	−476099.	−	824627.i	−0.517227	−	0.895863i
$244$		0			0
$245$	−327514.	+	567270.i	−0.348590	+	0.603775i
$246$		0			0
$247$	−662485.	+	830123.i	−0.690929	+	0.865765i
$248$		0			0
$249$	231819.	−	401523.i	0.236947	−	0.410404i
$250$		0			0
$251$	−448780.	−	777310.i	−0.449624	−	0.778771i	0.548738	−	0.835995i	$-0.315109\pi$
$251$	−448780.	−	777310.i	−0.449624	−	0.778771i	−0.998361	+	0.0572236i	$0.981775\pi$
$252$		0			0
$253$	1.15215e6	+	1.99558e6i	1.13164	+	1.96006i
$254$		0			0
$255$	875543.			0.843193
$256$		0			0
$257$	−552328.	−	956660.i	−0.521632	−	0.903493i	−0.999683	−	0.0251612i	$-0.991990\pi$
$257$	−552328.	−	956660.i	−0.521632	−	0.903493i	0.478051	−	0.878332i	$-0.341343\pi$
$258$		0			0
$259$	1.11982e6			1.03729
$260$		0			0
$261$	−428825.	+	742747.i	−0.389654	+	0.674901i
$262$		0			0
$263$	−306009.	+	530023.i	−0.272800	+	0.472504i	−0.969578	−	0.244783i	$-0.921283\pi$
$263$	−306009.	+	530023.i	−0.272800	+	0.472504i	0.696778	+	0.717287i	$0.254616\pi$
$264$		0			0
$265$	1.12844e6			0.987109
$266$		0			0
$267$	−131139.			−0.112578
$268$		0			0
$269$	−248820.	+	430969.i	−0.209655	+	0.363133i	−0.951606	−	0.307321i	$-0.900567\pi$
$269$	−248820.	+	430969.i	−0.209655	+	0.363133i	0.741951	+	0.670454i	$0.233901\pi$
$270$		0			0
$271$	724980.	−	1.25570e6i	0.599657	−	1.03864i	−0.393214	−	0.919447i	$-0.628637\pi$
$271$	724980.	−	1.25570e6i	0.599657	−	1.03864i	0.992871	−	0.119190i	$-0.0380297\pi$
$272$		0			0
$273$	−433060.			−0.351675
$274$		0			0
$275$	206853.	+	358281.i	0.164942	+	0.285688i
$276$		0			0
$277$	−87028.2			−0.0681492			−0.0340746	−	0.999419i	$-0.510848\pi$
$277$	−87028.2			−0.0681492			−0.0340746	+	0.999419i	$0.510848\pi$
$278$		0			0
$279$	−11393.6	−	19734.3i	−0.00876297	−	0.0151779i
$280$		0			0
$281$	949563.	+	1.64469e6i	0.717394	+	1.24256i	0.962029	+	0.272948i	$0.0879987\pi$
$281$	949563.	+	1.64469e6i	0.717394	+	1.24256i	−0.244635	+	0.969615i	$0.578668\pi$
$282$		0			0
$283$	−727473.	+	1.26002e6i	−0.539946	+	0.935214i	0.458960	+	0.888457i	$0.348222\pi$
$283$	−727473.	+	1.26002e6i	−0.539946	+	0.935214i	−0.998906	+	0.0467574i	$0.985111\pi$
$284$		0			0
$285$	495891.	−	621374.i	0.361638	−	0.453149i
$286$		0			0
$287$	−632846.	+	1.09612e6i	−0.453517	+	0.785514i
$288$		0			0
$289$	−791713.	−	1.37129e6i	−0.557600	−	0.965792i
$290$		0			0
$291$	525197.	+	909668.i	0.363572	+	0.629724i
$292$		0			0
$293$	795288.			0.541197			0.270598	−	0.962692i	$-0.412778\pi$
$293$	795288.			0.541197			0.270598	+	0.962692i	$0.412778\pi$
$294$		0			0
$295$	−532538.	−	922383.i	−0.356283	−	0.617101i
$296$		0			0
$297$	1.60313e6			1.05458
$298$		0			0
$299$	−1.63655e6	+	2.83459e6i	−1.05865	+	1.83363i
$300$		0			0
$301$	−77396.5	+	134055.i	−0.0492385	+	0.0852836i
$302$		0			0
$303$	736403.			0.460796
$304$		0			0
$305$	1.47177e6			0.905923
$306$		0			0
$307$	964887.	−	1.67123e6i	0.584293	−	1.01202i	−0.410670	−	0.911784i	$-0.634705\pi$
$307$	964887.	−	1.67123e6i	0.584293	−	1.01202i	0.994963	−	0.100241i	$-0.0319613\pi$
$308$		0			0
$309$	−598646.	+	1.03689e6i	−0.356676	+	0.617781i
$310$		0			0
$311$	1.42463e6			0.835220			0.417610	−	0.908626i	$-0.362868\pi$
$311$	1.42463e6			0.835220			0.417610	+	0.908626i	$0.362868\pi$
$312$		0			0
$313$	1.12004e6	+	1.93997e6i	0.646209	+	1.11927i	0.984021	+	0.178053i	$0.0569800\pi$
$313$	1.12004e6	+	1.93997e6i	0.646209	+	1.11927i	−0.337812	+	0.941214i	$0.609687\pi$
$314$		0			0
$315$	−908928.			−0.516123
$316$		0			0
$317$	−278493.	−	482363.i	−0.155656	−	0.269604i	0.777642	−	0.628708i	$-0.216416\pi$
$317$	−278493.	−	482363.i	−0.155656	−	0.269604i	−0.933298	+	0.359104i	$0.883082\pi$
$318$		0			0
$319$	−1.13759e6	−	1.97037e6i	−0.625908	−	1.08410i
$320$		0			0
$321$	−249251.	+	431715.i	−0.135012	+	0.233848i
$322$		0			0
$323$	−2.69638e6	−	407395.i	−1.43805	−	0.217275i
$324$		0			0
$325$	−293821.	+	508913.i	−0.154303	+	0.267261i
$326$		0			0
$327$	−218756.	−	378896.i	−0.113133	−	0.195953i
$328$		0			0
$329$	−650208.	−	1.12619e6i	−0.331179	−	0.573619i
$330$		0			0
$331$	−1.85079e6			−0.928511			−0.464256	−	0.885701i	$-0.653678\pi$
$331$	−1.85079e6			−0.928511			−0.464256	+	0.885701i	$0.653678\pi$
$332$		0			0
$333$	−1.24930e6	−	2.16385e6i	−0.617386	−	1.06934i
$334$		0			0
$335$	1.72168e6			0.838184
$336$		0			0
$337$	1.16626e6	−	2.02003e6i	0.559399	−	0.968907i	−0.438148	−	0.898903i	$-0.644365\pi$
$337$	1.16626e6	−	2.02003e6i	0.559399	−	0.968907i	0.997547	−	0.0700041i	$-0.0223013\pi$
$338$		0			0
$339$	337267.	−	584163.i	0.159395	−	0.276080i
$340$		0			0
$341$	60450.3			0.0281522
$342$		0			0
$343$	2.18110e6			1.00101
$344$		0			0
$345$	1.22501e6	−	2.12178e6i	0.554106	−	0.959739i
$346$		0			0
$347$	1.33391e6	−	2.31041e6i	0.594708	−	1.03006i	−0.398880	−	0.917003i	$-0.630601\pi$
$347$	1.33391e6	−	2.31041e6i	0.594708	−	1.03006i	0.993588	−	0.113062i	$-0.0360657\pi$
$348$		0			0
$349$	−2.33528e6			−1.02630			−0.513152	−	0.858298i	$-0.671522\pi$
$349$	−2.33528e6			−1.02630			−0.513152	+	0.858298i	$0.671522\pi$
$350$		0			0
$351$	1.13857e6	+	1.97206e6i	0.493278	+	0.854382i
$352$		0			0
$353$	−2.57168e6			−1.09845			−0.549225	−	0.835675i	$-0.685077\pi$
$353$	−2.57168e6			−1.09845			−0.549225	+	0.835675i	$0.685077\pi$
$354$		0			0
$355$	2.36722e6	+	4.10014e6i	0.996935	+	1.72674i
$356$		0			0
$357$	−555965.	−	962960.i	−0.230875	−	0.399887i
$358$		0			0
$359$	−2.06014e6	+	3.56826e6i	−0.843645	+	1.46124i	0.0431473	+	0.999069i	$0.486262\pi$
$359$	−2.06014e6	+	3.56826e6i	−0.843645	+	1.46124i	−0.886793	+	0.462168i	$0.847072\pi$
$360$		0			0
$361$	−1.81631e6	+	1.68288e6i	−0.733536	+	0.679651i
$362$		0			0
$363$	−258698.	+	448078.i	−0.103045	+	0.178479i
$364$		0			0
$365$	−2.20613e6	−	3.82112e6i	−0.866759	−	1.50127i
$366$		0			0
$367$	−1.76851e6	−	3.06315e6i	−0.685398	−	1.18714i	−0.973312	−	0.229487i	$-0.926295\pi$
$367$	−1.76851e6	−	3.06315e6i	−0.685398	−	1.18714i	0.287914	−	0.957656i	$-0.407038\pi$
$368$		0			0
$369$	2.82408e6			1.07972
$370$		0			0
$371$	−716555.	−	1.24111e6i	−0.270281	−	0.468140i
$372$		0			0
$373$	−3.14142e6			−1.16910			−0.584552	−	0.811356i	$-0.698730\pi$
$373$	−3.14142e6			−1.16910			−0.584552	+	0.811356i	$0.698730\pi$
$374$		0			0
$375$	−569469.	+	986350.i	−0.209118	+	0.362204i
$376$		0			0
$377$	1.61587e6	−	2.79878e6i	0.585537	−	1.01418i
$378$		0			0
$379$	1.24166e6			0.444021			0.222011	−	0.975044i	$-0.428738\pi$
$379$	1.24166e6			0.444021			0.222011	+	0.975044i	$0.428738\pi$
$380$		0			0
$381$	−946329.			−0.333987
$382$		0			0
$383$	1.41220e6	−	2.44600e6i	0.491924	−	0.852038i	−0.508032	−	0.861338i	$-0.669627\pi$
$383$	1.41220e6	−	2.44600e6i	0.491924	−	0.852038i	0.999957	+	0.00929990i	$0.00296029\pi$
$384$		0			0
$385$	1.20561e6	−	2.08817e6i	0.414528	−	0.717984i
$386$		0			0
$387$	345382.			0.117225
$388$		0			0
$389$	2.26664e6	+	3.92593e6i	0.759465	+	1.31543i	0.943124	+	0.332442i	$0.107873\pi$
$389$	2.26664e6	+	3.92593e6i	0.759465	+	1.31543i	−0.183658	+	0.982990i	$0.558794\pi$
$390$		0			0
$391$	−8.40405e6			−2.78001
$392$		0			0
$393$	−297550.	−	515371.i	−0.0971802	−	0.168321i
$394$		0			0
$395$	−721143.	−	1.24906e6i	−0.232557	−	0.402800i
$396$		0			0
$397$	968813.	−	1.67803e6i	0.308506	−	0.534348i	−0.669530	−	0.742785i	$-0.733504\pi$
$397$	968813.	−	1.67803e6i	0.308506	−	0.534348i	0.978036	+	0.208437i	$0.0668377\pi$
$398$		0			0
$399$	−998302.	−	150833.i	−0.313928	−	0.0474313i
$400$		0			0
$401$	2.21857e6	−	3.84268e6i	0.688990	−	1.19336i	−0.283176	−	0.959068i	$-0.591388\pi$
$401$	2.21857e6	−	3.84268e6i	0.688990	−	1.19336i	0.972165	−	0.234297i	$-0.0752788\pi$
$402$		0			0
$403$	42932.8	+	74361.7i	0.0131682	+	0.0228080i
$404$		0			0
$405$	523407.	+	906567.i	0.158563	+	0.274639i
$406$		0			0
$407$	6.62832e6			1.98343
$408$		0			0
$409$	3.20721e6	+	5.55506e6i	0.948025	+	1.64203i	0.749579	+	0.661915i	$0.230256\pi$
$409$	3.20721e6	+	5.55506e6i	0.948025	+	1.64203i	0.198446	+	0.980112i	$0.436411\pi$
$410$		0			0
$411$	1.12259e6			0.327805
$412$		0			0
$413$	−676317.	+	1.17142e6i	−0.195108	+	0.337937i
$414$		0			0
$415$	−1.83340e6	+	3.17555e6i	−0.522562	+	0.905103i
$416$		0			0
$417$	1.79548e6			0.505639
$418$		0			0
$419$	2.16492e6			0.602429			0.301215	−	0.953556i	$-0.402608\pi$
$419$	2.16492e6			0.602429			0.301215	+	0.953556i	$0.402608\pi$
$420$		0			0
$421$	3.39931e6	−	5.88777e6i	0.934727	−	1.61900i	0.159608	−	0.987180i	$-0.448977\pi$
$421$	3.39931e6	−	5.88777e6i	0.934727	−	1.61900i	0.775119	−	0.631815i	$-0.217690\pi$
$422$		0			0
$423$	−1.45078e6	+	2.51282e6i	−0.394230	+	0.682826i
$424$		0			0
$425$	−1.50884e6			−0.405201
$426$		0			0
$427$	−934567.	−	1.61872e6i	−0.248051	−	0.429637i
$428$		0			0
$429$	−2.56332e6			−0.672449
$430$		0			0
$431$	101699.	+	176148.i	0.0263708	+	0.0456756i	0.878910	−	0.476988i	$-0.158272\pi$
$431$	101699.	+	176148.i	0.0263708	+	0.0456756i	−0.852539	+	0.522664i	$0.824938\pi$
$432$		0			0
$433$	487850.	+	844981.i	0.125045	+	0.216584i	0.921751	−	0.387783i	$-0.126759\pi$
$433$	487850.	+	844981.i	0.125045	+	0.216584i	−0.796705	+	0.604368i	$0.793426\pi$
$434$		0			0
$435$	−1.20953e6	+	2.09497e6i	−0.306475	+	0.530830i
$436$		0			0
$437$	−4.75990e6	+	5.96437e6i	−1.19232	+	1.49404i
$438$		0			0
$439$	−1.96789e6	+	3.40848e6i	−0.487348	+	0.844111i	−0.999894	−	0.0145483i	$-0.995369\pi$
$439$	−1.96789e6	+	3.40848e6i	−0.487348	+	0.844111i	0.512546	+	0.858660i	$0.328702\pi$
$440$		0			0
$441$	−928063.	−	1.60745e6i	−0.227238	−	0.393588i
$442$		0			0
$443$	1.39091e6	+	2.40913e6i	0.336737	+	0.583246i	0.983817	−	0.179176i	$-0.0573433\pi$
$443$	1.39091e6	+	2.40913e6i	0.336737	+	0.583246i	−0.647080	+	0.762422i	$0.724010\pi$
$444$		0			0
$445$	1.03715e6			0.248279
$446$		0			0
$447$	−1.17486e6	−	2.03491e6i	−0.278110	−	0.481700i
$448$		0			0
$449$	6.91764e6			1.61936			0.809678	−	0.586875i	$-0.199642\pi$
$449$	6.91764e6			1.61936			0.809678	+	0.586875i	$0.199642\pi$
$450$		0			0
$451$	−3.74587e6	+	6.48804e6i	−0.867184	+	1.50201i
$452$		0			0
$453$	−1.46545e6	+	2.53823e6i	−0.335525	+	0.581146i
$454$		0			0
$455$	3.42497e6			0.775582
$456$		0			0
$457$	6.44928e6			1.44451			0.722256	−	0.691626i	$-0.243105\pi$
$457$	6.44928e6			1.44451			0.722256	+	0.691626i	$0.243105\pi$
$458$		0			0
$459$	−2.92340e6	+	5.06348e6i	−0.647675	+	1.12181i
$460$		0			0
$461$	610341.	−	1.05714e6i	0.133758	−	0.231676i	−0.791364	−	0.611345i	$-0.790629\pi$
$461$	610341.	−	1.05714e6i	0.133758	−	0.231676i	0.925122	+	0.379669i	$0.123962\pi$
$462$		0			0
$463$	847245.			0.183678			0.0918388	−	0.995774i	$-0.470726\pi$
$463$	847245.			0.183678			0.0918388	+	0.995774i	$0.470726\pi$
$464$		0			0
$465$	−32136.6	−	55662.2i	−0.00689235	−	0.0119379i
$466$		0			0
$467$	−76212.7			−0.0161709			−0.00808547	−	0.999967i	$-0.502574\pi$
$467$	−76212.7			−0.0161709			−0.00808547	+	0.999967i	$0.502574\pi$
$468$		0			0
$469$	−1.09325e6	−	1.89357e6i	−0.229503	−	0.397512i
$470$		0			0
$471$	114599.	+	198491.i	0.0238028	+	0.0412276i
$472$		0			0
$473$	−458116.	+	793481.i	−0.0941505	+	0.163074i
$474$		0			0
$475$	−854578.	+	1.07082e6i	−0.173787	+	0.217763i
$476$		0			0
$477$	−1.59881e6	+	2.76923e6i	−0.321738	+	0.557266i
$478$		0			0
$479$	−1.33045e6	−	2.30441e6i	−0.264947	−	0.458902i	0.702602	−	0.711583i	$-0.252021\pi$
$479$	−1.33045e6	−	2.30441e6i	−0.264947	−	0.458902i	−0.967550	+	0.252680i	$0.918688\pi$
$480$		0			0
$481$	4.70754e6	+	8.15370e6i	0.927750	+	1.60691i
$482$		0			0
$483$	−3.11150e6			−0.606879
$484$		0			0
$485$	−4.15366e6	−	7.19434e6i	−0.801819	−	1.38879i
$486$		0			0
$487$	5.81426e6			1.11089			0.555446	−	0.831552i	$-0.312547\pi$
$487$	5.81426e6			1.11089			0.555446	+	0.831552i	$0.312547\pi$
$488$		0			0
$489$	−51021.7	+	88372.2i	−0.00964901	+	0.0167126i
$490$		0			0
$491$	2.27968e6	−	3.94853e6i	0.426747	−	0.739148i	−0.569834	−	0.821760i	$-0.692993\pi$
$491$	2.27968e6	−	3.94853e6i	0.426747	−	0.739148i	0.996582	+	0.0826113i	$0.0263260\pi$
$492$		0			0
$493$	8.29787e6			1.53762
$494$		0			0
$495$	−5.38002e6			−0.986895
$496$		0			0
$497$	3.00634e6	−	5.20713e6i	0.545942	−	0.945600i
$498$		0			0
$499$	3.38613e6	−	5.86495e6i	0.608769	−	1.05442i	−0.382675	−	0.923883i	$-0.624997\pi$
$499$	3.38613e6	−	5.86495e6i	0.608769	−	1.05442i	0.991444	−	0.130536i	$-0.0416697\pi$
$500$		0			0
$501$	1.94295e6			0.345833
$502$		0			0
$503$	2.62169e6	+	4.54089e6i	0.462020	+	0.800242i	0.999062	−	0.0433140i	$-0.0137916\pi$
$503$	2.62169e6	+	4.54089e6i	0.462020	+	0.800242i	−0.537042	+	0.843556i	$0.680458\pi$
$504$		0			0
$505$	−5.82403e6			−1.01624
$506$		0			0
$507$	−336720.	−	583215.i	−0.0581766	−	0.100765i
$508$		0			0
$509$	−4.68578e6	−	8.11601e6i	−0.801655	−	1.38851i	−0.918526	−	0.395360i	$-0.870620\pi$
$509$	−4.68578e6	−	8.11601e6i	−0.801655	−	1.38851i	0.116872	−	0.993147i	$-0.462713\pi$
$510$		0			0
$511$	−2.80175e6	+	4.85278e6i	−0.474655	+	0.822126i
$512$		0			0
$513$	1.93780e6	+	4.94261e6i	0.325099	+	0.829206i
$514$		0			0
$515$	4.73455e6	−	8.20047e6i	0.786611	−	1.36245i
$516$		0			0
$517$	−3.84864e6	−	6.66604e6i	−0.633258	−	1.09683i
$518$		0			0
$519$	−1.70779e6	−	2.95798e6i	−0.278302	−	0.482032i
$520$		0			0
$521$	244496.			0.0394619			0.0197309	−	0.999805i	$-0.493719\pi$
$521$	244496.			0.0394619			0.0197309	+	0.999805i	$0.493719\pi$
$522$		0			0
$523$	−2.04939e6	−	3.54964e6i	−0.327619	−	0.567453i	0.654420	−	0.756131i	$-0.272913\pi$
$523$	−2.04939e6	−	3.54964e6i	−0.327619	−	0.567453i	−0.982039	+	0.188678i	$0.939580\pi$
$524$		0			0
$525$	−558630.			−0.0884557
$526$		0			0
$527$	−110235.	+	190932.i	−0.0172899	+	0.0299469i
$528$		0			0
$529$	−8.54032e6	+	1.47923e7i	−1.32689	+	2.29824i
$530$		0			0
$531$	3.01807e6			0.464507
$532$		0			0
$533$	−1.06415e7			−1.62250
$534$		0			0
$535$	1.97126e6	−	3.41433e6i	0.297756	−	0.515728i
$536$		0			0
$537$	−164543.	+	284997.i	−0.0246232	+	0.0426486i
$538$		0			0
$539$	4.92395e6			0.730032
$540$		0			0
$541$	227501.	+	394043.i	0.0334187	+	0.0578829i	0.882251	−	0.470779i	$-0.156027\pi$
$541$	227501.	+	394043.i	0.0334187	+	0.0578829i	−0.848832	+	0.528662i	$0.822694\pi$
$542$		0			0
$543$	3.85898e6			0.561660
$544$		0			0
$545$	1.73009e6	+	2.99660e6i	0.249503	+	0.432153i
$546$		0			0
$547$	−4.19066e6	−	7.25843e6i	−0.598844	−	1.03723i	−0.992992	−	0.118182i	$-0.962293\pi$
$547$	−4.19066e6	−	7.25843e6i	−0.598844	−	1.03723i	0.394148	−	0.919047i	$-0.371040\pi$
$548$		0			0
$549$	−2.08525e6	+	3.61176e6i	−0.295276	+	0.511433i
$550$		0			0
$551$	4.69976e6	−	5.88901e6i	0.659473	−	0.826349i
$552$		0			0
$553$	−915844.	+	1.58629e6i	−0.127353	+	0.220582i
$554$		0			0
$555$	−3.52375e6	−	6.10331e6i	−0.485593	−	0.841071i
$556$		0			0
$557$	−2.14702e6	−	3.71874e6i	−0.293222	−	0.507876i	0.681347	−	0.731960i	$-0.261394\pi$
$557$	−2.14702e6	−	3.71874e6i	−0.293222	−	0.507876i	−0.974570	+	0.224084i	$0.928061\pi$
$558$		0			0
$559$	−1.30145e6			−0.176156
$560$		0			0
$561$	−3.29080e6	−	5.69984e6i	−0.441464	−	0.764637i
$562$		0			0
$563$	−5.43360e6			−0.722465			−0.361232	−	0.932476i	$-0.617644\pi$
$563$	−5.43360e6			−0.722465			−0.361232	+	0.932476i	$0.617644\pi$
$564$		0			0
$565$	−2.66736e6	+	4.62001e6i	−0.351529	+	0.608866i
$566$		0			0
$567$	664720.	−	1.15133e6i	0.0868323	−	0.150398i
$568$		0			0
$569$	4.53732e6			0.587514			0.293757	−	0.955880i	$-0.405094\pi$
$569$	4.53732e6			0.587514			0.293757	+	0.955880i	$0.405094\pi$
$570$		0			0
$571$	−1.75132e6			−0.224789			−0.112395	−	0.993664i	$-0.535852\pi$
$571$	−1.75132e6			−0.224789			−0.112395	+	0.993664i	$0.535852\pi$
$572$		0			0
$573$	−871992.	+	1.51033e6i	−0.110950	+	0.192170i
$574$		0			0
$575$	−2.11108e6	+	3.65650e6i	−0.266278	+	0.461208i
$576$		0			0
$577$	2.69353e6			0.336808			0.168404	−	0.985718i	$-0.446139\pi$
$577$	2.69353e6			0.336808			0.168404	+	0.985718i	$0.446139\pi$
$578$		0			0
$579$	2.85790e6	+	4.95002e6i	0.354283	+	0.613636i
$580$		0			0
$581$	4.65680e6			0.572331
$582$		0			0
$583$	−4.24135e6	−	7.34624e6i	−0.516812	−	0.895145i
$584$		0			0
$585$	−3.82098e6	−	6.61812e6i	−0.461620	−	0.799549i
$586$		0			0
$587$	1.95802e6	−	3.39138e6i	0.234542	−	0.406239i	−0.724597	−	0.689172i	$-0.757974\pi$
$587$	1.95802e6	−	3.39138e6i	0.234542	−	0.406239i	0.959140	+	0.282934i	$0.0913076\pi$
$588$		0			0
$589$	73069.9	+	186374.i	0.00867862	+	0.0221359i
$590$		0			0
$591$	−70895.9	+	122795.i	−0.00834934	+	0.0144615i
$592$		0			0
$593$	−5.66866e6	−	9.81841e6i	−0.661978	−	1.14658i	−0.980095	−	0.198528i	$-0.936384\pi$
$593$	−5.66866e6	−	9.81841e6i	−0.661978	−	1.14658i	0.318117	−	0.948051i	$-0.396950\pi$
$594$		0			0
$595$	4.39699e6	+	7.61581e6i	0.509170	+	0.881909i
$596$		0			0
$597$	4.63729e6			0.532511
$598$		0			0
$599$	3.86543e6	+	6.69512e6i	0.440180	+	0.762414i	0.997702	−	0.0677475i	$-0.0215812\pi$
$599$	3.86543e6	+	6.69512e6i	0.440180	+	0.762414i	−0.557522	+	0.830162i	$0.688248\pi$
$600$		0			0
$601$	−6.87953e6			−0.776913			−0.388457	−	0.921467i	$-0.626992\pi$
$601$	−6.87953e6			−0.776913			−0.388457	+	0.921467i	$0.626992\pi$
$602$		0			0
$603$	−2.43932e6	+	4.22503e6i	−0.273197	+	0.473191i
$604$		0			0
$605$	2.04598e6	−	3.54374e6i	0.227255	−	0.393617i
$606$		0			0
$607$	1.19598e7			1.31750			0.658750	−	0.752362i	$-0.271085\pi$
$607$	1.19598e7			1.31750			0.658750	+	0.752362i	$0.271085\pi$
$608$		0			0
$609$	3.07219e6			0.335664
$610$		0			0
$611$	5.46673e6	−	9.46865e6i	0.592413	−	1.02609i
$612$		0			0
$613$	1.49181e6	−	2.58389e6i	0.160347	−	0.277730i	−0.774646	−	0.632395i	$-0.782072\pi$
$613$	1.49181e6	−	2.58389e6i	0.160347	−	0.277730i	0.934993	+	0.354666i	$0.115405\pi$
$614$		0			0
$615$	7.96552e6			0.849232
$616$		0			0
$617$	−2.62649e6	−	4.54922e6i	−0.277756	−	0.481087i	0.693071	−	0.720869i	$-0.256257\pi$
$617$	−2.62649e6	−	4.54922e6i	−0.277756	−	0.481087i	−0.970827	+	0.239782i	$0.922924\pi$
$618$		0			0
$619$	−1.09695e7			−1.15069			−0.575346	−	0.817910i	$-0.695133\pi$
$619$	−1.09695e7			−1.15069			−0.575346	+	0.817910i	$0.695133\pi$
$620$		0			0
$621$	8.18053e6	+	1.41691e7i	0.851241	+	1.47439i
$622$		0			0
$623$	−658583.	−	1.14070e6i	−0.0679815	−	0.117747i
$624$		0			0
$625$	5.86419e6	−	1.01571e7i	0.600493	−	1.04008i
$626$		0			0
$627$	−5.90904e6	−	892794.i	−0.600272	−	0.0906949i
$628$		0			0
$629$	−1.20871e7	+	2.09355e7i	−1.21814	+	2.10988i
$630$		0			0
$631$	−3.73436e6	−	6.46811e6i	−0.373373	−	0.646701i	0.616709	−	0.787191i	$-0.288466\pi$
$631$	−3.73436e6	−	6.46811e6i	−0.373373	−	0.646701i	−0.990082	+	0.140490i	$0.955132\pi$
$632$		0			0
$633$	3.34216e6	+	5.78879e6i	0.331526	+	0.574220i
$634$		0			0
$635$	7.48429e6			0.736573
$636$		0			0
$637$	3.49707e6	+	6.05710e6i	0.341473	+	0.591448i
$638$		0			0
$639$	−1.34158e7			−1.29976
$640$		0			0
$641$	−8.26419e6	+	1.43140e7i	−0.794430	+	1.37599i	0.128771	+	0.991674i	$0.458897\pi$
$641$	−8.26419e6	+	1.43140e7i	−0.794430	+	1.37599i	−0.923201	+	0.384318i	$0.874437\pi$
$642$		0			0
$643$	−6.29383e6	+	1.09012e7i	−0.600326	+	1.03980i	0.392445	+	0.919775i	$0.371629\pi$
$643$	−6.29383e6	+	1.09012e7i	−0.600326	+	1.03980i	−0.992771	+	0.120020i	$0.961704\pi$
$644$		0			0
$645$	974175.			0.0922014
$646$		0			0
$647$	1.21912e7			1.14494			0.572472	−	0.819924i	$-0.305985\pi$
$647$	1.21912e7			1.14494			0.572472	+	0.819924i	$0.305985\pi$
$648$		0			0
$649$	−4.00318e6	+	6.93371e6i	−0.373073	+	0.646181i
$650$		0			0
$651$	−40813.1	+	70690.4i	−0.00377439	+	0.00653744i
$652$		0			0
$653$	−7.52249e6			−0.690365			−0.345182	−	0.938536i	$-0.612183\pi$
$653$	−7.52249e6			−0.690365			−0.345182	+	0.938536i	$0.612183\pi$
$654$		0			0
$655$	2.35325e6	+	4.07594e6i	0.214321	+	0.371214i
$656$		0			0
$657$	1.25028e7			1.13004
$658$		0			0
$659$	8.02028e6	+	1.38915e7i	0.719409	+	1.24605i	0.961234	+	0.275733i	$0.0889206\pi$
$659$	8.02028e6	+	1.38915e7i	0.719409	+	1.24605i	−0.241825	+	0.970320i	$0.577746\pi$
$660$		0			0
$661$	6.26368e6	+	1.08490e7i	0.557604	+	0.965798i	0.997696	+	0.0678454i	$0.0216125\pi$
$661$	6.26368e6	+	1.08490e7i	0.557604	+	0.965798i	−0.440092	+	0.897953i	$0.645054\pi$
$662$		0			0
$663$	4.67436e6	−	8.09623e6i	0.412989	−	0.715318i
$664$		0			0
$665$	7.89533e6	+	1.19290e6i	0.692335	+	0.104605i
$666$		0			0
$667$	1.16099e7	−	2.01090e7i	1.01045	−	1.75015i
$668$		0			0
$669$	2.79368e6	+	4.83880e6i	0.241330	+	0.417996i
$670$		0			0
$671$	−5.53178e6	−	9.58133e6i	−0.474306	−	0.821523i
$672$		0			0
$673$	−7.50054e6			−0.638344			−0.319172	−	0.947697i	$-0.603405\pi$
$673$	−7.50054e6			−0.638344			−0.319172	+	0.947697i	$0.603405\pi$
$674$		0			0
$675$	1.46871e6	+	2.54388e6i	0.124073	+	0.214900i
$676$		0			0
$677$	1.19677e7			1.00355			0.501777	−	0.864997i	$-0.332680\pi$
$677$	1.19677e7			1.00355			0.501777	+	0.864997i	$0.332680\pi$
$678$		0			0
$679$	−5.27510e6	+	9.13673e6i	−0.439092	+	0.760530i
$680$		0			0
$681$	−3.25058e6	+	5.63017e6i	−0.268592	+	0.465215i
$682$		0			0
$683$	8.11577e6			0.665699			0.332850	−	0.942980i	$-0.391990\pi$
$683$	8.11577e6			0.665699			0.332850	+	0.942980i	$0.391990\pi$
$684$		0			0
$685$	−8.87827e6			−0.722939
$686$		0			0
$687$	4.75164e6	−	8.23009e6i	0.384107	−	0.665293i
$688$		0			0
$689$	6.02455e6	−	1.04348e7i	0.483478	−	0.837408i
$690$		0			0
$691$	−1.23034e7			−0.980235			−0.490117	−	0.871657i	$-0.663046\pi$
$691$	−1.23034e7			−0.980235			−0.490117	+	0.871657i	$0.663046\pi$
$692$		0			0
$693$	3.41628e6	+	5.91717e6i	0.270222	+	0.468038i
$694$		0			0
$695$	−1.42000e7			−1.11513
$696$		0			0
$697$	−1.36616e7	−	2.36626e7i	−1.06517	−	1.84494i
$698$		0			0
$699$	−853093.	−	1.47760e6i	−0.0660394	−	0.114384i
$700$		0			0
$701$	−7.04732e6	+	1.22063e7i	−0.541663	+	0.938188i	0.457146	+	0.889392i	$0.348872\pi$
$701$	−7.04732e6	+	1.22063e7i	−0.541663	+	0.938188i	−0.998809	+	0.0487959i	$0.984462\pi$
$702$		0			0
$703$	8.01205e6	+	2.04358e7i	0.611442	+	1.55956i
$704$		0			0
$705$	−4.09202e6	+	7.08759e6i	−0.310074	+	0.537064i
$706$		0			0
$707$	3.69823e6	+	6.40552e6i	0.278256	+	0.481954i
$708$		0			0
$709$	−2.13108e6	−	3.69113e6i	−0.159215	−	0.275768i	0.775371	−	0.631506i	$-0.217563\pi$
$709$	−2.13108e6	−	3.69113e6i	−0.159215	−	0.275768i	−0.934586	+	0.355738i	$0.884230\pi$
$710$		0			0
$711$	4.08695e6			0.303197
$712$		0			0
$713$	308469.	+	534283.i	0.0227241	+	0.0393593i
$714$		0			0
$715$	2.02727e7			1.48302
$716$		0			0
$717$	3.85950e6	−	6.68486e6i	0.280371	−	0.485617i
$718$		0			0
$719$	6.85763e6	−	1.18778e7i	0.494711	−	0.856865i	−0.505270	−	0.862961i	$-0.668607\pi$
$719$	6.85763e6	−	1.18778e7i	0.494711	−	0.856865i	0.999981	+	0.00609644i	$0.00194057\pi$
$720$		0			0
$721$	−1.20256e7			−0.861529
$722$		0			0
$723$	−6.25394e6			−0.444946
$724$		0			0
$725$	2.08441e6	−	3.61031e6i	0.147278	−	0.255093i
$726$		0			0
$727$	−1.05919e7	+	1.83457e7i	−0.743256	+	1.28736i	0.207749	+	0.978182i	$0.433386\pi$
$727$	−1.05919e7	+	1.83457e7i	−0.743256	+	1.28736i	−0.951005	+	0.309175i	$0.899947\pi$
$728$		0			0
$729$	3.58627e6			0.249933
$730$		0			0
$731$	−1.67080e6	−	2.89392e6i	−0.115646	−	0.200305i
$732$		0			0
$733$	6.01308e6			0.413368			0.206684	−	0.978408i	$-0.433733\pi$
$733$	6.01308e6			0.413368			0.206684	+	0.978408i	$0.433733\pi$
$734$		0			0
$735$	−2.61767e6	−	4.53394e6i	−0.178730	−	0.309569i
$736$		0			0
$737$	−6.47107e6	−	1.12082e7i	−0.438841	−	0.760095i
$738$		0			0
$739$	−8.41424e6	+	1.45739e7i	−0.566766	+	0.981667i	0.430117	+	0.902773i	$0.358472\pi$
$739$	−8.41424e6	+	1.45739e7i	−0.566766	+	0.981667i	−0.996883	+	0.0788942i	$0.974861\pi$
$740$		0			0
$741$	−3.09844e6	−	7.90296e6i	−0.207299	−	0.528742i
$742$		0			0
$743$	−2.01935e6	+	3.49762e6i	−0.134196	+	0.232434i	−0.925290	−	0.379260i	$-0.876179\pi$
$743$	−2.01935e6	+	3.49762e6i	−0.134196	+	0.232434i	0.791094	+	0.611695i	$0.209512\pi$
$744$		0			0
$745$	9.29165e6	+	1.60936e7i	0.613341	+	1.06234i
$746$		0			0
$747$	−5.19524e6	−	8.99842e6i	−0.340647	−	0.590018i
$748$		0			0
$749$	−5.00696e6			−0.326114
$750$		0			0
$751$	−351347.	−	608550.i	−0.0227319	−	0.0393728i	0.854436	−	0.519557i	$-0.173903\pi$
$751$	−351347.	−	608550.i	−0.0227319	−	0.0393728i	−0.877168	+	0.480184i	$0.840570\pi$
$752$		0			0
$753$	7.17380e6			0.461064
$754$		0			0
$755$	1.15899e7	−	2.00742e7i	0.739964	−	1.28166i
$756$		0			0
$757$	1.19882e7	−	2.07642e7i	0.760354	−	1.31697i	−0.182314	−	0.983240i	$-0.558359\pi$
$757$	1.19882e7	−	2.07642e7i	0.760354	−	1.31697i	0.942668	−	0.333731i	$-0.108308\pi$
$758$		0			0
$759$	−1.84172e7			−1.16043
$760$		0			0
$761$	−1.29063e7			−0.807869			−0.403934	−	0.914788i	$-0.632358\pi$
$761$	−1.29063e7			−0.807869			−0.403934	+	0.914788i	$0.632358\pi$
$762$		0			0
$763$	2.19719e6	−	3.80565e6i	0.136633	−	0.236656i
$764$		0			0
$765$	9.81078e6	−	1.69928e7i	0.606108	−	1.04981i
$766$		0			0
$767$	−1.13725e7			−0.698019
$768$		0			0
$769$	−1.05367e7	−	1.82501e7i	−0.642524	−	1.11288i	−0.984867	−	0.173310i	$-0.944554\pi$
$769$	−1.05367e7	−	1.82501e7i	−0.642524	−	1.11288i	0.342343	−	0.939575i	$-0.388779\pi$
$770$		0			0
$771$	8.82902e6			0.534905
$772$		0			0
$773$	4.35234e6	+	7.53848e6i	0.261984	+	0.453769i	0.966769	−	0.255652i	$-0.0822900\pi$
$773$	4.35234e6	+	7.53848e6i	0.261984	+	0.453769i	−0.704785	+	0.709421i	$0.748957\pi$
$774$		0			0
$775$	55381.5	+	95923.6i	0.00331215	+	0.00573682i
$776$		0			0
$777$	−4.47512e6	+	7.75113e6i	−0.265921	+	0.460588i
$778$		0			0
$779$	−2.45311e7	−	3.70640e6i	−1.44835	−	0.218831i
$780$		0			0
$781$	1.77948e7	−	3.08214e7i	1.04391	−	1.80811i
$782$		0			0
$783$	−8.07717e6	−	1.39901e7i	−0.470820	−	0.815484i
$784$		0			0
$785$	−906334.	−	1.56982e6i	−0.0524946	−	0.0909232i
$786$		0			0
$787$	−2.69329e6			−0.155005			−0.0775026	−	0.996992i	$-0.524695\pi$
$787$	−2.69329e6			−0.155005			−0.0775026	+	0.996992i	$0.524695\pi$
$788$		0			0
$789$	−2.44579e6	−	4.23624e6i	−0.139871	−	0.242263i
$790$		0			0
$791$	6.77504e6			0.385009
$792$		0			0
$793$	7.85752e6	−	1.36096e7i	0.443713	−	0.768534i
$794$		0			0
$795$	−4.50957e6	+	7.81081e6i	−0.253057	+	0.438307i
$796$		0			0
$797$	−4.67101e6			−0.260474			−0.130237	−	0.991483i	$-0.541574\pi$
$797$	−4.67101e6			−0.260474			−0.130237	+	0.991483i	$0.541574\pi$
$798$		0			0
$799$	2.80729e7			1.55568
$800$		0			0
$801$	−1.46946e6	+	2.54519e6i	−0.0809240	+	0.140165i
$802$		0			0
$803$	−1.65838e7	+	2.87240e7i	−0.907603	+	1.57201i
$804$		0			0
$805$	2.46081e7			1.33841
$806$		0			0
$807$	−1.98871e6	−	3.44455e6i	−0.107495	−	0.186186i
$808$		0			0
$809$	−1.82792e7			−0.981941			−0.490970	−	0.871176i	$-0.663358\pi$
$809$	−1.82792e7			−0.981941			−0.490970	+	0.871176i	$0.663358\pi$
$810$		0			0
$811$	−9.38560e6	−	1.62563e7i	−0.501083	−	0.867902i	−0.999999	−	0.00125119i	$-0.999602\pi$
$811$	−9.38560e6	−	1.62563e7i	−0.501083	−	0.867902i	0.498916	−	0.866650i	$-0.333732\pi$
$812$		0			0
$813$	5.79445e6	+	1.00363e7i	0.307458	+	0.532533i
$814$		0			0
$815$	403518.	−	698914.i	0.0212799	−	0.0368578i
$816$		0			0
$817$	−3.00013e6	−	453289.i	−0.157248	−	0.0237585i
$818$		0			0
$819$	−4.85260e6	+	8.40494e6i	−0.252793	+	0.437850i
$820$		0			0
$821$	5.00143e6	+	8.66273e6i	0.258962	+	0.448536i	0.965964	−	0.258676i	$-0.0832861\pi$
$821$	5.00143e6	+	8.66273e6i	0.258962	+	0.448536i	−0.707002	+	0.707212i	$0.749953\pi$
$822$		0			0
$823$	−5.31371e6	−	9.20361e6i	−0.273463	−	0.473651i	0.696283	−	0.717767i	$-0.254836\pi$
$823$	−5.31371e6	−	9.20361e6i	−0.273463	−	0.473651i	−0.969746	+	0.244116i	$0.921502\pi$
$824$		0			0
$825$	−3.30658e6			−0.169139
$826$		0			0
$827$	−2.74700e6	−	4.75795e6i	−0.139668	−	0.241911i	0.787703	−	0.616055i	$-0.211270\pi$
$827$	−2.74700e6	−	4.75795e6i	−0.139668	−	0.241911i	−0.927371	+	0.374144i	$0.877937\pi$
$828$		0			0
$829$	6.66282e6			0.336722			0.168361	−	0.985725i	$-0.446153\pi$
$829$	6.66282e6			0.336722			0.168361	+	0.985725i	$0.446153\pi$
$830$		0			0
$831$	347789.	−	602388.i	0.0174708	−	0.0302603i
$832$		0			0
$833$	−8.97912e6	+	1.55523e7i	−0.448354	+	0.776572i
$834$		0			0
$835$	−1.53663e7			−0.762699
$836$		0			0
$837$	429211.			0.0211766
$838$		0			0
$839$	−3.62638e6	+	6.28107e6i	−0.177856	+	0.308055i	−0.941146	−	0.338001i	$-0.890249\pi$
$839$	−3.62638e6	+	6.28107e6i	−0.177856	+	0.308055i	0.763290	+	0.646056i	$0.223583\pi$
$840$		0			0
$841$	−1.20767e6	+	2.09174e6i	−0.0588786	+	0.101981i
$842$		0			0
$843$	−1.51789e7			−0.735649
$844$		0			0
$845$	2.66303e6	+	4.61251e6i	0.128302	+	0.222226i
$846$		0			0
$847$	−5.19674e6			−0.248899
$848$		0			0
$849$	−5.81436e6	−	1.00708e7i	−0.276843	−	0.479506i
$850$		0			0
$851$	3.38233e7	+	5.85837e7i	1.60100	+	2.77302i
$852$		0			0
$853$	1.39644e7	−	2.41871e7i	0.657130	−	1.13818i	−0.324225	−	0.945980i	$-0.605104\pi$
$853$	1.39644e7	−	2.41871e7i	0.657130	−	1.13818i	0.981355	−	0.192202i	$-0.0615630\pi$
$854$		0			0
$855$	−6.50315e6	−	1.65871e7i	−0.304235	−	0.775989i
$856$		0			0
$857$	−1.35275e6	+	2.34304e6i	−0.0629169	+	0.108975i	−0.895768	−	0.444522i	$-0.853374\pi$
$857$	−1.35275e6	+	2.34304e6i	−0.0629169	+	0.108975i	0.832851	+	0.553497i	$0.186707\pi$
$858$		0			0
$859$	1.45030e7	+	2.51199e7i	0.670616	+	1.16154i	0.977730	+	0.209868i	$0.0673034\pi$
$859$	1.45030e7	+	2.51199e7i	0.670616	+	1.16154i	−0.307114	+	0.951673i	$0.599363\pi$
$860$		0			0
$861$	−5.05806e6	−	8.76081e6i	−0.232528	−	0.402751i
$862$		0			0
$863$	−8.44738e6			−0.386096			−0.193048	−	0.981189i	$-0.561837\pi$
$863$	−8.44738e6			−0.386096			−0.193048	+	0.981189i	$0.561837\pi$
$864$		0			0
$865$	1.35065e7	+	2.33939e7i	0.613765	+	1.06307i
$866$		0			0
$867$	1.26556e7			0.571789
$868$		0			0
$869$	−5.42096e6	+	9.38937e6i	−0.243515	+	0.421781i
$870$		0			0
$871$	9.19171e6	−	1.59205e7i	0.410536	−	0.711068i
$872$		0			0
$873$	2.35401e7			1.04538
$874$		0			0
$875$	−1.14395e7			−0.505113
$876$		0			0
$877$	−1.25597e7	+	2.17540e7i	−0.551416	+	0.955080i	0.446757	+	0.894655i	$0.352579\pi$
$877$	−1.25597e7	+	2.17540e7i	−0.551416	+	0.955080i	−0.998173	+	0.0604245i	$0.980755\pi$
$878$		0			0
$879$	−3.17819e6	+	5.50479e6i	−0.138742	+	0.240308i
$880$		0			0
$881$	−1.95758e7			−0.849728			−0.424864	−	0.905257i	$-0.639678\pi$
$881$	−1.95758e7			−0.849728			−0.424864	+	0.905257i	$0.639678\pi$
$882$		0			0
$883$	−1.40024e6	−	2.42528e6i	−0.0604366	−	0.104679i	0.834224	−	0.551426i	$-0.185916\pi$
$883$	−1.40024e6	−	2.42528e6i	−0.0604366	−	0.104679i	−0.894661	+	0.446746i	$0.852583\pi$
$884$		0			0
$885$	8.51268e6			0.365349
$886$		0			0
$887$	2.11985e7	+	3.67169e7i	0.904682	+	1.56696i	0.821343	+	0.570435i	$0.193225\pi$
$887$	2.11985e7	+	3.67169e7i	0.904682	+	1.56696i	0.0833393	+	0.996521i	$0.473441\pi$
$888$		0			0
$889$	−4.75248e6	−	8.23154e6i	−0.201681	−	0.349322i
$890$		0			0
$891$	3.93454e6	−	6.81482e6i	0.166035	−	0.287581i
$892$		0			0
$893$	1.59000e7	−	1.99234e7i	0.667217	−	0.836053i
$894$		0			0
$895$	1.30133e6	−	2.25397e6i	0.0543039	−	0.0940571i
$896$		0			0
$897$	−1.30802e7	−	2.26556e7i	−0.542793	−	0.940145i
$898$		0			0
$899$	−304571.	−	527533.i	−0.0125687	−	0.0217696i
$900$		0			0
$901$	3.09374e7			1.26962
$902$		0			0
$903$	−618595.	−	1.07144e6i	−0.0252457	−	0.0437268i
$904$		0			0
$905$	−3.05198e7			−1.23868
$906$		0			0
$907$	1.00865e7	−	1.74703e7i	0.407118	−	0.705149i	−0.587447	−	0.809262i	$-0.699867\pi$
$907$	1.00865e7	−	1.74703e7i	0.407118	−	0.705149i	0.994565	+	0.104113i	$0.0332004\pi$
$908$		0			0
$909$	8.25167e6	−	1.42923e7i	0.331232	−	0.573710i
$910$		0			0
$911$	−3.89915e7			−1.55659			−0.778294	−	0.627900i	$-0.783915\pi$
$911$	−3.89915e7			−1.55659			−0.778294	+	0.627900i	$0.783915\pi$
$912$		0			0
$913$	2.75640e7			1.09437
$914$		0			0
$915$	−5.88161e6	+	1.01873e7i	−0.232244	+	0.402258i
$916$		0			0
$917$	2.98860e6	−	5.17640e6i	0.117366	−	0.203285i
$918$		0			0
$919$	9.96447e6			0.389193			0.194597	−	0.980883i	$-0.437660\pi$
$919$	9.96447e6			0.389193			0.194597	+	0.980883i	$0.437660\pi$
$920$		0			0
$921$	7.71191e6	+	1.33574e7i	0.299580	+	0.518888i
$922$		0			0
$923$	5.05525e7			1.95316
$924$		0			0
$925$	6.07253e6	+	1.05179e7i	0.233354	+	0.404181i
$926$		0			0
$927$	1.34161e7	+	2.32374e7i	0.512775	+	0.888153i
$928$		0			0
$929$	6.00913e6	−	1.04081e7i	0.228440	−	0.395670i	−0.728906	−	0.684614i	$-0.759971\pi$
$929$	6.00913e6	−	1.04081e7i	0.228440	−	0.395670i	0.957346	+	0.288944i	$0.0933042\pi$
$930$		0			0
$931$	5.95188e6	+	1.51810e7i	0.225050	+	0.574020i
$932$		0			0
$933$	−5.69322e6	+	9.86094e6i	−0.214118	+	0.370864i
$934$		0			0
$935$	2.60262e7	+	4.50786e7i	0.973601	+	1.68633i
$936$		0			0
$937$	1.90689e7	+	3.30284e7i	0.709541	+	1.22896i	0.965027	+	0.262149i	$0.0844311\pi$
$937$	1.90689e7	+	3.30284e7i	0.709541	+	1.22896i	−0.255486	+	0.966813i	$0.582236\pi$
$938$		0			0
$939$	−1.79040e7			−0.662652
$940$		0			0
$941$	8.78331e6	+	1.52131e7i	0.323358	+	0.560073i	0.981179	−	0.193102i	$-0.0618548\pi$
$941$	8.78331e6	+	1.52131e7i	0.323358	+	0.560073i	−0.657820	+	0.753175i	$0.728521\pi$
$942$		0			0
$943$	−7.64584e7			−2.79992
$944$		0			0
$945$	8.56009e6	−	1.48265e7i	0.311816	−	0.540081i
$946$		0			0
$947$	2.41786e7	−	4.18786e7i	0.876106	−	1.51746i	0.0205267	−	0.999789i	$-0.493466\pi$
$947$	2.41786e7	−	4.18786e7i	0.876106	−	1.51746i	0.855580	−	0.517671i	$-0.173201\pi$
$948$		0			0
$949$	−4.71124e7			−1.69812
$950$		0			0
$951$	4.45174e6			0.159617
$952$		0			0
$953$	−1.89643e7	+	3.28471e7i	−0.676402	+	1.17156i	0.299656	+	0.954047i	$0.403128\pi$
$953$	−1.89643e7	+	3.28471e7i	−0.676402	+	1.17156i	−0.976057	+	0.217514i	$0.930205\pi$
$954$		0			0
$955$	6.89637e6	−	1.19449e7i	0.244688	−	0.423812i
$956$		0			0
$957$	1.81846e7			0.641834
$958$		0			0
$959$	5.63765e6	+	9.76470e6i	0.197948	+	0.342856i
$960$		0			0
$961$	−2.86130e7			−0.999435
$962$		0			0
$963$	5.58589e6	+	9.67504e6i	0.194100	+	0.336192i
$964$		0			0
$965$	−2.26024e7	−	3.91485e7i	−0.781333	−	1.35331i
$966$		0			0
$967$	−8.31734e6	+	1.44061e7i	−0.286034	+	0.495426i	−0.972859	−	0.231397i	$-0.925670\pi$
$967$	−8.31734e6	+	1.44061e7i	−0.286034	+	0.495426i	0.686825	+	0.726823i	$0.259004\pi$
$968$		0			0
$969$	1.35954e7	−	1.70356e7i	0.465138	−	0.582838i
$970$		0			0
$971$	−1.41242e7	+	2.44638e7i	−0.480746	+	0.832677i	−0.999756	−	0.0220914i	$-0.992968\pi$
$971$	−1.41242e7	+	2.44638e7i	−0.480746	+	0.832677i	0.519010	+	0.854768i	$0.326301\pi$
$972$		0			0
$973$	9.01694e6	+	1.56178e7i	0.305335	+	0.528856i
$974$		0			0
$975$	−2.34838e6	−	4.06752e6i	−0.0791147	−	0.137031i
$976$		0			0
$977$	−3.01881e7			−1.01181			−0.505906	−	0.862589i	$-0.668842\pi$
$977$	−3.01881e7			−1.01181			−0.505906	+	0.862589i	$0.668842\pi$
$978$		0			0
$979$	−3.89821e6	−	6.75190e6i	−0.129990	−	0.225149i
$980$		0			0
$981$	−9.80496e6			−0.325292
$982$		0			0
$983$	−2321.02	+	4020.12i	−7.66117e−5	+	0.000132695i	−0.866064	−	0.499934i	$-0.833358\pi$
$983$	−2321.02	+	4020.12i	−7.66117e−5	+	0.000132695i	0.865987	+	0.500066i	$0.166691\pi$
$984$		0			0
$985$	560698.	−	971158.i	0.0184136	−	0.0318933i
$986$		0			0
$987$	1.03936e7			0.339606
$988$		0			0
$989$	−9.35079e6			−0.303989
$990$		0			0
$991$	1.56708e7	−	2.71426e7i	0.506882	−	0.877945i	−0.493087	−	0.869980i	$-0.664131\pi$
$991$	1.56708e7	−	2.71426e7i	0.506882	−	0.877945i	0.999968	−	0.00796469i	$-0.00253527\pi$
$992$		0			0
$993$	7.39627e6	−	1.28107e7i	0.238034	−	0.412288i
$994$		0			0
$995$	−3.66752e7			−1.17440
$996$		0			0
$997$	−1.11856e7	−	1.93740e7i	−0.356387	−	0.617280i	0.630968	−	0.775809i	$-0.282658\pi$
$997$	−1.11856e7	−	1.93740e7i	−0.356387	−	0.617280i	−0.987354	+	0.158529i	$0.949325\pi$
$998$		0			0
$999$	4.70626e7			1.49198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.e.a.49.4	yes	18
3.2	odd	2		684.6.k.f.505.3		18
4.3	odd	2		304.6.i.d.49.6		18
19.7	even	3	inner	76.6.e.a.45.4	✓	18
57.26	odd	6		684.6.k.f.577.3		18
76.7	odd	6		304.6.i.d.273.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.e.a.45.4	✓	18	19.7	even	3	inner
76.6.e.a.49.4	yes	18	1.1	even	1	trivial
304.6.i.d.49.6		18	4.3	odd	2
304.6.i.d.273.6		18	76.7	odd	6
684.6.k.f.505.3		18	3.2	odd	2
684.6.k.f.577.3		18	57.26	odd	6

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.99628 + 6.92176i) q^{3} +(31.6056 - 54.7425i) q^{5} -80.2775 q^{7} +(89.5595 + 155.122i) q^{9} +O(q^{10})\)	\(q+(-3.99628 + 6.92176i) q^{3} +(31.6056 - 54.7425i) q^{5} -80.2775 q^{7} +(89.5595 + 155.122i) q^{9} -475.169 q^{11} +(-337.473 - 584.520i) q^{13} +(252.609 + 437.532i) q^{15} +(866.499 - 1500.82i) q^{17} +(-574.366 - 1464.99i) q^{19} +(320.811 - 555.661i) q^{21} +(-2424.72 - 4199.73i) q^{23} +(-435.326 - 754.007i) q^{25} -3373.81 q^{27} +(2394.08 + 4146.67i) q^{29} -127.218 q^{31} +(1898.91 - 3289.01i) q^{33} +(-2537.22 + 4394.59i) q^{35} -13949.4 q^{37} +5394.54 q^{39} +(7883.24 - 13654.2i) q^{41} +(964.112 - 1669.89i) q^{43} +11322.3 q^{45} +(8099.51 + 14028.8i) q^{47} -10362.5 q^{49} +(6925.54 + 11995.4i) q^{51} +(8925.98 + 15460.3i) q^{53} +(-15018.0 + 26011.9i) q^{55} +(12435.6 + 1878.90i) q^{57} +(8424.75 - 14592.1i) q^{59} +(11641.7 + 20164.0i) q^{61} +(-7189.61 - 12452.8i) q^{63} -42664.1 q^{65} +(13618.4 + 23587.8i) q^{67} +38759.3 q^{69} +(-37449.3 + 64864.1i) q^{71} +(34900.9 - 60450.1i) q^{73} +6958.73 q^{75} +38145.4 q^{77} +(11408.5 - 19760.1i) q^{79} +(-8280.29 + 14341.9i) q^{81} -58008.8 q^{83} +(-54772.4 - 94868.6i) q^{85} -38269.6 q^{87} +(8203.84 + 14209.5i) q^{89} +(27091.5 + 46923.8i) q^{91} +(508.400 - 880.575i) q^{93} +(-98350.5 - 14859.7i) q^{95} +(65710.8 - 113814. i) q^{97} +(-42555.9 - 73709.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 11 q^{3} + 11 q^{5} + 336 q^{7} - 902 q^{9}+O(q^{10}) \) 18 * q - 11 * q^3 + 11 * q^5 + 336 * q^7 - 902 * q^9	\( 18 q - 11 q^{3} + 11 q^{5} + 336 q^{7} - 902 q^{9} - 320 q^{11} + 227 q^{13} - 101 q^{15} + 179 q^{17} - 868 q^{19} - 5700 q^{21} - 3425 q^{23} - 7054 q^{25} + 14722 q^{27} - 7349 q^{29} - 9960 q^{31} - 2998 q^{33} + 15888 q^{35} + 26444 q^{37} - 30246 q^{39} - 7311 q^{41} - 8283 q^{43} - 62164 q^{45} + 37603 q^{47} + 124738 q^{49} + 47227 q^{51} - 20337 q^{53} + 716 q^{55} - 57555 q^{57} - 74455 q^{59} - 7569 q^{61} - 52544 q^{63} + 188998 q^{65} - 26177 q^{67} + 116282 q^{69} - 53463 q^{71} - 14103 q^{73} + 120912 q^{75} - 31960 q^{77} + 31825 q^{79} - 21137 q^{81} + 82600 q^{83} - 50787 q^{85} - 339766 q^{87} - 155197 q^{89} - 2800 q^{91} - 46460 q^{93} + 49315 q^{95} + 111241 q^{97} - 193544 q^{99}+O(q^{100}) \) 18 * q - 11 * q^3 + 11 * q^5 + 336 * q^7 - 902 * q^9 - 320 * q^11 + 227 * q^13 - 101 * q^15 + 179 * q^17 - 868 * q^19 - 5700 * q^21 - 3425 * q^23 - 7054 * q^25 + 14722 * q^27 - 7349 * q^29 - 9960 * q^31 - 2998 * q^33 + 15888 * q^35 + 26444 * q^37 - 30246 * q^39 - 7311 * q^41 - 8283 * q^43 - 62164 * q^45 + 37603 * q^47 + 124738 * q^49 + 47227 * q^51 - 20337 * q^53 + 716 * q^55 - 57555 * q^57 - 74455 * q^59 - 7569 * q^61 - 52544 * q^63 + 188998 * q^65 - 26177 * q^67 + 116282 * q^69 - 53463 * q^71 - 14103 * q^73 + 120912 * q^75 - 31960 * q^77 + 31825 * q^79 - 21137 * q^81 + 82600 * q^83 - 50787 * q^85 - 339766 * q^87 - 155197 * q^89 - 2800 * q^91 - 46460 * q^93 + 49315 * q^95 + 111241 * q^97 - 193544 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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