LMFDB - Embedded newform 33.6.e.b.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,6,Mod(4,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

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("33.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	33.e (of order $5$, degree $4$, 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:	$5.29266605383$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
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} + 78 x^{18} + 79 x^{17} + 10573 x^{16} - 33409 x^{15} + 1262953 x^{14} + \cdots + 25599187870096 $ x^20 - x^19 + 78x^18 + 79x^17 + 10573x^16 - 33409x^15 + 1262953x^14 - 1581925x^13 + 89291182x^12 - 100741271x^11 + 2277268901x^10 - 1144062486x^9 + 70677624924x^8 + 93641098134x^7 + 1732079176577x^6 + 1113900934906x^5 + 27749747552381x^4 + 4154923377746x^3 + 57625758470132x^2 + 60036938210920x + 25599187870096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			25.1
Root			$-8.59311 - 6.24326i$ of defining polynomial
Character	$\chi$	$=$	33.25
Dual form			33.6.e.b.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.78409 + 5.65548i) q^{2} +(-2.78115 - 8.55951i) q^{3} +(18.7192 - 57.6117i) q^{4} +(48.1408 + 34.9763i) q^{5} +(70.0568 + 50.8993i) q^{6} +(9.43666 - 29.0431i) q^{7} +(84.9654 + 261.497i) q^{8} +(-65.5304 + 47.6106i) q^{9} +O(q^{10})$	\(q+(-7.78409 + 5.65548i) q^{2} +(-2.78115 - 8.55951i) q^{3} +(18.7192 - 57.6117i) q^{4} +(48.1408 + 34.9763i) q^{5} +(70.0568 + 50.8993i) q^{6} +(9.43666 - 29.0431i) q^{7} +(84.9654 + 261.497i) q^{8} +(-65.5304 + 47.6106i) q^{9} -572.540 q^{10} +(-70.0591 + 395.149i) q^{11} -545.189 q^{12} +(-460.773 + 334.771i) q^{13} +(90.7964 + 279.443i) q^{14} +(165.493 - 509.336i) q^{15} +(-572.028 - 415.603i) q^{16} +(1619.20 + 1176.42i) q^{17} +(240.834 - 741.211i) q^{18} +(497.601 + 1531.46i) q^{19} +(2916.20 - 2118.74i) q^{20} -274.839 q^{21} +(-1689.41 - 3472.09i) q^{22} -1214.78 q^{23} +(2001.98 - 1454.52i) q^{24} +(128.514 + 395.526i) q^{25} +(1693.41 - 5211.78i) q^{26} +(589.773 + 428.495i) q^{27} +(-1496.57 - 1087.32i) q^{28} +(-2348.47 + 7227.84i) q^{29} +(1592.32 + 4900.66i) q^{30} +(5873.48 - 4267.33i) q^{31} -1995.37 q^{32} +(3577.13 - 499.298i) q^{33} -19257.3 q^{34} +(1470.11 - 1068.10i) q^{35} +(1516.25 + 4666.55i) q^{36} +(-406.300 + 1250.46i) q^{37} +(-12534.5 - 9106.84i) q^{38} +(4146.96 + 3012.94i) q^{39} +(-5055.89 + 15560.4i) q^{40} +(1804.73 + 5554.40i) q^{41} +(2139.37 - 1554.35i) q^{42} +6357.22 q^{43} +(21453.7 + 11433.1i) q^{44} -4819.93 q^{45} +(9455.97 - 6870.16i) q^{46} +(-9346.16 - 28764.5i) q^{47} +(-1966.46 + 6052.13i) q^{48} +(12842.7 + 9330.77i) q^{49} +(-3237.26 - 2352.01i) q^{50} +(5566.33 - 17131.4i) q^{51} +(10661.4 + 32812.6i) q^{52} +(-5785.79 + 4203.62i) q^{53} -7014.20 q^{54} +(-17193.6 + 16572.4i) q^{55} +8396.45 q^{56} +(11724.6 - 8518.44i) q^{57} +(-22596.2 - 69543.9i) q^{58} +(-6852.76 + 21090.6i) q^{59} +(-26245.8 - 19068.7i) q^{60} +(-20223.1 - 14693.0i) q^{61} +(-21585.9 + 66434.7i) q^{62} +(764.370 + 2352.49i) q^{63} +(33837.0 - 24584.1i) q^{64} -33891.1 q^{65} +(-25020.9 + 24116.9i) q^{66} +15543.8 q^{67} +(98085.7 - 71263.5i) q^{68} +(3378.49 + 10397.9i) q^{69} +(-5402.87 + 16628.3i) q^{70} +(52283.6 + 37986.3i) q^{71} +(-18017.8 - 13090.7i) q^{72} +(13634.4 - 41962.5i) q^{73} +(-3909.28 - 12031.5i) q^{74} +(3028.09 - 2200.04i) q^{75} +97544.6 q^{76} +(10815.2 + 5763.62i) q^{77} -49319.9 q^{78} +(14114.3 - 10254.6i) q^{79} +(-13001.6 - 40014.9i) q^{80} +(2027.46 - 6239.88i) q^{81} +(-45461.0 - 33029.3i) q^{82} +(-96187.9 - 69884.6i) q^{83} +(-5144.76 + 15833.9i) q^{84} +(36802.9 + 113268. i) q^{85} +(-49485.2 + 35953.1i) q^{86} +68398.2 q^{87} +(-109283. + 15253.8i) q^{88} -6612.00 q^{89} +(37518.8 - 27259.0i) q^{90} +(5374.62 + 16541.4i) q^{91} +(-22739.7 + 69985.6i) q^{92} +(-52861.3 - 38406.0i) q^{93} +(235428. + 171049. i) q^{94} +(-29609.9 + 91129.9i) q^{95} +(5549.43 + 17079.4i) q^{96} +(-103201. + 74979.8i) q^{97} -152739. q^{98} +(-14222.3 - 29229.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9}+O(q^{10}) $ 20 * q + 6 * q^2 + 45 * q^3 + 8 * q^4 - 11 * q^5 - 54 * q^6 - 139 * q^7 - 76 * q^8 - 405 * q^9	\( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9} - 424 q^{10} + 2289 q^{11} - 2682 q^{12} - 847 q^{13} + 2022 q^{14} - 396 q^{15} - 7148 q^{16} + 2482 q^{17} + 81 q^{18} + 2958 q^{19} + 8037 q^{20} - 1404 q^{21} + 7441 q^{22} + 8140 q^{23} - 4626 q^{24} - 13120 q^{25} - 13508 q^{26} + 3645 q^{27} + 27819 q^{28} - 20210 q^{29} + 11106 q^{30} + 5540 q^{31} - 4626 q^{32} + 639 q^{33} + 16540 q^{34} - 34101 q^{35} + 648 q^{36} - 25173 q^{37} - 55878 q^{38} + 7623 q^{39} + 22689 q^{40} + 54349 q^{41} + 32292 q^{42} - 21688 q^{43} + 24587 q^{44} - 5346 q^{45} + 44155 q^{46} - 48387 q^{47} - 43083 q^{48} - 78880 q^{49} + 19956 q^{50} + 7317 q^{51} + 109051 q^{52} - 74382 q^{53} + 10206 q^{54} - 47630 q^{55} + 168894 q^{56} + 52983 q^{57} + 1501 q^{58} - 108412 q^{59} - 72333 q^{60} + 16737 q^{61} + 132685 q^{62} - 11259 q^{63} - 157030 q^{64} - 134194 q^{65} - 127539 q^{66} + 20178 q^{67} + 387013 q^{68} + 19305 q^{69} - 411988 q^{70} + 143157 q^{71} + 41634 q^{72} + 164980 q^{73} + 286114 q^{74} - 96255 q^{75} + 46868 q^{76} - 367461 q^{77} - 152658 q^{78} + 369613 q^{79} - 107448 q^{80} - 32805 q^{81} - 184129 q^{82} + 267741 q^{83} + 279819 q^{84} + 379937 q^{85} - 290531 q^{86} + 214920 q^{87} - 740846 q^{88} + 205492 q^{89} + 117126 q^{90} + 394559 q^{91} - 483181 q^{92} - 49860 q^{93} + 561327 q^{94} + 267881 q^{95} + 228564 q^{96} - 300567 q^{97} - 2296174 q^{98} - 115506 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 + 45 * q^3 + 8 * q^4 - 11 * q^5 - 54 * q^6 - 139 * q^7 - 76 * q^8 - 405 * q^9 - 424 * q^10 + 2289 * q^11 - 2682 * q^12 - 847 * q^13 + 2022 * q^14 - 396 * q^15 - 7148 * q^16 + 2482 * q^17 + 81 * q^18 + 2958 * q^19 + 8037 * q^20 - 1404 * q^21 + 7441 * q^22 + 8140 * q^23 - 4626 * q^24 - 13120 * q^25 - 13508 * q^26 + 3645 * q^27 + 27819 * q^28 - 20210 * q^29 + 11106 * q^30 + 5540 * q^31 - 4626 * q^32 + 639 * q^33 + 16540 * q^34 - 34101 * q^35 + 648 * q^36 - 25173 * q^37 - 55878 * q^38 + 7623 * q^39 + 22689 * q^40 + 54349 * q^41 + 32292 * q^42 - 21688 * q^43 + 24587 * q^44 - 5346 * q^45 + 44155 * q^46 - 48387 * q^47 - 43083 * q^48 - 78880 * q^49 + 19956 * q^50 + 7317 * q^51 + 109051 * q^52 - 74382 * q^53 + 10206 * q^54 - 47630 * q^55 + 168894 * q^56 + 52983 * q^57 + 1501 * q^58 - 108412 * q^59 - 72333 * q^60 + 16737 * q^61 + 132685 * q^62 - 11259 * q^63 - 157030 * q^64 - 134194 * q^65 - 127539 * q^66 + 20178 * q^67 + 387013 * q^68 + 19305 * q^69 - 411988 * q^70 + 143157 * q^71 + 41634 * q^72 + 164980 * q^73 + 286114 * q^74 - 96255 * q^75 + 46868 * q^76 - 367461 * q^77 - 152658 * q^78 + 369613 * q^79 - 107448 * q^80 - 32805 * q^81 - 184129 * q^82 + 267741 * q^83 + 279819 * q^84 + 379937 * q^85 - 290531 * q^86 + 214920 * q^87 - 740846 * q^88 + 205492 * q^89 + 117126 * q^90 + 394559 * q^91 - 483181 * q^92 - 49860 * q^93 + 561327 * q^94 + 267881 * q^95 + 228564 * q^96 - 300567 * q^97 - 2296174 * q^98 - 115506 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−7.78409	+	5.65548i	−1.37605	+	0.999756i	−0.378809	+	0.925475i	$0.623666\pi$
$2$	−7.78409	+	5.65548i	−1.37605	+	0.999756i	−0.997237	+	0.0742813i	$0.976334\pi$
$3$	−2.78115	−	8.55951i	−0.178411	−	0.549093i
$3$	−2.78115	−	8.55951i	−0.178411	−	0.549093i
$4$	18.7192	−	57.6117i	0.584974	−	1.80037i
$5$	48.1408	+	34.9763i	0.861169	+	0.625676i	0.928203	−	0.372075i	$-0.121354\pi$
$5$	48.1408	+	34.9763i	0.861169	+	0.625676i	−0.0670339	+	0.997751i	$0.521354\pi$
$6$	70.0568	+	50.8993i	0.794461	+	0.577210i
$7$	9.43666	−	29.0431i	0.0727903	−	0.224025i	−0.908042	−	0.418879i	$-0.862423\pi$
$7$	9.43666	−	29.0431i	0.0727903	−	0.224025i	0.980832	+	0.194854i	$0.0624232\pi$
$8$	84.9654	+	261.497i	0.469372	+	1.44458i
$9$	−65.5304	+	47.6106i	−0.269672	+	0.195928i
$10$	−572.540			−1.81053
$11$	−70.0591	+	395.149i	−0.174575	+	0.984644i
$11$	−70.0591	+	395.149i	−0.174575	+	0.984644i
$12$	−545.189			−1.09293
$13$	−460.773	+	334.771i	−0.756186	+	0.549401i	−0.897738	−	0.440529i	$-0.854791\pi$
$13$	−460.773	+	334.771i	−0.756186	+	0.549401i	0.141552	+	0.989931i	$0.454791\pi$
$14$	90.7964	+	279.443i	0.123808	+	0.381042i
$15$	165.493	−	509.336i	0.189912	−	0.584489i
$16$	−572.028	−	415.603i	−0.558621	−	0.405862i
$17$	1619.20	+	1176.42i	1.35887	+	0.987280i	0.998516	+	0.0544664i	$0.0173458\pi$
$17$	1619.20	+	1176.42i	1.35887	+	0.987280i	0.360359	+	0.932814i	$0.382654\pi$
$18$	240.834	−	741.211i	0.175201	−	0.539213i
$19$	497.601	+	1531.46i	0.316226	+	0.973243i	0.975247	+	0.221118i	$0.0709707\pi$
$19$	497.601	+	1531.46i	0.316226	+	0.973243i	−0.659021	+	0.752124i	$0.729029\pi$
$20$	2916.20	−	2118.74i	1.63021	−	1.18441i
$21$	−274.839			−0.135997
$22$	−1689.41	−	3472.09i	−0.744180	−	1.52945i
$23$	−1214.78			−0.478827			−0.239413	−	0.970918i	$-0.576955\pi$
$23$	−1214.78			−0.478827			−0.239413	+	0.970918i	$0.576955\pi$
$24$	2001.98	−	1454.52i	0.709466	−	0.515457i
$25$	128.514	+	395.526i	0.0411246	+	0.126568i
$26$	1693.41	−	5211.78i	0.491280	−	1.51200i
$27$	589.773	+	428.495i	0.155695	+	0.113119i
$28$	−1496.57	−	1087.32i	−0.360747	−	0.262098i
$29$	−2348.47	+	7227.84i	−0.518549	+	1.59593i	0.258182	+	0.966096i	$0.416877\pi$
$29$	−2348.47	+	7227.84i	−0.518549	+	1.59593i	−0.776731	+	0.629833i	$0.783123\pi$
$30$	1592.32	+	4900.66i	0.323019	+	0.994150i
$31$	5873.48	−	4267.33i	1.09772	−	0.797540i	0.117034	−	0.993128i	$-0.462662\pi$
$31$	5873.48	−	4267.33i	1.09772	−	0.797540i	0.980686	+	0.195588i	$0.0626615\pi$
$32$	−1995.37			−0.344468
$33$	3577.13	−	499.298i	0.571807	−	0.0798132i
$34$	−19257.3			−2.85691
$35$	1470.11	−	1068.10i	0.202852	−	0.147381i
$36$	1516.25	+	4666.55i	0.194991	+	0.600122i
$37$	−406.300	+	1250.46i	−0.0487913	+	0.150164i	−0.972484	−	0.232970i	$-0.925155\pi$
$37$	−406.300	+	1250.46i	−0.0487913	+	0.150164i	0.923693	+	0.383135i	$0.125155\pi$
$38$	−12534.5	−	9106.84i	−1.40815	−	1.02308i
$39$	4146.96	+	3012.94i	0.436584	+	0.317197i
$40$	−5055.89	+	15560.4i	−0.499629	+	1.53770i
$41$	1804.73	+	5554.40i	0.167669	+	0.516033i	0.999223	−	0.0394114i	$-0.0125483\pi$
$41$	1804.73	+	5554.40i	0.167669	+	0.516033i	−0.831554	+	0.555444i	$0.812548\pi$
$42$	2139.37	−	1554.35i	0.187139	−	0.135964i
$43$	6357.22			0.524320			0.262160	−	0.965024i	$-0.415565\pi$
$43$	6357.22			0.524320			0.262160	+	0.965024i	$0.415565\pi$
$44$	21453.7	+	11433.1i	1.67060	+	0.890291i
$45$	−4819.93			−0.354821
$46$	9455.97	−	6870.16i	0.658888	−	0.478710i
$47$	−9346.16	−	28764.5i	−0.617147	−	1.89938i	−0.359516	−	0.933139i	$-0.617058\pi$
$47$	−9346.16	−	28764.5i	−0.617147	−	1.89938i	−0.257631	−	0.966243i	$-0.582942\pi$
$48$	−1966.46	+	6052.13i	−0.123192	+	0.379145i
$49$	12842.7	+	9330.77i	0.764128	+	0.555172i
$50$	−3237.26	−	2352.01i	−0.183127	−	0.133050i
$51$	5566.33	−	17131.4i	0.299670	−	0.922290i
$52$	10661.4	+	32812.6i	0.546774	+	1.68280i
$53$	−5785.79	+	4203.62i	−0.282926	+	0.205558i	−0.720193	−	0.693774i	$-0.755947\pi$
$53$	−5785.79	+	4203.62i	−0.282926	+	0.205558i	0.437267	+	0.899332i	$0.355947\pi$
$54$	−7014.20			−0.327336
$55$	−17193.6	+	16572.4i	−0.766407	+	0.738717i
$56$	8396.45			0.357788
$57$	11724.6	−	8518.44i	0.477982	−	0.347275i
$58$	−22596.2	−	69543.9i	−0.881993	−	2.71450i
$59$	−6852.76	+	21090.6i	−0.256292	+	0.788787i	0.737280	+	0.675587i	$0.236110\pi$
$59$	−6852.76	+	21090.6i	−0.256292	+	0.788787i	−0.993572	+	0.113199i	$0.963890\pi$
$60$	−26245.8	−	19068.7i	−0.941200	−	0.683822i
$61$	−20223.1	−	14693.0i	−0.695863	−	0.505574i	0.182719	−	0.983165i	$-0.441510\pi$
$61$	−20223.1	−	14693.0i	−0.695863	−	0.505574i	−0.878582	+	0.477591i	$0.841510\pi$
$62$	−21585.9	+	66434.7i	−0.713168	+	2.19490i
$63$	764.370	+	2352.49i	0.0242634	+	0.0746751i
$64$	33837.0	−	24584.1i	1.03262	−	0.750246i
$65$	−33891.1			−0.994951
$66$	−25020.9	+	24116.9i	−0.707039	+	0.681494i
$67$	15543.8			0.423028			0.211514	−	0.977375i	$-0.432161\pi$
$67$	15543.8			0.423028			0.211514	+	0.977375i	$0.432161\pi$
$68$	98085.7	−	71263.5i	2.57237	−	1.86894i
$69$	3378.49	+	10397.9i	0.0854280	+	0.262920i
$70$	−5402.87	+	16628.3i	−0.131789	+	0.405605i
$71$	52283.6	+	37986.3i	1.23089	+	0.894295i	0.996957	−	0.0779570i	$-0.0248397\pi$
$71$	52283.6	+	37986.3i	1.23089	+	0.894295i	0.233935	+	0.972252i	$0.424840\pi$
$72$	−18017.8	−	13090.7i	−0.409610	−	0.297599i
$73$	13634.4	−	41962.5i	0.299454	−	0.921625i	−0.682235	−	0.731133i	$-0.738992\pi$
$73$	13634.4	−	41962.5i	0.299454	−	0.921625i	0.981689	−	0.190492i	$-0.0610082\pi$
$74$	−3909.28	−	12031.5i	−0.0829885	−	0.255412i
$75$	3028.09	−	2200.04i	0.0621608	−	0.0451624i
$76$	97544.6			1.93718
$77$	10815.2	+	5763.62i	0.207878	+	0.110782i
$78$	−49319.9			−0.917880
$79$	14114.3	−	10254.6i	0.254444	−	0.184864i	−0.453250	−	0.891383i	$-0.649736\pi$
$79$	14114.3	−	10254.6i	0.254444	−	0.184864i	0.707694	+	0.706519i	$0.249736\pi$
$80$	−13001.6	−	40014.9i	−0.227129	−	0.699031i
$81$	2027.46	−	6239.88i	0.0343352	−	0.105673i
$82$	−45461.0	−	33029.3i	−0.746628	−	0.542457i
$83$	−96187.9	−	69884.6i	−1.53259	−	1.11349i	−0.954779	−	0.297316i	$-0.903908\pi$
$83$	−96187.9	−	69884.6i	−1.53259	−	1.11349i	−0.577808	−	0.816173i	$-0.696092\pi$
$84$	−5144.76	+	15833.9i	−0.0795549	+	0.244845i
$85$	36802.9	+	113268.i	0.552503	+	1.70043i
$86$	−49485.2	+	35953.1i	−0.721488	+	0.524192i
$87$	68398.2			0.968828
$88$	−109283.	+	15253.8i	−1.50434	+	0.209976i
$89$	−6612.00			−0.0884826			−0.0442413	−	0.999021i	$-0.514087\pi$
$89$	−6612.00			−0.0884826			−0.0442413	+	0.999021i	$0.514087\pi$
$90$	37518.8	−	27259.0i	0.488250	−	0.354735i
$91$	5374.62	+	16541.4i	0.0680369	+	0.209396i
$92$	−22739.7	+	69985.6i	−0.280101	+	0.862063i
$93$	−52861.3	−	38406.0i	−0.633769	−	0.460460i
$94$	235428.	+	171049.i	2.74814	+	1.99664i
$95$	−29609.9	+	91129.9i	−0.336611	+	1.03598i
$96$	5549.43	+	17079.4i	0.0614569	+	0.189145i
$97$	−103201.	+	74979.8i	−1.11366	+	0.809124i	−0.983237	−	0.182334i	$-0.941635\pi$
$97$	−103201.	+	74979.8i	−1.11366	+	0.809124i	−0.130427	+	0.991458i	$0.541635\pi$
$98$	−152739.			−1.60651
$99$	−14222.3	−	29229.8i	−0.145842	−	0.299735i
$100$	25192.6			0.251926
$101$	60612.2	−	44037.4i	0.591231	−	0.429554i	−0.251525	−	0.967851i	$-0.580932\pi$
$101$	60612.2	−	44037.4i	0.591231	−	0.429554i	0.842755	+	0.538297i	$0.180932\pi$
$102$	53557.4	+	164833.i	0.509705	+	1.56871i
$103$	16296.0	−	50153.8i	0.151352	−	0.465812i	−0.846421	−	0.532514i	$-0.821247\pi$
$103$	16296.0	−	50153.8i	0.151352	−	0.465812i	0.997773	+	0.0667013i	$0.0212475\pi$
$104$	−126691.	−	92046.6i	−1.14859	−	0.834496i
$105$	−13231.0	−	9612.87i	−0.117117	−	0.0850902i
$106$	21263.6	−	65442.7i	0.183812	−	0.565714i
$107$	−38090.9	−	117232.i	−0.321634	−	0.989888i	−0.972937	−	0.231070i	$-0.925777\pi$
$107$	−38090.9	−	117232.i	−0.321634	−	0.989888i	0.651303	−	0.758818i	$-0.274223\pi$
$108$	35726.4	−	25956.8i	0.294734	−	0.214137i
$109$	−134499.			−1.08431			−0.542153	−	0.840280i	$-0.682391\pi$
$109$	−134499.			−1.08431			−0.542153	+	0.840280i	$0.682391\pi$
$110$	40111.7	−	226239.i	0.316074	−	1.78273i
$111$	11833.3			0.0911589
$112$	−17468.4	+	12691.5i	−0.131586	+	0.0956025i
$113$	10405.9	+	32026.0i	0.0766623	+	0.235942i	0.982043	−	0.188659i	$-0.0604142\pi$
$113$	10405.9	+	32026.0i	0.0766623	+	0.235942i	−0.905380	+	0.424602i	$0.860414\pi$
$114$	−43089.8	+	132617.i	−0.310536	+	0.955732i
$115$	−58480.5	−	42488.6i	−0.412351	−	0.299590i
$116$	372447.	+	270598.i	2.56992	+	1.86715i
$117$	14256.0	−	43875.4i	0.0962792	−	0.296317i
$118$	−65935.0	−	202927.i	−0.435924	−	1.34164i
$119$	49446.7	−	35925.2i	0.320089	−	0.232558i
$120$	147251.			0.933479
$121$	−151234.	−	55367.6i	−0.939047	−	0.343789i
$122$	240514.			1.46299
$123$	42523.7	−	30895.3i	0.253436	−	0.184132i
$124$	−135902.	−	418262.i	−0.793726	−	2.44284i
$125$	49815.7	−	153317.i	0.285162	−	0.877637i
$126$	−19254.4	−	13989.1i	−0.108045	−	0.0784989i
$127$	189823.	+	137914.i	1.04433	+	0.758752i	0.971127	−	0.238565i	$-0.0766770\pi$
$127$	189823.	+	137914.i	1.04433	+	0.758752i	0.0732059	+	0.997317i	$0.476677\pi$
$128$	−104625.	+	322002.i	−0.564430	+	1.73714i
$129$	−17680.4	−	54414.7i	−0.0935444	−	0.287900i
$130$	263811.	−	191670.i	1.36910	−	0.994709i
$131$	204823.			1.04280			0.521399	−	0.853313i	$-0.325410\pi$
$131$	204823.			1.04280			0.521399	+	0.853313i	$0.325410\pi$
$132$	38195.4	−	215431.i	0.190799	−	1.07615i
$133$	49173.9			0.241049
$134$	−120994.	+	87907.4i	−0.582106	+	0.422925i
$135$	13405.0	+	41256.2i	0.0633040	+	0.194830i
$136$	−170054.	+	523371.i	−0.788386	+	2.42640i
$137$	39015.1	+	28346.1i	0.177595	+	0.129030i	0.673032	−	0.739614i	$-0.264992\pi$
$137$	39015.1	+	28346.1i	0.177595	+	0.129030i	−0.495436	+	0.868644i	$0.664992\pi$
$138$	−85103.7	−	61831.5i	−0.380409	−	0.276383i
$139$	36205.7	−	111430.i	0.158942	−	0.489174i	−0.839597	−	0.543210i	$-0.817209\pi$
$139$	36205.7	−	111430.i	0.158942	−	0.489174i	0.998539	+	0.0540363i	$0.0172087\pi$
$140$	−34015.6	−	104689.i	−0.146676	−	0.451421i
$141$	−220217.	+	159997.i	−0.932831	+	0.677742i
$142$	−621811.			−2.58784
$143$	−100003.	−	205528.i	−0.408953	−	0.840486i
$144$	57272.3			0.230164
$145$	−365861.	+	265813.i	−1.44509	+	1.04992i
$146$	131186.	+	403749.i	0.509337	+	1.56758i
$147$	44149.3	−	135877.i	0.168512	−	0.518626i
$148$	64435.6	+	46815.2i	0.241809	+	0.175684i
$149$	−167138.	−	121433.i	−0.616751	−	0.448096i	0.235034	−	0.971987i	$-0.424480\pi$
$149$	−167138.	−	121433.i	−0.616751	−	0.448096i	−0.851785	+	0.523891i	$0.824480\pi$
$150$	−11128.7	+	34250.6i	−0.0403847	+	0.124291i
$151$	31098.2	+	95710.5i	0.110992	+	0.341600i	0.991090	−	0.133193i	$-0.0425231\pi$
$151$	31098.2	+	95710.5i	0.110992	+	0.341600i	−0.880098	+	0.474793i	$0.842523\pi$
$152$	−358192.	+	260242.i	−1.25750	+	0.913625i
$153$	−162117.			−0.559887
$154$	−116783.	+	16300.6i	−0.396804	+	0.0553862i
$155$	432010.			1.44432
$156$	251208.	−	182513.i	0.826461	−	0.600459i
$157$	24801.2	+	76330.2i	0.0803014	+	0.247142i	0.983145	−	0.182826i	$-0.0585246\pi$
$157$	24801.2	+	76330.2i	0.0803014	+	0.247142i	−0.902844	+	0.429969i	$0.858525\pi$
$158$	−51872.2	+	159646.i	−0.165307	+	0.508763i
$159$	52072.1	+	37832.6i	0.163347	+	0.118679i
$160$	−96058.8	−	69790.8i	−0.296645	−	0.215525i
$161$	−11463.5	+	35281.0i	−0.0348539	+	0.107269i
$162$	19507.6	+	60038.1i	0.0584003	+	0.179738i
$163$	15438.1	−	11216.4i	0.0455118	−	0.0330663i	−0.564797	−	0.825230i	$-0.691045\pi$
$163$	15438.1	−	11216.4i	0.0455118	−	0.0330663i	0.610309	+	0.792164i	$0.291045\pi$
$164$	353781.			1.02713
$165$	189669.	+	101078.i	0.542360	+	0.289033i
$166$	1.14397e6			3.22213
$167$	354930.	−	257871.i	0.984807	−	0.715504i	0.0260291	−	0.999661i	$-0.491714\pi$
$167$	354930.	−	257871.i	0.984807	−	0.715504i	0.958778	+	0.284157i	$0.0917137\pi$
$168$	−23351.8	−	71869.5i	−0.0638333	−	0.196459i
$169$	−14495.8	+	44613.4i	−0.0390413	+	0.120157i
$170$	−927060.	−	673548.i	−2.46029	−	1.78750i
$171$	−105522.	−	76666.0i	−0.275963	−	0.200499i
$172$	119002.	−	366250.i	0.306713	−	0.943967i
$173$	125314.	+	385677.i	0.318335	+	0.979734i	0.974360	+	0.224995i	$0.0722366\pi$
$173$	125314.	+	385677.i	0.318335	+	0.979734i	−0.656025	+	0.754739i	$0.727763\pi$
$174$	−532418.	+	386824.i	−1.33315	+	0.968592i
$175$	12700.0			0.0313480
$176$	204301.	−	196919.i	0.497151	−	0.479189i
$177$	199584.			0.478843
$178$	51468.4	−	37394.0i	0.121756	−	0.0884610i
$179$	112272.	+	345539.i	0.261903	+	0.806054i	0.992391	+	0.123128i	$0.0392927\pi$
$179$	112272.	+	345539.i	0.261903	+	0.806054i	−0.730488	+	0.682926i	$0.760707\pi$
$180$	−90225.1	+	277684.i	−0.207561	+	0.638808i
$181$	506552.	+	368031.i	1.14928	+	0.835004i	0.988386	−	0.151967i	$-0.0485609\pi$
$181$	506552.	+	368031.i	1.14928	+	0.835004i	0.160898	+	0.986971i	$0.448561\pi$
$182$	−135386.	−	98363.6i	−0.302967	−	0.220118i
$183$	−69520.9	+	213963.i	−0.153457	+	0.472293i
$184$	−103214.	−	317661.i	−0.224748	−	0.691703i
$185$	−63296.2	+	45987.4i	−0.135972	+	0.0987891i
$186$	628682.			1.33244
$187$	−578302.	+	557408.i	−1.20935	+	1.16565i
$188$	−1.83212e6			−3.78060
$189$	18010.3	−	13085.3i	0.0366747	−	0.0266457i
$190$	−284897.	−	876822.i	−0.572537	−	1.76209i
$191$	151049.	−	464881.i	0.299595	−	0.922059i	−0.682044	−	0.731311i	$-0.738909\pi$
$191$	151049.	−	464881.i	0.299595	−	0.922059i	0.981639	−	0.190748i	$-0.0610912\pi$
$192$	−304533.	−	221256.i	−0.596186	−	0.433155i
$193$	109220.	+	79352.8i	0.211061	+	0.153345i	0.688294	−	0.725432i	$-0.258360\pi$
$193$	109220.	+	79352.8i	0.211061	+	0.153345i	−0.477233	+	0.878777i	$0.658360\pi$
$194$	379279.	−	1.16730e6i	0.723526	−	2.22678i
$195$	94256.2	+	290091.i	0.177510	+	0.546321i
$196$	777966.	−	565225.i	1.44651	−	1.05095i
$197$	−176847.			−0.324662			−0.162331	−	0.986736i	$-0.551901\pi$
$197$	−176847.			−0.324662			−0.162331	+	0.986736i	$0.551901\pi$
$198$	276016.	+	147094.i	0.500347	+	0.266644i
$199$	433048.			0.775181			0.387591	−	0.921832i	$-0.373307\pi$
$199$	433048.			0.775181			0.387591	+	0.921832i	$0.373307\pi$
$200$	−92509.5	+	67212.1i	−0.163535	+	0.118815i
$201$	−43229.6	−	133047.i	−0.0754729	−	0.232282i
$202$	−222759.	+	685582.i	−0.384111	+	1.18217i
$203$	187757.	+	136413.i	0.319783	+	0.232336i
$204$	−882772.	−	641371.i	−1.48516	−	1.07903i
$205$	−107391.	+	330516.i	−0.178478	+	0.549298i
$206$	156794.	+	482564.i	0.257432	+	0.792294i
$207$	79605.1	−	57836.5i	0.129126	−	0.0938158i
$208$	402707.			0.645403
$209$	−640016.	+	89333.8i	−1.01350	+	0.141465i
$210$	157356.			0.246227
$211$	108834.	−	79072.6i	0.168290	−	0.122270i	−0.500452	−	0.865764i	$-0.666833\pi$
$211$	108834.	−	79072.6i	0.168290	−	0.122270i	0.668742	+	0.743494i	$0.266833\pi$
$212$	133872.	+	412017.i	0.204575	+	0.629616i
$213$	179735.	−	553168.i	0.271446	−	0.835426i
$214$	959505.	+	697121.i	1.43223	+	1.04058i
$215$	306042.	+	222352.i	0.451528	+	0.328054i
$216$	−61939.8	+	190631.i	−0.0903306	+	0.278009i
$217$	−68510.4	−	210853.i	−0.0987659	−	0.303970i
$218$	1.04695e6	−	760654.i	1.49206	−	1.08404i
$219$	−397098.			−0.559483
$220$	632913.	+	1.30077e6i	0.881632	+	1.81194i
$221$	−1.13992e6			−1.56998
$222$	−92111.7	+	66923.1i	−0.125439	+	0.0911367i
$223$	−235726.	−	725489.i	−0.317428	−	0.976942i	−0.974744	−	0.223327i	$-0.928308\pi$
$223$	−235726.	−	725489.i	−0.317428	−	0.976942i	0.657316	−	0.753615i	$-0.271692\pi$
$224$	−18829.6	+	57951.7i	−0.0250739	+	0.0771695i
$225$	−27252.8	−	19800.4i	−0.0358885	−	0.0260745i
$226$	−262122.	−	190443.i	−0.341376	−	0.248024i
$227$	−33519.6	+	103163.i	−0.0431752	+	0.132880i	−0.970321	−	0.241822i	$-0.922255\pi$
$227$	−33519.6	+	103163.i	−0.0431752	+	0.132880i	0.927145	+	0.374702i	$0.122255\pi$
$228$	−271286.	−	834934.i	−0.345614	−	1.06369i
$229$	423208.	−	307479.i	0.533292	−	0.387459i	−0.288296	−	0.957541i	$-0.593089\pi$
$229$	423208.	−	307479.i	0.533292	−	0.387459i	0.821588	+	0.570082i	$0.193089\pi$
$230$	695511.			0.866931
$231$	19255.0	−	108602.i	0.0237418	−	0.133909i
$232$	−2.08959e6			−2.54884
$233$	−177464.	+	128935.i	−0.214152	+	0.155590i	−0.689690	−	0.724105i	$-0.742253\pi$
$233$	−177464.	+	128935.i	−0.214152	+	0.155590i	0.475539	+	0.879695i	$0.342253\pi$
$234$	137166.	+	422154.i	0.163760	+	0.504001i
$235$	556146.	−	1.71164e6i	0.656930	−	2.02182i
$236$	1.08679e6	+	789598.i	1.27018	+	0.922840i
$237$	−127029.	−	92291.8i	−0.146903	−	0.106731i
$238$	−181724.	+	559290.i	−0.207955	+	0.640021i
$239$	149117.	+	458935.i	0.168862	+	0.519704i	0.999300	−	0.0374068i	$-0.0119097\pi$
$239$	149117.	+	458935.i	0.168862	+	0.519704i	−0.830438	+	0.557111i	$0.811910\pi$
$240$	−306348.	+	222575.i	−0.343311	+	0.249430i
$241$	−472230.			−0.523734			−0.261867	−	0.965104i	$-0.584338\pi$
$241$	−472230.			−0.523734			−0.261867	+	0.965104i	$0.584338\pi$
$242$	1.49035e6	−	424316.i	1.63588	−	0.465748i
$243$	−59049.0			−0.0641500
$244$	−1.22505e6	+	890048.i	−1.31728	+	0.957060i
$245$	291902.	+	898381.i	0.310686	+	0.956193i
$246$	−156281.	+	480983.i	−0.164652	+	0.506748i
$247$	−741969.	−	539072.i	−0.773827	−	0.562218i
$248$	1.61494e6	+	1.17332e6i	1.66735	+	1.21140i
$249$	−330664.	+	1.01768e6i	−0.337979	+	1.04019i
$250$	479310.	+	1.47516e6i	0.485028	+	1.49276i
$251$	−296517.	+	215432.i	−0.297074	+	0.215837i	−0.726330	−	0.687346i	$-0.758776\pi$
$251$	−296517.	+	215432.i	−0.297074	+	0.215837i	0.429256	+	0.903183i	$0.358776\pi$
$252$	149839.			0.148636
$253$	85106.5	−	480020.i	0.0835914	−	0.471474i
$254$	−2.25757e6			−2.19562
$255$	867161.	−	630029.i	0.835121	−	0.606751i
$256$	−593079.	−	1.82531e6i	−0.565604	−	1.74075i
$257$	520203.	−	1.60102e6i	0.491292	−	1.51204i	−0.331363	−	0.943503i	$-0.607509\pi$
$257$	520203.	−	1.60102e6i	0.491292	−	1.51204i	0.822656	−	0.568540i	$-0.192491\pi$
$258$	445367.	+	323578.i	0.416551	+	0.302642i
$259$	32483.1	+	23600.4i	0.0300890	+	0.0218610i
$260$	−634413.	+	1.95252e6i	−0.582021	+	1.79128i
$261$	−190226.	−	585455.i	−0.172850	−	0.531976i
$262$	−1.59436e6	+	1.15837e6i	−1.43494	+	1.04254i
$263$	−1.52341e6			−1.35808			−0.679042	−	0.734100i	$-0.737604\pi$
$263$	−1.52341e6			−1.35808			−0.679042	+	0.734100i	$0.737604\pi$
$264$	434497.	+	892983.i	0.383686	+	0.788558i
$265$	−425560.			−0.372259
$266$	−382774.	+	278102.i	−0.331695	+	0.240990i
$267$	18389.0	+	56595.5i	0.0157863	+	0.0485851i
$268$	290966.	−	895502.i	0.247460	−	0.761605i
$269$	55575.7	+	40378.1i	0.0468278	+	0.0340224i	0.610953	−	0.791667i	$-0.290786\pi$
$269$	55575.7	+	40378.1i	0.0468278	+	0.0340224i	−0.564125	+	0.825689i	$0.690786\pi$
$270$	−337669.	−	245331.i	−0.281891	−	0.204806i
$271$	367114.	−	1.12986e6i	0.303653	−	0.934549i	−0.676523	−	0.736422i	$-0.736514\pi$
$271$	367114.	−	1.12986e6i	0.303653	−	0.934549i	0.980176	−	0.198128i	$-0.0634860\pi$
$272$	−437306.	−	1.34589e6i	−0.358396	−	1.10303i
$273$	126638.	−	92008.2i	0.102839	−	0.0747171i
$274$	−464008.			−0.373378
$275$	−165295.	+	23072.1i	−0.131804	+	0.0183973i
$276$	662285.			0.523326
$277$	1.22085e6	−	887001.i	0.956012	−	0.694583i	0.00379098	−	0.999993i	$-0.498793\pi$
$277$	1.22085e6	−	887001.i	0.956012	−	0.694583i	0.952221	+	0.305409i	$0.0987933\pi$
$278$	348359.	+	1.07214e6i	0.270343	+	0.832030i
$279$	−181721.	+	559280.i	−0.139764	+	0.430149i
$280$	404212.	+	293677.i	0.308116	+	0.223859i
$281$	−1.13878e6	−	827375.i	−0.860351	−	0.625081i	0.0676296	−	0.997710i	$-0.478456\pi$
$281$	−1.13878e6	−	827375.i	−0.860351	−	0.625081i	−0.927980	+	0.372629i	$0.878456\pi$
$282$	809331.	−	2.49086e6i	0.606043	−	1.86521i
$283$	99556.9	+	306405.i	0.0738933	+	0.227420i	0.981181	−	0.193090i	$-0.0618510\pi$
$283$	99556.9	+	306405.i	0.0738933	+	0.227420i	−0.907288	+	0.420510i	$0.861851\pi$
$284$	3.16716e6	−	2.30108e6i	2.33010	−	1.69292i
$285$	862377.			0.628905
$286$	1.94079e6	+	1.03428e6i	1.40302	+	0.747694i
$287$	178347.			0.127809
$288$	130757.	−	95000.8i	0.0928934	−	0.0674910i
$289$	799097.	+	2.45937e6i	0.562801	+	1.73212i
$290$	1.34459e6	−	4.13823e6i	0.938849	−	2.88948i
$291$	928808.	+	674818.i	0.642974	+	0.467148i
$292$	−2.16230e6	−	1.57101e6i	−1.48409	−	1.07825i
$293$	−437404.	+	1.34619e6i	−0.297656	+	0.916090i	0.684661	+	0.728862i	$0.259950\pi$
$293$	−437404.	+	1.34619e6i	−0.297656	+	0.916090i	−0.982317	+	0.187228i	$0.940050\pi$
$294$	424790.	+	1.30737e6i	0.286619	+	0.882124i
$295$	−1.06757e6	+	775636.i	−0.714236	+	0.518923i
$296$	−361513.			−0.239825
$297$	−210639.	+	203028.i	−0.138563	+	0.133557i
$298$	1.98778e6			1.29666
$299$	559739.	−	406674.i	0.362082	−	0.263068i
$300$	−70064.6	−	215637.i	−0.0449464	−	0.138331i
$301$	59990.9	−	184633.i	0.0381654	−	0.117461i
$302$	−783360.	−	569144.i	−0.494247	−	0.359091i
$303$	−545510.	−	396336.i	−0.341347	−	0.248003i
$304$	351836.	−	1.08284e6i	0.218352	−	0.672018i
$305$	−459652.	−	1.41466e6i	−0.282930	−	0.870769i
$306$	1.26194e6	−	916850.i	0.770431	−	0.559751i
$307$	637505.			0.386045			0.193022	−	0.981194i	$-0.438171\pi$
$307$	637505.			0.386045			0.193022	+	0.981194i	$0.438171\pi$
$308$	534504.	−	515192.i	0.321051	−	0.309451i
$309$	−474614.			−0.282777
$310$	−3.36281e6	+	2.44322e6i	−1.98746	+	1.44397i
$311$	−345172.	−	1.06233e6i	−0.202364	−	0.622814i	−0.999811	−	0.0194245i	$-0.993817\pi$
$311$	−345172.	−	1.06233e6i	−0.202364	−	0.622814i	0.797447	−	0.603389i	$-0.206183\pi$
$312$	−435526.	+	1.34041e6i	−0.253296	+	0.779563i
$313$	2.41362e6	+	1.75360e6i	1.39254	+	1.01174i	0.995581	+	0.0939055i	$0.0299352\pi$
$313$	2.41362e6	+	1.75360e6i	1.39254	+	1.01174i	0.396961	+	0.917836i	$0.370065\pi$
$314$	−624738.	−	453899.i	−0.357581	−	0.259798i
$315$	−45484.0	+	139985.i	−0.0258275	+	0.0794889i
$316$	−326579.	−	1.00511e6i	−0.183980	−	0.566232i
$317$	−1.58238e6	+	1.14966e6i	−0.884426	+	0.642573i	−0.934419	−	0.356177i	$-0.884080\pi$
$317$	−1.58238e6	+	1.14966e6i	−0.884426	+	0.642573i	0.0499930	+	0.998750i	$0.484080\pi$
$318$	−619295.			−0.343423
$319$	−2.69154e6	−	1.43437e6i	−1.48090	−	0.789196i
$320$	2.48880e6			1.35867
$321$	−897511.	+	652080.i	−0.486157	+	0.353214i
$322$	−110298.	−	339462.i	−0.0592826	−	0.182453i
$323$	−995922.	+	3.06513e6i	−0.531152	+	1.63472i
$324$	−321538.	−	233611.i	−0.170165	−	0.123632i
$325$	−191627.	−	139225.i	−0.100635	−	0.0731154i
$326$	−56737.3	+	174619.i	−0.0295682	+	0.0910014i
$327$	374062.	+	1.15124e6i	0.193452	+	0.595385i
$328$	−1.29912e6	+	943863.i	−0.666750	+	0.484422i
$329$	−923606.			−0.470432
$330$	−2.04805e6	+	285868.i	−1.03527	+	0.144504i
$331$	−340808.			−0.170978			−0.0854888	−	0.996339i	$-0.527245\pi$
$331$	−340808.			−0.170978			−0.0854888	+	0.996339i	$0.527245\pi$
$332$	−5.82672e6	+	4.23336e6i	−2.90121	+	2.10785i
$333$	−32910.3	−	101287.i	−0.0162638	−	0.0500547i
$334$	−1.30442e6	+	4.01459e6i	−0.639810	+	1.96913i
$335$	748289.	+	543664.i	0.364299	+	0.264678i
$336$	157216.	+	114224.i	0.0759709	+	0.0551961i
$337$	1.24336e6	−	3.82667e6i	0.596380	−	1.83547i	0.0486436	−	0.998816i	$-0.484510\pi$
$337$	1.24336e6	−	3.82667e6i	0.596380	−	1.83547i	0.547736	−	0.836651i	$-0.315490\pi$
$338$	−139473.	−	429255.i	−0.0664049	−	0.204373i
$339$	245186.	−	178138.i	0.115877	−	0.0841895i
$340$	7.21446e6			3.38459
$341$	1.27474e6	+	2.61987e6i	0.593658	+	1.22009i
$342$	1.25497e6			0.580188
$343$	807412.	−	586619.i	0.370561	−	0.269228i
$344$	540143.	+	1.66239e6i	0.246101	+	0.757420i
$345$	−201038.	+	618732.i	−0.0909350	+	0.279869i
$346$	−3.15664e6	−	2.29343e6i	−1.41754	−	1.02990i
$347$	3.21125e6	+	2.33311e6i	1.43170	+	1.04019i	0.989698	+	0.143173i	$0.0457306\pi$
$347$	3.21125e6	+	2.33311e6i	1.43170	+	1.04019i	0.441999	+	0.897015i	$0.354269\pi$
$348$	1.28036e6	−	3.94054e6i	0.566739	−	1.74424i
$349$	−590291.	−	1.81673e6i	−0.259420	−	0.798412i	−0.992927	−	0.118730i	$-0.962118\pi$
$349$	−590291.	−	1.81673e6i	−0.259420	−	0.798412i	0.733507	−	0.679682i	$-0.237882\pi$
$350$	−98858.3	+	71824.8i	−0.0431363	+	0.0313404i
$351$	−415200.			−0.179883
$352$	139794.	−	788469.i	0.0601356	−	0.339178i
$353$	4.22138e6			1.80309			0.901545	−	0.432686i	$-0.142434\pi$
$353$	4.22138e6			1.80309			0.901545	+	0.432686i	$0.142434\pi$
$354$	−1.55358e6	+	1.12874e6i	−0.658909	+	0.478726i
$355$	1.18835e6	+	3.65738e6i	0.500467	+	1.54028i
$356$	−123771.	+	380928.i	−0.0517600	+	0.159301i
$357$	−445021.	−	323326.i	−0.184803	−	0.134267i
$358$	−2.82812e6	−	2.05475e6i	−1.16625	−	0.847329i
$359$	473019.	−	1.45580e6i	0.193706	−	0.596165i	−0.806284	−	0.591529i	$-0.798524\pi$
$359$	473019.	−	1.45580e6i	0.193706	−	0.596165i	0.999989	−	0.00463543i	$-0.00147551\pi$
$360$	−409527.	−	1.26039e6i	−0.166543	−	0.512567i
$361$	−94551.5	+	68695.7i	−0.0381857	+	0.0277435i
$362$	−6.02444e6			−2.41627
$363$	−53313.4	+	1.44848e6i	−0.0212358	+	0.576960i
$364$	1.05359e6			0.416789
$365$	2.12407e6	−	1.54323e6i	0.834519	−	0.606313i
$366$	−668907.	−	2.05868e6i	−0.261014	−	0.803317i
$367$	−474852.	+	1.46144e6i	−0.184032	+	0.566392i	−0.999930	−	0.0118031i	$-0.996243\pi$
$367$	−474852.	+	1.46144e6i	−0.184032	+	0.566392i	0.815898	+	0.578195i	$0.196243\pi$
$368$	694889.	+	504866.i	0.267483	+	0.194338i
$369$	−382713.	−	278057.i	−0.146321	−	0.106309i
$370$	232623.	−	715940.i	0.0883382	−	0.271877i
$371$	67487.5	+	207705.i	0.0254559	+	0.0783452i
$372$	−3.20216e6	+	2.32650e6i	−1.19973	+	0.871658i
$373$	1.42900e6			0.531816			0.265908	−	0.963998i	$-0.414328\pi$
$373$	1.42900e6			0.531816			0.265908	+	0.963998i	$0.414328\pi$
$374$	1.34915e6	−	7.60949e6i	0.498747	−	2.81304i
$375$	−1.45086e6			−0.532780
$376$	6.72772e6	−	4.88798e6i	2.45413	−	1.78303i
$377$	−1.33756e6	−	4.11660e6i	−0.484686	−	1.49171i
$378$	−66190.6	+	203714.i	−0.0238269	+	0.0733315i
$379$	−2.31879e6	−	1.68470e6i	−0.829208	−	0.602455i	0.0901273	−	0.995930i	$-0.471273\pi$
$379$	−2.31879e6	−	1.68470e6i	−0.829208	−	0.602455i	−0.919335	+	0.393476i	$0.871273\pi$
$380$	4.69587e6	+	3.41175e6i	1.66824	+	1.21204i
$381$	652552.	−	2.00835e6i	0.230305	−	0.708805i
$382$	1.45334e6	+	4.47293e6i	0.509577	+	1.56832i
$383$	−2.30326e6	+	1.67341e6i	−0.802316	+	0.582917i	−0.911593	−	0.411095i	$-0.865147\pi$
$383$	−2.30326e6	+	1.67341e6i	−0.802316	+	0.582917i	0.109277	+	0.994011i	$0.465147\pi$
$384$	3.04716e6			1.05455
$385$	319063.	+	655742.i	0.109704	+	0.225466i
$386$	−1.29895e6			−0.443737
$387$	−416591.	+	302671.i	−0.141394	+	0.102729i
$388$	2.38788e6	+	7.34914e6i	0.805254	+	2.47832i
$389$	1.45681e6	−	4.48361e6i	0.488124	−	1.50229i	−0.339281	−	0.940685i	$-0.610184\pi$
$389$	1.45681e6	−	4.48361e6i	0.488124	−	1.50229i	0.827405	−	0.561606i	$-0.189816\pi$
$390$	−2.37430e6	−	1.72503e6i	−0.790450	−	0.574295i
$391$	−1.96698e6	−	1.42909e6i	−0.650665	−	0.472736i
$392$	−1.34878e6	+	4.15111e6i	−0.443328	+	1.36442i
$393$	−569644.	−	1.75318e6i	−0.186047	−	0.572593i
$394$	1.37659e6	−	1.00015e6i	0.446750	−	0.324583i
$395$	1.03814e6			0.334784
$396$	−1.95021e6	+	272212.i	−0.624947	+	0.0872305i
$397$	3.61747e6			1.15194			0.575968	−	0.817472i	$-0.304625\pi$
$397$	3.61747e6			1.15194			0.575968	+	0.817472i	$0.304625\pi$
$398$	−3.37089e6	+	2.44909e6i	−1.06669	+	0.774992i
$399$	−136760.	−	420905.i	−0.0430058	−	0.132358i
$400$	90868.0	−	279663.i	0.0283963	−	0.0873947i
$401$	2.81971e6	+	2.04864e6i	0.875677	+	0.636217i	0.932104	−	0.362190i	$-0.117971\pi$
$401$	2.81971e6	+	2.04864e6i	0.875677	+	0.636217i	−0.0564269	+	0.998407i	$0.517971\pi$
$402$	1.08895e6	+	791166.i	0.336079	+	0.244176i
$403$	−1.27776e6	+	3.93255e6i	−0.391911	+	1.20618i
$404$	−1.40246e6	−	4.31632e6i	−0.427500	−	1.31571i
$405$	315852.	−	229480.i	0.0956854	−	0.0695195i
$406$	−2.23300e6			−0.672316
$407$	−465654.	−	248155.i	−0.139340	−	0.0742570i
$408$	4.95275e6			1.47298
$409$	−2.68736e6	+	1.95248e6i	−0.794361	+	0.577137i	−0.909254	−	0.416241i	$-0.863347\pi$
$409$	−2.68736e6	+	1.95248e6i	−0.794361	+	0.577137i	0.114893	+	0.993378i	$0.463347\pi$
$410$	−1.03328e6	−	3.18012e6i	−0.303570	−	0.934294i
$411$	134122.	−	412785.i	0.0391648	−	0.120537i
$412$	−2.58440e6	−	1.87768e6i	−0.750096	−	0.544976i
$413$	547869.	+	398050.i	0.158053	+	0.114832i
$414$	−292561.	+	900409.i	−0.0838909	+	0.258190i
$415$	−2.18625e6	−	6.72860e6i	−0.623133	−	1.91780i
$416$	919413.	−	667993.i	0.260482	−	0.189251i
$417$	−1.05448e6			−0.296959
$418$	4.47672e6	−	4.31498e6i	1.25320	−	1.20792i
$419$	−5.09570e6			−1.41798			−0.708988	−	0.705221i	$-0.750848\pi$
$419$	−5.09570e6			−1.41798			−0.708988	+	0.705221i	$0.750848\pi$
$420$	−801486.	+	582314.i	−0.221704	+	0.161077i
$421$	988417.	+	3.04204e6i	0.271791	+	0.836487i	0.990051	+	0.140711i	$0.0449390\pi$
$421$	988417.	+	3.04204e6i	0.271791	+	0.836487i	−0.718260	+	0.695775i	$0.755061\pi$
$422$	−399982.	+	1.23102e6i	−0.109335	+	0.336498i
$423$	1.98195e6	+	1.43997e6i	0.538570	+	0.391294i
$424$	−1.59082e6	−	1.15580e6i	−0.429741	−	0.312225i
$425$	−257215.	+	791625.i	−0.0690754	+	0.212592i
$426$	1.72935e6	+	5.32240e6i	0.461699	+	1.42096i
$427$	−617567.	+	448689.i	−0.163913	+	0.119090i
$428$	−7.46696e6			−1.97031
$429$	−1.48109e6	+	1.42758e6i	−0.388543	+	0.374505i
$430$	−3.63976e6			−0.949297
$431$	1.32555e6	−	963072.i	0.343720	−	0.249727i	−0.402510	−	0.915416i	$-0.631862\pi$
$431$	1.32555e6	−	963072.i	0.343720	−	0.249727i	0.746230	+	0.665689i	$0.231862\pi$
$432$	−159283.	−	490223.i	−0.0410639	−	0.126382i
$433$	−69567.6	+	214107.i	−0.0178315	+	0.0548796i	−0.959576	−	0.281449i	$-0.909185\pi$
$433$	−69567.6	+	214107.i	−0.0178315	+	0.0548796i	0.941745	+	0.336328i	$0.109185\pi$
$434$	1.72577e6	+	1.25384e6i	0.439803	+	0.319535i
$435$	3.29275e6	+	2.39232e6i	0.834325	+	0.606172i
$436$	−2.51770e6	+	7.74870e6i	−0.634291	+	1.95215i
$437$	−604476.	−	1.86039e6i	−0.151417	−	0.466015i
$438$	3.09105e6	−	2.24578e6i	0.769875	−	0.559347i
$439$	119483.			0.0295899			0.0147950	−	0.999891i	$-0.495290\pi$
$439$	119483.			0.0295899			0.0147950	+	0.999891i	$0.495290\pi$
$440$	−5.79448e6	−	3.08798e6i	−1.42686	−	0.760401i
$441$	−1.28583e6			−0.314838
$442$	8.87323e6	−	6.44678e6i	2.16036	−	1.56959i
$443$	−287495.	−	884819.i	−0.0696019	−	0.214213i	0.910205	−	0.414157i	$-0.135924\pi$
$443$	−287495.	−	884819.i	−0.0696019	−	0.214213i	−0.979807	+	0.199945i	$0.935924\pi$
$444$	221510.	−	681738.i	0.0533256	−	0.164119i
$445$	−318307.	−	231264.i	−0.0761984	−	0.0553614i
$446$	5.93789e6	+	4.31413e6i	1.41350	+	1.02697i
$447$	−574570.	+	1.76834e6i	−0.136011	+	0.418599i
$448$	−394687.	−	1.21472e6i	−0.0929091	−	0.285945i
$449$	5.50754e6	−	4.00146e6i	1.28926	−	0.936705i	0.289473	−	0.957186i	$-0.406520\pi$
$449$	5.50754e6	−	4.00146e6i	1.28926	−	0.936705i	0.999790	+	0.0204816i	$0.00651996\pi$
$450$	324119.			0.0754525
$451$	−2.32125e6	+	324002.i	−0.537379	+	0.0750078i
$452$	2.03986e6			0.469628
$453$	732746.	−	532371.i	0.167768	−	0.121890i
$454$	−322515.	−	992599.i	−0.0734362	−	0.226013i
$455$	−319818.	+	984300.i	−0.0724228	+	0.222894i
$456$	3.22373e6	+	2.34218e6i	0.726016	+	0.527482i
$457$	6.73792e6	+	4.89539e6i	1.50916	+	1.09647i	0.966548	+	0.256487i	$0.0825651\pi$
$457$	6.73792e6	+	4.89539e6i	1.50916	+	1.09647i	0.542613	+	0.839983i	$0.317435\pi$
$458$	−1.55535e6	+	4.78689e6i	−0.346470	+	1.06632i
$459$	450873.	+	1.38764e6i	0.0998900	+	0.307430i
$460$	−3.54255e6	+	2.57381e6i	−0.780586	+	0.567129i
$461$	−164594.			−0.0360713			−0.0180356	−	0.999837i	$-0.505741\pi$
$461$	−164594.			−0.0360713			−0.0180356	+	0.999837i	$0.505741\pi$
$462$	464315.	+	954267.i	0.101206	+	0.208001i
$463$	−243247.			−0.0527345			−0.0263672	−	0.999652i	$-0.508394\pi$
$463$	−243247.			−0.0527345			−0.0263672	+	0.999652i	$0.508394\pi$
$464$	4.34730e6	−	3.15850e6i	0.937399	−	0.681060i
$465$	−1.20149e6	−	3.69779e6i	−0.257683	−	0.793068i
$466$	652208.	−	2.00729e6i	0.139130	−	0.428199i
$467$	−2.64014e6	−	1.91818e6i	−0.560190	−	0.407002i	0.271338	−	0.962484i	$-0.412534\pi$
$467$	−2.64014e6	−	1.91818e6i	−0.560190	−	0.407002i	−0.831529	+	0.555482i	$0.812534\pi$
$468$	−2.26087e6	−	1.64262e6i	−0.477158	−	0.346675i
$469$	146681.	−	451438.i	0.0307923	−	0.0947690i
$470$	5.35105e6	+	1.64688e7i	1.11736	+	3.43889i
$471$	584373.	−	424572.i	0.121377	−	0.0881859i
$472$	−6.09738e6			−1.25976
$473$	−445381.	+	2.51205e6i	−0.0915333	+	0.516268i
$474$	1.51076e6			0.308851
$475$	−541783.	+	393629.i	−0.110177	+	0.0800484i
$476$	−1.14411e6	−	3.52120e6i	−0.231446	−	0.712317i
$477$	179008.	−	550930.i	0.0360227	−	0.110866i
$478$	−3.75624e6	−	2.72906e6i	−0.751940	−	0.546316i
$479$	1.20525e6	+	875663.i	0.240014	+	0.174381i	0.701290	−	0.712876i	$-0.252608\pi$
$479$	1.20525e6	+	875663.i	0.240014	+	0.174381i	−0.461275	+	0.887257i	$0.652608\pi$
$480$	−330221.	+	1.01631e6i	−0.0654186	+	0.201338i
$481$	−231407.	−	712197.i	−0.0456051	−	0.140358i
$482$	3.67588e6	−	2.67068e6i	0.720682	−	0.523606i
$483$	333869.			0.0651191
$484$	−6.02080e6	+	7.67643e6i	−1.16826	+	1.48952i
$485$	−7.59069e6			−1.46530
$486$	459643.	−	333950.i	0.0882734	−	0.0641344i
$487$	−1.55402e6	−	4.78278e6i	−0.296916	−	0.913815i	−0.982571	−	0.185888i	$-0.940484\pi$
$487$	−1.55402e6	−	4.78278e6i	−0.296916	−	0.913815i	0.685654	−	0.727927i	$-0.259516\pi$
$488$	2.12389e6	−	6.53667e6i	0.403723	−	1.24253i
$489$	−138943.	−	100948.i	−0.0262763	−	0.0190908i
$490$	−7.35296e6	−	5.34224e6i	−1.38348	−	1.00516i
$491$	−1.37605e6	+	4.23504e6i	−0.257590	+	0.792781i	0.735718	+	0.677288i	$0.236845\pi$
$491$	−1.37605e6	+	4.23504e6i	−0.257590	+	0.792781i	−0.993308	+	0.115493i	$0.963155\pi$
$492$	−983920.	−	3.02819e6i	−0.183251	−	0.563989i
$493$	−1.23056e7	+	8.94057e6i	−2.28027	+	1.65671i
$494$	8.82427e6			1.62690
$495$	337680.	−	1.90459e6i	0.0619430	−	0.349372i
$496$	−5.13331e6			−0.936900
$497$	1.59662e6	−	1.16001e6i	0.289942	−	0.210655i
$498$	−3.18154e6	−	9.79178e6i	−0.574863	−	1.76925i
$499$	−2.40259e6	+	7.39441e6i	−0.431945	+	1.32939i	0.464241	+	0.885709i	$0.346327\pi$
$499$	−2.40259e6	+	7.39441e6i	−0.431945	+	1.32939i	−0.896185	+	0.443680i	$0.853673\pi$
$500$	−7.90034e6	−	5.73993e6i	−1.41326	−	1.02679i
$501$	−3.19437e6	−	2.32084e6i	−0.568578	−	0.413096i
$502$	1.08974e6	−	3.35389e6i	0.193004	−	0.594004i
$503$	−996062.	−	3.06556e6i	−0.175536	−	0.540244i	0.824122	−	0.566413i	$-0.191669\pi$
$503$	−996062.	−	3.06556e6i	−0.175536	−	0.540244i	−0.999658	+	0.0261687i	$0.991669\pi$
$504$	−550222.	+	399760.i	−0.0964855	+	0.0701008i
$505$	4.45819e6			0.777911
$506$	2.05226e6	+	4.21783e6i	0.356333	+	0.732341i
$507$	422184.			0.0729426
$508$	1.14988e7	−	8.35436e6i	1.97694	−	1.43633i
$509$	383192.	+	1.17934e6i	0.0655575	+	0.201765i	0.978470	−	0.206391i	$-0.0661719\pi$
$509$	383192.	+	1.17934e6i	0.0655575	+	0.201765i	−0.912912	+	0.408156i	$0.866172\pi$
$510$	−3.18695e6	+	9.80842e6i	−0.542562	+	1.66983i
$511$	−1.09006e6	−	791972.i	−0.184670	−	0.134171i
$512$	6.17441e6	+	4.48597e6i	1.04093	+	0.756278i
$513$	−362751.	+	1.11643e6i	−0.0608577	+	0.187301i
$514$	5.00522e6	+	1.54045e7i	0.835633	+	2.57181i
$515$	2.53870e6	−	1.84447e6i	0.421787	−	0.306446i
$516$	−3.46588e6			−0.573046
$517$	1.20211e7	−	1.67791e6i	1.97795	−	0.276084i
$518$	−386323.			−0.0632596
$519$	2.95269e6	−	2.14525e6i	0.481171	−	0.349591i
$520$	−2.87957e6	−	8.86240e6i	−0.467002	−	1.43728i
$521$	−1.39277e6	+	4.28651e6i	−0.224795	+	0.691846i	0.773518	+	0.633775i	$0.218495\pi$
$521$	−1.39277e6	+	4.28651e6i	−0.224795	+	0.691846i	−0.998312	+	0.0580720i	$0.981505\pi$
$522$	4.79176e6	+	3.48142e6i	0.769696	+	0.559217i
$523$	−1.83670e6	−	1.33444e6i	−0.293620	−	0.213327i	0.431216	−	0.902249i	$-0.358085\pi$
$523$	−1.83670e6	−	1.33444e6i	−0.293620	−	0.213327i	−0.724836	+	0.688921i	$0.758085\pi$
$524$	3.83412e6	−	1.18002e7i	0.610010	−	1.87742i
$525$	−35320.8	−	108706.i	−0.00559283	−	0.0172130i
$526$	1.18583e7	−	8.61559e6i	1.86879	−	1.35775i
$527$	1.45305e7			2.27906
$528$	−2.25373e6	−	1.20105e6i	−0.351816	−	0.187489i
$529$	−4.96065e6			−0.770725
$530$	3.31260e6	−	2.40674e6i	0.512246	−	0.372169i
$531$	−555074.	−	1.70834e6i	−0.0854308	−	0.262929i
$532$	920495.	−	2.83299e6i	0.141008	−	0.433977i
$533$	−2.69103e6	−	1.95514e6i	−0.410298	−	0.298099i
$534$	−463216.	−	336546.i	−0.0702959	−	0.0510730i
$535$	2.26661e6	−	6.97592e6i	0.342368	−	1.05370i
$536$	1.32068e6	+	4.06464e6i	0.198557	+	0.611097i
$537$	2.64540e6	−	1.92199e6i	0.395872	−	0.287618i
$538$	−660963.			−0.0984514
$539$	−4.58679e6	+	4.42107e6i	−0.680044	+	0.655475i
$540$	2.62777e6			0.387796
$541$	594522.	−	431945.i	0.0873322	−	0.0634506i	−0.543262	−	0.839563i	$-0.682811\pi$
$541$	594522.	−	431945.i	0.0873322	−	0.0634506i	0.630595	+	0.776112i	$0.282811\pi$
$542$	3.53225e6	+	1.08712e7i	0.516480	+	1.58956i
$543$	1.74137e6	−	5.35938e6i	0.253449	−	0.780037i
$544$	−3.23091e6	−	2.34740e6i	−0.468089	−	0.340086i
$545$	−6.47488e6	−	4.70427e6i	−0.933771	−	0.678424i
$546$	−465415.	+	1.43240e6i	−0.0668127	+	0.205628i
$547$	−3.11865e6	−	9.59822e6i	−0.445655	−	1.37158i	−0.881764	−	0.471690i	$-0.843644\pi$
$547$	−3.11865e6	−	9.59822e6i	−0.445655	−	1.37158i	0.436110	−	0.899894i	$-0.356356\pi$
$548$	2.36340e6	−	1.71711e6i	0.336191	−	0.244257i
$549$	2.02477e6			0.286711
$550$	1.15619e6	−	1.11442e6i	0.162976	−	0.157088i
$551$	−1.22377e7			−1.71721
$552$	−2.43197e6	+	1.76693e6i	−0.339711	+	0.246815i
$553$	−164634.	−	506692.i	−0.0228932	−	0.0704582i
$554$	−4.48681e6	+	1.38090e7i	−0.621103	+	1.91156i
$555$	569666.	+	413886.i	0.0785032	+	0.0570359i
$556$	−5.74190e6	−	4.17174e6i	−0.787715	−	0.572308i
$557$	−529373.	+	1.62924e6i	−0.0722976	+	0.222509i	−0.980676	−	0.195641i	$-0.937321\pi$
$557$	−529373.	+	1.62924e6i	−0.0722976	+	0.222509i	0.908378	+	0.418150i	$0.137321\pi$
$558$	−1.74846e6	−	5.38121e6i	−0.237723	−	0.731635i
$559$	−2.92924e6	+	2.12821e6i	−0.396483	+	0.288062i
$560$	−1.28485e6			−0.173134
$561$	6.37948e6	+	3.39974e6i	0.855812	+	0.456077i
$562$	1.35436e7			1.80881
$563$	3.57065e6	−	2.59423e6i	0.474763	−	0.344935i	−0.324532	−	0.945875i	$-0.605207\pi$
$563$	3.57065e6	−	2.59423e6i	0.474763	−	0.344935i	0.799294	+	0.600940i	$0.205207\pi$
$564$	5.09542e6	+	1.56821e7i	0.674500	+	2.07590i
$565$	−619204.	+	1.90571e6i	−0.0816042	+	0.251152i
$566$	−2.50782e6	−	1.82204e6i	−0.329045	−	0.239065i
$567$	−162093.	−	117767.i	−0.0211742	−	0.0153839i
$568$	−5.49098e6	+	1.68995e7i	−0.714133	+	2.19788i
$569$	−1.31326e6	−	4.04181e6i	−0.170048	−	0.523354i	0.829325	−	0.558767i	$-0.188725\pi$
$569$	−1.31326e6	−	4.04181e6i	−0.170048	−	0.523354i	−0.999373	+	0.0354130i	$0.988725\pi$
$570$	−6.71282e6	+	4.87715e6i	−0.865402	+	0.628751i
$571$	2.86179e6			0.367322			0.183661	−	0.982990i	$-0.441205\pi$
$571$	2.86179e6			0.367322			0.183661	+	0.982990i	$0.441205\pi$
$572$	−1.37128e7	+	1.91404e6i	−1.75241	+	0.244603i
$573$	−4.39925e6			−0.559747
$574$	−1.38827e6	+	1.00864e6i	−0.175871	+	0.127778i
$575$	−156117.	−	480478.i	−0.0196916	−	0.0606044i
$576$	−1.04689e6	+	3.22200e6i	−0.131476	+	0.404641i
$577$	7.56221e6	+	5.49427e6i	0.945604	+	0.687022i	0.949763	−	0.312970i	$-0.101324\pi$
$577$	7.56221e6	+	5.49427e6i	0.945604	+	0.687022i	−0.00415903	+	0.999991i	$0.501324\pi$
$578$	−2.01291e7	−	1.46247e7i	−2.50614	−	1.82082i
$579$	375464.	−	1.15556e6i	0.0465449	−	0.143250i
$580$	8.46534e6	+	2.60536e7i	1.04490	+	3.21587i
$581$	−2.93735e6	+	2.13411e6i	−0.361007	+	0.262287i
$582$	−1.10463e7			−1.35180
$583$	−1.25571e6	−	2.58075e6i	−0.153009	−	0.314467i
$584$	1.21315e7			1.47191
$585$	2.22089e6	−	1.61357e6i	0.268311	−	0.194939i
$586$	−4.20856e6	−	1.29526e7i	−0.506278	−	1.55816i
$587$	−81580.3	+	251078.i	−0.00977214	+	0.0300756i	−0.955824	−	0.293941i	$-0.905033\pi$
$587$	−81580.3	+	251078.i	−0.00977214	+	0.0300756i	0.946052	+	0.324016i	$0.105033\pi$
$588$	−7.00169e6	−	5.08703e6i	−0.835141	−	0.606765i
$589$	9.45790e6	+	6.87156e6i	1.12333	+	0.816145i
$590$	3.92348e6	−	1.20752e7i	0.464025	−	1.42812i
$591$	491837.	+	1.51372e6i	0.0579232	+	0.178269i
$592$	752110.	−	546440.i	0.0882017	−	0.0640823i
$593$	−1.46405e6			−0.170969			−0.0854846	−	0.996339i	$-0.527244\pi$
$593$	−1.46405e6			−0.170969			−0.0854846	+	0.996339i	$0.527244\pi$
$594$	491409.	−	2.77165e6i	0.0571448	−	0.322309i
$595$	3.63694e6			0.421156
$596$	−1.01246e7	+	7.35598e6i	−1.16752	+	0.848253i
$597$	−1.20437e6	−	3.70668e6i	−0.138301	−	0.425646i
$598$	−2.05712e6	+	6.33117e6i	−0.235238	+	0.723988i
$599$	−1.04245e6	−	757382.i	−0.118710	−	0.0862478i	0.526846	−	0.849961i	$-0.323374\pi$
$599$	−1.04245e6	−	757382.i	−0.118710	−	0.0862478i	−0.645556	+	0.763713i	$0.723374\pi$
$600$	832586.	+	604909.i	0.0944171	+	0.0685981i
$601$	−3.84287e6	+	1.18271e7i	−0.433980	+	1.33565i	0.460148	+	0.887842i	$0.347796\pi$
$601$	−3.84287e6	+	1.18271e7i	−0.433980	+	1.33565i	−0.894128	+	0.447811i	$0.852204\pi$
$602$	577213.	+	1.77648e6i	0.0649149	+	0.199788i
$603$	−1.01859e6	+	740048.i	−0.114079	+	0.0828832i
$604$	6.09618e6			0.679932
$605$	−5.34399e6	−	7.95507e6i	−0.593577	−	0.883599i
$606$	6.48777e6			0.717652
$607$	−1.14217e7	+	8.29837e6i	−1.25823	+	0.914157i	−0.998669	−	0.0515694i	$-0.983578\pi$
$607$	−1.14217e7	+	8.29837e6i	−1.25823	+	0.914157i	−0.259560	+	0.965727i	$0.583578\pi$
$608$	−992898.	−	3.05583e6i	−0.108930	−	0.335251i
$609$	645451.	−	1.98649e6i	0.0705212	−	0.217042i
$610$	1.15786e7	+	8.41231e6i	1.25988	+	0.915358i
$611$	1.39360e7	+	1.01251e7i	1.51020	+	1.09723i
$612$	−3.03470e6	+	9.33984e6i	−0.327519	+	1.00800i
$613$	−5.18824e6	−	1.59678e7i	−0.557659	−	1.71630i	−0.688815	−	0.724937i	$-0.741869\pi$
$613$	−5.18824e6	−	1.59678e7i	−0.557659	−	1.71630i	0.131156	−	0.991362i	$-0.458131\pi$
$614$	−4.96240e6	+	3.60539e6i	−0.531215	+	0.385950i
$615$	3.12773e6			0.333458
$616$	−588248.	+	3.31785e6i	−0.0624610	+	0.352294i
$617$	−1.49155e6			−0.157734			−0.0788670	−	0.996885i	$-0.525130\pi$
$617$	−1.49155e6			−0.157734			−0.0788670	+	0.996885i	$0.525130\pi$
$618$	3.69444e6	−	2.68417e6i	0.389114	−	0.282708i
$619$	2.45026e6	+	7.54111e6i	0.257031	+	0.791059i	0.993423	+	0.114504i	$0.0365278\pi$
$619$	2.45026e6	+	7.54111e6i	0.257031	+	0.791059i	−0.736392	+	0.676555i	$0.763472\pi$
$620$	8.08687e6	−	2.48888e7i	0.844892	−	2.60031i
$621$	−716446.	−	520528.i	−0.0745511	−	0.0541646i
$622$	8.69482e6	+	6.31716e6i	0.901125	+	0.654705i
$623$	−62395.2	+	192033.i	−0.00644067	+	0.0198223i
$624$	−1.11999e6	−	3.44697e6i	−0.115147	−	0.354386i
$625$	8.81205e6	−	6.40233e6i	0.902354	−	0.655599i
$626$	−2.87053e7			−2.92770
$627$	2.54464e6	+	5.22977e6i	0.258498	+	0.531268i
$628$	4.86177e6			0.491921
$629$	−2.12895e6	+	1.54677e6i	−0.214555	+	0.155884i
$630$	−437632.	−	1.34689e6i	−0.0439297	−	0.135202i
$631$	3.59807e6	−	1.10737e7i	0.359747	−	1.10719i	−0.593459	−	0.804864i	$-0.702238\pi$
$631$	3.59807e6	−	1.10737e7i	0.359747	−	1.10719i	0.953206	−	0.302322i	$-0.0977619\pi$
$632$	3.88078e6	+	2.81955e6i	0.386479	+	0.280794i
$633$	−979507.	−	711653.i	−0.0971624	−	0.0705926i
$634$	5.81547e6	−	1.78982e7i	0.574594	−	1.76842i
$635$	4.31448e6	+	1.32786e7i	0.424614	+	1.30683i
$636$	3.15434e6	−	2.29177e6i	0.309219	−	0.224661i
$637$	−9.04124e6			−0.882835
$638$	2.90633e7	−	4.05667e6i	2.82679	−	0.394565i
$639$	−5.23472e6			−0.507155
$640$	−1.62992e7	+	1.18421e7i	−1.57295	+	1.14282i
$641$	−1.70566e6	−	5.24949e6i	−0.163964	−	0.504628i	0.834995	−	0.550258i	$-0.185471\pi$
$641$	−1.70566e6	−	5.24949e6i	−0.163964	−	0.504628i	−0.998958	+	0.0456295i	$0.985471\pi$
$642$	3.29849e6	−	1.01517e7i	0.315847	−	0.972078i
$643$	4.00037e6	+	2.90644e6i	0.381569	+	0.277226i	0.761992	−	0.647587i	$-0.224222\pi$
$643$	4.00037e6	+	2.90644e6i	0.381569	+	0.277226i	−0.380423	+	0.924813i	$0.624222\pi$
$644$	1.81801e6	+	1.32086e6i	0.172735	+	0.125500i
$645$	1.05208e6	−	3.23796e6i	0.0995746	−	0.306459i
$646$	−9.58243e6	−	2.94917e7i	−0.903430	−	2.78047i
$647$	5.86897e6	−	4.26406e6i	0.551190	−	0.400463i	−0.277034	−	0.960860i	$-0.589351\pi$
$647$	5.86897e6	−	4.26406e6i	0.551190	−	0.400463i	0.828224	+	0.560397i	$0.189351\pi$
$648$	1.80397e6			0.168769
$649$	−7.85384e6	−	4.18545e6i	−0.731932	−	0.390060i
$650$	2.27903e6			0.211576
$651$	−1.61426e6	+	1.17283e6i	−0.149287	+	0.108463i
$652$	−357209.	−	1.09938e6i	−0.0329081	−	0.101281i
$653$	−6.04957e6	+	1.86186e7i	−0.555189	+	1.70870i	0.140253	+	0.990116i	$0.455208\pi$
$653$	−6.04957e6	+	1.86186e7i	−0.555189	+	1.70870i	−0.695443	+	0.718582i	$0.744792\pi$
$654$	−9.42256e6	−	6.84589e6i	−0.861439	−	0.625872i
$655$	9.86034e6	+	7.16396e6i	0.898025	+	0.652454i
$656$	1.27606e6	−	3.92732e6i	0.115774	−	0.356317i
$657$	1.10439e6	+	3.39896e6i	0.0998180	+	0.307208i
$658$	7.18943e6	−	5.22343e6i	0.647336	−	0.470317i
$659$	4.24342e6			0.380630			0.190315	−	0.981723i	$-0.439049\pi$
$659$	4.24342e6			0.380630			0.190315	+	0.981723i	$0.439049\pi$
$660$	9.37374e6	−	9.03507e6i	0.837631	−	0.807368i
$661$	1.86117e7			1.65685			0.828424	−	0.560101i	$-0.189238\pi$
$661$	1.86117e7			1.65685			0.828424	+	0.560101i	$0.189238\pi$
$662$	2.65288e6	−	1.92743e6i	0.235273	−	0.170936i
$663$	3.17029e6	+	9.75714e6i	0.280101	+	0.862062i
$664$	1.01019e7	−	3.10906e7i	0.889169	−	2.73658i
$665$	2.36727e6	+	1.71992e6i	0.207584	+	0.150819i
$666$	829005.	+	602308.i	0.0724222	+	0.0526178i
$667$	2.85287e6	−	8.78025e6i	0.248295	−	0.764174i
$668$	−8.21242e6	−	2.52752e7i	−0.712082	−	2.19156i
$669$	−5.55424e6	+	4.03539e6i	−0.479799	+	0.348594i
$670$	−8.89943e6			−0.765906
$671$	7.22272e6	−	6.96177e6i	0.619291	−	0.596916i
$672$	548406.			0.0468467
$673$	−1.23020e7	+	8.93791e6i	−1.04698	+	0.760674i	−0.971635	−	0.236484i	$-0.924005\pi$
$673$	−1.23020e7	+	8.93791e6i	−1.04698	+	0.760674i	−0.0753420	+	0.997158i	$0.524005\pi$
$674$	1.19632e7	+	3.68190e7i	1.01437	+	3.12192i
$675$	−93687.0	+	288339.i	−0.00791443	+	0.0243581i
$676$	2.29890e6	+	1.67025e6i	0.193488	+	0.140577i
$677$	6.61522e6	+	4.80624e6i	0.554719	+	0.403027i	0.829522	−	0.558474i	$-0.188613\pi$
$677$	6.61522e6	+	4.80624e6i	0.554719	+	0.403027i	−0.274803	+	0.961500i	$0.588613\pi$
$678$	−901096.	+	2.77329e6i	−0.0752830	+	0.231697i
$679$	1.20377e6	+	3.70483e6i	0.100200	+	0.308385i
$680$	−2.64921e7	+	1.92477e7i	−2.19707	+	1.59627i
$681$	976247.			0.0806662
$682$	−2.47393e7	−	1.31840e7i	−2.03670	−	1.08539i
$683$	7.72453e6			0.633608			0.316804	−	0.948491i	$-0.397390\pi$
$683$	7.72453e6			0.633608			0.316804	+	0.948491i	$0.397390\pi$
$684$	−6.39213e6	+	4.64416e6i	−0.522403	+	0.379548i
$685$	886774.	+	2.72921e6i	0.0722082	+	0.222234i
$686$	−2.96736e6	+	9.13259e6i	−0.240746	+	0.740941i
$687$	−3.80887e6	−	2.76731e6i	−0.307896	−	0.223700i
$688$	−3.63651e6	−	2.64208e6i	−0.292896	−	0.212801i
$689$	1.25868e6	−	3.87383e6i	0.101011	−	0.310880i
$690$	−1.93432e6	−	5.95323e6i	−0.154670	−	0.476025i
$691$	−1.62835e7	+	1.18307e7i	−1.29734	+	0.942573i	−0.999926	−	0.0121760i	$-0.996124\pi$
$691$	−1.62835e7	+	1.18307e7i	−1.29734	+	0.942573i	−0.297414	+	0.954749i	$0.596124\pi$
$692$	2.45653e7			1.95010
$693$	−983134.	+	137227.i	−0.0777642	+	0.0108544i
$694$	−3.81916e7			−3.01002
$695$	5.64037e6	−	4.09797e6i	0.442940	−	0.321815i
$696$	5.81148e6	+	1.78859e7i	0.454741	+	1.39955i
$697$	−3.61208e6	+	1.11168e7i	−0.281627	+	0.866760i
$698$	1.48694e7	+	1.08032e7i	1.15519	+	0.839295i
$699$	1.59718e6	+	1.16042e6i	0.123640	+	0.0898301i
$700$	237734.	−	731671.i	0.0183378	−	0.0564379i
$701$	−2.29781e6	−	7.07193e6i	−0.176611	−	0.543554i	0.823092	−	0.567908i	$-0.192247\pi$
$701$	−2.29781e6	−	7.07193e6i	−0.176611	−	0.543554i	−0.999703	+	0.0243541i	$0.992247\pi$
$702$	3.23195e6	−	2.34815e6i	0.247527	−	0.179839i
$703$	−2.11721e6			−0.161575
$704$	7.34377e6	+	1.50930e7i	0.558454	+	1.14774i
$705$	−1.61975e7			−1.22737
$706$	−3.28596e7	+	2.38739e7i	−2.48113	+	1.80265i
$707$	−707003.	−	2.17593e6i	−0.0531952	−	0.163718i
$708$	3.73605e6	−	1.14984e7i	0.280110	−	0.862091i
$709$	5.35574e6	+	3.89117e6i	0.400132	+	0.290713i	0.769595	−	0.638533i	$-0.220458\pi$
$709$	5.35574e6	+	3.89117e6i	0.400132	+	0.290713i	−0.369463	+	0.929246i	$0.620458\pi$
$710$	−2.99345e7	−	2.17487e7i	−2.22857	−	1.61915i
$711$	−436686.	+	1.34398e6i	−0.0323963	+	0.0997055i
$712$	−561791.	−	1.72901e6i	−0.0415312	−	0.127820i
$713$	−7.13500e6	+	5.18388e6i	−0.525618	+	0.381884i
$714$	5.29265e6			0.388533
$715$	2.37438e6	−	1.33920e7i	0.173694	−	0.979673i
$716$	2.20087e7			1.60440
$717$	3.51354e6	−	2.55274e6i	0.255239	−	0.185442i
$718$	4.55123e6	+	1.40072e7i	0.329471	+	1.01401i
$719$	5.35083e6	−	1.64682e7i	0.386010	−	1.18802i	−0.549735	−	0.835339i	$-0.685271\pi$
$719$	5.35083e6	−	1.64682e7i	0.386010	−	1.18802i	0.935745	−	0.352678i	$-0.114729\pi$
$720$	2.75713e6	+	2.00318e6i	0.198210	+	0.144008i
$721$	−1.30284e6	−	946569.i	−0.0933369	−	0.0678132i
$722$	347491.	−	1.06947e6i	0.0248085	−	0.0763528i
$723$	1.31334e6	+	4.04205e6i	0.0934399	+	0.287578i
$724$	3.06851e7	−	2.22941e7i	2.17561	−	1.58068i
$725$	−3.16061e6			−0.223319
$726$	−7.77684e6	−	1.15766e7i	−0.547597	−	0.815154i
$727$	1.02515e7			0.719366			0.359683	−	0.933075i	$-0.382885\pi$
$727$	1.02515e7			0.719366			0.359683	+	0.933075i	$0.382885\pi$
$728$	−3.86886e6	+	2.81089e6i	−0.270554	+	0.196569i
$729$	164224.	+	505430.i	0.0114451	+	0.0352243i
$730$	−7.80627e6	+	2.40252e7i	−0.542171	+	1.66863i
$731$	1.02936e7	+	7.47876e6i	0.712484	+	0.517650i
$732$	1.10254e7	+	8.01044e6i	0.760532	+	0.552559i
$733$	−885952.	+	2.72668e6i	−0.0609046	+	0.187445i	−0.976880	−	0.213790i	$-0.931419\pi$
$733$	−885952.	+	2.72668e6i	−0.0609046	+	0.187445i	0.915975	+	0.401235i	$0.131419\pi$
$734$	−4.56887e6	−	1.40615e7i	−0.313018	−	0.963369i
$735$	6.87788e6	−	4.99707e6i	0.469609	−	0.341191i
$736$	2.42394e6			0.164940
$737$	−1.08898e6	+	6.14210e6i	−0.0738503	+	0.416532i
$738$	4.55162e6			0.307627
$739$	−304632.	+	221328.i	−0.0205194	+	0.0149082i	−0.597998	−	0.801498i	$-0.704037\pi$
$739$	−304632.	+	221328.i	−0.0205194	+	0.0149082i	0.577478	+	0.816406i	$0.304037\pi$
$740$	1.46456e6	+	4.50745e6i	0.0983167	+	0.302588i
$741$	−2.55066e6	+	7.85014e6i	−0.170651	+	0.525208i
$742$	−1.70000e6	−	1.23512e6i	−0.113355	−	0.0823569i
$743$	−1.37323e7	−	9.97708e6i	−0.912579	−	0.663028i	0.0290867	−	0.999577i	$-0.490740\pi$
$743$	−1.37323e7	−	9.97708e6i	−0.912579	−	0.663028i	−0.941666	+	0.336549i	$0.890740\pi$
$744$	5.55166e6	−	1.70862e7i	0.367697	−	1.13166i
$745$	−3.79888e6	−	1.16918e7i	−0.250764	−	0.771772i
$746$	−1.11235e7	+	8.08169e6i	−0.731803	+	0.531686i
$747$	9.63047e6			0.631460
$748$	2.12879e7	+	4.37511e7i	1.39116	+	2.85914i
$749$	−3.76422e6			−0.245172
$750$	1.12936e7	−	8.20532e6i	0.733130	−	0.532650i
$751$	−8.33469e6	−	2.56515e7i	−0.539250	−	1.65964i	−0.734283	−	0.678843i	$-0.762482\pi$
$751$	−8.33469e6	−	2.56515e7i	−0.539250	−	1.65964i	0.195034	−	0.980797i	$-0.437518\pi$
$752$	−6.60834e6	+	2.03384e7i	−0.426136	+	1.31151i
$753$	2.66865e6	+	1.93889e6i	0.171516	+	0.124614i
$754$	3.36930e7	+	2.44794e7i	2.15830	+	1.56810i
$755$	−1.85051e6	+	5.69528e6i	−0.118147	+	0.363620i
$756$	−416726.	−	1.28255e6i	−0.0265183	−	0.0816149i
$757$	9.92063e6	−	7.20776e6i	0.629216	−	0.457152i	−0.226913	−	0.973915i	$-0.572863\pi$
$757$	9.92063e6	−	7.20776e6i	0.629216	−	0.457152i	0.856128	+	0.516763i	$0.172863\pi$
$758$	2.75775e7			1.74334
$759$	−4.34543e6	+	606538.i	−0.273796	+	0.0382167i
$760$	−2.63460e7			−1.65455
$761$	1.38569e7	−	1.00676e7i	0.867371	−	0.630182i	−0.0625089	−	0.998044i	$-0.519910\pi$
$761$	1.38569e7	−	1.00676e7i	0.867371	−	0.630182i	0.929880	+	0.367862i	$0.119910\pi$
$762$	6.27864e6	+	1.93237e7i	0.391722	+	1.20560i
$763$	−1.26922e6	+	3.90625e6i	−0.0789269	+	0.242912i
$764$	−2.39551e7	−	1.74044e7i	−1.48479	−	1.07876i
$765$	−7.80445e6	−	5.67027e6i	−0.482157	−	0.350308i
$766$	8.46482e6	−	2.60520e7i	0.521250	−	1.60424i
$767$	−3.90297e6	−	1.20121e7i	−0.239556	−	0.737277i
$768$	−1.39743e7	+	1.01529e7i	−0.854924	+	0.621138i
$769$	−1.67008e7			−1.01841			−0.509203	−	0.860647i	$-0.670060\pi$
$769$	−1.67008e7			−1.01841			−0.509203	+	0.860647i	$0.670060\pi$
$770$	−6.19214e6	−	3.29990e6i	−0.376369	−	0.200574i
$771$	−1.51507e7			−0.917904
$772$	6.61615e6	−	4.80691e6i	0.399542	−	0.290284i
$773$	−4.41732e6	−	1.35951e7i	−0.265895	−	0.818341i	−0.991486	−	0.130215i	$-0.958433\pi$
$773$	−4.41732e6	−	1.35951e7i	−0.265895	−	0.818341i	0.725591	−	0.688127i	$-0.241567\pi$
$774$	1.53103e6	−	4.71204e6i	0.0918613	−	0.282720i
$775$	2.44267e6	+	1.77470e6i	0.146087	+	0.106138i
$776$	−2.83755e7	−	2.06160e7i	−1.69157	−	1.22899i
$777$	111667.	−	343676.i	0.00663548	−	0.0204219i
$778$	1.40170e7	+	4.31398e7i	0.830244	+	2.55523i
$779$	−7.60829e6	+	5.52775e6i	−0.449204	+	0.326366i
$780$	1.84770e7			1.08742
$781$	−1.86732e7	+	1.79985e7i	−1.09545	+	1.05587i
$782$	2.33934e7			1.36797
$783$	−4.48216e6	+	3.25648e6i	−0.261266	+	0.189821i
$784$	−3.46849e6	−	1.06749e7i	−0.201535	−	0.620261i
$785$	−1.47580e6	+	4.54205e6i	−0.0854779	+	0.263074i
$786$	1.43492e7	+	1.04253e7i	0.828462	+	0.601913i
$787$	−2.27948e7	−	1.65614e7i	−1.31190	−	0.953148i	−0.999995	−	0.00303342i	$-0.999034\pi$
$787$	−2.27948e7	−	1.65614e7i	−1.31190	−	0.953148i	−0.311901	−	0.950115i	$-0.600966\pi$
$788$	−3.31042e6	+	1.01884e7i	−0.189919	+	0.584510i
$789$	4.23683e6	+	1.30396e7i	0.242297	+	0.745714i
$790$	−8.08101e6	+	5.87120e6i	−0.460678	+	0.334702i
$791$	1.02833e6			0.0584374
$792$	6.43510e6	−	6.20260e6i	0.364537	−	0.351367i
$793$	1.42371e7			0.803965
$794$	−2.81587e7	+	2.04585e7i	−1.58512	+	1.15165i
$795$	1.18355e6	+	3.64258e6i	0.0664152	+	0.204405i
$796$	8.10630e6	−	2.49486e7i	0.453461	−	1.39561i
$797$	−6.56832e6	−	4.77217e6i	−0.366276	−	0.266115i	0.389389	−	0.921073i	$-0.372686\pi$
$797$	−6.56832e6	−	4.77217e6i	−0.366276	−	0.266115i	−0.755665	+	0.654958i	$0.772686\pi$
$798$	3.44497e6	+	2.50292e6i	0.191504	+	0.139136i
$799$	1.87058e7	−	5.75706e7i	1.03660	−	3.19032i
$800$	−256434.	−	789222.i	−0.0141661	−	0.0435988i
$801$	433287.	−	314801.i	0.0238613	−	0.0173362i
$802$	−3.35350e7			−1.84103
$803$	1.56262e7	+	8.32749e6i	0.855195	+	0.455749i
$804$	−8.47428e6			−0.462341
$805$	−1.78586e6	+	1.29750e6i	−0.0971309	+	0.0705698i
$806$	−1.22942e7	−	3.78377e7i	−0.666596	−	2.05157i
$807$	191052.	−	587998.i	0.0103269	−	0.0317828i
$808$	1.66656e7	+	1.21082e7i	0.898031	+	0.652458i
$809$	−1.43065e7	−	1.03943e7i	−0.768534	−	0.558372i	0.132982	−	0.991118i	$-0.457545\pi$
$809$	−1.43065e7	−	1.03943e7i	−0.768534	−	0.558372i	−0.901516	+	0.432746i	$0.857545\pi$
$810$	−1.16080e6	+	3.57258e6i	−0.0621650	+	0.191324i
$811$	3.19470e6	+	9.83229e6i	0.170561	+	0.524931i	0.999403	−	0.0345508i	$-0.0110001\pi$
$811$	3.19470e6	+	9.83229e6i	0.170561	+	0.524931i	−0.828842	+	0.559482i	$0.811000\pi$
$812$	1.13737e7	−	8.26345e6i	0.605355	−	0.439816i
$813$	−1.06921e7			−0.567329
$814$	5.02813e6	−	701830.i	0.265978	−	0.0371254i
$815$	1.13551e6			0.0598821
$816$	−1.03039e7	+	7.48626e6i	−0.541724	+	0.393586i
$817$	3.16336e6	+	9.73582e6i	0.165803	+	0.510290i
$818$	9.87646e6	−	3.03966e7i	0.516081	−	1.58833i
$819$	−1.13975e6	−	828074.i	−0.0593743	−	0.0431379i
$820$	1.70313e7	+	1.23740e7i	0.884532	+	0.642650i
$821$	−4.38222e6	+	1.34871e7i	−0.226901	+	0.698330i	0.771192	+	0.636603i	$0.219661\pi$
$821$	−4.38222e6	+	1.34871e7i	−0.226901	+	0.698330i	−0.998093	+	0.0617272i	$0.980339\pi$
$822$	1.29048e6	+	3.97168e6i	0.0666148	+	0.205019i
$823$	−6.66919e6	+	4.84545e6i	−0.343221	+	0.249364i	−0.746019	−	0.665924i	$-0.768037\pi$
$823$	−6.66919e6	+	4.84545e6i	−0.343221	+	0.249364i	0.402799	+	0.915289i	$0.368037\pi$
$824$	1.44996e7			0.743942
$825$	657198.	+	1.35068e6i	0.0336172	+	0.0690904i
$826$	−6.51583e6			−0.332292
$827$	375203.	−	272601.i	0.0190767	−	0.0138600i	−0.578206	−	0.815891i	$-0.696247\pi$
$827$	375203.	−	272601.i	0.0190767	−	0.0138600i	0.597283	+	0.802031i	$0.296247\pi$
$828$	−1.84192e6	−	5.66883e6i	−0.0933671	−	0.287354i
$829$	1.05752e7	−	3.25472e7i	0.534445	−	1.64485i	−0.210401	−	0.977615i	$-0.567477\pi$
$829$	1.05752e7	−	3.25472e7i	0.534445	−	1.64485i	0.744846	−	0.667237i	$-0.232523\pi$
$830$	5.50714e7	+	4.00117e7i	2.77480	+	2.01601i
$831$	−1.09877e7	−	7.98300e6i	−0.551954	−	0.401018i
$832$	−7.36117e6	+	2.26553e7i	−0.368670	+	1.13465i
$833$	9.81805e6	+	3.02168e7i	0.490244	+	1.50882i
$834$	8.20814e6	−	5.96356e6i	0.408629	−	0.296887i
$835$	2.61060e7			1.29576
$836$	−6.83389e6	+	3.85446e7i	−0.338183	+	1.90743i
$837$	5.29256e6			0.261127
$838$	3.96654e7	−	2.88186e7i	1.95120	−	1.41763i
$839$	−2.19708e6	−	6.76193e6i	−0.107756	−	0.331639i	0.882611	−	0.470103i	$-0.155783\pi$
$839$	−2.19708e6	−	6.76193e6i	−0.107756	−	0.331639i	−0.990367	+	0.138464i	$0.955783\pi$
$840$	1.38956e6	−	4.27661e6i	0.0679482	−	0.209123i
$841$	−3.01325e7	−	2.18926e7i	−1.46908	−	1.06735i
$842$	−2.48981e7	−	1.80895e7i	−1.21028	−	0.879320i
$843$	−3.91479e6	+	1.20485e7i	−0.189732	+	0.583934i
$844$	−2.51822e6	−	7.75029e6i	−0.121685	−	0.374508i
$845$	−2.25825e6	+	1.64072e6i	−0.108800	+	0.0790481i
$846$	−2.35714e7			−1.13230
$847$	−3.03519e6	+	3.86982e6i	−0.145371	+	0.185346i
$848$	5.05667e6			0.241476
$849$	2.34579e6	−	1.70432e6i	0.111691	−	0.0811486i
$850$	−2.47483e6	−	7.61676e6i	−0.117489	−	0.361595i
$851$	493565.	−	1.51904e6i	0.0233626	−	0.0719026i
$852$	−2.85044e7	−	2.07097e7i	−1.34528	−	0.977405i
$853$	1.00383e7	+	7.29328e6i	0.472378	+	0.343203i	0.798367	−	0.602171i	$-0.205697\pi$
$853$	1.00383e7	+	7.29328e6i	0.472378	+	0.343203i	−0.325989	+	0.945373i	$0.605697\pi$
$854$	2.26965e6	−	6.98527e6i	0.106491	−	0.327747i
$855$	−2.39840e6	−	7.38152e6i	−0.112204	−	0.345327i
$856$	2.74193e7	−	1.99213e7i	1.27900	−	0.929251i
$857$	−9.60549e6			−0.446753			−0.223376	−	0.974732i	$-0.571708\pi$
$857$	−9.60549e6			−0.446753			−0.223376	+	0.974732i	$0.571708\pi$
$858$	3.45531e6	−	1.94887e7i	0.160239	−	0.903785i
$859$	1.35157e7			0.624964			0.312482	−	0.949924i	$-0.398840\pi$
$859$	1.35157e7			0.624964			0.312482	+	0.949924i	$0.398840\pi$
$860$	1.85389e7	−	1.34693e7i	0.854749	−	0.621012i
$861$	−496011.	−	1.52657e6i	−0.0228026	−	0.0701791i
$862$	−4.87161e6	+	1.49933e7i	−0.223308	+	0.687272i
$863$	−2.75417e7	−	2.00102e7i	−1.25882	−	0.914588i	−0.260123	−	0.965575i	$-0.583763\pi$
$863$	−2.75417e7	−	2.00102e7i	−1.25882	−	0.914588i	−0.998699	+	0.0509875i	$0.983763\pi$
$864$	−1.17682e6	−	855007.i	−0.0536321	−	0.0389660i
$865$	−7.45685e6	+	2.29498e7i	−0.338856	+	1.04289i
$866$	−669356.	−	2.06007e6i	−0.0303293	−	0.0933440i
$867$	1.88286e7	−	1.36798e7i	0.850686	−	0.618060i
$868$	−1.34301e7			−0.605033
$869$	3.06327e6	+	6.29568e6i	0.137606	+	0.282809i
$870$	−3.91607e7			−1.75409
$871$	−7.16215e6	+	5.20361e6i	−0.319888	+	0.232412i
$872$	−1.14277e7	−	3.51710e7i	−0.508943	−	1.56636i
$873$	3.19296e6	−	9.82691e6i	0.141794	−	0.436397i
$874$	1.52267e7	+	1.10628e7i	0.674258	+	0.489877i
$875$	−3.98270e6	−	2.89360e6i	−0.175856	−	0.127767i
$876$	−7.43334e6	+	2.28775e7i	−0.327283	+	1.00727i
$877$	−1.19668e6	−	3.68301e6i	−0.0525387	−	0.161698i	0.921344	−	0.388747i	$-0.127092\pi$
$877$	−1.19668e6	−	3.68301e6i	−0.0525387	−	0.161698i	−0.973883	+	0.227050i	$0.927092\pi$
$878$	−930065.	+	675732.i	−0.0407171	+	0.0295827i
$879$	1.27392e7			0.556123
$880$	1.67227e7	−	2.33417e6i	0.727948	−	0.101607i
$881$	2.91447e7			1.26509			0.632543	−	0.774525i	$-0.282011\pi$
$881$	2.91447e7			1.26509			0.632543	+	0.774525i	$0.282011\pi$
$882$	1.00090e7	−	7.27198e6i	0.433232	−	0.314761i
$883$	1.18195e7	+	3.63765e7i	0.510147	+	1.57007i	0.791941	+	0.610597i	$0.209070\pi$
$883$	1.18195e7	+	3.63765e7i	0.510147	+	1.57007i	−0.281794	+	0.959475i	$0.590930\pi$
$884$	−2.13383e7	+	6.56726e7i	−0.918395	+	2.82653i
$885$	9.60814e6	+	6.98072e6i	0.412364	+	0.299600i
$886$	7.24196e6	+	5.26159e6i	0.309936	+	0.225182i
$887$	−7.81116e6	+	2.40403e7i	−0.333354	+	1.02596i	0.634172	+	0.773192i	$0.281341\pi$
$887$	−7.81116e6	+	2.40403e7i	−0.333354	+	1.02596i	−0.967527	+	0.252768i	$0.918659\pi$
$888$	1.00542e6	+	3.09437e6i	0.0427874	+	0.131686i
$889$	5.79674e6	−	4.21158e6i	0.245997	−	0.178727i
$890$	3.78564e6			0.160200
$891$	2.32364e6	+	1.23831e6i	0.0980561	+	0.0522559i
$892$	−4.62092e7			−1.94454
$893$	3.94010e7	−	2.86265e7i	1.65340	−	1.20127i
$894$	−5.52832e6	−	1.70144e7i	−0.231339	−	0.711989i
$895$	−6.68080e6	+	2.05614e7i	−0.278786	+	0.858015i
$896$	8.36462e6	+	6.07725e6i	0.348078	+	0.252893i
$897$	−5.03765e6	−	3.66006e6i	−0.209048	−	0.151882i
$898$	−2.02410e7	+	6.22955e7i	−0.837610	+	2.57790i
$899$	1.70499e7	+	5.24743e7i	0.703596	+	2.16545i
$900$	−1.65088e6	+	1.19944e6i	−0.0679376	+	0.0493595i
$901$	−1.43136e7			−0.587404
$902$	1.62365e7	−	1.56498e7i	0.664469	−	0.640463i
$903$	−1.74721e6			−0.0713060
$904$	−7.49054e6	+	5.44219e6i	−0.304854	+	0.221489i
$905$	1.15134e7	+	3.54346e7i	0.467286	+	1.43816i
$906$	−2.69295e6	+	8.28805e6i	−0.108995	+	0.335453i
$907$	3.43290e7	+	2.49415e7i	1.38562	+	1.00671i	0.996330	+	0.0855944i	$0.0272789\pi$
$907$	3.43290e7	+	2.49415e7i	1.38562	+	1.00671i	0.389288	+	0.921116i	$0.372721\pi$
$908$	5.31593e6	+	3.86225e6i	0.213976	+	0.155462i
$909$	−1.87530e6	+	5.77157e6i	−0.0752767	+	0.231678i
$910$	−3.07719e6	−	9.47061e6i	−0.123183	−	0.379118i
$911$	3.70665e6	−	2.69304e6i	0.147974	−	0.107509i	−0.511335	−	0.859381i	$-0.670849\pi$
$911$	3.70665e6	−	2.69304e6i	0.147974	−	0.107509i	0.659309	+	0.751872i	$0.270849\pi$
$912$	−1.02471e7			−0.407956
$913$	3.43537e7	−	3.31125e7i	1.36394	−	1.31466i
$914$	−8.01344e7			−3.17288
$915$	−1.08304e7	+	7.86878e6i	−0.427655	+	0.310710i
$916$	−9.79226e6	−	3.01375e7i	−0.385606	−	1.18677i
$917$	1.93284e6	−	5.94868e6i	0.0759056	−	0.233613i
$918$	−1.13574e7	−	8.25165e6i	−0.444808	−	0.323172i
$919$	−1.49737e7	−	1.08790e7i	−0.584843	−	0.424913i	0.255624	−	0.966776i	$-0.417719\pi$
$919$	−1.49737e7	−	1.08790e7i	−0.584843	−	0.424913i	−0.840467	+	0.541863i	$0.817719\pi$
$920$	6.14180e6	−	1.89025e7i	0.239236	−	0.736292i
$921$	−1.77300e6	−	5.45673e6i	−0.0688746	−	0.211974i
$922$	1.28121e6	−	930857.i	0.0496357	−	0.0360625i
$923$	−3.68076e7			−1.42211
$924$	−5.89633e6	−	3.14226e6i	−0.227197	−	0.121077i
$925$	−546806.			−0.0210126
$926$	1.89346e6	−	1.37568e6i	0.0725651	−	0.0527216i
$927$	1.31997e6	+	4.06246e6i	0.0504505	+	0.155271i
$928$	4.68607e6	−	1.44222e7i	0.178623	−	0.549746i
$929$	−3.39555e7	−	2.46701e7i	−1.29084	−	0.937847i	−0.291014	−	0.956719i	$-0.593993\pi$
$929$	−3.39555e7	−	2.46701e7i	−1.29084	−	0.937847i	−0.999822	+	0.0188716i	$0.993993\pi$
$930$	3.02653e7	+	2.19890e7i	1.14746	+	0.833677i
$931$	−7.89914e6	+	2.43111e7i	−0.298680	+	0.919242i
$932$	4.10620e6	+	1.26376e7i	0.154846	+	0.476567i
$933$	−8.13304e6	+	5.90900e6i	−0.305878	+	0.222234i
$934$	3.13993e7			1.17775
$935$	−4.73360e7	+	6.60719e6i	−1.77077	+	0.247166i
$936$	1.26845e7			0.473243
$937$	−6.05508e6	+	4.39927e6i	−0.225305	+	0.163694i	−0.694711	−	0.719289i	$-0.744468\pi$
$937$	−6.05508e6	+	4.39927e6i	−0.225305	+	0.163694i	0.469406	+	0.882982i	$0.344468\pi$
$938$	1.41132e6	+	4.34359e6i	0.0523742	+	0.161191i
$939$	8.29729e6	−	2.55364e7i	0.307095	−	0.945140i
$940$	−8.81999e7	−	6.40810e7i	−3.25573	−	2.36543i
$941$	3.34949e7	+	2.43355e7i	1.23312	+	0.895912i	0.997120	−	0.0758412i	$-0.0241642\pi$
$941$	3.34949e7	+	2.43355e7i	1.23312	+	0.895912i	0.235998	+	0.971754i	$0.424164\pi$
$942$	−2.14766e6	+	6.60982e6i	−0.0788566	+	0.242696i
$943$	−2.19236e6	−	6.74738e6i	−0.0802845	−	0.247090i
$944$	1.26853e7	−	9.21641e6i	0.463309	−	0.336614i
$945$	1.32471e6			0.0482547
$946$	−1.07399e7	−	2.20729e7i	−0.390188	−	0.801920i
$947$	−4.38933e7			−1.59046			−0.795231	−	0.606307i	$-0.792650\pi$
$947$	−4.38933e7			−1.59046			−0.795231	+	0.606307i	$0.792650\pi$
$948$	−7.69496e6	+	5.59071e6i	−0.278090	+	0.202044i
$949$	7.76545e6	+	2.38996e7i	0.279899	+	0.861440i
$950$	1.99114e6	−	6.12809e6i	0.0715800	−	0.220301i
$951$	1.42414e7	+	1.03470e7i	0.510623	+	0.370990i
$952$	1.35956e7	+	9.87776e6i	0.486189	+	0.353237i
$953$	872998.	−	2.68681e6i	0.0311373	−	0.0958308i	−0.934280	−	0.356540i	$-0.883956\pi$
$953$	872998.	−	2.68681e6i	0.0311373	−	0.0958308i	0.965417	+	0.260709i	$0.0839564\pi$
$954$	1.72235e6	+	5.30086e6i	0.0612705	+	0.188571i
$955$	2.35315e7	−	1.70966e7i	0.834912	−	0.606599i
$956$	2.92314e7			1.03444
$957$	−4.79192e6	+	2.70275e7i	−0.169134	+	0.953951i
$958$	−1.43340e7			−0.504609
$959$	1.19143e6	−	865625.i	0.0418333	−	0.0303937i
$960$	−6.92174e6	−	2.13029e7i	−0.242403	−	0.746038i
$961$	7.44076e6	−	2.29003e7i	0.259901	−	0.799894i
$962$	5.82910e6	+	4.23509e6i	0.203079	+	0.147545i
$963$	8.07759e6	+	5.86872e6i	0.280683	+	0.203928i
$964$	−8.83975e6	+	2.72059e7i	−0.306371	+	0.942912i
$965$	2.48245e6	+	7.64021e6i	0.0858150	+	0.264111i
$966$	−2.59887e6	+	1.88819e6i	−0.0896070	+	0.0651033i
$967$	−1.10642e7			−0.380499			−0.190249	−	0.981736i	$-0.560930\pi$
$967$	−1.10642e7			−0.380499			−0.190249	+	0.981736i	$0.560930\pi$
$968$	1.62875e6	−	4.42516e7i	0.0558682	−	1.51789i
$969$	2.90058e7			0.992375
$970$	5.90867e7	−	4.29290e7i	2.01632	−	1.46494i
$971$	−4.55825e6	−	1.40289e7i	−0.155149	−	0.477501i	0.843027	−	0.537872i	$-0.180772\pi$
$971$	−4.55825e6	−	1.40289e7i	−0.155149	−	0.477501i	−0.998176	+	0.0603711i	$0.980772\pi$
$972$	−1.10535e6	+	3.40191e6i	−0.0375261	+	0.115493i
$973$	−2.89459e6	−	2.10305e6i	−0.0980179	−	0.0712142i
$974$	3.91456e7	+	2.84409e7i	1.32216	+	0.960608i
$975$	−658755.	+	2.02744e6i	−0.0221928	+	0.0683024i
$976$	5.46176e6	+	1.68096e7i	0.183530	+	0.564848i
$977$	1.50923e7	−	1.09652e7i	0.505848	−	0.367520i	−0.305398	−	0.952225i	$-0.598790\pi$
$977$	1.50923e7	−	1.09652e7i	0.505848	−	0.367520i	0.811246	+	0.584705i	$0.198790\pi$
$978$	1.65245e6			0.0552435
$979$	463231.	−	2.61272e6i	0.0154469	−	0.0871238i
$980$	5.72214e7			1.90324
$981$	8.81375e6	−	6.40357e6i	0.292407	−	0.212446i
$982$	−1.32399e7	−	4.07481e7i	−0.438132	−	1.34843i
$983$	4.42126e6	−	1.36072e7i	0.145936	−	0.449144i	−0.851194	−	0.524851i	$-0.824121\pi$
$983$	4.42126e6	−	1.36072e7i	0.145936	−	0.449144i	0.997130	+	0.0757064i	$0.0241212\pi$
$984$	1.16920e7	+	8.49477e6i	0.384948	+	0.279681i
$985$	−8.51354e6	−	6.18545e6i	−0.279589	−	0.203133i
$986$	4.52251e7	−	1.39188e8i	1.48145	−	4.55943i
$987$	2.56869e6	+	7.90561e6i	0.0839303	+	0.258311i
$988$	−4.49459e7	+	3.26551e7i	−1.46487	+	1.06429i
$989$	−7.72263e6			−0.251058
$990$	8.14283e6	+	1.67353e7i	0.264051	+	0.542681i
$991$	3.51472e7			1.13686			0.568429	−	0.822732i	$-0.307551\pi$
$991$	3.51472e7			1.13686			0.568429	+	0.822732i	$0.307551\pi$
$992$	−1.17198e7	+	8.51492e6i	−0.378129	+	0.274727i
$993$	947838.	+	2.91715e6i	0.0305043	+	0.0938826i
$994$	−5.86782e6	+	1.80593e7i	−0.188370	+	0.579742i
$995$	2.08473e7	+	1.51464e7i	0.667562	+	0.485012i
$996$	5.24405e7	+	3.81003e7i	1.67501	+	1.21697i
$997$	4.13366e6	−	1.27221e7i	0.131703	−	0.405341i	−0.863359	−	0.504589i	$-0.831644\pi$
$997$	4.13366e6	−	1.27221e7i	0.131703	−	0.405341i	0.995063	+	0.0992486i	$0.0316439\pi$
$998$	−2.31169e7	−	7.11466e7i	−0.734689	−	2.26114i
$999$	−775442.	+	563392.i	−0.0245830	+	0.0178606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.6.e.b.25.1	yes	20
3.2	odd	2		99.6.f.b.91.5		20
11.2	odd	10		363.6.a.t.1.1		10
11.4	even	5	inner	33.6.e.b.4.1	✓	20
11.9	even	5		363.6.a.r.1.10		10
33.2	even	10		1089.6.a.bi.1.10		10
33.20	odd	10		1089.6.a.bk.1.1		10
33.26	odd	10		99.6.f.b.37.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.6.e.b.4.1	✓	20	11.4	even	5	inner
33.6.e.b.25.1	yes	20	1.1	even	1	trivial
99.6.f.b.37.5		20	33.26	odd	10
99.6.f.b.91.5		20	3.2	odd	2
363.6.a.r.1.10		10	11.9	even	5
363.6.a.t.1.1		10	11.2	odd	10
1089.6.a.bi.1.10		10	33.2	even	10
1089.6.a.bk.1.1		10	33.20	odd	10

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.78409 + 5.65548i) q^{2} +(-2.78115 - 8.55951i) q^{3} +(18.7192 - 57.6117i) q^{4} +(48.1408 + 34.9763i) q^{5} +(70.0568 + 50.8993i) q^{6} +(9.43666 - 29.0431i) q^{7} +(84.9654 + 261.497i) q^{8} +(-65.5304 + 47.6106i) q^{9} +O(q^{10})\)	\(q+(-7.78409 + 5.65548i) q^{2} +(-2.78115 - 8.55951i) q^{3} +(18.7192 - 57.6117i) q^{4} +(48.1408 + 34.9763i) q^{5} +(70.0568 + 50.8993i) q^{6} +(9.43666 - 29.0431i) q^{7} +(84.9654 + 261.497i) q^{8} +(-65.5304 + 47.6106i) q^{9} -572.540 q^{10} +(-70.0591 + 395.149i) q^{11} -545.189 q^{12} +(-460.773 + 334.771i) q^{13} +(90.7964 + 279.443i) q^{14} +(165.493 - 509.336i) q^{15} +(-572.028 - 415.603i) q^{16} +(1619.20 + 1176.42i) q^{17} +(240.834 - 741.211i) q^{18} +(497.601 + 1531.46i) q^{19} +(2916.20 - 2118.74i) q^{20} -274.839 q^{21} +(-1689.41 - 3472.09i) q^{22} -1214.78 q^{23} +(2001.98 - 1454.52i) q^{24} +(128.514 + 395.526i) q^{25} +(1693.41 - 5211.78i) q^{26} +(589.773 + 428.495i) q^{27} +(-1496.57 - 1087.32i) q^{28} +(-2348.47 + 7227.84i) q^{29} +(1592.32 + 4900.66i) q^{30} +(5873.48 - 4267.33i) q^{31} -1995.37 q^{32} +(3577.13 - 499.298i) q^{33} -19257.3 q^{34} +(1470.11 - 1068.10i) q^{35} +(1516.25 + 4666.55i) q^{36} +(-406.300 + 1250.46i) q^{37} +(-12534.5 - 9106.84i) q^{38} +(4146.96 + 3012.94i) q^{39} +(-5055.89 + 15560.4i) q^{40} +(1804.73 + 5554.40i) q^{41} +(2139.37 - 1554.35i) q^{42} +6357.22 q^{43} +(21453.7 + 11433.1i) q^{44} -4819.93 q^{45} +(9455.97 - 6870.16i) q^{46} +(-9346.16 - 28764.5i) q^{47} +(-1966.46 + 6052.13i) q^{48} +(12842.7 + 9330.77i) q^{49} +(-3237.26 - 2352.01i) q^{50} +(5566.33 - 17131.4i) q^{51} +(10661.4 + 32812.6i) q^{52} +(-5785.79 + 4203.62i) q^{53} -7014.20 q^{54} +(-17193.6 + 16572.4i) q^{55} +8396.45 q^{56} +(11724.6 - 8518.44i) q^{57} +(-22596.2 - 69543.9i) q^{58} +(-6852.76 + 21090.6i) q^{59} +(-26245.8 - 19068.7i) q^{60} +(-20223.1 - 14693.0i) q^{61} +(-21585.9 + 66434.7i) q^{62} +(764.370 + 2352.49i) q^{63} +(33837.0 - 24584.1i) q^{64} -33891.1 q^{65} +(-25020.9 + 24116.9i) q^{66} +15543.8 q^{67} +(98085.7 - 71263.5i) q^{68} +(3378.49 + 10397.9i) q^{69} +(-5402.87 + 16628.3i) q^{70} +(52283.6 + 37986.3i) q^{71} +(-18017.8 - 13090.7i) q^{72} +(13634.4 - 41962.5i) q^{73} +(-3909.28 - 12031.5i) q^{74} +(3028.09 - 2200.04i) q^{75} +97544.6 q^{76} +(10815.2 + 5763.62i) q^{77} -49319.9 q^{78} +(14114.3 - 10254.6i) q^{79} +(-13001.6 - 40014.9i) q^{80} +(2027.46 - 6239.88i) q^{81} +(-45461.0 - 33029.3i) q^{82} +(-96187.9 - 69884.6i) q^{83} +(-5144.76 + 15833.9i) q^{84} +(36802.9 + 113268. i) q^{85} +(-49485.2 + 35953.1i) q^{86} +68398.2 q^{87} +(-109283. + 15253.8i) q^{88} -6612.00 q^{89} +(37518.8 - 27259.0i) q^{90} +(5374.62 + 16541.4i) q^{91} +(-22739.7 + 69985.6i) q^{92} +(-52861.3 - 38406.0i) q^{93} +(235428. + 171049. i) q^{94} +(-29609.9 + 91129.9i) q^{95} +(5549.43 + 17079.4i) q^{96} +(-103201. + 74979.8i) q^{97} -152739. q^{98} +(-14222.3 - 29229.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9}+O(q^{10}) \) 20 * q + 6 * q^2 + 45 * q^3 + 8 * q^4 - 11 * q^5 - 54 * q^6 - 139 * q^7 - 76 * q^8 - 405 * q^9	\( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9} - 424 q^{10} + 2289 q^{11} - 2682 q^{12} - 847 q^{13} + 2022 q^{14} - 396 q^{15} - 7148 q^{16} + 2482 q^{17} + 81 q^{18} + 2958 q^{19} + 8037 q^{20} - 1404 q^{21} + 7441 q^{22} + 8140 q^{23} - 4626 q^{24} - 13120 q^{25} - 13508 q^{26} + 3645 q^{27} + 27819 q^{28} - 20210 q^{29} + 11106 q^{30} + 5540 q^{31} - 4626 q^{32} + 639 q^{33} + 16540 q^{34} - 34101 q^{35} + 648 q^{36} - 25173 q^{37} - 55878 q^{38} + 7623 q^{39} + 22689 q^{40} + 54349 q^{41} + 32292 q^{42} - 21688 q^{43} + 24587 q^{44} - 5346 q^{45} + 44155 q^{46} - 48387 q^{47} - 43083 q^{48} - 78880 q^{49} + 19956 q^{50} + 7317 q^{51} + 109051 q^{52} - 74382 q^{53} + 10206 q^{54} - 47630 q^{55} + 168894 q^{56} + 52983 q^{57} + 1501 q^{58} - 108412 q^{59} - 72333 q^{60} + 16737 q^{61} + 132685 q^{62} - 11259 q^{63} - 157030 q^{64} - 134194 q^{65} - 127539 q^{66} + 20178 q^{67} + 387013 q^{68} + 19305 q^{69} - 411988 q^{70} + 143157 q^{71} + 41634 q^{72} + 164980 q^{73} + 286114 q^{74} - 96255 q^{75} + 46868 q^{76} - 367461 q^{77} - 152658 q^{78} + 369613 q^{79} - 107448 q^{80} - 32805 q^{81} - 184129 q^{82} + 267741 q^{83} + 279819 q^{84} + 379937 q^{85} - 290531 q^{86} + 214920 q^{87} - 740846 q^{88} + 205492 q^{89} + 117126 q^{90} + 394559 q^{91} - 483181 q^{92} - 49860 q^{93} + 561327 q^{94} + 267881 q^{95} + 228564 q^{96} - 300567 q^{97} - 2296174 q^{98} - 115506 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 + 45 * q^3 + 8 * q^4 - 11 * q^5 - 54 * q^6 - 139 * q^7 - 76 * q^8 - 405 * q^9 - 424 * q^10 + 2289 * q^11 - 2682 * q^12 - 847 * q^13 + 2022 * q^14 - 396 * q^15 - 7148 * q^16 + 2482 * q^17 + 81 * q^18 + 2958 * q^19 + 8037 * q^20 - 1404 * q^21 + 7441 * q^22 + 8140 * q^23 - 4626 * q^24 - 13120 * q^25 - 13508 * q^26 + 3645 * q^27 + 27819 * q^28 - 20210 * q^29 + 11106 * q^30 + 5540 * q^31 - 4626 * q^32 + 639 * q^33 + 16540 * q^34 - 34101 * q^35 + 648 * q^36 - 25173 * q^37 - 55878 * q^38 + 7623 * q^39 + 22689 * q^40 + 54349 * q^41 + 32292 * q^42 - 21688 * q^43 + 24587 * q^44 - 5346 * q^45 + 44155 * q^46 - 48387 * q^47 - 43083 * q^48 - 78880 * q^49 + 19956 * q^50 + 7317 * q^51 + 109051 * q^52 - 74382 * q^53 + 10206 * q^54 - 47630 * q^55 + 168894 * q^56 + 52983 * q^57 + 1501 * q^58 - 108412 * q^59 - 72333 * q^60 + 16737 * q^61 + 132685 * q^62 - 11259 * q^63 - 157030 * q^64 - 134194 * q^65 - 127539 * q^66 + 20178 * q^67 + 387013 * q^68 + 19305 * q^69 - 411988 * q^70 + 143157 * q^71 + 41634 * q^72 + 164980 * q^73 + 286114 * q^74 - 96255 * q^75 + 46868 * q^76 - 367461 * q^77 - 152658 * q^78 + 369613 * q^79 - 107448 * q^80 - 32805 * q^81 - 184129 * q^82 + 267741 * q^83 + 279819 * q^84 + 379937 * q^85 - 290531 * q^86 + 214920 * q^87 - 740846 * q^88 + 205492 * q^89 + 117126 * q^90 + 394559 * q^91 - 483181 * q^92 - 49860 * q^93 + 561327 * q^94 + 267881 * q^95 + 228564 * q^96 - 300567 * q^97 - 2296174 * q^98 - 115506 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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