LMFDB - Embedded newform 150.6.g.a.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,6,Mod(31,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("150.31");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	150.g (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:	$24.0575729719$
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} - 10 x^{19} + 67300 x^{18} - 605415 x^{17} + 1505002471 x^{16} - 12026298320 x^{15} + \cdots + 45\!\cdots\!05 $ x^20 - 10x^19 + 67300x^18 - 605415x^17 + 1505002471x^16 - 12026298320x^15 + 15161344295580x^14 - 105918997871590x^13 + 72521519492275041x^12 - 433752716999522710x^11 + 150954604904063839080x^10 - 750799480917962811625x^9 + 100084099910299358028076x^8 - 395836369710607771806480x^7 + 22144208384329171616972475x^6 - 65050346450081546072582845x^5 + 865137734840778899106150416x^4 - 1622318535480468844324766865x^3 + 11299132807307021058314145735x^2 - 10498749516125580450644510315*x + 45940690246932155189634577205
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 5^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			121.3
Root			$0.500000 - 19.6223i$ of defining polynomial
Character	$\chi$	$=$	150.121
Dual form			150.6.g.a.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23607 + 3.80423i) q^{2} +(7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-13.4674 - 54.2552i) q^{5} +(-29.1246 + 21.1603i) q^{6} +11.3383 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +O(q^{10})$	\(q+(-1.23607 + 3.80423i) q^{2} +(7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-13.4674 - 54.2552i) q^{5} +(-29.1246 + 21.1603i) q^{6} +11.3383 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +(223.046 + 15.8303i) q^{10} +(-11.0269 + 33.9372i) q^{11} +(-44.4984 - 136.952i) q^{12} +(18.6085 + 57.2711i) q^{13} +(-14.0149 + 43.1335i) q^{14} +(188.956 - 466.284i) q^{15} +(79.1084 + 243.470i) q^{16} +(-1223.94 + 889.243i) q^{17} -324.000 q^{18} +(-927.800 + 674.086i) q^{19} +(-335.922 + 828.949i) q^{20} +(82.5560 + 59.9805i) q^{21} +(-115.475 - 83.8975i) q^{22} +(-759.105 + 2336.28i) q^{23} +576.000 q^{24} +(-2762.26 + 1461.35i) q^{25} -240.874 q^{26} +(-225.273 + 693.320i) q^{27} +(-146.766 - 106.632i) q^{28} +(-1799.66 - 1307.53i) q^{29} +(1540.29 + 1295.19i) q^{30} +(-811.112 + 589.307i) q^{31} -1024.00 q^{32} +(-259.819 + 188.769i) q^{33} +(-1870.01 - 5755.30i) q^{34} +(-152.697 - 615.163i) q^{35} +(400.486 - 1232.57i) q^{36} +(1916.57 + 5898.58i) q^{37} +(-1417.55 - 4362.78i) q^{38} +(-167.477 + 515.440i) q^{39} +(-2738.29 - 2302.56i) q^{40} +(-1331.60 - 4098.25i) q^{41} +(-330.224 + 239.922i) q^{42} +1302.18 q^{43} +(461.900 - 335.590i) q^{44} +(3842.49 - 2395.49i) q^{45} +(-7949.45 - 5775.61i) q^{46} +(-11273.6 - 8190.72i) q^{47} +(-711.975 + 2191.23i) q^{48} -16678.4 q^{49} +(-2144.96 - 12314.6i) q^{50} -13615.8 q^{51} +(297.736 - 916.338i) q^{52} +(4339.78 + 3153.03i) q^{53} +(-2359.09 - 1713.98i) q^{54} +(1989.78 + 141.221i) q^{55} +(587.065 - 426.528i) q^{56} -10321.4 q^{57} +(7198.63 - 5230.11i) q^{58} +(-7961.61 - 24503.3i) q^{59} +(-6831.09 + 4258.66i) q^{60} +(-15449.1 + 47547.3i) q^{61} +(-1239.27 - 3814.08i) q^{62} +(283.802 + 873.454i) q^{63} +(1265.73 - 3895.53i) q^{64} +(2856.65 - 1780.90i) q^{65} +(-396.968 - 1221.74i) q^{66} +(-26171.3 + 19014.6i) q^{67} +24205.9 q^{68} +(-17886.3 + 12995.1i) q^{69} +(2528.96 + 179.489i) q^{70} +(-43979.2 - 31952.7i) q^{71} +(4193.94 + 3047.08i) q^{72} +(13.6152 - 41.9034i) q^{73} -24808.5 q^{74} +(-27843.1 - 3972.24i) q^{75} +18349.2 q^{76} +(-125.026 + 384.791i) q^{77} +(-1753.84 - 1274.24i) q^{78} +(18627.4 + 13533.6i) q^{79} +(12144.2 - 7570.95i) q^{80} +(-5307.96 + 3856.46i) q^{81} +17236.6 q^{82} +(53570.9 - 38921.6i) q^{83} +(-504.538 - 1552.81i) q^{84} +(64729.3 + 54429.3i) q^{85} +(-1609.58 + 4953.77i) q^{86} +(-6186.67 - 19040.6i) q^{87} +(705.720 + 2171.98i) q^{88} +(-4397.74 + 13534.8i) q^{89} +(4363.42 + 17578.7i) q^{90} +(210.989 + 649.358i) q^{91} +(31797.8 - 23102.4i) q^{92} -9023.31 q^{93} +(45094.2 - 32762.9i) q^{94} +(49067.7 + 41259.8i) q^{95} +(-7455.90 - 5417.03i) q^{96} +(-3815.08 - 2771.82i) q^{97} +(20615.7 - 63448.6i) q^{98} -2890.38 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} + 45 q^{3} - 80 q^{4} - 55 q^{5} - 180 q^{6} + 180 q^{7} + 320 q^{8} - 405 q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 + 45 * q^3 - 80 * q^4 - 55 * q^5 - 180 * q^6 + 180 * q^7 + 320 * q^8 - 405 * q^9	\( 20 q + 20 q^{2} + 45 q^{3} - 80 q^{4} - 55 q^{5} - 180 q^{6} + 180 q^{7} + 320 q^{8} - 405 q^{9} + 220 q^{10} + 380 q^{11} + 720 q^{12} - 230 q^{13} - 920 q^{14} - 630 q^{15} - 1280 q^{16} + 2870 q^{17} - 6480 q^{18} + 1560 q^{19} + 1120 q^{20} + 2880 q^{21} - 720 q^{22} + 760 q^{23} + 11520 q^{24} + 1725 q^{25} + 7320 q^{26} + 3645 q^{27} - 5120 q^{28} + 12000 q^{29} + 5220 q^{30} - 1710 q^{31} - 20480 q^{32} - 1620 q^{33} + 20620 q^{34} - 22440 q^{35} - 6480 q^{36} - 5595 q^{37} - 5240 q^{38} + 2070 q^{39} - 9280 q^{40} - 2820 q^{41} - 11520 q^{42} + 66020 q^{43} + 2880 q^{44} - 8505 q^{45} + 21960 q^{46} - 19630 q^{47} + 11520 q^{48} - 61780 q^{49} + 100 q^{50} - 41130 q^{51} - 3680 q^{52} + 62735 q^{53} - 14580 q^{54} + 66590 q^{55} + 20480 q^{56} + 51660 q^{57} - 48000 q^{58} + 105100 q^{59} + 15120 q^{60} + 34790 q^{61} - 28560 q^{62} + 18630 q^{63} - 20480 q^{64} - 44345 q^{65} + 13680 q^{66} - 19470 q^{67} + 73120 q^{68} + 49410 q^{69} - 81240 q^{70} - 111720 q^{71} + 25920 q^{72} - 198830 q^{73} - 104120 q^{74} + 60975 q^{75} - 91840 q^{76} + 144740 q^{77} + 41220 q^{78} + 71210 q^{79} - 26880 q^{80} - 32805 q^{81} + 166680 q^{82} - 288690 q^{83} - 33120 q^{84} + 338735 q^{85} + 39920 q^{86} + 108225 q^{87} - 24320 q^{88} + 114225 q^{89} + 17820 q^{90} - 155800 q^{91} - 87840 q^{92} + 97740 q^{93} + 78520 q^{94} - 416900 q^{95} - 46080 q^{96} - 446970 q^{97} - 123380 q^{98} - 90720 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 + 45 * q^3 - 80 * q^4 - 55 * q^5 - 180 * q^6 + 180 * q^7 + 320 * q^8 - 405 * q^9 + 220 * q^10 + 380 * q^11 + 720 * q^12 - 230 * q^13 - 920 * q^14 - 630 * q^15 - 1280 * q^16 + 2870 * q^17 - 6480 * q^18 + 1560 * q^19 + 1120 * q^20 + 2880 * q^21 - 720 * q^22 + 760 * q^23 + 11520 * q^24 + 1725 * q^25 + 7320 * q^26 + 3645 * q^27 - 5120 * q^28 + 12000 * q^29 + 5220 * q^30 - 1710 * q^31 - 20480 * q^32 - 1620 * q^33 + 20620 * q^34 - 22440 * q^35 - 6480 * q^36 - 5595 * q^37 - 5240 * q^38 + 2070 * q^39 - 9280 * q^40 - 2820 * q^41 - 11520 * q^42 + 66020 * q^43 + 2880 * q^44 - 8505 * q^45 + 21960 * q^46 - 19630 * q^47 + 11520 * q^48 - 61780 * q^49 + 100 * q^50 - 41130 * q^51 - 3680 * q^52 + 62735 * q^53 - 14580 * q^54 + 66590 * q^55 + 20480 * q^56 + 51660 * q^57 - 48000 * q^58 + 105100 * q^59 + 15120 * q^60 + 34790 * q^61 - 28560 * q^62 + 18630 * q^63 - 20480 * q^64 - 44345 * q^65 + 13680 * q^66 - 19470 * q^67 + 73120 * q^68 + 49410 * q^69 - 81240 * q^70 - 111720 * q^71 + 25920 * q^72 - 198830 * q^73 - 104120 * q^74 + 60975 * q^75 - 91840 * q^76 + 144740 * q^77 + 41220 * q^78 + 71210 * q^79 - 26880 * q^80 - 32805 * q^81 + 166680 * q^82 - 288690 * q^83 - 33120 * q^84 + 338735 * q^85 + 39920 * q^86 + 108225 * q^87 - 24320 * q^88 + 114225 * q^89 + 17820 * q^90 - 155800 * q^91 - 87840 * q^92 + 97740 * q^93 + 78520 * q^94 - 416900 * q^95 - 46080 * q^96 - 446970 * q^97 - 123380 * q^98 - 90720 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−1.23607	+	3.80423i	−0.218508	+	0.672499i
$2$	−1.23607	+	3.80423i	−0.218508	+	0.672499i
$3$	7.28115	+	5.29007i	0.467086	+	0.339358i
$3$	7.28115	+	5.29007i	0.467086	+	0.339358i
$4$	−12.9443	−	9.40456i	−0.404508	−	0.293893i
$5$	−13.4674	−	54.2552i	−0.240911	−	0.970547i
$5$	−13.4674	−	54.2552i	−0.240911	−	0.970547i
$6$	−29.1246	+	21.1603i	−0.330280	+	0.239962i
$7$	11.3383			0.0874588			0.0437294	−	0.999043i	$-0.486076\pi$
$7$	11.3383			0.0874588			0.0437294	+	0.999043i	$0.486076\pi$
$8$	51.7771	−	37.6183i	0.286031	−	0.207813i
$9$	25.0304	+	77.0356i	0.103006	+	0.317019i
$10$	223.046	+	15.8303i	0.705333	+	0.0500597i
$11$	−11.0269	+	33.9372i	−0.0274771	+	0.0845658i	−0.963855	−	0.266429i	$-0.914156\pi$
$11$	−11.0269	+	33.9372i	−0.0274771	+	0.0845658i	0.936378	+	0.350994i	$0.114156\pi$
$12$	−44.4984	−	136.952i	−0.0892055	−	0.274546i
$13$	18.6085	+	57.2711i	0.0305389	+	0.0939890i	0.965164	−	0.261645i	$-0.0842650\pi$
$13$	18.6085	+	57.2711i	0.0305389	+	0.0939890i	−0.934625	+	0.355634i	$0.884265\pi$
$14$	−14.0149	+	43.1335i	−0.0191104	+	0.0588159i
$15$	188.956	−	466.284i	0.216836	−	0.535084i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	−1223.94	+	889.243i	−1.02716	+	0.746274i	−0.967738	−	0.251959i	$-0.918925\pi$
$17$	−1223.94	+	889.243i	−1.02716	+	0.746274i	−0.0594199	+	0.998233i	$0.518925\pi$
$18$	−324.000			−0.235702
$19$	−927.800	+	674.086i	−0.589617	+	0.428382i	−0.842178	−	0.539199i	$-0.818727\pi$
$19$	−927.800	+	674.086i	−0.589617	+	0.428382i	0.252561	+	0.967581i	$0.418727\pi$
$20$	−335.922	+	828.949i	−0.187786	+	0.463397i
$21$	82.5560	+	59.9805i	0.0408508	+	0.0296798i
$22$	−115.475	−	83.8975i	−0.0508664	−	0.0369566i
$23$	−759.105	+	2336.28i	−0.299214	+	0.920886i	0.682559	+	0.730830i	$0.260867\pi$
$23$	−759.105	+	2336.28i	−0.299214	+	0.920886i	−0.981773	+	0.190056i	$0.939133\pi$
$24$	576.000			0.204124
$25$	−2762.26	+	1461.35i	−0.883923	+	0.467632i
$26$	−240.874			−0.0698805
$27$	−225.273	+	693.320i	−0.0594703	+	0.183031i
$28$	−146.766	−	106.632i	−0.0353778	−	0.0257035i
$29$	−1799.66	−	1307.53i	−0.397370	−	0.288706i	0.371099	−	0.928593i	$-0.378981\pi$
$29$	−1799.66	−	1307.53i	−0.397370	−	0.288706i	−0.768469	+	0.639887i	$0.778981\pi$
$30$	1540.29	+	1295.19i	0.312463	+	0.262742i
$31$	−811.112	+	589.307i	−0.151592	+	0.110138i	−0.660996	−	0.750389i	$-0.729866\pi$
$31$	−811.112	+	589.307i	−0.151592	+	0.110138i	0.509404	+	0.860528i	$0.329866\pi$
$32$	−1024.00			−0.176777
$33$	−259.819	+	188.769i	−0.0415322	+	0.0301749i
$34$	−1870.01	−	5755.30i	−0.277426	−	0.853829i
$35$	−152.697	−	615.163i	−0.0210698	−	0.0848829i
$36$	400.486	−	1232.57i	0.0515028	−	0.158509i
$37$	1916.57	+	5898.58i	0.230154	+	0.708342i	0.997727	+	0.0673808i	$0.0214642\pi$
$37$	1916.57	+	5898.58i	0.230154	+	0.708342i	−0.767573	+	0.640962i	$0.778536\pi$
$38$	−1417.55	−	4362.78i	−0.159250	−	0.490122i
$39$	−167.477	+	515.440i	−0.0176316	+	0.0542646i
$40$	−2738.29	−	2302.56i	−0.270601	−	0.227542i
$41$	−1331.60	−	4098.25i	−0.123713	−	0.380749i	0.869951	−	0.493137i	$-0.164150\pi$
$41$	−1331.60	−	4098.25i	−0.123713	−	0.380749i	−0.993664	+	0.112388i	$0.964150\pi$
$42$	−330.224	+	239.922i	−0.0288859	+	0.0209868i
$43$	1302.18			0.107399			0.0536993	−	0.998557i	$-0.482899\pi$
$43$	1302.18			0.107399			0.0536993	+	0.998557i	$0.482899\pi$
$44$	461.900	−	335.590i	0.0359680	−	0.0261323i
$45$	3842.49	−	2395.49i	0.282866	−	0.176345i
$46$	−7949.45	−	5775.61i	−0.553914	−	0.402442i
$47$	−11273.6	−	8190.72i	−0.744417	−	0.540851i	0.149674	−	0.988735i	$-0.452178\pi$
$47$	−11273.6	−	8190.72i	−0.744417	−	0.540851i	−0.894091	+	0.447884i	$0.852178\pi$
$48$	−711.975	+	2191.23i	−0.0446028	+	0.137273i
$49$	−16678.4			−0.992351
$50$	−2144.96	−	12314.6i	−0.121337	−	0.696618i
$51$	−13615.8			−0.733025
$52$	297.736	−	916.338i	0.0152694	−	0.0469945i
$53$	4339.78	+	3153.03i	0.212216	+	0.154184i	0.688816	−	0.724936i	$-0.258131\pi$
$53$	4339.78	+	3153.03i	0.212216	+	0.154184i	−0.476600	+	0.879120i	$0.658131\pi$
$54$	−2359.09	−	1713.98i	−0.110093	−	0.0799874i
$55$	1989.78	+	141.221i	0.0886946	+	0.00629494i
$56$	587.065	−	426.528i	0.0250159	−	0.0181751i
$57$	−10321.4			−0.420777
$58$	7198.63	−	5230.11i	0.280983	−	0.204146i
$59$	−7961.61	−	24503.3i	−0.297763	−	0.916420i	−0.982279	−	0.187423i	$-0.939987\pi$
$59$	−7961.61	−	24503.3i	−0.297763	−	0.916420i	0.684516	−	0.728998i	$-0.260013\pi$
$60$	−6831.09	+	4258.66i	−0.244970	+	0.152720i
$61$	−15449.1	+	47547.3i	−0.531591	+	1.63607i	0.219312	+	0.975655i	$0.429619\pi$
$61$	−15449.1	+	47547.3i	−0.531591	+	1.63607i	−0.750903	+	0.660413i	$0.770381\pi$
$62$	−1239.27	−	3814.08i	−0.0409436	−	0.126012i
$63$	283.802	+	873.454i	0.00900875	+	0.0277261i
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	2856.65	−	1780.90i	0.0838636	−	0.0522825i
$66$	−396.968	−	1221.74i	−0.0112175	−	0.0345238i
$67$	−26171.3	+	19014.6i	−0.712261	+	0.517488i	−0.883902	−	0.467672i	$-0.845093\pi$
$67$	−26171.3	+	19014.6i	−0.712261	+	0.517488i	0.171641	+	0.985159i	$0.445093\pi$
$68$	24205.9			0.634818
$69$	−17886.3	+	12995.1i	−0.452269	+	0.328593i
$70$	2528.96	+	179.489i	0.0616875	+	0.00437816i
$71$	−43979.2	−	31952.7i	−1.03538	−	0.752250i	−0.0660039	−	0.997819i	$-0.521025\pi$
$71$	−43979.2	−	31952.7i	−1.03538	−	0.752250i	−0.969379	+	0.245570i	$0.921025\pi$
$72$	4193.94	+	3047.08i	0.0953436	+	0.0692712i
$73$	13.6152	−	41.9034i	0.000299032	−	0.000920326i	−0.950907	−	0.309477i	$-0.899846\pi$
$73$	13.6152	−	41.9034i	0.000299032	−	0.000920326i	0.951206	+	0.308557i	$0.0998460\pi$
$74$	−24808.5			−0.526650
$75$	−27843.1	−	3972.24i	−0.571563	−	0.0815421i
$76$	18349.2			0.364404
$77$	−125.026	+	384.791i	−0.00240311	+	0.00739602i
$78$	−1753.84	−	1274.24i	−0.0326402	−	0.0237145i
$79$	18627.4	+	13533.6i	0.335802	+	0.243975i	0.742889	−	0.669415i	$-0.233455\pi$
$79$	18627.4	+	13533.6i	0.335802	+	0.243975i	−0.407086	+	0.913390i	$0.633455\pi$
$80$	12144.2	−	7570.95i	0.212150	−	0.132259i
$81$	−5307.96	+	3856.46i	−0.0898908	+	0.0653095i
$82$	17236.6			0.283086
$83$	53570.9	−	38921.6i	0.853560	−	0.620148i	−0.0725653	−	0.997364i	$-0.523119\pi$
$83$	53570.9	−	38921.6i	0.853560	−	0.620148i	0.926125	+	0.377216i	$0.123119\pi$
$84$	−504.538	−	1552.81i	−0.00780181	−	0.0240115i
$85$	64729.3	+	54429.3i	0.971748	+	0.817119i
$86$	−1609.58	+	4953.77i	−0.0234674	+	0.0722254i
$87$	−6186.67	−	19040.6i	−0.0876312	−	0.269701i
$88$	705.720	+	2171.98i	0.00971462	+	0.0298985i
$89$	−4397.74	+	13534.8i	−0.0588510	+	0.181125i	−0.976160	−	0.217050i	$-0.930356\pi$
$89$	−4397.74	+	13534.8i	−0.0588510	+	0.181125i	0.917309	+	0.398175i	$0.130356\pi$
$90$	4363.42	+	17578.7i	0.0567834	+	0.228760i
$91$	210.989	+	649.358i	0.00267089	+	0.00822017i
$92$	31797.8	−	23102.4i	0.391676	−	0.284570i
$93$	−9023.31			−0.108183
$94$	45094.2	−	32762.9i	0.526383	−	0.382439i
$95$	49067.7	+	41259.8i	0.557810	+	0.469049i
$96$	−7455.90	−	5417.03i	−0.0825700	−	0.0599906i
$97$	−3815.08	−	2771.82i	−0.0411694	−	0.0299113i	0.567010	−	0.823711i	$-0.308100\pi$
$97$	−3815.08	−	2771.82i	−0.0411694	−	0.0299113i	−0.608180	+	0.793799i	$0.708100\pi$
$98$	20615.7	−	63448.6i	0.216837	−	0.667355i
$99$	−2890.38			−0.0296392
$100$	49498.8	+	7061.75i	0.494988	+	0.0706175i
$101$	−18148.6			−0.177027			−0.0885136	−	0.996075i	$-0.528212\pi$
$101$	−18148.6			−0.177027			−0.0885136	+	0.996075i	$0.528212\pi$
$102$	16830.1	−	51797.7i	0.160172	−	0.492958i
$103$	140721.	+	102240.i	1.30697	+	0.949572i	0.999998	−	0.00214538i	$-0.000682895\pi$
$103$	140721.	+	102240.i	1.30697	+	0.949572i	0.306976	+	0.951717i	$0.400683\pi$
$104$	3117.93	+	2265.31i	0.0282673	+	0.0205374i
$105$	2142.44	−	5286.87i	0.0189643	−	0.0467978i
$106$	−17359.1	+	12612.1i	−0.150059	+	0.109024i
$107$	−35960.1			−0.303641			−0.151821	−	0.988408i	$-0.548514\pi$
$107$	−35960.1			−0.303641			−0.151821	+	0.988408i	$0.548514\pi$
$108$	9436.37	−	6855.93i	0.0778477	−	0.0565597i
$109$	44655.7	+	137436.i	0.360007	+	1.10799i	0.953049	+	0.302816i	$0.0979267\pi$
$109$	44655.7	+	137436.i	0.360007	+	1.10799i	−0.593042	+	0.805171i	$0.702073\pi$
$110$	−2996.73	+	7395.00i	−0.0236138	+	0.0582715i
$111$	−17249.1	+	53087.2i	−0.132880	+	0.408962i
$112$	896.956	+	2760.55i	0.00675656	+	0.0207946i
$113$	31346.6	+	96475.0i	0.230938	+	0.710753i	0.997634	+	0.0687436i	$0.0218990\pi$
$113$	31346.6	+	96475.0i	0.230938	+	0.710753i	−0.766697	+	0.642009i	$0.778101\pi$
$114$	12758.0	−	39265.0i	0.0919431	−	0.282972i
$115$	136979.	+	9721.83i	0.965848	+	0.0685493i
$116$	10998.5	+	33850.0i	0.0758909	+	0.233568i
$117$	−3946.14	+	2867.04i	−0.0266506	+	0.0193628i
$118$	103057.			0.681355
$119$	−13877.4	+	10082.5i	−0.0898340	+	0.0652682i
$120$	−7757.20	−	31251.0i	−0.0491758	−	0.198112i
$121$	129263.	+	93915.0i	0.802621	+	0.583138i
$122$	−161785.	−	117543.i	−0.984096	−	0.714988i
$123$	11984.4	−	36884.3i	0.0714257	−	0.219826i
$124$	16041.4			0.0936891
$125$	116486.	+	130187.i	0.666806	+	0.745231i
$126$	−3673.62			−0.0206142
$127$	24526.3	−	75484.2i	0.134935	−	0.415286i	−0.860645	−	0.509205i	$-0.829940\pi$
$127$	24526.3	−	75484.2i	0.134935	−	0.415286i	0.995580	+	0.0939192i	$0.0299395\pi$
$128$	13254.9	+	9630.27i	0.0715077	+	0.0519534i
$129$	9481.34	+	6888.60i	0.0501644	+	0.0364466i
$130$	3243.93	+	13068.7i	0.0168350	+	0.0678223i
$131$	−86269.0	+	62678.1i	−0.439214	+	0.319108i	−0.785323	−	0.619087i	$-0.787503\pi$
$131$	−86269.0	+	62678.1i	−0.439214	+	0.319108i	0.346108	+	0.938195i	$0.387503\pi$
$132$	5138.46			0.0256683
$133$	−10519.7	+	7643.00i	−0.0515672	+	0.0374658i
$134$	−39986.3	−	123065.i	−0.192375	−	0.592070i
$135$	40650.1	+	2885.07i	0.191967	+	0.0136245i
$136$	−29920.2	+	92084.8i	−0.138713	+	0.426914i
$137$	−98750.8	−	303924.i	−0.449510	−	1.38345i	−0.877461	−	0.479648i	$-0.840764\pi$
$137$	−98750.8	−	303924.i	−0.449510	−	1.38345i	0.427951	−	0.903802i	$-0.359236\pi$
$138$	−27327.8	−	84106.2i	−0.122154	−	0.375950i
$139$	−6465.58	+	19899.0i	−0.0283838	+	0.0873563i	−0.964245	−	0.265013i	$-0.914624\pi$
$139$	−6465.58	+	19899.0i	−0.0283838	+	0.0873563i	0.935861	+	0.352369i	$0.114624\pi$
$140$	−3808.79	+	9398.89i	−0.0164235	+	0.0405281i
$141$	−38755.1	−	119276.i	−0.164165	−	0.505248i
$142$	175917.	−	127811.i	0.732126	−	0.531921i
$143$	−2148.82			−0.00878738
$144$	−16775.8	+	12188.3i	−0.0674181	+	0.0489821i
$145$	−46703.6	+	115250.i	−0.184472	+	0.455219i
$146$	142.580	+	103.591i	0.000553577	+	0.000402197i
$147$	−121438.	−	88230.1i	−0.463513	−	0.336762i
$148$	30665.0	−	94377.3i	0.115077	−	0.354171i
$149$	−21498.1			−0.0793293			−0.0396647	−	0.999213i	$-0.512629\pi$
$149$	−21498.1			−0.0793293			−0.0396647	+	0.999213i	$0.512629\pi$
$150$	49527.2	−	101011.i	0.179728	−	0.366558i
$151$	−275612.			−0.983683			−0.491841	−	0.870685i	$-0.663676\pi$
$151$	−275612.			−0.983683			−0.491841	+	0.870685i	$0.663676\pi$
$152$	−22680.8	+	69804.4i	−0.0796251	+	0.245061i
$153$	−99139.0	−	72028.7i	−0.342386	−	0.248758i
$154$	−1309.29	−	951.256i	−0.00444871	−	0.00323218i
$155$	42896.5	+	36070.7i	0.143414	+	0.120594i
$156$	7015.35	−	5096.95i	0.0230801	−	0.0167687i
$157$	56786.0			0.183862			0.0919310	−	0.995765i	$-0.470696\pi$
$157$	56786.0			0.183862			0.0919310	+	0.995765i	$0.470696\pi$
$158$	−74509.5	+	54134.3i	−0.237448	+	0.172516i
$159$	14918.8	+	45915.5i	0.0467996	+	0.144034i
$160$	13790.6	+	55557.4i	0.0425875	+	0.171570i
$161$	−8606.97	+	26489.5i	−0.0261689	+	0.0805396i
$162$	−8109.84	−	24959.5i	−0.0242787	−	0.0747221i
$163$	−84160.3	−	259019.i	−0.248107	−	0.763593i	−0.995110	−	0.0987733i	$-0.968508\pi$
$163$	−84160.3	−	259019.i	−0.248107	−	0.763593i	0.747003	−	0.664820i	$-0.231492\pi$
$164$	−21305.7	+	65572.1i	−0.0618565	+	0.190375i
$165$	13740.8	+	11554.3i	0.0392918	+	0.0330395i
$166$	81849.1	+	251906.i	0.230539	+	0.709525i
$167$	−182494.	+	132589.i	−0.506357	+	0.367890i	−0.811440	−	0.584436i	$-0.801316\pi$
$167$	−182494.	+	132589.i	−0.506357	+	0.367890i	0.305083	+	0.952326i	$0.401316\pi$
$168$	6530.87			0.0178525
$169$	297449.	−	216109.i	0.801116	−	0.582045i
$170$	−287071.	+	178967.i	−0.761846	+	0.474952i
$171$	−75151.8	−	54601.0i	−0.196539	−	0.142794i
$172$	−16855.7	−	12246.4i	−0.0434436	−	0.0315636i
$173$	130063.	−	400294.i	0.330400	−	1.01687i	−0.638544	−	0.769585i	$-0.720463\pi$
$173$	130063.	−	400294.i	0.330400	−	1.01687i	0.968944	−	0.247280i	$-0.0795369\pi$
$174$	80081.9			0.200522
$175$	−31319.4	+	16569.2i	−0.0773069	+	0.0408985i
$176$	−9135.03			−0.0222294
$177$	71654.5	−	220530.i	0.171914	−	0.529096i
$178$	−46053.7	−	33460.0i	−0.108947	−	0.0791545i
$179$	280996.	+	204156.i	0.655493	+	0.476243i	0.865138	−	0.501534i	$-0.167231\pi$
$179$	280996.	+	204156.i	0.655493	+	0.476243i	−0.209645	+	0.977778i	$0.567231\pi$
$180$	−72266.8	−	5129.01i	−0.166248	−	0.0117992i
$181$	−465784.	+	338412.i	−1.05679	+	0.767801i	−0.973491	−	0.228724i	$-0.926545\pi$
$181$	−465784.	+	338412.i	−1.05679	+	0.767801i	−0.0832964	+	0.996525i	$0.526545\pi$
$182$	−2731.10			−0.00611166
$183$	−364015.	+	264473.i	−0.803511	+	0.583785i
$184$	48582.7	+	149522.i	0.105788	+	0.325583i
$185$	294218.	−	183422.i	0.632033	−	0.394023i
$186$	11153.4	−	34326.7i	0.0236388	−	0.0727528i
$187$	−16682.2	−	51342.6i	−0.0348859	−	0.107368i
$188$	68897.9	+	212046.i	0.142171	+	0.437558i
$189$	−2554.22	+	7861.08i	−0.00520121	+	0.0160077i
$190$	−217613.	+	135665.i	−0.437321	+	0.272636i
$191$	−67733.7	−	208463.i	−0.134345	−	0.413472i	0.861143	−	0.508364i	$-0.169749\pi$
$191$	−67733.7	−	208463.i	−0.134345	−	0.413472i	−0.995488	+	0.0948921i	$0.969749\pi$
$192$	29823.6	−	21668.1i	0.0583858	−	0.0424197i
$193$	363828.			0.703077			0.351538	−	0.936173i	$-0.385659\pi$
$193$	363828.			0.703077			0.351538	+	0.936173i	$0.385659\pi$
$194$	15260.3	−	11087.3i	0.0291112	−	0.0211505i
$195$	30220.8	+	2144.87i	0.0569140	+	0.00403937i
$196$	215890.	+	156853.i	0.401414	+	0.291645i
$197$	−836800.	−	607971.i	−1.53623	−	1.11614i	−0.952645	−	0.304085i	$-0.901649\pi$
$197$	−836800.	−	607971.i	−1.53623	−	1.11614i	−0.583585	−	0.812052i	$-0.698351\pi$
$198$	3572.71	−	10995.7i	0.00647641	−	0.0199323i
$199$	315273.			0.564357			0.282178	−	0.959362i	$-0.408943\pi$
$199$	315273.			0.564357			0.282178	+	0.959362i	$0.408943\pi$
$200$	−88048.4	+	179576.i	−0.155649	+	0.317448i
$201$	−291146.			−0.508301
$202$	22432.9	−	69041.4i	0.0386819	−	0.119051i
$203$	−20405.1	−	14825.2i	−0.0347535	−	0.0252499i
$204$	176247.	+	128051.i	0.296515	+	0.215431i
$205$	−204419.	+	127439.i	−0.339731	+	0.211796i
$206$	−562885.	+	408960.i	−0.924170	+	0.671449i
$207$	−198978.			−0.322759
$208$	−12471.7	+	9061.25i	−0.0199880	+	0.0145221i
$209$	−12645.9	−	38920.0i	−0.0200255	−	0.0616321i
$210$	17464.3	+	14685.3i	0.0273276	+	0.0229791i
$211$	−213991.	+	658597.i	−0.330894	+	1.01839i	0.637815	+	0.770190i	$0.279839\pi$
$211$	−213991.	+	658597.i	−0.330894	+	1.01839i	−0.968709	+	0.248199i	$0.920161\pi$
$212$	−26522.4	−	81627.5i	−0.0405296	−	0.124737i
$213$	−151187.	−	465305.i	−0.228331	−	0.702731i
$214$	44449.1	−	136800.i	0.0663481	−	0.204198i
$215$	−17536.9	−	70649.9i	−0.0258735	−	0.104235i
$216$	14417.5	+	44372.5i	0.0210259	+	0.0647112i
$217$	−9196.65	+	6681.75i	−0.0132581	+	0.00963255i
$218$	−578036.			−0.823784
$219$	320.806	−	233.079i	0.000451994	−	0.000328393i
$220$	−24428.1	−	20541.0i	−0.0340277	−	0.0286131i
$221$	−73703.6	−	53548.8i	−0.101510	−	0.0737512i
$222$	−180635.	−	131239.i	−0.245991	−	0.178723i
$223$	226119.	−	695922.i	0.304491	−	0.937127i	−0.675376	−	0.737474i	$-0.736019\pi$
$223$	226119.	−	695922.i	0.304491	−	0.937127i	0.979867	−	0.199653i	$-0.0639814\pi$
$224$	−11610.4			−0.0154607
$225$	−181716.	−	176214.i	−0.239297	−	0.232052i
$226$	−405759.			−0.528442
$227$	71862.3	−	221170.i	0.0925628	−	0.284879i	−0.894048	−	0.447971i	$-0.852147\pi$
$227$	71862.3	−	221170.i	0.0925628	−	0.284879i	0.986611	+	0.163092i	$0.0521467\pi$
$228$	133603.	+	97068.4i	0.170208	+	0.123663i
$229$	544594.	+	395671.i	0.686253	+	0.498592i	0.875426	−	0.483352i	$-0.160581\pi$
$229$	544594.	+	395671.i	0.686253	+	0.498592i	−0.189173	+	0.981944i	$0.560581\pi$
$230$	−206299.	+	509081.i	−0.257145	+	0.634553i
$231$	−2945.91	+	2140.33i	−0.00363236	+	0.00263906i
$232$	−142368.			−0.173657
$233$	864381.	−	628010.i	1.04308	−	0.757839i	0.0721918	−	0.997391i	$-0.477001\pi$
$233$	864381.	−	628010.i	1.04308	−	0.757839i	0.970883	+	0.239552i	$0.0770006\pi$
$234$	−6029.16	−	18555.8i	−0.00719809	−	0.0221534i
$235$	−292564.	+	721957.i	−0.345583	+	0.852789i
$236$	−127386.	+	392053.i	−0.148882	+	0.458210i
$237$	64035.2	+	197080.i	0.0740539	+	0.227914i
$238$	−21202.8	−	65255.4i	−0.0242633	−	0.0746748i
$239$	−242693.	+	746932.i	−0.274829	+	0.845837i	0.714436	+	0.699701i	$0.246684\pi$
$239$	−242693.	+	746932.i	−0.274829	+	0.845837i	−0.989265	+	0.146135i	$0.953316\pi$
$240$	128474.	+	9118.24i	0.143975	+	0.0102184i
$241$	−275302.	−	847292.i	−0.305328	−	0.939703i	−0.979555	−	0.201179i	$-0.935523\pi$
$241$	−275302.	−	847292.i	−0.305328	−	0.939703i	0.674227	−	0.738525i	$-0.264477\pi$
$242$	−517051.	+	375660.i	−0.567538	+	0.412341i
$243$	−59049.0			−0.0641500
$244$	647138.	−	470174.i	0.695861	−	0.505573i
$245$	224615.	+	904893.i	0.239069	+	0.963123i
$246$	125503.	+	91183.0i	0.132225	+	0.0960674i
$247$	−55870.6	−	40592.4i	−0.0582695	−	0.0423353i
$248$	−19828.3	+	61025.2i	−0.0204718	+	0.0630058i
$249$	595956.			0.609138
$250$	−639244.	+	282220.i	−0.646869	+	0.285587i
$251$	−475957.			−0.476852			−0.238426	−	0.971161i	$-0.576631\pi$
$251$	−475957.			−0.476852			−0.238426	+	0.971161i	$0.576631\pi$
$252$	4540.84	−	13975.3i	0.00450438	−	0.0138630i
$253$	−70916.5	−	51523.8i	−0.0696540	−	0.0506066i
$254$	256843.	+	186607.i	0.249795	+	0.181487i
$255$	183369.	+	738730.i	0.176594	+	0.711435i
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	272405.			0.257266			0.128633	−	0.991692i	$-0.458941\pi$
$257$	272405.			0.257266			0.128633	+	0.991692i	$0.458941\pi$
$258$	−37925.4	+	27554.4i	−0.0354716	+	0.0257716i
$259$	21730.6	+	66880.0i	0.0201290	+	0.0619508i
$260$	−53725.8	−	3813.10i	−0.0492890	−	0.00349820i
$261$	55680.0	−	171366.i	0.0505939	−	0.155712i
$262$	−131807.	−	405661.i	−0.118628	−	0.365099i
$263$	−331923.	−	1.02155e6i	−0.295902	−	0.910693i	−0.982917	−	0.184050i	$-0.941079\pi$
$263$	−331923.	−	1.02155e6i	−0.295902	−	0.910693i	0.687015	−	0.726643i	$-0.258921\pi$
$264$	−6351.48	+	19547.8i	−0.00560874	+	0.0172619i
$265$	112623.	−	277919.i	0.0985175	−	0.243110i
$266$	−16072.7	−	49466.5i	−0.0139278	−	0.0428655i
$267$	−103621.	+	75284.9i	−0.0889547	+	0.0646294i
$268$	517593.			0.440201
$269$	1.88066e6	−	1.36638e6i	1.58464	−	1.15131i	0.673514	−	0.739175i	$-0.264784\pi$
$269$	1.88066e6	−	1.36638e6i	1.58464	−	1.15131i	0.911124	−	0.412132i	$-0.135216\pi$
$270$	−61221.7	+	151076.i	−0.0511089	+	0.126121i
$271$	−1.16900e6	−	849326.i	−0.966919	−	0.702508i	−0.0121719	−	0.999926i	$-0.503875\pi$
$271$	−1.16900e6	−	849326.i	−0.966919	−	0.702508i	−0.954747	+	0.297418i	$0.903875\pi$
$272$	−313328.	−	227646.i	−0.256789	−	0.186568i
$273$	−1898.90	+	5844.22i	−0.00154204	+	0.00474592i
$274$	1.27826e6			1.02859
$275$	−19135.1	−	109858.i	−0.0152580	−	0.0875988i
$276$	353738.			0.279518
$277$	−315204.	+	970097.i	−0.246827	+	0.759654i	0.748504	+	0.663130i	$0.230772\pi$
$277$	−315204.	+	970097.i	−0.246827	+	0.759654i	−0.995331	+	0.0965240i	$0.969228\pi$
$278$	−67708.4	−	49193.0i	−0.0525449	−	0.0381761i
$279$	−65700.1	−	47733.9i	−0.0505307	−	0.0367127i
$280$	−31047.6	−	26107.2i	−0.0236664	−	0.0199005i
$281$	846452.	−	614983.i	0.639494	−	0.464620i	−0.220182	−	0.975459i	$-0.570665\pi$
$281$	846452.	−	614983.i	0.639494	−	0.464620i	0.859676	+	0.510839i	$0.170665\pi$
$282$	501656.			0.375650
$283$	973914.	−	707590.i	0.722861	−	0.525189i	−0.164436	−	0.986388i	$-0.552580\pi$
$283$	973914.	−	707590.i	0.722861	−	0.525189i	0.887297	+	0.461199i	$0.152580\pi$
$284$	268777.	+	827209.i	0.197741	+	0.608583i
$285$	139002.	+	559991.i	0.101370	+	0.408384i
$286$	2656.08	−	8174.58i	0.00192011	−	0.00590950i
$287$	−15098.1	−	46467.3i	−0.0108198	−	0.0332999i
$288$	−25631.1	−	78884.4i	−0.0182090	−	0.0560415i
$289$	268511.	−	826392.i	0.189111	−	0.582025i
$290$	−380707.	−	320127.i	−0.265825	−	0.223526i
$291$	−13115.1	−	40364.1i	−0.00907901	−	0.0279423i
$292$	−570.322	+	414.363i	−0.000391438	+	0.000284396i
$293$	2.60750e6			1.77441			0.887206	−	0.461373i	$-0.152643\pi$
$293$	2.60750e6			1.77441			0.887206	+	0.461373i	$0.152643\pi$
$294$	485753.	−	352920.i	0.327753	−	0.238127i
$295$	−1.22221e6	+	761954.i	−0.817695	+	0.509769i
$296$	321129.	+	233314.i	0.213034	+	0.154779i
$297$	−21045.3	−	15290.3i	−0.0138441	−	0.0100583i
$298$	26573.1	−	81783.5i	0.0173341	−	0.0533488i
$299$	−147927.			−0.0956909
$300$	323051.	+	313270.i	0.207237	+	0.200963i
$301$	14764.5			0.00939295
$302$	340675.	−	1.04849e6i	0.214943	−	0.661525i
$303$	−132143.	−	96007.4i	−0.0826870	−	0.0600756i
$304$	−237517.	−	172566.i	−0.147404	−	0.107096i
$305$	2.78775e6	+	197855.i	1.71595	+	0.121786i
$306$	396556.	−	288115.i	0.242103	−	0.175898i
$307$	239800.			0.145212			0.0726062	−	0.997361i	$-0.476868\pi$
$307$	239800.			0.145212			0.0726062	+	0.997361i	$0.476868\pi$
$308$	5237.17	−	3805.02i	0.00314572	−	0.00228550i
$309$	483757.	+	1.48885e6i	0.288225	+	0.887064i
$310$	−190244.	+	118602.i	−0.112436	+	0.0700953i
$311$	−21016.8	+	64682.9i	−0.0123215	+	0.0379218i	−0.957028	−	0.289995i	$-0.906346\pi$
$311$	−21016.8	+	64682.9i	−0.0123215	+	0.0379218i	0.944707	+	0.327916i	$0.106346\pi$
$312$	10718.5	+	32988.2i	0.00623373	+	0.0191854i
$313$	−870851.	−	2.68020e6i	−0.502439	−	1.54635i	−0.805034	−	0.593228i	$-0.797853\pi$
$313$	−870851.	−	2.68020e6i	−0.502439	−	1.54635i	0.302596	−	0.953119i	$-0.402147\pi$
$314$	−70191.4	+	216027.i	−0.0401753	+	0.123647i
$315$	43567.4	−	27160.9i	0.0247392	−	0.0154230i
$316$	−113840.	−	350364.i	−0.0641325	−	0.197380i
$317$	−44598.9	+	32403.0i	−0.0249273	+	0.0181108i	−0.600179	−	0.799866i	$-0.704904\pi$
$317$	−44598.9	+	32403.0i	−0.0249273	+	0.0181108i	0.575252	+	0.817976i	$0.304904\pi$
$318$	−193113.			−0.107089
$319$	64218.5	−	46657.4i	0.0353332	−	0.0256711i
$320$	−228399.	−	16210.2i	−0.124686	−	0.00884939i
$321$	−261831.	−	190231.i	−0.141827	−	0.103043i
$322$	−90133.4	−	65485.7i	−0.0484447	−	0.0351971i
$323$	536143.	−	1.65008e6i	0.285940	−	0.880032i
$324$	104976.			0.0555556
$325$	−135095.	−	131004.i	−0.0709463	−	0.0687982i
$326$	1.08939e6			0.567729
$327$	−401901.	+	1.23693e6i	−0.207850	+	0.639697i
$328$	−223116.	−	162103.i	−0.114511	−	0.0831968i
$329$	−127823.	−	92869.0i	−0.0651059	−	0.0473022i
$330$	−60939.7	+	37991.2i	−0.0308046	+	0.0192043i
$331$	−1.40684e6	+	1.02213e6i	−0.705788	+	0.512785i	−0.881812	−	0.471601i	$-0.843676\pi$
$331$	−1.40684e6	+	1.02213e6i	−0.705788	+	0.512785i	0.176024	+	0.984386i	$0.443676\pi$
$332$	−1.05948e6			−0.527529
$333$	−406428.	+	295287.i	−0.200851	+	0.145927i
$334$	−278826.	−	858137.i	−0.136762	−	0.420911i
$335$	1.38410e6	+	1.16386e6i	0.673838	+	0.566614i
$336$	−8072.60	+	24844.9i	−0.00390090	+	0.0120057i
$337$	768221.	+	2.36434e6i	0.368478	+	1.13406i	0.947775	+	0.318941i	$0.103327\pi$
$337$	768221.	+	2.36434e6i	0.368478	+	1.13406i	−0.579297	+	0.815117i	$0.696673\pi$
$338$	454461.	+	1.39869e6i	0.216374	+	0.665931i
$339$	−282120.	+	868275.i	−0.133332	+	0.410353i
$340$	−325990.	−	1.31330e6i	−0.152935	−	0.616121i
$341$	−11055.4	−	34025.1i	−0.00514861	−	0.0158458i
$342$	300607.	−	218404.i	0.138974	−	0.100971i
$343$	−379669.			−0.174249
$344$	67422.9	−	48985.6i	0.0307193	−	0.0223189i
$345$	945934.	+	795413.i	0.427871	+	0.359787i
$346$	1.36204e6	+	989581.i	0.611646	+	0.444387i
$347$	483094.	+	350988.i	0.215381	+	0.156484i	0.690245	−	0.723576i	$-0.257503\pi$
$347$	483094.	+	350988.i	0.215381	+	0.156484i	−0.474864	+	0.880059i	$0.657503\pi$
$348$	−98986.7	+	304650.i	−0.0438156	+	0.134851i
$349$	−1.87552e6			−0.824246			−0.412123	−	0.911128i	$-0.635213\pi$
$349$	−1.87552e6			−0.824246			−0.412123	+	0.911128i	$0.635213\pi$
$350$	−24320.3	−	139627.i	−0.0106120	−	0.0609254i
$351$	−43899.2			−0.0190191
$352$	11291.5	−	34751.7i	0.00485731	−	0.0149493i
$353$	81396.9	+	59138.3i	0.0347673	+	0.0252599i	0.605033	−	0.796200i	$-0.293160\pi$
$353$	81396.9	+	59138.3i	0.0347673	+	0.0252599i	−0.570266	+	0.821460i	$0.693160\pi$
$354$	750375.	+	545180.i	0.318251	+	0.231223i
$355$	−1.14132e6	+	2.81642e6i	−0.480658	+	1.18611i
$356$	184215.	−	133840.i	0.0770370	−	0.0559707i
$357$	−154381.			−0.0641095
$358$	−1.12398e6	+	816623.i	−0.463503	+	0.336755i
$359$	964109.	+	2.96722e6i	0.394812	+	1.21511i	0.929108	+	0.369808i	$0.120577\pi$
$359$	964109.	+	2.96722e6i	0.394812	+	1.21511i	−0.534296	+	0.845297i	$0.679423\pi$
$360$	108839.	−	268580.i	0.0442616	−	0.109224i
$361$	−358736.	+	1.10408e6i	−0.144880	+	0.445894i
$362$	−711654.	−	2.19025e6i	−0.285429	−	0.878459i
$363$	444366.	+	1.36762e6i	0.177000	+	0.544751i
$364$	3375.83	−	10389.7i	0.00133545	−	0.00411008i
$365$	−2456.84	−	174.370i	−0.000965260	−	6.85076e-5i
$366$	−556166.	−	1.71170e6i	−0.217021	−	0.667922i
$367$	−1.47976e6	+	1.07511e6i	−0.573492	+	0.416666i	−0.836372	−	0.548162i	$-0.815328\pi$
$367$	−1.47976e6	+	1.07511e6i	−0.573492	+	0.416666i	0.262880	+	0.964829i	$0.415328\pi$
$368$	−628868.			−0.242069
$369$	282381.	−	205162.i	0.107962	−	0.0784387i
$370$	334106.	+	1.34599e6i	0.126876	+	0.511138i
$371$	49205.8	+	35750.1i	0.0185602	+	0.0134847i
$372$	116800.	+	84860.3i	0.0437609	+	0.0317941i
$373$	1.01850e6	−	3.13461e6i	0.379042	−	1.16657i	−0.561670	−	0.827362i	$-0.689841\pi$
$373$	1.01850e6	−	3.13461e6i	0.379042	−	1.16657i	0.940711	−	0.339209i	$-0.110159\pi$
$374$	215939.			0.0798276
$375$	159458.	+	1.56413e6i	0.0585556	+	0.574373i
$376$	−891833.			−0.325322
$377$	41394.6	−	127399.i	0.0150000	−	0.0461652i
$378$	−26748.2	−	19433.7i	−0.00962863	−	0.00699561i
$379$	−3.92686e6	−	2.85303e6i	−1.40426	−	1.02026i	−0.994126	−	0.108231i	$-0.965481\pi$
$379$	−3.92686e6	−	2.85303e6i	−1.40426	−	1.02026i	−0.410136	−	0.912025i	$-0.634519\pi$
$380$	−247115.	−	995539.i	−0.0877890	−	0.353671i
$381$	577897.	−	419866.i	0.203957	−	0.148183i
$382$	876764.			0.307414
$383$	−2.85164e6	+	2.07184e6i	−0.993340	+	0.721704i	−0.960650	−	0.277762i	$-0.910407\pi$
$383$	−2.85164e6	+	2.07184e6i	−0.993340	+	0.721704i	−0.0326898	+	0.999466i	$0.510407\pi$
$384$	45566.4	+	140239.i	0.0157695	+	0.0485334i
$385$	22560.7	+	1601.21i	0.00775713	+	0.000550548i
$386$	−449716.	+	1.38408e6i	−0.153628	+	0.472818i
$387$	32594.0	+	100314.i	0.0110627	+	0.0340474i
$388$	23315.7	+	71758.4i	0.00786265	+	0.0241988i
$389$	−897099.	+	2.76099e6i	−0.300584	+	0.925103i	0.680704	+	0.732559i	$0.261674\pi$
$389$	−897099.	+	2.76099e6i	−0.300584	+	0.925103i	−0.981288	+	0.192545i	$0.938326\pi$
$390$	−45514.5	+	112315.i	−0.0151526	+	0.0373920i
$391$	−1.14843e6	−	3.53450e6i	−0.379893	−	1.16919i
$392$	−863561.	+	627414.i	−0.283843	+	0.206224i
$393$	−959709.			−0.313443
$394$	3.34720e6	−	2.43188e6i	1.08628	−	0.789228i
$395$	483406.	−	1.19289e6i	0.155890	−	0.384688i
$396$	37413.9	+	27182.8i	0.0119893	+	0.00871076i
$397$	585430.	+	425340.i	0.186423	+	0.135444i	0.677082	−	0.735907i	$-0.263244\pi$
$397$	585430.	+	425340.i	0.186423	+	0.135444i	−0.490660	+	0.871351i	$0.663244\pi$
$398$	−389698.	+	1.19937e6i	−0.123316	+	0.379529i
$399$	−117027.			−0.0368006
$400$	−574313.	−	556924.i	−0.179473	−	0.174039i
$401$	1.64020e6			0.509372			0.254686	−	0.967024i	$-0.418028\pi$
$401$	1.64020e6			0.509372			0.254686	+	0.967024i	$0.418028\pi$
$402$	359876.	−	1.10759e6i	0.111068	−	0.341831i
$403$	−48843.9	−	35487.2i	−0.0149812	−	0.0108845i
$404$	234921.	+	170680.i	0.0716090	+	0.0520270i
$405$	280717.	+	236048.i	0.0850416	+	0.0715094i
$406$	81620.3	−	59300.6i	0.0245744	−	0.0178544i
$407$	−221315.			−0.0662255
$408$	−704988.	+	512204.i	−0.209668	+	0.152332i
$409$	−1.11264e6	−	3.42435e6i	−0.328887	−	1.01221i	−0.969655	−	0.244476i	$-0.921384\pi$
$409$	−1.11264e6	−	3.42435e6i	−0.328887	−	1.01221i	0.640769	−	0.767734i	$-0.278616\pi$
$410$	−232132.	−	935178.i	−0.0681986	−	0.274748i
$411$	888758.	−	2.73531e6i	0.259525	−	0.798735i
$412$	−860012.	−	2.64685e6i	−0.249610	−	0.768220i
$413$	−90271.2	−	277826.i	−0.0260420	−	0.0801490i
$414$	245950.	−	756956.i	0.0705255	−	0.217055i
$415$	−2.83316e6	−	2.38233e6i	−0.807515	−	0.679020i
$416$	−19055.1	−	58645.6i	−0.00539856	−	0.0166151i
$417$	−152344.	+	110684.i	−0.0429027	+	0.0311707i
$418$	163692.			0.0458233
$419$	−5.37017e6	+	3.90166e6i	−1.49435	+	1.08571i	−0.521789	+	0.853075i	$0.674735\pi$
$419$	−5.37017e6	+	3.90166e6i	−1.49435	+	1.08571i	−0.972564	+	0.232636i	$0.925265\pi$
$420$	−77453.1	+	48286.0i	−0.0214247	+	0.0133567i
$421$	98056.2	+	71242.0i	0.0269631	+	0.0195898i	0.601185	−	0.799110i	$-0.294695\pi$
$421$	98056.2	+	71242.0i	0.0269631	+	0.0195898i	−0.574222	+	0.818700i	$0.694695\pi$
$422$	−2.24094e6	−	1.62814e6i	−0.612562	−	0.445052i
$423$	348796.	−	1.07348e6i	0.0947807	−	0.291705i
$424$	343313.			0.0927418
$425$	2.08134e6	−	4.24492e6i	0.558947	−	1.13998i
$426$	1.95700e6			0.522478
$427$	−175166.	+	539106.i	−0.0464923	+	0.143089i
$428$	465477.	+	338189.i	0.122826	+	0.0892380i
$429$	−15645.9	−	11367.4i	−0.00410446	−	0.00298207i
$430$	290445.	+	20613.8i	0.0757517	+	0.00537634i
$431$	−5.87534e6	+	4.26868e6i	−1.52349	+	1.10688i	−0.563768	+	0.825934i	$0.690649\pi$
$431$	−5.87534e6	+	4.26868e6i	−1.52349	+	1.10688i	−0.959723	+	0.280947i	$0.909351\pi$
$432$	−186624.			−0.0481125
$433$	−1.46164e6	+	1.06195e6i	−0.374647	+	0.272197i	−0.759135	−	0.650933i	$-0.774378\pi$
$433$	−1.46164e6	+	1.06195e6i	−0.374647	+	0.272197i	0.384488	+	0.923130i	$0.374378\pi$
$434$	−14051.2	−	43245.2i	−0.00358088	−	0.0110208i
$435$	−949735.	+	592086.i	−0.240646	+	0.150024i
$436$	714491.	−	2.19898e6i	0.180003	−	0.553994i
$437$	−870559.	−	2.67931e6i	−0.218069	−	0.671149i
$438$	490.148	+	1508.52i	0.000122079	+	0.000375721i
$439$	−820322.	+	2.52469e6i	−0.203153	+	0.625241i	0.796631	+	0.604466i	$0.206613\pi$
$439$	−820322.	+	2.52469e6i	−0.203153	+	0.625241i	−0.999784	+	0.0207749i	$0.993387\pi$
$440$	108337.	−	67539.9i	0.0266776	−	0.0166314i
$441$	−417468.	−	1.28483e6i	−0.102218	−	0.314594i
$442$	294814.	−	214195.i	0.0717783	−	0.0521500i
$443$	4.11331e6			0.995822			0.497911	−	0.867228i	$-0.334101\pi$
$443$	4.11331e6			0.995822			0.497911	+	0.867228i	$0.334101\pi$
$444$	722539.	−	524955.i	0.173942	−	0.126376i
$445$	793562.	+	56321.6i	0.189968	+	0.0134827i
$446$	2.36795e6	+	1.72041e6i	0.563683	+	0.409539i
$447$	−156531.	−	113726.i	−0.0370536	−	0.0269210i
$448$	14351.3	−	44168.7i	0.00337828	−	0.0103973i
$449$	−4.62186e6			−1.08193			−0.540967	−	0.841044i	$-0.681942\pi$
$449$	−4.62186e6			−1.08193			−0.540967	+	0.841044i	$0.681942\pi$
$450$	894972.	−	473477.i	0.208343	−	0.110222i
$451$	153767.			0.0355976
$452$	501546.	−	1.54360e6i	0.115469	−	0.355377i
$453$	−2.00677e6	−	1.45800e6i	−0.459465	−	0.333821i
$454$	752552.	+	546761.i	0.171355	+	0.124497i
$455$	32389.6	−	20192.4i	0.00733461	−	0.00457256i
$456$	−534413.	+	388273.i	−0.120355	+	0.0874431i
$457$	5.67741e6			1.27163			0.635813	−	0.771843i	$-0.280665\pi$
$457$	5.67741e6			1.27163			0.635813	+	0.771843i	$0.280665\pi$
$458$	−2.17838e6	+	1.58268e6i	−0.485254	+	0.352558i
$459$	−340809.	−	1.04890e6i	−0.0755057	−	0.232383i
$460$	−1.68166e6	−	1.41407e6i	−0.370548	−	0.311584i
$461$	−983440.	+	3.02672e6i	−0.215524	+	0.663315i	0.783592	+	0.621276i	$0.213385\pi$
$461$	−983440.	+	3.02672e6i	−0.215524	+	0.663315i	−0.999116	+	0.0420389i	$0.986615\pi$
$462$	−4500.94	−	13852.5i	−0.000981067	−	0.00301941i
$463$	1.88587e6	+	5.80410e6i	0.408845	+	1.25830i	0.917642	+	0.397409i	$0.130090\pi$
$463$	1.88587e6	+	5.80410e6i	0.408845	+	1.25830i	−0.508797	+	0.860887i	$0.669910\pi$
$464$	175976.	−	541600.i	0.0379454	−	0.116784i
$465$	121520.	+	489562.i	0.0260625	+	0.104997i
$466$	1.32066e6	+	4.06457e6i	0.281725	+	0.867060i
$467$	−2.81624e6	+	2.04611e6i	−0.597553	+	0.434148i	−0.845010	−	0.534751i	$-0.820405\pi$
$467$	−2.81624e6	+	2.04611e6i	−0.597553	+	0.434148i	0.247456	+	0.968899i	$0.420405\pi$
$468$	78043.1			0.0164710
$469$	−296739.	+	215594.i	−0.0622935	+	0.0452589i
$470$	−2.38486e6	−	2.00537e6i	−0.497987	−	0.418745i
$471$	413468.	+	300402.i	0.0858794	+	0.0623951i
$472$	−1.33400e6	−	969208.i	−0.275614	−	0.200245i
$473$	−14358.9	+	44192.2i	−0.00295100	+	0.00908225i
$474$	−828889.			−0.169453
$475$	1.57775e6	−	3.21784e6i	0.320851	−	0.654381i
$476$	274455.			0.0555205
$477$	−134270.	+	413239.i	−0.0270198	+	0.0831583i
$478$	−2.54151e6	−	1.84652e6i	−0.508772	−	0.369644i
$479$	−6.37759e6	−	4.63359e6i	−1.27004	−	0.922739i	−0.270837	−	0.962625i	$-0.587300\pi$
$479$	−6.37759e6	−	4.63359e6i	−1.27004	−	0.922739i	−0.999204	+	0.0398867i	$0.987300\pi$
$480$	−193491.	+	477475.i	−0.0383316	+	0.0945904i
$481$	−302154.	+	219528.i	−0.0595478	+	0.0432640i
$482$	3.56358e6			0.698666
$483$	−202800.	+	147343.i	−0.0395549	+	0.0287383i
$484$	−789984.	−	2.43132e6i	−0.153287	−	0.471769i
$485$	−99006.6	+	244317.i	−0.0191122	+	0.0471628i
$486$	72988.6	−	224636.i	0.0140173	−	0.0431408i
$487$	1.40003e6	+	4.30885e6i	0.267495	+	0.823264i	0.991108	+	0.133059i	$0.0424798\pi$
$487$	1.40003e6	+	4.30885e6i	0.267495	+	0.823264i	−0.723613	+	0.690205i	$0.757520\pi$
$488$	988739.	+	3.04303e6i	0.187946	+	0.578437i
$489$	757443.	−	2.33117e6i	0.143244	−	0.440861i
$490$	−3.72006e6	−	264024.i	−0.699937	−	0.0496768i
$491$	−242028.	−	744887.i	−0.0453067	−	0.139440i	0.925844	−	0.377905i	$-0.123356\pi$
$491$	−242028.	−	744887.i	−0.0453067	−	0.139440i	−0.971151	+	0.238466i	$0.923356\pi$
$492$	−502010.	+	364732.i	−0.0934975	+	0.0679299i
$493$	3.36538e6			0.623615
$494$	223482.	−	162370.i	0.0412027	−	0.0299355i
$495$	38925.8	+	156818.i	0.00714043	+	0.0287663i
$496$	−207645.	−	150863.i	−0.0378980	−	0.0275345i
$497$	−498650.	−	362290.i	−0.0905533	−	0.0657909i
$498$	−736642.	+	2.26715e6i	−0.133102	+	0.409644i
$499$	1.16779e6			0.209949			0.104975	−	0.994475i	$-0.466524\pi$
$499$	1.16779e6			0.209949			0.104975	+	0.994475i	$0.466524\pi$
$500$	−283481.	−	2.78067e6i	−0.0507106	−	0.497422i
$501$	−2.03017e6			−0.361359
$502$	588315.	−	1.81065e6i	0.104196	−	0.320682i
$503$	2.89638e6	+	2.10434e6i	0.510429	+	0.370849i	0.812986	−	0.582283i	$-0.197840\pi$
$503$	2.89638e6	+	2.10434e6i	0.510429	+	0.370849i	−0.302557	+	0.953131i	$0.597840\pi$
$504$	47552.3	+	34548.7i	0.00833863	+	0.00605837i
$505$	244414.	+	984657.i	0.0426479	+	0.171813i
$506$	283666.	−	206095.i	0.0492528	−	0.0357842i
$507$	3.30900e6			0.571712
$508$	−1.02737e6	+	746429.i	−0.176632	+	0.128330i
$509$	1.17839e6	+	3.62670e6i	0.201601	+	0.620464i	0.999836	+	0.0181179i	$0.00576743\pi$
$509$	1.17839e6	+	3.62670e6i	0.201601	+	0.620464i	−0.798235	+	0.602346i	$0.794233\pi$
$510$	−3.03695e6	−	215542.i	−0.517026	−	0.0366950i
$511$	154.374	−	475.114i	2.61530e−5	−	8.04906e-5i
$512$	−81007.0	−	249314.i	−0.0136568	−	0.0420312i
$513$	−258349.	−	795116.i	−0.0433424	−	0.133394i
$514$	−336711.	+	1.03629e6i	−0.0562146	+	0.173011i
$515$	3.65191e6	−	9.01177e6i	0.606739	−	1.49724i
$516$	−57944.8	−	178336.i	−0.00958055	−	0.0294859i
$517$	402283.	−	292275.i	0.0661919	−	0.0480912i
$518$	−281287.			−0.0460602
$519$	3.06459e6	−	2.22656e6i	0.499407	−	0.362840i
$520$	80914.7	−	199672.i	0.0131226	−	0.0323824i
$521$	8.07555e6	+	5.86723e6i	1.30340	+	0.946976i	0.999983	−	0.00588133i	$-0.00187210\pi$
$521$	8.07555e6	+	5.86723e6i	1.30340	+	0.946976i	0.303418	+	0.952857i	$0.401872\pi$
$522$	583089.	+	423639.i	0.0936609	+	0.0680487i
$523$	−1.44798e6	+	4.45641e6i	−0.231477	+	0.712412i	0.766093	+	0.642730i	$0.222198\pi$
$523$	−1.44798e6	+	4.45641e6i	−0.231477	+	0.712412i	−0.997569	+	0.0696817i	$0.977802\pi$
$524$	1.70615e6			0.271449
$525$	−315694.	−	45038.5i	−0.0499882	−	0.00713157i
$526$	4.29650e6			0.677097
$527$	468713.	−	1.44255e6i	0.0735158	−	0.226258i
$528$	−66513.6	−	48324.9i	−0.0103831	−	0.00754374i
$529$	325127.	+	236218.i	0.0505142	+	0.0367007i
$530$	918056.	+	771971.i	0.141964	+	0.119374i
$531$	1.68834e6	−	1.22665e6i	0.259851	−	0.188793i
$532$	208049.			0.0318703
$533$	209932.	−	152525.i	0.0320082	−	0.0232553i
$534$	−158318.	−	487254.i	−0.0240258	−	0.0739439i
$535$	484287.	+	1.95102e6i	0.0731507	+	0.294698i
$536$	−639780.	+	1.96904e6i	−0.0961875	+	0.296035i
$537$	965979.	+	2.97298e6i	0.144555	+	0.444893i
$538$	2.87340e6	+	8.84340e6i	0.427996	+	1.31724i
$539$	183911.	−	566020.i	0.0272669	−	0.0839189i
$540$	−499053.	−	419641.i	−0.0736482	−	0.0619290i
$541$	−2.71294e6	−	8.34959e6i	−0.398518	−	1.22651i	−0.926188	−	0.377062i	$-0.876934\pi$
$541$	−2.71294e6	−	8.34959e6i	−0.398518	−	1.22651i	0.527670	−	0.849449i	$-0.323066\pi$
$542$	4.67599e6	−	3.39730e6i	0.683715	−	0.496748i
$543$	−5.18166e6			−0.754170
$544$	1.25331e6	−	910585.i	0.181578	−	0.131924i
$545$	6.85523e6	−	4.27371e6i	0.988624	−	0.616330i
$546$	−19885.6	−	14447.7i	−0.00285467	−	0.00207404i
$547$	1.11572e7	+	8.10621e6i	1.59437	+	1.15838i	0.897347	+	0.441325i	$0.145491\pi$
$547$	1.11572e7	+	8.10621e6i	1.59437	+	1.15838i	0.697021	+	0.717051i	$0.254509\pi$
$548$	−1.58001e6	+	4.86278e6i	−0.224755	+	0.691725i
$549$	−4.04953e6			−0.573421
$550$	441575.	+	62997.4i	0.0622441	+	0.00888006i
$551$	2.55111e6			0.357972
$552$	−437244.	+	1.34570e6i	−0.0610768	+	0.187975i
$553$	211203.	+	153448.i	0.0293689	+	0.0213377i
$554$	−3.30086e6	−	2.39821e6i	−0.456933	−	0.331981i
$555$	3.11256e6	+	220908.i	0.428929	+	0.0304425i
$556$	270834.	−	196772.i	0.0371549	−	0.0269946i
$557$	4.37900e6			0.598050			0.299025	−	0.954245i	$-0.403339\pi$
$557$	4.37900e6			0.598050			0.299025	+	0.954245i	$0.403339\pi$
$558$	262800.	−	190936.i	0.0357306	−	0.0259598i
$559$	24231.6	+	74577.1i	0.00327983	+	0.0100943i
$560$	137694.	−	85841.8i	0.0185544	−	0.0115672i
$561$	150140.	−	462084.i	0.0201414	−	0.0619888i
$562$	1.29326e6	+	3.98026e6i	0.172721	+	0.531582i
$563$	1.18099e6	+	3.63471e6i	0.157027	+	0.483280i	0.998361	−	0.0572364i	$-0.0182289\pi$
$563$	1.18099e6	+	3.63471e6i	0.157027	+	0.483280i	−0.841333	+	0.540516i	$0.818229\pi$
$564$	−620081.	+	1.90841e6i	−0.0820825	+	0.252624i
$565$	4.81212e6	−	2.99998e6i	0.634184	−	0.395364i
$566$	1.48801e6	+	4.57962e6i	0.195238	+	0.600881i
$567$	−60183.3	+	43725.8i	−0.00786174	+	0.00571189i
$568$	−3.47912e6			−0.452479
$569$	−4.15605e6	+	3.01955e6i	−0.538146	+	0.390986i	−0.823396	−	0.567467i	$-0.807923\pi$
$569$	−4.15605e6	+	3.01955e6i	−0.538146	+	0.390986i	0.285250	+	0.958453i	$0.407923\pi$
$570$	−2.30215e6	−	163391.i	−0.296788	−	0.0210640i
$571$	2.72498e6	+	1.97982e6i	0.349763	+	0.254117i	0.748769	−	0.662831i	$-0.230645\pi$
$571$	2.72498e6	+	1.97982e6i	0.349763	+	0.254117i	−0.399007	+	0.916948i	$0.630645\pi$
$572$	27814.9	+	20208.7i	0.00355457	+	0.00258255i
$573$	609604.	−	1.87617e6i	0.0775641	−	0.238718i
$574$	195434.			0.0247583
$575$	−1.31728e6	−	7.56274e6i	−0.166153	−	0.953915i
$576$	331776.			0.0416667
$577$	−2.75723e6	+	8.48587e6i	−0.344773	+	1.06110i	0.616933	+	0.787016i	$0.288375\pi$
$577$	−2.75723e6	+	8.48587e6i	−0.344773	+	1.06110i	−0.961705	+	0.274085i	$0.911625\pi$
$578$	2.81189e6	+	2.04295e6i	0.350089	+	0.254354i
$579$	2.64909e6	+	1.92467e6i	0.328398	+	0.238595i
$580$	1.68842e6	−	1.05260e6i	0.208406	−	0.129925i
$581$	607404.	−	441305.i	0.0746513	−	0.0542374i
$582$	169765.			0.0207750
$583$	−154859.	+	112512.i	−0.0188698	+	0.0137097i
$584$	−871.374	−	2681.81i	−0.000105724	−	0.000325384i
$585$	208696.	+	175487.i	0.0252130	+	0.0212010i
$586$	−3.22304e6	+	9.91951e6i	−0.387723	+	1.19329i
$587$	−3.05921e6	−	9.41529e6i	−0.366450	−	1.12782i	−0.949068	−	0.315070i	$-0.897972\pi$
$587$	−3.05921e6	−	9.41529e6i	−0.366450	−	1.12782i	0.582619	−	0.812746i	$-0.302028\pi$
$588$	742165.	+	2.28415e6i	0.0885232	+	0.272446i
$589$	355306.	−	1.09352e6i	0.0422001	−	0.129879i
$590$	−1.38791e6	−	5.59139e6i	−0.164146	−	0.661287i
$591$	−2.87666e6	−	8.85346e6i	−0.338782	−	1.04266i
$592$	−1.28451e6	+	933254.i	−0.150638	+	0.109445i
$593$	1.03902e7			1.21335			0.606674	−	0.794951i	$-0.292503\pi$
$593$	1.03902e7			1.21335			0.606674	+	0.794951i	$0.292503\pi$
$594$	84181.2	−	61161.2i	0.00978924	−	0.00711230i
$595$	733921.	+	617137.i	0.0849879	+	0.0714643i
$596$	278277.	+	202180.i	0.0320894	+	0.0233143i
$597$	2.29555e6	+	1.66781e6i	0.263603	+	0.191519i
$598$	182848.	−	562749.i	0.0209092	−	0.0643520i
$599$	−1.40042e7			−1.59475			−0.797374	−	0.603486i	$-0.793778\pi$
$599$	−1.40042e7			−1.59475			−0.797374	+	0.603486i	$0.793778\pi$
$600$	−1.59106e6	+	841737.i	−0.180430	+	0.0954549i
$601$	8.87639e6			1.00242			0.501210	−	0.865325i	$-0.332888\pi$
$601$	8.87639e6			1.00242			0.501210	+	0.865325i	$0.332888\pi$
$602$	−18249.9	+	56167.4i	−0.00205243	+	0.00631675i
$603$	−2.11988e6	−	1.54018e6i	−0.237420	−	0.172496i
$604$	3.56759e6	+	2.59201e6i	0.397908	+	0.289097i
$605$	3.35455e6	−	8.27797e6i	0.372602	−	0.919466i
$606$	528571.	−	384030.i	0.0584685	−	0.0424799i
$607$	1.45159e7			1.59909			0.799545	−	0.600607i	$-0.205074\pi$
$607$	1.45159e7			1.59909			0.799545	+	0.600607i	$0.205074\pi$
$608$	950067.	−	690264.i	0.104231	−	0.0757280i
$609$	−70146.4	−	215889.i	−0.00766412	−	0.0235877i
$610$	−4.19853e6	+	1.03607e7i	−0.456849	+	1.12736i
$611$	259308.	−	798067.i	0.0281004	−	0.0864841i
$612$	605884.	+	1.86472e6i	0.0653899	+	0.201249i
$613$	−646769.	−	1.99055e6i	−0.0695181	−	0.213955i	0.910262	−	0.414033i	$-0.135880\pi$
$613$	−646769.	−	1.99055e6i	−0.0695181	−	0.213955i	−0.979780	+	0.200079i	$0.935880\pi$
$614$	−296409.	+	912254.i	−0.0317301	+	0.0976551i
$615$	−2.16256e6	−	153484.i	−0.230559	−	0.0163635i
$616$	8001.68	+	24626.6i	0.000849629	+	0.00261489i
$617$	−1.08331e7	+	7.87073e6i	−1.14562	+	0.832342i	−0.987892	−	0.155140i	$-0.950417\pi$
$617$	−1.08331e7	+	7.87073e6i	−1.14562	+	0.832342i	−0.157729	+	0.987482i	$0.550417\pi$
$618$	−6.26188e6			−0.659528
$619$	−4.84194e6	+	3.51787e6i	−0.507917	+	0.369023i	−0.812033	−	0.583612i	$-0.801639\pi$
$619$	−4.84194e6	+	3.51787e6i	−0.507917	+	0.369023i	0.304116	+	0.952635i	$0.401639\pi$
$620$	−216036.	−	870332.i	−0.0225708	−	0.0909297i
$621$	−1.44879e6	−	1.05261e6i	−0.150756	−	0.109531i
$622$	−220090.	−	159905.i	−0.0228100	−	0.0165724i
$623$	−49862.9	+	153462.i	−0.00514704	+	0.0158410i
$624$	−138743.			−0.0142643
$625$	5.49454e6	−	8.07326e6i	0.562641	−	0.826701i
$626$	1.12725e7			1.14970
$627$	113813.	−	350280.i	0.0115617	−	0.0355833i
$628$	−735053.	−	534048.i	−0.0743738	−	0.0540357i
$629$	−7.59103e6	−	5.51521e6i	−0.765022	−	0.555821i
$630$	49473.9	+	199313.i	0.00496621	+	0.0200071i
$631$	1.25166e7	−	9.09386e6i	1.25145	−	0.909232i	0.253146	−	0.967428i	$-0.418535\pi$
$631$	1.25166e7	−	9.09386e6i	1.25145	−	0.909232i	0.998305	+	0.0581959i	$0.0185348\pi$
$632$	1.47358e6			0.146751
$633$	−5.04212e6	+	3.66332e6i	−0.500154	+	0.363383i
$634$	−68141.0	−	209716.i	−0.00673264	−	0.0207209i
$635$	−4.42572e6	−	314108.i	−0.435562	−	0.0309132i
$636$	238701.	−	734647.i	0.0233998	−	0.0720172i
$637$	−310361.	−	955193.i	−0.0303053	−	0.0932701i
$638$	98117.1	+	301973.i	0.00954317	+	0.0293709i
$639$	1.36068e6	−	4.18775e6i	0.131827	−	0.405722i
$640$	343984.	−	848844.i	0.0331962	−	0.0819177i
$641$	−2.11571e6	−	6.51150e6i	−0.203382	−	0.625945i	−0.999776	−	0.0211668i	$-0.993262\pi$
$641$	−2.11571e6	−	6.51150e6i	−0.203382	−	0.625945i	0.796394	−	0.604778i	$-0.206738\pi$
$642$	1.04732e6	−	760925.i	0.100287	−	0.0728625i
$643$	−6.71374e6			−0.640379			−0.320190	−	0.947353i	$-0.603747\pi$
$643$	−6.71374e6			−0.640379			−0.320190	+	0.947353i	$0.603747\pi$
$644$	360533.	−	261943.i	0.0342556	−	0.0248881i
$645$	246054.	−	607184.i	0.0232879	−	0.0574673i
$646$	5.61456e6	+	4.07922e6i	0.529340	+	0.384588i
$647$	−8.06291e6	−	5.85805e6i	−0.757236	−	0.550164i	0.140825	−	0.990034i	$-0.455024\pi$
$647$	−8.06291e6	−	5.85805e6i	−0.757236	−	0.550164i	−0.898061	+	0.439870i	$0.855024\pi$
$648$	−129757.	+	399352.i	−0.0121393	+	0.0373610i
$649$	919366.			0.0856795
$650$	665356.	−	352001.i	0.0617690	−	0.0326783i
$651$	−102309.			−0.00946154
$652$	−1.34656e6	+	4.14430e6i	−0.124053	+	0.381797i
$653$	−4.19359e6	−	3.04682e6i	−0.384860	−	0.279617i	0.378486	−	0.925607i	$-0.376445\pi$
$653$	−4.19359e6	−	3.04682e6i	−0.384860	−	0.279617i	−0.763346	+	0.645990i	$0.776445\pi$
$654$	−4.20877e6	−	3.05785e6i	−0.384778	−	0.279558i
$655$	4.56243e6	+	3.83644e6i	0.415521	+	0.349401i
$656$	892463.	−	648412.i	0.0809712	−	0.0588290i
$657$	3568.84			0.000322563
$658$	511293.	−	371476.i	0.0460368	−	0.0334477i
$659$	−1.02922e6	−	3.16763e6i	−0.0923202	−	0.284132i	0.894226	−	0.447616i	$-0.147727\pi$
$659$	−1.02922e6	−	3.16763e6i	−0.0923202	−	0.284132i	−0.986546	+	0.163484i	$0.947727\pi$
$660$	−69201.4	−	278788.i	−0.00618380	−	0.0249123i
$661$	3.14712e6	−	9.68584e6i	0.280162	−	0.862251i	−0.707645	−	0.706568i	$-0.750242\pi$
$661$	3.14712e6	−	9.68584e6i	0.280162	−	0.862251i	0.987807	−	0.155682i	$-0.0497577\pi$
$662$	−2.14946e6	−	6.61535e6i	−0.190627	−	0.586689i
$663$	−253370.	−	779794.i	−0.0223858	−	0.0688963i
$664$	1.30959e6	−	4.03049e6i	0.115269	−	0.354763i
$665$	556345.	+	467817.i	0.0487854	+	0.0410225i
$666$	−620967.	−	1.91114e6i	−0.0542479	−	0.166958i
$667$	4.42088e6	−	3.21196e6i	0.384764	−	0.279547i
$668$	3.60919e6			0.312946
$669$	5.32788e6	−	3.87093e6i	0.460245	−	0.334387i
$670$	−6.13841e6	+	3.82682e6i	−0.528286	+	0.329345i
$671$	−1.44327e6	−	1.04860e6i	−0.123749	−	0.0899088i
$672$	−84537.4	−	61420.0i	−0.00722147	−	0.00524670i
$673$	−1.68567e6	+	5.18797e6i	−0.143462	+	0.441529i	−0.996810	−	0.0798118i	$-0.974568\pi$
$673$	−1.68567e6	+	5.18797e6i	−0.143462	+	0.441529i	0.853348	+	0.521341i	$0.174568\pi$
$674$	−9.94406e6			−0.843167
$675$	−390919.	−	2.24433e6i	−0.0330238	−	0.189596i
$676$	−5.88267e6			−0.495117
$677$	−4.63221e6	+	1.42565e7i	−0.388434	+	1.19548i	0.545525	+	0.838095i	$0.316330\pi$
$677$	−4.63221e6	+	1.42565e7i	−0.388434	+	1.19548i	−0.933959	+	0.357381i	$0.883670\pi$
$678$	−2.95440e6	−	2.14649e6i	−0.246828	−	0.179331i
$679$	−43256.6	−	31427.8i	−0.00360063	−	0.00261601i
$680$	5.39903e6	+	383187.i	0.447758	+	0.0317788i
$681$	1.69324e6	−	1.23021e6i	0.139911	−	0.101651i
$682$	143104.			0.0117813
$683$	−312541.	+	227075.i	−0.0256363	+	0.0186259i	−0.600530	−	0.799603i	$-0.705044\pi$
$683$	−312541.	+	227075.i	−0.0256363	+	0.0186259i	0.574893	+	0.818228i	$0.305044\pi$
$684$	459287.	+	1.41354e6i	0.0375356	+	0.115523i
$685$	−1.51595e7	+	9.45080e6i	−1.23441	+	0.769559i
$686$	469296.	−	1.44435e6i	0.0380747	−	0.117182i
$687$	1.87215e6	+	5.76188e6i	0.151338	+	0.465771i
$688$	103013.	+	317041.i	0.00829700	+	0.0255355i
$689$	−99821.0	+	307217.i	−0.00801076	+	0.0246546i
$690$	−4.19517e6	+	2.61536e6i	−0.335449	+	0.209127i
$691$	−6.74036e6	−	2.07447e7i	−0.537017	−	1.65277i	−0.739251	−	0.673430i	$-0.764820\pi$
$691$	−6.74036e6	−	2.07447e7i	−0.537017	−	1.65277i	0.202235	−	0.979337i	$-0.435180\pi$
$692$	−5.44816e6	+	3.95832e6i	−0.432499	+	0.314229i
$693$	−32772.1			−0.00259221
$694$	−1.93237e6	+	1.40395e6i	−0.152297	+	0.110651i
$695$	1.16670e6	+	82804.4i	0.0916214	+	0.00650267i
$696$	−1.03660e6	−	753136.i	−0.0811127	−	0.0589319i
$697$	5.27414e6	+	3.83189e6i	0.411216	+	0.298766i
$698$	2.31826e6	−	7.13488e6i	0.180104	−	0.554304i
$699$	9.61591e6			0.744385
$700$	561233.	+	80068.4i	0.0432911	+	0.00617612i
$701$	−6.07045e6			−0.466580			−0.233290	−	0.972407i	$-0.574949\pi$
$701$	−6.07045e6			−0.466580			−0.233290	+	0.972407i	$0.574949\pi$
$702$	54262.4	−	167003.i	0.00415582	−	0.0127903i
$703$	−5.75434e6	−	4.18077e6i	−0.439144	−	0.319057i
$704$	118246.	+	85911.0i	0.00899199	+	0.00653307i
$705$	−5.94941e6	+	3.70899e6i	−0.450818	+	0.281050i
$706$	−325587.	+	236553.i	−0.0245842	+	0.0178615i
$707$	−205775.			−0.0154826
$708$	−3.00150e6	+	2.18072e6i	−0.225038	+	0.163500i
$709$	1.63952e6	+	5.04593e6i	0.122490	+	0.376986i	0.993435	−	0.114394i	$-0.0364926\pi$
$709$	1.63952e6	+	5.04593e6i	0.122490	+	0.376986i	−0.870945	+	0.491380i	$0.836493\pi$
$710$	−9.30354e6	−	7.82312e6i	−0.692632	−	0.582417i
$711$	−576317.	+	1.77372e6i	−0.0427550	+	0.131586i
$712$	281455.	+	866230.i	0.0208070	+	0.0640373i
$713$	−761070.	−	2.34233e6i	−0.0560662	−	0.172554i
$714$	190825.	−	587299.i	0.0140084	−	0.0431135i
$715$	28938.9	+	116585.i	0.00211698	+	0.00852856i
$716$	−1.71730e6	−	5.28529e6i	−0.125188	−	0.385289i
$717$	−5.71841e6	+	4.15467e6i	−0.415410	+	0.301813i
$718$	−1.24797e7			−0.903426
$719$	−2.09181e7	+	1.51979e7i	−1.50904	+	1.09638i	−0.542439	+	0.840095i	$0.682499\pi$
$719$	−2.09181e7	+	1.51979e7i	−1.50904	+	1.09638i	−0.966601	+	0.256287i	$0.917501\pi$
$720$	887205.	+	746029.i	0.0637812	+	0.0536321i
$721$	1.59554e6	+	1.15923e6i	0.114306	+	0.0830484i
$722$	−3.75674e6	−	2.72943e6i	−0.268205	−	0.194863i
$723$	2.47772e6	−	7.62563e6i	0.176281	−	0.542538i
$724$	9.21184e6			0.653131
$725$	6.88188e6	+	981804.i	0.486252	+	0.0693713i
$726$	−5.75200e6			−0.405021
$727$	−4.19180e6	+	1.29010e7i	−0.294147	+	0.905291i	0.689360	+	0.724419i	$0.257892\pi$
$727$	−4.19180e6	+	1.29010e7i	−0.294147	+	0.905291i	−0.983507	+	0.180872i	$0.942108\pi$
$728$	35352.1	+	25684.8i	0.00247222	+	0.00179617i
$729$	−429945.	−	312373.i	−0.0299636	−	0.0217698i
$730$	3700.16	−	9130.83i	0.000256988	−	0.000634166i
$731$	−1.59378e6	+	1.15795e6i	−0.110315	+	0.0801487i
$732$	7.19916e6			0.496597
$733$	−1.22967e7	+	8.93410e6i	−0.845337	+	0.614173i	−0.923856	−	0.382739i	$-0.874981\pi$
$733$	−1.22967e7	+	8.93410e6i	−0.845337	+	0.614173i	0.0785194	+	0.996913i	$0.474981\pi$
$734$	−2.26088e6	−	6.95827e6i	−0.154895	−	0.476718i
$735$	−3.15149e6	+	7.77689e6i	−0.215178	+	0.530991i
$736$	777323.	−	2.39236e6i	0.0528941	−	0.162791i
$737$	−356715.	−	1.09785e6i	−0.0241909	−	0.0744519i
$738$	431440.	+	1.32783e6i	0.0291594	+	0.0897435i
$739$	−2.39552e6	+	7.37267e6i	−0.161358	+	0.496608i	−0.998749	−	0.0499954i	$-0.984079\pi$
$739$	−2.39552e6	+	7.37267e6i	−0.161358	+	0.496608i	0.837392	+	0.546603i	$0.184079\pi$
$740$	−5.53344e6	−	392726.i	−0.371463	−	0.0263640i
$741$	−192066.	−	591119.i	−0.0128501	−	0.0395484i
$742$	−196823.	+	143000.i	−0.0131240	+	0.00953515i
$743$	1.11864e7			0.743390			0.371695	−	0.928355i	$-0.378777\pi$
$743$	1.11864e7			0.743390			0.371695	+	0.928355i	$0.378777\pi$
$744$	−467200.	+	339441.i	−0.0309436	+	0.0224818i
$745$	289522.	+	1.16638e6i	0.0191113	+	0.0769928i
$746$	1.06658e7	+	7.74917e6i	0.701693	+	0.509810i
$747$	4.33925e6	+	3.15265e6i	0.284520	+	0.206716i
$748$	−266916.	+	821482.i	−0.0174430	+	0.0536839i
$749$	−407727.			−0.0265561
$750$	−6.14740e6	−	1.32675e6i	−0.399060	−	0.0861266i
$751$	−2.69780e6			−0.174546			−0.0872729	−	0.996184i	$-0.527815\pi$
$751$	−2.69780e6			−0.174546			−0.0872729	+	0.996184i	$0.527815\pi$
$752$	1.10237e6	−	3.39273e6i	0.0710855	−	0.218779i
$753$	−3.46552e6	−	2.51785e6i	−0.222731	−	0.161823i
$754$	433490.	+	314949.i	0.0277684	+	0.0201749i
$755$	3.71176e6	+	1.49534e7i	0.236980	+	0.954710i
$756$	106993.	−	77734.7i	0.00680847	−	0.00494664i
$757$	−1.26669e7			−0.803401			−0.401700	−	0.915771i	$-0.631581\pi$
$757$	−1.26669e7			−0.803401			−0.401700	+	0.915771i	$0.631581\pi$
$758$	1.57075e7	−	1.14121e7i	0.992963	−	0.721430i
$759$	−243789.	−	750306.i	−0.0153607	−	0.0472753i
$760$	4.09271e6	+	290473.i	0.257026	+	0.0182419i
$761$	−7.42688e6	+	2.28576e7i	−0.464884	+	1.43077i	0.394244	+	0.919006i	$0.371007\pi$
$761$	−7.42688e6	+	2.28576e7i	−0.464884	+	1.43077i	−0.859128	+	0.511761i	$0.828993\pi$
$762$	882947.	+	2.71743e6i	0.0550868	+	0.169540i
$763$	506321.	+	1.55829e6i	0.0314858	+	0.0969032i
$764$	−1.08374e6	+	3.33541e6i	−0.0671725	+	0.206736i
$765$	−2.57279e6	+	6.34884e6i	−0.158947	+	0.392230i
$766$	−4.35692e6	−	1.34092e7i	−0.268292	−	0.825717i
$767$	1.25518e6	−	911940.i	0.0770401	−	0.0559729i
$768$	−589824.			−0.0360844
$769$	−4.53963e6	+	3.29823e6i	−0.276824	+	0.201125i	−0.717531	−	0.696527i	$-0.754728\pi$
$769$	−4.53963e6	+	3.29823e6i	−0.276824	+	0.201125i	0.440707	+	0.897651i	$0.354728\pi$
$770$	−33977.9	+	83846.8i	−0.00206524	+	0.00509636i
$771$	1.98342e6	+	1.44104e6i	0.120165	+	0.0873051i
$772$	−4.70949e6	−	3.42164e6i	−0.284401	−	0.206629i
$773$	−452688.	+	1.39323e6i	−0.0272490	+	0.0838638i	−0.963756	−	0.266785i	$-0.914039\pi$
$773$	−452688.	+	1.39323e6i	−0.0272490	+	0.0838638i	0.936507	+	0.350648i	$0.114039\pi$
$774$	−421905.			−0.0253141
$775$	1.37932e6	−	2.81314e6i	0.0824917	−	0.168243i
$776$	−301805.			−0.0179917
$777$	−195576.	+	601920.i	−0.0116215	+	0.0357673i
$778$	−9.39454e6	−	6.82553e6i	−0.556450	−	0.404285i
$779$	3.99804e6	+	2.90474e6i	0.236050	+	0.171500i
$780$	−371015.	−	311977.i	−0.0218351	−	0.0183606i
$781$	1.56934e6	−	1.14019e6i	0.0920639	−	0.0668883i
$782$	1.48656e7			0.869289
$783$	1.31195e6	−	953187.i	0.0764738	−	0.0555615i
$784$	−1.31940e6	−	4.06071e6i	−0.0766633	−	0.235945i
$785$	−764757.	−	3.08094e6i	−0.0442945	−	0.178447i
$786$	1.18627e6	−	3.65095e6i	0.0684898	−	0.210790i
$787$	−7.14192e6	−	2.19806e7i	−0.411034	−	1.26503i	−0.915750	−	0.401748i	$-0.868403\pi$
$787$	−7.14192e6	−	2.19806e7i	−0.411034	−	1.26503i	0.504716	−	0.863285i	$-0.331597\pi$
$788$	5.11407e6	+	1.57395e7i	0.293394	+	0.902973i
$789$	2.98731e6	−	9.19399e6i	0.170839	−	0.525789i
$790$	3.94051e6	+	3.31348e6i	0.224639	+	0.188893i
$791$	355418.	+	1.09386e6i	0.0201975	+	0.0621616i
$792$	−149656.	+	108731.i	−0.00847773	+	0.00615943i
$793$	−3.01057e6			−0.170007
$794$	−2.34172e6	+	1.70136e6i	−0.131821	+	0.0957734i
$795$	2.29024e6	−	1.42778e6i	0.128518	−	0.0801207i
$796$	−4.08098e6	−	2.96500e6i	−0.228287	−	0.165860i
$797$	−1.74866e7	−	1.27047e7i	−0.975121	−	0.708467i	−0.0185079	−	0.999829i	$-0.505892\pi$
$797$	−1.74866e7	−	1.27047e7i	−0.975121	−	0.708467i	−0.956613	+	0.291362i	$0.905892\pi$
$798$	144654.	−	445199.i	0.00804124	−	0.0247484i
$799$	2.10817e7			1.16826
$800$	2.82855e6	−	1.49642e6i	0.156257	−	0.0826664i
$801$	−1.15274e6			−0.0634820
$802$	−2.02739e6	+	6.23968e6i	−0.111302	+	0.342552i
$803$	1271.95	+	924.126i	6.96116e−5	+	5.05758e-5i
$804$	3.76867e6	+	2.73810e6i	0.205612	+	0.149386i
$805$	1.55311e6	+	110229.i	0.0844719	+	0.00599524i
$806$	195375.	−	141949.i	0.0105933	−	0.00769650i
$807$	2.09216e7			1.13087
$808$	−939682.	+	682719.i	−0.0506352	+	0.0367886i
$809$	5.58531e6	+	1.71898e7i	0.300038	+	0.923421i	0.981483	+	0.191552i	$0.0613519\pi$
$809$	5.58531e6	+	1.71898e7i	0.300038	+	0.923421i	−0.681445	+	0.731869i	$0.738648\pi$
$810$	−1.24497e6	+	776140.i	−0.0666723	+	0.0415650i
$811$	2.87353e6	−	8.84383e6i	0.153414	−	0.472159i	−0.844583	−	0.535425i	$-0.820152\pi$
$811$	2.87353e6	−	8.84383e6i	0.153414	−	0.472159i	0.997997	+	0.0632657i	$0.0201516\pi$
$812$	124705.	+	383802.i	0.00663732	+	0.0204276i
$813$	−4.01865e6	−	1.23681e7i	−0.213233	−	0.656264i
$814$	273561.	−	841933.i	0.0144708	−	0.0445366i
$815$	−1.29197e7	+	8.05444e6i	−0.681332	+	0.424758i
$816$	−1.07713e6	−	3.31505e6i	−0.0566293	−	0.174287i
$817$	−1.20816e6	+	877778.i	−0.0633241	+	0.0460076i
$818$	1.44023e7			0.752574
$819$	−44742.5	+	32507.4i	−0.00233083	+	0.00169345i
$820$	3.84456e6	+	272861.i	0.199670	+	0.0141712i
$821$	2.50643e7	+	1.82103e7i	1.29777	+	0.942887i	0.999931	−	0.0117290i	$-0.00373353\pi$
$821$	2.50643e7	+	1.82103e7i	1.29777	+	0.942887i	0.297841	+	0.954616i	$0.403734\pi$
$822$	9.30719e6	+	6.76207e6i	0.480440	+	0.349060i
$823$	2.01645e6	−	6.20601e6i	0.103774	−	0.319384i	−0.885667	−	0.464322i	$-0.846298\pi$
$823$	2.01645e6	−	6.20601e6i	0.103774	−	0.319384i	0.989441	+	0.144938i	$0.0462982\pi$
$824$	1.11322e7			0.571168
$825$	441829.	−	901116.i	0.0226006	−	0.0460941i
$826$	1.16850e6			0.0595905
$827$	−5.71644e6	+	1.75934e7i	−0.290644	+	0.894512i	0.694005	+	0.719970i	$0.255844\pi$
$827$	−5.71644e6	+	1.75934e7i	−0.290644	+	0.894512i	−0.984650	+	0.174542i	$0.944156\pi$
$828$	2.57562e6	+	1.87130e6i	0.130559	+	0.0948565i
$829$	7.26194e6	+	5.27611e6i	0.367000	+	0.266641i	0.755966	−	0.654611i	$-0.227167\pi$
$829$	7.26194e6	+	5.27611e6i	0.367000	+	0.266641i	−0.388966	+	0.921252i	$0.627167\pi$
$830$	1.25649e7	−	7.83325e6i	0.633088	−	0.394681i
$831$	−7.42693e6	+	5.39598e6i	−0.373084	+	0.271061i
$832$	246655.			0.0123532
$833$	2.04134e7	−	1.48312e7i	1.01930	−	0.740565i
$834$	−232761.	−	716364.i	−0.0115876	−	0.0356631i
$835$	9.65138e6	+	8.11561e6i	0.479042	+	0.402814i
$836$	−202334.	+	622720.i	−0.0100127	+	0.0308161i
$837$	−225857.	−	695116.i	−0.0111434	−	0.0342960i
$838$	−8.20489e6	−	2.52521e7i	−0.403611	−	1.24219i
$839$	8.57120e6	−	2.63794e7i	0.420375	−	1.29378i	−0.486980	−	0.873413i	$-0.661901\pi$
$839$	8.57120e6	−	2.63794e7i	0.420375	−	1.29378i	0.907354	−	0.420367i	$-0.138099\pi$
$840$	−87953.6	−	354334.i	−0.00430086	−	0.0173266i
$841$	−4.80916e6	−	1.48011e7i	−0.234465	−	0.721611i
$842$	−392225.	+	284968.i	−0.0190658	+	0.0138521i
$843$	9.41645e6			0.456371
$844$	8.96377e6	−	6.51256e6i	0.433146	−	0.314699i
$845$	−1.57309e7	−	1.32277e7i	−0.757900	−	0.637299i
$846$	3.65263e6	+	2.65379e6i	0.175461	+	0.127480i
$847$	1.46562e6	+	1.06484e6i	0.0701962	+	0.0510006i
$848$	−424358.	+	1.30604e6i	−0.0202648	+	0.0623687i
$849$	1.08344e7			0.515865
$850$	1.35760e7	+	1.31649e7i	0.644501	+	0.624986i
$851$	−1.52356e7			−0.721168
$852$	−2.41899e6	+	7.44489e6i	−0.114166	+	0.351365i
$853$	−1.96667e7	−	1.42887e7i	−0.925462	−	0.672388i	0.0194154	−	0.999812i	$-0.493820\pi$
$853$	−1.96667e7	−	1.42887e7i	−0.925462	−	0.672388i	−0.944878	+	0.327424i	$0.893820\pi$
$854$	−1.83437e6	−	1.33274e6i	−0.0860679	−	0.0625320i
$855$	−1.95029e6	+	4.81271e6i	−0.0912398	+	0.225151i
$856$	−1.86191e6	+	1.35275e6i	−0.0868508	+	0.0631008i
$857$	5.81819e6			0.270605			0.135302	−	0.990804i	$-0.456799\pi$
$857$	5.81819e6			0.270605			0.135302	+	0.990804i	$0.456799\pi$
$858$	62583.5	−	45469.5i	0.00290229	−	0.00210864i
$859$	789894.	+	2.43104e6i	0.0365246	+	0.112411i	0.967657	−	0.252271i	$-0.0811775\pi$
$859$	789894.	+	2.43104e6i	0.0365246	+	0.112411i	−0.931132	+	0.364683i	$0.881178\pi$
$860$	−437429.	+	1.07944e6i	−0.0201679	+	0.0497681i
$861$	135883.	−	418206.i	0.00624681	−	0.0192257i
$862$	−8.97672e6	−	2.76275e7i	−0.411481	−	1.26641i
$863$	8.81621e6	+	2.71335e7i	0.402954	+	1.24016i	0.922592	+	0.385777i	$0.126067\pi$
$863$	8.81621e6	+	2.71335e7i	0.402954	+	1.24016i	−0.519638	+	0.854386i	$0.673933\pi$
$864$	230680.	−	709960.i	0.0105130	−	0.0323556i
$865$	−2.34696e7	−	1.66572e6i	−1.06651	−	0.0756939i
$866$	−2.23319e6	−	6.87306e6i	−0.101189	−	0.311427i
$867$	6.32674e6	−	4.59665e6i	0.285846	−	0.207679i
$868$	181883.			0.00819393
$869$	−664694.	+	482928.i	−0.0298588	+	0.0216937i
$870$	−1.07849e6	−	4.34486e6i	−0.0483080	−	0.194616i
$871$	−1.57600e6	−	1.14503e6i	−0.0703898	−	0.0511412i
$872$	7.48225e6	+	5.43617e6i	0.333228	+	0.242104i
$873$	118036.	−	363277.i	0.00524177	−	0.0161325i
$874$	1.12688e7			0.498996
$875$	1.32076e6	+	1.47610e6i	0.0583180	+	0.0651770i
$876$	−6344.61			−0.000279347
$877$	−7.73964e6	+	2.38202e7i	−0.339799	+	1.04579i	0.624511	+	0.781016i	$0.285298\pi$
$877$	−7.73964e6	+	2.38202e7i	−0.339799	+	1.04579i	−0.964310	+	0.264777i	$0.914702\pi$
$878$	−8.59053e6	−	6.24138e6i	−0.376083	−	0.273240i
$879$	1.89856e7	+	1.37938e7i	0.828804	+	0.602161i
$880$	123025.	+	495623.i	0.00535532	+	0.0215747i
$881$	−1.16837e7	+	8.48869e6i	−0.507154	+	0.368469i	−0.811743	−	0.584015i	$-0.801481\pi$
$881$	−1.16837e7	+	8.48869e6i	−0.507154	+	0.368469i	0.304589	+	0.952484i	$0.401481\pi$
$882$	5.40382e6			0.233899
$883$	−2.49344e7	+	1.81159e7i	−1.07621	+	0.781911i	−0.977018	−	0.213157i	$-0.931625\pi$
$883$	−2.49344e7	+	1.81159e7i	−1.07621	+	0.781911i	−0.0991904	+	0.995068i	$0.531625\pi$
$884$	450436.	+	1.38630e6i	0.0193866	+	0.0596660i
$885$	−1.29299e7	−	917676.i	−0.554928	−	0.0393850i
$886$	−5.08433e6	+	1.56479e7i	−0.217595	+	0.669689i
$887$	−9.14569e6	−	2.81476e7i	−0.390308	−	1.20125i	−0.932556	−	0.361026i	$-0.882426\pi$
$887$	−9.14569e6	−	2.81476e7i	−0.390308	−	1.20125i	0.542247	−	0.840219i	$-0.317574\pi$
$888$	1.10394e6	+	3.39758e6i	0.0469801	+	0.144590i
$889$	278087.	−	855864.i	0.0118012	−	0.0363204i
$890$	−1.19516e6	+	2.94927e6i	−0.0505766	+	0.124807i
$891$	−72347.3	−	222662.i	−0.00305301	−	0.00939620i
$892$	−9.47178e6	+	6.88165e6i	−0.398584	+	0.289588i
$893$	1.59809e7			0.670612
$894$	626123.	−	454905.i	0.0262009	−	0.0190360i
$895$	7.29224e6	−	1.79950e7i	0.304301	−	0.750919i
$896$	150289.	+	109191.i	0.00625398	+	0.00454378i
$897$	−1.07708e6	−	782546.i	−0.0446959	−	0.0324735i
$898$	5.71293e6	−	1.75826e7i	0.236411	−	0.727599i
$899$	2.23026e6			0.0920356
$900$	694968.	+	3.98993e6i	0.0285995	+	0.164195i
$901$	−8.11544e6			−0.333043
$902$	−190066.	+	584964.i	−0.00777837	+	0.0239394i
$903$	107502.	+	78105.1i	0.00438732	+	0.00318757i
$904$	5.25226e6	+	3.81599e6i	0.213759	+	0.155305i
$905$	2.46335e7	+	2.07137e7i	0.999780	+	0.840690i
$906$	8.02708e6	−	5.83201e6i	0.324891	−	0.236047i
$907$	3.12416e7			1.26100			0.630499	−	0.776190i	$-0.282850\pi$
$907$	3.12416e7			1.26100			0.630499	+	0.776190i	$0.282850\pi$
$908$	−3.01021e6	+	2.18704e6i	−0.121166	+	0.0880325i
$909$	−454267.	−	1.39809e6i	−0.0182348	−	0.0561210i
$910$	36780.7	+	148177.i	0.00147237	+	0.00593166i
$911$	−1.23567e7	+	3.80301e7i	−0.493296	+	1.51821i	0.326300	+	0.945266i	$0.394198\pi$
$911$	−1.23567e7	+	3.80301e7i	−0.493296	+	1.51821i	−0.819596	+	0.572942i	$0.805802\pi$
$912$	−816510.	−	2.51296e6i	−0.0325068	−	0.100046i
$913$	730170.	+	2.24723e6i	0.0289899	+	0.0892218i
$914$	−7.01766e6	+	2.15981e7i	−0.277861	+	0.855167i
$915$	1.92513e7	+	1.61880e7i	0.760166	+	0.639205i
$916$	−3.32826e6	−	1.02433e7i	−0.131063	−	0.403370i
$917$	−978145.	+	710664.i	−0.0384132	+	0.0279088i
$918$	4.41153e6			0.172776
$919$	1.88612e7	−	1.37035e7i	0.736684	−	0.535232i	−0.154987	−	0.987917i	$-0.549534\pi$
$919$	1.88612e7	−	1.37035e7i	0.736684	−	0.535232i	0.891671	+	0.452684i	$0.149534\pi$
$920$	7.45808e6	−	4.64954e6i	0.290508	−	0.181109i
$921$	1.74602e6	+	1.26856e6i	0.0678267	+	0.0492790i
$922$	−1.02987e7	−	7.48246e6i	−0.398984	−	0.289879i
$923$	1.01158e6	−	3.11333e6i	0.0390838	−	0.120288i
$924$	58261.4			0.00224492
$925$	−1.39139e7	−	1.34926e7i	−0.534682	−	0.518493i
$926$	−2.44112e7			−0.935537
$927$	−4.35381e6	+	1.33997e7i	−0.166406	+	0.512147i
$928$	1.84285e6	+	1.33891e6i	0.0702457	+	0.0510365i
$929$	1.37662e7	+	1.00017e7i	0.523327	+	0.380219i	0.817856	−	0.575423i	$-0.195163\pi$
$929$	1.37662e7	+	1.00017e7i	0.523327	+	0.380219i	−0.294529	+	0.955643i	$0.595163\pi$
$930$	−2.01261e6	−	142841.i	−0.0763049	−	0.00541560i
$931$	1.54743e7	−	1.12427e7i	0.585107	−	0.425105i
$932$	−1.70949e7			−0.644656
$933$	−495203.	+	359786.i	−0.0186243	+	0.0135313i
$934$	−4.30282e6	−	1.32427e7i	−0.161394	−	0.496719i
$935$	−2.56094e6	+	1.59655e6i	−0.0958011	+	0.0597246i
$936$	−96466.5	+	296893.i	−0.00359904	+	0.0110767i
$937$	−1.49189e7	−	4.59158e7i	−0.555123	−	1.70849i	−0.695619	−	0.718411i	$-0.744870\pi$
$937$	−1.49189e7	−	4.59158e7i	−0.555123	−	1.70849i	0.140497	−	0.990081i	$-0.455130\pi$
$938$	−453377.	−	1.39535e6i	−0.0168249	−	0.0517817i
$939$	7.83766e6	−	2.41218e7i	0.290083	−	0.892784i
$940$	1.05767e7	−	6.59377e6i	0.390420	−	0.243396i
$941$	1.03714e7	+	3.19197e7i	0.381822	+	1.17513i	0.938759	+	0.344573i	$0.111976\pi$
$941$	1.03714e7	+	3.19197e7i	0.381822	+	1.17513i	−0.556937	+	0.830555i	$0.688024\pi$
$942$	−1.65387e6	+	1.20161e6i	−0.0607259	+	0.0441200i
$943$	1.05855e7			0.387644
$944$	5.33600e6	−	3.87683e6i	0.194888	−	0.141595i
$945$	460904.	+	32711.8i	0.0167892	+	0.00119159i
$946$	−150369.	−	109249.i	−0.00546298	−	0.00396909i
$947$	−1.69775e7	−	1.23349e7i	−0.615175	−	0.446951i	0.236058	−	0.971739i	$-0.424145\pi$
$947$	−1.69775e7	−	1.23349e7i	−0.615175	−	0.446951i	−0.851233	+	0.524788i	$0.824145\pi$
$948$	1.02456e6	−	3.15328e6i	0.0370269	−	0.113957i
$949$	2653.21			9.56327e−5
$950$	1.02912e7	+	9.97958e6i	0.369961	+	0.358760i
$951$	−496145.			−0.0177892
$952$	−339244.	+	1.04409e6i	−0.0121317	+	0.0373374i
$953$	1.49279e7	+	1.08458e7i	0.532435	+	0.386837i	0.821268	−	0.570543i	$-0.193267\pi$
$953$	1.49279e7	+	1.08458e7i	0.532435	+	0.386837i	−0.288833	+	0.957380i	$0.593267\pi$
$954$	−1.40609e6	−	1.02158e6i	−0.0500198	−	0.0363415i
$955$	−1.03980e7	+	6.48236e6i	−0.368928	+	0.229998i
$956$	1.01661e7	−	7.38607e6i	0.359756	−	0.261378i
$957$	714405.			0.0252153
$958$	2.55104e7	−	1.85344e7i	0.898054	−	0.652475i
$959$	−1.11967e6	−	3.44598e6i	−0.0393136	−	0.120995i
$960$	−1.57725e6	−	1.32627e6i	−0.0552362	−	0.0464467i
$961$	−8.53627e6	+	2.62720e7i	−0.298167	+	0.917664i
$962$	−461650.	−	1.42081e6i	−0.0160833	−	0.0494993i
$963$	−900094.	−	2.77020e6i	−0.0312768	−	0.0962601i
$964$	−4.40483e6	+	1.35567e7i	−0.152664	+	0.469852i
$965$	−4.89980e6	−	1.97396e7i	−0.169379	−	0.682369i
$966$	−309851.	−	953623.i	−0.0106834	−	0.0328802i
$967$	3.51810e7	−	2.55605e7i	1.20988	−	0.879028i	0.214659	−	0.976689i	$-0.431136\pi$
$967$	3.51810e7	−	2.55605e7i	1.20988	−	0.879028i	0.995220	+	0.0976606i	$0.0311360\pi$
$968$	1.02258e7			0.350758
$969$	1.26328e7	−	9.17824e6i	0.432204	−	0.314015i
$970$	−807059.	−	678636.i	−0.0275408	−	0.0231584i
$971$	1.82651e7	+	1.32704e7i	0.621691	+	0.451685i	0.853512	−	0.521074i	$-0.174468\pi$
$971$	1.82651e7	+	1.32704e7i	0.621691	+	0.451685i	−0.231821	+	0.972759i	$0.574468\pi$
$972$	764346.	+	555330.i	0.0259492	+	0.0188532i
$973$	−73308.8	+	225621.i	−0.00248241	+	0.00764008i
$974$	−1.81224e7			−0.612094
$975$	−290624.	−	1.66852e6i	−0.00979084	−	0.0562109i
$976$	−1.27985e7			−0.430066
$977$	4.51052e6	−	1.38819e7i	0.151178	−	0.465280i	−0.846575	−	0.532269i	$-0.821339\pi$
$977$	4.51052e6	−	1.38819e7i	0.151178	−	0.465280i	0.997754	+	0.0669896i	$0.0213394\pi$
$978$	7.93204e6	+	5.76297e6i	0.265178	+	0.192663i
$979$	−410842.	−	298494.i	−0.0136999	−	0.00995357i
$980$	5.60265e6	−	1.38256e7i	0.186350	−	0.459852i
$981$	−9.46972e6	+	6.88016e6i	−0.314170	+	0.228258i
$982$	3.13288e6			0.103673
$983$	2.63701e7	−	1.91590e7i	0.870419	−	0.632396i	−0.0602804	−	0.998181i	$-0.519199\pi$
$983$	2.63701e7	−	1.91590e7i	0.870419	−	0.632396i	0.930699	+	0.365785i	$0.119199\pi$
$984$	−767004.	−	2.36059e6i	−0.0252528	−	0.0777202i
$985$	−2.17161e7	+	5.35886e7i	−0.713168	+	1.75987i
$986$	−4.15984e6	+	1.28027e7i	−0.136265	+	0.419380i
$987$	−439417.	−	1.35239e6i	−0.0143577	−	0.0441884i
$988$	341451.	+	1.05088e6i	0.0111285	+	0.0342499i
$989$	−988488.	+	3.04225e6i	−0.0321352	+	0.0989019i
$990$	−644687.	−	45755.5i	−0.0209055	−	0.00148373i
$991$	2.59952e6	+	8.00049e6i	0.0840830	+	0.258781i	0.984255	−	0.176753i	$-0.0565595\pi$
$991$	2.59952e6	+	8.00049e6i	0.0840830	+	0.258781i	−0.900172	+	0.435534i	$0.856559\pi$
$992$	830579.	−	603451.i	0.0267980	−	0.0194699i
$993$	−1.56505e7			−0.503681
$994$	1.99460e6	−	1.44916e6i	0.0640309	−	0.0465212i
$995$	−4.24589e6	−	1.71052e7i	−0.135960	−	0.547735i
$996$	−7.71422e6	−	5.60471e6i	−0.246402	−	0.179021i
$997$	−1.96472e7	−	1.42745e7i	−0.625984	−	0.454804i	0.229023	−	0.973421i	$-0.426447\pi$
$997$	−1.96472e7	−	1.42745e7i	−0.625984	−	0.454804i	−0.855007	+	0.518617i	$0.826447\pi$
$998$	−1.44347e6	+	4.44254e6i	−0.0458756	+	0.141190i
$999$	−4.52136e6			−0.143336

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.a.121.3	yes	20
25.6	even	5	inner	150.6.g.a.31.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.a.31.3	✓	20	25.6	even	5	inner
150.6.g.a.121.3	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	150.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23607 + 3.80423i) q^{2} +(7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-13.4674 - 54.2552i) q^{5} +(-29.1246 + 21.1603i) q^{6} +11.3383 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +O(q^{10})\)	\(q+(-1.23607 + 3.80423i) q^{2} +(7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-13.4674 - 54.2552i) q^{5} +(-29.1246 + 21.1603i) q^{6} +11.3383 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +(223.046 + 15.8303i) q^{10} +(-11.0269 + 33.9372i) q^{11} +(-44.4984 - 136.952i) q^{12} +(18.6085 + 57.2711i) q^{13} +(-14.0149 + 43.1335i) q^{14} +(188.956 - 466.284i) q^{15} +(79.1084 + 243.470i) q^{16} +(-1223.94 + 889.243i) q^{17} -324.000 q^{18} +(-927.800 + 674.086i) q^{19} +(-335.922 + 828.949i) q^{20} +(82.5560 + 59.9805i) q^{21} +(-115.475 - 83.8975i) q^{22} +(-759.105 + 2336.28i) q^{23} +576.000 q^{24} +(-2762.26 + 1461.35i) q^{25} -240.874 q^{26} +(-225.273 + 693.320i) q^{27} +(-146.766 - 106.632i) q^{28} +(-1799.66 - 1307.53i) q^{29} +(1540.29 + 1295.19i) q^{30} +(-811.112 + 589.307i) q^{31} -1024.00 q^{32} +(-259.819 + 188.769i) q^{33} +(-1870.01 - 5755.30i) q^{34} +(-152.697 - 615.163i) q^{35} +(400.486 - 1232.57i) q^{36} +(1916.57 + 5898.58i) q^{37} +(-1417.55 - 4362.78i) q^{38} +(-167.477 + 515.440i) q^{39} +(-2738.29 - 2302.56i) q^{40} +(-1331.60 - 4098.25i) q^{41} +(-330.224 + 239.922i) q^{42} +1302.18 q^{43} +(461.900 - 335.590i) q^{44} +(3842.49 - 2395.49i) q^{45} +(-7949.45 - 5775.61i) q^{46} +(-11273.6 - 8190.72i) q^{47} +(-711.975 + 2191.23i) q^{48} -16678.4 q^{49} +(-2144.96 - 12314.6i) q^{50} -13615.8 q^{51} +(297.736 - 916.338i) q^{52} +(4339.78 + 3153.03i) q^{53} +(-2359.09 - 1713.98i) q^{54} +(1989.78 + 141.221i) q^{55} +(587.065 - 426.528i) q^{56} -10321.4 q^{57} +(7198.63 - 5230.11i) q^{58} +(-7961.61 - 24503.3i) q^{59} +(-6831.09 + 4258.66i) q^{60} +(-15449.1 + 47547.3i) q^{61} +(-1239.27 - 3814.08i) q^{62} +(283.802 + 873.454i) q^{63} +(1265.73 - 3895.53i) q^{64} +(2856.65 - 1780.90i) q^{65} +(-396.968 - 1221.74i) q^{66} +(-26171.3 + 19014.6i) q^{67} +24205.9 q^{68} +(-17886.3 + 12995.1i) q^{69} +(2528.96 + 179.489i) q^{70} +(-43979.2 - 31952.7i) q^{71} +(4193.94 + 3047.08i) q^{72} +(13.6152 - 41.9034i) q^{73} -24808.5 q^{74} +(-27843.1 - 3972.24i) q^{75} +18349.2 q^{76} +(-125.026 + 384.791i) q^{77} +(-1753.84 - 1274.24i) q^{78} +(18627.4 + 13533.6i) q^{79} +(12144.2 - 7570.95i) q^{80} +(-5307.96 + 3856.46i) q^{81} +17236.6 q^{82} +(53570.9 - 38921.6i) q^{83} +(-504.538 - 1552.81i) q^{84} +(64729.3 + 54429.3i) q^{85} +(-1609.58 + 4953.77i) q^{86} +(-6186.67 - 19040.6i) q^{87} +(705.720 + 2171.98i) q^{88} +(-4397.74 + 13534.8i) q^{89} +(4363.42 + 17578.7i) q^{90} +(210.989 + 649.358i) q^{91} +(31797.8 - 23102.4i) q^{92} -9023.31 q^{93} +(45094.2 - 32762.9i) q^{94} +(49067.7 + 41259.8i) q^{95} +(-7455.90 - 5417.03i) q^{96} +(-3815.08 - 2771.82i) q^{97} +(20615.7 - 63448.6i) q^{98} -2890.38 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} + 45 q^{3} - 80 q^{4} - 55 q^{5} - 180 q^{6} + 180 q^{7} + 320 q^{8} - 405 q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 + 45 * q^3 - 80 * q^4 - 55 * q^5 - 180 * q^6 + 180 * q^7 + 320 * q^8 - 405 * q^9	\( 20 q + 20 q^{2} + 45 q^{3} - 80 q^{4} - 55 q^{5} - 180 q^{6} + 180 q^{7} + 320 q^{8} - 405 q^{9} + 220 q^{10} + 380 q^{11} + 720 q^{12} - 230 q^{13} - 920 q^{14} - 630 q^{15} - 1280 q^{16} + 2870 q^{17} - 6480 q^{18} + 1560 q^{19} + 1120 q^{20} + 2880 q^{21} - 720 q^{22} + 760 q^{23} + 11520 q^{24} + 1725 q^{25} + 7320 q^{26} + 3645 q^{27} - 5120 q^{28} + 12000 q^{29} + 5220 q^{30} - 1710 q^{31} - 20480 q^{32} - 1620 q^{33} + 20620 q^{34} - 22440 q^{35} - 6480 q^{36} - 5595 q^{37} - 5240 q^{38} + 2070 q^{39} - 9280 q^{40} - 2820 q^{41} - 11520 q^{42} + 66020 q^{43} + 2880 q^{44} - 8505 q^{45} + 21960 q^{46} - 19630 q^{47} + 11520 q^{48} - 61780 q^{49} + 100 q^{50} - 41130 q^{51} - 3680 q^{52} + 62735 q^{53} - 14580 q^{54} + 66590 q^{55} + 20480 q^{56} + 51660 q^{57} - 48000 q^{58} + 105100 q^{59} + 15120 q^{60} + 34790 q^{61} - 28560 q^{62} + 18630 q^{63} - 20480 q^{64} - 44345 q^{65} + 13680 q^{66} - 19470 q^{67} + 73120 q^{68} + 49410 q^{69} - 81240 q^{70} - 111720 q^{71} + 25920 q^{72} - 198830 q^{73} - 104120 q^{74} + 60975 q^{75} - 91840 q^{76} + 144740 q^{77} + 41220 q^{78} + 71210 q^{79} - 26880 q^{80} - 32805 q^{81} + 166680 q^{82} - 288690 q^{83} - 33120 q^{84} + 338735 q^{85} + 39920 q^{86} + 108225 q^{87} - 24320 q^{88} + 114225 q^{89} + 17820 q^{90} - 155800 q^{91} - 87840 q^{92} + 97740 q^{93} + 78520 q^{94} - 416900 q^{95} - 46080 q^{96} - 446970 q^{97} - 123380 q^{98} - 90720 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 + 45 * q^3 - 80 * q^4 - 55 * q^5 - 180 * q^6 + 180 * q^7 + 320 * q^8 - 405 * q^9 + 220 * q^10 + 380 * q^11 + 720 * q^12 - 230 * q^13 - 920 * q^14 - 630 * q^15 - 1280 * q^16 + 2870 * q^17 - 6480 * q^18 + 1560 * q^19 + 1120 * q^20 + 2880 * q^21 - 720 * q^22 + 760 * q^23 + 11520 * q^24 + 1725 * q^25 + 7320 * q^26 + 3645 * q^27 - 5120 * q^28 + 12000 * q^29 + 5220 * q^30 - 1710 * q^31 - 20480 * q^32 - 1620 * q^33 + 20620 * q^34 - 22440 * q^35 - 6480 * q^36 - 5595 * q^37 - 5240 * q^38 + 2070 * q^39 - 9280 * q^40 - 2820 * q^41 - 11520 * q^42 + 66020 * q^43 + 2880 * q^44 - 8505 * q^45 + 21960 * q^46 - 19630 * q^47 + 11520 * q^48 - 61780 * q^49 + 100 * q^50 - 41130 * q^51 - 3680 * q^52 + 62735 * q^53 - 14580 * q^54 + 66590 * q^55 + 20480 * q^56 + 51660 * q^57 - 48000 * q^58 + 105100 * q^59 + 15120 * q^60 + 34790 * q^61 - 28560 * q^62 + 18630 * q^63 - 20480 * q^64 - 44345 * q^65 + 13680 * q^66 - 19470 * q^67 + 73120 * q^68 + 49410 * q^69 - 81240 * q^70 - 111720 * q^71 + 25920 * q^72 - 198830 * q^73 - 104120 * q^74 + 60975 * q^75 - 91840 * q^76 + 144740 * q^77 + 41220 * q^78 + 71210 * q^79 - 26880 * q^80 - 32805 * q^81 + 166680 * q^82 - 288690 * q^83 - 33120 * q^84 + 338735 * q^85 + 39920 * q^86 + 108225 * q^87 - 24320 * q^88 + 114225 * q^89 + 17820 * q^90 - 155800 * q^91 - 87840 * q^92 + 97740 * q^93 + 78520 * q^94 - 416900 * q^95 - 46080 * q^96 - 446970 * q^97 - 123380 * q^98 - 90720 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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