LMFDB - Embedded newform 60.6.e.a.11.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,6,Mod(11,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("60.11");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	60.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.62302918878$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.20
Character	$\chi$	$=$	60.11
Dual form			60.6.e.a.11.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.00749860 + 5.65685i) q^{2} +(8.15586 + 13.2847i) q^{3} +(-31.9999 - 0.0848369i) q^{4} +25.0000i q^{5} +(-75.2104 + 46.0368i) q^{6} +55.6023i q^{7} +(0.719864 - 181.018i) q^{8} +(-109.964 + 216.695i) q^{9} +O(q^{10})$	\(q+(-0.00749860 + 5.65685i) q^{2} +(8.15586 + 13.2847i) q^{3} +(-31.9999 - 0.0848369i) q^{4} +25.0000i q^{5} +(-75.2104 + 46.0368i) q^{6} +55.6023i q^{7} +(0.719864 - 181.018i) q^{8} +(-109.964 + 216.695i) q^{9} +(-141.421 - 0.187465i) q^{10} -664.662 q^{11} +(-259.860 - 425.799i) q^{12} +725.981 q^{13} +(-314.534 - 0.416939i) q^{14} +(-332.116 + 203.896i) q^{15} +(1023.99 + 5.42954i) q^{16} -42.4946i q^{17} +(-1224.99 - 623.674i) q^{18} -829.934i q^{19} +(2.12092 - 799.997i) q^{20} +(-738.657 + 453.484i) q^{21} +(4.98404 - 3759.90i) q^{22} -1468.81 q^{23} +(2410.63 - 1466.79i) q^{24} -625.000 q^{25} +(-5.44384 + 4106.77i) q^{26} +(-3775.57 + 306.505i) q^{27} +(4.71713 - 1779.27i) q^{28} -365.246i q^{29} +(-1150.92 - 1880.26i) q^{30} +7944.20i q^{31} +(-38.3926 + 5792.49i) q^{32} +(-5420.89 - 8829.81i) q^{33} +(240.386 + 0.318650i) q^{34} -1390.06 q^{35} +(3537.22 - 6924.90i) q^{36} +7600.42 q^{37} +(4694.81 + 6.22334i) q^{38} +(5921.00 + 9644.40i) q^{39} +(4525.45 + 17.9966i) q^{40} +11692.6i q^{41} +(-2559.75 - 4181.87i) q^{42} +21398.8i q^{43} +(21269.1 + 56.3879i) q^{44} +(-5417.39 - 2749.10i) q^{45} +(11.0140 - 8308.84i) q^{46} -10901.7 q^{47} +(8279.35 + 13647.6i) q^{48} +13715.4 q^{49} +(4.68663 - 3535.53i) q^{50} +(564.526 - 346.580i) q^{51} +(-23231.3 - 61.5900i) q^{52} +17640.9i q^{53} +(-1705.54 - 21360.2i) q^{54} -16616.6i q^{55} +(10065.0 + 40.0261i) q^{56} +(11025.4 - 6768.82i) q^{57} +(2066.14 + 2.73883i) q^{58} +26087.0 q^{59} +(10645.0 - 6496.49i) q^{60} -39436.0 q^{61} +(-44939.1 - 59.5704i) q^{62} +(-12048.8 - 6114.25i) q^{63} +(-32767.0 - 260.617i) q^{64} +18149.5i q^{65} +(49989.5 - 30599.0i) q^{66} +2167.39i q^{67} +(-3.60511 + 1359.82i) q^{68} +(-11979.4 - 19512.6i) q^{69} +(10.4235 - 7863.34i) q^{70} +16194.4 q^{71} +(39146.6 + 20061.4i) q^{72} +68685.8 q^{73} +(-56.9925 + 42994.4i) q^{74} +(-5097.41 - 8302.91i) q^{75} +(-70.4090 + 26557.8i) q^{76} -36956.7i q^{77} +(-54601.3 + 33421.9i) q^{78} -104944. i q^{79} +(-135.739 + 25599.6i) q^{80} +(-34864.9 - 47657.4i) q^{81} +(-66143.5 - 87.6784i) q^{82} -92556.4 q^{83} +(23675.4 - 14448.8i) q^{84} +1062.37 q^{85} +(-121050. - 160.461i) q^{86} +(4852.16 - 2978.89i) q^{87} +(-478.467 + 120316. i) q^{88} +1638.28i q^{89} +(15591.9 - 30624.7i) q^{90} +40366.2i q^{91} +(47001.8 + 124.609i) q^{92} +(-105536. + 64791.8i) q^{93} +(81.7478 - 61669.5i) q^{94} +20748.3 q^{95} +(-77264.4 + 46732.7i) q^{96} +47203.9 q^{97} +(-102.846 + 77585.9i) q^{98} +(73088.9 - 144029. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 10 q^{4} - 114 q^{6} + 44 q^{9}+O(q^{10}) $ 40 * q - 10 * q^4 - 114 * q^6 + 44 * q^9	$ 40 q - 10 q^{4} - 114 q^{6} + 44 q^{9} + 50 q^{10} + 1876 q^{12} - 232 q^{13} - 2734 q^{16} - 3536 q^{18} + 820 q^{21} + 13684 q^{22} + 9550 q^{24} - 25000 q^{25} - 23188 q^{28} - 5800 q^{30} - 9424 q^{33} + 38972 q^{34} + 53754 q^{36} + 2152 q^{37} - 10850 q^{40} - 62868 q^{42} + 5900 q^{45} + 78748 q^{46} + 100956 q^{48} - 52144 q^{49} - 82528 q^{52} - 120862 q^{54} - 44424 q^{57} + 97476 q^{58} + 3850 q^{60} + 2072 q^{61} - 91234 q^{64} - 45784 q^{66} + 52764 q^{69} - 3300 q^{70} - 10344 q^{72} + 264960 q^{73} + 73356 q^{76} + 176440 q^{78} - 165120 q^{81} - 170920 q^{82} - 250544 q^{84} - 132400 q^{85} + 359116 q^{88} + 35550 q^{90} + 510368 q^{93} - 623100 q^{94} - 379254 q^{96} + 453648 q^{97}+O(q^{100}) $ 40 * q - 10 * q^4 - 114 * q^6 + 44 * q^9 + 50 * q^10 + 1876 * q^12 - 232 * q^13 - 2734 * q^16 - 3536 * q^18 + 820 * q^21 + 13684 * q^22 + 9550 * q^24 - 25000 * q^25 - 23188 * q^28 - 5800 * q^30 - 9424 * q^33 + 38972 * q^34 + 53754 * q^36 + 2152 * q^37 - 10850 * q^40 - 62868 * q^42 + 5900 * q^45 + 78748 * q^46 + 100956 * q^48 - 52144 * q^49 - 82528 * q^52 - 120862 * q^54 - 44424 * q^57 + 97476 * q^58 + 3850 * q^60 + 2072 * q^61 - 91234 * q^64 - 45784 * q^66 + 52764 * q^69 - 3300 * q^70 - 10344 * q^72 + 264960 * q^73 + 73356 * q^76 + 176440 * q^78 - 165120 * q^81 - 170920 * q^82 - 250544 * q^84 - 132400 * q^85 + 359116 * q^88 + 35550 * q^90 + 510368 * q^93 - 623100 * q^94 - 379254 * q^96 + 453648 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.00749860	+	5.65685i	−0.00132558	+	0.999999i
$2$	−0.00749860	+	5.65685i	−0.00132558	+	0.999999i
$3$	8.15586	+	13.2847i	0.523199	+	0.852211i
$3$	8.15586	+	13.2847i	0.523199	+	0.852211i
$4$	−31.9999	−	0.0848369i	−0.999996	−	0.00265115i
$5$			25.0000i			0.447214i
$5$			25.0000i			0.447214i
$6$	−75.2104	+	46.0368i	−0.852904	+	0.522068i
$7$			55.6023i			0.428892i	0.976736	+	0.214446i	$0.0687945\pi$
$7$			55.6023i			0.428892i	−0.976736	+	0.214446i	$0.931205\pi$
$8$	0.719864	−	181.018i	0.00397672	−	0.999992i
$9$	−109.964	+	216.695i	−0.452526	+	0.891751i
$10$	−141.421	−	0.187465i	−0.447213	−	0.000592817i
$11$	−664.662			−1.65623			−0.828113	−	0.560562i	$-0.810585\pi$
$11$	−664.662			−1.65623			−0.828113	+	0.560562i	$0.810585\pi$
$12$	−259.860	−	425.799i	−0.520937	−	0.853595i
$13$	725.981			1.19143			0.595713	−	0.803198i	$-0.296870\pi$
$13$	725.981			1.19143			0.595713	+	0.803198i	$0.296870\pi$
$14$	−314.534	−	0.416939i	−0.428891	−	0.000568529i
$15$	−332.116	+	203.896i	−0.381120	+	0.233982i
$16$	1023.99	+	5.42954i	0.999986	+	0.00530229i
$17$		−	42.4946i		−	0.0356625i	−0.999841	−	0.0178312i	$-0.994324\pi$
$17$		−	42.4946i		−	0.0356625i	0.999841	−	0.0178312i	$-0.00567616\pi$
$18$	−1224.99	−	623.674i	−0.891150	−	0.453708i
$19$		−	829.934i		−	0.527423i	−0.964602	−	0.263712i	$-0.915053\pi$
$19$		−	829.934i		−	0.527423i	0.964602	−	0.263712i	$-0.0849468\pi$
$20$	2.12092	−	799.997i	0.00118563	−	0.447212i
$21$	−738.657	+	453.484i	−0.365506	+	0.224395i
$22$	4.98404	−	3759.90i	0.00219546	−	1.65622i
$23$	−1468.81			−0.578957			−0.289478	−	0.957185i	$-0.593482\pi$
$23$	−1468.81			−0.578957			−0.289478	+	0.957185i	$0.593482\pi$
$24$	2410.63	−	1466.79i	0.854285	−	0.519805i
$25$	−625.000			−0.200000
$26$	−5.44384	+	4106.77i	−0.00157933	+	1.19142i
$27$	−3775.57	+	306.505i	−0.996721	+	0.0809149i
$28$	4.71713	−	1779.27i	0.00113706	−	0.428890i
$29$		−	365.246i		−	0.0806473i	−0.999187	−	0.0403237i	$-0.987161\pi$
$29$		−	365.246i		−	0.0806473i	0.999187	−	0.0403237i	$-0.0128389\pi$
$30$	−1150.92	−	1880.26i	−0.233476	−	0.381430i
$31$			7944.20i			1.48472i	0.669999	+	0.742362i	$0.266295\pi$
$31$			7944.20i			1.48472i	−0.669999	+	0.742362i	$0.733705\pi$
$32$	−38.3926	+	5792.49i	−0.00662784	+	0.999978i
$33$	−5420.89	−	8829.81i	−0.866535	−	1.41145i
$34$	240.386	+	0.318650i	0.0356625	+	4.72734e-5i
$35$	−1390.06			−0.191806
$36$	3537.22	−	6924.90i	0.454889	−	0.890548i
$37$	7600.42			0.912711			0.456356	−	0.889797i	$-0.349154\pi$
$37$	7600.42			0.912711			0.456356	+	0.889797i	$0.349154\pi$
$38$	4694.81	+	6.22334i	0.527423	+	0.000699141i
$39$	5921.00	+	9644.40i	0.623352	+	1.01535i
$40$	4525.45	+	17.9966i	0.447210	+	0.00177845i
$41$			11692.6i			1.08631i	0.839633	+	0.543154i	$0.182770\pi$
$41$			11692.6i			1.08631i	−0.839633	+	0.543154i	$0.817230\pi$
$42$	−2559.75	−	4181.87i	−0.223911	−	0.365803i
$43$			21398.8i			1.76490i	0.470411	+	0.882448i	$0.344106\pi$
$43$			21398.8i			1.76490i	−0.470411	+	0.882448i	$0.655894\pi$
$44$	21269.1	+	56.3879i	1.65622	+	0.00439091i
$45$	−5417.39	−	2749.10i	−0.398803	−	0.202376i
$46$	11.0140	−	8308.84i	0.000767453	−	0.578956i
$47$	−10901.7			−0.719865			−0.359933	−	0.932978i	$-0.617200\pi$
$47$	−10901.7			−0.719865			−0.359933	+	0.932978i	$0.617200\pi$
$48$	8279.35	+	13647.6i	0.518673	+	0.854973i
$49$	13715.4			0.816052
$50$	4.68663	−	3535.53i	0.000265116	−	0.200000i
$51$	564.526	−	346.580i	0.0303920	−	0.0186586i
$52$	−23231.3	−	61.5900i	−1.19142	−	0.00315865i
$53$			17640.9i			0.862643i	0.902198	+	0.431322i	$0.141953\pi$
$53$			17640.9i			0.862643i	−0.902198	+	0.431322i	$0.858047\pi$
$54$	−1705.54	−	21360.2i	−0.0795936	−	0.996827i
$55$		−	16616.6i		−	0.740686i
$56$	10065.0	+	40.0261i	0.428888	+	0.00170558i
$57$	11025.4	−	6768.82i	0.449476	−	0.275947i
$58$	2066.14	+	2.73883i	0.0806473	+	0.000106904i
$59$	26087.0			0.975650			0.487825	−	0.872941i	$-0.337790\pi$
$59$	26087.0			0.975650			0.487825	+	0.872941i	$0.337790\pi$
$60$	10645.0	−	6496.49i	0.381739	−	0.232970i
$61$	−39436.0			−1.35696			−0.678481	−	0.734618i	$-0.737361\pi$
$61$	−39436.0			−1.35696			−0.678481	+	0.734618i	$0.737361\pi$
$62$	−44939.1	−	59.5704i	−1.48472	−	0.00196812i
$63$	−12048.8	−	6114.25i	−0.382464	−	0.194085i
$64$	−32767.0	−	260.617i	−0.999968	−	0.00795339i
$65$			18149.5i			0.532822i
$66$	49989.5	−	30599.0i	1.41260	−	0.864663i
$67$			2167.39i			0.0589862i	0.999565	+	0.0294931i	$0.00938931\pi$
$67$			2167.39i			0.0589862i	−0.999565	+	0.0294931i	$0.990611\pi$
$68$	−3.60511	+	1359.82i	−9.45467e−5	+	0.0356624i
$69$	−11979.4	−	19512.6i	−0.302909	−	0.493393i
$70$	10.4235	−	7863.34i	0.000254254	−	0.191806i
$71$	16194.4			0.381259			0.190630	−	0.981662i	$-0.438947\pi$
$71$	16194.4			0.381259			0.190630	+	0.981662i	$0.438947\pi$
$72$	39146.6	+	20061.4i	0.889944	+	0.456069i
$73$	68685.8			1.50855			0.754275	−	0.656558i	$-0.227988\pi$
$73$	68685.8			1.50855			0.754275	+	0.656558i	$0.227988\pi$
$74$	−56.9925	+	42994.4i	−0.00120987	+	0.912710i
$75$	−5097.41	−	8302.91i	−0.104640	−	0.170442i
$76$	−70.4090	+	26557.8i	−0.00139828	+	0.527422i
$77$		−	36956.7i		−	0.710341i
$78$	−54601.3	+	33421.9i	−1.01617	+	0.622006i
$79$		−	104944.i		−	1.89186i	−0.324369	−	0.945931i	$-0.605152\pi$
$79$		−	104944.i		−	1.89186i	0.324369	−	0.945931i	$-0.394848\pi$
$80$	−135.739	+	25599.6i	−0.00237126	+	0.447207i
$81$	−34864.9	−	47657.4i	−0.590440	−	0.807082i
$82$	−66143.5	−	87.6784i	−1.08631	−	0.00143999i
$83$	−92556.4			−1.47473			−0.737363	−	0.675497i	$-0.763929\pi$
$83$	−92556.4			−1.47473			−0.737363	+	0.675497i	$0.763929\pi$
$84$	23675.4	−	14448.8i	0.366100	−	0.223426i
$85$	1062.37			0.0159487
$86$	−121050.	−	160.461i	−1.76489	−	0.00233951i
$87$	4852.16	−	2978.89i	0.0687285	−	0.0421946i
$88$	−478.467	+	120316.i	−0.00658635	+	1.65621i
$89$			1638.28i			0.0219237i	0.999940	+	0.0109618i	$0.00348933\pi$
$89$			1638.28i			0.0219237i	−0.999940	+	0.0109618i	$0.996511\pi$
$90$	15591.9	−	30624.7i	0.202904	−	0.398535i
$91$			40366.2i			0.510992i
$92$	47001.8	+	124.609i	0.578955	+	0.00153490i
$93$	−105536.	+	64791.8i	−1.26530	+	0.776806i
$94$	81.7478	−	61669.5i	0.000954238	−	0.719865i
$95$	20748.3			0.235871
$96$	−77264.4	+	46732.7i	−0.855660	+	0.517539i
$97$	47203.9			0.509388			0.254694	−	0.967022i	$-0.418025\pi$
$97$	47203.9			0.509388			0.254694	+	0.967022i	$0.418025\pi$
$98$	−102.846	+	77585.9i	−0.00108174	+	0.816051i
$99$	73088.9	−	144029.i	0.749486	−	1.47694i
$100$	19999.9	+	53.0231i	0.199999	+	0.000530231i
$101$			98799.8i			0.963724i	0.876247	+	0.481862i	$0.160039\pi$
$101$			98799.8i			0.963724i	−0.876247	+	0.481862i	$0.839961\pi$
$102$	1956.32	+	3196.04i	0.0186183	+	0.0304167i
$103$		−	71667.8i		−	0.665627i	−0.942993	−	0.332813i	$-0.892002\pi$
$103$		−	71667.8i		−	0.665627i	0.942993	−	0.332813i	$-0.107998\pi$
$104$	522.608	−	131416.i	0.00473797	−	1.19142i
$105$	−11337.1	−	18466.4i	−0.100353	−	0.163459i
$106$	−99791.9	−	132.282i	−0.862642	−	0.00114350i
$107$	218704.			1.84670			0.923351	−	0.383958i	$-0.125439\pi$
$107$	218704.			1.84670			0.923351	+	0.383958i	$0.125439\pi$
$108$	120844.	−	9487.82i	0.996932	−	0.0782721i
$109$	121729.			0.981356			0.490678	−	0.871341i	$-0.336749\pi$
$109$	121729.			0.981356			0.490678	+	0.871341i	$0.336749\pi$
$110$	93997.4	+	124.601i	0.740686	+	0.000981838i
$111$	61988.0	+	100969.i	0.477529	+	0.777822i
$112$	−301.895	+	56935.9i	−0.00227411	+	0.428886i
$113$		−	179453.i		−	1.32207i	−0.750356	−	0.661034i	$-0.770118\pi$
$113$		−	179453.i		−	1.32207i	0.750356	−	0.661034i	$-0.229882\pi$
$114$	38207.5	+	62419.7i	0.275351	+	0.449841i
$115$		−	36720.3i		−	0.258917i
$116$	−30.9863	+	11687.8i	−0.000213808	+	0.0806470i
$117$	−79831.7	+	157317.i	−0.539152	+	1.06245i
$118$	−195.616	+	147570.i	−0.00129330	+	0.975649i
$119$	2362.80			0.0152953
$120$	36669.8	+	60265.8i	0.232464	+	0.382048i
$121$	280725.			1.74308
$122$	295.715	−	223083.i	0.00179876	−	1.35696i
$123$	−155333.	+	95363.5i	−0.925763	+	0.568355i
$124$	673.961	−	254213.i	0.00393623	−	1.48472i
$125$		−	15625.0i		−	0.0894427i
$126$	34677.7	−	68112.2i	0.194592	−	0.382207i
$127$			138348.i			0.761136i	0.924753	+	0.380568i	$0.124272\pi$
$127$			138348.i			0.761136i	−0.924753	+	0.380568i	$0.875728\pi$
$128$	1719.98	−	185356.i	0.00927892	−	0.999957i
$129$	−284276.	+	174526.i	−1.50406	+	0.923391i
$130$	−102669.	−	136.096i	−0.532821	−	0.000706297i
$131$	168190.			0.856291			0.428145	−	0.903710i	$-0.359167\pi$
$131$	168190.			0.856291			0.428145	+	0.903710i	$0.359167\pi$
$132$	172719.	+	283013.i	0.862790	+	1.41375i
$133$	46146.2			0.226207
$134$	−12260.6	−	16.2524i	−0.0589861	−	7.81908e-5i
$135$	−7662.63	−	94389.4i	−0.0361862	−	0.445747i
$136$	−7692.29	−	30.5903i	−0.0356622	−	0.000141820i
$137$		−	107860.i		−	0.490975i	−0.969400	−	0.245488i	$-0.921052\pi$
$137$		−	107860.i		−	0.490975i	0.969400	−	0.245488i	$-0.0789480\pi$
$138$	110470.	−	67619.4i	0.493795	−	0.302255i
$139$			180035.i			0.790353i	0.918605	+	0.395176i	$0.129317\pi$
$139$			180035.i			0.790353i	−0.918605	+	0.395176i	$0.870683\pi$
$140$	44481.7	+	117.928i	0.191805	+	0.000508508i
$141$	−88913.1	−	144826.i	−0.376633	−	0.613477i
$142$	−121.436	+	91609.5i	−0.000505389	+	0.381259i
$143$	−482532.			−1.97327
$144$	−113778.	+	221296.i	−0.457248	+	0.889339i
$145$	9131.14			0.0360666
$146$	−515.048	+	388545.i	−0.00199970	+	1.50855i
$147$	111861.	+	182204.i	0.426957	+	0.695448i
$148$	−243213.	−	644.796i	−0.912708	−	0.00241974i
$149$		−	168796.i		−	0.622870i	−0.950268	−	0.311435i	$-0.899190\pi$
$149$		−	168796.i		−	0.622870i	0.950268	−	0.311435i	$-0.100810\pi$
$150$	47006.5	−	28773.0i	0.170581	−	0.104414i
$151$			236374.i			0.843642i	0.906679	+	0.421821i	$0.138609\pi$
$151$			236374.i			0.843642i	−0.906679	+	0.421821i	$0.861391\pi$
$152$	−150233.	−	597.439i	−0.527419	−	0.00209742i
$153$	9208.39	+	4672.87i	0.0318021	+	0.0161382i
$154$	209059.	+	277.124i	0.710340	+	0.000941613i
$155$	−198605.			−0.663989
$156$	−188653.	−	309122.i	−0.620658	−	1.01699i
$157$	−371974.			−1.20438			−0.602190	−	0.798353i	$-0.705705\pi$
$157$	−371974.			−1.20438			−0.602190	+	0.798353i	$0.705705\pi$
$158$	593652.	+	786.932i	1.89186	+	0.00250781i
$159$	−234353.	+	143877.i	−0.735154	+	0.451334i
$160$	−144812.	−	959.814i	−0.447204	−	0.00296406i
$161$		−	81669.2i		−	0.248310i
$162$	269852.	−	196868.i	0.807864	−	0.589369i
$163$		−	217145.i		−	0.640150i	−0.947392	−	0.320075i	$-0.896292\pi$
$163$		−	217145.i		−	0.640150i	0.947392	−	0.320075i	$-0.103708\pi$
$164$	991.967	−	374163.i	0.00287997	−	1.08630i
$165$	220745.	−	135522.i	0.631221	−	0.387526i
$166$	694.044	−	523578.i	0.00195486	−	1.47472i
$167$	−429501.			−1.19172			−0.595859	−	0.803089i	$-0.703188\pi$
$167$	−429501.			−1.19172			−0.595859	+	0.803089i	$0.703188\pi$
$168$	81557.1	+	134037.i	0.222940	+	0.366396i
$169$	155755.			0.419495
$170$	−7.96625	+	6009.64i	−2.11413e−5	+	0.0159487i
$171$	179843.	+	91262.8i	0.470330	+	0.238673i
$172$	1815.41	−	684760.i	0.00467901	−	1.76489i
$173$			317988.i			0.807785i	0.914806	+	0.403893i	$0.132343\pi$
$173$			317988.i			0.807785i	−0.914806	+	0.403893i	$0.867657\pi$
$174$	16814.8	+	27470.3i	0.0421034	+	0.0687844i
$175$		−	34751.4i		−	0.0857783i
$176$	−680605.	−	3608.81i	−1.65620	−	0.00878179i
$177$	212762.	+	346557.i	0.510459	+	0.831459i
$178$	−9267.52	−	12.2848i	−0.0219237	−	2.90616e-5i
$179$	175464.			0.409314			0.204657	−	0.978834i	$-0.434392\pi$
$179$	175464.			0.409314			0.204657	+	0.978834i	$0.434392\pi$
$180$	173123.	+	88430.4i	0.398265	+	0.203433i
$181$	268850.			0.609977			0.304989	−	0.952356i	$-0.401347\pi$
$181$	268850.			0.609977			0.304989	+	0.952356i	$0.401347\pi$
$182$	−228346.	−	302.690i	−0.510992	−	0.000677360i
$183$	−321634.	−	523893.i	−0.709961	−	1.15642i
$184$	−1057.34	+	265881.i	−0.00230235	+	0.578952i
$185$			190011.i			0.408177i
$186$	−365726.	−	597487.i	−0.775128	−	1.26633i
$187$			28244.6i			0.0590651i
$188$	348855.	+	924.870i	0.719863	+	0.00190847i
$189$	−17042.4	−	209931.i	−0.0347037	−	0.427485i
$190$	−155.584	+	117370.i	−0.000312665	+	0.235871i
$191$	692403.			1.37333			0.686666	−	0.726973i	$-0.259073\pi$
$191$	692403.			1.37333			0.686666	+	0.726973i	$0.259073\pi$
$192$	−263781.	−	437423.i	−0.516404	−	0.856345i
$193$	−225545.			−0.435853			−0.217926	−	0.975965i	$-0.569929\pi$
$193$	−225545.			−0.435853			−0.217926	+	0.975965i	$0.569929\pi$
$194$	−353.963	+	267025.i	−0.000675234	+	0.509388i
$195$	−241110.	+	148025.i	−0.454076	+	0.278772i
$196$	−438891.	−	1163.57i	−0.816049	−	0.00216348i
$197$		−	267203.i		−	0.490541i	−0.969455	−	0.245270i	$-0.921123\pi$
$197$		−	267203.i		−	0.490541i	0.969455	−	0.245270i	$-0.0788768\pi$
$198$	814204.	+	414533.i	1.47595	+	0.751443i
$199$			187238.i			0.335167i	0.985858	+	0.167583i	$0.0535964\pi$
$199$			187238.i			0.335167i	−0.985858	+	0.167583i	$0.946404\pi$
$200$	−449.915	+	113136.i	−0.000795345	+	0.199998i
$201$	−28793.0	+	17676.9i	−0.0502687	+	0.0308615i
$202$	−558895.	−	740.860i	−0.963723	−	0.00127749i
$203$	20308.5			0.0345890
$204$	−18094.2	+	11042.6i	−0.0304413	+	0.0185779i
$205$	−292316.			−0.485812
$206$	405414.	+	537.408i	0.665626	+	0.000882341i
$207$	161516.	−	318285.i	0.261993	−	0.516285i
$208$	743394.	+	3941.75i	1.19141	+	0.00631728i
$209$			551626.i			0.873532i
$210$	104547.	−	63993.8i	0.163592	−	0.100136i
$211$			483884.i			0.748230i	0.927382	+	0.374115i	$0.122054\pi$
$211$			483884.i			0.748230i	−0.927382	+	0.374115i	$0.877946\pi$
$212$	1496.60	−	564507.i	0.00228700	−	0.862640i
$213$	132080.	+	215138.i	0.199474	+	0.324913i
$214$	−1639.97	+	1.23717e6i	−0.00244795	+	1.84670i
$215$	−534971.			−0.789285
$216$	52765.0	+	683667.i	0.0769505	+	0.997035i
$217$	−441716.			−0.636786
$218$	−912.795	+	688601.i	−0.00130086	+	0.981355i
$219$	560192.	+	912467.i	0.789272	+	1.28560i
$220$	−1409.70	+	531728.i	−0.00196367	+	0.740684i
$221$		−	30850.3i		−	0.0424892i
$222$	−571631.	+	349899.i	−0.778455	+	0.476498i
$223$		−	1.03730e6i		−	1.39683i	−0.715694	−	0.698414i	$-0.753890\pi$
$223$		−	1.03730e6i		−	1.39683i	0.715694	−	0.698414i	$-0.246110\pi$
$224$	−322076.	−	2134.71i	−0.428882	−	0.00284263i
$225$	68727.5	−	135435.i	0.0905053	−	0.178350i
$226$	1.01514e6	+	1345.64i	1.32207	+	0.00175251i
$227$	1.19096e6			1.53402			0.767010	−	0.641635i	$-0.221744\pi$
$227$	1.19096e6			1.53402			0.767010	+	0.641635i	$0.221744\pi$
$228$	−353385.	+	215666.i	−0.450206	+	0.274755i
$229$	291881.			0.367804			0.183902	−	0.982945i	$-0.441127\pi$
$229$	291881.			0.367804			0.183902	+	0.982945i	$0.441127\pi$
$230$	207721.	+	275.351i	0.258917	+	0.000343215i
$231$	490958.	−	301414.i	0.605360	−	0.371649i
$232$	−66116.0	−	262.927i	−0.0806467	−	0.000320712i
$233$		−	686833.i		−	0.828822i	−0.910090	−	0.414411i	$-0.863988\pi$
$233$		−	686833.i		−	0.828822i	0.910090	−	0.414411i	$-0.136012\pi$
$234$	−889319.	−	452776.i	−1.06174	−	0.540559i
$235$		−	272544.i		−	0.321934i
$236$	−834781.	−	2213.14i	−0.975647	−	0.00258660i
$237$	1.39414e6	−	855907.i	1.61226	−	0.989819i
$238$	−17.7177	+	13366.0i	−2.02752e−5	+	0.0152953i
$239$	−220353.			−0.249531			−0.124765	−	0.992186i	$-0.539818\pi$
$239$	−220353.			−0.249531			−0.124765	+	0.992186i	$0.539818\pi$
$240$	−341189.	+	206984.i	−0.382356	+	0.231957i
$241$	−1.27250e6			−1.41129			−0.705643	−	0.708568i	$-0.749342\pi$
$241$	−1.27250e6			−1.41129			−0.705643	+	0.708568i	$0.749342\pi$
$242$	−2105.05	+	1.58802e6i	−0.00231059	+	1.74308i
$243$	348759.	−	851854.i	0.378887	−	0.925443i
$244$	1.26195e6	+	3345.63i	1.35696	+	0.00359752i
$245$			342885.i			0.364950i
$246$	−538292.	−	879408.i	−0.567127	−	0.926516i
$247$		−	602516.i		−	0.628386i
$248$	1.43804e6	+	5718.74i	1.48471	+	0.00590434i
$249$	−754877.	−	1.22958e6i	−0.771574	−	1.25678i
$250$	88388.3	+	117.166i	0.0894426	+	0.000118563i
$251$	1.04464e6			1.04660			0.523300	−	0.852149i	$-0.324701\pi$
$251$	1.04464e6			1.04660			0.523300	+	0.852149i	$0.324701\pi$
$252$	385040.	+	196677.i	0.381949	+	0.195098i
$253$	976263.			0.958883
$254$	−782612.	−	1037.41i	−0.761136	−	0.00100895i
$255$	8664.50	+	14113.2i	0.00834436	+	0.0135917i
$256$	1.04852e6	+	11119.5i	0.999944	+	0.0106044i
$257$			659519.i			0.622866i	0.950268	+	0.311433i	$0.100809\pi$
$257$			659519.i			0.622866i	−0.950268	+	0.311433i	$0.899191\pi$
$258$	−985135.	−	1.60942e6i	−0.921396	−	1.50529i
$259$			422601.i			0.391454i
$260$	1539.75	−	580783.i	0.00141259	−	0.532820i
$261$	79147.1	+	40163.8i	0.0719173	+	0.0364950i
$262$	−1261.19	+	951424.i	−0.00113508	+	0.856290i
$263$	−748412.			−0.667192			−0.333596	−	0.942716i	$-0.608262\pi$
$263$	−748412.			−0.667192			−0.333596	+	0.942716i	$0.608262\pi$
$264$	−1.60226e6	+	974922.i	−1.41489	+	0.860915i
$265$	−441023.			−0.385786
$266$	−346.032	+	261042.i	−0.000299856	+	0.226207i
$267$	−21764.0	+	13361.6i	−0.0186836	+	0.0114704i
$268$	183.875	−	69356.3i	0.000156381	−	0.0589860i
$269$			1.25684e6i			1.05901i	0.848307	+	0.529505i	$0.177622\pi$
$269$			1.25684e6i			1.05901i	−0.848307	+	0.529505i	$0.822378\pi$
$270$	534004.	−	42638.5i	0.445795	−	0.0355953i
$271$		−	1.45840e6i		−	1.20629i	−0.797631	−	0.603146i	$-0.793914\pi$
$271$		−	1.45840e6i		−	1.20629i	0.797631	−	0.603146i	$-0.206086\pi$
$272$	230.726	−	43513.9i	0.000189093	−	0.0356620i
$273$	−536251.	+	329221.i	−0.435473	+	0.267350i
$274$	610148.	+	808.800i	0.490975	+	0.000650826i
$275$	415414.			0.331245
$276$	381685.	+	625419.i	0.301600	+	0.494195i
$277$	−1.17575e6			−0.920694			−0.460347	−	0.887739i	$-0.652275\pi$
$277$	−1.17575e6			−0.920694			−0.460347	+	0.887739i	$0.652275\pi$
$278$	−1.01843e6	−	1350.01i	−0.790352	−	0.00104767i
$279$	−1.72147e6	−	873575.i	−1.32400	−	0.671877i
$280$	−1000.65	+	251625.i	−0.000762760	+	0.191805i
$281$			1.24530e6i			0.940827i	0.882446	+	0.470414i	$0.155895\pi$
$281$			1.24530e6i			0.940827i	−0.882446	+	0.470414i	$0.844105\pi$
$282$	819925.	−	501882.i	0.613976	−	0.375819i
$283$		−	665893.i		−	0.494241i	−0.968985	−	0.247120i	$-0.920516\pi$
$283$		−	665893.i		−	0.494241i	0.968985	−	0.247120i	$-0.0794843\pi$
$284$	−518220.	−	1373.89i	−0.381258	−	0.00101078i
$285$	169221.	+	275635.i	0.123407	+	0.201012i
$286$	3618.32	−	2.72961e6i	0.00261572	−	1.97327i
$287$	−650137.			−0.465908
$288$	−1.25098e6	−	645285.i	−0.888732	−	0.458427i
$289$	1.41805e6			0.998728
$290$	−68.4708	+	51653.5i	−4.78091e−5	+	0.0360665i
$291$	384988.	+	627088.i	0.266511	+	0.434106i
$292$	−2.19794e6	−	5827.09i	−1.50855	−	0.00399940i
$293$		−	963847.i		−	0.655902i	−0.944695	−	0.327951i	$-0.893642\pi$
$293$		−	963847.i		−	0.655902i	0.944695	−	0.327951i	$-0.106358\pi$
$294$	−1.03154e6	+	631413.i	−0.696014	+	0.426035i
$295$			652175.i			0.436324i
$296$	5471.27	−	1.37581e6i	0.00362960	−	0.912704i
$297$	2.50948e6	−	203722.i	1.65079	−	0.134013i
$298$	954855.	+	1265.74i	0.622869	+	0.000825662i
$299$	−1.06633e6			−0.689784
$300$	162412.	+	266125.i	0.104187	+	0.170719i
$301$	−1.18982e6			−0.756949
$302$	−1.33713e6	−	1772.48i	−0.843641	−	0.00111831i
$303$	−1.31252e6	+	805797.i	−0.821296	+	0.504219i
$304$	4506.16	−	849840.i	0.00279655	−	0.527416i
$305$		−	985899.i		−	0.606852i
$306$	−26502.8	+	52055.4i	−0.0161804	+	0.0317806i
$307$			2.63009e6i			1.59267i	0.604858	+	0.796333i	$0.293230\pi$
$307$			2.63009e6i			1.59267i	−0.604858	+	0.796333i	$0.706770\pi$
$308$	−3135.30	+	1.18261e6i	−0.00188322	+	0.710339i
$309$	952082.	−	584512.i	0.567255	−	0.348255i
$310$	1489.26	−	1.12348e6i	0.000880169	−	0.663988i
$311$	−1.76963e6			−1.03749			−0.518743	−	0.854930i	$-0.673600\pi$
$311$	−1.76963e6			−1.03749			−0.518743	+	0.854930i	$0.673600\pi$
$312$	1.75007e6	−	1.06486e6i	1.01782	−	0.619309i
$313$	−1.38503e6			−0.799092			−0.399546	−	0.916713i	$-0.630832\pi$
$313$	−1.38503e6			−0.799092			−0.399546	+	0.916713i	$0.630832\pi$
$314$	2789.28	−	2.10420e6i	0.00159650	−	1.20438i
$315$	152856.	−	301219.i	0.0867974	−	0.171043i
$316$	−8903.11	+	3.35819e6i	−0.00501561	+	1.89185i
$317$			179969.i			0.100589i	0.998734	+	0.0502944i	$0.0160159\pi$
$317$			179969.i			0.100589i	−0.998734	+	0.0502944i	$0.983984\pi$
$318$	−812132.	−	1.32678e6i	−0.450359	−	0.735751i
$319$			242765.i			0.133570i
$320$	6515.41	−	819174.i	0.00355686	−	0.447199i
$321$	1.78372e6	+	2.90540e6i	0.966191	+	1.57378i
$322$	461991.	+	612.405i	0.248310	+	0.000329154i
$323$	−35267.7			−0.0188092
$324$	1.11163e6	+	1.52799e6i	0.588298	+	0.808644i
$325$	−453738.			−0.238285
$326$	1.22836e6	+	1628.29i	0.640149	+	0.000848568i
$327$	992802.	+	1.61712e6i	0.513444	+	0.836322i
$328$	2.11658e6	+	8417.11i	1.08630	+	0.00431995i
$329$		−	606162.i		−	0.308744i
$330$	764974.	+	1.24974e6i	0.386689	+	0.631734i
$331$			2.05304e6i			1.02998i	0.857197	+	0.514989i	$0.172204\pi$
$331$			2.05304e6i			1.02998i	−0.857197	+	0.514989i	$0.827796\pi$
$332$	2.96179e6	+	7852.20i	1.47472	+	0.00390973i
$333$	−835772.	+	1.64698e6i	−0.413026	+	0.813911i
$334$	3220.66	−	2.42962e6i	0.00157971	−	1.19172i
$335$	−54184.8			−0.0263794
$336$	−758836.	+	460351.i	−0.366691	+	0.222454i
$337$	−2.34218e6			−1.12343			−0.561715	−	0.827331i	$-0.689858\pi$
$337$	−2.34218e6			−1.12343			−0.561715	+	0.827331i	$0.689858\pi$
$338$	−1167.95	+	881085.i	−0.000556073	+	0.419494i
$339$	2.38397e6	−	1.46359e6i	1.12668	−	0.691705i
$340$	−33995.6	−	90.1278i	−0.0159487	−	4.22826e-5i
$341$		−	5.28021e6i		−	2.45904i
$342$	−517608.	+	1.01666e6i	−0.239296	+	0.470014i
$343$			1.69711e6i			0.778889i
$344$	3.87357e6	+	15404.3i	1.76488	+	0.00701850i
$345$	487816.	−	299485.i	0.220652	−	0.135465i
$346$	−1.79881e6	−	2384.47i	−0.807785	−	0.00107078i
$347$	1.53654e6			0.685047			0.342524	−	0.939509i	$-0.388718\pi$
$347$	1.53654e6			0.685047			0.342524	+	0.939509i	$0.388718\pi$
$348$	−155521.	+	94912.5i	−0.0688401	+	0.0420122i
$349$	−2.19486e6			−0.964592			−0.482296	−	0.876008i	$-0.660197\pi$
$349$	−2.19486e6			−0.964592			−0.482296	+	0.876008i	$0.660197\pi$
$350$	196584.	+	260.587i	0.0857782	+	0.000113706i
$351$	−2.74100e6	+	222517.i	−1.18752	+	0.0964040i
$352$	25518.1	−	3.85005e6i	0.0109772	−	1.65619i
$353$		−	1.26277e6i		−	0.539372i	−0.962948	−	0.269686i	$-0.913080\pi$
$353$		−	1.26277e6i		−	0.539372i	0.962948	−	0.269686i	$-0.0869198\pi$
$354$	−1.96201e6	+	1.20096e6i	−0.832135	+	0.509356i
$355$			404861.i			0.170504i
$356$	138.987	−	52424.8i	5.81231e−5	−	0.0219236i
$357$	19270.6	+	31388.9i	0.00800250	+	0.0130349i
$358$	−1315.74	+	992576.i	−0.000542578	+	0.409314i
$359$	797258.			0.326485			0.163242	−	0.986586i	$-0.447805\pi$
$359$	797258.			0.326485			0.163242	+	0.986586i	$0.447805\pi$
$360$	−501536.	+	978665.i	−0.203960	+	0.397995i
$361$	1.78731e6			0.721825
$362$	−2016.00	+	1.52084e6i	−0.000808572	+	0.609977i
$363$	2.28955e6	+	3.72934e6i	0.911978	+	1.48547i
$364$	3424.54	−	1.29171e6i	0.00135472	−	0.510991i
$365$			1.71715e6i			0.674644i
$366$	2.96600e6	−	1.81551e6i	1.15736	−	0.708427i
$367$		−	3.16869e6i		−	1.22804i	−0.789289	−	0.614022i	$-0.789551\pi$
$367$		−	3.16869e6i		−	1.22804i	0.789289	−	0.614022i	$-0.210449\pi$
$368$	−1.50404e6	−	7974.97i	−0.578949	−	0.00306980i
$369$	−2.53374e6	−	1.28577e6i	−0.968716	−	0.491583i
$370$	−1.07486e6	−	1424.81i	−0.408177	−	0.000541070i
$371$	−980875.			−0.369980
$372$	3.38263e6	−	2.06438e6i	1.26735	−	0.773448i
$373$	3.89101e6			1.44807			0.724035	−	0.689763i	$-0.242285\pi$
$373$	3.89101e6			1.44807			0.724035	+	0.689763i	$0.242285\pi$
$374$	−159775.	−	211.795i	−0.0590651	−	7.82954e-5i
$375$	207573.	−	127435.i	0.0762241	−	0.0467963i
$376$	−7847.77	+	1.97341e6i	−0.00286271	+	0.719860i
$377$		−	265161.i		−	0.0960853i
$378$	1.18767e6	−	94832.0i	0.427531	−	0.0341370i
$379$		−	1.34697e6i		−	0.481683i	−0.970564	−	0.240841i	$-0.922577\pi$
$379$		−	1.34697e6i		−	0.481683i	0.970564	−	0.240841i	$-0.0774234\pi$
$380$	−663945.	−	1760.23i	−0.235870	−	0.000625330i
$381$	−1.83790e6	+	1.12834e6i	−0.648649	+	0.398225i
$382$	−5192.06	+	3.91682e6i	−0.00182046	+	1.37333i
$383$	1.74101e6			0.606464			0.303232	−	0.952917i	$-0.401934\pi$
$383$	1.74101e6			0.606464			0.303232	+	0.952917i	$0.401934\pi$
$384$	2.47642e6	−	1.48889e6i	0.857029	−	0.515268i
$385$	923919.			0.317674
$386$	1691.27	−	1.27587e6i	0.000577757	−	0.435853i
$387$	−4.63703e6	−	2.35310e6i	−1.57385	−	0.798662i
$388$	−1.51052e6	−	4004.63i	−0.509386	−	0.00135047i
$389$			5.46663e6i			1.83166i	0.401562	+	0.915832i	$0.368467\pi$
$389$			5.46663e6i			1.83166i	−0.401562	+	0.915832i	$0.631533\pi$
$390$	−835547.	−	1.36503e6i	−0.278169	−	0.454446i
$391$			62416.6i			0.0206470i
$392$	9873.21	−	2.48273e6i	0.00324521	−	0.816046i
$393$	1.37173e6	+	2.23434e6i	0.448010	+	0.729740i
$394$	1.51153e6	+	2003.65i	0.490540	+	0.000650250i
$395$	2.62360e6			0.846066
$396$	−2.35106e6	+	4.60272e6i	−0.753399	+	1.47495i
$397$	−1.98879e6			−0.633304			−0.316652	−	0.948542i	$-0.602559\pi$
$397$	−1.98879e6			−0.633304			−0.316652	+	0.948542i	$0.602559\pi$
$398$	−1.05918e6	−	1404.02i	−0.335167	−	0.000444290i
$399$	376362.	+	613036.i	0.118351	+	0.192776i
$400$	−639991.	−	3393.46i	−0.199997	−	0.00106046i
$401$		−	4.68836e6i		−	1.45600i	−0.685580	−	0.727998i	$-0.740451\pi$
$401$		−	4.68836e6i		−	1.45600i	0.685580	−	0.727998i	$-0.259549\pi$
$402$	−99779.9	−	163010.i	−0.0307948	−	0.0503095i
$403$			5.76734e6i			1.76894i
$404$	8381.87	−	3.16158e6i	0.00255498	−	0.963720i
$405$	1.19143e6	−	871622.i	0.360938	−	0.264053i
$406$	−152.285	+	114882.i	−4.58504e−5	+	0.0345889i
$407$	−5.05172e6			−1.51166
$408$	−62330.8	−	102439.i	−0.0185376	−	0.0304659i
$409$	5.05579e6			1.49445			0.747223	−	0.664573i	$-0.231387\pi$
$409$	5.05579e6			1.49445			0.747223	+	0.664573i	$0.231387\pi$
$410$	2191.96	−	1.65359e6i	0.000643981	−	0.485811i
$411$	1.43288e6	−	879692.i	0.418414	−	0.256877i
$412$	−6080.07	+	2.29336e6i	−0.00176468	+	0.665625i
$413$			1.45050e6i			0.418448i
$414$	1.79928e6	+	916060.i	0.515938	+	0.262678i
$415$		−	2.31391e6i		−	0.659517i
$416$	−27872.3	+	4.20524e6i	−0.00789658	+	1.19140i
$417$	−2.39171e6	+	1.46834e6i	−0.673547	+	0.413512i
$418$	−3.12046e6	−	4136.42i	−0.873531	−	0.00115793i
$419$	2.94984e6			0.820849			0.410424	−	0.911895i	$-0.365381\pi$
$419$	2.94984e6			0.820849			0.410424	+	0.911895i	$0.365381\pi$
$420$	361220.	+	591885.i	0.0999190	+	0.163725i
$421$	4.35743e6			1.19819			0.599095	−	0.800678i	$-0.295527\pi$
$421$	4.35743e6			1.19819			0.599095	+	0.800678i	$0.295527\pi$
$422$	−2.73726e6	−	3628.45i	−0.748230	−	0.000991838i
$423$	1.19880e6	−	2.36236e6i	0.325758	−	0.641941i
$424$	3.19332e6	+	12699.1i	0.862636	+	0.00343049i
$425$			26559.1i			0.00713250i
$426$	−1.21799e6	+	745541.i	−0.325177	+	0.199043i
$427$		−	2.19273e6i		−	0.581990i
$428$	−6.99849e6	−	18554.1i	−1.84669	−	0.00489589i
$429$	−3.93547e6	−	6.41027e6i	−1.03241	−	1.68164i
$430$	4011.53	−	3.02625e6i	0.00104626	−	0.789285i
$431$	−4.77234e6			−1.23748			−0.618740	−	0.785596i	$-0.712356\pi$
$431$	−4.77234e6			−1.23748			−0.618740	+	0.785596i	$0.712356\pi$
$432$	−3.86780e6	+	293357.i	−0.997136	+	0.0756288i
$433$	−3.59669e6			−0.921899			−0.460950	−	0.887426i	$-0.652491\pi$
$433$	−3.59669e6			−0.921899			−0.460950	+	0.887426i	$0.652491\pi$
$434$	3312.25	−	2.49872e6i	0.000844109	−	0.636785i
$435$	74472.3	+	121304.i	0.0188700	+	0.0307363i
$436$	−3.89530e6	−	10327.1i	−0.981353	−	0.00260173i
$437$			1.21902e6i			0.305355i
$438$	−5.16589e6	+	3.16208e6i	−1.28665	+	0.787567i
$439$		−	5.83722e6i		−	1.44559i	−0.691063	−	0.722795i	$-0.742857\pi$
$439$		−	5.83722e6i		−	1.44559i	0.691063	−	0.722795i	$-0.257143\pi$
$440$	−3.00790e6	−	11961.7i	−0.740681	−	0.00294551i
$441$	−1.50820e6	+	2.97206e6i	−0.369285	+	0.727715i
$442$	174515.	+	231.334i	0.0424892	+	5.63227e-5i
$443$	3.70541e6			0.897072			0.448536	−	0.893765i	$-0.351946\pi$
$443$	3.70541e6			0.897072			0.448536	+	0.893765i	$0.351946\pi$
$444$	−1.97504e6	−	3.23625e6i	−0.475465	−	0.779086i
$445$	−40957.1			−0.00980457
$446$	5.86786e6	+	7778.31i	1.39683	+	0.00185160i
$447$	2.24240e6	−	1.37668e6i	0.530816	−	0.325884i
$448$	14490.9	−	1.82192e6i	0.00341114	−	0.428878i
$449$			4.68460e6i			1.09662i	0.836275	+	0.548310i	$0.184729\pi$
$449$			4.68460e6i			1.09662i	−0.836275	+	0.548310i	$0.815271\pi$
$450$	765618.	+	389796.i	0.178230	+	0.0907416i
$451$		−	7.77166e6i		−	1.79917i
$452$	−15224.2	+	5.74247e6i	−0.00350501	+	1.32206i
$453$	−3.14015e6	+	1.92784e6i	−0.718960	+	0.441392i
$454$	−8930.51	+	6.73706e6i	−0.00203346	+	1.53402i
$455$	−1.00916e6			−0.228523
$456$	−1.21734e6	−	2.00066e6i	−0.274158	−	0.450570i
$457$	5.03914e6			1.12867			0.564333	−	0.825547i	$-0.309133\pi$
$457$	5.03914e6			1.12867			0.564333	+	0.825547i	$0.309133\pi$
$458$	−2188.70	+	1.65113e6i	−0.000487553	+	0.367804i
$459$	13024.8	+	160442.i	0.00288563	+	0.0355455i
$460$	−3115.23	+	1.17504e6i	−0.000686430	+	0.258917i
$461$			4.09644e6i			0.897748i	0.893595	+	0.448874i	$0.148175\pi$
$461$			4.09644e6i			0.897748i	−0.893595	+	0.448874i	$0.851825\pi$
$462$	1.70137e6	+	2.77953e6i	0.370847	+	0.605852i
$463$			1.67205e6i			0.362491i	0.983438	+	0.181246i	$0.0580129\pi$
$463$			1.67205e6i			0.362491i	−0.983438	+	0.181246i	$0.941987\pi$
$464$	1983.12	−	374006.i	0.000427615	−	0.0806462i
$465$	−1.61979e6	−	2.63840e6i	−0.347398	−	0.565859i
$466$	3.88531e6	+	5150.29i	0.828822	+	0.00109867i
$467$	−1.49689e6			−0.317613			−0.158806	−	0.987310i	$-0.550765\pi$
$467$	−1.49689e6			−0.317613			−0.158806	+	0.987310i	$0.550765\pi$
$468$	2.56795e6	−	5.02735e6i	0.541966	−	1.06102i
$469$	−120512.			−0.0252987
$470$	1.54174e6	+	2043.70i	0.321933	+	0.000426748i
$471$	−3.03377e6	−	4.94154e6i	−0.630130	−	1.02639i
$472$	18779.1	−	4.72221e6i	0.00387989	−	0.975642i
$473$		−	1.42230e7i		−	2.92306i
$474$	4.83128e6	+	7.89287e6i	0.987681	+	1.61358i
$475$			518709.i			0.105485i
$476$	−75609.3	−	200.452i	−0.0152953	−	4.05503e-5i
$477$	−3.82270e6	−	1.93986e6i	−0.769263	−	0.390369i
$478$	1652.34	−	1.24650e6i	0.000330773	−	0.249531i
$479$	2.55760e6			0.509325			0.254662	−	0.967030i	$-0.418036\pi$
$479$	2.55760e6			0.509325			0.254662	+	0.967030i	$0.418036\pi$
$480$	−1.16832e6	−	1.93161e6i	−0.231450	−	0.382663i
$481$	5.51776e6			1.08743
$482$	9541.96	−	7.19834e6i	0.00187077	−	1.41128i
$483$	1.08495e6	−	666083.i	0.211612	−	0.129915i
$484$	−8.98317e6	−	23815.9i	−1.74308	−	0.00462118i
$485$			1.18010e6i			0.227805i
$486$	4.81620e6	+	1.97926e6i	0.924940	+	0.380113i
$487$			3.14528e6i			0.600948i	0.953790	+	0.300474i	$0.0971449\pi$
$487$			3.14528e6i			0.600948i	−0.953790	+	0.300474i	$0.902855\pi$
$488$	−28388.5	+	7.13861e6i	−0.00539627	+	1.35695i
$489$	2.88470e6	−	1.77101e6i	0.545543	−	0.334925i
$490$	−1.93965e6	−	2571.16i	−0.364949	−	0.000483769i
$491$	−858259.			−0.160663			−0.0803313	−	0.996768i	$-0.525598\pi$
$491$	−858259.			−0.160663			−0.0803313	+	0.996768i	$0.525598\pi$
$492$	4.97872e6	−	3.03844e6i	0.927267	−	0.565898i
$493$	−15521.0			−0.00287608
$494$	3.40834e6	+	4518.03i	0.628385	+	0.000832974i
$495$	3.60073e6	+	1.82722e6i	0.660508	+	0.335180i
$496$	−43133.4	+	8.13474e6i	−0.00787244	+	1.48470i
$497$			900448.i			0.163519i
$498$	6.96121e6	−	4.26101e6i	1.25780	−	0.769908i
$499$		−	1.92537e6i		−	0.346148i	−0.984909	−	0.173074i	$-0.944630\pi$
$499$		−	1.92537e6i		−	0.346148i	0.984909	−	0.173074i	$-0.0553700\pi$
$500$	−1325.58	+	499998.i	−0.000237126	+	0.0894424i
$501$	−3.50295e6	−	5.70578e6i	−0.623505	−	1.01559i
$502$	−7833.31	+	5.90935e6i	−0.00138735	+	1.04660i
$503$	1.06310e7			1.87350			0.936751	−	0.349998i	$-0.113818\pi$
$503$	1.06310e7			1.87350			0.936751	+	0.349998i	$0.113818\pi$
$504$	−1.11546e6	+	2.17664e6i	−0.195604	+	0.381690i
$505$	−2.46999e6			−0.430990
$506$	−7320.61	+	5.52258e6i	−0.00127107	+	0.958882i
$507$	1.27032e6	+	2.06916e6i	0.219479	+	0.357498i
$508$	11737.0	−	4.42711e6i	0.00201789	−	0.761134i
$509$			1.38570e6i			0.237070i	0.992950	+	0.118535i	$0.0378197\pi$
$509$			1.38570e6i			0.237070i	−0.992950	+	0.118535i	$0.962180\pi$
$510$	−79901.0	+	48907.9i	−0.0136027	+	0.00832634i
$511$			3.81909e6i			0.647005i
$512$	−70764.0	+	5.93122e6i	−0.0119299	+	0.999929i
$513$	254379.	+	3.13348e6i	0.0426764	+	0.525694i
$514$	−3.73080e6	−	4945.47i	−0.622865	−	0.000825657i
$515$	1.79169e6			0.297677
$516$	9.11161e6	−	5.56069e6i	1.50651	−	0.919400i
$517$	7.24598e6			1.19226
$518$	−2.39059e6	−	3168.92i	−0.391454	−	0.000518903i
$519$	−4.22436e6	+	2.59347e6i	−0.688403	+	0.422632i
$520$	3.28539e6	+	13065.2i	0.532817	+	0.00211889i
$521$			8.57848e6i			1.38457i	0.721622	+	0.692287i	$0.243397\pi$
$521$			8.57848e6i			1.38457i	−0.721622	+	0.692287i	$0.756603\pi$
$522$	−227794.	+	447422.i	−0.0365903	+	0.0718689i
$523$			2.74327e6i			0.438544i	0.975664	+	0.219272i	$0.0703683\pi$
$523$			2.74327e6i			0.438544i	−0.975664	+	0.219272i	$0.929632\pi$
$524$	−5.38205e6	−	14268.7i	−0.856288	−	0.00227016i
$525$	461661.	−	283428.i	0.0731012	−	0.0448791i
$526$	5612.04	−	4.23365e6i	0.000884416	−	0.667192i
$527$	337586.			0.0529490
$528$	−5.50297e6	−	9.07103e6i	−0.859039	−	1.41603i
$529$	−4.27894e6			−0.664809
$530$	3307.05	−	2.49480e6i	0.000511389	−	0.385785i
$531$	−2.86863e6	+	5.65293e6i	−0.441507	+	0.870037i
$532$	−1.47667e6	−	3914.90i	−0.226207	−	0.000599711i
$533$			8.48863e6i			1.29425i
$534$	−75421.4	−	123216.i	−0.0114457	−	0.0186988i
$535$			5.46759e6i			0.825870i
$536$	392337.	+	1560.23i	0.0589857	+	0.000234572i
$537$	1.43106e6	+	2.33098e6i	0.214153	+	0.348822i
$538$	−7.10977e6	−	9424.56i	−1.05901	−	0.00140380i
$539$	−9.11610e6			−1.35157
$540$	237196.	+	3.02110e6i	0.0350044	+	0.445842i
$541$	−1.26762e7			−1.86207			−0.931037	−	0.364924i	$-0.881095\pi$
$541$	−1.26762e7			−1.86207			−0.931037	+	0.364924i	$0.881095\pi$
$542$	8.24993e6	+	10935.9i	1.20629	+	0.00159903i
$543$	2.19270e6	+	3.57158e6i	0.319139	+	0.519829i
$544$	246150.	+	1631.48i	0.0356617	+	0.000236365i
$545$			3.04322e6i			0.438876i
$546$	−1.85833e6	−	3.03596e6i	−0.266773	−	0.435827i
$547$		−	2.38700e6i		−	0.341101i	−0.985349	−	0.170551i	$-0.945445\pi$
$547$		−	2.38700e6i		−	0.341101i	0.985349	−	0.170551i	$-0.0545546\pi$
$548$	−9150.52	+	3.45151e6i	−0.00130165	+	0.490973i
$549$	4.33653e6	−	8.54559e6i	0.614061	−	1.21007i
$550$	−3115.02	+	2.34993e6i	−0.000439091	+	0.331245i
$551$	−303130.			−0.0425353
$552$	−3.54076e6	+	2.15444e6i	−0.494594	+	0.300945i
$553$	5.83512e6			0.811403
$554$	8816.47	−	6.65104e6i	0.00122045	−	0.920693i
$555$	−2.52422e6	+	1.54970e6i	−0.347853	+	0.213558i
$556$	15273.7	−	5.76111e6i	0.00209535	−	0.790350i
$557$		−	6.89726e6i		−	0.941973i	−0.882140	−	0.470986i	$-0.843898\pi$
$557$		−	6.89726e6i		−	0.941973i	0.882140	−	0.470986i	$-0.156102\pi$
$558$	4.95459e6	−	9.73156e6i	0.673632	−	1.32311i
$559$			1.55351e7i			2.10274i
$560$	−1.42340e6	−	7547.38i	−0.191803	−	0.00101701i
$561$	−375219.	+	230359.i	−0.0503359	+	0.0309028i
$562$	−7.04450e6	−	9338.04i	−0.940826	−	0.00124714i
$563$	−7.85350e6			−1.04422			−0.522110	−	0.852878i	$-0.674855\pi$
$563$	−7.85350e6			−1.04422			−0.522110	+	0.852878i	$0.674855\pi$
$564$	2.83292e6	+	4.64195e6i	0.375005	+	0.614473i
$565$	4.48632e6			0.591247
$566$	3.76686e6	+	4993.27i	0.494240	+	0.000655154i
$567$	2.64986e6	−	1.93857e6i	0.346151	−	0.253235i
$568$	11657.8	−	2.93148e6i	0.00151616	−	0.381256i
$569$			6.74205e6i			0.872994i	0.899706	+	0.436497i	$0.143781\pi$
$569$			6.74205e6i			0.872994i	−0.899706	+	0.436497i	$0.856219\pi$
$570$	−1.56049e6	+	955188.i	−0.201175	+	0.123141i
$571$		−	122502.i		−	0.0157236i	−0.999969	−	0.00786179i	$-0.997497\pi$
$571$		−	122502.i		−	0.0157236i	0.999969	−	0.00786179i	$-0.00250251\pi$
$572$	1.54410e7	+	40936.6i	1.97326	+	0.00523144i
$573$	5.64714e6	+	9.19834e6i	0.718526	+	1.17037i
$574$	4875.12	−	3.67773e6i	0.000617598	−	0.465908i
$575$	918007.			0.115791
$576$	3.65966e6	−	7.07179e6i	0.459605	−	0.888124i
$577$	−1.11918e6			−0.139946			−0.0699731	−	0.997549i	$-0.522291\pi$
$577$	−1.11918e6			−0.139946			−0.0699731	+	0.997549i	$0.522291\pi$
$578$	−10633.4	+	8.02170e6i	−0.00132389	+	0.998727i
$579$	−1.83951e6	−	2.99629e6i	−0.228038	−	0.371439i
$580$	−292195.	−	774.658i	−0.0360665	−	9.56180e-5i
$581$		−	5.14635e6i		−	0.632498i
$582$	−3.55023e6	+	2.17312e6i	−0.434459	+	0.265935i
$583$		−	1.17252e7i		−	1.42873i
$584$	49444.5	−	1.24334e7i	0.00599909	−	1.50854i
$585$	−3.93292e6	−	1.99579e6i	−0.475144	−	0.241116i
$586$	5.45234e6	+	7227.50i	0.655901	+	0.000869449i
$587$	4.44542e6			0.532497			0.266248	−	0.963904i	$-0.414216\pi$
$587$	4.44542e6			0.532497			0.266248	+	0.963904i	$0.414216\pi$
$588$	−3.56407e6	−	5.84000e6i	−0.425112	−	0.696578i
$589$	6.59316e6			0.783078
$590$	−3.68926e6	−	4890.40i	−0.436324	−	0.000578381i
$591$	3.54969e6	−	2.17927e6i	0.418044	−	0.256650i
$592$	7.78272e6	+	41266.8i	0.912698	+	0.00483946i
$593$		−	1.07084e7i		−	1.25052i	−0.780418	−	0.625258i	$-0.784994\pi$
$593$		−	1.07084e7i		−	1.25052i	0.780418	−	0.625258i	$-0.215006\pi$
$594$	1.13361e6	+	1.41973e7i	0.131825	+	1.65097i
$595$			59069.9i			0.00684028i
$596$	−14320.2	+	5.40146e6i	−0.00165132	+	0.622867i
$597$	−2.48739e6	+	1.52709e6i	−0.285633	+	0.175359i
$598$	7995.98	−	6.03206e6i	0.000914363	−	0.689783i
$599$	−9.96025e6			−1.13424			−0.567118	−	0.823637i	$-0.691942\pi$
$599$	−9.96025e6			−1.13424			−0.567118	+	0.823637i	$0.691942\pi$
$600$	−1.50664e6	+	916746.i	−0.170857	+	0.103961i
$601$	−8.63901e6			−0.975614			−0.487807	−	0.872952i	$-0.662203\pi$
$601$	−8.63901e6			−0.975614			−0.487807	+	0.872952i	$0.662203\pi$
$602$	8922.02	−	6.73065e6i	0.00100339	−	0.756948i
$603$	−469664.	−	238335.i	−0.0526010	−	0.0266928i
$604$	20053.3	−	7.56395e6i	0.00223662	−	0.843639i
$605$			7.01813e6i			0.779530i
$606$	−4.54843e6	−	7.43077e6i	−0.503130	−	0.821963i
$607$			2.62643e6i			0.289331i	0.989481	+	0.144665i	$0.0462105\pi$
$607$			2.62643e6i			0.289331i	−0.989481	+	0.144665i	$0.953789\pi$
$608$	4.80738e6	+	31863.3i	0.527412	+	0.00349568i
$609$	165633.	+	269791.i	0.0180969	+	0.0294771i
$610$	5.57708e6	+	7392.86i	0.606851	+	0.000804430i
$611$	−7.91446e6			−0.857666
$612$	−294271.	−	150313.i	−0.0317592	−	0.0162225i
$613$	−4.02955e6			−0.433117			−0.216559	−	0.976270i	$-0.569483\pi$
$613$	−4.02955e6			−0.433117			−0.216559	+	0.976270i	$0.569483\pi$
$614$	−1.48780e7	−	19722.0i	−1.59267	−	0.00211120i
$615$	−2.38409e6	−	3.88332e6i	−0.254176	−	0.414014i
$616$	−6.68983e6	−	26603.8i	−0.710335	−	0.00282483i
$617$		−	1.27536e7i		−	1.34872i	−0.738405	−	0.674358i	$-0.764420\pi$
$617$		−	1.27536e7i		−	1.34872i	0.738405	−	0.674358i	$-0.235580\pi$
$618$	3.29936e6	+	5.39016e6i	0.347503	+	0.567716i
$619$			6.65871e6i			0.698495i	0.937030	+	0.349248i	$0.113563\pi$
$619$			6.65871e6i			0.698495i	−0.937030	+	0.349248i	$0.886437\pi$
$620$	6.35534e6	+	16849.0i	0.663987	+	0.00176034i
$621$	5.54560e6	−	450198.i	0.577059	−	0.0468462i
$622$	13269.8	−	1.00105e7i	0.00137527	−	1.03748i
$623$	−91092.2			−0.00940289
$624$	6.01065e6	+	9.90788e6i	0.617960	+	1.01864i
$625$	390625.			0.0400000
$626$	10385.8	−	7.83488e6i	0.00105926	−	0.799092i
$627$	−7.32816e6	+	4.49898e6i	−0.744433	+	0.457031i
$628$	1.19031e7	+	31557.1i	1.20438	+	0.00319300i
$629$		−	322977.i		−	0.0325496i
$630$	1.70280e6	+	866943.i	0.170928	+	0.0870240i
$631$		−	6.98758e6i		−	0.698639i	−0.937004	−	0.349320i	$-0.886413\pi$
$631$		−	6.98758e6i		−	0.698639i	0.937004	−	0.349320i	$-0.113587\pi$
$632$	−1.89967e7	−	75545.3i	−1.89185	−	0.00752341i
$633$	−6.42823e6	+	3.94649e6i	−0.637650	+	0.391473i
$634$	−1.01806e6	−	1349.51i	−0.100589	−	0.000133338i
$635$	−3.45869e6			−0.340391
$636$	7.51148e6	−	4.58416e6i	0.736348	−	0.449383i
$637$	9.95711e6			0.972265
$638$	−1.37329e6	−	1820.40i	−0.133570	−	0.000177058i
$639$	−1.78080e6	+	3.50926e6i	−0.172530	+	0.339988i
$640$	4.63390e6	+	42999.4i	0.447194	+	0.00414966i
$641$		−	5.56451e6i		−	0.534911i	−0.963570	−	0.267456i	$-0.913817\pi$
$641$		−	5.56451e6i		−	0.534911i	0.963570	−	0.267456i	$-0.0861829\pi$
$642$	−1.64488e7	+	1.00684e7i	−1.57506	+	0.964104i
$643$		−	6.93962e6i		−	0.661924i	−0.943644	−	0.330962i	$-0.892627\pi$
$643$		−	6.93962e6i		−	0.661924i	0.943644	−	0.330962i	$-0.107373\pi$
$644$	−6928.57	+	2.61341e6i	−0.000658307	+	0.248309i
$645$	−4.36315e6	−	7.10690e6i	−0.412953	−	0.672637i
$646$	264.459	−	199504.i	2.49331e−5	−	0.0188092i
$647$	216869.			0.0203675			0.0101837	−	0.999948i	$-0.496758\pi$
$647$	216869.			0.0203675			0.0101837	+	0.999948i	$0.496758\pi$
$648$	−8.65194e6	+	6.27686e6i	−0.809424	+	0.587225i
$649$	−1.73390e7			−1.61590
$650$	3402.40	−	2.56673e6i	0.000315865	−	0.238285i
$651$	−3.60257e6	−	5.86804e6i	−0.333165	−	0.542676i
$652$	−18421.9	+	6.94863e6i	−0.00169714	+	0.640148i
$653$		−	7.99841e6i		−	0.734042i	−0.930213	−	0.367021i	$-0.880378\pi$
$653$		−	7.99841e6i		−	0.734042i	0.930213	−	0.367021i	$-0.119622\pi$
$654$	−9.15527e6	+	5.60400e6i	−0.837002	+	0.512335i
$655$			4.20474e6i			0.382945i
$656$	−63485.7	+	1.19731e7i	−0.00575992	+	1.08629i
$657$	−7.55296e6	+	1.48839e7i	−0.682659	+	1.34525i
$658$	3.42897e6	+	4545.37i	0.308744	+	0.000409265i
$659$	5.57495e6			0.500066			0.250033	−	0.968237i	$-0.419559\pi$
$659$	5.57495e6			0.500066			0.250033	+	0.968237i	$0.419559\pi$
$660$	−7.07532e6	+	4.31797e6i	−0.632246	+	0.385851i
$661$	7.42605e6			0.661080			0.330540	−	0.943792i	$-0.392769\pi$
$661$	7.42605e6			0.661080			0.330540	+	0.943792i	$0.392769\pi$
$662$	−1.16138e7	−	15395.0i	−1.02998	−	0.00136532i
$663$	409835.	−	251611.i	0.0362097	−	0.0222303i
$664$	−66628.0	+	1.67544e7i	−0.00586458	+	1.47471i
$665$			1.15366e6i			0.101163i
$666$	−9.31043e6	−	4.74019e6i	−0.813363	−	0.414105i
$667$			536477.i			0.0466913i
$668$	1.37440e7	+	36437.6i	1.19171	+	0.00315943i
$669$	1.37802e7	−	8.46008e6i	1.19039	−	0.730818i
$670$	406.310	−	306515.i	3.49680e−5	−	0.0263794i
$671$	2.62116e7			2.24744
$672$	−2.59845e6	−	4.29607e6i	−0.221968	−	0.366985i
$673$	−5.35800e6			−0.456000			−0.228000	−	0.973661i	$-0.573219\pi$
$673$	−5.35800e6			−0.456000			−0.228000	+	0.973661i	$0.573219\pi$
$674$	17563.1	−	1.32494e7i	0.00148919	−	1.12343i
$675$	2.35973e6	−	191566.i	0.199344	−	0.0161830i
$676$	−4.98416e6	−	13213.8i	−0.419493	−	0.00111214i
$677$			6.34280e6i			0.531875i	0.963990	+	0.265937i	$0.0856815\pi$
$677$			6.34280e6i			0.531875i	−0.963990	+	0.265937i	$0.914319\pi$
$678$	8.26144e6	+	1.34967e7i	0.690210	+	1.12760i
$679$			2.62465e6i			0.218472i
$680$	764.759	−	192307.i	6.34238e−5	−	0.0159486i
$681$	9.71327e6	+	1.58214e7i	0.802597	+	1.30731i
$682$	2.98694e7	+	39594.2i	2.45904	+	0.00325965i
$683$	1.66958e6			0.136948			0.0684740	−	0.997653i	$-0.478187\pi$
$683$	1.66958e6			0.136948			0.0684740	+	0.997653i	$0.478187\pi$
$684$	−5.74721e6	−	2.93566e6i	−0.469696	−	0.239919i
$685$	2.69650e6			0.219571
$686$	−9.60032e6	−	12726.0i	−0.778889	−	0.00103248i
$687$	2.38054e6	+	3.87753e6i	0.192435	+	0.313447i
$688$	−116186.	+	2.19121e7i	−0.00935799	+	1.76487i
$689$			1.28070e7i			1.02777i
$690$	1.69049e6	+	2.76175e6i	0.135173	+	0.220832i
$691$			594970.i			0.0474024i	0.999719	+	0.0237012i	$0.00754503\pi$
$691$			594970.i			0.0474024i	−0.999719	+	0.0237012i	$0.992455\pi$
$692$	26977.2	−	1.01756e7i	0.00214156	−	0.807782i
$693$	8.00836e6	+	4.06391e6i	0.633447	+	0.321448i
$694$	−11521.9	+	8.69198e6i	−0.000908083	+	0.685046i
$695$	−4.50089e6			−0.353457
$696$	−535740.	−	880472.i	−0.0419209	−	0.0688958i
$697$	496874.			0.0387404
$698$	16458.4	−	1.24160e7i	0.00127864	−	0.964591i
$699$	9.12434e6	−	5.60172e6i	0.706331	−	0.433639i
$700$	−2948.20	+	1.11204e6i	−0.000227412	+	0.0857780i
$701$		−	3.08250e6i		−	0.236923i	−0.992959	−	0.118462i	$-0.962204\pi$
$701$		−	3.08250e6i		−	0.236923i	0.992959	−	0.118462i	$-0.0377962\pi$
$702$	−1.23819e6	−	1.55071e7i	−0.0948298	−	1.18765i
$703$		−	6.30785e6i		−	0.481385i
$704$	2.17790e7	+	173222.i	1.65617	+	0.0131726i
$705$	3.62065e6	−	2.22283e6i	0.274355	−	0.168435i
$706$	7.14331e6	+	9469.02i	0.539371	+	0.000714979i
$707$	−5.49349e6			−0.413333
$708$	−6.77895e6	−	1.11078e7i	−0.508253	−	0.832810i
$709$	−2.09908e7			−1.56825			−0.784123	−	0.620606i	$-0.786887\pi$
$709$	−2.09908e7			−1.56825			−0.784123	+	0.620606i	$0.786887\pi$
$710$	−2.29024e6	−	3035.89i	−0.170504	−	0.000226017i
$711$	2.27409e7	+	1.15400e7i	1.68707	+	0.856117i
$712$	296558.	+	1179.34i	0.0219235	+	8.71845e-5i
$713$		−	1.16685e7i		−	0.859592i
$714$	−177707.	+	108776.i	−0.0130454	+	0.00798521i
$715$		−	1.20633e7i		−	0.882473i
$716$	−5.61484e6	−	14885.9i	−0.409313	−	0.00108515i
$717$	−1.79717e6	−	2.92731e6i	−0.130554	−	0.212653i
$718$	−5978.32	+	4.50997e6i	−0.000432781	+	0.326484i
$719$	1.76307e7			1.27188			0.635941	−	0.771738i	$-0.280612\pi$
$719$	1.76307e7			1.27188			0.635941	+	0.771738i	$0.280612\pi$
$720$	−5.53240e6	−	2.84445e6i	−0.397724	−	0.204488i
$721$	3.98489e6			0.285482
$722$	−13402.3	+	1.01105e7i	−0.000956835	+	0.721824i
$723$	−1.03783e7	−	1.69047e7i	−0.738383	−	1.20271i
$724$	−8.60317e6	−	22808.4i	−0.609975	−	0.00161714i
$725$			228278.i			0.0161295i
$726$	−2.11135e7	+	1.29237e7i	−1.48668	+	0.910008i
$727$		−	8.61050e6i		−	0.604216i	−0.953274	−	0.302108i	$-0.902310\pi$
$727$		−	8.61050e6i		−	0.604216i	0.953274	−	0.302108i	$-0.0976903\pi$
$728$	7.30700e6	+	29058.2i	0.510988	+	0.00203208i
$729$	1.41610e7	−	2.31447e6i	0.986906	−	0.161299i
$730$	−9.71363e6	−	12876.2i	−0.674644	−	0.000894294i
$731$	909335.			0.0629405
$732$	1.02478e7	+	1.67918e7i	0.706892	+	1.15830i
$733$	−2.42835e6			−0.166937			−0.0834684	−	0.996510i	$-0.526600\pi$
$733$	−2.42835e6			−0.166937			−0.0834684	+	0.996510i	$0.526600\pi$
$734$	1.79248e7	+	23760.7i	1.22804	+	0.00162787i
$735$	−4.55510e6	+	2.79652e6i	−0.311014	+	0.190941i
$736$	56391.4	−	8.50807e6i	0.00383724	−	0.578944i
$737$		−	1.44058e6i		−	0.0976944i
$738$	7.29240e6	−	1.43234e7i	0.492867	−	0.968063i
$739$		−	2.44656e7i		−	1.64795i	−0.566626	−	0.823975i	$-0.691752\pi$
$739$		−	2.44656e7i		−	1.64795i	0.566626	−	0.823975i	$-0.308248\pi$
$740$	16119.9	−	6.08032e6i	0.00108214	−	0.408175i
$741$	8.00422e6	−	4.91404e6i	0.535517	−	0.328770i
$742$	7355.19	−	5.54866e6i	0.000490438	−	0.369980i
$743$	−7.73014e6			−0.513707			−0.256853	−	0.966450i	$-0.582686\pi$
$743$	−7.73014e6			−0.513707			−0.256853	+	0.966450i	$0.582686\pi$
$744$	1.16525e7	+	1.91505e7i	0.771768	+	1.26838i
$745$	4.21991e6			0.278556
$746$	−29177.1	+	2.20108e7i	−0.00191953	+	1.44807i
$747$	1.01779e7	−	2.00566e7i	0.667353	−	1.31509i
$748$	2396.18	−	903823.i	0.000156591	−	0.0590649i
$749$			1.21604e7i			0.792035i
$750$	719326.	+	1.17516e6i	0.0466952	+	0.0762860i
$751$			1.55732e7i			1.00758i	0.863827	+	0.503789i	$0.168061\pi$
$751$			1.55732e7i			1.00758i	−0.863827	+	0.503789i	$0.831939\pi$
$752$	−1.11632e7	−	59191.5i	−0.719855	−	0.00381693i
$753$	8.51990e6	+	1.38776e7i	0.547579	+	0.891923i
$754$	1.49998e6	+	1988.34i	0.0960852	+	0.000127369i
$755$	−5.90936e6			−0.377288
$756$	527545.	+	6.71920e6i	0.0335703	+	0.427576i
$757$	−2.46665e7			−1.56447			−0.782236	−	0.622982i	$-0.785921\pi$
$757$	−2.46665e7			−1.56447			−0.782236	+	0.622982i	$0.785921\pi$
$758$	7.61963e6	+	10100.4i	0.481682	+	0.000638508i
$759$	7.96227e6	+	1.29693e7i	0.501686	+	0.817171i
$760$	14936.0	−	3.75582e6i	0.000937994	−	0.235869i
$761$		−	1.24949e7i		−	0.782118i	−0.920366	−	0.391059i	$-0.872109\pi$
$761$		−	1.24949e7i		−	0.782118i	0.920366	−	0.391059i	$-0.127891\pi$
$762$	−6.36909e6	−	1.04052e7i	−0.397365	−	0.649176i
$763$			6.76839e6i			0.420895i
$764$	−2.21568e7	−	58741.4i	−1.37333	−	0.00364092i
$765$	−116822.	+	230210.i	−0.00721723	+	0.0142223i
$766$	−13055.2	+	9.84864e6i	−0.000803915	+	0.606463i
$767$	1.89387e7			1.16241
$768$	8.40384e6	+	1.40199e7i	0.514132	+	0.857711i
$769$	6.79981e6			0.414649			0.207325	−	0.978272i	$-0.433524\pi$
$769$	6.79981e6			0.414649			0.207325	+	0.978272i	$0.433524\pi$
$770$	−6928.10	+	5.22647e6i	−0.000421102	+	0.317674i
$771$	−8.76148e6	+	5.37894e6i	−0.530813	+	0.325883i
$772$	7.21742e6	+	19134.5i	0.435851	+	0.00115551i
$773$			3.81527e6i			0.229655i	0.993385	+	0.114828i	$0.0366316\pi$
$773$			3.81527e6i			0.229655i	−0.993385	+	0.114828i	$0.963368\pi$
$774$	1.33459e7	−	2.62133e7i	0.800747	−	1.57279i
$775$		−	4.96512e6i		−	0.296945i
$776$	33980.4	−	8.54475e6i	0.00202570	−	0.509384i
$777$	−5.61410e6	+	3.44667e6i	−0.333601	+	0.204808i
$778$	−3.09239e7	−	40992.1i	−1.83166	−	0.00242801i
$779$	9.70411e6			0.572944
$780$	7.72805e6	−	4.71633e6i	0.454814	−	0.277567i
$781$	−1.07638e7			−0.631451
$782$	−353081.	−	468.037i	−0.0206470	−	2.73693e-5i
$783$	111950.	+	1.37901e6i	0.00652557	+	0.0803829i
$784$	1.40444e7	+	74468.3i	0.816041	+	0.00432694i
$785$		−	9.29935e6i		−	0.538615i
$786$	−1.26496e7	+	7.74292e6i	−0.730333	+	0.447042i
$787$			3.44192e6i			0.198091i	0.995083	+	0.0990454i	$0.0315789\pi$
$787$			3.44192e6i			0.198091i	−0.995083	+	0.0990454i	$0.968421\pi$
$788$	−22668.7	+	8.55046e6i	−0.00130050	+	0.490539i
$789$	−6.10394e6	−	9.94239e6i	−0.349074	−	0.568589i
$790$	−19673.3	+	1.48413e7i	−0.00112153	+	0.846065i
$791$	9.97798e6			0.567024
$792$	−2.60193e7	−	1.33341e7i	−1.47395	−	0.755353i
$793$	−2.86298e7			−1.61672
$794$	14913.1	−	1.12503e7i	0.000839494	−	0.633304i
$795$	−3.59692e6	−	5.85883e6i	−0.201843	−	0.328771i
$796$	15884.7	−	5.99159e6i	0.000888579	−	0.335166i
$797$			1.40126e7i			0.781400i	0.920518	+	0.390700i	$0.127767\pi$
$797$			1.40126e7i			0.781400i	−0.920518	+	0.390700i	$0.872233\pi$
$798$	−3.47068e6	+	2.12443e6i	−0.192933	+	0.118096i
$799$			463265.i			0.0256722i
$800$	23995.4	−	3.62031e6i	0.00132557	−	0.199996i
$801$	−355008.	−	180152.i	−0.0195505	−	0.00992105i
$802$	2.65213e7	+	35156.1i	1.45599	+	0.00193004i
$803$	−4.56529e7			−2.49850
$804$	922874.	−	563217.i	0.0503503	−	0.0307281i
$805$	2.04173e6			0.111048
$806$	−3.26250e7	−	43247.0i	−1.76894	−	0.00234487i
$807$	−1.66967e7	+	1.02506e7i	−0.902500	+	0.554073i
$808$	1.78845e7	+	71122.4i	0.963716	+	0.00383246i
$809$		−	2.75762e7i		−	1.48137i	−0.671852	−	0.740685i	$-0.734501\pi$
$809$		−	2.75762e7i		−	1.48137i	0.671852	−	0.740685i	$-0.265499\pi$
$810$	4.92170e6	+	6.74630e6i	0.263574	+	0.361288i
$811$			2.52683e7i			1.34903i	0.738259	+	0.674517i	$0.235648\pi$
$811$			2.52683e7i			1.34903i	−0.738259	+	0.674517i	$0.764352\pi$
$812$	−649869.	−	1722.91i	−0.0345888	−	9.17006e-5i
$813$	1.93743e7	−	1.18945e7i	1.02802	−	0.631130i
$814$	37880.8	−	2.85768e7i	0.00200382	−	1.51165i
$815$	5.42863e6			0.286284
$816$	579948.	−	351828.i	0.0304905	−	0.0184972i
$817$	1.77596e7			0.930847
$818$	−37911.3	+	2.85998e7i	−0.00198101	+	1.49445i
$819$	−8.74717e6	−	4.43883e6i	−0.455678	−	0.231238i
$820$	9.35408e6	+	24799.2i	0.485810	+	0.00128796i
$821$			1.00641e7i			0.521093i	0.965461	+	0.260547i	$0.0839028\pi$
$821$			1.00641e7i			0.521093i	−0.965461	+	0.260547i	$0.916097\pi$
$822$	4.96554e6	+	8.11220e6i	0.256323	+	0.418754i
$823$			1.24922e7i			0.642893i	0.946928	+	0.321446i	$0.104169\pi$
$823$			1.24922e7i			0.642893i	−0.946928	+	0.321446i	$0.895831\pi$
$824$	−1.29732e7	−	51591.1i	−0.665622	−	0.00264702i
$825$	3.38806e6	+	5.51863e6i	0.173307	+	0.282291i
$826$	−8.20524e6	−	10876.7i	−0.418448	−	0.000554686i
$827$	−4.91826e6			−0.250062			−0.125031	−	0.992153i	$-0.539903\pi$
$827$	−4.91826e6			−0.250062			−0.125031	+	0.992153i	$0.539903\pi$
$828$	−5.19550e6	+	1.01714e7i	−0.263361	+	0.515589i
$829$	−6.83098e6			−0.345220			−0.172610	−	0.984990i	$-0.555220\pi$
$829$	−6.83098e6			−0.345220			−0.172610	+	0.984990i	$0.555220\pi$
$830$	1.30894e7	+	17351.1i	0.659517	+	0.000874242i
$831$	−9.58924e6	−	1.56194e7i	−0.481706	−	0.784625i
$832$	−2.37882e7	−	189203.i	−1.19139	−	0.00947587i
$833$		−	582830.i		−	0.0291024i
$834$	−8.28827e6	−	1.35405e7i	−0.412618	−	0.674095i
$835$		−	1.07375e7i		−	0.532952i
$836$	46798.2	−	1.76520e7i	0.00231587	−	0.873529i
$837$	−2.43494e6	−	2.99939e7i	−0.120136	−	1.47986i
$838$	−22119.7	+	1.66868e7i	−0.00108810	+	0.820848i
$839$	−2.26376e7			−1.11026			−0.555131	−	0.831763i	$-0.687332\pi$
$839$	−2.26376e7			−1.11026			−0.555131	+	0.831763i	$0.687332\pi$
$840$	−3.35091e6	+	2.03893e6i	−0.163857	+	0.0997019i
$841$	2.03777e7			0.993496
$842$	−32674.7	+	2.46493e7i	−0.00158829	+	1.19819i
$843$	−1.65434e7	+	1.01565e7i	−0.801783	+	0.492239i
$844$	41051.2	−	1.54842e7i	0.00198367	−	0.748228i
$845$			3.89388e6i			0.187604i
$846$	1.33545e7	+	6.79914e6i	0.641508	+	0.326609i
$847$			1.56090e7i			0.747593i
$848$	−95782.1	+	1.80640e7i	−0.00457398	+	0.862631i
$849$	8.84616e6	−	5.43093e6i	0.421197	−	0.258586i
$850$	−150241.	−	199.156i	−0.00713249	−	9.45468e-6i
$851$	−1.11636e7			−0.528421
$852$	−4.20828e6	−	6.89558e6i	−0.198612	−	0.325441i
$853$	−9.88412e6			−0.465120			−0.232560	−	0.972582i	$-0.574710\pi$
$853$	−9.88412e6			−0.465120			−0.232560	+	0.972582i	$0.574710\pi$
$854$	1.24039e7	+	16442.4i	0.581989	+	0.000771473i
$855$	−2.28157e6	+	4.49607e6i	−0.106738	+	0.210338i
$856$	157437.	−	3.95893e7i	0.00734382	−	1.84669i
$857$			1.46705e7i			0.682329i	0.940004	+	0.341164i	$0.110821\pi$
$857$			1.46705e7i			0.682329i	−0.940004	+	0.341164i	$0.889179\pi$
$858$	3.62915e7	−	2.22143e7i	1.68301	−	1.03018i
$859$		−	2.29669e7i		−	1.06199i	−0.847376	−	0.530993i	$-0.821819\pi$
$859$		−	2.29669e7i		−	1.06199i	0.847376	−	0.530993i	$-0.178181\pi$
$860$	1.71190e7	+	45385.3i	0.789282	+	0.00209252i
$861$	−5.30243e6	−	8.63685e6i	−0.243763	−	0.397052i
$862$	35785.9	−	2.69964e7i	0.00164038	−	1.23748i
$863$	−2.08289e7			−0.952005			−0.476003	−	0.879444i	$-0.657915\pi$
$863$	−2.08289e7			−0.952005			−0.476003	+	0.879444i	$0.657915\pi$
$864$	−1.63047e6	−	2.18817e7i	−0.0743070	−	0.997235i
$865$	−7.94971e6			−0.361253
$866$	26970.2	−	2.03459e7i	0.00122205	−	0.921898i
$867$	1.15654e7	+	1.88383e7i	0.522533	+	0.851127i
$868$	1.41348e7	+	37473.8i	0.636784	+	0.00168822i
$869$			6.97522e7i			3.13335i
$870$	−686757.	+	420369.i	−0.0307613	+	0.0188292i
$871$			1.57349e6i			0.0702777i
$872$	87628.1	−	2.20351e7i	0.00390258	−	0.981348i
$873$	−5.19073e6	+	1.02289e7i	−0.230512	+	0.454247i
$874$	−6.89579e6	−	9140.91i	−0.305355	−	0.000404773i
$875$	868786.			0.0383612
$876$	−1.78487e7	−	2.92464e7i	−0.785861	−	1.28769i
$877$	2.31037e7			1.01434			0.507169	−	0.861846i	$-0.330692\pi$
$877$	2.31037e7			1.01434			0.507169	+	0.861846i	$0.330692\pi$
$878$	3.30203e7	+	43771.0i	1.44559	+	0.00191624i
$879$	1.28044e7	−	7.86100e6i	0.558967	−	0.343167i
$880$	90220.3	−	1.70151e7i	0.00392733	−	0.740676i
$881$		−	9.00201e6i		−	0.390751i	−0.980729	−	0.195375i	$-0.937407\pi$
$881$		−	9.00201e6i		−	0.390751i	0.980729	−	0.195375i	$-0.0625925\pi$
$882$	−1.68012e7	−	8.55393e6i	−0.727225	−	0.370249i
$883$		−	50228.4i		−	0.00216794i	−0.999999	−	0.00108397i	$-0.999655\pi$
$883$		−	50228.4i		−	0.00216794i	0.999999	−	0.00108397i	$-0.000345039\pi$
$884$	−2617.24	+	987206.i	−0.000112645	+	0.0424890i
$885$	−8.66392e6	+	5.31905e6i	−0.371840	+	0.228284i
$886$	−27785.4	+	2.09610e7i	−0.00118914	+	0.897071i
$887$	1.88607e7			0.804914			0.402457	−	0.915439i	$-0.368156\pi$
$887$	1.88607e7			0.804914			0.402457	+	0.915439i	$0.368156\pi$
$888$	1.83218e7	−	1.11482e7i	0.779715	−	0.474432i
$889$	−7.69245e6			−0.326445
$890$	307.121	−	231688.i	1.29967e−5	−	0.00980457i
$891$	2.31734e7	+	3.16761e7i	0.977901	+	1.33671i
$892$	−88001.4	+	3.31935e7i	−0.00370320	+	1.39682i
$893$			9.04772e6i			0.379674i
$894$	7.77085e6	+	1.26952e7i	0.325181	+	0.531248i
$895$			4.38661e6i			0.183051i
$896$	1.03062e7	+	95634.5i	0.428873	+	0.00397965i
$897$	−8.69683e6	−	1.41658e7i	−0.360894	−	0.587841i
$898$	−2.65001e7	−	35127.9i	−1.09662	−	0.00145366i
$899$	2.90158e6			0.119739
$900$	−2.21076e6	+	4.32806e6i	−0.0909778	+	0.178110i
$901$	749643.			0.0307640
$902$	4.39631e7	+	58276.6i	1.79917	+	0.00238494i
$903$	−9.70404e6	−	1.58064e7i	−0.396035	−	0.645080i
$904$	−3.24842e7	−	129182.i	−1.32206	−	0.00525750i
$905$			6.72125e6i			0.272790i
$906$	−1.08819e7	−	1.77778e7i	−0.440439	−	0.719545i
$907$			4.18579e7i			1.68950i	0.535158	+	0.844752i	$0.320252\pi$
$907$			4.18579e7i			1.68950i	−0.535158	+	0.844752i	$0.679748\pi$
$908$	−3.81105e7	−	101037.i	−1.53402	−	0.00406692i
$909$	−2.14095e7	−	1.08644e7i	−0.859402	−	0.436111i
$910$	7567.25	−	5.70864e6i	0.000302925	−	0.228523i
$911$	1.95415e7			0.780120			0.390060	−	0.920789i	$-0.372454\pi$
$911$	1.95415e7			0.780120			0.390060	+	0.920789i	$0.372454\pi$
$912$	1.13266e7	−	6.87131e6i	0.450933	−	0.273560i
$913$	6.15188e7			2.44248
$914$	−37786.5	+	2.85056e7i	−0.00149614	+	1.12867i
$915$	1.30973e7	−	8.04085e6i	0.517166	−	0.317504i
$916$	−9.34015e6	−	24762.3i	−0.367803	−	0.000975106i
$917$			9.35173e6i			0.367256i
$918$	−907691.	+	72476.3i	−0.0355493	+	0.00283850i
$919$			1.60894e7i			0.628422i	0.949353	+	0.314211i	$0.101740\pi$
$919$			1.60894e7i			0.628422i	−0.949353	+	0.314211i	$0.898260\pi$
$920$	−6.64703e6	−	26433.6i	−0.258915	−	0.00102964i
$921$	−3.49398e7	+	2.14507e7i	−1.35729	+	0.833281i
$922$	−2.31729e7	−	30717.6i	−0.897747	−	0.00119003i
$923$	1.17569e7			0.454242
$924$	−1.57362e7	+	9.60356e6i	−0.606344	+	0.370043i
$925$	−4.75026e6			−0.182542
$926$	−9.45855e6	−	12538.1i	−0.362491	−	0.000480510i
$927$	1.55301e7	+	7.88087e6i	0.593573	+	0.301214i
$928$	2.11568e6	+	14022.7i	0.0806456	+	0.000534518i
$929$		−	3.55762e7i		−	1.35245i	−0.736697	−	0.676223i	$-0.763615\pi$
$929$		−	3.55762e7i		−	1.35245i	0.736697	−	0.676223i	$-0.236385\pi$
$930$	1.49372e7	−	9.14315e6i	0.566319	−	0.346648i
$931$		−	1.13829e7i		−	0.430405i
$932$	−58268.8	+	2.19786e7i	−0.00219734	+	0.828820i
$933$	−1.44329e7	−	2.35089e7i	−0.542811	−	0.884156i
$934$	11224.6	−	8.46769e6i	0.000421021	−	0.317613i
$935$	−706114.			−0.0264147
$936$	2.84197e7	+	1.45642e7i	1.06030	+	0.543372i
$937$	1.37737e7			0.512509			0.256254	−	0.966609i	$-0.417512\pi$
$937$	1.37737e7			0.512509			0.256254	+	0.966609i	$0.417512\pi$
$938$	903.671	−	681718.i	3.35354e−5	−	0.0252987i
$939$	−1.12961e7	−	1.83996e7i	−0.418084	−	0.680995i
$940$	−23121.8	+	8.72136e6i	−0.000853495	+	0.321932i
$941$		−	4.54756e6i		−	0.167419i	−0.996490	−	0.0837094i	$-0.973323\pi$
$941$		−	4.54756e6i		−	0.167419i	0.996490	−	0.0837094i	$-0.0266767\pi$
$942$	2.79763e7	−	1.71245e7i	1.02722	−	0.628769i
$943$		−	1.71743e7i		−	0.628925i
$944$	2.67127e7	+	141640.i	0.975636	+	0.00517318i
$945$	5.24826e6	−	426060.i	0.191177	−	0.0155200i
$946$	8.04574e7	+	106653.i	2.92306	+	0.00387475i
$947$	−2.24329e7			−0.812849			−0.406425	−	0.913684i	$-0.633225\pi$
$947$	−2.24329e7			−0.812849			−0.406425	+	0.913684i	$0.633225\pi$
$948$	−4.46850e7	+	2.72707e7i	−1.61488	+	0.985541i
$949$	4.98646e7			1.79733
$950$	−2.93426e6	−	3889.59i	−0.105485	−	0.000139828i
$951$	−2.39082e6	+	1.46780e6i	−0.0857228	+	0.0526279i
$952$	1700.89	−	427709.i	6.08254e−5	−	0.0152952i
$953$			1.71245e7i			0.610780i	0.952227	+	0.305390i	$0.0987869\pi$
$953$			1.71245e7i			0.610780i	−0.952227	+	0.305390i	$0.901213\pi$
$954$	1.10022e7	−	2.16099e7i	0.391388	−	0.768745i
$955$			1.73101e7i			0.614173i
$956$	7.05127e6	+	18694.1i	0.249530	+	0.000661545i
$957$	−3.22505e6	+	1.97996e6i	−0.113830	+	0.0698837i
$958$	−19178.5	+	1.44680e7i	−0.000675150	+	0.509324i
$959$	5.99727e6			0.210575
$960$	1.09356e7	−	6.59451e6i	0.382969	−	0.230943i
$961$	−3.44811e7			−1.20441
$962$	−41375.5	+	3.12131e7i	−0.00144147	+	1.08743i
$963$	−2.40495e7	+	4.73921e7i	−0.835681	+	1.64680i
$964$	4.07198e7	+	107955.i	1.41128	+	0.00374153i
$965$		−	5.63863e6i		−	0.194919i
$966$	3.75979e6	+	6.14238e6i	0.129635	+	0.211784i
$967$		−	2.20356e7i		−	0.757807i	−0.925436	−	0.378904i	$-0.876301\pi$
$967$		−	2.20356e7i		−	0.757807i	0.925436	−	0.378904i	$-0.123699\pi$
$968$	202084.	−	5.08163e7i	0.00693176	−	1.74307i
$969$	−287638.	−	468519.i	−0.00984096	−	0.0160294i
$970$	−6.67564e6	−	8849.08i	−0.227805	−	0.000301974i
$971$	1.46244e7			0.497770			0.248885	−	0.968533i	$-0.419936\pi$
$971$	1.46244e7			0.497770			0.248885	+	0.968533i	$0.419936\pi$
$972$	−1.12325e7	+	2.72297e7i	−0.381339	+	0.924435i
$973$	−1.00104e7			−0.338976
$974$	−1.77924e7	−	23585.2i	−0.600947	−	0.000796604i
$975$	−3.70062e6	−	6.02775e6i	−0.124670	−	0.203069i
$976$	−4.03819e7	−	214119.i	−1.35694	−	0.00719501i
$977$		−	3.65007e7i		−	1.22339i	−0.791094	−	0.611695i	$-0.790488\pi$
$977$		−	3.65007e7i		−	1.22339i	0.791094	−	0.611695i	$-0.209512\pi$
$978$	9.99669e6	+	1.63316e7i	0.334202	+	0.545986i
$979$		−	1.08890e6i		−	0.0363106i
$980$	29089.3	−	1.09723e7i	0.000967537	−	0.364948i
$981$	−1.33858e7	+	2.63781e7i	−0.444090	+	0.875125i
$982$	6435.75	−	4.85504e6i	0.000212971	−	0.160662i
$983$	2.78247e7			0.918432			0.459216	−	0.888325i	$-0.348130\pi$
$983$	2.78247e7			0.918432			0.459216	+	0.888325i	$0.348130\pi$
$984$	1.71507e7	+	2.81866e7i	0.564669	+	0.928016i
$985$	6.68007e6			0.219377
$986$	116.386	−	87799.8i	3.81247e−6	−	0.00287608i
$987$	8.05265e6	−	4.94377e6i	0.263115	−	0.161535i
$988$	−51115.6	+	1.92804e7i	−0.00166595	+	0.628383i
$989$		−	3.14308e7i		−	1.02180i
$990$	−1.03633e7	+	2.03551e7i	−0.336056	+	0.660063i
$991$			6.59505e6i			0.213321i	0.994295	+	0.106661i	$0.0340158\pi$
$991$			6.59505e6i			0.213321i	−0.994295	+	0.106661i	$0.965984\pi$
$992$	−4.60167e7	−	304998.i	−1.48469	−	0.00984052i
$993$	−2.72740e7	+	1.67443e7i	−0.877759	+	0.538883i
$994$	−5.09370e6	−	6752.10i	−0.163519	−	0.000216757i
$995$	−4.68095e6			−0.149891
$996$	2.40517e7	+	3.94105e7i	0.768240	+	1.25882i
$997$	−1.47185e7			−0.468950			−0.234475	−	0.972122i	$-0.575337\pi$
$997$	−1.47185e7			−0.468950			−0.234475	+	0.972122i	$0.575337\pi$
$998$	1.08915e7	+	14437.6i	0.346148	+	0.000458847i
$999$	−2.86960e7	+	2.32957e6i	−0.909719	+	0.0738519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.6.e.a.11.20	yes	40
3.2	odd	2	inner	60.6.e.a.11.21	yes	40
4.3	odd	2	inner	60.6.e.a.11.22	yes	40
12.11	even	2	inner	60.6.e.a.11.19	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.6.e.a.11.19	✓	40	12.11	even	2	inner
60.6.e.a.11.20	yes	40	1.1	even	1	trivial
60.6.e.a.11.21	yes	40	3.2	odd	2	inner
60.6.e.a.11.22	yes	40	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	60.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.00749860 + 5.65685i) q^{2} +(8.15586 + 13.2847i) q^{3} +(-31.9999 - 0.0848369i) q^{4} +25.0000i q^{5} +(-75.2104 + 46.0368i) q^{6} +55.6023i q^{7} +(0.719864 - 181.018i) q^{8} +(-109.964 + 216.695i) q^{9} +O(q^{10})\)	\(q+(-0.00749860 + 5.65685i) q^{2} +(8.15586 + 13.2847i) q^{3} +(-31.9999 - 0.0848369i) q^{4} +25.0000i q^{5} +(-75.2104 + 46.0368i) q^{6} +55.6023i q^{7} +(0.719864 - 181.018i) q^{8} +(-109.964 + 216.695i) q^{9} +(-141.421 - 0.187465i) q^{10} -664.662 q^{11} +(-259.860 - 425.799i) q^{12} +725.981 q^{13} +(-314.534 - 0.416939i) q^{14} +(-332.116 + 203.896i) q^{15} +(1023.99 + 5.42954i) q^{16} -42.4946i q^{17} +(-1224.99 - 623.674i) q^{18} -829.934i q^{19} +(2.12092 - 799.997i) q^{20} +(-738.657 + 453.484i) q^{21} +(4.98404 - 3759.90i) q^{22} -1468.81 q^{23} +(2410.63 - 1466.79i) q^{24} -625.000 q^{25} +(-5.44384 + 4106.77i) q^{26} +(-3775.57 + 306.505i) q^{27} +(4.71713 - 1779.27i) q^{28} -365.246i q^{29} +(-1150.92 - 1880.26i) q^{30} +7944.20i q^{31} +(-38.3926 + 5792.49i) q^{32} +(-5420.89 - 8829.81i) q^{33} +(240.386 + 0.318650i) q^{34} -1390.06 q^{35} +(3537.22 - 6924.90i) q^{36} +7600.42 q^{37} +(4694.81 + 6.22334i) q^{38} +(5921.00 + 9644.40i) q^{39} +(4525.45 + 17.9966i) q^{40} +11692.6i q^{41} +(-2559.75 - 4181.87i) q^{42} +21398.8i q^{43} +(21269.1 + 56.3879i) q^{44} +(-5417.39 - 2749.10i) q^{45} +(11.0140 - 8308.84i) q^{46} -10901.7 q^{47} +(8279.35 + 13647.6i) q^{48} +13715.4 q^{49} +(4.68663 - 3535.53i) q^{50} +(564.526 - 346.580i) q^{51} +(-23231.3 - 61.5900i) q^{52} +17640.9i q^{53} +(-1705.54 - 21360.2i) q^{54} -16616.6i q^{55} +(10065.0 + 40.0261i) q^{56} +(11025.4 - 6768.82i) q^{57} +(2066.14 + 2.73883i) q^{58} +26087.0 q^{59} +(10645.0 - 6496.49i) q^{60} -39436.0 q^{61} +(-44939.1 - 59.5704i) q^{62} +(-12048.8 - 6114.25i) q^{63} +(-32767.0 - 260.617i) q^{64} +18149.5i q^{65} +(49989.5 - 30599.0i) q^{66} +2167.39i q^{67} +(-3.60511 + 1359.82i) q^{68} +(-11979.4 - 19512.6i) q^{69} +(10.4235 - 7863.34i) q^{70} +16194.4 q^{71} +(39146.6 + 20061.4i) q^{72} +68685.8 q^{73} +(-56.9925 + 42994.4i) q^{74} +(-5097.41 - 8302.91i) q^{75} +(-70.4090 + 26557.8i) q^{76} -36956.7i q^{77} +(-54601.3 + 33421.9i) q^{78} -104944. i q^{79} +(-135.739 + 25599.6i) q^{80} +(-34864.9 - 47657.4i) q^{81} +(-66143.5 - 87.6784i) q^{82} -92556.4 q^{83} +(23675.4 - 14448.8i) q^{84} +1062.37 q^{85} +(-121050. - 160.461i) q^{86} +(4852.16 - 2978.89i) q^{87} +(-478.467 + 120316. i) q^{88} +1638.28i q^{89} +(15591.9 - 30624.7i) q^{90} +40366.2i q^{91} +(47001.8 + 124.609i) q^{92} +(-105536. + 64791.8i) q^{93} +(81.7478 - 61669.5i) q^{94} +20748.3 q^{95} +(-77264.4 + 46732.7i) q^{96} +47203.9 q^{97} +(-102.846 + 77585.9i) q^{98} +(73088.9 - 144029. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 10 q^{4} - 114 q^{6} + 44 q^{9}+O(q^{10}) \) 40 * q - 10 * q^4 - 114 * q^6 + 44 * q^9	\( 40 q - 10 q^{4} - 114 q^{6} + 44 q^{9} + 50 q^{10} + 1876 q^{12} - 232 q^{13} - 2734 q^{16} - 3536 q^{18} + 820 q^{21} + 13684 q^{22} + 9550 q^{24} - 25000 q^{25} - 23188 q^{28} - 5800 q^{30} - 9424 q^{33} + 38972 q^{34} + 53754 q^{36} + 2152 q^{37} - 10850 q^{40} - 62868 q^{42} + 5900 q^{45} + 78748 q^{46} + 100956 q^{48} - 52144 q^{49} - 82528 q^{52} - 120862 q^{54} - 44424 q^{57} + 97476 q^{58} + 3850 q^{60} + 2072 q^{61} - 91234 q^{64} - 45784 q^{66} + 52764 q^{69} - 3300 q^{70} - 10344 q^{72} + 264960 q^{73} + 73356 q^{76} + 176440 q^{78} - 165120 q^{81} - 170920 q^{82} - 250544 q^{84} - 132400 q^{85} + 359116 q^{88} + 35550 q^{90} + 510368 q^{93} - 623100 q^{94} - 379254 q^{96} + 453648 q^{97}+O(q^{100}) \) 40 * q - 10 * q^4 - 114 * q^6 + 44 * q^9 + 50 * q^10 + 1876 * q^12 - 232 * q^13 - 2734 * q^16 - 3536 * q^18 + 820 * q^21 + 13684 * q^22 + 9550 * q^24 - 25000 * q^25 - 23188 * q^28 - 5800 * q^30 - 9424 * q^33 + 38972 * q^34 + 53754 * q^36 + 2152 * q^37 - 10850 * q^40 - 62868 * q^42 + 5900 * q^45 + 78748 * q^46 + 100956 * q^48 - 52144 * q^49 - 82528 * q^52 - 120862 * q^54 - 44424 * q^57 + 97476 * q^58 + 3850 * q^60 + 2072 * q^61 - 91234 * q^64 - 45784 * q^66 + 52764 * q^69 - 3300 * q^70 - 10344 * q^72 + 264960 * q^73 + 73356 * q^76 + 176440 * q^78 - 165120 * q^81 - 170920 * q^82 - 250544 * q^84 - 132400 * q^85 + 359116 * q^88 + 35550 * q^90 + 510368 * q^93 - 623100 * q^94 - 379254 * q^96 + 453648 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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