LMFDB - Embedded newform 60.7.l.a.23.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(23,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("60.23");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.4
Character	$\chi$	$=$	60.23
Dual form			60.7.l.a.47.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.90644 - 1.21994i) q^{2} +(25.6796 + 8.34012i) q^{3} +(61.0235 + 19.2908i) q^{4} +(88.2710 - 88.5055i) q^{5} +(-192.860 - 97.2682i) q^{6} +(-452.639 - 452.639i) q^{7} +(-458.945 - 226.966i) q^{8} +(589.885 + 428.342i) q^{9} +O(q^{10})$	\(q+(-7.90644 - 1.21994i) q^{2} +(25.6796 + 8.34012i) q^{3} +(61.0235 + 19.2908i) q^{4} +(88.2710 - 88.5055i) q^{5} +(-192.860 - 97.2682i) q^{6} +(-452.639 - 452.639i) q^{7} +(-458.945 - 226.966i) q^{8} +(589.885 + 428.342i) q^{9} +(-805.881 + 592.078i) q^{10} +285.789 q^{11} +(1406.17 + 1004.32i) q^{12} +(-1327.62 - 1327.62i) q^{13} +(3026.57 + 4130.95i) q^{14} +(3004.91 - 1536.60i) q^{15} +(3351.73 + 2354.38i) q^{16} +(-223.542 - 223.542i) q^{17} +(-4141.34 - 4106.28i) q^{18} -10242.0 q^{19} +(7093.94 - 3698.10i) q^{20} +(-7848.53 - 15398.6i) q^{21} +(-2259.57 - 348.645i) q^{22} +(-3784.27 - 3784.27i) q^{23} +(-9892.60 - 9656.05i) q^{24} +(-41.4567 - 15624.9i) q^{25} +(8877.10 + 12116.3i) q^{26} +(11575.6 + 15919.4i) q^{27} +(-18889.9 - 36353.3i) q^{28} +11728.4 q^{29} +(-25632.7 + 8483.20i) q^{30} -33953.5i q^{31} +(-23628.1 - 22703.7i) q^{32} +(7338.95 + 2383.51i) q^{33} +(1494.71 + 2040.13i) q^{34} +(-80015.9 + 106.151i) q^{35} +(27733.8 + 37518.2i) q^{36} +(42670.6 - 42670.6i) q^{37} +(80977.5 + 12494.6i) q^{38} +(-23020.2 - 45165.1i) q^{39} +(-60599.3 + 20584.6i) q^{40} -27497.6i q^{41} +(43268.5 + 131323. i) q^{42} +(31895.0 - 31895.0i) q^{43} +(17439.8 + 5513.08i) q^{44} +(89980.4 - 14397.9i) q^{45} +(25303.5 + 34536.7i) q^{46} +(-68677.9 + 68677.9i) q^{47} +(66435.4 + 88413.4i) q^{48} +292115. i q^{49} +(-18733.7 + 123588. i) q^{50} +(-3876.10 - 7604.84i) q^{51} +(-55405.0 - 106626. i) q^{52} +(130881. - 130881. i) q^{53} +(-72101.0 - 139987. i) q^{54} +(25226.9 - 25293.9i) q^{55} +(105003. + 310470. i) q^{56} +(-263010. - 85419.3i) q^{57} +(-92729.6 - 14307.9i) q^{58} +76661.9i q^{59} +(213012. - 35801.5i) q^{60} +254802. q^{61} +(-41421.2 + 268451. i) q^{62} +(-73120.6 - 460889. i) q^{63} +(159117. + 208330. i) q^{64} +(-234691. + 311.346i) q^{65} +(-55117.2 - 27798.2i) q^{66} +(-56172.9 - 56172.9i) q^{67} +(-9329.02 - 17953.6i) q^{68} +(-65617.3 - 128740. i) q^{69} +(632770. + 96775.3i) q^{70} -104651. q^{71} +(-173506. - 330469. i) q^{72} +(-205125. - 205125. i) q^{73} +(-389428. + 285317. i) q^{74} +(129249. - 401588. i) q^{75} +(-625001. - 197575. i) q^{76} +(-129359. - 129359. i) q^{77} +(126909. + 385178. i) q^{78} -284644. q^{79} +(504236. - 88823.6i) q^{80} +(164487. + 505345. i) q^{81} +(-33545.4 + 217408. i) q^{82} +(464813. + 464813. i) q^{83} +(-181893. - 1.09108e6i) q^{84} +(-39517.0 + 52.4239i) q^{85} +(-291086. + 213266. i) q^{86} +(301180. + 97815.9i) q^{87} +(-131161. - 64864.4i) q^{88} +1.31864e6 q^{89} +(-728989. + 4065.49i) q^{90} +1.20186e6i q^{91} +(-157928. - 303931. i) q^{92} +(283176. - 871912. i) q^{93} +(626780. - 459214. i) q^{94} +(-904069. + 906471. i) q^{95} +(-417409. - 780082. i) q^{96} +(88602.9 - 88602.9i) q^{97} +(356362. - 2.30959e6i) q^{98} +(168583. + 122415. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 4 q^{6}+O(q^{10}) $ 136 * q - 4 * q^6	$ 136 q - 4 q^{6} - 2092 q^{10} - 1460 q^{12} - 8 q^{13} - 932 q^{16} - 12744 q^{18} - 16056 q^{21} + 25444 q^{22} - 8 q^{25} - 52244 q^{28} + 82868 q^{30} - 2920 q^{33} - 69524 q^{36} - 113000 q^{37} + 99944 q^{40} + 19436 q^{42} - 62504 q^{45} + 145936 q^{46} - 82364 q^{48} + 219504 q^{52} - 286152 q^{57} - 351260 q^{58} + 466756 q^{60} + 652976 q^{61} - 61800 q^{66} + 243868 q^{70} - 145560 q^{72} - 316856 q^{73} + 269024 q^{76} + 613272 q^{78} + 1472232 q^{81} - 1652880 q^{82} - 1466984 q^{85} - 1084100 q^{88} + 448368 q^{90} - 2869552 q^{93} - 278860 q^{96} + 2135272 q^{97}+O(q^{100}) $ 136 * q - 4 * q^6 - 2092 * q^10 - 1460 * q^12 - 8 * q^13 - 932 * q^16 - 12744 * q^18 - 16056 * q^21 + 25444 * q^22 - 8 * q^25 - 52244 * q^28 + 82868 * q^30 - 2920 * q^33 - 69524 * q^36 - 113000 * q^37 + 99944 * q^40 + 19436 * q^42 - 62504 * q^45 + 145936 * q^46 - 82364 * q^48 + 219504 * q^52 - 286152 * q^57 - 351260 * q^58 + 466756 * q^60 + 652976 * q^61 - 61800 * q^66 + 243868 * q^70 - 145560 * q^72 - 316856 * q^73 + 269024 * q^76 + 613272 * q^78 + 1472232 * q^81 - 1652880 * q^82 - 1466984 * q^85 - 1084100 * q^88 + 448368 * q^90 - 2869552 * q^93 - 278860 * q^96 + 2135272 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−7.90644	−	1.21994i	−0.988305	−	0.152492i
$2$	−7.90644	−	1.21994i	−0.988305	−	0.152492i
$3$	25.6796	+	8.34012i	0.951097	+	0.308893i
$3$	25.6796	+	8.34012i	0.951097	+	0.308893i
$4$	61.0235	+	19.2908i	0.953492	+	0.301418i
$5$	88.2710	−	88.5055i	0.706168	−	0.708044i
$5$	88.2710	−	88.5055i	0.706168	−	0.708044i
$6$	−192.860	−	97.2682i	−0.892869	−	0.450316i
$7$	−452.639	−	452.639i	−1.31965	−	1.31965i	−0.914054	−	0.405593i	$-0.867065\pi$
$7$	−452.639	−	452.639i	−1.31965	−	1.31965i	−0.405593	−	0.914054i	$-0.632935\pi$
$8$	−458.945	−	226.966i	−0.896377	−	0.443293i
$9$	589.885	+	428.342i	0.809170	+	0.587575i
$10$	−805.881	+	592.078i	−0.805881	+	0.592078i
$11$	285.789			0.214717			0.107359	−	0.994220i	$-0.465761\pi$
$11$	285.789			0.214717			0.107359	+	0.994220i	$0.465761\pi$
$12$	1406.17	+	1004.32i	0.813757	+	0.581205i
$13$	−1327.62	−	1327.62i	−0.604286	−	0.604286i	0.337161	−	0.941447i	$-0.390533\pi$
$13$	−1327.62	−	1327.62i	−0.604286	−	0.604286i	−0.941447	+	0.337161i	$0.890533\pi$
$14$	3026.57	+	4130.95i	1.10298	+	1.50545i
$15$	3004.91	−	1536.60i	0.890344	−	0.455288i
$16$	3351.73	+	2354.38i	0.818294	+	0.574799i
$17$	−223.542	−	223.542i	−0.0455001	−	0.0455001i	0.683991	−	0.729491i	$-0.260243\pi$
$17$	−223.542	−	223.542i	−0.0455001	−	0.0455001i	−0.729491	+	0.683991i	$0.760243\pi$
$18$	−4141.34	−	4106.28i	−0.710106	−	0.704095i
$19$	−10242.0			−1.49322			−0.746608	−	0.665264i	$-0.768319\pi$
$19$	−10242.0			−1.49322			−0.746608	+	0.665264i	$0.768319\pi$
$20$	7093.94	−	3698.10i	0.886743	−	0.462263i
$21$	−7848.53	−	15398.6i	−0.847482	−	1.66274i
$22$	−2259.57	−	348.645i	−0.212206	−	0.0327428i
$23$	−3784.27	−	3784.27i	−0.311027	−	0.311027i	0.534280	−	0.845307i	$-0.320583\pi$
$23$	−3784.27	−	3784.27i	−0.311027	−	0.311027i	−0.845307	+	0.534280i	$0.820583\pi$
$24$	−9892.60	−	9656.05i	−0.715611	−	0.698499i
$25$	−41.4567	−	15624.9i	−0.00265323	−	0.999996i
$26$	8877.10	+	12116.3i	0.505069	+	0.689367i
$27$	11575.6	+	15919.4i	0.588101	+	0.808787i
$28$	−18889.9	−	36353.3i	−0.860507	−	1.65604i
$29$	11728.4			0.480887			0.240444	−	0.970663i	$-0.422707\pi$
$29$	11728.4			0.480887			0.240444	+	0.970663i	$0.422707\pi$
$30$	−25632.7	+	8483.20i	−0.949359	+	0.314192i
$31$		−	33953.5i		−	1.13972i	−0.821741	−	0.569861i	$-0.806997\pi$
$31$		−	33953.5i		−	1.13972i	0.821741	−	0.569861i	$-0.193003\pi$
$32$	−23628.1	−	22703.7i	−0.721072	−	0.692861i
$33$	7338.95	+	2383.51i	0.204217	+	0.0663248i
$34$	1494.71	+	2040.13i	0.0380295	+	0.0519064i
$35$	−80015.9	+	106.151i	−1.86626	+	0.00247582i
$36$	27733.8	+	37518.2i	0.594432	+	0.804146i
$37$	42670.6	−	42670.6i	0.842410	−	0.842410i	−0.146762	−	0.989172i	$-0.546885\pi$
$37$	42670.6	−	42670.6i	0.842410	−	0.842410i	0.989172	+	0.146762i	$0.0468851\pi$
$38$	80977.5	+	12494.6i	1.47575	+	0.227704i
$39$	−23020.2	−	45165.1i	−0.388074	−	0.761394i
$40$	−60599.3	+	20584.6i	−0.946864	+	0.321635i
$41$		−	27497.6i		−	0.398972i	−0.979901	−	0.199486i	$-0.936073\pi$
$41$		−	27497.6i		−	0.398972i	0.979901	−	0.199486i	$-0.0639273\pi$
$42$	43268.5	+	131323.i	0.584015	+	1.77253i
$43$	31895.0	−	31895.0i	0.401160	−	0.401160i	−0.477482	−	0.878642i	$-0.658450\pi$
$43$	31895.0	−	31895.0i	0.401160	−	0.401160i	0.878642	+	0.477482i	$0.158450\pi$
$44$	17439.8	+	5513.08i	0.204731	+	0.0647197i
$45$	89980.4	−	14397.9i	0.987439	−	0.158002i
$46$	25303.5	+	34536.7i	0.259960	+	0.354819i
$47$	−68677.9	+	68677.9i	−0.661490	+	0.661490i	−0.955731	−	0.294241i	$-0.904933\pi$
$47$	−68677.9	+	68677.9i	−0.661490	+	0.661490i	0.294241	+	0.955731i	$0.404933\pi$
$48$	66435.4	+	88413.4i	0.600726	+	0.799455i
$49$			292115.i			2.48293i
$50$	−18733.7	+	123588.i	−0.149870	+	0.988706i
$51$	−3876.10	−	7604.84i	−0.0292203	−	0.0573297i
$52$	−55405.0	−	106626.i	−0.394039	−	0.758324i
$53$	130881.	−	130881.i	0.879120	−	0.879120i	−0.114323	−	0.993444i	$-0.536470\pi$
$53$	130881.	−	130881.i	0.879120	−	0.879120i	0.993444	+	0.114323i	$0.0364700\pi$
$54$	−72101.0	−	139987.i	−0.457889	−	0.889009i
$55$	25226.9	−	25293.9i	0.151627	−	0.152029i
$56$	105003.	+	310470.i	0.597910	+	1.76789i
$57$	−263010.	−	85419.3i	−1.42019	−	0.461244i
$58$	−92729.6	−	14307.9i	−0.475263	−	0.0733317i
$59$			76661.9i			0.373270i	0.982429	+	0.186635i	$0.0597583\pi$
$59$			76661.9i			0.373270i	−0.982429	+	0.186635i	$0.940242\pi$
$60$	213012.	−	35801.5i	0.986168	−	0.165748i
$61$	254802.			1.12257			0.561284	−	0.827623i	$-0.310308\pi$
$61$	254802.			1.12257			0.561284	+	0.827623i	$0.310308\pi$
$62$	−41421.2	+	268451.i	−0.173799	+	1.12639i
$63$	−73120.6	−	460889.i	−0.292428	−	1.84321i
$64$	159117.	+	208330.i	0.606982	+	0.794715i
$65$	−234691.	+	311.346i	−0.854588	+	0.00113371i
$66$	−55117.2	−	27798.2i	−0.191715	−	0.0966906i
$67$	−56172.9	−	56172.9i	−0.186768	−	0.186768i	0.607529	−	0.794297i	$-0.292161\pi$
$67$	−56172.9	−	56172.9i	−0.186768	−	0.186768i	−0.794297	+	0.607529i	$0.792161\pi$
$68$	−9329.02	−	17953.6i	−0.0296694	−	0.0570985i
$69$	−65617.3	−	128740.i	−0.199743	−	0.391891i
$70$	632770.	+	96775.3i	1.84481	+	0.282144i
$71$	−104651.			−0.292395			−0.146197	−	0.989255i	$-0.546703\pi$
$71$	−104651.			−0.292395			−0.146197	+	0.989255i	$0.546703\pi$
$72$	−173506.	−	330469.i	−0.464853	−	0.885388i
$73$	−205125.	−	205125.i	−0.527289	−	0.527289i	0.392474	−	0.919763i	$-0.371619\pi$
$73$	−205125.	−	205125.i	−0.527289	−	0.527289i	−0.919763	+	0.392474i	$0.871619\pi$
$74$	−389428.	+	285317.i	−0.961019	+	0.704096i
$75$	129249.	−	401588.i	0.306369	−	0.951913i
$76$	−625001.	−	197575.i	−1.42377	−	0.450082i
$77$	−129359.	−	129359.i	−0.283351	−	0.283351i
$78$	126909.	+	385178.i	0.267429	+	0.811667i
$79$	−284644.			−0.577326			−0.288663	−	0.957431i	$-0.593211\pi$
$79$	−284644.			−0.577326			−0.288663	+	0.957431i	$0.593211\pi$
$80$	504236.	−	88823.6i	0.984837	−	0.173484i
$81$	164487.	+	505345.i	0.309512	+	0.950896i
$82$	−33545.4	+	217408.i	−0.0608403	+	0.394306i
$83$	464813.	+	464813.i	0.812913	+	0.812913i	0.985070	−	0.172156i	$-0.0550734\pi$
$83$	464813.	+	464813.i	0.812913	+	0.812913i	−0.172156	+	0.985070i	$0.555073\pi$
$84$	−181893.	−	1.09108e6i	−0.306887	−	1.84086i
$85$	−39517.0	+	52.4239i	−0.0643468	+	8.53636e-5i
$86$	−291086.	+	213266.i	−0.457642	+	0.335294i
$87$	301180.	+	97815.9i	0.457370	+	0.148543i
$88$	−131161.	−	64864.4i	−0.192468	−	0.0951828i
$89$	1.31864e6			1.87049			0.935244	−	0.354004i	$-0.115180\pi$
$89$	1.31864e6			1.87049			0.935244	+	0.354004i	$0.115180\pi$
$90$	−728989.	+	4065.49i	−0.999984	+	0.00557680i
$91$			1.20186e6i			1.59489i
$92$	−157928.	−	303931.i	−0.202813	−	0.390311i
$93$	283176.	−	871912.i	0.352052	−	1.08399i
$94$	626780.	−	459214.i	0.754626	−	0.552881i
$95$	−904069.	+	906471.i	−1.05446	+	1.05726i
$96$	−417409.	−	780082.i	−0.471789	−	0.881712i
$97$	88602.9	−	88602.9i	0.0970806	−	0.0970806i	−0.656898	−	0.753979i	$-0.728132\pi$
$97$	88602.9	−	88602.9i	0.0970806	−	0.0970806i	0.753979	+	0.656898i	$0.228132\pi$
$98$	356362.	−	2.30959e6i	0.378629	−	2.45390i
$99$	168583.	+	122415.i	0.173743	+	0.126163i
$100$	298887.	−	954288.i	0.298887	−	0.954288i
$101$			1.13152e6i			1.09824i	0.835743	+	0.549120i	$0.185037\pi$
$101$			1.13152e6i			1.09824i	−0.835743	+	0.549120i	$0.814963\pi$
$102$	21368.7	+	64855.8i	0.0201362	+	0.0611150i
$103$	−296630.	+	296630.i	−0.271459	+	0.271459i	−0.829687	−	0.558229i	$-0.811481\pi$
$103$	−296630.	+	296630.i	−0.271459	+	0.271459i	0.558229	+	0.829687i	$0.311481\pi$
$104$	307979.	+	910626.i	0.273792	+	0.809543i
$105$	−2.05566e6	−	664616.i	−1.77576	−	0.574121i
$106$	−1.19447e6	+	875134.i	−1.00290	+	0.734779i
$107$	1.03194e6	−	1.03194e6i	0.842374	−	0.842374i	−0.146794	−	0.989167i	$-0.546895\pi$
$107$	1.03194e6	−	1.03194e6i	0.842374	−	0.842374i	0.989167	+	0.146794i	$0.0468953\pi$
$108$	399287.	+	1.19476e6i	0.316967	+	0.948437i
$109$			1.15759e6i			0.893873i	0.894566	+	0.446936i	$0.147485\pi$
$109$			1.15759e6i			0.893873i	−0.894566	+	0.446936i	$0.852515\pi$
$110$	−230312.	+	169209.i	−0.173037	+	0.127130i
$111$	1.45164e6	−	739886.i	1.06143	−	0.540999i
$112$	−451442.	−	2.58281e6i	−0.321327	−	1.83839i
$113$	−1.34194e6	+	1.34194e6i	−0.930028	+	0.930028i	−0.997707	−	0.0676787i	$-0.978441\pi$
$113$	−1.34194e6	+	1.34194e6i	−0.930028	+	0.930028i	0.0676787	+	0.997707i	$0.478441\pi$
$114$	1.97526e6	+	996218.i	1.33325	+	0.672419i
$115$	−668970.	+	887.468i	−0.439859	+	0.000583525i
$116$	715706.	+	226249.i	0.458522	+	0.144948i
$117$	−214467.	−	1.35181e6i	−0.133907	−	0.844033i
$118$	93522.9	−	606123.i	0.0569209	−	0.368905i
$119$			202368.i			0.120088i
$120$	−1.72784e6	+	23200.3i	−0.999910	+	0.0134261i
$121$	−1.68989e6			−0.953896
$122$	−2.01457e6	−	310843.i	−1.10944	−	0.171183i
$123$	229333.	−	706127.i	0.123240	−	0.379461i
$124$	654988.	−	2.07196e6i	0.343533	−	1.08672i
$125$	−1.38655e6	−	1.37556e6i	−0.709915	−	0.704287i
$126$	15866.9	+	3.73319e6i	0.00793198	+	1.86625i
$127$	936695.	+	936695.i	0.457285	+	0.457285i	0.897763	−	0.440478i	$-0.145191\pi$
$127$	936695.	+	936695.i	0.457285	+	0.457285i	−0.440478	+	0.897763i	$0.645191\pi$
$128$	−1.00390e6	−	1.84126e6i	−0.478695	−	0.877981i
$129$	1.08506e6	−	553044.i	0.505458	−	0.257626i
$130$	1.85595e6	+	283847.i	0.844766	+	0.129198i
$131$	3.55001e6			1.57912			0.789561	−	0.613671i	$-0.210308\pi$
$131$	3.55001e6			1.57912			0.789561	+	0.613671i	$0.210308\pi$
$132$	401869.	+	287024.i	0.174728	+	0.124795i
$133$	4.63591e6	+	4.63591e6i	1.97052	+	1.97052i
$134$	375600.	+	512655.i	0.156103	+	0.213064i
$135$	2.43074e6	+	380714.i	0.987955	+	0.154738i
$136$	51857.0	+	153330.i	0.0206153	+	0.0609551i
$137$	213409.	+	213409.i	0.0829948	+	0.0829948i	0.747385	−	0.664391i	$-0.231309\pi$
$137$	213409.	+	213409.i	0.0829948	+	0.0829948i	−0.664391	+	0.747385i	$0.731309\pi$
$138$	361744.	+	1.09792e6i	0.137646	+	0.417767i
$139$	−3.48500e6			−1.29765			−0.648826	−	0.760937i	$-0.724740\pi$
$139$	−3.48500e6			−1.29765			−0.648826	+	0.760937i	$0.724740\pi$
$140$	−4.88490e6	−	1.53709e6i	−1.78021	−	0.560164i
$141$	−2.33640e6	+	1.19084e6i	−0.833471	+	0.424811i
$142$	827419.	+	127668.i	0.288975	+	0.0445880i
$143$	−379418.	−	379418.i	−0.129751	−	0.129751i
$144$	968658.	+	2.82450e6i	0.324402	+	0.945919i
$145$	1.03527e6	−	1.03803e6i	0.339587	−	0.340490i
$146$	1.37156e6	+	1.87204e6i	0.440715	+	0.601530i
$147$	−2.43627e6	+	7.50139e6i	−0.766962	+	2.36151i
$148$	3.42706e6	−	1.78076e6i	1.05715	−	0.549314i
$149$	−600669.			−0.181583			−0.0907917	−	0.995870i	$-0.528940\pi$
$149$	−600669.			−0.181583			−0.0907917	+	0.995870i	$0.528940\pi$
$150$	−1.51181e6	+	3.01746e6i	−0.447945	+	0.894061i
$151$		−	3.98522e6i		−	1.15750i	−0.815505	−	0.578751i	$-0.803540\pi$
$151$		−	3.98522e6i		−	1.15750i	0.815505	−	0.578751i	$-0.196460\pi$
$152$	4.70050e6	+	2.32458e6i	1.33848	+	0.661933i
$153$	−36111.6	−	227616.i	−0.0100826	−	0.0635520i
$154$	864960.	+	1.18058e6i	0.236828	+	0.323246i
$155$	−3.00507e6	−	2.99711e6i	−0.806974	−	0.804835i
$156$	−533503.	−	3.20021e6i	−0.140528	−	0.842955i
$157$	−1.38682e6	+	1.38682e6i	−0.358360	+	0.358360i	−0.863208	−	0.504848i	$-0.831549\pi$
$157$	−1.38682e6	+	1.38682e6i	−0.358360	+	0.358360i	0.504848	+	0.863208i	$0.331549\pi$
$158$	2.25052e6	+	347249.i	0.570574	+	0.0880379i
$159$	4.45253e6	−	2.26941e6i	1.10768	−	0.564574i
$160$	−4.09507e6	+	87140.6i	−0.999774	+	0.0212746i
$161$			3.42581e6i			0.820892i
$162$	−684019.	−	4.19614e6i	−0.160888	−	0.986973i
$163$	810130.	−	810130.i	0.187065	−	0.187065i	−0.607361	−	0.794426i	$-0.707772\pi$
$163$	810130.	−	810130.i	0.187065	−	0.187065i	0.794426	+	0.607361i	$0.207772\pi$
$164$	530449.	−	1.67800e6i	0.120257	−	0.380417i
$165$	858771.	−	439142.i	0.191172	−	0.0977583i
$166$	−3.10797e6	−	4.24206e6i	−0.679443	−	0.927369i
$167$	−1.56541e6	+	1.56541e6i	−0.336109	+	0.336109i	−0.854901	−	0.518792i	$-0.826382\pi$
$167$	−1.56541e6	+	1.56541e6i	−0.336109	+	0.336109i	0.518792	+	0.854901i	$0.326382\pi$
$168$	107071.	+	8.84848e6i	0.0225810	+	1.86613i
$169$		−	1.30168e6i		−	0.269678i
$170$	312502.	+	47793.8i	0.0636072	+	0.00972803i
$171$	−6.04159e6	−	4.38707e6i	−1.20827	−	0.877376i
$172$	2.56163e6	−	1.33107e6i	0.503420	−	0.261586i
$173$	5.87235e6	−	5.87235e6i	1.13416	−	1.13416i	0.144680	−	0.989479i	$-0.453785\pi$
$173$	5.87235e6	−	5.87235e6i	1.13416	−	1.13416i	0.989479	−	0.144680i	$-0.0462153\pi$
$174$	−2.26193e6	−	1.14080e6i	−0.429370	−	0.216551i
$175$	−7.05369e6	+	7.09122e6i	−1.31614	+	1.32314i
$176$	957888.	+	672855.i	0.175702	+	0.123419i
$177$	−639369.	+	1.96865e6i	−0.115301	+	0.355016i
$178$	−1.04257e7	−	1.60866e6i	−1.84861	−	0.285235i
$179$		−	5.34830e6i		−	0.932517i	−0.884649	−	0.466258i	$-0.845602\pi$
$179$		−	5.34830e6i		−	0.932517i	0.884649	−	0.466258i	$-0.154398\pi$
$180$	5.76866e6	+	857179.i	0.989140	+	0.146978i
$181$	8.16336e6			1.37668			0.688340	−	0.725388i	$-0.258340\pi$
$181$	8.16336e6			1.37668			0.688340	+	0.725388i	$0.258340\pi$
$182$	1.46620e6	−	9.50243e6i	0.243208	−	1.57623i
$183$	6.54321e6	+	2.12507e6i	1.06767	+	0.346754i
$184$	877870.	+	2.59567e6i	0.140921	+	0.416674i
$185$	−10006.9	−	7.54316e6i	−0.00158046	−	1.19135i
$186$	−3.30259e6	+	6.54826e6i	−0.513235	+	1.01762i
$187$	−63885.8	−	63885.8i	−0.00976966	−	0.00976966i
$188$	−5.51581e6	+	2.86612e6i	−0.830110	+	0.431340i
$189$	1.96616e6	−	1.24453e7i	0.291228	−	1.84340i
$190$	8.25381e6	−	6.06405e6i	1.20335	−	0.884101i
$191$	−1.67068e6			−0.239769			−0.119884	−	0.992788i	$-0.538252\pi$
$191$	−1.67068e6			−0.239769			−0.119884	+	0.992788i	$0.538252\pi$
$192$	2.34856e6	+	6.67688e6i	0.331817	+	0.943344i
$193$	357652.	+	357652.i	0.0497495	+	0.0497495i	0.731544	−	0.681794i	$-0.238800\pi$
$193$	357652.	+	357652.i	0.0497495	+	0.0497495i	−0.681794	+	0.731544i	$0.738800\pi$
$194$	−808623.	+	592443.i	−0.110749	+	0.0811412i
$195$	−6.02938e6	−	1.94936e6i	−0.813146	−	0.262898i
$196$	−5.63511e6	+	1.78259e7i	−0.748401	+	2.36746i
$197$	−4.51584e6	−	4.51584e6i	−0.590663	−	0.590663i	0.347148	−	0.937810i	$-0.387150\pi$
$197$	−4.51584e6	−	4.51584e6i	−0.590663	−	0.590663i	−0.937810	+	0.347148i	$0.887150\pi$
$198$	−1.18355e6	−	1.17353e6i	−0.152472	−	0.151182i
$199$	2.62759e6			0.333425			0.166712	−	0.986006i	$-0.446685\pi$
$199$	2.62759e6			0.333425			0.166712	+	0.986006i	$0.446685\pi$
$200$	−3.52731e6	+	7.18040e6i	−0.440913	+	0.897550i
$201$	−974010.	−	1.91099e6i	−0.119943	−	0.235326i
$202$	1.38038e6	−	8.94628e6i	0.167473	−	1.08540i
$203$	−5.30871e6	−	5.30871e6i	−0.634602	−	0.634602i
$204$	−89830.4	−	538847.i	−0.0105812	−	0.0634709i
$205$	−2.43369e6	−	2.42724e6i	−0.282490	−	0.281742i
$206$	2.70716e6	−	1.98342e6i	0.309679	−	0.226889i
$207$	−611322.	−	3.85324e6i	−0.0689222	−	0.434426i
$208$	−1.32410e6	−	7.57552e6i	−0.147141	−	0.841826i
$209$	−2.92704e6			−0.320620
$210$	1.54422e7	+	7.76253e6i	1.66744	+	0.838196i
$211$			1.80107e6i			0.191727i	0.995394	+	0.0958637i	$0.0305613\pi$
$211$			1.80107e6i			0.191727i	−0.995394	+	0.0958637i	$0.969439\pi$
$212$	1.05116e7	−	5.46201e6i	1.10322	−	0.573252i
$213$	−2.68740e6	−	872804.i	−0.278096	−	0.0903187i
$214$	−9.41791e6	+	6.90009e6i	−0.960977	+	0.704066i
$215$	−7479.86	−	5.63829e6i	−0.000752624	−	0.567325i
$216$	−1.69940e6	−	9.93338e6i	−0.168630	−	0.985679i
$217$	−1.53687e7	+	1.53687e7i	−1.50403	+	1.50403i
$218$	1.41219e6	−	9.15242e6i	0.136309	−	0.883419i
$219$	−3.55676e6	−	6.97828e6i	−0.338627	−	0.664379i
$220$	2.02737e6	−	1.05688e6i	0.190399	−	0.0992559i
$221$			593555.i			0.0549901i
$222$	−1.23799e7	+	4.07895e6i	−1.13151	+	0.372812i
$223$	1.33003e7	−	1.33003e7i	1.19935	−	1.19935i	0.224994	−	0.974360i	$-0.427764\pi$
$223$	1.33003e7	−	1.33003e7i	1.19935	−	1.19935i	0.974360	−	0.224994i	$-0.0722362\pi$
$224$	418428.	+	2.09715e7i	0.0372286	+	1.86589i
$225$	6.66836e6	−	9.23468e6i	0.585426	−	0.810726i
$226$	1.22470e7	−	8.97285e6i	1.06097	−	0.777329i
$227$	−3.68604e6	+	3.68604e6i	−0.315125	+	0.315125i	−0.846891	−	0.531766i	$-0.821528\pi$
$227$	−3.68604e6	+	3.68604e6i	−0.315125	+	0.315125i	0.531766	+	0.846891i	$0.321528\pi$
$228$	−1.44020e7	−	1.02862e7i	−1.21512	−	0.867865i
$229$			2.83216e6i			0.235837i	0.993023	+	0.117918i	$0.0376221\pi$
$229$			2.83216e6i			0.235837i	−0.993023	+	0.117918i	$0.962378\pi$
$230$	5.29025e6	+	809086.i	0.434803	+	0.0664984i
$231$	−2.24302e6	−	4.40076e6i	−0.181969	−	0.357020i
$232$	−5.38267e6	−	2.66194e6i	−0.431056	−	0.213174i
$233$	−9.22737e6	+	9.22737e6i	−0.729474	+	0.729474i	−0.970515	−	0.241041i	$-0.922511\pi$
$233$	−9.22737e6	+	9.22737e6i	−0.729474	+	0.729474i	0.241041	+	0.970515i	$0.422511\pi$
$234$	46538.6	+	1.09497e7i	0.00363217	+	0.854581i
$235$	16106.0	+	1.21406e7i	0.00124103	+	0.935487i
$236$	−1.47887e6	+	4.67818e6i	−0.112510	+	0.355910i
$237$	−7.30956e6	−	2.37397e6i	−0.549093	−	0.178332i
$238$	246876.	−	1.60001e6i	0.0183125	−	0.118684i
$239$			2.17935e7i			1.59637i	0.602412	+	0.798185i	$0.294206\pi$
$239$			2.17935e7i			1.59637i	−0.602412	+	0.798185i	$0.705794\pi$
$240$	1.36894e7	+	1.92443e6i	0.990263	+	0.139210i
$241$	2.02610e7			1.44747			0.723736	−	0.690077i	$-0.242423\pi$
$241$	2.02610e7			1.44747			0.723736	+	0.690077i	$0.242423\pi$
$242$	1.33610e7	+	2.06156e6i	0.942740	+	0.145462i
$243$	9337.61	+	1.43489e7i	0.000650754	+	1.00000i
$244$	1.55489e7	+	4.91531e6i	1.07036	+	0.338362i
$245$	2.58538e7	+	2.57853e7i	1.75803	+	1.75337i
$246$	−2.67464e6	+	5.30318e6i	−0.179663	+	0.356230i
$247$	1.35974e7	+	1.35974e7i	0.902329	+	0.902329i
$248$	−7.70628e6	+	1.55828e7i	−0.505231	+	1.02162i
$249$	8.05963e6	+	1.58128e7i	0.522056	+	1.02426i
$250$	9.28460e6	+	1.25673e7i	0.594214	+	0.804307i
$251$	1.86241e7			1.17775			0.588876	−	0.808223i	$-0.299570\pi$
$251$	1.86241e7			1.17775			0.588876	+	0.808223i	$0.299570\pi$
$252$	4.42882e6	−	2.95356e7i	0.276749	−	1.84563i
$253$	−1.08150e6	−	1.08150e6i	−0.0667830	−	0.0667830i
$254$	−6.26321e6	−	8.54863e6i	−0.382204	−	0.521669i
$255$	−1.01522e6	−	328230.i	−0.0612264	−	0.0197951i
$256$	5.69102e6	+	1.57825e7i	0.339211	+	0.940710i
$257$	5.91076e6	+	5.91076e6i	0.348212	+	0.348212i	0.859443	−	0.511231i	$-0.170810\pi$
$257$	5.91076e6	+	5.91076e6i	0.348212	+	0.348212i	−0.511231	+	0.859443i	$0.670810\pi$
$258$	−9.25364e6	+	3.04890e6i	−0.538832	+	0.177535i
$259$	−3.86287e7			−2.22337
$260$	−1.43277e7	−	4.50837e6i	−0.815185	−	0.256507i
$261$	6.91839e6	+	5.02375e6i	0.389120	+	0.282557i
$262$	−2.80679e7	−	4.33080e6i	−1.56065	−	0.240804i
$263$	9.26590e6	+	9.26590e6i	0.509355	+	0.509355i	0.914328	−	0.404974i	$-0.132719\pi$
$263$	9.26590e6	+	9.26590e6i	0.509355	+	0.509355i	−0.404974	+	0.914328i	$0.632719\pi$
$264$	−2.82720e6	−	2.75959e6i	−0.153654	−	0.149980i
$265$	−30693.5	−	2.31367e7i	−0.00164934	−	1.24326i
$266$	−3.09980e7	−	4.23091e7i	−1.64698	−	2.24796i
$267$	3.38621e7	+	1.09976e7i	1.77901	+	0.577781i
$268$	−2.34425e6	−	4.51148e6i	−0.121787	−	0.234377i
$269$	−3.19948e7			−1.64370			−0.821850	−	0.569703i	$-0.807058\pi$
$269$	−3.19948e7			−1.64370			−0.821850	+	0.569703i	$0.807058\pi$
$270$	−1.87541e7	−	5.97545e6i	−0.952805	−	0.303584i
$271$		−	2.79773e7i		−	1.40572i	−0.711329	−	0.702860i	$-0.751906\pi$
$271$		−	2.79773e7i		−	1.40572i	0.711329	−	0.702860i	$-0.248094\pi$
$272$	−222951.	−	1.27556e6i	−0.0110790	−	0.0633859i
$273$	−1.00237e7	+	3.08633e7i	−0.492650	+	1.51689i
$274$	−1.42696e6	−	1.94765e6i	−0.0693680	−	0.0946802i
$275$	−11847.9	−	4.46544e6i	−0.000569695	−	0.214717i
$276$	−1.52071e6	−	9.12196e6i	−0.0723301	−	0.433871i
$277$	−2.04646e6	+	2.04646e6i	−0.0962861	+	0.0962861i	−0.753609	−	0.657323i	$-0.771689\pi$
$277$	−2.04646e6	+	2.04646e6i	−0.0962861	+	0.0962861i	0.657323	+	0.753609i	$0.271689\pi$
$278$	2.75539e7	+	4.25149e6i	1.28248	+	0.197882i
$279$	1.45437e7	−	2.00286e7i	0.669672	−	0.922229i
$280$	3.67470e7	+	1.81122e7i	1.67397	+	0.825081i
$281$		−	1.99486e7i		−	0.899070i	−0.893263	−	0.449535i	$-0.851590\pi$
$281$		−	1.99486e7i		−	0.899070i	0.893263	−	0.449535i	$-0.148410\pi$
$282$	1.99254e7	−	6.56503e6i	0.888503	−	0.292745i
$283$	4.27001e6	−	4.27001e6i	0.188395	−	0.188395i	−0.606607	−	0.795002i	$-0.707470\pi$
$283$	4.27001e6	−	4.27001e6i	0.188395	−	0.188395i	0.795002	+	0.606607i	$0.207470\pi$
$284$	−6.38619e6	−	2.01880e6i	−0.278796	−	0.0881330i
$285$	−3.07762e7	+	1.57378e7i	−1.32948	+	0.679844i
$286$	2.53698e6	+	3.46271e6i	0.108447	+	0.148019i
$287$	−1.24465e7	+	1.24465e7i	−0.526503	+	0.526503i
$288$	−4.21292e6	−	2.35134e7i	−0.176362	−	0.984325i
$289$		−	2.40376e7i		−	0.995859i
$290$	−9.45166e6	+	6.94411e6i	−0.387538	+	0.284723i
$291$	3.01425e6	−	1.53633e6i	0.122321	−	0.0623455i
$292$	−8.56041e6	−	1.64744e7i	−0.343832	−	0.661701i
$293$	−5.77480e6	+	5.77480e6i	−0.229580	+	0.229580i	−0.812517	−	0.582937i	$-0.801903\pi$
$293$	−5.77480e6	+	5.77480e6i	−0.229580	+	0.229580i	0.582937	+	0.812517i	$0.301903\pi$
$294$	2.84135e7	−	5.63372e7i	1.11810	−	2.21694i
$295$	6.78500e6	+	6.76703e6i	0.264292	+	0.263592i
$296$	−2.92682e7	+	9.89867e6i	−1.12855	+	0.381682i
$297$	3.30818e6	+	4.54958e6i	0.126276	+	0.173661i
$298$	4.74915e6	+	732780.i	0.179460	+	0.0276901i
$299$			1.00481e7i			0.375899i
$300$	1.56342e7	−	2.20130e7i	0.579044	−	0.815296i
$301$	−2.88739e7			−1.05878
$302$	−4.86173e6	+	3.15089e7i	−0.176510	+	1.14396i
$303$	−9.43699e6	+	2.90569e7i	−0.339239	+	1.04453i
$304$	−3.43284e7	−	2.41135e7i	−1.22189	−	0.858300i
$305$	2.24916e7	−	2.25513e7i	0.792722	−	0.794828i
$306$	7836.11	+	1.84369e6i	0.000273487	+	0.0643463i
$307$	3.40438e6	+	3.40438e6i	0.117659	+	0.117659i	0.763485	−	0.645826i	$-0.223487\pi$
$307$	3.40438e6	+	3.40438e6i	0.117659	+	0.117659i	−0.645826	+	0.763485i	$0.723487\pi$
$308$	−5.39851e6	−	1.03894e7i	−0.184766	−	0.355580i
$309$	−1.00913e7	+	5.14342e6i	−0.342035	+	0.174332i
$310$	2.01031e7	+	2.73624e7i	0.674804	+	0.918480i
$311$	3.24882e7			1.08005			0.540026	−	0.841648i	$-0.318414\pi$
$311$	3.24882e7			1.08005			0.540026	+	0.841648i	$0.318414\pi$
$312$	314045.	+	2.59531e7i	0.0103402	+	0.854526i
$313$	−2.82866e7	−	2.82866e7i	−0.922461	−	0.922461i	0.0747423	−	0.997203i	$-0.476187\pi$
$313$	−2.82866e7	−	2.82866e7i	−0.922461	−	0.922461i	−0.997203	+	0.0747423i	$0.976187\pi$
$314$	1.26566e7	−	9.27295e6i	0.408817	−	0.299522i
$315$	−4.72457e7	−	3.42116e7i	−1.51158	−	1.09456i
$316$	−1.73700e7	−	5.49100e6i	−0.550476	−	0.174016i
$317$	−2.52642e6	−	2.52642e6i	−0.0793100	−	0.0793100i	0.666339	−	0.745649i	$-0.267860\pi$
$317$	−2.52642e6	−	2.52642e6i	−0.0793100	−	0.0793100i	−0.745649	+	0.666339i	$0.767860\pi$
$318$	−3.79722e7	+	1.25111e7i	−1.18082	+	0.389058i
$319$	3.35184e6			0.103255
$320$	3.24837e7	+	4.30677e6i	0.991325	+	0.131432i
$321$	3.51064e7	−	1.78934e7i	1.06138	−	0.540975i
$322$	4.17929e6	−	2.70860e7i	0.125180	−	0.811292i
$323$	2.28951e6	+	2.28951e6i	0.0679415	+	0.0679415i
$324$	289115.	+	3.40110e7i	0.00850032	+	0.999964i
$325$	−2.06889e7	+	2.07990e7i	−0.602680	+	0.605887i
$326$	−7.39355e6	+	5.41693e6i	−0.213403	+	0.156351i
$327$	−9.65445e6	+	2.97265e7i	−0.276111	+	0.850160i
$328$	−6.24102e6	+	1.26199e7i	−0.176862	+	0.357630i
$329$	6.21725e7			1.74587
$330$	−7.32554e6	+	2.42440e6i	−0.203844	+	0.0674626i
$331$			3.10450e7i			0.856065i	0.903763	+	0.428033i	$0.140793\pi$
$331$			3.10450e7i			0.856065i	−0.903763	+	0.428033i	$0.859207\pi$
$332$	1.93979e7	+	3.73311e7i	0.530080	+	1.02013i
$333$	4.34483e7	−	6.89313e6i	1.17663	−	0.186674i
$334$	1.42865e7	−	1.04671e7i	0.383432	−	0.280924i
$335$	−9.93005e6	+	13173.4i	−0.264130	+	0.000350399i
$336$	9.94806e6	−	7.00906e7i	0.262253	−	1.84774i
$337$	2.79312e6	−	2.79312e6i	0.0729793	−	0.0729793i	−0.669675	−	0.742654i	$-0.733567\pi$
$337$	2.79312e6	−	2.79312e6i	0.0729793	−	0.0729793i	0.742654	+	0.669675i	$0.233567\pi$
$338$	−1.58798e6	+	1.02917e7i	−0.0411239	+	0.266524i
$339$	−4.56523e7	+	2.32685e7i	−1.17183	+	0.597268i
$340$	−2.41247e6	−	759113.i	−0.0613799	−	0.0193139i
$341$		−	9.70352e6i		−	0.244718i
$342$	4.24155e7	+	4.20564e7i	1.06034	+	1.05137i
$343$	7.89700e7	−	7.89700e7i	1.95695	−	1.95695i
$344$	−2.18771e7	+	7.39897e6i	−0.537422	+	0.181759i
$345$	−1.71863e7	−	5.55650e6i	−0.418528	−	0.135314i
$346$	−5.35933e7	+	3.92655e7i	−1.29384	+	0.947943i
$347$	−2.54116e6	+	2.54116e6i	−0.0608196	+	0.0608196i	−0.736862	−	0.676043i	$-0.763693\pi$
$347$	−2.54116e6	+	2.54116e6i	−0.0608196	+	0.0608196i	0.676043	+	0.736862i	$0.263693\pi$
$348$	1.64921e7	+	1.17791e7i	0.391326	+	0.279494i
$349$		−	2.80364e7i		−	0.659548i	−0.944060	−	0.329774i	$-0.893027\pi$
$349$		−	2.80364e7i		−	0.659548i	0.944060	−	0.329774i	$-0.106973\pi$
$350$	6.44204e7	−	4.74612e7i	1.50252	−	1.10697i
$351$	5.76685e6	−	3.65027e7i	0.133358	−	0.844119i
$352$	−6.75264e6	−	6.48845e6i	−0.154827	−	0.148769i
$353$	−4.59272e7	+	4.59272e7i	−1.04411	+	1.04411i	−0.0451277	+	0.998981i	$0.514369\pi$
$353$	−4.59272e7	+	4.59272e7i	−1.04411	+	1.04411i	−0.998981	+	0.0451277i	$0.985631\pi$
$354$	7.45677e6	−	1.47850e7i	0.168090	−	0.333282i
$355$	−9.23767e6	+	9.26221e6i	−0.206480	+	0.207028i
$356$	8.04678e7	+	2.54375e7i	1.78350	+	0.563799i
$357$	−1.68777e6	+	5.19672e6i	−0.0370944	+	0.114215i
$358$	−6.52460e6	+	4.22860e7i	−0.142202	+	0.921611i
$359$		−	6.15150e7i		−	1.32953i	−0.747053	−	0.664764i	$-0.768532\pi$
$359$		−	6.15150e7i		−	1.32953i	0.747053	−	0.664764i	$-0.231468\pi$
$360$	−4.45639e7	−	1.38146e7i	−0.955158	−	0.296096i
$361$	5.78521e7			1.22970
$362$	−6.45431e7	−	9.95881e6i	−1.36058	−	0.209933i
$363$	−4.33956e7	−	1.40938e7i	−0.907248	−	0.294652i
$364$	−2.31848e7	+	7.33417e7i	−0.480728	+	1.52071i
$365$	−3.62612e7	+	48104.8i	−0.745699	+	0.000989258i
$366$	−4.91410e7	−	2.47841e7i	−1.00231	−	0.505510i
$367$	5.40702e6	+	5.40702e6i	0.109386	+	0.109386i	0.759681	−	0.650296i	$-0.225355\pi$
$367$	5.40702e6	+	5.40702e6i	0.109386	+	0.109386i	−0.650296	+	0.759681i	$0.725355\pi$
$368$	−3.77426e6	−	2.15935e7i	−0.0757336	−	0.433290i
$369$	1.17784e7	−	1.62204e7i	0.234426	−	0.322836i
$370$	−9.12308e6	+	5.96517e7i	−0.180109	+	1.17765i
$371$	−1.18483e8			−2.32026
$372$	3.41002e7	−	4.77444e7i	0.662412	−	0.927457i
$373$	6.70787e6	+	6.70787e6i	0.129258	+	0.129258i	0.768776	−	0.639518i	$-0.220866\pi$
$373$	6.70787e6	+	6.70787e6i	0.129258	+	0.129258i	−0.639518	+	0.768776i	$0.720866\pi$
$374$	427172.	+	583046.i	0.00816560	+	0.0111452i
$375$	−2.41338e7	−	4.68879e7i	−0.457649	−	0.889133i
$376$	4.71069e7	−	1.59318e7i	0.886178	−	0.299710i
$377$	−1.55708e7	−	1.55708e7i	−0.290593	−	0.290593i
$378$	−3.07278e7	+	9.59993e7i	−0.568926	+	1.77743i
$379$	2.58140e7			0.474174			0.237087	−	0.971488i	$-0.423807\pi$
$379$	2.58140e7			0.474174			0.237087	+	0.971488i	$0.423807\pi$
$380$	−7.26560e7	+	3.78759e7i	−1.32410	+	0.690259i
$381$	1.62418e7	+	3.18661e7i	0.293670	+	0.576174i
$382$	1.32091e7	+	2.03813e6i	0.236965	+	0.0365629i
$383$	9.70633e6	+	9.70633e6i	0.172766	+	0.172766i	0.788194	−	0.615427i	$-0.211017\pi$
$383$	9.70633e6	+	9.70633e6i	0.172766	+	0.172766i	−0.615427	+	0.788194i	$0.711017\pi$
$384$	−1.04234e7	−	5.56555e7i	−0.184083	−	0.982911i
$385$	−2.28677e7	+	30336.7i	−0.400719	+	0.000531601i
$386$	−2.39144e6	−	3.26407e6i	−0.0415813	−	0.0567541i
$387$	3.24764e7	−	5.15242e6i	0.560318	−	0.0888952i
$388$	7.11607e6	−	3.69764e6i	0.121827	−	0.0633038i
$389$	−7.58069e6			−0.128783			−0.0643917	−	0.997925i	$-0.520511\pi$
$389$	−7.58069e6			−0.128783			−0.0643917	+	0.997925i	$0.520511\pi$
$390$	4.52928e7	+	2.27679e7i	0.763546	+	0.383822i
$391$			1.69189e6i			0.0283035i
$392$	6.63002e7	−	1.34065e8i	1.10067	−	2.22565i
$393$	9.11629e7	+	2.96075e7i	1.50190	+	0.487780i
$394$	3.01951e7	+	4.12132e7i	0.493683	+	0.673826i
$395$	−2.51258e7	+	2.51926e7i	−0.407689	+	0.408772i
$396$	7.92601e6	+	1.07223e7i	0.127635	+	0.172664i
$397$	3.77517e7	−	3.77517e7i	0.603344	−	0.603344i	−0.337855	−	0.941198i	$-0.609701\pi$
$397$	3.77517e7	−	3.77517e7i	0.603344	−	0.603344i	0.941198	+	0.337855i	$0.109701\pi$
$398$	−2.07748e7	−	3.20550e6i	−0.329525	−	0.0508447i
$399$	8.03844e7	+	1.57713e8i	1.26547	+	2.48283i
$400$	3.66481e7	−	5.24683e7i	0.572626	−	0.819817i
$401$		−	4.13145e7i		−	0.640722i	−0.947296	−	0.320361i	$-0.896196\pi$
$401$		−	4.13145e7i		−	0.640722i	0.947296	−	0.320361i	$-0.103804\pi$
$402$	5.36966e6	+	1.62973e7i	0.0826549	+	0.250864i
$403$	−4.50771e7	+	4.50771e7i	−0.688718	+	0.688718i
$404$	−2.18278e7	+	6.90492e7i	−0.331029	+	1.04716i
$405$	5.92453e7	+	3.00493e7i	0.891844	+	0.452344i
$406$	3.54967e7	+	4.84493e7i	0.530408	+	0.723952i
$407$	1.21948e7	−	1.21948e7i	0.180880	−	0.180880i
$408$	52878.4	+	4.36994e6i	0.000778570	+	0.0643421i
$409$			7.92836e7i			1.15881i	0.815039	+	0.579406i	$0.196716\pi$
$409$			7.92836e7i			1.15881i	−0.815039	+	0.579406i	$0.803284\pi$
$410$	1.62807e7	+	2.21598e7i	0.236223	+	0.321524i
$411$	3.70040e6	+	7.26011e6i	0.0532995	+	0.104573i
$412$	−2.38236e7	+	1.23792e7i	−0.340656	+	0.177011i
$413$	3.47002e7	−	3.47002e7i	0.492585	−	0.492585i
$414$	132655.	+	3.12112e7i	0.00186949	+	0.439855i
$415$	8.21681e7	−	109006.i	1.14963	−	0.00152512i
$416$	1.22727e6	+	6.15107e7i	0.0170475	+	0.854419i
$417$	−8.94934e7	−	2.90653e7i	−1.23419	−	0.400836i
$418$	2.31425e7	+	3.57082e6i	0.316870	+	0.0488921i
$419$		−	1.37863e8i		−	1.87416i	−0.349115	−	0.937080i	$-0.613518\pi$
$419$		−	1.37863e8i		−	1.87416i	0.349115	−	0.937080i	$-0.386482\pi$
$420$	−1.12623e8	−	8.02125e7i	−1.52012	−	1.08267i
$421$	−7.45329e7			−0.998853			−0.499427	−	0.866356i	$-0.666456\pi$
$421$	−7.45329e7			−0.998853			−0.499427	+	0.866356i	$0.666456\pi$
$422$	2.19720e6	−	1.42401e7i	0.0292370	−	0.189485i
$423$	−6.99296e7	+	1.10944e7i	−0.923932	+	0.146583i
$424$	−8.97726e7	+	3.03616e7i	−1.17773	+	0.398315i
$425$	−3.48356e6	+	3.50210e6i	−0.0453792	+	0.0456206i
$426$	2.01830e7	+	1.01792e7i	0.261070	+	0.131670i
$427$	−1.15333e8	−	1.15333e8i	−1.48139	−	1.48139i
$428$	8.28798e7	−	4.30658e7i	1.05710	−	0.549290i
$429$	−6.57891e6	−	1.29077e7i	−0.0833263	−	0.163485i
$430$	−6.81924e6	+	4.45879e7i	−0.0857690	+	0.560805i
$431$	9.32320e7			1.16448			0.582242	−	0.813016i	$-0.302176\pi$
$431$	9.32320e7			1.16448			0.582242	+	0.813016i	$0.302176\pi$
$432$	1.31811e6	+	8.06108e7i	0.0163494	+	0.999866i
$433$	−2.20471e7	−	2.20471e7i	−0.271573	−	0.271573i	0.558160	−	0.829733i	$-0.311508\pi$
$433$	−2.20471e7	−	2.20471e7i	−0.271573	−	0.271573i	−0.829733	+	0.558160i	$0.811508\pi$
$434$	1.40260e8	−	1.02762e8i	1.71579	−	1.25709i
$435$	3.52427e7	−	1.80218e7i	0.428155	−	0.218942i
$436$	−2.23308e7	+	7.06403e7i	−0.269429	+	0.852301i
$437$	3.87584e7	+	3.87584e7i	0.464431	+	0.464431i
$438$	1.96082e7	+	5.95124e7i	0.233354	+	0.708247i
$439$	−4.15290e7			−0.490860			−0.245430	−	0.969414i	$-0.578929\pi$
$439$	−4.15290e7			−0.490860			−0.245430	+	0.969414i	$0.578929\pi$
$440$	−1.73186e7	+	5.88286e6i	−0.203308	+	0.0690606i
$441$	−1.25125e8	+	1.72314e8i	−1.45891	+	2.00912i
$442$	724102.	−	4.69291e6i	0.00838557	−	0.0543470i
$443$	−5.33212e7	−	5.33212e7i	−0.613322	−	0.613322i	0.330488	−	0.943810i	$-0.392787\pi$
$443$	−5.33212e7	−	5.33212e7i	−0.613322	−	0.613322i	−0.943810	+	0.330488i	$0.892787\pi$
$444$	1.02857e8	−	1.71472e7i	1.17513	−	0.195904i
$445$	1.16397e8	−	1.16707e8i	1.32088	−	1.32439i
$446$	−1.21384e8	+	8.89325e7i	−1.36822	+	1.00243i
$447$	−1.54249e7	−	5.00965e6i	−0.172703	−	0.0560899i
$448$	2.22757e7	−	1.66321e8i	0.247741	−	1.84975i
$449$	−5.18687e7			−0.573016			−0.286508	−	0.958078i	$-0.592494\pi$
$449$	−5.18687e7			−0.573016			−0.286508	+	0.958078i	$0.592494\pi$
$450$	−6.39887e7	+	6.48784e7i	−0.702208	+	0.711971i
$451$		−	7.85850e6i		−	0.0856663i
$452$	−1.07777e8	+	5.60026e7i	−1.16710	+	0.606447i
$453$	3.32372e7	−	1.02339e8i	0.357544	−	1.10090i
$454$	3.36402e7	−	2.46467e7i	0.359494	−	0.263385i
$455$	1.06371e8	+	1.06089e8i	1.12925	+	1.12626i
$456$	1.01320e8	+	9.88971e7i	1.06856	+	1.04301i
$457$	−4.62951e7	+	4.62951e7i	−0.485050	+	0.485050i	−0.906740	−	0.421690i	$-0.861437\pi$
$457$	−4.62951e7	+	4.62951e7i	−0.485050	+	0.485050i	0.421690	+	0.906740i	$0.361437\pi$
$458$	3.45506e6	−	2.23923e7i	0.0359633	−	0.233078i
$459$	971015.	−	6.14628e6i	0.0100412	−	0.0635585i
$460$	−4.08400e7	−	1.28508e7i	−0.419578	−	0.132025i
$461$		−	4.43814e7i		−	0.453000i	−0.974011	−	0.226500i	$-0.927272\pi$
$461$		−	4.43814e7i		−	0.453000i	0.974011	−	0.226500i	$-0.0727283\pi$
$462$	1.23657e7	+	3.75307e7i	0.125398	+	0.380593i
$463$	6.07712e7	−	6.07712e7i	0.612286	−	0.612286i	−0.331255	−	0.943541i	$-0.607472\pi$
$463$	6.07712e7	−	6.07712e7i	0.612286	−	0.612286i	0.943541	+	0.331255i	$0.107472\pi$
$464$	3.93104e7	+	2.76130e7i	0.393508	+	0.276414i
$465$	−5.21728e7	−	1.02027e8i	−0.518902	−	1.01474i
$466$	8.42124e7	−	6.16988e7i	0.832182	−	0.609704i
$467$	−1.92715e7	+	1.92715e7i	−0.189219	+	0.189219i	−0.795359	−	0.606139i	$-0.792717\pi$
$467$	−1.92715e7	+	1.92715e7i	−0.189219	+	0.189219i	0.606139	+	0.795359i	$0.292717\pi$
$468$	1.29900e7	−	8.66296e7i	0.126727	−	0.845140i
$469$			5.08521e7i			0.492935i
$470$	1.46835e7	−	9.60088e7i	0.141428	−	0.924735i
$471$	−4.71791e7	+	2.40467e7i	−0.451531	+	0.230140i
$472$	1.73997e7	−	3.51836e7i	0.165468	−	0.334591i
$473$	9.11525e6	−	9.11525e6i	0.0861361	−	0.0861361i
$474$	5.48964e7	+	2.76868e7i	0.515477	+	0.259979i
$475$	424599.	+	1.60030e8i	0.00396185	+	1.49321i
$476$	−3.90382e6	+	1.23492e7i	−0.0361967	+	0.114503i
$477$	1.33266e8	−	2.11429e7i	1.22791	−	0.194809i
$478$	2.65868e7	−	1.72309e8i	0.243434	−	1.57770i
$479$		−	2.88304e7i		−	0.262327i	−0.991361	−	0.131164i	$-0.958129\pi$
$479$		−	2.88304e7i		−	0.262327i	0.991361	−	0.131164i	$-0.0418713\pi$
$480$	−1.05887e8	−	3.19157e7i	−0.957453	−	0.288589i
$481$	−1.13300e8			−1.01811
$482$	−1.60192e8	−	2.47172e7i	−1.43054	−	0.220728i
$483$	−2.85717e7	+	8.79736e7i	−0.253568	+	0.780748i
$484$	−1.03123e8	−	3.25992e7i	−0.909533	−	0.287522i
$485$	−20778.7	−	1.56629e7i	−0.000182135	−	0.137293i
$486$	1.74310e7	−	1.13460e8i	0.151849	−	0.988404i
$487$	2.42727e6	+	2.42727e6i	0.0210151	+	0.0210151i	0.717536	−	0.696521i	$-0.245270\pi$
$487$	2.42727e6	+	2.42727e6i	0.0210151	+	0.0210151i	−0.696521	+	0.717536i	$0.745270\pi$
$488$	−1.16940e8	−	5.78313e7i	−1.00624	−	0.497627i
$489$	2.75604e7	−	1.40472e7i	0.235700	−	0.120134i
$490$	−1.72955e8	−	2.35410e8i	−1.47009	−	2.00095i
$491$	1.08622e8			0.917644			0.458822	−	0.888528i	$-0.348272\pi$
$491$	1.08622e8			0.917644			0.458822	+	0.888528i	$0.348272\pi$
$492$	2.76164e7	−	3.86663e7i	0.231885	−	0.324667i
$493$	−2.62178e6	−	2.62178e6i	−0.0218804	−	0.0218804i
$494$	−9.09190e7	−	1.24095e8i	−0.754178	−	1.02937i
$495$	2.57154e7	−	4.11476e6i	0.212020	−	0.0339257i
$496$	7.99393e7	−	1.13803e8i	0.655111	−	0.932628i
$497$	4.73692e7	+	4.73692e7i	0.385858	+	0.385858i
$498$	−4.44323e7	−	1.34855e8i	−0.359758	−	1.09189i
$499$	−6.85635e6			−0.0551812			−0.0275906	−	0.999619i	$-0.508783\pi$
$499$	−6.85635e6			−0.0551812			−0.0275906	+	0.999619i	$0.508783\pi$
$500$	−5.80767e7	−	1.10689e8i	−0.464614	−	0.885513i
$501$	−5.32549e7	+	2.71435e7i	−0.423493	+	0.215850i
$502$	−1.47250e8	−	2.27203e7i	−1.16398	−	0.179598i
$503$	8.05558e7	+	8.05558e7i	0.632984	+	0.632984i	0.948815	−	0.315831i	$-0.102283\pi$
$503$	8.05558e7	+	8.05558e7i	0.632984	+	0.632984i	−0.315831	+	0.948815i	$0.602283\pi$
$504$	−7.10478e7	+	2.28119e8i	−0.554957	+	1.78184i
$505$	1.00146e8	+	9.98802e7i	0.777603	+	0.775542i
$506$	7.23146e6	+	9.87020e6i	0.0558180	+	0.0761859i
$507$	1.08562e7	−	3.34268e7i	0.0833017	−	0.256490i
$508$	3.90908e7	+	7.52299e7i	0.298184	+	0.573851i
$509$	−8.06687e7			−0.611719			−0.305859	−	0.952077i	$-0.598944\pi$
$509$	−8.06687e7			−0.611719			−0.305859	+	0.952077i	$0.598944\pi$
$510$	7.62633e6	+	3.83363e6i	0.0574917	+	0.0289001i
$511$			1.85695e8i			1.39167i
$512$	−2.57420e7	−	1.31726e8i	−0.191793	−	0.981435i
$513$	−1.18557e8	−	1.63046e8i	−0.878162	−	1.20769i
$514$	−3.95223e7	−	5.39438e7i	−0.291040	−	0.397239i
$515$	69564.2	+	5.24373e7i	0.000509289	+	0.383900i
$516$	7.68828e7	−	1.28170e7i	0.559603	−	0.0932907i
$517$	−1.96274e7	+	1.96274e7i	−0.142033	+	0.142033i
$518$	3.05416e8	+	4.71247e7i	2.19736	+	0.339047i
$519$	1.99776e8	−	1.01824e8i	1.42903	−	0.728361i
$520$	1.07781e8	+	5.31241e7i	0.766535	+	0.377817i
$521$			2.38260e8i			1.68476i	0.538882	+	0.842382i	$0.318847\pi$
$521$			2.38260e8i			1.68476i	−0.538882	+	0.842382i	$0.681153\pi$
$522$	−4.85711e7	−	4.81600e7i	−0.341481	−	0.338590i
$523$	−1.43079e8	+	1.43079e8i	−1.00016	+	1.00016i	−0.000162259		1.00000i	$0.500052\pi$
$523$	−1.43079e8	+	1.43079e8i	−1.00016	+	1.00016i	−1.00000		0.000162259i	$0.999948\pi$
$524$	2.16634e8	+	6.84824e7i	1.50568	+	0.475976i
$525$	−2.40278e8	+	1.23271e8i	−1.66049	+	0.851890i
$526$	−6.19564e7	−	8.45641e7i	−0.425725	−	0.581070i
$527$	−7.59002e6	+	7.59002e6i	−0.0518575	+	0.0518575i
$528$	1.89865e7	+	2.52676e7i	0.128986	+	0.171657i
$529$		−	1.19394e8i		−	0.806524i
$530$	−2.79826e7	+	1.82966e8i	−0.187958	+	1.22897i
$531$	−3.28375e7	+	4.52217e7i	−0.219324	+	0.302039i
$532$	1.93469e8	+	3.72330e8i	1.28492	+	2.47282i
$533$	−3.65062e7	+	3.65062e7i	−0.241093	+	0.241093i
$534$	−2.54312e8	−	1.28261e8i	−1.67010	−	0.842310i
$535$	−242006.	−	1.82423e8i	−0.00158039	−	1.19130i
$536$	1.30309e7	+	3.85296e7i	0.0846215	+	0.250207i
$537$	4.46054e7	−	1.37342e8i	0.288048	−	0.886914i
$538$	2.52965e8	+	3.90317e7i	1.62448	+	0.250652i
$539$			8.34832e7i			0.533129i
$540$	1.40988e8	+	7.01233e7i	0.895367	+	0.445329i
$541$	9.03979e7			0.570909			0.285454	−	0.958392i	$-0.407856\pi$
$541$	9.03979e7			0.570909			0.285454	+	0.958392i	$0.407856\pi$
$542$	−3.41307e7	+	2.21201e8i	−0.214362	+	1.38928i
$543$	2.09632e8	+	6.80834e7i	1.30936	+	0.425247i
$544$	206646.	+	1.03571e7i	0.00128360	+	0.0643340i
$545$	1.02453e8	+	1.02182e8i	0.632902	+	0.631225i
$546$	1.16903e8	−	2.31791e8i	0.718202	−	1.42403i
$547$	−9.23890e7	−	9.23890e7i	−0.564493	−	0.564493i	0.366088	−	0.930580i	$-0.380697\pi$
$547$	−9.23890e7	−	9.23890e7i	−0.564493	−	0.564493i	−0.930580	+	0.366088i	$0.880697\pi$
$548$	8.90614e6	+	1.71398e7i	0.0541187	+	0.104151i
$549$	1.50304e8	+	1.09142e8i	0.908348	+	0.659592i
$550$	−5.35389e6	+	3.53201e7i	−0.0321796	+	0.212292i
$551$	−1.20122e8			−0.718069
$552$	895161.	+	7.39774e7i	0.00532211	+	0.439827i
$553$	1.28841e8	+	1.28841e8i	0.761867	+	0.761867i
$554$	1.86767e7	−	1.36836e7i	0.109843	−	0.0804771i
$555$	6.26539e7	−	1.93789e8i	0.366496	−	1.13357i
$556$	−2.12667e8	−	6.72283e7i	−1.23730	−	0.391136i
$557$	3.06078e7	+	3.06078e7i	0.177120	+	0.177120i	0.790099	−	0.612979i	$-0.210029\pi$
$557$	3.06078e7	+	3.06078e7i	0.177120	+	0.177120i	−0.612979	+	0.790099i	$0.710029\pi$
$558$	−1.39422e8	+	1.40613e8i	−0.802473	+	0.809323i
$559$	−8.46887e7			−0.484830
$560$	−2.68442e8	−	1.88032e8i	−1.52857	−	1.07070i
$561$	−1.10775e6	−	2.17338e6i	−0.00627411	−	0.0123097i
$562$	−2.43361e7	+	1.57722e8i	−0.137101	+	0.888555i
$563$	−7.37204e7	−	7.37204e7i	−0.413107	−	0.413107i	0.469712	−	0.882820i	$-0.344358\pi$
$563$	−7.37204e7	−	7.37204e7i	−0.413107	−	0.413107i	−0.882820	+	0.469712i	$0.844358\pi$
$564$	−1.65548e8	+	2.75982e7i	−0.922753	+	0.153831i
$565$	314704.	+	2.37223e8i	0.00174484	+	1.31526i
$566$	−3.89697e7	+	2.85514e7i	−0.214921	+	0.157463i
$567$	1.54285e8	−	3.03192e8i	0.846400	−	1.66329i
$568$	4.80292e7	+	2.37523e7i	0.262096	+	0.129617i
$569$	840002.			0.00455978			0.00227989	−	0.999997i	$-0.499274\pi$
$569$	840002.			0.00455978			0.00227989	+	0.999997i	$0.499274\pi$
$570$	2.62529e8	−	8.68847e7i	1.41760	−	0.469157i
$571$			1.05982e8i			0.569278i	0.958635	+	0.284639i	$0.0918737\pi$
$571$			1.05982e8i			0.569278i	−0.958635	+	0.284639i	$0.908126\pi$
$572$	−1.58341e7	−	3.04727e7i	−0.0846070	−	0.162825i
$573$	−4.29024e7	−	1.39336e7i	−0.228043	−	0.0740629i
$574$	1.13591e8	−	8.32233e7i	0.600633	−	0.440057i
$575$	−5.89721e7	+	5.92859e7i	−0.310201	+	0.311851i
$576$	4.62419e6	+	1.91047e8i	0.0241974	+	0.999707i
$577$	7.47801e6	−	7.47801e6i	0.0389277	−	0.0389277i	−0.687375	−	0.726303i	$-0.741237\pi$
$577$	7.47801e6	−	7.47801e6i	0.0389277	−	0.0389277i	0.726303	+	0.687375i	$0.241237\pi$
$578$	−2.93245e7	+	1.90052e8i	−0.151861	+	0.984213i
$579$	6.20151e6	+	1.21672e7i	0.0319493	+	0.0626839i
$580$	8.32004e7	−	4.33727e7i	0.426424	−	0.222296i
$581$		−	4.20785e8i		−	2.14552i
$582$	−2.57062e7	+	8.46969e6i	−0.130397	+	0.0429634i
$583$	3.74043e7	−	3.74043e7i	0.188762	−	0.188762i
$584$	4.75845e7	+	1.40697e8i	0.238906	+	0.706394i
$585$	−1.38574e8	−	1.00344e8i	−0.692173	−	0.501217i
$586$	5.27030e7	−	3.86132e7i	0.261904	−	0.191886i
$587$	−1.88432e7	+	1.88432e7i	−0.0931622	+	0.0931622i	−0.752152	−	0.658990i	$-0.770984\pi$
$587$	−1.88432e7	+	1.88432e7i	−0.0931622	+	0.0931622i	0.658990	+	0.752152i	$0.270984\pi$
$588$	−2.93377e8	+	4.10764e8i	−1.44309	+	2.02051i
$589$			3.47750e8i			1.70185i
$590$	−4.53898e7	−	6.17804e7i	−0.221005	−	0.300811i
$591$	−7.83023e7	−	1.53628e8i	−0.379326	−	0.744229i
$592$	2.43483e8	−	4.25578e7i	1.17356	−	0.205123i
$593$	9.29316e7	−	9.29316e7i	0.445655	−	0.445655i	−0.448252	−	0.893907i	$-0.647953\pi$
$593$	9.29316e7	−	9.29316e7i	0.445655	−	0.445655i	0.893907	+	0.448252i	$0.147953\pi$
$594$	−2.06057e7	−	4.00067e7i	−0.0983168	−	0.190886i
$595$	1.79106e7	+	1.78632e7i	0.0850277	+	0.0848024i
$596$	−3.66549e7	−	1.15874e7i	−0.173138	−	0.0547325i
$597$	6.74754e7	+	2.19144e7i	0.317119	+	0.102993i
$598$	1.22581e7	−	7.94447e7i	0.0573217	−	0.371502i
$599$			4.05044e8i			1.88461i	0.334753	+	0.942306i	$0.391347\pi$
$599$			4.05044e8i			1.88461i	−0.334753	+	0.942306i	$0.608653\pi$
$600$	−1.50465e8	+	1.54972e8i	−0.696598	+	0.717461i
$601$	1.93437e8			0.891077			0.445539	−	0.895263i	$-0.353012\pi$
$601$	1.93437e8			0.891077			0.445539	+	0.895263i	$0.353012\pi$
$602$	2.28289e8	+	3.52244e7i	1.04640	+	0.161456i
$603$	−9.07434e6	−	5.71968e7i	−0.0413869	−	0.260867i
$604$	7.68779e7	−	2.43192e8i	0.348892	−	1.10367i
$605$	−1.49168e8	+	1.49564e8i	−0.673611	+	0.675401i
$606$	1.10061e8	−	2.18224e8i	0.494555	−	0.980585i
$607$	−5.42456e6	−	5.42456e6i	−0.0242549	−	0.0242549i	0.694875	−	0.719130i	$-0.255460\pi$
$607$	−5.42456e6	−	5.42456e6i	−0.0242549	−	0.0242549i	−0.719130	+	0.694875i	$0.755460\pi$
$608$	2.41998e8	+	2.32530e8i	1.07672	+	1.03459i
$609$	−9.20504e7	−	1.80601e8i	−0.407543	−	0.799592i
$610$	−2.05340e8	+	1.50862e8i	−0.904656	+	0.664648i
$611$	1.82356e8			0.799457
$612$	2.18723e6	−	1.45866e7i	0.00954203	−	0.0636354i
$613$	−1.70284e8	−	1.70284e8i	−0.739251	−	0.739251i	0.233182	−	0.972433i	$-0.425086\pi$
$613$	−1.70284e8	−	1.70284e8i	−0.739251	−	0.739251i	−0.972433	+	0.233182i	$0.925086\pi$
$614$	−2.27634e7	−	3.10697e7i	−0.0983404	−	0.134225i
$615$	−4.22527e7	−	8.26278e7i	−0.181647	−	0.355223i
$616$	3.00086e7	+	8.87289e7i	0.128382	+	0.379597i
$617$	−1.10937e8	−	1.10937e8i	−0.472304	−	0.472304i	0.430355	−	0.902660i	$-0.358388\pi$
$617$	−1.10937e8	−	1.10937e8i	−0.472304	−	0.472304i	−0.902660	+	0.430355i	$0.858388\pi$
$618$	8.60607e7	−	2.83554e7i	0.364619	−	0.120135i
$619$	1.51815e8			0.640094			0.320047	−	0.947402i	$-0.396301\pi$
$619$	1.51815e8			0.640094			0.320047	+	0.947402i	$0.396301\pi$
$620$	−1.25563e8	−	2.40864e8i	−0.526851	−	1.01064i
$621$	1.64380e7	−	1.04048e8i	0.0686395	−	0.434471i
$622$	−2.56866e8	−	3.96336e7i	−1.06742	−	0.164700i
$623$	−5.96866e8	−	5.96866e8i	−2.46838	−	2.46838i
$624$	2.91782e7	−	2.05580e8i	0.120090	−	0.846109i
$625$	−2.44137e8	+	1.29552e6i	−0.999986	+	0.00530644i
$626$	1.89138e8	+	2.58154e8i	0.771004	+	1.05234i
$627$	−7.51653e7	−	2.44119e7i	−0.304940	−	0.0990372i
$628$	−1.11381e8	+	5.78757e7i	−0.449710	+	0.233678i
$629$	−1.90773e7			−0.0766594
$630$	3.31809e8	+	3.28128e8i	1.32699	+	1.31227i
$631$			1.74232e8i			0.693490i	0.937960	+	0.346745i	$0.112713\pi$
$631$			1.74232e8i			0.693490i	−0.937960	+	0.346745i	$0.887287\pi$
$632$	1.30636e8	+	6.46046e7i	0.517502	+	0.255925i
$633$	−1.50212e7	+	4.62509e7i	−0.0592233	+	0.182351i
$634$	1.68929e7	+	2.30571e7i	0.0662882	+	0.0904766i
$635$	1.65586e8	−	219669.i	0.646698	−	0.000857921i
$636$	3.15487e8	−	5.25945e7i	1.22634	−	0.204442i
$637$	3.87816e8	−	3.87816e8i	1.50040	−	1.50040i
$638$	−2.65011e7	−	4.08904e6i	−0.102047	−	0.0157456i
$639$	−6.17322e7	−	4.48265e7i	−0.236597	−	0.171804i
$640$	−2.51577e8	−	7.36794e7i	−0.959689	−	0.281065i
$641$		−	3.30004e8i		−	1.25298i	−0.779428	−	0.626492i	$-0.784490\pi$
$641$		−	3.30004e8i		−	1.25298i	0.779428	−	0.626492i	$-0.215510\pi$
$642$	−2.99396e8	+	9.86452e7i	−1.13146	+	0.372796i
$643$	−1.46799e8	+	1.46799e8i	−0.552190	+	0.552190i	−0.927072	−	0.374882i	$-0.877683\pi$
$643$	−1.46799e8	+	1.46799e8i	−0.552190	+	0.552190i	0.374882	+	0.927072i	$0.377683\pi$
$644$	−6.60865e7	+	2.09055e8i	−0.247432	+	0.782714i
$645$	4.68319e7	−	1.44852e8i	0.174527	−	0.539814i
$646$	−1.53088e7	−	2.08949e7i	−0.0567863	−	0.0775075i
$647$	−1.57568e8	+	1.57568e8i	−0.581777	+	0.581777i	−0.935391	−	0.353615i	$-0.884952\pi$
$647$	−1.57568e8	+	1.57568e8i	−0.581777	+	0.581777i	0.353615	+	0.935391i	$0.384952\pi$
$648$	3.92055e7	−	2.69258e8i	0.144086	−	0.989565i
$649$			2.19091e7i			0.0801477i
$650$	1.88949e8	−	1.39206e8i	0.688025	−	0.506896i
$651$	−5.22837e8	+	2.66485e8i	−1.89506	+	0.965894i
$652$	6.50650e7	−	3.38090e7i	0.234749	−	0.121980i
$653$	−2.29745e8	+	2.29745e8i	−0.825101	+	0.825101i	−0.986834	−	0.161733i	$-0.948292\pi$
$653$	−2.29745e8	+	2.29745e8i	−0.825101	+	0.825101i	0.161733	+	0.986834i	$0.448292\pi$
$654$	1.12597e8	−	2.23253e8i	0.402525	−	0.798112i
$655$	3.13363e8	−	3.14196e8i	1.11513	−	1.11809i
$656$	6.47397e7	−	9.21645e7i	0.229329	−	0.326477i
$657$	−3.31364e7	−	2.08863e8i	−0.116845	−	0.736489i
$658$	−4.91563e8	−	7.58467e7i	−1.72545	−	0.266231i
$659$		−	5.37703e7i		−	0.187882i	−0.995578	−	0.0939412i	$-0.970053\pi$
$659$		−	5.37703e7i		−	0.187882i	0.995578	−	0.0939412i	$-0.0299466\pi$
$660$	6.08766e7	−	1.02317e7i	0.211748	−	0.0355889i
$661$	−3.40889e8			−1.18034			−0.590172	−	0.807277i	$-0.700940\pi$
$661$	−3.40889e8			−1.18034			−0.590172	+	0.807277i	$0.700940\pi$
$662$	3.78730e7	−	2.45455e8i	0.130544	−	0.846053i
$663$	−4.95032e6	+	1.52423e7i	−0.0169861	+	0.0523009i
$664$	−1.07827e8	−	3.18821e8i	−0.368318	−	1.08904i
$665$	8.19521e8	−	1.08719e6i	2.78673	−	0.00369693i
$666$	−3.51931e8	+	1.49579e6i	−1.19134	+	0.00506346i
$667$	−4.43833e7	−	4.43833e7i	−0.149569	−	0.149569i
$668$	−1.25725e8	+	6.53290e7i	−0.421786	+	0.219168i
$669$	4.52473e8	−	2.30621e8i	1.51117	−	0.770229i
$670$	7.85274e7	+	1.20099e7i	0.261094	+	0.0399315i
$671$	7.28195e7			0.241035
$672$	−1.64160e8	+	5.42031e8i	−0.540953	+	1.78614i
$673$	2.86929e8	+	2.86929e8i	0.941302	+	0.941302i	0.998370	−	0.0570681i	$-0.0181752\pi$
$673$	2.86929e8	+	2.86929e8i	0.941302	+	0.941302i	−0.0570681	+	0.998370i	$0.518175\pi$
$674$	−2.54910e7	+	1.86762e7i	−0.0832546	+	0.0609970i
$675$	2.48259e8	−	1.81528e8i	0.807224	−	0.590245i
$676$	2.51105e7	−	7.94333e7i	0.0812858	−	0.257136i
$677$	3.55587e8	+	3.55587e8i	1.14599	+	1.14599i	0.987335	+	0.158652i	$0.0507148\pi$
$677$	3.55587e8	+	3.55587e8i	1.14599	+	1.14599i	0.158652	+	0.987335i	$0.449285\pi$
$678$	3.89333e8	−	1.28278e8i	1.24920	−	0.411588i
$679$	−8.02102e7			−0.256224
$680$	1.81480e7	+	8.94495e6i	0.0577168	+	0.0284480i
$681$	−1.25398e8	+	6.39141e7i	−0.397054	+	0.202374i
$682$	−1.18377e7	+	7.67203e7i	−0.0373177	+	0.241856i
$683$	1.87516e8	+	1.87516e8i	0.588539	+	0.588539i	0.937236	−	0.348697i	$-0.113376\pi$
$683$	1.87516e8	+	1.87516e8i	0.588539	+	0.588539i	−0.348697	+	0.937236i	$0.613376\pi$
$684$	−2.84049e8	−	3.84261e8i	−0.887615	−	1.20076i
$685$	3.77257e7	−	50047.6i	0.117372	−	0.000155708i
$686$	−7.20710e8	+	5.28033e8i	−2.23248	+	1.63564i
$687$	−2.36205e7	+	7.27288e7i	−0.0728483	+	0.224303i
$688$	1.81997e8	−	3.18107e7i	0.558853	−	0.0976805i
$689$	−3.47519e8			−1.06248
$690$	1.29104e8	+	6.48983e7i	0.392999	+	0.197554i
$691$		−	5.03609e8i		−	1.52637i	−0.646181	−	0.763184i	$-0.723635\pi$
$691$		−	5.03609e8i		−	1.52637i	0.646181	−	0.763184i	$-0.276365\pi$
$692$	4.71633e8	−	2.45069e8i	1.42327	−	0.739555i
$693$	−2.08971e7	−	1.31717e8i	−0.0627893	−	0.395769i
$694$	2.31916e7	−	1.69915e7i	0.0693829	−	0.0508338i
$695$	−3.07624e8	+	3.08442e8i	−0.916361	+	0.918795i
$696$	−1.16024e8	−	1.13250e8i	−0.344128	−	0.335900i
$697$	−6.14686e6	+	6.14686e6i	−0.0181533	+	0.0181533i
$698$	−3.42027e7	+	2.21668e8i	−0.100576	+	0.651834i
$699$	−3.13913e8	+	1.59998e8i	−0.919130	+	0.468471i
$700$	−5.67236e8	+	2.96660e8i	−1.65375	+	0.864898i
$701$		−	5.65385e8i		−	1.64131i	−0.571426	−	0.820654i	$-0.693609\pi$
$701$		−	5.65385e8i		−	1.64131i	0.571426	−	0.820654i	$-0.306391\pi$
$702$	−9.01264e7	+	2.81571e8i	−0.260520	+	0.813911i
$703$	−4.37031e8	+	4.37031e8i	−1.25790	+	1.25790i
$704$	4.54738e7	+	5.95384e7i	0.130330	+	0.170639i
$705$	−1.00841e8	+	3.11901e8i	−0.287785	+	0.890122i
$706$	4.19149e8	−	3.07092e8i	1.19112	−	0.872679i
$707$	5.12169e8	−	5.12169e8i	1.44929	−	1.44929i
$708$	−7.69933e7	+	1.07800e8i	−0.216947	+	0.303752i
$709$		−	3.87903e7i		−	0.108839i	−0.998518	−	0.0544195i	$-0.982669\pi$
$709$		−	3.87903e7i		−	0.108839i	0.998518	−	0.0544195i	$-0.0173308\pi$
$710$	8.43364e7	−	6.19617e7i	0.235635	−	0.173120i
$711$	−1.67907e8	−	1.21925e8i	−0.467155	−	0.339222i
$712$	−6.05181e8	−	2.99286e8i	−1.67666	−	0.829174i
$713$	−1.28489e8	+	1.28489e8i	−0.354485	+	0.354485i
$714$	1.96839e7	−	3.90286e7i	0.0540775	−	0.107223i
$715$	−6.70722e7	+	88979.1i	−0.183495	+	0.000243428i
$716$	1.03173e8	−	3.26372e8i	0.281077	−	0.889147i
$717$	−1.81760e8	+	5.59649e8i	−0.493108	+	1.51830i
$718$	−7.50446e7	+	4.86364e8i	−0.202743	+	1.31398i
$719$		−	5.01971e8i		−	1.35049i	−0.737592	−	0.675246i	$-0.764037\pi$
$719$		−	5.01971e8i		−	1.35049i	0.737592	−	0.675246i	$-0.235963\pi$
$720$	3.35488e8	+	1.63590e8i	0.898835	+	0.438287i
$721$	2.68533e8			0.716459
$722$	−4.57404e8	−	7.05761e7i	−1.21531	−	0.187519i
$723$	5.20295e8	+	1.68979e8i	1.37669	+	0.447114i
$724$	4.98157e8	+	1.57477e8i	1.31265	+	0.414956i
$725$	−486220.	−	1.83255e8i	−0.00127591	−	0.480886i
$726$	3.25911e8	+	1.64372e8i	0.851705	+	0.429554i
$727$	−9.64358e7	−	9.64358e7i	−0.250978	−	0.250978i	0.570394	−	0.821371i	$-0.306791\pi$
$727$	−9.64358e7	−	9.64358e7i	−0.250978	−	0.250978i	−0.821371	+	0.570394i	$0.806791\pi$
$728$	2.72782e8	−	5.51588e8i	0.707002	−	1.42962i
$729$	−1.19432e8	+	3.68552e8i	−0.308274	+	0.951298i
$730$	2.86756e8	+	4.38561e7i	0.737129	+	0.112736i
$731$	−1.42598e7			−0.0365056
$732$	3.58295e8	+	2.55903e8i	0.913498	+	0.652442i
$733$	−4.93212e8	−	4.93212e8i	−1.25234	−	1.25234i	−0.954669	−	0.297669i	$-0.903791\pi$
$733$	−4.93212e8	−	4.93212e8i	−1.25234	−	1.25234i	−0.297669	−	0.954669i	$-0.596209\pi$
$734$	−3.61540e7	−	4.93465e7i	−0.0914258	−	0.124787i
$735$	4.48863e8	+	8.77779e8i	1.13045	+	2.21067i
$736$	3.49825e6	+	1.75332e8i	0.00877440	+	0.439772i
$737$	−1.60536e7	−	1.60536e7i	−0.0401023	−	0.0401023i
$738$	−1.12913e8	+	1.13877e8i	−0.280914	+	0.283313i
$739$	3.91378e8			0.969758			0.484879	−	0.874581i	$-0.338864\pi$
$739$	3.91378e8			0.969758			0.484879	+	0.874581i	$0.338864\pi$
$740$	1.44903e8	−	4.60503e8i	0.357586	−	1.13642i
$741$	2.35772e8	+	4.62580e8i	0.579479	+	1.13693i
$742$	9.36782e8	+	1.44543e8i	2.29312	+	0.353822i
$743$	2.86567e8	+	2.86567e8i	0.698649	+	0.698649i	0.964119	−	0.265470i	$-0.0855271\pi$
$743$	2.86567e8	+	2.86567e8i	0.698649	+	0.698649i	−0.265470	+	0.964119i	$0.585527\pi$
$744$	−3.27856e8	+	3.35888e8i	−0.796095	+	0.815597i
$745$	−5.30217e7	+	5.31625e7i	−0.128228	+	0.128569i
$746$	−4.48521e7	−	6.12185e7i	−0.108036	−	0.147457i
$747$	7.50873e7	+	4.73285e8i	0.180138	+	1.13543i
$748$	−2.66613e6	−	5.13094e6i	−0.00637054	−	0.0122600i
$749$	−9.34196e8			−2.22327
$750$	1.33612e8	+	4.00158e8i	0.316710	+	0.948522i
$751$			8.02077e7i			0.189364i	0.995508	+	0.0946818i	$0.0301834\pi$
$751$			8.02077e7i			0.189364i	−0.995508	+	0.0946818i	$0.969817\pi$
$752$	−3.91884e8	+	6.84963e7i	−0.921517	+	0.161070i
$753$	4.78260e8	+	1.55327e8i	1.12016	+	0.363800i
$754$	1.04114e8	+	1.42105e8i	0.242881	+	0.331508i
$755$	−3.52714e8	−	3.51779e8i	−0.819562	−	0.817390i
$756$	3.60061e8	−	7.21526e8i	0.833317	−	1.66989i
$757$	−1.13386e8	+	1.13386e8i	−0.261380	+	0.261380i	−0.825614	−	0.564235i	$-0.809171\pi$
$757$	−1.13386e8	+	1.13386e8i	−0.261380	+	0.261380i	0.564235	+	0.825614i	$0.309171\pi$
$758$	−2.04097e8	−	3.14915e7i	−0.468628	−	0.0723079i
$759$	−1.87527e7	−	3.67924e7i	−0.0428883	−	0.0841459i
$760$	6.20656e8	−	2.10827e8i	1.41387	−	0.480271i
$761$		−	2.82272e7i		−	0.0640493i	−0.999487	−	0.0320246i	$-0.989804\pi$
$761$		−	2.82272e7i		−	0.0640493i	0.999487	−	0.0320246i	$-0.0101955\pi$
$762$	−8.95401e7	−	2.71761e8i	−0.202373	−	0.614218i
$763$	5.23971e8	−	5.23971e8i	1.17960	−	1.17960i
$764$	−1.01951e8	−	3.22286e7i	−0.228618	−	0.0722706i
$765$	−2.33329e7	−	1.68958e7i	−0.0521176	−	0.0377395i
$766$	−6.49013e7	−	8.85836e7i	−0.144400	−	0.197091i
$767$	1.01778e8	−	1.01778e8i	0.225562	−	0.225562i
$768$	1.45154e7	+	4.52752e8i	0.0320439	+	0.999486i
$769$		−	2.42825e8i		−	0.533966i	−0.963701	−	0.266983i	$-0.913973\pi$
$769$		−	2.42825e8i		−	0.533966i	0.963701	−	0.266983i	$-0.0860268\pi$
$770$	1.80839e8	+	2.76573e7i	0.396113	+	0.0605812i
$771$	1.02490e8	+	2.01082e8i	0.223623	+	0.438744i
$772$	1.49258e7	+	2.87246e7i	0.0324404	+	0.0624312i
$773$	−5.78242e8	+	5.78242e8i	−1.25190	+	1.25190i	−0.297039	+	0.954865i	$0.595999\pi$
$773$	−5.78242e8	+	5.78242e8i	−1.25190	+	1.25190i	−0.954865	+	0.297039i	$0.904001\pi$
$774$	−2.63058e8	+	1.11806e6i	−0.567321	+	0.00241125i
$775$	−5.30521e8	+	1.40760e6i	−1.13972	+	0.00302395i
$776$	−6.07737e7	+	2.05540e7i	−0.130056	+	0.0439856i
$777$	−9.91971e8	−	3.22168e8i	−2.11464	−	0.686783i
$778$	5.99363e7	+	9.24799e6i	0.127277	+	0.0196385i
$779$			2.81629e8i			0.595752i
$780$	−3.30329e8	−	2.35268e8i	−0.696086	−	0.495768i
$781$	−2.99082e7			−0.0627822
$782$	2.06400e6	−	1.33768e7i	0.00431608	−	0.0279725i
$783$	1.35763e8	+	1.86708e8i	0.282810	+	0.388936i
$784$	−6.87749e8	+	9.79091e8i	−1.42719	+	2.03177i
$785$	325229.	+	2.45157e8i	0.000672327	+	0.506798i
$786$	−6.84655e8	−	3.45303e8i	−1.40995	−	0.711104i
$787$	3.21710e8	+	3.21710e8i	0.659995	+	0.659995i	0.955379	−	0.295384i	$-0.0954474\pi$
$787$	3.21710e8	+	3.21710e8i	0.659995	+	0.659995i	−0.295384	+	0.955379i	$0.595447\pi$
$788$	−1.88458e8	−	3.62686e8i	−0.385156	−	0.741229i
$789$	1.60666e8	+	3.15223e8i	0.327109	+	0.641782i
$790$	2.29389e8	−	1.68532e8i	0.465256	−	0.341822i
$791$	1.21482e9			2.45462
$792$	−4.95860e7	−	9.44444e7i	−0.0998121	−	0.190108i
$793$	−3.38278e8	−	3.38278e8i	−0.678351	−	0.678351i
$794$	−3.44536e8	+	2.52427e8i	−0.688293	+	0.504282i
$795$	1.92174e8	−	5.94396e8i	0.382467	−	1.18297i
$796$	1.60344e8	+	5.06881e7i	0.317918	+	0.100500i
$797$	5.11316e8	+	5.11316e8i	1.00998	+	1.00998i	0.999950	+	0.0100335i	$0.00319380\pi$
$797$	5.11316e8	+	5.11316e8i	1.00998	+	1.00998i	0.0100335	+	0.999950i	$0.496806\pi$
$798$	−4.43155e8	−	1.34501e9i	−0.872060	−	2.64677i
$799$	3.07048e7			0.0601957
$800$	−3.53764e8	+	3.70129e8i	−0.690945	+	0.722907i
$801$	7.77843e8	+	5.64827e8i	1.51354	+	1.09905i
$802$	−5.04012e7	+	3.26651e8i	−0.0977053	+	0.633229i
$803$	−5.86223e7	−	5.86223e7i	−0.113218	−	0.113218i
$804$	−2.25731e7	−	1.35404e8i	−0.0434333	−	0.260534i
$805$	3.03204e8	+	3.02400e8i	0.581228	+	0.579688i
$806$	4.11391e8	−	3.01408e8i	0.785687	−	0.575638i
$807$	−8.21614e8	−	2.66840e8i	−1.56332	−	0.507728i
$808$	2.56816e8	−	5.19304e8i	0.486842	−	0.984437i
$809$	6.19730e8			1.17046			0.585230	−	0.810867i	$-0.301004\pi$
$809$	6.19730e8			1.17046			0.585230	+	0.810867i	$0.301004\pi$
$810$	−4.31761e8	−	3.09858e8i	−0.812434	−	0.583053i
$811$		−	1.21420e8i		−	0.227629i	−0.993502	−	0.113815i	$-0.963693\pi$
$811$		−	1.21420e8i		−	0.227629i	0.993502	−	0.113815i	$-0.0363070\pi$
$812$	−2.21547e8	−	4.26365e8i	−0.413807	−	0.796368i
$813$	2.33334e8	−	7.18447e8i	0.434217	−	1.33697i
$814$	−1.11294e8	+	8.15404e7i	−0.206348	+	0.151182i
$815$	−189988.	−	1.43212e8i	−0.000350956	−	0.264549i
$816$	4.91299e6	−	3.46152e7i	0.00904222	−	0.0637083i
$817$	−3.26668e8	+	3.26668e8i	−0.599019	+	0.599019i
$818$	9.67212e7	−	6.26851e8i	0.176710	−	1.14526i
$819$	−5.14807e8	+	7.08959e8i	−0.937115	+	1.29053i
$820$	−1.01689e8	−	1.95066e8i	−0.184430	−	0.353786i
$821$			3.96489e8i			0.716476i	0.933630	+	0.358238i	$0.116622\pi$
$821$			3.96489e8i			0.716476i	−0.933630	+	0.358238i	$0.883378\pi$
$822$	−2.04001e7	−	6.19159e7i	−0.0367296	−	0.111477i
$823$	−5.16923e7	+	5.16923e7i	−0.0927313	+	0.0927313i	−0.751951	−	0.659219i	$-0.770887\pi$
$823$	−5.16923e7	+	5.16923e7i	−0.0927313	+	0.0927313i	0.659219	+	0.751951i	$0.270887\pi$
$824$	2.03462e8	−	6.88119e7i	0.363665	−	0.122993i
$825$	3.69380e7	−	1.14769e8i	0.0657827	−	0.204392i
$826$	−3.16687e8	+	2.32023e8i	−0.561940	+	0.411709i
$827$	−6.18631e8	+	6.18631e8i	−1.09374	+	1.09374i	−0.0986169	+	0.995125i	$0.531442\pi$
$827$	−6.18631e8	+	6.18631e8i	−1.09374	+	1.09374i	−0.995125	+	0.0986169i	$0.968558\pi$
$828$	3.70270e7	−	2.46931e8i	0.0652270	−	0.434996i
$829$		−	9.07220e8i		−	1.59239i	−0.605041	−	0.796194i	$-0.706843\pi$
$829$		−	9.07220e8i		−	1.59239i	0.605041	−	0.796194i	$-0.293157\pi$
$830$	−6.49790e8	−	9.93783e7i	−1.13642	−	0.173803i
$831$	−6.96199e7	+	3.54845e7i	−0.121319	+	0.0618352i
$832$	6.53360e7	−	4.87828e8i	0.113444	−	0.847026i
$833$	6.52999e7	−	6.52999e7i	0.112974	−	0.112974i
$834$	6.72116e8	+	3.38980e8i	1.15863	+	0.584353i
$835$	367113.	+	2.76728e8i	0.000630580	+	0.475329i
$836$	−1.78618e8	−	5.64649e7i	−0.305708	−	0.0966405i
$837$	5.40517e8	−	3.93031e8i	0.921793	−	0.670272i
$838$	−1.68185e8	+	1.09001e9i	−0.285795	+	1.85224i
$839$		−	9.02190e8i		−	1.52761i	−0.645447	−	0.763805i	$-0.723329\pi$
$839$		−	9.02190e8i		−	1.52761i	0.645447	−	0.763805i	$-0.276671\pi$
$840$	7.92591e8	+	7.71588e8i	1.33725	+	1.30181i
$841$	−4.57269e8			−0.768747
$842$	5.89290e8	+	9.09256e7i	0.987171	+	0.152318i
$843$	1.66374e8	−	5.12273e8i	0.277717	−	0.855103i
$844$	−3.47441e7	+	1.09908e8i	−0.0577901	+	0.182811i
$845$	−1.15206e8	−	1.14901e8i	−0.190944	−	0.190438i
$846$	5.66429e8	−	2.40746e6i	0.935479	−	0.00397601i
$847$	7.64908e8	+	7.64908e8i	1.25881	+	1.25881i
$848$	7.46820e8	−	1.30535e8i	1.22470	−	0.214061i
$849$	1.45265e8	−	7.40399e7i	0.237376	−	0.120988i
$850$	3.18149e7	−	2.34394e7i	0.0518053	−	0.0381671i
$851$	−3.22954e8			−0.524025
$852$	−1.47158e8	−	1.05104e8i	−0.237938	−	0.169941i
$853$	5.83414e8	+	5.83414e8i	0.940004	+	0.940004i	0.998299	−	0.0582950i	$-0.0185664\pi$
$853$	5.83414e8	+	5.83414e8i	0.940004	+	0.940004i	−0.0582950	+	0.998299i	$0.518566\pi$
$854$	7.71174e8	+	1.05257e9i	1.23817	+	1.68997i
$855$	−9.21576e8	+	1.47463e8i	−1.47446	+	0.235931i
$856$	−7.07822e8	+	2.39389e8i	−1.12850	+	0.381666i
$857$	−9.88301e6	−	9.88301e6i	−0.0157017	−	0.0157017i	0.699212	−	0.714914i	$-0.253534\pi$
$857$	−9.88301e6	−	9.88301e6i	−0.0157017	−	0.0157017i	−0.714914	+	0.699212i	$0.753534\pi$
$858$	3.62692e7	+	1.10080e8i	0.0574216	+	0.174279i
$859$	7.23659e8			1.14171			0.570853	−	0.821052i	$-0.306613\pi$
$859$	7.23659e8			1.14171			0.570853	+	0.821052i	$0.306613\pi$
$860$	1.08310e8	−	3.44213e8i	0.170284	−	0.541167i
$861$	−4.23425e8	+	2.15815e8i	−0.663388	+	0.338122i
$862$	−7.37133e8	−	1.13737e8i	−1.15086	−	0.177575i
$863$	1.41020e8	+	1.41020e8i	0.219406	+	0.219406i	0.808248	−	0.588842i	$-0.200416\pi$
$863$	1.41020e8	+	1.41020e8i	0.219406	+	0.219406i	−0.588842	+	0.808248i	$0.700416\pi$
$864$	8.79187e7	−	6.38952e8i	0.136314	−	0.990666i
$865$	−1.37715e6	−	1.03809e9i	−0.00212782	−	1.60394i
$866$	1.47418e8	+	2.01210e8i	0.226984	+	0.309810i
$867$	2.00477e8	−	6.17277e8i	0.307614	−	0.947159i
$868$	−1.23432e9	+	6.41376e8i	−1.88742	+	0.980739i
$869$	−8.13482e7			−0.123962
$870$	−3.00630e8	+	9.94940e7i	−0.456535	+	0.151091i
$871$			1.49152e8i			0.225722i
$872$	2.62734e8	−	5.31271e8i	0.396248	−	0.801247i
$873$	9.02178e7	−	1.43132e7i	0.135597	−	0.0215126i
$874$	−2.59158e8	−	3.53724e8i	−0.388177	−	0.529822i
$875$	4.97580e6	+	1.25024e9i	0.00742743	+	1.86625i
$876$	−8.24294e7	−	4.94452e8i	−0.122622	−	0.735549i
$877$	−9.42275e8	+	9.42275e8i	−1.39694	+	1.39694i	−0.588305	+	0.808639i	$0.700205\pi$
$877$	−9.42275e8	+	9.42275e8i	−1.39694	+	1.39694i	−0.808639	+	0.588305i	$0.799795\pi$
$878$	3.28346e8	+	5.06629e7i	0.485120	+	0.0748525i
$879$	−1.96457e8	+	1.00132e8i	−0.289269	+	0.147437i
$880$	1.44105e8	−	2.53848e7i	0.211462	−	0.0372500i
$881$			2.21970e8i			0.324614i	0.986740	+	0.162307i	$0.0518934\pi$
$881$			2.21970e8i			0.324614i	−0.986740	+	0.162307i	$0.948107\pi$
$882$	1.19951e9	−	1.20975e9i	1.74822	−	1.76315i
$883$	−1.44680e7	+	1.44680e7i	−0.0210148	+	0.0210148i	−0.717536	−	0.696521i	$-0.754730\pi$
$883$	−1.44680e7	+	1.44680e7i	−0.0210148	+	0.0210148i	0.696521	+	0.717536i	$0.254730\pi$
$884$	−1.14501e7	+	3.62208e7i	−0.0165750	+	0.0524326i
$885$	1.17798e8	+	2.30362e8i	0.169946	+	0.332339i
$886$	3.56532e8	+	4.86629e8i	0.512622	+	0.699676i
$887$	5.66454e7	−	5.66454e7i	0.0811697	−	0.0811697i	−0.665356	−	0.746526i	$-0.731720\pi$
$887$	5.66454e7	−	5.66454e7i	0.0811697	−	0.0811697i	0.746526	+	0.665356i	$0.231720\pi$
$888$	−8.34153e8	+	1.00936e7i	−1.19126	+	0.0144148i
$889$		−	8.47969e8i		−	1.20691i
$890$	−1.06266e9	+	7.80735e8i	−1.50739	+	1.10747i
$891$	4.70087e7	+	1.44422e8i	0.0664576	+	0.204174i
$892$	1.06820e9	−	5.55059e8i	1.50508	−	0.782068i
$893$	7.03397e8	−	7.03397e8i	0.987748	−	0.987748i
$894$	1.15845e8	+	5.84260e7i	0.162130	+	0.0817699i
$895$	−4.73354e8	−	4.72100e8i	−0.660263	−	0.658514i
$896$	−3.79023e8	+	1.28783e9i	−0.526916	+	1.79033i
$897$	−8.38024e7	+	2.58032e8i	−0.116113	+	0.357516i
$898$	4.10097e8	+	6.32767e7i	0.566314	+	0.0873806i
$899$		−	3.98219e8i		−	0.548078i
$900$	5.85071e8	−	4.34895e8i	0.802566	−	0.596563i
$901$	−5.85147e7			−0.0800001
$902$	−9.58690e6	+	6.21328e7i	−0.0130635	+	0.0846644i
$903$	−7.41469e8	−	2.40811e8i	−1.00700	−	0.327050i
$904$	9.20448e8	−	3.11301e8i	1.24593	−	0.421381i
$905$	7.20588e8	−	7.22503e8i	0.972168	−	0.974751i
$906$	−3.87635e8	+	7.68589e8i	−0.521241	+	1.03350i
$907$	4.62532e8	+	4.62532e8i	0.619897	+	0.619897i	0.945505	−	0.325608i	$-0.105569\pi$
$907$	4.62532e8	+	4.62532e8i	0.619897	+	0.619897i	−0.325608	+	0.945505i	$0.605569\pi$
$908$	−2.96042e8	+	1.53829e8i	−0.395453	+	0.205485i
$909$	−4.84677e8	+	6.67465e8i	−0.645298	+	0.888663i
$910$	−7.11595e8	−	9.68556e8i	−0.944298	−	1.28529i
$911$	−8.34412e8			−1.10363			−0.551817	−	0.833965i	$-0.686065\pi$
$911$	−8.34412e8			−1.10363			−0.551817	+	0.833965i	$0.686065\pi$
$912$	−6.80430e8	−	9.05527e8i	−0.897013	−	1.19376i
$913$	1.32839e8	+	1.32839e8i	0.174547	+	0.174547i
$914$	4.22507e8	−	3.09552e8i	0.553344	−	0.405411i
$915$	7.65656e8	−	3.91527e8i	0.999472	−	0.511092i
$916$	−5.46345e7	+	1.72828e8i	−0.0710854	+	0.224868i
$917$	−1.60687e9	−	1.60687e9i	−2.08388	−	2.08388i
$918$	−1.51753e7	+	4.74106e7i	−0.0196160	+	0.0612840i
$919$	−5.45251e8			−0.702506			−0.351253	−	0.936281i	$-0.614244\pi$
$919$	−5.45251e8			−0.702506			−0.351253	+	0.936281i	$0.614244\pi$
$920$	3.07222e8	+	1.51426e8i	0.394538	+	0.194463i
$921$	5.90303e7	+	1.15816e8i	0.0755607	+	0.148249i
$922$	−5.41426e7	+	3.50899e8i	−0.0690791	+	0.447702i
$923$	1.38937e8	+	1.38937e8i	0.176690	+	0.176690i
$924$	−5.19830e7	−	3.11820e8i	−0.0658940	−	0.395264i
$925$	−6.68495e8	−	6.64957e8i	−0.844642	−	0.840172i
$926$	−5.54621e8	+	4.06346e8i	−0.698495	+	0.511756i
$927$	−3.02037e8	+	4.79185e7i	−0.379158	+	0.0601540i
$928$	−2.77119e8	−	2.66277e8i	−0.346754	−	0.333188i
$929$	1.05938e9			1.32131			0.660653	−	0.750692i	$-0.270280\pi$
$929$	1.05938e9			1.32131			0.660653	+	0.750692i	$0.270280\pi$
$930$	2.88034e8	+	8.70319e8i	0.358092	+	1.08201i
$931$		−	2.99183e9i		−	3.70756i
$932$	−7.41089e8	+	3.85083e8i	−0.915425	+	0.475671i
$933$	8.34285e8	+	2.70955e8i	1.02723	+	0.333621i
$934$	1.75879e8	−	1.28859e8i	0.215861	−	0.158152i
$935$	−1.12935e7	+	14982.2i	−0.0138164	+	1.83291e-5i
$936$	−2.08387e8	+	6.69085e8i	−0.254123	+	0.815931i
$937$	9.06124e8	−	9.06124e8i	1.10146	−	1.10146i	0.107225	−	0.994235i	$-0.465803\pi$
$937$	9.06124e8	−	9.06124e8i	1.10146	−	1.10146i	0.994235	−	0.107225i	$-0.0341966\pi$
$938$	6.20364e7	−	4.02059e8i	0.0751689	−	0.487170i
$939$	−4.90475e8	−	9.62303e8i	−0.592407	−	1.16229i
$940$	−2.33219e8	+	7.41175e8i	−0.280789	+	0.892354i
$941$		−	8.83593e8i		−	1.06043i	−0.847862	−	0.530217i	$-0.822110\pi$
$941$		−	8.83593e8i		−	1.06043i	0.847862	−	0.530217i	$-0.177890\pi$
$942$	4.02354e8	−	1.32568e8i	0.481344	−	0.158594i
$943$	−1.04058e8	+	1.04058e8i	−0.124091	+	0.124091i
$944$	−1.80491e8	+	2.56950e8i	−0.214556	+	0.305445i
$945$	−9.27922e8	−	1.27257e9i	−1.09955	−	1.50795i
$946$	−8.31892e7	+	6.09491e7i	−0.0982638	+	0.0719936i
$947$	−5.75855e8	+	5.75855e8i	−0.678052	+	0.678052i	−0.959559	−	0.281507i	$-0.909166\pi$
$947$	−5.75855e8	+	5.75855e8i	−0.678052	+	0.678052i	0.281507	+	0.959559i	$0.409166\pi$
$948$	−4.00259e8	−	2.85875e8i	−0.469803	−	0.335545i
$949$			5.44653e8i			0.637267i
$950$	1.91870e8	−	1.26579e9i	0.223788	−	1.47635i
$951$	−4.38068e7	−	8.59481e7i	−0.0509331	−	0.0999298i
$952$	4.59306e7	−	9.28755e7i	0.0532342	−	0.107644i
$953$	−1.02308e9	+	1.02308e9i	−1.18204	+	1.18204i	−0.202819	+	0.979216i	$0.565010\pi$
$953$	−1.02308e9	+	1.02308e9i	−1.18204	+	1.18204i	−0.979216	+	0.202819i	$0.934990\pi$
$954$	−1.07945e9	+	4.58794e6i	−1.24325	+	0.00528412i
$955$	−1.47472e8	+	1.47864e8i	−0.169317	+	0.169767i
$956$	−4.20413e8	+	1.32992e9i	−0.481175	+	1.52213i
$957$	8.60739e7	+	2.79547e7i	0.0982054	+	0.0318947i
$958$	−3.51713e7	+	2.27945e8i	−0.0400029	+	0.259259i
$959$		−	1.93194e8i		−	0.219048i
$960$	7.98251e8	+	3.81514e8i	0.902248	+	0.431218i
$961$	−2.65334e8			−0.298966
$962$	8.95801e8	+	1.38219e8i	1.00620	+	0.155254i
$963$	1.05075e9	−	1.66703e8i	1.17658	−	0.186666i
$964$	1.23640e9	+	3.90850e8i	1.38015	+	0.436294i
$965$	6.32245e7	−	83874.8i	0.0703564	−	9.33361e-5i
$966$	3.33223e8	−	6.60702e8i	0.369661	−	0.732950i
$967$	−4.94371e8	−	4.94371e8i	−0.546731	−	0.546731i	0.378763	−	0.925494i	$-0.376350\pi$
$967$	−4.94371e8	−	4.94371e8i	−0.546731	−	0.546731i	−0.925494	+	0.378763i	$0.876350\pi$
$968$	7.75564e8	+	3.83547e8i	0.855051	+	0.422856i
$969$	3.96990e7	+	7.78885e7i	0.0436323	+	0.0856056i
$970$	−1.89435e7	+	1.23863e8i	−0.0207561	+	0.135715i
$971$	7.35588e8			0.803484			0.401742	−	0.915753i	$-0.368405\pi$
$971$	7.35588e8			0.803484			0.401742	+	0.915753i	$0.368405\pi$
$972$	−2.76231e8	+	8.75800e8i	−0.300797	+	0.953688i
$973$	1.57745e9	+	1.57745e9i	1.71244	+	1.71244i
$974$	−1.62299e7	−	2.21522e7i	−0.0175647	−	0.0239740i
$975$	−7.04748e8	+	3.61561e8i	−0.760361	+	0.390093i
$976$	8.54027e8	+	5.99899e8i	0.918591	+	0.645251i
$977$	1.04690e9	+	1.04690e9i	1.12259	+	1.12259i	0.991350	+	0.131244i	$0.0418973\pi$
$977$	1.04690e9	+	1.04690e9i	1.12259	+	1.12259i	0.131244	+	0.991350i	$0.458103\pi$
$978$	−2.35041e8	+	7.74417e7i	−0.251263	+	0.0827862i
$979$	3.76852e8			0.401626
$980$	1.08027e9	+	2.07225e9i	1.14777	+	2.20173i
$981$	−4.95845e8	+	6.82846e8i	−0.525217	+	0.723295i
$982$	−8.58815e8	−	1.32513e8i	−0.906912	−	0.139934i
$983$	−1.09070e9	−	1.09070e9i	−1.14827	−	1.14827i	−0.986893	−	0.161376i	$-0.948407\pi$
$983$	−1.09070e9	−	1.09070e9i	−1.14827	−	1.14827i	−0.161376	−	0.986893i	$-0.551593\pi$
$984$	−2.65518e8	+	2.72023e8i	−0.278682	+	0.285509i
$985$	−7.98294e8	+	1.05903e6i	−0.835322	+	0.00110815i
$986$	1.75305e7	+	2.39274e7i	0.0182879	+	0.0249611i
$987$	1.59657e9	+	5.18526e8i	1.66049	+	0.539286i
$988$	5.67457e8	+	1.09206e9i	0.588386	+	1.13234i
$989$	−2.41399e8			−0.249543
$990$	−2.08337e8	+	1.16187e6i	−0.214714	+	0.00119744i
$991$			6.14718e8i			0.631619i	0.948823	+	0.315810i	$0.102276\pi$
$991$			6.14718e8i			0.631619i	−0.948823	+	0.315810i	$0.897724\pi$
$992$	−7.70868e8	+	8.02255e8i	−0.789668	+	0.821821i
$993$	−2.58919e8	+	7.97222e8i	−0.264433	+	0.814201i
$994$	−3.16734e8	−	4.32309e8i	−0.322504	−	0.440185i
$995$	2.31940e8	−	2.32556e8i	0.235454	−	0.236079i
$996$	1.86785e8	+	1.12043e9i	0.189045	+	1.13398i
$997$	1.01023e9	−	1.01023e9i	1.01938	−	1.01938i	0.0195719	−	0.999808i	$-0.493770\pi$
$997$	1.01023e9	−	1.01023e9i	1.01938	−	1.01938i	0.999808	−	0.0195719i	$-0.00623034\pi$
$998$	5.42093e7	+	8.36434e6i	0.0545359	+	0.00841472i
$999$	1.17323e9	+	1.85351e8i	1.17675	+	0.185908i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.l.a.23.4	✓	136
3.2	odd	2	inner	60.7.l.a.23.65	yes	136
4.3	odd	2	inner	60.7.l.a.23.31	yes	136
5.2	odd	4	inner	60.7.l.a.47.38	yes	136
12.11	even	2	inner	60.7.l.a.23.38	yes	136
15.2	even	4	inner	60.7.l.a.47.31	yes	136
20.7	even	4	inner	60.7.l.a.47.65	yes	136
60.47	odd	4	inner	60.7.l.a.47.4	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.l.a.23.4	✓	136	1.1	even	1	trivial
60.7.l.a.23.31	yes	136	4.3	odd	2	inner
60.7.l.a.23.38	yes	136	12.11	even	2	inner
60.7.l.a.23.65	yes	136	3.2	odd	2	inner
60.7.l.a.47.4	yes	136	60.47	odd	4	inner
60.7.l.a.47.31	yes	136	15.2	even	4	inner
60.7.l.a.47.38	yes	136	5.2	odd	4	inner
60.7.l.a.47.65	yes	136	20.7	even	4	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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.90644 - 1.21994i) q^{2} +(25.6796 + 8.34012i) q^{3} +(61.0235 + 19.2908i) q^{4} +(88.2710 - 88.5055i) q^{5} +(-192.860 - 97.2682i) q^{6} +(-452.639 - 452.639i) q^{7} +(-458.945 - 226.966i) q^{8} +(589.885 + 428.342i) q^{9} +O(q^{10})\)	\(q+(-7.90644 - 1.21994i) q^{2} +(25.6796 + 8.34012i) q^{3} +(61.0235 + 19.2908i) q^{4} +(88.2710 - 88.5055i) q^{5} +(-192.860 - 97.2682i) q^{6} +(-452.639 - 452.639i) q^{7} +(-458.945 - 226.966i) q^{8} +(589.885 + 428.342i) q^{9} +(-805.881 + 592.078i) q^{10} +285.789 q^{11} +(1406.17 + 1004.32i) q^{12} +(-1327.62 - 1327.62i) q^{13} +(3026.57 + 4130.95i) q^{14} +(3004.91 - 1536.60i) q^{15} +(3351.73 + 2354.38i) q^{16} +(-223.542 - 223.542i) q^{17} +(-4141.34 - 4106.28i) q^{18} -10242.0 q^{19} +(7093.94 - 3698.10i) q^{20} +(-7848.53 - 15398.6i) q^{21} +(-2259.57 - 348.645i) q^{22} +(-3784.27 - 3784.27i) q^{23} +(-9892.60 - 9656.05i) q^{24} +(-41.4567 - 15624.9i) q^{25} +(8877.10 + 12116.3i) q^{26} +(11575.6 + 15919.4i) q^{27} +(-18889.9 - 36353.3i) q^{28} +11728.4 q^{29} +(-25632.7 + 8483.20i) q^{30} -33953.5i q^{31} +(-23628.1 - 22703.7i) q^{32} +(7338.95 + 2383.51i) q^{33} +(1494.71 + 2040.13i) q^{34} +(-80015.9 + 106.151i) q^{35} +(27733.8 + 37518.2i) q^{36} +(42670.6 - 42670.6i) q^{37} +(80977.5 + 12494.6i) q^{38} +(-23020.2 - 45165.1i) q^{39} +(-60599.3 + 20584.6i) q^{40} -27497.6i q^{41} +(43268.5 + 131323. i) q^{42} +(31895.0 - 31895.0i) q^{43} +(17439.8 + 5513.08i) q^{44} +(89980.4 - 14397.9i) q^{45} +(25303.5 + 34536.7i) q^{46} +(-68677.9 + 68677.9i) q^{47} +(66435.4 + 88413.4i) q^{48} +292115. i q^{49} +(-18733.7 + 123588. i) q^{50} +(-3876.10 - 7604.84i) q^{51} +(-55405.0 - 106626. i) q^{52} +(130881. - 130881. i) q^{53} +(-72101.0 - 139987. i) q^{54} +(25226.9 - 25293.9i) q^{55} +(105003. + 310470. i) q^{56} +(-263010. - 85419.3i) q^{57} +(-92729.6 - 14307.9i) q^{58} +76661.9i q^{59} +(213012. - 35801.5i) q^{60} +254802. q^{61} +(-41421.2 + 268451. i) q^{62} +(-73120.6 - 460889. i) q^{63} +(159117. + 208330. i) q^{64} +(-234691. + 311.346i) q^{65} +(-55117.2 - 27798.2i) q^{66} +(-56172.9 - 56172.9i) q^{67} +(-9329.02 - 17953.6i) q^{68} +(-65617.3 - 128740. i) q^{69} +(632770. + 96775.3i) q^{70} -104651. q^{71} +(-173506. - 330469. i) q^{72} +(-205125. - 205125. i) q^{73} +(-389428. + 285317. i) q^{74} +(129249. - 401588. i) q^{75} +(-625001. - 197575. i) q^{76} +(-129359. - 129359. i) q^{77} +(126909. + 385178. i) q^{78} -284644. q^{79} +(504236. - 88823.6i) q^{80} +(164487. + 505345. i) q^{81} +(-33545.4 + 217408. i) q^{82} +(464813. + 464813. i) q^{83} +(-181893. - 1.09108e6i) q^{84} +(-39517.0 + 52.4239i) q^{85} +(-291086. + 213266. i) q^{86} +(301180. + 97815.9i) q^{87} +(-131161. - 64864.4i) q^{88} +1.31864e6 q^{89} +(-728989. + 4065.49i) q^{90} +1.20186e6i q^{91} +(-157928. - 303931. i) q^{92} +(283176. - 871912. i) q^{93} +(626780. - 459214. i) q^{94} +(-904069. + 906471. i) q^{95} +(-417409. - 780082. i) q^{96} +(88602.9 - 88602.9i) q^{97} +(356362. - 2.30959e6i) q^{98} +(168583. + 122415. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 4 q^{6}+O(q^{10}) \) 136 * q - 4 * q^6	\( 136 q - 4 q^{6} - 2092 q^{10} - 1460 q^{12} - 8 q^{13} - 932 q^{16} - 12744 q^{18} - 16056 q^{21} + 25444 q^{22} - 8 q^{25} - 52244 q^{28} + 82868 q^{30} - 2920 q^{33} - 69524 q^{36} - 113000 q^{37} + 99944 q^{40} + 19436 q^{42} - 62504 q^{45} + 145936 q^{46} - 82364 q^{48} + 219504 q^{52} - 286152 q^{57} - 351260 q^{58} + 466756 q^{60} + 652976 q^{61} - 61800 q^{66} + 243868 q^{70} - 145560 q^{72} - 316856 q^{73} + 269024 q^{76} + 613272 q^{78} + 1472232 q^{81} - 1652880 q^{82} - 1466984 q^{85} - 1084100 q^{88} + 448368 q^{90} - 2869552 q^{93} - 278860 q^{96} + 2135272 q^{97}+O(q^{100}) \) 136 * q - 4 * q^6 - 2092 * q^10 - 1460 * q^12 - 8 * q^13 - 932 * q^16 - 12744 * q^18 - 16056 * q^21 + 25444 * q^22 - 8 * q^25 - 52244 * q^28 + 82868 * q^30 - 2920 * q^33 - 69524 * q^36 - 113000 * q^37 + 99944 * q^40 + 19436 * q^42 - 62504 * q^45 + 145936 * q^46 - 82364 * q^48 + 219504 * q^52 - 286152 * q^57 - 351260 * q^58 + 466756 * q^60 + 652976 * q^61 - 61800 * q^66 + 243868 * q^70 - 145560 * q^72 - 316856 * q^73 + 269024 * q^76 + 613272 * q^78 + 1472232 * q^81 - 1652880 * q^82 - 1466984 * q^85 - 1084100 * q^88 + 448368 * q^90 - 2869552 * q^93 - 278860 * q^96 + 2135272 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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