LMFDB - Embedded newform 42.12.f.a.5.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [42,12,Mod(5,42)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("42.5"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	42.f (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$32.2704135835$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.8
Character	$\chi$	$=$	42.5
Dual form			42.12.f.a.17.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-27.7128 - 16.0000i) q^{2} +(-13.7199 - 420.665i) q^{3} +(512.000 + 886.810i) q^{4} +(5294.36 - 9170.11i) q^{5} +(-6350.42 + 11877.3i) q^{6} +(18339.4 + 40509.2i) q^{7} -32768.0i q^{8} +(-176771. + 11543.0i) q^{9} +(-293443. + 169420. i) q^{10} +(-264480. + 152698. i) q^{11} +(366025. - 227547. i) q^{12} -608159. i q^{13} +(139912. - 1.41605e6i) q^{14} +(-3.93018e6 - 2.10134e6i) q^{15} +(-524288. + 908093. i) q^{16} +(1.67187e6 + 2.89576e6i) q^{17} +(5.08350e6 + 2.50844e6i) q^{18} +(-1.49324e7 - 8.62124e6i) q^{19} +1.08429e7 q^{20} +(1.67892e7 - 8.27050e6i) q^{21} +9.77265e6 q^{22} +(-4.23940e7 - 2.44762e7i) q^{23} +(-1.37843e7 + 449575. i) q^{24} +(-3.16465e7 - 5.48134e7i) q^{25} +(-9.73055e6 + 1.68538e7i) q^{26} +(7.28100e6 + 7.42027e7i) q^{27} +(-2.65342e7 + 3.70042e7i) q^{28} +3.91221e7i q^{29} +(7.52949e7 + 1.21117e8i) q^{30} +(9.40293e7 - 5.42878e7i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(6.78632e7 + 1.09162e8i) q^{33} -1.07000e8i q^{34} +(4.68569e8 + 4.62965e7i) q^{35} +(-1.00743e8 - 1.50852e8i) q^{36} +(-3.92833e8 + 6.80407e8i) q^{37} +(2.75880e8 + 4.77838e8i) q^{38} +(-2.55831e8 + 8.34390e6i) q^{39} +(-3.00486e8 - 1.73486e8i) q^{40} -9.46696e8 q^{41} +(-5.97603e8 - 3.94278e7i) q^{42} -4.57397e8 q^{43} +(-2.70828e8 - 1.56362e8i) q^{44} +(-8.30037e8 + 1.68212e9i) q^{45} +(7.83238e8 + 1.35661e9i) q^{46} +(-6.01188e8 + 1.04129e9i) q^{47} +(3.89196e8 + 2.08090e8i) q^{48} +(-1.30466e9 + 1.48583e9i) q^{49} +2.02538e9i q^{50} +(1.19521e9 - 7.43025e8i) q^{51} +(5.39322e8 - 3.11378e8i) q^{52} +(3.86732e9 - 2.23280e9i) q^{53} +(9.85467e8 - 2.17286e9i) q^{54} +3.23375e9i q^{55} +(1.32741e9 - 6.00944e8i) q^{56} +(-3.42178e9 + 6.39983e9i) q^{57} +(6.25954e8 - 1.08418e9i) q^{58} +(2.02250e9 + 3.50308e9i) q^{59} +(-1.48763e8 - 4.56121e9i) q^{60} +(6.17240e9 + 3.56363e9i) q^{61} -3.47442e9 q^{62} +(-3.70946e9 - 6.94914e9i) q^{63} -1.07374e9 q^{64} +(-5.57689e9 - 3.21982e9i) q^{65} +(-1.34080e8 - 4.11101e9i) q^{66} +(-1.50560e9 - 2.60778e9i) q^{67} +(-1.71199e9 + 2.96526e9i) q^{68} +(-9.71462e9 + 1.81695e10i) q^{69} +(-1.22446e10 - 8.78011e9i) q^{70} -1.79670e10i q^{71} +(3.78240e8 + 5.79242e9i) q^{72} +(7.94868e9 - 4.58917e9i) q^{73} +(2.17730e10 - 1.25707e10i) q^{74} +(-2.26239e10 + 1.40646e10i) q^{75} -1.76563e10i q^{76} +(-1.10361e10 - 7.91350e9i) q^{77} +(7.22330e9 + 3.86207e9i) q^{78} +(2.41511e10 - 4.18309e10i) q^{79} +(5.55154e9 + 9.61555e9i) q^{80} +(3.11146e10 - 4.08092e9i) q^{81} +(2.62356e10 + 1.51471e10i) q^{82} -6.33073e10 q^{83} +(1.59304e10 + 1.06543e10i) q^{84} +3.54059e10 q^{85} +(1.26758e10 + 7.31836e9i) q^{86} +(1.64573e10 - 5.36753e8i) q^{87} +(5.00360e9 + 8.66649e9i) q^{88} +(-2.33441e10 + 4.04332e10i) q^{89} +(4.99165e10 - 3.33356e10i) q^{90} +(2.46360e10 - 1.11533e10i) q^{91} -5.01272e10i q^{92} +(-2.41271e10 - 3.88100e10i) q^{93} +(3.33212e10 - 1.92380e10i) q^{94} +(-1.58115e11 + 9.12879e10i) q^{95} +(-7.45627e9 - 1.19939e10i) q^{96} +6.38508e10i q^{97} +(5.99291e10 - 2.03018e10i) q^{98} +(4.49897e10 - 3.00453e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30720 q^{4} - 95298 q^{7} - 91434 q^{9} + 245184 q^{10} - 8480820 q^{15} - 31457280 q^{16} + 12170496 q^{18} + 1649724 q^{19} + 43254216 q^{21} + 20705664 q^{22} + 4521984 q^{24} - 336132444 q^{25}+ \cdots + 288758042496 q^{99}+O(q^{100}) $ 60 * q + 30720 * q^4 - 95298 * q^7 - 91434 * q^9 + 245184 * q^10 - 8480820 * q^15 - 31457280 * q^16 + 12170496 * q^18 + 1649724 * q^19 + 43254216 * q^21 + 20705664 * q^22 + 4521984 * q^24 - 336132444 * q^25 + 28121088 * q^28 - 77109120 * q^30 - 275992974 * q^31 + 1056712914 * q^33 - 187256832 * q^36 + 555437556 * q^37 - 563926680 * q^39 + 251068416 * q^40 + 1167043776 * q^42 + 2546594304 * q^43 + 544480776 * q^45 - 452472192 * q^46 - 1309143414 * q^49 + 2007979044 * q^51 + 3219419136 * q^52 - 9840998592 * q^54 + 17053196256 * q^57 + 12235419456 * q^58 - 4342179840 * q^60 - 3056592000 * q^61 - 42499692960 * q^63 - 64424509440 * q^64 + 48796070400 * q^66 + 27979853436 * q^67 - 4966503360 * q^70 - 12462587904 * q^72 - 105678747168 * q^73 + 173211633504 * q^75 - 16600538880 * q^78 - 27787555926 * q^79 - 71399556486 * q^81 + 31231064832 * q^82 - 25272410112 * q^84 + 12868048152 * q^85 + 137017459998 * q^87 + 10601299968 * q^88 + 333571182180 * q^91 - 14607989424 * q^93 - 430917051648 * q^94 + 4630511616 * q^96 + 288758042496 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−27.7128	−	16.0000i	−0.612372	−	0.353553i
$2$	−27.7128	−	16.0000i	−0.612372	−	0.353553i
$3$	−13.7199	−	420.665i	−0.0325976	−	0.999469i
$3$	−13.7199	−	420.665i	−0.0325976	−	0.999469i
$4$	512.000	+	886.810i	0.250000	+	0.433013i
$5$	5294.36	−	9170.11i	0.757668	−	1.31232i	−0.186370	−	0.982480i	$-0.559672\pi$
$5$	5294.36	−	9170.11i	0.757668	−	1.31232i	0.944037	−	0.329839i	$-0.106994\pi$
$6$	−6350.42	+	11877.3i	−0.333404	+	0.623572i
$7$	18339.4	+	40509.2i	0.412425	+	0.910992i
$7$	18339.4	+	40509.2i	0.412425	+	0.910992i
$8$		−	32768.0i		−	0.353553i
$9$	−176771.	+	11543.0i	−0.997875	+	0.0651605i
$10$	−293443.	+	169420.i	−0.927950	+	0.535752i
$11$	−264480.	+	152698.i	−0.495146	+	0.285873i	−0.726707	−	0.686948i	$-0.758950\pi$
$11$	−264480.	+	152698.i	−0.495146	+	0.285873i	0.231561	+	0.972820i	$0.425617\pi$
$12$	366025.	−	227547.i	0.424633	−	0.263982i
$13$		−	608159.i		−	0.454286i	−0.973861	−	0.227143i	$-0.927062\pi$
$13$		−	608159.i		−	0.454286i	0.973861	−	0.227143i	$-0.0729384\pi$
$14$	139912.	−	1.41605e6i	0.0695264	−	0.703680i
$15$	−3.93018e6	−	2.10134e6i	−1.33632	−	0.714487i
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	1.67187e6	+	2.89576e6i	0.285583	+	0.494645i	0.972750	−	0.231854i	$-0.0744793\pi$
$17$	1.67187e6	+	2.89576e6i	0.285583	+	0.494645i	−0.687167	+	0.726499i	$0.741146\pi$
$18$	5.08350e6	+	2.50844e6i	0.634109	+	0.312900i
$19$	−1.49324e7	−	8.62124e6i	−1.38352	−	0.798776i	−0.390946	−	0.920414i	$-0.627852\pi$
$19$	−1.49324e7	−	8.62124e6i	−1.38352	−	0.798776i	−0.992575	+	0.121638i	$0.961185\pi$
$20$	1.08429e7			0.757668
$21$	1.67892e7	−	8.27050e6i	0.897063	−	0.441902i
$22$	9.77265e6			0.404285
$23$	−4.23940e7	−	2.44762e7i	−1.37341	−	0.792940i	−0.382057	−	0.924139i	$-0.624784\pi$
$23$	−4.23940e7	−	2.44762e7i	−1.37341	−	0.792940i	−0.991356	+	0.131198i	$0.958118\pi$
$24$	−1.37843e7	+	449575.i	−0.353365	+	0.0115250i
$25$	−3.16465e7	−	5.48134e7i	−0.648120	−	1.12258i
$26$	−9.73055e6	+	1.68538e7i	−0.160614	+	0.278192i
$27$	7.28100e6	+	7.42027e7i	0.0976541	+	0.995220i
$28$	−2.65342e7	+	3.70042e7i	−0.291365	+	0.406333i
$29$			3.91221e7i			0.354188i	0.984194	+	0.177094i	$0.0566696\pi$
$29$			3.91221e7i			0.354188i	−0.984194	+	0.177094i	$0.943330\pi$
$30$	7.52949e7	+	1.21117e8i	0.565716	+	0.909992i
$31$	9.40293e7	−	5.42878e7i	0.589894	−	0.340575i	−0.175162	−	0.984540i	$-0.556045\pi$
$31$	9.40293e7	−	5.42878e7i	0.589894	−	0.340575i	0.765056	+	0.643964i	$0.222711\pi$
$32$	2.90590e7	−	1.67772e7i	0.153093	−	0.0883883i
$33$	6.78632e7	+	1.09162e8i	0.301861	+	0.485564i
$34$		−	1.07000e8i		−	0.403876i
$35$	4.68569e8	+	4.62965e7i	1.50799	+	0.148996i
$36$	−1.00743e8	−	1.50852e8i	−0.277684	−	0.415802i
$37$	−3.92833e8	+	6.80407e8i	−0.931319	+	1.61309i	−0.150250	+	0.988648i	$0.548008\pi$
$37$	−3.92833e8	+	6.80407e8i	−0.931319	+	1.61309i	−0.781069	+	0.624444i	$0.785326\pi$
$38$	2.75880e8	+	4.77838e8i	0.564820	+	0.978296i
$39$	−2.55831e8	+	8.34390e6i	−0.454044	+	0.0148086i
$40$	−3.00486e8	−	1.73486e8i	−0.463975	−	0.267876i
$41$	−9.46696e8			−1.27614			−0.638071	−	0.769977i	$-0.720268\pi$
$41$	−9.46696e8			−1.27614			−0.638071	+	0.769977i	$0.720268\pi$
$42$	−5.97603e8	−	3.94278e7i	−0.705573	−	0.0465512i
$43$	−4.57397e8			−0.474479			−0.237240	−	0.971451i	$-0.576243\pi$
$43$	−4.57397e8			−0.474479			−0.237240	+	0.971451i	$0.576243\pi$
$44$	−2.70828e8	−	1.56362e8i	−0.247573	−	0.142936i
$45$	−8.30037e8	+	1.68212e9i	−0.670546	+	1.35890i
$46$	7.83238e8	+	1.35661e9i	0.560694	+	0.971150i
$47$	−6.01188e8	+	1.04129e9i	−0.382359	+	0.662266i	−0.991399	−	0.130874i	$-0.958222\pi$
$47$	−6.01188e8	+	1.04129e9i	−0.382359	+	0.662266i	0.609040	+	0.793140i	$0.291555\pi$
$48$	3.89196e8	+	2.08090e8i	0.220466	+	0.117876i
$49$	−1.30466e9	+	1.48583e9i	−0.659811	+	0.751431i
$50$			2.02538e9i			0.916581i
$51$	1.19521e9	−	7.43025e8i	0.485073	−	0.301556i
$52$	5.39322e8	−	3.11378e8i	0.196711	−	0.113571i
$53$	3.86732e9	−	2.23280e9i	1.27026	−	0.733386i	0.295224	−	0.955428i	$-0.404606\pi$
$53$	3.86732e9	−	2.23280e9i	1.27026	−	0.733386i	0.975037	+	0.222042i	$0.0712722\pi$
$54$	9.85467e8	−	2.17286e9i	0.292063	−	0.643971i
$55$			3.23375e9i			0.866386i
$56$	1.32741e9	−	6.00944e8i	0.322084	−	0.145814i
$57$	−3.42178e9	+	6.39983e9i	−0.753252	+	1.40882i
$58$	6.25954e8	−	1.08418e9i	0.125224	−	0.216895i
$59$	2.02250e9	+	3.50308e9i	0.368301	+	0.637916i	0.989300	−	0.145895i	$-0.0466063\pi$
$59$	2.02250e9	+	3.50308e9i	0.368301	+	0.637916i	−0.620999	+	0.783811i	$0.713273\pi$
$60$	−1.48763e8	−	4.56121e9i	−0.0246981	−	0.757265i
$61$	6.17240e9	+	3.56363e9i	0.935706	+	0.540230i	0.888612	−	0.458660i	$-0.151670\pi$
$61$	6.17240e9	+	3.56363e9i	0.935706	+	0.540230i	0.0470946	+	0.998890i	$0.485004\pi$
$62$	−3.47442e9			−0.481646
$63$	−3.70946e9	−	6.94914e9i	−0.470909	−	0.882182i
$64$	−1.07374e9			−0.125000
$65$	−5.57689e9	−	3.21982e9i	−0.596168	−	0.344197i
$66$	−1.34080e8	−	4.11101e9i	−0.0131787	−	0.404070i
$67$	−1.50560e9	−	2.60778e9i	−0.136238	−	0.235971i	0.789832	−	0.613324i	$-0.210168\pi$
$67$	−1.50560e9	−	2.60778e9i	−0.136238	−	0.235971i	−0.926070	+	0.377353i	$0.876835\pi$
$68$	−1.71199e9	+	2.96526e9i	−0.142792	+	0.247322i
$69$	−9.71462e9	+	1.81695e10i	−0.747749	+	1.39853i
$70$	−1.22446e10	−	8.78011e9i	−0.870775	−	0.624397i
$71$		−	1.79670e10i		−	1.18183i	−0.806734	−	0.590914i	$-0.798767\pi$
$71$		−	1.79670e10i		−	1.18183i	0.806734	−	0.590914i	$-0.201233\pi$
$72$	3.78240e8	+	5.79242e9i	0.0230377	+	0.352802i
$73$	7.94868e9	−	4.58917e9i	0.448766	−	0.259095i	−0.258543	−	0.966000i	$-0.583242\pi$
$73$	7.94868e9	−	4.58917e9i	0.448766	−	0.259095i	0.707309	+	0.706905i	$0.249909\pi$
$74$	2.17730e10	−	1.25707e10i	1.14063	−	0.658542i
$75$	−2.26239e10	+	1.40646e10i	−1.10085	+	0.684369i
$76$		−	1.76563e10i		−	0.798776i
$77$	−1.10361e10	−	7.91350e9i	−0.464638	−	0.333173i
$78$	7.22330e9	+	3.86207e9i	0.283280	+	0.151460i
$79$	2.41511e10	−	4.18309e10i	0.883054	−	1.52949i	0.0351252	−	0.999383i	$-0.488817\pi$
$79$	2.41511e10	−	4.18309e10i	0.883054	−	1.52949i	0.847928	−	0.530111i	$-0.177850\pi$
$80$	5.55154e9	+	9.61555e9i	0.189417	+	0.328080i
$81$	3.11146e10	−	4.08092e9i	0.991508	−	0.130044i
$82$	2.62356e10	+	1.51471e10i	0.781475	+	0.451185i
$83$	−6.33073e10			−1.76410			−0.882052	−	0.471153i	$-0.843838\pi$
$83$	−6.33073e10			−1.76410			−0.882052	+	0.471153i	$0.843838\pi$
$84$	1.59304e10	+	1.06543e10i	0.415615	+	0.277964i
$85$	3.54059e10			0.865509
$86$	1.26758e10	+	7.31836e9i	0.290558	+	0.167754i
$87$	1.64573e10	−	5.36753e8i	0.353999	−	0.0115456i
$88$	5.00360e9	+	8.66649e9i	0.101071	+	0.175061i
$89$	−2.33441e10	+	4.04332e10i	−0.443131	+	0.767526i	−0.997920	−	0.0644654i	$-0.979466\pi$
$89$	−2.33441e10	+	4.04332e10i	−0.443131	+	0.767526i	0.554789	+	0.831991i	$0.312799\pi$
$90$	4.99165e10	−	3.33356e10i	0.891068	−	0.595079i
$91$	2.46360e10	−	1.11533e10i	0.413850	−	0.187359i
$92$		−	5.01272e10i		−	0.792940i
$93$	−2.41271e10	−	3.88100e10i	−0.359624	−	0.578479i
$94$	3.33212e10	−	1.92380e10i	0.468293	−	0.270369i
$95$	−1.58115e11	+	9.12879e10i	−2.09650	+	1.21041i
$96$	−7.45627e9	−	1.19939e10i	−0.0933318	−	0.150131i
$97$			6.38508e10i			0.754956i	0.926019	+	0.377478i	$0.123209\pi$
$97$			6.38508e10i			0.754956i	−0.926019	+	0.377478i	$0.876791\pi$
$98$	5.99291e10	−	2.03018e10i	0.669721	−	0.226877i
$99$	4.49897e10	−	3.00453e10i	0.475466	−	0.317529i
$100$	3.24060e10	−	5.61289e10i	0.324060	−	0.561289i
$101$	−3.57989e10	−	6.20056e10i	−0.338924	−	0.587034i	0.645306	−	0.763924i	$-0.276730\pi$
$101$	−3.57989e10	−	6.20056e10i	−0.338924	−	0.587034i	−0.984231	+	0.176890i	$0.943396\pi$
$102$	−4.50109e10	+	1.46803e9i	−0.403661	+	0.0131654i
$103$	7.95809e9	+	4.59461e9i	0.0676401	+	0.0390520i	0.533439	−	0.845839i	$-0.320900\pi$
$103$	7.95809e9	+	4.59461e9i	0.0676401	+	0.0390520i	−0.465799	+	0.884891i	$0.654233\pi$
$104$	−1.99282e10			−0.160614
$105$	1.30466e10	−	1.97746e11i	0.0997597	−	1.51205i
$106$	−1.42899e11			−1.03716
$107$	4.79003e10	+	2.76552e10i	0.330162	+	0.190619i	0.655913	−	0.754836i	$-0.272284\pi$
$107$	4.79003e10	+	2.76552e10i	0.330162	+	0.190619i	−0.325751	+	0.945456i	$0.605617\pi$
$108$	−6.20759e10	+	4.44487e10i	−0.406530	+	0.291091i
$109$	5.57927e10	+	9.66358e10i	0.347322	+	0.601579i	0.985773	−	0.168084i	$-0.0537579\pi$
$109$	5.57927e10	+	9.66358e10i	0.347322	+	0.601579i	−0.638451	+	0.769662i	$0.720425\pi$
$110$	5.17400e10	−	8.96163e10i	0.306314	−	0.530551i
$111$	2.91613e11	+	1.55916e11i	1.64259	+	0.878241i
$112$	−4.64012e10	−	4.58463e9i	−0.248789	−	0.0245813i
$113$		−	2.51334e11i		−	1.28328i	−0.767007	−	0.641639i	$-0.778255\pi$
$113$		−	2.51334e11i		−	1.28328i	0.767007	−	0.641639i	$-0.221745\pi$
$114$	1.97224e11	−	1.22609e11i	0.959365	−	0.596410i
$115$	−4.48898e11	+	2.59172e11i	−2.08118	+	1.20157i
$116$	−3.46939e10	+	2.00305e10i	−0.153368	+	0.0885469i
$117$	7.01997e9	+	1.07505e11i	0.0296015	+	0.453320i
$118$		−	1.29440e11i		−	0.520856i
$119$	−8.66439e10	+	1.20832e11i	−0.332836	+	0.464168i
$120$	−6.88567e10	+	1.28784e11i	−0.252609	+	0.472460i
$121$	−9.60226e10	+	1.66316e11i	−0.336554	+	0.582928i
$122$	−1.14036e11	−	1.97517e11i	−0.382001	−	0.661644i
$123$	1.29886e10	+	3.98242e11i	0.0415991	+	1.27546i
$124$	9.62860e10	+	5.55908e10i	0.294947	+	0.170288i
$125$	−1.53165e11			−0.448904
$126$	−8.38680e9	+	2.51932e11i	−0.0235266	+	0.706715i
$127$	−3.30288e11			−0.887100			−0.443550	−	0.896250i	$-0.646281\pi$
$127$	−3.30288e11			−0.887100			−0.443550	+	0.896250i	$0.646281\pi$
$128$	2.97564e10	+	1.71799e10i	0.0765466	+	0.0441942i
$129$	6.27546e9	+	1.92411e11i	0.0154669	+	0.474227i
$130$	1.03034e11	+	1.78460e11i	0.243384	+	0.421554i
$131$	−1.40328e11	+	2.43056e11i	−0.317799	+	0.550445i	−0.980029	−	0.198857i	$-0.936277\pi$
$131$	−1.40328e11	+	2.43056e11i	−0.317799	+	0.550445i	0.662229	+	0.749301i	$0.269611\pi$
$132$	−6.20604e10	+	1.16073e11i	−0.134790	+	0.252101i
$133$	7.53883e10	−	7.63008e11i	0.157080	−	1.58981i
$134$			9.63584e10i			0.192670i
$135$	7.18995e11	+	3.26089e11i	1.38004	+	0.625893i
$136$	9.48883e10	−	5.47838e10i	0.174883	−	0.100969i
$137$	−2.73382e11	+	1.57837e11i	−0.483957	+	0.279413i	−0.722064	−	0.691826i	$-0.756807\pi$
$137$	−2.73382e11	+	1.57837e11i	−0.483957	+	0.279413i	0.238107	+	0.971239i	$0.423473\pi$
$138$	5.59931e11	−	3.48093e11i	0.952356	−	0.592053i
$139$			1.34532e10i			0.0219910i	0.999940	+	0.0109955i	$0.00350005\pi$
$139$			1.34532e10i			0.0219910i	−0.999940	+	0.0109955i	$0.996500\pi$
$140$	1.98851e11	+	4.39235e11i	0.312481	+	0.690229i
$141$	4.46281e11	+	2.38612e11i	0.674378	+	0.360568i
$142$	−2.87472e11	+	4.97916e11i	−0.417839	+	0.723719i
$143$	9.28646e10	+	1.60846e11i	0.129868	+	0.224938i
$144$	8.21966e10	−	1.66576e11i	0.110627	−	0.224191i
$145$	3.58754e11	+	2.07127e11i	0.464807	+	0.268356i
$146$	−2.93707e11			−0.366416
$147$	6.42934e11	+	5.28440e11i	0.772540	+	0.634966i
$148$	−8.04522e11			−0.931319
$149$	−8.61099e11	−	4.97156e11i	−0.960569	−	0.554585i	−0.0642208	−	0.997936i	$-0.520456\pi$
$149$	−8.61099e11	−	4.97156e11i	−0.960569	−	0.554585i	−0.896348	+	0.443351i	$0.853790\pi$
$150$	8.52004e11	−	2.77880e10i	0.916094	−	0.0298783i
$151$	−3.12591e11	−	5.41424e11i	−0.324044	−	0.561260i	0.657275	−	0.753651i	$-0.271709\pi$
$151$	−3.12591e11	−	5.41424e11i	−0.324044	−	0.561260i	−0.981318	+	0.192391i	$0.938376\pi$
$152$	−2.82501e11	+	4.89306e11i	−0.282410	+	0.489148i
$153$	−3.28963e11	−	4.92587e11i	−0.317208	−	0.474985i
$154$	1.79224e11	+	3.95882e11i	0.166737	+	0.368300i
$155$		−	1.14968e12i		−	1.03217i
$156$	−1.38385e11	−	2.22602e11i	−0.119923	−	0.192905i
$157$	2.36349e11	−	1.36456e11i	0.197745	−	0.114168i	−0.397858	−	0.917447i	$-0.630246\pi$
$157$	2.36349e11	−	1.36456e11i	0.197745	−	0.114168i	0.595603	+	0.803279i	$0.296913\pi$
$158$	−1.33859e12	+	7.72834e11i	−1.08152	+	0.624413i
$159$	−9.92319e11	−	1.59621e12i	−0.774404	−	1.24568i
$160$		−	3.55299e11i		−	0.267876i
$161$	2.14032e11	−	2.16622e12i	0.155932	−	1.57820i
$162$	−9.27567e11	−	3.84740e11i	−0.653150	−	0.270916i
$163$	−5.64117e11	+	9.77080e11i	−0.384006	+	0.665117i	−0.991631	−	0.129107i	$-0.958789\pi$
$163$	−5.64117e11	+	9.77080e11i	−0.384006	+	0.665117i	0.607625	+	0.794224i	$0.292122\pi$
$164$	−4.84708e11	−	8.39539e11i	−0.319036	−	0.552586i
$165$	1.36032e12	−	4.43668e10i	0.865926	−	0.0282421i
$166$	1.75442e12	+	1.01292e12i	1.08029	+	0.623705i
$167$	−1.56850e12			−0.934423			−0.467211	−	0.884146i	$-0.654741\pi$
$167$	−1.56850e12			−0.934423			−0.467211	+	0.884146i	$0.654741\pi$
$168$	−2.71008e11	−	5.50148e11i	−0.156236	−	0.317160i
$169$	1.42230e12			0.793625
$170$	−9.81197e11	−	5.66495e11i	−0.530014	−	0.306004i
$171$	2.73913e12	+	1.35162e12i	1.43263	+	0.706927i
$172$	−2.34187e11	−	4.05624e11i	−0.118620	−	0.205455i
$173$	9.11255e11	−	1.57834e12i	0.447081	−	0.774367i	−0.551114	−	0.834430i	$-0.685797\pi$
$173$	9.11255e11	−	1.57834e12i	0.447081	−	0.774367i	0.998195	+	0.0600632i	$0.0191302\pi$
$174$	−4.64666e11	−	2.48442e11i	−0.220861	−	0.118087i
$175$	1.64007e12	−	2.28722e12i	0.755357	−	1.05341i
$176$		−	3.20230e11i		−	0.142936i
$177$	1.44587e12	−	8.98857e11i	0.625571	−	0.388900i
$178$	1.29386e12	−	7.47012e11i	0.542723	−	0.313341i
$179$	3.09428e11	−	1.78648e11i	0.125854	−	0.0726620i	−0.435751	−	0.900067i	$-0.643517\pi$
$179$	3.09428e11	−	1.78648e11i	0.125854	−	0.0726620i	0.561605	+	0.827405i	$0.310184\pi$
$180$	−1.91670e12	+	1.25159e11i	−0.756057	+	0.0493700i
$181$		−	2.65702e12i		−	1.01663i	−0.861171	−	0.508316i	$-0.830268\pi$
$181$		−	2.65702e12i		−	1.01663i	0.861171	−	0.508316i	$-0.169732\pi$
$182$	−8.61186e11	−	8.50887e10i	−0.319672	−	0.0315849i
$183$	1.41441e12	−	2.64540e12i	0.509442	−	0.952819i
$184$	−8.02035e11	+	1.38917e12i	−0.280347	+	0.485575i
$185$	4.15960e12	+	7.20464e12i	1.41126	+	2.44438i
$186$	4.76688e10	+	1.46157e12i	0.0157005	+	0.481390i
$187$	−8.84352e11	−	5.10581e11i	−0.282811	−	0.163281i
$188$	−1.23123e12			−0.382359
$189$	−2.87236e12	+	1.65578e12i	−0.866362	+	0.499416i
$190$	5.84243e12			1.71178
$191$	−3.73091e12	−	2.15404e12i	−1.06202	−	0.613155i	−0.136026	−	0.990705i	$-0.543433\pi$
$191$	−3.73091e12	−	2.15404e12i	−1.06202	−	0.613155i	−0.925989	+	0.377550i	$0.876767\pi$
$192$	1.47317e10	+	4.51685e11i	0.00407469	+	0.124934i
$193$	−1.30988e12	−	2.26878e12i	−0.352100	−	0.609855i	0.634517	−	0.772909i	$-0.281199\pi$
$193$	−1.30988e12	−	2.26878e12i	−0.352100	−	0.609855i	−0.986617	+	0.163054i	$0.947866\pi$
$194$	1.02161e12	−	1.76948e12i	0.266917	−	0.462314i
$195$	−1.27795e12	+	2.39017e12i	−0.324581	+	0.607071i
$196$	−1.98563e12	−	3.96245e11i	−0.490332	−	0.0978488i
$197$		−	9.50542e10i		−	0.0228248i	−0.999935	−	0.0114124i	$-0.996367\pi$
$197$		−	9.50542e10i		−	0.0228248i	0.999935	−	0.0114124i	$-0.00363276\pi$
$198$	−1.72752e12	+	1.12806e11i	−0.403426	+	0.0263434i
$199$	4.34281e12	−	2.50732e12i	0.986459	−	0.569532i	0.0822451	−	0.996612i	$-0.473791\pi$
$199$	4.34281e12	−	2.50732e12i	0.986459	−	0.569532i	0.904214	+	0.427080i	$0.140458\pi$
$200$	−1.79612e12	+	1.03699e12i	−0.396891	+	0.229145i
$201$	−1.07634e12	+	6.69131e11i	−0.231405	+	0.143858i
$202$			2.29113e12i			0.479311i
$203$	−1.58480e12	+	7.17474e11i	−0.322662	+	0.146076i
$204$	1.27087e12	+	6.79492e11i	0.251846	+	0.134654i
$205$	−5.01215e12	+	8.68130e12i	−0.966892	+	1.67471i
$206$	−1.47027e11	−	2.54659e11i	−0.0276140	−	0.0478288i
$207$	7.77654e12	+	3.83731e12i	1.42216	+	0.701763i
$208$	5.52266e11	+	3.18851e11i	0.0983557	+	0.0567857i
$209$	5.26577e12			0.913393
$210$	−3.52549e12	+	5.27134e12i	−0.595680	+	0.890666i
$211$	−9.43762e12			−1.55349			−0.776746	−	0.629814i	$-0.783131\pi$
$211$	−9.43762e12			−1.55349			−0.776746	+	0.629814i	$0.783131\pi$
$212$	3.96014e12	+	2.28639e12i	0.635131	+	0.366693i
$213$	−7.55808e12	+	2.46506e11i	−1.18120	+	0.0385247i
$214$	−8.84968e11	−	1.53281e12i	−0.134788	−	0.233460i
$215$	−2.42163e12	+	4.19438e12i	−0.359497	+	0.622668i
$216$	2.43148e12	−	2.38584e11i	0.351864	−	0.0345259i
$217$	3.92359e12	+	2.81345e12i	0.553548	+	0.396927i
$218$		−	3.57073e12i		−	0.491187i
$219$	−2.03956e12	−	3.28077e12i	−0.273586	−	0.440081i
$220$	−2.86772e12	+	1.65568e12i	−0.375156	+	0.216597i
$221$	1.76108e12	−	1.01676e12i	0.224710	−	0.129736i
$222$	−5.58676e12	−	8.98667e12i	−0.695374	−	1.11856i
$223$		−	1.32401e13i		−	1.60773i	−0.594809	−	0.803867i	$-0.702772\pi$
$223$		−	1.32401e13i		−	1.60773i	0.594809	−	0.803867i	$-0.297228\pi$
$224$	1.21255e12	+	8.69473e11i	0.143660	+	0.103013i
$225$	6.22688e12	+	9.32409e12i	0.719891	+	1.07796i
$226$	−4.02135e12	+	6.96519e12i	−0.453707	+	0.785844i
$227$	−7.95767e11	−	1.37831e12i	−0.0876282	−	0.151777i	0.818880	−	0.573965i	$-0.194595\pi$
$227$	−7.95767e11	−	1.37831e12i	−0.0876282	−	0.151777i	−0.906508	+	0.422188i	$0.861262\pi$
$228$	−7.42738e12	+	2.42243e11i	−0.798351	+	0.0260381i
$229$	−2.62987e12	−	1.51836e12i	−0.275956	−	0.159323i	0.355635	−	0.934625i	$-0.384265\pi$
$229$	−2.62987e12	−	1.51836e12i	−0.275956	−	0.159323i	−0.631591	+	0.775302i	$0.717598\pi$
$230$	1.65870e13			1.69928
$231$	−3.17752e12	+	4.75105e12i	−0.317850	+	0.475252i
$232$	1.28195e12			0.125224
$233$	9.80810e12	+	5.66271e12i	0.935680	+	0.540215i	0.888603	−	0.458676i	$-0.151676\pi$
$233$	9.80810e12	+	5.66271e12i	0.935680	+	0.540215i	0.0470765	+	0.998891i	$0.485010\pi$
$234$	1.52553e12	−	3.09158e12i	0.142146	−	0.288066i
$235$	6.36581e12	+	1.10259e13i	0.579403	+	1.00356i
$236$	−2.07104e12	+	3.58715e12i	−0.184150	+	0.318958i
$237$	−1.79281e13	−	9.58558e12i	−1.55747	−	0.832727i
$238$	4.33447e12	−	1.96230e12i	0.367928	−	0.166569i
$239$		−	1.22405e13i		−	1.01534i	−0.861552	−	0.507669i	$-0.830507\pi$
$239$		−	1.22405e13i		−	1.01534i	0.861552	−	0.507669i	$-0.169493\pi$
$240$	3.96876e12	−	2.46726e12i	0.321731	−	0.200011i
$241$	−1.32420e13	+	7.64529e12i	−1.04921	+	0.605759i	−0.922427	−	0.386171i	$-0.873797\pi$
$241$	−1.32420e13	+	7.64529e12i	−1.04921	+	0.605759i	−0.126779	+	0.991931i	$0.540464\pi$
$242$	5.32212e12	−	3.07272e12i	0.412192	−	0.237979i
$243$	−2.14359e12	−	1.30328e13i	−0.162296	−	0.986742i
$244$			7.29832e12i			0.540230i
$245$	6.71782e12	+	1.98304e13i	0.486200	+	1.43522i
$246$	6.01191e12	−	1.12442e13i	0.425471	−	0.795767i
$247$	−5.24309e12	+	9.08129e12i	−0.362872	+	0.628513i
$248$	−1.77890e12	−	3.08115e12i	−0.120412	−	0.208559i
$249$	8.68571e11	+	2.66311e13i	0.0575054	+	1.76317i
$250$	4.24462e12	+	2.45063e12i	0.274896	+	0.158712i
$251$	−1.96665e13			−1.24601			−0.623004	−	0.782219i	$-0.714088\pi$
$251$	−1.96665e13			−1.24601			−0.623004	+	0.782219i	$0.714088\pi$
$252$	4.26333e12	−	6.84754e12i	0.264269	−	0.424455i
$253$	1.49498e13			0.906720
$254$	9.15321e12	+	5.28461e12i	0.543235	+	0.313637i
$255$	−4.85767e11	−	1.48940e13i	−0.0282135	−	0.865049i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	6.99471e12	−	1.21152e13i	0.389168	−	0.674059i	−0.603170	−	0.797613i	$-0.706096\pi$
$257$	6.99471e12	−	1.21152e13i	0.389168	−	0.674059i	0.992338	+	0.123554i	$0.0394292\pi$
$258$	2.90466e12	−	5.43265e12i	0.158193	−	0.295872i
$259$	−3.47670e13	−	3.43512e12i	−1.85361	−	0.183144i
$260$		−	6.59418e12i		−	0.344197i
$261$	−4.51586e11	−	6.91564e12i	−0.0230790	−	0.353435i
$262$	7.77778e12	−	4.49051e12i	0.389223	−	0.224718i
$263$	1.97137e12	−	1.13817e12i	0.0966077	−	0.0557765i	−0.450918	−	0.892565i	$-0.648903\pi$
$263$	1.97137e12	−	1.13817e12i	0.0966077	−	0.0557765i	0.547525	+	0.836789i	$0.315570\pi$
$264$	3.57704e12	−	2.22374e12i	0.171673	−	0.106724i
$265$		−	4.72850e13i		−	2.22265i
$266$	−1.42974e13	+	1.99389e13i	−0.658274	+	0.918020i
$267$	1.73291e13	+	9.26530e12i	0.781563	+	0.417876i
$268$	1.54173e12	−	2.67036e12i	0.0681190	−	0.117986i
$269$	6.33364e12	+	1.09702e13i	0.274167	+	0.474872i	0.969925	−	0.243405i	$-0.0782645\pi$
$269$	6.33364e12	+	1.09702e13i	0.274167	+	0.474872i	−0.695757	+	0.718277i	$0.744931\pi$
$270$	−1.47080e13	−	2.05408e13i	−0.623809	−	0.871196i
$271$	3.29234e13	+	1.90083e13i	1.36828	+	0.789974i	0.990708	−	0.136008i	$-0.0434272\pi$
$271$	3.29234e13	+	1.90083e13i	1.36828	+	0.789974i	0.377568	+	0.925982i	$0.376761\pi$
$272$	−3.50616e12			−0.142792
$273$	−5.02979e12	−	1.02105e13i	−0.200750	−	0.407523i
$274$	1.01016e13			0.395150
$275$	1.67397e13	+	9.66470e12i	0.641829	+	0.370560i
$276$	−2.10867e13	+	6.87742e11i	−0.792519	+	0.0258479i
$277$	−1.21822e13	−	2.11001e13i	−0.448834	−	0.777403i	0.549477	−	0.835509i	$-0.314827\pi$
$277$	−1.21822e13	−	2.11001e13i	−0.448834	−	0.777403i	−0.998310	+	0.0581062i	$0.981494\pi$
$278$	2.15252e11	−	3.72827e11i	0.00777501	−	0.0134667i
$279$	−1.59950e13	+	1.06819e13i	−0.566448	+	0.378289i
$280$	1.51704e12	−	1.53541e13i	0.0526779	−	0.533156i
$281$			1.90923e11i			0.00650090i	0.999995	+	0.00325045i	$0.00103465\pi$
$281$			1.90923e11i			0.00650090i	−0.999995	+	0.00325045i	$0.998965\pi$
$282$	−8.54991e12	−	1.37531e13i	−0.285490	−	0.459231i
$283$	−3.00462e13	+	1.73472e13i	−0.983930	+	0.568073i	−0.903454	−	0.428684i	$-0.858977\pi$
$283$	−3.00462e13	+	1.73472e13i	−0.983930	+	0.568073i	−0.0804760	+	0.996757i	$0.525644\pi$
$284$	1.59333e13	−	9.19910e12i	0.511747	−	0.295457i
$285$	4.05709e13	+	6.52611e13i	1.27811	+	2.05593i
$286$		−	5.94333e12i		−	0.183661i
$287$	−1.73618e13	−	3.83499e13i	−0.526313	−	1.16256i
$288$	−4.94311e12	+	3.30114e12i	−0.147008	+	0.0981761i
$289$	1.15457e13	−	1.99977e13i	0.336884	−	0.583501i
$290$	−6.62805e12	−	1.14801e13i	−0.189757	−	0.328668i
$291$	2.68598e13	−	8.76028e11i	0.754555	−	0.0246097i
$292$	8.13945e12	+	4.69931e12i	0.224383	+	0.129547i
$293$	−1.77989e13			−0.481529			−0.240764	−	0.970584i	$-0.577398\pi$
$293$	−1.77989e13			−0.481529			−0.240764	+	0.970584i	$0.577398\pi$
$294$	−9.36247e12	−	2.49315e13i	−0.248588	−	0.661970i
$295$	4.28314e13			1.11620
$296$	2.22956e13	+	1.28724e13i	0.570314	+	0.329271i
$297$	−1.32563e13	−	1.85134e13i	−0.332859	−	0.464863i
$298$	1.59090e13	+	2.75552e13i	0.392151	+	0.679225i
$299$	−1.48854e13	+	2.57823e13i	−0.360221	+	0.623922i
$300$	−2.40560e13	−	1.28620e13i	−0.571554	−	0.305591i
$301$	−8.38837e12	−	1.85288e13i	−0.195687	−	0.432246i
$302$			2.00058e13i			0.458267i
$303$	−2.55924e13	+	1.59101e13i	−0.575674	+	0.357880i
$304$	1.56578e13	−	9.04002e12i	0.345880	−	0.199694i
$305$	6.53578e13	−	3.77343e13i	1.41791	−	0.818630i
$306$	1.23509e12	+	1.89144e13i	0.0263167	+	0.403018i
$307$		−	3.57716e13i		−	0.748648i	−0.927298	−	0.374324i	$-0.877875\pi$
$307$		−	3.57716e13i		−	0.748648i	0.927298	−	0.374324i	$-0.122125\pi$
$308$	1.36731e12	−	1.38386e13i	0.0281085	−	0.284488i
$309$	1.82360e12	−	3.41073e12i	0.0368264	−	0.0688772i
$310$	−1.83949e13	+	3.18608e13i	−0.364928	+	0.632074i
$311$	7.66288e12	+	1.32725e13i	0.149352	+	0.258684i	0.930988	−	0.365050i	$-0.118948\pi$
$311$	7.66288e12	+	1.32725e13i	0.149352	+	0.258684i	−0.781636	+	0.623734i	$0.785615\pi$
$312$	2.73413e11	+	8.38308e12i	0.00523563	+	0.160529i
$313$	−5.24061e13	−	3.02566e13i	−0.986024	−	0.569281i	−0.0819407	−	0.996637i	$-0.526112\pi$
$313$	−5.24061e13	−	3.02566e13i	−0.986024	−	0.569281i	−0.904084	+	0.427356i	$0.859445\pi$
$314$	−8.73319e12			−0.161458
$315$	−8.33636e13	−	2.77517e12i	−1.51450	−	0.0504176i
$316$	4.94614e13			0.883054
$317$	8.00164e13	+	4.61975e13i	1.40395	+	0.810574i	0.994796	−	0.101889i	$-0.0324888\pi$
$317$	8.00164e13	+	4.61975e13i	1.40395	+	0.810574i	0.409159	+	0.912463i	$0.365822\pi$
$318$	1.96057e12	+	6.01126e13i	0.0338090	+	1.03661i
$319$	−5.97386e12	−	1.03470e13i	−0.101253	−	0.175375i
$320$	−5.68478e12	+	9.84633e12i	−0.0947084	+	0.164040i
$321$	1.09764e13	−	2.05294e13i	0.179755	−	0.336201i
$322$	−4.05910e13	+	5.66076e13i	−0.653465	+	0.911314i
$323$		−	5.76543e13i		−	0.912468i
$324$	1.95497e13	+	2.55033e13i	0.304188	+	0.396825i
$325$	−3.33353e13	+	1.92461e13i	−0.509971	+	0.294432i
$326$	3.12666e13	−	1.80518e13i	0.470309	−	0.271533i
$327$	3.98858e13	−	2.47959e13i	0.589937	−	0.366747i
$328$			3.10213e13i			0.451185i
$329$	−5.32071e13	−	5.25708e12i	−0.761013	−	0.0751912i
$330$	−3.84083e13	−	2.05357e13i	−0.540254	−	0.288856i
$331$	−6.09815e13	+	1.05623e14i	−0.843615	+	1.46118i	0.0432034	+	0.999066i	$0.486244\pi$
$331$	−6.09815e13	+	1.05623e14i	−0.843615	+	1.46118i	−0.886818	+	0.462118i	$0.847090\pi$
$332$	−3.24133e13	−	5.61415e13i	−0.441026	−	0.763879i
$333$	6.15874e13	−	1.24810e14i	0.824230	−	1.67035i
$334$	4.34675e13	+	2.50960e13i	0.572215	+	0.330368i
$335$	−3.18848e13			−0.412892
$336$	−1.29197e12	+	1.95823e13i	−0.0164583	+	0.249458i
$337$	1.41025e14			1.76739			0.883696	−	0.468061i	$-0.155047\pi$
$337$	1.41025e14			1.76739			0.883696	+	0.468061i	$0.155047\pi$
$338$	−3.94160e13	−	2.27568e13i	−0.485994	−	0.280589i
$339$	−1.05728e14	+	3.44829e12i	−1.28260	+	0.0418317i
$340$	1.81278e13	+	3.13983e13i	0.216377	+	0.374776i
$341$	−1.65793e13	+	2.87161e13i	−0.194722	+	0.337269i
$342$	−5.42831e13	−	8.12831e13i	−0.627366	−	0.939413i
$343$	−8.41163e13	−	2.56017e13i	−0.956670	−	0.291173i
$344$			1.49880e13i			0.167754i
$345$	1.15183e14	+	1.85280e14i	1.26877	+	2.04091i
$346$	−5.05069e13	+	2.91602e13i	−0.547560	+	0.316134i
$347$	−1.18081e14	+	6.81739e13i	−1.25999	+	0.727455i	−0.973072	−	0.230500i	$-0.925964\pi$
$347$	−1.18081e14	+	6.81739e13i	−1.25999	+	0.727455i	−0.286917	+	0.957955i	$0.592630\pi$
$348$	8.90213e12	+	1.43197e13i	0.0934992	+	0.150400i
$349$			1.72135e13i			0.177963i	0.996033	+	0.0889815i	$0.0283612\pi$
$349$			1.72135e13i			0.177963i	−0.996033	+	0.0889815i	$0.971639\pi$
$350$	−8.20463e13	+	3.71441e13i	−0.834997	+	0.378021i
$351$	4.51271e13	−	4.42801e12i	0.452114	−	0.0443629i
$352$	−5.12369e12	+	8.87448e12i	−0.0505356	+	0.0875303i
$353$	7.13993e13	+	1.23667e14i	0.693319	+	1.20086i	0.970744	+	0.240117i	$0.0771857\pi$
$353$	7.13993e13	+	1.23667e14i	0.693319	+	1.20086i	−0.277425	+	0.960747i	$0.589481\pi$
$354$	−5.44509e13	+	1.77591e12i	−0.520579	+	0.0169786i
$355$	−1.64759e14	−	9.51238e13i	−1.55094	−	0.895433i
$356$	−4.78088e13			−0.443131
$357$	5.20187e13	+	3.47902e13i	0.474771	+	0.317528i
$358$	−1.14335e13			−0.102760
$359$	−3.12883e13	−	1.80643e13i	−0.276925	−	0.159883i	0.355105	−	0.934826i	$-0.384445\pi$
$359$	−3.12883e13	−	1.80643e13i	−0.276925	−	0.159883i	−0.632031	+	0.774943i	$0.717778\pi$
$360$	5.51196e13	+	2.71987e13i	0.480444	+	0.237074i
$361$	9.04064e13	+	1.56588e14i	0.776085	+	1.34422i
$362$	−4.25124e13	+	7.36336e13i	−0.359433	+	0.622557i
$363$	7.12807e13	+	3.81115e13i	0.593589	+	0.317373i
$364$	2.25045e13	+	1.61370e13i	0.184591	+	0.132363i
$365$		−	9.71870e13i		−	0.785231i
$366$	−8.15237e13	+	5.06810e13i	−0.648840	+	0.403366i
$367$	1.44753e14	−	8.35732e13i	1.13492	−	0.655245i	0.189751	−	0.981832i	$-0.439232\pi$
$367$	1.44753e14	−	8.35732e13i	1.13492	−	0.655245i	0.945167	+	0.326587i	$0.105899\pi$
$368$	4.44533e13	−	2.56651e13i	0.343353	−	0.198235i
$369$	1.67348e14	−	1.09277e13i	1.27343	−	0.0831540i
$370$		−	2.66215e14i		−	1.99582i
$371$	1.61373e14	+	1.15714e14i	1.19200	+	0.854731i
$372$	2.20640e13	−	4.12668e13i	0.160583	−	0.300341i
$373$	1.07460e14	−	1.86126e14i	0.770635	−	1.33478i	−0.166581	−	0.986028i	$-0.553273\pi$
$373$	1.07460e14	−	1.86126e14i	0.770635	−	1.33478i	0.937216	−	0.348751i	$-0.113394\pi$
$374$	1.63386e13	+	2.82993e13i	0.115457	+	0.199978i
$375$	2.10141e12	+	6.44310e13i	0.0146332	+	0.448665i
$376$	3.41209e13	+	1.96997e13i	0.234146	+	0.135184i
$377$	2.37925e13			0.160902
$378$	1.06094e14	+	7.15479e10i	0.707107	+	0.000476861i
$379$	7.62609e13			0.500940			0.250470	−	0.968124i	$-0.419415\pi$
$379$	7.62609e13			0.500940			0.250470	+	0.968124i	$0.419415\pi$
$380$	−1.61910e14	−	9.34788e13i	−1.04825	−	0.605206i
$381$	4.53153e12	+	1.38941e14i	0.0289173	+	0.886628i
$382$	6.89293e13	+	1.19389e14i	0.433566	+	0.750958i
$383$	1.37957e14	−	2.38948e14i	0.855360	−	1.48153i	−0.0209502	−	0.999781i	$-0.506669\pi$
$383$	1.37957e14	−	2.38948e14i	0.855360	−	1.48153i	0.876310	−	0.481747i	$-0.159998\pi$
$384$	6.81871e12	−	1.27532e13i	0.0416755	−	0.0779465i
$385$	−1.30997e14	+	5.93049e13i	−0.789270	+	0.357319i
$386$			8.38323e13i			0.497945i
$387$	8.08544e13	−	5.27973e12i	0.473471	−	0.0309173i
$388$	−5.66235e13	+	3.26916e13i	−0.326906	+	0.188739i
$389$	−2.18524e14	+	1.26165e14i	−1.24388	+	0.718152i	−0.969881	−	0.243579i	$-0.921678\pi$
$389$	−2.18524e14	+	1.26165e14i	−1.24388	+	0.718152i	−0.273995	+	0.961731i	$0.588345\pi$
$390$	7.36583e13	−	4.57913e13i	0.413396	−	0.256997i
$391$		−	1.63684e14i		−	0.905802i
$392$	4.86875e13	+	4.27512e13i	0.265671	+	0.233278i
$393$	1.04170e14	+	5.56964e13i	0.560512	+	0.299687i
$394$	−1.52087e12	+	2.63422e12i	−0.00806978	+	0.0139773i
$395$	−2.55729e14	−	4.42935e14i	−1.33812	−	2.31770i
$396$	4.96793e13	+	2.45141e13i	0.256361	+	0.126501i
$397$	−2.85368e14	−	1.64758e14i	−1.45231	−	0.838489i	−0.453694	−	0.891157i	$-0.649894\pi$
$397$	−2.85368e14	−	1.64758e14i	−1.45231	−	0.838489i	−0.998612	+	0.0526679i	$0.983228\pi$
$398$	−1.60469e14			−0.805440
$399$	−3.22005e14	−	2.12448e13i	−1.59409	−	0.105172i
$400$	6.63675e13			0.324060
$401$	−2.45334e14	−	1.41644e14i	−1.18158	−	0.682188i	−0.225203	−	0.974312i	$-0.572305\pi$
$401$	−2.45334e14	−	1.41644e14i	−1.18158	−	0.682188i	−0.956380	+	0.292124i	$0.905638\pi$
$402$	4.05346e13	−	1.32203e12i	0.192567	−	0.00628056i
$403$	−3.30157e13	−	5.71848e13i	−0.154719	−	0.267980i
$404$	3.66581e13	−	6.34937e13i	0.169462	−	0.293517i
$405$	1.27309e14	−	3.06930e14i	0.580575	−	1.39970i
$406$	5.53990e13	+	5.47364e12i	0.249235	+	0.0246254i
$407$		−	2.39939e14i		−	1.06496i
$408$	−2.43475e13	−	3.91645e13i	−0.106616	−	0.171499i
$409$	1.25239e14	−	7.23068e13i	0.541080	−	0.312393i	−0.204436	−	0.978880i	$-0.565536\pi$
$409$	1.25239e14	−	7.23068e13i	0.541080	−	0.312393i	0.745517	+	0.666487i	$0.232203\pi$
$410$	2.77802e14	−	1.60389e14i	1.18420	−	0.683696i
$411$	7.01474e13	+	1.12837e14i	0.295040	+	0.474592i
$412$			9.40976e12i			0.0390520i
$413$	−1.04815e14	+	1.46174e14i	−0.429239	+	0.598611i
$414$	−1.54113e14	−	2.30767e14i	−0.622783	−	0.932551i
$415$	−3.35172e14	+	5.80534e14i	−1.33660	+	2.31507i
$416$	−1.02032e13	−	1.76725e13i	−0.0401536	−	0.0695480i
$417$	5.65931e12	−	1.84578e11i	0.0219794	−	0.000716854i
$418$	−1.45929e14	−	8.42524e13i	−0.559337	−	0.322933i
$419$	−2.01759e14			−0.763232			−0.381616	−	0.924321i	$-0.624632\pi$
$419$	−2.01759e14			−0.763232			−0.381616	+	0.924321i	$0.624632\pi$
$420$	1.82043e14	−	8.96759e13i	0.679676	−	0.334815i
$421$	3.50407e14			1.29128			0.645642	−	0.763640i	$-0.276590\pi$
$421$	3.50407e14			1.29128			0.645642	+	0.763640i	$0.276590\pi$
$422$	2.61543e14	+	1.51002e14i	0.951316	+	0.549242i
$423$	9.42527e13	−	1.91008e14i	0.338393	−	0.685773i
$424$	−7.31644e13	−	1.26724e14i	−0.259291	−	0.449105i
$425$	1.05818e14	−	1.83281e14i	0.370185	−	0.641179i
$426$	2.13400e14	+	1.14098e14i	0.736955	+	0.394026i
$427$	−3.11621e13	+	3.15394e14i	−0.106237	+	1.07523i
$428$			5.66379e13i			0.190619i
$429$	6.63882e13	−	4.12716e13i	0.220585	−	0.137131i
$430$	1.34220e14	−	7.74921e13i	0.440293	−	0.254203i
$431$	−2.77195e14	+	1.60038e14i	−0.897759	+	0.518321i	−0.876472	−	0.481452i	$-0.840110\pi$
$431$	−2.77195e14	+	1.60038e14i	−0.897759	+	0.518321i	−0.0212864	+	0.999773i	$0.506776\pi$
$432$	−7.12004e13	−	3.22918e13i	−0.227678	−	0.103260i
$433$		−	4.15113e14i		−	1.31064i	−0.755352	−	0.655320i	$-0.772534\pi$
$433$		−	4.15113e14i		−	1.31064i	0.755352	−	0.655320i	$-0.227466\pi$
$434$	−6.37187e13	−	1.40746e14i	−0.198643	−	0.438776i
$435$	8.22088e13	−	1.53757e14i	0.253062	−	0.473308i
$436$	−5.71317e13	+	9.89551e13i	−0.173661	+	0.300789i
$437$	4.22030e14	+	7.30977e14i	1.26676	+	2.19410i
$438$	4.02964e12	+	1.23552e14i	0.0119442	+	0.366221i
$439$	2.13127e14	+	1.23049e14i	0.623854	+	0.360182i	0.778368	−	0.627808i	$-0.216048\pi$
$439$	2.13127e14	+	1.23049e14i	0.623854	+	0.360182i	−0.154514	+	0.987991i	$0.549381\pi$
$440$	1.05963e14			0.306314
$441$	2.13475e14	−	2.77710e14i	0.609445	−	0.792828i
$442$	−6.50728e13			−0.183475
$443$	1.02521e14	+	5.91904e13i	0.285490	+	0.164828i	0.635906	−	0.771766i	$-0.280626\pi$
$443$	1.02521e14	+	5.91904e13i	0.285490	+	0.164828i	−0.350416	+	0.936594i	$0.613960\pi$
$444$	1.10380e13	+	3.38434e14i	0.0303587	+	0.930824i
$445$	2.47184e14	+	4.28136e14i	0.671492	+	1.16306i
$446$	−2.11842e14	+	3.66920e14i	−0.568420	+	0.984532i
$447$	−1.97322e14	+	3.69055e14i	−0.522978	+	0.978137i
$448$	−1.96917e13	−	4.34964e13i	−0.0515531	−	0.113874i
$449$			3.05081e14i			0.788969i	0.918903	+	0.394484i	$0.129077\pi$
$449$			3.05081e14i			0.788969i	−0.918903	+	0.394484i	$0.870923\pi$
$450$	−2.33789e13	−	3.58027e14i	−0.0597248	−	0.914633i
$451$	2.50382e14	−	1.44558e14i	0.631877	−	0.364815i
$452$	2.22886e14	−	1.28683e14i	0.555676	−	0.320819i
$453$	−2.23469e14	+	1.38924e14i	−0.550399	+	0.342167i
$454$			5.09291e13i			0.123925i
$455$	2.81556e13	−	2.84965e14i	0.0676866	−	0.685059i
$456$	2.09709e14	+	1.12125e14i	0.498094	+	0.266315i
$457$	−1.61402e14	+	2.79557e14i	−0.378765	+	0.656041i	−0.990883	−	0.134726i	$-0.956985\pi$
$457$	−1.61402e14	+	2.79557e14i	−0.378765	+	0.656041i	0.612118	+	0.790767i	$0.290318\pi$
$458$	4.85874e13	+	8.41559e13i	0.112658	+	0.195130i
$459$	−2.02701e14	+	1.45141e14i	−0.464392	+	0.332523i
$460$	−4.59672e14	−	2.65392e14i	−1.04059	−	0.600785i
$461$	−6.50640e14			−1.45541			−0.727705	−	0.685890i	$-0.759413\pi$
$461$	−6.50640e14			−1.45541			−0.727705	+	0.685890i	$0.759413\pi$
$462$	1.64075e14	−	8.08248e13i	0.362669	−	0.178654i
$463$	−3.85783e14			−0.842650			−0.421325	−	0.906910i	$-0.638435\pi$
$463$	−3.85783e14			−0.842650			−0.421325	+	0.906910i	$0.638435\pi$
$464$	−3.55265e13	−	2.05113e13i	−0.0766838	−	0.0442734i
$465$	−4.83629e14	+	1.57735e13i	−1.03162	+	0.0336463i
$466$	−1.81207e14	−	3.13859e14i	−0.381990	−	0.661626i
$467$	5.80032e13	−	1.00465e14i	0.120840	−	0.209300i	−0.799259	−	0.600986i	$-0.794775\pi$
$467$	5.80032e13	−	1.00465e14i	0.120840	−	0.209300i	0.920099	+	0.391686i	$0.128108\pi$
$468$	−9.17420e13	+	6.12678e13i	−0.188893	+	0.126148i
$469$	7.80271e13	−	1.08816e14i	0.158780	−	0.221432i
$470$		−	4.07412e14i		−	0.819399i
$471$	−6.06450e13	−	9.75515e13i	−0.120553	−	0.193918i
$472$	1.14789e14	−	6.62733e13i	0.225537	−	0.130214i
$473$	1.20973e14	−	6.98435e13i	0.234936	−	0.135641i
$474$	3.43469e14	+	5.52493e14i	0.659336	+	1.06059i
$475$			1.09133e15i			2.07081i
$476$	−1.51517e14	−	1.49705e13i	−0.284200	−	0.0280801i
$477$	−6.57856e14	+	4.39334e14i	−1.21977	+	0.814598i
$478$	−1.95848e14	+	3.39219e14i	−0.358976	+	0.621765i
$479$	4.55625e14	+	7.89166e14i	0.825586	+	1.42996i	0.901470	+	0.432841i	$0.142489\pi$
$479$	4.55625e14	+	7.89166e14i	0.825586	+	1.42996i	−0.0758842	+	0.997117i	$0.524178\pi$
$480$	−1.49462e14	+	4.87467e12i	−0.267734	+	0.00873210i
$481$	4.13796e14	+	2.38905e14i	0.732805	+	0.423085i
$482$	4.89299e14			0.856673
$483$	−9.14190e14	−	6.03151e13i	−1.58244	−	0.104404i
$484$	−1.96654e14			−0.336554
$485$	5.85518e14	+	3.38049e14i	0.990743	+	0.572006i
$486$	−1.49120e14	+	3.95473e14i	−0.249481	+	0.661634i
$487$	−5.70832e14	−	9.88710e14i	−0.944276	−	1.63553i	−0.757194	−	0.653190i	$-0.773430\pi$
$487$	−5.70832e14	−	9.88710e14i	−0.944276	−	1.63553i	−0.187083	−	0.982344i	$-0.559903\pi$
$488$	1.16773e14	−	2.02257e14i	0.191000	−	0.330822i
$489$	4.18763e14	+	2.23899e14i	0.677282	+	0.362120i
$490$	1.31117e14	−	6.57041e14i	0.209691	−	1.05079i
$491$		−	8.67174e13i		−	0.137138i	−0.997646	−	0.0685691i	$-0.978157\pi$
$491$		−	8.67174e13i		−	0.137138i	0.997646	−	0.0685691i	$-0.0218434\pi$
$492$	−3.46514e14	+	2.15418e14i	−0.541893	+	0.336879i
$493$	−1.13288e14	+	6.54070e13i	−0.175197	+	0.101150i
$494$	2.90601e14	−	1.67779e14i	0.444426	−	0.256589i
$495$	−3.73271e13	−	5.71632e14i	−0.0564541	−	0.864545i
$496$			1.13850e14i			0.170288i
$497$	7.27828e14	−	3.29503e14i	1.07664	−	0.487416i
$498$	4.02027e14	−	7.51921e14i	0.588158	−	1.10005i
$499$	3.93263e14	−	6.81152e14i	0.569024	−	0.985579i	−0.427639	−	0.903950i	$-0.640654\pi$
$499$	3.93263e14	−	6.81152e14i	0.569024	−	0.985579i	0.996663	−	0.0816288i	$-0.0260122\pi$
$500$	−7.84203e13	−	1.35828e14i	−0.112226	−	0.194381i
$501$	2.15197e13	+	6.59812e14i	0.0304599	+	0.933926i
$502$	5.45013e14	+	3.14663e14i	0.763020	+	0.440530i
$503$	−1.33842e14			−0.185340			−0.0926700	−	0.995697i	$-0.529540\pi$
$503$	−1.33842e14			−0.185340			−0.0926700	+	0.995697i	$0.529540\pi$
$504$	−2.27709e14	+	1.21551e14i	−0.311898	+	0.166492i
$505$	−7.58130e14			−1.02717
$506$	−4.14302e14	−	2.39197e14i	−0.555251	−	0.320574i
$507$	−1.95139e13	−	5.98312e14i	−0.0258702	−	0.793203i
$508$	−1.69108e14	−	2.92903e14i	−0.221775	−	0.384125i
$509$	7.16650e13	−	1.24127e14i	0.0929735	−	0.161035i	−0.815788	−	0.578352i	$-0.803696\pi$
$509$	7.16650e13	−	1.24127e14i	0.0929735	−	0.161035i	0.908761	+	0.417317i	$0.137029\pi$
$510$	−2.24842e14	+	4.20527e14i	−0.288564	+	0.539707i
$511$	3.31678e14	+	2.37832e14i	0.421115	+	0.301964i
$512$			3.51844e13i			0.0441942i
$513$	5.30997e14	−	1.17080e15i	0.659851	−	1.45491i
$514$	−3.87686e14	+	2.23831e14i	−0.476632	+	0.275183i
$515$	8.42661e13	−	4.86510e13i	0.102497	−	0.0591769i
$516$	−1.67419e14	+	1.04079e14i	−0.201480	+	0.125254i
$517$		−	3.67200e14i		−	0.437225i
$518$	9.08531e14	+	6.51470e14i	1.07035	+	0.767504i
$519$	−6.76454e14	−	3.61678e14i	−0.788529	−	0.421601i
$520$	−1.05507e14	+	1.82743e14i	−0.121692	+	0.210777i
$521$	−8.96913e13	−	1.55350e14i	−0.102363	−	0.177298i	0.810295	−	0.586023i	$-0.199307\pi$
$521$	−8.96913e13	−	1.55350e14i	−0.102363	−	0.177298i	−0.912658	+	0.408725i	$0.865974\pi$
$522$	−9.81355e13	+	1.98877e14i	−0.110825	+	0.224593i
$523$	8.35707e14	+	4.82495e14i	0.933888	+	0.539180i	0.888039	−	0.459768i	$-0.152068\pi$
$523$	8.35707e14	+	4.82495e14i	0.933888	+	0.539180i	0.0458485	+	0.998948i	$0.485401\pi$
$524$	−2.87392e14			−0.317799
$525$	−9.84653e14	−	6.58538e14i	−1.07747	−	0.720617i
$526$	−7.28430e13			−0.0788798
$527$	3.14409e14	+	1.81524e14i	0.336928	+	0.194525i
$528$	−1.34710e14	+	4.39354e12i	−0.142860	+	0.00465938i
$529$	7.21762e14	+	1.25013e15i	0.757509	+	1.31204i
$530$	−7.56560e14	+	1.31040e15i	−0.785826	+	1.36109i
$531$	−3.97955e14	−	5.95895e14i	−0.409085	−	0.612562i
$532$	7.15242e14	−	3.23805e14i	0.727678	−	0.329435i
$533$			5.75742e14i			0.579733i
$534$	−3.31993e14	−	5.34033e14i	−0.330866	−	0.532220i
$535$	5.07203e14	−	2.92834e14i	0.500306	−	0.288852i
$536$	−8.54516e13	+	4.93355e13i	−0.0834284	+	0.0481674i
$537$	−7.93963e13	−	1.27714e14i	−0.0767259	−	0.123419i
$538$		−	4.05353e14i		−	0.387731i
$539$	1.18175e14	−	5.92190e14i	0.111889	−	0.560690i
$540$	7.89469e13	+	8.04570e14i	0.0739893	+	0.754046i
$541$	3.23525e14	−	5.60362e14i	0.300139	−	0.519857i	−0.676028	−	0.736876i	$-0.736300\pi$
$541$	3.23525e14	−	5.60362e14i	0.300139	−	0.519857i	0.976167	+	0.217019i	$0.0696335\pi$
$542$	−6.08267e14	−	1.05355e15i	−0.558596	−	0.967517i
$543$	−1.11772e15	+	3.64542e13i	−1.01609	+	0.0331397i
$544$	9.71656e13	+	5.60986e13i	0.0874417	+	0.0504845i
$545$	1.18155e15			1.05262
$546$	−2.39784e13	+	3.63438e14i	−0.0211476	+	0.320532i
$547$	1.10778e15			0.967217			0.483609	−	0.875284i	$-0.339326\pi$
$547$	1.10778e15			0.967217			0.483609	+	0.875284i	$0.339326\pi$
$548$	−2.79943e14	−	1.61625e14i	−0.241979	−	0.139706i
$549$	−1.13223e15	−	5.58698e14i	−0.968920	−	0.478111i
$550$	−3.09270e14	−	5.35672e14i	−0.262025	−	0.453841i
$551$	3.37281e14	−	5.84188e14i	0.282916	−	0.490026i
$552$	5.95377e14	+	3.18329e14i	0.494455	+	0.264369i
$553$	2.13745e15	+	2.11189e14i	1.75755	+	0.173653i
$554$			7.79658e14i			0.634747i
$555$	2.97367e15	−	1.84864e15i	2.39707	−	1.49019i
$556$	−1.19305e13	+	6.88806e12i	−0.00952240	+	0.00549776i
$557$	6.31890e14	−	3.64822e14i	0.499388	−	0.288322i	−0.229073	−	0.973409i	$-0.573569\pi$
$557$	6.31890e14	−	3.64822e14i	0.499388	−	0.288322i	0.728461	+	0.685088i	$0.240236\pi$
$558$	6.14175e14	−	4.01052e13i	0.480623	−	0.0313843i
$559$			2.78170e14i			0.215549i
$560$	−2.87707e14	+	4.01232e14i	−0.220758	+	0.307865i
$561$	−2.02650e14	+	3.79021e14i	−0.153975	+	0.287983i
$562$	3.05477e12	−	5.29101e12i	0.00229842	−	0.00398097i
$563$	−8.91377e14	−	1.54391e15i	−0.664149	−	1.15034i	−0.979515	−	0.201370i	$-0.935461\pi$
$563$	−8.91377e14	−	1.54391e15i	−0.664149	−	1.15034i	0.315366	−	0.948970i	$-0.397873\pi$
$564$	1.68924e13	+	5.17936e14i	0.0124640	+	0.382156i
$565$	−2.30476e15	−	1.33066e15i	−1.68407	−	0.972298i
$566$	1.11022e15			0.803376
$567$	7.35936e14	+	1.18559e15i	0.527392	+	0.849622i
$568$	−5.88742e14			−0.417839
$569$	−5.84865e13	−	3.37672e13i	−0.0411091	−	0.0237343i	0.479305	−	0.877649i	$-0.340889\pi$
$569$	−5.84865e13	−	3.37672e13i	−0.0411091	−	0.0237343i	−0.520414	+	0.853914i	$0.674222\pi$
$570$	−8.01577e13	−	2.45770e15i	−0.0557999	−	1.71087i
$571$	−8.29062e14	−	1.43598e15i	−0.571595	−	0.990031i	−0.996402	−	0.0847477i	$-0.972992\pi$
$571$	−8.29062e14	−	1.43598e15i	−0.571595	−	0.990031i	0.424808	−	0.905284i	$-0.360342\pi$
$572$	−9.50933e13	+	1.64706e14i	−0.0649339	+	0.112469i
$573$	−8.54941e14	+	1.59901e15i	−0.578210	+	1.08144i
$574$	−1.32454e14	+	1.34057e15i	−0.0887257	+	0.897997i
$575$			3.09834e15i			2.05568i
$576$	1.89806e14	−	1.23942e13i	0.124734	−	0.00814506i
$577$	3.41206e14	−	1.96996e14i	0.222101	−	0.128230i	−0.384822	−	0.922991i	$-0.625737\pi$
$577$	3.41206e14	−	1.96996e14i	0.222101	−	0.128230i	0.606923	+	0.794761i	$0.292404\pi$
$578$	−6.39926e14	+	3.69461e14i	−0.412597	+	0.238213i
$579$	−9.36423e14	+	5.82148e14i	−0.598054	+	0.371793i
$580$			4.24195e14i			0.268356i
$581$	−1.16101e15	−	2.56453e15i	−0.727560	−	1.60708i
$582$	−7.58376e14	−	4.05479e14i	−0.470769	−	0.251705i
$583$	−6.81887e14	+	1.18106e15i	−0.419310	+	0.726266i
$584$	−1.50378e14	−	2.60462e14i	−0.0916039	−	0.158663i
$585$	1.02300e15	+	5.04795e14i	0.617329	+	0.304619i
$586$	4.93258e14	+	2.84783e14i	0.294875	+	0.170246i
$587$	2.00240e15			1.18588			0.592940	−	0.805246i	$-0.297967\pi$
$587$	2.00240e15			1.18588			0.592940	+	0.805246i	$0.297967\pi$
$588$	−1.39444e14	+	8.40722e14i	−0.0818132	+	0.493261i
$589$	−1.87211e15			−1.08817
$590$	−1.18698e15	−	6.85303e14i	−0.683529	−	0.394636i
$591$	−3.99859e13	+	1.30414e12i	−0.0228127	+	0.000744033i
$592$	−4.11915e14	−	7.13458e14i	−0.232830	−	0.403273i
$593$	5.65610e14	−	9.79666e14i	0.316750	−	0.548627i	−0.663058	−	0.748568i	$-0.730742\pi$
$593$	5.65610e14	−	9.79666e14i	0.316750	−	0.548627i	0.979808	+	0.199941i	$0.0640751\pi$
$594$	7.11547e13	+	7.25158e14i	0.0394801	+	0.402353i
$595$	6.49322e14	+	1.43426e15i	0.356958	+	0.788472i
$596$		−	1.01817e15i		−	0.554585i
$597$	−1.11433e15	−	1.79247e15i	−0.601386	−	0.967369i
$598$	8.25034e14	−	4.76333e14i	0.441179	−	0.254715i
$599$	−8.19901e14	+	4.73370e14i	−0.434424	+	0.250815i	−0.701230	−	0.712935i	$-0.747365\pi$
$599$	−8.19901e14	+	4.73370e14i	−0.434424	+	0.250815i	0.266805	+	0.963750i	$0.414032\pi$
$600$	4.60869e14	+	7.41338e14i	0.241961	+	0.389211i
$601$			3.43895e14i			0.178902i	0.995991	+	0.0894511i	$0.0285113\pi$
$601$			3.43895e14i			0.178902i	−0.995991	+	0.0894511i	$0.971489\pi$
$602$	−6.39953e13	+	6.47699e14i	−0.0329888	+	0.333882i
$603$	2.96247e14	+	4.43599e14i	0.151324	+	0.226592i
$604$	3.20093e14	−	5.54418e14i	0.162022	−	0.280630i
$605$	1.01676e15	+	1.76108e15i	0.509991	+	0.883331i
$606$	9.63798e14	−	3.14342e13i	0.479056	−	0.0156244i
$607$	−2.05281e15	−	1.18519e15i	−1.01114	−	0.583781i	−0.0996132	−	0.995026i	$-0.531761\pi$
$607$	−2.05281e15	−	1.18519e15i	−1.01114	−	0.583781i	−0.911525	+	0.411246i	$0.865094\pi$
$608$	−5.78561e14			−0.282410
$609$	3.23560e14	+	6.56828e14i	0.156516	+	0.317729i
$610$	−2.41500e15			−1.15772
$611$	6.33269e14	+	3.65618e14i	0.300858	+	0.173700i
$612$	2.68402e14	−	5.43932e14i	0.126373	−	0.256101i
$613$	8.84983e13	+	1.53284e14i	0.0412955	+	0.0715258i	0.885934	−	0.463811i	$-0.153518\pi$
$613$	8.84983e13	+	1.53284e14i	0.0412955	+	0.0715258i	−0.844639	+	0.535336i	$0.820185\pi$
$614$	−5.72346e14	+	9.91332e14i	−0.264687	+	0.458451i
$615$	3.72068e15	+	1.98933e15i	1.70533	+	0.911787i
$616$	−2.59310e14	+	3.61630e14i	−0.117794	+	0.164274i
$617$		−	1.06953e15i		−	0.481533i	−0.970583	−	0.240766i	$-0.922601\pi$
$617$		−	1.06953e15i		−	0.481533i	0.970583	−	0.240766i	$-0.0773987\pi$
$618$	−1.05109e14	+	6.53432e13i	−0.0469032	+	0.0291584i
$619$	−1.89401e15	+	1.09351e15i	−0.837690	+	0.483640i	−0.856478	−	0.516183i	$-0.827352\pi$
$619$	−1.89401e15	+	1.09351e15i	−0.837690	+	0.483640i	0.0187884	+	0.999823i	$0.494019\pi$
$620$	1.01955e15	−	5.88635e14i	0.446944	−	0.258043i
$621$	1.50753e15	−	3.32396e15i	0.655031	−	1.44428i
$622$		−	4.90424e14i		−	0.211215i
$623$	−2.06603e15	−	2.04132e14i	−0.881968	−	0.0871420i
$624$	1.26552e14	−	2.36693e14i	0.0535494	−	0.100155i
$625$	7.34330e14	−	1.27190e15i	0.308000	−	0.533472i
$626$	9.68213e14	+	1.67699e15i	0.402543	+	0.697224i
$627$	−7.22460e13	−	2.21513e15i	−0.0297744	−	0.912907i
$628$	2.42021e14	+	1.39731e14i	0.0988725	+	0.0570841i
$629$	−2.62706e15			−1.06388
$630$	2.26584e15	+	1.41072e15i	0.909610	+	0.566330i
$631$	1.35727e15			0.540138			0.270069	−	0.962841i	$-0.412954\pi$
$631$	1.35727e15			0.540138			0.270069	+	0.962841i	$0.412954\pi$
$632$	−1.37071e15	−	7.91382e14i	−0.540758	−	0.312207i
$633$	1.29484e14	+	3.97007e15i	0.0506400	+	1.55267i
$634$	−1.47832e15	−	2.56053e15i	−0.573162	−	0.992746i
$635$	−1.74867e15	+	3.02878e15i	−0.672127	+	1.16416i
$636$	9.07469e14	−	1.69726e15i	0.345794	−	0.646747i
$637$	9.03619e14	+	7.93443e14i	0.341364	+	0.299743i
$638$			3.82327e14i			0.143193i
$639$	2.07393e14	+	3.17603e15i	0.0770085	+	1.17932i
$640$	3.15082e14	−	1.81913e14i	0.115994	−	0.0669690i
$641$	1.22129e15	−	7.05112e14i	0.445759	−	0.257359i	−0.260279	−	0.965534i	$-0.583814\pi$
$641$	1.22129e15	−	7.05112e14i	0.445759	−	0.257359i	0.706037	+	0.708175i	$0.250481\pi$
$642$	−6.32657e14	+	3.93305e14i	−0.228942	+	0.142327i
$643$			4.42566e15i			1.58788i	0.607996	+	0.793940i	$0.291974\pi$
$643$			4.42566e15i			1.58788i	−0.607996	+	0.793940i	$0.708026\pi$
$644$	2.03061e15	−	9.19301e14i	0.722362	−	0.327028i
$645$	1.79765e15	+	9.61146e14i	0.634056	+	0.339009i
$646$	−9.22469e14	+	1.59776e15i	−0.322606	+	0.558770i
$647$	1.12701e15	+	1.95204e15i	0.390801	+	0.676887i	0.992555	−	0.121794i	$-0.0388649\pi$
$647$	1.12701e15	+	1.95204e15i	0.390801	+	0.676887i	−0.601755	+	0.798681i	$0.705532\pi$
$648$	−1.33723e14	−	1.01956e15i	−0.0459775	−	0.350551i
$649$	−1.06982e15	−	6.17663e14i	−0.364726	−	0.210574i
$650$	1.23175e15			0.416389
$651$	1.12969e15	−	1.68912e15i	0.378671	−	0.566193i
$652$	−1.15531e15			−0.384006
$653$	−1.80302e15	−	1.04097e15i	−0.594262	−	0.343098i	0.172519	−	0.985006i	$-0.444809\pi$
$653$	−1.80302e15	−	1.04097e15i	−0.594262	−	0.343098i	−0.766781	+	0.641909i	$0.778143\pi$
$654$	−1.50208e15	+	4.89902e13i	−0.490926	+	0.0160115i
$655$	1.48590e15	+	2.57365e15i	0.481573	+	0.834108i
$656$	4.96341e14	−	8.59688e14i	0.159518	−	0.276293i
$657$	−1.35212e15	+	9.02982e14i	−0.430929	+	0.287786i
$658$	1.39041e15	+	9.97002e14i	0.439440	+	0.315104i
$659$			2.56530e15i			0.804024i	0.915634	+	0.402012i	$0.131689\pi$
$659$			2.56530e15i			0.804024i	−0.915634	+	0.402012i	$0.868311\pi$
$660$	7.35831e14	+	1.18363e15i	0.228711	+	0.367896i
$661$	7.38936e14	−	4.26625e14i	0.227771	−	0.131504i	−0.381772	−	0.924256i	$-0.624686\pi$
$661$	7.38936e14	−	4.26625e14i	0.227771	−	0.131504i	0.609543	+	0.792753i	$0.291353\pi$
$662$	3.37994e15	−	1.95141e15i	1.03321	−	0.596526i
$663$	−4.51878e14	−	7.26876e14i	−0.136992	−	0.220362i
$664$			2.07445e15i			0.623705i
$665$	−6.59773e15	−	4.73096e15i	−1.96732	−	1.41069i
$666$	−3.70373e15	+	2.47345e15i	−1.09529	+	0.731466i
$667$	9.57560e14	−	1.65854e15i	0.280850	−	0.486446i
$668$	−8.03071e14	−	1.39096e15i	−0.233606	−	0.404617i
$669$	−5.56964e15	+	1.81653e14i	−1.60688	+	0.0524082i
$670$	8.83617e14	+	5.10156e14i	0.252844	+	0.145980i
$671$	−2.17664e15			−0.617749
$672$	3.49120e14	−	5.22008e14i	0.0982752	−	0.146942i
$673$	−2.26876e15			−0.633441			−0.316721	−	0.948519i	$-0.602582\pi$
$673$	−2.26876e15			−0.633441			−0.316721	+	0.948519i	$0.602582\pi$
$674$	−3.90821e15	−	2.25641e15i	−1.08230	−	0.624867i
$675$	3.83688e15	−	2.74735e15i	1.05392	−	0.754647i
$676$	7.28219e14	+	1.26131e15i	0.198406	+	0.343650i
$677$	−1.20074e15	+	2.07975e15i	−0.324499	+	0.562048i	−0.981411	−	0.191919i	$-0.938529\pi$
$677$	−1.20074e15	+	2.07975e15i	−0.324499	+	0.562048i	0.656912	+	0.753967i	$0.271862\pi$
$678$	2.98518e15	+	1.59608e15i	0.800216	+	0.427849i
$679$	−2.58654e15	+	1.17098e15i	−0.687759	+	0.311363i
$680$		−	1.16018e15i		−	0.306004i
$681$	−5.68888e14	+	3.53662e14i	−0.148839	+	0.0925292i
$682$	9.18916e14	−	5.30536e14i	0.238485	−	0.137690i
$683$	−6.39265e14	+	3.69080e14i	−0.164576	+	0.0950181i	−0.580026	−	0.814598i	$-0.696958\pi$
$683$	−6.39265e14	+	3.69080e14i	−0.164576	+	0.0950181i	0.415450	+	0.909616i	$0.363624\pi$
$684$	2.03806e14	+	3.12111e15i	0.0520486	+	0.797078i
$685$			3.34259e15i			0.846809i
$686$	1.92147e15	+	2.05536e15i	0.482893	+	0.516541i
$687$	−6.02638e14	+	1.12713e15i	−0.150243	+	0.281003i
$688$	2.39808e14	−	4.15359e14i	0.0593099	−	0.102728i
$689$	−1.35790e15	−	2.35195e15i	−0.333167	−	0.577062i
$690$	−2.27572e14	−	6.97756e15i	−0.0553923	−	1.69837i
$691$	−4.46003e15	−	2.57500e15i	−1.07698	−	0.621796i	−0.146901	−	0.989151i	$-0.546930\pi$
$691$	−4.46003e15	−	2.57500e15i	−1.07698	−	0.621796i	−0.930081	+	0.367355i	$0.880263\pi$
$692$	1.86625e15			0.447081
$693$	2.04220e15	+	1.27148e15i	0.485361	+	0.302189i
$694$	4.36313e15			1.02878
$695$	1.23368e14	+	7.12264e13i	0.0288593	+	0.0166619i
$696$	−1.75883e13	−	5.39272e14i	−0.00408200	−	0.125158i
$697$	−1.58275e15	−	2.74140e15i	−0.364445	−	0.631238i
$698$	2.75416e14	−	4.77035e14i	0.0629194	−	0.108980i
$699$	2.24754e15	−	4.20361e15i	0.509427	−	0.952792i
$700$	2.86804e15	+	2.83374e14i	0.644980	+	0.0637266i
$701$			3.17280e15i			0.707936i	0.935258	+	0.353968i	$0.115168\pi$
$701$			3.17280e15i			0.707936i	−0.935258	+	0.353968i	$0.884832\pi$
$702$	−1.32145e15	−	5.99321e14i	−0.292547	−	0.132680i
$703$	1.17319e16	−	6.77342e15i	2.57700	−	1.48783i
$704$	2.83983e14	−	1.63958e14i	0.0618933	−	0.0357341i
$705$	4.55087e15	−	2.82915e15i	0.984135	−	0.611808i
$706$		−	4.56956e15i		−	0.980501i
$707$	1.85527e15	−	2.58733e15i	0.395002	−	0.550865i
$708$	1.53740e15	+	8.21999e14i	0.324791	+	0.173655i
$709$	2.41084e15	−	4.17570e15i	0.505376	−	0.875337i	−0.494604	−	0.869118i	$-0.664687\pi$
$709$	2.41084e15	−	4.17570e15i	0.505376	−	0.875337i	0.999981	−	0.00621903i	$-0.00197959\pi$
$710$	3.04396e15	+	5.27229e15i	0.633167	+	1.09668i
$711$	−3.78634e15	+	7.67324e15i	−0.781514	+	1.58378i
$712$	1.32491e15	+	7.64940e14i	0.271361	+	0.156671i
$713$	−5.31504e15			−1.08022
$714$	−8.84940e14	−	1.79643e15i	−0.178474	−	0.362302i
$715$	1.96663e15			0.393587
$716$	3.16854e14	+	1.82936e14i	0.0629271	+	0.0363310i
$717$	−5.14915e15	+	1.67939e14i	−1.01480	+	0.0330976i
$718$	5.78058e14	+	1.00123e15i	0.113054	+	0.195816i
$719$	2.24610e15	−	3.89035e15i	0.435933	−	0.755057i	−0.561439	−	0.827518i	$-0.689752\pi$
$719$	2.24610e15	−	3.89035e15i	0.435933	−	0.755057i	0.997371	+	0.0724610i	$0.0230853\pi$
$720$	−1.09234e15	−	1.63567e15i	−0.210392	−	0.315040i
$721$	−4.01775e13	+	4.06638e14i	−0.00767960	+	0.0777256i
$722$		−	5.78601e15i		−	1.09755i
$723$	3.39778e15	+	5.46556e15i	0.639639	+	1.02890i
$724$	2.35628e15	−	1.36040e15i	0.440214	−	0.254158i
$725$	2.14441e15	−	1.23808e15i	0.397603	−	0.229556i
$726$	−1.36561e15	−	2.19667e15i	−0.251289	−	0.404216i
$727$		−	4.88814e15i		−	0.892698i	−0.894859	−	0.446349i	$-0.852724\pi$
$727$		−	4.88814e15i		−	0.892698i	0.894859	−	0.446349i	$-0.147276\pi$
$728$	−3.65470e14	−	8.07274e14i	−0.0662413	−	0.146318i
$729$	−5.45303e15	+	1.08054e15i	−0.980927	+	0.194375i
$730$	−1.55499e15	+	2.69333e15i	−0.277621	+	0.480854i
$731$	−7.64708e14	−	1.32451e15i	−0.135503	−	0.234699i
$732$	3.07015e15	−	1.00132e14i	0.539943	−	0.0176102i
$733$	3.57698e15	+	2.06517e15i	0.624374	+	0.360483i	0.778570	−	0.627558i	$-0.215945\pi$
$733$	3.57698e15	+	2.06517e15i	0.624374	+	0.360483i	−0.154196	+	0.988040i	$0.549279\pi$
$734$	−5.34869e15			−0.926657
$735$	8.24978e15	−	3.09802e15i	1.41861	−	0.532726i
$736$	−1.64257e15			−0.280347
$737$	7.96403e14	+	4.59803e14i	0.134915	+	0.0778935i
$738$	−4.81253e15	−	2.37473e15i	−0.809213	−	0.399305i
$739$	−6.35134e14	−	1.10009e15i	−0.106004	−	0.183604i	0.808144	−	0.588985i	$-0.200472\pi$
$739$	−6.35134e14	−	1.10009e15i	−0.106004	−	0.183604i	−0.914148	+	0.405381i	$0.867139\pi$
$740$	−4.25943e15	+	7.37755e15i	−0.705630	+	1.22219i
$741$	3.89211e15	+	2.08099e15i	0.640008	+	0.342191i
$742$	−2.62068e15	−	5.78873e15i	−0.427752	−	0.944848i
$743$		−	3.51176e15i		−	0.568965i	−0.958681	−	0.284483i	$-0.908178\pi$
$743$		−	3.51176e15i		−	0.568965i	0.958681	−	0.284483i	$-0.0918218\pi$
$744$	−1.27173e15	+	7.90595e14i	−0.204523	+	0.127146i
$745$	−9.11794e15	+	5.26425e15i	−1.45558	+	0.840382i
$746$	−5.95604e15	+	3.43872e15i	−0.943831	+	0.544921i
$747$	1.11909e16	−	7.30754e14i	1.76035	−	0.114950i
$748$		−	1.04567e15i		−	0.163281i
$749$	−2.41831e14	+	2.44758e15i	−0.0374854	+	0.379391i
$750$	9.72659e14	−	1.81919e15i	0.149666	−	0.279924i
$751$	4.32232e15	−	7.48648e15i	0.660233	−	1.14356i	−0.320321	−	0.947309i	$-0.603791\pi$
$751$	4.32232e15	−	7.48648e15i	0.660233	−	1.14356i	0.980554	−	0.196249i	$-0.0628760\pi$
$752$	−6.30391e14	−	1.09187e15i	−0.0955899	−	0.165567i
$753$	2.69822e14	+	8.27298e15i	0.0406168	+	1.24535i
$754$	−6.59356e14	−	3.80680e14i	−0.0985321	−	0.0568876i
$755$	−6.61989e15			−0.982070
$756$	−2.93901e15	−	1.69948e15i	−0.432844	−	0.250292i
$757$	−1.15306e15			−0.168587			−0.0842933	−	0.996441i	$-0.526863\pi$
$757$	−1.15306e15			−0.168587			−0.0842933	+	0.996441i	$0.526863\pi$
$758$	−2.11340e15	−	1.22017e15i	−0.306762	−	0.177109i
$759$	−2.05111e14	−	6.28886e15i	−0.0295569	−	0.906238i
$760$	2.99132e15	+	5.18112e15i	0.427946	+	0.741223i
$761$	3.77696e15	−	6.54188e15i	0.536447	−	0.929153i	−0.462645	−	0.886543i	$-0.653100\pi$
$761$	3.77696e15	−	6.54188e15i	0.536447	−	0.929153i	0.999092	−	0.0426092i	$-0.0135670\pi$
$762$	2.09747e15	−	3.92294e15i	0.295762	−	0.553171i
$763$	−2.89144e15	+	4.03236e15i	−0.404789	+	0.564513i
$764$		−	4.41147e15i		−	0.613155i
$765$	−6.25872e15	+	4.08690e14i	−0.863670	+	0.0563970i
$766$	−7.64633e15	+	4.41461e15i	−1.04760	+	0.604831i
$767$	2.13043e15	−	1.23000e15i	0.289796	−	0.167314i
$768$	−3.93016e14	+	2.44327e14i	−0.0530791	+	0.0329978i
$769$		−	1.93150e15i		−	0.259000i	−0.991579	−	0.129500i	$-0.958663\pi$
$769$		−	1.93150e15i		−	0.259000i	0.991579	−	0.129500i	$-0.0413373\pi$
$770$	4.57916e15	+	4.52440e14i	0.609659	+	0.0602368i
$771$	−5.19240e15	−	2.77621e15i	−0.686387	−	0.366989i
$772$	1.34132e15	−	2.32323e15i	0.176050	−	0.304928i
$773$	3.86524e15	+	6.69480e15i	0.503720	+	0.872469i	0.999991	+	0.00430139i	$0.00136918\pi$
$773$	3.86524e15	+	6.69480e15i	0.503720	+	0.872469i	−0.496270	+	0.868168i	$0.665297\pi$
$774$	−2.32518e15	−	1.14735e15i	−0.300871	−	0.148464i
$775$	−5.95140e15	−	3.43604e15i	−0.764645	−	0.441468i
$776$	2.09226e15			0.266917
$777$	−9.68034e14	+	1.46724e16i	−0.122624	+	1.85860i
$778$	8.07457e15			1.01562
$779$	1.41365e16	+	8.16169e15i	1.76557	+	1.01935i
$780$	−2.77394e15	+	9.04718e13i	−0.344015	+	0.0112200i
$781$	2.74352e15	+	4.75191e15i	0.337853	+	0.585178i
$782$	−2.61894e15	+	4.53614e15i	−0.320250	+	0.554688i
$783$	−2.90297e15	+	2.84848e14i	−0.352495	+	0.0345879i
$784$	−6.65249e14	−	1.96376e15i	−0.0802133	−	0.236782i
$785$		−	2.88979e15i		−	0.346006i
$786$	−1.99571e15	−	3.21023e15i	−0.237286	−	0.381691i
$787$	−8.25561e15	+	4.76638e15i	−0.974738	+	0.562765i	−0.900677	−	0.434488i	$-0.856929\pi$
$787$	−8.25561e15	+	4.76638e15i	−0.974738	+	0.562765i	−0.0740609	+	0.997254i	$0.523596\pi$
$788$	8.42950e13	−	4.86677e13i	0.00988343	−	0.00570620i
$789$	−5.05836e14	−	8.13670e14i	−0.0588960	−	0.0947382i
$790$			1.63666e16i			1.89239i
$791$	1.01814e16	−	4.60931e15i	1.16906	−	0.529256i
$792$	−9.84526e14	−	1.47422e15i	−0.112264	−	0.168103i
$793$	2.16726e15	−	3.75380e15i	0.245419	−	0.425078i
$794$	5.27224e15	+	9.13179e15i	0.592902	+	1.02694i
$795$	−1.98911e16	+	6.48747e14i	−2.22147	+	0.0724530i
$796$	4.44704e15	+	2.56750e15i	0.493230	+	0.284766i
$797$	1.72959e16			1.90512			0.952561	−	0.304348i	$-0.0984386\pi$
$797$	1.72959e16			1.90512			0.952561	+	0.304348i	$0.0984386\pi$
$798$	8.58375e15	+	5.74083e15i	0.938990	+	0.627999i
$799$	−4.02043e15			−0.436782
$800$	−1.83923e15	−	1.06188e15i	−0.198446	−	0.114573i
$801$	3.65983e15	−	7.41686e15i	0.392177	−	0.794769i
$802$	4.53260e15	+	7.85070e15i	0.482379	+	0.835506i
$803$	−1.40151e15	+	2.42749e15i	−0.148136	+	0.256580i
$804$	−1.14448e15	−	6.11916e14i	−0.120143	−	0.0642368i
$805$	−1.87313e16	−	1.34315e16i	−1.95295	−	1.40038i
$806$			2.11300e15i			0.218805i
$807$	4.52787e15	−	2.81485e15i	0.465682	−	0.289501i
$808$	−2.03180e15	+	1.17306e15i	−0.207548	+	0.119828i
$809$	−1.45151e16	+	8.38031e15i	−1.47266	+	0.850244i	−0.999527	−	0.0307449i	$-0.990212\pi$
$809$	−1.45151e16	+	8.38031e15i	−1.47266	+	0.850244i	−0.473138	+	0.880988i	$0.656879\pi$
$810$	−8.43898e15	+	6.46894e15i	−0.850398	+	0.651877i
$811$		−	2.16723e14i		−	0.0216915i	−0.999941	−	0.0108458i	$-0.996548\pi$
$811$		−	2.16723e14i		−	0.0216915i	0.999941	−	0.0108458i	$-0.00345238\pi$
$812$	−1.44768e15	−	1.03807e15i	−0.143918	−	0.103198i
$813$	7.54443e15	−	1.41105e16i	0.744952	−	1.39330i
$814$	−3.83902e15	+	6.64938e15i	−0.376519	+	0.652149i
$815$	5.97328e15	+	1.03460e16i	0.581897	+	1.00788i
$816$	4.81043e13	+	1.47492e15i	0.00465466	+	0.142716i
$817$	6.83005e15	+	3.94333e15i	0.656451	+	0.379002i
$818$	−4.62764e15			−0.441790
$819$	−4.22618e15	+	2.25594e15i	−0.400762	+	0.213927i
$820$	−1.02649e16			−0.966892
$821$	1.62042e14	+	9.35547e13i	0.0151614	+	0.00875343i	0.507562	−	0.861616i	$-0.330547\pi$
$821$	1.62042e14	+	9.35547e13i	0.0151614	+	0.00875343i	−0.492400	+	0.870369i	$0.663880\pi$
$822$	−1.38593e14	−	4.24938e15i	−0.0128809	−	0.394940i
$823$	8.23349e15	+	1.42608e16i	0.760125	+	1.31658i	0.942786	+	0.333399i	$0.108196\pi$
$823$	8.23349e15	+	1.42608e16i	0.760125	+	1.31658i	−0.182661	+	0.983176i	$0.558471\pi$
$824$	1.50556e14	−	2.60771e14i	0.0138070	−	0.0239144i
$825$	3.83593e15	−	7.17442e15i	0.349441	−	0.653567i
$826$	5.24351e15	−	2.37385e15i	0.474496	−	0.214814i
$827$			6.68902e15i			0.601288i	0.953736	+	0.300644i	$0.0972016\pi$
$827$			6.68902e15i			0.601288i	−0.953736	+	0.300644i	$0.902798\pi$
$828$	5.78617e14	+	8.86101e15i	0.0516684	+	0.791255i
$829$	3.22601e14	−	1.86254e14i	0.0286165	−	0.0165217i	−0.485624	−	0.874168i	$-0.661407\pi$
$829$	3.22601e14	−	1.86254e14i	0.0286165	−	0.0165217i	0.514240	+	0.857646i	$0.328074\pi$
$830$	1.85771e16	−	1.07255e16i	1.63700	−	0.945122i
$831$	−8.70894e15	+	5.41410e15i	−0.762359	+	0.473937i
$832$			6.53006e14i			0.0567857i
$833$	−6.48382e15	−	1.29389e15i	−0.560123	−	0.111776i
$834$	−1.59789e14	−	8.54337e13i	−0.0137130	−	0.00733189i
$835$	−8.30420e15	+	1.43833e16i	−0.707982	+	1.22626i
$836$	2.69608e15	+	4.66974e15i	0.228348	+	0.395511i
$837$	4.71293e15	+	6.58196e15i	0.396553	+	0.553816i
$838$	5.59132e15	+	3.22815e15i	0.467382	+	0.269843i
$839$	−1.36707e16			−1.13527			−0.567634	−	0.823281i	$-0.692141\pi$
$839$	−1.36707e16			−1.13527			−0.567634	+	0.823281i	$0.692141\pi$
$840$	−6.47973e15	−	4.27510e14i	−0.534590	−	0.0352704i
$841$	1.06700e16			0.874551
$842$	−9.71078e15	−	5.60652e15i	−0.790747	−	0.456538i
$843$	8.03146e13	−	2.61945e12i	0.00649745	−	0.000211913i
$844$	−4.83206e15	−	8.36938e15i	−0.388373	−	0.672682i
$845$	7.53019e15	−	1.30427e16i	0.601304	−	1.04149i
$846$	−5.66814e15	+	3.78534e15i	−0.449680	+	0.300309i
$847$	−8.49832e15	−	8.39669e14i	−0.669845	−	0.0661834i
$848$			4.68252e15i			0.366693i
$849$	7.70958e15	+	1.24014e16i	0.599844	+	0.964890i
$850$	−5.86500e15	+	3.38616e15i	−0.453382	+	0.261760i
$851$	3.33075e16	−	1.92301e16i	2.55817	−	1.47696i
$852$	−4.08834e15	−	6.57637e15i	−0.311982	−	0.501843i
$853$		−	1.15284e16i		−	0.874075i	−0.899443	−	0.437037i	$-0.856028\pi$
$853$		−	1.15284e16i		−	0.874075i	0.899443	−	0.437037i	$-0.143972\pi$
$854$	5.90989e15	−	8.24185e15i	0.445206	−	0.620878i
$855$	2.68964e16	−	1.79621e16i	2.01317	−	1.34445i
$856$	9.06207e14	−	1.56960e15i	0.0673941	−	0.116730i
$857$	1.65695e15	+	2.86993e15i	0.122438	+	0.212069i	0.920729	−	0.390204i	$-0.127595\pi$
$857$	1.65695e15	+	2.86993e15i	0.122438	+	0.212069i	−0.798291	+	0.602272i	$0.794262\pi$
$858$	−2.50015e15	+	8.15421e13i	−0.183563	+	0.00598690i
$859$	−4.63505e15	−	2.67605e15i	−0.338136	−	0.195223i	0.321311	−	0.946974i	$-0.395876\pi$
$859$	−4.63505e15	−	2.67605e15i	−0.338136	−	0.195223i	−0.659448	+	0.751750i	$0.729210\pi$
$860$	−4.95949e15			−0.359497
$861$	−1.58942e16	+	7.82965e15i	−1.14478	+	0.563930i
$862$	1.02425e16			0.733017
$863$	1.34961e16	+	7.79199e15i	0.959731	+	0.554101i	0.896090	−	0.443872i	$-0.146396\pi$
$863$	1.34961e16	+	7.79199e15i	0.959731	+	0.554101i	0.0636407	+	0.997973i	$0.479729\pi$
$864$	1.45649e15	+	2.03410e15i	0.102916	+	0.143730i
$865$	−9.64903e15	−	1.67126e16i	−0.677478	−	1.17343i
$866$	−6.64181e15	+	1.15040e16i	−0.463381	+	0.802600i
$867$	−8.57072e15	−	4.58249e15i	−0.594172	−	0.317685i
$868$	−4.86113e14	+	4.91997e15i	−0.0334872	+	0.338925i
$869$			1.47512e16i			1.00976i
$870$	−4.73835e15	+	2.94569e15i	−0.322308	+	0.200370i
$871$	−1.58594e15	+	9.15645e14i	−0.107198	+	0.0618910i
$872$	3.16656e15	−	1.82822e15i	0.212690	−	0.122797i
$873$	−7.37028e14	−	1.12869e16i	−0.0491933	−	0.753352i
$874$		−	2.70099e16i		−	1.79147i
$875$	−2.80894e15	−	6.20458e15i	−0.185139	−	0.408948i
$876$	1.86516e15	−	3.48845e15i	0.122164	−	0.228486i
$877$	1.91903e15	−	3.32385e15i	0.124906	−	0.216343i	−0.796790	−	0.604256i	$-0.793470\pi$
$877$	1.91903e15	−	3.32385e15i	0.124906	−	0.216343i	0.921696	+	0.387913i	$0.126804\pi$
$878$	−3.93756e15	−	6.82006e15i	−0.254687	−	0.441131i
$879$	2.44200e14	+	7.48738e15i	0.0156967	+	0.481273i
$880$	−2.93655e15	−	1.69542e15i	−0.187578	−	0.108298i
$881$	−1.82088e16			−1.15588			−0.577940	−	0.816079i	$-0.696143\pi$
$881$	−1.82088e16			−1.15588			−0.577940	+	0.816079i	$0.696143\pi$
$882$	−1.03594e16	+	4.28052e15i	−0.653515	+	0.270035i
$883$	−2.84442e15			−0.178324			−0.0891620	−	0.996017i	$-0.528419\pi$
$883$	−2.84442e15			−0.178324			−0.0891620	+	0.996017i	$0.528419\pi$
$884$	1.80335e15	+	1.04116e15i	0.112355	+	0.0648682i
$885$	−5.87644e14	−	1.80177e16i	−0.0363853	−	1.11561i
$886$	−1.89409e15	−	3.28066e15i	−0.116551	−	0.201872i
$887$	−1.07493e16	+	1.86183e16i	−0.657355	+	1.13857i	0.323942	+	0.946077i	$0.394992\pi$
$887$	−1.07493e16	+	1.86183e16i	−0.657355	+	1.13857i	−0.981298	+	0.192496i	$0.938342\pi$
$888$	5.10905e15	−	9.55557e15i	0.310505	−	0.580745i
$889$	−6.05727e15	−	1.33797e16i	−0.365862	−	0.808140i
$890$		−	1.58198e16i		−	0.949634i
$891$	−7.60604e15	+	5.83045e15i	−0.453765	+	0.347836i
$892$	1.17414e16	−	6.77893e15i	0.696169	−	0.401934i
$893$	1.79544e16	−	1.03660e16i	1.05800	−	0.610839i
$894$	1.13732e16	−	7.07040e15i	0.666081	−	0.414083i
$895$		−	3.78331e15i		−	0.220214i
$896$	−1.50229e14	+	1.52048e15i	−0.00869081	+	0.0879600i
$897$	1.10499e16	+	5.90804e15i	0.635333	+	0.339692i
$898$	4.88129e15	−	8.45464e15i	0.278943	−	0.483143i
$899$	2.12385e15	+	3.67862e15i	0.120628	+	0.208933i
$900$	−5.08053e15	+	1.02960e16i	−0.286798	+	0.581212i
$901$	1.29313e16	+	7.46589e15i	0.725531	+	0.418886i
$902$	−9.25173e15			−0.515926
$903$	−7.67932e15	+	3.78291e15i	−0.425638	+	0.209673i
$904$	−8.23573e15			−0.453707
$905$	−2.43652e16	−	1.40673e16i	−1.33414	−	0.770269i
$906$	8.41575e15	−	2.74479e14i	0.458023	−	0.0149384i
$907$	1.32003e15	+	2.28636e15i	0.0714076	+	0.123682i	0.899518	−	0.436883i	$-0.143918\pi$
$907$	1.32003e15	+	2.28636e15i	0.0714076	+	0.123682i	−0.828111	+	0.560564i	$0.810584\pi$
$908$	8.14866e14	−	1.41139e15i	0.0438141	−	0.0758883i
$909$	7.04393e15	+	1.05475e16i	0.376455	+	0.563702i
$910$	−5.33970e15	+	7.44668e15i	−0.283654	+	0.395581i
$911$		−	1.06115e16i		−	0.560309i	−0.959955	−	0.280154i	$-0.909614\pi$
$911$		−	1.06115e16i		−	0.560309i	0.959955	−	0.280154i	$-0.0903857\pi$
$912$	−4.01764e15	−	6.46265e15i	−0.210863	−	0.339187i
$913$	1.67435e16	−	9.66687e15i	0.873489	−	0.504309i
$914$	8.94581e15	−	5.16487e15i	0.463891	−	0.267827i
$915$	−1.67702e16	−	2.69760e16i	−0.864415	−	1.39047i
$916$		−	3.10960e15i		−	0.159323i
$917$	−1.24195e16	−	1.22710e15i	−0.632519	−	0.0624954i
$918$	7.93966e15	−	7.79064e14i	0.401946	−	0.0394401i
$919$	−1.53256e16	+	2.65447e16i	−0.771225	+	1.33580i	0.165667	+	0.986182i	$0.447022\pi$
$919$	−1.53256e16	+	2.65447e16i	−0.771225	+	1.33580i	−0.936892	+	0.349619i	$0.886311\pi$
$920$	8.49253e15	+	1.47095e16i	0.424819	+	0.735809i
$921$	−1.50479e16	+	4.90784e14i	−0.748250	+	0.0244041i
$922$	1.80311e16	+	1.04102e16i	0.891253	+	0.514565i
$923$	−1.09268e16			−0.536888
$924$	−5.84017e15	−	3.85314e14i	−0.285253	−	0.0188200i
$925$	4.97272e16			2.41443
$926$	1.06911e16	+	6.17252e15i	0.516016	+	0.297922i
$927$	−1.45979e15	−	7.20331e14i	−0.0700410	−	0.0345616i
$928$	6.56360e14	+	1.13685e15i	0.0313060	+	0.0542237i
$929$	−3.02641e15	+	5.24189e15i	−0.143496	+	0.248543i	−0.928811	−	0.370554i	$-0.879168\pi$
$929$	−3.02641e15	+	5.24189e15i	−0.143496	+	0.248543i	0.785315	+	0.619097i	$0.212501\pi$
$930$	1.36551e16	+	7.30094e15i	0.643633	+	0.344130i
$931$	3.22914e16	−	1.09392e16i	1.51309	−	0.512579i
$932$			1.15972e16i			0.540215i
$933$	5.47813e15	−	3.40560e15i	0.253678	−	0.157705i
$934$	−3.21487e15	+	1.85610e15i	−0.147998	+	0.0854465i
$935$	−9.36416e15	+	5.40640e15i	−0.428554	+	0.247426i
$936$	3.52271e15	−	2.30030e14i	0.160273	−	0.0104657i
$937$		−	6.50444e15i		−	0.294200i	−0.989122	−	0.147100i	$-0.953006\pi$
$937$		−	6.50444e15i		−	0.294200i	0.989122	−	0.147100i	$-0.0469938\pi$
$938$	−3.90340e15	+	1.76715e15i	−0.175520	+	0.0794618i
$939$	−1.20089e16	+	2.24605e16i	−0.536837	+	1.00406i
$940$	−6.51859e15	+	1.12905e16i	−0.289701	+	0.501778i
$941$	1.81641e16	+	3.14611e16i	0.802547	+	1.39005i	0.917934	+	0.396732i	$0.129856\pi$
$941$	1.81641e16	+	3.14611e16i	0.802547	+	1.39005i	−0.115387	+	0.993321i	$0.536811\pi$
$942$	1.19819e14	+	3.67375e15i	0.00526314	+	0.161372i
$943$	4.01342e16	+	2.31715e16i	1.75267	+	1.01191i
$944$	−4.24149e15			−0.184150
$945$	−2.36750e13	+	3.51062e16i	−0.00102192	+	1.51533i
$946$	−4.46999e15			−0.191825
$947$	−2.51311e16	−	1.45095e16i	−1.07223	−	0.619051i	−0.143439	−	0.989659i	$-0.545816\pi$
$947$	−2.51311e16	−	1.45095e16i	−1.07223	−	0.619051i	−0.928789	+	0.370608i	$0.879149\pi$
$948$	−6.78606e14	−	2.08066e16i	−0.0287854	−	0.882584i
$949$	−2.79095e15	−	4.83407e15i	−0.117703	−	0.203868i
$950$	1.74612e16	−	3.02438e16i	0.732142	−	1.26811i
$951$	1.83358e16	−	3.42939e16i	0.764377	−	1.42963i
$952$	3.95944e15	+	2.83915e15i	0.164108	+	0.117675i
$953$			5.99344e15i			0.246982i	0.992346	+	0.123491i	$0.0394090\pi$
$953$			5.99344e15i			0.246982i	−0.992346	+	0.123491i	$0.960591\pi$
$954$	2.52604e16	−	1.64948e15i	1.03496	−	0.0675821i
$955$	−3.95055e16	+	2.28085e16i	−1.60931	+	0.929135i
$956$	1.08550e16	−	6.26714e15i	0.439655	−	0.253835i
$957$	−4.27067e15	+	2.65495e15i	−0.171981	+	0.106916i
$958$		−	2.91600e16i		−	1.16756i
$959$	−1.14075e16	−	8.17986e15i	−0.454139	−	0.325644i
$960$	4.22000e15	+	2.25629e15i	0.167040	+	0.0893108i
$961$	−6.80990e15	+	1.17951e16i	−0.268017	+	0.464219i
$962$	−7.64496e15	−	1.32415e16i	−0.299166	−	0.518171i
$963$	−8.78658e15	−	4.33572e15i	−0.341881	−	0.168701i
$964$	−1.35598e16	−	7.82878e15i	−0.524603	−	0.302880i
$965$	−2.77399e16			−1.06710
$966$	2.43697e16	+	1.62985e16i	0.932131	+	0.623411i
$967$	−6.20581e15			−0.236022			−0.118011	−	0.993012i	$-0.537652\pi$
$967$	−6.20581e15			−0.236022			−0.118011	+	0.993012i	$0.537652\pi$
$968$	5.44985e15	+	3.14647e15i	0.206096	+	0.118990i
$969$	−2.42531e16	+	7.91013e14i	−0.911983	+	0.0297442i
$970$	−1.08176e16	−	1.87366e16i	−0.404469	−	0.700561i
$971$	−5.51063e15	+	9.54468e15i	−0.204878	+	0.354859i	−0.950094	−	0.311964i	$-0.899013\pi$
$971$	−5.51063e15	+	9.54468e15i	−0.204878	+	0.354859i	0.745216	+	0.666823i	$0.232346\pi$
$972$	1.04601e16	−	8.57376e15i	0.386698	−	0.316962i
$973$	−5.44980e14	+	2.46724e14i	−0.0200337	+	0.00906966i
$974$			3.65333e16i			1.33541i
$975$	8.55352e15	+	1.37589e16i	0.310899	+	0.500102i
$976$	−6.47223e15	+	3.73674e15i	−0.233927	+	0.135058i
$977$	2.74247e16	−	1.58337e16i	0.985649	−	0.569065i	0.0816783	−	0.996659i	$-0.473972\pi$
$977$	2.74247e16	−	1.58337e16i	0.985649	−	0.569065i	0.903971	+	0.427594i	$0.140639\pi$
$978$	−8.02271e15	−	1.29051e16i	−0.286720	−	0.461208i
$979$		−	1.42584e16i		−	0.506717i
$980$	−1.41463e16	+	1.61106e16i	−0.499918	+	0.569335i
$981$	−1.09780e16	−	1.64383e16i	−0.385783	−	0.577668i
$982$	−1.38748e15	+	2.40318e15i	−0.0484857	+	0.0839796i
$983$	−1.14596e16	−	1.98486e16i	−0.398222	−	0.689741i	0.595284	−	0.803515i	$-0.297039\pi$
$983$	−1.14596e16	−	1.98486e16i	−0.398222	−	0.689741i	−0.993507	+	0.113774i	$0.963706\pi$
$984$	1.30496e16	−	4.25610e14i	0.450945	−	0.0147075i
$985$	−8.71657e14	−	5.03251e14i	−0.0299534	−	0.0172936i
$986$	4.18605e15			0.143048
$987$	−1.48147e15	+	2.24545e16i	−0.0503440	+	0.763060i
$988$	−1.07378e16			−0.362872
$989$	1.93909e16	+	1.11953e16i	0.651656	+	0.376234i
$990$	−8.11167e15	+	1.64388e16i	−0.271092	+	0.549383i
$991$	1.99610e16	+	3.45735e16i	0.663402	+	1.14905i	0.979716	+	0.200392i	$0.0642215\pi$
$991$	1.99610e16	+	3.45735e16i	0.663402	+	1.14905i	−0.316314	+	0.948655i	$0.602445\pi$
$992$	1.82160e15	−	3.15510e15i	0.0602058	−	0.104279i
$993$	4.52686e16	+	2.42036e16i	1.48791	+	0.795536i
$994$	−2.54422e16	−	2.51379e15i	−0.831629	−	0.0821683i
$995$		−	5.30987e16i		−	1.72607i
$996$	−2.31720e16	+	1.44054e16i	−0.749097	+	0.465692i
$997$	−9.37156e15	+	5.41067e15i	−0.301293	+	0.173951i	−0.643023	−	0.765846i	$-0.722320\pi$
$997$	−9.37156e15	+	5.41067e15i	−0.301293	+	0.173951i	0.341731	+	0.939798i	$0.388987\pi$
$998$	−2.17969e16	+	1.25844e16i	−0.696909	+	0.402361i
$999$	−5.33483e16	−	2.41952e16i	−1.69633	−	0.769343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.12.f.a.5.8	✓	60
3.2	odd	2	inner	42.12.f.a.5.28	yes	60
7.3	odd	6	inner	42.12.f.a.17.28	yes	60
21.17	even	6	inner	42.12.f.a.17.8	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.f.a.5.8	✓	60	1.1	even	1	trivial
42.12.f.a.5.28	yes	60	3.2	odd	2	inner
42.12.f.a.17.8	yes	60	21.17	even	6	inner
42.12.f.a.17.28	yes	60	7.3	odd	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	42.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-27.7128 - 16.0000i) q^{2} +(-13.7199 - 420.665i) q^{3} +(512.000 + 886.810i) q^{4} +(5294.36 - 9170.11i) q^{5} +(-6350.42 + 11877.3i) q^{6} +(18339.4 + 40509.2i) q^{7} -32768.0i q^{8} +(-176771. + 11543.0i) q^{9} +(-293443. + 169420. i) q^{10} +(-264480. + 152698. i) q^{11} +(366025. - 227547. i) q^{12} -608159. i q^{13} +(139912. - 1.41605e6i) q^{14} +(-3.93018e6 - 2.10134e6i) q^{15} +(-524288. + 908093. i) q^{16} +(1.67187e6 + 2.89576e6i) q^{17} +(5.08350e6 + 2.50844e6i) q^{18} +(-1.49324e7 - 8.62124e6i) q^{19} +1.08429e7 q^{20} +(1.67892e7 - 8.27050e6i) q^{21} +9.77265e6 q^{22} +(-4.23940e7 - 2.44762e7i) q^{23} +(-1.37843e7 + 449575. i) q^{24} +(-3.16465e7 - 5.48134e7i) q^{25} +(-9.73055e6 + 1.68538e7i) q^{26} +(7.28100e6 + 7.42027e7i) q^{27} +(-2.65342e7 + 3.70042e7i) q^{28} +3.91221e7i q^{29} +(7.52949e7 + 1.21117e8i) q^{30} +(9.40293e7 - 5.42878e7i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(6.78632e7 + 1.09162e8i) q^{33} -1.07000e8i q^{34} +(4.68569e8 + 4.62965e7i) q^{35} +(-1.00743e8 - 1.50852e8i) q^{36} +(-3.92833e8 + 6.80407e8i) q^{37} +(2.75880e8 + 4.77838e8i) q^{38} +(-2.55831e8 + 8.34390e6i) q^{39} +(-3.00486e8 - 1.73486e8i) q^{40} -9.46696e8 q^{41} +(-5.97603e8 - 3.94278e7i) q^{42} -4.57397e8 q^{43} +(-2.70828e8 - 1.56362e8i) q^{44} +(-8.30037e8 + 1.68212e9i) q^{45} +(7.83238e8 + 1.35661e9i) q^{46} +(-6.01188e8 + 1.04129e9i) q^{47} +(3.89196e8 + 2.08090e8i) q^{48} +(-1.30466e9 + 1.48583e9i) q^{49} +2.02538e9i q^{50} +(1.19521e9 - 7.43025e8i) q^{51} +(5.39322e8 - 3.11378e8i) q^{52} +(3.86732e9 - 2.23280e9i) q^{53} +(9.85467e8 - 2.17286e9i) q^{54} +3.23375e9i q^{55} +(1.32741e9 - 6.00944e8i) q^{56} +(-3.42178e9 + 6.39983e9i) q^{57} +(6.25954e8 - 1.08418e9i) q^{58} +(2.02250e9 + 3.50308e9i) q^{59} +(-1.48763e8 - 4.56121e9i) q^{60} +(6.17240e9 + 3.56363e9i) q^{61} -3.47442e9 q^{62} +(-3.70946e9 - 6.94914e9i) q^{63} -1.07374e9 q^{64} +(-5.57689e9 - 3.21982e9i) q^{65} +(-1.34080e8 - 4.11101e9i) q^{66} +(-1.50560e9 - 2.60778e9i) q^{67} +(-1.71199e9 + 2.96526e9i) q^{68} +(-9.71462e9 + 1.81695e10i) q^{69} +(-1.22446e10 - 8.78011e9i) q^{70} -1.79670e10i q^{71} +(3.78240e8 + 5.79242e9i) q^{72} +(7.94868e9 - 4.58917e9i) q^{73} +(2.17730e10 - 1.25707e10i) q^{74} +(-2.26239e10 + 1.40646e10i) q^{75} -1.76563e10i q^{76} +(-1.10361e10 - 7.91350e9i) q^{77} +(7.22330e9 + 3.86207e9i) q^{78} +(2.41511e10 - 4.18309e10i) q^{79} +(5.55154e9 + 9.61555e9i) q^{80} +(3.11146e10 - 4.08092e9i) q^{81} +(2.62356e10 + 1.51471e10i) q^{82} -6.33073e10 q^{83} +(1.59304e10 + 1.06543e10i) q^{84} +3.54059e10 q^{85} +(1.26758e10 + 7.31836e9i) q^{86} +(1.64573e10 - 5.36753e8i) q^{87} +(5.00360e9 + 8.66649e9i) q^{88} +(-2.33441e10 + 4.04332e10i) q^{89} +(4.99165e10 - 3.33356e10i) q^{90} +(2.46360e10 - 1.11533e10i) q^{91} -5.01272e10i q^{92} +(-2.41271e10 - 3.88100e10i) q^{93} +(3.33212e10 - 1.92380e10i) q^{94} +(-1.58115e11 + 9.12879e10i) q^{95} +(-7.45627e9 - 1.19939e10i) q^{96} +6.38508e10i q^{97} +(5.99291e10 - 2.03018e10i) q^{98} +(4.49897e10 - 3.00453e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30720 q^{4} - 95298 q^{7} - 91434 q^{9} + 245184 q^{10} - 8480820 q^{15} - 31457280 q^{16} + 12170496 q^{18} + 1649724 q^{19} + 43254216 q^{21} + 20705664 q^{22} + 4521984 q^{24} - 336132444 q^{25}+ \cdots + 288758042496 q^{99}+O(q^{100}) \) 60 * q + 30720 * q^4 - 95298 * q^7 - 91434 * q^9 + 245184 * q^10 - 8480820 * q^15 - 31457280 * q^16 + 12170496 * q^18 + 1649724 * q^19 + 43254216 * q^21 + 20705664 * q^22 + 4521984 * q^24 - 336132444 * q^25 + 28121088 * q^28 - 77109120 * q^30 - 275992974 * q^31 + 1056712914 * q^33 - 187256832 * q^36 + 555437556 * q^37 - 563926680 * q^39 + 251068416 * q^40 + 1167043776 * q^42 + 2546594304 * q^43 + 544480776 * q^45 - 452472192 * q^46 - 1309143414 * q^49 + 2007979044 * q^51 + 3219419136 * q^52 - 9840998592 * q^54 + 17053196256 * q^57 + 12235419456 * q^58 - 4342179840 * q^60 - 3056592000 * q^61 - 42499692960 * q^63 - 64424509440 * q^64 + 48796070400 * q^66 + 27979853436 * q^67 - 4966503360 * q^70 - 12462587904 * q^72 - 105678747168 * q^73 + 173211633504 * q^75 - 16600538880 * q^78 - 27787555926 * q^79 - 71399556486 * q^81 + 31231064832 * q^82 - 25272410112 * q^84 + 12868048152 * q^85 + 137017459998 * q^87 + 10601299968 * q^88 + 333571182180 * q^91 - 14607989424 * q^93 - 430917051648 * q^94 + 4630511616 * q^96 + 288758042496 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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