LMFDB - Embedded newform 43.11.b.b.42.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,11,Mod(42,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("43.42");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	43.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$27.3203618650$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			42.1
Character	$\chi$	$=$	43.42
Dual form			43.11.b.b.42.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-59.1014i q^{2} +419.853i q^{3} -2468.98 q^{4} -832.528i q^{5} +24813.9 q^{6} -31219.1i q^{7} +85400.1i q^{8} -117228. q^{9} +O(q^{10})$	\(q-59.1014i q^{2} +419.853i q^{3} -2468.98 q^{4} -832.528i q^{5} +24813.9 q^{6} -31219.1i q^{7} +85400.1i q^{8} -117228. q^{9} -49203.6 q^{10} -30601.5 q^{11} -1.03661e6i q^{12} -11019.9 q^{13} -1.84510e6 q^{14} +349540. q^{15} +2.51904e6 q^{16} +1.14659e6 q^{17} +6.92834e6i q^{18} +4.19962e6i q^{19} +2.05549e6i q^{20} +1.31075e7 q^{21} +1.80859e6i q^{22} -6.78637e6 q^{23} -3.58555e7 q^{24} +9.07252e6 q^{25} +651289. i q^{26} -2.44266e7i q^{27} +7.70793e7i q^{28} +2.48741e7i q^{29} -2.06583e7i q^{30} -3.61300e6 q^{31} -6.14288e7i q^{32} -1.28481e7i q^{33} -6.77651e7i q^{34} -2.59908e7 q^{35} +2.89433e8 q^{36} +1.01376e8i q^{37} +2.48203e8 q^{38} -4.62673e6i q^{39} +7.10980e7 q^{40} -3.57321e7 q^{41} -7.74670e8i q^{42} +(-1.34018e8 + 6.04208e7i) q^{43} +7.55544e7 q^{44} +9.75955e7i q^{45} +4.01084e8i q^{46} +2.71560e8 q^{47} +1.05763e9i q^{48} -6.92160e8 q^{49} -5.36199e8i q^{50} +4.81400e8i q^{51} +2.72078e7 q^{52} +4.96941e8 q^{53} -1.44365e9 q^{54} +2.54766e7i q^{55} +2.66612e9 q^{56} -1.76323e9 q^{57} +1.47010e9 q^{58} -6.47645e8 q^{59} -8.63005e8 q^{60} -5.21284e8i q^{61} +2.13533e8i q^{62} +3.65976e9i q^{63} -1.05104e9 q^{64} +9.17434e6i q^{65} -7.59343e8 q^{66} +1.81540e9 q^{67} -2.83090e9 q^{68} -2.84928e9i q^{69} +1.53609e9i q^{70} -6.55571e8i q^{71} -1.00113e10i q^{72} +2.34267e9i q^{73} +5.99147e9 q^{74} +3.80913e9i q^{75} -1.03688e10i q^{76} +9.55352e8i q^{77} -2.73446e8 q^{78} +3.31775e9 q^{79} -2.09717e9i q^{80} +3.33341e9 q^{81} +2.11182e9i q^{82} -3.83424e9 q^{83} -3.23620e10 q^{84} -9.54568e8i q^{85} +(3.57095e9 + 7.92065e9i) q^{86} -1.04435e10 q^{87} -2.61337e9i q^{88} +7.01136e9i q^{89} +5.76803e9 q^{90} +3.44031e8i q^{91} +1.67554e10 q^{92} -1.51693e9i q^{93} -1.60496e10i q^{94} +3.49630e9 q^{95} +2.57911e10 q^{96} -5.78385e9 q^{97} +4.09076e10i q^{98} +3.58735e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9}+O(q^{10}) $ 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9	$ 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9} - 254122 q^{10} - 218200 q^{11} - 191008 q^{13} - 1380228 q^{14} - 512732 q^{15} + 2224308 q^{16} - 1070678 q^{17} + 17857352 q^{21} + 8915254 q^{23} - 39666730 q^{24} - 82938284 q^{25} - 55042410 q^{31} - 179227232 q^{35} + 394381042 q^{36} + 709061882 q^{38} + 433255366 q^{40} + 80370626 q^{41} + 1585062 q^{43} + 324477888 q^{44} - 544910502 q^{47} - 2479345922 q^{49} - 987059452 q^{52} - 915886820 q^{53} - 297150836 q^{54} + 2172449592 q^{56} - 2398069428 q^{57} + 930519014 q^{58} + 3394816764 q^{59} - 5474941192 q^{60} + 2925325476 q^{64} + 455136192 q^{66} + 3405920388 q^{67} + 664008226 q^{68} + 16264108918 q^{74} - 17800086268 q^{78} - 13853150858 q^{79} + 20444701546 q^{81} + 113867236 q^{83} - 30401949428 q^{84} + 19291204884 q^{86} - 5221634730 q^{87} - 6984391876 q^{90} + 41423783058 q^{92} + 4107406010 q^{95} + 33148445474 q^{96} + 15795117154 q^{97} + 1345877600 q^{99}+O(q^{100}) $ 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9 - 254122 * q^10 - 218200 * q^11 - 191008 * q^13 - 1380228 * q^14 - 512732 * q^15 + 2224308 * q^16 - 1070678 * q^17 + 17857352 * q^21 + 8915254 * q^23 - 39666730 * q^24 - 82938284 * q^25 - 55042410 * q^31 - 179227232 * q^35 + 394381042 * q^36 + 709061882 * q^38 + 433255366 * q^40 + 80370626 * q^41 + 1585062 * q^43 + 324477888 * q^44 - 544910502 * q^47 - 2479345922 * q^49 - 987059452 * q^52 - 915886820 * q^53 - 297150836 * q^54 + 2172449592 * q^56 - 2398069428 * q^57 + 930519014 * q^58 + 3394816764 * q^59 - 5474941192 * q^60 + 2925325476 * q^64 + 455136192 * q^66 + 3405920388 * q^67 + 664008226 * q^68 + 16264108918 * q^74 - 17800086268 * q^78 - 13853150858 * q^79 + 20444701546 * q^81 + 113867236 * q^83 - 30401949428 * q^84 + 19291204884 * q^86 - 5221634730 * q^87 - 6984391876 * q^90 + 41423783058 * q^92 + 4107406010 * q^95 + 33148445474 * q^96 + 15795117154 * q^97 + 1345877600 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$		−	59.1014i		−	1.84692i	−0.383696	−	0.923459i	$-0.625349\pi$
$2$		−	59.1014i		−	1.84692i	0.383696	−	0.923459i	$-0.374651\pi$
$3$			419.853i			1.72779i	0.503670	+	0.863896i	$0.331983\pi$
$3$			419.853i			1.72779i	−0.503670	+	0.863896i	$0.668017\pi$
$4$	−2468.98			−2.41111
$5$		−	832.528i		−	0.266409i	−0.991089	−	0.133204i	$-0.957473\pi$
$5$		−	832.528i		−	0.266409i	0.991089	−	0.133204i	$-0.0425267\pi$
$6$	24813.9			3.19109
$7$		−	31219.1i		−	1.85751i	−0.370696	−	0.928754i	$-0.620881\pi$
$7$		−	31219.1i		−	1.85751i	0.370696	−	0.928754i	$-0.379119\pi$
$8$			85400.1i			2.60621i
$9$	−117228.			−1.98527
$10$	−49203.6			−0.492036
$11$	−30601.5			−0.190011			−0.0950056	−	0.995477i	$-0.530287\pi$
$11$	−30601.5			−0.190011			−0.0950056	+	0.995477i	$0.530287\pi$
$12$		−	1.03661e6i		−	4.16590i
$13$	−11019.9			−0.0296797			−0.0148398	−	0.999890i	$-0.504724\pi$
$13$	−11019.9			−0.0296797			−0.0148398	+	0.999890i	$0.504724\pi$
$14$	−1.84510e6			−3.43067
$15$	349540.			0.460299
$16$	2.51904e6			2.40234
$17$	1.14659e6			0.807539			0.403769	−	0.914861i	$-0.367700\pi$
$17$	1.14659e6			0.807539			0.403769	+	0.914861i	$0.367700\pi$
$18$			6.92834e6i			3.66662i
$19$			4.19962e6i			1.69606i	0.529946	+	0.848032i	$0.322212\pi$
$19$			4.19962e6i			1.69606i	−0.529946	+	0.848032i	$0.677788\pi$
$20$			2.05549e6i			0.642341i
$21$	1.31075e7			3.20939
$22$			1.80859e6i			0.350935i
$23$	−6.78637e6			−1.05438			−0.527192	−	0.849746i	$-0.676755\pi$
$23$	−6.78637e6			−1.05438			−0.527192	+	0.849746i	$0.676755\pi$
$24$	−3.58555e7			−4.50298
$25$	9.07252e6			0.929026
$26$			651289.i			0.0548160i
$27$		−	2.44266e7i		−	1.70233i
$28$			7.70793e7i			4.47866i
$29$			2.48741e7i			1.21271i	0.795193	+	0.606356i	$0.207369\pi$
$29$			2.48741e7i			1.21271i	−0.795193	+	0.606356i	$0.792631\pi$
$30$		−	2.06583e7i		−	0.850136i
$31$	−3.61300e6			−0.126200			−0.0631000	−	0.998007i	$-0.520099\pi$
$31$	−3.61300e6			−0.126200			−0.0631000	+	0.998007i	$0.520099\pi$
$32$		−	6.14288e7i		−	1.83072i
$33$		−	1.28481e7i		−	0.328300i
$34$		−	6.77651e7i		−	1.49146i
$35$	−2.59908e7			−0.494857
$36$	2.89433e8			4.78669
$37$			1.01376e8i			1.46193i	0.682414	+	0.730966i	$0.260930\pi$
$37$			1.01376e8i			1.46193i	−0.682414	+	0.730966i	$0.739070\pi$
$38$	2.48203e8			3.13249
$39$		−	4.62673e6i		−	0.0512803i
$40$	7.10980e7			0.694316
$41$	−3.57321e7			−0.308418			−0.154209	−	0.988038i	$-0.549283\pi$
$41$	−3.57321e7			−0.308418			−0.154209	+	0.988038i	$0.549283\pi$
$42$		−	7.74670e8i		−	5.92748i
$43$	−1.34018e8	+	6.04208e7i	−0.911634	+	0.411002i
$43$	−1.34018e8	+	6.04208e7i	−0.911634	+	0.411002i
$44$	7.55544e7			0.458138
$45$			9.75955e7i			0.528892i
$46$			4.01084e8i			1.94736i
$47$	2.71560e8			1.18407			0.592034	−	0.805913i	$-0.298325\pi$
$47$	2.71560e8			1.18407			0.592034	+	0.805913i	$0.298325\pi$
$48$			1.05763e9i			4.15074i
$49$	−6.92160e8			−2.45034
$50$		−	5.36199e8i		−	1.71584i
$51$			4.81400e8i			1.39526i
$52$	2.72078e7			0.0715610
$53$	4.96941e8			1.18830			0.594149	−	0.804355i	$-0.297489\pi$
$53$	4.96941e8			1.18830			0.594149	+	0.804355i	$0.297489\pi$
$54$	−1.44365e9			−3.14407
$55$			2.54766e7i			0.0506207i
$56$	2.66612e9			4.84105
$57$	−1.76323e9			−2.93044
$58$	1.47010e9			2.23978
$59$	−6.47645e8			−0.905893			−0.452946	−	0.891538i	$-0.649627\pi$
$59$	−6.47645e8			−0.905893			−0.452946	+	0.891538i	$0.649627\pi$
$60$	−8.63005e8			−1.10983
$61$		−	5.21284e8i		−	0.617199i	−0.951192	−	0.308599i	$-0.900140\pi$
$61$		−	5.21284e8i		−	0.617199i	0.951192	−	0.308599i	$-0.0998602\pi$
$62$			2.13533e8i			0.233081i
$63$			3.65976e9i			3.68765i
$64$	−1.05104e9			−0.978855
$65$			9.17434e6i			0.00790693i
$66$	−7.59343e8			−0.606343
$67$	1.81540e9			1.34461			0.672307	−	0.740272i	$-0.265303\pi$
$67$	1.81540e9			1.34461			0.672307	+	0.740272i	$0.265303\pi$
$68$	−2.83090e9			−1.94706
$69$		−	2.84928e9i		−	1.82176i
$70$			1.53609e9i			0.913961i
$71$		−	6.55571e8i		−	0.363353i	−0.983358	−	0.181676i	$-0.941848\pi$
$71$		−	6.55571e8i		−	0.363353i	0.983358	−	0.181676i	$-0.0581523\pi$
$72$		−	1.00113e10i		−	5.17401i
$73$			2.34267e9i			1.13005i	0.825074	+	0.565024i	$0.191133\pi$
$73$			2.34267e9i			1.13005i	−0.825074	+	0.565024i	$0.808867\pi$
$74$	5.99147e9			2.70007
$75$			3.80913e9i			1.60516i
$76$		−	1.03688e10i		−	4.08939i
$77$			9.55352e8i			0.352947i
$78$	−2.73446e8			−0.0947106
$79$	3.31775e9			1.07822			0.539110	−	0.842235i	$-0.318761\pi$
$79$	3.31775e9			1.07822			0.539110	+	0.842235i	$0.318761\pi$
$80$		−	2.09717e9i		−	0.640005i
$81$	3.33341e9			0.956013
$82$			2.11182e9i			0.569622i
$83$	−3.83424e9			−0.973393			−0.486697	−	0.873571i	$-0.661798\pi$
$83$	−3.83424e9			−0.973393			−0.486697	+	0.873571i	$0.661798\pi$
$84$	−3.23620e10			−7.73819
$85$		−	9.54568e8i		−	0.215136i
$86$	3.57095e9	+	7.92065e9i	0.759087	+	1.68371i
$87$	−1.04435e10			−2.09531
$88$		−	2.61337e9i		−	0.495208i
$89$			7.01136e9i			1.25560i	0.778373	+	0.627802i	$0.216045\pi$
$89$			7.01136e9i			1.25560i	−0.778373	+	0.627802i	$0.783955\pi$
$90$	5.76803e9			0.976822
$91$			3.44031e8i			0.0551303i
$92$	1.67554e10			2.54223
$93$		−	1.51693e9i		−	0.218047i
$94$		−	1.60496e10i		−	2.18688i
$95$	3.49630e9			0.451846
$96$	2.57911e10			3.16311
$97$	−5.78385e9			−0.673532			−0.336766	−	0.941588i	$-0.609333\pi$
$97$	−5.78385e9			−0.673532			−0.336766	+	0.941588i	$0.609333\pi$
$98$			4.09076e10i			4.52557i
$99$	3.58735e9			0.377223
$100$	−2.23998e10			−2.23998
$101$	−3.51511e9			−0.334451			−0.167226	−	0.985919i	$-0.553481\pi$
$101$	−3.51511e9			−0.334451			−0.167226	+	0.985919i	$0.553481\pi$
$102$	2.84514e10			2.57693
$103$	1.15282e10			0.994430			0.497215	−	0.867627i	$-0.334356\pi$
$103$	1.15282e10			0.994430			0.497215	+	0.867627i	$0.334356\pi$
$104$		−	9.41097e8i		−	0.0773513i
$105$		−	1.09123e10i		−	0.855010i
$106$		−	2.93699e10i		−	2.19469i
$107$	5.33567e9			0.380426			0.190213	−	0.981743i	$-0.439082\pi$
$107$	5.33567e9			0.380426			0.190213	+	0.981743i	$0.439082\pi$
$108$			6.03088e10i			4.10451i
$109$	−1.55469e10			−1.01044			−0.505221	−	0.862990i	$-0.668589\pi$
$109$	−1.55469e10			−1.01044			−0.505221	+	0.862990i	$0.668589\pi$
$110$	1.50570e9			0.0934923
$111$	−4.25631e10			−2.52591
$112$		−	7.86421e10i		−	4.46237i
$113$		−	1.28377e10i		−	0.696780i	−0.937350	−	0.348390i	$-0.886728\pi$
$113$		−	1.28377e10i		−	0.696780i	0.937350	−	0.348390i	$-0.113272\pi$
$114$			1.04209e11i			5.41229i
$115$			5.64985e9i			0.280897i
$116$		−	6.14136e10i		−	2.92398i
$117$	1.29184e9			0.0589220
$118$			3.82767e10i			1.67311i
$119$		−	3.57955e10i		−	1.50001i
$120$			2.98507e10i			1.19963i
$121$	−2.50010e10			−0.963896
$122$	−3.08086e10			−1.13992
$123$		−	1.50022e10i		−	0.532881i
$124$	8.92041e9			0.304282
$125$		−	1.56833e10i		−	0.513910i
$126$	2.16297e11			6.81078
$127$	2.04030e10			0.617554			0.308777	−	0.951134i	$-0.400080\pi$
$127$	2.04030e10			0.617554			0.308777	+	0.951134i	$0.400080\pi$
$128$		−	7.85315e8i		−	0.0228557i
$129$	−2.53679e10	−	5.62679e10i	−0.710126	−	1.57511i
$130$	5.42217e8			0.0146035
$131$			6.81112e10i			1.76548i	0.469864	+	0.882739i	$0.344303\pi$
$131$			6.81112e10i			1.76548i	−0.469864	+	0.882739i	$0.655697\pi$
$132$			3.17218e10i			0.791567i
$133$	1.31109e11			3.15045
$134$		−	1.07293e11i		−	2.48339i
$135$	−2.03358e10			−0.453517
$136$			9.79189e10i			2.10461i
$137$			1.98461e10i			0.411218i	0.978634	+	0.205609i	$0.0659175\pi$
$137$			1.98461e10i			0.411218i	−0.978634	+	0.205609i	$0.934083\pi$
$138$	−1.68397e11			−3.36464
$139$	−1.29281e10			−0.249150			−0.124575	−	0.992210i	$-0.539757\pi$
$139$	−1.29281e10			−0.249150			−0.124575	+	0.992210i	$0.539757\pi$
$140$	6.41707e10			1.19315
$141$			1.14016e11i			2.04582i
$142$	−3.87452e10			−0.671083
$143$	3.37224e8			0.00563947
$144$	−2.95301e11			−4.76928
$145$	2.07084e10			0.323077
$146$	1.38455e11			2.08711
$147$		−	2.90606e11i		−	4.23367i
$148$		−	2.50295e11i		−	3.52488i
$149$			8.07569e10i			1.09963i	0.835285	+	0.549817i	$0.185303\pi$
$149$			8.07569e10i			1.09963i	−0.835285	+	0.549817i	$0.814697\pi$
$150$	2.25125e11			2.96461
$151$		−	2.06213e10i		−	0.262682i	−0.991337	−	0.131341i	$-0.958072\pi$
$151$		−	2.06213e10i		−	0.262682i	0.991337	−	0.131341i	$-0.0419283\pi$
$152$	−3.58648e11			−4.42029
$153$	−1.34412e11			−1.60318
$154$	5.64627e10			0.651865
$155$			3.00792e9i			0.0336208i
$156$			1.14233e10i			0.123642i
$157$			5.75822e10i			0.603656i	0.953362	+	0.301828i	$0.0975969\pi$
$157$			5.75822e10i			0.603656i	−0.953362	+	0.301828i	$0.902403\pi$
$158$		−	1.96083e11i		−	1.99139i
$159$			2.08642e11i			2.05313i
$160$	−5.11412e10			−0.487721
$161$			2.11865e11i			1.95853i
$162$		−	1.97009e11i		−	1.76568i
$163$		−	1.01222e11i		−	0.879707i	−0.898070	−	0.439853i	$-0.855030\pi$
$163$		−	1.01222e11i		−	0.879707i	0.898070	−	0.439853i	$-0.144970\pi$
$164$	8.82217e10			0.743629
$165$	−1.06964e10			−0.0874620
$166$			2.26609e11i			1.79778i
$167$	−1.61243e11			−1.24136			−0.620681	−	0.784063i	$-0.713144\pi$
$167$	−1.61243e11			−1.24136			−0.620681	+	0.784063i	$0.713144\pi$
$168$			1.11938e12i			8.36432i
$169$	−1.37737e11			−0.999119
$170$	−5.64163e10			−0.397338
$171$		−	4.92313e11i		−	3.36714i
$172$	3.30887e11	−	1.49177e11i	2.19805	−	0.990971i
$173$	−5.74774e10			−0.370908			−0.185454	−	0.982653i	$-0.559376\pi$
$173$	−5.74774e10			−0.370908			−0.185454	+	0.982653i	$0.559376\pi$
$174$			6.17225e11i			3.86988i
$175$		−	2.83236e11i		−	1.72567i
$176$	−7.70863e10			−0.456472
$177$		−	2.71916e11i		−	1.56519i
$178$	4.14381e11			2.31900
$179$		−	4.14002e10i		−	0.225288i	−0.993635	−	0.112644i	$-0.964068\pi$
$179$		−	4.14002e10i		−	0.225288i	0.993635	−	0.112644i	$-0.0359319\pi$
$180$		−	2.40961e11i		−	1.27522i
$181$	1.16160e10			0.0597947			0.0298973	−	0.999553i	$-0.490482\pi$
$181$	1.16160e10			0.0597947			0.0298973	+	0.999553i	$0.490482\pi$
$182$	2.03327e10			0.101821
$183$	2.18863e11			1.06639
$184$		−	5.79557e11i		−	2.74794i
$185$	8.43985e10			0.389472
$186$	−8.96527e10			−0.402716
$187$	−3.50874e10			−0.153441
$188$	−6.70476e11			−2.85492
$189$	−7.62578e11			−3.16210
$190$		−	2.06636e11i		−	0.834524i
$191$			1.75795e11i			0.691575i	0.938313	+	0.345787i	$0.112388\pi$
$191$			1.75795e11i			0.691575i	−0.938313	+	0.345787i	$0.887612\pi$
$192$		−	4.41282e11i		−	1.69126i
$193$	−8.33306e10			−0.311184			−0.155592	−	0.987821i	$-0.549729\pi$
$193$	−8.33306e10			−0.311184			−0.155592	+	0.987821i	$0.549729\pi$
$194$			3.41834e11i			1.24396i
$195$	−3.85188e9			−0.0136615
$196$	1.70893e12			5.90803
$197$	4.38324e10			0.147728			0.0738641	−	0.997268i	$-0.476467\pi$
$197$	4.38324e10			0.147728			0.0738641	+	0.997268i	$0.476467\pi$
$198$		−	2.12017e11i		−	0.696700i
$199$		−	3.35527e11i		−	1.07513i	−0.843221	−	0.537566i	$-0.819344\pi$
$199$		−	3.35527e11i		−	1.07513i	0.843221	−	0.537566i	$-0.180656\pi$
$200$			7.74795e11i			2.42123i
$201$			7.62201e11i			2.32321i
$202$			2.07748e11i			0.617704i
$203$	7.76549e11			2.25262
$204$		−	1.18856e12i		−	3.36412i
$205$			2.97480e10i			0.0821652i
$206$		−	6.81331e11i		−	1.83663i
$207$	7.95553e11			2.09323
$208$	−2.77594e10			−0.0713007
$209$		−	1.28515e11i		−	0.322271i
$210$	−6.44934e11			−1.57913
$211$			3.28767e11i			0.786097i	0.919518	+	0.393048i	$0.128580\pi$
$211$			3.28767e11i			0.786097i	−0.919518	+	0.393048i	$0.871420\pi$
$212$	−1.22693e12			−2.86512
$213$	2.75244e11			0.627798
$214$		−	3.15346e11i		−	0.702616i
$215$	5.03020e10	+	1.11574e11i	0.109495	+	0.242868i
$216$	2.08604e12			4.43663
$217$			1.12795e11i			0.234417i
$218$			9.18844e11i			1.86621i
$219$	−9.83579e11			−1.95249
$220$		−	6.29011e10i		−	0.122052i
$221$	−1.26353e10			−0.0239675
$222$			2.51554e12i			4.66516i
$223$		−	2.39669e11i		−	0.434599i	−0.976105	−	0.217299i	$-0.930275\pi$
$223$		−	2.39669e11i		−	0.434599i	0.976105	−	0.217299i	$-0.0697248\pi$
$224$	−1.91776e12			−3.40058
$225$	−1.06355e12			−1.84436
$226$	−7.58728e11			−1.28690
$227$		−	1.85715e11i		−	0.308118i	−0.988062	−	0.154059i	$-0.950765\pi$
$227$		−	1.85715e11i		−	0.308118i	0.988062	−	0.154059i	$-0.0492346\pi$
$228$	4.35336e12			7.06562
$229$	1.47897e11			0.234846			0.117423	−	0.993082i	$-0.462537\pi$
$229$	1.47897e11			0.234846			0.117423	+	0.993082i	$0.462537\pi$
$230$	3.33914e11			0.518795
$231$	−4.01108e11			−0.609820
$232$	−2.12425e12			−3.16058
$233$		−	2.30728e11i		−	0.335985i	−0.985788	−	0.167992i	$-0.946272\pi$
$233$		−	2.30728e11i		−	0.335985i	0.985788	−	0.167992i	$-0.0537284\pi$
$234$		−	7.63493e10i		−	0.108824i
$235$		−	2.26082e11i		−	0.315447i
$236$	1.59902e12			2.18421
$237$			1.39297e12i			1.86294i
$238$	−2.11557e12			−2.77040
$239$	−4.08458e11			−0.523791			−0.261895	−	0.965096i	$-0.584348\pi$
$239$	−4.08458e11			−0.523791			−0.261895	+	0.965096i	$0.584348\pi$
$240$	8.80503e11			1.10580
$241$			8.99974e11i			1.10699i	0.832851	+	0.553497i	$0.186707\pi$
$241$			8.99974e11i			1.10699i	−0.832851	+	0.553497i	$0.813293\pi$
$242$			1.47759e12i			1.78024i
$243$		−	4.28238e10i		−	0.0505421i
$244$			1.28704e12i			1.48813i
$245$			5.76242e11i			0.652792i
$246$	−8.86654e11			−0.984189
$247$		−	4.62792e10i		−	0.0503386i
$248$		−	3.08550e11i		−	0.328903i
$249$		−	1.60982e12i		−	1.68182i
$250$	−9.26904e11			−0.949150
$251$	−1.12564e12			−1.12988			−0.564939	−	0.825133i	$-0.691100\pi$
$251$	−1.12564e12			−1.12988			−0.564939	+	0.825133i	$0.691100\pi$
$252$		−	9.03585e12i		−	8.89132i
$253$	2.07673e11			0.200345
$254$		−	1.20584e12i		−	1.14057i
$255$	4.00779e11			0.371710
$256$	−1.12268e12			−1.02107
$257$			2.02956e12i			1.81024i	0.425154	+	0.905121i	$0.360220\pi$
$257$			2.02956e12i			1.81024i	−0.425154	+	0.905121i	$0.639780\pi$
$258$	−3.32551e12	+	1.49928e12i	−2.90911	+	1.31155i
$259$	3.16488e12			2.71555
$260$		−	2.26512e10i		−	0.0190645i
$261$		−	2.91594e12i		−	2.40756i
$262$	4.02547e12			3.26069
$263$			1.35423e12i			1.07625i	0.842866	+	0.538124i	$0.180867\pi$
$263$			1.35423e12i			1.07625i	−0.842866	+	0.538124i	$0.819133\pi$
$264$	1.09723e12			0.855617
$265$		−	4.13717e11i		−	0.316573i
$266$		−	7.74870e12i		−	5.81863i
$267$	−2.94375e12			−2.16942
$268$	−4.48218e12			−3.24201
$269$	1.52798e12			1.08482			0.542408	−	0.840115i	$-0.317513\pi$
$269$	1.52798e12			1.08482			0.542408	+	0.840115i	$0.317513\pi$
$270$			1.20188e12i			0.837609i
$271$	−1.08870e12			−0.744839			−0.372420	−	0.928064i	$-0.621472\pi$
$271$	−1.08870e12			−0.744839			−0.372420	+	0.928064i	$0.621472\pi$
$272$	2.88830e12			1.93998
$273$	−1.44442e11			−0.0952536
$274$	1.17293e12			0.759486
$275$	−2.77633e11			−0.176525
$276$			7.03481e12i			4.39245i
$277$			1.26133e12i			0.773448i	0.922196	+	0.386724i	$0.126393\pi$
$277$			1.26133e12i			0.773448i	−0.922196	+	0.386724i	$0.873607\pi$
$278$			7.64070e11i			0.460160i
$279$	4.23544e11			0.250540
$280$		−	2.21962e12i		−	1.28970i
$281$	9.77086e11			0.557701			0.278850	−	0.960335i	$-0.410047\pi$
$281$	9.77086e11			0.557701			0.278850	+	0.960335i	$0.410047\pi$
$282$	6.73848e12			3.77847
$283$	1.67181e12			0.920989			0.460494	−	0.887663i	$-0.347672\pi$
$283$	1.67181e12			0.920989			0.460494	+	0.887663i	$0.347672\pi$
$284$			1.61859e12i			0.876083i
$285$			1.46793e12i			0.780697i
$286$		−	1.99304e10i		−	0.0104156i
$287$			1.11553e12i			0.572888i
$288$			7.20118e12i			3.63447i
$289$	−7.01326e11			−0.347881
$290$		−	1.22390e12i		−	0.596698i
$291$		−	2.42837e12i		−	1.16372i
$292$		−	5.78400e12i		−	2.72467i
$293$	2.94397e12			1.36331			0.681656	−	0.731673i	$-0.261260\pi$
$293$	2.94397e12			1.36331			0.681656	+	0.731673i	$0.261260\pi$
$294$	−1.71752e13			−7.81925
$295$			5.39182e11i			0.241338i
$296$	−8.65753e12			−3.81009
$297$			7.47491e11i			0.323462i
$298$	4.77285e12			2.03094
$299$	7.47849e10			0.0312938
$300$		−	9.40465e12i		−	3.87023i
$301$	1.88628e12	+	4.18393e12i	0.763440	+	1.69337i
$302$	−1.21875e12			−0.485152
$303$		−	1.47583e12i		−	0.577862i
$304$			1.05790e13i			4.07452i
$305$	−4.33983e11			−0.164427
$306$			7.94396e12i			2.96094i
$307$	−1.62167e11			−0.0594661			−0.0297330	−	0.999558i	$-0.509466\pi$
$307$	−1.62167e11			−0.0594661			−0.0297330	+	0.999558i	$0.509466\pi$
$308$		−	2.35874e12i		−	0.850995i
$309$			4.84014e12i			1.71817i
$310$	1.77772e11			0.0620949
$311$	−1.80279e12			−0.619646			−0.309823	−	0.950794i	$-0.600270\pi$
$311$	−1.80279e12			−0.619646			−0.309823	+	0.950794i	$0.600270\pi$
$312$	3.95123e11			0.133647
$313$		−	4.74297e12i		−	1.57881i	−0.613876	−	0.789403i	$-0.710390\pi$
$313$		−	4.74297e12i		−	1.57881i	0.613876	−	0.789403i	$-0.289610\pi$
$314$	3.40319e12			1.11490
$315$	3.04685e12			0.982422
$316$	−8.19144e12			−2.59971
$317$	3.23655e12			1.01108			0.505541	−	0.862803i	$-0.331293\pi$
$317$	3.23655e12			1.01108			0.505541	+	0.862803i	$0.331293\pi$
$318$	1.23310e13			3.79197
$319$		−	7.61185e11i		−	0.230429i
$320$			8.75018e11i			0.260776i
$321$			2.24020e12i			0.657297i
$322$	1.25215e13			3.61724
$323$			4.81524e12i			1.36964i
$324$	−8.23011e12			−2.30505
$325$	−9.99779e10			−0.0275732
$326$	−5.98238e12			−1.62475
$327$		−	6.52742e12i		−	1.74583i
$328$		−	3.05153e12i		−	0.803799i
$329$		−	8.47788e12i		−	2.19942i
$330$			6.32175e11i			0.161535i
$331$		−	5.02102e12i		−	1.26372i	−0.775081	−	0.631862i	$-0.782291\pi$
$331$		−	5.02102e12i		−	1.26372i	0.775081	−	0.631862i	$-0.217709\pi$
$332$	9.46664e12			2.34696
$333$		−	1.18841e13i		−	2.90232i
$334$			9.52969e12i			2.29270i
$335$		−	1.51137e12i		−	0.358217i
$336$	3.30182e13			7.71004
$337$	3.22069e12			0.740967			0.370483	−	0.928839i	$-0.379192\pi$
$337$	3.22069e12			0.740967			0.370483	+	0.928839i	$0.379192\pi$
$338$			8.14045e12i			1.84529i
$339$	5.38996e12			1.20389
$340$			2.35681e12i			0.518716i
$341$	1.10563e11			0.0239794
$342$	−2.90964e13			−6.21883
$343$			1.27900e13i			2.69401i
$344$	−5.15994e12	−	1.14452e13i	−1.07116	−	2.37591i
$345$	−2.37211e12			−0.485332
$346$			3.39699e12i			0.685037i
$347$		−	1.79363e12i		−	0.356521i	−0.983983	−	0.178260i	$-0.942953\pi$
$347$		−	1.79363e12i		−	0.356521i	0.983983	−	0.178260i	$-0.0570469\pi$
$348$	2.57847e13			5.05203
$349$			1.98981e12i			0.384312i	0.981364	+	0.192156i	$0.0615480\pi$
$349$			1.98981e12i			0.384312i	−0.981364	+	0.192156i	$0.938452\pi$
$350$	−1.67397e13			−3.18718
$351$			2.69178e11i			0.0505247i
$352$			1.87981e12i			0.347858i
$353$	−6.67536e12			−1.21787			−0.608935	−	0.793220i	$-0.708403\pi$
$353$	−6.67536e12			−1.21787			−0.608935	+	0.793220i	$0.708403\pi$
$354$	−1.60706e13			−2.89079
$355$	−5.45782e11			−0.0968004
$356$		−	1.73109e13i		−	3.02740i
$357$	1.50289e13			2.59171
$358$	−2.44681e12			−0.416088
$359$	−4.33742e12			−0.727376			−0.363688	−	0.931521i	$-0.618483\pi$
$359$	−4.33742e12			−0.727376			−0.363688	+	0.931521i	$0.618483\pi$
$360$	−8.33467e12			−1.37840
$361$	−1.15057e13			−1.87663
$362$		−	6.86520e11i		−	0.110436i
$363$		−	1.04967e13i		−	1.66541i
$364$		−	8.49403e11i		−	0.132925i
$365$	1.95034e12			0.301055
$366$		−	1.29351e13i		−	1.96954i
$367$	−6.86650e12			−1.03135			−0.515674	−	0.856785i	$-0.672458\pi$
$367$	−6.86650e12			−1.03135			−0.515674	+	0.856785i	$0.672458\pi$
$368$	−1.70951e13			−2.53299
$369$	4.18880e12			0.612291
$370$		−	4.98807e12i		−	0.719323i
$371$		−	1.55141e13i		−	2.20727i
$372$			3.74526e12i			0.525736i
$373$			3.72115e12i			0.515386i	0.966227	+	0.257693i	$0.0829623\pi$
$373$			3.72115e12i			0.515386i	−0.966227	+	0.257693i	$0.917038\pi$
$374$			2.07371e12i			0.283394i
$375$	6.58468e12			0.887929
$376$			2.31913e13i			3.08593i
$377$		−	2.74109e11i		−	0.0359929i
$378$			4.50694e13i			5.84014i
$379$	7.27747e12			0.930646			0.465323	−	0.885141i	$-0.345938\pi$
$379$	7.27747e12			0.930646			0.465323	+	0.885141i	$0.345938\pi$
$380$	−8.63229e12			−1.08945
$381$			8.56626e12i			1.06700i
$382$	1.03897e13			1.27728
$383$			1.39131e13i			1.68822i	0.536168	+	0.844112i	$0.319872\pi$
$383$			1.39131e13i			1.68822i	−0.536168	+	0.844112i	$0.680128\pi$
$384$	3.29717e11			0.0394899
$385$	7.95358e11			0.0940284
$386$			4.92496e12i			0.574732i
$387$	1.57106e13	−	7.08300e12i	1.80984	−	0.815948i
$388$	1.42802e13			1.62396
$389$			5.23131e12i			0.587303i	0.955912	+	0.293652i	$0.0948706\pi$
$389$			5.23131e12i			0.587303i	−0.955912	+	0.293652i	$0.905129\pi$
$390$			2.27651e11i			0.0252318i
$391$	−7.78119e12			−0.851456
$392$		−	5.91105e13i		−	6.38608i
$393$	−2.85967e13			−3.05038
$394$		−	2.59055e12i		−	0.272842i
$395$		−	2.76212e12i		−	0.287248i
$396$	−8.85708e12			−0.909525
$397$	−3.23534e12			−0.328071			−0.164035	−	0.986454i	$-0.552451\pi$
$397$	−3.23534e12			−0.328071			−0.164035	+	0.986454i	$0.552451\pi$
$398$	−1.98301e13			−1.98568
$399$			5.50464e13i			5.44333i
$400$	2.28540e13			2.23184
$401$	6.71315e12			0.647448			0.323724	−	0.946152i	$-0.395065\pi$
$401$	6.71315e12			0.647448			0.323724	+	0.946152i	$0.395065\pi$
$402$	4.50472e13			4.29079
$403$	3.98147e10			0.00374558
$404$	8.67873e12			0.806398
$405$		−	2.77516e12i		−	0.254690i
$406$		−	4.58951e13i		−	4.16041i
$407$		−	3.10226e12i		−	0.277783i
$408$	−4.11116e13			−3.63633
$409$		−	3.76964e12i		−	0.329369i	−0.986346	−	0.164685i	$-0.947339\pi$
$409$		−	3.76964e12i		−	0.329369i	0.986346	−	0.164685i	$-0.0526606\pi$
$410$	1.75815e12			0.151752
$411$	−8.33244e12			−0.710499
$412$	−2.84628e13			−2.39768
$413$			2.02189e13i			1.68270i
$414$		−	4.70183e13i		−	3.86603i
$415$			3.19211e12i			0.259321i
$416$			6.76937e11i			0.0543353i
$417$		−	5.42792e12i		−	0.430480i
$418$	−7.59540e12			−0.595208
$419$			5.70342e12i			0.441636i	0.975315	+	0.220818i	$0.0708728\pi$
$419$			5.70342e12i			0.441636i	−0.975315	+	0.220818i	$0.929127\pi$
$420$			2.69423e13i			2.06152i
$421$		−	6.78163e12i		−	0.512771i	−0.966575	−	0.256386i	$-0.917468\pi$
$421$		−	6.78163e12i		−	0.512771i	0.966575	−	0.256386i	$-0.0825317\pi$
$422$	1.94306e13			1.45186
$423$	−3.18345e13			−2.35069
$424$			4.24388e13i			3.09695i
$425$	1.04025e13			0.750225
$426$		−	1.62673e13i		−	1.15949i
$427$	−1.62740e13			−1.14645
$428$	−1.31736e13			−0.917249
$429$			1.41585e11i			0.00974384i
$430$	6.59416e12	−	2.97292e12i	0.448557	−	0.202228i
$431$	1.47502e13			0.991769			0.495884	−	0.868389i	$-0.334844\pi$
$431$	1.47502e13			0.991769			0.495884	+	0.868389i	$0.334844\pi$
$432$		−	6.15315e13i		−	4.08958i
$433$			4.40794e12i			0.289598i	0.989461	+	0.144799i	$0.0462536\pi$
$433$			4.40794e12i			0.289598i	−0.989461	+	0.144799i	$0.953746\pi$
$434$	6.66632e12			0.432950
$435$			8.69450e12i			0.558211i
$436$	3.83850e13			2.43629
$437$		−	2.85002e13i		−	1.78830i
$438$			5.81309e13i			3.60609i
$439$	−2.34447e13			−1.43788			−0.718938	−	0.695074i	$-0.755371\pi$
$439$	−2.34447e13			−1.43788			−0.718938	+	0.695074i	$0.755371\pi$
$440$	−2.17571e12			−0.131928
$441$	8.11404e13			4.86457
$442$			7.46761e11i			0.0442660i
$443$	−2.81507e13			−1.64995			−0.824975	−	0.565169i	$-0.808811\pi$
$443$	−2.81507e13			−1.64995			−0.824975	+	0.565169i	$0.808811\pi$
$444$	1.05087e14			6.09026
$445$	5.83716e12			0.334504
$446$	−1.41648e13			−0.802669
$447$	−3.39061e13			−1.89994
$448$			3.28125e13i			1.81823i
$449$			1.80546e13i			0.989363i	0.869074	+	0.494681i	$0.164715\pi$
$449$			1.80546e13i			0.989363i	−0.869074	+	0.494681i	$0.835285\pi$
$450$			6.28575e13i			3.40639i
$451$	1.09346e12			0.0586028
$452$			3.16960e13i			1.68001i
$453$	8.65791e12			0.453860
$454$	−1.09760e13			−0.569069
$455$	2.86415e11			0.0146872
$456$		−	1.50580e14i		−	7.63734i
$457$		−	1.63525e13i		−	0.820357i	−0.912005	−	0.410179i	$-0.865466\pi$
$457$		−	1.63525e13i		−	0.820357i	0.912005	−	0.410179i	$-0.134534\pi$
$458$		−	8.74093e12i		−	0.433741i
$459$		−	2.80073e13i		−	1.37470i
$460$		−	1.39493e13i		−	0.677274i
$461$	−2.03281e13			−0.976321			−0.488161	−	0.872754i	$-0.662332\pi$
$461$	−2.03281e13			−0.976321			−0.488161	+	0.872754i	$0.662332\pi$
$462$			2.37060e13i			1.12629i
$463$		−	1.17169e13i		−	0.550689i	−0.961346	−	0.275345i	$-0.911208\pi$
$463$		−	1.17169e13i		−	0.550689i	0.961346	−	0.275345i	$-0.0887919\pi$
$464$			6.26588e13i			2.91335i
$465$	−1.26289e12			−0.0580898
$466$	−1.36363e13			−0.620537
$467$			2.71597e13i			1.22276i	0.791337	+	0.611380i	$0.209385\pi$
$467$			2.71597e13i			1.22276i	−0.791337	+	0.611380i	$0.790615\pi$
$468$	−3.18951e12			−0.142068
$469$		−	5.66752e13i		−	2.49763i
$470$	−1.33617e13			−0.582604
$471$	−2.41761e13			−1.04299
$472$		−	5.53089e13i		−	2.36094i
$473$	4.10115e12	−	1.84897e12i	0.173221	−	0.0780950i
$474$	8.23263e13			3.44070
$475$			3.81012e13i			1.57569i
$476$			8.83784e13i			3.61669i
$477$	−5.82553e13			−2.35909
$478$			2.41404e13i			0.967399i
$479$	3.61505e13			1.43363			0.716815	−	0.697263i	$-0.245599\pi$
$479$	3.61505e13			1.43363			0.716815	+	0.697263i	$0.245599\pi$
$480$		−	2.14718e13i		−	0.842680i
$481$		−	1.11715e12i		−	0.0433897i
$482$	5.31897e13			2.04453
$483$	−8.89522e13			−3.38393
$484$	6.17268e13			2.32406
$485$			4.81522e12i			0.179435i
$486$	−2.53095e12			−0.0933472
$487$	−1.13607e13			−0.414727			−0.207363	−	0.978264i	$-0.566488\pi$
$487$	−1.13607e13			−0.414727			−0.207363	+	0.978264i	$0.566488\pi$
$488$	4.45177e13			1.60855
$489$	4.24985e13			1.51995
$490$	3.40567e13			1.20565
$491$		−	3.37611e13i		−	1.18307i	−0.806280	−	0.591534i	$-0.798523\pi$
$491$		−	3.37611e13i		−	1.18307i	0.806280	−	0.591534i	$-0.201477\pi$
$492$			3.70402e13i			1.28484i
$493$			2.85204e13i			0.979312i
$494$	−2.73517e12			−0.0929714
$495$		−	2.98657e12i		−	0.100496i
$496$	−9.10127e12			−0.303175
$497$	−2.04664e13			−0.674931
$498$	−9.51425e13			−3.10619
$499$		−	1.56284e13i		−	0.505142i	−0.967578	−	0.252571i	$-0.918724\pi$
$499$		−	1.56284e13i		−	0.505142i	0.967578	−	0.252571i	$-0.0812761\pi$
$500$			3.87217e13i			1.23909i
$501$		−	6.76985e13i		−	2.14482i
$502$			6.65269e13i			2.08679i
$503$			1.88419e13i			0.585172i	0.956239	+	0.292586i	$0.0945158\pi$
$503$			1.88419e13i			0.585172i	−0.956239	+	0.292586i	$0.905484\pi$
$504$	−3.12544e14			−9.61076
$505$			2.92643e12i			0.0891008i
$506$		−	1.22738e13i		−	0.370020i
$507$		−	5.78294e13i		−	1.72627i
$508$	−5.03744e13			−1.48899
$509$	−3.67101e13			−1.07448			−0.537238	−	0.843431i	$-0.680532\pi$
$509$	−3.67101e13			−1.07448			−0.537238	+	0.843431i	$0.680532\pi$
$510$		−	2.36866e13i		−	0.686517i
$511$	7.31362e13			2.09907
$512$			6.55476e13i			1.86297i
$513$	1.02583e14			2.88727
$514$	1.19950e14			3.34337
$515$		−	9.59752e12i		−	0.264925i
$516$	6.26327e13	+	1.38924e14i	1.71219	+	3.79777i
$517$	−8.31015e12			−0.224986
$518$		−	1.87049e14i		−	5.01540i
$519$		−	2.41321e13i		−	0.640852i
$520$	−7.83490e11			−0.0206071
$521$			5.47337e13i			1.42583i	0.701253	+	0.712913i	$0.252624\pi$
$521$			5.47337e13i			1.42583i	−0.701253	+	0.712913i	$0.747376\pi$
$522$	−1.72336e14			−4.44656
$523$		−	8.36353e12i		−	0.213738i	−0.994273	−	0.106869i	$-0.965917\pi$
$523$		−	8.36353e12i		−	0.213738i	0.994273	−	0.106869i	$-0.0340825\pi$
$524$		−	1.68165e14i		−	4.25676i
$525$	1.18918e14			2.98161
$526$	8.00367e13			1.98774
$527$	−4.14263e12			−0.101911
$528$		−	3.23649e13i		−	0.788688i
$529$	4.62837e12			0.111725
$530$	−2.44513e13			−0.584685
$531$	7.59220e13			1.79844
$532$	−3.23704e14			−7.59608
$533$	3.93763e11			0.00915374
$534$			1.73980e14i			4.00675i
$535$		−	4.44210e12i		−	0.101349i
$536$			1.55035e14i			3.50434i
$537$	1.73820e13			0.389251
$538$		−	9.03058e13i		−	2.00357i
$539$	2.11811e13			0.465592
$540$	5.02087e13			1.09348
$541$	−3.55836e13			−0.767828			−0.383914	−	0.923369i	$-0.625424\pi$
$541$	−3.55836e13			−0.767828			−0.383914	+	0.923369i	$0.625424\pi$
$542$			6.43438e13i			1.37566i
$543$			4.87700e12i			0.103313i
$544$		−	7.04337e13i		−	1.47838i
$545$			1.29432e13i			0.269191i
$546$			8.53675e12i			0.175926i
$547$	7.88966e13			1.61110			0.805548	−	0.592530i	$-0.201871\pi$
$547$	7.88966e13			1.61110			0.805548	+	0.592530i	$0.201871\pi$
$548$		−	4.89995e13i		−	0.991491i
$549$			6.11090e13i			1.22530i
$550$			1.64085e13i			0.326028i
$551$	−1.04462e14			−2.05684
$552$	2.43329e14			4.74787
$553$		−	1.03577e14i		−	2.00280i
$554$	7.45466e13			1.42850
$555$			3.54350e13i			0.672926i
$556$	3.19192e13			0.600729
$557$	−8.83010e13			−1.64699			−0.823493	−	0.567327i	$-0.807978\pi$
$557$	−8.83010e13			−1.64699			−0.823493	+	0.567327i	$0.807978\pi$
$558$		−	2.50321e13i		−	0.462728i
$559$	1.47686e12	−	6.65828e11i	0.0270570	−	0.0121984i
$560$	−6.54718e13			−1.18881
$561$		−	1.47315e13i		−	0.265115i
$562$		−	5.77472e13i		−	1.03003i
$563$	3.50978e13			0.620495			0.310247	−	0.950656i	$-0.399588\pi$
$563$	3.50978e13			0.620495			0.310247	+	0.950656i	$0.399588\pi$
$564$		−	2.81502e14i		−	4.93271i
$565$	−1.06878e13			−0.185629
$566$		−	9.88063e13i		−	1.70099i
$567$		−	1.04066e14i		−	1.77580i
$568$	5.59859e13			0.946971
$569$	−3.13808e13			−0.526141			−0.263071	−	0.964777i	$-0.584735\pi$
$569$	−3.13808e13			−0.526141			−0.263071	+	0.964777i	$0.584735\pi$
$570$	8.67570e13			1.44188
$571$		−	8.66236e13i		−	1.42710i	−0.700602	−	0.713552i	$-0.747085\pi$
$571$		−	8.66236e13i		−	1.42710i	0.700602	−	0.713552i	$-0.252915\pi$
$572$	−8.32598e11			−0.0135974
$573$	−7.38081e13			−1.19490
$574$	6.59291e13			1.05808
$575$	−6.15695e13			−0.979550
$576$	1.23211e14			1.94329
$577$			4.60046e13i			0.719321i	0.933083	+	0.359660i	$0.117107\pi$
$577$			4.60046e13i			0.719321i	−0.933083	+	0.359660i	$0.882893\pi$
$578$			4.14494e13i			0.642508i
$579$		−	3.49866e13i		−	0.537662i
$580$	−5.11286e13			−0.778975
$581$			1.19702e14i			1.80809i
$582$	−1.43520e14			−2.14930
$583$	−1.52071e13			−0.225790
$584$	−2.00064e14			−2.94514
$585$		−	1.07549e12i		−	0.0156974i
$586$		−	1.73993e14i		−	2.51793i
$587$			1.77739e12i			0.0255031i	0.999919	+	0.0127515i	$0.00405905\pi$
$587$			1.77739e12i			0.0255031i	−0.999919	+	0.0127515i	$0.995941\pi$
$588$			7.17498e14i			10.2079i
$589$		−	1.51732e13i		−	0.214043i
$590$	3.18664e13			0.445732
$591$			1.84032e13i			0.255244i
$592$			2.55370e14i			3.51206i
$593$			8.29707e12i			0.113149i	0.998398	+	0.0565746i	$0.0180179\pi$
$593$			8.29707e12i			0.113149i	−0.998398	+	0.0565746i	$0.981982\pi$
$594$	4.41778e13			0.597409
$595$	−2.98008e13			−0.399616
$596$		−	1.99387e14i		−	2.65134i
$597$	1.40872e14			1.85761
$598$		−	4.41989e12i		−	0.0577971i
$599$	−6.78681e13			−0.880100			−0.440050	−	0.897973i	$-0.645039\pi$
$599$	−6.78681e13			−0.880100			−0.440050	+	0.897973i	$0.645039\pi$
$600$	−3.25300e14			−4.18339
$601$			1.16255e13i			0.148265i	0.997248	+	0.0741325i	$0.0236188\pi$
$601$			1.16255e13i			0.148265i	−0.997248	+	0.0741325i	$0.976381\pi$
$602$	2.47276e14	−	1.11482e14i	3.12751	−	1.41001i
$603$	−2.12815e14			−2.66942
$604$			5.09134e13i			0.633355i
$605$			2.08140e13i			0.256790i
$606$	−8.72238e13			−1.06726
$607$		−	3.16649e13i		−	0.384269i	−0.981369	−	0.192134i	$-0.938459\pi$
$607$		−	3.16649e13i		−	0.384269i	0.981369	−	0.192134i	$-0.0615409\pi$
$608$	2.57978e14			3.10502
$609$			3.26037e14i			3.89206i
$610$			2.56490e13i			0.303684i
$611$	−2.99256e12			−0.0351428
$612$	3.31861e14			3.86544
$613$	8.80871e13			1.01768			0.508839	−	0.860862i	$-0.330075\pi$
$613$	8.80871e13			1.01768			0.508839	+	0.860862i	$0.330075\pi$
$614$			9.58427e12i			0.109829i
$615$	−1.24898e13			−0.141964
$616$	−8.15872e13			−0.919853
$617$	−8.82304e12			−0.0986717			−0.0493358	−	0.998782i	$-0.515710\pi$
$617$	−8.82304e12			−0.0986717			−0.0493358	+	0.998782i	$0.515710\pi$
$618$	2.86059e14			3.17332
$619$	5.83774e13			0.642380			0.321190	−	0.947015i	$-0.395917\pi$
$619$	5.83774e13			0.642380			0.321190	+	0.947015i	$0.395917\pi$
$620$		−	7.42649e12i		−	0.0810634i
$621$			1.65768e14i			1.79491i
$622$			1.06548e14i			1.14444i
$623$	2.18889e14			2.33229
$624$		−	1.16549e13i		−	0.123193i
$625$	7.55421e13			0.792116
$626$	−2.80316e14			−2.91593
$627$	5.39573e13			0.556817
$628$		−	1.42169e14i		−	1.45548i
$629$			1.16237e14i			1.18057i
$630$		−	1.80073e14i		−	1.81445i
$631$			6.00578e13i			0.600375i	0.953880	+	0.300188i	$0.0970493\pi$
$631$			6.00578e13i			0.600375i	−0.953880	+	0.300188i	$0.902951\pi$
$632$			2.83336e14i			2.81006i
$633$	−1.38034e14			−1.35821
$634$		−	1.91285e14i		−	1.86739i
$635$		−	1.69860e13i		−	0.164522i
$636$		−	5.15133e14i		−	4.95032i
$637$	7.62750e12			0.0727252
$638$	−4.49871e13			−0.425584
$639$			7.68513e13i			0.721351i
$640$	−6.53797e11			−0.00608896
$641$			1.93396e14i			1.78713i	0.448933	+	0.893565i	$0.351804\pi$
$641$			1.93396e14i			1.78713i	−0.448933	+	0.893565i	$0.648196\pi$
$642$	1.32399e14			1.21397
$643$	−9.91593e13			−0.902150			−0.451075	−	0.892486i	$-0.648959\pi$
$643$	−9.91593e13			−0.902150			−0.451075	+	0.892486i	$0.648959\pi$
$644$		−	5.23089e14i		−	4.72222i
$645$	−4.68446e13	+	2.11195e13i	−0.419625	+	0.189184i
$646$	2.84588e14			2.52961
$647$		−	1.71080e14i		−	1.50896i	−0.656324	−	0.754479i	$-0.727889\pi$
$647$		−	1.71080e14i		−	1.50896i	0.656324	−	0.754479i	$-0.272111\pi$
$648$			2.84674e14i			2.49157i
$649$	1.98189e13			0.172130
$650$			5.90884e12i			0.0509255i
$651$	−4.73572e13			−0.405025
$652$			2.49915e14i			2.12107i
$653$			8.58206e13i			0.722813i	0.932408	+	0.361406i	$0.117703\pi$
$653$			8.58206e13i			0.722813i	−0.932408	+	0.361406i	$0.882297\pi$
$654$	−3.85780e14			−3.22441
$655$	5.67045e13			0.470339
$656$	−9.00104e13			−0.740924
$657$		−	2.74626e14i		−	2.24345i
$658$	−5.01055e14			−4.06215
$659$	1.56412e14			1.25847			0.629235	−	0.777215i	$-0.283368\pi$
$659$	1.56412e14			1.25847			0.629235	+	0.777215i	$0.283368\pi$
$660$	2.64093e13			0.210881
$661$	1.56927e14			1.24363			0.621814	−	0.783165i	$-0.286396\pi$
$661$	1.56927e14			1.24363			0.621814	+	0.783165i	$0.286396\pi$
$662$	−2.96749e14			−2.33400
$663$		−	5.30496e12i		−	0.0414109i
$664$		−	3.27444e14i		−	2.53686i
$665$		−	1.09152e14i		−	0.839309i
$666$	−7.02368e14			−5.36035
$667$		−	1.68805e14i		−	1.27866i
$668$	3.98105e14			2.99306
$669$	1.00626e14			0.750896
$670$	−8.93241e13			−0.661599
$671$			1.59521e13i			0.117275i
$672$		−	8.05176e14i		−	5.87550i
$673$			2.20542e14i			1.59741i	0.601725	+	0.798703i	$0.294480\pi$
$673$			2.20542e14i			1.59741i	−0.601725	+	0.798703i	$0.705520\pi$
$674$		−	1.90347e14i		−	1.36851i
$675$		−	2.21611e14i		−	1.58151i
$676$	3.40070e14			2.40899
$677$			1.53249e14i			1.07759i	0.842436	+	0.538796i	$0.181121\pi$
$677$			1.53249e14i			1.07759i	−0.842436	+	0.538796i	$0.818879\pi$
$678$		−	3.18554e14i		−	2.22349i
$679$			1.80567e14i			1.25109i
$680$	8.15202e13			0.560687
$681$	7.79729e13			0.532363
$682$		−	6.53444e12i		−	0.0442880i
$683$	5.29142e13			0.356015			0.178008	−	0.984029i	$-0.443035\pi$
$683$	5.29142e13			0.356015			0.178008	+	0.984029i	$0.443035\pi$
$684$			1.21551e15i			8.11853i
$685$	1.65224e13			0.109552
$686$	7.55907e14			4.97562
$687$			6.20952e13i			0.405765i
$688$	−3.37596e14	+	1.52202e14i	−2.19006	+	0.987366i
$689$	−5.47622e12			−0.0352683
$690$			1.40195e14i			0.896369i
$691$		−	2.26934e14i		−	1.44049i	−0.693720	−	0.720245i	$-0.744029\pi$
$691$		−	2.26934e14i		−	1.44049i	0.693720	−	0.720245i	$-0.255971\pi$
$692$	1.41910e14			0.894300
$693$		−	1.11994e14i		−	0.700694i
$694$	−1.06006e14			−0.658465
$695$			1.07630e13i			0.0663759i
$696$		−	8.91875e14i		−	5.46082i
$697$	−4.09700e13			−0.249059
$698$	1.17601e14			0.709794
$699$	9.68718e13			0.580512
$700$			6.99304e14i			4.16079i
$701$	2.48822e14			1.46994			0.734968	−	0.678102i	$-0.237197\pi$
$701$	2.48822e14			1.46994			0.734968	+	0.678102i	$0.237197\pi$
$702$	1.59088e13			0.0933151
$703$	−4.25741e14			−2.47953
$704$	3.21633e13			0.185993
$705$	9.49211e13			0.545026
$706$			3.94523e14i			2.24931i
$707$			1.09739e14i			0.621246i
$708$			6.71354e14i			3.77385i
$709$	1.36841e14			0.763811			0.381906	−	0.924201i	$-0.375268\pi$
$709$	1.36841e14			0.763811			0.381906	+	0.924201i	$0.375268\pi$
$710$			3.22565e13i			0.178783i
$711$	−3.88933e14			−2.14055
$712$	−5.98771e14			−3.27236
$713$	2.45192e13			0.133063
$714$		−	8.88228e14i		−	4.78667i
$715$		−	2.80749e11i		−	0.00150241i
$716$			1.02216e14i			0.543194i
$717$		−	1.71493e14i		−	0.905002i
$718$			2.56347e14i			1.34340i
$719$	1.12409e14			0.585001			0.292500	−	0.956265i	$-0.405513\pi$
$719$	1.12409e14			0.585001			0.292500	+	0.956265i	$0.405513\pi$
$720$			2.45847e14i			1.27058i
$721$		−	3.59900e14i		−	1.84716i
$722$			6.80006e14i			3.46598i
$723$	−3.77857e14			−1.91265
$724$	−2.86795e13			−0.144172
$725$			2.25671e14i			1.12664i
$726$	−6.20372e14			−3.07588
$727$		−	3.16879e13i		−	0.156035i	−0.996952	−	0.0780173i	$-0.975141\pi$
$727$		−	3.16879e13i		−	0.156035i	0.996952	−	0.0780173i	$-0.0248589\pi$
$728$	−2.93803e13			−0.143681
$729$	2.14814e14			1.04334
$730$		−	1.15268e14i		−	0.556024i
$731$	−1.53664e14	+	6.92778e13i	−0.736180	+	0.331900i
$732$	−5.40367e14			−2.57119
$733$		−	1.08536e14i		−	0.512924i	−0.966554	−	0.256462i	$-0.917443\pi$
$733$		−	1.08536e14i		−	0.512924i	0.966554	−	0.256462i	$-0.0825568\pi$
$734$			4.05820e14i			1.90482i
$735$	−2.41937e14			−1.12789
$736$			4.16879e14i			1.93028i
$737$	−5.55539e13			−0.255492
$738$		−	2.47564e14i		−	1.13085i
$739$		−	1.36188e14i		−	0.617898i	−0.951079	−	0.308949i	$-0.900023\pi$
$739$		−	1.36188e14i		−	0.617898i	0.951079	−	0.308949i	$-0.0999773\pi$
$740$	−2.08378e14			−0.939059
$741$	1.94305e13			0.0869747
$742$	−9.16903e14			−4.07665
$743$		−	3.99392e13i		−	0.176383i	−0.996104	−	0.0881913i	$-0.971891\pi$
$743$		−	3.99392e13i		−	0.176383i	0.996104	−	0.0881913i	$-0.0281087\pi$
$744$	1.29546e14			0.568276
$745$	6.72324e13			0.292952
$746$	2.19925e14			0.951876
$747$	4.49480e14			1.93244
$748$	8.66299e13			0.369964
$749$		−	1.66575e14i		−	0.706644i
$750$		−	3.89164e14i		−	1.63993i
$751$		−	1.85094e14i		−	0.774806i	−0.921910	−	0.387403i	$-0.873372\pi$
$751$		−	1.85094e14i		−	0.774806i	0.921910	−	0.387403i	$-0.126628\pi$
$752$	6.84070e14			2.84454
$753$		−	4.72604e14i		−	1.95219i
$754$	−1.62002e13			−0.0664760
$755$	−1.71678e13			−0.0699809
$756$	1.88279e15			7.62417
$757$		−	4.67882e14i		−	1.88216i	−0.338183	−	0.941080i	$-0.609812\pi$
$757$		−	4.67882e14i		−	1.88216i	0.338183	−	0.941080i	$-0.390188\pi$
$758$		−	4.30109e14i		−	1.71883i
$759$			8.71923e13i			0.346154i
$760$			2.98585e14i			1.17760i
$761$			6.00935e13i			0.235453i	0.993046	+	0.117726i	$0.0375606\pi$
$761$			6.00935e13i			0.235453i	−0.993046	+	0.117726i	$0.962439\pi$
$762$	5.06278e14			1.97067
$763$			4.85361e14i			1.87691i
$764$		−	4.34033e14i		−	1.66746i
$765$			1.11902e14i			0.427101i
$766$	8.22283e14			3.11801
$767$	7.13695e12			0.0268866
$768$		−	4.71359e14i		−	1.76419i
$769$	4.69428e14			1.74557			0.872785	−	0.488104i	$-0.162311\pi$
$769$	4.69428e14			1.74557			0.872785	+	0.488104i	$0.162311\pi$
$770$		−	4.70068e13i		−	0.173663i
$771$	−8.52118e14			−3.12772
$772$	2.05741e14			0.750300
$773$		−	1.61620e14i		−	0.585595i	−0.956174	−	0.292798i	$-0.905414\pi$
$773$		−	1.61620e14i		−	0.585595i	0.956174	−	0.292798i	$-0.0945862\pi$
$774$	−4.18615e14	−	9.28521e14i	−1.50699	−	3.34262i
$775$	−3.27790e13			−0.117243
$776$		−	4.93942e14i		−	1.75536i
$777$			1.32878e15i			4.69191i
$778$	3.09178e14			1.08470
$779$		−	1.50061e14i		−	0.523096i
$780$	9.51020e12			0.0329395
$781$			2.00615e13i			0.0690411i
$782$			4.59879e14i			1.57257i
$783$	6.07591e14			2.06444
$784$	−1.74358e15			−5.88654
$785$	4.79388e13			0.160820
$786$			1.69011e15i			5.63380i
$787$	−6.16446e13			−0.204184			−0.102092	−	0.994775i	$-0.532554\pi$
$787$	−6.16446e13			−0.204184			−0.102092	+	0.994775i	$0.532554\pi$
$788$	−1.08221e14			−0.356189
$789$	−5.68577e14			−1.85953
$790$	−1.63245e14			−0.530523
$791$	−4.00783e14			−1.29428
$792$			3.06360e14i			0.983120i
$793$			5.74447e12i			0.0183183i
$794$			1.91213e14i			0.605920i
$795$	1.73701e14			0.546972
$796$			8.28408e14i			2.59226i
$797$	2.44080e14			0.758999			0.379499	−	0.925192i	$-0.376096\pi$
$797$	2.44080e14			0.758999			0.379499	+	0.925192i	$0.376096\pi$
$798$	3.25332e15			10.0534
$799$	3.11368e14			0.956182
$800$		−	5.57314e14i		−	1.70079i
$801$		−	8.21928e14i		−	2.49271i
$802$		−	3.96757e14i		−	1.19578i
$803$		−	7.16892e13i		−	0.214722i
$804$		−	1.88186e15i		−	5.60153i
$805$	1.76383e14			0.521769
$806$		−	2.35311e12i		−	0.00691777i
$807$			6.41528e14i			1.87434i
$808$		−	3.00191e14i		−	0.871648i
$809$	2.67926e14			0.773165			0.386583	−	0.922255i	$-0.373655\pi$
$809$	2.67926e14			0.773165			0.386583	+	0.922255i	$0.373655\pi$
$810$	−1.64016e14			−0.470393
$811$		−	2.27265e14i		−	0.647781i	−0.946095	−	0.323890i	$-0.895009\pi$
$811$		−	2.27265e14i		−	0.647781i	0.946095	−	0.323890i	$-0.104991\pi$
$812$	−1.91728e15			−5.43132
$813$		−	4.57095e14i		−	1.28693i
$814$	−1.83348e14			−0.513043
$815$	−8.42704e13			−0.234362
$816$			1.21266e15i			3.35189i
$817$	−2.53744e14	−	5.62825e14i	−0.697085	−	1.54619i
$818$	−2.22791e14			−0.608318
$819$		−	4.03300e13i		−	0.109448i
$820$		−	7.34470e13i		−	0.198109i
$821$	−1.33376e14			−0.357572			−0.178786	−	0.983888i	$-0.557217\pi$
$821$	−1.33376e14			−0.357572			−0.178786	+	0.983888i	$0.557217\pi$
$822$			4.92459e14i			1.31223i
$823$	4.07315e14			1.07878			0.539388	−	0.842057i	$-0.318655\pi$
$823$	4.07315e14			1.07878			0.539388	+	0.842057i	$0.318655\pi$
$824$			9.84507e14i			2.59169i
$825$		−	1.16565e14i		−	0.304999i
$826$	1.19497e15			3.10782
$827$	5.89117e14			1.52291			0.761455	−	0.648218i	$-0.224485\pi$
$827$	5.89117e14			1.52291			0.761455	+	0.648218i	$0.224485\pi$
$828$	−1.96420e15			−5.04701
$829$			3.25159e13i			0.0830469i	0.999138	+	0.0415235i	$0.0132211\pi$
$829$			3.25159e13i			0.0830469i	−0.999138	+	0.0415235i	$0.986779\pi$
$830$	1.88658e14			0.478944
$831$	−5.29575e14			−1.33636
$832$	1.15823e13			0.0290521
$833$	−7.93623e14			−1.97874
$834$	−3.20797e14			−0.795061
$835$			1.34239e14i			0.330710i
$836$			3.17300e14i			0.777031i
$837$			8.82533e13i			0.214834i
$838$	3.37080e14			0.815667
$839$		−	3.43628e14i		−	0.826568i	−0.910602	−	0.413284i	$-0.864382\pi$
$839$		−	3.43628e14i		−	0.826568i	0.910602	−	0.413284i	$-0.135618\pi$
$840$	9.31915e14			2.22833
$841$	−1.98015e14			−0.470671
$842$	−4.00804e14			−0.947047
$843$			4.10233e14i			0.963591i
$844$		−	8.11718e14i		−	1.89537i
$845$			1.14670e14i			0.266174i
$846$			1.88146e15i			4.34154i
$847$			7.80509e14i			1.79044i
$848$	1.25181e15			2.85469
$849$			7.01915e14i			1.59128i
$850$		−	6.14800e14i		−	1.38560i
$851$		−	6.87976e14i		−	1.54144i
$852$	−6.79571e14			−1.51369
$853$	−2.06413e14			−0.457079			−0.228539	−	0.973535i	$-0.573395\pi$
$853$	−2.06413e14			−0.457079			−0.228539	+	0.973535i	$0.573395\pi$
$854$			9.61818e14i			2.11740i
$855$	−4.09864e14			−0.897035
$856$			4.55667e14i			0.991468i
$857$	−6.70424e14			−1.45026			−0.725130	−	0.688612i	$-0.758220\pi$
$857$	−6.70424e14			−1.45026			−0.725130	+	0.688612i	$0.758220\pi$
$858$	8.36786e12			0.0179961
$859$			2.44866e14i			0.523556i	0.965128	+	0.261778i	$0.0843089\pi$
$859$			2.44866e14i			0.523556i	−0.965128	+	0.261778i	$0.915691\pi$
$860$	−1.24194e14	−	2.75473e14i	−0.264004	−	0.585580i
$861$	−4.68357e14			−0.989832
$862$		−	8.71755e14i		−	1.83172i
$863$		−	4.00211e14i		−	0.836055i	−0.908434	−	0.418027i	$-0.862722\pi$
$863$		−	4.00211e14i		−	0.836055i	0.908434	−	0.418027i	$-0.137278\pi$
$864$	−1.50050e15			−3.11650
$865$			4.78515e13i			0.0988133i
$866$	2.60515e14			0.534865
$867$		−	2.94454e14i		−	0.601066i
$868$		−	2.78487e14i		−	0.565206i
$869$	−1.01528e14			−0.204874
$870$	5.13857e14			1.03097
$871$	−2.00054e13			−0.0399077
$872$		−	1.32771e15i		−	2.63342i
$873$	6.78029e14			1.33714
$874$	−1.68440e15			−3.30285
$875$	−4.89619e14			−0.954592
$876$	2.42843e15			4.70766
$877$	1.65134e14			0.318302			0.159151	−	0.987254i	$-0.449124\pi$
$877$	1.65134e14			0.318302			0.159151	+	0.987254i	$0.449124\pi$
$878$			1.38561e15i			2.65564i
$879$			1.23604e15i			2.35552i
$880$			6.41765e13i			0.121608i
$881$	6.20546e14			1.16921			0.584607	−	0.811316i	$-0.301249\pi$
$881$	6.20546e14			1.16921			0.584607	+	0.811316i	$0.301249\pi$
$882$		−	4.79551e15i		−	8.98447i
$883$	−7.21211e14			−1.34357			−0.671783	−	0.740748i	$-0.734471\pi$
$883$	−7.21211e14			−1.34357			−0.671783	+	0.740748i	$0.734471\pi$
$884$	3.11961e13			0.0577883
$885$	−2.26378e14			−0.416982
$886$			1.66375e15i			3.04732i
$887$		−	2.10658e14i		−	0.383672i	−0.981427	−	0.191836i	$-0.938556\pi$
$887$		−	2.10658e14i		−	0.383672i	0.981427	−	0.191836i	$-0.0614441\pi$
$888$		−	3.63490e15i		−	6.58305i
$889$		−	6.36963e14i		−	1.14711i
$890$		−	3.44984e14i		−	0.617802i
$891$	−1.02007e14			−0.181653
$892$			5.91738e14i			1.04787i
$893$			1.14045e15i			2.00826i
$894$			2.00390e15i			3.50903i
$895$	−3.44669e13			−0.0600187
$896$	−2.45169e13			−0.0424546
$897$			3.13987e13i			0.0540691i
$898$	1.06705e15			1.82727
$899$		−	8.98702e13i		−	0.153044i
$900$	2.62589e15			4.44696
$901$	5.69787e14			0.959596
$902$		−	6.46248e13i		−	0.108235i
$903$	−1.75664e15	+	7.91963e14i	−2.92579	+	1.31906i
$904$	1.09634e15			1.81595
$905$		−	9.67062e12i		−	0.0159298i
$906$		−	5.11694e14i		−	0.838243i
$907$	5.78575e14			0.942592			0.471296	−	0.881975i	$-0.343786\pi$
$907$	5.78575e14			0.942592			0.471296	+	0.881975i	$0.343786\pi$
$908$			4.58525e14i			0.742906i
$909$	4.12070e14			0.663974
$910$		−	1.69275e13i		−	0.0271261i
$911$		−	1.30023e14i		−	0.207218i	−0.994618	−	0.103609i	$-0.966961\pi$
$911$		−	1.30023e14i		−	0.207218i	0.994618	−	0.103609i	$-0.0330391\pi$
$912$	−4.44163e15			−7.03992
$913$	1.17333e14			0.184956
$914$	−9.66455e14			−1.51513
$915$		−	1.82209e14i		−	0.284096i
$916$	−3.65155e14			−0.566239
$917$	2.12637e15			3.27939
$918$	−1.65527e15			−2.53896
$919$	2.06256e14			0.314651			0.157326	−	0.987547i	$-0.449713\pi$
$919$	2.06256e14			0.314651			0.157326	+	0.987547i	$0.449713\pi$
$920$	−4.82498e14			−0.732076
$921$		−	6.80862e13i		−	0.102745i
$922$			1.20142e15i			1.80319i
$923$			7.22431e12i			0.0107842i
$924$	9.90326e14			1.47034
$925$			9.19737e14i			1.35817i
$926$	−6.92483e14			−1.01708
$927$	−1.35142e15			−1.97421
$928$	1.52799e15			2.22014
$929$		−	3.31265e14i		−	0.478737i	−0.970929	−	0.239368i	$-0.923060\pi$
$929$		−	3.31265e14i		−	0.478737i	0.970929	−	0.239368i	$-0.0769404\pi$
$930$			7.46384e13i			0.107287i
$931$		−	2.90681e15i		−	4.15593i
$932$			5.69661e14i			0.810097i
$933$		−	7.56908e14i		−	1.07062i
$934$	1.60518e15			2.25834
$935$			2.92112e13i			0.0408782i
$936$			1.10323e14i			0.153563i
$937$		−	1.13419e15i		−	1.57032i	−0.619291	−	0.785161i	$-0.712580\pi$
$937$		−	1.13419e15i		−	1.57032i	0.619291	−	0.785161i	$-0.287420\pi$
$938$	−3.34958e15			−4.61293
$939$	1.99135e15			2.72785
$940$			5.58190e14i			0.760576i
$941$	−4.36022e14			−0.590962			−0.295481	−	0.955349i	$-0.595480\pi$
$941$	−4.36022e14			−0.590962			−0.295481	+	0.955349i	$0.595480\pi$
$942$			1.42884e15i			1.92632i
$943$	2.42491e14			0.325190
$944$	−1.63144e15			−2.17626
$945$			6.34868e14i			0.842411i
$946$	−1.09276e14	−	2.42384e14i	−0.144235	−	0.319925i
$947$	−1.13238e15			−1.48676			−0.743381	−	0.668868i	$-0.766779\pi$
$947$	−1.13238e15			−1.48676			−0.743381	+	0.668868i	$0.766779\pi$
$948$		−	3.43920e15i		−	4.49176i
$949$		−	2.58159e13i		−	0.0335395i
$950$	2.25183e15			2.91017
$951$			1.35888e15i			1.74694i
$952$	3.05694e15			3.90933
$953$			1.16938e15i			1.48762i	0.668393	+	0.743808i	$0.266982\pi$
$953$			1.16938e15i			1.48762i	−0.668393	+	0.743808i	$0.733018\pi$
$954$			3.44297e15i			4.35704i
$955$	1.46354e14			0.184242
$956$	1.00847e15			1.26292
$957$	3.19586e14			0.398133
$958$		−	2.13655e15i		−	2.64780i
$959$	6.19578e14			0.763840
$960$	−3.67380e14			−0.450566
$961$	−8.06575e14			−0.984074
$962$	−6.60252e13			−0.0801372
$963$	−6.25490e14			−0.755246
$964$		−	2.22202e15i		−	2.66908i
$965$			6.93751e13i			0.0829023i
$966$			5.25720e15i			6.24984i
$967$	−1.58671e15			−1.87657			−0.938284	−	0.345865i	$-0.887585\pi$
$967$	−1.58671e15			−1.87657			−0.938284	+	0.345865i	$0.887585\pi$
$968$		−	2.13509e15i		−	2.51211i
$969$	−2.02170e15			−2.36645
$970$	2.84586e14			0.331402
$971$	3.24791e14			0.376278			0.188139	−	0.982142i	$-0.439755\pi$
$971$	3.24791e14			0.376278			0.188139	+	0.982142i	$0.439755\pi$
$972$			1.05731e14i			0.121863i
$973$			4.03605e14i			0.462799i
$974$			6.71436e14i			0.765967i
$975$		−	4.19761e13i		−	0.0476408i
$976$		−	1.31313e15i		−	1.48272i
$977$	−8.18240e14			−0.919196			−0.459598	−	0.888127i	$-0.652006\pi$
$977$	−8.18240e14			−0.919196			−0.459598	+	0.888127i	$0.652006\pi$
$978$		−	2.51172e15i		−	2.80723i
$979$		−	2.14558e14i		−	0.238579i
$980$		−	1.42273e15i		−	1.57395i
$981$	1.82253e15			2.00600
$982$	−1.99533e15			−2.18503
$983$			3.27838e14i			0.357183i	0.983923	+	0.178592i	$0.0571541\pi$
$983$			3.27838e14i			0.357183i	−0.983923	+	0.178592i	$0.942846\pi$
$984$	1.28119e15			1.38880
$985$		−	3.64917e13i		−	0.0393561i
$986$	1.68560e15			1.80871
$987$	3.55947e15			3.80014
$988$			1.14262e14i			0.121372i
$989$	9.09496e14	−	4.10038e14i	0.961212	−	0.433354i
$990$	−1.76510e14			−0.185607
$991$			1.84522e14i			0.193054i	0.995330	+	0.0965271i	$0.0307734\pi$
$991$			1.84522e14i			0.193054i	−0.995330	+	0.0965271i	$0.969227\pi$
$992$			2.21942e14i			0.231037i
$993$	2.10809e15			2.18345
$994$			1.20959e15i			1.24654i
$995$	−2.79336e14			−0.286425
$996$			3.97460e15i			4.05506i
$997$		−	8.17869e14i		−	0.830248i	−0.909765	−	0.415124i	$-0.863738\pi$
$997$		−	8.17869e14i		−	0.830248i	0.909765	−	0.415124i	$-0.136262\pi$
$998$	−9.23663e14			−0.932956
$999$	2.47628e15			2.48870

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.b.b.42.1	✓	34
43.42	odd	2	inner	43.11.b.b.42.34	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.b.b.42.1	✓	34	1.1	even	1	trivial
43.11.b.b.42.34	yes	34	43.42	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-59.1014i q^{2} +419.853i q^{3} -2468.98 q^{4} -832.528i q^{5} +24813.9 q^{6} -31219.1i q^{7} +85400.1i q^{8} -117228. q^{9} +O(q^{10})\)	\(q-59.1014i q^{2} +419.853i q^{3} -2468.98 q^{4} -832.528i q^{5} +24813.9 q^{6} -31219.1i q^{7} +85400.1i q^{8} -117228. q^{9} -49203.6 q^{10} -30601.5 q^{11} -1.03661e6i q^{12} -11019.9 q^{13} -1.84510e6 q^{14} +349540. q^{15} +2.51904e6 q^{16} +1.14659e6 q^{17} +6.92834e6i q^{18} +4.19962e6i q^{19} +2.05549e6i q^{20} +1.31075e7 q^{21} +1.80859e6i q^{22} -6.78637e6 q^{23} -3.58555e7 q^{24} +9.07252e6 q^{25} +651289. i q^{26} -2.44266e7i q^{27} +7.70793e7i q^{28} +2.48741e7i q^{29} -2.06583e7i q^{30} -3.61300e6 q^{31} -6.14288e7i q^{32} -1.28481e7i q^{33} -6.77651e7i q^{34} -2.59908e7 q^{35} +2.89433e8 q^{36} +1.01376e8i q^{37} +2.48203e8 q^{38} -4.62673e6i q^{39} +7.10980e7 q^{40} -3.57321e7 q^{41} -7.74670e8i q^{42} +(-1.34018e8 + 6.04208e7i) q^{43} +7.55544e7 q^{44} +9.75955e7i q^{45} +4.01084e8i q^{46} +2.71560e8 q^{47} +1.05763e9i q^{48} -6.92160e8 q^{49} -5.36199e8i q^{50} +4.81400e8i q^{51} +2.72078e7 q^{52} +4.96941e8 q^{53} -1.44365e9 q^{54} +2.54766e7i q^{55} +2.66612e9 q^{56} -1.76323e9 q^{57} +1.47010e9 q^{58} -6.47645e8 q^{59} -8.63005e8 q^{60} -5.21284e8i q^{61} +2.13533e8i q^{62} +3.65976e9i q^{63} -1.05104e9 q^{64} +9.17434e6i q^{65} -7.59343e8 q^{66} +1.81540e9 q^{67} -2.83090e9 q^{68} -2.84928e9i q^{69} +1.53609e9i q^{70} -6.55571e8i q^{71} -1.00113e10i q^{72} +2.34267e9i q^{73} +5.99147e9 q^{74} +3.80913e9i q^{75} -1.03688e10i q^{76} +9.55352e8i q^{77} -2.73446e8 q^{78} +3.31775e9 q^{79} -2.09717e9i q^{80} +3.33341e9 q^{81} +2.11182e9i q^{82} -3.83424e9 q^{83} -3.23620e10 q^{84} -9.54568e8i q^{85} +(3.57095e9 + 7.92065e9i) q^{86} -1.04435e10 q^{87} -2.61337e9i q^{88} +7.01136e9i q^{89} +5.76803e9 q^{90} +3.44031e8i q^{91} +1.67554e10 q^{92} -1.51693e9i q^{93} -1.60496e10i q^{94} +3.49630e9 q^{95} +2.57911e10 q^{96} -5.78385e9 q^{97} +4.09076e10i q^{98} +3.58735e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9}+O(q^{10}) \) 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9	\( 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9} - 254122 q^{10} - 218200 q^{11} - 191008 q^{13} - 1380228 q^{14} - 512732 q^{15} + 2224308 q^{16} - 1070678 q^{17} + 17857352 q^{21} + 8915254 q^{23} - 39666730 q^{24} - 82938284 q^{25} - 55042410 q^{31} - 179227232 q^{35} + 394381042 q^{36} + 709061882 q^{38} + 433255366 q^{40} + 80370626 q^{41} + 1585062 q^{43} + 324477888 q^{44} - 544910502 q^{47} - 2479345922 q^{49} - 987059452 q^{52} - 915886820 q^{53} - 297150836 q^{54} + 2172449592 q^{56} - 2398069428 q^{57} + 930519014 q^{58} + 3394816764 q^{59} - 5474941192 q^{60} + 2925325476 q^{64} + 455136192 q^{66} + 3405920388 q^{67} + 664008226 q^{68} + 16264108918 q^{74} - 17800086268 q^{78} - 13853150858 q^{79} + 20444701546 q^{81} + 113867236 q^{83} - 30401949428 q^{84} + 19291204884 q^{86} - 5221634730 q^{87} - 6984391876 q^{90} + 41423783058 q^{92} + 4107406010 q^{95} + 33148445474 q^{96} + 15795117154 q^{97} + 1345877600 q^{99}+O(q^{100}) \) 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9 - 254122 * q^10 - 218200 * q^11 - 191008 * q^13 - 1380228 * q^14 - 512732 * q^15 + 2224308 * q^16 - 1070678 * q^17 + 17857352 * q^21 + 8915254 * q^23 - 39666730 * q^24 - 82938284 * q^25 - 55042410 * q^31 - 179227232 * q^35 + 394381042 * q^36 + 709061882 * q^38 + 433255366 * q^40 + 80370626 * q^41 + 1585062 * q^43 + 324477888 * q^44 - 544910502 * q^47 - 2479345922 * q^49 - 987059452 * q^52 - 915886820 * q^53 - 297150836 * q^54 + 2172449592 * q^56 - 2398069428 * q^57 + 930519014 * q^58 + 3394816764 * q^59 - 5474941192 * q^60 + 2925325476 * q^64 + 455136192 * q^66 + 3405920388 * q^67 + 664008226 * q^68 + 16264108918 * q^74 - 17800086268 * q^78 - 13853150858 * q^79 + 20444701546 * q^81 + 113867236 * q^83 - 30401949428 * q^84 + 19291204884 * q^86 - 5221634730 * q^87 - 6984391876 * q^90 + 41423783058 * q^92 + 4107406010 * q^95 + 33148445474 * q^96 + 15795117154 * q^97 + 1345877600 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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