LMFDB - Embedded newform 43.11.b.b.42.33

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			42.33
Character	$\chi$	$=$	43.42
Dual form			43.11.b.b.42.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+58.7853i q^{2} +301.513i q^{3} -2431.72 q^{4} +2781.13i q^{5} -17724.6 q^{6} -4095.06i q^{7} -82753.1i q^{8} -31861.2 q^{9} +O(q^{10})$	\(q+58.7853i q^{2} +301.513i q^{3} -2431.72 q^{4} +2781.13i q^{5} -17724.6 q^{6} -4095.06i q^{7} -82753.1i q^{8} -31861.2 q^{9} -163489. q^{10} -123581. q^{11} -733195. i q^{12} +347183. q^{13} +240730. q^{14} -838546. q^{15} +2.37459e6 q^{16} -82597.3 q^{17} -1.87297e6i q^{18} -1.73289e6i q^{19} -6.76291e6i q^{20} +1.23471e6 q^{21} -7.26474e6i q^{22} -1.02592e7 q^{23} +2.49512e7 q^{24} +2.03096e6 q^{25} +2.04093e7i q^{26} +8.19747e6i q^{27} +9.95803e6i q^{28} +6.06720e6i q^{29} -4.92942e7i q^{30} -4.26574e7 q^{31} +5.48521e7i q^{32} -3.72613e7i q^{33} -4.85551e6i q^{34} +1.13889e7 q^{35} +7.74775e7 q^{36} +1.00476e8i q^{37} +1.01868e8 q^{38} +1.04680e8i q^{39} +2.30147e8 q^{40} +9.51556e7 q^{41} +7.25831e7i q^{42} +(-1.46887e8 + 5.98259e6i) q^{43} +3.00514e8 q^{44} -8.86101e7i q^{45} -6.03091e8i q^{46} +6.18096e6 q^{47} +7.15971e8i q^{48} +2.65706e8 q^{49} +1.19391e8i q^{50} -2.49042e7i q^{51} -8.44251e8 q^{52} -3.72498e8 q^{53} -4.81891e8 q^{54} -3.43694e8i q^{55} -3.38879e8 q^{56} +5.22488e8 q^{57} -3.56662e8 q^{58} +7.30905e8 q^{59} +2.03911e9 q^{60} -5.55615e8i q^{61} -2.50763e9i q^{62} +1.30474e8i q^{63} -7.92916e8 q^{64} +9.65560e8i q^{65} +2.19042e9 q^{66} -1.30656e9 q^{67} +2.00853e8 q^{68} -3.09328e9i q^{69} +6.69499e8i q^{70} -2.26506e9i q^{71} +2.63662e9i q^{72} +1.19629e9i q^{73} -5.90651e9 q^{74} +6.12362e8i q^{75} +4.21389e9i q^{76} +5.06071e8i q^{77} -6.15367e9 q^{78} -5.10251e9 q^{79} +6.60404e9i q^{80} -4.35302e9 q^{81} +5.59375e9i q^{82} +7.51268e9 q^{83} -3.00248e9 q^{84} -2.29714e8i q^{85} +(-3.51689e8 - 8.63478e9i) q^{86} -1.82934e9 q^{87} +1.02267e10i q^{88} -5.82403e9i q^{89} +5.20898e9 q^{90} -1.42174e9i q^{91} +2.49475e10 q^{92} -1.28618e10i q^{93} +3.63350e8i q^{94} +4.81938e9 q^{95} -1.65386e10 q^{96} -8.05991e9 q^{97} +1.56196e10i q^{98} +3.93744e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			58.7853i			1.83704i	0.395372	+	0.918521i	$0.370616\pi$
$2$			58.7853i			1.83704i	−0.395372	+	0.918521i	$0.629384\pi$
$3$			301.513i			1.24080i	0.784287	+	0.620398i	$0.213029\pi$
$3$			301.513i			1.24080i	−0.784287	+	0.620398i	$0.786971\pi$
$4$	−2431.72			−2.37472
$5$			2781.13i			0.889960i	0.895540	+	0.444980i	$0.146789\pi$
$5$			2781.13i			0.889960i	−0.895540	+	0.444980i	$0.853211\pi$
$6$	−17724.6			−2.27939
$7$		−	4095.06i		−	0.243652i	−0.992551	−	0.121826i	$-0.961125\pi$
$7$		−	4095.06i		−	0.243652i	0.992551	−	0.121826i	$-0.0388750\pi$
$8$		−	82753.1i		−	2.52543i
$9$	−31861.2			−0.539573
$10$	−163489.			−1.63489
$11$	−123581.			−0.767340			−0.383670	−	0.923470i	$-0.625340\pi$
$11$	−123581.			−0.767340			−0.383670	+	0.923470i	$0.625340\pi$
$12$		−	733195.i		−	2.94655i
$13$	347183.			0.935065			0.467533	−	0.883976i	$-0.345143\pi$
$13$	347183.			0.935065			0.467533	+	0.883976i	$0.345143\pi$
$14$	240730.			0.447599
$15$	−838546.			−1.10426
$16$	2.37459e6			2.26459
$17$	−82597.3			−0.0581730			−0.0290865	−	0.999577i	$-0.509260\pi$
$17$	−82597.3			−0.0581730			−0.0290865	+	0.999577i	$0.509260\pi$
$18$		−	1.87297e6i		−	0.991218i
$19$		−	1.73289e6i		−	0.699846i	−0.936779	−	0.349923i	$-0.886208\pi$
$19$		−	1.73289e6i		−	0.699846i	0.936779	−	0.349923i	$-0.113792\pi$
$20$		−	6.76291e6i		−	2.11341i
$21$	1.23471e6			0.302322
$22$		−	7.26474e6i		−	1.40964i
$23$	−1.02592e7			−1.59395			−0.796974	−	0.604013i	$-0.793567\pi$
$23$	−1.02592e7			−1.59395			−0.796974	+	0.604013i	$0.793567\pi$
$24$	2.49512e7			3.13354
$25$	2.03096e6			0.207970
$26$			2.04093e7i			1.71775i
$27$			8.19747e6i			0.571296i
$28$			9.95803e6i			0.578606i
$29$			6.06720e6i			0.295800i	0.989002	+	0.147900i	$0.0472514\pi$
$29$			6.06720e6i			0.295800i	−0.989002	+	0.147900i	$0.952749\pi$
$30$		−	4.92942e7i		−	2.02857i
$31$	−4.26574e7			−1.49000			−0.745000	−	0.667064i	$-0.767551\pi$
$31$	−4.26574e7			−1.49000			−0.745000	+	0.667064i	$0.767551\pi$
$32$			5.48521e7i			1.63472i
$33$		−	3.72613e7i		−	0.952112i
$34$		−	4.85551e6i		−	0.106866i
$35$	1.13889e7			0.216841
$36$	7.74775e7			1.28134
$37$			1.00476e8i			1.44895i	0.689301	+	0.724475i	$0.257918\pi$
$37$			1.00476e8i			1.44895i	−0.689301	+	0.724475i	$0.742082\pi$
$38$	1.01868e8			1.28565
$39$			1.04680e8i			1.16022i
$40$	2.30147e8			2.24753
$41$	9.51556e7			0.821325			0.410662	−	0.911787i	$-0.365298\pi$
$41$	9.51556e7			0.821325			0.410662	+	0.911787i	$0.365298\pi$
$42$			7.25831e7i			0.555379i
$43$	−1.46887e8	+	5.98259e6i	−0.999172	+	0.0406956i
$43$	−1.46887e8	+	5.98259e6i	−0.999172	+	0.0406956i
$44$	3.00514e8			1.82222
$45$		−	8.86101e7i		−	0.480198i
$46$		−	6.03091e8i		−	2.92815i
$47$	6.18096e6			0.0269505			0.0134752	−	0.999909i	$-0.495711\pi$
$47$	6.18096e6			0.0269505			0.0134752	+	0.999909i	$0.495711\pi$
$48$			7.15971e8i			2.80989i
$49$	2.65706e8			0.940634
$50$			1.19391e8i			0.382050i
$51$		−	2.49042e7i		−	0.0721808i
$52$	−8.44251e8			−2.22052
$53$	−3.72498e8			−0.890726			−0.445363	−	0.895350i	$-0.646925\pi$
$53$	−3.72498e8			−0.890726			−0.445363	+	0.895350i	$0.646925\pi$
$54$	−4.81891e8			−1.04949
$55$		−	3.43694e8i		−	0.682902i
$56$	−3.38879e8			−0.615325
$57$	5.22488e8			0.868365
$58$	−3.56662e8			−0.543397
$59$	7.30905e8			1.02235			0.511177	−	0.859476i	$-0.329210\pi$
$59$	7.30905e8			1.02235			0.511177	+	0.859476i	$0.329210\pi$
$60$	2.03911e9			2.62231
$61$		−	5.55615e8i		−	0.657847i	−0.944357	−	0.328924i	$-0.893314\pi$
$61$		−	5.55615e8i		−	0.657847i	0.944357	−	0.328924i	$-0.106686\pi$
$62$		−	2.50763e9i		−	2.73719i
$63$			1.30474e8i			0.131468i
$64$	−7.92916e8			−0.738460
$65$			9.65560e8i			0.832171i
$66$	2.19042e9			1.74907
$67$	−1.30656e9			−0.967734			−0.483867	−	0.875142i	$-0.660768\pi$
$67$	−1.30656e9			−0.967734			−0.483867	+	0.875142i	$0.660768\pi$
$68$	2.00853e8			0.138145
$69$		−	3.09328e9i		−	1.97776i
$70$			6.69499e8i			0.398345i
$71$		−	2.26506e9i		−	1.25541i	−0.778449	−	0.627707i	$-0.783993\pi$
$71$		−	2.26506e9i		−	1.25541i	0.778449	−	0.627707i	$-0.216007\pi$
$72$			2.63662e9i			1.36265i
$73$			1.19629e9i			0.577062i	0.957471	+	0.288531i	$0.0931668\pi$
$73$			1.19629e9i			0.577062i	−0.957471	+	0.288531i	$0.906833\pi$
$74$	−5.90651e9			−2.66178
$75$			6.12362e8i			0.258049i
$76$			4.21389e9i			1.66194i
$77$			5.06071e8i			0.186964i
$78$	−6.15367e9			−2.13138
$79$	−5.10251e9			−1.65824			−0.829122	−	0.559067i	$-0.811159\pi$
$79$	−5.10251e9			−1.65824			−0.829122	+	0.559067i	$0.811159\pi$
$80$			6.60404e9i			2.01539i
$81$	−4.35302e9			−1.24843
$82$			5.59375e9i			1.50881i
$83$	7.51268e9			1.90724			0.953618	−	0.301020i	$-0.0973272\pi$
$83$	7.51268e9			1.90724			0.953618	+	0.301020i	$0.0973272\pi$
$84$	−3.00248e9			−0.717932
$85$		−	2.29714e8i		−	0.0517716i
$86$	−3.51689e8	−	8.63478e9i	−0.0747595	−	1.83552i
$87$	−1.82934e9			−0.367027
$88$			1.02267e10i			1.93786i
$89$		−	5.82403e9i		−	1.04297i	−0.853259	−	0.521487i	$-0.825377\pi$
$89$		−	5.82403e9i		−	1.04297i	0.853259	−	0.521487i	$-0.174623\pi$
$90$	5.20898e9			0.882145
$91$		−	1.42174e9i		−	0.227831i
$92$	2.49475e10			3.78519
$93$		−	1.28618e10i		−	1.84879i
$94$			3.63350e8i			0.0495092i
$95$	4.81938e9			0.622835
$96$	−1.65386e10			−2.02835
$97$	−8.05991e9			−0.938580			−0.469290	−	0.883044i	$-0.655490\pi$
$97$	−8.05991e9			−0.938580			−0.469290	+	0.883044i	$0.655490\pi$
$98$			1.56196e10i			1.72798i
$99$	3.93744e9			0.414036
$100$	−4.93872e9			−0.493872
$101$	4.21055e8			0.0400620			0.0200310	−	0.999799i	$-0.493624\pi$
$101$	4.21055e8			0.0400620			0.0200310	+	0.999799i	$0.493624\pi$
$102$	1.46400e9			0.132599
$103$	2.05118e9			0.176936			0.0884682	−	0.996079i	$-0.471803\pi$
$103$	2.05118e9			0.176936			0.0884682	+	0.996079i	$0.471803\pi$
$104$		−	2.87305e10i		−	2.36144i
$105$			3.43390e9i			0.269055i
$106$		−	2.18974e10i		−	1.63630i
$107$	1.77156e10			1.26309			0.631547	−	0.775337i	$-0.282420\pi$
$107$	1.77156e10			1.26309			0.631547	+	0.775337i	$0.282420\pi$
$108$		−	1.99339e10i		−	1.35667i
$109$	1.07286e10			0.697288			0.348644	−	0.937255i	$-0.386642\pi$
$109$	1.07286e10			0.697288			0.348644	+	0.937255i	$0.386642\pi$
$110$	2.02042e10			1.25452
$111$	−3.02948e10			−1.79785
$112$		−	9.72410e9i		−	0.551772i
$113$		−	2.05731e10i		−	1.11663i	−0.829630	−	0.558314i	$-0.811449\pi$
$113$		−	2.05731e10i		−	1.11663i	0.829630	−	0.558314i	$-0.188551\pi$
$114$			3.07147e10i			1.59522i
$115$		−	2.85321e10i		−	1.41855i
$116$		−	1.47537e10i		−	0.702443i
$117$	−1.10617e10			−0.504536
$118$			4.29665e10i			1.87811i
$119$			3.38241e8i			0.0141740i
$120$			6.93923e10i			2.78872i
$121$	−1.06652e10			−0.411190
$122$	3.26620e10			1.20849
$123$			2.86907e10i			1.01910i
$124$	1.03731e11			3.53834
$125$			3.28078e10i			1.07505i
$126$	−7.66994e9			−0.241512
$127$	−1.51740e10			−0.459283			−0.229641	−	0.973275i	$-0.573755\pi$
$127$	−1.51740e10			−0.459283			−0.229641	+	0.973275i	$0.573755\pi$
$128$			9.55672e9i			0.278137i
$129$	−1.80383e9	−	4.42883e10i	−0.0504949	−	1.23977i
$130$	−5.67608e10			−1.52873
$131$			1.12052e10i			0.290443i	0.989399	+	0.145222i	$0.0463895\pi$
$131$			1.12052e10i			0.290443i	−0.989399	+	0.145222i	$0.953610\pi$
$132$			9.06088e10i			2.26100i
$133$	−7.09628e9			−0.170519
$134$		−	7.68067e10i		−	1.77777i
$135$	−2.27982e10			−0.508431
$136$			6.83519e9i			0.146912i
$137$			7.63190e10i			1.58136i	0.612231	+	0.790679i	$0.290272\pi$
$137$			7.63190e10i			1.58136i	−0.612231	+	0.790679i	$0.709728\pi$
$138$	1.81840e11			3.63324
$139$	−7.87273e10			−1.51723			−0.758615	−	0.651539i	$-0.774123\pi$
$139$	−7.87273e10			−1.51723			−0.758615	+	0.651539i	$0.774123\pi$
$140$	−2.76945e10			−0.514937
$141$			1.86364e9i			0.0334400i
$142$	1.33152e11			2.30625
$143$	−4.29052e10			−0.717513
$144$	−7.56575e10			−1.22191
$145$	−1.68736e10			−0.263250
$146$	−7.03244e10			−1.06009
$147$			8.01138e10i			1.16713i
$148$		−	2.44329e11i		−	3.44086i
$149$			3.16960e10i			0.431592i	0.976438	+	0.215796i	$0.0692346\pi$
$149$			3.16960e10i			0.431592i	−0.976438	+	0.215796i	$0.930765\pi$
$150$	−3.59979e10			−0.474046
$151$			1.06479e11i			1.35638i	0.734888	+	0.678188i	$0.237234\pi$
$151$			1.06479e11i			1.35638i	−0.734888	+	0.678188i	$0.762766\pi$
$152$	−1.43402e11			−1.76741
$153$	2.63165e9			0.0313886
$154$	−2.97496e10			−0.343461
$155$		−	1.18636e11i		−	1.32604i
$156$		−	2.54553e11i		−	2.75521i
$157$			1.03422e11i			1.08421i	0.840311	+	0.542105i	$0.182372\pi$
$157$			1.03422e11i			1.08421i	−0.840311	+	0.542105i	$0.817628\pi$
$158$		−	2.99953e11i		−	3.04626i
$159$		−	1.12313e11i		−	1.10521i
$160$	−1.52551e11			−1.45484
$161$			4.20120e10i			0.388369i
$162$		−	2.55894e11i		−	2.29343i
$163$			1.65963e11i			1.44236i	0.692748	+	0.721180i	$0.256400\pi$
$163$			1.65963e11i			1.44236i	−0.692748	+	0.721180i	$0.743600\pi$
$164$	−2.31391e11			−1.95042
$165$	1.03628e11			0.847342
$166$			4.41635e11i			3.50367i
$167$	−1.88099e10			−0.144812			−0.0724061	−	0.997375i	$-0.523068\pi$
$167$	−1.88099e10			−0.144812			−0.0724061	+	0.997375i	$0.523068\pi$
$168$		−	1.02177e11i		−	0.763492i
$169$	−1.73223e10			−0.125653
$170$	1.35038e10			0.0951067
$171$			5.52119e10i			0.377618i
$172$	3.57187e11	−	1.45480e10i	2.37276	−	0.0966408i
$173$	3.76642e10			0.243052			0.121526	−	0.992588i	$-0.461221\pi$
$173$	3.76642e10			0.243052			0.121526	+	0.992588i	$0.461221\pi$
$174$		−	1.07538e11i		−	0.674245i
$175$		−	8.31691e9i		−	0.0506724i
$176$	−2.93454e11			−1.73771
$177$			2.20378e11i			1.26853i
$178$	3.42368e11			1.91599
$179$		−	1.05319e11i		−	0.573116i	−0.958063	−	0.286558i	$-0.907489\pi$
$179$		−	1.05319e11i		−	0.573116i	0.958063	−	0.286558i	$-0.0925111\pi$
$180$			2.15475e11i			1.14034i
$181$	−9.42249e10			−0.485035			−0.242517	−	0.970147i	$-0.577973\pi$
$181$	−9.42249e10			−0.485035			−0.242517	+	0.970147i	$0.577973\pi$
$182$	8.35773e10			0.418534
$183$	1.67525e11			0.816254
$184$			8.48981e11i			4.02540i
$185$	−2.79436e11			−1.28951
$186$	7.56084e11			3.39630
$187$	1.02074e10			0.0446384
$188$	−1.50303e10			−0.0639999
$189$	3.35691e10			0.139197
$190$			2.83309e11i			1.14417i
$191$		−	2.21542e10i		−	0.0871542i	−0.999050	−	0.0435771i	$-0.986125\pi$
$191$		−	2.21542e10i		−	0.0871542i	0.999050	−	0.0435771i	$-0.0138754\pi$
$192$		−	2.39075e11i		−	0.916278i
$193$	−3.99665e11			−1.49248			−0.746241	−	0.665676i	$-0.768143\pi$
$193$	−3.99665e11			−1.49248			−0.746241	+	0.665676i	$0.768143\pi$
$194$		−	4.73804e11i		−	1.72421i
$195$	−2.91129e11			−1.03255
$196$	−6.46121e11			−2.23375
$197$	−2.90810e11			−0.980117			−0.490059	−	0.871689i	$-0.663025\pi$
$197$	−2.90810e11			−0.980117			−0.490059	+	0.871689i	$0.663025\pi$
$198$			2.31464e11i			0.760601i
$199$		−	4.67310e11i		−	1.49741i	−0.662904	−	0.748704i	$-0.730676\pi$
$199$		−	4.67310e11i		−	1.49741i	0.662904	−	0.748704i	$-0.269324\pi$
$200$		−	1.68068e11i		−	0.525214i
$201$		−	3.93946e11i		−	1.20076i
$202$			2.47519e10i			0.0735955i
$203$	2.48455e10			0.0720723
$204$			6.05599e10i			0.171409i
$205$			2.64640e11i			0.730946i
$206$			1.20579e11i			0.325040i
$207$	3.26871e11			0.860051
$208$	8.24419e11			2.11754
$209$			2.14152e11i			0.537019i
$210$	−2.01863e11			−0.494265
$211$		−	6.62830e11i		−	1.58486i	−0.609965	−	0.792428i	$-0.708817\pi$
$211$		−	6.62830e11i		−	1.58486i	0.609965	−	0.792428i	$-0.291183\pi$
$212$	9.05809e11			2.11523
$213$	6.82944e11			1.55771
$214$			1.04141e12i			2.32036i
$215$	−1.66384e10	−	4.08510e11i	−0.0362175	−	0.889223i
$216$	6.78367e11			1.44277
$217$			1.74685e11i			0.363042i
$218$			6.30687e11i			1.28095i
$219$	−3.60697e11			−0.716016
$220$			8.35766e11i			1.62170i
$221$	−2.86764e10			−0.0543955
$222$		−	1.78089e12i		−	3.30273i
$223$		−	2.54463e11i		−	0.461424i	−0.973022	−	0.230712i	$-0.925894\pi$
$223$		−	2.54463e11i		−	0.461424i	0.973022	−	0.230712i	$-0.0741056\pi$
$224$	2.24623e11			0.398303
$225$	−6.47089e10			−0.112215
$226$	1.20940e12			2.05129
$227$		−	8.55296e11i		−	1.41902i	−0.704698	−	0.709508i	$-0.748917\pi$
$227$		−	8.55296e11i		−	1.41902i	0.704698	−	0.709508i	$-0.251083\pi$
$228$	−1.27054e12			−2.06213
$229$	−1.39540e11			−0.221575			−0.110787	−	0.993844i	$-0.535337\pi$
$229$	−1.39540e11			−0.221575			−0.110787	+	0.993844i	$0.535337\pi$
$230$	1.67727e12			2.60594
$231$	−1.52587e11			−0.231984
$232$	5.02080e11			0.747021
$233$			4.38920e11i			0.639154i	0.947560	+	0.319577i	$0.103541\pi$
$233$			4.38920e11i			0.639154i	−0.947560	+	0.319577i	$0.896459\pi$
$234$		−	6.50265e11i		−	0.926854i
$235$			1.71900e10i			0.0239849i
$236$	−1.77735e12			−2.42781
$237$		−	1.53847e12i		−	2.05754i
$238$	−1.98836e10			−0.0260382
$239$	−1.22437e12			−1.57008			−0.785041	−	0.619444i	$-0.787358\pi$
$239$	−1.22437e12			−1.57008			−0.785041	+	0.619444i	$0.787358\pi$
$240$	−1.99121e12			−2.50069
$241$		−	1.20039e11i		−	0.147652i	−0.997271	−	0.0738259i	$-0.976479\pi$
$241$		−	1.20039e11i		−	0.147652i	0.997271	−	0.0738259i	$-0.0235209\pi$
$242$		−	6.26958e11i		−	0.755373i
$243$		−	8.28441e11i		−	0.977755i
$244$			1.35110e12i			1.56221i
$245$			7.38961e11i			0.837127i
$246$	−1.68659e12			−1.87212
$247$		−	6.01629e11i		−	0.654401i
$248$			3.53004e12i			3.76288i
$249$			2.26517e12i			2.36649i
$250$	−1.92862e12			−1.97490
$251$	8.36159e11			0.839306			0.419653	−	0.907685i	$-0.362152\pi$
$251$	8.36159e11			0.839306			0.419653	+	0.907685i	$0.362152\pi$
$252$		−	3.17275e11i		−	0.312200i
$253$	1.26784e12			1.22310
$254$		−	8.92006e11i		−	0.843722i
$255$	6.92617e10			0.0642380
$256$	−1.37374e12			−1.24941
$257$		−	5.72904e10i		−	0.0510994i	−0.999674	−	0.0255497i	$-0.991866\pi$
$257$		−	5.72904e10i		−	0.0510994i	0.999674	−	0.0255497i	$-0.00813361\pi$
$258$	2.60350e12	−	1.06039e11i	2.27750	−	0.0927612i
$259$	4.11455e11			0.353040
$260$		−	2.34797e12i		−	1.97618i
$261$		−	1.93308e11i		−	0.159606i
$262$	−6.58699e11			−0.533557
$263$			1.94524e12i			1.54594i	0.634441	+	0.772971i	$0.281230\pi$
$263$			1.94524e12i			1.54594i	−0.634441	+	0.772971i	$0.718770\pi$
$264$	−3.08349e12			−2.40449
$265$		−	1.03596e12i		−	0.792711i
$266$		−	4.17157e11i		−	0.313250i
$267$	1.75602e12			1.29412
$268$	3.17719e12			2.29810
$269$	−2.22693e11			−0.158105			−0.0790525	−	0.996870i	$-0.525189\pi$
$269$	−2.22693e11			−0.158105			−0.0790525	+	0.996870i	$0.525189\pi$
$270$		−	1.34020e12i		−	0.934009i
$271$	1.96371e12			1.34348			0.671741	−	0.740786i	$-0.265547\pi$
$271$	1.96371e12			1.34348			0.671741	+	0.740786i	$0.265547\pi$
$272$	−1.96135e11			−0.131738
$273$	4.28672e11			0.282691
$274$	−4.48644e12			−2.90502
$275$	−2.50988e11			−0.159584
$276$			7.52199e12i			4.69664i
$277$			2.96481e12i			1.81802i	0.416774	+	0.909010i	$0.363160\pi$
$277$			2.96481e12i			1.81802i	−0.416774	+	0.909010i	$0.636840\pi$
$278$		−	4.62801e12i		−	2.78721i
$279$	1.35912e12			0.803963
$280$		−	9.42466e11i		−	0.547615i
$281$	1.19276e12			0.680803			0.340401	−	0.940280i	$-0.389437\pi$
$281$	1.19276e12			0.680803			0.340401	+	0.940280i	$0.389437\pi$
$282$	−1.09555e11			−0.0614307
$283$	−1.85174e12			−1.02011			−0.510056	−	0.860141i	$-0.670375\pi$
$283$	−1.85174e12			−1.02011			−0.510056	+	0.860141i	$0.670375\pi$
$284$			5.50798e12i			2.98126i
$285$			1.45311e12i			0.772810i
$286$		−	2.52220e12i		−	1.31810i
$287$		−	3.89668e11i		−	0.200117i
$288$		−	1.74766e12i		−	0.882050i
$289$	−2.00917e12			−0.996616
$290$		−	9.91923e11i		−	0.483602i
$291$		−	2.43017e12i		−	1.16459i
$292$		−	2.90904e12i		−	1.37036i
$293$	1.59940e12			0.740662			0.370331	−	0.928900i	$-0.379244\pi$
$293$	1.59940e12			0.740662			0.370331	+	0.928900i	$0.379244\pi$
$294$	−4.70952e12			−2.14407
$295$			2.03274e12i			0.909854i
$296$	8.31470e12			3.65921
$297$		−	1.01305e12i		−	0.438378i
$298$	−1.86326e12			−0.792853
$299$	−3.56182e12			−1.49045
$300$		−	1.48909e12i		−	0.612794i
$301$	2.44991e10	+	6.01510e11i	0.00991556	+	0.243450i
$302$	−6.25942e12			−2.49172
$303$			1.26954e11i			0.0497087i
$304$		−	4.11490e12i		−	1.58486i
$305$	1.54524e12			0.585458
$306$			1.54703e11i			0.0576621i
$307$	−4.23749e12			−1.55388			−0.776938	−	0.629577i	$-0.783228\pi$
$307$	−4.23749e12			−1.55388			−0.776938	+	0.629577i	$0.783228\pi$
$308$		−	1.23062e12i		−	0.443988i
$309$			6.18457e11i			0.219542i
$310$	6.97404e12			2.43599
$311$	1.81080e12			0.622400			0.311200	−	0.950345i	$-0.399269\pi$
$311$	1.81080e12			0.622400			0.311200	+	0.950345i	$0.399269\pi$
$312$	8.66263e12			2.93006
$313$		−	2.35705e12i		−	0.784597i	−0.919838	−	0.392299i	$-0.871680\pi$
$313$		−	2.35705e12i		−	0.784597i	0.919838	−	0.392299i	$-0.128320\pi$
$314$	−6.07968e12			−1.99174
$315$	−3.62864e11			−0.117001
$316$	1.24079e13			3.93787
$317$	−2.44343e11			−0.0763315			−0.0381657	−	0.999271i	$-0.512151\pi$
$317$	−2.44343e11			−0.0763315			−0.0381657	+	0.999271i	$0.512151\pi$
$318$	6.60236e12			2.03032
$319$		−	7.49789e11i		−	0.226979i
$320$		−	2.20520e12i		−	0.657201i
$321$			5.34147e12i			1.56724i
$322$	−2.46969e12			−0.713450
$323$			1.43132e11i			0.0407121i
$324$	1.05853e13			2.96469
$325$	7.05116e11			0.194466
$326$	−9.75620e12			−2.64968
$327$			3.23483e12i			0.865192i
$328$		−	7.87442e12i		−	2.07419i
$329$		−	2.53114e10i		−	0.00656654i
$330$			6.09182e12i			1.55660i
$331$			4.84332e12i			1.21900i	0.792787	+	0.609499i	$0.208629\pi$
$331$			4.84332e12i			1.21900i	−0.792787	+	0.609499i	$0.791371\pi$
$332$	−1.82687e13			−4.52916
$333$		−	3.20129e12i		−	0.781814i
$334$		−	1.10575e12i		−	0.266026i
$335$		−	3.63371e12i		−	0.861245i
$336$	2.93195e12			0.684636
$337$	1.12548e12			0.258934			0.129467	−	0.991584i	$-0.458673\pi$
$337$	1.12548e12			0.258934			0.129467	+	0.991584i	$0.458673\pi$
$338$		−	1.01830e12i		−	0.230829i
$339$	6.20307e12			1.38551
$340$			5.58598e11i			0.122943i
$341$	5.27164e12			1.14334
$342$	−3.24565e12			−0.693699
$343$		−	2.24483e12i		−	0.472839i
$344$	4.95078e11	+	1.21553e13i	0.102774	+	2.52333i
$345$	8.60282e12			1.76013
$346$			2.21410e12i			0.446496i
$347$			7.96450e12i			1.58311i	0.611098	+	0.791555i	$0.290728\pi$
$347$			7.96450e12i			1.58311i	−0.611098	+	0.791555i	$0.709272\pi$
$348$	4.44844e12			0.871588
$349$		−	6.88437e12i		−	1.32965i	−0.747000	−	0.664825i	$-0.768506\pi$
$349$		−	6.88437e12i		−	1.32965i	0.747000	−	0.664825i	$-0.231494\pi$
$350$	4.88912e11			0.0930874
$351$			2.84602e12i			0.534199i
$352$		−	6.77867e12i		−	1.25439i
$353$	−7.60397e12			−1.38729			−0.693644	−	0.720318i	$-0.743996\pi$
$353$	−7.60397e12			−1.38729			−0.693644	+	0.720318i	$0.743996\pi$
$354$	−1.29550e13			−2.33035
$355$	6.29941e12			1.11727
$356$			1.41624e13i			2.47678i
$357$	−1.01984e11			−0.0175870
$358$	6.19123e12			1.05284
$359$	1.16452e12			0.195287			0.0976434	−	0.995221i	$-0.468870\pi$
$359$	1.16452e12			0.195287			0.0976434	+	0.995221i	$0.468870\pi$
$360$	−7.33276e12			−1.21271
$361$	3.12817e12			0.510216
$362$		−	5.53904e12i		−	0.891029i
$363$		−	3.21570e12i		−	0.510202i
$364$			3.45726e12i			0.541035i
$365$	−3.32704e12			−0.513562
$366$			9.84804e12i			1.49949i
$367$	−2.37467e11			−0.0356675			−0.0178338	−	0.999841i	$-0.505677\pi$
$367$	−2.37467e11			−0.0356675			−0.0178338	+	0.999841i	$0.505677\pi$
$368$	−2.43614e13			−3.60964
$369$	−3.03177e12			−0.443164
$370$		−	1.64268e13i		−	2.36888i
$371$			1.52540e12i			0.217027i
$372$			3.12762e13i			4.39035i
$373$		−	7.65200e12i		−	1.05982i	−0.848055	−	0.529908i	$-0.822226\pi$
$373$		−	7.65200e12i		−	1.05982i	0.848055	−	0.529908i	$-0.177774\pi$
$374$			6.00048e11i			0.0820027i
$375$	−9.89199e12			−1.33391
$376$		−	5.11494e11i		−	0.0680614i
$377$			2.10643e12i			0.276592i
$378$			1.97337e12i			0.255712i
$379$	2.37829e12			0.304136			0.152068	−	0.988370i	$-0.451407\pi$
$379$	2.37829e12			0.304136			0.152068	+	0.988370i	$0.451407\pi$
$380$	−1.17194e13			−1.47906
$381$		−	4.57515e12i		−	0.569876i
$382$	1.30234e12			0.160106
$383$			1.19635e13i			1.45166i	0.687876	+	0.725829i	$0.258543\pi$
$383$			1.19635e13i			1.45166i	−0.687876	+	0.725829i	$0.741457\pi$
$384$	−2.88148e12			−0.345111
$385$	−1.40745e12			−0.166390
$386$		−	2.34944e13i		−	2.74175i
$387$	4.67999e12	−	1.90613e11i	0.539126	−	0.0219582i
$388$	1.95994e13			2.22887
$389$		−	3.01793e12i		−	0.338814i	−0.985546	−	0.169407i	$-0.945815\pi$
$389$		−	3.01793e12i		−	0.338814i	0.985546	−	0.169407i	$-0.0541853\pi$
$390$		−	1.71141e13i		−	1.89685i
$391$	8.47382e11			0.0927247
$392$		−	2.19880e13i		−	2.37550i
$393$	−3.37850e12			−0.360381
$394$		−	1.70954e13i		−	1.80052i
$395$		−	1.41907e13i		−	1.47577i
$396$	−9.57473e12			−0.983220
$397$	−3.39287e12			−0.344045			−0.172022	−	0.985093i	$-0.555030\pi$
$397$	−3.39287e12			−0.344045			−0.172022	+	0.985093i	$0.555030\pi$
$398$	2.74710e13			2.75080
$399$		−	2.13962e12i		−	0.211579i
$400$	4.82271e12			0.470968
$401$	1.35236e13			1.30428			0.652141	−	0.758098i	$-0.273871\pi$
$401$	1.35236e13			1.30428			0.652141	+	0.758098i	$0.273871\pi$
$402$	2.31582e13			2.20585
$403$	−1.48099e13			−1.39325
$404$	−1.02389e12			−0.0951361
$405$		−	1.21063e13i		−	1.11106i
$406$			1.46055e12i			0.132400i
$407$		−	1.24169e13i		−	1.11184i
$408$	−2.06090e12			−0.182287
$409$			8.00571e12i			0.699493i	0.936844	+	0.349746i	$0.113732\pi$
$409$			8.00571e12i			0.699493i	−0.936844	+	0.349746i	$0.886268\pi$
$410$	−1.55569e13			−1.34278
$411$	−2.30112e13			−1.96214
$412$	−4.98789e12			−0.420175
$413$		−	2.99310e12i		−	0.249099i
$414$			1.92152e13i			1.57995i
$415$			2.08937e13i			1.69736i
$416$			1.90437e13i			1.52857i
$417$		−	2.37373e13i		−	1.88257i
$418$	−1.25890e13			−0.986527
$419$			2.17731e13i			1.68597i	0.537936	+	0.842986i	$0.319204\pi$
$419$			2.17731e13i			1.68597i	−0.537936	+	0.842986i	$0.680796\pi$
$420$		−	8.35027e12i		−	0.638931i
$421$		−	3.22439e11i		−	0.0243802i	−0.999926	−	0.0121901i	$-0.996120\pi$
$421$		−	3.22439e11i		−	0.0243802i	0.999926	−	0.0121901i	$-0.00388033\pi$
$422$	3.89647e13			2.91145
$423$	−1.96933e11			−0.0145417
$424$			3.08254e13i			2.24946i
$425$	−1.67752e11			−0.0120983
$426$			4.01471e13i			2.86158i
$427$	−2.27528e12			−0.160286
$428$	−4.30792e13			−2.99950
$429$		−	1.29365e13i		−	0.890287i
$430$	2.40144e13	−	9.78091e11i	1.63354	−	0.0665330i
$431$	−1.35035e13			−0.907947			−0.453974	−	0.891015i	$-0.649994\pi$
$431$	−1.35035e13			−0.907947			−0.453974	+	0.891015i	$0.649994\pi$
$432$			1.94657e13i			1.29375i
$433$		−	8.25814e12i		−	0.542554i	−0.962501	−	0.271277i	$-0.912554\pi$
$433$		−	8.25814e12i		−	0.542554i	0.962501	−	0.271277i	$-0.0874459\pi$
$434$	−1.02689e13			−0.666923
$435$		−	5.08763e12i		−	0.326640i
$436$	−2.60890e13			−1.65587
$437$			1.77780e13i			1.11552i
$438$		−	2.12037e13i		−	1.31535i
$439$	7.62272e12			0.467506			0.233753	−	0.972296i	$-0.424899\pi$
$439$	7.62272e12			0.467506			0.233753	+	0.972296i	$0.424899\pi$
$440$	−2.84418e13			−1.72462
$441$	−8.46571e12			−0.507540
$442$		−	1.68575e12i		−	0.0999269i
$443$	2.83041e13			1.65894			0.829469	−	0.558553i	$-0.188643\pi$
$443$	2.83041e13			1.65894			0.829469	+	0.558553i	$0.188643\pi$
$444$	7.36684e13			4.26940
$445$	1.61974e13			0.928206
$446$	1.49587e13			0.847656
$447$	−9.55677e12			−0.535518
$448$			3.24704e12i			0.179927i
$449$		−	1.76773e13i		−	0.968690i	−0.874877	−	0.484345i	$-0.839058\pi$
$449$		−	1.76773e13i		−	0.968690i	0.874877	−	0.484345i	$-0.160942\pi$
$450$		−	3.80394e12i		−	0.206144i
$451$	−1.17594e13			−0.630235
$452$			5.00280e13i			2.65168i
$453$	−3.21049e13			−1.68298
$454$	5.02789e13			2.60679
$455$	3.95403e12			0.202760
$456$		−	4.32375e13i		−	2.19299i
$457$			3.19607e13i			1.60338i	0.597742	+	0.801689i	$0.296065\pi$
$457$			3.19607e13i			1.60338i	−0.597742	+	0.801689i	$0.703935\pi$
$458$		−	8.20289e12i		−	0.407042i
$459$		−	6.77089e11i		−	0.0332340i
$460$			6.93821e13i			3.36867i
$461$	2.66536e13			1.28012			0.640061	−	0.768324i	$-0.278909\pi$
$461$	2.66536e13			1.28012			0.640061	+	0.768324i	$0.278909\pi$
$462$		−	8.96989e12i		−	0.426164i
$463$			8.75833e12i			0.411639i	0.978590	+	0.205820i	$0.0659860\pi$
$463$			8.75833e12i			0.411639i	−0.978590	+	0.205820i	$0.934014\pi$
$464$			1.44071e13i			0.669865i
$465$	3.57702e13			1.64535
$466$	−2.58021e13			−1.17415
$467$		−	2.30755e13i		−	1.03889i	−0.854505	−	0.519443i	$-0.826140\pi$
$467$		−	2.30755e13i		−	1.03889i	0.854505	−	0.519443i	$-0.173860\pi$
$468$	2.68989e13			1.19813
$469$			5.35045e12i			0.235790i
$470$	−1.01052e12			−0.0440612
$471$	−3.11830e13			−1.34528
$472$		−	6.04847e13i		−	2.58188i
$473$	1.81524e13	−	7.39334e11i	0.766704	−	0.0312273i
$474$	9.04398e13			3.77979
$475$		−	3.51943e12i		−	0.145547i
$476$		−	8.22506e11i		−	0.0336593i
$477$	1.18682e13			0.480612
$478$		−	7.19749e13i		−	2.88431i
$479$	−2.26972e13			−0.900110			−0.450055	−	0.893001i	$-0.648596\pi$
$479$	−2.26972e13			−0.900110			−0.450055	+	0.893001i	$0.648596\pi$
$480$		−	4.59960e13i		−	1.80515i
$481$			3.48836e13i			1.35486i
$482$	7.05656e12			0.271242
$483$	−1.26672e13			−0.481886
$484$	2.59348e13			0.976462
$485$		−	2.24156e13i		−	0.835299i
$486$	4.87002e13			1.79618
$487$	−3.49809e13			−1.27698			−0.638492	−	0.769628i	$-0.720442\pi$
$487$	−3.49809e13			−1.27698			−0.638492	+	0.769628i	$0.720442\pi$
$488$	−4.59789e13			−1.66134
$489$	−5.00401e13			−1.78967
$490$	−4.34401e13			−1.53784
$491$		−	1.18333e13i		−	0.414666i	−0.978270	−	0.207333i	$-0.933522\pi$
$491$		−	1.18333e13i		−	0.414666i	0.978270	−	0.207333i	$-0.0664784\pi$
$492$		−	6.97676e13i		−	2.42007i
$493$		−	5.01134e11i		−	0.0172076i
$494$	3.53670e13			1.20216
$495$			1.09505e13i			0.368475i
$496$	−1.01294e14			−3.37424
$497$	−9.27554e12			−0.305884
$498$	−1.33159e14			−4.34734
$499$			2.21676e13i			0.716501i	0.933625	+	0.358251i	$0.116627\pi$
$499$			2.21676e13i			0.716501i	−0.933625	+	0.358251i	$0.883373\pi$
$500$		−	7.97793e13i		−	2.55294i
$501$		−	5.67145e12i		−	0.179682i
$502$			4.91539e13i			1.54184i
$503$			4.12286e12i			0.128044i	0.997948	+	0.0640220i	$0.0203928\pi$
$503$			4.12286e12i			0.128044i	−0.997948	+	0.0640220i	$0.979607\pi$
$504$	1.07971e13			0.332013
$505$			1.17101e12i			0.0356536i
$506$			7.45305e13i			2.24689i
$507$		−	5.22290e12i		−	0.155909i
$508$	3.68988e13			1.09067
$509$	−2.25492e13			−0.659997			−0.329999	−	0.943981i	$-0.607048\pi$
$509$	−2.25492e13			−0.659997			−0.329999	+	0.943981i	$0.607048\pi$
$510$			4.07157e12i			0.118008i
$511$	4.89888e12			0.140602
$512$		−	7.09697e13i		−	2.01708i
$513$	1.42053e13			0.399819
$514$	3.36783e12			0.0938718
$515$			5.70459e12i			0.157466i
$516$	4.38641e12	+	1.07697e14i	0.119911	+	2.94410i
$517$	−7.63848e11			−0.0206802
$518$			2.41875e13i			0.648549i
$519$			1.13563e13i			0.301577i
$520$	7.99032e13			2.10159
$521$			2.68827e13i			0.700299i	0.936694	+	0.350150i	$0.113869\pi$
$521$			2.68827e13i			0.700299i	−0.936694	+	0.350150i	$0.886131\pi$
$522$	1.13637e13			0.293202
$523$		−	2.93357e13i		−	0.749700i	−0.927085	−	0.374850i	$-0.877694\pi$
$523$		−	2.93357e13i		−	0.749700i	0.927085	−	0.374850i	$-0.122306\pi$
$524$		−	2.72478e13i		−	0.689723i
$525$	2.50766e12			0.0628741
$526$	−1.14351e14			−2.83996
$527$	3.52339e12			0.0866777
$528$		−	8.84803e13i		−	2.15614i
$529$	6.38247e13			1.54067
$530$	6.08995e13			1.45624
$531$	−2.32875e13			−0.551634
$532$	1.72561e13			0.404935
$533$	3.30364e13			0.767992
$534$			1.03228e14i			2.37735i
$535$			4.92692e13i			1.12410i
$536$			1.08122e14i			2.44394i
$537$	3.17552e13			0.711120
$538$		−	1.30911e13i		−	0.290445i
$539$	−3.28361e13			−0.721786
$540$	5.54388e13			1.20738
$541$	1.04143e13			0.224722			0.112361	−	0.993667i	$-0.464159\pi$
$541$	1.04143e13			0.224722			0.112361	+	0.993667i	$0.464159\pi$
$542$			1.15438e14i			2.46803i
$543$		−	2.84101e13i		−	0.601829i
$544$		−	4.53064e12i		−	0.0950965i
$545$			2.98377e13i			0.620559i
$546$			2.51997e13i			0.519316i
$547$	−2.26544e13			−0.462611			−0.231306	−	0.972881i	$-0.574300\pi$
$547$	−2.26544e13			−0.462611			−0.231306	+	0.972881i	$0.574300\pi$
$548$		−	1.85586e14i		−	3.75529i
$549$			1.77026e13i			0.354957i
$550$		−	1.47544e13i		−	0.293163i
$551$	1.05138e13			0.207014
$552$	−2.55979e14			−4.99470
$553$			2.08951e13i			0.404035i
$554$	−1.74288e14			−3.33978
$555$		−	8.42537e13i		−	1.60002i
$556$	1.91442e14			3.60300
$557$	−7.42359e13			−1.38464			−0.692322	−	0.721589i	$-0.743412\pi$
$557$	−7.42359e13			−1.38464			−0.692322	+	0.721589i	$0.743412\pi$
$558$			7.98963e13i			1.47691i
$559$	−5.09966e13	+	2.07706e12i	−0.934291	+	0.0380530i
$560$	2.70440e13			0.491055
$561$			3.07768e12i			0.0553872i
$562$			7.01168e13i			1.25066i
$563$	6.40693e13			1.13268			0.566341	−	0.824171i	$-0.308359\pi$
$563$	6.40693e13			1.13268			0.566341	+	0.824171i	$0.308359\pi$
$564$		−	4.53185e12i		−	0.0794108i
$565$	5.72165e13			0.993754
$566$		−	1.08855e14i		−	1.87399i
$567$			1.78259e13i			0.304184i
$568$	−1.87441e14			−3.17046
$569$	−3.19302e13			−0.535352			−0.267676	−	0.963509i	$-0.586256\pi$
$569$	−3.19302e13			−0.535352			−0.267676	+	0.963509i	$0.586256\pi$
$570$	−8.54213e13			−1.41969
$571$			9.43273e13i			1.55402i	0.629488	+	0.777011i	$0.283265\pi$
$571$			9.43273e13i			1.55402i	−0.629488	+	0.777011i	$0.716735\pi$
$572$	1.04333e14			1.70389
$573$	6.67977e12			0.108141
$574$	2.29068e13			0.367624
$575$	−2.08360e13			−0.331494
$576$	2.52633e13			0.398453
$577$			6.67376e13i			1.04350i	0.853099	+	0.521749i	$0.174720\pi$
$577$			6.67376e13i			1.04350i	−0.853099	+	0.521749i	$0.825280\pi$
$578$		−	1.18110e14i		−	1.83083i
$579$		−	1.20504e14i		−	1.85186i
$580$	4.10319e13			0.625147
$581$		−	3.07649e13i		−	0.464702i
$582$	1.42858e14			2.13939
$583$	4.60336e13			0.683490
$584$	9.89968e13			1.45733
$585$		−	3.07639e13i		−	0.449017i
$586$			9.40215e13i			1.36063i
$587$		−	3.87372e13i		−	0.555825i	−0.960606	−	0.277912i	$-0.910357\pi$
$587$		−	3.87372e13i		−	0.555825i	0.960606	−	0.277912i	$-0.0896425\pi$
$588$		−	1.94814e14i		−	2.77162i
$589$			7.39205e13i			1.04277i
$590$	−1.19495e14			−1.67144
$591$		−	8.76830e13i		−	1.21612i
$592$			2.38589e14i			3.28128i
$593$			2.58904e13i			0.353073i	0.984294	+	0.176537i	$0.0564894\pi$
$593$			2.58904e13i			0.353073i	−0.984294	+	0.176537i	$0.943511\pi$
$594$	5.95525e13			0.805319
$595$	−9.40691e11			−0.0126143
$596$		−	7.70758e13i		−	1.02491i
$597$	1.40900e14			1.85798
$598$		−	2.09383e14i		−	2.73801i
$599$	3.67692e12			0.0476815			0.0238407	−	0.999716i	$-0.492411\pi$
$599$	3.67692e12			0.0476815			0.0238407	+	0.999716i	$0.492411\pi$
$600$	5.06749e13			0.651683
$601$			1.31596e14i			1.67830i	0.543902	+	0.839148i	$0.316946\pi$
$601$			1.31596e14i			1.67830i	−0.543902	+	0.839148i	$0.683054\pi$
$602$	−3.53600e13	+	1.44019e12i	−0.447228	+	0.0182153i
$603$	4.16287e13			0.522163
$604$		−	2.58927e14i		−	3.22102i
$605$		−	2.96613e13i		−	0.365943i
$606$	−7.46302e12			−0.0913170
$607$		−	9.60688e12i		−	0.116584i	−0.998300	−	0.0582920i	$-0.981435\pi$
$607$		−	9.60688e12i		−	0.116584i	0.998300	−	0.0582920i	$-0.0185654\pi$
$608$	9.50525e13			1.14405
$609$			7.49126e12i			0.0894269i
$610$			9.08373e13i			1.07551i
$611$	2.14593e12			0.0252005
$612$	−6.39943e12			−0.0745391
$613$	5.67285e12			0.0655388			0.0327694	−	0.999463i	$-0.489567\pi$
$613$	5.67285e12			0.0655388			0.0327694	+	0.999463i	$0.489567\pi$
$614$		−	2.49102e14i		−	2.85454i
$615$	−7.97924e13			−0.906955
$616$	4.18790e13			0.472163
$617$	6.89629e13			0.771240			0.385620	−	0.922658i	$-0.373988\pi$
$617$	6.89629e13			0.771240			0.385620	+	0.922658i	$0.373988\pi$
$618$	−3.63562e13			−0.403308
$619$	8.35140e13			0.918980			0.459490	−	0.888183i	$-0.348032\pi$
$619$	8.35140e13			0.918980			0.459490	+	0.888183i	$0.348032\pi$
$620$			2.88489e14i			3.14898i
$621$		−	8.40995e13i		−	0.910616i
$622$			1.06449e14i			1.14337i
$623$	−2.38498e13			−0.254123
$624$			2.48573e14i			2.62743i
$625$	−7.14090e13			−0.748778
$626$	1.38560e14			1.44134
$627$	−6.45695e13			−0.666331
$628$		−	2.51492e14i		−	2.57470i
$629$		−	8.29904e12i		−	0.0842897i
$630$		−	2.13311e13i		−	0.214936i
$631$		−	1.17694e13i		−	0.117654i	−0.998268	−	0.0588271i	$-0.981264\pi$
$631$		−	1.17694e13i		−	0.117654i	0.998268	−	0.0588271i	$-0.0187361\pi$
$632$			4.22249e14i			4.18777i
$633$	1.99852e14			1.96648
$634$		−	1.43638e13i		−	0.140224i
$635$		−	4.22007e13i		−	0.408743i
$636$			2.73113e14i			2.62457i
$637$	9.22486e13			0.879554
$638$	4.40766e13			0.416970
$639$			7.21675e13i			0.677388i
$640$	−2.65784e13			−0.247531
$641$		−	1.39288e14i		−	1.28713i	−0.765392	−	0.643565i	$-0.777455\pi$
$641$		−	1.39288e14i		−	1.28713i	0.765392	−	0.643565i	$-0.222545\pi$
$642$	−3.14000e14			−2.87909
$643$	−8.45328e13			−0.769078			−0.384539	−	0.923109i	$-0.625640\pi$
$643$	−8.45328e13			−0.769078			−0.384539	+	0.923109i	$0.625640\pi$
$644$		−	1.02161e14i		−	0.922269i
$645$	1.23171e14	−	5.01668e12i	1.10334	−	0.0449385i
$646$	−8.41405e12			−0.0747898
$647$			7.54213e13i			0.665231i	0.943063	+	0.332615i	$0.107931\pi$
$647$			7.54213e13i			0.665231i	−0.943063	+	0.332615i	$0.892069\pi$
$648$			3.60226e14i			3.15283i
$649$	−9.03259e13			−0.784492
$650$			4.14505e13i			0.357242i
$651$	−5.26698e13			−0.450460
$652$		−	4.03575e14i		−	3.42521i
$653$		−	5.99341e13i		−	0.504787i	−0.967625	−	0.252393i	$-0.918782\pi$
$653$		−	5.99341e13i		−	0.504787i	0.967625	−	0.252393i	$-0.0812177\pi$
$654$	−1.90161e14			−1.58939
$655$	−3.11630e13			−0.258483
$656$	2.25956e14			1.85996
$657$		−	3.81153e13i		−	0.311367i
$658$	1.48794e12			0.0120630
$659$	−2.14727e14			−1.72766			−0.863832	−	0.503781i	$-0.831942\pi$
$659$	−2.14727e14			−1.72766			−0.863832	+	0.503781i	$0.831942\pi$
$660$	−2.51995e14			−2.01220
$661$	4.43828e13			0.351728			0.175864	−	0.984414i	$-0.443728\pi$
$661$	4.43828e13			0.351728			0.175864	+	0.984414i	$0.443728\pi$
$662$	−2.84716e14			−2.23935
$663$		−	8.64632e12i		−	0.0674937i
$664$		−	6.21698e14i		−	4.81658i
$665$		−	1.97356e13i		−	0.151755i
$666$	1.88189e14			1.43622
$667$		−	6.22446e13i		−	0.471490i
$668$	4.57404e13			0.343889
$669$	7.67240e13			0.572533
$670$	2.13609e14			1.58214
$671$			6.86634e13i			0.504792i
$672$			6.77267e13i			0.494212i
$673$			2.10395e13i			0.152392i	0.997093	+	0.0761958i	$0.0242774\pi$
$673$			2.10395e13i			0.152392i	−0.997093	+	0.0761958i	$0.975723\pi$
$674$			6.61617e13i			0.475672i
$675$			1.66487e13i			0.118813i
$676$	4.21229e13			0.298390
$677$			1.41079e14i			0.992018i	0.868317	+	0.496009i	$0.165202\pi$
$677$			1.41079e14i			0.992018i	−0.868317	+	0.496009i	$0.834798\pi$
$678$			3.64650e14i			2.54523i
$679$			3.30058e13i			0.228687i
$680$	−1.90095e13			−0.130745
$681$	2.57883e14			1.76071
$682$			3.09895e14i			2.10036i
$683$	−9.61331e13			−0.646799			−0.323400	−	0.946263i	$-0.604826\pi$
$683$	−9.61331e13			−0.646799			−0.323400	+	0.946263i	$0.604826\pi$
$684$		−	1.34260e14i		−	0.896737i
$685$	−2.12253e14			−1.40735
$686$	1.31963e14			0.868626
$687$		−	4.20731e13i		−	0.274929i
$688$	−3.48796e14	+	1.42062e13i	−2.26271	+	0.0921588i
$689$	−1.29325e14			−0.832887
$690$			5.05720e14i			3.23344i
$691$		−	2.58847e14i		−	1.64306i	−0.570168	−	0.821528i	$-0.693122\pi$
$691$		−	2.58847e14i		−	1.64306i	0.570168	−	0.821528i	$-0.306878\pi$
$692$	−9.15887e13			−0.577180
$693$		−	1.61240e13i		−	0.100881i
$694$	−4.68196e14			−2.90824
$695$		−	2.18951e14i		−	1.35027i
$696$			1.51384e14i			0.926900i
$697$	−7.85959e12			−0.0477789
$698$	4.04700e14			2.44262
$699$	−1.32340e14			−0.793060
$700$			2.02244e13i			0.120333i
$701$	2.64616e14			1.56324			0.781621	−	0.623753i	$-0.214393\pi$
$701$	2.64616e14			1.56324			0.781621	+	0.623753i	$0.214393\pi$
$702$	−1.67305e14			−0.981346
$703$	1.74113e14			1.01404
$704$	9.79892e13			0.566650
$705$	−5.18302e12			−0.0297603
$706$		−	4.47002e14i		−	2.54851i
$707$		−	1.72425e12i		−	0.00976118i
$708$		−	5.35896e14i		−	3.01241i
$709$	−1.70519e14			−0.951790			−0.475895	−	0.879502i	$-0.657876\pi$
$709$	−1.70519e14			−0.951790			−0.475895	+	0.879502i	$0.657876\pi$
$710$			3.70313e14i			2.05247i
$711$	1.62572e14			0.894744
$712$	−4.81957e14			−2.63395
$713$	4.37631e14			2.37498
$714$		−	5.99517e12i		−	0.0323080i
$715$		−	1.19325e14i		−	0.638558i
$716$			2.56107e14i			1.36099i
$717$		−	3.69163e14i		−	1.94815i
$718$			6.84564e13i			0.358750i
$719$	5.08876e13			0.264830			0.132415	−	0.991194i	$-0.457727\pi$
$719$	5.08876e13			0.264830			0.132415	+	0.991194i	$0.457727\pi$
$720$		−	2.10413e14i		−	1.08745i
$721$		−	8.39970e12i		−	0.0431109i
$722$			1.83891e14i			0.937289i
$723$	3.61935e13			0.183206
$724$	2.29128e14			1.15182
$725$			1.23222e13i			0.0615177i
$726$	1.89036e14			0.937263
$727$			1.03917e14i			0.511700i	0.966716	+	0.255850i	$0.0823554\pi$
$727$			1.03917e14i			0.511700i	−0.966716	+	0.255850i	$0.917645\pi$
$728$	−1.17653e14			−0.575369
$729$	−7.25565e12			−0.0352402
$730$		−	1.95581e14i		−	0.943435i
$731$	1.21324e13	−	4.94146e11i	0.0581248	−	0.00236738i
$732$	−4.07374e14			−1.93838
$733$			3.08035e14i			1.45573i	0.685722	+	0.727863i	$0.259486\pi$
$733$			3.08035e14i			1.45573i	−0.685722	+	0.727863i	$0.740514\pi$
$734$		−	1.39596e13i		−	0.0655227i
$735$	−2.22807e14			−1.03870
$736$		−	5.62739e14i		−	2.60566i
$737$	1.61466e14			0.742581
$738$		−	1.78224e14i		−	0.814112i
$739$			2.65696e14i			1.20549i	0.797934	+	0.602744i	$0.205926\pi$
$739$			2.65696e14i			1.20549i	−0.797934	+	0.602744i	$0.794074\pi$
$740$	6.79510e14			3.06222
$741$	1.81399e14			0.811978
$742$	−8.96712e13			−0.398688
$743$			4.04479e13i			0.178629i	0.996003	+	0.0893145i	$0.0284676\pi$
$743$			4.04479e13i			0.178629i	−0.996003	+	0.0893145i	$0.971532\pi$
$744$	−1.06435e15			−4.66897
$745$	−8.81507e13			−0.384100
$746$	4.49826e14			1.94693
$747$	−2.39363e14			−1.02909
$748$	−2.48216e13			−0.106004
$749$		−	7.25462e13i		−	0.307756i
$750$		−	5.81504e14i		−	2.45045i
$751$			4.55885e14i			1.90834i	0.299267	+	0.954169i	$0.403258\pi$
$751$			4.55885e14i			1.90834i	−0.299267	+	0.954169i	$0.596742\pi$
$752$	1.46773e13			0.0610318
$753$			2.52113e14i			1.04141i
$754$	−1.23827e14			−0.508112
$755$	−2.96132e14			−1.20712
$756$	−8.16307e13			−0.330555
$757$		−	1.68937e14i		−	0.679589i	−0.940500	−	0.339794i	$-0.889643\pi$
$757$		−	1.68937e14i		−	0.679589i	0.940500	−	0.339794i	$-0.110357\pi$
$758$			1.39808e14i			0.558711i
$759$			3.82271e14i			1.51762i
$760$		−	3.98819e14i		−	1.57292i
$761$		−	1.58991e14i		−	0.622944i	−0.950255	−	0.311472i	$-0.899178\pi$
$761$		−	1.58991e14i		−	0.622944i	0.950255	−	0.311472i	$-0.100822\pi$
$762$	2.68952e14			1.04689
$763$		−	4.39345e13i		−	0.169896i
$764$			5.38726e13i			0.206967i
$765$			7.31896e12i			0.0279346i
$766$	−7.03278e14			−2.66676
$767$	2.53758e14			0.955967
$768$		−	4.14201e14i		−	1.55026i
$769$	−5.15268e13			−0.191603			−0.0958013	−	0.995400i	$-0.530541\pi$
$769$	−5.15268e13			−0.191603			−0.0958013	+	0.995400i	$0.530541\pi$
$770$		−	8.27373e13i		−	0.305666i
$771$	1.72738e13			0.0634039
$772$	9.71871e14			3.54423
$773$			1.55645e14i			0.563944i	0.959423	+	0.281972i	$0.0909886\pi$
$773$			1.55645e14i			0.563944i	−0.959423	+	0.281972i	$0.909011\pi$
$774$	1.12052e13	+	2.75115e14i	0.0403382	+	0.990397i
$775$	−8.66356e13			−0.309876
$776$			6.66983e14i			2.37031i
$777$			1.24059e14i			0.438050i
$778$	1.77410e14			0.622416
$779$		−	1.64894e14i		−	0.574800i
$780$	7.07944e14			2.45203
$781$			2.79918e14i			0.963330i
$782$			4.98137e13i			0.170339i
$783$	−4.97357e13			−0.168989
$784$	6.30943e14			2.13015
$785$	−2.87629e14			−0.964903
$786$		−	1.98607e14i		−	0.662035i
$787$	−3.72738e14			−1.23461			−0.617306	−	0.786723i	$-0.711776\pi$
$787$	−3.72738e14			−1.23461			−0.617306	+	0.786723i	$0.711776\pi$
$788$	7.07167e14			2.32751
$789$	−5.86514e14			−1.91820
$790$	8.34207e14			2.71106
$791$	−8.42482e13			−0.272069
$792$		−	3.25835e14i		−	1.04562i
$793$		−	1.92900e14i		−	0.615130i
$794$		−	1.99451e14i		−	0.632025i
$795$	3.12357e14			0.983592
$796$			1.13637e15i			3.55593i
$797$	4.58075e14			1.42444			0.712221	−	0.701955i	$-0.247689\pi$
$797$	4.58075e14			1.42444			0.712221	+	0.701955i	$0.247689\pi$
$798$	1.25778e14			0.388679
$799$	−5.10530e11			−0.00156779
$800$			1.11402e14i			0.339973i
$801$			1.85561e14i			0.562761i
$802$			7.94991e14i			2.39602i
$803$		−	1.47839e14i		−	0.442803i
$804$			9.57964e14i			2.85147i
$805$	−1.16841e14			−0.345633
$806$		−	8.70608e14i		−	2.55945i
$807$		−	6.71449e13i		−	0.196176i
$808$		−	3.48436e13i		−	0.101174i
$809$	−3.19110e14			−0.920870			−0.460435	−	0.887693i	$-0.652307\pi$
$809$	−3.19110e14			−0.920870			−0.460435	+	0.887693i	$0.652307\pi$
$810$	7.11673e14			2.04106
$811$			6.85724e14i			1.95454i	0.211994	+	0.977271i	$0.432004\pi$
$811$			6.85724e14i			1.95454i	−0.211994	+	0.977271i	$0.567996\pi$
$812$	−6.04173e13			−0.171152
$813$			5.92086e14i			1.66699i
$814$	7.29932e14			2.04249
$815$	−4.61565e14			−1.28364
$816$		−	5.91373e13i		−	0.163460i
$817$	1.03672e13	+	2.54538e14i	0.0284806	+	0.699266i
$818$	−4.70618e14			−1.28500
$819$			4.52983e13i			0.122931i
$820$		−	6.43529e14i		−	1.73580i
$821$	−5.04315e14			−1.35203			−0.676014	−	0.736889i	$-0.736294\pi$
$821$	−5.04315e14			−1.35203			−0.676014	+	0.736889i	$0.736294\pi$
$822$		−	1.35272e15i		−	3.60453i
$823$	1.37810e14			0.364989			0.182495	−	0.983207i	$-0.441583\pi$
$823$	1.37810e14			0.364989			0.182495	+	0.983207i	$0.441583\pi$
$824$		−	1.69741e14i		−	0.446840i
$825$		−	7.56762e13i		−	0.198011i
$826$	1.75950e14			0.457604
$827$	5.27371e13			0.136329			0.0681646	−	0.997674i	$-0.478286\pi$
$827$	5.27371e13			0.136329			0.0681646	+	0.997674i	$0.478286\pi$
$828$	−7.94857e14			−2.04238
$829$		−	5.77696e14i		−	1.47546i	−0.675097	−	0.737729i	$-0.735898\pi$
$829$		−	5.77696e14i		−	1.47546i	0.675097	−	0.737729i	$-0.264102\pi$
$830$	−1.22824e15			−3.11813
$831$	−8.93931e14			−2.25579
$832$	−2.75287e14			−0.690509
$833$	−2.19466e13			−0.0547195
$834$	1.39541e15			3.45836
$835$		−	5.23128e13i		−	0.128877i
$836$		−	5.20756e14i		−	1.27527i
$837$		−	3.49683e14i		−	0.851231i
$838$	−1.27994e15			−3.09720
$839$			6.52424e14i			1.56935i	0.619906	+	0.784676i	$0.287171\pi$
$839$			6.52424e14i			1.56935i	−0.619906	+	0.784676i	$0.712829\pi$
$840$	2.84166e14			0.679478
$841$	3.83896e14			0.912502
$842$	1.89547e13			0.0447875
$843$			3.59633e14i			0.844737i
$844$			1.61182e15i			3.76360i
$845$		−	4.81754e13i		−	0.111826i
$846$		−	1.15768e13i		−	0.0267138i
$847$			4.36746e13i			0.100187i
$848$	−8.84531e14			−2.01713
$849$		−	5.58325e14i		−	1.26575i
$850$		−	9.86136e12i		−	0.0222250i
$851$		−	1.03080e15i		−	2.30955i
$852$	−1.66073e15			−3.69914
$853$	6.82643e14			1.51164			0.755820	−	0.654780i	$-0.227239\pi$
$853$	6.82643e14			1.51164			0.755820	+	0.654780i	$0.227239\pi$
$854$		−	1.33753e14i		−	0.294452i
$855$	−1.53551e14			−0.336065
$856$		−	1.46602e15i		−	3.18985i
$857$	6.37037e14			1.37804			0.689018	−	0.724744i	$-0.258042\pi$
$857$	6.37037e14			1.37804			0.689018	+	0.724744i	$0.258042\pi$
$858$	7.60476e14			1.63549
$859$		−	8.80906e14i		−	1.88349i	−0.336324	−	0.941746i	$-0.609184\pi$
$859$		−	8.80906e14i		−	1.88349i	0.336324	−	0.941746i	$-0.390816\pi$
$860$	4.04598e13	+	9.93382e14i	0.0860065	+	2.11166i
$861$	1.17490e14			0.248305
$862$		−	7.93809e14i		−	1.66794i
$863$		−	6.01567e13i		−	0.125669i	−0.998024	−	0.0628347i	$-0.979986\pi$
$863$		−	6.01567e13i		−	0.125669i	0.998024	−	0.0628347i	$-0.0200141\pi$
$864$	−4.49649e14			−0.933909
$865$			1.04749e14i			0.216306i
$866$	4.85458e14			0.996694
$867$		−	6.05792e14i		−	1.23660i
$868$		−	4.24784e14i		−	0.862123i
$869$	6.30573e14			1.27244
$870$	2.99078e14			0.600051
$871$	−4.53616e14			−0.904895
$872$		−	8.87829e14i		−	1.76095i
$873$	2.56799e14			0.506432
$874$	−1.04509e15			−2.04925
$875$	1.34350e14			0.261937
$876$	8.77114e14			1.70034
$877$	5.17228e13			0.0996975			0.0498488	−	0.998757i	$-0.484126\pi$
$877$	5.17228e13			0.0996975			0.0498488	+	0.998757i	$0.484126\pi$
$878$			4.48104e14i			0.858828i
$879$			4.82241e14i			0.919009i
$880$		−	8.16133e14i		−	1.54649i
$881$	−2.76177e14			−0.520365			−0.260183	−	0.965559i	$-0.583783\pi$
$881$	−2.76177e14			−0.520365			−0.260183	+	0.965559i	$0.583783\pi$
$882$		−	4.97660e14i		−	0.932373i
$883$	8.44714e14			1.57364			0.786821	−	0.617181i	$-0.211725\pi$
$883$	8.44714e14			1.57364			0.786821	+	0.617181i	$0.211725\pi$
$884$	6.97329e13			0.129174
$885$	−6.12898e14			−1.12894
$886$			1.66386e15i			3.04754i
$887$			8.28143e14i			1.50830i	0.656703	+	0.754149i	$0.271951\pi$
$887$			8.28143e14i			1.50830i	−0.656703	+	0.754149i	$0.728049\pi$
$888$			2.50699e15i			4.54034i
$889$			6.21383e13i			0.111905i
$890$			9.52168e14i			1.70515i
$891$	5.37950e14			0.957973
$892$			6.18782e14i			1.09576i
$893$		−	1.07109e13i		−	0.0188612i
$894$		−	5.61798e14i		−	0.983768i
$895$	2.92906e14			0.510051
$896$	3.91353e13			0.0677687
$897$		−	1.07394e15i		−	1.84934i
$898$	1.03917e15			1.77952
$899$		−	2.58811e14i		−	0.440742i
$900$	1.57354e14			0.266480
$901$	3.07673e13			0.0518162
$902$		−	6.91281e14i		−	1.15777i
$903$	−1.81363e14	+	7.38680e12i	−0.302072	+	0.0123032i
$904$	−1.70249e15			−2.81996
$905$		−	2.62051e14i		−	0.431662i
$906$		−	1.88730e15i		−	3.09171i
$907$	−4.46460e14			−0.727355			−0.363677	−	0.931525i	$-0.618479\pi$
$907$	−4.46460e14			−0.727355			−0.363677	+	0.931525i	$0.618479\pi$
$908$			2.07984e15i			3.36977i
$909$	−1.34153e13			−0.0216163
$910$			2.32439e14i			0.372479i
$911$		−	4.71740e14i		−	0.751815i	−0.926657	−	0.375907i	$-0.877331\pi$
$911$		−	4.71740e14i		−	0.751815i	0.926657	−	0.375907i	$-0.122669\pi$
$912$	1.24070e15			1.96649
$913$	−9.28423e14			−1.46350
$914$	−1.87882e15			−2.94547
$915$			4.65909e14i			0.726434i
$916$	3.39321e14			0.526179
$917$	4.58858e13			0.0707671
$918$	3.98029e13			0.0610522
$919$	−5.22957e14			−0.797790			−0.398895	−	0.916997i	$-0.630606\pi$
$919$	−5.22957e14			−0.797790			−0.398895	+	0.916997i	$0.630606\pi$
$920$	−2.36112e15			−3.58245
$921$		−	1.27766e15i		−	1.92804i
$922$			1.56684e15i			2.35164i
$923$		−	7.86390e14i		−	1.17390i
$924$	3.71049e14			0.550898
$925$			2.04063e14i			0.301339i
$926$	−5.14862e14			−0.756198
$927$	−6.53531e13			−0.0954701
$928$	−3.32799e14			−0.483550
$929$		−	3.65317e13i		−	0.0527949i	−0.999652	−	0.0263974i	$-0.991596\pi$
$929$		−	3.65317e13i		−	0.0527949i	0.999652	−	0.0263974i	$-0.00840354\pi$
$930$			2.10277e15i			3.02257i
$931$		−	4.60438e14i		−	0.658298i
$932$		−	1.06733e15i		−	1.51781i
$933$			5.45981e14i			0.772270i
$934$	1.35650e15			1.90848
$935$			2.83882e13i			0.0397264i
$936$			9.15389e14i			1.27417i
$937$			7.96238e14i			1.10242i	0.834368	+	0.551208i	$0.185833\pi$
$937$			7.96238e14i			1.10242i	−0.834368	+	0.551208i	$0.814167\pi$
$938$	−3.14528e14			−0.433157
$939$	7.10681e14			0.973525
$940$		−	4.18013e13i		−	0.0569574i
$941$	−8.04190e14			−1.08996			−0.544980	−	0.838449i	$-0.683463\pi$
$941$	−8.04190e14			−1.08996			−0.544980	+	0.838449i	$0.683463\pi$
$942$		−	1.83310e15i		−	2.47134i
$943$	−9.76220e14			−1.30915
$944$	1.73560e15			2.31521
$945$			9.33600e13i			0.123880i
$946$	4.34620e13	+	1.06709e15i	0.0573659	+	1.40847i
$947$	−8.33991e14			−1.09499			−0.547497	−	0.836808i	$-0.684419\pi$
$947$	−8.33991e14			−1.09499			−0.547497	+	0.836808i	$0.684419\pi$
$948$			3.74114e15i			4.88609i
$949$			4.15332e14i			0.539591i
$950$	2.06891e14			0.267376
$951$		−	7.36727e13i		−	0.0947117i
$952$	2.79905e13			0.0357953
$953$		−	1.28028e14i		−	0.162870i	−0.996679	−	0.0814349i	$-0.974050\pi$
$953$		−	1.28028e14i		−	0.162870i	0.996679	−	0.0814349i	$-0.0259503\pi$
$954$			6.97678e14i			0.882904i
$955$	6.16135e13			0.0775638
$956$	2.97731e15			3.72851
$957$	2.26071e14			0.281635
$958$		−	1.33426e15i		−	1.65354i
$959$	3.12531e14			0.385301
$960$	6.64897e14			0.815451
$961$	1.00003e15			1.22010
$962$	−2.05064e15			−2.48894
$963$	−5.64439e14			−0.681531
$964$			2.91902e14i			0.350632i
$965$		−	1.11152e15i		−	1.32825i
$966$		−	7.44645e14i		−	0.885245i
$967$	8.55354e14			1.01161			0.505806	−	0.862647i	$-0.331195\pi$
$967$	8.55354e14			1.01161			0.505806	+	0.862647i	$0.331195\pi$
$968$			8.82579e14i			1.03843i
$969$	−4.31561e13			−0.0505154
$970$	1.31771e15			1.53448
$971$	1.44645e15			1.67575			0.837873	−	0.545866i	$-0.183799\pi$
$971$	1.44645e15			1.67575			0.837873	+	0.545866i	$0.183799\pi$
$972$			2.01453e15i			2.32190i
$973$			3.22393e14i			0.369676i
$974$		−	2.05636e15i		−	2.34587i
$975$			2.12602e14i			0.241292i
$976$		−	1.31936e15i		−	1.48975i
$977$	−7.97820e13			−0.0896256			−0.0448128	−	0.998995i	$-0.514269\pi$
$977$	−7.97820e13			−0.0896256			−0.0448128	+	0.998995i	$0.514269\pi$
$978$		−	2.94162e15i		−	3.28771i
$979$			7.19739e14i			0.800316i
$980$		−	1.79694e15i		−	1.98794i
$981$	−3.41828e14			−0.376238
$982$	6.95625e14			0.761760
$983$		−	2.94771e14i		−	0.321157i	−0.987023	−	0.160578i	$-0.948664\pi$
$983$		−	2.94771e14i		−	0.321157i	0.987023	−	0.160578i	$-0.0513359\pi$
$984$	2.37424e15			2.57365
$985$		−	8.08779e14i		−	0.872266i
$986$	2.94594e13			0.0316110
$987$	7.63172e12			0.00814773
$988$			1.46299e15i			1.55402i
$989$	1.50694e15	−	6.13766e13i	1.59263	−	0.0648667i
$990$	−6.43730e14			−0.676905
$991$			2.67544e13i			0.0279915i	0.999902	+	0.0139958i	$0.00445513\pi$
$991$			2.67544e13i			0.0279915i	−0.999902	+	0.0139958i	$0.995545\pi$
$992$		−	2.33985e15i		−	2.43573i
$993$	−1.46032e15			−1.51253
$994$		−	5.45266e14i		−	0.561923i
$995$	1.29965e15			1.33263
$996$		−	5.50826e15i		−	5.61976i
$997$			7.46679e13i			0.0757980i	0.999282	+	0.0378990i	$0.0120665\pi$
$997$			7.46679e13i			0.0757980i	−0.999282	+	0.0378990i	$0.987933\pi$
$998$	−1.30313e15			−1.31624
$999$	−8.23648e14			−0.827779

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.b.b.42.33	yes	34
43.42	odd	2	inner	43.11.b.b.42.2	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.b.b.42.2	✓	34	43.42	odd	2	inner
43.11.b.b.42.33	yes	34	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+58.7853i q^{2} +301.513i q^{3} -2431.72 q^{4} +2781.13i q^{5} -17724.6 q^{6} -4095.06i q^{7} -82753.1i q^{8} -31861.2 q^{9} +O(q^{10})\)	\(q+58.7853i q^{2} +301.513i q^{3} -2431.72 q^{4} +2781.13i q^{5} -17724.6 q^{6} -4095.06i q^{7} -82753.1i q^{8} -31861.2 q^{9} -163489. q^{10} -123581. q^{11} -733195. i q^{12} +347183. q^{13} +240730. q^{14} -838546. q^{15} +2.37459e6 q^{16} -82597.3 q^{17} -1.87297e6i q^{18} -1.73289e6i q^{19} -6.76291e6i q^{20} +1.23471e6 q^{21} -7.26474e6i q^{22} -1.02592e7 q^{23} +2.49512e7 q^{24} +2.03096e6 q^{25} +2.04093e7i q^{26} +8.19747e6i q^{27} +9.95803e6i q^{28} +6.06720e6i q^{29} -4.92942e7i q^{30} -4.26574e7 q^{31} +5.48521e7i q^{32} -3.72613e7i q^{33} -4.85551e6i q^{34} +1.13889e7 q^{35} +7.74775e7 q^{36} +1.00476e8i q^{37} +1.01868e8 q^{38} +1.04680e8i q^{39} +2.30147e8 q^{40} +9.51556e7 q^{41} +7.25831e7i q^{42} +(-1.46887e8 + 5.98259e6i) q^{43} +3.00514e8 q^{44} -8.86101e7i q^{45} -6.03091e8i q^{46} +6.18096e6 q^{47} +7.15971e8i q^{48} +2.65706e8 q^{49} +1.19391e8i q^{50} -2.49042e7i q^{51} -8.44251e8 q^{52} -3.72498e8 q^{53} -4.81891e8 q^{54} -3.43694e8i q^{55} -3.38879e8 q^{56} +5.22488e8 q^{57} -3.56662e8 q^{58} +7.30905e8 q^{59} +2.03911e9 q^{60} -5.55615e8i q^{61} -2.50763e9i q^{62} +1.30474e8i q^{63} -7.92916e8 q^{64} +9.65560e8i q^{65} +2.19042e9 q^{66} -1.30656e9 q^{67} +2.00853e8 q^{68} -3.09328e9i q^{69} +6.69499e8i q^{70} -2.26506e9i q^{71} +2.63662e9i q^{72} +1.19629e9i q^{73} -5.90651e9 q^{74} +6.12362e8i q^{75} +4.21389e9i q^{76} +5.06071e8i q^{77} -6.15367e9 q^{78} -5.10251e9 q^{79} +6.60404e9i q^{80} -4.35302e9 q^{81} +5.59375e9i q^{82} +7.51268e9 q^{83} -3.00248e9 q^{84} -2.29714e8i q^{85} +(-3.51689e8 - 8.63478e9i) q^{86} -1.82934e9 q^{87} +1.02267e10i q^{88} -5.82403e9i q^{89} +5.20898e9 q^{90} -1.42174e9i q^{91} +2.49475e10 q^{92} -1.28618e10i q^{93} +3.63350e8i q^{94} +4.81938e9 q^{95} -1.65386e10 q^{96} -8.05991e9 q^{97} +1.56196e10i q^{98} +3.93744e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more