LMFDB - Embedded newform 43.11.b.b.42.5

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			42.5
Character	$\chi$	$=$	43.42
Dual form			43.11.b.b.42.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-46.2007i q^{2} +372.330i q^{3} -1110.50 q^{4} +2517.50i q^{5} +17201.9 q^{6} +25292.2i q^{7} +3996.58i q^{8} -79580.9 q^{9} +O(q^{10})$	\(q-46.2007i q^{2} +372.330i q^{3} -1110.50 q^{4} +2517.50i q^{5} +17201.9 q^{6} +25292.2i q^{7} +3996.58i q^{8} -79580.9 q^{9} +116310. q^{10} +71323.6 q^{11} -413475. i q^{12} +305041. q^{13} +1.16852e6 q^{14} -937343. q^{15} -952512. q^{16} -1.86577e6 q^{17} +3.67669e6i q^{18} -250385. i q^{19} -2.79570e6i q^{20} -9.41705e6 q^{21} -3.29520e6i q^{22} -7.17521e6 q^{23} -1.48805e6 q^{24} +3.42780e6 q^{25} -1.40931e7i q^{26} -7.64463e6i q^{27} -2.80871e7i q^{28} -7.03624e6i q^{29} +4.33059e7i q^{30} -2.56657e7 q^{31} +4.80992e7i q^{32} +2.65559e7i q^{33} +8.61999e7i q^{34} -6.36732e7 q^{35} +8.83749e7 q^{36} -4.75251e7i q^{37} -1.15680e7 q^{38} +1.13576e8i q^{39} -1.00614e7 q^{40} +9.96282e7 q^{41} +4.35074e8i q^{42} +(9.73908e7 + 1.10120e8i) q^{43} -7.92052e7 q^{44} -2.00345e8i q^{45} +3.31500e8i q^{46} +8.53994e7 q^{47} -3.54649e8i q^{48} -3.57220e8 q^{49} -1.58367e8i q^{50} -6.94683e8i q^{51} -3.38749e8 q^{52} -6.32854e8 q^{53} -3.53187e8 q^{54} +1.79557e8i q^{55} -1.01082e8 q^{56} +9.32259e7 q^{57} -3.25079e8 q^{58} -1.36284e9 q^{59} +1.04092e9 q^{60} -5.18564e8i q^{61} +1.18577e9i q^{62} -2.01278e9i q^{63} +1.24685e9 q^{64} +7.67942e8i q^{65} +1.22690e9 q^{66} +7.52892e8 q^{67} +2.07195e9 q^{68} -2.67155e9i q^{69} +2.94175e9i q^{70} +2.82572e9i q^{71} -3.18051e8i q^{72} -3.11851e9i q^{73} -2.19569e9 q^{74} +1.27627e9i q^{75} +2.78053e8i q^{76} +1.80393e9i q^{77} +5.24729e9 q^{78} +1.02175e9 q^{79} -2.39795e9i q^{80} -1.85284e9 q^{81} -4.60289e9i q^{82} -5.19494e9 q^{83} +1.04577e10 q^{84} -4.69709e9i q^{85} +(5.08764e9 - 4.49952e9i) q^{86} +2.61980e9 q^{87} +2.85050e8i q^{88} +4.43923e9i q^{89} -9.25609e9 q^{90} +7.71516e9i q^{91} +7.96810e9 q^{92} -9.55610e9i q^{93} -3.94551e9i q^{94} +6.30345e8 q^{95} -1.79088e10 q^{96} +6.65798e9 q^{97} +1.65038e10i q^{98} -5.67599e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	46.2007i		−	1.44377i	−0.692012	−	0.721886i	$-0.743276\pi$
$2$		−	46.2007i		−	1.44377i	0.692012	−	0.721886i	$-0.256724\pi$
$3$			372.330i			1.53222i	0.642707	+	0.766112i	$0.277811\pi$
$3$			372.330i			1.53222i	−0.642707	+	0.766112i	$0.722189\pi$
$4$	−1110.50			−1.08448
$5$			2517.50i			0.805601i	0.915288	+	0.402801i	$0.131963\pi$
$5$			2517.50i			0.805601i	−0.915288	+	0.402801i	$0.868037\pi$
$6$	17201.9			2.21218
$7$			25292.2i			1.50486i	0.658671	+	0.752431i	$0.271119\pi$
$7$			25292.2i			1.50486i	−0.658671	+	0.752431i	$0.728881\pi$
$8$			3996.58i			0.121966i
$9$	−79580.9			−1.34771
$10$	116310.			1.16310
$11$	71323.6			0.442863			0.221432	−	0.975176i	$-0.428927\pi$
$11$	71323.6			0.442863			0.221432	+	0.975176i	$0.428927\pi$
$12$		−	413475.i		−	1.66166i
$13$	305041.			0.821564			0.410782	−	0.911734i	$-0.365256\pi$
$13$	305041.			0.821564			0.410782	+	0.911734i	$0.365256\pi$
$14$	1.16852e6			2.17268
$15$	−937343.			−1.23436
$16$	−952512.			−0.908386
$17$	−1.86577e6			−1.31406			−0.657028	−	0.753866i	$-0.728187\pi$
$17$	−1.86577e6			−1.31406			−0.657028	+	0.753866i	$0.728187\pi$
$18$			3.67669e6i			1.94578i
$19$		−	250385.i		−	0.101121i	−0.998721	−	0.0505603i	$-0.983899\pi$
$19$		−	250385.i		−	0.101121i	0.998721	−	0.0505603i	$-0.0161007\pi$
$20$		−	2.79570e6i		−	0.873656i
$21$	−9.41705e6			−2.30578
$22$		−	3.29520e6i		−	0.639394i
$23$	−7.17521e6			−1.11480			−0.557398	−	0.830245i	$-0.688200\pi$
$23$	−7.17521e6			−1.11480			−0.557398	+	0.830245i	$0.688200\pi$
$24$	−1.48805e6			−0.186879
$25$	3.42780e6			0.351006
$26$		−	1.40931e7i		−	1.18615i
$27$		−	7.64463e6i		−	0.532768i
$28$		−	2.80871e7i		−	1.63199i
$29$		−	7.03624e6i		−	0.343045i	−0.985180	−	0.171522i	$-0.945131\pi$
$29$		−	7.03624e6i		−	0.343045i	0.985180	−	0.171522i	$-0.0548685\pi$
$30$			4.33059e7i			1.78214i
$31$	−2.56657e7			−0.896487			−0.448244	−	0.893911i	$-0.647950\pi$
$31$	−2.56657e7			−0.896487			−0.448244	+	0.893911i	$0.647950\pi$
$32$			4.80992e7i			1.43347i
$33$			2.65559e7i			0.678566i
$34$			8.61999e7i			1.89720i
$35$	−6.36732e7			−1.21232
$36$	8.83749e7			1.46156
$37$		−	4.75251e7i		−	0.685353i	−0.939454	−	0.342676i	$-0.888667\pi$
$37$		−	4.75251e7i		−	0.685353i	0.939454	−	0.342676i	$-0.111333\pi$
$38$	−1.15680e7			−0.145995
$39$			1.13576e8i			1.25882i
$40$	−1.00614e7			−0.0982558
$41$	9.96282e7			0.859930			0.429965	−	0.902846i	$-0.358526\pi$
$41$	9.96282e7			0.859930			0.429965	+	0.902846i	$0.358526\pi$
$42$			4.35074e8i			3.32903i
$43$	9.73908e7	+	1.10120e8i	0.662484	+	0.749076i
$43$	9.73908e7	+	1.10120e8i	0.662484	+	0.749076i
$44$	−7.92052e7			−0.480275
$45$		−	2.00345e8i		−	1.08572i
$46$			3.31500e8i			1.60951i
$47$	8.53994e7			0.372362			0.186181	−	0.982515i	$-0.440389\pi$
$47$	8.53994e7			0.372362			0.186181	+	0.982515i	$0.440389\pi$
$48$		−	3.54649e8i		−	1.39185i
$49$	−3.57220e8			−1.26461
$50$		−	1.58367e8i		−	0.506773i
$51$		−	6.94683e8i		−	2.01343i
$52$	−3.38749e8			−0.890967
$53$	−6.32854e8			−1.51330			−0.756649	−	0.653821i	$-0.773165\pi$
$53$	−6.32854e8			−1.51330			−0.756649	+	0.653821i	$0.773165\pi$
$54$	−3.53187e8			−0.769195
$55$			1.79557e8i			0.356771i
$56$	−1.01082e8			−0.183542
$57$	9.32259e7			0.154939
$58$	−3.25079e8			−0.495278
$59$	−1.36284e9			−1.90627			−0.953134	−	0.302550i	$-0.902162\pi$
$59$	−1.36284e9			−1.90627			−0.953134	+	0.302550i	$0.902162\pi$
$60$	1.04092e9			1.33864
$61$		−	5.18564e8i		−	0.613978i	−0.951713	−	0.306989i	$-0.900678\pi$
$61$		−	5.18564e8i		−	0.613978i	0.951713	−	0.306989i	$-0.0993216\pi$
$62$			1.18577e9i			1.29432i
$63$		−	2.01278e9i		−	2.02811i
$64$	1.24685e9			1.16122
$65$			7.67942e8i			0.661853i
$66$	1.22690e9			0.979694
$67$	7.52892e8			0.557646			0.278823	−	0.960342i	$-0.410056\pi$
$67$	7.52892e8			0.557646			0.278823	+	0.960342i	$0.410056\pi$
$68$	2.07195e9			1.42506
$69$		−	2.67155e9i		−	1.70812i
$70$			2.94175e9i			1.75031i
$71$			2.82572e9i			1.56617i	0.621917	+	0.783083i	$0.286354\pi$
$71$			2.82572e9i			1.56617i	−0.621917	+	0.783083i	$0.713646\pi$
$72$		−	3.18051e8i		−	0.164374i
$73$		−	3.11851e9i		−	1.50430i	−0.658994	−	0.752148i	$-0.729018\pi$
$73$		−	3.11851e9i		−	1.50430i	0.658994	−	0.752148i	$-0.270982\pi$
$74$	−2.19569e9			−0.989493
$75$			1.27627e9i			0.537820i
$76$			2.78053e8i			0.109663i
$77$			1.80393e9i			0.666448i
$78$	5.24729e9			1.81745
$79$	1.02175e9			0.332056			0.166028	−	0.986121i	$-0.446906\pi$
$79$	1.02175e9			0.332056			0.166028	+	0.986121i	$0.446906\pi$
$80$		−	2.39795e9i		−	0.731797i
$81$	−1.85284e9			−0.531390
$82$		−	4.60289e9i		−	1.24154i
$83$	−5.19494e9			−1.31883			−0.659416	−	0.751778i	$-0.729197\pi$
$83$	−5.19494e9			−1.31883			−0.659416	+	0.751778i	$0.729197\pi$
$84$	1.04577e10			2.50057
$85$		−	4.69709e9i		−	1.05861i
$86$	5.08764e9	−	4.49952e9i	1.08149	−	0.956476i
$87$	2.61980e9			0.525621
$88$			2.85050e8i			0.0540142i
$89$			4.43923e9i			0.794983i	0.917606	+	0.397491i	$0.130119\pi$
$89$			4.43923e9i			0.794983i	−0.917606	+	0.397491i	$0.869881\pi$
$90$	−9.25609e9			−1.56753
$91$			7.71516e9i			1.23634i
$92$	7.96810e9			1.20897
$93$		−	9.55610e9i		−	1.37362i
$94$		−	3.94551e9i		−	0.537606i
$95$	6.30345e8			0.0814630
$96$	−1.79088e10			−2.19639
$97$	6.65798e9			0.775325			0.387662	−	0.921801i	$-0.373283\pi$
$97$	6.65798e9			0.775325			0.387662	+	0.921801i	$0.373283\pi$
$98$			1.65038e10i			1.82580i
$99$	−5.67599e9			−0.596851
$100$	−3.80658e9			−0.380658
$101$	−7.20535e9			−0.685564			−0.342782	−	0.939415i	$-0.611369\pi$
$101$	−7.20535e9			−0.685564			−0.342782	+	0.939415i	$0.611369\pi$
$102$	−3.20948e10			−2.90693
$103$	−1.00832e10			−0.869785			−0.434892	−	0.900482i	$-0.643214\pi$
$103$	−1.00832e10			−0.869785			−0.434892	+	0.900482i	$0.643214\pi$
$104$			1.21912e9i			0.100203i
$105$		−	2.37075e10i		−	1.85754i
$106$			2.92383e10i			2.18486i
$107$	1.52468e10			1.08708			0.543540	−	0.839384i	$-0.317084\pi$
$107$	1.52468e10			1.08708			0.543540	+	0.839384i	$0.317084\pi$
$108$			8.48940e9i			0.577774i
$109$	2.99019e10			1.94342			0.971710	−	0.236177i	$-0.0758947\pi$
$109$	2.99019e10			1.94342			0.971710	+	0.236177i	$0.0758947\pi$
$110$	8.29568e9			0.515096
$111$	1.76950e10			1.05011
$112$		−	2.40911e10i		−	1.36700i
$113$			7.48999e9i			0.406527i	0.979124	+	0.203263i	$0.0651548\pi$
$113$			7.48999e9i			0.406527i	−0.979124	+	0.203263i	$0.934845\pi$
$114$		−	4.30710e9i		−	0.223697i
$115$		−	1.80636e10i		−	0.898081i
$116$			7.81377e9i			0.372024i
$117$	−2.42754e10			−1.10723
$118$			6.29640e10i			2.75222i
$119$		−	4.71895e10i		−	1.97747i
$120$		−	3.74616e9i		−	0.150550i
$121$	−2.08504e10			−0.803872
$122$	−2.39580e10			−0.886445
$123$			3.70946e10i			1.31760i
$124$	2.85018e10			0.972220
$125$			3.32145e10i			1.08837i
$126$	−9.29916e10			−2.92814
$127$	6.20334e10			1.87762			0.938809	−	0.344438i	$-0.111931\pi$
$127$	6.20334e10			1.87762			0.938809	+	0.344438i	$0.111931\pi$
$128$		−	8.35152e9i		−	0.243061i
$129$	−4.10012e10	+	3.62615e10i	−1.14775	+	1.01507i
$130$	3.54794e10			0.955565
$131$			2.92734e10i			0.758782i	0.925236	+	0.379391i	$0.123867\pi$
$131$			2.92734e10i			0.758782i	−0.925236	+	0.379391i	$0.876133\pi$
$132$		−	2.94905e10i		−	0.735889i
$133$	6.33278e9			0.152173
$134$		−	3.47841e10i		−	0.805114i
$135$	1.92454e10			0.429198
$136$		−	7.45669e9i		−	0.160270i
$137$			3.44989e10i			0.714830i	0.933946	+	0.357415i	$0.116342\pi$
$137$			3.44989e10i			0.714830i	−0.933946	+	0.357415i	$0.883658\pi$
$138$	−1.23427e11			−2.46613
$139$	−3.91308e9			−0.0754127			−0.0377063	−	0.999289i	$-0.512005\pi$
$139$	−3.91308e9			−0.0754127			−0.0377063	+	0.999289i	$0.512005\pi$
$140$	7.07094e10			1.31473
$141$			3.17968e10i			0.570542i
$142$	1.30550e11			2.26119
$143$	2.17566e10			0.363840
$144$	7.58017e10			1.22424
$145$	1.77138e10			0.276357
$146$	−1.44078e11			−2.17186
$147$		−	1.33004e11i		−	1.93766i
$148$			5.27768e10i			0.743249i
$149$		−	1.10802e11i		−	1.50875i	−0.656446	−	0.754373i	$-0.727941\pi$
$149$		−	1.10802e11i		−	1.50875i	0.656446	−	0.754373i	$-0.272059\pi$
$150$	5.89647e10			0.776489
$151$			7.24649e10i			0.923088i	0.887117	+	0.461544i	$0.152704\pi$
$151$			7.24649e10i			0.923088i	−0.887117	+	0.461544i	$0.847296\pi$
$152$	1.00068e9			0.0123333
$153$	1.48480e11			1.77096
$154$	8.33429e10			0.962199
$155$		−	6.46134e10i		−	0.722211i
$156$		−	1.26127e11i		−	1.36516i
$157$			1.17646e11i			1.23333i	0.787227	+	0.616664i	$0.211516\pi$
$157$			1.17646e11i			1.23333i	−0.787227	+	0.616664i	$0.788484\pi$
$158$		−	4.72058e10i		−	0.479413i
$159$		−	2.35631e11i		−	2.31871i
$160$	−1.21090e11			−1.15480
$161$		−	1.81477e11i		−	1.67761i
$162$			8.56026e10i			0.767205i
$163$			1.40912e11i			1.22465i	0.790608	+	0.612323i	$0.209765\pi$
$163$			1.40912e11i			1.22465i	−0.790608	+	0.612323i	$0.790235\pi$
$164$	−1.10638e11			−0.932574
$165$	−6.68547e10			−0.546654
$166$			2.40010e11i			1.90409i
$167$	1.36599e10			0.105164			0.0525818	−	0.998617i	$-0.483255\pi$
$167$	1.36599e10			0.105164			0.0525818	+	0.998617i	$0.483255\pi$
$168$		−	3.76360e10i		−	0.281227i
$169$	−4.48086e10			−0.325033
$170$	−2.17009e11			−1.52838
$171$			1.99258e10i			0.136281i
$172$	−1.08153e11	−	1.22289e11i	−0.718449	−	0.812356i
$173$	1.77902e11			1.14802			0.574010	−	0.818848i	$-0.305387\pi$
$173$	1.77902e11			1.14802			0.574010	+	0.818848i	$0.305387\pi$
$174$		−	1.21037e11i		−	0.758877i
$175$			8.66965e10i			0.528216i
$176$	−6.79366e10			−0.402291
$177$		−	5.07425e11i		−	2.92083i
$178$	2.05096e11			1.14777
$179$			1.67525e11i			0.911621i	0.890077	+	0.455811i	$0.150651\pi$
$179$			1.67525e11i			0.911621i	−0.890077	+	0.455811i	$0.849349\pi$
$180$			2.22484e11i			1.17743i
$181$	−2.07998e11			−1.07070			−0.535348	−	0.844632i	$-0.679819\pi$
$181$	−2.07998e11			−1.07070			−0.535348	+	0.844632i	$0.679819\pi$
$182$	3.56446e11			1.78499
$183$	1.93077e11			0.940752
$184$		−	2.86763e10i		−	0.135967i
$185$	1.19645e11			0.552121
$186$	−4.41499e11			−1.98319
$187$	−1.33073e11			−0.581947
$188$	−9.48364e10			−0.403818
$189$	1.93350e11			0.801741
$190$		−	2.91224e10i		−	0.117614i
$191$		−	5.41486e10i		−	0.213020i	−0.994312	−	0.106510i	$-0.966032\pi$
$191$		−	5.41486e10i		−	0.213020i	0.994312	−	0.106510i	$-0.0339676\pi$
$192$			4.64238e11i			1.77924i
$193$	4.49258e11			1.67768			0.838841	−	0.544377i	$-0.183234\pi$
$193$	4.49258e11			1.67768			0.838841	+	0.544377i	$0.183234\pi$
$194$		−	3.07603e11i		−	1.11939i
$195$	−2.85928e11			−1.01411
$196$	3.96695e11			1.37144
$197$	−1.20058e10			−0.0404631			−0.0202316	−	0.999795i	$-0.506440\pi$
$197$	−1.20058e10			−0.0404631			−0.0202316	+	0.999795i	$0.506440\pi$
$198$			2.62235e11i			0.861717i
$199$			1.99312e11i			0.638658i	0.947644	+	0.319329i	$0.103457\pi$
$199$			1.99312e11i			0.638658i	−0.947644	+	0.319329i	$0.896543\pi$
$200$			1.36994e10i			0.0428108i
$201$			2.80325e11i			0.854439i
$202$			3.32892e11i			0.989798i
$203$	1.77962e11			0.516234
$204$			7.71449e11i			2.18352i
$205$			2.50814e11i			0.692761i
$206$			4.65850e11i			1.25577i
$207$	5.71009e11			1.50242
$208$	−2.90555e11			−0.746297
$209$		−	1.78583e10i		−	0.0447826i
$210$	−1.09530e12			−2.68187
$211$			3.66095e11i			0.875349i	0.899134	+	0.437674i	$0.144198\pi$
$211$			3.66095e11i			0.875349i	−0.899134	+	0.437674i	$0.855802\pi$
$212$	7.02788e11			1.64114
$213$	−1.05210e12			−2.39972
$214$		−	7.04415e11i		−	1.56949i
$215$	−2.77229e11	+	2.45182e11i	−0.603457	+	0.533698i
$216$	3.05524e10			0.0649794
$217$		−	6.49141e11i		−	1.34909i
$218$		−	1.38149e12i		−	2.80585i
$219$	1.16112e12			2.30492
$220$		−	1.99399e11i		−	0.386910i
$221$	−5.69136e11			−1.07958
$222$		−	8.17522e11i		−	1.51612i
$223$			1.10099e11i			0.199645i	0.995005	+	0.0998227i	$0.0318276\pi$
$223$			1.10099e11i			0.199645i	−0.995005	+	0.0998227i	$0.968172\pi$
$224$	−1.21654e12			−2.15717
$225$	−2.72787e11			−0.473054
$226$	3.46043e11			0.586932
$227$			8.36307e10i			0.138751i	0.997591	+	0.0693756i	$0.0221007\pi$
$227$			8.36307e10i			0.138751i	−0.997591	+	0.0693756i	$0.977899\pi$
$228$	−1.03528e11			−0.168028
$229$	−6.58580e11			−1.04576			−0.522879	−	0.852407i	$-0.675142\pi$
$229$	−6.58580e11			−1.04576			−0.522879	+	0.852407i	$0.675142\pi$
$230$	−8.34552e11			−1.29662
$231$	−6.71658e11			−1.02115
$232$	2.81209e10			0.0418397
$233$		−	5.69687e11i		−	0.829577i	−0.909918	−	0.414789i	$-0.863856\pi$
$233$		−	5.69687e11i		−	0.829577i	0.909918	−	0.414789i	$-0.136144\pi$
$234$			1.12154e12i			1.59859i
$235$			2.14993e11i			0.299976i
$236$	1.51344e12			2.06730
$237$			3.80430e11i			0.508784i
$238$	−2.18019e12			−2.85502
$239$	6.54291e11			0.839038			0.419519	−	0.907747i	$-0.362199\pi$
$239$	6.54291e11			0.839038			0.419519	+	0.907747i	$0.362199\pi$
$240$	8.92831e11			1.12128
$241$		−	1.47198e11i		−	0.181058i	−0.995894	−	0.0905288i	$-0.971144\pi$
$241$		−	1.47198e11i		−	0.181058i	0.995894	−	0.0905288i	$-0.0288557\pi$
$242$			9.63302e11i			1.16061i
$243$		−	1.14128e12i		−	1.34698i
$244$			5.75868e11i			0.665846i
$245$		−	8.99304e11i		−	1.01877i
$246$	1.71380e12			1.90232
$247$		−	7.63776e10i		−	0.0830771i
$248$		−	1.02575e11i		−	0.109341i
$249$		−	1.93423e12i		−	2.02075i
$250$	1.53453e12			1.57136
$251$	−5.57229e11			−0.559326			−0.279663	−	0.960098i	$-0.590223\pi$
$251$	−5.57229e11			−0.559326			−0.279663	+	0.960098i	$0.590223\pi$
$252$			2.23520e12i			2.19944i
$253$	−5.11762e11			−0.493702
$254$		−	2.86599e12i		−	2.71085i
$255$	1.74887e12			1.62202
$256$	8.90923e11			0.810290
$257$			1.63650e11i			0.145966i	0.997333	+	0.0729828i	$0.0232518\pi$
$257$			1.63650e11i			0.145966i	−0.997333	+	0.0729828i	$0.976748\pi$
$258$	1.67531e12	+	1.89428e12i	1.46554	+	1.65709i
$259$	1.20201e12			1.03136
$260$		−	8.52803e11i		−	0.717764i
$261$			5.59950e11i			0.462324i
$262$	1.35245e12			1.09551
$263$			2.20675e12i			1.75377i	0.480696	+	0.876887i	$0.340384\pi$
$263$			2.20675e12i			1.75377i	−0.480696	+	0.876887i	$0.659616\pi$
$264$	−1.06133e11			−0.0827618
$265$		−	1.59321e12i		−	1.21912i
$266$		−	2.92579e11i		−	0.219703i
$267$	−1.65286e12			−1.21809
$268$	−8.36090e11			−0.604755
$269$	−2.28588e12			−1.62290			−0.811451	−	0.584421i	$-0.801322\pi$
$269$	−2.28588e12			−1.62290			−0.811451	+	0.584421i	$0.801322\pi$
$270$		−	8.89151e11i		−	0.619665i
$271$	2.10457e12			1.43985			0.719924	−	0.694053i	$-0.244177\pi$
$271$	2.10457e12			1.43985			0.719924	+	0.694053i	$0.244177\pi$
$272$	1.77717e12			1.19367
$273$	−2.87259e12			−1.89435
$274$	1.59387e12			1.03205
$275$	2.44483e11			0.155448
$276$			2.96677e12i			1.85241i
$277$			1.69302e12i			1.03816i	0.854726	+	0.519080i	$0.173725\pi$
$277$			1.69302e12i			1.03816i	−0.854726	+	0.519080i	$0.826275\pi$
$278$			1.80787e11i			0.108879i
$279$	2.04250e12			1.20820
$280$		−	2.54475e11i		−	0.147861i
$281$	−1.67292e12			−0.954867			−0.477433	−	0.878668i	$-0.658433\pi$
$281$	−1.67292e12			−0.954867			−0.477433	+	0.878668i	$0.658433\pi$
$282$	1.46903e12			0.823733
$283$	−2.59661e12			−1.43046			−0.715229	−	0.698890i	$-0.753678\pi$
$283$	−2.59661e12			−1.43046			−0.715229	+	0.698890i	$0.753678\pi$
$284$		−	3.13798e12i		−	1.69847i
$285$			2.34697e11i			0.124819i
$286$		−	1.00517e12i		−	0.525303i
$287$			2.51982e12i			1.29408i
$288$		−	3.82778e12i		−	1.93190i
$289$	1.46511e12			0.726742
$290$		−	8.18388e11i		−	0.398997i
$291$			2.47897e12i			1.18797i
$292$			3.46313e12i			1.63138i
$293$	2.22776e12			1.03165			0.515823	−	0.856695i	$-0.327486\pi$
$293$	2.22776e12			1.03165			0.515823	+	0.856695i	$0.327486\pi$
$294$	−6.14488e12			−2.79754
$295$		−	3.43095e12i		−	1.53569i
$296$	1.89937e11			0.0835896
$297$		−	5.45243e11i		−	0.235943i
$298$	−5.11913e12			−2.17829
$299$	−2.18873e12			−0.915876
$300$		−	1.41731e12i		−	0.583254i
$301$	−2.78519e12	+	2.46323e12i	−1.12726	+	0.996947i
$302$	3.34793e12			1.33273
$303$		−	2.68277e12i		−	1.05044i
$304$			2.38495e11i			0.0918566i
$305$	1.30549e12			0.494622
$306$		−	6.85986e12i		−	2.55687i
$307$	1.96871e12			0.721922			0.360961	−	0.932581i	$-0.382449\pi$
$307$	1.96871e12			0.721922			0.360961	+	0.932581i	$0.382449\pi$
$308$		−	2.00327e12i		−	0.722748i
$309$		−	3.75428e12i		−	1.33270i
$310$	−2.98519e12			−1.04271
$311$	−4.26791e12			−1.46694			−0.733472	−	0.679720i	$-0.762101\pi$
$311$	−4.26791e12			−1.46694			−0.733472	+	0.679720i	$0.762101\pi$
$312$	−4.53915e11			−0.153533
$313$			4.54518e12i			1.51297i	0.654012	+	0.756484i	$0.273085\pi$
$313$			4.54518e12i			1.51297i	−0.654012	+	0.756484i	$0.726915\pi$
$314$	5.43532e12			1.78064
$315$	5.06717e12			1.63385
$316$	−1.13466e12			−0.360107
$317$	1.59917e12			0.499571			0.249786	−	0.968301i	$-0.419640\pi$
$317$	1.59917e12			0.499571			0.249786	+	0.968301i	$0.419640\pi$
$318$	−1.08863e13			−3.34769
$319$		−	5.01850e11i		−	0.151922i
$320$			3.13894e12i			0.935477i
$321$			5.67686e12i			1.66565i
$322$	−8.38436e12			−2.42209
$323$			4.67161e11i			0.132878i
$324$	2.05759e12			0.576280
$325$	1.04562e12			0.288374
$326$	6.51024e12			1.76811
$327$			1.11334e13i			2.97775i
$328$			3.98172e11i			0.104882i
$329$			2.15994e12i			0.560353i
$330$			3.08873e12i			0.789243i
$331$			2.83663e12i			0.713942i	0.934115	+	0.356971i	$0.116191\pi$
$331$			2.83663e12i			0.713942i	−0.934115	+	0.356971i	$0.883809\pi$
$332$	5.76900e12			1.43024
$333$			3.78209e12i			0.923656i
$334$		−	6.31098e11i		−	0.151832i
$335$			1.89541e12i			0.449241i
$336$	8.96986e12			2.09454
$337$	−6.48421e12			−1.49179			−0.745895	−	0.666064i	$-0.767978\pi$
$337$	−6.48421e12			−1.49179			−0.745895	+	0.666064i	$0.767978\pi$
$338$			2.07019e12i			0.469274i
$339$	−2.78875e12			−0.622890
$340$			5.21614e12i			1.14803i
$341$	−1.83057e12			−0.397021
$342$	9.20588e11			0.196759
$343$		−	1.89047e12i		−	0.398197i
$344$	−4.40105e11	+	3.89230e11i	−0.0913616	+	0.0808004i
$345$	6.72563e12			1.37606
$346$		−	8.21918e12i		−	1.65748i
$347$		−	7.21366e12i		−	1.43387i	−0.697142	−	0.716933i	$-0.745545\pi$
$347$		−	7.21366e12i		−	1.43387i	0.697142	−	0.716933i	$-0.254455\pi$
$348$	−2.90931e12			−0.570024
$349$		−	2.31109e12i		−	0.446364i	−0.974777	−	0.223182i	$-0.928356\pi$
$349$		−	2.31109e12i		−	0.446364i	0.974777	−	0.223182i	$-0.0716445\pi$
$350$	4.00544e12			0.762623
$351$		−	2.33193e12i		−	0.437703i
$352$			3.43061e12i			0.634831i
$353$	2.26403e12			0.413056			0.206528	−	0.978441i	$-0.433784\pi$
$353$	2.26403e12			0.413056			0.206528	+	0.978441i	$0.433784\pi$
$354$	−2.34434e13			−4.21701
$355$	−7.11377e12			−1.26171
$356$		−	4.92979e12i		−	0.862140i
$357$	1.75701e13			3.02993
$358$	7.73977e12			1.31617
$359$	6.50793e12			1.09137			0.545683	−	0.837992i	$-0.316270\pi$
$359$	6.50793e12			1.09137			0.545683	+	0.837992i	$0.316270\pi$
$360$	8.00695e11			0.132420
$361$	6.06837e12			0.989775
$362$			9.60965e12i			1.54584i
$363$		−	7.76322e12i		−	1.23171i
$364$		−	8.56772e12i		−	1.34078i
$365$	7.85088e12			1.21186
$366$		−	8.92030e12i		−	1.35823i
$367$	−6.62772e12			−0.995483			−0.497741	−	0.867326i	$-0.665837\pi$
$367$	−6.62772e12			−0.995483			−0.497741	+	0.867326i	$0.665837\pi$
$368$	6.83447e12			1.01267
$369$	−7.92850e12			−1.15893
$370$		−	5.52766e12i		−	0.797137i
$371$		−	1.60063e13i		−	2.27730i
$372$			1.06121e13i			1.48966i
$373$		−	1.15355e12i		−	0.159769i	−0.996804	−	0.0798844i	$-0.974545\pi$
$373$		−	1.15355e12i		−	0.159769i	0.996804	−	0.0798844i	$-0.0254551\pi$
$374$			6.14809e12i			0.840199i
$375$	−1.23668e13			−1.66763
$376$			3.41305e11i			0.0454154i
$377$		−	2.14634e12i		−	0.281833i
$378$		−	8.93289e12i		−	1.15753i
$379$	1.20748e12			0.154413			0.0772067	−	0.997015i	$-0.475400\pi$
$379$	1.20748e12			0.154413			0.0772067	+	0.997015i	$0.475400\pi$
$380$	−7.00001e11			−0.0883447
$381$			2.30969e13i			2.87693i
$382$	−2.50170e12			−0.307552
$383$			3.74979e9i			0.000455002i	1.00000		0.000227501i	$7.24158e-5\pi$
$383$			3.74979e9i			0.000455002i	−1.00000		0.000227501i	$0.999928\pi$
$384$	3.10952e12			0.372424
$385$	−4.54140e12			−0.536891
$386$		−	2.07560e13i		−	2.42219i
$387$	−7.75044e12	−	8.76348e12i	−0.892836	−	1.00954i
$388$	−7.39371e12			−0.840822
$389$			9.33224e12i			1.04770i	0.851810	+	0.523851i	$0.175505\pi$
$389$			9.33224e12i			1.04770i	−0.851810	+	0.523851i	$0.824495\pi$
$390$			1.32101e13i			1.46414i
$391$	1.33873e13			1.46490
$392$		−	1.42766e12i		−	0.154239i
$393$	−1.08994e13			−1.16262
$394$			5.54676e11i			0.0584195i
$395$			2.57227e12i			0.267505i
$396$	6.30322e12			0.647271
$397$	−7.85222e12			−0.796233			−0.398116	−	0.917335i	$-0.630336\pi$
$397$	−7.85222e12			−0.796233			−0.398116	+	0.917335i	$0.630336\pi$
$398$	9.20836e12			0.922076
$399$			2.35789e12i			0.233162i
$400$	−3.26502e12			−0.318849
$401$	1.05265e13			1.01522			0.507612	−	0.861586i	$-0.330528\pi$
$401$	1.05265e13			1.01522			0.507612	+	0.861586i	$0.330528\pi$
$402$	1.29512e13			1.23361
$403$	−7.82908e12			−0.736521
$404$	8.00157e12			0.743479
$405$		−	4.66454e12i		−	0.428088i
$406$		−	8.22197e12i		−	0.745325i
$407$		−	3.38966e12i		−	0.303518i
$408$	2.77635e12			0.245569
$409$			1.33735e13i			1.16850i	0.811573	+	0.584250i	$0.198611\pi$
$409$			1.33735e13i			1.16850i	−0.811573	+	0.584250i	$0.801389\pi$
$410$	1.15878e13			1.00019
$411$	−1.28450e13			−1.09528
$412$	1.11974e13			0.943262
$413$		−	3.44691e13i		−	2.86867i
$414$		−	2.63810e13i		−	2.16915i
$415$		−	1.30783e13i		−	1.06245i
$416$			1.46722e13i			1.17769i
$417$		−	1.45696e12i		−	0.115549i
$418$	−8.25068e11			−0.0646559
$419$		−	1.85553e13i		−	1.43680i	−0.695629	−	0.718401i	$-0.744874\pi$
$419$		−	1.85553e13i		−	1.43680i	0.695629	−	0.718401i	$-0.255126\pi$
$420$			2.63273e13i			2.01446i
$421$			2.02826e13i			1.53360i	0.641884	+	0.766802i	$0.278153\pi$
$421$			2.02826e13i			1.53360i	−0.641884	+	0.766802i	$0.721847\pi$
$422$	1.69138e13			1.26380
$423$	−6.79616e12			−0.501836
$424$		−	2.52925e12i		−	0.184571i
$425$	−6.39548e12			−0.461242
$426$			4.86078e13i			3.46464i
$427$	1.31156e13			0.923952
$428$	−1.69317e13			−1.17891
$429$			8.10064e12i			0.557485i
$430$	1.13276e13	+	1.28082e13i	0.770539	+	0.871254i
$431$	−4.60294e12			−0.309492			−0.154746	−	0.987954i	$-0.549456\pi$
$431$	−4.60294e12			−0.309492			−0.154746	+	0.987954i	$0.549456\pi$
$432$			7.28161e12i			0.483959i
$433$		−	1.00692e13i		−	0.661540i	−0.943711	−	0.330770i	$-0.892692\pi$
$433$		−	1.00692e13i		−	0.661540i	0.943711	−	0.330770i	$-0.107308\pi$
$434$	−2.99908e13			−1.94778
$435$			6.59537e12i			0.423441i
$436$	−3.32062e13			−2.10759
$437$			1.79656e12i			0.112729i
$438$		−	5.36444e13i		−	3.32778i
$439$	2.63240e12			0.161447			0.0807234	−	0.996737i	$-0.474277\pi$
$439$	2.63240e12			0.161447			0.0807234	+	0.996737i	$0.474277\pi$
$440$	−7.17615e11			−0.0435139
$441$	2.84279e13			1.70432
$442$			2.62945e13i			1.55867i
$443$	−8.76270e12			−0.513593			−0.256797	−	0.966465i	$-0.582667\pi$
$443$	−8.76270e12			−0.513593			−0.256797	+	0.966465i	$0.582667\pi$
$444$	−1.96504e13			−1.13882
$445$	−1.11758e13			−0.640439
$446$	5.08666e12			0.288242
$447$	4.12550e13			2.31174
$448$			3.15355e13i			1.74747i
$449$		−	2.25448e13i		−	1.23542i	−0.786406	−	0.617710i	$-0.788060\pi$
$449$		−	2.25448e13i		−	1.23542i	0.786406	−	0.617710i	$-0.211940\pi$
$450$			1.26029e13i			0.682982i
$451$	7.10584e12			0.380831
$452$		−	8.31767e12i		−	0.440869i
$453$	−2.69809e13			−1.41438
$454$	3.86380e12			0.200325
$455$	−1.94229e13			−0.995997
$456$			3.72584e11i			0.0188973i
$457$		−	6.81262e12i		−	0.341769i	−0.985291	−	0.170885i	$-0.945337\pi$
$457$		−	6.81262e12i		−	0.341769i	0.985291	−	0.170885i	$-0.0546626\pi$
$458$			3.04268e13i			1.50984i
$459$			1.42631e13i			0.700086i
$460$			2.00597e13i			0.973949i
$461$	−2.33485e13			−1.12138			−0.560692	−	0.828025i	$-0.689465\pi$
$461$	−2.33485e13			−1.12138			−0.560692	+	0.828025i	$0.689465\pi$
$462$			3.10311e13i			1.47430i
$463$		−	3.70670e13i		−	1.74214i	−0.491160	−	0.871070i	$-0.663427\pi$
$463$		−	3.70670e13i		−	1.74214i	0.491160	−	0.871070i	$-0.336573\pi$
$464$			6.70210e12i			0.311617i
$465$	2.40575e13			1.10659
$466$	−2.63199e13			−1.19772
$467$		−	2.89598e13i		−	1.30380i	−0.758305	−	0.651900i	$-0.773972\pi$
$467$		−	2.89598e13i		−	1.30380i	0.758305	−	0.651900i	$-0.226028\pi$
$468$	2.69580e13			1.20076
$469$			1.90423e13i			0.839180i
$470$	9.93284e12			0.433096
$471$	−4.38031e13			−1.88973
$472$		−	5.44668e12i		−	0.232499i
$473$	6.94626e12	+	7.85419e12i	0.293390	+	0.331738i
$474$	1.75761e13			0.734568
$475$		−	8.58268e11i		−	0.0354940i
$476$			5.24041e13i			2.14452i
$477$	5.03631e13			2.03949
$478$		−	3.02287e13i		−	1.21138i
$479$	−5.00231e12			−0.198378			−0.0991888	−	0.995069i	$-0.531625\pi$
$479$	−5.00231e12			−0.198378			−0.0991888	+	0.995069i	$0.531625\pi$
$480$		−	4.50855e13i		−	1.76942i
$481$		−	1.44971e13i		−	0.563061i
$482$	−6.80065e12			−0.261406
$483$	6.75693e13			2.57048
$484$	2.31544e13			0.871781
$485$			1.67615e13i			0.624603i
$486$	−5.27278e13			−1.94473
$487$	4.68407e13			1.70993			0.854965	−	0.518685i	$-0.173578\pi$
$487$	4.68407e13			1.70993			0.854965	+	0.518685i	$0.173578\pi$
$488$	2.07248e12			0.0748844
$489$	−5.24659e13			−1.87643
$490$	−4.15485e13			−1.47087
$491$			4.76896e13i			1.67115i	0.549373	+	0.835577i	$0.314867\pi$
$491$			4.76896e13i			1.67115i	−0.549373	+	0.835577i	$0.685133\pi$
$492$		−	4.11937e13i		−	1.42891i
$493$			1.31280e13i			0.450780i
$494$	−3.52870e12			−0.119944
$495$		−	1.42893e13i		−	0.480824i
$496$	2.44469e13			0.814357
$497$	−7.14687e13			−2.35686
$498$	−8.93629e13			−2.91750
$499$			5.25062e12i			0.169710i	0.996393	+	0.0848551i	$0.0270427\pi$
$499$			5.25062e12i			0.169710i	−0.996393	+	0.0848551i	$0.972957\pi$
$500$		−	3.68849e13i		−	1.18032i
$501$			5.08600e12i			0.161134i
$502$			2.57444e13i			0.807539i
$503$		−	1.87015e13i		−	0.580814i	−0.956903	−	0.290407i	$-0.906209\pi$
$503$		−	1.87015e13i		−	0.580814i	0.956903	−	0.290407i	$-0.0937907\pi$
$504$	8.04421e12			0.247361
$505$		−	1.81395e13i		−	0.552291i
$506$			2.36437e13i			0.712793i
$507$		−	1.66836e13i		−	0.498023i
$508$	−6.88884e13			−2.03623
$509$	4.81590e13			1.40958			0.704788	−	0.709418i	$-0.251042\pi$
$509$	4.81590e13			1.40958			0.704788	+	0.709418i	$0.251042\pi$
$510$		−	8.07989e13i		−	2.34183i
$511$	7.88741e13			2.26376
$512$		−	4.97132e13i		−	1.41294i
$513$	−1.91410e12			−0.0538738
$514$	7.56075e12			0.210741
$515$		−	2.53845e13i		−	0.700700i
$516$	4.55320e13	−	4.02686e13i	1.24471	−	1.10082i
$517$	6.09099e12			0.164906
$518$		−	5.55339e13i		−	1.48905i
$519$			6.62382e13i			1.75902i
$520$	−3.06914e12			−0.0807234
$521$			4.77518e13i			1.24395i	0.783039	+	0.621973i	$0.213669\pi$
$521$			4.77518e13i			1.24395i	−0.783039	+	0.621973i	$0.786331\pi$
$522$	2.58701e13			0.667491
$523$		−	3.62939e12i		−	0.0927524i	−0.998924	−	0.0463762i	$-0.985233\pi$
$523$		−	3.62939e12i		−	0.0927524i	0.998924	−	0.0463762i	$-0.0147673\pi$
$524$		−	3.25083e13i		−	0.822882i
$525$	−3.22797e13			−0.809345
$526$	1.01953e14			2.53205
$527$	4.78862e13			1.17803
$528$		−	2.52949e13i		−	0.616400i
$529$	1.00571e13			0.242770
$530$	−7.36076e13			−1.76012
$531$	1.08456e14			2.56909
$532$	−7.03259e12			−0.165028
$533$	3.03907e13			0.706487
$534$			7.63633e13i			1.75865i
$535$			3.83840e13i			0.875753i
$536$			3.00899e12i			0.0680138i
$537$	−6.23746e13			−1.39681
$538$			1.05609e14i			2.34310i
$539$	−2.54782e13			−0.560048
$540$	−2.13721e13			−0.465456
$541$	−3.40244e13			−0.734183			−0.367092	−	0.930185i	$-0.619646\pi$
$541$	−3.40244e13			−0.734183			−0.367092	+	0.930185i	$0.619646\pi$
$542$		−	9.72326e13i		−	2.07881i
$543$		−	7.74439e13i		−	1.64055i
$544$		−	8.97421e13i		−	1.88366i
$545$			7.52782e13i			1.56562i
$546$			1.32715e14i			2.73501i
$547$	−7.53319e13			−1.53831			−0.769153	−	0.639065i	$-0.779321\pi$
$547$	−7.53319e13			−1.53831			−0.769153	+	0.639065i	$0.779321\pi$
$548$		−	3.83112e13i		−	0.775217i
$549$			4.12678e13i			0.827464i
$550$		−	1.12953e13i		−	0.224431i
$551$	−1.76177e12			−0.0346889
$552$	1.06770e13			0.208332
$553$			2.58424e13i			0.499698i
$554$	7.82189e13			1.49887
$555$			4.45473e13i			0.845973i
$556$	4.34549e12			0.0817833
$557$	5.40321e13			1.00780			0.503901	−	0.863761i	$-0.331897\pi$
$557$	5.40321e13			1.00780			0.503901	+	0.863761i	$0.331897\pi$
$558$		−	9.43647e13i		−	1.74437i
$559$	2.97082e13	+	3.35912e13i	0.544273	+	0.615413i
$560$	6.06495e13			1.10125
$561$		−	4.95473e13i		−	0.891673i
$562$			7.72899e13i			1.37861i
$563$	−1.21882e12			−0.0215476			−0.0107738	−	0.999942i	$-0.503429\pi$
$563$	−1.21882e12			−0.0215476			−0.0107738	+	0.999942i	$0.503429\pi$
$564$		−	3.53105e13i		−	0.618740i
$565$	−1.88561e13			−0.327498
$566$			1.19965e14i			2.06526i
$567$		−	4.68624e13i		−	0.799668i
$568$	−1.12932e13			−0.191019
$569$	−1.25274e12			−0.0210039			−0.0105020	−	0.999945i	$-0.503343\pi$
$569$	−1.25274e12			−0.0210039			−0.0105020	+	0.999945i	$0.503343\pi$
$570$	1.08431e13			0.180211
$571$		−	7.69973e13i		−	1.26851i	−0.773122	−	0.634257i	$-0.781306\pi$
$571$		−	7.69973e13i		−	1.26851i	0.773122	−	0.634257i	$-0.218694\pi$
$572$	−2.41608e13			−0.394577
$573$	2.01612e13			0.326394
$574$	1.16417e14			1.86835
$575$	−2.45951e13			−0.391300
$576$	−9.92250e13			−1.56498
$577$			6.44502e13i			1.00773i	0.863782	+	0.503866i	$0.168090\pi$
$577$			6.44502e13i			1.00773i	−0.863782	+	0.503866i	$0.831910\pi$
$578$		−	6.76890e13i		−	1.04925i
$579$			1.67272e14i			2.57058i
$580$	−1.96712e13			−0.299703
$581$		−	1.31391e14i		−	1.98466i
$582$	1.14530e14			1.71516
$583$	−4.51374e13			−0.670184
$584$	1.24634e13			0.183473
$585$		−	6.11135e13i		−	0.891985i
$586$		−	1.02924e14i		−	1.48946i
$587$		−	5.33136e13i		−	0.764976i	−0.923960	−	0.382488i	$-0.875067\pi$
$587$		−	5.33136e13i		−	0.764976i	0.923960	−	0.382488i	$-0.124933\pi$
$588$			1.47702e14i			2.10135i
$589$			6.42629e12i			0.0906534i
$590$	−1.58512e14			−2.21719
$591$		−	4.47012e12i		−	0.0619986i
$592$			4.52682e13i			0.622565i
$593$		−	1.02559e14i		−	1.39862i	−0.714817	−	0.699312i	$-0.753490\pi$
$593$		−	1.02559e14i		−	1.39862i	0.714817	−	0.699312i	$-0.246510\pi$
$594$	−2.51906e13			−0.340648
$595$	1.18800e14			1.59305
$596$			1.23046e14i			1.63620i
$597$	−7.42099e13			−0.978567
$598$			1.01121e14i			1.32232i
$599$	−1.12585e14			−1.45998			−0.729992	−	0.683456i	$-0.760476\pi$
$599$	−1.12585e14			−1.45998			−0.729992	+	0.683456i	$0.760476\pi$
$600$	−5.10072e12			−0.0655957
$601$			5.45771e12i			0.0696046i	0.999394	+	0.0348023i	$0.0110802\pi$
$601$			5.45771e12i			0.0696046i	−0.999394	+	0.0348023i	$0.988920\pi$
$602$	1.13803e14	+	1.28678e14i	1.43936	+	1.62750i
$603$	−5.99158e13			−0.751545
$604$		−	8.04726e13i		−	1.00107i
$605$		−	5.24909e13i		−	0.647601i
$606$	−1.23946e14			−1.51659
$607$		−	1.42238e14i		−	1.72612i	−0.505101	−	0.863060i	$-0.668545\pi$
$607$		−	1.42238e14i		−	1.72612i	0.505101	−	0.863060i	$-0.331455\pi$
$608$	1.20433e13			0.144953
$609$			6.62606e13i			0.790987i
$610$		−	6.03144e13i		−	0.714121i
$611$	2.60503e13			0.305919
$612$	−1.64887e14			−1.92057
$613$	4.10317e13			0.474042			0.237021	−	0.971505i	$-0.423829\pi$
$613$	4.10317e13			0.474042			0.237021	+	0.971505i	$0.423829\pi$
$614$		−	9.09559e13i		−	1.04229i
$615$	−9.33858e13			−1.06146
$616$	−7.20955e12			−0.0812839
$617$	−1.66102e14			−1.85759			−0.928793	−	0.370598i	$-0.879153\pi$
$617$	−1.66102e14			−1.85759			−0.928793	+	0.370598i	$0.879153\pi$
$618$	−1.73450e14			−1.92412
$619$	1.21414e13			0.133603			0.0668015	−	0.997766i	$-0.478721\pi$
$619$	1.21414e13			0.133603			0.0668015	+	0.997766i	$0.478721\pi$
$620$			7.17535e13i			0.783222i
$621$			5.48518e13i			0.593927i
$622$			1.97181e14i			2.11793i
$623$	−1.12278e14			−1.19634
$624$		−	1.08182e14i		−	1.14349i
$625$	−5.01431e13			−0.525788
$626$	2.09991e14			2.18438
$627$	6.64920e12			0.0686170
$628$		−	1.30646e14i		−	1.33752i
$629$			8.86709e13i			0.900591i
$630$		−	2.34107e14i		−	2.35891i
$631$			5.98910e13i			0.598708i	0.954142	+	0.299354i	$0.0967711\pi$
$631$			5.98910e13i			0.598708i	−0.954142	+	0.299354i	$0.903229\pi$
$632$			4.08352e12i			0.0404995i
$633$	−1.36308e14			−1.34123
$634$		−	7.38826e13i		−	0.721267i
$635$			1.56169e14i			1.51261i
$636$			2.61669e14i			2.51459i
$637$	−1.08967e14			−1.03896
$638$	−2.31858e13			−0.219340
$639$		−	2.24873e14i		−	2.11074i
$640$	2.10250e13			0.195810
$641$			1.27984e14i			1.18267i	0.806425	+	0.591336i	$0.201399\pi$
$641$			1.27984e14i			1.18267i	−0.806425	+	0.591336i	$0.798601\pi$
$642$	2.62275e14			2.40482
$643$	1.20161e14			1.09323			0.546613	−	0.837386i	$-0.315917\pi$
$643$	1.20161e14			1.09323			0.546613	+	0.837386i	$0.315917\pi$
$644$			2.01531e14i			1.81933i
$645$	−9.12886e13	−	1.03221e14i	−0.817745	−	0.924630i
$646$	2.15832e13			0.191846
$647$		−	2.11239e13i		−	0.186317i	−0.995651	−	0.0931586i	$-0.970304\pi$
$647$		−	2.11239e13i		−	0.186317i	0.995651	−	0.0931586i	$-0.0296964\pi$
$648$		−	7.40502e12i		−	0.0648114i
$649$	−9.72024e13			−0.844216
$650$		−	4.83083e13i		−	0.416346i
$651$	2.41695e14			2.06711
$652$		−	1.56484e14i		−	1.32810i
$653$			1.49697e14i			1.26080i	0.776270	+	0.630401i	$0.217109\pi$
$653$			1.49697e14i			1.26080i	−0.776270	+	0.630401i	$0.782891\pi$
$654$	5.14371e14			4.29920
$655$	−7.36960e13			−0.611276
$656$	−9.48971e13			−0.781149
$657$			2.48174e14i			2.02735i
$658$	9.97907e13			0.809022
$659$	1.56549e14			1.25957			0.629786	−	0.776769i	$-0.283143\pi$
$659$	1.56549e14			1.25957			0.629786	+	0.776769i	$0.283143\pi$
$660$	7.42424e13			0.592833
$661$	1.48883e14			1.17988			0.589940	−	0.807447i	$-0.299151\pi$
$661$	1.48883e14			1.17988			0.589940	+	0.807447i	$0.299151\pi$
$662$	1.31054e14			1.03077
$663$		−	2.11907e14i		−	1.65416i
$664$		−	2.07620e13i		−	0.160853i
$665$			1.59428e13i			0.122590i
$666$	1.74735e14			1.33355
$667$			5.04865e13i			0.382425i
$668$	−1.51694e13			−0.114048
$669$	−4.09932e13			−0.305901
$670$	8.75692e13			0.648601
$671$		−	3.69858e13i		−	0.271909i
$672$		−	4.52953e14i		−	3.30527i
$673$			2.94088e13i			0.213011i	0.994312	+	0.106506i	$0.0339662\pi$
$673$			2.94088e13i			0.213011i	−0.994312	+	0.106506i	$0.966034\pi$
$674$			2.99575e14i			2.15380i
$675$		−	2.62042e13i		−	0.187005i
$676$	4.97601e13			0.352491
$677$			1.54013e14i			1.08297i	0.840711	+	0.541484i	$0.182137\pi$
$677$			1.54013e14i			1.08297i	−0.840711	+	0.541484i	$0.817863\pi$
$678$			1.28842e14i			0.899311i
$679$			1.68395e14i			1.16676i
$680$	1.87723e13			0.129114
$681$	−3.11383e13			−0.212598
$682$			8.45735e13i			0.573208i
$683$	8.90638e13			0.599235			0.299618	−	0.954059i	$-0.403141\pi$
$683$	8.90638e13			0.599235			0.299618	+	0.954059i	$0.403141\pi$
$684$		−	2.21277e13i		−	0.147794i
$685$	−8.68512e13			−0.575868
$686$	−8.73409e13			−0.574906
$687$		−	2.45209e14i		−	1.60233i
$688$	−9.27659e13	−	1.04891e14i	−0.601792	−	0.680450i
$689$	−1.93046e14			−1.24327
$690$		−	3.10729e14i		−	1.98672i
$691$			2.05726e14i			1.30587i	0.757415	+	0.652934i	$0.226462\pi$
$691$			2.05726e14i			1.30587i	−0.757415	+	0.652934i	$0.773538\pi$
$692$	−1.97561e14			−1.24500
$693$		−	1.43558e14i		−	0.898178i
$694$	−3.33276e14			−2.07017
$695$		−	9.85119e12i		−	0.0607526i
$696$			1.04702e13i			0.0641078i
$697$	−1.85883e14			−1.13000
$698$	−1.06774e14			−0.644448
$699$	2.12112e14			1.27110
$700$		−	9.62769e13i		−	0.572838i
$701$	−2.83348e13			−0.167390			−0.0836950	−	0.996491i	$-0.526672\pi$
$701$	−2.83348e13			−0.167390			−0.0836950	+	0.996491i	$0.526672\pi$
$702$	−1.07737e14			−0.631943
$703$	−1.18996e13			−0.0693033
$704$	8.89295e13			0.514260
$705$	−8.00486e13			−0.459630
$706$		−	1.04600e14i		−	0.596359i
$707$		−	1.82239e14i		−	1.03168i
$708$			5.63498e14i			3.16757i
$709$	5.65638e13			0.315724			0.157862	−	0.987461i	$-0.449540\pi$
$709$	5.65638e13			0.315724			0.157862	+	0.987461i	$0.449540\pi$
$710$			3.28661e14i			1.82161i
$711$	−8.13121e13			−0.447515
$712$	−1.77417e13			−0.0969607
$713$	1.84156e14			0.999400
$714$		−	8.11749e14i		−	4.37452i
$715$			5.47724e13i			0.293110i
$716$		−	1.86037e14i		−	0.988632i
$717$			2.43612e14i			1.28559i
$718$		−	3.00671e14i		−	1.57568i
$719$	1.57454e14			0.819424			0.409712	−	0.912215i	$-0.365629\pi$
$719$	1.57454e14			0.819424			0.409712	+	0.912215i	$0.365629\pi$
$720$			1.90831e14i			0.986250i
$721$		−	2.55026e14i		−	1.30891i
$722$		−	2.80363e14i		−	1.42901i
$723$	5.48063e13			0.277421
$724$	2.30983e14			1.16115
$725$		−	2.41188e13i		−	0.120411i
$726$	−3.58666e14			−1.77831
$727$		−	8.96966e13i		−	0.441676i	−0.975310	−	0.220838i	$-0.929121\pi$
$727$		−	8.96966e13i		−	0.441676i	0.975310	−	0.220838i	$-0.0708793\pi$
$728$	−3.08342e13			−0.150791
$729$	3.15524e14			1.53248
$730$		−	3.62716e14i		−	1.74965i
$731$	−1.81709e14	−	2.05460e14i	−0.870541	−	0.984327i
$732$	−2.14413e14			−1.02022
$733$		−	2.97971e14i		−	1.40817i	−0.710116	−	0.704084i	$-0.751358\pi$
$733$		−	2.97971e14i		−	1.40817i	0.710116	−	0.704084i	$-0.248642\pi$
$734$			3.06205e14i			1.43725i
$735$	3.34838e14			1.56098
$736$		−	3.45122e14i		−	1.59802i
$737$	5.36990e13			0.246961
$738$			3.66302e14i			1.67324i
$739$		−	1.09759e13i		−	0.0497987i	−0.999690	−	0.0248994i	$-0.992073\pi$
$739$		−	1.09759e13i		−	0.0497987i	0.999690	−	0.0248994i	$-0.00792653\pi$
$740$	−1.32866e14			−0.598763
$741$	2.84377e13			0.127293
$742$	−7.39501e14			−3.28791
$743$			1.78778e14i			0.789533i	0.918781	+	0.394766i	$0.129175\pi$
$743$			1.78778e14i			0.789533i	−0.918781	+	0.394766i	$0.870825\pi$
$744$	3.81917e13			0.167534
$745$	2.78945e14			1.21545
$746$	−5.32948e13			−0.230670
$747$	4.13417e14			1.77740
$748$	1.47779e14			0.631108
$749$			3.85626e14i			1.63590i
$750$			5.71353e14i			2.40768i
$751$			1.49336e14i			0.625121i	0.949898	+	0.312561i	$0.101187\pi$
$751$			1.49336e14i			0.625121i	−0.949898	+	0.312561i	$0.898813\pi$
$752$	−8.13440e13			−0.338249
$753$		−	2.07473e14i		−	0.857012i
$754$	−9.91624e13			−0.406902
$755$	−1.82431e14			−0.743641
$756$	−2.14716e14			−0.869470
$757$		−	2.40950e14i		−	0.969278i	−0.874714	−	0.484639i	$-0.838951\pi$
$757$		−	2.40950e14i		−	0.969278i	0.874714	−	0.484639i	$-0.161049\pi$
$758$		−	5.57865e13i		−	0.222938i
$759$		−	1.90544e14i		−	0.756462i
$760$			2.51922e12i			0.00993570i
$761$			1.15549e13i			0.0452735i	0.999744	+	0.0226367i	$0.00720611\pi$
$761$			1.15549e13i			0.0452735i	−0.999744	+	0.0226367i	$0.992794\pi$
$762$	1.06709e15			4.15363
$763$			7.56286e14i			2.92458i
$764$			6.01323e13i			0.231015i
$765$			3.73798e14i			1.42669i
$766$	1.73243e11			0.000656919
$767$	−4.15721e14			−1.56612
$768$			3.31718e14i			1.24155i
$769$	2.51778e13			0.0936237			0.0468118	−	0.998904i	$-0.485094\pi$
$769$	2.51778e13			0.0936237			0.0468118	+	0.998904i	$0.485094\pi$
$770$			2.09816e14i			0.775149i
$771$	−6.09319e13			−0.223652
$772$	−4.98903e14			−1.81941
$773$		−	4.49217e13i		−	0.162764i	−0.996683	−	0.0813821i	$-0.974067\pi$
$773$		−	4.49217e13i		−	0.162764i	0.996683	−	0.0813821i	$-0.0259334\pi$
$774$	−4.04879e14	+	3.58076e14i	−1.45754	+	1.28905i
$775$	−8.79766e13			−0.314673
$776$			2.66091e13i			0.0945631i
$777$			4.47546e14i			1.58027i
$778$	4.31156e14			1.51264
$779$		−	2.49454e13i		−	0.0869567i
$780$	3.17524e14			1.09978
$781$			2.01541e14i			0.693597i
$782$		−	6.18502e14i		−	2.11499i
$783$	−5.37895e13			−0.182763
$784$	3.40257e14			1.14875
$785$	−2.96174e14			−0.993570
$786$			5.03559e14i			1.67856i
$787$	5.27561e14			1.74743			0.873713	−	0.486442i	$-0.161705\pi$
$787$	5.27561e14			1.74743			0.873713	+	0.486442i	$0.161705\pi$
$788$	1.33325e13			0.0438813
$789$	−8.21639e14			−2.68717
$790$	1.18841e14			0.386216
$791$	−1.89438e14			−0.611766
$792$		−	2.26845e13i		−	0.0727954i
$793$		−	1.58183e14i		−	0.504422i
$794$			3.62778e14i			1.14958i
$795$	5.93202e14			1.86796
$796$		−	2.21337e14i		−	0.692610i
$797$	−2.94350e12			−0.00915319			−0.00457660	−	0.999990i	$-0.501457\pi$
$797$	−2.94350e12			−0.00915319			−0.00457660	+	0.999990i	$0.501457\pi$
$798$	1.08936e14			0.336633
$799$	−1.59336e14			−0.489305
$800$			1.64874e14i			0.503156i
$801$		−	3.53278e14i		−	1.07141i
$802$		−	4.86332e14i		−	1.46575i
$803$		−	2.22424e14i		−	0.666198i
$804$		−	3.11302e14i		−	0.926619i
$805$	4.56869e14			1.35149
$806$			3.61709e14i			1.06337i
$807$		−	8.51103e14i		−	2.48665i
$808$		−	2.87967e13i		−	0.0836154i
$809$	2.90862e14			0.839352			0.419676	−	0.907674i	$-0.362144\pi$
$809$	2.90862e14			0.839352			0.419676	+	0.907674i	$0.362144\pi$
$810$	−2.15505e14			−0.618062
$811$			2.22538e14i			0.634309i	0.948374	+	0.317154i	$0.102727\pi$
$811$			2.22538e14i			0.634309i	−0.948374	+	0.317154i	$0.897273\pi$
$812$	−1.97628e14			−0.559844
$813$			7.83595e14i			2.20617i
$814$	−1.56605e14			−0.438210
$815$	−3.54747e14			−0.986577
$816$			6.61694e14i			1.82897i
$817$	2.75725e13	−	2.43852e13i	0.0757470	−	0.0669909i
$818$	6.17866e14			1.68705
$819$		−	6.13979e14i		−	1.66623i
$820$		−	2.78531e14i		−	0.751283i
$821$	−5.96467e14			−1.59908			−0.799541	−	0.600611i	$-0.794924\pi$
$821$	−5.96467e14			−1.59908			−0.799541	+	0.600611i	$0.794924\pi$
$822$			5.93448e14i			1.58133i
$823$	1.08070e14			0.286225			0.143112	−	0.989706i	$-0.454289\pi$
$823$	1.08070e14			0.286225			0.143112	+	0.989706i	$0.454289\pi$
$824$		−	4.02982e13i		−	0.106084i
$825$			9.10283e13i			0.238181i
$826$	−1.59250e15			−4.14170
$827$	2.13035e14			0.550711			0.275356	−	0.961342i	$-0.411204\pi$
$827$	2.13035e14			0.550711			0.275356	+	0.961342i	$0.411204\pi$
$828$	−6.34109e14			−1.62934
$829$		−	1.56752e14i		−	0.400352i	−0.979760	−	0.200176i	$-0.935849\pi$
$829$		−	1.56752e14i		−	0.400352i	0.979760	−	0.200176i	$-0.0641514\pi$
$830$	−6.04226e14			−1.53394
$831$	−6.30364e14			−1.59069
$832$	3.80339e14			0.954012
$833$	6.66491e14			1.66176
$834$	−6.73124e13			−0.166826
$835$			3.43889e13i			0.0847200i
$836$			1.98318e13i			0.0485658i
$837$			1.96205e14i			0.477619i
$838$	−8.57266e14			−2.07441
$839$		−	6.72146e14i		−	1.61679i	−0.588640	−	0.808395i	$-0.700336\pi$
$839$		−	6.72146e14i		−	1.61679i	0.588640	−	0.808395i	$-0.299664\pi$
$840$	9.47487e13			0.226557
$841$	3.71199e14			0.882320
$842$	9.37070e14			2.21417
$843$		−	6.22878e14i		−	1.46307i
$844$		−	4.06550e14i		−	0.949296i
$845$		−	1.12806e14i		−	0.261847i
$846$			3.13987e14i			0.724536i
$847$		−	5.27352e14i		−	1.20972i
$848$	6.02802e14			1.37466
$849$		−	9.66798e14i		−	2.19178i
$850$			2.95476e14i			0.665928i
$851$			3.41002e14i			0.764028i
$852$	1.16836e15			2.60244
$853$	1.54715e14			0.342601			0.171300	−	0.985219i	$-0.445203\pi$
$853$	1.54715e14			0.342601			0.171300	+	0.985219i	$0.445203\pi$
$854$		−	6.05951e14i		−	1.33398i
$855$	−5.01634e13			−0.109788
$856$			6.09352e13i			0.132586i
$857$	1.30387e14			0.282052			0.141026	−	0.990006i	$-0.454960\pi$
$857$	1.30387e14			0.282052			0.141026	+	0.990006i	$0.454960\pi$
$858$	3.74255e14			0.804881
$859$			2.82035e13i			0.0603027i	0.999545	+	0.0301513i	$0.00959893\pi$
$859$			2.82035e13i			0.0603027i	−0.999545	+	0.0301513i	$0.990401\pi$
$860$	3.07864e14	−	2.72276e14i	0.654435	−	0.578784i
$861$	−9.38204e14			−1.98281
$862$			2.12659e14i			0.446836i
$863$		−	5.28391e14i		−	1.10383i	−0.833901	−	0.551914i	$-0.813898\pi$
$863$		−	5.28391e14i		−	1.10383i	0.833901	−	0.551914i	$-0.186102\pi$
$864$	3.67701e14			0.763706
$865$			4.47868e14i			0.924847i
$866$	−4.65205e14			−0.955113
$867$			5.45504e14i			1.11353i
$868$			7.20874e14i			1.46306i
$869$	7.28752e13			0.147055
$870$	3.04711e14			0.611352
$871$	2.29663e14			0.458142
$872$			1.19505e14i			0.237031i
$873$	−5.29848e14			−1.04491
$874$	8.30025e13			0.162755
$875$	−8.40068e14			−1.63785
$876$	−1.28943e15			−2.49963
$877$	−4.15573e14			−0.801030			−0.400515	−	0.916290i	$-0.631169\pi$
$877$	−4.15573e14			−0.801030			−0.400515	+	0.916290i	$0.631169\pi$
$878$		−	1.21619e14i		−	0.233092i
$879$			8.29464e14i			1.58071i
$880$		−	1.71031e14i		−	0.324086i
$881$	8.88986e14			1.67500			0.837501	−	0.546436i	$-0.184016\pi$
$881$	8.88986e14			1.67500			0.837501	+	0.546436i	$0.184016\pi$
$882$		−	1.31339e15i		−	2.46065i
$883$	9.80960e14			1.82746			0.913729	−	0.406323i	$-0.133189\pi$
$883$	9.80960e14			1.82746			0.913729	+	0.406323i	$0.133189\pi$
$884$	6.32029e14			1.17078
$885$	1.27745e15			2.35302
$886$			4.04843e14i			0.741511i
$887$		−	6.46997e14i		−	1.17838i	−0.807995	−	0.589189i	$-0.799447\pi$
$887$		−	6.46997e14i		−	1.17838i	0.807995	−	0.589189i	$-0.200553\pi$
$888$			7.07195e13i			0.128078i
$889$			1.56896e15i			2.82555i
$890$			5.16329e14i			0.924648i
$891$	−1.32151e14			−0.235333
$892$		−	1.22266e14i		−	0.216511i
$893$		−	2.13827e13i		−	0.0376535i
$894$		−	1.90601e15i		−	3.33762i
$895$	−4.21745e14			−0.734403
$896$	2.11228e14			0.365773
$897$		−	8.14931e14i		−	1.40333i
$898$	−1.04159e15			−1.78367
$899$			1.80590e14i			0.307535i
$900$	3.02931e14			0.513017
$901$	1.18076e15			1.98856
$902$		−	3.28295e14i		−	0.549834i
$903$	−9.17134e14	−	1.03701e15i	−1.52755	−	1.72721i
$904$	−2.99343e13			−0.0495824
$905$		−	5.23636e14i		−	0.862554i
$906$			1.24654e15i			2.04204i
$907$	4.23106e14			0.689308			0.344654	−	0.938730i	$-0.387996\pi$
$907$	4.23106e14			0.689308			0.344654	+	0.938730i	$0.387996\pi$
$908$		−	9.28723e13i		−	0.150472i
$909$	5.73408e14			0.923941
$910$			8.97353e14i			1.43799i
$911$		−	4.15578e14i		−	0.662310i	−0.943576	−	0.331155i	$-0.892562\pi$
$911$		−	4.15578e14i		−	0.662310i	0.943576	−	0.331155i	$-0.107438\pi$
$912$	−8.87988e13			−0.140745
$913$	−3.70522e14			−0.584063
$914$	−3.14748e14			−0.493437
$915$			4.86072e14i			0.757871i
$916$	7.31356e14			1.13410
$917$	−7.40390e14			−1.14186
$918$	6.58967e14			1.01076
$919$	7.66389e14			1.16915			0.584577	−	0.811338i	$-0.301261\pi$
$919$	7.66389e14			1.16915			0.584577	+	0.811338i	$0.301261\pi$
$920$	7.21926e13			0.109535
$921$			7.33012e14i			1.10615i
$922$			1.07872e15i			1.61902i
$923$			8.61961e14i			1.28670i
$924$	7.45879e14			1.10741
$925$		−	1.62906e14i		−	0.240563i
$926$	−1.71252e15			−2.51525
$927$	8.02429e14			1.17222
$928$	3.38438e14			0.491744
$929$			1.11731e15i			1.61471i	0.590067	+	0.807354i	$0.299101\pi$
$929$			1.11731e15i			1.61471i	−0.590067	+	0.807354i	$0.700899\pi$
$930$		−	1.11147e15i		−	1.59766i
$931$			8.94425e13i			0.127878i
$932$			6.32640e14i			0.899658i
$933$		−	1.58907e15i		−	2.24769i
$934$	−1.33796e15			−1.88239
$935$		−	3.35013e14i		−	0.468817i
$936$		−	9.70185e13i		−	0.135044i
$937$			1.30507e12i			0.00180690i	1.00000		0.000903450i	$0.000287577\pi$
$937$			1.30507e12i			0.00180690i	−1.00000		0.000903450i	$0.999712\pi$
$938$	8.79768e14			1.21158
$939$	−1.69231e15			−2.31821
$940$		−	2.38751e14i		−	0.325317i
$941$	7.08175e14			0.959826			0.479913	−	0.877316i	$-0.340668\pi$
$941$	7.08175e14			0.959826			0.479913	+	0.877316i	$0.340668\pi$
$942$			2.02373e15i			2.72834i
$943$	−7.14853e14			−0.958646
$944$	1.29812e15			1.73163
$945$			4.86759e14i			0.645884i
$946$	3.62869e14	−	3.20922e14i	0.478954	−	0.423588i
$947$	6.64127e14			0.871969			0.435985	−	0.899954i	$-0.356400\pi$
$947$	6.64127e14			0.871969			0.435985	+	0.899954i	$0.356400\pi$
$948$		−	4.22470e14i		−	0.551765i
$949$		−	9.51274e14i		−	1.23588i
$950$	−3.96526e13			−0.0512452
$951$			5.95418e14i			0.765455i
$952$	1.88596e14			0.241184
$953$			3.18745e14i			0.405489i	0.979232	+	0.202745i	$0.0649861\pi$
$953$			3.18745e14i			0.405489i	−0.979232	+	0.202745i	$0.935014\pi$
$954$		−	2.32681e15i		−	2.94455i
$955$	1.36319e14			0.171609
$956$	−7.26593e14			−0.909917
$957$	1.86854e14			0.232778
$958$			2.31110e14i			0.286412i
$959$	−8.72554e14			−1.07572
$960$	−1.16872e15			−1.43336
$961$	−1.60902e14			−0.196311
$962$	−6.69775e14			−0.812931
$963$	−1.21336e15			−1.46507
$964$			1.63464e14i			0.196353i
$965$			1.13101e15i			1.35154i
$966$		−	3.12175e15i		−	3.71118i
$967$	1.28449e15			1.51914			0.759570	−	0.650425i	$-0.225409\pi$
$967$	1.28449e15			1.51914			0.759570	+	0.650425i	$0.225409\pi$
$968$		−	8.33301e13i		−	0.0980449i
$969$	−1.73938e14			−0.203599
$970$	7.74392e14			0.901784
$971$	−1.67405e14			−0.193942			−0.0969711	−	0.995287i	$-0.530915\pi$
$971$	−1.67405e14			−0.193942			−0.0969711	+	0.995287i	$0.530915\pi$
$972$			1.26739e15i			1.46076i
$973$		−	9.89703e13i		−	0.113486i
$974$		−	2.16407e15i		−	2.46875i
$975$			3.89315e14i			0.441853i
$976$			4.93938e14i			0.557730i
$977$	−7.53068e14			−0.845983			−0.422991	−	0.906134i	$-0.639020\pi$
$977$	−7.53068e14			−0.845983			−0.422991	+	0.906134i	$0.639020\pi$
$978$			2.42396e15i			2.70914i
$979$			3.16622e14i			0.352069i
$980$			9.98681e14i			1.10483i
$981$	−2.37962e15			−2.61916
$982$	2.20329e15			2.41277
$983$		−	6.84141e13i		−	0.0745380i	−0.999305	−	0.0372690i	$-0.988134\pi$
$983$		−	6.84141e13i		−	0.0745380i	0.999305	−	0.0372690i	$-0.0118658\pi$
$984$	−1.48251e14			−0.160703
$985$		−	3.02246e13i		−	0.0325972i
$986$	6.06523e14			0.650823
$987$	−8.04211e14			−0.858587
$988$			8.48177e13i			0.0900952i
$989$	−6.98799e14	−	7.90137e14i	−0.738535	−	0.835067i
$990$	−6.60177e14			−0.694200
$991$			2.94800e14i			0.308432i	0.988037	+	0.154216i	$0.0492852\pi$
$991$			2.94800e14i			0.308432i	−0.988037	+	0.154216i	$0.950715\pi$
$992$		−	1.23450e15i		−	1.28509i
$993$	−1.05616e15			−1.09392
$994$			3.30191e15i			3.40277i
$995$	−5.01769e14			−0.514504
$996$			2.14797e15i			2.19145i
$997$		−	1.12900e12i		−	0.00114609i	−1.00000		0.000573046i	$-0.999818\pi$
$997$		−	1.12900e12i		−	0.00114609i	1.00000		0.000573046i	$-0.000182406\pi$
$998$	2.42582e14			0.245023
$999$	−3.63312e14			−0.365134

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.b.b.42.5	✓	34
43.42	odd	2	inner	43.11.b.b.42.30	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.b.b.42.5	✓	34	1.1	even	1	trivial
43.11.b.b.42.30	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)

\(f(q)\)	\(=\)	\(q-46.2007i q^{2} +372.330i q^{3} -1110.50 q^{4} +2517.50i q^{5} +17201.9 q^{6} +25292.2i q^{7} +3996.58i q^{8} -79580.9 q^{9} +O(q^{10})\)	\(q-46.2007i q^{2} +372.330i q^{3} -1110.50 q^{4} +2517.50i q^{5} +17201.9 q^{6} +25292.2i q^{7} +3996.58i q^{8} -79580.9 q^{9} +116310. q^{10} +71323.6 q^{11} -413475. i q^{12} +305041. q^{13} +1.16852e6 q^{14} -937343. q^{15} -952512. q^{16} -1.86577e6 q^{17} +3.67669e6i q^{18} -250385. i q^{19} -2.79570e6i q^{20} -9.41705e6 q^{21} -3.29520e6i q^{22} -7.17521e6 q^{23} -1.48805e6 q^{24} +3.42780e6 q^{25} -1.40931e7i q^{26} -7.64463e6i q^{27} -2.80871e7i q^{28} -7.03624e6i q^{29} +4.33059e7i q^{30} -2.56657e7 q^{31} +4.80992e7i q^{32} +2.65559e7i q^{33} +8.61999e7i q^{34} -6.36732e7 q^{35} +8.83749e7 q^{36} -4.75251e7i q^{37} -1.15680e7 q^{38} +1.13576e8i q^{39} -1.00614e7 q^{40} +9.96282e7 q^{41} +4.35074e8i q^{42} +(9.73908e7 + 1.10120e8i) q^{43} -7.92052e7 q^{44} -2.00345e8i q^{45} +3.31500e8i q^{46} +8.53994e7 q^{47} -3.54649e8i q^{48} -3.57220e8 q^{49} -1.58367e8i q^{50} -6.94683e8i q^{51} -3.38749e8 q^{52} -6.32854e8 q^{53} -3.53187e8 q^{54} +1.79557e8i q^{55} -1.01082e8 q^{56} +9.32259e7 q^{57} -3.25079e8 q^{58} -1.36284e9 q^{59} +1.04092e9 q^{60} -5.18564e8i q^{61} +1.18577e9i q^{62} -2.01278e9i q^{63} +1.24685e9 q^{64} +7.67942e8i q^{65} +1.22690e9 q^{66} +7.52892e8 q^{67} +2.07195e9 q^{68} -2.67155e9i q^{69} +2.94175e9i q^{70} +2.82572e9i q^{71} -3.18051e8i q^{72} -3.11851e9i q^{73} -2.19569e9 q^{74} +1.27627e9i q^{75} +2.78053e8i q^{76} +1.80393e9i q^{77} +5.24729e9 q^{78} +1.02175e9 q^{79} -2.39795e9i q^{80} -1.85284e9 q^{81} -4.60289e9i q^{82} -5.19494e9 q^{83} +1.04577e10 q^{84} -4.69709e9i q^{85} +(5.08764e9 - 4.49952e9i) q^{86} +2.61980e9 q^{87} +2.85050e8i q^{88} +4.43923e9i q^{89} -9.25609e9 q^{90} +7.71516e9i q^{91} +7.96810e9 q^{92} -9.55610e9i q^{93} -3.94551e9i q^{94} +6.30345e8 q^{95} -1.79088e10 q^{96} +6.65798e9 q^{97} +1.65038e10i q^{98} -5.67599e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9}+O(q^{10}) \) 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

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