LMFDB - Embedded newform 43.11.b.b.42.24

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			42.24
Character	$\chi$	$=$	43.42
Dual form			43.11.b.b.42.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+29.9454i q^{2} -271.957i q^{3} +127.271 q^{4} +203.516i q^{5} +8143.86 q^{6} +3479.85i q^{7} +34475.3i q^{8} -14911.3 q^{9} +O(q^{10})$	\(q+29.9454i q^{2} -271.957i q^{3} +127.271 q^{4} +203.516i q^{5} +8143.86 q^{6} +3479.85i q^{7} +34475.3i q^{8} -14911.3 q^{9} -6094.37 q^{10} -186733. q^{11} -34612.1i q^{12} +180877. q^{13} -104206. q^{14} +55347.4 q^{15} -902053. q^{16} +2.31205e6 q^{17} -446527. i q^{18} +1.81781e6i q^{19} +25901.6i q^{20} +946367. q^{21} -5.59179e6i q^{22} +3.25182e6 q^{23} +9.37578e6 q^{24} +9.72421e6 q^{25} +5.41644e6i q^{26} -1.20035e7i q^{27} +442883. i q^{28} -1.93209e6i q^{29} +1.65740e6i q^{30} +1.24335e7 q^{31} +8.29034e6i q^{32} +5.07832e7i q^{33} +6.92353e7i q^{34} -708204. q^{35} -1.89778e6 q^{36} +1.29307e8i q^{37} -5.44351e7 q^{38} -4.91907e7i q^{39} -7.01627e6 q^{40} +5.75466e7 q^{41} +2.83394e7i q^{42} +(-8.81905e7 + 1.17618e8i) q^{43} -2.37656e7 q^{44} -3.03469e6i q^{45} +9.73771e7i q^{46} +2.19743e8 q^{47} +2.45319e8i q^{48} +2.70366e8 q^{49} +2.91196e8i q^{50} -6.28776e8i q^{51} +2.30204e7 q^{52} +2.24365e8 q^{53} +3.59451e8 q^{54} -3.80030e7i q^{55} -1.19969e8 q^{56} +4.94366e8 q^{57} +5.78574e7 q^{58} +4.63656e8 q^{59} +7.04411e6 q^{60} -1.32372e9i q^{61} +3.72327e8i q^{62} -5.18892e7i q^{63} -1.17196e9 q^{64} +3.68113e7i q^{65} -1.52072e9 q^{66} -9.00383e8 q^{67} +2.94256e8 q^{68} -8.84353e8i q^{69} -2.12075e7i q^{70} +5.54119e8i q^{71} -5.14073e8i q^{72} +2.21796e9i q^{73} -3.87215e9 q^{74} -2.64456e9i q^{75} +2.31354e8i q^{76} -6.49801e8i q^{77} +1.47304e9 q^{78} +1.15303e9 q^{79} -1.83582e8i q^{80} -4.14494e9 q^{81} +1.72326e9i q^{82} +1.02782e9 q^{83} +1.20445e8 q^{84} +4.70538e8i q^{85} +(-3.52211e9 - 2.64090e9i) q^{86} -5.25445e8 q^{87} -6.43767e9i q^{88} -6.93215e9i q^{89} +9.08752e7 q^{90} +6.29425e8i q^{91} +4.13861e8 q^{92} -3.38138e9i q^{93} +6.58031e9i q^{94} -3.69953e8 q^{95} +2.25461e9 q^{96} +9.01632e9 q^{97} +8.09623e9i q^{98} +2.78443e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			29.9454i			0.935795i	0.883783	+	0.467897i	$0.154988\pi$
$2$			29.9454i			0.935795i	−0.883783	+	0.467897i	$0.845012\pi$
$3$		−	271.957i		−	1.11916i	−0.828775	−	0.559581i	$-0.810962\pi$
$3$		−	271.957i		−	1.11916i	0.828775	−	0.559581i	$-0.189038\pi$
$4$	127.271			0.124288
$5$			203.516i			0.0651250i	0.999470	+	0.0325625i	$0.0103668\pi$
$5$			203.516i			0.0651250i	−0.999470	+	0.0325625i	$0.989633\pi$
$6$	8143.86			1.04731
$7$			3479.85i			0.207048i	0.994627	+	0.103524i	$0.0330118\pi$
$7$			3479.85i			0.207048i	−0.994627	+	0.103524i	$0.966988\pi$
$8$			34475.3i			1.05210i
$9$	−14911.3			−0.252525
$10$	−6094.37			−0.0609437
$11$	−186733.			−1.15946			−0.579731	−	0.814808i	$-0.696843\pi$
$11$	−186733.			−1.15946			−0.579731	+	0.814808i	$0.696843\pi$
$12$		−	34612.1i		−	0.139098i
$13$	180877.			0.487155			0.243577	−	0.969881i	$-0.421679\pi$
$13$	180877.			0.487155			0.243577	+	0.969881i	$0.421679\pi$
$14$	−104206.			−0.193754
$15$	55347.4			0.0728855
$16$	−902053.			−0.860265
$17$	2.31205e6			1.62837			0.814183	−	0.580608i	$-0.197185\pi$
$17$	2.31205e6			1.62837			0.814183	+	0.580608i	$0.197185\pi$
$18$		−	446527.i		−	0.236311i
$19$			1.81781e6i			0.734143i	0.930193	+	0.367072i	$0.119640\pi$
$19$			1.81781e6i			0.734143i	−0.930193	+	0.367072i	$0.880360\pi$
$20$			25901.6i			0.00809425i
$21$	946367.			0.231720
$22$		−	5.59179e6i		−	1.08502i
$23$	3.25182e6			0.505227			0.252614	−	0.967567i	$-0.418710\pi$
$23$	3.25182e6			0.505227			0.252614	+	0.967567i	$0.418710\pi$
$24$	9.37578e6			1.17747
$25$	9.72421e6			0.995759
$26$			5.41644e6i			0.455877i
$27$		−	1.20035e7i		−	0.836546i
$28$			442883.i			0.0257335i
$29$		−	1.93209e6i		−	0.0941972i	−0.998890	−	0.0470986i	$-0.985002\pi$
$29$		−	1.93209e6i		−	0.0941972i	0.998890	−	0.0470986i	$-0.0149975\pi$
$30$			1.65740e6i			0.0682059i
$31$	1.24335e7			0.434296			0.217148	−	0.976139i	$-0.430325\pi$
$31$	1.24335e7			0.434296			0.217148	+	0.976139i	$0.430325\pi$
$32$			8.29034e6i			0.247071i
$33$			5.07832e7i			1.29763i
$34$			6.92353e7i			1.52382i
$35$	−708204.			−0.0134840
$36$	−1.89778e6			−0.0313858
$37$			1.29307e8i			1.86472i	0.361535	+	0.932359i	$0.382253\pi$
$37$			1.29307e8i			1.86472i	−0.361535	+	0.932359i	$0.617747\pi$
$38$	−5.44351e7			−0.687007
$39$		−	4.91907e7i		−	0.545205i
$40$	−7.01627e6			−0.0685182
$41$	5.75466e7			0.496707			0.248354	−	0.968669i	$-0.420111\pi$
$41$	5.75466e7			0.496707			0.248354	+	0.968669i	$0.420111\pi$
$42$			2.83394e7i			0.216842i
$43$	−8.81905e7	+	1.17618e8i	−0.599901	+	0.800075i
$43$	−8.81905e7	+	1.17618e8i	−0.599901	+	0.800075i
$44$	−2.37656e7			−0.144107
$45$		−	3.03469e6i		−	0.0164457i
$46$			9.73771e7i			0.472789i
$47$	2.19743e8			0.958134			0.479067	−	0.877778i	$-0.340975\pi$
$47$	2.19743e8			0.958134			0.479067	+	0.877778i	$0.340975\pi$
$48$			2.45319e8i			0.962776i
$49$	2.70366e8			0.957131
$50$			2.91196e8i			0.931826i
$51$		−	6.28776e8i		−	1.82241i
$52$	2.30204e7			0.0605474
$53$	2.24365e8			0.536508			0.268254	−	0.963348i	$-0.413553\pi$
$53$	2.24365e8			0.536508			0.268254	+	0.963348i	$0.413553\pi$
$54$	3.59451e8			0.782836
$55$		−	3.80030e7i		−	0.0755101i
$56$	−1.19969e8			−0.217835
$57$	4.94366e8			0.821625
$58$	5.78574e7			0.0881493
$59$	4.63656e8			0.648538			0.324269	−	0.945965i	$-0.394882\pi$
$59$	4.63656e8			0.648538			0.324269	+	0.945965i	$0.394882\pi$
$60$	7.04411e6			0.00905878
$61$		−	1.32372e9i		−	1.56729i	−0.621212	−	0.783643i	$-0.713359\pi$
$61$		−	1.32372e9i		−	1.56729i	0.621212	−	0.783643i	$-0.286641\pi$
$62$			3.72327e8i			0.406412i
$63$		−	5.18892e7i		−	0.0522846i
$64$	−1.17196e9			−1.09147
$65$			3.68113e7i			0.0317260i
$66$	−1.52072e9			−1.21431
$67$	−9.00383e8			−0.666888			−0.333444	−	0.942770i	$-0.608211\pi$
$67$	−9.00383e8			−0.666888			−0.333444	+	0.942770i	$0.608211\pi$
$68$	2.94256e8			0.202386
$69$		−	8.84353e8i		−	0.565432i
$70$		−	2.12075e7i		−	0.0126182i
$71$			5.54119e8i			0.307122i	0.988139	+	0.153561i	$0.0490742\pi$
$71$			5.54119e8i			0.307122i	−0.988139	+	0.153561i	$0.950926\pi$
$72$		−	5.14073e8i		−	0.265682i
$73$			2.21796e9i			1.06989i	0.844887	+	0.534944i	$0.179667\pi$
$73$			2.21796e9i			1.06989i	−0.844887	+	0.534944i	$0.820333\pi$
$74$	−3.87215e9			−1.74499
$75$		−	2.64456e9i		−	1.11442i
$76$			2.31354e8i			0.0912450i
$77$		−	6.49801e8i		−	0.240064i
$78$	1.47304e9			0.510200
$79$	1.15303e9			0.374718			0.187359	−	0.982292i	$-0.440007\pi$
$79$	1.15303e9			0.374718			0.187359	+	0.982292i	$0.440007\pi$
$80$		−	1.83582e8i		−	0.0560248i
$81$	−4.14494e9			−1.18876
$82$			1.72326e9i			0.464816i
$83$	1.02782e9			0.260931			0.130465	−	0.991453i	$-0.458353\pi$
$83$	1.02782e9			0.260931			0.130465	+	0.991453i	$0.458353\pi$
$84$	1.20445e8			0.0288000
$85$			4.70538e8i			0.106047i
$86$	−3.52211e9	−	2.64090e9i	−0.748706	−	0.561384i
$87$	−5.25445e8			−0.105422
$88$		−	6.43767e9i		−	1.21987i
$89$		−	6.93215e9i		−	1.24142i	−0.784041	−	0.620709i	$-0.786845\pi$
$89$		−	6.93215e9i		−	1.24142i	0.784041	−	0.620709i	$-0.213155\pi$
$90$	9.08752e7			0.0153898
$91$			6.29425e8i			0.100864i
$92$	4.13861e8			0.0627936
$93$		−	3.38138e9i		−	0.486047i
$94$			6.58031e9i			0.896617i
$95$	−3.69953e8			−0.0478111
$96$	2.25461e9			0.276513
$97$	9.01632e9			1.04996			0.524978	−	0.851116i	$-0.324074\pi$
$97$	9.01632e9			1.04996			0.524978	+	0.851116i	$0.324074\pi$
$98$			8.09623e9i			0.895679i
$99$	2.78443e9			0.292793
$100$	1.23761e9			0.123761
$101$	1.02554e9			0.0975768			0.0487884	−	0.998809i	$-0.484464\pi$
$101$	1.02554e9			0.0975768			0.0487884	+	0.998809i	$0.484464\pi$
$102$	1.88290e10			1.70540
$103$	−1.17742e10			−1.01566			−0.507828	−	0.861458i	$-0.669552\pi$
$103$	−1.17742e10			−1.01566			−0.507828	+	0.861458i	$0.669552\pi$
$104$			6.23579e9i			0.512537i
$105$			1.92601e8i			0.0150908i
$106$			6.71871e9i			0.502061i
$107$	−1.00033e10			−0.713222			−0.356611	−	0.934253i	$-0.616068\pi$
$107$	−1.00033e10			−0.713222			−0.356611	+	0.934253i	$0.616068\pi$
$108$		−	1.52770e9i		−	0.103973i
$109$	−2.28161e10			−1.48289			−0.741444	−	0.671015i	$-0.765858\pi$
$109$	−2.28161e10			−1.48289			−0.741444	+	0.671015i	$0.765858\pi$
$110$	1.13802e9			0.0706619
$111$	3.51658e10			2.08692
$112$		−	3.13901e9i		−	0.178116i
$113$			5.09756e9i			0.276675i	0.990385	+	0.138338i	$0.0441759\pi$
$113$			5.09756e9i			0.276675i	−0.990385	+	0.138338i	$0.955824\pi$
$114$			1.48040e10i			0.768873i
$115$			6.61796e8i			0.0329029i
$116$		−	2.45899e8i		−	0.0117076i
$117$	−2.69712e9			−0.123019
$118$			1.38844e10i			0.606899i
$119$			8.04557e9i			0.337149i
$120$			1.90812e9i			0.0766830i
$121$	8.93167e9			0.344354
$122$	3.96395e10			1.46666
$123$		−	1.56502e10i		−	0.555896i
$124$	1.58242e9			0.0539777
$125$			3.96649e9i			0.129974i
$126$	1.55384e9			0.0489277
$127$	−4.69853e10			−1.42214			−0.711072	−	0.703119i	$-0.751790\pi$
$127$	−4.69853e10			−1.42214			−0.711072	+	0.703119i	$0.751790\pi$
$128$		−	2.66055e10i		−	0.774323i
$129$	3.19869e10	+	2.39840e10i	0.895413	+	0.671386i
$130$	−1.10233e9			−0.0296890
$131$			4.29874e10i			1.11426i	0.830426	+	0.557128i	$0.188097\pi$
$131$			4.29874e10i			1.11426i	−0.830426	+	0.557128i	$0.811903\pi$
$132$			6.46321e9i			0.161279i
$133$	−6.32571e9			−0.152003
$134$		−	2.69624e10i		−	0.624071i
$135$	2.44291e9			0.0544801
$136$			7.97086e10i			1.71321i
$137$		−	3.02579e10i		−	0.626954i	−0.949596	−	0.313477i	$-0.898506\pi$
$137$		−	3.02579e10i		−	0.626954i	0.949596	−	0.313477i	$-0.101494\pi$
$138$	2.64823e10			0.529128
$139$	−6.74771e10			−1.30042			−0.650208	−	0.759756i	$-0.725318\pi$
$139$	−6.74771e10			−1.30042			−0.650208	+	0.759756i	$0.725318\pi$
$140$	−9.01336e7			−0.00167589
$141$		−	5.97606e10i		−	1.07231i
$142$	−1.65933e10			−0.287403
$143$	−3.37757e10			−0.564838
$144$	1.34508e10			0.217238
$145$	3.93211e8			0.00613460
$146$	−6.64176e10			−1.00120
$147$		−	7.35278e10i		−	1.07119i
$148$			1.64570e10i			0.231762i
$149$		−	6.07433e10i		−	0.827117i	−0.910478	−	0.413558i	$-0.864286\pi$
$149$		−	6.07433e10i		−	0.827117i	0.910478	−	0.413558i	$-0.135714\pi$
$150$	7.91925e10			1.04286
$151$			4.24289e10i			0.540477i	0.962793	+	0.270238i	$0.0871025\pi$
$151$			4.24289e10i			0.540477i	−0.962793	+	0.270238i	$0.912898\pi$
$152$	−6.26696e10			−0.772394
$153$	−3.44757e10			−0.411203
$154$	1.94586e10			0.224651
$155$			2.53042e9i			0.0282835i
$156$		−	6.26054e9i		−	0.0677624i
$157$		−	6.74501e10i		−	0.707105i	−0.935415	−	0.353553i	$-0.884973\pi$
$157$		−	6.74501e10i		−	0.707105i	0.935415	−	0.353553i	$-0.115027\pi$
$158$			3.45279e10i			0.350659i
$159$		−	6.10175e10i		−	0.600439i
$160$	−1.68721e9			−0.0160905
$161$			1.13158e10i			0.104606i
$162$		−	1.24122e11i		−	1.11243i
$163$		−	4.69429e10i		−	0.407973i	−0.978974	−	0.203987i	$-0.934610\pi$
$163$		−	4.69429e10i		−	0.407973i	0.978974	−	0.203987i	$-0.0653899\pi$
$164$	7.32400e9			0.0617346
$165$	−1.03352e10			−0.0845080
$166$			3.07784e10i			0.244178i
$167$	2.47736e10			0.190725			0.0953623	−	0.995443i	$-0.469599\pi$
$167$	2.47736e10			0.190725			0.0953623	+	0.995443i	$0.469599\pi$
$168$			3.26263e10i			0.243793i
$169$	−1.05142e11			−0.762680
$170$	−1.40905e10			−0.0992386
$171$		−	2.71060e10i		−	0.185389i
$172$	−1.12241e10	+	1.49693e10i	−0.0745603	+	0.0994395i
$173$	1.71294e11			1.10538			0.552690	−	0.833387i	$-0.313601\pi$
$173$	1.71294e11			1.10538			0.552690	+	0.833387i	$0.313601\pi$
$174$		−	1.57347e10i		−	0.0986534i
$175$			3.38388e10i			0.206169i
$176$	1.68443e11			0.997445
$177$		−	1.26094e11i		−	0.725820i
$178$	2.07586e11			1.16171
$179$		−	2.81260e11i		−	1.53054i	−0.643712	−	0.765268i	$-0.722606\pi$
$179$		−	2.81260e11i		−	1.53054i	0.643712	−	0.765268i	$-0.277394\pi$
$180$		−	3.86227e8i		−	0.00204400i
$181$	−9.21860e10			−0.474539			−0.237270	−	0.971444i	$-0.576252\pi$
$181$	−9.21860e10			−0.474539			−0.237270	+	0.971444i	$0.576252\pi$
$182$	−1.88484e10			−0.0943882
$183$	−3.59995e11			−1.75405
$184$			1.12107e11i			0.531551i
$185$	−2.63160e10			−0.121440
$186$	1.01257e11			0.454841
$187$	−4.31735e11			−1.88803
$188$	2.79669e10			0.119084
$189$	4.17704e10			0.173205
$190$		−	1.10784e10i		−	0.0447414i
$191$			1.41848e11i			0.558029i	0.960287	+	0.279015i	$0.0900078\pi$
$191$			1.41848e11i			0.558029i	−0.960287	+	0.279015i	$0.909992\pi$
$192$			3.18722e11i			1.22154i
$193$	3.49463e11			1.30501			0.652507	−	0.757783i	$-0.273717\pi$
$193$	3.49463e11			1.30501			0.652507	+	0.757783i	$0.273717\pi$
$194$			2.69998e11i			0.982543i
$195$	1.00111e10			0.0355065
$196$	3.44097e10			0.118960
$197$	−7.75830e10			−0.261478			−0.130739	−	0.991417i	$-0.541735\pi$
$197$	−7.75830e10			−0.261478			−0.130739	+	0.991417i	$0.541735\pi$
$198$			8.33811e10i			0.273994i
$199$			5.02411e11i			1.60988i	0.593356	+	0.804940i	$0.297803\pi$
$199$			5.02411e11i			1.60988i	−0.593356	+	0.804940i	$0.702197\pi$
$200$			3.35245e11i			1.04764i
$201$			2.44865e11i			0.746357i
$202$			3.07103e10i			0.0913119i
$203$	6.72339e9			0.0195033
$204$		−	8.00248e10i		−	0.226503i
$205$			1.17116e10i			0.0323481i
$206$		−	3.52585e11i		−	0.950446i
$207$	−4.84889e10			−0.127582
$208$	−1.63161e11			−0.419082
$209$		−	3.39445e11i		−	0.851212i
$210$	−5.76751e9			−0.0141219
$211$			6.06724e11i			1.45070i	0.688378	+	0.725352i	$0.258323\pi$
$211$			6.06724e11i			1.45070i	−0.688378	+	0.725352i	$0.741677\pi$
$212$	2.85551e10			0.0666814
$213$	1.50696e11			0.343720
$214$		−	2.99553e11i		−	0.667430i
$215$	−2.39370e10	−	1.79481e10i	−0.0521049	−	0.0390685i
$216$	4.13825e11			0.880133
$217$			4.32667e10i			0.0899199i
$218$		−	6.83237e11i		−	1.38768i
$219$	6.03187e11			1.19738
$220$		−	4.83667e9i		−	0.00938498i
$221$	4.18197e11			0.793266
$222$			1.05306e12i			1.95293i
$223$		−	3.47401e11i		−	0.629951i	−0.949100	−	0.314976i	$-0.898004\pi$
$223$		−	3.47401e11i		−	0.629951i	0.949100	−	0.314976i	$-0.101996\pi$
$224$	−2.88491e10			−0.0511555
$225$	−1.45001e11			−0.251454
$226$	−1.52649e11			−0.258911
$227$		−	2.92541e11i		−	0.485352i	−0.970107	−	0.242676i	$-0.921975\pi$
$227$		−	2.92541e11i		−	0.485352i	0.970107	−	0.242676i	$-0.0780252\pi$
$228$	6.29183e10			0.102118
$229$	3.34745e11			0.531540			0.265770	−	0.964036i	$-0.414374\pi$
$229$	3.34745e11			0.531540			0.265770	+	0.964036i	$0.414374\pi$
$230$	−1.98178e10			−0.0307904
$231$	−1.76718e11			−0.268671
$232$	6.66095e10			0.0991052
$233$		−	9.55518e11i		−	1.39142i	−0.718321	−	0.695711i	$-0.755089\pi$
$233$		−	9.55518e11i		−	1.39142i	0.718321	−	0.695711i	$-0.244911\pi$
$234$		−	8.07664e10i		−	0.115120i
$235$			4.47212e10i			0.0623985i
$236$	5.90098e10			0.0806054
$237$		−	3.13573e11i		−	0.419370i
$238$	−2.40928e11			−0.315503
$239$	1.01652e12			1.30355			0.651773	−	0.758414i	$-0.274026\pi$
$239$	1.01652e12			1.30355			0.651773	+	0.758414i	$0.274026\pi$
$240$	−4.99263e10			−0.0627008
$241$		−	4.87485e11i		−	0.599620i	−0.953999	−	0.299810i	$-0.903077\pi$
$241$		−	4.87485e11i		−	0.599620i	0.953999	−	0.299810i	$-0.0969233\pi$
$242$			2.67463e11i			0.322245i
$243$			4.18446e11i			0.493865i
$244$		−	1.68471e11i		−	0.194795i
$245$			5.50237e10i			0.0623332i
$246$	4.68651e11			0.520205
$247$			3.28800e11i			0.357641i
$248$			4.28649e11i			0.456924i
$249$		−	2.79521e11i		−	0.292024i
$250$	−1.18778e11			−0.121629
$251$	−1.82489e12			−1.83176			−0.915880	−	0.401453i	$-0.868505\pi$
$251$	−1.82489e12			−1.83176			−0.915880	+	0.401453i	$0.868505\pi$
$252$		−	6.60398e9i		−	0.00649834i
$253$	−6.07220e11			−0.585792
$254$		−	1.40700e12i		−	1.33084i
$255$	1.27966e11			0.118684
$256$	−4.03372e11			−0.366865
$257$		−	2.84410e11i		−	0.253676i	−0.991923	−	0.126838i	$-0.959517\pi$
$257$		−	2.84410e11i		−	0.253676i	0.991923	−	0.126838i	$-0.0404828\pi$
$258$	−7.18210e11	+	9.57862e11i	−0.628280	+	0.837923i
$259$	−4.49968e11			−0.386085
$260$			4.68500e9i			0.00394315i
$261$			2.88101e10i			0.0237871i
$262$	−1.28728e12			−1.04272
$263$		−	3.79504e11i		−	0.301604i	−0.988564	−	0.150802i	$-0.951814\pi$
$263$		−	3.79504e11i		−	0.301604i	0.988564	−	0.150802i	$-0.0481856\pi$
$264$	−1.75077e12			−1.36524
$265$			4.56618e10i			0.0349401i
$266$		−	1.89426e11i		−	0.142243i
$267$	−1.88524e12			−1.38935
$268$	−1.14592e11			−0.0828861
$269$	4.04745e11			0.287356			0.143678	−	0.989625i	$-0.454107\pi$
$269$	4.04745e11			0.287356			0.143678	+	0.989625i	$0.454107\pi$
$270$			7.31539e10i			0.0509822i
$271$	2.37135e12			1.62237			0.811183	−	0.584793i	$-0.198824\pi$
$271$	2.37135e12			1.62237			0.811183	+	0.584793i	$0.198824\pi$
$272$	−2.08559e12			−1.40083
$273$	1.71176e11			0.112883
$274$	9.06085e11			0.586700
$275$	−1.81583e12			−1.15455
$276$		−	1.12552e11i		−	0.0702763i
$277$			2.24997e12i			1.37968i	0.723964	+	0.689838i	$0.242318\pi$
$277$			2.24997e12i			1.37968i	−0.723964	+	0.689838i	$0.757682\pi$
$278$		−	2.02063e12i		−	1.21692i
$279$	−1.85400e11			−0.109670
$280$		−	2.44155e10i		−	0.0141865i
$281$	−7.18647e11			−0.410189			−0.205094	−	0.978742i	$-0.565750\pi$
$281$	−7.18647e11			−0.410189			−0.205094	+	0.978742i	$0.565750\pi$
$282$	1.78956e12			1.00346
$283$	2.12573e12			1.17105			0.585527	−	0.810653i	$-0.300888\pi$
$283$	2.12573e12			1.17105			0.585527	+	0.810653i	$0.300888\pi$
$284$			7.05231e10i			0.0381715i
$285$			1.00611e11i			0.0535084i
$286$		−	1.01143e12i		−	0.528572i
$287$			2.00253e11i			0.102842i
$288$		−	1.23620e11i		−	0.0623917i
$289$	3.32957e12			1.65158
$290$			1.17749e10i			0.00574072i
$291$		−	2.45205e12i		−	1.17507i
$292$			2.82281e11i			0.132974i
$293$	3.97847e12			1.84237			0.921187	−	0.389121i	$-0.127221\pi$
$293$	3.97847e12			1.84237			0.921187	+	0.389121i	$0.127221\pi$
$294$	2.20182e12			1.00241
$295$			9.43612e10i			0.0422361i
$296$	−4.45789e12			−1.96187
$297$			2.24145e12i			0.969944i
$298$	1.81898e12			0.774012
$299$	5.88179e11			0.246124
$300$		−	3.36575e11i		−	0.138508i
$301$	−4.09292e11	−	3.06889e11i	−0.165653	−	0.124208i
$302$	−1.27055e12			−0.505775
$303$		−	2.78903e11i		−	0.109204i
$304$		−	1.63976e12i		−	0.631557i
$305$	2.69399e11			0.102070
$306$		−	1.03239e12i		−	0.384802i
$307$	2.68118e11			0.0983183			0.0491591	−	0.998791i	$-0.484346\pi$
$307$	2.68118e11			0.0983183			0.0491591	+	0.998791i	$0.484346\pi$
$308$		−	8.27007e10i		−	0.0298370i
$309$			3.20208e12i			1.13668i
$310$	−7.57744e10			−0.0264676
$311$	−1.56641e12			−0.538399			−0.269199	−	0.963084i	$-0.586759\pi$
$311$	−1.56641e12			−0.538399			−0.269199	+	0.963084i	$0.586759\pi$
$312$	1.69586e12			0.573612
$313$			2.16661e11i			0.0721205i	0.999350	+	0.0360602i	$0.0114808\pi$
$313$			2.16661e11i			0.0721205i	−0.999350	+	0.0360602i	$0.988519\pi$
$314$	2.01982e12			0.661706
$315$	1.05603e10			0.00340504
$316$	1.46747e11			0.0465729
$317$	−4.92724e11			−0.153924			−0.0769622	−	0.997034i	$-0.524522\pi$
$317$	−4.92724e11			−0.153924			−0.0769622	+	0.997034i	$0.524522\pi$
$318$	1.82720e12			0.561888
$319$			3.60785e11i			0.109218i
$320$		−	2.38512e11i		−	0.0710822i
$321$			2.72046e12i			0.798211i
$322$	−3.38857e11			−0.0978898
$323$			4.20287e12i			1.19545i
$324$	−5.27529e11			−0.147748
$325$	1.75889e12			0.485089
$326$	1.40572e12			0.381779
$327$			6.20497e12i			1.65959i
$328$			1.98394e12i			0.522587i
$329$			7.64673e11i			0.198379i
$330$		−	3.09491e11i		−	0.0790822i
$331$		−	9.92385e11i		−	0.249770i	−0.992171	−	0.124885i	$-0.960144\pi$
$331$		−	9.92385e11i		−	0.249770i	0.992171	−	0.124885i	$-0.0398562\pi$
$332$	1.30811e11			0.0324305
$333$		−	1.92814e12i		−	0.470887i
$334$			7.41856e11i			0.178479i
$335$		−	1.83242e11i		−	0.0434311i
$336$	−8.53673e11			−0.199340
$337$	−5.53124e12			−1.27254			−0.636272	−	0.771465i	$-0.719524\pi$
$337$	−5.53124e12			−1.27254			−0.636272	+	0.771465i	$0.719524\pi$
$338$		−	3.14852e12i		−	0.713712i
$339$	1.38632e12			0.309645
$340$			5.98857e10i			0.0131804i
$341$	−2.32174e12			−0.503550
$342$	8.11701e11			0.173486
$343$			1.92380e12i			0.405219i
$344$	−4.05491e12	−	3.04039e12i	−0.841761	−	0.631157i
$345$	1.79980e11			0.0368237
$346$			5.12947e12i			1.03441i
$347$			1.35809e12i			0.269948i	0.990849	+	0.134974i	$0.0430951\pi$
$347$			1.35809e12i			0.269948i	−0.990849	+	0.134974i	$0.956905\pi$
$348$	−6.68738e10			−0.0131027
$349$			5.27222e12i			1.01828i	0.860684	+	0.509139i	$0.170036\pi$
$349$			5.27222e12i			1.01828i	−0.860684	+	0.509139i	$0.829964\pi$
$350$	−1.01332e12			−0.192932
$351$		−	2.17116e12i		−	0.407527i
$352$		−	1.54808e12i		−	0.286470i
$353$	−7.41122e12			−1.35212			−0.676062	−	0.736845i	$-0.736315\pi$
$353$	−7.41122e12			−1.35212			−0.676062	+	0.736845i	$0.736315\pi$
$354$	3.77595e12			0.679218
$355$	−1.12772e11			−0.0200013
$356$		−	8.82259e11i		−	0.154293i
$357$	2.18805e12			0.377325
$358$	8.42247e12			1.43227
$359$	−6.00592e12			−1.00718			−0.503591	−	0.863942i	$-0.667988\pi$
$359$	−6.00592e12			−1.00718			−0.503591	+	0.863942i	$0.667988\pi$
$360$	1.04622e11			0.0173026
$361$	2.82663e12			0.461034
$362$		−	2.76055e12i		−	0.444071i
$363$		−	2.42902e12i		−	0.385389i
$364$			8.01074e10i			0.0125362i
$365$	−4.51389e11			−0.0696765
$366$		−	1.07802e13i		−	1.64143i
$367$	9.10870e11			0.136813			0.0684063	−	0.997658i	$-0.478209\pi$
$367$	9.10870e11			0.136813			0.0684063	+	0.997658i	$0.478209\pi$
$368$	−2.93331e12			−0.434629
$369$	−8.58097e11			−0.125431
$370$		−	7.88043e11i		−	0.113643i
$371$			7.80756e11i			0.111083i
$372$		−	4.30350e11i		−	0.0604098i
$373$		−	1.18703e13i		−	1.64406i	−0.569443	−	0.822031i	$-0.692841\pi$
$373$		−	1.18703e13i		−	1.64406i	0.569443	−	0.822031i	$-0.307159\pi$
$374$		−	1.29285e13i		−	1.76681i
$375$	1.07871e12			0.145462
$376$			7.57572e12i			1.00806i
$377$		−	3.49471e11i		−	0.0458886i
$378$			1.25083e12i			0.162084i
$379$	6.13117e12			0.784056			0.392028	−	0.919953i	$-0.371774\pi$
$379$	6.13117e12			0.784056			0.392028	+	0.919953i	$0.371774\pi$
$380$	−4.70842e10			−0.00594234
$381$			1.27780e13i			1.59161i
$382$	−4.24771e12			−0.522201
$383$		−	1.63650e13i		−	1.98574i	−0.119205	−	0.992870i	$-0.538035\pi$
$383$		−	1.63650e13i		−	1.98574i	0.119205	−	0.992870i	$-0.461965\pi$
$384$	−7.23555e12			−0.866594
$385$	1.32245e11			0.0156342
$386$			1.04648e13i			1.22123i
$387$	1.31504e12	−	1.75384e12i	0.151490	−	0.202039i
$388$	1.14751e12			0.130497
$389$		−	7.49710e12i		−	0.841677i	−0.907136	−	0.420839i	$-0.861736\pi$
$389$		−	7.49710e12i		−	0.841677i	0.907136	−	0.420839i	$-0.138264\pi$
$390$			2.99786e11i			0.0332268i
$391$	7.51836e12			0.822695
$392$			9.32095e12i			1.00700i
$393$	1.16907e13			1.24703
$394$		−	2.32326e12i		−	0.244690i
$395$			2.34659e11i			0.0244035i
$396$	3.54377e11			0.0363906
$397$	−1.07340e13			−1.08845			−0.544227	−	0.838938i	$-0.683177\pi$
$397$	−1.07340e13			−1.08845			−0.544227	+	0.838938i	$0.683177\pi$
$398$	−1.50449e13			−1.50652
$399$			1.72032e12i			0.170116i
$400$	−8.77175e12			−0.856616
$401$	−8.46435e12			−0.816341			−0.408171	−	0.912906i	$-0.633833\pi$
$401$	−8.46435e12			−0.816341			−0.408171	+	0.912906i	$0.633833\pi$
$402$	−7.33259e12			−0.698437
$403$	2.24894e12			0.211569
$404$	1.30521e11			0.0121276
$405$		−	8.43560e11i		−	0.0774178i
$406$			2.01335e11i			0.0182511i
$407$		−	2.41458e13i		−	2.16207i
$408$	2.16773e13			1.91736
$409$		−	6.90427e12i		−	0.603255i	−0.953426	−	0.301628i	$-0.902470\pi$
$409$		−	6.90427e12i		−	0.603255i	0.953426	−	0.301628i	$-0.0975299\pi$
$410$	−3.50710e11			−0.0302711
$411$	−8.22882e12			−0.701663
$412$	−1.49852e12			−0.126234
$413$			1.61345e12i			0.134278i
$414$		−	1.45202e12i		−	0.119391i
$415$			2.09177e11i			0.0169931i
$416$			1.49953e12i			0.120362i
$417$			1.83508e13i			1.45538i
$418$	1.01648e13			0.796560
$419$		−	3.78990e12i		−	0.293466i	−0.989176	−	0.146733i	$-0.953124\pi$
$419$		−	3.78990e12i		−	0.293466i	0.989176	−	0.146733i	$-0.0468758\pi$
$420$			2.45124e10i			0.00187560i
$421$		−	2.61396e12i		−	0.197646i	−0.995105	−	0.0988229i	$-0.968492\pi$
$421$		−	2.61396e12i		−	0.197646i	0.995105	−	0.0988229i	$-0.0315077\pi$
$422$	−1.81686e13			−1.35756
$423$	−3.27667e12			−0.241953
$424$			7.73505e12i			0.564461i
$425$	2.24828e13			1.62146
$426$			4.51266e12i			0.321651i
$427$	4.60636e12			0.324503
$428$	−1.27313e12			−0.0886448
$429$			9.18551e12i			0.632145i
$430$	5.37465e11	−	7.16805e11i	0.0365601	−	0.0487595i
$431$	5.30690e12			0.356824			0.178412	−	0.983956i	$-0.442904\pi$
$431$	5.30690e12			0.356824			0.178412	+	0.983956i	$0.442904\pi$
$432$			1.08278e13i			0.719651i
$433$		−	9.50518e12i		−	0.624484i	−0.950003	−	0.312242i	$-0.898920\pi$
$433$		−	9.50518e12i		−	0.624484i	0.950003	−	0.312242i	$-0.101080\pi$
$434$	−1.29564e12			−0.0841465
$435$		−	1.06936e11i		−	0.00686561i
$436$	−2.90382e12			−0.184305
$437$			5.91119e12i			0.370909i
$438$			1.80627e13i			1.12050i
$439$	2.23920e13			1.37332			0.686658	−	0.726980i	$-0.259077\pi$
$439$	2.23920e13			1.37332			0.686658	+	0.726980i	$0.259077\pi$
$440$	1.31017e12			0.0794443
$441$	−4.03152e12			−0.241699
$442$			1.25231e13i			0.742335i
$443$	−1.73807e12			−0.101870			−0.0509352	−	0.998702i	$-0.516220\pi$
$443$	−1.73807e12			−0.101870			−0.0509352	+	0.998702i	$0.516220\pi$
$444$	4.47558e12			0.259379
$445$	1.41080e12			0.0808473
$446$	1.04031e13			0.589505
$447$	−1.65195e13			−0.925678
$448$		−	4.07824e12i		−	0.225987i
$449$			1.71473e13i			0.939647i	0.882760	+	0.469823i	$0.155682\pi$
$449$			1.71473e13i			0.939647i	−0.882760	+	0.469823i	$0.844318\pi$
$450$		−	4.34212e12i		−	0.235309i
$451$	−1.07458e13			−0.575913
$452$			6.48770e11i			0.0343874i
$453$	1.15388e13			0.604881
$454$	8.76025e12			0.454190
$455$	−1.28098e11			−0.00656878
$456$			1.70434e13i			0.864435i
$457$			2.13148e13i			1.06930i	0.845073	+	0.534651i	$0.179557\pi$
$457$			2.13148e13i			1.06930i	−0.845073	+	0.534651i	$0.820443\pi$
$458$			1.00241e13i			0.497413i
$459$		−	2.77527e13i		−	1.36220i
$460$			8.42272e10i			0.00408944i
$461$	−2.53916e13			−1.21951			−0.609754	−	0.792590i	$-0.708732\pi$
$461$	−2.53916e13			−1.21951			−0.609754	+	0.792590i	$0.708732\pi$
$462$		−	5.29189e12i		−	0.251421i
$463$		−	1.86225e13i		−	0.875254i	−0.899157	−	0.437627i	$-0.855819\pi$
$463$		−	1.86225e13i		−	0.875254i	0.899157	−	0.437627i	$-0.144181\pi$
$464$			1.74285e12i			0.0810346i
$465$	6.88163e11			0.0316539
$466$	2.86134e13			1.30209
$467$		−	2.68346e13i		−	1.20812i	−0.796938	−	0.604062i	$-0.793548\pi$
$467$		−	2.68346e13i		−	1.20812i	0.796938	−	0.604062i	$-0.206452\pi$
$468$	−3.43264e11			−0.0152897
$469$		−	3.13320e12i		−	0.138078i
$470$	−1.33920e12			−0.0583922
$471$	−1.83435e13			−0.791366
$472$			1.59847e13i			0.682329i
$473$	1.64680e13	−	2.19631e13i	0.695563	−	0.927657i
$474$	9.39009e12			0.392444
$475$			1.76768e13i			0.731029i
$476$			1.02397e12i			0.0419035i
$477$	−3.34558e12			−0.135482
$478$			3.04401e13i			1.21985i
$479$	−7.59261e12			−0.301102			−0.150551	−	0.988602i	$-0.548105\pi$
$479$	−7.59261e12			−0.301102			−0.150551	+	0.988602i	$0.548105\pi$
$480$			4.58849e11i			0.0180079i
$481$			2.33887e13i			0.908406i
$482$	1.45980e13			0.561121
$483$	3.07741e12			0.117071
$484$	1.13674e12			0.0427991
$485$			1.83496e12i			0.0683784i
$486$	−1.25306e13			−0.462156
$487$	−2.06304e13			−0.753116			−0.376558	−	0.926393i	$-0.622892\pi$
$487$	−2.06304e13			−0.753116			−0.376558	+	0.926393i	$0.622892\pi$
$488$	4.56358e13			1.64895
$489$	−1.27664e13			−0.456588
$490$	−1.64771e12			−0.0583311
$491$		−	5.74792e10i		−	0.00201420i	−0.999999	−	0.00100710i	$-0.999679\pi$
$491$		−	5.74792e10i		−	0.00201420i	0.999999	−	0.00100710i	$-0.000320570\pi$
$492$		−	1.99181e12i		−	0.0690911i
$493$		−	4.46709e12i		−	0.153388i
$494$	−9.84607e12			−0.334679
$495$			5.66676e11i			0.0190682i
$496$	−1.12157e13			−0.373609
$497$	−1.92825e12			−0.0635889
$498$	8.37039e12			0.273274
$499$			3.88299e13i			1.25506i	0.778594	+	0.627528i	$0.215933\pi$
$499$			3.88299e13i			1.25506i	−0.778594	+	0.627528i	$0.784067\pi$
$500$			5.04818e11i			0.0161542i
$501$		−	6.73734e12i		−	0.213452i
$502$		−	5.46472e13i		−	1.71415i
$503$		−	5.96465e13i		−	1.85244i	−0.376978	−	0.926222i	$-0.623037\pi$
$503$		−	5.96465e13i		−	1.85244i	0.376978	−	0.926222i	$-0.376963\pi$
$504$	1.78890e12			0.0550088
$505$			2.08714e11i			0.00635469i
$506$		−	1.81835e13i		−	0.548182i
$507$			2.85940e13i			0.853563i
$508$	−5.97986e12			−0.176755
$509$	9.68042e12			0.283338			0.141669	−	0.989914i	$-0.454753\pi$
$509$	9.68042e12			0.283338			0.141669	+	0.989914i	$0.454753\pi$
$510$			3.83199e12i			0.111064i
$511$	−7.71815e12			−0.221518
$512$		−	3.93232e13i		−	1.11763i
$513$	2.18201e13			0.614145
$514$	8.51677e12			0.237388
$515$		−	2.39624e12i		−	0.0661446i
$516$	4.07100e12	+	3.05246e12i	0.111289	+	0.0834451i
$517$	−4.10333e13			−1.11092
$518$		−	1.34745e13i		−	0.361297i
$519$		−	4.65845e13i		−	1.23710i
$520$	−1.26908e12			−0.0333790
$521$			2.61386e13i			0.680916i	0.940260	+	0.340458i	$0.110582\pi$
$521$			2.61386e13i			0.680916i	−0.940260	+	0.340458i	$0.889418\pi$
$522$	−8.62731e11			−0.0222599
$523$		−	4.15936e12i		−	0.106296i	−0.998587	−	0.0531482i	$-0.983074\pi$
$523$		−	4.15936e12i		−	0.106296i	0.998587	−	0.0531482i	$-0.0169256\pi$
$524$			5.47104e12i			0.138489i
$525$	9.20267e12			0.230737
$526$	1.13644e13			0.282239
$527$	2.87469e13			0.707193
$528$		−	4.58091e13i		−	1.11630i
$529$	−3.08522e13			−0.744745
$530$	−1.36736e12			−0.0326967
$531$	−6.91373e12			−0.163772
$532$	−8.05077e11			−0.0188921
$533$	1.04089e13			0.241973
$534$		−	5.64544e13i		−	1.30014i
$535$		−	2.03583e12i		−	0.0464486i
$536$		−	3.10410e13i		−	0.701635i
$537$	−7.64906e13			−1.71292
$538$			1.21203e13i			0.268906i
$539$	−5.04861e13			−1.10976
$540$	3.10910e11			0.00677121
$541$	2.48861e13			0.536995			0.268497	−	0.963280i	$-0.413473\pi$
$541$	2.48861e13			0.536995			0.268497	+	0.963280i	$0.413473\pi$
$542$			7.10110e13i			1.51820i
$543$			2.50706e13i			0.531086i
$544$			1.91677e13i			0.402323i
$545$		−	4.64343e12i		−	0.0965731i
$546$			5.12595e12i			0.105636i
$547$	−8.18220e13			−1.67083			−0.835417	−	0.549616i	$-0.814774\pi$
$547$	−8.18220e13			−1.67083			−0.835417	+	0.549616i	$0.814774\pi$
$548$		−	3.85094e12i		−	0.0779227i
$549$			1.97385e13i			0.395779i
$550$		−	5.43757e13i		−	1.08042i
$551$	3.51218e12			0.0691542
$552$	3.04883e13			0.594892
$553$			4.01236e12i			0.0775844i
$554$	−6.73762e13			−1.29109
$555$			7.15680e12i			0.135911i
$556$	−8.58786e12			−0.161626
$557$	4.67918e13			0.872758			0.436379	−	0.899763i	$-0.356261\pi$
$557$	4.67918e13			0.872758			0.436379	+	0.899763i	$0.356261\pi$
$558$		−	5.55190e12i		−	0.102629i
$559$	−1.59516e13	+	2.12744e13i	−0.292244	+	0.389760i
$560$	6.38837e11			0.0115998
$561$			1.17413e14i			2.11301i
$562$		−	2.15202e13i		−	0.383853i
$563$	−5.92155e13			−1.04687			−0.523436	−	0.852065i	$-0.675350\pi$
$563$	−5.92155e13			−1.04687			−0.523436	+	0.852065i	$0.675350\pi$
$564$		−	7.60578e12i		−	0.133275i
$565$	−1.03743e12			−0.0180185
$566$			6.36560e13i			1.09587i
$567$		−	1.44237e13i		−	0.246129i
$568$	−1.91034e13			−0.323124
$569$	1.03745e14			1.73943			0.869714	−	0.493556i	$-0.164303\pi$
$569$	1.03745e14			1.73943			0.869714	+	0.493556i	$0.164303\pi$
$570$	−3.01284e12			−0.0500729
$571$			5.54780e12i			0.0913988i	0.998955	+	0.0456994i	$0.0145516\pi$
$571$			5.54780e12i			0.0913988i	−0.998955	+	0.0456994i	$0.985448\pi$
$572$	−4.29865e12			−0.0702025
$573$	3.85765e13			0.624525
$574$	−5.99668e12			−0.0962390
$575$	3.16213e13			0.503085
$576$	1.74755e13			0.275624
$577$		−	1.06287e14i		−	1.66189i	−0.556355	−	0.830945i	$-0.687800\pi$
$577$		−	1.06287e14i		−	1.66189i	0.556355	−	0.830945i	$-0.312200\pi$
$578$			9.97055e13i			1.54554i
$579$		−	9.50388e13i		−	1.46052i
$580$	5.00443e10			0.000762456
$581$			3.57665e12i			0.0540251i
$582$	7.34276e13			1.09963
$583$	−4.18963e13			−0.622061
$584$	−7.64647e13			−1.12563
$585$		−	5.48906e11i		−	0.00801159i
$586$			1.19137e14i			1.72408i
$587$			5.54347e13i			0.795411i	0.917513	+	0.397705i	$0.130193\pi$
$587$			5.54347e13i			0.795411i	−0.917513	+	0.397705i	$0.869807\pi$
$588$		−	9.35793e12i		−	0.133135i
$589$			2.26018e13i			0.318835i
$590$	−2.82569e12			−0.0395243
$591$			2.10992e13i			0.292637i
$592$		−	1.16642e14i		−	1.60415i
$593$		−	1.23403e14i		−	1.68288i	−0.540349	−	0.841441i	$-0.681708\pi$
$593$		−	1.23403e14i		−	1.68288i	0.540349	−	0.841441i	$-0.318292\pi$
$594$	−6.71212e13			−0.907669
$595$	−1.63740e12			−0.0219569
$596$		−	7.73084e12i		−	0.102801i
$597$	1.36634e14			1.80172
$598$			1.76133e13i			0.230321i
$599$	5.75412e13			0.746182			0.373091	−	0.927795i	$-0.378298\pi$
$599$	5.75412e13			0.746182			0.373091	+	0.927795i	$0.378298\pi$
$600$	9.11721e13			1.17248
$601$			1.12470e14i			1.43437i	0.696881	+	0.717187i	$0.254571\pi$
$601$			1.12470e14i			1.43437i	−0.696881	+	0.717187i	$0.745429\pi$
$602$	9.18994e12	−	1.22564e13i	0.116233	−	0.155018i
$603$	1.34259e13			0.168406
$604$			5.39996e12i			0.0671747i
$605$			1.81773e12i			0.0224261i
$606$	8.35187e12			0.102193
$607$		−	1.14155e13i		−	0.138532i	−0.997598	−	0.0692659i	$-0.977934\pi$
$607$		−	1.14155e13i		−	0.138532i	0.997598	−	0.0692659i	$-0.0220657\pi$
$608$	−1.50703e13			−0.181386
$609$		−	1.82847e12i		−	0.0218274i
$610$			8.06726e12i			0.0955161i
$611$	3.97465e13			0.466760
$612$	−4.38775e12			−0.0511075
$613$	1.42106e14			1.64177			0.820883	−	0.571096i	$-0.193482\pi$
$613$	1.42106e14			1.64177			0.820883	+	0.571096i	$0.193482\pi$
$614$			8.02892e12i			0.0920058i
$615$	3.18506e12			0.0362027
$616$	2.24021e13			0.252572
$617$	6.74557e13			0.754384			0.377192	−	0.926135i	$-0.376890\pi$
$617$	6.74557e13			0.754384			0.377192	+	0.926135i	$0.376890\pi$
$618$	−9.58877e13			−1.06370
$619$	2.48391e13			0.273327			0.136664	−	0.990618i	$-0.456362\pi$
$619$	2.48391e13			0.273327			0.136664	+	0.990618i	$0.456362\pi$
$620$			3.22048e11i			0.00351530i
$621$		−	3.90333e13i		−	0.422646i
$622$		−	4.69069e13i		−	0.503831i
$623$	2.41228e13			0.257032
$624$			4.43726e13i			0.469021i
$625$	9.41557e13			0.987294
$626$	−6.48800e12			−0.0674900
$627$	−9.23142e13			−0.952644
$628$		−	8.58442e12i		−	0.0878846i
$629$			2.98964e14i			3.03644i
$630$			3.16232e11i			0.00318642i
$631$		−	6.71070e13i		−	0.670843i	−0.942068	−	0.335422i	$-0.891121\pi$
$631$		−	6.71070e13i		−	0.670843i	0.942068	−	0.335422i	$-0.108879\pi$
$632$			3.97510e13i			0.394242i
$633$	1.65003e14			1.62357
$634$		−	1.47548e13i		−	0.144042i
$635$		−	9.56225e12i		−	0.0926172i
$636$		−	7.76575e12i		−	0.0746273i
$637$	4.89030e13			0.466271
$638$	−1.08039e13			−0.102206
$639$		−	8.26265e12i		−	0.0775560i
$640$	5.41465e12			0.0504278
$641$		−	1.30587e14i		−	1.20673i	−0.797465	−	0.603365i	$-0.793826\pi$
$641$		−	1.30587e14i		−	1.20673i	0.797465	−	0.603365i	$-0.206174\pi$
$642$	−8.14655e13			−0.746962
$643$	−8.09113e13			−0.736130			−0.368065	−	0.929800i	$-0.619980\pi$
$643$	−8.09113e13			−0.736130			−0.368065	+	0.929800i	$0.619980\pi$
$644$			1.44017e12i			0.0130013i
$645$	−4.88111e12	+	6.50984e12i	−0.0437240	+	0.0583138i
$646$	−1.25857e14			−1.11870
$647$			8.55615e13i			0.754669i	0.926077	+	0.377335i	$0.123159\pi$
$647$			8.55615e13i			0.754669i	−0.926077	+	0.377335i	$0.876841\pi$
$648$		−	1.42898e14i		−	1.25069i
$649$	−8.65797e13			−0.751956
$650$			5.26706e13i			0.453943i
$651$	1.17667e13			0.100635
$652$		−	5.97445e12i		−	0.0507061i
$653$			1.61973e14i			1.36420i	0.731259	+	0.682100i	$0.238933\pi$
$653$			1.61973e14i			1.36420i	−0.731259	+	0.682100i	$0.761067\pi$
$654$	−1.85811e14			−1.55304
$655$	−8.74862e12			−0.0725660
$656$	−5.19101e13			−0.427300
$657$		−	3.30727e13i		−	0.270173i
$658$	−2.28985e13			−0.185642
$659$	−8.60337e13			−0.692216			−0.346108	−	0.938195i	$-0.612497\pi$
$659$	−8.60337e13			−0.692216			−0.346108	+	0.938195i	$0.612497\pi$
$660$	−1.31536e12			−0.0105033
$661$	−1.67477e14			−1.32723			−0.663617	−	0.748073i	$-0.730979\pi$
$661$	−1.67477e14			−1.32723			−0.663617	+	0.748073i	$0.730979\pi$
$662$	2.97174e13			0.233734
$663$		−	1.13731e14i		−	0.887794i
$664$			3.54343e13i			0.274526i
$665$		−	1.28738e12i		−	0.00989917i
$666$	5.77390e13			0.440654
$667$		−	6.28281e12i		−	0.0475910i
$668$	3.15295e12			0.0237047
$669$	−9.44780e13			−0.705018
$670$	5.48726e12			0.0406426
$671$			2.47182e14i			1.81721i
$672$			7.84571e12i			0.0572514i
$673$			2.30784e14i			1.67159i	0.549039	+	0.835797i	$0.314994\pi$
$673$			2.30784e14i			1.67159i	−0.549039	+	0.835797i	$0.685006\pi$
$674$		−	1.65635e14i		−	1.19084i
$675$		−	1.16725e14i		−	0.832998i
$676$	−1.33815e13			−0.0947919
$677$		−	8.43691e13i		−	0.593253i	−0.954994	−	0.296627i	$-0.904138\pi$
$677$		−	8.43691e13i		−	0.593253i	0.954994	−	0.296627i	$-0.0958617\pi$
$678$			4.15138e13i			0.289764i
$679$			3.13754e13i			0.217391i
$680$	−1.62219e13			−0.111573
$681$	−7.95583e13			−0.543188
$682$		−	6.95256e13i		−	0.471219i
$683$	1.33475e14			0.898038			0.449019	−	0.893522i	$-0.351773\pi$
$683$	1.33475e14			0.898038			0.449019	+	0.893522i	$0.351773\pi$
$684$		−	3.44980e12i		−	0.0230416i
$685$	6.15795e12			0.0408304
$686$	−5.76091e13			−0.379202
$687$		−	9.10360e13i		−	0.594880i
$688$	7.95525e13	−	1.06097e14i	0.516073	−	0.688276i
$689$	4.05825e13			0.261362
$690$			5.38957e12i			0.0344595i
$691$		−	2.31962e14i		−	1.47240i	−0.676764	−	0.736200i	$-0.736618\pi$
$691$		−	2.31962e14i		−	1.47240i	0.676764	−	0.736200i	$-0.263382\pi$
$692$	2.18007e13			0.137385
$693$			9.68941e12i			0.0606221i
$694$	−4.06685e13			−0.252616
$695$		−	1.37327e13i		−	0.0846897i
$696$		−	1.81149e13i		−	0.110915i
$697$	1.33050e14			0.808821
$698$	−1.57879e14			−0.952900
$699$	−2.59859e14			−1.55723
$700$			4.30668e12i			0.0256243i
$701$	5.99175e13			0.353968			0.176984	−	0.984214i	$-0.443366\pi$
$701$	5.99175e13			0.353968			0.176984	+	0.984214i	$0.443366\pi$
$702$	6.50164e13			0.381362
$703$	−2.35055e14			−1.36897
$704$	2.18843e14			1.26552
$705$	1.21622e13			0.0698341
$706$		−	2.21932e14i		−	1.26531i
$707$			3.56873e12i			0.0202030i
$708$		−	1.60481e13i		−	0.0902106i
$709$	2.44977e14			1.36740			0.683698	−	0.729765i	$-0.260370\pi$
$709$	2.44977e14			1.36740			0.683698	+	0.729765i	$0.260370\pi$
$710$		−	3.37700e12i		−	0.0187171i
$711$	−1.71932e13			−0.0946256
$712$	2.38988e14			1.30610
$713$	4.04315e13			0.219418
$714$			6.55220e13i			0.353099i
$715$		−	6.87388e12i		−	0.0367851i
$716$		−	3.57962e13i		−	0.190227i
$717$		−	2.76449e14i		−	1.45888i
$718$		−	1.79850e14i		−	0.942515i
$719$	1.12367e14			0.584785			0.292392	−	0.956298i	$-0.405549\pi$
$719$	1.12367e14			0.584785			0.292392	+	0.956298i	$0.405549\pi$
$720$			2.73745e12i			0.0141476i
$721$		−	4.09726e13i		−	0.210289i
$722$			8.46447e13i			0.431433i
$723$	−1.32575e14			−0.671072
$724$	−1.17326e13			−0.0589794
$725$		−	1.87881e13i		−	0.0937977i
$726$	7.27382e13			0.360645
$727$		−	2.03887e14i		−	1.00396i	−0.864878	−	0.501982i	$-0.832604\pi$
$727$		−	2.03887e14i		−	1.00396i	0.864878	−	0.501982i	$-0.167396\pi$
$728$	−2.16996e13			−0.106119
$729$	−1.30955e14			−0.636041
$730$		−	1.35170e13i		−	0.0652029i
$731$	−2.03901e14	+	2.71938e14i	−0.976858	+	1.30281i
$732$	−4.58169e13			−0.218007
$733$			1.40792e14i			0.665362i	0.943039	+	0.332681i	$0.107953\pi$
$733$			1.40792e14i			0.665362i	−0.943039	+	0.332681i	$0.892047\pi$
$734$			2.72764e13i			0.128028i
$735$	1.49641e13			0.0697610
$736$			2.69587e13i			0.124827i
$737$	1.68131e14			0.773233
$738$		−	2.56961e13i		−	0.117378i
$739$			5.06958e13i			0.230012i	0.993365	+	0.115006i	$0.0366887\pi$
$739$			5.06958e13i			0.230012i	−0.993365	+	0.115006i	$0.963311\pi$
$740$	−3.34925e12			−0.0150935
$741$	8.94194e13			0.400259
$742$	−2.33801e13			−0.103951
$743$		−	3.77080e14i		−	1.66529i	−0.553810	−	0.832643i	$-0.686827\pi$
$743$		−	3.77080e14i		−	1.66529i	0.553810	−	0.832643i	$-0.313173\pi$
$744$	1.16574e14			0.511372
$745$	1.23622e13			0.0538660
$746$	3.55462e14			1.53850
$747$	−1.53261e13			−0.0658915
$748$	−5.49472e13			−0.234659
$749$		−	3.48100e13i		−	0.147671i
$750$			3.23025e13i			0.136122i
$751$		−	3.16255e14i		−	1.32385i	−0.749571	−	0.661923i	$-0.769740\pi$
$751$		−	3.16255e14i		−	1.32385i	0.749571	−	0.661923i	$-0.230260\pi$
$752$	−1.98220e14			−0.824249
$753$			4.96291e14i			2.05004i
$754$	1.04651e13			0.0429423
$755$	−8.63494e12			−0.0351985
$756$	5.31615e12			0.0215273
$757$			1.69500e14i			0.681853i	0.940090	+	0.340927i	$0.110741\pi$
$757$			1.69500e14i			0.681853i	−0.940090	+	0.340927i	$0.889259\pi$
$758$			1.83601e14i			0.733716i
$759$			1.65138e14i			0.655597i
$760$		−	1.27542e13i		−	0.0503022i
$761$			4.88591e14i			1.91435i	0.289507	+	0.957176i	$0.406509\pi$
$761$			4.88591e14i			1.91435i	−0.289507	+	0.957176i	$0.593491\pi$
$762$	−3.82642e14			−1.48942
$763$		−	7.93964e13i		−	0.307028i
$764$			1.80531e13i			0.0693562i
$765$		−	7.01635e12i		−	0.0267796i
$766$	4.90057e14			1.85824
$767$	8.38647e13			0.315938
$768$			1.09700e14i			0.410582i
$769$	−5.11989e14			−1.90383			−0.951917	−	0.306356i	$-0.900890\pi$
$769$	−5.11989e14			−1.90383			−0.951917	+	0.306356i	$0.900890\pi$
$770$			3.96013e12i			0.0146304i
$771$	−7.73470e13			−0.283904
$772$	4.44764e13			0.162197
$773$			1.45115e14i			0.525792i	0.964824	+	0.262896i	$0.0846777\pi$
$773$			1.45115e14i			0.525792i	−0.964824	+	0.262896i	$0.915322\pi$
$774$	5.25194e13	+	3.93794e13i	0.189067	+	0.141763i
$775$	1.20906e14			0.432454
$776$			3.10840e14i			1.10466i
$777$			1.22372e14i			0.432092i
$778$	2.24504e14			0.787637
$779$			1.04609e14i			0.364654i
$780$	1.27412e12			0.00441303
$781$		−	1.03472e14i		−	0.356097i
$782$			2.25140e14i			0.769874i
$783$	−2.31919e13			−0.0788003
$784$	−2.43884e14			−0.823386
$785$	1.37271e13			0.0460503
$786$			3.50084e14i			1.16697i
$787$	−1.46059e14			−0.483789			−0.241894	−	0.970303i	$-0.577769\pi$
$787$	−1.46059e14			−0.483789			−0.241894	+	0.970303i	$0.577769\pi$
$788$	−9.87404e12			−0.0324985
$789$	−1.03208e14			−0.337544
$790$	−7.02697e12			−0.0228367
$791$	−1.77387e13			−0.0572849
$792$			9.59942e13i			0.308049i
$793$		−	2.39431e14i		−	0.763510i
$794$		−	3.21435e14i		−	1.01857i
$795$	1.24180e13			0.0391036
$796$			6.39422e13i			0.200088i
$797$	−5.63988e14			−1.75379			−0.876896	−	0.480680i	$-0.840390\pi$
$797$	−5.63988e14			−1.75379			−0.876896	+	0.480680i	$0.840390\pi$
$798$	−5.15156e13			−0.159193
$799$	5.08057e14			1.56019
$800$			8.06170e13i			0.246024i
$801$			1.03368e14i			0.313489i
$802$		−	2.53469e14i		−	0.763928i
$803$		−	4.14165e14i		−	1.24050i
$804$			3.11641e13i			0.0927630i
$805$	−2.30295e12			−0.00681247
$806$			6.73455e13i			0.197985i
$807$		−	1.10073e14i		−	0.321598i
$808$			3.53559e13i			0.102661i
$809$	3.18933e14			0.920359			0.460180	−	0.887826i	$-0.347785\pi$
$809$	3.18933e14			0.920359			0.460180	+	0.887826i	$0.347785\pi$
$810$	2.52608e13			0.0724471
$811$			4.60416e14i			1.31234i	0.754614	+	0.656169i	$0.227824\pi$
$811$			4.60416e14i			1.31234i	−0.754614	+	0.656169i	$0.772176\pi$
$812$	8.55691e11			0.00242402
$813$		−	6.44903e14i		−	1.81569i
$814$	7.23057e14			2.02325
$815$	9.55361e12			0.0265693
$816$			5.67190e14i			1.56775i
$817$	−2.13807e14	−	1.60314e14i	−0.587369	−	0.440413i
$818$	2.06751e14			0.564523
$819$		−	9.38557e12i		−	0.0254707i
$820$			1.49055e12i			0.00402047i
$821$	2.17005e14			0.581772			0.290886	−	0.956758i	$-0.406050\pi$
$821$	2.17005e14			0.581772			0.290886	+	0.956758i	$0.406050\pi$
$822$		−	2.46416e14i		−	0.656613i
$823$	−1.74147e14			−0.461230			−0.230615	−	0.973045i	$-0.574074\pi$
$823$	−1.74147e14			−0.461230			−0.230615	+	0.973045i	$0.574074\pi$
$824$		−	4.05921e14i		−	1.06858i
$825$			4.93826e14i			1.29212i
$826$	−4.83155e13			−0.125657
$827$	−8.11856e13			−0.209870			−0.104935	−	0.994479i	$-0.533464\pi$
$827$	−8.11856e13			−0.209870			−0.104935	+	0.994479i	$0.533464\pi$
$828$	−6.17122e12			−0.0158569
$829$			1.27790e14i			0.326381i	0.986595	+	0.163190i	$0.0521785\pi$
$829$			1.27790e14i			0.326381i	−0.986595	+	0.163190i	$0.947822\pi$
$830$	−6.26389e12			−0.0159021
$831$	6.11893e14			1.54408
$832$	−2.11981e14			−0.531716
$833$	6.25099e14			1.55856
$834$	−5.49524e14			−1.36194
$835$			5.04182e12i			0.0124209i
$836$		−	4.32014e13i		−	0.105795i
$837$		−	1.49246e14i		−	0.363308i
$838$	1.13490e14			0.274624
$839$		−	5.42822e14i		−	1.30571i	−0.757481	−	0.652857i	$-0.773570\pi$
$839$		−	5.42822e14i		−	1.30571i	0.757481	−	0.652857i	$-0.226430\pi$
$840$	−6.63996e12			−0.0158770
$841$	4.16974e14			0.991127
$842$	7.82760e13			0.184956
$843$			1.95441e14i			0.459068i
$844$			7.72182e13i			0.180305i
$845$		−	2.13980e13i		−	0.0496696i
$846$		−	9.81212e13i		−	0.226418i
$847$			3.10808e13i			0.0712977i
$848$	−2.02389e14			−0.461539
$849$		−	5.78107e14i		−	1.31060i
$850$			6.73258e14i			1.51735i
$851$			4.20482e14i			0.942106i
$852$	1.91792e13			0.0427202
$853$	−5.87310e14			−1.30053			−0.650267	−	0.759706i	$-0.725343\pi$
$853$	−5.87310e14			−1.30053			−0.650267	+	0.759706i	$0.725343\pi$
$854$			1.37939e14i			0.303668i
$855$	5.51650e12			0.0120735
$856$		−	3.44867e14i		−	0.750383i
$857$	−5.55311e14			−1.20125			−0.600623	−	0.799532i	$-0.705081\pi$
$857$	−5.55311e14			−1.20125			−0.600623	+	0.799532i	$0.705081\pi$
$858$	−2.75064e14			−0.591558
$859$		−	2.54422e14i		−	0.543988i	−0.962299	−	0.271994i	$-0.912317\pi$
$859$		−	2.54422e14i		−	0.543988i	0.962299	−	0.271994i	$-0.0876831\pi$
$860$	−3.04649e12	−	2.28427e12i	−0.00647600	−	0.00485574i
$861$	5.44602e13			0.115097
$862$			1.58917e14i			0.333914i
$863$		−	5.36575e14i		−	1.12093i	−0.828180	−	0.560463i	$-0.810623\pi$
$863$		−	5.36575e14i		−	1.12093i	0.828180	−	0.560463i	$-0.189377\pi$
$864$	9.95133e13			0.206687
$865$			3.48610e13i			0.0719879i
$866$	2.84637e14			0.584389
$867$		−	9.05498e14i		−	1.84838i
$868$			5.50659e12i			0.0111759i
$869$	−2.15308e14			−0.434471
$870$	3.20226e12			0.00642480
$871$	−1.62859e14			−0.324878
$872$		−	7.86591e14i		−	1.56015i
$873$	−1.34445e14			−0.265140
$874$	−1.77013e14			−0.347095
$875$	−1.38028e13			−0.0269108
$876$	7.67681e13			0.148820
$877$	−4.93296e14			−0.950844			−0.475422	−	0.879758i	$-0.657705\pi$
$877$	−4.93296e14			−0.950844			−0.475422	+	0.879758i	$0.657705\pi$
$878$			6.70539e14i			1.28514i
$879$		−	1.08197e15i		−	2.06192i
$880$			3.42807e13i			0.0649586i
$881$	9.18966e13			0.173149			0.0865744	−	0.996245i	$-0.472408\pi$
$881$	9.18966e13			0.173149			0.0865744	+	0.996245i	$0.472408\pi$
$882$		−	1.20726e14i		−	0.226181i
$883$	−9.39719e14			−1.75063			−0.875315	−	0.483553i	$-0.839346\pi$
$883$	−9.39719e14			−1.75063			−0.875315	+	0.483553i	$0.839346\pi$
$884$	5.32242e13			0.0985933
$885$	2.56621e13			0.0472690
$886$		−	5.20472e13i		−	0.0953298i
$887$			5.78866e14i			1.05429i	0.849776	+	0.527145i	$0.176737\pi$
$887$			5.78866e14i			1.05429i	−0.849776	+	0.527145i	$0.823263\pi$
$888$			1.21235e15i			2.19566i
$889$		−	1.63502e14i		−	0.294452i
$890$			4.22470e13i			0.0756565i
$891$	7.73995e14			1.37832
$892$		−	4.42140e13i		−	0.0782953i
$893$			3.99452e14i			0.703408i
$894$		−	4.94684e14i		−	0.866245i
$895$	5.72409e13			0.0996762
$896$	9.25833e13			0.160322
$897$		−	1.59959e14i		−	0.275453i
$898$	−5.13484e14			−0.879317
$899$		−	2.40227e13i		−	0.0409095i
$900$	−1.84544e13			−0.0312526
$901$	5.18743e14			0.873631
$902$		−	3.21789e14i		−	0.538937i
$903$	−8.34606e13	+	1.11310e14i	−0.139009	+	0.185393i
$904$	−1.75740e14			−0.291091
$905$		−	1.87613e13i		−	0.0309044i
$906$			3.45535e14i			0.566045i
$907$	−5.34411e14			−0.870641			−0.435321	−	0.900275i	$-0.643365\pi$
$907$	−5.34411e14			−0.870641			−0.435321	+	0.900275i	$0.643365\pi$
$908$		−	3.72318e13i		−	0.0603233i
$909$	−1.52922e13			−0.0246406
$910$		−	3.83595e12i		−	0.00614703i
$911$		−	8.04949e14i		−	1.28285i	−0.767185	−	0.641426i	$-0.778343\pi$
$911$		−	8.04949e14i		−	1.28285i	0.767185	−	0.641426i	$-0.221657\pi$
$912$	−4.45944e14			−0.706815
$913$	−1.91927e14			−0.302539
$914$	−6.38282e14			−1.00065
$915$		−	7.32647e13i		−	0.114232i
$916$	4.26032e13			0.0660640
$917$	−1.49590e14			−0.230704
$918$	8.31067e14			1.27474
$919$	−8.09171e14			−1.23442			−0.617209	−	0.786799i	$-0.711737\pi$
$919$	−8.09171e14			−1.23442			−0.617209	+	0.786799i	$0.711737\pi$
$920$	−2.28156e13			−0.0346173
$921$		−	7.29165e13i		−	0.110034i
$922$		−	7.60362e14i		−	1.14121i
$923$			1.00227e14i			0.149616i
$924$	−2.24910e13			−0.0333925
$925$			1.25741e15i			1.85681i
$926$	5.57660e14			0.819058
$927$	1.75570e14			0.256478
$928$	1.60177e13			0.0232734
$929$			1.50256e14i			0.217146i	0.994088	+	0.108573i	$0.0346282\pi$
$929$			1.50256e14i			0.217146i	−0.994088	+	0.108573i	$0.965372\pi$
$930$			2.06073e13i			0.0296215i
$931$			4.91474e14i			0.702671i
$932$		−	1.21609e14i		−	0.172937i
$933$			4.25996e14i			0.602556i
$934$	8.03575e14			1.13056
$935$		−	8.78648e13i		−	0.122958i
$936$		−	9.29840e13i		−	0.129428i
$937$			5.48073e14i			0.758822i	0.925228	+	0.379411i	$0.123873\pi$
$937$			5.48073e14i			0.758822i	−0.925228	+	0.379411i	$0.876127\pi$
$938$	9.38249e13			0.129212
$939$	5.89223e13			0.0807145
$940$			5.69170e12i			0.00775538i
$941$	1.40204e15			1.90026			0.950131	−	0.311851i	$-0.100949\pi$
$941$	1.40204e15			1.90026			0.950131	+	0.311851i	$0.100949\pi$
$942$		−	5.49304e14i		−	0.740556i
$943$	1.87131e14			0.250950
$944$	−4.18242e14			−0.557915
$945$			8.50094e12i			0.0112800i
$946$	6.57694e14	+	4.93143e14i	0.868097	+	0.650904i
$947$	−3.00078e13			−0.0393989			−0.0196995	−	0.999806i	$-0.506271\pi$
$947$	−3.00078e13			−0.0393989			−0.0196995	+	0.999806i	$0.506271\pi$
$948$		−	3.99087e13i		−	0.0521226i
$949$			4.01177e14i			0.521201i
$950$	−5.29339e14			−0.684094
$951$			1.33999e14i			0.172266i
$952$	−2.77374e14			−0.354716
$953$		−	8.16681e14i		−	1.03893i	−0.854490	−	0.519467i	$-0.826130\pi$
$953$		−	8.16681e14i		−	1.03893i	0.854490	−	0.519467i	$-0.173870\pi$
$954$		−	1.00185e14i		−	0.126783i
$955$	−2.88683e13			−0.0363417
$956$	1.29373e14			0.162015
$957$	9.81178e13			0.122233
$958$		−	2.27364e14i		−	0.281770i
$959$	1.05293e14			0.129809
$960$	−6.48650e13			−0.0795525
$961$	−6.65036e14			−0.811387
$962$	−7.00384e14			−0.850081
$963$	1.49163e14			0.180106
$964$		−	6.20426e13i		−	0.0745254i
$965$			7.11213e13i			0.0849890i
$966$			9.21545e13i			0.109555i
$967$	1.31271e15			1.55251			0.776257	−	0.630417i	$-0.217116\pi$
$967$	1.31271e15			1.55251			0.776257	+	0.630417i	$0.217116\pi$
$968$			3.07922e14i			0.362296i
$969$	1.14300e15			1.33791
$970$	−5.49488e13			−0.0639881
$971$	−1.04586e15			−1.21165			−0.605827	−	0.795596i	$-0.707158\pi$
$971$	−1.04586e15			−1.21165			−0.605827	+	0.795596i	$0.707158\pi$
$972$			5.32560e13i			0.0613814i
$973$		−	2.34810e14i		−	0.269248i
$974$		−	6.17785e14i		−	0.704762i
$975$		−	4.78341e14i		−	0.542893i
$976$			1.19407e15i			1.34828i
$977$	−6.00194e14			−0.674247			−0.337123	−	0.941460i	$-0.609454\pi$
$977$	−6.00194e14			−0.674247			−0.337123	+	0.941460i	$0.609454\pi$
$978$		−	3.82296e14i		−	0.427273i
$979$			1.29446e15i			1.43938i
$980$			7.00291e12i			0.00774726i
$981$	3.40218e14			0.374466
$982$	1.72124e12			0.00188488
$983$			2.00636e14i			0.218595i	0.994009	+	0.109298i	$0.0348601\pi$
$983$			2.00636e14i			0.218595i	−0.994009	+	0.109298i	$0.965140\pi$
$984$	5.39544e14			0.584860
$985$		−	1.57894e13i		−	0.0170288i
$986$	1.33769e14			0.143539
$987$	2.07958e14			0.222019
$988$			4.18467e13i			0.0444504i
$989$	−2.86779e14	+	3.82471e14i	−0.303086	+	0.404220i
$990$	−1.69694e13			−0.0178439
$991$			1.24930e15i			1.30707i	0.756896	+	0.653535i	$0.226715\pi$
$991$			1.24930e15i			1.30707i	−0.756896	+	0.653535i	$0.773285\pi$
$992$			1.03078e14i			0.107302i
$993$	−2.69886e14			−0.279533
$994$		−	5.77423e13i		−	0.0595062i
$995$	−1.02248e14			−0.104843
$996$		−	3.55749e13i		−	0.0362950i
$997$			7.32543e14i			0.743631i	0.928307	+	0.371815i	$0.121265\pi$
$997$			7.32543e14i			0.743631i	−0.928307	+	0.371815i	$0.878735\pi$
$998$	−1.16278e15			−1.17448
$999$	1.55214e15			1.55992

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.b.b.42.24	yes	34
43.42	odd	2	inner	43.11.b.b.42.11	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.b.b.42.11	✓	34	43.42	odd	2	inner
43.11.b.b.42.24	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)

\(f(q)\)	\(=\)	\(q+29.9454i q^{2} -271.957i q^{3} +127.271 q^{4} +203.516i q^{5} +8143.86 q^{6} +3479.85i q^{7} +34475.3i q^{8} -14911.3 q^{9} +O(q^{10})\)	\(q+29.9454i q^{2} -271.957i q^{3} +127.271 q^{4} +203.516i q^{5} +8143.86 q^{6} +3479.85i q^{7} +34475.3i q^{8} -14911.3 q^{9} -6094.37 q^{10} -186733. q^{11} -34612.1i q^{12} +180877. q^{13} -104206. q^{14} +55347.4 q^{15} -902053. q^{16} +2.31205e6 q^{17} -446527. i q^{18} +1.81781e6i q^{19} +25901.6i q^{20} +946367. q^{21} -5.59179e6i q^{22} +3.25182e6 q^{23} +9.37578e6 q^{24} +9.72421e6 q^{25} +5.41644e6i q^{26} -1.20035e7i q^{27} +442883. i q^{28} -1.93209e6i q^{29} +1.65740e6i q^{30} +1.24335e7 q^{31} +8.29034e6i q^{32} +5.07832e7i q^{33} +6.92353e7i q^{34} -708204. q^{35} -1.89778e6 q^{36} +1.29307e8i q^{37} -5.44351e7 q^{38} -4.91907e7i q^{39} -7.01627e6 q^{40} +5.75466e7 q^{41} +2.83394e7i q^{42} +(-8.81905e7 + 1.17618e8i) q^{43} -2.37656e7 q^{44} -3.03469e6i q^{45} +9.73771e7i q^{46} +2.19743e8 q^{47} +2.45319e8i q^{48} +2.70366e8 q^{49} +2.91196e8i q^{50} -6.28776e8i q^{51} +2.30204e7 q^{52} +2.24365e8 q^{53} +3.59451e8 q^{54} -3.80030e7i q^{55} -1.19969e8 q^{56} +4.94366e8 q^{57} +5.78574e7 q^{58} +4.63656e8 q^{59} +7.04411e6 q^{60} -1.32372e9i q^{61} +3.72327e8i q^{62} -5.18892e7i q^{63} -1.17196e9 q^{64} +3.68113e7i q^{65} -1.52072e9 q^{66} -9.00383e8 q^{67} +2.94256e8 q^{68} -8.84353e8i q^{69} -2.12075e7i q^{70} +5.54119e8i q^{71} -5.14073e8i q^{72} +2.21796e9i q^{73} -3.87215e9 q^{74} -2.64456e9i q^{75} +2.31354e8i q^{76} -6.49801e8i q^{77} +1.47304e9 q^{78} +1.15303e9 q^{79} -1.83582e8i q^{80} -4.14494e9 q^{81} +1.72326e9i q^{82} +1.02782e9 q^{83} +1.20445e8 q^{84} +4.70538e8i q^{85} +(-3.52211e9 - 2.64090e9i) q^{86} -5.25445e8 q^{87} -6.43767e9i q^{88} -6.93215e9i q^{89} +9.08752e7 q^{90} +6.29425e8i q^{91} +4.13861e8 q^{92} -3.38138e9i q^{93} +6.58031e9i q^{94} -3.69953e8 q^{95} +2.25461e9 q^{96} +9.01632e9 q^{97} +8.09623e9i q^{98} +2.78443e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9}+O(q^{10}) \) 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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