LMFDB - Embedded newform 43.11.b.b.42.10

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			42.10
Character	$\chi$	$=$	43.42
Dual form			43.11.b.b.42.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-30.3109i q^{2} -212.897i q^{3} +105.247 q^{4} -1632.05i q^{5} -6453.11 q^{6} +7423.10i q^{7} -34228.5i q^{8} +13723.9 q^{9} +O(q^{10})$	\(q-30.3109i q^{2} -212.897i q^{3} +105.247 q^{4} -1632.05i q^{5} -6453.11 q^{6} +7423.10i q^{7} -34228.5i q^{8} +13723.9 q^{9} -49468.9 q^{10} -129685. q^{11} -22406.7i q^{12} -477616. q^{13} +225001. q^{14} -347458. q^{15} -929727. q^{16} -239065. q^{17} -415984. i q^{18} -2.40703e6i q^{19} -171768. i q^{20} +1.58035e6 q^{21} +3.93086e6i q^{22} -1.07661e7 q^{23} -7.28715e6 q^{24} +7.10204e6 q^{25} +1.44770e7i q^{26} -1.54931e7i q^{27} +781256. i q^{28} +3.05676e7i q^{29} +1.05318e7i q^{30} +1.70986e7 q^{31} -6.86913e6i q^{32} +2.76094e7i q^{33} +7.24629e6i q^{34} +1.21149e7 q^{35} +1.44439e6 q^{36} +2.92417e7i q^{37} -7.29593e7 q^{38} +1.01683e8i q^{39} -5.58626e7 q^{40} -6.33921e7 q^{41} -4.79020e7i q^{42} +(5.97263e7 + 1.34329e8i) q^{43} -1.36489e7 q^{44} -2.23981e7i q^{45} +3.26331e8i q^{46} +1.73838e7 q^{47} +1.97936e8i q^{48} +2.27373e8 q^{49} -2.15270e8i q^{50} +5.08962e7i q^{51} -5.02674e7 q^{52} -9.26195e7 q^{53} -4.69611e8 q^{54} +2.11651e8i q^{55} +2.54082e8 q^{56} -5.12449e8 q^{57} +9.26533e8 q^{58} -8.79381e8 q^{59} -3.65688e7 q^{60} -1.35810e9i q^{61} -5.18273e8i q^{62} +1.01874e8i q^{63} -1.16025e9 q^{64} +7.79492e8i q^{65} +8.36868e8 q^{66} +1.86000e8 q^{67} -2.51608e7 q^{68} +2.29207e9i q^{69} -3.67213e8i q^{70} -3.17203e9i q^{71} -4.69749e8i q^{72} -2.67560e9i q^{73} +8.86342e8 q^{74} -1.51200e9i q^{75} -2.53332e8i q^{76} -9.62661e8i q^{77} +3.08210e9 q^{78} +5.12315e9 q^{79} +1.51736e9i q^{80} -2.48806e9 q^{81} +1.92148e9i q^{82} -9.86767e8 q^{83} +1.66327e8 q^{84} +3.90166e8i q^{85} +(4.07164e9 - 1.81036e9i) q^{86} +6.50775e9 q^{87} +4.43891e9i q^{88} +5.62804e8i q^{89} -6.78906e8 q^{90} -3.54539e9i q^{91} -1.13310e9 q^{92} -3.64023e9i q^{93} -5.26918e8i q^{94} -3.92839e9 q^{95} -1.46242e9 q^{96} -1.18206e10 q^{97} -6.89189e9i q^{98} -1.77978e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	30.3109i		−	0.947217i	−0.880735	−	0.473609i	$-0.842951\pi$
$2$		−	30.3109i		−	0.947217i	0.880735	−	0.473609i	$-0.157049\pi$
$3$		−	212.897i		−	0.876119i	−0.898946	−	0.438060i	$-0.855666\pi$
$3$		−	212.897i		−	0.876119i	0.898946	−	0.438060i	$-0.144334\pi$
$4$	105.247			0.102780
$5$		−	1632.05i		−	0.522256i	−0.965304	−	0.261128i	$-0.915906\pi$
$5$		−	1632.05i		−	0.522256i	0.965304	−	0.261128i	$-0.0840944\pi$
$6$	−6453.11			−0.829875
$7$			7423.10i			0.441667i	0.975312	+	0.220833i	$0.0708777\pi$
$7$			7423.10i			0.441667i	−0.975312	+	0.220833i	$0.929122\pi$
$8$		−	34228.5i		−	1.04457i
$9$	13723.9			0.232415
$10$	−49468.9			−0.494689
$11$	−129685.			−0.805239			−0.402619	−	0.915367i	$-0.631900\pi$
$11$	−129685.			−0.805239			−0.402619	+	0.915367i	$0.631900\pi$
$12$		−	22406.7i		−	0.0900475i
$13$	−477616.			−1.28636			−0.643179	−	0.765716i	$-0.722385\pi$
$13$	−477616.			−1.28636			−0.643179	+	0.765716i	$0.722385\pi$
$14$	225001.			0.418354
$15$	−347458.			−0.457558
$16$	−929727.			−0.886656
$17$	−239065.			−0.168373			−0.0841863	−	0.996450i	$-0.526829\pi$
$17$	−239065.			−0.168373			−0.0841863	+	0.996450i	$0.526829\pi$
$18$		−	415984.i		−	0.220148i
$19$		−	2.40703e6i		−	0.972105i	−0.873929	−	0.486053i	$-0.838436\pi$
$19$		−	2.40703e6i		−	0.972105i	0.873929	−	0.486053i	$-0.161564\pi$
$20$		−	171768.i		−	0.0536774i
$21$	1.58035e6			0.386953
$22$			3.93086e6i			0.762736i
$23$	−1.07661e7			−1.67271			−0.836353	−	0.548192i	$-0.815316\pi$
$23$	−1.07661e7			−1.67271			−0.836353	+	0.548192i	$0.815316\pi$
$24$	−7.28715e6			−0.915169
$25$	7.10204e6			0.727249
$26$			1.44770e7i			1.21846i
$27$		−	1.54931e7i		−	1.07974i
$28$			781256.i			0.0453945i
$29$			3.05676e7i			1.49029i	0.666901	+	0.745146i	$0.267620\pi$
$29$			3.05676e7i			1.49029i	−0.666901	+	0.745146i	$0.732380\pi$
$30$			1.05318e7i			0.433407i
$31$	1.70986e7			0.597243			0.298621	−	0.954372i	$-0.403473\pi$
$31$	1.70986e7			0.597243			0.298621	+	0.954372i	$0.403473\pi$
$32$		−	6.86913e6i		−	0.204716i
$33$			2.76094e7i			0.705485i
$34$			7.24629e6i			0.159485i
$35$	1.21149e7			0.230663
$36$	1.44439e6			0.0238876
$37$			2.92417e7i			0.421690i	0.977519	+	0.210845i	$0.0676216\pi$
$37$			2.92417e7i			0.421690i	−0.977519	+	0.210845i	$0.932378\pi$
$38$	−7.29593e7			−0.920795
$39$			1.01683e8i			1.12700i
$40$	−5.58626e7			−0.545533
$41$	−6.33921e7			−0.547162			−0.273581	−	0.961849i	$-0.588208\pi$
$41$	−6.33921e7			−0.547162			−0.273581	+	0.961849i	$0.588208\pi$
$42$		−	4.79020e7i		−	0.366528i
$43$	5.97263e7	+	1.34329e8i	0.406278	+	0.913749i
$43$	5.97263e7	+	1.34329e8i	0.406278	+	0.913749i
$44$	−1.36489e7			−0.0827624
$45$		−	2.23981e7i		−	0.121380i
$46$			3.26331e8i			1.58442i
$47$	1.73838e7			0.0757974			0.0378987	−	0.999282i	$-0.487934\pi$
$47$	1.73838e7			0.0757974			0.0378987	+	0.999282i	$0.487934\pi$
$48$			1.97936e8i			0.776817i
$49$	2.27373e8			0.804930
$50$		−	2.15270e8i		−	0.688863i
$51$			5.08962e7i			0.147514i
$52$	−5.02674e7			−0.132212
$53$	−9.26195e7			−0.221474			−0.110737	−	0.993850i	$-0.535321\pi$
$53$	−9.26195e7			−0.221474			−0.110737	+	0.993850i	$0.535321\pi$
$54$	−4.69611e8			−1.02275
$55$			2.11651e8i			0.420540i
$56$	2.54082e8			0.461353
$57$	−5.12449e8			−0.851680
$58$	9.26533e8			1.41163
$59$	−8.79381e8			−1.23003			−0.615017	−	0.788514i	$-0.710851\pi$
$59$	−8.79381e8			−1.23003			−0.615017	+	0.788514i	$0.710851\pi$
$60$	−3.65688e7			−0.0470278
$61$		−	1.35810e9i		−	1.60799i	−0.594634	−	0.803996i	$-0.702703\pi$
$61$		−	1.35810e9i		−	1.60799i	0.594634	−	0.803996i	$-0.297297\pi$
$62$		−	5.18273e8i		−	0.565719i
$63$			1.01874e8i			0.102650i
$64$	−1.16025e9			−1.08057
$65$			7.79492e8i			0.671807i
$66$	8.36868e8			0.668247
$67$	1.86000e8			0.137765			0.0688824	−	0.997625i	$-0.478057\pi$
$67$	1.86000e8			0.137765			0.0688824	+	0.997625i	$0.478057\pi$
$68$	−2.51608e7			−0.0173053
$69$			2.29207e9i			1.46549i
$70$		−	3.67213e8i		−	0.218488i
$71$		−	3.17203e9i		−	1.75811i	−0.476721	−	0.879055i	$-0.658175\pi$
$71$		−	3.17203e9i		−	1.75811i	0.476721	−	0.879055i	$-0.341825\pi$
$72$		−	4.69749e8i		−	0.242775i
$73$		−	2.67560e9i		−	1.29064i	−0.763911	−	0.645321i	$-0.776723\pi$
$73$		−	2.67560e9i		−	1.29064i	0.763911	−	0.645321i	$-0.223277\pi$
$74$	8.86342e8			0.399432
$75$		−	1.51200e9i		−	0.637157i
$76$		−	2.53332e8i		−	0.0999129i
$77$		−	9.62661e8i		−	0.355647i
$78$	3.08210e9			1.06752
$79$	5.12315e9			1.66495			0.832477	−	0.554060i	$-0.186922\pi$
$79$	5.12315e9			1.66495			0.832477	+	0.554060i	$0.186922\pi$
$80$			1.51736e9i			0.463061i
$81$	−2.48806e9			−0.713568
$82$			1.92148e9i			0.518281i
$83$	−9.86767e8			−0.250509			−0.125255	−	0.992125i	$-0.539975\pi$
$83$	−9.86767e8			−0.250509			−0.125255	+	0.992125i	$0.539975\pi$
$84$	1.66327e8			0.0397710
$85$			3.90166e8i			0.0879336i
$86$	4.07164e9	−	1.81036e9i	0.865519	−	0.384834i
$87$	6.50775e9			1.30567
$88$			4.43891e9i			0.841130i
$89$			5.62804e8i			0.100788i	0.998729	+	0.0503938i	$0.0160476\pi$
$89$			5.62804e8i			0.100788i	−0.998729	+	0.0503938i	$0.983952\pi$
$90$	−6.78906e8			−0.114973
$91$		−	3.54539e9i		−	0.568142i
$92$	−1.13310e9			−0.171921
$93$		−	3.64023e9i		−	0.523256i
$94$		−	5.26918e8i		−	0.0717966i
$95$	−3.92839e9			−0.507687
$96$	−1.46242e9			−0.179356
$97$	−1.18206e10			−1.37651			−0.688256	−	0.725468i	$-0.741624\pi$
$97$	−1.18206e10			−1.37651			−0.688256	+	0.725468i	$0.741624\pi$
$98$		−	6.89189e9i		−	0.762444i
$99$	−1.77978e9			−0.187150
$100$	7.47466e8			0.0747466
$101$	4.69755e9			0.446956			0.223478	−	0.974709i	$-0.428259\pi$
$101$	4.69755e9			0.446956			0.223478	+	0.974709i	$0.428259\pi$
$102$	1.54271e9			0.139728
$103$	−1.46350e10			−1.26243			−0.631213	−	0.775609i	$-0.717443\pi$
$103$	−1.46350e10			−1.26243			−0.631213	+	0.775609i	$0.717443\pi$
$104$			1.63481e10i			1.34369i
$105$		−	2.57922e9i		−	0.202088i
$106$			2.80738e9i			0.209784i
$107$	−2.01715e10			−1.43820			−0.719101	−	0.694906i	$-0.755446\pi$
$107$	−2.01715e10			−1.43820			−0.719101	+	0.694906i	$0.755446\pi$
$108$		−	1.63060e9i		−	0.110976i
$109$	−7.33490e8			−0.0476718			−0.0238359	−	0.999716i	$-0.507588\pi$
$109$	−7.33490e8			−0.0476718			−0.0238359	+	0.999716i	$0.507588\pi$
$110$	6.41535e9			0.398343
$111$	6.22546e9			0.369451
$112$		−	6.90145e9i		−	0.391607i
$113$		−	1.80819e9i		−	0.0981412i	−0.998795	−	0.0490706i	$-0.984374\pi$
$113$		−	1.80819e9i		−	0.0981412i	0.998795	−	0.0490706i	$-0.0156259\pi$
$114$			1.55328e10i			0.806726i
$115$			1.75708e10i			0.873580i
$116$			3.21714e9i			0.153172i
$117$	−6.55474e9			−0.298969
$118$			2.66549e10i			1.16511i
$119$		−	1.77460e9i		−	0.0743646i
$120$			1.18930e10i			0.477952i
$121$	−9.11935e9			−0.351590
$122$	−4.11654e10			−1.52312
$123$			1.34960e10i			0.479379i
$124$	1.79957e9			0.0613846
$125$		−	2.75289e10i		−	0.902065i
$126$	3.08789e9			0.0972320
$127$	6.50848e10			1.96998			0.984989	−	0.172619i	$-0.0552231\pi$
$127$	6.50848e10			1.96998			0.984989	+	0.172619i	$0.0552231\pi$
$128$			2.81343e10i			0.818815i
$129$	2.85982e10	−	1.27156e10i	0.800553	−	0.355948i
$130$	2.36271e10			0.636347
$131$		−	7.67234e9i		−	0.198871i	−0.995044	−	0.0994355i	$-0.968296\pi$
$131$		−	7.67234e9i		−	0.198871i	0.995044	−	0.0994355i	$-0.0317037\pi$
$132$			2.90580e9i			0.0725097i
$133$	1.78676e10			0.429347
$134$		−	5.63783e9i		−	0.130493i
$135$	−2.52855e10			−0.563902
$136$			8.18285e9i			0.175877i
$137$			3.77817e10i			0.782850i	0.920210	+	0.391425i	$0.128018\pi$
$137$			3.77817e10i			0.782850i	−0.920210	+	0.391425i	$0.871982\pi$
$138$	6.94748e10			1.38814
$139$	1.48235e10			0.285679			0.142839	−	0.989746i	$-0.454377\pi$
$139$	1.48235e10			0.285679			0.142839	+	0.989746i	$0.454377\pi$
$140$	1.27505e9			0.0237075
$141$		−	3.70095e9i		−	0.0664076i
$142$	−9.61473e10			−1.66531
$143$	6.19393e10			1.03582
$144$	−1.27595e10			−0.206073
$145$	4.98878e10			0.778314
$146$	−8.10998e10			−1.22252
$147$		−	4.84070e10i		−	0.705215i
$148$			3.07759e9i			0.0433413i
$149$		−	3.79213e10i		−	0.516359i	−0.966097	−	0.258179i	$-0.916877\pi$
$149$		−	3.79213e10i		−	0.516359i	0.966097	−	0.258179i	$-0.0831226\pi$
$150$	−4.58302e10			−0.603526
$151$		−	1.08043e11i		−	1.37629i	−0.725571	−	0.688147i	$-0.758424\pi$
$151$		−	1.08043e11i		−	1.37629i	0.725571	−	0.688147i	$-0.241576\pi$
$152$	−8.23891e10			−1.01543
$153$	−3.28090e9			−0.0391324
$154$	−2.91792e10			−0.336875
$155$		−	2.79057e10i		−	0.311913i
$156$			1.07018e10i			0.115833i
$157$		−	6.90568e10i		−	0.723950i	−0.932188	−	0.361975i	$-0.882103\pi$
$157$		−	6.90568e10i		−	0.723950i	0.932188	−	0.361975i	$-0.117897\pi$
$158$		−	1.55288e11i		−	1.57707i
$159$			1.97184e10i			0.194038i
$160$	−1.12107e10			−0.106914
$161$		−	7.99178e10i		−	0.738779i
$162$			7.54154e10i			0.675904i
$163$			4.29270e10i			0.373071i	0.982448	+	0.186536i	$0.0597260\pi$
$163$			4.29270e10i			0.373071i	−0.982448	+	0.186536i	$0.940274\pi$
$164$	−6.67181e9			−0.0562373
$165$	4.50599e10			0.368443
$166$			2.99098e10i			0.237287i
$167$	2.11428e10			0.162772			0.0813861	−	0.996683i	$-0.474065\pi$
$167$	2.11428e10			0.162772			0.0813861	+	0.996683i	$0.474065\pi$
$168$		−	5.40932e10i		−	0.404200i
$169$	9.02581e10			0.654716
$170$	1.18263e10			0.0832922
$171$		−	3.30338e10i		−	0.225932i
$172$	6.28600e9	+	1.41377e10i	0.0417572	+	0.0939151i
$173$	8.80695e10			0.568323			0.284161	−	0.958776i	$-0.408285\pi$
$173$	8.80695e10			0.568323			0.284161	+	0.958776i	$0.408285\pi$
$174$		−	1.97256e11i		−	1.23676i
$175$			5.27192e10i			0.321202i
$176$	1.20571e11			0.713970
$177$			1.87217e11i			1.07766i
$178$	1.70591e10			0.0954677
$179$		−	1.34447e11i		−	0.731623i	−0.930689	−	0.365811i	$-0.880792\pi$
$179$		−	1.34447e11i		−	0.731623i	0.930689	−	0.365811i	$-0.119208\pi$
$180$		−	2.35732e9i		−	0.0124754i
$181$	2.75284e11			1.41706			0.708529	−	0.705682i	$-0.249359\pi$
$181$	2.75284e11			1.41706			0.708529	+	0.705682i	$0.249359\pi$
$182$	−1.07464e11			−0.538153
$183$	−2.89136e11			−1.40879
$184$			3.68508e11i			1.74726i
$185$	4.77238e10			0.220230
$186$	−1.10339e11			−0.495637
$187$	3.10030e10			0.135580
$188$	1.82958e9			0.00779045
$189$	1.15007e11			0.476887
$190$			1.19073e11i			0.480890i
$191$		−	8.67688e10i		−	0.341347i	−0.985328	−	0.170674i	$-0.945406\pi$
$191$		−	8.67688e10i		−	0.341347i	0.985328	−	0.170674i	$-0.0545944\pi$
$192$			2.47014e11i			0.946705i
$193$	−2.71466e10			−0.101374			−0.0506872	−	0.998715i	$-0.516141\pi$
$193$	−2.71466e10			−0.101374			−0.0506872	+	0.998715i	$0.516141\pi$
$194$			3.58293e11i			1.30386i
$195$	1.65951e11			0.588583
$196$	2.39302e10			0.0827307
$197$	−2.23494e11			−0.753244			−0.376622	−	0.926367i	$-0.622914\pi$
$197$	−2.23494e11			−0.753244			−0.376622	+	0.926367i	$0.622914\pi$
$198$			5.39467e10i			0.177272i
$199$		−	3.59302e11i		−	1.15132i	−0.817691	−	0.575658i	$-0.804746\pi$
$199$		−	3.59302e11i		−	1.15132i	0.817691	−	0.575658i	$-0.195254\pi$
$200$		−	2.43092e11i		−	0.759664i
$201$		−	3.95988e10i		−	0.120698i
$202$		−	1.42387e11i		−	0.423364i
$203$	−2.26906e11			−0.658213
$204$			5.35666e9i			0.0151615i
$205$			1.03459e11i			0.285759i
$206$			4.43600e11i			1.19579i
$207$	−1.47753e11			−0.388762
$208$	4.44052e11			1.14056
$209$			3.12154e11i			0.782777i
$210$	−7.81785e10			−0.191421
$211$		−	2.78564e11i		−	0.666060i	−0.942916	−	0.333030i	$-0.891929\pi$
$211$		−	2.78564e11i		−	0.666060i	0.942916	−	0.333030i	$-0.108071\pi$
$212$	−9.74789e9			−0.0227631
$213$	−6.75316e11			−1.54031
$214$			6.11418e11i			1.36229i
$215$	2.19231e11	−	9.74763e10i	0.477211	−	0.212181i
$216$	−5.30307e11			−1.12787
$217$			1.26924e11i			0.263782i
$218$			2.22328e10i			0.0451555i
$219$	−5.69626e11			−1.13076
$220$			2.22756e10i			0.0432231i
$221$	1.14181e11			0.216587
$222$		−	1.88700e11i		−	0.349950i
$223$			1.02679e12i			1.86191i	0.365136	+	0.930954i	$0.381023\pi$
$223$			1.02679e12i			1.86191i	−0.365136	+	0.930954i	$0.618977\pi$
$224$	5.09902e10			0.0904163
$225$	9.74677e10			0.169024
$226$	−5.48079e10			−0.0929610
$227$		−	1.07728e12i		−	1.78731i	−0.448756	−	0.893654i	$-0.648133\pi$
$227$		−	1.07728e12i		−	1.78731i	0.448756	−	0.893654i	$-0.351867\pi$
$228$	−5.39336e10			−0.0875356
$229$	1.64721e11			0.261561			0.130780	−	0.991411i	$-0.458252\pi$
$229$	1.64721e11			0.261561			0.130780	+	0.991411i	$0.458252\pi$
$230$	5.32588e11			0.827470
$231$	−2.04948e11			−0.311589
$232$	1.04628e12			1.55672
$233$			8.24421e10i			0.120052i	0.998197	+	0.0600260i	$0.0191184\pi$
$233$			8.24421e10i			0.120052i	−0.998197	+	0.0600260i	$0.980882\pi$
$234$			1.98681e11i			0.283189i
$235$		−	2.83711e10i		−	0.0395856i
$236$	−9.25519e10			−0.126423
$237$		−	1.09070e12i		−	1.45870i
$238$	−5.37899e10			−0.0704395
$239$	−1.36817e12			−1.75448			−0.877241	−	0.480049i	$-0.840619\pi$
$239$	−1.36817e12			−1.75448			−0.877241	+	0.480049i	$0.840619\pi$
$240$	3.23041e11			0.405697
$241$		−	1.06468e11i		−	0.130959i	−0.997854	−	0.0654796i	$-0.979142\pi$
$241$		−	1.06468e11i		−	0.130959i	0.997854	−	0.0654796i	$-0.0208577\pi$
$242$			2.76416e11i			0.333033i
$243$		−	3.85154e11i		−	0.454572i
$244$		−	1.42936e11i		−	0.165269i
$245$		−	3.71084e11i		−	0.420379i
$246$	4.09076e11			0.454076
$247$			1.14963e12i			1.25048i
$248$		−	5.85258e11i		−	0.623863i
$249$			2.10080e11i			0.219476i
$250$	−8.34426e11			−0.854452
$251$	8.97688e11			0.901066			0.450533	−	0.892760i	$-0.351234\pi$
$251$	8.97688e11			0.901066			0.450533	+	0.892760i	$0.351234\pi$
$252$			1.07219e10i			0.0105504i
$253$	1.39620e12			1.34693
$254$		−	1.97278e12i		−	1.86600i
$255$	8.30651e10			0.0770403
$256$	−3.35319e11			−0.304971
$257$			7.32413e11i			0.653266i	0.945151	+	0.326633i	$0.105914\pi$
$257$			7.32413e11i			0.653266i	−0.945151	+	0.326633i	$0.894086\pi$
$258$	−3.85420e11	−	8.66839e11i	−0.337160	−	0.758298i
$259$	−2.17064e11			−0.186247
$260$			8.20389e10i			0.0690483i
$261$			4.19507e11i			0.346367i
$262$	−2.32556e11			−0.188374
$263$		−	6.19909e11i		−	0.492662i	−0.969186	−	0.246331i	$-0.920775\pi$
$263$		−	6.19909e11i		−	0.492662i	0.969186	−	0.246331i	$-0.0792250\pi$
$264$	9.45030e11			0.736930
$265$			1.51159e11i			0.115666i
$266$		−	5.41584e11i		−	0.406685i
$267$	1.19819e11			0.0883019
$268$	1.95758e10			0.0141595
$269$	2.54278e12			1.80529			0.902647	−	0.430383i	$-0.141621\pi$
$269$	2.54278e12			1.80529			0.902647	+	0.430383i	$0.141621\pi$
$270$			7.66428e11i			0.534137i
$271$	−3.45095e11			−0.236098			−0.118049	−	0.993008i	$-0.537664\pi$
$271$	−3.45095e11			−0.236098			−0.118049	+	0.993008i	$0.537664\pi$
$272$	2.22265e11			0.149289
$273$	−7.54802e11			−0.497760
$274$	1.14520e12			0.741529
$275$	−9.21025e11			−0.585609
$276$			2.41233e11i			0.150623i
$277$		−	8.63431e11i		−	0.529455i	−0.964323	−	0.264727i	$-0.914718\pi$
$277$		−	8.63431e11i		−	0.529455i	0.964323	−	0.264727i	$-0.0852820\pi$
$278$		−	4.49315e11i		−	0.270600i
$279$	2.34659e11			0.138808
$280$		−	4.14674e11i		−	0.240944i
$281$	1.86458e12			1.06426			0.532131	−	0.846662i	$-0.321391\pi$
$281$	1.86458e12			1.06426			0.532131	+	0.846662i	$0.321391\pi$
$282$	−1.12179e11			−0.0629024
$283$	−1.56730e12			−0.863414			−0.431707	−	0.902014i	$-0.642089\pi$
$283$	−1.56730e12			−0.863414			−0.431707	+	0.902014i	$0.642089\pi$
$284$		−	3.33846e11i		−	0.180698i
$285$			8.36342e11i			0.444795i
$286$		−	1.87744e12i		−	0.981151i
$287$		−	4.70566e11i		−	0.241664i
$288$		−	9.42712e10i		−	0.0475791i
$289$	−1.95884e12			−0.971651
$290$		−	1.51215e12i		−	0.737232i
$291$			2.51657e12i			1.20599i
$292$		−	2.81597e11i		−	0.132652i
$293$	2.56310e11			0.118694			0.0593469	−	0.998237i	$-0.481098\pi$
$293$	2.56310e11			0.118694			0.0593469	+	0.998237i	$0.481098\pi$
$294$	−1.46726e12			−0.667991
$295$			1.43519e12i			0.642392i
$296$	1.00090e12			0.440486
$297$			2.00922e12i			0.869451i
$298$	−1.14943e12			−0.489104
$299$	5.14206e12			2.15170
$300$		−	1.59133e11i		−	0.0654869i
$301$	−9.97136e11	+	4.43354e11i	−0.403573	+	0.179440i
$302$	−3.27488e12			−1.30365
$303$		−	1.00009e12i		−	0.391586i
$304$			2.23788e12i			0.861923i
$305$	−2.21649e12			−0.839783
$306$			9.94473e10i			0.0370669i
$307$	−3.71438e12			−1.36205			−0.681027	−	0.732258i	$-0.738466\pi$
$307$	−3.71438e12			−1.36205			−0.681027	+	0.732258i	$0.738466\pi$
$308$		−	1.01317e11i		−	0.0365534i
$309$			3.11574e12i			1.10604i
$310$	−8.45847e11			−0.295450
$311$	3.09364e12			1.06333			0.531665	−	0.846955i	$-0.321567\pi$
$311$	3.09364e12			1.06333			0.531665	+	0.846955i	$0.321567\pi$
$312$	3.48046e12			1.17724
$313$		−	2.23969e11i		−	0.0745530i	−0.999305	−	0.0372765i	$-0.988132\pi$
$313$		−	2.23969e11i		−	0.0745530i	0.999305	−	0.0372765i	$-0.0118682\pi$
$314$	−2.09318e12			−0.685738
$315$	1.66263e11			0.0536096
$316$	5.39195e11			0.171124
$317$	−4.04325e12			−1.26309			−0.631545	−	0.775339i	$-0.717579\pi$
$317$	−4.04325e12			−1.26309			−0.631545	+	0.775339i	$0.717579\pi$
$318$	5.97683e11			0.183796
$319$		−	3.96415e12i		−	1.20004i
$320$			1.89358e12i			0.564332i
$321$			4.29446e12i			1.26004i
$322$	−2.42239e12			−0.699784
$323$			5.75437e11i			0.163676i
$324$	−2.61860e11			−0.0733404
$325$	−3.39205e12			−0.935502
$326$	1.30116e12			0.353380
$327$			1.56158e11i			0.0417662i
$328$			2.16982e12i			0.571550i
$329$			1.29041e11i			0.0334772i
$330$		−	1.36581e12i		−	0.348996i
$331$			5.99907e11i			0.150988i	0.997146	+	0.0754942i	$0.0240534\pi$
$331$			5.99907e11i			0.150988i	−0.997146	+	0.0754942i	$0.975947\pi$
$332$	−1.03854e11			−0.0257473
$333$			4.01309e11i			0.0980073i
$334$		−	6.40859e11i		−	0.154181i
$335$		−	3.03561e11i		−	0.0719484i
$336$	−1.46930e12			−0.343094
$337$	3.55603e12			0.818118			0.409059	−	0.912508i	$-0.365857\pi$
$337$	3.55603e12			0.818118			0.409059	+	0.912508i	$0.365857\pi$
$338$		−	2.73581e12i		−	0.620158i
$339$	−3.84958e11			−0.0859833
$340$			4.10636e10i			0.00903780i
$341$	−2.21742e12			−0.480923
$342$	−1.00129e12			−0.214007
$343$			3.78465e12i			0.797178i
$344$	4.59788e12	−	2.04434e12i	0.954477	−	0.424387i
$345$	3.74077e12			0.765360
$346$		−	2.66947e12i		−	0.538325i
$347$		−	5.19453e12i		−	1.03252i	−0.856432	−	0.516261i	$-0.827324\pi$
$347$		−	5.19453e12i		−	1.03252i	0.856432	−	0.516261i	$-0.172676\pi$
$348$	6.84919e11			0.134197
$349$			7.54441e12i			1.45713i	0.684977	+	0.728565i	$0.259812\pi$
$349$			7.54441e12i			1.45713i	−0.684977	+	0.728565i	$0.740188\pi$
$350$	1.59797e12			0.304248
$351$			7.39976e12i			1.38894i
$352$			8.90819e11i			0.164845i
$353$	2.57237e12			0.469310			0.234655	−	0.972079i	$-0.424604\pi$
$353$	2.57237e12			0.469310			0.234655	+	0.972079i	$0.424604\pi$
$354$	5.67474e12			1.02077
$355$	−5.17691e12			−0.918182
$356$			5.92332e10i			0.0103589i
$357$	−3.77808e11			−0.0651523
$358$	−4.07523e12			−0.693005
$359$	8.39475e12			1.40778			0.703891	−	0.710308i	$-0.251444\pi$
$359$	8.39475e12			1.40778			0.703891	+	0.710308i	$0.251444\pi$
$360$	−7.66653e11			−0.126790
$361$	3.37276e11			0.0550110
$362$		−	8.34411e12i		−	1.34226i
$363$			1.94148e12i			0.308035i
$364$		−	3.73140e11i		−	0.0583936i
$365$	−4.36670e12			−0.674045
$366$			8.76400e12i			1.33443i
$367$	4.84782e12			0.728142			0.364071	−	0.931371i	$-0.381386\pi$
$367$	4.84782e12			0.728142			0.364071	+	0.931371i	$0.381386\pi$
$368$	1.00095e13			1.48311
$369$	−8.69987e11			−0.127169
$370$		−	1.44655e12i		−	0.208606i
$371$		−	6.87523e11i		−	0.0978178i
$372$		−	3.83122e11i		−	0.0537802i
$373$		−	2.39635e12i		−	0.331899i	−0.986134	−	0.165949i	$-0.946931\pi$
$373$		−	2.39635e12i		−	0.331899i	0.986134	−	0.165949i	$-0.0530688\pi$
$374$		−	9.39731e11i		−	0.128424i
$375$	−5.86081e12			−0.790317
$376$		−	5.95021e11i		−	0.0791759i
$377$		−	1.45996e13i		−	1.91705i
$378$		−	3.48597e12i		−	0.451715i
$379$	1.05843e12			0.135352			0.0676759	−	0.997707i	$-0.478442\pi$
$379$	1.05843e12			0.135352			0.0676759	+	0.997707i	$0.478442\pi$
$380$	−4.13450e11			−0.0521801
$381$		−	1.38564e13i		−	1.72593i
$382$	−2.63004e12			−0.323330
$383$		−	6.61173e12i		−	0.802271i	−0.916019	−	0.401135i	$-0.868616\pi$
$383$		−	6.61173e12i		−	0.802271i	0.916019	−	0.401135i	$-0.131384\pi$
$384$	5.98970e12			0.717380
$385$	−1.57111e12			−0.185739
$386$			8.22838e11i			0.0960236i
$387$	8.19678e11	+	1.84352e12i	0.0944253	+	0.212369i
$388$	−1.24408e12			−0.141478
$389$			1.12412e13i			1.26202i	0.775774	+	0.631010i	$0.217359\pi$
$389$			1.12412e13i			1.26202i	−0.775774	+	0.631010i	$0.782641\pi$
$390$		−	5.03014e12i		−	0.557516i
$391$	2.57380e12			0.281638
$392$		−	7.78264e12i		−	0.840808i
$393$	−1.63342e12			−0.174235
$394$			6.77433e12i			0.713485i
$395$		−	8.36124e12i		−	0.869531i
$396$	−1.87315e11			−0.0192352
$397$	−6.78427e12			−0.687940			−0.343970	−	0.938981i	$-0.611772\pi$
$397$	−6.78427e12			−0.687940			−0.343970	+	0.938981i	$0.611772\pi$
$398$	−1.08908e13			−1.09055
$399$		−	3.80396e12i		−	0.376159i
$400$	−6.60296e12			−0.644820
$401$	−6.72300e12			−0.648398			−0.324199	−	0.945989i	$-0.605095\pi$
$401$	−6.72300e12			−0.648398			−0.324199	+	0.945989i	$0.605095\pi$
$402$	−1.20028e12			−0.114328
$403$	−8.16653e12			−0.768268
$404$	4.94401e11			0.0459381
$405$			4.06063e12i			0.372665i
$406$			6.87775e12i			0.623471i
$407$		−	3.79219e12i		−	0.339561i
$408$	1.74210e12			0.154090
$409$		−	1.25823e13i		−	1.09937i	−0.835374	−	0.549683i	$-0.814749\pi$
$409$		−	1.25823e13i		−	1.09937i	0.835374	−	0.549683i	$-0.185251\pi$
$410$	3.13594e12			0.270675
$411$	8.04361e12			0.685870
$412$	−1.54028e12			−0.129752
$413$		−	6.52773e12i		−	0.543265i
$414$			4.47853e12i			0.368242i
$415$			1.61045e12i			0.130830i
$416$			3.28080e12i			0.263338i
$417$		−	3.15588e12i		−	0.250288i
$418$	9.46170e12			0.741460
$419$			8.22754e12i			0.637089i	0.947908	+	0.318545i	$0.103194\pi$
$419$			8.22754e12i			0.637089i	−0.947908	+	0.318545i	$0.896806\pi$
$420$		−	2.71454e11i		−	0.0207706i
$421$		−	1.51716e12i		−	0.114715i	−0.998354	−	0.0573577i	$-0.981732\pi$
$421$		−	1.51716e12i		−	0.114715i	0.998354	−	0.0573577i	$-0.0182676\pi$
$422$	−8.44355e12			−0.630903
$423$	2.38573e11			0.0176165
$424$			3.17023e12i			0.231346i
$425$	−1.69785e12			−0.122449
$426$			2.04695e13i			1.45901i
$427$	1.00813e13			0.710197
$428$	−2.12299e12			−0.147818
$429$		−	1.31867e13i		−	0.907506i
$430$	−2.95460e12	−	6.64511e12i	−0.200982	−	0.452022i
$431$	2.29491e13			1.54304			0.771522	−	0.636202i	$-0.219496\pi$
$431$	2.29491e13			1.54304			0.771522	+	0.636202i	$0.219496\pi$
$432$			1.44044e13i			0.957361i
$433$			1.61671e13i			1.06216i	0.847321	+	0.531082i	$0.178214\pi$
$433$			1.61671e13i			1.06216i	−0.847321	+	0.531082i	$0.821786\pi$
$434$	3.84719e12			0.249859
$435$		−	1.06210e13i		−	0.681895i
$436$	−7.71973e10			−0.00489970
$437$			2.59143e13i			1.62605i
$438$			1.72659e13i			1.07107i
$439$	8.69720e12			0.533404			0.266702	−	0.963779i	$-0.414066\pi$
$439$	8.69720e12			0.533404			0.266702	+	0.963779i	$0.414066\pi$
$440$	7.24452e12			0.439285
$441$	3.12044e12			0.187078
$442$		−	3.46094e12i		−	0.205155i
$443$	3.97589e11			0.0233032			0.0116516	−	0.999932i	$-0.496291\pi$
$443$	3.97589e11			0.0233032			0.0116516	+	0.999932i	$0.496291\pi$
$444$	6.55209e11			0.0379721
$445$	9.18523e11			0.0526369
$446$	3.11230e13			1.76363
$447$	−8.07333e12			−0.452392
$448$		−	8.61265e12i		−	0.477251i
$449$			9.74296e12i			0.533899i	0.963711	+	0.266949i	$0.0860157\pi$
$449$			9.74296e12i			0.533899i	−0.963711	+	0.266949i	$0.913984\pi$
$450$		−	2.95434e12i		−	0.160102i
$451$	8.22098e12			0.440596
$452$		−	1.90306e11i		−	0.0100869i
$453$	−2.30020e13			−1.20580
$454$	−3.26534e13			−1.69297
$455$	−5.78624e12			−0.296715
$456$			1.75404e13i			0.889641i
$457$			3.12316e13i			1.56680i	0.621517	+	0.783400i	$0.286517\pi$
$457$			3.12316e13i			1.56680i	−0.621517	+	0.783400i	$0.713483\pi$
$458$		−	4.99286e12i		−	0.247755i
$459$			3.70387e12i			0.181799i
$460$			1.84927e12i			0.0897865i
$461$	−2.87113e12			−0.137895			−0.0689474	−	0.997620i	$-0.521964\pi$
$461$	−2.87113e12			−0.137895			−0.0689474	+	0.997620i	$0.521964\pi$
$462$			6.21215e12i			0.295143i
$463$		−	5.12515e11i		−	0.0240881i	−0.999927	−	0.0120440i	$-0.996166\pi$
$463$		−	5.12515e11i		−	0.0240881i	0.999927	−	0.0120440i	$-0.00383383\pi$
$464$		−	2.84195e13i		−	1.32138i
$465$	−5.94103e12			−0.273273
$466$	2.49890e12			0.113715
$467$		−	1.78913e13i		−	0.805487i	−0.915313	−	0.402743i	$-0.868057\pi$
$467$		−	1.78913e13i		−	0.805487i	0.915313	−	0.402743i	$-0.131943\pi$
$468$	−6.89865e11			−0.0307280
$469$			1.38069e12i			0.0608462i
$470$	−8.59956e11			−0.0374962
$471$	−1.47020e13			−0.634266
$472$			3.00999e13i			1.28486i
$473$	−7.74558e12	−	1.74204e13i	−0.327151	−	0.735786i
$474$	−3.30603e13			−1.38170
$475$		−	1.70948e13i		−	0.706963i
$476$		−	1.86771e11i		−	0.00764319i
$477$	−1.27110e12			−0.0514740
$478$			4.14704e13i			1.66188i
$479$	1.85935e13			0.737365			0.368683	−	0.929555i	$-0.379809\pi$
$479$	1.85935e13			0.737365			0.368683	+	0.929555i	$0.379809\pi$
$480$			2.38673e12i			0.0936694i
$481$		−	1.39663e13i		−	0.542444i
$482$	−3.22716e12			−0.124047
$483$	−1.70143e13			−0.647258
$484$	−9.59781e11			−0.0361364
$485$			1.92918e13i			0.718891i
$486$	−1.16744e13			−0.430579
$487$	3.72914e13			1.36133			0.680666	−	0.732594i	$-0.261691\pi$
$487$	3.72914e13			1.36133			0.680666	+	0.732594i	$0.261691\pi$
$488$	−4.64859e13			−1.67966
$489$	9.13902e12			0.326855
$490$	−1.12479e13			−0.398190
$491$		−	4.75070e13i		−	1.66475i	−0.554210	−	0.832377i	$-0.686980\pi$
$491$		−	4.75070e13i		−	1.66475i	0.554210	−	0.832377i	$-0.313020\pi$
$492$			1.42041e12i			0.0492706i
$493$		−	7.30765e12i		−	0.250925i
$494$	3.48465e13			1.18447
$495$			2.90468e12i			0.0977400i
$496$	−1.58970e13			−0.529549
$497$	2.35463e13			0.776499
$498$	6.36771e12			0.207891
$499$			2.21002e13i			0.714322i	0.934043	+	0.357161i	$0.116255\pi$
$499$			2.21002e13i			0.714322i	−0.934043	+	0.357161i	$0.883745\pi$
$500$		−	2.89732e12i		−	0.0927142i
$501$		−	4.50124e12i		−	0.142608i
$502$		−	2.72098e13i		−	0.853505i
$503$		−	5.70484e13i		−	1.77176i	−0.463918	−	0.885878i	$-0.653557\pi$
$503$		−	5.70484e13i		−	1.77176i	0.463918	−	0.885878i	$-0.346443\pi$
$504$	3.48699e12			0.107226
$505$		−	7.66663e12i		−	0.233425i
$506$		−	4.23201e13i		−	1.27583i
$507$		−	1.92157e13i		−	0.573609i
$508$	6.84996e12			0.202474
$509$	−3.84448e13			−1.12525			−0.562625	−	0.826713i	$-0.690208\pi$
$509$	−3.84448e13			−1.12525			−0.562625	+	0.826713i	$0.690208\pi$
$510$		−	2.51778e12i		−	0.0729739i
$511$	1.98612e13			0.570034
$512$			3.89733e13i			1.10769i
$513$	−3.72924e13			−1.04962
$514$	2.22001e13			0.618785
$515$			2.38850e13i			0.659309i
$516$	3.00987e12	−	1.33827e12i	0.0822808	−	0.0365843i
$517$	−2.25440e12			−0.0610350
$518$			6.57941e12i			0.176416i
$519$		−	1.87497e13i		−	0.497918i
$520$	2.66809e13			0.701751
$521$			4.87724e13i			1.27053i	0.772294	+	0.635266i	$0.219109\pi$
$521$			4.87724e13i			1.27053i	−0.772294	+	0.635266i	$0.780891\pi$
$522$	1.27156e13			0.328085
$523$			4.72530e12i			0.120759i	0.998175	+	0.0603797i	$0.0192311\pi$
$523$			4.72530e12i			0.120759i	−0.998175	+	0.0603797i	$0.980769\pi$
$524$		−	8.07488e11i		−	0.0204399i
$525$	1.12237e13			0.281411
$526$	−1.87900e13			−0.466658
$527$	−4.08767e12			−0.100559
$528$		−	2.56692e13i		−	0.625523i
$529$	7.44825e13			1.79794
$530$	4.58179e12			0.109561
$531$	−1.20685e13			−0.285879
$532$	1.88051e12			0.0441282
$533$	3.02771e13			0.703846
$534$		−	3.63183e12i		−	0.0836411i
$535$			3.29209e13i			0.751109i
$536$		−	6.36650e12i		−	0.143905i
$537$	−2.86234e13			−0.640989
$538$		−	7.70741e13i		−	1.71000i
$539$	−2.94867e13			−0.648161
$540$	−2.66122e12			−0.0579578
$541$	9.01800e13			1.94592			0.972958	−	0.230982i	$-0.0741940\pi$
$541$	9.01800e13			1.94592			0.972958	+	0.230982i	$0.0741940\pi$
$542$			1.04602e13i			0.223636i
$543$		−	5.86071e13i		−	1.24151i
$544$			1.64217e12i			0.0344686i
$545$			1.19709e12i			0.0248969i
$546$			2.28788e13i			0.471487i
$547$	4.49477e13			0.917848			0.458924	−	0.888476i	$-0.348235\pi$
$547$	4.49477e13			0.917848			0.458924	+	0.888476i	$0.348235\pi$
$548$			3.97640e12i			0.0804613i
$549$		−	1.86385e13i		−	0.373722i
$550$			2.79171e13i			0.554699i
$551$	7.35771e13			1.44872
$552$	7.84542e13			1.53081
$553$			3.80297e13i			0.735355i
$554$	−2.61714e13			−0.501509
$555$		−	1.01603e13i		−	0.192948i
$556$	1.56013e12			0.0293620
$557$	−2.31786e12			−0.0432325			−0.0216163	−	0.999766i	$-0.506881\pi$
$557$	−2.31786e12			−0.0432325			−0.0216163	+	0.999766i	$0.506881\pi$
$558$		−	7.11273e12i		−	0.131482i
$559$	−2.85262e13	−	6.41576e13i	−0.522619	−	1.17541i
$560$	−1.12635e13			−0.204519
$561$		−	6.60045e12i		−	0.118784i
$562$		−	5.65170e13i		−	1.00809i
$563$	−6.76439e13			−1.19588			−0.597939	−	0.801542i	$-0.704013\pi$
$563$	−6.76439e13			−1.19588			−0.597939	+	0.801542i	$0.704013\pi$
$564$		−	3.89512e11i		−	0.00682536i
$565$	−2.95105e12			−0.0512548
$566$			4.75063e13i			0.817841i
$567$		−	1.84691e13i		−	0.315159i
$568$	−1.08574e14			−1.83647
$569$	−3.69123e13			−0.618885			−0.309442	−	0.950918i	$-0.600142\pi$
$569$	−3.69123e13			−0.618885			−0.309442	+	0.950918i	$0.600142\pi$
$570$	2.53503e13			0.421317
$571$			7.73272e13i			1.27395i	0.770885	+	0.636974i	$0.219814\pi$
$571$			7.73272e13i			1.27395i	−0.770885	+	0.636974i	$0.780186\pi$
$572$	6.51891e12			0.106462
$573$	−1.84728e13			−0.299061
$574$	−1.42633e13			−0.228908
$575$	−7.64613e13			−1.21647
$576$	−1.59231e13			−0.251140
$577$			7.14931e13i			1.11785i	0.829217	+	0.558927i	$0.188787\pi$
$577$			7.14931e13i			1.11785i	−0.829217	+	0.558927i	$0.811213\pi$
$578$			5.93743e13i			0.920364i
$579$			5.77942e12i			0.0888161i
$580$	5.25053e12			0.0799950
$581$		−	7.32487e12i		−	0.110642i
$582$	7.62795e13			1.14233
$583$	1.20113e13			0.178340
$584$	−9.15817e13			−1.34817
$585$			1.06977e13i			0.156138i
$586$		−	7.76901e12i		−	0.112429i
$587$		−	5.18469e13i		−	0.743930i	−0.928247	−	0.371965i	$-0.878684\pi$
$587$		−	5.18469e13i		−	0.743930i	0.928247	−	0.371965i	$-0.121316\pi$
$588$		−	5.09467e12i		−	0.0724819i
$589$		−	4.11567e13i		−	0.580583i
$590$	4.35020e13			0.608484
$591$			4.75813e13i			0.659931i
$592$		−	2.71868e13i		−	0.373894i
$593$			4.78819e13i			0.652977i	0.945201	+	0.326488i	$0.105865\pi$
$593$			4.78819e13i			0.652977i	−0.945201	+	0.326488i	$0.894135\pi$
$594$	6.09013e13			0.823558
$595$	−2.89624e12			−0.0388373
$596$		−	3.99109e12i		−	0.0530713i
$597$	−7.64943e13			−1.00869
$598$		−	1.55861e14i		−	2.03812i
$599$	−3.77465e13			−0.489489			−0.244744	−	0.969588i	$-0.578704\pi$
$599$	−3.77465e13			−0.489489			−0.244744	+	0.969588i	$0.578704\pi$
$600$	−5.17536e13			−0.665556
$601$			9.77475e13i			1.24662i	0.781976	+	0.623309i	$0.214212\pi$
$601$			9.77475e13i			1.24662i	−0.781976	+	0.623309i	$0.785788\pi$
$602$	1.34385e13	+	3.02241e13i	0.169968	+	0.382271i
$603$	2.55264e12			0.0320187
$604$		−	1.13711e13i		−	0.141455i
$605$			1.48832e13i			0.183620i
$606$	−3.03138e13			−0.370917
$607$			8.67443e13i			1.05268i	0.850273	+	0.526341i	$0.176437\pi$
$607$			8.67443e13i			1.05268i	−0.850273	+	0.526341i	$0.823563\pi$
$608$	−1.65342e13			−0.199005
$609$			4.83077e13i			0.576673i
$610$			6.71840e13i			0.795457i
$611$	−8.30275e12			−0.0975026
$612$	−3.45304e11			−0.00402202
$613$	−9.99251e13			−1.15444			−0.577221	−	0.816588i	$-0.695863\pi$
$613$	−9.99251e13			−1.15444			−0.577221	+	0.816588i	$0.695863\pi$
$614$			1.12586e14i			1.29016i
$615$	2.20261e13			0.250358
$616$	−3.29505e13			−0.371499
$617$	1.05976e14			1.18517			0.592587	−	0.805506i	$-0.298107\pi$
$617$	1.05976e14			1.18517			0.592587	+	0.805506i	$0.298107\pi$
$618$	9.44411e13			1.04766
$619$	−3.85612e13			−0.424324			−0.212162	−	0.977235i	$-0.568050\pi$
$619$	−3.85612e13			−0.424324			−0.212162	+	0.977235i	$0.568050\pi$
$620$		−	2.93698e12i		−	0.0320584i
$621$			1.66801e14i			1.80609i
$622$		−	9.37712e13i		−	1.00720i
$623$	−4.17775e12			−0.0445146
$624$		−	9.45373e13i		−	0.999264i
$625$	2.44275e13			0.256140
$626$	−6.78870e12			−0.0706179
$627$	6.64567e13			0.685806
$628$		−	7.26800e12i		−	0.0744075i
$629$		−	6.99066e12i		−	0.0710011i
$630$		−	5.03959e12i		−	0.0507800i
$631$		−	5.20514e13i		−	0.520338i	−0.965563	−	0.260169i	$-0.916222\pi$
$631$		−	5.20514e13i		−	0.520338i	0.965563	−	0.260169i	$-0.0837783\pi$
$632$		−	1.75358e14i		−	1.73916i
$633$	−5.93055e13			−0.583548
$634$			1.22555e14i			1.19642i
$635$		−	1.06222e14i		−	1.02883i
$636$			2.07530e12i			0.0199432i
$637$	−1.08597e14			−1.03543
$638$	−1.20157e14			−1.13670
$639$		−	4.35326e13i		−	0.408612i
$640$	4.59165e13			0.427631
$641$			1.95638e14i			1.80785i	0.427689	+	0.903926i	$0.359328\pi$
$641$			1.95638e14i			1.80785i	−0.427689	+	0.903926i	$0.640672\pi$
$642$	1.30169e14			1.19353
$643$	9.21963e13			0.838800			0.419400	−	0.907802i	$-0.362240\pi$
$643$	9.21963e13			0.838800			0.419400	+	0.907802i	$0.362240\pi$
$644$		−	8.41108e12i		−	0.0759316i
$645$	−2.07524e13	−	4.66737e13i	−0.185896	−	0.418093i
$646$	1.74420e13			0.155037
$647$		−	6.37692e13i		−	0.562458i	−0.959641	−	0.281229i	$-0.909258\pi$
$647$		−	6.37692e13i		−	0.562458i	0.959641	−	0.281229i	$-0.0907420\pi$
$648$			8.51625e13i			0.745373i
$649$	1.14042e14			0.990470
$650$			1.02816e14i			0.886124i
$651$	2.70218e13			0.231105
$652$			4.51792e12i			0.0383443i
$653$			2.02229e14i			1.70325i	0.524155	+	0.851623i	$0.324381\pi$
$653$			2.02229e14i			1.70325i	−0.524155	+	0.851623i	$0.675619\pi$
$654$	4.73329e12			0.0395616
$655$	−1.25216e13			−0.103861
$656$	5.89374e13			0.485145
$657$		−	3.67196e13i		−	0.299965i
$658$	3.91137e12			0.0317102
$659$	−8.46543e13			−0.681118			−0.340559	−	0.940223i	$-0.610616\pi$
$659$	−8.46543e13			−0.681118			−0.340559	+	0.940223i	$0.610616\pi$
$660$	4.74241e12			0.0378686
$661$	−1.47490e14			−1.16884			−0.584419	−	0.811452i	$-0.698678\pi$
$661$	−1.47490e14			−1.16884			−0.584419	+	0.811452i	$0.698678\pi$
$662$	1.81837e13			0.143019
$663$		−	2.43088e13i		−	0.189756i
$664$			3.37756e13i			0.261675i
$665$		−	2.91608e13i		−	0.224229i
$666$	1.21641e13			0.0928341
$667$		−	3.29094e14i		−	2.49282i
$668$	2.22521e12			0.0167297
$669$	2.18601e14			1.63125
$670$	−9.20121e12			−0.0681508
$671$			1.76125e14i			1.29482i
$672$		−	1.08557e13i		−	0.0792154i
$673$		−	1.06345e14i		−	0.770264i	−0.922861	−	0.385132i	$-0.874156\pi$
$673$		−	1.06345e14i		−	0.770264i	0.922861	−	0.385132i	$-0.125844\pi$
$674$		−	1.07787e14i		−	0.774936i
$675$		−	1.10033e14i		−	0.785242i
$676$	9.49936e12			0.0672916
$677$			1.02179e14i			0.718488i	0.933244	+	0.359244i	$0.116965\pi$
$677$			1.02179e14i			0.718488i	−0.933244	+	0.359244i	$0.883035\pi$
$678$			1.16684e13i			0.0814449i
$679$		−	8.77453e13i		−	0.607960i
$680$	1.33548e13			0.0918529
$681$	−2.29350e14			−1.56590
$682$			6.72120e13i			0.455538i
$683$	−3.50693e13			−0.235952			−0.117976	−	0.993016i	$-0.537641\pi$
$683$	−3.50693e13			−0.235952			−0.117976	+	0.993016i	$0.537641\pi$
$684$		−	3.47670e12i		−	0.0232213i
$685$	6.16616e13			0.408848
$686$	1.14716e14			0.755101
$687$		−	3.50687e13i		−	0.229158i
$688$	−5.55292e13	−	1.24889e14i	−0.360229	−	0.810182i
$689$	4.42365e13			0.284895
$690$		−	1.13386e14i		−	0.724962i
$691$		−	6.02940e13i		−	0.382722i	−0.981520	−	0.191361i	$-0.938710\pi$
$691$		−	6.02940e13i		−	0.382722i	0.981520	−	0.191361i	$-0.0612901\pi$
$692$	9.26902e12			0.0584122
$693$		−	1.32115e13i		−	0.0826579i
$694$	−1.57451e14			−0.978022
$695$		−	2.41927e13i		−	0.149197i
$696$		−	2.22751e14i		−	1.36387i
$697$	1.51548e13			0.0921272
$698$	2.28678e14			1.38022
$699$	1.75517e13			0.105180
$700$			5.54851e12i			0.0330131i
$701$	−2.04936e14			−1.21068			−0.605338	−	0.795968i	$-0.706962\pi$
$701$	−2.04936e14			−1.21068			−0.605338	+	0.795968i	$0.706962\pi$
$702$	2.24294e14			1.31562
$703$	7.03855e13			0.409927
$704$	1.50466e14			0.870114
$705$	−6.04013e12			−0.0346817
$706$		−	7.79709e13i		−	0.444538i
$707$			3.48704e13i			0.197406i
$708$			1.97040e13i			0.110761i
$709$	4.40105e13			0.245655			0.122827	−	0.992428i	$-0.460804\pi$
$709$	4.40105e13			0.245655			0.122827	+	0.992428i	$0.460804\pi$
$710$			1.56917e14i			0.869718i
$711$	7.03096e13			0.386961
$712$	1.92640e13			0.105280
$713$	−1.84085e14			−0.999011
$714$			1.14517e13i			0.0617134i
$715$		−	1.01088e14i		−	0.540965i
$716$		−	1.41501e13i		−	0.0751961i
$717$			2.91278e14i			1.53714i
$718$		−	2.54453e14i		−	1.33347i
$719$	9.39253e13			0.488808			0.244404	−	0.969674i	$-0.421408\pi$
$719$	9.39253e13			0.488808			0.244404	+	0.969674i	$0.421408\pi$
$720$			2.08241e13i			0.107623i
$721$		−	1.08637e14i		−	0.557572i
$722$		−	1.02232e13i		−	0.0521073i
$723$	−2.26668e13			−0.114736
$724$	2.89727e13			0.145645
$725$			2.17092e14i			1.08381i
$726$	5.88482e13			0.291776
$727$			2.05262e14i			1.01074i	0.862904	+	0.505368i	$0.168643\pi$
$727$			2.05262e14i			1.01074i	−0.862904	+	0.505368i	$0.831357\pi$
$728$	−1.21353e14			−0.593465
$729$	−2.28915e14			−1.11183
$730$			1.32359e14i			0.638467i
$731$	−1.42785e13	−	3.21133e13i	−0.0684061	−	0.153850i
$732$	−3.04306e13			−0.144796
$733$		−	3.06949e14i		−	1.45059i	−0.688436	−	0.725297i	$-0.741703\pi$
$733$		−	3.06949e14i		−	1.45059i	0.688436	−	0.725297i	$-0.258297\pi$
$734$		−	1.46942e14i		−	0.689709i
$735$	−7.90026e13			−0.368302
$736$			7.39537e13i			0.342429i
$737$	−2.41213e13			−0.110934
$738$			2.63701e13i			0.120457i
$739$		−	1.84860e14i		−	0.838728i	−0.907818	−	0.419364i	$-0.862253\pi$
$739$		−	1.84860e14i		−	0.838728i	0.907818	−	0.419364i	$-0.137747\pi$
$740$	5.02277e12			0.0226352
$741$	2.44754e14			1.09557
$742$	−2.08395e13			−0.0926547
$743$			2.60027e14i			1.14835i	0.818732	+	0.574175i	$0.194677\pi$
$743$			2.60027e14i			1.14835i	−0.818732	+	0.574175i	$0.805323\pi$
$744$	−1.24600e14			−0.546578
$745$	−6.18894e13			−0.269671
$746$	−7.26355e13			−0.314380
$747$	−1.35423e13			−0.0582222
$748$	3.26297e12			0.0139349
$749$		−	1.49735e14i		−	0.635206i
$750$			1.77647e14i			0.748601i
$751$			3.93218e14i			1.64601i	0.568031	+	0.823007i	$0.307705\pi$
$751$			3.93218e14i			1.64601i	−0.568031	+	0.823007i	$0.692295\pi$
$752$	−1.61621e13			−0.0672063
$753$		−	1.91115e14i		−	0.789441i
$754$	−4.42527e14			−1.81586
$755$	−1.76331e14			−0.718777
$756$	1.21041e13			0.0490144
$757$		−	1.83250e14i		−	0.737163i	−0.929595	−	0.368582i	$-0.879843\pi$
$757$		−	1.83250e14i		−	0.737163i	0.929595	−	0.368582i	$-0.120157\pi$
$758$		−	3.20819e13i		−	0.128208i
$759$		−	2.97246e14i		−	1.18007i
$760$			1.34463e14i			0.530316i
$761$		−	7.87814e13i		−	0.308674i	−0.988018	−	0.154337i	$-0.950676\pi$
$761$		−	7.87814e13i		−	0.308674i	0.988018	−	0.154337i	$-0.0493242\pi$
$762$	−4.19999e14			−1.63483
$763$		−	5.44477e12i		−	0.0210551i
$764$		−	9.13212e12i		−	0.0350837i
$765$			5.35459e12i			0.0204371i
$766$	−2.00408e14			−0.759925
$767$	4.20006e14			1.58226
$768$			7.13884e13i			0.267191i
$769$	3.29751e14			1.22618			0.613091	−	0.790012i	$-0.289926\pi$
$769$	3.29751e14			1.22618			0.613091	+	0.790012i	$0.289926\pi$
$770$			4.76218e13i			0.175935i
$771$	1.55928e14			0.572339
$772$	−2.85709e12			−0.0104193
$773$			5.25997e13i			0.190584i	0.995449	+	0.0952919i	$0.0303785\pi$
$773$			5.25997e13i			0.190584i	−0.995449	+	0.0952919i	$0.969622\pi$
$774$	5.58787e13	−	2.48452e13i	0.201160	−	0.0894412i
$775$	1.21435e14			0.434344
$776$			4.04601e14i			1.43787i
$777$			4.62122e13i			0.163174i
$778$	3.40733e14			1.19541
$779$			1.52587e14i			0.531899i
$780$	1.74658e13			0.0604945
$781$			4.11363e14i			1.41570i
$782$		−	7.80143e13i		−	0.266772i
$783$	4.73588e14			1.60913
$784$	−2.11395e14			−0.713697
$785$	−1.12704e14			−0.378087
$786$			4.95104e13i			0.165038i
$787$	−8.26230e13			−0.273670			−0.136835	−	0.990594i	$-0.543693\pi$
$787$	−8.26230e13			−0.273670			−0.136835	+	0.990594i	$0.543693\pi$
$788$	−2.35220e13			−0.0774183
$789$	−1.31977e14			−0.431631
$790$	−2.53437e14			−0.823635
$791$	1.34224e13			0.0433457
$792$			6.09191e13i			0.195491i
$793$			6.48652e14i			2.06845i
$794$			2.05638e14i			0.651629i
$795$	3.21814e13			0.101337
$796$		−	3.78153e13i		−	0.118332i
$797$	3.00379e14			0.934068			0.467034	−	0.884239i	$-0.345323\pi$
$797$	3.00379e14			0.934068			0.467034	+	0.884239i	$0.345323\pi$
$798$	−1.15302e14			−0.356304
$799$	−4.15585e12			−0.0127622
$800$		−	4.87848e13i		−	0.148879i
$801$			7.72386e12i			0.0234246i
$802$			2.03781e14i			0.614173i
$803$			3.46983e14i			1.03928i
$804$		−	4.16764e12i		−	0.0124054i
$805$	−1.30430e14			−0.385831
$806$			2.47535e14i			0.727716i
$807$		−	5.41351e14i		−	1.58165i
$808$		−	1.60790e14i		−	0.466877i
$809$	5.08376e14			1.46704			0.733521	−	0.679666i	$-0.237875\pi$
$809$	5.08376e14			1.46704			0.733521	+	0.679666i	$0.237875\pi$
$810$	1.23082e14			0.352994
$811$		−	3.96814e14i		−	1.13105i	−0.824731	−	0.565526i	$-0.808673\pi$
$811$		−	3.96814e14i		−	1.13105i	0.824731	−	0.565526i	$-0.191327\pi$
$812$	−2.38811e13			−0.0676511
$813$			7.34697e13i			0.206850i
$814$	−1.14945e14			−0.321638
$815$	7.00589e13			0.194839
$816$		−	4.73196e13i		−	0.130795i
$817$	3.23334e14	−	1.43763e14i	0.888261	−	0.394945i
$818$	−3.81380e14			−1.04134
$819$		−	4.86565e13i		−	0.132045i
$820$			1.08887e13i			0.0293702i
$821$	−7.28379e14			−1.95273			−0.976363	−	0.216137i	$-0.930654\pi$
$821$	−7.28379e14			−1.95273			−0.976363	+	0.216137i	$0.930654\pi$
$822$		−	2.43809e14i		−	0.649668i
$823$	2.64290e14			0.699973			0.349987	−	0.936755i	$-0.386186\pi$
$823$	2.64290e14			0.699973			0.349987	+	0.936755i	$0.386186\pi$
$824$			5.00934e14i			1.31870i
$825$			1.96083e14i			0.513063i
$826$	−1.97862e14			−0.514590
$827$	−1.47340e14			−0.380885			−0.190443	−	0.981698i	$-0.560992\pi$
$827$	−1.47340e14			−0.380885			−0.190443	+	0.981698i	$0.560992\pi$
$828$	−1.55505e13			−0.0399570
$829$		−	1.62568e13i		−	0.0415206i	−0.999784	−	0.0207603i	$-0.993391\pi$
$829$		−	1.62568e13i		−	0.0415206i	0.999784	−	0.0207603i	$-0.00660868\pi$
$830$	4.88143e13			0.123924
$831$	−1.83822e14			−0.463865
$832$	5.54153e14			1.39000
$833$	−5.43569e13			−0.135528
$834$	−9.56578e13			−0.237077
$835$		−	3.45061e13i		−	0.0850087i
$836$			3.28532e13i			0.0804538i
$837$		−	2.64910e14i		−	0.644868i
$838$	2.49385e14			0.603462
$839$		−	3.92672e14i		−	0.944541i	−0.881454	−	0.472270i	$-0.843435\pi$
$839$		−	3.92672e14i		−	0.944541i	0.881454	−	0.472270i	$-0.156565\pi$
$840$	−8.82828e13			−0.211096
$841$	−5.13672e14			−1.22097
$842$	−4.59867e13			−0.108660
$843$		−	3.96962e14i		−	0.932420i
$844$		−	2.93180e13i		−	0.0684576i
$845$		−	1.47306e14i		−	0.341929i
$846$		−	7.23137e12i		−	0.0166866i
$847$		−	6.76938e13i		−	0.155286i
$848$	8.61108e13			0.196371
$849$			3.33673e14i			0.756454i
$850$			5.14635e13i			0.115986i
$851$		−	3.14819e14i		−	0.705363i
$852$	−7.10747e13			−0.158313
$853$	8.18682e14			1.81288			0.906442	−	0.422330i	$-0.138788\pi$
$853$	8.18682e14			1.81288			0.906442	+	0.422330i	$0.138788\pi$
$854$		−	3.05575e14i		−	0.672711i
$855$	−5.39128e13			−0.117994
$856$			6.90442e14i			1.50231i
$857$	−1.87875e13			−0.0406411			−0.0203206	−	0.999794i	$-0.506469\pi$
$857$	−1.87875e13			−0.0406411			−0.0203206	+	0.999794i	$0.506469\pi$
$858$	−3.99701e14			−0.859605
$859$		−	4.82515e14i		−	1.03168i	−0.856685	−	0.515840i	$-0.827480\pi$
$859$		−	4.82515e14i		−	1.03168i	0.856685	−	0.515840i	$-0.172520\pi$
$860$	2.30734e13	−	1.02591e13i	0.0490477	−	0.0218080i
$861$	−1.00182e14			−0.211726
$862$		−	6.95608e14i		−	1.46160i
$863$		−	1.60742e14i		−	0.335795i	−0.985804	−	0.167898i	$-0.946302\pi$
$863$		−	1.60742e14i		−	0.335795i	0.985804	−	0.167898i	$-0.0536978\pi$
$864$	−1.06424e14			−0.221040
$865$		−	1.43734e14i		−	0.296810i
$866$	4.90039e14			1.00610
$867$			4.17031e14i			0.851282i
$868$			1.33583e13i			0.0271115i
$869$	−6.64394e14			−1.34068
$870$	−3.21932e14			−0.645903
$871$	−8.88364e13			−0.177215
$872$			2.51063e13i			0.0497966i
$873$	−1.62224e14			−0.319923
$874$	7.85488e14			1.54022
$875$	2.04349e14			0.398413
$876$	−5.99512e13			−0.116219
$877$	−3.52329e14			−0.679125			−0.339563	−	0.940583i	$-0.610279\pi$
$877$	−3.52329e14			−0.679125			−0.339563	+	0.940583i	$0.610279\pi$
$878$		−	2.63620e14i		−	0.505250i
$879$		−	5.45677e13i		−	0.103990i
$880$		−	1.96778e14i		−	0.372875i
$881$	−5.41193e14			−1.01970			−0.509851	−	0.860263i	$-0.670299\pi$
$881$	−5.41193e14			−1.01970			−0.509851	+	0.860263i	$0.670299\pi$
$882$		−	9.45835e13i		−	0.177204i
$883$	−6.95756e13			−0.129615			−0.0648073	−	0.997898i	$-0.520643\pi$
$883$	−6.95756e13			−0.129615			−0.0648073	+	0.997898i	$0.520643\pi$
$884$	1.20172e13			0.0222608
$885$	3.05548e14			0.562812
$886$		−	1.20513e13i		−	0.0220732i
$887$		−	9.97444e14i		−	1.81665i	−0.418268	−	0.908323i	$-0.637363\pi$
$887$		−	9.97444e14i		−	1.81665i	0.418268	−	0.908323i	$-0.362637\pi$
$888$		−	2.13088e14i		−	0.385918i
$889$			4.83131e14i			0.870074i
$890$		−	2.78413e13i		−	0.0498585i
$891$	3.22662e14			0.574592
$892$			1.08066e14i			0.191367i
$893$		−	4.18432e13i		−	0.0736831i
$894$			2.44710e14i			0.428513i
$895$	−2.19425e14			−0.382094
$896$	−2.08843e14			−0.361644
$897$		−	1.09473e15i		−	1.88514i
$898$	2.95318e14			0.505718
$899$			5.22662e14i			0.890066i
$900$	1.02581e13			0.0173723
$901$	2.21421e13			0.0372902
$902$		−	2.49186e14i		−	0.417340i
$903$	9.43888e13	+	2.12287e14i	0.157211	+	0.353578i
$904$	−6.18916e13			−0.102516
$905$		−	4.49276e14i		−	0.740066i
$906$			6.97212e14i			1.14215i
$907$	−1.01421e14			−0.165231			−0.0826155	−	0.996582i	$-0.526327\pi$
$907$	−1.01421e14			−0.165231			−0.0826155	+	0.996582i	$0.526327\pi$
$908$		−	1.13380e14i		−	0.183699i
$909$	6.44687e13			0.103879
$910$			1.75386e14i			0.281054i
$911$		−	7.56002e14i		−	1.20484i	−0.798178	−	0.602422i	$-0.794202\pi$
$911$		−	7.56002e14i		−	1.20484i	0.798178	−	0.602422i	$-0.205798\pi$
$912$	4.76438e14			0.755148
$913$	1.27968e14			0.201720
$914$	9.46661e14			1.48410
$915$			4.71885e14i			0.735750i
$916$	1.73364e13			0.0268832
$917$	5.69525e13			0.0878347
$918$	1.12268e14			0.172203
$919$	6.32181e14			0.964415			0.482207	−	0.876057i	$-0.339835\pi$
$919$	6.32181e14			0.964415			0.482207	+	0.876057i	$0.339835\pi$
$920$	6.01423e14			0.912517
$921$			7.90780e14i			1.19332i
$922$			8.70266e13i			0.130616i
$923$			1.51501e15i			2.26156i
$924$	−2.15700e13			−0.0320251
$925$			2.07676e14i			0.306674i
$926$	−1.55348e13			−0.0228166
$927$	−2.00849e14			−0.293407
$928$	2.09973e14			0.305087
$929$		−	1.19303e15i		−	1.72415i	−0.506784	−	0.862073i	$-0.669166\pi$
$929$		−	1.19303e15i		−	1.72415i	0.506784	−	0.862073i	$-0.330834\pi$
$930$			1.80078e14i			0.258849i
$931$		−	5.47293e14i		−	0.782477i
$932$			8.67675e12i			0.0123389i
$933$		−	6.58627e14i		−	0.931604i
$934$	−5.42303e14			−0.762971
$935$		−	5.05985e13i		−	0.0708075i
$936$			2.24359e14i			0.312295i
$937$		−	1.35714e14i		−	0.187900i	−0.995577	−	0.0939501i	$-0.970051\pi$
$937$		−	1.35714e14i		−	0.187900i	0.995577	−	0.0939501i	$-0.0299494\pi$
$938$	4.18501e13			0.0576345
$939$	−4.76822e13			−0.0653173
$940$		−	2.98597e12i		−	0.00406861i
$941$	1.10068e15			1.49181			0.745903	−	0.666054i	$-0.232018\pi$
$941$	1.10068e15			1.49181			0.745903	+	0.666054i	$0.232018\pi$
$942$			4.45631e14i			0.600788i
$943$	6.82486e14			0.915241
$944$	8.17584e14			1.09062
$945$		−	1.87697e14i		−	0.249057i
$946$	−5.28028e14	+	2.34776e14i	−0.696949	+	0.309883i
$947$	−6.50543e14			−0.854134			−0.427067	−	0.904220i	$-0.640453\pi$
$947$	−6.50543e14			−0.854134			−0.427067	+	0.904220i	$0.640453\pi$
$948$		−	1.14793e14i		−	0.149925i
$949$			1.27791e15i			1.66023i
$950$	−5.18160e14			−0.669647
$951$			8.60795e14i			1.10662i
$952$	−6.07421e13			−0.0776792
$953$			5.30358e14i			0.674691i	0.941381	+	0.337346i	$0.109529\pi$
$953$			5.30358e14i			0.674691i	−0.941381	+	0.337346i	$0.890471\pi$
$954$			3.85282e13i			0.0487570i
$955$	−1.41611e14			−0.178271
$956$	−1.43995e14			−0.180326
$957$	−8.43955e14			−1.05138
$958$		−	5.63585e14i		−	0.698445i
$959$	−2.80457e14			−0.345759
$960$	4.03138e14			0.494422
$961$	−5.27268e14			−0.643301
$962$	−4.23331e14			−0.513812
$963$	−2.76832e14			−0.334260
$964$		−	1.12054e13i		−	0.0134600i
$965$			4.43045e13i			0.0529434i
$966$			5.15718e14i			0.613094i
$967$	2.45396e14			0.290225			0.145112	−	0.989415i	$-0.453646\pi$
$967$	2.45396e14			0.290225			0.145112	+	0.989415i	$0.453646\pi$
$968$			3.12142e14i			0.367262i
$969$	1.22509e14			0.143400
$970$	5.84752e14			0.680946
$971$	−1.21172e15			−1.40381			−0.701904	−	0.712271i	$-0.747667\pi$
$971$	−1.21172e15			−1.40381			−0.701904	+	0.712271i	$0.747667\pi$
$972$		−	4.05362e13i		−	0.0467209i
$973$			1.10036e14i			0.126175i
$974$		−	1.13034e15i		−	1.28948i
$975$			7.22156e14i			0.819612i
$976$			1.26267e15i			1.42574i
$977$	−8.00962e14			−0.899785			−0.449893	−	0.893083i	$-0.648538\pi$
$977$	−8.00962e14			−0.899785			−0.449893	+	0.893083i	$0.648538\pi$
$978$		−	2.77012e14i		−	0.309603i
$979$		−	7.29869e13i		−	0.0811581i
$980$		−	3.90553e13i		−	0.0432066i
$981$	−1.00663e13			−0.0110797
$982$	−1.43998e15			−1.57688
$983$			5.98841e14i			0.652445i	0.945293	+	0.326222i	$0.105776\pi$
$983$			5.98841e14i			0.652445i	−0.945293	+	0.326222i	$0.894224\pi$
$984$	4.61948e14			0.500746
$985$			3.64754e14i			0.393386i
$986$	−2.21502e14			−0.237680
$987$	2.74725e13			0.0293300
$988$			1.20995e14i			0.128524i
$989$	−6.43020e14	−	1.44620e15i	−0.679584	−	1.52843i
$990$	8.80436e13			0.0925810
$991$			3.97317e14i			0.415689i	0.978162	+	0.207845i	$0.0666448\pi$
$991$			3.97317e14i			0.415689i	−0.978162	+	0.207845i	$0.933355\pi$
$992$		−	1.17452e14i		−	0.122265i
$993$	1.27718e14			0.132284
$994$		−	7.13711e14i		−	0.735513i
$995$	−5.86399e14			−0.601281
$996$			2.21102e13i			0.0225577i
$997$		−	7.76136e14i		−	0.787884i	−0.919135	−	0.393942i	$-0.871111\pi$
$997$		−	7.76136e14i		−	0.787884i	0.919135	−	0.393942i	$-0.128889\pi$
$998$	6.69878e14			0.676618
$999$	4.53045e14			0.455317

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.b.b.42.10	✓	34
43.42	odd	2	inner	43.11.b.b.42.25	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.b.b.42.10	✓	34	1.1	even	1	trivial
43.11.b.b.42.25	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)

\(f(q)\)	\(=\)	\(q-30.3109i q^{2} -212.897i q^{3} +105.247 q^{4} -1632.05i q^{5} -6453.11 q^{6} +7423.10i q^{7} -34228.5i q^{8} +13723.9 q^{9} +O(q^{10})\)	\(q-30.3109i q^{2} -212.897i q^{3} +105.247 q^{4} -1632.05i q^{5} -6453.11 q^{6} +7423.10i q^{7} -34228.5i q^{8} +13723.9 q^{9} -49468.9 q^{10} -129685. q^{11} -22406.7i q^{12} -477616. q^{13} +225001. q^{14} -347458. q^{15} -929727. q^{16} -239065. q^{17} -415984. i q^{18} -2.40703e6i q^{19} -171768. i q^{20} +1.58035e6 q^{21} +3.93086e6i q^{22} -1.07661e7 q^{23} -7.28715e6 q^{24} +7.10204e6 q^{25} +1.44770e7i q^{26} -1.54931e7i q^{27} +781256. i q^{28} +3.05676e7i q^{29} +1.05318e7i q^{30} +1.70986e7 q^{31} -6.86913e6i q^{32} +2.76094e7i q^{33} +7.24629e6i q^{34} +1.21149e7 q^{35} +1.44439e6 q^{36} +2.92417e7i q^{37} -7.29593e7 q^{38} +1.01683e8i q^{39} -5.58626e7 q^{40} -6.33921e7 q^{41} -4.79020e7i q^{42} +(5.97263e7 + 1.34329e8i) q^{43} -1.36489e7 q^{44} -2.23981e7i q^{45} +3.26331e8i q^{46} +1.73838e7 q^{47} +1.97936e8i q^{48} +2.27373e8 q^{49} -2.15270e8i q^{50} +5.08962e7i q^{51} -5.02674e7 q^{52} -9.26195e7 q^{53} -4.69611e8 q^{54} +2.11651e8i q^{55} +2.54082e8 q^{56} -5.12449e8 q^{57} +9.26533e8 q^{58} -8.79381e8 q^{59} -3.65688e7 q^{60} -1.35810e9i q^{61} -5.18273e8i q^{62} +1.01874e8i q^{63} -1.16025e9 q^{64} +7.79492e8i q^{65} +8.36868e8 q^{66} +1.86000e8 q^{67} -2.51608e7 q^{68} +2.29207e9i q^{69} -3.67213e8i q^{70} -3.17203e9i q^{71} -4.69749e8i q^{72} -2.67560e9i q^{73} +8.86342e8 q^{74} -1.51200e9i q^{75} -2.53332e8i q^{76} -9.62661e8i q^{77} +3.08210e9 q^{78} +5.12315e9 q^{79} +1.51736e9i q^{80} -2.48806e9 q^{81} +1.92148e9i q^{82} -9.86767e8 q^{83} +1.66327e8 q^{84} +3.90166e8i q^{85} +(4.07164e9 - 1.81036e9i) q^{86} +6.50775e9 q^{87} +4.43891e9i q^{88} +5.62804e8i q^{89} -6.78906e8 q^{90} -3.54539e9i q^{91} -1.13310e9 q^{92} -3.64023e9i q^{93} -5.26918e8i q^{94} -3.92839e9 q^{95} -1.46242e9 q^{96} -1.18206e10 q^{97} -6.89189e9i q^{98} -1.77978e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9}+O(q^{10}) \) 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

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Database

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