LMFDB - Embedded newform 43.11.b.b.42.28

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			42.28
Character	$\chi$	$=$	43.42
Dual form			43.11.b.b.42.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+43.4520i q^{2} +375.725i q^{3} -864.079 q^{4} +561.891i q^{5} -16326.0 q^{6} +26275.3i q^{7} +6948.90i q^{8} -82120.5 q^{9} +O(q^{10})$	\(q+43.4520i q^{2} +375.725i q^{3} -864.079 q^{4} +561.891i q^{5} -16326.0 q^{6} +26275.3i q^{7} +6948.90i q^{8} -82120.5 q^{9} -24415.3 q^{10} +176463. q^{11} -324656. i q^{12} -466723. q^{13} -1.14171e6 q^{14} -211117. q^{15} -1.18676e6 q^{16} +237914. q^{17} -3.56830e6i q^{18} -519568. i q^{19} -485518. i q^{20} -9.87229e6 q^{21} +7.66767e6i q^{22} +1.16024e7 q^{23} -2.61088e6 q^{24} +9.44990e6 q^{25} -2.02801e7i q^{26} -8.66853e6i q^{27} -2.27039e7i q^{28} +2.76466e7i q^{29} -9.17344e6i q^{30} +6.10392e6 q^{31} -4.44515e7i q^{32} +6.63016e7i q^{33} +1.03379e7i q^{34} -1.47638e7 q^{35} +7.09586e7 q^{36} +1.86749e7i q^{37} +2.25763e7 q^{38} -1.75360e8i q^{39} -3.90452e6 q^{40} +1.74564e8 q^{41} -4.28971e8i q^{42} +(-4.17760e7 - 1.40948e8i) q^{43} -1.52478e8 q^{44} -4.61427e7i q^{45} +5.04148e8i q^{46} +3.46204e8 q^{47} -4.45896e8i q^{48} -4.07916e8 q^{49} +4.10617e8i q^{50} +8.93904e7i q^{51} +4.03285e8 q^{52} +2.36698e8 q^{53} +3.76665e8 q^{54} +9.91528e7i q^{55} -1.82584e8 q^{56} +1.95215e8 q^{57} -1.20130e9 q^{58} -8.09457e8 q^{59} +1.82421e8 q^{60} -4.73248e8i q^{61} +2.65227e8i q^{62} -2.15774e9i q^{63} +7.16264e8 q^{64} -2.62247e8i q^{65} -2.88094e9 q^{66} +2.10865e8 q^{67} -2.05577e8 q^{68} +4.35932e9i q^{69} -6.41519e8i q^{70} -1.02027e9i q^{71} -5.70647e8i q^{72} +7.03992e8i q^{73} -8.11462e8 q^{74} +3.55057e9i q^{75} +4.48948e8i q^{76} +4.63661e9i q^{77} +7.61973e9 q^{78} -1.85363e9 q^{79} -6.66830e8i q^{80} -1.59214e9 q^{81} +7.58515e9i q^{82} +9.78789e8 q^{83} +8.53044e9 q^{84} +1.33682e8i q^{85} +(6.12446e9 - 1.81525e9i) q^{86} -1.03875e10 q^{87} +1.22622e9i q^{88} -4.53014e9i q^{89} +2.00499e9 q^{90} -1.22633e10i q^{91} -1.00254e10 q^{92} +2.29340e9i q^{93} +1.50433e10i q^{94} +2.91941e8 q^{95} +1.67015e10 q^{96} +1.30294e10 q^{97} -1.77248e10i q^{98} -1.44912e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			43.4520i			1.35788i	0.734196	+	0.678938i	$0.237559\pi$
$2$			43.4520i			1.35788i	−0.734196	+	0.678938i	$0.762441\pi$
$3$			375.725i			1.54619i	0.634288	+	0.773097i	$0.281294\pi$
$3$			375.725i			1.54619i	−0.634288	+	0.773097i	$0.718706\pi$
$4$	−864.079			−0.843827
$5$			561.891i			0.179805i	0.995951	+	0.0899025i	$0.0286555\pi$
$5$			561.891i			0.179805i	−0.995951	+	0.0899025i	$0.971344\pi$
$6$	−16326.0			−2.09954
$7$			26275.3i			1.56335i	0.623683	+	0.781677i	$0.285635\pi$
$7$			26275.3i			1.56335i	−0.623683	+	0.781677i	$0.714365\pi$
$8$			6948.90i			0.212064i
$9$	−82120.5			−1.39072
$10$	−24415.3			−0.244153
$11$	176463.			1.09570			0.547848	−	0.836578i	$-0.315447\pi$
$11$	176463.			1.09570			0.547848	+	0.836578i	$0.315447\pi$
$12$		−	324656.i		−	1.30472i
$13$	−466723.			−1.25702			−0.628510	−	0.777801i	$-0.716335\pi$
$13$	−466723.			−1.25702			−0.628510	+	0.777801i	$0.716335\pi$
$14$	−1.14171e6			−2.12284
$15$	−211117.			−0.278014
$16$	−1.18676e6			−1.13178
$17$	237914.			0.167562			0.0837810	−	0.996484i	$-0.473300\pi$
$17$	237914.			0.167562			0.0837810	+	0.996484i	$0.473300\pi$
$18$		−	3.56830e6i		−	1.88842i
$19$		−	519568.i		−	0.209833i	−0.994481	−	0.104917i	$-0.966542\pi$
$19$		−	519568.i		−	0.209833i	0.994481	−	0.104917i	$-0.0334576\pi$
$20$		−	485518.i		−	0.151724i
$21$	−9.87229e6			−2.41725
$22$			7.66767e6i			1.48782i
$23$	1.16024e7			1.80264			0.901320	−	0.433155i	$-0.142600\pi$
$23$	1.16024e7			1.80264			0.901320	+	0.433155i	$0.142600\pi$
$24$	−2.61088e6			−0.327892
$25$	9.44990e6			0.967670
$26$		−	2.02801e7i		−	1.70688i
$27$		−	8.66853e6i		−	0.604125i
$28$		−	2.27039e7i		−	1.31920i
$29$			2.76466e7i			1.34788i	0.738786	+	0.673940i	$0.235399\pi$
$29$			2.76466e7i			1.34788i	−0.738786	+	0.673940i	$0.764601\pi$
$30$		−	9.17344e6i		−	0.377508i
$31$	6.10392e6			0.213206			0.106603	−	0.994302i	$-0.466003\pi$
$31$	6.10392e6			0.213206			0.106603	+	0.994302i	$0.466003\pi$
$32$		−	4.44515e7i		−	1.32476i
$33$			6.63016e7i			1.69416i
$34$			1.03379e7i			0.227528i
$35$	−1.47638e7			−0.281099
$36$	7.09586e7			1.17352
$37$			1.86749e7i			0.269308i	0.990893	+	0.134654i	$0.0429923\pi$
$37$			1.86749e7i			0.269308i	−0.990893	+	0.134654i	$0.957008\pi$
$38$	2.25763e7			0.284928
$39$		−	1.75360e8i		−	1.94360i
$40$	−3.90452e6			−0.0381301
$41$	1.74564e8			1.50673			0.753364	−	0.657603i	$-0.228430\pi$
$41$	1.74564e8			1.50673			0.753364	+	0.657603i	$0.228430\pi$
$42$		−	4.28971e8i		−	3.28232i
$43$	−4.17760e7	−	1.40948e8i	−0.284174	−	0.958773i
$43$	−4.17760e7	−	1.40948e8i	−0.284174	−	0.958773i
$44$	−1.52478e8			−0.924578
$45$		−	4.61427e7i		−	0.250058i
$46$			5.04148e8i			2.44776i
$47$	3.46204e8			1.50953			0.754767	−	0.655993i	$-0.227750\pi$
$47$	3.46204e8			1.50953			0.754767	+	0.655993i	$0.227750\pi$
$48$		−	4.45896e8i		−	1.74996i
$49$	−4.07916e8			−1.44408
$50$			4.10617e8i			1.31398i
$51$			8.93904e7i			0.259084i
$52$	4.03285e8			1.06071
$53$	2.36698e8			0.565998			0.282999	−	0.959120i	$-0.408671\pi$
$53$	2.36698e8			0.565998			0.282999	+	0.959120i	$0.408671\pi$
$54$	3.76665e8			0.820327
$55$			9.91528e7i			0.197012i
$56$	−1.82584e8			−0.331531
$57$	1.95215e8			0.324443
$58$	−1.20130e9			−1.83025
$59$	−8.09457e8			−1.13223			−0.566114	−	0.824327i	$-0.691554\pi$
$59$	−8.09457e8			−1.13223			−0.566114	+	0.824327i	$0.691554\pi$
$60$	1.82421e8			0.234595
$61$		−	4.73248e8i		−	0.560324i	−0.959953	−	0.280162i	$-0.909612\pi$
$61$		−	4.73248e8i		−	0.560324i	0.959953	−	0.280162i	$-0.0903882\pi$
$62$			2.65227e8i			0.289508i
$63$		−	2.15774e9i		−	2.17418i
$64$	7.16264e8			0.667073
$65$		−	2.62247e8i		−	0.226019i
$66$	−2.88094e9			−2.30046
$67$	2.10865e8			0.156182			0.0780909	−	0.996946i	$-0.475118\pi$
$67$	2.10865e8			0.156182			0.0780909	+	0.996946i	$0.475118\pi$
$68$	−2.05577e8			−0.141393
$69$			4.35932e9i			2.78723i
$70$		−	6.41519e8i		−	0.381697i
$71$		−	1.02027e9i		−	0.565488i	−0.959195	−	0.282744i	$-0.908755\pi$
$71$		−	1.02027e9i		−	0.565488i	0.959195	−	0.282744i	$-0.0912447\pi$
$72$		−	5.70647e8i		−	0.294921i
$73$			7.03992e8i			0.339589i	0.985480	+	0.169794i	$0.0543103\pi$
$73$			7.03992e8i			0.339589i	−0.985480	+	0.169794i	$0.945690\pi$
$74$	−8.11462e8			−0.365687
$75$			3.55057e9i			1.49621i
$76$			4.48948e8i			0.177063i
$77$			4.63661e9i			1.71296i
$78$	7.61973e9			2.63916
$79$	−1.85363e9			−0.602402			−0.301201	−	0.953561i	$-0.597388\pi$
$79$	−1.85363e9			−0.602402			−0.301201	+	0.953561i	$0.597388\pi$
$80$		−	6.66830e8i		−	0.203500i
$81$	−1.59214e9			−0.456623
$82$			7.58515e9i			2.04595i
$83$	9.78789e8			0.248484			0.124242	−	0.992252i	$-0.460350\pi$
$83$	9.78789e8			0.248484			0.124242	+	0.992252i	$0.460350\pi$
$84$	8.53044e9			2.03974
$85$			1.33682e8i			0.0301285i
$86$	6.12446e9	−	1.81525e9i	1.30189	−	0.385873i
$87$	−1.03875e10			−2.08409
$88$			1.22622e9i			0.232357i
$89$		−	4.53014e9i		−	0.811263i	−0.914037	−	0.405631i	$-0.867052\pi$
$89$		−	4.53014e9i		−	0.811263i	0.914037	−	0.405631i	$-0.132948\pi$
$90$	2.00499e9			0.339548
$91$		−	1.22633e10i		−	1.96517i
$92$	−1.00254e10			−1.52112
$93$			2.29340e9i			0.329658i
$94$			1.50433e10i			2.04976i
$95$	2.91941e8			0.0377291
$96$	1.67015e10			2.04833
$97$	1.30294e10			1.51728			0.758640	−	0.651510i	$-0.225864\pi$
$97$	1.30294e10			1.51728			0.758640	+	0.651510i	$0.225864\pi$
$98$		−	1.77248e10i		−	1.96088i
$99$	−1.44912e10			−1.52380
$100$	−8.16546e9			−0.816546
$101$	−1.99566e10			−1.89881			−0.949403	−	0.314059i	$-0.898311\pi$
$101$	−1.99566e10			−1.89881			−0.949403	+	0.314059i	$0.898311\pi$
$102$	−3.88419e9			−0.351803
$103$	4.65480e9			0.401527			0.200764	−	0.979640i	$-0.435658\pi$
$103$	4.65480e9			0.401527			0.200764	+	0.979640i	$0.435658\pi$
$104$		−	3.24321e9i		−	0.266568i
$105$		−	5.54715e9i		−	0.434634i
$106$			1.02850e10i			0.768556i
$107$	−1.84503e10			−1.31548			−0.657739	−	0.753246i	$-0.728487\pi$
$107$	−1.84503e10			−1.31548			−0.657739	+	0.753246i	$0.728487\pi$
$108$			7.49029e9i			0.509777i
$109$	−1.22798e10			−0.798100			−0.399050	−	0.916929i	$-0.630660\pi$
$109$	−1.22798e10			−0.798100			−0.399050	+	0.916929i	$0.630660\pi$
$110$	−4.30839e9			−0.267517
$111$	−7.01663e9			−0.416403
$112$		−	3.11825e10i		−	1.76938i
$113$		−	3.19317e10i		−	1.73312i	−0.499069	−	0.866562i	$-0.666324\pi$
$113$		−	3.19317e10i		−	1.73312i	0.499069	−	0.866562i	$-0.333676\pi$
$114$			8.48248e9i			0.440554i
$115$			6.51928e9i			0.324124i
$116$		−	2.38888e10i		−	1.13738i
$117$	3.83275e10			1.74816
$118$		−	3.51725e10i		−	1.53742i
$119$			6.25126e9i			0.261959i
$120$		−	1.46703e9i		−	0.0589566i
$121$	5.20173e9			0.200549
$122$	2.05636e10			0.760851
$123$			6.55881e10i			2.32970i
$124$	−5.27426e9			−0.179909
$125$			1.07970e10i			0.353797i
$126$	9.37581e10			2.95227
$127$	−1.15922e10			−0.350870			−0.175435	−	0.984491i	$-0.556133\pi$
$127$	−1.15922e10			−0.350870			−0.175435	+	0.984491i	$0.556133\pi$
$128$		−	1.43952e10i		−	0.418955i
$129$	5.29576e10	−	1.56963e10i	1.48245	−	0.439388i
$130$	1.13952e10			0.306905
$131$			5.90260e10i			1.52998i	0.644039	+	0.764992i	$0.277257\pi$
$131$			5.90260e10i			1.52998i	−0.644039	+	0.764992i	$0.722743\pi$
$132$		−	5.72898e10i		−	1.42958i
$133$	1.36518e10			0.328044
$134$			9.16252e9i			0.212076i
$135$	4.87077e9			0.108625
$136$			1.65324e9i			0.0355338i
$137$		−	1.69458e10i		−	0.351123i	−0.984468	−	0.175562i	$-0.943826\pi$
$137$		−	1.69458e10i		−	0.351123i	0.984468	−	0.175562i	$-0.0561742\pi$
$138$	−1.89421e11			−3.78471
$139$	9.47193e10			1.82543			0.912714	−	0.408600i	$-0.133983\pi$
$139$	9.47193e10			1.82543			0.912714	+	0.408600i	$0.133983\pi$
$140$	1.27571e10			0.237199
$141$			1.30078e11i			2.33403i
$142$	4.43328e10			0.767862
$143$	−8.23592e10			−1.37731
$144$	9.74573e10			1.57399
$145$	−1.55344e10			−0.242356
$146$	−3.05899e10			−0.461119
$147$		−	1.53264e11i		−	2.23282i
$148$		−	1.61366e10i		−	0.227249i
$149$			1.91153e10i			0.260285i	0.991495	+	0.130142i	$0.0415435\pi$
$149$			1.91153e10i			0.260285i	−0.991495	+	0.130142i	$0.958457\pi$
$150$	−1.54279e11			−2.03166
$151$		−	5.07838e10i		−	0.646905i	−0.946244	−	0.323452i	$-0.895156\pi$
$151$		−	5.07838e10i		−	0.646905i	0.946244	−	0.323452i	$-0.104844\pi$
$152$	3.61043e9			0.0444980
$153$	−1.95376e10			−0.233031
$154$	−2.01470e11			−2.32599
$155$			3.42973e9i			0.0383356i
$156$			1.51524e11i			1.64006i
$157$			6.24319e10i			0.654498i	0.944938	+	0.327249i	$0.106122\pi$
$157$			6.24319e10i			0.654498i	−0.944938	+	0.327249i	$0.893878\pi$
$158$		−	8.05438e10i		−	0.817987i
$159$			8.89334e10i			0.875144i
$160$	2.49769e10			0.238198
$161$			3.04857e11i			2.81816i
$162$		−	6.91819e10i		−	0.620037i
$163$			5.90994e10i			0.513624i	0.966461	+	0.256812i	$0.0826721\pi$
$163$			5.90994e10i			0.513624i	−0.966461	+	0.256812i	$0.917328\pi$
$164$	−1.50837e11			−1.27142
$165$	−3.72542e10			−0.304618
$166$			4.25304e10i			0.337410i
$167$	7.76679e10			0.597942			0.298971	−	0.954262i	$-0.403357\pi$
$167$	7.76679e10			0.597942			0.298971	+	0.954262i	$0.403357\pi$
$168$		−	6.86016e10i		−	0.512611i
$169$	7.99717e10			0.580100
$170$	−5.80874e9			−0.0409108
$171$			4.26672e10i			0.291819i
$172$	3.60977e10	+	1.21790e11i	0.239794	+	0.809038i
$173$	−3.37221e10			−0.217613			−0.108806	−	0.994063i	$-0.534703\pi$
$173$	−3.37221e10			−0.217613			−0.108806	+	0.994063i	$0.534703\pi$
$174$		−	4.51359e11i		−	2.82993i
$175$			2.48299e11i			1.51281i
$176$	−2.09419e11			−1.24009
$177$		−	3.04133e11i		−	1.75064i
$178$	1.96844e11			1.10159
$179$		−	1.44240e11i		−	0.784909i	−0.919771	−	0.392455i	$-0.871626\pi$
$179$		−	1.44240e11i		−	0.784909i	0.919771	−	0.392455i	$-0.128374\pi$
$180$			3.98709e10i			0.211006i
$181$	2.04299e11			1.05166			0.525829	−	0.850590i	$-0.323755\pi$
$181$	2.04299e11			1.05166			0.525829	+	0.850590i	$0.323755\pi$
$182$	5.32864e11			2.66845
$183$	1.77811e11			0.866370
$184$			8.06240e10i			0.382274i
$185$	−1.04932e10			−0.0484229
$186$	−9.96527e10			−0.447635
$187$	4.19830e10			0.183597
$188$	−2.99148e11			−1.27379
$189$	2.27768e11			0.944461
$190$			1.26854e10i			0.0512314i
$191$		−	5.85874e9i		−	0.0230482i	−0.999934	−	0.0115241i	$-0.996332\pi$
$191$		−	5.85874e9i		−	0.0230482i	0.999934	−	0.0115241i	$-0.00366832\pi$
$192$			2.69118e11i			1.03142i
$193$	1.76086e11			0.657565			0.328783	−	0.944406i	$-0.393362\pi$
$193$	1.76086e11			0.657565			0.328783	+	0.944406i	$0.393362\pi$
$194$			5.66154e11i			2.06028i
$195$	9.85329e10			0.349469
$196$	3.52471e11			1.21855
$197$	−5.11182e11			−1.72284			−0.861419	−	0.507895i	$-0.830424\pi$
$197$	−5.11182e11			−1.72284			−0.861419	+	0.507895i	$0.830424\pi$
$198$		−	6.29673e11i		−	2.06914i
$199$			1.88481e11i			0.603951i	0.953316	+	0.301975i	$0.0976460\pi$
$199$			1.88481e11i			0.603951i	−0.953316	+	0.301975i	$0.902354\pi$
$200$			6.56665e10i			0.205208i
$201$			7.92273e10i			0.241488i
$202$		−	8.67157e11i		−	2.57834i
$203$	−7.26422e11			−2.10721
$204$		−	7.72403e10i		−	0.218622i
$205$			9.80858e10i			0.270917i
$206$			2.02261e11i			0.545224i
$207$	−9.52795e11			−2.50696
$208$	5.53888e11			1.42267
$209$		−	9.16845e10i		−	0.229914i
$210$	2.41035e11			0.590178
$211$		−	4.33240e11i		−	1.03590i	−0.855412	−	0.517949i	$-0.826696\pi$
$211$		−	4.33240e11i		−	1.03590i	0.855412	−	0.517949i	$-0.173304\pi$
$212$	−2.04526e11			−0.477605
$213$	3.83341e11			0.874354
$214$		−	8.01702e11i		−	1.78626i
$215$	7.91972e10	−	2.34735e10i	0.172392	−	0.0510959i
$216$	6.02368e10			0.128113
$217$			1.60382e11i			0.333317i
$218$		−	5.33581e11i		−	1.08372i
$219$	−2.64507e11			−0.525070
$220$		−	8.56759e10i		−	0.166244i
$221$	−1.11040e11			−0.210629
$222$		−	3.04887e11i		−	0.565423i
$223$			5.26107e11i			0.954003i	0.878903	+	0.477001i	$0.158276\pi$
$223$			5.26107e11i			0.954003i	−0.878903	+	0.477001i	$0.841724\pi$
$224$	1.16798e12			2.07106
$225$	−7.76031e11			−1.34576
$226$	1.38750e12			2.35337
$227$		−	7.92335e11i		−	1.31456i	−0.753647	−	0.657279i	$-0.771707\pi$
$227$		−	7.92335e11i		−	1.31456i	0.753647	−	0.657279i	$-0.228293\pi$
$228$	−1.68681e11			−0.273774
$229$	5.71371e11			0.907278			0.453639	−	0.891185i	$-0.350125\pi$
$229$	5.71371e11			0.907278			0.453639	+	0.891185i	$0.350125\pi$
$230$	−2.83276e11			−0.440120
$231$	−1.74209e12			−2.64857
$232$	−1.92113e11			−0.285836
$233$			5.38816e11i			0.784623i	0.919833	+	0.392311i	$0.128324\pi$
$233$			5.38816e11i			0.784623i	−0.919833	+	0.392311i	$0.871676\pi$
$234$			1.66541e12i			2.37378i
$235$			1.94529e11i			0.271422i
$236$	6.99434e11			0.955404
$237$		−	6.96454e11i		−	0.931431i
$238$	−2.71630e11			−0.355708
$239$	4.82176e10			0.0618324			0.0309162	−	0.999522i	$-0.490157\pi$
$239$	4.82176e10			0.0618324			0.0309162	+	0.999522i	$0.490157\pi$
$240$	2.50545e11			0.314651
$241$			1.10028e12i			1.35338i	0.736269	+	0.676689i	$0.236586\pi$
$241$			1.10028e12i			1.35338i	−0.736269	+	0.676689i	$0.763414\pi$
$242$			2.26026e11i			0.272321i
$243$		−	1.11008e12i		−	1.31015i
$244$			4.08923e11i			0.472817i
$245$		−	2.29204e11i		−	0.259652i
$246$	−2.84993e12			−3.16344
$247$			2.42494e11i			0.263765i
$248$			4.24155e10i			0.0452133i
$249$			3.67756e11i			0.384205i
$250$	−4.69153e11			−0.480412
$251$	3.93709e11			0.395191			0.197596	−	0.980284i	$-0.436687\pi$
$251$	3.93709e11			0.395191			0.197596	+	0.980284i	$0.436687\pi$
$252$			1.86446e12i			1.83463i
$253$	2.04739e12			1.97514
$254$		−	5.03704e11i		−	0.476438i
$255$	−5.02276e10			−0.0465845
$256$	1.35895e12			1.23596
$257$			1.34133e12i			1.19638i	0.801354	+	0.598191i	$0.204113\pi$
$257$			1.34133e12i			1.19638i	−0.801354	+	0.598191i	$0.795887\pi$
$258$	6.82036e11	+	2.30112e12i	0.596635	+	2.01298i
$259$	−4.90688e11			−0.421024
$260$			2.26602e11i			0.190721i
$261$		−	2.27035e12i		−	1.87452i
$262$	−2.56480e12			−2.07753
$263$		−	2.02530e12i		−	1.60957i	−0.593567	−	0.804785i	$-0.702281\pi$
$263$		−	2.02530e12i		−	1.60957i	0.593567	−	0.804785i	$-0.297719\pi$
$264$	−4.60723e11			−0.359269
$265$			1.32998e11i			0.101769i
$266$			5.93199e11i			0.445443i
$267$	1.70209e12			1.25437
$268$	−1.82204e11			−0.131790
$269$	6.43203e11			0.456653			0.228327	−	0.973585i	$-0.426675\pi$
$269$	6.43203e11			0.456653			0.228327	+	0.973585i	$0.426675\pi$
$270$			2.11645e11i			0.147499i
$271$	−2.70274e12			−1.84909			−0.924544	−	0.381075i	$-0.875554\pi$
$271$	−2.70274e12			−1.84909			−0.924544	+	0.381075i	$0.875554\pi$
$272$	−2.82347e11			−0.189644
$273$	4.60762e12			3.03853
$274$	7.36330e11			0.476782
$275$	1.66756e12			1.06027
$276$		−	3.76679e12i		−	2.35194i
$277$		−	8.73863e11i		−	0.535851i	−0.963440	−	0.267926i	$-0.913662\pi$
$277$		−	8.73863e11i		−	0.535851i	0.963440	−	0.267926i	$-0.0863382\pi$
$278$			4.11575e12i			2.47870i
$279$	−5.01256e11			−0.296510
$280$		−	1.02592e11i		−	0.0596109i
$281$	2.33248e12			1.33133			0.665665	−	0.746251i	$-0.268148\pi$
$281$	2.33248e12			1.33133			0.665665	+	0.746251i	$0.268148\pi$
$282$	−5.65214e12			−3.16933
$283$	−7.70322e11			−0.424366			−0.212183	−	0.977230i	$-0.568057\pi$
$283$	−7.70322e11			−0.424366			−0.212183	+	0.977230i	$0.568057\pi$
$284$			8.81593e11i			0.477174i
$285$			1.09689e11i			0.0583365i
$286$		−	3.57868e12i		−	1.87022i
$287$			4.58672e12i			2.35555i
$288$			3.65038e12i			1.84236i
$289$	−1.95939e12			−0.971923
$290$		−	6.74999e11i		−	0.329089i
$291$			4.89547e12i			2.34601i
$292$		−	6.08304e11i		−	0.286554i
$293$	−3.93334e12			−1.82148			−0.910738	−	0.412985i	$-0.864486\pi$
$293$	−3.93334e12			−1.82148			−0.910738	+	0.412985i	$0.864486\pi$
$294$	6.65964e12			3.03190
$295$		−	4.54826e11i		−	0.203580i
$296$	−1.29770e11			−0.0571104
$297$		−	1.52967e12i		−	0.661937i
$298$	−8.30597e11			−0.353435
$299$	−5.41511e12			−2.26595
$300$		−	3.06797e12i		−	1.26254i
$301$	3.70344e12	−	1.09768e12i	1.49890	−	0.444265i
$302$	2.20666e12			0.878416
$303$		−	7.49822e12i		−	2.93592i
$304$			6.16603e11i			0.237486i
$305$	2.65913e11			0.100749
$306$		−	8.48949e11i		−	0.316428i
$307$	3.55464e12			1.30348			0.651740	−	0.758443i	$-0.274039\pi$
$307$	3.55464e12			1.30348			0.651740	+	0.758443i	$0.274039\pi$
$308$		−	4.00640e12i		−	1.44544i
$309$			1.74893e12i			0.620839i
$310$	−1.49029e11			−0.0520549
$311$	8.84075e11			0.303870			0.151935	−	0.988391i	$-0.451450\pi$
$311$	8.84075e11			0.303870			0.151935	+	0.988391i	$0.451450\pi$
$312$	1.21856e12			0.412166
$313$		−	2.78961e12i		−	0.928587i	−0.885681	−	0.464293i	$-0.846308\pi$
$313$		−	2.78961e12i		−	0.928587i	0.885681	−	0.464293i	$-0.153692\pi$
$314$	−2.71279e12			−0.888727
$315$	1.21241e12			0.390929
$316$	1.60168e12			0.508323
$317$	2.58249e12			0.806758			0.403379	−	0.915033i	$-0.367836\pi$
$317$	2.58249e12			0.806758			0.403379	+	0.915033i	$0.367836\pi$
$318$	−3.86434e12			−1.18834
$319$			4.87859e12i			1.47687i
$320$			4.02462e11i			0.119943i
$321$		−	6.93223e12i		−	2.03399i
$322$	−1.32466e13			−3.82672
$323$		−	1.23613e11i		−	0.0351601i
$324$	1.37574e12			0.385311
$325$	−4.41049e12			−1.21638
$326$	−2.56799e12			−0.697438
$327$		−	4.61382e12i		−	1.23402i
$328$			1.21303e12i			0.319522i
$329$			9.09662e12i			2.35994i
$330$		−	1.61877e12i		−	0.413634i
$331$		−	6.69456e12i		−	1.68493i	−0.538751	−	0.842465i	$-0.681104\pi$
$331$		−	6.69456e12i		−	1.68493i	0.538751	−	0.842465i	$-0.318896\pi$
$332$	−8.45750e11			−0.209678
$333$		−	1.53359e12i		−	0.374531i
$334$			3.37483e12i			0.811931i
$335$			1.18483e11i			0.0280823i
$336$	1.17160e13			2.73580
$337$	−4.74772e12			−1.09228			−0.546142	−	0.837693i	$-0.683904\pi$
$337$	−4.74772e12			−1.09228			−0.546142	+	0.837693i	$0.683904\pi$
$338$			3.47493e12i			0.787703i
$339$	1.19975e13			2.67975
$340$		−	1.15512e11i		−	0.0254232i
$341$	1.07711e12			0.233609
$342$	−1.85398e12			−0.396254
$343$		−	3.29599e12i		−	0.694248i
$344$	9.79432e11	−	2.90297e11i	0.203321	−	0.0602630i
$345$	−2.44946e12			−0.501158
$346$		−	1.46529e12i		−	0.295491i
$347$			2.39973e12i			0.476996i	0.971143	+	0.238498i	$0.0766550\pi$
$347$			2.39973e12i			0.476996i	−0.971143	+	0.238498i	$0.923345\pi$
$348$	8.97563e12			1.75861
$349$		−	2.58521e12i		−	0.499309i	−0.968335	−	0.249655i	$-0.919683\pi$
$349$		−	2.58521e12i		−	0.499309i	0.968335	−	0.249655i	$-0.0803171\pi$
$350$	−1.07891e13			−2.05421
$351$			4.04580e12i			0.759397i
$352$		−	7.84404e12i		−	1.45153i
$353$	4.03701e12			0.736522			0.368261	−	0.929722i	$-0.379953\pi$
$353$	4.03701e12			0.736522			0.368261	+	0.929722i	$0.379953\pi$
$354$	1.32152e13			2.37716
$355$	5.73280e11			0.101678
$356$			3.91440e12i			0.684565i
$357$	−2.34876e12			−0.405039
$358$	6.26751e12			1.06581
$359$	8.09958e12			1.35828			0.679141	−	0.734007i	$-0.262352\pi$
$359$	8.09958e12			1.35828			0.679141	+	0.734007i	$0.262352\pi$
$360$	3.20641e11			0.0530282
$361$	5.86112e12			0.955970
$362$			8.87723e12i			1.42802i
$363$			1.95442e12i			0.310088i
$364$			1.05964e13i			1.65826i
$365$	−3.95566e11			−0.0610597
$366$			7.72625e12i			1.17642i
$367$	2.38660e11			0.0358467			0.0179233	−	0.999839i	$-0.494295\pi$
$367$	2.38660e11			0.0358467			0.0179233	+	0.999839i	$0.494295\pi$
$368$	−1.37693e13			−2.04020
$369$	−1.43353e13			−2.09543
$370$		−	4.55953e11i		−	0.0657523i
$371$			6.21931e12i			0.884856i
$372$		−	1.98167e12i		−	0.278175i
$373$		−	1.04130e13i		−	1.44222i	−0.692819	−	0.721112i	$-0.743631\pi$
$373$		−	1.04130e13i		−	1.44222i	0.692819	−	0.721112i	$-0.256369\pi$
$374$			1.82425e12i			0.249302i
$375$	−4.05672e12			−0.547039
$376$			2.40574e12i			0.320117i
$377$		−	1.29033e13i		−	1.69431i
$378$			9.89699e12i			1.28246i
$379$	−4.27776e12			−0.547041			−0.273521	−	0.961866i	$-0.588188\pi$
$379$	−4.27776e12			−0.547041			−0.273521	+	0.961866i	$0.588188\pi$
$380$	−2.52260e11			−0.0318368
$381$		−	4.35547e12i		−	0.542514i
$382$	2.54574e11			0.0312966
$383$		−	2.12063e12i		−	0.257318i	−0.991689	−	0.128659i	$-0.958933\pi$
$383$		−	2.12063e12i		−	0.257318i	0.991689	−	0.128659i	$-0.0410673\pi$
$384$	5.40863e12			0.647786
$385$	−2.60527e12			−0.307999
$386$			7.65130e12i			0.892892i
$387$	3.43066e12	+	1.15747e13i	0.395206	+	1.33338i
$388$	−1.12584e13			−1.28032
$389$			1.74998e13i			1.96465i	0.187190	+	0.982324i	$0.440062\pi$
$389$			1.74998e13i			1.96465i	−0.187190	+	0.982324i	$0.559938\pi$
$390$			4.28145e12i			0.474535i
$391$	2.76038e12			0.302054
$392$		−	2.83457e12i		−	0.306236i
$393$	−2.21776e13			−2.36565
$394$		−	2.22119e13i		−	2.33940i
$395$		−	1.04153e12i		−	0.108315i
$396$	1.25216e13			1.28583
$397$	−1.30082e13			−1.31906			−0.659532	−	0.751677i	$-0.729245\pi$
$397$	−1.30082e13			−1.31906			−0.659532	+	0.751677i	$0.729245\pi$
$398$	−8.18987e12			−0.820090
$399$			5.12933e12i			0.507220i
$400$	−1.12148e13			−1.09519
$401$	−1.61167e12			−0.155437			−0.0777184	−	0.996975i	$-0.524764\pi$
$401$	−1.61167e12			−0.155437			−0.0777184	+	0.996975i	$0.524764\pi$
$402$	−3.44259e12			−0.327910
$403$	−2.84884e12			−0.268005
$404$	1.72441e13			1.60226
$405$		−	8.94611e11i		−	0.0821031i
$406$		−	3.15645e13i		−	2.86134i
$407$			3.29542e12i			0.295080i
$408$	−6.21165e11			−0.0549422
$409$			1.49548e12i			0.130667i	0.997864	+	0.0653333i	$0.0208110\pi$
$409$			1.49548e12i			0.130667i	−0.997864	+	0.0653333i	$0.979189\pi$
$410$	−4.26203e12			−0.367872
$411$	6.36697e12			0.542905
$412$	−4.02211e12			−0.338819
$413$		−	2.12687e13i		−	1.77007i
$414$		−	4.14009e13i		−	3.40414i
$415$			5.49972e11i			0.0446787i
$416$			2.07465e13i			1.66525i
$417$			3.55884e13i			2.82247i
$418$	3.98388e12			0.312194
$419$			1.62703e13i			1.25987i	0.776650	+	0.629933i	$0.216918\pi$
$419$			1.62703e13i			1.25987i	−0.776650	+	0.629933i	$0.783082\pi$
$420$			4.79317e12i			0.366756i
$421$			6.86747e12i			0.519262i	0.965708	+	0.259631i	$0.0836009\pi$
$421$			6.86747e12i			0.519262i	−0.965708	+	0.259631i	$0.916399\pi$
$422$	1.88252e13			1.40662
$423$	−2.84304e13			−2.09934
$424$			1.64479e12i			0.120028i
$425$	2.24827e12			0.162145
$426$			1.66569e13i			1.18726i
$427$	1.24347e13			0.875985
$428$	1.59425e13			1.11004
$429$		−	3.09444e13i		−	2.12959i
$430$	1.01997e12	+	3.44128e12i	0.0693819	+	0.234087i
$431$	7.11864e12			0.478642			0.239321	−	0.970941i	$-0.423075\pi$
$431$	7.11864e12			0.478642			0.239321	+	0.970941i	$0.423075\pi$
$432$			1.02875e13i			0.683738i
$433$			2.59233e13i			1.70314i	0.524240	+	0.851570i	$0.324349\pi$
$433$			2.59233e13i			1.70314i	−0.524240	+	0.851570i	$0.675651\pi$
$434$	−6.96893e12			−0.452603
$435$		−	5.83665e12i		−	0.374729i
$436$	1.06107e13			0.673459
$437$		−	6.02824e12i		−	0.378254i
$438$		−	1.14934e13i		−	0.712980i
$439$	5.68385e12			0.348594			0.174297	−	0.984693i	$-0.444235\pi$
$439$	5.68385e12			0.348594			0.174297	+	0.984693i	$0.444235\pi$
$440$	−6.89003e11			−0.0417790
$441$	3.34982e13			2.00830
$442$		−	4.82491e12i		−	0.286008i
$443$	2.10962e13			1.23648			0.618238	−	0.785991i	$-0.287847\pi$
$443$	2.10962e13			1.23648			0.618238	+	0.785991i	$0.287847\pi$
$444$	6.06292e12			0.351372
$445$	2.54544e12			0.145869
$446$	−2.28604e13			−1.29542
$447$	−7.18209e12			−0.402451
$448$			1.88200e13i			1.04287i
$449$		−	2.64710e13i		−	1.45057i	−0.688448	−	0.725285i	$-0.741708\pi$
$449$		−	2.64710e13i		−	1.45057i	0.688448	−	0.725285i	$-0.258292\pi$
$450$		−	3.37201e13i		−	1.82737i
$451$	3.08040e13			1.65092
$452$			2.75915e13i			1.46246i
$453$	1.90808e13			1.00024
$454$	3.44286e13			1.78501
$455$	6.89062e12			0.353347
$456$			1.35653e12i			0.0688026i
$457$		−	1.62983e13i		−	0.817638i	−0.912616	−	0.408819i	$-0.865941\pi$
$457$		−	1.62983e13i		−	0.817638i	0.912616	−	0.408819i	$-0.134059\pi$
$458$			2.48272e13i			1.23197i
$459$		−	2.06237e12i		−	0.101228i
$460$		−	5.63317e12i		−	0.273504i
$461$	−1.08374e13			−0.520499			−0.260249	−	0.965541i	$-0.583805\pi$
$461$	−1.08374e13			−0.520499			−0.260249	+	0.965541i	$0.583805\pi$
$462$		−	7.56975e13i		−	3.59643i
$463$			2.34477e13i			1.10204i	0.834493	+	0.551018i	$0.185761\pi$
$463$			2.34477e13i			1.10204i	−0.834493	+	0.551018i	$0.814239\pi$
$464$		−	3.28099e13i		−	1.52551i
$465$	−1.28864e12			−0.0592742
$466$	−2.34126e13			−1.06542
$467$			5.80691e12i			0.261433i	0.991420	+	0.130717i	$0.0417278\pi$
$467$			5.80691e12i			0.261433i	−0.991420	+	0.130717i	$0.958272\pi$
$468$	−3.31180e13			−1.47514
$469$			5.54054e12i			0.244168i
$470$	−8.45267e12			−0.368557
$471$	−2.34572e13			−1.01198
$472$		−	5.62484e12i		−	0.240104i
$473$	−7.37191e12	−	2.48720e13i	−0.311368	−	1.05052i
$474$	3.02623e13			1.26477
$475$		−	4.90987e12i		−	0.203050i
$476$		−	5.40158e12i		−	0.221048i
$477$	−1.94377e13			−0.787144
$478$			2.09515e12i			0.0839608i
$479$	−1.59691e13			−0.633289			−0.316645	−	0.948544i	$-0.602556\pi$
$479$	−1.59691e13			−0.633289			−0.316645	+	0.948544i	$0.602556\pi$
$480$			9.38444e12i			0.368300i
$481$		−	8.71599e12i		−	0.338526i
$482$	−4.78095e13			−1.83772
$483$	−1.14542e14			−4.35743
$484$	−4.49470e12			−0.169229
$485$			7.32110e12i			0.272815i
$486$	4.82351e13			1.77902
$487$	3.83538e13			1.40012			0.700058	−	0.714086i	$-0.253158\pi$
$487$	3.83538e13			1.40012			0.700058	+	0.714086i	$0.253158\pi$
$488$	3.28855e12			0.118824
$489$	−2.22051e13			−0.794162
$490$	9.95938e12			0.352575
$491$			2.92677e13i			1.02561i	0.858506	+	0.512803i	$0.171393\pi$
$491$			2.92677e13i			1.02561i	−0.858506	+	0.512803i	$0.828607\pi$
$492$		−	5.66732e13i		−	1.96586i
$493$			6.57751e12i			0.225854i
$494$	−1.05369e13			−0.358160
$495$		−	8.14248e12i		−	0.273987i
$496$	−7.24389e12			−0.241303
$497$	2.68079e13			0.884058
$498$	−1.59797e13			−0.521702
$499$			4.70754e13i			1.52157i	0.649005	+	0.760784i	$0.275185\pi$
$499$			4.70754e13i			1.52157i	−0.649005	+	0.760784i	$0.724815\pi$
$500$		−	9.32948e12i		−	0.298543i
$501$			2.91818e13i			0.924535i
$502$			1.71075e13i			0.536621i
$503$			3.71078e13i			1.15246i	0.817288	+	0.576229i	$0.195476\pi$
$503$			3.71078e13i			1.15246i	−0.817288	+	0.576229i	$0.804524\pi$
$504$	1.49939e13			0.461065
$505$		−	1.12135e13i		−	0.341415i
$506$			8.89634e13i			2.68200i
$507$			3.00474e13i			0.896947i
$508$	1.00166e13			0.296074
$509$	1.67021e13			0.488859			0.244429	−	0.969667i	$-0.421399\pi$
$509$	1.67021e13			0.488859			0.244429	+	0.969667i	$0.421399\pi$
$510$		−	2.18249e12i		−	0.0632560i
$511$	−1.84976e13			−0.530897
$512$			4.43087e13i			1.25933i
$513$	−4.50389e12			−0.126766
$514$	−5.82835e13			−1.62454
$515$			2.61549e12i			0.0721966i
$516$	−4.57595e13	+	1.35628e13i	−1.25093	+	0.370768i
$517$	6.10922e13			1.65399
$518$		−	2.13214e13i		−	0.571698i
$519$		−	1.26703e13i		−	0.336472i
$520$	1.82233e12			0.0479303
$521$		−	4.21766e13i		−	1.09871i	−0.835589	−	0.549355i	$-0.814874\pi$
$521$		−	4.21766e13i		−	1.09871i	0.835589	−	0.549355i	$-0.185126\pi$
$522$	9.86513e13			2.54537
$523$		−	3.37686e13i		−	0.862989i	−0.902116	−	0.431494i	$-0.857986\pi$
$523$		−	3.37686e13i		−	0.862989i	0.902116	−	0.431494i	$-0.142014\pi$
$524$		−	5.10031e13i		−	1.29104i
$525$	−9.32922e13			−2.33910
$526$	8.80032e13			2.18560
$527$	1.45221e12			0.0357253
$528$		−	7.86841e13i		−	1.91742i
$529$	9.31893e13			2.24951
$530$	−5.77905e12			−0.138190
$531$	6.64730e13			1.57461
$532$	−1.17962e13			−0.276812
$533$	−8.14729e13			−1.89399
$534$			7.39592e13i			1.70328i
$535$		−	1.03670e13i		−	0.236530i
$536$			1.46528e12i			0.0331205i
$537$	5.41945e13			1.21362
$538$			2.79485e13i			0.620078i
$539$	−7.19820e13			−1.58227
$540$	−4.20873e12			−0.0916604
$541$	5.98775e13			1.29204			0.646022	−	0.763319i	$-0.276431\pi$
$541$	5.98775e13			1.29204			0.646022	+	0.763319i	$0.276431\pi$
$542$		−	1.17439e14i		−	2.51083i
$543$			7.67605e13i			1.62607i
$544$		−	1.05756e13i		−	0.221979i
$545$		−	6.89988e12i		−	0.143502i
$546$			2.00211e14i			4.12595i
$547$	−1.75237e13			−0.357840			−0.178920	−	0.983864i	$-0.557260\pi$
$547$	−1.75237e13			−0.357840			−0.178920	+	0.983864i	$0.557260\pi$
$548$			1.46425e13i			0.296287i
$549$			3.88633e13i			0.779252i
$550$			7.24587e13i			1.43972i
$551$	1.43643e13			0.282830
$552$	−3.02925e13			−0.591070
$553$		−	4.87045e13i		−	0.941768i
$554$	3.79711e13			0.727620
$555$		−	3.94258e12i		−	0.0748713i
$556$	−8.18449e13			−1.54034
$557$	5.45729e13			1.01789			0.508946	−	0.860799i	$-0.330035\pi$
$557$	5.45729e13			1.01789			0.508946	+	0.860799i	$0.330035\pi$
$558$		−	2.17806e13i		−	0.402623i
$559$	1.94978e13	+	6.57835e13i	0.357212	+	1.20520i
$560$	1.75211e13			0.318143
$561$			1.57741e13i			0.283877i
$562$			1.01351e14i			1.80778i
$563$	−2.58971e13			−0.457835			−0.228917	−	0.973446i	$-0.573519\pi$
$563$	−2.58971e13			−0.457835			−0.228917	+	0.973446i	$0.573519\pi$
$564$		−	1.12397e14i		−	1.96952i
$565$	1.79421e13			0.311625
$566$		−	3.34721e13i		−	0.576236i
$567$		−	4.18341e13i		−	0.713863i
$568$	7.08975e12			0.119919
$569$	−4.99939e13			−0.838216			−0.419108	−	0.907936i	$-0.637657\pi$
$569$	−4.99939e13			−0.838216			−0.419108	+	0.907936i	$0.637657\pi$
$570$	−4.76623e12			−0.0792138
$571$		−	1.15462e14i		−	1.90220i	−0.308877	−	0.951102i	$-0.599953\pi$
$571$		−	1.15462e14i		−	1.90220i	0.308877	−	0.951102i	$-0.400047\pi$
$572$	7.11649e13			1.16221
$573$	2.20128e12			0.0356370
$574$	−1.99302e14			−3.19855
$575$	1.09642e14			1.74436
$576$	−5.88199e13			−0.927710
$577$			8.08399e13i			1.26400i	0.774969	+	0.632000i	$0.217766\pi$
$577$			8.08399e13i			1.26400i	−0.774969	+	0.632000i	$0.782234\pi$
$578$		−	8.51395e13i		−	1.31975i
$579$			6.61600e13i			1.01672i
$580$	1.34229e13			0.204506
$581$			2.57180e13i			0.388469i
$582$	−2.12718e14			−3.18559
$583$	4.17684e13			0.620162
$584$	−4.89197e12			−0.0720144
$585$			2.15359e13i			0.314328i
$586$		−	1.70912e14i		−	2.47334i
$587$			7.86996e12i			0.112923i	0.998405	+	0.0564614i	$0.0179818\pi$
$587$			7.86996e12i			0.112923i	−0.998405	+	0.0564614i	$0.982018\pi$
$588$			1.32432e14i			1.88412i
$589$		−	3.17140e12i		−	0.0447378i
$590$	1.97631e13			0.276437
$591$		−	1.92064e14i		−	2.66384i
$592$		−	2.21626e13i		−	0.304798i
$593$		−	8.56253e13i		−	1.16769i	−0.811864	−	0.583847i	$-0.801547\pi$
$593$		−	8.56253e13i		−	1.16769i	0.811864	−	0.583847i	$-0.198453\pi$
$594$	6.64674e13			0.898828
$595$	−3.51253e12			−0.0471015
$596$		−	1.65171e13i		−	0.219635i
$597$	−7.08170e13			−0.933825
$598$		−	2.35297e14i		−	3.07688i
$599$	−1.48717e13			−0.192852			−0.0964262	−	0.995340i	$-0.530741\pi$
$599$	−1.48717e13			−0.192852			−0.0964262	+	0.995340i	$0.530741\pi$
$600$	−2.46725e13			−0.317291
$601$		−	8.31585e13i		−	1.06056i	−0.847823	−	0.530279i	$-0.822087\pi$
$601$		−	8.31585e13i		−	1.06056i	0.847823	−	0.530279i	$-0.177913\pi$
$602$	4.76962e13	+	1.60922e14i	0.603256	+	2.03532i
$603$	−1.73163e13			−0.217205
$604$			4.38812e13i			0.545876i
$605$			2.92280e12i			0.0360597i
$606$	3.25813e14			3.98662
$607$			1.20141e14i			1.45797i	0.684529	+	0.728985i	$0.260008\pi$
$607$			1.20141e14i			1.45797i	−0.684529	+	0.728985i	$0.739992\pi$
$608$	−2.30956e13			−0.277978
$609$		−	2.72935e14i		−	3.25816i
$610$			1.15545e13i			0.136805i
$611$	−1.61581e14			−1.89751
$612$	1.68820e13			0.196638
$613$	1.06650e14			1.23213			0.616066	−	0.787694i	$-0.288725\pi$
$613$	1.06650e14			1.23213			0.616066	+	0.787694i	$0.288725\pi$
$614$			1.54457e14i			1.76996i
$615$	−3.68533e13			−0.418891
$616$	−3.22194e13			−0.363257
$617$	−1.07278e14			−1.19973			−0.599865	−	0.800101i	$-0.704779\pi$
$617$	−1.07278e14			−1.19973			−0.599865	+	0.800101i	$0.704779\pi$
$618$	−7.59944e13			−0.843023
$619$	−9.90190e13			−1.08960			−0.544798	−	0.838568i	$-0.683394\pi$
$619$	−9.90190e13			−1.08960			−0.544798	+	0.838568i	$0.683394\pi$
$620$		−	2.96356e12i		−	0.0323486i
$621$		−	1.00576e14i		−	1.08902i
$622$			3.84149e13i			0.412617i
$623$	1.19031e14			1.26829
$624$			2.08110e14i			2.19973i
$625$	8.62175e13			0.904056
$626$	1.21214e14			1.26091
$627$	3.44482e13			0.355491
$628$		−	5.39461e13i		−	0.552283i
$629$			4.44302e12i			0.0451258i
$630$			5.26818e13i			0.530833i
$631$			2.23891e13i			0.223815i	0.993719	+	0.111908i	$0.0356961\pi$
$631$			2.23891e13i			0.223815i	−0.993719	+	0.111908i	$0.964304\pi$
$632$		−	1.28807e13i		−	0.127748i
$633$	1.62779e14			1.60170
$634$			1.12215e14i			1.09548i
$635$		−	6.51354e12i		−	0.0630882i
$636$		−	7.68455e13i		−	0.738470i
$637$	1.90384e14			1.81523
$638$	−2.11985e14			−2.00540
$639$			8.37850e13i			0.786434i
$640$	8.08852e12			0.0753302
$641$		−	6.25113e13i		−	0.577654i	−0.957381	−	0.288827i	$-0.906735\pi$
$641$		−	6.25113e13i		−	0.577654i	0.957381	−	0.288827i	$-0.0932653\pi$
$642$	3.01220e14			2.76190
$643$	−2.02908e14			−1.84606			−0.923028	−	0.384732i	$-0.874294\pi$
$643$	−2.02908e14			−1.84606			−0.923028	+	0.384732i	$0.874294\pi$
$644$		−	2.63420e14i		−	2.37804i
$645$	8.81960e12	+	2.97564e13i	0.0790042	+	0.266552i
$646$	5.37122e12			0.0477431
$647$			1.49018e13i			0.131437i	0.997838	+	0.0657184i	$0.0209339\pi$
$647$			1.49018e13i			0.131437i	−0.997838	+	0.0657184i	$0.979066\pi$
$648$		−	1.10637e13i		−	0.0968331i
$649$	−1.42839e14			−1.24058
$650$		−	1.91645e14i		−	1.65169i
$651$	−6.02596e13			−0.515373
$652$		−	5.10666e13i		−	0.433410i
$653$			1.18155e14i			0.995141i	0.867423	+	0.497571i	$0.165774\pi$
$653$			1.18155e14i			0.995141i	−0.867423	+	0.497571i	$0.834226\pi$
$654$	2.00480e14			1.67564
$655$	−3.31662e13			−0.275099
$656$	−2.07166e14			−1.70529
$657$		−	5.78121e13i		−	0.472272i
$658$	−3.95266e14			−3.20450
$659$	−1.21811e13			−0.0980078			−0.0490039	−	0.998799i	$-0.515605\pi$
$659$	−1.21811e13			−0.0980078			−0.0490039	+	0.998799i	$0.515605\pi$
$660$	3.21906e13			0.257045
$661$	3.48800e13			0.276420			0.138210	−	0.990403i	$-0.455865\pi$
$661$	3.48800e13			0.276420			0.138210	+	0.990403i	$0.455865\pi$
$662$	2.90892e14			2.28793
$663$		−	4.17205e13i		−	0.325673i
$664$			6.80151e12i			0.0526944i
$665$			7.67082e12i			0.0589839i
$666$	6.66376e13			0.508567
$667$			3.20767e14i			2.42974i
$668$	−6.71112e13			−0.504560
$669$	−1.97672e14			−1.47507
$670$	−5.14833e12			−0.0381323
$671$		−	8.35106e13i		−	0.613945i
$672$			4.38838e14i			3.20227i
$673$		−	1.15973e14i		−	0.840001i	−0.907524	−	0.420001i	$-0.862030\pi$
$673$		−	1.15973e14i		−	0.840001i	0.907524	−	0.420001i	$-0.137970\pi$
$674$		−	2.06298e14i		−	1.48319i
$675$		−	8.19168e13i		−	0.584594i
$676$	−6.91018e13			−0.489504
$677$		−	6.79252e13i		−	0.477626i	−0.971066	−	0.238813i	$-0.923242\pi$
$677$		−	6.79252e13i		−	0.477626i	0.971066	−	0.238813i	$-0.0767583\pi$
$678$			5.21318e14i			3.63877i
$679$			3.42351e14i			2.37205i
$680$	−9.28941e11			−0.00638916
$681$	2.97700e14			2.03256
$682$			4.68028e13i			0.317212i
$683$	3.79254e13			0.255168			0.127584	−	0.991828i	$-0.459278\pi$
$683$	3.79254e13			0.255168			0.127584	+	0.991828i	$0.459278\pi$
$684$		−	3.68678e13i		−	0.246245i
$685$	9.52170e12			0.0631338
$686$	1.43217e14			0.942703
$687$			2.14678e14i			1.40283i
$688$	4.95781e13	+	1.67271e14i	0.321623	+	1.08512i
$689$	−1.10472e14			−0.711471
$690$		−	1.06434e14i		−	0.680510i
$691$		−	1.15244e14i		−	0.731521i	−0.930709	−	0.365760i	$-0.880809\pi$
$691$		−	1.15244e14i		−	0.731521i	0.930709	−	0.365760i	$-0.119191\pi$
$692$	2.91386e13			0.183628
$693$		−	3.80761e14i		−	2.38224i
$694$	−1.04273e14			−0.647701
$695$			5.32219e13i			0.328221i
$696$		−	7.21818e13i		−	0.441959i
$697$	4.15312e13			0.252471
$698$	1.12333e14			0.678000
$699$	−2.02447e14			−1.21318
$700$		−	2.14550e14i		−	1.27655i
$701$	3.65272e13			0.215787			0.107894	−	0.994162i	$-0.465589\pi$
$701$	3.65272e13			0.215787			0.107894	+	0.994162i	$0.465589\pi$
$702$	−1.75798e14			−1.03117
$703$	9.70288e12			0.0565098
$704$	1.26394e14			0.730909
$705$	−7.30894e13			−0.419671
$706$			1.75416e14i			1.00011i
$707$		−	5.24367e14i		−	2.96851i
$708$			2.62795e14i			1.47724i
$709$	−1.34678e14			−0.751737			−0.375868	−	0.926673i	$-0.622656\pi$
$709$	−1.34678e14			−0.751737			−0.375868	+	0.926673i	$0.622656\pi$
$710$			2.49102e13i			0.138065i
$711$	1.52221e14			0.837771
$712$	3.14795e13			0.172039
$713$	7.08201e13			0.384334
$714$		−	1.02058e14i		−	0.549993i
$715$		−	4.62769e13i		−	0.247648i
$716$			1.24634e14i			0.662328i
$717$			1.81166e13i			0.0956050i
$718$			3.51943e14i			1.84438i
$719$	−1.03604e14			−0.539177			−0.269588	−	0.962976i	$-0.586888\pi$
$719$	−1.03604e14			−0.539177			−0.269588	+	0.962976i	$0.586888\pi$
$720$			5.47604e13i			0.283011i
$721$			1.22306e14i			0.627729i
$722$			2.54677e14i			1.29809i
$723$	−4.13404e14			−2.09258
$724$	−1.76531e14			−0.887417
$725$			2.61257e14i			1.30430i
$726$	−8.49235e13			−0.421061
$727$			4.43628e13i			0.218447i	0.994017	+	0.109224i	$0.0348365\pi$
$727$			4.43628e13i			0.218447i	−0.994017	+	0.109224i	$0.965164\pi$
$728$	8.52163e13			0.416741
$729$	3.23069e14			1.56913
$730$		−	1.71882e13i		−	0.0829116i
$731$	−9.93909e12	−	3.35334e13i	−0.0476168	−	0.160654i
$732$	−1.53643e14			−0.731066
$733$		−	1.70067e14i		−	0.803713i	−0.915703	−	0.401856i	$-0.868365\pi$
$733$		−	1.70067e14i		−	0.803713i	0.915703	−	0.401856i	$-0.131635\pi$
$734$			1.03702e13i			0.0486753i
$735$	8.61178e13			0.401473
$736$		−	5.15744e14i		−	2.38806i
$737$	3.72099e13			0.171128
$738$		−	6.22896e14i		−	2.84534i
$739$			1.97546e14i			0.896283i	0.893963	+	0.448142i	$0.147914\pi$
$739$			1.97546e14i			0.896283i	−0.893963	+	0.448142i	$0.852086\pi$
$740$	9.06699e12			0.0408606
$741$	−9.11112e13			−0.407832
$742$	−2.70242e14			−1.20152
$743$			1.19187e14i			0.526363i	0.964746	+	0.263182i	$0.0847719\pi$
$743$			1.19187e14i			0.526363i	−0.964746	+	0.263182i	$0.915228\pi$
$744$	−1.59366e13			−0.0699086
$745$	−1.07407e13			−0.0468005
$746$	4.52467e14			1.95836
$747$	−8.03786e13			−0.345571
$748$	−3.62766e13			−0.154924
$749$		−	4.84786e14i		−	2.05656i
$750$		−	1.76273e14i		−	0.742811i
$751$		−	1.42115e14i		−	0.594893i	−0.954738	−	0.297447i	$-0.903865\pi$
$751$		−	1.42115e14i		−	0.594893i	0.954738	−	0.297447i	$-0.0961350\pi$
$752$	−4.10861e14			−1.70847
$753$			1.47927e14i			0.611042i
$754$	5.60674e14			2.30067
$755$	2.85349e13			0.116317
$756$	−1.96810e14			−0.796962
$757$			9.54159e13i			0.383832i	0.981411	+	0.191916i	$0.0614701\pi$
$757$			9.54159e13i			0.383832i	−0.981411	+	0.191916i	$0.938530\pi$
$758$		−	1.85877e14i		−	0.742814i
$759$			7.69258e14i			3.05396i
$760$			2.02867e12i			0.00800097i
$761$			4.55346e14i			1.78410i	0.451939	+	0.892049i	$0.350732\pi$
$761$			4.55346e14i			1.78410i	−0.451939	+	0.892049i	$0.649268\pi$
$762$	1.89254e14			0.736666
$763$		−	3.22654e14i		−	1.24771i
$764$			5.06241e12i			0.0194487i
$765$		−	1.09780e13i		−	0.0419002i
$766$	9.21455e13			0.349406
$767$	3.77792e14			1.42323
$768$			5.10593e14i			1.91104i
$769$	−1.21914e13			−0.0453338			−0.0226669	−	0.999743i	$-0.507216\pi$
$769$	−1.21914e13			−0.0453338			−0.0226669	+	0.999743i	$0.507216\pi$
$770$		−	1.13204e14i		−	0.418224i
$771$	−5.03971e14			−1.84984
$772$	−1.52152e14			−0.554871
$773$		−	3.40763e14i		−	1.23468i	−0.786696	−	0.617340i	$-0.788210\pi$
$773$		−	3.40763e14i		−	1.23468i	0.786696	−	0.617340i	$-0.211790\pi$
$774$	−5.02944e14	+	1.49069e14i	−1.81057	+	0.536640i
$775$	5.76814e13			0.206313
$776$			9.05400e13i			0.321760i
$777$		−	1.84364e14i		−	0.650985i
$778$	−7.60401e14			−2.66775
$779$		−	9.06978e13i		−	0.316162i
$780$	−8.51402e13			−0.294891
$781$		−	1.80040e14i		−	0.619603i
$782$			1.19944e14i			0.410152i
$783$	2.39655e14			0.814288
$784$	4.84098e14			1.63438
$785$	−3.50799e13			−0.117682
$786$		−	9.63660e14i		−	3.21226i
$787$	−3.82760e12			−0.0126781			−0.00633904	−	0.999980i	$-0.502018\pi$
$787$	−3.82760e12			−0.0126781			−0.00633904	+	0.999980i	$0.502018\pi$
$788$	4.41702e14			1.45378
$789$	7.60955e14			2.48871
$790$	4.52568e13			0.147078
$791$	8.39015e14			2.70949
$792$		−	1.00698e14i		−	0.323143i
$793$			2.20875e14i			0.704339i
$794$		−	5.65234e14i		−	1.79112i
$795$	−4.99708e13			−0.157355
$796$		−	1.62862e14i		−	0.509630i
$797$	4.48459e14			1.39454			0.697270	−	0.716809i	$-0.254398\pi$
$797$	4.48459e14			1.39454			0.697270	+	0.716809i	$0.254398\pi$
$798$	−2.22880e14			−0.688741
$799$	8.23669e13			0.252941
$800$		−	4.20062e14i		−	1.28193i
$801$			3.72017e14i			1.12824i
$802$		−	7.00303e13i		−	0.211064i
$803$			1.24228e14i			0.372086i
$804$		−	6.84587e13i		−	0.203774i
$805$	−1.71296e14			−0.506720
$806$		−	1.23788e14i		−	0.363917i
$807$			2.41668e14i			0.706075i
$808$		−	1.38677e14i		−	0.402668i
$809$	−5.13952e14			−1.48313			−0.741567	−	0.670879i	$-0.765917\pi$
$809$	−5.13952e14			−1.48313			−0.741567	+	0.670879i	$0.765917\pi$
$810$	3.88727e13			0.111486
$811$		−	5.48339e13i		−	0.156295i	−0.996942	−	0.0781475i	$-0.975099\pi$
$811$		−	5.48339e13i		−	0.156295i	0.996942	−	0.0781475i	$-0.0249005\pi$
$812$	6.27686e14			1.77812
$813$		−	1.01549e15i		−	2.85905i
$814$	−1.43193e14			−0.400682
$815$	−3.32074e13			−0.0923522
$816$		−	1.06085e14i		−	0.293226i
$817$	−7.32319e13	+	2.17055e13i	−0.201183	+	0.0596292i
$818$	−6.49817e13			−0.177429
$819$			1.00707e15i			2.73299i
$820$		−	8.47539e13i		−	0.228607i
$821$	−4.04743e14			−1.08508			−0.542542	−	0.840029i	$-0.682538\pi$
$821$	−4.04743e14			−1.08508			−0.542542	+	0.840029i	$0.682538\pi$
$822$			2.76658e14i			0.737198i
$823$	5.41285e14			1.43360			0.716798	−	0.697281i	$-0.245607\pi$
$823$	5.41285e14			1.43360			0.716798	+	0.697281i	$0.245607\pi$
$824$			3.23458e13i			0.0851493i
$825$			6.26543e14i			1.63939i
$826$	9.24169e14			2.40354
$827$	8.43510e13			0.218053			0.109027	−	0.994039i	$-0.465227\pi$
$827$	8.43510e13			0.218053			0.109027	+	0.994039i	$0.465227\pi$
$828$	8.23290e14			2.11544
$829$			6.43376e14i			1.64321i	0.570060	+	0.821603i	$0.306920\pi$
$829$			6.43376e14i			1.64321i	−0.570060	+	0.821603i	$0.693080\pi$
$830$	−2.38974e13			−0.0606681
$831$	3.28332e14			0.828530
$832$	−3.34297e14			−0.838524
$833$	−9.70489e13			−0.241972
$834$	−1.54639e15			−3.83256
$835$			4.36409e13i			0.107513i
$836$			7.92226e13i			0.194007i
$837$		−	5.29120e13i		−	0.128803i
$838$	−7.06975e14			−1.71074
$839$			3.10596e14i			0.747113i	0.927607	+	0.373557i	$0.121862\pi$
$839$			3.10596e14i			0.747113i	−0.927607	+	0.373557i	$0.878138\pi$
$840$	3.85466e13			0.0921700
$841$	−3.43626e14			−0.816782
$842$	−2.98405e14			−0.705093
$843$			8.76370e14i			2.05849i
$844$			3.74354e14i			0.874118i
$845$			4.49353e13i			0.104305i
$846$		−	1.23536e15i		−	2.85064i
$847$			1.36677e14i			0.313529i
$848$	−2.80904e14			−0.640587
$849$		−	2.89430e14i		−	0.656152i
$850$			9.76917e13i			0.220173i
$851$			2.16674e14i			0.485465i
$852$	−3.31237e14			−0.737804
$853$	7.58596e14			1.67983			0.839915	−	0.542718i	$-0.182605\pi$
$853$	7.58596e14			1.67983			0.839915	+	0.542718i	$0.182605\pi$
$854$			5.40314e14i			1.18948i
$855$	−2.39743e13			−0.0524705
$856$		−	1.28209e14i		−	0.278965i
$857$	−6.62973e14			−1.43414			−0.717070	−	0.697001i	$-0.754517\pi$
$857$	−6.62973e14			−1.43414			−0.717070	+	0.697001i	$0.754517\pi$
$858$	1.34460e15			2.89172
$859$		−	1.63017e14i		−	0.348552i	−0.984697	−	0.174276i	$-0.944242\pi$
$859$		−	1.63017e14i		−	0.348552i	0.984697	−	0.174276i	$-0.0557584\pi$
$860$	−6.84326e13	+	2.02830e13i	−0.145469	+	0.0431161i
$861$	−1.72335e15			−3.64214
$862$			3.09319e14i			0.649936i
$863$		−	7.02053e14i		−	1.46661i	−0.679897	−	0.733307i	$-0.737976\pi$
$863$		−	7.02053e14i		−	1.46661i	0.679897	−	0.733307i	$-0.262024\pi$
$864$	−3.85329e14			−0.800319
$865$		−	1.89481e13i		−	0.0391279i
$866$	−1.12642e15			−2.31265
$867$		−	7.36193e14i		−	1.50278i
$868$		−	1.38583e14i		−	0.281262i
$869$	−3.27096e14			−0.660049
$870$	2.53614e14			0.508835
$871$	−9.84155e13			−0.196324
$872$		−	8.53309e13i		−	0.169248i
$873$	−1.06998e15			−2.11011
$874$	2.61939e14			0.513622
$875$	−2.83695e14			−0.553110
$876$	2.28555e14			0.443068
$877$	6.41274e14			1.23608			0.618039	−	0.786148i	$-0.287927\pi$
$877$	6.41274e14			1.23608			0.618039	+	0.786148i	$0.287927\pi$
$878$			2.46975e14i			0.473348i
$879$		−	1.47786e15i		−	2.81636i
$880$		−	1.17671e14i		−	0.222974i
$881$	2.43911e14			0.459569			0.229785	−	0.973241i	$-0.426198\pi$
$881$	2.43911e14			0.459569			0.229785	+	0.973241i	$0.426198\pi$
$882$			1.45557e15i			2.72702i
$883$	4.53277e13			0.0844423			0.0422212	−	0.999108i	$-0.486557\pi$
$883$	4.53277e13			0.0844423			0.0422212	+	0.999108i	$0.486557\pi$
$884$	9.59473e13			0.177734
$885$	1.70890e14			0.314774
$886$			9.16673e14i			1.67898i
$887$			5.06160e14i			0.921870i	0.887434	+	0.460935i	$0.152486\pi$
$887$			5.06160e14i			0.921870i	−0.887434	+	0.460935i	$0.847514\pi$
$888$		−	4.87578e13i		−	0.0883038i
$889$		−	3.04588e14i		−	0.548534i
$890$			1.10605e14i			0.198072i
$891$	−2.80955e14			−0.500320
$892$		−	4.54598e14i		−	0.805013i
$893$		−	1.79877e14i		−	0.316751i
$894$		−	3.12076e14i		−	0.546479i
$895$	8.10469e13			0.141131
$896$	3.78238e14			0.654975
$897$		−	2.03459e15i		−	3.50361i
$898$	1.15022e15			1.96970
$899$			1.68752e14i			0.287377i
$900$	6.70551e14			1.13558
$901$	5.63138e13			0.0948398
$902$			1.33850e15i			2.24174i
$903$	4.12425e14	+	1.39148e15i	0.686919	+	2.31759i
$904$	2.21890e14			0.367533
$905$			1.14794e14i			0.189093i
$906$			8.29097e14i			1.35820i
$907$	−8.87671e14			−1.44616			−0.723079	−	0.690765i	$-0.757274\pi$
$907$	−8.87671e14			−1.44616			−0.723079	+	0.690765i	$0.757274\pi$
$908$			6.84640e14i			1.10926i
$909$	1.63885e15			2.64070
$910$			2.99411e14i			0.479801i
$911$		−	5.73997e14i		−	0.914782i	−0.889266	−	0.457391i	$-0.848784\pi$
$911$		−	5.73997e14i		−	0.914782i	0.889266	−	0.457391i	$-0.151216\pi$
$912$	−2.31673e14			−0.367199
$913$	1.72720e14			0.272263
$914$	7.08193e14			1.11025
$915$			9.99104e13i			0.155778i
$916$	−4.93709e14			−0.765586
$917$	−1.55093e15			−2.39191
$918$	8.96140e13			0.137456
$919$	−8.77444e14			−1.33857			−0.669286	−	0.743005i	$-0.733400\pi$
$919$	−8.77444e14			−1.33857			−0.669286	+	0.743005i	$0.733400\pi$
$920$	−4.53019e13			−0.0687348
$921$			1.33557e15i			2.01543i
$922$		−	4.70906e14i		−	0.706773i
$923$			4.76183e14i			0.710830i
$924$	1.50531e15			2.23493
$925$			1.76476e14i			0.260601i
$926$	−1.01885e15			−1.49643
$927$	−3.82254e14			−0.558411
$928$	1.22893e15			1.78561
$929$			7.49667e14i			1.08340i	0.840571	+	0.541701i	$0.182220\pi$
$929$			7.49667e14i			1.08340i	−0.840571	+	0.541701i	$0.817780\pi$
$930$		−	5.59939e13i		−	0.0804870i
$931$			2.11940e14i			0.303015i
$932$		−	4.65579e14i		−	0.662086i
$933$			3.32169e14i			0.469841i
$934$	−2.52322e14			−0.354994
$935$			2.35899e13i			0.0330117i
$936$			2.66334e14i			0.370721i
$937$		−	8.33868e14i		−	1.15452i	−0.816562	−	0.577258i	$-0.804123\pi$
$937$		−	8.33868e14i		−	1.15452i	0.816562	−	0.577258i	$-0.195877\pi$
$938$	−2.40748e14			−0.331549
$939$	1.04813e15			1.43578
$940$		−	1.68088e14i		−	0.229033i
$941$	−8.84335e14			−1.19858			−0.599292	−	0.800530i	$-0.704551\pi$
$941$	−8.84335e14			−1.19858			−0.599292	+	0.800530i	$0.704551\pi$
$942$		−	1.01926e15i		−	1.37414i
$943$	2.02536e15			2.71609
$944$	9.60631e14			1.28144
$945$			1.27981e14i			0.169819i
$946$	1.08074e15	−	3.20324e14i	1.42648	−	0.422799i
$947$	−3.25234e14			−0.427018			−0.213509	−	0.976941i	$-0.568489\pi$
$947$	−3.25234e14			−0.427018			−0.213509	+	0.976941i	$0.568489\pi$
$948$			6.01791e14i			0.785966i
$949$		−	3.28569e14i		−	0.426870i
$950$	2.13344e14			0.275716
$951$			9.70308e14i			1.24740i
$952$	−4.34394e13			−0.0555519
$953$		−	9.76252e14i		−	1.24193i	−0.783838	−	0.620965i	$-0.786741\pi$
$953$		−	9.76252e14i		−	1.24193i	0.783838	−	0.620965i	$-0.213259\pi$
$954$		−	8.44610e14i		−	1.06884i
$955$	3.29197e12			0.00414418
$956$	−4.16638e13			−0.0521759
$957$	−1.83301e15			−2.28352
$958$		−	6.93888e14i		−	0.859928i
$959$	4.45257e14			0.548930
$960$	−1.51215e14			−0.185455
$961$	−7.82371e14			−0.954543
$962$	3.78728e14			0.459676
$963$	1.51514e15			1.82946
$964$		−	9.50730e14i		−	1.14202i
$965$			9.89412e13i			0.118234i
$966$		−	4.97710e15i		−	5.91685i
$967$	−3.27941e14			−0.387850			−0.193925	−	0.981016i	$-0.562122\pi$
$967$	−3.27941e14			−0.387850			−0.193925	+	0.981016i	$0.562122\pi$
$968$			3.61463e13i			0.0425292i
$969$	4.64444e13			0.0543644
$970$	−3.18117e14			−0.370448
$971$	−1.00150e15			−1.16026			−0.580129	−	0.814525i	$-0.696998\pi$
$971$	−1.00150e15			−1.16026			−0.580129	+	0.814525i	$0.696998\pi$
$972$			9.59194e14i			1.10554i
$973$			2.48878e15i			2.85379i
$974$			1.66655e15i			1.90118i
$975$		−	1.65713e15i		−	1.88076i
$976$			5.61632e14i			0.634165i
$977$	6.86520e14			0.771224			0.385612	−	0.922661i	$-0.373990\pi$
$977$	6.86520e14			0.771224			0.385612	+	0.922661i	$0.373990\pi$
$978$		−	9.64859e14i		−	1.07837i
$979$		−	7.99402e14i		−	0.888897i
$980$			1.98050e14i			0.219101i
$981$	1.00842e15			1.10993
$982$	−1.27174e15			−1.39265
$983$			1.63261e14i			0.177875i	0.996037	+	0.0889374i	$0.0283471\pi$
$983$			1.63261e14i			0.177875i	−0.996037	+	0.0889374i	$0.971653\pi$
$984$	−4.55765e14			−0.494044
$985$		−	2.87228e14i		−	0.309775i
$986$	−2.85806e14			−0.306681
$987$	−3.41783e15			−3.64892
$988$		−	2.09534e14i		−	0.222572i
$989$	−4.84702e14	−	1.63533e15i	−0.512263	−	1.72832i
$990$	3.53807e14			0.372041
$991$			3.21742e13i			0.0336620i	0.999858	+	0.0168310i	$0.00535772\pi$
$991$			3.21742e13i			0.0336620i	−0.999858	+	0.0168310i	$0.994642\pi$
$992$		−	2.71328e14i		−	0.282447i
$993$	2.51531e15			2.60523
$994$			1.16486e15i			1.20044i
$995$	−1.05906e14			−0.108593
$996$		−	3.17770e14i		−	0.324202i
$997$			1.23567e15i			1.25438i	0.778867	+	0.627189i	$0.215795\pi$
$997$			1.23567e15i			1.25438i	−0.778867	+	0.627189i	$0.784205\pi$
$998$	−2.04552e15			−2.06610
$999$	1.61884e14			0.162696

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.b.b.42.28	yes	34
43.42	odd	2	inner	43.11.b.b.42.7	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.b.b.42.7	✓	34	43.42	odd	2	inner
43.11.b.b.42.28	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)

\(f(q)\)	\(=\)	\(q+43.4520i q^{2} +375.725i q^{3} -864.079 q^{4} +561.891i q^{5} -16326.0 q^{6} +26275.3i q^{7} +6948.90i q^{8} -82120.5 q^{9} +O(q^{10})\)	\(q+43.4520i q^{2} +375.725i q^{3} -864.079 q^{4} +561.891i q^{5} -16326.0 q^{6} +26275.3i q^{7} +6948.90i q^{8} -82120.5 q^{9} -24415.3 q^{10} +176463. q^{11} -324656. i q^{12} -466723. q^{13} -1.14171e6 q^{14} -211117. q^{15} -1.18676e6 q^{16} +237914. q^{17} -3.56830e6i q^{18} -519568. i q^{19} -485518. i q^{20} -9.87229e6 q^{21} +7.66767e6i q^{22} +1.16024e7 q^{23} -2.61088e6 q^{24} +9.44990e6 q^{25} -2.02801e7i q^{26} -8.66853e6i q^{27} -2.27039e7i q^{28} +2.76466e7i q^{29} -9.17344e6i q^{30} +6.10392e6 q^{31} -4.44515e7i q^{32} +6.63016e7i q^{33} +1.03379e7i q^{34} -1.47638e7 q^{35} +7.09586e7 q^{36} +1.86749e7i q^{37} +2.25763e7 q^{38} -1.75360e8i q^{39} -3.90452e6 q^{40} +1.74564e8 q^{41} -4.28971e8i q^{42} +(-4.17760e7 - 1.40948e8i) q^{43} -1.52478e8 q^{44} -4.61427e7i q^{45} +5.04148e8i q^{46} +3.46204e8 q^{47} -4.45896e8i q^{48} -4.07916e8 q^{49} +4.10617e8i q^{50} +8.93904e7i q^{51} +4.03285e8 q^{52} +2.36698e8 q^{53} +3.76665e8 q^{54} +9.91528e7i q^{55} -1.82584e8 q^{56} +1.95215e8 q^{57} -1.20130e9 q^{58} -8.09457e8 q^{59} +1.82421e8 q^{60} -4.73248e8i q^{61} +2.65227e8i q^{62} -2.15774e9i q^{63} +7.16264e8 q^{64} -2.62247e8i q^{65} -2.88094e9 q^{66} +2.10865e8 q^{67} -2.05577e8 q^{68} +4.35932e9i q^{69} -6.41519e8i q^{70} -1.02027e9i q^{71} -5.70647e8i q^{72} +7.03992e8i q^{73} -8.11462e8 q^{74} +3.55057e9i q^{75} +4.48948e8i q^{76} +4.63661e9i q^{77} +7.61973e9 q^{78} -1.85363e9 q^{79} -6.66830e8i q^{80} -1.59214e9 q^{81} +7.58515e9i q^{82} +9.78789e8 q^{83} +8.53044e9 q^{84} +1.33682e8i q^{85} +(6.12446e9 - 1.81525e9i) q^{86} -1.03875e10 q^{87} +1.22622e9i q^{88} -4.53014e9i q^{89} +2.00499e9 q^{90} -1.22633e10i q^{91} -1.00254e10 q^{92} +2.29340e9i q^{93} +1.50433e10i q^{94} +2.91941e8 q^{95} +1.67015e10 q^{96} +1.30294e10 q^{97} -1.77248e10i q^{98} -1.44912e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9}+O(q^{10}) \) 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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