LMFDB - Embedded newform 43.9.b.b.42.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,9,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, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("43.42");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 9 $
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:	$17.5172802326$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			42.27
Character	$\chi$	$=$	43.42
Dual form			43.9.b.b.42.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+31.0929i q^{2} -76.9602i q^{3} -710.770 q^{4} +309.101i q^{5} +2392.92 q^{6} -1604.82i q^{7} -14140.1i q^{8} +638.125 q^{9} +O(q^{10})$	\(q+31.0929i q^{2} -76.9602i q^{3} -710.770 q^{4} +309.101i q^{5} +2392.92 q^{6} -1604.82i q^{7} -14140.1i q^{8} +638.125 q^{9} -9610.84 q^{10} -7356.08 q^{11} +54701.0i q^{12} +42183.4 q^{13} +49898.6 q^{14} +23788.4 q^{15} +257701. q^{16} -57088.6 q^{17} +19841.2i q^{18} +127050. i q^{19} -219700. i q^{20} -123507. q^{21} -228722. i q^{22} +287238. q^{23} -1.08823e6 q^{24} +295082. q^{25} +1.31161e6i q^{26} -554046. i q^{27} +1.14066e6i q^{28} -292238. i q^{29} +739653. i q^{30} -478095. q^{31} +4.39281e6i q^{32} +566125. i q^{33} -1.77505e6i q^{34} +496051. q^{35} -453560. q^{36} -1.22416e6i q^{37} -3.95036e6 q^{38} -3.24645e6i q^{39} +4.37073e6 q^{40} +5.52026e6 q^{41} -3.84021e6i q^{42} +(1.30315e6 - 3.16070e6i) q^{43} +5.22848e6 q^{44} +197245. i q^{45} +8.93108e6i q^{46} -1.51306e6 q^{47} -1.98328e7i q^{48} +3.18935e6 q^{49} +9.17496e6i q^{50} +4.39355e6i q^{51} -2.99827e7 q^{52} +7.83616e6 q^{53} +1.72269e7 q^{54} -2.27377e6i q^{55} -2.26924e7 q^{56} +9.77780e6 q^{57} +9.08655e6 q^{58} +1.53013e7 q^{59} -1.69081e7 q^{60} -3.41732e6i q^{61} -1.48654e7i q^{62} -1.02408e6i q^{63} -7.06139e7 q^{64} +1.30389e7i q^{65} -1.76025e7 q^{66} -3.26404e7 q^{67} +4.05769e7 q^{68} -2.21059e7i q^{69} +1.54237e7i q^{70} +4.27345e7i q^{71} -9.02318e6i q^{72} -5.32427e7i q^{73} +3.80629e7 q^{74} -2.27096e7i q^{75} -9.03034e7i q^{76} +1.18052e7i q^{77} +1.00942e8 q^{78} +4.22399e7 q^{79} +7.96556e7i q^{80} -3.84528e7 q^{81} +1.71641e8i q^{82} -4.72358e7 q^{83} +8.77854e7 q^{84} -1.76461e7i q^{85} +(9.82753e7 + 4.05188e7i) q^{86} -2.24907e7 q^{87} +1.04016e8i q^{88} -7.79613e7i q^{89} -6.13292e6 q^{90} -6.76969e7i q^{91} -2.04161e8 q^{92} +3.67943e7i q^{93} -4.70453e7i q^{94} -3.92712e7 q^{95} +3.38072e8 q^{96} +5.35770e7 q^{97} +9.91662e7i q^{98} -4.69410e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9}+O(q^{10}) $ 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9	$ 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9} + 24982 q^{10} + 4538 q^{11} + 22086 q^{13} + 24732 q^{14} + 15388 q^{15} + 525812 q^{16} - 135136 q^{17} - 261352 q^{21} - 184432 q^{23} + 1770326 q^{24} - 2640434 q^{25} - 110272 q^{31} + 10947816 q^{35} + 11602066 q^{36} - 7189158 q^{38} - 21389338 q^{40} + 1301336 q^{41} + 2473420 q^{43} - 8818480 q^{44} + 1983566 q^{47} - 15560936 q^{49} + 12927876 q^{52} + 23942594 q^{53} - 13757972 q^{54} + 34967256 q^{56} + 35225148 q^{57} + 22565734 q^{58} - 5554336 q^{59} - 44902072 q^{60} - 170444572 q^{64} - 48457584 q^{66} - 130953802 q^{67} + 150021122 q^{68} + 205870278 q^{74} + 267860612 q^{78} + 7380250 q^{79} - 57601004 q^{81} - 42603970 q^{83} + 251931292 q^{84} - 45482652 q^{86} - 106687410 q^{87} - 255044692 q^{90} - 409532014 q^{92} + 123322986 q^{95} - 692987086 q^{96} - 318744840 q^{97} - 609707206 q^{99}+O(q^{100}) $ 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9 + 24982 * q^10 + 4538 * q^11 + 22086 * q^13 + 24732 * q^14 + 15388 * q^15 + 525812 * q^16 - 135136 * q^17 - 261352 * q^21 - 184432 * q^23 + 1770326 * q^24 - 2640434 * q^25 - 110272 * q^31 + 10947816 * q^35 + 11602066 * q^36 - 7189158 * q^38 - 21389338 * q^40 + 1301336 * q^41 + 2473420 * q^43 - 8818480 * q^44 + 1983566 * q^47 - 15560936 * q^49 + 12927876 * q^52 + 23942594 * q^53 - 13757972 * q^54 + 34967256 * q^56 + 35225148 * q^57 + 22565734 * q^58 - 5554336 * q^59 - 44902072 * q^60 - 170444572 * q^64 - 48457584 * q^66 - 130953802 * q^67 + 150021122 * q^68 + 205870278 * q^74 + 267860612 * q^78 + 7380250 * q^79 - 57601004 * q^81 - 42603970 * q^83 + 251931292 * q^84 - 45482652 * q^86 - 106687410 * q^87 - 255044692 * q^90 - 409532014 * q^92 + 123322986 * q^95 - 692987086 * q^96 - 318744840 * q^97 - 609707206 * 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 $

$2$			31.0929i			1.94331i	0.236407	+	0.971654i	$0.424030\pi$
$2$			31.0929i			1.94331i	−0.236407	+	0.971654i	$0.575970\pi$
$3$		−	76.9602i		−	0.950126i	−0.879952	−	0.475063i	$-0.842425\pi$
$3$		−	76.9602i		−	0.950126i	0.879952	−	0.475063i	$-0.157575\pi$
$4$	−710.770			−2.77645
$5$			309.101i			0.494561i	0.968944	+	0.247280i	$0.0795369\pi$
$5$			309.101i			0.494561i	−0.968944	+	0.247280i	$0.920463\pi$
$6$	2392.92			1.84639
$7$		−	1604.82i		−	0.668397i	−0.942503	−	0.334199i	$-0.891534\pi$
$7$		−	1604.82i		−	0.668397i	0.942503	−	0.334199i	$-0.108466\pi$
$8$		−	14140.1i		−	3.45218i
$9$	638.125			0.0972603
$10$	−9610.84			−0.961084
$11$	−7356.08			−0.502430			−0.251215	−	0.967931i	$-0.580830\pi$
$11$	−7356.08			−0.502430			−0.251215	+	0.967931i	$0.580830\pi$
$12$			54701.0i			2.63797i
$13$	42183.4			1.47696			0.738480	−	0.674275i	$-0.235544\pi$
$13$	42183.4			1.47696			0.738480	+	0.674275i	$0.235544\pi$
$14$	49898.6			1.29890
$15$	23788.4			0.469895
$16$	257701.			3.93221
$17$	−57088.6			−0.683524			−0.341762	−	0.939787i	$-0.611024\pi$
$17$	−57088.6			−0.683524			−0.341762	+	0.939787i	$0.611024\pi$
$18$			19841.2i			0.189007i
$19$			127050.i			0.974901i	0.873151	+	0.487450i	$0.162073\pi$
$19$			127050.i			0.974901i	−0.873151	+	0.487450i	$0.837927\pi$
$20$		−	219700.i		−	1.37312i
$21$	−123507.			−0.635062
$22$		−	228722.i		−	0.976377i
$23$	287238.			1.02643			0.513217	−	0.858259i	$-0.328454\pi$
$23$	287238.			1.02643			0.513217	+	0.858259i	$0.328454\pi$
$24$	−1.08823e6			−3.28001
$25$	295082.			0.755410
$26$			1.31161e6i			2.87019i
$27$		−	554046.i		−	1.04254i
$28$			1.14066e6i			1.85577i
$29$		−	292238.i		−	0.413186i	−0.978427	−	0.206593i	$-0.933762\pi$
$29$		−	292238.i		−	0.413186i	0.978427	−	0.206593i	$-0.0662375\pi$
$30$			739653.i			0.913151i
$31$	−478095.			−0.517687			−0.258844	−	0.965919i	$-0.583341\pi$
$31$	−478095.			−0.517687			−0.258844	+	0.965919i	$0.583341\pi$
$32$			4.39281e6i			4.18931i
$33$			566125.i			0.477372i
$34$		−	1.77505e6i		−	1.32830i
$35$	496051.			0.330563
$36$	−453560.			−0.270038
$37$		−	1.22416e6i		−	0.653180i	−0.945166	−	0.326590i	$-0.894100\pi$
$37$		−	1.22416e6i		−	0.653180i	0.945166	−	0.326590i	$-0.105900\pi$
$38$	−3.95036e6			−1.89453
$39$		−	3.24645e6i		−	1.40330i
$40$	4.37073e6			1.70732
$41$	5.52026e6			1.95355			0.976775	−	0.214270i	$-0.0687371\pi$
$41$	5.52026e6			1.95355			0.976775	+	0.214270i	$0.0687371\pi$
$42$		−	3.84021e6i		−	1.23412i
$43$	1.30315e6	−	3.16070e6i	0.381172	−	0.924504i
$43$	1.30315e6	−	3.16070e6i	0.381172	−	0.924504i
$44$	5.22848e6			1.39497
$45$			197245.i			0.0481011i
$46$			8.93108e6i			1.99468i
$47$	−1.51306e6			−0.310073			−0.155036	−	0.987909i	$-0.549549\pi$
$47$	−1.51306e6			−0.310073			−0.155036	+	0.987909i	$0.549549\pi$
$48$		−	1.98328e7i		−	3.73610i
$49$	3.18935e6			0.553245
$50$			9.17496e6i			1.46799i
$51$			4.39355e6i			0.649434i
$52$	−2.99827e7			−4.10070
$53$	7.83616e6			0.993116			0.496558	−	0.868004i	$-0.334597\pi$
$53$	7.83616e6			0.993116			0.496558	+	0.868004i	$0.334597\pi$
$54$	1.72269e7			2.02597
$55$		−	2.27377e6i		−	0.248482i
$56$	−2.26924e7			−2.30743
$57$	9.77780e6			0.926279
$58$	9.08655e6			0.802947
$59$	1.53013e7			1.26276			0.631378	−	0.775475i	$-0.282489\pi$
$59$	1.53013e7			1.26276			0.631378	+	0.775475i	$0.282489\pi$
$60$	−1.69081e7			−1.30464
$61$		−	3.41732e6i		−	0.246812i	−0.992356	−	0.123406i	$-0.960618\pi$
$61$		−	3.41732e6i		−	0.246812i	0.992356	−	0.123406i	$-0.0393817\pi$
$62$		−	1.48654e7i		−	1.00603i
$63$		−	1.02408e6i		−	0.0650085i
$64$	−7.06139e7			−4.20892
$65$			1.30389e7i			0.730447i
$66$	−1.76025e7			−0.927681
$67$	−3.26404e7			−1.61978			−0.809892	−	0.586580i	$-0.800474\pi$
$67$	−3.26404e7			−1.61978			−0.809892	+	0.586580i	$0.800474\pi$
$68$	4.05769e7			1.89777
$69$		−	2.21059e7i		−	0.975242i
$70$			1.54237e7i			0.642386i
$71$			4.27345e7i			1.68169i	0.541279	+	0.840843i	$0.317940\pi$
$71$			4.27345e7i			1.68169i	−0.541279	+	0.840843i	$0.682060\pi$
$72$		−	9.02318e6i		−	0.335761i
$73$		−	5.32427e7i		−	1.87486i	−0.348175	−	0.937430i	$-0.613198\pi$
$73$		−	5.32427e7i		−	1.87486i	0.348175	−	0.937430i	$-0.386802\pi$
$74$	3.80629e7			1.26933
$75$		−	2.27096e7i		−	0.717734i
$76$		−	9.03034e7i		−	2.70676i
$77$			1.18052e7i			0.335823i
$78$	1.00942e8			2.72704
$79$	4.22399e7			1.08446			0.542231	−	0.840230i	$-0.317580\pi$
$79$	4.22399e7			1.08446			0.542231	+	0.840230i	$0.317580\pi$
$80$			7.96556e7i			1.94472i
$81$	−3.84528e7			−0.893280
$82$			1.71641e8i			3.79635i
$83$	−4.72358e7			−0.995311			−0.497656	−	0.867375i	$-0.665806\pi$
$83$	−4.72358e7			−0.995311			−0.497656	+	0.867375i	$0.665806\pi$
$84$	8.77854e7			1.76322
$85$		−	1.76461e7i		−	0.338044i
$86$	9.82753e7	+	4.05188e7i	1.79660	+	0.740735i
$87$	−2.24907e7			−0.392578
$88$			1.04016e8i			1.73448i
$89$		−	7.79613e7i		−	1.24256i	−0.783587	−	0.621282i	$-0.786612\pi$
$89$		−	7.79613e7i		−	1.24256i	0.783587	−	0.621282i	$-0.213388\pi$
$90$	−6.13292e6			−0.0934754
$91$		−	6.76969e7i		−	0.987196i
$92$	−2.04161e8			−2.84984
$93$			3.67943e7i			0.491868i
$94$		−	4.70453e7i		−	0.602567i
$95$	−3.92712e7			−0.482148
$96$	3.38072e8			3.98038
$97$	5.35770e7			0.605190			0.302595	−	0.953119i	$-0.402147\pi$
$97$	5.35770e7			0.605190			0.302595	+	0.953119i	$0.402147\pi$
$98$			9.91662e7i			1.07513i
$99$	−4.69410e6			−0.0488665
$100$	−2.09735e8			−2.09735
$101$	4.84542e7			0.465635			0.232818	−	0.972520i	$-0.425205\pi$
$101$	4.84542e7			0.465635			0.232818	+	0.972520i	$0.425205\pi$
$102$	−1.36608e8			−1.26205
$103$	−1.76149e8			−1.56506			−0.782531	−	0.622612i	$-0.786072\pi$
$103$	−1.76149e8			−1.56506			−0.782531	+	0.622612i	$0.786072\pi$
$104$		−	5.96480e8i		−	5.09874i
$105$		−	3.81762e7i		−	0.314077i
$106$			2.43649e8i			1.92993i
$107$	−4.01578e7			−0.306362			−0.153181	−	0.988198i	$-0.548952\pi$
$107$	−4.01578e7			−0.306362			−0.153181	+	0.988198i	$0.548952\pi$
$108$			3.93800e8i			2.89455i
$109$	4.85598e7			0.344010			0.172005	−	0.985096i	$-0.444976\pi$
$109$	4.85598e7			0.344010			0.172005	+	0.985096i	$0.444976\pi$
$110$	7.06981e7			0.482878
$111$	−9.42120e7			−0.620603
$112$		−	4.13565e8i		−	2.62828i
$113$			7.49574e7i			0.459728i	0.973223	+	0.229864i	$0.0738281\pi$
$113$			7.49574e7i			0.459728i	−0.973223	+	0.229864i	$0.926172\pi$
$114$			3.04020e8i			1.80005i
$115$			8.87855e7i			0.507634i
$116$			2.07714e8i			1.14719i
$117$	2.69183e7			0.143650
$118$			4.75762e8i			2.45393i
$119$			9.16170e7i			0.456865i
$120$		−	3.36372e8i		−	1.62216i
$121$	−1.60247e8			−0.747564
$122$	1.06254e8			0.479632
$123$		−	4.24841e8i		−	1.85612i
$124$	3.39816e8			1.43733
$125$			2.11952e8i			0.868157i
$126$	3.18416e7			0.126332
$127$	−7.98391e7			−0.306903			−0.153451	−	0.988156i	$-0.549039\pi$
$127$	−7.98391e7			−0.306903			−0.153451	+	0.988156i	$0.549039\pi$
$128$		−	1.07103e9i		−	3.98991i
$129$	−2.43248e8	−	1.00291e8i	−0.878395	−	0.362162i
$130$	−4.05418e8			−1.41948
$131$			1.37065e8i			0.465415i	0.972547	+	0.232707i	$0.0747584\pi$
$131$			1.37065e8i			0.465415i	−0.972547	+	0.232707i	$0.925242\pi$
$132$		−	4.02385e8i		−	1.32540i
$133$	2.03893e8			0.651621
$134$		−	1.01489e9i		−	3.14774i
$135$	1.71256e8			0.515597
$136$			8.07241e8i			2.35965i
$137$		−	3.72743e8i		−	1.05810i	−0.848590	−	0.529051i	$-0.822548\pi$
$137$		−	3.72743e8i		−	1.05810i	0.848590	−	0.529051i	$-0.177452\pi$
$138$	6.87338e8			1.89520
$139$	−1.21246e8			−0.324794			−0.162397	−	0.986726i	$-0.551922\pi$
$139$	−1.21246e8			−0.324794			−0.162397	+	0.986726i	$0.551922\pi$
$140$	−3.52579e8			−0.917791
$141$			1.16445e8i			0.294608i
$142$	−1.32874e9			−3.26803
$143$	−3.10305e8			−0.742069
$144$	1.64446e8			0.382448
$145$	9.03310e7			0.204345
$146$	1.65547e9			3.64343
$147$		−	2.45453e8i		−	0.525653i
$148$			8.70100e8i			1.81352i
$149$		−	5.70992e8i		−	1.15847i	−0.815160	−	0.579235i	$-0.803351\pi$
$149$		−	5.70992e8i		−	1.15847i	0.815160	−	0.579235i	$-0.196649\pi$
$150$	7.06107e8			1.39478
$151$			5.19180e8i			0.998644i	0.866417	+	0.499322i	$0.166417\pi$
$151$			5.19180e8i			0.998644i	−0.866417	+	0.499322i	$0.833583\pi$
$152$	1.79651e9			3.36554
$153$	−3.64297e7			−0.0664797
$154$	−3.67058e8			−0.652607
$155$		−	1.47779e8i		−	0.256028i
$156$			2.30748e9i			3.89618i
$157$			7.05045e8i			1.16043i	0.814464	+	0.580214i	$0.197031\pi$
$157$			7.05045e8i			1.16043i	−0.814464	+	0.580214i	$0.802969\pi$
$158$			1.31336e9i			2.10744i
$159$		−	6.03073e8i		−	0.943585i
$160$	−1.35782e9			−2.07187
$161$		−	4.60966e8i		−	0.686066i
$162$		−	1.19561e9i		−	1.73592i
$163$		−	2.10320e8i		−	0.297940i	−0.988842	−	0.148970i	$-0.952404\pi$
$163$		−	2.10320e8i		−	0.297940i	0.988842	−	0.148970i	$-0.0475958\pi$
$164$	−3.92364e9			−5.42393
$165$	−1.74990e8			−0.236090
$166$		−	1.46870e9i		−	1.93420i
$167$	1.19295e8			0.153375			0.0766877	−	0.997055i	$-0.475566\pi$
$167$	1.19295e8			0.153375			0.0766877	+	0.997055i	$0.475566\pi$
$168$			1.74641e9i			2.19235i
$169$	9.63713e8			1.18141
$170$	5.48670e8			0.656924
$171$			8.10738e7i			0.0948192i
$172$	−9.26242e8	+	2.24653e9i	−1.05830	+	2.56684i
$173$	1.83412e8			0.204759			0.102380	−	0.994745i	$-0.467354\pi$
$173$	1.83412e8			0.204759			0.102380	+	0.994745i	$0.467354\pi$
$174$		−	6.99303e8i		−	0.762901i
$175$		−	4.73554e8i		−	0.504914i
$176$	−1.89567e9			−1.97566
$177$		−	1.17759e9i		−	1.19978i
$178$	2.42404e9			2.41469
$179$			1.83639e9i			1.78876i	0.447304	+	0.894382i	$0.352384\pi$
$179$			1.83639e9i			1.78876i	−0.447304	+	0.894382i	$0.647616\pi$
$180$		−	1.40196e8i		−	0.133550i
$181$	7.96225e8			0.741859			0.370930	−	0.928661i	$-0.379039\pi$
$181$	7.96225e8			0.741859			0.370930	+	0.928661i	$0.379039\pi$
$182$	2.10490e9			1.91843
$183$	−2.62998e8			−0.234502
$184$		−	4.06159e9i		−	3.54344i
$185$	3.78390e8			0.323037
$186$	−1.14404e9			−0.955852
$187$	4.19948e8			0.343423
$188$	1.07544e9			0.860900
$189$	−8.89145e8			−0.696828
$190$		−	1.22106e9i		−	0.936962i
$191$			1.27800e9i			0.960279i	0.877192	+	0.480140i	$0.159414\pi$
$191$			1.27800e9i			0.960279i	−0.877192	+	0.480140i	$0.840586\pi$
$192$			5.43446e9i			3.99900i
$193$	−2.03388e8			−0.146587			−0.0732937	−	0.997310i	$-0.523351\pi$
$193$	−2.03388e8			−0.146587			−0.0732937	+	0.997310i	$0.523351\pi$
$194$			1.66587e9i			1.17607i
$195$	1.00348e9			0.694016
$196$	−2.26689e9			−1.53606
$197$	1.84082e9			1.22221			0.611107	−	0.791548i	$-0.290725\pi$
$197$	1.84082e9			1.22221			0.611107	+	0.791548i	$0.290725\pi$
$198$		−	1.45953e8i		−	0.0949627i
$199$		−	3.93508e8i		−	0.250923i	−0.992098	−	0.125462i	$-0.959959\pi$
$199$		−	3.93508e8i		−	0.250923i	0.992098	−	0.125462i	$-0.0400412\pi$
$200$		−	4.17250e9i		−	2.60781i
$201$			2.51202e9i			1.53900i
$202$			1.50658e9i			0.904873i
$203$	−4.68990e8			−0.276172
$204$		−	3.12281e9i		−	1.80312i
$205$			1.70632e9i			0.966149i
$206$		−	5.47699e9i		−	3.04140i
$207$	1.83294e8			0.0998313
$208$	1.08707e10			5.80772
$209$		−	9.34590e8i		−	0.489820i
$210$	1.18701e9			0.610348
$211$		−	3.33053e9i		−	1.68029i	−0.542362	−	0.840145i	$-0.682470\pi$
$211$		−	3.33053e9i		−	1.68029i	0.542362	−	0.840145i	$-0.317530\pi$
$212$	−5.56971e9			−2.75733
$213$	3.28885e9			1.59781
$214$		−	1.24862e9i		−	0.595355i
$215$	9.76973e8	+	4.02805e8i	0.457224	+	0.188513i
$216$	−7.83429e9			−3.59903
$217$			7.67258e8i			0.346021i
$218$			1.50987e9i			0.668517i
$219$	−4.09757e9			−1.78135
$220$			1.61613e9i			0.689898i
$221$	−2.40819e9			−1.00954
$222$		−	2.92933e9i		−	1.20602i
$223$		−	2.90423e9i		−	1.17439i	−0.809446	−	0.587195i	$-0.800232\pi$
$223$		−	2.90423e9i		−	1.17439i	0.809446	−	0.587195i	$-0.199768\pi$
$224$	7.04968e9			2.80013
$225$	1.88299e8			0.0734714
$226$	−2.33065e9			−0.893393
$227$			2.65538e9i			1.00005i	0.866010	+	0.500027i	$0.166677\pi$
$227$			2.65538e9i			1.00005i	−0.866010	+	0.500027i	$0.833323\pi$
$228$	−6.94977e9			−2.57176
$229$	−6.07345e8			−0.220848			−0.110424	−	0.993885i	$-0.535221\pi$
$229$	−6.07345e8			−0.220848			−0.110424	+	0.993885i	$0.535221\pi$
$230$	−2.76060e9			−0.986490
$231$	9.08531e8			0.319074
$232$	−4.13229e9			−1.42639
$233$			9.56751e8i			0.324620i	0.986740	+	0.162310i	$0.0518944\pi$
$233$			9.56751e8i			0.324620i	−0.986740	+	0.162310i	$0.948106\pi$
$234$			8.36969e8i			0.279155i
$235$		−	4.67686e8i		−	0.153350i
$236$	−1.08757e10			−3.50598
$237$		−	3.25079e9i		−	1.03037i
$238$	−2.84864e9			−0.887830
$239$	1.06815e8			0.0327373			0.0163686	−	0.999866i	$-0.494789\pi$
$239$	1.06815e8			0.0327373			0.0163686	+	0.999866i	$0.494789\pi$
$240$	6.13032e9			1.84773
$241$			5.00348e9i			1.48321i	0.670835	+	0.741607i	$0.265936\pi$
$241$			5.00348e9i			1.48321i	−0.670835	+	0.741607i	$0.734064\pi$
$242$		−	4.98255e9i		−	1.45275i
$243$		−	6.75763e8i		−	0.193807i
$244$			2.42893e9i			0.685260i
$245$			9.85829e8i			0.273613i
$246$	1.32095e10			3.60701
$247$			5.35941e9i			1.43989i
$248$			6.76034e9i			1.78715i
$249$			3.63528e9i			0.945671i
$250$	−6.59022e9			−1.68710
$251$	6.27266e9			1.58036			0.790182	−	0.612872i	$-0.209986\pi$
$251$	6.27266e9			1.58036			0.790182	+	0.612872i	$0.209986\pi$
$252$			7.27884e8i			0.180493i
$253$	−2.11295e9			−0.515712
$254$		−	2.48243e9i		−	0.596407i
$255$	−1.35805e9			−0.321185
$256$	1.52244e10			3.54471
$257$			3.46689e9i			0.794708i	0.917665	+	0.397354i	$0.130072\pi$
$257$			3.46689e9i			0.794708i	−0.917665	+	0.397354i	$0.869928\pi$
$258$	3.11834e9	−	7.56329e9i	0.703792	−	1.70699i
$259$	−1.96457e9			−0.436584
$260$		−	9.26768e9i		−	2.02805i
$261$		−	1.86485e8i		−	0.0401866i
$262$	−4.26174e9			−0.904444
$263$			1.63128e9i			0.340961i	0.985361	+	0.170480i	$0.0545319\pi$
$263$			1.63128e9i			0.340961i	−0.985361	+	0.170480i	$0.945468\pi$
$264$	8.00510e9			1.64798
$265$			2.42216e9i			0.491156i
$266$			6.33962e9i			1.26630i
$267$	−5.99992e9			−1.18059
$268$	2.31999e10			4.49724
$269$	3.80777e8			0.0727212			0.0363606	−	0.999339i	$-0.488424\pi$
$269$	3.80777e8			0.0727212			0.0363606	+	0.999339i	$0.488424\pi$
$270$			5.32485e9i			1.00196i
$271$	−4.98415e9			−0.924089			−0.462045	−	0.886857i	$-0.652884\pi$
$271$	−4.98415e9			−0.924089			−0.462045	+	0.886857i	$0.652884\pi$
$272$	−1.47118e10			−2.68776
$273$	−5.20997e9			−0.937961
$274$	1.15897e10			2.05622
$275$	−2.17065e9			−0.379541
$276$			1.57122e10i			2.70771i
$277$		−	1.03473e10i		−	1.75755i	−0.477233	−	0.878777i	$-0.658360\pi$
$277$		−	1.03473e10i		−	1.75755i	0.477233	−	0.878777i	$-0.341640\pi$
$278$		−	3.76989e9i		−	0.631174i
$279$	−3.05084e8			−0.0503504
$280$		−	7.01424e9i		−	1.14116i
$281$	5.27555e9			0.846140			0.423070	−	0.906097i	$-0.360952\pi$
$281$	5.27555e9			0.846140			0.423070	+	0.906097i	$0.360952\pi$
$282$	−3.62062e9			−0.572515
$283$	6.87347e9			1.07159			0.535797	−	0.844347i	$-0.320011\pi$
$283$	6.87347e9			1.07159			0.535797	+	0.844347i	$0.320011\pi$
$284$		−	3.03744e10i		−	4.66911i
$285$			3.02232e9i			0.458101i
$286$		−	9.64829e9i		−	1.44207i
$287$		−	8.85904e9i		−	1.30575i
$288$			2.80316e9i			0.407454i
$289$	−3.71665e9			−0.532795
$290$			2.80866e9i			0.397106i
$291$		−	4.12330e9i		−	0.575007i
$292$			3.78433e10i			5.20545i
$293$	−1.19152e10			−1.61671			−0.808355	−	0.588696i	$-0.799642\pi$
$293$	−1.19152e10			−1.61671			−0.808355	+	0.588696i	$0.799642\pi$
$294$	7.63185e9			1.02151
$295$			4.72963e9i			0.624510i
$296$	−1.73099e10			−2.25490
$297$			4.07561e9i			0.523801i
$298$	1.77538e10			2.25127
$299$	1.21167e10			1.51600
$300$			1.61413e10i			1.99275i
$301$	−5.07235e9	−	2.09133e9i	−0.617936	−	0.254775i
$302$	−1.61428e10			−1.94067
$303$		−	3.72904e9i		−	0.442412i
$304$			3.27410e10i			3.83352i
$305$	1.05629e9			0.122064
$306$		−	1.13270e9i		−	0.129191i
$307$	6.03350e9			0.679229			0.339614	−	0.940565i	$-0.389703\pi$
$307$	6.03350e9			0.679229			0.339614	+	0.940565i	$0.389703\pi$
$308$		−	8.39079e9i		−	0.932395i
$309$			1.35565e10i			1.48701i
$310$	4.59490e9			0.497541
$311$	−1.24617e10			−1.33209			−0.666046	−	0.745911i	$-0.732015\pi$
$311$	−1.24617e10			−1.33209			−0.666046	+	0.745911i	$0.732015\pi$
$312$	−4.59052e10			−4.84444
$313$		−	6.35655e9i		−	0.662283i	−0.943581	−	0.331142i	$-0.892566\pi$
$313$		−	6.35655e9i		−	0.662283i	0.943581	−	0.331142i	$-0.107434\pi$
$314$	−2.19219e10			−2.25507
$315$	3.16543e8			0.0321507
$316$	−3.00228e10			−3.01095
$317$	1.40297e10			1.38935			0.694676	−	0.719323i	$-0.255548\pi$
$317$	1.40297e10			1.38935			0.694676	+	0.719323i	$0.255548\pi$
$318$	1.87513e10			1.83368
$319$			2.14973e9i			0.207597i
$320$		−	2.18268e10i		−	2.08157i
$321$			3.09055e9i			0.291082i
$322$	1.43328e10			1.33324
$323$		−	7.25311e9i		−	0.666368i
$324$	2.73311e10			2.48014
$325$	1.24476e10			1.11571
$326$	6.53945e9			0.578990
$327$		−	3.73717e9i		−	0.326853i
$328$		−	7.80573e10i		−	6.74401i
$329$			2.42819e9i			0.207252i
$330$		−	5.44094e9i		−	0.458795i
$331$		−	1.45095e10i		−	1.20876i	−0.796696	−	0.604380i	$-0.793421\pi$
$331$		−	1.45095e10i		−	1.20876i	0.796696	−	0.604380i	$-0.206579\pi$
$332$	3.35738e10			2.76343
$333$		−	7.81170e8i		−	0.0635285i
$334$			3.70923e9i			0.298056i
$335$		−	1.00892e10i		−	0.801081i
$336$	−3.18280e10			−2.49720
$337$	−1.52910e10			−1.18554			−0.592772	−	0.805370i	$-0.701966\pi$
$337$	−1.52910e10			−1.18554			−0.592772	+	0.805370i	$0.701966\pi$
$338$			2.99647e10i			2.29584i
$339$	5.76874e9			0.436800
$340$			1.25423e10i			0.938562i
$341$	3.51691e9			0.260102
$342$	−2.52082e9			−0.184263
$343$		−	1.43698e10i		−	1.03818i
$344$	−4.46927e10	−	1.84268e10i	−3.19156	−	1.31588i
$345$	6.83295e9			0.482317
$346$			5.70282e9i			0.397910i
$347$			3.46237e8i			0.0238812i	0.999929	+	0.0119406i	$0.00380090\pi$
$347$			3.46237e8i			0.0238812i	−0.999929	+	0.0119406i	$0.996199\pi$
$348$	1.59857e10			1.08997
$349$			2.52716e10i			1.70346i	0.523983	+	0.851729i	$0.324446\pi$
$349$			2.52716e10i			1.70346i	−0.523983	+	0.851729i	$0.675554\pi$
$350$	1.47242e10			0.981203
$351$		−	2.33716e10i		−	1.53978i
$352$		−	3.23139e10i		−	2.10484i
$353$	2.62821e9			0.169263			0.0846315	−	0.996412i	$-0.473029\pi$
$353$	2.62821e9			0.169263			0.0846315	+	0.996412i	$0.473029\pi$
$354$	3.66147e10			2.33154
$355$	−1.32092e10			−0.831696
$356$			5.54126e10i			3.44991i
$357$	7.05087e9			0.434080
$358$	−5.70988e10			−3.47612
$359$	2.51278e10			1.51278			0.756392	−	0.654119i	$-0.226960\pi$
$359$	2.51278e10			1.51278			0.756392	+	0.654119i	$0.226960\pi$
$360$	2.78907e9			0.166054
$361$	8.41845e8			0.0495682
$362$			2.47570e10i			1.44166i
$363$			1.23326e10i			0.710280i
$364$			4.81170e10i			2.74090i
$365$	1.64574e10			0.927232
$366$		−	8.17736e9i		−	0.455710i
$367$	9.39858e9			0.518081			0.259041	−	0.965866i	$-0.416594\pi$
$367$	9.39858e9			0.518081			0.259041	+	0.965866i	$0.416594\pi$
$368$	7.40217e10			4.03616
$369$	3.52262e9			0.190003
$370$			1.17653e10i			0.627761i
$371$		−	1.25756e10i		−	0.663796i
$372$		−	2.61523e10i		−	1.36565i
$373$		−	5.81508e9i		−	0.300414i	−0.988655	−	0.150207i	$-0.952006\pi$
$373$		−	5.81508e9i		−	0.300414i	0.988655	−	0.150207i	$-0.0479940\pi$
$374$			1.30574e10i			0.667377i
$375$	1.63119e10			0.824859
$376$			2.13948e10i			1.07043i
$377$		−	1.23276e10i		−	0.610258i
$378$		−	2.76461e10i		−	1.35415i
$379$	−2.73939e10			−1.32769			−0.663845	−	0.747871i	$-0.731076\pi$
$379$	−2.73939e10			−1.32769			−0.663845	+	0.747871i	$0.731076\pi$
$380$	2.79128e10			1.33866
$381$			6.14444e9i			0.291596i
$382$	−3.97368e10			−1.86612
$383$		−	1.63024e9i		−	0.0757627i	−0.999282	−	0.0378813i	$-0.987939\pi$
$383$		−	1.63024e9i		−	0.0757627i	0.999282	−	0.0378813i	$-0.0120609\pi$
$384$	−8.24270e10			−3.79092
$385$	−3.64899e9			−0.166085
$386$		−	6.32393e9i		−	0.284864i
$387$	8.31574e8	−	2.01692e9i	0.0370729	−	0.0899176i
$388$	−3.80810e10			−1.68028
$389$		−	5.91193e9i		−	0.258185i	−0.991633	−	0.129092i	$-0.958794\pi$
$389$		−	5.91193e9i		−	0.258185i	0.991633	−	0.129092i	$-0.0412064\pi$
$390$			3.12011e10i			1.34869i
$391$	−1.63980e10			−0.701592
$392$		−	4.50978e10i		−	1.90990i
$393$	1.05485e10			0.442202
$394$			5.72366e10i			2.37514i
$395$			1.30564e10i			0.536332i
$396$	3.33643e9			0.135675
$397$	−2.24349e10			−0.903154			−0.451577	−	0.892232i	$-0.649138\pi$
$397$	−2.24349e10			−0.903154			−0.451577	+	0.892232i	$0.649138\pi$
$398$	1.22353e10			0.487622
$399$		−	1.56916e10i		−	0.619122i
$400$	7.60430e10			2.97043
$401$	−1.52627e10			−0.590272			−0.295136	−	0.955455i	$-0.595365\pi$
$401$	−1.52627e10			−0.590272			−0.295136	+	0.955455i	$0.595365\pi$
$402$	−7.81059e10			−2.99075
$403$	−2.01677e10			−0.764603
$404$	−3.44398e10			−1.29281
$405$		−	1.18858e10i		−	0.441781i
$406$		−	1.45823e10i		−	0.536688i
$407$			9.00505e9i			0.328177i
$408$	6.21255e10			2.24197
$409$		−	7.64531e9i		−	0.273213i	−0.990625	−	0.136607i	$-0.956380\pi$
$409$		−	7.64531e9i		−	0.273213i	0.990625	−	0.136607i	$-0.0436196\pi$
$410$	−5.30544e10			−1.87753
$411$	−2.86864e10			−1.00533
$412$	1.25202e11			4.34531
$413$		−	2.45558e10i		−	0.844023i
$414$			5.69915e9i			0.194003i
$415$		−	1.46006e10i		−	0.492242i
$416$			1.85304e11i			6.18745i
$417$			9.33111e9i			0.308595i
$418$	2.90592e10			0.951870
$419$		−	2.18738e10i		−	0.709689i	−0.934925	−	0.354844i	$-0.884534\pi$
$419$		−	2.18738e10i		−	0.709689i	0.934925	−	0.354844i	$-0.115466\pi$
$420$			2.71345e10i			0.872017i
$421$			1.91405e10i			0.609291i	0.952466	+	0.304645i	$0.0985380\pi$
$421$			1.91405e10i			0.609291i	−0.952466	+	0.304645i	$0.901462\pi$
$422$	1.03556e11			3.26532
$423$	−9.65519e8			−0.0301578
$424$		−	1.10804e11i		−	3.42842i
$425$	−1.68458e10			−0.516340
$426$			1.02260e11i			3.10504i
$427$	−5.48419e9			−0.164968
$428$	2.85430e10			0.850597
$429$			2.38811e10i			0.705059i
$430$	−1.25244e10	+	3.03769e10i	−0.366339	+	0.888526i
$431$	1.65854e10			0.480636			0.240318	−	0.970694i	$-0.422748\pi$
$431$	1.65854e10			0.480636			0.240318	+	0.970694i	$0.422748\pi$
$432$		−	1.42778e11i		−	4.09947i
$433$			2.27110e8i			0.00646078i	0.999995	+	0.00323039i	$0.00102827\pi$
$433$			2.27110e8i			0.00646078i	−0.999995	+	0.00323039i	$0.998972\pi$
$434$	−2.38563e10			−0.672425
$435$		−	6.95190e9i		−	0.194154i
$436$	−3.45148e10			−0.955125
$437$			3.64937e10i			1.00067i
$438$		−	1.27405e11i		−	3.46172i
$439$	−3.63557e10			−0.978846			−0.489423	−	0.872046i	$-0.662793\pi$
$439$	−3.63557e10			−0.978846			−0.489423	+	0.872046i	$0.662793\pi$
$440$	−3.21514e10			−0.857807
$441$	2.03520e9			0.0538088
$442$		−	7.48778e10i		−	1.96184i
$443$	−5.00268e10			−1.29894			−0.649468	−	0.760389i	$-0.725008\pi$
$443$	−5.00268e10			−1.29894			−0.649468	+	0.760389i	$0.725008\pi$
$444$	6.69631e10			1.72307
$445$	2.40979e10			0.614524
$446$	9.03012e10			2.28220
$447$	−4.39437e10			−1.10069
$448$			1.13323e11i			2.81323i
$449$			6.46660e10i			1.59108i	0.605904	+	0.795538i	$0.292812\pi$
$449$			6.46660e10i			1.59108i	−0.605904	+	0.795538i	$0.707188\pi$
$450$			5.85477e9i			0.142778i
$451$	−4.06075e10			−0.981522
$452$		−	5.32775e10i		−	1.27641i
$453$	3.99562e10			0.948837
$454$	−8.25636e10			−1.94341
$455$	2.09252e10			0.488228
$456$		−	1.38260e11i		−	3.19769i
$457$			7.15621e10i			1.64066i	0.571891	+	0.820330i	$0.306210\pi$
$457$			7.15621e10i			1.64066i	−0.571891	+	0.820330i	$0.693790\pi$
$458$		−	1.88841e10i		−	0.429176i
$459$			3.16297e10i			0.712598i
$460$		−	6.31061e10i		−	1.40942i
$461$	−9.56302e9			−0.211734			−0.105867	−	0.994380i	$-0.533762\pi$
$461$	−9.56302e9			−0.211734			−0.105867	+	0.994380i	$0.533762\pi$
$462$			2.82489e10i			0.620059i
$463$		−	1.69947e10i		−	0.369819i	−0.982756	−	0.184909i	$-0.940801\pi$
$463$		−	1.69947e10i		−	0.369819i	0.982756	−	0.184909i	$-0.0591991\pi$
$464$		−	7.53102e10i		−	1.62473i
$465$	−1.13731e10			−0.243259
$466$	−2.97482e10			−0.630837
$467$		−	4.90505e10i		−	1.03128i	−0.856806	−	0.515640i	$-0.827554\pi$
$467$		−	4.90505e10i		−	1.03128i	0.856806	−	0.515640i	$-0.172446\pi$
$468$	−1.91327e10			−0.398835
$469$			5.23821e10i			1.08266i
$470$	1.45417e10			0.298006
$471$	5.42604e10			1.10255
$472$		−	2.16362e11i		−	4.35927i
$473$	−9.58609e9	+	2.32503e10i	−0.191512	+	0.464499i
$474$	1.01077e11			2.00234
$475$			3.74902e10i			0.736449i
$476$		−	6.51187e10i		−	1.26846i
$477$	5.00045e9			0.0965908
$478$			3.32121e9i			0.0636186i
$479$	3.24807e10			0.616997			0.308499	−	0.951225i	$-0.400174\pi$
$479$	3.24807e10			0.616997			0.308499	+	0.951225i	$0.400174\pi$
$480$			1.04498e11i			1.96854i
$481$		−	5.16395e10i		−	0.964721i
$482$	−1.55573e11			−2.88234
$483$	−3.54761e10			−0.651849
$484$	1.13899e11			2.07557
$485$			1.65607e10i			0.299303i
$486$	2.10115e10			0.376627
$487$	6.76777e10			1.20318			0.601589	−	0.798806i	$-0.294535\pi$
$487$	6.76777e10			1.20318			0.601589	+	0.798806i	$0.294535\pi$
$488$	−4.83214e10			−0.852040
$489$	−1.61862e10			−0.283081
$490$	−3.06523e10			−0.531715
$491$		−	5.31270e10i		−	0.914091i	−0.889443	−	0.457046i	$-0.848908\pi$
$491$		−	5.31270e10i		−	0.914091i	0.889443	−	0.457046i	$-0.151092\pi$
$492$			3.01964e11i			5.15341i
$493$			1.66835e10i			0.282422i
$494$	−1.66640e11			−2.79815
$495$		−	1.45095e9i		−	0.0241675i
$496$	−1.23206e11			−2.03566
$497$	6.85812e10			1.12403
$498$	−1.13031e11			−1.83773
$499$			8.54031e10i			1.37744i	0.725029	+	0.688718i	$0.241826\pi$
$499$			8.54031e10i			1.37744i	−0.725029	+	0.688718i	$0.758174\pi$
$500$		−	1.50649e11i		−	2.41039i
$501$		−	9.18096e9i		−	0.145726i
$502$			1.95036e11i			3.07113i
$503$			3.93175e10i			0.614206i	0.951676	+	0.307103i	$0.0993596\pi$
$503$			3.93175e10i			0.614206i	−0.951676	+	0.307103i	$0.900640\pi$
$504$	−1.44806e10			−0.224421
$505$			1.49772e10i			0.230285i
$506$		−	6.56978e10i		−	1.00219i
$507$		−	7.41675e10i		−	1.12249i
$508$	5.67473e10			0.852100
$509$	4.01712e10			0.598471			0.299236	−	0.954179i	$-0.403268\pi$
$509$	4.01712e10			0.598471			0.299236	+	0.954179i	$0.403268\pi$
$510$		−	4.22257e10i		−	0.624161i
$511$	−8.54451e10			−1.25315
$512$			1.99187e11i			2.89855i
$513$	7.03916e10			1.01637
$514$	−1.07796e11			−1.54436
$515$		−	5.44478e10i		−	0.774018i
$516$	1.72893e11	+	7.12838e10i	2.43882	+	1.00552i
$517$	1.11302e10			0.155790
$518$		−	6.10841e10i		−	0.848417i
$519$		−	1.41154e10i		−	0.194547i
$520$	1.84372e11			2.52164
$521$		−	2.34037e10i		−	0.317639i	−0.987308	−	0.158819i	$-0.949231\pi$
$521$		−	2.34037e10i		−	0.317639i	0.987308	−	0.158819i	$-0.0507687\pi$
$522$	5.79835e9			0.0780949
$523$			1.53893e9i			0.0205689i	0.999947	+	0.0102844i	$0.00327370\pi$
$523$			1.53893e9i			0.0205689i	−0.999947	+	0.0102844i	$0.996726\pi$
$524$		−	9.74214e10i		−	1.29220i
$525$	−3.64448e10			−0.479732
$526$	−5.07211e10			−0.662592
$527$	2.72938e10			0.353852
$528$			1.45891e11i			1.87713i
$529$	4.19490e9			0.0535673
$530$	−7.53121e10			−0.954468
$531$	9.76413e9			0.122816
$532$	−1.44921e11			−1.80919
$533$	2.32864e11			2.88531
$534$		−	1.86555e11i		−	2.29426i
$535$		−	1.24128e10i		−	0.151515i
$536$			4.61541e11i			5.59179i
$537$	1.41329e11			1.69955
$538$			1.18395e10i			0.141320i
$539$	−2.34611e10			−0.277967
$540$	−1.21724e11			−1.43153
$541$	−2.14855e10			−0.250816			−0.125408	−	0.992105i	$-0.540024\pi$
$541$	−2.14855e10			−0.250816			−0.125408	+	0.992105i	$0.540024\pi$
$542$		−	1.54972e11i		−	1.79579i
$543$		−	6.12776e10i		−	0.704860i
$544$		−	2.50780e11i		−	2.86350i
$545$			1.50099e10i			0.170134i
$546$		−	1.61993e11i		−	1.82275i
$547$	−7.55950e10			−0.844391			−0.422196	−	0.906505i	$-0.638741\pi$
$547$	−7.55950e10			−0.844391			−0.422196	+	0.906505i	$0.638741\pi$
$548$			2.64935e11i			2.93777i
$549$		−	2.18068e9i		−	0.0240050i
$550$		−	6.74917e10i		−	0.737564i
$551$	3.71289e10			0.402815
$552$	−3.12581e11			−3.36671
$553$		−	6.77874e10i		−	0.724851i
$554$	3.21728e11			3.41547
$555$		−	2.91210e10i		−	0.306926i
$556$	8.61780e10			0.901773
$557$	−1.76314e11			−1.83175			−0.915877	−	0.401459i	$-0.868503\pi$
$557$	−1.76314e11			−1.83175			−0.915877	+	0.401459i	$0.868503\pi$
$558$		−	9.48597e9i		−	0.0978464i
$559$	5.49715e10	−	1.33329e11i	0.562976	−	1.36546i
$560$	1.27833e11			1.29984
$561$		−	3.23193e10i		−	0.326295i
$562$			1.64032e11i			1.64431i
$563$	4.11955e9			0.0410031			0.0205015	−	0.999790i	$-0.493474\pi$
$563$	4.11955e9			0.0410031			0.0205015	+	0.999790i	$0.493474\pi$
$564$		−	8.27657e10i		−	0.817964i
$565$	−2.31694e10			−0.227364
$566$			2.13716e11i			2.08244i
$567$			6.17099e10i			0.597066i
$568$	6.04271e11			5.80549
$569$	−5.45267e10			−0.520188			−0.260094	−	0.965583i	$-0.583754\pi$
$569$	−5.45267e10			−0.520188			−0.260094	+	0.965583i	$0.583754\pi$
$570$	−9.39729e10			−0.890232
$571$			1.57005e11i			1.47697i	0.674272	+	0.738483i	$0.264457\pi$
$571$			1.57005e11i			1.47697i	−0.674272	+	0.738483i	$0.735543\pi$
$572$	2.20555e11			2.06032
$573$	9.83552e10			0.912387
$574$	2.75453e11			2.53747
$575$	8.47588e10			0.775378
$576$	−4.50605e10			−0.409361
$577$			1.19552e11i			1.07858i	0.842120	+	0.539291i	$0.181308\pi$
$577$			1.19552e11i			1.07858i	−0.842120	+	0.539291i	$0.818692\pi$
$578$		−	1.15562e11i		−	1.03539i
$579$			1.56528e10i			0.139276i
$580$	−6.42046e10			−0.567354
$581$			7.58050e10i			0.665263i
$582$	1.28205e11			1.11742
$583$	−5.76434e10			−0.498971
$584$	−7.52860e11			−6.47236
$585$			8.32046e9i			0.0710435i
$586$		−	3.70480e11i		−	3.14177i
$587$			9.65927e10i			0.813564i	0.913525	+	0.406782i	$0.133349\pi$
$587$			9.65927e10i			0.813564i	−0.913525	+	0.406782i	$0.866651\pi$
$588$			1.74461e11i			1.45945i
$589$		−	6.07420e10i		−	0.504694i
$590$	−1.47058e11			−1.21362
$591$		−	1.41670e11i		−	1.16126i
$592$		−	3.15469e11i		−	2.56844i
$593$			1.38229e11i			1.11784i	0.829222	+	0.558920i	$0.188784\pi$
$593$			1.38229e11i			1.11784i	−0.829222	+	0.558920i	$0.811216\pi$
$594$	−1.26723e11			−1.01791
$595$	−2.83189e10			−0.225948
$596$			4.05844e11i			3.21643i
$597$	−3.02845e10			−0.238409
$598$			3.76744e11i			2.94606i
$599$	7.61743e10			0.591700			0.295850	−	0.955234i	$-0.404397\pi$
$599$	7.61743e10			0.591700			0.295850	+	0.955234i	$0.404397\pi$
$600$	−3.21117e11			−2.47775
$601$			1.66678e11i			1.27756i	0.769391	+	0.638778i	$0.220560\pi$
$601$			1.66678e11i			1.27756i	−0.769391	+	0.638778i	$0.779440\pi$
$602$	6.50255e10	−	1.57714e11i	0.495106	−	1.20084i
$603$	−2.08287e10			−0.157541
$604$		−	3.69018e11i		−	2.77268i
$605$		−	4.95324e10i		−	0.369716i
$606$	1.15947e11			0.859743
$607$		−	7.27298e10i		−	0.535745i	−0.963454	−	0.267872i	$-0.913679\pi$
$607$		−	7.27298e10i		−	0.535745i	0.963454	−	0.267872i	$-0.0863205\pi$
$608$	−5.58107e11			−4.08417
$609$			3.60936e10i			0.262398i
$610$			3.28433e10i			0.237207i
$611$	−6.38259e10			−0.457965
$612$	2.58931e10			0.184577
$613$	−1.54770e11			−1.09608			−0.548042	−	0.836451i	$-0.684627\pi$
$613$	−1.54770e11			−1.09608			−0.548042	+	0.836451i	$0.684627\pi$
$614$			1.87599e11i			1.31995i
$615$	1.31318e11			0.917963
$616$	1.66927e11			1.15932
$617$	9.53827e10			0.658156			0.329078	−	0.944303i	$-0.393262\pi$
$617$	9.53827e10			0.658156			0.329078	+	0.944303i	$0.393262\pi$
$618$	−4.21510e11			−2.88971
$619$	−6.89842e9			−0.0469880			−0.0234940	−	0.999724i	$-0.507479\pi$
$619$	−6.89842e9			−0.0469880			−0.0234940	+	0.999724i	$0.507479\pi$
$620$			1.05037e11i			0.710848i
$621$		−	1.59143e11i		−	1.07009i
$622$		−	3.87469e11i		−	2.58867i
$623$	−1.25114e11			−0.830527
$624$		−	8.36614e11i		−	5.51806i
$625$	4.97518e10			0.326053
$626$	1.97644e11			1.28702
$627$	−7.19263e10			−0.465390
$628$		−	5.01125e11i		−	3.22187i
$629$			6.98858e10i			0.446464i
$630$			9.84224e9i			0.0624787i
$631$			7.55488e10i			0.476552i	0.971198	+	0.238276i	$0.0765823\pi$
$631$			7.55488e10i			0.476552i	−0.971198	+	0.238276i	$0.923418\pi$
$632$		−	5.97278e11i		−	3.74376i
$633$	−2.56319e11			−1.59649
$634$			4.36225e11i			2.69994i
$635$		−	2.46783e10i		−	0.151782i
$636$			4.28646e11i			2.61981i
$637$	1.34538e11			0.817121
$638$	−6.68414e10			−0.403425
$639$			2.72699e10i			0.163561i
$640$	3.31057e11			1.97325
$641$		−	6.44169e10i		−	0.381564i	−0.981632	−	0.190782i	$-0.938898\pi$
$641$		−	6.44169e10i		−	0.381564i	0.981632	−	0.190782i	$-0.0611024\pi$
$642$	−9.60943e10			−0.565663
$643$	−8.74404e10			−0.511527			−0.255763	−	0.966739i	$-0.582327\pi$
$643$	−8.74404e10			−0.511527			−0.255763	+	0.966739i	$0.582327\pi$
$644$			3.27641e11i			1.90483i
$645$	3.10000e10	−	7.51880e10i	0.179111	−	0.434420i
$646$	2.25520e11			1.29496
$647$		−	2.45475e11i		−	1.40085i	−0.713728	−	0.700423i	$-0.752995\pi$
$647$		−	2.45475e11i		−	1.40085i	0.713728	−	0.700423i	$-0.247005\pi$
$648$			5.43728e11i			3.08377i
$649$	−1.12557e11			−0.634447
$650$			3.87031e11i			2.16817i
$651$	5.90483e10			0.328763
$652$			1.49489e11i			0.827215i
$653$		−	2.93482e10i		−	0.161410i	−0.996738	−	0.0807048i	$-0.974283\pi$
$653$		−	2.93482e10i		−	0.161410i	0.996738	−	0.0807048i	$-0.0257171\pi$
$654$	1.16200e11			0.635175
$655$	−4.23667e10			−0.230176
$656$	1.42258e12			7.68177
$657$		−	3.39755e10i		−	0.182349i
$658$	−7.54994e10			−0.402754
$659$	−2.33390e11			−1.23749			−0.618744	−	0.785593i	$-0.712358\pi$
$659$	−2.33390e11			−1.23749			−0.618744	+	0.785593i	$0.712358\pi$
$660$	1.24378e11			0.655490
$661$	−2.66026e11			−1.39353			−0.696767	−	0.717297i	$-0.745379\pi$
$661$	−2.66026e11			−1.39353			−0.696767	+	0.717297i	$0.745379\pi$
$662$	4.51143e11			2.34900
$663$			1.85335e11i			0.959188i
$664$			6.67921e11i			3.43600i
$665$			6.30233e10i			0.322266i
$666$	2.42889e10			0.123455
$667$		−	8.39421e10i		−	0.424108i
$668$	−8.47913e10			−0.425839
$669$	−2.23511e11			−1.11582
$670$	3.13702e11			1.55675
$671$			2.51381e10i			0.124006i
$672$		−	5.42545e11i		−	2.66047i
$673$		−	2.88073e11i		−	1.40424i	−0.712058	−	0.702121i	$-0.752237\pi$
$673$		−	2.88073e11i		−	1.40424i	0.712058	−	0.702121i	$-0.247763\pi$
$674$		−	4.75443e11i		−	2.30388i
$675$		−	1.63489e11i		−	0.787541i
$676$	−6.84978e11			−3.28012
$677$			2.49369e11i			1.18710i	0.804796	+	0.593551i	$0.202275\pi$
$677$			2.49369e11i			1.18710i	−0.804796	+	0.593551i	$0.797725\pi$
$678$			1.79367e11i			0.848836i
$679$		−	8.59816e10i		−	0.404507i
$680$	−2.49519e11			−1.16699
$681$	2.04359e11			0.950178
$682$			1.09351e11i			0.505458i
$683$	−7.43209e10			−0.341530			−0.170765	−	0.985312i	$-0.554624\pi$
$683$	−7.43209e10			−0.341530			−0.170765	+	0.985312i	$0.554624\pi$
$684$		−	5.76249e10i		−	0.263260i
$685$	1.15215e11			0.523296
$686$	4.46800e11			2.01751
$687$			4.67414e10i			0.209834i
$688$	3.35824e11	−	8.14515e11i	1.49885	−	3.63534i
$689$	3.30556e11			1.46679
$690$			2.12457e11i			0.937290i
$691$		−	1.05148e11i		−	0.461200i	−0.973049	−	0.230600i	$-0.925931\pi$
$691$		−	1.05148e11i		−	0.461200i	0.973049	−	0.230600i	$-0.0740689\pi$
$692$	−1.30364e11			−0.568503
$693$			7.53319e9i			0.0326622i
$694$	−1.07655e10			−0.0464085
$695$		−	3.74772e10i		−	0.160630i
$696$			3.18022e11i			1.35525i
$697$	−3.15144e11			−1.33530
$698$	−7.85769e11			−3.31034
$699$	7.36318e10			0.308430
$700$			3.36588e11i			1.40187i
$701$	−3.01602e11			−1.24900			−0.624501	−	0.781024i	$-0.714697\pi$
$701$	−3.01602e11			−1.24900			−0.624501	+	0.781024i	$0.714697\pi$
$702$	7.26691e11			2.99227
$703$	1.55530e11			0.636786
$704$	5.19442e11			2.11469
$705$	−3.59932e10			−0.145702
$706$			8.17189e10i			0.328930i
$707$		−	7.77603e10i		−	0.311229i
$708$			8.36996e11i			3.33112i
$709$	−3.95499e11			−1.56516			−0.782582	−	0.622547i	$-0.786098\pi$
$709$	−3.95499e11			−1.56516			−0.782582	+	0.622547i	$0.786098\pi$
$710$		−	4.10714e11i		−	1.61624i
$711$	2.69543e10			0.105475
$712$	−1.10238e12			−4.28956
$713$	−1.37327e11			−0.531372
$714$			2.19232e11i			0.843551i
$715$		−	9.59154e10i		−	0.366998i
$716$		−	1.30525e12i		−	4.96641i
$717$		−	8.22054e9i		−	0.0311045i
$718$			7.81297e11i			2.93981i
$719$	3.76466e11			1.40867			0.704337	−	0.709866i	$-0.251244\pi$
$719$	3.76466e11			1.40867			0.704337	+	0.709866i	$0.251244\pi$
$720$			5.08302e10i			0.189144i
$721$			2.82688e11i			1.04608i
$722$			2.61754e10i			0.0963263i
$723$	3.85069e11			1.40924
$724$	−5.65933e11			−2.05973
$725$		−	8.62342e10i		−	0.312124i
$726$	−3.83458e11			−1.38029
$727$		−	1.34308e11i		−	0.480800i	−0.970674	−	0.240400i	$-0.922721\pi$
$727$		−	1.34308e11i		−	0.480800i	0.970674	−	0.240400i	$-0.0772785\pi$
$728$	−9.57244e11			−3.40798
$729$	−3.04296e11			−1.07742
$730$			5.11707e11i			1.80190i
$731$	−7.43951e10	+	1.80440e11i	−0.260540	+	0.631921i
$732$	1.86931e11			0.651084
$733$			1.41612e10i			0.0490550i	0.999699	+	0.0245275i	$0.00780813\pi$
$733$			1.41612e10i			0.0490550i	−0.999699	+	0.0245275i	$0.992192\pi$
$734$			2.92229e11i			1.00679i
$735$	7.58696e10			0.259967
$736$			1.26178e12i			4.30006i
$737$	2.40106e11			0.813828
$738$			1.09529e11i			0.369234i
$739$			1.01671e11i			0.340893i	0.985367	+	0.170447i	$0.0545210\pi$
$739$			1.01671e11i			0.340893i	−0.985367	+	0.170447i	$0.945479\pi$
$740$	−2.68948e11			−0.896896
$741$	4.12461e11			1.36808
$742$	3.91014e11			1.28996
$743$		−	7.42954e10i		−	0.243785i	−0.992543	−	0.121892i	$-0.961104\pi$
$743$		−	7.42954e10i		−	0.243785i	0.992543	−	0.121892i	$-0.0388963\pi$
$744$	5.20277e11			1.69802
$745$	1.76494e11			0.572934
$746$	1.80808e11			0.583797
$747$	−3.01423e10			−0.0968043
$748$	−2.98487e11			−0.953496
$749$			6.44461e10i			0.204771i
$750$			5.07185e11i			1.60295i
$751$		−	3.61993e10i		−	0.113799i	−0.998380	−	0.0568997i	$-0.981878\pi$
$751$		−	3.61993e10i		−	0.113799i	0.998380	−	0.0568997i	$-0.0181215\pi$
$752$	−3.89917e11			−1.21927
$753$		−	4.82746e11i		−	1.50155i
$754$	3.83302e11			1.18592
$755$	−1.60479e11			−0.493890
$756$	6.31978e11			1.93471
$757$		−	1.37097e11i		−	0.417489i	−0.977970	−	0.208744i	$-0.933062\pi$
$757$		−	1.37097e11i		−	0.417489i	0.977970	−	0.208744i	$-0.0669377\pi$
$758$		−	8.51755e11i		−	2.58011i
$759$			1.62613e11i			0.489991i
$760$			5.55301e11i			1.66446i
$761$		−	3.33327e10i		−	0.0993876i	−0.998764	−	0.0496938i	$-0.984175\pi$
$761$		−	3.33327e10i		−	0.0993876i	0.998764	−	0.0496938i	$-0.0158245\pi$
$762$	−1.91049e11			−0.566662
$763$		−	7.79298e10i		−	0.229935i
$764$		−	9.08365e11i		−	2.66617i
$765$		−	1.12604e10i		−	0.0328783i
$766$	5.06888e10			0.147230
$767$	6.45461e11			1.86504
$768$		−	1.17167e12i		−	3.36792i
$769$	−2.60316e11			−0.744381			−0.372190	−	0.928156i	$-0.621393\pi$
$769$	−2.60316e11			−0.744381			−0.372190	+	0.928156i	$0.621393\pi$
$770$		−	1.13458e11i		−	0.322754i
$771$	2.66813e11			0.755073
$772$	1.44562e11			0.406992
$773$		−	4.75435e11i		−	1.33160i	−0.746131	−	0.665799i	$-0.768091\pi$
$773$		−	4.75435e11i		−	1.33160i	0.746131	−	0.665799i	$-0.231909\pi$
$774$	6.27119e10	+	2.58561e10i	0.174738	+	0.0720442i
$775$	−1.41077e11			−0.391066
$776$		−	7.57587e11i		−	2.08923i
$777$			1.51193e11i			0.414810i
$778$	1.83819e11			0.501733
$779$			7.01350e11i			1.90452i
$780$	−7.13243e11			−1.92690
$781$		−	3.14358e11i		−	0.844929i
$782$		−	5.09863e11i		−	1.36341i
$783$	−1.61914e11			−0.430761
$784$	8.21899e11			2.17548
$785$	−2.17930e11			−0.573903
$786$			3.27984e11i			0.859336i
$787$	1.32872e11			0.346365			0.173182	−	0.984890i	$-0.444595\pi$
$787$	1.32872e11			0.346365			0.173182	+	0.984890i	$0.444595\pi$
$788$	−1.30840e12			−3.39341
$789$	1.25543e11			0.323956
$790$	−4.05961e11			−1.04226
$791$	1.20293e11			0.307281
$792$			6.63752e10i			0.168696i
$793$		−	1.44154e11i		−	0.364531i
$794$		−	6.97566e11i		−	1.75511i
$795$	1.86410e11			0.466660
$796$			2.79694e11i			0.696676i
$797$	−2.24404e10			−0.0556157			−0.0278079	−	0.999613i	$-0.508853\pi$
$797$	−2.24404e10			−0.0556157			−0.0278079	+	0.999613i	$0.508853\pi$
$798$	4.87899e11			1.20315
$799$	8.63782e10			0.211942
$800$			1.29624e12i			3.16465i
$801$		−	4.97490e10i		−	0.120852i
$802$		−	4.74561e11i		−	1.14708i
$803$			3.91658e11i			0.941986i
$804$		−	1.78547e12i		−	4.27295i
$805$	1.42485e11			0.339301
$806$		−	6.27073e11i		−	1.48586i
$807$		−	2.93047e10i		−	0.0690943i
$808$		−	6.85149e11i		−	1.60746i
$809$	5.81192e11			1.35683			0.678415	−	0.734679i	$-0.262667\pi$
$809$	5.81192e11			1.35683			0.678415	+	0.734679i	$0.262667\pi$
$810$	3.69564e11			0.858517
$811$			1.37076e11i			0.316867i	0.987370	+	0.158434i	$0.0506444\pi$
$811$			1.37076e11i			0.316867i	−0.987370	+	0.158434i	$0.949356\pi$
$812$	3.33345e11			0.766777
$813$			3.83581e11i			0.878001i
$814$	−2.79993e11			−0.637750
$815$	6.50099e10			0.147350
$816$			1.13222e12i			2.55371i
$817$	4.01567e11	+	1.65566e11i	0.901300	+	0.371605i
$818$	2.37715e11			0.530938
$819$		−	4.31991e10i		−	0.0960150i
$820$		−	1.21280e12i		−	2.68246i
$821$	−1.00200e11			−0.220544			−0.110272	−	0.993901i	$-0.535172\pi$
$821$	−1.00200e11			−0.220544			−0.110272	+	0.993901i	$0.535172\pi$
$822$		−	8.91945e11i		−	1.95367i
$823$	5.38250e11			1.17323			0.586617	−	0.809865i	$-0.300460\pi$
$823$	5.38250e11			1.17323			0.586617	+	0.809865i	$0.300460\pi$
$824$			2.49077e12i			5.40288i
$825$			1.67053e11i			0.360611i
$826$	7.63513e11			1.64020
$827$	−7.72181e11			−1.65081			−0.825405	−	0.564541i	$-0.809053\pi$
$827$	−7.72181e11			−1.65081			−0.825405	+	0.564541i	$0.809053\pi$
$828$	−1.30280e11			−0.277176
$829$		−	4.98666e11i		−	1.05582i	−0.849299	−	0.527912i	$-0.822975\pi$
$829$		−	4.98666e11i		−	1.05582i	0.849299	−	0.527912i	$-0.177025\pi$
$830$	4.53976e11			0.956578
$831$	−7.96332e11			−1.66990
$832$	−2.97874e12			−6.21640
$833$	−1.82075e11			−0.378156
$834$	−2.90131e11			−0.599695
$835$			3.68741e10i			0.0758535i
$836$			6.64279e11i			1.35996i
$837$			2.64887e11i			0.539708i
$838$	6.80120e11			1.37914
$839$			4.50167e10i			0.0908503i	0.998968	+	0.0454251i	$0.0144642\pi$
$839$			4.50167e10i			0.0908503i	−0.998968	+	0.0454251i	$0.985536\pi$
$840$	−5.39817e11			−1.08425
$841$	4.14843e11			0.829278
$842$	−5.95134e11			−1.18404
$843$		−	4.06007e11i		−	0.803940i
$844$			2.36725e12i			4.66524i
$845$			2.97884e11i			0.584279i
$846$		−	3.00208e10i		−	0.0586058i
$847$			2.57168e11i			0.499670i
$848$	2.01939e12			3.90514
$849$		−	5.28983e11i		−	1.01815i
$850$		−	5.23786e11i		−	1.00341i
$851$		−	3.51627e11i		−	0.670446i
$852$	−2.33762e12			−4.43624
$853$	6.35607e10			0.120058			0.0600292	−	0.998197i	$-0.480881\pi$
$853$	6.35607e10			0.120058			0.0600292	+	0.998197i	$0.480881\pi$
$854$		−	1.70519e11i		−	0.320584i
$855$	−2.50600e10			−0.0468939
$856$			5.67837e11i			1.05762i
$857$	−3.04132e11			−0.563818			−0.281909	−	0.959441i	$-0.590968\pi$
$857$	−3.04132e11			−0.563818			−0.281909	+	0.959441i	$0.590968\pi$
$858$	−7.42534e11			−1.37015
$859$		−	8.70514e10i		−	0.159883i	−0.996800	−	0.0799417i	$-0.974527\pi$
$859$		−	8.70514e10i		−	0.159883i	0.996800	−	0.0799417i	$-0.0254734\pi$
$860$	−6.94403e11	−	2.86302e11i	−1.26946	−	0.523396i
$861$	−6.81794e11			−1.24062
$862$			5.15688e11i			0.934024i
$863$			6.30779e11i			1.13719i	0.822617	+	0.568596i	$0.192513\pi$
$863$			6.30779e11i			1.13719i	−0.822617	+	0.568596i	$0.807487\pi$
$864$	2.43382e12			4.36751
$865$			5.66928e10i			0.101266i
$866$	−7.06152e9			−0.0125553
$867$			2.86034e11i			0.506223i
$868$		−	5.45344e11i		−	0.960708i
$869$	−3.10720e11			−0.544866
$870$	2.16155e11			0.377301
$871$	−1.37689e12			−2.39235
$872$		−	6.86642e11i		−	1.18758i
$873$	3.41888e10			0.0588610
$874$	−1.13469e12			−1.94461
$875$	3.40146e11			0.580274
$876$	2.91243e12			4.94583
$877$	7.43976e11			1.25765			0.628826	−	0.777546i	$-0.283536\pi$
$877$	7.43976e11			1.25765			0.628826	+	0.777546i	$0.283536\pi$
$878$		−	1.13041e12i		−	1.90220i
$879$			9.16999e11i			1.53608i
$880$		−	5.85953e11i		−	0.977085i
$881$	2.51985e11			0.418283			0.209142	−	0.977885i	$-0.432933\pi$
$881$	2.51985e11			0.418283			0.209142	+	0.977885i	$0.432933\pi$
$882$			6.32804e10i			0.104567i
$883$	7.60754e11			1.25142			0.625708	−	0.780058i	$-0.284810\pi$
$883$	7.60754e11			1.25142			0.625708	+	0.780058i	$0.284810\pi$
$884$	1.71167e12			2.80293
$885$	3.63994e11			0.593363
$886$		−	1.55548e12i		−	2.52423i
$887$			6.24953e11i			1.00961i	0.863234	+	0.504804i	$0.168435\pi$
$887$			6.24953e11i			1.00961i	−0.863234	+	0.504804i	$0.831565\pi$
$888$			1.33217e12i			2.14244i
$889$			1.28128e11i			0.205133i
$890$			7.49273e11i			1.19421i
$891$	2.82862e11			0.448811
$892$			2.06424e12i			3.26063i
$893$		−	1.92234e11i		−	0.302290i
$894$		−	1.36634e12i		−	2.13899i
$895$	−5.67629e11			−0.884653
$896$	−1.71882e12			−2.66684
$897$		−	9.32504e11i		−	1.44039i
$898$	−2.01066e12			−3.09195
$899$			1.39718e11i			0.213901i
$900$	−1.33837e11			−0.203989
$901$	−4.47355e11			−0.678818
$902$		−	1.26261e12i		−	1.90740i
$903$	−1.60949e11	+	3.90369e11i	−0.242068	+	0.587117i
$904$	1.05991e12			1.58707
$905$			2.46114e11i			0.366894i
$906$			1.24236e12i			1.84388i
$907$	9.82966e10			0.145248			0.0726238	−	0.997359i	$-0.476863\pi$
$907$	9.82966e10			0.145248			0.0726238	+	0.997359i	$0.476863\pi$
$908$		−	1.88737e12i		−	2.77660i
$909$	3.09198e10			0.0452878
$910$			6.50624e11i			0.948778i
$911$		−	1.06133e11i		−	0.154092i	−0.997028	−	0.0770458i	$-0.975451\pi$
$911$		−	1.06133e11i		−	0.154092i	0.997028	−	0.0770458i	$-0.0245488\pi$
$912$	2.51975e12			3.64232
$913$	3.47470e11			0.500074
$914$	−2.22508e12			−3.18831
$915$		−	8.12927e10i		−	0.115976i
$916$	4.31683e11			0.613173
$917$	2.19964e11			0.311082
$918$	−9.83461e11			−1.38480
$919$	−4.81945e11			−0.675671			−0.337836	−	0.941205i	$-0.609695\pi$
$919$	−4.81945e11			−0.675671			−0.337836	+	0.941205i	$0.609695\pi$
$920$	1.25544e12			1.75245
$921$		−	4.64340e11i		−	0.645353i
$922$		−	2.97342e11i		−	0.411465i
$923$			1.80269e12i			2.48378i
$924$	−6.45757e11			−0.885892
$925$		−	3.61229e11i		−	0.493418i
$926$	5.28414e11			0.718671
$927$	−1.12405e11			−0.152218
$928$	1.28375e12			1.73096
$929$			8.60540e11i			1.15534i	0.816272	+	0.577668i	$0.196037\pi$
$929$			8.60540e11i			1.15534i	−0.816272	+	0.577668i	$0.803963\pi$
$930$		−	3.53624e11i		−	0.472727i
$931$			4.05207e11i			0.539359i
$932$		−	6.80030e11i		−	0.901290i
$933$			9.59052e11i			1.26566i
$934$	1.52513e12			2.00409
$935$			1.29806e11i			0.169844i
$936$		−	3.80629e11i		−	0.495905i
$937$			4.51510e11i			0.585745i	0.956151	+	0.292873i	$0.0946112\pi$
$937$			4.51510e11i			0.585745i	−0.956151	+	0.292873i	$0.905389\pi$
$938$	−1.62871e12			−2.10394
$939$	−4.89201e11			−0.629253
$940$			3.32418e11i			0.425768i
$941$	−1.02846e11			−0.131168			−0.0655840	−	0.997847i	$-0.520891\pi$
$941$	−1.02846e11			−0.131168			−0.0655840	+	0.997847i	$0.520891\pi$
$942$			1.68712e12i			2.14260i
$943$	1.58563e12			2.00519
$944$	3.94316e12			4.96543
$945$		−	2.74835e11i		−	0.344624i
$946$	−7.22921e11	−	2.98060e11i	−0.902664	−	0.372168i
$947$	−7.66897e11			−0.953536			−0.476768	−	0.879029i	$-0.658192\pi$
$947$	−7.66897e11			−0.953536			−0.476768	+	0.879029i	$0.658192\pi$
$948$			2.31056e12i			2.86078i
$949$		−	2.24596e12i		−	2.76909i
$950$	−1.16568e12			−1.43115
$951$		−	1.07973e12i		−	1.32006i
$952$	1.29548e12			1.57718
$953$		−	1.03653e12i		−	1.25663i	−0.777958	−	0.628317i	$-0.783744\pi$
$953$		−	1.03653e12i		−	1.25663i	0.777958	−	0.628317i	$-0.216256\pi$
$954$			1.55479e11i			0.187706i
$955$	−3.95031e11			−0.474917
$956$	−7.59213e10			−0.0908933
$957$	1.65444e11			0.197243
$958$			1.00992e12i			1.19902i
$959$	−5.98187e11			−0.707233
$960$	−1.67980e12			−1.97775
$961$	−6.24316e11			−0.732000
$962$	1.60562e12			1.87475
$963$	−2.56257e10			−0.0297968
$964$		−	3.55632e12i		−	4.11806i
$965$		−	6.28674e10i		−	0.0724963i
$966$		−	1.10306e12i		−	1.26674i
$967$	3.67231e11			0.419984			0.209992	−	0.977703i	$-0.432656\pi$
$967$	3.67231e11			0.419984			0.209992	+	0.977703i	$0.432656\pi$
$968$			2.26592e12i			2.58073i
$969$	−5.58201e11			−0.633134
$970$	−5.14920e11			−0.581638
$971$	1.05490e12			1.18668			0.593341	−	0.804951i	$-0.297809\pi$
$971$	1.05490e12			1.18668			0.593341	+	0.804951i	$0.297809\pi$
$972$			4.80312e11i			0.538095i
$973$			1.94578e11i			0.217091i
$974$			2.10430e12i			2.33815i
$975$		−	9.57968e11i		−	1.06006i
$976$		−	8.80648e11i		−	0.970516i
$977$	−3.10125e11			−0.340376			−0.170188	−	0.985412i	$-0.554438\pi$
$977$	−3.10125e11			−0.340376			−0.170188	+	0.985412i	$0.554438\pi$
$978$		−	5.03278e11i		−	0.550113i
$979$			5.73489e11i			0.624302i
$980$		−	7.00698e11i		−	0.759673i
$981$	3.09872e10			0.0334585
$982$	1.65187e12			1.77636
$983$			5.39951e11i			0.578282i	0.957286	+	0.289141i	$0.0933697\pi$
$983$			5.39951e11i			0.578282i	−0.957286	+	0.289141i	$0.906630\pi$
$984$	−6.00731e12			−6.40766
$985$			5.68999e11i			0.604459i
$986$	−5.18738e11			−0.548833
$987$	1.86874e11			0.196915
$988$		−	3.80931e12i		−	3.99778i
$989$	3.74315e11	−	9.07873e11i	0.391248	−	0.948943i
$990$	4.51142e10			0.0469648
$991$		−	1.96408e11i		−	0.203641i	−0.994803	−	0.101821i	$-0.967533\pi$
$991$		−	1.96408e11i		−	0.203641i	0.994803	−	0.101821i	$-0.0324667\pi$
$992$		−	2.10018e12i		−	2.16875i
$993$	−1.11665e12			−1.14848
$994$			2.13239e12i			2.18434i
$995$	1.21634e11			0.124097
$996$		−	2.58385e12i		−	2.62561i
$997$		−	1.02710e12i		−	1.03952i	−0.854313	−	0.519758i	$-0.826022\pi$
$997$		−	1.02710e12i		−	1.03952i	0.854313	−	0.519758i	$-0.173978\pi$
$998$	−2.65543e12			−2.67678
$999$	−6.78244e11			−0.680964

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.9.b.b.42.27	yes	28
43.42	odd	2	inner	43.9.b.b.42.2	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.9.b.b.42.2	✓	28	43.42	odd	2	inner
43.9.b.b.42.27	yes	28	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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+31.0929i q^{2} -76.9602i q^{3} -710.770 q^{4} +309.101i q^{5} +2392.92 q^{6} -1604.82i q^{7} -14140.1i q^{8} +638.125 q^{9} +O(q^{10})\)	\(q+31.0929i q^{2} -76.9602i q^{3} -710.770 q^{4} +309.101i q^{5} +2392.92 q^{6} -1604.82i q^{7} -14140.1i q^{8} +638.125 q^{9} -9610.84 q^{10} -7356.08 q^{11} +54701.0i q^{12} +42183.4 q^{13} +49898.6 q^{14} +23788.4 q^{15} +257701. q^{16} -57088.6 q^{17} +19841.2i q^{18} +127050. i q^{19} -219700. i q^{20} -123507. q^{21} -228722. i q^{22} +287238. q^{23} -1.08823e6 q^{24} +295082. q^{25} +1.31161e6i q^{26} -554046. i q^{27} +1.14066e6i q^{28} -292238. i q^{29} +739653. i q^{30} -478095. q^{31} +4.39281e6i q^{32} +566125. i q^{33} -1.77505e6i q^{34} +496051. q^{35} -453560. q^{36} -1.22416e6i q^{37} -3.95036e6 q^{38} -3.24645e6i q^{39} +4.37073e6 q^{40} +5.52026e6 q^{41} -3.84021e6i q^{42} +(1.30315e6 - 3.16070e6i) q^{43} +5.22848e6 q^{44} +197245. i q^{45} +8.93108e6i q^{46} -1.51306e6 q^{47} -1.98328e7i q^{48} +3.18935e6 q^{49} +9.17496e6i q^{50} +4.39355e6i q^{51} -2.99827e7 q^{52} +7.83616e6 q^{53} +1.72269e7 q^{54} -2.27377e6i q^{55} -2.26924e7 q^{56} +9.77780e6 q^{57} +9.08655e6 q^{58} +1.53013e7 q^{59} -1.69081e7 q^{60} -3.41732e6i q^{61} -1.48654e7i q^{62} -1.02408e6i q^{63} -7.06139e7 q^{64} +1.30389e7i q^{65} -1.76025e7 q^{66} -3.26404e7 q^{67} +4.05769e7 q^{68} -2.21059e7i q^{69} +1.54237e7i q^{70} +4.27345e7i q^{71} -9.02318e6i q^{72} -5.32427e7i q^{73} +3.80629e7 q^{74} -2.27096e7i q^{75} -9.03034e7i q^{76} +1.18052e7i q^{77} +1.00942e8 q^{78} +4.22399e7 q^{79} +7.96556e7i q^{80} -3.84528e7 q^{81} +1.71641e8i q^{82} -4.72358e7 q^{83} +8.77854e7 q^{84} -1.76461e7i q^{85} +(9.82753e7 + 4.05188e7i) q^{86} -2.24907e7 q^{87} +1.04016e8i q^{88} -7.79613e7i q^{89} -6.13292e6 q^{90} -6.76969e7i q^{91} -2.04161e8 q^{92} +3.67943e7i q^{93} -4.70453e7i q^{94} -3.92712e7 q^{95} +3.38072e8 q^{96} +5.35770e7 q^{97} +9.91662e7i q^{98} -4.69410e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9}+O(q^{10}) \) 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9	\( 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9} + 24982 q^{10} + 4538 q^{11} + 22086 q^{13} + 24732 q^{14} + 15388 q^{15} + 525812 q^{16} - 135136 q^{17} - 261352 q^{21} - 184432 q^{23} + 1770326 q^{24} - 2640434 q^{25} - 110272 q^{31} + 10947816 q^{35} + 11602066 q^{36} - 7189158 q^{38} - 21389338 q^{40} + 1301336 q^{41} + 2473420 q^{43} - 8818480 q^{44} + 1983566 q^{47} - 15560936 q^{49} + 12927876 q^{52} + 23942594 q^{53} - 13757972 q^{54} + 34967256 q^{56} + 35225148 q^{57} + 22565734 q^{58} - 5554336 q^{59} - 44902072 q^{60} - 170444572 q^{64} - 48457584 q^{66} - 130953802 q^{67} + 150021122 q^{68} + 205870278 q^{74} + 267860612 q^{78} + 7380250 q^{79} - 57601004 q^{81} - 42603970 q^{83} + 251931292 q^{84} - 45482652 q^{86} - 106687410 q^{87} - 255044692 q^{90} - 409532014 q^{92} + 123322986 q^{95} - 692987086 q^{96} - 318744840 q^{97} - 609707206 q^{99}+O(q^{100}) \) 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9 + 24982 * q^10 + 4538 * q^11 + 22086 * q^13 + 24732 * q^14 + 15388 * q^15 + 525812 * q^16 - 135136 * q^17 - 261352 * q^21 - 184432 * q^23 + 1770326 * q^24 - 2640434 * q^25 - 110272 * q^31 + 10947816 * q^35 + 11602066 * q^36 - 7189158 * q^38 - 21389338 * q^40 + 1301336 * q^41 + 2473420 * q^43 - 8818480 * q^44 + 1983566 * q^47 - 15560936 * q^49 + 12927876 * q^52 + 23942594 * q^53 - 13757972 * q^54 + 34967256 * q^56 + 35225148 * q^57 + 22565734 * q^58 - 5554336 * q^59 - 44902072 * q^60 - 170444572 * q^64 - 48457584 * q^66 - 130953802 * q^67 + 150021122 * q^68 + 205870278 * q^74 + 267860612 * q^78 + 7380250 * q^79 - 57601004 * q^81 - 42603970 * q^83 + 251931292 * q^84 - 45482652 * q^86 - 106687410 * q^87 - 255044692 * q^90 - 409532014 * q^92 + 123322986 * q^95 - 692987086 * q^96 - 318744840 * q^97 - 609707206 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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