LMFDB - Embedded newform 43.9.b.b.42.19

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			42.19
Character	$\chi$	$=$	43.42
Dual form			43.9.b.b.42.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11.2266i q^{2} -77.9859i q^{3} +129.962 q^{4} -278.075i q^{5} +875.519 q^{6} -3160.13i q^{7} +4333.06i q^{8} +479.207 q^{9} +O(q^{10})$	\(q+11.2266i q^{2} -77.9859i q^{3} +129.962 q^{4} -278.075i q^{5} +875.519 q^{6} -3160.13i q^{7} +4333.06i q^{8} +479.207 q^{9} +3121.85 q^{10} -16312.7 q^{11} -10135.2i q^{12} -529.246 q^{13} +35477.7 q^{14} -21685.9 q^{15} -15375.4 q^{16} -122717. q^{17} +5379.88i q^{18} -126881. i q^{19} -36139.4i q^{20} -246446. q^{21} -183137. i q^{22} -33289.9 q^{23} +337918. q^{24} +313299. q^{25} -5941.65i q^{26} -549037. i q^{27} -410699. i q^{28} -1.14051e6i q^{29} -243460. i q^{30} +737944. q^{31} +936650. i q^{32} +1.27216e6i q^{33} -1.37770e6i q^{34} -878755. q^{35} +62278.9 q^{36} -1.37860e6i q^{37} +1.42445e6 q^{38} +41273.7i q^{39} +1.20492e6 q^{40} -5.06776e6 q^{41} -2.76676e6i q^{42} +(-586993. + 3.36803e6i) q^{43} -2.12004e6 q^{44} -133256. i q^{45} -373734. i q^{46} -3.40496e6 q^{47} +1.19906e6i q^{48} -4.22164e6 q^{49} +3.51730e6i q^{50} +9.57019e6i q^{51} -68782.1 q^{52} +8.04889e6 q^{53} +6.16384e6 q^{54} +4.53617e6i q^{55} +1.36931e7 q^{56} -9.89495e6 q^{57} +1.28041e7 q^{58} +1.77965e7 q^{59} -2.81836e6 q^{60} +8.79447e6i q^{61} +8.28463e6i q^{62} -1.51436e6i q^{63} -1.44515e7 q^{64} +147170. i q^{65} -1.42821e7 q^{66} +2.55566e6 q^{67} -1.59486e7 q^{68} +2.59614e6i q^{69} -9.86547e6i q^{70} -1.00216e7i q^{71} +2.07643e6i q^{72} +7.54723e6i q^{73} +1.54770e7 q^{74} -2.44329e7i q^{75} -1.64898e7i q^{76} +5.15505e7i q^{77} -463365. q^{78} +1.30718e7 q^{79} +4.27551e6i q^{80} -3.96730e7 q^{81} -5.68939e7i q^{82} +7.73406e7 q^{83} -3.20287e7 q^{84} +3.41246e7i q^{85} +(-3.78117e7 - 6.58996e6i) q^{86} -8.89439e7 q^{87} -7.06842e7i q^{88} -3.53743e7i q^{89} +1.49601e6 q^{90} +1.67249e6i q^{91} -4.32643e6 q^{92} -5.75492e7i q^{93} -3.82263e7i q^{94} -3.52826e7 q^{95} +7.30455e7 q^{96} +1.12025e8 q^{97} -4.73948e7i q^{98} -7.81718e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			11.2266i			0.701665i	0.936438	+	0.350833i	$0.114101\pi$
$2$			11.2266i			0.701665i	−0.936438	+	0.350833i	$0.885899\pi$
$3$		−	77.9859i		−	0.962788i	−0.876504	−	0.481394i	$-0.840131\pi$
$3$		−	77.9859i		−	0.962788i	0.876504	−	0.481394i	$-0.159869\pi$
$4$	129.962			0.507666
$5$		−	278.075i		−	0.444921i	−0.974942	−	0.222460i	$-0.928591\pi$
$5$		−	278.075i		−	0.444921i	0.974942	−	0.222460i	$-0.0714088\pi$
$6$	875.519			0.675555
$7$		−	3160.13i		−	1.31617i	−0.752942	−	0.658087i	$-0.771366\pi$
$7$		−	3160.13i		−	1.31617i	0.752942	−	0.658087i	$-0.228634\pi$
$8$			4333.06i			1.05788i
$9$	479.207			0.0730387
$10$	3121.85			0.312185
$11$	−16312.7			−1.11418			−0.557091	−	0.830451i	$-0.688083\pi$
$11$	−16312.7			−1.11418			−0.557091	+	0.830451i	$0.688083\pi$
$12$		−	10135.2i		−	0.488775i
$13$	−529.246			−0.0185304			−0.00926518	−	0.999957i	$-0.502949\pi$
$13$	−529.246			−0.0185304			−0.00926518	+	0.999957i	$0.502949\pi$
$14$	35477.7			0.923513
$15$	−21685.9			−0.428364
$16$	−15375.4			−0.234610
$17$	−122717.			−1.46930			−0.734648	−	0.678449i	$-0.762653\pi$
$17$	−122717.			−1.46930			−0.734648	+	0.678449i	$0.762653\pi$
$18$			5379.88i			0.0512487i
$19$		−	126881.i		−	0.973606i	−0.873512	−	0.486803i	$-0.838163\pi$
$19$		−	126881.i		−	0.973606i	0.873512	−	0.486803i	$-0.161837\pi$
$20$		−	36139.4i		−	0.225871i
$21$	−246446.			−1.26720
$22$		−	183137.i		−	0.781783i
$23$	−33289.9			−0.118960			−0.0594800	−	0.998229i	$-0.518944\pi$
$23$	−33289.9			−0.118960			−0.0594800	+	0.998229i	$0.518944\pi$
$24$	337918.			1.01851
$25$	313299.			0.802046
$26$		−	5941.65i		−	0.0130021i
$27$		−	549037.i		−	1.03311i
$28$		−	410699.i		−	0.668176i
$29$		−	1.14051e6i		−	1.61253i	−0.591553	−	0.806266i	$-0.701485\pi$
$29$		−	1.14051e6i		−	1.61253i	0.591553	−	0.806266i	$-0.298515\pi$
$30$		−	243460.i		−	0.300568i
$31$	737944.			0.799055			0.399527	−	0.916721i	$-0.369174\pi$
$31$	737944.			0.799055			0.399527	+	0.916721i	$0.369174\pi$
$32$			936650.i			0.893259i
$33$			1.27216e6i			1.07272i
$34$		−	1.37770e6i		−	1.03095i
$35$	−878755.			−0.585593
$36$	62278.9			0.0370792
$37$		−	1.37860e6i		−	0.735581i	−0.929909	−	0.367790i	$-0.880114\pi$
$37$		−	1.37860e6i		−	0.735581i	0.929909	−	0.367790i	$-0.119886\pi$
$38$	1.42445e6			0.683146
$39$			41273.7i			0.0178408i
$40$	1.20492e6			0.470671
$41$	−5.06776e6			−1.79341			−0.896707	−	0.442625i	$-0.854047\pi$
$41$	−5.06776e6			−1.79341			−0.896707	+	0.442625i	$0.854047\pi$
$42$		−	2.76676e6i		−	0.889148i
$43$	−586993.	+	3.36803e6i	−0.171695	+	0.985150i
$43$	−586993.	+	3.36803e6i	−0.171695	+	0.985150i
$44$	−2.12004e6			−0.565632
$45$		−	133256.i		−	0.0324964i
$46$		−	373734.i		−	0.0834701i
$47$	−3.40496e6			−0.697783			−0.348892	−	0.937163i	$-0.613442\pi$
$47$	−3.40496e6			−0.697783			−0.348892	+	0.937163i	$0.613442\pi$
$48$			1.19906e6i			0.225879i
$49$	−4.22164e6			−0.732313
$50$			3.51730e6i			0.562768i
$51$			9.57019e6i			1.41462i
$52$	−68782.1			−0.00940723
$53$	8.04889e6			1.02008			0.510038	−	0.860152i	$-0.329631\pi$
$53$	8.04889e6			1.02008			0.510038	+	0.860152i	$0.329631\pi$
$54$	6.16384e6			0.724897
$55$			4.53617e6i			0.495723i
$56$	1.36931e7			1.39235
$57$	−9.89495e6			−0.937377
$58$	1.28041e7			1.13146
$59$	1.77965e7			1.46868			0.734341	−	0.678781i	$-0.237491\pi$
$59$	1.77965e7			1.46868			0.734341	+	0.678781i	$0.237491\pi$
$60$	−2.81836e6			−0.217466
$61$			8.79447e6i			0.635170i	0.948230	+	0.317585i	$0.102872\pi$
$61$			8.79447e6i			0.635170i	−0.948230	+	0.317585i	$0.897128\pi$
$62$			8.28463e6i			0.560669i
$63$		−	1.51436e6i		−	0.0961316i
$64$	−1.44515e7			−0.861379
$65$			147170.i			0.00824454i
$66$	−1.42821e7			−0.752692
$67$	2.55566e6			0.126825			0.0634123	−	0.997987i	$-0.479802\pi$
$67$	2.55566e6			0.126825			0.0634123	+	0.997987i	$0.479802\pi$
$68$	−1.59486e7			−0.745911
$69$			2.59614e6i			0.114533i
$70$		−	9.86547e6i		−	0.410890i
$71$		−	1.00216e7i		−	0.394372i	−0.980366	−	0.197186i	$-0.936820\pi$
$71$		−	1.00216e7i		−	0.394372i	0.980366	−	0.197186i	$-0.0631802\pi$
$72$			2.07643e6i			0.0772659i
$73$			7.54723e6i			0.265764i	0.991132	+	0.132882i	$0.0424231\pi$
$73$			7.54723e6i			0.265764i	−0.991132	+	0.132882i	$0.957577\pi$
$74$	1.54770e7			0.516131
$75$		−	2.44329e7i		−	0.772200i
$76$		−	1.64898e7i		−	0.494267i
$77$			5.15505e7i			1.46646i
$78$	−463365.			−0.0125183
$79$	1.30718e7			0.335605			0.167802	−	0.985821i	$-0.446333\pi$
$79$	1.30718e7			0.335605			0.167802	+	0.985821i	$0.446333\pi$
$80$			4.27551e6i			0.104383i
$81$	−3.96730e7			−0.921627
$82$		−	5.68939e7i		−	1.25838i
$83$	7.73406e7			1.62965			0.814826	−	0.579705i	$-0.196832\pi$
$83$	7.73406e7			1.62965			0.814826	+	0.579705i	$0.196832\pi$
$84$	−3.20287e7			−0.643312
$85$			3.41246e7i			0.653720i
$86$	−3.78117e7	−	6.58996e6i	−0.691246	−	0.120473i
$87$	−8.89439e7			−1.55253
$88$		−	7.06842e7i		−	1.17867i
$89$		−	3.53743e7i		−	0.563804i	−0.959443	−	0.281902i	$-0.909035\pi$
$89$		−	3.53743e7i		−	0.563804i	0.959443	−	0.281902i	$-0.0909653\pi$
$90$	1.49601e6			0.0228016
$91$			1.67249e6i			0.0243892i
$92$	−4.32643e6			−0.0603919
$93$		−	5.75492e7i		−	0.769320i
$94$		−	3.82263e7i		−	0.489610i
$95$	−3.52826e7			−0.433178
$96$	7.30455e7			0.860020
$97$	1.12025e8			1.26540			0.632702	−	0.774395i	$-0.281946\pi$
$97$	1.12025e8			1.26540			0.632702	+	0.774395i	$0.281946\pi$
$98$		−	4.73948e7i		−	0.513839i
$99$	−7.81718e6			−0.0813784
$100$	4.07171e7			0.407171
$101$	−6.20802e7			−0.596579			−0.298289	−	0.954475i	$-0.596416\pi$
$101$	−6.20802e7			−0.596579			−0.298289	+	0.954475i	$0.596416\pi$
$102$	−1.07441e8			−0.992590
$103$	2.13424e8			1.89625			0.948124	−	0.317900i	$-0.102977\pi$
$103$	2.13424e8			1.89625			0.948124	+	0.317900i	$0.102977\pi$
$104$		−	2.29325e6i		−	0.0196028i
$105$			6.85305e7i			0.563802i
$106$			9.03620e7i			0.715752i
$107$	−7.15021e7			−0.545486			−0.272743	−	0.962087i	$-0.587931\pi$
$107$	−7.15021e7			−0.545486			−0.272743	+	0.962087i	$0.587931\pi$
$108$		−	7.13541e7i		−	0.524474i
$109$	2.45917e7			0.174214			0.0871068	−	0.996199i	$-0.472238\pi$
$109$	2.45917e7			0.174214			0.0871068	+	0.996199i	$0.472238\pi$
$110$	−5.09260e7			−0.347832
$111$	−1.07511e8			−0.708208
$112$			4.85882e7i			0.308787i
$113$			4.74022e7i			0.290726i	0.989378	+	0.145363i	$0.0464351\pi$
$113$			4.74022e7i			0.290726i	−0.989378	+	0.145363i	$0.953565\pi$
$114$		−	1.11087e8i		−	0.657725i
$115$			9.25709e6i			0.0529277i
$116$		−	1.48224e8i		−	0.818628i
$117$	−253618.			−0.00135343
$118$			1.99796e8i			1.03052i
$119$			3.87802e8i			1.93385i
$120$		−	9.39666e7i		−	0.453157i
$121$	5.17469e7			0.241403
$122$	−9.87324e7			−0.445677
$123$			3.95213e8i			1.72668i
$124$	9.59050e7			0.405653
$125$		−	1.95744e8i		−	0.801767i
$126$	1.70011e7			0.0674522
$127$	4.11369e8			1.58131			0.790654	−	0.612263i	$-0.209741\pi$
$127$	4.11369e8			1.58131			0.790654	+	0.612263i	$0.209741\pi$
$128$			7.75402e7i			0.288860i
$129$	2.62659e8	+	4.57771e7i	0.948491	+	0.165306i
$130$	−1.65223e6			−0.00578491
$131$		−	1.97954e8i		−	0.672171i	−0.941831	−	0.336086i	$-0.890897\pi$
$131$		−	1.97954e8i		−	0.672171i	0.941831	−	0.336086i	$-0.109103\pi$
$132$			1.65334e8i			0.544584i
$133$	−4.00962e8			−1.28143
$134$			2.86914e7i			0.0889884i
$135$	−1.52674e8			−0.459652
$136$		−	5.31741e8i		−	1.55433i
$137$			6.49306e8i			1.84318i	0.388169	+	0.921588i	$0.373108\pi$
$137$			6.49306e8i			1.84318i	−0.388169	+	0.921588i	$0.626892\pi$
$138$	−2.91459e7			−0.0803640
$139$	−1.38946e8			−0.372208			−0.186104	−	0.982530i	$-0.559586\pi$
$139$	−1.38946e8			−0.372208			−0.186104	+	0.982530i	$0.559586\pi$
$140$	−1.14205e8			−0.297285
$141$			2.65539e8i			0.671818i
$142$	1.12509e8			0.276717
$143$	8.63345e6			0.0206462
$144$	−7.36798e6			−0.0171356
$145$	−3.17149e8			−0.717449
$146$	−8.47301e7			−0.186477
$147$			3.29228e8i			0.705063i
$148$		−	1.79166e8i		−	0.373429i
$149$			8.69163e7i			0.176342i	0.996105	+	0.0881710i	$0.0281022\pi$
$149$			8.69163e7i			0.176342i	−0.996105	+	0.0881710i	$0.971898\pi$
$150$	2.74299e8			0.541826
$151$		−	5.75666e8i		−	1.10729i	−0.832752	−	0.553646i	$-0.813236\pi$
$151$		−	5.75666e8i		−	1.10729i	0.832752	−	0.553646i	$-0.186764\pi$
$152$	5.49785e8			1.02996
$153$	−5.88068e7			−0.107315
$154$	−5.78739e8			−1.02896
$155$		−	2.05204e8i		−	0.355516i
$156$			5.36403e6i			0.00905717i
$157$		−	8.00910e8i		−	1.31821i	−0.752050	−	0.659106i	$-0.770935\pi$
$157$		−	8.00910e8i		−	1.31821i	0.752050	−	0.659106i	$-0.229065\pi$
$158$			1.46753e8i			0.235482i
$159$		−	6.27700e8i		−	0.982117i
$160$	2.60459e8			0.397430
$161$			1.05200e8i			0.156572i
$162$		−	4.45395e8i		−	0.646673i
$163$			1.22821e9i			1.73989i	0.493147	+	0.869946i	$0.335847\pi$
$163$			1.22821e9i			1.73989i	−0.493147	+	0.869946i	$0.664153\pi$
$164$	−6.58618e8			−0.910455
$165$	3.53757e8			0.477276
$166$			8.68275e8i			1.14347i
$167$	1.02872e9			1.32260			0.661302	−	0.750120i	$-0.270004\pi$
$167$	1.02872e9			1.32260			0.661302	+	0.750120i	$0.270004\pi$
$168$		−	1.06786e9i		−	1.34054i
$169$	−8.15451e8			−0.999657
$170$	−3.83105e8			−0.458693
$171$		−	6.08024e7i		−	0.0711109i
$172$	−7.62870e7	+	4.37718e8i	−0.0871639	+	0.500127i
$173$	1.79583e8			0.200485			0.100242	−	0.994963i	$-0.468038\pi$
$173$	1.79583e8			0.200485			0.100242	+	0.994963i	$0.468038\pi$
$174$		−	9.98542e8i		−	1.08935i
$175$		−	9.90067e8i		−	1.05563i
$176$	2.50815e8			0.261398
$177$		−	1.38788e9i		−	1.41403i
$178$	3.97135e8			0.395602
$179$		−	6.29234e8i		−	0.612915i	−0.951884	−	0.306457i	$-0.900856\pi$
$179$		−	6.29234e8i		−	0.612915i	0.951884	−	0.306457i	$-0.0991437\pi$
$180$		−	1.73182e7i		−	0.0164973i
$181$	6.87327e8			0.640396			0.320198	−	0.947351i	$-0.396251\pi$
$181$	6.87327e8			0.640396			0.320198	+	0.947351i	$0.396251\pi$
$182$	−1.87764e7			−0.0171130
$183$	6.85844e8			0.611535
$184$		−	1.44247e8i		−	0.125845i
$185$	−3.83354e8			−0.327275
$186$	6.46084e8			0.539805
$187$	2.00185e9			1.63706
$188$	−4.42517e8			−0.354241
$189$	−1.73503e9			−1.35975
$190$		−	3.96105e8i		−	0.303946i
$191$			1.44589e9i			1.08643i	0.839595	+	0.543214i	$0.182793\pi$
$191$			1.44589e9i			1.08643i	−0.839595	+	0.543214i	$0.817207\pi$
$192$			1.12702e9i			0.829325i
$193$	−2.20464e9			−1.58894			−0.794472	−	0.607301i	$-0.792252\pi$
$193$	−2.20464e9			−1.58894			−0.794472	+	0.607301i	$0.792252\pi$
$194$			1.25767e9i			0.887890i
$195$	1.14772e7			0.00793775
$196$	−5.48655e8			−0.371770
$197$	4.52647e8			0.300535			0.150267	−	0.988645i	$-0.451987\pi$
$197$	4.52647e8			0.300535			0.150267	+	0.988645i	$0.451987\pi$
$198$		−	8.77607e7i		−	0.0571004i
$199$		−	1.89007e9i		−	1.20522i	−0.798036	−	0.602610i	$-0.794128\pi$
$199$		−	1.89007e9i		−	1.20522i	0.798036	−	0.602610i	$-0.205872\pi$
$200$			1.35754e9i			0.848465i
$201$		−	1.99305e8i		−	0.122105i
$202$		−	6.96953e8i		−	0.418599i
$203$	−3.60418e9			−2.12237
$204$			1.24377e9i			0.718155i
$205$			1.40922e9i			0.797927i
$206$			2.39604e9i			1.33053i
$207$	−1.59527e7			−0.00868867
$208$	8.13735e6			0.00434740
$209$			2.06978e9i			1.08478i
$210$	−7.69367e8			−0.395600
$211$		−	2.76711e8i		−	0.139603i	−0.997561	−	0.0698017i	$-0.977763\pi$
$211$		−	2.76711e8i		−	0.139603i	0.997561	−	0.0698017i	$-0.0222367\pi$
$212$	1.04605e9			0.517858
$213$	−7.81547e8			−0.379696
$214$		−	8.02729e8i		−	0.382749i
$215$	9.36567e8	+	1.63228e8i	0.438314	+	0.0763909i
$216$	2.37901e9			1.09290
$217$		−	2.33200e9i		−	1.05169i
$218$			2.76082e8i			0.122240i
$219$	5.88577e8			0.255875
$220$			5.89532e8i			0.251662i
$221$	6.49475e7			0.0272266
$222$		−	1.20699e9i		−	0.496925i
$223$			7.54321e8i			0.305026i	0.988301	+	0.152513i	$0.0487366\pi$
$223$			7.54321e8i			0.305026i	−0.988301	+	0.152513i	$0.951263\pi$
$224$	2.95994e9			1.17568
$225$	1.50135e8			0.0585803
$226$	−5.32167e8			−0.203993
$227$			2.68891e9i			1.01268i	0.862333	+	0.506342i	$0.169002\pi$
$227$			2.68891e9i			1.01268i	−0.862333	+	0.506342i	$0.830998\pi$
$228$	−1.28597e9			−0.475874
$229$	−6.23178e8			−0.226605			−0.113303	−	0.993561i	$-0.536143\pi$
$229$	−6.23178e8			−0.226605			−0.113303	+	0.993561i	$0.536143\pi$
$230$	−1.03926e8			−0.0371376
$231$	4.02021e9			1.41189
$232$	4.94192e9			1.70586
$233$			1.32982e9i			0.451199i	0.974220	+	0.225600i	$0.0724341\pi$
$233$			1.32982e9i			0.451199i	−0.974220	+	0.225600i	$0.927566\pi$
$234$		−	2.84728e6i		−	0.000949657i
$235$			9.46836e8i			0.310458i
$236$	2.31288e9			0.745600
$237$		−	1.01942e9i		−	0.323116i
$238$	−4.35372e9			−1.35691
$239$	−1.85605e9			−0.568850			−0.284425	−	0.958698i	$-0.591803\pi$
$239$	−1.85605e9			−0.568850			−0.284425	+	0.958698i	$0.591803\pi$
$240$	3.33430e8			0.100498
$241$		−	2.51423e9i		−	0.745310i	−0.927970	−	0.372655i	$-0.878448\pi$
$241$		−	2.51423e9i		−	0.745310i	0.927970	−	0.372655i	$-0.121552\pi$
$242$			5.80944e8i			0.169384i
$243$		−	5.08295e8i		−	0.145778i
$244$			1.14295e9i			0.322454i
$245$			1.17393e9i			0.325821i
$246$	−4.43692e9			−1.21155
$247$			6.71514e7i			0.0180413i
$248$			3.19756e9i			0.845301i
$249$		−	6.03147e9i		−	1.56901i
$250$	2.19755e9			0.562572
$251$	2.38831e9			0.601723			0.300862	−	0.953668i	$-0.402726\pi$
$251$	2.38831e9			0.601723			0.300862	+	0.953668i	$0.402726\pi$
$252$		−	1.96809e8i		−	0.0488027i
$253$	5.43049e8			0.132543
$254$			4.61829e9i			1.10955i
$255$	2.66124e9			0.629394
$256$	−4.57011e9			−1.06406
$257$		−	5.77650e9i		−	1.32414i	−0.749444	−	0.662068i	$-0.769679\pi$
$257$		−	5.77650e9i		−	1.32414i	0.749444	−	0.662068i	$-0.230321\pi$
$258$	−5.13923e8	+	2.94878e9i	−0.115990	+	0.665523i
$259$	−4.35655e9			−0.968152
$260$			1.91266e7i			0.00418547i
$261$		−	5.46542e8i		−	0.117777i
$262$	2.22236e9			0.471639
$263$		−	5.48436e9i		−	1.14631i	−0.819446	−	0.573156i	$-0.805719\pi$
$263$		−	5.48436e9i		−	1.14631i	0.819446	−	0.573156i	$-0.194281\pi$
$264$	−5.51237e9			−1.13481
$265$		−	2.23820e9i		−	0.453853i
$266$		−	4.50146e9i		−	0.899138i
$267$	−2.75870e9			−0.542824
$268$	3.32139e8			0.0643845
$269$	5.81055e9			1.10971			0.554853	−	0.831948i	$-0.312774\pi$
$269$	5.81055e9			1.10971			0.554853	+	0.831948i	$0.312774\pi$
$270$		−	1.71401e9i		−	0.322522i
$271$	−4.93446e9			−0.914877			−0.457439	−	0.889241i	$-0.651233\pi$
$271$	−4.93446e9			−0.914877			−0.457439	+	0.889241i	$0.651233\pi$
$272$	1.88682e9			0.344711
$273$	1.30430e8			0.0234816
$274$	−7.28952e9			−1.29329
$275$	−5.11077e9			−0.893625
$276$			3.37401e8i			0.0581446i
$277$		−	6.54007e9i		−	1.11087i	−0.831560	−	0.555435i	$-0.812552\pi$
$277$		−	6.54007e9i		−	1.11087i	0.831560	−	0.555435i	$-0.187448\pi$
$278$		−	1.55989e9i		−	0.261166i
$279$	3.53628e8			0.0583619
$280$		−	3.80770e9i		−	0.619485i
$281$	5.69943e9			0.914126			0.457063	−	0.889434i	$-0.348901\pi$
$281$	5.69943e9			0.914126			0.457063	+	0.889434i	$0.348901\pi$
$282$	−2.98111e9			−0.471391
$283$	−2.71819e9			−0.423774			−0.211887	−	0.977294i	$-0.567961\pi$
$283$	−2.71819e9			−0.423774			−0.211887	+	0.977294i	$0.567961\pi$
$284$		−	1.30244e9i		−	0.200209i
$285$			2.75154e9i			0.417058i
$286$			9.69247e7i			0.0144867i
$287$			1.60148e10i			2.36044i
$288$			4.48849e8i			0.0652425i
$289$	8.08372e9			1.15883
$290$		−	3.56052e9i		−	0.503409i
$291$		−	8.73639e9i		−	1.21832i
$292$			9.80857e8i			0.134919i
$293$	1.69386e9			0.229830			0.114915	−	0.993375i	$-0.463340\pi$
$293$	1.69386e9			0.229830			0.114915	+	0.993375i	$0.463340\pi$
$294$	−3.69613e9			−0.494718
$295$		−	4.94878e9i		−	0.653447i
$296$	5.97355e9			0.778154
$297$			8.95629e9i			1.15107i
$298$	−9.75778e8			−0.123733
$299$	1.76185e7			0.00220437
$300$		−	3.17536e9i		−	0.392020i
$301$	1.06434e10	+	1.85497e9i	1.29663	+	0.225981i
$302$	6.46279e9			0.776949
$303$			4.84138e9i			0.574379i
$304$			1.95085e9i			0.228417i
$305$	2.44553e9			0.282600
$306$		−	6.60203e8i		−	0.0752995i
$307$	−1.07653e9			−0.121192			−0.0605961	−	0.998162i	$-0.519300\pi$
$307$	−1.07653e9			−0.121192			−0.0605961	+	0.998162i	$0.519300\pi$
$308$			6.69962e9i			0.744471i
$309$		−	1.66441e10i		−	1.82569i
$310$	2.30375e9			0.249453
$311$	−6.92038e9			−0.739756			−0.369878	−	0.929080i	$-0.620601\pi$
$311$	−6.92038e9			−0.739756			−0.369878	+	0.929080i	$0.620601\pi$
$312$	−1.78841e8			−0.0188734
$313$		−	4.87540e9i		−	0.507964i	−0.967209	−	0.253982i	$-0.918260\pi$
$313$		−	4.87540e9i		−	0.507964i	0.967209	−	0.253982i	$-0.0817403\pi$
$314$	8.99154e9			0.924944
$315$	−4.21105e8			−0.0427709
$316$	1.69885e9			0.170375
$317$	−4.22998e9			−0.418892			−0.209446	−	0.977820i	$-0.567166\pi$
$317$	−4.22998e9			−0.418892			−0.209446	+	0.977820i	$0.567166\pi$
$318$	7.04696e9			0.689118
$319$			1.86049e10i			1.79666i
$320$			4.01862e9i			0.383245i
$321$			5.57615e9i			0.525188i
$322$	−1.18105e9			−0.109861
$323$			1.55705e10i			1.43052i
$324$	−5.15600e9			−0.467878
$325$	−1.65812e8			−0.0148622
$326$	−1.37887e10			−1.22082
$327$		−	1.91780e9i		−	0.167731i
$328$		−	2.19589e10i		−	1.89721i
$329$			1.07601e10i			0.918404i
$330$			3.97151e9i			0.334888i
$331$			1.00613e10i			0.838186i	0.907943	+	0.419093i	$0.137652\pi$
$331$			1.00613e10i			0.838186i	−0.907943	+	0.419093i	$0.862348\pi$
$332$	1.00514e10			0.827319
$333$		−	6.60632e8i		−	0.0537258i
$334$			1.15490e10i			0.928025i
$335$		−	7.10665e8i		−	0.0564268i
$336$	3.78919e9			0.297296
$337$	−1.58839e10			−1.23151			−0.615753	−	0.787939i	$-0.711148\pi$
$337$	−1.58839e10			−1.23151			−0.615753	+	0.787939i	$0.711148\pi$
$338$		−	9.15477e9i		−	0.701424i
$339$	3.69670e9			0.279908
$340$			4.43492e9i			0.331871i
$341$	−1.20379e10			−0.890293
$342$	6.82607e8			0.0498960
$343$		−	4.87660e9i		−	0.352322i
$344$	−1.45939e10	−	2.54348e9i	−1.04217	−	0.181633i
$345$	7.21922e8			0.0509582
$346$			2.01612e9i			0.140673i
$347$			2.05288e10i			1.41595i	0.706240	+	0.707973i	$0.250390\pi$
$347$			2.05288e10i			1.41595i	−0.706240	+	0.707973i	$0.749610\pi$
$348$	−1.15594e10			−0.788165
$349$			4.83149e9i			0.325671i	0.986653	+	0.162835i	$0.0520640\pi$
$349$			4.83149e9i			0.325671i	−0.986653	+	0.162835i	$0.947936\pi$
$350$	1.11151e10			0.740700
$351$			2.90575e8i			0.0191439i
$352$		−	1.52793e10i		−	0.995254i
$353$	−2.45055e10			−1.57821			−0.789105	−	0.614258i	$-0.789455\pi$
$353$	−2.45055e10			−1.57821			−0.789105	+	0.614258i	$0.789455\pi$
$354$	1.55812e10			0.992176
$355$	−2.78677e9			−0.175464
$356$		−	4.59733e9i		−	0.286224i
$357$	3.02431e10			1.86189
$358$	7.06419e9			0.430061
$359$	−2.54268e9			−0.153079			−0.0765393	−	0.997067i	$-0.524387\pi$
$359$	−2.54268e9			−0.153079			−0.0765393	+	0.997067i	$0.524387\pi$
$360$	5.77405e8			0.0343772
$361$	8.84687e8			0.0520908
$362$			7.71637e9i			0.449344i
$363$		−	4.03553e9i		−	0.232420i
$364$			2.17360e8i			0.0123815i
$365$	2.09870e9			0.118244
$366$			7.69973e9i			0.429093i
$367$	1.75953e10			0.969914			0.484957	−	0.874538i	$-0.338835\pi$
$367$	1.75953e10			0.969914			0.484957	+	0.874538i	$0.338835\pi$
$368$	5.11844e8			0.0279091
$369$	−2.42850e9			−0.130989
$370$		−	4.30378e9i		−	0.229637i
$371$		−	2.54356e10i		−	1.34260i
$372$		−	7.47923e9i		−	0.390558i
$373$			1.05811e10i			0.546635i	0.961924	+	0.273318i	$0.0881210\pi$
$373$			1.05811e10i			0.546635i	−0.961924	+	0.273318i	$0.911879\pi$
$374$			2.24741e10i			1.14867i
$375$	−1.52653e10			−0.771932
$376$		−	1.47539e10i		−	0.738169i
$377$			6.03612e8i			0.0298808i
$378$		−	1.94785e10i		−	0.954090i
$379$	2.81900e9			0.136628			0.0683138	−	0.997664i	$-0.478238\pi$
$379$	2.81900e9			0.136628			0.0683138	+	0.997664i	$0.478238\pi$
$380$	−4.58541e9			−0.219909
$381$		−	3.20810e10i		−	1.52247i
$382$	−1.62325e10			−0.762308
$383$			3.93346e10i			1.82801i	0.405699	+	0.914007i	$0.367028\pi$
$383$			3.93346e10i			1.82801i	−0.405699	+	0.914007i	$0.632972\pi$
$384$	6.04704e9			0.278111
$385$	1.43349e10			0.652457
$386$		−	2.47507e10i		−	1.11491i
$387$	−2.81291e8	+	1.61398e9i	−0.0125404	+	0.0719540i
$388$	1.45591e10			0.642403
$389$		−	2.95328e10i		−	1.28975i	−0.764288	−	0.644875i	$-0.776909\pi$
$389$		−	2.95328e10i		−	1.28975i	0.764288	−	0.644875i	$-0.223091\pi$
$390$			1.28850e8i			0.00556964i
$391$	4.08523e9			0.174787
$392$		−	1.82926e10i		−	0.774697i
$393$	−1.54376e10			−0.647159
$394$			5.08171e9i			0.210875i
$395$		−	3.63495e9i		−	0.149317i
$396$	−1.01594e9			−0.0413130
$397$	−4.05863e10			−1.63387			−0.816935	−	0.576730i	$-0.804329\pi$
$397$	−4.05863e10			−1.63387			−0.816935	+	0.576730i	$0.804329\pi$
$398$	2.12192e10			0.845661
$399$			3.12694e10i			1.23375i
$400$	−4.81709e9			−0.188168
$401$	1.60282e10			0.619881			0.309940	−	0.950756i	$-0.399691\pi$
$401$	1.60282e10			0.619881			0.309940	+	0.950756i	$0.399691\pi$
$402$	2.23753e9			0.0856770
$403$	−3.90553e8			−0.0148068
$404$	−8.06810e9			−0.302863
$405$			1.10321e10i			0.410051i
$406$		−	4.04628e10i		−	1.48920i
$407$			2.24887e10i			0.819571i
$408$	−4.14683e10			−1.49649
$409$		−	4.50915e10i		−	1.61139i	−0.592328	−	0.805697i	$-0.701791\pi$
$409$		−	4.50915e10i		−	1.61139i	0.592328	−	0.805697i	$-0.298209\pi$
$410$	−1.58208e10			−0.559877
$411$	5.06367e10			1.77459
$412$	2.77372e10			0.962661
$413$		−	5.62395e10i		−	1.93304i
$414$		−	1.79096e8i		−	0.00609654i
$415$		−	2.15065e10i		−	0.725066i
$416$		−	4.95718e8i		−	0.0165524i
$417$			1.08358e10i			0.358358i
$418$	−2.32367e10			−0.761149
$419$		−	5.81410e9i		−	0.188637i	−0.995542	−	0.0943184i	$-0.969933\pi$
$419$		−	5.81410e9i		−	0.188637i	0.995542	−	0.0943184i	$-0.0300672\pi$
$420$			8.90639e9i			0.286223i
$421$			4.04666e10i			1.28815i	0.764960	+	0.644077i	$0.222759\pi$
$421$			4.04666e10i			1.28815i	−0.764960	+	0.644077i	$0.777241\pi$
$422$	3.10653e9			0.0979549
$423$	−1.63168e9			−0.0509652
$424$			3.48763e10i			1.07911i
$425$	−3.84471e10			−1.17844
$426$		−	8.77415e9i		−	0.266420i
$427$	2.77917e10			0.835994
$428$	−9.29259e9			−0.276925
$429$		−	6.73287e8i		−	0.0198779i
$430$	−1.83251e9	+	1.05145e10i	−0.0536008	+	0.307549i
$431$	−1.24158e10			−0.359803			−0.179901	−	0.983685i	$-0.557578\pi$
$431$	−1.24158e10			−0.359803			−0.179901	+	0.983685i	$0.557578\pi$
$432$			8.44164e9i			0.242377i
$433$			4.05793e10i			1.15439i	0.816606	+	0.577195i	$0.195853\pi$
$433$			4.05793e10i			1.15439i	−0.816606	+	0.577195i	$0.804147\pi$
$434$	2.61805e10			0.737938
$435$			2.47331e10i			0.690752i
$436$	3.19600e9			0.0884423
$437$			4.22386e9i			0.115820i
$438$			6.60775e9i			0.179538i
$439$	4.33049e10			1.16595			0.582973	−	0.812491i	$-0.301889\pi$
$439$	4.33049e10			1.16595			0.582973	+	0.812491i	$0.301889\pi$
$440$	−1.96555e10			−0.524414
$441$	−2.02304e9			−0.0534872
$442$			7.29142e8i			0.0191039i
$443$	5.62607e9			0.146080			0.0730400	−	0.997329i	$-0.476730\pi$
$443$	5.62607e9			0.146080			0.0730400	+	0.997329i	$0.476730\pi$
$444$	−1.39724e10			−0.359533
$445$	−9.83673e9			−0.250848
$446$	−8.46850e9			−0.214026
$447$	6.77824e9			0.169780
$448$			4.56688e10i			1.13372i
$449$		−	3.19821e10i		−	0.786903i	−0.919345	−	0.393451i	$-0.871281\pi$
$449$		−	3.19821e10i		−	0.786903i	0.919345	−	0.393451i	$-0.128719\pi$
$450$			1.68551e9i			0.0411038i
$451$	8.26691e10			1.99819
$452$			6.16050e9i			0.147592i
$453$	−4.48938e10			−1.06609
$454$	−3.01875e10			−0.710565
$455$	4.65077e8			0.0108512
$456$		−	4.28754e10i		−	0.991629i
$457$		−	7.26146e10i		−	1.66479i	−0.554184	−	0.832394i	$-0.686970\pi$
$457$		−	7.26146e10i		−	1.66479i	0.554184	−	0.832394i	$-0.313030\pi$
$458$		−	6.99620e9i		−	0.159001i
$459$			6.73761e10i			1.51794i
$460$			1.20307e9i			0.0268696i
$461$	5.17863e10			1.14660			0.573299	−	0.819346i	$-0.305663\pi$
$461$	5.17863e10			1.14660			0.573299	+	0.819346i	$0.305663\pi$
$462$			4.51334e10i			0.990673i
$463$			3.23815e10i			0.704650i	0.935878	+	0.352325i	$0.114609\pi$
$463$			3.23815e10i			0.704650i	−0.935878	+	0.352325i	$0.885391\pi$
$464$			1.75358e10i			0.378316i
$465$	−1.60030e10			−0.342287
$466$	−1.49294e10			−0.316591
$467$			3.11892e10i			0.655747i	0.944722	+	0.327873i	$0.106332\pi$
$467$			3.11892e10i			0.655747i	−0.944722	+	0.327873i	$0.893668\pi$
$468$	−3.29608e7			−0.000687091
$469$		−	8.07621e9i		−	0.166923i
$470$	−1.06298e10			−0.217838
$471$	−6.24597e10			−1.26916
$472$			7.71136e10i			1.55368i
$473$	9.57546e9	−	5.49419e10i	0.191300	−	1.09764i
$474$	1.14446e10			0.226719
$475$		−	3.97518e10i		−	0.780877i
$476$			5.03997e10i			0.981749i
$477$	3.85708e9			0.0745050
$478$		−	2.08372e10i		−	0.399143i
$479$	−9.30639e9			−0.176782			−0.0883912	−	0.996086i	$-0.528173\pi$
$479$	−9.30639e9			−0.176782			−0.0883912	+	0.996086i	$0.528173\pi$
$480$		−	2.03122e10i		−	0.382641i
$481$			7.29616e8i			0.0136306i
$482$	2.82264e10			0.522958
$483$	8.20414e9			0.150746
$484$	6.72515e9			0.122552
$485$		−	3.11515e10i		−	0.563004i
$486$	5.70645e9			0.102287
$487$	−9.25780e10			−1.64586			−0.822928	−	0.568146i	$-0.807661\pi$
$487$	−9.25780e10			−1.64586			−0.822928	+	0.568146i	$0.807661\pi$
$488$	−3.81070e10			−0.671932
$489$	9.57830e10			1.67515
$490$	−1.31793e10			−0.228617
$491$			5.31182e9i			0.0913939i	0.998955	+	0.0456970i	$0.0145509\pi$
$491$			5.31182e9i			0.0913939i	−0.998955	+	0.0456970i	$0.985449\pi$
$492$			5.13629e10i			0.876575i
$493$			1.39960e11i			2.36929i
$494$	−7.53885e8			−0.0126589
$495$			2.17376e9i			0.0362069i
$496$	−1.13462e10			−0.187466
$497$	−3.16697e10			−0.519062
$498$	6.77132e10			1.10092
$499$		−	1.79703e10i		−	0.289837i	−0.989444	−	0.144918i	$-0.953708\pi$
$499$		−	1.79703e10i		−	0.289837i	0.989444	−	0.144918i	$-0.0462920\pi$
$500$		−	2.54394e10i		−	0.407030i
$501$		−	8.02253e10i		−	1.27339i
$502$			2.68128e10i			0.422208i
$503$		−	8.02520e10i		−	1.25367i	−0.779151	−	0.626836i	$-0.784350\pi$
$503$		−	8.02520e10i		−	1.25367i	0.779151	−	0.626836i	$-0.215650\pi$
$504$	6.56180e9			0.101695
$505$			1.72630e10i			0.265430i
$506$			6.09662e9i			0.0930009i
$507$			6.35936e10i			0.962458i
$508$	5.34625e10			0.802776
$509$	6.47170e10			0.964156			0.482078	−	0.876128i	$-0.339882\pi$
$509$	6.47170e10			0.964156			0.482078	+	0.876128i	$0.339882\pi$
$510$			2.98767e10i			0.441624i
$511$	2.38503e10			0.349792
$512$		−	3.14567e10i		−	0.457755i
$513$	−6.96625e10			−1.00584
$514$	6.48507e10			0.929100
$515$		−	5.93481e10i		−	0.843680i
$516$	3.41358e10	+	5.94931e9i	0.481516	+	0.0839204i
$517$	5.55443e10			0.777458
$518$		−	4.89094e10i		−	0.679318i
$519$		−	1.40050e10i		−	0.193025i
$520$	−6.37698e8			−0.00872171
$521$		−	1.28872e11i		−	1.74908i	−0.484955	−	0.874539i	$-0.661164\pi$
$521$		−	1.28872e11i		−	1.74908i	0.484955	−	0.874539i	$-0.338836\pi$
$522$	6.13583e9			0.0826402
$523$		−	2.50640e10i		−	0.334999i	−0.985872	−	0.167500i	$-0.946431\pi$
$523$		−	2.50640e10i		−	0.334999i	0.985872	−	0.167500i	$-0.0535693\pi$
$524$		−	2.57266e10i		−	0.341238i
$525$	−7.72112e10			−1.01635
$526$	6.15710e10			0.804327
$527$	−9.05583e10			−1.17405
$528$		−	1.95600e10i		−	0.251671i
$529$	−7.72028e10			−0.985849
$530$	2.51275e10			0.318453
$531$	8.52822e9			0.107271
$532$	−5.21100e10			−0.650541
$533$	2.68209e9			0.0332326
$534$		−	3.09709e10i		−	0.380881i
$535$			1.98830e10i			0.242698i
$536$			1.10738e10i			0.134165i
$537$	−4.90714e10			−0.590107
$538$			6.52330e10i			0.778643i
$539$	6.88665e10			0.815931
$540$	−1.98418e10			−0.233349
$541$	−8.94644e10			−1.04439			−0.522193	−	0.852827i	$-0.674886\pi$
$541$	−8.94644e10			−1.04439			−0.522193	+	0.852827i	$0.674886\pi$
$542$		−	5.53975e10i		−	0.641938i
$543$		−	5.36017e10i		−	0.616566i
$544$		−	1.14943e11i		−	1.31246i
$545$		−	6.83834e9i		−	0.0775113i
$546$			1.46429e9i			0.0164762i
$547$	−2.63222e9			−0.0294018			−0.0147009	−	0.999892i	$-0.504680\pi$
$547$	−2.63222e9			−0.0294018			−0.0147009	+	0.999892i	$0.504680\pi$
$548$			8.43854e10i			0.935718i
$549$			4.21437e9i			0.0463920i
$550$		−	5.73768e10i		−	0.627026i
$551$	−1.44710e11			−1.56997
$552$	−1.12492e10			−0.121162
$553$		−	4.13087e10i		−	0.441714i
$554$	7.34230e10			0.779459
$555$			2.98962e10i			0.315097i
$556$	−1.80577e10			−0.188957
$557$	−9.49214e10			−0.986151			−0.493075	−	0.869987i	$-0.664127\pi$
$557$	−9.49214e10			−0.986151			−0.493075	+	0.869987i	$0.664127\pi$
$558$			3.97005e9i			0.0409505i
$559$	3.10663e8	−	1.78252e9i	0.00318158	−	0.0182552i
$560$	1.35112e10			0.137386
$561$		−	1.56116e11i		−	1.57615i
$562$			6.39855e10i			0.641411i
$563$	1.59291e11			1.58547			0.792734	−	0.609568i	$-0.208657\pi$
$563$	1.59291e11			1.58547			0.792734	+	0.609568i	$0.208657\pi$
$564$			3.45101e10i			0.341059i
$565$	1.31814e10			0.129350
$566$		−	3.05161e10i		−	0.297347i
$567$			1.25372e11i			1.21302i
$568$	4.34244e10			0.417197
$569$	6.53976e10			0.623897			0.311949	−	0.950099i	$-0.399018\pi$
$569$	6.53976e10			0.623897			0.311949	+	0.950099i	$0.399018\pi$
$570$	−3.08906e10			−0.292635
$571$			1.38007e11i			1.29825i	0.760683	+	0.649124i	$0.224864\pi$
$571$			1.38007e11i			1.29825i	−0.760683	+	0.649124i	$0.775136\pi$
$572$	1.12202e9			0.0104814
$573$	1.12759e11			1.04600
$574$	−1.79792e11			−1.65624
$575$	−1.04297e10			−0.0954113
$576$	−6.92527e9			−0.0629139
$577$		−	6.28157e9i		−	0.0566716i	−0.999598	−	0.0283358i	$-0.990979\pi$
$577$		−	6.28157e9i		−	0.0566716i	0.999598	−	0.0283358i	$-0.00902077\pi$
$578$			9.07530e10i			0.813111i
$579$			1.71931e11i			1.52982i
$580$	−4.12174e10			−0.364224
$581$		−	2.44407e11i		−	2.14491i
$582$	9.80804e10			0.854850
$583$	−1.31300e11			−1.13655
$584$	−3.27026e10			−0.281146
$585$			7.05249e7i			0.000602170i
$586$			1.90164e10i			0.161264i
$587$		−	7.97093e10i		−	0.671362i	−0.941976	−	0.335681i	$-0.891034\pi$
$587$		−	7.97093e10i		−	0.671362i	0.941976	−	0.335681i	$-0.108966\pi$
$588$			4.27873e10i			0.357936i
$589$		−	9.36313e10i		−	0.777965i
$590$	5.55582e10			0.458501
$591$		−	3.53001e10i		−	0.289351i
$592$			2.11964e10i			0.172574i
$593$			1.09184e11i			0.882960i	0.897271	+	0.441480i	$0.145546\pi$
$593$			1.09184e11i			0.882960i	−0.897271	+	0.441480i	$0.854454\pi$
$594$	−1.00549e11			−0.807667
$595$	1.07838e11			0.860409
$596$			1.12958e10i			0.0895228i
$597$	−1.47399e11			−1.16037
$598$			1.97797e8i			0.00154673i
$599$	−6.17501e10			−0.479656			−0.239828	−	0.970815i	$-0.577091\pi$
$599$	−6.17501e10			−0.479656			−0.239828	+	0.970815i	$0.577091\pi$
$600$	1.05869e11			0.816893
$601$		−	6.83095e10i		−	0.523580i	−0.965125	−	0.261790i	$-0.915687\pi$
$601$		−	6.83095e10i		−	0.523580i	0.965125	−	0.261790i	$-0.0843128\pi$
$602$	−2.08251e10	+	1.19490e11i	−0.158563	+	0.909799i
$603$	1.22469e9			0.00926309
$604$		−	7.48149e10i		−	0.562135i
$605$		−	1.43895e10i		−	0.107405i
$606$	−5.43525e10			−0.403022
$607$			9.53091e10i			0.702068i	0.936363	+	0.351034i	$0.114170\pi$
$607$			9.53091e10i			0.702068i	−0.936363	+	0.351034i	$0.885830\pi$
$608$	1.18843e11			0.869683
$609$			2.81075e11i			2.04340i
$610$			2.74550e10i			0.198291i
$611$	1.80206e9			0.0129302
$612$	−7.64268e9			−0.0544804
$613$	2.29649e11			1.62638			0.813190	−	0.581998i	$-0.197729\pi$
$613$	2.29649e11			1.62638			0.813190	+	0.581998i	$0.197729\pi$
$614$		−	1.20859e10i		−	0.0850363i
$615$	1.09899e11			0.768235
$616$	−2.23371e11			−1.55133
$617$	1.63025e11			1.12490			0.562451	−	0.826831i	$-0.309859\pi$
$617$	1.63025e11			1.12490			0.562451	+	0.826831i	$0.309859\pi$
$618$	1.86857e11			1.28102
$619$	2.44766e11			1.66720			0.833600	−	0.552368i	$-0.186276\pi$
$619$	2.44766e11			1.66720			0.833600	+	0.552368i	$0.186276\pi$
$620$		−	2.66688e10i		−	0.180483i
$621$			1.82774e10i			0.122899i
$622$		−	7.76927e10i		−	0.519061i
$623$	−1.11788e11			−0.742064
$624$		−	6.34598e8i		−	0.00418563i
$625$	6.79509e10			0.445323
$626$	5.47343e10			0.356420
$627$	1.61414e11			1.04441
$628$		−	1.04088e11i		−	0.669211i
$629$			1.69177e11i			1.08079i
$630$		−	4.72760e9i		−	0.0300109i
$631$			2.93871e11i			1.85370i	0.375432	+	0.926850i	$0.377494\pi$
$631$			2.93871e11i			1.85370i	−0.375432	+	0.926850i	$0.622506\pi$
$632$			5.66410e10i			0.355028i
$633$	−2.15795e10			−0.134409
$634$		−	4.74885e10i		−	0.293922i
$635$		−	1.14392e11i		−	0.703557i
$636$		−	8.15774e10i		−	0.498587i
$637$	2.23428e9			0.0135700
$638$	−2.08871e11			−1.26065
$639$		−	4.80244e9i		−	0.0288044i
$640$	2.15620e10			0.128520
$641$			1.49515e11i			0.885629i	0.896613	+	0.442815i	$0.146020\pi$
$641$			1.49515e11i			0.885629i	−0.896613	+	0.442815i	$0.853980\pi$
$642$	−6.26015e10			−0.368506
$643$	3.12896e11			1.83045			0.915223	−	0.402948i	$-0.132015\pi$
$643$	3.12896e11			1.83045			0.915223	+	0.402948i	$0.132015\pi$
$644$			1.36721e10i			0.0794862i
$645$	1.27295e10	−	7.30390e10i	0.0735482	−	0.422003i
$646$	−1.74805e11			−1.00374
$647$			4.68994e10i			0.267639i	0.991006	+	0.133820i	$0.0427243\pi$
$647$			4.68994e10i			0.267639i	−0.991006	+	0.133820i	$0.957276\pi$
$648$		−	1.71906e11i		−	0.974967i
$649$	−2.90311e11			−1.63638
$650$		−	1.86151e9i		−	0.0104283i
$651$	−1.81863e11			−1.01256
$652$			1.59621e11i			0.883284i
$653$		−	1.20001e11i		−	0.659982i	−0.943984	−	0.329991i	$-0.892954\pi$
$653$		−	1.20001e11i		−	0.659982i	0.943984	−	0.329991i	$-0.107046\pi$
$654$	2.15305e10			0.117691
$655$	−5.50462e10			−0.299063
$656$	7.79187e10			0.420752
$657$			3.61668e9i			0.0194110i
$658$	−1.20800e11			−0.644412
$659$	−2.66563e11			−1.41338			−0.706688	−	0.707526i	$-0.749811\pi$
$659$	−2.66563e11			−1.41338			−0.706688	+	0.707526i	$0.749811\pi$
$660$	4.59752e10			0.242297
$661$	−3.28604e11			−1.72134			−0.860671	−	0.509162i	$-0.829955\pi$
$661$	−3.28604e11			−1.72134			−0.860671	+	0.509162i	$0.829955\pi$
$662$	−1.12954e11			−0.588126
$663$		−	5.06498e9i		−	0.0262134i
$664$			3.35122e11i			1.72397i
$665$			1.11498e11i			0.570137i
$666$	7.41669e9			0.0376975
$667$			3.79676e10i			0.191827i
$668$	1.33694e11			0.671440
$669$	5.88264e10			0.293676
$670$	7.97838e9			0.0395928
$671$		−	1.43462e11i		−	0.707696i
$672$		−	2.30833e11i		−	1.13194i
$673$			2.06329e11i			1.00577i	0.864352	+	0.502887i	$0.167729\pi$
$673$			2.06329e11i			1.00577i	−0.864352	+	0.502887i	$0.832271\pi$
$674$		−	1.78323e11i		−	0.864106i
$675$		−	1.72013e11i		−	0.828601i
$676$	−1.05978e11			−0.507492
$677$			3.04887e11i			1.45139i	0.688016	+	0.725695i	$0.258482\pi$
$677$			3.04887e11i			1.45139i	−0.688016	+	0.725695i	$0.741518\pi$
$678$			4.15015e10i			0.196402i
$679$		−	3.54015e11i		−	1.66549i
$680$	−1.47864e11			−0.691555
$681$	2.09697e11			0.974999
$682$		−	1.35145e11i		−	0.624688i
$683$	−2.76020e11			−1.26840			−0.634202	−	0.773168i	$-0.718671\pi$
$683$	−2.76020e11			−1.26840			−0.634202	+	0.773168i	$0.718671\pi$
$684$		−	7.90203e9i		−	0.0361006i
$685$	1.80556e11			0.820067
$686$	5.47478e10			0.247212
$687$			4.85991e10i			0.218173i
$688$	9.02523e9	−	5.17848e10i	0.0402814	−	0.231126i
$689$	−4.25984e9			−0.0189024
$690$			8.10477e9i			0.0357556i
$691$		−	1.83321e11i		−	0.804080i	−0.915622	−	0.402040i	$-0.868301\pi$
$691$		−	1.83321e11i		−	0.804080i	0.915622	−	0.402040i	$-0.131699\pi$
$692$	2.33391e10			0.101779
$693$			2.47033e10i			0.107108i
$694$	−2.30470e11			−0.993520
$695$			3.86374e10i			0.165603i
$696$		−	3.85400e11i		−	1.64238i
$697$	6.21900e11			2.63505
$698$	−5.42414e10			−0.228512
$699$	1.03707e11			0.434409
$700$		−	1.28671e11i		−	0.535908i
$701$	2.61721e11			1.08384			0.541922	−	0.840429i	$-0.317697\pi$
$701$	2.61721e11			1.08384			0.541922	+	0.840429i	$0.317697\pi$
$702$	−3.26218e9			−0.0134326
$703$	−1.74918e11			−0.716166
$704$	2.35744e11			0.959733
$705$	7.38398e10			0.298906
$706$		−	2.75115e11i		−	1.10738i
$707$			1.96182e11i			0.785201i
$708$		−	1.80372e11i		−	0.717855i
$709$	−2.88387e11			−1.14127			−0.570637	−	0.821202i	$-0.693304\pi$
$709$	−2.88387e11			−1.14127			−0.570637	+	0.821202i	$0.693304\pi$
$710$		−	3.12861e10i		−	0.123117i
$711$	6.26410e9			0.0245121
$712$	1.53279e11			0.596435
$713$	−2.45661e10			−0.0950555
$714$			3.39528e11i			1.30642i
$715$		−	2.40075e9i		−	0.00918592i
$716$		−	8.17768e10i		−	0.311156i
$717$			1.44746e11i			0.547683i
$718$		−	2.85458e10i		−	0.107410i
$719$	−1.09961e10			−0.0411456			−0.0205728	−	0.999788i	$-0.506549\pi$
$719$	−1.09961e10			−0.0411456			−0.0205728	+	0.999788i	$0.506549\pi$
$720$			2.04885e9i			0.00762397i
$721$		−	6.74450e11i		−	2.49579i
$722$			9.93207e9i			0.0365503i
$723$	−1.96074e11			−0.717575
$724$	8.93266e10			0.325107
$725$		−	3.57322e11i		−	1.29332i
$726$	4.53054e10			0.163081
$727$			5.25195e11i			1.88011i	0.341024	+	0.940054i	$0.389226\pi$
$727$			5.25195e11i			1.88011i	−0.341024	+	0.940054i	$0.610774\pi$
$728$	−7.24699e9			−0.0258007
$729$	−2.99934e11			−1.06198
$730$			2.35614e10i			0.0829677i
$731$	7.20340e10	−	4.13315e11i	0.252271	−	1.44748i
$732$	8.91340e10			0.310455
$733$			8.73247e10i			0.302497i	0.988496	+	0.151249i	$0.0483294\pi$
$733$			8.73247e10i			0.302497i	−0.988496	+	0.151249i	$0.951671\pi$
$734$			1.97537e11i			0.680555i
$735$	9.15503e10			0.313697
$736$		−	3.11810e10i		−	0.106262i
$737$	−4.16898e10			−0.141306
$738$		−	2.72639e10i		−	0.0919101i
$739$		−	2.90510e10i		−	0.0974054i	−0.998813	−	0.0487027i	$-0.984491\pi$
$739$		−	2.90510e10i		−	0.0974054i	0.998813	−	0.0487027i	$-0.0155087\pi$
$740$	−4.98216e10			−0.166146
$741$	5.23686e9			0.0173699
$742$	2.85556e11			0.942054
$743$			4.72649e11i			1.55090i	0.631409	+	0.775450i	$0.282477\pi$
$743$			4.72649e11i			1.55090i	−0.631409	+	0.775450i	$0.717523\pi$
$744$	2.49364e11			0.813846
$745$	2.41693e10			0.0784582
$746$	−1.18791e11			−0.383555
$747$	3.70621e10			0.119028
$748$	2.60166e11			0.831081
$749$			2.25956e11i			0.717955i
$750$		−	1.71378e11i		−	0.541638i
$751$		−	1.12217e11i		−	0.352777i	−0.984321	−	0.176389i	$-0.943558\pi$
$751$		−	1.12217e11i		−	0.352777i	0.984321	−	0.176389i	$-0.0564416\pi$
$752$	5.23525e10			0.163707
$753$		−	1.86255e11i		−	0.579332i
$754$	−6.77654e9			−0.0209663
$755$	−1.60078e11			−0.492657
$756$	−2.25489e11			−0.690299
$757$			4.09584e11i			1.24727i	0.781717	+	0.623634i	$0.214344\pi$
$757$			4.09584e11i			1.24727i	−0.781717	+	0.623634i	$0.785656\pi$
$758$			3.16479e10i			0.0958669i
$759$		−	4.23502e10i		−	0.127611i
$760$		−	1.52882e11i		−	0.458248i
$761$		−	3.43697e11i		−	1.02480i	−0.858748	−	0.512398i	$-0.828757\pi$
$761$		−	3.43697e11i		−	1.02480i	0.858748	−	0.512398i	$-0.171243\pi$
$762$	3.60162e11			1.06826
$763$		−	7.77130e10i		−	0.229295i
$764$			1.87911e11i			0.551542i
$765$			1.63527e10i			0.0477468i
$766$	−4.41595e11			−1.28265
$767$	−9.41874e9			−0.0272152
$768$			3.56404e11i			1.02447i
$769$	−2.31427e10			−0.0661774			−0.0330887	−	0.999452i	$-0.510534\pi$
$769$	−2.31427e10			−0.0661774			−0.0330887	+	0.999452i	$0.510534\pi$
$770$			1.60933e11i			0.457807i
$771$	−4.50485e11			−1.27486
$772$	−2.86520e11			−0.806653
$773$			4.68931e10i			0.131338i	0.997841	+	0.0656690i	$0.0209182\pi$
$773$			4.68931e10i			0.131338i	−0.997841	+	0.0656690i	$0.979082\pi$
$774$	−1.81196e10	−	3.15795e9i	−0.0504876	−	0.00879917i
$775$	2.31197e11			0.640878
$776$			4.85413e11i			1.33864i
$777$			3.39749e11i			0.932125i
$778$	3.31554e11			0.904974
$779$			6.43004e11i			1.74608i
$780$	1.49160e9			0.00402972
$781$			1.63481e11i			0.439402i
$782$			4.58635e10i			0.122642i
$783$	−6.26184e11			−1.66592
$784$	6.49093e10			0.171808
$785$	−2.22714e11			−0.586500
$786$		−	1.73313e11i		−	0.454089i
$787$	−5.05846e10			−0.131862			−0.0659309	−	0.997824i	$-0.521002\pi$
$787$	−5.05846e10			−0.131862			−0.0659309	+	0.997824i	$0.521002\pi$
$788$	5.88271e10			0.152571
$789$	−4.27702e11			−1.10366
$790$	4.08083e10			0.104771
$791$	1.49797e11			0.382647
$792$		−	3.38723e10i		−	0.0860883i
$793$		−	4.65443e9i		−	0.0117699i
$794$		−	4.55648e11i		−	1.14643i
$795$	−1.74548e11			−0.436964
$796$		−	2.45638e11i		−	0.611849i
$797$	9.69494e10			0.240277			0.120138	−	0.992757i	$-0.461666\pi$
$797$	9.69494e10			0.240277			0.120138	+	0.992757i	$0.461666\pi$
$798$	−3.51050e11			−0.865680
$799$	4.17847e11			1.02525
$800$			2.93452e11i			0.716435i
$801$		−	1.69516e10i		−	0.0411795i
$802$			1.79943e11i			0.434949i
$803$		−	1.23116e11i		−	0.296110i
$804$		−	2.59022e10i		−	0.0619886i
$805$	2.92536e10			0.0696621
$806$		−	4.38461e9i		−	0.0103894i
$807$		−	4.53141e11i		−	1.06841i
$808$		−	2.68998e11i		−	0.631107i
$809$	2.26260e11			0.528219			0.264110	−	0.964493i	$-0.414922\pi$
$809$	2.26260e11			0.528219			0.264110	+	0.964493i	$0.414922\pi$
$810$	−1.23853e11			−0.287718
$811$		−	3.66726e11i		−	0.847731i	−0.905725	−	0.423865i	$-0.860673\pi$
$811$		−	3.66726e11i		−	0.847731i	0.905725	−	0.423865i	$-0.139327\pi$
$812$	−4.68407e11			−1.07746
$813$			3.84818e11i			0.880833i
$814$	−2.52473e11			−0.575065
$815$	3.41535e11			0.774114
$816$		−	1.47145e11i		−	0.331884i
$817$	4.27340e11	+	7.44784e10i	0.959148	+	0.167164i
$818$	5.06227e11			1.13066
$819$			8.01467e8i			0.00178135i
$820$			1.83146e11i			0.405080i
$821$	5.96621e11			1.31318			0.656592	−	0.754246i	$-0.271997\pi$
$821$	5.96621e11			1.31318			0.656592	+	0.754246i	$0.271997\pi$
$822$			5.68480e11i			1.24517i
$823$	6.85970e11			1.49522			0.747612	−	0.664136i	$-0.231200\pi$
$823$	6.85970e11			1.49522			0.747612	+	0.664136i	$0.231200\pi$
$824$			9.24782e11i			2.00600i
$825$			3.98568e11i			0.860372i
$826$	6.31380e11			1.35635
$827$	1.16755e11			0.249605			0.124802	−	0.992182i	$-0.460170\pi$
$827$	1.16755e11			0.249605			0.124802	+	0.992182i	$0.460170\pi$
$828$	−2.07326e9			−0.00441094
$829$			4.41596e11i			0.934990i	0.883996	+	0.467495i	$0.154843\pi$
$829$			4.41596e11i			0.934990i	−0.883996	+	0.467495i	$0.845157\pi$
$830$	2.41446e11			0.508754
$831$	−5.10033e11			−1.06953
$832$	7.64841e9			0.0159617
$833$	5.18067e11			1.07598
$834$	−1.21650e11			−0.251447
$835$		−	2.86061e11i		−	0.588453i
$836$			2.68994e11i			0.550703i
$837$		−	4.05158e11i		−	0.825511i
$838$	6.52728e10			0.132360
$839$		−	4.98702e11i		−	1.00645i	−0.864155	−	0.503226i	$-0.832146\pi$
$839$		−	4.98702e11i		−	1.00645i	0.864155	−	0.503226i	$-0.167854\pi$
$840$	−2.96947e11			−0.596433
$841$	−8.00525e11			−1.60026
$842$	−4.54304e11			−0.903853
$843$		−	4.44475e11i		−	0.880110i
$844$		−	3.59620e10i		−	0.0708719i
$845$			2.26757e11i			0.444768i
$846$		−	1.83183e10i		−	0.0357605i
$847$		−	1.63527e11i		−	0.317728i
$848$	−1.23755e11			−0.239320
$849$			2.11980e11i			0.408004i
$850$		−	4.31632e11i		−	0.826872i
$851$			4.58933e10i			0.0875046i
$852$	−1.01572e11			−0.192759
$853$	−5.90043e11			−1.11452			−0.557260	−	0.830338i	$-0.688147\pi$
$853$	−5.90043e11			−1.11452			−0.557260	+	0.830338i	$0.688147\pi$
$854$			3.12007e11i			0.586588i
$855$	−1.69076e10			−0.0316387
$856$		−	3.09823e11i		−	0.577057i
$857$	−3.07077e11			−0.569278			−0.284639	−	0.958635i	$-0.591874\pi$
$857$	−3.07077e11			−0.569278			−0.284639	+	0.958635i	$0.591874\pi$
$858$	7.55875e9			0.0139477
$859$			3.98532e11i			0.731965i	0.930622	+	0.365983i	$0.119267\pi$
$859$			3.98532e11i			0.731965i	−0.930622	+	0.365983i	$0.880733\pi$
$860$	1.21719e11	+	2.12135e10i	0.222517	+	0.0387810i
$861$	1.24893e12			2.27261
$862$		−	1.39387e11i		−	0.252461i
$863$		−	8.10893e11i		−	1.46191i	−0.682426	−	0.730955i	$-0.739075\pi$
$863$		−	8.10893e11i		−	1.46191i	0.682426	−	0.730955i	$-0.260925\pi$
$864$	5.14255e11			0.922834
$865$		−	4.99377e10i		−	0.0891999i
$866$	−4.55569e11			−0.809995
$867$		−	6.30416e11i		−	1.11571i
$868$		−	3.03072e11i		−	0.533909i
$869$	−2.13237e11			−0.373925
$870$	−2.77670e11			−0.484676
$871$	−1.35257e9			−0.00235010
$872$			1.06557e11i			0.184297i
$873$	5.36833e10			0.0924234
$874$	−4.74198e10			−0.0812670
$875$	−6.18577e11			−1.05527
$876$	7.64930e10			0.129899
$877$	2.92778e11			0.494926			0.247463	−	0.968897i	$-0.420403\pi$
$877$	2.92778e11			0.494926			0.247463	+	0.968897i	$0.420403\pi$
$878$			4.86168e11i			0.818104i
$879$		−	1.32097e11i		−	0.221278i
$880$		−	6.97454e10i		−	0.116301i
$881$	−3.96387e10			−0.0657984			−0.0328992	−	0.999459i	$-0.510474\pi$
$881$	−3.96387e10			−0.0657984			−0.0328992	+	0.999459i	$0.510474\pi$
$882$		−	2.27119e10i		−	0.0375301i
$883$	2.37019e11			0.389889			0.194944	−	0.980814i	$-0.437547\pi$
$883$	2.37019e11			0.389889			0.194944	+	0.980814i	$0.437547\pi$
$884$	8.44073e9			0.0138220
$885$	−3.85935e11			−0.629131
$886$			6.31619e10i			0.102499i
$887$		−	3.27646e11i		−	0.529310i	−0.964343	−	0.264655i	$-0.914742\pi$
$887$		−	3.27646e11i		−	0.529310i	0.964343	−	0.264655i	$-0.0852581\pi$
$888$		−	4.65852e11i		−	0.749197i
$889$		−	1.29998e12i		−	2.08128i
$890$		−	1.10433e11i		−	0.176011i
$891$	6.47176e11			1.02686
$892$			9.80335e10i			0.154851i
$893$			4.32026e11i			0.679366i
$894$			7.60969e10i			0.119129i
$895$	−1.74975e11			−0.272698
$896$	2.45037e11			0.380190
$897$		−	1.37400e9i		−	0.00212234i
$898$	3.59051e11			0.552142
$899$		−	8.41635e11i		−	1.28850i
$900$	1.95119e10			0.0297392
$901$	−9.87736e11			−1.49879
$902$			9.28096e11i			1.40206i
$903$	1.44662e11	−	8.30037e11i	0.217572	−	1.24838i
$904$	−2.05397e11			−0.307553
$905$		−	1.91129e11i		−	0.284926i
$906$		−	5.04006e11i		−	0.748037i
$907$	3.22719e11			0.476865			0.238432	−	0.971159i	$-0.423366\pi$
$907$	3.22719e11			0.476865			0.238432	+	0.971159i	$0.423366\pi$
$908$			3.49458e11i			0.514105i
$909$	−2.97493e10			−0.0435733
$910$			5.22126e9i			0.00761394i
$911$			3.01171e11i			0.437260i	0.975808	+	0.218630i	$0.0701588\pi$
$911$			3.01171e11i			0.437260i	−0.975808	+	0.218630i	$0.929841\pi$
$912$	1.52139e11			0.219918
$913$	−1.26164e12			−1.81573
$914$	8.15218e11			1.16812
$915$		−	1.90716e11i		−	0.272084i
$916$	−8.09898e10			−0.115040
$917$	−6.25562e11			−0.884694
$918$	−7.56408e11			−1.06509
$919$	−2.30684e11			−0.323411			−0.161706	−	0.986839i	$-0.551699\pi$
$919$	−2.30684e11			−0.323411			−0.161706	+	0.986839i	$0.551699\pi$
$920$	−4.01116e10			−0.0559910
$921$			8.39545e10i			0.116682i
$922$			5.81387e11i			0.804528i
$923$			5.30391e9i			0.00730785i
$924$	5.22476e11			0.716768
$925$		−	4.31913e11i		−	0.589969i
$926$	−3.63536e11			−0.494428
$927$	1.02274e11			0.138499
$928$	1.06826e12			1.44041
$929$			7.61974e11i			1.02300i	0.859282	+	0.511502i	$0.170911\pi$
$929$			7.61974e11i			1.02300i	−0.859282	+	0.511502i	$0.829089\pi$
$930$		−	1.79660e11i		−	0.240171i
$931$			5.35647e11i			0.712985i
$932$			1.72826e11i			0.229058i
$933$			5.39692e11i			0.712229i
$934$	−3.50150e11			−0.460115
$935$		−	5.56666e11i		−	0.728364i
$936$		−	1.09894e9i		−	0.00143176i
$937$			3.07766e11i			0.399266i	0.979871	+	0.199633i	$0.0639750\pi$
$937$			3.07766e11i			0.399266i	−0.979871	+	0.199633i	$0.936025\pi$
$938$	9.06688e10			0.117124
$939$	−3.80212e11			−0.489061
$940$			1.23053e11i			0.157609i
$941$	−9.51909e11			−1.21405			−0.607026	−	0.794682i	$-0.707638\pi$
$941$	−9.51909e11			−1.21405			−0.607026	+	0.794682i	$0.707638\pi$
$942$		−	7.01213e11i		−	0.890525i
$943$	1.68705e11			0.213344
$944$	−2.73629e11			−0.344567
$945$			4.82469e11i			0.604981i
$946$	6.16813e11	+	1.07500e11i	0.770174	+	0.134229i
$947$	4.01176e11			0.498810			0.249405	−	0.968399i	$-0.419765\pi$
$947$	4.01176e11			0.498810			0.249405	+	0.968399i	$0.419765\pi$
$948$		−	1.32486e11i		−	0.164035i
$949$		−	3.99434e9i		−	0.00492470i
$950$	4.46279e11			0.547914
$951$			3.29879e11i			0.403304i
$952$	−1.68037e12			−2.04577
$953$		−	3.56865e11i		−	0.432646i	−0.976322	−	0.216323i	$-0.930594\pi$
$953$		−	3.56865e11i		−	0.432646i	0.976322	−	0.216323i	$-0.0694064\pi$
$954$			4.33021e10i			0.0522776i
$955$	4.02065e11			0.483374
$956$	−2.41217e11			−0.288786
$957$	1.45092e12			1.72980
$958$		−	1.04480e11i		−	0.124042i
$959$	2.05189e12			2.42594
$960$	3.13395e11			0.368984
$961$	−3.08330e11			−0.361512
$962$	−8.19114e9			−0.00956410
$963$	−3.42643e10			−0.0398416
$964$		−	3.26755e11i		−	0.378368i
$965$			6.13056e11i			0.706954i
$966$			9.21050e10i			0.105773i
$967$	−1.50708e12			−1.72358			−0.861788	−	0.507268i	$-0.830655\pi$
$967$	−1.50708e12			−1.72358			−0.861788	+	0.507268i	$0.830655\pi$
$968$			2.24223e11i			0.255375i
$969$	1.21428e12			1.37728
$970$	3.49727e11			0.395041
$971$	1.37739e12			1.54946			0.774731	−	0.632291i	$-0.217885\pi$
$971$	1.37739e12			1.54946			0.774731	+	0.632291i	$0.217885\pi$
$972$		−	6.60593e10i		−	0.0740063i
$973$			4.39087e11i			0.489891i
$974$		−	1.03934e12i		−	1.15484i
$975$			1.29310e10i			0.0143091i
$976$		−	1.35218e11i		−	0.149017i
$977$	−6.81980e11			−0.748503			−0.374251	−	0.927327i	$-0.622100\pi$
$977$	−6.81980e11			−0.748503			−0.374251	+	0.927327i	$0.622100\pi$
$978$			1.07532e12i			1.17539i
$979$			5.77052e11i			0.628181i
$980$			1.52567e11i			0.165408i
$981$	1.17845e10			0.0127243
$982$	−5.96339e10			−0.0641279
$983$			5.00165e11i			0.535673i	0.963464	+	0.267836i	$0.0863086\pi$
$983$			5.00165e11i			0.535673i	−0.963464	+	0.267836i	$0.913691\pi$
$984$	−1.71248e12			−1.82661
$985$		−	1.25870e11i		−	0.133714i
$986$	−1.57129e12			−1.66245
$987$	8.39138e11			0.884229
$988$			8.72716e9i			0.00915894i
$989$	1.95409e10	−	1.12121e11i	0.0204249	−	0.117193i
$990$	−2.44041e10			−0.0254051
$991$		−	5.26328e11i		−	0.545710i	−0.962055	−	0.272855i	$-0.912032\pi$
$991$		−	5.26328e11i		−	0.545710i	0.962055	−	0.272855i	$-0.0879680\pi$
$992$			6.91195e11i			0.713763i
$993$	7.84636e11			0.806996
$994$		−	3.55545e11i		−	0.364208i
$995$	−5.25583e11			−0.536227
$996$		−	7.83865e11i		−	0.796533i
$997$			1.63339e12i			1.65314i	0.562834	+	0.826570i	$0.309711\pi$
$997$			1.63339e12i			1.65314i	−0.562834	+	0.826570i	$0.690289\pi$
$998$	2.01746e11			0.203368
$999$	−7.56900e11			−0.759935

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.9.b.b.42.19	yes	28
43.42	odd	2	inner	43.9.b.b.42.10	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.9.b.b.42.10	✓	28	43.42	odd	2	inner
43.9.b.b.42.19	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)

\(f(q)\)	\(=\)	\(q+11.2266i q^{2} -77.9859i q^{3} +129.962 q^{4} -278.075i q^{5} +875.519 q^{6} -3160.13i q^{7} +4333.06i q^{8} +479.207 q^{9} +O(q^{10})\)	\(q+11.2266i q^{2} -77.9859i q^{3} +129.962 q^{4} -278.075i q^{5} +875.519 q^{6} -3160.13i q^{7} +4333.06i q^{8} +479.207 q^{9} +3121.85 q^{10} -16312.7 q^{11} -10135.2i q^{12} -529.246 q^{13} +35477.7 q^{14} -21685.9 q^{15} -15375.4 q^{16} -122717. q^{17} +5379.88i q^{18} -126881. i q^{19} -36139.4i q^{20} -246446. q^{21} -183137. i q^{22} -33289.9 q^{23} +337918. q^{24} +313299. q^{25} -5941.65i q^{26} -549037. i q^{27} -410699. i q^{28} -1.14051e6i q^{29} -243460. i q^{30} +737944. q^{31} +936650. i q^{32} +1.27216e6i q^{33} -1.37770e6i q^{34} -878755. q^{35} +62278.9 q^{36} -1.37860e6i q^{37} +1.42445e6 q^{38} +41273.7i q^{39} +1.20492e6 q^{40} -5.06776e6 q^{41} -2.76676e6i q^{42} +(-586993. + 3.36803e6i) q^{43} -2.12004e6 q^{44} -133256. i q^{45} -373734. i q^{46} -3.40496e6 q^{47} +1.19906e6i q^{48} -4.22164e6 q^{49} +3.51730e6i q^{50} +9.57019e6i q^{51} -68782.1 q^{52} +8.04889e6 q^{53} +6.16384e6 q^{54} +4.53617e6i q^{55} +1.36931e7 q^{56} -9.89495e6 q^{57} +1.28041e7 q^{58} +1.77965e7 q^{59} -2.81836e6 q^{60} +8.79447e6i q^{61} +8.28463e6i q^{62} -1.51436e6i q^{63} -1.44515e7 q^{64} +147170. i q^{65} -1.42821e7 q^{66} +2.55566e6 q^{67} -1.59486e7 q^{68} +2.59614e6i q^{69} -9.86547e6i q^{70} -1.00216e7i q^{71} +2.07643e6i q^{72} +7.54723e6i q^{73} +1.54770e7 q^{74} -2.44329e7i q^{75} -1.64898e7i q^{76} +5.15505e7i q^{77} -463365. q^{78} +1.30718e7 q^{79} +4.27551e6i q^{80} -3.96730e7 q^{81} -5.68939e7i q^{82} +7.73406e7 q^{83} -3.20287e7 q^{84} +3.41246e7i q^{85} +(-3.78117e7 - 6.58996e6i) q^{86} -8.89439e7 q^{87} -7.06842e7i q^{88} -3.53743e7i q^{89} +1.49601e6 q^{90} +1.67249e6i q^{91} -4.32643e6 q^{92} -5.75492e7i q^{93} -3.82263e7i q^{94} -3.52826e7 q^{95} +7.30455e7 q^{96} +1.12025e8 q^{97} -4.73948e7i q^{98} -7.81718e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9}+O(q^{10}) \) 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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