LMFDB - Embedded newform 43.9.b.b.42.7

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			42.7
Character	$\chi$	$=$	43.42
Dual form			43.9.b.b.42.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-23.0076i q^{2} -78.5211i q^{3} -273.350 q^{4} -548.269i q^{5} -1806.58 q^{6} -2213.93i q^{7} +399.191i q^{8} +395.432 q^{9} +O(q^{10})$	\(q-23.0076i q^{2} -78.5211i q^{3} -273.350 q^{4} -548.269i q^{5} -1806.58 q^{6} -2213.93i q^{7} +399.191i q^{8} +395.432 q^{9} -12614.4 q^{10} -22302.0 q^{11} +21463.8i q^{12} +25711.7 q^{13} -50937.3 q^{14} -43050.7 q^{15} -60793.3 q^{16} +94860.8 q^{17} -9097.95i q^{18} -13775.7i q^{19} +149870. i q^{20} -173841. q^{21} +513115. i q^{22} +444307. q^{23} +31345.0 q^{24} +90025.7 q^{25} -591564. i q^{26} -546227. i q^{27} +605180. i q^{28} +843909. i q^{29} +990495. i q^{30} +557250. q^{31} +1.50090e6i q^{32} +1.75117e6i q^{33} -2.18252e6i q^{34} -1.21383e6 q^{35} -108092. q^{36} +1.34789e6i q^{37} -316945. q^{38} -2.01891e6i q^{39} +218864. q^{40} -2.42209e6 q^{41} +3.99966e6i q^{42} +(-493656. - 3.38297e6i) q^{43} +6.09625e6 q^{44} -216803. i q^{45} -1.02224e7i q^{46} -4.12862e6 q^{47} +4.77356e6i q^{48} +863301. q^{49} -2.07128e6i q^{50} -7.44857e6i q^{51} -7.02829e6 q^{52} +717126. q^{53} -1.25674e7 q^{54} +1.22275e7i q^{55} +883783. q^{56} -1.08168e6 q^{57} +1.94163e7 q^{58} -1.58674e7 q^{59} +1.17679e7 q^{60} -1.76056e7i q^{61} -1.28210e7i q^{62} -875460. i q^{63} +1.89691e7 q^{64} -1.40969e7i q^{65} +4.02904e7 q^{66} +2.33402e7 q^{67} -2.59302e7 q^{68} -3.48875e7i q^{69} +2.79274e7i q^{70} +1.27010e7i q^{71} +157853. i q^{72} -4.05442e6i q^{73} +3.10116e7 q^{74} -7.06892e6i q^{75} +3.76559e6i q^{76} +4.93750e7i q^{77} -4.64503e7 q^{78} -6.41487e7 q^{79} +3.33311e7i q^{80} -4.02959e7 q^{81} +5.57265e7i q^{82} -4.42985e7 q^{83} +4.75194e7 q^{84} -5.20092e7i q^{85} +(-7.78341e7 + 1.13579e7i) q^{86} +6.62647e7 q^{87} -8.90275e6i q^{88} +8.42809e7i q^{89} -4.98813e6 q^{90} -5.69239e7i q^{91} -1.21451e8 q^{92} -4.37559e7i q^{93} +9.49898e7i q^{94} -7.55278e6 q^{95} +1.17852e8 q^{96} +6.90318e7 q^{97} -1.98625e7i q^{98} -8.81891e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	23.0076i		−	1.43798i	−0.695022	−	0.718988i	$-0.744606\pi$
$2$		−	23.0076i		−	1.43798i	0.695022	−	0.718988i	$-0.255394\pi$
$3$		−	78.5211i		−	0.969397i	−0.874681	−	0.484698i	$-0.838929\pi$
$3$		−	78.5211i		−	0.969397i	0.874681	−	0.484698i	$-0.161071\pi$
$4$	−273.350			−1.06778
$5$		−	548.269i		−	0.877231i	−0.898675	−	0.438616i	$-0.855469\pi$
$5$		−	548.269i		−	0.877231i	0.898675	−	0.438616i	$-0.144531\pi$
$6$	−1806.58			−1.39397
$7$		−	2213.93i		−	0.922088i	−0.887377	−	0.461044i	$-0.847475\pi$
$7$		−	2213.93i		−	0.922088i	0.887377	−	0.461044i	$-0.152525\pi$
$8$			399.191i			0.0974589i
$9$	395.432			0.0602701
$10$	−12614.4			−1.26144
$11$	−22302.0			−1.52325			−0.761627	−	0.648016i	$-0.775599\pi$
$11$	−22302.0			−1.52325			−0.761627	+	0.648016i	$0.775599\pi$
$12$			21463.8i			1.03510i
$13$	25711.7			0.900237			0.450118	−	0.892969i	$-0.351382\pi$
$13$	25711.7			0.900237			0.450118	+	0.892969i	$0.351382\pi$
$14$	−50937.3			−1.32594
$15$	−43050.7			−0.850385
$16$	−60793.3			−0.927632
$17$	94860.8			1.13577			0.567886	−	0.823107i	$-0.307762\pi$
$17$	94860.8			1.13577			0.567886	+	0.823107i	$0.307762\pi$
$18$		−	9097.95i		−	0.0866670i
$19$		−	13775.7i		−	0.105706i	−0.998602	−	0.0528528i	$-0.983169\pi$
$19$		−	13775.7i		−	0.105706i	0.998602	−	0.0528528i	$-0.0168314\pi$
$20$			149870.i			0.936685i
$21$	−173841.			−0.893869
$22$			513115.i			2.19040i
$23$	444307.			1.58771			0.793856	−	0.608106i	$-0.208070\pi$
$23$	444307.			1.58771			0.793856	+	0.608106i	$0.208070\pi$
$24$	31345.0			0.0944763
$25$	90025.7			0.230466
$26$		−	591564.i		−	1.29452i
$27$		−	546227.i		−	1.02782i
$28$			605180.i			0.984582i
$29$			843909.i			1.19317i	0.802549	+	0.596587i	$0.203477\pi$
$29$			843909.i			1.19317i	−0.802549	+	0.596587i	$0.796523\pi$
$30$			990495.i			1.22283i
$31$	557250.			0.603398			0.301699	−	0.953403i	$-0.402446\pi$
$31$	557250.			0.603398			0.301699	+	0.953403i	$0.402446\pi$
$32$			1.50090e6i			1.43137i
$33$			1.75117e6i			1.47664i
$34$		−	2.18252e6i		−	1.63321i
$35$	−1.21383e6			−0.808884
$36$	−108092.			−0.0643549
$37$			1.34789e6i			0.719194i	0.933108	+	0.359597i	$0.117086\pi$
$37$			1.34789e6i			0.719194i	−0.933108	+	0.359597i	$0.882914\pi$
$38$	−316945.			−0.152002
$39$		−	2.01891e6i		−	0.872687i
$40$	218864.			0.0854939
$41$	−2.42209e6			−0.857146			−0.428573	−	0.903507i	$-0.640984\pi$
$41$	−2.42209e6			−0.857146			−0.428573	+	0.903507i	$0.640984\pi$
$42$			3.99966e6i			1.28536i
$43$	−493656.	−	3.38297e6i	−0.144395	−	0.989520i
$43$	−493656.	−	3.38297e6i	−0.144395	−	0.989520i
$44$	6.09625e6			1.62649
$45$		−	216803.i		−	0.0528708i
$46$		−	1.02224e7i		−	2.28309i
$47$	−4.12862e6			−0.846084			−0.423042	−	0.906110i	$-0.639038\pi$
$47$	−4.12862e6			−0.846084			−0.423042	+	0.906110i	$0.639038\pi$
$48$			4.77356e6i			0.899243i
$49$	863301.			0.149754
$50$		−	2.07128e6i		−	0.331404i
$51$		−	7.44857e6i		−	1.10101i
$52$	−7.02829e6			−0.961250
$53$	717126.			0.0908849			0.0454425	−	0.998967i	$-0.485530\pi$
$53$	717126.			0.0908849			0.0454425	+	0.998967i	$0.485530\pi$
$54$	−1.25674e7			−1.47798
$55$			1.22275e7i			1.33625i
$56$	883783.			0.0898656
$57$	−1.08168e6			−0.102471
$58$	1.94163e7			1.71575
$59$	−1.58674e7			−1.30947			−0.654737	−	0.755856i	$-0.727221\pi$
$59$	−1.58674e7			−1.30947			−0.654737	+	0.755856i	$0.727221\pi$
$60$	1.17679e7			0.908020
$61$		−	1.76056e7i		−	1.27154i	−0.771877	−	0.635772i	$-0.780682\pi$
$61$		−	1.76056e7i		−	1.27154i	0.771877	−	0.635772i	$-0.219318\pi$
$62$		−	1.28210e7i		−	0.867671i
$63$		−	875460.i		−	0.0555743i
$64$	1.89691e7			1.13065
$65$		−	1.40969e7i		−	0.789716i
$66$	4.02904e7			2.12337
$67$	2.33402e7			1.15826			0.579129	−	0.815236i	$-0.303393\pi$
$67$	2.33402e7			1.15826			0.579129	+	0.815236i	$0.303393\pi$
$68$	−2.59302e7			−1.21275
$69$		−	3.48875e7i		−	1.53912i
$70$			2.79274e7i			1.16316i
$71$			1.27010e7i			0.499811i	0.968270	+	0.249905i	$0.0803995\pi$
$71$			1.27010e7i			0.499811i	−0.968270	+	0.249905i	$0.919600\pi$
$72$			157853.i			0.00587386i
$73$		−	4.05442e6i		−	0.142770i	−0.997449	−	0.0713851i	$-0.977258\pi$
$73$		−	4.05442e6i		−	0.142770i	0.997449	−	0.0713851i	$-0.0227419\pi$
$74$	3.10116e7			1.03418
$75$		−	7.06892e6i		−	0.223413i
$76$			3.76559e6i			0.112870i
$77$			4.93750e7i			1.40457i
$78$	−4.64503e7			−1.25490
$79$	−6.41487e7			−1.64695			−0.823473	−	0.567356i	$-0.807966\pi$
$79$	−6.41487e7			−1.64695			−0.823473	+	0.567356i	$0.807966\pi$
$80$			3.33311e7i			0.813747i
$81$	−4.02959e7			−0.936097
$82$			5.57265e7i			1.23256i
$83$	−4.42985e7			−0.933420			−0.466710	−	0.884410i	$-0.654561\pi$
$83$	−4.42985e7			−0.933420			−0.466710	+	0.884410i	$0.654561\pi$
$84$	4.75194e7			0.954451
$85$		−	5.20092e7i		−	0.996334i
$86$	−7.78341e7	+	1.13579e7i	−1.42291	+	0.207636i
$87$	6.62647e7			1.15666
$88$		−	8.90275e6i		−	0.148455i
$89$			8.42809e7i			1.34329i	0.740874	+	0.671644i	$0.234412\pi$
$89$			8.42809e7i			1.34329i	−0.740874	+	0.671644i	$0.765588\pi$
$90$	−4.98813e6			−0.0760270
$91$		−	5.69239e7i		−	0.830098i
$92$	−1.21451e8			−1.69532
$93$		−	4.37559e7i		−	0.584932i
$94$			9.49898e7i			1.21665i
$95$	−7.55278e6			−0.0927283
$96$	1.17852e8			1.38757
$97$	6.90318e7			0.779762			0.389881	−	0.920865i	$-0.372516\pi$
$97$	6.90318e7			0.779762			0.389881	+	0.920865i	$0.372516\pi$
$98$		−	1.98625e7i		−	0.215342i
$99$	−8.81891e6			−0.0918067
$100$	−2.46086e7			−0.246086
$101$	5.71873e6			0.0549558			0.0274779	−	0.999622i	$-0.491252\pi$
$101$	5.71873e6			0.0549558			0.0274779	+	0.999622i	$0.491252\pi$
$102$	−1.71374e8			−1.58323
$103$	4.67582e7			0.415441			0.207720	−	0.978188i	$-0.433396\pi$
$103$	4.67582e7			0.415441			0.207720	+	0.978188i	$0.433396\pi$
$104$			1.02639e7i			0.0877361i
$105$			9.53114e7i			0.784130i
$106$		−	1.64994e7i		−	0.130690i
$107$	1.33766e8			1.02050			0.510248	−	0.860027i	$-0.329554\pi$
$107$	1.33766e8			1.02050			0.510248	+	0.860027i	$0.329554\pi$
$108$			1.49311e8i			1.09748i
$109$	9.33602e7			0.661387			0.330694	−	0.943738i	$-0.392717\pi$
$109$	9.33602e7			0.661387			0.330694	+	0.943738i	$0.392717\pi$
$110$	2.81325e8			1.92149
$111$	1.05837e8			0.697184
$112$			1.34592e8i			0.855358i
$113$		−	2.60559e8i		−	1.59806i	−0.601294	−	0.799028i	$-0.705348\pi$
$113$		−	2.60559e8i		−	1.59806i	0.601294	−	0.799028i	$-0.294652\pi$
$114$			2.48869e7i			0.147350i
$115$		−	2.43600e8i		−	1.39279i
$116$		−	2.30683e8i		−	1.27404i
$117$	1.01672e7			0.0542574
$118$			3.65071e8i			1.88299i
$119$		−	2.10015e8i		−	1.04728i
$120$		−	1.71855e7i		−	0.0828775i
$121$	2.83018e8			1.32030
$122$	−4.05063e8			−1.82845
$123$			1.90185e8i			0.830914i
$124$	−1.52325e8			−0.644293
$125$		−	2.63526e8i		−	1.07940i
$126$	−2.01423e7			−0.0799146
$127$	2.42053e8			0.930457			0.465229	−	0.885191i	$-0.345972\pi$
$127$	2.42053e8			0.930457			0.465229	+	0.885191i	$0.345972\pi$
$128$		−	5.22027e7i		−	0.194470i
$129$	−2.65635e8	+	3.87624e7i	−0.959238	+	0.139976i
$130$	−3.24337e8			−1.13559
$131$			3.17260e7i			0.107728i	0.998548	+	0.0538642i	$0.0171538\pi$
$131$			3.17260e7i			0.107728i	−0.998548	+	0.0538642i	$0.982846\pi$
$132$		−	4.78684e8i		−	1.57672i
$133$	−3.04984e7			−0.0974700
$134$		−	5.37003e8i		−	1.66555i
$135$	−2.99479e8			−0.901638
$136$			3.78676e7i			0.110691i
$137$		−	4.48682e7i		−	0.127367i	−0.997970	−	0.0636834i	$-0.979715\pi$
$137$		−	4.48682e7i		−	0.127367i	0.997970	−	0.0636834i	$-0.0202848\pi$
$138$	−8.02678e8			−2.21322
$139$	2.23751e8			0.599384			0.299692	−	0.954036i	$-0.403116\pi$
$139$	2.23751e8			0.599384			0.299692	+	0.954036i	$0.403116\pi$
$140$	3.31801e8			0.863706
$141$			3.24184e8i			0.820191i
$142$	2.92220e8			0.718716
$143$	−5.73421e8			−1.37129
$144$	−2.40396e7			−0.0559085
$145$	4.62689e8			1.04669
$146$	−9.32826e7			−0.205300
$147$		−	6.77874e7i		−	0.145171i
$148$		−	3.68445e8i		−	0.767937i
$149$			5.16841e8i			1.04861i	0.851532	+	0.524303i	$0.175674\pi$
$149$			5.16841e8i			1.04861i	−0.851532	+	0.524303i	$0.824326\pi$
$150$	−1.62639e8			−0.321262
$151$		−	2.26895e8i		−	0.436432i	−0.975900	−	0.218216i	$-0.929976\pi$
$151$		−	2.26895e8i		−	0.436432i	0.975900	−	0.218216i	$-0.0700238\pi$
$152$	5.49913e6			0.0103020
$153$	3.75110e7			0.0684531
$154$	1.13600e9			2.01974
$155$		−	3.05523e8i		−	0.529319i
$156$			5.51870e8i			0.931833i
$157$			1.47899e8i			0.243426i	0.992565	+	0.121713i	$0.0388387\pi$
$157$			1.47899e8i			0.243426i	−0.992565	+	0.121713i	$0.961161\pi$
$158$			1.47591e9i			2.36827i
$159$		−	5.63095e7i		−	0.0881035i
$160$	8.22898e8			1.25564
$161$		−	9.83666e8i		−	1.46401i
$162$			9.27113e8i			1.34609i
$163$			5.39395e8i			0.764111i	0.924139	+	0.382056i	$0.124784\pi$
$163$			5.39395e8i			0.764111i	−0.924139	+	0.382056i	$0.875216\pi$
$164$	6.62079e8			0.915239
$165$	9.60116e8			1.29535
$166$			1.01920e9i			1.34224i
$167$	−1.17007e9			−1.50434			−0.752171	−	0.658968i	$-0.770993\pi$
$167$	−1.17007e9			−1.50434			−0.752171	+	0.658968i	$0.770993\pi$
$168$		−	6.93957e7i		−	0.0871155i
$169$	−1.54641e8			−0.189573
$170$	−1.19661e9			−1.43270
$171$		−	5.44734e6i		−	0.00637089i
$172$	1.34941e8	+	9.24737e8i	0.154181	+	1.05658i
$173$	−7.41901e7			−0.0828250			−0.0414125	−	0.999142i	$-0.513186\pi$
$173$	−7.41901e7			−0.0828250			−0.0414125	+	0.999142i	$0.513186\pi$
$174$		−	1.52459e9i		−	1.66325i
$175$		−	1.99311e8i		−	0.212510i
$176$	1.35581e9			1.41302
$177$			1.24592e9i			1.26940i
$178$	1.93910e9			1.93162
$179$		−	1.95172e9i		−	1.90110i	−0.310566	−	0.950552i	$-0.600519\pi$
$179$		−	1.95172e9i		−	1.90110i	0.310566	−	0.950552i	$-0.399481\pi$
$180$			5.92633e7i			0.0564541i
$181$	−1.70935e9			−1.59264			−0.796319	−	0.604877i	$-0.793222\pi$
$181$	−1.70935e9			−1.59264			−0.796319	+	0.604877i	$0.793222\pi$
$182$	−1.30968e9			−1.19366
$183$	−1.38241e9			−1.23263
$184$			1.77363e8i			0.154737i
$185$	7.39004e8			0.630899
$186$	−1.00672e9			−0.841118
$187$	−2.11558e9			−1.73007
$188$	1.12856e9			0.903428
$189$	−1.20931e9			−0.947743
$190$			1.73771e8i			0.133341i
$191$			2.52030e9i			1.89373i	0.321628	+	0.946866i	$0.395770\pi$
$191$			2.52030e9i			1.89373i	−0.321628	+	0.946866i	$0.604230\pi$
$192$		−	1.48947e9i		−	1.09604i
$193$	1.25620e9			0.905380			0.452690	−	0.891668i	$-0.350464\pi$
$193$	1.25620e9			0.905380			0.452690	+	0.891668i	$0.350464\pi$
$194$		−	1.58826e9i		−	1.12128i
$195$	−1.10691e9			−0.765548
$196$	−2.35984e8			−0.159903
$197$	7.03003e8			0.466758			0.233379	−	0.972386i	$-0.425022\pi$
$197$	7.03003e8			0.466758			0.233379	+	0.972386i	$0.425022\pi$
$198$			2.02902e8i			0.132016i
$199$			1.62062e9i			1.03340i	0.856166	+	0.516701i	$0.172840\pi$
$199$			1.62062e9i			1.03340i	−0.856166	+	0.516701i	$0.827160\pi$
$200$			3.59375e7i			0.0224609i
$201$		−	1.83270e9i		−	1.12281i
$202$		−	1.31574e8i		−	0.0790252i
$203$	1.86836e9			1.10021
$204$			2.03607e9i			1.17563i
$205$			1.32796e9i			0.751915i
$206$		−	1.07579e9i		−	0.597394i
$207$	1.75693e8			0.0956916
$208$	−1.56310e9			−0.835088
$209$			3.07224e8i			0.161017i
$210$	2.19289e9			1.12756
$211$			2.02893e8i			0.102362i	0.998689	+	0.0511808i	$0.0162985\pi$
$211$			2.02893e8i			0.102362i	−0.998689	+	0.0511808i	$0.983702\pi$
$212$	−1.96027e8			−0.0970446
$213$	9.97299e8			0.484515
$214$		−	3.07764e9i		−	1.46745i
$215$	−1.85478e9	+	2.70657e8i	−0.868038	+	0.126667i
$216$	2.18049e8			0.100170
$217$		−	1.23371e9i		−	0.556386i
$218$		−	2.14800e9i		−	0.951059i
$219$	−3.18358e8			−0.138401
$220$		−	3.34239e9i		−	1.42681i
$221$	2.43903e9			1.02246
$222$		−	2.43507e9i		−	1.00253i
$223$		−	2.20052e9i		−	0.889827i	−0.895573	−	0.444914i	$-0.853234\pi$
$223$		−	2.20052e9i		−	0.889827i	0.895573	−	0.444914i	$-0.146766\pi$
$224$	3.32289e9			1.31985
$225$	3.55990e7			0.0138902
$226$	−5.99484e9			−2.29797
$227$		−	3.11333e9i		−	1.17252i	−0.810122	−	0.586262i	$-0.800599\pi$
$227$		−	3.11333e9i		−	1.17252i	0.810122	−	0.586262i	$-0.199401\pi$
$228$	2.95678e8			0.109416
$229$	4.08434e9			1.48518			0.742592	−	0.669744i	$-0.233596\pi$
$229$	4.08434e9			1.48518			0.742592	+	0.669744i	$0.233596\pi$
$230$	−5.60465e9			−2.00280
$231$	3.87698e9			1.36159
$232$	−3.36881e8			−0.116285
$233$			3.98505e9i			1.35210i	0.736854	+	0.676052i	$0.236311\pi$
$233$			3.98505e9i			1.35210i	−0.736854	+	0.676052i	$0.763689\pi$
$234$		−	2.33924e8i		−	0.0780208i
$235$			2.26360e9i			0.742212i
$236$	4.33735e9			1.39822
$237$			5.03702e9i			1.59654i
$238$	−4.83195e9			−1.50596
$239$	3.61698e9			1.10855			0.554274	−	0.832334i	$-0.312996\pi$
$239$	3.61698e9			1.10855			0.554274	+	0.832334i	$0.312996\pi$
$240$	2.61719e9			0.788844
$241$			5.13891e9i			1.52336i	0.647953	+	0.761680i	$0.275625\pi$
$241$			5.13891e9i			1.52336i	−0.647953	+	0.761680i	$0.724375\pi$
$242$		−	6.51158e9i		−	1.89856i
$243$		−	4.19713e8i		−	0.120373i
$244$			4.81250e9i			1.35772i
$245$		−	4.73321e8i		−	0.131369i
$246$	4.37571e9			1.19483
$247$		−	3.54195e8i		−	0.0951602i
$248$			2.22450e8i			0.0588064i
$249$			3.47837e9i			0.904854i
$250$	−6.06311e9			−1.55216
$251$	3.59876e9			0.906688			0.453344	−	0.891336i	$-0.350231\pi$
$251$	3.59876e9			0.906688			0.453344	+	0.891336i	$0.350231\pi$
$252$			2.39307e8i			0.0593409i
$253$	−9.90891e9			−2.41849
$254$		−	5.56907e9i		−	1.33798i
$255$	−4.08382e9			−0.965843
$256$	3.65503e9			0.851002
$257$		−	3.58551e9i		−	0.821898i	−0.911658	−	0.410949i	$-0.865197\pi$
$257$		−	3.58551e9i		−	0.821898i	0.911658	−	0.410949i	$-0.134803\pi$
$258$	8.91832e8	+	6.11162e9i	0.201282	+	1.37936i
$259$	2.98413e9			0.663160
$260$			3.85340e9i			0.843239i
$261$			3.33709e8i			0.0719127i
$262$	7.29939e8			0.154911
$263$		−	2.72133e9i		−	0.568799i	−0.958706	−	0.284400i	$-0.908206\pi$
$263$		−	2.72133e9i		−	0.568799i	0.958706	−	0.284400i	$-0.0917942\pi$
$264$	−6.99054e8			−0.143911
$265$		−	3.93178e8i		−	0.0797271i
$266$			7.01696e8i			0.140159i
$267$	6.61783e9			1.30218
$268$	−6.38006e9			−1.23676
$269$	−5.51586e9			−1.05343			−0.526713	−	0.850043i	$-0.676576\pi$
$269$	−5.51586e9			−1.05343			−0.526713	+	0.850043i	$0.676576\pi$
$270$			6.89031e9i			1.29653i
$271$	−2.83300e9			−0.525255			−0.262627	−	0.964897i	$-0.584589\pi$
$271$	−2.83300e9			−0.525255			−0.262627	+	0.964897i	$0.584589\pi$
$272$	−5.76689e9			−1.05358
$273$	−4.46973e9			−0.804694
$274$	−1.03231e9			−0.183150
$275$	−2.00775e9			−0.351058
$276$			9.53650e9i			1.64344i
$277$		−	9.20304e9i		−	1.56319i	−0.623785	−	0.781596i	$-0.714406\pi$
$277$		−	9.20304e9i		−	1.56319i	0.623785	−	0.781596i	$-0.285594\pi$
$278$		−	5.14797e9i		−	0.861900i
$279$	2.20355e8			0.0363668
$280$		−	4.84551e8i		−	0.0788329i
$281$	4.72092e9			0.757184			0.378592	−	0.925564i	$-0.376408\pi$
$281$	4.72092e9			0.757184			0.378592	+	0.925564i	$0.376408\pi$
$282$	7.45870e9			1.17942
$283$	1.11248e9			0.173439			0.0867194	−	0.996233i	$-0.472362\pi$
$283$	1.11248e9			0.173439			0.0867194	+	0.996233i	$0.472362\pi$
$284$		−	3.47183e9i		−	0.533685i
$285$			5.93053e8i			0.0898905i
$286$			1.31930e10i			1.97188i
$287$			5.36234e9i			0.790364i
$288$			5.93505e8i			0.0862689i
$289$	2.02281e9			0.289976
$290$		−	1.06454e10i		−	1.50511i
$291$		−	5.42045e9i		−	0.755899i
$292$			1.10828e9i			0.152446i
$293$	−6.59517e9			−0.894860			−0.447430	−	0.894319i	$-0.647661\pi$
$293$	−6.59517e9			−0.894860			−0.447430	+	0.894319i	$0.647661\pi$
$294$	−1.55963e9			−0.208752
$295$			8.69960e9i			1.14871i
$296$	−5.38064e8			−0.0700918
$297$			1.21819e10i			1.56563i
$298$	1.18913e10			1.50787
$299$	1.14239e10			1.42932
$300$			1.93229e9i			0.238555i
$301$	−7.48968e9	+	1.09292e9i	−0.912425	+	0.133144i
$302$	−5.22031e9			−0.627579
$303$		−	4.49041e8i		−	0.0532740i
$304$			8.37468e8i			0.0980559i
$305$	−9.65261e9			−1.11544
$306$		−	8.63039e8i		−	0.0984339i
$307$	2.40305e9			0.270526			0.135263	−	0.990810i	$-0.456812\pi$
$307$	2.40305e9			0.270526			0.135263	+	0.990810i	$0.456812\pi$
$308$		−	1.34967e10i		−	1.49977i
$309$		−	3.67151e9i		−	0.402727i
$310$	−7.02936e9			−0.761148
$311$	1.25145e10			1.33774			0.668870	−	0.743380i	$-0.266778\pi$
$311$	1.25145e10			1.33774			0.668870	+	0.743380i	$0.266778\pi$
$312$	8.05931e8			0.0850510
$313$			2.72482e9i			0.283897i	0.989874	+	0.141948i	$0.0453367\pi$
$313$			2.72482e9i			0.283897i	−0.989874	+	0.141948i	$0.954663\pi$
$314$	3.40280e9			0.350040
$315$	−4.79988e8			−0.0487515
$316$	1.75351e10			1.75857
$317$	2.40399e9			0.238065			0.119033	−	0.992890i	$-0.462021\pi$
$317$	2.40399e9			0.238065			0.119033	+	0.992890i	$0.462021\pi$
$318$	−1.29555e9			−0.126691
$319$		−	1.88208e10i		−	1.81751i
$320$		−	1.04002e10i		−	0.991837i
$321$		−	1.05035e10i		−	0.989265i
$322$	−2.26318e10			−2.10521
$323$		−	1.30677e9i		−	0.120057i
$324$	1.10149e10			0.999541
$325$	2.31471e9			0.207474
$326$	1.24102e10			1.09877
$327$		−	7.33075e9i		−	0.641147i
$328$		−	9.66878e8i		−	0.0835365i
$329$			9.14049e9i			0.780164i
$330$		−	2.20900e10i		−	1.86268i
$331$			1.85040e10i			1.54153i	0.637118	+	0.770766i	$0.280126\pi$
$331$			1.85040e10i			1.54153i	−0.637118	+	0.770766i	$0.719874\pi$
$332$	1.21090e10			0.996683
$333$			5.32997e8i			0.0433459i
$334$			2.69206e10i			2.16321i
$335$		−	1.27967e10i		−	1.01606i
$336$	1.05683e10			0.829181
$337$	1.84917e10			1.43370			0.716849	−	0.697229i	$-0.245584\pi$
$337$	1.84917e10			1.43370			0.716849	+	0.697229i	$0.245584\pi$
$338$			3.55792e9i			0.272602i
$339$	−2.04594e10			−1.54915
$340$			1.42167e10i			1.06386i
$341$	−1.24278e10			−0.919128
$342$	−1.25330e8			−0.00916119
$343$		−	1.46742e10i		−	1.06017i
$344$	1.35045e9	−	1.97063e8i	0.0964375	−	0.0140725i
$345$	−1.91277e10			−1.35017
$346$			1.70694e9i			0.119100i
$347$			2.21431e9i			0.152729i	0.997080	+	0.0763643i	$0.0243312\pi$
$347$			2.21431e9i			0.152729i	−0.997080	+	0.0763643i	$0.975669\pi$
$348$	−1.81135e10			−1.23505
$349$		−	1.01146e10i		−	0.681787i	−0.940102	−	0.340893i	$-0.889270\pi$
$349$		−	1.01146e10i		−	0.681787i	0.940102	−	0.340893i	$-0.110730\pi$
$350$	−4.58567e9			−0.305584
$351$		−	1.40444e10i		−	0.925284i
$352$		−	3.34730e10i		−	2.18034i
$353$	−1.17769e10			−0.758461			−0.379230	−	0.925302i	$-0.623811\pi$
$353$	−1.17769e10			−0.758461			−0.379230	+	0.925302i	$0.623811\pi$
$354$	2.86658e10			1.82537
$355$	6.96359e9			0.438449
$356$		−	2.30382e10i		−	1.43433i
$357$	−1.64906e10			−1.01523
$358$	−4.49045e10			−2.73374
$359$	−2.45068e9			−0.147540			−0.0737700	−	0.997275i	$-0.523503\pi$
$359$	−2.45068e9			−0.147540			−0.0737700	+	0.997275i	$0.523503\pi$
$360$	8.65461e7			0.00515273
$361$	1.67938e10			0.988826
$362$			3.93281e10i			2.29017i
$363$		−	2.22229e10i		−	1.27990i
$364$			1.55602e10i			0.886358i
$365$	−2.22291e9			−0.125242
$366$			3.18060e10i			1.77249i
$367$	1.88958e10			1.04160			0.520800	−	0.853678i	$-0.325634\pi$
$367$	1.88958e10			1.04160			0.520800	+	0.853678i	$0.325634\pi$
$368$	−2.70109e10			−1.47281
$369$	−9.57772e8			−0.0516603
$370$		−	1.70027e10i		−	0.907218i
$371$		−	1.58767e9i		−	0.0838039i
$372$			1.19607e10i			0.624575i
$373$			6.77386e9i			0.349946i	0.984573	+	0.174973i	$0.0559838\pi$
$373$			6.77386e9i			0.349946i	−0.984573	+	0.174973i	$0.944016\pi$
$374$			4.86745e10i			2.48780i
$375$	−2.06924e10			−1.04637
$376$		−	1.64811e9i		−	0.0824584i
$377$			2.16983e10i			1.07414i
$378$			2.78233e10i			1.36283i
$379$	−3.86135e10			−1.87147			−0.935735	−	0.352704i	$-0.885262\pi$
$379$	−3.86135e10			−1.87147			−0.935735	+	0.352704i	$0.885262\pi$
$380$	2.06456e9			0.0990130
$381$		−	1.90063e10i		−	0.901982i
$382$	5.79861e10			2.72314
$383$		−	3.90536e10i		−	1.81495i	−0.420101	−	0.907477i	$-0.638005\pi$
$383$		−	3.90536e10i		−	1.81495i	0.420101	−	0.907477i	$-0.361995\pi$
$384$	−4.09901e9			−0.188519
$385$	2.70708e10			1.23214
$386$		−	2.89023e10i		−	1.30192i
$387$	−1.95208e8	−	1.33774e9i	−0.00870268	−	0.0596385i
$388$	−1.88699e10			−0.832610
$389$			2.51473e10i			1.09823i	0.835747	+	0.549115i	$0.185035\pi$
$389$			2.51473e10i			1.09823i	−0.835747	+	0.549115i	$0.814965\pi$
$390$			2.54673e10i			1.10084i
$391$	4.21473e10			1.80328
$392$			3.44622e8i			0.0145948i
$393$	2.49116e9			0.104432
$394$		−	1.61744e10i		−	0.671187i
$395$			3.51707e10i			1.44475i
$396$	2.41065e9			0.0980289
$397$	3.45068e10			1.38913			0.694565	−	0.719430i	$-0.255597\pi$
$397$	3.45068e10			1.38913			0.694565	+	0.719430i	$0.255597\pi$
$398$	3.72866e10			1.48601
$399$			2.39477e9i			0.0944870i
$400$	−5.47295e9			−0.213787
$401$	2.43097e10			0.940162			0.470081	−	0.882623i	$-0.344225\pi$
$401$	2.43097e10			0.940162			0.470081	+	0.882623i	$0.344225\pi$
$402$	−4.21661e10			−1.61458
$403$	1.43278e10			0.543201
$404$	−1.56322e9			−0.0586805
$405$			2.20930e10i			0.821174i
$406$		−	4.29865e10i		−	1.58208i
$407$		−	3.00605e10i		−	1.09552i
$408$	2.97341e9			0.107303
$409$			2.52284e10i			0.901564i	0.892634	+	0.450782i	$0.148855\pi$
$409$			2.52284e10i			0.901564i	−0.892634	+	0.450782i	$0.851145\pi$
$410$	3.05531e10			1.08124
$411$	−3.52310e9			−0.123469
$412$	−1.27814e10			−0.443597
$413$			3.51293e10i			1.20745i
$414$		−	4.04228e9i		−	0.137602i
$415$			2.42875e10i			0.818825i
$416$			3.85907e10i			1.28857i
$417$		−	1.75692e10i		−	0.581041i
$418$	7.06850e9			0.231538
$419$		−	4.21693e10i		−	1.36817i	−0.729402	−	0.684085i	$-0.760202\pi$
$419$		−	4.21693e10i		−	1.36817i	0.729402	−	0.684085i	$-0.239798\pi$
$420$		−	2.60534e10i		−	0.837274i
$421$			2.56731e10i			0.817239i	0.912705	+	0.408620i	$0.133990\pi$
$421$			2.56731e10i			0.817239i	−0.912705	+	0.408620i	$0.866010\pi$
$422$	4.66808e9			0.147194
$423$	−1.63259e9			−0.0509936
$424$			2.86270e8i			0.00885754i
$425$	8.53990e9			0.261756
$426$		−	2.29455e10i		−	0.696721i
$427$	−3.89776e10			−1.17248
$428$	−3.65650e10			−1.08966
$429$			4.50256e10i			1.32932i
$430$	6.22716e9	+	4.26741e10i	0.182145	+	1.24822i
$431$	−4.50399e10			−1.30523			−0.652617	−	0.757688i	$-0.726329\pi$
$431$	−4.50399e10			−1.30523			−0.652617	+	0.757688i	$0.726329\pi$
$432$			3.32069e10i			0.953440i
$433$		−	3.23102e10i		−	0.919153i	−0.888138	−	0.459577i	$-0.848001\pi$
$433$		−	3.23102e10i		−	0.919153i	0.888138	−	0.459577i	$-0.151999\pi$
$434$	−2.83848e10			−0.800069
$435$		−	3.63309e10i		−	1.01466i
$436$	−2.55201e10			−0.706213
$437$		−	6.12062e9i		−	0.167830i
$438$			7.32465e9i			0.199017i
$439$	2.51931e10			0.678303			0.339151	−	0.940732i	$-0.389860\pi$
$439$	2.51931e10			0.678303			0.339151	+	0.940732i	$0.389860\pi$
$440$	−4.88111e9			−0.130229
$441$	3.41377e8			0.00902568
$442$		−	5.61162e10i		−	1.47028i
$443$	−5.96388e10			−1.54851			−0.774255	−	0.632874i	$-0.781875\pi$
$443$	−5.96388e10			−1.54851			−0.774255	+	0.632874i	$0.781875\pi$
$444$	−2.89307e10			−0.744436
$445$	4.62086e10			1.17837
$446$	−5.06287e10			−1.27955
$447$	4.05830e10			1.01651
$448$		−	4.19963e10i		−	1.04255i
$449$		−	4.63343e10i		−	1.14003i	−0.821633	−	0.570016i	$-0.806937\pi$
$449$		−	4.63343e10i		−	1.14003i	0.821633	−	0.570016i	$-0.193063\pi$
$450$		−	8.19049e8i		−	0.0199738i
$451$	5.40173e10			1.30565
$452$			7.12239e10i			1.70636i
$453$	−1.78160e10			−0.423076
$454$	−7.16303e10			−1.68606
$455$	−3.12096e10			−0.728187
$456$		−	4.31798e8i		−	0.00998668i
$457$			2.64600e10i			0.606631i	0.952890	+	0.303316i	$0.0980937\pi$
$457$			2.64600e10i			0.606631i	−0.952890	+	0.303316i	$0.901906\pi$
$458$		−	9.39710e10i		−	2.13566i
$459$		−	5.18155e10i		−	1.16737i
$460$			6.65881e10i			1.48719i
$461$	−4.70971e10			−1.04278			−0.521388	−	0.853320i	$-0.674585\pi$
$461$	−4.70971e10			−1.04278			−0.521388	+	0.853320i	$0.674585\pi$
$462$		−	8.92002e10i		−	1.95793i
$463$			4.28757e10i			0.933013i	0.884518	+	0.466507i	$0.154488\pi$
$463$			4.28757e10i			0.933013i	−0.884518	+	0.466507i	$0.845512\pi$
$464$		−	5.13040e10i		−	1.10683i
$465$	−2.39900e10			−0.513120
$466$	9.16865e10			1.94429
$467$		−	5.17139e10i		−	1.08727i	−0.839320	−	0.543637i	$-0.817047\pi$
$467$		−	5.17139e10i		−	1.08727i	0.839320	−	0.543637i	$-0.182953\pi$
$468$	−2.77921e9			−0.0579347
$469$		−	5.16737e10i		−	1.06802i
$470$	5.20800e10			1.06728
$471$	1.16132e10			0.235976
$472$		−	6.33412e9i		−	0.127620i
$473$	1.10095e10	+	7.54469e10i	0.219950	+	1.50729i
$474$	1.15890e11			2.29579
$475$		−	1.24016e9i		−	0.0243615i
$476$			5.74078e10i			1.11826i
$477$	2.83575e8			0.00547764
$478$		−	8.32181e10i		−	1.59407i
$479$	5.36737e10			1.01958			0.509788	−	0.860300i	$-0.329724\pi$
$479$	5.36737e10			1.01958			0.509788	+	0.860300i	$0.329724\pi$
$480$		−	6.46149e10i		−	1.21722i
$481$			3.46564e10i			0.647445i
$482$	1.18234e11			2.19055
$483$	−7.72385e10			−1.41921
$484$	−7.73632e10			−1.40979
$485$		−	3.78480e10i		−	0.684031i
$486$	−9.65660e9			−0.173093
$487$	3.86141e10			0.686483			0.343242	−	0.939247i	$-0.388475\pi$
$487$	3.86141e10			0.686483			0.343242	+	0.939247i	$0.388475\pi$
$488$	7.02800e9			0.123923
$489$	4.23539e10			0.740727
$490$	−1.08900e10			−0.188905
$491$			8.61031e10i			1.48147i	0.671797	+	0.740735i	$0.265523\pi$
$491$			8.61031e10i			1.48147i	−0.671797	+	0.740735i	$0.734477\pi$
$492$		−	5.19872e10i		−	0.887230i
$493$			8.00538e10i			1.35517i
$494$	−8.14919e9			−0.136838
$495$			4.83514e9i			0.0805357i
$496$	−3.38771e10			−0.559731
$497$	2.81192e10			0.460869
$498$	8.00290e10			1.30116
$499$		−	7.90191e10i		−	1.27447i	−0.770669	−	0.637235i	$-0.780078\pi$
$499$		−	7.90191e10i		−	1.27447i	0.770669	−	0.637235i	$-0.219922\pi$
$500$			7.20350e10i			1.15256i
$501$			9.18753e10i			1.45830i
$502$		−	8.27988e10i		−	1.30380i
$503$			9.92805e10i			1.55093i	0.631391	+	0.775464i	$0.282484\pi$
$503$			9.92805e10i			1.55093i	−0.631391	+	0.775464i	$0.717516\pi$
$504$	3.49476e8			0.00541621
$505$		−	3.13540e9i		−	0.0482090i
$506$			2.27980e11i			3.47773i
$507$			1.21426e10i			0.183772i
$508$	−6.61654e10			−0.993519
$509$	−8.82552e10			−1.31483			−0.657414	−	0.753529i	$-0.728350\pi$
$509$	−8.82552e10			−1.31483			−0.657414	+	0.753529i	$0.728350\pi$
$510$			9.39591e10i			1.38886i
$511$	−8.97622e9			−0.131647
$512$		−	9.74573e10i		−	1.41819i
$513$	−7.52464e9			−0.108647
$514$	−8.24940e10			−1.18187
$515$		−	2.56361e10i		−	0.364437i
$516$	7.26114e10	−	1.05957e10i	1.02425	−	0.149462i
$517$	9.20764e10			1.28880
$518$		−	6.86577e10i		−	0.953608i
$519$			5.82549e9i			0.0802903i
$520$	5.62737e9			0.0769648
$521$			3.93047e10i			0.533450i	0.963773	+	0.266725i	$0.0859415\pi$
$521$			3.93047e10i			0.533450i	−0.963773	+	0.266725i	$0.914059\pi$
$522$	7.67784e9			0.103409
$523$		−	1.06896e11i		−	1.42875i	−0.699763	−	0.714375i	$-0.746711\pi$
$523$		−	1.06896e11i		−	1.42875i	0.699763	−	0.714375i	$-0.253289\pi$
$524$		−	8.67231e9i		−	0.115030i
$525$	−1.56501e10			−0.206006
$526$	−6.26114e10			−0.817920
$527$	5.28612e10			0.685322
$528$		−	1.06460e11i		−	1.36978i
$529$	1.19098e11			1.52083
$530$	−9.04609e9			−0.114646
$531$	−6.27447e9			−0.0789222
$532$	8.33675e9			0.104076
$533$	−6.22760e10			−0.771634
$534$		−	1.52261e11i		−	1.87250i
$535$		−	7.33399e10i		−	0.895211i
$536$			9.31721e9i			0.112883i
$537$	−1.53251e11			−1.84292
$538$			1.26907e11i			1.51480i
$539$	−1.92533e10			−0.228113
$540$	8.18628e10			0.962746
$541$	−1.27179e11			−1.48466			−0.742331	−	0.670034i	$-0.766280\pi$
$541$	−1.27179e11			−1.48466			−0.742331	+	0.670034i	$0.766280\pi$
$542$			6.51807e10i			0.755304i
$543$			1.34220e11i			1.54390i
$544$			1.42377e11i			1.62571i
$545$		−	5.11866e10i		−	0.580190i
$546$			1.02838e11i			1.15713i
$547$	−1.10966e11			−1.23949			−0.619744	−	0.784804i	$-0.712763\pi$
$547$	−1.10966e11			−1.23949			−0.619744	+	0.784804i	$0.712763\pi$
$548$			1.22647e10i			0.135999i
$549$		−	6.96182e9i		−	0.0766361i
$550$			4.61935e10i			0.504813i
$551$	1.16254e10			0.126125
$552$	1.39268e10			0.150001
$553$			1.42021e11i			1.51863i
$554$	−2.11740e11			−2.24783
$555$		−	5.80275e10i		−	0.611592i
$556$	−6.11624e10			−0.640007
$557$	1.70704e10			0.177347			0.0886734	−	0.996061i	$-0.471737\pi$
$557$	1.70704e10			0.177347			0.0886734	+	0.996061i	$0.471737\pi$
$558$		−	5.06984e9i		−	0.0522946i
$559$	−1.26927e10	−	8.69819e10i	−0.129989	−	0.890803i
$560$	7.37928e10			0.750346
$561$			1.66118e11i			1.67712i
$562$		−	1.08617e11i		−	1.08881i
$563$	6.49015e10			0.645983			0.322992	−	0.946402i	$-0.395311\pi$
$563$	6.49015e10			0.645983			0.322992	+	0.946402i	$0.395311\pi$
$564$		−	8.86159e10i		−	0.875780i
$565$	−1.42856e11			−1.40186
$566$		−	2.55955e10i		−	0.249401i
$567$			8.92125e10i			0.863164i
$568$	−5.07014e9			−0.0487110
$569$	−9.81338e10			−0.936202			−0.468101	−	0.883675i	$-0.655062\pi$
$569$	−9.81338e10			−0.936202			−0.468101	+	0.883675i	$0.655062\pi$
$570$	1.36447e10			0.129260
$571$			1.38488e10i			0.130277i	0.997876	+	0.0651385i	$0.0207489\pi$
$571$			1.38488e10i			0.130277i	−0.997876	+	0.0651385i	$0.979251\pi$
$572$	1.56745e11			1.46423
$573$	1.97897e11			1.83578
$574$	1.23375e11			1.13652
$575$	3.99990e10			0.365913
$576$	7.50098e9			0.0681441
$577$		−	1.02819e11i		−	0.927621i	−0.885934	−	0.463811i	$-0.846482\pi$
$577$		−	1.02819e11i		−	0.927621i	0.885934	−	0.463811i	$-0.153518\pi$
$578$		−	4.65399e10i		−	0.416979i
$579$		−	9.86386e10i		−	0.877673i
$580$	−1.26476e11			−1.11763
$581$			9.80740e10i			0.860695i
$582$	−1.24712e11			−1.08696
$583$	−1.59933e10			−0.138441
$584$	1.61849e9			0.0139142
$585$		−	5.57438e9i		−	0.0475963i
$586$			1.51739e11i			1.28679i
$587$			2.83893e10i			0.239113i	0.992827	+	0.119556i	$0.0381472\pi$
$587$			2.83893e10i			0.239113i	−0.992827	+	0.119556i	$0.961853\pi$
$588$			1.85297e10i			0.155010i
$589$		−	7.67650e9i		−	0.0637826i
$590$	2.00157e11			1.65182
$591$		−	5.52006e10i		−	0.452474i
$592$		−	8.19424e10i		−	0.667147i
$593$			1.97060e11i			1.59360i	0.604242	+	0.796801i	$0.293476\pi$
$593$			1.97060e11i			1.59360i	−0.604242	+	0.796801i	$0.706524\pi$
$594$	2.80277e11			2.25134
$595$	−1.15145e11			−0.918707
$596$		−	1.41279e11i		−	1.11968i
$597$	1.27253e11			1.00178
$598$		−	2.62836e11i		−	2.05532i
$599$	1.92220e11			1.49311			0.746553	−	0.665326i	$-0.231708\pi$
$599$	1.92220e11			1.49311			0.746553	+	0.665326i	$0.231708\pi$
$600$	2.82185e9			0.0217735
$601$		−	7.87414e10i		−	0.603539i	−0.953381	−	0.301769i	$-0.902423\pi$
$601$		−	7.87414e10i		−	0.603539i	0.953381	−	0.301769i	$-0.0975772\pi$
$602$	2.51455e10	+	1.72320e11i	0.191459	+	1.31204i
$603$	9.22947e9			0.0698084
$604$			6.20218e10i			0.466012i
$605$		−	1.55170e11i		−	1.15821i
$606$	−1.03314e10			−0.0766067
$607$		−	1.66376e11i		−	1.22556i	−0.790252	−	0.612781i	$-0.790051\pi$
$607$		−	1.66376e11i		−	1.22556i	0.790252	−	0.612781i	$-0.209949\pi$
$608$	2.06759e10			0.151304
$609$		−	1.46706e11i		−	1.06654i
$610$			2.22084e11i			1.60397i
$611$	−1.06154e11			−0.761676
$612$	−1.02536e10			−0.0730925
$613$	1.70299e11			1.20606			0.603031	−	0.797718i	$-0.293960\pi$
$613$	1.70299e11			1.20606			0.603031	+	0.797718i	$0.293960\pi$
$614$		−	5.52885e10i		−	0.389011i
$615$	1.04273e11			0.728904
$616$	−1.97101e10			−0.136888
$617$	−2.65299e11			−1.83060			−0.915302	−	0.402767i	$-0.868048\pi$
$617$	−2.65299e11			−1.83060			−0.915302	+	0.402767i	$0.868048\pi$
$618$	−8.44726e10			−0.579111
$619$	−1.78200e11			−1.21379			−0.606896	−	0.794781i	$-0.707586\pi$
$619$	−1.78200e11			−1.21379			−0.606896	+	0.794781i	$0.707586\pi$
$620$			8.35149e10i			0.565194i
$621$		−	2.42692e11i		−	1.63189i
$622$		−	2.87929e11i		−	1.92364i
$623$	1.86592e11			1.23863
$624$			1.22736e11i			0.809532i
$625$	−1.09317e11			−0.716420
$626$	6.26916e10			0.408236
$627$	2.41236e10			0.156089
$628$		−	4.04282e10i		−	0.259924i
$629$			1.27861e11i			0.816840i
$630$			1.10434e10i			0.0701035i
$631$		−	1.59654e11i		−	1.00708i	−0.863973	−	0.503538i	$-0.832031\pi$
$631$		−	1.59654e11i		−	1.00708i	0.863973	−	0.503538i	$-0.167969\pi$
$632$		−	2.56076e10i		−	0.160509i
$633$	1.59314e10			0.0992290
$634$		−	5.53101e10i		−	0.342332i
$635$		−	1.32711e11i		−	0.816226i
$636$			1.53922e10i			0.0940747i
$637$	2.21969e10			0.134814
$638$	−4.33022e11			−2.61353
$639$			5.02240e9i			0.0301236i
$640$	−2.86211e10			−0.170595
$641$			2.14549e10i			0.127085i	0.997979	+	0.0635425i	$0.0202398\pi$
$641$			2.14549e10i			0.127085i	−0.997979	+	0.0635425i	$0.979760\pi$
$642$	−2.41660e11			−1.42254
$643$	1.26797e11			0.741763			0.370882	−	0.928680i	$-0.379056\pi$
$643$	1.26797e11			0.741763			0.370882	+	0.928680i	$0.379056\pi$
$644$			2.68885e11i			1.56323i
$645$	2.12523e10	+	1.45639e11i	0.122791	+	0.841473i
$646$	−3.00657e10			−0.172640
$647$			2.05924e11i			1.17514i	0.809173	+	0.587570i	$0.199916\pi$
$647$			2.05924e11i			1.17514i	−0.809173	+	0.587570i	$0.800084\pi$
$648$		−	1.60858e10i		−	0.0912310i
$649$	3.53874e11			1.99466
$650$		−	5.32560e10i		−	0.298342i
$651$	−9.68727e10			−0.539358
$652$		−	1.47444e11i		−	0.815899i
$653$		−	9.69391e10i		−	0.533146i	−0.963815	−	0.266573i	$-0.914109\pi$
$653$		−	9.69391e10i		−	0.533146i	0.963815	−	0.266573i	$-0.0858913\pi$
$654$	−1.68663e11			−0.921954
$655$	1.73944e10			0.0945026
$656$	1.47247e11			0.795116
$657$		−	1.60325e9i		−	0.00860477i
$658$	2.10301e11			1.12186
$659$	−2.33344e11			−1.23725			−0.618623	−	0.785688i	$-0.712309\pi$
$659$	−2.33344e11			−1.23725			−0.618623	+	0.785688i	$0.712309\pi$
$660$	−2.62448e11			−1.38314
$661$	9.21767e10			0.482854			0.241427	−	0.970419i	$-0.422385\pi$
$661$	9.21767e10			0.482854			0.241427	+	0.970419i	$0.422385\pi$
$662$	4.25732e11			2.21669
$663$		−	1.91515e11i		−	0.991172i
$664$		−	1.76836e10i		−	0.0909700i
$665$			1.67213e10i			0.0855037i
$666$	1.22630e10			0.0623304
$667$			3.74954e11i			1.89442i
$668$	3.19839e11			1.60630
$669$	−1.72787e11			−0.862596
$670$	−2.94422e11			−1.46107
$671$			3.92639e11i			1.93688i
$672$		−	2.60917e11i		−	1.27946i
$673$			8.74582e10i			0.426324i	0.977017	+	0.213162i	$0.0683763\pi$
$673$			8.74582e10i			0.426324i	−0.977017	+	0.213162i	$0.931624\pi$
$674$		−	4.25450e11i		−	2.06162i
$675$		−	4.91744e10i		−	0.236878i
$676$	4.22712e10			0.202422
$677$		−	1.78736e11i		−	0.850861i	−0.904991	−	0.425430i	$-0.860123\pi$
$677$		−	1.78736e11i		−	0.850861i	0.904991	−	0.425430i	$-0.139877\pi$
$678$			4.70721e11i			2.22764i
$679$		−	1.52832e11i		−	0.719009i
$680$	2.07616e10			0.0971016
$681$	−2.44462e11			−1.13664
$682$			2.85933e11i			1.32168i
$683$	5.16028e10			0.237132			0.118566	−	0.992946i	$-0.462170\pi$
$683$	5.16028e10			0.237132			0.118566	+	0.992946i	$0.462170\pi$
$684$			1.48903e9i			0.00680268i
$685$	−2.45998e10			−0.111730
$686$	−3.37618e11			−1.52450
$687$		−	3.20707e11i		−	1.43973i
$688$	3.00110e10	+	2.05662e11i	0.133945	+	0.917910i
$689$	1.84385e10			0.0818180
$690$			4.40084e11i			1.94151i
$691$			1.07652e11i			0.472183i	0.971731	+	0.236091i	$0.0758665\pi$
$691$			1.07652e11i			0.472183i	−0.971731	+	0.236091i	$0.924134\pi$
$692$	2.02799e10			0.0884385
$693$			1.95245e10i			0.0846538i
$694$	5.09460e10			0.219620
$695$		−	1.22676e11i		−	0.525798i
$696$			2.64523e10i			0.112727i
$697$	−2.29761e11			−0.973522
$698$	−2.32714e11			−0.980393
$699$	3.12911e11			1.31073
$700$			5.44817e10i			0.226913i
$701$	2.84901e11			1.17984			0.589918	−	0.807463i	$-0.299160\pi$
$701$	2.84901e11			1.17984			0.589918	+	0.807463i	$0.299160\pi$
$702$	−3.23128e11			−1.33054
$703$	1.85680e10			0.0760229
$704$	−4.23048e11			−1.72226
$705$	1.77740e11			0.719497
$706$			2.70959e11i			1.09065i
$707$		−	1.26609e10i		−	0.0506741i
$708$		−	3.40574e11i		−	1.35543i
$709$	1.31805e11			0.521611			0.260805	−	0.965391i	$-0.416012\pi$
$709$	1.31805e11			0.521611			0.260805	+	0.965391i	$0.416012\pi$
$710$		−	1.60216e11i		−	0.630480i
$711$	−2.53664e10			−0.0992616
$712$	−3.36442e10			−0.130915
$713$	2.47590e11			0.958021
$714$			3.79410e11i			1.45988i
$715$			3.14389e11i			1.20294i
$716$			5.33504e11i			2.02995i
$717$		−	2.84010e11i		−	1.07462i
$718$			5.63844e10i			0.212159i
$719$	4.05208e11			1.51622			0.758110	−	0.652127i	$-0.226123\pi$
$719$	4.05208e11			1.51622			0.758110	+	0.652127i	$0.226123\pi$
$720$			1.31802e10i			0.0490446i
$721$		−	1.03520e11i		−	0.383073i
$722$		−	3.86385e11i		−	1.42191i
$723$	4.03513e11			1.47674
$724$	4.67252e11			1.70058
$725$			7.59735e10i			0.274986i
$726$	−5.11297e11			−1.84046
$727$		−	5.30950e10i		−	0.190071i	−0.995474	−	0.0950355i	$-0.969704\pi$
$727$		−	5.30950e10i		−	0.190071i	0.995474	−	0.0950355i	$-0.0302965\pi$
$728$	2.27235e10			0.0809004
$729$	−2.97338e11			−1.05279
$730$			5.11440e10i			0.180096i
$731$	−4.68286e10	−	3.20911e11i	−0.163999	−	1.12387i
$732$	3.77883e11			1.31617
$733$		−	2.64810e11i		−	0.917314i	−0.888613	−	0.458657i	$-0.848331\pi$
$733$		−	2.64810e11i		−	0.917314i	0.888613	−	0.458657i	$-0.151669\pi$
$734$		−	4.34748e11i		−	1.49780i
$735$	−3.71657e10			−0.127348
$736$			6.66861e11i			2.27260i
$737$	−5.20532e11			−1.76432
$738$			2.20361e10i			0.0742862i
$739$			3.49177e11i			1.17076i	0.810759	+	0.585381i	$0.199055\pi$
$739$			3.49177e11i			1.17076i	−0.810759	+	0.585381i	$0.800945\pi$
$740$	−2.02007e11			−0.673659
$741$	−2.78118e10			−0.0922480
$742$	−3.65285e10			−0.120508
$743$		−	3.40681e11i		−	1.11787i	−0.829210	−	0.558937i	$-0.811209\pi$
$743$		−	3.40681e11i		−	1.11787i	0.829210	−	0.558937i	$-0.188791\pi$
$744$	1.74670e10			0.0570068
$745$	2.83368e11			0.919869
$746$	1.55850e11			0.503214
$747$	−1.75171e10			−0.0562573
$748$	5.78295e11			1.84732
$749$		−	2.96149e11i		−	0.940987i
$750$			4.76082e11i			1.50465i
$751$		−	1.73741e11i		−	0.546188i	−0.961987	−	0.273094i	$-0.911953\pi$
$751$		−	1.73741e11i		−	0.546188i	0.961987	−	0.273094i	$-0.0880470\pi$
$752$	2.50992e11			0.784855
$753$		−	2.82579e11i		−	0.878940i
$754$	4.99226e11			1.54459
$755$	−1.24400e11			−0.382852
$756$	3.30565e11			1.01198
$757$			5.97510e11i			1.81954i	0.415114	+	0.909769i	$0.363742\pi$
$757$			5.97510e11i			1.81954i	−0.415114	+	0.909769i	$0.636258\pi$
$758$			8.88406e11i			2.69113i
$759$			7.78059e11i			2.34447i
$760$		−	3.01501e9i		−	0.00903720i
$761$			3.40017e11i			1.01382i	0.861998	+	0.506912i	$0.169213\pi$
$761$			3.40017e11i			1.01382i	−0.861998	+	0.506912i	$0.830787\pi$
$762$	−4.37290e11			−1.29703
$763$		−	2.06693e11i		−	0.609857i
$764$		−	6.88925e11i		−	2.02208i
$765$		−	2.05661e10i		−	0.0600491i
$766$	−8.98530e11			−2.60986
$767$	−4.07977e11			−1.17884
$768$		−	2.86997e11i		−	0.824959i
$769$	3.42285e11			0.978774			0.489387	−	0.872067i	$-0.337221\pi$
$769$	3.42285e11			0.978774			0.489387	+	0.872067i	$0.337221\pi$
$770$		−	6.22835e11i		−	1.77178i
$771$	−2.81538e11			−0.796746
$772$	−3.43384e11			−0.966742
$773$			3.41450e10i			0.0956332i	0.998856	+	0.0478166i	$0.0152263\pi$
$773$			3.41450e10i			0.0956332i	−0.998856	+	0.0478166i	$0.984774\pi$
$774$	−3.07781e10	+	4.49126e9i	−0.0857587	+	0.0125142i
$775$	5.01668e10			0.139062
$776$			2.75569e10i			0.0759947i
$777$		−	2.34317e11i		−	0.642865i
$778$	5.78580e11			1.57923
$779$			3.33659e10i			0.0906052i
$780$	3.02573e11			0.817433
$781$		−	2.83258e11i		−	0.761339i
$782$		−	9.69708e11i		−	2.59307i
$783$	4.60966e11			1.22637
$784$	−5.24829e10			−0.138916
$785$	8.10884e10			0.213540
$786$		−	5.73157e10i		−	0.150170i
$787$	−5.26327e11			−1.37201			−0.686004	−	0.727598i	$-0.740637\pi$
$787$	−5.26327e11			−1.37201			−0.686004	+	0.727598i	$0.740637\pi$
$788$	−1.92166e11			−0.498393
$789$	−2.13682e11			−0.551392
$790$	8.09195e11			2.07752
$791$	−5.76860e11			−1.47355
$792$		−	3.52043e9i		−	0.00894737i
$793$		−	4.52669e11i		−	1.14469i
$794$		−	7.93919e11i		−	1.99754i
$795$	−3.08728e10			−0.0772871
$796$		−	4.42997e11i		−	1.10344i
$797$	−2.80203e11			−0.694449			−0.347224	−	0.937782i	$-0.612876\pi$
$797$	−2.80203e11			−0.694449			−0.347224	+	0.937782i	$0.612876\pi$
$798$	5.50980e10			0.135870
$799$	−3.91644e11			−0.960958
$800$			1.35120e11i			0.329882i
$801$			3.33274e10i			0.0809601i
$802$		−	5.59309e11i		−	1.35193i
$803$			9.04215e10i			0.217475i
$804$			5.00969e11i			1.19891i
$805$	−5.39314e11			−1.28427
$806$		−	3.29649e11i		−	0.781110i
$807$			4.33111e11i			1.02119i
$808$			2.28287e9i			0.00535593i
$809$	−4.95228e11			−1.15614			−0.578071	−	0.815986i	$-0.696195\pi$
$809$	−4.95228e11			−1.15614			−0.578071	+	0.815986i	$0.696195\pi$
$810$	5.08308e11			1.18083
$811$		−	2.66342e11i		−	0.615683i	−0.951438	−	0.307841i	$-0.900393\pi$
$811$		−	2.66342e11i		−	0.615683i	0.951438	−	0.307841i	$-0.0996066\pi$
$812$	−5.10716e11			−1.17478
$813$			2.22451e11i			0.509180i
$814$	−6.91620e11			−1.57532
$815$	2.95734e11			0.670302
$816$			4.52823e11i			1.02133i
$817$	−4.66027e10	+	6.80045e9i	−0.104598	+	0.0152633i
$818$	5.80446e11			1.29643
$819$		−	2.25095e10i		−	0.0500301i
$820$		−	3.62998e11i		−	0.802876i
$821$	−5.99275e11			−1.31903			−0.659513	−	0.751693i	$-0.729237\pi$
$821$	−5.99275e11			−1.31903			−0.659513	+	0.751693i	$0.729237\pi$
$822$			8.10581e10i			0.177545i
$823$	3.34555e11			0.729237			0.364619	−	0.931157i	$-0.381199\pi$
$823$	3.34555e11			0.729237			0.364619	+	0.931157i	$0.381199\pi$
$824$			1.86655e10i			0.0404884i
$825$			1.57651e11i			0.340314i
$826$	8.08242e11			1.73629
$827$	6.97838e11			1.49187			0.745937	−	0.666016i	$-0.232002\pi$
$827$	6.97838e11			1.49187			0.745937	+	0.666016i	$0.232002\pi$
$828$	−4.80258e10			−0.102177
$829$			3.06723e11i			0.649423i	0.945813	+	0.324712i	$0.105267\pi$
$829$			3.06723e11i			0.649423i	−0.945813	+	0.324712i	$0.894733\pi$
$830$	5.58798e11			1.17745
$831$	−7.22633e11			−1.51535
$832$	4.87727e11			1.01785
$833$	8.18934e10			0.170086
$834$	−4.04224e11			−0.835523
$835$			6.41514e11i			1.31966i
$836$		−	8.39799e10i		−	0.171930i
$837$		−	3.04385e11i		−	0.620185i
$838$	−9.70215e11			−1.96740
$839$			5.67989e11i			1.14628i	0.819456	+	0.573142i	$0.194276\pi$
$839$			5.67989e11i			1.14628i	−0.819456	+	0.573142i	$0.805724\pi$
$840$	−3.80475e10			−0.0764204
$841$	−2.11936e11			−0.423663
$842$	5.90676e11			1.17517
$843$		−	3.70692e11i		−	0.734012i
$844$		−	5.54609e10i		−	0.109299i
$845$			8.47849e10i			0.166300i
$846$			3.75620e10i			0.0733276i
$847$		−	6.26584e11i		−	1.21743i
$848$	−4.35964e10			−0.0843077
$849$		−	8.73531e10i		−	0.168131i
$850$		−	1.96483e11i		−	0.376399i
$851$			5.98875e11i			1.14187i
$852$	−2.72612e11			−0.517353
$853$	5.54160e11			1.04674			0.523370	−	0.852106i	$-0.324675\pi$
$853$	5.54160e11			1.04674			0.523370	+	0.852106i	$0.324675\pi$
$854$			8.96782e11i			1.68599i
$855$	−2.98661e9			−0.00558875
$856$			5.33983e10i			0.0994564i
$857$	6.57798e10			0.121946			0.0609732	−	0.998139i	$-0.480580\pi$
$857$	6.57798e10			0.121946			0.0609732	+	0.998139i	$0.480580\pi$
$858$	1.03593e12			1.91153
$859$			5.78007e11i			1.06160i	0.847497	+	0.530800i	$0.178108\pi$
$859$			5.78007e11i			1.06160i	−0.847497	+	0.530800i	$0.821892\pi$
$860$	5.07005e11	−	7.39841e10i	0.926869	−	0.135252i
$861$	4.21057e11			0.766176
$862$			1.03626e12i			1.87690i
$863$		−	2.50288e11i		−	0.451228i	−0.974217	−	0.225614i	$-0.927561\pi$
$863$		−	2.50288e11i		−	0.451228i	0.974217	−	0.225614i	$-0.0724388\pi$
$864$	8.19833e11			1.47119
$865$			4.06762e10i			0.0726567i
$866$	−7.43380e11			−1.32172
$867$		−	1.58833e11i		−	0.281102i
$868$			3.37236e11i			0.594095i
$869$	1.43064e12			2.50872
$870$	−8.35887e11			−1.45905
$871$	6.00116e11			1.04271
$872$			3.72686e10i			0.0644581i
$873$	2.72974e10			0.0469963
$874$	−1.40821e11			−0.241336
$875$	−5.83429e11			−0.995304
$876$	8.70232e10			0.147781
$877$	3.47482e11			0.587400			0.293700	−	0.955898i	$-0.405113\pi$
$877$	3.47482e11			0.587400			0.293700	+	0.955898i	$0.405113\pi$
$878$		−	5.79633e11i		−	0.975383i
$879$			5.17860e11i			0.867475i
$880$		−	7.43348e11i		−	1.23954i
$881$	−7.52008e11			−1.24830			−0.624150	−	0.781305i	$-0.714554\pi$
$881$	−7.52008e11			−1.24830			−0.624150	+	0.781305i	$0.714554\pi$
$882$		−	7.85427e9i		−	0.0129787i
$883$	−1.91526e11			−0.315054			−0.157527	−	0.987515i	$-0.550352\pi$
$883$	−1.91526e11			−0.315054			−0.157527	+	0.987515i	$0.550352\pi$
$884$	−6.66709e11			−1.09176
$885$	6.83102e11			1.11356
$886$			1.37215e12i			2.22672i
$887$		−	7.30905e11i		−	1.18077i	−0.807121	−	0.590387i	$-0.798975\pi$
$887$		−	7.30905e11i		−	1.18077i	0.807121	−	0.590387i	$-0.201025\pi$
$888$			4.22494e10i			0.0679468i
$889$		−	5.35890e11i		−	0.857963i
$890$		−	1.06315e12i		−	1.69447i
$891$	8.98678e11			1.42591
$892$			6.01513e11i			0.950136i
$893$			5.68745e10i			0.0894359i
$894$		−	9.33717e11i		−	1.46172i
$895$	−1.07007e12			−1.66771
$896$	−1.15573e11			−0.179318
$897$		−	8.97015e11i		−	1.38557i
$898$	−1.06604e12			−1.63934
$899$			4.70268e11i			0.719958i
$900$	−9.73101e9			−0.0148316
$901$	6.80271e10			0.103224
$902$		−	1.24281e12i		−	1.87749i
$903$	8.58175e10	+	5.88098e11i	0.129070	+	0.884501i
$904$	1.04013e11			0.155745
$905$			9.37185e11i			1.39711i
$906$			4.09905e11i			0.608373i
$907$	−5.37136e11			−0.793698			−0.396849	−	0.917884i	$-0.629896\pi$
$907$	−5.37136e11			−0.793698			−0.396849	+	0.917884i	$0.629896\pi$
$908$			8.51030e11i			1.25199i
$909$	2.26137e9			0.00331219
$910$			7.18059e11i			1.04712i
$911$			1.02946e12i			1.49464i	0.664465	+	0.747319i	$0.268659\pi$
$911$			1.02946e12i			1.49464i	−0.664465	+	0.747319i	$0.731341\pi$
$912$	6.57589e10			0.0950551
$913$	9.87944e11			1.42184
$914$	6.08781e11			0.872321
$915$			7.57934e11i			1.08130i
$916$	−1.11646e12			−1.58584
$917$	7.02392e10			0.0993350
$918$	−1.19215e12			−1.67865
$919$	4.12836e11			0.578782			0.289391	−	0.957211i	$-0.406547\pi$
$919$	4.12836e11			0.578782			0.289391	+	0.957211i	$0.406547\pi$
$920$	9.72430e10			0.135740
$921$		−	1.88690e11i		−	0.262247i
$922$			1.08359e12i			1.49949i
$923$			3.26565e11i			0.449948i
$924$	−1.05978e12			−1.45387
$925$			1.21344e11i			0.165750i
$926$	9.86469e11			1.34165
$927$	1.84897e10			0.0250386
$928$	−1.26662e12			−1.70787
$929$		−	5.80653e11i		−	0.779568i	−0.920906	−	0.389784i	$-0.872550\pi$
$929$		−	5.80653e11i		−	0.779568i	0.920906	−	0.389784i	$-0.127450\pi$
$930$			5.51953e11i			0.737854i
$931$		−	1.18925e10i		−	0.0158298i
$932$		−	1.08932e12i		−	1.44374i
$933$		−	9.82652e11i		−	1.29680i
$934$	−1.18981e12			−1.56348
$935$			1.15991e12i			1.51767i
$936$			4.05867e9i			0.00528786i
$937$			4.56529e10i			0.0592257i	0.999561	+	0.0296128i	$0.00942744\pi$
$937$			4.56529e10i			0.0592257i	−0.999561	+	0.0296128i	$0.990573\pi$
$938$	−1.18889e12			−1.53578
$939$	2.13956e11			0.275208
$940$		−	6.18755e11i		−	0.792515i
$941$	1.00537e12			1.28224			0.641119	−	0.767441i	$-0.278470\pi$
$941$	1.00537e12			1.28224			0.641119	+	0.767441i	$0.278470\pi$
$942$		−	2.67192e11i		−	0.339328i
$943$	−1.07615e12			−1.36090
$944$	9.64630e11			1.21471
$945$			6.63028e11i			0.831389i
$946$	1.73585e12	−	2.53302e11i	2.16745	−	0.316282i
$947$	−9.74784e11			−1.21202			−0.606008	−	0.795458i	$-0.707230\pi$
$947$	−9.74784e11			−1.21202			−0.606008	+	0.795458i	$0.707230\pi$
$948$		−	1.37687e12i		−	1.70475i
$949$		−	1.04246e11i		−	0.128527i
$950$	−2.85332e10			−0.0350313
$951$		−	1.88764e11i		−	0.230780i
$952$	8.38363e10			0.102067
$953$			4.92276e11i			0.596812i	0.954439	+	0.298406i	$0.0964549\pi$
$953$			4.92276e11i			0.596812i	−0.954439	+	0.298406i	$0.903545\pi$
$954$		−	6.52437e9i		−	0.00787672i
$955$	1.38180e12			1.66124
$956$	−9.88703e11			−1.18368
$957$	−1.47783e12			−1.76188
$958$		−	1.23490e12i		−	1.46613i
$959$	−9.93351e10			−0.117443
$960$	−8.16633e11			−0.961484
$961$	−5.42363e11			−0.635911
$962$	7.97361e11			0.931010
$963$	5.28955e10			0.0615054
$964$		−	1.40472e12i		−	1.62661i
$965$		−	6.88738e11i		−	0.794228i
$966$			1.77707e12i			2.04078i
$967$	−1.72742e11			−0.197557			−0.0987785	−	0.995109i	$-0.531494\pi$
$967$	−1.72742e11			−0.197557			−0.0987785	+	0.995109i	$0.531494\pi$
$968$			1.12979e11i			0.128675i
$969$	−1.02609e11			−0.116383
$970$	−8.70792e11			−0.983621
$971$	2.24845e10			0.0252934			0.0126467	−	0.999920i	$-0.495974\pi$
$971$	2.24845e10			0.0252934			0.0126467	+	0.999920i	$0.495974\pi$
$972$			1.14729e11i			0.128531i
$973$		−	4.95369e11i		−	0.552685i
$974$		−	8.88418e11i		−	0.987146i
$975$		−	1.81754e11i		−	0.201124i
$976$			1.07030e12i			1.17952i
$977$	1.68860e12			1.85331			0.926653	−	0.375917i	$-0.122672\pi$
$977$	1.68860e12			1.85331			0.926653	+	0.375917i	$0.122672\pi$
$978$		−	9.74463e11i		−	1.06515i
$979$		−	1.87963e12i		−	2.04617i
$980$			1.29383e11i			0.140272i
$981$	3.69176e10			0.0398619
$982$	1.98103e12			2.13032
$983$			1.80594e12i			1.93415i	0.254493	+	0.967075i	$0.418091\pi$
$983$			1.80594e12i			1.93415i	−0.254493	+	0.967075i	$0.581909\pi$
$984$	−7.59203e10			−0.0809800
$985$		−	3.85435e11i		−	0.409455i
$986$	1.84185e12			1.94870
$987$	7.17722e11			0.756289
$988$			9.68195e10i			0.101610i
$989$	−2.19335e11	−	1.50308e12i	−0.229257	−	1.57107i
$990$	1.11245e11			0.115808
$991$		−	4.93967e11i		−	0.512157i	−0.966656	−	0.256078i	$-0.917569\pi$
$991$		−	4.93967e11i		−	0.512157i	0.966656	−	0.256078i	$-0.0824305\pi$
$992$			8.36377e11i			0.863686i
$993$	1.45295e12			1.49436
$994$		−	6.46957e11i		−	0.662719i
$995$	8.88536e11			0.906532
$996$		−	9.50814e11i		−	0.966181i
$997$		−	3.45858e11i		−	0.350040i	−0.984565	−	0.175020i	$-0.944001\pi$
$997$		−	3.45858e11i		−	0.350040i	0.984565	−	0.175020i	$-0.0559990\pi$
$998$	−1.81804e12			−1.83266
$999$	7.36251e11			0.739204

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.9.b.b.42.7	✓	28
43.42	odd	2	inner	43.9.b.b.42.22	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.9.b.b.42.7	✓	28	1.1	even	1	trivial
43.9.b.b.42.22	yes	28	43.42	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-23.0076i q^{2} -78.5211i q^{3} -273.350 q^{4} -548.269i q^{5} -1806.58 q^{6} -2213.93i q^{7} +399.191i q^{8} +395.432 q^{9} +O(q^{10})\)	\(q-23.0076i q^{2} -78.5211i q^{3} -273.350 q^{4} -548.269i q^{5} -1806.58 q^{6} -2213.93i q^{7} +399.191i q^{8} +395.432 q^{9} -12614.4 q^{10} -22302.0 q^{11} +21463.8i q^{12} +25711.7 q^{13} -50937.3 q^{14} -43050.7 q^{15} -60793.3 q^{16} +94860.8 q^{17} -9097.95i q^{18} -13775.7i q^{19} +149870. i q^{20} -173841. q^{21} +513115. i q^{22} +444307. q^{23} +31345.0 q^{24} +90025.7 q^{25} -591564. i q^{26} -546227. i q^{27} +605180. i q^{28} +843909. i q^{29} +990495. i q^{30} +557250. q^{31} +1.50090e6i q^{32} +1.75117e6i q^{33} -2.18252e6i q^{34} -1.21383e6 q^{35} -108092. q^{36} +1.34789e6i q^{37} -316945. q^{38} -2.01891e6i q^{39} +218864. q^{40} -2.42209e6 q^{41} +3.99966e6i q^{42} +(-493656. - 3.38297e6i) q^{43} +6.09625e6 q^{44} -216803. i q^{45} -1.02224e7i q^{46} -4.12862e6 q^{47} +4.77356e6i q^{48} +863301. q^{49} -2.07128e6i q^{50} -7.44857e6i q^{51} -7.02829e6 q^{52} +717126. q^{53} -1.25674e7 q^{54} +1.22275e7i q^{55} +883783. q^{56} -1.08168e6 q^{57} +1.94163e7 q^{58} -1.58674e7 q^{59} +1.17679e7 q^{60} -1.76056e7i q^{61} -1.28210e7i q^{62} -875460. i q^{63} +1.89691e7 q^{64} -1.40969e7i q^{65} +4.02904e7 q^{66} +2.33402e7 q^{67} -2.59302e7 q^{68} -3.48875e7i q^{69} +2.79274e7i q^{70} +1.27010e7i q^{71} +157853. i q^{72} -4.05442e6i q^{73} +3.10116e7 q^{74} -7.06892e6i q^{75} +3.76559e6i q^{76} +4.93750e7i q^{77} -4.64503e7 q^{78} -6.41487e7 q^{79} +3.33311e7i q^{80} -4.02959e7 q^{81} +5.57265e7i q^{82} -4.42985e7 q^{83} +4.75194e7 q^{84} -5.20092e7i q^{85} +(-7.78341e7 + 1.13579e7i) q^{86} +6.62647e7 q^{87} -8.90275e6i q^{88} +8.42809e7i q^{89} -4.98813e6 q^{90} -5.69239e7i q^{91} -1.21451e8 q^{92} -4.37559e7i q^{93} +9.49898e7i q^{94} -7.55278e6 q^{95} +1.17852e8 q^{96} +6.90318e7 q^{97} -1.98625e7i q^{98} -8.81891e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9}+O(q^{10}) \) 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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