LMFDB - Embedded newform 43.9.b.b.42.8

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			42.8
Character	$\chi$	$=$	43.42
Dual form			43.9.b.b.42.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-17.7707i q^{2} +152.462i q^{3} -59.7986 q^{4} -783.269i q^{5} +2709.35 q^{6} +1147.99i q^{7} -3486.64i q^{8} -16683.5 q^{9} +O(q^{10})$	\(q-17.7707i q^{2} +152.462i q^{3} -59.7986 q^{4} -783.269i q^{5} +2709.35 q^{6} +1147.99i q^{7} -3486.64i q^{8} -16683.5 q^{9} -13919.3 q^{10} +21355.1 q^{11} -9116.98i q^{12} +16947.7 q^{13} +20400.5 q^{14} +119418. q^{15} -77268.6 q^{16} +104612. q^{17} +296478. i q^{18} +142642. i q^{19} +46838.4i q^{20} -175024. q^{21} -379495. i q^{22} +376231. q^{23} +531579. q^{24} -222885. q^{25} -301172. i q^{26} -1.54329e6i q^{27} -68647.9i q^{28} +245109. i q^{29} -2.12215e6i q^{30} +373811. q^{31} +480538. i q^{32} +3.25582e6i q^{33} -1.85903e6i q^{34} +899182. q^{35} +997650. q^{36} -1.72624e6i q^{37} +2.53484e6 q^{38} +2.58387e6i q^{39} -2.73098e6 q^{40} -3.57800e6 q^{41} +3.11030e6i q^{42} +(3.19345e6 + 1.22070e6i) q^{43} -1.27700e6 q^{44} +1.30677e7i q^{45} -6.68589e6i q^{46} +6.89105e6 q^{47} -1.17805e7i q^{48} +4.44693e6 q^{49} +3.96083e6i q^{50} +1.59493e7i q^{51} -1.01345e6 q^{52} -3.52143e6 q^{53} -2.74255e7 q^{54} -1.67268e7i q^{55} +4.00262e6 q^{56} -2.17474e7 q^{57} +4.35576e6 q^{58} -1.55268e6 q^{59} -7.14105e6 q^{60} -3.86782e6i q^{61} -6.64288e6i q^{62} -1.91524e7i q^{63} -1.12412e7 q^{64} -1.32746e7i q^{65} +5.78584e7 q^{66} -1.77748e7 q^{67} -6.25565e6 q^{68} +5.73607e7i q^{69} -1.59791e7i q^{70} -3.92801e7i q^{71} +5.81694e7i q^{72} +2.65149e7i q^{73} -3.06764e7 q^{74} -3.39814e7i q^{75} -8.52976e6i q^{76} +2.45153e7i q^{77} +4.59172e7 q^{78} -6.70808e7 q^{79} +6.05221e7i q^{80} +1.25832e8 q^{81} +6.35836e7i q^{82} -1.73713e7 q^{83} +1.04662e7 q^{84} -8.19394e7i q^{85} +(2.16926e7 - 5.67499e7i) q^{86} -3.73696e7 q^{87} -7.44574e7i q^{88} -1.06480e7i q^{89} +2.32222e8 q^{90} +1.94557e7i q^{91} -2.24981e7 q^{92} +5.69917e7i q^{93} -1.22459e8i q^{94} +1.11727e8 q^{95} -7.32636e7 q^{96} -1.23822e8 q^{97} -7.90251e7i q^{98} -3.56277e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	17.7707i		−	1.11067i	−0.831627	−	0.555335i	$-0.812590\pi$
$2$		−	17.7707i		−	1.11067i	0.831627	−	0.555335i	$-0.187410\pi$
$3$			152.462i			1.88224i	0.338071	+	0.941121i	$0.390225\pi$
$3$			152.462i			1.88224i	−0.338071	+	0.941121i	$0.609775\pi$
$4$	−59.7986			−0.233588
$5$		−	783.269i		−	1.25323i	−0.779329	−	0.626615i	$-0.784440\pi$
$5$		−	783.269i		−	1.25323i	0.779329	−	0.626615i	$-0.215560\pi$
$6$	2709.35			2.09055
$7$			1147.99i			0.478128i	0.971004	+	0.239064i	$0.0768406\pi$
$7$			1147.99i			0.478128i	−0.971004	+	0.239064i	$0.923159\pi$
$8$		−	3486.64i		−	0.851231i
$9$	−16683.5			−2.54283
$10$	−13919.3			−1.39193
$11$	21355.1			1.45858			0.729290	−	0.684205i	$-0.239851\pi$
$11$	21355.1			1.45858			0.729290	+	0.684205i	$0.239851\pi$
$12$		−	9116.98i		−	0.439669i
$13$	16947.7			0.593385			0.296693	−	0.954973i	$-0.404116\pi$
$13$	16947.7			0.593385			0.296693	+	0.954973i	$0.404116\pi$
$14$	20400.5			0.531043
$15$	119418.			2.35888
$16$	−77268.6			−1.17902
$17$	104612.			1.25252			0.626262	−	0.779613i	$-0.284584\pi$
$17$	104612.			1.25252			0.626262	+	0.779613i	$0.284584\pi$
$18$			296478.i			2.82425i
$19$			142642.i			1.09454i	0.836956	+	0.547270i	$0.184333\pi$
$19$			142642.i			1.09454i	−0.836956	+	0.547270i	$0.815667\pi$
$20$			46838.4i			0.292740i
$21$	−175024.			−0.899953
$22$		−	379495.i		−	1.62000i
$23$	376231.			1.34444			0.672222	−	0.740349i	$-0.265340\pi$
$23$	376231.			1.34444			0.672222	+	0.740349i	$0.265340\pi$
$24$	531579.			1.60222
$25$	−222885.			−0.570586
$26$		−	301172.i		−	0.659055i
$27$		−	1.54329e6i		−	2.90398i
$28$		−	68647.9i		−	0.111685i
$29$			245109.i			0.346551i	0.984873	+	0.173275i	$0.0554350\pi$
$29$			245109.i			0.346551i	−0.984873	+	0.173275i	$0.944565\pi$
$30$		−	2.12215e6i		−	2.61994i
$31$	373811.			0.404767			0.202383	−	0.979306i	$-0.435131\pi$
$31$	373811.			0.404767			0.202383	+	0.979306i	$0.435131\pi$
$32$			480538.i			0.458277i
$33$			3.25582e6i			2.74540i
$34$		−	1.85903e6i		−	1.39114i
$35$	899182.			0.599205
$36$	997650.			0.593975
$37$		−	1.72624e6i		−	0.921071i	−0.887641	−	0.460535i	$-0.847657\pi$
$37$		−	1.72624e6i		−	0.921071i	0.887641	−	0.460535i	$-0.152343\pi$
$38$	2.53484e6			1.21567
$39$			2.58387e6i			1.11689i
$40$	−2.73098e6			−1.06679
$41$	−3.57800e6			−1.26621			−0.633103	−	0.774067i	$-0.718219\pi$
$41$	−3.57800e6			−1.26621			−0.633103	+	0.774067i	$0.718219\pi$
$42$			3.11030e6i			0.999551i
$43$	3.19345e6	+	1.22070e6i	0.934084	+	0.357054i
$43$	3.19345e6	+	1.22070e6i	0.934084	+	0.357054i
$44$	−1.27700e6			−0.340707
$45$			1.30677e7i			3.18675i
$46$		−	6.68589e6i		−	1.49323i
$47$	6.89105e6			1.41219			0.706096	−	0.708116i	$-0.250455\pi$
$47$	6.89105e6			1.41219			0.706096	+	0.708116i	$0.250455\pi$
$48$		−	1.17805e7i		−	2.21921i
$49$	4.44693e6			0.771393
$50$			3.96083e6i			0.633733i
$51$			1.59493e7i			2.35755i
$52$	−1.01345e6			−0.138608
$53$	−3.52143e6			−0.446288			−0.223144	−	0.974785i	$-0.571632\pi$
$53$	−3.52143e6			−0.446288			−0.223144	+	0.974785i	$0.571632\pi$
$54$	−2.74255e7			−3.22536
$55$		−	1.67268e7i		−	1.82794i
$56$	4.00262e6			0.406998
$57$	−2.17474e7			−2.06019
$58$	4.35576e6			0.384903
$59$	−1.55268e6			−0.128137			−0.0640685	−	0.997946i	$-0.520408\pi$
$59$	−1.55268e6			−0.128137			−0.0640685	+	0.997946i	$0.520408\pi$
$60$	−7.14105e6			−0.551007
$61$		−	3.86782e6i		−	0.279349i	−0.990197	−	0.139674i	$-0.955394\pi$
$61$		−	3.86782e6i		−	0.279349i	0.990197	−	0.139674i	$-0.0446056\pi$
$62$		−	6.64288e6i		−	0.449562i
$63$		−	1.91524e7i		−	1.21580i
$64$	−1.12412e7			−0.670030
$65$		−	1.32746e7i		−	0.743648i
$66$	5.78584e7			3.04923
$67$	−1.77748e7			−0.882074			−0.441037	−	0.897489i	$-0.645389\pi$
$67$	−1.77748e7			−0.882074			−0.441037	+	0.897489i	$0.645389\pi$
$68$	−6.25565e6			−0.292575
$69$			5.73607e7i			2.53057i
$70$		−	1.59791e7i		−	0.665519i
$71$		−	3.92801e7i		−	1.54575i	−0.634557	−	0.772876i	$-0.718818\pi$
$71$		−	3.92801e7i		−	1.54575i	0.634557	−	0.772876i	$-0.281182\pi$
$72$			5.81694e7i			2.16454i
$73$			2.65149e7i			0.933680i	0.884342	+	0.466840i	$0.154608\pi$
$73$			2.65149e7i			0.933680i	−0.884342	+	0.466840i	$0.845392\pi$
$74$	−3.06764e7			−1.02301
$75$		−	3.39814e7i		−	1.07398i
$76$		−	8.52976e6i		−	0.255672i
$77$			2.45153e7i			0.697388i
$78$	4.59172e7			1.24050
$79$	−6.70808e7			−1.72223			−0.861113	−	0.508414i	$-0.830232\pi$
$79$	−6.70808e7			−1.72223			−0.861113	+	0.508414i	$0.830232\pi$
$80$			6.05221e7i			1.47759i
$81$	1.25832e8			2.92316
$82$			6.35836e7i			1.40634i
$83$	−1.73713e7			−0.366033			−0.183017	−	0.983110i	$-0.558586\pi$
$83$	−1.73713e7			−0.366033			−0.183017	+	0.983110i	$0.558586\pi$
$84$	1.04662e7			0.210218
$85$		−	8.19394e7i		−	1.56970i
$86$	2.16926e7	−	5.67499e7i	0.396569	−	1.03746i
$87$	−3.73696e7			−0.652292
$88$		−	7.44574e7i		−	1.24159i
$89$		−	1.06480e7i		−	0.169709i	−0.996393	−	0.0848547i	$-0.972957\pi$
$89$		−	1.06480e7i		−	0.169709i	0.996393	−	0.0848547i	$-0.0270426\pi$
$90$	2.32222e8			3.53943
$91$			1.94557e7i			0.283714i
$92$	−2.24981e7			−0.314046
$93$			5.69917e7i			0.761869i
$94$		−	1.22459e8i		−	1.56848i
$95$	1.11727e8			1.37171
$96$	−7.32636e7			−0.862587
$97$	−1.23822e8			−1.39866			−0.699330	−	0.714799i	$-0.746518\pi$
$97$	−1.23822e8			−1.39866			−0.699330	+	0.714799i	$0.746518\pi$
$98$		−	7.90251e7i		−	0.856763i
$99$	−3.56277e8			−3.70892
$100$	1.33282e7			0.133282
$101$	2.90612e7			0.279273			0.139636	−	0.990203i	$-0.455407\pi$
$101$	2.90612e7			0.279273			0.139636	+	0.990203i	$0.455407\pi$
$102$	2.83431e8			2.61846
$103$	1.02737e7			0.0912806			0.0456403	−	0.998958i	$-0.485467\pi$
$103$	1.02737e7			0.0912806			0.0456403	+	0.998958i	$0.485467\pi$
$104$		−	5.90905e7i		−	0.505108i
$105$			1.37091e8i			1.12785i
$106$			6.25783e7i			0.495679i
$107$	−1.22323e8			−0.933195			−0.466597	−	0.884470i	$-0.654520\pi$
$107$	−1.22323e8			−0.933195			−0.466597	+	0.884470i	$0.654520\pi$
$108$			9.22868e7i			0.678335i
$109$	2.58957e8			1.83451			0.917257	−	0.398296i	$-0.130398\pi$
$109$	2.58957e8			1.83451			0.917257	+	0.398296i	$0.130398\pi$
$110$	−2.97246e8			−2.03023
$111$	2.63184e8			1.73368
$112$		−	8.87033e7i		−	0.563725i
$113$			2.22666e8i			1.36565i	0.730581	+	0.682826i	$0.239249\pi$
$113$			2.22666e8i			1.36565i	−0.730581	+	0.682826i	$0.760751\pi$
$114$			3.86466e8i			2.28819i
$115$		−	2.94690e8i		−	1.68490i
$116$		−	1.46571e7i		−	0.0809501i
$117$	−2.82747e8			−1.50888
$118$			2.75923e7i			0.142318i
$119$			1.20093e8i			0.598867i
$120$		−	4.16369e8i		−	2.00795i
$121$	2.41680e8			1.12745
$122$	−6.87339e7			−0.310264
$123$		−	5.45507e8i		−	2.38331i
$124$	−2.23533e7			−0.0945487
$125$		−	1.31385e8i		−	0.538155i
$126$	−3.40353e8			−1.35035
$127$	−7.23723e7			−0.278200			−0.139100	−	0.990278i	$-0.544421\pi$
$127$	−7.23723e7			−0.278200			−0.139100	+	0.990278i	$0.544421\pi$
$128$			3.22783e8i			1.20246i
$129$	−1.86109e8	+	4.86878e8i	−0.672061	+	1.75817i
$130$	−2.35899e8			−0.825948
$131$			2.13462e8i			0.724828i	0.932017	+	0.362414i	$0.118047\pi$
$131$			2.13462e8i			0.724828i	−0.932017	+	0.362414i	$0.881953\pi$
$132$		−	1.94694e8i		−	0.641292i
$133$	−1.63751e8			−0.523331
$134$			3.15871e8i			0.979693i
$135$	−1.20881e9			−3.63936
$136$		−	3.64745e8i		−	1.06619i
$137$		−	2.73201e8i		−	0.775532i	−0.921758	−	0.387766i	$-0.873247\pi$
$137$		−	2.73201e8i		−	0.775532i	0.921758	−	0.387766i	$-0.126753\pi$
$138$	1.01934e9			2.81063
$139$	3.27177e8			0.876442			0.438221	−	0.898867i	$-0.355609\pi$
$139$	3.27177e8			0.876442			0.438221	+	0.898867i	$0.355609\pi$
$140$	−5.37698e7			−0.139967
$141$			1.05062e9i			2.65809i
$142$	−6.98037e8			−1.71682
$143$	3.61919e8			0.865499
$144$	1.28911e9			2.99806
$145$	1.91986e8			0.434308
$146$	4.71189e8			1.03701
$147$			6.77985e8i			1.45195i
$148$			1.03226e8i			0.215151i
$149$		−	6.32543e8i		−	1.28335i	−0.766977	−	0.641675i	$-0.778240\pi$
$149$		−	6.32543e8i		−	1.28335i	0.766977	−	0.641675i	$-0.221760\pi$
$150$	−6.03874e8			−1.19284
$151$		−	4.30577e8i		−	0.828214i	−0.910228	−	0.414107i	$-0.864094\pi$
$151$		−	4.30577e8i		−	0.828214i	0.910228	−	0.414107i	$-0.135906\pi$
$152$	4.97340e8			0.931706
$153$	−1.74530e9			−3.18496
$154$	4.35655e8			0.774568
$155$		−	2.92794e8i		−	0.507266i
$156$		−	1.54512e8i		−	0.260893i
$157$			2.11312e8i			0.347797i	0.984764	+	0.173898i	$0.0556364\pi$
$157$			2.11312e8i			0.347797i	−0.984764	+	0.173898i	$0.944364\pi$
$158$			1.19207e9i			1.91282i
$159$		−	5.36882e8i		−	0.840022i
$160$	3.76391e8			0.574326
$161$			4.31908e8i			0.642817i
$162$		−	2.23613e9i		−	3.24667i
$163$			3.17331e7i			0.0449534i	0.999747	+	0.0224767i	$0.00715516\pi$
$163$			3.17331e7i			0.0449534i	−0.999747	+	0.0224767i	$0.992845\pi$
$164$	2.13959e8			0.295771
$165$	2.55019e9			3.44062
$166$			3.08701e8i			0.406542i
$167$	1.72754e8			0.222107			0.111053	−	0.993814i	$-0.464578\pi$
$167$	1.72754e8			0.222107			0.111053	+	0.993814i	$0.464578\pi$
$168$			6.10245e8i			0.766068i
$169$	−5.28507e8			−0.647894
$170$	−1.45612e9			−1.74342
$171$		−	2.37976e9i		−	2.78323i
$172$	−1.90964e8	−	7.29958e7i	−0.218191	−	0.0834035i
$173$	3.49848e8			0.390567			0.195283	−	0.980747i	$-0.437437\pi$
$173$	3.49848e8			0.390567			0.195283	+	0.980747i	$0.437437\pi$
$174$			6.64086e8i			0.724481i
$175$		−	2.55869e8i		−	0.272813i
$176$	−1.65007e9			−1.71970
$177$		−	2.36724e8i		−	0.241185i
$178$	−1.89222e8			−0.188491
$179$			1.61233e9i			1.57052i	0.619169	+	0.785258i	$0.287469\pi$
$179$			1.61233e9i			1.57052i	−0.619169	+	0.785258i	$0.712531\pi$
$180$		−	7.81428e8i		−	0.744388i
$181$	1.47130e9			1.37084			0.685419	−	0.728149i	$-0.259619\pi$
$181$	1.47130e9			1.37084			0.685419	+	0.728149i	$0.259619\pi$
$182$	3.45742e8			0.315113
$183$	5.89693e8			0.525802
$184$		−	1.31178e9i		−	1.14443i
$185$	−1.35211e9			−1.15431
$186$	1.01278e9			0.846185
$187$	2.23400e9			1.82691
$188$	−4.12075e8			−0.329871
$189$	1.77168e9			1.38848
$190$		−	1.98546e9i		−	1.52352i
$191$			4.60059e8i			0.345685i	0.984949	+	0.172842i	$0.0552951\pi$
$191$			4.60059e8i			0.345685i	−0.984949	+	0.172842i	$0.944705\pi$
$192$		−	1.71386e9i		−	1.26116i
$193$	−1.75432e9			−1.26439			−0.632193	−	0.774811i	$-0.717845\pi$
$193$	−1.75432e9			−1.26439			−0.632193	+	0.774811i	$0.717845\pi$
$194$			2.20041e9i			1.55345i
$195$	2.02386e9			1.39973
$196$	−2.65920e8			−0.180188
$197$	−2.67417e9			−1.77551			−0.887756	−	0.460314i	$-0.847737\pi$
$197$	−2.67417e9			−1.77551			−0.887756	+	0.460314i	$0.847737\pi$
$198$			6.33131e9i			4.11939i
$199$			9.42028e8i			0.600692i	0.953830	+	0.300346i	$0.0971021\pi$
$199$			9.42028e8i			0.600692i	−0.953830	+	0.300346i	$0.902898\pi$
$200$			7.77120e8i			0.485700i
$201$		−	2.70997e9i		−	1.66028i
$202$		−	5.16439e8i		−	0.310180i
$203$	−2.81381e8			−0.165696
$204$		−	9.53746e8i		−	0.550696i
$205$			2.80253e9i			1.58685i
$206$		−	1.82571e8i		−	0.101383i
$207$	−6.27685e9			−3.41870
$208$	−1.30952e9			−0.699616
$209$			3.04612e9i			1.59647i
$210$	2.43620e9			1.25267
$211$			3.63936e9i			1.83610i	0.396469	+	0.918048i	$0.370236\pi$
$211$			3.63936e9i			1.83610i	−0.396469	+	0.918048i	$0.629764\pi$
$212$	2.10576e8			0.104248
$213$	5.98871e9			2.90948
$214$			2.17376e9i			1.03647i
$215$	9.56133e8	−	2.50133e9i	0.447470	−	1.17062i
$216$	−5.38091e9			−2.47196
$217$			4.29129e8i			0.193530i
$218$		−	4.60184e9i		−	2.03754i
$219$	−4.04250e9			−1.75741
$220$			1.00024e9i			0.426984i
$221$	1.77293e9			0.743229
$222$		−	4.67698e9i		−	1.92554i
$223$			1.86717e8i			0.0755032i	0.999287	+	0.0377516i	$0.0120196\pi$
$223$			1.86717e8i			0.0755032i	−0.999287	+	0.0377516i	$0.987980\pi$
$224$	−5.51651e8			−0.219115
$225$	3.71851e9			1.45090
$226$	3.95694e9			1.51679
$227$		−	2.20237e9i		−	0.829445i	−0.909948	−	0.414722i	$-0.863879\pi$
$227$		−	2.20237e9i		−	0.829445i	0.909948	−	0.414722i	$-0.136121\pi$
$228$	1.30046e9			0.481236
$229$	−1.37546e9			−0.500155			−0.250077	−	0.968226i	$-0.580456\pi$
$229$	−1.37546e9			−0.500155			−0.250077	+	0.968226i	$0.580456\pi$
$230$	−5.23685e9			−1.87137
$231$	−3.73764e9			−1.31265
$232$	8.54606e8			0.294995
$233$			1.56426e9i			0.530743i	0.964146	+	0.265372i	$0.0854946\pi$
$233$			1.56426e9i			0.530743i	−0.964146	+	0.265372i	$0.914505\pi$
$234$			5.02462e9i			1.67587i
$235$		−	5.39754e9i		−	1.76980i
$236$	9.28482e7			0.0299313
$237$		−	1.02272e10i		−	3.24164i
$238$	2.13414e9			0.665144
$239$	−2.61367e9			−0.801048			−0.400524	−	0.916286i	$-0.631172\pi$
$239$	−2.61367e9			−0.801048			−0.400524	+	0.916286i	$0.631172\pi$
$240$	−9.22729e9			−2.78118
$241$			3.69579e8i			0.109557i	0.998499	+	0.0547784i	$0.0174453\pi$
$241$			3.69579e8i			0.109557i	−0.998499	+	0.0547784i	$0.982555\pi$
$242$		−	4.29482e9i		−	1.25223i
$243$			9.05905e9i			2.59811i
$244$			2.31290e8i			0.0652526i
$245$		−	3.48314e9i		−	0.966733i
$246$	−9.69405e9			−2.64707
$247$			2.41744e9i			0.649484i
$248$		−	1.30334e9i		−	0.344550i
$249$		−	2.64846e9i		−	0.688962i
$250$	−2.33481e9			−0.597713
$251$	2.82275e9			0.711177			0.355588	−	0.934643i	$-0.384280\pi$
$251$	2.82275e9			0.711177			0.355588	+	0.934643i	$0.384280\pi$
$252$			1.14529e9i			0.283996i
$253$	8.03443e9			1.96098
$254$			1.28611e9i			0.308989i
$255$	1.24926e10			2.95456
$256$	2.85832e9			0.665506
$257$			1.95053e9i			0.447115i	0.974691	+	0.223558i	$0.0717671\pi$
$257$			1.95053e9i			0.447115i	−0.974691	+	0.223558i	$0.928233\pi$
$258$	8.65217e9	+	3.30729e9i	1.95275	+	0.746438i
$259$	1.98169e9			0.440390
$260$			7.93801e8i			0.173707i
$261$		−	4.08927e9i		−	0.881220i
$262$	3.79337e9			0.805045
$263$			1.40497e9i			0.293659i	0.989162	+	0.146830i	$0.0469069\pi$
$263$			1.40497e9i			0.293659i	−0.989162	+	0.146830i	$0.953093\pi$
$264$	1.13519e10			2.33697
$265$			2.75822e9i			0.559302i
$266$			2.90997e9i			0.581248i
$267$	1.62340e9			0.319434
$268$	1.06291e9			0.206042
$269$	−8.25785e8			−0.157709			−0.0788547	−	0.996886i	$-0.525126\pi$
$269$	−8.25785e8			−0.157709			−0.0788547	+	0.996886i	$0.525126\pi$
$270$			2.14815e10i			4.04212i
$271$	6.82085e8			0.126462			0.0632312	−	0.997999i	$-0.479859\pi$
$271$	6.82085e8			0.126462			0.0632312	+	0.997999i	$0.479859\pi$
$272$	−8.08322e9			−1.47676
$273$	−2.96625e9			−0.534019
$274$	−4.85498e9			−0.861360
$275$	−4.75972e9			−0.832245
$276$		−	3.43009e9i		−	0.591111i
$277$			1.59599e9i			0.271089i	0.990771	+	0.135544i	$0.0432784\pi$
$277$			1.59599e9i			0.271089i	−0.990771	+	0.135544i	$0.956722\pi$
$278$		−	5.81417e9i		−	0.973438i
$279$	−6.23647e9			−1.02925
$280$		−	3.13512e9i		−	0.510062i
$281$	−9.84477e9			−1.57899			−0.789497	−	0.613755i	$-0.789658\pi$
$281$	−9.84477e9			−1.57899			−0.789497	+	0.613755i	$0.789658\pi$
$282$	1.86703e10			2.95226
$283$	5.66632e9			0.883395			0.441698	−	0.897164i	$-0.354376\pi$
$283$	5.66632e9			0.883395			0.441698	+	0.897164i	$0.354376\pi$
$284$			2.34890e9i			0.361069i
$285$			1.70340e10i			2.58189i
$286$		−	6.43156e9i		−	0.961284i
$287$		−	4.10749e9i		−	0.605409i
$288$		−	8.01706e9i		−	1.16532i
$289$	3.96793e9			0.568816
$290$		−	3.41173e9i		−	0.482373i
$291$		−	1.88781e10i		−	2.63261i
$292$		−	1.58555e9i		−	0.218097i
$293$	−8.29340e9			−1.12528			−0.562642	−	0.826701i	$-0.690215\pi$
$293$	−8.29340e9			−1.12528			−0.562642	+	0.826701i	$0.690215\pi$
$294$	1.20483e10			1.61264
$295$			1.21617e9i			0.160585i
$296$	−6.01876e9			−0.784044
$297$		−	3.29571e10i		−	4.23569i
$298$	−1.12407e10			−1.42538
$299$	6.37624e9			0.797774
$300$			2.03204e9i			0.250869i
$301$	−1.40134e9	+	3.66603e9i	−0.170717	+	0.446612i
$302$	−7.65166e9			−0.919873
$303$			4.43072e9i			0.525659i
$304$		−	1.10217e10i		−	1.29049i
$305$	−3.02954e9			−0.350088
$306$			3.10152e10i			3.53744i
$307$	−2.49145e9			−0.280478			−0.140239	−	0.990118i	$-0.544787\pi$
$307$	−2.49145e9			−0.280478			−0.140239	+	0.990118i	$0.544787\pi$
$308$		−	1.46598e9i		−	0.162902i
$309$			1.56635e9i			0.171812i
$310$	−5.20316e9			−0.563405
$311$	8.34587e9			0.892134			0.446067	−	0.894999i	$-0.352824\pi$
$311$	8.34587e9			0.892134			0.446067	+	0.894999i	$0.352824\pi$
$312$	9.00902e9			0.950735
$313$		−	1.49570e10i		−	1.55836i	−0.626803	−	0.779178i	$-0.715637\pi$
$313$		−	1.49570e10i		−	1.55836i	0.626803	−	0.779178i	$-0.284363\pi$
$314$	3.75517e9			0.386288
$315$	−1.50015e10			−1.52368
$316$	4.01134e9			0.402292
$317$	−4.93098e9			−0.488311			−0.244156	−	0.969736i	$-0.578511\pi$
$317$	−4.93098e9			−0.488311			−0.244156	+	0.969736i	$0.578511\pi$
$318$	−9.54078e9			−0.932987
$319$			5.23431e9i			0.505472i
$320$			8.80492e9i			0.839702i
$321$		−	1.86495e10i		−	1.75650i
$322$	7.67531e9			0.713958
$323$			1.49220e10i			1.37094i
$324$	−7.52460e9			−0.682815
$325$	−3.77738e9			−0.338577
$326$	5.63921e8			0.0499284
$327$			3.94809e10i			3.45300i
$328$			1.24752e10i			1.07783i
$329$			7.91083e9i			0.675209i
$330$		−	4.53186e10i		−	3.82139i
$331$		−	1.01229e10i		−	0.843322i	−0.906754	−	0.421661i	$-0.861447\pi$
$331$		−	1.01229e10i		−	0.843322i	0.906754	−	0.421661i	$-0.138553\pi$
$332$	1.03878e9			0.0855010
$333$			2.87997e10i			2.34213i
$334$		−	3.06996e9i		−	0.246687i
$335$			1.39224e10i			1.10544i
$336$	1.35238e10			1.06107
$337$	−2.62618e9			−0.203613			−0.101807	−	0.994804i	$-0.532462\pi$
$337$	−2.62618e9			−0.203613			−0.101807	+	0.994804i	$0.532462\pi$
$338$			9.39195e9i			0.719596i
$339$	−3.39480e10			−2.57049
$340$			4.89986e9i			0.366664i
$341$	7.98275e9			0.590384
$342$	−4.22901e10			−3.09125
$343$			1.17229e10i			0.846953i
$344$	4.25613e9	−	1.11344e10i	0.303935	−	0.795121i
$345$	4.49289e10			3.17139
$346$		−	6.21706e9i		−	0.433791i
$347$			5.33379e9i			0.367890i	0.982937	+	0.183945i	$0.0588868\pi$
$347$			5.33379e9i			0.367890i	−0.982937	+	0.183945i	$0.941113\pi$
$348$	2.23465e9			0.152368
$349$		−	1.76395e9i		−	0.118901i	−0.998231	−	0.0594504i	$-0.981065\pi$
$349$		−	1.76395e9i		−	0.118901i	0.998231	−	0.0594504i	$-0.0189348\pi$
$350$	−4.54698e9			−0.303006
$351$		−	2.61553e10i		−	1.72318i
$352$			1.02619e10i			0.668433i
$353$	−1.49693e10			−0.964056			−0.482028	−	0.876156i	$-0.660100\pi$
$353$	−1.49693e10			−0.964056			−0.482028	+	0.876156i	$0.660100\pi$
$354$	−4.20676e9			−0.267877
$355$	−3.07669e10			−1.93718
$356$			6.36732e8i			0.0396421i
$357$	−1.83096e10			−1.12721
$358$	2.86523e10			1.74432
$359$	1.00539e10			0.605279			0.302639	−	0.953105i	$-0.402132\pi$
$359$	1.00539e10			0.605279			0.302639	+	0.953105i	$0.402132\pi$
$360$	4.55623e10			2.71266
$361$	−3.36306e9			−0.198018
$362$		−	2.61460e10i		−	1.52255i
$363$			3.68468e10i			2.12214i
$364$		−	1.16342e9i		−	0.0662723i
$365$	2.07683e10			1.17012
$366$		−	1.04793e10i		−	0.583992i
$367$	−2.25533e10			−1.24321			−0.621606	−	0.783330i	$-0.713519\pi$
$367$	−2.25533e10			−1.24321			−0.621606	+	0.783330i	$0.713519\pi$
$368$	−2.90708e10			−1.58513
$369$	5.96936e10			3.21975
$370$			2.40279e10i			1.28206i
$371$		−	4.04255e9i		−	0.213383i
$372$		−	3.40802e9i		−	0.177963i
$373$		−	4.92003e9i		−	0.254175i	−0.991892	−	0.127087i	$-0.959437\pi$
$373$		−	4.92003e9i		−	0.254175i	0.991892	−	0.127087i	$-0.0405629\pi$
$374$		−	3.96997e10i		−	2.02909i
$375$	2.00312e10			1.01294
$376$		−	2.40266e10i		−	1.20210i
$377$			4.15402e9i			0.205638i
$378$		−	3.14840e10i		−	1.54214i
$379$	1.13510e9			0.0550147			0.0275073	−	0.999622i	$-0.491243\pi$
$379$	1.13510e9			0.0550147			0.0275073	+	0.999622i	$0.491243\pi$
$380$	−6.68110e9			−0.320415
$381$		−	1.10340e10i		−	0.523640i
$382$	8.17558e9			0.383942
$383$			2.87658e10i			1.33685i	0.743782	+	0.668423i	$0.233030\pi$
$383$			2.87658e10i			1.33685i	−0.743782	+	0.668423i	$0.766970\pi$
$384$	−4.92120e10			−2.26332
$385$	1.92021e10			0.873988
$386$			3.11755e10i			1.40432i
$387$	−5.32779e10	−	2.03655e10i	−2.37522	−	0.907927i
$388$	7.40440e9			0.326710
$389$			2.92780e10i			1.27862i	0.768947	+	0.639312i	$0.220781\pi$
$389$			2.92780e10i			1.27862i	−0.768947	+	0.639312i	$0.779219\pi$
$390$		−	3.59655e10i		−	1.55463i
$391$	3.93583e10			1.68395
$392$		−	1.55048e10i		−	0.656634i
$393$	−3.25447e10			−1.36430
$394$			4.75219e10i			1.97201i
$395$			5.25423e10i			2.15835i
$396$	2.13049e10			0.866360
$397$	−2.75612e10			−1.10952			−0.554761	−	0.832009i	$-0.687190\pi$
$397$	−2.75612e10			−1.10952			−0.554761	+	0.832009i	$0.687190\pi$
$398$	1.67405e10			0.667170
$399$		−	2.49657e10i		−	0.985035i
$400$	1.72220e10			0.672735
$401$	2.55883e10			0.989608			0.494804	−	0.869005i	$-0.335240\pi$
$401$	2.55883e10			0.989608			0.494804	+	0.869005i	$0.335240\pi$
$402$	−4.81581e10			−1.84402
$403$	6.33522e9			0.240183
$404$	−1.73782e9			−0.0652348
$405$		−	9.85606e10i		−	3.66339i
$406$			5.00035e9i			0.184033i
$407$		−	3.68639e10i		−	1.34345i
$408$	5.56095e10			2.00682
$409$		−	4.26629e10i		−	1.52461i	−0.647220	−	0.762303i	$-0.724069\pi$
$409$		−	4.26629e10i		−	1.52461i	0.647220	−	0.762303i	$-0.275931\pi$
$410$	4.98031e10			1.76247
$411$	4.16526e10			1.45974
$412$	−6.14354e8			−0.0213221
$413$		−	1.78246e9i		−	0.0612659i
$414$			1.11544e11i			3.79704i
$415$			1.36064e10i			0.458724i
$416$			8.14400e9i			0.271935i
$417$			4.98819e10i			1.64968i
$418$	5.41317e10			1.77316
$419$		−	5.09397e10i		−	1.65272i	−0.563140	−	0.826362i	$-0.690407\pi$
$419$		−	5.09397e10i		−	1.65272i	0.563140	−	0.826362i	$-0.309593\pi$
$420$		−	8.19782e9i		−	0.263452i
$421$		−	3.53233e8i		−	0.0112443i	−0.999984	−	0.00562216i	$-0.998210\pi$
$421$		−	3.53233e8i		−	0.0112443i	0.999984	−	0.00562216i	$-0.00178960\pi$
$422$	6.46741e10			2.03930
$423$	−1.14967e11			−3.59097
$424$			1.22780e10i			0.379894i
$425$	−2.33165e10			−0.714672
$426$		−	1.06424e11i		−	3.23147i
$427$	4.44020e9			0.133565
$428$	7.31473e9			0.217983
$429$			5.51787e10i			1.62908i
$430$	−4.44504e10	−	1.69912e10i	−1.30017	−	0.496992i
$431$	−1.09238e9			−0.0316566			−0.0158283	−	0.999875i	$-0.505039\pi$
$431$	−1.09238e9			−0.0316566			−0.0158283	+	0.999875i	$0.505039\pi$
$432$			1.19248e11i			3.42386i
$433$		−	6.70639e10i		−	1.90782i	−0.300092	−	0.953910i	$-0.597017\pi$
$433$		−	6.70639e10i		−	1.90782i	0.300092	−	0.953910i	$-0.402983\pi$
$434$	7.62594e9			0.214949
$435$			2.92705e10i			0.817472i
$436$	−1.54852e10			−0.428521
$437$			5.36662e10i			1.47155i
$438$			7.18381e10i			1.95190i
$439$	−3.53135e10			−0.950785			−0.475393	−	0.879774i	$-0.657694\pi$
$439$	−3.53135e10			−0.950785			−0.475393	+	0.879774i	$0.657694\pi$
$440$	−5.83202e10			−1.55599
$441$	−7.41904e10			−1.96152
$442$		−	3.15063e10i		−	0.825483i
$443$	−6.26941e9			−0.162784			−0.0813921	−	0.996682i	$-0.525937\pi$
$443$	−6.26941e9			−0.162784			−0.0813921	+	0.996682i	$0.525937\pi$
$444$	−1.57381e10			−0.404967
$445$	−8.34021e9			−0.212685
$446$	3.31810e9			0.0838592
$447$	9.64384e10			2.41557
$448$		−	1.29048e10i		−	0.320361i
$449$		−	7.40849e10i		−	1.82282i	−0.411497	−	0.911411i	$-0.634994\pi$
$449$		−	7.40849e10i		−	1.82282i	0.411497	−	0.911411i	$-0.365006\pi$
$450$		−	6.60805e10i		−	1.61147i
$451$	−7.64083e10			−1.84686
$452$		−	1.33151e10i		−	0.319000i
$453$	6.56464e10			1.55890
$454$	−3.91378e10			−0.921240
$455$	1.52390e10			0.355559
$456$			7.58252e10i			1.75370i
$457$			6.33445e10i			1.45226i	0.687558	+	0.726129i	$0.258683\pi$
$457$			6.33445e10i			1.45226i	−0.687558	+	0.726129i	$0.741317\pi$
$458$			2.44428e10i			0.555507i
$459$		−	1.61447e11i		−	3.63730i
$460$			1.76220e10i			0.393572i
$461$	4.30565e10			0.953313			0.476656	−	0.879090i	$-0.341849\pi$
$461$	4.30565e10			0.953313			0.476656	+	0.879090i	$0.341849\pi$
$462$			6.64206e10i			1.45792i
$463$		−	2.59095e10i		−	0.563812i	−0.959442	−	0.281906i	$-0.909033\pi$
$463$		−	2.59095e10i		−	0.563812i	0.959442	−	0.281906i	$-0.0909667\pi$
$464$		−	1.89392e10i		−	0.408592i
$465$	4.46398e10			0.954797
$466$	2.77980e10			0.589481
$467$			3.07472e10i			0.646455i	0.946321	+	0.323228i	$0.104768\pi$
$467$			3.07472e10i			0.646455i	−0.946321	+	0.323228i	$0.895232\pi$
$468$	1.69079e10			0.352456
$469$		−	2.04052e10i		−	0.421745i
$470$	−9.59182e10			−1.96567
$471$	−3.22170e10			−0.654637
$472$			5.41365e9i			0.109074i
$473$	6.81962e10	+	2.60680e10i	1.36244	+	0.520791i
$474$	−1.81746e11			−3.60040
$475$		−	3.17927e10i		−	0.624529i
$476$		−	7.18140e9i		−	0.139888i
$477$	5.87498e10			1.13484
$478$			4.64467e10i			0.889700i
$479$	4.25414e10			0.808109			0.404054	−	0.914735i	$-0.367601\pi$
$479$	4.25414e10			0.808109			0.404054	+	0.914735i	$0.367601\pi$
$480$			5.73851e10i			1.08102i
$481$		−	2.92557e10i		−	0.546550i
$482$	6.56769e9			0.121682
$483$	−6.58493e10			−1.20994
$484$	−1.44521e10			−0.263360
$485$			9.69862e10i			1.75284i
$486$	1.60986e11			2.88564
$487$	−8.19028e10			−1.45607			−0.728036	−	0.685539i	$-0.759567\pi$
$487$	−8.19028e10			−1.45607			−0.728036	+	0.685539i	$0.759567\pi$
$488$	−1.34857e10			−0.237790
$489$	−4.83808e9			−0.0846132
$490$	−6.18979e10			−1.07372
$491$		−	9.90164e10i		−	1.70365i	−0.523824	−	0.851827i	$-0.675495\pi$
$491$		−	9.90164e10i		−	1.70365i	0.523824	−	0.851827i	$-0.324505\pi$
$492$			3.26205e10i			0.556712i
$493$			2.56413e10i			0.434063i
$494$	4.29597e10			0.721363
$495$			2.79061e11i			4.64813i
$496$	−2.88838e10			−0.477230
$497$	4.50931e10			0.739068
$498$	−4.70650e10			−0.765210
$499$		−	2.10144e10i		−	0.338934i	−0.985536	−	0.169467i	$-0.945795\pi$
$499$		−	2.10144e10i		−	0.338934i	0.985536	−	0.169467i	$-0.0542046\pi$
$500$			7.85666e9i			0.125707i
$501$			2.63383e10i			0.418058i
$502$		−	5.01623e10i		−	0.789883i
$503$		−	4.46332e10i		−	0.697246i	−0.937263	−	0.348623i	$-0.886649\pi$
$503$		−	4.46332e10i		−	0.697246i	0.937263	−	0.348623i	$-0.113351\pi$
$504$	−6.67777e10			−1.03493
$505$		−	2.27628e10i		−	0.349993i
$506$		−	1.42778e11i		−	2.17800i
$507$		−	8.05770e10i		−	1.21949i
$508$	4.32776e9			0.0649842
$509$	−8.81999e10			−1.31400			−0.657002	−	0.753889i	$-0.728176\pi$
$509$	−8.81999e10			−1.31400			−0.657002	+	0.753889i	$0.728176\pi$
$510$		−	2.22003e11i		−	3.28154i
$511$	−3.04387e10			−0.446419
$512$			3.18379e10i			0.463302i
$513$	2.20138e11			3.17852
$514$	3.46623e10			0.496597
$515$		−	8.04708e9i		−	0.114396i
$516$	1.11291e10	−	2.91146e10i	0.156985	−	0.410688i
$517$	1.47159e11			2.05979
$518$		−	3.52161e10i		−	0.489128i
$519$			5.33384e10i			0.735141i
$520$	−4.62837e10			−0.633016
$521$			7.84546e10i			1.06480i	0.846493	+	0.532400i	$0.178710\pi$
$521$			7.84546e10i			1.06480i	−0.846493	+	0.532400i	$0.821290\pi$
$522$	−7.26694e10			−0.978744
$523$		−	7.85221e10i		−	1.04951i	−0.851254	−	0.524753i	$-0.824158\pi$
$523$		−	7.85221e10i		−	1.04951i	0.851254	−	0.524753i	$-0.175842\pi$
$524$		−	1.27647e10i		−	0.169311i
$525$	3.90102e10			0.513500
$526$	2.49673e10			0.326158
$527$	3.91051e10			0.506980
$528$		−	2.51573e11i		−	3.23689i
$529$	6.32386e10			0.807532
$530$	4.90156e10			0.621200
$531$	2.59042e10			0.325831
$532$	9.79205e9			0.122244
$533$	−6.06387e10			−0.751348
$534$		−	2.88490e10i		−	0.354786i
$535$			9.58116e10i			1.16951i
$536$			6.19743e10i			0.750848i
$537$	−2.45818e11			−2.95609
$538$			1.46748e10i			0.175163i
$539$	9.49644e10			1.12514
$540$	7.22854e10			0.850110
$541$	−1.01935e11			−1.18997			−0.594984	−	0.803737i	$-0.702842\pi$
$541$	−1.01935e11			−1.18997			−0.594984	+	0.803737i	$0.702842\pi$
$542$		−	1.21211e10i		−	0.140458i
$543$			2.24316e11i			2.58025i
$544$			5.02701e10i			0.574003i
$545$		−	2.02833e11i		−	2.29907i
$546$			5.27123e10i			0.593119i
$547$	3.06187e10			0.342009			0.171004	−	0.985270i	$-0.445299\pi$
$547$	3.06187e10			0.342009			0.171004	+	0.985270i	$0.445299\pi$
$548$			1.63370e10i			0.181155i
$549$			6.45288e10i			0.710337i
$550$			8.45837e10i			0.924349i
$551$	−3.49627e10			−0.379314
$552$	1.99996e11			2.15410
$553$		−	7.70079e10i		−	0.823445i
$554$	2.83619e10			0.301090
$555$		−	2.06144e11i		−	2.17270i
$556$	−1.95647e10			−0.204727
$557$	1.28205e11			1.33194			0.665971	−	0.745978i	$-0.268017\pi$
$557$	1.28205e11			1.33194			0.665971	+	0.745978i	$0.268017\pi$
$558$			1.10827e11i			1.14316i
$559$	5.41215e10	+	2.06879e10i	0.554272	+	0.211870i
$560$	−6.94785e10			−0.706477
$561$			3.40599e11i			3.43868i
$562$			1.74949e11i			1.75374i
$563$	−1.75852e11			−1.75031			−0.875153	−	0.483847i	$-0.839239\pi$
$563$	−1.75852e11			−1.75031			−0.875153	+	0.483847i	$0.839239\pi$
$564$		−	6.28255e10i		−	0.620897i
$565$	1.74407e11			1.71148
$566$		−	1.00695e11i		−	0.981161i
$567$			1.44454e11i			1.39765i
$568$	−1.36956e11			−1.31579
$569$	1.96827e11			1.87774			0.938872	−	0.344266i	$-0.111872\pi$
$569$	1.96827e11			1.87774			0.938872	+	0.344266i	$0.111872\pi$
$570$	3.02707e11			2.86763
$571$			8.11931e10i			0.763791i	0.924205	+	0.381896i	$0.124729\pi$
$571$			8.11931e10i			0.763791i	−0.924205	+	0.381896i	$0.875271\pi$
$572$	−2.16422e10			−0.202170
$573$	−7.01413e10			−0.650662
$574$	−7.29931e10			−0.672410
$575$	−8.38562e10			−0.767121
$576$	1.87543e11			1.70377
$577$		−	3.27137e10i		−	0.295139i	−0.989052	−	0.147569i	$-0.952855\pi$
$577$		−	3.27137e10i		−	0.295139i	0.989052	−	0.147569i	$-0.0471449\pi$
$578$		−	7.05129e10i		−	0.631768i
$579$		−	2.67466e11i		−	2.37988i
$580$	−1.14805e10			−0.101449
$581$		−	1.99420e10i		−	0.175011i
$582$	−3.35478e11			−2.92397
$583$	−7.52003e10			−0.650946
$584$	9.24479e10			0.794777
$585$			2.21467e11i			1.89097i
$586$			1.47380e11i			1.24982i
$587$		−	4.75906e10i		−	0.400838i	−0.979710	−	0.200419i	$-0.935770\pi$
$587$		−	4.75906e10i		−	0.400838i	0.979710	−	0.200419i	$-0.0642303\pi$
$588$		−	4.05426e10i		−	0.339158i
$589$			5.33209e10i			0.443033i
$590$	2.16122e10			0.178357
$591$		−	4.07708e11i		−	3.34194i
$592$			1.33384e11i			1.08597i
$593$			3.97667e9i			0.0321589i	0.999871	+	0.0160794i	$0.00511847\pi$
$593$			3.97667e9i			0.0321589i	−0.999871	+	0.0160794i	$0.994882\pi$
$594$	−5.85672e11			−4.70445
$595$	9.40653e10			0.750519
$596$			3.78252e10i			0.299775i
$597$	−1.43623e11			−1.13065
$598$		−	1.13310e11i		−	0.886064i
$599$	1.36562e11			1.06077			0.530387	−	0.847756i	$-0.322047\pi$
$599$	1.36562e11			1.06077			0.530387	+	0.847756i	$0.322047\pi$
$600$	−1.18481e11			−0.914205
$601$			3.99717e10i			0.306376i	0.988197	+	0.153188i	$0.0489540\pi$
$601$			3.99717e10i			0.306376i	−0.988197	+	0.153188i	$0.951046\pi$
$602$	6.51481e10	+	2.49029e10i	0.496039	+	0.189611i
$603$	2.96546e11			2.24297
$604$			2.57479e10i			0.193461i
$605$		−	1.89300e11i		−	1.41296i
$606$	7.87371e10			0.583833
$607$		−	1.12940e11i		−	0.831945i	−0.909377	−	0.415973i	$-0.863441\pi$
$607$		−	1.12940e11i		−	0.831945i	0.909377	−	0.415973i	$-0.136559\pi$
$608$	−6.85447e10			−0.501602
$609$		−	4.28998e10i		−	0.311879i
$610$			5.38371e10i			0.388833i
$611$	1.16787e11			0.837974
$612$	1.04366e11			0.743968
$613$	8.37139e10			0.592865			0.296432	−	0.955054i	$-0.404203\pi$
$613$	8.37139e10			0.592865			0.296432	+	0.955054i	$0.404203\pi$
$614$			4.42748e10i			0.311518i
$615$	−4.27279e11			−2.98683
$616$	8.54761e10			0.593638
$617$	1.29479e11			0.893423			0.446712	−	0.894678i	$-0.352595\pi$
$617$	1.29479e11			0.893423			0.446712	+	0.894678i	$0.352595\pi$
$618$	2.78351e10			0.190827
$619$	−1.67421e11			−1.14037			−0.570187	−	0.821515i	$-0.693129\pi$
$619$	−1.67421e11			−1.14037			−0.570187	+	0.821515i	$0.693129\pi$
$620$			1.75087e10i			0.118491i
$621$		−	5.80635e11i		−	3.90424i
$622$		−	1.48312e11i		−	0.990867i
$623$	1.22237e10			0.0811429
$624$		−	1.99652e11i		−	1.31685i
$625$	−1.89975e11			−1.24502
$626$	−2.65796e11			−1.73082
$627$	−4.64416e11			−3.00495
$628$		−	1.26362e10i		−	0.0812412i
$629$		−	1.80585e11i		−	1.15366i
$630$			2.66588e11i			1.69230i
$631$			3.06797e11i			1.93523i	0.252427	+	0.967616i	$0.418771\pi$
$631$			3.06797e11i			1.93523i	−0.252427	+	0.967616i	$0.581229\pi$
$632$			2.33887e11i			1.46601i
$633$	−5.54863e11			−3.45598
$634$			8.76271e10i			0.542352i
$635$			5.66869e10i			0.348649i
$636$			3.21048e10i			0.196219i
$637$	7.53651e10			0.457733
$638$	9.30175e10			0.561412
$639$			6.55331e11i			3.93059i
$640$	2.52826e11			1.50696
$641$			9.47904e9i			0.0561477i	0.999606	+	0.0280739i	$0.00893736\pi$
$641$			9.47904e9i			0.0561477i	−0.999606	+	0.0280739i	$0.991063\pi$
$642$	−3.31415e11			−1.95089
$643$	−6.87672e10			−0.402288			−0.201144	−	0.979562i	$-0.564466\pi$
$643$	−6.87672e10			−0.402288			−0.201144	+	0.979562i	$0.564466\pi$
$644$		−	2.58275e10i		−	0.150155i
$645$	3.81356e11	+	1.45773e11i	2.20339	+	0.842247i
$646$	2.65175e11			1.52266
$647$			2.26638e11i			1.29335i	0.762767	+	0.646673i	$0.223840\pi$
$647$			2.26638e11i			1.29335i	−0.762767	+	0.646673i	$0.776160\pi$
$648$		−	4.38732e11i		−	2.48828i
$649$	−3.31576e10			−0.186898
$650$			6.71268e10i			0.376048i
$651$	−6.54257e10			−0.364271
$652$		−	1.89760e9i		−	0.0105006i
$653$		−	1.26350e11i		−	0.694898i	−0.937699	−	0.347449i	$-0.887048\pi$
$653$		−	1.26350e11i		−	0.694898i	0.937699	−	0.347449i	$-0.112952\pi$
$654$	7.01604e11			3.83514
$655$	1.67198e11			0.908377
$656$	2.76467e11			1.49289
$657$		−	4.42361e11i		−	2.37419i
$658$	1.40581e11			0.749935
$659$	5.31715e10			0.281927			0.140964	−	0.990015i	$-0.454980\pi$
$659$	5.31715e10			0.281927			0.140964	+	0.990015i	$0.454980\pi$
$660$	−1.52497e11			−0.803687
$661$	−2.49891e11			−1.30901			−0.654506	−	0.756056i	$-0.727124\pi$
$661$	−2.49891e11			−1.30901			−0.654506	+	0.756056i	$0.727124\pi$
$662$	−1.79891e11			−0.936653
$663$			2.70304e11i			1.39894i
$664$			6.05675e10i			0.311579i
$665$			1.28261e11i			0.655854i
$666$	5.11791e11			2.60133
$667$			9.22174e10i			0.465918i
$668$	−1.03304e10			−0.0518815
$669$	−2.84672e10			−0.142115
$670$	2.47412e11			1.22778
$671$		−	8.25975e10i		−	0.407452i
$672$		−	8.41056e10i		−	0.412428i
$673$		−	6.74617e10i		−	0.328849i	−0.986390	−	0.164425i	$-0.947423\pi$
$673$		−	6.74617e10i		−	0.328849i	0.986390	−	0.164425i	$-0.0525768\pi$
$674$			4.66692e10i			0.226147i
$675$			3.43977e11i			1.65697i
$676$	3.16040e10			0.151340
$677$			3.99956e11i			1.90396i	0.306164	+	0.951979i	$0.400954\pi$
$677$			3.99956e11i			1.90396i	−0.306164	+	0.951979i	$0.599046\pi$
$678$			6.03281e11i			2.85496i
$679$		−	1.42146e11i		−	0.668739i
$680$	−2.85693e11			−1.33618
$681$	3.35777e11			1.56122
$682$		−	1.41859e11i		−	0.655722i
$683$	−2.49767e11			−1.14776			−0.573882	−	0.818938i	$-0.694563\pi$
$683$	−2.49767e11			−1.14776			−0.573882	+	0.818938i	$0.694563\pi$
$684$			1.42306e11i			0.650130i
$685$	−2.13990e11			−0.971920
$686$	2.08325e11			0.940686
$687$		−	2.09704e11i		−	0.941412i
$688$	−2.46753e11	−	9.43214e10i	−1.10131	−	0.420975i
$689$	−5.96800e10			−0.264821
$690$		−	7.98418e11i		−	3.52236i
$691$			8.07032e10i			0.353980i	0.984213	+	0.176990i	$0.0566360\pi$
$691$			8.07032e10i			0.353980i	−0.984213	+	0.176990i	$0.943364\pi$
$692$	−2.09204e10			−0.0912318
$693$		−	4.09002e11i		−	1.77334i
$694$	9.47853e10			0.408604
$695$		−	2.56267e11i		−	1.09838i
$696$			1.30295e11i			0.555251i
$697$	−3.74302e11			−1.58595
$698$	−3.13467e10			−0.132059
$699$	−2.38489e11			−0.998987
$700$			1.53006e10i			0.0637260i
$701$	−1.82574e11			−0.756078			−0.378039	−	0.925790i	$-0.623401\pi$
$701$	−1.82574e11			−0.756078			−0.378039	+	0.925790i	$0.623401\pi$
$702$	−4.64798e11			−1.91388
$703$	2.46233e11			1.00815
$704$	−2.40057e11			−0.977292
$705$	8.22918e11			3.33119
$706$			2.66015e11i			1.07075i
$707$			3.33619e10i			0.133528i
$708$			1.41558e10i			0.0563379i
$709$	−2.09260e11			−0.828137			−0.414069	−	0.910246i	$-0.635893\pi$
$709$	−2.09260e11			−0.828137			−0.414069	+	0.910246i	$0.635893\pi$
$710$			5.46750e11i			2.15157i
$711$	1.11914e12			4.37933
$712$	−3.71256e10			−0.144462
$713$	1.40639e11			0.544187
$714$			3.25375e11i			1.25196i
$715$		−	2.83480e11i		−	1.08467i
$716$		−	9.64151e10i		−	0.366854i
$717$		−	3.98484e11i		−	1.50777i
$718$		−	1.78665e11i		−	0.672265i
$719$	2.93803e10			0.109936			0.0549682	−	0.998488i	$-0.482494\pi$
$719$	2.93803e10			0.109936			0.0549682	+	0.998488i	$0.482494\pi$
$720$		−	1.00972e12i		−	3.75726i
$721$			1.17941e10i			0.0436439i
$722$			5.97639e10i			0.219933i
$723$	−5.63467e10			−0.206212
$724$	−8.79815e10			−0.320211
$725$		−	5.46311e10i		−	0.197737i
$726$	6.54795e11			2.35700
$727$		−	2.83587e11i		−	1.01519i	−0.861595	−	0.507597i	$-0.830534\pi$
$727$		−	2.83587e11i		−	1.01519i	0.861595	−	0.507597i	$-0.169466\pi$
$728$	6.78351e10			0.241506
$729$	−5.55570e11			−1.96711
$730$		−	3.69067e11i		−	1.29961i
$731$	3.34073e11	+	1.27699e11i	1.16996	+	0.447218i
$732$	−3.52628e10			−0.122821
$733$			1.36753e11i			0.473720i	0.971544	+	0.236860i	$0.0761183\pi$
$733$			1.36753e11i			0.473720i	−0.971544	+	0.236860i	$0.923882\pi$
$734$			4.00788e11i			1.38080i
$735$	5.31045e11			1.81962
$736$			1.80793e11i			0.616128i
$737$	−3.79581e11			−1.28657
$738$		−	1.06080e12i		−	3.57608i
$739$			1.82315e10i			0.0611285i	0.999533	+	0.0305643i	$0.00973042\pi$
$739$			1.82315e10i			0.0611285i	−0.999533	+	0.0305643i	$0.990270\pi$
$740$	8.08540e10			0.269634
$741$	−3.68567e11			−1.22249
$742$	−7.18390e10			−0.236998
$743$			2.39818e11i			0.786913i	0.919343	+	0.393456i	$0.128721\pi$
$743$			2.39818e11i			0.786913i	−0.919343	+	0.393456i	$0.871279\pi$
$744$	1.98710e11			0.648526
$745$	−4.95451e11			−1.60833
$746$	−8.74325e10			−0.282304
$747$	2.89815e11			0.930760
$748$	−1.33590e11			−0.426744
$749$		−	1.40425e11i		−	0.446187i
$750$		−	3.55969e11i		−	1.12504i
$751$		−	2.50813e11i		−	0.788478i	−0.919008	−	0.394239i	$-0.871008\pi$
$751$		−	2.50813e11i		−	0.788478i	0.919008	−	0.394239i	$-0.128992\pi$
$752$	−5.32461e11			−1.66501
$753$			4.30361e11i			1.33861i
$754$	7.38200e10			0.228396
$755$	−3.37257e11			−1.03794
$756$	−1.05944e11			−0.324331
$757$		−	2.52893e11i		−	0.770111i	−0.922893	−	0.385056i	$-0.874182\pi$
$757$		−	2.52893e11i		−	0.770111i	0.922893	−	0.385056i	$-0.125818\pi$
$758$		−	2.01716e10i		−	0.0611032i
$759$			1.22494e12i			3.69104i
$760$		−	3.89551e11i		−	1.16764i
$761$			2.33691e10i			0.0696791i	0.999393	+	0.0348396i	$0.0110920\pi$
$761$			2.33691e10i			0.0696791i	−0.999393	+	0.0348396i	$0.988908\pi$
$762$	−1.96082e11			−0.581591
$763$			2.97279e11i			0.877133i
$764$		−	2.75109e10i		−	0.0807479i
$765$			1.36704e12i			3.99148i
$766$	5.11189e11			1.48479
$767$	−2.63144e10			−0.0760346
$768$			4.35785e11i			1.25264i
$769$	−2.10074e11			−0.600713			−0.300356	−	0.953827i	$-0.597106\pi$
$769$	−2.10074e11			−0.600713			−0.300356	+	0.953827i	$0.597106\pi$
$770$		−	3.41235e11i		−	0.970712i
$771$	−2.97380e11			−0.841578
$772$	1.04906e11			0.295346
$773$		−	6.38984e10i		−	0.178966i	−0.995988	−	0.0894832i	$-0.971478\pi$
$773$		−	6.38984e10i		−	0.178966i	0.995988	−	0.0894832i	$-0.0285215\pi$
$774$	−3.61909e11	+	9.46787e11i	−1.00841	+	2.63808i
$775$	−8.33168e10			−0.230954
$776$			4.31724e11i			1.19058i
$777$			3.02132e11i			0.828921i
$778$	5.20291e11			1.42013
$779$		−	5.10371e11i		−	1.38591i
$780$	−1.21024e11			−0.326959
$781$		−	8.38830e11i		−	2.25460i
$782$		−	6.99425e11i		−	1.87031i
$783$	3.78275e11			1.00638
$784$	−3.43608e11			−0.909492
$785$	1.65514e11			0.435869
$786$			5.78343e11i			1.51529i
$787$	1.89152e11			0.493074			0.246537	−	0.969133i	$-0.420707\pi$
$787$	1.89152e11			0.493074			0.246537	+	0.969133i	$0.420707\pi$
$788$	1.59911e11			0.414739
$789$	−2.14204e11			−0.552737
$790$	9.33715e11			2.39721
$791$	−2.55618e11			−0.652957
$792$			1.24221e12i			3.15715i
$793$		−	6.55505e10i		−	0.165761i
$794$			4.89783e11i			1.23231i
$795$	−4.20523e11			−1.05274
$796$		−	5.63319e10i		−	0.140314i
$797$	3.38421e11			0.838733			0.419367	−	0.907817i	$-0.362252\pi$
$797$	3.38421e11			0.838733			0.419367	+	0.907817i	$0.362252\pi$
$798$	−4.43658e11			−1.09405
$799$	7.20887e11			1.76880
$800$		−	1.07105e11i		−	0.261486i
$801$			1.77645e11i			0.431543i
$802$		−	4.54722e11i		−	1.09913i
$803$			5.66227e11i			1.36185i
$804$			1.62052e11i			0.387821i
$805$	3.38300e11			0.805598
$806$		−	1.12581e11i		−	0.266764i
$807$		−	1.25900e11i		−	0.296847i
$808$		−	1.01326e11i		−	0.237725i
$809$	1.68821e11			0.394124			0.197062	−	0.980391i	$-0.436860\pi$
$809$	1.68821e11			0.394124			0.197062	+	0.980391i	$0.436860\pi$
$810$	−1.75149e12			−4.06882
$811$		−	1.70198e11i		−	0.393433i	−0.980460	−	0.196716i	$-0.936972\pi$
$811$		−	1.70198e11i		−	0.393433i	0.980460	−	0.196716i	$-0.0630278\pi$
$812$	1.68262e10			0.0387046
$813$			1.03992e11i			0.238033i
$814$	−6.55097e11			−1.49214
$815$	2.48556e10			0.0563370
$816$		−	1.23238e12i		−	2.77961i
$817$	−1.74122e11	+	4.55518e11i	−0.390810	+	1.02239i
$818$	−7.58151e11			−1.69333
$819$		−	3.24590e11i		−	0.721438i
$820$		−	1.67588e11i		−	0.370669i
$821$	−2.88857e11			−0.635784			−0.317892	−	0.948127i	$-0.602975\pi$
$821$	−2.88857e11			−0.635784			−0.317892	+	0.948127i	$0.602975\pi$
$822$		−	7.40197e11i		−	1.62129i
$823$	1.78540e11			0.389168			0.194584	−	0.980886i	$-0.437664\pi$
$823$	1.78540e11			0.389168			0.194584	+	0.980886i	$0.437664\pi$
$824$		−	3.58208e10i		−	0.0777009i
$825$		−	7.25675e11i		−	1.56648i
$826$	−3.16756e10			−0.0680463
$827$	−6.03486e11			−1.29016			−0.645082	−	0.764113i	$-0.723177\pi$
$827$	−6.03486e11			−1.29016			−0.645082	+	0.764113i	$0.723177\pi$
$828$	3.75347e11			0.798567
$829$			1.35042e11i			0.285923i	0.989728	+	0.142962i	$0.0456625\pi$
$829$			1.35042e11i			0.285923i	−0.989728	+	0.142962i	$0.954337\pi$
$830$	2.41796e11			0.509491
$831$	−2.43327e11			−0.510255
$832$	−1.90513e11			−0.397586
$833$	4.65202e11			0.966189
$834$	8.86437e11			1.83225
$835$		−	1.35313e11i		−	0.278351i
$836$		−	1.82154e11i		−	0.372917i
$837$		−	5.76900e11i		−	1.17543i
$838$	−9.05235e11			−1.83563
$839$		−	6.57720e11i		−	1.32737i	−0.748011	−	0.663687i	$-0.768991\pi$
$839$		−	6.57720e11i		−	1.32737i	0.748011	−	0.663687i	$-0.231009\pi$
$840$	4.77986e11			0.960059
$841$	4.40168e11			0.879903
$842$	−6.27721e9			−0.0124887
$843$		−	1.50095e12i		−	2.97205i
$844$		−	2.17629e11i		−	0.428890i
$845$			4.13963e11i			0.811960i
$846$			2.04304e12i			3.98838i
$847$			2.77445e11i			0.539068i
$848$	2.72096e11			0.526185
$849$			8.63895e11i			1.66276i
$850$			4.14350e11i			0.793765i
$851$		−	6.49463e11i		−	1.23833i
$852$	−3.58116e11			−0.679619
$853$	−1.56198e11			−0.295039			−0.147519	−	0.989059i	$-0.547129\pi$
$853$	−1.56198e11			−0.295039			−0.147519	+	0.989059i	$0.547129\pi$
$854$		−	7.89056e10i		−	0.148346i
$855$	−1.86399e12			−3.48803
$856$			4.26496e11i			0.794364i
$857$	8.56166e11			1.58721			0.793606	−	0.608433i	$-0.208201\pi$
$857$	8.56166e11			1.58721			0.793606	+	0.608433i	$0.208201\pi$
$858$	9.80565e11			1.80937
$859$		−	4.18036e11i		−	0.767788i	−0.923377	−	0.383894i	$-0.874583\pi$
$859$		−	4.18036e11i		−	0.767788i	0.923377	−	0.383894i	$-0.125417\pi$
$860$	−5.71754e10	+	1.49576e11i	−0.104524	+	0.273443i
$861$	6.26235e11			1.13953
$862$			1.94123e10i			0.0351600i
$863$			6.84673e10i			0.123435i	0.998094	+	0.0617177i	$0.0196579\pi$
$863$			6.84673e10i			0.123435i	−0.998094	+	0.0617177i	$0.980342\pi$
$864$	7.41612e11			1.33083
$865$		−	2.74025e11i		−	0.489470i
$866$	−1.19177e12			−2.11896
$867$			6.04956e11i			1.07065i
$868$		−	2.56613e10i		−	0.0452064i
$869$	−1.43252e12			−2.51200
$870$	5.20157e11			0.907941
$871$	−3.01241e11			−0.523410
$872$		−	9.02889e11i		−	1.56159i
$873$	2.06579e12			3.55656
$874$	9.53686e11			1.63441
$875$	1.50829e11			0.257307
$876$	2.41736e11			0.410511
$877$	2.69660e11			0.455846			0.227923	−	0.973679i	$-0.426807\pi$
$877$	2.69660e11			0.455846			0.227923	+	0.973679i	$0.426807\pi$
$878$			6.27546e11i			1.05601i
$879$		−	1.26442e12i		−	2.11806i
$880$			1.29245e12i			2.15518i
$881$	2.94267e11			0.488470			0.244235	−	0.969716i	$-0.421463\pi$
$881$	2.94267e11			0.488470			0.244235	+	0.969716i	$0.421463\pi$
$882$			1.31842e12i			2.17860i
$883$	−5.62272e11			−0.924919			−0.462460	−	0.886640i	$-0.653033\pi$
$883$	−5.62272e11			−0.924919			−0.462460	+	0.886640i	$0.653033\pi$
$884$	−1.06019e11			−0.173610
$885$	−1.85419e11			−0.302260
$886$			1.11412e11i			0.180799i
$887$		−	4.38832e11i		−	0.708930i	−0.935069	−	0.354465i	$-0.884663\pi$
$887$		−	4.38832e11i		−	0.708930i	0.935069	−	0.354465i	$-0.115337\pi$
$888$		−	9.17630e11i		−	1.47576i
$889$		−	8.30824e10i		−	0.133015i
$890$			1.48212e11i			0.236223i
$891$	2.68716e12			4.26366
$892$		−	1.11654e10i		−	0.0176367i
$893$			9.82950e11i			1.54570i
$894$		−	1.71378e12i		−	2.68290i
$895$	1.26289e12			1.96822
$896$	−3.70550e11			−0.574930
$897$			9.72131e11i			1.50160i
$898$	−1.31654e12			−2.02455
$899$			9.16242e10i			0.140272i
$900$	−2.22361e11			−0.338914
$901$	−3.68384e11			−0.558987
$902$			1.35783e12i			2.05126i
$903$	−5.58929e11	−	2.13651e11i	−0.840632	−	0.321331i
$904$	7.76357e11			1.16249
$905$		−	1.15242e12i		−	1.71798i
$906$		−	1.16658e12i		−	1.73142i
$907$	−1.26315e11			−0.186649			−0.0933247	−	0.995636i	$-0.529749\pi$
$907$	−1.26315e11			−0.186649			−0.0933247	+	0.995636i	$0.529749\pi$
$908$			1.31699e11i			0.193749i
$909$	−4.84843e11			−0.710143
$910$		−	2.70809e11i		−	0.394909i
$911$			1.02478e12i			1.48784i	0.668267	+	0.743922i	$0.267036\pi$
$911$			1.02478e12i			1.48784i	−0.668267	+	0.743922i	$0.732964\pi$
$912$	1.68039e12			2.42901
$913$	−3.70965e11			−0.533888
$914$	1.12568e12			1.61298
$915$		−	4.61888e11i		−	0.658950i
$916$	8.22503e10			0.116830
$917$	−2.45051e11			−0.346561
$918$	−2.86903e12			−4.03985
$919$	2.36982e11			0.332241			0.166121	−	0.986105i	$-0.446876\pi$
$919$	2.36982e11			0.332241			0.166121	+	0.986105i	$0.446876\pi$
$920$	−1.02748e12			−1.43424
$921$		−	3.79850e11i		−	0.527927i
$922$		−	7.65146e11i		−	1.05882i
$923$		−	6.65707e11i		−	0.917226i
$924$	2.23506e11			0.306620
$925$			3.84752e11i			0.525550i
$926$	−4.60430e11			−0.626209
$927$	−1.71402e11			−0.232111
$928$	−1.17784e11			−0.158816
$929$			1.05586e12i			1.41756i	0.705429	+	0.708781i	$0.250754\pi$
$929$			1.05586e12i			1.41756i	−0.705429	+	0.708781i	$0.749246\pi$
$930$		−	7.93282e11i		−	1.06046i
$931$			6.34317e11i			0.844321i
$932$		−	9.35403e10i		−	0.123975i
$933$			1.27242e12i			1.67921i
$934$	5.46401e11			0.717999
$935$		−	1.74982e12i		−	2.28953i
$936$			9.85837e11i			1.28440i
$937$			1.35732e12i			1.76086i	0.474178	+	0.880429i	$0.342745\pi$
$937$			1.35732e12i			1.76086i	−0.474178	+	0.880429i	$0.657255\pi$
$938$	−3.62615e11			−0.468419
$939$	2.28036e12			2.93320
$940$			3.22765e11i			0.413405i
$941$	4.33635e11			0.553052			0.276526	−	0.961007i	$-0.410817\pi$
$941$	4.33635e11			0.553052			0.276526	+	0.961007i	$0.410817\pi$
$942$			5.72519e11i			0.727086i
$943$	−1.34615e12			−1.70235
$944$	1.19974e11			0.151077
$945$		−	1.38770e12i		−	1.74008i
$946$	4.63248e11	−	1.21190e12i	0.578427	−	1.51322i
$947$	−1.71955e11			−0.213803			−0.106902	−	0.994270i	$-0.534093\pi$
$947$	−1.71955e11			−0.213803			−0.106902	+	0.994270i	$0.534093\pi$
$948$			6.11575e11i			0.757210i
$949$			4.49366e11i			0.554032i
$950$	−5.64979e11			−0.693646
$951$		−	7.51785e11i		−	0.919119i
$952$	4.18722e11			0.509774
$953$		−	8.64002e10i		−	0.104747i	−0.998628	−	0.0523737i	$-0.983321\pi$
$953$		−	8.64002e10i		−	0.104747i	0.998628	−	0.0523737i	$-0.0166787\pi$
$954$		−	1.04403e12i		−	1.26043i
$955$	3.60350e11			0.433223
$956$	1.56294e11			0.187115
$957$	−7.98031e11			−0.951419
$958$		−	7.55991e11i		−	0.897542i
$959$	3.13631e11			0.370804
$960$	−1.34241e12			−1.58052
$961$	−7.13157e11			−0.836164
$962$	−5.19895e11			−0.607037
$963$	2.04077e12			2.37296
$964$		−	2.21003e10i		−	0.0255912i
$965$			1.37410e12i			1.58457i
$966$			1.17019e12i			1.34384i
$967$	1.00018e12			1.14386			0.571930	−	0.820302i	$-0.306195\pi$
$967$	1.00018e12			1.14386			0.571930	+	0.820302i	$0.306195\pi$
$968$		−	8.42650e11i		−	0.959723i
$969$	−2.27504e12			−2.58044
$970$	1.72351e12			1.94683
$971$	1.18350e12			1.33135			0.665676	−	0.746241i	$-0.268143\pi$
$971$	1.18350e12			1.33135			0.665676	+	0.746241i	$0.268143\pi$
$972$		−	5.41718e11i		−	0.606888i
$973$			3.75594e11i			0.419052i
$974$			1.45547e12i			1.61722i
$975$		−	5.75906e11i		−	0.637284i
$976$			2.98861e11i			0.329359i
$977$	1.52625e11			0.167513			0.0837565	−	0.996486i	$-0.473308\pi$
$977$	1.52625e11			0.167513			0.0837565	+	0.996486i	$0.473308\pi$
$978$			8.59762e10i			0.0939773i
$979$		−	2.27388e11i		−	0.247535i
$980$			2.08287e11i			0.225817i
$981$	−4.32031e12			−4.66486
$982$	−1.75959e12			−1.89220
$983$		−	4.71920e11i		−	0.505422i	−0.967542	−	0.252711i	$-0.918678\pi$
$983$		−	4.71920e11i		−	0.505422i	0.967542	−	0.252711i	$-0.0813222\pi$
$984$	−1.90199e12			−2.02874
$985$			2.09459e12i			2.22513i
$986$	4.55665e11			0.482101
$987$	−1.20610e12			−1.27091
$988$		−	1.44560e11i		−	0.151712i
$989$	1.20147e12	+	4.59263e11i	1.25582	+	0.480039i
$990$	4.95912e12			5.16254
$991$			1.02642e12i			1.06422i	0.846674	+	0.532111i	$0.178601\pi$
$991$			1.02642e12i			1.06422i	−0.846674	+	0.532111i	$0.821399\pi$
$992$			1.79630e11i			0.185495i
$993$	1.54335e12			1.58734
$994$		−	8.01336e11i		−	0.820861i
$995$	7.37861e11			0.752805
$996$			1.58374e11i			0.160933i
$997$		−	8.69664e11i		−	0.880179i	−0.897954	−	0.440090i	$-0.854947\pi$
$997$		−	8.69664e11i		−	0.880179i	0.897954	−	0.440090i	$-0.145053\pi$
$998$	−3.73441e11			−0.376444
$999$	−2.66409e12			−2.67477

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.9.b.b.42.8	✓	28
43.42	odd	2	inner	43.9.b.b.42.21	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.9.b.b.42.8	✓	28	1.1	even	1	trivial
43.9.b.b.42.21	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)

\(f(q)\)	\(=\)	\(q-17.7707i q^{2} +152.462i q^{3} -59.7986 q^{4} -783.269i q^{5} +2709.35 q^{6} +1147.99i q^{7} -3486.64i q^{8} -16683.5 q^{9} +O(q^{10})\)	\(q-17.7707i q^{2} +152.462i q^{3} -59.7986 q^{4} -783.269i q^{5} +2709.35 q^{6} +1147.99i q^{7} -3486.64i q^{8} -16683.5 q^{9} -13919.3 q^{10} +21355.1 q^{11} -9116.98i q^{12} +16947.7 q^{13} +20400.5 q^{14} +119418. q^{15} -77268.6 q^{16} +104612. q^{17} +296478. i q^{18} +142642. i q^{19} +46838.4i q^{20} -175024. q^{21} -379495. i q^{22} +376231. q^{23} +531579. q^{24} -222885. q^{25} -301172. i q^{26} -1.54329e6i q^{27} -68647.9i q^{28} +245109. i q^{29} -2.12215e6i q^{30} +373811. q^{31} +480538. i q^{32} +3.25582e6i q^{33} -1.85903e6i q^{34} +899182. q^{35} +997650. q^{36} -1.72624e6i q^{37} +2.53484e6 q^{38} +2.58387e6i q^{39} -2.73098e6 q^{40} -3.57800e6 q^{41} +3.11030e6i q^{42} +(3.19345e6 + 1.22070e6i) q^{43} -1.27700e6 q^{44} +1.30677e7i q^{45} -6.68589e6i q^{46} +6.89105e6 q^{47} -1.17805e7i q^{48} +4.44693e6 q^{49} +3.96083e6i q^{50} +1.59493e7i q^{51} -1.01345e6 q^{52} -3.52143e6 q^{53} -2.74255e7 q^{54} -1.67268e7i q^{55} +4.00262e6 q^{56} -2.17474e7 q^{57} +4.35576e6 q^{58} -1.55268e6 q^{59} -7.14105e6 q^{60} -3.86782e6i q^{61} -6.64288e6i q^{62} -1.91524e7i q^{63} -1.12412e7 q^{64} -1.32746e7i q^{65} +5.78584e7 q^{66} -1.77748e7 q^{67} -6.25565e6 q^{68} +5.73607e7i q^{69} -1.59791e7i q^{70} -3.92801e7i q^{71} +5.81694e7i q^{72} +2.65149e7i q^{73} -3.06764e7 q^{74} -3.39814e7i q^{75} -8.52976e6i q^{76} +2.45153e7i q^{77} +4.59172e7 q^{78} -6.70808e7 q^{79} +6.05221e7i q^{80} +1.25832e8 q^{81} +6.35836e7i q^{82} -1.73713e7 q^{83} +1.04662e7 q^{84} -8.19394e7i q^{85} +(2.16926e7 - 5.67499e7i) q^{86} -3.73696e7 q^{87} -7.44574e7i q^{88} -1.06480e7i q^{89} +2.32222e8 q^{90} +1.94557e7i q^{91} -2.24981e7 q^{92} +5.69917e7i q^{93} -1.22459e8i q^{94} +1.11727e8 q^{95} -7.32636e7 q^{96} -1.23822e8 q^{97} -7.90251e7i q^{98} -3.56277e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9}+O(q^{10}) \) 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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