LMFDB - Embedded newform 43.11.b.b.42.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,11,Mod(42,43)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("43.42");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	43.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$27.3203618650$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			42.17
Character	$\chi$	$=$	43.42
Dual form			43.11.b.b.42.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.846054i q^{2} -54.5873i q^{3} +1023.28 q^{4} -4881.88i q^{5} -46.1839 q^{6} -30624.2i q^{7} -1732.11i q^{8} +56069.2 q^{9} +O(q^{10})$	\(q-0.846054i q^{2} -54.5873i q^{3} +1023.28 q^{4} -4881.88i q^{5} -46.1839 q^{6} -30624.2i q^{7} -1732.11i q^{8} +56069.2 q^{9} -4130.34 q^{10} -179422. q^{11} -55858.4i q^{12} -338315. q^{13} -25909.7 q^{14} -266489. q^{15} +1.04638e6 q^{16} +766203. q^{17} -47437.6i q^{18} +3.89726e6i q^{19} -4.99555e6i q^{20} -1.67169e6 q^{21} +151801. i q^{22} +3.13921e6 q^{23} -94551.5 q^{24} -1.40672e7 q^{25} +286232. i q^{26} -6.28400e6i q^{27} -3.13372e7i q^{28} +1.81741e7i q^{29} +225464. i q^{30} -2.96757e7 q^{31} -2.65898e6i q^{32} +9.79419e6i q^{33} -648249. i q^{34} -1.49504e8 q^{35} +5.73747e7 q^{36} -8.05730e7i q^{37} +3.29729e6 q^{38} +1.84677e7i q^{39} -8.45598e6 q^{40} +4.52023e7 q^{41} +1.41434e6i q^{42} +(1.20044e8 - 8.48586e7i) q^{43} -1.83600e8 q^{44} -2.73723e8i q^{45} -2.65594e6i q^{46} +1.36443e8 q^{47} -5.71190e7i q^{48} -6.55365e8 q^{49} +1.19016e7i q^{50} -4.18250e7i q^{51} -3.46192e8 q^{52} -3.81746e8 q^{53} -5.31660e6 q^{54} +8.75919e8i q^{55} -5.30445e7 q^{56} +2.12741e8 q^{57} +1.53763e7 q^{58} +1.06201e9 q^{59} -2.72694e8 q^{60} -7.22078e8i q^{61} +2.51072e7i q^{62} -1.71707e9i q^{63} +1.06924e9 q^{64} +1.65161e9i q^{65} +8.28642e6 q^{66} +1.44131e9 q^{67} +7.84044e8 q^{68} -1.71361e8i q^{69} +1.26488e8i q^{70} -3.79857e8i q^{71} -9.71183e7i q^{72} +1.13814e9i q^{73} -6.81691e7 q^{74} +7.67889e8i q^{75} +3.98800e9i q^{76} +5.49466e9i q^{77} +1.56247e7 q^{78} -4.58342e9 q^{79} -5.10829e9i q^{80} +2.96780e9 q^{81} -3.82436e7i q^{82} +6.19566e9 q^{83} -1.71062e9 q^{84} -3.74051e9i q^{85} +(-7.17950e7 - 1.01563e8i) q^{86} +9.92077e8 q^{87} +3.10780e8i q^{88} -7.46570e9i q^{89} -2.31585e8 q^{90} +1.03606e10i q^{91} +3.21231e9 q^{92} +1.61992e9i q^{93} -1.15438e8i q^{94} +1.90259e10 q^{95} -1.45146e8 q^{96} -3.79259e9 q^{97} +5.54474e8i q^{98} -1.00601e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9}+O(q^{10}) $ 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9	$ 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9} - 254122 q^{10} - 218200 q^{11} - 191008 q^{13} - 1380228 q^{14} - 512732 q^{15} + 2224308 q^{16} - 1070678 q^{17} + 17857352 q^{21} + 8915254 q^{23} - 39666730 q^{24} - 82938284 q^{25} - 55042410 q^{31} - 179227232 q^{35} + 394381042 q^{36} + 709061882 q^{38} + 433255366 q^{40} + 80370626 q^{41} + 1585062 q^{43} + 324477888 q^{44} - 544910502 q^{47} - 2479345922 q^{49} - 987059452 q^{52} - 915886820 q^{53} - 297150836 q^{54} + 2172449592 q^{56} - 2398069428 q^{57} + 930519014 q^{58} + 3394816764 q^{59} - 5474941192 q^{60} + 2925325476 q^{64} + 455136192 q^{66} + 3405920388 q^{67} + 664008226 q^{68} + 16264108918 q^{74} - 17800086268 q^{78} - 13853150858 q^{79} + 20444701546 q^{81} + 113867236 q^{83} - 30401949428 q^{84} + 19291204884 q^{86} - 5221634730 q^{87} - 6984391876 q^{90} + 41423783058 q^{92} + 4107406010 q^{95} + 33148445474 q^{96} + 15795117154 q^{97} + 1345877600 q^{99}+O(q^{100}) $ 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9 - 254122 * q^10 - 218200 * q^11 - 191008 * q^13 - 1380228 * q^14 - 512732 * q^15 + 2224308 * q^16 - 1070678 * q^17 + 17857352 * q^21 + 8915254 * q^23 - 39666730 * q^24 - 82938284 * q^25 - 55042410 * q^31 - 179227232 * q^35 + 394381042 * q^36 + 709061882 * q^38 + 433255366 * q^40 + 80370626 * q^41 + 1585062 * q^43 + 324477888 * q^44 - 544910502 * q^47 - 2479345922 * q^49 - 987059452 * q^52 - 915886820 * q^53 - 297150836 * q^54 + 2172449592 * q^56 - 2398069428 * q^57 + 930519014 * q^58 + 3394816764 * q^59 - 5474941192 * q^60 + 2925325476 * q^64 + 455136192 * q^66 + 3405920388 * q^67 + 664008226 * q^68 + 16264108918 * q^74 - 17800086268 * q^78 - 13853150858 * q^79 + 20444701546 * q^81 + 113867236 * q^83 - 30401949428 * q^84 + 19291204884 * q^86 - 5221634730 * q^87 - 6984391876 * q^90 + 41423783058 * q^92 + 4107406010 * q^95 + 33148445474 * q^96 + 15795117154 * q^97 + 1345877600 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	0.846054i		−	0.0264392i	−0.999913	−	0.0132196i	$-0.995792\pi$
$2$		−	0.846054i		−	0.0264392i	0.999913	−	0.0132196i	$-0.00420805\pi$
$3$		−	54.5873i		−	0.224639i	−0.993672	−	0.112320i	$-0.964172\pi$
$3$		−	54.5873i		−	0.224639i	0.993672	−	0.112320i	$-0.0358281\pi$
$4$	1023.28			0.999301
$5$		−	4881.88i		−	1.56220i	−0.624404	−	0.781101i	$-0.714658\pi$
$5$		−	4881.88i		−	1.56220i	0.624404	−	0.781101i	$-0.285342\pi$
$6$	−46.1839			−0.00593928
$7$		−	30624.2i		−	1.82211i	−0.412287	−	0.911054i	$-0.635270\pi$
$7$		−	30624.2i		−	1.82211i	0.412287	−	0.911054i	$-0.364730\pi$
$8$		−	1732.11i		−	0.0528599i
$9$	56069.2			0.949537
$10$	−4130.34			−0.0413034
$11$	−179422.			−1.11407			−0.557036	−	0.830488i	$-0.688061\pi$
$11$	−179422.			−1.11407			−0.557036	+	0.830488i	$0.688061\pi$
$12$		−	55858.4i		−	0.224482i
$13$	−338315.			−0.911179			−0.455590	−	0.890190i	$-0.650572\pi$
$13$	−338315.			−0.911179			−0.455590	+	0.890190i	$0.650572\pi$
$14$	−25909.7			−0.0481751
$15$	−266489.			−0.350932
$16$	1.04638e6			0.997903
$17$	766203.			0.539634			0.269817	−	0.962912i	$-0.413037\pi$
$17$	766203.			0.539634			0.269817	+	0.962912i	$0.413037\pi$
$18$		−	47437.6i		−	0.0251050i
$19$			3.89726e6i			1.57395i	0.616985	+	0.786975i	$0.288354\pi$
$19$			3.89726e6i			1.57395i	−0.616985	+	0.786975i	$0.711646\pi$
$20$		−	4.99555e6i		−	1.56111i
$21$	−1.67169e6			−0.409317
$22$			151801.i			0.0294552i
$23$	3.13921e6			0.487732			0.243866	−	0.969809i	$-0.421584\pi$
$23$	3.13921e6			0.487732			0.243866	+	0.969809i	$0.421584\pi$
$24$	−94551.5			−0.0118744
$25$	−1.40672e7			−1.44048
$26$			286232.i			0.0240908i
$27$		−	6.28400e6i		−	0.437943i
$28$		−	3.13372e7i		−	1.82083i
$29$			1.81741e7i			0.886060i	0.896507	+	0.443030i	$0.146097\pi$
$29$			1.81741e7i			0.886060i	−0.896507	+	0.443030i	$0.853903\pi$
$30$			225464.i			0.00927836i
$31$	−2.96757e7			−1.03656			−0.518278	−	0.855212i	$-0.673427\pi$
$31$	−2.96757e7			−1.03656			−0.518278	+	0.855212i	$0.673427\pi$
$32$		−	2.65898e6i		−	0.0792437i
$33$			9.79419e6i			0.250264i
$34$		−	648249.i		−	0.0142675i
$35$	−1.49504e8			−2.84650
$36$	5.73747e7			0.948873
$37$		−	8.05730e7i		−	1.16193i	−0.813928	−	0.580966i	$-0.802675\pi$
$37$		−	8.05730e7i		−	1.16193i	0.813928	−	0.580966i	$-0.197325\pi$
$38$	3.29729e6			0.0416140
$39$			1.84677e7i			0.204687i
$40$	−8.45598e6			−0.0825779
$41$	4.52023e7			0.390159			0.195079	−	0.980787i	$-0.437504\pi$
$41$	4.52023e7			0.390159			0.195079	+	0.980787i	$0.437504\pi$
$42$			1.41434e6i			0.0108220i
$43$	1.20044e8	−	8.48586e7i	0.816577	−	0.577237i
$43$	1.20044e8	−	8.48586e7i	0.816577	−	0.577237i
$44$	−1.83600e8			−1.11329
$45$		−	2.73723e8i		−	1.48337i
$46$		−	2.65594e6i		−	0.0128952i
$47$	1.36443e8			0.594925			0.297463	−	0.954733i	$-0.403860\pi$
$47$	1.36443e8			0.594925			0.297463	+	0.954733i	$0.403860\pi$
$48$		−	5.71190e7i		−	0.224168i
$49$	−6.55365e8			−2.32008
$50$			1.19016e7i			0.0380850i
$51$		−	4.18250e7i		−	0.121223i
$52$	−3.46192e8			−0.910542
$53$	−3.81746e8			−0.912842			−0.456421	−	0.889764i	$-0.650869\pi$
$53$	−3.81746e8			−0.912842			−0.456421	+	0.889764i	$0.650869\pi$
$54$	−5.31660e6			−0.0115789
$55$			8.75919e8i			1.74041i
$56$	−5.30445e7			−0.0963165
$57$	2.12741e8			0.353571
$58$	1.53763e7			0.0234267
$59$	1.06201e9			1.48548			0.742740	−	0.669580i	$-0.233526\pi$
$59$	1.06201e9			1.48548			0.742740	+	0.669580i	$0.233526\pi$
$60$	−2.72694e8			−0.350687
$61$		−	7.22078e8i		−	0.854939i	−0.904030	−	0.427470i	$-0.859405\pi$
$61$		−	7.22078e8i		−	0.854939i	0.904030	−	0.427470i	$-0.140595\pi$
$62$			2.51072e7i			0.0274057i
$63$		−	1.71707e9i		−	1.73016i
$64$	1.06924e9			0.995808
$65$			1.65161e9i			1.42345i
$66$	8.28642e6			0.00661679
$67$	1.44131e9			1.06753			0.533767	−	0.845631i	$-0.320776\pi$
$67$	1.44131e9			1.06753			0.533767	+	0.845631i	$0.320776\pi$
$68$	7.84044e8			0.539257
$69$		−	1.71361e8i		−	0.109564i
$70$			1.26488e8i			0.0752592i
$71$		−	3.79857e8i		−	0.210537i	−0.994444	−	0.105268i	$-0.966430\pi$
$71$		−	3.79857e8i		−	0.210537i	0.994444	−	0.105268i	$-0.0335702\pi$
$72$		−	9.71183e7i		−	0.0501925i
$73$			1.13814e9i			0.549013i	0.961585	+	0.274507i	$0.0885145\pi$
$73$			1.13814e9i			0.549013i	−0.961585	+	0.274507i	$0.911485\pi$
$74$	−6.81691e7			−0.0307206
$75$			7.67889e8i			0.323588i
$76$			3.98800e9i			1.57285i
$77$			5.49466e9i			2.02996i
$78$	1.56247e7			0.00541175
$79$	−4.58342e9			−1.48955			−0.744773	−	0.667318i	$-0.767442\pi$
$79$	−4.58342e9			−1.48955			−0.744773	+	0.667318i	$0.767442\pi$
$80$		−	5.10829e9i		−	1.55893i
$81$	2.96780e9			0.851158
$82$		−	3.82436e7i		−	0.0103155i
$83$	6.19566e9			1.57289			0.786443	−	0.617663i	$-0.211920\pi$
$83$	6.19566e9			1.57289			0.786443	+	0.617663i	$0.211920\pi$
$84$	−1.71062e9			−0.409031
$85$		−	3.74051e9i		−	0.843018i
$86$	−7.17950e7	−	1.01563e8i	−0.0152617	−	0.0215896i
$87$	9.92077e8			0.199044
$88$			3.10780e8i			0.0588898i
$89$		−	7.46570e9i		−	1.33697i	−0.743727	−	0.668483i	$-0.766944\pi$
$89$		−	7.46570e9i		−	1.33697i	0.743727	−	0.668483i	$-0.233056\pi$
$90$	−2.31585e8			−0.0392191
$91$			1.03606e10i			1.66027i
$92$	3.21231e9			0.487391
$93$			1.61992e9i			0.232851i
$94$		−	1.15438e8i		−	0.0157293i
$95$	1.90259e10			2.45883
$96$	−1.45146e8			−0.0178012
$97$	−3.79259e9			−0.441649			−0.220825	−	0.975314i	$-0.570875\pi$
$97$	−3.79259e9			−0.441649			−0.220825	+	0.975314i	$0.570875\pi$
$98$			5.54474e8i			0.0613410i
$99$	−1.00601e10			−1.05785
$100$	−1.43947e10			−1.43947
$101$	−1.53422e9			−0.145976			−0.0729878	−	0.997333i	$-0.523253\pi$
$101$	−1.53422e9			−0.145976			−0.0729878	+	0.997333i	$0.523253\pi$
$102$	−3.53862e7			−0.00320504
$103$	−2.62038e9			−0.226036			−0.113018	−	0.993593i	$-0.536052\pi$
$103$	−2.62038e9			−0.226036			−0.113018	+	0.993593i	$0.536052\pi$
$104$			5.85999e8i			0.0481649i
$105$			8.16101e9i			0.639436i
$106$			3.22978e8i			0.0241348i
$107$	−1.32447e10			−0.944326			−0.472163	−	0.881511i	$-0.656527\pi$
$107$	−1.32447e10			−0.944326			−0.472163	+	0.881511i	$0.656527\pi$
$108$		−	6.43032e9i		−	0.437637i
$109$	−2.14660e8			−0.0139514			−0.00697570	−	0.999976i	$-0.502220\pi$
$109$	−2.14660e8			−0.0139514			−0.00697570	+	0.999976i	$0.502220\pi$
$110$	7.41075e8			0.0460149
$111$	−4.39827e9			−0.261016
$112$		−	3.20444e10i		−	1.81829i
$113$		−	1.52894e10i		−	0.829846i	−0.909857	−	0.414923i	$-0.863809\pi$
$113$		−	1.52894e10i		−	0.829846i	0.909857	−	0.414923i	$-0.136191\pi$
$114$		−	1.79990e8i		−	0.00934813i
$115$		−	1.53253e10i		−	0.761937i
$116$			1.85973e10i			0.885441i
$117$	−1.89690e10			−0.865199
$118$		−	8.98514e8i		−	0.0392749i
$119$		−	2.34643e10i		−	0.983272i
$120$			4.61589e8i			0.0185502i
$121$	6.25498e9			0.241157
$122$	−6.10918e8			−0.0226039
$123$		−	2.46747e9i		−	0.0876450i
$124$	−3.03667e10			−1.03583
$125$			2.09996e10i			0.688113i
$126$	−1.45274e9			−0.0457440
$127$	−1.09606e10			−0.331754			−0.165877	−	0.986146i	$-0.553045\pi$
$127$	−1.09606e10			−0.331754			−0.165877	+	0.986146i	$0.553045\pi$
$128$		−	3.62743e9i		−	0.105572i
$129$	−4.63221e9	−	6.55287e9i	−0.129670	−	0.183435i
$130$	1.39735e9			0.0376348
$131$			4.01825e10i			1.04155i	0.853694	+	0.520776i	$0.174357\pi$
$131$			4.01825e10i			1.04155i	−0.853694	+	0.520776i	$0.825643\pi$
$132$			1.00222e10i			0.250089i
$133$	1.19350e11			2.86791
$134$		−	1.21942e9i		−	0.0282248i
$135$	−3.06777e10			−0.684155
$136$		−	1.32715e9i		−	0.0285250i
$137$			1.58617e10i			0.328661i	0.986405	+	0.164330i	$0.0525463\pi$
$137$			1.58617e10i			0.328661i	−0.986405	+	0.164330i	$0.947454\pi$
$138$	−1.44981e8			−0.00289678
$139$	−2.51826e10			−0.485318			−0.242659	−	0.970112i	$-0.578020\pi$
$139$	−2.51826e10			−0.485318			−0.242659	+	0.970112i	$0.578020\pi$
$140$	−1.52985e11			−2.84451
$141$		−	7.44807e9i		−	0.133644i
$142$	−3.21380e8			−0.00556643
$143$	6.07012e10			1.01512
$144$	5.86696e10			0.947546
$145$	8.87239e10			1.38421
$146$	9.62931e8			0.0145155
$147$			3.57746e10i			0.521181i
$148$		−	8.24491e10i		−	1.16112i
$149$		−	2.12604e10i		−	0.289495i	−0.989469	−	0.144747i	$-0.953763\pi$
$149$		−	2.12604e10i		−	0.289495i	0.989469	−	0.144747i	$-0.0462369\pi$
$150$	6.49675e8			0.00855540
$151$			1.47453e10i			0.187831i	0.995580	+	0.0939157i	$0.0299384\pi$
$151$			1.47453e10i			0.187831i	−0.995580	+	0.0939157i	$0.970062\pi$
$152$	6.75049e9			0.0831988
$153$	4.29604e10			0.512403
$154$	4.64878e9			0.0536705
$155$			1.44873e11i			1.61931i
$156$			1.88977e10i			0.204544i
$157$			6.49091e10i			0.680467i	0.940341	+	0.340233i	$0.110506\pi$
$157$			6.49091e10i			0.680467i	−0.940341	+	0.340233i	$0.889494\pi$
$158$			3.87782e9i			0.0393824i
$159$			2.08385e10i			0.205060i
$160$	−1.29808e10			−0.123795
$161$		−	9.61358e10i		−	0.888701i
$162$		−	2.51092e9i		−	0.0225039i
$163$		−	1.68483e11i		−	1.46426i	−0.681167	−	0.732128i	$-0.738527\pi$
$163$		−	1.68483e11i		−	1.46426i	0.681167	−	0.732128i	$-0.261473\pi$
$164$	4.62548e10			0.389886
$165$	4.78141e10			0.390964
$166$		−	5.24186e9i		−	0.0415858i
$167$	8.66424e10			0.667034			0.333517	−	0.942744i	$-0.391765\pi$
$167$	8.66424e10			0.667034			0.333517	+	0.942744i	$0.391765\pi$
$168$			2.89556e9i			0.0216365i
$169$	−2.34018e10			−0.169752
$170$	−3.16468e9			−0.0222887
$171$			2.18516e11i			1.49452i
$172$	1.22839e11	−	8.68345e10i	0.816006	−	0.576833i
$173$	1.37685e11			0.888496			0.444248	−	0.895904i	$-0.353471\pi$
$173$	1.37685e11			0.888496			0.444248	+	0.895904i	$0.353471\pi$
$174$		−	8.39351e8i		−	0.00526256i
$175$			4.30795e11i			2.62470i
$176$	−1.87744e11			−1.11174
$177$		−	5.79720e10i		−	0.333697i
$178$	−6.31639e9			−0.0353483
$179$			2.72920e11i			1.48515i	0.669763	+	0.742575i	$0.266396\pi$
$179$			2.72920e11i			1.48515i	−0.669763	+	0.742575i	$0.733604\pi$
$180$		−	2.80097e11i		−	1.48233i
$181$	2.81034e11			1.44666			0.723328	−	0.690505i	$-0.242612\pi$
$181$	2.81034e11			1.44666			0.723328	+	0.690505i	$0.242612\pi$
$182$	8.76563e9			0.0438961
$183$	−3.94163e10			−0.192053
$184$		−	5.43747e9i		−	0.0257815i
$185$	−3.93348e11			−1.81517
$186$	1.37054e9			0.00615639
$187$	−1.37474e11			−0.601191
$188$	1.39620e11			0.594509
$189$	−1.92442e11			−0.797979
$190$		−	1.60970e10i		−	0.0650094i
$191$		−	4.74206e11i		−	1.86552i	−0.360495	−	0.932761i	$-0.617392\pi$
$191$		−	4.74206e11i		−	1.86552i	0.360495	−	0.932761i	$-0.382608\pi$
$192$		−	5.83670e10i		−	0.223698i
$193$	−3.33550e11			−1.24559			−0.622794	−	0.782386i	$-0.714002\pi$
$193$	−3.33550e11			−1.24559			−0.622794	+	0.782386i	$0.714002\pi$
$194$			3.20874e9i			0.0116769i
$195$	9.01571e10			0.319762
$196$	−6.70624e11			−2.31846
$197$	4.59036e11			1.54709			0.773545	−	0.633742i	$-0.218482\pi$
$197$	4.59036e11			1.54709			0.773545	+	0.633742i	$0.218482\pi$
$198$			8.51137e9i			0.0279688i
$199$		−	3.09195e11i		−	0.990756i	−0.868677	−	0.495378i	$-0.835029\pi$
$199$		−	3.09195e11i		−	0.990756i	0.868677	−	0.495378i	$-0.164971\pi$
$200$			2.43659e10i			0.0761435i
$201$		−	7.86770e10i		−	0.239810i
$202$			1.29803e9i			0.00385948i
$203$	5.56567e11			1.61450
$204$		−	4.27989e10i		−	0.121138i
$205$		−	2.20672e11i		−	0.609507i
$206$			2.21699e9i			0.00597622i
$207$	1.76013e11			0.463120
$208$	−3.54005e11			−0.909269
$209$		−	6.99255e11i		−	1.75349i
$210$	6.90465e9			0.0169062
$211$			5.38365e11i			1.28725i	0.765339	+	0.643627i	$0.222571\pi$
$211$			5.38365e11i			1.28725i	−0.765339	+	0.643627i	$0.777429\pi$
$212$	−3.90635e11			−0.912204
$213$	−2.07354e10			−0.0472949
$214$			1.12057e10i			0.0249672i
$215$	−4.14270e11	−	5.86039e11i	−0.901760	−	1.27566i
$216$	−1.08846e10			−0.0231496
$217$			9.08793e11i			1.88872i
$218$			1.81614e8i			0.000368864i
$219$	6.21283e10			0.123330
$220$			8.96314e11i			1.73919i
$221$	−2.59218e11			−0.491703
$222$			3.72117e9i			0.00690105i
$223$			8.51101e10i			0.154332i	0.997018	+	0.0771661i	$0.0245872\pi$
$223$			8.51101e10i			0.154332i	−0.997018	+	0.0771661i	$0.975413\pi$
$224$	−8.14290e10			−0.144391
$225$	−7.88734e11			−1.36779
$226$	−1.29356e10			−0.0219405
$227$		−	5.77929e11i		−	0.958837i	−0.877586	−	0.479419i	$-0.840848\pi$
$227$		−	5.77929e11i		−	0.958837i	0.877586	−	0.479419i	$-0.159152\pi$
$228$	2.17694e11			0.353324
$229$	3.46320e11			0.549920			0.274960	−	0.961456i	$-0.411335\pi$
$229$	3.46320e11			0.549920			0.274960	+	0.961456i	$0.411335\pi$
$230$	−1.29660e10			−0.0201450
$231$	2.99939e11			0.456009
$232$	3.14796e10			0.0468371
$233$			5.72808e11i			0.834121i	0.908879	+	0.417061i	$0.136940\pi$
$233$			5.72808e11i			0.834121i	−0.908879	+	0.417061i	$0.863060\pi$
$234$			1.60488e10i			0.0228752i
$235$		−	6.66099e11i		−	0.929393i
$236$	1.08673e12			1.48444
$237$			2.50197e11i			0.334611i
$238$	−1.98521e10			−0.0259969
$239$	3.40057e11			0.436076			0.218038	−	0.975940i	$-0.430034\pi$
$239$	3.40057e11			0.436076			0.218038	+	0.975940i	$0.430034\pi$
$240$	−2.78848e11			−0.350196
$241$		−	1.25721e12i		−	1.54641i	−0.634158	−	0.773204i	$-0.718653\pi$
$241$		−	1.25721e12i		−	1.54641i	0.634158	−	0.773204i	$-0.281347\pi$
$242$		−	5.29205e9i		−	0.00637599i
$243$		−	5.33068e11i		−	0.629146i
$244$		−	7.38891e11i		−	0.854342i
$245$			3.19941e12i			3.62443i
$246$	−2.08762e9			−0.00231726
$247$		−	1.31850e12i		−	1.43415i
$248$			5.14017e10i			0.0547922i
$249$		−	3.38205e11i		−	0.353332i
$250$	1.77668e10			0.0181932
$251$	1.80908e12			1.81589			0.907945	−	0.419089i	$-0.137650\pi$
$251$	1.80908e12			1.81589			0.907945	+	0.419089i	$0.137650\pi$
$252$		−	1.75705e12i		−	1.72895i
$253$	−5.63245e11			−0.543369
$254$			9.27326e9i			0.00877130i
$255$	−2.04185e11			−0.189375
$256$	1.09183e12			0.993017
$257$			8.85258e11i			0.789595i	0.918768	+	0.394797i	$0.129185\pi$
$257$			8.85258e11i			0.789595i	−0.918768	+	0.394797i	$0.870815\pi$
$258$	−5.54408e9	+	3.91910e9i	−0.00484988	+	0.00342837i
$259$	−2.46748e12			−2.11717
$260$			1.69007e12i			1.42245i
$261$			1.01901e12i			0.841347i
$262$	3.39966e10			0.0275378
$263$			2.32424e12i			1.84715i	0.383413	+	0.923577i	$0.374748\pi$
$263$			2.32424e12i			1.84715i	−0.383413	+	0.923577i	$0.625252\pi$
$264$	1.69647e10			0.0132290
$265$			1.86364e12i			1.42604i
$266$		−	1.00977e11i		−	0.0758251i
$267$	−4.07533e11			−0.300335
$268$	1.47487e12			1.06679
$269$	−8.13151e10			−0.0577311			−0.0288656	−	0.999583i	$-0.509189\pi$
$269$	−8.13151e10			−0.0577311			−0.0288656	+	0.999583i	$0.509189\pi$
$270$			2.59550e10i			0.0180885i
$271$	1.01982e12			0.697711			0.348856	−	0.937177i	$-0.386570\pi$
$271$	1.01982e12			0.697711			0.348856	+	0.937177i	$0.386570\pi$
$272$	8.01738e11			0.538503
$273$	5.65558e11			0.372961
$274$	1.34199e10			0.00868953
$275$	2.52396e12			1.60479
$276$		−	1.75351e11i		−	0.109487i
$277$		−	2.04163e12i		−	1.25192i	−0.779854	−	0.625961i	$-0.784707\pi$
$277$		−	2.04163e12i		−	1.25192i	0.779854	−	0.625961i	$-0.215293\pi$
$278$			2.13058e10i			0.0128314i
$279$	−1.66389e12			−0.984248
$280$			2.58957e11i			0.150466i
$281$	1.27867e12			0.729836			0.364918	−	0.931040i	$-0.381097\pi$
$281$	1.27867e12			0.729836			0.364918	+	0.931040i	$0.381097\pi$
$282$	−6.30147e9			−0.00353343
$283$	7.72221e11			0.425412			0.212706	−	0.977116i	$-0.431772\pi$
$283$	7.72221e11			0.425412			0.212706	+	0.977116i	$0.431772\pi$
$284$		−	3.88702e11i		−	0.210390i
$285$		−	1.03858e12i		−	0.552349i
$286$		−	5.13565e10i		−	0.0268389i
$287$		−	1.38428e12i		−	0.710911i
$288$		−	1.49087e11i		−	0.0752448i
$289$	−1.42893e12			−0.708795
$290$		−	7.50652e10i		−	0.0365973i
$291$			2.07028e11i			0.0992118i
$292$			1.16464e12i			0.548629i
$293$	−1.94950e12			−0.902788			−0.451394	−	0.892325i	$-0.649073\pi$
$293$	−1.94950e12			−0.902788			−0.451394	+	0.892325i	$0.649073\pi$
$294$	3.02673e10			0.0137796
$295$		−	5.18458e12i		−	2.32062i
$296$	−1.39562e11			−0.0614196
$297$			1.12749e12i			0.487900i
$298$	−1.79875e10			−0.00765400
$299$	−1.06204e12			−0.444412
$300$			7.85768e11i			0.323361i
$301$	−2.59873e12	−	3.67624e12i	−1.05179	−	1.48789i
$302$	1.24753e10			0.00496611
$303$			8.37489e10i			0.0327919i
$304$			4.07800e12i			1.57065i
$305$	−3.52510e12			−1.33559
$306$		−	3.63468e10i		−	0.0135475i
$307$	3.18628e12			1.16840			0.584201	−	0.811609i	$-0.301408\pi$
$307$	3.18628e12			1.16840			0.584201	+	0.811609i	$0.301408\pi$
$308$			5.62260e12i			2.02854i
$309$			1.43040e11i			0.0507767i
$310$	1.22571e11			0.0428132
$311$	2.38175e12			0.818641			0.409321	−	0.912391i	$-0.365766\pi$
$311$	2.38175e12			0.818641			0.409321	+	0.912391i	$0.365766\pi$
$312$	3.19881e10			0.0108197
$313$		−	1.24263e12i		−	0.413638i	−0.978379	−	0.206819i	$-0.933689\pi$
$313$		−	1.24263e12i		−	0.413638i	0.978379	−	0.206819i	$-0.0663112\pi$
$314$	5.49166e10			0.0179910
$315$	−8.38255e12			−2.70286
$316$	−4.69014e12			−1.48850
$317$	−1.03858e12			−0.324447			−0.162224	−	0.986754i	$-0.551867\pi$
$317$	−1.03858e12			−0.324447			−0.162224	+	0.986754i	$0.551867\pi$
$318$	1.76305e10			0.00542163
$319$		−	3.26084e12i		−	0.987135i
$320$		−	5.21991e12i		−	1.55565i
$321$			7.22991e11i			0.212133i
$322$	−8.13361e10			−0.0234965
$323$			2.98609e12i			0.849357i
$324$	3.03691e12			0.850563
$325$	4.75912e12			1.31253
$326$	−1.42545e11			−0.0387137
$327$			1.17177e10i			0.00313403i
$328$		−	7.82955e10i		−	0.0206238i
$329$		−	4.17846e12i		−	1.08402i
$330$		−	4.04533e10i		−	0.0103368i
$331$			3.52483e12i			0.887153i	0.896236	+	0.443577i	$0.146291\pi$
$331$			3.52483e12i			0.887153i	−0.896236	+	0.443577i	$0.853709\pi$
$332$	6.33992e12			1.57179
$333$		−	4.51766e12i		−	1.10330i
$334$		−	7.33042e10i		−	0.0176358i
$335$		−	7.03628e12i		−	1.66771i
$336$	−1.74922e12			−0.408459
$337$	−6.83158e12			−1.57171			−0.785854	−	0.618412i	$-0.787776\pi$
$337$	−6.83158e12			−1.57171			−0.785854	+	0.618412i	$0.787776\pi$
$338$			1.97992e10i			0.00448811i
$339$	−8.34606e11			−0.186416
$340$		−	3.82761e12i		−	0.842428i
$341$	5.32448e12			1.15480
$342$	1.84876e11			0.0395140
$343$			1.14194e13i			2.40533i
$344$	−1.46985e11	−	2.07929e11i	−0.0305127	−	0.0431642i
$345$	−8.36566e11			−0.171161
$346$		−	1.16489e11i		−	0.0234911i
$347$			8.64593e12i			1.71856i	0.511507	+	0.859279i	$0.329087\pi$
$347$			8.64593e12i			1.71856i	−0.511507	+	0.859279i	$0.670913\pi$
$348$	1.01518e12			0.198905
$349$		−	5.68975e12i		−	1.09892i	−0.835520	−	0.549460i	$-0.814834\pi$
$349$		−	5.68975e12i		−	1.09892i	0.835520	−	0.549460i	$-0.185166\pi$
$350$	3.64476e11			0.0693951
$351$			2.12597e12i			0.399044i
$352$			4.77080e11i			0.0882832i
$353$	−1.01878e12			−0.185868			−0.0929342	−	0.995672i	$-0.529625\pi$
$353$	−1.01878e12			−0.185868			−0.0929342	+	0.995672i	$0.529625\pi$
$354$	−4.90475e10			−0.00882268
$355$	−1.85442e12			−0.328901
$356$		−	7.63953e12i		−	1.33603i
$357$	−1.28086e12			−0.220881
$358$	2.30905e11			0.0392662
$359$	2.44894e12			0.410682			0.205341	−	0.978691i	$-0.434170\pi$
$359$	2.44894e12			0.410682			0.205341	+	0.978691i	$0.434170\pi$
$360$	−4.74120e11			−0.0784108
$361$	−9.05753e12			−1.47732
$362$		−	2.37770e11i		−	0.0382484i
$363$		−	3.41443e11i		−	0.0541733i
$364$			1.06018e13i			1.65911i
$365$	5.55628e12			0.857670
$366$			3.33484e10i			0.00507773i
$367$	−5.29017e12			−0.794584			−0.397292	−	0.917692i	$-0.630050\pi$
$367$	−5.29017e12			−0.794584			−0.397292	+	0.917692i	$0.630050\pi$
$368$	3.28480e12			0.486710
$369$	2.53446e12			0.370470
$370$			3.32794e11i			0.0479917i
$371$			1.16907e13i			1.66330i
$372$			1.65764e12i			0.232688i
$373$		−	4.24662e12i		−	0.588165i	−0.955780	−	0.294083i	$-0.904986\pi$
$373$		−	4.24662e12i		−	0.588165i	0.955780	−	0.294083i	$-0.0950141\pi$
$374$			1.16310e11i			0.0158950i
$375$	1.14631e12			0.154577
$376$		−	2.36335e11i		−	0.0314477i
$377$		−	6.14857e12i		−	0.807360i
$378$			1.62817e11i			0.0210979i
$379$	−1.42309e13			−1.81986			−0.909929	−	0.414764i	$-0.863864\pi$
$379$	−1.42309e13			−1.81986			−0.909929	+	0.414764i	$0.863864\pi$
$380$	1.94689e13			2.45711
$381$			5.98310e11i			0.0745249i
$382$	−4.01204e11			−0.0493229
$383$		−	4.75530e12i		−	0.577011i	−0.957478	−	0.288505i	$-0.906842\pi$
$383$		−	4.75530e12i		−	0.577011i	0.957478	−	0.288505i	$-0.0931583\pi$
$384$	−1.98012e11			−0.0237156
$385$	2.68243e13			3.17121
$386$			2.82201e11i			0.0329323i
$387$	6.73076e12	−	4.75796e12i	0.775370	−	0.548108i
$388$	−3.88090e12			−0.441341
$389$			1.25209e13i			1.40568i	0.711349	+	0.702839i	$0.248085\pi$
$389$			1.25209e13i			1.40568i	−0.711349	+	0.702839i	$0.751915\pi$
$390$		−	7.62778e10i		−	0.00845425i
$391$	2.40527e12			0.263197
$392$			1.13517e12i			0.122639i
$393$	2.19346e12			0.233973
$394$		−	3.88369e11i		−	0.0409038i
$395$			2.23757e13i			2.32697i
$396$	−1.02943e13			−1.05711
$397$	1.80073e13			1.82598			0.912992	−	0.407978i	$-0.133766\pi$
$397$	1.80073e13			1.82598			0.912992	+	0.407978i	$0.133766\pi$
$398$	−2.61596e11			−0.0261948
$399$		−	6.51501e12i		−	0.644245i
$400$	−1.47196e13			−1.43746
$401$	−4.77325e12			−0.460355			−0.230177	−	0.973149i	$-0.573931\pi$
$401$	−4.77325e12			−0.460355			−0.230177	+	0.973149i	$0.573931\pi$
$402$	−6.65651e10			−0.00634039
$403$	1.00397e13			0.944488
$404$	−1.56994e12			−0.145874
$405$		−	1.44885e13i		−	1.32968i
$406$		−	4.70886e11i		−	0.0426860i
$407$			1.44566e13i			1.29448i
$408$	−7.24457e10			−0.00640784
$409$			9.20218e12i			0.804034i	0.915632	+	0.402017i	$0.131691\pi$
$409$			9.20218e12i			0.804034i	−0.915632	+	0.402017i	$0.868309\pi$
$410$	−1.86701e11			−0.0161149
$411$	8.65850e11			0.0738301
$412$	−2.68140e12			−0.225878
$413$		−	3.25230e13i		−	2.70670i
$414$		−	1.48917e11i		−	0.0122445i
$415$		−	3.02465e13i		−	2.45717i
$416$			8.99570e11i			0.0722052i
$417$			1.37465e12i			0.109021i
$418$	−5.91608e11			−0.0463610
$419$			1.75815e13i			1.36140i	0.732562	+	0.680700i	$0.238324\pi$
$419$			1.75815e13i			1.36140i	−0.732562	+	0.680700i	$0.761676\pi$
$420$			8.35103e12i			0.638989i
$421$			1.52384e13i			1.15220i	0.817379	+	0.576100i	$0.195426\pi$
$421$			1.52384e13i			1.15220i	−0.817379	+	0.576100i	$0.804574\pi$
$422$	4.55486e11			0.0340340
$423$	7.65026e12			0.564904
$424$			6.61228e11i			0.0482528i
$425$	−1.07783e13			−0.777330
$426$			1.75433e10i			0.00125044i
$427$	−2.21131e13			−1.55779
$428$	−1.35531e13			−0.943666
$429$		−	3.31352e12i		−	0.228036i
$430$	−4.95821e11	+	3.50495e11i	−0.0337274	+	0.0238418i
$431$	8.76785e12			0.589531			0.294766	−	0.955570i	$-0.404758\pi$
$431$	8.76785e12			0.589531			0.294766	+	0.955570i	$0.404758\pi$
$432$		−	6.57543e12i		−	0.437024i
$433$		−	9.25042e12i		−	0.607746i	−0.952713	−	0.303873i	$-0.901720\pi$
$433$		−	9.25042e12i		−	0.607746i	0.952713	−	0.303873i	$-0.0982798\pi$
$434$	7.68889e11			0.0499361
$435$		−	4.84320e12i		−	0.310947i
$436$	−2.19658e11			−0.0139416
$437$			1.22343e13i			0.767666i
$438$		−	5.25639e10i		−	0.00326075i
$439$	2.41481e13			1.48102			0.740510	−	0.672045i	$-0.234584\pi$
$439$	2.41481e13			1.48102			0.740510	+	0.672045i	$0.234584\pi$
$440$	1.51719e12			0.0919977
$441$	−3.67458e13			−2.20300
$442$			2.19312e11i			0.0130002i
$443$	−8.01561e12			−0.469805			−0.234903	−	0.972019i	$-0.575477\pi$
$443$	−8.01561e12			−0.469805			−0.234903	+	0.972019i	$0.575477\pi$
$444$	−4.50068e12			−0.260833
$445$	−3.64467e13			−2.08861
$446$	7.20077e10			0.00408042
$447$	−1.16055e12			−0.0650319
$448$		−	3.27446e13i		−	1.81447i
$449$			2.13102e13i			1.16777i	0.811838	+	0.583883i	$0.198467\pi$
$449$			2.13102e13i			1.16777i	−0.811838	+	0.583883i	$0.801533\pi$
$450$			6.67312e11i			0.0361632i
$451$	−8.11031e12			−0.434665
$452$		−	1.56454e13i		−	0.829266i
$453$	8.04905e11			0.0421943
$454$	−4.88959e11			−0.0253509
$455$	5.05792e13			2.59367
$456$		−	3.68491e11i		−	0.0186897i
$457$			1.95013e13i			0.978323i	0.872193	+	0.489161i	$0.162697\pi$
$457$			1.95013e13i			0.978323i	−0.872193	+	0.489161i	$0.837303\pi$
$458$		−	2.93005e11i		−	0.0145395i
$459$		−	4.81482e12i		−	0.236329i
$460$		−	1.56821e13i		−	0.761404i
$461$	1.21083e13			0.581541			0.290770	−	0.956793i	$-0.406088\pi$
$461$	1.21083e13			0.581541			0.290770	+	0.956793i	$0.406088\pi$
$462$		−	2.53765e11i		−	0.0120565i
$463$			2.45524e13i			1.15395i	0.816761	+	0.576977i	$0.195768\pi$
$463$			2.45524e13i			1.15395i	−0.816761	+	0.576977i	$0.804232\pi$
$464$			1.90170e13i			0.884202i
$465$	7.90825e12			0.363760
$466$	4.84626e11			0.0220535
$467$		−	1.20191e13i		−	0.541113i	−0.962704	−	0.270556i	$-0.912792\pi$
$467$		−	1.20191e13i		−	0.541113i	0.962704	−	0.270556i	$-0.0872076\pi$
$468$	−1.94107e13			−0.864594
$469$		−	4.41388e13i		−	1.94516i
$470$	−5.63556e11			−0.0245724
$471$	3.54321e12			0.152860
$472$		−	1.83951e12i		−	0.0785223i
$473$	−2.15385e13	+	1.52255e13i	−0.909726	+	0.643083i
$474$	2.11680e11			0.00884683
$475$		−	5.48233e13i		−	2.26724i
$476$		−	2.40107e13i		−	0.982584i
$477$	−2.14042e13			−0.866778
$478$		−	2.87707e11i		−	0.0115295i
$479$	4.15981e13			1.64967			0.824833	−	0.565377i	$-0.191269\pi$
$479$	4.15981e13			1.64967			0.824833	+	0.565377i	$0.191269\pi$
$480$			7.08588e11i			0.0278091i
$481$			2.72590e13i			1.05873i
$482$	−1.06367e12			−0.0408858
$483$	−5.24780e12			−0.199637
$484$	6.40062e12			0.240988
$485$			1.85150e13i			0.689946i
$486$	−4.51005e11			−0.0166341
$487$	−8.49956e12			−0.310278			−0.155139	−	0.987893i	$-0.549583\pi$
$487$	−8.49956e12			−0.310278			−0.155139	+	0.987893i	$0.549583\pi$
$488$	−1.25072e12			−0.0451920
$489$	−9.19702e12			−0.328929
$490$	2.70688e12			0.0958271
$491$		−	5.57689e12i		−	0.195427i	−0.995215	−	0.0977135i	$-0.968847\pi$
$491$		−	5.57689e12i		−	0.195427i	0.995215	−	0.0977135i	$-0.0311529\pi$
$492$		−	2.52493e12i		−	0.0875837i
$493$			1.39251e13i			0.478148i
$494$	−1.11552e12			−0.0379178
$495$			4.91121e13i			1.65258i
$496$	−3.10520e13			−1.03438
$497$	−1.16328e13			−0.383621
$498$	−2.86139e11			−0.00934181
$499$			2.12718e13i			0.687545i	0.939053	+	0.343772i	$0.111705\pi$
$499$			2.12718e13i			0.687545i	−0.939053	+	0.343772i	$0.888295\pi$
$500$			2.14885e13i			0.687632i
$501$		−	4.72958e12i		−	0.149842i
$502$		−	1.53058e12i		−	0.0480107i
$503$		−	1.61237e13i		−	0.500753i	−0.968148	−	0.250377i	$-0.919446\pi$
$503$		−	1.61237e13i		−	0.500753i	0.968148	−	0.250377i	$-0.0805545\pi$
$504$	−2.97417e12			−0.0914561
$505$			7.48987e12i			0.228043i
$506$			4.76536e11i			0.0143662i
$507$			1.27744e12i			0.0381330i
$508$	−1.12158e13			−0.331522
$509$	4.96346e13			1.45277			0.726383	−	0.687290i	$-0.241200\pi$
$509$	4.96346e13			1.45277			0.726383	+	0.687290i	$0.241200\pi$
$510$			1.72751e11i			0.00500692i
$511$	3.48547e13			1.00036
$512$		−	4.63824e12i		−	0.131827i
$513$	2.44903e13			0.689300
$514$	7.48976e11			0.0208763
$515$			1.27924e13i			0.353115i
$516$	−4.74007e12	−	6.70545e12i	−0.129579	−	0.183307i
$517$	−2.44810e13			−0.662789
$518$			2.08762e12i			0.0559762i
$519$		−	7.51585e12i		−	0.199591i
$520$	2.86078e12			0.0752433
$521$		−	5.19063e13i		−	1.35217i	−0.736823	−	0.676086i	$-0.763675\pi$
$521$		−	5.19063e13i		−	1.35217i	0.736823	−	0.676086i	$-0.236325\pi$
$522$	8.62136e11			0.0222445
$523$		−	2.70715e13i		−	0.691836i	−0.938265	−	0.345918i	$-0.887568\pi$
$523$		−	2.70715e13i		−	0.691836i	0.938265	−	0.345918i	$-0.112432\pi$
$524$			4.11181e13i			1.04082i
$525$	2.35160e13			0.589612
$526$	1.96644e12			0.0488373
$527$	−2.27376e13			−0.559360
$528$			1.02484e13i			0.249740i
$529$	−3.15719e13			−0.762117
$530$	1.57674e12			0.0377035
$531$	5.95458e13			1.41052
$532$	1.22129e14			2.86590
$533$	−1.52926e13			−0.355505
$534$			3.44795e11i			0.00794062i
$535$			6.46589e13i			1.47523i
$536$		−	2.49650e12i		−	0.0564298i
$537$	1.48980e13			0.333623
$538$			6.87970e10i			0.00152636i
$539$	1.17587e14			2.58473
$540$	−3.13920e13			−0.683677
$541$	−4.82709e11			−0.0104160			−0.00520798	−	0.999986i	$-0.501658\pi$
$541$	−4.82709e11			−0.0104160			−0.00520798	+	0.999986i	$0.501658\pi$
$542$		−	8.62820e11i		−	0.0184469i
$543$		−	1.53409e13i		−	0.324976i
$544$		−	2.03732e12i		−	0.0427626i
$545$			1.04794e12i			0.0217949i
$546$		−	4.78493e11i		−	0.00986080i
$547$	5.07801e13			1.03695			0.518474	−	0.855093i	$-0.326500\pi$
$547$	5.07801e13			1.03695			0.518474	+	0.855093i	$0.326500\pi$
$548$			1.62311e13i			0.328431i
$549$		−	4.04864e13i		−	0.811797i
$550$		−	2.13541e12i		−	0.0424295i
$551$	−7.08292e13			−1.39461
$552$	−2.96817e11			−0.00579153
$553$			1.40363e14i			2.71411i
$554$	−1.72733e12			−0.0330998
$555$			2.14718e13i			0.407759i
$556$	−2.57689e13			−0.484978
$557$	1.93646e13			0.361188			0.180594	−	0.983558i	$-0.442198\pi$
$557$	1.93646e13			0.361188			0.180594	+	0.983558i	$0.442198\pi$
$558$			1.40774e12i			0.0260227i
$559$	−4.06125e13	+	2.87089e13i	−0.744048	+	0.525966i
$560$	−1.56437e14			−2.84053
$561$			7.50434e12i			0.135051i
$562$		−	1.08182e12i		−	0.0192963i
$563$	1.67892e13			0.296817			0.148409	−	0.988926i	$-0.452585\pi$
$563$	1.67892e13			0.296817			0.148409	+	0.988926i	$0.452585\pi$
$564$		−	7.62149e12i		−	0.133550i
$565$	−7.46409e13			−1.29639
$566$		−	6.53341e11i		−	0.0112475i
$567$		−	9.08866e13i		−	1.55090i
$568$	−6.57955e11			−0.0111290
$569$	−7.06796e13			−1.18504			−0.592520	−	0.805556i	$-0.701867\pi$
$569$	−7.06796e13			−1.18504			−0.592520	+	0.805556i	$0.701867\pi$
$570$	−8.78692e11			−0.0146037
$571$		−	3.18030e13i		−	0.523947i	−0.965075	−	0.261974i	$-0.915627\pi$
$571$		−	3.18030e13i		−	0.523947i	0.965075	−	0.261974i	$-0.0843733\pi$
$572$	6.21146e13			1.01441
$573$	−2.58857e13			−0.419070
$574$	−1.17118e12			−0.0187959
$575$	−4.41598e13			−0.702567
$576$	5.99515e13			0.945557
$577$			2.25287e13i			0.352255i	0.984367	+	0.176128i	$0.0563571\pi$
$577$			2.25287e13i			0.352255i	−0.984367	+	0.176128i	$0.943643\pi$
$578$			1.20895e12i			0.0187400i
$579$			1.82076e13i			0.279808i
$580$	9.07898e13			1.38324
$581$		−	1.89737e14i		−	2.86597i
$582$	1.75157e11			0.00262308
$583$	6.84939e13			1.01697
$584$	1.97139e12			0.0290208
$585$			9.26046e13i			1.35162i
$586$			1.64939e12i			0.0238690i
$587$			9.42670e13i			1.35260i	0.736627	+	0.676300i	$0.236418\pi$
$587$			9.42670e13i			1.35260i	−0.736627	+	0.676300i	$0.763582\pi$
$588$			3.66076e13i			0.520816i
$589$		−	1.15654e14i		−	1.63149i
$590$	−4.38644e12			−0.0613553
$591$		−	2.50576e13i		−	0.347537i
$592$		−	8.43098e13i		−	1.15950i
$593$		−	1.31494e14i		−	1.79321i	−0.442832	−	0.896605i	$-0.646026\pi$
$593$		−	1.31494e14i		−	1.79321i	0.442832	−	0.896605i	$-0.353974\pi$
$594$	9.53918e11			0.0128997
$595$	−1.14550e14			−1.53607
$596$		−	2.17554e13i		−	0.289292i
$597$	−1.68781e13			−0.222563
$598$			8.98544e11i			0.0117499i
$599$	1.15805e12			0.0150174			0.00750868	−	0.999972i	$-0.497610\pi$
$599$	1.15805e12			0.0150174			0.00750868	+	0.999972i	$0.497610\pi$
$600$	1.33007e12			0.0171048
$601$		−	3.04760e13i		−	0.388674i	−0.980935	−	0.194337i	$-0.937745\pi$
$601$		−	3.04760e13i		−	0.388674i	0.980935	−	0.194337i	$-0.0622555\pi$
$602$	−3.11030e12	+	2.19866e12i	−0.0393387	+	0.0278084i
$603$	8.08129e13			1.01366
$604$			1.50886e13i			0.187700i
$605$		−	3.05361e13i		−	0.376735i
$606$	7.08561e10			0.000866991
$607$			1.14536e14i			1.38995i	0.719035	+	0.694974i	$0.244584\pi$
$607$			1.14536e14i			1.38995i	−0.719035	+	0.694974i	$0.755416\pi$
$608$	1.03627e13			0.124726
$609$		−	3.03815e13i		−	0.362680i
$610$			2.98243e12i			0.0353119i
$611$	−4.61607e13			−0.542083
$612$	4.39607e13			0.512044
$613$	−3.22409e13			−0.372481			−0.186241	−	0.982504i	$-0.559630\pi$
$613$	−3.22409e13			−0.372481			−0.186241	+	0.982504i	$0.559630\pi$
$614$		−	2.69577e12i		−	0.0308916i
$615$	−1.20459e13			−0.136919
$616$	9.51738e12			0.107304
$617$	−1.54437e14			−1.72713			−0.863567	−	0.504235i	$-0.831775\pi$
$617$	−1.54437e14			−1.72713			−0.863567	+	0.504235i	$0.831775\pi$
$618$	1.21019e11			0.00134249
$619$	1.73772e13			0.191217			0.0956086	−	0.995419i	$-0.469520\pi$
$619$	1.73772e13			0.191217			0.0956086	+	0.995419i	$0.469520\pi$
$620$			1.48246e14i			1.61818i
$621$		−	1.97268e13i		−	0.213599i
$622$		−	2.01509e12i		−	0.0216442i
$623$	−2.28631e14			−2.43610
$624$			1.93242e13i			0.204258i
$625$	−3.48572e13			−0.365504
$626$	−1.05133e12			−0.0109363
$627$	−3.81705e13			−0.393904
$628$			6.64204e13i			0.679991i
$629$		−	6.17353e13i		−	0.627018i
$630$			7.09209e12i			0.0714614i
$631$		−	6.14662e12i		−	0.0614454i	−0.999528	−	0.0307227i	$-0.990219\pi$
$631$		−	6.14662e12i		−	0.0614454i	0.999528	−	0.0307227i	$-0.00978088\pi$
$632$			7.93900e12i			0.0787373i
$633$	2.93879e13			0.289168
$634$			8.78696e11i			0.00857813i
$635$			5.35084e13i			0.518266i
$636$			2.13237e13i			0.204917i
$637$	2.21719e14			2.11401
$638$	−2.75885e12			−0.0260991
$639$		−	2.12983e13i		−	0.199913i
$640$	−1.77087e13			−0.164925
$641$			9.01040e13i			0.832633i	0.909220	+	0.416317i	$0.136679\pi$
$641$			9.01040e13i			0.832633i	−0.909220	+	0.416317i	$0.863321\pi$
$642$	6.11690e11			0.00560862
$643$	5.02415e13			0.457096			0.228548	−	0.973533i	$-0.426602\pi$
$643$	5.02415e13			0.457096			0.228548	+	0.973533i	$0.426602\pi$
$644$		−	9.83742e13i		−	0.888080i
$645$	−3.19903e13	+	2.26139e13i	−0.286563	+	0.202571i
$646$	2.52639e12			0.0224563
$647$			1.07660e14i			0.949583i	0.880098	+	0.474791i	$0.157476\pi$
$647$			1.07660e14i			0.949583i	−0.880098	+	0.474791i	$0.842524\pi$
$648$		−	5.14057e12i		−	0.0449921i
$649$	−1.90548e14			−1.65493
$650$		−	4.02648e12i		−	0.0347023i
$651$	4.96086e13			0.424280
$652$		−	1.72406e14i		−	1.46323i
$653$		−	2.03675e14i		−	1.71542i	−0.514132	−	0.857711i	$-0.671886\pi$
$653$		−	2.03675e14i		−	1.71542i	0.514132	−	0.857711i	$-0.328114\pi$
$654$	9.91381e9			8.28613e−5
$655$	1.96166e14			1.62711
$656$	4.72987e13			0.389341
$657$			6.38148e13i			0.521309i
$658$	−3.53520e12			−0.0286606
$659$	9.42998e13			0.758723			0.379362	−	0.925248i	$-0.376144\pi$
$659$	9.42998e13			0.758723			0.379362	+	0.925248i	$0.376144\pi$
$660$	4.89274e13			0.390690
$661$	−2.15781e14			−1.71004			−0.855018	−	0.518598i	$-0.826454\pi$
$661$	−2.15781e14			−1.71004			−0.855018	+	0.518598i	$0.826454\pi$
$662$	2.98220e12			0.0234556
$663$			1.41500e13i			0.110456i
$664$		−	1.07316e13i		−	0.0831426i
$665$		−	5.82654e14i		−	4.48025i
$666$	−3.82219e12			−0.0291703
$667$			5.70524e13i			0.432160i
$668$	8.86598e13			0.666568
$669$	4.64593e12			0.0346691
$670$	−5.95308e12			−0.0440928
$671$			1.29557e14i			0.952464i
$672$			4.44499e12i			0.0324358i
$673$			1.04309e14i			0.755519i	0.925904	+	0.377759i	$0.123305\pi$
$673$			1.04309e14i			0.755519i	−0.925904	+	0.377759i	$0.876695\pi$
$674$			5.77989e12i			0.0415547i
$675$			8.83980e13i			0.630846i
$676$	−2.39467e13			−0.169634
$677$			1.52663e14i			1.07347i	0.843750	+	0.536737i	$0.180343\pi$
$677$			1.52663e14i			1.07347i	−0.843750	+	0.536737i	$0.819657\pi$
$678$			7.06122e11i			0.00492869i
$679$			1.16145e14i			0.804733i
$680$	−6.47900e12			−0.0445618
$681$	−3.15476e13			−0.215393
$682$		−	4.50480e12i		−	0.0305319i
$683$	7.96363e13			0.535806			0.267903	−	0.963446i	$-0.413669\pi$
$683$	7.96363e13			0.535806			0.267903	+	0.963446i	$0.413669\pi$
$684$			2.23604e14i			1.49348i
$685$	7.74351e13			0.513435
$686$	9.66146e12			0.0635949
$687$		−	1.89047e13i		−	0.123534i
$688$	1.25611e14	−	8.87942e13i	0.814865	−	0.576026i
$689$	1.29150e14			0.831763
$690$			7.07780e11i			0.00452536i
$691$		−	1.80567e14i		−	1.14617i	−0.819496	−	0.573085i	$-0.805747\pi$
$691$		−	1.80567e14i		−	1.14617i	0.819496	−	0.573085i	$-0.194253\pi$
$692$	1.40891e14			0.887875
$693$			3.08081e14i			1.92752i
$694$	7.31492e12			0.0454373
$695$			1.22938e14i			0.758164i
$696$		−	1.71839e12i		−	0.0105214i
$697$	3.46341e13			0.210543
$698$	−4.81384e12			−0.0290546
$699$	3.12681e13			0.187376
$700$			4.40826e14i			2.62287i
$701$	−6.31483e13			−0.373054			−0.186527	−	0.982450i	$-0.559723\pi$
$701$	−6.31483e13			−0.373054			−0.186527	+	0.982450i	$0.559723\pi$
$702$	1.79868e12			0.0105504
$703$	3.14014e14			1.82882
$704$	−1.91846e14			−1.10940
$705$	−3.63606e13			−0.208778
$706$			8.61941e11i			0.00491421i
$707$			4.69842e13i			0.265983i
$708$		−	5.93219e13i		−	0.333464i
$709$	1.41239e14			0.788358			0.394179	−	0.919034i	$-0.371029\pi$
$709$	1.41239e14			0.788358			0.394179	+	0.919034i	$0.371029\pi$
$710$			1.56894e12i			0.00869589i
$711$	−2.56989e14			−1.41438
$712$	−1.29314e13			−0.0706719
$713$	−9.31583e13			−0.505561
$714$			1.08367e12i			0.00583993i
$715$		−	2.96336e14i		−	1.58582i
$716$			2.79275e14i			1.48411i
$717$		−	1.85628e13i		−	0.0979599i
$718$		−	2.07193e12i		−	0.0108581i
$719$	−8.58193e13			−0.446623			−0.223311	−	0.974747i	$-0.571687\pi$
$719$	−8.58193e13			−0.446623			−0.223311	+	0.974747i	$0.571687\pi$
$720$		−	2.86418e14i		−	1.48026i
$721$			8.02470e13i			0.411863i
$722$			7.66316e12i			0.0390591i
$723$	−6.86280e13			−0.347384
$724$	2.87577e14			1.44564
$725$		−	2.55658e14i		−	1.27635i
$726$	−2.88879e11			−0.00143230
$727$			1.46830e14i			0.723005i	0.932371	+	0.361503i	$0.117736\pi$
$727$			1.46830e14i			0.723005i	−0.932371	+	0.361503i	$0.882264\pi$
$728$	1.79457e13			0.0877616
$729$	1.46147e14			0.709827
$730$		−	4.70092e12i		−	0.0226761i
$731$	9.19779e13	−	6.50190e13i	0.440653	−	0.311496i
$732$	−4.03341e13			−0.191919
$733$		−	6.49570e13i		−	0.306977i	−0.988150	−	0.153488i	$-0.950949\pi$
$733$		−	6.49570e13i		−	0.306977i	0.988150	−	0.153488i	$-0.0490508\pi$
$734$			4.47577e12i			0.0210082i
$735$	1.74647e14			0.814190
$736$		−	8.34709e12i		−	0.0386497i
$737$	−2.58603e14			−1.18931
$738$		−	2.14429e12i		−	0.00979493i
$739$		−	2.94890e14i		−	1.33794i	−0.743288	−	0.668972i	$-0.766735\pi$
$739$		−	2.94890e14i		−	1.33794i	0.743288	−	0.668972i	$-0.233265\pi$
$740$	−4.02507e14			−1.81390
$741$	−7.19733e13			−0.322167
$742$	9.89094e12			0.0439762
$743$		−	1.44160e14i		−	0.636651i	−0.947981	−	0.318326i	$-0.896880\pi$
$743$		−	1.44160e14i		−	0.636651i	0.947981	−	0.318326i	$-0.103120\pi$
$744$	2.80588e12			0.0123085
$745$	−1.03791e14			−0.452249
$746$	−3.59287e12			−0.0155506
$747$	3.47386e14			1.49351
$748$	−1.40675e14			−0.600771
$749$			4.05607e14i			1.72066i
$750$		−	9.69841e11i		−	0.00408690i
$751$		−	8.92427e12i		−	0.0373571i	−0.999826	−	0.0186785i	$-0.994054\pi$
$751$		−	8.92427e12i		−	0.0373571i	0.999826	−	0.0186785i	$-0.00594591\pi$
$752$	1.42771e14			0.593678
$753$		−	9.87530e13i		−	0.407920i
$754$	−5.20202e12			−0.0213459
$755$	7.19847e13			0.293431
$756$	−1.96923e14			−0.797421
$757$			9.64872e13i			0.388142i	0.980988	+	0.194071i	$0.0621691\pi$
$757$			9.64872e13i			0.388142i	−0.980988	+	0.194071i	$0.937831\pi$
$758$			1.20401e13i			0.0481156i
$759$			3.07461e13i			0.122062i
$760$		−	3.29551e13i		−	0.129973i
$761$			1.69309e14i			0.663370i	0.943390	+	0.331685i	$0.107617\pi$
$761$			1.69309e14i			0.663370i	−0.943390	+	0.331685i	$0.892383\pi$
$762$	5.06203e11			0.00197038
$763$			6.57377e12i			0.0254210i
$764$		−	4.85248e14i		−	1.86422i
$765$		−	2.09728e14i		−	0.800477i
$766$	−4.02324e12			−0.0152557
$767$	−3.59292e14			−1.35354
$768$		−	5.96003e13i		−	0.223071i
$769$	−3.58143e14			−1.33176			−0.665878	−	0.746061i	$-0.731943\pi$
$769$	−3.58143e14			−1.33176			−0.665878	+	0.746061i	$0.731943\pi$
$770$		−	2.26948e13i		−	0.0838442i
$771$	4.83239e13			0.177374
$772$	−3.41316e14			−1.24472
$773$		−	1.36760e14i		−	0.495522i	−0.968821	−	0.247761i	$-0.920305\pi$
$773$		−	1.36760e14i		−	0.495522i	0.968821	−	0.247761i	$-0.0796948\pi$
$774$	−4.02549e12	−	5.69459e12i	−0.0144915	−	0.0205002i
$775$	4.17452e14			1.49313
$776$			6.56920e12i			0.0233455i
$777$			1.34693e14i			0.475599i
$778$	1.05933e13			0.0371650
$779$			1.76165e14i			0.614090i
$780$	9.22563e13			0.319539
$781$			6.81548e13i			0.234553i
$782$		−	2.03499e12i		−	0.00695872i
$783$	1.14206e14			0.388044
$784$	−6.85759e14			−2.31521
$785$	3.16878e14			1.06303
$786$		−	1.85578e12i		−	0.00618607i
$787$	1.36777e14			0.453042			0.226521	−	0.974006i	$-0.427265\pi$
$787$	1.36777e14			0.453042			0.226521	+	0.974006i	$0.427265\pi$
$788$	4.69724e14			1.54601
$789$	1.26874e14			0.414943
$790$	1.89311e13			0.0615233
$791$	−4.68224e14			−1.51207
$792$			1.74252e13i			0.0559180i
$793$			2.44290e14i			0.779003i
$794$		−	1.52352e13i		−	0.0482775i
$795$	1.01731e14			0.320346
$796$		−	3.16394e14i		−	0.990064i
$797$	−5.67827e14			−1.76573			−0.882866	−	0.469626i	$-0.844389\pi$
$797$	−5.67827e14			−1.76573			−0.882866	+	0.469626i	$0.844389\pi$
$798$	−5.51205e12			−0.0170333
$799$	1.04543e14			0.321042
$800$			3.74042e13i			0.114149i
$801$		−	4.18596e14i		−	1.26950i
$802$			4.03843e12i			0.0121714i
$803$		−	2.04209e14i		−	0.611640i
$804$		−	8.05090e13i		−	0.239643i
$805$	−4.69324e14			−1.38833
$806$		−	8.49415e12i		−	0.0249715i
$807$			4.43878e12i			0.0129687i
$808$			2.65744e12i			0.00771626i
$809$	7.98438e13			0.230409			0.115204	−	0.993342i	$-0.463248\pi$
$809$	7.98438e13			0.230409			0.115204	+	0.993342i	$0.463248\pi$
$810$	−1.22580e13			−0.0351557
$811$			5.12445e14i			1.46064i	0.683106	+	0.730320i	$0.260629\pi$
$811$			5.12445e14i			1.46064i	−0.683106	+	0.730320i	$0.739371\pi$
$812$	5.69526e14			1.61337
$813$		−	5.56691e13i		−	0.156733i
$814$	1.22311e13			0.0342249
$815$	−8.22512e14			−2.28746
$816$		−	4.37647e13i		−	0.120969i
$817$	3.30716e14	+	4.67841e14i	0.908541	+	1.28525i
$818$	7.78555e12			0.0212580
$819$			5.80911e14i			1.57649i
$820$		−	2.25811e14i		−	0.609081i
$821$	−3.48244e14			−0.933614			−0.466807	−	0.884359i	$-0.654596\pi$
$821$	−3.48244e14			−0.933614			−0.466807	+	0.884359i	$0.654596\pi$
$822$		−	7.32556e11i		−	0.00195201i
$823$	4.68372e14			1.24049			0.620243	−	0.784409i	$-0.287034\pi$
$823$	4.68372e14			1.24049			0.620243	+	0.784409i	$0.287034\pi$
$824$			4.53880e12i			0.0119483i
$825$		−	1.37776e14i		−	0.360500i
$826$	−2.75162e13			−0.0715631
$827$	6.08475e14			1.57295			0.786476	−	0.617621i	$-0.211904\pi$
$827$	6.08475e14			1.57295			0.786476	+	0.617621i	$0.211904\pi$
$828$	1.80112e14			0.462796
$829$		−	5.02721e14i		−	1.28397i	−0.766718	−	0.641984i	$-0.778112\pi$
$829$		−	5.02721e14i		−	1.28397i	0.766718	−	0.641984i	$-0.221888\pi$
$830$	−2.55902e13			−0.0649655
$831$	−1.11447e14			−0.281231
$832$	−3.61740e14			−0.907360
$833$	−5.02142e14			−1.25199
$834$	1.16303e12			0.00288244
$835$		−	4.22978e14i		−	1.04204i
$836$		−	7.15537e14i		−	1.75227i
$837$			1.86482e14i			0.453952i
$838$	1.48749e13			0.0359943
$839$			9.63376e13i			0.231732i	0.993265	+	0.115866i	$0.0369643\pi$
$839$			9.63376e13i			0.231732i	−0.993265	+	0.115866i	$0.963036\pi$
$840$	1.41358e13			0.0338005
$841$	9.04089e13			0.214897
$842$	1.28925e13			0.0304632
$843$		−	6.97990e13i		−	0.163950i
$844$			5.50900e14i			1.28635i
$845$			1.14245e14i			0.265187i
$846$		−	6.47253e12i		−	0.0149356i
$847$		−	1.91554e14i		−	0.439413i
$848$	−3.99451e14			−0.910928
$849$		−	4.21535e13i		−	0.0955641i
$850$			9.11902e12i			0.0205520i
$851$		−	2.52936e14i		−	0.566712i
$852$	−2.12182e13			−0.0472618
$853$	−8.44718e13			−0.187054			−0.0935269	−	0.995617i	$-0.529814\pi$
$853$	−8.44718e13			−0.187054			−0.0935269	+	0.995617i	$0.529814\pi$
$854$			1.87088e13i			0.0411868i
$855$	1.06677e15			2.33475
$856$			2.29413e13i			0.0499170i
$857$	7.23095e14			1.56420			0.782098	−	0.623155i	$-0.214149\pi$
$857$	7.23095e14			1.56420			0.782098	+	0.623155i	$0.214149\pi$
$858$	−2.80342e12			−0.00602908
$859$			5.32248e14i			1.13802i	0.822332	+	0.569008i	$0.192673\pi$
$859$			5.32248e14i			1.13802i	−0.822332	+	0.569008i	$0.807327\pi$
$860$	−4.23916e14	−	5.99685e14i	−0.901130	−	1.27477i
$861$	−7.55643e13			−0.159699
$862$		−	7.41808e12i		−	0.0155867i
$863$			8.60293e14i			1.79718i	0.438786	+	0.898591i	$0.355409\pi$
$863$			8.60293e14i			1.79718i	−0.438786	+	0.898591i	$0.644591\pi$
$864$	−1.67090e13			−0.0347042
$865$		−	6.72161e14i		−	1.38801i
$866$	−7.82636e12			−0.0160683
$867$			7.80013e13i			0.159223i
$868$			9.29954e14i			1.88740i
$869$	8.22368e14			1.65946
$870$	−4.09761e12			−0.00822119
$871$	−4.87615e14			−0.972716
$872$			3.71815e11i			0.000737470i
$873$	−2.12648e14			−0.419362
$874$	1.03509e13			0.0202965
$875$	6.43094e14			1.25382
$876$	6.35749e13			0.123244
$877$	9.30571e14			1.79371			0.896854	−	0.442327i	$-0.145847\pi$
$877$	9.30571e14			1.79371			0.896854	+	0.442327i	$0.145847\pi$
$878$		−	2.04306e13i		−	0.0391570i
$879$			1.06418e14i			0.202802i
$880$			9.16542e14i			1.73676i
$881$	2.02031e14			0.380661			0.190330	−	0.981720i	$-0.439044\pi$
$881$	2.02031e14			0.380661			0.190330	+	0.981720i	$0.439044\pi$
$882$			3.10889e13i			0.0582456i
$883$	1.95016e14			0.363301			0.181651	−	0.983363i	$-0.441856\pi$
$883$	1.95016e14			0.363301			0.181651	+	0.983363i	$0.441856\pi$
$884$	−2.65253e14			−0.491360
$885$	−2.83013e14			−0.521302
$886$			6.78164e12i			0.0124213i
$887$			6.85090e14i			1.24775i	0.781522	+	0.623877i	$0.214444\pi$
$887$			6.85090e14i			1.24775i	−0.781522	+	0.623877i	$0.785556\pi$
$888$			7.61830e12i			0.0137973i
$889$			3.35659e14i			0.604491i
$890$			3.08359e13i			0.0552212i
$891$	−5.32491e14			−0.948251
$892$			8.70918e13i			0.154224i
$893$			5.31754e14i			0.936382i
$894$			9.81888e11i			0.00171939i
$895$	1.33236e15			2.32011
$896$	−1.11087e14			−0.192364
$897$			5.79740e13i			0.0998323i
$898$	1.80296e13			0.0308748
$899$		−	5.39329e14i		−	0.918450i
$900$	−8.07099e14			−1.36683
$901$	−2.92495e14			−0.492601
$902$			6.86176e12i			0.0114922i
$903$	−2.00676e14	+	1.41858e14i	−0.334239	+	0.236273i
$904$	−2.64829e13			−0.0438656
$905$		−	1.37197e15i		−	2.25997i
$906$		−	6.80994e11i		−	0.00111558i
$907$	6.84032e14			1.11440			0.557199	−	0.830379i	$-0.311876\pi$
$907$	6.84032e14			1.11440			0.557199	+	0.830379i	$0.311876\pi$
$908$		−	5.91385e14i		−	0.958167i
$909$	−8.60224e13			−0.138609
$910$		−	4.27928e13i		−	0.0685746i
$911$			1.35076e14i			0.215271i	0.994190	+	0.107635i	$0.0343279\pi$
$911$			1.35076e14i			0.215271i	−0.994190	+	0.107635i	$0.965672\pi$
$912$	2.22607e14			0.352830
$913$	−1.11164e15			−1.75231
$914$	1.64991e13			0.0258661
$915$			1.92426e14i			0.300026i
$916$	3.54383e14			0.549536
$917$	1.23056e15			1.89782
$918$	−4.07360e12			−0.00624834
$919$	−2.36775e14			−0.361209			−0.180604	−	0.983556i	$-0.557805\pi$
$919$	−2.36775e14			−0.361209			−0.180604	+	0.983556i	$0.557805\pi$
$920$	−2.65451e13			−0.0402759
$921$		−	1.73931e14i		−	0.262469i
$922$		−	1.02443e13i		−	0.0153755i
$923$			1.28511e14i			0.191837i
$924$	3.06923e14			0.455690
$925$			1.13343e15i			1.67374i
$926$	2.07726e13			0.0305096
$927$	−1.46923e14			−0.214630
$928$	4.83245e13			0.0702147
$929$		−	5.37530e14i		−	0.776827i	−0.921485	−	0.388413i	$-0.873023\pi$
$929$		−	5.37530e14i		−	0.776827i	0.921485	−	0.388413i	$-0.126977\pi$
$930$		−	6.69081e12i		−	0.00961753i
$931$		−	2.55412e15i		−	3.65169i
$932$			5.86145e14i			0.833538i
$933$		−	1.30013e14i		−	0.183899i
$934$	−1.01688e13			−0.0143066
$935$			6.71132e14i			0.939182i
$936$			3.28565e13i			0.0457343i
$937$		−	5.74508e14i		−	0.795423i	−0.917510	−	0.397712i	$-0.869804\pi$
$937$		−	5.74508e14i		−	0.795423i	0.917510	−	0.397712i	$-0.130196\pi$
$938$	−3.73438e13			−0.0514286
$939$	−6.78320e13			−0.0929194
$940$		−	6.81609e14i		−	0.928744i
$941$	−1.18983e15			−1.61264			−0.806322	−	0.591477i	$-0.798545\pi$
$941$	−1.18983e15			−1.61264			−0.806322	+	0.591477i	$0.798545\pi$
$942$		−	2.99775e12i		−	0.00404149i
$943$	1.41900e14			0.190293
$944$	1.11126e15			1.48236
$945$			9.39480e14i			1.24660i
$946$	1.28816e13	+	1.82228e13i	0.0170026	+	0.0240524i
$947$	−1.05265e15			−1.38208			−0.691040	−	0.722817i	$-0.742847\pi$
$947$	−1.05265e15			−1.38208			−0.691040	+	0.722817i	$0.742847\pi$
$948$			2.56022e14i			0.334377i
$949$		−	3.85051e14i		−	0.500250i
$950$	−4.63835e13			−0.0599439
$951$			5.66934e13i			0.0728836i
$952$	−4.06429e13			−0.0519756
$953$			4.60655e14i			0.586019i	0.956110	+	0.293009i	$0.0946567\pi$
$953$			4.60655e14i			0.586019i	−0.956110	+	0.293009i	$0.905343\pi$
$954$			1.81091e13i			0.0229169i
$955$	−2.31502e15			−2.91432
$956$	3.47975e14			0.435771
$957$	−1.78001e14			−0.221749
$958$		−	3.51942e13i		−	0.0436158i
$959$	4.85753e14			0.598856
$960$	−2.84941e14			−0.349461
$961$	6.10183e13			0.0744463
$962$	2.30626e13			0.0279919
$963$	−7.42618e14			−0.896673
$964$		−	1.28649e15i		−	1.54533i
$965$			1.62835e15i			1.94586i
$966$			4.43992e12i			0.00527825i
$967$	−4.77240e14			−0.564422			−0.282211	−	0.959352i	$-0.591068\pi$
$967$	−4.77240e14			−0.564422			−0.282211	+	0.959352i	$0.591068\pi$
$968$		−	1.08343e13i		−	0.0127475i
$969$	1.63003e14			0.190799
$970$	1.56647e13			0.0182416
$971$	−1.14694e15			−1.32875			−0.664377	−	0.747398i	$-0.731303\pi$
$971$	−1.14694e15			−1.32875			−0.664377	+	0.747398i	$0.731303\pi$
$972$		−	5.45480e14i		−	0.628706i
$973$			7.71195e14i			0.884301i
$974$			7.19109e12i			0.00820351i
$975$		−	2.59788e14i		−	0.294846i
$976$		−	7.55567e14i		−	0.853147i
$977$	1.69978e15			1.90950			0.954748	−	0.297417i	$-0.0961251\pi$
$977$	1.69978e15			1.90950			0.954748	+	0.297417i	$0.0961251\pi$
$978$			7.78118e12i			0.00869663i
$979$			1.33951e15i			1.48948i
$980$			3.27391e15i			3.62190i
$981$	−1.20358e13			−0.0132474
$982$	−4.71835e12			−0.00516693
$983$		−	4.99631e14i		−	0.544354i	−0.962247	−	0.272177i	$-0.912256\pi$
$983$		−	4.99631e14i		−	0.544354i	0.962247	−	0.272177i	$-0.0877437\pi$
$984$	−4.27395e12			−0.00463291
$985$		−	2.24096e15i		−	2.41687i
$986$	1.17814e13			0.0126419
$987$	−2.28091e14			−0.243513
$988$		−	1.34920e15i		−	1.43315i
$989$	3.76843e14	−	2.66389e14i	0.398271	−	0.281537i
$990$	4.15515e13			0.0436929
$991$		−	3.18035e14i		−	0.332741i	−0.986063	−	0.166371i	$-0.946795\pi$
$991$		−	3.18035e14i		−	0.332741i	0.986063	−	0.166371i	$-0.0532048\pi$
$992$			7.89070e13i			0.0821404i
$993$	1.92411e14			0.199289
$994$			9.84198e12i			0.0101426i
$995$	−1.50945e15			−1.54776
$996$		−	3.46079e14i		−	0.353085i
$997$			8.99024e14i			0.912632i	0.889818	+	0.456316i	$0.150831\pi$
$997$			8.99024e14i			0.912632i	−0.889818	+	0.456316i	$0.849169\pi$
$998$	1.79971e13			0.0181781
$999$	−5.06321e14			−0.508860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.b.b.42.17	✓	34
43.42	odd	2	inner	43.11.b.b.42.18	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.b.b.42.17	✓	34	1.1	even	1	trivial
43.11.b.b.42.18	yes	34	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:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.846054i q^{2} -54.5873i q^{3} +1023.28 q^{4} -4881.88i q^{5} -46.1839 q^{6} -30624.2i q^{7} -1732.11i q^{8} +56069.2 q^{9} +O(q^{10})\)	\(q-0.846054i q^{2} -54.5873i q^{3} +1023.28 q^{4} -4881.88i q^{5} -46.1839 q^{6} -30624.2i q^{7} -1732.11i q^{8} +56069.2 q^{9} -4130.34 q^{10} -179422. q^{11} -55858.4i q^{12} -338315. q^{13} -25909.7 q^{14} -266489. q^{15} +1.04638e6 q^{16} +766203. q^{17} -47437.6i q^{18} +3.89726e6i q^{19} -4.99555e6i q^{20} -1.67169e6 q^{21} +151801. i q^{22} +3.13921e6 q^{23} -94551.5 q^{24} -1.40672e7 q^{25} +286232. i q^{26} -6.28400e6i q^{27} -3.13372e7i q^{28} +1.81741e7i q^{29} +225464. i q^{30} -2.96757e7 q^{31} -2.65898e6i q^{32} +9.79419e6i q^{33} -648249. i q^{34} -1.49504e8 q^{35} +5.73747e7 q^{36} -8.05730e7i q^{37} +3.29729e6 q^{38} +1.84677e7i q^{39} -8.45598e6 q^{40} +4.52023e7 q^{41} +1.41434e6i q^{42} +(1.20044e8 - 8.48586e7i) q^{43} -1.83600e8 q^{44} -2.73723e8i q^{45} -2.65594e6i q^{46} +1.36443e8 q^{47} -5.71190e7i q^{48} -6.55365e8 q^{49} +1.19016e7i q^{50} -4.18250e7i q^{51} -3.46192e8 q^{52} -3.81746e8 q^{53} -5.31660e6 q^{54} +8.75919e8i q^{55} -5.30445e7 q^{56} +2.12741e8 q^{57} +1.53763e7 q^{58} +1.06201e9 q^{59} -2.72694e8 q^{60} -7.22078e8i q^{61} +2.51072e7i q^{62} -1.71707e9i q^{63} +1.06924e9 q^{64} +1.65161e9i q^{65} +8.28642e6 q^{66} +1.44131e9 q^{67} +7.84044e8 q^{68} -1.71361e8i q^{69} +1.26488e8i q^{70} -3.79857e8i q^{71} -9.71183e7i q^{72} +1.13814e9i q^{73} -6.81691e7 q^{74} +7.67889e8i q^{75} +3.98800e9i q^{76} +5.49466e9i q^{77} +1.56247e7 q^{78} -4.58342e9 q^{79} -5.10829e9i q^{80} +2.96780e9 q^{81} -3.82436e7i q^{82} +6.19566e9 q^{83} -1.71062e9 q^{84} -3.74051e9i q^{85} +(-7.17950e7 - 1.01563e8i) q^{86} +9.92077e8 q^{87} +3.10780e8i q^{88} -7.46570e9i q^{89} -2.31585e8 q^{90} +1.03606e10i q^{91} +3.21231e9 q^{92} +1.61992e9i q^{93} -1.15438e8i q^{94} +1.90259e10 q^{95} -1.45146e8 q^{96} -3.79259e9 q^{97} +5.54474e8i q^{98} -1.00601e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9}+O(q^{10}) \) 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9	\( 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9} - 254122 q^{10} - 218200 q^{11} - 191008 q^{13} - 1380228 q^{14} - 512732 q^{15} + 2224308 q^{16} - 1070678 q^{17} + 17857352 q^{21} + 8915254 q^{23} - 39666730 q^{24} - 82938284 q^{25} - 55042410 q^{31} - 179227232 q^{35} + 394381042 q^{36} + 709061882 q^{38} + 433255366 q^{40} + 80370626 q^{41} + 1585062 q^{43} + 324477888 q^{44} - 544910502 q^{47} - 2479345922 q^{49} - 987059452 q^{52} - 915886820 q^{53} - 297150836 q^{54} + 2172449592 q^{56} - 2398069428 q^{57} + 930519014 q^{58} + 3394816764 q^{59} - 5474941192 q^{60} + 2925325476 q^{64} + 455136192 q^{66} + 3405920388 q^{67} + 664008226 q^{68} + 16264108918 q^{74} - 17800086268 q^{78} - 13853150858 q^{79} + 20444701546 q^{81} + 113867236 q^{83} - 30401949428 q^{84} + 19291204884 q^{86} - 5221634730 q^{87} - 6984391876 q^{90} + 41423783058 q^{92} + 4107406010 q^{95} + 33148445474 q^{96} + 15795117154 q^{97} + 1345877600 q^{99}+O(q^{100}) \) 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9 - 254122 * q^10 - 218200 * q^11 - 191008 * q^13 - 1380228 * q^14 - 512732 * q^15 + 2224308 * q^16 - 1070678 * q^17 + 17857352 * q^21 + 8915254 * q^23 - 39666730 * q^24 - 82938284 * q^25 - 55042410 * q^31 - 179227232 * q^35 + 394381042 * q^36 + 709061882 * q^38 + 433255366 * q^40 + 80370626 * q^41 + 1585062 * q^43 + 324477888 * q^44 - 544910502 * q^47 - 2479345922 * q^49 - 987059452 * q^52 - 915886820 * q^53 - 297150836 * q^54 + 2172449592 * q^56 - 2398069428 * q^57 + 930519014 * q^58 + 3394816764 * q^59 - 5474941192 * q^60 + 2925325476 * q^64 + 455136192 * q^66 + 3405920388 * q^67 + 664008226 * q^68 + 16264108918 * q^74 - 17800086268 * q^78 - 13853150858 * q^79 + 20444701546 * q^81 + 113867236 * q^83 - 30401949428 * q^84 + 19291204884 * q^86 - 5221634730 * q^87 - 6984391876 * q^90 + 41423783058 * q^92 + 4107406010 * q^95 + 33148445474 * q^96 + 15795117154 * q^97 + 1345877600 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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