LMFDB - Embedded newform 11.9.b.b.10.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,9,Mod(10,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, 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("11.10");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	11.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:	$4.48116471067$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 1374x^{4} + 436560x^{2} + 40320000 $ x^6 + 1374x^4 + 436560x^2 + 40320000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			10.3
Root			$-14.0233i$ of defining polynomial
Character	$\chi$	$=$	11.10
Dual form			11.9.b.b.10.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-14.0233i q^{2} +84.5196 q^{3} +59.3467 q^{4} +63.0464 q^{5} -1185.25i q^{6} -1667.89i q^{7} -4422.21i q^{8} +582.567 q^{9} +O(q^{10})$	\(q-14.0233i q^{2} +84.5196 q^{3} +59.3467 q^{4} +63.0464 q^{5} -1185.25i q^{6} -1667.89i q^{7} -4422.21i q^{8} +582.567 q^{9} -884.120i q^{10} +(4865.29 + 13809.0i) q^{11} +5015.96 q^{12} +16178.3i q^{13} -23389.3 q^{14} +5328.66 q^{15} -46821.2 q^{16} +58233.1i q^{17} -8169.52i q^{18} +17200.1i q^{19} +3741.60 q^{20} -140969. i q^{21} +(193648. - 68227.4i) q^{22} +290115. q^{23} -373763. i q^{24} -386650. q^{25} +226874. q^{26} -505295. q^{27} -98983.7i q^{28} +1.15736e6i q^{29} -74725.5i q^{30} -504456. q^{31} -475496. i q^{32} +(411212. + 1.16713e6i) q^{33} +816620. q^{34} -105154. i q^{35} +34573.5 q^{36} -562440. q^{37} +241202. q^{38} +1.36739e6i q^{39} -278804. i q^{40} -957088. i q^{41} -1.97686e6 q^{42} -6.28563e6i q^{43} +(288739. + 819518. i) q^{44} +36728.8 q^{45} -4.06838e6i q^{46} +7.14150e6 q^{47} -3.95731e6 q^{48} +2.98295e6 q^{49} +5.42212e6i q^{50} +4.92184e6i q^{51} +960132. i q^{52} -5.44472e6 q^{53} +7.08591e6i q^{54} +(306739. + 870607. i) q^{55} -7.37574e6 q^{56} +1.45374e6i q^{57} +1.62300e7 q^{58} -1.63227e7 q^{59} +316239. q^{60} -1.66903e7i q^{61} +7.07414e6i q^{62} -971657. i q^{63} -1.86543e7 q^{64} +1.01999e6i q^{65} +(1.63670e7 - 5.76656e6i) q^{66} +2.30970e7 q^{67} +3.45594e6i q^{68} +2.45204e7 q^{69} -1.47461e6 q^{70} -1.66778e7 q^{71} -2.57623e6i q^{72} -5.01077e7i q^{73} +7.88728e6i q^{74} -3.26795e7 q^{75} +1.02077e6i q^{76} +(2.30318e7 - 8.11475e6i) q^{77} +1.91753e7 q^{78} +4.05105e7i q^{79} -2.95191e6 q^{80} -4.65296e7 q^{81} -1.34215e7 q^{82} +4.65927e7i q^{83} -8.36606e6i q^{84} +3.67139e6i q^{85} -8.81453e7 q^{86} +9.78196e7i q^{87} +(6.10661e7 - 2.15153e7i) q^{88} +9.49493e7 q^{89} -515059. i q^{90} +2.69837e7 q^{91} +1.72174e7 q^{92} -4.26364e7 q^{93} -1.00148e8i q^{94} +1.08440e6i q^{95} -4.01888e7i q^{96} -3.42056e7 q^{97} -4.18309e7i q^{98} +(2.83436e6 + 8.04466e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 36 q^{3} - 1212 q^{4} - 448 q^{5} - 13578 q^{9}+O(q^{10}) $ 6 * q - 36 * q^3 - 1212 * q^4 - 448 * q^5 - 13578 * q^9	$ 6 q - 36 q^{3} - 1212 q^{4} - 448 q^{5} - 13578 q^{9} - 32318 q^{11} + 54564 q^{12} - 33768 q^{14} + 85824 q^{15} + 312264 q^{16} - 894868 q^{20} - 550440 q^{22} + 683084 q^{23} - 141498 q^{25} - 657432 q^{26} + 988848 q^{27} + 942684 q^{31} + 2992704 q^{33} - 1345128 q^{34} + 7401360 q^{36} - 3804816 q^{37} - 8900760 q^{38} - 8158920 q^{42} + 14210284 q^{44} - 2499684 q^{45} + 15828644 q^{47} - 19028376 q^{48} - 10066602 q^{49} - 35477956 q^{53} + 7335372 q^{55} + 68829936 q^{56} + 65482560 q^{58} - 29614804 q^{59} + 35069244 q^{60} - 212921520 q^{64} + 75167400 q^{66} + 39419484 q^{67} + 62859468 q^{69} - 168190680 q^{70} + 3219212 q^{71} - 110874276 q^{75} + 91605360 q^{77} + 111889320 q^{78} + 383392952 q^{80} - 103764906 q^{81} - 163977720 q^{82} - 261274512 q^{86} + 328724880 q^{88} + 38785664 q^{89} + 355260528 q^{91} - 456128956 q^{92} - 182572452 q^{93} - 222185616 q^{97} + 159125406 q^{99}+O(q^{100}) $ 6 * q - 36 * q^3 - 1212 * q^4 - 448 * q^5 - 13578 * q^9 - 32318 * q^11 + 54564 * q^12 - 33768 * q^14 + 85824 * q^15 + 312264 * q^16 - 894868 * q^20 - 550440 * q^22 + 683084 * q^23 - 141498 * q^25 - 657432 * q^26 + 988848 * q^27 + 942684 * q^31 + 2992704 * q^33 - 1345128 * q^34 + 7401360 * q^36 - 3804816 * q^37 - 8900760 * q^38 - 8158920 * q^42 + 14210284 * q^44 - 2499684 * q^45 + 15828644 * q^47 - 19028376 * q^48 - 10066602 * q^49 - 35477956 * q^53 + 7335372 * q^55 + 68829936 * q^56 + 65482560 * q^58 - 29614804 * q^59 + 35069244 * q^60 - 212921520 * q^64 + 75167400 * q^66 + 39419484 * q^67 + 62859468 * q^69 - 168190680 * q^70 + 3219212 * q^71 - 110874276 * q^75 + 91605360 * q^77 + 111889320 * q^78 + 383392952 * q^80 - 103764906 * q^81 - 163977720 * q^82 - 261274512 * q^86 + 328724880 * q^88 + 38785664 * q^89 + 355260528 * q^91 - 456128956 * q^92 - 182572452 * q^93 - 222185616 * q^97 + 159125406 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	14.0233i		−	0.876457i	−0.898864	−	0.438228i	$-0.855606\pi$
$2$		−	14.0233i		−	0.876457i	0.898864	−	0.438228i	$-0.144394\pi$
$3$	84.5196			1.04345			0.521726	−	0.853113i	$-0.325288\pi$
$3$	84.5196			1.04345			0.521726	+	0.853113i	$0.325288\pi$
$4$	59.3467			0.231823
$5$	63.0464			0.100874			0.0504371	−	0.998727i	$-0.483939\pi$
$5$	63.0464			0.100874			0.0504371	+	0.998727i	$0.483939\pi$
$6$		−	1185.25i		−	0.914541i
$7$		−	1667.89i		−	0.694664i	−0.937742	−	0.347332i	$-0.887088\pi$
$7$		−	1667.89i		−	0.694664i	0.937742	−	0.347332i	$-0.112912\pi$
$8$		−	4422.21i		−	1.07964i
$9$	582.567			0.0887925
$10$		−	884.120i		−	0.0884120i
$11$	4865.29	+	13809.0i	0.332306	+	0.943172i
$11$	4865.29	+	13809.0i	0.332306	+	0.943172i
$12$	5015.96			0.241896
$13$			16178.3i			0.566449i	0.959054	+	0.283224i	$0.0914041\pi$
$13$			16178.3i			0.566449i	−0.959054	+	0.283224i	$0.908596\pi$
$14$	−23389.3			−0.608843
$15$	5328.66			0.105257
$16$	−46821.2			−0.714435
$17$			58233.1i			0.697227i	0.937267	+	0.348613i	$0.113347\pi$
$17$			58233.1i			0.697227i	−0.937267	+	0.348613i	$0.886653\pi$
$18$		−	8169.52i		−	0.0778228i
$19$			17200.1i			0.131982i	0.997820	+	0.0659911i	$0.0210209\pi$
$19$			17200.1i			0.131982i	−0.997820	+	0.0659911i	$0.978979\pi$
$20$	3741.60			0.0233850
$21$		−	140969.i		−	0.724848i
$22$	193648.	−	68227.4i	0.826649	−	0.291252i
$23$	290115.			1.03671			0.518357	−	0.855164i	$-0.326544\pi$
$23$	290115.			1.03671			0.518357	+	0.855164i	$0.326544\pi$
$24$		−	373763.i		−	1.12655i
$25$	−386650.			−0.989824
$26$	226874.			0.496468
$27$	−505295.			−0.950801
$28$		−	98983.7i		−	0.161039i
$29$			1.15736e6i			1.63635i	0.574969	+	0.818175i	$0.305014\pi$
$29$			1.15736e6i			1.63635i	−0.574969	+	0.818175i	$0.694986\pi$
$30$		−	74725.5i		−	0.0922536i
$31$	−504456.			−0.546231			−0.273116	−	0.961981i	$-0.588054\pi$
$31$	−504456.			−0.546231			−0.273116	+	0.961981i	$0.588054\pi$
$32$		−	475496.i		−	0.453469i
$33$	411212.	+	1.16713e6i	0.346745	+	0.984155i
$34$	816620.			0.611089
$35$		−	105154.i		−	0.0700737i
$36$	34573.5			0.0205841
$37$	−562440.			−0.300103			−0.150051	−	0.988678i	$-0.547944\pi$
$37$	−562440.			−0.300103			−0.150051	+	0.988678i	$0.547944\pi$
$38$	241202.			0.115677
$39$			1.36739e6i			0.591062i
$40$		−	278804.i		−	0.108908i
$41$		−	957088.i		−	0.338701i	−0.985556	−	0.169351i	$-0.945833\pi$
$41$		−	957088.i		−	0.338701i	0.985556	−	0.169351i	$-0.0541670\pi$
$42$	−1.97686e6			−0.635298
$43$		−	6.28563e6i		−	1.83855i	−0.393618	−	0.919274i	$-0.628777\pi$
$43$		−	6.28563e6i		−	1.83855i	0.393618	−	0.919274i	$-0.371223\pi$
$44$	288739.	+	819518.i	0.0770361	+	0.218649i
$45$	36728.8			0.00895687
$46$		−	4.06838e6i		−	0.908635i
$47$	7.14150e6			1.46352			0.731759	−	0.681563i	$-0.238700\pi$
$47$	7.14150e6			1.46352			0.731759	+	0.681563i	$0.238700\pi$
$48$	−3.95731e6			−0.745479
$49$	2.98295e6			0.517443
$50$			5.42212e6i			0.867538i
$51$			4.92184e6i			0.727523i
$52$			960132.i			0.131316i
$53$	−5.44472e6			−0.690037			−0.345018	−	0.938596i	$-0.612127\pi$
$53$	−5.44472e6			−0.690037			−0.345018	+	0.938596i	$0.612127\pi$
$54$			7.08591e6i			0.833337i
$55$	306739.	+	870607.i	0.0335211	+	0.0951418i
$56$	−7.37574e6			−0.749987
$57$			1.45374e6i			0.137717i
$58$	1.62300e7			1.43419
$59$	−1.63227e7			−1.34705			−0.673523	−	0.739166i	$-0.735220\pi$
$59$	−1.63227e7			−1.34705			−0.673523	+	0.739166i	$0.735220\pi$
$60$	316239.			0.0244011
$61$		−	1.66903e7i		−	1.20544i	−0.797954	−	0.602718i	$-0.794085\pi$
$61$		−	1.66903e7i		−	1.20544i	0.797954	−	0.602718i	$-0.205915\pi$
$62$			7.07414e6i			0.478748i
$63$		−	971657.i		−	0.0616809i
$64$	−1.86543e7			−1.11188
$65$			1.01999e6i			0.0571401i
$66$	1.63670e7	−	5.76656e6i	0.862569	−	0.303907i
$67$	2.30970e7			1.14619			0.573095	−	0.819489i	$-0.305743\pi$
$67$	2.30970e7			1.14619			0.573095	+	0.819489i	$0.305743\pi$
$68$			3.45594e6i			0.161633i
$69$	2.45204e7			1.08176
$70$	−1.47461e6			−0.0614166
$71$	−1.66778e7			−0.656304			−0.328152	−	0.944625i	$-0.606426\pi$
$71$	−1.66778e7			−0.656304			−0.328152	+	0.944625i	$0.606426\pi$
$72$		−	2.57623e6i		−	0.0958639i
$73$		−	5.01077e7i		−	1.76446i	−0.470814	−	0.882232i	$-0.656040\pi$
$73$		−	5.01077e7i		−	1.76446i	0.470814	−	0.882232i	$-0.343960\pi$
$74$			7.88728e6i			0.263027i
$75$	−3.26795e7			−1.03283
$76$			1.02077e6i			0.0305966i
$77$	2.30318e7	−	8.11475e6i	0.655187	−	0.230841i
$78$	1.91753e7			0.518041
$79$			4.05105e7i			1.04006i	0.854147	+	0.520031i	$0.174080\pi$
$79$			4.05105e7i			1.04006i	−0.854147	+	0.520031i	$0.825920\pi$
$80$	−2.95191e6			−0.0720681
$81$	−4.65296e7			−1.08091
$82$	−1.34215e7			−0.296857
$83$			4.65927e7i			0.981760i	0.871227	+	0.490880i	$0.163325\pi$
$83$			4.65927e7i			0.981760i	−0.871227	+	0.490880i	$0.836675\pi$
$84$		−	8.36606e6i		−	0.168037i
$85$			3.67139e6i			0.0703322i
$86$	−8.81453e7			−1.61141
$87$			9.78196e7i			1.70745i
$88$	6.10661e7	−	2.15153e7i	1.01829	−	0.358770i
$89$	9.49493e7			1.51332			0.756662	−	0.653806i	$-0.226829\pi$
$89$	9.49493e7			1.51332			0.756662	+	0.653806i	$0.226829\pi$
$90$		−	515059.i		−	0.00785031i
$91$	2.69837e7			0.393491
$92$	1.72174e7			0.240334
$93$	−4.26364e7			−0.569966
$94$		−	1.00148e8i		−	1.28271i
$95$			1.08440e6i			0.0133136i
$96$		−	4.01888e7i		−	0.473173i
$97$	−3.42056e7			−0.386376			−0.193188	−	0.981162i	$-0.561883\pi$
$97$	−3.42056e7			−0.386376			−0.193188	+	0.981162i	$0.561883\pi$
$98$		−	4.18309e7i		−	0.453516i
$99$	2.83436e6	+	8.04466e6i	0.0295062	+	0.0837465i
$100$	−2.29464e7			−0.229464
$101$		−	7.13647e7i		−	0.685801i	−0.939372	−	0.342900i	$-0.888591\pi$
$101$		−	7.13647e7i		−	0.685801i	0.939372	−	0.342900i	$-0.111409\pi$
$102$	6.90204e7			0.637642
$103$	−1.18765e8			−1.05521			−0.527605	−	0.849490i	$-0.676910\pi$
$103$	−1.18765e8			−1.05521			−0.527605	+	0.849490i	$0.676910\pi$
$104$	7.15440e7			0.611561
$105$		−	8.88760e6i		−	0.0731185i
$106$			7.63530e7i			0.604787i
$107$			3.02687e7i			0.230918i	0.993312	+	0.115459i	$0.0368339\pi$
$107$			3.02687e7i			0.230918i	−0.993312	+	0.115459i	$0.963166\pi$
$108$	−2.99876e7			−0.220418
$109$		−	1.16680e8i		−	0.826592i	−0.910597	−	0.413296i	$-0.864378\pi$
$109$		−	1.16680e8i		−	0.826592i	0.910597	−	0.413296i	$-0.135622\pi$
$110$	1.22088e7	−	4.30149e6i	0.0833877	−	0.0293798i
$111$	−4.75373e7			−0.313143
$112$			7.80925e7i			0.496292i
$113$	1.54630e8			0.948377			0.474188	−	0.880423i	$-0.342742\pi$
$113$	1.54630e8			0.948377			0.474188	+	0.880423i	$0.342742\pi$
$114$	2.03863e7			0.120703
$115$	1.82907e7			0.104578
$116$			6.86855e7i			0.379344i
$117$			9.42498e6i			0.0502964i
$118$			2.28898e8i			1.18063i
$119$	9.71262e7			0.484338
$120$		−	2.35644e7i		−	0.113640i
$121$	−1.67017e8	+	1.34369e8i	−0.779146	+	0.626843i
$122$	−2.34053e8			−1.05651
$123$		−	8.08927e7i		−	0.353418i
$124$	−2.99378e7			−0.126629
$125$	−4.90044e7			−0.200722
$126$	−1.36258e7			−0.0540606
$127$			4.05063e8i			1.55707i	0.627603	+	0.778534i	$0.284036\pi$
$127$			4.05063e8i			1.55707i	−0.627603	+	0.778534i	$0.715964\pi$
$128$			1.39867e8i			0.521047i
$129$		−	5.31259e8i		−	1.91844i
$130$	1.43036e7			0.0500809
$131$		−	3.12044e8i		−	1.05957i	−0.848131	−	0.529786i	$-0.822272\pi$
$131$		−	3.12044e8i		−	1.05957i	0.848131	−	0.529786i	$-0.177728\pi$
$132$	2.44041e7	+	6.92653e7i	0.0803835	+	0.228150i
$133$	2.86878e7			0.0916833
$134$		−	3.23896e8i		−	1.00459i
$135$	−3.18570e7			−0.0959114
$136$	2.57519e8			0.752754
$137$	1.92514e8			0.546488			0.273244	−	0.961945i	$-0.411903\pi$
$137$	1.92514e8			0.546488			0.273244	+	0.961945i	$0.411903\pi$
$138$		−	3.43858e8i		−	0.948118i
$139$		−	6.71831e7i		−	0.179970i	−0.995943	−	0.0899852i	$-0.971318\pi$
$139$		−	6.71831e7i		−	0.179970i	0.995943	−	0.0899852i	$-0.0286820\pi$
$140$		−	6.24057e6i		−	0.0162447i
$141$	6.03597e8			1.52711
$142$			2.33878e8i			0.575222i
$143$	−2.23406e8	+	7.87123e7i	−0.534259	+	0.188234i
$144$	−2.72765e7			−0.0634364
$145$			7.29674e7i			0.165066i
$146$	−7.02676e8			−1.54648
$147$	2.52118e8			0.539927
$148$	−3.33790e7			−0.0695707
$149$		−	1.25764e8i		−	0.255158i	−0.991828	−	0.127579i	$-0.959279\pi$
$149$		−	1.25764e8i		−	0.255158i	0.991828	−	0.127579i	$-0.0407207\pi$
$150$			4.58275e8i			0.905235i
$151$			3.79672e8i			0.730300i	0.930949	+	0.365150i	$0.118982\pi$
$151$			3.79672e8i			0.730300i	−0.930949	+	0.365150i	$0.881018\pi$
$152$	7.60622e7			0.142493
$153$			3.39247e7i			0.0619085i
$154$	−1.13796e8	−	3.22982e8i	−0.202322	−	0.574243i
$155$	−3.18041e7			−0.0551007
$156$			8.11500e7i			0.137022i
$157$	−9.60738e8			−1.58127			−0.790635	−	0.612287i	$-0.790250\pi$
$157$	−9.60738e8			−1.58127			−0.790635	+	0.612287i	$0.790250\pi$
$158$	5.68092e8			0.911570
$159$	−4.60186e8			−0.720020
$160$		−	2.99783e7i		−	0.0457433i
$161$		−	4.83879e8i		−	0.720168i
$162$			6.52499e8i			0.947370i
$163$	2.02925e8			0.287465			0.143733	−	0.989617i	$-0.454089\pi$
$163$	2.02925e8			0.287465			0.143733	+	0.989617i	$0.454089\pi$
$164$		−	5.68001e7i		−	0.0785188i
$165$	2.59255e7	+	7.35833e7i	0.0349776	+	0.0992759i
$166$	6.53383e8			0.860470
$167$			1.20544e9i			1.54981i	0.632078	+	0.774905i	$0.282202\pi$
$167$			1.20544e9i			1.54981i	−0.632078	+	0.774905i	$0.717798\pi$
$168$	−6.23395e8			−0.782575
$169$	5.53992e8			0.679136
$170$	5.14850e7			0.0616432
$171$			1.00202e7i			0.0117190i
$172$		−	3.73032e8i		−	0.426218i
$173$		−	3.88863e8i		−	0.434122i	−0.976158	−	0.217061i	$-0.930353\pi$
$173$		−	3.88863e8i		−	0.434122i	0.976158	−	0.217061i	$-0.0696471\pi$
$174$	1.37176e9			1.49651
$175$			6.44889e8i			0.687595i
$176$	−2.27799e8	−	6.46553e8i	−0.237411	−	0.673835i
$177$	−1.37958e9			−1.40558
$178$		−	1.33150e9i		−	1.32636i
$179$	−6.73331e7			−0.0655868			−0.0327934	−	0.999462i	$-0.510440\pi$
$179$	−6.73331e7			−0.0655868			−0.0327934	+	0.999462i	$0.510440\pi$
$180$	2.17973e6			0.00207641
$181$	1.01723e9			0.947776			0.473888	−	0.880585i	$-0.342850\pi$
$181$	1.01723e9			0.947776			0.473888	+	0.880585i	$0.342850\pi$
$182$		−	3.78400e8i		−	0.344878i
$183$		−	1.41066e9i		−	1.25781i
$184$		−	1.28295e9i		−	1.11928i
$185$	−3.54599e7			−0.0302726
$186$			5.97904e8i			0.499551i
$187$	−8.04139e8	+	2.83321e8i	−0.657604	+	0.231692i
$188$	4.23825e8			0.339277
$189$			8.42775e8i			0.660487i
$190$	1.52069e7			0.0116688
$191$	4.97059e8			0.373486			0.186743	−	0.982409i	$-0.440207\pi$
$191$	4.97059e8			0.373486			0.186743	+	0.982409i	$0.440207\pi$
$192$	−1.57665e9			−1.16019
$193$			2.85362e8i			0.205668i	0.994699	+	0.102834i	$0.0327911\pi$
$193$			2.85362e8i			0.205668i	−0.994699	+	0.102834i	$0.967209\pi$
$194$			4.79676e8i			0.338642i
$195$			8.62089e7i			0.0596230i
$196$	1.77029e8			0.119955
$197$			1.51685e9i			1.00711i	0.863963	+	0.503556i	$0.167975\pi$
$197$			1.51685e9i			1.00711i	−0.863963	+	0.503556i	$0.832025\pi$
$198$	1.12813e8	−	3.97471e7i	0.0734002	−	0.0258609i
$199$	−1.40903e9			−0.898477			−0.449238	−	0.893412i	$-0.648305\pi$
$199$	−1.40903e9			−0.898477			−0.449238	+	0.893412i	$0.648305\pi$
$200$			1.70985e9i			1.06865i
$201$	1.95215e9			1.19599
$202$	−1.00077e9			−0.601075
$203$	1.93035e9			1.13671
$204$			2.92095e8i			0.168657i
$205$		−	6.03410e7i		−	0.0341662i
$206$			1.66547e9i			0.924845i
$207$	1.69012e8			0.0920524
$208$		−	7.57490e8i		−	0.404691i
$209$	−2.37515e8	+	8.36832e7i	−0.124482	+	0.0438585i
$210$	−1.24634e8			−0.0640853
$211$		−	2.51119e9i		−	1.26692i	−0.773776	−	0.633460i	$-0.781634\pi$
$211$		−	2.51119e9i		−	1.26692i	0.773776	−	0.633460i	$-0.218366\pi$
$212$	−3.23126e8			−0.159966
$213$	−1.40960e9			−0.684821
$214$	4.24467e8			0.202390
$215$		−	3.96286e8i		−	0.185462i
$216$			2.23452e9i			1.02652i
$217$			8.41376e8i			0.379447i
$218$	−1.63624e9			−0.724472
$219$		−	4.23508e9i		−	1.84113i
$220$	1.82039e7	+	5.16677e7i	0.00777096	+	0.0220561i
$221$	−9.42115e8			−0.394943
$222$			6.66630e8i			0.274456i
$223$	3.04505e9			1.23133			0.615666	−	0.788007i	$-0.288887\pi$
$223$	3.04505e9			1.23133			0.615666	+	0.788007i	$0.288887\pi$
$224$	−7.93074e8			−0.315008
$225$	−2.25250e8			−0.0878889
$226$		−	2.16843e9i		−	0.831212i
$227$			5.73736e8i			0.216077i	0.994147	+	0.108038i	$0.0344570\pi$
$227$			5.73736e8i			0.216077i	−0.994147	+	0.108038i	$0.965543\pi$
$228$			8.62749e7i			0.0319260i
$229$	−2.73896e9			−0.995966			−0.497983	−	0.867187i	$-0.665926\pi$
$229$	−2.73896e9			−0.995966			−0.497983	+	0.867187i	$0.665926\pi$
$230$		−	2.56496e8i		−	0.0916579i
$231$	1.94664e9	−	6.85856e8i	0.683656	−	0.240871i
$232$	5.11808e9			1.76667
$233$		−	2.15337e9i		−	0.730625i	−0.930885	−	0.365312i	$-0.880962\pi$
$233$		−	2.15337e9i		−	0.730625i	0.930885	−	0.365312i	$-0.119038\pi$
$234$	1.32169e8			0.0440826
$235$	4.50246e8			0.147631
$236$	−9.68696e8			−0.312277
$237$			3.42393e9i			1.08526i
$238$		−	1.36203e9i		−	0.424501i
$239$		−	4.41753e9i		−	1.35390i	−0.736027	−	0.676952i	$-0.763300\pi$
$239$		−	4.41753e9i		−	1.35390i	0.736027	−	0.676952i	$-0.236700\pi$
$240$	−2.49494e8			−0.0751996
$241$			1.15334e9i			0.341892i	0.985280	+	0.170946i	$0.0546824\pi$
$241$			1.15334e9i			0.341892i	−0.985280	+	0.170946i	$0.945318\pi$
$242$	1.88430e9	+	2.34213e9i	0.549401	+	0.682888i
$243$	−6.17421e8			−0.177075
$244$		−	9.90513e8i		−	0.279448i
$245$	1.88065e8			0.0521966
$246$	−1.13438e9			−0.309756
$247$	−2.78269e8			−0.0747612
$248$			2.23081e9i			0.589733i
$249$			3.93799e9i			1.02442i
$250$			6.87204e8i			0.175924i
$251$	−5.58001e9			−1.40585			−0.702927	−	0.711262i	$-0.748124\pi$
$251$	−5.58001e9			−1.40585			−0.702927	+	0.711262i	$0.748124\pi$
$252$		−	5.76646e7i		−	0.0142991i
$253$	1.41149e9	+	4.00619e9i	0.344506	+	0.977800i
$254$	5.68032e9			1.36470
$255$			3.10304e8i			0.0733883i
$256$	−2.81409e9			−0.655205
$257$	−4.39750e9			−1.00803			−0.504015	−	0.863695i	$-0.668144\pi$
$257$	−4.39750e9			−1.00803			−0.504015	+	0.863695i	$0.668144\pi$
$258$	−7.45001e9			−1.68143
$259$			9.38087e8i			0.208470i
$260$			6.05329e7i			0.0132464i
$261$			6.74240e8i			0.145296i
$262$	−4.37589e9			−0.928669
$263$		−	7.83149e8i		−	0.163690i	−0.996645	−	0.0818448i	$-0.973919\pi$
$263$		−	7.83149e8i		−	0.163690i	0.996645	−	0.0818448i	$-0.0260812\pi$
$264$	5.16129e9	−	1.81846e9i	1.06253	−	0.374360i
$265$	−3.43270e8			−0.0696069
$266$		−	4.02297e8i		−	0.0803565i
$267$	8.02508e9			1.57908
$268$	1.37073e9			0.265713
$269$	4.51881e9			0.863008			0.431504	−	0.902111i	$-0.357983\pi$
$269$	4.51881e9			0.863008			0.431504	+	0.902111i	$0.357983\pi$
$270$			4.46741e8i			0.0840622i
$271$		−	3.01131e8i		−	0.0558314i	−0.999610	−	0.0279157i	$-0.991113\pi$
$271$		−	3.01131e8i		−	0.0558314i	0.999610	−	0.0279157i	$-0.00888699\pi$
$272$		−	2.72654e9i		−	0.498123i
$273$	2.28065e9			0.410589
$274$		−	2.69969e9i		−	0.478973i
$275$	−1.88116e9	−	5.33924e9i	−0.328924	−	0.933574i
$276$	1.45521e9			0.250777
$277$			2.47663e9i			0.420670i	0.977629	+	0.210335i	$0.0674554\pi$
$277$			2.47663e9i			0.420670i	−0.977629	+	0.210335i	$0.932545\pi$
$278$	−9.42130e8			−0.157736
$279$	−2.93880e8			−0.0485012
$280$	−4.65014e8			−0.0756544
$281$		−	6.32351e9i		−	1.01422i	−0.861881	−	0.507111i	$-0.830713\pi$
$281$		−	6.32351e9i		−	1.01422i	0.861881	−	0.507111i	$-0.169287\pi$
$282$		−	8.46443e9i		−	1.33845i
$283$			1.03618e10i			1.61544i	0.589567	+	0.807719i	$0.299298\pi$
$283$			1.03618e10i			1.61544i	−0.589567	+	0.807719i	$0.700702\pi$
$284$	−9.89772e8			−0.152146
$285$			9.16533e7i			0.0138921i
$286$	1.10381e9	+	3.13290e9i	0.164979	+	0.468255i
$287$	−1.59632e9			−0.235283
$288$		−	2.77009e8i		−	0.0402646i
$289$	3.58467e9			0.513875
$290$	1.02324e9			0.144673
$291$	−2.89104e9			−0.403165
$292$		−	2.97373e9i		−	0.409044i
$293$			3.95819e9i			0.537065i	0.963271	+	0.268532i	$0.0865386\pi$
$293$			3.95819e9i			0.537065i	−0.963271	+	0.268532i	$0.913461\pi$
$294$		−	3.53553e9i		−	0.473222i
$295$	−1.02908e9			−0.135882
$296$			2.48723e9i			0.324003i
$297$	−2.45840e9	−	6.97761e9i	−0.315957	−	0.896769i
$298$	−1.76362e9			−0.223635
$299$			4.69358e9i			0.587246i
$300$	−1.93942e9			−0.239435
$301$	−1.04837e10			−1.27717
$302$	5.32427e9			0.640077
$303$		−	6.03172e9i		−	0.715600i
$304$		−	8.05328e8i		−	0.0942927i
$305$		−	1.05226e9i		−	0.121597i
$306$	4.75736e8			0.0542601
$307$			1.70429e10i			1.91862i	0.282352	+	0.959311i	$0.408885\pi$
$307$			1.70429e10i			1.91862i	−0.282352	+	0.959311i	$0.591115\pi$
$308$	1.36686e9	−	4.81584e8i	0.151888	−	0.0535142i
$309$	−1.00380e10			−1.10106
$310$			4.45999e8i			0.0482934i
$311$	8.58227e9			0.917404			0.458702	−	0.888590i	$-0.348315\pi$
$311$	8.58227e9			0.917404			0.458702	+	0.888590i	$0.348315\pi$
$312$	6.04687e9			0.638134
$313$	1.01813e10			1.06078			0.530390	−	0.847754i	$-0.322046\pi$
$313$	1.01813e10			1.06078			0.530390	+	0.847754i	$0.322046\pi$
$314$			1.34727e10i			1.38592i
$315$		−	6.12595e7i		−	0.00622201i
$316$			2.40417e9i			0.241111i
$317$	1.19438e10			1.18278			0.591391	−	0.806385i	$-0.298579\pi$
$317$	1.19438e10			1.18278			0.591391	+	0.806385i	$0.298579\pi$
$318$			6.45333e9i			0.631067i
$319$	−1.59820e10	+	5.63089e9i	−1.54336	+	0.543769i
$320$	−1.17608e9			−0.112160
$321$			2.55830e9i			0.240952i
$322$	−6.78559e9			−0.631196
$323$	−1.00161e9			−0.0920216
$324$	−2.76138e9			−0.250580
$325$		−	6.25536e9i		−	0.560685i
$326$		−	2.84568e9i		−	0.251951i
$327$		−	9.86176e9i		−	0.862509i
$328$	−4.23244e9			−0.365675
$329$		−	1.19112e10i		−	1.01665i
$330$	1.03188e9	−	3.63561e8i	0.0870110	−	0.0306564i
$331$	−2.28423e9			−0.190295			−0.0951477	−	0.995463i	$-0.530332\pi$
$331$	−2.28423e9			−0.190295			−0.0951477	+	0.995463i	$0.530332\pi$
$332$			2.76512e9i			0.227595i
$333$	−3.27659e8			−0.0266468
$334$	1.69042e10			1.35834
$335$	1.45618e9			0.115621
$336$			6.60035e9i			0.517857i
$337$		−	2.32635e10i		−	1.80366i	−0.432087	−	0.901832i	$-0.642222\pi$
$337$		−	2.32635e10i		−	1.80366i	0.432087	−	0.901832i	$-0.357778\pi$
$338$		−	7.76880e9i		−	0.595233i
$339$	1.30693e10			0.989586
$340$			2.17885e8i			0.0163046i
$341$	−2.45432e9	−	6.96602e9i	−0.181516	−	0.515190i
$342$	1.40516e8			0.0102712
$343$		−	1.45903e10i		−	1.05411i
$344$	−2.77963e10			−1.98497
$345$	1.54592e9			0.109122
$346$	−5.45315e9			−0.380490
$347$		−	5.44834e9i		−	0.375791i	−0.982189	−	0.187895i	$-0.939833\pi$
$347$		−	5.44834e9i		−	0.375791i	0.982189	−	0.187895i	$-0.0601666\pi$
$348$			5.80527e9i			0.395827i
$349$			2.00322e10i			1.35029i	0.737684	+	0.675146i	$0.235919\pi$
$349$			2.00322e10i			1.35029i	−0.737684	+	0.675146i	$0.764081\pi$
$350$	9.04348e9			0.602647
$351$		−	8.17484e9i		−	0.538580i
$352$	6.56612e9	−	2.31343e9i	0.427699	−	0.150690i
$353$	2.24777e9			0.144762			0.0723809	−	0.997377i	$-0.476940\pi$
$353$	2.24777e9			0.144762			0.0723809	+	0.997377i	$0.476940\pi$
$354$			1.93463e10i			1.23193i
$355$	−1.05147e9			−0.0662041
$356$	5.63493e9			0.350824
$357$	8.20907e9			0.505383
$358$			9.44233e8i			0.0574840i
$359$			2.86395e10i			1.72420i	0.506740	+	0.862099i	$0.330850\pi$
$359$			2.86395e10i			1.72420i	−0.506740	+	0.862099i	$0.669150\pi$
$360$		−	1.62422e8i		−	0.00967020i
$361$	1.66877e10			0.982581
$362$		−	1.42650e10i		−	0.830685i
$363$	−1.41162e10	+	1.13568e10i	−0.813002	+	0.654080i
$364$	1.60139e9			0.0912204
$365$		−	3.15911e9i		−	0.177989i
$366$	−1.97821e10			−1.10242
$367$	1.82833e10			1.00784			0.503919	−	0.863751i	$-0.331891\pi$
$367$	1.82833e10			1.00784			0.503919	+	0.863751i	$0.331891\pi$
$368$	−1.35835e10			−0.740665
$369$		−	5.57568e8i		−	0.0300741i
$370$			4.97265e8i			0.0265327i
$371$			9.08118e9i			0.479343i
$372$	−2.53033e9			−0.132131
$373$		−	3.74963e9i		−	0.193711i	−0.995298	−	0.0968553i	$-0.969122\pi$
$373$		−	3.74963e9i		−	0.193711i	0.995298	−	0.0968553i	$-0.0308784\pi$
$374$	3.97309e9	+	1.12767e10i	0.203068	+	0.576362i
$375$	−4.14183e9			−0.209444
$376$		−	3.15812e10i		−	1.58007i
$377$	−1.87242e10			−0.926909
$378$	1.18185e10			0.578889
$379$	−1.76725e10			−0.856529			−0.428265	−	0.903653i	$-0.640875\pi$
$379$	−1.76725e10			−0.856529			−0.428265	+	0.903653i	$0.640875\pi$
$380$			6.43557e7i			0.00308640i
$381$			3.42358e10i			1.62473i
$382$		−	6.97041e9i		−	0.327344i
$383$	1.82722e9			0.0849174			0.0424587	−	0.999098i	$-0.486481\pi$
$383$	1.82722e9			0.0849174			0.0424587	+	0.999098i	$0.486481\pi$
$384$			1.18215e10i			0.543688i
$385$	1.45207e9	−	5.11606e8i	0.0660915	−	0.0232859i
$386$	4.00172e9			0.180259
$387$		−	3.66180e9i		−	0.163249i
$388$	−2.02999e9			−0.0895709
$389$	−2.27004e10			−0.991369			−0.495684	−	0.868503i	$-0.665083\pi$
$389$	−2.27004e10			−0.991369			−0.495684	+	0.868503i	$0.665083\pi$
$390$	1.20893e9			0.0522570
$391$			1.68943e10i			0.722825i
$392$		−	1.31912e10i		−	0.558652i
$393$		−	2.63738e10i		−	1.10561i
$394$	2.12713e10			0.882690
$395$			2.55404e9i			0.104916i
$396$	1.68210e8	+	4.77424e8i	0.00684023	+	0.0194144i
$397$	−9.72569e9			−0.391524			−0.195762	−	0.980651i	$-0.562718\pi$
$397$	−9.72569e9			−0.391524			−0.195762	+	0.980651i	$0.562718\pi$
$398$			1.97592e10i			0.787476i
$399$	2.42468e9			0.0956671
$400$	1.81034e10			0.707165
$401$	3.11555e10			1.20492			0.602458	−	0.798150i	$-0.294188\pi$
$401$	3.11555e10			1.20492			0.602458	+	0.798150i	$0.294188\pi$
$402$		−	2.73756e10i		−	1.04824i
$403$		−	8.16126e9i		−	0.309412i
$404$		−	4.23526e9i		−	0.158985i
$405$	−2.93352e9			−0.109036
$406$		−	2.70698e10i		−	0.996280i
$407$	−2.73643e9	−	7.76673e9i	−0.0997257	−	0.283048i
$408$	2.17654e10			0.785462
$409$		−	3.59011e10i		−	1.28297i	−0.767138	−	0.641483i	$-0.778320\pi$
$409$		−	3.59011e10i		−	1.28297i	0.767138	−	0.641483i	$-0.221680\pi$
$410$	−8.46180e8			−0.0299452
$411$	1.62712e10			0.570234
$412$	−7.04830e9			−0.244622
$413$			2.72243e10i			0.935744i
$414$		−	2.37010e9i		−	0.0806800i
$415$			2.93750e9i			0.0990343i
$416$	7.69274e9			0.256867
$417$		−	5.67829e9i		−	0.187791i
$418$	1.17352e9	+	3.33075e9i	0.0384400	+	0.109103i
$419$	−3.57228e10			−1.15902			−0.579508	−	0.814967i	$-0.696755\pi$
$419$	−3.57228e10			−1.15902			−0.579508	+	0.814967i	$0.696755\pi$
$420$		−	5.27450e8i		−	0.0169506i
$421$	2.93298e10			0.933643			0.466822	−	0.884352i	$-0.345399\pi$
$421$	2.93298e10			0.933643			0.466822	+	0.884352i	$0.345399\pi$
$422$	−3.52151e10			−1.11040
$423$	4.16041e9			0.129949
$424$			2.40777e10i			0.744991i
$425$		−	2.25158e10i		−	0.690132i
$426$			1.97673e10i			0.600217i
$427$	−2.78375e10			−0.837372
$428$			1.79635e9i			0.0535322i
$429$	−1.88822e10	+	6.65273e9i	−0.557473	+	0.196413i
$430$	−5.55725e9			−0.162550
$431$			5.31220e10i			1.53945i	0.638376	+	0.769725i	$0.279607\pi$
$431$			5.31220e10i			1.53945i	−0.638376	+	0.769725i	$0.720393\pi$
$432$	2.36585e10			0.679286
$433$	−3.61292e10			−1.02780			−0.513898	−	0.857851i	$-0.671799\pi$
$433$	−3.61292e10			−1.02780			−0.513898	+	0.857851i	$0.671799\pi$
$434$	1.17989e10			0.332569
$435$			6.16718e9i			0.172238i
$436$		−	6.92459e9i		−	0.191623i
$437$			4.99000e9i			0.136828i
$438$	−5.93899e10			−1.61368
$439$			2.53113e10i			0.681485i	0.940157	+	0.340743i	$0.110678\pi$
$439$			2.53113e10i			0.681485i	−0.940157	+	0.340743i	$0.889322\pi$
$440$	3.85000e9	−	1.35646e9i	0.102719	−	0.0361907i
$441$	1.73777e9			0.0459450
$442$			1.32116e10i			0.346151i
$443$	5.78458e10			1.50196			0.750978	−	0.660328i	$-0.229583\pi$
$443$	5.78458e10			1.50196			0.750978	+	0.660328i	$0.229583\pi$
$444$	−2.82118e9			−0.0725937
$445$	5.98622e9			0.152655
$446$		−	4.27017e10i		−	1.07921i
$447$		−	1.06295e10i		−	0.266246i
$448$			3.11132e10i			0.772383i
$449$	2.14220e10			0.527079			0.263539	−	0.964649i	$-0.415110\pi$
$449$	2.14220e10			0.527079			0.263539	+	0.964649i	$0.415110\pi$
$450$			3.15875e9i			0.0770309i
$451$	1.32164e10	−	4.65651e9i	0.319453	−	0.112552i
$452$	9.17681e9			0.219856
$453$			3.20898e10i			0.762033i
$454$	8.04567e9			0.189382
$455$	1.70122e9			0.0396932
$456$	6.42875e9			0.148685
$457$		−	4.39882e10i		−	1.00849i	−0.863561	−	0.504245i	$-0.831771\pi$
$457$		−	4.39882e10i		−	1.00849i	0.863561	−	0.504245i	$-0.168229\pi$
$458$			3.84094e10i			0.872921i
$459$		−	2.94249e10i		−	0.662924i
$460$	1.08549e9			0.0242436
$461$			3.47144e10i			0.768610i	0.923206	+	0.384305i	$0.125559\pi$
$461$			3.47144e10i			0.768610i	−0.923206	+	0.384305i	$0.874441\pi$
$462$	−9.61797e9	−	2.72983e10i	−0.211113	−	0.599195i
$463$	1.12849e10			0.245568			0.122784	−	0.992433i	$-0.460818\pi$
$463$	1.12849e10			0.245568			0.122784	+	0.992433i	$0.460818\pi$
$464$		−	5.41890e10i		−	1.16907i
$465$	−2.68807e9			−0.0574949
$466$	−3.01973e10			−0.640361
$467$	−3.00630e9			−0.0632070			−0.0316035	−	0.999500i	$-0.510061\pi$
$467$	−3.00630e9			−0.0632070			−0.0316035	+	0.999500i	$0.510061\pi$
$468$			5.59341e8i			0.0116599i
$469$		−	3.85232e10i		−	0.796216i
$470$		−	6.31394e9i		−	0.129393i
$471$	−8.12012e10			−1.64998
$472$			7.21821e10i			1.45433i
$473$	8.67981e10	−	3.05814e10i	1.73407	−	0.610960i
$474$	4.80149e10			0.951180
$475$		−	6.65041e9i		−	0.130639i
$476$	5.76412e9			0.112281
$477$	−3.17192e9			−0.0612700
$478$	−6.19484e10			−1.18664
$479$		−	4.11124e10i		−	0.780963i	−0.920611	−	0.390481i	$-0.872309\pi$
$479$		−	4.11124e10i		−	0.780963i	0.920611	−	0.390481i	$-0.127691\pi$
$480$		−	2.53376e9i		−	0.0477310i
$481$		−	9.09936e9i		−	0.169993i
$482$	1.61737e10			0.299654
$483$		−	4.08973e10i		−	0.751460i
$484$	−9.91190e9	+	7.97438e9i	−0.180624	+	0.145317i
$485$	−2.15654e9			−0.0389754
$486$			8.65829e9i			0.155198i
$487$	3.65862e10			0.650432			0.325216	−	0.945640i	$-0.394563\pi$
$487$	3.65862e10			0.650432			0.325216	+	0.945640i	$0.394563\pi$
$488$	−7.38078e10			−1.30144
$489$	1.71512e10			0.299956
$490$		−	2.63729e9i		−	0.0457481i
$491$		−	7.01731e10i		−	1.20738i	−0.797219	−	0.603691i	$-0.793696\pi$
$491$		−	7.01731e10i		−	1.20738i	0.797219	−	0.603691i	$-0.206304\pi$
$492$		−	4.80072e9i		−	0.0819306i
$493$	−6.73966e10			−1.14091
$494$			3.90225e9i			0.0655250i
$495$	1.78696e8	+	5.07187e8i	0.00297642	+	0.00844787i
$496$	2.36192e10			0.390247
$497$			2.78167e10i			0.455910i
$498$	5.52237e10			0.897859
$499$	8.42315e10			1.35854			0.679270	−	0.733888i	$-0.262296\pi$
$499$	8.42315e10			1.35854			0.679270	+	0.733888i	$0.262296\pi$
$500$	−2.90825e9			−0.0465320
$501$			1.01883e11i			1.61715i
$502$			7.82502e10i			1.23217i
$503$		−	1.03618e10i		−	0.161868i	−0.996719	−	0.0809341i	$-0.974210\pi$
$503$		−	1.03618e10i		−	0.161868i	0.996719	−	0.0809341i	$-0.0257903\pi$
$504$	−4.29687e9			−0.0665932
$505$		−	4.49929e9i		−	0.0691797i
$506$	5.61801e10	−	1.97938e10i	0.856999	−	0.301945i
$507$	4.68232e10			0.708646
$508$			2.40392e10i			0.360964i
$509$	−1.10325e11			−1.64363			−0.821814	−	0.569756i	$-0.807038\pi$
$509$	−1.10325e11			−1.64363			−0.821814	+	0.569756i	$0.807038\pi$
$510$	4.35149e9			0.0643217
$511$	−8.35740e10			−1.22571
$512$			7.52689e10i			1.09531i
$513$		−	8.69110e9i		−	0.125489i
$514$			6.16676e10i			0.883495i
$515$	−7.48769e9			−0.106443
$516$		−	3.15285e10i		−	0.444738i
$517$	3.47455e10	+	9.86168e10i	0.486335	+	1.38035i
$518$	1.31551e10			0.182715
$519$		−	3.28666e10i		−	0.452986i
$520$	4.51059e9			0.0616908
$521$	−1.00574e11			−1.36501			−0.682506	−	0.730880i	$-0.739110\pi$
$521$	−1.00574e11			−1.36501			−0.682506	+	0.730880i	$0.739110\pi$
$522$	9.45508e9			0.127345
$523$		−	7.00997e9i		−	0.0936934i	−0.998902	−	0.0468467i	$-0.985083\pi$
$523$		−	7.00997e9i		−	0.0936934i	0.998902	−	0.0468467i	$-0.0149172\pi$
$524$		−	1.85188e10i		−	0.245633i
$525$			5.45058e10i			0.717472i
$526$	−1.09823e10			−0.143467
$527$		−	2.93760e10i		−	0.380847i
$528$	−1.92534e10	−	5.46464e10i	−0.247727	−	0.703114i
$529$	5.85581e9			0.0747764
$530$			4.81378e9i			0.0610075i
$531$	−9.50905e9			−0.119608
$532$	1.70253e9			0.0212543
$533$	1.54841e10			0.191857
$534$		−	1.12538e11i		−	1.38400i
$535$			1.90833e9i			0.0232937i
$536$		−	1.02140e11i		−	1.23747i
$537$	−5.69097e9			−0.0684367
$538$		−	6.33687e10i		−	0.756389i
$539$	1.45129e10	+	4.11915e10i	0.171949	+	0.488037i
$540$	−1.89061e9			−0.0222345
$541$			3.53605e10i			0.412790i	0.978469	+	0.206395i	$0.0661731\pi$
$541$			3.53605e10i			0.412790i	−0.978469	+	0.206395i	$0.933827\pi$
$542$	−4.22285e9			−0.0489338
$543$	8.59761e10			0.988959
$544$	2.76896e10			0.316170
$545$		−	7.35627e9i		−	0.0833818i
$546$		−	3.19822e10i		−	0.359864i
$547$		−	5.06602e10i		−	0.565871i	−0.959139	−	0.282935i	$-0.908692\pi$
$547$		−	5.06602e10i		−	0.565871i	0.959139	−	0.282935i	$-0.0913082\pi$
$548$	1.14251e10			0.126689
$549$		−	9.72320e9i		−	0.107034i
$550$	−7.48739e10	+	2.63801e10i	−0.818238	+	0.288288i
$551$	−1.99067e10			−0.215969
$552$		−	1.08434e11i		−	1.16791i
$553$	6.75670e10			0.722493
$554$	3.47305e10			0.368699
$555$	−2.99705e9			−0.0315880
$556$		−	3.98710e9i		−	0.0417213i
$557$			1.81892e11i			1.88970i	0.327510	+	0.944848i	$0.393790\pi$
$557$			1.81892e11i			1.88970i	−0.327510	+	0.944848i	$0.606210\pi$
$558$			4.12116e9i			0.0425092i
$559$	1.01691e11			1.04144
$560$			4.92345e9i			0.0500631i
$561$	−6.79655e10	+	2.39461e10i	−0.686179	+	0.241760i
$562$	−8.86765e10			−0.888922
$563$		−	1.01736e11i		−	1.01261i	−0.862355	−	0.506304i	$-0.831011\pi$
$563$		−	1.01736e11i		−	1.01261i	0.862355	−	0.506304i	$-0.168989\pi$
$564$	3.58215e10			0.354020
$565$	9.74889e9			0.0956668
$566$	1.45307e11			1.41586
$567$			7.76061e10i			0.750868i
$568$			7.37526e10i			0.708572i
$569$		−	1.46963e10i		−	0.140203i	−0.997540	−	0.0701017i	$-0.977668\pi$
$569$		−	1.46963e10i		−	0.140203i	0.997540	−	0.0701017i	$-0.0223324\pi$
$570$	1.28528e9			0.0121758
$571$		−	7.61093e10i		−	0.715967i	−0.933728	−	0.357984i	$-0.883464\pi$
$571$		−	7.61093e10i		−	0.715967i	0.933728	−	0.357984i	$-0.116536\pi$
$572$	−1.32584e10	+	4.67132e9i	−0.123854	+	0.0436370i
$573$	4.20112e10			0.389715
$574$			2.23856e10i			0.206216i
$575$	−1.12173e11			−1.02617
$576$	−1.08674e10			−0.0987266
$577$	−5.07456e10			−0.457820			−0.228910	−	0.973448i	$-0.573516\pi$
$577$	−5.07456e10			−0.457820			−0.228910	+	0.973448i	$0.573516\pi$
$578$		−	5.02689e10i		−	0.450389i
$579$			2.41187e10i			0.214605i
$580$			4.33038e9i			0.0382661i
$581$	7.77113e10			0.681993
$582$			4.05420e10i			0.353357i
$583$	−2.64901e10	−	7.51860e10i	−0.229303	−	0.650823i
$584$	−2.21587e11			−1.90499
$585$			5.94211e8i			0.00507361i
$586$	5.55070e10			0.470714
$587$	−7.57213e10			−0.637773			−0.318886	−	0.947793i	$-0.603309\pi$
$587$	−7.57213e10			−0.637773			−0.318886	+	0.947793i	$0.603309\pi$
$588$	1.49624e10			0.125167
$589$		−	8.67668e9i		−	0.0720928i
$590$			1.44312e10i			0.119095i
$591$			1.28204e11i			1.05087i
$592$	2.63341e10			0.214404
$593$			5.47583e10i			0.442824i	0.975180	+	0.221412i	$0.0710665\pi$
$593$			5.47583e10i			0.442824i	−0.975180	+	0.221412i	$0.928933\pi$
$594$	−9.78491e10	+	3.44750e10i	−0.785980	+	0.276922i
$595$	6.12346e9			0.0488572
$596$		−	7.46366e9i		−	0.0591516i
$597$	−1.19090e11			−0.937518
$598$	6.58196e10			0.514695
$599$	8.95361e10			0.695490			0.347745	−	0.937589i	$-0.386948\pi$
$599$	8.95361e10			0.695490			0.347745	+	0.937589i	$0.386948\pi$
$600$			1.44516e11i			1.11509i
$601$		−	1.32990e11i		−	1.01934i	−0.860369	−	0.509672i	$-0.829767\pi$
$601$		−	1.32990e11i		−	1.01934i	0.860369	−	0.509672i	$-0.170233\pi$
$602$			1.47016e11i			1.11939i
$603$	1.34556e10			0.101773
$604$			2.25323e10i			0.169300i
$605$	−1.05298e10	+	8.47150e9i	−0.0785958	+	0.0632323i
$606$	−8.45847e10			−0.627193
$607$			5.87534e10i			0.432791i	0.976306	+	0.216396i	$0.0694301\pi$
$607$			5.87534e10i			0.432791i	−0.976306	+	0.216396i	$0.930570\pi$
$608$	8.17857e9			0.0598498
$609$	1.63152e11			1.18611
$610$	−1.47562e10			−0.106575
$611$			1.15538e11i			0.829008i
$612$			2.01332e9i			0.0143518i
$613$		−	2.29689e11i		−	1.62667i	−0.581798	−	0.813333i	$-0.697651\pi$
$613$		−	2.29689e11i		−	1.62667i	0.581798	−	0.813333i	$-0.302349\pi$
$614$	2.38998e11			1.68159
$615$		−	5.10000e9i		−	0.0356508i
$616$	−3.58851e10	−	1.01851e11i	−0.249225	−	0.707366i
$617$	1.20115e11			0.828812			0.414406	−	0.910092i	$-0.363989\pi$
$617$	1.20115e11			0.828812			0.414406	+	0.910092i	$0.363989\pi$
$618$			1.40765e11i			0.965032i
$619$	−1.51533e11			−1.03215			−0.516076	−	0.856543i	$-0.672608\pi$
$619$	−1.51533e11			−1.03215			−0.516076	+	0.856543i	$0.672608\pi$
$620$	−1.88747e9			−0.0127736
$621$	−1.46594e11			−0.985709
$622$		−	1.20352e11i		−	0.804065i
$623$		−	1.58365e11i		−	1.05125i
$624$		−	6.40227e10i		−	0.422275i
$625$	1.47946e11			0.969577
$626$		−	1.42775e11i		−	0.929728i
$627$	−2.00747e10	+	7.07288e9i	−0.129891	+	0.0457642i
$628$	−5.70166e10			−0.366575
$629$		−	3.27526e10i		−	0.209239i
$630$	−8.59061e8			−0.00545333
$631$	1.42844e11			0.901042			0.450521	−	0.892766i	$-0.351238\pi$
$631$	1.42844e11			0.901042			0.450521	+	0.892766i	$0.351238\pi$
$632$	1.79146e11			1.12289
$633$		−	2.12245e11i		−	1.32197i
$634$		−	1.67491e11i		−	1.03666i
$635$			2.55378e10i			0.157068i
$636$	−2.73105e10			−0.166917
$637$			4.82592e10i			0.293105i
$638$	7.89637e10	+	2.24120e11i	0.476590	+	1.35269i
$639$	−9.71593e9			−0.0582748
$640$			8.81814e9i			0.0525602i
$641$	−1.79831e11			−1.06520			−0.532602	−	0.846366i	$-0.678786\pi$
$641$	−1.79831e11			−1.06520			−0.532602	+	0.846366i	$0.678786\pi$
$642$	3.58758e10			0.211184
$643$	−9.90179e10			−0.579255			−0.289627	−	0.957139i	$-0.593531\pi$
$643$	−9.90179e10			−0.579255			−0.289627	+	0.957139i	$0.593531\pi$
$644$		−	2.87167e10i		−	0.166952i
$645$		−	3.34940e10i		−	0.193521i
$646$			1.40459e10i			0.0806529i
$647$	−1.65940e10			−0.0946967			−0.0473484	−	0.998878i	$-0.515077\pi$
$647$	−1.65940e10			−0.0946967			−0.0473484	+	0.998878i	$0.515077\pi$
$648$			2.05763e11i			1.16699i
$649$	−7.94144e10	−	2.25399e11i	−0.447631	−	1.27050i
$650$	−8.77209e10			−0.491416
$651$			7.11128e10i			0.395935i
$652$	1.20429e10			0.0666411
$653$	−1.97237e11			−1.08476			−0.542382	−	0.840132i	$-0.682477\pi$
$653$	−1.97237e11			−1.08476			−0.542382	+	0.840132i	$0.682477\pi$
$654$	−1.38295e11			−0.755952
$655$		−	1.96732e10i		−	0.106884i
$656$			4.48120e10i			0.241980i
$657$		−	2.91911e10i		−	0.156671i
$658$	−1.67035e11			−0.891052
$659$			2.48431e11i			1.31724i	0.752477	+	0.658619i	$0.228859\pi$
$659$			2.48431e11i			1.31724i	−0.752477	+	0.658619i	$0.771141\pi$
$660$	1.53859e9	+	4.36693e9i	0.00810863	+	0.0230144i
$661$	3.14531e11			1.64762			0.823812	−	0.566864i	$-0.191843\pi$
$661$	3.14531e11			1.64762			0.823812	+	0.566864i	$0.191843\pi$
$662$			3.20325e10i			0.166786i
$663$	−7.96272e10			−0.412104
$664$	2.06042e11			1.05995
$665$	1.80866e9			0.00924848
$666$			4.59487e9i			0.0233548i
$667$			3.35768e11i			1.69643i
$668$			7.15387e10i			0.359282i
$669$	2.57366e11			1.28484
$670$		−	2.04205e10i		−	0.101337i
$671$	2.30476e11	−	8.12029e10i	1.13693	−	0.400573i
$672$	−6.70303e10			−0.328696
$673$			4.09481e10i			0.199606i	0.995007	+	0.0998030i	$0.0318213\pi$
$673$			4.09481e10i			0.199606i	−0.995007	+	0.0998030i	$0.968179\pi$
$674$	−3.26232e11			−1.58083
$675$	1.95372e11			0.941127
$676$	3.28776e10			0.157439
$677$		−	9.93802e10i		−	0.473092i	−0.971620	−	0.236546i	$-0.923985\pi$
$677$		−	9.93802e10i		−	0.473092i	0.971620	−	0.236546i	$-0.0760153\pi$
$678$		−	1.83275e11i		−	0.867330i
$679$			5.70511e10i			0.268401i
$680$	1.62356e10			0.0759335
$681$			4.84919e10i			0.225466i
$682$	−9.76867e10	+	3.44177e10i	−0.451542	+	0.159091i
$683$	1.21146e11			0.556707			0.278354	−	0.960479i	$-0.410211\pi$
$683$	1.21146e11			0.556707			0.278354	+	0.960479i	$0.410211\pi$
$684$			5.94666e8i			0.00271674i
$685$	1.21373e10			0.0551266
$686$	−2.04604e11			−0.923884
$687$	−2.31496e11			−1.03924
$688$			2.94301e11i			1.31352i
$689$		−	8.80866e10i		−	0.390870i
$690$		−	2.16790e10i		−	0.0956407i
$691$	−2.91228e11			−1.27738			−0.638690	−	0.769464i	$-0.720523\pi$
$691$	−2.91228e11			−1.27738			−0.638690	+	0.769464i	$0.720523\pi$
$692$		−	2.30777e10i		−	0.100640i
$693$	1.34176e10	−	4.72739e9i	0.0581757	−	0.0204969i
$694$	−7.64037e10			−0.329364
$695$		−	4.23566e9i		−	0.0181544i
$696$	4.32578e11			1.84344
$697$	5.57342e10			0.236151
$698$	2.80918e11			1.18347
$699$		−	1.82002e11i		−	0.762372i
$700$			3.82720e10i			0.159400i
$701$			4.01798e11i			1.66393i	0.554826	+	0.831967i	$0.312785\pi$
$701$			4.01798e11i			1.66393i	−0.554826	+	0.831967i	$0.687215\pi$
$702$	−1.14638e11			−0.472043
$703$		−	9.67401e9i		−	0.0396082i
$704$	−9.07583e10	−	2.57596e11i	−0.369484	−	1.04869i
$705$	3.80546e10			0.154046
$706$		−	3.15212e10i		−	0.126877i
$707$	−1.19028e11			−0.476401
$708$	−8.18738e10			−0.325846
$709$	−9.24268e10			−0.365774			−0.182887	−	0.983134i	$-0.558544\pi$
$709$	−9.24268e10			−0.365774			−0.182887	+	0.983134i	$0.558544\pi$
$710$			1.47451e10i			0.0580251i
$711$			2.36001e10i			0.0923497i
$712$		−	4.19885e11i		−	1.63384i
$713$	−1.46350e11			−0.566286
$714$		−	1.15118e11i		−	0.442947i
$715$	−1.40850e10	+	4.96253e9i	−0.0538929	+	0.0189880i
$716$	−3.99600e9			−0.0152045
$717$		−	3.73368e11i		−	1.41273i
$718$	4.01620e11			1.51119
$719$	−3.26859e11			−1.22305			−0.611525	−	0.791225i	$-0.709444\pi$
$719$	−3.26859e11			−1.22305			−0.611525	+	0.791225i	$0.709444\pi$
$720$	−1.71969e9			−0.00639910
$721$			1.98086e11i			0.733015i
$722$		−	2.34017e11i		−	0.861190i
$723$			9.74799e10i			0.356748i
$724$	6.03694e10			0.219716
$725$		−	4.47493e11i		−	1.61970i
$726$	1.59261e11	+	1.97956e11i	0.573273	+	0.712561i
$727$	−5.39902e10			−0.193276			−0.0966378	−	0.995320i	$-0.530809\pi$
$727$	−5.39902e10			−0.193276			−0.0966378	+	0.995320i	$0.530809\pi$
$728$		−	1.19327e11i		−	0.424829i
$729$	2.53096e11			0.896139
$730$	−4.43012e10			−0.156000
$731$	3.66031e11			1.28188
$732$		−	8.37178e10i		−	0.291590i
$733$			2.99494e11i			1.03746i	0.854938	+	0.518731i	$0.173595\pi$
$733$			2.99494e11i			1.03746i	−0.854938	+	0.518731i	$0.826405\pi$
$734$		−	2.56393e11i		−	0.883326i
$735$	1.58951e10			0.0544647
$736$		−	1.37949e11i		−	0.470117i
$737$	1.12374e11	+	3.18946e11i	0.380885	+	1.08105i
$738$	−7.81895e9			−0.0263587
$739$			4.41447e11i			1.48013i	0.672534	+	0.740066i	$0.265206\pi$
$739$			4.41447e11i			1.48013i	−0.672534	+	0.740066i	$0.734794\pi$
$740$	−2.10443e9			−0.00701790
$741$	−2.35192e10			−0.0780098
$742$	1.27348e11			0.420124
$743$		−	8.87043e10i		−	0.291064i	−0.989354	−	0.145532i	$-0.953511\pi$
$743$		−	8.87043e10i		−	0.291064i	0.989354	−	0.145532i	$-0.0464894\pi$
$744$			1.88547e11i			0.615358i
$745$		−	7.92894e9i		−	0.0257389i
$746$	−5.25823e10			−0.169779
$747$			2.71434e10i			0.0871728i
$748$	−4.77230e10	+	1.68141e10i	−0.152448	+	0.0537116i
$749$	5.04847e10			0.160411
$750$			5.80822e10i			0.183569i
$751$	1.59587e11			0.501693			0.250847	−	0.968027i	$-0.419291\pi$
$751$	1.59587e11			0.501693			0.250847	+	0.968027i	$0.419291\pi$
$752$	−3.34374e11			−1.04559
$753$	−4.71620e11			−1.46694
$754$			2.62575e11i			0.812396i
$755$			2.39370e10i			0.0736685i
$756$			5.00159e10i			0.153116i
$757$	−5.66092e11			−1.72387			−0.861933	−	0.507022i	$-0.830746\pi$
$757$	−5.66092e11			−1.72387			−0.861933	+	0.507022i	$0.830746\pi$
$758$			2.47828e11i			0.750711i
$759$	1.19299e11	+	3.38602e11i	0.359475	+	1.02029i
$760$	4.79545e9			0.0143739
$761$		−	8.18216e10i		−	0.243966i	−0.992532	−	0.121983i	$-0.961075\pi$
$761$		−	8.18216e10i		−	0.243966i	0.992532	−	0.121983i	$-0.0389253\pi$
$762$	4.80099e11			1.42400
$763$	−1.94609e11			−0.574203
$764$	2.94988e10			0.0865827
$765$			2.13883e9i			0.00624497i
$766$		−	2.56237e10i		−	0.0744265i
$767$		−	2.64074e11i		−	0.763033i
$768$	−2.37845e11			−0.683675
$769$			2.57446e10i			0.0736175i	0.999322	+	0.0368088i	$0.0117192\pi$
$769$			2.57446e10i			0.0736175i	−0.999322	+	0.0368088i	$0.988281\pi$
$770$	−7.17441e9	−	2.03629e10i	−0.0204091	−	0.0579264i
$771$	−3.71675e11			−1.05183
$772$			1.69353e10i			0.0476787i
$773$	3.21906e11			0.901594			0.450797	−	0.892626i	$-0.351140\pi$
$773$	3.21906e11			0.901594			0.450797	+	0.892626i	$0.351140\pi$
$774$	−5.13506e10			−0.143081
$775$	1.95048e11			0.540673
$776$			1.51264e11i			0.417147i
$777$			7.92868e10i			0.217529i
$778$			3.18335e11i			0.868892i
$779$	1.64620e10			0.0447025
$780$			5.11622e9i			0.0138220i
$781$	−8.11422e10	−	2.30303e11i	−0.218093	−	0.619007i
$782$	2.36914e11			0.633525
$783$		−	5.84808e11i		−	1.55584i
$784$	−1.39665e11			−0.369679
$785$	−6.05711e10			−0.159510
$786$	−3.69848e11			−0.969022
$787$		−	2.24961e11i		−	0.586421i	−0.956048	−	0.293210i	$-0.905276\pi$
$787$		−	2.24961e11i		−	0.586421i	0.956048	−	0.293210i	$-0.0947236\pi$
$788$			9.00201e10i			0.233472i
$789$		−	6.61914e10i		−	0.170802i
$790$	3.58161e10			0.0919539
$791$		−	2.57906e11i		−	0.658803i
$792$	3.55751e10	−	1.25341e10i	0.0904161	−	0.0318561i
$793$	2.70021e11			0.682818
$794$			1.36386e11i			0.343154i
$795$	−2.90131e10			−0.0726315
$796$	−8.36211e10			−0.208288
$797$	4.06334e11			1.00705			0.503523	−	0.863982i	$-0.332037\pi$
$797$	4.06334e11			1.00705			0.503523	+	0.863982i	$0.332037\pi$
$798$		−	3.40020e10i		−	0.0838481i
$799$			4.15872e11i			1.02040i
$800$			1.83851e11i			0.448854i
$801$	5.53144e10			0.134372
$802$		−	4.36903e11i		−	1.05606i
$803$	6.91936e11	−	2.43788e11i	1.66419	−	0.586342i
$804$	1.15854e11			0.277259
$805$		−	3.05069e10i		−	0.0726464i
$806$	−1.14448e11			−0.271186
$807$	3.81928e11			0.900508
$808$	−3.15589e11			−0.740418
$809$			4.70967e10i			0.109950i	0.998488	+	0.0549752i	$0.0175080\pi$
$809$			4.70967e10i			0.109950i	−0.998488	+	0.0549752i	$0.982492\pi$
$810$			4.11377e10i			0.0955652i
$811$			1.47347e11i			0.340611i	0.985391	+	0.170305i	$0.0544754\pi$
$811$			1.47347e11i			0.340611i	−0.985391	+	0.170305i	$0.945525\pi$
$812$	1.14560e11			0.263516
$813$		−	2.54515e10i		−	0.0582574i
$814$	−1.08915e11	+	3.83739e10i	−0.248080	+	0.0874053i
$815$	1.27937e10			0.0289979
$816$		−	2.30446e11i		−	0.519767i
$817$	1.08113e11			0.242656
$818$	−5.03453e11			−1.12446
$819$	1.57198e10			0.0349391
$820$		−	3.58104e9i		−	0.00792052i
$821$		−	3.94096e11i		−	0.867421i	−0.901052	−	0.433710i	$-0.857204\pi$
$821$		−	3.94096e11i		−	0.867421i	0.901052	−	0.433710i	$-0.142796\pi$
$822$		−	2.28177e11i		−	0.499786i
$823$	−5.47738e11			−1.19392			−0.596958	−	0.802273i	$-0.703624\pi$
$823$	−5.47738e11			−1.19392			−0.596958	+	0.802273i	$0.703624\pi$
$824$			5.25202e11i			1.13925i
$825$	−1.58995e11	−	4.51271e11i	−0.343217	−	0.974140i
$826$	3.81776e11			0.820140
$827$		−	2.41764e11i		−	0.516855i	−0.966031	−	0.258428i	$-0.916796\pi$
$827$		−	2.41764e11i		−	0.516855i	0.966031	−	0.258428i	$-0.0832044\pi$
$828$	1.00303e10			0.0213399
$829$	5.49011e11			1.16242			0.581209	−	0.813754i	$-0.302580\pi$
$829$	5.49011e11			1.16242			0.581209	+	0.813754i	$0.302580\pi$
$830$	4.11935e10			0.0867993
$831$			2.09323e11i			0.438949i
$832$		−	3.01795e11i		−	0.629823i
$833$			1.73706e11i			0.360775i
$834$	−7.96285e10			−0.164590
$835$			7.59984e10i			0.156336i
$836$	−1.40958e10	+	4.96633e9i	−0.0288578	+	0.0101674i
$837$	2.54899e11			0.519357
$838$			5.00952e11i			1.01583i
$839$	−6.53079e11			−1.31801			−0.659004	−	0.752139i	$-0.729022\pi$
$839$	−6.53079e11			−1.31801			−0.659004	+	0.752139i	$0.729022\pi$
$840$	−3.93028e10			−0.0789417
$841$	−8.39235e11			−1.67764
$842$		−	4.11301e11i		−	0.818298i
$843$		−	5.34461e11i		−	1.05829i
$844$		−	1.49031e11i		−	0.293701i
$845$	3.49272e10			0.0685073
$846$		−	5.83427e10i		−	0.113895i
$847$	2.24113e11	+	2.78565e11i	0.435445	+	0.541244i
$848$	2.54928e11			0.492986
$849$			8.75777e11i			1.68563i
$850$	−3.15746e11			−0.604871
$851$	−1.63172e11			−0.311121
$852$	−8.36551e10			−0.158757
$853$		−	1.79803e11i		−	0.339626i	−0.985476	−	0.169813i	$-0.945684\pi$
$853$		−	1.79803e11i		−	0.339626i	0.985476	−	0.169813i	$-0.0543164\pi$
$854$			3.90374e11i			0.733921i
$855$			6.31737e8i			0.00118215i
$856$	1.33854e11			0.249309
$857$			8.78924e11i			1.62940i	0.579882	+	0.814701i	$0.303099\pi$
$857$			8.78924e11i			1.62940i	−0.579882	+	0.814701i	$0.696901\pi$
$858$	9.32933e10	+	2.64791e11i	0.172148	+	0.488601i
$859$	−5.86303e11			−1.07684			−0.538418	−	0.842678i	$-0.680978\pi$
$859$	−5.86303e11			−1.07684			−0.538418	+	0.842678i	$0.680978\pi$
$860$		−	2.35183e10i		−	0.0429944i
$861$	−1.34920e11			−0.245507
$862$	7.44947e11			1.34926
$863$	7.68092e11			1.38475			0.692373	−	0.721540i	$-0.256565\pi$
$863$	7.68092e11			1.38475			0.692373	+	0.721540i	$0.256565\pi$
$864$			2.40266e11i			0.431159i
$865$		−	2.45164e10i		−	0.0437918i
$866$			5.06651e11i			0.900819i
$867$	3.02975e11			0.536204
$868$			4.99329e10i			0.0879646i
$869$	−5.59409e11	+	1.97095e11i	−0.980957	+	0.345619i
$870$	8.64842e10			0.150959
$871$			3.73671e11i			0.649258i
$872$	−5.15984e11			−0.892422
$873$	−1.99271e10			−0.0343073
$874$	6.99763e10			0.119924
$875$			8.17338e10i			0.139434i
$876$		−	2.51338e11i		−	0.426818i
$877$		−	8.29806e11i		−	1.40274i	−0.712796	−	0.701371i	$-0.752572\pi$
$877$		−	8.29806e11i		−	1.40274i	0.712796	−	0.701371i	$-0.247428\pi$
$878$	3.54948e11			0.597293
$879$			3.34545e11i			0.560401i
$880$	−1.43619e10	−	4.07628e10i	−0.0239486	−	0.0679726i
$881$	−2.57568e11			−0.427551			−0.213775	−	0.976883i	$-0.568576\pi$
$881$	−2.57568e11			−0.427551			−0.213775	+	0.976883i	$0.568576\pi$
$882$		−	2.43693e10i		−	0.0402688i
$883$	3.20195e11			0.526710			0.263355	−	0.964699i	$-0.415171\pi$
$883$	3.20195e11			0.526710			0.263355	+	0.964699i	$0.415171\pi$
$884$	−5.59114e10			−0.0915570
$885$	−8.69779e10			−0.141787
$886$		−	8.11190e11i		−	1.31640i
$887$		−	4.40679e11i		−	0.711914i	−0.934502	−	0.355957i	$-0.884155\pi$
$887$		−	4.40679e11i		−	0.711914i	0.934502	−	0.355957i	$-0.115845\pi$
$888$			2.10220e11i			0.338081i
$889$	6.75599e11			1.08164
$890$		−	8.39466e10i		−	0.133796i
$891$	−2.26380e11	−	6.42526e11i	−0.359192	−	1.01948i
$892$	1.80714e11			0.285451
$893$			1.22834e11i			0.193158i
$894$	−1.49061e11			−0.233353
$895$	−4.24511e9			−0.00661602
$896$	2.33283e11			0.361952
$897$			3.96700e11i			0.612763i
$898$		−	3.00408e11i		−	0.461962i
$899$		−	5.83837e11i		−	0.893826i
$900$	−1.33678e10			−0.0203747
$901$		−	3.17063e11i		−	0.481112i
$902$	−6.52997e10	−	1.85338e11i	−0.0986472	−	0.279987i
$903$	−8.86080e11			−1.33267
$904$		−	6.83807e11i		−	1.02391i
$905$	6.41328e10			0.0956062
$906$	4.50005e11			0.667889
$907$	6.71059e11			0.991588			0.495794	−	0.868440i	$-0.334877\pi$
$907$	6.71059e11			0.991588			0.495794	+	0.868440i	$0.334877\pi$
$908$			3.40493e10i			0.0500916i
$909$		−	4.15747e10i		−	0.0608939i
$910$		−	2.38568e10i		−	0.0347893i
$911$	1.60483e11			0.232999			0.116500	−	0.993191i	$-0.462833\pi$
$911$	1.60483e11			0.232999			0.116500	+	0.993191i	$0.462833\pi$
$912$		−	6.80660e10i		−	0.0983900i
$913$	−6.43397e11	+	2.26687e11i	−0.925968	+	0.326244i
$914$	−6.16861e11			−0.883898
$915$		−	8.89368e10i		−	0.126881i
$916$	−1.62549e11			−0.230888
$917$	−5.20454e11			−0.736046
$918$	−4.12634e11			−0.581024
$919$		−	1.15774e11i		−	0.162312i	−0.996701	−	0.0811559i	$-0.974139\pi$
$919$		−	1.15774e11i		−	0.162312i	0.996701	−	0.0811559i	$-0.0258612\pi$
$920$		−	8.08853e10i		−	0.112906i
$921$			1.44046e12i			2.00199i
$922$	4.86811e11			0.673653
$923$		−	2.69819e11i		−	0.371762i
$924$	1.15527e11	−	4.07033e10i	0.158487	−	0.0558395i
$925$	2.17468e11			0.297049
$926$		−	1.58251e11i		−	0.215230i
$927$	−6.91884e10			−0.0936946
$928$	5.50320e11			0.742034
$929$	−1.83139e11			−0.245877			−0.122938	−	0.992414i	$-0.539232\pi$
$929$	−1.83139e11			−0.245877			−0.122938	+	0.992414i	$0.539232\pi$
$930$			3.76957e10i			0.0503918i
$931$			5.13070e10i			0.0682932i
$932$		−	1.27795e11i		−	0.169376i
$933$	7.25370e11			0.957267
$934$			4.21583e10i			0.0553982i
$935$	−5.06981e10	+	1.78623e10i	−0.0663354	+	0.0233718i
$936$	4.16792e10			0.0543020
$937$		−	2.01715e10i		−	0.0261686i	−0.999914	−	0.0130843i	$-0.995835\pi$
$937$		−	2.01715e10i		−	0.0261686i	0.999914	−	0.0130843i	$-0.00416498\pi$
$938$	−5.40223e11			−0.697849
$939$	8.60519e11			1.10687
$940$	2.67206e10			0.0342244
$941$			9.65288e11i			1.23111i	0.788092	+	0.615557i	$0.211069\pi$
$941$			9.65288e11i			1.23111i	−0.788092	+	0.615557i	$0.788931\pi$
$942$			1.13871e12i			1.44614i
$943$		−	2.77666e11i		−	0.351136i
$944$	7.64246e11			0.962377
$945$			5.31339e10i			0.0666262i
$946$	−4.28852e11	−	1.21720e12i	−0.535480	−	1.51983i
$947$	−8.01947e11			−0.997117			−0.498558	−	0.866856i	$-0.666137\pi$
$947$	−8.01947e11			−0.997117			−0.498558	+	0.866856i	$0.666137\pi$
$948$			2.03199e11i			0.251587i
$949$	8.10660e11			0.999479
$950$	−9.32607e10			−0.114500
$951$	1.00948e12			1.23418
$952$		−	4.29512e11i		−	0.522911i
$953$			8.67576e11i			1.05181i	0.850544	+	0.525904i	$0.176273\pi$
$953$			8.67576e11i			1.05181i	−0.850544	+	0.525904i	$0.823727\pi$
$954$			4.44808e10i			0.0537006i
$955$	3.13378e10			0.0376751
$956$		−	2.62166e11i		−	0.313866i
$957$	−1.35079e12	+	4.75920e11i	−1.61042	+	0.567396i
$958$	−5.76532e11			−0.684480
$959$		−	3.21092e11i		−	0.379625i
$960$	−9.94022e10			−0.117034
$961$	−5.98415e11			−0.701631
$962$	−1.27603e11			−0.148991
$963$			1.76335e10i			0.0205038i
$964$			6.84470e10i			0.0792586i
$965$			1.79911e10i			0.0207466i
$966$	−5.73516e11			−0.658623
$967$			8.21102e11i			0.939055i	0.882918	+	0.469528i	$0.155576\pi$
$967$			8.21102e11i			0.939055i	−0.882918	+	0.469528i	$0.844424\pi$
$968$	5.94208e11	+	7.38583e11i	0.676764	+	0.841197i
$969$	−8.46559e10			−0.0960201
$970$			3.02418e10i			0.0341602i
$971$	−2.10268e11			−0.236536			−0.118268	−	0.992982i	$-0.537734\pi$
$971$	−2.10268e11			−0.236536			−0.118268	+	0.992982i	$0.537734\pi$
$972$	−3.66419e10			−0.0410500
$973$	−1.12054e11			−0.125019
$974$		−	5.13060e11i		−	0.570075i
$975$		−	5.28701e11i		−	0.585048i
$976$			7.81458e11i			0.861205i
$977$	4.12602e11			0.452849			0.226424	−	0.974029i	$-0.427296\pi$
$977$	4.12602e11			0.452849			0.226424	+	0.974029i	$0.427296\pi$
$978$		−	2.40516e11i		−	0.262899i
$979$	4.61956e11	+	1.31115e12i	0.502886	+	1.42732i
$980$	1.11610e10			0.0121004
$981$		−	6.79741e10i		−	0.0733951i
$982$	−9.84059e11			−1.05822
$983$	9.64520e10			0.103299			0.0516496	−	0.998665i	$-0.483552\pi$
$983$	9.64520e10			0.103299			0.0516496	+	0.998665i	$0.483552\pi$
$984$	−3.57724e11			−0.381565
$985$			9.56319e10i			0.101592i
$986$			9.45124e11i			0.999956i
$987$		−	1.00673e12i		−	1.06083i
$988$	−1.65143e10			−0.0173314
$989$		−	1.82356e12i		−	1.90605i
$990$	7.11244e9	−	2.50591e9i	0.00740420	−	0.00260870i
$991$	−3.85251e11			−0.399437			−0.199719	−	0.979853i	$-0.564003\pi$
$991$	−3.85251e11			−0.399437			−0.199719	+	0.979853i	$0.564003\pi$
$992$			2.39867e11i			0.247699i
$993$	−1.93062e11			−0.198564
$994$	3.90082e11			0.399586
$995$	−8.88341e10			−0.0906332
$996$			2.33707e11i			0.237484i
$997$		−	7.54081e11i		−	0.763198i	−0.924328	−	0.381599i	$-0.875374\pi$
$997$		−	7.54081e11i		−	0.763198i	0.924328	−	0.381599i	$-0.124626\pi$
$998$		−	1.18121e12i		−	1.19070i
$999$	2.84198e11			0.285338

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.9.b.b.10.3	✓	6
3.2	odd	2		99.9.c.b.10.4		6
4.3	odd	2		176.9.h.c.65.2		6
11.10	odd	2	inner	11.9.b.b.10.4	yes	6
33.32	even	2		99.9.c.b.10.3		6
44.43	even	2		176.9.h.c.65.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.9.b.b.10.3	✓	6	1.1	even	1	trivial
11.9.b.b.10.4	yes	6	11.10	odd	2	inner
99.9.c.b.10.3		6	33.32	even	2
99.9.c.b.10.4		6	3.2	odd	2
176.9.h.c.65.1		6	44.43	even	2
176.9.h.c.65.2		6	4.3	odd	2

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:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	11.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-14.0233i q^{2} +84.5196 q^{3} +59.3467 q^{4} +63.0464 q^{5} -1185.25i q^{6} -1667.89i q^{7} -4422.21i q^{8} +582.567 q^{9} +O(q^{10})\)	\(q-14.0233i q^{2} +84.5196 q^{3} +59.3467 q^{4} +63.0464 q^{5} -1185.25i q^{6} -1667.89i q^{7} -4422.21i q^{8} +582.567 q^{9} -884.120i q^{10} +(4865.29 + 13809.0i) q^{11} +5015.96 q^{12} +16178.3i q^{13} -23389.3 q^{14} +5328.66 q^{15} -46821.2 q^{16} +58233.1i q^{17} -8169.52i q^{18} +17200.1i q^{19} +3741.60 q^{20} -140969. i q^{21} +(193648. - 68227.4i) q^{22} +290115. q^{23} -373763. i q^{24} -386650. q^{25} +226874. q^{26} -505295. q^{27} -98983.7i q^{28} +1.15736e6i q^{29} -74725.5i q^{30} -504456. q^{31} -475496. i q^{32} +(411212. + 1.16713e6i) q^{33} +816620. q^{34} -105154. i q^{35} +34573.5 q^{36} -562440. q^{37} +241202. q^{38} +1.36739e6i q^{39} -278804. i q^{40} -957088. i q^{41} -1.97686e6 q^{42} -6.28563e6i q^{43} +(288739. + 819518. i) q^{44} +36728.8 q^{45} -4.06838e6i q^{46} +7.14150e6 q^{47} -3.95731e6 q^{48} +2.98295e6 q^{49} +5.42212e6i q^{50} +4.92184e6i q^{51} +960132. i q^{52} -5.44472e6 q^{53} +7.08591e6i q^{54} +(306739. + 870607. i) q^{55} -7.37574e6 q^{56} +1.45374e6i q^{57} +1.62300e7 q^{58} -1.63227e7 q^{59} +316239. q^{60} -1.66903e7i q^{61} +7.07414e6i q^{62} -971657. i q^{63} -1.86543e7 q^{64} +1.01999e6i q^{65} +(1.63670e7 - 5.76656e6i) q^{66} +2.30970e7 q^{67} +3.45594e6i q^{68} +2.45204e7 q^{69} -1.47461e6 q^{70} -1.66778e7 q^{71} -2.57623e6i q^{72} -5.01077e7i q^{73} +7.88728e6i q^{74} -3.26795e7 q^{75} +1.02077e6i q^{76} +(2.30318e7 - 8.11475e6i) q^{77} +1.91753e7 q^{78} +4.05105e7i q^{79} -2.95191e6 q^{80} -4.65296e7 q^{81} -1.34215e7 q^{82} +4.65927e7i q^{83} -8.36606e6i q^{84} +3.67139e6i q^{85} -8.81453e7 q^{86} +9.78196e7i q^{87} +(6.10661e7 - 2.15153e7i) q^{88} +9.49493e7 q^{89} -515059. i q^{90} +2.69837e7 q^{91} +1.72174e7 q^{92} -4.26364e7 q^{93} -1.00148e8i q^{94} +1.08440e6i q^{95} -4.01888e7i q^{96} -3.42056e7 q^{97} -4.18309e7i q^{98} +(2.83436e6 + 8.04466e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 36 q^{3} - 1212 q^{4} - 448 q^{5} - 13578 q^{9}+O(q^{10}) \) 6 * q - 36 * q^3 - 1212 * q^4 - 448 * q^5 - 13578 * q^9	\( 6 q - 36 q^{3} - 1212 q^{4} - 448 q^{5} - 13578 q^{9} - 32318 q^{11} + 54564 q^{12} - 33768 q^{14} + 85824 q^{15} + 312264 q^{16} - 894868 q^{20} - 550440 q^{22} + 683084 q^{23} - 141498 q^{25} - 657432 q^{26} + 988848 q^{27} + 942684 q^{31} + 2992704 q^{33} - 1345128 q^{34} + 7401360 q^{36} - 3804816 q^{37} - 8900760 q^{38} - 8158920 q^{42} + 14210284 q^{44} - 2499684 q^{45} + 15828644 q^{47} - 19028376 q^{48} - 10066602 q^{49} - 35477956 q^{53} + 7335372 q^{55} + 68829936 q^{56} + 65482560 q^{58} - 29614804 q^{59} + 35069244 q^{60} - 212921520 q^{64} + 75167400 q^{66} + 39419484 q^{67} + 62859468 q^{69} - 168190680 q^{70} + 3219212 q^{71} - 110874276 q^{75} + 91605360 q^{77} + 111889320 q^{78} + 383392952 q^{80} - 103764906 q^{81} - 163977720 q^{82} - 261274512 q^{86} + 328724880 q^{88} + 38785664 q^{89} + 355260528 q^{91} - 456128956 q^{92} - 182572452 q^{93} - 222185616 q^{97} + 159125406 q^{99}+O(q^{100}) \) 6 * q - 36 * q^3 - 1212 * q^4 - 448 * q^5 - 13578 * q^9 - 32318 * q^11 + 54564 * q^12 - 33768 * q^14 + 85824 * q^15 + 312264 * q^16 - 894868 * q^20 - 550440 * q^22 + 683084 * q^23 - 141498 * q^25 - 657432 * q^26 + 988848 * q^27 + 942684 * q^31 + 2992704 * q^33 - 1345128 * q^34 + 7401360 * q^36 - 3804816 * q^37 - 8900760 * q^38 - 8158920 * q^42 + 14210284 * q^44 - 2499684 * q^45 + 15828644 * q^47 - 19028376 * q^48 - 10066602 * q^49 - 35477956 * q^53 + 7335372 * q^55 + 68829936 * q^56 + 65482560 * q^58 - 29614804 * q^59 + 35069244 * q^60 - 212921520 * q^64 + 75167400 * q^66 + 39419484 * q^67 + 62859468 * q^69 - 168190680 * q^70 + 3219212 * q^71 - 110874276 * q^75 + 91605360 * q^77 + 111889320 * q^78 + 383392952 * q^80 - 103764906 * q^81 - 163977720 * q^82 - 261274512 * q^86 + 328724880 * q^88 + 38785664 * q^89 + 355260528 * q^91 - 456128956 * q^92 - 182572452 * q^93 - 222185616 * q^97 + 159125406 * q^99

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