LMFDB - Embedded newform 180.9.c.b.91.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [180,9,Mod(91,180)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("180.91"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	180.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$73.3281498110$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.8
Character	$\chi$	$=$	180.91
Dual form			180.9.c.b.91.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-12.7138 + 9.71382i) q^{2} +(67.2836 - 247.000i) q^{4} -279.508 q^{5} +3004.85i q^{7} +(1543.88 + 3793.90i) q^{8} +(3553.63 - 2715.09i) q^{10} +831.945i q^{11} -21654.4 q^{13} +(-29188.5 - 38203.2i) q^{14} +(-56481.8 - 33238.1i) q^{16} -20325.2 q^{17} +157797. i q^{19} +(-18806.3 + 69038.6i) q^{20} +(-8081.36 - 10577.2i) q^{22} -32500.8i q^{23} +78125.0 q^{25} +(275311. - 210347. i) q^{26} +(742197. + 202177. i) q^{28} +896260. q^{29} +1.07076e6i q^{31} +(1.04097e6 - 126071. i) q^{32} +(258412. - 197436. i) q^{34} -839881. i q^{35} -2.90012e6 q^{37} +(-1.53281e6 - 2.00621e6i) q^{38} +(-431527. - 1.06043e6i) q^{40} +2.72580e6 q^{41} +3.95277e6i q^{43} +(205490. + 55976.2i) q^{44} +(315707. + 413210. i) q^{46} +2.00923e6i q^{47} -3.26431e6 q^{49} +(-993269. + 758892. i) q^{50} +(-1.45699e6 + 5.34863e6i) q^{52} -1.23248e7 q^{53} -232536. i q^{55} +(-1.14001e7 + 4.63912e6i) q^{56} +(-1.13949e7 + 8.70611e6i) q^{58} +2.93018e6i q^{59} +1.68909e7 q^{61} +(-1.04011e7 - 1.36135e7i) q^{62} +(-1.20101e7 + 1.17146e7i) q^{64} +6.05259e6 q^{65} +9.10735e6i q^{67} +(-1.36756e6 + 5.02033e6i) q^{68} +(8.15845e6 + 1.06781e7i) q^{70} -2.41855e7i q^{71} -2.42567e7 q^{73} +(3.68717e7 - 2.81712e7i) q^{74} +(3.89759e7 + 1.06172e7i) q^{76} -2.49987e6 q^{77} +1.23467e7i q^{79} +(1.57872e7 + 9.29032e6i) q^{80} +(-3.46554e7 + 2.64779e7i) q^{82} -5.46013e7i q^{83} +5.68108e6 q^{85} +(-3.83965e7 - 5.02549e7i) q^{86} +(-3.15631e6 + 1.28442e6i) q^{88} -4.56533e6 q^{89} -6.50682e7i q^{91} +(-8.02770e6 - 2.18677e6i) q^{92} +(-1.95173e7 - 2.55451e7i) q^{94} -4.41056e7i q^{95} -6.48434e7 q^{97} +(4.15020e7 - 3.17089e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 610 q^{4} - 8750 q^{10} - 51392 q^{13} + 11986 q^{16} - 758068 q^{22} + 2500000 q^{25} + 976324 q^{28} - 6117428 q^{34} + 5152064 q^{37} - 96250 q^{40} - 10391752 q^{46} - 11002976 q^{49} + 13976584 q^{52}+ \cdots + 80579520 q^{97}+O(q^{100}) $ 32 * q + 610 * q^4 - 8750 * q^10 - 51392 * q^13 + 11986 * q^16 - 758068 * q^22 + 2500000 * q^25 + 976324 * q^28 - 6117428 * q^34 + 5152064 * q^37 - 96250 * q^40 - 10391752 * q^46 - 11002976 * q^49 + 13976584 * q^52 - 36333948 * q^58 - 7802048 * q^61 + 116259994 * q^64 - 49897500 * q^70 - 94303680 * q^73 + 248840592 * q^76 - 428557904 * q^82 + 106960000 * q^85 + 510719924 * q^88 - 692727576 * q^94 + 80579520 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−12.7138	+	9.71382i	−0.794615	+	0.607113i
$2$	−12.7138	+	9.71382i	−0.794615	+	0.607113i
$3$		0			0
$3$		0			0
$4$	67.2836	−	247.000i	0.262827	−	0.964843i
$5$	−279.508			−0.447214
$5$	−279.508			−0.447214
$6$		0			0
$7$			3004.85i			1.25150i	0.780024	+	0.625749i	$0.215207\pi$
$7$			3004.85i			1.25150i	−0.780024	+	0.625749i	$0.784793\pi$
$8$	1543.88	+	3793.90i	0.376923	+	0.926244i
$9$		0			0
$10$	3553.63	−	2715.09i	0.355363	−	0.271509i
$11$			831.945i			0.0568229i	0.999596	+	0.0284115i	$0.00904487\pi$
$11$			831.945i			0.0568229i	−0.999596	+	0.0284115i	$0.990955\pi$
$12$		0			0
$13$	−21654.4			−0.758181			−0.379090	−	0.925360i	$-0.623763\pi$
$13$	−21654.4			−0.758181			−0.379090	+	0.925360i	$0.623763\pi$
$14$	−29188.5	−	38203.2i	−0.759802	−	0.994460i
$15$		0			0
$16$	−56481.8	−	33238.1i	−0.861844	−	0.507173i
$17$	−20325.2			−0.243355			−0.121677	−	0.992570i	$-0.538827\pi$
$17$	−20325.2			−0.243355			−0.121677	+	0.992570i	$0.538827\pi$
$18$		0			0
$19$			157797.i			1.21083i	0.795908	+	0.605417i	$0.206994\pi$
$19$			157797.i			1.21083i	−0.795908	+	0.605417i	$0.793006\pi$
$20$	−18806.3	+	69038.6i	−0.117540	+	0.431491i
$21$		0			0
$22$	−8081.36	−	10577.2i	−0.0344980	−	0.0451524i
$23$		−	32500.8i		−	0.116140i	−0.998313	−	0.0580701i	$-0.981505\pi$
$23$		−	32500.8i		−	0.116140i	0.998313	−	0.0580701i	$-0.0184947\pi$
$24$		0			0
$25$	78125.0			0.200000
$26$	275311.	−	210347.i	0.602462	−	0.460302i
$27$		0			0
$28$	742197.	+	202177.i	1.20750	+	0.328927i
$29$	896260.			1.26719			0.633596	−	0.773664i	$-0.281578\pi$
$29$	896260.			1.26719			0.633596	+	0.773664i	$0.281578\pi$
$30$		0			0
$31$			1.07076e6i			1.15943i	0.814819	+	0.579715i	$0.196836\pi$
$31$			1.07076e6i			1.15943i	−0.814819	+	0.579715i	$0.803164\pi$
$32$	1.04097e6	−	126071.i	0.992746	−	0.120230i
$33$		0			0
$34$	258412.	−	197436.i	0.193373	−	0.147744i
$35$		−	839881.i		−	0.559687i
$36$		0			0
$37$	−2.90012e6			−1.54742			−0.773712	−	0.633538i	$-0.781602\pi$
$37$	−2.90012e6			−1.54742			−0.773712	+	0.633538i	$0.781602\pi$
$38$	−1.53281e6	−	2.00621e6i	−0.735114	−	0.962147i
$39$		0			0
$40$	−431527.	−	1.06043e6i	−0.168565	−	0.414229i
$41$	2.72580e6			0.964626			0.482313	−	0.875999i	$-0.339797\pi$
$41$	2.72580e6			0.964626			0.482313	+	0.875999i	$0.339797\pi$
$42$		0			0
$43$			3.95277e6i			1.15619i	0.815971	+	0.578093i	$0.196203\pi$
$43$			3.95277e6i			1.15619i	−0.815971	+	0.578093i	$0.803797\pi$
$44$	205490.	+	55976.2i	0.0548252	+	0.0149346i
$45$		0			0
$46$	315707.	+	413210.i	0.0705103	+	0.0922868i
$47$			2.00923e6i			0.411755i	0.978578	+	0.205878i	$0.0660049\pi$
$47$			2.00923e6i			0.411755i	−0.978578	+	0.205878i	$0.933995\pi$
$48$		0			0
$49$	−3.26431e6			−0.566249
$50$	−993269.	+	758892.i	−0.158923	+	0.121423i
$51$		0			0
$52$	−1.45699e6	+	5.34863e6i	−0.199270	+	0.731526i
$53$	−1.23248e7			−1.56198			−0.780990	−	0.624544i	$-0.785285\pi$
$53$	−1.23248e7			−1.56198			−0.780990	+	0.624544i	$0.785285\pi$
$54$		0			0
$55$		−	232536.i		−	0.0254120i
$56$	−1.14001e7	+	4.63912e6i	−1.15919	+	0.471719i
$57$		0			0
$58$	−1.13949e7	+	8.70611e6i	−1.00693	+	0.769329i
$59$			2.93018e6i			0.241817i	0.992664	+	0.120908i	$0.0385807\pi$
$59$			2.93018e6i			0.241817i	−0.992664	+	0.120908i	$0.961419\pi$
$60$		0			0
$61$	1.68909e7			1.21993			0.609964	−	0.792429i	$-0.291184\pi$
$61$	1.68909e7			1.21993			0.609964	+	0.792429i	$0.291184\pi$
$62$	−1.04011e7	−	1.36135e7i	−0.703906	−	0.921301i
$63$		0			0
$64$	−1.20101e7	+	1.17146e7i	−0.715858	+	0.698246i
$65$	6.05259e6			0.339069
$66$		0			0
$67$			9.10735e6i			0.451952i	0.974133	+	0.225976i	$0.0725572\pi$
$67$			9.10735e6i			0.451952i	−0.974133	+	0.225976i	$0.927443\pi$
$68$	−1.36756e6	+	5.02033e6i	−0.0639601	+	0.234799i
$69$		0			0
$70$	8.15845e6	+	1.06781e7i	0.339794	+	0.444736i
$71$		−	2.41855e7i		−	0.951746i	−0.879514	−	0.475873i	$-0.842132\pi$
$71$		−	2.41855e7i		−	0.951746i	0.879514	−	0.475873i	$-0.157868\pi$
$72$		0			0
$73$	−2.42567e7			−0.854164			−0.427082	−	0.904213i	$-0.640458\pi$
$73$	−2.42567e7			−0.854164			−0.427082	+	0.904213i	$0.640458\pi$
$74$	3.68717e7	−	2.81712e7i	1.22961	−	0.939461i
$75$		0			0
$76$	3.89759e7	+	1.06172e7i	1.16826	+	0.318239i
$77$	−2.49987e6			−0.0711138
$78$		0			0
$79$			1.23467e7i			0.316988i	0.987360	+	0.158494i	$0.0506639\pi$
$79$			1.23467e7i			0.316988i	−0.987360	+	0.158494i	$0.949336\pi$
$80$	1.57872e7	+	9.29032e6i	0.385429	+	0.226815i
$81$		0			0
$82$	−3.46554e7	+	2.64779e7i	−0.766506	+	0.585637i
$83$		−	5.46013e7i		−	1.15051i	−0.817974	−	0.575256i	$-0.804903\pi$
$83$		−	5.46013e7i		−	1.15051i	0.817974	−	0.575256i	$-0.195097\pi$
$84$		0			0
$85$	5.68108e6			0.108832
$86$	−3.83965e7	−	5.02549e7i	−0.701936	−	0.918723i
$87$		0			0
$88$	−3.15631e6	+	1.28442e6i	−0.0526319	+	0.0214179i
$89$	−4.56533e6			−0.0727633			−0.0363817	−	0.999338i	$-0.511583\pi$
$89$	−4.56533e6			−0.0727633			−0.0363817	+	0.999338i	$0.511583\pi$
$90$		0			0
$91$		−	6.50682e7i		−	0.948862i
$92$	−8.02770e6	−	2.18677e6i	−0.112057	−	0.0305247i
$93$		0			0
$94$	−1.95173e7	−	2.55451e7i	−0.249982	−	0.327187i
$95$		−	4.41056e7i		−	0.541501i
$96$		0			0
$97$	−6.48434e7			−0.732451			−0.366226	−	0.930526i	$-0.619350\pi$
$97$	−6.48434e7			−0.732451			−0.366226	+	0.930526i	$0.619350\pi$
$98$	4.15020e7	−	3.17089e7i	0.449950	−	0.343777i
$99$		0			0
$100$	5.25653e6	−	1.92969e7i	0.0525653	−	0.192969i
$101$	−2.28685e7			−0.219762			−0.109881	−	0.993945i	$-0.535047\pi$
$101$	−2.28685e7			−0.219762			−0.109881	+	0.993945i	$0.535047\pi$
$102$		0			0
$103$			2.85108e6i			0.0253315i	0.999920	+	0.0126658i	$0.00403174\pi$
$103$			2.85108e6i			0.0253315i	−0.999920	+	0.0126658i	$0.995968\pi$
$104$	−3.34318e7	−	8.21546e7i	−0.285776	−	0.702261i
$105$		0			0
$106$	1.56695e8	−	1.19721e8i	1.24117	−	0.948299i
$107$		−	2.45987e8i		−	1.87662i	−0.345795	−	0.938310i	$-0.612391\pi$
$107$		−	2.45987e8i		−	1.87662i	0.345795	−	0.938310i	$-0.387609\pi$
$108$		0			0
$109$	−4.12110e7			−0.291949			−0.145975	−	0.989288i	$-0.546632\pi$
$109$	−4.12110e7			−0.291949			−0.145975	+	0.989288i	$0.546632\pi$
$110$	2.25881e6	+	2.95642e6i	0.0154280	+	0.0201928i
$111$		0			0
$112$	9.98754e7	−	1.69719e8i	0.634726	−	1.07860i
$113$	−1.76282e8			−1.08117			−0.540584	−	0.841290i	$-0.681797\pi$
$113$	−1.76282e8			−1.08117			−0.540584	+	0.841290i	$0.681797\pi$
$114$		0			0
$115$			9.08425e6i			0.0519395i
$116$	6.03036e7	−	2.21376e8i	0.333051	−	1.22264i
$117$		0			0
$118$	−2.84632e7	−	3.72538e7i	−0.146810	−	0.192151i
$119$		−	6.10743e7i		−	0.304558i
$120$		0			0
$121$	2.13667e8			0.996771
$122$	−2.14749e8	+	1.64075e8i	−0.969373	+	0.740635i
$123$		0			0
$124$	2.64477e8	+	7.20445e7i	1.11867	+	0.304729i
$125$	−2.18366e7			−0.0894427
$126$		0			0
$127$		−	2.66109e8i		−	1.02293i	−0.859305	−	0.511463i	$-0.829104\pi$
$127$		−	2.66109e8i		−	1.02293i	0.859305	−	0.511463i	$-0.170896\pi$
$128$	3.89008e7	−	2.65602e8i	0.144917	−	0.989444i
$129$		0			0
$130$	−7.69517e7	+	5.87937e7i	−0.269429	+	0.205853i
$131$		−	9.42652e7i		−	0.320086i	−0.987110	−	0.160043i	$-0.948837\pi$
$131$		−	9.42652e7i		−	0.320086i	0.987110	−	0.160043i	$-0.0511632\pi$
$132$		0			0
$133$	−4.74156e8			−1.51536
$134$	−8.84671e7	−	1.15789e8i	−0.274386	−	0.359128i
$135$		0			0
$136$	−3.13797e7	−	7.71119e7i	−0.0917261	−	0.225406i
$137$	4.24530e8			1.20511			0.602554	−	0.798078i	$-0.294150\pi$
$137$	4.24530e8			1.20511			0.602554	+	0.798078i	$0.294150\pi$
$138$		0			0
$139$		−	4.84797e8i		−	1.29868i	−0.760500	−	0.649338i	$-0.775046\pi$
$139$		−	4.84797e8i		−	1.29868i	0.760500	−	0.649338i	$-0.224954\pi$
$140$	−2.07450e8	−	5.65102e7i	−0.540010	−	0.147101i
$141$		0			0
$142$	2.34933e8	+	3.07490e8i	0.577818	+	0.756272i
$143$		−	1.80153e7i		−	0.0430821i
$144$		0			0
$145$	−2.50512e8			−0.566705
$146$	3.08396e8	−	2.35626e8i	0.678731	−	0.518574i
$147$		0			0
$148$	−1.95131e8	+	7.16329e8i	−0.406704	+	1.49302i
$149$	−8.59503e8			−1.74382			−0.871912	−	0.489663i	$-0.837120\pi$
$149$	−8.59503e8			−1.74382			−0.871912	+	0.489663i	$0.837120\pi$
$150$		0			0
$151$		−	4.35660e8i		−	0.837991i	−0.907988	−	0.418996i	$-0.862382\pi$
$151$		−	4.35660e8i		−	0.837991i	0.907988	−	0.418996i	$-0.137618\pi$
$152$	−5.98666e8	+	2.43619e8i	−1.12153	+	0.456392i
$153$		0			0
$154$	3.17829e7	−	2.42833e7i	0.0565081	−	0.0431742i
$155$		−	2.99286e8i		−	0.518513i
$156$		0			0
$157$	4.96389e8			0.817003			0.408502	−	0.912758i	$-0.366051\pi$
$157$	4.96389e8			0.817003			0.408502	+	0.912758i	$0.366051\pi$
$158$	−1.19934e8	−	1.56974e8i	−0.192448	−	0.251884i
$159$		0			0
$160$	−2.90960e8	+	3.52378e7i	−0.443970	+	0.0537686i
$161$	9.76600e7			0.145349
$162$		0			0
$163$			8.92254e7i			0.126397i	0.998001	+	0.0631987i	$0.0201302\pi$
$163$			8.92254e7i			0.126397i	−0.998001	+	0.0631987i	$0.979870\pi$
$164$	1.83402e8	−	6.73273e8i	0.253529	−	0.930712i
$165$		0			0
$166$	5.30387e8	+	6.94193e8i	0.698491	+	0.914214i
$167$		−	7.04032e8i		−	0.905162i	−0.891723	−	0.452581i	$-0.850503\pi$
$167$		−	7.04032e8i		−	0.905162i	0.891723	−	0.452581i	$-0.149497\pi$
$168$		0			0
$169$	−3.46817e8			−0.425162
$170$	−7.22283e7	+	5.51849e7i	−0.0864792	+	0.0660731i
$171$		0			0
$172$	9.76333e8	+	2.65957e8i	1.11554	+	0.303876i
$173$	8.48441e8			0.947191			0.473595	−	0.880743i	$-0.342956\pi$
$173$	8.48441e8			0.947191			0.473595	+	0.880743i	$0.342956\pi$
$174$		0			0
$175$			2.34754e8i			0.250300i
$176$	2.76522e7	−	4.69898e7i	0.0288190	−	0.0489725i
$177$		0			0
$178$	5.80429e7	−	4.43468e7i	0.0578188	−	0.0441756i
$179$			1.79485e9i			1.74830i	0.485660	+	0.874148i	$0.338579\pi$
$179$			1.79485e9i			1.74830i	−0.485660	+	0.874148i	$0.661421\pi$
$180$		0			0
$181$	−1.98774e9			−1.85202			−0.926009	−	0.377500i	$-0.876784\pi$
$181$	−1.98774e9			−1.85202			−0.926009	+	0.377500i	$0.876784\pi$
$182$	6.32061e8	+	8.27267e8i	0.576067	+	0.753980i
$183$		0			0
$184$	1.23305e8	−	5.01773e7i	0.107574	−	0.0437760i
$185$	8.10608e8			0.692029
$186$		0			0
$187$		−	1.69095e7i		−	0.0138281i
$188$	4.96280e8	+	1.35188e8i	0.397279	+	0.108220i
$189$		0			0
$190$	4.28434e8	+	5.60752e8i	0.328753	+	0.430285i
$191$		−	2.15341e9i		−	1.61805i	−0.587772	−	0.809027i	$-0.699995\pi$
$191$		−	2.15341e9i		−	1.61805i	0.587772	−	0.809027i	$-0.300005\pi$
$192$		0			0
$193$	−1.90715e9			−1.37453			−0.687266	−	0.726406i	$-0.741189\pi$
$193$	−1.90715e9			−1.37453			−0.687266	+	0.726406i	$0.741189\pi$
$194$	8.24409e8	−	6.29877e8i	0.582017	−	0.444681i
$195$		0			0
$196$	−2.19635e8	+	8.06285e8i	−0.148825	+	0.546341i
$197$	−6.77481e8			−0.449813			−0.224907	−	0.974380i	$-0.572208\pi$
$197$	−6.77481e8			−0.449813			−0.224907	+	0.974380i	$0.572208\pi$
$198$		0			0
$199$			3.02491e8i			0.192885i	0.995339	+	0.0964427i	$0.0307465\pi$
$199$			3.02491e8i			0.192885i	−0.995339	+	0.0964427i	$0.969254\pi$
$200$	1.20615e8	+	2.96398e8i	0.0753847	+	0.185249i
$201$		0			0
$202$	2.90747e8	−	2.22141e8i	0.174626	−	0.133421i
$203$			2.69313e9i			1.58589i
$204$		0			0
$205$	−7.61885e8			−0.431394
$206$	−2.76949e7	−	3.62482e7i	−0.0153791	−	0.0201288i
$207$		0			0
$208$	1.22308e9	+	7.19751e8i	0.653434	+	0.384529i
$209$	−1.31278e8			−0.0688032
$210$		0			0
$211$		−	6.70422e8i		−	0.338235i	−0.985596	−	0.169117i	$-0.945908\pi$
$211$		−	6.70422e8i		−	0.338235i	0.985596	−	0.169117i	$-0.0540917\pi$
$212$	−8.29255e8	+	3.04422e9i	−0.410530	+	1.50707i
$213$		0			0
$214$	2.38947e9	+	3.12743e9i	1.13932	+	1.49119i
$215$		−	1.10483e9i		−	0.517062i
$216$		0			0
$217$	−3.21747e9			−1.45103
$218$	5.23950e8	−	4.00316e8i	0.231987	−	0.177246i
$219$		0			0
$220$	−5.74363e7	−	1.56458e7i	−0.0245186	−	0.00667895i
$221$	4.40131e8			0.184507
$222$		0			0
$223$		−	1.95800e9i		−	0.791759i	−0.918302	−	0.395880i	$-0.870440\pi$
$223$		−	1.95800e9i		−	0.791759i	0.918302	−	0.395880i	$-0.129560\pi$
$224$	3.78823e8	+	3.12796e9i	0.150468	+	1.24242i
$225$		0			0
$226$	2.24122e9	−	1.71237e9i	0.859113	−	0.656392i
$227$			4.48603e9i			1.68950i	0.535160	+	0.844750i	$0.320251\pi$
$227$			4.48603e9i			1.68950i	−0.535160	+	0.844750i	$0.679749\pi$
$228$		0			0
$229$	−2.86592e9			−1.04213			−0.521065	−	0.853517i	$-0.674465\pi$
$229$	−2.86592e9			−1.04213			−0.521065	+	0.853517i	$0.674465\pi$
$230$	−8.82428e7	−	1.15496e8i	−0.0315332	−	0.0412719i
$231$		0			0
$232$	1.38372e9	+	3.40032e9i	0.477634	+	1.17373i
$233$	−4.07226e9			−1.38169			−0.690846	−	0.723002i	$-0.742762\pi$
$233$	−4.07226e9			−1.38169			−0.690846	+	0.723002i	$0.742762\pi$
$234$		0			0
$235$		−	5.61598e8i		−	0.184142i
$236$	7.23754e8	+	1.97153e8i	0.233315	+	0.0635558i
$237$		0			0
$238$	5.93264e8	+	7.76489e8i	0.184901	+	0.242007i
$239$			3.15737e9i			0.967685i	0.875155	+	0.483843i	$0.160759\pi$
$239$			3.15737e9i			0.967685i	−0.875155	+	0.483843i	$0.839241\pi$
$240$		0			0
$241$	1.40791e9			0.417356			0.208678	−	0.977984i	$-0.433084\pi$
$241$	1.40791e9			0.417356			0.208678	+	0.977984i	$0.433084\pi$
$242$	−2.71653e9	+	2.07552e9i	−0.792049	+	0.605153i
$243$		0			0
$244$	1.13648e9	−	4.17206e9i	0.320629	−	1.17704i
$245$	9.12403e8			0.253234
$246$		0			0
$247$		−	3.41700e9i		−	0.918031i
$248$	−4.06235e9	+	1.65312e9i	−1.07392	+	0.437016i
$249$		0			0
$250$	2.77627e8	−	2.12117e8i	0.0710725	−	0.0543019i
$251$			1.54170e9i			0.388423i	0.980960	+	0.194211i	$0.0622148\pi$
$251$			1.54170e9i			0.388423i	−0.980960	+	0.194211i	$0.937785\pi$
$252$		0			0
$253$	2.70389e7			0.00659943
$254$	2.58493e9	+	3.38327e9i	0.621032	+	0.812833i
$255$		0			0
$256$	2.08543e9	+	3.75469e9i	0.485552	+	0.874208i
$257$	1.96925e9			0.451408			0.225704	−	0.974196i	$-0.427532\pi$
$257$	1.96925e9			0.451408			0.225704	+	0.974196i	$0.427532\pi$
$258$		0			0
$259$		−	8.71442e9i		−	1.93660i
$260$	4.07240e8	−	1.49499e9i	0.0891163	−	0.327148i
$261$		0			0
$262$	9.15675e8	+	1.19847e9i	0.194328	+	0.254345i
$263$		−	1.76226e9i		−	0.368338i	−0.982895	−	0.184169i	$-0.941041\pi$
$263$		−	1.76226e9i		−	0.368338i	0.982895	−	0.184169i	$-0.0589593\pi$
$264$		0			0
$265$	3.44488e9			0.698539
$266$	6.02835e9	−	4.60587e9i	1.20413	−	0.919994i
$267$		0			0
$268$	2.24951e9	+	6.12775e8i	0.436063	+	0.118785i
$269$	4.10833e9			0.784614			0.392307	−	0.919834i	$-0.371677\pi$
$269$	4.10833e9			0.784614			0.392307	+	0.919834i	$0.371677\pi$
$270$		0			0
$271$		−	5.69300e9i		−	1.05551i	−0.849395	−	0.527757i	$-0.823033\pi$
$271$		−	5.69300e9i		−	1.05551i	0.849395	−	0.527757i	$-0.176967\pi$
$272$	1.14801e9	+	6.75572e8i	0.209734	+	0.123423i
$273$		0			0
$274$	−5.39740e9	+	4.12380e9i	−0.957596	+	0.731637i
$275$			6.49957e7i			0.0113646i
$276$		0			0
$277$	−5.52101e9			−0.937777			−0.468889	−	0.883257i	$-0.655345\pi$
$277$	−5.52101e9			−0.937777			−0.468889	+	0.883257i	$0.655345\pi$
$278$	4.70923e9	+	6.16363e9i	0.788443	+	1.03195i
$279$		0			0
$280$	3.18642e9	−	1.29667e9i	0.518407	−	0.210959i
$281$	6.98839e9			1.12086			0.560430	−	0.828202i	$-0.310636\pi$
$281$	6.98839e9			1.12086			0.560430	+	0.828202i	$0.310636\pi$
$282$		0			0
$283$		−	1.06220e10i		−	1.65600i	−0.560726	−	0.828002i	$-0.689478\pi$
$283$		−	1.06220e10i		−	1.65600i	0.560726	−	0.828002i	$-0.310522\pi$
$284$	−5.97380e9	−	1.62728e9i	−0.918285	−	0.250144i
$285$		0			0
$286$	1.74997e8	+	2.29043e8i	0.0261557	+	0.0342337i
$287$			8.19062e9i			1.20723i
$288$		0			0
$289$	−6.56264e9			−0.940778
$290$	3.18498e9	−	2.43343e9i	0.450313	−	0.344054i
$291$		0			0
$292$	−1.63208e9	+	5.99141e9i	−0.224497	+	0.824134i
$293$	6.36222e9			0.863254			0.431627	−	0.902052i	$-0.357940\pi$
$293$	6.36222e9			0.863254			0.431627	+	0.902052i	$0.357940\pi$
$294$		0			0
$295$		−	8.19010e8i		−	0.108144i
$296$	−4.47743e9	−	1.10028e10i	−0.583260	−	1.43329i
$297$		0			0
$298$	1.09276e10	−	8.34906e9i	1.38567	−	1.05870i
$299$			7.03786e8i			0.0880553i
$300$		0			0
$301$	−1.18775e10			−1.44697
$302$	4.23192e9	+	5.53891e9i	0.508756	+	0.665880i
$303$		0			0
$304$	5.24487e9	−	8.91267e9i	0.614102	−	1.04355i
$305$	−4.72116e9			−0.545568
$306$		0			0
$307$			1.36857e10i			1.54069i	0.637629	+	0.770344i	$0.279915\pi$
$307$			1.36857e10i			1.54069i	−0.637629	+	0.770344i	$0.720085\pi$
$308$	−1.68200e8	+	6.17467e8i	−0.0186906	+	0.0686137i
$309$		0			0
$310$	2.90721e9	+	3.80508e9i	0.314796	+	0.412018i
$311$		−	1.40040e10i		−	1.49696i	−0.663159	−	0.748478i	$-0.730785\pi$
$311$		−	1.40040e10i		−	1.49696i	0.663159	−	0.748478i	$-0.269215\pi$
$312$		0			0
$313$	2.00876e9			0.209291			0.104645	−	0.994510i	$-0.466629\pi$
$313$	2.00876e9			0.209291			0.104645	+	0.994510i	$0.466629\pi$
$314$	−6.31102e9	+	4.82183e9i	−0.649203	+	0.496014i
$315$		0			0
$316$	3.04964e9	+	8.30731e8i	0.305844	+	0.0833129i
$317$	−1.48021e10			−1.46584			−0.732918	−	0.680317i	$-0.761842\pi$
$317$	−1.48021e10			−1.46584			−0.732918	+	0.680317i	$0.761842\pi$
$318$		0			0
$319$			7.45639e8i			0.0720055i
$320$	3.35692e9	−	3.27434e9i	0.320141	−	0.312265i
$321$		0			0
$322$	−1.24163e9	+	9.48651e8i	−0.115497	+	0.0882436i
$323$		−	3.20726e9i		−	0.294662i
$324$		0			0
$325$	−1.69175e9			−0.151636
$326$	−8.66719e8	−	1.13440e9i	−0.0767375	−	0.100437i
$327$		0			0
$328$	4.20830e9	+	1.03414e10i	0.363590	+	0.893479i
$329$	−6.03744e9			−0.515311
$330$		0			0
$331$			9.55249e9i			0.795801i	0.917428	+	0.397901i	$0.130261\pi$
$331$			9.55249e9i			0.795801i	−0.917428	+	0.397901i	$0.869739\pi$
$332$	−1.34865e10	−	3.67377e9i	−1.11006	−	0.302385i
$333$		0			0
$334$	6.83883e9	+	8.95095e9i	0.549536	+	0.719255i
$335$		−	2.54558e9i		−	0.202119i
$336$		0			0
$337$	3.83170e9			0.297079			0.148539	−	0.988906i	$-0.452543\pi$
$337$	3.83170e9			0.297079			0.148539	+	0.988906i	$0.452543\pi$
$338$	4.40938e9	−	3.36892e9i	0.337840	−	0.258121i
$339$		0			0
$340$	3.82243e8	−	1.40323e9i	0.0286038	−	0.105005i
$341$	−8.90812e8			−0.0658823
$342$		0			0
$343$			7.51359e9i			0.542839i
$344$	−1.49964e10	+	6.10259e9i	−1.07091	+	0.435793i
$345$		0			0
$346$	−1.07870e10	+	8.24160e9i	−0.752652	+	0.575052i
$347$			2.16493e10i			1.49323i	0.665256	+	0.746615i	$0.268322\pi$
$347$			2.16493e10i			1.49323i	−0.665256	+	0.746615i	$0.731678\pi$
$348$		0			0
$349$	−7.79586e8			−0.0525488			−0.0262744	−	0.999655i	$-0.508364\pi$
$349$	−7.79586e8			−0.0525488			−0.0262744	+	0.999655i	$0.508364\pi$
$350$	−2.28035e9	−	2.98462e9i	−0.151960	−	0.198892i
$351$		0			0
$352$	1.04884e8	+	8.66029e8i	0.00683184	+	0.0564108i
$353$	−1.69740e9			−0.109317			−0.0546583	−	0.998505i	$-0.517407\pi$
$353$	−1.69740e9			−0.109317			−0.0546583	+	0.998505i	$0.517407\pi$
$354$		0			0
$355$			6.76004e9i			0.425634i
$356$	−3.07172e8	+	1.12764e9i	−0.0191241	+	0.0702052i
$357$		0			0
$358$	−1.74348e10	−	2.28194e10i	−1.06141	−	1.38922i
$359$		−	2.25393e10i		−	1.35694i	−0.734626	−	0.678472i	$-0.762642\pi$
$359$		−	2.25393e10i		−	1.35694i	0.734626	−	0.678472i	$-0.237358\pi$
$360$		0			0
$361$	−7.91636e9			−0.466119
$362$	2.52718e10	−	1.93085e10i	1.47164	−	1.12439i
$363$		0			0
$364$	−1.60718e10	−	4.37802e9i	−0.915503	−	0.249386i
$365$	6.77997e9			0.381994
$366$		0			0
$367$			6.10333e9i			0.336436i	0.985750	+	0.168218i	$0.0538013\pi$
$367$			6.10333e9i			0.336436i	−0.985750	+	0.168218i	$0.946199\pi$
$368$	−1.08026e9	+	1.83571e9i	−0.0589032	+	0.100095i
$369$		0			0
$370$	−1.03059e10	+	7.87410e9i	−0.549897	+	0.420140i
$371$		−	3.70341e10i		−	1.95482i
$372$		0			0
$373$	−9.43858e8			−0.0487609			−0.0243804	−	0.999703i	$-0.507761\pi$
$373$	−9.43858e8			−0.0487609			−0.0243804	+	0.999703i	$0.507761\pi$
$374$	1.64256e8	+	2.14984e8i	0.00839525	+	0.0109881i
$375$		0			0
$376$	−7.62283e9	+	3.10201e9i	−0.381386	+	0.155200i
$377$	−1.94080e10			−0.960760
$378$		0			0
$379$		−	8.90445e9i		−	0.431569i	−0.976441	−	0.215784i	$-0.930769\pi$
$379$		−	8.90445e9i		−	0.431569i	0.976441	−	0.215784i	$-0.0692308\pi$
$380$	−1.08941e10	−	2.96759e9i	−0.522464	−	0.142321i
$381$		0			0
$382$	2.09178e10	+	2.73781e10i	0.982342	+	1.28573i
$383$		−	1.74695e10i		−	0.811866i	−0.913903	−	0.405933i	$-0.866947\pi$
$383$		−	1.74695e10i		−	0.811866i	0.913903	−	0.405933i	$-0.133053\pi$
$384$		0			0
$385$	6.98734e8			0.0318031
$386$	2.42472e10	−	1.85257e10i	1.09222	−	0.834497i
$387$		0			0
$388$	−4.36290e9	+	1.60163e10i	−0.192508	+	0.706701i
$389$	5.20057e9			0.227118			0.113559	−	0.993531i	$-0.463775\pi$
$389$	5.20057e9			0.227118			0.113559	+	0.993531i	$0.463775\pi$
$390$		0			0
$391$			6.60587e8i			0.0282633i
$392$	−5.03970e9	−	1.23845e10i	−0.213432	−	0.524485i
$393$		0			0
$394$	8.61339e9	−	6.58093e9i	0.357429	−	0.273088i
$395$		−	3.45101e9i		−	0.141761i
$396$		0			0
$397$	2.61454e10			1.05253			0.526264	−	0.850321i	$-0.323592\pi$
$397$	2.61454e10			1.05253			0.526264	+	0.850321i	$0.323592\pi$
$398$	−2.93834e9	−	3.84582e9i	−0.117103	−	0.153270i
$399$		0			0
$400$	−4.41264e9	−	2.59672e9i	−0.172369	−	0.101435i
$401$	1.05639e10			0.408553			0.204277	−	0.978913i	$-0.434516\pi$
$401$	1.05639e10			0.408553			0.204277	+	0.978913i	$0.434516\pi$
$402$		0			0
$403$		−	2.31866e10i		−	0.879058i
$404$	−1.53868e9	+	5.64853e9i	−0.0577593	+	0.212036i
$405$		0			0
$406$	−2.61605e10	−	3.42400e10i	−0.962814	−	1.26017i
$407$		−	2.41274e9i		−	0.0879292i
$408$		0			0
$409$	2.75141e10			0.983247			0.491623	−	0.870808i	$-0.336404\pi$
$409$	2.75141e10			0.983247			0.491623	+	0.870808i	$0.336404\pi$
$410$	9.68648e9	−	7.40081e9i	0.342792	−	0.261905i
$411$		0			0
$412$	7.04217e8	+	1.91831e8i	0.0244409	+	0.00665779i
$413$	−8.80474e9			−0.302633
$414$		0			0
$415$			1.52615e10i			0.514524i
$416$	−2.25416e10	+	2.72998e9i	−0.752681	+	0.0911563i
$417$		0			0
$418$	1.66905e9	−	1.27521e9i	0.0546720	−	0.0417713i
$419$			8.27123e9i			0.268358i	0.990957	+	0.134179i	$0.0428396\pi$
$419$			8.27123e9i			0.268358i	−0.990957	+	0.134179i	$0.957160\pi$
$420$		0			0
$421$	3.35248e10			1.06718			0.533589	−	0.845744i	$-0.320843\pi$
$421$	3.35248e10			1.06718			0.533589	+	0.845744i	$0.320843\pi$
$422$	6.51235e9	+	8.52364e9i	0.205347	+	0.268767i
$423$		0			0
$424$	−1.90279e10	−	4.67589e10i	−0.588746	−	1.44677i
$425$	−1.58791e9			−0.0486710
$426$		0			0
$427$			5.07547e10i			1.52674i
$428$	−6.07586e10	−	1.65509e10i	−1.81064	−	0.493225i
$429$		0			0
$430$	1.07321e10	+	1.40467e10i	0.313915	+	0.410865i
$431$			8.28161e8i			0.0239997i	0.999928	+	0.0119998i	$0.00381976\pi$
$431$			8.28161e8i			0.0239997i	−0.999928	+	0.0119998i	$0.996180\pi$
$432$		0			0
$433$	9.93872e9			0.282735			0.141367	−	0.989957i	$-0.454850\pi$
$433$	9.93872e9			0.282735			0.141367	+	0.989957i	$0.454850\pi$
$434$	4.09064e10	−	3.12539e10i	1.15301	−	0.880937i
$435$		0			0
$436$	−2.77282e9	+	1.01791e10i	−0.0767320	+	0.281685i
$437$	5.12853e9			0.140627
$438$		0			0
$439$		−	5.26817e10i		−	1.41841i	−0.705002	−	0.709205i	$-0.749054\pi$
$439$		−	5.26817e10i		−	1.41841i	0.705002	−	0.709205i	$-0.250946\pi$
$440$	8.82216e8	−	3.59007e8i	0.0235377	−	0.00957837i
$441$		0			0
$442$	−5.59576e9	+	4.27535e9i	−0.146612	+	0.112017i
$443$			3.82644e9i			0.0993528i	0.998765	+	0.0496764i	$0.0158190\pi$
$443$			3.82644e9i			0.0993528i	−0.998765	+	0.0496764i	$0.984181\pi$
$444$		0			0
$445$	1.27605e9			0.0325407
$446$	1.90196e10	+	2.48937e10i	0.480688	+	0.629144i
$447$		0			0
$448$	−3.52007e10	−	3.60885e10i	−0.873854	−	0.895895i
$449$	4.83070e10			1.18857			0.594285	−	0.804255i	$-0.297435\pi$
$449$	4.83070e10			1.18857			0.594285	+	0.804255i	$0.297435\pi$
$450$		0			0
$451$			2.26772e9i			0.0548129i
$452$	−1.18609e10	+	4.35415e10i	−0.284160	+	1.04316i
$453$		0			0
$454$	−4.35764e10	−	5.70346e10i	−1.02572	−	1.34250i
$455$			1.81871e10i			0.424344i
$456$		0			0
$457$	6.09494e10			1.39735			0.698674	−	0.715440i	$-0.253774\pi$
$457$	6.09494e10			1.39735			0.698674	+	0.715440i	$0.253774\pi$
$458$	3.64368e10	−	2.78390e10i	0.828092	−	0.632691i
$459$		0			0
$460$	2.24381e9	+	6.11221e8i	0.0501135	+	0.0136511i
$461$	−4.59730e10			−1.01789			−0.508943	−	0.860800i	$-0.669963\pi$
$461$	−4.59730e10			−1.01789			−0.508943	+	0.860800i	$0.669963\pi$
$462$		0			0
$463$			6.46853e10i			1.40761i	0.710395	+	0.703804i	$0.248516\pi$
$463$			6.46853e10i			1.40761i	−0.710395	+	0.703804i	$0.751484\pi$
$464$	−5.06224e10	−	2.97900e10i	−1.09212	−	0.642685i
$465$		0			0
$466$	5.17740e10	−	3.95572e10i	1.09791	−	0.838844i
$467$		−	5.92180e10i		−	1.24505i	−0.782601	−	0.622524i	$-0.786107\pi$
$467$		−	5.92180e10i		−	1.24505i	0.782601	−	0.622524i	$-0.213893\pi$
$468$		0			0
$469$	−2.73662e10			−0.565618
$470$	5.45526e9	+	7.14007e9i	0.111795	+	0.146322i
$471$		0			0
$472$	−1.11168e10	+	4.52384e9i	−0.223981	+	0.0911463i
$473$	−3.28849e9			−0.0656979
$474$		0			0
$475$			1.23279e10i			0.242167i
$476$	−1.50853e10	−	4.10930e9i	−0.293851	−	0.0800460i
$477$		0			0
$478$	−3.06701e10	−	4.01423e10i	−0.587495	−	0.768938i
$479$			7.06180e10i			1.34145i	0.741707	+	0.670724i	$0.234016\pi$
$479$			7.06180e10i			1.34145i	−0.741707	+	0.670724i	$0.765984\pi$
$480$		0			0
$481$	6.28004e10			1.17323
$482$	−1.79000e10	+	1.36762e10i	−0.331638	+	0.253383i
$483$		0			0
$484$	1.43763e10	−	5.27757e10i	0.261978	−	0.961728i
$485$	1.81243e10			0.327562
$486$		0			0
$487$			9.59650e10i			1.70607i	0.521854	+	0.853035i	$0.325241\pi$
$487$			9.59650e10i			1.70607i	−0.521854	+	0.853035i	$0.674759\pi$
$488$	2.60775e10	+	6.40825e10i	0.459819	+	1.12995i
$489$		0			0
$490$	−1.16002e10	+	8.86292e9i	−0.201224	+	0.153742i
$491$			8.92833e10i			1.53619i	0.640337	+	0.768094i	$0.278795\pi$
$491$			8.92833e10i			1.53619i	−0.640337	+	0.768094i	$0.721205\pi$
$492$		0			0
$493$	−1.82167e10			−0.308377
$494$	3.31921e10	+	4.34432e10i	0.557349	+	0.729482i
$495$		0			0
$496$	3.55899e10	−	6.04784e10i	0.588031	−	0.999249i
$497$	7.26736e10			1.19111
$498$		0			0
$499$			1.56949e10i			0.253137i	0.991958	+	0.126568i	$0.0403963\pi$
$499$			1.56949e10i			0.253137i	−0.991958	+	0.126568i	$0.959604\pi$
$500$	−1.46924e9	+	5.39364e9i	−0.0235079	+	0.0862982i
$501$		0			0
$502$	−1.49758e10	−	1.96009e10i	−0.235817	−	0.308647i
$503$			4.98620e10i			0.778928i	0.921042	+	0.389464i	$0.127340\pi$
$503$			4.98620e10i			0.778928i	−0.921042	+	0.389464i	$0.872660\pi$
$504$		0			0
$505$	6.39195e9			0.0982807
$506$	−3.43768e8	+	2.62651e8i	−0.00524401	+	0.00400660i
$507$		0			0
$508$	−6.57288e10	−	1.79048e10i	−0.986964	−	0.268852i
$509$	−4.86041e10			−0.724105			−0.362052	−	0.932158i	$-0.617924\pi$
$509$	−4.86041e10			−0.724105			−0.362052	+	0.932158i	$0.617924\pi$
$510$		0			0
$511$		−	7.28878e10i		−	1.06898i
$512$	−6.29862e10	−	2.74791e10i	−0.916570	−	0.399874i
$513$		0			0
$514$	−2.50368e10	+	1.91290e10i	−0.358695	+	0.274056i
$515$		−	7.96902e8i		−	0.0113286i
$516$		0			0
$517$	−1.67157e9			−0.0233971
$518$	8.46503e10	+	1.10794e11i	1.17573	+	1.53885i
$519$		0			0
$520$	9.34446e9	+	2.29629e10i	0.127803	+	0.314061i
$521$	−4.81707e10			−0.653781			−0.326891	−	0.945062i	$-0.606001\pi$
$521$	−4.81707e10			−0.653781			−0.326891	+	0.945062i	$0.606001\pi$
$522$		0			0
$523$		−	7.13512e10i		−	0.953662i	−0.878995	−	0.476831i	$-0.841785\pi$
$523$		−	7.13512e10i		−	0.953662i	0.878995	−	0.476831i	$-0.158215\pi$
$524$	−2.32835e10	−	6.34250e9i	−0.308832	−	0.0841270i
$525$		0			0
$526$	1.71182e10	+	2.24051e10i	0.223623	+	0.292687i
$527$		−	2.17634e10i		−	0.282153i
$528$		0			0
$529$	7.72547e10			0.986511
$530$	−4.37976e10	+	3.34629e10i	−0.555069	+	0.424092i
$531$		0			0
$532$	−3.19029e10	+	1.17117e11i	−0.398276	+	1.46208i
$533$	−5.90256e10			−0.731361
$534$		0			0
$535$			6.87553e10i			0.839250i
$536$	−3.45523e10	+	1.40606e10i	−0.418618	+	0.170351i
$537$		0			0
$538$	−5.22327e10	+	3.99076e10i	−0.623467	+	0.476350i
$539$		−	2.71573e9i		−	0.0321759i
$540$		0			0
$541$	1.33403e11			1.55731			0.778656	−	0.627451i	$-0.215902\pi$
$541$	1.33403e11			1.55731			0.778656	+	0.627451i	$0.215902\pi$
$542$	5.53008e10	+	7.23800e10i	0.640817	+	0.838728i
$543$		0			0
$544$	−2.11580e10	+	2.56241e9i	−0.241590	+	0.0292586i
$545$	1.15188e10			0.130564
$546$		0			0
$547$			1.12962e11i			1.26178i	0.775872	+	0.630891i	$0.217310\pi$
$547$			1.12962e11i			1.26178i	−0.775872	+	0.630891i	$0.782690\pi$
$548$	2.85639e10	−	1.04859e11i	0.316734	−	1.16274i
$549$		0			0
$550$	−6.31356e8	−	8.26345e8i	−0.00689960	−	0.00903048i
$551$			1.41427e11i			1.53436i
$552$		0			0
$553$	−3.71000e10			−0.396710
$554$	7.01933e10	−	5.36301e10i	0.745172	−	0.569337i
$555$		0			0
$556$	−1.19745e11	−	3.26189e10i	−1.25302	−	0.341326i
$557$	9.91223e10			1.02979			0.514897	−	0.857252i	$-0.327830\pi$
$557$	9.91223e10			1.02979			0.514897	+	0.857252i	$0.327830\pi$
$558$		0			0
$559$		−	8.55949e10i		−	0.876598i
$560$	−2.79160e10	+	4.74380e10i	−0.283858	+	0.482363i
$561$		0			0
$562$	−8.88493e10	+	6.78839e10i	−0.890653	+	0.680490i
$563$		−	5.62703e10i		−	0.560075i	−0.959989	−	0.280037i	$-0.909653\pi$
$563$		−	5.62703e10i		−	0.560075i	0.959989	−	0.280037i	$-0.0903468\pi$
$564$		0			0
$565$	4.92722e10			0.483513
$566$	1.03180e11	+	1.35047e11i	1.00538	+	1.31589i
$567$		0			0
$568$	9.17571e10	−	3.73394e10i	0.881549	−	0.358735i
$569$	2.67326e10			0.255031			0.127515	−	0.991837i	$-0.459300\pi$
$569$	2.67326e10			0.255031			0.127515	+	0.991837i	$0.459300\pi$
$570$		0			0
$571$			1.70013e11i			1.59933i	0.600446	+	0.799666i	$0.294990\pi$
$571$			1.70013e11i			1.59933i	−0.600446	+	0.799666i	$0.705010\pi$
$572$	−4.44977e9	−	1.21213e9i	−0.0415674	−	0.0113231i
$573$		0			0
$574$	−7.95622e10	−	1.04134e11i	−0.732924	−	0.959281i
$575$		−	2.53913e9i		−	0.0232281i
$576$		0			0
$577$	5.21900e10			0.470852			0.235426	−	0.971892i	$-0.424352\pi$
$577$	5.21900e10			0.470852			0.235426	+	0.971892i	$0.424352\pi$
$578$	8.34364e10	−	6.37483e10i	0.747557	−	0.571159i
$579$		0			0
$580$	−1.68554e10	+	6.18765e10i	−0.148945	+	0.546782i
$581$	1.64069e11			1.43986
$582$		0			0
$583$		−	1.02535e10i		−	0.0887563i
$584$	−3.74494e10	−	9.20276e10i	−0.321954	−	0.791164i
$585$		0			0
$586$	−8.08883e10	+	6.18015e10i	−0.685954	+	0.524093i
$587$		−	1.32515e11i		−	1.11612i	−0.829800	−	0.558060i	$-0.811546\pi$
$587$		−	1.32515e11i		−	1.11612i	0.829800	−	0.558060i	$-0.188454\pi$
$588$		0			0
$589$	−1.68963e11			−1.40388
$590$	7.95571e9	+	1.04128e10i	0.0656555	+	0.0859326i
$591$		0			0
$592$	1.63804e11	+	9.63944e10i	1.33364	+	0.784811i
$593$	−4.90676e10			−0.396804			−0.198402	−	0.980121i	$-0.563575\pi$
$593$	−4.90676e10			−0.396804			−0.198402	+	0.980121i	$0.563575\pi$
$594$		0			0
$595$			1.70708e10i			0.136203i
$596$	−5.78305e10	+	2.12297e11i	−0.458323	+	1.68252i
$597$		0			0
$598$	−6.83644e9	−	8.94782e9i	−0.0534596	−	0.0699701i
$599$			1.81971e11i			1.41350i	0.707463	+	0.706750i	$0.249840\pi$
$599$			1.81971e11i			1.41350i	−0.707463	+	0.706750i	$0.750160\pi$
$600$		0			0
$601$	−2.45349e11			−1.88056			−0.940279	−	0.340404i	$-0.889436\pi$
$601$	−2.45349e11			−1.88056			−0.940279	+	0.340404i	$0.889436\pi$
$602$	1.51008e11	−	1.15376e11i	1.14978	−	0.878472i
$603$		0			0
$604$	−1.07608e11	−	2.93127e10i	−0.808530	−	0.220246i
$605$	−5.97217e10			−0.445770
$606$		0			0
$607$			2.67477e11i			1.97029i	0.171713	+	0.985147i	$0.445070\pi$
$607$			2.67477e11i			1.97029i	−0.171713	+	0.985147i	$0.554930\pi$
$608$	1.98936e10	+	1.64262e11i	0.145579	+	1.20205i
$609$		0			0
$610$	6.00241e10	−	4.58605e10i	0.433517	−	0.331222i
$611$		−	4.35088e10i		−	0.312185i
$612$		0			0
$613$	1.87562e11			1.32832			0.664159	−	0.747591i	$-0.268790\pi$
$613$	1.87562e11			1.32832			0.664159	+	0.747591i	$0.268790\pi$
$614$	−1.32941e11	−	1.73998e11i	−0.935372	−	1.22425i
$615$		0			0
$616$	−3.85949e9	−	9.48424e9i	−0.0268045	−	0.0658688i
$617$	−4.25269e10			−0.293442			−0.146721	−	0.989178i	$-0.546872\pi$
$617$	−4.25269e10			−0.293442			−0.146721	+	0.989178i	$0.546872\pi$
$618$		0			0
$619$		−	2.22095e11i		−	1.51278i	−0.654120	−	0.756390i	$-0.726961\pi$
$619$		−	2.22095e11i		−	1.51278i	0.654120	−	0.756390i	$-0.273039\pi$
$620$	−7.39236e10	−	2.01370e10i	−0.500284	−	0.136279i
$621$		0			0
$622$	1.36032e11	+	1.78044e11i	0.908822	+	1.18950i
$623$		−	1.37181e10i		−	0.0910632i
$624$		0			0
$625$	6.10352e9			0.0400000
$626$	−2.55390e10	+	1.95127e10i	−0.166306	+	0.127063i
$627$		0			0
$628$	3.33989e10	−	1.22608e11i	0.214730	−	0.788280i
$629$	5.89456e10			0.376573
$630$		0			0
$631$		−	1.04087e11i		−	0.656569i	−0.944579	−	0.328285i	$-0.893530\pi$
$631$		−	1.04087e11i		−	0.656569i	0.944579	−	0.328285i	$-0.106470\pi$
$632$	−4.68422e10	+	1.90618e10i	−0.293609	+	0.119480i
$633$		0			0
$634$	1.88191e11	−	1.43785e11i	1.16478	−	0.889929i
$635$			7.43797e10i			0.457467i
$636$		0			0
$637$	7.06868e10			0.429319
$638$	−7.24300e9	−	9.47994e9i	−0.0437155	−	0.0572167i
$639$		0			0
$640$	−1.08731e10	+	7.42380e10i	−0.0648087	+	0.442493i
$641$	−2.56180e11			−1.51744			−0.758721	−	0.651415i	$-0.774176\pi$
$641$	−2.56180e11			−1.51744			−0.758721	+	0.651415i	$0.774176\pi$
$642$		0			0
$643$		−	1.12785e11i		−	0.659793i	−0.944017	−	0.329897i	$-0.892986\pi$
$643$		−	1.12785e11i		−	0.659793i	0.944017	−	0.329897i	$-0.107014\pi$
$644$	6.57092e9	−	2.41220e10i	0.0382017	−	0.140239i
$645$		0			0
$646$	3.11548e10	+	4.07767e10i	0.178893	+	0.234143i
$647$		−	7.84013e10i		−	0.447410i	−0.974657	−	0.223705i	$-0.928185\pi$
$647$		−	7.84013e10i		−	0.447410i	0.974657	−	0.223705i	$-0.0718153\pi$
$648$		0			0
$649$	−2.43775e9			−0.0137407
$650$	2.15086e10	−	1.64334e10i	0.120492	−	0.0920604i
$651$		0			0
$652$	2.20387e10	+	6.00340e9i	0.121954	+	0.0332206i
$653$	−4.72264e10			−0.259736			−0.129868	−	0.991531i	$-0.541455\pi$
$653$	−4.72264e10			−0.259736			−0.129868	+	0.991531i	$0.541455\pi$
$654$		0			0
$655$			2.63479e10i			0.143147i
$656$	−1.53958e11	−	9.06004e10i	−0.831357	−	0.489232i
$657$		0			0
$658$	7.67591e10	−	5.86466e10i	0.409474	−	0.312852i
$659$		−	6.47551e10i		−	0.343346i	−0.985154	−	0.171673i	$-0.945083\pi$
$659$		−	6.47551e10i		−	0.343346i	0.985154	−	0.171673i	$-0.0549173\pi$
$660$		0			0
$661$	−2.89406e11			−1.51601			−0.758004	−	0.652250i	$-0.773825\pi$
$661$	−2.89406e11			−1.51601			−0.758004	+	0.652250i	$0.773825\pi$
$662$	−9.27911e10	−	1.21449e11i	−0.483142	−	0.632356i
$663$		0			0
$664$	2.07152e11	−	8.42978e10i	1.06565	−	0.433655i
$665$	1.32531e11			0.677688
$666$		0			0
$667$		−	2.91292e10i		−	0.147172i
$668$	−1.73896e11	−	4.73698e10i	−0.873339	−	0.237901i
$669$		0			0
$670$	2.47273e10	+	3.23641e10i	0.122709	+	0.160607i
$671$			1.40523e10i			0.0693199i
$672$		0			0
$673$	−2.02037e11			−0.984850			−0.492425	−	0.870355i	$-0.663889\pi$
$673$	−2.02037e11			−0.984850			−0.492425	+	0.870355i	$0.663889\pi$
$674$	−4.87156e10	+	3.72204e10i	−0.236063	+	0.180360i
$675$		0			0
$676$	−2.33351e10	+	8.56639e10i	−0.111744	+	0.410214i
$677$	−1.05704e11			−0.503194			−0.251597	−	0.967832i	$-0.580956\pi$
$677$	−1.05704e11			−0.503194			−0.251597	+	0.967832i	$0.580956\pi$
$678$		0			0
$679$		−	1.94845e11i		−	0.916662i
$680$	8.77089e9	+	2.15534e10i	0.0410212	+	0.100805i
$681$		0			0
$682$	1.13256e10	−	8.65318e9i	0.0523510	−	0.0399980i
$683$		−	2.21093e11i		−	1.01600i	−0.861358	−	0.507999i	$-0.830385\pi$
$683$		−	2.21093e11i		−	1.01600i	0.861358	−	0.507999i	$-0.169615\pi$
$684$		0			0
$685$	−1.18660e11			−0.538940
$686$	−7.29856e10	−	9.55266e10i	−0.329565	−	0.431348i
$687$		0			0
$688$	1.31382e11	−	2.23260e11i	0.586386	−	0.996452i
$689$	2.66886e11			1.18426
$690$		0			0
$691$		−	6.28628e10i		−	0.275728i	−0.990451	−	0.137864i	$-0.955976\pi$
$691$		−	6.28628e10i		−	0.275728i	0.990451	−	0.137864i	$-0.0440237\pi$
$692$	5.70862e10	−	2.09565e11i	0.248947	−	0.913890i
$693$		0			0
$694$	−2.10298e11	−	2.75246e11i	−0.906560	−	1.18654i
$695$			1.35505e11i			0.580785i
$696$		0			0
$697$	−5.54026e10			−0.234746
$698$	9.91154e9	−	7.57276e9i	0.0417560	−	0.0319031i
$699$		0			0
$700$	5.79841e10	+	1.57951e10i	0.241500	+	0.0657854i
$701$	−3.50718e11			−1.45240			−0.726200	−	0.687484i	$-0.758715\pi$
$701$	−3.50718e11			−1.45240			−0.726200	+	0.687484i	$0.758715\pi$
$702$		0			0
$703$		−	4.57631e11i		−	1.87367i
$704$	−9.74592e9	−	9.99174e9i	−0.0396764	−	0.0406771i
$705$		0			0
$706$	2.15805e10	−	1.64883e10i	0.0868646	−	0.0663676i
$707$		−	6.87165e10i		−	0.275032i
$708$		0			0
$709$	6.64455e10			0.262955			0.131477	−	0.991319i	$-0.458028\pi$
$709$	6.64455e10			0.262955			0.131477	+	0.991319i	$0.458028\pi$
$710$	−6.56658e10	−	8.59461e10i	−0.258408	−	0.338215i
$711$		0			0
$712$	−7.04832e9	−	1.73204e10i	−0.0274262	−	0.0673966i
$713$	3.48005e10			0.134657
$714$		0			0
$715$			5.03542e9i			0.0192669i
$716$	4.43326e11	+	1.20764e11i	1.68683	+	0.459498i
$717$		0			0
$718$	2.18942e11	+	2.86561e11i	0.823819	+	1.07825i
$719$		−	5.29534e11i		−	1.98143i	−0.135969	−	0.990713i	$-0.543415\pi$
$719$		−	5.29534e11i		−	1.98143i	0.135969	−	0.990713i	$-0.456585\pi$
$720$		0			0
$721$	−8.56708e9			−0.0317024
$722$	1.00647e11	−	7.68981e10i	0.370385	−	0.282987i
$723$		0			0
$724$	−1.33742e11	+	4.90972e11i	−0.486760	+	1.78691i
$725$	7.00203e10			0.253438
$726$		0			0
$727$			5.50891e10i			0.197210i	0.995127	+	0.0986048i	$0.0314380\pi$
$727$			5.50891e10i			0.197210i	−0.995127	+	0.0986048i	$0.968562\pi$
$728$	2.46862e11	−	1.00457e11i	0.878879	−	0.357648i
$729$		0			0
$730$	−8.61994e10	+	6.58593e10i	−0.303538	+	0.231913i
$731$		−	8.03410e10i		−	0.281363i
$732$		0			0
$733$	1.00150e11			0.346925			0.173462	−	0.984840i	$-0.444504\pi$
$733$	1.00150e11			0.346925			0.173462	+	0.984840i	$0.444504\pi$
$734$	−5.92867e10	−	7.75968e10i	−0.204255	−	0.267337i
$735$		0			0
$736$	−4.09739e9	−	3.38324e10i	−0.0139636	−	0.115298i
$737$	−7.57681e9			−0.0256813
$738$		0			0
$739$		−	3.32835e11i		−	1.11597i	−0.829852	−	0.557984i	$-0.811575\pi$
$739$		−	3.32835e11i		−	1.11597i	0.829852	−	0.557984i	$-0.188425\pi$
$740$	5.45406e10	−	2.00220e11i	0.181883	−	0.667699i
$741$		0			0
$742$	3.59742e11	+	4.70845e11i	1.18679	+	1.55333i
$743$		−	3.73853e11i		−	1.22672i	−0.789803	−	0.613361i	$-0.789817\pi$
$743$		−	3.73853e11i		−	1.22672i	0.789803	−	0.613361i	$-0.210183\pi$
$744$		0			0
$745$	2.40238e11			0.779862
$746$	1.20001e10	−	9.16847e9i	0.0387461	−	0.0296034i
$747$		0			0
$748$	−4.17664e9	−	1.13773e9i	−0.0133420	−	0.00363440i
$749$	7.39152e11			2.34859
$750$		0			0
$751$		−	3.24815e11i		−	1.02112i	−0.859843	−	0.510559i	$-0.829438\pi$
$751$		−	3.24815e11i		−	1.02112i	0.859843	−	0.510559i	$-0.170562\pi$
$752$	6.67830e10	−	1.13485e11i	0.208831	−	0.354869i
$753$		0			0
$754$	2.46750e11	−	1.88526e11i	0.763435	−	0.583290i
$755$			1.21771e11i			0.374761i
$756$		0			0
$757$	−1.97773e11			−0.602261			−0.301130	−	0.953583i	$-0.597364\pi$
$757$	−1.97773e11			−0.602261			−0.301130	+	0.953583i	$0.597364\pi$
$758$	8.64961e10	+	1.13210e11i	0.262011	+	0.342931i
$759$		0			0
$760$	1.67332e11	−	6.80937e10i	0.501563	−	0.204105i
$761$	−3.73737e10			−0.111436			−0.0557182	−	0.998447i	$-0.517745\pi$
$761$	−3.73737e10			−0.111436			−0.0557182	+	0.998447i	$0.517745\pi$
$762$		0			0
$763$		−	1.23833e11i		−	0.365374i
$764$	−5.31891e11	−	1.44889e11i	−1.56117	−	0.425267i
$765$		0			0
$766$	1.69695e11	+	2.22104e11i	0.492895	+	0.645121i
$767$		−	6.34513e10i		−	0.183341i
$768$		0			0
$769$	−5.76381e11			−1.64818			−0.824089	−	0.566461i	$-0.808312\pi$
$769$	−5.76381e11			−1.64818			−0.824089	+	0.566461i	$0.808312\pi$
$770$	−8.88360e9	+	6.78738e9i	−0.0252712	+	0.0193081i
$771$		0			0
$772$	−1.28320e11	+	4.71065e11i	−0.361264	+	1.32621i
$773$	−6.50692e11			−1.82246			−0.911229	−	0.411901i	$-0.864865\pi$
$773$	−6.50692e11			−1.82246			−0.911229	+	0.411901i	$0.864865\pi$
$774$		0			0
$775$			8.36530e10i			0.231886i
$776$	−1.00110e11	−	2.46009e11i	−0.276078	−	0.678429i
$777$		0			0
$778$	−6.61192e10	+	5.05174e10i	−0.180472	+	0.137887i
$779$			4.30124e11i			1.16800i
$780$		0			0
$781$	2.01210e10			0.0540810
$782$	−6.41682e9	−	8.39860e9i	−0.0171590	−	0.0224584i
$783$		0			0
$784$	1.84374e11	+	1.08499e11i	0.488019	+	0.287186i
$785$	−1.38745e11			−0.365375
$786$		0			0
$787$			4.70164e10i			0.122560i	0.998121	+	0.0612802i	$0.0195183\pi$
$787$			4.70164e10i			0.122560i	−0.998121	+	0.0612802i	$0.980482\pi$
$788$	−4.55834e10	+	1.67338e11i	−0.118223	+	0.433999i
$789$		0			0
$790$	3.35225e10	+	4.38756e10i	0.0860653	+	0.112646i
$791$		−	5.29700e11i		−	1.35308i
$792$		0			0
$793$	−3.65763e11			−0.924926
$794$	−3.32409e11	+	2.53972e11i	−0.836355	+	0.639004i
$795$		0			0
$796$	7.47151e10	+	2.03527e10i	0.186104	+	0.0506954i
$797$	−6.03770e11			−1.49637			−0.748184	−	0.663491i	$-0.769074\pi$
$797$	−6.03770e11			−1.49637			−0.748184	+	0.663491i	$0.769074\pi$
$798$		0			0
$799$		−	4.08382e10i		−	0.100203i
$800$	8.13258e10	−	9.84926e9i	0.198549	−	0.0240460i
$801$		0			0
$802$	−1.34308e11	+	1.02616e11i	−0.324643	+	0.248038i
$803$		−	2.01803e10i		−	0.0485361i
$804$		0			0
$805$	−2.72968e10			−0.0650022
$806$	2.25231e11	+	2.94791e11i	0.533688	+	0.698513i
$807$		0			0
$808$	−3.53062e10	−	8.67609e10i	−0.0828335	−	0.203554i
$809$	−7.70557e10			−0.179891			−0.0899457	−	0.995947i	$-0.528669\pi$
$809$	−7.70557e10			−0.179891			−0.0899457	+	0.995947i	$0.528669\pi$
$810$		0			0
$811$			1.94344e11i			0.449249i	0.974445	+	0.224625i	$0.0721156\pi$
$811$			1.94344e11i			0.449249i	−0.974445	+	0.224625i	$0.927884\pi$
$812$	6.65202e11	+	1.81203e11i	1.53013	+	0.416814i
$813$		0			0
$814$	2.34369e10	+	3.06752e10i	0.0533830	+	0.0698698i
$815$		−	2.49393e10i		−	0.0565266i
$816$		0			0
$817$	−6.23736e11			−1.39995
$818$	−3.49810e11	+	2.67267e11i	−0.781303	+	0.596942i
$819$		0			0
$820$	−5.12623e10	+	1.88185e11i	−0.113382	+	0.416227i
$821$	3.09723e11			0.681711			0.340855	−	0.940116i	$-0.389283\pi$
$821$	3.09723e11			0.681711			0.340855	+	0.940116i	$0.389283\pi$
$822$		0			0
$823$			2.51180e11i			0.547501i	0.961801	+	0.273751i	$0.0882643\pi$
$823$			2.51180e11i			0.547501i	−0.961801	+	0.273751i	$0.911736\pi$
$824$	−1.08167e10	+	4.40173e9i	−0.0234632	+	0.00954804i
$825$		0			0
$826$	1.11942e11	−	8.55277e10i	0.240477	−	0.183733i
$827$			7.61654e11i			1.62830i	0.580652	+	0.814152i	$0.302798\pi$
$827$			7.61654e11i			1.62830i	−0.580652	+	0.814152i	$0.697202\pi$
$828$		0			0
$829$	−5.23232e11			−1.10784			−0.553919	−	0.832570i	$-0.686868\pi$
$829$	−5.23232e11			−1.10784			−0.553919	+	0.832570i	$0.686868\pi$
$830$	−1.48248e11	−	1.94033e11i	−0.312375	−	0.408849i
$831$		0			0
$832$	2.60072e11	−	2.53673e11i	0.542750	−	0.529397i
$833$	6.63479e10			0.137799
$834$		0			0
$835$			1.96783e11i			0.404801i
$836$	−8.83289e9	+	3.24258e10i	−0.0180833	+	0.0663843i
$837$		0			0
$838$	−8.03452e10	−	1.05159e11i	−0.162923	−	0.213241i
$839$			6.98976e11i			1.41063i	0.708892	+	0.705317i	$0.249195\pi$
$839$			6.98976e11i			1.41063i	−0.708892	+	0.705317i	$0.750805\pi$
$840$		0			0
$841$	3.03036e11			0.605774
$842$	−4.26228e11	+	3.25653e11i	−0.847996	+	0.647899i
$843$		0			0
$844$	−1.65594e11	−	4.51084e10i	−0.326344	−	0.0888971i
$845$	9.69384e10			0.190138
$846$		0			0
$847$			6.42036e11i			1.24746i
$848$	6.96126e11	+	4.09652e11i	1.34618	+	0.792193i
$849$		0			0
$850$	2.01884e10	−	1.54247e10i	0.0386747	−	0.0295488i
$851$			9.42563e10i			0.179718i
$852$		0			0
$853$	−7.55391e11			−1.42684			−0.713421	−	0.700736i	$-0.752855\pi$
$853$	−7.55391e11			−1.42684			−0.713421	+	0.700736i	$0.752855\pi$
$854$	−4.93022e11	−	6.45287e11i	−0.926903	−	1.21317i
$855$		0			0
$856$	9.33248e11	−	3.79773e11i	1.73821	−	0.707342i
$857$	8.88963e10			0.164801			0.0824006	−	0.996599i	$-0.473741\pi$
$857$	8.88963e10			0.164801			0.0824006	+	0.996599i	$0.473741\pi$
$858$		0			0
$859$		−	9.88172e10i		−	0.181493i	−0.995874	−	0.0907465i	$-0.971075\pi$
$859$		−	9.88172e10i		−	0.181493i	0.995874	−	0.0907465i	$-0.0289253\pi$
$860$	−2.72893e11	−	7.43371e10i	−0.498884	−	0.135898i
$861$		0			0
$862$	−8.04460e9	−	1.05291e10i	−0.0145705	−	0.0190705i
$863$		−	7.06320e11i		−	1.27338i	−0.771119	−	0.636691i	$-0.780303\pi$
$863$		−	7.06320e11i		−	1.27338i	0.771119	−	0.636691i	$-0.219697\pi$
$864$		0			0
$865$	−2.37147e11			−0.423597
$866$	−1.26359e11	+	9.65429e10i	−0.224665	+	0.171652i
$867$		0			0
$868$	−2.16483e11	+	7.94714e11i	−0.381368	+	1.40001i
$869$	−1.02718e10			−0.0180122
$870$		0			0
$871$		−	1.97214e11i		−	0.342662i
$872$	−6.36248e10	−	1.56350e11i	−0.110042	−	0.270416i
$873$		0			0
$874$	−6.52034e10	+	4.98176e10i	−0.111744	+	0.0853763i
$875$		−	6.56157e10i		−	0.111937i
$876$		0			0
$877$	8.57602e11			1.44973			0.724865	−	0.688891i	$-0.241902\pi$
$877$	8.57602e11			1.44973			0.724865	+	0.688891i	$0.241902\pi$
$878$	5.11741e11	+	6.69787e11i	0.861136	+	1.12709i
$879$		0			0
$880$	−7.72904e9	+	1.31340e10i	−0.0128883	+	0.0219012i
$881$	6.85802e11			1.13840			0.569201	−	0.822199i	$-0.307253\pi$
$881$	6.85802e11			1.13840			0.569201	+	0.822199i	$0.307253\pi$
$882$		0			0
$883$			4.88217e11i			0.803101i	0.915837	+	0.401551i	$0.131529\pi$
$883$			4.88217e11i			0.803101i	−0.915837	+	0.401551i	$0.868471\pi$
$884$	2.96136e10	−	1.08712e11i	0.0484933	−	0.178020i
$885$		0			0
$886$	−3.71693e10	−	4.86487e10i	−0.0603184	−	0.0789472i
$887$			1.02206e12i			1.65113i	0.564308	+	0.825564i	$0.309143\pi$
$887$			1.02206e12i			1.65113i	−0.564308	+	0.825564i	$0.690857\pi$
$888$		0			0
$889$	7.99617e11			1.28019
$890$	−1.62235e10	+	1.23953e10i	−0.0258574	+	0.0197559i
$891$		0			0
$892$	−4.83625e11	−	1.31741e11i	−0.763923	−	0.208095i
$893$	−3.17051e11			−0.498567
$894$		0			0
$895$		−	5.01674e11i		−	0.781862i
$896$	7.98093e11	+	1.16891e11i	1.23829	+	0.181363i
$897$		0			0
$898$	−6.14167e11	+	4.69245e11i	−0.944455	+	0.721597i
$899$			9.59678e11i			1.46922i
$900$		0			0
$901$	2.50504e11			0.380115
$902$	−2.20282e10	−	2.88314e10i	−0.0332776	−	0.0435551i
$903$		0			0
$904$	−2.72157e11	−	6.68794e11i	−0.407517	−	1.00143i
$905$	5.55590e11			0.828248
$906$		0			0
$907$		−	7.83608e11i		−	1.15790i	−0.815364	−	0.578949i	$-0.803463\pi$
$907$		−	7.83608e11i		−	1.15790i	0.815364	−	0.578949i	$-0.196537\pi$
$908$	1.10805e12	+	3.01836e11i	1.63010	+	0.444046i
$909$		0			0
$910$	−1.76666e11	−	2.31228e11i	−0.257625	−	0.337190i
$911$		−	7.34304e11i		−	1.06611i	−0.846080	−	0.533056i	$-0.821044\pi$
$911$		−	7.34304e11i		−	1.06611i	0.846080	−	0.533056i	$-0.178956\pi$
$912$		0			0
$913$	4.54253e10			0.0653754
$914$	−7.74901e11	+	5.92051e11i	−1.11035	+	0.848349i
$915$		0			0
$916$	−1.92829e11	+	7.07881e11i	−0.273899	+	1.00549i
$917$	2.83253e11			0.400587
$918$		0			0
$919$			4.92475e11i			0.690434i	0.938523	+	0.345217i	$0.112195\pi$
$919$			4.92475e11i			0.690434i	−0.938523	+	0.345217i	$0.887805\pi$
$920$	−3.44647e10	+	1.40250e10i	−0.0481087	+	0.0195772i
$921$		0			0
$922$	5.84493e11	−	4.46573e11i	0.808827	−	0.617972i
$923$			5.23722e11i			0.721595i
$924$		0			0
$925$	−2.26572e11			−0.309485
$926$	−6.28341e11	−	8.22398e11i	−0.854577	−	1.11851i
$927$		0			0
$928$	9.32980e11	−	1.12992e11i	1.25800	−	0.152355i
$929$	1.45211e12			1.94956			0.974779	−	0.223173i	$-0.0716415\pi$
$929$	1.45211e12			1.94956			0.974779	+	0.223173i	$0.0716415\pi$
$930$		0			0
$931$		−	5.15099e11i		−	0.685634i
$932$	−2.73996e11	+	1.00585e12i	−0.363146	+	1.33312i
$933$		0			0
$934$	5.75233e11	+	7.52888e11i	0.755886	+	0.989334i
$935$			4.72634e9i			0.00618413i
$936$		0			0
$937$	9.33377e10			0.121087			0.0605437	−	0.998166i	$-0.480717\pi$
$937$	9.33377e10			0.121087			0.0605437	+	0.998166i	$0.480717\pi$
$938$	3.47930e11	−	2.65830e11i	0.449448	−	0.343394i
$939$		0			0
$940$	−1.38715e11	−	3.77863e10i	−0.177669	−	0.0483975i
$941$	−1.02235e12			−1.30389			−0.651946	−	0.758265i	$-0.726047\pi$
$941$	−1.02235e12			−1.30389			−0.651946	+	0.758265i	$0.726047\pi$
$942$		0			0
$943$		−	8.85908e10i		−	0.112032i
$944$	9.73935e10	−	1.65502e11i	0.122643	−	0.208408i
$945$		0			0
$946$	4.18093e10	−	3.19437e10i	0.0522045	−	0.0398861i
$947$		−	1.02824e11i		−	0.127849i	−0.997955	−	0.0639243i	$-0.979638\pi$
$947$		−	1.02824e11i		−	0.127849i	0.997955	−	0.0639243i	$-0.0203616\pi$
$948$		0			0
$949$	5.25265e11			0.647611
$950$	−1.19751e11	−	1.56735e11i	−0.147023	−	0.192429i
$951$		0			0
$952$	2.31710e11	−	9.42912e10i	0.282095	−	0.114795i
$953$	−1.13956e12			−1.38154			−0.690771	−	0.723074i	$-0.742729\pi$
$953$	−1.13956e12			−1.38154			−0.690771	+	0.723074i	$0.742729\pi$
$954$		0			0
$955$			6.01896e11i			0.723615i
$956$	7.79871e11	+	2.12439e11i	0.933665	+	0.254333i
$957$		0			0
$958$	−6.85970e11	−	8.97827e11i	−0.814411	−	1.06593i
$959$			1.27565e12i			1.50819i
$960$		0			0
$961$	−2.93633e11			−0.344279
$962$	−7.98434e11	+	6.10031e11i	−0.932264	+	0.712282i
$963$		0			0
$964$	9.47293e10	−	3.47754e11i	0.109692	−	0.402683i
$965$	5.33064e11			0.614710
$966$		0			0
$967$		−	1.18968e12i		−	1.36058i	−0.732942	−	0.680291i	$-0.761853\pi$
$967$		−	1.18968e12i		−	1.36058i	0.732942	−	0.680291i	$-0.238147\pi$
$968$	3.29875e11	+	8.10630e11i	0.375706	+	0.923254i
$969$		0			0
$970$	−2.30429e11	+	1.76056e11i	−0.260286	+	0.198867i
$971$		−	8.30442e11i		−	0.934184i	−0.884209	−	0.467092i	$-0.845302\pi$
$971$		−	8.30442e11i		−	0.934184i	0.884209	−	0.467092i	$-0.154698\pi$
$972$		0			0
$973$	1.45674e12			1.62529
$974$	−9.32186e11	−	1.22008e12i	−1.03578	−	1.35567i
$975$		0			0
$976$	−9.54031e11	−	5.61422e11i	−1.05139	−	0.618714i
$977$	6.84728e10			0.0751518			0.0375759	−	0.999294i	$-0.488036\pi$
$977$	6.84728e10			0.0751518			0.0375759	+	0.999294i	$0.488036\pi$
$978$		0			0
$979$		−	3.79811e9i		−	0.00413463i
$980$	6.13898e10	−	2.25363e11i	0.0665567	−	0.244331i
$981$		0			0
$982$	−8.67282e11	−	1.13513e12i	−0.932640	−	1.22068i
$983$			7.69855e11i			0.824508i	0.911069	+	0.412254i	$0.135258\pi$
$983$			7.69855e11i			0.824508i	−0.911069	+	0.412254i	$0.864742\pi$
$984$		0			0
$985$	1.89362e11			0.201163
$986$	2.31604e11	−	1.76954e11i	0.245041	−	0.187220i
$987$		0			0
$988$	−8.43999e11	−	2.29908e11i	−0.885756	−	0.241283i
$989$	1.28468e11			0.134280
$990$		0			0
$991$			5.04152e11i			0.522717i	0.965242	+	0.261359i	$0.0841705\pi$
$991$			5.04152e11i			0.522717i	−0.965242	+	0.261359i	$0.915829\pi$
$992$	1.34991e11	+	1.11463e12i	0.139399	+	1.15102i
$993$		0			0
$994$	−9.23961e11	+	7.05938e11i	−0.946473	+	0.723138i
$995$		−	8.45487e10i		−	0.0862610i
$996$		0			0
$997$	3.36752e11			0.340823			0.170412	−	0.985373i	$-0.445490\pi$
$997$	3.36752e11			0.340823			0.170412	+	0.985373i	$0.445490\pi$
$998$	−1.52457e11	−	1.99542e11i	−0.153683	−	0.201146i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.9.c.b.91.8	yes	32
3.2	odd	2	inner	180.9.c.b.91.25	yes	32
4.3	odd	2	inner	180.9.c.b.91.7	✓	32
12.11	even	2	inner	180.9.c.b.91.26	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.9.c.b.91.7	✓	32	4.3	odd	2	inner
180.9.c.b.91.8	yes	32	1.1	even	1	trivial
180.9.c.b.91.25	yes	32	3.2	odd	2	inner
180.9.c.b.91.26	yes	32	12.11	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	180.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-12.7138 + 9.71382i) q^{2} +(67.2836 - 247.000i) q^{4} -279.508 q^{5} +3004.85i q^{7} +(1543.88 + 3793.90i) q^{8} +(3553.63 - 2715.09i) q^{10} +831.945i q^{11} -21654.4 q^{13} +(-29188.5 - 38203.2i) q^{14} +(-56481.8 - 33238.1i) q^{16} -20325.2 q^{17} +157797. i q^{19} +(-18806.3 + 69038.6i) q^{20} +(-8081.36 - 10577.2i) q^{22} -32500.8i q^{23} +78125.0 q^{25} +(275311. - 210347. i) q^{26} +(742197. + 202177. i) q^{28} +896260. q^{29} +1.07076e6i q^{31} +(1.04097e6 - 126071. i) q^{32} +(258412. - 197436. i) q^{34} -839881. i q^{35} -2.90012e6 q^{37} +(-1.53281e6 - 2.00621e6i) q^{38} +(-431527. - 1.06043e6i) q^{40} +2.72580e6 q^{41} +3.95277e6i q^{43} +(205490. + 55976.2i) q^{44} +(315707. + 413210. i) q^{46} +2.00923e6i q^{47} -3.26431e6 q^{49} +(-993269. + 758892. i) q^{50} +(-1.45699e6 + 5.34863e6i) q^{52} -1.23248e7 q^{53} -232536. i q^{55} +(-1.14001e7 + 4.63912e6i) q^{56} +(-1.13949e7 + 8.70611e6i) q^{58} +2.93018e6i q^{59} +1.68909e7 q^{61} +(-1.04011e7 - 1.36135e7i) q^{62} +(-1.20101e7 + 1.17146e7i) q^{64} +6.05259e6 q^{65} +9.10735e6i q^{67} +(-1.36756e6 + 5.02033e6i) q^{68} +(8.15845e6 + 1.06781e7i) q^{70} -2.41855e7i q^{71} -2.42567e7 q^{73} +(3.68717e7 - 2.81712e7i) q^{74} +(3.89759e7 + 1.06172e7i) q^{76} -2.49987e6 q^{77} +1.23467e7i q^{79} +(1.57872e7 + 9.29032e6i) q^{80} +(-3.46554e7 + 2.64779e7i) q^{82} -5.46013e7i q^{83} +5.68108e6 q^{85} +(-3.83965e7 - 5.02549e7i) q^{86} +(-3.15631e6 + 1.28442e6i) q^{88} -4.56533e6 q^{89} -6.50682e7i q^{91} +(-8.02770e6 - 2.18677e6i) q^{92} +(-1.95173e7 - 2.55451e7i) q^{94} -4.41056e7i q^{95} -6.48434e7 q^{97} +(4.15020e7 - 3.17089e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 610 q^{4} - 8750 q^{10} - 51392 q^{13} + 11986 q^{16} - 758068 q^{22} + 2500000 q^{25} + 976324 q^{28} - 6117428 q^{34} + 5152064 q^{37} - 96250 q^{40} - 10391752 q^{46} - 11002976 q^{49} + 13976584 q^{52}+ \cdots + 80579520 q^{97}+O(q^{100}) \) 32 * q + 610 * q^4 - 8750 * q^10 - 51392 * q^13 + 11986 * q^16 - 758068 * q^22 + 2500000 * q^25 + 976324 * q^28 - 6117428 * q^34 + 5152064 * q^37 - 96250 * q^40 - 10391752 * q^46 - 11002976 * q^49 + 13976584 * q^52 - 36333948 * q^58 - 7802048 * q^61 + 116259994 * q^64 - 49897500 * q^70 - 94303680 * q^73 + 248840592 * q^76 - 428557904 * q^82 + 106960000 * q^85 + 510719924 * q^88 - 692727576 * q^94 + 80579520 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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