LMFDB - Embedded newform 234.8.h.c.55.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,8,Mod(55,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.55"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	234.h (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-32,0,-256,386] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$73.0980959633$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3 x^{7} - 14114 x^{6} + 42351 x^{5} + 205543918 x^{4} + 13390412127 x^{3} + \cdots + 28150431267204 $ x^8 - 3x^7 - 14114x^6 + 42351x^5 + 205543918x^4 + 13390412127x^3 + 374804224653x^2 + 5032619029638*x + 28150431267204
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{3}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.3
Root			$-80.7401 + 46.6153i$ of defining polynomial
Character	$\chi$	$=$	234.55
Dual form			234.8.h.c.217.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.00000 - 6.92820i) q^{2} +(-32.0000 + 55.4256i) q^{4} +292.365 q^{5} +(682.601 - 1182.30i) q^{7} +512.000 q^{8} +(-1169.46 - 2025.56i) q^{10} +(-3147.44 - 5451.52i) q^{11} +(-519.190 - 7904.36i) q^{13} -10921.6 q^{14} +(-2048.00 - 3547.24i) q^{16} +(7071.69 - 12248.5i) q^{17} +(-24494.2 + 42425.1i) q^{19} +(-9355.67 + 16204.5i) q^{20} +(-25179.5 + 43612.2i) q^{22} +(-27761.4 - 48084.2i) q^{23} +7352.11 q^{25} +(-52686.3 + 35214.5i) q^{26} +(43686.5 + 75667.2i) q^{28} +(-29134.9 - 50463.2i) q^{29} +96117.8 q^{31} +(-16384.0 + 28377.9i) q^{32} -113147. q^{34} +(199568. - 345663. i) q^{35} +(126083. + 218382. i) q^{37} +391907. q^{38} +149691. q^{40} +(-226376. - 392094. i) q^{41} +(-298773. + 517491. i) q^{43} +402872. q^{44} +(-222092. + 384674. i) q^{46} +879720. q^{47} +(-520116. - 900868. i) q^{49} +(-29408.4 - 50936.9i) q^{50} +(454718. + 224163. i) q^{52} -1.19574e6 q^{53} +(-920200. - 1.59383e6i) q^{55} +(349492. - 605337. i) q^{56} +(-233080. + 403706. i) q^{58} +(366838. - 635382. i) q^{59} +(37257.1 - 64531.2i) q^{61} +(-384471. - 665924. i) q^{62} +262144. q^{64} +(-151793. - 2.31096e6i) q^{65} +(295983. + 512658. i) q^{67} +(452588. + 783906. i) q^{68} -3.19309e6 q^{70} +(-298650. + 517277. i) q^{71} +602204. q^{73} +(1.00866e6 - 1.74705e6i) q^{74} +(-1.56763e6 - 2.71521e6i) q^{76} -8.59377e6 q^{77} +5.60729e6 q^{79} +(-598763. - 1.03709e6i) q^{80} +(-1.81100e6 + 3.13675e6i) q^{82} -6.43871e6 q^{83} +(2.06751e6 - 3.58104e6i) q^{85} +4.78037e6 q^{86} +(-1.61149e6 - 2.79118e6i) q^{88} +(5.94525e6 + 1.02975e7i) q^{89} +(-9.69972e6 - 4.78169e6i) q^{91} +3.55346e6 q^{92} +(-3.51888e6 - 6.09488e6i) q^{94} +(-7.16123e6 + 1.24036e7i) q^{95} +(-7.90111e6 + 1.36851e7i) q^{97} +(-4.16093e6 + 7.20694e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{2} - 256 q^{4} + 386 q^{5} + 757 q^{7} + 4096 q^{8} - 1544 q^{10} - 4524 q^{11} + 13272 q^{13} - 12112 q^{14} - 16384 q^{16} + 12775 q^{17} + 38646 q^{19} - 12352 q^{20} - 36192 q^{22} - 24428 q^{23}+ \cdots + 4224696 q^{98}+O(q^{100}) $ 8 * q - 32 * q^2 - 256 * q^4 + 386 * q^5 + 757 * q^7 + 4096 * q^8 - 1544 * q^10 - 4524 * q^11 + 13272 * q^13 - 12112 * q^14 - 16384 * q^16 + 12775 * q^17 + 38646 * q^19 - 12352 * q^20 - 36192 * q^22 - 24428 * q^23 + 305798 * q^25 - 90552 * q^26 + 48448 * q^28 - 22109 * q^29 + 42558 * q^31 - 131072 * q^32 - 204400 * q^34 + 190892 * q^35 + 372411 * q^37 - 618336 * q^38 + 197632 * q^40 - 266009 * q^41 - 399935 * q^43 + 579072 * q^44 - 195424 * q^46 + 487344 * q^47 + 528087 * q^49 - 1223192 * q^50 - 124992 * q^52 - 3351434 * q^53 - 1572842 * q^55 + 387584 * q^56 - 176872 * q^58 - 1025370 * q^59 + 260650 * q^61 - 170232 * q^62 + 2097152 * q^64 + 59673 * q^65 - 2382807 * q^67 + 817600 * q^68 - 3054272 * q^70 - 1773980 * q^71 - 3903260 * q^73 + 2979288 * q^74 + 2473344 * q^76 - 17541708 * q^77 + 11678674 * q^79 - 790528 * q^80 - 2128072 * q^82 + 20314044 * q^83 - 5236237 * q^85 + 6398960 * q^86 - 2316288 * q^88 + 1108942 * q^89 - 29498671 * q^91 + 3126784 * q^92 - 1949376 * q^94 - 10481054 * q^95 - 7003183 * q^97 + 4224696 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−4.00000	−	6.92820i	−0.353553	−	0.612372i
$2$	−4.00000	−	6.92820i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−32.0000	+	55.4256i	−0.250000	+	0.433013i
$5$	292.365			1.04600			0.522998	−	0.852334i	$-0.324814\pi$
$5$	292.365			1.04600			0.522998	+	0.852334i	$0.324814\pi$
$6$		0			0
$7$	682.601	−	1182.30i	0.752183	−	1.30282i	−0.194579	−	0.980887i	$-0.562334\pi$
$7$	682.601	−	1182.30i	0.752183	−	1.30282i	0.946763	−	0.321933i	$-0.104333\pi$
$8$	512.000			0.353553
$9$		0			0
$10$	−1169.46	−	2025.56i	−0.369815	−	0.640539i
$11$	−3147.44	−	5451.52i	−0.712989	−	1.23493i	−0.963730	−	0.266879i	$-0.914008\pi$
$11$	−3147.44	−	5451.52i	−0.712989	−	1.23493i	0.250741	−	0.968054i	$-0.419326\pi$
$12$		0			0
$13$	−519.190	−	7904.36i	−0.0655428	−	0.997850i
$13$	−519.190	−	7904.36i	−0.0655428	−	0.997850i
$14$	−10921.6			−1.06375
$15$		0			0
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	7071.69	−	12248.5i	0.349102	−	0.604662i	−0.636988	−	0.770873i	$-0.719820\pi$
$17$	7071.69	−	12248.5i	0.349102	−	0.604662i	0.986090	+	0.166212i	$0.0531534\pi$
$18$		0			0
$19$	−24494.2	+	42425.1i	−0.819266	+	1.41901i	0.0869571	+	0.996212i	$0.472286\pi$
$19$	−24494.2	+	42425.1i	−0.819266	+	1.41901i	−0.906224	+	0.422799i	$0.861048\pi$
$20$	−9355.67	+	16204.5i	−0.261499	+	0.452929i
$21$		0			0
$22$	−25179.5	+	43612.2i	−0.504159	+	0.873229i
$23$	−27761.4	−	48084.2i	−0.475767	−	0.824053i	0.523847	−	0.851812i	$-0.324496\pi$
$23$	−27761.4	−	48084.2i	−0.475767	−	0.824053i	−0.999615	+	0.0277591i	$0.991163\pi$
$24$		0			0
$25$	7352.11			0.0941070
$26$	−52686.3	+	35214.5i	−0.587883	+	0.392930i
$27$		0			0
$28$	43686.5	+	75667.2i	0.376092	+	0.651410i
$29$	−29134.9	−	50463.2i	−0.221831	−	0.384222i	0.733533	−	0.679653i	$-0.237870\pi$
$29$	−29134.9	−	50463.2i	−0.221831	−	0.384222i	−0.955364	+	0.295432i	$0.904537\pi$
$30$		0			0
$31$	96117.8			0.579479			0.289740	−	0.957105i	$-0.406431\pi$
$31$	96117.8			0.579479			0.289740	+	0.957105i	$0.406431\pi$
$32$	−16384.0	+	28377.9i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−113147.			−0.493704
$35$	199568.	−	345663.i	0.786780	−	1.36274i
$36$		0			0
$37$	126083.	+	218382.i	0.409213	+	0.708778i	0.994802	−	0.101831i	$-0.0324700\pi$
$37$	126083.	+	218382.i	0.409213	+	0.708778i	−0.585589	+	0.810608i	$0.699137\pi$
$38$	391907.			1.15862
$39$		0			0
$40$	149691.			0.369815
$41$	−226376.	−	392094.i	−0.512963	−	0.888478i	−0.999887	−	0.0150337i	$-0.995214\pi$
$41$	−226376.	−	392094.i	−0.512963	−	0.888478i	0.486924	−	0.873444i	$-0.338119\pi$
$42$		0			0
$43$	−298773.	+	517491.i	−0.573063	+	0.992574i	0.423186	+	0.906043i	$0.360912\pi$
$43$	−298773.	+	517491.i	−0.573063	+	0.992574i	−0.996249	+	0.0865313i	$0.972422\pi$
$44$	402872.			0.712989
$45$		0			0
$46$	−222092.	+	384674.i	−0.336418	+	0.582694i
$47$	879720.			1.23595			0.617977	−	0.786196i	$-0.287953\pi$
$47$	879720.			1.23595			0.617977	+	0.786196i	$0.287953\pi$
$48$		0			0
$49$	−520116.	−	900868.i	−0.631559	−	1.09389i
$50$	−29408.4	−	50936.9i	−0.0332718	−	0.0576285i
$51$		0			0
$52$	454718.	+	224163.i	0.448467	+	0.221082i
$53$	−1.19574e6			−1.10324			−0.551622	−	0.834094i	$-0.685991\pi$
$53$	−1.19574e6			−1.10324			−0.551622	+	0.834094i	$0.685991\pi$
$54$		0			0
$55$	−920200.	−	1.59383e6i	−0.745783	−	1.29173i
$56$	349492.	−	605337.i	0.265937	−	0.460616i
$57$		0			0
$58$	−233080.	+	403706.i	−0.156858	+	0.271686i
$59$	366838.	−	635382.i	0.232537	−	0.402766i	−0.726017	−	0.687677i	$-0.758631\pi$
$59$	366838.	−	635382.i	0.232537	−	0.402766i	0.958554	+	0.284911i	$0.0919640\pi$
$60$		0			0
$61$	37257.1	−	64531.2i	0.0210162	−	0.0364011i	−0.855326	−	0.518090i	$-0.826643\pi$
$61$	37257.1	−	64531.2i	0.0210162	−	0.0364011i	0.876342	+	0.481689i	$0.159977\pi$
$62$	−384471.	−	665924.i	−0.204877	−	0.354857i
$63$		0			0
$64$	262144.			0.125000
$65$	−151793.	−	2.31096e6i	−0.0685574	−	1.04375i
$66$		0			0
$67$	295983.	+	512658.i	0.120228	+	0.208241i	0.919857	−	0.392253i	$-0.128304\pi$
$67$	295983.	+	512658.i	0.120228	+	0.208241i	−0.799630	+	0.600494i	$0.794971\pi$
$68$	452588.	+	783906.i	0.174551	+	0.302331i
$69$		0			0
$70$	−3.19309e6			−1.11268
$71$	−298650.	+	517277.i	−0.0990280	+	0.171521i	−0.911283	−	0.411782i	$-0.864907\pi$
$71$	−298650.	+	517277.i	−0.0990280	+	0.171521i	0.812255	+	0.583303i	$0.198240\pi$
$72$		0			0
$73$	602204.			0.181182			0.0905908	−	0.995888i	$-0.471124\pi$
$73$	602204.			0.181182			0.0905908	+	0.995888i	$0.471124\pi$
$74$	1.00866e6	−	1.74705e6i	0.289357	−	0.501181i
$75$		0			0
$76$	−1.56763e6	−	2.71521e6i	−0.409633	−	0.709505i
$77$	−8.59377e6			−2.14519
$78$		0			0
$79$	5.60729e6			1.27955			0.639776	−	0.768561i	$-0.279027\pi$
$79$	5.60729e6			1.27955			0.639776	+	0.768561i	$0.279027\pi$
$80$	−598763.	−	1.03709e6i	−0.130749	−	0.226465i
$81$		0			0
$82$	−1.81100e6	+	3.13675e6i	−0.362720	+	0.628249i
$83$	−6.43871e6			−1.23602			−0.618010	−	0.786170i	$-0.712061\pi$
$83$	−6.43871e6			−1.23602			−0.618010	+	0.786170i	$0.712061\pi$
$84$		0			0
$85$	2.06751e6	−	3.58104e6i	0.365159	−	0.632474i
$86$	4.78037e6			0.810433
$87$		0			0
$88$	−1.61149e6	−	2.79118e6i	−0.252080	−	0.436615i
$89$	5.94525e6	+	1.02975e7i	0.893933	+	1.54834i	0.835119	+	0.550069i	$0.185399\pi$
$89$	5.94525e6	+	1.02975e7i	0.893933	+	1.54834i	0.0588141	+	0.998269i	$0.481268\pi$
$90$		0			0
$91$	−9.69972e6	−	4.78169e6i	−1.34932	−	0.665175i
$92$	3.55346e6			0.475767
$93$		0			0
$94$	−3.51888e6	−	6.09488e6i	−0.436975	−	0.756864i
$95$	−7.16123e6	+	1.24036e7i	−0.856949	+	1.48428i
$96$		0			0
$97$	−7.90111e6	+	1.36851e7i	−0.878996	+	1.52247i	−0.0265515	+	0.999647i	$0.508453\pi$
$97$	−7.90111e6	+	1.36851e7i	−0.878996	+	1.52247i	−0.852444	+	0.522818i	$0.824881\pi$
$98$	−4.16093e6	+	7.20694e6i	−0.446580	+	0.773499i
$99$		0			0
$100$	−235267.	+	407495.i	−0.0235267	+	0.0407495i
$101$	6.12652e6	+	1.06114e7i	0.591683	+	1.02482i	0.994006	+	0.109327i	$0.0348695\pi$
$101$	6.12652e6	+	1.06114e7i	0.591683	+	1.02482i	−0.402323	+	0.915498i	$0.631797\pi$
$102$		0			0
$103$	9.45306e6			0.852398			0.426199	−	0.904629i	$-0.359852\pi$
$103$	9.45306e6			0.852398			0.426199	+	0.904629i	$0.359852\pi$
$104$	−265825.	−	4.04703e6i	−0.0231729	−	0.352793i
$105$		0			0
$106$	4.78296e6	+	8.28433e6i	0.390056	+	0.675596i
$107$	−1.06857e7	−	1.85082e7i	−0.843260	−	1.46057i	−0.887124	−	0.461531i	$-0.847300\pi$
$107$	−1.06857e7	−	1.85082e7i	−0.843260	−	1.46057i	0.0438646	−	0.999037i	$-0.486033\pi$
$108$		0			0
$109$	−1.40494e7			−1.03912			−0.519559	−	0.854435i	$-0.673904\pi$
$109$	−1.40494e7			−1.03912			−0.519559	+	0.854435i	$0.673904\pi$
$110$	−7.36160e6	+	1.27507e7i	−0.527348	+	0.913394i
$111$		0			0
$112$	−5.59187e6			−0.376092
$113$	2.00220e6	−	3.46791e6i	0.130537	−	0.226096i	−0.793347	−	0.608770i	$-0.791663\pi$
$113$	2.00220e6	−	3.46791e6i	0.130537	−	0.226096i	0.923884	+	0.382674i	$0.124997\pi$
$114$		0			0
$115$	−8.11646e6	−	1.40581e7i	−0.497651	−	0.861956i
$116$	3.72927e6			0.221831
$117$		0			0
$118$	−5.86941e6			−0.328857
$119$	−9.65428e6	−	1.67217e7i	−0.525177	−	0.909633i
$120$		0			0
$121$	−1.00691e7	+	1.74403e7i	−0.516706	+	0.894961i
$122$	−596113.			−0.0297214
$123$		0			0
$124$	−3.07577e6	+	5.32739e6i	−0.144870	+	0.250922i
$125$	−2.06915e7			−0.947560
$126$		0			0
$127$	−1.99573e7	−	3.45671e7i	−0.864548	−	1.49744i	−0.867495	−	0.497446i	$-0.834271\pi$
$127$	−1.99573e7	−	3.45671e7i	−0.864548	−	1.49744i	0.00294673	−	0.999996i	$-0.499062\pi$
$128$	−1.04858e6	−	1.81619e6i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−1.54036e7	+	1.02955e7i	−0.614923	+	0.411003i
$131$	2.63495e7			1.02405			0.512027	−	0.858969i	$-0.328895\pi$
$131$	2.63495e7			1.02405			0.512027	+	0.858969i	$0.328895\pi$
$132$		0			0
$133$	3.34395e7	+	5.79189e7i	1.23248	+	2.13471i
$134$	2.36786e6	−	4.10126e6i	0.0850139	−	0.147248i
$135$		0			0
$136$	3.62070e6	−	6.27124e6i	0.123426	−	0.213780i
$137$	2.14607e7	−	3.71710e7i	0.713052	−	1.23504i	−0.250654	−	0.968077i	$-0.580646\pi$
$137$	2.14607e7	−	3.71710e7i	0.713052	−	1.23504i	0.963706	−	0.266966i	$-0.0860210\pi$
$138$		0			0
$139$	−2.04074e7	+	3.53466e7i	−0.644518	+	1.11634i	0.339895	+	0.940463i	$0.389608\pi$
$139$	−2.04074e7	+	3.53466e7i	−0.644518	+	1.11634i	−0.984413	+	0.175874i	$0.943725\pi$
$140$	1.27724e7	+	2.21224e7i	0.393390	+	0.681372i
$141$		0			0
$142$	4.77840e6			0.140047
$143$	−4.14567e7	+	2.77089e7i	−1.18555	+	0.792397i
$144$		0			0
$145$	−8.51803e6	−	1.47537e7i	−0.232034	−	0.401894i
$146$	−2.40882e6	−	4.17219e6i	−0.0640573	−	0.110951i
$147$		0			0
$148$	−1.61386e7			−0.409213
$149$	−9.52509e6	+	1.64979e7i	−0.235894	+	0.408581i	−0.959532	−	0.281599i	$-0.909135\pi$
$149$	−9.52509e6	+	1.64979e7i	−0.235894	+	0.408581i	0.723638	+	0.690180i	$0.242469\pi$
$150$		0			0
$151$	−3.29124e7			−0.777929			−0.388965	−	0.921253i	$-0.627167\pi$
$151$	−3.29124e7			−0.777929			−0.388965	+	0.921253i	$0.627167\pi$
$152$	−1.25410e7	+	2.17217e7i	−0.289654	+	0.501696i
$153$		0			0
$154$	3.43751e7	+	5.95394e7i	0.758440	+	1.31366i
$155$	2.81015e7			0.606133
$156$		0			0
$157$	−9.18409e7			−1.89403			−0.947016	−	0.321187i	$-0.895918\pi$
$157$	−9.18409e7			−1.89403			−0.947016	+	0.321187i	$0.895918\pi$
$158$	−2.24292e7	−	3.88484e7i	−0.452390	−	0.783563i
$159$		0			0
$160$	−4.79010e6	+	8.29670e6i	−0.0924538	+	0.160135i
$161$	−7.57999e7			−1.43146
$162$		0			0
$163$	1.40858e7	−	2.43972e7i	0.254755	−	0.441249i	−0.710074	−	0.704127i	$-0.751338\pi$
$163$	1.40858e7	−	2.43972e7i	0.254755	−	0.441249i	0.964829	+	0.262878i	$0.0846717\pi$
$164$	2.89761e7			0.512963
$165$		0			0
$166$	2.57549e7	+	4.46087e7i	0.436999	+	0.756905i
$167$	−1.93187e7	−	3.34610e7i	−0.320975	−	0.555945i	0.659714	−	0.751516i	$-0.270677\pi$
$167$	−1.93187e7	−	3.34610e7i	−0.320975	−	0.555945i	−0.980689	+	0.195571i	$0.937344\pi$
$168$		0			0
$169$	−6.22094e7	+	8.20774e6i	−0.991408	+	0.130804i
$170$	−3.30802e7			−0.516413
$171$		0			0
$172$	−1.91215e7	−	3.31194e7i	−0.286531	−	0.496287i
$173$	130701.	−	226380.i	0.00191918	−	0.00332412i	−0.865064	−	0.501661i	$-0.832722\pi$
$173$	130701.	−	226380.i	0.00191918	−	0.00332412i	0.866983	+	0.498337i	$0.166056\pi$
$174$		0			0
$175$	5.01855e6	−	8.69239e6i	0.0707857	−	0.122604i
$176$	−1.28919e7	+	2.23294e7i	−0.178247	+	0.308733i
$177$		0			0
$178$	4.75620e7	−	8.23798e7i	0.632106	−	1.09484i
$179$	−2.19120e6	−	3.79527e6i	−0.0285560	−	0.0494604i	0.851394	−	0.524526i	$-0.175758\pi$
$179$	−2.19120e6	−	3.79527e6i	−0.0285560	−	0.0494604i	−0.879950	+	0.475066i	$0.842424\pi$
$180$		0			0
$181$	−2.70440e7			−0.338997			−0.169499	−	0.985530i	$-0.554215\pi$
$181$	−2.70440e7			−0.338997			−0.169499	+	0.985530i	$0.554215\pi$
$182$	5.67039e6	+	8.63284e7i	0.0697210	+	1.06146i
$183$		0			0
$184$	−1.42139e7	−	2.46191e7i	−0.168209	−	0.291347i
$185$	3.68621e7	+	6.38471e7i	0.428035	+	0.741378i
$186$		0			0
$187$	−8.90308e7			−0.995622
$188$	−2.81510e7	+	4.87590e7i	−0.308988	+	0.535183i
$189$		0			0
$190$	1.14580e8			1.21191
$191$	4.82447e7	−	8.35623e7i	0.500995	−	0.867748i	−0.499005	−	0.866599i	$-0.666301\pi$
$191$	4.82447e7	−	8.35623e7i	0.500995	−	0.867748i	0.999999	−	0.00114877i	$-0.000365666\pi$
$192$		0			0
$193$	−1.05389e7	−	1.82539e7i	−0.105523	−	0.182770i	0.808429	−	0.588594i	$-0.200318\pi$
$193$	−1.05389e7	−	1.82539e7i	−0.105523	−	0.182770i	−0.913952	+	0.405823i	$0.866985\pi$
$194$	1.26418e8			1.24309
$195$		0			0
$196$	6.65749e7			0.631559
$197$	−8.09174e7	−	1.40153e8i	−0.754068	−	1.30608i	−0.945837	−	0.324643i	$-0.894756\pi$
$197$	−8.09174e7	−	1.40153e8i	−0.754068	−	1.30608i	0.191769	−	0.981440i	$-0.438578\pi$
$198$		0			0
$199$	1.08635e8	−	1.88161e8i	0.977201	−	1.69256i	0.304728	−	0.952440i	$-0.401435\pi$
$199$	1.08635e8	−	1.88161e8i	0.977201	−	1.69256i	0.672473	−	0.740122i	$-0.265232\pi$
$200$	3.76428e6			0.0332718
$201$		0			0
$202$	4.90121e7	−	8.48915e7i	0.418383	−	0.724660i
$203$	−7.95502e7			−0.667429
$204$		0			0
$205$	−6.61842e7	−	1.14634e8i	−0.536557	−	0.929344i
$206$	−3.78123e7	−	6.54927e7i	−0.301368	−	0.521985i
$207$		0			0
$208$	−2.69754e7	+	1.80298e7i	−0.207848	+	0.138922i
$209$	3.08375e8			2.33651
$210$		0			0
$211$	1.01779e8	+	1.76286e8i	0.745881	+	1.29190i	0.949782	+	0.312913i	$0.101305\pi$
$211$	1.01779e8	+	1.76286e8i	0.745881	+	1.29190i	−0.203901	+	0.978992i	$0.565362\pi$
$212$	3.82637e7	−	6.62747e7i	0.275811	−	0.477718i
$213$		0			0
$214$	−8.54859e7	+	1.48066e8i	−0.596275	+	1.03278i
$215$	−8.73508e7	+	1.51296e8i	−0.599421	+	1.03823i
$216$		0			0
$217$	6.56101e7	−	1.13640e8i	0.435875	−	0.754957i
$218$	5.61975e7	+	9.73370e7i	0.367383	+	0.636327i
$219$		0			0
$220$	1.17786e8			0.745783
$221$	−1.00488e8	−	4.95379e7i	−0.626243	−	0.308720i
$222$		0			0
$223$	−1.74200e7	−	3.01723e7i	−0.105192	−	0.182197i	0.808625	−	0.588325i	$-0.200212\pi$
$223$	−1.74200e7	−	3.01723e7i	−0.105192	−	0.182197i	−0.913816	+	0.406127i	$0.866879\pi$
$224$	2.23675e7	+	3.87416e7i	0.132968	+	0.230308i
$225$		0			0
$226$	−3.20352e7			−0.184607
$227$	4.81864e7	−	8.34613e7i	0.273422	−	0.473581i	−0.696314	−	0.717738i	$-0.745178\pi$
$227$	4.81864e7	−	8.34613e7i	0.273422	−	0.473581i	0.969736	+	0.244156i	$0.0785110\pi$
$228$		0			0
$229$	1.90546e8			1.04852			0.524260	−	0.851559i	$-0.324342\pi$
$229$	1.90546e8			1.04852			0.524260	+	0.851559i	$0.324342\pi$
$230$	−6.49317e7	+	1.12465e8i	−0.351892	+	0.609495i
$231$		0			0
$232$	−1.49171e7	−	2.58372e7i	−0.0784289	−	0.135843i
$233$	4.84822e7			0.251094			0.125547	−	0.992088i	$-0.459931\pi$
$233$	4.84822e7			0.251094			0.125547	+	0.992088i	$0.459931\pi$
$234$		0			0
$235$	2.57199e8			1.29280
$236$	2.34776e7	+	4.06644e7i	0.116269	+	0.201383i
$237$		0			0
$238$	−7.72343e7	+	1.33774e8i	−0.371356	+	0.643208i
$239$	9.77332e7			0.463073			0.231537	−	0.972826i	$-0.425625\pi$
$239$	9.77332e7			0.463073			0.231537	+	0.972826i	$0.425625\pi$
$240$		0			0
$241$	1.40752e8	−	2.43789e8i	0.647731	−	1.12190i	−0.335932	−	0.941886i	$-0.609051\pi$
$241$	1.40752e8	−	2.43789e8i	0.647731	−	1.12190i	0.983663	−	0.180017i	$-0.0576153\pi$
$242$	1.61106e8			0.730733
$243$		0			0
$244$	2.38445e6	+	4.12999e6i	0.0105081	+	0.0182006i
$245$	−1.52064e8	−	2.63382e8i	−0.660608	−	1.14421i
$246$		0			0
$247$	3.48061e8	+	1.71584e8i	1.46966	+	0.724499i
$248$	4.92123e7			0.204877
$249$		0			0
$250$	8.27660e7	+	1.43355e8i	0.335013	+	0.580260i
$251$	4.65639e7	−	8.06511e7i	0.185863	−	0.321923i	−0.758004	−	0.652250i	$-0.773825\pi$
$251$	4.65639e7	−	8.06511e7i	0.185863	−	0.321923i	0.943867	+	0.330326i	$0.107159\pi$
$252$		0			0
$253$	−1.74755e8	+	3.02684e8i	−0.678434	+	1.17508i
$254$	−1.59659e8	+	2.76537e8i	−0.611328	+	1.05885i
$255$		0			0
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	−1.66536e8	−	2.88448e8i	−0.611986	−	1.05999i	−0.990905	−	0.134561i	$-0.957038\pi$
$257$	−1.66536e8	−	2.88448e8i	−0.611986	−	1.05999i	0.378920	−	0.925430i	$-0.376296\pi$
$258$		0			0
$259$	3.44257e8			1.23121
$260$	1.32944e8	+	6.55374e7i	0.469095	+	0.231250i
$261$		0			0
$262$	−1.05398e8	−	1.82555e8i	−0.362058	−	0.627102i
$263$	6.25613e7	+	1.08359e8i	0.212061	+	0.367300i	0.952359	−	0.304978i	$-0.0986491\pi$
$263$	6.25613e7	+	1.08359e8i	0.212061	+	0.367300i	−0.740298	+	0.672278i	$0.765316\pi$
$264$		0			0
$265$	−3.49592e8			−1.15399
$266$	2.67516e8	−	4.63351e8i	0.871493	−	1.50947i
$267$		0			0
$268$	−3.78858e7			−0.120228
$269$	1.50279e8	−	2.60291e8i	0.470723	−	0.815317i	−0.528716	−	0.848799i	$-0.677326\pi$
$269$	1.50279e8	−	2.60291e8i	0.470723	−	0.815317i	0.999439	+	0.0334822i	$0.0106597\pi$
$270$		0			0
$271$	−2.43902e8	−	4.22451e8i	−0.744428	−	1.28939i	−0.950461	−	0.310843i	$-0.899389\pi$
$271$	−2.43902e8	−	4.22451e8i	−0.744428	−	1.28939i	0.206033	−	0.978545i	$-0.433945\pi$
$272$	−5.79313e7			−0.174551
$273$		0			0
$274$	−3.43371e8			−1.00841
$275$	−2.31403e7	−	4.00802e7i	−0.0670972	−	0.116216i
$276$		0			0
$277$	−1.83303e8	+	3.17491e8i	−0.518193	+	0.897537i	0.481584	+	0.876400i	$0.340062\pi$
$277$	−1.83303e8	+	3.17491e8i	−0.518193	+	0.897537i	−0.999777	+	0.0211365i	$0.993272\pi$
$278$	3.26518e8			0.911486
$279$		0			0
$280$	1.02179e8	−	1.76979e8i	0.278169	−	0.481803i
$281$	−1.05557e6			−0.00283802			−0.00141901	−	0.999999i	$-0.500452\pi$
$281$	−1.05557e6			−0.00283802			−0.00141901	+	0.999999i	$0.500452\pi$
$282$		0			0
$283$	−3.05192e8	−	5.28608e8i	−0.800425	−	1.38638i	−0.919336	−	0.393472i	$-0.871274\pi$
$283$	−3.05192e8	−	5.28608e8i	−0.800425	−	1.38638i	0.118911	−	0.992905i	$-0.462060\pi$
$284$	−1.91136e7	−	3.31057e7i	−0.0495140	−	0.0857607i
$285$		0			0
$286$	3.57799e8	+	1.76385e8i	0.904396	+	0.445841i
$287$	−6.18097e8			−1.54337
$288$		0			0
$289$	1.05152e8	+	1.82128e8i	0.256256	+	0.443848i
$290$	−6.81442e7	+	1.18029e8i	−0.164073	+	0.284182i
$291$		0			0
$292$	−1.92705e7	+	3.33776e7i	−0.0452954	+	0.0784539i
$293$	−2.49118e8	+	4.31485e8i	−0.578587	+	1.00214i	0.417055	+	0.908881i	$0.363062\pi$
$293$	−2.49118e8	+	4.31485e8i	−0.578587	+	1.00214i	−0.995642	+	0.0932602i	$0.970271\pi$
$294$		0			0
$295$	1.07250e8	−	1.85763e8i	0.243233	−	0.421291i
$296$	6.45543e7	+	1.11811e8i	0.144679	+	0.250591i
$297$		0			0
$298$	1.52401e8			0.333605
$299$	−3.65662e8	+	2.44401e8i	−0.791098	+	0.528755i
$300$		0			0
$301$	4.07886e8	+	7.06479e8i	0.862097	+	1.49320i
$302$	1.31650e8	+	2.28024e8i	0.275040	+	0.476382i
$303$		0			0
$304$	2.00656e8			0.409633
$305$	1.08927e7	−	1.88666e7i	0.0219829	−	0.0380754i
$306$		0			0
$307$	4.97378e8			0.981075			0.490537	−	0.871420i	$-0.336801\pi$
$307$	4.97378e8			0.981075			0.490537	+	0.871420i	$0.336801\pi$
$308$	2.75001e8	−	4.76315e8i	0.536298	−	0.928896i
$309$		0			0
$310$	−1.12406e8	−	1.94693e8i	−0.214300	−	0.371179i
$311$	1.05279e9			1.98463			0.992317	−	0.123721i	$-0.0394829\pi$
$311$	1.05279e9			1.98463			0.992317	+	0.123721i	$0.0394829\pi$
$312$		0			0
$313$	−2.19688e8			−0.404950			−0.202475	−	0.979287i	$-0.564899\pi$
$313$	−2.19688e8			−0.404950			−0.202475	+	0.979287i	$0.564899\pi$
$314$	3.67364e8	+	6.36292e8i	0.669641	+	1.15985i
$315$		0			0
$316$	−1.79433e8	+	3.10787e8i	−0.319888	+	0.554062i
$317$	−9.50641e8			−1.67614			−0.838068	−	0.545567i	$-0.816315\pi$
$317$	−9.50641e8			−1.67614			−0.838068	+	0.545567i	$0.816315\pi$
$318$		0			0
$319$	−1.83401e8	+	3.17660e8i	−0.316325	+	0.547892i
$320$	7.66416e7			0.130749
$321$		0			0
$322$	3.03200e8	+	5.25157e8i	0.506096	+	0.876585i
$323$	3.46430e8	+	6.00035e8i	0.572015	+	0.990758i
$324$		0			0
$325$	−3.81714e6	−	5.81137e7i	−0.00616803	−	0.0939046i
$326$	−2.25372e8			−0.360279
$327$		0			0
$328$	−1.15904e8	−	2.00752e8i	−0.181360	−	0.314124i
$329$	6.00498e8	−	1.04009e9i	0.929663	−	1.61022i
$330$		0			0
$331$	5.48701e8	−	9.50379e8i	0.831645	−	1.44045i	−0.0650879	−	0.997880i	$-0.520733\pi$
$331$	5.48701e8	−	9.50379e8i	0.831645	−	1.44045i	0.896733	−	0.442572i	$-0.145934\pi$
$332$	2.06039e8	−	3.56870e8i	0.309005	−	0.535213i
$333$		0			0
$334$	−1.54550e8	+	2.67688e8i	−0.226964	+	0.393112i
$335$	8.65350e7	+	1.49883e8i	0.125758	+	0.217819i
$336$		0			0
$337$	4.21771e8			0.600305			0.300153	−	0.953891i	$-0.402962\pi$
$337$	4.21771e8			0.600305			0.300153	+	0.953891i	$0.402962\pi$
$338$	3.05702e8	+	3.98168e8i	0.430616	+	0.560865i
$339$		0			0
$340$	1.32321e8	+	2.29186e8i	0.182579	+	0.316237i
$341$	−3.02525e8	−	5.23989e8i	−0.413162	−	0.715618i
$342$		0			0
$343$	−2.95825e8			−0.395827
$344$	−1.52972e8	+	2.64955e8i	−0.202608	+	0.350928i
$345$		0			0
$346$	−2.09121e6			−0.00271414
$347$	−2.86132e8	+	4.95594e8i	−0.367631	+	0.636756i	−0.989195	−	0.146608i	$-0.953165\pi$
$347$	−2.86132e8	+	4.95594e8i	−0.367631	+	0.636756i	0.621563	+	0.783364i	$0.286498\pi$
$348$		0			0
$349$	5.47641e8	+	9.48542e8i	0.689616	+	1.19445i	0.971962	+	0.235137i	$0.0755539\pi$
$349$	5.47641e8	+	9.48542e8i	0.689616	+	1.19445i	−0.282347	+	0.959312i	$0.591113\pi$
$350$	−8.02969e7			−0.100106
$351$		0			0
$352$	2.06270e8			0.252080
$353$	−1.38676e8	−	2.40193e8i	−0.167799	−	0.290636i	0.769847	−	0.638229i	$-0.220332\pi$
$353$	−1.38676e8	−	2.40193e8i	−0.167799	−	0.290636i	−0.937646	+	0.347593i	$0.886999\pi$
$354$		0			0
$355$	−8.73146e7	+	1.51233e8i	−0.103583	+	0.179411i
$356$	−7.60992e8			−0.893933
$357$		0			0
$358$	−1.75296e7	+	3.03622e7i	−0.0201921	+	0.0349738i
$359$	−3.61517e8			−0.412380			−0.206190	−	0.978512i	$-0.566107\pi$
$359$	−3.61517e8			−0.412380			−0.206190	+	0.978512i	$0.566107\pi$
$360$		0			0
$361$	−7.52993e8	−	1.30422e9i	−0.842395	−	1.45907i
$362$	1.08176e8	+	1.87366e8i	0.119854	+	0.207592i
$363$		0			0
$364$	5.75419e8	−	3.84599e8i	0.625359	−	0.417978i
$365$	1.76063e8			0.189515
$366$		0			0
$367$	2.97065e8	+	5.14531e8i	0.313704	+	0.543351i	0.979161	−	0.203085i	$-0.0650967\pi$
$367$	2.97065e8	+	5.14531e8i	0.313704	+	0.543351i	−0.665457	+	0.746436i	$0.731763\pi$
$368$	−1.13711e8	+	1.96953e8i	−0.118942	+	0.206013i
$369$		0			0
$370$	2.94897e8	−	5.10777e8i	0.302666	−	0.524234i
$371$	−8.16213e8	+	1.41372e9i	−0.829841	+	1.43733i
$372$		0			0
$373$	2.49132e8	−	4.31510e8i	0.248570	−	0.430536i	−0.714559	−	0.699575i	$-0.753373\pi$
$373$	2.49132e8	−	4.31510e8i	0.248570	−	0.430536i	0.963129	+	0.269039i	$0.0867060\pi$
$374$	3.56123e8	+	6.16823e8i	0.352006	+	0.609692i
$375$		0			0
$376$	4.50417e8			0.436975
$377$	−3.83753e8	+	2.56493e8i	−0.368856	+	0.246536i
$378$		0			0
$379$	−8.71895e8	−	1.51017e9i	−0.822672	−	1.42491i	−0.903685	−	0.428197i	$-0.859149\pi$
$379$	−8.71895e8	−	1.51017e9i	−0.822672	−	1.42491i	0.0810133	−	0.996713i	$-0.474184\pi$
$380$	−4.58319e8	−	7.93831e8i	−0.428475	−	0.742140i
$381$		0			0
$382$	−7.71915e8			−0.708513
$383$	−5.61251e8	+	9.72116e8i	−0.510460	+	0.884143i	0.489466	+	0.872022i	$0.337192\pi$
$383$	−5.61251e8	+	9.72116e8i	−0.510460	+	0.884143i	−0.999927	+	0.0121206i	$0.996142\pi$
$384$		0			0
$385$	−2.51252e9			−2.24386
$386$	−8.43113e7	+	1.46031e8i	−0.0746157	+	0.129238i
$387$		0			0
$388$	−5.05671e8	−	8.75848e8i	−0.439498	−	0.761233i
$389$	1.36537e9			1.17605			0.588025	−	0.808843i	$-0.299906\pi$
$389$	1.36537e9			1.17605			0.588025	+	0.808843i	$0.299906\pi$
$390$		0			0
$391$	−7.85281e8			−0.664365
$392$	−2.66300e8	−	4.61244e8i	−0.223290	−	0.386750i
$393$		0			0
$394$	−6.47339e8	+	1.12122e9i	−0.533206	+	0.923540i
$395$	1.63937e9			1.33841
$396$		0			0
$397$	−1.36988e8	+	2.37270e8i	−0.109879	+	0.190316i	−0.915721	−	0.401814i	$-0.868380\pi$
$397$	−1.36988e8	+	2.37270e8i	−0.109879	+	0.190316i	0.805842	+	0.592131i	$0.201713\pi$
$398$	−1.73816e9			−1.38197
$399$		0			0
$400$	−1.50571e7	−	2.60797e7i	−0.0117634	−	0.0203748i
$401$	−4.37653e8	−	7.58037e8i	−0.338942	−	0.587064i	0.645292	−	0.763936i	$-0.276736\pi$
$401$	−4.37653e8	−	7.58037e8i	−0.338942	−	0.587064i	−0.984234	+	0.176872i	$0.943402\pi$
$402$		0			0
$403$	−4.99034e7	−	7.59750e8i	−0.0379807	−	0.578233i
$404$	−7.84194e8			−0.591683
$405$		0			0
$406$	3.18201e8	+	5.51140e8i	0.235972	+	0.408715i
$407$	7.93675e8	−	1.37468e9i	0.583529	−	1.01070i
$408$		0			0
$409$	−9.25251e6	+	1.60258e7i	−0.00668695	+	0.0115821i	−0.869350	−	0.494198i	$-0.835462\pi$
$409$	−9.25251e6	+	1.60258e7i	−0.00668695	+	0.0115821i	0.862663	+	0.505780i	$0.168795\pi$
$410$	−5.29474e8	+	9.17076e8i	−0.379403	+	0.657146i
$411$		0			0
$412$	−3.02498e8	+	5.23942e8i	−0.213099	+	0.369099i
$413$	−5.00808e8	−	8.67424e8i	−0.349821	−	0.605908i
$414$		0			0
$415$	−1.88245e9			−1.29287
$416$	2.32816e8	+	1.14772e8i	0.158557	+	0.0781641i
$417$		0			0
$418$	−1.23350e9	−	2.13649e9i	−0.826081	−	1.43082i
$419$	−8.70914e8	−	1.50847e9i	−0.578397	−	1.00181i	−0.995663	−	0.0930289i	$-0.970345\pi$
$419$	−8.70914e8	−	1.50847e9i	−0.578397	−	1.00181i	0.417266	−	0.908784i	$-0.362988\pi$
$420$		0			0
$421$	−1.06714e8			−0.0697005			−0.0348503	−	0.999393i	$-0.511095\pi$
$421$	−1.06714e8			−0.0697005			−0.0348503	+	0.999393i	$0.511095\pi$
$422$	8.14232e8	−	1.41029e9i	0.527418	−	0.913514i
$423$		0			0
$424$	−6.12219e8			−0.390056
$425$	5.19918e7	−	9.00525e7i	0.0328529	−	0.0569029i
$426$		0			0
$427$	−5.08634e7	−	8.80981e7i	−0.0316161	−	0.0547607i
$428$	1.36777e9			0.843260
$429$		0			0
$430$	1.39761e9			0.847710
$431$	−5.17174e8	−	8.95771e8i	−0.311147	−	0.538923i	0.667464	−	0.744642i	$-0.267380\pi$
$431$	−5.17174e8	−	8.95771e8i	−0.311147	−	0.538923i	−0.978611	+	0.205720i	$0.934047\pi$
$432$		0			0
$433$	−6.21572e8	+	1.07659e9i	−0.367946	+	0.637301i	−0.989244	−	0.146273i	$-0.953272\pi$
$433$	−6.21572e8	+	1.07659e9i	−0.367946	+	0.637301i	0.621298	+	0.783574i	$0.286605\pi$
$434$	−1.04976e9			−0.616420
$435$		0			0
$436$	4.49580e8	−	7.78696e8i	0.259779	−	0.449951i
$437$	2.71997e9			1.55912
$438$		0			0
$439$	1.10839e9	+	1.91980e9i	0.625272	+	1.08300i	0.988488	+	0.151297i	$0.0483451\pi$
$439$	1.10839e9	+	1.91980e9i	0.625272	+	1.08300i	−0.363217	+	0.931705i	$0.618322\pi$
$440$	−4.71142e8	−	8.16042e8i	−0.263674	−	0.456697i
$441$		0			0
$442$	5.87448e7	+	8.94355e8i	0.0323587	+	0.492643i
$443$	2.79640e8			0.152822			0.0764110	−	0.997076i	$-0.475654\pi$
$443$	2.79640e8			0.152822			0.0764110	+	0.997076i	$0.475654\pi$
$444$		0			0
$445$	1.73818e9	+	3.01062e9i	0.935050	+	1.61955i
$446$	−1.39360e8	+	2.41379e8i	−0.0743817	+	0.128833i
$447$		0			0
$448$	1.78940e8	−	3.09933e8i	0.0940229	−	0.162852i
$449$	−9.14533e8	+	1.58402e9i	−0.476801	+	0.825843i	−0.999647	−	0.0265839i	$-0.991537\pi$
$449$	−9.14533e8	+	1.58402e9i	−0.476801	+	0.825843i	0.522846	+	0.852427i	$0.324870\pi$
$450$		0			0
$451$	−1.42501e9	+	2.46818e9i	−0.731474	+	1.26695i
$452$	1.28141e8	+	2.21946e8i	0.0652684	+	0.113048i
$453$		0			0
$454$	−7.70982e8			−0.386678
$455$	−2.83586e9	−	1.39800e9i	−1.41138	−	0.695771i
$456$		0			0
$457$	3.61757e8	+	6.26581e8i	0.177301	+	0.307094i	0.940955	−	0.338532i	$-0.109930\pi$
$457$	3.61757e8	+	6.26581e8i	0.177301	+	0.307094i	−0.763654	+	0.645625i	$0.776597\pi$
$458$	−7.62185e8	−	1.32014e9i	−0.370707	−	0.642084i
$459$		0			0
$460$	1.03891e9			0.497651
$461$	1.73367e8	−	3.00281e8i	0.0824164	−	0.142749i	−0.821871	−	0.569674i	$-0.807070\pi$
$461$	1.73367e8	−	3.00281e8i	0.0824164	−	0.142749i	0.904287	+	0.426924i	$0.140403\pi$
$462$		0			0
$463$	−3.24685e9			−1.52030			−0.760149	−	0.649749i	$-0.774874\pi$
$463$	−3.24685e9			−1.52030			−0.760149	+	0.649749i	$0.774874\pi$
$464$	−1.19337e8	+	2.06697e8i	−0.0554576	+	0.0960554i
$465$		0			0
$466$	−1.93929e8	−	3.35895e8i	−0.0887752	−	0.153763i
$467$	9.84550e8			0.447331			0.223665	−	0.974666i	$-0.428198\pi$
$467$	9.84550e8			0.447331			0.223665	+	0.974666i	$0.428198\pi$
$468$		0			0
$469$	8.08153e8			0.361733
$470$	−1.02880e9	−	1.78193e9i	−0.457074	−	0.791676i
$471$		0			0
$472$	1.87821e8	−	3.25316e8i	0.0822143	−	0.142399i
$473$	3.76148e9			1.63435
$474$		0			0
$475$	−1.80084e8	+	3.11914e8i	−0.0770987	+	0.133539i
$476$	1.23575e9			0.525177
$477$		0			0
$478$	−3.90933e8	−	6.77116e8i	−0.163721	−	0.283573i
$479$	1.94101e9	+	3.36193e9i	0.806964	+	1.39770i	0.914957	+	0.403552i	$0.132224\pi$
$479$	1.94101e9	+	3.36193e9i	0.806964	+	1.39770i	−0.107993	+	0.994152i	$0.534442\pi$
$480$		0			0
$481$	1.66071e9	−	1.10998e9i	0.680433	−	0.454788i
$482$	−2.25203e9			−0.916030
$483$		0			0
$484$	−6.44425e8	−	1.11618e9i	−0.258353	−	0.447481i
$485$	−2.31000e9	+	4.00104e9i	−0.919426	+	1.59249i
$486$		0			0
$487$	−5.77838e8	+	1.00084e9i	−0.226702	+	0.392659i	−0.956829	−	0.290653i	$-0.906128\pi$
$487$	−5.77838e8	+	1.00084e9i	−0.226702	+	0.392659i	0.730127	+	0.683312i	$0.239461\pi$
$488$	1.90756e7	−	3.30400e7i	0.00743035	−	0.0128697i
$489$		0			0
$490$	−1.21651e9	+	2.10706e9i	−0.467121	+	0.809077i
$491$	−1.27998e9	−	2.21700e9i	−0.488000	−	0.845240i	0.511905	−	0.859042i	$-0.328940\pi$
$491$	−1.27998e9	−	2.21700e9i	−0.488000	−	0.845240i	−0.999905	+	0.0138019i	$0.995607\pi$
$492$		0			0
$493$	−8.24133e8			−0.309766
$494$	−2.03474e8	−	3.09777e9i	−0.0759390	−	1.15613i
$495$		0			0
$496$	−1.96849e8	−	3.40953e8i	−0.0724349	−	0.125461i
$497$	4.07717e8	+	7.06187e8i	0.148974	+	0.258031i
$498$		0			0
$499$	4.46390e9			1.60828			0.804142	−	0.594437i	$-0.202625\pi$
$499$	4.46390e9			1.60828			0.804142	+	0.594437i	$0.202625\pi$
$500$	6.62128e8	−	1.14684e9i	0.236890	−	0.410306i
$501$		0			0
$502$	−7.45023e8			−0.262849
$503$	−9.56502e8	+	1.65671e9i	−0.335118	+	0.580442i	−0.983508	−	0.180867i	$-0.942110\pi$
$503$	−9.56502e8	+	1.65671e9i	−0.335118	+	0.580442i	0.648389	+	0.761309i	$0.275443\pi$
$504$		0			0
$505$	1.79118e9	+	3.10241e9i	0.618898	+	1.07196i
$506$	2.79608e9			0.959450
$507$		0			0
$508$	2.55454e9			0.864548
$509$	1.30078e9	+	2.25303e9i	0.437213	+	0.757275i	0.997473	−	0.0710413i	$-0.0226322\pi$
$509$	1.30078e9	+	2.25303e9i	0.437213	+	0.757275i	−0.560260	+	0.828317i	$0.689299\pi$
$510$		0			0
$511$	4.11065e8	−	7.11986e8i	0.136282	−	0.236047i
$512$	1.34218e8			0.0441942
$513$		0			0
$514$	−1.33228e9	+	2.30759e9i	−0.432739	+	0.749526i
$515$	2.76374e9			0.891604
$516$		0			0
$517$	−2.76886e9	−	4.79581e9i	−0.881221	−	1.52632i
$518$	−1.37703e9	−	2.38508e9i	−0.435299	−	0.753961i
$519$		0			0
$520$	−7.77179e7	−	1.18321e9i	−0.0242387	−	0.369020i
$521$	7.28323e8			0.225627			0.112814	−	0.993616i	$-0.464014\pi$
$521$	7.28323e8			0.225627			0.112814	+	0.993616i	$0.464014\pi$
$522$		0			0
$523$	−5.32945e8	−	9.23087e8i	−0.162902	−	0.282154i	0.773006	−	0.634398i	$-0.218752\pi$
$523$	−5.32945e8	−	9.23087e8i	−0.162902	−	0.282154i	−0.935908	+	0.352244i	$0.885419\pi$
$524$	−8.43184e8	+	1.46044e9i	−0.256013	+	0.443428i
$525$		0			0
$526$	5.00491e8	−	8.66875e8i	0.149950	−	0.259721i
$527$	6.79715e8	−	1.17730e9i	0.202297	−	0.350389i
$528$		0			0
$529$	1.61018e8	−	2.78891e8i	0.0472910	−	0.0819104i
$530$	1.39837e9	+	2.42205e9i	0.407996	+	0.706670i
$531$		0			0
$532$	−4.28025e9			−1.23248
$533$	−2.98172e9	+	1.99293e9i	−0.852947	+	0.570093i
$534$		0			0
$535$	−3.12413e9	−	5.41116e9i	−0.882046	−	1.52775i
$536$	1.51543e8	+	2.62481e8i	0.0425070	+	0.0736242i
$537$		0			0
$538$	−2.40447e9			−0.665703
$539$	−3.27407e9	+	5.67085e9i	−0.900590	+	1.55987i
$540$		0			0
$541$	−3.60800e9			−0.979663			−0.489831	−	0.871817i	$-0.662942\pi$
$541$	−3.60800e9			−0.979663			−0.489831	+	0.871817i	$0.662942\pi$
$542$	−1.95122e9	+	3.37961e9i	−0.526390	+	0.911735i
$543$		0			0
$544$	2.31725e8	+	4.01360e8i	0.0617130	+	0.106890i
$545$	−4.10754e9			−1.08691
$546$		0			0
$547$	4.38462e9			1.14545			0.572726	−	0.819747i	$-0.305886\pi$
$547$	4.38462e9			1.14545			0.572726	+	0.819747i	$0.305886\pi$
$548$	1.37348e9	+	2.37894e9i	0.356526	+	0.617521i
$549$		0			0
$550$	−1.85122e8	+	3.20641e8i	−0.0474449	+	0.0821770i
$551$	2.85455e9			0.726953
$552$		0			0
$553$	3.82754e9	−	6.62949e9i	0.962458	−	1.66703i
$554$	2.93286e9			0.732836
$555$		0			0
$556$	−1.30607e9	−	2.26218e9i	−0.322259	−	0.558169i
$557$	−3.21953e9	−	5.57639e9i	−0.789405	−	1.36729i	−0.926332	−	0.376708i	$-0.877056\pi$
$557$	−3.21953e9	−	5.57639e9i	−0.789405	−	1.36729i	0.136927	−	0.990581i	$-0.456277\pi$
$558$		0			0
$559$	4.24555e9	+	2.09294e9i	1.02800	+	0.506775i
$560$	−1.63486e9			−0.393390
$561$		0			0
$562$	4.22228e6	+	7.31320e6i	0.00100339	+	0.00173792i
$563$	−7.73951e8	+	1.34052e9i	−0.182782	+	0.316588i	−0.942827	−	0.333283i	$-0.891844\pi$
$563$	−7.73951e8	+	1.34052e9i	−0.182782	+	0.316588i	0.760045	+	0.649871i	$0.225177\pi$
$564$		0			0
$565$	5.85373e8	−	1.01390e9i	0.136541	−	0.236496i
$566$	−2.44154e9	+	4.22887e9i	−0.565986	+	0.980317i
$567$		0			0
$568$	−1.52909e8	+	2.64846e8i	−0.0350117	+	0.0606420i
$569$	−1.33315e8	−	2.30909e8i	−0.0303380	−	0.0525469i	0.850458	−	0.526043i	$-0.176325\pi$
$569$	−1.33315e8	−	2.30909e8i	−0.0303380	−	0.0525469i	−0.880796	+	0.473496i	$0.842992\pi$
$570$		0			0
$571$	2.24474e9			0.504591			0.252296	−	0.967650i	$-0.418814\pi$
$571$	2.24474e9			0.504591			0.252296	+	0.967650i	$0.418814\pi$
$572$	−2.09167e8	−	3.18445e9i	−0.0467313	−	0.711456i
$573$		0			0
$574$	2.47239e9	+	4.28230e9i	0.545663	+	0.945117i
$575$	−2.04105e8	−	3.53520e8i	−0.0447730	−	0.0775491i
$576$		0			0
$577$	8.35240e9			1.81007			0.905036	−	0.425335i	$-0.139844\pi$
$577$	8.35240e9			1.81007			0.905036	+	0.425335i	$0.139844\pi$
$578$	8.41214e8	−	1.45703e9i	0.181200	−	0.313848i
$579$		0			0
$580$	1.09031e9			0.232034
$581$	−4.39507e9	+	7.61249e9i	−0.929714	+	1.61031i
$582$		0			0
$583$	3.76352e9	+	6.51861e9i	0.786600	+	1.36243i
$584$	3.08329e8			0.0640573
$585$		0			0
$586$	3.98589e9			0.818245
$587$	1.28658e9	+	2.22843e9i	0.262546	+	0.454742i	0.966918	−	0.255089i	$-0.0821046\pi$
$587$	1.28658e9	+	2.22843e9i	0.262546	+	0.454742i	−0.704372	+	0.709831i	$0.748771\pi$
$588$		0			0
$589$	−2.35433e9	+	4.07781e9i	−0.474748	+	0.822288i
$590$	−1.71601e9			−0.343983
$591$		0			0
$592$	5.16435e8	−	8.94491e8i	0.102303	−	0.177194i
$593$	5.94741e9			1.17121			0.585607	−	0.810595i	$-0.300856\pi$
$593$	5.94741e9			1.17121			0.585607	+	0.810595i	$0.300856\pi$
$594$		0			0
$595$	−2.82257e9	−	4.88884e9i	−0.549333	−	0.951472i
$596$	−6.09606e8	−	1.05587e9i	−0.117947	−	0.204290i
$597$		0			0
$598$	3.15591e9	+	1.55577e9i	0.603490	+	0.297504i
$599$	5.25374e9			0.998792			0.499396	−	0.866374i	$-0.333555\pi$
$599$	5.25374e9			0.998792			0.499396	+	0.866374i	$0.333555\pi$
$600$		0			0
$601$	3.66219e9	+	6.34309e9i	0.688145	+	1.19190i	0.972437	+	0.233164i	$0.0749079\pi$
$601$	3.66219e9	+	6.34309e9i	0.688145	+	1.19190i	−0.284293	+	0.958737i	$0.591759\pi$
$602$	3.26309e9	−	5.65183e9i	0.609594	−	1.05585i
$603$		0			0
$604$	1.05320e9	−	1.82419e9i	0.194482	−	0.336853i
$605$	−2.94386e9	+	5.09892e9i	−0.540472	+	0.936126i
$606$		0			0
$607$	−2.86675e9	+	4.96536e9i	−0.520271	+	0.901136i	0.479451	+	0.877568i	$0.340836\pi$
$607$	−2.86675e9	+	4.96536e9i	−0.520271	+	0.901136i	−0.999722	+	0.0235672i	$0.992498\pi$
$608$	−8.02625e8	−	1.39019e9i	−0.144827	−	0.250848i
$609$		0			0
$610$	−1.74283e8			−0.0310885
$611$	−4.56742e8	−	6.95363e9i	−0.0810078	−	1.23330i
$612$		0			0
$613$	−9.33205e8	−	1.61636e9i	−0.163631	−	0.283417i	0.772537	−	0.634969i	$-0.218987\pi$
$613$	−9.33205e8	−	1.61636e9i	−0.163631	−	0.283417i	−0.936168	+	0.351552i	$0.885654\pi$
$614$	−1.98951e9	−	3.44593e9i	−0.346862	−	0.600783i
$615$		0			0
$616$	−4.40001e9			−0.758440
$617$	2.88453e9	−	4.99615e9i	0.494398	−	0.856322i	−0.505581	−	0.862779i	$-0.668722\pi$
$617$	2.88453e9	−	4.99615e9i	0.494398	−	0.856322i	0.999979	+	0.00645676i	$0.00205527\pi$
$618$		0			0
$619$	9.91957e9			1.68103			0.840515	−	0.541788i	$-0.182252\pi$
$619$	9.91957e9			1.68103			0.840515	+	0.541788i	$0.182252\pi$
$620$	−8.99247e8	+	1.55754e9i	−0.151533	+	0.262463i
$621$		0			0
$622$	−4.21116e9	−	7.29394e9i	−0.701674	−	1.21534i
$623$	1.62329e10			2.68961
$624$		0			0
$625$	−6.62385e9			−1.08525
$626$	8.78753e8	+	1.52205e9i	0.143172	+	0.247980i
$627$		0			0
$628$	2.93891e9	−	5.09034e9i	0.473508	−	0.820140i
$629$	3.56647e9			0.571428
$630$		0			0
$631$	3.92902e9	−	6.80526e9i	0.622560	−	1.07831i	−0.366447	−	0.930439i	$-0.619426\pi$
$631$	3.92902e9	−	6.80526e9i	0.622560	−	1.07831i	0.989007	−	0.147867i	$-0.0472408\pi$
$632$	2.87093e9			0.452390
$633$		0			0
$634$	3.80256e9	+	6.58623e9i	0.592603	+	1.02642i
$635$	−5.83482e9	−	1.01062e10i	−0.904314	−	1.56632i
$636$		0			0
$637$	−6.85075e9	+	4.57891e9i	−1.05015	+	0.701898i
$638$	2.93441e9			0.447352
$639$		0			0
$640$	−3.06567e8	−	5.30989e8i	−0.0462269	−	0.0800674i
$641$	4.40339e8	−	7.62689e8i	0.0660365	−	0.114379i	−0.831117	−	0.556098i	$-0.812298\pi$
$641$	4.40339e8	−	7.62689e8i	0.0660365	−	0.114379i	0.897153	+	0.441719i	$0.145631\pi$
$642$		0			0
$643$	5.32881e9	−	9.22976e9i	0.790481	−	1.36915i	−0.135188	−	0.990820i	$-0.543164\pi$
$643$	5.32881e9	−	9.22976e9i	0.790481	−	1.36915i	0.925669	−	0.378333i	$-0.123503\pi$
$644$	2.42560e9	−	4.20126e9i	0.357864	−	0.619839i
$645$		0			0
$646$	2.77144e9	−	4.80028e9i	0.404475	−	0.700572i
$647$	2.08426e9	+	3.61004e9i	0.302543	+	0.524020i	0.976711	−	0.214558i	$-0.0688311\pi$
$647$	2.08426e9	+	3.61004e9i	0.302543	+	0.524020i	−0.674168	+	0.738578i	$0.735498\pi$
$648$		0			0
$649$	−4.61840e9			−0.663185
$650$	−3.87355e8	+	2.58901e8i	−0.0553239	+	0.0369774i
$651$		0			0
$652$	9.01488e8	+	1.56142e9i	0.127378	+	0.220625i
$653$	−6.66949e9	−	1.15519e10i	−0.937338	−	1.62352i	−0.770411	−	0.637548i	$-0.779949\pi$
$653$	−6.66949e9	−	1.15519e10i	−0.937338	−	1.62352i	−0.166928	−	0.985969i	$-0.553385\pi$
$654$		0			0
$655$	7.70366e9			1.07116
$656$	−9.27234e8	+	1.60602e9i	−0.128241	+	0.222120i
$657$		0			0
$658$	−9.60796e9			−1.31474
$659$	4.89479e9	−	8.47803e9i	0.666247	−	1.15397i	−0.312699	−	0.949852i	$-0.601233\pi$
$659$	4.89479e9	−	8.47803e9i	0.666247	−	1.15397i	0.978946	−	0.204121i	$-0.0654337\pi$
$660$		0			0
$661$	−1.53489e9	−	2.65851e9i	−0.206715	−	0.358041i	0.743963	−	0.668221i	$-0.232944\pi$
$661$	−1.53489e9	−	2.65851e9i	−0.206715	−	0.358041i	−0.950678	+	0.310180i	$0.899611\pi$
$662$	−8.77922e9			−1.17612
$663$		0			0
$664$	−3.29662e9			−0.436999
$665$	9.77652e9	+	1.69334e10i	1.28917	+	2.23290i
$666$		0			0
$667$	−1.61766e9	+	2.80186e9i	−0.211079	+	0.365600i
$668$	2.47280e9			0.320975
$669$		0			0
$670$	6.92280e8	−	1.19906e9i	0.0889242	−	0.154021i
$671$	−4.69057e8			−0.0599373
$672$		0			0
$673$	2.02392e9	+	3.50552e9i	0.255941	+	0.443303i	0.965151	−	0.261695i	$-0.0842814\pi$
$673$	2.02392e9	+	3.50552e9i	0.255941	+	0.443303i	−0.709210	+	0.704998i	$0.750948\pi$
$674$	−1.68708e9	−	2.92212e9i	−0.212240	−	0.367610i
$675$		0			0
$676$	1.53578e9	−	3.71064e9i	0.191212	−	0.461993i
$677$	−5.88970e9			−0.729513			−0.364756	−	0.931103i	$-0.618848\pi$
$677$	−5.88970e9			−0.729513			−0.364756	+	0.931103i	$0.618848\pi$
$678$		0			0
$679$	1.07866e10	+	1.86829e10i	1.32233	+	2.29035i
$680$	1.05857e9	−	1.83349e9i	0.129103	−	0.223613i
$681$		0			0
$682$	−2.42020e9	+	4.19191e9i	−0.292150	+	0.506019i
$683$	7.98001e9	−	1.38218e10i	0.958365	−	1.65994i	0.231891	−	0.972742i	$-0.425509\pi$
$683$	7.98001e9	−	1.38218e10i	0.958365	−	1.65994i	0.726473	−	0.687194i	$-0.241158\pi$
$684$		0			0
$685$	6.27434e9	−	1.08675e10i	0.745849	−	1.29185i
$686$	1.18330e9	+	2.04953e9i	0.139946	+	0.242393i
$687$		0			0
$688$	2.44755e9			0.286531
$689$	6.20817e8	+	9.45157e9i	0.0723096	+	1.10087i
$690$		0			0
$691$	3.48893e9	+	6.04300e9i	0.402271	+	0.696754i	0.994000	−	0.109383i	$-0.0348876\pi$
$691$	3.48893e9	+	6.04300e9i	0.402271	+	0.696754i	−0.591729	+	0.806137i	$0.701554\pi$
$692$	8.36485e6	+	1.44883e7i	0.000959592	+	0.00166206i
$693$		0			0
$694$	4.57811e9			0.519909
$695$	−5.96639e9	+	1.03341e10i	−0.674163	+	1.16768i
$696$		0			0
$697$	−6.40343e9			−0.716305
$698$	4.38113e9	−	7.58834e9i	0.487632	−	0.844603i
$699$		0			0
$700$	3.21188e8	+	5.56313e8i	0.0353928	+	0.0613022i
$701$	−1.42783e10			−1.56554			−0.782770	−	0.622311i	$-0.786194\pi$
$701$	−1.42783e10			−1.56554			−0.782770	+	0.622311i	$0.786194\pi$
$702$		0			0
$703$	−1.23532e10			−1.34102
$704$	−8.25082e8	−	1.42908e9i	−0.0891236	−	0.154367i
$705$		0			0
$706$	−1.10940e9	+	1.92154e9i	−0.118652	+	0.205510i
$707$	1.67279e10			1.78022
$708$		0			0
$709$	1.90818e8	−	3.30507e8i	0.0201075	−	0.0348272i	−0.855797	−	0.517313i	$-0.826932\pi$
$709$	1.90818e8	−	3.30507e8i	0.0201075	−	0.0348272i	0.875904	+	0.482485i	$0.160266\pi$
$710$	1.39703e9			0.146488
$711$		0			0
$712$	3.04397e9	+	5.27231e9i	0.316053	+	0.547420i
$713$	−2.66837e9	−	4.62175e9i	−0.275697	−	0.477522i
$714$		0			0
$715$	−1.21205e10	+	8.10109e9i	−1.24008	+	0.828843i
$716$	2.80474e8			0.0285560
$717$		0			0
$718$	1.44607e9	+	2.50466e9i	0.145799	+	0.252530i
$719$	6.43024e9	−	1.11375e10i	0.645173	−	1.11747i	−0.339089	−	0.940754i	$-0.610119\pi$
$719$	6.43024e9	−	1.11375e10i	0.645173	−	1.11747i	0.984262	−	0.176718i	$-0.0565479\pi$
$720$		0			0
$721$	6.45267e9	−	1.11764e10i	0.641159	−	1.11052i
$722$	−6.02394e9	+	1.04338e10i	−0.595663	+	1.03172i
$723$		0			0
$724$	8.65408e8	−	1.49893e9i	0.0847493	−	0.146790i
$725$	−2.14203e8	−	3.71011e8i	−0.0208758	−	0.0361579i
$726$		0			0
$727$	−3.31616e9			−0.320085			−0.160043	−	0.987110i	$-0.551163\pi$
$727$	−3.31616e9			−0.320085			−0.160043	+	0.987110i	$0.551163\pi$
$728$	−4.96626e9	−	2.44822e9i	−0.477056	−	0.235175i
$729$		0			0
$730$	−7.04253e8	−	1.21980e9i	−0.0670037	−	0.116054i
$731$	4.22566e9	+	7.31907e9i	0.400114	+	0.693019i
$732$		0			0
$733$	−3.96951e9			−0.372282			−0.186141	−	0.982523i	$-0.559598\pi$
$733$	−3.96951e9			−0.372282			−0.186141	+	0.982523i	$0.559598\pi$
$734$	2.37652e9	−	4.11625e9i	0.221822	−	0.384207i
$735$		0			0
$736$	1.81937e9			0.168209
$737$	1.86318e9	−	3.22712e9i	0.171442	−	0.296947i
$738$		0			0
$739$	−6.72157e9	−	1.16421e10i	−0.612654	−	1.06115i	−0.990791	−	0.135398i	$-0.956769\pi$
$739$	−6.72157e9	−	1.16421e10i	−0.612654	−	1.06115i	0.378138	−	0.925749i	$-0.376565\pi$
$740$	−4.71835e9			−0.428035
$741$		0			0
$742$	1.30594e10			1.17357
$743$	3.25521e9	+	5.63819e9i	0.291151	+	0.504288i	0.974082	−	0.226194i	$-0.0726284\pi$
$743$	3.25521e9	+	5.63819e9i	0.291151	+	0.504288i	−0.682931	+	0.730483i	$0.739295\pi$
$744$		0			0
$745$	−2.78480e9	+	4.82341e9i	−0.246744	+	0.427374i
$746$	−3.98612e9			−0.351531
$747$		0			0
$748$	2.84899e9	−	4.93459e9i	0.248906	−	0.431117i
$749$	−2.91764e10			−2.53714
$750$		0			0
$751$	−1.90147e9	−	3.29345e9i	−0.163814	−	0.283734i	0.772420	−	0.635113i	$-0.219046\pi$
$751$	−1.90147e9	−	3.29345e9i	−0.163814	−	0.283734i	−0.936233	+	0.351379i	$0.885713\pi$
$752$	−1.80167e9	−	3.12058e9i	−0.154494	−	0.267592i
$753$		0			0
$754$	3.31205e9	+	1.63275e9i	0.281382	+	0.138714i
$755$	−9.62242e9			−0.813711
$756$		0			0
$757$	−5.22825e9	−	9.05559e9i	−0.438047	−	0.758719i	0.559492	−	0.828836i	$-0.310996\pi$
$757$	−5.22825e9	−	9.05559e9i	−0.438047	−	0.758719i	−0.997539	+	0.0701166i	$0.977663\pi$
$758$	−6.97516e9	+	1.20813e10i	−0.581717	+	1.00756i
$759$		0			0
$760$	−3.66655e9	+	6.35065e9i	−0.302977	+	0.524772i
$761$	1.16308e9	−	2.01451e9i	0.0956673	−	0.165701i	−0.814220	−	0.580557i	$-0.802835\pi$
$761$	1.16308e9	−	2.01451e9i	0.0956673	−	0.165701i	0.909887	+	0.414856i	$0.136168\pi$
$762$		0			0
$763$	−9.59012e9	+	1.66106e10i	−0.781606	+	1.35378i
$764$	3.08766e9	+	5.34799e9i	0.250497	+	0.433874i
$765$		0			0
$766$	8.98002e9			0.721900
$767$	−5.21275e9	−	2.56974e9i	−0.417141	−	0.205639i
$768$		0			0
$769$	−2.45269e9	−	4.24819e9i	−0.194492	−	0.336869i	0.752242	−	0.658887i	$-0.228972\pi$
$769$	−2.45269e9	−	4.24819e9i	−0.194492	−	0.336869i	−0.946734	+	0.322017i	$0.895639\pi$
$770$	1.00501e10	+	1.74072e10i	0.793325	+	1.37408i
$771$		0			0
$772$	1.34898e9			0.105523
$773$	−2.33679e9	+	4.04744e9i	−0.181967	+	0.315176i	−0.942550	−	0.334065i	$-0.891580\pi$
$773$	−2.33679e9	+	4.04744e9i	−0.181967	+	0.315176i	0.760584	+	0.649240i	$0.224913\pi$
$774$		0			0
$775$	7.06669e8			0.0545331
$776$	−4.04537e9	+	7.00678e9i	−0.310772	+	0.538273i
$777$		0			0
$778$	−5.46147e9	−	9.45954e9i	−0.415796	−	0.720181i
$779$	2.21795e10			1.68101
$780$		0			0
$781$	3.75993e9			0.282423
$782$	3.14112e9	+	5.44059e9i	0.234888	+	0.406839i
$783$		0			0
$784$	−2.13040e9	+	3.68995e9i	−0.157890	+	0.273473i
$785$	−2.68510e10			−1.98115
$786$		0			0
$787$	2.51214e9	−	4.35115e9i	0.183710	−	0.318195i	−0.759431	−	0.650588i	$-0.774523\pi$
$787$	2.51214e9	−	4.35115e9i	0.183710	−	0.318195i	0.943141	+	0.332393i	$0.107856\pi$
$788$	1.03574e10			0.754068
$789$		0			0
$790$	−6.55749e9	−	1.13579e10i	−0.473198	−	0.819603i
$791$	−2.73341e9	−	4.73440e9i	−0.196375	−	0.340132i
$792$		0			0
$793$	−5.29421e8	−	2.60990e8i	−0.0377003	−	0.0185852i
$794$	2.19181e9			0.155393
$795$		0			0
$796$	6.95264e9	+	1.20423e10i	0.488600	+	0.846281i
$797$	6.10661e9	−	1.05770e10i	0.427264	−	0.740042i	−0.569365	−	0.822085i	$-0.692811\pi$
$797$	6.10661e9	−	1.05770e10i	0.427264	−	0.740042i	0.996629	+	0.0820424i	$0.0261443\pi$
$798$		0			0
$799$	6.22111e9	−	1.07753e10i	0.431473	−	0.747334i
$800$	−1.20457e8	+	2.08638e8i	−0.00831796	+	0.0144071i
$801$		0			0
$802$	−3.50123e9	+	6.06430e9i	−0.239668	+	0.415117i
$803$	−1.89540e9	−	3.28293e9i	−0.129180	−	0.223747i
$804$		0			0
$805$	−2.21612e10			−1.49730
$806$	−5.06409e9	+	3.38474e9i	−0.340666	+	0.227695i
$807$		0			0
$808$	3.13678e9	+	5.43306e9i	0.209191	+	0.362330i
$809$	4.86777e9	+	8.43123e9i	0.323229	+	0.559849i	0.981152	−	0.193236i	$-0.0618983\pi$
$809$	4.86777e9	+	8.43123e9i	0.323229	+	0.559849i	−0.657923	+	0.753085i	$0.728565\pi$
$810$		0			0
$811$	−1.50013e10			−0.987542			−0.493771	−	0.869592i	$-0.664382\pi$
$811$	−1.50013e10			−0.987542			−0.493771	+	0.869592i	$0.664382\pi$
$812$	2.54561e9	−	4.40912e9i	0.166857	−	0.289005i
$813$		0			0
$814$	−1.26988e10			−0.825234
$815$	4.11818e9	−	7.13289e9i	0.266473	−	0.461545i
$816$		0			0
$817$	−1.46364e10	−	2.53510e10i	−0.938982	−	1.62637i
$818$	1.48040e8			0.00945678
$819$		0			0
$820$	8.47158e9			0.536557
$821$	−3.31998e9	−	5.75037e9i	−0.209380	−	0.362656i	0.742140	−	0.670245i	$-0.233811\pi$
$821$	−3.31998e9	−	5.75037e9i	−0.209380	−	0.362656i	−0.951519	+	0.307589i	$0.900478\pi$
$822$		0			0
$823$	1.55815e9	−	2.69879e9i	0.0974336	−	0.168760i	−0.813188	−	0.582001i	$-0.802270\pi$
$823$	1.55815e9	−	2.69879e9i	0.0974336	−	0.168760i	0.910622	+	0.413241i	$0.135603\pi$
$824$	4.83997e9			0.301368
$825$		0			0
$826$	−4.00646e9	+	6.93939e9i	−0.247361	+	0.428441i
$827$	−4.14743e9			−0.254982			−0.127491	−	0.991840i	$-0.540692\pi$
$827$	−4.14743e9			−0.254982			−0.127491	+	0.991840i	$0.540692\pi$
$828$		0			0
$829$	3.42521e9	+	5.93264e9i	0.208808	+	0.361665i	0.951339	−	0.308146i	$-0.0997084\pi$
$829$	3.42521e9	+	5.93264e9i	0.208808	+	0.361665i	−0.742532	+	0.669811i	$0.766375\pi$
$830$	7.52981e9	+	1.30420e10i	0.457099	+	0.791719i
$831$		0			0
$832$	−1.36103e8	−	2.07208e9i	−0.00819285	−	0.124731i
$833$	−1.47124e10			−0.881914
$834$		0			0
$835$	−5.64812e9	−	9.78283e9i	−0.335738	−	0.581516i
$836$	−9.86802e9	+	1.70919e10i	−0.584128	+	1.01174i
$837$		0			0
$838$	−6.96731e9	+	1.20677e10i	−0.408989	+	0.708389i
$839$	−1.69365e10	+	2.93348e10i	−0.990048	+	1.71481i	−0.373145	+	0.927773i	$0.621721\pi$
$839$	−1.69365e10	+	2.93348e10i	−0.990048	+	1.71481i	−0.616903	+	0.787039i	$0.711613\pi$
$840$		0			0
$841$	6.92725e9	−	1.19983e10i	0.401582	−	0.695561i
$842$	4.26858e8	+	7.39340e8i	0.0246429	+	0.0426827i
$843$		0			0
$844$	−1.30277e10			−0.745881
$845$	−1.81878e10	+	2.39965e9i	−1.03701	+	0.136820i
$846$		0			0
$847$	1.37464e10	+	2.38095e10i	0.777316	+	1.34635i
$848$	2.44888e9	+	4.24158e9i	0.137905	+	0.238859i
$849$		0			0
$850$	−8.31869e8			−0.0464610
$851$	7.00047e9	−	1.21252e10i	0.389380	−	0.674426i
$852$		0			0
$853$	2.53792e10			1.40009			0.700046	−	0.714098i	$-0.253163\pi$
$853$	2.53792e10			1.40009			0.700046	+	0.714098i	$0.253163\pi$
$854$	−4.06907e8	+	7.04784e8i	−0.0223560	+	0.0387216i
$855$		0			0
$856$	−5.47110e9	−	9.47622e9i	−0.298137	−	0.516389i
$857$	1.15439e10			0.626496			0.313248	−	0.949671i	$-0.398583\pi$
$857$	1.15439e10			0.626496			0.313248	+	0.949671i	$0.398583\pi$
$858$		0			0
$859$	−2.20284e10			−1.18579			−0.592893	−	0.805281i	$-0.702014\pi$
$859$	−2.20284e10			−1.18579			−0.592893	+	0.805281i	$0.702014\pi$
$860$	−5.59045e9	−	9.68294e9i	−0.299711	−	0.519114i
$861$		0			0
$862$	−4.13739e9	+	7.16617e9i	−0.220014	+	0.381076i
$863$	1.33248e10			0.705707			0.352853	−	0.935679i	$-0.385211\pi$
$863$	1.33248e10			0.705707			0.352853	+	0.935679i	$0.385211\pi$
$864$		0			0
$865$	3.82123e7	−	6.61856e7i	0.00200746	−	0.00347702i
$866$	9.94515e9			0.520354
$867$		0			0
$868$	4.19905e9	+	7.27296e9i	0.217937	+	0.377479i
$869$	−1.76486e10	−	3.05683e10i	−0.912307	−	1.58016i
$870$		0			0
$871$	3.89856e9	−	2.60572e9i	0.199913	−	0.133618i
$872$	−7.19328e9			−0.367383
$873$		0			0
$874$	−1.08799e10	−	1.88445e10i	−0.551232	−	0.954762i
$875$	−1.41240e10	+	2.44635e10i	−0.712739	+	1.23450i
$876$		0			0
$877$	−1.09078e10	+	1.88929e10i	−0.546059	+	0.945802i	0.452480	+	0.891774i	$0.350539\pi$
$877$	−1.09078e10	+	1.88929e10i	−0.546059	+	0.945802i	−0.998539	+	0.0540276i	$0.982794\pi$
$878$	8.86716e9	−	1.53584e10i	0.442134	−	0.765798i
$879$		0			0
$880$	−3.76914e9	+	6.52834e9i	−0.186446	+	0.322934i
$881$	1.42858e10	+	2.47438e10i	0.703865	+	1.21913i	0.967100	+	0.254398i	$0.0818772\pi$
$881$	1.42858e10	+	2.47438e10i	0.703865	+	1.21913i	−0.263235	+	0.964732i	$0.584789\pi$
$882$		0			0
$883$	1.94977e10			0.953061			0.476531	−	0.879158i	$-0.341894\pi$
$883$	1.94977e10			0.953061			0.476531	+	0.879158i	$0.341894\pi$
$884$	5.96130e9	−	3.98442e9i	0.290240	−	0.193991i
$885$		0			0
$886$	−1.11856e9	−	1.93740e9i	−0.0540308	−	0.0935840i
$887$	−1.16099e10	−	2.01090e10i	−0.558595	−	0.967514i	−0.997614	−	0.0690368i	$-0.978007\pi$
$887$	−1.16099e10	−	2.01090e10i	−0.558595	−	0.967514i	0.439019	−	0.898478i	$-0.355326\pi$
$888$		0			0
$889$	−5.44915e10			−2.60119
$890$	1.39054e10	−	2.40849e10i	0.661180	−	1.14520i
$891$		0			0
$892$	2.22976e9			0.105192
$893$	−2.15480e10	+	3.73223e10i	−1.01258	+	1.75383i
$894$		0			0
$895$	−6.40630e8	−	1.10960e9i	−0.0298694	−	0.0517354i
$896$	−2.86304e9			−0.132968
$897$		0			0
$898$	1.46325e10			0.674298
$899$	−2.80039e9	−	4.85041e9i	−0.128546	−	0.222649i
$900$		0			0
$901$	−8.45591e9	+	1.46461e10i	−0.385144	+	0.667089i
$902$	2.28001e10			1.03446
$903$		0			0
$904$	1.02513e9	−	1.77557e9i	0.0461517	−	0.0799371i
$905$	−7.90671e9			−0.354590
$906$		0			0
$907$	−2.86411e8	−	4.96078e8i	−0.0127457	−	0.0220762i	0.859582	−	0.510997i	$-0.170724\pi$
$907$	−2.86411e8	−	4.96078e8i	−0.0127457	−	0.0220762i	−0.872328	+	0.488921i	$0.837391\pi$
$908$	3.08393e9	+	5.34152e9i	0.136711	+	0.236791i
$909$		0			0
$910$	1.65782e9	+	2.52394e10i	0.0729278	+	1.11028i
$911$	1.07211e10			0.469815			0.234907	−	0.972018i	$-0.424521\pi$
$911$	1.07211e10			0.469815			0.234907	+	0.972018i	$0.424521\pi$
$912$		0			0
$913$	2.02654e10	+	3.51008e10i	0.881269	+	1.52640i
$914$	2.89405e9	−	5.01265e9i	0.125370	−	0.217148i
$915$		0			0
$916$	−6.09748e9	+	1.05611e10i	−0.262130	+	0.454022i
$917$	1.79862e10	−	3.11530e10i	0.770276	−	1.33416i
$918$		0			0
$919$	−1.79597e10	+	3.11071e10i	−0.763299	+	1.32207i	0.177842	+	0.984059i	$0.443089\pi$
$919$	−1.79597e10	+	3.11071e10i	−0.763299	+	1.32207i	−0.941141	+	0.338014i	$0.890245\pi$
$920$	−4.15563e9	−	7.19776e9i	−0.175946	−	0.304747i
$921$		0			0
$922$	−2.77388e9			−0.116554
$923$	4.24380e9	+	2.09207e9i	0.177643	+	0.0875731i
$924$		0			0
$925$	9.26973e8	+	1.60556e9i	0.0385098	+	0.0667009i
$926$	1.29874e10	+	2.24948e10i	0.537506	+	0.930988i
$927$		0			0
$928$	1.90939e9			0.0784289
$929$	1.22473e10	−	2.12129e10i	0.501168	−	0.868049i	−0.498831	−	0.866699i	$-0.666237\pi$
$929$	1.22473e10	−	2.12129e10i	0.501168	−	0.868049i	0.999999	−	0.00134967i	$-0.000429614\pi$
$930$		0			0
$931$	5.09593e10			2.06966
$932$	−1.55143e9	+	2.68716e9i	−0.0627736	+	0.108727i
$933$		0			0
$934$	−3.93820e9	−	6.82116e9i	−0.158155	−	0.273933i
$935$	−2.60295e10			−1.04142
$936$		0			0
$937$	1.00234e9			0.0398041			0.0199021	−	0.999802i	$-0.493665\pi$
$937$	1.00234e9			0.0398041			0.0199021	+	0.999802i	$0.493665\pi$
$938$	−3.23261e9	−	5.59905e9i	−0.127892	−	0.221516i
$939$		0			0
$940$	−8.23037e9	+	1.42554e10i	−0.323200	+	0.559800i
$941$	1.00328e10			0.392515			0.196258	−	0.980552i	$-0.437121\pi$
$941$	1.00328e10			0.392515			0.196258	+	0.980552i	$0.437121\pi$
$942$		0			0
$943$	−1.25690e10	+	2.17702e10i	−0.488102	+	0.845418i
$944$	−3.00514e9			−0.116269
$945$		0			0
$946$	−1.50459e10	−	2.60603e10i	−0.577830	−	1.00083i
$947$	−8.33758e9	−	1.44411e10i	−0.319018	−	0.552555i	0.661265	−	0.750152i	$-0.270020\pi$
$947$	−8.33758e9	−	1.44411e10i	−0.319018	−	0.552555i	−0.980283	+	0.197597i	$0.936686\pi$
$948$		0			0
$949$	−3.12659e8	−	4.76004e9i	−0.0118751	−	0.180792i
$950$	2.88134e9			0.109034
$951$		0			0
$952$	−4.94299e9	−	8.56151e9i	−0.185678	−	0.321604i
$953$	−1.47576e10	+	2.55609e10i	−0.552321	+	0.956647i	0.445786	+	0.895140i	$0.352924\pi$
$953$	−1.47576e10	+	2.55609e10i	−0.552321	+	0.956647i	−0.998107	+	0.0615077i	$0.980409\pi$
$954$		0			0
$955$	1.41051e10	−	2.44307e10i	0.524038	−	0.907661i
$956$	−3.12746e9	+	5.41693e9i	−0.115768	+	0.200517i
$957$		0			0
$958$	1.55281e10	−	2.68955e10i	0.570610	−	0.988325i
$959$	−2.92981e10	−	5.07459e10i	−1.07269	−	1.85796i
$960$		0			0
$961$	−1.82740e10			−0.664204
$962$	−1.43330e10	−	7.06577e9i	−0.519069	−	0.255886i
$963$		0			0
$964$	9.00812e9	+	1.56025e10i	0.323866	+	0.560952i
$965$	−3.08121e9	−	5.33680e9i	−0.110376	−	0.191177i
$966$		0			0
$967$	1.18090e9			0.0419973			0.0209987	−	0.999780i	$-0.493315\pi$
$967$	1.18090e9			0.0419973			0.0209987	+	0.999780i	$0.493315\pi$
$968$	−5.15540e9	+	8.92942e9i	−0.182683	+	0.316417i
$969$		0			0
$970$	3.69601e10			1.30026
$971$	−2.01714e10	+	3.49378e10i	−0.707079	+	1.22470i	0.258857	+	0.965916i	$0.416654\pi$
$971$	−2.01714e10	+	3.49378e10i	−0.707079	+	1.22470i	−0.965936	+	0.258781i	$0.916679\pi$
$972$		0			0
$973$	2.78601e10	+	4.82552e10i	0.969591	+	1.67938i
$974$	9.24541e9			0.320605
$975$		0			0
$976$	−3.05210e8			−0.0105081
$977$	−7.68842e9	−	1.33167e10i	−0.263758	−	0.456843i	0.703479	−	0.710716i	$-0.251629\pi$
$977$	−7.68842e9	−	1.33167e10i	−0.263758	−	0.456843i	−0.967238	+	0.253873i	$0.918295\pi$
$978$		0			0
$979$	3.74246e10	−	6.48213e10i	1.27473	−	2.20790i
$980$	1.94641e10			0.660608
$981$		0			0
$982$	−1.02399e10	+	1.77360e10i	−0.345068	+	0.597675i
$983$	8.11574e9			0.272515			0.136258	−	0.990673i	$-0.456493\pi$
$983$	8.11574e9			0.272515			0.136258	+	0.990673i	$0.456493\pi$
$984$		0			0
$985$	−2.36574e10	−	4.09758e10i	−0.788751	−	1.36616i
$986$	3.29653e9	+	5.70976e9i	0.109519	+	0.189692i
$987$		0			0
$988$	−2.06481e10	+	1.38008e10i	−0.681131	+	0.455255i
$989$	3.31775e10			1.09058
$990$		0			0
$991$	−2.50954e10	−	4.34665e10i	−0.819100	−	1.41872i	−0.906346	−	0.422536i	$-0.861140\pi$
$991$	−2.50954e10	−	4.34665e10i	−0.819100	−	1.41872i	0.0872467	−	0.996187i	$-0.472193\pi$
$992$	−1.57479e9	+	2.72762e9i	−0.0512192	+	0.0887143i
$993$		0			0
$994$	3.26174e9	−	5.64949e9i	0.105341	−	0.182456i
$995$	3.17610e10	−	5.50117e10i	1.02215	−	1.77041i
$996$		0			0
$997$	−1.22870e10	+	2.12817e10i	−0.392657	+	0.680102i	−0.992799	−	0.119792i	$-0.961777\pi$
$997$	−1.22870e10	+	2.12817e10i	−0.392657	+	0.680102i	0.600142	+	0.799893i	$0.295111\pi$
$998$	−1.78556e10	−	3.09268e10i	−0.568614	−	0.984869i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.8.h.c.55.3		8
3.2	odd	2		78.8.e.a.55.2	✓	8
13.9	even	3	inner	234.8.h.c.217.3		8
39.35	odd	6		78.8.e.a.61.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.8.e.a.55.2	✓	8	3.2	odd	2
78.8.e.a.61.2	yes	8	39.35	odd	6
234.8.h.c.55.3		8	1.1	even	1	trivial
234.8.h.c.217.3		8	13.9	even	3	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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	234.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 - 6.92820i) q^{2} +(-32.0000 + 55.4256i) q^{4} +292.365 q^{5} +(682.601 - 1182.30i) q^{7} +512.000 q^{8} +(-1169.46 - 2025.56i) q^{10} +(-3147.44 - 5451.52i) q^{11} +(-519.190 - 7904.36i) q^{13} -10921.6 q^{14} +(-2048.00 - 3547.24i) q^{16} +(7071.69 - 12248.5i) q^{17} +(-24494.2 + 42425.1i) q^{19} +(-9355.67 + 16204.5i) q^{20} +(-25179.5 + 43612.2i) q^{22} +(-27761.4 - 48084.2i) q^{23} +7352.11 q^{25} +(-52686.3 + 35214.5i) q^{26} +(43686.5 + 75667.2i) q^{28} +(-29134.9 - 50463.2i) q^{29} +96117.8 q^{31} +(-16384.0 + 28377.9i) q^{32} -113147. q^{34} +(199568. - 345663. i) q^{35} +(126083. + 218382. i) q^{37} +391907. q^{38} +149691. q^{40} +(-226376. - 392094. i) q^{41} +(-298773. + 517491. i) q^{43} +402872. q^{44} +(-222092. + 384674. i) q^{46} +879720. q^{47} +(-520116. - 900868. i) q^{49} +(-29408.4 - 50936.9i) q^{50} +(454718. + 224163. i) q^{52} -1.19574e6 q^{53} +(-920200. - 1.59383e6i) q^{55} +(349492. - 605337. i) q^{56} +(-233080. + 403706. i) q^{58} +(366838. - 635382. i) q^{59} +(37257.1 - 64531.2i) q^{61} +(-384471. - 665924. i) q^{62} +262144. q^{64} +(-151793. - 2.31096e6i) q^{65} +(295983. + 512658. i) q^{67} +(452588. + 783906. i) q^{68} -3.19309e6 q^{70} +(-298650. + 517277. i) q^{71} +602204. q^{73} +(1.00866e6 - 1.74705e6i) q^{74} +(-1.56763e6 - 2.71521e6i) q^{76} -8.59377e6 q^{77} +5.60729e6 q^{79} +(-598763. - 1.03709e6i) q^{80} +(-1.81100e6 + 3.13675e6i) q^{82} -6.43871e6 q^{83} +(2.06751e6 - 3.58104e6i) q^{85} +4.78037e6 q^{86} +(-1.61149e6 - 2.79118e6i) q^{88} +(5.94525e6 + 1.02975e7i) q^{89} +(-9.69972e6 - 4.78169e6i) q^{91} +3.55346e6 q^{92} +(-3.51888e6 - 6.09488e6i) q^{94} +(-7.16123e6 + 1.24036e7i) q^{95} +(-7.90111e6 + 1.36851e7i) q^{97} +(-4.16093e6 + 7.20694e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{2} - 256 q^{4} + 386 q^{5} + 757 q^{7} + 4096 q^{8} - 1544 q^{10} - 4524 q^{11} + 13272 q^{13} - 12112 q^{14} - 16384 q^{16} + 12775 q^{17} + 38646 q^{19} - 12352 q^{20} - 36192 q^{22} - 24428 q^{23}+ \cdots + 4224696 q^{98}+O(q^{100}) \) 8 * q - 32 * q^2 - 256 * q^4 + 386 * q^5 + 757 * q^7 + 4096 * q^8 - 1544 * q^10 - 4524 * q^11 + 13272 * q^13 - 12112 * q^14 - 16384 * q^16 + 12775 * q^17 + 38646 * q^19 - 12352 * q^20 - 36192 * q^22 - 24428 * q^23 + 305798 * q^25 - 90552 * q^26 + 48448 * q^28 - 22109 * q^29 + 42558 * q^31 - 131072 * q^32 - 204400 * q^34 + 190892 * q^35 + 372411 * q^37 - 618336 * q^38 + 197632 * q^40 - 266009 * q^41 - 399935 * q^43 + 579072 * q^44 - 195424 * q^46 + 487344 * q^47 + 528087 * q^49 - 1223192 * q^50 - 124992 * q^52 - 3351434 * q^53 - 1572842 * q^55 + 387584 * q^56 - 176872 * q^58 - 1025370 * q^59 + 260650 * q^61 - 170232 * q^62 + 2097152 * q^64 + 59673 * q^65 - 2382807 * q^67 + 817600 * q^68 - 3054272 * q^70 - 1773980 * q^71 - 3903260 * q^73 + 2979288 * q^74 + 2473344 * q^76 - 17541708 * q^77 + 11678674 * q^79 - 790528 * q^80 - 2128072 * q^82 + 20314044 * q^83 - 5236237 * q^85 + 6398960 * q^86 - 2316288 * q^88 + 1108942 * q^89 - 29498671 * q^91 + 3126784 * q^92 - 1949376 * q^94 - 10481054 * q^95 - 7003183 * q^97 + 4224696 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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