LMFDB - Embedded newform 162.12.c.l.109.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [162,12,Mod(55,162)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(162, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 12, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("162.55"); S:= CuspForms(chi, 12); N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	162.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-64,0,-2048,3720] 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:	$124.471595251$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{109})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 28x^{2} + 27x + 729 $ x^4 - x^3 + 28x^2 + 27x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.1
Root			$-2.36008 + 4.08777i$ of defining polynomial
Character	$\chi$	$=$	162.109
Dual form			162.12.c.l.55.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-16.0000 - 27.7128i) q^{2} +(-512.000 + 886.810i) q^{4} +(-1888.88 + 3271.64i) q^{5} +(26504.7 + 45907.4i) q^{7} +32768.0 q^{8} +120888. q^{10} +(-95717.6 - 165788. i) q^{11} +(662649. - 1.14774e6i) q^{13} +(848149. - 1.46904e6i) q^{14} +(-524288. - 908093. i) q^{16} -7.39161e6 q^{17} -6.06542e6 q^{19} +(-1.93422e6 - 3.35016e6i) q^{20} +(-3.06296e6 + 5.30521e6i) q^{22} +(-2.32666e7 + 4.02989e7i) q^{23} +(1.72783e7 + 2.99269e7i) q^{25} -4.24096e7 q^{26} -5.42816e7 q^{28} +(3.25031e7 + 5.62970e7i) q^{29} +(2.79570e7 - 4.84230e7i) q^{31} +(-1.67772e7 + 2.90590e7i) q^{32} +(1.18266e8 + 2.04842e8i) q^{34} -2.00257e8 q^{35} -2.00878e8 q^{37} +(9.70467e7 + 1.68090e8i) q^{38} +(-6.18949e7 + 1.07205e8i) q^{40} +(2.86262e8 - 4.95820e8i) q^{41} +(-4.83786e7 - 8.37942e7i) q^{43} +1.96030e8 q^{44} +1.48906e9 q^{46} +(1.19837e9 + 2.07563e9i) q^{47} +(-4.16332e8 + 7.21107e8i) q^{49} +(5.52906e8 - 9.57661e8i) q^{50} +(6.78553e8 + 1.17529e9i) q^{52} -3.14068e9 q^{53} +7.23197e8 q^{55} +(8.68505e8 + 1.50429e9i) q^{56} +(1.04010e9 - 1.80150e9i) q^{58} +(1.10233e9 - 1.90930e9i) q^{59} +(-5.47943e9 - 9.49066e9i) q^{61} -1.78925e9 q^{62} +1.07374e9 q^{64} +(2.50333e9 + 4.33590e9i) q^{65} +(5.31673e9 - 9.20885e9i) q^{67} +(3.78450e9 - 6.55495e9i) q^{68} +(3.20411e9 + 5.54968e9i) q^{70} -2.95131e10 q^{71} +2.30487e10 q^{73} +(3.21404e9 + 5.56689e9i) q^{74} +(3.10550e9 - 5.37888e9i) q^{76} +(5.07392e9 - 8.78829e9i) q^{77} +(1.66109e10 + 2.87710e10i) q^{79} +3.96127e9 q^{80} -1.83207e10 q^{82} +(-1.17076e10 - 2.02782e10i) q^{83} +(1.39619e10 - 2.41827e10i) q^{85} +(-1.54812e9 + 2.68142e9i) q^{86} +(-3.13647e9 - 5.43253e9i) q^{88} +4.47401e10 q^{89} +7.02532e10 q^{91} +(-2.38250e10 - 4.12660e10i) q^{92} +(3.83477e10 - 6.64202e10i) q^{94} +(1.14569e10 - 1.98439e10i) q^{95} +(-1.23184e10 - 2.13361e10i) q^{97} +2.66452e10 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 64 q^{2} - 2048 q^{4} + 3720 q^{5} + 6794 q^{7} + 131072 q^{8} - 238080 q^{10} + 832632 q^{11} - 984634 q^{13} + 217408 q^{14} - 2097152 q^{16} - 10222128 q^{17} - 45838540 q^{19} + 3809280 q^{20}+ \cdots + 63436390656 q^{98}+O(q^{100}) $ 4 * q - 64 * q^2 - 2048 * q^4 + 3720 * q^5 + 6794 * q^7 + 131072 * q^8 - 238080 * q^10 + 832632 * q^11 - 984634 * q^13 + 217408 * q^14 - 2097152 * q^16 - 10222128 * q^17 - 45838540 * q^19 + 3809280 * q^20 + 26644224 * q^22 - 5263656 * q^23 + 27168250 * q^25 + 63016576 * q^26 - 13914112 * q^28 + 37534848 * q^29 + 328859480 * q^31 - 67108864 * q^32 + 163554048 * q^34 - 1093537200 * q^35 - 193134772 * q^37 + 733416640 * q^38 + 121896960 * q^40 + 478653312 * q^41 - 133709104 * q^43 - 1705230336 * q^44 + 336873984 * q^46 + 4431713208 * q^47 - 991193604 * q^49 + 869384000 * q^50 - 1008265216 * q^52 - 9509944032 * q^53 + 16802824320 * q^55 + 222625792 * q^56 + 1201115136 * q^58 + 9940537848 * q^59 - 6058984510 * q^61 - 21047006720 * q^62 + 4294967296 * q^64 + 22326000360 * q^65 + 6772264670 * q^67 + 5233729536 * q^68 + 17496595200 * q^70 - 51162730848 * q^71 + 31615248932 * q^73 + 3090156352 * q^74 + 23469332480 * q^76 + 57475455528 * q^77 + 28139021846 * q^79 - 7801405440 * q^80 - 30633811968 * q^82 - 77207454480 * q^83 + 45022737600 * q^85 - 4278691328 * q^86 + 27283685376 * q^88 + 76591168272 * q^89 + 354015024316 * q^91 - 5389983744 * q^92 + 141814822656 * q^94 - 103452470040 * q^95 - 109290600874 * q^97 + 63436390656 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−16.0000	−	27.7128i	−0.353553	−	0.612372i
$2$	−16.0000	−	27.7128i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−512.000	+	886.810i	−0.250000	+	0.433013i
$5$	−1888.88	+	3271.64i	−0.270315	+	0.468199i	−0.968942	−	0.247286i	$-0.920461\pi$
$5$	−1888.88	+	3271.64i	−0.270315	+	0.468199i	0.698628	+	0.715486i	$0.253794\pi$
$6$		0			0
$7$	26504.7	+	45907.4i	0.596051	+	1.03239i	0.993398	+	0.114722i	$0.0365976\pi$
$7$	26504.7	+	45907.4i	0.596051	+	1.03239i	−0.397347	+	0.917668i	$0.630069\pi$
$8$	32768.0			0.353553
$9$		0			0
$10$	120888.			0.382283
$11$	−95717.6	−	165788.i	−0.179197	−	0.310379i	0.762408	−	0.647096i	$-0.224017\pi$
$11$	−95717.6	−	165788.i	−0.179197	−	0.310379i	−0.941606	+	0.336717i	$0.890683\pi$
$12$		0			0
$13$	662649.	−	1.14774e6i	0.494989	−	0.857346i	−0.504995	−	0.863123i	$-0.668506\pi$
$13$	662649.	−	1.14774e6i	0.494989	−	0.857346i	0.999983	+	0.00577689i	$0.00183885\pi$
$14$	848149.	−	1.46904e6i	0.421471	−	0.730010i
$15$		0			0
$16$	−524288.	−	908093.i	−0.125000	−	0.216506i
$17$	−7.39161e6			−1.26261			−0.631306	−	0.775534i	$-0.717481\pi$
$17$	−7.39161e6			−1.26261			−0.631306	+	0.775534i	$0.717481\pi$
$18$		0			0
$19$	−6.06542e6			−0.561974			−0.280987	−	0.959712i	$-0.590662\pi$
$19$	−6.06542e6			−0.561974			−0.280987	+	0.959712i	$0.590662\pi$
$20$	−1.93422e6	−	3.35016e6i	−0.135157	−	0.234100i
$21$		0			0
$22$	−3.06296e6	+	5.30521e6i	−0.126712	+	0.219471i
$23$	−2.32666e7	+	4.02989e7i	−0.753753	+	1.30554i	0.192239	+	0.981348i	$0.438425\pi$
$23$	−2.32666e7	+	4.02989e7i	−0.753753	+	1.30554i	−0.945992	+	0.324190i	$0.894908\pi$
$24$		0			0
$25$	1.72783e7	+	2.99269e7i	0.353860	+	0.612903i
$26$	−4.24096e7			−0.700020
$27$		0			0
$28$	−5.42816e7			−0.596051
$29$	3.25031e7	+	5.62970e7i	0.294263	+	0.509678i	0.974813	−	0.223023i	$-0.0715926\pi$
$29$	3.25031e7	+	5.62970e7i	0.294263	+	0.509678i	−0.680550	+	0.732701i	$0.738259\pi$
$30$		0			0
$31$	2.79570e7	−	4.84230e7i	0.175389	−	0.303782i	−0.764907	−	0.644141i	$-0.777215\pi$
$31$	2.79570e7	−	4.84230e7i	0.175389	−	0.303782i	0.940296	+	0.340359i	$0.110548\pi$
$32$	−1.67772e7	+	2.90590e7i	−0.0883883	+	0.153093i
$33$		0			0
$34$	1.18266e8	+	2.04842e8i	0.446401	+	0.773189i
$35$	−2.00257e8			−0.644485
$36$		0			0
$37$	−2.00878e8			−0.476236			−0.238118	−	0.971236i	$-0.576531\pi$
$37$	−2.00878e8			−0.476236			−0.238118	+	0.971236i	$0.576531\pi$
$38$	9.70467e7	+	1.68090e8i	0.198688	+	0.344137i
$39$		0			0
$40$	−6.18949e7	+	1.07205e8i	−0.0955707	+	0.165533i
$41$	2.86262e8	−	4.95820e8i	0.385880	−	0.668363i	−0.606011	−	0.795456i	$-0.707231\pi$
$41$	2.86262e8	−	4.95820e8i	0.385880	−	0.668363i	0.991891	+	0.127093i	$0.0405647\pi$
$42$		0			0
$43$	−4.83786e7	−	8.37942e7i	−0.0501854	−	0.0869236i	0.839841	−	0.542832i	$-0.182648\pi$
$43$	−4.83786e7	−	8.37942e7i	−0.0501854	−	0.0869236i	−0.890027	+	0.455908i	$0.849315\pi$
$44$	1.96030e8			0.179197
$45$		0			0
$46$	1.48906e9			1.06597
$47$	1.19837e9	+	2.07563e9i	0.762169	+	1.32011i	0.941731	+	0.336368i	$0.109199\pi$
$47$	1.19837e9	+	2.07563e9i	0.762169	+	1.32011i	−0.179562	+	0.983747i	$0.557468\pi$
$48$		0			0
$49$	−4.16332e8	+	7.21107e8i	−0.210553	+	0.364688i
$50$	5.52906e8	−	9.57661e8i	0.250217	−	0.433388i
$51$		0			0
$52$	6.78553e8	+	1.17529e9i	0.247494	+	0.428673i
$53$	−3.14068e9			−1.03159			−0.515794	−	0.856713i	$-0.672503\pi$
$53$	−3.14068e9			−1.03159			−0.515794	+	0.856713i	$0.672503\pi$
$54$		0			0
$55$	7.23197e8			0.193759
$56$	8.68505e8	+	1.50429e9i	0.210736	+	0.365005i
$57$		0			0
$58$	1.04010e9	−	1.80150e9i	0.208075	−	0.360397i
$59$	1.10233e9	−	1.90930e9i	0.200737	−	0.347686i	−0.748029	−	0.663666i	$-0.769000\pi$
$59$	1.10233e9	−	1.90930e9i	0.200737	−	0.347686i	0.948766	+	0.315980i	$0.102333\pi$
$60$		0			0
$61$	−5.47943e9	−	9.49066e9i	−0.830657	−	1.43874i	−0.897518	−	0.440977i	$-0.854632\pi$
$61$	−5.47943e9	−	9.49066e9i	−0.830657	−	1.43874i	0.0668618	−	0.997762i	$-0.478701\pi$
$62$	−1.78925e9			−0.248037
$63$		0			0
$64$	1.07374e9			0.125000
$65$	2.50333e9	+	4.33590e9i	0.267606	+	0.463507i
$66$		0			0
$67$	5.31673e9	−	9.20885e9i	0.481098	−	0.833286i	−0.518667	−	0.854976i	$-0.673571\pi$
$67$	5.31673e9	−	9.20885e9i	0.481098	−	0.833286i	0.999765	+	0.0216904i	$0.00690483\pi$
$68$	3.78450e9	−	6.55495e9i	0.315653	−	0.546727i
$69$		0			0
$70$	3.20411e9	+	5.54968e9i	0.227860	+	0.394665i
$71$	−2.95131e10			−1.94131			−0.970653	−	0.240486i	$-0.922693\pi$
$71$	−2.95131e10			−1.94131			−0.970653	+	0.240486i	$0.922693\pi$
$72$		0			0
$73$	2.30487e10			1.30128			0.650641	−	0.759386i	$-0.274500\pi$
$73$	2.30487e10			1.30128			0.650641	+	0.759386i	$0.274500\pi$
$74$	3.21404e9	+	5.56689e9i	0.168375	+	0.291634i
$75$		0			0
$76$	3.10550e9	−	5.37888e9i	0.140493	−	0.243342i
$77$	5.07392e9	−	8.78829e9i	0.213622	−	0.370003i
$78$		0			0
$79$	1.66109e10	+	2.87710e10i	0.607358	+	1.05198i	0.991674	+	0.128774i	$0.0411041\pi$
$79$	1.66109e10	+	2.87710e10i	0.607358	+	1.05198i	−0.384316	+	0.923202i	$0.625563\pi$
$80$	3.96127e9			0.135157
$81$		0			0
$82$	−1.83207e10			−0.545716
$83$	−1.17076e10	−	2.02782e10i	−0.326242	−	0.565067i	0.655521	−	0.755177i	$-0.272449\pi$
$83$	−1.17076e10	−	2.02782e10i	−0.326242	−	0.565067i	−0.981763	+	0.190109i	$0.939116\pi$
$84$		0			0
$85$	1.39619e10	−	2.41827e10i	0.341303	−	0.591154i
$86$	−1.54812e9	+	2.68142e9i	−0.0354864	+	0.0614643i
$87$		0			0
$88$	−3.13647e9	−	5.43253e9i	−0.0633559	−	0.109736i
$89$	4.47401e10			0.849281			0.424641	−	0.905362i	$-0.360400\pi$
$89$	4.47401e10			0.849281			0.424641	+	0.905362i	$0.360400\pi$
$90$		0			0
$91$	7.02532e10			1.18015
$92$	−2.38250e10	−	4.12660e10i	−0.376876	−	0.652769i
$93$		0			0
$94$	3.83477e10	−	6.64202e10i	0.538935	−	0.933462i
$95$	1.14569e10	−	1.98439e10i	0.151910	−	0.263116i
$96$		0			0
$97$	−1.23184e10	−	2.13361e10i	−0.145650	−	0.252273i	0.783965	−	0.620805i	$-0.213194\pi$
$97$	−1.23184e10	−	2.13361e10i	−0.145650	−	0.252273i	−0.929615	+	0.368532i	$0.879861\pi$
$98$	2.66452e10			0.297767
$99$		0			0
$100$	−3.53860e10			−0.353860
$101$	−4.17542e10	−	7.23205e10i	−0.395306	−	0.684689i	0.597835	−	0.801620i	$-0.296028\pi$
$101$	−4.17542e10	−	7.23205e10i	−0.395306	−	0.684689i	−0.993140	+	0.116930i	$0.962695\pi$
$102$		0			0
$103$	−8.77375e10	+	1.51966e11i	−0.745728	+	1.29164i	0.204125	+	0.978945i	$0.434565\pi$
$103$	−8.77375e10	+	1.51966e11i	−0.745728	+	1.29164i	−0.949854	+	0.312695i	$0.898768\pi$
$104$	2.17137e10	−	3.76092e10i	0.175005	−	0.303117i
$105$		0			0
$106$	5.02509e10	+	8.70371e10i	0.364721	+	0.631716i
$107$	2.96445e10			0.204330			0.102165	−	0.994767i	$-0.467423\pi$
$107$	2.96445e10			0.204330			0.102165	+	0.994767i	$0.467423\pi$
$108$		0			0
$109$	2.52394e11			1.57120			0.785602	−	0.618732i	$-0.212353\pi$
$109$	2.52394e11			1.57120			0.785602	+	0.618732i	$0.212353\pi$
$110$	−1.15712e10	−	2.00418e10i	−0.0685041	−	0.118653i
$111$		0			0
$112$	2.77922e10	−	4.81374e10i	0.149013	−	0.258097i
$113$	−1.75265e11	+	3.03568e11i	−0.894877	+	1.54997i	−0.0609200	+	0.998143i	$0.519403\pi$
$113$	−1.75265e11	+	3.03568e11i	−0.894877	+	1.54997i	−0.833957	+	0.551830i	$0.813930\pi$
$114$		0			0
$115$	−8.78956e10	−	1.52240e11i	−0.407501	−	0.705813i
$116$	−6.65663e10			−0.294263
$117$		0			0
$118$	−7.05493e10			−0.283885
$119$	−1.95912e11	−	3.39330e11i	−0.752581	−	1.30351i
$120$		0			0
$121$	1.24332e11	−	2.15350e11i	0.435777	−	0.754787i
$122$	−1.75342e11	+	3.03701e11i	−0.587363	+	1.01734i
$123$		0			0
$124$	2.86280e10	+	4.95851e10i	0.0876943	+	0.151891i
$125$	−3.15008e11			−0.923244
$126$		0			0
$127$	8.86417e9			0.0238077			0.0119039	−	0.999929i	$-0.496211\pi$
$127$	8.86417e9			0.0238077			0.0119039	+	0.999929i	$0.496211\pi$
$128$	−1.71799e10	−	2.97564e10i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	8.01067e10	−	1.38749e11i	0.189226	−	0.327749i
$131$	1.22666e11	−	2.12463e11i	0.277799	−	0.481162i	−0.693038	−	0.720901i	$-0.743728\pi$
$131$	1.22666e11	−	2.12463e11i	0.277799	−	0.481162i	0.970837	+	0.239739i	$0.0770617\pi$
$132$		0			0
$133$	−1.60762e11	−	2.78448e11i	−0.334965	−	0.580176i
$134$	−3.40271e11			−0.680375
$135$		0			0
$136$	−2.42208e11			−0.446401
$137$	−2.18990e11	−	3.79302e11i	−0.387670	−	0.671463i	0.604466	−	0.796631i	$-0.293387\pi$
$137$	−2.18990e11	−	3.79302e11i	−0.387670	−	0.671463i	−0.992136	+	0.125167i	$0.960053\pi$
$138$		0			0
$139$	−2.08201e11	+	3.60615e11i	−0.340331	+	0.589470i	−0.984494	−	0.175418i	$-0.943872\pi$
$139$	−2.08201e11	+	3.60615e11i	−0.340331	+	0.589470i	0.644163	+	0.764888i	$0.277206\pi$
$140$	1.02532e11	−	1.77590e11i	0.161121	−	0.279070i
$141$		0			0
$142$	4.72209e11	+	8.17891e11i	0.686355	+	1.18880i
$143$	−2.53709e11			−0.354803
$144$		0			0
$145$	−2.45578e11			−0.318174
$146$	−3.68780e11	−	6.38745e11i	−0.460073	−	0.796869i
$147$		0			0
$148$	1.02849e11	−	1.78140e11i	0.119059	−	0.206216i
$149$	6.58285e11	−	1.14018e12i	0.734327	−	1.27189i	−0.220691	−	0.975344i	$-0.570831\pi$
$149$	6.58285e11	−	1.14018e12i	0.734327	−	1.27189i	0.955018	−	0.296548i	$-0.0958354\pi$
$150$		0			0
$151$	−3.10088e11	−	5.37088e11i	−0.321449	−	0.556766i	0.659338	−	0.751846i	$-0.270837\pi$
$151$	−3.10088e11	−	5.37088e11i	−0.321449	−	0.556766i	−0.980787	+	0.195081i	$0.937503\pi$
$152$	−1.98752e11			−0.198688
$153$		0			0
$154$	−3.24731e11			−0.302106
$155$	1.05615e11	+	1.82931e11i	0.0948203	+	0.164234i
$156$		0			0
$157$	−2.98794e11	+	5.17527e11i	−0.249991	+	0.432997i	−0.963523	−	0.267625i	$-0.913761\pi$
$157$	−2.98794e11	+	5.17527e11i	−0.249991	+	0.432997i	0.713532	+	0.700623i	$0.247094\pi$
$158$	5.31550e11	−	9.20671e11i	0.429467	−	0.743859i
$159$		0			0
$160$	−6.33804e10	−	1.09778e11i	−0.0477854	−	0.0827667i
$161$	−2.46669e12			−1.79710
$162$		0			0
$163$	−1.93116e12			−1.31458			−0.657290	−	0.753638i	$-0.728297\pi$
$163$	−1.93116e12			−1.31458			−0.657290	+	0.753638i	$0.728297\pi$
$164$	2.93132e11	+	5.07719e11i	0.192940	+	0.334182i
$165$		0			0
$166$	−3.74644e11	+	6.48903e11i	−0.230688	+	0.399563i
$167$	4.50210e11	−	7.79786e11i	0.268210	−	0.464553i	−0.700190	−	0.713957i	$-0.746901\pi$
$167$	4.50210e11	−	7.79786e11i	0.268210	−	0.464553i	0.968400	+	0.249404i	$0.0802347\pi$
$168$		0			0
$169$	1.78720e10	+	3.09552e10i	0.00997232	+	0.0172726i
$170$	−8.93560e11			−0.482675
$171$		0			0
$172$	9.90794e10			0.0501854
$173$	−1.77155e12	−	3.06841e12i	−0.869158	−	1.50543i	−0.862859	−	0.505445i	$-0.831328\pi$
$173$	−1.77155e12	−	3.06841e12i	−0.869158	−	1.50543i	−0.00629914	−	0.999980i	$-0.502005\pi$
$174$		0			0
$175$	−9.15912e11	+	1.58641e12i	−0.421837	+	0.730642i
$176$	−1.00367e11	+	1.73841e11i	−0.0447994	+	0.0775948i
$177$		0			0
$178$	−7.15841e11	−	1.23987e12i	−0.300266	−	0.520076i
$179$	−3.54131e12			−1.44036			−0.720182	−	0.693785i	$-0.755942\pi$
$179$	−3.54131e12			−1.44036			−0.720182	+	0.693785i	$0.755942\pi$
$180$		0			0
$181$	2.51189e12			0.961098			0.480549	−	0.876968i	$-0.340437\pi$
$181$	2.51189e12			0.961098			0.480549	+	0.876968i	$0.340437\pi$
$182$	−1.12405e12	−	1.94691e12i	−0.417247	−	0.722693i
$183$		0			0
$184$	−7.62398e11	+	1.32051e12i	−0.266492	+	0.461577i
$185$	3.79434e11	−	6.57200e11i	0.128734	−	0.222973i
$186$		0			0
$187$	7.07507e11	+	1.22544e12i	0.226257	+	0.391888i
$188$	−2.45425e12			−0.762169
$189$		0			0
$190$	−7.33240e11			−0.214833
$191$	−3.15663e12	−	5.46745e12i	−0.898546	−	1.55633i	−0.829353	−	0.558724i	$-0.811291\pi$
$191$	−3.15663e12	−	5.46745e12i	−0.898546	−	1.55633i	−0.0691926	−	0.997603i	$-0.522042\pi$
$192$		0			0
$193$	5.44962e11	−	9.43902e11i	0.146488	−	0.253724i	−0.783439	−	0.621468i	$-0.786536\pi$
$193$	5.44962e11	−	9.43902e11i	0.146488	−	0.253724i	0.929927	+	0.367744i	$0.119870\pi$
$194$	−3.94189e11	+	6.82756e11i	−0.102990	+	0.178384i
$195$		0			0
$196$	−4.26323e11	−	7.38414e11i	−0.105276	−	0.182344i
$197$	−4.77834e12			−1.14740			−0.573698	−	0.819067i	$-0.694492\pi$
$197$	−4.77834e12			−1.14740			−0.573698	+	0.819067i	$0.694492\pi$
$198$		0			0
$199$	−3.39102e12			−0.770261			−0.385130	−	0.922862i	$-0.625844\pi$
$199$	−3.39102e12			−0.770261			−0.385130	+	0.922862i	$0.625844\pi$
$200$	5.66176e11	+	9.80645e11i	0.125108	+	0.216694i
$201$		0			0
$202$	−1.33614e12	+	2.31425e12i	−0.279523	+	0.484149i
$203$	−1.72297e12	+	2.98426e12i	−0.350791	+	0.607588i
$204$		0			0
$205$	1.08143e12	+	1.87309e12i	0.208618	+	0.361337i
$206$	5.61520e12			1.05462
$207$		0			0
$208$	−1.38968e12			−0.247494
$209$	5.80567e11	+	1.00557e12i	0.100704	+	0.174425i
$210$		0			0
$211$	5.35886e12	−	9.28182e12i	0.882102	−	1.52785i	0.0331032	−	0.999452i	$-0.489461\pi$
$211$	5.35886e12	−	9.28182e12i	0.882102	−	1.52785i	0.848999	−	0.528394i	$-0.177206\pi$
$212$	1.60803e12	−	2.78519e12i	0.257897	−	0.446691i
$213$		0			0
$214$	−4.74311e11	−	8.21531e11i	−0.0722417	−	0.125126i
$215$	3.65526e11			0.0542634
$216$		0			0
$217$	2.96397e12			0.418162
$218$	−4.03830e12	−	6.99454e12i	−0.555505	−	0.962162i
$219$		0			0
$220$	−3.70277e11	+	6.41338e11i	−0.0484397	+	0.0839001i
$221$	−4.89804e12	+	8.48366e12i	−0.624979	+	1.08249i
$222$		0			0
$223$	−9.87717e11	−	1.71078e12i	−0.119938	−	0.207738i	0.799805	−	0.600260i	$-0.204936\pi$
$223$	−9.87717e11	−	1.71078e12i	−0.119938	−	0.207738i	−0.919743	+	0.392522i	$0.871603\pi$
$224$	−1.77870e12			−0.210736
$225$		0			0
$226$	1.12169e13			1.26555
$227$	−8.21078e12	−	1.42215e13i	−0.904154	−	1.56604i	−0.822049	−	0.569417i	$-0.807169\pi$
$227$	−8.21078e12	−	1.42215e13i	−0.904154	−	1.56604i	−0.0821051	−	0.996624i	$-0.526164\pi$
$228$		0			0
$229$	8.30337e12	−	1.43819e13i	0.871283	−	1.50911i	0.0106134	−	0.999944i	$-0.496622\pi$
$229$	8.30337e12	−	1.43819e13i	0.871283	−	1.50911i	0.860670	−	0.509163i	$-0.170045\pi$
$230$	−2.81266e12	+	4.87167e12i	−0.288147	+	0.499085i
$231$		0			0
$232$	1.06506e12	+	1.84474e12i	0.104038	+	0.180198i
$233$	1.39122e13			1.32721			0.663605	−	0.748083i	$-0.269026\pi$
$233$	1.39122e13			1.32721			0.663605	+	0.748083i	$0.269026\pi$
$234$		0			0
$235$	−9.05429e12			−0.824102
$236$	1.12879e12	+	1.95512e12i	0.100368	+	0.173843i
$237$		0			0
$238$	−6.26919e12	+	1.08586e13i	−0.532155	+	0.921719i
$239$	7.86403e12	−	1.36209e13i	0.652314	−	1.12984i	−0.330246	−	0.943895i	$-0.607132\pi$
$239$	7.86403e12	−	1.36209e13i	0.652314	−	1.12984i	0.982560	−	0.185946i	$-0.0595349\pi$
$240$		0			0
$241$	−7.90047e11	−	1.36840e12i	−0.0625978	−	0.108423i	0.833028	−	0.553231i	$-0.186605\pi$
$241$	−7.90047e11	−	1.36840e12i	−0.0625978	−	0.108423i	−0.895626	+	0.444808i	$0.853272\pi$
$242$	−7.95726e12			−0.616281
$243$		0			0
$244$	1.12219e13			0.830657
$245$	−1.57280e12	−	2.72417e12i	−0.113831	−	0.197161i
$246$		0			0
$247$	−4.01925e12	+	6.96154e12i	−0.278171	+	0.481806i
$248$	9.16095e11	−	1.58672e12i	0.0620093	−	0.107403i
$249$		0			0
$250$	5.04013e12	+	8.72976e12i	0.326416	+	0.565369i
$251$	−1.45264e13			−0.920351			−0.460176	−	0.887828i	$-0.652214\pi$
$251$	−1.45264e13			−0.920351			−0.460176	+	0.887828i	$0.652214\pi$
$252$		0			0
$253$	8.90807e12			0.540282
$254$	−1.41827e11	−	2.45651e11i	−0.00841729	−	0.0145792i
$255$		0			0
$256$	−5.49756e11	+	9.52205e11i	−0.0312500	+	0.0541266i
$257$	−2.43750e12	+	4.22187e12i	−0.135616	+	0.234895i	−0.925833	−	0.377933i	$-0.876635\pi$
$257$	−2.43750e12	+	4.22187e12i	−0.135616	+	0.234895i	0.790216	+	0.612828i	$0.209968\pi$
$258$		0			0
$259$	−5.32420e12	−	9.22178e12i	−0.283861	−	0.491661i
$260$	−5.12683e12			−0.267606
$261$		0			0
$262$	−7.85060e12			−0.392867
$263$	7.13284e12	+	1.23544e13i	0.349547	+	0.605434i	0.986169	−	0.165742i	$-0.0530020\pi$
$263$	7.13284e12	+	1.23544e13i	0.349547	+	0.605434i	−0.636622	+	0.771176i	$0.719669\pi$
$264$		0			0
$265$	5.93238e12	−	1.02752e13i	0.278854	−	0.482989i
$266$	−5.14438e12	+	8.91033e12i	−0.236856	+	0.410247i
$267$		0			0
$268$	5.44433e12	+	9.42986e12i	0.240549	+	0.416643i
$269$	−1.72215e13			−0.745475			−0.372737	−	0.927937i	$-0.621581\pi$
$269$	−1.72215e13			−0.745475			−0.372737	+	0.927937i	$0.621581\pi$
$270$		0			0
$271$	2.46849e13			1.02589			0.512944	−	0.858422i	$-0.328555\pi$
$271$	2.46849e13			1.02589			0.512944	+	0.858422i	$0.328555\pi$
$272$	3.87533e12	+	6.71227e12i	0.157826	+	0.273363i
$273$		0			0
$274$	−7.00769e12	+	1.21377e13i	−0.274124	+	0.474796i
$275$	3.30767e12	−	5.72906e12i	0.126822	−	0.219661i
$276$		0			0
$277$	−4.80945e12	−	8.33021e12i	−0.177197	−	0.306914i	0.763722	−	0.645545i	$-0.223370\pi$
$277$	−4.80945e12	−	8.33021e12i	−0.177197	−	0.306914i	−0.940919	+	0.338631i	$0.890036\pi$
$278$	1.33249e13			0.481300
$279$		0			0
$280$	−6.56202e12			−0.227860
$281$	1.66223e13	+	2.87907e13i	0.565988	+	0.980321i	0.996957	+	0.0779537i	$0.0248386\pi$
$281$	1.66223e13	+	2.87907e13i	0.565988	+	0.980321i	−0.430969	+	0.902367i	$0.641828\pi$
$282$		0			0
$283$	1.46871e13	−	2.54388e13i	0.480962	−	0.833051i	−0.518799	−	0.854896i	$-0.673621\pi$
$283$	1.46871e13	−	2.54388e13i	0.480962	−	0.833051i	0.999761	+	0.0218449i	$0.00695401\pi$
$284$	1.51107e13	−	2.61725e13i	0.485326	−	0.840610i
$285$		0			0
$286$	4.05934e12	+	7.03098e12i	0.125442	+	0.217272i
$287$	3.03491e13			0.920015
$288$		0			0
$289$	2.03640e13			0.594188
$290$	3.92925e12	+	6.80565e12i	0.112492	+	0.194841i
$291$		0			0
$292$	−1.18010e13	+	2.04398e13i	−0.325320	+	0.563472i
$293$	2.37463e13	−	4.11298e13i	0.642428	−	1.11272i	−0.342461	−	0.939532i	$-0.611261\pi$
$293$	2.37463e13	−	4.11298e13i	0.642428	−	1.11272i	0.984889	−	0.173186i	$-0.0554061\pi$
$294$		0			0
$295$	4.16436e12	+	7.21288e12i	0.108524	+	0.187970i
$296$	−6.58236e12			−0.168375
$297$		0			0
$298$	−4.21302e13			−1.03850
$299$	3.08351e13	+	5.34080e13i	0.746198	+	1.29245i
$300$		0			0
$301$	2.56452e12	−	4.44188e12i	0.0598260	−	0.103622i
$302$	−9.92282e12	+	1.71868e13i	−0.227299	+	0.393693i
$303$		0			0
$304$	3.18003e12	+	5.50797e12i	0.0702467	+	0.121671i
$305$	4.14000e13			0.898155
$306$		0			0
$307$	−6.85550e13			−1.43476			−0.717378	−	0.696684i	$-0.754658\pi$
$307$	−6.85550e13			−1.43476			−0.717378	+	0.696684i	$0.754658\pi$
$308$	5.19570e12	+	8.99921e12i	0.106811	+	0.185002i
$309$		0			0
$310$	3.37968e12	−	5.85378e12i	0.0670481	−	0.116131i
$311$	−2.82350e12	+	4.89045e12i	−0.0550308	+	0.0953161i	−0.892228	−	0.451584i	$-0.850859\pi$
$311$	−2.82350e12	+	4.89045e12i	−0.0550308	+	0.0953161i	0.837198	+	0.546900i	$0.184192\pi$
$312$		0			0
$313$	−4.79841e13	−	8.31109e13i	−0.902825	−	1.56374i	−0.823810	−	0.566865i	$-0.808156\pi$
$313$	−4.79841e13	−	8.31109e13i	−0.902825	−	1.56374i	−0.0790147	−	0.996873i	$-0.525177\pi$
$314$	1.91228e13			0.353541
$315$		0			0
$316$	−3.40192e13			−0.607358
$317$	1.37213e13	+	2.37659e13i	0.240751	+	0.416993i	0.960928	−	0.276797i	$-0.0892729\pi$
$317$	1.37213e13	+	2.37659e13i	0.240751	+	0.416993i	−0.720177	+	0.693790i	$0.755940\pi$
$318$		0			0
$319$	6.22223e12	−	1.07772e13i	0.105462	−	0.182666i
$320$	−2.02817e12	+	3.51290e12i	−0.0337894	+	0.0585249i
$321$		0			0
$322$	3.94670e13	+	6.83589e13i	0.635371	+	1.10049i
$323$	4.48332e13			0.709555
$324$		0			0
$325$	4.57978e13			0.700626
$326$	3.08986e13	+	5.35180e13i	0.464774	+	0.805013i
$327$		0			0
$328$	9.38022e12	−	1.62470e13i	0.136429	−	0.236302i
$329$	−6.35246e13	+	1.10028e14i	−0.908582	+	1.57371i
$330$		0			0
$331$	5.95979e12	+	1.03227e13i	0.0824474	+	0.142803i	0.904301	−	0.426896i	$-0.140393\pi$
$331$	5.95979e12	+	1.03227e13i	0.0824474	+	0.142803i	−0.821853	+	0.569699i	$0.807060\pi$
$332$	2.39772e13			0.326242
$333$		0			0
$334$	−2.88134e13			−0.379306
$335$	2.00854e13	+	3.47889e13i	0.260096	+	0.450499i
$336$		0			0
$337$	−5.60348e13	+	9.70551e13i	−0.702252	+	1.21634i	0.265421	+	0.964132i	$0.414489\pi$
$337$	−5.60348e13	+	9.70551e13i	−0.702252	+	1.21634i	−0.967674	+	0.252205i	$0.918844\pi$
$338$	5.71904e11	−	9.90567e11i	0.00705150	−	0.0122136i
$339$		0			0
$340$	1.42970e13	+	2.47631e13i	0.170651	+	0.295577i
$341$	−1.07039e13			−0.125717
$342$		0			0
$343$	6.06779e13			0.690101
$344$	−1.58527e12	−	2.74577e12i	−0.0177432	−	0.0307321i
$345$		0			0
$346$	−5.66894e13	+	9.81890e13i	−0.614587	+	1.06450i
$347$	−4.05120e13	+	7.01688e13i	−0.432286	+	0.748741i	−0.997070	−	0.0764975i	$-0.975626\pi$
$347$	−4.05120e13	+	7.01688e13i	−0.432286	+	0.748741i	0.564784	+	0.825239i	$0.308960\pi$
$348$		0			0
$349$	−8.99111e13	−	1.55731e14i	−0.929551	−	1.61003i	−0.784073	−	0.620668i	$-0.786861\pi$
$349$	−8.99111e13	−	1.55731e14i	−0.929551	−	1.61003i	−0.145478	−	0.989361i	$-0.546472\pi$
$350$	5.86183e13			0.596567
$351$		0			0
$352$	6.42350e12			0.0633559
$353$	3.91733e13	+	6.78502e13i	0.380390	+	0.658855i	0.991118	−	0.132985i	$-0.0424564\pi$
$353$	3.91733e13	+	6.78502e13i	0.380390	+	0.658855i	−0.610728	+	0.791841i	$0.709123\pi$
$354$		0			0
$355$	5.57468e13	−	9.65562e13i	0.524764	−	0.908917i
$356$	−2.29069e13	+	3.96759e13i	−0.212320	+	0.367750i
$357$		0			0
$358$	5.66610e13	+	9.81397e13i	0.509246	+	0.882039i
$359$	1.87927e14			1.66329			0.831646	−	0.555306i	$-0.187399\pi$
$359$	1.87927e14			1.66329			0.831646	+	0.555306i	$0.187399\pi$
$360$		0			0
$361$	−7.97009e13			−0.684185
$362$	−4.01902e13	−	6.96114e13i	−0.339799	−	0.588550i
$363$		0			0
$364$	−3.59696e13	+	6.23012e13i	−0.295038	+	0.511021i
$365$	−4.35364e13	+	7.54072e13i	−0.351756	+	0.609259i
$366$		0			0
$367$	−2.96521e13	−	5.13589e13i	−0.232483	−	0.402673i	0.726055	−	0.687637i	$-0.241352\pi$
$367$	−2.96521e13	−	5.13589e13i	−0.232483	−	0.402673i	−0.958538	+	0.284964i	$0.908018\pi$
$368$	4.87935e13			0.376876
$369$		0			0
$370$	−2.42838e13			−0.182057
$371$	−8.32427e13	−	1.44181e14i	−0.614879	−	1.06500i
$372$		0			0
$373$	6.15276e11	−	1.06569e12i	0.00441237	−	0.00764245i	−0.863811	−	0.503816i	$-0.831929\pi$
$373$	6.15276e11	−	1.06569e12i	0.00441237	−	0.00764245i	0.868223	+	0.496174i	$0.165262\pi$
$374$	2.26402e13	−	3.92140e13i	0.159988	−	0.277107i
$375$		0			0
$376$	3.92680e13	+	6.80142e13i	0.269467	+	0.466731i
$377$	8.61525e13			0.582627
$378$		0			0
$379$	1.21423e13			0.0797600			0.0398800	−	0.999204i	$-0.487302\pi$
$379$	1.21423e13			0.0797600			0.0398800	+	0.999204i	$0.487302\pi$
$380$	1.17318e13	+	2.03201e13i	0.0759550	+	0.131558i
$381$		0			0
$382$	−1.01012e14	+	1.74958e14i	−0.635368	+	1.10049i
$383$	1.06199e14	−	1.83942e14i	0.658457	−	1.14048i	−0.322559	−	0.946550i	$-0.604543\pi$
$383$	1.06199e14	−	1.83942e14i	0.658457	−	1.14048i	0.981015	−	0.193931i	$-0.0621237\pi$
$384$		0			0
$385$	1.91681e13	+	3.32001e13i	0.115490	+	0.200035i
$386$	−3.48776e13			−0.207165
$387$		0			0
$388$	2.52281e13			0.145650
$389$	8.40877e13	+	1.45644e14i	0.478641	+	0.829030i	0.999700	−	0.0244903i	$-0.00779627\pi$
$389$	8.40877e13	+	1.45644e14i	0.478641	+	0.829030i	−0.521059	+	0.853521i	$0.674463\pi$
$390$		0			0
$391$	1.71977e14	−	2.97873e14i	0.951697	−	1.64839i
$392$	−1.36424e13	+	2.36292e13i	−0.0744416	+	0.128937i
$393$		0			0
$394$	7.64535e13	+	1.32421e14i	0.405666	+	0.702633i
$395$	−1.25504e14			−0.656712
$396$		0			0
$397$	−1.43772e13			−0.0731691			−0.0365845	−	0.999331i	$-0.511648\pi$
$397$	−1.43772e13			−0.0731691			−0.0365845	+	0.999331i	$0.511648\pi$
$398$	5.42562e13	+	9.39746e13i	0.272328	+	0.471687i
$399$		0			0
$400$	1.81176e13	−	3.13806e13i	0.0884649	−	0.153226i
$401$	6.31228e13	−	1.09332e14i	0.304013	−	0.526566i	−0.673028	−	0.739617i	$-0.735007\pi$
$401$	6.31228e13	−	1.09332e14i	0.304013	−	0.526566i	0.977041	+	0.213051i	$0.0683401\pi$
$402$		0			0
$403$	−3.70514e13	−	6.41749e13i	−0.173631	−	0.300737i
$404$	8.55127e13			0.395306
$405$		0			0
$406$	1.10270e14			0.496093
$407$	1.92275e13	+	3.33030e13i	0.0853403	+	0.147814i
$408$		0			0
$409$	5.21006e13	−	9.02410e13i	0.225095	−	0.389875i	−0.731253	−	0.682106i	$-0.761064\pi$
$409$	5.21006e13	−	9.02410e13i	0.225095	−	0.389875i	0.956348	+	0.292231i	$0.0943976\pi$
$410$	3.46057e13	−	5.99389e13i	0.147515	−	0.255504i
$411$		0			0
$412$	−8.98432e13	−	1.55613e14i	−0.372864	−	0.645820i
$413$	1.16868e14			0.478597
$414$		0			0
$415$	8.84574e13			0.352752
$416$	2.22348e13	+	3.85118e13i	0.0875025	+	0.151559i
$417$		0			0
$418$	1.85782e13	−	3.21783e13i	0.0712087	−	0.123337i
$419$	−2.24905e12	+	3.89548e12i	−0.00850791	+	0.0147361i	−0.870248	−	0.492614i	$-0.836042\pi$
$419$	−2.24905e12	+	3.89548e12i	−0.00850791	+	0.0147361i	0.861740	+	0.507350i	$0.169375\pi$
$420$		0			0
$421$	−6.92552e13	−	1.19953e14i	−0.255212	−	0.442040i	0.709741	−	0.704462i	$-0.248812\pi$
$421$	−6.92552e13	−	1.19953e14i	−0.255212	−	0.442040i	−0.964953	+	0.262423i	$0.915479\pi$
$422$	−3.42967e14			−1.24748
$423$		0			0
$424$	−1.02914e14			−0.364721
$425$	−1.27714e14	−	2.21208e14i	−0.446787	−	0.773859i
$426$		0			0
$427$	2.90461e14	−	5.03093e14i	0.990227	−	1.71512i
$428$	−1.51780e13	+	2.62890e13i	−0.0510826	+	0.0884776i
$429$		0			0
$430$	−5.84842e12	−	1.01298e13i	−0.0191850	−	0.0332294i
$431$	−3.59012e14			−1.16275			−0.581373	−	0.813637i	$-0.697484\pi$
$431$	−3.59012e14			−1.16275			−0.581373	+	0.813637i	$0.697484\pi$
$432$		0			0
$433$	2.15274e14			0.679684			0.339842	−	0.940482i	$-0.389626\pi$
$433$	2.15274e14			0.679684			0.339842	+	0.940482i	$0.389626\pi$
$434$	−4.74234e13	−	8.21398e13i	−0.147843	−	0.256071i
$435$		0			0
$436$	−1.29226e14	+	2.23825e14i	−0.392801	+	0.680351i
$437$	1.41121e14	−	2.44430e14i	0.423589	−	0.733678i
$438$		0			0
$439$	2.78955e14	+	4.83164e14i	0.816543	+	1.41429i	0.908215	+	0.418504i	$0.137446\pi$
$439$	2.78955e14	+	4.83164e14i	0.816543	+	1.41429i	−0.0916720	+	0.995789i	$0.529221\pi$
$440$	2.36977e13			0.0685041
$441$		0			0
$442$	3.13475e14			0.883853
$443$	1.38874e14	+	2.40537e14i	0.386723	+	0.669824i	0.992007	−	0.126186i	$-0.0402736\pi$
$443$	1.38874e14	+	2.40537e14i	0.386723	+	0.669824i	−0.605283	+	0.796010i	$0.706940\pi$
$444$		0			0
$445$	−8.45087e13	+	1.46373e14i	−0.229573	+	0.397633i
$446$	−3.16069e13	+	5.47448e13i	−0.0848087	+	0.146893i
$447$		0			0
$448$	2.84592e13	+	4.92927e13i	0.0745063	+	0.129049i
$449$	−5.80134e14			−1.50028			−0.750142	−	0.661277i	$-0.770015\pi$
$449$	−5.80134e14			−1.50028			−0.750142	+	0.661277i	$0.770015\pi$
$450$		0			0
$451$	−1.09601e14			−0.276595
$452$	−1.79471e14	−	3.10853e14i	−0.447438	−	0.774986i
$453$		0			0
$454$	−2.62745e14	+	4.55088e14i	−0.639333	+	1.10736i
$455$	−1.32700e14	+	2.29843e14i	−0.319013	+	0.552547i
$456$		0			0
$457$	−8.13864e13	−	1.40965e14i	−0.190991	−	0.330806i	0.754588	−	0.656199i	$-0.227837\pi$
$457$	−8.13864e13	−	1.40965e14i	−0.190991	−	0.330806i	−0.945579	+	0.325393i	$0.894503\pi$
$458$	−5.31416e14			−1.23218
$459$		0			0
$460$	1.80010e14			0.407501
$461$	−5.65219e13	−	9.78988e13i	−0.126433	−	0.218989i	0.795859	−	0.605482i	$-0.207020\pi$
$461$	−5.65219e13	−	9.78988e13i	−0.126433	−	0.218989i	−0.922292	+	0.386493i	$0.873686\pi$
$462$		0			0
$463$	2.75506e14	−	4.77190e14i	0.601776	−	1.04231i	−0.390776	−	0.920486i	$-0.627793\pi$
$463$	2.75506e14	−	4.77190e14i	0.601776	−	1.04231i	0.992552	−	0.121821i	$-0.0388735\pi$
$464$	3.40819e13	−	5.90316e13i	0.0735657	−	0.127420i
$465$		0			0
$466$	−2.22596e14	−	3.85548e14i	−0.469240	−	0.812747i
$467$	−4.19636e14			−0.874238			−0.437119	−	0.899404i	$-0.644001\pi$
$467$	−4.19636e14			−0.874238			−0.437119	+	0.899404i	$0.644001\pi$
$468$		0			0
$469$	5.63673e14			1.14703
$470$	1.44869e14	+	2.50920e14i	0.291364	+	0.504657i
$471$		0			0
$472$	3.61213e13	−	6.25638e13i	0.0709711	−	0.122926i
$473$	−9.26137e12	+	1.60412e13i	−0.0179862	+	0.0311530i
$474$		0			0
$475$	−1.04800e14	−	1.81519e14i	−0.198860	−	0.344435i
$476$	4.01228e14			0.752581
$477$		0			0
$478$	−5.03298e14			−0.922511
$479$	−2.38849e14	−	4.13699e14i	−0.432791	−	0.749616i	0.564322	−	0.825555i	$-0.309138\pi$
$479$	−2.38849e14	−	4.13699e14i	−0.432791	−	0.749616i	−0.997112	+	0.0759394i	$0.975804\pi$
$480$		0			0
$481$	−1.33111e14	+	2.30556e14i	−0.235731	+	0.408299i
$482$	−2.52815e13	+	4.37888e13i	−0.0442633	+	0.0766663i
$483$		0			0
$484$	1.27316e14	+	2.20518e14i	0.217888	+	0.377394i
$485$	9.30721e13			0.157485
$486$		0			0
$487$	−9.07190e14			−1.50068			−0.750342	−	0.661050i	$-0.770111\pi$
$487$	−9.07190e14			−1.50068			−0.750342	+	0.661050i	$0.770111\pi$
$488$	−1.79550e14	−	3.10990e14i	−0.293681	−	0.508671i
$489$		0			0
$490$	−5.03297e13	+	8.71736e13i	−0.0804907	+	0.139414i
$491$	3.02857e13	−	5.24563e13i	0.0478948	−	0.0829563i	−0.841084	−	0.540904i	$-0.818082\pi$
$491$	3.02857e13	−	5.24563e13i	0.0478948	−	0.0829563i	0.888979	+	0.457948i	$0.151415\pi$
$492$		0			0
$493$	−2.40250e14	−	4.16125e14i	−0.371540	−	0.643525i
$494$	2.57232e14			0.393393
$495$		0			0
$496$	−5.86301e13			−0.0876943
$497$	−7.82235e14	−	1.35487e15i	−1.15712	−	2.00418i
$498$		0			0
$499$	−3.99825e14	+	6.92517e14i	−0.578518	+	1.00202i	0.417132	+	0.908846i	$0.363035\pi$
$499$	−3.99825e14	+	6.92517e14i	−0.578518	+	1.00202i	−0.995650	+	0.0931762i	$0.970298\pi$
$500$	1.61284e14	−	2.79352e14i	0.230811	−	0.399776i
$501$		0			0
$502$	2.32423e14	+	4.02568e14i	0.325393	+	0.563598i
$503$	3.09482e14			0.428560			0.214280	−	0.976772i	$-0.431259\pi$
$503$	3.09482e14			0.428560			0.214280	+	0.976772i	$0.431259\pi$
$504$		0			0
$505$	3.15475e14			0.427428
$506$	−1.42529e14	−	2.46868e14i	−0.191019	−	0.330854i
$507$		0			0
$508$	−4.53845e12	+	7.86083e12i	−0.00595193	+	0.0103090i
$509$	1.60238e14	−	2.77540e14i	0.207882	−	0.360063i	−0.743165	−	0.669108i	$-0.766676\pi$
$509$	1.60238e14	−	2.77540e14i	0.207882	−	0.360063i	0.951047	+	0.309045i	$0.100010\pi$
$510$		0			0
$511$	6.10899e14	+	1.05811e15i	0.775630	+	1.34343i
$512$	3.51844e13			0.0441942
$513$		0			0
$514$	1.56000e14			0.191791
$515$	−3.31452e14	−	5.74091e14i	−0.403163	−	0.698299i
$516$		0			0
$517$	2.29409e14	−	3.97348e14i	0.273157	−	0.473122i
$518$	−1.70374e14	+	2.95097e14i	−0.200720	+	0.347657i
$519$		0			0
$520$	8.20292e13	+	1.42079e14i	0.0946129	+	0.163874i
$521$	−1.59747e14			−0.182317			−0.0911583	−	0.995836i	$-0.529057\pi$
$521$	−1.59747e14			−0.182317			−0.0911583	+	0.995836i	$0.529057\pi$
$522$		0			0
$523$	−1.60413e15			−1.79259			−0.896293	−	0.443462i	$-0.853750\pi$
$523$	−1.60413e15			−1.79259			−0.896293	+	0.443462i	$0.853750\pi$
$524$	1.25610e14	+	2.17562e14i	0.138899	+	0.240581i
$525$		0			0
$526$	2.28251e14	−	3.95342e14i	0.247167	−	0.428106i
$527$	−2.06647e14	+	3.57924e14i	−0.221448	+	0.383559i
$528$		0			0
$529$	−6.06260e14	−	1.05007e15i	−0.636287	−	1.10208i
$530$	−3.79672e14			−0.394359
$531$		0			0
$532$	3.29241e14			0.334965
$533$	−3.79382e14	−	6.57109e14i	−0.382012	−	0.661664i
$534$		0			0
$535$	−5.59949e13	+	9.69860e13i	−0.0552335	+	0.0956673i
$536$	1.74219e14	−	3.01756e14i	0.170094	−	0.294611i
$537$		0			0
$538$	2.75544e14	+	4.77256e14i	0.263565	+	0.456508i
$539$	1.59401e14			0.150922
$540$		0			0
$541$	1.42984e14			0.132649			0.0663243	−	0.997798i	$-0.478873\pi$
$541$	1.42984e14			0.132649			0.0663243	+	0.997798i	$0.478873\pi$
$542$	−3.94958e14	−	6.84088e14i	−0.362706	−	0.628226i
$543$		0			0
$544$	1.24011e14	−	2.14793e14i	0.111600	−	0.193297i
$545$	−4.76742e14	+	8.25741e14i	−0.424720	+	0.735636i
$546$		0			0
$547$	−1.08411e14	−	1.87774e14i	−0.0946550	−	0.163947i	0.814810	−	0.579729i	$-0.196841\pi$
$547$	−1.08411e14	−	1.87774e14i	−0.0946550	−	0.163947i	−0.909465	+	0.415781i	$0.863508\pi$
$548$	4.48492e14			0.387670
$549$		0			0
$550$	−2.11691e14			−0.179353
$551$	−1.97145e14	−	3.41465e14i	−0.165368	−	0.286426i
$552$		0			0
$553$	−8.80534e14	+	1.52513e15i	−0.724033	+	1.25406i
$554$	−1.53902e14	+	2.66567e14i	−0.125297	+	0.217021i
$555$		0			0
$556$	−2.13198e14	−	3.69269e14i	−0.170165	−	0.294735i
$557$	−1.11565e15			−0.881707			−0.440853	−	0.897579i	$-0.645324\pi$
$557$	−1.11565e15			−0.881707			−0.440853	+	0.897579i	$0.645324\pi$
$558$		0			0
$559$	−1.28232e14			−0.0993648
$560$	1.04992e14	+	1.81852e14i	0.0805607	+	0.139535i
$561$		0			0
$562$	5.31915e14	−	9.21304e14i	0.400214	−	0.693191i
$563$	−7.34687e13	+	1.27251e14i	−0.0547402	+	0.0948127i	−0.892097	−	0.451844i	$-0.850766\pi$
$563$	−7.34687e13	+	1.27251e14i	−0.0547402	+	0.0948127i	0.837357	+	0.546657i	$0.184100\pi$
$564$		0			0
$565$	−6.62109e14	−	1.14681e15i	−0.483797	−	0.837961i
$566$	−9.39975e14			−0.680184
$567$		0			0
$568$	−9.67085e14			−0.686355
$569$	1.07662e15	+	1.86476e15i	0.756738	+	1.31071i	0.944506	+	0.328495i	$0.106542\pi$
$569$	1.07662e15	+	1.86476e15i	0.756738	+	1.31071i	−0.187767	+	0.982214i	$0.560125\pi$
$570$		0			0
$571$	−5.58642e14	+	9.67597e14i	−0.385155	+	0.667107i	−0.991791	−	0.127872i	$-0.959185\pi$
$571$	−5.58642e14	+	9.67597e14i	−0.385155	+	0.667107i	0.606636	+	0.794980i	$0.292519\pi$
$572$	1.29899e14	−	2.24991e14i	0.0887007	−	0.153634i
$573$		0			0
$574$	−4.85585e14	−	8.41058e14i	−0.325274	−	0.563392i
$575$	−1.60803e15			−1.06689
$576$		0			0
$577$	1.96428e15			1.27860			0.639301	−	0.768956i	$-0.279224\pi$
$577$	1.96428e15			1.27860			0.639301	+	0.768956i	$0.279224\pi$
$578$	−3.25823e14	−	5.64343e14i	−0.210077	−	0.363865i
$579$		0			0
$580$	1.25736e14	−	2.17781e14i	0.0795436	−	0.137774i
$581$	6.20614e14	−	1.07493e15i	0.388913	−	0.673618i
$582$		0			0
$583$	3.00618e14	+	5.20686e14i	0.184858	+	0.320183i
$584$	7.55261e14			0.460073
$585$		0			0
$586$	−1.51976e15			−0.908530
$587$	6.26342e14	+	1.08486e15i	0.370939	+	0.642485i	0.989710	−	0.143086i	$-0.0457027\pi$
$587$	6.26342e14	+	1.08486e15i	0.370939	+	0.642485i	−0.618772	+	0.785571i	$0.712369\pi$
$588$		0			0
$589$	−1.69571e14	+	2.93706e14i	−0.0985638	+	0.170718i
$590$	1.33259e14	−	2.30812e14i	0.0767382	−	0.132915i
$591$		0			0
$592$	1.05318e14	+	1.82416e14i	0.0595295	+	0.103108i
$593$	1.44789e15			0.810837			0.405418	−	0.914131i	$-0.367126\pi$
$593$	1.44789e15			0.810837			0.405418	+	0.914131i	$0.367126\pi$
$594$		0			0
$595$	1.48022e15			0.813735
$596$	6.74084e14	+	1.16755e15i	0.367163	+	0.635946i
$597$		0			0
$598$	9.86724e14	−	1.70906e15i	0.527642	−	0.913903i
$599$	1.71290e14	−	2.96682e14i	0.0907578	−	0.157197i	−0.817072	−	0.576535i	$-0.804404\pi$
$599$	1.71290e14	−	2.96682e14i	0.0907578	−	0.157197i	0.907830	+	0.419338i	$0.137738\pi$
$600$		0			0
$601$	1.22917e15	+	2.12898e15i	0.639443	+	1.10755i	0.985555	+	0.169354i	$0.0541682\pi$
$601$	1.22917e15	+	2.12898e15i	0.639443	+	1.10755i	−0.346113	+	0.938193i	$0.612498\pi$
$602$	−1.64129e14			−0.0846068
$603$		0			0
$604$	6.35061e14			0.321449
$605$	4.69698e14	+	8.13540e14i	0.235594	+	0.408060i
$606$		0			0
$607$	−1.00431e15	+	1.73951e15i	−0.494686	+	0.856821i	−0.999981	−	0.00612539i	$-0.998050\pi$
$607$	−1.00431e15	+	1.73951e15i	−0.494686	+	0.856821i	0.505295	+	0.862946i	$0.331384\pi$
$608$	1.01761e14	−	1.76255e14i	0.0496719	−	0.0860343i
$609$		0			0
$610$	−6.62400e14	−	1.14731e15i	−0.317546	−	0.550006i
$611$	3.17638e15			1.50906
$612$		0			0
$613$	1.54595e14			0.0721379			0.0360689	−	0.999349i	$-0.488516\pi$
$613$	1.54595e14			0.0721379			0.0360689	+	0.999349i	$0.488516\pi$
$614$	1.09688e15	+	1.89985e15i	0.507263	+	0.878605i
$615$		0			0
$616$	1.66262e14	−	2.87975e14i	0.0755266	−	0.130816i
$617$	1.31836e15	−	2.28347e15i	0.593562	−	1.02808i	−0.400186	−	0.916434i	$-0.631055\pi$
$617$	1.31836e15	−	2.28347e15i	0.593562	−	1.02808i	0.993748	−	0.111645i	$-0.0356120\pi$
$618$		0			0
$619$	7.74322e14	+	1.34117e15i	0.342470	+	0.593176i	0.984891	−	0.173176i	$-0.0554030\pi$
$619$	7.74322e14	+	1.34117e15i	0.342470	+	0.593176i	−0.642420	+	0.766352i	$0.722070\pi$
$620$	−2.16300e14			−0.0948203
$621$		0			0
$622$	1.80704e14			0.0778253
$623$	1.18582e15	+	2.05390e15i	0.506215	+	0.876790i
$624$		0			0
$625$	−2.48654e14	+	4.30682e14i	−0.104293	+	0.180641i
$626$	−1.53549e15	+	2.65955e15i	−0.638394	+	1.10573i
$627$		0			0
$628$	−3.05966e14	−	5.29948e14i	−0.124996	−	0.216499i
$629$	1.48481e15			0.601301
$630$		0			0
$631$	9.61087e12			0.00382473			0.00191237	−	0.999998i	$-0.499391\pi$
$631$	9.61087e12			0.00382473			0.00191237	+	0.999998i	$0.499391\pi$
$632$	5.44307e14	+	9.42767e14i	0.214734	+	0.371929i
$633$		0			0
$634$	4.39080e14	−	7.60510e14i	0.170237	−	0.294859i
$635$	−1.67434e13	+	2.90004e13i	−0.00643558	+	0.0111467i
$636$		0			0
$637$	5.51764e14	+	9.55683e14i	0.208442	+	0.361033i
$638$	−3.98223e14			−0.149146
$639$		0			0
$640$	1.29803e14			0.0477854
$641$	1.97963e15	+	3.42882e15i	0.722544	+	1.25148i	0.959977	+	0.280079i	$0.0903606\pi$
$641$	1.97963e15	+	3.42882e15i	0.722544	+	1.25148i	−0.237433	+	0.971404i	$0.576306\pi$
$642$		0			0
$643$	1.61670e15	−	2.80020e15i	0.580054	−	1.00468i	−0.415419	−	0.909630i	$-0.636365\pi$
$643$	1.61670e15	−	2.80020e15i	0.580054	−	1.00468i	0.995472	−	0.0950520i	$-0.0303017\pi$
$644$	1.26294e15	−	2.18748e15i	0.449275	−	0.778167i
$645$		0			0
$646$	−7.17331e14	−	1.24245e15i	−0.250866	−	0.434512i
$647$	−1.30706e15			−0.453234			−0.226617	−	0.973984i	$-0.572767\pi$
$647$	−1.30706e15			−0.453234			−0.226617	+	0.973984i	$0.572767\pi$
$648$		0			0
$649$	−4.22051e14			−0.143886
$650$	−7.32765e14	−	1.26919e15i	−0.247709	−	0.429044i
$651$		0			0
$652$	9.88755e14	−	1.71257e15i	0.328645	−	0.569230i
$653$	−1.49130e15	+	2.58301e15i	−0.491523	+	0.851342i	−0.999952	−	0.00976141i	$-0.996893\pi$
$653$	−1.49130e15	+	2.58301e15i	−0.491523	+	0.851342i	0.508430	+	0.861103i	$0.330226\pi$
$654$		0			0
$655$	4.63402e14	+	8.02636e14i	0.150186	+	0.260130i
$656$	−6.00334e14			−0.192940
$657$		0			0
$658$	4.06557e15			1.28493
$659$	1.35575e15	+	2.34823e15i	0.424923	+	0.735988i	0.996413	−	0.0846209i	$-0.0269679\pi$
$659$	1.35575e15	+	2.34823e15i	0.424923	+	0.735988i	−0.571490	+	0.820609i	$0.693635\pi$
$660$		0			0
$661$	−7.96824e14	+	1.38014e15i	−0.245615	+	0.425417i	−0.962304	−	0.271975i	$-0.912323\pi$
$661$	−7.96824e14	+	1.38014e15i	−0.245615	+	0.425417i	0.716690	+	0.697392i	$0.245656\pi$
$662$	1.90713e14	−	3.30325e14i	0.0582991	−	0.100977i
$663$		0			0
$664$	−3.83636e14	−	6.64477e14i	−0.115344	−	0.199782i
$665$	1.21464e15			0.362184
$666$		0			0
$667$	−3.02494e15			−0.887206
$668$	4.61015e14	+	7.98501e14i	0.134105	+	0.232276i
$669$		0			0
$670$	6.42732e14	−	1.11324e15i	0.183916	−	0.318551i
$671$	−1.04896e15	+	1.81684e15i	−0.297703	+	0.515637i
$672$		0			0
$673$	2.05247e15	+	3.55498e15i	0.573052	+	0.992555i	0.996250	+	0.0865183i	$0.0275741\pi$
$673$	2.05247e15	+	3.55498e15i	0.573052	+	0.992555i	−0.423198	+	0.906037i	$0.639093\pi$
$674$	3.58623e15			0.993135
$675$		0			0
$676$	−3.66019e13			−0.00997232
$677$	−2.31200e15	−	4.00450e15i	−0.624814	−	1.08221i	−0.988577	−	0.150718i	$-0.951842\pi$
$677$	−2.31200e15	−	4.00450e15i	−0.624814	−	1.08221i	0.363763	−	0.931491i	$-0.381492\pi$
$678$		0			0
$679$	6.52991e14	−	1.13101e15i	0.173629	−	0.300735i
$680$	4.57503e14	−	7.92418e14i	0.120669	−	0.209004i
$681$		0			0
$682$	1.71263e14	+	2.96635e14i	0.0444476	+	0.0769855i
$683$	2.30592e15			0.593651			0.296825	−	0.954932i	$-0.404072\pi$
$683$	2.30592e15			0.593651			0.296825	+	0.954932i	$0.404072\pi$
$684$		0			0
$685$	1.65459e15			0.419171
$686$	−9.70846e14	−	1.68155e15i	−0.243988	−	0.422599i
$687$		0			0
$688$	−5.07287e13	+	8.78646e13i	−0.0125463	+	0.0217309i
$689$	−2.08117e15	+	3.60469e15i	−0.510624	+	0.884428i
$690$		0			0
$691$	6.06069e14	+	1.04974e15i	0.146350	+	0.253486i	0.929876	−	0.367874i	$-0.119914\pi$
$691$	6.06069e14	+	1.04974e15i	0.146350	+	0.253486i	−0.783526	+	0.621359i	$0.786581\pi$
$692$	3.62812e15			0.869158
$693$		0			0
$694$	2.59277e15			0.611345
$695$	−7.86534e14	−	1.36232e15i	−0.183993	−	0.318685i
$696$		0			0
$697$	−2.11593e15	+	3.66490e15i	−0.487216	+	0.843883i
$698$	−2.87715e15	+	4.98338e15i	−0.657292	+	1.13846i
$699$		0			0
$700$	−9.37893e14	−	1.62448e15i	−0.210918	−	0.365321i
$701$	4.25099e15			0.948507			0.474254	−	0.880388i	$-0.342718\pi$
$701$	4.25099e15			0.948507			0.474254	+	0.880388i	$0.342718\pi$
$702$		0			0
$703$	1.21841e15			0.267632
$704$	−1.02776e14	−	1.78013e14i	−0.0223997	−	0.0387974i
$705$		0			0
$706$	1.25355e15	−	2.17120e15i	0.268976	−	0.465881i
$707$	2.21336e15	−	3.83366e15i	0.471244	−	0.816219i
$708$		0			0
$709$	−4.07734e15	−	7.06215e15i	−0.854717	−	1.48041i	−0.876908	−	0.480659i	$-0.840398\pi$
$709$	−4.07734e15	−	7.06215e15i	−0.854717	−	1.48041i	0.0221910	−	0.999754i	$-0.492936\pi$
$710$	−3.56779e15			−0.742128
$711$		0			0
$712$	1.46604e15			0.300266
$713$	1.30093e15	+	2.25327e15i	0.264399	+	0.457953i
$714$		0			0
$715$	4.79226e14	−	8.30044e14i	0.0959085	−	0.166118i
$716$	1.81315e15	−	3.14047e15i	0.360091	−	0.623696i
$717$		0			0
$718$	−3.00682e15	−	5.20797e15i	−0.588063	−	1.01855i
$719$	6.49021e15			1.25965			0.629825	−	0.776737i	$-0.283127\pi$
$719$	6.49021e15			1.25965			0.629825	+	0.776737i	$0.283127\pi$
$720$		0			0
$721$	−9.30182e15			−1.77797
$722$	1.27521e15	+	2.20874e15i	0.241896	+	0.418976i
$723$		0			0
$724$	−1.28609e15	+	2.22757e15i	−0.240275	+	0.416168i
$725$	−1.12320e15	+	1.94543e15i	−0.208255	+	0.360709i
$726$		0			0
$727$	1.11414e15	+	1.92974e15i	0.203470	+	0.352420i	0.949644	−	0.313331i	$-0.101445\pi$
$727$	1.11414e15	+	1.92974e15i	0.203470	+	0.352420i	−0.746174	+	0.665750i	$0.768112\pi$
$728$	2.30206e15			0.417247
$729$		0			0
$730$	2.78633e15			0.497458
$731$	3.57596e14	+	6.19374e14i	0.0633646	+	0.109751i
$732$		0			0
$733$	2.90019e15	−	5.02327e15i	0.506237	−	0.876829i	−0.493737	−	0.869611i	$-0.664369\pi$
$733$	2.90019e15	−	5.02327e15i	0.506237	−	0.876829i	0.999974	−	0.00721720i	$-0.00229733\pi$
$734$	−9.48867e14	+	1.64349e15i	−0.164391	+	0.284733i
$735$		0			0
$736$	−7.80696e14	−	1.35221e15i	−0.133246	−	0.230789i
$737$	−2.03562e15			−0.344846
$738$		0			0
$739$	5.26802e15			0.879231			0.439615	−	0.898186i	$-0.355115\pi$
$739$	5.26802e15			0.879231			0.439615	+	0.898186i	$0.355115\pi$
$740$	3.88541e14	+	6.72973e14i	0.0643668	+	0.111487i
$741$		0			0
$742$	−2.66377e15	+	4.61378e15i	−0.434785	+	0.753070i
$743$	−6.79730e14	+	1.17733e15i	−0.110128	+	0.190747i	−0.915822	−	0.401585i	$-0.868459\pi$
$743$	−6.79730e14	+	1.17733e15i	−0.110128	+	0.190747i	0.805694	+	0.592332i	$0.201793\pi$
$744$		0			0
$745$	2.48685e15	+	4.30734e15i	0.396999	+	0.687623i
$746$	−3.93777e13			−0.00624003
$747$		0			0
$748$	−1.44897e15			−0.226257
$749$	7.85717e14	+	1.36090e15i	0.121791	+	0.210949i
$750$		0			0
$751$	−3.24157e15	+	5.61456e15i	−0.495148	+	0.857622i	−0.999984	−	0.00559339i	$-0.998220\pi$
$751$	−3.24157e15	+	5.61456e15i	−0.495148	+	0.857622i	0.504836	+	0.863215i	$0.331553\pi$
$752$	1.25658e15	−	2.17646e15i	0.190542	−	0.330029i
$753$		0			0
$754$	−1.37844e15	−	2.38753e15i	−0.205990	−	0.356785i
$755$	2.34288e15			0.347570
$756$		0			0
$757$	−7.16904e15			−1.04817			−0.524087	−	0.851664i	$-0.675594\pi$
$757$	−7.16904e15			−1.04817			−0.524087	+	0.851664i	$0.675594\pi$
$758$	−1.94277e14	−	3.36497e14i	−0.0281994	−	0.0488428i
$759$		0			0
$760$	3.75419e14	−	6.50244e14i	0.0537083	−	0.0930254i
$761$	1.10296e15	−	1.91038e15i	0.156655	−	0.271334i	−0.777006	−	0.629494i	$-0.783262\pi$
$761$	1.10296e15	−	1.91038e15i	0.156655	−	0.271334i	0.933660	+	0.358160i	$0.116596\pi$
$762$		0			0
$763$	6.68961e15	+	1.15867e16i	0.936517	+	1.62210i
$764$	6.46478e15			0.898546
$765$		0			0
$766$	−6.79674e15			−0.931198
$767$	−1.46092e15	−	2.53039e15i	−0.198725	−	0.344202i
$768$		0			0
$769$	−5.11710e15	+	8.86308e15i	−0.686166	+	1.18847i	0.286903	+	0.957960i	$0.407374\pi$
$769$	−5.11710e15	+	8.86308e15i	−0.686166	+	1.18847i	−0.973069	+	0.230515i	$0.925959\pi$
$770$	6.13379e14	−	1.06240e15i	0.0816639	−	0.141446i
$771$		0			0
$772$	5.58041e14	+	9.66555e14i	0.0732438	+	0.126862i
$773$	−9.26990e15			−1.20806			−0.604029	−	0.796962i	$-0.706439\pi$
$773$	−9.26990e15			−1.20806			−0.604029	+	0.796962i	$0.706439\pi$
$774$		0			0
$775$	1.93220e15			0.248252
$776$	−4.03650e14	−	6.99142e14i	−0.0514950	−	0.0891920i
$777$		0			0
$778$	2.69081e15	−	4.66061e15i	0.338450	−	0.586213i
$779$	−1.73630e15	+	3.00735e15i	−0.216854	+	0.375603i
$780$		0			0
$781$	2.82492e15	+	4.89291e15i	0.347877	+	0.602541i
$782$	−1.10065e16			−1.34590
$783$		0			0
$784$	8.73110e14			0.105276
$785$	−1.12878e15	−	1.95510e15i	−0.135153	−	0.234091i
$786$		0			0
$787$	−3.63589e15	+	6.29755e15i	−0.429289	+	0.743551i	−0.996810	−	0.0798083i	$-0.974569\pi$
$787$	−3.63589e15	+	6.29755e15i	−0.429289	+	0.743551i	0.567521	+	0.823359i	$0.307903\pi$
$788$	2.44651e15	−	4.23748e15i	0.286849	−	0.496837i
$789$		0			0
$790$	2.00807e15	+	3.47808e15i	0.232183	+	0.402152i
$791$	−1.85813e16			−2.13357
$792$		0			0
$793$	−1.45238e16			−1.64466
$794$	2.30036e14	+	3.98434e14i	0.0258692	+	0.0448067i
$795$		0			0
$796$	1.73620e15	−	3.00719e15i	0.192565	−	0.333533i
$797$	1.02973e15	−	1.78355e15i	0.113424	−	0.196455i	−0.803725	−	0.595001i	$-0.797152\pi$
$797$	1.02973e15	−	1.78355e15i	0.113424	−	0.196455i	0.917148	+	0.398546i	$0.130485\pi$
$798$		0			0
$799$	−8.85785e15	−	1.53422e16i	−0.962323	−	1.66679i
$800$	−1.15953e15			−0.125108
$801$		0			0
$802$	−4.03986e15			−0.429939
$803$	−2.20617e15	−	3.82120e15i	−0.233186	−	0.403891i
$804$		0			0
$805$	4.65929e15	−	8.07012e15i	0.485783	−	0.841400i
$806$	−1.18564e15	+	2.05360e15i	−0.122776	+	0.212653i
$807$		0			0
$808$	−1.36820e15	−	2.36980e15i	−0.139762	−	0.242074i
$809$	−4.11963e14			−0.0417966			−0.0208983	−	0.999782i	$-0.506653\pi$
$809$	−4.11963e14			−0.0417966			−0.0208983	+	0.999782i	$0.506653\pi$
$810$		0			0
$811$	1.59926e16			1.60068			0.800341	−	0.599545i	$-0.204652\pi$
$811$	1.59926e16			1.60068			0.800341	+	0.599545i	$0.204652\pi$
$812$	−1.76432e15	−	3.05589e15i	−0.175395	−	0.303794i
$813$		0			0
$814$	6.15281e14	−	1.06570e15i	0.0603447	−	0.104520i
$815$	3.64774e15	−	6.31807e15i	0.355351	−	0.615485i
$816$		0			0
$817$	2.93437e14	+	5.08247e14i	0.0282029	+	0.0488488i
$818$	−3.33444e15			−0.318332
$819$		0			0
$820$	−2.21477e15			−0.208618
$821$	4.58116e15	+	7.93480e15i	0.428635	+	0.742418i	0.996752	−	0.0805296i	$-0.0256612\pi$
$821$	4.58116e15	+	7.93480e15i	0.428635	+	0.742418i	−0.568117	+	0.822948i	$0.692328\pi$
$822$		0			0
$823$	−2.67931e15	+	4.64070e15i	−0.247357	+	0.428435i	−0.962792	−	0.270245i	$-0.912895\pi$
$823$	−2.67931e15	+	4.64070e15i	−0.247357	+	0.428435i	0.715435	+	0.698680i	$0.246229\pi$
$824$	−2.87498e15	+	4.97962e15i	−0.263655	+	0.456664i
$825$		0			0
$826$	−1.86989e15	−	3.23874e15i	−0.169210	−	0.293080i
$827$	−1.52149e16			−1.36770			−0.683849	−	0.729624i	$-0.739695\pi$
$827$	−1.52149e16			−1.36770			−0.683849	+	0.729624i	$0.739695\pi$
$828$		0			0
$829$	−7.51363e15			−0.666500			−0.333250	−	0.942839i	$-0.608145\pi$
$829$	−7.51363e15			−0.666500			−0.333250	+	0.942839i	$0.608145\pi$
$830$	−1.41532e15	−	2.45140e15i	−0.124717	−	0.216016i
$831$		0			0
$832$	7.11514e14	−	1.23238e15i	0.0618736	−	0.107168i
$833$	3.07736e15	−	5.33014e15i	0.265846	−	0.460459i
$834$		0			0
$835$	1.70079e15	+	2.94585e15i	0.145002	+	0.251151i
$836$	−1.18900e15			−0.100704
$837$		0			0
$838$	1.43939e14			0.0120320
$839$	−3.11876e15	−	5.40184e15i	−0.258994	−	0.448592i	0.706978	−	0.707235i	$-0.250058\pi$
$839$	−3.11876e15	−	5.40184e15i	−0.258994	−	0.448592i	−0.965973	+	0.258644i	$0.916724\pi$
$840$		0			0
$841$	3.98736e15	−	6.90630e15i	0.326819	−	0.566067i
$842$	−2.21617e15	+	3.83851e15i	−0.180462	+	0.312569i
$843$		0			0
$844$	5.48747e15	+	9.50458e15i	0.441051	+	0.763923i
$845$	−1.35032e14			−0.0107827
$846$		0			0
$847$	1.31815e16			1.03898
$848$	1.64662e15	+	2.85203e15i	0.128949	+	0.223345i
$849$		0			0
$850$	−4.08686e15	+	7.07865e15i	−0.315926	+	0.547201i
$851$	4.67373e15	−	8.09514e15i	0.358964	−	0.621744i
$852$		0			0
$853$	−9.28192e15	−	1.60768e16i	−0.703749	−	1.21893i	−0.967141	−	0.254241i	$-0.918174\pi$
$853$	−9.28192e15	−	1.60768e16i	−0.703749	−	1.21893i	0.263391	−	0.964689i	$-0.415159\pi$
$854$	−1.85895e16			−1.40039
$855$		0			0
$856$	9.71390e14			0.0722417
$857$	−8.68618e15	−	1.50449e16i	−0.641851	−	1.11172i	−0.985019	−	0.172445i	$-0.944833\pi$
$857$	−8.68618e15	−	1.50449e16i	−0.641851	−	1.11172i	0.343168	−	0.939274i	$-0.388500\pi$
$858$		0			0
$859$	−5.83406e15	+	1.01049e16i	−0.425607	+	0.737173i	−0.996477	−	0.0838676i	$-0.973273\pi$
$859$	−5.83406e15	+	1.01049e16i	−0.425607	+	0.737173i	0.570870	+	0.821041i	$0.306606\pi$
$860$	−1.87149e14	+	3.24152e14i	−0.0135659	+	0.0234967i
$861$		0			0
$862$	5.74420e15	+	9.94925e15i	0.411093	+	0.712033i
$863$	1.75417e16			1.24742			0.623709	−	0.781657i	$-0.285625\pi$
$863$	1.75417e16			1.24742			0.623709	+	0.781657i	$0.285625\pi$
$864$		0			0
$865$	1.33850e16			0.939785
$866$	−3.44438e15	−	5.96584e15i	−0.240305	−	0.416220i
$867$		0			0
$868$	−1.51755e15	+	2.62847e15i	−0.104541	+	0.181069i
$869$	3.17992e15	−	5.50778e15i	0.217674	−	0.377023i
$870$		0			0
$871$	−7.04626e15	−	1.22045e16i	−0.476276	−	0.824934i
$872$	8.27043e15			0.555505
$873$		0			0
$874$	−9.03177e15			−0.599046
$875$	−8.34918e15	−	1.44612e16i	−0.550300	−	0.953148i
$876$		0			0
$877$	1.06994e16	−	1.85319e16i	0.696403	−	1.20621i	−0.273302	−	0.961928i	$-0.588116\pi$
$877$	1.06994e16	−	1.85319e16i	0.696403	−	1.20621i	0.969705	−	0.244278i	$-0.0785508\pi$
$878$	8.92655e15	−	1.54612e16i	0.577383	−	1.00006i
$879$		0			0
$880$	−3.79164e14	−	6.56730e14i	−0.0242199	−	0.0419500i
$881$	−1.47188e16			−0.934338			−0.467169	−	0.884168i	$-0.654726\pi$
$881$	−1.47188e16			−0.934338			−0.467169	+	0.884168i	$0.654726\pi$
$882$		0			0
$883$	−4.13136e15			−0.259006			−0.129503	−	0.991579i	$-0.541338\pi$
$883$	−4.13136e15			−0.259006			−0.129503	+	0.991579i	$0.541338\pi$
$884$	−5.01560e15	−	8.68727e15i	−0.312489	−	0.541247i
$885$		0			0
$886$	4.44396e15	−	7.69717e15i	0.273455	−	0.473637i
$887$	2.97729e15	−	5.15681e15i	0.182071	−	0.315356i	−0.760515	−	0.649321i	$-0.775053\pi$
$887$	2.97729e15	−	5.15681e15i	0.182071	−	0.315356i	0.942586	+	0.333965i	$0.108387\pi$
$888$		0			0
$889$	2.34942e14	+	4.06931e14i	0.0141906	+	0.0245788i
$890$	5.40856e15			0.324666
$891$		0			0
$892$	2.02284e15			0.119938
$893$	−7.26859e15	−	1.25896e16i	−0.428319	−	0.741870i
$894$		0			0
$895$	6.68912e15	−	1.15859e16i	0.389352	−	0.674377i
$896$	9.10693e14	−	1.57737e15i	0.0526839	−	0.0912512i
$897$		0			0
$898$	9.28214e15	+	1.60771e16i	0.530430	+	0.918733i
$899$	3.63475e15			0.206441
$900$		0			0
$901$	2.32147e16			1.30250
$902$	1.75362e15	+	3.03735e15i	0.0977910	+	0.169379i
$903$		0			0
$904$	−5.74308e15	+	9.94730e15i	−0.316387	+	0.547998i
$905$	−4.74466e15	+	8.21799e15i	−0.259799	+	0.449985i
$906$		0			0
$907$	−1.10715e16	−	1.91764e16i	−0.598918	−	1.03736i	−0.992981	−	0.118273i	$-0.962264\pi$
$907$	−1.10715e16	−	1.91764e16i	−0.598918	−	1.03736i	0.394063	−	0.919083i	$-0.371069\pi$
$908$	1.68157e16			0.904154
$909$		0			0
$910$	8.49280e15			0.451153
$911$	−1.03450e16	−	1.79181e16i	−0.546235	−	0.946107i	−0.998528	−	0.0542375i	$-0.982727\pi$
$911$	−1.03450e16	−	1.79181e16i	−0.546235	−	0.946107i	0.452293	−	0.891869i	$-0.350606\pi$
$912$		0			0
$913$	−2.24125e15	+	3.88196e15i	−0.116923	+	0.202517i
$914$	−2.60436e15	+	4.51089e15i	−0.135051	+	0.233915i
$915$		0			0
$916$	8.50265e15	+	1.47270e16i	0.435642	+	0.754553i
$917$	1.30048e16			0.662329
$918$		0			0
$919$	9.82530e15			0.494436			0.247218	−	0.968960i	$-0.420484\pi$
$919$	9.82530e15			0.494436			0.247218	+	0.968960i	$0.420484\pi$
$920$	−2.88016e15	−	4.98859e15i	−0.144073	−	0.249543i
$921$		0			0
$922$	−1.80870e15	+	3.13276e15i	−0.0894019	+	0.154849i
$923$	−1.95568e16	+	3.38734e16i	−0.960924	+	1.66437i
$924$		0			0
$925$	−3.47083e15	−	6.01165e15i	−0.168521	−	0.291887i
$926$	−1.76324e16			−0.851040
$927$		0			0
$928$	−2.18124e15			−0.104038
$929$	−8.48895e13	−	1.47033e14i	−0.00402502	−	0.00697153i	0.864006	−	0.503482i	$-0.167948\pi$
$929$	−8.48895e13	−	1.47033e14i	−0.00402502	−	0.00697153i	−0.868031	+	0.496510i	$0.834615\pi$
$930$		0			0
$931$	2.52523e15	−	4.37382e15i	0.118325	−	0.204945i
$932$	−7.12307e15	+	1.23375e16i	−0.331803	+	0.574699i
$933$		0			0
$934$	6.71417e15	+	1.16293e16i	0.309090	+	0.535359i
$935$	−5.34559e15			−0.244642
$936$		0			0
$937$	−3.07118e16			−1.38911			−0.694556	−	0.719439i	$-0.744399\pi$
$937$	−3.07118e16			−1.38911			−0.694556	+	0.719439i	$0.744399\pi$
$938$	−9.01877e15	−	1.56210e16i	−0.405538	−	0.702412i
$939$		0			0
$940$	4.63579e15	−	8.02943e15i	0.206026	−	0.356847i
$941$	−1.02605e16	+	1.77716e16i	−0.453340	+	0.785207i	−0.998591	−	0.0530652i	$-0.983101\pi$
$941$	−1.02605e16	+	1.77716e16i	−0.453340	+	0.785207i	0.545251	+	0.838273i	$0.316434\pi$
$942$		0			0
$943$	1.33206e16	+	2.30720e16i	0.581716	+	1.00756i
$944$	−2.31176e15			−0.100368
$945$		0			0
$946$	5.92728e14			0.0254363
$947$	1.30951e16	+	2.26814e16i	0.558707	+	0.967708i	0.997605	+	0.0691714i	$0.0220355\pi$
$947$	1.30951e16	+	2.26814e16i	0.558707	+	0.967708i	−0.438898	+	0.898537i	$0.644631\pi$
$948$		0			0
$949$	1.52732e16	−	2.64540e16i	0.644120	−	1.11565i
$950$	−3.35361e15	+	5.80862e15i	−0.140615	+	0.243553i
$951$		0			0
$952$	−6.41965e15	−	1.11192e16i	−0.266077	−	0.460860i
$953$	−5.86183e15			−0.241558			−0.120779	−	0.992679i	$-0.538539\pi$
$953$	−5.86183e15			−0.241558			−0.120779	+	0.992679i	$0.538539\pi$
$954$		0			0
$955$	2.38500e16			0.971562
$956$	8.05276e15	+	1.39478e16i	0.326157	+	0.564920i
$957$		0			0
$958$	−7.64317e15	+	1.32384e16i	−0.306029	+	0.530058i
$959$	1.16085e16	−	2.01066e16i	0.462141	−	0.800452i
$960$		0			0
$961$	1.11410e16	+	1.92969e16i	0.438478	+	0.759466i
$962$	8.51913e15			0.333375
$963$		0			0
$964$	1.61802e15			0.0625978
$965$	2.05874e15	+	3.56584e15i	0.0791956	+	0.137171i
$966$		0			0
$967$	1.57336e15	−	2.72514e15i	0.0598387	−	0.103644i	−0.834554	−	0.550926i	$-0.814275\pi$
$967$	1.57336e15	−	2.72514e15i	0.0598387	−	0.103644i	0.894393	+	0.447282i	$0.147608\pi$
$968$	4.07412e15	−	7.05657e15i	0.154070	−	0.266858i
$969$		0			0
$970$	−1.48915e15	−	2.57929e15i	−0.0556795	−	0.0964397i
$971$	−2.12016e16			−0.788249			−0.394124	−	0.919057i	$-0.628952\pi$
$971$	−2.12016e16			−0.788249			−0.394124	+	0.919057i	$0.628952\pi$
$972$		0			0
$973$	−2.20732e16			−0.811417
$974$	1.45150e16	+	2.51408e16i	0.530572	+	0.918977i
$975$		0			0
$976$	−5.74560e15	+	9.95167e15i	−0.207664	+	0.359685i
$977$	−4.91653e15	+	8.51568e15i	−0.176701	+	0.306055i	−0.940749	−	0.339105i	$-0.889876\pi$
$977$	−4.91653e15	+	8.51568e15i	−0.176701	+	0.306055i	0.764048	+	0.645160i	$0.223209\pi$
$978$		0			0
$979$	−4.28241e15	−	7.41735e15i	−0.152189	−	0.263599i
$980$	3.22110e15			0.113831
$981$		0			0
$982$	−1.93828e15			−0.0677335
$983$	4.71005e15	+	8.15804e15i	0.163674	+	0.283492i	0.936184	−	0.351511i	$-0.114332\pi$
$983$	4.71005e15	+	8.15804e15i	0.163674	+	0.283492i	−0.772509	+	0.635003i	$0.780999\pi$
$984$		0			0
$985$	9.02573e15	−	1.56330e16i	0.310158	−	0.537210i
$986$	−7.68800e15	+	1.33160e16i	−0.262718	+	0.455041i
$987$		0			0
$988$	−4.11571e15	−	7.12862e15i	−0.139085	−	0.240903i
$989$	4.50242e15			0.151309
$990$		0			0
$991$	−1.54334e16			−0.512928			−0.256464	−	0.966554i	$-0.582557\pi$
$991$	−1.54334e16			−0.512928			−0.256464	+	0.966554i	$0.582557\pi$
$992$	9.38082e14	+	1.62481e15i	0.0310046	+	0.0537016i
$993$		0			0
$994$	−2.50315e16	+	4.33558e16i	−0.818205	+	1.41717i
$995$	6.40523e15	−	1.10942e16i	0.208213	−	0.360635i
$996$		0			0
$997$	−1.36635e16	−	2.36659e16i	−0.439277	−	0.760850i	0.558357	−	0.829601i	$-0.311432\pi$
$997$	−1.36635e16	−	2.36659e16i	−0.439277	−	0.760850i	−0.997634	+	0.0687511i	$0.978099\pi$
$998$	2.55888e16			0.818148
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.12.c.l.109.1		4
3.2	odd	2		162.12.c.q.109.2		4
9.2	odd	6		162.12.c.q.55.2		4
9.4	even	3		54.12.a.g.1.2	yes	2
9.5	odd	6		54.12.a.d.1.1	✓	2
9.7	even	3	inner	162.12.c.l.55.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.12.a.d.1.1	✓	2	9.5	odd	6
54.12.a.g.1.2	yes	2	9.4	even	3
162.12.c.l.55.1		4	9.7	even	3	inner
162.12.c.l.109.1		4	1.1	even	1	trivial
162.12.c.q.55.2		4	9.2	odd	6
162.12.c.q.109.2		4	3.2	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	162.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-16.0000 - 27.7128i) q^{2} +(-512.000 + 886.810i) q^{4} +(-1888.88 + 3271.64i) q^{5} +(26504.7 + 45907.4i) q^{7} +32768.0 q^{8} +120888. q^{10} +(-95717.6 - 165788. i) q^{11} +(662649. - 1.14774e6i) q^{13} +(848149. - 1.46904e6i) q^{14} +(-524288. - 908093. i) q^{16} -7.39161e6 q^{17} -6.06542e6 q^{19} +(-1.93422e6 - 3.35016e6i) q^{20} +(-3.06296e6 + 5.30521e6i) q^{22} +(-2.32666e7 + 4.02989e7i) q^{23} +(1.72783e7 + 2.99269e7i) q^{25} -4.24096e7 q^{26} -5.42816e7 q^{28} +(3.25031e7 + 5.62970e7i) q^{29} +(2.79570e7 - 4.84230e7i) q^{31} +(-1.67772e7 + 2.90590e7i) q^{32} +(1.18266e8 + 2.04842e8i) q^{34} -2.00257e8 q^{35} -2.00878e8 q^{37} +(9.70467e7 + 1.68090e8i) q^{38} +(-6.18949e7 + 1.07205e8i) q^{40} +(2.86262e8 - 4.95820e8i) q^{41} +(-4.83786e7 - 8.37942e7i) q^{43} +1.96030e8 q^{44} +1.48906e9 q^{46} +(1.19837e9 + 2.07563e9i) q^{47} +(-4.16332e8 + 7.21107e8i) q^{49} +(5.52906e8 - 9.57661e8i) q^{50} +(6.78553e8 + 1.17529e9i) q^{52} -3.14068e9 q^{53} +7.23197e8 q^{55} +(8.68505e8 + 1.50429e9i) q^{56} +(1.04010e9 - 1.80150e9i) q^{58} +(1.10233e9 - 1.90930e9i) q^{59} +(-5.47943e9 - 9.49066e9i) q^{61} -1.78925e9 q^{62} +1.07374e9 q^{64} +(2.50333e9 + 4.33590e9i) q^{65} +(5.31673e9 - 9.20885e9i) q^{67} +(3.78450e9 - 6.55495e9i) q^{68} +(3.20411e9 + 5.54968e9i) q^{70} -2.95131e10 q^{71} +2.30487e10 q^{73} +(3.21404e9 + 5.56689e9i) q^{74} +(3.10550e9 - 5.37888e9i) q^{76} +(5.07392e9 - 8.78829e9i) q^{77} +(1.66109e10 + 2.87710e10i) q^{79} +3.96127e9 q^{80} -1.83207e10 q^{82} +(-1.17076e10 - 2.02782e10i) q^{83} +(1.39619e10 - 2.41827e10i) q^{85} +(-1.54812e9 + 2.68142e9i) q^{86} +(-3.13647e9 - 5.43253e9i) q^{88} +4.47401e10 q^{89} +7.02532e10 q^{91} +(-2.38250e10 - 4.12660e10i) q^{92} +(3.83477e10 - 6.64202e10i) q^{94} +(1.14569e10 - 1.98439e10i) q^{95} +(-1.23184e10 - 2.13361e10i) q^{97} +2.66452e10 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 64 q^{2} - 2048 q^{4} + 3720 q^{5} + 6794 q^{7} + 131072 q^{8} - 238080 q^{10} + 832632 q^{11} - 984634 q^{13} + 217408 q^{14} - 2097152 q^{16} - 10222128 q^{17} - 45838540 q^{19} + 3809280 q^{20}+ \cdots + 63436390656 q^{98}+O(q^{100}) \) 4 * q - 64 * q^2 - 2048 * q^4 + 3720 * q^5 + 6794 * q^7 + 131072 * q^8 - 238080 * q^10 + 832632 * q^11 - 984634 * q^13 + 217408 * q^14 - 2097152 * q^16 - 10222128 * q^17 - 45838540 * q^19 + 3809280 * q^20 + 26644224 * q^22 - 5263656 * q^23 + 27168250 * q^25 + 63016576 * q^26 - 13914112 * q^28 + 37534848 * q^29 + 328859480 * q^31 - 67108864 * q^32 + 163554048 * q^34 - 1093537200 * q^35 - 193134772 * q^37 + 733416640 * q^38 + 121896960 * q^40 + 478653312 * q^41 - 133709104 * q^43 - 1705230336 * q^44 + 336873984 * q^46 + 4431713208 * q^47 - 991193604 * q^49 + 869384000 * q^50 - 1008265216 * q^52 - 9509944032 * q^53 + 16802824320 * q^55 + 222625792 * q^56 + 1201115136 * q^58 + 9940537848 * q^59 - 6058984510 * q^61 - 21047006720 * q^62 + 4294967296 * q^64 + 22326000360 * q^65 + 6772264670 * q^67 + 5233729536 * q^68 + 17496595200 * q^70 - 51162730848 * q^71 + 31615248932 * q^73 + 3090156352 * q^74 + 23469332480 * q^76 + 57475455528 * q^77 + 28139021846 * q^79 - 7801405440 * q^80 - 30633811968 * q^82 - 77207454480 * q^83 + 45022737600 * q^85 - 4278691328 * q^86 + 27283685376 * q^88 + 76591168272 * q^89 + 354015024316 * q^91 - 5389983744 * q^92 + 141814822656 * q^94 - 103452470040 * q^95 - 109290600874 * q^97 + 63436390656 * q^98

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