LMFDB - Embedded newform 126.8.g.e.37.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,8,Mod(37,126)] 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("126.37"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,16,0,-128,-238] 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:	$39.3605132110$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{2389})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 598x^{2} + 597x + 356409 $ x^4 - x^3 + 598x^2 + 597x + 356409
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.2
Root			$-11.9693 - 20.7315i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.8.g.e.109.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.00000 - 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-10.6226 + 18.3989i) q^{5} +(-642.284 + 641.104i) q^{7} -512.000 q^{8} +(84.9808 + 147.191i) q^{10} +(1633.07 + 2828.56i) q^{11} +10238.0 q^{13} +(1872.57 + 7014.29i) q^{14} +(-2048.00 + 3547.24i) q^{16} +(-18264.6 - 31635.1i) q^{17} +(16200.6 - 28060.3i) q^{19} +1359.69 q^{20} +26129.1 q^{22} +(8370.58 - 14498.3i) q^{23} +(38836.8 + 67267.3i) q^{25} +(40951.9 - 70930.7i) q^{26} +(56086.7 + 15083.6i) q^{28} -43984.4 q^{29} +(-66921.6 - 115912. i) q^{31} +(16384.0 + 28377.9i) q^{32} -292233. q^{34} +(-4972.88 - 18627.5i) q^{35} +(289939. - 502188. i) q^{37} +(-129605. - 224482. i) q^{38} +(5438.77 - 9420.23i) q^{40} +532967. q^{41} -365375. q^{43} +(104517. - 181028. i) q^{44} +(-66964.6 - 115986. i) q^{46} +(-103432. + 179149. i) q^{47} +(1513.36 - 823542. i) q^{49} +621389. q^{50} +(-327615. - 567446. i) q^{52} +(-544104. - 942416. i) q^{53} -69389.9 q^{55} +(328849. - 328245. i) q^{56} +(-175938. + 304733. i) q^{58} +(80826.2 + 139995. i) q^{59} +(422154. - 731192. i) q^{61} -1.07075e6 q^{62} +262144. q^{64} +(-108754. + 188367. i) q^{65} +(-613923. - 1.06335e6i) q^{67} +(-1.16893e6 + 2.02465e6i) q^{68} +(-148947. - 40056.8i) q^{70} -1.10759e6 q^{71} +(-819423. - 1.41928e6i) q^{73} +(-2.31951e6 - 4.01751e6i) q^{74} -2.07368e6 q^{76} +(-2.86230e6 - 769770. i) q^{77} +(2.49711e6 - 4.32512e6i) q^{79} +(-43510.2 - 75361.8i) q^{80} +(2.13187e6 - 3.69251e6i) q^{82} +3.38355e6 q^{83} +776069. q^{85} +(-1.46150e6 + 2.53139e6i) q^{86} +(-836132. - 1.44822e6i) q^{88} +(3.26848e6 - 5.66118e6i) q^{89} +(-6.57568e6 + 6.56361e6i) q^{91} -1.07143e6 q^{92} +(827454. + 1.43319e6i) q^{94} +(344185. + 596146. i) q^{95} +1.35914e6 q^{97} +(-5.69961e6 - 3.30465e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 16 q^{2} - 128 q^{4} - 238 q^{5} + 168 q^{7} - 2048 q^{8} + 1904 q^{10} + 5848 q^{11} + 2632 q^{13} + 2016 q^{14} - 8192 q^{16} - 47642 q^{17} + 41048 q^{19} + 30464 q^{20} + 93568 q^{22} - 49316 q^{23}+ \cdots - 20499248 q^{98}+O(q^{100}) $ 4 * q + 16 * q^2 - 128 * q^4 - 238 * q^5 + 168 * q^7 - 2048 * q^8 + 1904 * q^10 + 5848 * q^11 + 2632 * q^13 + 2016 * q^14 - 8192 * q^16 - 47642 * q^17 + 41048 * q^19 + 30464 * q^20 + 93568 * q^22 - 49316 * q^23 + 108816 * q^25 + 10528 * q^26 + 5376 * q^28 - 345640 * q^29 + 70252 * q^31 + 65536 * q^32 - 762272 * q^34 + 36904 * q^35 + 88166 * q^37 - 328384 * q^38 + 121856 * q^40 + 2312520 * q^41 + 115088 * q^43 + 374272 * q^44 + 394528 * q^46 - 1412292 * q^47 + 465892 * q^49 + 1741056 * q^50 - 84224 * q^52 - 2361174 * q^53 - 1258040 * q^55 - 86016 * q^56 - 1382560 * q^58 + 1842512 * q^59 - 1278242 * q^61 + 1124032 * q^62 + 1048576 * q^64 + 1716372 * q^65 + 2121480 * q^67 - 3049088 * q^68 + 2595712 * q^70 - 7200320 * q^71 + 1634682 * q^73 - 705328 * q^74 - 5254144 * q^76 - 1416226 * q^77 + 9192604 * q^79 - 974848 * q^80 + 9250080 * q^82 + 56560 * q^83 + 6369676 * q^85 + 460352 * q^86 - 2994176 * q^88 + 8936550 * q^89 - 26111120 * q^91 + 6312448 * q^92 + 11298336 * q^94 + 2562604 * q^95 + 11748408 * q^97 - 20499248 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	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
$5$	−10.6226	+	18.3989i	−0.0380046	+	0.0658259i	−0.884402	−	0.466726i	$-0.845433\pi$
$5$	−10.6226	+	18.3989i	−0.0380046	+	0.0658259i	0.846397	+	0.532552i	$0.178767\pi$
$6$		0			0
$7$	−642.284	+	641.104i	−0.707756	+	0.706457i
$7$	−642.284	+	641.104i	−0.707756	+	0.706457i
$8$	−512.000			−0.353553
$9$		0			0
$10$	84.9808	+	147.191i	0.0268733	+	0.0465459i
$11$	1633.07	+	2828.56i	0.369939	+	0.640754i	0.989556	−	0.144151i	$-0.0460451\pi$
$11$	1633.07	+	2828.56i	0.369939	+	0.640754i	−0.619616	+	0.784905i	$0.712712\pi$
$12$		0			0
$13$	10238.0			1.29245			0.646223	−	0.763149i	$-0.276348\pi$
$13$	10238.0			1.29245			0.646223	+	0.763149i	$0.276348\pi$
$14$	1872.57	+	7014.29i	0.182385	+	0.683181i
$15$		0			0
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	−18264.6	−	31635.1i	−0.901650	−	1.56170i	−0.825352	−	0.564619i	$-0.809023\pi$
$17$	−18264.6	−	31635.1i	−0.901650	−	1.56170i	−0.0762982	−	0.997085i	$-0.524310\pi$
$18$		0			0
$19$	16200.6	−	28060.3i	0.541868	−	0.938543i	−0.456929	−	0.889503i	$-0.651051\pi$
$19$	16200.6	−	28060.3i	0.541868	−	0.938543i	0.998797	−	0.0490398i	$-0.0156161\pi$
$20$	1359.69			0.0380046
$21$		0			0
$22$	26129.1			0.523173
$23$	8370.58	−	14498.3i	0.143452	−	0.248467i	−0.785342	−	0.619062i	$-0.787513\pi$
$23$	8370.58	−	14498.3i	0.143452	−	0.248467i	0.928795	+	0.370595i	$0.120846\pi$
$24$		0			0
$25$	38836.8	+	67267.3i	0.497111	+	0.861022i
$26$	40951.9	−	70930.7i	0.456948	−	0.791458i
$27$		0			0
$28$	56086.7	+	15083.6i	0.482844	+	0.129853i
$29$	−43984.4			−0.334893			−0.167446	−	0.985881i	$-0.553552\pi$
$29$	−43984.4			−0.334893			−0.167446	+	0.985881i	$0.553552\pi$
$30$		0			0
$31$	−66921.6	−	115912.i	−0.403460	−	0.698813i	0.590681	−	0.806905i	$-0.298859\pi$
$31$	−66921.6	−	115912.i	−0.403460	−	0.698813i	−0.994141	+	0.108092i	$0.965526\pi$
$32$	16384.0	+	28377.9i	0.0883883	+	0.153093i
$33$		0			0
$34$	−292233.			−1.27513
$35$	−4972.88	−	18627.5i	−0.0196052	−	0.0734373i
$36$		0			0
$37$	289939.	−	502188.i	0.941022	−	1.62990i	0.177496	−	0.984122i	$-0.443200\pi$
$37$	289939.	−	502188.i	0.941022	−	1.62990i	0.763526	−	0.645777i	$-0.223466\pi$
$38$	−129605.	−	224482.i	−0.383159	−	0.663650i
$39$		0			0
$40$	5438.77	−	9420.23i	0.0134366	−	0.0232730i
$41$	532967.			1.20769			0.603847	−	0.797100i	$-0.293634\pi$
$41$	532967.			1.20769			0.603847	+	0.797100i	$0.293634\pi$
$42$		0			0
$43$	−365375.			−0.700809			−0.350404	−	0.936598i	$-0.613956\pi$
$43$	−365375.			−0.700809			−0.350404	+	0.936598i	$0.613956\pi$
$44$	104517.	−	181028.i	0.184970	−	0.320377i
$45$		0			0
$46$	−66964.6	−	115986.i	−0.101436	−	0.175693i
$47$	−103432.	+	179149.i	−0.145315	+	0.251693i	−0.929491	−	0.368846i	$-0.879753\pi$
$47$	−103432.	+	179149.i	−0.145315	+	0.251693i	0.784175	+	0.620539i	$0.213086\pi$
$48$		0			0
$49$	1513.36	−	823542.i	0.00183762	−	0.999998i
$50$	621389.			0.703022
$51$		0			0
$52$	−327615.	−	567446.i	−0.323111	−	0.559645i
$53$	−544104.	−	942416.i	−0.502015	−	0.869515i	−0.999997	−	0.00232824i	$-0.999259\pi$
$53$	−544104.	−	942416.i	−0.502015	−	0.869515i	0.497982	−	0.867187i	$-0.334074\pi$
$54$		0			0
$55$	−69389.9			−0.0562376
$56$	328849.	−	328245.i	0.250230	−	0.249770i
$57$		0			0
$58$	−175938.	+	304733.i	−0.118402	+	0.205079i
$59$	80826.2	+	139995.i	0.0512354	+	0.0887423i	0.890506	−	0.454972i	$-0.150351\pi$
$59$	80826.2	+	139995.i	0.0512354	+	0.0887423i	−0.839270	+	0.543714i	$0.817017\pi$
$60$		0			0
$61$	422154.	−	731192.i	0.238131	−	0.412456i	−0.722047	−	0.691844i	$-0.756798\pi$
$61$	422154.	−	731192.i	0.238131	−	0.412456i	0.960178	+	0.279389i	$0.0901318\pi$
$62$	−1.07075e6			−0.570578
$63$		0			0
$64$	262144.			0.125000
$65$	−108754.	+	188367.i	−0.0491188	+	0.0850763i
$66$		0			0
$67$	−613923.	−	1.06335e6i	−0.249375	−	0.431929i	0.713978	−	0.700168i	$-0.246892\pi$
$67$	−613923.	−	1.06335e6i	−0.249375	−	0.431929i	−0.963352	+	0.268239i	$0.913558\pi$
$68$	−1.16893e6	+	2.02465e6i	−0.450825	+	0.780852i
$69$		0			0
$70$	−148947.	−	40056.8i	−0.0519024	−	0.0139583i
$71$	−1.10759e6			−0.367259			−0.183630	−	0.982995i	$-0.558785\pi$
$71$	−1.10759e6			−0.367259			−0.183630	+	0.982995i	$0.558785\pi$
$72$		0			0
$73$	−819423.	−	1.41928e6i	−0.246535	−	0.427011i	0.716027	−	0.698072i	$-0.245959\pi$
$73$	−819423.	−	1.41928e6i	−0.246535	−	0.427011i	−0.962562	+	0.271062i	$0.912625\pi$
$74$	−2.31951e6	−	4.01751e6i	−0.665403	−	1.15251i
$75$		0			0
$76$	−2.07368e6			−0.541868
$77$	−2.86230e6	−	769770.i	−0.714492	−	0.192151i
$78$		0			0
$79$	2.49711e6	−	4.32512e6i	0.569826	−	0.986968i	−0.426757	−	0.904366i	$-0.640344\pi$
$79$	2.49711e6	−	4.32512e6i	0.569826	−	0.986968i	0.996583	−	0.0826011i	$-0.0263227\pi$
$80$	−43510.2	−	75361.8i	−0.00950114	−	0.0164565i
$81$		0			0
$82$	2.13187e6	−	3.69251e6i	0.426984	−	0.739559i
$83$	3.38355e6			0.649531			0.324765	−	0.945795i	$-0.394715\pi$
$83$	3.38355e6			0.649531			0.324765	+	0.945795i	$0.394715\pi$
$84$		0			0
$85$	776069.			0.137067
$86$	−1.46150e6	+	2.53139e6i	−0.247773	+	0.429156i
$87$		0			0
$88$	−836132.	−	1.44822e6i	−0.130793	−	0.226541i
$89$	3.26848e6	−	5.66118e6i	0.491452	−	0.851220i	−0.508500	−	0.861062i	$-0.669800\pi$
$89$	3.26848e6	−	5.66118e6i	0.491452	−	0.851220i	0.999952	+	0.00984263i	$0.00313306\pi$
$90$		0			0
$91$	−6.57568e6	+	6.56361e6i	−0.914736	+	0.913057i
$92$	−1.07143e6			−0.143452
$93$		0			0
$94$	827454.	+	1.43319e6i	0.102753	+	0.177974i
$95$	344185.	+	596146.i	0.0411869	+	0.0713379i
$96$		0			0
$97$	1.35914e6			0.151204			0.0756022	−	0.997138i	$-0.475912\pi$
$97$	1.35914e6			0.151204			0.0756022	+	0.997138i	$0.475912\pi$
$98$	−5.69961e6	−	3.30465e6i	−0.611722	−	0.354678i
$99$		0			0
$100$	2.48556e6	−	4.30511e6i	0.248556	−	0.430511i
$101$	5.84618e6	+	1.01259e7i	0.564608	+	0.977930i	0.997086	+	0.0762853i	$0.0243060\pi$
$101$	5.84618e6	+	1.01259e7i	0.564608	+	0.977930i	−0.432478	+	0.901644i	$0.642361\pi$
$102$		0			0
$103$	1.08658e6	−	1.88202e6i	0.0979790	−	0.169705i	−0.812869	−	0.582447i	$-0.802096\pi$
$103$	1.08658e6	−	1.88202e6i	0.0979790	−	0.169705i	0.910848	+	0.412742i	$0.135429\pi$
$104$	−5.24184e6			−0.456948
$105$		0			0
$106$	−8.70567e6			−0.709956
$107$	5.38290e6	−	9.32345e6i	0.424789	−	0.735756i	−0.571612	−	0.820524i	$-0.693682\pi$
$107$	5.38290e6	−	9.32345e6i	0.424789	−	0.735756i	0.996401	+	0.0847685i	$0.0270151\pi$
$108$		0			0
$109$	6.18768e6	+	1.07174e7i	0.457652	+	0.792676i	0.998836	−	0.0482280i	$-0.0153574\pi$
$109$	6.18768e6	+	1.07174e7i	0.457652	+	0.792676i	−0.541185	+	0.840904i	$0.682024\pi$
$110$	−277559.	+	480747.i	−0.0198830	+	0.0344383i
$111$		0			0
$112$	−958754.	−	3.59132e6i	−0.0644829	−	0.241541i
$113$	1.93909e7			1.26422			0.632112	−	0.774877i	$-0.282188\pi$
$113$	1.93909e7			1.26422			0.632112	+	0.774877i	$0.282188\pi$
$114$		0			0
$115$	177835.	+	308019.i	0.0109037	+	0.0188858i
$116$	1.40750e6	+	2.43786e6i	0.0837232	+	0.145013i
$117$		0			0
$118$	1.29322e6			0.0724578
$119$	3.20125e7	+	8.60925e6i	1.74142	+	0.468329i
$120$		0			0
$121$	4.40974e6	−	7.63790e6i	0.226290	−	0.391945i
$122$	−3.37723e6	−	5.84954e6i	−0.168384	−	0.291650i
$123$		0			0
$124$	−4.28298e6	+	7.41834e6i	−0.201730	+	0.349406i
$125$	−3.30997e6			−0.151579
$126$		0			0
$127$	−1.41475e6			−0.0612868			−0.0306434	−	0.999530i	$-0.509756\pi$
$127$	−1.41475e6			−0.0612868			−0.0306434	+	0.999530i	$0.509756\pi$
$128$	1.04858e6	−	1.81619e6i	0.0441942	−	0.0765466i
$129$		0			0
$130$	870031.	+	1.50694e6i	0.0347323	+	0.0601580i
$131$	−1.77615e7	+	3.07638e7i	−0.690287	+	1.19561i	0.281457	+	0.959574i	$0.409182\pi$
$131$	−1.77615e7	+	3.07638e7i	−0.690287	+	1.19561i	−0.971744	+	0.236038i	$0.924151\pi$
$132$		0			0
$133$	7.58418e6	+	2.84089e7i	0.279530	+	1.04707i
$134$	−9.82277e6			−0.352669
$135$		0			0
$136$	9.35146e6	+	1.61972e7i	0.318781	+	0.552146i
$137$	−2.21508e7	−	3.83663e7i	−0.735982	−	1.27476i	−0.954291	−	0.298878i	$-0.903387\pi$
$137$	−2.21508e7	−	3.83663e7i	−0.735982	−	1.27476i	0.218309	−	0.975880i	$-0.429946\pi$
$138$		0			0
$139$	2.97789e7			0.940496			0.470248	−	0.882534i	$-0.344164\pi$
$139$	2.97789e7			0.940496			0.470248	+	0.882534i	$0.344164\pi$
$140$	−873309.	+	871705.i	−0.0268980	+	0.0268486i
$141$		0			0
$142$	−4.43034e6	+	7.67357e6i	−0.129846	+	0.224900i
$143$	1.67193e7	+	2.89587e7i	0.478126	+	0.828139i
$144$		0			0
$145$	467229.	−	809264.i	0.0127275	−	0.0220446i
$146$	−1.31108e7			−0.348653
$147$		0			0
$148$	−3.71121e7			−0.941022
$149$	−2.04028e7	+	3.53387e7i	−0.505286	+	0.875181i	0.494695	+	0.869067i	$0.335280\pi$
$149$	−2.04028e7	+	3.53387e7i	−0.505286	+	0.875181i	−0.999981	+	0.00611484i	$0.998054\pi$
$150$		0			0
$151$	1.78291e7	+	3.08810e7i	0.421416	+	0.729914i	0.996078	−	0.0884767i	$-0.0281999\pi$
$151$	1.78291e7	+	3.08810e7i	0.421416	+	0.729914i	−0.574662	+	0.818391i	$0.694867\pi$
$152$	−8.29471e6	+	1.43669e7i	−0.191579	+	0.331825i
$153$		0			0
$154$	−1.67823e7	+	1.67515e7i	−0.370279	+	0.369599i
$155$	2.84353e6			0.0613333
$156$		0			0
$157$	2.60341e7	+	4.50923e7i	0.536899	+	0.929937i	0.999069	+	0.0431455i	$0.0137379\pi$
$157$	2.60341e7	+	4.50923e7i	0.536899	+	0.929937i	−0.462169	+	0.886792i	$0.652929\pi$
$158$	−1.99769e7	−	3.46009e7i	−0.402928	−	0.697891i
$159$		0			0
$160$	−696163.			−0.0134366
$161$	3.91862e6	+	1.46784e7i	0.0740018	+	0.277197i
$162$		0			0
$163$	−2.72230e7	+	4.71516e7i	−0.492356	+	0.852785i	−0.999961	−	0.00880425i	$-0.997197\pi$
$163$	−2.72230e7	+	4.71516e7i	−0.492356	+	0.852785i	0.507605	+	0.861590i	$0.330531\pi$
$164$	−1.70550e7	−	2.95400e7i	−0.301924	−	0.522947i
$165$		0			0
$166$	1.35342e7	−	2.34419e7i	0.229644	−	0.397755i
$167$	3.69146e7			0.613325			0.306662	−	0.951818i	$-0.400788\pi$
$167$	3.69146e7			0.613325			0.306662	+	0.951818i	$0.400788\pi$
$168$		0			0
$169$	4.20675e7			0.670414
$170$	3.10427e6	−	5.37676e6i	0.0484606	−	0.0839363i
$171$		0			0
$172$	1.16920e7	+	2.02512e7i	0.175202	+	0.303459i
$173$	−3.84918e7	+	6.66697e7i	−0.565206	+	0.978965i	0.431825	+	0.901958i	$0.357870\pi$
$173$	−3.84918e7	+	6.66697e7i	−0.565206	+	0.978965i	−0.997031	+	0.0770076i	$0.975463\pi$
$174$		0			0
$175$	−6.80696e7	−	1.83063e7i	−0.960108	−	0.258206i
$176$	−1.33781e7			−0.184970
$177$		0			0
$178$	−2.61478e7	−	4.52894e7i	−0.347509	−	0.601903i
$179$	2.50183e7	+	4.33329e7i	0.326041	+	0.564719i	0.981722	−	0.190318i	$-0.0609520\pi$
$179$	2.50183e7	+	4.33329e7i	0.326041	+	0.564719i	−0.655682	+	0.755037i	$0.727619\pi$
$180$		0			0
$181$	1.63228e7			0.204606			0.102303	−	0.994753i	$-0.467379\pi$
$181$	1.63228e7			0.204606			0.102303	+	0.994753i	$0.467379\pi$
$182$	1.91713e7	+	7.18121e7i	0.235723	+	0.882973i
$183$		0			0
$184$	−4.28574e6	+	7.42311e6i	−0.0507181	+	0.0878463i
$185$	6.15980e6	+	1.06691e7i	0.0715263	+	0.123887i
$186$		0			0
$187$	5.96546e7	−	1.03325e8i	0.667112	−	1.15547i
$188$	1.32393e7			0.145315
$189$		0			0
$190$	5.50696e6			0.0582471
$191$	7.45240e7	−	1.29079e8i	0.773890	−	1.34042i	−0.161526	−	0.986869i	$-0.551641\pi$
$191$	7.45240e7	−	1.29079e8i	0.773890	−	1.34042i	0.935416	−	0.353549i	$-0.115025\pi$
$192$		0			0
$193$	−3.16993e7	−	5.49049e7i	−0.317395	−	0.549744i	0.662549	−	0.749019i	$-0.269475\pi$
$193$	−3.16993e7	−	5.49049e7i	−0.317395	−	0.549744i	−0.979944	+	0.199275i	$0.936141\pi$
$194$	5.43658e6	−	9.41643e6i	0.0534588	−	0.0925934i
$195$		0			0
$196$	−4.56937e7	+	2.62695e7i	−0.433471	+	0.249204i
$197$	−2.93791e7			−0.273783			−0.136892	−	0.990586i	$-0.543711\pi$
$197$	−2.93791e7			−0.273783			−0.136892	+	0.990586i	$0.543711\pi$
$198$		0			0
$199$	−2.45848e7	−	4.25821e7i	−0.221147	−	0.383037i	0.734010	−	0.679139i	$-0.237647\pi$
$199$	−2.45848e7	−	4.25821e7i	−0.221147	−	0.383037i	−0.955156	+	0.296102i	$0.904313\pi$
$200$	−1.98845e7	−	3.44409e7i	−0.175755	−	0.304417i
$201$		0			0
$202$	9.35388e7			0.798476
$203$	2.82505e7	−	2.81986e7i	0.237022	−	0.236587i
$204$		0			0
$205$	−5.66150e6	+	9.80600e6i	−0.0458979	+	0.0794975i
$206$	−8.69268e6	−	1.50562e7i	−0.0692816	−	0.119999i
$207$		0			0
$208$	−2.09674e7	+	3.63165e7i	−0.161556	+	0.279823i
$209$	1.05827e8			0.801834
$210$		0			0
$211$	−2.55314e8			−1.87105			−0.935526	−	0.353258i	$-0.885074\pi$
$211$	−2.55314e8			−1.87105			−0.935526	+	0.353258i	$0.885074\pi$
$212$	−3.48227e7	+	6.03146e7i	−0.251007	+	0.434758i
$213$		0			0
$214$	−4.30632e7	−	7.45876e7i	−0.300371	−	0.520258i
$215$	3.88124e6	−	6.72250e6i	0.0266339	−	0.0461314i
$216$		0			0
$217$	1.17294e8	+	3.15444e7i	0.779232	+	0.209562i
$218$	9.90028e7			0.647217
$219$		0			0
$220$	2.22048e6	+	3.84598e6i	0.0140594	+	0.0243516i
$221$	−1.86992e8	−	3.23880e8i	−1.16533	−	2.01842i
$222$		0			0
$223$	−3.35491e7			−0.202588			−0.101294	−	0.994857i	$-0.532298\pi$
$223$	−3.35491e7			−0.202588			−0.101294	+	0.994857i	$0.532298\pi$
$224$	−2.87164e7	−	7.72282e6i	−0.170711	−	0.0459100i
$225$		0			0
$226$	7.75638e7	−	1.34344e8i	0.446971	−	0.774177i
$227$	7.55391e6	+	1.30838e7i	0.0428629	+	0.0742407i	0.886661	−	0.462420i	$-0.153019\pi$
$227$	7.55391e6	+	1.30838e7i	0.0428629	+	0.0742407i	−0.843798	+	0.536661i	$0.819685\pi$
$228$		0			0
$229$	5.15808e7	−	8.93406e7i	0.283834	−	0.491615i	−0.688492	−	0.725244i	$-0.741727\pi$
$229$	5.15808e7	−	8.93406e7i	0.283834	−	0.491615i	0.972326	+	0.233629i	$0.0750603\pi$
$230$	2.84535e6			0.0154202
$231$		0			0
$232$	2.25200e7			0.118402
$233$	5.19814e7	−	9.00345e7i	0.269217	−	0.466298i	−0.699443	−	0.714689i	$-0.746568\pi$
$233$	5.19814e7	−	9.00345e7i	0.269217	−	0.466298i	0.968660	+	0.248391i	$0.0799018\pi$
$234$		0			0
$235$	−2.19743e6	−	3.80606e6i	−0.0110453	−	0.0191310i
$236$	5.17288e6	−	8.95968e6i	0.0256177	−	0.0443711i
$237$		0			0
$238$	1.87696e8	−	1.87352e8i	0.902478	−	0.900821i
$239$	−1.40545e8			−0.665919			−0.332960	−	0.942941i	$-0.608047\pi$
$239$	−1.40545e8			−0.665919			−0.332960	+	0.942941i	$0.608047\pi$
$240$		0			0
$241$	−1.52501e8	−	2.64139e8i	−0.701798	−	1.21555i	−0.967835	−	0.251587i	$-0.919047\pi$
$241$	−1.52501e8	−	2.64139e8i	−0.701798	−	1.21555i	0.266036	−	0.963963i	$-0.414286\pi$
$242$	−3.52780e7	−	6.11032e7i	−0.160011	−	0.277147i
$243$		0			0
$244$	−5.40357e7			−0.238131
$245$	1.51362e7	+	8.77600e6i	0.0657559	+	0.0381255i
$246$		0			0
$247$	1.65861e8	−	2.87280e8i	0.700335	−	1.21302i
$248$	3.42638e7	+	5.93467e7i	0.142645	+	0.247068i
$249$		0			0
$250$	−1.32399e7	+	2.29322e7i	−0.0535913	+	0.0928229i
$251$	−7.20544e7			−0.287609			−0.143804	−	0.989606i	$-0.545934\pi$
$251$	−7.20544e7			−0.287609			−0.143804	+	0.989606i	$0.545934\pi$
$252$		0			0
$253$	5.46790e7			0.212275
$254$	−5.65901e6	+	9.80169e6i	−0.0216682	+	0.0375304i
$255$		0			0
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	−2.89343e6	+	5.01156e6i	−0.0106328	+	0.0184165i	−0.871293	−	0.490763i	$-0.836718\pi$
$257$	−2.89343e6	+	5.01156e6i	−0.0106328	+	0.0184165i	0.860660	+	0.509180i	$0.170051\pi$
$258$		0			0
$259$	1.35732e8	+	5.08428e8i	0.485438	+	1.81836i
$260$	1.39205e7			0.0491188
$261$		0			0
$262$	1.42092e8	+	2.46110e8i	0.488106	+	0.845425i
$263$	1.16636e8	+	2.02020e8i	0.395356	+	0.684778i	0.993147	−	0.116875i	$-0.0372877\pi$
$263$	1.16636e8	+	2.02020e8i	0.395356	+	0.684778i	−0.597790	+	0.801653i	$0.703954\pi$
$264$		0			0
$265$	2.31192e7			0.0763155
$266$	2.27160e8	+	6.10910e7i	0.740023	+	0.199018i
$267$		0			0
$268$	−3.92911e7	+	6.80542e7i	−0.124687	+	0.215965i
$269$	−2.06500e8	−	3.57668e8i	−0.646825	−	1.12033i	−0.983877	−	0.178848i	$-0.942763\pi$
$269$	−2.06500e8	−	3.57668e8i	−0.646825	−	1.12033i	0.337051	−	0.941486i	$-0.390570\pi$
$270$		0			0
$271$	−1.45930e7	+	2.52758e7i	−0.0445401	+	0.0771457i	−0.887436	−	0.460931i	$-0.847516\pi$
$271$	−1.45930e7	+	2.52758e7i	−0.0445401	+	0.0771457i	0.842896	+	0.538077i	$0.180849\pi$
$272$	1.49623e8			0.450825
$273$		0			0
$274$	−3.54413e8			−1.04084
$275$	−1.26847e8	+	2.19705e8i	−0.367802	+	0.637052i
$276$		0			0
$277$	−3.26538e8	−	5.65581e8i	−0.923113	−	1.59888i	−0.794568	−	0.607175i	$-0.792303\pi$
$277$	−3.26538e8	−	5.65581e8i	−0.923113	−	1.59888i	−0.128545	−	0.991704i	$-0.541031\pi$
$278$	1.19116e8	−	2.06314e8i	0.332516	−	0.575934i
$279$		0			0
$280$	2.54612e6	+	9.53728e6i	0.00693147	+	0.0259640i
$281$	−5.17554e8			−1.39150			−0.695750	−	0.718284i	$-0.744928\pi$
$281$	−5.17554e8			−1.39150			−0.695750	+	0.718284i	$0.744928\pi$
$282$		0			0
$283$	−7.16532e6	−	1.24107e7i	−0.0187924	−	0.0325494i	0.856476	−	0.516186i	$-0.172649\pi$
$283$	−7.16532e6	−	1.24107e7i	−0.0187924	−	0.0325494i	−0.875269	+	0.483637i	$0.839315\pi$
$284$	3.54427e7	+	6.13886e7i	0.0918148	+	0.159028i
$285$		0			0
$286$	2.67509e8			0.676173
$287$	−3.42316e8	+	3.41688e8i	−0.854753	+	0.853184i
$288$		0			0
$289$	−4.62019e8	+	8.00241e8i	−1.12595	+	1.95020i
$290$	−3.73783e6	−	6.47411e6i	−0.00899967	−	0.0155879i
$291$		0			0
$292$	−5.24431e7	+	9.08341e7i	−0.123267	+	0.213505i
$293$	4.59597e8			1.06743			0.533716	−	0.845664i	$-0.320795\pi$
$293$	4.59597e8			1.06743			0.533716	+	0.845664i	$0.320795\pi$
$294$		0			0
$295$	−3.43434e6			−0.00778872
$296$	−1.48449e8	+	2.57120e8i	−0.332702	+	0.576256i
$297$		0			0
$298$	1.63222e8	+	2.82709e8i	0.357291	+	0.618847i
$299$	8.56977e7	−	1.48433e8i	0.185404	−	0.321130i
$300$		0			0
$301$	2.34675e8	−	2.34244e8i	0.496002	−	0.495091i
$302$	2.85266e8			0.595972
$303$		0			0
$304$	6.63577e7	+	1.14935e8i	0.135467	+	0.234636i
$305$	8.96875e6	+	1.55343e7i	0.0181002	+	0.0313504i
$306$		0			0
$307$	−2.28161e8			−0.450046			−0.225023	−	0.974354i	$-0.572246\pi$
$307$	−2.28161e8			−0.450046			−0.225023	+	0.974354i	$0.572246\pi$
$308$	4.89286e7	+	1.83277e8i	0.0954190	+	0.357422i
$309$		0			0
$310$	1.13741e7	−	1.97005e7i	0.0216846	−	0.0375588i
$311$	3.56536e8	+	6.17538e8i	0.672112	+	1.16413i	0.977304	+	0.211842i	$0.0679462\pi$
$311$	3.56536e8	+	6.17538e8i	0.672112	+	1.16413i	−0.305192	+	0.952291i	$0.598720\pi$
$312$		0			0
$313$	6.97714e7	−	1.20848e8i	0.128609	−	0.222758i	−0.794529	−	0.607226i	$-0.792282\pi$
$313$	6.97714e7	−	1.20848e8i	0.128609	−	0.222758i	0.923138	+	0.384469i	$0.125615\pi$
$314$	4.16545e8			0.759291
$315$		0			0
$316$	−3.19630e8			−0.569826
$317$	−7.69441e7	+	1.33271e8i	−0.135665	+	0.234979i	−0.925851	−	0.377888i	$-0.876650\pi$
$317$	−7.69441e7	+	1.33271e8i	−0.135665	+	0.234979i	0.790186	+	0.612867i	$0.209984\pi$
$318$		0			0
$319$	−7.18297e7	−	1.24413e8i	−0.123890	−	0.214584i
$320$	−2.78465e6	+	4.82316e6i	−0.00475057	+	0.00822823i
$321$		0			0
$322$	1.17369e8	+	3.15647e7i	0.195911	+	0.0526873i
$323$	−1.18359e9			−1.95430
$324$		0			0
$325$	3.97610e8	+	6.88681e8i	0.642489	+	1.11282i
$326$	2.17784e8	+	3.77213e8i	0.348148	+	0.603010i
$327$		0			0
$328$	−2.72879e8			−0.426984
$329$	−4.84207e7	−	1.81375e8i	−0.0749627	−	0.280796i
$330$		0			0
$331$	−6.99907e7	+	1.21227e8i	−0.106082	+	0.183740i	−0.914180	−	0.405309i	$-0.867164\pi$
$331$	−6.99907e7	+	1.21227e8i	−0.106082	+	0.183740i	0.808098	+	0.589048i	$0.200497\pi$
$332$	−1.08274e8	−	1.87536e8i	−0.162383	−	0.281255i
$333$		0			0
$334$	1.47658e8	−	2.55752e8i	0.216843	−	0.375583i
$335$	2.60858e7			0.0379095
$336$		0			0
$337$	−9.36806e7			−0.133335			−0.0666676	−	0.997775i	$-0.521237\pi$
$337$	−9.36806e7			−0.133335			−0.0666676	+	0.997775i	$0.521237\pi$
$338$	1.68270e8	−	2.91452e8i	0.237027	−	0.410543i
$339$		0			0
$340$	−2.48342e7	−	4.30141e7i	−0.0342668	−	0.0593519i
$341$	2.18575e8	−	3.78584e8i	0.298511	−	0.517037i
$342$		0			0
$343$	5.27004e8	+	5.29917e8i	0.705155	+	0.709053i
$344$	1.87072e8			0.247773
$345$		0			0
$346$	3.07934e8	+	5.33358e8i	0.399661	+	0.692233i
$347$	−2.85722e8	−	4.94886e8i	−0.367106	−	0.635846i	0.622006	−	0.783012i	$-0.286318\pi$
$347$	−2.85722e8	−	4.94886e8i	−0.367106	−	0.635846i	−0.989112	+	0.147167i	$0.952985\pi$
$348$		0			0
$349$	−2.32123e8			−0.292300			−0.146150	−	0.989262i	$-0.546688\pi$
$349$	−2.32123e8			−0.292300			−0.146150	+	0.989262i	$0.546688\pi$
$350$	−3.99108e8	+	3.98375e8i	−0.497568	+	0.496654i
$351$		0			0
$352$	−5.35125e7	+	9.26863e7i	−0.0653967	+	0.113270i
$353$	5.79874e8	+	1.00437e9i	0.701653	+	1.21530i	0.967886	+	0.251390i	$0.0808876\pi$
$353$	5.79874e8	+	1.00437e9i	0.701653	+	1.21530i	−0.266233	+	0.963909i	$0.585779\pi$
$354$		0			0
$355$	1.17654e7	−	2.03783e7i	0.0139575	−	0.0241752i
$356$	−4.18366e8			−0.491452
$357$		0			0
$358$	4.00292e8			0.461091
$359$	4.85816e8	−	8.41458e8i	0.554168	−	0.959847i	−0.443800	−	0.896126i	$-0.646370\pi$
$359$	4.85816e8	−	8.41458e8i	0.554168	−	0.959847i	0.997968	−	0.0637210i	$-0.0202968\pi$
$360$		0			0
$361$	−7.79833e7	−	1.35071e8i	−0.0872421	−	0.151108i
$362$	6.52911e7	−	1.13087e8i	0.0723392	−	0.125295i
$363$		0			0
$364$	5.74214e8	+	1.54426e8i	0.624049	+	0.167828i
$365$	3.48176e7			0.0374778
$366$		0			0
$367$	8.51399e8	+	1.47467e9i	0.899088	+	1.55727i	0.828663	+	0.559749i	$0.189102\pi$
$367$	8.51399e8	+	1.47467e9i	0.899088	+	1.55727i	0.0704252	+	0.997517i	$0.477564\pi$
$368$	3.42859e7	+	5.93849e7i	0.0358631	+	0.0621167i
$369$		0			0
$370$	9.85569e7			0.101153
$371$	9.53657e8	+	2.56471e8i	0.969579	+	0.260753i
$372$		0			0
$373$	−1.88494e8	+	3.26481e8i	−0.188068	+	0.325744i	−0.944606	−	0.328206i	$-0.893556\pi$
$373$	−1.88494e8	+	3.26481e8i	−0.188068	+	0.325744i	0.756538	+	0.653950i	$0.226889\pi$
$374$	−4.77237e8	−	8.26599e8i	−0.471719	−	0.817042i
$375$		0			0
$376$	5.29570e7	−	9.17243e7i	0.0513767	−	0.0889870i
$377$	−4.50311e8			−0.432831
$378$		0			0
$379$	8.86999e8			0.836924			0.418462	−	0.908234i	$-0.362569\pi$
$379$	8.86999e8			0.836924			0.418462	+	0.908234i	$0.362569\pi$
$380$	2.20278e7	−	3.81534e7i	0.0205935	−	0.0356689i
$381$		0			0
$382$	−5.96192e8	−	1.03264e9i	−0.547223	−	0.947818i
$383$	−2.17148e8	+	3.76111e8i	−0.197497	+	0.342074i	−0.947716	−	0.319115i	$-0.896614\pi$
$383$	−2.17148e8	+	3.76111e8i	−0.197497	+	0.342074i	0.750220	+	0.661189i	$0.229948\pi$
$384$		0			0
$385$	4.45680e7	−	4.44861e7i	0.0398025	−	0.0397294i
$386$	−5.07189e8			−0.448864
$387$		0			0
$388$	−4.34926e7	−	7.53314e7i	−0.0378011	−	0.0654734i
$389$	7.57986e7	+	1.31287e8i	0.0652886	+	0.113083i	0.896822	−	0.442392i	$-0.145870\pi$
$389$	7.57986e7	+	1.31287e8i	0.0652886	+	0.113083i	−0.831533	+	0.555475i	$0.812537\pi$
$390$		0			0
$391$	−6.11540e8			−0.517376
$392$	−774841.	+	4.21653e8i	−0.000649697	+	0.353553i
$393$		0			0
$394$	−1.17517e8	+	2.03545e8i	−0.0967971	+	0.167657i
$395$	5.30515e7	+	9.18880e7i	0.0433120	+	0.0750186i
$396$		0			0
$397$	8.52585e8	−	1.47672e9i	0.683866	−	1.18449i	−0.289926	−	0.957049i	$-0.593631\pi$
$397$	8.52585e8	−	1.47672e9i	0.683866	−	1.18449i	0.973792	−	0.227441i	$-0.0730360\pi$
$398$	−3.93357e8			−0.312749
$399$		0			0
$400$	−3.18151e8			−0.248556
$401$	5.75883e8	−	9.97459e8i	0.445994	−	0.772484i	−0.552127	−	0.833760i	$-0.686184\pi$
$401$	5.75883e8	−	9.97459e8i	0.445994	−	0.772484i	0.998121	+	0.0612759i	$0.0195169\pi$
$402$		0			0
$403$	−6.85141e8	−	1.18670e9i	−0.521450	−	0.903177i
$404$	3.74155e8	−	6.48056e8i	0.282304	−	0.488965i
$405$		0			0
$406$	−8.23638e7	−	3.08519e8i	−0.0610795	−	0.228792i
$407$	1.89396e9			1.39248
$408$		0			0
$409$	−5.71985e8	−	9.90706e8i	−0.413383	−	0.716001i	0.581874	−	0.813279i	$-0.302320\pi$
$409$	−5.71985e8	−	9.90706e8i	−0.413383	−	0.716001i	−0.995257	+	0.0972783i	$0.968986\pi$
$410$	4.52920e7	+	7.84480e7i	0.0324547	+	0.0562132i
$411$		0			0
$412$	−1.39083e8			−0.0979790
$413$	−1.41665e8	−	3.80985e7i	−0.0989548	−	0.0266123i
$414$		0			0
$415$	−3.59421e7	+	6.22536e7i	−0.0246851	+	0.0427559i
$416$	1.67739e8	+	2.90532e8i	0.114237	+	0.197864i
$417$		0			0
$418$	4.23308e8	−	7.33191e8i	0.283491	−	0.491021i
$419$	−1.72282e9			−1.14417			−0.572084	−	0.820195i	$-0.693865\pi$
$419$	−1.72282e9			−1.14417			−0.572084	+	0.820195i	$0.693865\pi$
$420$		0			0
$421$	−2.50496e9			−1.63611			−0.818056	−	0.575139i	$-0.804948\pi$
$421$	−2.50496e9			−1.63611			−0.818056	+	0.575139i	$0.804948\pi$
$422$	−1.02126e9	+	1.76887e9i	−0.661517	+	1.14578i
$423$		0			0
$424$	2.78581e8	+	4.82517e8i	0.177489	+	0.307420i
$425$	1.41868e9	−	2.45722e9i	0.896441	−	1.55268i
$426$		0			0
$427$	1.97628e8	+	7.40278e8i	0.122843	+	0.460147i
$428$	−6.89011e8			−0.424789
$429$		0			0
$430$	−3.10499e7	−	5.37800e7i	−0.0188330	−	0.0326198i
$431$	1.14303e9	+	1.97978e9i	0.687679	+	1.19110i	0.972587	+	0.232541i	$0.0747039\pi$
$431$	1.14303e9	+	1.97978e9i	0.687679	+	1.19110i	−0.284907	+	0.958555i	$0.591963\pi$
$432$		0			0
$433$	−2.07332e9			−1.22732			−0.613660	−	0.789570i	$-0.710303\pi$
$433$	−2.07332e9			−1.22732			−0.613660	+	0.789570i	$0.710303\pi$
$434$	6.87722e8	−	6.86460e8i	0.403830	−	0.403089i
$435$		0			0
$436$	3.96011e8	−	6.85912e8i	0.228826	−	0.396338i
$437$	−2.71217e8	−	4.69761e8i	−0.155465	−	0.269273i
$438$		0			0
$439$	8.79323e8	−	1.52303e9i	0.496047	−	0.859178i	−0.503943	−	0.863737i	$-0.668118\pi$
$439$	8.79323e8	−	1.52303e9i	0.496047	−	0.859178i	0.999990	+	0.00455873i	$0.00145109\pi$
$440$	3.55276e7			0.0198830
$441$		0			0
$442$	−2.99187e9			−1.64803
$443$	−9.64736e8	+	1.67097e9i	−0.527224	+	0.913179i	0.472272	+	0.881453i	$0.343434\pi$
$443$	−9.64736e8	+	1.67097e9i	−0.527224	+	0.913179i	−0.999497	+	0.0317264i	$0.989899\pi$
$444$		0			0
$445$	6.94395e7	+	1.20273e8i	0.0373548	+	0.0647005i
$446$	−1.34196e8	+	2.32435e8i	−0.0716257	+	0.124059i
$447$		0			0
$448$	−1.68371e8	+	1.68062e8i	−0.0884695	+	0.0883071i
$449$	−3.29325e9			−1.71697			−0.858484	−	0.512840i	$-0.828593\pi$
$449$	−3.29325e9			−1.71697			−0.858484	+	0.512840i	$0.828593\pi$
$450$		0			0
$451$	8.70373e8	+	1.50753e9i	0.446774	+	0.773835i
$452$	−6.20510e8	−	1.07476e9i	−0.316056	−	0.547425i
$453$		0			0
$454$	1.20863e8			0.0606172
$455$	−5.09122e7	−	1.90708e8i	−0.0253386	−	0.0949136i
$456$		0			0
$457$	9.57310e8	−	1.65811e9i	0.469187	−	0.812655i	−0.530193	−	0.847877i	$-0.677880\pi$
$457$	9.57310e8	−	1.65811e9i	0.469187	−	0.812655i	0.999380	+	0.0352218i	$0.0112138\pi$
$458$	−4.12647e8	−	7.14725e8i	−0.200701	−	0.347624i
$459$		0			0
$460$	1.13814e7	−	1.97132e7i	0.00545185	−	0.00944288i
$461$	1.84068e9			0.875032			0.437516	−	0.899211i	$-0.355858\pi$
$461$	1.84068e9			0.875032			0.437516	+	0.899211i	$0.355858\pi$
$462$		0			0
$463$	−1.67942e8			−0.0786367			−0.0393184	−	0.999227i	$-0.512519\pi$
$463$	−1.67942e8			−0.0786367			−0.0393184	+	0.999227i	$0.512519\pi$
$464$	9.00801e7	−	1.56023e8i	0.0418616	−	0.0725064i
$465$		0			0
$466$	−4.15852e8	−	7.20276e8i	−0.190365	−	0.329722i
$467$	6.89538e8	−	1.19432e9i	0.313292	−	0.542638i	−0.665781	−	0.746147i	$-0.731901\pi$
$467$	6.89538e8	−	1.19432e9i	0.313292	−	0.542638i	0.979073	+	0.203510i	$0.0652348\pi$
$468$		0			0
$469$	1.07603e9	+	2.89381e8i	0.481636	+	0.129528i
$470$	−3.51588e7			−0.0156204
$471$		0			0
$472$	−4.13830e7	−	7.16775e7i	−0.0181144	−	0.0313751i
$473$	−5.96684e8	−	1.03349e9i	−0.259257	−	0.449046i
$474$		0			0
$475$	2.51672e9			1.07748
$476$	−5.47226e8	−	2.04981e9i	−0.232564	−	0.871141i
$477$		0			0
$478$	−5.62179e8	+	9.73722e8i	−0.235438	+	0.407791i
$479$	2.26505e9	+	3.92318e9i	0.941679	+	1.63104i	0.762268	+	0.647261i	$0.224086\pi$
$479$	2.26505e9	+	3.92318e9i	0.941679	+	1.63104i	0.179411	+	0.983774i	$0.442581\pi$
$480$		0			0
$481$	2.96838e9	−	5.14139e9i	1.21622	−	2.10655i
$482$	−2.44001e9			−0.992493
$483$		0			0
$484$	−5.64447e8			−0.226290
$485$	−1.44376e7	+	2.50067e7i	−0.00574646	+	0.00995316i
$486$		0			0
$487$	−7.69774e8	−	1.33329e9i	−0.302003	−	0.523085i	0.674586	−	0.738196i	$-0.264322\pi$
$487$	−7.69774e8	−	1.33329e9i	−0.302003	−	0.523085i	−0.976590	+	0.215111i	$0.930989\pi$
$488$	−2.16143e8	+	3.74370e8i	−0.0841921	+	0.145825i
$489$		0			0
$490$	1.21347e8	−	6.97625e7i	0.0465952	−	0.0267877i
$491$	1.85780e9			0.708295			0.354148	−	0.935190i	$-0.384771\pi$
$491$	1.85780e9			0.708295			0.354148	+	0.935190i	$0.384771\pi$
$492$		0			0
$493$	8.03356e8	+	1.39145e9i	0.301956	+	0.523003i
$494$	−1.32689e9	−	2.29824e9i	−0.495211	−	0.857731i
$495$		0			0
$496$	5.48222e8			0.201730
$497$	7.11384e8	−	7.10078e8i	0.259930	−	0.259453i
$498$		0			0
$499$	−2.67677e9	+	4.63630e9i	−0.964405	+	1.67040i	−0.253198	+	0.967414i	$0.581482\pi$
$499$	−2.67677e9	+	4.63630e9i	−0.964405	+	1.67040i	−0.711206	+	0.702983i	$0.751851\pi$
$500$	1.05919e8	+	1.83457e8i	0.0378948	+	0.0656357i
$501$		0			0
$502$	−2.88218e8	+	4.99207e8i	−0.101685	+	0.176124i
$503$	−5.43979e9			−1.90587			−0.952936	−	0.303170i	$-0.901955\pi$
$503$	−5.43979e9			−1.90587			−0.952936	+	0.303170i	$0.901955\pi$
$504$		0			0
$505$	−2.48406e8			−0.0858308
$506$	2.18716e8	−	3.78827e8i	0.0750505	−	0.129991i
$507$		0			0
$508$	4.52721e7	+	7.84135e7i	0.0153217	+	0.0265380i
$509$	9.12084e8	−	1.57978e9i	0.306565	−	0.530986i	−0.671044	−	0.741418i	$-0.734154\pi$
$509$	9.12084e8	−	1.57978e9i	0.306565	−	0.530986i	0.977609	+	0.210432i	$0.0674870\pi$
$510$		0			0
$511$	1.43621e9	+	3.86246e8i	0.476151	+	0.128053i
$512$	−1.34218e8			−0.0441942
$513$		0			0
$514$	2.31474e7	+	4.00925e7i	0.00751850	+	0.0130224i
$515$	2.30847e7	+	3.99839e7i	0.00744730	+	0.0128991i
$516$		0			0
$517$	−6.75645e8			−0.215031
$518$	4.06542e9	+	1.09333e9i	1.28514	+	0.345619i
$519$		0			0
$520$	5.56820e7	−	9.64440e7i	0.0173661	−	0.0300790i
$521$	−2.07430e8	−	3.59280e8i	−0.0642599	−	0.111301i	0.832106	−	0.554617i	$-0.187135\pi$
$521$	−2.07430e8	−	3.59280e8i	−0.0642599	−	0.111301i	−0.896365	+	0.443316i	$0.853802\pi$
$522$		0			0
$523$	1.60836e9	−	2.78576e9i	0.491616	−	0.851505i	−0.508337	−	0.861158i	$-0.669740\pi$
$523$	1.60836e9	−	2.78576e9i	0.491616	−	0.851505i	0.999953	+	0.00965354i	$0.00307287\pi$
$524$	2.27347e9			0.690287
$525$		0			0
$526$	1.86618e9			0.559118
$527$	−2.44459e9	+	4.23415e9i	−0.727559	+	1.26017i
$528$		0			0
$529$	1.56228e9	+	2.70595e9i	0.458843	+	0.794739i
$530$	9.24769e7	−	1.60175e8i	0.0269816	−	0.0467335i
$531$		0			0
$532$	1.33189e9	−	1.32944e9i	0.383511	−	0.382806i
$533$	5.45650e9			1.56088
$534$		0			0
$535$	1.14361e8	+	1.98079e8i	0.0322878	+	0.0559242i
$536$	3.14329e8	+	5.44433e8i	0.0881672	+	0.152710i
$537$		0			0
$538$	−3.30400e9			−0.914749
$539$	2.33191e9	−	1.34062e9i	0.641433	−	0.368761i
$540$		0			0
$541$	1.14907e9	−	1.99025e9i	0.312002	−	0.540403i	−0.666794	−	0.745242i	$-0.732334\pi$
$541$	1.14907e9	−	1.99025e9i	0.312002	−	0.540403i	0.978796	+	0.204839i	$0.0656672\pi$
$542$	1.16744e8	+	2.02206e8i	0.0314946	+	0.0545503i
$543$		0			0
$544$	5.98493e8	−	1.03662e9i	0.159391	−	0.276073i
$545$	−2.62917e8			−0.0695714
$546$		0			0
$547$	−6.33362e9			−1.65461			−0.827306	−	0.561752i	$-0.810128\pi$
$547$	−6.33362e9			−1.65461			−0.827306	+	0.561752i	$0.810128\pi$
$548$	−1.41765e9	+	2.45544e9i	−0.367991	+	0.637379i
$549$		0			0
$550$	1.01477e9	+	1.75764e9i	0.260075	+	0.450464i
$551$	−7.12574e8	+	1.23421e9i	−0.181468	+	0.314311i
$552$		0			0
$553$	1.16900e9	+	4.37886e9i	0.293952	+	1.10109i
$554$	−5.22461e9			−1.30548
$555$		0			0
$556$	−9.52925e8	−	1.65051e9i	−0.235124	−	0.407247i
$557$	−3.75684e9	−	6.50705e9i	−0.921149	−	1.59548i	−0.797640	−	0.603134i	$-0.793918\pi$
$557$	−3.75684e9	−	6.50705e9i	−0.921149	−	1.59548i	−0.123510	−	0.992343i	$-0.539415\pi$
$558$		0			0
$559$	−3.74070e9			−0.905757
$560$	7.62607e7	+	2.05091e7i	0.0183503	+	0.00493502i
$561$		0			0
$562$	−2.07022e9	+	3.58572e9i	−0.491970	+	0.852117i
$563$	2.39314e9	+	4.14504e9i	0.565183	+	0.978926i	0.997033	+	0.0769801i	$0.0245278\pi$
$563$	2.39314e9	+	4.14504e9i	0.565183	+	0.978926i	−0.431850	+	0.901946i	$0.642139\pi$
$564$		0			0
$565$	−2.05982e8	+	3.56772e8i	−0.0480463	+	0.0832187i
$566$	−1.14645e8			−0.0265765
$567$		0			0
$568$	5.67084e8			0.129846
$569$	2.60548e9	−	4.51283e9i	0.592919	−	1.02697i	−0.400918	−	0.916114i	$-0.631309\pi$
$569$	2.60548e9	−	4.51283e9i	0.592919	−	1.02697i	0.993837	−	0.110852i	$-0.0353580\pi$
$570$		0			0
$571$	3.04516e9	+	5.27437e9i	0.684516	+	1.18562i	0.973589	+	0.228310i	$0.0733199\pi$
$571$	3.04516e9	+	5.27437e9i	0.684516	+	1.18562i	−0.289072	+	0.957307i	$0.593347\pi$
$572$	1.07004e9	−	1.85336e9i	0.239063	−	0.414070i
$573$		0			0
$574$	9.98017e8	+	3.73839e9i	0.220265	+	0.825073i
$575$	1.30035e9			0.285247
$576$		0			0
$577$	1.01575e9	+	1.75934e9i	0.220127	+	0.381271i	0.954846	−	0.297100i	$-0.0960195\pi$
$577$	1.01575e9	+	1.75934e9i	0.220127	+	0.381271i	−0.734719	+	0.678371i	$0.762686\pi$
$578$	3.69615e9	+	6.40192e9i	0.796164	+	1.37900i
$579$		0			0
$580$	−5.98053e7			−0.0127275
$581$	−2.17320e9	+	2.16921e9i	−0.459709	+	0.458865i
$582$		0			0
$583$	1.77712e9	−	3.07807e9i	0.371430	−	0.643336i
$584$	4.19545e8	+	7.26673e8i	0.0871632	+	0.150971i
$585$		0			0
$586$	1.83839e9	−	3.18418e9i	0.377394	−	0.653666i
$587$	7.84037e9			1.59994			0.799970	−	0.600041i	$-0.204849\pi$
$587$	7.84037e9			1.59994			0.799970	+	0.600041i	$0.204849\pi$
$588$		0			0
$589$	−4.33668e9			−0.874488
$590$	−1.37374e7	+	2.37938e7i	−0.00275373	+	0.00476960i
$591$		0			0
$592$	1.18759e9	+	2.05696e9i	0.235256	+	0.407475i
$593$	−7.96578e8	+	1.37971e9i	−0.156869	+	0.271705i	−0.933738	−	0.357957i	$-0.883473\pi$
$593$	−7.96578e8	+	1.37971e9i	−0.156869	+	0.271705i	0.776869	+	0.629662i	$0.216807\pi$
$594$		0			0
$595$	−4.98456e8	+	4.97541e8i	−0.0970102	+	0.0968321i
$596$	2.61156e9			0.505286
$597$		0			0
$598$	−6.85582e8	−	1.18746e9i	−0.131101	−	0.227073i
$599$	3.97790e8	+	6.88992e8i	0.0756240	+	0.130985i	0.901357	−	0.433076i	$-0.142572\pi$
$599$	3.97790e8	+	6.88992e8i	0.0756240	+	0.130985i	−0.825733	+	0.564060i	$0.809238\pi$
$600$		0			0
$601$	6.44884e8			0.121177			0.0605886	−	0.998163i	$-0.480702\pi$
$601$	6.44884e8			0.121177			0.0605886	+	0.998163i	$0.480702\pi$
$602$	−6.84190e8	−	2.56285e9i	−0.127817	−	0.478779i
$603$		0			0
$604$	1.14106e9	−	1.97638e9i	0.210708	−	0.364957i
$605$	9.36859e7	+	1.62269e8i	0.0172001	+	0.0297914i
$606$		0			0
$607$	−1.62737e9	+	2.81869e9i	−0.295343	+	0.511549i	−0.975065	−	0.221921i	$-0.928767\pi$
$607$	−1.62737e9	+	2.81869e9i	−0.295343	+	0.511549i	0.679721	+	0.733470i	$0.262101\pi$
$608$	1.06172e9			0.191579
$609$		0			0
$610$	1.43500e8			0.0255975
$611$	−1.05893e9	+	1.83412e9i	−0.187812	+	0.325300i
$612$		0			0
$613$	−1.95906e9	−	3.39319e9i	−0.343508	−	0.594973i	0.641574	−	0.767061i	$-0.278282\pi$
$613$	−1.95906e9	−	3.39319e9i	−0.343508	−	0.594973i	−0.985081	+	0.172089i	$0.944948\pi$
$614$	−9.12643e8	+	1.58074e9i	−0.159115	+	0.275596i
$615$		0			0
$616$	1.46550e9	+	3.94122e8i	0.252611	+	0.0679357i
$617$	−6.38504e9			−1.09437			−0.547187	−	0.837010i	$-0.684301\pi$
$617$	−6.38504e9			−1.09437			−0.547187	+	0.837010i	$0.684301\pi$
$618$		0			0
$619$	5.48911e9	+	9.50741e9i	0.930217	+	1.61118i	0.782948	+	0.622087i	$0.213715\pi$
$619$	5.48911e9	+	9.50741e9i	0.930217	+	1.61118i	0.147269	+	0.989096i	$0.452952\pi$
$620$	−9.09928e7	−	1.57604e8i	−0.0153333	−	0.0265581i
$621$		0			0
$622$	5.70457e9			0.950510
$623$	1.53011e9	+	5.73152e9i	0.253522	+	0.949645i
$624$		0			0
$625$	−2.99897e9	+	5.19436e9i	−0.491351	+	0.851044i
$626$	−5.58171e8	−	9.66780e8i	−0.0909404	−	0.157513i
$627$		0			0
$628$	1.66618e9	−	2.88591e9i	0.268450	−	0.464969i
$629$	−2.11824e10			−3.39389
$630$		0			0
$631$	−6.75136e9			−1.06977			−0.534883	−	0.844926i	$-0.679644\pi$
$631$	−6.75136e9			−1.06977			−0.534883	+	0.844926i	$0.679644\pi$
$632$	−1.27852e9	+	2.21446e9i	−0.201464	+	0.348946i
$633$		0			0
$634$	6.15553e8	+	1.06617e9i	0.0959297	+	0.166155i
$635$	1.50283e7	−	2.60299e7i	0.00232918	−	0.00403426i
$636$		0			0
$637$	1.54937e7	−	8.43139e9i	0.00237503	−	1.29244i
$638$	−1.14927e9			−0.175207
$639$		0			0
$640$	2.22772e7	+	3.85853e7i	0.00335916	+	0.00581824i
$641$	2.66451e9	+	4.61507e9i	0.399590	+	0.692110i	0.993675	−	0.112292i	$-0.0358192\pi$
$641$	2.66451e9	+	4.61507e9i	0.399590	+	0.692110i	−0.594085	+	0.804402i	$0.702486\pi$
$642$		0			0
$643$	3.64486e9			0.540683			0.270342	−	0.962764i	$-0.412863\pi$
$643$	3.64486e9			0.540683			0.270342	+	0.962764i	$0.412863\pi$
$644$	6.88164e8	−	6.86901e8i	0.101529	−	0.101343i
$645$		0			0
$646$	−4.73435e9	+	8.20014e9i	−0.690950	+	1.19676i
$647$	−4.98373e8	−	8.63207e8i	−0.0723418	−	0.125300i	0.827585	−	0.561340i	$-0.189714\pi$
$647$	−4.98373e8	−	8.63207e8i	−0.0723418	−	0.125300i	−0.899927	+	0.436040i	$0.856381\pi$
$648$		0			0
$649$	−2.63990e8	+	4.57244e8i	−0.0379080	+	0.0656585i
$650$	6.36176e9			0.908617
$651$		0			0
$652$	3.48454e9			0.492356
$653$	1.25807e9	−	2.17905e9i	0.176811	−	0.306246i	−0.763975	−	0.645245i	$-0.776755\pi$
$653$	1.25807e9	−	2.17905e9i	0.176811	−	0.306246i	0.940787	+	0.338999i	$0.110088\pi$
$654$		0			0
$655$	−3.77346e8	−	6.53583e8i	−0.0524681	−	0.0908774i
$656$	−1.09152e9	+	1.89056e9i	−0.150962	+	0.261474i
$657$		0			0
$658$	−1.45029e9	−	3.90031e8i	−0.198455	−	0.0533714i
$659$	−2.14485e9			−0.291944			−0.145972	−	0.989289i	$-0.546631\pi$
$659$	−2.14485e9			−0.291944			−0.145972	+	0.989289i	$0.546631\pi$
$660$		0			0
$661$	2.15616e9	+	3.73457e9i	0.290386	+	0.502962i	0.973901	−	0.226974i	$-0.0728831\pi$
$661$	2.15616e9	+	3.73457e9i	0.290386	+	0.502962i	−0.683515	+	0.729936i	$0.739550\pi$
$662$	5.59925e8	+	9.69819e8i	0.0750114	+	0.129924i
$663$		0			0
$664$	−1.73238e9			−0.229644
$665$	−6.03256e8	−	1.62236e8i	−0.0795474	−	0.0213930i
$666$		0			0
$667$	−3.68175e8	+	6.37698e8i	−0.0480412	+	0.0832098i
$668$	−1.18127e9	−	2.04601e9i	−0.153331	−	0.265577i
$669$		0			0
$670$	1.04343e8	−	1.80728e8i	0.0134030	−	0.0232147i
$671$	2.75763e9			0.352377
$672$		0			0
$673$	8.49626e9			1.07442			0.537211	−	0.843448i	$-0.319478\pi$
$673$	8.49626e9			1.07442			0.537211	+	0.843448i	$0.319478\pi$
$674$	−3.74722e8	+	6.49038e8i	−0.0471411	+	0.0816509i
$675$		0			0
$676$	−1.34616e9	−	2.33162e9i	−0.167604	−	0.290298i
$677$	3.85081e9	−	6.66980e9i	0.476971	−	0.826138i	−0.522681	−	0.852528i	$-0.675068\pi$
$677$	3.85081e9	−	6.66980e9i	0.476971	−	0.826138i	0.999652	+	0.0263906i	$0.00840138\pi$
$678$		0			0
$679$	−8.72956e8	+	8.71353e8i	−0.107016	+	0.106819i
$680$	−3.97347e8			−0.0484606
$681$		0			0
$682$	−1.74860e9	−	3.02867e9i	−0.211079	−	0.365600i
$683$	−4.85022e9	−	8.40083e9i	−0.582491	−	1.00890i	−0.995183	−	0.0980333i	$-0.968745\pi$
$683$	−4.85022e9	−	8.40083e9i	−0.582491	−	1.00890i	0.412692	−	0.910871i	$-0.364588\pi$
$684$		0			0
$685$	9.41196e8			0.111883
$686$	5.77939e9	−	1.53152e9i	0.683515	−	0.181129i
$687$		0			0
$688$	7.48289e8	−	1.29607e9i	0.0876011	−	0.151730i
$689$	−5.57052e9	−	9.64843e9i	−0.648827	−	1.12380i
$690$		0			0
$691$	1.42444e9	−	2.46720e9i	0.164237	−	0.284466i	−0.772147	−	0.635444i	$-0.780817\pi$
$691$	1.42444e9	−	2.46720e9i	0.164237	−	0.284466i	0.936384	+	0.350977i	$0.114151\pi$
$692$	4.92695e9			0.565206
$693$		0			0
$694$	−4.57156e9			−0.519166
$695$	−3.16329e8	+	5.47899e8i	−0.0357432	+	0.0619090i
$696$		0			0
$697$	−9.73441e9	−	1.68605e10i	−1.08892	−	1.88606i
$698$	−9.28491e8	+	1.60819e9i	−0.103344	+	0.178996i
$699$		0			0
$700$	1.16359e9	+	4.35860e9i	0.128221	+	0.480291i
$701$	4.47816e9			0.491006			0.245503	−	0.969396i	$-0.421047\pi$
$701$	4.47816e9			0.491006			0.245503	+	0.969396i	$0.421047\pi$
$702$		0			0
$703$	−9.39436e9	−	1.62715e10i	−1.01982	−	1.76638i
$704$	4.28100e8	+	7.41490e8i	0.0462424	+	0.0800942i
$705$		0			0
$706$	9.27799e9			0.992287
$707$	−1.02466e10	−	2.75567e9i	−1.09047	−	0.293265i
$708$		0			0
$709$	4.19450e9	−	7.26510e9i	0.441997	−	0.765560i	−0.555841	−	0.831289i	$-0.687604\pi$
$709$	4.19450e9	−	7.26510e9i	0.441997	−	0.765560i	0.997838	+	0.0657281i	$0.0209370\pi$
$710$	−9.41235e7	−	1.63027e8i	−0.00986947	−	0.0170944i
$711$		0			0
$712$	−1.67346e9	+	2.89852e9i	−0.173754	+	0.300952i
$713$	−2.24069e9			−0.231509
$714$		0			0
$715$	−7.10411e8			−0.0726840
$716$	1.60117e9	−	2.77331e9i	0.163020	−	0.282360i
$717$		0			0
$718$	−3.88653e9	−	6.73167e9i	−0.391856	−	0.678714i
$719$	−6.19091e8	+	1.07230e9i	−0.0621160	+	0.107588i	−0.895411	−	0.445240i	$-0.853118\pi$
$719$	−6.19091e8	+	1.07230e9i	−0.0621160	+	0.107588i	0.833295	+	0.552829i	$0.186452\pi$
$720$		0			0
$721$	5.08676e8	+	1.90540e9i	0.0505437	+	0.189327i
$722$	−1.24773e9			−0.123379
$723$		0			0
$724$	−5.22329e8	−	9.04700e8i	−0.0511516	−	0.0885971i
$725$	−1.70821e9	−	2.95872e9i	−0.166479	−	0.288350i
$726$		0			0
$727$	−3.52132e9			−0.339888			−0.169944	−	0.985454i	$-0.554359\pi$
$727$	−3.52132e9			−0.339888			−0.169944	+	0.985454i	$0.554359\pi$
$728$	3.36675e9	−	3.36057e9i	0.323408	−	0.322814i
$729$		0			0
$730$	1.39270e8	−	2.41224e8i	0.0132504	−	0.0229504i
$731$	6.67342e9	+	1.15587e10i	0.631884	+	1.09446i
$732$		0			0
$733$	−3.95436e9	+	6.84915e9i	−0.370862	+	0.642352i	−0.989698	−	0.143168i	$-0.954271\pi$
$733$	−3.95436e9	+	6.84915e9i	−0.370862	+	0.642352i	0.618836	+	0.785520i	$0.287604\pi$
$734$	1.36224e10			1.27150
$735$		0			0
$736$	5.48574e8			0.0507181
$737$	2.00516e9	−	3.47304e9i	0.184507	−	0.319576i
$738$		0			0
$739$	−2.24356e9	−	3.88597e9i	−0.204495	−	0.354196i	0.745477	−	0.666532i	$-0.232222\pi$
$739$	−2.24356e9	−	3.88597e9i	−0.204495	−	0.354196i	−0.949972	+	0.312336i	$0.898889\pi$
$740$	3.94227e8	−	6.82822e8i	0.0357632	−	0.0619436i
$741$		0			0
$742$	5.59151e9	−	5.58124e9i	0.502476	−	0.501553i
$743$	4.33508e9			0.387736			0.193868	−	0.981028i	$-0.437897\pi$
$743$	4.33508e9			0.387736			0.193868	+	0.981028i	$0.437897\pi$
$744$		0			0
$745$	−4.33461e8	−	7.50777e8i	−0.0384064	−	0.0665218i
$746$	1.50795e9	+	2.61185e9i	0.132984	+	0.230336i
$747$		0			0
$748$	−7.63579e9			−0.667112
$749$	2.51996e9	+	9.43930e9i	0.219133	+	0.820830i
$750$		0			0
$751$	5.94199e9	−	1.02918e10i	0.511908	−	0.886651i	−0.487997	−	0.872845i	$-0.662272\pi$
$751$	5.94199e9	−	1.02918e10i	0.511908	−	0.886651i	0.999905	−	0.0138052i	$-0.00439447\pi$
$752$	−4.23656e8	−	7.33794e8i	−0.0363288	−	0.0629233i
$753$		0			0
$754$	−1.80124e9	+	3.11985e9i	−0.153029	+	0.265054i
$755$	−7.57567e8			−0.0640630
$756$		0			0
$757$	1.37796e10			1.15452			0.577260	−	0.816560i	$-0.304122\pi$
$757$	1.37796e10			1.15452			0.577260	+	0.816560i	$0.304122\pi$
$758$	3.54799e9	−	6.14531e9i	0.295897	−	0.512509i
$759$		0			0
$760$	−1.76223e8	−	3.05227e8i	−0.0145618	−	0.0252217i
$761$	4.26500e9	−	7.38719e9i	0.350810	−	0.607622i	−0.635581	−	0.772034i	$-0.719239\pi$
$761$	4.26500e9	−	7.38719e9i	0.350810	−	0.607622i	0.986392	+	0.164412i	$0.0525728\pi$
$762$		0			0
$763$	−1.08452e10	−	2.91664e9i	−0.883897	−	0.237710i
$764$	−9.53907e9			−0.773890
$765$		0			0
$766$	1.73718e9	+	3.00889e9i	0.139651	+	0.241883i
$767$	8.27496e8	+	1.43327e9i	0.0662189	+	0.114695i
$768$		0			0
$769$	−1.57605e10			−1.24976			−0.624881	−	0.780720i	$-0.714853\pi$
$769$	−1.57605e10			−1.24976			−0.624881	+	0.780720i	$0.714853\pi$
$770$	−1.29937e8	−	4.86720e8i	−0.0102569	−	0.0384204i
$771$		0			0
$772$	−2.02876e9	+	3.51391e9i	−0.158697	+	0.274872i
$773$	−1.87506e9	−	3.24770e9i	−0.146011	−	0.252899i	0.783738	−	0.621091i	$-0.213310\pi$
$773$	−1.87506e9	−	3.24770e9i	−0.146011	−	0.252899i	−0.929750	+	0.368192i	$0.879977\pi$
$774$		0			0
$775$	5.19804e9	−	9.00327e9i	0.401129	−	0.694776i
$776$	−6.95882e8			−0.0534588
$777$		0			0
$778$	1.21278e9			0.0923320
$779$	8.63439e9	−	1.49552e10i	0.654411	−	1.13347i
$780$		0			0
$781$	−1.80876e9	−	3.13287e9i	−0.135864	−	0.235323i
$782$	−2.44616e9	+	4.23687e9i	−0.182920	+	0.316827i
$783$		0			0
$784$	2.91820e9	+	1.69198e9i	0.216276	+	0.125398i
$785$	−1.10620e9			−0.0816186
$786$		0			0
$787$	1.01205e10	+	1.75292e10i	0.740099	+	1.28189i	0.952450	+	0.304696i	$0.0985549\pi$
$787$	1.01205e10	+	1.75292e10i	0.740099	+	1.28189i	−0.212350	+	0.977194i	$0.568112\pi$
$788$	9.40132e8	+	1.62836e9i	0.0684459	+	0.118552i
$789$		0			0
$790$	8.48825e8			0.0612524
$791$	−1.24545e10	+	1.24316e10i	−0.894763	+	0.893120i
$792$		0			0
$793$	4.32200e9	−	7.48592e9i	0.307772	−	0.533076i
$794$	−6.82068e9	−	1.18138e10i	−0.483566	−	0.837561i
$795$		0			0
$796$	−1.57343e9	+	2.72525e9i	−0.110573	+	0.191519i
$797$	1.96658e10			1.37597			0.687983	−	0.725727i	$-0.258496\pi$
$797$	1.96658e10			1.37597			0.687983	+	0.725727i	$0.258496\pi$
$798$		0			0
$799$	7.55654e9			0.524094
$800$	−1.27260e9	+	2.20422e9i	−0.0878777	+	0.152209i
$801$		0			0
$802$	−4.60706e9	−	7.97967e9i	−0.315365	−	0.546229i
$803$	2.67635e9	−	4.63558e9i	0.182406	−	0.315936i
$804$		0			0
$805$	−3.11692e8	−	8.38247e7i	−0.0210591	−	0.00566352i
$806$	−1.09623e10			−0.737441
$807$		0			0
$808$	−2.99324e9	−	5.18445e9i	−0.199619	−	0.345750i
$809$	2.91367e9	+	5.04662e9i	0.193473	+	0.335105i	0.946399	−	0.323000i	$-0.104692\pi$
$809$	2.91367e9	+	5.04662e9i	0.193473	+	0.335105i	−0.752926	+	0.658105i	$0.771358\pi$
$810$		0			0
$811$	1.13903e10			0.749829			0.374914	−	0.927059i	$-0.377672\pi$
$811$	1.13903e10			0.749829			0.374914	+	0.927059i	$0.377672\pi$
$812$	−2.46694e9	−	6.63445e8i	−0.161701	−	0.0434869i
$813$		0			0
$814$	7.57584e9	−	1.31217e10i	0.492318	−	0.852719i
$815$	−5.78358e8	−	1.00175e9i	−0.0374236	−	0.0648195i
$816$		0			0
$817$	−5.91930e9	+	1.02525e10i	−0.379746	+	0.657739i
$818$	−9.15175e9			−0.584612
$819$		0			0
$820$	7.24672e8			0.0458979
$821$	5.98364e9	−	1.03640e10i	0.377367	−	0.653619i	−0.613311	−	0.789841i	$-0.710163\pi$
$821$	5.98364e9	−	1.03640e10i	0.377367	−	0.653619i	0.990678	+	0.136222i	$0.0434961\pi$
$822$		0			0
$823$	1.24348e10	+	2.15376e10i	0.777568	+	1.34679i	0.933340	+	0.358994i	$0.116880\pi$
$823$	1.24348e10	+	2.15376e10i	0.777568	+	1.34679i	−0.155772	+	0.987793i	$0.549787\pi$
$824$	−5.56331e8	+	9.63594e8i	−0.0346408	+	0.0599997i
$825$		0			0
$826$	−8.30613e8	+	8.29088e8i	−0.0512824	+	0.0511883i
$827$	−1.05586e10			−0.649137			−0.324569	−	0.945862i	$-0.605219\pi$
$827$	−1.05586e10			−0.649137			−0.324569	+	0.945862i	$0.605219\pi$
$828$		0			0
$829$	5.93269e9	+	1.02757e10i	0.361668	+	0.626428i	0.988236	−	0.152939i	$-0.0488739\pi$
$829$	5.93269e9	+	1.02757e10i	0.361668	+	0.626428i	−0.626567	+	0.779367i	$0.715541\pi$
$830$	2.87537e8	+	4.98029e8i	0.0174550	+	0.0302330i
$831$		0			0
$832$	2.68382e9			0.161556
$833$	−2.60805e10	+	1.49938e10i	−1.56336	+	0.898779i
$834$		0			0
$835$	−3.92129e8	+	6.79188e8i	−0.0233092	+	0.0403726i
$836$	−3.38646e9	−	5.86552e9i	−0.200458	−	0.347204i
$837$		0			0
$838$	−6.89127e9	+	1.19360e10i	−0.404525	+	0.700657i
$839$	−4.68285e9			−0.273743			−0.136872	−	0.990589i	$-0.543705\pi$
$839$	−4.68285e9			−0.273743			−0.136872	+	0.990589i	$0.543705\pi$
$840$		0			0
$841$	−1.53152e10			−0.887847
$842$	−1.00198e10	+	1.73548e10i	−0.578453	+	1.00191i
$843$		0			0
$844$	8.17004e9	+	1.41509e10i	0.467763	+	0.810189i
$845$	−4.46866e8	+	7.73995e8i	−0.0254788	+	0.0441306i
$846$		0			0
$847$	2.06439e9	+	7.73280e9i	0.116734	+	0.437265i
$848$	4.45730e9			0.251007
$849$		0			0
$850$	−1.13494e10	−	1.96577e10i	−0.633879	−	1.09791i
$851$	−4.85391e9	−	8.40721e9i	−0.269984	−	0.467626i
$852$		0			0
$853$	−5.76473e9			−0.318022			−0.159011	−	0.987277i	$-0.550831\pi$
$853$	−5.76473e9			−0.318022			−0.159011	+	0.987277i	$0.550831\pi$
$854$	5.91930e9	+	1.59190e9i	0.325213	+	0.0874610i
$855$		0			0
$856$	−2.75604e9	+	4.77361e9i	−0.150185	+	0.260129i
$857$	1.23111e10	+	2.13235e10i	0.668135	+	1.15724i	0.978425	+	0.206602i	$0.0662406\pi$
$857$	1.23111e10	+	2.13235e10i	0.668135	+	1.15724i	−0.310290	+	0.950642i	$0.600426\pi$
$858$		0			0
$859$	−1.49943e10	+	2.59709e10i	−0.807144	+	1.39801i	0.107691	+	0.994184i	$0.465654\pi$
$859$	−1.49943e10	+	2.59709e10i	−0.807144	+	1.39801i	−0.914834	+	0.403829i	$0.867679\pi$
$860$	−4.96798e8			−0.0266339
$861$		0			0
$862$	1.82884e10			0.972526
$863$	4.28994e8	−	7.43040e8i	0.0227203	−	0.0393527i	−0.854442	−	0.519547i	$-0.826101\pi$
$863$	4.28994e8	−	7.43040e8i	0.0227203	−	0.0393527i	0.877162	+	0.480195i	$0.159434\pi$
$864$		0			0
$865$	−8.17766e8	−	1.41641e9i	−0.0429608	−	0.0744103i
$866$	−8.29326e9	+	1.43644e10i	−0.433923	+	0.751577i
$867$		0			0
$868$	−2.00504e9	−	7.51052e9i	−0.104065	−	0.389808i
$869$	1.63118e10			0.843204
$870$		0			0
$871$	−6.28533e9	−	1.08865e10i	−0.322303	−	0.558245i
$872$	−3.16809e9	−	5.48729e9i	−0.161804	−	0.280253i
$873$		0			0
$874$	−4.33947e9			−0.219860
$875$	2.12594e9	−	2.12204e9i	0.107281	−	0.107084i
$876$		0			0
$877$	2.82487e9	−	4.89282e9i	0.141416	−	0.244940i	−0.786614	−	0.617445i	$-0.788168\pi$
$877$	2.82487e9	−	4.89282e9i	0.141416	−	0.244940i	0.928030	+	0.372505i	$0.121501\pi$
$878$	−7.03459e9	−	1.21843e10i	−0.350758	−	0.607531i
$879$		0			0
$880$	1.42110e8	−	2.46142e8i	0.00702970	−	0.0121758i
$881$	2.87116e10			1.41462			0.707312	−	0.706902i	$-0.249908\pi$
$881$	2.87116e10			1.41462			0.707312	+	0.706902i	$0.249908\pi$
$882$		0			0
$883$	1.38023e10			0.674668			0.337334	−	0.941385i	$-0.390475\pi$
$883$	1.38023e10			0.674668			0.337334	+	0.941385i	$0.390475\pi$
$884$	−1.19675e10	+	2.07283e10i	−0.582667	+	1.00921i
$885$		0			0
$886$	7.71789e9	+	1.33678e10i	0.372804	+	0.645715i
$887$	−1.86125e10	+	3.22378e10i	−0.895513	+	1.55107i	−0.0623449	+	0.998055i	$0.519858\pi$
$887$	−1.86125e10	+	3.22378e10i	−0.895513	+	1.55107i	−0.833168	+	0.553020i	$0.813475\pi$
$888$		0			0
$889$	9.08672e8	−	9.07003e8i	0.0433761	−	0.0432965i
$890$	1.11103e9			0.0528277
$891$		0			0
$892$	1.07357e9	+	1.85948e9i	0.0506470	+	0.0877232i
$893$	3.35131e9	+	5.80464e9i	0.157483	+	0.272769i
$894$		0			0
$895$	−1.06304e9			−0.0495642
$896$	4.90882e8	+	1.83875e9i	0.0227981	+	0.0853976i
$897$		0			0
$898$	−1.31730e10	+	2.28163e10i	−0.607040	+	1.05142i
$899$	2.94351e9	+	5.09830e9i	0.135116	+	0.234027i
$900$		0			0
$901$	−1.98757e10	+	3.44256e10i	−0.905284	+	1.56800i
$902$	1.39260e10			0.631834
$903$		0			0
$904$	−9.92816e9			−0.446971
$905$	−1.73390e8	+	3.00321e8i	−0.00777597	+	0.0134684i
$906$		0			0
$907$	2.80129e9	+	4.85198e9i	0.124662	+	0.215920i	0.921601	−	0.388139i	$-0.126882\pi$
$907$	2.80129e9	+	4.85198e9i	0.124662	+	0.215920i	−0.796939	+	0.604060i	$0.793549\pi$
$908$	4.83450e8	−	8.37360e8i	0.0214314	−	0.0371203i
$909$		0			0
$910$	−1.52491e9	−	4.10101e8i	−0.0670810	−	0.0180404i
$911$	3.57046e10			1.56462			0.782312	−	0.622886i	$-0.214040\pi$
$911$	3.57046e10			1.56462			0.782312	+	0.622886i	$0.214040\pi$
$912$		0			0
$913$	5.52558e9	+	9.57059e9i	0.240287	+	0.416189i
$914$	−7.65848e9	−	1.32649e10i	−0.331765	−	0.574634i
$915$		0			0
$916$	−6.60235e9			−0.283834
$917$	−8.31489e9	−	3.11460e10i	−0.356093	−	1.33386i
$918$		0			0
$919$	−2.19020e9	+	3.79354e9i	−0.0930850	+	0.161228i	−0.908808	−	0.417215i	$-0.863006\pi$
$919$	−2.19020e9	+	3.79354e9i	−0.0930850	+	0.161228i	0.815723	+	0.578443i	$0.196340\pi$
$920$	−9.10513e7	−	1.57706e8i	−0.00385504	−	0.00667713i
$921$		0			0
$922$	7.36270e9	−	1.27526e10i	0.309371	−	0.535845i
$923$	−1.13394e10			−0.474663
$924$		0			0
$925$	4.50412e10			1.87117
$926$	−6.71767e8	+	1.16353e9i	−0.0278023	+	0.0481550i
$927$		0			0
$928$	−7.20641e8	−	1.24819e9i	−0.0296006	−	0.0512698i
$929$	−9.08246e9	+	1.57313e10i	−0.371662	+	0.643738i	−0.989821	−	0.142315i	$-0.954545\pi$
$929$	−9.08246e9	+	1.57313e10i	−0.371662	+	0.643738i	0.618159	+	0.786053i	$0.287879\pi$
$930$		0			0
$931$	−2.30843e10	−	1.33843e10i	−0.937546	−	0.543592i
$932$	−6.65362e9			−0.269217
$933$		0			0
$934$	−5.51631e9	−	9.55452e9i	−0.221531	−	0.383703i
$935$	1.26738e9	+	2.19516e9i	0.0507066	+	0.0878264i
$936$		0			0
$937$	2.55925e10			1.01631			0.508153	−	0.861267i	$-0.330328\pi$
$937$	2.55925e10			1.01631			0.508153	+	0.861267i	$0.330328\pi$
$938$	6.30900e9	−	6.29742e9i	0.249604	−	0.249145i
$939$		0			0
$940$	−1.40635e8	+	2.43588e8i	−0.00552264	+	0.00956550i
$941$	1.53193e10	+	2.65338e10i	0.599343	+	1.03809i	0.992918	+	0.118800i	$0.0379046\pi$
$941$	1.53193e10	+	2.65338e10i	0.599343	+	1.03809i	−0.393576	+	0.919292i	$0.628762\pi$
$942$		0			0
$943$	4.46124e9	−	7.72710e9i	0.173247	−	0.300072i
$944$	−6.62128e8			−0.0256177
$945$		0			0
$946$	−9.54694e9			−0.366645
$947$	1.13440e10	−	1.96484e10i	0.434052	−	0.751800i	−0.563166	−	0.826344i	$-0.690417\pi$
$947$	1.13440e10	−	1.96484e10i	0.434052	−	0.751800i	0.997218	+	0.0745437i	$0.0237500\pi$
$948$		0			0
$949$	−8.38923e9	−	1.45306e10i	−0.318633	−	0.551888i
$950$	1.00669e10	−	1.74363e10i	0.380945	−	0.659816i
$951$		0			0
$952$	−1.63904e10	−	4.40793e9i	−0.615687	−	0.165579i
$953$	2.31130e10			0.865030			0.432515	−	0.901627i	$-0.357626\pi$
$953$	2.31130e10			0.865030			0.432515	+	0.901627i	$0.357626\pi$
$954$		0			0
$955$	1.58328e9	+	2.74232e9i	0.0588228	+	0.101884i
$956$	4.49743e9	+	7.78977e9i	0.166480	+	0.288352i
$957$		0			0
$958$	3.62407e10			1.33173
$959$	3.88239e10	+	1.04411e10i	1.42146	+	0.382278i
$960$		0			0
$961$	4.79931e9	−	8.31265e9i	0.174440	−	0.302140i
$962$	−2.37471e10	−	4.11311e10i	−0.859997	−	1.48956i
$963$		0			0
$964$	−9.76005e9	+	1.69049e10i	−0.350899	+	0.607775i
$965$	1.34692e9			0.0482498
$966$		0			0
$967$	1.63381e10			0.581043			0.290521	−	0.956868i	$-0.406171\pi$
$967$	1.63381e10			0.581043			0.290521	+	0.956868i	$0.406171\pi$
$968$	−2.25779e9	+	3.91061e9i	−0.0800055	+	0.138574i
$969$		0			0
$970$	1.15501e8	+	2.00054e8i	0.00406336	+	0.00703795i
$971$	−2.36893e9	+	4.10311e9i	−0.0830396	+	0.143829i	−0.904554	−	0.426359i	$-0.859796\pi$
$971$	−2.36893e9	+	4.10311e9i	−0.0830396	+	0.143829i	0.821515	+	0.570188i	$0.193129\pi$
$972$		0			0
$973$	−1.91265e10	+	1.90914e10i	−0.665642	+	0.664420i
$974$	−1.23164e10			−0.427097
$975$		0			0
$976$	1.72914e9	+	2.99496e9i	0.0595328	+	0.103114i
$977$	8.57370e9	+	1.48501e10i	0.294129	+	0.509446i	0.974782	−	0.223160i	$-0.0716373\pi$
$977$	8.57370e9	+	1.48501e10i	0.294129	+	0.509446i	−0.680653	+	0.732606i	$0.738304\pi$
$978$		0			0
$979$	2.13506e10			0.727230
$980$	2.05771e6	−	1.11976e9i	6.98380e−5	−	0.0380045i
$981$		0			0
$982$	7.43121e9	−	1.28712e10i	0.250420	−	0.433741i
$983$	−2.27209e10	−	3.93537e10i	−0.762935	−	1.32144i	−0.941332	−	0.337483i	$-0.890425\pi$
$983$	−2.27209e10	−	3.93537e10i	−0.762935	−	1.32144i	0.178397	−	0.983959i	$-0.442909\pi$
$984$		0			0
$985$	3.12083e8	−	5.40543e8i	0.0104050	−	0.0180220i
$986$	1.28537e10			0.427030
$987$		0			0
$988$	−2.12302e10			−0.700335
$989$	−3.05840e9	+	5.29731e9i	−0.100533	+	0.174128i
$990$		0			0
$991$	1.63460e10	+	2.83122e10i	0.533525	+	0.924092i	0.999233	+	0.0391537i	$0.0124662\pi$
$991$	1.63460e10	+	2.83122e10i	0.533525	+	0.924092i	−0.465708	+	0.884938i	$0.654200\pi$
$992$	2.19289e9	−	3.79819e9i	0.0713223	−	0.123534i
$993$		0			0
$994$	−2.07403e9	−	7.76892e9i	−0.0669826	−	0.250904i
$995$	1.04462e9			0.0336184
$996$		0			0
$997$	−2.70222e10	−	4.68038e10i	−0.863550	−	1.49571i	−0.868480	−	0.495724i	$-0.834903\pi$
$997$	−2.70222e10	−	4.68038e10i	−0.863550	−	1.49571i	0.00493036	−	0.999988i	$-0.498431\pi$
$998$	2.14142e10	+	3.70904e10i	0.681937	+	1.18115i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.8.g.e.37.2		4
3.2	odd	2		14.8.c.a.9.2	✓	4
7.4	even	3	inner	126.8.g.e.109.2		4
12.11	even	2		112.8.i.a.65.1		4
21.2	odd	6		98.8.a.h.1.1		2
21.5	even	6		98.8.a.k.1.2		2
21.11	odd	6		14.8.c.a.11.2	yes	4
21.17	even	6		98.8.c.h.67.1		4
21.20	even	2		98.8.c.h.79.1		4
84.11	even	6		112.8.i.a.81.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.8.c.a.9.2	✓	4	3.2	odd	2
14.8.c.a.11.2	yes	4	21.11	odd	6
98.8.a.h.1.1		2	21.2	odd	6
98.8.a.k.1.2		2	21.5	even	6
98.8.c.h.67.1		4	21.17	even	6
98.8.c.h.79.1		4	21.20	even	2
112.8.i.a.65.1		4	12.11	even	2
112.8.i.a.81.1		4	84.11	even	6
126.8.g.e.37.2		4	1.1	even	1	trivial
126.8.g.e.109.2		4	7.4	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 - 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-10.6226 + 18.3989i) q^{5} +(-642.284 + 641.104i) q^{7} -512.000 q^{8} +(84.9808 + 147.191i) q^{10} +(1633.07 + 2828.56i) q^{11} +10238.0 q^{13} +(1872.57 + 7014.29i) q^{14} +(-2048.00 + 3547.24i) q^{16} +(-18264.6 - 31635.1i) q^{17} +(16200.6 - 28060.3i) q^{19} +1359.69 q^{20} +26129.1 q^{22} +(8370.58 - 14498.3i) q^{23} +(38836.8 + 67267.3i) q^{25} +(40951.9 - 70930.7i) q^{26} +(56086.7 + 15083.6i) q^{28} -43984.4 q^{29} +(-66921.6 - 115912. i) q^{31} +(16384.0 + 28377.9i) q^{32} -292233. q^{34} +(-4972.88 - 18627.5i) q^{35} +(289939. - 502188. i) q^{37} +(-129605. - 224482. i) q^{38} +(5438.77 - 9420.23i) q^{40} +532967. q^{41} -365375. q^{43} +(104517. - 181028. i) q^{44} +(-66964.6 - 115986. i) q^{46} +(-103432. + 179149. i) q^{47} +(1513.36 - 823542. i) q^{49} +621389. q^{50} +(-327615. - 567446. i) q^{52} +(-544104. - 942416. i) q^{53} -69389.9 q^{55} +(328849. - 328245. i) q^{56} +(-175938. + 304733. i) q^{58} +(80826.2 + 139995. i) q^{59} +(422154. - 731192. i) q^{61} -1.07075e6 q^{62} +262144. q^{64} +(-108754. + 188367. i) q^{65} +(-613923. - 1.06335e6i) q^{67} +(-1.16893e6 + 2.02465e6i) q^{68} +(-148947. - 40056.8i) q^{70} -1.10759e6 q^{71} +(-819423. - 1.41928e6i) q^{73} +(-2.31951e6 - 4.01751e6i) q^{74} -2.07368e6 q^{76} +(-2.86230e6 - 769770. i) q^{77} +(2.49711e6 - 4.32512e6i) q^{79} +(-43510.2 - 75361.8i) q^{80} +(2.13187e6 - 3.69251e6i) q^{82} +3.38355e6 q^{83} +776069. q^{85} +(-1.46150e6 + 2.53139e6i) q^{86} +(-836132. - 1.44822e6i) q^{88} +(3.26848e6 - 5.66118e6i) q^{89} +(-6.57568e6 + 6.56361e6i) q^{91} -1.07143e6 q^{92} +(827454. + 1.43319e6i) q^{94} +(344185. + 596146. i) q^{95} +1.35914e6 q^{97} +(-5.69961e6 - 3.30465e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 16 q^{2} - 128 q^{4} - 238 q^{5} + 168 q^{7} - 2048 q^{8} + 1904 q^{10} + 5848 q^{11} + 2632 q^{13} + 2016 q^{14} - 8192 q^{16} - 47642 q^{17} + 41048 q^{19} + 30464 q^{20} + 93568 q^{22} - 49316 q^{23}+ \cdots - 20499248 q^{98}+O(q^{100}) \) 4 * q + 16 * q^2 - 128 * q^4 - 238 * q^5 + 168 * q^7 - 2048 * q^8 + 1904 * q^10 + 5848 * q^11 + 2632 * q^13 + 2016 * q^14 - 8192 * q^16 - 47642 * q^17 + 41048 * q^19 + 30464 * q^20 + 93568 * q^22 - 49316 * q^23 + 108816 * q^25 + 10528 * q^26 + 5376 * q^28 - 345640 * q^29 + 70252 * q^31 + 65536 * q^32 - 762272 * q^34 + 36904 * q^35 + 88166 * q^37 - 328384 * q^38 + 121856 * q^40 + 2312520 * q^41 + 115088 * q^43 + 374272 * q^44 + 394528 * q^46 - 1412292 * q^47 + 465892 * q^49 + 1741056 * q^50 - 84224 * q^52 - 2361174 * q^53 - 1258040 * q^55 - 86016 * q^56 - 1382560 * q^58 + 1842512 * q^59 - 1278242 * q^61 + 1124032 * q^62 + 1048576 * q^64 + 1716372 * q^65 + 2121480 * q^67 - 3049088 * q^68 + 2595712 * q^70 - 7200320 * q^71 + 1634682 * q^73 - 705328 * q^74 - 5254144 * q^76 - 1416226 * q^77 + 9192604 * q^79 - 974848 * q^80 + 9250080 * q^82 + 56560 * q^83 + 6369676 * q^85 + 460352 * q^86 - 2994176 * q^88 + 8936550 * q^89 - 26111120 * q^91 + 6312448 * q^92 + 11298336 * q^94 + 2562604 * q^95 + 11748408 * q^97 - 20499248 * q^98

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