LMFDB - Embedded newform 126.8.g.j.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,8,Mod(37,126)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$39.3605132110$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 1111x^{4} + 2838x^{3} + 1231236x^{2} + 959040x + 746496 $ x^6 - x^5 + 1111x^4 + 2838x^3 + 1231236x^2 + 959040x + 746496
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.2
Root			$-16.2090 - 28.0749i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.8.g.j.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.00000 - 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-95.0129 + 164.567i) q^{5} +(-515.817 - 746.643i) q^{7} -512.000 q^{8} +(760.103 + 1316.54i) q^{10} +(3127.15 + 5416.38i) q^{11} -4182.79 q^{13} +(-7236.16 + 587.110i) q^{14} +(-2048.00 + 3547.24i) q^{16} +(288.449 + 499.608i) q^{17} +(7721.88 - 13374.7i) q^{19} +12161.7 q^{20} +50034.3 q^{22} +(29335.5 - 50810.6i) q^{23} +(21007.6 + 36386.2i) q^{25} +(-16731.2 + 28979.2i) q^{26} +(-24877.0 + 52482.0i) q^{28} +23161.9 q^{29} +(151094. + 261703. i) q^{31} +(16384.0 + 28377.9i) q^{32} +4615.18 q^{34} +(171882. - 13945.8i) q^{35} +(111538. - 193190. i) q^{37} +(-61775.1 - 106998. i) q^{38} +(48646.6 - 84258.4i) q^{40} +330003. q^{41} +284765. q^{43} +(200137. - 346648. i) q^{44} +(-234684. - 406485. i) q^{46} +(653080. - 1.13117e6i) q^{47} +(-291409. + 770262. i) q^{49} +336122. q^{50} +(133849. + 231834. i) q^{52} +(551149. + 954618. i) q^{53} -1.18848e6 q^{55} +(264098. + 382281. i) q^{56} +(92647.6 - 160470. i) q^{58} +(17976.0 + 31135.3i) q^{59} +(602384. - 1.04336e6i) q^{61} +2.41751e6 q^{62} +262144. q^{64} +(397419. - 688350. i) q^{65} +(111437. + 193014. i) q^{67} +(18460.7 - 31974.9i) q^{68} +(590910. - 1.24662e6i) q^{70} +4.83371e6 q^{71} +(-1.74021e6 - 3.01414e6i) q^{73} +(-892306. - 1.54552e6i) q^{74} -988401. q^{76} +(2.43107e6 - 5.12872e6i) q^{77} +(-3.72576e6 + 6.45321e6i) q^{79} +(-389173. - 674067. i) q^{80} +(1.32001e6 - 2.28633e6i) q^{82} +4.70492e6 q^{83} -109625. q^{85} +(1.13906e6 - 1.97291e6i) q^{86} +(-1.60110e6 - 2.77318e6i) q^{88} +(1.71735e6 - 2.97453e6i) q^{89} +(2.15755e6 + 3.12305e6i) q^{91} -3.75495e6 q^{92} +(-5.22464e6 - 9.04935e6i) q^{94} +(1.46736e6 + 2.54154e6i) q^{95} +3.79727e6 q^{97} +(4.17090e6 + 5.09999e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 24 q^{2} - 192 q^{4} - 718 q^{5} - 1471 q^{7} - 3072 q^{8} + 5744 q^{10} + 208 q^{11} + 19394 q^{13} - 4504 q^{14} - 12288 q^{16} - 19244 q^{17} - 25419 q^{19} + 91904 q^{20} + 3328 q^{22} - 67400 q^{23}+ \cdots + 20461248 q^{98}+O(q^{100}) $ 6 * q + 24 * q^2 - 192 * q^4 - 718 * q^5 - 1471 * q^7 - 3072 * q^8 + 5744 * q^10 + 208 * q^11 + 19394 * q^13 - 4504 * q^14 - 12288 * q^16 - 19244 * q^17 - 25419 * q^19 + 91904 * q^20 + 3328 * q^22 - 67400 * q^23 - 93931 * q^25 + 77576 * q^26 + 58112 * q^28 + 33476 * q^29 + 78449 * q^31 + 98304 * q^32 - 307904 * q^34 - 602072 * q^35 - 496599 * q^37 + 203352 * q^38 + 367616 * q^40 + 1953168 * q^41 + 697470 * q^43 + 13312 * q^44 + 539200 * q^46 + 701328 * q^47 + 959673 * q^49 - 1502896 * q^50 - 620608 * q^52 + 2917374 * q^53 - 3275696 * q^55 + 753152 * q^56 + 133904 * q^58 - 492040 * q^59 + 3649370 * q^61 + 1255184 * q^62 + 1572864 * q^64 - 2707764 * q^65 - 3647153 * q^67 - 1231616 * q^68 - 503936 * q^70 + 3541216 * q^71 - 6183557 * q^73 + 3972792 * q^74 + 3253632 * q^76 + 13092290 * q^77 - 12453589 * q^79 - 2940928 * q^80 + 7812672 * q^82 + 11611120 * q^83 + 38154616 * q^85 + 2789880 * q^86 - 106496 * q^88 - 8292612 * q^89 + 366581 * q^91 + 8627200 * q^92 - 5610624 * q^94 - 8691056 * q^95 - 55949528 * q^97 + 20461248 * 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
$5$	−95.0129	+	164.567i	−0.339928	+	0.588773i	−0.984419	−	0.175839i	$-0.943736\pi$
$5$	−95.0129	+	164.567i	−0.339928	+	0.588773i	0.644490	+	0.764612i	$0.277070\pi$
$6$		0			0
$7$	−515.817	−	746.643i	−0.568398	−	0.822754i
$7$	−515.817	−	746.643i	−0.568398	−	0.822754i
$8$	−512.000			−0.353553
$9$		0			0
$10$	760.103	+	1316.54i	0.240366	+	0.416326i
$11$	3127.15	+	5416.38i	0.708392	+	1.22697i	0.965453	+	0.260576i	$0.0839125\pi$
$11$	3127.15	+	5416.38i	0.708392	+	1.22697i	−0.257061	+	0.966395i	$0.582754\pi$
$12$		0			0
$13$	−4182.79			−0.528037			−0.264018	−	0.964518i	$-0.585048\pi$
$13$	−4182.79			−0.528037			−0.264018	+	0.964518i	$0.585048\pi$
$14$	−7236.16	+	587.110i	−0.704791	+	0.0571836i
$15$		0			0
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	288.449	+	499.608i	0.0142396	+	0.0246637i	0.873057	−	0.487617i	$-0.162134\pi$
$17$	288.449	+	499.608i	0.0142396	+	0.0246637i	−0.858818	+	0.512281i	$0.828801\pi$
$18$		0			0
$19$	7721.88	−	13374.7i	0.258277	−	0.447349i	−0.707503	−	0.706710i	$-0.750179\pi$
$19$	7721.88	−	13374.7i	0.258277	−	0.447349i	0.965780	+	0.259361i	$0.0835120\pi$
$20$	12161.7			0.339928
$21$		0			0
$22$	50034.3			1.00182
$23$	29335.5	−	50810.6i	0.502744	−	0.870777i	−0.497251	−	0.867606i	$-0.665657\pi$
$23$	29335.5	−	50810.6i	0.502744	−	0.870777i	0.999995	−	0.00317085i	$-0.00100932\pi$
$24$		0			0
$25$	21007.6	+	36386.2i	0.268897	+	0.465744i
$26$	−16731.2	+	28979.2i	−0.186689	+	0.323355i
$27$		0			0
$28$	−24877.0	+	52482.0i	−0.214163	+	0.451812i
$29$	23161.9			0.176352			0.0881762	−	0.996105i	$-0.471896\pi$
$29$	23161.9			0.176352			0.0881762	+	0.996105i	$0.471896\pi$
$30$		0			0
$31$	151094.	+	261703.i	0.910923	+	1.57776i	0.812764	+	0.582593i	$0.197962\pi$
$31$	151094.	+	261703.i	0.910923	+	1.57776i	0.0981589	+	0.995171i	$0.468705\pi$
$32$	16384.0	+	28377.9i	0.0883883	+	0.153093i
$33$		0			0
$34$	4615.18			0.0201378
$35$	171882.	−	13945.8i	0.677630	−	0.0549799i
$36$		0			0
$37$	111538.	−	193190.i	0.362008	−	0.627015i	−0.626284	−	0.779595i	$-0.715425\pi$
$37$	111538.	−	193190.i	0.362008	−	0.627015i	0.988291	+	0.152580i	$0.0487581\pi$
$38$	−61775.1	−	106998.i	−0.182629	−	0.316323i
$39$		0			0
$40$	48646.6	−	84258.4i	0.120183	−	0.208163i
$41$	330003.			0.747782			0.373891	−	0.927473i	$-0.378023\pi$
$41$	330003.			0.747782			0.373891	+	0.927473i	$0.378023\pi$
$42$		0			0
$43$	284765.			0.546194			0.273097	−	0.961986i	$-0.411952\pi$
$43$	284765.			0.546194			0.273097	+	0.961986i	$0.411952\pi$
$44$	200137.	−	346648.i	0.354196	−	0.613486i
$45$		0			0
$46$	−234684.	−	406485.i	−0.355493	−	0.615733i
$47$	653080.	−	1.13117e6i	0.917538	−	1.58922i	0.114396	−	0.993435i	$-0.463507\pi$
$47$	653080.	−	1.13117e6i	0.917538	−	1.58922i	0.803142	−	0.595788i	$-0.203160\pi$
$48$		0			0
$49$	−291409.	+	770262.i	−0.353848	+	0.935303i
$50$	336122.			0.380278
$51$		0			0
$52$	133849.	+	231834.i	0.132009	+	0.228647i
$53$	551149.	+	954618.i	0.508514	+	0.880773i	0.999951	+	0.00985975i	$0.00313851\pi$
$53$	551149.	+	954618.i	0.508514	+	0.880773i	−0.491437	+	0.870913i	$0.663528\pi$
$54$		0			0
$55$	−1.18848e6			−0.963211
$56$	264098.	+	382281.i	0.200959	+	0.290887i
$57$		0			0
$58$	92647.6	−	160470.i	0.0623500	−	0.107993i
$59$	17976.0	+	31135.3i	0.0113949	+	0.0197366i	0.871667	−	0.490099i	$-0.163039\pi$
$59$	17976.0	+	31135.3i	0.0113949	+	0.0197366i	−0.860272	+	0.509836i	$0.829706\pi$
$60$		0			0
$61$	602384.	−	1.04336e6i	0.339797	−	0.588545i	−0.644598	−	0.764522i	$-0.722975\pi$
$61$	602384.	−	1.04336e6i	0.339797	−	0.588545i	0.984394	+	0.175977i	$0.0563085\pi$
$62$	2.41751e6			1.28824
$63$		0			0
$64$	262144.			0.125000
$65$	397419.	−	688350.i	0.179495	−	0.310894i
$66$		0			0
$67$	111437.	+	193014.i	0.0452654	+	0.0784020i	0.887770	−	0.460287i	$-0.152253\pi$
$67$	111437.	+	193014.i	0.0452654	+	0.0784020i	−0.842505	+	0.538688i	$0.818920\pi$
$68$	18460.7	−	31974.9i	0.00711980	−	0.0123319i
$69$		0			0
$70$	590910.	−	1.24662e6i	0.205910	−	0.434400i
$71$	4.83371e6			1.60279			0.801395	−	0.598135i	$-0.204091\pi$
$71$	4.83371e6			1.60279			0.801395	+	0.598135i	$0.204091\pi$
$72$		0			0
$73$	−1.74021e6	−	3.01414e6i	−0.523567	−	0.906844i	−0.999624	−	0.0274299i	$-0.991268\pi$
$73$	−1.74021e6	−	3.01414e6i	−0.523567	−	0.906844i	0.476057	−	0.879414i	$-0.342066\pi$
$74$	−892306.	−	1.54552e6i	−0.255978	−	0.443367i
$75$		0			0
$76$	−988401.			−0.258277
$77$	2.43107e6	−	5.12872e6i	0.606847	−	1.28024i
$78$		0			0
$79$	−3.72576e6	+	6.45321e6i	−0.850198	+	1.47259i	0.0308315	+	0.999525i	$0.490184\pi$
$79$	−3.72576e6	+	6.45321e6i	−0.850198	+	1.47259i	−0.881029	+	0.473061i	$0.843149\pi$
$80$	−389173.	−	674067.i	−0.0849821	−	0.147193i
$81$		0			0
$82$	1.32001e6	−	2.28633e6i	0.264381	−	0.457921i
$83$	4.70492e6			0.903189			0.451594	−	0.892223i	$-0.350855\pi$
$83$	4.70492e6			0.903189			0.451594	+	0.892223i	$0.350855\pi$
$84$		0			0
$85$	−109625.			−0.0193618
$86$	1.13906e6	−	1.97291e6i	0.193109	−	0.334474i
$87$		0			0
$88$	−1.60110e6	−	2.77318e6i	−0.250454	−	0.433800i
$89$	1.71735e6	−	2.97453e6i	0.258222	−	0.447253i	−0.707544	−	0.706669i	$-0.750197\pi$
$89$	1.71735e6	−	2.97453e6i	0.258222	−	0.447253i	0.965766	+	0.259416i	$0.0835301\pi$
$90$		0			0
$91$	2.15755e6	+	3.12305e6i	0.300135	+	0.434444i
$92$	−3.75495e6			−0.502744
$93$		0			0
$94$	−5.22464e6	−	9.04935e6i	−0.648797	−	1.12375i
$95$	1.46736e6	+	2.54154e6i	0.175591	+	0.304133i
$96$		0			0
$97$	3.79727e6			0.422445			0.211223	−	0.977438i	$-0.432256\pi$
$97$	3.79727e6			0.422445			0.211223	+	0.977438i	$0.432256\pi$
$98$	4.17090e6	+	5.09999e6i	0.447649	+	0.547366i
$99$		0			0
$100$	1.34449e6	−	2.32872e6i	0.134449	−	0.232872i
$101$	−1.98781e6	−	3.44299e6i	−0.191977	−	0.332514i	0.753928	−	0.656957i	$-0.228157\pi$
$101$	−1.98781e6	−	3.44299e6i	−0.191977	−	0.332514i	−0.945905	+	0.324442i	$0.894823\pi$
$102$		0			0
$103$	−3.47204e6	+	6.01376e6i	−0.313080	+	0.542270i	−0.979027	−	0.203728i	$-0.934694\pi$
$103$	−3.47204e6	+	6.01376e6i	−0.313080	+	0.542270i	0.665948	+	0.745998i	$0.268027\pi$
$104$	2.14159e6			0.186689
$105$		0			0
$106$	8.81838e6			0.719148
$107$	−7.61733e6	+	1.31936e7i	−0.601118	+	1.04117i	0.391534	+	0.920164i	$0.371945\pi$
$107$	−7.61733e6	+	1.31936e7i	−0.601118	+	1.04117i	−0.992652	+	0.121003i	$0.961389\pi$
$108$		0			0
$109$	9.79401e6	+	1.69637e7i	0.724382	+	1.25467i	0.959228	+	0.282634i	$0.0912082\pi$
$109$	9.79401e6	+	1.69637e7i	0.724382	+	1.25467i	−0.234846	+	0.972033i	$0.575458\pi$
$110$	−4.75391e6	+	8.23401e6i	−0.340546	+	0.589844i
$111$		0			0
$112$	3.70492e6	−	300600.i	0.249181	−	0.0202175i
$113$	−8.75407e6			−0.570736			−0.285368	−	0.958418i	$-0.592116\pi$
$113$	−8.75407e6			−0.570736			−0.285368	+	0.958418i	$0.592116\pi$
$114$		0			0
$115$	5.57451e6	+	9.65533e6i	0.341794	+	0.592004i
$116$	−741181.	−	1.28376e6i	−0.0440881	−	0.0763628i
$117$		0			0
$118$	287616.			0.0161148
$119$	224242.	−	473075.i	0.0121984	−	0.0257345i
$120$		0			0
$121$	−9.81450e6	+	1.69992e7i	−0.503639	+	0.872329i
$122$	−4.81907e6	−	8.34688e6i	−0.240272	−	0.416164i
$123$		0			0
$124$	9.67002e6	−	1.67490e7i	0.455461	−	0.788882i
$125$	−2.28297e7			−1.04548
$126$		0			0
$127$	3.12686e7			1.35455			0.677275	−	0.735730i	$-0.263161\pi$
$127$	3.12686e7			1.35455			0.677275	+	0.735730i	$0.263161\pi$
$128$	1.04858e6	−	1.81619e6i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−3.17935e6	−	5.50680e6i	−0.126922	−	0.219835i
$131$	−1.44504e7	+	2.50288e7i	−0.561605	+	0.972728i	0.435752	+	0.900067i	$0.356482\pi$
$131$	−1.44504e7	+	2.50288e7i	−0.561605	+	0.972728i	−0.997357	+	0.0726610i	$0.976851\pi$
$132$		0			0
$133$	−1.39692e7	+	1.13340e6i	−0.514862	+	0.0417736i
$134$	1.78299e6			0.0640149
$135$		0			0
$136$	−147686.	−	255799.i	−0.00503446	−	0.00871994i
$137$	−1.90023e6	−	3.29130e6i	−0.0631371	−	0.109357i	0.832729	−	0.553681i	$-0.186777\pi$
$137$	−1.90023e6	−	3.29130e6i	−0.0631371	−	0.109357i	−0.895866	+	0.444324i	$0.853444\pi$
$138$		0			0
$139$	−5.87608e7			−1.85582			−0.927911	−	0.372803i	$-0.878397\pi$
$139$	−5.87608e7			−1.85582			−0.927911	+	0.372803i	$0.878397\pi$
$140$	−6.27318e6	−	9.08041e6i	−0.193215	−	0.279678i
$141$		0			0
$142$	1.93349e7	−	3.34890e7i	0.566672	−	0.981505i
$143$	−1.30802e7	−	2.26556e7i	−0.374057	−	0.647886i
$144$		0			0
$145$	−2.20068e6	+	3.81169e6i	−0.0599472	+	0.103832i
$146$	−2.78434e7			−0.740435
$147$		0			0
$148$	−1.42769e7			−0.362008
$149$	−2.18958e7	+	3.79246e7i	−0.542261	+	0.939224i	0.456512	+	0.889717i	$0.349098\pi$
$149$	−2.18958e7	+	3.79246e7i	−0.542261	+	0.939224i	−0.998774	+	0.0495073i	$0.984235\pi$
$150$		0			0
$151$	5.34472e6	+	9.25733e6i	0.126330	+	0.218810i	0.922252	−	0.386589i	$-0.126347\pi$
$151$	5.34472e6	+	9.25733e6i	0.126330	+	0.218810i	−0.795922	+	0.605399i	$0.793014\pi$
$152$	−3.95360e6	+	6.84784e6i	−0.0913147	+	0.158162i
$153$		0			0
$154$	−2.58086e7	−	3.73578e7i	−0.569431	−	0.824250i
$155$	−5.74235e7			−1.23859
$156$		0			0
$157$	2.54849e7	+	4.41411e7i	0.525574	+	0.910320i	0.999556	+	0.0297861i	$0.00948262\pi$
$157$	2.54849e7	+	4.41411e7i	0.525574	+	0.910320i	−0.473983	+	0.880534i	$0.657184\pi$
$158$	2.98061e7	+	5.16256e7i	0.601181	+	1.04128i
$159$		0			0
$160$	−6.22677e6			−0.120183
$161$	−5.30692e7	+	4.30580e6i	−1.00219	+	0.0813136i
$162$		0			0
$163$	−2.77491e6	+	4.80629e6i	−0.0501872	+	0.0869268i	−0.890028	−	0.455907i	$-0.849315\pi$
$163$	−2.77491e6	+	4.80629e6i	−0.0501872	+	0.0869268i	0.839840	+	0.542833i	$0.182648\pi$
$164$	−1.05601e7	−	1.82906e7i	−0.186945	−	0.323799i
$165$		0			0
$166$	1.88197e7	−	3.25966e7i	0.319325	−	0.553088i
$167$	8.69574e7			1.44477			0.722385	−	0.691491i	$-0.243046\pi$
$167$	8.69574e7			1.44477			0.722385	+	0.691491i	$0.243046\pi$
$168$		0			0
$169$	−4.52528e7			−0.721177
$170$	−438502.	+	759507.i	−0.00684542	+	0.0118566i
$171$		0			0
$172$	−9.11248e6	−	1.57833e7i	−0.136549	−	0.236509i
$173$	−5.88732e6	+	1.01971e7i	−0.0864483	+	0.149733i	−0.906007	−	0.423262i	$-0.860885\pi$
$173$	−5.88732e6	+	1.01971e7i	−0.0864483	+	0.149733i	0.819559	+	0.572995i	$0.194218\pi$
$174$		0			0
$175$	1.63315e7	−	3.44538e7i	0.230352	−	0.485964i
$176$	−2.56176e7			−0.354196
$177$		0			0
$178$	−1.37388e7	−	2.37962e7i	−0.182590	−	0.316256i
$179$	−2.28592e7	−	3.95932e7i	−0.297903	−	0.515983i	0.677753	−	0.735290i	$-0.262954\pi$
$179$	−2.28592e7	−	3.95932e7i	−0.297903	−	0.515983i	−0.975656	+	0.219307i	$0.929620\pi$
$180$		0			0
$181$	−1.74679e7			−0.218960			−0.109480	−	0.993989i	$-0.534919\pi$
$181$	−1.74679e7			−0.218960			−0.109480	+	0.993989i	$0.534919\pi$
$182$	3.02673e7	−	2.45576e6i	0.372155	−	0.0301950i
$183$		0			0
$184$	−1.50198e7	+	2.60150e7i	−0.177747	+	0.307866i
$185$	2.11951e7	+	3.67110e7i	0.246113	+	0.426281i
$186$		0			0
$187$	−1.80404e6	+	3.12470e6i	−0.0201744	+	0.0349431i
$188$	−8.35943e7			−0.917538
$189$		0			0
$190$	2.34777e7			0.248324
$191$	1.92433e7	−	3.33304e7i	0.199831	−	0.346117i	−0.748643	−	0.662974i	$-0.769294\pi$
$191$	1.92433e7	−	3.33304e7i	0.199831	−	0.346117i	0.948473	+	0.316857i	$0.102627\pi$
$192$		0			0
$193$	5.12431e7	+	8.87557e7i	0.513080	+	0.888681i	0.999885	+	0.0151698i	$0.00482890\pi$
$193$	5.12431e7	+	8.87557e7i	0.513080	+	0.888681i	−0.486805	+	0.873511i	$0.661838\pi$
$194$	1.51891e7	−	2.63083e7i	0.149357	−	0.258694i
$195$		0			0
$196$	5.20174e7	−	8.49685e6i	0.493460	−	0.0806050i
$197$	1.77214e8			1.65145			0.825725	−	0.564072i	$-0.190766\pi$
$197$	1.77214e8			1.65145			0.825725	+	0.564072i	$0.190766\pi$
$198$		0			0
$199$	2.01052e6	+	3.48233e6i	0.0180852	+	0.0313245i	0.874926	−	0.484256i	$-0.160910\pi$
$199$	2.01052e6	+	3.48233e6i	0.0180852	+	0.0313245i	−0.856841	+	0.515580i	$0.827576\pi$
$200$	−1.07559e7	−	1.86297e7i	−0.0950695	−	0.164665i
$201$		0			0
$202$	−3.18049e7			−0.271497
$203$	−1.19473e7	−	1.72937e7i	−0.100238	−	0.145095i
$204$		0			0
$205$	−3.13546e7	+	5.43077e7i	−0.254192	+	0.440274i
$206$	2.77764e7	+	4.81101e7i	0.221381	+	0.383443i
$207$		0			0
$208$	8.56635e6	−	1.48374e7i	0.0660046	−	0.114323i
$209$	9.65898e7			0.731846
$210$		0			0
$211$	−1.04790e8			−0.767944			−0.383972	−	0.923345i	$-0.625444\pi$
$211$	−1.04790e8			−0.767944			−0.383972	+	0.923345i	$0.625444\pi$
$212$	3.52735e7	−	6.10955e7i	0.254257	−	0.440386i
$213$		0			0
$214$	6.09387e7	+	1.05549e8i	0.425055	+	0.736216i
$215$	−2.70564e7	+	4.68630e7i	−0.185667	+	0.321585i
$216$		0			0
$217$	1.17462e8	−	2.47804e8i	0.780345	−	1.64626i
$218$	1.56704e8			1.02443
$219$		0			0
$220$	3.80313e7	+	6.58721e7i	0.240803	+	0.417083i
$221$	−1.20652e6	−	2.08975e6i	−0.00751903	−	0.0130233i
$222$		0			0
$223$	−3.55298e7			−0.214548			−0.107274	−	0.994229i	$-0.534212\pi$
$223$	−3.55298e7			−0.214548			−0.107274	+	0.994229i	$0.534212\pi$
$224$	1.27370e7	−	2.68708e7i	0.0757182	−	0.159740i
$225$		0			0
$226$	−3.50163e7	+	6.06500e7i	−0.201786	+	0.349503i
$227$	−5.81207e7	−	1.00668e8i	−0.329792	−	0.571217i	0.652678	−	0.757635i	$-0.273645\pi$
$227$	−5.81207e7	−	1.00668e8i	−0.329792	−	0.571217i	−0.982470	+	0.186418i	$0.940312\pi$
$228$		0			0
$229$	9.46205e7	−	1.63888e8i	0.520668	−	0.901824i	−0.479043	−	0.877792i	$-0.659016\pi$
$229$	9.46205e7	−	1.63888e8i	0.520668	−	0.901824i	0.999711	−	0.0240325i	$-0.00765052\pi$
$230$	8.91921e7			0.483369
$231$		0			0
$232$	−1.18589e7			−0.0623500
$233$	1.51010e8	−	2.61556e8i	0.782094	−	1.35463i	−0.148626	−	0.988894i	$-0.547485\pi$
$233$	1.51010e8	−	2.61556e8i	0.782094	−	1.35463i	0.930720	−	0.365733i	$-0.119182\pi$
$234$		0			0
$235$	1.24102e8	+	2.14951e8i	0.623795	+	1.08044i
$236$	1.15046e6	−	1.99266e6i	0.00569746	−	0.00986828i
$237$		0			0
$238$	−2.38059e6	−	3.44589e6i	−0.0114463	−	0.0165685i
$239$	3.00671e8			1.42462			0.712309	−	0.701866i	$-0.247649\pi$
$239$	3.00671e8			1.42462			0.712309	+	0.701866i	$0.247649\pi$
$240$		0			0
$241$	1.91754e7	+	3.32127e7i	0.0882437	+	0.152843i	0.906769	−	0.421628i	$-0.138541\pi$
$241$	1.91754e7	+	3.32127e7i	0.0882437	+	0.152843i	−0.818525	+	0.574471i	$0.805208\pi$
$242$	7.85160e7	+	1.35994e8i	0.356127	+	0.616829i
$243$		0			0
$244$	−7.71051e7			−0.339797
$245$	−9.90722e7	−	1.21141e8i	−0.430398	−	0.526272i
$246$		0			0
$247$	−3.22990e7	+	5.59435e7i	−0.136380	+	0.236217i
$248$	−7.73602e7	−	1.33992e8i	−0.322060	−	0.557824i
$249$		0			0
$250$	−9.13189e7	+	1.58169e8i	−0.369633	+	0.640223i
$251$	1.78185e7			0.0711234			0.0355617	−	0.999367i	$-0.488678\pi$
$251$	1.78185e7			0.0711234			0.0355617	+	0.999367i	$0.488678\pi$
$252$		0			0
$253$	3.66946e8			1.42456
$254$	1.25074e8	−	2.16635e8i	0.478906	−	0.829490i
$255$		0			0
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	169674.	−	293884.i	0.000623518	−	0.00107996i	−0.865713	−	0.500540i	$-0.833135\pi$
$257$	169674.	−	293884.i	0.000623518	−	0.00107996i	0.866337	+	0.499460i	$0.166468\pi$
$258$		0			0
$259$	−2.01777e8	+	1.63713e7i	−0.721644	+	0.0585510i
$260$	−5.08696e7			−0.179495
$261$		0			0
$262$	1.15603e8	+	2.00231e8i	0.397114	+	0.687822i
$263$	9.01614e7	+	1.56164e8i	0.305616	+	0.529342i	0.977398	−	0.211407i	$-0.0678044\pi$
$263$	9.01614e7	+	1.56164e8i	0.305616	+	0.529342i	−0.671783	+	0.740748i	$0.734471\pi$
$264$		0			0
$265$	−2.09465e8			−0.691434
$266$	−4.80244e7	+	1.01315e8i	−0.156450	+	0.330057i
$267$		0			0
$268$	7.13195e6	−	1.23529e7i	0.0226327	−	0.0392010i
$269$	1.96057e8	+	3.39581e8i	0.614115	+	1.06368i	0.990539	+	0.137230i	$0.0438201\pi$
$269$	1.96057e8	+	3.39581e8i	0.614115	+	1.06368i	−0.376424	+	0.926447i	$0.622847\pi$
$270$		0			0
$271$	1.92498e8	−	3.33417e8i	0.587536	−	1.01764i	−0.407018	−	0.913420i	$-0.633431\pi$
$271$	1.92498e8	−	3.33417e8i	0.587536	−	1.01764i	0.994554	−	0.104222i	$-0.0332353\pi$
$272$	−2.36297e6			−0.00711980
$273$		0			0
$274$	−3.04037e7			−0.0892894
$275$	−1.31388e8	+	2.27570e8i	−0.380969	+	0.659858i
$276$		0			0
$277$	−2.10950e8	−	3.65375e8i	−0.596348	−	1.03290i	−0.993355	−	0.115089i	$-0.963285\pi$
$277$	−2.10950e8	−	3.65375e8i	−0.596348	−	1.03290i	0.397008	−	0.917815i	$-0.370049\pi$
$278$	−2.35043e8	+	4.07107e8i	−0.656132	+	1.13645i
$279$		0			0
$280$	−8.80037e7	+	7.14023e6i	−0.239578	+	0.0194383i
$281$	1.48141e8			0.398294			0.199147	−	0.979970i	$-0.436183\pi$
$281$	1.48141e8			0.398294			0.199147	+	0.979970i	$0.436183\pi$
$282$		0			0
$283$	−1.95211e8	−	3.38115e8i	−0.511977	−	0.886771i	−0.999904	−	0.0138859i	$-0.995580\pi$
$283$	−1.95211e8	−	3.38115e8i	−0.511977	−	0.886771i	0.487926	−	0.872885i	$-0.337753\pi$
$284$	−1.54679e8	−	2.67912e8i	−0.400698	−	0.694029i
$285$		0			0
$286$	−2.09283e8			−0.528997
$287$	−1.70221e8	−	2.46395e8i	−0.425037	−	0.615240i
$288$		0			0
$289$	2.05003e8	−	3.55075e8i	0.499594	−	0.865323i
$290$	1.76054e7	+	3.04935e7i	0.0423891	+	0.0734200i
$291$		0			0
$292$	−1.11374e8	+	1.92905e8i	−0.261783	+	0.453422i
$293$	−4.41291e8			−1.02492			−0.512458	−	0.858712i	$-0.671265\pi$
$293$	−4.41291e8			−1.02492			−0.512458	+	0.858712i	$0.671265\pi$
$294$		0			0
$295$	−6.83181e6			−0.0154938
$296$	−5.71076e7	+	9.89132e7i	−0.127989	+	0.221683i
$297$		0			0
$298$	1.75166e8	+	3.03397e8i	0.383437	+	0.664132i
$299$	−1.22704e8	+	2.12530e8i	−0.265467	+	0.459802i
$300$		0			0
$301$	−1.46887e8	−	2.12618e8i	−0.310456	−	0.449383i
$302$	8.55156e7			0.178657
$303$		0			0
$304$	3.16288e7	+	5.47827e7i	0.0645692	+	0.111837i
$305$	1.14468e8	+	1.98265e8i	0.231013	+	0.400126i
$306$		0			0
$307$	−8.55663e8			−1.68779			−0.843895	−	0.536509i	$-0.819743\pi$
$307$	−8.55663e8			−1.68779			−0.843895	+	0.536509i	$0.819743\pi$
$308$	−3.62057e8	+	2.93757e7i	−0.706072	+	0.0572876i
$309$		0			0
$310$	−2.29694e8	+	3.97842e8i	−0.437909	+	0.758481i
$311$	−5.01999e8	−	8.69488e8i	−0.946328	−	1.63909i	−0.753070	−	0.657941i	$-0.771428\pi$
$311$	−5.01999e8	−	8.69488e8i	−0.946328	−	1.63909i	−0.193258	−	0.981148i	$-0.561906\pi$
$312$		0			0
$313$	1.73099e8	−	2.99817e8i	0.319073	−	0.552650i	−0.661222	−	0.750190i	$-0.729962\pi$
$313$	1.73099e8	−	2.99817e8i	0.319073	−	0.552650i	0.980295	+	0.197540i	$0.0632952\pi$
$314$	4.07758e8			0.743273
$315$		0			0
$316$	4.76897e8			0.850198
$317$	2.01572e8	−	3.49132e8i	0.355404	−	0.615578i	−0.631783	−	0.775145i	$-0.717677\pi$
$317$	2.01572e8	−	3.49132e8i	0.355404	−	0.615578i	0.987187	+	0.159568i	$0.0510100\pi$
$318$		0			0
$319$	7.24307e7	+	1.25454e8i	0.124927	+	0.216379i
$320$	−2.49071e7	+	4.31403e7i	−0.0424911	+	0.0735967i
$321$		0			0
$322$	−1.82445e8	+	3.84897e8i	−0.304535	+	0.642465i
$323$	8.90947e6			0.0147110
$324$		0			0
$325$	−8.78703e7	−	1.52196e8i	−0.141988	−	0.245930i
$326$	2.21993e7	+	3.84503e7i	0.0354877	+	0.0614665i
$327$		0			0
$328$	−1.68962e8			−0.264381
$329$	−1.18145e9	+	9.58576e7i	−1.82907	+	0.148402i
$330$		0			0
$331$	−1.43426e8	+	2.48421e8i	−0.217385	+	0.376521i	−0.954008	−	0.299782i	$-0.903086\pi$
$331$	−1.43426e8	+	2.48421e8i	−0.217385	+	0.376521i	0.736623	+	0.676304i	$0.236419\pi$
$332$	−1.50557e8	−	2.60773e8i	−0.225797	−	0.391092i
$333$		0			0
$334$	3.47830e8	−	6.02459e8i	0.510804	−	0.884738i
$335$	−4.23517e7			−0.0615480
$336$		0			0
$337$	5.69157e8			0.810078			0.405039	−	0.914299i	$-0.367258\pi$
$337$	5.69157e8			0.810078			0.405039	+	0.914299i	$0.367258\pi$
$338$	−1.81011e8	+	3.13521e8i	−0.254975	+	0.441629i
$339$		0			0
$340$	3.50801e6	+	6.07606e6i	0.00484044	+	0.00838389i
$341$	−9.44986e8	+	1.63676e9i	−1.29058	+	2.23535i
$342$		0			0
$343$	7.25425e8	−	1.79735e8i	0.970651	−	0.240494i
$344$	−1.45800e8			−0.193109
$345$		0			0
$346$	4.70986e7	+	8.15771e7i	0.0611282	+	0.105877i
$347$	5.53764e8	+	9.59148e8i	0.711495	+	1.23234i	0.964296	+	0.264827i	$0.0853148\pi$
$347$	5.53764e8	+	9.59148e8i	0.711495	+	1.23234i	−0.252801	+	0.967518i	$0.581352\pi$
$348$		0			0
$349$	1.46957e9			1.85055			0.925274	−	0.379300i	$-0.123835\pi$
$349$	1.46957e9			1.85055			0.925274	+	0.379300i	$0.123835\pi$
$350$	−1.73377e8	−	2.50963e8i	−0.216149	−	0.312875i
$351$		0			0
$352$	−1.02470e8	+	1.77484e8i	−0.125227	+	0.216900i
$353$	−4.35007e8	−	7.53453e8i	−0.526362	−	0.911685i	−0.999528	−	0.0307123i	$-0.990222\pi$
$353$	−4.35007e8	−	7.53453e8i	−0.526362	−	0.911685i	0.473166	−	0.880973i	$-0.343111\pi$
$354$		0			0
$355$	−4.59265e8	+	7.95471e8i	−0.544834	+	0.943680i
$356$	−2.19820e8			−0.258222
$357$		0			0
$358$	−3.65747e8			−0.421298
$359$	−4.00315e8	+	6.93366e8i	−0.456638	+	0.790919i	−0.998781	−	0.0493667i	$-0.984280\pi$
$359$	−4.00315e8	+	6.93366e8i	−0.456638	+	0.790919i	0.542143	+	0.840286i	$0.317613\pi$
$360$		0			0
$361$	3.27681e8	+	5.67560e8i	0.366586	+	0.634946i
$362$	−6.98715e7	+	1.21021e8i	−0.0774140	+	0.134085i
$363$		0			0
$364$	1.04055e8	−	2.19521e8i	0.113086	−	0.238573i
$365$	6.61370e8			0.711901
$366$		0			0
$367$	−2.49769e8	−	4.32612e8i	−0.263759	−	0.456844i	0.703479	−	0.710716i	$-0.251629\pi$
$367$	−2.49769e8	−	4.32612e8i	−0.263759	−	0.456844i	−0.967238	+	0.253873i	$0.918296\pi$
$368$	1.20158e8	+	2.08120e8i	0.125686	+	0.217694i
$369$		0			0
$370$	3.39122e8			0.348057
$371$	4.28467e8	−	9.03919e8i	0.435621	−	0.919012i
$372$		0			0
$373$	−5.15842e8	+	8.93464e8i	−0.514678	+	0.891448i	0.485177	+	0.874416i	$0.338755\pi$
$373$	−5.15842e8	+	8.93464e8i	−0.514678	+	0.891448i	−0.999855	+	0.0170324i	$0.994578\pi$
$374$	1.44323e7	+	2.49976e7i	0.0142655	+	0.0247085i
$375$		0			0
$376$	−3.34377e8	+	5.79158e8i	−0.324399	+	0.561875i
$377$	−9.68814e7			−0.0931205
$378$		0			0
$379$	−8.35481e8			−0.788314			−0.394157	−	0.919043i	$-0.628963\pi$
$379$	−8.35481e8			−0.788314			−0.394157	+	0.919043i	$0.628963\pi$
$380$	9.39109e7	−	1.62658e8i	0.0877957	−	0.152067i
$381$		0			0
$382$	−1.53946e8	−	2.66643e8i	−0.141302	−	0.244742i
$383$	−9.98853e8	+	1.73006e9i	−0.908460	+	1.57350i	−0.0922557	+	0.995735i	$0.529408\pi$
$383$	−9.98853e8	+	1.73006e9i	−0.908460	+	1.57350i	−0.816204	+	0.577763i	$0.803926\pi$
$384$		0			0
$385$	6.13036e8	+	8.87368e8i	0.547487	+	0.792485i
$386$	8.19890e8			0.725605
$387$		0			0
$388$	−1.21513e8	−	2.10466e8i	−0.105611	−	0.182924i
$389$	−2.25421e8	−	3.90441e8i	−0.194165	−	0.336304i	0.752462	−	0.658636i	$-0.228866\pi$
$389$	−2.25421e8	−	3.90441e8i	−0.194165	−	0.336304i	−0.946626	+	0.322333i	$0.895533\pi$
$390$		0			0
$391$	3.38472e7			0.0286355
$392$	1.49202e8	−	3.94374e8i	0.125104	−	0.330680i
$393$		0			0
$394$	7.08855e8	−	1.22777e9i	0.583876	−	1.01130i
$395$	−7.07991e8	−	1.22628e9i	−0.578013	−	1.00115i
$396$		0			0
$397$	4.83785e8	−	8.37940e8i	0.388048	−	0.672119i	−0.604139	−	0.796879i	$-0.706483\pi$
$397$	4.83785e8	−	8.37940e8i	0.388048	−	0.672119i	0.992187	+	0.124760i	$0.0398160\pi$
$398$	3.21684e7			0.0255763
$399$		0			0
$400$	−1.72094e8			−0.134449
$401$	1.24216e9	−	2.15149e9i	0.961996	−	1.66623i	0.244517	−	0.969645i	$-0.421371\pi$
$401$	1.24216e9	−	2.15149e9i	0.961996	−	1.66623i	0.717479	−	0.696580i	$-0.245296\pi$
$402$		0			0
$403$	−6.31994e8	−	1.09465e9i	−0.481001	−	0.833117i
$404$	−1.27220e8	+	2.20351e8i	−0.0959887	+	0.166257i
$405$		0			0
$406$	−1.67603e8	+	1.35986e7i	−0.124292	+	0.0100845i
$407$	1.39518e9			1.02577
$408$		0			0
$409$	3.68300e6	+	6.37914e6i	0.00266176	+	0.00461031i	0.867353	−	0.497693i	$-0.165819\pi$
$409$	3.68300e6	+	6.37914e6i	0.00266176	+	0.00461031i	−0.864691	+	0.502303i	$0.832486\pi$
$410$	2.50837e8	+	4.34462e8i	0.179741	+	0.311321i
$411$		0			0
$412$	4.44422e8			0.313080
$413$	1.39747e7	−	2.94818e7i	0.00976150	−	0.0205934i
$414$		0			0
$415$	−4.47028e8	+	7.74275e8i	−0.307020	+	0.531773i
$416$	−6.85308e7	−	1.18699e8i	−0.0466723	−	0.0808388i
$417$		0			0
$418$	3.86359e8	−	6.69194e8i	0.258746	−	0.448162i
$419$	2.18245e9			1.44942			0.724712	−	0.689051i	$-0.241973\pi$
$419$	2.18245e9			1.44942			0.724712	+	0.689051i	$0.241973\pi$
$420$		0			0
$421$	−2.74780e8			−0.179472			−0.0897362	−	0.995966i	$-0.528602\pi$
$421$	−2.74780e8			−0.179472			−0.0897362	+	0.995966i	$0.528602\pi$
$422$	−4.19158e8	+	7.26003e8i	−0.271509	+	0.470268i
$423$		0			0
$424$	−2.82188e8	−	4.88764e8i	−0.179787	−	0.311400i
$425$	−1.21192e7	+	2.09911e7i	−0.00765798	+	0.0132640i
$426$		0			0
$427$	−1.08974e9	+	8.84165e7i	−0.677367	+	0.0549586i
$428$	9.75019e8			0.601118
$429$		0			0
$430$	2.16451e8	+	3.74904e8i	0.131286	+	0.227395i
$431$	7.95998e8	+	1.37871e9i	0.478897	+	0.829473i	0.999707	−	0.0241991i	$-0.00770357\pi$
$431$	7.95998e8	+	1.37871e9i	0.478897	+	0.829473i	−0.520811	+	0.853672i	$0.674370\pi$
$432$		0			0
$433$	4.93795e8			0.292307			0.146154	−	0.989262i	$-0.453311\pi$
$433$	4.93795e8			0.292307			0.146154	+	0.989262i	$0.453311\pi$
$434$	−1.24699e9	−	1.80501e9i	−0.732232	−	1.05990i
$435$		0			0
$436$	6.26817e8	−	1.08568e9i	0.362191	−	0.627333i
$437$	−4.53051e8	−	7.84707e8i	−0.259694	−	0.449803i
$438$		0			0
$439$	−1.62501e9	+	2.81460e9i	−0.916708	+	1.58778i	−0.112326	+	0.993671i	$0.535830\pi$
$439$	−1.62501e9	+	2.81460e9i	−0.916708	+	1.58778i	−0.804382	+	0.594113i	$0.797503\pi$
$440$	6.08500e8			0.340546
$441$		0			0
$442$	−1.93043e7			−0.0106335
$443$	1.24877e9	−	2.16294e9i	0.682450	−	1.18204i	−0.291782	−	0.956485i	$-0.594248\pi$
$443$	1.24877e9	−	2.16294e9i	0.682450	−	1.18204i	0.974231	−	0.225552i	$-0.0724187\pi$
$444$		0			0
$445$	3.26340e8	+	5.65238e8i	0.175554	+	0.304068i
$446$	−1.42119e8	+	2.46157e8i	−0.0758543	+	0.131383i
$447$		0			0
$448$	−1.35218e8	−	1.95728e8i	−0.0710497	−	0.102844i
$449$	2.71722e9			1.41665			0.708325	−	0.705887i	$-0.249451\pi$
$449$	2.71722e9			1.41665			0.708325	+	0.705887i	$0.249451\pi$
$450$		0			0
$451$	1.03197e9	+	1.78742e9i	0.529723	+	0.917507i
$452$	2.80130e8	+	4.85200e8i	0.142684	+	0.247136i
$453$		0			0
$454$	−9.29931e8			−0.466397
$455$	−7.18947e8	+	5.83322e7i	−0.357814	+	0.0290314i
$456$		0			0
$457$	1.56358e9	−	2.70820e9i	0.766326	−	1.32731i	−0.173217	−	0.984884i	$-0.555416\pi$
$457$	1.56358e9	−	2.70820e9i	0.766326	−	1.32731i	0.939543	−	0.342431i	$-0.111250\pi$
$458$	−7.56964e8	−	1.31110e9i	−0.368168	−	0.637686i
$459$		0			0
$460$	3.56768e8	−	6.17941e8i	0.170897	−	0.296002i
$461$	2.90548e9			1.38123			0.690614	−	0.723224i	$-0.257341\pi$
$461$	2.90548e9			1.38123			0.690614	+	0.723224i	$0.257341\pi$
$462$		0			0
$463$	−3.47147e9			−1.62547			−0.812736	−	0.582632i	$-0.802023\pi$
$463$	−3.47147e9			−1.62547			−0.812736	+	0.582632i	$0.802023\pi$
$464$	−4.74356e7	+	8.21609e7i	−0.0220441	+	0.0381814i
$465$		0			0
$466$	−1.20808e9	−	2.09245e9i	−0.553024	−	0.957866i
$467$	−1.31417e9	+	2.27621e9i	−0.597094	+	1.03420i	0.396154	+	0.918184i	$0.370345\pi$
$467$	−1.31417e9	+	2.27621e9i	−0.597094	+	1.03420i	−0.993248	+	0.116013i	$0.962989\pi$
$468$		0			0
$469$	8.66317e7	−	1.82763e8i	0.0387768	−	0.0818058i
$470$	1.98563e9			0.882179
$471$		0			0
$472$	−9.20371e6	−	1.59413e7i	−0.00402871	−	0.00697793i
$473$	8.90502e8	+	1.54239e9i	0.386920	+	0.670165i
$474$		0			0
$475$	6.48873e8			0.277800
$476$	−3.33962e7	+	2.70962e6i	−0.0141930	+	0.00115155i
$477$		0			0
$478$	1.20268e9	−	2.08311e9i	0.503679	−	0.872397i
$479$	−2.03983e9	−	3.53309e9i	−0.848046	−	1.46886i	−0.882950	−	0.469468i	$-0.844446\pi$
$479$	−2.03983e9	−	3.53309e9i	−0.848046	−	1.46886i	0.0349039	−	0.999391i	$-0.488887\pi$
$480$		0			0
$481$	−4.66541e8	+	8.08072e8i	−0.191153	+	0.331087i
$482$	3.06806e8			0.124795
$483$		0			0
$484$	1.25626e9			0.503639
$485$	−3.60790e8	+	6.24906e8i	−0.143601	+	0.248725i
$486$		0			0
$487$	7.56219e7	+	1.30981e8i	0.0296685	+	0.0513874i	0.880478	−	0.474086i	$-0.157221\pi$
$487$	7.56219e7	+	1.30981e8i	0.0296685	+	0.0513874i	−0.850810	+	0.525474i	$0.823888\pi$
$488$	−3.08421e8	+	5.34200e8i	−0.120136	+	0.208082i
$489$		0			0
$490$	−1.23558e9	+	2.01828e8i	−0.474444	+	0.0774987i
$491$	4.20636e9			1.60369			0.801846	−	0.597531i	$-0.203851\pi$
$491$	4.20636e9			1.60369			0.801846	+	0.597531i	$0.203851\pi$
$492$		0			0
$493$	6.68103e6	+	1.15719e7i	0.00251119	+	0.00434950i
$494$	2.58392e8	+	4.47548e8i	0.0964350	+	0.167030i
$495$		0			0
$496$	−1.23776e9			−0.455461
$497$	−2.49331e9	−	3.60906e9i	−0.911022	−	1.31870i
$498$		0			0
$499$	−9.65358e8	+	1.67205e9i	−0.347806	+	0.602417i	−0.985859	−	0.167575i	$-0.946406\pi$
$499$	−9.65358e8	+	1.67205e9i	−0.347806	+	0.602417i	0.638054	+	0.769992i	$0.279740\pi$
$500$	7.30552e8	+	1.26535e9i	0.261370	+	0.452706i
$501$		0			0
$502$	7.12739e7	−	1.23450e8i	0.0251459	−	0.0435540i
$503$	−1.22595e9			−0.429522			−0.214761	−	0.976667i	$-0.568897\pi$
$503$	−1.22595e9			−0.429522			−0.214761	+	0.976667i	$0.568897\pi$
$504$		0			0
$505$	7.55470e8			0.261034
$506$	1.46778e9	−	2.54228e9i	0.503657	−	0.872360i
$507$		0			0
$508$	−1.00059e9	−	1.73308e9i	−0.338638	−	0.586538i
$509$	−2.11547e9	+	3.66410e9i	−0.711041	+	1.23156i	0.253426	+	0.967355i	$0.418443\pi$
$509$	−2.11547e9	+	3.66410e9i	−0.711041	+	1.23156i	−0.964467	+	0.264204i	$0.914891\pi$
$510$		0			0
$511$	−1.35285e9	+	2.85406e9i	−0.448516	+	0.946215i
$512$	−1.34218e8			−0.0441942
$513$		0			0
$514$	−1.35739e6	−	2.35107e6i	−0.000440894	−	0.000763650i
$515$	−6.59778e8	−	1.14277e9i	−0.212849	−	0.368666i
$516$		0			0
$517$	8.16911e9			2.59991
$518$	−6.93685e8	+	1.46344e9i	−0.219285	+	0.462616i
$519$		0			0
$520$	−2.03478e8	+	3.52435e8i	−0.0634610	+	0.109918i
$521$	1.32387e9	+	2.29302e9i	0.410123	+	0.710355i	0.994903	−	0.100838i	$-0.0321523\pi$
$521$	1.32387e9	+	2.29302e9i	0.410123	+	0.710355i	−0.584779	+	0.811192i	$0.698819\pi$
$522$		0			0
$523$	−2.30857e9	+	3.99856e9i	−0.705647	+	1.22222i	0.260810	+	0.965390i	$0.416010\pi$
$523$	−2.30857e9	+	3.99856e9i	−0.705647	+	1.22222i	−0.966458	+	0.256827i	$0.917323\pi$
$524$	1.84965e9			0.561605
$525$		0			0
$526$	1.44258e9			0.432206
$527$	−8.71658e7	+	1.50976e8i	−0.0259423	+	0.0449334i
$528$		0			0
$529$	−1.87337e7	−	3.24477e7i	−0.00550211	−	0.00952993i
$530$	−8.37860e8	+	1.45122e9i	−0.244459	+	0.423415i
$531$		0			0
$532$	5.09834e8	+	7.37983e8i	0.146804	+	0.212498i
$533$	−1.38033e9			−0.394856
$534$		0			0
$535$	−1.44749e9	−	2.50713e9i	−0.408674	−	0.707845i
$536$	−5.70556e7	−	9.88231e7i	−0.0160037	−	0.0277193i
$537$		0			0
$538$	3.13691e9			0.868489
$539$	−5.08331e9	+	8.30341e8i	−1.39825	+	0.228400i
$540$		0			0
$541$	1.09381e8	−	1.89453e8i	0.0296996	−	0.0514412i	−0.850794	−	0.525500i	$-0.823878\pi$
$541$	1.09381e8	−	1.89453e8i	0.0296996	−	0.0514412i	0.880493	+	0.474059i	$0.157212\pi$
$542$	−1.53999e9	−	2.66734e9i	−0.415451	−	0.719582i
$543$		0			0
$544$	−9.45189e6	+	1.63712e7i	−0.00251723	+	0.00435997i
$545$	−3.72223e9			−0.984953
$546$		0			0
$547$	−2.39779e9			−0.626405			−0.313203	−	0.949686i	$-0.601402\pi$
$547$	−2.39779e9			−0.626405			−0.313203	+	0.949686i	$0.601402\pi$
$548$	−1.21615e8	+	2.10643e8i	−0.0315686	+	0.0546784i
$549$		0			0
$550$	1.05110e9	+	1.82056e9i	0.269386	+	0.466590i
$551$	1.78854e8	−	3.09783e8i	0.0455478	−	0.0788910i
$552$		0			0
$553$	6.74005e9	−	5.46858e8i	1.69483	−	0.137511i
$554$	−3.37519e9			−0.843363
$555$		0			0
$556$	1.88035e9	+	3.25686e9i	0.463955	+	0.803594i
$557$	3.92372e9	+	6.79609e9i	0.962067	+	1.66635i	0.717297	+	0.696768i	$0.245379\pi$
$557$	3.92372e9	+	6.79609e9i	0.962067	+	1.66635i	0.244770	+	0.969581i	$0.421288\pi$
$558$		0			0
$559$	−1.19111e9			−0.288411
$560$	−3.02546e8	+	6.38268e8i	−0.0728003	+	0.153584i
$561$		0			0
$562$	5.92565e8	−	1.02635e9i	0.140818	−	0.243904i
$563$	−1.39537e9	−	2.41685e9i	−0.329541	−	0.570782i	0.652880	−	0.757462i	$-0.273561\pi$
$563$	−1.39537e9	−	2.41685e9i	−0.329541	−	0.570782i	−0.982421	+	0.186679i	$0.940227\pi$
$564$		0			0
$565$	8.31749e8	−	1.44063e9i	0.194009	−	0.336034i
$566$	−3.12337e9			−0.724045
$567$		0			0
$568$	−2.47486e9			−0.566672
$569$	1.85983e9	−	3.22131e9i	0.423233	−	0.733061i	−0.573021	−	0.819541i	$-0.694229\pi$
$569$	1.85983e9	−	3.22131e9i	0.423233	−	0.733061i	0.996254	+	0.0864801i	$0.0275619\pi$
$570$		0			0
$571$	2.04386e8	+	3.54007e8i	0.0459435	+	0.0795765i	0.888083	−	0.459684i	$-0.152037\pi$
$571$	2.04386e8	+	3.54007e8i	0.0459435	+	0.0795765i	−0.842139	+	0.539260i	$0.818704\pi$
$572$	−8.37132e8	+	1.44996e9i	−0.187029	+	0.323943i
$573$		0			0
$574$	−2.38796e9	+	1.93748e8i	−0.527030	+	0.0427609i
$575$	2.46508e9			0.540745
$576$		0			0
$577$	−3.64920e9	−	6.32059e9i	−0.790828	−	1.36975i	−0.925455	−	0.378857i	$-0.876317\pi$
$577$	−3.64920e9	−	6.32059e9i	−0.790828	−	1.36975i	0.134628	−	0.990896i	$-0.457016\pi$
$578$	−1.64002e9	−	2.84060e9i	−0.353267	−	0.611876i
$579$		0			0
$580$	2.81687e8			0.0599472
$581$	−2.42687e9	−	3.51289e9i	−0.513370	−	0.743102i
$582$		0			0
$583$	−3.44705e9	+	5.97046e9i	−0.720455	+	1.24787i
$584$	8.90989e8	+	1.54324e9i	0.185109	+	0.320618i
$585$		0			0
$586$	−1.76516e9	+	3.05735e9i	−0.362362	+	0.627630i
$587$	−4.58500e9			−0.935633			−0.467817	−	0.883826i	$-0.654959\pi$
$587$	−4.58500e9			−0.935633			−0.467817	+	0.883826i	$0.654959\pi$
$588$		0			0
$589$	4.66692e9			0.941081
$590$	−2.73272e7	+	4.73321e7i	−0.00547789	+	0.00948799i
$591$		0			0
$592$	4.56860e8	+	7.91306e8i	0.0905019	+	0.156754i
$593$	−4.14382e9	+	7.17731e9i	−0.816037	+	1.41342i	0.0925446	+	0.995709i	$0.470500\pi$
$593$	−4.14382e9	+	7.17731e9i	−0.816037	+	1.41342i	−0.908581	+	0.417708i	$0.862833\pi$
$594$		0			0
$595$	5.65466e7	+	8.18511e7i	0.0110052	+	0.0159300i
$596$	2.80266e9			0.542261
$597$		0			0
$598$	9.81634e8	+	1.70024e9i	0.187714	+	0.325129i
$599$	−1.17488e9	−	2.03496e9i	−0.223358	−	0.386867i	0.732468	−	0.680802i	$-0.238369\pi$
$599$	−1.17488e9	−	2.03496e9i	−0.223358	−	0.386867i	−0.955826	+	0.293935i	$0.905035\pi$
$600$		0			0
$601$	−9.61955e8			−0.180757			−0.0903783	−	0.995908i	$-0.528808\pi$
$601$	−9.61955e8			−0.180757			−0.0903783	+	0.995908i	$0.528808\pi$
$602$	−2.06061e9	+	1.67189e8i	−0.384953	+	0.0312334i
$603$		0			0
$604$	3.42062e8	−	5.92469e8i	0.0631649	−	0.109405i
$605$	−1.86501e9	−	3.23029e9i	−0.342403	−	0.593059i
$606$		0			0
$607$	2.84283e9	−	4.92392e9i	0.515929	−	0.893615i	−0.483900	−	0.875123i	$-0.660780\pi$
$607$	2.84283e9	−	4.92392e9i	0.515929	−	0.893615i	0.999829	−	0.0184920i	$-0.00588652\pi$
$608$	5.06061e8			0.0913147
$609$		0			0
$610$	1.83150e9			0.326702
$611$	−2.73170e9	+	4.73144e9i	−0.484494	+	0.839168i
$612$		0			0
$613$	−1.64257e9	−	2.84502e9i	−0.288013	−	0.498853i	0.685322	−	0.728240i	$-0.259661\pi$
$613$	−1.64257e9	−	2.84502e9i	−0.288013	−	0.498853i	−0.973335	+	0.229387i	$0.926328\pi$
$614$	−3.42265e9	+	5.92820e9i	−0.596724	+	1.03356i
$615$		0			0
$616$	−1.24471e9	+	2.62590e9i	−0.214553	+	0.452633i
$617$	3.69864e9			0.633933			0.316967	−	0.948437i	$-0.397336\pi$
$617$	3.69864e9			0.633933			0.316967	+	0.948437i	$0.397336\pi$
$618$		0			0
$619$	−4.78155e9	−	8.28188e9i	−0.810310	−	1.40350i	−0.912647	−	0.408748i	$-0.865965\pi$
$619$	−4.78155e9	−	8.28188e9i	−0.810310	−	1.40350i	0.102337	−	0.994750i	$-0.467368\pi$
$620$	1.83755e9	+	3.18274e9i	0.309649	+	0.536327i
$621$		0			0
$622$	−8.03199e9			−1.33831
$623$	−3.10675e9	+	2.52068e8i	−0.514752	+	0.0417647i
$624$		0			0
$625$	5.27901e8	−	9.14351e8i	0.0864913	−	0.149807i
$626$	−1.38479e9	−	2.39853e9i	−0.225619	−	0.390783i
$627$		0			0
$628$	1.63103e9	−	2.82503e9i	0.262787	−	0.455160i
$629$	1.28692e8			0.0206194
$630$		0			0
$631$	−5.85026e9			−0.926985			−0.463492	−	0.886101i	$-0.653404\pi$
$631$	−5.85026e9			−0.926985			−0.463492	+	0.886101i	$0.653404\pi$
$632$	1.90759e9	−	3.30404e9i	0.300590	−	0.520638i
$633$		0			0
$634$	−1.61257e9	−	2.79306e9i	−0.251308	−	0.435279i
$635$	−2.97092e9	+	5.14578e9i	−0.460450	+	0.797524i
$636$		0			0
$637$	1.21890e9	−	3.22184e9i	0.186845	−	0.493874i
$638$	1.15889e9			0.176673
$639$		0			0
$640$	1.99256e8	+	3.45122e8i	0.0300457	+	0.0520407i
$641$	−3.63568e9	−	6.29718e9i	−0.545233	−	0.944371i	−0.998592	−	0.0530435i	$-0.983108\pi$
$641$	−3.63568e9	−	6.29718e9i	−0.545233	−	0.944371i	0.453359	−	0.891328i	$-0.350226\pi$
$642$		0			0
$643$	2.50221e9			0.371181			0.185591	−	0.982627i	$-0.440580\pi$
$643$	2.50221e9			0.371181			0.185591	+	0.982627i	$0.440580\pi$
$644$	1.93686e9	+	2.80361e9i	0.285758	+	0.413634i
$645$		0			0
$646$	3.56379e7	−	6.17266e7i	0.00520114	−	0.00900863i
$647$	4.44048e9	+	7.69115e9i	0.644563	+	1.11642i	0.984402	+	0.175932i	$0.0562940\pi$
$647$	4.44048e9	+	7.69115e9i	0.644563	+	1.11642i	−0.339839	+	0.940484i	$0.610373\pi$
$648$		0			0
$649$	−1.12427e8	+	1.94730e8i	−0.0161441	+	0.0279625i
$650$	−1.40593e9			−0.200801
$651$		0			0
$652$	3.55189e8			0.0501872
$653$	−2.43457e9	+	4.21681e9i	−0.342158	+	0.592635i	−0.984833	−	0.173504i	$-0.944491\pi$
$653$	−2.43457e9	+	4.21681e9i	−0.342158	+	0.592635i	0.642675	+	0.766139i	$0.277824\pi$
$654$		0			0
$655$	−2.74595e9	−	4.75613e9i	−0.381811	−	0.661316i
$656$	−6.75847e8	+	1.17060e9i	−0.0934727	+	0.161899i
$657$		0			0
$658$	−4.06168e9	+	8.56875e9i	−0.555795	+	1.17254i
$659$	5.44124e9			0.740627			0.370313	−	0.928907i	$-0.379250\pi$
$659$	5.44124e9			0.740627			0.370313	+	0.928907i	$0.379250\pi$
$660$		0			0
$661$	2.58734e9	+	4.48140e9i	0.348456	+	0.603544i	0.985975	−	0.166891i	$-0.0533726\pi$
$661$	2.58734e9	+	4.48140e9i	0.348456	+	0.603544i	−0.637519	+	0.770435i	$0.720039\pi$
$662$	1.14741e9	+	1.98737e9i	0.153714	+	0.266241i
$663$		0			0
$664$	−2.40892e9			−0.319325
$665$	1.14073e9	−	2.40656e9i	0.150421	−	0.317337i
$666$		0			0
$667$	6.79467e8	−	1.17687e9i	0.0886600	−	0.153564i
$668$	−2.78264e9	−	4.81967e9i	−0.361193	−	0.625604i
$669$		0			0
$670$	−1.69407e8	+	2.93421e8i	−0.0217605	+	0.0376903i
$671$	7.53497e9			0.962837
$672$		0			0
$673$	3.74132e9			0.473121			0.236561	−	0.971617i	$-0.423980\pi$
$673$	3.74132e9			0.473121			0.236561	+	0.971617i	$0.423980\pi$
$674$	2.27663e9	−	3.94323e9i	0.286406	−	0.496070i
$675$		0			0
$676$	1.44809e9	+	2.50816e9i	0.180294	+	0.312279i
$677$	6.36566e9	−	1.10257e10i	0.788467	−	1.36566i	−0.138440	−	0.990371i	$-0.544209\pi$
$677$	6.36566e9	−	1.10257e10i	0.788467	−	1.36566i	0.926906	−	0.375293i	$-0.122458\pi$
$678$		0			0
$679$	−1.95870e9	−	2.83521e9i	−0.240117	−	0.347568i
$680$	5.61282e7			0.00684542
$681$		0			0
$682$	7.55989e9	+	1.30941e10i	0.912579	+	1.58063i
$683$	8.00307e8	+	1.38617e9i	0.0961135	+	0.166473i	0.910073	−	0.414448i	$-0.136026\pi$
$683$	8.00307e8	+	1.38617e9i	0.0961135	+	0.166473i	−0.813959	+	0.580922i	$0.802692\pi$
$684$		0			0
$685$	7.22187e8			0.0858484
$686$	1.65646e9	−	5.74483e9i	0.195905	−	0.679427i
$687$		0			0
$688$	−5.83199e8	+	1.01013e9i	−0.0682743	+	0.118255i
$689$	−2.30534e9	−	3.99296e9i	−0.268514	−	0.465080i
$690$		0			0
$691$	1.93237e9	−	3.34697e9i	0.222801	−	0.385903i	−0.732856	−	0.680384i	$-0.761813\pi$
$691$	1.93237e9	−	3.34697e9i	0.222801	−	0.385903i	0.955658	+	0.294480i	$0.0951465\pi$
$692$	7.53577e8			0.0864483
$693$		0			0
$694$	8.86023e9			1.00621
$695$	5.58304e9	−	9.67010e9i	0.630847	−	1.09266i
$696$		0			0
$697$	9.51891e7	+	1.64872e8i	0.0106481	+	0.0184431i
$698$	5.87826e9	−	1.01815e10i	0.654267	−	1.13322i
$699$		0			0
$700$	−2.43223e9	+	1.97340e8i	−0.268017	+	0.0217457i
$701$	−9.59194e9			−1.05170			−0.525852	−	0.850576i	$-0.676253\pi$
$701$	−9.59194e9			−1.05170			−0.525852	+	0.850576i	$0.676253\pi$
$702$		0			0
$703$	−1.72257e9	−	2.98358e9i	−0.186996	−	0.323887i
$704$	8.19763e8	+	1.41987e9i	0.0885490	+	0.153371i
$705$		0			0
$706$	−6.96011e9			−0.744388
$707$	−1.54534e9	+	3.26013e9i	−0.164458	+	0.346951i
$708$		0			0
$709$	1.80143e9	−	3.12016e9i	0.189826	−	0.328787i	−0.755366	−	0.655303i	$-0.772541\pi$
$709$	1.80143e9	−	3.12016e9i	0.189826	−	0.328787i	0.945192	+	0.326515i	$0.105874\pi$
$710$	3.67412e9	+	6.36376e9i	0.385256	+	0.667283i
$711$		0			0
$712$	−8.79281e8	+	1.52296e9i	−0.0912952	+	0.158128i
$713$	1.77297e10			1.83184
$714$		0			0
$715$	4.97115e9			0.508611
$716$	−1.46299e9	+	2.53397e9i	−0.148951	+	0.257991i
$717$		0			0
$718$	3.20252e9	+	5.54693e9i	0.322892	+	0.559265i
$719$	4.41578e9	−	7.64835e9i	0.443053	−	0.767391i	−0.554861	−	0.831943i	$-0.687229\pi$
$719$	4.41578e9	−	7.64835e9i	0.443053	−	0.767391i	0.997914	+	0.0645520i	$0.0205618\pi$
$720$		0			0
$721$	6.28107e9	−	5.09618e8i	0.624109	−	0.0506374i
$722$	5.24289e9			0.518431
$723$		0			0
$724$	5.58972e8	+	9.68167e8i	0.0547400	+	0.0948125i
$725$	4.86576e8	+	8.42775e8i	0.0474207	+	0.0821350i
$726$		0			0
$727$	−8.30116e9			−0.801250			−0.400625	−	0.916242i	$-0.631207\pi$
$727$	−8.30116e9			−0.801250			−0.400625	+	0.916242i	$0.631207\pi$
$728$	−1.10467e9	−	1.59900e9i	−0.106114	−	0.153599i
$729$		0			0
$730$	2.64548e9	−	4.58211e9i	0.251695	−	0.435949i
$731$	8.21402e7	+	1.42271e8i	0.00777758	+	0.0134712i
$732$		0			0
$733$	4.74120e9	−	8.21199e9i	0.444656	−	0.770166i	−0.553372	−	0.832934i	$-0.686659\pi$
$733$	4.74120e9	−	8.21199e9i	0.444656	−	0.770166i	0.998028	+	0.0627676i	$0.0199927\pi$
$734$	−3.99630e9			−0.373011
$735$		0			0
$736$	1.92253e9			0.177747
$737$	−6.96957e8	+	1.20717e9i	−0.0641313	+	0.111079i
$738$		0			0
$739$	6.12549e9	+	1.06097e10i	0.558323	+	0.967043i	0.997637	+	0.0687097i	$0.0218882\pi$
$739$	6.12549e9	+	1.06097e10i	0.558323	+	0.967043i	−0.439314	+	0.898334i	$0.644778\pi$
$740$	1.35649e9	−	2.34951e9i	0.123057	−	0.213140i
$741$		0			0
$742$	−4.54867e9	−	6.58418e9i	−0.408762	−	0.591682i
$743$	1.06325e10			0.950989			0.475495	−	0.879719i	$-0.342269\pi$
$743$	1.06325e10			0.950989			0.475495	+	0.879719i	$0.342269\pi$
$744$		0			0
$745$	−4.16077e9	−	7.20666e9i	−0.368660	−	0.638538i
$746$	4.12673e9	+	7.14771e9i	0.363932	+	0.630349i
$747$		0			0
$748$	2.30918e8			0.0201744
$749$	1.37801e10	−	1.11805e9i	1.19830	−	0.0972246i
$750$		0			0
$751$	−9.99189e9	+	1.73065e10i	−0.860811	+	1.49097i	0.0103358	+	0.999947i	$0.496710\pi$
$751$	−9.99189e9	+	1.73065e10i	−0.860811	+	1.49097i	−0.871147	+	0.491022i	$0.836623\pi$
$752$	2.67502e9	+	4.63327e9i	0.229385	+	0.397306i
$753$		0			0
$754$	−3.87525e8	+	6.71214e8i	−0.0329231	+	0.0570245i
$755$	−2.03127e9			−0.171772
$756$		0			0
$757$	−1.08884e10			−0.912281			−0.456140	−	0.889908i	$-0.650769\pi$
$757$	−1.08884e10			−0.912281			−0.456140	+	0.889908i	$0.650769\pi$
$758$	−3.34192e9	+	5.78838e9i	−0.278711	+	0.482742i
$759$		0			0
$760$	−7.51287e8	−	1.30127e9i	−0.0620809	−	0.107527i
$761$	−8.29514e9	+	1.43676e10i	−0.682303	+	1.18178i	0.291973	+	0.956427i	$0.405688\pi$
$761$	−8.29514e9	+	1.43676e10i	−0.682303	+	1.18178i	−0.974276	+	0.225357i	$0.927645\pi$
$762$		0			0
$763$	7.61393e9	−	1.60628e10i	0.620545	−	1.30914i
$764$	−2.46314e9			−0.199831
$765$		0			0
$766$	7.99082e9	+	1.38405e10i	0.642378	+	1.11263i
$767$	−7.51898e7	−	1.30233e8i	−0.00601693	−	0.0104216i
$768$		0			0
$769$	1.24893e10			0.990363			0.495182	−	0.868790i	$-0.335102\pi$
$769$	1.24893e10			0.990363			0.495182	+	0.868790i	$0.335102\pi$
$770$	8.60001e9	−	6.97767e8i	0.678862	−	0.0550799i
$771$		0			0
$772$	3.27956e9	−	5.68036e9i	0.256540	−	0.444340i
$773$	−3.53844e9	−	6.12877e9i	−0.275540	−	0.477249i	0.694731	−	0.719269i	$-0.255523\pi$
$773$	−3.53844e9	−	6.12877e9i	−0.275540	−	0.477249i	−0.970271	+	0.242020i	$0.922190\pi$
$774$		0			0
$775$	−6.34825e9	+	1.09955e10i	−0.489889	+	0.848513i
$776$	−1.94420e9			−0.149357
$777$		0			0
$778$	−3.60674e9			−0.274591
$779$	2.54825e9	−	4.41369e9i	0.193135	−	0.334519i
$780$		0			0
$781$	1.51157e10	+	2.61812e10i	1.13540	+	1.96658i
$782$	1.35389e8	−	2.34500e8i	0.0101242	−	0.0175356i
$783$		0			0
$784$	−2.13550e9	−	2.61120e9i	−0.158268	−	0.193523i
$785$	−9.68556e9			−0.714630
$786$		0			0
$787$	−2.89271e9	−	5.01033e9i	−0.211541	−	0.366399i	0.740656	−	0.671884i	$-0.234515\pi$
$787$	−2.89271e9	−	5.01033e9i	−0.211541	−	0.366399i	−0.952197	+	0.305485i	$0.901181\pi$
$788$	−5.67084e9	−	9.82218e9i	−0.412863	−	0.715099i
$789$		0			0
$790$	−1.13278e10			−0.817434
$791$	4.51550e9	+	6.53617e9i	0.324405	+	0.469575i
$792$		0			0
$793$	−2.51964e9	+	4.36415e9i	−0.179425	+	0.310773i
$794$	−3.87028e9	−	6.70352e9i	−0.274392	−	0.475260i
$795$		0			0
$796$	1.28674e8	−	2.22869e8i	0.00904260	−	0.0156622i
$797$	1.60066e10			1.11994			0.559969	−	0.828514i	$-0.310813\pi$
$797$	1.60066e10			1.11994			0.559969	+	0.828514i	$0.310813\pi$
$798$		0			0
$799$	7.53521e8			0.0522615
$800$	−6.88377e8	+	1.19230e9i	−0.0475348	+	0.0823326i
$801$		0			0
$802$	−9.93730e9	−	1.72119e10i	−0.680234	−	1.17820i
$803$	1.08838e10	−	1.88513e10i	0.741781	−	1.28480i
$804$		0			0
$805$	4.33366e9	−	9.14255e9i	0.292799	−	0.617706i
$806$	−1.01119e10			−0.680238
$807$		0			0
$808$	1.01776e9	+	1.76281e9i	0.0678742	+	0.117562i
$809$	2.59877e9	+	4.50120e9i	0.172563	+	0.298888i	0.939315	−	0.343055i	$-0.111462\pi$
$809$	2.59877e9	+	4.50120e9i	0.172563	+	0.298888i	−0.766752	+	0.641943i	$0.778128\pi$
$810$		0			0
$811$	2.58012e9			0.169850			0.0849252	−	0.996387i	$-0.472935\pi$
$811$	2.58012e9			0.169850			0.0849252	+	0.996387i	$0.472935\pi$
$812$	−5.76200e8	+	1.21558e9i	−0.0377683	+	0.0796781i
$813$		0			0
$814$	5.58074e9	−	9.66613e9i	0.362666	−	0.628155i
$815$	−5.27305e8	−	9.13320e8i	−0.0341201	−	0.0590978i
$816$		0			0
$817$	2.19892e9	−	3.80865e9i	0.141069	−	0.244339i
$818$	5.89279e7			0.00376430
$819$		0			0
$820$	4.01339e9			0.254192
$821$	−3.25385e9	+	5.63583e9i	−0.205209	+	0.355432i	−0.950199	−	0.311643i	$-0.899121\pi$
$821$	−3.25385e9	+	5.63583e9i	−0.205209	+	0.355432i	0.744990	+	0.667075i	$0.232454\pi$
$822$		0			0
$823$	3.83450e9	+	6.64155e9i	0.239778	+	0.415308i	0.960651	−	0.277760i	$-0.0895920\pi$
$823$	3.83450e9	+	6.64155e9i	0.239778	+	0.415308i	−0.720872	+	0.693068i	$0.756259\pi$
$824$	1.77769e9	−	3.07904e9i	0.110690	−	0.191721i
$825$		0			0
$826$	−1.48357e8	−	2.14746e8i	−0.00915964	−	0.0132585i
$827$	−2.19638e9			−0.135032			−0.0675162	−	0.997718i	$-0.521507\pi$
$827$	−2.19638e9			−0.135032			−0.0675162	+	0.997718i	$0.521507\pi$
$828$		0			0
$829$	−9.64024e9	−	1.66974e10i	−0.587688	−	1.01791i	−0.994534	−	0.104409i	$-0.966705\pi$
$829$	−9.64024e9	−	1.66974e10i	−0.587688	−	1.01791i	0.406846	−	0.913497i	$-0.366628\pi$
$830$	3.57622e9	+	6.19420e9i	0.217096	+	0.376021i
$831$		0			0
$832$	−1.09649e9			−0.0660046
$833$	−4.68886e8	+	7.65909e7i	−0.0281067	+	0.00459113i
$834$		0			0
$835$	−8.26207e9	+	1.43103e10i	−0.491119	+	0.850642i
$836$	−3.09087e9	−	5.35355e9i	−0.182961	−	0.316898i
$837$		0			0
$838$	8.72981e9	−	1.51205e10i	0.512449	−	0.887588i
$839$	−3.19760e10			−1.86921			−0.934604	−	0.355689i	$-0.884246\pi$
$839$	−3.19760e10			−1.86921			−0.934604	+	0.355689i	$0.884246\pi$
$840$		0			0
$841$	−1.67134e10			−0.968900
$842$	−1.09912e9	+	1.90373e9i	−0.0634531	+	0.109904i
$843$		0			0
$844$	3.35327e9	+	5.80803e9i	0.191986	+	0.332529i
$845$	4.29960e9	−	7.44713e9i	0.245149	−	0.424610i
$846$		0			0
$847$	1.77548e10	−	1.44055e9i	1.00398	−	0.0814584i
$848$	−4.51501e9			−0.254257
$849$		0			0
$850$	9.69539e7	+	1.67929e8i	0.00541501	+	0.00937907i
$851$	−6.54406e9	−	1.13347e10i	−0.363994	−	0.630456i
$852$		0			0
$853$	−1.06299e10			−0.586416			−0.293208	−	0.956049i	$-0.594723\pi$
$853$	−1.06299e10			−0.586416			−0.293208	+	0.956049i	$0.594723\pi$
$854$	−3.74638e9	+	7.90359e9i	−0.205830	+	0.434232i
$855$		0			0
$856$	3.90008e9	−	6.75513e9i	0.212527	−	0.368108i
$857$	9.42668e9	+	1.63275e10i	0.511594	+	0.886108i	0.999910	+	0.0134403i	$0.00427830\pi$
$857$	9.42668e9	+	1.63275e10i	0.511594	+	0.886108i	−0.488315	+	0.872667i	$0.662388\pi$
$858$		0			0
$859$	−9.45689e9	+	1.63798e10i	−0.509064	+	0.881725i	0.490881	+	0.871227i	$0.336675\pi$
$859$	−9.45689e9	+	1.63798e10i	−0.509064	+	0.881725i	−0.999945	+	0.0104981i	$0.996658\pi$
$860$	3.46321e9			0.185667
$861$		0			0
$862$	1.27360e10			0.677262
$863$	−1.60330e10	+	2.77700e10i	−0.849137	+	1.47075i	0.0328428	+	0.999461i	$0.489544\pi$
$863$	−1.60330e10	+	2.77700e10i	−0.849137	+	1.47075i	−0.881980	+	0.471288i	$0.843789\pi$
$864$		0			0
$865$	−1.11874e9	−	1.93772e9i	−0.0587725	−	0.101797i
$866$	1.97518e9	−	3.42111e9i	0.103346	−	0.179001i
$867$		0			0
$868$	−1.74935e10	+	1.41934e9i	−0.907939	+	0.0736662i
$869$	−4.66040e10			−2.40909
$870$		0			0
$871$	−4.66116e8	−	8.07336e8i	−0.0239018	−	0.0413991i
$872$	−5.01453e9	−	8.68542e9i	−0.256108	−	0.443592i
$873$		0			0
$874$	−7.24882e9			−0.367263
$875$	1.17760e10	+	1.70457e10i	0.594249	+	0.860173i
$876$		0			0
$877$	−1.35871e10	+	2.35335e10i	−0.680186	+	1.17812i	0.294738	+	0.955578i	$0.404767\pi$
$877$	−1.35871e10	+	2.35335e10i	−0.680186	+	1.17812i	−0.974924	+	0.222538i	$0.928566\pi$
$878$	1.30001e10	+	2.25168e10i	0.648210	+	1.12273i
$879$		0			0
$880$	2.43400e9	−	4.21581e9i	0.120401	−	0.208541i
$881$	−2.80664e10			−1.38284			−0.691418	−	0.722455i	$-0.743014\pi$
$881$	−2.80664e10			−1.38284			−0.691418	+	0.722455i	$0.743014\pi$
$882$		0			0
$883$	−2.55368e10			−1.24826			−0.624129	−	0.781321i	$-0.714546\pi$
$883$	−2.55368e10			−1.24826			−0.624129	+	0.781321i	$0.714546\pi$
$884$	−7.72173e7	+	1.33744e8i	−0.00375951	+	0.00651167i
$885$		0			0
$886$	−9.99019e9	−	1.73035e10i	−0.482565	−	0.835827i
$887$	−1.08146e8	+	1.87315e8i	−0.00520330	+	0.00901238i	−0.868615	−	0.495487i	$-0.834990\pi$
$887$	−1.08146e8	+	1.87315e8i	−0.00520330	+	0.00901238i	0.863412	+	0.504499i	$0.168323\pi$
$888$		0			0
$889$	−1.61289e10	−	2.33465e10i	−0.769924	−	1.11446i
$890$	5.22144e9			0.248271
$891$		0			0
$892$	1.13695e9	+	1.96926e9i	0.0536371	+	0.0929022i
$893$	−1.00860e10	−	1.74695e10i	−0.473958	−	0.820919i
$894$		0			0
$895$	8.68766e9			0.405063
$896$	−1.89692e9	+	1.53907e8i	−0.0880988	+	0.00714795i
$897$		0			0
$898$	1.08689e10	−	1.88254e10i	0.500861	−	0.867517i
$899$	3.49963e9	+	6.06153e9i	0.160643	+	0.278243i
$900$		0			0
$901$	−3.17957e8	+	5.50717e8i	−0.0144821	+	0.0250837i
$902$	1.65115e10			0.749141
$903$		0			0
$904$	4.48208e9			0.201786
$905$	1.65967e9	−	2.87464e9i	0.0744307	−	0.128918i
$906$		0			0
$907$	2.60424e9	+	4.51068e9i	0.115893	+	0.200732i	0.918136	−	0.396265i	$-0.129694\pi$
$907$	2.60424e9	+	4.51068e9i	0.115893	+	0.200732i	−0.802244	+	0.596997i	$0.796360\pi$
$908$	−3.71972e9	+	6.44275e9i	−0.164896	+	0.285608i
$909$		0			0
$910$	−2.47165e9	+	5.21434e9i	−0.108728	+	0.229379i
$911$	−3.10115e10			−1.35896			−0.679482	−	0.733692i	$-0.737795\pi$
$911$	−3.10115e10			−1.35896			−0.679482	+	0.733692i	$0.737795\pi$
$912$		0			0
$913$	1.47130e10	+	2.54836e10i	0.639812	+	1.10819i
$914$	−1.25086e10	−	2.16656e10i	−0.541874	−	0.938553i
$915$		0			0
$916$	−1.21114e10			−0.520668
$917$	2.61414e10	−	2.12100e9i	1.11953	−	0.0908338i
$918$		0			0
$919$	1.24346e10	−	2.15373e10i	0.528477	−	0.915349i	−0.470972	−	0.882148i	$-0.656097\pi$
$919$	1.24346e10	−	2.15373e10i	0.528477	−	0.915349i	0.999449	−	0.0332005i	$-0.0105700\pi$
$920$	−2.85415e9	−	4.94353e9i	−0.120842	−	0.209305i
$921$		0			0
$922$	1.16219e10	−	2.01298e10i	0.488338	−	0.845826i
$923$	−2.02184e10			−0.846332
$924$		0			0
$925$	9.37260e9			0.389371
$926$	−1.38859e10	+	2.40510e10i	−0.574691	+	0.995394i
$927$		0			0
$928$	3.79485e8	+	6.57287e8i	0.0155875	+	0.0269983i
$929$	7.19722e9	−	1.24660e10i	0.294517	−	0.510118i	−0.680356	−	0.732882i	$-0.738175\pi$
$929$	7.19722e9	−	1.24660e10i	0.294517	−	0.510118i	0.974872	+	0.222764i	$0.0715080\pi$
$930$		0			0
$931$	8.05179e9	+	9.84538e9i	0.327016	+	0.399861i
$932$	−1.93292e10			−0.782094
$933$		0			0
$934$	1.05134e10	+	1.82097e10i	0.422209	+	0.731288i
$935$	−3.42815e8	−	5.93773e8i	−0.0137157	−	0.0237563i
$936$		0			0
$937$	−1.25268e10			−0.497451			−0.248726	−	0.968574i	$-0.580012\pi$
$937$	−1.25268e10			−0.497451			−0.248726	+	0.968574i	$0.580012\pi$
$938$	−9.19694e8	−	1.33125e9i	−0.0363859	−	0.0526685i
$939$		0			0
$940$	7.94254e9	−	1.37569e10i	0.311897	−	0.540222i
$941$	2.06675e10	+	3.57971e10i	0.808581	+	1.40050i	0.913847	+	0.406059i	$0.133097\pi$
$941$	2.06675e10	+	3.57971e10i	0.808581	+	1.40050i	−0.105266	+	0.994444i	$0.533569\pi$
$942$		0			0
$943$	9.68082e9	−	1.67677e10i	0.375942	−	0.651151i
$944$	−1.47259e8			−0.00569746
$945$		0			0
$946$	1.42480e10			0.547187
$947$	−1.24770e10	+	2.16108e10i	−0.477402	+	0.826885i	−0.999665	−	0.0258999i	$-0.991755\pi$
$947$	−1.24770e10	+	2.16108e10i	−0.477402	+	0.826885i	0.522262	+	0.852785i	$0.325088\pi$
$948$		0			0
$949$	7.27894e9	+	1.26075e10i	0.276463	+	0.478847i
$950$	2.59549e9	−	4.49552e9i	0.0982171	−	0.170117i
$951$		0			0
$952$	−1.14812e8	+	2.42214e8i	−0.00431279	+	0.00909851i
$953$	7.15422e9			0.267755			0.133877	−	0.990998i	$-0.457257\pi$
$953$	7.15422e9			0.267755			0.133877	+	0.990998i	$0.457257\pi$
$954$		0			0
$955$	3.65672e9	+	6.33363e9i	0.135856	+	0.235310i
$956$	−9.62146e9	−	1.66649e10i	−0.356155	−	0.616878i
$957$		0			0
$958$	−3.26373e10			−1.19932
$959$	−1.47726e9	+	3.11650e9i	−0.0540867	+	0.114104i
$960$		0			0
$961$	−3.19025e10	+	5.52568e10i	−1.15956	+	2.00842i
$962$	3.73232e9	+	6.46458e9i	0.135166	+	0.234114i
$963$		0			0
$964$	1.22722e9	−	2.12561e9i	0.0441219	−	0.0764213i
$965$	−1.94750e10			−0.697642
$966$		0			0
$967$	4.41476e10			1.57006			0.785028	−	0.619461i	$-0.212649\pi$
$967$	4.41476e10			1.57006			0.785028	+	0.619461i	$0.212649\pi$
$968$	5.02502e9	−	8.70360e9i	0.178063	−	0.308415i
$969$		0			0
$970$	2.88632e9	+	4.99925e9i	0.101541	+	0.175875i
$971$	1.93951e10	−	3.35933e10i	0.679869	−	1.17757i	−0.295152	−	0.955450i	$-0.595370\pi$
$971$	1.93951e10	−	3.35933e10i	0.679869	−	1.17757i	0.975020	−	0.222116i	$-0.0712965\pi$
$972$		0			0
$973$	3.03098e10	+	4.38734e10i	1.05484	+	1.52688i
$974$	1.20995e9			0.0419576
$975$		0			0
$976$	2.46736e9	+	4.27360e9i	0.0849491	+	0.147136i
$977$	1.28118e10	+	2.21907e10i	0.439521	+	0.761272i	0.997652	−	0.0684801i	$-0.0218150\pi$
$977$	1.28118e10	+	2.21907e10i	0.439521	+	0.761272i	−0.558132	+	0.829752i	$0.688482\pi$
$978$		0			0
$979$	2.14816e10			0.731689
$980$	−3.54402e9	+	9.36766e9i	−0.120283	+	0.317936i
$981$		0			0
$982$	1.68254e10	−	2.91425e10i	0.566991	−	0.982057i
$983$	−1.75271e9	−	3.03578e9i	−0.0588534	−	0.101937i	0.835098	−	0.550102i	$-0.185411\pi$
$983$	−1.75271e9	−	3.03578e9i	−0.0588534	−	0.101937i	−0.893951	+	0.448165i	$0.852078\pi$
$984$		0			0
$985$	−1.68376e10	+	2.91636e10i	−0.561375	+	0.972330i
$986$	1.06896e8			0.00355135
$987$		0			0
$988$	4.13427e9			0.136380
$989$	8.35373e9	−	1.44691e10i	0.274596	−	0.475614i
$990$		0			0
$991$	1.11508e10	+	1.93137e10i	0.363954	+	0.630387i	0.988608	−	0.150515i	$-0.0480931\pi$
$991$	1.11508e10	+	1.93137e10i	0.363954	+	0.630387i	−0.624654	+	0.780902i	$0.714760\pi$
$992$	−4.95105e9	+	8.57547e9i	−0.161030	+	0.278912i
$993$		0			0
$994$	−3.49775e10	+	2.83792e9i	−1.12963	+	0.0916533i
$995$	−7.64103e8			−0.0245907
$996$		0			0
$997$	−2.39697e10	−	4.15168e10i	−0.766002	−	1.32676i	−0.939715	−	0.341959i	$-0.888910\pi$
$997$	−2.39697e10	−	4.15168e10i	−0.766002	−	1.32676i	0.173712	−	0.984796i	$-0.444424\pi$
$998$	7.72286e9	+	1.33764e10i	0.245936	+	0.425973i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.8.g.j.37.2	yes	6
3.2	odd	2		126.8.g.i.37.2	✓	6
7.4	even	3	inner	126.8.g.j.109.2	yes	6
21.11	odd	6		126.8.g.i.109.2	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.8.g.i.37.2	✓	6	3.2	odd	2
126.8.g.i.109.2	yes	6	21.11	odd	6
126.8.g.j.37.2	yes	6	1.1	even	1	trivial
126.8.g.j.109.2	yes	6	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(4.00000 - 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-95.0129 + 164.567i) q^{5} +(-515.817 - 746.643i) q^{7} -512.000 q^{8} +(760.103 + 1316.54i) q^{10} +(3127.15 + 5416.38i) q^{11} -4182.79 q^{13} +(-7236.16 + 587.110i) q^{14} +(-2048.00 + 3547.24i) q^{16} +(288.449 + 499.608i) q^{17} +(7721.88 - 13374.7i) q^{19} +12161.7 q^{20} +50034.3 q^{22} +(29335.5 - 50810.6i) q^{23} +(21007.6 + 36386.2i) q^{25} +(-16731.2 + 28979.2i) q^{26} +(-24877.0 + 52482.0i) q^{28} +23161.9 q^{29} +(151094. + 261703. i) q^{31} +(16384.0 + 28377.9i) q^{32} +4615.18 q^{34} +(171882. - 13945.8i) q^{35} +(111538. - 193190. i) q^{37} +(-61775.1 - 106998. i) q^{38} +(48646.6 - 84258.4i) q^{40} +330003. q^{41} +284765. q^{43} +(200137. - 346648. i) q^{44} +(-234684. - 406485. i) q^{46} +(653080. - 1.13117e6i) q^{47} +(-291409. + 770262. i) q^{49} +336122. q^{50} +(133849. + 231834. i) q^{52} +(551149. + 954618. i) q^{53} -1.18848e6 q^{55} +(264098. + 382281. i) q^{56} +(92647.6 - 160470. i) q^{58} +(17976.0 + 31135.3i) q^{59} +(602384. - 1.04336e6i) q^{61} +2.41751e6 q^{62} +262144. q^{64} +(397419. - 688350. i) q^{65} +(111437. + 193014. i) q^{67} +(18460.7 - 31974.9i) q^{68} +(590910. - 1.24662e6i) q^{70} +4.83371e6 q^{71} +(-1.74021e6 - 3.01414e6i) q^{73} +(-892306. - 1.54552e6i) q^{74} -988401. q^{76} +(2.43107e6 - 5.12872e6i) q^{77} +(-3.72576e6 + 6.45321e6i) q^{79} +(-389173. - 674067. i) q^{80} +(1.32001e6 - 2.28633e6i) q^{82} +4.70492e6 q^{83} -109625. q^{85} +(1.13906e6 - 1.97291e6i) q^{86} +(-1.60110e6 - 2.77318e6i) q^{88} +(1.71735e6 - 2.97453e6i) q^{89} +(2.15755e6 + 3.12305e6i) q^{91} -3.75495e6 q^{92} +(-5.22464e6 - 9.04935e6i) q^{94} +(1.46736e6 + 2.54154e6i) q^{95} +3.79727e6 q^{97} +(4.17090e6 + 5.09999e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 24 q^{2} - 192 q^{4} - 718 q^{5} - 1471 q^{7} - 3072 q^{8} + 5744 q^{10} + 208 q^{11} + 19394 q^{13} - 4504 q^{14} - 12288 q^{16} - 19244 q^{17} - 25419 q^{19} + 91904 q^{20} + 3328 q^{22} - 67400 q^{23}+ \cdots + 20461248 q^{98}+O(q^{100}) \) 6 * q + 24 * q^2 - 192 * q^4 - 718 * q^5 - 1471 * q^7 - 3072 * q^8 + 5744 * q^10 + 208 * q^11 + 19394 * q^13 - 4504 * q^14 - 12288 * q^16 - 19244 * q^17 - 25419 * q^19 + 91904 * q^20 + 3328 * q^22 - 67400 * q^23 - 93931 * q^25 + 77576 * q^26 + 58112 * q^28 + 33476 * q^29 + 78449 * q^31 + 98304 * q^32 - 307904 * q^34 - 602072 * q^35 - 496599 * q^37 + 203352 * q^38 + 367616 * q^40 + 1953168 * q^41 + 697470 * q^43 + 13312 * q^44 + 539200 * q^46 + 701328 * q^47 + 959673 * q^49 - 1502896 * q^50 - 620608 * q^52 + 2917374 * q^53 - 3275696 * q^55 + 753152 * q^56 + 133904 * q^58 - 492040 * q^59 + 3649370 * q^61 + 1255184 * q^62 + 1572864 * q^64 - 2707764 * q^65 - 3647153 * q^67 - 1231616 * q^68 - 503936 * q^70 + 3541216 * q^71 - 6183557 * q^73 + 3972792 * q^74 + 3253632 * q^76 + 13092290 * q^77 - 12453589 * q^79 - 2940928 * q^80 + 7812672 * q^82 + 11611120 * q^83 + 38154616 * q^85 + 2789880 * q^86 - 106496 * q^88 - 8292612 * q^89 + 366581 * q^91 + 8627200 * q^92 - 5610624 * q^94 - 8691056 * q^95 - 55949528 * q^97 + 20461248 * q^98

Introduction

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