LMFDB - Embedded newform 126.8.g.j.109.2

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			109.2
Root			$-16.2090 + 28.0749i$ of defining polynomial
Character	$\chi$	$=$	126.109
Dual form			126.8.g.j.37.2

$q$-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 $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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	0.644490	−	0.764612i	$-0.277070\pi$
$5$	−95.0129	−	164.567i	−0.339928	−	0.588773i	−0.984419	+	0.175839i	$0.943736\pi$
$6$		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	−0.257061	−	0.966395i	$-0.582754\pi$
$11$	3127.15	−	5416.38i	0.708392	−	1.22697i	0.965453	−	0.260576i	$-0.0839125\pi$
$12$		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	−0.858818	−	0.512281i	$-0.828801\pi$
$17$	288.449	−	499.608i	0.0142396	−	0.0246637i	0.873057	+	0.487617i	$0.162134\pi$
$18$		0			0
$19$	7721.88	+	13374.7i	0.258277	+	0.447349i	0.965780	−	0.259361i	$-0.0835120\pi$
$19$	7721.88	+	13374.7i	0.258277	+	0.447349i	−0.707503	+	0.706710i	$0.750179\pi$
$20$	12161.7			0.339928
$21$		0			0
$22$	50034.3			1.00182
$23$	29335.5	+	50810.6i	0.502744	+	0.870777i	0.999995	+	0.00317085i	$0.00100932\pi$
$23$	29335.5	+	50810.6i	0.502744	+	0.870777i	−0.497251	+	0.867606i	$0.665657\pi$
$24$		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	0.0981589	−	0.995171i	$-0.468705\pi$
$31$	151094.	−	261703.i	0.910923	−	1.57776i	0.812764	−	0.582593i	$-0.197962\pi$
$32$	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	0.988291	−	0.152580i	$-0.0487581\pi$
$37$	111538.	+	193190.i	0.362008	+	0.627015i	−0.626284	+	0.779595i	$0.715425\pi$
$38$	−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	0.803142	+	0.595788i	$0.203160\pi$
$47$	653080.	+	1.13117e6i	0.917538	+	1.58922i	0.114396	+	0.993435i	$0.463507\pi$
$48$		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	−0.491437	−	0.870913i	$-0.663528\pi$
$53$	551149.	−	954618.i	0.508514	−	0.880773i	0.999951	−	0.00985975i	$-0.00313851\pi$
$54$		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	−0.860272	−	0.509836i	$-0.829706\pi$
$59$	17976.0	−	31135.3i	0.0113949	−	0.0197366i	0.871667	+	0.490099i	$0.163039\pi$
$60$		0			0
$61$	602384.	+	1.04336e6i	0.339797	+	0.588545i	0.984394	−	0.175977i	$-0.0563085\pi$
$61$	602384.	+	1.04336e6i	0.339797	+	0.588545i	−0.644598	+	0.764522i	$0.722975\pi$
$62$	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	−0.842505	−	0.538688i	$-0.818920\pi$
$67$	111437.	−	193014.i	0.0452654	−	0.0784020i	0.887770	+	0.460287i	$0.152253\pi$
$68$	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	0.476057	+	0.879414i	$0.342066\pi$
$73$	−1.74021e6	+	3.01414e6i	−0.523567	+	0.906844i	−0.999624	+	0.0274299i	$0.991268\pi$
$74$	−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	−0.881029	−	0.473061i	$-0.843149\pi$
$79$	−3.72576e6	−	6.45321e6i	−0.850198	−	1.47259i	0.0308315	−	0.999525i	$-0.490184\pi$
$80$	−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	0.965766	−	0.259416i	$-0.0835301\pi$
$89$	1.71735e6	+	2.97453e6i	0.258222	+	0.447253i	−0.707544	+	0.706669i	$0.750197\pi$
$90$		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	−0.945905	−	0.324442i	$-0.894823\pi$
$101$	−1.98781e6	+	3.44299e6i	−0.191977	+	0.332514i	0.753928	+	0.656957i	$0.228157\pi$
$102$		0			0
$103$	−3.47204e6	−	6.01376e6i	−0.313080	−	0.542270i	0.665948	−	0.745998i	$-0.268027\pi$
$103$	−3.47204e6	−	6.01376e6i	−0.313080	−	0.542270i	−0.979027	+	0.203728i	$0.934694\pi$
$104$	2.14159e6			0.186689
$105$		0			0
$106$	8.81838e6			0.719148
$107$	−7.61733e6	−	1.31936e7i	−0.601118	−	1.04117i	−0.992652	−	0.121003i	$-0.961389\pi$
$107$	−7.61733e6	−	1.31936e7i	−0.601118	−	1.04117i	0.391534	−	0.920164i	$-0.371945\pi$
$108$		0			0
$109$	9.79401e6	−	1.69637e7i	0.724382	−	1.25467i	−0.234846	−	0.972033i	$-0.575458\pi$
$109$	9.79401e6	−	1.69637e7i	0.724382	−	1.25467i	0.959228	−	0.282634i	$-0.0912082\pi$
$110$	−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	−0.997357	−	0.0726610i	$-0.976851\pi$
$131$	−1.44504e7	−	2.50288e7i	−0.561605	−	0.972728i	0.435752	−	0.900067i	$-0.356482\pi$
$132$		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	−0.895866	−	0.444324i	$-0.853444\pi$
$137$	−1.90023e6	+	3.29130e6i	−0.0631371	+	0.109357i	0.832729	+	0.553681i	$0.186777\pi$
$138$		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	−0.998774	−	0.0495073i	$-0.984235\pi$
$149$	−2.18958e7	−	3.79246e7i	−0.542261	−	0.939224i	0.456512	−	0.889717i	$-0.349098\pi$
$150$		0			0
$151$	5.34472e6	−	9.25733e6i	0.126330	−	0.218810i	−0.795922	−	0.605399i	$-0.793014\pi$
$151$	5.34472e6	−	9.25733e6i	0.126330	−	0.218810i	0.922252	+	0.386589i	$0.126347\pi$
$152$	−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	−0.473983	−	0.880534i	$-0.657184\pi$
$157$	2.54849e7	−	4.41411e7i	0.525574	−	0.910320i	0.999556	−	0.0297861i	$-0.00948262\pi$
$158$	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	0.839840	−	0.542833i	$-0.182648\pi$
$163$	−2.77491e6	−	4.80629e6i	−0.0501872	−	0.0869268i	−0.890028	+	0.455907i	$0.849315\pi$
$164$	−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	0.819559	−	0.572995i	$-0.194218\pi$
$173$	−5.88732e6	−	1.01971e7i	−0.0864483	−	0.149733i	−0.906007	+	0.423262i	$0.860885\pi$
$174$		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	−0.975656	−	0.219307i	$-0.929620\pi$
$179$	−2.28592e7	+	3.95932e7i	−0.297903	+	0.515983i	0.677753	+	0.735290i	$0.262954\pi$
$180$		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	0.948473	−	0.316857i	$-0.102627\pi$
$191$	1.92433e7	+	3.33304e7i	0.199831	+	0.346117i	−0.748643	+	0.662974i	$0.769294\pi$
$192$		0			0
$193$	5.12431e7	−	8.87557e7i	0.513080	−	0.888681i	−0.486805	−	0.873511i	$-0.661838\pi$
$193$	5.12431e7	−	8.87557e7i	0.513080	−	0.888681i	0.999885	−	0.0151698i	$-0.00482890\pi$
$194$	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	−0.856841	−	0.515580i	$-0.827576\pi$
$199$	2.01052e6	−	3.48233e6i	0.0180852	−	0.0313245i	0.874926	+	0.484256i	$0.160910\pi$
$200$	−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	−0.982470	−	0.186418i	$-0.940312\pi$
$227$	−5.81207e7	+	1.00668e8i	−0.329792	+	0.571217i	0.652678	+	0.757635i	$0.273645\pi$
$228$		0			0
$229$	9.46205e7	+	1.63888e8i	0.520668	+	0.901824i	0.999711	+	0.0240325i	$0.00765052\pi$
$229$	9.46205e7	+	1.63888e8i	0.520668	+	0.901824i	−0.479043	+	0.877792i	$0.659016\pi$
$230$	8.91921e7			0.483369
$231$		0			0
$232$	−1.18589e7			−0.0623500
$233$	1.51010e8	+	2.61556e8i	0.782094	+	1.35463i	0.930720	+	0.365733i	$0.119182\pi$
$233$	1.51010e8	+	2.61556e8i	0.782094	+	1.35463i	−0.148626	+	0.988894i	$0.547485\pi$
$234$		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	−0.818525	−	0.574471i	$-0.805208\pi$
$241$	1.91754e7	−	3.32127e7i	0.0882437	−	0.152843i	0.906769	+	0.421628i	$0.138541\pi$
$242$	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	0.866337	−	0.499460i	$-0.166468\pi$
$257$	169674.	+	293884.i	0.000623518	+	0.00107996i	−0.865713	+	0.500540i	$0.833135\pi$
$258$		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	−0.671783	−	0.740748i	$-0.734471\pi$
$263$	9.01614e7	−	1.56164e8i	0.305616	−	0.529342i	0.977398	+	0.211407i	$0.0678044\pi$
$264$		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	−0.376424	−	0.926447i	$-0.622847\pi$
$269$	1.96057e8	−	3.39581e8i	0.614115	−	1.06368i	0.990539	−	0.137230i	$-0.0438201\pi$
$270$		0			0
$271$	1.92498e8	+	3.33417e8i	0.587536	+	1.01764i	0.994554	+	0.104222i	$0.0332353\pi$
$271$	1.92498e8	+	3.33417e8i	0.587536	+	1.01764i	−0.407018	+	0.913420i	$0.633431\pi$
$272$	−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	0.397008	+	0.917815i	$0.370049\pi$
$277$	−2.10950e8	+	3.65375e8i	−0.596348	+	1.03290i	−0.993355	+	0.115089i	$0.963285\pi$
$278$	−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	0.487926	+	0.872885i	$0.337753\pi$
$283$	−1.95211e8	+	3.38115e8i	−0.511977	+	0.886771i	−0.999904	+	0.0138859i	$0.995580\pi$
$284$	−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	−0.193258	+	0.981148i	$0.561906\pi$
$311$	−5.01999e8	+	8.69488e8i	−0.946328	+	1.63909i	−0.753070	+	0.657941i	$0.771428\pi$
$312$		0			0
$313$	1.73099e8	+	2.99817e8i	0.319073	+	0.552650i	0.980295	−	0.197540i	$-0.0632952\pi$
$313$	1.73099e8	+	2.99817e8i	0.319073	+	0.552650i	−0.661222	+	0.750190i	$0.729962\pi$
$314$	4.07758e8			0.743273
$315$		0			0
$316$	4.76897e8			0.850198
$317$	2.01572e8	+	3.49132e8i	0.355404	+	0.615578i	0.987187	−	0.159568i	$-0.0510100\pi$
$317$	2.01572e8	+	3.49132e8i	0.355404	+	0.615578i	−0.631783	+	0.775145i	$0.717677\pi$
$318$		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	0.736623	−	0.676304i	$-0.236419\pi$
$331$	−1.43426e8	−	2.48421e8i	−0.217385	−	0.376521i	−0.954008	+	0.299782i	$0.903086\pi$
$332$	−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	−0.252801	−	0.967518i	$-0.581352\pi$
$347$	5.53764e8	−	9.59148e8i	0.711495	−	1.23234i	0.964296	−	0.264827i	$-0.0853148\pi$
$348$		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	0.473166	+	0.880973i	$0.343111\pi$
$353$	−4.35007e8	+	7.53453e8i	−0.526362	+	0.911685i	−0.999528	+	0.0307123i	$0.990222\pi$
$354$		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	0.542143	−	0.840286i	$-0.317613\pi$
$359$	−4.00315e8	−	6.93366e8i	−0.456638	−	0.790919i	−0.998781	+	0.0493667i	$0.984280\pi$
$360$		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	−0.967238	−	0.253873i	$-0.918296\pi$
$367$	−2.49769e8	+	4.32612e8i	−0.263759	+	0.456844i	0.703479	+	0.710716i	$0.251629\pi$
$368$	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	−0.999855	−	0.0170324i	$-0.994578\pi$
$373$	−5.15842e8	−	8.93464e8i	−0.514678	−	0.891448i	0.485177	−	0.874416i	$-0.338755\pi$
$374$	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	−0.816204	−	0.577763i	$-0.803926\pi$
$383$	−9.98853e8	−	1.73006e9i	−0.908460	−	1.57350i	−0.0922557	−	0.995735i	$-0.529408\pi$
$384$		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	−0.946626	−	0.322333i	$-0.895533\pi$
$389$	−2.25421e8	+	3.90441e8i	−0.194165	+	0.336304i	0.752462	+	0.658636i	$0.228866\pi$
$390$		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	0.992187	−	0.124760i	$-0.0398160\pi$
$397$	4.83785e8	+	8.37940e8i	0.388048	+	0.672119i	−0.604139	+	0.796879i	$0.706483\pi$
$398$	3.21684e7			0.0255763
$399$		0			0
$400$	−1.72094e8			−0.134449
$401$	1.24216e9	+	2.15149e9i	0.961996	+	1.66623i	0.717479	+	0.696580i	$0.245296\pi$
$401$	1.24216e9	+	2.15149e9i	0.961996	+	1.66623i	0.244517	+	0.969645i	$0.421371\pi$
$402$		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	−0.864691	−	0.502303i	$-0.832486\pi$
$409$	3.68300e6	−	6.37914e6i	0.00266176	−	0.00461031i	0.867353	+	0.497693i	$0.165819\pi$
$410$	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	−0.520811	−	0.853672i	$-0.674370\pi$
$431$	7.95998e8	−	1.37871e9i	0.478897	−	0.829473i	0.999707	+	0.0241991i	$0.00770357\pi$
$432$		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	−0.804382	−	0.594113i	$-0.797503\pi$
$439$	−1.62501e9	−	2.81460e9i	−0.916708	−	1.58778i	−0.112326	−	0.993671i	$-0.535830\pi$
$440$	6.08500e8			0.340546
$441$		0			0
$442$	−1.93043e7			−0.0106335
$443$	1.24877e9	+	2.16294e9i	0.682450	+	1.18204i	0.974231	+	0.225552i	$0.0724187\pi$
$443$	1.24877e9	+	2.16294e9i	0.682450	+	1.18204i	−0.291782	+	0.956485i	$0.594248\pi$
$444$		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	0.939543	+	0.342431i	$0.111250\pi$
$457$	1.56358e9	+	2.70820e9i	0.766326	+	1.32731i	−0.173217	+	0.984884i	$0.555416\pi$
$458$	−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	−0.993248	−	0.116013i	$-0.962989\pi$
$467$	−1.31417e9	−	2.27621e9i	−0.597094	−	1.03420i	0.396154	−	0.918184i	$-0.370345\pi$
$468$		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	0.0349039	+	0.999391i	$0.488887\pi$
$479$	−2.03983e9	+	3.53309e9i	−0.848046	+	1.46886i	−0.882950	+	0.469468i	$0.844446\pi$
$480$		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	−0.850810	−	0.525474i	$-0.823888\pi$
$487$	7.56219e7	−	1.30981e8i	0.0296685	−	0.0513874i	0.880478	+	0.474086i	$0.157221\pi$
$488$	−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	0.638054	−	0.769992i	$-0.279740\pi$
$499$	−9.65358e8	−	1.67205e9i	−0.347806	−	0.602417i	−0.985859	+	0.167575i	$0.946406\pi$
$500$	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	−0.964467	−	0.264204i	$-0.914891\pi$
$509$	−2.11547e9	−	3.66410e9i	−0.711041	−	1.23156i	0.253426	−	0.967355i	$-0.418443\pi$
$510$		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	−0.584779	−	0.811192i	$-0.698819\pi$
$521$	1.32387e9	−	2.29302e9i	0.410123	−	0.710355i	0.994903	+	0.100838i	$0.0321523\pi$
$522$		0			0
$523$	−2.30857e9	−	3.99856e9i	−0.705647	−	1.22222i	−0.966458	−	0.256827i	$-0.917323\pi$
$523$	−2.30857e9	−	3.99856e9i	−0.705647	−	1.22222i	0.260810	−	0.965390i	$-0.416010\pi$
$524$	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	0.880493	−	0.474059i	$-0.157212\pi$
$541$	1.09381e8	+	1.89453e8i	0.0296996	+	0.0514412i	−0.850794	+	0.525500i	$0.823878\pi$
$542$	−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	0.244770	−	0.969581i	$-0.421288\pi$
$557$	3.92372e9	−	6.79609e9i	0.962067	−	1.66635i	0.717297	−	0.696768i	$-0.245379\pi$
$558$		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	−0.982421	−	0.186679i	$-0.940227\pi$
$563$	−1.39537e9	+	2.41685e9i	−0.329541	+	0.570782i	0.652880	+	0.757462i	$0.273561\pi$
$564$		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	0.996254	−	0.0864801i	$-0.0275619\pi$
$569$	1.85983e9	+	3.22131e9i	0.423233	+	0.733061i	−0.573021	+	0.819541i	$0.694229\pi$
$570$		0			0
$571$	2.04386e8	−	3.54007e8i	0.0459435	−	0.0795765i	−0.842139	−	0.539260i	$-0.818704\pi$
$571$	2.04386e8	−	3.54007e8i	0.0459435	−	0.0795765i	0.888083	+	0.459684i	$0.152037\pi$
$572$	−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	0.134628	+	0.990896i	$0.457016\pi$
$577$	−3.64920e9	+	6.32059e9i	−0.790828	+	1.36975i	−0.925455	+	0.378857i	$0.876317\pi$
$578$	−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	−0.908581	−	0.417708i	$-0.862833\pi$
$593$	−4.14382e9	−	7.17731e9i	−0.816037	−	1.41342i	0.0925446	−	0.995709i	$-0.470500\pi$
$594$		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	−0.955826	−	0.293935i	$-0.905035\pi$
$599$	−1.17488e9	+	2.03496e9i	−0.223358	+	0.386867i	0.732468	+	0.680802i	$0.238369\pi$
$600$		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	0.999829	+	0.0184920i	$0.00588652\pi$
$607$	2.84283e9	+	4.92392e9i	0.515929	+	0.893615i	−0.483900	+	0.875123i	$0.660780\pi$
$608$	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	−0.973335	−	0.229387i	$-0.926328\pi$
$613$	−1.64257e9	+	2.84502e9i	−0.288013	+	0.498853i	0.685322	+	0.728240i	$0.259661\pi$
$614$	−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	0.102337	+	0.994750i	$0.467368\pi$
$619$	−4.78155e9	+	8.28188e9i	−0.810310	+	1.40350i	−0.912647	+	0.408748i	$0.865965\pi$
$620$	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	0.453359	+	0.891328i	$0.350226\pi$
$641$	−3.63568e9	+	6.29718e9i	−0.545233	+	0.944371i	−0.998592	+	0.0530435i	$0.983108\pi$
$642$		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	−0.339839	−	0.940484i	$-0.610373\pi$
$647$	4.44048e9	−	7.69115e9i	0.644563	−	1.11642i	0.984402	−	0.175932i	$-0.0562940\pi$
$648$		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	0.642675	−	0.766139i	$-0.277824\pi$
$653$	−2.43457e9	−	4.21681e9i	−0.342158	−	0.592635i	−0.984833	+	0.173504i	$0.944491\pi$
$654$		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	−0.637519	−	0.770435i	$-0.720039\pi$
$661$	2.58734e9	−	4.48140e9i	0.348456	−	0.603544i	0.985975	+	0.166891i	$0.0533726\pi$
$662$	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	0.926906	+	0.375293i	$0.122458\pi$
$677$	6.36566e9	+	1.10257e10i	0.788467	+	1.36566i	−0.138440	+	0.990371i	$0.544209\pi$
$678$		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	−0.813959	−	0.580922i	$-0.802692\pi$
$683$	8.00307e8	−	1.38617e9i	0.0961135	−	0.166473i	0.910073	+	0.414448i	$0.136026\pi$
$684$		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	0.955658	−	0.294480i	$-0.0951465\pi$
$691$	1.93237e9	+	3.34697e9i	0.222801	+	0.385903i	−0.732856	+	0.680384i	$0.761813\pi$
$692$	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	0.945192	−	0.326515i	$-0.105874\pi$
$709$	1.80143e9	+	3.12016e9i	0.189826	+	0.328787i	−0.755366	+	0.655303i	$0.772541\pi$
$710$	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	0.997914	−	0.0645520i	$-0.0205618\pi$
$719$	4.41578e9	+	7.64835e9i	0.443053	+	0.767391i	−0.554861	+	0.831943i	$0.687229\pi$
$720$		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	0.998028	−	0.0627676i	$-0.0199927\pi$
$733$	4.74120e9	+	8.21199e9i	0.444656	+	0.770166i	−0.553372	+	0.832934i	$0.686659\pi$
$734$	−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	−0.439314	−	0.898334i	$-0.644778\pi$
$739$	6.12549e9	−	1.06097e10i	0.558323	−	0.967043i	0.997637	−	0.0687097i	$-0.0218882\pi$
$740$	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	−0.871147	−	0.491022i	$-0.836623\pi$
$751$	−9.99189e9	−	1.73065e10i	−0.860811	−	1.49097i	0.0103358	−	0.999947i	$-0.496710\pi$
$752$	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	−0.974276	−	0.225357i	$-0.927645\pi$
$761$	−8.29514e9	−	1.43676e10i	−0.682303	−	1.18178i	0.291973	−	0.956427i	$-0.405688\pi$
$762$		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	−0.970271	−	0.242020i	$-0.922190\pi$
$773$	−3.53844e9	+	6.12877e9i	−0.275540	+	0.477249i	0.694731	+	0.719269i	$0.255523\pi$
$774$		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	−0.952197	−	0.305485i	$-0.901181\pi$
$787$	−2.89271e9	+	5.01033e9i	−0.211541	+	0.366399i	0.740656	+	0.671884i	$0.234515\pi$
$788$	−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	−0.766752	−	0.641943i	$-0.778128\pi$
$809$	2.59877e9	−	4.50120e9i	0.172563	−	0.298888i	0.939315	+	0.343055i	$0.111462\pi$
$810$		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	0.744990	−	0.667075i	$-0.232454\pi$
$821$	−3.25385e9	−	5.63583e9i	−0.205209	−	0.355432i	−0.950199	+	0.311643i	$0.899121\pi$
$822$		0			0
$823$	3.83450e9	−	6.64155e9i	0.239778	−	0.415308i	−0.720872	−	0.693068i	$-0.756259\pi$
$823$	3.83450e9	−	6.64155e9i	0.239778	−	0.415308i	0.960651	+	0.277760i	$0.0895920\pi$
$824$	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	0.406846	+	0.913497i	$0.366628\pi$
$829$	−9.64024e9	+	1.66974e10i	−0.587688	+	1.01791i	−0.994534	+	0.104409i	$0.966705\pi$
$830$	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	−0.488315	−	0.872667i	$-0.662388\pi$
$857$	9.42668e9	−	1.63275e10i	0.511594	−	0.886108i	0.999910	−	0.0134403i	$-0.00427830\pi$
$858$		0			0
$859$	−9.45689e9	−	1.63798e10i	−0.509064	−	0.881725i	−0.999945	−	0.0104981i	$-0.996658\pi$
$859$	−9.45689e9	−	1.63798e10i	−0.509064	−	0.881725i	0.490881	−	0.871227i	$-0.336675\pi$
$860$	3.46321e9			0.185667
$861$		0			0
$862$	1.27360e10			0.677262
$863$	−1.60330e10	−	2.77700e10i	−0.849137	−	1.47075i	−0.881980	−	0.471288i	$-0.843789\pi$
$863$	−1.60330e10	−	2.77700e10i	−0.849137	−	1.47075i	0.0328428	−	0.999461i	$-0.489544\pi$
$864$		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	−0.974924	−	0.222538i	$-0.928566\pi$
$877$	−1.35871e10	−	2.35335e10i	−0.680186	−	1.17812i	0.294738	−	0.955578i	$-0.404767\pi$
$878$	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	0.863412	−	0.504499i	$-0.168323\pi$
$887$	−1.08146e8	−	1.87315e8i	−0.00520330	−	0.00901238i	−0.868615	+	0.495487i	$0.834990\pi$
$888$		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	−0.802244	−	0.596997i	$-0.796360\pi$
$907$	2.60424e9	−	4.51068e9i	0.115893	−	0.200732i	0.918136	+	0.396265i	$0.129694\pi$
$908$	−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	0.999449	+	0.0332005i	$0.0105700\pi$
$919$	1.24346e10	+	2.15373e10i	0.528477	+	0.915349i	−0.470972	+	0.882148i	$0.656097\pi$
$920$	−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	0.974872	−	0.222764i	$-0.0715080\pi$
$929$	7.19722e9	+	1.24660e10i	0.294517	+	0.510118i	−0.680356	+	0.732882i	$0.738175\pi$
$930$		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	−0.105266	−	0.994444i	$-0.533569\pi$
$941$	2.06675e10	−	3.57971e10i	0.808581	−	1.40050i	0.913847	−	0.406059i	$-0.133097\pi$
$942$		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	0.522262	−	0.852785i	$-0.325088\pi$
$947$	−1.24770e10	−	2.16108e10i	−0.477402	−	0.826885i	−0.999665	+	0.0258999i	$0.991755\pi$
$948$		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	0.975020	+	0.222116i	$0.0712965\pi$
$971$	1.93951e10	+	3.35933e10i	0.679869	+	1.17757i	−0.295152	+	0.955450i	$0.595370\pi$
$972$		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	−0.558132	−	0.829752i	$-0.688482\pi$
$977$	1.28118e10	−	2.21907e10i	0.439521	−	0.761272i	0.997652	+	0.0684801i	$0.0218150\pi$
$978$		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	−0.893951	−	0.448165i	$-0.852078\pi$
$983$	−1.75271e9	+	3.03578e9i	−0.0588534	+	0.101937i	0.835098	+	0.550102i	$0.185411\pi$
$984$		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	−0.624654	−	0.780902i	$-0.714760\pi$
$991$	1.11508e10	−	1.93137e10i	0.363954	−	0.630387i	0.988608	+	0.150515i	$0.0480931\pi$
$992$	−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	0.173712	+	0.984796i	$0.444424\pi$
$997$	−2.39697e10	+	4.15168e10i	−0.766002	+	1.32676i	−0.939715	+	0.341959i	$0.888910\pi$
$998$	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.109.2	yes	6
3.2	odd	2		126.8.g.i.109.2	yes	6
7.2	even	3	inner	126.8.g.j.37.2	yes	6
21.2	odd	6		126.8.g.i.37.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.8.g.i.37.2	✓	6	21.2	odd	6
126.8.g.i.109.2	yes	6	3.2	odd	2
126.8.g.j.37.2	yes	6	7.2	even	3	inner
126.8.g.j.109.2	yes	6	1.1	even	1	trivial

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more