LMFDB - Embedded newform 62.8.d.a.33.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,8,Mod(33,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.33"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	62.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,-80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$19.3678715800$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			33.9
Character	$\chi$	$=$	62.33
Dual form			62.8.d.a.47.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.47214 - 4.70228i) q^{2} +(66.2571 - 48.1386i) q^{3} +(19.7771 + 60.8676i) q^{4} +520.167 q^{5} -655.187 q^{6} +(-313.887 - 966.043i) q^{7} +(158.217 - 486.941i) q^{8} +(1396.86 - 4299.10i) q^{9} +(-3366.59 - 2445.97i) q^{10} +(1816.34 + 5590.13i) q^{11} +(4240.46 + 3080.87i) q^{12} +(6729.45 - 4889.23i) q^{13} +(-2511.09 + 7728.35i) q^{14} +(34464.8 - 25040.1i) q^{15} +(-3313.73 + 2407.57i) q^{16} +(-9414.90 + 28976.1i) q^{17} +(-29256.2 + 21255.9i) q^{18} +(2605.78 + 1893.21i) q^{19} +(10287.4 + 31661.3i) q^{20} +(-67301.2 - 48897.2i) q^{21} +(14530.8 - 44721.1i) q^{22} +(-9984.04 + 30727.7i) q^{23} +(-12957.7 - 39879.7i) q^{24} +192449. q^{25} -66544.5 q^{26} +(-59052.0 - 181743. i) q^{27} +(52593.0 - 38211.1i) q^{28} +(-80198.8 - 58267.8i) q^{29} -340807. q^{30} +(-158828. + 47814.3i) q^{31} +32768.0 q^{32} +(389447. + 282950. i) q^{33} +(197188. - 143266. i) q^{34} +(-163273. - 502504. i) q^{35} +289302. q^{36} -114560. q^{37} +(-7962.55 - 24506.2i) q^{38} +(210513. - 647893. i) q^{39} +(82299.1 - 253291. i) q^{40} +(-132162. - 96021.2i) q^{41} +(205654. + 632939. i) q^{42} +(-485237. - 352545. i) q^{43} +(-304336. + 221113. i) q^{44} +(726601. - 2.23625e6i) q^{45} +(209108. - 151926. i) q^{46} +(-559409. + 406435. i) q^{47} +(-103661. + 319037. i) q^{48} +(-168455. + 122390. i) q^{49} +(-1.24555e6 - 904948. i) q^{50} +(771065. + 2.37309e6i) q^{51} +(430685. + 312911. i) q^{52} +(-110961. + 341504. i) q^{53} +(-472416. + 1.45395e6i) q^{54} +(944803. + 2.90780e6i) q^{55} -520068. q^{56} +263788. q^{57} +(245066. + 754235. i) q^{58} +(-278813. + 202570. i) q^{59} +(2.20575e6 + 1.60257e6i) q^{60} -1.59522e6 q^{61} +(1.25279e6 + 437395. i) q^{62} -4.59157e6 q^{63} +(-212079. - 154084. i) q^{64} +(3.50044e6 - 2.54322e6i) q^{65} +(-1.19004e6 - 3.66258e6i) q^{66} +2.74179e6 q^{67} -1.94990e6 q^{68} +(817676. + 2.51655e6i) q^{69} +(-1.30619e6 + 4.02003e6i) q^{70} +(-1.37282e6 + 4.22512e6i) q^{71} +(-1.87240e6 - 1.36038e6i) q^{72} +(-976121. - 3.00419e6i) q^{73} +(741449. + 538694. i) q^{74} +(1.27511e7 - 9.26422e6i) q^{75} +(-63700.4 + 196050. i) q^{76} +(4.83019e6 - 3.50934e6i) q^{77} +(-4.40905e6 + 3.20336e6i) q^{78} +(1.27690e6 - 3.92990e6i) q^{79} +(-1.72370e6 + 1.25234e6i) q^{80} +(-4.66358e6 - 3.38829e6i) q^{81} +(403851. + 1.24293e6i) q^{82} +(3.50488e6 + 2.54645e6i) q^{83} +(1.64523e6 - 5.06351e6i) q^{84} +(-4.89732e6 + 1.50724e7i) q^{85} +(1.48275e6 + 4.56344e6i) q^{86} -8.11868e6 q^{87} +3.00944e6 q^{88} +(-259986. - 800155. i) q^{89} +(-1.52181e7 + 1.10566e7i) q^{90} +(-6.83550e6 - 4.96628e6i) q^{91} -2.06778e6 q^{92} +(-8.22179e6 + 1.08138e7i) q^{93} +5.53174e6 q^{94} +(1.35544e6 + 984784. i) q^{95} +(2.17111e6 - 1.57741e6i) q^{96} +(-1.97459e6 - 6.07716e6i) q^{97} +1.66577e6 q^{98} +2.65697e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) $ 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−6.47214	−	4.70228i	−0.572061	−	0.415627i
$2$	−6.47214	−	4.70228i	−0.572061	−	0.415627i
$3$	66.2571	−	48.1386i	1.41680	−	1.02936i	0.424510	−	0.905423i	$-0.360446\pi$
$3$	66.2571	−	48.1386i	1.41680	−	1.02936i	0.992290	−	0.123942i	$-0.0395535\pi$
$4$	19.7771	+	60.8676i	0.154508	+	0.475528i
$5$	520.167			1.86101			0.930503	−	0.366284i	$-0.119370\pi$
$5$	520.167			1.86101			0.930503	+	0.366284i	$0.119370\pi$
$6$	−655.187			−1.23833
$7$	−313.887	−	966.043i	−0.345883	−	1.06452i	−0.961109	−	0.276168i	$-0.910935\pi$
$7$	−313.887	−	966.043i	−0.345883	−	1.06452i	0.615226	−	0.788351i	$-0.289065\pi$
$8$	158.217	−	486.941i	0.109254	−	0.336249i
$9$	1396.86	−	4299.10i	0.638711	−	1.96575i
$10$	−3366.59	−	2445.97i	−1.06461	−	0.773484i
$11$	1816.34	+	5590.13i	0.411456	+	1.26633i	0.915382	+	0.402586i	$0.131888\pi$
$11$	1816.34	+	5590.13i	0.411456	+	1.26633i	−0.503926	+	0.863747i	$0.668112\pi$
$12$	4240.46	+	3080.87i	0.708400	+	0.514682i
$13$	6729.45	−	4889.23i	0.849529	−	0.617219i	−0.0754874	−	0.997147i	$-0.524051\pi$
$13$	6729.45	−	4889.23i	0.849529	−	0.617219i	0.925016	+	0.379928i	$0.124051\pi$
$14$	−2511.09	+	7728.35i	−0.244576	+	0.752729i
$15$	34464.8	−	25040.1i	2.63667	−	1.91565i
$16$	−3313.73	+	2407.57i	−0.202254	+	0.146946i
$17$	−9414.90	+	28976.1i	−0.464777	+	1.43044i	0.394486	+	0.918902i	$0.370923\pi$
$17$	−9414.90	+	28976.1i	−0.464777	+	1.43044i	−0.859263	+	0.511534i	$0.829077\pi$
$18$	−29256.2	+	21255.9i	−1.18240	+	0.859064i
$19$	2605.78	+	1893.21i	0.0871565	+	0.0633229i	0.630510	−	0.776181i	$-0.282846\pi$
$19$	2605.78	+	1893.21i	0.0871565	+	0.0633229i	−0.543354	+	0.839504i	$0.682846\pi$
$20$	10287.4	+	31661.3i	0.287541	+	0.884961i
$21$	−67301.2	−	48897.2i	−1.58583	−	1.15217i
$22$	14530.8	−	44721.1i	0.290944	−	0.895432i
$23$	−9984.04	+	30727.7i	−0.171104	+	0.526602i	−0.999434	−	0.0336372i	$-0.989291\pi$
$23$	−9984.04	+	30727.7i	−0.171104	+	0.526602i	0.828331	+	0.560240i	$0.189291\pi$
$24$	−12957.7	−	39879.7i	−0.191332	−	0.588860i
$25$	192449.			2.46334
$26$	−66544.5			−0.742515
$27$	−59052.0	−	181743.i	−0.577380	−	1.77699i
$28$	52593.0	−	38211.1i	0.452767	−	0.328955i
$29$	−80198.8	−	58267.8i	−0.610626	−	0.443645i	0.239009	−	0.971017i	$-0.423177\pi$
$29$	−80198.8	−	58267.8i	−0.610626	−	0.443645i	−0.849635	+	0.527372i	$0.823177\pi$
$30$	−340807.			−2.30454
$31$	−158828.	+	47814.3i	−0.957551	+	0.288265i
$31$	−158828.	+	47814.3i	−0.957551	+	0.288265i
$32$	32768.0			0.176777
$33$	389447.	+	282950.i	1.88647	+	1.37060i
$34$	197188.	−	143266.i	0.860409	−	0.625123i
$35$	−163273.	−	502504.i	−0.643691	−	1.98108i
$36$	289302.			1.03346
$37$	−114560.			−0.371816			−0.185908	−	0.982567i	$-0.559523\pi$
$37$	−114560.			−0.371816			−0.185908	+	0.982567i	$0.559523\pi$
$38$	−7962.55	−	24506.2i	−0.0235402	−	0.0724492i
$39$	210513.	−	647893.i	0.568268	−	1.74895i
$40$	82299.1	−	253291.i	0.203322	−	0.625762i
$41$	−132162.	−	96021.2i	−0.299477	−	0.217582i	0.427891	−	0.903830i	$-0.359257\pi$
$41$	−132162.	−	96021.2i	−0.299477	−	0.217582i	−0.727368	+	0.686248i	$0.759257\pi$
$42$	205654.	+	632939.i	0.428317	+	1.31822i
$43$	−485237.	−	352545.i	−0.930710	−	0.676200i	0.0154567	−	0.999881i	$-0.495080\pi$
$43$	−485237.	−	352545.i	−0.930710	−	0.676200i	−0.946167	+	0.323680i	$0.895080\pi$
$44$	−304336.	+	221113.i	−0.538603	+	0.391318i
$45$	726601.	−	2.23625e6i	1.18865	−	3.65827i
$46$	209108.	−	151926.i	0.316752	−	0.230134i
$47$	−559409.	+	406435.i	−0.785936	+	0.571016i	−0.906755	−	0.421659i	$-0.861448\pi$
$47$	−559409.	+	406435.i	−0.785936	+	0.571016i	0.120819	+	0.992675i	$0.461448\pi$
$48$	−103661.	+	319037.i	−0.135292	+	0.416387i
$49$	−168455.	+	122390.i	−0.204549	+	0.148614i
$50$	−1.24555e6	−	904948.i	−1.40918	−	1.02383i
$51$	771065.	+	2.37309e6i	0.813945	+	2.50507i
$52$	430685.	+	312911.i	0.424764	+	0.308609i
$53$	−110961.	+	341504.i	−0.102378	+	0.315087i	−0.989106	−	0.147204i	$-0.952972\pi$
$53$	−110961.	+	341504.i	−0.102378	+	0.315087i	0.886728	+	0.462291i	$0.152972\pi$
$54$	−472416.	+	1.45395e6i	−0.408269	+	1.25652i
$55$	944803.	+	2.90780e6i	0.765723	+	2.35665i
$56$	−520068.			−0.395733
$57$	263788.			0.188666
$58$	245066.	+	754235.i	0.164924	+	0.507585i
$59$	−278813.	+	202570.i	−0.176739	+	0.128408i	−0.672638	−	0.739972i	$-0.734839\pi$
$59$	−278813.	+	202570.i	−0.176739	+	0.128408i	0.495899	+	0.868380i	$0.334839\pi$
$60$	2.20575e6	+	1.60257e6i	1.31834	+	0.957827i
$61$	−1.59522e6			−0.899844			−0.449922	−	0.893068i	$-0.648548\pi$
$61$	−1.59522e6			−0.899844			−0.449922	+	0.893068i	$0.648548\pi$
$62$	1.25279e6	+	437395.i	0.667588	+	0.233079i
$63$	−4.59157e6			−2.31350
$64$	−212079.	−	154084.i	−0.101127	−	0.0734732i
$65$	3.50044e6	−	2.54322e6i	1.58098	−	1.14865i
$66$	−1.19004e6	−	3.66258e6i	−0.509518	−	1.56814i
$67$	2.74179e6			1.11371			0.556855	−	0.830610i	$-0.312008\pi$
$67$	2.74179e6			1.11371			0.556855	+	0.830610i	$0.312008\pi$
$68$	−1.94990e6			−0.752025
$69$	817676.	+	2.51655e6i	0.299647	+	0.922218i
$70$	−1.30619e6	+	4.02003e6i	−0.455158	+	1.40083i
$71$	−1.37282e6	+	4.22512e6i	−0.455209	+	1.40099i	0.415680	+	0.909511i	$0.363543\pi$
$71$	−1.37282e6	+	4.22512e6i	−0.455209	+	1.40099i	−0.870890	+	0.491479i	$0.836457\pi$
$72$	−1.87240e6	−	1.36038e6i	−0.591200	−	0.429532i
$73$	−976121.	−	3.00419e6i	−0.293680	−	0.903853i	−0.983662	−	0.180026i	$-0.942382\pi$
$73$	−976121.	−	3.00419e6i	−0.293680	−	0.903853i	0.689982	−	0.723826i	$-0.257618\pi$
$74$	741449.	+	538694.i	0.212701	+	0.154537i
$75$	1.27511e7	−	9.26422e6i	3.49006	−	2.53568i
$76$	−63700.4	+	196050.i	−0.0166454	+	0.0512293i
$77$	4.83019e6	−	3.50934e6i	1.20572	−	0.876006i
$78$	−4.40905e6	+	3.20336e6i	−1.05200	+	0.764319i
$79$	1.27690e6	−	3.92990e6i	0.291382	−	0.896781i	−0.693031	−	0.720908i	$-0.743725\pi$
$79$	1.27690e6	−	3.92990e6i	0.291382	−	0.896781i	0.984413	−	0.175874i	$-0.0562750\pi$
$80$	−1.72370e6	+	1.25234e6i	−0.376396	+	0.273468i
$81$	−4.66358e6	−	3.38829e6i	−0.975039	−	0.708407i
$82$	403851.	+	1.24293e6i	0.0808858	+	0.248941i
$83$	3.50488e6	+	2.54645e6i	0.672822	+	0.488834i	0.870969	−	0.491339i	$-0.163492\pi$
$83$	3.50488e6	+	2.54645e6i	0.672822	+	0.488834i	−0.198147	+	0.980172i	$0.563492\pi$
$84$	1.64523e6	−	5.06351e6i	0.302866	−	0.932125i
$85$	−4.89732e6	+	1.50724e7i	−0.864953	+	2.66205i
$86$	1.48275e6	+	4.56344e6i	0.251376	+	0.773656i
$87$	−8.11868e6			−1.32181
$88$	3.00944e6			0.470757
$89$	−259986.	−	800155.i	−0.0390918	−	0.120312i	0.929606	−	0.368554i	$-0.120147\pi$
$89$	−259986.	−	800155.i	−0.0390918	−	0.120312i	−0.968698	+	0.248242i	$0.920147\pi$
$90$	−1.52181e7	+	1.10566e7i	−2.20046	+	1.59872i
$91$	−6.83550e6	−	4.96628e6i	−0.950879	−	0.690854i
$92$	−2.06778e6			−0.276851
$93$	−8.22179e6	+	1.08138e7i	−1.05993	+	1.39408i
$94$	5.53174e6			0.686933
$95$	1.35544e6	+	984784.i	0.162199	+	0.117844i
$96$	2.17111e6	−	1.57741e6i	0.250457	−	0.181968i
$97$	−1.97459e6	−	6.07716e6i	−0.219673	−	0.676083i	−0.998789	−	0.0492031i	$-0.984332\pi$
$97$	−1.97459e6	−	6.07716e6i	−0.219673	−	0.676083i	0.779116	−	0.626879i	$-0.215668\pi$
$98$	1.66577e6			0.178782
$99$	2.65697e7			2.75210
$100$	3.80608e6	+	1.17139e7i	0.380608	+	1.17139i
$101$	3.82643e6	−	1.17766e7i	0.369547	−	1.13735i	−0.577538	−	0.816364i	$-0.695986\pi$
$101$	3.82643e6	−	1.17766e7i	0.369547	−	1.13735i	0.947085	−	0.320984i	$-0.104014\pi$
$102$	6.16852e6	−	1.89847e7i	0.575546	−	1.77135i
$103$	1.58521e6	+	1.15172e6i	0.142941	+	0.103853i	0.656957	−	0.753928i	$-0.271843\pi$
$103$	1.58521e6	+	1.15172e6i	0.142941	+	0.103853i	−0.514017	+	0.857780i	$0.671843\pi$
$104$	−1.31606e6	−	4.05040e6i	−0.114725	−	0.353087i
$105$	−3.50079e7	−	2.54347e7i	−2.95123	−	2.14420i
$106$	2.32400e6	−	1.68849e6i	0.189525	−	0.137698i
$107$	−7.35188e6	+	2.26268e7i	−0.580170	+	1.78558i	0.0376877	+	0.999290i	$0.488001\pi$
$107$	−7.35188e6	+	2.26268e7i	−0.580170	+	1.78558i	−0.617858	+	0.786290i	$0.711999\pi$
$108$	9.89442e6	−	7.18871e6i	0.755800	−	0.549121i
$109$	1.67037e7	−	1.21359e7i	1.23543	−	0.897595i	0.238148	−	0.971229i	$-0.423460\pi$
$109$	1.67037e7	−	1.21359e7i	1.23543	−	0.897595i	0.997285	+	0.0736339i	$0.0234596\pi$
$110$	7.55842e6	−	2.32624e7i	0.541448	−	1.66641i
$111$	−7.59043e6	+	5.51477e6i	−0.526788	+	0.382734i
$112$	3.36595e6	+	2.44551e6i	0.226384	+	0.164477i
$113$	7.23229e6	+	2.22587e7i	0.471521	+	1.45119i	0.850593	+	0.525825i	$0.176243\pi$
$113$	7.23229e6	+	2.22587e7i	0.471521	+	1.45119i	−0.379072	+	0.925367i	$0.623757\pi$
$114$	−1.70727e6	−	1.24040e6i	−0.107928	−	0.0784145i
$115$	−5.19337e6	+	1.59835e7i	−0.318425	+	0.980010i
$116$	1.96053e6	−	6.03388e6i	0.116619	−	0.358917i
$117$	−1.16192e7	−	3.57601e7i	−0.670695	−	2.06419i
$118$	2.75706e6			0.154475
$119$	3.09474e7			1.68349
$120$	−6.74016e6	−	2.07441e7i	−0.356070	−	1.09587i
$121$	−1.21850e7	+	8.85294e6i	−0.625285	+	0.454296i
$122$	1.03245e7	+	7.50119e6i	0.514766	+	0.373999i
$123$	−1.33790e7			−0.648270
$124$	−6.05150e6	−	8.72187e6i	−0.285028	−	0.410803i
$125$	5.94675e7			2.72329
$126$	2.97173e7	+	2.15909e7i	1.32346	+	0.961552i
$127$	−2.20656e7	+	1.60316e7i	−0.955879	+	0.694487i	−0.952190	−	0.305506i	$-0.901174\pi$
$127$	−2.20656e7	+	1.60316e7i	−0.955879	+	0.694487i	−0.00368903	+	0.999993i	$0.501174\pi$
$128$	648056.	+	1.99451e6i	0.0273135	+	0.0840623i
$129$	−4.91215e7			−2.01469
$130$	−3.46143e7			−1.38183
$131$	6.33357e6	+	1.94927e7i	0.246150	+	0.757570i	0.995445	+	0.0953349i	$0.0303922\pi$
$131$	6.33357e6	+	1.94927e7i	0.246150	+	0.757570i	−0.749296	+	0.662236i	$0.769608\pi$
$132$	−9.52036e6	+	2.93006e7i	−0.360284	+	1.10884i
$133$	1.01100e6	−	3.11155e6i	0.0372625	−	0.114682i
$134$	−1.77452e7	−	1.28927e7i	−0.637111	−	0.462888i
$135$	−3.07169e7	−	9.45370e7i	−1.07451	−	3.30700i
$136$	1.26200e7	+	9.16900e6i	0.430204	+	0.312562i
$137$	2.03161e7	−	1.47605e7i	0.675022	−	0.490432i	−0.196681	−	0.980468i	$-0.563016\pi$
$137$	2.03161e7	−	1.47605e7i	0.675022	−	0.490432i	0.871702	+	0.490036i	$0.163016\pi$
$138$	6.54141e6	−	2.01324e7i	0.211882	−	0.652107i
$139$	5.19990e6	−	3.77795e6i	0.164226	−	0.119317i	−0.502637	−	0.864498i	$-0.667637\pi$
$139$	5.19990e6	−	3.77795e6i	0.164226	−	0.119317i	0.666863	+	0.745180i	$0.267637\pi$
$140$	2.73571e7	−	1.98761e7i	0.842602	−	0.612186i
$141$	−1.74997e7	+	5.38584e7i	−0.525730	+	1.61803i
$142$	2.87528e7	−	2.08901e7i	0.842697	−	0.612255i
$143$	3.95545e7	+	2.87380e7i	1.13115	+	0.821827i
$144$	5.72154e6	+	1.76091e7i	0.159678	+	0.491438i
$145$	−4.17168e7	−	3.03090e7i	−1.13638	−	0.825627i
$146$	−7.80897e6	+	2.40335e7i	−0.207663	+	0.639120i
$147$	−5.26967e6	+	1.62184e7i	−0.136827	+	0.421111i
$148$	−2.26567e6	−	6.97301e6i	−0.0574487	−	0.176809i
$149$	−1.13185e7			−0.280309			−0.140154	−	0.990130i	$-0.544760\pi$
$149$	−1.13185e7			−0.280309			−0.140154	+	0.990130i	$0.544760\pi$
$150$	−1.26090e8			−3.05043
$151$	−3.84165e6	−	1.18234e7i	−0.0908026	−	0.279462i	0.895334	−	0.445394i	$-0.146937\pi$
$151$	−3.84165e6	−	1.18234e7i	−0.0908026	−	0.279462i	−0.986137	+	0.165933i	$0.946937\pi$
$152$	1.33416e6	−	969322.i	0.0308145	−	0.0223880i
$153$	1.11420e8	+	8.09511e7i	2.51502	+	1.82727i
$154$	−4.77635e7			−1.05384
$155$	−8.26172e7	+	2.48714e7i	−1.78201	+	0.536463i
$156$	4.35991e7			0.919477
$157$	−1.90617e7	−	1.38491e7i	−0.393109	−	0.285610i	0.373619	−	0.927582i	$-0.378117\pi$
$157$	−1.90617e7	−	1.38491e7i	−0.393109	−	0.285610i	−0.766728	+	0.641972i	$0.778117\pi$
$158$	−2.67438e7	+	1.94305e7i	−0.539415	+	0.391908i
$159$	9.08755e6	+	2.79686e7i	0.179290	+	0.551799i
$160$	1.70448e7			0.328983
$161$	3.28182e7			0.619760
$162$	1.42506e7	+	4.38589e7i	0.263349	+	0.810505i
$163$	−3.09802e7	+	9.53473e7i	−0.560309	+	1.72445i	0.121184	+	0.992630i	$0.461331\pi$
$163$	−3.09802e7	+	9.53473e7i	−0.560309	+	1.72445i	−0.681493	+	0.731825i	$0.738669\pi$
$164$	3.23081e6	−	9.94340e6i	0.0571949	−	0.176028i
$165$	2.02578e8	+	1.47181e8i	3.51073	+	2.55070i
$166$	−1.07100e7	−	3.29619e7i	−0.181723	−	0.559286i
$167$	−6.79416e7	−	4.93625e7i	−1.12883	−	0.820142i	−0.143305	−	0.989679i	$-0.545773\pi$
$167$	−6.79416e7	−	4.93625e7i	−1.12883	−	0.820142i	−0.985524	+	0.169536i	$0.945773\pi$
$168$	−3.44582e7	+	2.50354e7i	−0.560674	+	0.407354i
$169$	1.99057e6	−	6.12635e6i	0.0317230	−	0.0976334i
$170$	1.02571e8	−	7.45221e7i	1.60123	−	1.16336i
$171$	1.17790e7	−	8.55794e6i	0.180145	−	0.130883i
$172$	1.18620e7	−	3.65075e7i	0.177750	−	0.547058i
$173$	−2.13251e7	+	1.54936e7i	−0.313133	+	0.227505i	−0.733240	−	0.679970i	$-0.761993\pi$
$173$	−2.13251e7	+	1.54936e7i	−0.313133	+	0.227505i	0.420106	+	0.907475i	$0.361993\pi$
$174$	5.25452e7	+	3.81763e7i	0.756155	+	0.549378i
$175$	−6.04071e7	−	1.85914e8i	−0.852030	−	2.62228i
$176$	−1.94775e7	−	1.41512e7i	−0.269302	−	0.195659i
$177$	−8.72194e6	+	2.68434e7i	−0.118224	+	0.363857i
$178$	−2.07989e6	+	6.40124e6i	−0.0276420	+	0.0850735i
$179$	−6.62804e6	−	2.03990e7i	−0.0863773	−	0.265842i	0.898533	−	0.438905i	$-0.144634\pi$
$179$	−6.62804e6	−	2.03990e7i	−0.0863773	−	0.265842i	−0.984911	+	0.173063i	$0.944634\pi$
$180$	1.50485e8			1.92327
$181$	1.04688e8			1.31227			0.656136	−	0.754643i	$-0.272190\pi$
$181$	1.04688e8			1.31227			0.656136	+	0.754643i	$0.272190\pi$
$182$	2.08874e7	+	6.42849e7i	0.256824	+	0.790422i
$183$	−1.05695e8	+	7.67919e7i	−1.27490	+	0.926268i
$184$	1.33829e7	+	9.72328e6i	0.158376	+	0.115067i
$185$	−5.95905e7			−0.691952
$186$	1.04062e8	−	3.13273e7i	1.18576	−	0.356966i
$187$	−1.79081e8			−2.00264
$188$	−3.58022e7	−	2.60118e7i	−0.392968	−	0.285508i
$189$	−1.57036e8	+	1.14094e8i	−1.69194	+	1.22926i
$190$	−4.14185e6	−	1.27473e7i	−0.0438084	−	0.134828i
$191$	8.58321e7			0.891318			0.445659	−	0.895203i	$-0.352969\pi$
$191$	8.58321e7			0.891318			0.445659	+	0.895203i	$0.352969\pi$
$192$	−2.14692e7			−0.218908
$193$	3.85387e7	+	1.18610e8i	0.385874	+	1.18760i	0.935844	+	0.352415i	$0.114639\pi$
$193$	3.85387e7	+	1.18610e8i	0.385874	+	1.18760i	−0.549969	+	0.835185i	$0.685361\pi$
$194$	−1.57967e7	+	4.86173e7i	−0.155332	+	0.478063i
$195$	1.09502e8	−	3.37013e8i	1.05755	−	3.25481i
$196$	−1.07811e7	−	7.83294e6i	−0.102274	−	0.0743068i
$197$	−3.05266e7	−	9.39511e7i	−0.284476	−	0.875528i	−0.986555	−	0.163429i	$-0.947745\pi$
$197$	−3.05266e7	−	9.39511e7i	−0.284476	−	0.875528i	0.702079	−	0.712099i	$-0.252255\pi$
$198$	−1.71963e8	−	1.24938e8i	−1.57437	−	1.14384i
$199$	5.12068e7	−	3.72039e7i	0.460619	−	0.334660i	−0.333155	−	0.942872i	$-0.608113\pi$
$199$	5.12068e7	−	3.72039e7i	0.460619	−	0.334660i	0.793774	+	0.608213i	$0.208113\pi$
$200$	3.04486e7	−	9.37112e7i	0.269130	−	0.828298i
$201$	1.81663e8	−	1.31986e8i	1.57790	−	1.14641i
$202$	−8.01419e7	+	5.82265e7i	−0.684116	+	0.497039i
$203$	−3.11159e7	+	9.57650e7i	−0.261064	+	0.803472i
$204$	−1.29195e8	+	9.38657e7i	−1.06547	+	0.774108i
$205$	−6.87463e7	−	4.99471e7i	−0.557328	−	0.404922i
$206$	−4.84397e6	−	1.49082e7i	−0.0386070	−	0.118820i
$207$	1.18155e8	+	8.58447e7i	0.925883	+	0.672694i
$208$	−1.05284e7	+	3.24032e7i	−0.0811228	+	0.249670i
$209$	−5.85030e6	+	1.80054e7i	−0.0443267	+	0.136424i
$210$	1.06975e8	+	3.29234e8i	0.797100	+	2.45322i
$211$	5.72260e7			0.419377			0.209689	−	0.977768i	$-0.432755\pi$
$211$	5.72260e7			0.419377			0.209689	+	0.977768i	$0.432755\pi$
$212$	−2.29810e7			−0.165651
$213$	1.12432e8	+	3.46030e8i	0.797190	+	2.45350i
$214$	1.53980e8	−	1.11873e8i	1.07403	−	0.780327i
$215$	−2.52404e8	−	1.83382e8i	−1.73206	−	1.25841i
$216$	−9.78414e7			−0.660594
$217$	9.60447e7	+	1.38427e8i	0.638064	+	0.919625i
$218$	−1.65175e8			−1.07981
$219$	−2.09293e8	−	1.52060e8i	−1.34648	−	0.978275i
$220$	−1.58306e8	+	1.15016e8i	−1.00234	+	0.728246i
$221$	7.83137e7	+	2.41025e8i	0.488051	+	1.50207i
$222$	7.50583e7			0.460430
$223$	−2.58560e8			−1.56133			−0.780666	−	0.624949i	$-0.785120\pi$
$223$	−2.58560e8			−1.56133			−0.780666	+	0.624949i	$0.785120\pi$
$224$	−1.02854e7	−	3.16553e7i	−0.0611441	−	0.188182i
$225$	2.68824e8	−	8.27356e8i	1.57337	−	4.84232i
$226$	5.78583e7	−	1.78070e8i	0.333416	−	1.02615i
$227$	−3.91850e7	−	2.84696e7i	−0.222346	−	0.161544i	0.471036	−	0.882114i	$-0.343880\pi$
$227$	−3.91850e7	−	2.84696e7i	−0.222346	−	0.161544i	−0.693382	+	0.720570i	$0.743880\pi$
$228$	5.21695e6	+	1.60561e7i	0.0291504	+	0.0897158i
$229$	1.85159e8	+	1.34526e8i	1.01887	+	0.740255i	0.966052	−	0.258349i	$-0.0831783\pi$
$229$	1.85159e8	+	1.34526e8i	1.01887	+	0.740255i	0.0528223	+	0.998604i	$0.483178\pi$
$230$	1.08771e8	−	7.90270e7i	0.589477	−	0.428280i
$231$	1.51100e8	−	4.65037e8i	0.806532	−	2.48225i
$232$	−4.10618e7	+	2.98331e7i	−0.215889	+	0.156852i
$233$	2.56590e8	−	1.86424e8i	1.32891	−	0.965507i	0.329131	−	0.944284i	$-0.393244\pi$
$233$	2.56590e8	−	1.86424e8i	1.32891	−	0.965507i	0.999775	−	0.0212227i	$-0.00675589\pi$
$234$	−9.29534e7	+	2.86081e8i	−0.474253	+	1.45960i
$235$	−2.90986e8	+	2.11414e8i	−1.46263	+	1.06266i
$236$	−1.78440e7	−	1.29645e7i	−0.0883693	−	0.0642040i
$237$	−1.04576e8	−	3.21852e8i	−0.510286	−	1.57050i
$238$	−2.00296e8	−	1.45523e8i	−0.963057	−	0.699702i
$239$	7.56441e7	−	2.32809e8i	0.358412	−	1.10308i	−0.595593	−	0.803287i	$-0.703083\pi$
$239$	7.56441e7	−	2.32809e8i	0.358412	−	1.10308i	0.954005	−	0.299792i	$-0.0969173\pi$
$240$	−5.39213e7	+	1.65953e8i	−0.251780	+	0.774899i
$241$	−6.04992e7	−	1.86197e8i	−0.278413	−	0.856868i	−0.988296	−	0.152548i	$-0.951252\pi$
$241$	−6.04992e7	−	1.86197e8i	−0.278413	−	0.856868i	0.709883	−	0.704320i	$-0.248748\pi$
$242$	1.20492e8			0.546519
$243$	−5.41752e7			−0.242202
$244$	−3.15489e7	−	9.70974e7i	−0.139033	−	0.427901i
$245$	−8.76247e7	+	6.36631e7i	−0.380667	+	0.276571i
$246$	8.65907e7	+	6.29118e7i	0.370850	+	0.269438i
$247$	2.67918e7			0.113126
$248$	−1.84655e6	+	8.49050e7i	−0.00768740	+	0.353470i
$249$	3.54806e8			1.45644
$250$	−3.84882e8	−	2.79633e8i	−1.55789	−	1.13187i
$251$	2.79688e8	−	2.03205e8i	1.11639	−	0.811105i	0.132732	−	0.991152i	$-0.457625\pi$
$251$	2.79688e8	−	2.03205e8i	1.11639	−	0.811105i	0.983658	+	0.180047i	$0.0576250\pi$
$252$	−9.08079e7	−	2.79478e8i	−0.357455	−	1.10013i
$253$	−1.89906e8			−0.737255
$254$	2.18197e8			0.835469
$255$	4.01082e8	+	1.23440e9i	1.51476	+	4.66194i
$256$	5.18444e6	−	1.59561e7i	0.0193136	−	0.0594410i
$257$	−111971.	+	344610.i	−0.000411470	+	0.00126637i	−0.951262	−	0.308384i	$-0.900212\pi$
$257$	−111971.	+	344610.i	−0.000411470	+	0.00126637i	0.950851	+	0.309650i	$0.100212\pi$
$258$	3.17921e8	+	2.30983e8i	1.15252	+	0.837358i
$259$	3.59589e7	+	1.10670e8i	0.128605	+	0.395805i
$260$	2.24028e8	+	1.62766e8i	0.790489	+	0.574324i
$261$	−3.62526e8	+	2.63390e8i	−1.26211	+	0.916976i
$262$	5.06686e7	−	1.55942e8i	0.174054	−	0.535683i
$263$	1.56680e8	−	1.13834e8i	0.531089	−	0.385859i	−0.289676	−	0.957125i	$-0.593547\pi$
$263$	1.56680e8	−	1.13834e8i	0.531089	−	0.385859i	0.820765	+	0.571266i	$0.193547\pi$
$264$	1.99397e8	−	1.44870e8i	0.666968	−	0.484580i
$265$	−5.77184e7	+	1.77639e8i	−0.190526	+	0.586378i
$266$	−2.11747e7	+	1.53843e7i	−0.0689814	+	0.0501179i
$267$	−5.57443e7	−	4.05006e7i	−0.179230	−	0.130218i
$268$	5.42246e7	+	1.66886e8i	0.172078	+	0.529601i
$269$	−1.92425e8	−	1.39805e8i	−0.602739	−	0.437915i	0.244111	−	0.969747i	$-0.421504\pi$
$269$	−1.92425e8	−	1.39805e8i	−0.602739	−	0.437915i	−0.846850	+	0.531832i	$0.821504\pi$
$270$	−2.45735e8	+	7.56296e8i	−0.759792	+	2.33840i
$271$	1.33718e8	−	4.11541e8i	0.408129	−	1.25609i	−0.510126	−	0.860100i	$-0.670401\pi$
$271$	1.33718e8	−	4.11541e8i	0.408129	−	1.25609i	0.918254	−	0.395991i	$-0.129599\pi$
$272$	−3.85634e7	−	1.18686e8i	−0.116194	−	0.357609i
$273$	−6.91970e8			−2.05835
$274$	−2.00896e8			−0.589991
$275$	3.49553e8	+	1.07581e9i	1.01356	+	3.11941i
$276$	−1.37005e8	+	9.95400e7i	−0.392243	+	0.284981i
$277$	1.98468e8	+	1.44195e8i	0.561062	+	0.407635i	0.831847	−	0.555004i	$-0.187283\pi$
$277$	1.98468e8	+	1.44195e8i	0.561062	+	0.407635i	−0.270786	+	0.962640i	$0.587283\pi$
$278$	−5.14194e7			−0.143539
$279$	−1.63028e7	+	7.49608e8i	−0.0449414	+	2.06642i
$280$	−2.70522e8			−0.736461
$281$	5.36952e7	+	3.90118e7i	0.144365	+	0.104888i	0.657624	−	0.753347i	$-0.271562\pi$
$281$	5.36952e7	+	3.90118e7i	0.144365	+	0.104888i	−0.513258	+	0.858234i	$0.671562\pi$
$282$	3.66518e8	−	2.66291e8i	0.973246	−	0.707105i
$283$	5.47726e7	+	1.68573e8i	0.143652	+	0.442114i	0.996835	−	0.0794966i	$-0.0253313\pi$
$283$	5.47726e7	+	1.68573e8i	0.143652	+	0.442114i	−0.853183	+	0.521611i	$0.825331\pi$
$284$	−2.84324e8			−0.736544
$285$	1.37214e8			0.351108
$286$	−1.20868e8	−	3.71993e8i	−0.305513	−	0.940271i
$287$	−5.12768e7	+	1.57814e8i	−0.128037	+	0.394057i
$288$	4.57723e7	−	1.40873e8i	0.112909	−	0.347499i
$289$	−4.19002e8	−	3.04423e8i	−1.02111	−	0.741882i
$290$	1.27475e8	+	3.92328e8i	0.306925	+	0.944619i
$291$	−4.23377e8	−	3.07601e8i	−1.00717	−	0.731750i
$292$	1.63553e8	−	1.18828e8i	0.384432	−	0.279306i
$293$	2.46052e7	−	7.57270e7i	0.0571466	−	0.175879i	−0.918409	−	0.395633i	$-0.870525\pi$
$293$	2.46052e7	−	7.57270e7i	0.0571466	−	0.175879i	0.975555	+	0.219754i	$0.0705253\pi$
$294$	1.10369e8	−	8.01881e7i	0.253299	−	0.184032i
$295$	−1.45029e8	+	1.05370e8i	−0.328912	+	0.238968i
$296$	−1.81253e7	+	5.57841e7i	−0.0406224	+	0.125023i
$297$	9.08712e8	−	6.60218e8i	2.01270	−	1.46231i
$298$	7.32549e7	+	5.32228e7i	0.160354	+	0.116504i
$299$	8.30479e7	+	2.55595e8i	0.179672	+	0.552972i
$300$	8.16071e8	+	5.92910e8i	1.74503	+	1.26784i
$301$	−1.88265e8	+	5.79419e8i	−0.397911	+	1.22464i
$302$	−3.07332e7	+	9.45871e7i	−0.0642072	+	0.197609i
$303$	−3.13379e8	−	9.64480e8i	−0.647173	−	1.99179i
$304$	−1.31929e7			−0.0269328
$305$	−8.29783e8			−1.67461
$306$	−3.40468e8	−	1.04785e9i	−0.679284	−	2.09062i
$307$	−1.78326e8	+	1.29562e8i	−0.351747	+	0.255559i	−0.749602	−	0.661889i	$-0.769755\pi$
$307$	−1.78326e8	+	1.29562e8i	−0.351747	+	0.255559i	0.397854	+	0.917449i	$0.369755\pi$
$308$	3.09132e8	+	2.24597e8i	0.602860	+	0.438003i
$309$	1.60474e8			0.309421
$310$	6.51662e8	+	2.27518e8i	1.24239	+	0.433761i
$311$	1.54615e8			0.291468			0.145734	−	0.989324i	$-0.453446\pi$
$311$	1.54615e8			0.291468			0.145734	+	0.989324i	$0.453446\pi$
$312$	−2.82179e8	−	2.05015e8i	−0.525998	−	0.382160i
$313$	−2.44234e8	+	1.77446e8i	−0.450195	+	0.327086i	−0.789673	−	0.613528i	$-0.789750\pi$
$313$	−2.44234e8	+	1.77446e8i	−0.450195	+	0.327086i	0.339478	+	0.940614i	$0.389750\pi$
$314$	5.82474e7	+	1.79267e8i	0.106175	+	0.326773i
$315$	−2.38838e9			−4.30544
$316$	2.64457e8			0.471466
$317$	2.51395e7	+	7.73715e7i	0.0443251	+	0.136419i	0.970770	−	0.240012i	$-0.0771513\pi$
$317$	2.51395e7	+	7.73715e7i	0.0443251	+	0.136419i	−0.926445	+	0.376431i	$0.877151\pi$
$318$	7.27004e7	−	2.23749e8i	0.126777	−	0.390181i
$319$	1.80056e8	−	5.54157e8i	0.310557	−	0.955796i
$320$	−1.10316e8	−	8.01496e7i	−0.188198	−	0.136734i
$321$	6.02107e8	+	1.85309e9i	1.01603	+	3.12701i
$322$	−2.12404e8	−	1.54320e8i	−0.354541	−	0.257589i
$323$	−7.93909e7	+	5.76808e7i	−0.131088	+	0.0952408i
$324$	1.14005e8	−	3.50871e8i	0.186216	−	0.573113i
$325$	1.29508e9	−	9.40927e8i	2.09268	−	1.52042i
$326$	6.48858e8	−	4.71423e8i	1.03726	−	0.753614i
$327$	5.22531e8	−	1.60818e9i	0.826408	−	2.54342i
$328$	−6.76669e7	+	4.91629e7i	−0.105881	+	0.0769270i
$329$	5.68225e8	+	4.12839e8i	0.879700	+	0.639139i
$330$	−6.19022e8	−	1.90515e9i	−0.948216	−	2.91831i
$331$	−7.18710e8	−	5.22174e8i	−1.08932	−	0.791438i	−0.110037	−	0.993928i	$-0.535097\pi$
$331$	−7.18710e8	−	5.22174e8i	−1.08932	−	0.791438i	−0.979284	+	0.202489i	$0.935097\pi$
$332$	−8.56798e7	+	2.63695e8i	−0.128498	+	0.395475i
$333$	−1.60025e8	+	4.92505e8i	−0.237483	+	0.730897i
$334$	2.07611e8	+	6.38961e8i	0.304886	+	0.938344i
$335$	1.42619e9			2.07262
$336$	3.40742e8			0.490047
$337$	−9.37215e7	−	2.88445e8i	−0.133393	−	0.410543i	0.861943	−	0.507005i	$-0.169247\pi$
$337$	−9.37215e7	−	2.88445e8i	−0.133393	−	0.410543i	−0.995337	+	0.0964620i	$0.969247\pi$
$338$	−4.16911e7	+	3.02904e7i	−0.0587266	+	0.0426674i
$339$	1.55069e9	+	1.12664e9i	2.16186	+	1.57068i
$340$	−1.01428e9			−1.39952
$341$	−5.55775e8	−	8.01024e8i	−0.759030	−	1.09397i
$342$	−1.16477e8			−0.157452
$343$	−5.05650e8	−	3.67376e8i	−0.676582	−	0.491566i
$344$	−2.48441e8	+	1.80503e8i	−0.329056	+	0.239073i
$345$	4.25328e8	+	1.30903e9i	0.557644	+	1.71625i
$346$	2.10874e8			0.273689
$347$	2.41612e7			0.0310432			0.0155216	−	0.999880i	$-0.495059\pi$
$347$	2.41612e7			0.0310432			0.0155216	+	0.999880i	$0.495059\pi$
$348$	−1.60564e8	−	4.94165e8i	−0.204230	−	0.628556i
$349$	−2.90931e8	+	8.95395e8i	−0.366355	+	1.12752i	0.582774	+	0.812634i	$0.301967\pi$
$349$	−2.90931e8	+	8.95395e8i	−0.366355	+	1.12752i	−0.949128	+	0.314889i	$0.898033\pi$
$350$	−4.83257e8	+	1.48731e9i	−0.602476	+	1.85423i
$351$	−1.28597e9	−	9.34315e8i	−1.58729	−	1.15324i
$352$	5.95180e7	+	1.83177e8i	0.0727359	+	0.223858i
$353$	−6.30877e7	−	4.58359e7i	−0.0763367	−	0.0554618i	0.548962	−	0.835847i	$-0.315023\pi$
$353$	−6.30877e7	−	4.58359e7i	−0.0763367	−	0.0554618i	−0.625299	+	0.780385i	$0.715023\pi$
$354$	1.82675e8	−	1.32721e8i	0.218860	−	0.159011i
$355$	−7.14098e8	+	2.19777e9i	−0.847147	+	2.60725i
$356$	4.35618e7	−	3.16495e7i	0.0511718	−	0.0371785i
$357$	2.05048e9	−	1.48976e9i	2.38516	−	1.73292i
$358$	−5.30243e7	+	1.63192e8i	−0.0610780	+	0.187979i
$359$	−9.72346e8	+	7.06451e8i	−1.10915	+	0.805844i	−0.982530	−	0.186107i	$-0.940413\pi$
$359$	−9.72346e8	+	7.06451e8i	−1.10915	+	0.805844i	−0.126620	+	0.991951i	$0.540413\pi$
$360$	−9.73960e8	−	7.07624e8i	−1.10023	−	0.799362i
$361$	−2.73016e8	−	8.40256e8i	−0.305431	−	0.940019i
$362$	−6.77558e8	−	4.92274e8i	−0.750700	−	0.545415i
$363$	−3.81177e8	+	1.17314e9i	−0.418267	+	1.28729i
$364$	1.67099e8	−	5.14279e8i	0.181602	−	0.558913i
$365$	−5.07746e8	−	1.56268e9i	−0.546540	−	1.68208i
$366$	1.04517e9			1.11430
$367$	−8.84891e8			−0.934455			−0.467228	−	0.884137i	$-0.654747\pi$
$367$	−8.84891e8			−0.934455			−0.467228	+	0.884137i	$0.654747\pi$
$368$	−4.08946e7	−	1.25861e8i	−0.0427759	−	0.131651i
$369$	−5.97416e8	+	4.34048e8i	−0.618992	+	0.449724i
$370$	3.85678e8	+	2.80211e8i	0.395839	+	0.287594i
$371$	3.64737e8			0.370827
$372$	−8.20814e8	−	2.86575e8i	−0.826693	−	0.288628i
$373$	−3.06171e8			−0.305480			−0.152740	−	0.988266i	$-0.548810\pi$
$373$	−3.06171e8			−0.305480			−0.152740	+	0.988266i	$0.548810\pi$
$374$	1.15904e9	+	8.42089e8i	1.14563	+	0.832352i
$375$	3.94014e9	−	2.86268e9i	3.85836	−	2.80326i
$376$	1.09402e8	+	3.36704e8i	0.106137	+	0.326656i
$377$	−8.24579e8			−0.792570
$378$	1.55286e9			1.47881
$379$	−2.69945e8	−	8.30805e8i	−0.254705	−	0.783902i	−0.993888	−	0.110397i	$-0.964788\pi$
$379$	−2.69945e8	−	8.30805e8i	−0.254705	−	0.783902i	0.739182	−	0.673505i	$-0.235212\pi$
$380$	−3.31348e7	+	1.01979e8i	−0.0309772	+	0.0953380i
$381$	−6.90265e8	+	2.12442e9i	−0.639408	+	1.96790i
$382$	−5.55517e8	−	4.03607e8i	−0.509889	−	0.370456i
$383$	1.13854e8	+	3.50406e8i	0.103550	+	0.318695i	0.989387	−	0.145301i	$-0.0464151\pi$
$383$	1.13854e8	+	3.50406e8i	0.103550	+	0.318695i	−0.885837	+	0.463996i	$0.846415\pi$
$384$	1.38951e8	+	1.00954e8i	0.125229	+	0.0909839i
$385$	2.51250e9	−	1.82544e9i	2.24385	−	1.63025i
$386$	3.08309e8	−	9.48878e8i	0.272854	−	0.839760i
$387$	−2.19343e9	+	1.59362e9i	−1.92370	+	1.39765i
$388$	3.30851e8	−	2.40377e8i	0.287555	−	0.208921i
$389$	2.88804e8	−	8.88848e8i	0.248760	−	0.765604i	−0.746236	−	0.665682i	$-0.768141\pi$
$389$	2.88804e8	−	8.88848e8i	0.248760	−	0.765604i	0.994995	−	0.0999218i	$-0.0318593\pi$
$390$	−2.29344e9	+	1.66628e9i	−1.95777	+	1.42240i
$391$	−7.96370e8	−	5.78597e8i	−0.673746	−	0.489505i
$392$	3.29441e7	+	1.01392e8i	0.0276234	+	0.0850161i
$393$	1.35800e9	+	9.86643e8i	1.12856	+	0.819948i
$394$	−2.44212e8	+	7.51609e8i	−0.201155	+	0.619092i
$395$	6.64202e8	−	2.04420e9i	0.542264	−	1.66892i
$396$	5.25471e8	+	1.61723e9i	0.425222	+	1.30870i
$397$	1.06984e9			0.858130			0.429065	−	0.903274i	$-0.358843\pi$
$397$	1.06984e9			0.858130			0.429065	+	0.903274i	$0.358843\pi$
$398$	−5.06361e8			−0.402596
$399$	−8.27994e7	−	2.54830e8i	−0.0652563	−	0.200838i
$400$	−6.37724e8	+	4.63334e8i	−0.498222	+	0.361979i
$401$	−1.10620e8	−	8.03703e7i	−0.0856701	−	0.0622430i	0.544126	−	0.839004i	$-0.316861\pi$
$401$	−1.10620e8	−	8.03703e7i	−0.0856701	−	0.0622430i	−0.629796	+	0.776761i	$0.716861\pi$
$402$	−1.79638e9			−1.37914
$403$	−8.35052e8	+	1.09831e9i	−0.635544	+	0.835907i
$404$	7.92486e8			0.597939
$405$	−2.42584e9	−	1.76248e9i	−1.81455	−	1.31835i
$406$	6.51701e8	−	4.73488e8i	0.483289	−	0.351130i
$407$	−2.08081e8	−	6.40407e8i	−0.152986	−	0.470842i
$408$	1.27755e9			0.931253
$409$	−2.68101e9			−1.93762			−0.968808	−	0.247814i	$-0.920288\pi$
$409$	−2.68101e9			−1.93762			−0.968808	+	0.247814i	$0.920288\pi$
$410$	2.10070e8	+	6.46529e8i	0.150529	+	0.463281i
$411$	6.35535e8	−	1.95598e9i	0.451537	−	1.38969i
$412$	−3.87517e7	+	1.19266e8i	−0.0272993	+	0.0840185i
$413$	2.83207e8	+	2.05762e8i	0.197824	+	0.143727i
$414$	−3.61050e8	−	1.11120e9i	−0.250073	−	0.769644i
$415$	1.82312e9	+	1.32458e9i	1.25213	+	0.909723i
$416$	2.20511e8	−	1.60210e8i	0.150177	−	0.109110i
$417$	1.62665e8	−	5.00632e8i	0.109855	−	0.338098i
$418$	1.22530e8	−	8.90234e7i	0.0820590	−	0.0596193i
$419$	−4.96348e8	+	3.60618e8i	−0.329638	+	0.239496i	−0.740277	−	0.672302i	$-0.765306\pi$
$419$	−4.96348e8	+	3.60618e8i	−0.329638	+	0.239496i	0.410639	+	0.911798i	$0.365306\pi$
$420$	8.55797e8	−	2.63387e9i	0.563635	−	1.73469i
$421$	2.42551e9	−	1.76224e9i	1.58422	−	1.15100i	0.672575	−	0.740029i	$-0.265188\pi$
$421$	2.42551e9	−	1.76224e9i	1.58422	−	1.15100i	0.911647	−	0.410975i	$-0.134812\pi$
$422$	−3.70375e8	−	2.69093e8i	−0.239910	−	0.174305i
$423$	9.65885e8	+	2.97269e9i	0.620489	+	1.90967i
$424$	1.48736e8	+	1.08063e8i	0.0947624	+	0.0688489i
$425$	−1.81189e9	+	5.57641e9i	−1.14491	+	3.52366i
$426$	8.99457e8	−	2.76824e9i	0.563698	−	1.73488i
$427$	5.00719e8	+	1.54106e9i	0.311241	+	0.957901i
$428$	−1.52264e9			−0.938735
$429$	4.00417e9			2.44857
$430$	7.71279e8	+	2.37375e9i	0.467813	+	1.43978i
$431$	−1.90063e7	+	1.38089e7i	−0.0114347	+	0.00830783i	−0.593488	−	0.804843i	$-0.702250\pi$
$431$	−1.90063e7	+	1.38089e7i	−0.0114347	+	0.00830783i	0.582053	+	0.813151i	$0.302250\pi$
$432$	6.33243e8	+	4.60078e8i	0.377900	+	0.274561i
$433$	−1.40568e9			−0.832106			−0.416053	−	0.909340i	$-0.636587\pi$
$433$	−1.40568e9			−0.832106			−0.416053	+	0.909340i	$0.636587\pi$
$434$	2.93070e7	−	1.34755e9i	0.0172090	−	0.791279i
$435$	−4.22307e9			−2.45989
$436$	1.06904e9	+	7.76700e8i	0.617717	+	0.448797i
$437$	−8.41901e7	+	6.11677e7i	−0.0482588	+	0.0350620i
$438$	6.39542e8	+	1.96831e9i	0.363672	+	1.11927i
$439$	−1.01187e9			−0.570818			−0.285409	−	0.958406i	$-0.592130\pi$
$439$	−1.01187e9			−0.570818			−0.285409	+	0.958406i	$0.592130\pi$
$440$	1.56541e9			0.876081
$441$	2.90857e8	+	8.95165e8i	0.161489	+	0.497013i
$442$	6.26510e8	−	1.92820e9i	0.345104	−	1.06212i
$443$	8.16819e8	−	2.51391e9i	0.446388	−	1.37384i	−0.434565	−	0.900640i	$-0.643098\pi$
$443$	8.16819e8	−	2.51391e9i	0.446388	−	1.37384i	0.880954	−	0.473202i	$-0.156902\pi$
$444$	−4.85788e8	−	3.52945e8i	−0.263394	−	0.191367i
$445$	−1.35236e8	−	4.16214e8i	−0.0727500	−	0.223901i
$446$	1.67344e9	+	1.21582e9i	0.893177	+	0.648931i
$447$	−7.49932e8	+	5.44857e8i	−0.397142	+	0.288540i
$448$	−8.22835e7	+	2.53242e8i	−0.0432354	+	0.133065i
$449$	−6.00222e8	+	4.36087e8i	−0.312932	+	0.227358i	−0.733153	−	0.680063i	$-0.761952\pi$
$449$	−6.00222e8	+	4.36087e8i	−0.312932	+	0.227358i	0.420222	+	0.907421i	$0.361952\pi$
$450$	−5.63033e9	+	4.09067e9i	−2.91266	+	2.11617i
$451$	2.96720e8	−	9.13210e8i	0.152310	−	0.468763i
$452$	−1.21180e9	+	8.80424e8i	−0.617229	+	0.448443i
$453$	−8.23698e8	−	5.98452e8i	−0.416317	−	0.302472i
$454$	1.19739e8	+	3.68518e8i	0.0600536	+	0.184826i
$455$	−3.55560e9	−	2.58329e9i	−1.76959	−	1.28568i
$456$	4.17356e7	−	1.28449e8i	0.0206125	−	0.0634387i
$457$	1.43680e8	−	4.42202e8i	0.0704191	−	0.216728i	−0.909653	−	0.415368i	$-0.863653\pi$
$457$	1.43680e8	−	4.42202e8i	0.0704191	−	0.216728i	0.980072	+	0.198641i	$0.0636527\pi$
$458$	−5.65795e8	−	1.74134e9i	−0.275188	−	0.846943i
$459$	5.82218e9			2.81023
$460$	−1.07559e9			−0.515222
$461$	1.05642e9	+	3.25134e9i	0.502209	+	1.54564i	0.805412	+	0.592715i	$0.201944\pi$
$461$	1.05642e9	+	3.25134e9i	0.502209	+	1.54564i	−0.303203	+	0.952926i	$0.598056\pi$
$462$	−3.16467e9	+	2.29927e9i	−1.49308	+	1.08478i
$463$	1.56092e9	+	1.13407e9i	0.730882	+	0.531017i	0.889842	−	0.456268i	$-0.150814\pi$
$463$	1.56092e9	+	1.13407e9i	0.730882	+	0.531017i	−0.158960	+	0.987285i	$0.550814\pi$
$464$	4.06041e8			0.188694
$465$	−4.27671e9	+	5.62499e9i	−1.97253	+	2.59440i
$466$	−2.53730e9			−1.16151
$467$	2.01029e7	+	1.46056e7i	0.00913374	+	0.00663605i	0.592343	−	0.805686i	$-0.298203\pi$
$467$	2.01029e7	+	1.46056e7i	0.00913374	+	0.00663605i	−0.583209	+	0.812322i	$0.698203\pi$
$468$	1.94684e9	−	1.41446e9i	0.877951	−	0.637868i
$469$	−8.60611e8	−	2.64869e9i	−0.385214	−	1.18557i
$470$	2.87743e9			1.27839
$471$	−1.92965e9			−0.850954
$472$	5.45266e7	+	1.67815e8i	0.0238677	+	0.0734573i
$473$	1.08942e9	−	3.35288e9i	0.473348	−	1.45682i
$474$	−8.36609e8	+	2.57482e9i	−0.360826	+	1.11051i
$475$	5.01479e8	+	3.64346e8i	0.214696	+	0.155986i
$476$	6.12049e8	+	1.88369e9i	0.260113	+	0.800545i
$477$	1.31316e9	+	9.54067e8i	0.553992	+	0.402499i
$478$	−1.58431e9	+	1.15107e9i	−0.663503	+	0.482063i
$479$	−4.41165e7	+	1.35777e8i	−0.0183412	+	0.0564483i	−0.959808	−	0.280657i	$-0.909448\pi$
$479$	−4.41165e7	+	1.35777e8i	−0.0183412	+	0.0564483i	0.941467	+	0.337105i	$0.109448\pi$
$480$	1.12934e9	−	8.20515e8i	0.466102	−	0.338643i
$481$	−7.70928e8	+	5.60112e8i	−0.315868	+	0.229492i
$482$	−4.83993e8	+	1.48958e9i	−0.196868	+	0.605897i
$483$	2.17444e9	−	1.57982e9i	0.878076	−	0.637959i
$484$	−7.79842e8	−	5.66588e8i	−0.312642	−	0.227148i
$485$	−1.02712e9	−	3.16114e9i	−0.408812	−	1.25819i
$486$	3.50629e8	+	2.54747e8i	0.138555	+	0.100666i
$487$	7.83550e8	−	2.41152e9i	0.307408	−	0.946105i	−0.671359	−	0.741132i	$-0.734289\pi$
$487$	7.83550e8	−	2.41152e9i	0.307408	−	0.946105i	0.978768	−	0.204973i	$-0.0657108\pi$
$488$	−2.52391e8	+	7.76780e8i	−0.0983115	+	0.302572i
$489$	2.53723e9	+	7.80878e9i	0.981247	+	3.01997i
$490$	8.66481e8			0.332715
$491$	1.21917e9			0.464813			0.232407	−	0.972619i	$-0.425340\pi$
$491$	1.21917e9			0.464813			0.232407	+	0.972619i	$0.425340\pi$
$492$	−2.64598e8	−	8.14348e8i	−0.100163	−	0.308271i
$493$	2.44344e9	−	1.77526e9i	0.918411	−	0.667265i
$494$	−1.73400e8	−	1.25983e8i	−0.0647150	−	0.0470182i
$495$	1.38207e10			5.12167
$496$	4.11198e8	−	5.40834e8i	0.151309	−	0.199011i
$497$	4.51256e9			1.64883
$498$	−2.29635e9	−	1.66840e9i	−0.833174	−	0.605337i
$499$	6.19046e8	−	4.49763e8i	0.223034	−	0.162044i	−0.470657	−	0.882316i	$-0.655983\pi$
$499$	6.19046e8	−	4.49763e8i	0.223034	−	0.162044i	0.693691	+	0.720272i	$0.255983\pi$
$500$	1.17609e9	+	3.61964e9i	0.420772	+	1.29500i
$501$	−6.87786e9			−2.44355
$502$	−2.76571e9			−0.975761
$503$	−1.49250e9	−	4.59345e9i	−0.522910	−	1.60935i	−0.768412	−	0.639955i	$-0.778953\pi$
$503$	−1.49250e9	−	4.59345e9i	−0.522910	−	1.60935i	0.245502	−	0.969396i	$-0.421047\pi$
$504$	−7.26463e8	+	2.23582e9i	−0.252759	+	0.777912i
$505$	1.99039e9	−	6.12578e9i	0.687729	−	2.11661i
$506$	1.22910e9	+	8.92994e8i	0.421755	+	0.306423i
$507$	−1.63025e8	−	5.01738e8i	−0.0555553	−	0.170982i
$508$	−1.41220e9	−	1.02602e9i	−0.477940	−	0.347243i
$509$	1.12078e9	−	8.14291e8i	0.376709	−	0.273695i	−0.383278	−	0.923633i	$-0.625205\pi$
$509$	1.12078e9	−	8.14291e8i	0.376709	−	0.273695i	0.759988	+	0.649938i	$0.225205\pi$
$510$	3.20866e9	−	9.87524e9i	1.07110	−	3.29649i
$511$	−2.59579e9	+	1.88595e9i	−0.860590	+	0.625255i
$512$	−1.08584e8	+	7.88912e7i	−0.0357538	+	0.0259767i
$513$	1.90202e8	−	5.85381e8i	0.0622019	−	0.191438i
$514$	2.34514e6	−	1.70385e6i	0.000761725	−	0.000553426i
$515$	8.24573e8	+	5.99088e8i	0.266014	+	0.193270i
$516$	−9.71480e8	−	2.98991e9i	−0.311286	−	0.958040i
$517$	−3.28810e9	−	2.38895e9i	−1.04647	−	0.760308i
$518$	2.87671e8	−	8.85361e8i	0.0909374	−	0.279876i
$519$	−6.67099e8	+	2.05312e9i	−0.209462	+	0.644657i
$520$	−6.84569e8	−	2.10689e9i	−0.213504	−	0.657097i
$521$	−4.03808e9			−1.25096			−0.625479	−	0.780241i	$-0.715096\pi$
$521$	−4.03808e9			−1.25096			−0.625479	+	0.780241i	$0.715096\pi$
$522$	3.58485e9			1.10312
$523$	8.21857e7	+	2.52942e8i	0.0251212	+	0.0773151i	0.962831	−	0.270104i	$-0.0870581\pi$
$523$	8.21857e7	+	2.52942e8i	0.0251212	+	0.0773151i	−0.937710	+	0.347419i	$0.887058\pi$
$524$	−1.06122e9	+	7.71019e8i	−0.322214	+	0.234102i
$525$	−1.29520e10	−	9.41021e9i	−3.90644	−	2.83819i
$526$	−1.54933e9			−0.464189
$527$	1.09881e8	−	5.05239e9i	0.0327029	−	1.50369i
$528$	−1.97175e9			−0.582951
$529$	1.91005e9	+	1.38773e9i	0.560983	+	0.407578i
$530$	1.20887e9	−	8.78296e8i	0.352707	−	0.256257i
$531$	4.81403e8	+	1.48161e9i	0.139533	+	0.429440i
$532$	2.09387e8			0.0602919
$533$	−1.35885e9			−0.388710
$534$	1.70339e8	+	5.24251e8i	0.0484084	+	0.148986i
$535$	−3.82421e9	+	1.17697e10i	−1.07970	+	3.32297i
$536$	4.33797e8	−	1.33509e9i	0.121677	−	0.374484i
$537$	−1.42114e9	−	1.03252e9i	−0.396028	−	0.287731i
$538$	5.87999e8	+	1.80968e9i	0.162794	+	0.501029i
$539$	−9.90147e8	−	7.19384e8i	−0.272357	−	0.197879i
$540$	5.14675e9	−	3.73933e9i	1.40655	−	1.02192i
$541$	−2.39224e8	+	7.36255e8i	−0.0649552	+	0.199912i	−0.978267	−	0.207350i	$-0.933516\pi$
$541$	−2.39224e8	+	7.36255e8i	−0.0649552	+	0.199912i	0.913312	+	0.407261i	$0.133516\pi$
$542$	−2.80062e9	+	2.03477e9i	−0.755540	+	0.548932i
$543$	6.93636e9	−	5.03956e9i	1.85922	−	1.35081i
$544$	−3.08507e8	+	9.49488e8i	−0.0821617	+	0.252868i
$545$	8.68870e9	−	6.31271e9i	2.29915	−	1.67043i
$546$	4.47853e9	+	3.25384e9i	1.17750	+	0.855504i
$547$	3.73673e8	+	1.15005e9i	0.0976195	+	0.300442i	0.987928	−	0.154917i	$-0.0495110\pi$
$547$	3.73673e8	+	1.15005e9i	0.0976195	+	0.300442i	−0.890308	+	0.455359i	$0.849511\pi$
$548$	1.30023e9	+	9.44671e8i	0.337511	+	0.245216i
$549$	−2.22831e9	+	6.85802e9i	−0.574740	+	1.76887i
$550$	2.79643e9	−	8.60652e9i	0.716694	−	2.20576i
$551$	−9.86671e7	−	3.03666e8i	−0.0251271	−	0.0773331i
$552$	1.35478e9			0.342833
$553$	−4.19726e9			−1.05543
$554$	−6.06463e8	−	1.86650e9i	−0.151538	−	0.466385i
$555$	−3.94829e9	+	2.86860e9i	−0.980356	+	0.712271i
$556$	3.32793e8	+	2.41789e8i	0.0821132	+	0.0596587i
$557$	−1.04073e7			−0.00255179			−0.00127590	−	0.999999i	$-0.500406\pi$
$557$	−1.04073e7			−0.00255179			−0.00127590	+	0.999999i	$0.500406\pi$
$558$	3.63038e9	−	4.77490e9i	0.884571	−	1.16344i
$559$	−4.98906e9			−1.20803
$560$	1.75086e9	+	1.27207e9i	0.421301	+	0.306093i
$561$	−1.18654e10	+	8.62071e9i	−2.83734	+	2.06145i
$562$	−1.64078e8	−	5.04980e8i	−0.0389918	−	0.120004i
$563$	−3.70132e9			−0.874132			−0.437066	−	0.899429i	$-0.643982\pi$
$563$	−3.70132e9			−0.874132			−0.437066	+	0.899429i	$0.643982\pi$
$564$	−3.62432e9			−0.850649
$565$	3.76200e9	+	1.15782e10i	0.877504	+	2.70068i
$566$	4.38181e8	−	1.34858e9i	0.101577	−	0.312622i
$567$	−1.80940e9	+	5.56876e9i	−0.416863	+	1.28297i
$568$	1.84018e9	+	1.33697e9i	0.421348	+	0.306127i
$569$	−1.41911e9	−	4.36758e9i	−0.322942	−	0.993913i	−0.972361	−	0.233482i	$-0.924988\pi$
$569$	−1.41911e9	−	4.36758e9i	−0.322942	−	0.993913i	0.649419	−	0.760431i	$-0.275012\pi$
$570$	−8.88066e8	−	6.45218e8i	−0.200855	−	0.145930i
$571$	−7.11845e9	+	5.17186e9i	−1.60015	+	1.16257i	−0.712910	+	0.701255i	$0.752623\pi$
$571$	−7.11845e9	+	5.17186e9i	−1.60015	+	1.16257i	−0.887235	+	0.461318i	$0.847377\pi$
$572$	−9.66942e8	+	2.97594e9i	−0.216030	+	0.664872i
$573$	5.68699e9	−	4.13184e9i	1.26282	−	0.917492i
$574$	1.07396e9	−	7.80275e8i	0.237025	−	0.172209i
$575$	−1.92142e9	+	5.91351e9i	−0.421487	+	1.29720i
$576$	−9.58668e8	+	6.96513e8i	−0.209021	+	0.151863i
$577$	5.73980e9	+	4.17021e9i	1.24389	+	0.903738i	0.997851	−	0.0655229i	$-0.0208716\pi$
$577$	5.73980e9	+	4.17021e9i	1.24389	+	0.903738i	0.246037	+	0.969260i	$0.420872\pi$
$578$	1.28036e9	+	3.94053e9i	0.275793	+	0.848804i
$579$	8.26318e9	+	6.00355e9i	1.76918	+	1.28538i
$580$	1.01980e9	−	3.13863e9i	0.217029	−	0.667946i
$581$	1.35984e9	−	4.18516e9i	0.287655	−	0.885311i
$582$	1.29372e9	+	3.98168e9i	0.272027	+	0.837212i
$583$	−2.11060e9			−0.441128
$584$	−1.61730e9			−0.336006
$585$	−6.04391e9	−	1.86013e10i	−1.24817	−	3.84146i
$586$	−5.15338e8	+	3.74415e8i	−0.105791	+	0.0768620i
$587$	3.16484e9	+	2.29939e9i	0.645830	+	0.469223i	0.861848	−	0.507167i	$-0.169307\pi$
$587$	3.16484e9	+	2.29939e9i	0.645830	+	0.469223i	−0.216018	+	0.976389i	$0.569307\pi$
$588$	−1.09139e9			−0.221391
$589$	−5.04393e8	−	1.76102e8i	−0.101711	−	0.0355107i
$590$	1.43413e9			0.287479
$591$	−6.54528e9	−	4.75542e9i	−1.30428	−	0.947617i
$592$	3.79622e8	−	2.75812e8i	0.0752013	−	0.0546370i
$593$	3.16867e8	+	9.75215e8i	0.0624001	+	0.192048i	0.977397	−	0.211414i	$-0.0678068\pi$
$593$	3.16867e8	+	9.75215e8i	0.0624001	+	0.192048i	−0.914997	+	0.403462i	$0.867807\pi$
$594$	−8.98583e9			−1.75916
$595$	1.60978e10			3.13298
$596$	−2.23847e8	−	6.88930e8i	−0.0433101	−	0.133295i
$597$	1.60187e9	−	4.93005e9i	0.308118	−	0.948291i
$598$	6.64383e8	−	2.04476e9i	0.127047	−	0.391010i
$599$	−1.37848e9	−	1.00152e9i	−0.262063	−	0.190400i	0.448993	−	0.893535i	$-0.351783\pi$
$599$	−1.37848e9	−	1.00152e9i	−0.262063	−	0.190400i	−0.711056	+	0.703135i	$0.751783\pi$
$600$	−2.49369e9	−	7.67479e9i	−0.471317	−	1.45056i
$601$	7.63549e9	+	5.54751e9i	1.43475	+	1.04241i	0.989107	+	0.147196i	$0.0470249\pi$
$601$	7.63549e9	+	5.54751e9i	1.43475	+	1.04241i	0.445643	+	0.895211i	$0.352975\pi$
$602$	3.94307e9	−	2.86481e9i	0.736625	−	0.535189i
$603$	3.82990e9	−	1.17872e10i	0.711339	−	2.18928i
$604$	6.43685e8	−	4.67664e8i	0.118862	−	0.0863584i
$605$	−6.33825e9	+	4.60501e9i	−1.16366	+	0.845448i
$606$	−2.50703e9	+	7.71584e9i	−0.457620	+	1.40841i
$607$	4.46688e9	−	3.24538e9i	0.810670	−	0.588986i	−0.103355	−	0.994645i	$-0.532958\pi$
$607$	4.46688e9	−	3.24538e9i	0.810670	−	0.588986i	0.914025	+	0.405658i	$0.132958\pi$
$608$	8.53861e7	+	6.20366e7i	0.0154072	+	0.0111940i
$609$	2.54834e9	+	7.84300e9i	0.457191	+	1.40709i
$610$	5.37047e9	+	3.90187e9i	0.957982	+	0.696015i
$611$	−1.77736e9	+	5.47017e9i	−0.315233	+	0.970189i
$612$	−2.72375e9	+	8.38283e9i	−0.480326	+	1.47829i
$613$	−1.85025e9	−	5.69447e9i	−0.324427	−	0.998485i	−0.971698	−	0.236225i	$-0.924090\pi$
$613$	−1.85025e9	−	5.69447e9i	−0.324427	−	0.998485i	0.647271	−	0.762260i	$-0.275910\pi$
$614$	1.76339e9			0.307439
$615$	−6.95932e9			−1.20643
$616$	−9.44623e8	−	2.90725e9i	−0.162827	−	0.501130i
$617$	−4.56635e9	+	3.31765e9i	−0.782656	+	0.568633i	−0.905775	−	0.423759i	$-0.860710\pi$
$617$	−4.56635e9	+	3.31765e9i	−0.782656	+	0.568633i	0.123119	+	0.992392i	$0.460710\pi$
$618$	−1.03861e9	−	7.54592e8i	−0.177008	−	0.128604i
$619$	5.24500e9			0.888849			0.444425	−	0.895816i	$-0.353408\pi$
$619$	5.24500e9			0.888849			0.444425	+	0.895816i	$0.353408\pi$
$620$	−3.14779e9	−	4.53683e9i	−0.530439	−	0.764507i
$621$	6.17414e9			1.03456
$622$	−1.00069e9	−	7.27044e8i	−0.166738	−	0.121142i
$623$	−6.91378e8	+	5.02316e8i	−0.114553	+	0.0832278i
$624$	8.62263e8	+	2.65377e9i	0.142067	+	0.437237i
$625$	1.58980e10			2.60472
$626$	2.41512e9			0.393485
$627$	4.79129e8	+	1.47461e9i	0.0776277	+	0.238913i
$628$	4.65979e8	−	1.43414e9i	0.0750772	−	0.231064i
$629$	1.07857e9	−	3.31951e9i	0.172811	−	0.531859i
$630$	1.54579e10	+	1.12309e10i	2.46297	+	1.78945i
$631$	−1.89611e9	−	5.83561e9i	−0.300441	−	0.924664i	−0.981339	−	0.192285i	$-0.938410\pi$
$631$	−1.89611e9	−	5.83561e9i	−0.300441	−	0.924664i	0.680898	−	0.732379i	$-0.261590\pi$
$632$	−1.71160e9	−	1.24355e9i	−0.269707	−	0.195954i
$633$	3.79163e9	−	2.75478e9i	0.594174	−	0.431692i
$634$	2.01116e8	−	6.18972e8i	0.0313426	−	0.0964626i
$635$	−1.14778e10	+	8.33911e9i	−1.77890	+	1.29244i
$636$	−1.52266e9	+	1.10627e9i	−0.234694	+	0.170515i
$637$	−5.35218e8	+	1.64723e9i	−0.0820432	+	0.252503i
$638$	−3.77115e9	+	2.73990e9i	−0.574912	+	0.417698i
$639$	1.62466e10	+	1.18038e10i	2.46325	+	1.78965i
$640$	3.37097e8	+	1.03748e9i	0.0508306	+	0.156440i
$641$	−9.23070e9	−	6.70650e9i	−1.38430	−	1.00576i	−0.996463	−	0.0840296i	$-0.973221\pi$
$641$	−9.23070e9	−	6.70650e9i	−1.38430	−	1.00576i	−0.387841	−	0.921726i	$-0.626779\pi$
$642$	4.81685e9	−	1.48248e10i	0.718441	−	2.21113i
$643$	−2.31847e9	+	7.13552e9i	−0.343925	+	1.05849i	0.618232	+	0.785996i	$0.287849\pi$
$643$	−2.31847e9	+	7.13552e9i	−0.343925	+	1.05849i	−0.962157	+	0.272496i	$0.912151\pi$
$644$	6.49048e8	+	1.99756e9i	0.0957582	+	0.294714i
$645$	−2.55514e10			−3.74934
$646$	7.85060e8			0.114575
$647$	−1.33095e9	−	4.09624e9i	−0.193195	−	0.594593i	−0.999993	−	0.00376572i	$-0.998801\pi$
$647$	−1.33095e9	−	4.09624e9i	−0.193195	−	0.594593i	0.806798	−	0.590828i	$-0.201199\pi$
$648$	−2.38775e9	+	1.73480e9i	−0.344728	+	0.250460i
$649$	−1.63881e9	−	1.19067e9i	−0.235328	−	0.170975i
$650$	−1.28064e10			−1.82907
$651$	1.30273e10	+	4.54830e9i	1.85064	+	0.646123i
$652$	−6.41626e9			−0.906599
$653$	1.07554e10	+	7.81429e9i	1.51158	+	1.09823i	0.965468	+	0.260521i	$0.0838942\pi$
$653$	1.07554e10	+	7.81429e9i	1.51158	+	1.09823i	0.546116	+	0.837710i	$0.316106\pi$
$654$	−1.09440e10	+	7.95130e9i	−1.52987	+	1.11152i
$655$	3.29451e9	+	1.01395e10i	0.458086	+	1.40984i
$656$	6.69127e8			0.0925433
$657$	−1.42788e10			−1.96433
$658$	−1.73634e9	−	5.34390e9i	−0.237599	−	0.731254i
$659$	−2.39764e9	+	7.37918e9i	−0.326351	+	1.00441i	0.644476	+	0.764625i	$0.277076\pi$
$659$	−2.39764e9	+	7.37918e9i	−0.326351	+	1.00441i	−0.970827	+	0.239781i	$0.922924\pi$
$660$	−4.95218e9	+	1.52412e10i	−0.670490	+	2.06356i
$661$	1.10332e10	+	8.01611e9i	1.48593	+	1.07959i	0.975586	+	0.219617i	$0.0704807\pi$
$661$	1.10332e10	+	8.01611e9i	1.48593	+	1.07959i	0.510341	+	0.859972i	$0.329519\pi$
$662$	2.19618e9	+	6.75916e9i	0.294216	+	0.905502i
$663$	1.67914e10	+	1.21997e10i	2.23764	+	1.62574i
$664$	1.79450e9	−	1.30378e9i	0.237879	−	0.172829i
$665$	5.25890e8	−	1.61852e9i	0.0693457	−	0.213424i
$666$	3.35160e9	−	2.43508e9i	0.439635	−	0.319414i
$667$	2.59115e9	−	1.88258e9i	0.338105	−	0.245648i
$668$	1.66089e9	−	5.11169e9i	0.215587	−	0.663509i
$669$	−1.71315e10	+	1.24467e10i	−2.21209	+	1.60718i
$670$	−9.23049e9	−	6.70634e9i	−1.18567	−	0.861438i
$671$	−2.89748e9	−	8.91751e9i	−0.370246	−	1.13950i
$672$	−2.20533e9	−	1.60226e9i	−0.280337	−	0.203677i
$673$	2.23130e9	−	6.86725e9i	0.282167	−	0.868421i	−0.705067	−	0.709141i	$-0.749083\pi$
$673$	2.23130e9	−	6.86725e9i	0.282167	−	0.868421i	0.987234	−	0.159280i	$-0.0509171\pi$
$674$	−7.49772e8	+	2.30756e9i	−0.0943234	+	0.290298i
$675$	−1.13645e10	−	3.49763e10i	−1.42229	−	4.37735i
$676$	4.12264e8			0.0513289
$677$	−8.56054e9			−1.06033			−0.530165	−	0.847895i	$-0.677870\pi$
$677$	−8.56054e9			−1.06033			−0.530165	+	0.847895i	$0.677870\pi$
$678$	−4.73850e9	−	1.45836e10i	−0.583898	−	1.79705i
$679$	−5.25101e9	+	3.81508e9i	−0.643722	+	0.467691i
$680$	6.56453e9	+	4.76941e9i	0.800613	+	0.581679i
$681$	−3.96677e9			−0.481307
$682$	−1.69588e8	+	7.79775e9i	−0.0204716	+	0.941291i
$683$	−7.98380e9			−0.958821			−0.479410	−	0.877591i	$-0.659149\pi$
$683$	−7.98380e9			−0.958821			−0.479410	+	0.877591i	$0.659149\pi$
$684$	7.53855e8	+	5.47708e8i	0.0900724	+	0.0654414i
$685$	1.05678e10	−	7.67792e9i	1.25622	−	0.912697i
$686$	1.54513e9	+	4.75542e9i	0.182739	+	0.562412i
$687$	1.87440e10			2.20553
$688$	2.45672e9			0.287605
$689$	9.22983e8	+	2.84065e9i	0.107504	+	0.330865i
$690$	3.40263e9	−	1.04722e10i	0.394314	−	1.21357i
$691$	3.27835e9	−	1.00897e10i	0.377992	−	1.16334i	−0.563446	−	0.826153i	$-0.690525\pi$
$691$	3.27835e9	−	1.00897e10i	0.377992	−	1.16334i	0.941438	−	0.337186i	$-0.109475\pi$
$692$	−1.36481e9	−	9.91589e8i	−0.156567	−	0.113752i
$693$	−8.33987e9	−	2.56675e10i	−0.951904	−	2.92966i
$694$	−1.56375e8	−	1.13613e8i	−0.0177586	−	0.0129024i
$695$	2.70482e9	−	1.96516e9i	0.305626	−	0.222051i
$696$	−1.28451e9	+	3.95332e9i	−0.144413	+	0.444457i
$697$	4.02661e9	−	2.92550e9i	0.450427	−	0.327255i
$698$	6.09335e9	−	4.42708e9i	0.678206	−	0.492746i
$699$	8.02675e9	−	2.47038e10i	0.888934	−	2.73586i
$700$	1.01215e10	−	7.35367e9i	1.11532	−	0.810328i
$701$	9.06108e9	+	6.58326e9i	0.993498	+	0.721818i	0.960684	−	0.277643i	$-0.0895533\pi$
$701$	9.06108e9	+	6.58326e9i	0.993498	+	0.721818i	0.0328133	+	0.999461i	$0.489553\pi$
$702$	3.92959e9	+	1.20940e10i	0.428713	+	1.31944i
$703$	−2.98518e8	−	2.16886e8i	−0.0324062	−	0.0235444i
$704$	4.76144e8	−	1.46542e9i	0.0514320	−	0.158292i
$705$	−9.10274e9	+	2.80154e10i	−0.978386	+	3.01116i
$706$	1.92779e8	+	5.93312e8i	0.0206178	+	0.0634552i
$707$	−1.25777e10			−1.33855
$708$	−1.80639e9			−0.191291
$709$	3.37179e9	+	1.03773e10i	0.355303	+	1.09351i	0.955833	+	0.293909i	$0.0949563\pi$
$709$	3.37179e9	+	1.03773e10i	0.355303	+	1.09351i	−0.600530	+	0.799602i	$0.705044\pi$
$710$	1.49563e10	−	1.08664e10i	1.56826	−	1.13941i
$711$	−1.51114e10	−	1.09790e10i	−1.57674	−	1.14557i
$712$	−4.30762e8			−0.0447258
$713$	1.16524e8	−	5.35781e9i	0.0120393	−	0.553572i
$714$	−2.02763e10			−2.08471
$715$	2.05749e10	+	1.49486e10i	2.10507	+	1.52943i
$716$	1.11056e9	−	8.06866e8i	0.113069	−	0.0821497i
$717$	−6.19513e9	−	1.90666e10i	−0.627673	−	1.93178i
$718$	9.61508e9			0.969432
$719$	−1.37863e10			−1.38324			−0.691618	−	0.722264i	$-0.743102\pi$
$719$	−1.37863e10			−1.38324			−0.691618	+	0.722264i	$0.743102\pi$
$720$	2.97616e9	+	9.15967e9i	0.297161	+	0.914568i
$721$	6.15037e8	−	1.89289e9i	0.0611122	−	0.188084i
$722$	−2.18413e9	+	6.72205e9i	−0.215972	+	0.664693i
$723$	−1.29718e10	−	9.42456e9i	−1.27649	−	0.927421i
$724$	2.07043e9	+	6.37213e9i	0.202757	+	0.624022i
$725$	−1.54342e10	−	1.12136e10i	−1.50418	−	1.09285i
$726$	7.98347e9	−	5.80033e9i	0.774308	−	0.562567i
$727$	−1.84173e9	+	5.66825e9i	−0.177769	+	0.547115i	−0.999749	−	0.0224003i	$-0.992869\pi$
$727$	−1.84173e9	+	5.66825e9i	−0.177769	+	0.547115i	0.821981	+	0.569516i	$0.192869\pi$
$728$	−3.49977e9	+	2.54273e9i	−0.336186	+	0.244254i
$729$	6.60976e9	−	4.80227e9i	0.631887	−	0.459092i
$730$	−4.06197e9	+	1.25015e10i	−0.386462	+	1.18941i
$731$	1.47838e10	−	1.07411e10i	1.39983	−	1.01704i
$732$	−6.76448e9	−	4.91468e9i	−0.637449	−	0.463134i
$733$	1.33919e9	+	4.12161e9i	0.125597	+	0.386547i	0.994009	−	0.109295i	$-0.0348593\pi$
$733$	1.33919e9	+	4.12161e9i	0.125597	+	0.386547i	−0.868412	+	0.495843i	$0.834859\pi$
$734$	5.72714e9	+	4.16101e9i	0.534566	+	0.388385i
$735$	−2.74111e9	+	8.43627e9i	−0.254636	+	0.783690i
$736$	−3.27157e8	+	1.00689e9i	−0.0302471	+	0.0930910i
$737$	4.98003e9	+	1.53270e10i	0.458243	+	1.41033i
$738$	5.90758e9			0.541019
$739$	1.40869e10			1.28399			0.641994	−	0.766709i	$-0.278107\pi$
$739$	1.40869e10			1.28399			0.641994	+	0.766709i	$0.278107\pi$
$740$	−1.17853e9	−	3.62713e9i	−0.106912	−	0.329042i
$741$	1.77515e9	−	1.28972e9i	0.160277	−	0.116448i
$742$	−2.36063e9	−	1.71509e9i	−0.212136	−	0.154125i
$743$	−2.21507e9			−0.198120			−0.0990598	−	0.995081i	$-0.531584\pi$
$743$	−2.21507e9			−0.198120			−0.0990598	+	0.995081i	$0.531584\pi$
$744$	3.96486e9	+	5.71445e9i	0.352958	+	0.508709i
$745$	−5.88751e9			−0.521657
$746$	1.98158e9	+	1.43970e9i	0.174754	+	0.126966i
$747$	1.58433e10	−	1.15108e10i	1.39066	−	1.01038i
$748$	−3.54170e9	−	1.09002e10i	−0.309425	−	0.952313i
$749$	2.41661e10			2.10145
$750$	−3.89623e10			−3.37233
$751$	−1.40714e9	−	4.33073e9i	−0.121226	−	0.373097i	0.871968	−	0.489562i	$-0.162843\pi$
$751$	−1.40714e9	−	4.33073e9i	−0.121226	−	0.373097i	−0.993195	+	0.116466i	$0.962843\pi$
$752$	8.75214e8	−	2.69363e9i	0.0750502	−	0.230981i
$753$	8.74931e9	−	2.69276e10i	0.746778	−	2.29835i
$754$	5.33679e9	+	3.87740e9i	0.453399	+	0.329413i
$755$	−1.99830e9	−	6.15013e9i	−0.168984	−	0.520080i
$756$	−1.00503e10	−	7.30200e9i	−0.845969	−	0.614632i
$757$	1.35646e10	−	9.85527e9i	1.13651	−	0.825720i	0.149878	−	0.988705i	$-0.452112\pi$
$757$	1.35646e10	−	9.85527e9i	1.13651	−	0.825720i	0.986629	+	0.162984i	$0.0521120\pi$
$758$	−2.15956e9	+	6.64644e9i	−0.180104	+	0.554302i
$759$	−1.25827e10	+	9.14184e9i	−1.04454	+	0.758905i
$760$	6.93985e8	−	5.04210e8i	0.0573459	−	0.0416642i
$761$	−2.56088e9	+	7.88158e9i	−0.210641	+	0.648287i	0.788793	+	0.614658i	$0.210706\pi$
$761$	−2.56088e9	+	7.88158e9i	−0.210641	+	0.648287i	−0.999434	+	0.0336280i	$0.989294\pi$
$762$	1.44571e10	−	1.05037e10i	1.18369	−	0.860002i
$763$	−1.69669e10	−	1.23272e10i	−1.38282	−	1.00468i
$764$	1.69751e9	+	5.22439e9i	0.137716	+	0.423847i
$765$	5.79568e10	+	4.21081e10i	4.68047	+	3.40056i
$766$	9.10830e8	−	2.80325e9i	0.0732212	−	0.225352i
$767$	−8.85850e8	+	2.72637e9i	−0.0708886	+	0.218173i
$768$	−4.24597e8	−	1.30678e9i	−0.0338231	−	0.104097i
$769$	−1.65579e10			−1.31299			−0.656496	−	0.754330i	$-0.727962\pi$
$769$	−1.65579e10			−1.31299			−0.656496	+	0.754330i	$0.727962\pi$
$770$	−2.48450e10			−1.96120
$771$	9.17020e6	+	2.82230e7i	0.000720591	+	0.00221775i
$772$	−6.45731e9	+	4.69151e9i	−0.505116	+	0.366988i
$773$	−2.19118e8	−	1.59199e8i	−0.0170628	−	0.0123969i	0.579221	−	0.815170i	$-0.303357\pi$
$773$	−2.19118e8	−	1.59199e8i	−0.0170628	−	0.0123969i	−0.596284	+	0.802774i	$0.703357\pi$
$774$	2.16899e10			1.68137
$775$	−3.05663e10	+	9.20180e9i	−2.35878	+	0.710096i
$776$	−3.27163e9			−0.251332
$777$	7.71004e9	+	5.60168e9i	0.589635	+	0.428395i
$778$	−6.04880e9	+	4.39471e9i	−0.460511	+	0.334581i
$779$	−1.62596e8	−	5.00420e8i	−0.0123234	−	0.0379274i
$780$	2.26788e10			1.71115
$781$	−2.61125e10			−1.96142
$782$	2.43349e9	+	7.48951e9i	0.181973	+	0.560054i
$783$	−5.85390e9	+	1.80164e10i	−0.435792	+	1.34123i
$784$	2.63553e8	−	8.11133e8i	0.0195327	−	0.0601154i
$785$	−9.91527e9	−	7.20387e9i	−0.731579	−	0.531523i
$786$	−4.14967e9	−	1.27714e10i	−0.304814	−	0.938121i
$787$	−5.91845e9	−	4.30001e9i	−0.432809	−	0.314454i	0.349962	−	0.936764i	$-0.386195\pi$
$787$	−5.91845e9	−	4.30001e9i	−0.432809	−	0.314454i	−0.782771	+	0.622309i	$0.786195\pi$
$788$	5.11485e9	−	3.71616e9i	0.372384	−	0.270553i
$789$	4.90131e9	−	1.50847e10i	0.355257	−	1.09337i
$790$	−1.39112e10	+	1.01071e10i	−1.00385	+	0.729343i
$791$	1.92327e10	−	1.39734e10i	1.38173	−	1.00389i
$792$	4.20377e9	−	1.29379e10i	0.300677	−	0.925390i
$793$	−1.07350e10	+	7.79942e9i	−0.764443	+	0.555400i
$794$	−6.92416e9	−	5.03070e9i	−0.490903	−	0.356662i
$795$	4.72704e9	+	1.45483e10i	0.333660	+	1.02690i
$796$	3.27724e9	+	2.38105e9i	0.230310	+	0.167330i
$797$	−2.79798e8	+	8.61130e8i	−0.0195768	+	0.0602510i	−0.960368	−	0.278736i	$-0.910084\pi$
$797$	−2.79798e8	+	8.61130e8i	−0.0195768	+	0.0602510i	0.940791	+	0.338987i	$0.110084\pi$
$798$	−6.62395e8	+	2.03864e9i	−0.0461432	+	0.142014i
$799$	−6.51010e9	−	2.00360e10i	−0.451517	−	1.38963i
$800$	6.30616e9			0.435462
$801$	−3.80311e9			−0.261472
$802$	3.38025e8	+	1.04033e9i	0.0231387	+	0.0712136i
$803$	1.50209e10	−	1.09133e10i	1.02374	−	0.743792i
$804$	1.16264e10	+	8.44710e9i	0.788952	+	0.573207i
$805$	1.70709e10			1.15338
$806$	1.05691e10	−	3.18178e9i	0.710996	−	0.214041i
$807$	−1.94796e10			−1.30473
$808$	−5.12908e9	−	3.72649e9i	−0.342058	−	0.248520i
$809$	−1.76172e10	+	1.27997e10i	−1.16982	+	0.849921i	−0.990987	−	0.133959i	$-0.957231\pi$
$809$	−1.76172e10	+	1.27997e10i	−1.16982	+	0.849921i	−0.178829	+	0.983880i	$0.557231\pi$
$810$	7.41271e9	+	2.28140e10i	0.490094	+	1.50835i
$811$	1.08856e10			0.716602			0.358301	−	0.933606i	$-0.383356\pi$
$811$	1.08856e10			0.716602			0.358301	+	0.933606i	$0.383356\pi$
$812$	−6.44437e9			−0.422410
$813$	−1.09513e10	−	3.37046e10i	−0.714739	−	2.19974i
$814$	−1.66465e9	+	5.12326e9i	−0.108177	+	0.332936i
$815$	−1.61149e10	+	4.95965e10i	−1.04274	+	3.20922i
$816$	−8.26849e9	−	6.00741e9i	−0.532734	−	0.387054i
$817$	−5.96978e8	−	1.83731e9i	−0.0382984	−	0.117870i
$818$	1.73519e10	+	1.26069e10i	1.10843	+	0.805325i
$819$	−3.08988e10	+	2.24493e10i	−1.96538	+	1.42793i
$820$	1.68056e9	−	5.17223e9i	0.106440	−	0.327589i
$821$	−2.13708e9	+	1.55268e9i	−0.134779	+	0.0979223i	−0.653132	−	0.757244i	$-0.726545\pi$
$821$	−2.13708e9	+	1.55268e9i	−0.134779	+	0.0979223i	0.518353	+	0.855167i	$0.326545\pi$
$822$	−1.33108e10	+	9.67088e9i	−0.835898	+	0.607316i
$823$	−2.02526e9	+	6.23312e9i	−0.126643	+	0.389768i	−0.994197	−	0.107576i	$-0.965691\pi$
$823$	−2.02526e9	+	6.23312e9i	−0.126643	+	0.389768i	0.867554	+	0.497344i	$0.165691\pi$
$824$	8.11627e8	−	5.89681e8i	0.0505372	−	0.0367174i
$825$	7.49486e10	+	5.44534e10i	4.64702	+	3.37626i
$826$	−8.65403e8	−	2.66344e9i	−0.0534304	−	0.164442i
$827$	1.56006e8	+	1.13345e8i	0.00959119	+	0.00696841i	0.592571	−	0.805519i	$-0.298113\pi$
$827$	1.56006e8	+	1.13345e8i	0.00959119	+	0.00696841i	−0.582979	+	0.812487i	$0.698113\pi$
$828$	−2.88840e9	+	8.88958e9i	−0.176828	+	0.544221i
$829$	−2.43604e9	+	7.49735e9i	−0.148506	+	0.457054i	−0.997445	−	0.0714366i	$-0.977242\pi$
$829$	−2.43604e9	+	7.49735e9i	−0.148506	+	0.457054i	0.848939	+	0.528490i	$0.177242\pi$
$830$	−5.57097e9	−	1.71457e10i	−0.338188	−	1.04083i
$831$	2.00913e10			1.21452
$832$	−2.18053e9			−0.131259
$833$	−1.96039e9	−	6.03345e9i	−0.117513	−	0.361666i
$834$	−3.40690e9	+	2.47526e9i	−0.203366	+	0.147754i
$835$	−3.53410e10	−	2.56767e10i	−2.10076	−	1.52629i
$836$	−1.21165e9			−0.0717222
$837$	1.80691e10	+	2.60425e10i	1.06512	+	1.53512i
$838$	4.90816e9			0.288114
$839$	−1.33291e9	−	9.68414e8i	−0.0779171	−	0.0566101i	0.548145	−	0.836383i	$-0.315334\pi$
$839$	−1.33291e9	−	9.68414e8i	−0.0779171	−	0.0566101i	−0.626062	+	0.779773i	$0.715334\pi$
$840$	−1.79240e10	+	1.30226e10i	−1.04342	+	0.758088i
$841$	−2.29380e9	−	7.05958e9i	−0.132975	−	0.409254i
$842$	−2.39848e10			−1.38466
$843$	5.43567e9			0.312504
$844$	1.13176e9	+	3.48321e9i	0.0647974	+	0.199426i
$845$	1.03543e9	−	3.18673e9i	0.0590367	−	0.181696i
$846$	7.72708e9	−	2.37815e10i	0.438752	−	1.35034i
$847$	1.23770e10	+	8.99245e9i	0.699882	+	0.508494i
$848$	−4.54497e8	−	1.39880e9i	−0.0255945	−	0.0787717i
$849$	1.17439e10	+	8.53247e9i	0.658623	+	0.478517i
$850$	3.79486e10	−	2.75713e10i	2.11948	−	1.53989i
$851$	1.14377e9	−	3.52017e9i	0.0636190	−	0.195799i
$852$	−1.88385e10	+	1.36869e10i	−1.04353	+	0.758172i
$853$	−1.16939e9	+	8.49614e8i	−0.0645118	+	0.0468706i	−0.619574	−	0.784938i	$-0.712695\pi$
$853$	−1.16939e9	+	8.49614e8i	−0.0645118	+	0.0468706i	0.555062	+	0.831809i	$0.312695\pi$
$854$	4.00575e9	−	1.23284e10i	0.220081	−	0.677338i
$855$	6.12704e9	−	4.45156e9i	0.335251	−	0.243574i
$856$	9.85471e9	+	7.15986e9i	0.537014	+	0.390163i
$857$	−8.26340e9	−	2.54321e10i	−0.448462	−	1.38022i	−0.878642	−	0.477481i	$-0.841550\pi$
$857$	−8.26340e9	−	2.54321e10i	−0.448462	−	1.38022i	0.430180	−	0.902743i	$-0.358450\pi$
$858$	−2.59156e10	−	1.88288e10i	−1.40073	−	1.01769i
$859$	1.38510e8	−	4.26291e8i	0.00745600	−	0.0229472i	−0.947259	−	0.320468i	$-0.896160\pi$
$859$	1.38510e8	−	4.26291e8i	0.00745600	−	0.0229472i	0.954715	+	0.297521i	$0.0961598\pi$
$860$	6.17023e9	−	1.89900e10i	0.330793	−	1.01808i
$861$	4.19949e9	+	1.29247e10i	0.224226	+	0.690096i
$862$	1.87944e8			0.00999434
$863$	−2.87729e8			−0.0152386			−0.00761930	−	0.999971i	$-0.502425\pi$
$863$	−2.87729e8			−0.0152386			−0.00761930	+	0.999971i	$0.502425\pi$
$864$	−1.93502e9	−	5.95537e9i	−0.102067	−	0.314131i
$865$	−1.10926e10	+	8.05925e9i	−0.582743	+	0.423388i
$866$	9.09774e9	+	6.60990e9i	0.476015	+	0.345845i
$867$	−4.24164e10			−2.21038
$868$	−6.52622e9	+	8.58369e9i	−0.338721	+	0.445507i
$869$	2.42880e10			1.25551
$870$	2.73323e10	+	1.98581e10i	1.40721	+	1.02240i
$871$	1.84507e10	−	1.34052e10i	0.946129	−	0.687403i
$872$	−3.26668e9	−	1.00538e10i	−0.166840	−	0.513479i
$873$	−2.88845e10			−1.46932
$874$	8.32518e8			0.0421797
$875$	−1.86660e10	−	5.74482e10i	−0.941942	−	2.89900i
$876$	5.11633e9	−	1.57465e10i	0.257155	−	0.791441i
$877$	3.77810e9	−	1.16278e10i	0.189136	−	0.582101i	−0.810859	−	0.585242i	$-0.801000\pi$
$877$	3.77810e9	−	1.16278e10i	0.189136	−	0.582101i	0.999995	+	0.00314053i	$0.000999664\pi$
$878$	6.54895e9	+	4.75809e9i	0.326543	+	0.237248i
$879$	−2.01512e9	−	6.20192e9i	−0.100079	−	0.308010i
$880$	−1.01316e10	−	7.36101e9i	−0.501172	−	0.364123i
$881$	−4.66512e9	+	3.38941e9i	−0.229851	+	0.166997i	−0.696750	−	0.717314i	$-0.745371\pi$
$881$	−4.66512e9	+	3.38941e9i	−0.229851	+	0.166997i	0.466899	+	0.884311i	$0.345371\pi$
$882$	2.32685e9	−	7.16132e9i	0.114190	−	0.351442i
$883$	−2.44091e10	+	1.77342e10i	−1.19313	+	0.866861i	−0.993592	−	0.113028i	$-0.963945\pi$
$883$	−2.44091e10	+	1.77342e10i	−1.19313	+	0.866861i	−0.199541	+	0.979890i	$0.563945\pi$
$884$	−1.31218e10	+	9.53354e9i	−0.638867	+	0.464164i
$885$	−4.53687e9	+	1.39630e10i	−0.220016	+	0.677140i
$886$	−1.71077e10	+	1.24295e10i	−0.826367	+	0.600391i
$887$	1.78016e10	+	1.29336e10i	0.856499	+	0.622283i	0.926930	−	0.375234i	$-0.122438\pi$
$887$	1.78016e10	+	1.29336e10i	0.856499	+	0.622283i	−0.0704312	+	0.997517i	$0.522438\pi$
$888$	1.48444e9	+	4.56862e9i	0.0711403	+	0.218947i
$889$	2.24133e10	+	1.62842e10i	1.06992	+	0.777340i
$890$	−1.08189e9	+	3.32971e9i	−0.0514420	+	0.158322i
$891$	1.04703e10	−	3.22243e10i	0.495893	−	1.52620i
$892$	−5.11357e9	−	1.57380e10i	−0.241239	−	0.742457i
$893$	−2.22716e9			−0.104658
$894$	7.41573e9			0.347114
$895$	−3.44769e9	−	1.06109e10i	−0.160749	−	0.494733i
$896$	1.72337e9	−	1.25210e9i	0.0800387	−	0.0581515i
$897$	1.78065e10	+	1.29372e10i	0.823769	+	0.598503i
$898$	5.93532e9			0.273512
$899$	1.55239e10	+	5.41993e9i	0.712592	+	0.248791i
$900$	5.56757e10			2.54576
$901$	−8.85075e9	−	6.43045e9i	−0.403128	−	0.292890i
$902$	−6.21458e9	+	4.51516e9i	−0.281961	+	0.204857i
$903$	1.54186e10	+	4.74535e10i	0.696846	+	2.14467i
$904$	1.19829e10			0.539478
$905$	5.44555e10			2.44215
$906$	2.51700e9	+	7.74652e9i	0.112443	+	0.346065i
$907$	−2.93417e8	+	9.03044e8i	−0.0130575	+	0.0401868i	−0.957373	−	0.288855i	$-0.906726\pi$
$907$	−2.93417e8	+	9.03044e8i	−0.0130575	+	0.0401868i	0.944315	+	0.329041i	$0.106726\pi$
$908$	9.57909e8	−	2.94814e9i	0.0424643	−	0.130692i
$909$	−4.52835e10	−	3.29004e10i	−1.99971	−	1.45287i
$910$	1.08649e10	+	3.34389e10i	0.477950	+	1.47098i
$911$	−2.68046e9	−	1.94747e9i	−0.117461	−	0.0853406i	0.527504	−	0.849553i	$-0.323128\pi$
$911$	−2.68046e9	−	1.94747e9i	−0.117461	−	0.0853406i	−0.644965	+	0.764212i	$0.723128\pi$
$912$	−8.74122e8	+	6.35087e8i	−0.0381584	+	0.0277237i
$913$	−7.86890e9	+	2.42180e10i	−0.342189	+	1.05315i
$914$	−3.00928e9	+	2.18637e9i	−0.130362	+	0.0947134i
$915$	−5.49790e10	+	3.99446e10i	−2.37259	+	1.72379i
$916$	−4.52636e9	+	1.39307e10i	−0.194588	+	0.598879i
$917$	1.68428e10	−	1.22370e10i	0.721309	−	0.524062i
$918$	−3.76820e10	−	2.73775e10i	−1.60762	−	1.16801i
$919$	−1.24569e10	−	3.83383e10i	−0.529425	−	1.62940i	−0.755396	−	0.655269i	$-0.772555\pi$
$919$	−1.24569e10	−	3.83383e10i	−0.529425	−	1.62940i	0.225971	−	0.974134i	$-0.427445\pi$
$920$	6.96137e9	+	5.05773e9i	0.294739	+	0.214140i
$921$	−5.57847e9	+	1.71688e10i	−0.235292	+	0.724153i
$922$	8.45138e9	−	2.60107e10i	0.355116	−	1.09293i
$923$	1.14192e10	+	3.51448e10i	0.478004	+	1.47114i
$924$	3.12940e10			1.30500
$925$	−2.20470e10			−0.915910
$926$	−4.76975e9	−	1.46798e10i	−0.197404	−	0.607548i
$927$	7.16568e9	−	5.20617e9i	0.295446	−	0.214654i
$928$	−2.62795e9	−	1.90932e9i	−0.107944	−	0.0784262i
$929$	6.35137e9			0.259904			0.129952	−	0.991520i	$-0.458518\pi$
$929$	6.35137e9			0.259904			0.129952	+	0.991520i	$0.458518\pi$
$930$	5.41297e10	−	1.62954e10i	2.20671	−	0.664317i
$931$	−6.70665e8			−0.0272384
$932$	1.64218e10	+	1.19311e10i	0.664453	+	0.482753i
$933$	1.02444e10	−	7.44296e9i	0.412952	−	0.300027i
$934$	−6.14289e7	−	1.89059e8i	−0.00246694	−	0.00759246i
$935$	−9.31520e10			−3.72693
$936$	−1.92514e10			−0.767357
$937$	6.00260e9	+	1.84741e10i	0.238370	+	0.733626i	0.996657	+	0.0817052i	$0.0260366\pi$
$937$	6.00260e9	+	1.84741e10i	0.238370	+	0.733626i	−0.758287	+	0.651921i	$0.773963\pi$
$938$	−6.88489e9	+	2.11895e10i	−0.272387	+	0.838322i
$939$	−7.64021e9	+	2.35142e10i	−0.301145	+	0.926830i
$940$	−1.86231e10	−	1.35305e10i	−0.731316	−	0.531332i
$941$	−9.21872e9	−	2.83723e10i	−0.360667	−	1.11002i	−0.952650	−	0.304069i	$-0.901655\pi$
$941$	−9.21872e9	−	2.83723e10i	−0.360667	−	1.11002i	0.591983	−	0.805951i	$-0.298345\pi$
$942$	1.24890e10	+	9.07377e9i	0.486798	+	0.353679i
$943$	4.27002e9	−	3.10235e9i	0.165821	−	0.120476i
$944$	4.36212e8	−	1.34252e9i	0.0168770	−	0.0519422i
$945$	−8.16852e10	+	5.93478e10i	−3.14871	+	2.28767i
$946$	−2.28171e10	+	1.65776e10i	−0.876276	+	0.636652i
$947$	−1.16589e10	+	3.58825e10i	−0.446102	+	1.37296i	0.435168	+	0.900349i	$0.356689\pi$
$947$	−1.16589e10	+	3.58825e10i	−0.446102	+	1.37296i	−0.881271	+	0.472612i	$0.843311\pi$
$948$	1.75222e10	−	1.27306e10i	0.667973	−	0.485310i
$949$	−2.12570e10	−	1.54441e10i	−0.807364	−	0.586584i
$950$	−1.53238e9	−	4.71619e9i	−0.0579875	−	0.178467i
$951$	5.39023e9	+	3.91623e9i	0.203224	+	0.147651i
$952$	4.89639e9	−	1.50695e10i	0.183927	−	0.566071i
$953$	2.41305e9	−	7.42659e9i	0.0903109	−	0.277948i	−0.895692	−	0.444674i	$-0.853319\pi$
$953$	2.41305e9	−	7.42659e9i	0.0903109	−	0.277948i	0.986003	+	0.166726i	$0.0533195\pi$
$954$	−4.01266e9	−	1.23497e10i	−0.149628	−	0.460508i
$955$	4.46470e10			1.65875
$956$	1.56665e10			0.579923
$957$	−1.47463e10	−	4.53845e10i	−0.543866	−	1.67385i
$958$	9.23989e8	−	6.71317e8i	0.0339537	−	0.0246688i
$959$	−2.06362e10	−	1.49931e10i	−0.755553	−	0.548941i
$960$	−1.11675e10			−0.407388
$961$	2.29402e10	−	1.51885e10i	0.833807	−	0.552056i
$962$	7.62335e9			0.276079
$963$	8.70051e10	+	6.32129e10i	3.13944	+	2.28094i
$964$	1.01369e10	−	7.36488e9i	0.364448	−	0.264787i
$965$	2.00465e10	+	6.16969e10i	0.718115	+	2.21013i
$966$	−2.15020e10			−0.767466
$967$	2.11578e10			0.752452			0.376226	−	0.926528i	$-0.377222\pi$
$967$	2.11578e10			0.752452			0.376226	+	0.926528i	$0.377222\pi$
$968$	2.38299e9	+	7.33407e9i	0.0844418	+	0.259885i
$969$	−2.48354e9	+	7.64354e9i	−0.0876874	+	0.269874i
$970$	−8.21693e9	+	2.52891e10i	−0.289074	+	0.889677i
$971$	9.99021e9	+	7.25831e9i	0.350193	+	0.254430i	0.748950	−	0.662627i	$-0.230558\pi$
$971$	9.99021e9	+	7.25831e9i	0.350193	+	0.254430i	−0.398757	+	0.917057i	$0.630558\pi$
$972$	−1.07143e9	−	3.29751e9i	−0.0374223	−	0.115174i
$973$	−5.28184e9	−	3.83748e9i	−0.183819	−	0.133552i
$974$	−1.64109e10	+	1.19232e10i	−0.569083	+	0.413463i
$975$	4.05130e10	−	1.24686e11i	1.39984	−	4.30827i
$976$	5.28615e9	−	3.84061e9i	0.181997	−	0.132229i
$977$	3.58806e10	−	2.60688e10i	1.23092	−	0.894313i	0.233958	−	0.972247i	$-0.424832\pi$
$977$	3.58806e10	−	2.60688e10i	1.23092	−	0.894313i	0.996959	+	0.0779331i	$0.0248321\pi$
$978$	2.02978e10	−	6.24703e10i	0.693847	−	2.13544i
$979$	4.00075e9	−	2.90671e9i	0.136271	−	0.0990063i
$980$	−5.60798e9	−	4.07444e9i	−0.190333	−	0.138285i
$981$	−2.88408e10	−	8.87629e10i	−0.975363	−	3.00186i
$982$	−7.89063e9	−	5.73288e9i	−0.265902	−	0.193189i
$983$	3.99344e9	−	1.22905e10i	0.134094	−	0.412699i	−0.861354	−	0.508005i	$-0.830383\pi$
$983$	3.99344e9	−	1.22905e10i	0.134094	−	0.412699i	0.995448	+	0.0953062i	$0.0303830\pi$
$984$	−2.11678e9	+	6.51478e9i	−0.0708261	+	0.217980i
$985$	−1.58789e10	−	4.88703e10i	−0.529412	−	1.62936i
$986$	−2.41620e10			−0.802721
$987$	5.75225e10			1.90427
$988$	5.29864e8	+	1.63075e9i	0.0174789	+	0.0537946i
$989$	1.56775e10	−	1.13904e10i	0.515336	−	0.374414i
$990$	−8.94493e10	−	6.49888e10i	−2.92991	−	2.12870i
$991$	2.51114e10			0.819620			0.409810	−	0.912171i	$-0.365595\pi$
$991$	2.51114e10			0.819620			0.409810	+	0.912171i	$0.365595\pi$
$992$	−5.20448e9	+	1.56678e9i	−0.169273	+	0.0509585i
$993$	−7.27564e10			−2.35803
$994$	−2.92059e10	−	2.12193e10i	−0.943232	−	0.685298i
$995$	2.66361e10	−	1.93523e10i	0.857215	−	0.622804i
$996$	7.01703e9	+	2.15962e10i	0.225033	+	0.692579i
$997$	−3.64886e10			−1.16607			−0.583034	−	0.812448i	$-0.698135\pi$
$997$	−3.64886e10			−1.16607			−0.583034	+	0.812448i	$0.698135\pi$
$998$	−6.12147e9			−0.194939
$999$	6.76501e9	+	2.08206e10i	0.214679	+	0.660714i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.8.d.a.33.9	✓	40
31.16	even	5	inner	62.8.d.a.47.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.8.d.a.33.9	✓	40	1.1	even	1	trivial
62.8.d.a.47.9	yes	40	31.16	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.47214 - 4.70228i) q^{2} +(66.2571 - 48.1386i) q^{3} +(19.7771 + 60.8676i) q^{4} +520.167 q^{5} -655.187 q^{6} +(-313.887 - 966.043i) q^{7} +(158.217 - 486.941i) q^{8} +(1396.86 - 4299.10i) q^{9} +(-3366.59 - 2445.97i) q^{10} +(1816.34 + 5590.13i) q^{11} +(4240.46 + 3080.87i) q^{12} +(6729.45 - 4889.23i) q^{13} +(-2511.09 + 7728.35i) q^{14} +(34464.8 - 25040.1i) q^{15} +(-3313.73 + 2407.57i) q^{16} +(-9414.90 + 28976.1i) q^{17} +(-29256.2 + 21255.9i) q^{18} +(2605.78 + 1893.21i) q^{19} +(10287.4 + 31661.3i) q^{20} +(-67301.2 - 48897.2i) q^{21} +(14530.8 - 44721.1i) q^{22} +(-9984.04 + 30727.7i) q^{23} +(-12957.7 - 39879.7i) q^{24} +192449. q^{25} -66544.5 q^{26} +(-59052.0 - 181743. i) q^{27} +(52593.0 - 38211.1i) q^{28} +(-80198.8 - 58267.8i) q^{29} -340807. q^{30} +(-158828. + 47814.3i) q^{31} +32768.0 q^{32} +(389447. + 282950. i) q^{33} +(197188. - 143266. i) q^{34} +(-163273. - 502504. i) q^{35} +289302. q^{36} -114560. q^{37} +(-7962.55 - 24506.2i) q^{38} +(210513. - 647893. i) q^{39} +(82299.1 - 253291. i) q^{40} +(-132162. - 96021.2i) q^{41} +(205654. + 632939. i) q^{42} +(-485237. - 352545. i) q^{43} +(-304336. + 221113. i) q^{44} +(726601. - 2.23625e6i) q^{45} +(209108. - 151926. i) q^{46} +(-559409. + 406435. i) q^{47} +(-103661. + 319037. i) q^{48} +(-168455. + 122390. i) q^{49} +(-1.24555e6 - 904948. i) q^{50} +(771065. + 2.37309e6i) q^{51} +(430685. + 312911. i) q^{52} +(-110961. + 341504. i) q^{53} +(-472416. + 1.45395e6i) q^{54} +(944803. + 2.90780e6i) q^{55} -520068. q^{56} +263788. q^{57} +(245066. + 754235. i) q^{58} +(-278813. + 202570. i) q^{59} +(2.20575e6 + 1.60257e6i) q^{60} -1.59522e6 q^{61} +(1.25279e6 + 437395. i) q^{62} -4.59157e6 q^{63} +(-212079. - 154084. i) q^{64} +(3.50044e6 - 2.54322e6i) q^{65} +(-1.19004e6 - 3.66258e6i) q^{66} +2.74179e6 q^{67} -1.94990e6 q^{68} +(817676. + 2.51655e6i) q^{69} +(-1.30619e6 + 4.02003e6i) q^{70} +(-1.37282e6 + 4.22512e6i) q^{71} +(-1.87240e6 - 1.36038e6i) q^{72} +(-976121. - 3.00419e6i) q^{73} +(741449. + 538694. i) q^{74} +(1.27511e7 - 9.26422e6i) q^{75} +(-63700.4 + 196050. i) q^{76} +(4.83019e6 - 3.50934e6i) q^{77} +(-4.40905e6 + 3.20336e6i) q^{78} +(1.27690e6 - 3.92990e6i) q^{79} +(-1.72370e6 + 1.25234e6i) q^{80} +(-4.66358e6 - 3.38829e6i) q^{81} +(403851. + 1.24293e6i) q^{82} +(3.50488e6 + 2.54645e6i) q^{83} +(1.64523e6 - 5.06351e6i) q^{84} +(-4.89732e6 + 1.50724e7i) q^{85} +(1.48275e6 + 4.56344e6i) q^{86} -8.11868e6 q^{87} +3.00944e6 q^{88} +(-259986. - 800155. i) q^{89} +(-1.52181e7 + 1.10566e7i) q^{90} +(-6.83550e6 - 4.96628e6i) q^{91} -2.06778e6 q^{92} +(-8.22179e6 + 1.08138e7i) q^{93} +5.53174e6 q^{94} +(1.35544e6 + 984784. i) q^{95} +(2.17111e6 - 1.57741e6i) q^{96} +(-1.97459e6 - 6.07716e6i) q^{97} +1.66577e6 q^{98} +2.65697e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) \) 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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