LMFDB - Embedded newform 100.9.b.g.51.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(51,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.51"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0] 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:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 94 x^{18} + 5343 x^{16} - 172772 x^{14} + 36131456 x^{12} - 3044563968 x^{10} + \cdots + 11\!\cdots\!76 $ x^20 - 94x^18 + 5343x^16 - 172772x^14 + 36131456x^12 - 3044563968x^10 + 147994443776x^8 - 2898633162752x^6 + 367168164200448x^4 - 26458647810801664*x^2 + 1152921504606846976
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{75}\cdot 3^{4}\cdot 5^{14} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.6
Root			$-7.13604 + 3.61621i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.9.b.g.51.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-14.2721 + 7.23243i) q^{2} +44.3270i q^{3} +(151.384 - 206.443i) q^{4} +(-320.592 - 632.638i) q^{6} -2826.75i q^{7} +(-667.476 + 4041.25i) q^{8} +4596.11 q^{9} -18327.2i q^{11} +(9151.02 + 6710.40i) q^{12} +13946.9 q^{13} +(20444.3 + 40343.6i) q^{14} +(-19701.8 - 62504.5i) q^{16} -96189.1 q^{17} +(-65596.1 + 33241.1i) q^{18} -153485. i q^{19} +125301. q^{21} +(132550. + 261567. i) q^{22} +339368. i q^{23} +(-179137. - 29587.2i) q^{24} +(-199051. + 100870. i) q^{26} +494562. i q^{27} +(-583564. - 427925. i) q^{28} -758065. q^{29} +1.01418e6i q^{31} +(733244. + 749577. i) q^{32} +812389. q^{33} +(1.37282e6 - 695681. i) q^{34} +(695778. - 948838. i) q^{36} -135354. q^{37} +(1.11007e6 + 2.19055e6i) q^{38} +618224. i q^{39} -2.56309e6 q^{41} +(-1.78831e6 + 906233. i) q^{42} -852539. i q^{43} +(-3.78352e6 - 2.77444e6i) q^{44} +(-2.45445e6 - 4.84348e6i) q^{46} +1.25626e6i q^{47} +(2.77064e6 - 873321. i) q^{48} -2.22572e6 q^{49} -4.26378e6i q^{51} +(2.11134e6 - 2.87925e6i) q^{52} -1.00203e7 q^{53} +(-3.57688e6 - 7.05842e6i) q^{54} +(1.14236e7 + 1.88679e6i) q^{56} +6.80354e6 q^{57} +(1.08192e7 - 5.48265e6i) q^{58} -2.35908e7i q^{59} -5.69128e6 q^{61} +(-7.33498e6 - 1.44744e7i) q^{62} -1.29921e7i q^{63} +(-1.58862e7 - 5.39488e6i) q^{64} +(-1.15945e7 + 5.87554e6i) q^{66} -1.76526e7i q^{67} +(-1.45615e7 + 1.98576e7i) q^{68} -1.50432e7 q^{69} -3.89940e6i q^{71} +(-3.06780e6 + 1.85740e7i) q^{72} -9.62921e6 q^{73} +(1.93178e6 - 978938. i) q^{74} +(-3.16860e7 - 2.32352e7i) q^{76} -5.18063e7 q^{77} +(-4.47126e6 - 8.82334e6i) q^{78} +2.34959e6i q^{79} +8.23266e6 q^{81} +(3.65806e7 - 1.85374e7i) q^{82} +1.26930e7i q^{83} +(1.89686e7 - 2.58677e7i) q^{84} +(6.16593e6 + 1.21675e7i) q^{86} -3.36028e7i q^{87} +(7.40646e7 + 1.22330e7i) q^{88} -6.42709e7 q^{89} -3.94244e7i q^{91} +(7.00603e7 + 5.13749e7i) q^{92} -4.49555e7 q^{93} +(-9.08579e6 - 1.79294e7i) q^{94} +(-3.32265e7 + 3.25025e7i) q^{96} -6.62485e6 q^{97} +(3.17656e7 - 1.60973e7i) q^{98} -8.42338e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 752 q^{4} + 3408 q^{6} - 2556 q^{9} - 8848 q^{14} - 59200 q^{16} + 410256 q^{21} + 156672 q^{24} - 440448 q^{26} - 660136 q^{29} - 4342528 q^{34} - 7191312 q^{36} + 7068520 q^{41} - 2666880 q^{44}+ \cdots + 28850688 q^{96}+O(q^{100}) $ 20 * q + 752 * q^4 + 3408 * q^6 - 2556 * q^9 - 8848 * q^14 - 59200 * q^16 + 410256 * q^21 + 156672 * q^24 - 440448 * q^26 - 660136 * q^29 - 4342528 * q^34 - 7191312 * q^36 + 7068520 * q^41 - 2666880 * q^44 + 561168 * q^46 - 11719036 * q^49 - 37110816 * q^54 - 35044352 * q^56 - 17660440 * q^61 - 20201728 * q^64 + 31902720 * q^66 - 111747216 * q^69 - 19114368 * q^74 - 54998400 * q^76 - 154212444 * q^81 - 101289216 * q^84 + 94429648 * q^86 - 105006376 * q^89 + 192757872 * q^94 + 28850688 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

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 $

$2$	−14.2721	+	7.23243i	−0.892004	+	0.452027i
$2$	−14.2721	+	7.23243i	−0.892004	+	0.452027i
$3$			44.3270i			0.547247i	0.961837	+	0.273624i	$0.0882223\pi$
$3$			44.3270i			0.547247i	−0.961837	+	0.273624i	$0.911778\pi$
$4$	151.384	−	206.443i	0.591344	−	0.806420i
$5$		0			0
$5$		0			0
$6$	−320.592	−	632.638i	−0.247370	−	0.488147i
$7$		−	2826.75i		−	1.17732i	−0.808380	−	0.588661i	$-0.799655\pi$
$7$		−	2826.75i		−	1.17732i	0.808380	−	0.588661i	$-0.200345\pi$
$8$	−667.476	+	4041.25i	−0.162958	+	0.986633i
$9$	4596.11			0.700520
$10$		0			0
$11$		−	18327.2i		−	1.25177i	−0.779915	−	0.625885i	$-0.784738\pi$
$11$		−	18327.2i		−	1.25177i	0.779915	−	0.625885i	$-0.215262\pi$
$12$	9151.02	+	6710.40i	0.441311	+	0.323611i
$13$	13946.9			0.488320			0.244160	−	0.969735i	$-0.421488\pi$
$13$	13946.9			0.488320			0.244160	+	0.969735i	$0.421488\pi$
$14$	20444.3	+	40343.6i	0.532181	+	1.05018i
$15$		0			0
$16$	−19701.8	−	62504.5i	−0.300625	−	0.953742i
$17$	−96189.1			−1.15168			−0.575838	−	0.817564i	$-0.695324\pi$
$17$	−96189.1			−1.15168			−0.575838	+	0.817564i	$0.695324\pi$
$18$	−65596.1	+	33241.1i	−0.624867	+	0.316654i
$19$		−	153485.i		−	1.17775i	−0.808225	−	0.588873i	$-0.799572\pi$
$19$		−	153485.i		−	1.17775i	0.808225	−	0.588873i	$-0.200428\pi$
$20$		0			0
$21$	125301.			0.644286
$22$	132550.	+	261567.i	0.565833	+	1.11658i
$23$			339368.i			1.21272i	0.795191	+	0.606358i	$0.207370\pi$
$23$			339368.i			1.21272i	−0.795191	+	0.606358i	$0.792630\pi$
$24$	−179137.	−	29587.2i	−0.539932	−	0.0891784i
$25$		0			0
$26$	−199051.	+	100870.i	−0.435583	+	0.220734i
$27$			494562.i			0.930605i
$28$	−583564.	−	427925.i	−0.949416	−	0.696202i
$29$	−758065.			−1.07180			−0.535901	−	0.844281i	$-0.680028\pi$
$29$	−758065.			−1.07180			−0.535901	+	0.844281i	$0.680028\pi$
$30$		0			0
$31$			1.01418e6i			1.09817i	0.835768	+	0.549083i	$0.185023\pi$
$31$			1.01418e6i			1.09817i	−0.835768	+	0.549083i	$0.814977\pi$
$32$	733244.	+	749577.i	0.699276	+	0.714852i
$33$	812389.			0.685028
$34$	1.37282e6	−	695681.i	1.02730	−	0.520588i
$35$		0			0
$36$	695778.	−	948838.i	0.414248	−	0.564913i
$37$	−135354.			−0.0722211			−0.0361106	−	0.999348i	$-0.511497\pi$
$37$	−135354.			−0.0722211			−0.0361106	+	0.999348i	$0.511497\pi$
$38$	1.11007e6	+	2.19055e6i	0.532373	+	1.05056i
$39$			618224.i			0.267232i
$40$		0			0
$41$	−2.56309e6			−0.907045			−0.453523	−	0.891245i	$-0.649833\pi$
$41$	−2.56309e6			−0.907045			−0.453523	+	0.891245i	$0.649833\pi$
$42$	−1.78831e6	+	906233.i	−0.574706	+	0.291235i
$43$		−	852539.i		−	0.249368i	−0.992197	−	0.124684i	$-0.960208\pi$
$43$		−	852539.i		−	0.249368i	0.992197	−	0.124684i	$-0.0397917\pi$
$44$	−3.78352e6	−	2.77444e6i	−1.00945	−	0.740226i
$45$		0			0
$46$	−2.45445e6	−	4.84348e6i	−0.548180	−	1.08175i
$47$			1.25626e6i			0.257447i	0.991681	+	0.128723i	$0.0410879\pi$
$47$			1.25626e6i			0.257447i	−0.991681	+	0.128723i	$0.958912\pi$
$48$	2.77064e6	−	873321.i	0.521933	−	0.164516i
$49$	−2.22572e6			−0.386087
$50$		0			0
$51$		−	4.26378e6i		−	0.630251i
$52$	2.11134e6	−	2.87925e6i	0.288765	−	0.393791i
$53$	−1.00203e7			−1.26993			−0.634963	−	0.772542i	$-0.718985\pi$
$53$	−1.00203e7			−1.26993			−0.634963	+	0.772542i	$0.718985\pi$
$54$	−3.57688e6	−	7.05842e6i	−0.420658	−	0.830104i
$55$		0			0
$56$	1.14236e7	+	1.88679e6i	1.16158	+	0.191854i
$57$	6.80354e6			0.644519
$58$	1.08192e7	−	5.48265e6i	0.956052	−	0.484483i
$59$		−	2.35908e7i		−	1.94686i	−0.228979	−	0.973431i	$-0.573539\pi$
$59$		−	2.35908e7i		−	1.94686i	0.228979	−	0.973431i	$-0.426461\pi$
$60$		0			0
$61$	−5.69128e6			−0.411046			−0.205523	−	0.978652i	$-0.565890\pi$
$61$	−5.69128e6			−0.411046			−0.205523	+	0.978652i	$0.565890\pi$
$62$	−7.33498e6	−	1.44744e7i	−0.496400	−	0.979569i
$63$		−	1.29921e7i		−	0.824738i
$64$	−1.58862e7	−	5.39488e6i	−0.946889	−	0.321560i
$65$		0			0
$66$	−1.15945e7	+	5.87554e6i	−0.611048	+	0.309651i
$67$		−	1.76526e7i		−	0.876010i	−0.898973	−	0.438005i	$-0.855685\pi$
$67$		−	1.76526e7i		−	0.876010i	0.898973	−	0.438005i	$-0.144315\pi$
$68$	−1.45615e7	+	1.98576e7i	−0.681036	+	0.928734i
$69$	−1.50432e7			−0.663656
$70$		0			0
$71$		−	3.89940e6i		−	0.153449i	−0.997052	−	0.0767246i	$-0.975554\pi$
$71$		−	3.89940e6i		−	0.153449i	0.997052	−	0.0767246i	$-0.0244462\pi$
$72$	−3.06780e6	+	1.85740e7i	−0.114156	+	0.691157i
$73$	−9.62921e6			−0.339078			−0.169539	−	0.985523i	$-0.554228\pi$
$73$	−9.62921e6			−0.339078			−0.169539	+	0.985523i	$0.554228\pi$
$74$	1.93178e6	−	978938.i	0.0644216	−	0.0326459i
$75$		0			0
$76$	−3.16860e7	−	2.32352e7i	−0.949758	−	0.696453i
$77$	−5.18063e7			−1.47374
$78$	−4.47126e6	−	8.82334e6i	−0.120796	−	0.238372i
$79$			2.34959e6i			0.0603232i	0.999545	+	0.0301616i	$0.00960220\pi$
$79$			2.34959e6i			0.0603232i	−0.999545	+	0.0301616i	$0.990398\pi$
$80$		0			0
$81$	8.23266e6			0.191249
$82$	3.65806e7	−	1.85374e7i	0.809088	−	0.410009i
$83$			1.26930e7i			0.267456i	0.991018	+	0.133728i	$0.0426948\pi$
$83$			1.26930e7i			0.267456i	−0.991018	+	0.133728i	$0.957305\pi$
$84$	1.89686e7	−	2.58677e7i	0.380995	−	0.519565i
$85$		0			0
$86$	6.16593e6	+	1.21675e7i	0.112721	+	0.222437i
$87$		−	3.36028e7i		−	0.586541i
$88$	7.40646e7	+	1.22330e7i	1.23504	+	0.203986i
$89$	−6.42709e7			−1.02436			−0.512182	−	0.858877i	$-0.671163\pi$
$89$	−6.42709e7			−1.02436			−0.512182	+	0.858877i	$0.671163\pi$
$90$		0			0
$91$		−	3.94244e7i		−	0.574910i
$92$	7.00603e7	+	5.13749e7i	0.977959	+	0.717133i
$93$	−4.49555e7			−0.600968
$94$	−9.08579e6	−	1.79294e7i	−0.116373	−	0.229643i
$95$		0			0
$96$	−3.32265e7	+	3.25025e7i	−0.391201	+	0.382677i
$97$	−6.62485e6			−0.0748323			−0.0374161	−	0.999300i	$-0.511913\pi$
$97$	−6.62485e6			−0.0748323			−0.0374161	+	0.999300i	$0.511913\pi$
$98$	3.17656e7	−	1.60973e7i	0.344392	−	0.174522i
$99$		−	8.42338e7i		−	0.876891i
$100$		0			0
$101$	5.22160e7			0.501786			0.250893	−	0.968015i	$-0.419276\pi$
$101$	5.22160e7			0.501786			0.250893	+	0.968015i	$0.419276\pi$
$102$	3.08374e7	+	6.08529e7i	0.284890	+	0.562187i
$103$		−	1.19619e8i		−	1.06280i	−0.847120	−	0.531401i	$-0.821666\pi$
$103$		−	1.19619e8i		−	1.06280i	0.847120	−	0.531401i	$-0.178334\pi$
$104$	−9.30923e6	+	5.63629e7i	−0.0795757	+	0.481792i
$105$		0			0
$106$	1.43011e8	−	7.24713e7i	1.13278	−	0.574041i
$107$			1.97409e8i			1.50602i	0.658008	+	0.753011i	$0.271399\pi$
$107$			1.97409e8i			1.50602i	−0.658008	+	0.753011i	$0.728601\pi$
$108$	1.02099e8	+	7.48687e7i	0.750458	+	0.550308i
$109$	2.24099e8			1.58758			0.793788	−	0.608195i	$-0.208106\pi$
$109$	2.24099e8			1.58758			0.793788	+	0.608195i	$0.208106\pi$
$110$		0			0
$111$		−	5.99984e6i		−	0.0395228i
$112$	−1.76685e8	+	5.56920e7i	−1.12286	+	0.353933i
$113$	−3.24514e8			−1.99031			−0.995153	−	0.0983370i	$-0.968648\pi$
$113$	−3.24514e8			−1.99031			−0.995153	+	0.0983370i	$0.968648\pi$
$114$	−9.71006e7	+	4.92061e7i	−0.574913	+	0.291340i
$115$		0			0
$116$	−1.14759e8	+	1.56498e8i	−0.633804	+	0.864322i
$117$	6.41015e7			0.342078
$118$	1.70619e8	+	3.36690e8i	0.880034	+	1.73661i
$119$			2.71903e8i			1.35589i
$120$		0			0
$121$	−1.21526e8			−0.566928
$122$	8.12264e7	−	4.11618e7i	0.366655	−	0.185804i
$123$		−	1.13614e8i		−	0.496378i
$124$	2.09371e8	+	1.53530e8i	0.885582	+	0.649393i
$125$		0			0
$126$	9.39642e7	+	1.85424e8i	0.372804	+	0.735670i
$127$		−	3.41089e8i		−	1.31115i	−0.755129	−	0.655576i	$-0.772426\pi$
$127$		−	3.41089e8i		−	1.31115i	0.755129	−	0.655576i	$-0.227574\pi$
$128$	2.65747e8	−	3.78995e7i	0.989983	−	0.141187i
$129$	3.77905e7			0.136466
$130$		0			0
$131$			2.72281e8i			0.924553i	0.886736	+	0.462277i	$0.152967\pi$
$131$			2.72281e8i			0.924553i	−0.886736	+	0.462277i	$0.847033\pi$
$132$	1.22983e8	−	1.67712e8i	0.405087	−	0.552420i
$133$	−4.33864e8			−1.38659
$134$	1.27671e8	+	2.51939e8i	0.395980	+	0.781404i
$135$		0			0
$136$	6.42040e7	−	3.88724e8i	0.187675	−	1.13628i
$137$	−3.75590e8			−1.06618			−0.533092	−	0.846057i	$-0.678970\pi$
$137$	−3.75590e8			−1.06618			−0.533092	+	0.846057i	$0.678970\pi$
$138$	2.14697e8	−	1.08799e8i	0.591984	−	0.299990i
$139$			5.07197e8i			1.35868i	0.733823	+	0.679340i	$0.237734\pi$
$139$			5.07197e8i			1.35868i	−0.733823	+	0.679340i	$0.762266\pi$
$140$		0			0
$141$	−5.56861e7			−0.140887
$142$	2.82022e7	+	5.56526e7i	0.0693632	+	0.136877i
$143$		−	2.55607e8i		−	0.611264i
$144$	−9.05516e7	−	2.87278e8i	−0.210594	−	0.668116i
$145$		0			0
$146$	1.37429e8	−	6.96426e7i	0.302459	−	0.153272i
$147$		−	9.86594e7i		−	0.211285i
$148$	−2.04904e7	+	2.79429e7i	−0.0427075	+	0.0582405i
$149$	7.01900e7			0.142407			0.0712033	−	0.997462i	$-0.477316\pi$
$149$	7.01900e7			0.142407			0.0712033	+	0.997462i	$0.477316\pi$
$150$		0			0
$151$			3.99910e8i			0.769228i	0.923078	+	0.384614i	$0.125665\pi$
$151$			3.99910e8i			0.769228i	−0.923078	+	0.384614i	$0.874335\pi$
$152$	6.20272e8	+	1.02448e8i	1.16200	+	0.191923i
$153$	−4.42096e8			−0.806772
$154$	7.39383e8	−	3.74685e8i	1.31458	−	0.666168i
$155$		0			0
$156$	1.27628e8	+	9.35893e7i	0.215501	+	0.158026i
$157$	−6.98489e8			−1.14964			−0.574819	−	0.818281i	$-0.694927\pi$
$157$	−6.98489e8			−1.14964			−0.574819	+	0.818281i	$0.694927\pi$
$158$	−1.69933e7	−	3.35336e7i	−0.0272677	−	0.0538086i
$159$		−	4.44171e8i		−	0.694964i
$160$		0			0
$161$	9.59308e8			1.42776
$162$	−1.17497e8	+	5.95421e7i	−0.170595	+	0.0864498i
$163$		−	3.45753e8i		−	0.489796i	−0.969549	−	0.244898i	$-0.921245\pi$
$163$		−	3.45753e8i		−	0.489796i	0.969549	−	0.244898i	$-0.0787545\pi$
$164$	−3.88011e8	+	5.29134e8i	−0.536375	+	0.731459i
$165$		0			0
$166$	−9.18013e7	−	1.81156e8i	−0.120897	−	0.238572i
$167$		−	9.80032e8i		−	1.26001i	−0.776591	−	0.630006i	$-0.783053\pi$
$167$		−	9.80032e8i		−	1.26001i	0.776591	−	0.630006i	$-0.216947\pi$
$168$	−8.36358e7	+	5.06374e8i	−0.104992	+	0.635674i
$169$	−6.21215e8			−0.761544
$170$		0			0
$171$		−	7.05435e8i		−	0.825036i
$172$	−1.76001e8	−	1.29061e8i	−0.201095	−	0.147462i
$173$	9.30284e8			1.03856			0.519280	−	0.854604i	$-0.326200\pi$
$173$	9.30284e8			1.03856			0.519280	+	0.854604i	$0.326200\pi$
$174$	2.43030e8	+	4.79581e8i	0.265132	+	0.523197i
$175$		0			0
$176$	−1.14553e9	+	3.61077e8i	−1.19387	+	0.376313i
$177$	1.04571e9			1.06542
$178$	9.17279e8	−	4.64835e8i	0.913737	−	0.463040i
$179$		−	3.62399e8i		−	0.353000i	−0.984301	−	0.176500i	$-0.943522\pi$
$179$		−	3.62399e8i		−	0.353000i	0.984301	−	0.176500i	$-0.0564776\pi$
$180$		0			0
$181$	−1.52080e9			−1.41696			−0.708479	−	0.705732i	$-0.750618\pi$
$181$	−1.52080e9			−1.41696			−0.708479	+	0.705732i	$0.750618\pi$
$182$	2.85134e8	+	5.62668e8i	0.259874	+	0.512822i
$183$		−	2.52278e8i		−	0.224944i
$184$	−1.37147e9	−	2.26520e8i	−1.19651	−	0.197622i
$185$		0			0
$186$	6.41609e8	−	3.25138e8i	0.536066	−	0.271654i
$187$			1.76287e9i			1.44163i
$188$	2.59346e8	+	1.90177e8i	0.207610	+	0.152239i
$189$	1.39800e9			1.09562
$190$		0			0
$191$		−	8.08221e8i		−	0.607290i	−0.952785	−	0.303645i	$-0.901796\pi$
$191$		−	8.08221e8i		−	0.607290i	0.952785	−	0.303645i	$-0.0982037\pi$
$192$	2.39139e8	−	7.04186e8i	0.175973	−	0.518183i
$193$	−2.18420e9			−1.57421			−0.787107	−	0.616817i	$-0.788422\pi$
$193$	−2.18420e9			−1.57421			−0.787107	+	0.616817i	$0.788422\pi$
$194$	9.45503e7	−	4.79137e7i	0.0667507	−	0.0338262i
$195$		0			0
$196$	−3.36938e8	+	4.59485e8i	−0.228310	+	0.311348i
$197$	−1.02380e9			−0.679751			−0.339875	−	0.940470i	$-0.610385\pi$
$197$	−1.02380e9			−0.679751			−0.339875	+	0.940470i	$0.610385\pi$
$198$	6.09214e8	+	1.20219e9i	0.396378	+	0.782190i
$199$		−	1.22571e9i		−	0.781585i	−0.920479	−	0.390792i	$-0.872201\pi$
$199$		−	1.22571e9i		−	0.781585i	0.920479	−	0.390792i	$-0.127799\pi$
$200$		0			0
$201$	7.82486e8			0.479394
$202$	−7.45231e8	+	3.77649e8i	−0.447595	+	0.226820i
$203$			2.14286e9i			1.26186i
$204$	−8.80229e8	−	6.45468e8i	−0.508247	−	0.372695i
$205$		0			0
$206$	8.65138e8	+	1.70722e9i	0.480415	+	0.948025i
$207$			1.55977e9i			0.849533i
$208$	−2.74778e8	−	8.71743e8i	−0.146801	−	0.465731i
$209$	−2.81295e9			−1.47427
$210$		0			0
$211$			2.22607e8i			0.112307i	0.998422	+	0.0561537i	$0.0178837\pi$
$211$			2.22607e8i			0.112307i	−0.998422	+	0.0561537i	$0.982116\pi$
$212$	−1.51692e9	+	2.06863e9i	−0.750963	+	1.02409i
$213$	1.72849e8			0.0839747
$214$	−1.42774e9	−	2.81743e9i	−0.680762	−	1.34338i
$215$		0			0
$216$	−1.99865e9	−	3.30108e8i	−0.918166	−	0.151650i
$217$	2.86683e9			1.29289
$218$	−3.19836e9	+	1.62078e9i	−1.41612	+	0.717626i
$219$		−	4.26834e8i		−	0.185559i
$220$		0			0
$221$	−1.34154e9			−0.562386
$222$	4.33934e7	+	8.56302e7i	0.0178654	+	0.0352545i
$223$		−	2.66616e9i		−	1.07812i	−0.842268	−	0.539059i	$-0.818780\pi$
$223$		−	2.66616e9i		−	1.07812i	0.842268	−	0.539059i	$-0.181220\pi$
$224$	2.11887e9	−	2.07270e9i	0.841611	−	0.823273i
$225$		0			0
$226$	4.63149e9	−	2.34703e9i	1.77536	−	0.899672i
$227$		−	1.45410e9i		−	0.547636i	−0.961782	−	0.273818i	$-0.911713\pi$
$227$		−	1.45410e9i		−	0.547636i	0.961782	−	0.273818i	$-0.0882866\pi$
$228$	1.02995e9	−	1.40455e9i	0.381132	−	0.519752i
$229$	−1.32962e7			−0.00483488			−0.00241744	−	0.999997i	$-0.500769\pi$
$229$	−1.32962e7			−0.00483488			−0.00241744	+	0.999997i	$0.500769\pi$
$230$		0			0
$231$		−	2.29642e9i		−	0.806498i
$232$	5.05991e8	−	3.06353e9i	0.174659	−	1.05748i
$233$	5.53873e9			1.87926			0.939628	−	0.342196i	$-0.111171\pi$
$233$	5.53873e9			1.87926			0.939628	+	0.342196i	$0.111171\pi$
$234$	−9.14862e8	+	4.63610e8i	−0.305135	+	0.154628i
$235$		0			0
$236$	−4.87017e9	−	3.57128e9i	−1.56999	−	1.15127i
$237$	−1.04151e8			−0.0330117
$238$	−1.96652e9	−	3.88061e9i	−0.612900	−	1.20946i
$239$		−	7.06175e8i		−	0.216432i	−0.994127	−	0.108216i	$-0.965486\pi$
$239$		−	7.06175e8i		−	0.216432i	0.994127	−	0.108216i	$-0.0345137\pi$
$240$		0			0
$241$	2.23345e9			0.662075			0.331038	−	0.943618i	$-0.392601\pi$
$241$	2.23345e9			0.662075			0.331038	+	0.943618i	$0.392601\pi$
$242$	1.73443e9	−	8.78928e8i	0.505702	−	0.256267i
$243$			3.60975e9i			1.03527i
$244$	−8.61569e8	+	1.17493e9i	−0.243070	+	0.331476i
$245$		0			0
$246$	8.21707e8	+	1.62151e9i	0.224376	+	0.442771i
$247$		−	2.14064e9i		−	0.575117i
$248$	−4.09855e9	−	6.76941e8i	−1.08349	−	0.178955i
$249$	−5.62643e8			−0.146365
$250$		0			0
$251$			3.22973e9i			0.813713i	0.913492	+	0.406857i	$0.133375\pi$
$251$			3.22973e9i			0.813713i	−0.913492	+	0.406857i	$0.866625\pi$
$252$	−2.68213e9	−	1.96679e9i	−0.665085	−	0.487704i
$253$	6.21965e9			1.51804
$254$	2.46690e9	+	4.86805e9i	0.592676	+	1.16955i
$255$		0			0
$256$	−3.51865e9	+	2.46290e9i	−0.819249	+	0.573438i
$257$	−3.73492e9			−0.856148			−0.428074	−	0.903744i	$-0.640808\pi$
$257$	−3.73492e9			−0.856148			−0.428074	+	0.903744i	$0.640808\pi$
$258$	−5.39349e8	+	2.73317e8i	−0.121728	+	0.0616862i
$259$			3.82612e8i			0.0850275i
$260$		0			0
$261$	−3.48416e9			−0.750819
$262$	−1.96925e9	−	3.88601e9i	−0.417923	−	0.824706i
$263$			5.87828e9i			1.22865i	0.789054	+	0.614324i	$0.210571\pi$
$263$			5.87828e9i			1.22865i	−0.789054	+	0.614324i	$0.789429\pi$
$264$	−5.42250e8	+	3.28306e9i	−0.111631	+	0.675871i
$265$		0			0
$266$	6.19214e9	−	3.13789e9i	1.23684	−	0.626774i
$267$		−	2.84894e9i		−	0.560580i
$268$	−3.64426e9	−	2.67232e9i	−0.706431	−	0.518023i
$269$	2.61826e9			0.500039			0.250019	−	0.968241i	$-0.419563\pi$
$269$	2.61826e9			0.500039			0.250019	+	0.968241i	$0.419563\pi$
$270$		0			0
$271$			4.66174e9i			0.864312i	0.901799	+	0.432156i	$0.142247\pi$
$271$			4.66174e9i			0.864312i	−0.901799	+	0.432156i	$0.857753\pi$
$272$	1.89509e9	+	6.01225e9i	0.346223	+	1.09840i
$273$	1.74757e9			0.314618
$274$	5.36045e9	−	2.71643e9i	0.951041	−	0.481944i
$275$		0			0
$276$	−2.27730e9	+	3.10556e9i	−0.392449	+	0.535185i
$277$	3.79455e9			0.644526			0.322263	−	0.946650i	$-0.395556\pi$
$277$	3.79455e9			0.644526			0.322263	+	0.946650i	$0.395556\pi$
$278$	−3.66826e9	−	7.23875e9i	−0.614160	−	1.21195i
$279$			4.66128e9i			0.769288i
$280$		0			0
$281$	5.95287e9			0.954776			0.477388	−	0.878693i	$-0.341584\pi$
$281$	5.95287e9			0.954776			0.477388	+	0.878693i	$0.341584\pi$
$282$	7.94756e8	−	4.02746e8i	0.125672	−	0.0636846i
$283$		−	6.09829e9i		−	0.950742i	−0.879785	−	0.475371i	$-0.842314\pi$
$283$		−	6.09829e9i		−	0.950742i	0.879785	−	0.475371i	$-0.157686\pi$
$284$	−8.05006e8	−	5.90307e8i	−0.123744	−	0.0907413i
$285$		0			0
$286$	1.84866e9	+	3.64804e9i	0.276308	+	0.545250i
$287$			7.24522e9i			1.06788i
$288$	3.37007e9	+	3.44514e9i	0.489857	+	0.500768i
$289$	2.27658e9			0.326357
$290$		0			0
$291$		−	2.93660e8i		−	0.0409517i
$292$	−1.45771e9	+	1.98789e9i	−0.200512	+	0.273439i
$293$	3.58577e9			0.486533			0.243266	−	0.969960i	$-0.421781\pi$
$293$	3.58577e9			0.486533			0.243266	+	0.969960i	$0.421781\pi$
$294$	7.13547e8	+	1.40807e9i	0.0955066	+	0.188467i
$295$		0			0
$296$	9.03456e7	−	5.46999e8i	0.0117690	−	0.0712557i
$297$	9.06391e9			1.16490
$298$	−1.00176e9	+	5.07644e8i	−0.127027	+	0.0643716i
$299$			4.73313e9i			0.592194i
$300$		0			0
$301$	−2.40992e9			−0.293586
$302$	−2.89232e9	−	5.70755e9i	−0.347711	−	0.686155i
$303$			2.31458e9i			0.274601i
$304$	−9.59351e9	+	3.02393e9i	−1.12327	+	0.354060i
$305$		0			0
$306$	6.30963e9	−	3.19743e9i	0.719644	−	0.364683i
$307$			5.11579e9i			0.575917i	0.957643	+	0.287958i	$0.0929765\pi$
$307$			5.11579e9i			0.575917i	−0.957643	+	0.287958i	$0.907024\pi$
$308$	−7.84265e9	+	1.06951e10i	−0.871485	+	1.18845i
$309$	5.30237e9			0.581616
$310$		0			0
$311$			2.80934e9i			0.300305i	0.988663	+	0.150152i	$0.0479764\pi$
$311$			2.80934e9i			0.300305i	−0.988663	+	0.150152i	$0.952024\pi$
$312$	−2.49840e9	−	4.12650e8i	−0.263659	−	0.0435476i
$313$	−4.69101e9			−0.488753			−0.244376	−	0.969680i	$-0.578583\pi$
$313$	−4.69101e9			−0.488753			−0.244376	+	0.969680i	$0.578583\pi$
$314$	9.96888e9	−	5.05177e9i	1.02548	−	0.519667i
$315$		0			0
$316$	4.85058e8	+	3.55691e8i	0.0486458	+	0.0356718i
$317$	2.44480e9			0.242107			0.121053	−	0.992646i	$-0.461373\pi$
$317$	2.44480e9			0.242107			0.121053	+	0.992646i	$0.461373\pi$
$318$	3.21244e9	+	6.33925e9i	0.314142	+	0.619911i
$319$			1.38932e10i			1.34165i
$320$		0			0
$321$	−8.75054e9			−0.824166
$322$	−1.36913e10	+	6.93813e9i	−1.27357	+	0.645385i
$323$			1.47636e10i			1.35638i
$324$	1.24629e9	−	1.69958e9i	0.113094	−	0.154227i
$325$		0			0
$326$	2.50063e9	+	4.93461e9i	0.221401	+	0.436900i
$327$			9.93365e9i			0.868796i
$328$	1.71080e9	−	1.03581e10i	0.147810	−	0.894921i
$329$	3.55112e9			0.303097
$330$		0			0
$331$		−	2.14898e10i		−	1.79028i	−0.445786	−	0.895139i	$-0.647076\pi$
$331$		−	2.14898e10i		−	1.79028i	0.445786	−	0.895139i	$-0.352924\pi$
$332$	2.62039e9	+	1.92152e9i	0.215682	+	0.158158i
$333$	−6.22103e8			−0.0505924
$334$	7.08801e9	+	1.39871e10i	0.569559	+	1.12394i
$335$		0			0
$336$	−2.46866e9	−	7.83190e9i	−0.193689	−	0.614483i
$337$	−4.77773e9			−0.370426			−0.185213	−	0.982698i	$-0.559298\pi$
$337$	−4.77773e9			−0.370426			−0.185213	+	0.982698i	$0.559298\pi$
$338$	8.86602e9	−	4.49289e9i	0.679301	−	0.344238i
$339$		−	1.43847e10i		−	1.08919i
$340$		0			0
$341$	1.85870e10			1.37465
$342$	5.10201e9	+	1.00680e10i	0.372938	+	0.735936i
$343$		−	1.00041e10i		−	0.722773i
$344$	3.44532e9	+	5.69050e8i	0.246035	+	0.0406365i
$345$		0			0
$346$	−1.32771e10	+	6.72821e9i	−0.926399	+	0.469456i
$347$		−	7.28826e9i		−	0.502696i	−0.967897	−	0.251348i	$-0.919126\pi$
$347$		−	7.28826e9i		−	0.502696i	0.967897	−	0.251348i	$-0.0808739\pi$
$348$	−6.93707e9	−	5.08692e9i	−0.472998	−	0.346847i
$349$	−2.60410e9			−0.175532			−0.0877660	−	0.996141i	$-0.527973\pi$
$349$	−2.60410e9			−0.175532			−0.0877660	+	0.996141i	$0.527973\pi$
$350$		0			0
$351$			6.89760e9i			0.454433i
$352$	1.37376e10	−	1.34383e10i	0.894830	−	0.875333i
$353$	7.30914e9			0.470725			0.235363	−	0.971908i	$-0.424372\pi$
$353$	7.30914e9			0.470725			0.235363	+	0.971908i	$0.424372\pi$
$354$	−1.49245e10	+	7.56303e9i	−0.950355	+	0.481596i
$355$		0			0
$356$	−9.72959e9	+	1.32683e10i	−0.605751	+	0.826067i
$357$	−1.20526e10			−0.742009
$358$	2.62102e9	+	5.17218e9i	0.159565	+	0.314878i
$359$		−	1.69103e10i		−	1.01806i	−0.860749	−	0.509029i	$-0.830004\pi$
$359$		−	1.69103e10i		−	1.01806i	0.860749	−	0.509029i	$-0.169996\pi$
$360$		0			0
$361$	−6.57413e9			−0.387088
$362$	2.17049e10	−	1.09991e10i	1.26393	−	0.640503i
$363$		−	5.38689e9i		−	0.310250i
$364$	−8.13891e9	−	5.96822e9i	−0.463618	−	0.339969i
$365$		0			0
$366$	1.82458e9	+	3.60052e9i	0.101681	+	0.200651i
$367$		−	3.03452e10i		−	1.67273i	−0.548174	−	0.836364i	$-0.684677\pi$
$367$		−	3.03452e10i		−	1.67273i	0.548174	−	0.836364i	$-0.315323\pi$
$368$	2.12120e10	−	6.68615e9i	1.15662	−	0.364573i
$369$	−1.17803e10			−0.635404
$370$		0			0
$371$			2.83250e10i			1.49511i
$372$	−6.80555e9	+	9.28077e9i	−0.355379	+	0.484632i
$373$	−9.46195e9			−0.488816			−0.244408	−	0.969673i	$-0.578594\pi$
$373$	−9.46195e9			−0.488816			−0.244408	+	0.969673i	$0.578594\pi$
$374$	−1.27499e10	−	2.51599e10i	−0.651657	−	1.28594i
$375$		0			0
$376$	−5.07685e9	−	8.38522e8i	−0.254005	−	0.0419530i
$377$	−1.05727e10			−0.523382
$378$	−1.99524e10	+	1.01110e10i	−0.977300	+	0.495250i
$379$		−	1.10814e10i		−	0.537078i	−0.963269	−	0.268539i	$-0.913459\pi$
$379$		−	1.10814e10i		−	0.537078i	0.963269	−	0.268539i	$-0.0865409\pi$
$380$		0			0
$381$	1.51195e10			0.717525
$382$	5.84540e9	+	1.15350e10i	0.274511	+	0.541706i
$383$		−	3.17801e10i		−	1.47693i	−0.674292	−	0.738465i	$-0.735551\pi$
$383$		−	3.17801e10i		−	1.47693i	0.674292	−	0.738465i	$-0.264449\pi$
$384$	1.67997e9	+	1.17798e10i	0.0772639	+	0.541765i
$385$		0			0
$386$	3.11731e10	−	1.57971e10i	1.40421	−	0.711586i
$387$		−	3.91837e9i		−	0.174687i
$388$	−1.00290e9	+	1.36766e9i	−0.0442516	+	0.0603462i
$389$	−2.63166e10			−1.14929			−0.574647	−	0.818402i	$-0.694860\pi$
$389$	−2.63166e10			−1.14929			−0.574647	+	0.818402i	$0.694860\pi$
$390$		0			0
$391$		−	3.26435e10i		−	1.39666i
$392$	1.48561e9	−	8.99468e9i	0.0629161	−	0.380927i
$393$	−1.20694e10			−0.505959
$394$	1.46117e10	−	7.40455e9i	0.606341	−	0.307266i
$395$		0			0
$396$	−1.73895e10	−	1.27516e10i	−0.707142	−	0.518544i
$397$	−1.18226e9			−0.0475937			−0.0237969	−	0.999717i	$-0.507575\pi$
$397$	−1.18226e9			−0.0475937			−0.0237969	+	0.999717i	$0.507575\pi$
$398$	8.86487e9	+	1.74934e10i	0.353297	+	0.697177i
$399$		−	1.92319e10i		−	0.758806i
$400$		0			0
$401$	−4.04552e10			−1.56458			−0.782289	−	0.622916i	$-0.785948\pi$
$401$	−4.04552e10			−1.56458			−0.782289	+	0.622916i	$0.785948\pi$
$402$	−1.11677e10	+	5.65927e9i	−0.427621	+	0.216699i
$403$			1.41447e10i			0.536256i
$404$	7.90467e9	−	1.07797e10i	0.296728	−	0.404650i
$405$		0			0
$406$	−1.54981e10	−	3.05831e10i	−0.570393	−	1.12558i
$407$			2.48066e9i			0.0904042i
$408$	1.72310e10	+	2.84597e9i	0.621827	+	0.102705i
$409$	2.26640e9			0.0809921			0.0404960	−	0.999180i	$-0.487106\pi$
$409$	2.26640e9			0.0809921			0.0404960	+	0.999180i	$0.487106\pi$
$410$		0			0
$411$		−	1.66488e10i		−	0.583466i
$412$	−2.46946e10	−	1.81085e10i	−0.857065	−	0.628482i
$413$	−6.66854e10			−2.29208
$414$	−1.12810e10	−	2.22612e10i	−0.384012	−	0.757787i
$415$		0			0
$416$	1.02265e10	+	1.04543e10i	0.341470	+	0.349076i
$417$	−2.24825e10			−0.743534
$418$	4.01466e10	−	2.03444e10i	1.31505	−	0.666408i
$419$			5.97866e10i			1.93976i	0.243587	+	0.969879i	$0.421676\pi$
$419$			5.97866e10i			1.93976i	−0.243587	+	0.969879i	$0.578324\pi$
$420$		0			0
$421$	1.37859e8			0.00438841			0.00219421	−	0.999998i	$-0.499302\pi$
$421$	1.37859e8			0.00438841			0.00219421	+	0.999998i	$0.499302\pi$
$422$	−1.60999e9	−	3.17706e9i	−0.0507659	−	0.100179i
$423$			5.77390e9i			0.180347i
$424$	6.68834e9	−	4.04947e10i	0.206945	−	1.25295i
$425$		0			0
$426$	−2.46691e9	+	1.25012e9i	−0.0749058	+	0.0379588i
$427$			1.60878e10i			0.483934i
$428$	4.07537e10	+	2.98845e10i	1.21449	+	0.890577i
$429$	1.13303e10			0.334512
$430$		0			0
$431$			1.87046e10i			0.542051i	0.962572	+	0.271026i	$0.0873628\pi$
$431$			1.87046e10i			0.542051i	−0.962572	+	0.271026i	$0.912637\pi$
$432$	3.09123e10	−	9.74374e9i	0.887558	−	0.279763i
$433$	−1.46857e10			−0.417776			−0.208888	−	0.977940i	$-0.566984\pi$
$433$	−1.46857e10			−0.417776			−0.208888	+	0.977940i	$0.566984\pi$
$434$	−4.09156e10	+	2.07341e10i	−1.15327	+	0.584423i
$435$		0			0
$436$	3.39250e10	−	4.62638e10i	0.938803	−	1.28025i
$437$	5.20879e10			1.42827
$438$	3.08705e9	+	6.09181e9i	0.0838778	+	0.165520i
$439$		−	2.58143e10i		−	0.695029i	−0.937675	−	0.347514i	$-0.887026\pi$
$439$		−	2.58143e10i		−	0.695029i	0.937675	−	0.347514i	$-0.112974\pi$
$440$		0			0
$441$	−1.02297e10			−0.270462
$442$	1.91465e10	−	9.70259e9i	0.501651	−	0.254213i
$443$		−	3.46551e10i		−	0.899813i	−0.893076	−	0.449906i	$-0.851457\pi$
$443$		−	3.46551e10i		−	0.899813i	0.893076	−	0.449906i	$-0.148543\pi$
$444$	−1.23863e9	−	9.08280e8i	−0.0318720	−	0.0233716i
$445$		0			0
$446$	1.92828e10	+	3.80516e10i	0.487338	+	0.961686i
$447$			3.11131e9i			0.0779316i
$448$	−1.52500e10	+	4.49062e10i	−0.378579	+	1.11479i
$449$	3.50756e10			0.863018			0.431509	−	0.902109i	$-0.357981\pi$
$449$	3.50756e10			0.863018			0.431509	+	0.902109i	$0.357981\pi$
$450$		0			0
$451$			4.69742e10i			1.13541i
$452$	−4.91263e10	+	6.69938e10i	−1.17696	+	1.60502i
$453$	−1.77268e10			−0.420958
$454$	1.05167e10	+	2.07531e10i	0.247546	+	0.488494i
$455$		0			0
$456$	−4.54120e9	+	2.74948e10i	−0.105030	+	0.635903i
$457$	−1.80923e10			−0.414791			−0.207395	−	0.978257i	$-0.566499\pi$
$457$	−1.80923e10			−0.414791			−0.207395	+	0.978257i	$0.566499\pi$
$458$	1.89764e8	−	9.61638e7i	0.00431274	−	0.00218550i
$459$		−	4.75714e10i		−	1.07176i
$460$		0			0
$461$	2.22531e10			0.492704			0.246352	−	0.969180i	$-0.420768\pi$
$461$	2.22531e10			0.492704			0.246352	+	0.969180i	$0.420768\pi$
$462$	1.66087e10	+	3.27747e10i	0.364559	+	0.719400i
$463$		−	4.13307e10i		−	0.899391i	−0.893182	−	0.449695i	$-0.851533\pi$
$463$		−	4.13307e10i		−	0.899391i	0.893182	−	0.449695i	$-0.148467\pi$
$464$	1.49352e10	+	4.73825e10i	0.322211	+	1.02222i
$465$		0			0
$466$	−7.90491e10	+	4.00584e10i	−1.67631	+	0.849474i
$467$			3.60193e10i			0.757300i	0.925540	+	0.378650i	$0.123612\pi$
$467$			3.60193e10i			0.757300i	−0.925540	+	0.378650i	$0.876388\pi$
$468$	9.70395e9	−	1.32333e10i	0.202286	−	0.275858i
$469$	−4.98994e10			−1.03135
$470$		0			0
$471$		−	3.09619e10i		−	0.629136i
$472$	9.53365e10	+	1.57463e10i	1.92084	+	0.317257i
$473$	−1.56246e10			−0.312151
$474$	1.48644e9	−	7.53261e8i	0.0294466	−	0.0149222i
$475$		0			0
$476$	5.61325e10	+	4.11617e10i	1.09342	+	0.801799i
$477$	−4.60546e10			−0.889610
$478$	5.10736e9	+	1.00786e10i	0.0978328	+	0.193058i
$479$			5.31999e10i			1.01058i	0.862951	+	0.505288i	$0.168614\pi$
$479$			5.31999e10i			1.01058i	−0.862951	+	0.505288i	$0.831386\pi$
$480$		0			0
$481$	−1.88777e9			−0.0352670
$482$	−3.18759e10	+	1.61532e10i	−0.590574	+	0.299276i
$483$			4.25233e10i			0.781337i
$484$	−1.83971e10	+	2.50883e10i	−0.335249	+	0.457182i
$485$		0			0
$486$	−2.61072e10	−	5.15186e10i	−0.467968	−	0.923462i
$487$		−	2.16155e10i		−	0.384281i	−0.981367	−	0.192140i	$-0.938457\pi$
$487$		−	2.16155e10i		−	0.384281i	0.981367	−	0.192140i	$-0.0615429\pi$
$488$	3.79880e9	−	2.29999e10i	0.0669833	−	0.405552i
$489$	1.53262e10			0.268040
$490$		0			0
$491$		−	6.94657e9i		−	0.119521i	−0.998213	−	0.0597606i	$-0.980966\pi$
$491$		−	6.94657e9i		−	0.119521i	0.998213	−	0.0597606i	$-0.0190337\pi$
$492$	−2.34549e10	−	1.71994e10i	−0.400289	−	0.293530i
$493$	7.29176e10			1.23437
$494$	1.54820e10	+	3.05514e10i	0.259968	+	0.513007i
$495$		0			0
$496$	6.33907e10	−	1.99811e10i	1.04737	−	0.330136i
$497$	−1.10226e10			−0.180659
$498$	8.03009e9	−	4.06928e9i	0.130558	−	0.0661607i
$499$			3.04616e10i			0.491304i	0.969358	+	0.245652i	$0.0790021\pi$
$499$			3.04616e10i			0.491304i	−0.969358	+	0.245652i	$0.920998\pi$
$500$		0			0
$501$	4.34419e10			0.689538
$502$	−2.33588e10	−	4.60949e10i	−0.367820	−	0.725836i
$503$			2.80844e10i			0.438725i	0.975643	+	0.219363i	$0.0703978\pi$
$503$			2.80844e10i			0.438725i	−0.975643	+	0.219363i	$0.929602\pi$
$504$	5.25042e10	+	8.67190e9i	0.813714	+	0.134398i
$505$		0			0
$506$	−8.87673e10	+	4.49832e10i	−1.35410	+	0.686196i
$507$		−	2.75366e10i		−	0.416753i
$508$	−7.04157e10	−	5.16355e10i	−1.05734	−	0.775342i
$509$	1.09246e11			1.62755			0.813773	−	0.581183i	$-0.197410\pi$
$509$	1.09246e11			1.62755			0.813773	+	0.581183i	$0.197410\pi$
$510$		0			0
$511$			2.72194e10i			0.399204i
$512$	3.24057e10	−	6.05990e10i	0.471565	−	0.881831i
$513$	7.59079e10			1.09602
$514$	5.33051e10	−	2.70126e10i	0.763688	−	0.387002i
$515$		0			0
$516$	5.72088e9	−	7.80160e9i	0.0806982	−	0.110049i
$517$	2.30236e10			0.322264
$518$	−2.76721e9	−	5.46067e9i	−0.0384347	−	0.0758449i
$519$			4.12367e10i			0.568349i
$520$		0			0
$521$	7.86075e10			1.06687			0.533437	−	0.845840i	$-0.320900\pi$
$521$	7.86075e10			1.06687			0.533437	+	0.845840i	$0.320900\pi$
$522$	4.97261e10	−	2.51989e10i	0.669734	−	0.339390i
$523$			7.29827e10i			0.975468i	0.872992	+	0.487734i	$0.162176\pi$
$523$			7.29827e10i			0.975468i	−0.872992	+	0.487734i	$0.837824\pi$
$524$	5.62106e10	+	4.12190e10i	0.745578	+	0.546729i
$525$		0			0
$526$	−4.25143e10	−	8.38953e10i	−0.555382	−	1.09596i
$527$		−	9.75530e10i		−	1.26473i
$528$	−1.60055e10	−	5.07779e10i	−0.205936	−	0.653340i
$529$	−3.68596e10			−0.470682
$530$		0			0
$531$		−	1.08426e11i		−	1.36382i
$532$	−6.56801e10	+	8.95684e10i	−0.819950	+	1.11817i
$533$	−3.57472e10			−0.442928
$534$	2.06047e10	+	4.06602e10i	0.253397	+	0.500040i
$535$		0			0
$536$	7.13385e10	+	1.17827e10i	0.864300	+	0.142753i
$537$	1.60641e10			0.193178
$538$	−3.73680e10	+	1.89364e10i	−0.446037	+	0.226031i
$539$			4.07911e10i			0.483293i
$540$		0			0
$541$	−6.69135e10			−0.781133			−0.390566	−	0.920575i	$-0.627721\pi$
$541$	−6.69135e10			−0.781133			−0.390566	+	0.920575i	$0.627721\pi$
$542$	−3.37157e10	−	6.65327e10i	−0.390692	−	0.770970i
$543$		−	6.74124e10i		−	0.775426i
$544$	−7.05301e10	−	7.21011e10i	−0.805339	−	0.823277i
$545$		0			0
$546$	−2.49414e10	+	1.26391e10i	−0.280640	+	0.142216i
$547$			1.11865e11i			1.24953i	0.780813	+	0.624765i	$0.214805\pi$
$547$			1.11865e11i			1.24953i	−0.780813	+	0.624765i	$0.785195\pi$
$548$	−5.68584e10	+	7.75382e10i	−0.630481	+	0.859792i
$549$	−2.61578e10			−0.287946
$550$		0			0
$551$			1.16352e11i			1.26231i
$552$	1.00410e10	−	6.07932e10i	0.108148	−	0.654785i
$553$	6.64172e9			0.0710199
$554$	−5.41560e10	+	2.74438e10i	−0.574920	+	0.291343i
$555$		0			0
$556$	1.04707e11	+	7.67815e10i	1.09567	+	0.803447i
$557$	2.01090e8			0.00208915			0.00104458	−	0.999999i	$-0.499668\pi$
$557$	2.01090e8			0.00208915			0.00104458	+	0.999999i	$0.499668\pi$
$558$	−3.37124e10	−	6.65262e10i	−0.347738	−	0.686208i
$559$		−	1.18903e10i		−	0.121771i
$560$		0			0
$561$	−7.81429e10			−0.788930
$562$	−8.49598e10	+	4.30537e10i	−0.851664	+	0.431584i
$563$		−	7.36627e10i		−	0.733185i	−0.930382	−	0.366593i	$-0.880524\pi$
$563$		−	7.36627e10i		−	0.733185i	0.930382	−	0.366593i	$-0.119476\pi$
$564$	−8.42999e9	+	1.14960e10i	−0.0833126	+	0.113614i
$565$		0			0
$566$	4.41055e10	+	8.70353e10i	0.429761	+	0.848066i
$567$		−	2.32717e10i		−	0.225162i
$568$	1.57585e10	+	2.60276e9i	0.151398	+	0.0250058i
$569$	−5.53549e10			−0.528089			−0.264045	−	0.964510i	$-0.585057\pi$
$569$	−5.53549e10			−0.528089			−0.264045	+	0.964510i	$0.585057\pi$
$570$		0			0
$571$			2.98777e10i			0.281063i	0.990076	+	0.140531i	$0.0448811\pi$
$571$			2.98777e10i			0.281063i	−0.990076	+	0.140531i	$0.955119\pi$
$572$	−5.27684e10	−	3.86948e10i	−0.492935	−	0.361467i
$573$	3.58260e10			0.332338
$574$	−5.24005e10	−	1.03404e11i	−0.482712	−	0.952557i
$575$		0			0
$576$	−7.30146e10	−	2.47955e10i	−0.663315	−	0.225259i
$577$	1.20418e11			1.08640			0.543200	−	0.839603i	$-0.317212\pi$
$577$	1.20418e11			1.08640			0.543200	+	0.839603i	$0.317212\pi$
$578$	−3.24916e10	+	1.64652e10i	−0.291112	+	0.147522i
$579$		−	9.68192e10i		−	0.861484i
$580$		0			0
$581$	3.58800e10			0.314882
$582$	2.12387e9	+	4.19113e9i	0.0185113	+	0.0365291i
$583$			1.83644e11i			1.58966i
$584$	6.42727e9	−	3.89141e10i	0.0552555	−	0.334545i
$585$		0			0
$586$	−5.11764e10	+	2.59338e10i	−0.433989	+	0.219926i
$587$		−	1.26290e10i		−	0.106369i	−0.998585	−	0.0531845i	$-0.983063\pi$
$587$		−	1.26290e10i		−	0.106369i	0.998585	−	0.0531845i	$-0.0169371\pi$
$588$	−2.03676e10	−	1.49355e10i	−0.170385	−	0.124942i
$589$	1.55661e11			1.29336
$590$		0			0
$591$		−	4.53820e10i		−	0.371992i
$592$	2.66671e9	+	8.46023e9i	0.0217115	+	0.0688804i
$593$	9.56312e10			0.773359			0.386679	−	0.922214i	$-0.373622\pi$
$593$	9.56312e10			0.773359			0.386679	+	0.922214i	$0.373622\pi$
$594$	−1.29361e11	+	6.55541e10i	−1.03910	+	0.526567i
$595$		0			0
$596$	1.06256e10	−	1.44903e10i	0.0842113	−	0.114839i
$597$	5.43322e10			0.427720
$598$	−3.42320e10	−	6.75516e10i	−0.267687	−	0.528239i
$599$		−	5.13440e9i		−	0.0398825i	−0.999801	−	0.0199413i	$-0.993652\pi$
$599$		−	5.13440e9i		−	0.0398825i	0.999801	−	0.0199413i	$-0.00634792\pi$
$600$		0			0
$601$	−9.84800e8			−0.00754832			−0.00377416	−	0.999993i	$-0.501201\pi$
$601$	−9.84800e8			−0.00754832			−0.00377416	+	0.999993i	$0.501201\pi$
$602$	3.43945e10	−	1.74295e10i	0.261880	−	0.132709i
$603$		−	8.11333e10i		−	0.613663i
$604$	8.25589e10	+	6.05400e10i	0.620320	+	0.454878i
$605$		0			0
$606$	−1.67400e10	−	3.30339e10i	−0.124127	−	0.244945i
$607$			2.29100e11i			1.68760i	0.536654	+	0.843802i	$0.319688\pi$
$607$			2.29100e11i			1.68760i	−0.536654	+	0.843802i	$0.680312\pi$
$608$	1.15049e11	−	1.12542e11i	0.841915	−	0.823570i
$609$	−9.49867e10			−0.690547
$610$		0			0
$611$			1.75209e10i			0.125716i
$612$	−6.69263e10	+	9.12678e10i	−0.477080	+	0.650597i
$613$	1.82859e11			1.29502			0.647508	−	0.762058i	$-0.275811\pi$
$613$	1.82859e11			1.29502			0.647508	+	0.762058i	$0.275811\pi$
$614$	−3.69996e10	−	7.30130e10i	−0.260330	−	0.513720i
$615$		0			0
$616$	3.45795e10	−	2.09362e11i	0.240157	−	1.45404i
$617$	4.78934e10			0.330472			0.165236	−	0.986254i	$-0.447161\pi$
$617$	4.78934e10			0.330472			0.165236	+	0.986254i	$0.447161\pi$
$618$	−7.56758e10	+	3.83490e10i	−0.518804	+	0.262906i
$619$		−	8.75787e10i		−	0.596535i	−0.954482	−	0.298267i	$-0.903591\pi$
$619$		−	8.75787e10i		−	0.596535i	0.954482	−	0.298267i	$-0.0964087\pi$
$620$		0			0
$621$	−1.67838e11			−1.12856
$622$	−2.03183e10	−	4.00951e10i	−0.135746	−	0.267873i
$623$			1.81678e11i			1.20601i
$624$	3.86418e10	−	1.21801e10i	0.254870	−	0.0803365i
$625$		0			0
$626$	6.69505e10	−	3.39274e10i	0.435970	−	0.220929i
$627$		−	1.24690e11i		−	0.806789i
$628$	−1.05740e11	+	1.44198e11i	−0.679831	+	0.927090i
$629$	1.30196e10			0.0831753
$630$		0			0
$631$		−	1.79020e11i		−	1.12923i	−0.825354	−	0.564616i	$-0.809024\pi$
$631$		−	1.79020e11i		−	1.12923i	0.825354	−	0.564616i	$-0.190976\pi$
$632$	−9.49530e9	−	1.56830e9i	−0.0595169	−	0.00983016i
$633$	−9.86749e9			−0.0614599
$634$	−3.48924e10	+	1.76819e10i	−0.215960	+	0.109439i
$635$		0			0
$636$	−9.16963e10	−	6.72405e10i	−0.560432	−	0.410963i
$637$	−3.10418e10			−0.188534
$638$	−1.00481e11	−	1.98285e11i	−0.606462	−	1.19676i
$639$		−	1.79221e10i		−	0.107494i
$640$		0			0
$641$	9.29527e10			0.550592			0.275296	−	0.961360i	$-0.411224\pi$
$641$	9.29527e10			0.550592			0.275296	+	0.961360i	$0.411224\pi$
$642$	1.24888e11	−	6.32877e10i	0.735160	−	0.372545i
$643$			1.76187e11i			1.03069i	0.856982	+	0.515347i	$0.172337\pi$
$643$			1.76187e11i			1.03069i	−0.856982	+	0.515347i	$0.827663\pi$
$644$	1.45224e11	−	1.98043e11i	0.844296	−	1.15137i
$645$		0			0
$646$	−1.06777e11	−	2.10707e11i	−0.613121	−	1.20990i
$647$			2.37613e11i			1.35598i	0.735071	+	0.677990i	$0.237149\pi$
$647$			2.37613e11i			1.35598i	−0.735071	+	0.677990i	$0.762851\pi$
$648$	−5.49511e9	+	3.32702e10i	−0.0311657	+	0.188693i
$649$	−4.32353e11			−2.43702
$650$		0			0
$651$			1.27078e11i			0.707533i
$652$	−7.13784e10	−	5.23415e10i	−0.394981	−	0.289638i
$653$	2.96902e11			1.63290			0.816451	−	0.577415i	$-0.195938\pi$
$653$	2.96902e11			1.63290			0.816451	+	0.577415i	$0.195938\pi$
$654$	−7.18444e10	−	1.41774e11i	−0.392719	−	0.774970i
$655$		0			0
$656$	5.04974e10	+	1.60205e11i	0.272680	+	0.865087i
$657$	−4.42570e10			−0.237531
$658$	−5.06819e10	+	2.56832e10i	−0.270364	+	0.137008i
$659$		−	1.31179e11i		−	0.695541i	−0.937580	−	0.347771i	$-0.886939\pi$
$659$		−	1.31179e11i		−	0.695541i	0.937580	−	0.347771i	$-0.113061\pi$
$660$		0			0
$661$	5.54817e10			0.290632			0.145316	−	0.989385i	$-0.453580\pi$
$661$	5.54817e10			0.290632			0.145316	+	0.989385i	$0.453580\pi$
$662$	1.55423e11	+	3.06704e11i	0.809254	+	1.59694i
$663$		−	5.94665e10i		−	0.307764i
$664$	−5.12956e10	−	8.47229e9i	−0.263881	−	0.0435841i
$665$		0			0
$666$	8.87869e9	−	4.49931e9i	0.0451286	−	0.0228691i
$667$		−	2.57263e11i		−	1.29979i
$668$	−2.02321e11	−	1.48361e11i	−1.01610	−	0.745100i
$669$	1.18183e11			0.589997
$670$		0			0
$671$			1.04305e11i			0.514535i
$672$	9.18765e10	+	9.39230e10i	0.450534	+	0.460569i
$673$	−5.91921e10			−0.288538			−0.144269	−	0.989538i	$-0.546083\pi$
$673$	−5.91921e10			−0.288538			−0.144269	+	0.989538i	$0.546083\pi$
$674$	6.81881e10	−	3.45546e10i	0.330422	−	0.167443i
$675$		0			0
$676$	−9.40420e10	+	1.28246e11i	−0.450334	+	0.614124i
$677$	−2.84457e11			−1.35413			−0.677066	−	0.735922i	$-0.736749\pi$
$677$	−2.84457e11			−1.35413			−0.677066	+	0.735922i	$0.736749\pi$
$678$	1.04037e11	+	2.05300e11i	0.492343	+	0.971562i
$679$			1.87268e10i			0.0881017i
$680$		0			0
$681$	6.44561e10			0.299692
$682$	−2.65275e11	+	1.34429e11i	−1.22619	+	0.621379i
$683$		−	3.01776e11i		−	1.38676i	−0.720571	−	0.693381i	$-0.756120\pi$
$683$		−	3.01776e11i		−	1.38676i	0.720571	−	0.693381i	$-0.243880\pi$
$684$	−1.45632e11	−	1.06792e11i	−0.665325	−	0.487880i
$685$		0			0
$686$	7.23540e10	+	1.42779e11i	0.326713	+	0.644717i
$687$		−	5.89381e8i		−	0.00264588i
$688$	−5.32875e10	+	1.67965e10i	−0.237833	+	0.0749662i
$689$	−1.39753e11			−0.620130
$690$		0			0
$691$		−	1.07258e11i		−	0.470455i	−0.971940	−	0.235227i	$-0.924417\pi$
$691$		−	1.07258e11i		−	0.470455i	0.971940	−	0.235227i	$-0.0755835\pi$
$692$	1.40830e11	−	1.92051e11i	0.614145	−	0.837514i
$693$	−2.38108e11			−1.03238
$694$	5.27118e10	+	1.04019e11i	0.227232	+	0.448407i
$695$		0			0
$696$	1.35797e11	+	2.24291e10i	0.578701	+	0.0955816i
$697$	2.46542e11			1.04462
$698$	3.71659e10	−	1.88340e10i	0.156575	−	0.0793452i
$699$			2.45515e11i			1.02842i
$700$		0			0
$701$	1.01471e11			0.420213			0.210107	−	0.977678i	$-0.432619\pi$
$701$	1.01471e11			0.420213			0.210107	+	0.977678i	$0.432619\pi$
$702$	−4.98864e10	−	9.84431e10i	−0.205416	−	0.405356i
$703$			2.07748e10i			0.0850582i
$704$	−9.88728e10	+	2.91148e11i	−0.402519	+	1.18529i
$705$		0			0
$706$	−1.04317e11	+	5.28628e10i	−0.419889	+	0.212780i
$707$		−	1.47602e11i		−	0.590763i
$708$	1.58304e11	−	2.15880e11i	0.630027	−	0.859172i
$709$	4.73489e11			1.87381			0.936904	−	0.349587i	$-0.113678\pi$
$709$	4.73489e11			1.87381			0.936904	+	0.349587i	$0.113678\pi$
$710$		0			0
$711$			1.07990e10i			0.0422577i
$712$	4.28993e10	−	2.59735e11i	0.166928	−	1.01067i
$713$	−3.44180e11			−1.33176
$714$	1.72016e11	−	8.71698e10i	0.661875	−	0.335408i
$715$		0			0
$716$	−7.48149e10	−	5.48614e10i	−0.284666	−	0.208744i
$717$	3.13026e10			0.118442
$718$	1.22302e11	+	2.41345e11i	0.460190	+	0.908113i
$719$		−	3.14505e11i		−	1.17683i	−0.808561	−	0.588413i	$-0.799753\pi$
$719$		−	3.14505e11i		−	1.17683i	0.808561	−	0.588413i	$-0.200247\pi$
$720$		0			0
$721$	−3.38134e11			−1.25126
$722$	9.38264e10	−	4.75469e10i	0.345284	−	0.174974i
$723$			9.90021e10i			0.362319i
$724$	−2.30224e11	+	3.13959e11i	−0.837909	+	1.14266i
$725$		0			0
$726$	3.89603e10	+	7.68821e10i	0.140241	+	0.276744i
$727$		−	3.23780e10i		−	0.115908i	−0.998319	−	0.0579538i	$-0.981542\pi$
$727$		−	3.23780e10i		−	0.115908i	0.998319	−	0.0579538i	$-0.0184576\pi$
$728$	1.59324e11	+	2.63149e10i	0.567225	+	0.0936862i
$729$	−1.05995e11			−0.375297
$730$		0			0
$731$			8.20050e10i			0.287191i
$732$	−5.20810e10	−	3.81908e10i	−0.181399	−	0.133019i
$733$	−9.11504e10			−0.315749			−0.157875	−	0.987459i	$-0.550464\pi$
$733$	−9.11504e10			−0.315749			−0.157875	+	0.987459i	$0.550464\pi$
$734$	2.19469e11	+	4.33088e11i	0.756118	+	1.49208i
$735$		0			0
$736$	−2.54382e11	+	2.48839e11i	−0.866913	+	0.848024i
$737$	−3.23522e11			−1.09656
$738$	1.68129e11	−	8.51999e10i	0.566783	−	0.287219i
$739$			2.00083e11i			0.670860i	0.942065	+	0.335430i	$0.108882\pi$
$739$			2.00083e11i			0.670860i	−0.942065	+	0.335430i	$0.891118\pi$
$740$		0			0
$741$	9.48883e10			0.314731
$742$	−2.04858e11	−	4.04256e11i	−0.675831	−	1.33365i
$743$			5.50175e10i			0.180528i	0.995918	+	0.0902642i	$0.0287712\pi$
$743$			5.50175e10i			0.180528i	−0.995918	+	0.0902642i	$0.971229\pi$
$744$	3.00068e10	−	1.81677e11i	0.0979326	−	0.592935i
$745$		0			0
$746$	1.35042e11	−	6.84329e10i	0.436026	−	0.220958i
$747$			5.83385e10i			0.187358i
$748$	3.63934e11	+	2.66871e11i	1.16256	+	0.852501i
$749$	5.58025e11			1.77307
$750$		0			0
$751$		−	5.26277e11i		−	1.65445i	−0.561869	−	0.827226i	$-0.689917\pi$
$751$		−	5.26277e11i		−	1.65445i	0.561869	−	0.827226i	$-0.310083\pi$
$752$	7.85217e10	−	2.47505e10i	0.245538	−	0.0773949i
$753$	−1.43164e11			−0.445302
$754$	1.50894e11	−	7.64660e10i	0.466859	−	0.236583i
$755$		0			0
$756$	2.11635e11	−	2.88608e11i	0.647889	−	0.883531i
$757$	4.33728e11			1.32079			0.660395	−	0.750919i	$-0.270389\pi$
$757$	4.33728e11			1.32079			0.660395	+	0.750919i	$0.270389\pi$
$758$	8.01454e10	+	1.58154e11i	0.242774	+	0.479076i
$759$			2.75699e11i			0.830745i
$760$		0			0
$761$	3.18871e11			0.950771			0.475385	−	0.879778i	$-0.342309\pi$
$761$	3.18871e11			0.950771			0.475385	+	0.879778i	$0.342309\pi$
$762$	−2.15786e11	+	1.09351e11i	−0.640035	+	0.324340i
$763$		−	6.33472e11i		−	1.86909i
$764$	−1.66852e11	−	1.22352e11i	−0.489731	−	0.359117i
$765$		0			0
$766$	2.29847e11	+	4.53567e11i	0.667611	+	1.31743i
$767$		−	3.29019e11i		−	0.950691i
$768$	−1.09173e11	−	1.55971e11i	−0.313812	−	0.448332i
$769$	1.36365e11			0.389941			0.194970	−	0.980809i	$-0.437539\pi$
$769$	1.36365e11			0.389941			0.194970	+	0.980809i	$0.437539\pi$
$770$		0			0
$771$		−	1.65558e11i		−	0.468525i
$772$	−3.30653e11	+	4.50914e11i	−0.930901	+	1.26948i
$773$	−2.93754e11			−0.822746			−0.411373	−	0.911467i	$-0.634951\pi$
$773$	−2.93754e11			−0.822746			−0.411373	+	0.911467i	$0.634951\pi$
$774$	2.83393e10	+	5.59232e10i	0.0789633	+	0.155822i
$775$		0			0
$776$	4.42193e9	−	2.67727e10i	0.0121945	−	0.0738320i
$777$	−1.69601e10			−0.0465311
$778$	3.75592e11	−	1.90333e11i	1.02517	−	0.519511i
$779$			3.93397e11i			1.06827i
$780$		0			0
$781$	−7.14650e10			−0.192083
$782$	2.36092e11	+	4.65890e11i	0.631326	+	1.24582i
$783$		−	3.74910e11i		−	0.997425i
$784$	4.38505e10	+	1.39117e11i	0.116068	+	0.368228i
$785$		0			0
$786$	1.72255e11	−	8.72911e10i	0.451318	−	0.228707i
$787$			4.49406e11i			1.17149i	0.810494	+	0.585747i	$0.199199\pi$
$787$			4.49406e11i			1.17149i	−0.810494	+	0.585747i	$0.800801\pi$
$788$	−1.54987e11	+	2.11357e11i	−0.401966	+	0.548164i
$789$	−2.60567e11			−0.672374
$790$		0			0
$791$			9.17321e11i			2.34323i
$792$	3.40410e11	+	5.62240e10i	0.865169	+	0.142896i
$793$	−7.93757e10			−0.200722
$794$	1.68732e10	−	8.55058e9i	0.0424538	−	0.0215136i
$795$		0			0
$796$	−2.53040e11	−	1.85553e11i	−0.630285	−	0.462185i
$797$	−4.56927e11			−1.13244			−0.566218	−	0.824256i	$-0.691594\pi$
$797$	−4.56927e11			−1.13244			−0.566218	+	0.824256i	$0.691594\pi$
$798$	1.39093e11	+	2.74479e11i	0.343001	+	0.676858i
$799$		−	1.20838e11i		−	0.296495i
$800$		0			0
$801$	−2.95396e11			−0.717588
$802$	5.77380e11	−	2.92589e11i	1.39561	−	0.707231i
$803$			1.76476e11i			0.424447i
$804$	1.18456e11	−	1.61539e11i	0.283487	−	0.386593i
$805$		0			0
$806$	−1.02300e11	−	2.01873e11i	−0.242402	−	0.478343i
$807$			1.16060e11i			0.273645i
$808$	−3.48530e10	+	2.11018e11i	−0.0817700	+	0.495078i
$809$	−7.90117e11			−1.84458			−0.922289	−	0.386500i	$-0.873684\pi$
$809$	−7.90117e11			−1.84458			−0.922289	+	0.386500i	$0.873684\pi$
$810$		0			0
$811$			1.98385e11i			0.458590i	0.973357	+	0.229295i	$0.0736420\pi$
$811$			1.98385e11i			0.458590i	−0.973357	+	0.229295i	$0.926358\pi$
$812$	4.42380e11	+	3.24395e11i	1.01759	+	0.746191i
$813$	−2.06641e11			−0.472993
$814$	−1.79412e10	−	3.54041e10i	−0.0408651	−	0.0806410i
$815$		0			0
$816$	−2.66505e11	+	8.40039e10i	−0.601097	+	0.189469i
$817$	−1.30852e11			−0.293692
$818$	−3.23462e10	+	1.63915e10i	−0.0722453	+	0.0366106i
$819$		−	1.81199e11i		−	0.402736i
$820$		0			0
$821$	4.89572e11			1.07757			0.538783	−	0.842445i	$-0.318884\pi$
$821$	4.89572e11			1.07757			0.538783	+	0.842445i	$0.318884\pi$
$822$	1.20411e11	+	2.37613e11i	0.263742	+	0.520455i
$823$			4.10873e11i			0.895587i	0.894137	+	0.447793i	$0.147790\pi$
$823$			4.10873e11i			0.895587i	−0.894137	+	0.447793i	$0.852210\pi$
$824$	4.83412e11	+	7.98431e10i	1.04860	+	0.173192i
$825$		0			0
$826$	9.51739e11	−	4.82297e11i	2.04455	−	1.03608i
$827$		−	4.15118e11i		−	0.887461i	−0.896160	−	0.443731i	$-0.853655\pi$
$827$		−	4.15118e11i		−	0.887461i	0.896160	−	0.443731i	$-0.146345\pi$
$828$	3.22005e11	+	2.36125e11i	0.685080	+	0.502366i
$829$	4.32301e11			0.915310			0.457655	−	0.889130i	$-0.348690\pi$
$829$	4.32301e11			0.915310			0.457655	+	0.889130i	$0.348690\pi$
$830$		0			0
$831$			1.68201e11i			0.352715i
$832$	−2.21563e11	−	7.52418e10i	−0.462385	−	0.157024i
$833$	2.14090e11			0.444647
$834$	3.20872e11	−	1.62603e11i	0.663236	−	0.336097i
$835$		0			0
$836$	−4.25835e11	+	5.80714e11i	−0.871799	+	1.18888i
$837$	−5.01574e11			−1.02196
$838$	−4.32402e11	−	8.53278e11i	−0.876822	−	1.73027i
$839$			4.22053e11i			0.851764i	0.904779	+	0.425882i	$0.140036\pi$
$839$			4.22053e11i			0.851764i	−0.904779	+	0.425882i	$0.859964\pi$
$840$		0			0
$841$	7.44167e10			0.148760
$842$	−1.96754e9	+	9.97057e8i	−0.00391448	+	0.00198368i
$843$			2.63873e11i			0.522498i
$844$	4.59557e10	+	3.36991e10i	0.0905668	+	0.0664122i
$845$		0			0
$846$	−4.17593e10	−	8.24055e10i	−0.0815215	−	0.160870i
$847$			3.43524e11i			0.667457i
$848$	1.97418e11	+	6.26315e11i	0.381772	+	1.21118i
$849$	2.70319e11			0.520291
$850$		0			0
$851$		−	4.59348e10i		−	0.0875838i
$852$	2.61666e10	−	3.56835e10i	0.0496579	−	0.0677188i
$853$	−4.91131e11			−0.927687			−0.463843	−	0.885917i	$-0.653530\pi$
$853$	−4.91131e11			−0.927687			−0.463843	+	0.885917i	$0.653530\pi$
$854$	−1.16354e11	−	2.29607e11i	−0.218751	−	0.431671i
$855$		0			0
$856$	−7.97778e11	−	1.31766e11i	−1.48589	−	0.245419i
$857$	−2.87979e10			−0.0533873			−0.0266936	−	0.999644i	$-0.508498\pi$
$857$	−2.87979e10			−0.0533873			−0.0266936	+	0.999644i	$0.508498\pi$
$858$	−1.61707e11	+	8.19456e10i	−0.298387	+	0.151209i
$859$		−	3.71560e11i		−	0.682428i	−0.939986	−	0.341214i	$-0.889162\pi$
$859$		−	3.71560e11i		−	0.682428i	0.939986	−	0.341214i	$-0.110838\pi$
$860$		0			0
$861$	−3.21159e11			−0.584397
$862$	−1.35280e11	−	2.66954e11i	−0.245022	−	0.483512i
$863$			8.63937e10i			0.155754i	0.996963	+	0.0778769i	$0.0248141\pi$
$863$			8.63937e10i			0.155754i	−0.996963	+	0.0778769i	$0.975186\pi$
$864$	−3.70712e11	+	3.62634e11i	−0.665245	+	0.650750i
$865$		0			0
$866$	2.09596e11	−	1.06213e11i	0.372658	−	0.188846i
$867$			1.00914e11i			0.178598i
$868$	4.33992e11	−	5.91838e11i	0.764545	−	1.04262i
$869$	4.30614e10			0.0755108
$870$		0			0
$871$		−	2.46199e11i		−	0.427773i
$872$	−1.49581e11	+	9.05641e11i	−0.258708	+	1.56635i
$873$	−3.04486e10			−0.0524215
$874$	−7.43403e11	+	3.76722e11i	−1.27403	+	0.645618i
$875$		0			0
$876$	−8.81172e10	−	6.46159e10i	−0.149639	−	0.109729i
$877$	3.79999e11			0.642369			0.321184	−	0.947017i	$-0.395919\pi$
$877$	3.79999e11			0.642369			0.321184	+	0.947017i	$0.395919\pi$
$878$	1.86700e11	+	3.68424e11i	0.314172	+	0.619969i
$879$			1.58946e11i			0.266254i
$880$		0			0
$881$	−9.51956e11			−1.58020			−0.790102	−	0.612975i	$-0.789973\pi$
$881$	−9.51956e11			−1.58020			−0.790102	+	0.612975i	$0.789973\pi$
$882$	1.45998e11	−	7.39852e10i	0.241253	−	0.122256i
$883$		−	5.76893e11i		−	0.948971i	−0.880263	−	0.474485i	$-0.842634\pi$
$883$		−	5.76893e11i		−	0.948971i	0.880263	−	0.474485i	$-0.157366\pi$
$884$	−2.03088e11	+	2.76952e11i	−0.332563	+	0.453519i
$885$		0			0
$886$	2.50640e11	+	4.94600e11i	0.406739	+	0.802637i
$887$		−	6.27370e11i		−	1.01351i	−0.862089	−	0.506756i	$-0.830844\pi$
$887$		−	6.27370e11i		−	1.01351i	0.862089	−	0.506756i	$-0.169156\pi$
$888$	2.42469e10	+	4.00475e9i	0.0389945	+	0.00644056i
$889$	−9.64175e11			−1.54365
$890$		0			0
$891$		−	1.50881e11i		−	0.239400i
$892$	−5.50410e11	−	4.03613e11i	−0.869415	−	0.637538i
$893$	1.92817e11			0.303207
$894$	−2.25023e10	−	4.44049e10i	−0.0352272	−	0.0695153i
$895$		0			0
$896$	−1.07132e11	−	7.51199e11i	−0.166222	−	1.16553i
$897$	−2.09806e11			−0.324076
$898$	−5.00602e11	+	2.53682e11i	−0.769816	+	0.390107i
$899$		−	7.68814e11i		−	1.17702i
$900$		0			0
$901$	9.63847e11			1.46254
$902$	−3.39738e11	−	6.70419e11i	−0.513236	−	1.01279i
$903$		−	1.06824e11i		−	0.160664i
$904$	2.16606e11	−	1.31144e12i	0.324337	−	1.96370i
$905$		0			0
$906$	2.52999e11	−	1.28208e11i	0.375496	−	0.190284i
$907$			3.89597e11i			0.575688i	0.957677	+	0.287844i	$0.0929384\pi$
$907$			3.89597e11i			0.575688i	−0.957677	+	0.287844i	$0.907062\pi$
$908$	−3.00190e11	−	2.20128e11i	−0.441624	−	0.323841i
$909$	2.39991e11			0.351511
$910$		0			0
$911$		−	1.13330e12i		−	1.64540i	−0.568475	−	0.822700i	$-0.692467\pi$
$911$		−	1.13330e12i		−	1.64540i	0.568475	−	0.822700i	$-0.307533\pi$
$912$	−1.34042e11	−	4.25252e11i	−0.193758	−	0.614705i
$913$	2.32627e11			0.334793
$914$	2.58215e11	−	1.30851e11i	0.369995	−	0.187497i
$915$		0			0
$916$	−2.01283e9	+	2.74491e9i	−0.00285908	+	0.00389894i
$917$	7.69670e11			1.08850
$918$	3.44057e11	+	6.78943e11i	0.484462	+	0.956010i
$919$		−	1.35023e12i		−	1.89298i	−0.322739	−	0.946488i	$-0.604604\pi$
$919$		−	1.35023e12i		−	1.89298i	0.322739	−	0.946488i	$-0.395396\pi$
$920$		0			0
$921$	−2.26768e11			−0.315169
$922$	−3.17597e11	+	1.60944e11i	−0.439494	+	0.222715i
$923$		−	5.43846e10i		−	0.0749323i
$924$	−4.74081e11	−	3.47641e11i	−0.650376	−	0.476918i
$925$		0			0
$926$	2.98921e11	+	5.89874e11i	0.406549	+	0.802260i
$927$		−	5.49784e11i		−	0.744515i
$928$	−5.55847e11	−	5.68228e11i	−0.749485	−	0.766180i
$929$	3.18334e11			0.427387			0.213693	−	0.976901i	$-0.431451\pi$
$929$	3.18334e11			0.427387			0.213693	+	0.976901i	$0.431451\pi$
$930$		0			0
$931$			3.41614e11i			0.454713i
$932$	8.38474e11	−	1.14343e12i	1.11129	−	1.51547i
$933$	−1.24530e11			−0.164341
$934$	−2.60507e11	−	5.14070e11i	−0.342320	−	0.675515i
$935$		0			0
$936$	−4.27863e10	+	2.59050e11i	−0.0557444	+	0.337505i
$937$	1.14781e12			1.48906			0.744532	−	0.667587i	$-0.232673\pi$
$937$	1.14781e12			1.48906			0.744532	+	0.667587i	$0.232673\pi$
$938$	7.12168e11	−	3.60894e11i	0.919965	−	0.466196i
$939$		−	2.07939e11i		−	0.267469i
$940$		0			0
$941$	−2.67245e11			−0.340840			−0.170420	−	0.985372i	$-0.554512\pi$
$941$	−2.67245e11			−0.340840			−0.170420	+	0.985372i	$0.554512\pi$
$942$	2.23930e11	+	4.41891e11i	0.284386	+	0.561192i
$943$		−	8.69831e11i		−	1.09999i
$944$	−1.47453e12	+	4.64781e11i	−1.85681	+	0.585276i
$945$		0			0
$946$	2.22996e11	−	1.13004e11i	0.278440	−	0.141101i
$947$			5.74285e11i			0.714049i	0.934095	+	0.357024i	$0.116209\pi$
$947$			5.74285e11i			0.714049i	−0.934095	+	0.357024i	$0.883791\pi$
$948$	−1.57667e10	+	2.15012e10i	−0.0195213	+	0.0266213i
$949$	−1.34298e11			−0.165578
$950$		0			0
$951$			1.08371e11i			0.132492i
$952$	−1.09883e12	−	1.81489e11i	−1.33777	−	0.220954i
$953$	−1.67118e11			−0.202605			−0.101303	−	0.994856i	$-0.532301\pi$
$953$	−1.67118e11			−0.202605			−0.101303	+	0.994856i	$0.532301\pi$
$954$	6.57294e11	−	3.33086e11i	0.793536	−	0.402127i
$955$		0			0
$956$	−1.45785e11	−	1.06904e11i	−0.174535	−	0.127985i
$957$	−6.15844e11			−0.734214
$958$	−3.84764e11	−	7.59273e11i	−0.456807	−	0.901438i
$959$			1.06170e12i			1.25524i
$960$		0			0
$961$	−1.75668e11			−0.205968
$962$	2.69424e10	−	1.36531e10i	0.0314583	−	0.0159416i
$963$			9.07313e11i			1.05500i
$964$	3.38108e11	−	4.61080e11i	0.391514	−	0.533911i
$965$		0			0
$966$	−3.07547e11	−	6.06895e11i	−0.353185	−	0.696956i
$967$		−	8.24444e11i		−	0.942877i	−0.881899	−	0.471439i	$-0.843735\pi$
$967$		−	8.24444e11i		−	0.942877i	0.881899	−	0.471439i	$-0.156265\pi$
$968$	8.11158e10	−	4.91117e11i	0.0923855	−	0.559350i
$969$	−6.54426e11			−0.742276
$970$		0			0
$971$		−	8.36736e11i		−	0.941264i	−0.882330	−	0.470632i	$-0.844026\pi$
$971$		−	8.36736e11i		−	0.941264i	0.882330	−	0.470632i	$-0.155974\pi$
$972$	7.45209e11	+	5.46458e11i	0.834859	+	0.612198i
$973$	1.43372e12			1.59960
$974$	1.56332e11	+	3.08498e11i	0.173705	+	0.342780i
$975$		0			0
$976$	1.12128e11	+	3.55730e11i	0.123571	+	0.392032i
$977$	−1.09033e12			−1.19669			−0.598344	−	0.801239i	$-0.704174\pi$
$977$	−1.09033e12			−1.19669			−0.598344	+	0.801239i	$0.704174\pi$
$978$	−2.18737e11	+	1.10846e11i	−0.239093	+	0.121161i
$979$			1.17790e12i			1.28227i
$980$		0			0
$981$	1.02999e12			1.11213
$982$	5.02406e10	+	9.91420e10i	0.0540267	+	0.106613i
$983$			1.28853e11i			0.138000i	0.997617	+	0.0690001i	$0.0219809\pi$
$983$			1.28853e11i			0.138000i	−0.997617	+	0.0690001i	$0.978019\pi$
$984$	4.59143e11	+	7.58348e10i	0.489743	+	0.0808888i
$985$		0			0
$986$	−1.04069e12	+	5.27371e11i	−1.10106	+	0.557967i
$987$			1.57411e11i			0.165869i
$988$	−4.41921e11	−	3.24059e11i	−0.463786	−	0.340092i
$989$	2.89324e11			0.302413
$990$		0			0
$991$			1.29472e12i			1.34240i	0.741276	+	0.671201i	$0.234221\pi$
$991$			1.29472e12i			1.34240i	−0.741276	+	0.671201i	$0.765779\pi$
$992$	−7.60205e11	+	7.43641e11i	−0.785026	+	0.767921i
$993$	9.52579e11			0.979725
$994$	1.57316e11	−	7.97204e10i	0.161149	−	0.0816628i
$995$		0			0
$996$	−8.51752e10	+	1.16154e11i	−0.0865518	+	0.118031i
$997$	1.46628e12			1.48401			0.742006	−	0.670393i	$-0.233875\pi$
$997$	1.46628e12			1.48401			0.742006	+	0.670393i	$0.233875\pi$
$998$	−2.20311e11	−	4.34750e11i	−0.222083	−	0.438246i
$999$		−	6.69409e10i		−	0.0672094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.b.g.51.6		20
4.3	odd	2	inner	100.9.b.g.51.5		20
5.2	odd	4		20.9.d.c.19.5	✓	20
5.3	odd	4		20.9.d.c.19.16	yes	20
5.4	even	2	inner	100.9.b.g.51.15		20
20.3	even	4		20.9.d.c.19.6	yes	20
20.7	even	4		20.9.d.c.19.15	yes	20
20.19	odd	2	inner	100.9.b.g.51.16		20
40.3	even	4		320.9.h.g.319.7		20
40.13	odd	4		320.9.h.g.319.13		20
40.27	even	4		320.9.h.g.319.14		20
40.37	odd	4		320.9.h.g.319.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.d.c.19.5	✓	20	5.2	odd	4
20.9.d.c.19.6	yes	20	20.3	even	4
20.9.d.c.19.15	yes	20	20.7	even	4
20.9.d.c.19.16	yes	20	5.3	odd	4
100.9.b.g.51.5		20	4.3	odd	2	inner
100.9.b.g.51.6		20	1.1	even	1	trivial
100.9.b.g.51.15		20	5.4	even	2	inner
100.9.b.g.51.16		20	20.19	odd	2	inner
320.9.h.g.319.7		20	40.3	even	4
320.9.h.g.319.8		20	40.37	odd	4
320.9.h.g.319.13		20	40.13	odd	4
320.9.h.g.319.14		20	40.27	even	4

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-14.2721 + 7.23243i) q^{2} +44.3270i q^{3} +(151.384 - 206.443i) q^{4} +(-320.592 - 632.638i) q^{6} -2826.75i q^{7} +(-667.476 + 4041.25i) q^{8} +4596.11 q^{9} -18327.2i q^{11} +(9151.02 + 6710.40i) q^{12} +13946.9 q^{13} +(20444.3 + 40343.6i) q^{14} +(-19701.8 - 62504.5i) q^{16} -96189.1 q^{17} +(-65596.1 + 33241.1i) q^{18} -153485. i q^{19} +125301. q^{21} +(132550. + 261567. i) q^{22} +339368. i q^{23} +(-179137. - 29587.2i) q^{24} +(-199051. + 100870. i) q^{26} +494562. i q^{27} +(-583564. - 427925. i) q^{28} -758065. q^{29} +1.01418e6i q^{31} +(733244. + 749577. i) q^{32} +812389. q^{33} +(1.37282e6 - 695681. i) q^{34} +(695778. - 948838. i) q^{36} -135354. q^{37} +(1.11007e6 + 2.19055e6i) q^{38} +618224. i q^{39} -2.56309e6 q^{41} +(-1.78831e6 + 906233. i) q^{42} -852539. i q^{43} +(-3.78352e6 - 2.77444e6i) q^{44} +(-2.45445e6 - 4.84348e6i) q^{46} +1.25626e6i q^{47} +(2.77064e6 - 873321. i) q^{48} -2.22572e6 q^{49} -4.26378e6i q^{51} +(2.11134e6 - 2.87925e6i) q^{52} -1.00203e7 q^{53} +(-3.57688e6 - 7.05842e6i) q^{54} +(1.14236e7 + 1.88679e6i) q^{56} +6.80354e6 q^{57} +(1.08192e7 - 5.48265e6i) q^{58} -2.35908e7i q^{59} -5.69128e6 q^{61} +(-7.33498e6 - 1.44744e7i) q^{62} -1.29921e7i q^{63} +(-1.58862e7 - 5.39488e6i) q^{64} +(-1.15945e7 + 5.87554e6i) q^{66} -1.76526e7i q^{67} +(-1.45615e7 + 1.98576e7i) q^{68} -1.50432e7 q^{69} -3.89940e6i q^{71} +(-3.06780e6 + 1.85740e7i) q^{72} -9.62921e6 q^{73} +(1.93178e6 - 978938. i) q^{74} +(-3.16860e7 - 2.32352e7i) q^{76} -5.18063e7 q^{77} +(-4.47126e6 - 8.82334e6i) q^{78} +2.34959e6i q^{79} +8.23266e6 q^{81} +(3.65806e7 - 1.85374e7i) q^{82} +1.26930e7i q^{83} +(1.89686e7 - 2.58677e7i) q^{84} +(6.16593e6 + 1.21675e7i) q^{86} -3.36028e7i q^{87} +(7.40646e7 + 1.22330e7i) q^{88} -6.42709e7 q^{89} -3.94244e7i q^{91} +(7.00603e7 + 5.13749e7i) q^{92} -4.49555e7 q^{93} +(-9.08579e6 - 1.79294e7i) q^{94} +(-3.32265e7 + 3.25025e7i) q^{96} -6.62485e6 q^{97} +(3.17656e7 - 1.60973e7i) q^{98} -8.42338e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 752 q^{4} + 3408 q^{6} - 2556 q^{9} - 8848 q^{14} - 59200 q^{16} + 410256 q^{21} + 156672 q^{24} - 440448 q^{26} - 660136 q^{29} - 4342528 q^{34} - 7191312 q^{36} + 7068520 q^{41} - 2666880 q^{44}+ \cdots + 28850688 q^{96}+O(q^{100}) \) 20 * q + 752 * q^4 + 3408 * q^6 - 2556 * q^9 - 8848 * q^14 - 59200 * q^16 + 410256 * q^21 + 156672 * q^24 - 440448 * q^26 - 660136 * q^29 - 4342528 * q^34 - 7191312 * q^36 + 7068520 * q^41 - 2666880 * q^44 + 561168 * q^46 - 11719036 * q^49 - 37110816 * q^54 - 35044352 * q^56 - 17660440 * q^61 - 20201728 * q^64 + 31902720 * q^66 - 111747216 * q^69 - 19114368 * q^74 - 54998400 * q^76 - 154212444 * q^81 - 101289216 * q^84 + 94429648 * q^86 - 105006376 * q^89 + 192757872 * q^94 + 28850688 * q^96

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