LMFDB - Embedded newform 9.9.d.a.5.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9,9,Mod(2,9)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9.2"); S:= CuspForms(chi, 9); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 9, names="a")

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	9.d (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.66640749055$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 427 x^{12} - 1362 x^{11} + 135762 x^{10} - 371244 x^{9} + 18261508 x^{8} + \cdots + 872385888256 $ x^14 - x^13 + 427x^12 - 1362x^11 + 135762x^10 - 371244x^9 + 18261508x^8 - 29352736x^7 + 1757083840x^6 - 1434930432x^5 + 61638378240x^4 + 183604924416x^3 + 1254910111744x^2 + 1078377512960x + 872385888256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{21} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.1
Root			$7.38374 - 12.7890i$ of defining polynomial
Character	$\chi$	$=$	9.5
Dual form			9.9.d.a.2.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-22.1512 + 12.7890i) q^{2} +(-80.9424 + 3.05302i) q^{3} +(199.117 - 344.881i) q^{4} +(570.352 + 329.293i) q^{5} +(1753.93 - 1102.80i) q^{6} +(-1512.41 - 2619.58i) q^{7} +3638.08i q^{8} +(6542.36 - 494.238i) q^{9} -16845.3 q^{10} +(-8016.93 + 4628.57i) q^{11} +(-15064.1 + 28523.5i) q^{12} +(21771.9 - 37710.0i) q^{13} +(67003.6 + 38684.6i) q^{14} +(-47171.1 - 24912.5i) q^{15} +(4446.57 + 7701.69i) q^{16} -107702. i q^{17} +(-138600. + 94618.2i) q^{18} -22386.6 q^{19} +(227134. - 131136. i) q^{20} +(130416. + 207418. i) q^{21} +(118390. - 205057. i) q^{22} +(-115959. - 66949.2i) q^{23} +(-11107.2 - 294475. i) q^{24} +(21555.4 + 37335.0i) q^{25} +1.11376e6i q^{26} +(-528046. + 59978.8i) q^{27} -1.20459e6 q^{28} +(-219270. + 126596. i) q^{29} +(1.36350e6 - 51429.2i) q^{30} +(393886. - 682230. i) q^{31} +(-1.00357e6 - 579409. i) q^{32} +(634778. - 399124. i) q^{33} +(1.37740e6 + 2.38573e6i) q^{34} -1.99211e6i q^{35} +(1.13224e6 - 2.35475e6i) q^{36} +1.55379e6 q^{37} +(495890. - 286302. i) q^{38} +(-1.64714e6 + 3.11881e6i) q^{39} +(-1.19800e6 + 2.07499e6i) q^{40} +(-1.91891e6 - 1.10788e6i) q^{41} +(-5.54154e6 - 2.92666e6i) q^{42} +(-277061. - 479883. i) q^{43} +3.68652e6i q^{44} +(3.89420e6 + 1.87246e6i) q^{45} +3.42486e6 q^{46} +(2.05696e6 - 1.18759e6i) q^{47} +(-383430. - 609818. i) q^{48} +(-1.69239e6 + 2.93131e6i) q^{49} +(-954955. - 551344. i) q^{50} +(328817. + 8.71766e6i) q^{51} +(-8.67033e6 - 1.50175e7i) q^{52} +7.83903e6i q^{53} +(1.09298e7 - 8.08178e6i) q^{54} -6.09663e6 q^{55} +(9.53025e6 - 5.50229e6i) q^{56} +(1.81203e6 - 68346.8i) q^{57} +(3.23806e6 - 5.60849e6i) q^{58} +(4.48638e6 + 2.59021e6i) q^{59} +(-1.79844e7 + 1.13079e7i) q^{60} +(-4.77454e6 - 8.26974e6i) q^{61} +2.01496e7i q^{62} +(-1.11895e7 - 1.63907e7i) q^{63} +2.73636e7 q^{64} +(2.48353e7 - 1.43387e7i) q^{65} +(-8.95671e6 + 1.69593e7i) q^{66} +(-4.31500e6 + 7.47380e6i) q^{67} +(-3.71444e7 - 2.14453e7i) q^{68} +(9.59044e6 + 5.06501e6i) q^{69} +(2.54771e7 + 4.41277e7i) q^{70} -3.31572e7i q^{71} +(1.79808e6 + 2.38016e7i) q^{72} -5.28831e7 q^{73} +(-3.44184e7 + 1.98715e7i) q^{74} +(-1.85873e6 - 2.95618e6i) q^{75} +(-4.45756e6 + 7.72072e6i) q^{76} +(2.42498e7 + 1.40006e7i) q^{77} +(-3.40035e6 - 9.01508e7i) q^{78} +(4.50350e6 + 7.80029e6i) q^{79} +5.85691e6i q^{80} +(4.25582e7 - 6.46697e6i) q^{81} +5.66748e7 q^{82} +(-3.31421e7 + 1.91346e7i) q^{83} +(9.75026e7 - 3.67765e6i) q^{84} +(3.54655e7 - 6.14281e7i) q^{85} +(1.22745e7 + 7.08666e6i) q^{86} +(1.73617e7 - 1.09164e7i) q^{87} +(-1.68391e7 - 2.91662e7i) q^{88} +1.41720e7i q^{89} +(-1.10208e8 + 8.32560e6i) q^{90} -1.31713e8 q^{91} +(-4.61791e7 + 2.66615e7i) q^{92} +(-2.97992e7 + 5.64239e7i) q^{93} +(-3.03761e7 + 5.26130e7i) q^{94} +(-1.27682e7 - 7.37175e6i) q^{95} +(8.30001e7 + 4.38349e7i) q^{96} +(7.52257e7 + 1.30295e8i) q^{97} -8.65761e7i q^{98} +(-5.01620e7 + 3.42441e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{2} - 93 q^{3} + 767 q^{4} + 438 q^{5} - 2259 q^{6} + 922 q^{7} + 17973 q^{9} - 516 q^{10} - 28677 q^{11} - 55110 q^{12} + 1684 q^{13} + 120966 q^{14} - 75276 q^{15} - 65281 q^{16} + 243324 q^{18}+ \cdots - 511060752 q^{99}+O(q^{100}) $ 14 * q - 3 * q^2 - 93 * q^3 + 767 * q^4 + 438 * q^5 - 2259 * q^6 + 922 * q^7 + 17973 * q^9 - 516 * q^10 - 28677 * q^11 - 55110 * q^12 + 1684 * q^13 + 120966 * q^14 - 75276 * q^15 - 65281 * q^16 + 243324 * q^18 - 269630 * q^19 + 539454 * q^20 + 354054 * q^21 + 61311 * q^22 - 1000452 * q^23 - 1125513 * q^24 + 65177 * q^25 - 524826 * q^27 + 1075708 * q^28 + 3797682 * q^29 + 2372562 * q^30 - 164132 * q^31 - 8461881 * q^32 - 5761521 * q^33 + 654993 * q^34 + 12958047 * q^36 - 1671668 * q^37 + 10967691 * q^38 + 3383976 * q^39 + 613326 * q^40 - 10239447 * q^41 - 35844228 * q^42 + 791815 * q^43 + 27631638 * q^45 + 1189536 * q^46 + 31148628 * q^47 + 17088189 * q^48 - 4826637 * q^49 - 63849453 * q^50 - 47946573 * q^51 - 5552720 * q^52 + 36967995 * q^54 + 8107476 * q^55 + 116638674 * q^56 + 37276797 * q^57 + 14211822 * q^58 - 83493795 * q^59 - 109012050 * q^60 - 5255600 * q^61 + 38322432 * q^63 - 26813830 * q^64 + 69232992 * q^65 + 36133866 * q^66 - 8288855 * q^67 - 77746743 * q^68 - 62108640 * q^69 + 27813756 * q^70 + 88821171 * q^72 - 36721682 * q^73 - 10383450 * q^74 + 13792011 * q^75 - 42822959 * q^76 + 56158710 * q^77 + 27355140 * q^78 - 32771822 * q^79 - 16336971 * q^81 + 236099418 * q^82 - 198915996 * q^83 - 187060614 * q^84 + 97486146 * q^85 + 146190669 * q^86 + 114294006 * q^87 + 24955827 * q^88 - 222035850 * q^90 - 201514504 * q^91 - 295365804 * q^92 + 94187784 * q^93 - 36698244 * q^94 + 386813838 * q^95 + 768275928 * q^96 + 127049161 * q^97 - 511060752 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−22.1512	+	12.7890i	−1.38445	+	0.799313i	−0.992683	−	0.120751i	$-0.961470\pi$
$2$	−22.1512	+	12.7890i	−1.38445	+	0.799313i	−0.391768	+	0.920064i	$0.628136\pi$
$3$	−80.9424	+	3.05302i	−0.999289	+	0.0376916i
$3$	−80.9424	+	3.05302i	−0.999289	+	0.0376916i
$4$	199.117	−	344.881i	0.777802	−	1.34719i
$5$	570.352	+	329.293i	0.912564	+	0.526869i	0.881255	−	0.472641i	$-0.156699\pi$
$5$	570.352	+	329.293i	0.912564	+	0.526869i	0.0313086	+	0.999510i	$0.490033\pi$
$6$	1753.93	−	1102.80i	1.35334	−	0.850927i
$7$	−1512.41	−	2619.58i	−0.629910	−	1.09104i	−0.987569	−	0.157184i	$-0.949758\pi$
$7$	−1512.41	−	2619.58i	−0.629910	−	1.09104i	0.357659	−	0.933852i	$-0.383575\pi$
$8$			3638.08i			0.888204i
$9$	6542.36	−	494.238i	0.997159	−	0.0753297i
$10$	−16845.3			−1.68453
$11$	−8016.93	+	4628.57i	−0.547567	+	0.316138i	−0.748140	−	0.663541i	$-0.769053\pi$
$11$	−8016.93	+	4628.57i	−0.547567	+	0.316138i	0.200573	+	0.979679i	$0.435720\pi$
$12$	−15064.1	+	28523.5i	−0.726472	+	1.37555i
$13$	21771.9	−	37710.0i	0.762295	−	1.32033i	−0.179370	−	0.983782i	$-0.557406\pi$
$13$	21771.9	−	37710.0i	0.762295	−	1.32033i	0.941665	−	0.336552i	$-0.109261\pi$
$14$	67003.6	+	38684.6i	1.74416	+	1.00699i
$15$	−47171.1	−	24912.5i	−0.931774	−	0.492099i
$16$	4446.57	+	7701.69i	0.0678493	+	0.117519i
$17$		−	107702.i		−	1.28952i	−0.764385	−	0.644760i	$-0.776957\pi$
$17$		−	107702.i		−	1.28952i	0.764385	−	0.644760i	$-0.223043\pi$
$18$	−138600.	+	94618.2i	−1.32030	+	0.901332i
$19$	−22386.6			−0.171780			−0.0858902	−	0.996305i	$-0.527373\pi$
$19$	−22386.6			−0.171780			−0.0858902	+	0.996305i	$0.527373\pi$
$20$	227134.	−	131136.i	1.41959	−	0.819600i
$21$	130416.	+	207418.i	0.670585	+	1.06652i
$22$	118390.	−	205057.i	0.505386	−	0.875354i
$23$	−115959.	−	66949.2i	−0.414376	−	0.239240i	0.278292	−	0.960496i	$-0.410232\pi$
$23$	−115959.	−	66949.2i	−0.414376	−	0.239240i	−0.692668	+	0.721256i	$0.743565\pi$
$24$	−11107.2	−	294475.i	−0.0334779	−	0.887573i
$25$	21555.4	+	37335.0i	0.0551818	+	0.0955776i
$26$			1.11376e6i			2.43725i
$27$	−528046.	+	59978.8i	−0.993611	+	0.112861i
$28$	−1.20459e6			−1.95978
$29$	−219270.	+	126596.i	−0.310018	+	0.178989i	−0.646935	−	0.762546i	$-0.723949\pi$
$29$	−219270.	+	126596.i	−0.310018	+	0.178989i	0.336916	+	0.941535i	$0.390616\pi$
$30$	1.36350e6	−	51429.2i	1.68334	−	0.0634928i
$31$	393886.	−	682230.i	0.426504	−	0.738727i	−0.570055	−	0.821606i	$-0.693078\pi$
$31$	393886.	−	682230.i	0.426504	−	0.738727i	0.996560	+	0.0828793i	$0.0264116\pi$
$32$	−1.00357e6	−	579409.i	−0.957075	−	0.552568i
$33$	634778.	−	399124.i	0.535262	−	0.336552i
$34$	1.37740e6	+	2.38573e6i	1.03073	+	1.78528i
$35$		−	1.99211e6i		−	1.32752i
$36$	1.13224e6	−	2.35475e6i	0.674109	−	1.40196i
$37$	1.55379e6			0.829062			0.414531	−	0.910035i	$-0.363946\pi$
$37$	1.55379e6			0.829062			0.414531	+	0.910035i	$0.363946\pi$
$38$	495890.	−	286302.i	0.237822	−	0.137306i
$39$	−1.64714e6	+	3.11881e6i	−0.711988	+	1.34813i
$40$	−1.19800e6	+	2.07499e6i	−0.467967	+	0.810543i
$41$	−1.91891e6	−	1.10788e6i	−0.679076	−	0.392065i	0.120431	−	0.992722i	$-0.461572\pi$
$41$	−1.91891e6	−	1.10788e6i	−0.679076	−	0.392065i	−0.799507	+	0.600657i	$0.794906\pi$
$42$	−5.54154e6	−	2.92666e6i	−1.78087	−	0.940535i
$43$	−277061.	−	479883.i	−0.0810403	−	0.140366i	0.822657	−	0.568538i	$-0.192491\pi$
$43$	−277061.	−	479883.i	−0.0810403	−	0.140366i	−0.903697	+	0.428172i	$0.859158\pi$
$44$			3.68652e6i			0.983571i
$45$	3.89420e6	+	1.87246e6i	0.949660	+	0.456629i
$46$	3.42486e6			0.764911
$47$	2.05696e6	−	1.18759e6i	0.421536	−	0.243374i	−0.274198	−	0.961673i	$-0.588413\pi$
$47$	2.05696e6	−	1.18759e6i	0.421536	−	0.243374i	0.695734	+	0.718299i	$0.255079\pi$
$48$	−383430.	−	609818.i	−0.0722306	−	0.114878i
$49$	−1.69239e6	+	2.93131e6i	−0.293574	+	0.508484i
$50$	−954955.	−	551344.i	−0.152793	−	0.0882150i
$51$	328817.	+	8.71766e6i	0.0486041	+	1.28860i
$52$	−8.67033e6	−	1.50175e7i	−1.18583	−	2.05392i
$53$			7.83903e6i			0.993480i	0.867899	+	0.496740i	$0.165470\pi$
$53$			7.83903e6i			0.993480i	−0.867899	+	0.496740i	$0.834530\pi$
$54$	1.09298e7	−	8.08178e6i	1.28539	−	0.950456i
$55$	−6.09663e6			−0.666253
$56$	9.53025e6	−	5.50229e6i	0.969063	−	0.559489i
$57$	1.81203e6	−	68346.8i	0.171658	−	0.00647469i
$58$	3.23806e6	−	5.60849e6i	0.286136	−	0.495603i
$59$	4.48638e6	+	2.59021e6i	0.370244	+	0.213760i	0.673565	−	0.739128i	$-0.264762\pi$
$59$	4.48638e6	+	2.59021e6i	0.370244	+	0.213760i	−0.303321	+	0.952888i	$0.598096\pi$
$60$	−1.79844e7	+	1.13079e7i	−1.38769	+	0.872524i
$61$	−4.77454e6	−	8.26974e6i	−0.344836	−	0.597273i	0.640488	−	0.767968i	$-0.278732\pi$
$61$	−4.77454e6	−	8.26974e6i	−0.344836	−	0.597273i	−0.985324	+	0.170695i	$0.945399\pi$
$62$			2.01496e7i			1.36364i
$63$	−1.11895e7	−	1.63907e7i	−0.710308	−	1.04049i
$64$	2.73636e7			1.63100
$65$	2.48353e7	−	1.43387e7i	1.39129	−	0.803259i
$66$	−8.95671e6	+	1.69593e7i	−0.472033	+	0.893781i
$67$	−4.31500e6	+	7.47380e6i	−0.214132	+	0.370887i	−0.953004	−	0.302959i	$-0.902026\pi$
$67$	−4.31500e6	+	7.47380e6i	−0.214132	+	0.370887i	0.738872	+	0.673846i	$0.235359\pi$
$68$	−3.71444e7	−	2.14453e7i	−1.73723	−	1.00299i
$69$	9.59044e6	+	5.06501e6i	0.423099	+	0.223452i
$70$	2.54771e7	+	4.41277e7i	1.06110	+	1.83789i
$71$		−	3.31572e7i		−	1.30480i	−0.757873	−	0.652402i	$-0.773762\pi$
$71$		−	3.31572e7i		−	1.30480i	0.757873	−	0.652402i	$-0.226238\pi$
$72$	1.79808e6	+	2.38016e7i	0.0669082	+	0.885680i
$73$	−5.28831e7			−1.86219			−0.931097	−	0.364770i	$-0.881147\pi$
$73$	−5.28831e7			−1.86219			−0.931097	+	0.364770i	$0.881147\pi$
$74$	−3.44184e7	+	1.98715e7i	−1.14779	+	0.662680i
$75$	−1.85873e6	−	2.95618e6i	−0.0587450	−	0.0934298i
$76$	−4.45756e6	+	7.72072e6i	−0.133611	+	0.231421i
$77$	2.42498e7	+	1.40006e7i	0.689836	+	0.398277i
$78$	−3.40035e6	−	9.01508e7i	−0.0918639	−	2.43552i
$79$	4.50350e6	+	7.80029e6i	0.115622	+	0.200264i	0.918028	−	0.396515i	$-0.129780\pi$
$79$	4.50350e6	+	7.80029e6i	0.115622	+	0.200264i	−0.802406	+	0.596778i	$0.796447\pi$
$80$			5.85691e6i			0.142991i
$81$	4.25582e7	−	6.46697e6i	0.988651	−	0.150231i
$82$	5.66748e7			1.25353
$83$	−3.31421e7	+	1.91346e7i	−0.698341	+	0.403188i	−0.806729	−	0.590921i	$-0.798764\pi$
$83$	−3.31421e7	+	1.91346e7i	−0.698341	+	0.403188i	0.108388	+	0.994109i	$0.465431\pi$
$84$	9.75026e7	−	3.67765e6i	1.95839	−	0.0738674i
$85$	3.54655e7	−	6.14281e7i	0.679408	−	1.17677i
$86$	1.22745e7	+	7.08666e6i	0.224393	+	0.129553i
$87$	1.73617e7	−	1.09164e7i	0.303051	−	0.190547i
$88$	−1.68391e7	−	2.91662e7i	−0.280795	−	0.486351i
$89$			1.41720e7i			0.225876i	0.993602	+	0.112938i	$0.0360262\pi$
$89$			1.41720e7i			0.225876i	−0.993602	+	0.112938i	$0.963974\pi$
$90$	−1.10208e8	+	8.32560e6i	−1.67975	+	0.126895i
$91$	−1.31713e8			−1.92071
$92$	−4.61791e7	+	2.66615e7i	−0.644605	+	0.372163i
$93$	−2.97992e7	+	5.64239e7i	−0.398357	+	0.754278i
$94$	−3.03761e7	+	5.26130e7i	−0.389064	+	0.673878i
$95$	−1.27682e7	−	7.37175e6i	−0.156761	−	0.0905058i
$96$	8.30001e7	+	4.38349e7i	0.977223	+	0.516101i
$97$	7.52257e7	+	1.30295e8i	0.849727	+	1.47177i	0.881452	+	0.472273i	$0.156566\pi$
$97$	7.52257e7	+	1.30295e8i	0.849727	+	1.47177i	−0.0317254	+	0.999497i	$0.510100\pi$
$98$		−	8.65761e7i		−	0.938629i
$99$	−5.01620e7	+	3.42441e7i	−0.522196	+	0.356488i
$100$	1.71682e7			0.171682
$101$	8.40858e7	−	4.85470e7i	0.808048	−	0.466527i	−0.0382294	−	0.999269i	$-0.512172\pi$
$101$	8.40858e7	−	4.85470e7i	0.808048	−	0.466527i	0.846278	+	0.532742i	$0.178838\pi$
$102$	−1.18774e8	−	1.88902e8i	−1.09729	−	1.74516i
$103$	4.24958e7	−	7.36049e7i	0.377570	−	0.653970i	−0.613138	−	0.789976i	$-0.710093\pi$
$103$	4.24958e7	−	7.36049e7i	0.377570	−	0.653970i	0.990708	+	0.136006i	$0.0434265\pi$
$104$	1.37192e8	+	7.92080e7i	1.17273	+	0.677073i
$105$	6.08196e6	+	1.61246e8i	0.0500364	+	1.32658i
$106$	−1.00253e8	−	1.73644e8i	−0.794101	−	1.37542i
$107$		−	4.67026e7i		−	0.356292i	−0.984004	−	0.178146i	$-0.942990\pi$
$107$		−	4.67026e7i		−	0.356292i	0.984004	−	0.178146i	$-0.0570099\pi$
$108$	−8.44575e7	+	1.94056e8i	−0.620788	+	1.42637i
$109$	2.22397e8			1.57551			0.787757	−	0.615987i	$-0.211243\pi$
$109$	2.22397e8			1.57551			0.787757	+	0.615987i	$0.211243\pi$
$110$	1.35048e8	−	7.79698e7i	0.922394	−	0.532544i
$111$	−1.25768e8	+	4.74377e6i	−0.828472	+	0.0312487i
$112$	1.34501e7	−	2.32963e7i	0.0854780	−	0.148052i
$113$	−2.58364e7	−	1.49166e7i	−0.158459	−	0.0914866i	0.418673	−	0.908137i	$-0.362495\pi$
$113$	−2.58364e7	−	1.49166e7i	−0.158459	−	0.0914866i	−0.577133	+	0.816650i	$0.695829\pi$
$114$	−3.92645e7	+	2.46880e7i	−0.232477	+	0.146173i
$115$	−4.40918e7	−	7.63693e7i	−0.252096	−	0.436644i
$116$			1.00829e8i			0.556872i
$117$	1.23802e8	−	2.57473e8i	0.660669	−	1.37401i
$118$	−1.32505e8			−0.683445
$119$	−2.82134e8	+	1.62890e8i	−1.40691	+	0.812282i
$120$	9.06337e7	−	1.71612e8i	0.437084	−	0.827605i
$121$	−6.43320e7	+	1.11426e8i	−0.300114	+	0.519812i
$122$	2.11524e8	+	1.22123e8i	0.954816	+	0.551263i
$123$	1.58703e8	+	8.38161e7i	0.693371	+	0.366191i
$124$	−1.56859e8	−	2.71688e8i	−0.663472	−	1.14917i
$125$		−	2.28868e8i		−	0.937444i
$126$	4.57481e8	+	2.19972e8i	1.81506	+	0.872742i
$127$	7.78822e7			0.299381			0.149690	−	0.988733i	$-0.452172\pi$
$127$	7.78822e7			0.299381			0.149690	+	0.988733i	$0.452172\pi$
$128$	−3.49225e8	+	2.01625e8i	−1.30096	+	0.751111i
$129$	2.38911e7	+	3.79971e7i	0.0862734	+	0.137212i
$130$	−3.66755e8	+	6.35238e8i	−1.28411	+	2.22414i
$131$	1.49752e8	+	8.64595e7i	0.508497	+	0.293581i	0.732215	−	0.681073i	$-0.238486\pi$
$131$	1.49752e8	+	8.64595e7i	0.508497	+	0.293581i	−0.223719	+	0.974654i	$0.571820\pi$
$132$	−1.12550e7	−	2.98396e8i	−0.0370724	−	0.982872i
$133$	3.38578e7	+	5.86434e7i	0.108206	+	0.187419i
$134$		−	2.20738e8i		−	0.684634i
$135$	−3.20923e8	−	1.39673e8i	−0.966196	−	0.420510i
$136$	3.91829e8			1.14536
$137$	−2.81349e8	+	1.62437e8i	−0.798662	+	0.461108i	−0.843003	−	0.537908i	$-0.819215\pi$
$137$	−2.81349e8	+	1.62437e8i	−0.798662	+	0.461108i	0.0443408	+	0.999016i	$0.485881\pi$
$138$	−2.77216e8	+	1.04562e7i	−0.764368	+	0.0288308i
$139$	2.69917e8	−	4.67509e8i	0.723054	−	1.25237i	−0.236717	−	0.971579i	$-0.576071\pi$
$139$	2.69917e8	−	4.67509e8i	0.723054	−	1.25237i	0.959770	−	0.280787i	$-0.0905954\pi$
$140$	−6.87042e8	−	3.96664e8i	−1.78843	−	1.03255i
$141$	−1.62870e8	+	1.02406e8i	−0.412063	+	0.259089i
$142$	4.24048e8	+	7.34473e8i	1.04295	+	1.80644i
$143$			4.03091e8i			0.963961i
$144$	3.28976e7	+	4.81896e7i	0.0765092	+	0.112074i
$145$	−1.66748e8			−0.377215
$146$	1.17142e9	−	6.76322e8i	2.57812	−	1.48848i
$147$	1.28037e8	−	2.42434e8i	0.274199	−	0.519188i
$148$	3.09388e8	−	5.35875e8i	0.644846	−	1.11691i
$149$	−2.88344e8	−	1.66475e8i	−0.585013	−	0.337757i	0.178110	−	0.984011i	$-0.443002\pi$
$149$	−2.88344e8	−	1.66475e8i	−0.585013	−	0.337757i	−0.763123	+	0.646253i	$0.776335\pi$
$150$	7.89797e7	+	4.17116e7i	0.156009	+	0.0823933i
$151$	3.59005e8	+	6.21816e8i	0.690547	+	1.19606i	0.971659	+	0.236388i	$0.0759635\pi$
$151$	3.59005e8	+	6.21816e8i	0.690547	+	1.19606i	−0.281112	+	0.959675i	$0.590703\pi$
$152$		−	8.14443e7i		−	0.152576i
$153$	−5.32304e7	−	7.04625e8i	−0.0971392	−	1.28586i
$154$	−7.16217e8			−1.27339
$155$	4.49307e8	−	2.59408e8i	0.778425	−	0.449424i
$156$	7.47646e8	+	1.18908e9i	1.26240	+	2.00776i
$157$	−2.46878e8	+	4.27605e8i	−0.406334	+	0.703792i	−0.994476	−	0.104966i	$-0.966527\pi$
$157$	−2.46878e8	+	4.27605e8i	−0.406334	+	0.703792i	0.588141	+	0.808758i	$0.299860\pi$
$158$	−1.99516e8	−	1.15191e8i	−0.320147	−	0.184837i
$159$	−2.39328e7	−	6.34511e8i	−0.0374459	−	0.992774i
$160$	−3.81591e8	−	6.60935e8i	−0.582262	−	1.00851i
$161$			4.05020e8i			0.602799i
$162$	−8.60009e8	+	6.87528e8i	−1.24866	+	0.998229i
$163$	−3.60955e8			−0.511331			−0.255666	−	0.966765i	$-0.582295\pi$
$163$	−3.60955e8			−0.511331			−0.255666	+	0.966765i	$0.582295\pi$
$164$	−7.64175e8	+	4.41197e8i	−1.05637	+	0.609898i
$165$	4.93476e8	−	1.86131e7i	0.665779	−	0.0251122i
$166$	4.89425e8	−	8.47709e8i	0.644546	−	1.11639i
$167$	7.75381e8	+	4.47667e8i	0.996895	+	0.575558i	0.907328	−	0.420423i	$-0.138118\pi$
$167$	7.75381e8	+	4.47667e8i	0.996895	+	0.575558i	0.0895670	+	0.995981i	$0.471452\pi$
$168$	−7.54603e8	+	4.74465e8i	−0.947286	+	0.595617i
$169$	−5.40166e8	−	9.35595e8i	−0.662187	−	1.14694i
$170$			1.81428e9i			2.17224i
$171$	−1.46461e8	+	1.10643e7i	−0.171292	+	0.0129402i
$172$	−2.20670e8			−0.252133
$173$	−2.83205e8	+	1.63508e8i	−0.316167	+	0.182539i	−0.649683	−	0.760206i	$-0.725098\pi$
$173$	−2.83205e8	+	1.63508e8i	−0.316167	+	0.182539i	0.333516	+	0.942744i	$0.391765\pi$
$174$	−2.44974e8	+	4.63851e8i	−0.267253	+	0.506036i
$175$	6.52013e7	−	1.12932e8i	0.0695191	−	0.120411i
$176$	−7.12957e7	−	4.11626e7i	−0.0743041	−	0.0428995i
$177$	−3.71046e8	−	1.95961e8i	−0.378038	−	0.199653i
$178$	−1.81246e8	−	3.13927e8i	−0.180546	−	0.312715i
$179$		−	6.26395e8i		−	0.610150i	−0.952328	−	0.305075i	$-0.901319\pi$
$179$		−	6.26395e8i		−	0.610150i	0.952328	−	0.305075i	$-0.0986815\pi$
$180$	1.42118e9	−	9.70197e8i	1.35381	−	0.924208i
$181$	1.46351e8			0.136359			0.0681793	−	0.997673i	$-0.478281\pi$
$181$	1.46351e8			0.136359			0.0681793	+	0.997673i	$0.478281\pi$
$182$	2.91759e9	−	1.68447e9i	2.65913	−	1.53525i
$183$	4.11711e8	+	6.54797e8i	0.367103	+	0.583851i
$184$	2.43567e8	−	4.21870e8i	0.212494	−	0.368051i
$185$	8.86211e8	+	5.11654e8i	0.756572	+	0.436807i
$186$	−6.15173e7	−	1.63096e9i	−0.0513979	−	1.36267i
$187$	4.98507e8	+	8.63439e8i	0.407666	+	0.706098i
$188$		−	9.45876e8i		−	0.757187i
$189$	9.55743e8	+	1.29254e9i	0.749021	+	1.01297i
$190$	3.77110e8			0.289370
$191$	−1.93012e9	+	1.11436e9i	−1.45028	+	0.837320i	−0.998497	−	0.0548082i	$-0.982545\pi$
$191$	−1.93012e9	+	1.11436e9i	−1.45028	+	0.837320i	−0.451783	+	0.892128i	$0.649212\pi$
$192$	−2.21488e9	+	8.35418e7i	−1.62984	+	0.0614750i
$193$	−8.57309e8	+	1.48490e9i	−0.617886	+	1.07021i	0.371985	+	0.928239i	$0.378677\pi$
$193$	−8.57309e8	+	1.48490e9i	−0.617886	+	1.07021i	−0.989871	+	0.141971i	$0.954656\pi$
$194$	−3.33268e9	−	1.92412e9i	−2.35281	−	1.35840i
$195$	−1.96645e9	+	1.23643e9i	−1.36002	+	0.855128i
$196$	6.73970e8	+	1.16735e9i	0.456684	+	0.791001i
$197$		−	1.93330e9i		−	1.28361i	−0.766866	−	0.641807i	$-0.778185\pi$
$197$		−	1.93330e9i		−	1.28361i	0.766866	−	0.641807i	$-0.221815\pi$
$198$	6.73201e8	−	1.40007e9i	0.438010	−	0.910938i
$199$	2.64799e9			1.68851			0.844254	−	0.535943i	$-0.180044\pi$
$199$	2.64799e9			1.68851			0.844254	+	0.535943i	$0.180044\pi$
$200$	−1.35828e8	+	7.84203e7i	−0.0848924	+	0.0490127i
$201$	3.26449e8	−	6.18121e8i	0.200000	−	0.378695i
$202$	−1.24174e9	+	2.15075e9i	−0.745802	+	1.29177i
$203$	6.63254e8	+	3.82930e8i	0.390567	+	0.225494i
$204$	3.07203e9	+	1.62244e9i	1.77380	+	0.936800i
$205$	−7.29635e8	−	1.26377e9i	−0.413133	−	0.715568i
$206$			2.17392e9i			1.20719i
$207$	−7.91737e8	−	3.80694e8i	−0.431221	−	0.207346i
$208$	3.87242e8			0.206885
$209$	1.79472e8	−	1.03618e8i	0.0940613	−	0.0543063i
$210$	−2.19690e9	−	3.49402e9i	−1.12962	−	1.79659i
$211$	9.38787e8	−	1.62603e9i	0.473628	−	0.820347i	−0.525916	−	0.850536i	$-0.676278\pi$
$211$	9.38787e8	−	1.62603e9i	0.473628	−	0.820347i	0.999544	+	0.0301889i	$0.00961089\pi$
$212$	2.70354e9	+	1.56089e9i	1.33841	+	0.772731i
$213$	1.01230e8	+	2.68383e9i	0.0491802	+	1.30388i
$214$	5.97280e8	+	1.03452e9i	0.284789	+	0.493268i
$215$		−	3.64937e8i		−	0.170791i
$216$	−2.18208e8	−	1.92107e9i	−0.100243	−	0.882529i
$217$	−2.38287e9			−1.07464
$218$	−4.92635e9	+	2.84423e9i	−2.18122	+	1.25933i
$219$	4.28048e9	−	1.61453e8i	1.86087	−	0.0701892i
$220$	−1.21395e9	+	2.10261e9i	−0.518213	+	0.897571i
$221$	−4.06145e9	−	2.34488e9i	−1.70260	−	0.982994i
$222$	2.72524e9	−	1.71353e9i	1.12200	−	0.705471i
$223$	−1.91832e9	−	3.32263e9i	−0.775713	−	1.34358i	−0.934393	−	0.356245i	$-0.884057\pi$
$223$	−1.91832e9	−	3.32263e9i	−0.775713	−	1.34358i	0.158679	−	0.987330i	$-0.449276\pi$
$224$			3.50523e9i			1.39227i
$225$	1.59475e8	+	2.33605e8i	0.0622248	+	0.0911492i
$226$	7.63076e8			0.292506
$227$	3.45300e9	−	1.99359e9i	1.30045	−	0.750813i	0.319966	−	0.947429i	$-0.396329\pi$
$227$	3.45300e9	−	1.99359e9i	1.30045	−	0.750813i	0.980481	+	0.196616i	$0.0629952\pi$
$228$	3.37234e8	−	6.38543e8i	0.124794	−	0.236293i
$229$	−9.26279e8	+	1.60436e9i	−0.336821	+	0.583392i	−0.983833	−	0.179088i	$-0.942685\pi$
$229$	−9.26279e8	+	1.60436e9i	−0.336821	+	0.583392i	0.647012	+	0.762480i	$0.276019\pi$
$230$	1.95337e9	+	1.12778e9i	0.698030	+	0.403008i
$231$	−2.00558e9	−	1.05921e9i	−0.704357	−	0.371993i
$232$	−4.60565e8	−	7.97722e8i	−0.158979	−	0.275359i
$233$		−	5.85169e9i		−	1.98544i	−0.120431	−	0.992722i	$-0.538428\pi$
$233$		−	5.85169e9i		−	1.98544i	0.120431	−	0.992722i	$-0.461572\pi$
$234$	5.50465e8	+	7.28664e9i	0.183597	+	2.43032i
$235$	1.56426e9			0.512904
$236$	1.78663e9	−	1.03151e9i	0.575953	−	0.332526i
$237$	−3.88339e8	−	6.17625e8i	−0.123088	−	0.195763i
$238$	4.16640e9	−	7.21642e9i	1.29853	−	2.24913i
$239$	3.97738e9	+	2.29634e9i	1.21901	+	0.703793i	0.964705	−	0.263332i	$-0.0848215\pi$
$239$	3.97738e9	+	2.29634e9i	1.21901	+	0.703793i	0.254300	+	0.967125i	$0.418155\pi$
$240$	−1.78813e7	−	4.74072e8i	−0.00538956	−	0.142889i
$241$	1.07396e9	+	1.86015e9i	0.318361	+	0.551417i	0.980146	−	0.198276i	$-0.0635343\pi$
$241$	1.07396e9	+	1.86015e9i	0.318361	+	0.551417i	−0.661785	+	0.749693i	$0.730201\pi$
$242$		−	3.29097e9i		−	0.959539i
$243$	−3.42502e9	+	6.53383e8i	−0.982286	+	0.187388i
$244$	−3.80278e9			−1.07286
$245$	−1.93052e9	+	1.11459e9i	−0.535809	+	0.309350i
$246$	−4.58740e9	+	1.73029e8i	−1.25264	+	0.0472476i
$247$	−4.87399e8	+	8.44200e8i	−0.130947	+	0.226807i
$248$	2.48201e9	+	1.43299e9i	0.656140	+	0.378823i
$249$	2.62419e9	−	1.64999e9i	0.682648	−	0.429223i
$250$	2.92700e9	+	5.06970e9i	0.749311	+	1.29784i
$251$			6.17017e9i			1.55454i	0.629166	+	0.777271i	$0.283397\pi$
$251$			6.17017e9i			1.55454i	−0.629166	+	0.777271i	$0.716603\pi$
$252$	−7.88087e9	+	5.95355e8i	−1.95421	+	0.147630i
$253$	1.23952e9			0.302531
$254$	−1.72519e9	+	9.96037e8i	−0.414478	+	0.239299i
$255$	−2.68312e9	+	5.08042e9i	−0.634571	+	1.20154i
$256$	1.65462e9	−	2.86589e9i	0.385246	−	0.667266i
$257$	4.17836e9	+	2.41238e9i	0.957797	+	0.552984i	0.895494	−	0.445073i	$-0.146822\pi$
$257$	4.17836e9	+	2.41238e9i	0.957797	+	0.552984i	0.0623027	+	0.998057i	$0.480156\pi$
$258$	−1.01516e9	−	5.36138e8i	−0.229116	−	0.121003i
$259$	−2.34998e9	−	4.07029e9i	−0.522234	−	0.904536i
$260$		−	1.14203e10i		−	2.49911i
$261$	−1.37197e9	+	9.36605e8i	−0.295654	+	0.201834i
$262$	−4.42292e9			−0.938651
$263$	−2.74533e9	+	1.58501e9i	−0.573814	+	0.331292i	−0.758671	−	0.651474i	$-0.774151\pi$
$263$	−2.74533e9	+	1.58501e9i	−0.573814	+	0.331292i	0.184857	+	0.982765i	$0.440818\pi$
$264$	1.45205e9	+	2.30938e9i	0.298927	+	0.475422i
$265$	−2.58134e9	+	4.47101e9i	−0.523434	+	0.906614i
$266$	−1.49998e9	−	8.66016e8i	−0.299612	−	0.172981i
$267$	−4.32674e7	−	1.14712e9i	−0.00851366	−	0.225716i
$268$	1.71838e9	+	2.97633e9i	0.333105	+	0.576954i
$269$		−	4.01247e9i		−	0.766306i	−0.923685	−	0.383153i	$-0.874838\pi$
$269$		−	4.01247e9i		−	0.766306i	0.923685	−	0.383153i	$-0.125162\pi$
$270$	8.89510e9	−	1.01036e9i	1.67377	−	0.190118i
$271$	−5.85354e9			−1.08528			−0.542640	−	0.839966i	$-0.682575\pi$
$271$	−5.85354e9			−1.08528			−0.542640	+	0.839966i	$0.682575\pi$
$272$	8.29488e8	−	4.78905e8i	0.151542	−	0.0874931i
$273$	1.06611e10	−	4.02121e8i	1.91934	−	0.0723947i
$274$	4.15482e9	−	7.19635e9i	0.737139	−	1.27676i
$275$	−3.45616e8	−	1.99541e8i	−0.0604314	−	0.0348901i
$276$	3.65645e9	−	2.29903e9i	0.630120	−	0.396195i
$277$	2.71626e9	+	4.70470e9i	0.461373	+	0.799121i	0.999030	−	0.0440427i	$-0.0140238\pi$
$277$	2.71626e9	+	4.70470e9i	0.461373	+	0.799121i	−0.537657	+	0.843164i	$0.680690\pi$
$278$			1.38079e10i			2.31178i
$279$	2.23976e9	−	4.65807e9i	0.369644	−	0.768756i
$280$	7.24746e9			1.17911
$281$	9.77406e7	−	5.64306e7i	0.0156765	−	0.00905084i	−0.492141	−	0.870515i	$-0.663786\pi$
$281$	9.77406e7	−	5.64306e7i	0.0156765	−	0.00905084i	0.507818	+	0.861465i	$0.330452\pi$
$282$	2.29809e9	−	4.35136e9i	0.363388	−	0.688064i
$283$	3.05787e9	−	5.29639e9i	0.476732	−	0.825723i	−0.522913	−	0.852386i	$-0.675155\pi$
$283$	3.05787e9	−	5.29639e9i	0.476732	−	0.825723i	0.999644	+	0.0266628i	$0.00848805\pi$
$284$	−1.14353e10	−	6.60218e9i	−1.75782	−	1.01488i
$285$	1.05600e9	+	5.57706e8i	0.160061	+	0.0845329i
$286$	−5.15514e9	−	8.92896e9i	−0.770506	−	1.33456i
$287$			6.70230e9i			0.987862i
$288$	−6.85206e9	−	3.29470e9i	−0.995981	−	0.478902i
$289$	−4.62396e9			−0.662861
$290$	3.69367e9	−	2.13254e9i	0.522236	−	0.301513i
$291$	−6.48674e9	−	1.03167e10i	−0.904596	−	1.43870i
$292$	−1.05299e10	+	1.82384e10i	−1.44842	+	2.50874i
$293$	5.72464e9	+	3.30512e9i	0.776744	+	0.448453i	0.835275	−	0.549832i	$-0.185308\pi$
$293$	5.72464e9	+	3.30512e9i	0.776744	+	0.448453i	−0.0585311	+	0.998286i	$0.518642\pi$
$294$	2.64319e8	+	7.00768e9i	0.0353785	+	0.937962i
$295$	1.70588e9	+	2.95467e9i	0.225247	+	0.390140i
$296$			5.65284e9i			0.736376i
$297$	3.95569e9	−	2.92494e9i	0.508389	−	0.375917i
$298$	8.51622e9			1.07990
$299$	−5.04932e9	+	2.91522e9i	−0.631754	+	0.364743i
$300$	−1.38964e9	+	5.24149e7i	−0.171560	+	0.00647098i
$301$	−8.38061e8	+	1.45156e9i	−0.102096	+	0.176836i
$302$	−1.59048e10	−	9.18265e9i	−1.91206	−	1.10393i
$303$	−6.65790e9	+	4.18623e9i	−0.789890	+	0.496652i
$304$	−9.95437e7	−	1.72415e8i	−0.0116552	−	0.0201874i
$305$		−	6.28889e9i		−	0.726733i
$306$	1.01906e10	+	1.49275e10i	1.16229	+	1.70256i
$307$	1.46067e10			1.64437			0.822184	−	0.569222i	$-0.192755\pi$
$307$	1.46067e10			1.64437			0.822184	+	0.569222i	$0.192755\pi$
$308$	9.65712e9	−	5.57554e9i	1.07311	−	0.619561i
$309$	−3.21500e9	+	6.08750e9i	−0.352652	+	0.667736i
$310$	−6.63513e9	+	1.14924e10i	−0.718460	+	1.24441i
$311$	−6.95108e9	−	4.01321e9i	−0.743038	−	0.428993i	0.0801351	−	0.996784i	$-0.474465\pi$
$311$	−6.95108e9	−	4.01321e9i	−0.743038	−	0.428993i	−0.823173	+	0.567791i	$0.807798\pi$
$312$	−1.13465e10	−	5.99244e9i	−1.19741	−	0.632390i
$313$	1.74799e9	+	3.02760e9i	0.182121	+	0.315443i	0.942603	−	0.333916i	$-0.108370\pi$
$313$	1.74799e9	+	3.02760e9i	0.182121	+	0.315443i	−0.760481	+	0.649360i	$0.775037\pi$
$314$		−	1.26293e10i		−	1.29915i
$315$	−9.84577e8	−	1.30331e10i	−0.100002	−	1.32375i
$316$	3.58690e9			0.359725
$317$	3.16758e9	−	1.82880e9i	0.313683	−	0.181105i	−0.334890	−	0.942257i	$-0.608699\pi$
$317$	3.16758e9	−	1.82880e9i	0.313683	−	0.181105i	0.648573	+	0.761152i	$0.275366\pi$
$318$	8.64490e9	+	1.37491e10i	0.845379	+	1.34452i
$319$	1.17191e9	−	2.02981e9i	0.113170	−	0.196017i
$320$	1.56069e10	+	9.01065e9i	1.48839	+	0.859323i
$321$	1.42584e8	+	3.78022e9i	0.0134292	+	0.356039i
$322$	−5.17980e9	−	8.97168e9i	−0.481825	−	0.834546i
$323$			2.41108e9i			0.221514i
$324$	6.24374e9	−	1.59652e10i	0.566584	−	1.44875i
$325$	1.87721e9			0.168259
$326$	7.99559e9	−	4.61625e9i	0.707913	−	0.408714i
$327$	−1.80013e10	+	6.78982e8i	−1.57439	+	0.0593837i
$328$	4.03056e9	−	6.98114e9i	0.348233	−	0.603158i
$329$	−6.22195e9	−	3.59225e9i	−0.531059	−	0.306607i
$330$	−1.06930e10	+	6.72337e9i	−0.901666	+	0.566933i
$331$	1.28320e9	+	2.22257e9i	0.106901	+	0.185159i	0.914513	−	0.404555i	$-0.132574\pi$
$331$	1.28320e9	+	2.22257e9i	0.106901	+	0.185159i	−0.807612	+	0.589714i	$0.799240\pi$
$332$			1.52401e10i			1.25440i
$333$	1.01655e10	−	7.67945e8i	0.826706	−	0.0624530i
$334$	−2.29008e10			−1.84020
$335$	−4.92214e9	+	2.84180e9i	−0.390818	+	0.225639i
$336$	−1.01756e9	+	1.92672e9i	−0.0798369	+	0.151169i
$337$	8.78453e9	−	1.52153e10i	0.681081	−	1.17967i	−0.293570	−	0.955938i	$-0.594843\pi$
$337$	8.78453e9	−	1.52153e10i	0.681081	−	1.17967i	0.974651	−	0.223730i	$-0.0718233\pi$
$338$	2.39307e10	+	1.38164e10i	1.83353	+	1.05859i
$339$	2.13680e9	+	1.12851e9i	0.161795	+	0.0854490i
$340$	−1.41236e10	−	2.44628e10i	−1.05689	−	1.83059i
$341$			7.29251e9i			0.539336i
$342$	3.10279e9	−	2.11818e9i	0.226803	−	0.154831i
$343$	−7.19914e9			−0.520120
$344$	1.74586e9	−	1.00797e9i	0.124674	−	0.0719804i
$345$	3.80206e9	+	6.04690e9i	0.268375	+	0.426832i
$346$	4.18222e9	−	7.24381e9i	0.291811	−	0.505432i
$347$	−3.87244e9	−	2.23576e9i	−0.267096	−	0.154208i	0.360471	−	0.932770i	$-0.382616\pi$
$347$	−3.87244e9	−	2.23576e9i	−0.267096	−	0.154208i	−0.627567	+	0.778562i	$0.715949\pi$
$348$	−3.07835e8	−	8.16139e9i	−0.0209894	−	0.556477i
$349$	3.34797e9	+	5.79885e9i	0.225673	+	0.390877i	0.956521	−	0.291663i	$-0.0942086\pi$
$349$	3.34797e9	+	5.79885e9i	0.225673	+	0.390877i	−0.730848	+	0.682540i	$0.760875\pi$
$350$			3.33544e9i			0.222270i
$351$	−9.23475e9	+	2.12185e10i	−0.608411	+	1.39793i
$352$	1.07274e10			0.698750
$353$	−5.93593e9	+	3.42711e9i	−0.382287	+	0.220714i	−0.678813	−	0.734311i	$-0.737505\pi$
$353$	−5.93593e9	+	3.42711e9i	−0.382287	+	0.220714i	0.296526	+	0.955025i	$0.404172\pi$
$354$	1.07253e10	−	4.04540e8i	0.682960	−	0.0257602i
$355$	1.09185e10	−	1.89113e10i	0.687460	−	1.19072i
$356$	4.88766e9	+	2.82189e9i	0.304299	+	0.175687i
$357$	2.23393e10	−	1.40461e10i	1.37530	−	0.864733i
$358$	8.01098e9	+	1.38754e10i	0.487701	+	0.844722i
$359$		−	1.73526e9i		−	0.104469i	−0.998635	−	0.0522343i	$-0.983366\pi$
$359$		−	1.73526e9i		−	0.104469i	0.998635	−	0.0522343i	$-0.0166343\pi$
$360$	−6.81218e9	+	1.41674e10i	−0.405580	+	0.843492i
$361$	−1.64824e10			−0.970491
$362$	−3.24186e9	+	1.87169e9i	−0.188782	+	0.108993i
$363$	4.86701e9	−	9.21553e9i	0.280308	−	0.530755i
$364$	−2.62263e10	+	4.54252e10i	−1.49393	+	2.58757i
$365$	−3.01620e10	−	1.74140e10i	−1.69937	−	0.981133i
$366$	−1.74941e10	−	9.23917e9i	−0.974915	−	0.514883i
$367$	5.88774e9	+	1.01979e10i	0.324552	+	0.562140i	0.981422	−	0.191864i	$-0.0614532\pi$
$367$	5.88774e9	+	1.01979e10i	0.324552	+	0.562140i	−0.656870	+	0.754004i	$0.728120\pi$
$368$		−	1.19078e9i		−	0.0649292i
$369$	−1.31017e10	−	6.29976e9i	−0.706681	−	0.339796i
$370$	−2.61742e10			−1.39658
$371$	2.05350e10	−	1.18559e10i	1.08392	−	0.625803i
$372$	1.35260e10	+	2.15122e10i	0.706314	+	1.12334i
$373$	−3.90182e9	+	6.75815e9i	−0.201573	+	0.349134i	−0.949035	−	0.315170i	$-0.897939\pi$
$373$	−3.90182e9	+	6.75815e9i	−0.201573	+	0.349134i	0.747463	+	0.664304i	$0.231272\pi$
$374$	−2.20850e10	−	1.27508e10i	−1.12879	−	0.651705i
$375$	6.98739e8	+	1.85251e10i	0.0353338	+	0.936778i
$376$	4.32054e9	+	7.48339e9i	0.216166	+	0.374410i
$377$			1.10249e10i			0.545770i
$378$	−3.77012e10	−	1.64084e10i	−1.84666	−	0.803710i
$379$	2.60617e10			1.26312			0.631561	−	0.775326i	$-0.282415\pi$
$379$	2.60617e10			1.26312			0.631561	+	0.775326i	$0.282415\pi$
$380$	−5.08476e9	+	2.93569e9i	−0.243858	+	0.140791i
$381$	−6.30398e9	+	2.37776e8i	−0.299168	+	0.0112841i
$382$	2.85031e10	−	4.93688e10i	1.33856	−	2.31846i
$383$	3.06119e10	+	1.76738e10i	1.42264	+	0.821361i	0.996524	−	0.0833079i	$-0.0265485\pi$
$383$	3.06119e10	+	1.76738e10i	1.42264	+	0.821361i	0.426115	+	0.904669i	$0.359882\pi$
$384$	2.76515e10	−	1.73862e10i	1.27173	−	0.799613i
$385$	9.22063e9	+	1.59706e10i	0.419679	+	0.726906i
$386$		−	4.38565e10i		−	1.97554i
$387$	−2.04981e9	−	3.00263e9i	−0.0913838	−	0.133862i
$388$	5.99150e10			2.64368
$389$	1.63388e10	−	9.43321e9i	0.713545	−	0.411966i	−0.0988271	−	0.995105i	$-0.531509\pi$
$389$	1.63388e10	−	9.43321e9i	0.713545	−	0.411966i	0.812372	+	0.583139i	$0.198176\pi$
$390$	2.77466e10	−	5.25374e10i	1.19937	−	2.27096i
$391$	−7.21056e9	+	1.24891e10i	−0.308505	+	0.534346i
$392$	−1.06644e10	−	6.15707e9i	−0.451638	−	0.260753i
$393$	−1.23853e10	−	6.54104e9i	−0.519201	−	0.274206i
$394$	2.47250e10	+	4.28250e10i	1.02601	+	1.77710i
$395$			5.93188e9i			0.243671i
$396$	1.82202e9	+	2.41185e10i	0.0740921	+	0.980776i
$397$	−3.41481e10			−1.37469			−0.687345	−	0.726331i	$-0.741224\pi$
$397$	−3.41481e10			−1.37469			−0.687345	+	0.726331i	$0.741224\pi$
$398$	−5.86561e10	+	3.38651e10i	−2.33766	+	1.34965i
$399$	−2.91957e9	−	4.64338e9i	−0.115193	−	0.183207i
$400$	−1.91695e8	+	3.32026e8i	−0.00748809	+	0.0129698i
$401$	3.01595e9	+	1.74126e9i	0.116640	+	0.0673420i	0.557185	−	0.830388i	$-0.311881\pi$
$401$	3.01595e9	+	1.74126e9i	0.116640	+	0.0673420i	−0.440545	+	0.897730i	$0.645215\pi$
$402$	6.73919e8	+	1.78671e10i	0.0258050	+	0.684147i
$403$	−1.71513e10	−	2.97069e10i	−0.650244	−	1.12626i
$404$		−	3.86662e10i		−	1.45146i
$405$	2.64027e10	+	1.03257e10i	0.981359	+	0.383794i
$406$	−1.95892e10			−0.720961
$407$	−1.24567e10	+	7.19185e9i	−0.453967	+	0.262098i
$408$	−3.17156e10	+	1.19626e9i	−1.14454	+	0.0431704i
$409$	−1.46758e10	+	2.54192e10i	−0.524455	+	0.908382i	0.475140	+	0.879910i	$0.342397\pi$
$409$	−1.46758e10	+	2.54192e10i	−0.524455	+	0.908382i	−0.999595	+	0.0284717i	$0.990936\pi$
$410$	3.23246e10	+	1.86626e10i	1.14393	+	0.660446i
$411$	2.22772e10	−	1.40070e10i	0.780715	−	0.490883i
$412$	−1.69233e10	−	2.93120e10i	−0.587349	−	1.01732i
$413$		−	1.56699e10i		−	0.538599i
$414$	2.24066e10	−	1.69269e9i	0.762738	−	0.0576205i
$415$	−2.52036e10			−0.849708
$416$	−4.36991e10	+	2.52297e10i	−1.45915	+	0.842439i
$417$	−2.04204e10	+	3.86654e10i	−0.675336	+	1.27873i
$418$	−2.65034e9	+	4.59053e9i	−0.0868154	+	0.150369i
$419$	2.87848e10	+	1.66189e10i	0.933914	+	0.539195i	0.888047	−	0.459752i	$-0.152062\pi$
$419$	2.87848e10	+	1.66189e10i	0.933914	+	0.539195i	0.0458666	+	0.998948i	$0.485395\pi$
$420$	5.68219e10	+	3.00094e10i	1.82607	+	0.964406i
$421$	−1.38303e10	−	2.39548e10i	−0.440254	−	0.762542i	0.557454	−	0.830208i	$-0.311778\pi$
$421$	−1.38303e10	−	2.39548e10i	−0.440254	−	0.762542i	−0.997708	+	0.0676654i	$0.978445\pi$
$422$			4.80246e10i			1.51431i
$423$	1.28704e10	−	8.78624e9i	0.402005	−	0.274436i
$424$	−2.85191e10			−0.882413
$425$	4.02105e9	−	2.32156e9i	0.123249	−	0.0711580i
$426$	−3.65659e10	−	5.81554e10i	−1.11029	−	1.76584i
$427$	−1.44422e10	+	2.50146e10i	−0.434431	+	0.752456i
$428$	−1.61069e10	−	9.29929e9i	−0.479994	−	0.277125i
$429$	−1.23065e9	−	3.26272e10i	−0.0363333	−	0.963276i
$430$	4.66718e9	+	8.08379e9i	0.136515	+	0.236451i
$431$			3.24621e10i			0.940734i	0.882471	+	0.470367i	$0.155879\pi$
$431$			3.24621e10i			0.940734i	−0.882471	+	0.470367i	$0.844121\pi$
$432$	−2.80993e9	−	3.80014e9i	−0.0806791	−	0.109110i
$433$	2.13330e10			0.606876			0.303438	−	0.952851i	$-0.401865\pi$
$433$	2.13330e10			0.606876			0.303438	+	0.952851i	$0.401865\pi$
$434$	5.27835e10	−	3.04746e10i	1.48778	−	0.858972i
$435$	1.34970e10	−	5.09086e8i	0.376947	−	0.0142179i
$436$	4.42830e10	−	7.67004e10i	1.22544	−	2.12252i
$437$	2.59594e9	+	1.49877e9i	0.0711817	+	0.0410968i
$438$	−9.27531e10	+	5.83195e10i	−2.52018	+	1.58459i
$439$	−9.84950e9	−	1.70598e10i	−0.265189	−	0.459322i	0.702424	−	0.711759i	$-0.252101\pi$
$439$	−9.84950e9	−	1.70598e10i	−0.265189	−	0.459322i	−0.967613	+	0.252437i	$0.918768\pi$
$440$		−	2.21800e10i		−	0.591768i
$441$	−9.62348e9	+	2.00141e10i	−0.254435	+	0.529154i
$442$	1.19955e11			3.14288
$443$	2.42267e10	−	1.39873e10i	0.629042	−	0.363177i	−0.151339	−	0.988482i	$-0.548359\pi$
$443$	2.42267e10	−	1.39873e10i	0.629042	−	0.363177i	0.780381	+	0.625305i	$0.215025\pi$
$444$	−2.34065e10	+	4.43196e10i	−0.602290	+	1.14042i
$445$	−4.66674e9	+	8.08303e9i	−0.119007	+	0.206127i
$446$	8.49862e10	+	4.90668e10i	2.14787	+	1.24008i
$447$	2.38475e10	+	1.25946e10i	0.597328	+	0.315467i
$448$	−4.13851e10	−	7.16812e10i	−1.02738	−	1.77948i
$449$		−	3.38588e10i		−	0.833080i	−0.909117	−	0.416540i	$-0.863243\pi$
$449$		−	3.38588e10i		−	0.833080i	0.909117	−	0.416540i	$-0.136757\pi$
$450$	−6.52015e9	−	3.13511e9i	−0.159004	−	0.0764545i
$451$	2.05116e10			0.495786
$452$	−1.02889e10	+	5.94033e9i	−0.246500	+	0.142317i
$453$	−3.09572e10	−	4.92352e10i	−0.735138	−	1.16918i
$454$	−5.09920e10	+	8.83208e10i	−1.20027	+	2.07893i
$455$	−7.51226e10	−	4.33720e10i	−1.75277	−	1.01196i
$456$	2.48651e8	+	6.59230e9i	0.00575084	+	0.152468i
$457$	−2.42880e10	−	4.20680e10i	−0.556834	−	0.964466i	−0.997758	−	0.0669210i	$-0.978682\pi$
$457$	−2.42880e10	−	4.20680e10i	−0.556834	−	0.964466i	0.440924	−	0.897545i	$-0.354651\pi$
$458$		−	4.73847e10i		−	1.07690i
$459$	6.45984e9	+	5.68715e10i	0.145536	+	1.28128i
$460$	−3.51178e10			−0.784325
$461$	3.83976e10	−	2.21689e10i	0.850159	−	0.490840i	−0.0105452	−	0.999944i	$-0.503357\pi$
$461$	3.83976e10	−	2.21689e10i	0.850159	−	0.490840i	0.860705	+	0.509105i	$0.170023\pi$
$462$	5.79724e10	−	2.18663e9i	1.27249	−	0.0479962i
$463$	7.25514e9	−	1.25663e10i	0.157878	−	0.273453i	−0.776225	−	0.630456i	$-0.782868\pi$
$463$	7.25514e9	−	1.25663e10i	0.157878	−	0.273453i	0.934103	+	0.357003i	$0.116201\pi$
$464$	−1.95000e9	−	1.12583e9i	−0.0420690	−	0.0242886i
$465$	−3.55760e10	+	2.23688e10i	−0.760932	+	0.478444i
$466$	7.48373e10	+	1.29622e11i	1.58699	+	2.74875i
$467$		−	5.53421e10i		−	1.16356i	−0.813347	−	0.581779i	$-0.802357\pi$
$467$		−	5.53421e10i		−	1.16356i	0.813347	−	0.581779i	$-0.197643\pi$
$468$	−6.41466e10	−	9.39643e10i	−1.33718	−	1.95875i
$469$	2.61043e10			0.539535
$470$	−3.46502e10	+	2.00053e10i	−0.710091	+	0.409971i
$471$	1.86774e10	−	3.53651e10i	0.379519	−	0.718607i
$472$	−9.42340e9	+	1.63218e10i	−0.189863	+	0.328852i
$473$	4.44235e9	+	2.56479e9i	0.0887500	+	0.0512398i
$474$	1.65010e10	+	8.71468e9i	0.326886	+	0.172639i
$475$	−4.82552e8	−	8.35804e8i	−0.00947915	−	0.0164184i
$476$			1.29737e11i			2.52718i
$477$	3.87435e9	+	5.12858e10i	0.0748386	+	0.990657i
$478$	−1.17472e11			−2.25020
$479$	3.37571e10	−	1.94897e10i	0.641243	−	0.370222i	−0.143850	−	0.989599i	$-0.545948\pi$
$479$	3.37571e10	−	1.94897e10i	0.641243	−	0.370222i	0.785093	+	0.619378i	$0.212615\pi$
$480$	3.29048e10	+	5.23327e10i	0.619860	+	0.985844i
$481$	3.38291e10	−	5.85937e10i	0.631989	−	1.09464i
$482$	−4.75790e10	−	2.74697e10i	−0.881510	−	0.508940i
$483$	−1.23653e9	−	3.27833e10i	−0.0227205	−	0.602371i
$484$	2.56193e10	+	4.43739e10i	0.466858	+	0.808622i
$485$			9.90852e10i			1.79078i
$486$	6.75122e10	−	5.82758e10i	1.21014	−	1.04458i
$487$	−2.22852e10			−0.396188			−0.198094	−	0.980183i	$-0.563475\pi$
$487$	−2.22852e10			−0.396188			−0.198094	+	0.980183i	$0.563475\pi$
$488$	3.00860e10	−	1.73702e10i	0.530500	−	0.306284i
$489$	2.92166e10	−	1.10200e9i	0.510968	−	0.0192729i
$490$	2.85089e10	−	4.93789e10i	0.494534	−	0.856559i
$491$	−5.32333e10	−	3.07343e10i	−0.915920	−	0.528807i	−0.0335890	−	0.999436i	$-0.510694\pi$
$491$	−5.32333e10	−	3.07343e10i	−0.915920	−	0.528807i	−0.882331	+	0.470629i	$0.844027\pi$
$492$	6.05072e10	−	3.80446e10i	1.03263	−	0.649281i
$493$	1.36346e10	+	2.36158e10i	0.230810	+	0.399774i
$494$		−	2.49334e10i		−	0.418672i
$495$	−3.98863e10	+	3.01319e9i	−0.664360	+	0.0501886i
$496$	7.00577e9			0.115752
$497$	−8.68580e10	+	5.01475e10i	−1.42359	+	0.821909i
$498$	−3.70272e10	+	7.01099e10i	−0.602010	+	1.13989i
$499$	−2.77415e10	+	4.80496e10i	−0.447432	+	0.774975i	−0.998218	−	0.0596714i	$-0.980995\pi$
$499$	−2.77415e10	+	4.80496e10i	−0.447432	+	0.774975i	0.550786	+	0.834647i	$0.314328\pi$
$500$	−7.89324e10	−	4.55716e10i	−1.26292	−	0.729146i
$501$	−6.41280e10	−	3.38680e10i	−1.01788	−	0.537574i
$502$	−7.89104e10	−	1.36677e11i	−1.24257	−	2.15219i
$503$			9.38955e10i			1.46681i	0.679794	+	0.733403i	$0.262069\pi$
$503$			9.38955e10i			1.46681i	−0.679794	+	0.733403i	$0.737931\pi$
$504$	5.96308e10	−	4.07082e10i	0.924163	−	0.630898i
$505$	6.39447e10			0.983194
$506$	−2.74568e10	+	1.58522e10i	−0.418840	+	0.241817i
$507$	4.65788e10	+	7.40802e10i	0.704946	+	1.12117i
$508$	1.55077e10	−	2.68601e10i	0.232859	−	0.403323i
$509$	2.97149e10	+	1.71559e10i	0.442693	+	0.255589i	0.704739	−	0.709466i	$-0.251064\pi$
$509$	2.97149e10	+	1.71559e10i	0.442693	+	0.255589i	−0.262046	+	0.965055i	$0.584397\pi$
$510$	−5.53902e9	−	1.46852e11i	−0.0818752	−	2.17069i
$511$	7.99811e10	+	1.38531e11i	1.17302	+	2.03172i
$512$		−	1.85882e10i		−	0.270494i
$513$	1.18211e10	−	1.34272e9i	0.170683	−	0.0193873i
$514$	−1.23408e11			−1.76803
$515$	4.84752e10	−	2.79871e10i	0.689113	−	0.397860i
$516$	1.78616e10	−	6.73712e8i	0.251954	−	0.00950332i
$517$	−1.09937e10	+	1.90416e10i	−0.153879	+	0.266527i
$518$	1.04110e11	+	6.01079e10i	1.44602	+	0.834857i
$519$	2.24241e10	−	1.40994e10i	0.309062	−	0.194326i
$520$	5.21653e10	+	9.03530e10i	0.713458	+	1.23575i
$521$		−	1.04659e11i		−	1.42045i	−0.703975	−	0.710225i	$-0.748593\pi$
$521$		−	1.04659e11i		−	1.42045i	0.703975	−	0.710225i	$-0.251407\pi$
$522$	1.84126e10	−	3.82931e10i	0.247990	−	0.515749i
$523$	−6.66398e8			−0.00890690			−0.00445345	−	0.999990i	$-0.501418\pi$
$523$	−6.66398e8			−0.00890690			−0.00445345	+	0.999990i	$0.501418\pi$
$524$	5.96365e10	−	3.44312e10i	0.791020	−	0.456695i
$525$	−4.93277e9	+	9.34005e9i	−0.0649312	+	0.122945i
$526$	4.05415e10	−	7.02200e10i	0.529611	−	0.917314i
$527$	−7.34775e10	−	4.24223e10i	−0.952603	−	0.549986i
$528$	5.89652e9	+	3.11413e9i	0.0758683	+	0.0400684i
$529$	−3.01911e10	−	5.22925e10i	−0.385528	−	0.667755i
$530$		−	1.32051e11i		−	1.67355i
$531$	3.06317e10	+	1.47287e10i	0.385294	+	0.185263i
$532$	2.69667e10			0.336652
$533$	−8.35565e10	+	4.82414e10i	−1.03531	+	0.597738i
$534$	1.56289e10	+	2.48567e10i	0.192204	+	0.305688i
$535$	1.53788e10	−	2.66369e10i	0.187719	−	0.325139i
$536$	−2.71903e10	−	1.56983e10i	−0.329424	−	0.190193i
$537$	1.91240e9	+	5.07020e10i	0.0229975	+	0.609716i
$538$	5.13155e10	+	8.88810e10i	0.612518	+	1.06091i
$539$		−	3.13335e10i		−	0.371239i
$540$	−1.12072e11	+	8.28690e10i	−1.31802	+	0.974579i
$541$	5.96762e10			0.696646			0.348323	−	0.937375i	$-0.386751\pi$
$541$	5.96762e10			0.696646			0.348323	+	0.937375i	$0.386751\pi$
$542$	1.29663e11	−	7.48610e10i	1.50252	−	0.867478i
$543$	−1.18460e10	+	4.46814e8i	−0.136262	+	0.00513958i
$544$	−6.24035e10	+	1.08086e11i	−0.712547	+	1.23417i
$545$	1.26844e11	+	7.32336e10i	1.43776	+	0.830089i
$546$	−2.31014e11	+	1.45253e11i	−2.59937	+	1.63438i
$547$	−2.65388e10	−	4.59665e10i	−0.296436	−	0.513443i	0.678882	−	0.734248i	$-0.262465\pi$
$547$	−2.65388e10	−	4.59665e10i	−0.296436	−	0.513443i	−0.975318	+	0.220805i	$0.929132\pi$
$548$			1.29376e11i			1.43460i
$549$	−3.53240e10	−	5.17439e10i	−0.388848	−	0.569599i
$550$	1.02077e10			0.111552
$551$	4.90871e9	−	2.83404e9i	0.0532550	−	0.0307468i
$552$	−1.84269e10	+	3.48908e10i	−0.198471	+	0.375798i
$553$	1.36223e10	−	2.35945e10i	0.145663	−	0.252296i
$554$	−1.20337e11	−	6.94765e10i	−1.27750	−	0.737562i
$555$	−7.32941e10	−	3.87089e10i	−0.772498	−	0.407980i
$556$	−1.07490e11	−	1.86178e11i	−1.12479	−	1.94819i
$557$			1.10596e11i			1.14900i	0.818504	+	0.574500i	$0.194804\pi$
$557$			1.10596e11i			1.14900i	−0.818504	+	0.574500i	$0.805196\pi$
$558$	9.95871e9	+	1.31826e11i	0.102723	+	1.35977i
$559$	−2.41286e10			−0.247107
$560$	1.53426e10	−	8.85807e9i	0.156008	−	0.0900714i
$561$	−4.29864e10	−	6.83669e10i	−0.433990	−	0.690231i
$562$	−1.44338e9	+	2.50001e9i	−0.0144689	+	0.0250609i
$563$	−3.72727e10	−	2.15194e10i	−0.370986	−	0.214189i	0.302903	−	0.953021i	$-0.402044\pi$
$563$	−3.72727e10	−	2.15194e10i	−0.370986	−	0.214189i	−0.673889	+	0.738832i	$0.735377\pi$
$564$	2.88778e9	+	7.65616e10i	0.0285396	+	0.756649i
$565$	−9.82390e9	−	1.70155e10i	−0.0964029	−	0.166975i
$566$			1.56429e11i			1.52423i
$567$	−8.13063e10	−	1.01704e11i	−0.786669	−	0.984022i
$568$	1.20629e11			1.15893
$569$	−7.58502e9	+	4.37922e9i	−0.0723616	+	0.0417780i	−0.535744	−	0.844380i	$-0.679969\pi$
$569$	−7.58502e9	+	4.37922e9i	−0.0723616	+	0.0417780i	0.463383	+	0.886158i	$0.346636\pi$
$570$	−3.05242e10	+	1.15132e9i	−0.289164	+	0.0109068i
$571$	1.64763e9	−	2.85377e9i	0.0154994	−	0.0268457i	−0.858172	−	0.513363i	$-0.828400\pi$
$571$	1.64763e9	−	2.85377e9i	0.0154994	−	0.0268457i	0.873671	+	0.486517i	$0.161733\pi$
$572$	1.39019e11	+	8.02625e10i	1.29864	+	0.749771i
$573$	1.52827e11	−	9.60916e10i	1.41769	−	0.891388i
$574$	−8.57158e10	−	1.48464e11i	−0.789611	−	1.36765i
$575$		−	5.77246e9i		−	0.0528068i
$576$	1.79023e11	−	1.35242e10i	1.62637	−	0.122863i
$577$	7.03112e10			0.634338			0.317169	−	0.948369i	$-0.397268\pi$
$577$	7.03112e10			0.634338			0.317169	+	0.948369i	$0.397268\pi$
$578$	1.02426e11	−	5.91358e10i	0.917699	−	0.529834i
$579$	6.48593e10	−	1.22809e11i	0.577109	−	1.09274i
$580$	−3.32025e10	+	5.75083e10i	−0.293399	+	0.508182i
$581$	1.00249e11	+	5.78789e10i	0.879785	+	0.507944i
$582$	2.75630e11	+	1.45569e11i	2.40234	+	1.26875i
$583$	−3.62836e10	−	6.28450e10i	−0.314077	−	0.543997i
$584$		−	1.92393e11i		−	1.65401i
$585$	1.55395e11	−	1.06083e11i	1.32682	−	0.905782i
$586$	−1.69077e11			−1.43382
$587$	−9.15067e9	+	5.28314e9i	−0.0770726	+	0.0444979i	−0.538041	−	0.842919i	$-0.680835\pi$
$587$	−9.15067e9	+	5.28314e9i	−0.0770726	+	0.0444979i	0.460968	+	0.887417i	$0.347502\pi$
$588$	−5.81167e10	−	9.24305e10i	−0.486174	−	0.773225i
$589$	−8.81776e9	+	1.52728e10i	−0.0732651	+	0.126899i
$590$	−7.55745e10	−	4.36329e10i	−0.623688	−	0.360086i
$591$	5.90241e9	+	1.56486e11i	0.0483816	+	1.28270i
$592$	6.90906e9	+	1.19669e10i	0.0562513	+	0.0974301i
$593$			6.75771e10i			0.546488i	0.961945	+	0.273244i	$0.0880967\pi$
$593$			6.75771e10i			0.546488i	−0.961945	+	0.273244i	$0.911903\pi$
$594$	−5.02161e10	+	1.15380e11i	−0.403364	+	0.926800i
$595$	−2.14554e11			−1.71186
$596$	−1.14829e11	+	6.62963e10i	−0.910049	+	0.525417i
$597$	−2.14334e11	+	8.08436e9i	−1.68731	+	0.0636427i
$598$	7.45656e10	−	1.29151e11i	0.583088	−	1.00994i
$599$	−1.08819e11	−	6.28266e10i	−0.845273	−	0.488019i	0.0137800	−	0.999905i	$-0.495614\pi$
$599$	−1.08819e11	−	6.28266e10i	−0.845273	−	0.488019i	−0.859053	+	0.511886i	$0.828947\pi$
$600$	1.07548e10	−	6.76221e9i	0.0829847	−	0.0521776i
$601$	4.01255e10	+	6.94994e10i	0.307555	+	0.532701i	0.977827	−	0.209415i	$-0.0671558\pi$
$601$	4.01255e10	+	6.94994e10i	0.307555	+	0.532701i	−0.670272	+	0.742116i	$0.733823\pi$
$602$		−	4.28719e10i		−	0.326427i
$603$	−2.45364e10	+	5.10289e10i	−0.185585	+	0.385964i
$604$	2.85937e11			2.14844
$605$	−7.33839e10	+	4.23682e10i	−0.547746	+	0.316241i
$606$	9.39428e10	−	1.77878e11i	0.696583	−	1.31896i
$607$	−1.03080e11	+	1.78540e11i	−0.759313	+	1.31517i	0.183888	+	0.982947i	$0.441132\pi$
$607$	−1.03080e11	+	1.78540e11i	−0.759313	+	1.31517i	−0.943201	+	0.332222i	$0.892202\pi$
$608$	2.24664e10	+	1.29710e10i	0.164407	+	0.0949203i
$609$	−5.48545e10	−	2.89703e10i	−0.398789	−	0.210613i
$610$	8.04287e10	+	1.39307e11i	0.580887	+	1.00613i
$611$		−	1.03424e11i		−	0.742090i
$612$	−2.53611e11	−	1.21945e11i	−1.80785	−	0.869276i
$613$	7.28984e10			0.516269			0.258134	−	0.966109i	$-0.416892\pi$
$613$	7.28984e10			0.516269			0.258134	+	0.966109i	$0.416892\pi$
$614$	−3.23556e11	+	1.86805e11i	−2.27655	+	1.31436i
$615$	6.29168e10	+	1.00065e11i	0.439811	+	0.699488i
$616$	−5.09355e10	+	8.82229e10i	−0.353751	+	0.612715i
$617$	2.23320e11	+	1.28934e11i	1.54094	+	0.889663i	0.998780	+	0.0493888i	$0.0157273\pi$
$617$	2.23320e11	+	1.28934e11i	1.54094	+	0.889663i	0.542162	+	0.840274i	$0.317606\pi$
$618$	−6.63702e9	−	1.75962e11i	−0.0455008	−	1.20633i
$619$	1.06461e10	+	1.84395e10i	0.0725148	+	0.125599i	0.900003	−	0.435884i	$-0.143564\pi$
$619$	1.06461e10	+	1.84395e10i	0.0725148	+	0.125599i	−0.827488	+	0.561483i	$0.810231\pi$
$620$		−	2.06610e11i		−	1.39825i
$621$	6.52474e10	+	2.83971e10i	0.438729	+	0.190945i
$622$	2.05300e11			1.37160
$623$	3.71247e10	−	2.14339e10i	0.246439	−	0.142282i
$624$	−3.13443e10	+	1.18226e9i	−0.206738	+	0.00779783i
$625$	8.37847e10	−	1.45119e11i	0.549092	−	0.951055i
$626$	−7.74400e10	−	4.47100e10i	−0.504276	−	0.291144i
$627$	−1.42105e10	+	8.93503e9i	−0.0919475	+	0.0578130i
$628$	9.83154e10	+	1.70287e11i	0.632096	+	1.09482i
$629$		−	1.67347e11i		−	1.06909i
$630$	1.88490e11	+	2.76107e11i	1.19654	+	1.75273i
$631$	−9.46727e10			−0.597183			−0.298591	−	0.954381i	$-0.596517\pi$
$631$	−9.46727e10			−0.597183			−0.298591	+	0.954381i	$0.596517\pi$
$632$	−2.83781e10	+	1.63841e10i	−0.177875	+	0.102696i
$633$	−7.10234e10	+	1.34481e11i	−0.442371	+	0.837616i
$634$	−4.67772e10	+	8.10205e10i	−0.289519	+	0.501462i
$635$	4.44203e10	+	2.56461e10i	0.273204	+	0.157734i
$636$	−2.23596e11	−	1.18088e11i	−1.36658	−	0.721735i
$637$	7.36933e10	+	1.27640e11i	0.447579	+	0.775230i
$638$			5.99504e10i			0.361834i
$639$	−1.63876e10	−	2.16927e11i	−0.0982905	−	1.30110i
$640$	−2.65575e11			−1.58295
$641$	9.25489e10	−	5.34331e10i	0.548200	−	0.316504i	−0.200196	−	0.979756i	$-0.564158\pi$
$641$	9.25489e10	−	5.34331e10i	0.548200	−	0.316504i	0.748396	+	0.663252i	$0.230824\pi$
$642$	−5.15037e10	−	8.19129e10i	−0.303178	−	0.482184i
$643$	−2.30544e10	+	3.99314e10i	−0.134868	+	0.233599i	−0.925547	−	0.378632i	$-0.876395\pi$
$643$	−2.30544e10	+	3.99314e10i	−0.134868	+	0.233599i	0.790679	+	0.612231i	$0.209728\pi$
$644$	1.39684e11	+	8.06465e10i	0.812087	+	0.468859i
$645$	1.11416e9	+	2.95389e10i	0.00643738	+	0.170669i
$646$	−3.08353e10	−	5.34084e10i	−0.177059	−	0.306676i
$647$		−	1.54353e11i		−	0.880842i	−0.897791	−	0.440421i	$-0.854829\pi$
$647$		−	1.54353e11i		−	0.880842i	0.897791	−	0.440421i	$-0.145171\pi$
$648$	2.35274e10	+	1.54830e11i	0.133436	+	0.878124i
$649$	−4.79559e10			−0.270311
$650$	−4.15824e10	+	2.40076e10i	−0.232946	+	0.134492i
$651$	1.92876e11	−	7.27496e9i	1.07387	−	0.0405048i
$652$	−7.18724e10	+	1.24487e11i	−0.397715	+	0.688862i
$653$	−2.92739e11	−	1.69013e11i	−1.61001	−	0.929539i	−0.989366	−	0.145446i	$-0.953538\pi$
$653$	−2.92739e11	−	1.69013e11i	−1.61001	−	0.929539i	−0.620643	−	0.784093i	$-0.713128\pi$
$654$	3.90067e11	−	2.45259e11i	2.13220	−	1.34065i
$655$	5.69410e10	+	9.86247e10i	0.309357	+	0.535822i
$656$		−	1.97051e10i		−	0.106405i
$657$	−3.45980e11	+	2.61368e10i	−1.85690	+	0.140279i
$658$	1.83765e11			0.980300
$659$	−1.65476e11	+	9.55374e10i	−0.877389	+	0.506561i	−0.869797	−	0.493410i	$-0.835750\pi$
$659$	−1.65476e11	+	9.55374e10i	−0.877389	+	0.506561i	−0.00759244	+	0.999971i	$0.502417\pi$
$660$	9.18403e10	−	1.73897e11i	0.484014	−	0.916466i
$661$	1.43958e11	−	2.49342e11i	0.754099	−	1.30614i	−0.191721	−	0.981449i	$-0.561407\pi$
$661$	1.43958e11	−	2.49342e11i	0.754099	−	1.30614i	0.945821	−	0.324689i	$-0.105260\pi$
$662$	−5.68490e10	−	3.28218e10i	−0.296000	−	0.170895i
$663$	3.35902e11	+	1.77400e11i	1.73844	+	0.918122i
$664$	−6.96133e10	−	1.20574e11i	−0.358113	−	0.620270i
$665$			4.45966e10i			0.228042i
$666$	−2.15356e11	+	1.47017e11i	−1.09461	+	0.747260i
$667$	3.39019e10			0.171285
$668$	3.08784e11	−	1.78276e11i	1.55077	−	0.895340i
$669$	1.65417e11	+	2.63085e11i	0.825804	+	1.31338i
$670$	7.26876e10	−	1.25899e11i	0.360712	−	0.624772i
$671$	7.65542e10	+	4.41986e10i	0.377641	+	0.218031i
$672$	−1.07015e10	−	2.83722e11i	−0.0524770	−	1.39128i
$673$	−1.61459e11	−	2.79655e11i	−0.787050	−	1.36321i	−0.927767	−	0.373160i	$-0.878274\pi$
$673$	−1.61459e11	−	2.79655e11i	−0.787050	−	1.36321i	0.140717	−	0.990050i	$-0.455059\pi$
$674$			4.49382e11i			2.17759i
$675$	−1.36215e10	−	1.84217e10i	−0.0656162	−	0.0887391i
$676$	−4.30226e11			−2.06020
$677$	−1.05215e11	+	6.07462e10i	−0.500870	+	0.289177i	−0.729073	−	0.684436i	$-0.760048\pi$
$677$	−1.05215e11	+	6.07462e10i	−0.500870	+	0.289177i	0.228203	+	0.973614i	$0.426715\pi$
$678$	−6.17653e10	+	2.32969e9i	−0.292298	+	0.0110250i
$679$	2.27545e11	−	3.94119e11i	1.07050	−	1.85417i
$680$	2.23481e11	+	1.29027e11i	1.04521	+	0.603453i
$681$	−2.73407e11	+	1.71908e11i	−1.27122	+	0.799296i
$682$	−9.32640e10	−	1.61538e11i	−0.431099	−	0.746685i
$683$			2.88173e11i			1.32425i	0.749393	+	0.662126i	$0.230346\pi$
$683$			2.88173e11i			1.32425i	−0.749393	+	0.662126i	$0.769654\pi$
$684$	−2.53471e10	+	5.27148e10i	−0.115799	+	0.240829i
$685$	−2.13957e11			−0.971774
$686$	1.59470e11	−	9.20698e10i	0.720081	−	0.415739i
$687$	7.00771e10	−	1.32689e11i	0.314593	−	0.595673i
$688$	2.46394e9	−	4.26767e9i	0.0109971	−	0.0190475i
$689$	2.95610e11	+	1.70671e11i	1.31172	+	0.757325i
$690$	−1.61554e11	−	8.53217e10i	−0.712724	−	0.376412i
$691$	1.41426e11	+	2.44956e11i	0.620320	+	1.07443i	0.989426	+	0.145039i	$0.0463306\pi$
$691$	1.41426e11	+	2.44956e11i	0.620320	+	1.07443i	−0.369106	+	0.929387i	$0.620336\pi$
$692$			1.30229e11i			0.567917i
$693$	1.65571e11	+	7.96120e10i	0.717878	+	0.345180i
$694$	1.14372e11			0.493042
$695$	3.07895e11	−	1.77763e11i	1.31966	−	0.761909i
$696$	3.97147e10	+	6.31635e10i	0.169245	+	0.269171i
$697$	−1.19321e11	+	2.06670e11i	−0.505575	+	0.875682i
$698$	−1.48323e11	−	8.56343e10i	−0.624866	−	0.360767i
$699$	1.78653e10	+	4.73650e11i	0.0748346	+	1.98403i
$700$	−2.59654e10	−	4.49734e10i	−0.108144	−	0.187311i
$701$		−	4.37155e11i		−	1.81035i	−0.425035	−	0.905177i	$-0.639738\pi$
$701$		−	4.37155e11i		−	1.81035i	0.425035	−	0.905177i	$-0.360262\pi$
$702$	−6.68023e10	−	5.88118e11i	−0.275070	−	2.42168i
$703$	−3.47842e10			−0.142417
$704$	−2.19372e11	+	1.26655e11i	−0.893081	+	0.515621i
$705$	−1.26615e11	+	4.77571e9i	−0.512540	+	0.0193322i
$706$	8.76587e10	−	1.51829e11i	0.352839	−	0.611134i
$707$	−2.54345e11	−	1.46846e11i	−1.01800	−	0.587740i
$708$	−1.41465e11	+	8.89477e10i	−0.563010	+	0.353999i
$709$	1.01719e11	+	1.76183e11i	0.402549	+	0.697235i	0.994033	−	0.109082i	$-0.0347911\pi$
$709$	1.01719e11	+	1.76183e11i	0.402549	+	0.697235i	−0.591484	+	0.806317i	$0.701458\pi$
$710$			5.58545e11i			2.19798i
$711$	3.33187e10	+	4.88065e10i	0.130380	+	0.190985i
$712$	−5.15589e10			−0.200624
$713$	−9.13495e10	+	5.27407e10i	−0.353466	+	0.204074i
$714$	−3.15207e11	+	5.96835e11i	−1.21284	+	2.29647i
$715$	−1.32735e11	+	2.29904e11i	−0.507881	+	0.879676i
$716$	−2.16032e11	−	1.24726e11i	−0.821990	−	0.474576i
$717$	−3.28950e11	−	1.73729e11i	−1.24467	−	0.657347i
$718$	2.21922e10	+	3.84380e10i	0.0835031	+	0.144632i
$719$		−	3.44324e11i		−	1.28840i	−0.764856	−	0.644201i	$-0.777190\pi$
$719$		−	3.44324e11i		−	1.28840i	0.764856	−	0.644201i	$-0.222810\pi$
$720$	2.89471e9	+	3.83180e10i	0.0107715	+	0.142585i
$721$	−2.57085e11			−0.951340
$722$	3.65105e11	−	2.10794e11i	1.34360	−	0.775726i
$723$	−9.26080e10	−	1.47286e11i	−0.338918	−	0.539026i
$724$	2.91411e10	−	5.04739e10i	0.106060	−	0.183701i
$725$	−9.45289e9	−	5.45763e9i	−0.0342147	−	0.0197539i
$726$	1.00474e10	+	2.66379e11i	0.0361666	+	0.958857i
$727$	−5.98468e10	−	1.03658e11i	−0.214241	−	0.371077i	0.738796	−	0.673929i	$-0.235395\pi$
$727$	−5.98468e10	−	1.03658e11i	−0.214241	−	0.371077i	−0.953038	+	0.302852i	$0.902061\pi$
$728$		−	4.79181e11i		−	1.70598i
$729$	2.75235e11	−	6.33431e10i	0.974525	−	0.224279i
$730$	8.90832e11			3.13693
$731$	−5.16844e10	+	2.98400e10i	−0.181005	+	0.104503i
$732$	3.07806e11	−	1.16100e10i	1.07209	−	0.0404377i
$733$	−8.94181e10	+	1.54877e11i	−0.309749	+	0.536500i	−0.978307	−	0.207159i	$-0.933578\pi$
$733$	−8.94181e10	+	1.54877e11i	−0.309749	+	0.536500i	0.668559	+	0.743659i	$0.266912\pi$
$734$	−2.60841e11	−	1.50597e11i	−0.898652	−	0.518837i
$735$	1.52858e11	−	9.61113e10i	0.523769	−	0.329325i
$736$	7.75820e10	+	1.34376e11i	0.264393	+	0.457942i
$737$		−	7.98891e10i		−	0.270781i
$738$	3.70787e11	−	2.80108e10i	1.24997	−	0.0944280i
$739$	3.08096e11			1.03302			0.516509	−	0.856282i	$-0.327231\pi$
$739$	3.08096e11			1.03302			0.516509	+	0.856282i	$0.327231\pi$
$740$	3.52920e11	−	2.03758e11i	1.17693	−	0.679499i
$741$	3.68739e10	−	6.98196e10i	0.122306	−	0.231582i
$742$	−3.03250e11	+	5.25244e11i	−1.00043	+	1.73279i
$743$	3.63187e11	+	2.09686e11i	1.19172	+	0.688041i	0.958697	−	0.284430i	$-0.0918042\pi$
$743$	3.63187e11	+	2.09686e11i	1.19172	+	0.688041i	0.233025	+	0.972471i	$0.425138\pi$
$744$	−2.05275e11	−	1.08412e11i	−0.669953	−	0.353823i
$745$	−1.09638e11	−	1.89899e11i	−0.355908	−	0.616450i
$746$		−	1.99602e11i		−	0.644479i
$747$	−2.07371e11	+	1.41566e11i	−0.665985	+	0.454648i
$748$	3.97045e11			1.26833
$749$	−1.22341e11	+	7.06336e10i	−0.388727	+	0.224432i
$750$	−2.52396e11	−	4.01418e11i	−0.797696	−	1.26868i
$751$	3.24484e9	−	5.62023e9i	0.0102008	−	0.0176683i	−0.860880	−	0.508808i	$-0.830086\pi$
$751$	3.24484e9	−	5.62023e9i	0.0102008	−	0.0176683i	0.871081	+	0.491140i	$0.163420\pi$
$752$	1.82929e10	+	1.05614e10i	0.0572019	+	0.0330255i
$753$	−1.88377e10	−	4.99429e11i	−0.0585932	−	1.55344i
$754$	−1.40998e11	−	2.44215e11i	−0.436241	−	0.755591i
$755$			4.72872e11i			1.45531i
$756$	6.36079e11	−	7.22500e10i	1.94726	−	0.221182i
$757$	2.62150e11			0.798299			0.399150	−	0.916886i	$-0.369305\pi$
$757$	2.62150e11			0.798299			0.399150	+	0.916886i	$0.369305\pi$
$758$	−5.77297e11	+	3.33303e11i	−1.74873	+	1.00963i
$759$	−1.00330e11	+	3.78427e9i	−0.302316	+	0.0114029i
$760$	2.68191e10	−	4.64520e10i	0.0803876	−	0.139235i
$761$	−9.29283e10	−	5.36522e10i	−0.277083	−	0.159974i	0.355019	−	0.934859i	$-0.384474\pi$
$761$	−9.29283e10	−	5.36522e10i	−0.277083	−	0.159974i	−0.632102	+	0.774885i	$0.717808\pi$
$762$	1.36600e11	−	8.58887e10i	0.405163	−	0.254751i
$763$	−3.36356e11	−	5.82585e11i	−0.992432	−	1.71894i
$764$			8.87552e11i			2.60508i
$765$	2.01668e11	−	4.19413e11i	0.588832	−	1.22461i
$766$	−9.04120e11			−2.62610
$767$	1.95354e11	−	1.12788e11i	0.564470	−	0.325897i
$768$	−1.25179e11	+	2.37023e11i	−0.359822	+	0.681312i
$769$	1.20233e11	−	2.08249e11i	0.343808	−	0.595494i	−0.641328	−	0.767267i	$-0.721616\pi$
$769$	1.20233e11	−	2.08249e11i	0.343808	−	0.595494i	0.985137	+	0.171773i	$0.0549496\pi$
$770$	−4.08496e11	−	2.35845e11i	−1.16205	−	0.670910i
$771$	−3.45572e11	−	1.82507e11i	−0.977959	−	0.516490i
$772$	3.41410e11	+	5.91340e11i	0.961186	+	1.66482i
$773$			1.08257e11i			0.303206i	0.988441	+	0.151603i	$0.0484436\pi$
$773$			1.08257e11i			0.303206i	−0.988441	+	0.151603i	$0.951556\pi$
$774$	8.38064e10	+	4.02970e10i	0.233514	+	0.112282i
$775$	3.39614e10			0.0941410
$776$	−4.74023e11	+	2.73677e11i	−1.30723	+	0.754731i
$777$	2.02640e11	+	3.22284e11i	0.555957	+	0.884210i
$778$	−2.41283e11	+	4.17914e11i	−0.658579	+	1.14069i
$779$	4.29578e10	+	2.48017e10i	0.116652	+	0.0673490i
$780$	3.48665e10	+	9.24388e11i	0.0941954	+	2.49733i
$781$	1.53471e11	+	2.65819e11i	0.412498	+	0.714467i
$782$		−	3.68864e11i		−	0.986368i
$783$	1.08191e11	−	7.99998e10i	0.287836	−	0.212834i
$784$	−3.01014e10			−0.0796751
$785$	−2.81615e11	+	1.62590e11i	−0.741612	+	0.428170i
$786$	3.58002e11	−	1.35033e10i	0.937984	−	0.0353793i
$787$	−3.25844e11	+	5.64378e11i	−0.849397	+	1.47120i	0.0323497	+	0.999477i	$0.489701\pi$
$787$	−3.25844e11	+	5.64378e11i	−0.849397	+	1.47120i	−0.881747	+	0.471723i	$0.843632\pi$
$788$	−6.66760e11	−	3.84954e11i	−1.72928	−	0.998399i
$789$	2.17374e11	−	1.36677e11i	0.560919	−	0.352684i
$790$	−7.58629e10	−	1.31398e11i	−0.194770	−	0.337351i
$791$			9.02406e10i			0.230513i
$792$	−1.24583e11	−	1.82493e11i	−0.316634	−	0.463817i
$793$	−4.15803e11			−1.05147
$794$	7.56422e11	−	4.36721e11i	1.90319	−	1.09881i
$795$	1.95290e11	−	3.69776e11i	0.488890	−	0.925699i
$796$	5.27260e11	−	9.13241e11i	1.31333	−	2.27475i
$797$	3.93581e10	+	2.27234e10i	0.0975440	+	0.0563170i	0.547978	−	0.836492i	$-0.315398\pi$
$797$	3.93581e10	+	2.27234e10i	0.0975440	+	0.0563170i	−0.450434	+	0.892809i	$0.648731\pi$
$798$	1.24056e11	+	6.55179e10i	0.305919	+	0.161565i
$799$	−1.27905e11	−	2.21539e11i	−0.313835	−	0.543579i
$800$		−	4.99575e10i		−	0.121967i
$801$	7.00434e9	+	9.27183e10i	0.0170152	+	0.225235i
$802$	−8.90759e10			−0.215309
$803$	4.23960e11	−	2.44773e11i	1.01968	−	0.588710i
$804$	−1.48177e11	−	2.35665e11i	−0.354614	−	0.563989i
$805$	−1.33370e11	+	2.31004e11i	−0.317596	+	0.550093i
$806$	7.59843e11	+	4.38696e11i	1.80046	+	1.03950i
$807$	1.22502e10	+	3.24779e11i	0.0288833	+	0.765762i
$808$	1.76618e11	+	3.05911e11i	0.414371	+	0.717712i
$809$			1.21628e11i			0.283948i	0.989870	+	0.141974i	$0.0453449\pi$
$809$			1.21628e11i			0.283948i	−0.989870	+	0.141974i	$0.954655\pi$
$810$	−7.16906e11	+	1.08938e11i	−1.66541	+	0.253070i
$811$	8.42541e11			1.94764			0.973818	−	0.227330i	$-0.0729997\pi$
$811$	8.42541e11			1.94764			0.973818	+	0.227330i	$0.0729997\pi$
$812$	2.64131e11	−	1.52496e11i	0.607568	−	0.350780i
$813$	4.73800e11	−	1.78710e10i	1.08451	−	0.0409060i
$814$	1.83953e11	−	3.18617e11i	0.418996	−	0.725723i
$815$	−2.05871e11	−	1.18860e11i	−0.466622	−	0.269405i
$816$	−6.56787e10	+	4.12962e10i	−0.148137	+	0.0931428i
$817$	6.20245e9	+	1.07430e10i	0.0139211	+	0.0241121i
$818$		−	7.50754e11i		−	1.67681i
$819$	−8.61711e11	+	6.50974e10i	−1.91525	+	0.144686i
$820$	−5.81132e11			−1.28534
$821$	−6.43734e11	+	3.71660e11i	−1.41688	+	0.818037i	−0.996024	−	0.0890890i	$-0.971604\pi$
$821$	−6.43734e11	+	3.71660e11i	−1.41688	+	0.818037i	−0.420859	+	0.907126i	$0.638271\pi$
$822$	−3.14330e11	+	5.95175e11i	−0.688492	+	1.30364i
$823$	1.94548e11	−	3.36968e11i	0.424061	−	0.734495i	−0.572271	−	0.820064i	$-0.693938\pi$
$823$	1.94548e11	−	3.36968e11i	0.424061	−	0.734495i	0.996332	+	0.0855694i	$0.0272709\pi$
$824$	2.67781e11	+	1.54603e11i	0.580859	+	0.335359i
$825$	2.85842e10	+	1.50962e10i	0.0617035	+	0.0325875i
$826$	2.00402e11	+	3.47107e11i	0.430509	+	0.745664i
$827$			4.56038e11i			0.974942i	0.873139	+	0.487471i	$0.162080\pi$
$827$			4.56038e11i			0.974942i	−0.873139	+	0.487471i	$0.837920\pi$
$828$	−2.88943e11	+	1.97253e11i	−0.614739	+	0.419664i
$829$	1.17595e11			0.248983			0.124491	−	0.992221i	$-0.460270\pi$
$829$	1.17595e11			0.248983			0.124491	+	0.992221i	$0.460270\pi$
$830$	5.58290e11	−	3.22329e11i	1.17638	−	0.679183i
$831$	−2.34224e11	−	3.72517e11i	−0.491165	−	0.781163i
$832$	5.95758e11	−	1.03188e12i	1.24330	−	2.15346i
$833$	3.15708e11	+	1.82274e11i	0.655701	+	0.378569i
$834$	−4.21557e10	−	1.11764e12i	−0.0871349	−	2.31014i
$835$	2.94827e11	+	5.10655e11i	0.606487	+	1.05047i
$836$		−	8.25286e10i		−	0.168958i
$837$	−1.67070e11	+	3.83873e11i	−0.340406	+	0.782143i
$838$	−8.50157e11			−1.72394
$839$	−2.58758e11	+	1.49394e11i	−0.522212	+	0.301499i	−0.737839	−	0.674977i	$-0.764154\pi$
$839$	−2.58758e11	+	1.49394e11i	−0.522212	+	0.301499i	0.215627	+	0.976476i	$0.430820\pi$
$840$	−5.86627e11	+	2.21267e10i	−1.17827	+	0.0444426i
$841$	−2.18070e11	+	3.77709e11i	−0.435926	+	0.755046i
$842$	6.12716e11	+	3.53752e11i	1.21902	+	0.703802i
$843$	−7.73908e9	+	4.86603e9i	−0.0153242	+	0.00963529i
$844$	−3.73858e11	−	6.47540e11i	−0.736778	−	1.27614i
$845$		−	7.11492e11i		−	1.39554i
$846$	−1.72728e11	+	3.59226e11i	−0.337195	+	0.701271i
$847$	3.89187e11			0.756179
$848$	−6.03738e10	+	3.48569e10i	−0.116752	+	0.0674070i
$849$	−2.31342e11	+	4.38039e11i	−0.445270	+	0.843105i
$850$	−5.93808e10	+	1.02851e11i	−0.113755	+	0.197029i
$851$	−1.80177e11	−	1.04025e11i	−0.343543	−	0.198345i
$852$	9.45759e11	+	4.99485e11i	1.79483	+	0.947903i
$853$	9.91795e10	+	1.71784e11i	0.187338	+	0.324479i	0.944362	−	0.328908i	$-0.106681\pi$
$853$	9.91795e10	+	1.71784e11i	0.187338	+	0.324479i	−0.757024	+	0.653387i	$0.773347\pi$
$854$		−	7.38804e11i		−	1.38898i
$855$	−8.71779e10	−	4.19181e10i	−0.163133	−	0.0784399i
$856$	1.69908e11			0.316460
$857$	6.49453e11	−	3.74962e11i	1.20399	−	0.695127i	0.242554	−	0.970138i	$-0.422015\pi$
$857$	6.49453e11	−	3.74962e11i	1.20399	−	0.695127i	0.961441	+	0.275011i	$0.0886816\pi$
$858$	4.44530e11	+	7.06993e11i	0.820261	+	1.30457i
$859$	1.95861e11	−	3.39241e11i	0.359728	−	0.623068i	−0.628187	−	0.778063i	$-0.716203\pi$
$859$	1.95861e11	−	3.39241e11i	0.359728	−	0.623068i	0.987915	+	0.154994i	$0.0495360\pi$
$860$	−1.25860e11	−	7.26653e10i	−0.230088	−	0.132841i
$861$	−2.04623e10	−	5.42501e11i	−0.0372341	−	0.987160i
$862$	−4.15158e11	−	7.19074e11i	−0.751941	−	1.30240i
$863$			7.72271e11i			1.39228i	0.717906	+	0.696140i	$0.245101\pi$
$863$			7.72271e11i			1.39228i	−0.717906	+	0.696140i	$0.754899\pi$
$864$	5.64681e11	+	2.45762e11i	1.01332	+	0.441021i
$865$	−2.15369e11			−0.384696
$866$	−4.72552e11	+	2.72828e11i	−0.840191	+	0.485084i
$867$	3.74275e11	−	1.41171e10i	0.662390	−	0.0249843i
$868$	−4.74471e11	+	8.21809e11i	−0.835855	+	1.44774i
$869$	−7.22084e10	−	4.16896e10i	−0.126622	−	0.0731052i
$870$	−2.92464e11	+	1.83890e11i	−0.510500	+	0.320983i
$871$	1.87891e11	+	3.25438e11i	0.326463	+	0.565451i
$872$			8.09097e11i			1.39938i
$873$	5.56550e11	+	8.15255e11i	0.958180	+	1.40358i
$874$	−7.66709e10			−0.131397
$875$	−5.99538e11	+	3.46143e11i	−1.02279	+	0.590505i
$876$	7.96637e11	−	1.50841e12i	1.35283	−	2.56155i
$877$	1.02235e11	−	1.77075e11i	0.172822	−	0.299337i	−0.766583	−	0.642145i	$-0.778045\pi$
$877$	1.02235e11	−	1.77075e11i	0.172822	−	0.299337i	0.939405	+	0.342808i	$0.111378\pi$
$878$	4.36357e11	+	2.51931e11i	0.734283	+	0.423939i
$879$	−4.73457e11	−	2.50047e11i	−0.793095	−	0.418858i
$880$	−2.71091e10	−	4.69544e10i	−0.0452048	−	0.0782970i
$881$		−	4.46549e11i		−	0.741251i	−0.928782	−	0.370625i	$-0.879143\pi$
$881$		−	4.46549e11i		−	0.741251i	0.928782	−	0.370625i	$-0.120857\pi$
$882$	−4.27892e10	−	5.66412e11i	−0.0707066	−	0.935962i
$883$	−3.48668e11			−0.573547			−0.286774	−	0.957998i	$-0.592583\pi$
$883$	−3.48668e11			−0.573547			−0.286774	+	0.957998i	$0.592583\pi$
$884$	−1.61741e12	+	9.33812e11i	−2.64857	+	1.52915i
$885$	−1.47098e11	−	2.33950e11i	−0.239792	−	0.381373i
$886$	−3.57767e11	+	6.19671e11i	−0.580585	+	1.00560i
$887$	−4.44551e11	−	2.56662e11i	−0.718171	−	0.414636i	0.0959084	−	0.995390i	$-0.469424\pi$
$887$	−4.44551e11	−	2.56662e11i	−0.718171	−	0.414636i	−0.814079	+	0.580754i	$0.802758\pi$
$888$	−1.72582e10	−	4.57554e11i	−0.0277552	−	0.735853i
$889$	−1.17790e11	−	2.04019e11i	−0.188583	−	0.326635i
$890$		−	2.38732e11i		−	0.380496i
$891$	−3.11253e11	+	2.48829e11i	−0.493859	+	0.394812i
$892$	−1.52788e12			−2.41341
$893$	−4.60483e10	+	2.65860e10i	−0.0724116	+	0.0418069i
$894$	−6.89323e11	+	2.60002e10i	−1.07913	+	0.0407030i
$895$	2.06268e11	−	3.57266e11i	0.321469	−	0.556801i
$896$	1.05634e12	+	6.09881e11i	1.63898	+	0.946265i
$897$	3.99804e11	−	2.51381e11i	0.617557	−	0.388296i
$898$	4.33021e11	+	7.50014e11i	0.665892	+	1.15336i
$899$			1.99457e11i			0.305358i
$900$	1.12321e11	−	8.48518e9i	0.171194	−	0.0129328i
$901$	8.44280e11			1.28111
$902$	−4.54358e11	+	2.62323e11i	−0.686391	+	0.396288i
$903$	6.34031e10	−	1.20052e11i	0.0953585	−	0.180558i
$904$	5.42680e10	−	9.39949e10i	0.0812587	−	0.140744i
$905$	8.34718e10	+	4.81925e10i	0.124436	+	0.0718431i
$906$	1.31541e12	+	6.94708e11i	1.95231	+	1.03107i
$907$	−6.59250e11	−	1.14185e12i	−0.974139	−	1.68726i	−0.682746	−	0.730656i	$-0.739214\pi$
$907$	−6.59250e11	−	1.14185e12i	−0.974139	−	1.68726i	−0.291393	−	0.956603i	$-0.594119\pi$
$908$		−	1.58783e12i		−	2.33594i
$909$	5.26126e11	−	3.59170e11i	0.770609	−	0.526071i
$910$	2.21874e12			3.23550
$911$	5.13588e11	−	2.96520e11i	0.745661	−	0.430508i	−0.0784630	−	0.996917i	$-0.525001\pi$
$911$	5.13588e11	−	2.96520e11i	0.745661	−	0.430508i	0.824124	+	0.566409i	$0.191668\pi$
$912$	8.58370e9	+	1.36518e10i	0.0124078	+	0.0197337i
$913$	1.77132e11	−	3.06801e11i	0.254926	−	0.441544i
$914$	1.07602e12	+	6.21238e11i	1.54182	+	0.890170i
$915$	1.92001e10	+	5.09038e11i	0.0273917	+	0.726216i
$916$	3.68876e11	+	6.38913e11i	0.523961	+	0.907527i
$917$		−	5.23050e11i		−	0.739718i
$918$	−8.70424e11	−	1.17716e12i	−1.22563	−	1.65754i
$919$	1.29362e11			0.181361			0.0906807	−	0.995880i	$-0.471096\pi$
$919$	1.29362e11			0.181361			0.0906807	+	0.995880i	$0.471096\pi$
$920$	2.77838e11	−	1.60410e11i	0.387829	−	0.223913i
$921$	−1.18230e12	+	4.45946e10i	−1.64320	+	0.0619789i
$922$	−5.67036e11	+	9.82134e11i	−0.784669	+	1.35909i
$923$	−1.25036e12	−	7.21896e11i	−1.72278	−	0.994645i
$924$	−7.64649e11	+	4.80781e11i	−1.04900	+	0.659568i
$925$	3.34926e10	+	5.80109e10i	0.0457491	+	0.0792397i
$926$			3.71144e11i			0.504776i
$927$	2.41644e11	−	5.02553e11i	0.327234	−	0.680554i
$928$	2.93403e11			0.395614
$929$	6.57533e11	−	3.79627e11i	0.882785	−	0.509676i	0.0112093	−	0.999937i	$-0.496432\pi$
$929$	6.57533e11	−	3.79627e11i	0.882785	−	0.509676i	0.871576	+	0.490261i	$0.163099\pi$
$930$	5.01977e11	−	9.50479e11i	0.671046	−	1.27061i
$931$	3.78869e10	−	6.56221e10i	0.0504302	−	0.0873477i
$932$	−2.01814e12	−	1.16517e12i	−2.67478	−	1.54428i
$933$	5.74890e11	+	3.03617e11i	0.758679	+	0.400682i
$934$	7.07771e11	+	1.22589e12i	0.930048	+	1.61089i
$935$			6.56619e11i			0.859146i
$936$	9.36709e11	+	4.50401e11i	1.22040	+	0.586809i
$937$	8.60250e11			1.11601			0.558003	−	0.829839i	$-0.311568\pi$
$937$	8.60250e11			1.11601			0.558003	+	0.829839i	$0.311568\pi$
$938$	−5.78241e11	+	3.33848e11i	−0.746960	+	0.431258i
$939$	−1.50730e11	−	2.39725e11i	−0.193881	−	0.308355i
$940$	3.11471e11	−	5.39483e11i	0.398938	−	0.690981i
$941$	−7.69338e11	−	4.44178e11i	−0.981203	−	0.566498i	−0.0785697	−	0.996909i	$-0.525035\pi$
$941$	−7.69338e11	−	4.44178e11i	−0.981203	−	0.566498i	−0.902633	+	0.430411i	$0.858369\pi$
$942$	3.85575e10	+	1.02225e12i	0.0489672	+	1.29823i
$943$	1.48344e11	+	2.56938e11i	0.187595	+	0.324924i
$944$			4.60703e10i			0.0580140i
$945$	1.19484e11	+	1.05192e12i	0.149825	+	1.31904i
$946$	−1.31205e11			−0.163827
$947$	1.09842e12	−	6.34171e11i	1.36574	−	0.788509i	0.375357	−	0.926880i	$-0.377520\pi$
$947$	1.09842e12	−	6.34171e11i	1.36574	−	0.788509i	0.990380	+	0.138371i	$0.0441867\pi$
$948$	−2.90332e11	+	1.09509e10i	−0.359470	+	0.0135586i
$949$	−1.15136e12	+	1.99422e12i	−1.41954	+	2.45872i
$950$	2.13782e10	+	1.23427e10i	0.0262468	+	0.0151536i
$951$	−2.50808e11	+	1.57699e11i	−0.306634	+	0.192799i
$952$	−5.92608e11	−	1.02643e12i	−0.721472	−	1.24963i
$953$		−	6.14560e11i		−	0.745062i	−0.928020	−	0.372531i	$-0.878490\pi$
$953$		−	6.14560e11i		−	0.745062i	0.928020	−	0.372531i	$-0.121510\pi$
$954$	−7.41716e11	−	1.08649e12i	−0.895455	−	1.31170i
$955$	−1.46780e12			−1.76463
$956$	1.58393e12	−	9.14484e11i	1.89629	−	1.09482i
$957$	−8.86605e10	+	1.67876e11i	−0.105702	+	0.200143i
$958$	−4.98507e11	+	8.63439e11i	−0.591846	+	1.02511i
$959$	8.51033e11	+	4.91344e11i	1.00617	+	0.580913i
$960$	−1.29077e12	−	6.81696e11i	−1.51972	−	0.802612i
$961$	1.16154e11	+	2.01184e11i	0.136188	+	0.235885i
$962$			1.73056e12i			2.02063i
$963$	−2.30822e10	−	3.05545e11i	−0.0268394	−	0.355279i
$964$	8.55376e11			0.990487
$965$	−9.77937e11	+	5.64612e11i	−1.12772	+	0.651090i
$966$	4.46656e11	+	7.10375e11i	0.512938	+	0.815792i
$967$	4.23691e11	−	7.33855e11i	0.484555	−	0.839275i	−0.515287	−	0.857018i	$-0.672315\pi$
$967$	4.23691e11	−	7.33855e11i	0.484555	−	0.839275i	0.999843	+	0.0177429i	$0.00564804\pi$
$968$	−4.05379e11	−	2.34045e11i	−0.461699	−	0.266562i
$969$	−7.36109e9	−	1.95159e11i	−0.00834924	−	0.221357i
$970$	−1.26720e12	−	2.19486e12i	−1.43139	−	2.47924i
$971$			9.02982e11i			1.01579i	0.861420	+	0.507893i	$0.169576\pi$
$971$			9.02982e11i			1.01579i	−0.861420	+	0.507893i	$0.830424\pi$
$972$	−4.56641e11	+	1.31133e12i	−0.511576	+	1.46908i
$973$	−1.63290e12			−1.82184
$974$	4.93645e11	−	2.85006e11i	0.548503	−	0.316678i
$975$	−1.51946e11	+	5.73115e9i	−0.168140	+	0.00634196i
$976$	4.24607e10	−	7.35441e10i	0.0467937	−	0.0810491i
$977$	7.67027e11	+	4.42844e11i	0.841846	+	0.486040i	0.857891	−	0.513831i	$-0.171774\pi$
$977$	7.67027e11	+	4.42844e11i	0.841846	+	0.486040i	−0.0160453	+	0.999871i	$0.505108\pi$
$978$	−6.33089e11	+	3.98062e11i	−0.692005	+	0.435106i
$979$	−6.55961e10	−	1.13616e11i	−0.0714081	−	0.123682i
$980$			8.87735e11i			0.962451i
$981$	1.45500e12	−	1.09917e11i	1.57104	−	0.118683i
$982$	1.57224e12			1.69073
$983$	−7.45908e11	+	4.30650e11i	−0.798861	+	0.461223i	−0.843073	−	0.537800i	$-0.819256\pi$
$983$	−7.45908e11	+	4.30650e11i	−0.798861	+	0.461223i	0.0442118	+	0.999022i	$0.485922\pi$
$984$	−3.04930e11	+	5.77376e11i	−0.325252	+	0.615855i
$985$	6.36623e11	−	1.10266e12i	0.676297	−	1.17138i
$986$	−6.04045e11	−	3.48746e11i	−0.639090	−	0.368979i
$987$	5.14587e11	+	2.71769e11i	0.542238	+	0.286373i
$988$	1.94099e11	+	3.36190e11i	0.203702	+	0.352823i
$989$			7.41960e10i			0.0775524i
$990$	8.44995e11	−	5.76852e11i	0.879657	−	0.600515i
$991$	−1.05517e12			−1.09403			−0.547013	−	0.837124i	$-0.684235\pi$
$991$	−1.05517e12			−1.09403			−0.547013	+	0.837124i	$0.684235\pi$
$992$	−7.90581e11	+	4.56442e11i	−0.816393	+	0.471345i
$993$	−1.10651e11	−	1.75983e11i	−0.113804	−	0.180998i
$994$	1.28267e12	−	2.22166e12i	1.31392	−	2.27578i
$995$	1.51028e12	+	8.71963e11i	1.54087	+	0.889623i
$996$	−4.65285e10	−	1.23357e12i	−0.0472804	−	1.25351i
$997$	4.03544e11	+	6.98959e11i	0.408423	+	0.707410i	0.994713	−	0.102691i	$-0.0327454\pi$
$997$	4.03544e11	+	6.98959e11i	0.408423	+	0.707410i	−0.586290	+	0.810101i	$0.699412\pi$
$998$		−	1.41914e12i		−	1.43055i
$999$	−8.20474e11	+	9.31948e10i	−0.823764	+	0.0935685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.9.d.a.5.1	yes	14
3.2	odd	2		27.9.d.a.17.7		14
4.3	odd	2		144.9.q.a.113.7		14
9.2	odd	6	inner	9.9.d.a.2.1	✓	14
9.4	even	3		81.9.b.a.80.2		14
9.5	odd	6		81.9.b.a.80.13		14
9.7	even	3		27.9.d.a.8.7		14
12.11	even	2		432.9.q.a.17.2		14
36.7	odd	6		432.9.q.a.305.2		14
36.11	even	6		144.9.q.a.65.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.9.d.a.2.1	✓	14	9.2	odd	6	inner
9.9.d.a.5.1	yes	14	1.1	even	1	trivial
27.9.d.a.8.7		14	9.7	even	3
27.9.d.a.17.7		14	3.2	odd	2
81.9.b.a.80.2		14	9.4	even	3
81.9.b.a.80.13		14	9.5	odd	6
144.9.q.a.65.7		14	36.11	even	6
144.9.q.a.113.7		14	4.3	odd	2
432.9.q.a.17.2		14	12.11	even	2
432.9.q.a.305.2		14	36.7	odd	6

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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	9.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-22.1512 + 12.7890i) q^{2} +(-80.9424 + 3.05302i) q^{3} +(199.117 - 344.881i) q^{4} +(570.352 + 329.293i) q^{5} +(1753.93 - 1102.80i) q^{6} +(-1512.41 - 2619.58i) q^{7} +3638.08i q^{8} +(6542.36 - 494.238i) q^{9} -16845.3 q^{10} +(-8016.93 + 4628.57i) q^{11} +(-15064.1 + 28523.5i) q^{12} +(21771.9 - 37710.0i) q^{13} +(67003.6 + 38684.6i) q^{14} +(-47171.1 - 24912.5i) q^{15} +(4446.57 + 7701.69i) q^{16} -107702. i q^{17} +(-138600. + 94618.2i) q^{18} -22386.6 q^{19} +(227134. - 131136. i) q^{20} +(130416. + 207418. i) q^{21} +(118390. - 205057. i) q^{22} +(-115959. - 66949.2i) q^{23} +(-11107.2 - 294475. i) q^{24} +(21555.4 + 37335.0i) q^{25} +1.11376e6i q^{26} +(-528046. + 59978.8i) q^{27} -1.20459e6 q^{28} +(-219270. + 126596. i) q^{29} +(1.36350e6 - 51429.2i) q^{30} +(393886. - 682230. i) q^{31} +(-1.00357e6 - 579409. i) q^{32} +(634778. - 399124. i) q^{33} +(1.37740e6 + 2.38573e6i) q^{34} -1.99211e6i q^{35} +(1.13224e6 - 2.35475e6i) q^{36} +1.55379e6 q^{37} +(495890. - 286302. i) q^{38} +(-1.64714e6 + 3.11881e6i) q^{39} +(-1.19800e6 + 2.07499e6i) q^{40} +(-1.91891e6 - 1.10788e6i) q^{41} +(-5.54154e6 - 2.92666e6i) q^{42} +(-277061. - 479883. i) q^{43} +3.68652e6i q^{44} +(3.89420e6 + 1.87246e6i) q^{45} +3.42486e6 q^{46} +(2.05696e6 - 1.18759e6i) q^{47} +(-383430. - 609818. i) q^{48} +(-1.69239e6 + 2.93131e6i) q^{49} +(-954955. - 551344. i) q^{50} +(328817. + 8.71766e6i) q^{51} +(-8.67033e6 - 1.50175e7i) q^{52} +7.83903e6i q^{53} +(1.09298e7 - 8.08178e6i) q^{54} -6.09663e6 q^{55} +(9.53025e6 - 5.50229e6i) q^{56} +(1.81203e6 - 68346.8i) q^{57} +(3.23806e6 - 5.60849e6i) q^{58} +(4.48638e6 + 2.59021e6i) q^{59} +(-1.79844e7 + 1.13079e7i) q^{60} +(-4.77454e6 - 8.26974e6i) q^{61} +2.01496e7i q^{62} +(-1.11895e7 - 1.63907e7i) q^{63} +2.73636e7 q^{64} +(2.48353e7 - 1.43387e7i) q^{65} +(-8.95671e6 + 1.69593e7i) q^{66} +(-4.31500e6 + 7.47380e6i) q^{67} +(-3.71444e7 - 2.14453e7i) q^{68} +(9.59044e6 + 5.06501e6i) q^{69} +(2.54771e7 + 4.41277e7i) q^{70} -3.31572e7i q^{71} +(1.79808e6 + 2.38016e7i) q^{72} -5.28831e7 q^{73} +(-3.44184e7 + 1.98715e7i) q^{74} +(-1.85873e6 - 2.95618e6i) q^{75} +(-4.45756e6 + 7.72072e6i) q^{76} +(2.42498e7 + 1.40006e7i) q^{77} +(-3.40035e6 - 9.01508e7i) q^{78} +(4.50350e6 + 7.80029e6i) q^{79} +5.85691e6i q^{80} +(4.25582e7 - 6.46697e6i) q^{81} +5.66748e7 q^{82} +(-3.31421e7 + 1.91346e7i) q^{83} +(9.75026e7 - 3.67765e6i) q^{84} +(3.54655e7 - 6.14281e7i) q^{85} +(1.22745e7 + 7.08666e6i) q^{86} +(1.73617e7 - 1.09164e7i) q^{87} +(-1.68391e7 - 2.91662e7i) q^{88} +1.41720e7i q^{89} +(-1.10208e8 + 8.32560e6i) q^{90} -1.31713e8 q^{91} +(-4.61791e7 + 2.66615e7i) q^{92} +(-2.97992e7 + 5.64239e7i) q^{93} +(-3.03761e7 + 5.26130e7i) q^{94} +(-1.27682e7 - 7.37175e6i) q^{95} +(8.30001e7 + 4.38349e7i) q^{96} +(7.52257e7 + 1.30295e8i) q^{97} -8.65761e7i q^{98} +(-5.01620e7 + 3.42441e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{2} - 93 q^{3} + 767 q^{4} + 438 q^{5} - 2259 q^{6} + 922 q^{7} + 17973 q^{9} - 516 q^{10} - 28677 q^{11} - 55110 q^{12} + 1684 q^{13} + 120966 q^{14} - 75276 q^{15} - 65281 q^{16} + 243324 q^{18}+ \cdots - 511060752 q^{99}+O(q^{100}) \) 14 * q - 3 * q^2 - 93 * q^3 + 767 * q^4 + 438 * q^5 - 2259 * q^6 + 922 * q^7 + 17973 * q^9 - 516 * q^10 - 28677 * q^11 - 55110 * q^12 + 1684 * q^13 + 120966 * q^14 - 75276 * q^15 - 65281 * q^16 + 243324 * q^18 - 269630 * q^19 + 539454 * q^20 + 354054 * q^21 + 61311 * q^22 - 1000452 * q^23 - 1125513 * q^24 + 65177 * q^25 - 524826 * q^27 + 1075708 * q^28 + 3797682 * q^29 + 2372562 * q^30 - 164132 * q^31 - 8461881 * q^32 - 5761521 * q^33 + 654993 * q^34 + 12958047 * q^36 - 1671668 * q^37 + 10967691 * q^38 + 3383976 * q^39 + 613326 * q^40 - 10239447 * q^41 - 35844228 * q^42 + 791815 * q^43 + 27631638 * q^45 + 1189536 * q^46 + 31148628 * q^47 + 17088189 * q^48 - 4826637 * q^49 - 63849453 * q^50 - 47946573 * q^51 - 5552720 * q^52 + 36967995 * q^54 + 8107476 * q^55 + 116638674 * q^56 + 37276797 * q^57 + 14211822 * q^58 - 83493795 * q^59 - 109012050 * q^60 - 5255600 * q^61 + 38322432 * q^63 - 26813830 * q^64 + 69232992 * q^65 + 36133866 * q^66 - 8288855 * q^67 - 77746743 * q^68 - 62108640 * q^69 + 27813756 * q^70 + 88821171 * q^72 - 36721682 * q^73 - 10383450 * q^74 + 13792011 * q^75 - 42822959 * q^76 + 56158710 * q^77 + 27355140 * q^78 - 32771822 * q^79 - 16336971 * q^81 + 236099418 * q^82 - 198915996 * q^83 - 187060614 * q^84 + 97486146 * q^85 + 146190669 * q^86 + 114294006 * q^87 + 24955827 * q^88 - 222035850 * q^90 - 201514504 * q^91 - 295365804 * q^92 + 94187784 * q^93 - 36698244 * q^94 + 386813838 * q^95 + 768275928 * q^96 + 127049161 * q^97 - 511060752 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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