LMFDB - Embedded newform 21.9.f.b.10.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,9,Mod(10,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("21.10");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	21.f (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.55495081128$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 1331 x^{10} + 1482 x^{9} + 1359381 x^{8} + 1222227 x^{7} + 474169529 x^{6} + \cdots + 556282980265104 $ x^12 - 3x^11 + 1331x^10 + 1482x^9 + 1359381x^8 + 1222227x^7 + 474169529x^6 + 1911324162x^5 + 121870629463x^4 + 259296590901x^3 + 9508380016437x^2 - 12075311354004*x + 556282980265104
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{5}\cdot 7^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.3
Root			$3.88954 - 6.73687i$ of defining polynomial
Character	$\chi$	$=$	21.10
Dual form			21.9.f.b.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.38954 - 5.87085i) q^{2} +(40.5000 + 23.3827i) q^{3} +(105.022 - 181.904i) q^{4} +(-231.653 + 133.745i) q^{5} -317.026i q^{6} +(2354.84 - 468.558i) q^{7} -3159.35 q^{8} +(1093.50 + 1894.00i) q^{9} +O(q^{10})$	\(q+(-3.38954 - 5.87085i) q^{2} +(40.5000 + 23.3827i) q^{3} +(105.022 - 181.904i) q^{4} +(-231.653 + 133.745i) q^{5} -317.026i q^{6} +(2354.84 - 468.558i) q^{7} -3159.35 q^{8} +(1093.50 + 1894.00i) q^{9} +(1570.39 + 906.668i) q^{10} +(9586.51 - 16604.3i) q^{11} +(8506.79 - 4911.40i) q^{12} -40724.3i q^{13} +(-10732.6 - 12236.7i) q^{14} -12509.3 q^{15} +(-16176.9 - 28019.3i) q^{16} +(-7569.41 - 4370.20i) q^{17} +(7412.92 - 12839.5i) q^{18} +(107434. - 62026.8i) q^{19} +56184.8i q^{20} +(106327. + 36085.8i) q^{21} -129975. q^{22} +(188368. + 326263. i) q^{23} +(-127954. - 73874.0i) q^{24} +(-159537. + 276326. i) q^{25} +(-239086. + 138036. i) q^{26} +102276. i q^{27} +(162078. - 477562. i) q^{28} -927223. q^{29} +(42400.6 + 73440.1i) q^{30} +(837032. + 483261. i) q^{31} +(-514061. + 890380. i) q^{32} +(776507. - 448316. i) q^{33} +59251.8i q^{34} +(-482838. + 423491. i) q^{35} +459367. q^{36} +(-461288. - 798974. i) q^{37} +(-728300. - 420484. i) q^{38} +(952243. - 1.64933e6i) q^{39} +(731873. - 422547. i) q^{40} +2.47157e6i q^{41} +(-148545. - 746544. i) q^{42} +1.37320e6 q^{43} +(-2.01359e6 - 3.48764e6i) q^{44} +(-506626. - 292500. i) q^{45} +(1.27696e6 - 2.21176e6i) q^{46} +(2.78766e6 - 1.60946e6i) q^{47} -1.51304e6i q^{48} +(5.32571e6 - 2.20675e6i) q^{49} +2.16303e6 q^{50} +(-204374. - 353986. i) q^{51} +(-7.40789e6 - 4.27695e6i) q^{52} +(-7.69978e6 + 1.33364e7i) q^{53} +(600446. - 346668. i) q^{54} +5.12859e6i q^{55} +(-7.43975e6 + 1.48034e6i) q^{56} +5.80142e6 q^{57} +(3.14285e6 + 5.44358e6i) q^{58} +(-2.49651e6 - 1.44136e6i) q^{59} +(-1.31375e6 + 2.27548e6i) q^{60} +(1.44479e6 - 834148. i) q^{61} -6.55212e6i q^{62} +(3.46246e6 + 3.94769e6i) q^{63} -1.31288e6 q^{64} +(5.44667e6 + 9.43391e6i) q^{65} +(-5.26400e6 - 3.03917e6i) q^{66} +(-8.55413e6 + 1.48162e7i) q^{67} +(-1.58991e6 + 917935. i) q^{68} +1.76182e7i q^{69} +(4.12285e6 + 1.39923e6i) q^{70} +3.12574e7 q^{71} +(-3.45475e6 - 5.98380e6i) q^{72} +(-2.38356e7 - 1.37615e7i) q^{73} +(-3.12711e6 + 5.41631e6i) q^{74} +(-1.29225e7 + 7.46081e6i) q^{75} -2.60567e7i q^{76} +(1.47946e7 - 4.35923e7i) q^{77} -1.29106e7 q^{78} +(1.23733e7 + 2.14311e7i) q^{79} +(7.49488e6 + 4.32717e6i) q^{80} +(-2.39148e6 + 4.14217e6i) q^{81} +(1.45102e7 - 8.37746e6i) q^{82} -5.98657e7i q^{83} +(1.77308e7 - 1.55515e7i) q^{84} +2.33797e6 q^{85} +(-4.65450e6 - 8.06182e6i) q^{86} +(-3.75525e7 - 2.16810e7i) q^{87} +(-3.02871e7 + 5.24588e7i) q^{88} +(5.94265e7 - 3.43099e7i) q^{89} +3.96576e6i q^{90} +(-1.90817e7 - 9.58990e7i) q^{91} +7.91313e7 q^{92} +(2.25999e7 + 3.91441e7i) q^{93} +(-1.88977e7 - 1.09106e7i) q^{94} +(-1.65916e7 + 2.87374e7i) q^{95} +(-4.16389e7 + 2.40403e7i) q^{96} +1.66923e8i q^{97} +(-3.10072e7 - 2.37866e7i) q^{98} +4.19314e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9	\( 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9} - 19731 q^{10} + 18081 q^{11} - 90477 q^{12} - 175188 q^{14} + 75006 q^{15} - 298849 q^{16} + 63306 q^{17} - 6561 q^{18} + 476265 q^{19} - 154953 q^{21} + 419258 q^{22} - 66384 q^{23} + 144099 q^{24} + 792375 q^{25} + 1890762 q^{26} - 4229651 q^{28} + 671106 q^{29} - 532737 q^{30} + 717240 q^{31} + 895149 q^{32} + 1464561 q^{33} + 3454614 q^{35} - 4885758 q^{36} + 2289443 q^{37} - 6275988 q^{38} - 930933 q^{39} + 8773863 q^{40} - 4123629 q^{42} - 10119958 q^{43} + 14123901 q^{44} + 3037743 q^{45} - 19926544 q^{46} - 4198782 q^{47} + 8565642 q^{49} - 1162248 q^{50} + 1709262 q^{51} - 26384844 q^{52} - 209511 q^{53} - 531441 q^{54} + 70081743 q^{56} + 25718310 q^{57} + 1938935 q^{58} - 97052259 q^{59} - 51464727 q^{60} - 24195864 q^{61} - 9869931 q^{63} + 272849458 q^{64} + 30440562 q^{65} + 16979949 q^{66} - 57546057 q^{67} - 32476050 q^{68} - 108189027 q^{70} + 224566620 q^{71} + 3890673 q^{72} - 193344135 q^{73} - 71015400 q^{74} + 64182375 q^{75} + 92041617 q^{77} + 102101148 q^{78} - 29314488 q^{79} - 735358533 q^{80} - 28697814 q^{81} + 321118926 q^{82} - 120939804 q^{84} + 248647620 q^{85} + 127268268 q^{86} + 27179793 q^{87} - 487070897 q^{88} + 119863098 q^{89} + 100090965 q^{91} + 364039200 q^{92} + 19365480 q^{93} - 191086092 q^{94} - 95584488 q^{95} + 72507069 q^{96} + 24200217 q^{98} + 79086294 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9 - 19731 * q^10 + 18081 * q^11 - 90477 * q^12 - 175188 * q^14 + 75006 * q^15 - 298849 * q^16 + 63306 * q^17 - 6561 * q^18 + 476265 * q^19 - 154953 * q^21 + 419258 * q^22 - 66384 * q^23 + 144099 * q^24 + 792375 * q^25 + 1890762 * q^26 - 4229651 * q^28 + 671106 * q^29 - 532737 * q^30 + 717240 * q^31 + 895149 * q^32 + 1464561 * q^33 + 3454614 * q^35 - 4885758 * q^36 + 2289443 * q^37 - 6275988 * q^38 - 930933 * q^39 + 8773863 * q^40 - 4123629 * q^42 - 10119958 * q^43 + 14123901 * q^44 + 3037743 * q^45 - 19926544 * q^46 - 4198782 * q^47 + 8565642 * q^49 - 1162248 * q^50 + 1709262 * q^51 - 26384844 * q^52 - 209511 * q^53 - 531441 * q^54 + 70081743 * q^56 + 25718310 * q^57 + 1938935 * q^58 - 97052259 * q^59 - 51464727 * q^60 - 24195864 * q^61 - 9869931 * q^63 + 272849458 * q^64 + 30440562 * q^65 + 16979949 * q^66 - 57546057 * q^67 - 32476050 * q^68 - 108189027 * q^70 + 224566620 * q^71 + 3890673 * q^72 - 193344135 * q^73 - 71015400 * q^74 + 64182375 * q^75 + 92041617 * q^77 + 102101148 * q^78 - 29314488 * q^79 - 735358533 * q^80 - 28697814 * q^81 + 321118926 * q^82 - 120939804 * q^84 + 248647620 * q^85 + 127268268 * q^86 + 27179793 * q^87 - 487070897 * q^88 + 119863098 * q^89 + 100090965 * q^91 + 364039200 * q^92 + 19365480 * q^93 - 191086092 * q^94 - 95584488 * q^95 + 72507069 * q^96 + 24200217 * q^98 + 79086294 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−3.38954	−	5.87085i	−0.211846	−	0.366928i	0.740446	−	0.672116i	$-0.234614\pi$
$2$	−3.38954	−	5.87085i	−0.211846	−	0.366928i	−0.952292	+	0.305188i	$0.901281\pi$
$3$	40.5000	+	23.3827i	0.500000	+	0.288675i
$3$	40.5000	+	23.3827i	0.500000	+	0.288675i
$4$	105.022	−	181.904i	0.410243	−	0.710561i
$5$	−231.653	+	133.745i	−0.370645	+	0.213992i	−0.673740	−	0.738968i	$-0.735313\pi$
$5$	−231.653	+	133.745i	−0.370645	+	0.213992i	0.303095	+	0.952960i	$0.401980\pi$
$6$		−	317.026i		−	0.244619i
$7$	2354.84	−	468.558i	0.980773	−	0.195151i
$7$	2354.84	−	468.558i	0.980773	−	0.195151i
$8$	−3159.35			−0.771325
$9$	1093.50	+	1894.00i	0.166667	+	0.288675i
$10$	1570.39	+	906.668i	0.157039	+	0.0906668i
$11$	9586.51	−	16604.3i	0.654771	−	1.13410i	−0.327180	−	0.944962i	$-0.606098\pi$
$11$	9586.51	−	16604.3i	0.654771	−	1.13410i	0.981951	−	0.189135i	$-0.0605684\pi$
$12$	8506.79	−	4911.40i	0.410243	−	0.236854i
$13$		−	40724.3i		−	1.42587i	−0.701230	−	0.712935i	$-0.747366\pi$
$13$		−	40724.3i		−	1.42587i	0.701230	−	0.712935i	$-0.252634\pi$
$14$	−10732.6	−	12236.7i	−0.279379	−	0.318531i
$15$	−12509.3			−0.247097
$16$	−16176.9	−	28019.3i	−0.246840	−	0.427540i
$17$	−7569.41	−	4370.20i	−0.0906288	−	0.0523246i	0.454001	−	0.891001i	$-0.349996\pi$
$17$	−7569.41	−	4370.20i	−0.0906288	−	0.0523246i	−0.544629	+	0.838677i	$0.683330\pi$
$18$	7412.92	−	12839.5i	0.0706153	−	0.122309i
$19$	107434.	−	62026.8i	0.824377	−	0.475954i	−0.0275466	−	0.999621i	$-0.508769\pi$
$19$	107434.	−	62026.8i	0.824377	−	0.475954i	0.851923	+	0.523666i	$0.175436\pi$
$20$			56184.8i			0.351155i
$21$	106327.	+	36085.8i	0.546722	+	0.185549i
$22$	−129975.			−0.554843
$23$	188368.	+	326263.i	0.673126	+	1.16589i	0.977013	+	0.213180i	$0.0683820\pi$
$23$	188368.	+	326263.i	0.673126	+	1.16589i	−0.303887	+	0.952708i	$0.598285\pi$
$24$	−127954.	−	73874.0i	−0.385662	−	0.222662i
$25$	−159537.	+	276326.i	−0.408415	+	0.707395i
$26$	−239086.	+	138036.i	−0.523192	+	0.302065i
$27$			102276.i			0.192450i
$28$	162078.	−	477562.i	0.263688	−	0.776958i
$29$	−927223.			−1.31097			−0.655484	−	0.755209i	$-0.727535\pi$
$29$	−927223.			−1.31097			−0.655484	+	0.755209i	$0.727535\pi$
$30$	42400.6	+	73440.1i	0.0523465	+	0.0906668i
$31$	837032.	+	483261.i	0.906349	+	0.523281i	0.879255	−	0.476352i	$-0.158041\pi$
$31$	837032.	+	483261.i	0.906349	+	0.523281i	0.0270943	+	0.999633i	$0.491375\pi$
$32$	−514061.	+	890380.i	−0.490247	+	0.849132i
$33$	776507.	−	448316.i	0.654771	−	0.378032i
$34$			59251.8i			0.0443390i
$35$	−482838.	+	423491.i	−0.321758	+	0.282210i
$36$	459367.			0.273495
$37$	−461288.	−	798974.i	−0.246130	−	0.426310i	0.716318	−	0.697774i	$-0.245826\pi$
$37$	−461288.	−	798974.i	−0.246130	−	0.426310i	−0.962449	+	0.271463i	$0.912493\pi$
$38$	−728300.	−	420484.i	−0.349282	−	0.201658i
$39$	952243.	−	1.64933e6i	0.411613	−	0.712935i
$40$	731873.	−	422547.i	0.285888	−	0.165057i
$41$			2.47157e6i			0.874655i	0.899302	+	0.437327i	$0.144075\pi$
$41$			2.47157e6i			0.874655i	−0.899302	+	0.437327i	$0.855925\pi$
$42$	−148545.	−	746544.i	−0.0477376	−	0.239915i
$43$	1.37320e6			0.401660			0.200830	−	0.979626i	$-0.435636\pi$
$43$	1.37320e6			0.401660			0.200830	+	0.979626i	$0.435636\pi$
$44$	−2.01359e6	−	3.48764e6i	−0.537230	−	0.930510i
$45$	−506626.	−	292500.i	−0.123548	−	0.0713307i
$46$	1.27696e6	−	2.21176e6i	0.285198	−	0.493977i
$47$	2.78766e6	−	1.60946e6i	0.571279	−	0.329828i	−0.186381	−	0.982478i	$-0.559676\pi$
$47$	2.78766e6	−	1.60946e6i	0.571279	−	0.329828i	0.757660	+	0.652649i	$0.226343\pi$
$48$		−	1.51304e6i		−	0.285027i
$49$	5.32571e6	−	2.20675e6i	0.923832	−	0.382798i
$50$	2.16303e6			0.346084
$51$	−204374.	−	353986.i	−0.0302096	−	0.0523246i
$52$	−7.40789e6	−	4.27695e6i	−1.01317	−	0.584952i
$53$	−7.69978e6	+	1.33364e7i	−0.975832	+	1.69019i	−0.298670	+	0.954356i	$0.596543\pi$
$53$	−7.69978e6	+	1.33364e7i	−0.975832	+	1.69019i	−0.677162	+	0.735834i	$0.736790\pi$
$54$	600446.	−	346668.i	0.0706153	−	0.0407698i
$55$			5.12859e6i			0.560464i
$56$	−7.43975e6	+	1.48034e6i	−0.756495	+	0.150525i
$57$	5.80142e6			0.549585
$58$	3.14285e6	+	5.44358e6i	0.277723	+	0.481031i
$59$	−2.49651e6	−	1.44136e6i	−0.206028	−	0.118950i	0.393436	−	0.919352i	$-0.371286\pi$
$59$	−2.49651e6	−	1.44136e6i	−0.206028	−	0.118950i	−0.599464	+	0.800402i	$0.704620\pi$
$60$	−1.31375e6	+	2.27548e6i	−0.101370	+	0.175577i
$61$	1.44479e6	−	834148.i	0.104348	−	0.0602454i	−0.446918	−	0.894575i	$-0.647478\pi$
$61$	1.44479e6	−	834148.i	0.104348	−	0.0602454i	0.551266	+	0.834330i	$0.314145\pi$
$62$		−	6.55212e6i		−	0.443420i
$63$	3.46246e6	+	3.94769e6i	0.219797	+	0.250600i
$64$	−1.31288e6			−0.0782535
$65$	5.44667e6	+	9.43391e6i	0.305125	+	0.528492i
$66$	−5.26400e6	−	3.03917e6i	−0.277421	−	0.160169i
$67$	−8.55413e6	+	1.48162e7i	−0.424499	+	0.735254i	−0.996374	−	0.0850872i	$-0.972883\pi$
$67$	−8.55413e6	+	1.48162e7i	−0.424499	+	0.735254i	0.571874	+	0.820341i	$0.306216\pi$
$68$	−1.58991e6	+	917935.i	−0.0743596	+	0.0429315i
$69$			1.76182e7i			0.777258i
$70$	4.12285e6	+	1.39923e6i	0.171714	+	0.0582771i
$71$	3.12574e7			1.23004			0.615020	−	0.788511i	$-0.289148\pi$
$71$	3.12574e7			1.23004			0.615020	+	0.788511i	$0.289148\pi$
$72$	−3.45475e6	−	5.98380e6i	−0.128554	−	0.222662i
$73$	−2.38356e7	−	1.37615e7i	−0.839333	−	0.484589i	0.0177042	−	0.999843i	$-0.494364\pi$
$73$	−2.38356e7	−	1.37615e7i	−0.839333	−	0.484589i	−0.857038	+	0.515254i	$0.827698\pi$
$74$	−3.12711e6	+	5.41631e6i	−0.104284	+	0.180624i
$75$	−1.29225e7	+	7.46081e6i	−0.408415	+	0.235798i
$76$		−	2.60567e7i		−	0.781027i
$77$	1.47946e7	−	4.35923e7i	0.420862	−	1.24007i
$78$	−1.29106e7			−0.348794
$79$	1.23733e7	+	2.14311e7i	0.317670	+	0.550220i	0.980001	−	0.198991i	$-0.0637663\pi$
$79$	1.23733e7	+	2.14311e7i	0.317670	+	0.550220i	−0.662332	+	0.749211i	$0.730433\pi$
$80$	7.49488e6	+	4.32717e6i	0.182980	+	0.105644i
$81$	−2.39148e6	+	4.14217e6i	−0.0555556	+	0.0962250i
$82$	1.45102e7	−	8.37746e6i	0.320935	−	0.185292i
$83$		−	5.98657e7i		−	1.26144i	−0.776012	−	0.630718i	$-0.782760\pi$
$83$		−	5.98657e7i		−	1.26144i	0.776012	−	0.630718i	$-0.217240\pi$
$84$	1.77308e7	−	1.55515e7i	0.356133	−	0.312359i
$85$	2.33797e6			0.0447882
$86$	−4.65450e6	−	8.06182e6i	−0.0850901	−	0.147380i
$87$	−3.75525e7	−	2.16810e7i	−0.655484	−	0.378444i
$88$	−3.02871e7	+	5.24588e7i	−0.505041	+	0.874757i
$89$	5.94265e7	−	3.43099e7i	0.947153	−	0.546839i	0.0549574	−	0.998489i	$-0.482498\pi$
$89$	5.94265e7	−	3.43099e7i	0.947153	−	0.546839i	0.892195	+	0.451650i	$0.149164\pi$
$90$			3.96576e6i			0.0604445i
$91$	−1.90817e7	−	9.58990e7i	−0.278260	−	1.39845i
$92$	7.91313e7			1.10458
$93$	2.25999e7	+	3.91441e7i	0.302116	+	0.523281i
$94$	−1.88977e7	−	1.09106e7i	−0.242046	−	0.139746i
$95$	−1.65916e7	+	2.87374e7i	−0.203701	+	0.352820i
$96$	−4.16389e7	+	2.40403e7i	−0.490247	+	0.283044i
$97$			1.66923e8i			1.88551i	0.333482	+	0.942757i	$0.391776\pi$
$97$			1.66923e8i			1.88551i	−0.333482	+	0.942757i	$0.608224\pi$
$98$	−3.10072e7	−	2.37866e7i	−0.336169	−	0.257886i
$99$	4.19314e7			0.436514
$100$	3.35098e7	+	5.80407e7i	0.335098	+	0.580407i
$101$	−1.23598e8	−	7.13591e7i	−1.18775	−	0.685747i	−0.229954	−	0.973201i	$-0.573858\pi$
$101$	−1.23598e8	−	7.13591e7i	−1.18775	−	0.685747i	−0.957794	+	0.287454i	$0.907191\pi$
$102$	−1.38547e6	+	2.39970e6i	−0.0127996	+	0.0221695i
$103$	−5.00884e7	+	2.89186e7i	−0.445029	+	0.256938i	−0.705729	−	0.708482i	$-0.749380\pi$
$103$	−5.00884e7	+	2.89186e7i	−0.445029	+	0.256938i	0.260699	+	0.965420i	$0.416047\pi$
$104$			1.28662e8i			1.09981i
$105$	−2.94573e7	+	5.86132e6i	−0.242346	+	0.0482212i
$106$	1.04395e8			0.826904
$107$	4.47179e7	+	7.74538e7i	0.341151	+	0.590891i	0.984647	−	0.174559i	$-0.0558499\pi$
$107$	4.47179e7	+	7.74538e7i	0.341151	+	0.590891i	−0.643496	+	0.765450i	$0.722517\pi$
$108$	1.86043e7	+	1.07412e7i	0.136748	+	0.0789512i
$109$	1.75975e7	−	3.04797e7i	0.124665	−	0.215926i	−0.796937	−	0.604062i	$-0.793548\pi$
$109$	1.75975e7	−	3.04797e7i	0.124665	−	0.215926i	0.921602	+	0.388136i	$0.126881\pi$
$110$	3.01092e7	−	1.73835e7i	0.205650	−	0.118732i
$111$		−	4.31446e7i		−	0.284207i
$112$	−5.12227e7	−	5.84010e7i	−0.325529	−	0.371149i
$113$	−6.70322e7			−0.411121			−0.205560	−	0.978644i	$-0.565902\pi$
$113$	−6.70322e7			−0.411121			−0.205560	+	0.978644i	$0.565902\pi$
$114$	−1.96641e7	−	3.40592e7i	−0.116427	−	0.201658i
$115$	−8.72722e7	−	5.03866e7i	−0.498982	−	0.288087i
$116$	−9.73789e7	+	1.68665e8i	−0.537815	+	0.931522i
$117$	7.71317e7	−	4.45320e7i	0.411613	−	0.237645i
$118$			1.95422e7i			0.100796i
$119$	−1.98724e7	−	6.74440e6i	−0.0990975	−	0.0336322i
$120$	3.95211e7			0.190592
$121$	−7.66227e7	−	1.32714e8i	−0.357451	−	0.619123i
$122$	−9.79431e6	−	5.65475e6i	−0.0442114	−	0.0255255i
$123$	−5.77918e7	+	1.00098e8i	−0.252491	+	0.437327i
$124$	1.75814e8	−	1.01506e8i	0.743646	−	0.429344i
$125$		−	1.89838e8i		−	0.777574i
$126$	1.14401e7	−	3.37084e7i	0.0453888	−	0.133738i
$127$	5.97711e7			0.229761			0.114881	−	0.993379i	$-0.463351\pi$
$127$	5.97711e7			0.229761			0.114881	+	0.993379i	$0.463351\pi$
$128$	1.36050e8	+	2.35645e8i	0.506825	+	0.877846i
$129$	5.56144e7	+	3.21090e7i	0.200830	+	0.115949i
$130$	3.69234e7	−	6.39531e7i	0.129279	−	0.223918i
$131$	−1.81198e8	+	1.04615e8i	−0.615273	+	0.355228i	−0.775026	−	0.631929i	$-0.782264\pi$
$131$	−1.81198e8	+	1.04615e8i	−0.615273	+	0.355228i	0.159753	+	0.987157i	$0.448930\pi$
$132$		−	1.88333e8i		−	0.620340i
$133$	2.23925e8	−	1.96402e8i	0.715644	−	0.627681i
$134$	1.15978e8			0.359714
$135$	−1.36789e7	−	2.36925e7i	−0.0411828	−	0.0713307i
$136$	2.39144e7	+	1.38070e7i	0.0699043	+	0.0403592i
$137$	3.50307e7	−	6.06750e7i	0.0994414	−	0.172238i	−0.812012	−	0.583640i	$-0.801628\pi$
$137$	3.50307e7	−	6.06750e7i	0.0994414	−	0.172238i	0.911454	+	0.411403i	$0.134961\pi$
$138$	1.03434e8	−	5.97176e7i	0.285198	−	0.164659i
$139$		−	1.28614e7i		−	0.0344531i	−0.999852	−	0.0172265i	$-0.994516\pi$
$139$		−	1.28614e7i		−	0.0344531i	0.999852	−	0.0172265i	$-0.00548365\pi$
$140$	2.63258e7	+	1.32306e8i	0.0685282	+	0.344403i
$141$	1.50534e8			0.380853
$142$	−1.05948e8	−	1.83508e8i	−0.260579	−	0.451336i
$143$	−6.76198e8	−	3.90403e8i	−1.61707	−	0.933618i
$144$	3.53790e7	−	6.12781e7i	0.0822801	−	0.142513i
$145$	2.14794e8	−	1.24011e8i	0.485904	−	0.280537i
$146$			1.86580e8i			0.410633i
$147$	2.67291e8	+	3.51559e7i	0.572420	+	0.0752885i
$148$	−1.93782e8			−0.403893
$149$	−4.46096e7	−	7.72661e7i	−0.0905072	−	0.156763i	0.817217	−	0.576329i	$-0.195515\pi$
$149$	−4.46096e7	−	7.72661e7i	−0.0905072	−	0.156763i	−0.907725	+	0.419566i	$0.862182\pi$
$150$	8.76025e7	+	5.05774e7i	0.173042	+	0.0999059i
$151$	−2.79390e8	+	4.83918e8i	−0.537407	+	0.930816i	0.461636	+	0.887070i	$0.347263\pi$
$151$	−2.79390e8	+	4.83918e8i	−0.537407	+	0.930816i	−0.999043	+	0.0437467i	$0.986071\pi$
$152$	−3.39420e8	+	1.95964e8i	−0.635862	+	0.367115i
$153$		−	1.91153e7i		−	0.0348830i
$154$	−3.06070e8	+	6.09009e7i	−0.544175	+	0.108278i
$155$	−2.58535e8			−0.447912
$156$	−2.00013e8	−	3.46433e8i	−0.337722	−	0.584952i
$157$	9.34000e8	+	5.39245e8i	1.53726	+	0.887539i	0.998998	+	0.0447635i	$0.0142534\pi$
$157$	9.34000e8	+	5.39245e8i	1.53726	+	0.887539i	0.538265	+	0.842776i	$0.319080\pi$
$158$	8.38792e7	−	1.45283e8i	0.134594	−	0.233124i
$159$	−6.23682e8	+	3.60083e8i	−0.975832	+	0.563397i
$160$		−	2.75013e8i		−	0.419636i
$161$	5.96449e8	+	6.80035e8i	0.887708	+	1.01211i
$162$	3.24241e7			0.0470769
$163$	2.72747e8	+	4.72411e8i	0.386375	+	0.669222i	0.991959	−	0.126560i	$-0.0403936\pi$
$163$	2.72747e8	+	4.72411e8i	0.386375	+	0.669222i	−0.605584	+	0.795782i	$0.707060\pi$
$164$	4.49587e8	+	2.59569e8i	0.621495	+	0.358821i
$165$	−1.19920e8	+	2.07708e8i	−0.161792	+	0.280232i
$166$	−3.51462e8	+	2.02917e8i	−0.462856	+	0.267230i
$167$		−	2.98358e7i		−	0.0383594i	−0.999816	−	0.0191797i	$-0.993895\pi$
$167$		−	2.98358e7i		−	0.0383594i	0.999816	−	0.0191797i	$-0.00610546\pi$
$168$	−3.35924e8	−	1.14008e8i	−0.421700	−	0.143119i
$169$	−8.42735e8			−1.03310
$170$	−7.92464e6	−	1.37259e7i	−0.00948820	−	0.0164340i
$171$	2.34957e8	+	1.35653e8i	0.274792	+	0.158651i
$172$	1.44216e8	−	2.49789e8i	0.164778	−	0.285404i
$173$	1.36675e9	−	7.89093e8i	1.52582	−	0.880935i	0.526294	−	0.850303i	$-0.323581\pi$
$173$	1.36675e9	−	7.89093e8i	1.52582	−	0.880935i	0.999531	−	0.0306326i	$-0.00975219\pi$
$174$			2.93954e8i			0.320687i
$175$	−2.46209e8	+	7.25455e8i	−0.262513	+	0.773497i
$176$	−6.20321e8			−0.646496
$177$	−6.74058e7	−	1.16750e8i	−0.0686759	−	0.118950i
$178$	−4.02856e8	−	2.32589e8i	−0.401301	−	0.231691i
$179$	7.89835e8	−	1.36804e9i	0.769351	−	1.33256i	−0.168564	−	0.985691i	$-0.553913\pi$
$179$	7.89835e8	−	1.36804e9i	0.769351	−	1.33256i	0.937915	−	0.346864i	$-0.112754\pi$
$180$	−1.06414e8	+	6.14380e7i	−0.101370	+	0.0585258i
$181$			6.13370e8i			0.571490i	0.958306	+	0.285745i	$0.0922410\pi$
$181$			6.13370e8i			0.571490i	−0.958306	+	0.285745i	$0.907759\pi$
$182$	−4.98330e8	+	4.37079e8i	−0.454184	+	0.398358i
$183$	7.80185e7			0.0695654
$184$	−5.95120e8	−	1.03078e9i	−0.519199	−	0.899278i
$185$	2.13718e8	+	1.23390e8i	0.182454	+	0.105340i
$186$	1.53206e8	−	2.65361e8i	0.128004	−	0.221710i
$187$	−1.45128e8	+	8.37899e7i	−0.118682	+	0.0685212i
$188$		−	6.76114e8i		−	0.541238i
$189$	4.79221e7	+	2.40843e8i	0.0375568	+	0.188750i
$190$	2.24951e8			0.172613
$191$	−3.00465e8	−	5.20420e8i	−0.225767	−	0.391039i	0.730782	−	0.682610i	$-0.239155\pi$
$191$	−3.00465e8	−	5.20420e8i	−0.225767	−	0.391039i	−0.956549	+	0.291571i	$0.905822\pi$
$192$	−5.31715e7	−	3.06986e7i	−0.0391268	−	0.0225898i
$193$	9.28691e8	−	1.60854e9i	0.669332	−	1.15932i	−0.308759	−	0.951140i	$-0.599914\pi$
$193$	9.28691e8	−	1.60854e9i	0.669332	−	1.15932i	0.978091	−	0.208177i	$-0.0667531\pi$
$194$	9.79980e8	−	5.65792e8i	0.691848	−	0.399438i
$195$			5.09431e8i			0.352328i
$196$	1.57901e8	−	1.20052e9i	0.106994	−	0.813479i
$197$	7.08218e8			0.470221			0.235111	−	0.971969i	$-0.424455\pi$
$197$	7.08218e8			0.470221			0.235111	+	0.971969i	$0.424455\pi$
$198$	−1.42128e8	−	2.46173e8i	−0.0924738	−	0.160169i
$199$	1.52211e9	+	8.78793e8i	0.970588	+	0.560369i	0.899415	−	0.437095i	$-0.143993\pi$
$199$	1.52211e9	+	8.78793e8i	0.970588	+	0.560369i	0.0711725	+	0.997464i	$0.477326\pi$
$200$	5.04033e8	−	8.73010e8i	0.315020	−	0.545632i
$201$	−6.92885e8	+	4.00037e8i	−0.424499	+	0.245085i
$202$			9.67497e8i			0.581091i
$203$	−2.18346e9	+	4.34457e8i	−1.28576	+	0.255837i
$204$	−8.58552e7			−0.0495731
$205$	−3.30560e8	−	5.72546e8i	−0.187169	−	0.324187i
$206$	3.39553e8	+	1.96041e8i	0.188555	+	0.108862i
$207$	−4.11961e8	+	7.13538e8i	−0.224375	+	0.388629i
$208$	−1.14106e9	+	6.58794e8i	−0.609617	+	0.351962i
$209$		−	2.37848e9i		−	1.24656i
$210$	1.34257e8	+	1.53072e8i	0.0690337	+	0.0787081i
$211$	−3.43205e9			−1.73151			−0.865753	−	0.500472i	$-0.833160\pi$
$211$	−3.43205e9			−1.73151			−0.865753	+	0.500472i	$0.833160\pi$
$212$	1.61729e9	+	2.80124e9i	0.800656	+	1.38678i
$213$	1.26592e9	+	7.30882e8i	0.615020	+	0.355082i
$214$	3.03146e8	−	5.25065e8i	0.144543	−	0.250356i
$215$	−3.18105e8	+	1.83658e8i	−0.148873	+	0.0859521i
$216$		−	3.23125e8i		−	0.148442i
$217$	2.19751e9	+	7.45802e8i	0.991042	+	0.336345i
$218$	−2.38589e8			−0.105639
$219$	−6.43561e8	−	1.11468e9i	−0.279778	−	0.484589i
$220$	9.32909e8	+	5.38615e8i	0.398243	+	0.229926i
$221$	−1.77973e8	+	3.08259e8i	−0.0746080	+	0.129225i
$222$	−2.53296e8	+	1.46240e8i	−0.104284	+	0.0602081i
$223$		−	1.86934e8i		−	0.0755907i	−0.999286	−	0.0377953i	$-0.987967\pi$
$223$		−	1.86934e8i		−	0.0755907i	0.999286	−	0.0377953i	$-0.0120335\pi$
$224$	−7.93335e8	+	2.33757e9i	−0.315112	+	0.928478i
$225$	−6.97815e8			−0.272276
$226$	2.27208e8	+	3.93536e8i	0.0870943	+	0.150852i
$227$	6.54720e8	+	3.78003e8i	0.246577	+	0.142361i	0.618196	−	0.786024i	$-0.287864\pi$
$227$	6.54720e8	+	3.78003e8i	0.246577	+	0.142361i	−0.371619	+	0.928385i	$0.621197\pi$
$228$	6.09277e8	−	1.05530e9i	0.225463	−	0.390513i
$229$	−2.96305e9	+	1.71072e9i	−1.07745	+	0.622067i	−0.930208	−	0.367034i	$-0.880373\pi$
$229$	−2.96305e9	+	1.71072e9i	−1.07745	+	0.622067i	−0.147244	+	0.989100i	$0.547040\pi$
$230$			6.83149e8i			0.244120i
$231$	1.61848e9	−	1.41955e9i	0.568409	−	0.498543i
$232$	2.92942e9			1.01118
$233$	1.27863e9	+	2.21466e9i	0.433833	+	0.751420i	0.997200	−	0.0747866i	$-0.0238276\pi$
$233$	1.27863e9	+	2.21466e9i	0.433833	+	0.751420i	−0.563367	+	0.826207i	$0.690494\pi$
$234$	−5.22881e8	−	3.01886e8i	−0.174397	−	0.100688i
$235$	−4.30514e8	+	7.45672e8i	−0.141161	+	0.244498i
$236$	−5.24378e8	+	3.02750e8i	−0.169043	+	0.0975968i
$237$			1.15728e9i			0.366813i
$238$	2.77629e7	+	1.39528e8i	0.00865280	+	0.0434865i
$239$	−6.23455e9			−1.91079			−0.955396	−	0.295328i	$-0.904571\pi$
$239$	−6.23455e9			−1.91079			−0.955396	+	0.295328i	$0.904571\pi$
$240$	2.02362e8	+	3.50501e8i	0.0609935	+	0.105644i
$241$	6.76231e8	+	3.90422e8i	0.200460	+	0.115735i	0.596870	−	0.802338i	$-0.296411\pi$
$241$	6.76231e8	+	3.90422e8i	0.200460	+	0.115735i	−0.396410	+	0.918073i	$0.629744\pi$
$242$	−5.19431e8	+	8.99681e8i	−0.151449	+	0.262317i
$243$	−1.93710e8	+	1.11839e8i	−0.0555556	+	0.0320750i
$244$		−	3.50416e8i		−	0.0988608i
$245$	−9.38575e8	+	1.22349e9i	−0.260498	+	0.339575i
$246$	7.83550e8			0.213957
$247$	−2.52600e9	−	4.37515e9i	−0.678649	−	1.17545i
$248$	−2.64448e9	−	1.52679e9i	−0.699090	−	0.403620i
$249$	1.39982e9	−	2.42456e9i	0.364145	−	0.630718i
$250$	−1.11451e9	+	6.43461e8i	−0.285314	+	0.164726i
$251$		−	3.15325e9i		−	0.794445i	−0.917722	−	0.397222i	$-0.869974\pi$
$251$		−	3.15325e9i		−	0.794445i	0.917722	−	0.397222i	$-0.130026\pi$
$252$	1.08173e9	−	2.15240e8i	0.268237	−	0.0533728i
$253$	7.22317e9			1.76297
$254$	−2.02596e8	−	3.50907e8i	−0.0486740	−	0.0843058i
$255$	9.46878e7	+	5.46680e7i	0.0223941	+	0.0129292i
$256$	7.54242e8	−	1.30639e9i	0.175611	−	0.304167i
$257$	6.57968e9	−	3.79878e9i	1.50825	−	0.870786i	0.508292	−	0.861185i	$-0.330277\pi$
$257$	6.57968e9	−	3.79878e9i	1.50825	−	0.870786i	0.999954	−	0.00960166i	$-0.00305635\pi$
$258$		−	4.35339e8i		−	0.0982536i
$259$	−1.46062e9	−	1.66531e9i	−0.324593	−	0.370081i
$260$	2.28808e9			0.500701
$261$	−1.01392e9	−	1.75616e9i	−0.218495	−	0.378444i
$262$	1.22835e9	+	7.09191e8i	0.260686	+	0.150507i
$263$	−3.51345e9	+	6.08547e9i	−0.734363	+	1.27195i	0.220640	+	0.975355i	$0.429186\pi$
$263$	−3.51345e9	+	6.08547e9i	−0.734363	+	1.27195i	−0.955002	+	0.296598i	$0.904148\pi$
$264$	−2.45325e9	+	1.41639e9i	−0.505041	+	0.291586i
$265$		−	4.11923e9i		−	0.835281i
$266$	−1.91205e9	−	6.48921e8i	−0.381920	−	0.129618i
$267$	3.20903e9			0.631435
$268$	1.79675e9	+	3.11205e9i	0.348295	+	0.603265i
$269$	−7.13899e9	−	4.12170e9i	−1.36341	−	0.787167i	−0.373337	−	0.927696i	$-0.621786\pi$
$269$	−7.13899e9	−	4.12170e9i	−1.36341	−	0.787167i	−0.990077	+	0.140529i	$0.955120\pi$
$270$	−9.27302e7	+	1.60613e8i	−0.0174488	+	0.0302223i
$271$	5.99220e9	−	3.45960e9i	1.11099	−	0.641429i	0.171903	−	0.985114i	$-0.445009\pi$
$271$	5.99220e9	−	3.45960e9i	1.11099	−	0.641429i	0.939085	+	0.343685i	$0.111675\pi$
$272$			2.82786e8i			0.0516633i
$273$	1.46957e9	−	4.33009e9i	0.264569	−	0.779554i
$274$	−4.74952e8			−0.0842650
$275$	3.05880e9	+	5.29801e9i	0.534836	+	0.926364i
$276$	3.20482e9	+	1.85030e9i	0.552289	+	0.318864i
$277$	−2.83448e9	+	4.90947e9i	−0.481454	+	0.833903i	−0.999773	−	0.0212843i	$-0.993224\pi$
$277$	−2.83448e9	+	4.90947e9i	−0.481454	+	0.833903i	0.518319	+	0.855187i	$0.326558\pi$
$278$	−7.55072e7	+	4.35941e7i	−0.0126418	+	0.00729875i
$279$			2.11378e9i			0.348854i
$280$	1.52545e9	−	1.33795e9i	0.248180	−	0.217675i
$281$	−2.39953e7			−0.00384858			−0.00192429	−	0.999998i	$-0.500613\pi$
$281$	−2.39953e7			−0.00384858			−0.00192429	+	0.999998i	$0.500613\pi$
$282$	−5.10239e8	−	8.83760e8i	−0.0806821	−	0.139746i
$283$	−7.65100e9	−	4.41731e9i	−1.19281	−	0.688671i	−0.233869	−	0.972268i	$-0.575139\pi$
$283$	−7.65100e9	−	4.41731e9i	−1.19281	−	0.688671i	−0.958943	+	0.283597i	$0.908472\pi$
$284$	3.28272e9	−	5.68583e9i	0.504615	−	0.874019i
$285$	−1.34392e9	+	7.75911e8i	−0.203701	+	0.117607i
$286$			5.29315e9i			0.791133i
$287$	1.15807e9	+	5.82013e9i	0.170690	+	0.857838i
$288$	−2.24850e9			−0.326831
$289$	−3.44968e9	−	5.97502e9i	−0.494524	−	0.856541i
$290$	−1.45611e9	−	8.40683e8i	−0.205874	−	0.118861i
$291$	−3.90311e9	+	6.76039e9i	−0.544301	+	0.942757i
$292$	−5.00653e9	+	2.89052e9i	−0.688661	+	0.397598i
$293$			8.07016e9i			1.09499i	0.836808	+	0.547497i	$0.184419\pi$
$293$			8.07016e9i			1.09499i	−0.836808	+	0.547497i	$0.815581\pi$
$294$	−6.99598e8	−	1.68839e9i	−0.0936395	−	0.225987i
$295$	7.71100e8			0.101818
$296$	1.45737e9	+	2.52424e9i	0.189847	+	0.328824i
$297$	1.69822e9	+	9.80468e8i	0.218257	+	0.126011i
$298$	−3.02412e8	+	5.23793e8i	−0.0383472	+	0.0664193i
$299$	1.32868e10	−	7.67115e9i	1.66240	−	0.959789i
$300$			3.13420e9i			0.386938i
$301$	3.23365e9	−	6.43421e8i	0.393937	−	0.0783844i
$302$	3.78801e9			0.455390
$303$	−3.33714e9	−	5.78009e9i	−0.395916	−	0.685747i
$304$	−3.47589e9	−	2.00681e9i	−0.406979	−	0.234969i
$305$	−2.23126e8	+	3.86466e8i	−0.0257841	+	0.0446593i
$306$	−1.12223e8	+	6.47919e7i	−0.0127996	+	0.00738983i
$307$			1.00925e10i			1.13617i	0.822968	+	0.568087i	$0.192316\pi$
$307$			1.00925e10i			1.13617i	−0.822968	+	0.568087i	$0.807684\pi$
$308$	−6.37583e9	−	7.26934e9i	−0.708491	−	0.807778i
$309$	−2.70478e9			−0.296686
$310$	8.76314e8	+	1.51782e9i	0.0948884	+	0.164351i
$311$	−6.13405e9	−	3.54149e9i	−0.655701	−	0.378569i	0.134936	−	0.990854i	$-0.456917\pi$
$311$	−6.13405e9	−	3.54149e9i	−0.655701	−	0.378569i	−0.790637	+	0.612285i	$0.790250\pi$
$312$	−3.00847e9	+	5.21081e9i	−0.317487	+	0.549904i
$313$	−6.76423e9	+	3.90533e9i	−0.704759	+	0.406893i	−0.809118	−	0.587647i	$-0.800054\pi$
$313$	−6.76423e9	+	3.90533e9i	−0.704759	+	0.406893i	0.104358	+	0.994540i	$0.466721\pi$
$314$		−	7.31116e9i		−	0.752086i
$315$	−1.33007e9	−	4.51407e8i	−0.135093	−	0.0458486i
$316$	5.19786e9			0.521287
$317$	7.52195e9	+	1.30284e10i	0.744892	+	1.29019i	0.950245	+	0.311504i	$0.100833\pi$
$317$	7.52195e9	+	1.30284e10i	0.744892	+	1.29019i	−0.205353	+	0.978688i	$0.565834\pi$
$318$	4.22799e9	+	2.44103e9i	0.413452	+	0.238707i
$319$	−8.88882e9	+	1.53959e10i	−0.858384	+	1.48676i
$320$	3.04132e8	−	1.75591e8i	0.0290043	−	0.0167456i
$321$			4.18250e9i			0.393927i
$322$	1.97070e9	−	5.80667e9i	0.183314	−	0.540136i
$323$	−1.08428e9			−0.0996164
$324$	5.02317e8	+	8.70039e8i	0.0455825	+	0.0789512i
$325$	1.12532e10	+	6.49703e9i	1.00865	+	0.582346i
$326$	1.84897e9	−	3.20251e9i	0.163704	−	0.283544i
$327$	1.42539e9	−	8.22952e8i	0.124665	−	0.0719753i
$328$		−	7.80853e9i		−	0.674643i
$329$	5.81036e9	−	5.09619e9i	0.495929	−	0.434972i
$330$	1.62590e9			0.137100
$331$	−4.19026e9	−	7.25774e9i	−0.349083	−	0.604629i	0.637004	−	0.770861i	$-0.280174\pi$
$331$	−4.19026e9	−	7.25774e9i	−0.349083	−	0.604629i	−0.986087	+	0.166231i	$0.946840\pi$
$332$	−1.08898e10	−	6.28722e9i	−0.896327	−	0.517495i
$333$	1.00884e9	−	1.74736e9i	0.0820435	−	0.142103i
$334$	−1.75161e8	+	1.01129e8i	−0.0140751	+	0.00812628i
$335$		−	4.57629e9i		−	0.363358i
$336$	−7.08947e8	−	3.56296e9i	−0.0556233	−	0.279547i
$337$	4.79019e9			0.371392			0.185696	−	0.982607i	$-0.440546\pi$
$337$	4.79019e9			0.371392			0.185696	+	0.982607i	$0.440546\pi$
$338$	2.85648e9	+	4.94757e9i	0.218859	+	0.379075i
$339$	−2.71480e9	−	1.56739e9i	−0.205560	−	0.118680i
$340$	2.45539e8	−	4.25285e8i	0.0183740	−	0.0318247i
$341$	1.60484e10	−	9.26556e9i	1.18690	−	0.685258i
$342$		−	1.83920e9i		−	0.134439i
$343$	1.15072e10	−	7.69194e9i	0.831366	−	0.555725i
$344$	−4.33840e9			−0.309810
$345$	−2.35635e9	−	4.08132e9i	−0.166327	−	0.288087i
$346$	−9.26530e9	−	5.34932e9i	−0.646480	−	0.373245i
$347$	2.20690e9	−	3.82247e9i	0.152218	−	0.263649i	−0.779825	−	0.625998i	$-0.784692\pi$
$347$	2.20690e9	−	3.82247e9i	0.152218	−	0.263649i	0.932042	+	0.362349i	$0.118025\pi$
$348$	−7.88769e9	+	4.55396e9i	−0.537815	+	0.310507i
$349$		−	1.02728e10i		−	0.692448i	−0.938152	−	0.346224i	$-0.887464\pi$
$349$		−	1.02728e10i		−	0.692448i	0.938152	−	0.346224i	$-0.112536\pi$
$350$	5.09357e9	−	1.01350e9i	0.339430	−	0.0675387i
$351$	4.16511e9			0.274409
$352$	9.85610e9	+	1.70713e10i	0.641999	+	1.11197i
$353$	−1.27695e10	−	7.37247e9i	−0.822385	−	0.474804i	0.0288534	−	0.999584i	$-0.490814\pi$
$353$	−1.27695e10	−	7.37247e9i	−0.822385	−	0.474804i	−0.851238	+	0.524780i	$0.824148\pi$
$354$	−4.56949e8	+	7.91459e8i	−0.0290974	+	0.0503982i
$355$	−7.24088e9	+	4.18052e9i	−0.455909	+	0.263219i
$356$		−	1.44132e10i		−	0.897346i
$357$	−6.47130e8	−	7.37819e8i	−0.0398400	−	0.0454231i
$358$	−1.07087e10			−0.651936
$359$	3.32597e9	+	5.76074e9i	0.200235	+	0.346817i	0.948604	−	0.316465i	$-0.102496\pi$
$359$	3.32597e9	+	5.76074e9i	0.200235	+	0.346817i	−0.748369	+	0.663283i	$0.769163\pi$
$360$	1.60061e9	+	9.24111e8i	0.0952960	+	0.0550192i
$361$	−7.97128e8	+	1.38067e9i	−0.0469352	+	0.0812942i
$362$	3.60100e9	−	2.07904e9i	0.209696	−	0.121068i
$363$		−	7.16658e9i		−	0.412748i
$364$	−1.94484e10	−	6.60049e9i	−1.10784	−	0.375985i
$365$	7.36212e9			0.414793
$366$	−2.64446e8	−	4.58035e8i	−0.0147371	−	0.0255255i
$367$	1.59310e10	+	9.19776e9i	0.878169	+	0.507011i	0.870054	−	0.492956i	$-0.164084\pi$
$367$	1.59310e10	+	9.19776e9i	0.878169	+	0.507011i	0.00811490	+	0.999967i	$0.497417\pi$
$368$	6.09444e9	−	1.05559e10i	0.332309	−	0.575576i
$369$	−4.68114e9	+	2.70266e9i	−0.252491	+	0.145776i
$370$		−	1.67294e9i		−	0.0892634i
$371$	−1.18829e10	+	3.50129e10i	−0.627227	+	1.84813i
$372$	9.49394e9			0.495764
$373$	−1.32605e10	−	2.29678e10i	−0.685052	−	1.18655i	−0.973420	−	0.229026i	$-0.926446\pi$
$373$	−1.32605e10	−	2.29678e10i	−0.685052	−	1.18655i	0.288368	−	0.957520i	$-0.406887\pi$
$374$	9.83836e8	+	5.68018e8i	0.0502847	+	0.0290319i
$375$	4.43891e9	−	7.68842e9i	0.224466	−	0.388787i
$376$	−8.80719e9	+	5.08483e9i	−0.440642	+	0.254405i
$377$			3.77605e10i			1.86927i
$378$	1.25152e9	−	1.09769e9i	0.0613014	−	0.0537666i
$379$	1.90327e10			0.922454			0.461227	−	0.887282i	$-0.347409\pi$
$379$	1.90327e10			0.922454			0.461227	+	0.887282i	$0.347409\pi$
$380$	3.48496e9	+	6.03613e9i	0.167134	+	0.289484i
$381$	2.42073e9	+	1.39761e9i	0.114881	+	0.0663263i
$382$	−2.03687e9	+	3.52797e9i	−0.0956556	+	0.165680i
$383$	−1.30082e10	+	7.51027e9i	−0.604535	+	0.349028i	−0.770823	−	0.637049i	$-0.780155\pi$
$383$	−1.30082e10	+	7.51027e9i	−0.604535	+	0.349028i	0.166289	+	0.986077i	$0.446822\pi$
$384$			1.27248e10i			0.585231i
$385$	2.40304e9	+	1.20770e10i	0.109375	+	0.549688i
$386$	−1.25913e10			−0.567182
$387$	1.50159e9	+	2.60083e9i	0.0669433	+	0.115949i
$388$	3.03639e10	+	1.75306e10i	1.33977	+	0.773518i
$389$	−1.19641e10	+	2.07225e10i	−0.522496	+	0.904989i	0.477162	+	0.878815i	$0.341666\pi$
$389$	−1.19641e10	+	2.07225e10i	−0.522496	+	0.904989i	−0.999657	+	0.0261734i	$0.991668\pi$
$390$	2.99079e9	−	1.72674e9i	0.129279	−	0.0746393i
$391$		−	3.29283e9i		−	0.140884i
$392$	−1.68258e10	+	6.97190e9i	−0.712575	+	0.295262i
$393$	−9.78469e9			−0.410182
$394$	−2.40053e9	−	4.15784e9i	−0.0996145	−	0.172537i
$395$	−5.73261e9	−	3.30973e9i	−0.235486	−	0.135958i
$396$	4.40372e9	−	7.62747e9i	0.179077	−	0.310170i
$397$	1.10835e10	−	6.39904e9i	0.446183	−	0.257604i	−0.260034	−	0.965600i	$-0.583734\pi$
$397$	1.10835e10	−	6.39904e9i	0.446183	−	0.257604i	0.706217	+	0.707996i	$0.250400\pi$
$398$		−	1.19148e10i		−	0.474848i
$399$	1.36614e10	−	2.71830e9i	0.539018	−	0.107252i
$400$	1.03233e10			0.403253
$401$	−8.49974e9	−	1.47220e10i	−0.328721	−	0.569362i	0.653537	−	0.756895i	$-0.273284\pi$
$401$	−8.49974e9	−	1.47220e10i	−0.328721	−	0.569362i	−0.982258	+	0.187532i	$0.939951\pi$
$402$	4.69712e9	+	2.71188e9i	0.179857	+	0.103840i
$403$	1.96804e10	−	3.40875e10i	0.746130	−	1.29234i
$404$	−2.59610e10	+	1.49886e10i	−0.974530	+	0.562645i
$405$		−	1.27940e9i		−	0.0475538i
$406$	9.95154e9	+	1.13461e10i	0.366257	+	0.417584i
$407$	−1.76886e10			−0.644637
$408$	6.45689e8	+	1.11837e9i	0.0233014	+	0.0403592i
$409$	−4.31951e10	−	2.49387e10i	−1.54362	−	0.891212i	−0.998606	−	0.0527885i	$-0.983189\pi$
$409$	−4.31951e10	−	2.49387e10i	−1.54362	−	0.891212i	−0.545019	−	0.838424i	$-0.683478\pi$
$410$	−2.24089e9	+	3.88133e9i	−0.0793021	+	0.137355i
$411$	2.83749e9	−	1.63823e9i	0.0994414	−	0.0574125i
$412$			1.21484e10i			0.421627i
$413$	−6.55424e9	−	2.22441e9i	−0.225280	−	0.0764566i
$414$	5.58543e9			0.190132
$415$	8.00674e9	+	1.38681e10i	0.269937	+	0.467545i
$416$	3.62601e10	+	2.09348e10i	1.21075	+	0.699028i
$417$	3.00733e8	−	5.20885e8i	0.00994575	−	0.0172265i
$418$	−1.39637e10	+	8.06195e9i	−0.457399	+	0.264080i
$419$		−	3.21565e10i		−	1.04331i	−0.853157	−	0.521655i	$-0.825315\pi$
$419$		−	3.21565e10i		−	1.04331i	0.853157	−	0.521655i	$-0.174685\pi$
$420$	−2.02747e9	+	5.97396e9i	−0.0651565	+	0.191984i
$421$	−5.71409e10			−1.81894			−0.909471	−	0.415767i	$-0.863513\pi$
$421$	−5.71409e10			−1.81894			−0.909471	+	0.415767i	$0.863513\pi$
$422$	1.16331e10	+	2.01491e10i	0.366813	+	0.635338i
$423$	6.09661e9	+	3.51988e9i	0.190426	+	0.109943i
$424$	2.43263e10	−	4.21344e10i	0.752684	−	1.30369i
$425$	2.41520e9	−	1.39442e9i	0.0740283	−	0.0427402i
$426$		−	9.90941e9i		−	0.300891i
$427$	3.01139e9	−	2.64125e9i	0.0905848	−	0.0794507i
$428$	1.87855e10			0.559819
$429$	−1.82574e10	−	3.16227e10i	−0.539025	−	0.933618i
$430$	2.15646e9	+	1.24503e9i	0.0630765	+	0.0364172i
$431$	1.48286e10	−	2.56839e10i	0.429726	−	0.744307i	−0.567123	−	0.823633i	$-0.691944\pi$
$431$	1.48286e10	−	2.56839e10i	0.429726	−	0.744307i	0.996849	+	0.0793263i	$0.0252769\pi$
$432$	2.86570e9	−	1.65451e9i	0.0822801	−	0.0475045i
$433$			3.29153e10i			0.936368i	0.883631	+	0.468184i	$0.155092\pi$
$433$			3.29153e10i			0.936368i	−0.883631	+	0.468184i	$0.844908\pi$
$434$	−3.07005e9	−	1.54292e10i	−0.0865338	−	0.434894i
$435$	1.15989e10			0.323936
$436$	−3.69625e9	−	6.40208e9i	−0.102286	−	0.177164i
$437$	4.04741e10	+	2.33678e10i	1.10982	+	0.640754i
$438$	−4.36275e9	+	7.55650e9i	−0.118540	+	0.205317i
$439$	5.76158e10	−	3.32645e10i	1.55126	−	0.895619i	0.553218	−	0.833037i	$-0.313400\pi$
$439$	5.76158e10	−	3.32645e10i	1.55126	−	0.895619i	0.998040	−	0.0625821i	$-0.0199335\pi$
$440$		−	1.62030e10i		−	0.432300i
$441$	1.00032e10	+	7.67379e9i	0.264476	+	0.202888i
$442$	2.41299e9			0.0632216
$443$	−3.44935e10	−	5.97444e10i	−0.895616	−	1.55125i	−0.833041	−	0.553212i	$-0.813402\pi$
$443$	−3.44935e10	−	5.97444e10i	−0.895616	−	1.55125i	−0.0625754	−	0.998040i	$-0.519931\pi$
$444$	−7.84816e9	−	4.53114e9i	−0.201946	−	0.116594i
$445$	−9.17756e9	+	1.58960e10i	−0.234038	+	0.405366i
$446$	−1.09746e9	+	6.33619e8i	−0.0277363	+	0.0160136i
$447$		−	4.17237e9i		−	0.104509i
$448$	−3.09161e9	+	6.15158e8i	−0.0767489	+	0.0152713i
$449$	−4.11572e10			−1.01265			−0.506326	−	0.862342i	$-0.668997\pi$
$449$	−4.11572e10			−1.01265			−0.506326	+	0.862342i	$0.668997\pi$
$450$	2.36527e9	+	4.09677e9i	0.0576807	+	0.0999059i
$451$	4.10386e10	+	2.36937e10i	0.991943	+	0.572699i
$452$	−7.03986e9	+	1.21934e10i	−0.168659	+	0.292126i
$453$	−2.26306e10	+	1.30658e10i	−0.537407	+	0.310272i
$454$		−	5.12501e9i		−	0.120635i
$455$	1.72463e10	+	1.96632e10i	0.402394	+	0.458785i
$456$	−1.83287e10			−0.423908
$457$	−1.63130e10	−	2.82550e10i	−0.373998	−	0.647784i	0.616178	−	0.787607i	$-0.288680\pi$
$457$	−1.63130e10	−	2.82550e10i	−0.373998	−	0.647784i	−0.990177	+	0.139823i	$0.955347\pi$
$458$	2.00868e10	+	1.15971e10i	0.456507	+	0.263565i
$459$	4.46966e8	−	7.74168e8i	0.0100699	−	0.0174415i
$460$	−1.83310e10	+	1.05834e10i	−0.409407	+	0.236371i
$461$		−	5.26181e9i		−	0.116502i	−0.998302	−	0.0582508i	$-0.981448\pi$
$461$		−	5.26181e9i		−	0.116502i	0.998302	−	0.0582508i	$-0.0185523\pi$
$462$	−1.38199e10	−	4.69026e9i	−0.303345	−	0.102951i
$463$	−5.12482e10			−1.11520			−0.557602	−	0.830108i	$-0.688278\pi$
$463$	−5.12482e10			−1.11520			−0.557602	+	0.830108i	$0.688278\pi$
$464$	1.49996e10	+	2.59801e10i	0.323600	+	0.560491i
$465$	−1.04707e10	−	6.04524e9i	−0.223956	−	0.129301i
$466$	8.66795e9	−	1.50133e10i	0.183811	−	0.318371i
$467$	4.94910e10	−	2.85736e10i	1.04054	−	0.600756i	0.120554	−	0.992707i	$-0.461533\pi$
$467$	4.94910e10	−	2.85736e10i	1.04054	−	0.600756i	0.919986	+	0.391951i	$0.128200\pi$
$468$		−	1.87074e10i		−	0.389968i
$469$	−1.32013e10	+	3.88978e10i	−0.272852	+	0.803959i
$470$	5.83697e9			0.119618
$471$	2.52180e10	+	4.36788e10i	0.512421	+	0.887539i
$472$	7.88735e9	+	4.55376e9i	0.158914	+	0.0917492i
$473$	1.31641e10	−	2.28010e10i	0.262995	−	0.455521i
$474$	6.79422e9	−	3.92264e9i	0.134594	−	0.0777080i
$475$			3.95823e10i			0.777547i
$476$	−3.31387e9	+	2.90655e9i	−0.0645518	+	0.0566174i
$477$	−3.36789e10			−0.650555
$478$	2.11322e10	+	3.66021e10i	0.404794	+	0.701123i
$479$	−1.22340e9	−	7.06331e8i	−0.0232395	−	0.0134173i	0.488335	−	0.872656i	$-0.337604\pi$
$479$	−1.22340e9	−	7.06331e8i	−0.0232395	−	0.0134173i	−0.511575	+	0.859239i	$0.670938\pi$
$480$	6.43053e9	−	1.11380e10i	0.121138	−	0.209818i
$481$	−3.25376e10	+	1.87856e10i	−0.607863	+	0.350950i
$482$		−	5.29340e9i		−	0.0980723i
$483$	8.25515e9	+	4.14880e10i	0.151683	+	0.762314i
$484$	−3.21883e10			−0.586566
$485$	−2.23251e10	−	3.86683e10i	−0.403485	−	0.698856i
$486$	1.31318e9	+	7.58162e8i	0.0235384	+	0.0135899i
$487$	−2.05546e10	+	3.56016e10i	−0.365420	+	0.632926i	−0.988844	−	0.148958i	$-0.952408\pi$
$487$	−2.05546e10	+	3.56016e10i	−0.365420	+	0.632926i	0.623423	+	0.781885i	$0.285741\pi$
$488$	−4.56458e9	+	2.63536e9i	−0.0804862	+	0.0464688i
$489$			2.55102e10i			0.446148i
$490$	1.03643e10	+	1.36317e9i	0.179785	+	0.0236465i
$491$	7.29089e9			0.125445			0.0627226	−	0.998031i	$-0.480022\pi$
$491$	7.29089e9			0.125445			0.0627226	+	0.998031i	$0.480022\pi$
$492$	1.21388e10	+	2.10251e10i	0.207165	+	0.358821i
$493$	7.01853e9	+	4.05215e9i	0.118811	+	0.0685958i
$494$	−1.71239e10	+	2.96595e10i	−0.287538	+	0.498030i
$495$	−9.71354e9	+	5.60811e9i	−0.161792	+	0.0934106i
$496$		−	3.12707e10i		−	0.516667i
$497$	7.36061e10	−	1.46459e10i	1.20639	−	0.240044i
$498$	−1.89790e10			−0.308571
$499$	1.66296e10	+	2.88034e10i	0.268214	+	0.464560i	0.968401	−	0.249400i	$-0.0802334\pi$
$499$	1.66296e10	+	2.88034e10i	0.268214	+	0.464560i	−0.700187	+	0.713960i	$0.746900\pi$
$500$	−3.45321e10	−	1.99371e10i	−0.552514	−	0.318994i
$501$	6.97641e8	−	1.20835e9i	0.0110734	−	0.0191797i
$502$	−1.85123e10	+	1.06881e10i	−0.291504	+	0.168300i
$503$			2.23813e10i			0.349633i	0.984601	+	0.174817i	$0.0559332\pi$
$503$			2.23813e10i			0.349633i	−0.984601	+	0.174817i	$0.944067\pi$
$504$	−1.09391e10	−	1.24721e10i	−0.169535	−	0.193294i
$505$	3.81757e10			0.586978
$506$	−2.44832e10	−	4.24061e10i	−0.373479	−	0.646884i
$507$	−3.41308e10	−	1.97054e10i	−0.516552	−	0.298231i
$508$	6.27729e9	−	1.08726e10i	0.0942578	−	0.163259i
$509$	−5.60138e10	+	3.23396e10i	−0.834495	+	0.481796i	−0.855389	−	0.517986i	$-0.826682\pi$
$509$	−5.60138e10	+	3.23396e10i	−0.834495	+	0.481796i	0.0208945	+	0.999782i	$0.493349\pi$
$510$		−	7.41197e8i		−	0.0109560i
$511$	−6.25770e10	−	2.12377e10i	−0.917764	−	0.311475i
$512$	5.94313e10			0.864839
$513$	6.34385e9	+	1.09879e10i	0.0915974	+	0.158651i
$514$	−4.46041e10	−	2.57522e10i	−0.639032	−	0.368945i
$515$	7.73543e9	−	1.33982e10i	0.109965	−	0.190466i
$516$	1.16815e10	−	6.74431e9i	0.164778	−	0.0951346i
$517$		−	6.17162e10i		−	0.863848i
$518$	−4.82597e9	+	1.42197e10i	−0.0670294	+	0.197503i
$519$	7.38045e10			1.01722
$520$	−1.72079e10	−	2.98050e10i	−0.235350	−	0.407639i
$521$	5.03381e10	+	2.90627e10i	0.683197	+	0.394444i	0.801059	−	0.598586i	$-0.204270\pi$
$521$	5.03381e10	+	2.90627e10i	0.683197	+	0.394444i	−0.117861	+	0.993030i	$0.537604\pi$
$522$	−6.87342e9	+	1.19051e10i	−0.0925744	+	0.160344i
$523$	9.86806e10	−	5.69733e10i	1.31894	−	0.761491i	0.335382	−	0.942082i	$-0.391134\pi$
$523$	9.86806e10	−	5.69733e10i	1.31894	−	0.761491i	0.983558	+	0.180591i	$0.0578012\pi$
$524$			4.39474e10i			0.582919i
$525$	−2.69346e10	+	2.36239e10i	−0.354546	+	0.310967i
$526$	4.76358e10			0.622287
$527$	−4.22389e9	−	7.31600e9i	−0.0547609	−	0.0948486i
$528$	−2.51230e10	−	1.45048e10i	−0.323248	−	0.186627i
$529$	−3.18096e10	+	5.50959e10i	−0.406196	+	0.703552i
$530$	−2.41834e10	+	1.39623e10i	−0.306488	+	0.176951i
$531$		−	6.30451e9i		−	0.0793001i
$532$	−1.22091e10	−	6.13594e10i	−0.152418	−	0.766010i
$533$	1.00653e11			1.24714
$534$	−1.08771e10	−	1.88397e10i	−0.133767	−	0.231691i
$535$	−2.07181e10	−	1.19616e10i	−0.252892	−	0.146007i
$536$	2.70255e10	−	4.68095e10i	0.327427	−	0.567120i
$537$	6.39767e10	−	3.69370e10i	0.769351	−	0.444185i
$538$			5.58826e10i			0.667033i
$539$	1.44133e10	−	1.09585e11i	0.170769	−	1.29836i
$540$	−5.74634e9			−0.0675798
$541$	−6.99025e9	−	1.21075e10i	−0.0816025	−	0.141340i	0.822336	−	0.569002i	$-0.192670\pi$
$541$	−6.99025e9	−	1.21075e10i	−0.0816025	−	0.141340i	−0.903938	+	0.427663i	$0.859337\pi$
$542$	−4.06216e10	−	2.34529e10i	−0.470717	−	0.271768i
$543$	−1.43422e10	+	2.48415e10i	−0.164975	+	0.285745i
$544$	7.78228e9	−	4.49310e9i	0.0888610	−	0.0513039i
$545$			9.41430e9i			0.106709i
$546$	−3.04025e10	+	6.04938e9i	−0.342088	+	0.0680676i
$547$	6.43329e10			0.718594			0.359297	−	0.933223i	$-0.383017\pi$
$547$	6.43329e10			0.718594			0.359297	+	0.933223i	$0.383017\pi$
$548$	−7.35800e9	−	1.27444e10i	−0.0815902	−	0.141318i
$549$	3.15975e9	+	1.82428e9i	0.0347827	+	0.0200818i
$550$	2.07359e10	−	3.59156e10i	0.226606	−	0.392493i
$551$	−9.96149e10	+	5.75127e10i	−1.08073	+	0.623961i
$552$		−	5.56620e10i		−	0.599519i
$553$	3.91787e10	+	4.46692e10i	0.418938	+	0.477648i
$554$	3.84303e10			0.407976
$555$	5.77038e9	+	9.99459e9i	0.0608181	+	0.105340i
$556$	−2.33953e9	−	1.35073e9i	−0.0244810	−	0.0141341i
$557$	−2.74849e10	+	4.76053e10i	−0.285544	+	0.494577i	−0.972741	−	0.231894i	$-0.925508\pi$
$557$	−2.74849e10	+	4.76053e10i	−0.285544	+	0.494577i	0.687197	+	0.726471i	$0.258841\pi$
$558$	1.24097e10	−	7.16474e9i	0.128004	−	0.0739033i
$559$		−	5.59224e10i		−	0.572715i
$560$	1.96767e10	+	6.67800e9i	0.200079	+	0.0679038i
$561$	−7.83693e9			−0.0791215
$562$	8.13328e7	+	1.40873e8i	0.000815305	+	0.00141215i
$563$	−7.43985e10	−	4.29540e10i	−0.740509	−	0.427533i	0.0817454	−	0.996653i	$-0.473951\pi$
$563$	−7.43985e10	−	4.29540e10i	−0.740509	−	0.427533i	−0.822254	+	0.569120i	$0.807284\pi$
$564$	1.58094e10	−	2.73826e10i	0.156242	−	0.270619i
$565$	1.55282e10	−	8.96522e9i	0.152380	−	0.0879766i
$566$			5.98905e10i			0.583569i
$567$	−3.69071e9	+	1.08747e10i	−0.0357090	+	0.105217i
$568$	−9.87530e10			−0.948761
$569$	1.88137e10	+	3.25863e10i	0.179484	+	0.310875i	0.941704	−	0.336443i	$-0.109224\pi$
$569$	1.88137e10	+	3.25863e10i	0.179484	+	0.310875i	−0.762220	+	0.647318i	$0.775891\pi$
$570$	9.11051e9	+	5.25995e9i	0.0863064	+	0.0498290i
$571$	−1.88677e10	+	3.26798e10i	−0.177490	+	0.307422i	−0.941020	−	0.338350i	$-0.890131\pi$
$571$	−1.88677e10	+	3.26798e10i	−0.177490	+	0.307422i	0.763530	+	0.645772i	$0.223464\pi$
$572$	−1.42032e11	+	8.20020e10i	−1.32679	+	0.766020i
$573$		−	2.81027e10i		−	0.260693i
$574$	3.02438e10	−	2.65264e10i	0.278605	−	0.244360i
$575$	−1.20207e11			−1.09966
$576$	−1.43563e9	−	2.48658e9i	−0.0130423	−	0.0225898i
$577$	−8.38562e10	−	4.84144e10i	−0.756540	−	0.436788i	0.0715123	−	0.997440i	$-0.477217\pi$
$577$	−8.38562e10	−	4.84144e10i	−0.756540	−	0.436788i	−0.828052	+	0.560651i	$0.810551\pi$
$578$	−2.33856e10	+	4.05051e10i	−0.209526	+	0.362910i
$579$	7.52239e10	−	4.34306e10i	0.669332	−	0.386439i
$580$		−	5.20958e10i		−	0.460352i
$581$	−2.80505e10	−	1.40974e11i	−0.246171	−	1.23718i
$582$	5.29189e10			0.461232
$583$	1.47628e11	+	2.55699e11i	1.27789	+	2.21338i
$584$	7.53049e10	+	4.34773e10i	0.647399	+	0.373776i
$585$	−1.19119e10	+	2.06320e10i	−0.101708	+	0.176164i
$586$	4.73787e10	−	2.73541e10i	0.401784	−	0.231970i
$587$			1.01539e11i			0.855223i	0.903963	+	0.427612i	$0.140645\pi$
$587$			1.01539e11i			0.855223i	−0.903963	+	0.427612i	$0.859355\pi$
$588$	3.44664e10	−	4.49291e10i	0.288328	−	0.375853i
$589$	1.19901e11			0.996231
$590$	−2.61367e9	−	4.52701e9i	−0.0215696	−	0.0373597i
$591$	2.86828e10	+	1.65600e10i	0.235111	+	0.135741i
$592$	−1.49245e10	+	2.58499e10i	−0.121510	+	0.210461i
$593$	−1.82032e10	+	1.05096e10i	−0.147207	+	0.0849899i	−0.571794	−	0.820397i	$-0.693752\pi$
$593$	−1.82032e10	+	1.05096e10i	−0.147207	+	0.0849899i	0.424587	+	0.905387i	$0.360419\pi$
$594$		−	1.32933e10i		−	0.106780i
$595$	5.50554e9	−	1.09547e9i	0.0439271	−	0.00874046i
$596$	−1.87400e10			−0.148520
$597$	4.10971e10	+	7.11822e10i	0.323529	+	0.560369i
$598$	−9.00724e10	−	5.20033e10i	−0.704347	−	0.406655i
$599$	−1.08341e11	+	1.87653e11i	−0.841563	+	1.45763i	0.0470100	+	0.998894i	$0.485031\pi$
$599$	−1.08341e11	+	1.87653e11i	−0.841563	+	1.45763i	−0.888573	+	0.458735i	$0.848303\pi$
$600$	4.08267e10	−	2.35713e10i	0.315020	−	0.181877i
$601$		−	3.99391e10i		−	0.306126i	−0.988216	−	0.153063i	$-0.951086\pi$
$601$		−	3.99391e10i		−	0.306126i	0.988216	−	0.153063i	$-0.0489138\pi$
$602$	−1.47380e10	−	1.68034e10i	−0.112215	−	0.127941i
$603$	−3.74158e10			−0.282999
$604$	5.86843e10	+	1.01644e11i	0.440934	+	0.763721i
$605$	3.54998e10	+	2.04958e10i	0.264975	+	0.152983i
$606$	−2.26227e10	+	3.91836e10i	−0.167747	+	0.290546i
$607$	−4.68557e10	+	2.70521e10i	−0.345150	+	0.199272i	−0.662547	−	0.749020i	$-0.730524\pi$
$607$	−4.68557e10	+	2.70521e10i	−0.345150	+	0.199272i	0.317397	+	0.948293i	$0.397191\pi$
$608$			1.27542e11i			0.933340i
$609$	−9.85888e10	−	3.34596e10i	−0.716735	−	0.243249i
$610$	3.02518e9			0.0218490
$611$	−6.55439e10	−	1.13525e11i	−0.470292	−	0.814570i
$612$	−3.47713e9	−	2.00752e9i	−0.0247865	−	0.0143105i
$613$	−4.75233e10	+	8.23128e10i	−0.336562	+	0.582942i	−0.983784	−	0.179359i	$-0.942597\pi$
$613$	−4.75233e10	+	8.23128e10i	−0.336562	+	0.582942i	0.647222	+	0.762302i	$0.275931\pi$
$614$	5.92515e10	−	3.42089e10i	0.416894	−	0.240694i
$615$		−	3.09175e10i		−	0.216124i
$616$	−4.67412e10	+	1.37723e11i	−0.324621	+	0.956498i
$617$	9.30288e10			0.641914			0.320957	−	0.947094i	$-0.395996\pi$
$617$	9.30288e10			0.641914			0.320957	+	0.947094i	$0.395996\pi$
$618$	9.16793e9	+	1.58793e10i	0.0628518	+	0.108862i
$619$	−6.05185e10	−	3.49403e10i	−0.412216	−	0.237993i	0.279525	−	0.960138i	$-0.409823\pi$
$619$	−6.05185e10	−	3.49403e10i	−0.412216	−	0.237993i	−0.691742	+	0.722145i	$0.743156\pi$
$620$	−2.71519e10	+	4.70285e10i	−0.183753	+	0.318269i
$621$	−3.33688e10	+	1.92655e10i	−0.224375	+	0.129543i
$622$			4.80161e10i			0.320793i
$623$	1.23863e11	−	1.08639e11i	0.822226	−	0.721163i
$624$	−6.16175e10			−0.406411
$625$	−3.69293e10	−	6.39634e10i	−0.242020	−	0.419191i
$626$	4.58552e10	+	2.64745e10i	0.298601	+	0.172397i
$627$	5.56153e10	−	9.63285e10i	0.359852	−	0.623282i
$628$	1.96181e11	−	1.13265e11i	1.26130	−	0.728213i
$629$			8.06369e9i			0.0515147i
$630$	1.85819e9	+	9.33873e9i	0.0117958	+	0.0592824i
$631$	−8.99980e10			−0.567695			−0.283848	−	0.958869i	$-0.591611\pi$
$631$	−8.99980e10			−0.567695			−0.283848	+	0.958869i	$0.591611\pi$
$632$	−3.90914e10	−	6.77083e10i	−0.245027	−	0.424399i
$633$	−1.38998e11	−	8.02506e10i	−0.865753	−	0.499843i
$634$	5.09919e10	−	8.83205e10i	0.315605	−	0.546644i
$635$	−1.38462e10	+	7.99409e9i	−0.0851599	+	0.0491671i
$636$			1.51267e11i			0.924517i
$637$	−8.98684e10	−	2.16886e11i	−0.545820	−	1.31726i
$638$	1.20516e11			0.727381
$639$	3.41800e10	+	5.92015e10i	0.205007	+	0.355082i
$640$	−6.30327e10	−	3.63919e10i	−0.375704	−	0.216913i
$641$	1.01466e11	−	1.75744e11i	0.601019	−	1.04100i	−0.391648	−	0.920115i	$-0.628095\pi$
$641$	1.01466e11	−	1.75744e11i	0.601019	−	1.04100i	0.992667	−	0.120880i	$-0.0385717\pi$
$642$	2.45548e10	−	1.41767e10i	0.144543	−	0.0834519i
$643$		−	1.99065e11i		−	1.16453i	−0.812999	−	0.582265i	$-0.802167\pi$
$643$		−	1.99065e11i		−	1.16453i	0.812999	−	0.582265i	$-0.197833\pi$
$644$	1.86341e11	−	3.70776e10i	1.08334	−	0.215560i
$645$	−1.71777e10			−0.0992489
$646$	3.67520e9	+	6.36564e9i	0.0211033	+	0.0365520i
$647$	−9.44003e10	−	5.45021e10i	−0.538712	−	0.311025i	0.205845	−	0.978585i	$-0.434006\pi$
$647$	−9.44003e10	−	5.45021e10i	−0.538712	−	0.311025i	−0.744557	+	0.667559i	$0.767339\pi$
$648$	7.55553e9	−	1.30866e10i	0.0428514	−	0.0742208i
$649$	−4.78656e10	+	2.76352e10i	−0.269802	+	0.155770i
$650$		−	8.80876e10i		−	0.493471i
$651$	7.15603e10	+	8.15887e10i	0.398426	+	0.454262i
$652$	1.14578e11			0.634030
$653$	−4.34249e10	−	7.52141e10i	−0.238828	−	0.413663i	0.721550	−	0.692362i	$-0.243430\pi$
$653$	−4.34249e10	−	7.52141e10i	−0.238828	−	0.413663i	−0.960378	+	0.278700i	$0.910097\pi$
$654$	−9.66285e9	−	5.57885e9i	−0.0528195	−	0.0304954i
$655$	2.79834e10	−	4.84687e10i	0.152032	−	0.263327i
$656$	6.92515e10	−	3.99823e10i	0.373950	−	0.215900i
$657$		−	6.01927e10i		−	0.323060i
$658$	−4.96134e10	−	1.68380e10i	−0.264664	−	0.0898231i
$659$	−1.49313e11			−0.791689			−0.395845	−	0.918317i	$-0.629548\pi$
$659$	−1.49313e11			−0.791689			−0.395845	+	0.918317i	$0.629548\pi$
$660$	2.51885e10	+	4.36278e10i	0.132748	+	0.229926i
$661$	2.17164e11	+	1.25380e11i	1.13758	+	0.656781i	0.945830	−	0.324663i	$-0.105251\pi$
$661$	2.17164e11	+	1.25380e11i	1.13758	+	0.656781i	0.191749	+	0.981444i	$0.438584\pi$
$662$	−2.84061e10	+	4.92007e10i	−0.147904	+	0.256177i
$663$	−1.44158e10	+	8.32298e9i	−0.0746080	+	0.0430750i
$664$			1.89136e11i			0.972977i
$665$	−2.56053e10	+	7.54461e10i	−0.130931	+	0.385789i
$666$	−1.36780e10			−0.0695223
$667$	−1.74659e11	−	3.02519e11i	−0.882446	−	1.52844i
$668$	−5.42724e9	−	3.13342e9i	−0.0272567	−	0.0157366i
$669$	4.37101e9	−	7.57082e9i	0.0218211	−	0.0377953i
$670$	−2.68667e10	+	1.55115e10i	−0.133326	+	0.0769759i
$671$		−	3.19862e10i		−	0.157788i
$672$	−8.67887e10	+	7.61211e10i	−0.425585	+	0.373274i
$673$	2.52426e10			0.123048			0.0615240	−	0.998106i	$-0.480404\pi$
$673$	2.52426e10			0.123048			0.0615240	+	0.998106i	$0.480404\pi$
$674$	−1.62365e10	−	2.81225e10i	−0.0786780	−	0.136274i
$675$	−2.82615e10	−	1.63168e10i	−0.136138	−	0.0785995i
$676$	−8.85058e10	+	1.53296e11i	−0.423823	+	0.734083i
$677$	7.78426e10	−	4.49424e10i	0.370564	−	0.213945i	−0.303141	−	0.952946i	$-0.598035\pi$
$677$	7.78426e10	−	4.49424e10i	0.370564	−	0.213945i	0.673705	+	0.739001i	$0.264702\pi$
$678$			2.12509e10i			0.100568i
$679$	7.82131e10	+	3.93077e11i	0.367960	+	1.84926i
$680$	−7.38646e9			−0.0345462
$681$	1.76774e10	+	3.06182e10i	0.0821922	+	0.142361i
$682$	−1.08793e11	−	6.28119e10i	−0.502881	−	0.290339i
$683$	3.85503e10	−	6.67711e10i	0.177152	−	0.306835i	−0.763752	−	0.645510i	$-0.776645\pi$
$683$	3.85503e10	−	6.67711e10i	0.177152	−	0.306835i	0.940904	+	0.338674i	$0.109978\pi$
$684$	4.93514e10	−	2.84931e10i	0.225463	−	0.130171i
$685$			1.87408e10i			0.0851187i
$686$	−8.41622e10	−	4.14848e10i	−0.380033	−	0.187324i
$687$	−1.60005e11			−0.718301
$688$	−2.22141e10	−	3.84759e10i	−0.0991459	−	0.171726i
$689$	5.43116e11	+	3.13568e11i	2.40999	+	1.39141i
$690$	−1.59739e10	+	2.76675e10i	−0.0704715	+	0.122060i
$691$	−1.52741e11	+	8.81853e10i	−0.669954	+	0.386798i	−0.796059	−	0.605219i	$-0.793086\pi$
$691$	−1.52741e11	+	8.81853e10i	−0.669954	+	0.386798i	0.126105	+	0.992017i	$0.459752\pi$
$692$		−	3.31489e11i		−	1.44559i
$693$	9.87415e10	−	1.96473e10i	0.428121	−	0.0851862i
$694$	−2.99215e10			−0.128987
$695$	1.72014e9	+	2.97938e9i	0.00737269	+	0.0127699i
$696$	1.18641e11	+	6.84977e10i	0.505591	+	0.291903i
$697$	1.08012e10	−	1.87083e10i	0.0457659	−	0.0792689i
$698$	−6.03101e10	+	3.48200e10i	−0.254079	+	0.146692i
$699$			1.19592e11i			0.500947i
$700$	1.06106e11	+	1.20975e11i	0.441922	+	0.503853i
$701$	2.37032e11			0.981599			0.490800	−	0.871272i	$-0.336705\pi$
$701$	2.37032e11			0.981599			0.490800	+	0.871272i	$0.336705\pi$
$702$	−1.41178e10	−	2.44527e10i	−0.0581324	−	0.100688i
$703$	−9.91157e10	−	5.72245e10i	−0.405808	−	0.234294i
$704$	−1.25859e10	+	2.17994e10i	−0.0512381	+	0.0887471i
$705$	−3.48716e10	+	2.01331e10i	−0.141161	+	0.0814995i
$706$			9.99571e10i			0.402341i
$707$	−3.24488e11	−	1.10126e11i	−1.29874	−	0.440772i
$708$	−2.83164e10			−0.112695
$709$	2.97998e10	+	5.16148e10i	0.117931	+	0.204263i	0.918948	−	0.394379i	$-0.129040\pi$
$709$	2.97998e10	+	5.16148e10i	0.117931	+	0.204263i	−0.801016	+	0.598642i	$0.795707\pi$
$710$	4.90865e10	+	2.83401e10i	0.193165	+	0.111524i
$711$	−2.70603e10	+	4.68699e10i	−0.105890	+	0.183407i
$712$	−1.87749e11	+	1.08397e11i	−0.730563	+	0.421790i
$713$			3.64124e11i			1.40893i
$714$	−2.13815e9	+	6.30007e9i	−0.00822707	+	0.0242411i
$715$	2.08858e11			0.799148
$716$	−1.65900e11	−	2.87348e11i	−0.631241	−	1.09334i
$717$	−2.52499e11	−	1.45781e11i	−0.955396	−	0.551598i
$718$	2.25470e10	−	3.90525e10i	0.0848380	−	0.146944i
$719$	−1.65282e11	+	9.54254e10i	−0.618456	+	0.357066i	−0.776268	−	0.630403i	$-0.782890\pi$
$719$	−1.65282e11	+	9.54254e10i	−0.618456	+	0.357066i	0.157811	+	0.987469i	$0.449556\pi$
$720$			1.89270e10i			0.0704292i
$721$	−1.04400e11	+	9.15678e10i	−0.386331	+	0.338846i
$722$	1.08076e10			0.0397722
$723$	1.82582e10	+	3.16242e10i	0.0668199	+	0.115735i
$724$	1.11574e11	+	6.44174e10i	0.406078	+	0.234449i
$725$	1.47926e11	−	2.56216e11i	0.535419	−	0.927372i
$726$	−4.20739e10	+	2.42914e10i	−0.151449	+	0.0874391i
$727$		−	8.50700e10i		−	0.304536i	−0.988339	−	0.152268i	$-0.951342\pi$
$727$		−	8.50700e10i		−	0.304536i	0.988339	−	0.152268i	$-0.0486577\pi$
$728$	6.02856e10	+	3.02978e11i	0.214629	+	1.07866i
$729$	−1.04604e10			−0.0370370
$730$	−2.49542e10	−	4.32219e10i	−0.0878723	−	0.152199i
$731$	−1.03943e10	−	6.00114e9i	−0.0364020	−	0.0210167i
$732$	8.19366e9	−	1.41918e10i	0.0285387	−	0.0494304i
$733$	−8.47822e9	+	4.89490e9i	−0.0293690	+	0.0169562i	−0.514613	−	0.857423i	$-0.672064\pi$
$733$	−8.47822e9	+	4.89490e9i	−0.0293690	+	0.0169562i	0.485244	+	0.874379i	$0.338731\pi$
$734$		−	1.24704e11i		−	0.429633i
$735$	−6.66208e10	+	2.76049e10i	−0.228276	+	0.0945881i
$736$	−3.87331e11			−1.31999
$737$	1.64008e11	+	2.84071e11i	0.555899	+	0.962846i
$738$	3.17338e10	+	1.83215e10i	0.106978	+	0.0617640i
$739$	1.64891e11	−	2.85599e11i	0.552864	−	0.957588i	−0.445203	−	0.895430i	$-0.646868\pi$
$739$	1.64891e11	−	2.85599e11i	0.552864	−	0.957588i	0.998066	−	0.0621581i	$-0.0197983\pi$
$740$	4.48902e10	−	2.59174e10i	0.149701	−	0.0864299i
$741$		−	2.36258e11i		−	0.783636i
$742$	2.45833e11	−	4.89150e10i	0.811006	−	0.161371i
$743$	−3.93745e11			−1.29199			−0.645996	−	0.763341i	$-0.723558\pi$
$743$	−3.93745e11			−1.29199			−0.645996	+	0.763341i	$0.723558\pi$
$744$	−7.14008e10	−	1.23670e11i	−0.233030	−	0.403620i
$745$	2.06679e10	+	1.19326e10i	0.0670922	+	0.0387357i
$746$	−8.98937e10	+	1.55701e11i	−0.290251	+	0.502730i
$747$	1.13385e11	−	6.54631e10i	0.364145	−	0.210239i
$748$			3.51992e10i			0.112441i
$749$	1.41595e11	+	1.61438e11i	0.449905	+	0.512954i
$750$	−6.01834e10			−0.190209
$751$	2.67018e11	+	4.62489e11i	0.839423	+	1.45392i	0.890377	+	0.455223i	$0.150441\pi$
$751$	2.67018e11	+	4.62489e11i	0.839423	+	1.45392i	−0.0509539	+	0.998701i	$0.516226\pi$
$752$	−9.01916e10	−	5.20721e10i	−0.282030	−	0.162830i
$753$	7.37315e10	−	1.27707e11i	0.229336	−	0.397222i
$754$	2.21686e11	−	1.27990e11i	0.685887	−	0.395997i
$755$		−	1.49468e11i		−	0.460004i
$756$	4.88431e10	+	1.65766e10i	0.149526	+	0.0507468i
$757$	−3.48900e11			−1.06247			−0.531236	−	0.847224i	$-0.678272\pi$
$757$	−3.48900e11			−1.06247			−0.531236	+	0.847224i	$0.678272\pi$
$758$	−6.45122e10	−	1.11738e11i	−0.195418	−	0.338474i
$759$	2.92538e11	+	1.68897e11i	0.881486	+	0.508926i
$760$	5.24185e10	−	9.07915e10i	0.157120	−	0.272139i
$761$	1.24626e11	−	7.19527e10i	0.371594	−	0.214540i	−0.302561	−	0.953130i	$-0.597841\pi$
$761$	1.24626e11	−	7.19527e10i	0.371594	−	0.214540i	0.674155	+	0.738590i	$0.264508\pi$
$762$		−	1.89490e10i		−	0.0562039i
$763$	2.71577e10	−	8.00201e10i	0.0801298	−	0.236103i
$764$	−1.26222e11			−0.370476
$765$	2.55657e9	+	4.42811e9i	0.00746470	+	0.0129292i
$766$	8.81833e10	+	5.09127e10i	0.256136	+	0.147880i
$767$	−5.86984e10	+	1.01669e11i	−0.169607	+	0.293769i
$768$	6.10936e10	−	3.52724e10i	0.175611	−	0.101389i
$769$		−	2.83112e11i		−	0.809567i	−0.914413	−	0.404783i	$-0.867347\pi$
$769$		−	2.83112e11i		−	0.809567i	0.914413	−	0.404783i	$-0.132653\pi$
$770$	6.27570e10	−	5.50433e10i	0.178525	−	0.156582i
$771$	3.55303e11			1.00550
$772$	−1.95066e11	−	3.37864e11i	−0.549177	−	0.951203i
$773$	1.18891e11	+	6.86416e10i	0.332989	+	0.192251i	0.657167	−	0.753745i	$-0.271754\pi$
$773$	1.18891e11	+	6.86416e10i	0.332989	+	0.192251i	−0.324178	+	0.945996i	$0.605088\pi$
$774$	1.01794e10	−	1.76312e10i	0.0283634	−	0.0491268i
$775$	−2.67075e11	+	1.54196e11i	−0.740333	+	0.427431i
$776$		−	5.27368e11i		−	1.45434i
$777$	−2.02157e10	−	1.01599e11i	−0.0554633	−	0.278743i
$778$	1.62211e11			0.442754
$779$	1.53303e11	+	2.65529e11i	0.416296	+	0.721045i
$780$	9.26673e10	+	5.35015e10i	0.250350	+	0.144540i
$781$	2.99649e11	−	5.19008e11i	0.805395	−	1.39499i
$782$	−1.93317e10	+	1.11612e10i	−0.0516943	+	0.0298457i
$783$		−	9.48325e10i		−	0.252296i
$784$	−1.47985e11	−	1.13524e11i	−0.391701	−	0.300485i
$785$	−2.88485e11			−0.759706
$786$	3.31656e10	+	5.74444e10i	0.0868955	+	0.150507i
$787$	2.96173e11	+	1.70995e11i	0.772051	+	0.445744i	0.833606	−	0.552360i	$-0.186272\pi$
$787$	2.96173e11	+	1.70995e11i	0.772051	+	0.445744i	−0.0615545	+	0.998104i	$0.519606\pi$
$788$	7.43786e10	−	1.28827e11i	0.192905	−	0.334121i
$789$	−2.84589e11	+	1.64308e11i	−0.734363	+	0.423985i
$790$			4.48737e10i			0.115208i
$791$	−1.57850e11	+	3.14084e10i	−0.403216	+	0.0802307i
$792$	−1.32476e11			−0.336694
$793$	−3.39701e10	−	5.88379e10i	−0.0859020	−	0.148787i
$794$	−7.51356e10	−	4.33795e10i	−0.189044	−	0.109145i
$795$	9.63187e10	−	1.66829e11i	0.241125	−	0.417641i
$796$	3.19711e11	−	1.84585e11i	0.796353	−	0.459775i
$797$			5.90299e11i			1.46298i	0.681852	+	0.731491i	$0.261175\pi$
$797$			5.90299e11i			1.46298i	−0.681852	+	0.731491i	$0.738825\pi$
$798$	−6.22645e10	−	7.09902e10i	−0.153543	−	0.175060i
$799$	−2.81346e10			−0.0690325
$800$	−1.64024e11	−	2.84097e11i	−0.400448	−	0.693596i
$801$	1.29966e11	+	7.50357e10i	0.315718	+	0.182280i
$802$	−5.76203e10	+	9.98013e10i	−0.139277	+	0.241234i
$803$	−4.57000e11	+	2.63849e11i	−1.09914	+	0.634590i
$804$			1.68051e11i			0.402177i
$805$	−2.29121e11	−	7.77602e10i	−0.545608	−	0.185171i
$806$	−2.66830e11			−0.632259
$807$	−1.92753e11	−	3.33857e11i	−0.454471	−	0.787167i
$808$	3.90488e11	+	2.25448e11i	0.916140	+	0.528934i
$809$	4.80422e10	−	8.32115e10i	0.112158	−	0.194263i	−0.804482	−	0.593976i	$-0.797557\pi$
$809$	4.80422e10	−	8.32115e10i	0.112158	−	0.194263i	0.916640	+	0.399714i	$0.130891\pi$
$810$	−7.51115e9	+	4.33656e9i	−0.0174488	+	0.0100741i
$811$		−	2.61119e11i		−	0.603608i	−0.953370	−	0.301804i	$-0.902411\pi$
$811$		−	2.61119e11i		−	0.603608i	0.953370	−	0.301804i	$-0.0975888\pi$
$812$	−1.50282e11	+	4.42806e11i	−0.345687	+	1.01857i
$813$	3.23579e11			0.740658
$814$	5.99560e10	+	1.03847e11i	0.136564	+	0.236535i
$815$	−1.26365e11	−	7.29571e10i	−0.286416	−	0.165363i
$816$	−6.61229e9	+	1.14528e10i	−0.0149139	+	0.0258316i
$817$	1.47527e11	−	8.51750e10i	0.331119	−	0.191172i
$818$			3.38123e11i			0.755199i
$819$	1.60767e11	−	1.41006e11i	0.357322	−	0.313403i
$820$	−1.38864e11			−0.307139
$821$	1.69853e11	+	2.94194e11i	0.373853	+	0.647532i	0.990155	−	0.139978i	$-0.0447032\pi$
$821$	1.69853e11	+	2.94194e11i	0.373853	+	0.647532i	−0.616302	+	0.787510i	$0.711370\pi$
$822$	−1.92356e10	−	1.11057e10i	−0.0421325	−	0.0243252i
$823$	−6.89538e10	+	1.19432e11i	−0.150300	+	0.260327i	−0.931338	−	0.364157i	$-0.881357\pi$
$823$	−6.89538e10	+	1.19432e11i	−0.150300	+	0.260327i	0.781038	+	0.624484i	$0.214691\pi$
$824$	1.58247e11	−	9.13638e10i	0.343262	−	0.198183i
$825$			2.86092e11i			0.617576i
$826$	9.15664e9	+	4.60187e10i	0.0196705	+	0.0988584i
$827$	1.03179e11			0.220582			0.110291	−	0.993899i	$-0.464822\pi$
$827$	1.03179e11			0.220582			0.110291	+	0.993899i	$0.464822\pi$
$828$	8.65300e10	+	1.49874e11i	0.184096	+	0.318864i
$829$	−2.61446e11	−	1.50946e11i	−0.553559	−	0.319598i	0.196997	−	0.980404i	$-0.436881\pi$
$829$	−2.61446e11	−	1.50946e11i	−0.553559	−	0.319598i	−0.750556	+	0.660806i	$0.770214\pi$
$830$	5.42782e10	−	9.40127e10i	0.114370	−	0.198095i
$831$	−2.29593e11	+	1.32556e11i	−0.481454	+	0.277968i
$832$			5.34659e10i			0.111579i
$833$	−4.99564e10	−	6.57060e9i	−0.103756	−	0.0136466i
$834$	−4.07739e9			−0.00842787
$835$	3.99039e9	+	6.91156e9i	0.00820860	+	0.0142177i
$836$	−4.32654e11	−	2.49793e11i	−0.885760	−	0.511394i
$837$	−4.94259e10	+	8.56082e10i	−0.100705	+	0.174427i
$838$	−1.88786e11	+	1.08996e11i	−0.382820	+	0.221021i
$839$			4.99916e11i			1.00890i	0.863440	+	0.504451i	$0.168305\pi$
$839$			4.99916e11i			1.00890i	−0.863440	+	0.504451i	$0.831695\pi$
$840$	9.30658e10	−	1.85179e10i	0.186927	−	0.0371942i
$841$	3.59495e11			0.718636
$842$	1.93681e11	+	3.35466e11i	0.385336	+	0.667421i
$843$	−9.71808e8	−	5.61073e8i	−0.00192429	−	0.00111099i
$844$	−3.60441e11	+	6.24302e11i	−0.710337	+	1.23034i
$845$	1.95222e11	−	1.12712e11i	0.382915	−	0.221076i
$846$		−	4.77231e10i		−	0.0931637i
$847$	−2.42618e11	−	2.76619e11i	−0.471400	−	0.537462i
$848$	4.98236e11			0.963499
$849$	−2.06577e11	−	3.57802e11i	−0.397604	−	0.688671i
$850$	−1.63728e10	−	9.45286e9i	−0.0313652	−	0.0181087i
$851$	1.73784e11	−	3.01003e11i	0.331353	−	0.573921i
$852$	2.65900e11	−	1.53518e11i	0.504615	−	0.291340i
$853$			6.64273e11i			1.25473i	0.778725	+	0.627365i	$0.215867\pi$
$853$			6.64273e11i			1.25473i	−0.778725	+	0.627365i	$0.784133\pi$
$854$	−2.57136e10	−	8.72681e9i	−0.0483427	−	0.0164068i
$855$	−7.25715e10			−0.135801
$856$	−1.41280e11	−	2.44703e11i	−0.263138	−	0.455769i
$857$	−3.73865e11	−	2.15851e11i	−0.693092	−	0.400157i	0.111677	−	0.993745i	$-0.464378\pi$
$857$	−3.73865e11	−	2.15851e11i	−0.693092	−	0.400157i	−0.804769	+	0.593587i	$0.797711\pi$
$858$	−1.23768e11	+	2.14372e11i	−0.228381	+	0.395567i
$859$	−3.15583e11	+	1.82202e11i	−0.579618	+	0.334642i	−0.760981	−	0.648774i	$-0.775282\pi$
$859$	−3.15583e11	+	1.82202e11i	−0.579618	+	0.334642i	0.181364	+	0.983416i	$0.441949\pi$
$860$			7.71527e10i			0.141045i
$861$	−8.91884e10	+	2.62794e11i	−0.162292	+	0.478193i
$862$	−2.01048e11			−0.364143
$863$	3.50506e11	+	6.07094e11i	0.631906	+	1.09449i	0.987162	+	0.159724i	$0.0510604\pi$
$863$	3.50506e11	+	6.07094e11i	0.631906	+	1.09449i	−0.355256	+	0.934769i	$0.615606\pi$
$864$	−9.10644e10	−	5.25760e10i	−0.163416	−	0.0943480i
$865$	−2.11075e11	+	3.65592e11i	−0.377026	+	0.653029i
$866$	1.93241e11	−	1.11568e11i	0.343580	−	0.198366i
$867$		−	3.22651e11i		−	0.571027i
$868$	3.66451e11	−	3.21409e11i	0.645561	−	0.566212i
$869$	4.74465e11			0.832004
$870$	−3.93148e10	−	6.80953e10i	−0.0686245	−	0.118861i
$871$	6.03378e11	+	3.48361e11i	1.04838	+	0.605280i
$872$	−5.55965e10	+	9.62960e10i	−0.0961571	+	0.166549i
$873$	−3.16152e11	+	1.82530e11i	−0.544301	+	0.314252i
$874$		−	3.16823e11i		−	0.542965i
$875$	−8.89498e10	−	4.47036e11i	−0.151744	−	0.762624i
$876$	−2.70352e11			−0.459107
$877$	−2.68814e11	−	4.65600e11i	−0.454416	−	0.787072i	0.544238	−	0.838931i	$-0.316819\pi$
$877$	−2.68814e11	−	4.65600e11i	−0.454416	−	0.787072i	−0.998654	+	0.0518586i	$0.983486\pi$
$878$	−3.90582e11	−	2.25503e11i	−0.657255	−	0.379467i
$879$	−1.88702e11	+	3.26842e11i	−0.316098	+	0.547497i
$880$	1.43699e11	−	8.29649e10i	0.239621	−	0.138345i
$881$		−	1.18727e12i		−	1.97081i	−0.170220	−	0.985406i	$-0.554448\pi$
$881$		−	1.18727e12i		−	1.97081i	0.170220	−	0.985406i	$-0.445552\pi$
$882$	1.11453e10	−	8.47382e10i	0.0184170	−	0.140025i
$883$	1.03398e11			0.170086			0.0850429	−	0.996377i	$-0.472897\pi$
$883$	1.03398e11			0.170086			0.0850429	+	0.996377i	$0.472897\pi$
$884$	3.73822e10	+	6.47479e10i	0.0612148	+	0.106027i
$885$	3.12295e10	+	1.80304e10i	0.0509088	+	0.0293922i
$886$	−2.33834e11	+	4.05012e11i	−0.379465	+	0.657253i
$887$	7.38676e11	−	4.26475e11i	1.19333	−	0.688967i	0.234267	−	0.972172i	$-0.424731\pi$
$887$	7.38676e11	−	4.26475e11i	1.19333	−	0.688967i	0.959059	+	0.283205i	$0.0913977\pi$
$888$			1.36309e11i			0.219216i
$889$	1.40751e11	−	2.80062e10i	0.225344	−	0.0448381i
$890$	1.24431e11			0.198320
$891$	4.58520e10	+	7.94179e10i	0.0727524	+	0.126011i
$892$	−3.40039e10	−	1.96322e10i	−0.0537118	−	0.0310105i
$893$	1.99659e11	−	3.45819e11i	0.313966	−	0.543805i
$894$	−2.44954e10	+	1.41424e10i	−0.0383472	+	0.0221398i
$895$			4.22546e11i			0.658540i
$896$	4.30788e11	+	4.91158e11i	0.668392	+	0.762060i
$897$	7.17489e11			1.10827
$898$	1.39504e11	+	2.41628e11i	0.214526	+	0.371571i
$899$	−7.76115e11	−	4.48090e11i	−1.18819	−	0.686004i
$900$	−7.32860e10	+	1.26935e11i	−0.111699	+	0.193469i
$901$	1.16566e11	−	6.72992e10i	0.176877	−	0.102120i
$902$		−	3.21242e11i		−	0.485296i
$903$	1.46008e11	+	4.95529e10i	0.219596	+	0.0745278i
$904$	2.11778e11			0.317108
$905$	−8.20353e10	−	1.42089e11i	−0.122294	−	0.211820i
$906$	1.53415e11	+	8.85739e10i	0.227695	+	0.131460i
$907$	1.20799e11	−	2.09230e11i	0.178498	−	0.309168i	−0.762868	−	0.646554i	$-0.776209\pi$
$907$	1.20799e11	−	2.09230e11i	0.178498	−	0.309168i	0.941366	+	0.337386i	$0.109543\pi$
$908$	1.37520e11	−	7.93973e10i	0.202313	−	0.116805i
$909$		−	3.12125e11i		−	0.457165i
$910$	5.69828e10	−	1.67900e11i	0.0830956	−	0.244841i
$911$	−3.40518e11			−0.494386			−0.247193	−	0.968966i	$-0.579508\pi$
$911$	−3.40518e11			−0.494386			−0.247193	+	0.968966i	$0.579508\pi$
$912$	−9.38491e10	−	1.62551e11i	−0.135660	−	0.234969i
$913$	−9.94028e11	−	5.73902e11i	−1.43059	−	0.825952i
$914$	−1.10587e11	+	1.91543e11i	−0.158460	+	0.274461i
$915$	−1.80732e10	+	1.04346e10i	−0.0257841	+	0.0148864i
$916$			7.18654e11i			1.02079i
$917$	−3.77674e11	+	3.31252e11i	−0.534120	+	0.468470i
$918$	−6.06003e9			−0.00853305
$919$	−1.70782e11	−	2.95802e11i	−0.239430	−	0.414705i	0.721121	−	0.692809i	$-0.243627\pi$
$919$	−1.70782e11	−	2.95802e11i	−0.239430	−	0.414705i	−0.960551	+	0.278104i	$0.910294\pi$
$920$	2.75723e11	+	1.59189e11i	0.384877	+	0.222209i
$921$	−2.35990e11	+	4.08746e11i	−0.327985	+	0.568087i
$922$	−3.08913e10	+	1.78351e10i	−0.0427477	+	0.0246804i
$923$		−	1.27293e12i		−	1.75388i
$924$	−8.82446e10	−	4.43492e11i	−0.121060	−	0.608413i
$925$	2.94370e11			0.402093
$926$	1.73708e11	+	3.00870e11i	0.236252	+	0.409200i
$927$	−1.09543e11	−	6.32449e10i	−0.148343	−	0.0856459i
$928$	4.76649e11	−	8.25580e11i	0.642698	−	1.11319i
$929$	7.66008e11	−	4.42255e11i	1.02842	−	0.593759i	0.111889	−	0.993721i	$-0.464310\pi$
$929$	7.66008e11	−	4.42255e11i	1.02842	−	0.593759i	0.916532	+	0.399962i	$0.130977\pi$
$930$			8.19623e10i			0.109568i
$931$	4.35282e11	−	5.67416e11i	0.579392	−	0.755271i
$932$	5.37139e11			0.711907
$933$	−1.65619e11	−	2.86861e11i	−0.218567	−	0.378569i
$934$	−3.35503e11	−	1.93703e11i	−0.440868	−	0.254535i
$935$	2.24130e10	−	3.88204e10i	0.0293260	−	0.0507941i
$936$	−2.43686e11	+	1.40692e11i	−0.317487	+	0.183301i
$937$			4.85369e11i			0.629671i	0.949146	+	0.314836i	$0.101949\pi$
$937$			4.85369e11i			0.629671i	−0.949146	+	0.314836i	$0.898051\pi$
$938$	2.73110e11	−	5.43424e10i	0.352798	−	0.0701985i
$939$	−3.65268e11			−0.469840
$940$	9.04269e10	+	1.56624e11i	0.115821	+	0.200607i
$941$	−7.31010e11	−	4.22049e11i	−0.932320	−	0.538275i	−0.0447755	−	0.998997i	$-0.514257\pi$
$941$	−7.31010e11	−	4.22049e11i	−0.932320	−	0.538275i	−0.887545	+	0.460722i	$0.847591\pi$
$942$	1.70955e11	−	2.96102e11i	0.217109	−	0.376043i
$943$	−8.06381e11	+	4.65564e11i	−1.01975	+	0.588752i
$944$			9.32672e10i			0.117447i
$945$	−4.33129e10	−	4.93827e10i	−0.0543113	−	0.0619224i
$946$	−1.78481e11			−0.222858
$947$	3.11821e11	+	5.40090e11i	0.387709	+	0.671531i	0.992141	−	0.125126i	$-0.0399334\pi$
$947$	3.11821e11	+	5.40090e11i	0.387709	+	0.671531i	−0.604432	+	0.796656i	$0.706600\pi$
$948$	2.10513e11	+	1.21540e11i	0.260643	+	0.150482i
$949$	−5.60426e11	+	9.70687e11i	−0.690961	+	1.19678i
$950$	2.32382e11	−	1.34166e11i	0.285304	−	0.164720i
$951$			7.03534e11i			0.860128i
$952$	6.27838e10	+	2.13079e10i	0.0764364	+	0.0259414i
$953$	−5.74523e11			−0.696524			−0.348262	−	0.937397i	$-0.613228\pi$
$953$	−5.74523e11			−0.696524			−0.348262	+	0.937397i	$0.613228\pi$
$954$	1.14156e11	+	1.97723e11i	0.137817	+	0.238707i
$955$	1.39207e11	+	8.03713e10i	0.167359	+	0.0966246i
$956$	−6.54765e11	+	1.13409e12i	−0.783888	+	1.35773i
$957$	−7.19995e11	+	4.15689e11i	−0.858384	+	0.495588i
$958$			9.57653e9i			0.0113696i
$959$	5.40619e10	−	1.59294e11i	0.0639171	−	0.188332i
$960$	1.64231e10			0.0193362
$961$	4.06366e10	+	7.03846e10i	0.0476457	+	0.0825247i
$962$	2.20575e11	+	1.27349e11i	0.257547	+	0.148695i
$963$	−9.77982e10	+	1.69391e11i	−0.113717	+	0.196964i
$964$	1.42038e11	−	8.20059e10i	0.164474	−	0.0949592i
$965$			4.96831e11i			0.572927i
$966$	2.15589e11	−	1.89090e11i	0.247581	−	0.217150i
$967$	1.02285e12			1.16978			0.584892	−	0.811111i	$-0.301137\pi$
$967$	1.02285e12			1.16978			0.584892	+	0.811111i	$0.301137\pi$
$968$	2.42078e11	+	4.19291e11i	0.275711	+	0.477545i
$969$	−4.39133e10	−	2.53533e10i	−0.0498082	−	0.0287568i
$970$	−1.51344e11	+	2.62135e11i	−0.170953	+	0.296100i
$971$	1.43260e12	−	8.27112e11i	1.61157	−	0.930438i	0.622558	−	0.782574i	$-0.286094\pi$
$971$	1.43260e12	−	8.27112e11i	1.61157	−	0.930438i	0.989008	−	0.147864i	$-0.0472397\pi$
$972$			4.69821e10i			0.0526341i
$973$	−6.02629e9	−	3.02864e10i	−0.00672355	−	0.0337907i
$974$	2.78682e11			0.309651
$975$	3.03836e11	+	5.26259e11i	0.336218	+	0.582346i
$976$	−4.67444e10	−	2.69879e10i	−0.0515146	−	0.0297420i
$977$	−7.08767e11	+	1.22762e12i	−0.777902	+	1.34737i	0.155247	+	0.987876i	$0.450383\pi$
$977$	−7.08767e11	+	1.22762e12i	−0.777902	+	1.34737i	−0.933149	+	0.359490i	$0.882951\pi$
$978$	1.49767e11	−	8.64678e10i	0.163704	−	0.0945146i
$979$		−	1.31565e12i		−	1.43222i
$980$	1.23986e11	+	2.99224e11i	0.134421	+	0.324408i
$981$	7.69713e10			0.0831099
$982$	−2.47127e10	−	4.28037e10i	−0.0265751	−	0.0460294i
$983$	6.10227e11	+	3.52315e11i	0.653548	+	0.377326i	0.789814	−	0.613346i	$-0.210177\pi$
$983$	6.10227e11	+	3.52315e11i	0.653548	+	0.377326i	−0.136266	+	0.990672i	$0.543510\pi$
$984$	1.82584e11	−	3.16246e11i	0.194753	−	0.337322i
$985$	−1.64061e11	+	9.47207e10i	−0.174285	+	0.100624i
$986$		−	5.49396e10i		−	0.0581270i
$987$	3.54482e11	−	7.05337e10i	0.373530	−	0.0743238i
$988$	−1.06114e12			−1.11364
$989$	2.58666e11	+	4.48023e11i	0.270368	+	0.468291i
$990$	6.58488e10	+	3.80178e10i	0.0685499	+	0.0395773i
$991$	−6.48285e11	+	1.12286e12i	−0.672158	+	1.16421i	0.305133	+	0.952310i	$0.401299\pi$
$991$	−6.48285e11	+	1.12286e12i	−0.672158	+	1.16421i	−0.977291	+	0.211902i	$0.932034\pi$
$992$	−8.60571e11	+	4.96851e11i	−0.888669	+	0.513074i
$993$		−	3.91918e11i		−	0.403086i
$994$	−3.35474e11	−	3.82487e11i	−0.343648	−	0.391806i
$995$	−4.70137e11			−0.479658
$996$	−2.94024e11	−	5.09264e11i	−0.298776	−	0.517495i
$997$	1.85093e11	+	1.06863e11i	0.187331	+	0.108155i	0.590732	−	0.806868i	$-0.298839\pi$
$997$	1.85093e11	+	1.06863e11i	0.187331	+	0.108155i	−0.403402	+	0.915023i	$0.632172\pi$
$998$	1.12734e11	−	1.95260e11i	0.113640	−	0.196830i
$999$	8.17158e10	−	4.71786e10i	0.0820435	−	0.0473678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.9.f.b.10.3	✓	12
3.2	odd	2		63.9.m.d.10.4		12
7.3	odd	6		147.9.d.b.97.8		12
7.4	even	3		147.9.d.b.97.7		12
7.5	odd	6	inner	21.9.f.b.19.3	yes	12
21.5	even	6		63.9.m.d.19.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.9.f.b.10.3	✓	12	1.1	even	1	trivial
21.9.f.b.19.3	yes	12	7.5	odd	6	inner
63.9.m.d.10.4		12	3.2	odd	2
63.9.m.d.19.4		12	21.5	even	6
147.9.d.b.97.7		12	7.4	even	3
147.9.d.b.97.8		12	7.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	21.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.38954 - 5.87085i) q^{2} +(40.5000 + 23.3827i) q^{3} +(105.022 - 181.904i) q^{4} +(-231.653 + 133.745i) q^{5} -317.026i q^{6} +(2354.84 - 468.558i) q^{7} -3159.35 q^{8} +(1093.50 + 1894.00i) q^{9} +O(q^{10})\)	\(q+(-3.38954 - 5.87085i) q^{2} +(40.5000 + 23.3827i) q^{3} +(105.022 - 181.904i) q^{4} +(-231.653 + 133.745i) q^{5} -317.026i q^{6} +(2354.84 - 468.558i) q^{7} -3159.35 q^{8} +(1093.50 + 1894.00i) q^{9} +(1570.39 + 906.668i) q^{10} +(9586.51 - 16604.3i) q^{11} +(8506.79 - 4911.40i) q^{12} -40724.3i q^{13} +(-10732.6 - 12236.7i) q^{14} -12509.3 q^{15} +(-16176.9 - 28019.3i) q^{16} +(-7569.41 - 4370.20i) q^{17} +(7412.92 - 12839.5i) q^{18} +(107434. - 62026.8i) q^{19} +56184.8i q^{20} +(106327. + 36085.8i) q^{21} -129975. q^{22} +(188368. + 326263. i) q^{23} +(-127954. - 73874.0i) q^{24} +(-159537. + 276326. i) q^{25} +(-239086. + 138036. i) q^{26} +102276. i q^{27} +(162078. - 477562. i) q^{28} -927223. q^{29} +(42400.6 + 73440.1i) q^{30} +(837032. + 483261. i) q^{31} +(-514061. + 890380. i) q^{32} +(776507. - 448316. i) q^{33} +59251.8i q^{34} +(-482838. + 423491. i) q^{35} +459367. q^{36} +(-461288. - 798974. i) q^{37} +(-728300. - 420484. i) q^{38} +(952243. - 1.64933e6i) q^{39} +(731873. - 422547. i) q^{40} +2.47157e6i q^{41} +(-148545. - 746544. i) q^{42} +1.37320e6 q^{43} +(-2.01359e6 - 3.48764e6i) q^{44} +(-506626. - 292500. i) q^{45} +(1.27696e6 - 2.21176e6i) q^{46} +(2.78766e6 - 1.60946e6i) q^{47} -1.51304e6i q^{48} +(5.32571e6 - 2.20675e6i) q^{49} +2.16303e6 q^{50} +(-204374. - 353986. i) q^{51} +(-7.40789e6 - 4.27695e6i) q^{52} +(-7.69978e6 + 1.33364e7i) q^{53} +(600446. - 346668. i) q^{54} +5.12859e6i q^{55} +(-7.43975e6 + 1.48034e6i) q^{56} +5.80142e6 q^{57} +(3.14285e6 + 5.44358e6i) q^{58} +(-2.49651e6 - 1.44136e6i) q^{59} +(-1.31375e6 + 2.27548e6i) q^{60} +(1.44479e6 - 834148. i) q^{61} -6.55212e6i q^{62} +(3.46246e6 + 3.94769e6i) q^{63} -1.31288e6 q^{64} +(5.44667e6 + 9.43391e6i) q^{65} +(-5.26400e6 - 3.03917e6i) q^{66} +(-8.55413e6 + 1.48162e7i) q^{67} +(-1.58991e6 + 917935. i) q^{68} +1.76182e7i q^{69} +(4.12285e6 + 1.39923e6i) q^{70} +3.12574e7 q^{71} +(-3.45475e6 - 5.98380e6i) q^{72} +(-2.38356e7 - 1.37615e7i) q^{73} +(-3.12711e6 + 5.41631e6i) q^{74} +(-1.29225e7 + 7.46081e6i) q^{75} -2.60567e7i q^{76} +(1.47946e7 - 4.35923e7i) q^{77} -1.29106e7 q^{78} +(1.23733e7 + 2.14311e7i) q^{79} +(7.49488e6 + 4.32717e6i) q^{80} +(-2.39148e6 + 4.14217e6i) q^{81} +(1.45102e7 - 8.37746e6i) q^{82} -5.98657e7i q^{83} +(1.77308e7 - 1.55515e7i) q^{84} +2.33797e6 q^{85} +(-4.65450e6 - 8.06182e6i) q^{86} +(-3.75525e7 - 2.16810e7i) q^{87} +(-3.02871e7 + 5.24588e7i) q^{88} +(5.94265e7 - 3.43099e7i) q^{89} +3.96576e6i q^{90} +(-1.90817e7 - 9.58990e7i) q^{91} +7.91313e7 q^{92} +(2.25999e7 + 3.91441e7i) q^{93} +(-1.88977e7 - 1.09106e7i) q^{94} +(-1.65916e7 + 2.87374e7i) q^{95} +(-4.16389e7 + 2.40403e7i) q^{96} +1.66923e8i q^{97} +(-3.10072e7 - 2.37866e7i) q^{98} +4.19314e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9	\( 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9} - 19731 q^{10} + 18081 q^{11} - 90477 q^{12} - 175188 q^{14} + 75006 q^{15} - 298849 q^{16} + 63306 q^{17} - 6561 q^{18} + 476265 q^{19} - 154953 q^{21} + 419258 q^{22} - 66384 q^{23} + 144099 q^{24} + 792375 q^{25} + 1890762 q^{26} - 4229651 q^{28} + 671106 q^{29} - 532737 q^{30} + 717240 q^{31} + 895149 q^{32} + 1464561 q^{33} + 3454614 q^{35} - 4885758 q^{36} + 2289443 q^{37} - 6275988 q^{38} - 930933 q^{39} + 8773863 q^{40} - 4123629 q^{42} - 10119958 q^{43} + 14123901 q^{44} + 3037743 q^{45} - 19926544 q^{46} - 4198782 q^{47} + 8565642 q^{49} - 1162248 q^{50} + 1709262 q^{51} - 26384844 q^{52} - 209511 q^{53} - 531441 q^{54} + 70081743 q^{56} + 25718310 q^{57} + 1938935 q^{58} - 97052259 q^{59} - 51464727 q^{60} - 24195864 q^{61} - 9869931 q^{63} + 272849458 q^{64} + 30440562 q^{65} + 16979949 q^{66} - 57546057 q^{67} - 32476050 q^{68} - 108189027 q^{70} + 224566620 q^{71} + 3890673 q^{72} - 193344135 q^{73} - 71015400 q^{74} + 64182375 q^{75} + 92041617 q^{77} + 102101148 q^{78} - 29314488 q^{79} - 735358533 q^{80} - 28697814 q^{81} + 321118926 q^{82} - 120939804 q^{84} + 248647620 q^{85} + 127268268 q^{86} + 27179793 q^{87} - 487070897 q^{88} + 119863098 q^{89} + 100090965 q^{91} + 364039200 q^{92} + 19365480 q^{93} - 191086092 q^{94} - 95584488 q^{95} + 72507069 q^{96} + 24200217 q^{98} + 79086294 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9 - 19731 * q^10 + 18081 * q^11 - 90477 * q^12 - 175188 * q^14 + 75006 * q^15 - 298849 * q^16 + 63306 * q^17 - 6561 * q^18 + 476265 * q^19 - 154953 * q^21 + 419258 * q^22 - 66384 * q^23 + 144099 * q^24 + 792375 * q^25 + 1890762 * q^26 - 4229651 * q^28 + 671106 * q^29 - 532737 * q^30 + 717240 * q^31 + 895149 * q^32 + 1464561 * q^33 + 3454614 * q^35 - 4885758 * q^36 + 2289443 * q^37 - 6275988 * q^38 - 930933 * q^39 + 8773863 * q^40 - 4123629 * q^42 - 10119958 * q^43 + 14123901 * q^44 + 3037743 * q^45 - 19926544 * q^46 - 4198782 * q^47 + 8565642 * q^49 - 1162248 * q^50 + 1709262 * q^51 - 26384844 * q^52 - 209511 * q^53 - 531441 * q^54 + 70081743 * q^56 + 25718310 * q^57 + 1938935 * q^58 - 97052259 * q^59 - 51464727 * q^60 - 24195864 * q^61 - 9869931 * q^63 + 272849458 * q^64 + 30440562 * q^65 + 16979949 * q^66 - 57546057 * q^67 - 32476050 * q^68 - 108189027 * q^70 + 224566620 * q^71 + 3890673 * q^72 - 193344135 * q^73 - 71015400 * q^74 + 64182375 * q^75 + 92041617 * q^77 + 102101148 * q^78 - 29314488 * q^79 - 735358533 * q^80 - 28697814 * q^81 + 321118926 * q^82 - 120939804 * q^84 + 248647620 * q^85 + 127268268 * q^86 + 27179793 * q^87 - 487070897 * q^88 + 119863098 * q^89 + 100090965 * q^91 + 364039200 * q^92 + 19365480 * q^93 - 191086092 * q^94 - 95584488 * q^95 + 72507069 * q^96 + 24200217 * q^98 + 79086294 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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