LMFDB - Embedded newform 43.9.d.a.7.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,9,Mod(7,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("43.7");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	43.d (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:	$17.5172802326$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.8
Character	$\chi$	$=$	43.7
Dual form			43.9.d.a.37.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-15.0304i q^{2} +(10.2856 - 5.93838i) q^{3} +30.0883 q^{4} +(-349.334 + 201.688i) q^{5} +(-89.2560 - 154.596i) q^{6} +(764.498 + 441.383i) q^{7} -4300.01i q^{8} +(-3209.97 + 5559.83i) q^{9} +O(q^{10})$	\(q-15.0304i q^{2} +(10.2856 - 5.93838i) q^{3} +30.0883 q^{4} +(-349.334 + 201.688i) q^{5} +(-89.2560 - 154.596i) q^{6} +(764.498 + 441.383i) q^{7} -4300.01i q^{8} +(-3209.97 + 5559.83i) q^{9} +(3031.45 + 5250.62i) q^{10} -18871.7 q^{11} +(309.476 - 178.676i) q^{12} +(-17940.3 + 31073.5i) q^{13} +(6634.14 - 11490.7i) q^{14} +(-2395.41 + 4148.96i) q^{15} -56928.1 q^{16} +(16596.3 - 28745.7i) q^{17} +(83566.3 + 48247.0i) q^{18} +(-58765.0 + 33928.0i) q^{19} +(-10510.9 + 6068.46i) q^{20} +10484.4 q^{21} +283648. i q^{22} +(40618.5 + 70353.4i) q^{23} +(-25535.1 - 44228.1i) q^{24} +(-113956. + 197378. i) q^{25} +(467046. + 269649. i) q^{26} +154172. i q^{27} +(23002.5 + 13280.5i) q^{28} +(892041. + 515020. i) q^{29} +(62360.4 + 36003.8i) q^{30} +(227470. + 393990. i) q^{31} -245153. i q^{32} +(-194106. + 112067. i) q^{33} +(-432058. - 249449. i) q^{34} -356087. q^{35} +(-96582.6 + 167286. i) q^{36} +(-729373. + 421103. i) q^{37} +(509950. + 883260. i) q^{38} +426145. i q^{39} +(867262. + 1.50214e6i) q^{40} +2.08913e6 q^{41} -157584. i q^{42} +(-3.33700e6 - 743370. i) q^{43} -567817. q^{44} -2.58966e6i q^{45} +(1.05744e6 - 610511. i) q^{46} -8.62960e6 q^{47} +(-585538. + 338061. i) q^{48} +(-2.49276e6 - 4.31759e6i) q^{49} +(2.96666e6 + 1.71280e6i) q^{50} -394221. i q^{51} +(-539793. + 934949. i) q^{52} +(-3.56207e6 - 6.16968e6i) q^{53} +2.31725e6 q^{54} +(6.59252e6 - 3.80619e6i) q^{55} +(1.89795e6 - 3.28735e6i) q^{56} +(-402955. + 697939. i) q^{57} +(7.74094e6 - 1.34077e7i) q^{58} +932693. q^{59} +(-72073.7 + 124835. i) q^{60} +(9.32479e6 + 5.38367e6i) q^{61} +(5.92181e6 - 3.41896e6i) q^{62} +(-4.90803e6 + 2.83365e6i) q^{63} -1.82583e7 q^{64} -1.44734e7i q^{65} +(1.68441e6 + 2.91748e6i) q^{66} +(-8.50977e6 - 1.47393e7i) q^{67} +(499355. - 864909. i) q^{68} +(835570. + 482417. i) q^{69} +5.35212e6i q^{70} +(2.19596e7 + 1.26784e7i) q^{71} +(2.39073e7 + 1.38029e7i) q^{72} +(-1.61275e7 - 9.31122e6i) q^{73} +(6.32934e6 + 1.09627e7i) q^{74} +2.70686e6i q^{75} +(-1.76814e6 + 1.02084e6i) q^{76} +(-1.44273e7 - 8.32963e6i) q^{77} +6.40511e6 q^{78} +(-2.46478e7 + 4.26912e7i) q^{79} +(1.98869e7 - 1.14817e7i) q^{80} +(-2.01451e7 - 3.48923e7i) q^{81} -3.14003e7i q^{82} +(4.70896e6 + 8.15616e6i) q^{83} +315458. q^{84} +1.33891e7i q^{85} +(-1.11731e7 + 5.01564e7i) q^{86} +1.22335e7 q^{87} +8.11483e7i q^{88} +(-7.45097e7 + 4.30182e7i) q^{89} -3.89234e7 q^{90} +(-2.74306e7 + 1.58371e7i) q^{91} +(1.22214e6 + 2.11682e6i) q^{92} +(4.67933e6 + 2.70161e6i) q^{93} +1.29706e8i q^{94} +(1.36858e7 - 2.37044e7i) q^{95} +(-1.45581e6 - 2.52154e6i) q^{96} +1.19244e8 q^{97} +(-6.48950e7 + 3.74671e7i) q^{98} +(6.05775e7 - 1.04923e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 84 q^{3} - 6474 q^{4} - 3 q^{5} + 1791 q^{6} - 5031 q^{7} + 57858 q^{9}+O(q^{10}) $ 56 * q - 84 * q^3 - 6474 * q^4 - 3 * q^5 + 1791 * q^6 - 5031 * q^7 + 57858 * q^9	\( 56 q - 84 q^{3} - 6474 q^{4} - 3 q^{5} + 1791 q^{6} - 5031 q^{7} + 57858 q^{9} + 12491 q^{10} + 31928 q^{11} + 56574 q^{12} - 24868 q^{13} + 106830 q^{14} - 11989 q^{15} + 655366 q^{16} + 5963 q^{17} + 326445 q^{18} - 67476 q^{19} - 713343 q^{20} - 187232 q^{21} - 210724 q^{23} - 1651574 q^{24} + 1650473 q^{25} + 765 q^{26} + 684492 q^{28} - 5568699 q^{29} - 3412593 q^{30} + 2602959 q^{31} - 554514 q^{33} - 584967 q^{34} + 8137398 q^{35} - 3035428 q^{36} - 3541812 q^{37} + 6280356 q^{38} - 2473841 q^{40} + 7375370 q^{41} + 15490227 q^{43} - 2983894 q^{44} + 3217584 q^{46} - 7588210 q^{47} + 5844987 q^{48} + 33155723 q^{49} - 9064422 q^{50} + 3837506 q^{52} - 5366122 q^{53} - 45158560 q^{54} + 40061478 q^{55} - 39705477 q^{56} + 13330347 q^{57} + 19271684 q^{58} + 18367244 q^{59} - 36808121 q^{60} - 6722484 q^{61} - 15483591 q^{62} - 40574925 q^{63} - 87236036 q^{64} - 33263013 q^{66} - 8581935 q^{67} - 123045082 q^{68} - 26516709 q^{69} - 132304098 q^{71} - 100762446 q^{72} + 278404467 q^{73} + 182026410 q^{74} + 179327130 q^{76} + 143930505 q^{77} - 143413472 q^{78} - 62931368 q^{79} + 121842717 q^{80} - 65032540 q^{81} - 29005780 q^{83} + 370916864 q^{84} + 73281798 q^{86} + 137580504 q^{87} - 124655943 q^{89} + 63835252 q^{90} + 287393496 q^{91} - 215232271 q^{92} - 124327923 q^{93} + 413979855 q^{95} + 51391714 q^{96} - 446400270 q^{97} - 351696195 q^{98} - 146664065 q^{99}+O(q^{100}) \) 56 * q - 84 * q^3 - 6474 * q^4 - 3 * q^5 + 1791 * q^6 - 5031 * q^7 + 57858 * q^9 + 12491 * q^10 + 31928 * q^11 + 56574 * q^12 - 24868 * q^13 + 106830 * q^14 - 11989 * q^15 + 655366 * q^16 + 5963 * q^17 + 326445 * q^18 - 67476 * q^19 - 713343 * q^20 - 187232 * q^21 - 210724 * q^23 - 1651574 * q^24 + 1650473 * q^25 + 765 * q^26 + 684492 * q^28 - 5568699 * q^29 - 3412593 * q^30 + 2602959 * q^31 - 554514 * q^33 - 584967 * q^34 + 8137398 * q^35 - 3035428 * q^36 - 3541812 * q^37 + 6280356 * q^38 - 2473841 * q^40 + 7375370 * q^41 + 15490227 * q^43 - 2983894 * q^44 + 3217584 * q^46 - 7588210 * q^47 + 5844987 * q^48 + 33155723 * q^49 - 9064422 * q^50 + 3837506 * q^52 - 5366122 * q^53 - 45158560 * q^54 + 40061478 * q^55 - 39705477 * q^56 + 13330347 * q^57 + 19271684 * q^58 + 18367244 * q^59 - 36808121 * q^60 - 6722484 * q^61 - 15483591 * q^62 - 40574925 * q^63 - 87236036 * q^64 - 33263013 * q^66 - 8581935 * q^67 - 123045082 * q^68 - 26516709 * q^69 - 132304098 * q^71 - 100762446 * q^72 + 278404467 * q^73 + 182026410 * q^74 + 179327130 * q^76 + 143930505 * q^77 - 143413472 * q^78 - 62931368 * q^79 + 121842717 * q^80 - 65032540 * q^81 - 29005780 * q^83 + 370916864 * q^84 + 73281798 * q^86 + 137580504 * q^87 - 124655943 * q^89 + 63835252 * q^90 + 287393496 * q^91 - 215232271 * q^92 - 124327923 * q^93 + 413979855 * q^95 + 51391714 * q^96 - 446400270 * q^97 - 351696195 * q^98 - 146664065 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	15.0304i		−	0.939397i	−0.882827	−	0.469699i	$-0.844363\pi$
$2$		−	15.0304i		−	0.939397i	0.882827	−	0.469699i	$-0.155637\pi$
$3$	10.2856	−	5.93838i	0.126982	−	0.0733134i	−0.435163	−	0.900352i	$-0.643309\pi$
$3$	10.2856	−	5.93838i	0.126982	−	0.0733134i	0.562146	+	0.827038i	$0.309976\pi$
$4$	30.0883			0.117533
$5$	−349.334	+	201.688i	−0.558935	+	0.322701i	−0.752718	−	0.658343i	$-0.771258\pi$
$5$	−349.334	+	201.688i	−0.558935	+	0.322701i	0.193783	+	0.981044i	$0.437924\pi$
$6$	−89.2560	−	154.596i	−0.0688704	−	0.119287i
$7$	764.498	+	441.383i	0.318408	+	0.183833i	0.650683	−	0.759350i	$-0.274483\pi$
$7$	764.498	+	441.383i	0.318408	+	0.183833i	−0.332275	+	0.943183i	$0.607816\pi$
$8$		−	4300.01i		−	1.04981i
$9$	−3209.97	+	5559.83i	−0.489250	+	0.847406i
$10$	3031.45	+	5250.62i	0.303145	+	0.525062i
$11$	−18871.7			−1.28896			−0.644480	−	0.764621i	$-0.722926\pi$
$11$	−18871.7			−1.28896			−0.644480	+	0.764621i	$0.722926\pi$
$12$	309.476	−	178.676i	0.0149246	−	0.00861670i
$13$	−17940.3	+	31073.5i	−0.628139	+	1.08797i	0.359786	+	0.933035i	$0.382850\pi$
$13$	−17940.3	+	31073.5i	−0.628139	+	1.08797i	−0.987925	+	0.154934i	$0.950483\pi$
$14$	6634.14	−	11490.7i	0.172692	−	0.299112i
$15$	−2395.41	+	4148.96i	−0.0473166	+	0.0819548i
$16$	−56928.1			−0.868654
$17$	16596.3	−	28745.7i	0.198708	−	0.344173i	−0.749402	−	0.662116i	$-0.769659\pi$
$17$	16596.3	−	28745.7i	0.198708	−	0.344173i	0.948110	+	0.317943i	$0.102992\pi$
$18$	83566.3	+	48247.0i	0.796051	+	0.459600i
$19$	−58765.0	+	33928.0i	−0.450925	+	0.260342i	−0.708221	−	0.705991i	$-0.750502\pi$
$19$	−58765.0	+	33928.0i	−0.450925	+	0.260342i	0.257296	+	0.966333i	$0.417169\pi$
$20$	−10510.9	+	6068.46i	−0.0656930	+	0.0379279i
$21$	10484.4			0.0539096
$22$			283648.i			1.21085i
$23$	40618.5	+	70353.4i	0.145149	+	0.251405i	0.929428	−	0.369003i	$-0.120301\pi$
$23$	40618.5	+	70353.4i	0.145149	+	0.251405i	−0.784280	+	0.620407i	$0.786967\pi$
$24$	−25535.1	−	44228.1i	−0.0769649	−	0.133307i
$25$	−113956.	+	197378.i	−0.291728	+	0.505287i
$26$	467046.	+	269649.i	1.02204	+	0.590072i
$27$			154172.i			0.290101i
$28$	23002.5	+	13280.5i	0.0374233	+	0.0216063i
$29$	892041.	+	515020.i	1.26123	+	0.728169i	0.973312	−	0.229487i	$-0.0737048\pi$
$29$	892041.	+	515020.i	1.26123	+	0.728169i	0.287914	+	0.957656i	$0.407038\pi$
$30$	62360.4	+	36003.8i	0.0769882	+	0.0444491i
$31$	227470.	+	393990.i	0.246308	+	0.426617i	0.962498	−	0.271287i	$-0.0874493\pi$
$31$	227470.	+	393990.i	0.246308	+	0.426617i	−0.716191	+	0.697904i	$0.754116\pi$
$32$		−	245153.i		−	0.233796i
$33$	−194106.	+	112067.i	−0.163675	+	0.0944980i
$34$	−432058.	−	249449.i	−0.323315	−	0.186666i
$35$	−356087.			−0.237293
$36$	−96582.6	+	167286.i	−0.0575028	+	0.0995978i
$37$	−729373.	+	421103.i	−0.389173	+	0.224689i	−0.681802	−	0.731537i	$-0.738803\pi$
$37$	−729373.	+	421103.i	−0.389173	+	0.224689i	0.292629	+	0.956226i	$0.405470\pi$
$38$	509950.	+	883260.i	0.244564	+	0.423598i
$39$			426145.i			0.184204i
$40$	867262.	+	1.50214e6i	0.338774	+	0.586774i
$41$	2.08913e6			0.739315			0.369657	−	0.929168i	$-0.379475\pi$
$41$	2.08913e6			0.739315			0.369657	+	0.929168i	$0.379475\pi$
$42$		−	157584.i		−	0.0506426i
$43$	−3.33700e6	−	743370.i	−0.976075	−	0.217436i
$43$	−3.33700e6	−	743370.i	−0.976075	−	0.217436i
$44$	−567817.			−0.151495
$45$		−	2.58966e6i		−	0.631527i
$46$	1.05744e6	−	610511.i	0.236169	−	0.136352i
$47$	−8.62960e6			−1.76848			−0.884238	−	0.467036i	$-0.845322\pi$
$47$	−8.62960e6			−1.76848			−0.884238	+	0.467036i	$0.845322\pi$
$48$	−585538.	+	338061.i	−0.110304	+	0.0636839i
$49$	−2.49276e6	−	4.31759e6i	−0.432411	−	0.748958i
$50$	2.96666e6	+	1.71280e6i	0.474665	+	0.274048i
$51$		−	394221.i		−	0.0582719i
$52$	−539793.	+	934949.i	−0.0738268	+	0.127872i
$53$	−3.56207e6	−	6.16968e6i	−0.451439	−	0.781914i	0.547037	−	0.837108i	$-0.315756\pi$
$53$	−3.56207e6	−	6.16968e6i	−0.451439	−	0.781914i	−0.998476	+	0.0551939i	$0.982422\pi$
$54$	2.31725e6			0.272520
$55$	6.59252e6	−	3.80619e6i	0.720445	−	0.415949i
$56$	1.89795e6	−	3.28735e6i	0.192989	−	0.334267i
$57$	−402955.	+	697939.i	−0.0381731	+	0.0661177i
$58$	7.74094e6	−	1.34077e7i	0.684040	−	1.18479i
$59$	932693.			0.0769716			0.0384858	−	0.999259i	$-0.487747\pi$
$59$	932693.			0.0769716			0.0384858	+	0.999259i	$0.487747\pi$
$60$	−72073.7	+	124835.i	−0.00556124	+	0.00963236i
$61$	9.32479e6	+	5.38367e6i	0.673472	+	0.388829i	0.797391	−	0.603463i	$-0.206213\pi$
$61$	9.32479e6	+	5.38367e6i	0.673472	+	0.388829i	−0.123919	+	0.992292i	$0.539546\pi$
$62$	5.92181e6	−	3.41896e6i	0.400763	−	0.231381i
$63$	−4.90803e6	+	2.83365e6i	−0.311562	+	0.179881i
$64$	−1.82583e7			−1.08828
$65$		−	1.44734e7i		−	0.810806i
$66$	1.68441e6	+	2.91748e6i	0.0887712	+	0.153756i
$67$	−8.50977e6	−	1.47393e7i	−0.422297	−	0.731440i	0.573866	−	0.818949i	$-0.305443\pi$
$67$	−8.50977e6	−	1.47393e7i	−0.422297	−	0.731440i	−0.996164	+	0.0875084i	$0.972110\pi$
$68$	499355.	−	864909.i	0.0233547	−	0.0404515i
$69$	835570.	+	482417.i	0.0368627	+	0.0212827i
$70$			5.35212e6i			0.222912i
$71$	2.19596e7	+	1.26784e7i	0.864152	+	0.498918i	0.865400	−	0.501081i	$-0.167064\pi$
$71$	2.19596e7	+	1.26784e7i	0.864152	+	0.498918i	−0.00124854	+	0.999999i	$0.500397\pi$
$72$	2.39073e7	+	1.38029e7i	0.889613	+	0.513618i
$73$	−1.61275e7	−	9.31122e6i	−0.567905	−	0.327880i	0.188407	−	0.982091i	$-0.439668\pi$
$73$	−1.61275e7	−	9.31122e6i	−0.567905	−	0.327880i	−0.756312	+	0.654211i	$0.773001\pi$
$74$	6.32934e6	+	1.09627e7i	0.211072	+	0.365588i
$75$			2.70686e6i			0.0855501i
$76$	−1.76814e6	+	1.02084e6i	−0.0529984	+	0.0305986i
$77$	−1.44273e7	−	8.32963e6i	−0.410415	−	0.236953i
$78$	6.40511e6			0.173041
$79$	−2.46478e7	+	4.26912e7i	−0.632804	+	1.09605i	0.354172	+	0.935180i	$0.384763\pi$
$79$	−2.46478e7	+	4.26912e7i	−0.632804	+	1.09605i	−0.986976	+	0.160868i	$0.948571\pi$
$80$	1.98869e7	−	1.14817e7i	0.485521	−	0.280316i
$81$	−2.01451e7	−	3.48923e7i	−0.467982	−	0.810569i
$82$		−	3.14003e7i		−	0.694510i
$83$	4.70896e6	+	8.15616e6i	0.0992231	+	0.171859i	0.911363	−	0.411603i	$-0.135031\pi$
$83$	4.70896e6	+	8.15616e6i	0.0992231	+	0.171859i	−0.812140	+	0.583462i	$0.801698\pi$
$84$	315458.			0.00633614
$85$			1.33891e7i			0.256494i
$86$	−1.11731e7	+	5.01564e7i	−0.204259	+	0.916922i
$87$	1.22335e7			0.213538
$88$			8.11483e7i			1.35316i
$89$	−7.45097e7	+	4.30182e7i	−1.18755	+	0.685634i	−0.957749	−	0.287604i	$-0.907141\pi$
$89$	−7.45097e7	+	4.30182e7i	−1.18755	+	0.685634i	−0.229803	+	0.973237i	$0.573808\pi$
$90$	−3.89234e7			−0.593255
$91$	−2.74306e7	+	1.58371e7i	−0.400009	+	0.230945i
$92$	1.22214e6	+	2.11682e6i	0.0170597	+	0.0295482i
$93$	4.67933e6	+	2.70161e6i	0.0625535	+	0.0361153i
$94$			1.29706e8i			1.66130i
$95$	1.36858e7	−	2.37044e7i	0.168025	−	0.291028i
$96$	−1.45581e6	−	2.52154e6i	−0.0171404	−	0.0296880i
$97$	1.19244e8			1.34695			0.673475	−	0.739210i	$-0.264801\pi$
$97$	1.19244e8			1.34695			0.673475	+	0.739210i	$0.264801\pi$
$98$	−6.48950e7	+	3.74671e7i	−0.703569	+	0.406206i
$99$	6.05775e7	−	1.04923e8i	0.630624	−	1.09227i
$100$	−3.42875e6	+	5.93877e6i	−0.0342875	+	0.0593877i
$101$	9.39474e7	−	1.62722e8i	0.902816	−	1.56372i	0.0789928	−	0.996875i	$-0.474830\pi$
$101$	9.39474e7	−	1.62722e8i	0.902816	−	1.56372i	0.823823	−	0.566847i	$-0.191837\pi$
$102$	−5.92528e6			−0.0547405
$103$	−8.76893e6	+	1.51882e7i	−0.0779108	+	0.134945i	−0.902348	−	0.431007i	$-0.858158\pi$
$103$	−8.76893e6	+	1.51882e7i	−0.0779108	+	0.134945i	0.824438	+	0.565953i	$0.191492\pi$
$104$	1.33616e8	+	7.71434e7i	1.14216	+	0.659425i
$105$	−3.66256e6	+	2.11458e6i	−0.0301320	+	0.0173967i
$106$	−9.27325e7	+	5.35391e7i	−0.734528	+	0.424080i
$107$	3.16416e7			0.241392			0.120696	−	0.992689i	$-0.461487\pi$
$107$	3.16416e7			0.241392			0.120696	+	0.992689i	$0.461487\pi$
$108$			4.63876e6i			0.0340963i
$109$	7.64422e7	+	1.32402e8i	0.541536	+	0.937967i	0.998816	+	0.0486448i	$0.0154902\pi$
$109$	7.64422e7	+	1.32402e8i	0.541536	+	0.937967i	−0.457280	+	0.889323i	$0.651176\pi$
$110$	−5.72085e7	−	9.90880e7i	−0.390742	−	0.676784i
$111$	−5.00135e6	+	8.66259e6i	−0.0329454	+	0.0570631i
$112$	−4.35214e7	−	2.51271e7i	−0.276586	−	0.159687i
$113$		−	1.77312e8i		−	1.08749i	−0.839252	−	0.543743i	$-0.817007\pi$
$113$		−	1.77312e8i		−	1.08749i	0.839252	−	0.543743i	$-0.182993\pi$
$114$	1.04903e7	+	6.05656e6i	0.0621108	+	0.0358597i
$115$	−2.83789e7	−	1.63846e7i	−0.162257	−	0.0936793i
$116$	2.68400e7	+	1.54961e7i	0.148235	+	0.0855836i
$117$	−1.15176e8	−	1.99490e8i	−0.614635	−	1.06458i
$118$		−	1.40187e7i		−	0.0723070i
$119$	2.53757e7	−	1.46507e7i	0.126541	−	0.0730583i
$120$	1.78406e7	+	1.03003e7i	0.0860368	+	0.0496733i
$121$	1.41781e8			0.661418
$122$	8.09185e7	−	1.40155e8i	0.365265	−	0.632658i
$123$	2.14879e7	−	1.24060e7i	0.0938800	−	0.0542017i
$124$	6.84420e6	+	1.18545e7i	0.0289491	+	0.0501414i
$125$		−	2.49504e8i		−	1.02197i
$126$	4.25908e7	+	7.37695e7i	0.168979	+	0.292681i
$127$	−1.93308e8			−0.743078			−0.371539	−	0.928417i	$-0.621170\pi$
$127$	−1.93308e8			−0.743078			−0.371539	+	0.928417i	$0.621170\pi$
$128$			2.11670e8i			0.788532i
$129$	−3.87374e7	+	1.21704e7i	−0.139885	+	0.0439488i
$130$	−2.17540e8			−0.761669
$131$		−	2.22292e8i		−	0.754812i	−0.926048	−	0.377406i	$-0.876816\pi$
$131$		−	2.22292e8i		−	0.754812i	0.926048	−	0.377406i	$-0.123184\pi$
$132$	−5.84032e6	+	3.37191e6i	−0.0192372	+	0.0111066i
$133$	−5.99010e7			−0.191438
$134$	−2.21538e8	+	1.27905e8i	−0.687113	+	0.396705i
$135$	−3.10946e7	−	5.38575e7i	−0.0936160	−	0.162148i
$136$	−1.23607e8	−	7.13643e7i	−0.361315	−	0.208605i
$137$			5.90691e8i			1.67679i	0.545064	+	0.838394i	$0.316505\pi$
$137$			5.90691e8i			1.67679i	−0.545064	+	0.838394i	$0.683495\pi$
$138$	7.25090e6	−	1.25589e7i	0.0199929	−	0.0346287i
$139$	−2.42944e8	−	4.20791e8i	−0.650798	−	1.12722i	−0.982930	−	0.183982i	$-0.941101\pi$
$139$	−2.42944e8	−	4.20791e8i	−0.650798	−	1.12722i	0.332132	−	0.943233i	$-0.392232\pi$
$140$	−1.07141e7			−0.0278896
$141$	−8.87605e7	+	5.12459e7i	−0.224566	+	0.129653i
$142$	1.90560e8	−	3.30060e8i	0.468683	−	0.811782i
$143$	3.38563e8	−	5.86408e8i	0.809646	−	1.40235i
$144$	1.82738e8	−	3.16511e8i	0.424989	−	0.736103i
$145$	−4.15494e8			−0.939925
$146$	−1.39951e8	+	2.42402e8i	−0.308010	+	0.533489i
$147$	−5.12790e7	−	2.96060e7i	−0.109817	−	0.0634030i
$148$	−2.19456e7	+	1.26703e7i	−0.0457405	+	0.0264083i
$149$	3.98584e8	−	2.30123e8i	0.808677	−	0.466890i	−0.0378195	−	0.999285i	$-0.512041\pi$
$149$	3.98584e8	−	2.30123e8i	0.808677	−	0.466890i	0.846496	+	0.532395i	$0.178708\pi$
$150$	4.06851e7			0.0803656
$151$			6.96477e8i			1.33967i	0.742509	+	0.669837i	$0.233636\pi$
$151$			6.96477e8i			1.33967i	−0.742509	+	0.669837i	$0.766364\pi$
$152$	1.45891e8	+	2.52690e8i	0.273309	+	0.473385i
$153$	1.06547e8	+	1.84546e8i	0.194436	+	0.336773i
$154$	−1.25197e8	+	2.16848e8i	−0.222593	+	0.385543i
$155$	−1.58926e8	−	9.17562e7i	−0.275340	−	0.158968i
$156$			1.28220e7i			0.0216500i
$157$	4.23370e8	+	2.44433e8i	0.696822	+	0.402310i	0.806163	−	0.591694i	$-0.201541\pi$
$157$	4.23370e8	+	2.44433e8i	0.696822	+	0.402310i	−0.109341	+	0.994004i	$0.534874\pi$
$158$	6.41664e8	+	3.70465e8i	1.02962	+	0.594454i
$159$	−7.32758e7	−	4.23058e7i	−0.114650	−	0.0661929i
$160$	4.94445e7	+	8.56404e7i	0.0754464	+	0.130677i
$161$			7.17133e7i			0.106732i
$162$	−5.24444e8	+	3.02788e8i	−0.761446	+	0.439621i
$163$	3.52122e7	+	2.03298e7i	0.0498819	+	0.0287993i	0.524734	−	0.851267i	$-0.324165\pi$
$163$	3.52122e7	+	2.03298e7i	0.0498819	+	0.0287993i	−0.474852	+	0.880066i	$0.657498\pi$
$164$	6.28583e7			0.0868935
$165$	4.52053e7	−	7.82978e7i	0.0609893	−	0.105636i
$166$	1.22590e8	−	7.07774e7i	0.161444	−	0.0932099i
$167$	6.00960e8	+	1.04089e9i	0.772644	+	1.33826i	0.936109	+	0.351710i	$0.114400\pi$
$167$	6.00960e8	+	1.04089e9i	0.772644	+	1.33826i	−0.163465	+	0.986549i	$0.552267\pi$
$168$		−	4.50830e7i		−	0.0565947i
$169$	−2.35842e8	−	4.08491e8i	−0.289118	−	0.500767i
$170$	2.01243e8			0.240950
$171$		−	4.35632e8i		−	0.509489i
$172$	−1.00405e8	−	2.23667e7i	−0.114720	−	0.0255558i
$173$	−5.93068e8			−0.662095			−0.331047	−	0.943614i	$-0.607402\pi$
$173$	−5.93068e8			−0.662095			−0.331047	+	0.943614i	$0.607402\pi$
$174$		−	1.83875e8i		−	0.200597i
$175$	−1.74238e8	+	1.00597e8i	−0.185777	+	0.107258i
$176$	1.07433e9			1.11966
$177$	9.59329e6	−	5.53869e6i	0.00977405	−	0.00564305i
$178$	6.46579e8	+	1.11991e9i	0.644082	+	1.11558i
$179$	−1.18544e8	−	6.84415e7i	−0.115470	−	0.0666665i	0.441153	−	0.897432i	$-0.354570\pi$
$179$	−1.18544e8	−	6.84415e7i	−0.115470	−	0.0666665i	−0.556623	+	0.830766i	$0.687903\pi$
$180$		−	7.79184e7i		−	0.0742249i
$181$	−4.43254e8	+	7.67739e8i	−0.412989	+	0.715318i	−0.995215	−	0.0977088i	$-0.968849\pi$
$181$	−4.43254e8	+	7.67739e8i	−0.412989	+	0.715318i	0.582226	+	0.813027i	$0.302182\pi$
$182$	2.38037e8	+	4.12292e8i	0.216950	+	0.375768i
$183$	1.27881e8			0.114026
$184$	3.02520e8	−	1.74660e8i	0.263927	−	0.152378i
$185$	1.69863e8	−	2.94212e8i	0.145015	−	0.251173i
$186$	4.06062e7	−	7.03319e7i	0.0339266	−	0.0587626i
$187$	−3.13200e8	+	5.42478e8i	−0.256127	+	0.443625i
$188$	−2.59650e8			−0.207853
$189$	−6.80487e7	+	1.17864e8i	−0.0533301	+	0.0923705i
$190$	−3.56286e8	−	2.05702e8i	−0.273391	−	0.157843i
$191$	−1.10942e9	+	6.40523e8i	−0.833609	+	0.481284i	−0.855087	−	0.518485i	$-0.826496\pi$
$191$	−1.10942e9	+	6.40523e8i	−0.833609	+	0.481284i	0.0214780	+	0.999769i	$0.493163\pi$
$192$	−1.87797e8	+	1.08425e8i	−0.138193	+	0.0797855i
$193$	−1.86936e8			−0.134730			−0.0673648	−	0.997728i	$-0.521459\pi$
$193$	−1.86936e8			−0.134730			−0.0673648	+	0.997728i	$0.521459\pi$
$194$		−	1.79229e9i		−	1.26532i
$195$	−8.59485e7	−	1.48867e8i	−0.0594429	−	0.102958i
$196$	−7.50030e7	−	1.29909e8i	−0.0508223	−	0.0880269i
$197$	−1.60537e8	+	2.78058e8i	−0.106588	+	0.184616i	−0.914386	−	0.404843i	$-0.867326\pi$
$197$	−1.60537e8	+	2.78058e8i	−0.106588	+	0.184616i	0.807798	+	0.589460i	$0.200659\pi$
$198$	−1.57703e9	−	9.10501e8i	−1.02608	−	0.592407i
$199$			9.71297e8i			0.619355i	0.950842	+	0.309678i	$0.100221\pi$
$199$			9.71297e8i			0.619355i	−0.950842	+	0.309678i	$0.899779\pi$
$200$	8.48726e8	+	4.90012e8i	0.530454	+	0.306258i
$201$	−1.75056e8	−	1.01068e8i	−0.107249	−	0.0619201i
$202$	−2.44576e9	−	1.41206e9i	−1.46896	−	0.848103i
$203$	4.54642e8	+	7.87464e8i	0.267723	+	0.463710i
$204$		−	1.18615e7i		−	0.00684884i
$205$	−7.29804e8	+	4.21353e8i	−0.413229	+	0.238578i
$206$	2.28285e8	+	1.31800e8i	0.126767	+	0.0731892i
$207$	−5.21537e8			−0.284056
$208$	1.02131e9	−	1.76895e9i	0.545635	−	0.945068i
$209$	1.10899e9	−	6.40278e8i	0.581225	−	0.335570i
$210$	3.17829e7	+	5.50496e7i	0.0163424	+	0.0283059i
$211$		−	1.68864e9i		−	0.851936i	−0.904738	−	0.425968i	$-0.859934\pi$
$211$		−	1.68864e9i		−	0.851936i	0.904738	−	0.425968i	$-0.140066\pi$
$212$	−1.07177e8	−	1.85635e8i	−0.0530587	−	0.0919004i
$213$	3.01156e8			0.146310
$214$		−	4.75585e8i		−	0.226763i
$215$	1.31566e9	−	4.13350e8i	0.615729	−	0.193448i
$216$	6.62939e8			0.304550
$217$			4.01606e8i			0.181118i
$218$	1.99005e9	−	1.14895e9i	0.881124	−	0.508717i
$219$	−2.21174e8			−0.0961520
$220$	1.98358e8	−	1.14522e8i	0.0846757	−	0.0488875i
$221$	5.95485e8	+	1.03141e9i	0.249633	+	0.432377i
$222$	1.30202e8	+	7.51720e7i	0.0536050	+	0.0309488i
$223$		−	4.36772e9i		−	1.76618i	−0.469203	−	0.883090i	$-0.655459\pi$
$223$		−	4.36772e9i		−	1.76618i	0.469203	−	0.883090i	$-0.344541\pi$
$224$	1.08206e8	−	1.87419e8i	0.0429794	−	0.0744426i
$225$	−7.31592e8	−	1.26715e9i	−0.285456	−	0.494424i
$226$	−2.66506e9			−1.02158
$227$	−6.56201e8	+	3.78858e8i	−0.247135	+	0.142683i	−0.618452	−	0.785823i	$-0.712240\pi$
$227$	−6.56201e8	+	3.78858e8i	−0.247135	+	0.142683i	0.371317	+	0.928506i	$0.378906\pi$
$228$	−1.21242e7	+	2.09998e7i	−0.00448658	+	0.00777098i
$229$	−1.54937e9	+	2.68358e9i	−0.563394	+	0.975828i	0.433803	+	0.901008i	$0.357171\pi$
$229$	−1.54937e9	+	2.68358e9i	−0.563394	+	0.975828i	−0.997197	+	0.0748198i	$0.976162\pi$
$230$	−2.46266e8	+	4.26545e8i	−0.0880021	+	0.152424i
$231$	−1.97858e8			−0.0694874
$232$	2.21459e9	−	3.83579e9i	0.764437	−	1.32404i
$233$	1.01716e9	+	5.87259e8i	0.345117	+	0.199253i	0.662533	−	0.749033i	$-0.269482\pi$
$233$	1.01716e9	+	5.87259e8i	0.345117	+	0.199253i	−0.317415	+	0.948287i	$0.602815\pi$
$234$	−2.99841e9	+	1.73113e9i	−1.00006	+	0.577386i
$235$	3.01462e9	−	1.74049e9i	0.988464	−	0.570690i
$236$	2.80632e7			0.00904667
$237$			5.85471e8i			0.185572i
$238$	−2.20205e8	−	3.81406e8i	−0.0686308	−	0.118872i
$239$	2.72175e9	+	4.71421e9i	0.834175	+	1.44483i	0.894700	+	0.446667i	$0.147389\pi$
$239$	2.72175e9	+	4.71421e9i	0.834175	+	1.44483i	−0.0605256	+	0.998167i	$0.519278\pi$
$240$	1.36366e8	−	2.36193e8i	0.0411018	−	0.0711904i
$241$	3.58486e9	+	2.06972e9i	1.06268	+	0.613541i	0.926173	−	0.377098i	$-0.123078\pi$
$241$	3.58486e9	+	2.06972e9i	1.06268	+	0.613541i	0.136510	+	0.990639i	$0.456411\pi$
$242$		−	2.13102e9i		−	0.621334i
$243$	−1.29041e9	−	7.45018e8i	−0.370086	−	0.213669i
$244$	2.80567e8	+	1.61986e8i	0.0791549	+	0.0457001i
$245$	1.74162e9	+	1.00552e9i	0.483379	+	0.279079i
$246$	−1.86467e8	−	3.22971e8i	−0.0509169	−	0.0881906i
$247$		−	2.43471e9i		−	0.654124i
$248$	1.69416e9	−	9.78124e8i	0.447866	−	0.258575i
$249$	9.68688e7	+	5.59272e7i	0.0251992	+	0.0145488i
$250$	−3.75013e9			−0.960033
$251$	−8.11165e8	+	1.40498e9i	−0.204369	+	0.353977i	−0.949931	−	0.312459i	$-0.898847\pi$
$251$	−8.11165e8	+	1.40498e9i	−0.204369	+	0.353977i	0.745563	+	0.666435i	$0.232181\pi$
$252$	−1.47674e8	+	8.52599e7i	−0.0366187	+	0.0211418i
$253$	−7.66539e8	−	1.32769e9i	−0.187091	−	0.324051i
$254$			2.90549e9i			0.698046i
$255$	7.95098e7	+	1.37715e8i	0.0188044	+	0.0325702i
$256$	−1.49266e9			−0.347536
$257$			3.84981e9i			0.882484i	0.897388	+	0.441242i	$0.145462\pi$
$257$			3.84981e9i			0.882484i	−0.897388	+	0.441242i	$0.854538\pi$
$258$	1.82926e8	+	5.82238e8i	0.0412854	+	0.131408i
$259$	−7.43472e8			−0.165221
$260$		−	4.35480e8i		−	0.0952960i
$261$	−5.72685e9	+	3.30640e9i	−1.23411	+	0.712514i
$262$	−3.34113e9			−0.709068
$263$	3.56626e9	−	2.05898e9i	0.745400	−	0.430357i	−0.0786292	−	0.996904i	$-0.525054\pi$
$263$	3.56626e9	−	2.05898e9i	0.745400	−	0.430357i	0.824030	+	0.566547i	$0.191721\pi$
$264$	4.81890e8	+	8.34658e8i	0.0992047	+	0.171828i
$265$	2.48871e9	+	1.43685e9i	0.504650	+	0.291360i
$266$			9.00333e8i			0.179836i
$267$	−5.10917e8	+	8.84934e8i	−0.100532	+	0.174127i
$268$	−2.56045e8	−	4.43482e8i	−0.0496337	−	0.0859680i
$269$	−2.93062e9			−0.559695			−0.279847	−	0.960045i	$-0.590284\pi$
$269$	−2.93062e9			−0.559695			−0.279847	+	0.960045i	$0.590284\pi$
$270$	−8.09497e8	+	4.67363e8i	−0.152321	+	0.0879426i
$271$	−2.09431e9	+	3.62746e9i	−0.388297	+	0.672551i	−0.992221	−	0.124492i	$-0.960270\pi$
$271$	−2.09431e9	+	3.62746e9i	−0.388297	+	0.672551i	0.603923	+	0.797043i	$0.293603\pi$
$272$	−9.44796e8	+	1.63644e9i	−0.172609	+	0.298967i
$273$	−1.88093e8	+	3.25787e8i	−0.0338628	+	0.0586520i
$274$	8.87830e9			1.57517
$275$	2.15054e9	−	3.72485e9i	0.376025	−	0.651295i
$276$	2.51409e7	+	1.45151e7i	0.00433256	+	0.00250141i
$277$	3.00093e9	−	1.73259e9i	0.509725	−	0.294290i	−0.222995	−	0.974820i	$-0.571583\pi$
$277$	3.00093e9	−	1.73259e9i	0.509725	−	0.294290i	0.732721	+	0.680529i	$0.238250\pi$
$278$	−6.32463e9	+	3.65153e9i	−1.05890	+	0.611358i
$279$	−2.92069e9			−0.482024
$280$			1.53118e9i			0.249111i
$281$	1.26127e9	+	2.18458e9i	0.202294	+	0.350383i	0.949267	−	0.314471i	$-0.101827\pi$
$281$	1.26127e9	+	2.18458e9i	0.202294	+	0.350383i	−0.746973	+	0.664854i	$0.768494\pi$
$282$	7.70244e8	+	1.33410e9i	0.121796	+	0.210956i
$283$	−9.88147e8	+	1.71152e9i	−0.154055	+	0.266831i	−0.932715	−	0.360616i	$-0.882567\pi$
$283$	−9.88147e8	+	1.71152e9i	−0.154055	+	0.266831i	0.778659	+	0.627447i	$0.215900\pi$
$284$	6.60726e8	+	3.81470e8i	0.101566	+	0.0586391i
$285$		−	3.25085e8i		−	0.0492740i
$286$	−8.81393e9	−	5.08872e9i	−1.31736	−	0.760580i
$287$	1.59713e9	+	9.22105e8i	0.235404	+	0.135910i
$288$	1.36301e9	+	7.86934e8i	0.198120	+	0.114385i
$289$	2.93700e9	+	5.08704e9i	0.421030	+	0.729245i
$290$			6.24503e9i			0.882963i
$291$	1.22650e9	−	7.08119e8i	0.171039	−	0.0987494i
$292$	−4.85250e8	−	2.80159e8i	−0.0667473	−	0.0385366i
$293$	5.21378e9			0.707427			0.353714	−	0.935354i	$-0.384919\pi$
$293$	5.21378e9			0.707427			0.353714	+	0.935354i	$0.384919\pi$
$294$	−4.44988e8	+	7.70742e8i	−0.0595606	+	0.103162i
$295$	−3.25822e8	+	1.88113e8i	−0.0430222	+	0.0248389i
$296$	1.81075e9	+	3.13631e9i	0.235880	+	0.408556i
$297$		−	2.90947e9i		−	0.373929i
$298$	−3.45883e9	−	5.99086e9i	−0.438595	−	0.759669i
$299$	−2.91483e9			−0.364694
$300$			8.14449e7i			0.0100549i
$301$	−2.22302e9	−	2.04120e9i	−0.270818	−	0.248668i
$302$	1.04683e10			1.25849
$303$		−	2.23158e9i		−	0.264754i
$304$	3.34538e9	−	1.93146e9i	0.391698	−	0.226147i
$305$	−4.34329e9			−0.501903
$306$	2.77379e9	−	1.60145e9i	0.316364	−	0.182653i
$307$	−6.20418e8	−	1.07460e9i	−0.0698443	−	0.120974i	0.828988	−	0.559266i	$-0.188917\pi$
$307$	−6.20418e8	−	1.07460e9i	−0.0698443	−	0.120974i	−0.898833	+	0.438292i	$0.855584\pi$
$308$	−4.34094e8	−	2.50625e8i	−0.0482371	−	0.0278497i
$309$			2.08293e8i			0.0228476i
$310$	−1.37913e9	+	2.38872e9i	−0.149334	+	0.258654i
$311$	−4.18340e8	−	7.24586e8i	−0.0447186	−	0.0774548i	0.842800	−	0.538227i	$-0.180906\pi$
$311$	−4.18340e8	−	7.24586e8i	−0.0447186	−	0.0774548i	−0.887518	+	0.460772i	$0.847572\pi$
$312$	1.83243e9			0.193379
$313$	5.18954e9	−	2.99618e9i	0.540694	−	0.312170i	−0.204666	−	0.978832i	$-0.565611\pi$
$313$	5.18954e9	−	2.99618e9i	0.540694	−	0.312170i	0.745360	+	0.666662i	$0.232278\pi$
$314$	3.67391e9	−	6.36341e9i	0.377929	−	0.654593i
$315$	1.14303e9	−	1.97979e9i	0.116095	−	0.201083i
$316$	−7.41610e8	+	1.28451e9i	−0.0743750	+	0.128821i
$317$	1.38617e10			1.37271			0.686355	−	0.727267i	$-0.259210\pi$
$317$	1.38617e10			1.37271			0.686355	+	0.727267i	$0.259210\pi$
$318$	−6.35872e8	+	1.10136e9i	−0.0621815	+	0.107701i
$319$	−1.68343e10	−	9.71929e9i	−1.62567	−	0.938581i
$320$	6.37826e9	−	3.68249e9i	0.608279	−	0.351190i
$321$	3.25452e8	−	1.87900e8i	0.0306526	−	0.0176973i
$322$	1.07788e9			0.100264
$323$			2.25232e9i			0.206928i
$324$	−6.06132e8	−	1.04985e9i	−0.0550031	−	0.0952682i
$325$	−4.08881e9	−	7.08203e9i	−0.366491	−	0.634781i
$326$	3.05564e8	−	5.29252e8i	0.0270540	−	0.0468589i
$327$	1.57250e9	+	9.07886e8i	0.137531	+	0.0794036i
$328$		−	8.98327e9i		−	0.776138i
$329$	−6.59731e9	−	3.80896e9i	−0.563097	−	0.325104i
$330$	−1.17684e9	−	6.79451e8i	−0.0992346	−	0.0572931i
$331$	−5.06626e9	−	2.92501e9i	−0.422061	−	0.243677i	0.273898	−	0.961759i	$-0.411687\pi$
$331$	−5.06626e9	−	2.92501e9i	−0.422061	−	0.243677i	−0.695959	+	0.718082i	$0.745020\pi$
$332$	1.41685e8	+	2.45405e8i	0.0116619	+	0.0201991i
$333$		−	5.40692e9i		−	0.439717i
$334$	1.56450e10	−	9.03264e9i	1.25716	−	0.725820i
$335$	5.94551e9	+	3.43264e9i	0.472074	+	0.272552i
$336$	−5.96857e8			−0.0468288
$337$	−8.17798e9	+	1.41647e10i	−0.634054	+	1.09821i	0.352660	+	0.935751i	$0.385277\pi$
$337$	−8.17798e9	+	1.41647e10i	−0.634054	+	1.09821i	−0.986715	+	0.162463i	$0.948056\pi$
$338$	−6.13976e9	+	3.54479e9i	−0.470419	+	0.271596i
$339$	−1.05294e9	−	1.82375e9i	−0.0797273	−	0.138092i
$340$			4.02857e8i			0.0301464i
$341$	−4.29274e9	−	7.43524e9i	−0.317481	−	0.549892i
$342$	−6.54770e9			−0.478613
$343$		−	9.49002e9i		−	0.685631i
$344$	−3.19650e9	+	1.43492e10i	−0.228266	+	1.02469i
$345$	−3.89191e8			−0.0274718
$346$			8.91403e9i			0.621970i
$347$	−9.31216e9	+	5.37638e9i	−0.642292	+	0.370828i	−0.785497	−	0.618865i	$-0.787593\pi$
$347$	−9.31216e9	+	5.37638e9i	−0.642292	+	0.370828i	0.143205	+	0.989693i	$0.454259\pi$
$348$	3.68087e8			0.0250977
$349$	−1.11008e10	+	6.40905e9i	−0.748261	+	0.432008i	−0.825065	−	0.565038i	$-0.808862\pi$
$349$	−1.11008e10	+	6.40905e9i	−0.748261	+	0.432008i	0.0768044	+	0.997046i	$0.475528\pi$
$350$	1.51200e9	+	2.61887e9i	0.100758	+	0.174518i
$351$	−4.79065e9	−	2.76588e9i	−0.315621	−	0.182224i
$352$			4.62645e9i			0.301354i
$353$	1.10243e10	−	1.90947e10i	0.709993	−	1.22974i	−0.254867	−	0.966976i	$-0.582032\pi$
$353$	1.10243e10	−	1.90947e10i	0.709993	−	1.22974i	0.964859	−	0.262767i	$-0.0846351\pi$
$354$	−8.32485e7	−	1.44191e8i	−0.00530107	−	0.00918172i
$355$	−1.02283e10			−0.644007
$356$	−2.24187e9	+	1.29434e9i	−0.139576	+	0.0805842i
$357$	1.74002e8	−	3.01381e8i	0.0107123	−	0.0185542i
$358$	−1.02870e9	+	1.78176e9i	−0.0626263	+	0.108472i
$359$	1.52241e10	−	2.63689e10i	0.916544	−	1.58750i	0.111918	−	0.993717i	$-0.464301\pi$
$359$	1.52241e10	−	2.63689e10i	0.916544	−	1.58750i	0.804625	−	0.593783i	$-0.202366\pi$
$360$	−1.11355e10			−0.662982
$361$	−6.18956e9	+	1.07206e10i	−0.364444	+	0.631236i
$362$	1.15394e10	+	6.66227e9i	0.671968	+	0.387961i
$363$	1.45830e9	−	8.41948e8i	0.0839884	−	0.0484907i
$364$	−8.25341e8	+	4.76511e8i	−0.0470141	+	0.0271436i
$365$	7.51186e9			0.423229
$366$		−	1.92210e9i		−	0.107115i
$367$	−9.43635e9	−	1.63442e10i	−0.520164	−	0.900950i	−0.999725	−	0.0234416i	$-0.992538\pi$
$367$	−9.43635e9	−	1.63442e10i	−0.520164	−	0.900950i	0.479562	−	0.877508i	$-0.340796\pi$
$368$	−2.31234e9	−	4.00508e9i	−0.126084	−	0.218384i
$369$	−6.70604e9	+	1.16152e10i	−0.361710	+	0.626500i
$370$	−4.42211e9	−	2.55311e9i	−0.235951	−	0.136227i
$371$		−	6.28894e9i		−	0.331957i
$372$	1.40793e8	+	8.12869e7i	0.00735207	+	0.00424472i
$373$	1.82476e10	+	1.05353e10i	0.942693	+	0.544264i	0.890803	−	0.454389i	$-0.150142\pi$
$373$	1.82476e10	+	1.05353e10i	0.942693	+	0.544264i	0.0518895	+	0.998653i	$0.483476\pi$
$374$	8.15365e9	+	4.70751e9i	0.416740	+	0.240605i
$375$	−1.48165e9	−	2.56629e9i	−0.0749238	−	0.129772i
$376$			3.71074e10i			1.85656i
$377$	−3.20069e10	+	1.84792e10i	−1.58445	+	0.914783i
$378$	1.77154e9	+	1.02280e9i	0.0867726	+	0.0500982i
$379$	2.95748e10			1.43339			0.716695	−	0.697386i	$-0.245654\pi$
$379$	2.95748e10			1.43339			0.716695	+	0.697386i	$0.245654\pi$
$380$	4.11782e8	−	7.13227e8i	0.0197484	−	0.0342053i
$381$	−1.98828e9	+	1.14794e9i	−0.0943579	+	0.0544776i
$382$	9.62730e9	+	1.66750e10i	0.452117	+	0.783090i
$383$		−	3.65174e9i		−	0.169709i	−0.996393	−	0.0848545i	$-0.972957\pi$
$383$		−	3.65174e9i		−	0.169709i	0.996393	−	0.0848545i	$-0.0270425\pi$
$384$	1.25698e9	+	2.17715e9i	0.0578100	+	0.100130i
$385$	6.71996e9			0.305861
$386$			2.80971e9i			0.126565i
$387$	1.48447e10	−	1.61670e10i	0.661801	−	0.720751i
$388$	3.58787e9			0.158310
$389$		−	8.75462e9i		−	0.382331i	−0.981558	−	0.191165i	$-0.938773\pi$
$389$		−	8.75462e9i		−	0.382331i	0.981558	−	0.191165i	$-0.0612266\pi$
$390$	−2.23753e9	+	1.29184e9i	−0.0967186	+	0.0558405i
$391$	2.69647e9			0.115369
$392$	−1.85657e10	+	1.07189e10i	−0.786261	+	0.453948i
$393$	−1.32006e9	−	2.28640e9i	−0.0553378	−	0.0958479i
$394$	4.17931e9	+	2.41293e9i	0.173428	+	0.100129i
$395$		−	1.98847e10i		−	0.816826i
$396$	1.82268e9	−	3.15697e9i	0.0741188	−	0.128378i
$397$	2.02659e10	+	3.51016e10i	0.815838	+	1.41307i	0.908725	+	0.417396i	$0.137057\pi$
$397$	2.02659e10	+	3.51016e10i	0.815838	+	1.41307i	−0.0928871	+	0.995677i	$0.529610\pi$
$398$	1.45989e10			0.581821
$399$	−6.16116e8	+	3.55715e8i	−0.0243092	+	0.0140349i
$400$	6.48730e9	−	1.12363e10i	0.253410	−	0.438919i
$401$	−2.04995e10	+	3.55062e10i	−0.792804	+	1.37318i	0.131420	+	0.991327i	$0.458046\pi$
$401$	−2.04995e10	+	3.55062e10i	−0.792804	+	1.37318i	−0.924224	+	0.381851i	$0.875287\pi$
$402$	−1.51910e9	+	2.63115e9i	−0.0581676	+	0.100749i
$403$	−1.63235e10			−0.618862
$404$	2.82672e9	−	4.89602e9i	0.106110	−	0.183788i
$405$	1.40747e10	+	8.12606e9i	0.523143	+	0.302037i
$406$	1.18359e10	−	6.83344e9i	0.435608	−	0.251498i
$407$	1.37645e10	−	7.94692e9i	0.501628	−	0.289615i
$408$	−1.69515e9			−0.0611743
$409$			3.08180e10i			1.10131i	0.834732	+	0.550657i	$0.185623\pi$
$409$			3.08180e10i			1.10131i	−0.834732	+	0.550657i	$0.814377\pi$
$410$	6.33308e9	+	1.09692e10i	0.224119	+	0.388186i
$411$	3.50775e9	+	6.07560e9i	0.122931	+	0.212923i
$412$	−2.63842e8	+	4.56988e8i	−0.00915705	+	0.0158605i
$413$	7.13042e8	+	4.11675e8i	0.0245084	+	0.0141499i
$414$			7.83889e9i			0.266842i
$415$	−3.29001e9	−	1.89949e9i	−0.110919	−	0.0640389i
$416$	7.61776e9	+	4.39812e9i	0.254363	+	0.146857i
$417$	−4.99763e9	−	2.88538e9i	−0.165280	−	0.0954244i
$418$	−9.62361e9	−	1.66686e10i	−0.315234	−	0.546001i
$419$		−	5.08993e9i		−	0.165141i	−0.996585	−	0.0825706i	$-0.973687\pi$
$419$		−	5.08993e9i		−	0.165141i	0.996585	−	0.0825706i	$-0.0263130\pi$
$420$	−1.10200e8	+	6.36242e7i	−0.00354149	+	0.00204468i
$421$	3.27508e8	+	1.89087e8i	0.0104254	+	0.00601912i	0.505204	−	0.863000i	$-0.331417\pi$
$421$	3.27508e8	+	1.89087e8i	0.0104254	+	0.00601912i	−0.494778	+	0.869019i	$0.664751\pi$
$422$	−2.53808e10			−0.800306
$423$	2.77008e10	−	4.79791e10i	0.865228	−	1.49862i
$424$	−2.65297e10	+	1.53169e10i	−0.820859	+	0.473923i
$425$	3.78250e9	+	6.55149e9i	0.115937	+	0.200809i
$426$		−	4.52648e9i		−	0.137443i
$427$	4.75252e9	+	8.23160e9i	0.142959	+	0.247613i
$428$	9.52043e8			0.0283715
$429$		−	8.04207e9i		−	0.237432i
$430$	−6.21281e9	−	1.97748e10i	−0.181725	−	0.578414i
$431$	−1.17733e10			−0.341184			−0.170592	−	0.985342i	$-0.554568\pi$
$431$	−1.17733e10			−0.341184			−0.170592	+	0.985342i	$0.554568\pi$
$432$		−	8.77669e9i		−	0.251997i
$433$	−2.48178e10	+	1.43286e10i	−0.706011	+	0.407616i	−0.809582	−	0.587006i	$-0.800306\pi$
$433$	−2.48178e10	+	1.43286e10i	−0.706011	+	0.407616i	0.103571	+	0.994622i	$0.466973\pi$
$434$	6.03628e9			0.170142
$435$	−4.27360e9	+	2.46736e9i	−0.119354	+	0.0689090i
$436$	2.30002e9	+	3.98375e9i	0.0636480	+	0.110242i
$437$	−4.77390e9	−	2.75621e9i	−0.130902	−	0.0755765i
$438$			3.32433e9i			0.0903249i
$439$	3.13388e8	−	5.42804e8i	0.00843771	−	0.0146145i	−0.861776	−	0.507289i	$-0.830647\pi$
$439$	3.13388e8	−	5.42804e8i	0.00843771	−	0.0146145i	0.870213	+	0.492675i	$0.163981\pi$
$440$	−1.63667e10	−	2.83479e10i	−0.436666	−	0.756328i
$441$	3.20068e10			0.846229
$442$	1.55025e10	−	8.95036e9i	0.406174	−	0.234505i
$443$	1.32186e10	−	2.28952e10i	0.343217	−	0.594470i	−0.641811	−	0.766863i	$-0.721817\pi$
$443$	1.32186e10	−	2.28952e10i	0.343217	−	0.594470i	0.985028	+	0.172393i	$0.0551499\pi$
$444$	−1.50482e8	+	2.60643e8i	−0.00387216	+	0.00670677i
$445$	1.73525e10	−	3.00555e10i	0.442510	−	0.766449i
$446$	−6.56484e10			−1.65915
$447$	2.73311e9	−	4.73389e9i	0.0684585	−	0.118574i
$448$	−1.39584e10	−	8.05891e9i	−0.346517	−	0.200062i
$449$	−2.20562e9	+	1.27342e9i	−0.0542682	+	0.0313318i	−0.526889	−	0.849934i	$-0.676642\pi$
$449$	−2.20562e9	+	1.27342e9i	−0.0542682	+	0.0313318i	0.472620	+	0.881266i	$0.343308\pi$
$450$	−1.90458e10	+	1.09961e10i	−0.464460	+	0.268156i
$451$	−3.94253e10			−0.952947
$452$		−	5.33501e9i		−	0.127815i
$453$	4.13595e9	+	7.16367e9i	0.0982159	+	0.170115i
$454$	5.69437e9	+	9.86294e9i	0.134036	+	0.232158i
$455$	6.38831e9	−	1.10649e10i	0.149053	−	0.258167i
$456$	3.00114e9	+	1.73271e9i	0.0694108	+	0.0400744i
$457$			6.11511e10i			1.40197i	0.713174	+	0.700987i	$0.247257\pi$
$457$			6.11511e10i			1.40197i	−0.713174	+	0.700987i	$0.752743\pi$
$458$	4.03352e10	+	2.32875e10i	0.916690	+	0.529251i
$459$	4.43176e9	+	2.55868e9i	0.0998449	+	0.0576455i
$460$	−8.53874e8	−	4.92984e8i	−0.0190705	−	0.0110104i
$461$	−3.03485e10	−	5.25651e10i	−0.671944	−	1.16384i	−0.977352	−	0.211619i	$-0.932126\pi$
$461$	−3.03485e10	−	5.25651e10i	−0.671944	−	1.16384i	0.305408	−	0.952221i	$-0.401207\pi$
$462$			2.97388e9i			0.0652763i
$463$	−7.45898e10	+	4.30644e10i	−1.62314	+	0.937119i	−0.637063	+	0.770811i	$0.719851\pi$
$463$	−7.45898e10	+	4.30644e10i	−1.62314	+	0.937119i	−0.986074	+	0.166307i	$0.946816\pi$
$464$	−5.07822e10	−	2.93191e10i	−1.09557	−	0.632527i
$465$	−2.17953e9			−0.0466178
$466$	8.82671e9	−	1.52883e10i	0.187178	−	0.324202i
$467$	2.15662e10	−	1.24513e10i	0.453426	−	0.261786i	−0.255850	−	0.966717i	$-0.582355\pi$
$467$	2.15662e10	−	1.24513e10i	0.453426	−	0.261786i	0.709276	+	0.704931i	$0.249022\pi$
$468$	−3.46544e9	−	6.00232e9i	−0.0722395	−	0.125123i
$469$		−	1.50243e10i		−	0.310529i
$470$	−2.61602e10	−	4.53108e10i	−0.536104	−	0.928560i
$471$	5.80614e9			0.117979
$472$		−	4.01059e9i		−	0.0808054i
$473$	6.29748e10	+	1.40286e10i	1.25812	+	0.280266i
$474$	8.79984e9			0.174326
$475$		−	1.54652e10i		−	0.303796i
$476$	7.63512e8	−	4.40814e8i	0.0148726	−	0.00858672i
$477$	4.57365e10			0.883466
$478$	7.08563e10	−	4.09089e10i	1.35727	−	0.783622i
$479$	2.19226e10	+	3.79711e10i	0.416438	+	0.721291i	0.995578	−	0.0939366i	$-0.0299451\pi$
$479$	2.19226e10	+	3.79711e10i	0.416438	+	0.721291i	−0.579141	+	0.815228i	$0.696612\pi$
$480$	1.01713e9	+	5.87241e8i	0.0191607	+	0.0110625i
$481$		−	3.02189e10i		−	0.564544i
$482$	3.11086e10	−	5.38817e10i	0.576359	−	0.998282i
$483$	4.25861e8	+	7.37613e8i	0.00782491	+	0.0135531i
$484$	4.26594e9			0.0777381
$485$	−4.16562e10	+	2.40502e10i	−0.752857	+	0.434662i
$486$	−1.11979e10	+	1.93953e10i	−0.200720	+	0.347658i
$487$	1.27128e10	−	2.20193e10i	0.226009	−	0.391460i	−0.730612	−	0.682792i	$-0.760765\pi$
$487$	1.27128e10	−	2.20193e10i	0.226009	−	0.391460i	0.956622	+	0.291333i	$0.0940987\pi$
$488$	2.31498e10	−	4.00967e10i	0.408196	−	0.707016i
$489$	4.82904e8			0.00844550
$490$	1.51134e10	−	2.61771e10i	0.262166	−	0.454085i
$491$	−9.41603e10	−	5.43635e10i	−1.62010	−	0.935365i	−0.986892	−	0.161384i	$-0.948404\pi$
$491$	−9.41603e10	−	5.43635e10i	−1.62010	−	0.935365i	−0.633208	−	0.773981i	$-0.718262\pi$
$492$	6.46534e8	−	3.73277e8i	0.0110340	−	0.00637046i
$493$	2.96092e10	−	1.70949e10i	0.501232	−	0.289387i
$494$	−3.65946e10			−0.614482
$495$			4.88711e10i			0.814013i
$496$	−1.29494e10	−	2.24291e10i	−0.213956	−	0.370583i
$497$	1.11920e10	+	1.93851e10i	0.183435	+	0.317719i
$498$	8.40606e8	−	1.45597e9i	0.0136671	−	0.0236721i
$499$	7.95243e10	+	4.59134e10i	1.28262	+	0.740520i	0.977326	−	0.211738i	$-0.0679125\pi$
$499$	7.95243e10	+	4.59134e10i	1.28262	+	0.740520i	0.305292	+	0.952259i	$0.401246\pi$
$500$		−	7.50714e9i		−	0.120114i
$501$	1.23624e10	+	7.13746e9i	0.196225	+	0.113290i
$502$	2.11173e10	+	1.21921e10i	0.332525	+	0.191983i
$503$	−2.31797e10	−	1.33828e10i	−0.362106	−	0.209062i	0.307898	−	0.951419i	$-0.400374\pi$
$503$	−2.31797e10	−	1.33828e10i	−0.362106	−	0.209062i	−0.670004	+	0.742357i	$0.733708\pi$
$504$	1.21847e10	+	2.11046e10i	0.188840	+	0.327080i
$505$			7.57923e10i			1.16536i
$506$	−1.99556e10	+	1.15214e10i	−0.304412	+	0.175753i
$507$	−4.85155e9	−	2.80104e9i	−0.0734258	−	0.0423924i
$508$	−5.81631e9			−0.0873359
$509$	−1.79537e10	+	3.10967e10i	−0.267474	+	0.463279i	−0.968209	−	0.250143i	$-0.919522\pi$
$509$	−1.79537e10	+	3.10967e10i	−0.267474	+	0.463279i	0.700735	+	0.713422i	$0.252856\pi$
$510$	2.06991e9	−	1.19506e9i	0.0305964	−	0.0176648i
$511$	−8.21963e9	−	1.42368e10i	−0.120550	−	0.208799i
$512$			7.66227e10i			1.11501i
$513$	−5.23074e9	−	9.05990e9i	−0.0755255	−	0.130814i
$514$	5.78641e10			0.829004
$515$		−	7.07436e9i		−	0.100568i
$516$	−1.16554e9	+	3.66188e8i	−0.0164411	+	0.00516541i
$517$	1.62855e11			2.27950
$518$			1.11746e10i			0.155208i
$519$	−6.10005e9	+	3.52186e9i	−0.0840744	+	0.0485404i
$520$	−6.22357e10			−0.851189
$521$	−6.43859e10	+	3.71732e10i	−0.873856	+	0.504521i	−0.868628	−	0.495466i	$-0.834997\pi$
$521$	−6.43859e10	+	3.71732e10i	−0.873856	+	0.504521i	−0.00522796	+	0.999986i	$0.501664\pi$
$522$	4.96964e10	+	8.60767e10i	0.669334	+	1.15932i
$523$	−8.34150e10	−	4.81597e10i	−1.11490	−	0.643690i	−0.174809	−	0.984602i	$-0.555931\pi$
$523$	−8.34150e10	−	4.81597e10i	−1.11490	−	0.643690i	−0.940095	+	0.340912i	$0.889264\pi$
$524$		−	6.68839e9i		−	0.0887149i
$525$	−1.19476e9	+	2.06939e9i	−0.0157269	+	0.0272399i
$526$	−3.09472e10	−	5.36021e10i	−0.404276	−	0.700227i
$527$	1.51007e10			0.195773
$528$	1.10501e10	−	6.37977e9i	0.142177	−	0.0820860i
$529$	3.58558e10	−	6.21040e10i	0.457864	−	0.793043i
$530$	2.15964e10	−	3.74061e10i	0.273702	−	0.474067i
$531$	−2.99392e9	+	5.18562e9i	−0.0376584	+	0.0652263i
$532$	−1.80232e9			−0.0225001
$533$	−3.74795e10	+	6.49165e10i	−0.464393	+	0.804352i
$534$	1.33009e10	+	7.67926e9i	0.163574	+	0.0944397i
$535$	−1.10535e10	+	6.38175e9i	−0.134923	+	0.0778977i
$536$	−6.33793e10	+	3.65921e10i	−0.767871	+	0.443331i
$537$	−1.62573e9			−0.0195502
$538$			4.40483e10i			0.525776i
$539$	4.70426e10	+	8.14801e10i	0.557360	+	0.965376i
$540$	−9.35585e8	−	1.62048e9i	−0.0110029	−	0.0190576i
$541$	−6.74491e10	+	1.16825e11i	−0.787385	+	1.36379i	0.140179	+	0.990126i	$0.455232\pi$
$541$	−6.74491e10	+	1.16825e11i	−0.787385	+	1.36379i	−0.927564	+	0.373665i	$0.878101\pi$
$542$	5.45220e10	+	3.14783e10i	0.631793	+	0.364766i
$543$			1.05289e10i			0.121111i
$544$	−7.04709e9	−	4.06864e9i	−0.0804663	−	0.0464572i
$545$	−5.34078e10	−	3.08350e10i	−0.605367	−	0.349509i
$546$	4.89669e9	+	2.82711e9i	0.0550976	+	0.0318106i
$547$	3.84001e10	+	6.65110e10i	0.428927	+	0.742923i	0.996778	−	0.0802079i	$-0.0255584\pi$
$547$	3.84001e10	+	6.65110e10i	0.428927	+	0.742923i	−0.567851	+	0.823131i	$0.692225\pi$
$548$			1.77729e10i			0.197077i
$549$	−5.98646e10	+	3.45628e10i	−0.658993	+	0.380470i
$550$	−5.59858e10	−	3.23234e10i	−0.611825	−	0.353237i
$551$	−6.98945e10			−0.758292
$552$	2.07440e9	−	3.59296e9i	0.0223427	−	0.0386987i
$553$	−3.76863e10	+	2.17582e10i	−0.402980	+	0.232660i
$554$	−2.60414e10	−	4.51050e10i	−0.276455	−	0.478835i
$555$		−	4.03485e9i		−	0.0425261i
$556$	−7.30976e9	−	1.26609e10i	−0.0764899	−	0.132484i
$557$	−7.34170e10			−0.762739			−0.381370	−	0.924423i	$-0.624547\pi$
$557$	−7.34170e10			−0.762739			−0.381370	+	0.924423i	$0.624547\pi$
$558$			4.38990e10i			0.452812i
$559$	8.29659e10	−	9.03561e10i	0.849674	−	0.925359i
$560$	2.02714e10			0.206125
$561$			7.43961e9i			0.0751101i
$562$	3.28350e10	−	1.89573e10i	0.329149	−	0.190034i
$563$	−6.49914e10			−0.646878			−0.323439	−	0.946249i	$-0.604839\pi$
$563$	−6.49914e10			−0.646878			−0.323439	+	0.946249i	$0.604839\pi$
$564$	−2.67065e9	+	1.54190e9i	−0.0263937	+	0.0152384i
$565$	3.57617e10	+	6.19411e10i	0.350933	+	0.607834i
$566$	2.57248e10	+	1.48522e10i	0.250661	+	0.144719i
$567$		−	3.55668e10i		−	0.344122i
$568$	5.45170e10	−	9.44263e10i	0.523768	−	0.907193i
$569$	5.01659e10	+	8.68899e10i	0.478585	+	0.828934i	0.999699	−	0.0245535i	$-0.00781640\pi$
$569$	5.01659e10	+	8.68899e10i	0.478585	+	0.828934i	−0.521113	+	0.853488i	$0.674483\pi$
$570$	−4.88615e9			−0.0462879
$571$	5.03792e10	−	2.90864e10i	0.473922	−	0.273619i	−0.243958	−	0.969786i	$-0.578446\pi$
$571$	5.03792e10	−	2.90864e10i	0.473922	−	0.273619i	0.717880	+	0.696167i	$0.245113\pi$
$572$	1.01868e10	−	1.76440e10i	0.0951598	−	0.164822i
$573$	−7.60735e9	+	1.31763e10i	−0.0705691	+	0.122229i
$574$	1.38596e10	−	2.40055e10i	0.127674	−	0.221138i
$575$	−1.85149e10			−0.169375
$576$	5.86087e10	−	1.01513e11i	0.532442	−	0.922216i
$577$	−5.17010e10	−	2.98496e10i	−0.466440	−	0.269299i	0.248308	−	0.968681i	$-0.420125\pi$
$577$	−5.17010e10	−	2.98496e10i	−0.466440	−	0.269299i	−0.714748	+	0.699382i	$0.753459\pi$
$578$	7.64600e10	−	4.41442e10i	0.685051	−	0.395515i
$579$	−1.92274e9	+	1.11010e9i	−0.0171083	+	0.00987748i
$580$	−1.25015e10			−0.110472
$581$			8.31382e9i			0.0729619i
$582$	−1.06433e10	−	1.84347e10i	−0.0927649	−	0.160674i
$583$	6.72221e10	+	1.16432e11i	0.581886	+	1.00786i
$584$	−4.00383e10	+	6.93484e10i	−0.344211	+	0.596191i
$585$	8.04696e10	+	4.64592e10i	0.687082	+	0.396687i
$586$		−	7.83649e10i		−	0.664555i
$587$	−1.74522e11	−	1.00760e11i	−1.46993	−	0.848665i	−0.470500	−	0.882400i	$-0.655926\pi$
$587$	−1.74522e11	−	1.00760e11i	−1.46993	−	0.848665i	−0.999431	+	0.0337356i	$0.989260\pi$
$588$	−1.54290e9	−	8.90794e8i	−0.0129071	−	0.00745191i
$589$	−2.67346e10	−	1.54352e10i	−0.222133	−	0.128248i
$590$	2.82741e9	+	4.89722e9i	0.0233336	+	0.0404149i
$591$			3.81332e9i			0.0312574i
$592$	4.15218e10	−	2.39726e10i	0.338056	−	0.195177i
$593$	8.36862e10	+	4.83163e10i	0.676761	+	0.390728i	0.798634	−	0.601818i	$-0.205557\pi$
$593$	8.36862e10	+	4.83163e10i	0.676761	+	0.390728i	−0.121873	+	0.992546i	$0.538890\pi$
$594$	−4.37304e10			−0.351268
$595$	−5.90974e9	+	1.02360e10i	−0.0471520	+	0.0816697i
$596$	1.19927e10	−	6.92400e9i	0.0950458	−	0.0548747i
$597$	5.76793e9	+	9.99035e9i	0.0454070	+	0.0786472i
$598$			4.38110e10i			0.342593i
$599$	−9.33774e10	−	1.61734e11i	−0.725328	−	1.25631i	−0.958839	−	0.283951i	$-0.908355\pi$
$599$	−9.33774e10	−	1.61734e11i	−0.725328	−	1.25631i	0.233511	−	0.972354i	$-0.424979\pi$
$600$	1.16395e10			0.0898112
$601$		−	4.21091e10i		−	0.322759i	−0.986892	−	0.161379i	$-0.948406\pi$
$601$		−	4.21091e10i		−	0.322759i	0.986892	−	0.161379i	$-0.0515943\pi$
$602$	−3.06800e10	+	3.34128e10i	−0.233598	+	0.254406i
$603$	1.09264e11			0.826436
$604$			2.09558e10i			0.157455i
$605$	−4.95289e10	+	2.85955e10i	−0.369690	+	0.213440i
$606$	−3.35415e10			−0.248709
$607$	2.22104e10	−	1.28232e10i	0.163607	−	0.0944584i	−0.415961	−	0.909382i	$-0.636555\pi$
$607$	2.22104e10	−	1.28232e10i	0.163607	−	0.0944584i	0.579568	+	0.814924i	$0.303221\pi$
$608$	8.31756e9	+	1.44064e10i	0.0608669	+	0.105425i
$609$	9.35252e9	+	5.39968e9i	0.0679923	+	0.0392553i
$610$			6.52813e10i			0.471486i
$611$	1.54817e11	−	2.68152e11i	1.11085	−	1.92405i
$612$	3.20583e9	+	5.55266e9i	0.0228526	+	0.0395818i
$613$	−1.35362e11			−0.958636			−0.479318	−	0.877641i	$-0.659116\pi$
$613$	−1.35362e11			−0.958636			−0.479318	+	0.877641i	$0.659116\pi$
$614$	−1.61516e10	+	9.32511e9i	−0.113643	+	0.0656116i
$615$	−5.00431e9	+	8.66771e9i	−0.0349819	+	0.0605904i
$616$	−3.58175e10	+	6.20377e10i	−0.248755	+	0.430857i
$617$	1.02873e11	−	1.78182e11i	0.709843	−	1.22948i	−0.255072	−	0.966922i	$-0.582099\pi$
$617$	1.02873e11	−	1.78182e11i	0.709843	−	1.22948i	0.964915	−	0.262562i	$-0.0845674\pi$
$618$	3.13072e9			0.0214630
$619$	9.87347e10	−	1.71013e11i	0.672523	−	1.16484i	−0.304664	−	0.952460i	$-0.598544\pi$
$619$	9.87347e10	−	1.71013e11i	0.672523	−	1.16484i	0.977186	−	0.212384i	$-0.0681227\pi$
$620$	−4.78183e9	−	2.76079e9i	−0.0323614	−	0.0186839i
$621$	−1.08465e10	+	6.26223e9i	−0.0729328	+	0.0421078i
$622$	−1.08908e10	+	6.28780e9i	−0.0727609	+	0.0420085i
$623$	−7.59500e10			−0.504168
$624$		−	2.42596e10i		−	0.160009i
$625$	5.80784e9	+	1.00595e10i	0.0380623	+	0.0659258i
$626$	−4.50337e10	−	7.80006e10i	−0.293251	−	0.507926i
$627$	7.60443e9	−	1.31713e10i	0.0492036	−	0.0852231i
$628$	1.27385e10	+	7.35458e9i	0.0818992	+	0.0472845i
$629$			2.79551e10i			0.178590i
$630$	−2.97569e10	−	1.71801e10i	−0.188897	−	0.109060i
$631$	2.24145e11	+	1.29410e11i	1.41388	+	0.816302i	0.995751	−	0.0920880i	$-0.0293541\pi$
$631$	2.24145e11	+	1.29410e11i	1.41388	+	0.816302i	0.418125	+	0.908390i	$0.362687\pi$
$632$	1.83572e11	+	1.05986e11i	1.15064	+	0.664322i
$633$	−1.00278e10	−	1.73686e10i	−0.0624583	−	0.108181i
$634$		−	2.08346e11i		−	1.28952i
$635$	6.75291e10	−	3.89879e10i	0.415333	−	0.239792i
$636$	−2.20475e9	−	1.27291e9i	−0.0134750	−	0.00777982i
$637$	1.78883e11			1.08646
$638$	−1.46084e11	+	2.53026e11i	−0.881700	+	1.52715i
$639$	−1.40979e11	+	8.13943e10i	−0.845573	+	0.488192i
$640$	−4.26914e10	−	7.39436e10i	−0.254460	−	0.440738i
$641$		−	1.93544e11i		−	1.14643i	−0.819405	−	0.573215i	$-0.805696\pi$
$641$		−	1.93544e11i		−	1.14643i	0.819405	−	0.573215i	$-0.194304\pi$
$642$	−2.82421e9	−	4.89167e9i	−0.0166248	−	0.0287950i
$643$	−1.13810e11			−0.665787			−0.332894	−	0.942964i	$-0.608025\pi$
$643$	−1.13810e11			−0.665787			−0.332894	+	0.942964i	$0.608025\pi$
$644$			2.15773e9i			0.0125445i
$645$	1.10777e10	−	1.20644e10i	0.0640045	−	0.0697057i
$646$	3.38532e10			0.194388
$647$		−	2.81970e11i		−	1.60911i	−0.593878	−	0.804555i	$-0.702404\pi$
$647$		−	2.81970e11i		−	1.60911i	0.593878	−	0.804555i	$-0.297596\pi$
$648$	−1.50037e11	+	8.66241e10i	−0.850941	+	0.491291i
$649$	−1.76015e10			−0.0992134
$650$	−1.06445e11	+	6.14563e10i	−0.596312	+	0.344281i
$651$	2.38489e9	+	4.13075e9i	0.0132784	+	0.0229988i
$652$	1.05948e9	+	6.11689e8i	0.00586275	+	0.00338486i
$653$		−	1.80174e11i		−	0.990923i	−0.868630	−	0.495461i	$-0.834999\pi$
$653$		−	1.80174e11i		−	0.990923i	0.868630	−	0.495461i	$-0.165001\pi$
$654$	1.36458e10	−	2.36353e10i	0.0745915	−	0.129196i
$655$	4.48337e10	+	7.76543e10i	0.243579	+	0.421891i
$656$	−1.18930e11			−0.642208
$657$	1.03538e11	−	5.97775e10i	0.555695	−	0.320831i
$658$	−5.72500e10	+	9.91599e10i	−0.305402	+	0.528972i
$659$	−1.37043e11	+	2.37366e11i	−0.726635	+	1.25857i	0.231662	+	0.972796i	$0.425584\pi$
$659$	−1.37043e11	+	2.37366e11i	−0.726635	+	1.25857i	−0.958297	+	0.285773i	$0.907750\pi$
$660$	1.36015e9	−	2.35585e9i	0.00716822	−	0.0124157i
$661$	−2.41838e11			−1.26683			−0.633416	−	0.773811i	$-0.718348\pi$
$661$	−2.41838e11			−1.26683			−0.633416	+	0.773811i	$0.718348\pi$
$662$	−4.39639e10	+	7.61477e10i	−0.228910	+	0.396483i
$663$	1.22498e10	+	7.07244e9i	0.0633980	+	0.0366029i
$664$	3.50716e10	−	2.02486e10i	0.180419	−	0.104165i
$665$	2.09255e10	−	1.20813e10i	0.107001	−	0.0617772i
$666$	−8.12679e10			−0.413069
$667$			8.36775e10i			0.422771i
$668$	1.80819e10	+	3.13187e10i	0.0908108	+	0.157289i
$669$	−2.59372e10	−	4.49245e10i	−0.129485	−	0.224274i
$670$	5.15938e10	−	8.93631e10i	0.256035	−	0.443465i
$671$	−1.75974e11	−	1.01599e11i	−0.868079	−	0.501185i
$672$		−	2.57028e9i		−	0.0126039i
$673$	−1.30999e11	−	7.56324e10i	−0.638569	−	0.368678i	0.145494	−	0.989359i	$-0.453523\pi$
$673$	−1.30999e11	−	7.56324e10i	−0.638569	−	0.368678i	−0.784063	+	0.620681i	$0.786856\pi$
$674$	2.12900e11	+	1.22918e11i	1.03166	+	0.595629i
$675$	−3.04300e10	−	1.75688e10i	−0.146584	−	0.0846305i
$676$	−7.09610e9	−	1.22908e10i	−0.0339807	−	0.0588564i
$677$			3.79167e11i			1.80499i	0.430695	+	0.902497i	$0.358268\pi$
$677$			3.79167e11i			1.80499i	−0.430695	+	0.902497i	$0.641732\pi$
$678$	−2.74117e10	+	1.58261e10i	−0.129723	+	0.0748956i
$679$	9.11621e10	+	5.26325e10i	0.428880	+	0.247614i
$680$	5.75734e10			0.269269
$681$	−4.49961e9	+	7.79355e9i	−0.0209212	+	0.0362366i
$682$	−1.11754e11	+	6.45214e10i	−0.516568	+	0.298240i
$683$	1.78467e11	+	3.09113e11i	0.820114	+	1.42048i	0.905597	+	0.424139i	$0.139423\pi$
$683$	1.78467e11	+	3.09113e11i	0.820114	+	1.42048i	−0.0854829	+	0.996340i	$0.527243\pi$
$684$		−	1.31074e10i		−	0.0598816i
$685$	−1.19136e11	−	2.06349e11i	−0.541102	−	0.937216i
$686$	−1.42638e11			−0.644080
$687$			3.68029e10i			0.165217i
$688$	1.89969e11	+	4.23186e10i	0.847871	+	0.188876i
$689$	2.55618e11			1.13426
$690$			5.84969e9i			0.0258069i
$691$	−2.30404e11	+	1.33024e11i	−1.01060	+	0.583468i	−0.911366	−	0.411597i	$-0.864971\pi$
$691$	−2.30404e11	+	1.33024e11i	−1.01060	+	0.583468i	−0.0992299	+	0.995065i	$0.531638\pi$
$692$	−1.78444e10			−0.0778177
$693$	9.26227e10	−	5.34757e10i	0.401592	−	0.231859i
$694$	8.08089e10	+	1.39965e11i	0.348355	+	0.603368i
$695$	1.69737e11	+	9.79978e10i	0.727508	+	0.420027i
$696$		−	5.26044e10i		−	0.224174i
$697$	3.46718e10	−	6.00533e10i	0.146908	−	0.254452i
$698$	9.63304e10	+	1.66849e11i	0.405828	+	0.702914i
$699$	1.39495e10			0.0584317
$700$	−5.24254e9	+	3.02678e9i	−0.0218348	+	0.0126063i
$701$	3.26568e10	−	5.65633e10i	0.135239	−	0.234241i	−0.790450	−	0.612527i	$-0.790153\pi$
$701$	3.26568e10	−	5.65633e10i	0.135239	−	0.234241i	0.925689	+	0.378286i	$0.123486\pi$
$702$	−4.15722e10	+	7.20052e10i	−0.171181	+	0.296494i
$703$	2.85744e10	−	4.94923e10i	0.116992	−	0.202636i
$704$	3.44565e11			1.40275
$705$	2.06714e10	−	3.58039e10i	0.0836784	−	0.144935i
$706$	−2.87001e11	−	1.65700e11i	−1.15522	−	0.666965i
$707$	1.43645e11	−	8.29335e10i	0.574927	−	0.331935i
$708$	2.88646e8	−	1.66650e8i	0.00114877	−	0.000663242i
$709$	1.36083e11			0.538542			0.269271	−	0.963064i	$-0.413217\pi$
$709$	1.36083e11			0.538542			0.269271	+	0.963064i	$0.413217\pi$
$710$			1.53735e11i			0.604978i
$711$	−1.58237e11	−	2.74075e11i	−0.619199	−	1.07248i
$712$	1.84979e11	+	3.20392e11i	0.719783	+	1.24670i
$713$	−1.84790e10	+	3.20066e10i	−0.0715024	+	0.123846i
$714$	−4.52987e9	−	2.61532e9i	−0.0174298	−	0.0100631i
$715$			2.73137e11i			1.04510i
$716$	−3.56680e9	−	2.05929e9i	−0.0135714	−	0.00783548i
$717$	5.59896e10	+	3.23256e10i	0.211851	+	0.122312i
$718$	−3.96334e11	−	2.28823e11i	−1.49129	−	0.860999i
$719$	−1.65445e11	−	2.86560e11i	−0.619069	−	1.07226i	−0.989656	−	0.143461i	$-0.954177\pi$
$719$	−1.65445e11	−	2.86560e11i	−0.619069	−	1.07226i	0.370587	−	0.928798i	$-0.379156\pi$
$720$			1.47424e11i			0.548578i
$721$	−1.34077e10	+	7.74091e9i	−0.0496149	+	0.0286451i
$722$	1.61135e11	+	9.30313e10i	0.592981	+	0.342358i
$723$	4.91631e10			0.179923
$724$	−1.33368e10	+	2.31000e10i	−0.0485397	+	0.0840732i
$725$	−2.03307e11	+	1.17379e11i	−0.735869	+	0.424854i
$726$	−1.26548e10	−	2.19187e10i	−0.0455521	−	0.0788985i
$727$		−	1.15403e11i		−	0.413124i	−0.978433	−	0.206562i	$-0.933772\pi$
$727$		−	1.15403e11i		−	0.413124i	0.978433	−	0.206562i	$-0.0662276\pi$
$728$	6.80996e10	+	1.17952e11i	0.242448	+	0.419932i
$729$	2.46647e11			0.873305
$730$		−	1.12906e11i		−	0.397581i
$731$	−7.67506e10	+	8.35872e10i	−0.268790	+	0.292732i
$732$	3.84773e9			0.0134017
$733$			2.28267e10i			0.0790727i	0.999218	+	0.0395363i	$0.0125881\pi$
$733$			2.28267e10i			0.0790727i	−0.999218	+	0.0395363i	$0.987412\pi$
$734$	−2.45660e11	+	1.41832e11i	−0.846350	+	0.488640i
$735$	2.38847e10			0.0818409
$736$	1.72473e10	−	9.95776e9i	0.0587775	−	0.0339352i
$737$	1.60593e11	+	2.78156e11i	0.544324	+	0.942797i
$738$	1.74581e11	+	1.00794e11i	0.588533	+	0.339789i
$739$		−	4.55875e10i		−	0.152851i	−0.997075	−	0.0764254i	$-0.975649\pi$
$739$		−	4.55875e10i		−	0.152851i	0.997075	−	0.0764254i	$-0.0243507\pi$
$740$	5.11090e9	−	8.85234e9i	0.0170440	−	0.0295210i
$741$	−1.44583e10	−	2.50424e10i	−0.0479560	−	0.0830622i
$742$	−9.45251e10			−0.311840
$743$	2.76835e11	−	1.59831e11i	0.908377	−	0.524452i	0.0284684	−	0.999595i	$-0.490937\pi$
$743$	2.76835e11	−	1.59831e11i	0.908377	−	0.524452i	0.879909	+	0.475143i	$0.157604\pi$
$744$	1.16169e10	−	2.01211e10i	0.0379141	−	0.0656691i
$745$	−9.28261e10	+	1.60780e11i	−0.301332	+	0.521922i
$746$	1.58349e11	−	2.74268e11i	0.511280	−	0.885563i
$747$	−6.04625e10			−0.194180
$748$	−9.42366e9	+	1.63223e10i	−0.0301033	+	0.0521404i
$749$	2.41899e10	+	1.39661e10i	0.0768613	+	0.0443759i
$750$	−3.85722e10	+	2.22697e10i	−0.121907	+	0.0703832i
$751$	1.38722e11	−	8.00910e10i	0.436098	−	0.251782i	−0.265843	−	0.964016i	$-0.585650\pi$
$751$	1.38722e11	−	8.00910e10i	0.436098	−	0.251782i	0.701941	+	0.712235i	$0.252317\pi$
$752$	4.91267e11			1.53619
$753$			1.92680e10i			0.0599318i
$754$	2.77749e11	+	4.81076e11i	0.859345	+	1.48843i
$755$	−1.40471e11	−	2.43303e11i	−0.432314	−	0.748790i
$756$	−2.04747e9	+	3.54632e9i	−0.00626802	+	0.0108565i
$757$	3.50001e10	+	2.02073e10i	0.106582	+	0.0615354i	0.552344	−	0.833616i	$-0.313734\pi$
$757$	3.50001e10	+	2.02073e10i	0.106582	+	0.0615354i	−0.445761	+	0.895152i	$0.647067\pi$
$758$		−	4.44519e11i		−	1.34652i
$759$	−1.57686e10	−	9.10401e9i	−0.0475145	−	0.0274325i
$760$	−1.01929e11	−	5.88489e10i	−0.305524	−	0.176394i
$761$	−3.27264e11	−	1.88946e11i	−0.975798	−	0.563377i	−0.0747992	−	0.997199i	$-0.523832\pi$
$761$	−3.27264e11	−	1.88946e11i	−0.975798	−	0.563377i	−0.900999	+	0.433821i	$0.857165\pi$
$762$	1.72539e10	+	2.98846e10i	0.0511761	+	0.0886396i
$763$			1.34961e11i			0.398208i
$764$	−3.33806e10	+	1.92723e10i	−0.0979761	+	0.0565665i
$765$	−7.44414e10	−	4.29787e10i	−0.217354	−	0.125490i
$766$	−5.48870e10			−0.159424
$767$	−1.67328e10	+	2.89820e10i	−0.0483489	+	0.0837428i
$768$	−1.53528e10	+	8.86396e9i	−0.0441310	+	0.0254790i
$769$	−1.12870e11	−	1.95496e11i	−0.322755	−	0.559028i	0.658300	−	0.752755i	$-0.271276\pi$
$769$	−1.12870e11	−	1.95496e11i	−0.322755	−	0.559028i	−0.981055	+	0.193727i	$0.937942\pi$
$770$		−	1.01003e11i		−	0.287325i
$771$	2.28617e10	+	3.95975e10i	0.0646979	+	0.112060i
$772$	−5.62458e9			−0.0158351
$773$			7.81990e10i			0.219020i	0.993986	+	0.109510i	$0.0349281\pi$
$773$			7.81990e10i			0.219020i	−0.993986	+	0.109510i	$0.965072\pi$
$774$	−2.42996e11	−	2.23121e11i	−0.677072	−	0.621694i
$775$	−1.03686e11			−0.287419
$776$		−	5.12752e11i		−	1.41404i
$777$	−7.64704e9	+	4.41502e9i	−0.0209802	+	0.0121129i
$778$	−1.31585e11			−0.359160
$779$	−1.22768e11	+	7.08799e10i	−0.333376	+	0.192475i
$780$	−2.58605e9	−	4.47916e9i	−0.00698647	−	0.0121009i
$781$	−4.14413e11	−	2.39262e11i	−1.11386	−	0.643086i
$782$		−	4.05289e10i		−	0.108377i
$783$	−7.94015e10	+	1.37527e11i	−0.211243	+	0.365883i
$784$	1.41908e11	+	2.45792e11i	0.375615	+	0.650585i
$785$	−1.97197e11			−0.519304
$786$	−3.43654e10	+	1.98409e10i	−0.0900392	+	0.0519842i
$787$	1.54778e11	−	2.68084e11i	0.403470	−	0.698830i	−0.590672	−	0.806911i	$-0.701137\pi$
$787$	1.54778e11	−	2.68084e11i	0.403470	−	0.698830i	0.994142	+	0.108082i	$0.0344708\pi$
$788$	−4.83028e9	+	8.36630e9i	−0.0125276	+	0.0216984i
$789$	2.44540e10	−	4.23556e10i	0.0631018	−	0.109296i
$790$	−2.98874e11			−0.767325
$791$	7.82624e10	−	1.35554e11i	0.199916	−	0.346264i
$792$	−4.51171e11	−	2.60484e11i	−1.14668	−	0.662034i
$793$	−3.34579e11	+	1.93169e11i	−0.846069	+	0.488478i
$794$	5.27589e11	−	3.04604e11i	1.32744	−	0.766396i
$795$	3.41304e10			0.0854422
$796$			2.92247e10i			0.0727944i
$797$	−4.06130e10	−	7.03438e10i	−0.100654	−	0.174338i	0.811300	−	0.584630i	$-0.198760\pi$
$797$	−4.06130e10	−	7.03438e10i	−0.100654	−	0.174338i	−0.911954	+	0.410292i	$0.865427\pi$
$798$	5.34652e9	+	9.26045e9i	0.0131844	+	0.0228360i
$799$	−1.43220e11	+	2.48064e11i	−0.351411	+	0.608662i
$800$	4.83878e10	+	2.79367e10i	0.118134	+	0.0682048i
$801$		−	5.52349e11i		−	1.34179i
$802$	5.33671e11	+	3.08115e11i	1.28996	+	0.744758i
$803$	3.04353e11	+	1.75718e11i	0.732007	+	0.422624i
$804$	−5.26713e9	−	3.04098e9i	−0.0126052	−	0.00727762i
$805$	−1.44637e10	−	2.50519e10i	−0.0344427	−	0.0596565i
$806$			2.45348e11i			0.581357i
$807$	−3.01432e10	+	1.74032e10i	−0.0710714	+	0.0410331i
$808$	−6.99704e11	−	4.03975e11i	−1.64161	−	0.947782i
$809$	6.33168e10			0.147817			0.0739086	−	0.997265i	$-0.476453\pi$
$809$	6.33168e10			0.147817			0.0739086	+	0.997265i	$0.476453\pi$
$810$	1.22138e11	−	2.11549e11i	0.283733	−	0.491439i
$811$	−2.63696e11	+	1.52245e11i	−0.609566	+	0.351933i	−0.772796	−	0.634655i	$-0.781142\pi$
$811$	−2.63696e11	+	1.52245e11i	−0.609566	+	0.351933i	0.163230	+	0.986588i	$0.447809\pi$
$812$	1.36794e10	+	2.36935e10i	0.0314662	+	0.0545010i
$813$			4.97473e10i			0.113870i
$814$	−1.19445e11	−	2.06885e11i	−0.272064	−	0.471228i
$815$	−1.64011e10			−0.0371743
$816$			2.24423e10i			0.0506181i
$817$	2.21320e11	−	6.95338e10i	0.496744	−	0.156066i
$818$	4.63205e11			1.03457
$819$		−	2.03346e11i		−	0.451960i
$820$	−2.19586e10	+	1.26778e10i	−0.0485678	+	0.0280407i
$821$	−2.33895e10			−0.0514812			−0.0257406	−	0.999669i	$-0.508194\pi$
$821$	−2.33895e10			−0.0514812			−0.0257406	+	0.999669i	$0.508194\pi$
$822$	9.13185e10	−	5.27228e10i	0.200019	−	0.115481i
$823$	3.01820e11	+	5.22768e11i	0.657884	+	1.13949i	0.981162	+	0.193184i	$0.0618816\pi$
$823$	3.01820e11	+	5.22768e11i	0.657884	+	1.13949i	−0.323279	+	0.946304i	$0.604785\pi$
$824$	6.53095e10	+	3.77065e10i	0.141667	+	0.0817913i
$825$		−	5.10829e10i		−	0.110271i
$826$	6.18762e9	−	1.07173e10i	0.0132924	−	0.0230231i
$827$	−1.42533e11	−	2.46874e11i	−0.304714	−	0.527780i	0.672484	−	0.740112i	$-0.265228\pi$
$827$	−1.42533e11	−	2.46874e11i	−0.304714	−	0.527780i	−0.977198	+	0.212332i	$0.931894\pi$
$828$	−1.56922e10			−0.0333858
$829$	−1.93929e10	+	1.11965e10i	−0.0410605	+	0.0237063i	−0.520390	−	0.853929i	$-0.674213\pi$
$829$	−1.93929e10	+	1.11965e10i	−0.0410605	+	0.0237063i	0.479329	+	0.877635i	$0.340880\pi$
$830$	−2.85499e10	+	4.94500e10i	−0.0601579	+	0.104197i
$831$	2.05775e10	−	3.56413e10i	0.0431508	−	0.0747394i
$832$	3.27560e11	−	5.67350e11i	0.683592	−	1.18402i
$833$	−1.65483e11			−0.343695
$834$	−4.33684e10	+	7.51162e10i	−0.0896414	+	0.155263i
$835$	−4.19872e11	−	2.42413e11i	−0.863716	−	0.498667i
$836$	3.33678e10	−	1.92649e10i	0.0683128	−	0.0394404i
$837$	−6.07421e10	+	3.50694e10i	−0.123762	+	0.0714541i
$838$	−7.65034e10			−0.155133
$839$			7.69841e11i			1.55365i	0.629716	+	0.776825i	$0.283171\pi$
$839$			7.69841e11i			1.55365i	−0.629716	+	0.776825i	$0.716829\pi$
$840$	9.09272e9	+	1.57491e10i	0.0182632	+	0.0316328i
$841$	2.80369e11	+	4.85613e11i	0.560461	+	0.970747i
$842$	2.84204e9	−	4.92257e9i	0.00565435	−	0.00979362i
$843$	2.59458e10	+	1.49798e10i	0.0513755	+	0.0296617i
$844$		−	5.08083e10i		−	0.100130i
$845$	1.64776e11	+	9.51333e10i	0.323196	+	0.186597i
$846$	−7.21144e11	−	4.16353e11i	−1.40780	−	0.812793i
$847$	1.08391e11	+	6.25796e10i	0.210601	+	0.121590i
$848$	2.02782e11	+	3.51228e11i	0.392144	+	0.679213i
$849$			2.34720e10i			0.0451772i
$850$	9.84712e10	−	5.68524e10i	0.188640	−	0.108911i
$851$	−5.92521e10	−	3.42092e10i	−0.112976	−	0.0652266i
$852$	9.06127e9			0.0171961
$853$	3.41344e11	−	5.91225e11i	0.644757	−	1.11675i	−0.339600	−	0.940570i	$-0.610292\pi$
$853$	3.41344e11	−	5.91225e11i	0.644757	−	1.11675i	0.984358	−	0.176182i	$-0.0563749\pi$
$854$	1.23724e11	−	7.14321e10i	0.232607	−	0.134296i
$855$	8.78619e10	+	1.52181e11i	0.164413	+	0.284772i
$856$		−	1.36059e11i		−	0.253416i
$857$	1.78558e11	+	3.09272e11i	0.331022	+	0.573347i	0.982713	−	0.185138i	$-0.0592732\pi$
$857$	1.78558e11	+	3.09272e11i	0.331022	+	0.573347i	−0.651690	+	0.758485i	$0.725940\pi$
$858$	−1.20875e11			−0.223043
$859$			1.00529e12i			1.84637i	0.384354	+	0.923186i	$0.374424\pi$
$859$			1.00529e12i			1.84637i	−0.384354	+	0.923186i	$0.625576\pi$
$860$	3.95860e10	−	1.24370e10i	0.0723682	−	0.0227364i
$861$	2.19032e10			0.0398562
$862$			1.76957e11i			0.320508i
$863$	−4.02381e11	+	2.32315e11i	−0.725428	+	0.418826i	−0.816747	−	0.576995i	$-0.804225\pi$
$863$	−4.02381e11	+	2.32315e11i	−0.725428	+	0.418826i	0.0913190	+	0.995822i	$0.470892\pi$
$864$	3.77956e10			0.0678245
$865$	2.07179e11	−	1.19615e11i	0.370068	−	0.213659i
$866$	2.15363e11	+	3.73020e11i	0.382913	+	0.663225i
$867$	6.04176e10	+	3.48821e10i	0.106927	+	0.0617343i
$868$			1.20836e10i			0.0212872i
$869$	4.65144e11	−	8.05653e11i	0.815659	−	1.41276i
$870$	3.70854e10	+	6.42337e10i	0.0647330	+	0.112121i
$871$	6.10670e11			1.06105
$872$	5.69329e11	−	3.28702e11i	0.984685	−	0.568508i
$873$	−3.82771e11	+	6.62979e11i	−0.658995	+	1.14141i
$874$	−4.14269e10	+	7.17534e10i	−0.0709964	+	0.122969i
$875$	1.10127e11	−	1.90745e11i	0.187871	−	0.325402i
$876$	−6.65476e9			−0.0113010
$877$	4.60602e11	−	7.97785e11i	0.778623	−	1.34861i	−0.154113	−	0.988053i	$-0.549252\pi$
$877$	4.60602e11	−	7.97785e11i	0.778623	−	1.34861i	0.932736	−	0.360561i	$-0.117415\pi$
$878$	−8.15854e9	−	4.71034e9i	−0.0137289	−	0.00792636i
$879$	5.36267e10	−	3.09614e10i	0.0898309	−	0.0518639i
$880$	−3.75300e11	+	2.16679e11i	−0.625817	+	0.361316i
$881$	−5.94163e11			−0.986284			−0.493142	−	0.869949i	$-0.664152\pi$
$881$	−5.94163e11			−0.986284			−0.493142	+	0.869949i	$0.664152\pi$
$882$		−	4.81073e11i		−	0.794945i
$883$	3.69532e11	+	6.40048e11i	0.607868	+	1.05286i	0.991591	+	0.129410i	$0.0413082\pi$
$883$	3.69532e11	+	6.40048e11i	0.607868	+	1.05286i	−0.383724	+	0.923448i	$0.625358\pi$
$884$	1.79172e10	+	3.10334e10i	0.0293400	+	0.0508183i
$885$	−2.23418e9	+	3.86971e9i	−0.00364204	+	0.00630820i
$886$	−3.44123e11	−	1.98680e11i	−0.558443	−	0.322417i
$887$			7.61348e11i			1.22995i	0.788545	+	0.614977i	$0.210835\pi$
$887$			7.61348e11i			1.22995i	−0.788545	+	0.614977i	$0.789165\pi$
$888$	3.72492e10	+	2.15058e10i	0.0599053	+	0.0345863i
$889$	−1.47783e11	−	8.53228e10i	−0.236602	−	0.136602i
$890$	−4.51744e11	−	2.60815e11i	−0.720001	−	0.415692i
$891$	3.80171e11	+	6.58476e11i	0.603210	+	1.04479i
$892$		−	1.31417e11i		−	0.207584i
$893$	5.07119e11	−	2.92785e11i	0.797451	−	0.460408i
$894$	−7.11520e10	−	4.10797e10i	−0.111388	−	0.0643097i
$895$	5.52154e10			0.0860534
$896$	−9.34275e10	+	1.61821e11i	−0.144958	+	0.251075i
$897$	−2.99807e10	+	1.73094e10i	−0.0463098	+	0.0267370i
$898$	1.91399e10	+	3.31513e10i	0.0294330	+	0.0509794i
$899$			4.68607e11i			0.717414i
$900$	−2.20124e10	−	3.81265e10i	−0.0335503	−	0.0581109i
$901$	−2.36469e11			−0.358818
$902$			5.92576e11i			0.895196i
$903$	−3.49865e10	−	7.79379e9i	−0.0526198	−	0.0117219i
$904$	−7.62442e11			−1.14165
$905$		−	3.57597e11i		−	0.533089i
$906$	1.07672e11	−	6.21647e10i	0.159806	−	0.0922638i
$907$	−1.98188e11			−0.292852			−0.146426	−	0.989222i	$-0.546777\pi$
$907$	−1.98188e11			−0.292852			−0.146426	+	0.989222i	$0.546777\pi$
$908$	−1.97440e10	+	1.13992e10i	−0.0290464	+	0.0167699i
$909$	6.03137e11	+	1.04466e12i	0.883406	+	1.53010i
$910$	−1.66309e11	−	9.60185e10i	−0.242521	−	0.140020i
$911$			8.66507e11i			1.25805i	0.777384	+	0.629026i	$0.216546\pi$
$911$			8.66507e11i			1.25805i	−0.777384	+	0.629026i	$0.783454\pi$
$912$	2.29395e10	−	3.97323e10i	0.0331592	−	0.0574334i
$913$	−8.88659e10	−	1.53920e11i	−0.127895	−	0.221520i
$914$	9.19124e11			1.31701
$915$	−4.46733e10	+	2.57921e10i	−0.0637329	+	0.0367962i
$916$	−4.66179e10	+	8.07445e10i	−0.0662171	+	0.114691i
$917$	9.81159e10	−	1.69942e11i	0.138759	−	0.240338i
$918$	3.84579e10	−	6.66110e10i	0.0541520	−	0.0937941i
$919$	−8.21844e11			−1.15220			−0.576100	−	0.817379i	$-0.695426\pi$
$919$	−8.21844e11			−1.15220			−0.576100	+	0.817379i	$0.695426\pi$
$920$	−7.04538e10	+	1.22030e11i	−0.0983452	+	0.170339i
$921$	−1.27627e10	−	7.36856e9i	−0.0177380	−	0.0102410i
$922$	−7.90072e11	+	4.56148e11i	−1.09331	+	0.631222i
$923$	−7.87921e11	+	4.54907e11i	−1.08562	+	0.626780i
$924$	−5.95322e9			−0.00816703
$925$		−	1.91949e11i		−	0.262192i
$926$	6.47274e11	+	1.12111e12i	0.880327	+	1.52477i
$927$	−5.62960e10	−	9.75076e10i	−0.0762358	−	0.132044i
$928$	1.26259e11	−	2.18687e11i	0.170243	−	0.294870i
$929$	−8.63638e11	−	4.98622e11i	−1.15950	−	0.669435i	−0.208312	−	0.978062i	$-0.566797\pi$
$929$	−8.63638e11	−	4.98622e11i	−1.15950	−	0.669435i	−0.951183	+	0.308627i	$0.900130\pi$
$930$			3.27592e10i			0.0437926i
$931$	2.92975e11	+	1.69149e11i	0.389970	+	0.225149i
$932$	3.06047e10	+	1.76696e10i	0.0405625	+	0.0234188i
$933$	−8.60574e9	−	4.96853e9i	−0.0113569	−	0.00655694i
$934$	−1.87147e11	−	3.24148e11i	−0.245921	−	0.425947i
$935$		−	2.52675e11i		−	0.330610i
$936$	−8.57809e11	+	4.95256e11i	−1.11760	+	0.645248i
$937$	−6.33236e11	−	3.65599e11i	−0.821500	−	0.474293i	0.0294335	−	0.999567i	$-0.490630\pi$
$937$	−6.33236e11	−	3.65599e11i	−0.821500	−	0.474293i	−0.850933	+	0.525274i	$0.823963\pi$
$938$	−2.25820e11			−0.291710
$939$	3.55849e10	−	6.16349e10i	0.0457724	−	0.0792801i
$940$	9.07048e10	−	5.23684e10i	0.116177	−	0.0670746i
$941$	−4.64096e11	−	8.03838e11i	−0.591902	−	1.02520i	−0.993976	−	0.109597i	$-0.965044\pi$
$941$	−4.64096e11	−	8.03838e11i	−0.591902	−	1.02520i	0.402075	−	0.915607i	$-0.368289\pi$
$942$		−	8.72684e10i		−	0.110829i
$943$	8.48573e10	+	1.46977e11i	0.107311	+	0.185867i
$944$	−5.30964e10			−0.0668617
$945$		−	5.48985e10i		−	0.0688388i
$946$	2.10855e11	−	9.46534e11i	0.263281	−	1.18188i
$947$	6.71883e11			0.835399			0.417700	−	0.908585i	$-0.362836\pi$
$947$	6.71883e11			0.835399			0.417700	+	0.908585i	$0.362836\pi$
$948$			1.76158e10i			0.0218107i
$949$	5.78664e11	−	3.34092e11i	0.713447	−	0.411909i
$950$	−2.32448e11			−0.285385
$951$	1.42575e11	−	8.23159e10i	0.174310	−	0.100638i
$952$	−6.29980e10	−	1.09116e11i	−0.0766971	−	0.132843i
$953$	6.94879e11	+	4.01189e11i	0.842438	+	0.486382i	0.858092	−	0.513496i	$-0.171650\pi$
$953$	6.94879e11	+	4.01189e11i	0.842438	+	0.486382i	−0.0156544	+	0.999877i	$0.504983\pi$
$954$		−	6.87436e11i		−	0.829925i
$955$	2.58372e11	−	4.47514e11i	0.310622	−	0.538013i
$956$	8.18930e10	+	1.41843e11i	0.0980427	+	0.169815i
$957$	−2.30867e11			−0.275242
$958$	5.70719e11	−	3.29505e11i	0.677579	−	0.391200i
$959$	−2.60721e11	+	4.51582e11i	−0.308249	+	0.533903i
$960$	4.37361e10	−	7.57531e10i	0.0514938	−	0.0891899i
$961$	3.22960e11	−	5.59383e11i	0.378665	−	0.655867i
$962$	−4.54200e11			−0.530331
$963$	−1.01569e11	+	1.75922e11i	−0.118101	+	0.204557i
$964$	1.07862e11	+	6.22744e10i	0.124900	+	0.0721110i
$965$	6.53031e10	−	3.77028e10i	0.0753051	−	0.0434774i
$966$	1.10866e10	−	6.40085e9i	0.0127318	−	0.00735070i
$967$	9.77891e11			1.11837			0.559184	−	0.829044i	$-0.311115\pi$
$967$	9.77891e11			1.11837			0.559184	+	0.829044i	$0.311115\pi$
$968$		−	6.09659e11i		−	0.694361i
$969$	1.33751e10	+	2.31664e10i	0.0151706	+	0.0262763i
$970$	3.61483e11	+	6.26108e11i	0.408321	+	0.707232i
$971$	2.73943e11	−	4.74483e11i	0.308165	−	0.533757i	−0.669796	−	0.742545i	$-0.733619\pi$
$971$	2.73943e11	−	4.74483e11i	0.308165	−	0.533757i	0.977961	+	0.208788i	$0.0669518\pi$
$972$	−3.88263e10	−	2.24164e10i	−0.0434971	−	0.0251131i
$973$		−	4.28925e11i		−	0.478553i
$974$	−3.30957e11	−	1.91078e11i	−0.367736	−	0.212313i
$975$	−8.41116e10	−	4.85618e10i	−0.0930759	−	0.0537374i
$976$	−5.30842e11	−	3.06482e11i	−0.585014	−	0.337758i
$977$	3.64770e11	+	6.31800e11i	0.400351	+	0.693428i	0.993768	−	0.111467i	$-0.0355549\pi$
$977$	3.64770e11	+	6.31800e11i	0.400351	+	0.693428i	−0.593417	+	0.804895i	$0.702222\pi$
$978$		−	7.25822e9i		−	0.00793368i
$979$	1.40612e12	−	8.11825e11i	1.53071	−	0.883754i
$980$	5.24023e10	+	3.02545e10i	0.0568128	+	0.0328009i
$981$	−9.81509e11			−1.05979
$982$	−8.17102e11	+	1.41526e12i	−0.878680	+	1.52192i
$983$	−8.93379e11	+	5.15792e11i	−0.956801	+	0.552409i	−0.895187	−	0.445691i	$-0.852958\pi$
$983$	−8.93379e11	+	5.15792e11i	−0.956801	+	0.552409i	−0.0616137	+	0.998100i	$0.519625\pi$
$984$	−5.33461e10	−	9.23981e10i	−0.0569013	−	0.0985559i
$985$		−	1.29514e11i		−	0.137585i
$986$	−2.56942e11	−	4.45037e11i	−0.271849	−	0.470856i
$987$	−9.04762e10			−0.0953379
$988$		−	7.32564e10i		−	0.0768808i
$989$	−8.32457e10	−	2.64964e11i	−0.0870115	−	0.276950i
$990$	7.34550e11			0.764682
$991$		−	6.12231e11i		−	0.634777i	−0.948296	−	0.317388i	$-0.897194\pi$
$991$		−	6.12231e11i		−	0.634777i	0.948296	−	0.317388i	$-0.102806\pi$
$992$	9.65878e10	−	5.57650e10i	0.0997415	−	0.0575858i
$993$	−6.94792e10			−0.0714592
$994$	2.91366e11	−	1.68220e11i	0.298465	−	0.172319i
$995$	−1.95899e11	−	3.39308e11i	−0.199867	−	0.346179i
$996$	2.91462e9	+	1.68276e9i	0.00296172	+	0.00170995i
$997$			9.84240e11i			0.996140i	0.867137	+	0.498070i	$0.165958\pi$
$997$			9.84240e11i			0.996140i	−0.867137	+	0.498070i	$0.834042\pi$
$998$	6.90094e11	−	1.19528e12i	0.695643	−	1.20489i
$999$	−6.49222e10	−	1.12449e11i	−0.0651825	−	0.112899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.9.d.a.7.8	✓	56
43.37	odd	6	inner	43.9.d.a.37.21	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.9.d.a.7.8	✓	56	1.1	even	1	trivial
43.9.d.a.37.21	yes	56	43.37	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-15.0304i q^{2} +(10.2856 - 5.93838i) q^{3} +30.0883 q^{4} +(-349.334 + 201.688i) q^{5} +(-89.2560 - 154.596i) q^{6} +(764.498 + 441.383i) q^{7} -4300.01i q^{8} +(-3209.97 + 5559.83i) q^{9} +O(q^{10})\)	\(q-15.0304i q^{2} +(10.2856 - 5.93838i) q^{3} +30.0883 q^{4} +(-349.334 + 201.688i) q^{5} +(-89.2560 - 154.596i) q^{6} +(764.498 + 441.383i) q^{7} -4300.01i q^{8} +(-3209.97 + 5559.83i) q^{9} +(3031.45 + 5250.62i) q^{10} -18871.7 q^{11} +(309.476 - 178.676i) q^{12} +(-17940.3 + 31073.5i) q^{13} +(6634.14 - 11490.7i) q^{14} +(-2395.41 + 4148.96i) q^{15} -56928.1 q^{16} +(16596.3 - 28745.7i) q^{17} +(83566.3 + 48247.0i) q^{18} +(-58765.0 + 33928.0i) q^{19} +(-10510.9 + 6068.46i) q^{20} +10484.4 q^{21} +283648. i q^{22} +(40618.5 + 70353.4i) q^{23} +(-25535.1 - 44228.1i) q^{24} +(-113956. + 197378. i) q^{25} +(467046. + 269649. i) q^{26} +154172. i q^{27} +(23002.5 + 13280.5i) q^{28} +(892041. + 515020. i) q^{29} +(62360.4 + 36003.8i) q^{30} +(227470. + 393990. i) q^{31} -245153. i q^{32} +(-194106. + 112067. i) q^{33} +(-432058. - 249449. i) q^{34} -356087. q^{35} +(-96582.6 + 167286. i) q^{36} +(-729373. + 421103. i) q^{37} +(509950. + 883260. i) q^{38} +426145. i q^{39} +(867262. + 1.50214e6i) q^{40} +2.08913e6 q^{41} -157584. i q^{42} +(-3.33700e6 - 743370. i) q^{43} -567817. q^{44} -2.58966e6i q^{45} +(1.05744e6 - 610511. i) q^{46} -8.62960e6 q^{47} +(-585538. + 338061. i) q^{48} +(-2.49276e6 - 4.31759e6i) q^{49} +(2.96666e6 + 1.71280e6i) q^{50} -394221. i q^{51} +(-539793. + 934949. i) q^{52} +(-3.56207e6 - 6.16968e6i) q^{53} +2.31725e6 q^{54} +(6.59252e6 - 3.80619e6i) q^{55} +(1.89795e6 - 3.28735e6i) q^{56} +(-402955. + 697939. i) q^{57} +(7.74094e6 - 1.34077e7i) q^{58} +932693. q^{59} +(-72073.7 + 124835. i) q^{60} +(9.32479e6 + 5.38367e6i) q^{61} +(5.92181e6 - 3.41896e6i) q^{62} +(-4.90803e6 + 2.83365e6i) q^{63} -1.82583e7 q^{64} -1.44734e7i q^{65} +(1.68441e6 + 2.91748e6i) q^{66} +(-8.50977e6 - 1.47393e7i) q^{67} +(499355. - 864909. i) q^{68} +(835570. + 482417. i) q^{69} +5.35212e6i q^{70} +(2.19596e7 + 1.26784e7i) q^{71} +(2.39073e7 + 1.38029e7i) q^{72} +(-1.61275e7 - 9.31122e6i) q^{73} +(6.32934e6 + 1.09627e7i) q^{74} +2.70686e6i q^{75} +(-1.76814e6 + 1.02084e6i) q^{76} +(-1.44273e7 - 8.32963e6i) q^{77} +6.40511e6 q^{78} +(-2.46478e7 + 4.26912e7i) q^{79} +(1.98869e7 - 1.14817e7i) q^{80} +(-2.01451e7 - 3.48923e7i) q^{81} -3.14003e7i q^{82} +(4.70896e6 + 8.15616e6i) q^{83} +315458. q^{84} +1.33891e7i q^{85} +(-1.11731e7 + 5.01564e7i) q^{86} +1.22335e7 q^{87} +8.11483e7i q^{88} +(-7.45097e7 + 4.30182e7i) q^{89} -3.89234e7 q^{90} +(-2.74306e7 + 1.58371e7i) q^{91} +(1.22214e6 + 2.11682e6i) q^{92} +(4.67933e6 + 2.70161e6i) q^{93} +1.29706e8i q^{94} +(1.36858e7 - 2.37044e7i) q^{95} +(-1.45581e6 - 2.52154e6i) q^{96} +1.19244e8 q^{97} +(-6.48950e7 + 3.74671e7i) q^{98} +(6.05775e7 - 1.04923e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 84 q^{3} - 6474 q^{4} - 3 q^{5} + 1791 q^{6} - 5031 q^{7} + 57858 q^{9}+O(q^{10}) \) 56 * q - 84 * q^3 - 6474 * q^4 - 3 * q^5 + 1791 * q^6 - 5031 * q^7 + 57858 * q^9	\( 56 q - 84 q^{3} - 6474 q^{4} - 3 q^{5} + 1791 q^{6} - 5031 q^{7} + 57858 q^{9} + 12491 q^{10} + 31928 q^{11} + 56574 q^{12} - 24868 q^{13} + 106830 q^{14} - 11989 q^{15} + 655366 q^{16} + 5963 q^{17} + 326445 q^{18} - 67476 q^{19} - 713343 q^{20} - 187232 q^{21} - 210724 q^{23} - 1651574 q^{24} + 1650473 q^{25} + 765 q^{26} + 684492 q^{28} - 5568699 q^{29} - 3412593 q^{30} + 2602959 q^{31} - 554514 q^{33} - 584967 q^{34} + 8137398 q^{35} - 3035428 q^{36} - 3541812 q^{37} + 6280356 q^{38} - 2473841 q^{40} + 7375370 q^{41} + 15490227 q^{43} - 2983894 q^{44} + 3217584 q^{46} - 7588210 q^{47} + 5844987 q^{48} + 33155723 q^{49} - 9064422 q^{50} + 3837506 q^{52} - 5366122 q^{53} - 45158560 q^{54} + 40061478 q^{55} - 39705477 q^{56} + 13330347 q^{57} + 19271684 q^{58} + 18367244 q^{59} - 36808121 q^{60} - 6722484 q^{61} - 15483591 q^{62} - 40574925 q^{63} - 87236036 q^{64} - 33263013 q^{66} - 8581935 q^{67} - 123045082 q^{68} - 26516709 q^{69} - 132304098 q^{71} - 100762446 q^{72} + 278404467 q^{73} + 182026410 q^{74} + 179327130 q^{76} + 143930505 q^{77} - 143413472 q^{78} - 62931368 q^{79} + 121842717 q^{80} - 65032540 q^{81} - 29005780 q^{83} + 370916864 q^{84} + 73281798 q^{86} + 137580504 q^{87} - 124655943 q^{89} + 63835252 q^{90} + 287393496 q^{91} - 215232271 q^{92} - 124327923 q^{93} + 413979855 q^{95} + 51391714 q^{96} - 446400270 q^{97} - 351696195 q^{98} - 146664065 q^{99}+O(q^{100}) \) 56 * q - 84 * q^3 - 6474 * q^4 - 3 * q^5 + 1791 * q^6 - 5031 * q^7 + 57858 * q^9 + 12491 * q^10 + 31928 * q^11 + 56574 * q^12 - 24868 * q^13 + 106830 * q^14 - 11989 * q^15 + 655366 * q^16 + 5963 * q^17 + 326445 * q^18 - 67476 * q^19 - 713343 * q^20 - 187232 * q^21 - 210724 * q^23 - 1651574 * q^24 + 1650473 * q^25 + 765 * q^26 + 684492 * q^28 - 5568699 * q^29 - 3412593 * q^30 + 2602959 * q^31 - 554514 * q^33 - 584967 * q^34 + 8137398 * q^35 - 3035428 * q^36 - 3541812 * q^37 + 6280356 * q^38 - 2473841 * q^40 + 7375370 * q^41 + 15490227 * q^43 - 2983894 * q^44 + 3217584 * q^46 - 7588210 * q^47 + 5844987 * q^48 + 33155723 * q^49 - 9064422 * q^50 + 3837506 * q^52 - 5366122 * q^53 - 45158560 * q^54 + 40061478 * q^55 - 39705477 * q^56 + 13330347 * q^57 + 19271684 * q^58 + 18367244 * q^59 - 36808121 * q^60 - 6722484 * q^61 - 15483591 * q^62 - 40574925 * q^63 - 87236036 * q^64 - 33263013 * q^66 - 8581935 * q^67 - 123045082 * q^68 - 26516709 * q^69 - 132304098 * q^71 - 100762446 * q^72 + 278404467 * q^73 + 182026410 * q^74 + 179327130 * q^76 + 143930505 * q^77 - 143413472 * q^78 - 62931368 * q^79 + 121842717 * q^80 - 65032540 * q^81 - 29005780 * q^83 + 370916864 * q^84 + 73281798 * q^86 + 137580504 * q^87 - 124655943 * q^89 + 63835252 * q^90 + 287393496 * q^91 - 215232271 * q^92 - 124327923 * q^93 + 413979855 * q^95 + 51391714 * q^96 - 446400270 * q^97 - 351696195 * q^98 - 146664065 * q^99

Introduction

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