LMFDB - Embedded newform 43.10.c.a.6.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,10,Mod(6,43)]

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([4]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("43.6");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	43.c (of order $3$, 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:	$22.1465409550$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			6.15
Character	$\chi$	$=$	43.6
Dual form			43.10.c.a.36.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.29691 q^{2} +(-0.107179 + 0.185640i) q^{3} -458.755 q^{4} +(1142.50 - 1978.86i) q^{5} +(0.782078 - 1.35460i) q^{6} +(-5889.33 - 10200.6i) q^{7} +7083.52 q^{8} +(9841.48 + 17045.9i) q^{9} +O(q^{10})$	\(q-7.29691 q^{2} +(-0.107179 + 0.185640i) q^{3} -458.755 q^{4} +(1142.50 - 1978.86i) q^{5} +(0.782078 - 1.35460i) q^{6} +(-5889.33 - 10200.6i) q^{7} +7083.52 q^{8} +(9841.48 + 17045.9i) q^{9} +(-8336.70 + 14439.6i) q^{10} +24167.2 q^{11} +(49.1690 - 85.1632i) q^{12} +(-6025.36 - 10436.2i) q^{13} +(42974.0 + 74433.1i) q^{14} +(244.904 + 424.186i) q^{15} +183195. q^{16} +(-302170. - 523375. i) q^{17} +(-71812.4 - 124383. i) q^{18} +(-296845. + 514150. i) q^{19} +(-524126. + 907814. i) q^{20} +2524.86 q^{21} -176346. q^{22} +(232004. - 401842. i) q^{23} +(-759.206 + 1314.98i) q^{24} +(-1.63404e6 - 2.83024e6i) q^{25} +(43966.6 + 76152.3i) q^{26} -8438.43 q^{27} +(2.70176e6 + 4.67959e6i) q^{28} +(-714164. - 1.23697e6i) q^{29} +(-1787.04 - 3095.25i) q^{30} +(-3.09357e6 + 5.35821e6i) q^{31} -4.96352e6 q^{32} +(-2590.22 + 4486.40i) q^{33} +(2.20491e6 + 3.81902e6i) q^{34} -2.69142e7 q^{35} +(-4.51483e6 - 7.81991e6i) q^{36} +(-7.27165e6 + 1.25949e7i) q^{37} +(2.16605e6 - 3.75171e6i) q^{38} +2583.18 q^{39} +(8.09290e6 - 1.40173e7i) q^{40} -3.11049e7 q^{41} -18423.7 q^{42} +(1.97701e7 - 1.05706e7i) q^{43} -1.10868e7 q^{44} +4.49754e7 q^{45} +(-1.69291e6 + 2.93221e6i) q^{46} +3.11810e7 q^{47} +(-19634.7 + 34008.3i) q^{48} +(-4.91917e7 + 8.52025e7i) q^{49} +(1.19234e7 + 2.06520e7i) q^{50} +129546. q^{51} +(2.76417e6 + 4.78768e6i) q^{52} +(3.06638e7 - 5.31113e7i) q^{53} +61574.5 q^{54} +(2.76110e7 - 4.78236e7i) q^{55} +(-4.17172e7 - 7.22563e7i) q^{56} +(-63631.2 - 110212. i) q^{57} +(5.21119e6 + 9.02605e6i) q^{58} -1.40505e7 q^{59} +(-112351. - 194598. i) q^{60} +(4.27646e7 + 7.40705e7i) q^{61} +(2.25735e7 - 3.90984e7i) q^{62} +(1.15919e8 - 2.00778e8i) q^{63} -5.75774e7 q^{64} -2.75358e7 q^{65} +(18900.6 - 32736.9i) q^{66} +(-2.84713e7 + 4.93137e7i) q^{67} +(1.38622e8 + 2.40101e8i) q^{68} +(49732.0 + 86138.3i) q^{69} +1.96391e8 q^{70} +(-5.05815e7 - 8.76096e7i) q^{71} +(6.97123e7 + 1.20745e8i) q^{72} +(1.87812e8 + 3.25301e8i) q^{73} +(5.30606e7 - 9.19036e7i) q^{74} +700540. q^{75} +(1.36179e8 - 2.35869e8i) q^{76} +(-1.42329e8 - 2.46521e8i) q^{77} -18849.2 q^{78} +(2.59061e7 + 4.48707e7i) q^{79} +(2.09300e8 - 3.62517e8i) q^{80} +(-1.93709e8 + 3.35514e8i) q^{81} +2.26970e8 q^{82} +(2.56642e8 - 4.44517e8i) q^{83} -1.15829e6 q^{84} -1.38092e9 q^{85} +(-1.44260e8 + 7.71325e7i) q^{86} +306174. q^{87} +1.71189e8 q^{88} +(1.95232e6 - 3.38152e6i) q^{89} -3.28182e8 q^{90} +(-7.09707e7 + 1.22925e8i) q^{91} +(-1.06433e8 + 1.84347e8i) q^{92} +(-663132. - 1.14858e6i) q^{93} -2.27525e8 q^{94} +(6.78288e8 + 1.17483e9i) q^{95} +(531986. - 921427. i) q^{96} -1.04675e9 q^{97} +(3.58947e8 - 6.21715e8i) q^{98} +(2.37841e8 + 4.11953e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9}+O(q^{10}) $ 64 * q - 70 * q^2 + 307 * q^3 + 16038 * q^4 + 681 * q^5 - 1281 * q^6 + 957 * q^7 - 10920 * q^8 - 255339 * q^9	\( 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9} - 6237 q^{10} - 180682 q^{11} + 274344 q^{12} + 115245 q^{13} - 171208 q^{14} + 138833 q^{15} + 4289206 q^{16} + 65180 q^{17} + 603985 q^{18} + 39150 q^{19} - 2709775 q^{20} - 3105162 q^{21} + 598456 q^{22} + 1285907 q^{23} - 292550 q^{24} - 14709917 q^{25} + 5332695 q^{26} - 20118002 q^{27} - 5475298 q^{28} + 1274091 q^{29} + 28424751 q^{30} + 2899781 q^{31} - 16322030 q^{32} + 30668912 q^{33} + 6822099 q^{34} - 14750922 q^{35} - 113819232 q^{36} - 13772217 q^{37} + 2700532 q^{38} + 49876982 q^{39} - 55802359 q^{40} + 5375394 q^{41} - 62768266 q^{42} - 4250879 q^{43} - 125171958 q^{44} + 74719384 q^{45} - 91405220 q^{46} + 46104596 q^{47} + 294588191 q^{48} - 233221733 q^{49} + 380339342 q^{50} + 229598406 q^{51} + 166281612 q^{52} + 125396641 q^{53} - 137752484 q^{54} + 139471854 q^{55} + 41104589 q^{56} - 289586721 q^{57} - 183782516 q^{58} - 637949078 q^{59} - 70735747 q^{60} - 95573327 q^{61} + 181277053 q^{62} + 226632970 q^{63} + 712599660 q^{64} - 498753718 q^{65} - 349240445 q^{66} - 276270786 q^{67} + 1034771928 q^{68} - 199705103 q^{69} + 1780847990 q^{70} + 651945247 q^{71} - 270063054 q^{72} - 182725322 q^{73} - 193737672 q^{74} - 3155252572 q^{75} + 492133584 q^{76} + 216024528 q^{77} + 2562586420 q^{78} - 376932221 q^{79} - 783129021 q^{80} - 2146956496 q^{81} + 2373824428 q^{82} + 1008544071 q^{83} - 9413139208 q^{84} - 1131353054 q^{85} - 1641459050 q^{86} + 5060470018 q^{87} + 369936980 q^{88} + 2244184366 q^{89} + 3302428348 q^{90} + 3951711 q^{91} + 4361095637 q^{92} + 3133616089 q^{93} + 3002217406 q^{94} + 1515822931 q^{95} + 69408612 q^{96} - 6951085934 q^{97} + 1120193981 q^{98} + 1264470179 q^{99}+O(q^{100}) \) 64 * q - 70 * q^2 + 307 * q^3 + 16038 * q^4 + 681 * q^5 - 1281 * q^6 + 957 * q^7 - 10920 * q^8 - 255339 * q^9 - 6237 * q^10 - 180682 * q^11 + 274344 * q^12 + 115245 * q^13 - 171208 * q^14 + 138833 * q^15 + 4289206 * q^16 + 65180 * q^17 + 603985 * q^18 + 39150 * q^19 - 2709775 * q^20 - 3105162 * q^21 + 598456 * q^22 + 1285907 * q^23 - 292550 * q^24 - 14709917 * q^25 + 5332695 * q^26 - 20118002 * q^27 - 5475298 * q^28 + 1274091 * q^29 + 28424751 * q^30 + 2899781 * q^31 - 16322030 * q^32 + 30668912 * q^33 + 6822099 * q^34 - 14750922 * q^35 - 113819232 * q^36 - 13772217 * q^37 + 2700532 * q^38 + 49876982 * q^39 - 55802359 * q^40 + 5375394 * q^41 - 62768266 * q^42 - 4250879 * q^43 - 125171958 * q^44 + 74719384 * q^45 - 91405220 * q^46 + 46104596 * q^47 + 294588191 * q^48 - 233221733 * q^49 + 380339342 * q^50 + 229598406 * q^51 + 166281612 * q^52 + 125396641 * q^53 - 137752484 * q^54 + 139471854 * q^55 + 41104589 * q^56 - 289586721 * q^57 - 183782516 * q^58 - 637949078 * q^59 - 70735747 * q^60 - 95573327 * q^61 + 181277053 * q^62 + 226632970 * q^63 + 712599660 * q^64 - 498753718 * q^65 - 349240445 * q^66 - 276270786 * q^67 + 1034771928 * q^68 - 199705103 * q^69 + 1780847990 * q^70 + 651945247 * q^71 - 270063054 * q^72 - 182725322 * q^73 - 193737672 * q^74 - 3155252572 * q^75 + 492133584 * q^76 + 216024528 * q^77 + 2562586420 * q^78 - 376932221 * q^79 - 783129021 * q^80 - 2146956496 * q^81 + 2373824428 * q^82 + 1008544071 * q^83 - 9413139208 * q^84 - 1131353054 * q^85 - 1641459050 * q^86 + 5060470018 * q^87 + 369936980 * q^88 + 2244184366 * q^89 + 3302428348 * q^90 + 3951711 * q^91 + 4361095637 * q^92 + 3133616089 * q^93 + 3002217406 * q^94 + 1515822931 * q^95 + 69408612 * q^96 - 6951085934 * q^97 + 1120193981 * q^98 + 1264470179 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−7.29691			−0.322481			−0.161241	−	0.986915i	$-0.551549\pi$
$2$	−7.29691			−0.322481			−0.161241	+	0.986915i	$0.551549\pi$
$3$	−0.107179	+	0.185640i	−0.000763950	+	0.00132320i	−0.866407	−	0.499338i	$-0.833577\pi$
$3$	−0.107179	+	0.185640i	−0.000763950	+	0.00132320i	0.865643	+	0.500661i	$0.166910\pi$
$4$	−458.755			−0.896006
$5$	1142.50	−	1978.86i	0.817505	−	1.41596i	−0.0900109	−	0.995941i	$-0.528690\pi$
$5$	1142.50	−	1978.86i	0.817505	−	1.41596i	0.907515	−	0.420019i	$-0.137976\pi$
$6$	0.782078	−	1.35460i	0.000246359	−	0.000426707i
$7$	−5889.33	−	10200.6i	−0.927097	−	1.60578i	−0.788154	−	0.615478i	$-0.788963\pi$
$7$	−5889.33	−	10200.6i	−0.927097	−	1.60578i	−0.138942	−	0.990300i	$-0.544370\pi$
$8$	7083.52			0.611426
$9$	9841.48	+	17045.9i	0.499999	+	0.866023i
$10$	−8336.70	+	14439.6i	−0.263630	+	0.456620i
$11$	24167.2			0.497691			0.248845	−	0.968543i	$-0.419949\pi$
$11$	24167.2			0.497691			0.248845	+	0.968543i	$0.419949\pi$
$12$	49.1690	−	85.1632i	0.000684504	−	0.00118560i
$13$	−6025.36	−	10436.2i	−0.0585111	−	0.101344i	0.835286	−	0.549815i	$-0.185302\pi$
$13$	−6025.36	−	10436.2i	−0.0585111	−	0.101344i	−0.893797	+	0.448471i	$0.851969\pi$
$14$	42974.0	+	74433.1i	0.298971	+	0.517833i
$15$	244.904	+	424.186i	0.00124907	+	0.00216344i
$16$	183195.			0.698833
$17$	−302170.	−	523375.i	−0.877469	−	1.51982i	−0.854109	−	0.520094i	$-0.825897\pi$
$17$	−302170.	−	523375.i	−0.877469	−	1.51982i	−0.0233600	−	0.999727i	$-0.507436\pi$
$18$	−71812.4	−	124383.i	−0.161240	−	0.279276i
$19$	−296845.	+	514150.i	−0.522562	+	0.905104i	0.477093	+	0.878853i	$0.341690\pi$
$19$	−296845.	+	514150.i	−0.522562	+	0.905104i	−0.999655	+	0.0262516i	$0.991643\pi$
$20$	−524126.	+	907814.i	−0.732489	+	1.26871i
$21$	2524.86			0.00283302
$22$	−176346.			−0.160496
$23$	232004.	−	401842.i	0.172870	−	0.299420i	−0.766552	−	0.642182i	$-0.778029\pi$
$23$	232004.	−	401842.i	0.172870	−	0.299420i	0.939422	+	0.342763i	$0.111363\pi$
$24$	−759.206	+	1314.98i	−0.000467099	+	0.000809039i
$25$	−1.63404e6	−	2.83024e6i	−0.836627	−	1.44908i
$26$	43966.6	+	76152.3i	0.0188687	+	0.0326816i
$27$	−8438.43			−0.00305580
$28$	2.70176e6	+	4.67959e6i	0.830684	+	1.43879i
$29$	−714164.	−	1.23697e6i	−0.187502	−	0.324764i	0.756915	−	0.653514i	$-0.226706\pi$
$29$	−714164.	−	1.23697e6i	−0.187502	−	0.324764i	−0.944417	+	0.328750i	$0.893373\pi$
$30$	−1787.04	−	3095.25i	−0.000402800	−	0.000697670i
$31$	−3.09357e6	+	5.35821e6i	−0.601633	+	1.04206i	0.390941	+	0.920416i	$0.372150\pi$
$31$	−3.09357e6	+	5.35821e6i	−0.601633	+	1.04206i	−0.992574	+	0.121643i	$0.961184\pi$
$32$	−4.96352e6			−0.836786
$33$	−2590.22	+	4486.40i	−0.000380211	+	0.000658544i
$34$	2.20491e6	+	3.81902e6i	0.282967	+	0.490114i
$35$	−2.69142e7			−3.03162
$36$	−4.51483e6	−	7.81991e6i	−0.448002	−	0.775962i
$37$	−7.27165e6	+	1.25949e7i	−0.637860	+	1.10481i	0.348042	+	0.937479i	$0.386847\pi$
$37$	−7.27165e6	+	1.25949e7i	−0.637860	+	1.10481i	−0.985902	+	0.167326i	$0.946487\pi$
$38$	2.16605e6	−	3.75171e6i	0.168516	−	0.291879i
$39$	2583.18			0.000178798
$40$	8.09290e6	−	1.40173e7i	0.499844	−	0.865754i
$41$	−3.11049e7			−1.71910			−0.859550	−	0.511052i	$-0.829256\pi$
$41$	−3.11049e7			−1.71910			−0.859550	+	0.511052i	$0.829256\pi$
$42$	−18423.7			−0.000913596
$43$	1.97701e7	−	1.05706e7i	0.881861	−	0.471509i
$43$	1.97701e7	−	1.05706e7i	0.881861	−	0.471509i
$44$	−1.10868e7			−0.445934
$45$	4.49754e7			1.63501
$46$	−1.69291e6	+	2.93221e6i	−0.0557473	+	0.0965572i
$47$	3.11810e7			0.932074			0.466037	−	0.884765i	$-0.345681\pi$
$47$	3.11810e7			0.932074			0.466037	+	0.884765i	$0.345681\pi$
$48$	−19634.7	+	34008.3i	−0.000533873	+	0.000924696i
$49$	−4.91917e7	+	8.52025e7i	−1.21902	+	2.11140i
$50$	1.19234e7	+	2.06520e7i	0.269797	+	0.467301i
$51$	129546.			0.00268137
$52$	2.76417e6	+	4.78768e6i	0.0524263	+	0.0908050i
$53$	3.06638e7	−	5.31113e7i	0.533808	−	0.924583i	−0.465412	−	0.885094i	$-0.654094\pi$
$53$	3.06638e7	−	5.31113e7i	0.533808	−	0.924583i	0.999220	−	0.0394884i	$-0.0125728\pi$
$54$	61574.5			0.000985437
$55$	2.76110e7	−	4.78236e7i	0.406864	−	0.704710i
$56$	−4.17172e7	−	7.22563e7i	−0.566851	−	0.981815i
$57$	−63631.2	−	110212.i	−0.000798423	−	0.00138291i
$58$	5.21119e6	+	9.02605e6i	0.0604660	+	0.104730i
$59$	−1.40505e7			−0.150958			−0.0754790	−	0.997147i	$-0.524049\pi$
$59$	−1.40505e7			−0.150958			−0.0754790	+	0.997147i	$0.524049\pi$
$60$	−112351.	−	194598.i	−0.00111917	−	0.00193846i
$61$	4.27646e7	+	7.40705e7i	0.395458	+	0.684953i	0.993160	−	0.116766i	$-0.0372526\pi$
$61$	4.27646e7	+	7.40705e7i	0.395458	+	0.684953i	−0.597702	+	0.801719i	$0.703919\pi$
$62$	2.25735e7	−	3.90984e7i	0.194015	−	0.336044i
$63$	1.15919e8	−	2.00778e8i	0.927094	−	1.60577i
$64$	−5.75774e7			−0.428985
$65$	−2.75358e7			−0.191332
$66$	18900.6	−	32736.9i	0.000122611	−	0.000212368i
$67$	−2.84713e7	+	4.93137e7i	−0.172612	+	0.298972i	−0.939332	−	0.343009i	$-0.888554\pi$
$67$	−2.84713e7	+	4.93137e7i	−0.172612	+	0.298972i	0.766720	+	0.641981i	$0.221887\pi$
$68$	1.38622e8	+	2.40101e8i	0.786218	+	1.36177i
$69$	49732.0	+	86138.3i	0.000264128	+	0.000457483i
$70$	1.96391e8			0.977641
$71$	−5.05815e7	−	8.76096e7i	−0.236227	−	0.409156i	0.723402	−	0.690427i	$-0.242577\pi$
$71$	−5.05815e7	−	8.76096e7i	−0.236227	−	0.409156i	−0.959628	+	0.281271i	$0.909244\pi$
$72$	6.97123e7	+	1.20745e8i	0.305712	+	0.529509i
$73$	1.87812e8	+	3.25301e8i	0.774054	+	1.34070i	0.935325	+	0.353791i	$0.115108\pi$
$73$	1.87812e8	+	3.25301e8i	0.774054	+	1.34070i	−0.161270	+	0.986910i	$0.551559\pi$
$74$	5.30606e7	−	9.19036e7i	0.205698	−	0.356279i
$75$	700540.			0.00255657
$76$	1.36179e8	−	2.35869e8i	0.468219	−	0.810979i
$77$	−1.42329e8	−	2.46521e8i	−0.461407	−	0.799181i
$78$	−18849.2			−5.76590e−5
$79$	2.59061e7	+	4.48707e7i	0.0748309	+	0.129611i	0.901013	−	0.433793i	$-0.142825\pi$
$79$	2.59061e7	+	4.48707e7i	0.0748309	+	0.129611i	−0.826182	+	0.563404i	$0.809492\pi$
$80$	2.09300e8	−	3.62517e8i	0.571299	−	0.989519i
$81$	−1.93709e8	+	3.35514e8i	−0.499996	+	0.866019i
$82$	2.26970e8			0.554377
$83$	2.56642e8	−	4.44517e8i	0.593576	−	1.02810i	−0.400170	−	0.916441i	$-0.631049\pi$
$83$	2.56642e8	−	4.44517e8i	0.593576	−	1.02810i	0.993746	−	0.111663i	$-0.0356178\pi$
$84$	−1.15829e6			−0.00253840
$85$	−1.38092e9			−2.86934
$86$	−1.44260e8	+	7.71325e7i	−0.284383	+	0.152053i
$87$	306174.			0.000572970
$88$	1.71189e8			0.304301
$89$	1.95232e6	−	3.38152e6i	0.00329835	−	0.00571291i	−0.864372	−	0.502854i	$-0.832283\pi$
$89$	1.95232e6	−	3.38152e6i	0.00329835	−	0.00571291i	0.867670	+	0.497141i	$0.165617\pi$
$90$	−3.28182e8			−0.527258
$91$	−7.09707e7	+	1.22925e8i	−0.108491	+	0.187912i
$92$	−1.06433e8	+	1.84347e8i	−0.154893	+	0.268282i
$93$	−663132.	−	1.14858e6i	−0.000919235	−	0.00159216i
$94$	−2.27525e8			−0.300576
$95$	6.78288e8	+	1.17483e9i	0.854394	+	1.47985i
$96$	531986.	−	921427.i	0.000639263	−	0.00110724i
$97$	−1.04675e9			−1.20052			−0.600262	−	0.799803i	$-0.704937\pi$
$97$	−1.04675e9			−1.20052			−0.600262	+	0.799803i	$0.704937\pi$
$98$	3.58947e8	−	6.21715e8i	0.393110	−	0.680886i
$99$	2.37841e8	+	4.11953e8i	0.248845	+	0.431012i
$100$	7.49623e8	+	1.29839e9i	0.749623	+	1.29839i
$101$	−4.50327e8	−	7.79989e8i	−0.430607	−	0.745834i	0.566318	−	0.824187i	$-0.308367\pi$
$101$	−4.50327e8	−	7.79989e8i	−0.430607	−	0.745834i	−0.996926	+	0.0783528i	$0.975034\pi$
$102$	−945283.			−0.000864691
$103$	−1.78583e8	−	3.09315e8i	−0.156341	−	0.270790i	0.777206	−	0.629247i	$-0.216636\pi$
$103$	−1.78583e8	−	3.09315e8i	−0.156341	−	0.270790i	−0.933546	+	0.358456i	$0.883303\pi$
$104$	−4.26808e7	−	7.39252e7i	−0.0357752	−	0.0619645i
$105$	2.88464e6	−	4.99635e6i	0.00231601	−	0.00401144i
$106$	−2.23751e8	+	3.87549e8i	−0.172143	+	0.298160i
$107$	−1.17368e9			−0.865609			−0.432804	−	0.901488i	$-0.642476\pi$
$107$	−1.17368e9			−0.865609			−0.432804	+	0.901488i	$0.642476\pi$
$108$	3.87117e6			0.00273801
$109$	9.04957e8	−	1.56743e9i	0.614057	−	1.06358i	−0.376492	−	0.926420i	$-0.622870\pi$
$109$	9.04957e8	−	1.56743e9i	0.614057	−	1.06358i	0.990549	−	0.137158i	$-0.0437969\pi$
$110$	−2.01475e8	+	3.48965e8i	−0.131206	+	0.227256i
$111$	−1.55874e6	−	2.69982e6i	−0.000974586	−	0.00168803i
$112$	−1.07890e9	−	1.86870e9i	−0.647885	−	1.12217i
$113$	−2.03728e8			−0.117543			−0.0587716	−	0.998271i	$-0.518718\pi$
$113$	−2.03728e8			−0.117543			−0.0587716	+	0.998271i	$0.518718\pi$
$114$	464311.	+	804210.i	0.000257476	+	0.000445962i
$115$	−5.30127e8	−	9.18207e8i	−0.282644	−	0.489554i
$116$	3.27626e8	+	5.67465e8i	0.168003	+	0.290990i
$117$	1.18597e8	−	2.05416e8i	0.0585109	−	0.101344i
$118$	1.02525e8			0.0486811
$119$	−3.55916e9	+	6.16465e9i	−1.62700	+	2.81804i
$120$	1.73478e6	+	3.00473e6i	0.000763711	+	0.00132279i
$121$	−1.77389e9			−0.752304
$122$	−3.12050e8	−	5.40486e8i	−0.127528	−	0.220884i
$123$	3.33380e6	−	5.77431e6i	0.00131331	−	0.00227471i
$124$	1.41919e9	−	2.45811e9i	0.539067	−	0.933691i
$125$	−3.00466e9			−1.10078
$126$	−8.45854e8	+	1.46506e9i	−0.298970	+	0.517832i
$127$	4.27455e9			1.45805			0.729026	−	0.684486i	$-0.239973\pi$
$127$	4.27455e9			1.45805			0.729026	+	0.684486i	$0.239973\pi$
$128$	2.96146e9			0.975126
$129$	−156621.	+	4.80306e6i	−4.97963e−5	+	0.00152709i
$130$	2.00927e8			0.0617010
$131$	2.48351e9			0.736792			0.368396	−	0.929669i	$-0.379907\pi$
$131$	2.48351e9			0.736792			0.368396	+	0.929669i	$0.379907\pi$
$132$	1.18828e6	−	2.05816e6i	0.000340671	−	0.000590060i
$133$	6.99287e9			1.93786
$134$	2.07753e8	−	3.59838e8i	0.0556640	−	0.0964130i
$135$	−9.64088e6	+	1.66985e7i	−0.00249813	+	0.00432688i
$136$	−2.14043e9	−	3.70733e9i	−0.536507	−	0.929258i
$137$	−3.96429e9			−0.961442			−0.480721	−	0.876874i	$-0.659625\pi$
$137$	−3.96429e9			−0.961442			−0.480721	+	0.876874i	$0.659625\pi$
$138$	−362890.	−	628544.i	−8.51763e−5	−	0.000147530i
$139$	8.75120e8	−	1.51575e9i	0.198839	−	0.344399i	−0.749313	−	0.662216i	$-0.769616\pi$
$139$	8.75120e8	−	1.51575e9i	0.198839	−	0.344399i	0.948152	+	0.317817i	$0.102950\pi$
$140$	1.23470e10			2.71635
$141$	−3.34196e6	+	5.78845e6i	−0.000712058	+	0.00123332i
$142$	3.69088e8	+	6.39280e8i	0.0761786	+	0.131945i
$143$	−1.45616e8	−	2.52215e8i	−0.0291204	−	0.0504380i
$144$	1.80291e9	+	3.12273e9i	0.349416	+	0.605205i
$145$	−3.26372e9			−0.613136
$146$	−1.37045e9	−	2.37369e9i	−0.249618	−	0.432351i
$147$	−1.05447e7	−	1.82639e7i	−0.00186253	−	0.00322600i
$148$	3.33591e9	−	5.77796e9i	0.571526	−	0.989912i
$149$	−1.24380e8	+	2.15432e8i	−0.0206734	+	0.0358074i	−0.876177	−	0.481989i	$-0.839914\pi$
$149$	−1.24380e8	+	2.15432e8i	−0.0206734	+	0.0358074i	0.855504	+	0.517797i	$0.173248\pi$
$150$	−5.11178e6			−0.000824444
$151$	−6.61314e9			−1.03517			−0.517585	−	0.855632i	$-0.673169\pi$
$151$	−6.61314e9			−1.03517			−0.517585	+	0.855632i	$0.673169\pi$
$152$	−2.10270e9	+	3.64199e9i	−0.319508	+	0.553404i
$153$	5.94761e9	−	1.03016e10i	0.877467	−	1.51982i
$154$	1.03856e9	+	1.79884e9i	0.148795	+	0.257721i
$155$	7.06878e9	+	1.22435e10i	0.983676	+	1.70378i
$156$	−1.18504e6			−0.000160204
$157$	−2.64893e9	−	4.58808e9i	−0.347954	−	0.602674i	0.637932	−	0.770093i	$-0.279790\pi$
$157$	−2.64893e9	−	4.58808e9i	−0.347954	−	0.602674i	−0.985886	+	0.167419i	$0.946457\pi$
$158$	−1.89035e8	−	3.27418e8i	−0.0241315	−	0.0417970i
$159$	6.57305e6	+	1.13849e7i	0.000815605	+	0.00141267i
$160$	−5.67080e9	+	9.82212e9i	−0.684077	+	1.18486i
$161$	−5.46539e9			−0.641069
$162$	1.41348e9	−	2.44821e9i	0.161239	−	0.279275i
$163$	−2.77340e9	−	4.80367e9i	−0.307729	−	0.533002i	0.670136	−	0.742238i	$-0.266236\pi$
$163$	−2.77340e9	−	4.80367e9i	−0.307729	−	0.533002i	−0.977865	+	0.209236i	$0.932902\pi$
$164$	1.42695e10			1.54032
$165$	5.91865e6	+	1.02514e7i	0.000621648	+	0.00107673i
$166$	−1.87270e9	+	3.24360e9i	−0.191417	+	0.331544i
$167$	5.34442e9	−	9.25680e9i	0.531712	−	0.920952i	−0.467603	−	0.883939i	$-0.654882\pi$
$167$	5.34442e9	−	9.25680e9i	0.531712	−	0.920952i	0.999315	−	0.0370133i	$-0.0117844\pi$
$168$	1.78849e7			0.00173218
$169$	5.22964e9	−	9.05800e9i	0.493153	−	0.854166i
$170$	1.00764e10			0.925308
$171$	−1.16856e10			−1.04512
$172$	−9.06962e9	+	4.84930e9i	−0.790153	+	0.422475i
$173$	−8.30913e9			−0.705258			−0.352629	−	0.935763i	$-0.614712\pi$
$173$	−8.30913e9			−0.705258			−0.352629	+	0.935763i	$0.614712\pi$
$174$	−2.23413e6			−0.000184772
$175$	−1.92468e10	+	3.33364e10i	−1.55127	+	2.68688i
$176$	4.42731e9			0.347802
$177$	1.50592e6	−	2.60833e6i	0.000115324	−	0.000199748i
$178$	−1.42459e7	+	2.46747e7i	−0.00106366	+	0.00184231i
$179$	−6.74226e9	−	1.16779e10i	−0.490871	−	0.850213i	0.509074	−	0.860723i	$-0.329988\pi$
$179$	−6.74226e9	−	1.16779e10i	−0.490871	−	0.850213i	−0.999945	+	0.0105096i	$0.996655\pi$
$180$	−2.06327e10			−1.46497
$181$	1.48581e9	+	2.57350e9i	0.102899	+	0.178226i	0.912878	−	0.408233i	$-0.133855\pi$
$181$	1.48581e9	+	2.57350e9i	0.102899	+	0.178226i	−0.809979	+	0.586459i	$0.800522\pi$
$182$	5.17867e8	−	8.96973e8i	0.0349862	−	0.0605980i
$183$	−1.83339e7			−0.00120844
$184$	1.64340e9	−	2.84646e9i	0.105697	−	0.183073i
$185$	1.66157e10	+	2.87792e10i	1.04291	+	1.80637i
$186$	4.83882e6	+	8.38108e6i	0.000296436	+	0.000513442i
$187$	−7.30262e9	−	1.26485e10i	−0.436708	−	0.756401i
$188$	−1.43045e10			−0.835144
$189$	4.96967e7	+	8.60772e7i	0.00283302	+	0.00490693i
$190$	−4.94941e9	−	8.57263e9i	−0.275526	−	0.477225i
$191$	7.64524e9	−	1.32419e10i	0.415663	−	0.719949i	−0.579835	−	0.814734i	$-0.696883\pi$
$191$	7.64524e9	−	1.32419e10i	0.415663	−	0.719949i	0.995498	+	0.0947851i	$0.0302164\pi$
$192$	6.17110e6	−	1.06887e7i	0.000327723	−	0.000567633i
$193$	−2.79186e10			−1.44839			−0.724194	−	0.689596i	$-0.757788\pi$
$193$	−2.79186e10			−1.44839			−0.724194	+	0.689596i	$0.757788\pi$
$194$	7.63806e9			0.387147
$195$	2.95127e6	−	5.11175e6i	0.000146168	−	0.000253171i
$196$	2.25669e10	−	3.90871e10i	1.09225	−	1.89182i
$197$	5.61460e9	+	9.72478e9i	0.265596	+	0.460025i	0.967720	−	0.252030i	$-0.0810981\pi$
$197$	5.61460e9	+	9.72478e9i	0.265596	+	0.460025i	−0.702124	+	0.712055i	$0.747765\pi$
$198$	−1.73551e9	−	3.00598e9i	−0.0802477	−	0.138993i
$199$	2.92130e9			0.132049			0.0660247	−	0.997818i	$-0.478968\pi$
$199$	2.92130e9			0.132049			0.0660247	+	0.997818i	$0.478968\pi$
$200$	−1.15747e10	−	2.00480e10i	−0.511536	−	0.886006i
$201$	−6.10306e6	−	1.05708e7i	−0.000263734	−	0.000456800i
$202$	3.28599e9	+	5.69151e9i	0.138863	+	0.240517i
$203$	−8.41190e9	+	1.45698e10i	−0.347666	+	0.602174i
$204$	−5.94297e7			−0.00240252
$205$	−3.55372e10	+	6.15523e10i	−1.40537	+	2.43418i
$206$	1.30310e9	+	2.25704e9i	0.0504170	+	0.0873247i
$207$	9.13304e9			0.345739
$208$	−1.10382e9	−	1.91186e9i	−0.0408895	−	0.0708226i
$209$	−7.17391e9	+	1.24256e10i	−0.260074	+	0.450462i
$210$	−2.10490e7	+	3.64579e7i	−0.000746869	+	0.00129361i
$211$	2.46193e10			0.855076			0.427538	−	0.903997i	$-0.359381\pi$
$211$	2.46193e10			0.855076			0.427538	+	0.903997i	$0.359381\pi$
$212$	−1.40672e10	+	2.43651e10i	−0.478295	+	0.828431i
$213$	2.16851e7			0.000721861
$214$	8.56422e9			0.279142
$215$	1.66954e9	−	5.11991e10i	0.0532872	−	1.63414i
$216$	−5.97737e7			−0.00186839
$217$	7.28762e10			2.23109
$218$	−6.60339e9	+	1.14374e10i	−0.198022	+	0.342984i
$219$	−8.05183e7			−0.00236536
$220$	−1.26667e10	+	2.19393e10i	−0.364553	+	0.631424i
$221$	−3.64137e9	+	6.30704e9i	−0.102683	+	0.177853i
$222$	1.13740e7	+	1.97003e7i	0.000314285	+	0.000544358i
$223$	−6.51547e10			−1.76431			−0.882153	−	0.470964i	$-0.843906\pi$
$223$	−6.51547e10			−1.76431			−0.882153	+	0.470964i	$0.843906\pi$
$224$	2.92318e10	+	5.06310e10i	0.775782	+	1.34369i
$225$	3.21627e10	−	5.57074e10i	0.836625	−	1.44908i
$226$	1.48658e9			0.0379054
$227$	3.86357e10	−	6.69191e10i	0.965768	−	1.67276i	0.258232	−	0.966083i	$-0.416860\pi$
$227$	3.86357e10	−	6.69191e10i	0.965768	−	1.67276i	0.707537	−	0.706677i	$-0.249806\pi$
$228$	2.91911e7	+	5.05605e7i	0.000715392	+	0.00123909i
$229$	5.78678e9	+	1.00230e10i	0.139052	+	0.240845i	0.927138	−	0.374720i	$-0.122261\pi$
$229$	5.78678e9	+	1.00230e10i	0.139052	+	0.240845i	−0.788086	+	0.615565i	$0.788928\pi$
$230$	3.86829e9	+	6.70008e9i	0.0911473	+	0.157872i
$231$	6.10188e7			0.00140997
$232$	−5.05879e9	−	8.76208e9i	−0.114644	−	0.198569i
$233$	−2.67583e10	−	4.63468e10i	−0.594781	−	1.03019i	−0.993578	−	0.113151i	$-0.963905\pi$
$233$	−2.67583e10	−	4.63468e10i	−0.594781	−	1.03019i	0.398797	−	0.917039i	$-0.369428\pi$
$234$	−8.65392e8	+	1.49890e9i	−0.0188687	+	0.0326815i
$235$	3.56243e10	−	6.17030e10i	0.761975	−	1.31978i
$236$	6.44572e9			0.135259
$237$	−1.11064e7			−0.000228668
$238$	2.59709e10	−	4.49829e10i	0.524676	−	0.908765i
$239$	4.02221e9	−	6.96667e9i	0.0797396	−	0.138113i	−0.823398	−	0.567464i	$-0.807924\pi$
$239$	4.02221e9	−	6.96667e9i	0.0797396	−	0.138113i	0.903138	+	0.429351i	$0.141258\pi$
$240$	4.48651e7	+	7.77087e7i	0.000872888	+	0.00151189i
$241$	−1.31265e10	−	2.27358e10i	−0.250653	−	0.434143i	0.713053	−	0.701110i	$-0.247312\pi$
$241$	−1.31265e10	−	2.27358e10i	−0.250653	−	0.434143i	−0.963706	+	0.266967i	$0.913979\pi$
$242$	1.29439e10			0.242604
$243$	−1.24570e8	−	2.15761e8i	−0.00229184	−	0.00396959i
$244$	−1.96185e10	−	3.39802e10i	−0.354333	−	0.613722i
$245$	1.12403e11	+	1.94687e11i	1.99310	+	3.45215i
$246$	−2.43264e7	+	4.21346e7i	−0.000423517	+	0.000733552i
$247$	7.15439e9			0.122303
$248$	−2.19133e10	+	3.79550e10i	−0.367854	+	0.637142i
$249$	5.50134e7	+	9.52860e7i	0.000906925	+	0.00157084i
$250$	2.19247e10			0.354980
$251$	−4.76670e7	−	8.25616e7i	−0.000758029	−	0.00131294i	0.865646	−	0.500656i	$-0.166908\pi$
$251$	−4.76670e7	−	8.25616e7i	−0.000758029	−	0.00131294i	−0.866404	+	0.499343i	$0.833575\pi$
$252$	−5.31786e10	+	9.21081e10i	−0.830682	+	1.43878i
$253$	5.60688e9	−	9.71141e9i	0.0860358	−	0.149018i
$254$	−3.11910e10			−0.470194
$255$	1.48005e8	−	2.56353e8i	0.00219203	−	0.00379671i
$256$	7.87012e9			0.114525
$257$	−7.13842e10			−1.02071			−0.510356	−	0.859963i	$-0.670486\pi$
$257$	−7.13842e10			−1.02071			−0.510356	+	0.859963i	$0.670486\pi$
$258$	1.14285e6	−	3.50475e7i	1.60584e−5	−	0.000492457i
$259$	1.71301e11			2.36543
$260$	1.26322e10			0.171435
$261$	1.40569e10	−	2.43472e10i	0.187502	−	0.324763i
$262$	−1.81219e10			−0.237601
$263$	−3.91720e10	+	6.78479e10i	−0.504865	+	0.874451i	0.495120	+	0.868825i	$0.335124\pi$
$263$	−3.91720e10	+	6.78479e10i	−0.504865	+	0.874451i	−0.999984	+	0.00562627i	$0.998209\pi$
$264$	−1.83479e7	+	3.17795e7i	−0.000232471	+	0.000402651i
$265$	−7.00667e10	−	1.21359e11i	−0.872781	−	1.51170i
$266$	−5.10264e10			−0.624924
$267$	418497.	+	724858.i	5.03955e−6	+	8.72876e-6i
$268$	1.30613e10	−	2.26229e10i	0.154661	−	0.267881i
$269$	−4.13973e9			−0.0482044			−0.0241022	−	0.999709i	$-0.507673\pi$
$269$	−4.13973e9			−0.0482044			−0.0241022	+	0.999709i	$0.507673\pi$
$270$	7.03487e7	−	1.21847e8i	0.000805599	−	0.00139534i
$271$	3.39885e10	+	5.88698e10i	0.382799	+	0.663026i	0.991461	−	0.130403i	$-0.0416270\pi$
$271$	3.39885e10	+	5.88698e10i	0.382799	+	0.663026i	−0.608663	+	0.793429i	$0.708294\pi$
$272$	−5.53560e10	−	9.58795e10i	−0.613204	−	1.06210i
$273$	−1.52132e7	−	2.63500e7i	−0.000165763	−	0.000287110i
$274$	2.89271e10			0.310047
$275$	−3.94901e10	−	6.83989e10i	−0.416382	−	0.721194i
$276$	−2.28148e7	−	3.95164e7i	−0.000236660	−	0.000409908i
$277$	3.78331e10	−	6.55288e10i	0.386111	−	0.668765i	−0.605811	−	0.795608i	$-0.707151\pi$
$277$	3.78331e10	−	6.55288e10i	0.386111	−	0.668765i	0.991923	+	0.126844i	$0.0404847\pi$
$278$	−6.38568e9	+	1.10603e10i	−0.0641217	+	0.111062i
$279$	−1.21781e11			−1.20326
$280$	−1.90647e11			−1.85361
$281$	8.12419e10	−	1.40715e11i	0.777323	−	1.34636i	−0.156157	−	0.987732i	$-0.549910\pi$
$281$	8.12419e10	−	1.40715e11i	0.777323	−	1.34636i	0.933480	−	0.358631i	$-0.116756\pi$
$282$	2.43860e7	−	4.22378e7i	0.000229625	−	0.000397722i
$283$	4.57712e9	+	7.92780e9i	0.0424183	+	0.0734706i	0.886455	−	0.462815i	$-0.153160\pi$
$283$	4.57712e9	+	7.92780e9i	0.0424183	+	0.0734706i	−0.844037	+	0.536285i	$0.819827\pi$
$284$	2.32045e10	+	4.01914e10i	0.211660	+	0.366607i
$285$	−2.90794e8			−0.00261086
$286$	1.06255e9	+	1.84039e9i	0.00939078	+	0.0162653i
$287$	1.83187e11	+	3.17289e11i	1.59377	+	2.76049i
$288$	−4.88483e10	−	8.46078e10i	−0.418392	−	0.724677i
$289$	−1.23320e11	+	2.13597e11i	−1.03990	+	1.80117i
$290$	2.38151e10			0.197725
$291$	1.12190e8	−	1.94319e8i	0.000917141	−	0.00158854i
$292$	−8.61599e10	−	1.49233e11i	−0.693557	−	1.20128i
$293$	2.23923e11			1.77498			0.887492	−	0.460824i	$-0.152446\pi$
$293$	2.23923e11			1.77498			0.887492	+	0.460824i	$0.152446\pi$
$294$	7.69434e7	+	1.33270e8i	0.000600632	+	0.00104033i
$295$	−1.60526e10	+	2.78039e10i	−0.123409	+	0.213751i
$296$	−5.15088e10	+	8.92159e10i	−0.390004	+	0.675507i
$297$	−2.03933e8			−0.00152084
$298$	9.07589e8	−	1.57199e9i	0.00666678	−	0.0115472i
$299$	−5.59163e9			−0.0404592
$300$	−3.21376e8			−0.00229070
$301$	−2.24259e11	−	1.39413e11i	−1.57471	−	0.978938i
$302$	4.82555e10			0.333822
$303$	1.93063e8			0.00131585
$304$	−5.43804e10	+	9.41896e10i	−0.365184	+	0.632516i
$305$	1.95434e11			1.29315
$306$	−4.33992e10	+	7.51696e10i	−0.282967	+	0.490112i
$307$	−4.40246e10	+	7.62529e10i	−0.282861	+	0.489930i	−0.972088	−	0.234616i	$-0.924617\pi$
$307$	−4.40246e10	+	7.62529e10i	−0.282861	+	0.489930i	0.689227	+	0.724545i	$0.257950\pi$
$308$	6.52940e10	+	1.13093e11i	0.413424	+	0.716071i
$309$	7.65615e7			0.000477746
$310$	−5.15803e10	−	8.93397e10i	−0.317217	−	0.549436i
$311$	−2.16857e9	+	3.75607e9i	−0.0131447	+	0.0227673i	−0.872523	−	0.488573i	$-0.837518\pi$
$311$	−2.16857e9	+	3.75607e9i	−0.0131447	+	0.0227673i	0.859378	+	0.511340i	$0.170851\pi$
$312$	1.82980e7			0.000109322
$313$	−8.83311e10	+	1.52994e11i	−0.520192	+	0.900999i	0.479532	+	0.877524i	$0.340806\pi$
$313$	−8.83311e10	+	1.52994e11i	−0.520192	+	0.900999i	−0.999724	+	0.0234751i	$0.992527\pi$
$314$	1.93290e10	+	3.34788e10i	0.112208	+	0.194351i
$315$	−2.64875e11	−	4.58778e11i	−1.51581	−	2.62546i
$316$	−1.18846e10	−	2.05847e10i	−0.0670489	−	0.116132i
$317$	−1.19116e11			−0.662526			−0.331263	−	0.943538i	$-0.607475\pi$
$317$	−1.19116e11			−0.662526			−0.331263	+	0.943538i	$0.607475\pi$
$318$	−4.79630e7	−	8.30744e7i	−0.000263017	−	0.000455559i
$319$	−1.72593e10	−	2.98941e10i	−0.0933182	−	0.161632i
$320$	−6.57820e10	+	1.13938e11i	−0.350697	+	0.607425i
$321$	1.25794e8	−	2.17881e8i	0.000661282	−	0.00114537i
$322$	3.98805e10			0.206733
$323$	3.58791e11			1.83413
$324$	8.88649e10	−	1.53919e11i	0.448000	−	0.775958i
$325$	−1.96913e10	+	3.41064e10i	−0.0979040	+	0.169575i
$326$	2.02373e10	+	3.50519e10i	0.0992367	+	0.171883i
$327$	1.93985e8	+	3.35992e8i	0.000938218	+	0.00162504i
$328$	−2.20332e11			−1.05110
$329$	−1.83636e11	−	3.18066e11i	−0.864122	−	1.49670i
$330$	−4.31879e7	−	7.48036e7i	−0.000200470	−	0.000347224i
$331$	1.19548e11	+	2.07063e11i	0.547414	+	0.948149i	0.998451	+	0.0556434i	$0.0177210\pi$
$331$	1.19548e11	+	2.07063e11i	0.547414	+	0.948149i	−0.451037	+	0.892505i	$0.648946\pi$
$332$	−1.17736e11	+	2.03924e11i	−0.531848	+	0.921187i
$333$	−2.86255e11			−1.27572
$334$	−3.89978e10	+	6.75461e10i	−0.171467	+	0.296990i
$335$	6.50567e10	+	1.12682e11i	0.282222	+	0.488823i
$336$	4.62541e8			0.00197981
$337$	−2.07051e11	−	3.58623e11i	−0.874467	−	1.51462i	−0.857330	−	0.514768i	$-0.827878\pi$
$337$	−2.07051e11	−	3.58623e11i	−0.874467	−	1.51462i	−0.0171372	−	0.999853i	$-0.505455\pi$
$338$	−3.81602e10	+	6.60955e10i	−0.159032	+	0.275452i
$339$	2.18354e7	−	3.78200e7i	8.97971e−5	−	0.000155533i
$340$	6.33502e11			2.57095
$341$	−7.47629e10	+	1.29493e11i	−0.299427	+	0.518623i
$342$	8.52685e10			0.337032
$343$	6.83513e11			2.66639
$344$	1.40042e11	−	7.48768e10i	0.539193	−	0.288293i
$345$	2.27275e8			0.000863704
$346$	6.06310e10			0.227432
$347$	1.75315e11	−	3.03654e11i	0.649135	−	1.12434i	−0.334194	−	0.942504i	$-0.608464\pi$
$347$	1.75315e11	−	3.03654e11i	0.649135	−	1.12434i	0.983330	−	0.181831i	$-0.0582025\pi$
$348$	−1.40459e8			−0.000513384
$349$	−1.18739e11	+	2.05661e11i	−0.428428	+	0.742059i	−0.996734	−	0.0807587i	$-0.974266\pi$
$349$	−1.18739e11	+	2.05661e11i	−0.428428	+	0.742059i	0.568306	+	0.822817i	$0.307599\pi$
$350$	1.40442e11	−	2.43253e11i	0.500255	−	0.866467i
$351$	5.08446e7	+	8.80654e7i	0.000178798	+	0.000309687i
$352$	−1.19954e11			−0.416461
$353$	8.07943e10	+	1.39940e11i	0.276946	+	0.479684i	0.970624	−	0.240601i	$-0.0773444\pi$
$353$	8.07943e10	+	1.39940e11i	0.276946	+	0.479684i	−0.693678	+	0.720285i	$0.744011\pi$
$354$	−1.09885e7	+	1.90327e7i	−3.71900e−5	+	6.44149e-5i
$355$	−2.31157e11			−0.772465
$356$	−8.95638e8	+	1.55129e9i	−0.00295534	+	0.00511880i
$357$	−7.62937e8	−	1.32145e9i	−0.00248589	−	0.00430569i
$358$	4.91977e10	+	8.52130e10i	0.158297	+	0.274178i
$359$	2.78574e11	+	4.82505e11i	0.885148	+	1.53312i	0.845544	+	0.533906i	$0.179276\pi$
$359$	2.78574e11	+	4.82505e11i	0.885148	+	1.53312i	0.0396045	+	0.999215i	$0.487390\pi$
$360$	3.18584e11			0.999685
$361$	−1.48896e10	−	2.57896e10i	−0.0461425	−	0.0799212i
$362$	−1.08418e10	−	1.87786e10i	−0.0331829	−	0.0574744i
$363$	1.90125e8	−	3.29305e8i	0.000574723	−	0.000995449i
$364$	3.25582e10	−	5.63924e10i	0.0972084	−	0.168370i
$365$	8.58301e11			2.53117
$366$	1.33781e8			0.000389699
$367$	−3.93216e10	+	6.81071e10i	−0.113145	+	0.195972i	−0.917037	−	0.398803i	$-0.869426\pi$
$367$	−3.93216e10	+	6.81071e10i	−0.113145	+	0.195972i	0.803892	+	0.594775i	$0.202759\pi$
$368$	4.25019e10	−	7.36154e10i	0.120807	−	0.209244i
$369$	−3.06118e11	−	5.30212e11i	−0.859548	−	1.48878i
$370$	−1.21243e11	−	2.09999e11i	−0.336317	−	0.582519i
$371$	−7.22358e11			−1.97957
$372$	3.04215e8	+	5.26916e8i	0.000823640	+	0.00142659i
$373$	6.89043e9	+	1.19346e10i	0.0184313	+	0.0319240i	0.875094	−	0.483953i	$-0.160799\pi$
$373$	6.89043e9	+	1.19346e10i	0.0184313	+	0.0319240i	−0.856663	+	0.515877i	$0.827466\pi$
$374$	5.32866e10	+	9.22950e10i	0.140830	+	0.243925i
$375$	3.22037e8	−	5.57784e8i	0.000840939	−	0.00145655i
$376$	2.20871e11			0.569894
$377$	−8.60619e9	+	1.49064e10i	−0.0219419	+	0.0380045i
$378$	−3.62633e8	−	6.28098e8i	−0.000913595	−	0.00158239i
$379$	4.01889e11			1.00053			0.500265	−	0.865872i	$-0.333236\pi$
$379$	4.01889e11			1.00053			0.500265	+	0.865872i	$0.333236\pi$
$380$	−3.11168e11	−	5.38959e11i	−0.765542	−	1.32596i
$381$	−4.58143e8	+	7.93526e8i	−0.00111388	+	0.00192930i
$382$	−5.57866e10	+	9.66253e10i	−0.134043	+	0.232170i
$383$	−2.15611e11			−0.512008			−0.256004	−	0.966676i	$-0.582406\pi$
$383$	−2.15611e11			−0.512008			−0.256004	+	0.966676i	$0.582406\pi$
$384$	−3.17407e8	+	5.49765e8i	−0.000744948	+	0.00129029i
$385$	−6.50441e11			−1.50881
$386$	2.03719e11			0.467078
$387$	3.74752e11	+	2.32969e11i	0.849268	+	0.527958i
$388$	4.80203e11			1.07568
$389$	−3.48571e11			−0.771824			−0.385912	−	0.922536i	$-0.626113\pi$
$389$	−3.48571e11			−0.771824			−0.385912	+	0.922536i	$0.626113\pi$
$390$	−2.15352e7	+	3.73000e7i	−4.71365e−5	+	8.16429e-5i
$391$	−2.80419e11			−0.606752
$392$	−3.48450e11	+	6.03533e11i	−0.745338	+	1.29096i
$393$	−2.66180e8	+	4.61038e8i	−0.000562872	+	0.000974923i
$394$	−4.09693e10	−	7.09608e10i	−0.0856496	−	0.148349i
$395$	1.18391e11			0.244698
$396$	−1.09111e11	−	1.88985e11i	−0.222966	−	0.386189i
$397$	−1.92350e11	+	3.33161e11i	−0.388630	+	0.673126i	−0.992265	−	0.124134i	$-0.960385\pi$
$397$	−1.92350e11	+	3.33161e11i	−0.388630	+	0.673126i	0.603636	+	0.797260i	$0.293718\pi$
$398$	−2.13164e10			−0.0425834
$399$	−7.49490e8	+	1.29816e9i	−0.00148043	+	0.00256418i
$400$	−2.99347e11	−	5.18485e11i	−0.584663	−	1.01267i
$401$	−7.65453e10	−	1.32580e11i	−0.147832	−	0.256053i	0.782594	−	0.622533i	$-0.213896\pi$
$401$	−7.65453e10	−	1.32580e11i	−0.147832	−	0.256053i	−0.930426	+	0.366480i	$0.880563\pi$
$402$	4.45335e7	+	7.71343e7i	8.50491e−5	+	0.000147309i
$403$	7.45594e10			0.140809
$404$	2.06590e11	+	3.57824e11i	0.385827	+	0.668272i
$405$	4.42624e11	+	7.66647e11i	0.817499	+	1.41595i
$406$	6.13809e10	−	1.06315e11i	0.112116	−	0.194190i
$407$	−1.75735e11	+	3.04383e11i	−0.317457	+	0.549851i
$408$	9.17638e8			0.00163946
$409$	−7.97910e10			−0.140994			−0.0704968	−	0.997512i	$-0.522458\pi$
$409$	−7.97910e10			−0.140994			−0.0704968	+	0.997512i	$0.522458\pi$
$410$	2.59312e11	−	4.49142e11i	0.453206	−	0.784976i
$411$	4.24890e8	−	7.35931e8i	0.000734494	−	0.00127218i
$412$	8.19258e10	+	1.41900e11i	0.140082	+	0.242630i
$413$	8.27478e10	+	1.43323e11i	0.139953	+	0.242405i
$414$	−6.66430e10			−0.111494
$415$	−5.86426e11	−	1.01572e12i	−0.970502	−	1.68096i
$416$	2.99070e10	+	5.18004e10i	0.0489613	+	0.0848034i
$417$	1.87589e8	+	3.24914e8i	0.000303806	+	0.000526207i
$418$	5.23474e10	−	9.06683e10i	0.0838690	−	0.145265i
$419$	−1.23159e11			−0.195211			−0.0976055	−	0.995225i	$-0.531118\pi$
$419$	−1.23159e11			−0.195211			−0.0976055	+	0.995225i	$0.531118\pi$
$420$	−1.32334e9	+	2.29210e9i	−0.00207516	+	0.00359428i
$421$	−2.58542e11	−	4.47808e11i	−0.401108	−	0.694740i	0.592751	−	0.805385i	$-0.298042\pi$
$421$	−2.58542e11	−	4.47808e11i	−0.401108	−	0.694740i	−0.993860	+	0.110645i	$0.964708\pi$
$422$	−1.79645e11			−0.275746
$423$	3.06868e11	+	5.31510e11i	0.466036	+	0.807198i
$424$	2.17208e11	−	3.76215e11i	0.326384	−	0.565314i
$425$	−9.87516e11	+	1.71043e12i	−1.46823	+	2.54305i
$426$	−1.58234e8			−0.000232787
$427$	5.03710e11	−	8.72451e11i	0.733255	−	1.27003i
$428$	5.38430e11			0.775591
$429$	6.24281e7			8.89862e−5
$430$	−1.21825e10	+	3.73596e11i	−0.0171841	+	0.526979i
$431$	−2.93693e11			−0.409964			−0.204982	−	0.978766i	$-0.565714\pi$
$431$	−2.93693e11			−0.409964			−0.204982	+	0.978766i	$0.565714\pi$
$432$	−1.54588e9			−0.00213549
$433$	−3.92237e11	+	6.79374e11i	−0.536232	+	0.928781i	0.462871	+	0.886426i	$0.346819\pi$
$433$	−3.92237e11	+	6.79374e11i	−0.536232	+	0.928781i	−0.999103	+	0.0423551i	$0.986514\pi$
$434$	−5.31771e11			−0.719484
$435$	3.49803e8	−	6.05877e8i	0.000468405	−	0.000811302i
$436$	−4.15154e11	+	7.19067e11i	−0.550199	+	0.952972i
$437$	1.37738e11	+	2.38569e11i	0.180671	+	0.312931i
$438$	5.87535e8			0.000762782
$439$	−6.97447e11	−	1.20801e12i	−0.896232	−	1.55232i	−0.832272	−	0.554368i	$-0.812960\pi$
$439$	−6.97447e11	−	1.20801e12i	−0.896232	−	1.55232i	−0.0639604	−	0.997952i	$-0.520373\pi$
$440$	1.95583e11	−	3.38759e11i	0.248767	−	0.430878i
$441$	−1.93648e12			−2.43803
$442$	2.65708e10	−	4.60220e10i	0.0331134	−	0.0573541i
$443$	−3.43597e11	−	5.95128e11i	−0.423870	−	0.734165i	0.572444	−	0.819944i	$-0.305995\pi$
$443$	−3.43597e11	−	5.95128e11i	−0.423870	−	0.734165i	−0.996314	+	0.0857791i	$0.972662\pi$
$444$	7.15080e8	+	1.23855e9i	0.000873235	+	0.00151249i
$445$	−4.46105e9	−	7.72677e9i	−0.00539283	−	0.00934066i
$446$	4.75428e11			0.568955
$447$	−2.66619e7	−	4.61797e7i	−3.15869e−5	−	5.47101e-5i
$448$	3.39092e11	+	5.87325e11i	0.397710	+	0.688855i
$449$	2.45776e11	−	4.25696e11i	0.285385	−	0.494301i	−0.687318	−	0.726357i	$-0.741212\pi$
$449$	2.45776e11	−	4.25696e11i	0.285385	−	0.494301i	0.972702	+	0.232056i	$0.0745453\pi$
$450$	−2.34688e11	+	4.06492e11i	−0.269796	+	0.467300i
$451$	−7.51718e11			−0.855580
$452$	9.34612e10			0.105319
$453$	7.08791e8	−	1.22766e9i	0.000790818	−	0.00136974i
$454$	−2.81922e11	+	4.88303e11i	−0.311442	+	0.539433i
$455$	1.62168e11	+	2.80883e11i	0.177384	+	0.307237i
$456$	−4.50732e8	−	7.80691e8i	−0.000488177	−	0.000845547i
$457$	7.02364e11			0.753250			0.376625	−	0.926366i	$-0.377085\pi$
$457$	7.02364e11			0.753250			0.376625	+	0.926366i	$0.377085\pi$
$458$	−4.22256e10	−	7.31370e10i	−0.0448417	−	0.0776680i
$459$	2.54984e9	+	4.41646e9i	0.00268137	+	0.00464426i
$460$	2.43199e11	+	4.21232e11i	0.253251	+	0.438643i
$461$	4.59875e11	−	7.96527e11i	0.474226	−	0.821384i	−0.525338	−	0.850894i	$-0.676061\pi$
$461$	4.59875e11	−	7.96527e11i	0.474226	−	0.821384i	0.999565	+	0.0295093i	$0.00939445\pi$
$462$	−4.45249e8			−0.000454688
$463$	1.61615e11	−	2.79925e11i	0.163443	−	0.283092i	−0.772658	−	0.634822i	$-0.781073\pi$
$463$	1.61615e11	−	2.79925e11i	0.163443	−	0.283092i	0.936101	+	0.351730i	$0.114407\pi$
$464$	−1.30831e11	−	2.26606e11i	−0.131033	−	0.226955i
$465$	−3.03051e9			−0.00300592
$466$	1.95253e11	+	3.38188e11i	0.191806	+	0.332217i
$467$	6.48053e11	−	1.12246e12i	0.630499	−	1.09206i	−0.356950	−	0.934123i	$-0.616184\pi$
$467$	6.48053e11	−	1.12246e12i	0.630499	−	1.09206i	0.987450	−	0.157934i	$-0.0504832\pi$
$468$	−5.44070e10	+	9.42356e10i	−0.0524262	+	0.0908048i
$469$	6.70708e11			0.640111
$470$	−2.59947e11	+	4.50242e11i	−0.245722	+	0.425604i
$471$	1.13564e9			0.00106328
$472$	−9.95266e10			−0.0922997
$473$	4.77787e11	−	2.55461e11i	0.438894	−	0.234666i
$474$	8.10424e7			7.37412e−5
$475$	1.94022e12			1.74876
$476$	1.63278e12	−	2.82807e12i	1.45780	−	2.52498i
$477$	1.20711e12			1.06761
$478$	−2.93497e10	+	5.08352e10i	−0.0257145	+	0.0445389i
$479$	−6.48082e10	+	1.12251e11i	−0.0562497	+	0.0974273i	−0.892779	−	0.450495i	$-0.851248\pi$
$479$	−6.48082e10	+	1.12251e11i	−0.0562497	+	0.0974273i	0.836529	+	0.547922i	$0.184581\pi$
$480$	−1.21559e9	−	2.10546e9i	−0.00104520	−	0.00181034i
$481$	1.75257e11			0.149287
$482$	9.57830e10	+	1.65901e11i	0.0808308	+	0.140003i
$483$	5.85776e8	−	1.01459e9i	0.000489745	−	0.000848262i
$484$	8.13783e11			0.674069
$485$	−1.19591e12	+	2.07138e12i	−0.981435	+	1.69989i
$486$	9.08976e8	+	1.57439e9i	0.000739076	+	0.00128012i
$487$	5.04508e11	+	8.73833e11i	0.406432	+	0.703961i	0.994487	−	0.104860i	$-0.0334395\pi$
$487$	5.04508e11	+	8.73833e11i	0.406432	+	0.703961i	−0.588055	+	0.808821i	$0.700106\pi$
$488$	3.02924e11	+	5.24679e11i	0.241793	+	0.418798i
$489$	1.18900e9			0.000940358
$490$	−8.20193e11	−	1.42062e12i	−0.642738	−	1.11325i
$491$	8.28350e11	+	1.43474e12i	0.643202	+	1.11406i	0.984714	+	0.174181i	$0.0557277\pi$
$491$	8.28350e11	+	1.43474e12i	0.643202	+	1.11406i	−0.341512	+	0.939877i	$0.610939\pi$
$492$	−1.52940e9	+	2.64899e9i	−0.00117673	+	0.00203816i
$493$	−4.31598e11	+	7.47550e11i	−0.329055	+	0.569940i
$494$	−5.22049e10			−0.0394403
$495$	1.08693e12			0.813727
$496$	−5.66725e11	+	9.81597e11i	−0.420441	+	0.728225i
$497$	−5.95782e11	+	1.03192e12i	−0.438010	+	0.758655i
$498$	−4.01428e8	−	6.95294e8i	−0.000292466	−	0.000506566i
$499$	1.61086e11	+	2.79009e11i	0.116307	+	0.201449i	0.918301	−	0.395882i	$-0.129561\pi$
$499$	1.61086e11	+	2.79009e11i	0.116307	+	0.201449i	−0.801995	+	0.597331i	$0.796228\pi$
$500$	1.37840e12			0.986304
$501$	1.14562e9	+	1.98427e9i	0.000812403	+	0.00140712i
$502$	3.47822e8	+	6.02445e8i	0.000244450	+	0.000423400i
$503$	−5.24354e11	−	9.08208e11i	−0.365232	−	0.632600i	0.623581	−	0.781758i	$-0.285677\pi$
$503$	−5.24354e11	−	9.08208e11i	−0.365232	−	0.632600i	−0.988813	+	0.149158i	$0.952344\pi$
$504$	8.21117e11	−	1.42222e12i	0.566850	−	0.981812i
$505$	−2.05799e12			−1.40809
$506$	−4.09129e10	+	7.08633e10i	−0.0277449	+	0.0480556i
$507$	1.12102e9	+	1.94166e9i	0.000753488	+	0.00130508i
$508$	−1.96097e12			−1.30642
$509$	−1.09267e12	−	1.89257e12i	−0.721541	−	1.24974i	−0.960382	−	0.278686i	$-0.910101\pi$
$509$	−1.09267e12	−	1.89257e12i	−0.721541	−	1.24974i	0.238842	−	0.971059i	$-0.423232\pi$
$510$	−1.07998e9	+	1.87059e9i	−0.000706889	+	0.00122437i
$511$	2.21218e12	−	3.83161e12i	1.43525	−	2.48592i
$512$	−1.57369e12			−1.01206
$513$	2.50490e9	−	4.33862e9i	0.00159684	−	0.00276582i
$514$	5.20885e11			0.329160
$515$	−8.16122e11			−0.511237
$516$	7.18509e7	−	2.20343e9i	4.46178e−5	−	0.00136828i
$517$	7.53559e11			0.463884
$518$	−1.24997e12			−0.762806
$519$	8.90566e8	−	1.54251e9i	0.000538782	−	0.000933198i
$520$	−1.95051e11			−0.116986
$521$	1.38985e12	−	2.40728e12i	0.826413	−	1.43139i	−0.0744221	−	0.997227i	$-0.523711\pi$
$521$	1.38985e12	−	2.40728e12i	0.826413	−	1.43139i	0.900835	−	0.434162i	$-0.142955\pi$
$522$	−1.02572e11	+	1.77659e11i	−0.0604658	+	0.104730i
$523$	7.72909e11	+	1.33872e12i	0.451721	+	0.782404i	0.998493	−	0.0548774i	$-0.0174768\pi$
$523$	7.72909e11	+	1.33872e12i	0.451721	+	0.782404i	−0.546772	+	0.837282i	$0.684143\pi$
$524$	−1.13932e12			−0.660170
$525$	−4.12571e9	−	7.14594e9i	−0.00237018	−	0.00410528i
$526$	2.85835e11	−	4.95080e11i	0.162809	−	0.281994i
$527$	3.73914e12			2.11166
$528$	−4.74515e8	+	8.21885e8i	−0.000265704	+	0.000460212i
$529$	7.92925e11	+	1.37339e12i	0.440232	+	0.762504i
$530$	5.11271e11	+	8.85547e11i	0.281455	+	0.487495i
$531$	−1.38277e11	−	2.39503e11i	−0.0754789	−	0.130733i
$532$	−3.20801e12			−1.73634
$533$	1.87418e11	+	3.24618e11i	0.100586	+	0.174221i
$534$	−3.05374e6	−	5.28923e6i	−1.62516e−6	−	2.81486e-6i
$535$	−1.34092e12	+	2.32255e12i	−0.707639	+	1.22567i
$536$	−2.01677e11	+	3.49315e11i	−0.105539	+	0.182800i
$537$	2.89052e9			0.00150000
$538$	3.02072e10			0.0155450
$539$	−1.18883e12	+	2.05911e12i	−0.606693	+	1.05082i
$540$	4.42280e9	−	7.66052e9i	0.00223834	−	0.00387691i
$541$	1.14616e12	+	1.98521e12i	0.575251	+	0.996365i	0.996014	+	0.0891939i	$0.0284291\pi$
$541$	1.14616e12	+	1.98521e12i	0.575251	+	0.996365i	−0.420763	+	0.907171i	$0.638238\pi$
$542$	−2.48011e11	−	4.29568e11i	−0.123445	−	0.213813i
$543$	−6.36992e8			−0.000314438
$544$	1.49983e12	+	2.59778e12i	0.734254	+	1.27177i
$545$	−2.06782e12	−	3.58157e12i	−1.00399	−	1.73896i
$546$	1.11009e8	+	1.92274e8i	5.34555e−5	+	9.25876e-5i
$547$	6.18202e11	−	1.07076e12i	0.295248	−	0.511385i	−0.679794	−	0.733403i	$-0.737931\pi$
$547$	6.18202e11	−	1.07076e12i	0.295248	−	0.511385i	0.975043	+	0.222018i	$0.0712642\pi$
$548$	1.81864e12			0.861458
$549$	−8.41734e11	+	1.45793e12i	−0.395457	+	0.684951i
$550$	2.88156e11	+	4.99101e11i	0.134275	+	0.232571i
$551$	8.47983e11			0.391927
$552$	3.52277e8	+	6.10162e8i	0.000161495	+	0.000279717i
$553$	3.05140e11	−	5.28518e11i	0.138751	−	0.240324i
$554$	−2.76065e11	+	4.78158e11i	−0.124514	+	0.215664i
$555$	−7.12342e9			−0.00318691
$556$	−4.01466e11	+	6.95359e11i	−0.178161	+	0.308583i
$557$	1.28862e12			0.567252			0.283626	−	0.958935i	$-0.408463\pi$
$557$	1.28862e12			0.567252			0.283626	+	0.958935i	$0.408463\pi$
$558$	8.88626e11			0.388030
$559$	−2.29439e11	−	1.42634e11i	−0.0993834	−	0.0617829i
$560$	−4.93054e12			−2.11860
$561$	3.13076e9			0.00133449
$562$	−5.92815e11	+	1.02679e12i	−0.250672	+	0.434177i
$563$	−3.34868e12			−1.40471			−0.702354	−	0.711828i	$-0.747868\pi$
$563$	−3.34868e12			−1.40471			−0.702354	+	0.711828i	$0.747868\pi$
$564$	1.53314e9	−	2.65548e9i	0.000638008	−	0.00110506i
$565$	−2.32759e11	+	4.03150e11i	−0.0960921	+	0.166436i
$566$	−3.33988e10	−	5.78484e10i	−0.0136791	−	0.0236929i
$567$	4.56326e12			1.85418
$568$	−3.58295e11	−	6.20584e11i	−0.144435	−	0.250169i
$569$	7.85296e10	−	1.36017e11i	0.0314071	−	0.0543987i	−0.849895	−	0.526953i	$-0.823334\pi$
$569$	7.85296e10	−	1.36017e11i	0.0314071	−	0.0543987i	0.881302	+	0.472554i	$0.156668\pi$
$570$	2.12190e9			0.000841952
$571$	7.94410e11	−	1.37596e12i	0.312739	−	0.541680i	−0.666215	−	0.745759i	$-0.732087\pi$
$571$	7.94410e11	−	1.37596e12i	0.312739	−	0.541680i	0.978954	+	0.204080i	$0.0654201\pi$
$572$	6.68022e10	+	1.15705e11i	0.0260921	+	0.0451928i
$573$	1.63882e9	+	2.83852e9i	0.000635091	+	0.00110001i
$574$	−1.33670e12	−	2.31523e12i	−0.513961	−	0.890207i
$575$	−1.51641e12			−0.578511
$576$	−5.66646e11	−	9.81460e11i	−0.214492	−	0.371511i
$577$	−2.41895e12	−	4.18975e12i	−0.908524	−	1.57361i	−0.816116	−	0.577888i	$-0.803877\pi$
$577$	−2.41895e12	−	4.18975e12i	−0.908524	−	1.57361i	−0.0924077	−	0.995721i	$-0.529456\pi$
$578$	8.99855e11	−	1.55860e12i	0.335349	−	0.580842i
$579$	2.99229e9	−	5.18280e9i	0.00110650	−	0.00191651i
$580$	1.49725e12			0.549374
$581$	−6.04580e12			−2.20121
$582$	−8.18642e8	+	1.41793e9i	−0.000295761	+	0.000512272i
$583$	7.41059e11	−	1.28355e12i	0.265671	−	0.460156i
$584$	1.33037e12	+	2.30427e12i	0.473277	+	0.819740i
$585$	−2.70993e11	−	4.69374e11i	−0.0956659	−	0.165698i
$586$	−1.63395e12			−0.572398
$587$	−1.62361e12	−	2.81218e12i	−0.564430	−	0.977622i	−0.997102	−	0.0760707i	$-0.975763\pi$
$587$	−1.62361e12	−	2.81218e12i	−0.564430	−	0.977622i	0.432672	−	0.901551i	$-0.357571\pi$
$588$	4.83741e9	+	8.37865e9i	0.00166884	+	0.00289052i
$589$	−1.83662e12	−	3.18111e12i	−0.628781	−	1.08908i
$590$	1.17135e11	−	2.02883e11i	0.0397970	−	0.0689305i
$591$	−2.40707e9			−0.000811607
$592$	−1.33213e12	+	2.30731e12i	−0.445757	+	0.772074i
$593$	−7.12641e11	−	1.23433e12i	−0.236660	−	0.409907i	0.723094	−	0.690750i	$-0.242719\pi$
$593$	−7.12641e11	−	1.23433e12i	−0.236660	−	0.409907i	−0.959754	+	0.280843i	$0.909386\pi$
$594$	1.48808e9			0.000490443
$595$	8.13267e12	+	1.40862e13i	2.66016	+	4.60752i
$596$	5.70599e10	−	9.88306e10i	0.0185235	−	0.0320836i
$597$	−3.13102e8	+	5.42309e8i	−0.000100879	+	0.000174728i
$598$	4.08016e10			0.0130473
$599$	−1.51863e12	+	2.63034e12i	−0.481982	+	0.834818i	−0.999786	−	0.0206814i	$-0.993416\pi$
$599$	−1.51863e12	+	2.63034e12i	−0.481982	+	0.834818i	0.517804	+	0.855499i	$0.326750\pi$
$600$	4.96228e9			0.00156315
$601$	−3.56596e12			−1.11491			−0.557457	−	0.830206i	$-0.688223\pi$
$601$	−3.56596e12			−1.11491			−0.557457	+	0.830206i	$0.688223\pi$
$602$	1.63640e12	+	1.01729e12i	0.507814	+	0.315689i
$603$	−1.12080e12			−0.345223
$604$	3.03381e12			0.927518
$605$	−2.02667e12	+	3.51029e12i	−0.615012	+	1.06523i
$606$	−1.40876e9			−0.000424337
$607$	1.65269e12	−	2.86254e12i	0.494130	−	0.855859i	−0.505847	−	0.862623i	$-0.668820\pi$
$607$	1.65269e12	−	2.86254e12i	0.494130	−	0.855859i	0.999977	+	0.00676469i	$0.00215328\pi$
$608$	1.47339e12	−	2.55199e12i	0.437273	−	0.757379i
$609$	−1.80316e9	−	3.12317e9i	−0.000531198	−	0.000920063i
$610$	−1.42606e12			−0.417018
$611$	−1.87877e11	−	3.25413e11i	−0.0545366	−	0.0944602i
$612$	−2.72849e12	+	4.72589e12i	−0.786216	+	1.36177i
$613$	6.46079e11			0.184805			0.0924024	−	0.995722i	$-0.470545\pi$
$613$	6.46079e11			0.184805			0.0924024	+	0.995722i	$0.470545\pi$
$614$	3.21244e11	−	5.56411e11i	0.0912173	−	0.157993i
$615$	−7.61771e9	−	1.31943e10i	−0.00214727	−	0.00371918i
$616$	−1.00819e12	−	1.74623e12i	−0.282116	−	0.488640i
$617$	1.38286e12	+	2.39519e12i	0.384145	+	0.665359i	0.991650	−	0.128957i	$-0.0411629\pi$
$617$	1.38286e12	+	2.39519e12i	0.384145	+	0.665359i	−0.607505	+	0.794316i	$0.707830\pi$
$618$	−5.58663e8			−0.000154064
$619$	1.62497e12	+	2.81452e12i	0.444873	+	0.770543i	0.998043	−	0.0625254i	$-0.0199154\pi$
$619$	1.62497e12	+	2.81452e12i	0.444873	+	0.770543i	−0.553170	+	0.833068i	$0.686582\pi$
$620$	−3.24284e12	−	5.61676e12i	−0.881379	−	1.52659i
$621$	−1.95775e9	+	3.39092e9i	−0.000528256	+	0.000914966i
$622$	1.58238e10	−	2.74077e10i	0.00423892	−	0.00734202i
$623$	−4.59915e10			−0.0122316
$624$	4.73224e8			0.000124950
$625$	−2.41331e11	+	4.17998e11i	−0.0632635	+	0.109576i
$626$	6.44544e11	−	1.11638e12i	0.167752	−	0.290555i
$627$	−1.53779e9	−	2.66353e9i	−0.000397368	−	0.000688261i
$628$	1.21521e12	+	2.10480e12i	0.311769	+	0.539999i
$629$	8.78911e12			2.23881
$630$	1.93277e12	+	3.34766e12i	0.488819	+	0.846660i
$631$	−3.32270e12	−	5.75508e12i	−0.834370	−	1.44517i	−0.894542	−	0.446984i	$-0.852498\pi$
$631$	−3.32270e12	−	5.75508e12i	−0.834370	−	1.44517i	0.0601720	−	0.998188i	$-0.480835\pi$
$632$	1.83507e11	+	3.17843e11i	0.0457535	+	0.0792474i
$633$	−2.63868e9	+	4.57033e9i	−0.000653236	+	0.00113144i
$634$	8.69178e11			0.213652
$635$	4.88366e12	−	8.45874e12i	1.19196	−	2.06454i
$636$	−3.01542e9	−	5.22286e9i	−0.000730787	−	0.00126576i
$637$	1.18559e12			0.285304
$638$	1.25940e11	+	2.18134e11i	0.0300933	+	0.0521232i
$639$	9.95592e11	−	1.72442e12i	0.236226	−	0.409155i
$640$	3.38346e12	−	5.86032e12i	0.797170	−	1.38074i
$641$	−5.99684e12			−1.40301			−0.701506	−	0.712663i	$-0.747489\pi$
$641$	−5.99684e12			−1.40301			−0.701506	+	0.712663i	$0.747489\pi$
$642$	−9.17907e8	+	1.58986e9i	−0.000213251	+	0.000369361i
$643$	5.40547e12			1.24705			0.623525	−	0.781803i	$-0.285700\pi$
$643$	5.40547e12			1.24705			0.623525	+	0.781803i	$0.285700\pi$
$644$	2.50727e12			0.574401
$645$	9.32566e9	+	5.79741e9i	0.00212159	+	0.00131891i
$646$	−2.61806e12			−0.591472
$647$	1.19793e12			0.268757			0.134379	−	0.990930i	$-0.457096\pi$
$647$	1.19793e12			0.268757			0.134379	+	0.990930i	$0.457096\pi$
$648$	−1.37214e12	+	2.37662e12i	−0.305711	+	0.529507i
$649$	−3.39560e11			−0.0751304
$650$	1.43686e11	−	2.48872e11i	0.0315722	−	0.0546846i
$651$	−7.81081e9	+	1.35287e10i	−0.00170444	+	0.00295218i
$652$	1.27231e12	+	2.20371e12i	0.275727	+	0.477573i
$653$	−3.61822e12			−0.778728			−0.389364	−	0.921084i	$-0.627305\pi$
$653$	−3.61822e12			−0.778728			−0.389364	+	0.921084i	$0.627305\pi$
$654$	−1.41549e9	−	2.45171e9i	−0.000302558	−	0.000524045i
$655$	2.83740e12	−	4.91452e12i	0.602330	−	1.04327i
$656$	−5.69825e12			−1.20136
$657$	−3.69670e12	+	6.40288e12i	−0.774052	+	1.34070i
$658$	1.33997e12	+	2.32090e12i	0.278663	+	0.482659i
$659$	1.97595e12	+	3.42244e12i	0.408123	+	0.706890i	0.994679	−	0.103019i	$-0.0328501\pi$
$659$	1.97595e12	+	3.42244e12i	0.408123	+	0.706890i	−0.586557	+	0.809908i	$0.699517\pi$
$660$	−2.71521e9	−	4.70288e9i	−0.000557000	−	0.000964753i
$661$	−2.65917e12			−0.541801			−0.270901	−	0.962607i	$-0.587321\pi$
$661$	−2.65917e12			−0.541801			−0.270901	+	0.962607i	$0.587321\pi$
$662$	−8.72330e11	−	1.51092e12i	−0.176531	−	0.305760i
$663$	−7.80559e8	−	1.35197e9i	−0.000156890	−	0.000271741i
$664$	1.81793e12	−	3.14874e12i	0.362928	−	0.628610i
$665$	7.98933e12	−	1.38379e13i	1.58421	−	2.74393i
$666$	2.08878e12			0.411394
$667$	−6.62754e11			−0.129654
$668$	−2.45178e12	+	4.24661e12i	−0.476417	+	0.825178i
$669$	6.98323e9	−	1.20953e10i	0.00134784	−	0.00233453i
$670$	−4.74713e11	−	8.22228e11i	−0.0910112	−	0.157636i
$671$	1.03350e12	+	1.79008e12i	0.196816	+	0.340895i
$672$	−1.25322e10			−0.00237063
$673$	1.99803e12	+	3.46068e12i	0.375434	+	0.650270i	0.990392	−	0.138289i	$-0.0441604\pi$
$673$	1.99803e12	+	3.46068e12i	0.375434	+	0.650270i	−0.614958	+	0.788560i	$0.710827\pi$
$674$	1.51084e12	+	2.61684e12i	0.281999	+	0.488437i
$675$	1.37887e10	+	2.38827e10i	0.00255656	+	0.00442810i
$676$	−2.39912e12	+	4.15540e12i	−0.441868	+	0.765338i
$677$	−1.31547e12			−0.240675			−0.120338	−	0.992733i	$-0.538398\pi$
$677$	−1.31547e12			−0.240675			−0.120338	+	0.992733i	$0.538398\pi$
$678$	−1.59331e8	+	2.75969e8i	−2.89579e−5	+	5.01565e-5i
$679$	6.16467e12	+	1.06775e13i	1.11300	+	1.92778i
$680$	−9.78174e12			−1.75439
$681$	8.28190e9	+	1.43447e10i	0.00147560	+	0.00255581i
$682$	5.45538e11	−	9.44900e11i	0.0965596	−	0.167246i
$683$	2.27981e12	−	3.94874e12i	0.400871	−	0.694329i	−0.592960	−	0.805232i	$-0.702041\pi$
$683$	2.27981e12	−	3.94874e12i	0.400871	−	0.694329i	0.993831	+	0.110903i	$0.0353742\pi$
$684$	5.36081e12			0.936436
$685$	−4.52919e12	+	7.84479e12i	−0.785983	+	1.36136i
$686$	−4.98754e12			−0.859860
$687$	−2.48089e9			−0.000424915
$688$	3.62177e12	−	1.93647e12i	0.616273	−	0.329506i
$689$	−7.39043e11			−0.124935
$690$	−1.65840e9			−0.000278528
$691$	3.82961e12	−	6.63308e12i	0.639003	−	1.10679i	−0.346648	−	0.937995i	$-0.612680\pi$
$691$	3.82961e12	−	6.63308e12i	0.639003	−	1.10679i	0.985652	−	0.168791i	$-0.0539864\pi$
$692$	3.81186e12			0.631916
$693$	2.80145e12	−	4.85225e12i	0.461406	−	0.799179i
$694$	−1.27926e12	+	2.21573e12i	−0.209334	+	0.362577i
$695$	−1.99965e12	−	3.46349e12i	−0.325103	−	0.563095i
$696$	2.16879e9			0.000350329
$697$	9.39897e12	+	1.62795e13i	1.50846	+	2.61272i
$698$	8.66425e11	−	1.50069e12i	0.138160	−	0.239300i
$699$	1.14717e10			0.00181753
$700$	8.82956e12	−	1.52932e13i	1.38995	−	2.40746i
$701$	−3.40474e12	−	5.89718e12i	−0.532541	−	0.922388i	−0.999278	−	0.0379919i	$-0.987904\pi$
$701$	−3.40474e12	−	5.89718e12i	−0.532541	−	0.922388i	0.466737	−	0.884396i	$-0.345429\pi$
$702$	−3.71009e8	−	6.42606e8i	−5.76590e−5	−	9.98683e-5i
$703$	−4.31710e12	−	7.47743e12i	−0.666643	−	1.15466i
$704$	−1.39148e12			−0.213502
$705$	7.63636e9	+	1.32266e10i	0.00116422	+	0.00201649i
$706$	−5.89549e11	−	1.02113e12i	−0.0893098	−	0.154689i
$707$	−5.30425e12	+	9.18723e12i	−0.798429	+	1.38292i
$708$	−6.90847e8	+	1.19658e9i	−0.000103331	+	0.000178975i
$709$	−5.35362e12			−0.795682			−0.397841	−	0.917454i	$-0.630240\pi$
$709$	−5.35362e12			−0.795682			−0.397841	+	0.917454i	$0.630240\pi$
$710$	1.68673e12			0.249105
$711$	−5.09909e11	+	8.83189e11i	−0.0748307	+	0.129611i
$712$	1.38293e10	−	2.39531e10i	0.00201670	−	0.00349302i
$713$	1.43544e12	+	2.48625e12i	0.208009	+	0.360282i
$714$	5.56709e9	+	9.64248e9i	0.000801652	+	0.00138850i
$715$	−6.65465e11			−0.0952243
$716$	3.09305e12	+	5.35732e12i	0.439823	+	0.761796i
$717$	8.62195e8	+	1.49337e9i	0.000121834	+	0.000211023i
$718$	−2.03273e12	−	3.52080e12i	−0.285444	−	0.494403i
$719$	2.33455e12	−	4.04355e12i	0.325778	−	0.564265i	−0.655891	−	0.754855i	$-0.727707\pi$
$719$	2.33455e12	−	4.04355e12i	0.325778	−	0.564265i	0.981670	+	0.190591i	$0.0610403\pi$
$720$	8.23927e12			1.14260
$721$	−2.10347e12	+	3.64331e12i	−0.289886	+	0.502097i
$722$	1.08648e11	+	1.88184e11i	0.0148801	+	0.0257731i
$723$	5.62756e9			0.000765945
$724$	−6.81623e11	−	1.18061e12i	−0.0921978	−	0.159691i
$725$	−2.33394e12	+	4.04250e12i	−0.313739	+	0.543412i
$726$	−1.38732e9	+	2.40291e9i	−0.000185337	+	0.000321013i
$727$	−6.37217e12			−0.846023			−0.423012	−	0.906124i	$-0.639027\pi$
$727$	−6.37217e12			−0.846023			−0.423012	+	0.906124i	$0.639027\pi$
$728$	−5.02722e11	+	8.70741e11i	−0.0663341	+	0.114894i
$729$	−7.62549e12			−0.999986
$730$	−6.26294e12			−0.816255
$731$	−1.15063e13	−	7.15304e12i	−1.49042	−	0.926536i
$732$	8.41077e9			0.00108277
$733$	−7.41486e12			−0.948713			−0.474356	−	0.880333i	$-0.657319\pi$
$733$	−7.41486e12			−0.948713			−0.474356	+	0.880333i	$0.657319\pi$
$734$	2.86927e11	−	4.96971e11i	0.0364870	−	0.0631974i
$735$	−4.81890e10			−0.00609052
$736$	−1.15155e12	+	1.99455e12i	−0.144655	+	0.250550i
$737$	−6.88072e11	+	1.19178e12i	−0.0859073	+	0.148796i
$738$	2.23372e12	+	3.86891e12i	0.277188	+	0.480104i
$739$	−1.35604e13			−1.67252			−0.836260	−	0.548333i	$-0.815263\pi$
$739$	−1.35604e13			−1.67252			−0.836260	+	0.548333i	$0.815263\pi$
$740$	−7.62253e12	−	1.32026e13i	−0.934450	−	1.61852i
$741$	−7.66802e8	+	1.32814e9i	−9.34332e−5	+	0.000161831i
$742$	5.27099e12			0.638373
$743$	−2.64483e12	+	4.58098e12i	−0.318382	+	0.551454i	−0.980151	−	0.198254i	$-0.936473\pi$
$743$	−2.64483e12	+	4.58098e12i	−0.318382	+	0.551454i	0.661769	+	0.749708i	$0.269806\pi$
$744$	−4.69731e9	−	8.13597e9i	−0.000562044	−	0.000973490i
$745$	2.84207e11	+	4.92261e11i	0.0338012	+	0.0585454i
$746$	−5.02789e10	−	8.70855e10i	−0.00594375	−	0.0102949i
$747$	1.01029e13			1.18715
$748$	3.35011e12	+	5.80256e12i	0.391293	+	0.677740i
$749$	6.91218e12	+	1.19722e13i	0.802503	+	1.38998i
$750$	−2.34987e9	+	4.07010e9i	−0.000271187	+	0.000469710i
$751$	3.23674e12	−	5.60620e12i	0.371303	−	0.643115i	−0.618464	−	0.785813i	$-0.712245\pi$
$751$	3.23674e12	−	5.60620e12i	0.371303	−	0.643115i	0.989766	+	0.142698i	$0.0455779\pi$
$752$	5.71220e12			0.651364
$753$	2.04356e7			2.31639e−6
$754$	6.27986e10	−	1.08770e11i	0.00707586	−	0.0122557i
$755$	−7.55549e12	+	1.30865e13i	−0.846256	+	1.46576i
$756$	−2.27986e10	−	3.94884e10i	−0.00253840	−	0.00439664i
$757$	−1.33506e12	−	2.31240e12i	−0.147765	−	0.255936i	0.782636	−	0.622479i	$-0.213874\pi$
$757$	−1.33506e12	−	2.31240e12i	−0.147765	−	0.255936i	−0.930401	+	0.366543i	$0.880541\pi$
$758$	−2.93255e12			−0.322652
$759$	1.20188e9	+	2.08172e9i	0.000131454	+	0.000227685i
$760$	4.80467e12	+	8.32193e12i	0.522399	+	0.904821i
$761$	6.81646e11	+	1.18065e12i	0.0736763	+	0.127611i	0.900510	−	0.434836i	$-0.143193\pi$
$761$	6.81646e11	+	1.18065e12i	0.0736763	+	0.127611i	−0.826834	+	0.562447i	$0.809860\pi$
$762$	3.34303e9	−	5.79029e9i	0.000359205	−	0.000622161i
$763$	−2.13184e13			−2.27716
$764$	−3.50729e12	+	6.07481e12i	−0.372436	+	0.645078i
$765$	−1.35903e13	−	2.35390e13i	−1.43467	−	2.48492i
$766$	1.57330e12			0.165113
$767$	8.46591e10	+	1.46634e11i	0.00883272	+	0.0152987i
$768$	−8.43513e8	+	1.46101e9i	−8.74916e−5	+	0.000151540i
$769$	−6.09592e12	+	1.05584e13i	−0.628595	+	1.08876i	0.359239	+	0.933245i	$0.383036\pi$
$769$	−6.09592e12	+	1.05584e13i	−0.628595	+	1.08876i	−0.987834	+	0.155512i	$0.950297\pi$
$770$	4.74621e12			0.486563
$771$	7.65091e9	−	1.32518e10i	0.000779773	−	0.00135061i
$772$	1.28078e13			1.29776
$773$	3.65849e12			0.368548			0.184274	−	0.982875i	$-0.441007\pi$
$773$	3.65849e12			0.368548			0.184274	+	0.982875i	$0.441007\pi$
$774$	−2.73453e12	−	1.69996e12i	−0.273873	−	0.170256i
$775$	2.02200e13			2.01337
$776$	−7.41469e12			−0.734032
$777$	−1.83599e10	+	3.18002e10i	−0.00180707	+	0.00312994i
$778$	2.54350e12			0.248899
$779$	9.23332e12	−	1.59926e13i	0.898337	−	1.55596i
$780$	−1.35391e9	+	2.34504e9i	−0.000130968	+	0.000226843i
$781$	−1.22241e12	−	2.11728e12i	−0.117568	−	0.203633i
$782$	2.04619e12			0.195666
$783$	6.02642e9	+	1.04381e10i	0.000572969	+	0.000992412i
$784$	−9.01166e12	+	1.56087e13i	−0.851888	+	1.47551i
$785$	−1.21056e13			−1.13782
$786$	1.94230e9	−	3.36415e9i	0.000181516	−	0.000314394i
$787$	8.15169e11	+	1.41191e12i	0.0757463	+	0.131196i	0.901411	−	0.432965i	$-0.142533\pi$
$787$	8.15169e11	+	1.41191e12i	0.0757463	+	0.131196i	−0.825664	+	0.564162i	$0.809199\pi$
$788$	−2.57573e12	−	4.46129e12i	−0.237975	−	0.412185i
$789$	−8.39685e9	−	1.45438e10i	−0.000771383	−	0.00133607i
$790$	−8.63887e11			−0.0789106
$791$	1.19982e12	+	2.07815e12i	0.108974	+	0.188748i
$792$	1.68475e12	+	2.91807e12i	0.152150	+	0.263532i
$793$	5.15344e11	−	8.92603e11i	0.0462773	−	0.0801547i
$794$	1.40356e12	−	2.43105e12i	0.125326	−	0.217071i
$795$	3.00388e10			0.00266704
$796$	−1.34016e12			−0.118317
$797$	4.32370e12	−	7.48887e12i	0.379571	−	0.657437i	−0.611429	−	0.791300i	$-0.709405\pi$
$797$	4.32370e12	−	7.48887e12i	0.379571	−	0.657437i	0.991000	+	0.133863i	$0.0427381\pi$
$798$	5.46897e9	−	9.47253e9i	0.000477411	−	0.000826900i
$799$	−9.42199e12	−	1.63194e13i	−0.817866	−	1.41659i
$800$	8.11057e12	+	1.40479e13i	0.700078	+	1.21257i
$801$	7.68550e10			0.00659669
$802$	5.58544e11	+	9.67427e11i	0.0476730	+	0.0825721i
$803$	4.53890e12	+	7.86161e12i	0.385239	+	0.667254i
$804$	2.79981e9	+	4.84941e9i	0.000236307	+	0.000409296i
$805$	−6.24419e12	+	1.08153e13i	−0.524077	+	0.907727i
$806$	−5.44054e11			−0.0454082
$807$	4.43693e8	−	7.68499e8i	3.68258e−5	−	6.37841e-5i
$808$	−3.18990e12	−	5.52506e12i	−0.263285	−	0.456022i
$809$	2.20551e13			1.81026			0.905129	−	0.425137i	$-0.139774\pi$
$809$	2.20551e13			1.81026			0.905129	+	0.425137i	$0.139774\pi$
$810$	−3.22979e12	−	5.59416e12i	−0.263628	−	0.456617i
$811$	7.35078e12	−	1.27319e13i	0.596677	−	1.03348i	−0.396631	−	0.917978i	$-0.629821\pi$
$811$	7.35078e12	−	1.27319e13i	0.596677	−	1.03348i	0.993308	−	0.115497i	$-0.0368461\pi$
$812$	3.85900e12	−	6.68398e12i	0.311510	−	0.539552i
$813$	−1.45714e10			−0.00116976
$814$	1.28233e12	−	2.22105e12i	0.102374	−	0.177317i
$815$	−1.26744e13			−1.00628
$816$	2.37321e10			0.00187383
$817$	−4.33780e11	+	1.33026e13i	−0.0340620	+	1.04457i
$818$	5.82228e11			0.0454677
$819$	−2.79383e12			−0.216981
$820$	1.63029e13	−	2.82374e13i	1.25922	−	2.18104i
$821$	2.09102e13			1.60625			0.803126	−	0.595809i	$-0.203168\pi$
$821$	2.09102e13			1.60625			0.803126	+	0.595809i	$0.203168\pi$
$822$	−3.10038e9	+	5.37002e9i	−0.000236860	+	0.000410254i
$823$	−2.80554e12	+	4.85933e12i	−0.213165	+	0.369213i	−0.952703	−	0.303902i	$-0.901711\pi$
$823$	−2.80554e12	+	4.85933e12i	−0.213165	+	0.369213i	0.739538	+	0.673115i	$0.235044\pi$
$824$	−1.26499e12	−	2.19104e12i	−0.0955908	−	0.165568i
$825$	1.69301e10			0.00127238
$826$	−6.03804e11	−	1.04582e12i	−0.0451321	−	0.0781711i
$827$	−1.24996e13	+	2.16500e13i	−0.929228	+	1.60947i	−0.144613	+	0.989488i	$0.546194\pi$
$827$	−1.24996e13	+	2.16500e13i	−0.929228	+	1.60947i	−0.784616	+	0.619982i	$0.787140\pi$
$828$	−4.18983e12			−0.309784
$829$	−5.10417e12	+	8.84069e12i	−0.375344	+	0.650116i	−0.990379	−	0.138385i	$-0.955809\pi$
$829$	−5.10417e12	+	8.84069e12i	−0.375344	+	0.650116i	0.615034	+	0.788500i	$0.289142\pi$
$830$	4.27910e12	+	7.41162e12i	0.312969	+	0.542078i
$831$	8.10984e9	+	1.40467e10i	0.000589940	+	0.00102181i
$832$	3.46925e11	+	6.00891e11i	0.0251004	+	0.0434751i
$833$	5.94571e13			4.27859
$834$	−1.36882e9	−	2.37087e9i	−9.79716e−5	−	0.000169692i
$835$	−1.22120e13	−	2.11517e13i	−0.869354	−	1.50576i
$836$	3.29107e12	−	5.70029e12i	0.233028	−	0.403617i
$837$	2.61048e10	−	4.52149e10i	0.00183847	−	0.00318432i
$838$	8.98683e11			0.0629519
$839$	1.24122e13			0.864811			0.432406	−	0.901679i	$-0.357665\pi$
$839$	1.24122e13			0.864811			0.432406	+	0.901679i	$0.357665\pi$
$840$	2.04334e10	−	3.53917e10i	0.00141607	−	0.00245270i
$841$	6.23351e12	−	1.07968e13i	0.429686	−	0.744238i
$842$	1.88656e12	+	3.26762e12i	0.129350	+	0.224041i
$843$	1.74149e10	+	3.01635e10i	0.00118767	+	0.00205711i
$844$	−1.12942e13			−0.766153
$845$	−1.19497e13	−	2.06975e13i	−0.806310	−	1.39657i
$846$	−2.23919e12	−	3.87838e12i	−0.150288	−	0.260306i
$847$	1.04471e13	+	1.80948e13i	0.697458	+	1.20803i
$848$	5.61745e12	−	9.72972e12i	0.373042	−	0.646128i
$849$	−1.96229e9			−0.000129622
$850$	7.20582e12	−	1.24808e13i	0.473476	−	0.820085i
$851$	3.37410e12	+	5.84411e12i	0.220534	+	0.381975i
$852$	−9.94816e9			−0.000646792
$853$	−3.20805e12	−	5.55650e12i	−0.207477	−	0.359361i	0.743442	−	0.668800i	$-0.233192\pi$
$853$	−3.20805e12	−	5.55650e12i	−0.207477	−	0.359361i	−0.950919	+	0.309439i	$0.899859\pi$
$854$	−3.67553e12	+	6.36620e12i	−0.236461	+	0.409562i
$855$	−1.33507e13	+	2.31241e13i	−0.854392	+	1.47985i
$856$	−8.31376e12			−0.529256
$857$	7.39879e12	−	1.28151e13i	0.468540	−	0.811536i	−0.530813	−	0.847489i	$-0.678113\pi$
$857$	7.39879e12	−	1.28151e13i	0.468540	−	0.811536i	0.999353	+	0.0359531i	$0.0114467\pi$
$858$	−4.55533e8			−2.86964e−5
$859$	2.36639e13			1.48292			0.741459	−	0.670998i	$-0.234134\pi$
$859$	2.36639e13			1.48292			0.741459	+	0.670998i	$0.234134\pi$
$860$	−7.65908e11	+	2.34879e13i	−0.0477456	+	1.46420i
$861$	−7.85354e10			−0.00487025
$862$	2.14305e12			0.132206
$863$	−1.00336e13	+	1.73788e13i	−0.615758	+	1.06652i	0.374493	+	0.927230i	$0.377817\pi$
$863$	−1.00336e13	+	1.73788e13i	−0.615758	+	1.06652i	−0.990251	+	0.139295i	$0.955516\pi$
$864$	4.18843e10			0.00255705
$865$	−9.49316e12	+	1.64426e13i	−0.576552	+	0.998617i
$866$	2.86212e12	−	4.95733e12i	0.172925	−	0.299514i
$867$	−2.64347e10	−	4.57862e10i	−0.00158887	−	0.00275200i
$868$	−3.34323e13			−1.99907
$869$	6.26079e11	+	1.08440e12i	0.0372426	+	0.0645061i
$870$	−2.55248e9	+	4.42103e9i	−0.000151052	+	0.000261630i
$871$	6.86199e11			0.0403988
$872$	6.41028e12	−	1.11029e13i	0.375451	−	0.650299i
$873$	−1.03016e13	−	1.78429e13i	−0.600261	−	1.03968i
$874$	−1.00506e12	−	1.74082e12i	−0.0582629	−	0.100914i
$875$	1.76954e13	+	3.06494e13i	1.02053	+	1.76761i
$876$	3.69382e10			0.00211937
$877$	3.04200e12	+	5.26891e12i	0.173645	+	0.300761i	0.939691	−	0.342023i	$-0.111112\pi$
$877$	3.04200e12	+	5.26891e12i	0.173645	+	0.300761i	−0.766047	+	0.642785i	$0.777779\pi$
$878$	5.08921e12	+	8.81477e12i	0.289018	+	0.500594i
$879$	−2.39999e10	+	4.15690e10i	−0.00135600	+	0.00234866i
$880$	5.05819e12	−	8.76104e12i	0.284330	−	0.492474i
$881$	1.79047e12			0.100133			0.0500663	−	0.998746i	$-0.484057\pi$
$881$	1.79047e12			0.100133			0.0500663	+	0.998746i	$0.484057\pi$
$882$	1.41303e13			0.786217
$883$	8.71327e12	−	1.50918e13i	0.482345	−	0.835446i	−0.517449	−	0.855714i	$-0.673118\pi$
$883$	8.71327e12	−	1.50918e13i	0.482345	−	0.835446i	0.999795	+	0.0202675i	$0.00645179\pi$
$884$	1.67050e12	−	2.89339e12i	0.0920049	−	0.159357i
$885$	−3.44101e9	−	5.96001e9i	−0.000188557	−	0.000326590i
$886$	2.50720e12	+	4.34260e12i	0.136690	+	0.236754i
$887$	−3.43304e13			−1.86218			−0.931092	−	0.364785i	$-0.881142\pi$
$887$	−3.43304e13			−1.86218			−0.931092	+	0.364785i	$0.881142\pi$
$888$	−1.10414e10	−	1.91242e10i	−0.000595887	−	0.00103211i
$889$	−2.51742e13	−	4.36030e13i	−1.35176	−	2.34131i
$890$	3.25519e10	+	5.63815e10i	0.00173909	+	0.00301219i
$891$	−4.68140e12	+	8.10843e12i	−0.248844	+	0.431010i
$892$	2.98900e13			1.58083
$893$	−9.25592e12	+	1.60317e13i	−0.487066	+	0.843624i
$894$	1.94549e8	+	3.36969e8i	1.01862e−5	+	1.76430e-5i
$895$	−3.08121e13			−1.60516
$896$	−1.74410e13	−	3.02087e13i	−0.904036	−	1.56584i
$897$	5.99306e8	−	1.03803e9i	3.09088e−5	−	5.35357e-5i
$898$	−1.79341e12	+	3.10627e12i	−0.0920312	+	0.159403i
$899$	8.83725e12			0.451231
$900$	−1.47548e13	+	2.55561e13i	−0.749621	+	1.29838i
$901$	−3.70628e13			−1.87360
$902$	5.48522e12			0.275908
$903$	4.99166e10	−	2.66892e10i	0.00249833	−	0.00133580i
$904$	−1.44311e12			−0.0718690
$905$	6.79014e12			0.336481
$906$	−5.17199e9	+	8.95815e9i	−0.000255024	+	0.000441714i
$907$	3.35099e13			1.64415			0.822074	−	0.569380i	$-0.192817\pi$
$907$	3.35099e13			1.64415			0.822074	+	0.569380i	$0.192817\pi$
$908$	−1.77243e13	+	3.06995e13i	−0.865334	+	1.49880i
$909$	8.86376e12	−	1.53525e13i	0.430606	−	0.745832i
$910$	−1.18332e12	−	2.04958e12i	−0.0572028	−	0.0990782i
$911$	1.35752e13			0.653002			0.326501	−	0.945197i	$-0.394130\pi$
$911$	1.35752e13			0.653002			0.326501	+	0.945197i	$0.394130\pi$
$912$	−1.16569e10	−	2.01903e10i	−0.000557964	−	0.000966422i
$913$	6.20232e12	−	1.07427e13i	0.295417	−	0.511678i
$914$	−5.12509e12			−0.242909
$915$	−2.09464e10	+	3.62803e10i	−0.000987905	+	0.00171110i
$916$	−2.65472e12	−	4.59810e12i	−0.124591	−	0.215799i
$917$	−1.46262e13	−	2.53333e13i	−0.683077	−	1.18312i
$918$	−1.86060e10	−	3.22265e10i	−0.000864690	−	0.00149769i
$919$	1.08916e13			0.503700			0.251850	−	0.967766i	$-0.418961\pi$
$919$	1.08916e13			0.503700			0.251850	+	0.967766i	$0.418961\pi$
$920$	−3.75516e12	−	6.50414e12i	−0.172816	−	0.299326i
$921$	−9.43705e9	−	1.63455e10i	−0.000432183	−	0.000748564i
$922$	−3.35567e12	+	5.81219e12i	−0.152929	+	0.264881i
$923$	−6.09543e11	+	1.05576e12i	−0.0276437	+	0.0478804i
$924$	−2.79927e10			−0.00126334
$925$	4.75286e13			2.13460
$926$	−1.17929e12	+	2.04259e12i	−0.0527074	+	0.0912919i
$927$	3.51504e12	−	6.08823e12i	0.156340	−	0.270790i
$928$	3.54476e12	+	6.13971e12i	0.156899	+	0.271758i
$929$	1.47196e13	+	2.54951e13i	0.648373	+	1.12302i	0.983511	+	0.180847i	$0.0578837\pi$
$929$	1.47196e13	+	2.54951e13i	0.648373	+	1.12302i	−0.335138	+	0.942169i	$0.608783\pi$
$930$	2.21133e10			0.000969351
$931$	−2.92046e13	−	5.05838e13i	−1.27402	−	2.20667i
$932$	1.22755e13	+	2.12618e13i	0.532927	+	0.923057i
$933$	−4.64851e8	−	8.05145e8i	−2.00838e−5	−	3.47862e-5i
$934$	−4.72879e12	+	8.19050e12i	−0.203324	+	0.352168i
$935$	−3.33729e13			−1.42804
$936$	8.40083e11	−	1.45507e12i	0.0357751	−	0.0619643i
$937$	2.44266e12	+	4.23082e12i	0.103523	+	0.179307i	0.913134	−	0.407660i	$-0.133655\pi$
$937$	2.44266e12	+	4.23082e12i	0.103523	+	0.179307i	−0.809611	+	0.586967i	$0.800322\pi$
$938$	−4.89410e12			−0.206424
$939$	−1.89345e10	−	3.27955e10i	−0.000794802	−	0.00137664i
$940$	−1.63428e13	+	2.83066e13i	−0.682734	+	1.18253i
$941$	−2.06511e12	+	3.57687e12i	−0.0858598	+	0.148714i	−0.905757	−	0.423797i	$-0.860697\pi$
$941$	−2.06511e12	+	3.57687e12i	−0.0858598	+	0.148714i	0.819897	+	0.572510i	$0.194030\pi$
$942$	−8.28667e9			−0.000342887
$943$	−7.21645e12	+	1.24993e13i	−0.297181	+	0.514732i
$944$	−2.57397e12			−0.105494
$945$	2.27113e11			0.00926402
$946$	−3.48637e12	+	1.86408e12i	−0.141535	+	0.0756753i
$947$	−2.68672e11			−0.0108554			−0.00542772	−	0.999985i	$-0.501728\pi$
$947$	−2.68672e11			−0.0108554			−0.00542772	+	0.999985i	$0.501728\pi$
$948$	5.09512e9			0.000204888
$949$	2.26328e12	−	3.92011e12i	0.0905815	−	0.156892i
$950$	−1.41576e13			−0.563942
$951$	1.27667e10	−	2.21127e10i	0.000506137	−	0.000876655i
$952$	−2.52114e13	+	4.36674e13i	−0.994788	+	1.72302i
$953$	1.27512e13	+	2.20858e13i	0.500765	+	0.867350i	1.00000		0.000883122i	$0.000281106\pi$
$953$	1.27512e13	+	2.20858e13i	0.500765	+	0.867350i	−0.499235	+	0.866467i	$0.666386\pi$
$954$	−8.80818e12			−0.344285
$955$	−1.74693e13	−	3.02578e13i	−0.679612	−	1.17712i
$956$	−1.84521e12	+	3.19600e12i	−0.0714472	+	0.123750i
$957$	7.39937e9			0.000285162
$958$	4.72900e11	−	8.19086e11i	0.0181395	−	0.0314185i
$959$	2.33470e13	+	4.04383e13i	0.891350	+	1.54386i
$960$	−1.41009e10	−	2.44235e10i	−0.000535830	−	0.000928085i
$961$	−5.92049e12	−	1.02546e13i	−0.223925	−	0.387849i
$962$	−1.27884e12			−0.0481424
$963$	−1.15507e13	−	2.00064e13i	−0.432803	−	0.749637i
$964$	6.02185e12	+	1.04302e13i	0.224586	+	0.388995i
$965$	−3.18969e13	+	5.52470e13i	−1.18406	+	2.05086i
$966$	−4.27436e9	+	7.40341e9i	−0.000157933	+	0.000273549i
$967$	4.21350e13			1.54961			0.774807	−	0.632198i	$-0.217847\pi$
$967$	4.21350e13			1.54961			0.774807	+	0.632198i	$0.217847\pi$
$968$	−1.25654e13			−0.459978
$969$	−3.84549e10	+	6.66059e10i	−0.00140118	+	0.00242692i
$970$	8.72646e12	−	1.51147e13i	0.316494	−	0.548184i
$971$	−1.04440e13	−	1.80895e13i	−0.377033	−	0.653040i	0.613596	−	0.789620i	$-0.289722\pi$
$971$	−1.04440e13	−	1.80895e13i	−0.377033	−	0.653040i	−0.990629	+	0.136580i	$0.956389\pi$
$972$	5.71471e10	+	9.89816e10i	0.00205351	+	0.00355678i
$973$	−2.06155e13			−0.737371
$974$	−3.68135e12	−	6.37629e12i	−0.131067	−	0.227014i
$975$	−4.22101e9	−	7.31100e9i	−0.000149587	−	0.000259093i
$976$	7.83425e12	+	1.35693e13i	0.276359	+	0.478667i
$977$	−7.23049e11	+	1.25236e12i	−0.0253888	+	0.0439747i	−0.878441	−	0.477851i	$-0.841416\pi$
$977$	−7.23049e11	+	1.25236e12i	−0.0253888	+	0.0439747i	0.853052	+	0.521826i	$0.174749\pi$
$978$	−8.67605e9			−0.000303248
$979$	4.71822e10	−	8.17220e10i	0.00164156	−	0.00284326i
$980$	−5.15653e13	−	8.93138e13i	−1.78583	−	3.09315i
$981$	3.56245e13			1.22811
$982$	−6.04440e12	−	1.04692e13i	−0.207420	−	0.359263i
$983$	1.86737e13	−	3.23438e13i	0.637880	−	1.10484i	−0.348017	−	0.937488i	$-0.613145\pi$
$983$	1.86737e13	−	3.23438e13i	0.637880	−	1.10484i	0.985897	−	0.167353i	$-0.0535219\pi$
$984$	2.36150e10	−	4.09024e10i	0.000802990	−	0.00139082i
$985$	2.56587e13			0.868503
$986$	3.14934e12	−	5.45481e12i	0.106114	−	0.183795i
$987$	7.87277e10			0.00264059
$988$	−3.28211e12			−0.109584
$989$	3.39028e11	−	1.03969e13i	0.0112681	−	0.345556i
$990$	−7.93124e12			−0.262411
$991$	3.18730e13			1.04976			0.524881	−	0.851176i	$-0.324110\pi$
$991$	3.18730e13			1.04976			0.524881	+	0.851176i	$0.324110\pi$
$992$	1.53550e13	−	2.65956e13i	0.503438	−	0.871981i
$993$	−5.12522e10			−0.00167279
$994$	4.34737e12	−	7.52987e12i	0.141250	−	0.244652i
$995$	3.33757e12	−	5.78084e12i	0.107951	−	0.186977i
$996$	−2.52377e10	−	4.37129e10i	−0.000812610	−	0.00140748i
$997$	−3.28430e13			−1.05273			−0.526363	−	0.850260i	$-0.676445\pi$
$997$	−3.28430e13			−1.05273			−0.526363	+	0.850260i	$0.676445\pi$
$998$	−1.17543e12	−	2.03590e12i	−0.0375067	−	0.0649635i
$999$	6.13613e10	−	1.06281e11i	0.00194917	−	0.00337606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.c.a.6.15	✓	64
43.36	even	3	inner	43.10.c.a.36.15	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.c.a.6.15	✓	64	1.1	even	1	trivial
43.10.c.a.36.15	yes	64	43.36	even	3	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-7.29691 q^{2} +(-0.107179 + 0.185640i) q^{3} -458.755 q^{4} +(1142.50 - 1978.86i) q^{5} +(0.782078 - 1.35460i) q^{6} +(-5889.33 - 10200.6i) q^{7} +7083.52 q^{8} +(9841.48 + 17045.9i) q^{9} +O(q^{10})\)	\(q-7.29691 q^{2} +(-0.107179 + 0.185640i) q^{3} -458.755 q^{4} +(1142.50 - 1978.86i) q^{5} +(0.782078 - 1.35460i) q^{6} +(-5889.33 - 10200.6i) q^{7} +7083.52 q^{8} +(9841.48 + 17045.9i) q^{9} +(-8336.70 + 14439.6i) q^{10} +24167.2 q^{11} +(49.1690 - 85.1632i) q^{12} +(-6025.36 - 10436.2i) q^{13} +(42974.0 + 74433.1i) q^{14} +(244.904 + 424.186i) q^{15} +183195. q^{16} +(-302170. - 523375. i) q^{17} +(-71812.4 - 124383. i) q^{18} +(-296845. + 514150. i) q^{19} +(-524126. + 907814. i) q^{20} +2524.86 q^{21} -176346. q^{22} +(232004. - 401842. i) q^{23} +(-759.206 + 1314.98i) q^{24} +(-1.63404e6 - 2.83024e6i) q^{25} +(43966.6 + 76152.3i) q^{26} -8438.43 q^{27} +(2.70176e6 + 4.67959e6i) q^{28} +(-714164. - 1.23697e6i) q^{29} +(-1787.04 - 3095.25i) q^{30} +(-3.09357e6 + 5.35821e6i) q^{31} -4.96352e6 q^{32} +(-2590.22 + 4486.40i) q^{33} +(2.20491e6 + 3.81902e6i) q^{34} -2.69142e7 q^{35} +(-4.51483e6 - 7.81991e6i) q^{36} +(-7.27165e6 + 1.25949e7i) q^{37} +(2.16605e6 - 3.75171e6i) q^{38} +2583.18 q^{39} +(8.09290e6 - 1.40173e7i) q^{40} -3.11049e7 q^{41} -18423.7 q^{42} +(1.97701e7 - 1.05706e7i) q^{43} -1.10868e7 q^{44} +4.49754e7 q^{45} +(-1.69291e6 + 2.93221e6i) q^{46} +3.11810e7 q^{47} +(-19634.7 + 34008.3i) q^{48} +(-4.91917e7 + 8.52025e7i) q^{49} +(1.19234e7 + 2.06520e7i) q^{50} +129546. q^{51} +(2.76417e6 + 4.78768e6i) q^{52} +(3.06638e7 - 5.31113e7i) q^{53} +61574.5 q^{54} +(2.76110e7 - 4.78236e7i) q^{55} +(-4.17172e7 - 7.22563e7i) q^{56} +(-63631.2 - 110212. i) q^{57} +(5.21119e6 + 9.02605e6i) q^{58} -1.40505e7 q^{59} +(-112351. - 194598. i) q^{60} +(4.27646e7 + 7.40705e7i) q^{61} +(2.25735e7 - 3.90984e7i) q^{62} +(1.15919e8 - 2.00778e8i) q^{63} -5.75774e7 q^{64} -2.75358e7 q^{65} +(18900.6 - 32736.9i) q^{66} +(-2.84713e7 + 4.93137e7i) q^{67} +(1.38622e8 + 2.40101e8i) q^{68} +(49732.0 + 86138.3i) q^{69} +1.96391e8 q^{70} +(-5.05815e7 - 8.76096e7i) q^{71} +(6.97123e7 + 1.20745e8i) q^{72} +(1.87812e8 + 3.25301e8i) q^{73} +(5.30606e7 - 9.19036e7i) q^{74} +700540. q^{75} +(1.36179e8 - 2.35869e8i) q^{76} +(-1.42329e8 - 2.46521e8i) q^{77} -18849.2 q^{78} +(2.59061e7 + 4.48707e7i) q^{79} +(2.09300e8 - 3.62517e8i) q^{80} +(-1.93709e8 + 3.35514e8i) q^{81} +2.26970e8 q^{82} +(2.56642e8 - 4.44517e8i) q^{83} -1.15829e6 q^{84} -1.38092e9 q^{85} +(-1.44260e8 + 7.71325e7i) q^{86} +306174. q^{87} +1.71189e8 q^{88} +(1.95232e6 - 3.38152e6i) q^{89} -3.28182e8 q^{90} +(-7.09707e7 + 1.22925e8i) q^{91} +(-1.06433e8 + 1.84347e8i) q^{92} +(-663132. - 1.14858e6i) q^{93} -2.27525e8 q^{94} +(6.78288e8 + 1.17483e9i) q^{95} +(531986. - 921427. i) q^{96} -1.04675e9 q^{97} +(3.58947e8 - 6.21715e8i) q^{98} +(2.37841e8 + 4.11953e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9}+O(q^{10}) \) 64 * q - 70 * q^2 + 307 * q^3 + 16038 * q^4 + 681 * q^5 - 1281 * q^6 + 957 * q^7 - 10920 * q^8 - 255339 * q^9	\( 64 q - 70 q^{2} + 307 q^{3} + 16038 q^{4} + 681 q^{5} - 1281 q^{6} + 957 q^{7} - 10920 q^{8} - 255339 q^{9} - 6237 q^{10} - 180682 q^{11} + 274344 q^{12} + 115245 q^{13} - 171208 q^{14} + 138833 q^{15} + 4289206 q^{16} + 65180 q^{17} + 603985 q^{18} + 39150 q^{19} - 2709775 q^{20} - 3105162 q^{21} + 598456 q^{22} + 1285907 q^{23} - 292550 q^{24} - 14709917 q^{25} + 5332695 q^{26} - 20118002 q^{27} - 5475298 q^{28} + 1274091 q^{29} + 28424751 q^{30} + 2899781 q^{31} - 16322030 q^{32} + 30668912 q^{33} + 6822099 q^{34} - 14750922 q^{35} - 113819232 q^{36} - 13772217 q^{37} + 2700532 q^{38} + 49876982 q^{39} - 55802359 q^{40} + 5375394 q^{41} - 62768266 q^{42} - 4250879 q^{43} - 125171958 q^{44} + 74719384 q^{45} - 91405220 q^{46} + 46104596 q^{47} + 294588191 q^{48} - 233221733 q^{49} + 380339342 q^{50} + 229598406 q^{51} + 166281612 q^{52} + 125396641 q^{53} - 137752484 q^{54} + 139471854 q^{55} + 41104589 q^{56} - 289586721 q^{57} - 183782516 q^{58} - 637949078 q^{59} - 70735747 q^{60} - 95573327 q^{61} + 181277053 q^{62} + 226632970 q^{63} + 712599660 q^{64} - 498753718 q^{65} - 349240445 q^{66} - 276270786 q^{67} + 1034771928 q^{68} - 199705103 q^{69} + 1780847990 q^{70} + 651945247 q^{71} - 270063054 q^{72} - 182725322 q^{73} - 193737672 q^{74} - 3155252572 q^{75} + 492133584 q^{76} + 216024528 q^{77} + 2562586420 q^{78} - 376932221 q^{79} - 783129021 q^{80} - 2146956496 q^{81} + 2373824428 q^{82} + 1008544071 q^{83} - 9413139208 q^{84} - 1131353054 q^{85} - 1641459050 q^{86} + 5060470018 q^{87} + 369936980 q^{88} + 2244184366 q^{89} + 3302428348 q^{90} + 3951711 q^{91} + 4361095637 q^{92} + 3133616089 q^{93} + 3002217406 q^{94} + 1515822931 q^{95} + 69408612 q^{96} - 6951085934 q^{97} + 1120193981 q^{98} + 1264470179 q^{99}+O(q^{100}) \) 64 * q - 70 * q^2 + 307 * q^3 + 16038 * q^4 + 681 * q^5 - 1281 * q^6 + 957 * q^7 - 10920 * q^8 - 255339 * q^9 - 6237 * q^10 - 180682 * q^11 + 274344 * q^12 + 115245 * q^13 - 171208 * q^14 + 138833 * q^15 + 4289206 * q^16 + 65180 * q^17 + 603985 * q^18 + 39150 * q^19 - 2709775 * q^20 - 3105162 * q^21 + 598456 * q^22 + 1285907 * q^23 - 292550 * q^24 - 14709917 * q^25 + 5332695 * q^26 - 20118002 * q^27 - 5475298 * q^28 + 1274091 * q^29 + 28424751 * q^30 + 2899781 * q^31 - 16322030 * q^32 + 30668912 * q^33 + 6822099 * q^34 - 14750922 * q^35 - 113819232 * q^36 - 13772217 * q^37 + 2700532 * q^38 + 49876982 * q^39 - 55802359 * q^40 + 5375394 * q^41 - 62768266 * q^42 - 4250879 * q^43 - 125171958 * q^44 + 74719384 * q^45 - 91405220 * q^46 + 46104596 * q^47 + 294588191 * q^48 - 233221733 * q^49 + 380339342 * q^50 + 229598406 * q^51 + 166281612 * q^52 + 125396641 * q^53 - 137752484 * q^54 + 139471854 * q^55 + 41104589 * q^56 - 289586721 * q^57 - 183782516 * q^58 - 637949078 * q^59 - 70735747 * q^60 - 95573327 * q^61 + 181277053 * q^62 + 226632970 * q^63 + 712599660 * q^64 - 498753718 * q^65 - 349240445 * q^66 - 276270786 * q^67 + 1034771928 * q^68 - 199705103 * q^69 + 1780847990 * q^70 + 651945247 * q^71 - 270063054 * q^72 - 182725322 * q^73 - 193737672 * q^74 - 3155252572 * q^75 + 492133584 * q^76 + 216024528 * q^77 + 2562586420 * q^78 - 376932221 * q^79 - 783129021 * q^80 - 2146956496 * q^81 + 2373824428 * q^82 + 1008544071 * q^83 - 9413139208 * q^84 - 1131353054 * q^85 - 1641459050 * q^86 + 5060470018 * q^87 + 369936980 * q^88 + 2244184366 * q^89 + 3302428348 * q^90 + 3951711 * q^91 + 4361095637 * q^92 + 3133616089 * q^93 + 3002217406 * q^94 + 1515822931 * q^95 + 69408612 * q^96 - 6951085934 * q^97 + 1120193981 * q^98 + 1264470179 * q^99

Introduction

L-functions

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