LMFDB - Embedded newform 43.10.c.a.36.18

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			36.18
Character	$\chi$	$=$	43.36
Dual form			43.10.c.a.6.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.09785 q^{2} +(102.202 + 177.020i) q^{3} -507.599 q^{4} +(-192.277 - 333.034i) q^{5} +(214.405 + 371.361i) q^{6} +(2053.75 - 3557.19i) q^{7} -2138.97 q^{8} +(-11049.2 + 19137.7i) q^{9} +O(q^{10})$	\(q+2.09785 q^{2} +(102.202 + 177.020i) q^{3} -507.599 q^{4} +(-192.277 - 333.034i) q^{5} +(214.405 + 371.361i) q^{6} +(2053.75 - 3557.19i) q^{7} -2138.97 q^{8} +(-11049.2 + 19137.7i) q^{9} +(-403.369 - 698.655i) q^{10} -71976.0 q^{11} +(-51877.8 - 89855.0i) q^{12} +(58452.9 - 101243. i) q^{13} +(4308.45 - 7462.46i) q^{14} +(39302.4 - 68073.7i) q^{15} +255403. q^{16} +(-50468.0 + 87413.1i) q^{17} +(-23179.5 + 40148.0i) q^{18} +(-478542. - 828858. i) q^{19} +(97599.7 + 169048. i) q^{20} +839591. q^{21} -150995. q^{22} +(1.31140e6 + 2.27141e6i) q^{23} +(-218608. - 378639. i) q^{24} +(902621. - 1.56339e6i) q^{25} +(122626. - 212394. i) q^{26} -493701. q^{27} +(-1.04248e6 + 1.80563e6i) q^{28} +(2.71377e6 - 4.70039e6i) q^{29} +(82450.5 - 142808. i) q^{30} +(-3.22702e6 - 5.58936e6i) q^{31} +1.63095e6 q^{32} +(-7.35612e6 - 1.27412e7i) q^{33} +(-105874. + 183380. i) q^{34} -1.57955e6 q^{35} +(5.60854e6 - 9.71428e6i) q^{36} +(-1.12717e6 - 1.95231e6i) q^{37} +(-1.00391e6 - 1.73882e6i) q^{38} +2.38961e7 q^{39} +(411274. + 712348. i) q^{40} -3.25017e7 q^{41} +1.76134e6 q^{42} +(1.00494e7 - 2.00400e7i) q^{43} +3.65350e7 q^{44} +8.49800e6 q^{45} +(2.75113e6 + 4.76509e6i) q^{46} -4.35786e7 q^{47} +(2.61028e7 + 4.52115e7i) q^{48} +(1.17411e7 + 2.03361e7i) q^{49} +(1.89357e6 - 3.27975e6i) q^{50} -2.06318e7 q^{51} +(-2.96706e7 + 5.13911e7i) q^{52} +(-8.12950e6 - 1.40807e7i) q^{53} -1.03571e6 q^{54} +(1.38393e7 + 2.39704e7i) q^{55} +(-4.39290e6 + 7.60872e6i) q^{56} +(9.78162e7 - 1.69423e8i) q^{57} +(5.69308e6 - 9.86071e6i) q^{58} -5.01615e7 q^{59} +(-1.99498e7 + 3.45541e7i) q^{60} +(-3.51956e7 + 6.09605e7i) q^{61} +(-6.76981e6 - 1.17257e7i) q^{62} +(4.53843e7 + 7.86080e7i) q^{63} -1.27345e8 q^{64} -4.49566e7 q^{65} +(-1.54320e7 - 2.67291e7i) q^{66} +(-3.17585e7 - 5.50073e7i) q^{67} +(2.56175e7 - 4.43708e7i) q^{68} +(-2.68057e8 + 4.64288e8i) q^{69} -3.31367e6 q^{70} +(-3.46313e7 + 5.99832e7i) q^{71} +(2.36338e7 - 4.09349e7i) q^{72} +(7.99681e7 - 1.38509e8i) q^{73} +(-2.36463e6 - 4.09566e6i) q^{74} +3.69000e8 q^{75} +(2.42907e8 + 4.20728e8i) q^{76} +(-1.47821e8 + 2.56033e8i) q^{77} +5.01305e7 q^{78} +(-5.78269e7 + 1.00159e8i) q^{79} +(-4.91083e7 - 8.50580e7i) q^{80} +(1.67023e8 + 2.89292e8i) q^{81} -6.81837e7 q^{82} +(-1.99146e8 - 3.44931e8i) q^{83} -4.26176e8 q^{84} +3.88153e7 q^{85} +(2.10821e7 - 4.20410e7i) q^{86} +1.10941e9 q^{87} +1.53954e8 q^{88} +(2.72020e7 + 4.71152e7i) q^{89} +1.78275e7 q^{90} +(-2.40095e8 - 4.15857e8i) q^{91} +(-6.65666e8 - 1.15297e9i) q^{92} +(6.59618e8 - 1.14249e9i) q^{93} -9.14214e7 q^{94} +(-1.84025e8 + 3.18741e8i) q^{95} +(1.66687e8 + 2.88710e8i) q^{96} -1.64409e9 q^{97} +(2.46310e7 + 4.26621e7i) q^{98} +(7.95274e8 - 1.37746e9i) 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 $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.09785			0.0927128			0.0463564	−	0.998925i	$-0.485239\pi$
$2$	2.09785			0.0927128			0.0463564	+	0.998925i	$0.485239\pi$
$3$	102.202	+	177.020i	0.728476	+	1.26176i	0.957527	+	0.288343i	$0.0931045\pi$
$3$	102.202	+	177.020i	0.728476	+	1.26176i	−0.229051	+	0.973414i	$0.573562\pi$
$4$	−507.599			−0.991404
$5$	−192.277	−	333.034i	−0.137582	−	0.238300i	0.788999	−	0.614395i	$-0.210600\pi$
$5$	−192.277	−	333.034i	−0.137582	−	0.238300i	−0.926581	+	0.376095i	$0.877267\pi$
$6$	214.405	+	371.361i	0.0675391	+	0.116981i
$7$	2053.75	−	3557.19i	0.323300	−	0.559972i	−0.657867	−	0.753134i	$-0.728541\pi$
$7$	2053.75	−	3557.19i	0.323300	−	0.559972i	0.981167	+	0.193162i	$0.0618744\pi$
$8$	−2138.97			−0.184629
$9$	−11049.2	+	19137.7i	−0.561355	+	0.972296i
$10$	−403.369	−	698.655i	−0.0127556	−	0.0220934i
$11$	−71976.0			−1.48225			−0.741124	−	0.671368i	$-0.765707\pi$
$11$	−71976.0			−1.48225			−0.741124	+	0.671368i	$0.765707\pi$
$12$	−51877.8	−	89855.0i	−0.722215	−	1.25091i
$13$	58452.9	−	101243.i	0.567624	−	0.983154i	−0.429176	−	0.903221i	$-0.641196\pi$
$13$	58452.9	−	101243.i	0.567624	−	0.983154i	0.996800	−	0.0799334i	$-0.0254708\pi$
$14$	4308.45	−	7462.46i	0.0299740	−	0.0519166i
$15$	39302.4	−	68073.7i	0.200451	−	0.347191i
$16$	255403.			0.974287
$17$	−50468.0	+	87413.1i	−0.146553	+	0.253838i	−0.929951	−	0.367683i	$-0.880151\pi$
$17$	−50468.0	+	87413.1i	−0.146553	+	0.253838i	0.783398	+	0.621520i	$0.213485\pi$
$18$	−23179.5	+	40148.0i	−0.0520448	+	0.0901443i
$19$	−478542.	−	828858.i	−0.842420	−	1.45911i	−0.887843	−	0.460146i	$-0.847797\pi$
$19$	−478542.	−	828858.i	−0.842420	−	1.45911i	0.0454235	−	0.998968i	$-0.485536\pi$
$20$	97599.7	+	169048.i	0.136400	+	0.236251i
$21$	839591.			0.942065
$22$	−150995.			−0.137423
$23$	1.31140e6	+	2.27141e6i	0.977148	+	1.69247i	0.672656	+	0.739955i	$0.265153\pi$
$23$	1.31140e6	+	2.27141e6i	0.977148	+	1.69247i	0.304492	+	0.952515i	$0.401513\pi$
$24$	−218608.	−	378639.i	−0.134498	−	0.232957i
$25$	902621.	−	1.56339e6i	0.462142	−	0.800454i
$26$	122626.	−	212394.i	0.0526260	−	0.0911510i
$27$	−493701.			−0.178783
$28$	−1.04248e6	+	1.80563e6i	−0.320521	+	0.555159i
$29$	2.71377e6	−	4.70039e6i	0.712495	−	1.23408i	−0.251422	−	0.967877i	$-0.580898\pi$
$29$	2.71377e6	−	4.70039e6i	0.712495	−	1.23408i	0.963918	−	0.266200i	$-0.0857683\pi$
$30$	82450.5	−	142808.i	0.0185844	−	0.0321891i
$31$	−3.22702e6	−	5.58936e6i	−0.627587	−	1.08701i	−0.988034	−	0.154233i	$-0.950709\pi$
$31$	−3.22702e6	−	5.58936e6i	−0.627587	−	1.08701i	0.360447	−	0.932780i	$-0.382624\pi$
$32$	1.63095e6			0.274958
$33$	−7.35612e6	−	1.27412e7i	−1.07978	−	1.87024i
$34$	−105874.	+	183380.i	−0.0135874	+	0.0235340i
$35$	−1.57955e6			−0.177921
$36$	5.60854e6	−	9.71428e6i	0.556530	−	0.963938i
$37$	−1.12717e6	−	1.95231e6i	−0.0988738	−	0.171254i	0.812345	−	0.583177i	$-0.198191\pi$
$37$	−1.12717e6	−	1.95231e6i	−0.0988738	−	0.171254i	−0.911219	+	0.411923i	$0.864857\pi$
$38$	−1.00391e6	−	1.73882e6i	−0.0781031	−	0.135279i
$39$	2.38961e7			1.65400
$40$	411274.	+	712348.i	0.0254016	+	0.0439969i
$41$	−3.25017e7			−1.79630			−0.898149	−	0.439692i	$-0.855088\pi$
$41$	−3.25017e7			−1.79630			−0.898149	+	0.439692i	$0.855088\pi$
$42$	1.76134e6			0.0873415
$43$	1.00494e7	−	2.00400e7i	0.448261	−	0.893903i
$43$	1.00494e7	−	2.00400e7i	0.448261	−	0.893903i
$44$	3.65350e7			1.46951
$45$	8.49800e6			0.308930
$46$	2.75113e6	+	4.76509e6i	0.0905941	+	0.156914i
$47$	−4.35786e7			−1.30267			−0.651333	−	0.758792i	$-0.725790\pi$
$47$	−4.35786e7			−1.30267			−0.651333	+	0.758792i	$0.725790\pi$
$48$	2.61028e7	+	4.52115e7i	0.709745	+	1.22931i
$49$	1.17411e7	+	2.03361e7i	0.290954	+	0.503948i
$50$	1.89357e6	−	3.27975e6i	0.0428465	−	0.0742123i
$51$	−2.06318e7			−0.427042
$52$	−2.96706e7	+	5.13911e7i	−0.562745	+	0.974703i
$53$	−8.12950e6	−	1.40807e7i	−0.141522	−	0.245123i	0.786548	−	0.617529i	$-0.211866\pi$
$53$	−8.12950e6	−	1.40807e7i	−0.141522	−	0.245123i	−0.928070	+	0.372406i	$0.878533\pi$
$54$	−1.03571e6			−0.0165755
$55$	1.38393e7	+	2.39704e7i	0.203931	+	0.353219i
$56$	−4.39290e6	+	7.60872e6i	−0.0596904	+	0.103387i
$57$	9.78162e7	−	1.69423e8i	1.22737	−	2.12586i
$58$	5.69308e6	−	9.86071e6i	0.0660574	−	0.114415i
$59$	−5.01615e7			−0.538935			−0.269467	−	0.963010i	$-0.586848\pi$
$59$	−5.01615e7			−0.538935			−0.269467	+	0.963010i	$0.586848\pi$
$60$	−1.99498e7	+	3.45541e7i	−0.198728	+	0.344207i
$61$	−3.51956e7	+	6.09605e7i	−0.325464	+	0.563721i	−0.981606	−	0.190917i	$-0.938854\pi$
$61$	−3.51956e7	+	6.09605e7i	−0.325464	+	0.563721i	0.656142	+	0.754638i	$0.272187\pi$
$62$	−6.76981e6	−	1.17257e7i	−0.0581854	−	0.100780i
$63$	4.53843e7	+	7.86080e7i	0.362972	+	0.628686i
$64$	−1.27345e8			−0.948795
$65$	−4.49566e7			−0.312380
$66$	−1.54320e7	−	2.67291e7i	−0.100110	−	0.173395i
$67$	−3.17585e7	−	5.50073e7i	−0.192541	−	0.333490i	0.753551	−	0.657390i	$-0.228339\pi$
$67$	−3.17585e7	−	5.50073e7i	−0.192541	−	0.333490i	−0.946092	+	0.323899i	$0.895006\pi$
$68$	2.56175e7	−	4.43708e7i	0.145294	−	0.251656i
$69$	−2.68057e8	+	4.64288e8i	−1.42366	+	2.46585i
$70$	−3.31367e6			−0.0164956
$71$	−3.46313e7	+	5.99832e7i	−0.161736	+	0.280135i	−0.935491	−	0.353350i	$-0.885043\pi$
$71$	−3.46313e7	+	5.99832e7i	−0.161736	+	0.280135i	0.773755	+	0.633484i	$0.218376\pi$
$72$	2.36338e7	−	4.09349e7i	0.103642	−	0.179514i
$73$	7.99681e7	−	1.38509e8i	0.329582	−	0.570853i	−0.652847	−	0.757490i	$-0.726425\pi$
$73$	7.99681e7	−	1.38509e8i	0.329582	−	0.570853i	0.982429	+	0.186637i	$0.0597587\pi$
$74$	−2.36463e6	−	4.09566e6i	−0.00916686	−	0.0158775i
$75$	3.69000e8			1.34664
$76$	2.42907e8	+	4.20728e8i	0.835179	+	1.44657i
$77$	−1.47821e8	+	2.56033e8i	−0.479211	+	0.830017i
$78$	5.01305e7			0.153347
$79$	−5.78269e7	+	1.00159e8i	−0.167035	+	0.289314i	−0.937376	−	0.348319i	$-0.886753\pi$
$79$	−5.78269e7	+	1.00159e8i	−0.167035	+	0.289314i	0.770341	+	0.637632i	$0.220086\pi$
$80$	−4.91083e7	−	8.50580e7i	−0.134045	−	0.232172i
$81$	1.67023e8	+	2.89292e8i	0.431116	+	0.746714i
$82$	−6.81837e7			−0.166540
$83$	−1.99146e8	−	3.44931e8i	−0.460596	−	0.797776i	0.538395	−	0.842693i	$-0.319031\pi$
$83$	−1.99146e8	−	3.44931e8i	−0.460596	−	0.797776i	−0.998991	+	0.0449170i	$0.985698\pi$
$84$	−4.26176e8			−0.933968
$85$	3.88153e7			0.0806526
$86$	2.10821e7	−	4.20410e7i	0.0415595	−	0.0828762i
$87$	1.10941e9			2.07614
$88$	1.53954e8			0.273665
$89$	2.72020e7	+	4.71152e7i	0.0459564	+	0.0795987i	0.888089	−	0.459672i	$-0.152033\pi$
$89$	2.72020e7	+	4.71152e7i	0.0459564	+	0.0795987i	−0.842132	+	0.539271i	$0.818700\pi$
$90$	1.78275e7			0.0286418
$91$	−2.40095e8	−	4.15857e8i	−0.367026	−	0.635708i
$92$	−6.65666e8	−	1.15297e9i	−0.968749	−	1.67792i
$93$	6.59618e8	−	1.14249e9i	0.914365	−	1.58373i
$94$	−9.14214e7			−0.120774
$95$	−1.84025e8	+	3.18741e8i	−0.231804	+	0.401497i
$96$	1.66687e8	+	2.88710e8i	0.200300	+	0.346930i
$97$	−1.64409e9			−1.88561			−0.942804	−	0.333347i	$-0.891822\pi$
$97$	−1.64409e9			−1.88561			−0.942804	+	0.333347i	$0.891822\pi$
$98$	2.46310e7	+	4.26621e7i	0.0269752	+	0.0467224i
$99$	7.95274e8	−	1.37746e9i	0.832067	−	1.44118i
$100$	−4.58170e8	+	7.93573e8i	−0.458170	+	0.793573i
$101$	4.22842e8	−	7.32383e8i	0.404326	−	0.700313i	−0.589917	−	0.807464i	$-0.700839\pi$
$101$	4.22842e8	−	7.32383e8i	0.404326	−	0.700313i	0.994243	+	0.107151i	$0.0341728\pi$
$102$	−4.32824e7			−0.0395923
$103$	2.98571e8	−	5.17140e8i	0.261385	−	0.452732i	−0.705225	−	0.708983i	$-0.749154\pi$
$103$	2.98571e8	−	5.17140e8i	0.261385	−	0.452732i	0.966610	+	0.256251i	$0.0824875\pi$
$104$	−1.25029e8	+	2.16556e8i	−0.104800	+	0.181518i
$105$	−1.61434e8	−	2.79612e8i	−0.129612	−	0.224494i
$106$	−1.70545e7	−	2.95392e7i	−0.0131209	−	0.0227260i
$107$	−1.37700e9			−1.01556			−0.507782	−	0.861485i	$-0.669535\pi$
$107$	−1.37700e9			−1.01556			−0.507782	+	0.861485i	$0.669535\pi$
$108$	2.50602e8			0.177247
$109$	4.63494e8	+	8.02795e8i	0.314503	+	0.544735i	0.979332	−	0.202261i	$-0.0648288\pi$
$109$	4.63494e8	+	8.02795e8i	0.314503	+	0.544735i	−0.664829	+	0.746996i	$0.731495\pi$
$110$	2.90329e7	+	5.02864e7i	0.0189070	+	0.0327479i
$111$	2.30399e8	−	3.99062e8i	0.144054	−	0.249509i
$112$	5.24534e8	−	9.08520e8i	0.314987	−	0.545573i
$113$	2.49872e9			1.44167			0.720833	−	0.693109i	$-0.243760\pi$
$113$	2.49872e9			1.44167			0.720833	+	0.693109i	$0.243760\pi$
$114$	2.05204e8	−	3.55423e8i	0.113792	−	0.197094i
$115$	5.04305e8	−	8.73482e8i	0.268877	−	0.465708i
$116$	−1.37751e9	+	2.38591e9i	−0.706371	+	1.22347i
$117$	1.29171e9	+	2.23731e9i	0.637278	+	1.10380i
$118$	−1.05231e8			−0.0499661
$119$	2.07297e8	+	3.59049e8i	0.0947614	+	0.164131i
$120$	−8.40665e7	+	1.45607e8i	−0.0370090	+	0.0641014i
$121$	2.82260e9			1.19706
$122$	−7.38350e7	+	1.27886e8i	−0.0301747	+	0.0522641i
$123$	−3.32175e9	−	5.75344e9i	−1.30856	−	2.26649i
$124$	1.63803e9	+	2.83716e9i	0.622193	+	1.07767i
$125$	−1.44530e9			−0.529495
$126$	9.52096e7	+	1.64908e8i	0.0336522	+	0.0582873i
$127$	−3.78555e9			−1.29126			−0.645628	−	0.763652i	$-0.723404\pi$
$127$	−3.78555e9			−1.29126			−0.645628	+	0.763652i	$0.723404\pi$
$128$	−1.10220e9			−0.362923
$129$	4.57455e9	−	2.69200e8i	1.45444	−	0.0855897i
$130$	−9.43123e7			−0.0289617
$131$	−3.58114e9			−1.06243			−0.531216	−	0.847237i	$-0.678265\pi$
$131$	−3.58114e9			−1.06243			−0.531216	+	0.847237i	$0.678265\pi$
$132$	3.73396e9	+	6.46741e9i	1.07050	+	1.85416i
$133$	−3.93121e9			−1.08942
$134$	−6.66245e7	−	1.15397e8i	−0.0178510	−	0.0309188i
$135$	9.49275e7	+	1.64419e8i	0.0245974	+	0.0426040i
$136$	1.07949e8	−	1.86974e8i	0.0270579	−	0.0468657i
$137$	6.10056e9			1.47954			0.739771	−	0.672859i	$-0.234934\pi$
$137$	6.10056e9			1.47954			0.739771	+	0.672859i	$0.234934\pi$
$138$	−5.62343e8	+	9.74007e8i	−0.131991	+	0.228616i
$139$	−2.08146e9	−	3.60519e9i	−0.472935	−	0.819147i	0.526585	−	0.850122i	$-0.323472\pi$
$139$	−2.08146e9	−	3.60519e9i	−0.472935	−	0.819147i	−0.999520	+	0.0309753i	$0.990139\pi$
$140$	8.01780e8			0.176392
$141$	−4.45384e9	−	7.71427e9i	−0.948961	−	1.64365i
$142$	−7.26513e7	+	1.25836e8i	−0.0149950	+	0.0259721i
$143$	−4.20721e9	+	7.28710e9i	−0.841360	+	1.45728i
$144$	−2.82199e9	+	4.88783e9i	−0.546921	+	0.947295i
$145$	−2.08718e9			−0.392107
$146$	1.67761e8	−	2.90571e8i	0.0305565	−	0.0529254i
$147$	−2.39993e9	+	4.15680e9i	−0.423907	+	0.734228i
$148$	5.72150e8	+	9.90992e8i	0.0980239	+	0.169782i
$149$	3.36419e9	+	5.82695e9i	0.559168	+	0.968507i	0.997566	+	0.0697262i	$0.0222126\pi$
$149$	3.36419e9	+	5.82695e9i	0.559168	+	0.968507i	−0.438398	+	0.898781i	$0.644454\pi$
$150$	7.74108e8			0.124851
$151$	2.75354e9			0.431018			0.215509	−	0.976502i	$-0.430859\pi$
$151$	2.75354e9			0.431018			0.215509	+	0.976502i	$0.430859\pi$
$152$	1.02358e9	+	1.77290e9i	0.155535	+	0.269394i
$153$	−1.11526e9	−	1.93168e9i	−0.164537	−	0.284986i
$154$	−3.10105e8	+	5.37118e8i	−0.0444290	+	0.0769532i
$155$	−1.24096e9	+	2.14941e9i	−0.172690	+	0.299108i
$156$	−1.21296e10			−1.63979
$157$	2.39539e9	−	4.14893e9i	0.314649	−	0.544989i	−0.664713	−	0.747098i	$-0.731446\pi$
$157$	2.39539e9	−	4.14893e9i	0.314649	−	0.544989i	0.979363	+	0.202110i	$0.0647797\pi$
$158$	−1.21312e8	+	2.10119e8i	−0.0154863	+	0.0268231i
$159$	1.66171e9	−	2.87817e9i	0.206190	−	0.357132i
$160$	−3.13594e8	−	5.43161e8i	−0.0378293	−	0.0655223i
$161$	1.07731e10			1.26365
$162$	3.50390e8	+	6.06892e8i	0.0399699	+	0.0692300i
$163$	2.95276e9	−	5.11434e9i	0.327631	−	0.567473i	−0.654411	−	0.756139i	$-0.727083\pi$
$163$	2.95276e9	−	5.11434e9i	0.327631	−	0.567473i	0.982041	+	0.188667i	$0.0604165\pi$
$164$	1.64978e10			1.78086
$165$	−2.82883e9	+	4.89967e9i	−0.297118	+	0.514623i
$166$	−4.17779e8	−	7.23614e8i	−0.0427032	−	0.0739640i
$167$	−7.72856e8	−	1.33863e9i	−0.0768908	−	0.133179i	0.825016	−	0.565109i	$-0.191166\pi$
$167$	−7.72856e8	−	1.33863e9i	−0.0768908	−	0.133179i	−0.901907	+	0.431930i	$0.857833\pi$
$168$	−1.79586e9			−0.173932
$169$	−1.53124e9	−	2.65218e9i	−0.144395	−	0.250099i
$170$	8.14288e7			0.00747753
$171$	2.11499e10			1.89159
$172$	−5.10105e9	+	1.01723e10i	−0.444408	+	0.886219i
$173$	3.70899e9			0.314810			0.157405	−	0.987534i	$-0.449687\pi$
$173$	3.70899e9			0.314810			0.157405	+	0.987534i	$0.449687\pi$
$174$	2.32739e9			0.192485
$175$	−3.70751e9	−	6.42160e9i	−0.298821	−	0.517573i
$176$	−1.83829e10			−1.44413
$177$	−5.12662e9	−	8.87957e9i	−0.392601	−	0.680005i
$178$	5.70657e7	+	9.88407e7i	0.00426074	+	0.00737982i
$179$	9.61112e9	−	1.66469e10i	0.699738	−	1.21198i	−0.268820	−	0.963190i	$-0.586634\pi$
$179$	9.61112e9	−	1.66469e10i	0.699738	−	1.21198i	0.968557	−	0.248790i	$-0.0800330\pi$
$180$	−4.31358e9			−0.306275
$181$	−1.07709e10	+	1.86558e10i	−0.745932	+	1.29199i	0.203826	+	0.979007i	$0.434662\pi$
$181$	−1.07709e10	+	1.86558e10i	−0.745932	+	1.29199i	−0.949758	+	0.312985i	$0.898671\pi$
$182$	−5.03683e8	−	8.72405e8i	−0.0340280	−	0.0589382i
$183$	−1.43883e10			−0.948373
$184$	−2.80504e9	−	4.85848e9i	−0.180410	−	0.312479i
$185$	−4.33457e8	+	7.50770e8i	−0.0272066	+	0.0471232i
$186$	1.38378e9	−	2.39678e9i	0.0847733	−	0.146832i
$187$	3.63248e9	−	6.29164e9i	0.217228	−	0.376250i
$188$	2.21205e10			1.29147
$189$	−1.01394e9	+	1.75619e9i	−0.0578007	+	0.100114i
$190$	−3.86058e8	+	6.68671e8i	−0.0214912	+	0.0372239i
$191$	−7.37604e9	−	1.27757e10i	−0.401026	−	0.694598i	0.592824	−	0.805332i	$-0.298013\pi$
$191$	−7.37604e9	−	1.27757e10i	−0.401026	−	0.694598i	−0.993850	+	0.110734i	$0.964680\pi$
$192$	−1.30150e10	−	2.25426e10i	−0.691174	−	1.19715i
$193$	2.34774e10			1.21799			0.608993	−	0.793176i	$-0.291574\pi$
$193$	2.34774e10			1.21799			0.608993	+	0.793176i	$0.291574\pi$
$194$	−3.44905e9			−0.174820
$195$	−4.59468e9	−	7.95821e9i	−0.227562	−	0.394148i
$196$	−5.95975e9	−	1.03226e10i	−0.288453	−	0.499616i
$197$	3.78640e8	−	6.55824e8i	0.0179114	−	0.0310234i	−0.856931	−	0.515431i	$-0.827632\pi$
$197$	3.78640e8	−	6.55824e8i	0.0179114	−	0.0310234i	0.874842	+	0.484408i	$0.160965\pi$
$198$	1.66837e9	−	2.88970e9i	0.0771433	−	0.133616i
$199$	8.97673e9			0.405769			0.202885	−	0.979203i	$-0.434968\pi$
$199$	8.97673e9			0.405769			0.202885	+	0.979203i	$0.434968\pi$
$200$	−1.93068e9	+	3.34403e9i	−0.0853247	+	0.147787i
$201$	6.49158e9	−	1.12437e10i	0.280523	−	0.485880i
$202$	8.87059e8	−	1.53643e9i	0.0374862	−	0.0649280i
$203$	−1.11468e10	−	1.93068e10i	−0.460699	−	0.797955i
$204$	1.04727e10			0.423372
$205$	6.24933e9	+	1.08242e10i	0.247139	+	0.428057i
$206$	6.26358e8	−	1.08488e9i	0.0242337	−	0.0419740i
$207$	−5.79595e10			−2.19411
$208$	1.49291e10	−	2.58579e10i	0.553029	−	0.957874i
$209$	3.44435e10	+	5.96579e10i	1.24867	+	2.16277i
$210$	−3.38665e8	−	5.86585e8i	−0.0120166	−	0.0208134i
$211$	2.66918e10			0.927058			0.463529	−	0.886082i	$-0.346583\pi$
$211$	2.66918e10			0.927058			0.463529	+	0.886082i	$0.346583\pi$
$212$	4.12653e9	+	7.14736e9i	0.140305	+	0.243016i
$213$	−1.41576e10			−0.471283
$214$	−2.88874e9			−0.0941558
$215$	−8.60627e9	+	5.06456e8i	−0.274689	+	0.0161647i
$216$	1.05601e9			0.0330086
$217$	−2.65099e10			−0.811596
$218$	9.72341e8	+	1.68414e9i	0.0291585	+	0.0505039i
$219$	3.26917e10			0.960372
$220$	−7.02484e9	−	1.21674e10i	−0.202178	−	0.350183i
$221$	5.90000e9	+	1.02191e10i	0.166374	+	0.288169i
$222$	4.83342e8	−	8.37173e8i	0.0133557	−	0.0231327i
$223$	3.78351e10			1.02453			0.512263	−	0.858828i	$-0.328807\pi$
$223$	3.78351e10			1.02453			0.512263	+	0.858828i	$0.328807\pi$
$224$	3.34956e9	−	5.80160e9i	0.0888938	−	0.153969i
$225$	1.99464e10	+	3.45482e10i	0.518852	+	0.898678i
$226$	5.24194e9			0.133661
$227$	7.85919e9	+	1.36125e10i	0.196454	+	0.340269i	0.947376	−	0.320122i	$-0.103724\pi$
$227$	7.85919e9	+	1.36125e10i	0.196454	+	0.340269i	−0.750922	+	0.660391i	$0.770391\pi$
$228$	−4.96514e10	+	8.59988e10i	−1.21682	+	2.10759i
$229$	−3.61632e9	+	6.26364e9i	−0.0868974	+	0.150511i	−0.906198	−	0.422853i	$-0.861029\pi$
$229$	−3.61632e9	+	6.26364e9i	−0.0868974	+	0.150511i	0.819301	+	0.573364i	$0.194362\pi$
$230$	1.05796e9	−	1.83244e9i	0.0249283	−	0.0431771i
$231$	−6.04304e10			−1.39637
$232$	−5.80466e9	+	1.00540e10i	−0.131547	+	0.227846i
$233$	1.83960e10	−	3.18629e10i	0.408905	−	0.708244i	−0.585862	−	0.810411i	$-0.699244\pi$
$233$	1.83960e10	−	3.18629e10i	0.408905	−	0.708244i	0.994767	+	0.102166i	$0.0325774\pi$
$234$	2.70982e9	+	4.69354e9i	0.0590838	+	0.102336i
$235$	8.37917e9	+	1.45132e10i	0.179224	+	0.310425i
$236$	2.54619e10			0.534302
$237$	−2.36402e10			−0.486725
$238$	4.34878e8	+	7.53230e8i	0.00878559	+	0.0152171i
$239$	2.45119e10	+	4.24558e10i	0.485943	+	0.841679i	0.999869	−	0.0161557i	$-0.00514275\pi$
$239$	2.45119e10	+	4.24558e10i	0.485943	+	0.841679i	−0.513926	+	0.857835i	$0.671809\pi$
$240$	1.00380e10	−	1.73863e10i	0.195297	−	0.338264i
$241$	−3.49049e10	+	6.04570e10i	−0.666514	+	1.15444i	0.312358	+	0.949964i	$0.398881\pi$
$241$	−3.49049e10	+	6.04570e10i	−0.666514	+	1.15444i	−0.978872	+	0.204472i	$0.934452\pi$
$242$	5.92139e9			0.110983
$243$	−3.89991e10	+	6.75484e10i	−0.717507	+	1.24276i
$244$	1.78652e10	−	3.09435e10i	0.322667	−	0.558875i
$245$	4.51507e9	−	7.82034e9i	0.0800603	−	0.138669i
$246$	−6.96853e9	−	1.20699e10i	−0.121320	−	0.210133i
$247$	−1.11889e11			−1.91271
$248$	6.90249e9	+	1.19555e10i	0.115871	+	0.200694i
$249$	4.07064e10	−	7.05056e10i	0.671067	−	1.16232i
$250$	−3.03202e9			−0.0490910
$251$	−1.71416e10	+	2.96902e10i	−0.272596	+	0.472151i	−0.969526	−	0.244989i	$-0.921216\pi$
$251$	−1.71416e10	+	2.96902e10i	−0.272596	+	0.472151i	0.696929	+	0.717140i	$0.254549\pi$
$252$	−2.30370e10	−	3.99013e10i	−0.359852	−	0.623283i
$253$	−9.43895e10	−	1.63487e11i	−1.44838	−	2.50866i
$254$	−7.94152e9			−0.119716
$255$	3.96702e9	+	6.87108e9i	0.0587535	+	0.101764i
$256$	6.28884e10			0.915147
$257$	−1.41797e10			−0.202754			−0.101377	−	0.994848i	$-0.532325\pi$
$257$	−1.41797e10			−0.202754			−0.101377	+	0.994848i	$0.532325\pi$
$258$	9.59672e9	−	5.64742e8i	0.134845	−	0.00793526i
$259$	−9.25967e9			−0.127864
$260$	2.28199e10			0.309695
$261$	5.99697e10	+	1.03871e11i	0.799926	+	1.38551i
$262$	−7.51270e9			−0.0985010
$263$	1.16737e10	+	2.02195e10i	0.150455	+	0.260596i	0.931395	−	0.364010i	$-0.118593\pi$
$263$	1.16737e10	+	2.02195e10i	0.150455	+	0.260596i	−0.780940	+	0.624607i	$0.785259\pi$
$264$	1.57345e10	+	2.72530e10i	0.199359	+	0.345299i
$265$	−3.12624e9	+	5.41480e9i	−0.0389417	+	0.0674491i
$266$	−8.24710e9			−0.101003
$267$	−5.56022e9	+	9.63058e9i	−0.0669562	+	0.115972i
$268$	1.61206e10	+	2.79216e10i	0.190886	+	0.330624i
$269$	−2.33180e10			−0.271522			−0.135761	−	0.990742i	$-0.543348\pi$
$269$	−2.33180e10			−0.271522			−0.135761	+	0.990742i	$0.543348\pi$
$270$	1.99144e8	+	3.44927e8i	0.00228050	+	0.00394994i
$271$	2.75236e10	−	4.76723e10i	0.309987	−	0.536913i	−0.668372	−	0.743827i	$-0.733009\pi$
$271$	2.75236e10	−	4.76723e10i	0.309987	−	0.536913i	0.978359	+	0.206914i	$0.0663420\pi$
$272$	−1.28897e10	+	2.23256e10i	−0.142785	+	0.247311i
$273$	4.90766e10	−	8.50031e10i	0.534739	−	0.926196i
$274$	1.27981e10			0.137172
$275$	−6.49671e10	+	1.12526e11i	−0.685009	+	1.18647i
$276$	1.36065e11	−	2.35672e11i	1.41142	−	2.44465i
$277$	4.92249e10	+	8.52601e10i	0.502373	+	0.870136i	0.999996	+	0.00274229i	$0.000872901\pi$
$277$	4.92249e10	+	8.52601e10i	0.502373	+	0.870136i	−0.497623	+	0.867393i	$0.665794\pi$
$278$	−4.36659e9	−	7.56316e9i	−0.0438471	−	0.0759454i
$279$	1.42623e11			1.40920
$280$	3.37861e9			0.0328494
$281$	1.08836e10	+	1.88509e10i	0.104134	+	0.180365i	0.913384	−	0.407099i	$-0.133460\pi$
$281$	1.08836e10	+	1.88509e10i	0.104134	+	0.180365i	−0.809250	+	0.587464i	$0.800126\pi$
$282$	−9.34349e9	−	1.61834e10i	−0.0879808	−	0.152387i
$283$	−1.53008e9	+	2.65018e9i	−0.0141800	+	0.0245604i	−0.873028	−	0.487670i	$-0.837847\pi$
$283$	−1.53008e9	+	2.65018e9i	−0.0141800	+	0.0245604i	0.858848	+	0.512230i	$0.171180\pi$
$284$	1.75788e10	−	3.04474e10i	0.160346	−	0.277727i
$285$	−7.52313e10			−0.675455
$286$	−8.82610e9	+	1.52872e10i	−0.0780048	+	0.135108i
$287$	−6.67502e10	+	1.15615e11i	−0.580743	+	1.00588i
$288$	−1.80206e10	+	3.12126e10i	−0.154349	+	0.267340i
$289$	5.41999e10	+	9.38770e10i	0.457044	+	0.791624i
$290$	−4.37860e9			−0.0363533
$291$	−1.68029e11	−	2.91036e11i	−1.37362	−	2.37918i
$292$	−4.05917e10	+	7.03069e10i	−0.326749	+	0.565946i
$293$	−1.06330e10			−0.0842855			−0.0421427	−	0.999112i	$-0.513418\pi$
$293$	−1.06330e10			−0.0842855			−0.0421427	+	0.999112i	$0.513418\pi$
$294$	−5.03469e9	+	8.72034e9i	−0.0393016	+	0.0680723i
$295$	9.64490e9	+	1.67055e10i	0.0741479	+	0.128428i
$296$	2.41098e9	+	4.17593e9i	0.0182549	+	0.0316185i
$297$	3.55347e10			0.265001
$298$	7.05757e9	+	1.22241e10i	0.0518420	+	0.0897930i
$299$	3.06621e11			2.21861
$300$	−1.87304e11			−1.33506
$301$	−5.06474e10	−	7.69047e10i	−0.355638	−	0.540012i
$302$	5.77653e9			0.0399609
$303$	1.72862e11			1.17817
$304$	−1.22221e11	−	2.11693e11i	−0.820759	−	1.42160i
$305$	2.70692e10			0.179113
$306$	−2.33964e9	−	4.05238e9i	−0.0152547	−	0.0264219i
$307$	−1.34034e11	−	2.32153e11i	−0.861175	−	1.49160i	−0.870796	−	0.491645i	$-0.836396\pi$
$307$	−1.34034e11	−	2.32153e11i	−0.861175	−	1.49160i	0.00962040	−	0.999954i	$-0.496938\pi$
$308$	7.50335e10	−	1.29962e11i	0.475091	−	0.822883i
$309$	1.22059e11			0.761650
$310$	−2.60336e9	+	4.50915e9i	−0.0160106	+	0.0277311i
$311$	6.08213e10	+	1.05346e11i	0.368667	+	0.638549i	0.989357	−	0.145506i	$-0.0464811\pi$
$311$	6.08213e10	+	1.05346e11i	0.368667	+	0.638549i	−0.620691	+	0.784056i	$0.713148\pi$
$312$	−5.11130e10			−0.305376
$313$	−1.53204e11	−	2.65358e11i	−0.902238	−	1.56272i	−0.824582	−	0.565742i	$-0.808590\pi$
$313$	−1.53204e11	−	2.65358e11i	−0.902238	−	1.56272i	−0.0776563	−	0.996980i	$-0.524744\pi$
$314$	5.02516e9	−	8.70384e9i	0.0291720	−	0.0505274i
$315$	1.74527e10	−	3.02290e10i	0.0998772	−	0.172992i
$316$	2.93529e10	−	5.08407e10i	0.165599	−	0.286827i
$317$	8.56329e10			0.476293			0.238146	−	0.971229i	$-0.423460\pi$
$317$	8.56329e10			0.476293			0.238146	+	0.971229i	$0.423460\pi$
$318$	3.48602e9	−	6.03796e9i	0.0191165	−	0.0331107i
$319$	−1.95326e11	+	3.38315e11i	−1.05609	+	1.82921i
$320$	2.44856e10	+	4.24102e10i	0.130537	+	0.226097i
$321$	−1.40733e11	−	2.43756e11i	−0.739815	−	1.28140i
$322$	2.26005e10			0.117156
$323$	9.66041e10			0.493838
$324$	−8.47808e10	−	1.46845e11i	−0.427410	−	0.740296i
$325$	−1.05522e11	−	1.82769e11i	−0.524646	−	0.908714i
$326$	6.19446e9	−	1.07291e10i	0.0303755	−	0.0526120i
$327$	−9.47404e10	+	1.64095e11i	−0.458216	+	0.793654i
$328$	6.95200e10			0.331648
$329$	−8.94994e10	+	1.55018e11i	−0.421152	+	0.729456i
$330$	−5.93446e9	+	1.02788e10i	−0.0275466	+	0.0477122i
$331$	−1.09373e11	+	1.89439e11i	−0.500822	+	0.867449i	0.499178	+	0.866500i	$0.333636\pi$
$331$	−1.09373e11	+	1.89439e11i	−0.500822	+	0.867449i	−1.00000		0.000949478i	$0.999698\pi$
$332$	1.01086e11	+	1.75087e11i	0.456637	+	0.790918i
$333$	4.98170e10			0.222013
$334$	−1.62134e9	−	2.80824e9i	−0.00712876	−	0.0123474i
$335$	−1.22129e10	+	2.11533e10i	−0.0529804	+	0.0917648i
$336$	2.14435e11			0.917842
$337$	−5.99690e10	+	1.03869e11i	−0.253275	+	0.438685i	−0.964426	−	0.264354i	$-0.914841\pi$
$337$	−5.99690e10	+	1.03869e11i	−0.253275	+	0.438685i	0.711150	+	0.703040i	$0.248174\pi$
$338$	−3.21231e9	−	5.56388e9i	−0.0133873	−	0.0231874i
$339$	2.55375e11	+	4.42323e11i	1.05022	+	1.81903i
$340$	−1.97026e10			−0.0799593
$341$	2.32268e11	+	4.02300e11i	0.930240	+	1.61122i
$342$	4.43694e10			0.175374
$343$	2.62205e11			1.02286
$344$	−2.14953e10	+	4.28649e10i	−0.0827619	+	0.165040i
$345$	2.06165e11			0.783481
$346$	7.78091e9			0.0291869
$347$	4.84899e10	+	8.39870e10i	0.179543	+	0.310978i	0.941724	−	0.336386i	$-0.109205\pi$
$347$	4.84899e10	+	8.39870e10i	0.179543	+	0.310978i	−0.762181	+	0.647364i	$0.775871\pi$
$348$	−5.63138e11			−2.05830
$349$	−2.08617e11	−	3.61336e11i	−0.752724	−	1.30376i	−0.946498	−	0.322711i	$-0.895406\pi$
$349$	−2.08617e11	−	3.61336e11i	−0.752724	−	1.30376i	0.193773	−	0.981046i	$-0.437927\pi$
$350$	−7.77781e9	−	1.34716e10i	−0.0277045	−	0.0479857i
$351$	−2.88583e10	+	4.99840e10i	−0.101482	+	0.175772i
$352$	−1.17389e11			−0.407555
$353$	−1.74442e11	+	3.02143e11i	−0.597951	+	1.03568i	0.395173	+	0.918607i	$0.370685\pi$
$353$	−1.74442e11	+	3.02143e11i	−0.597951	+	1.03568i	−0.993123	+	0.117074i	$0.962649\pi$
$354$	−1.07549e10	−	1.86280e10i	−0.0363991	−	0.0630452i
$355$	2.66352e10			0.0890080
$356$	−1.38077e10	−	2.39156e10i	−0.0455613	−	0.0789145i
$357$	−4.23725e10	+	7.33912e10i	−0.138063	+	0.239132i
$358$	2.01627e10	−	3.49228e10i	0.0648746	−	0.112366i
$359$	1.64719e11	−	2.85301e11i	0.523381	−	0.906522i	−0.476249	−	0.879311i	$-0.658004\pi$
$359$	1.64719e11	−	2.85301e11i	0.523381	−	0.906522i	0.999630	−	0.0272118i	$-0.00866285\pi$
$360$	−1.81769e10			−0.0570374
$361$	−2.96660e11	+	5.13831e11i	−0.919342	+	1.59235i
$362$	−2.25958e10	+	3.91371e10i	−0.0691575	+	0.119784i
$363$	2.88476e11	+	4.99656e11i	0.872028	+	1.51040i
$364$	1.21872e11	+	2.11088e11i	0.363871	+	0.630243i
$365$	−6.15042e10			−0.181379
$366$	−3.01845e10			−0.0879263
$367$	−2.45259e11	−	4.24802e11i	−0.705714	−	1.22233i	−0.966433	−	0.256917i	$-0.917293\pi$
$367$	−2.45259e11	−	4.24802e11i	−0.705714	−	1.22233i	0.260720	−	0.965414i	$-0.416040\pi$
$368$	3.34936e11	+	5.80127e11i	0.952023	+	1.64895i
$369$	3.59116e11	−	6.22007e11i	1.00836	−	1.74653i
$370$	−9.09329e8	+	1.57500e9i	−0.00252240	+	0.00436892i
$371$	−6.67838e10			−0.183016
$372$	−3.34822e11	+	5.79928e11i	−0.906505	+	1.57011i
$373$	1.53612e11	−	2.66064e11i	0.410899	−	0.711698i	−0.584089	−	0.811689i	$-0.698548\pi$
$373$	1.53612e11	−	2.66064e11i	0.410899	−	0.711698i	0.994988	+	0.0999914i	$0.0318815\pi$
$374$	7.62041e9	−	1.31989e10i	0.0201398	−	0.0348832i
$375$	−1.47713e11	−	2.55846e11i	−0.385725	−	0.668095i
$376$	9.32132e10			0.240509
$377$	−3.17255e11	−	5.49503e11i	−0.808859	−	1.40099i
$378$	−2.12709e9	+	3.68423e9i	−0.00535886	+	0.00928182i
$379$	−2.19420e11			−0.546261			−0.273131	−	0.961977i	$-0.588059\pi$
$379$	−2.19420e11			−0.546261			−0.273131	+	0.961977i	$0.588059\pi$
$380$	9.34110e10	−	1.61793e11i	0.229812	−	0.398045i
$381$	−3.86892e11	−	6.70117e11i	−0.940649	−	1.62925i
$382$	−1.54738e10	−	2.68014e10i	−0.0371803	−	0.0643981i
$383$	−6.85500e10			−0.162785			−0.0813923	−	0.996682i	$-0.525937\pi$
$383$	−6.85500e10			−0.162785			−0.0813923	+	0.996682i	$0.525937\pi$
$384$	−1.12647e11	−	1.95111e11i	−0.264381	−	0.457921i
$385$	1.13690e11			0.263724
$386$	4.92521e10			0.112923
$387$	2.72483e11	+	4.13747e11i	0.617504	+	0.937639i
$388$	8.34536e11			1.86940
$389$	1.10820e11			0.245383			0.122692	−	0.992445i	$-0.460847\pi$
$389$	1.10820e11			0.245383			0.122692	+	0.992445i	$0.460847\pi$
$390$	−9.63895e9	−	1.66951e10i	−0.0210979	−	0.0365426i
$391$	−2.64735e11			−0.572817
$392$	−2.51137e10	−	4.34982e10i	−0.0537185	−	0.0930432i
$393$	−3.66001e11	−	6.33933e11i	−0.773956	−	1.34053i
$394$	7.94331e8	−	1.37582e9i	0.00166061	−	0.00287627i
$395$	4.44752e10			0.0919244
$396$	−4.03680e11	+	6.99195e11i	−0.824915	+	1.42880i
$397$	1.47821e11	+	2.56034e11i	0.298662	+	0.517298i	0.975830	−	0.218531i	$-0.0701264\pi$
$397$	1.47821e11	+	2.56034e11i	0.298662	+	0.517298i	−0.677168	+	0.735828i	$0.736793\pi$
$398$	1.88318e10			0.0376200
$399$	−4.01779e11	−	6.95902e11i	−0.793615	−	1.37458i
$400$	2.30533e11	−	3.99294e11i	0.450259	−	0.779872i
$401$	−8.29182e10	+	1.43618e11i	−0.160140	+	0.277371i	−0.934919	−	0.354862i	$-0.884528\pi$
$401$	−8.29182e10	+	1.43618e11i	−0.160140	+	0.277371i	0.774779	+	0.632233i	$0.217861\pi$
$402$	1.36184e10	−	2.35877e10i	0.0260081	−	0.0450473i
$403$	−7.54515e11			−1.42494
$404$	−2.14634e11	+	3.71757e11i	−0.400851	+	0.694294i
$405$	6.42294e10	−	1.11249e11i	0.118628	−	0.205469i
$406$	−2.33843e10	−	4.05028e10i	−0.0427127	−	0.0739806i
$407$	8.11291e10	+	1.40520e11i	0.146555	+	0.253841i
$408$	4.41307e10			0.0788443
$409$	9.27923e11			1.63967			0.819836	−	0.572599i	$-0.194065\pi$
$409$	9.27923e11			1.63967			0.819836	+	0.572599i	$0.194065\pi$
$410$	1.31102e10	+	2.27075e10i	0.0229129	+	0.0396864i
$411$	6.23492e11	+	1.07992e12i	1.07781	+	1.86682i
$412$	−1.51554e11	+	2.62500e11i	−0.259138	+	0.448840i
$413$	−1.03019e11	+	1.78434e11i	−0.174238	+	0.301788i
$414$	−1.21590e11			−0.203422
$415$	−7.65825e10	+	1.32645e11i	−0.126740	+	0.219520i
$416$	9.53337e10	−	1.65123e11i	0.156073	−	0.270326i
$417$	4.25460e11	−	7.36918e11i	0.689043	−	1.19346i
$418$	7.22574e10	+	1.25153e11i	0.115768	+	0.200516i
$419$	4.97140e11			0.787981			0.393991	−	0.919114i	$-0.371094\pi$
$419$	4.97140e11			0.787981			0.393991	+	0.919114i	$0.371094\pi$
$420$	8.19438e10	+	1.41931e11i	0.128497	+	0.222564i
$421$	4.50371e11	−	7.80065e11i	0.698716	−	1.21021i	−0.270196	−	0.962805i	$-0.587088\pi$
$421$	4.50371e11	−	7.80065e11i	0.698716	−	1.21021i	0.968912	−	0.247407i	$-0.0795783\pi$
$422$	5.59954e10			0.0859501
$423$	4.81507e11	−	8.33994e11i	0.731258	−	1.26658i
$424$	1.73887e10	+	3.01182e10i	0.0261289	+	0.0452567i
$425$	9.11069e10	+	1.57802e11i	0.135457	+	0.234618i
$426$	−2.97006e10			−0.0436940
$427$	1.44566e11	+	2.50395e11i	0.210445	+	0.364502i
$428$	6.98965e11			1.00684
$429$	−1.71995e12			−2.45164
$430$	−1.80547e10	+	1.06247e9i	−0.0254672	+	0.00149868i
$431$	−2.31786e11			−0.323549			−0.161775	−	0.986828i	$-0.551722\pi$
$431$	−2.31786e11			−0.323549			−0.161775	+	0.986828i	$0.551722\pi$
$432$	−1.26093e11			−0.174186
$433$	2.65136e11	+	4.59228e11i	0.362470	+	0.627817i	0.988367	−	0.152089i	$-0.0486000\pi$
$433$	2.65136e11	+	4.59228e11i	0.362470	+	0.627817i	−0.625896	+	0.779906i	$0.715267\pi$
$434$	−5.56139e10			−0.0752453
$435$	−2.13315e11	−	3.69473e11i	−0.285641	−	0.494744i
$436$	−2.35269e11	−	4.07498e11i	−0.311800	−	0.540053i
$437$	1.25512e12	−	2.17393e12i	1.64634	−	2.85154i
$438$	6.85824e10			0.0890387
$439$	−5.44892e9	+	9.43780e9i	−0.00700197	+	0.0121278i	−0.869505	−	0.493924i	$-0.835562\pi$
$439$	−5.44892e9	+	9.43780e9i	−0.00700197	+	0.0121278i	0.862503	+	0.506052i	$0.168895\pi$
$440$	−2.96019e10	−	5.12720e10i	−0.0376515	−	0.0652143i
$441$	−5.18915e11			−0.653315
$442$	1.23773e10	+	2.14381e10i	0.0154250	+	0.0267170i
$443$	−2.48498e11	+	4.30412e11i	−0.306554	+	0.530966i	−0.977606	−	0.210443i	$-0.932509\pi$
$443$	−2.48498e11	+	4.30412e11i	−0.306554	+	0.530966i	0.671052	+	0.741410i	$0.265843\pi$
$444$	−1.16950e11	+	2.02564e11i	−0.142816	+	0.247365i
$445$	1.04606e10	−	1.81184e10i	0.0126456	−	0.0219028i
$446$	7.93725e10			0.0949867
$447$	−6.87656e11	+	1.19106e12i	−0.814681	+	1.41107i
$448$	−2.61535e11	+	4.52991e11i	−0.306745	+	0.531299i
$449$	−6.95008e11	−	1.20379e12i	−0.807015	−	1.39779i	−0.914922	−	0.403630i	$-0.867748\pi$
$449$	−6.95008e11	−	1.20379e12i	−0.807015	−	1.39779i	0.107908	−	0.994161i	$-0.465585\pi$
$450$	4.18446e10	+	7.24770e10i	0.0481042	+	0.0833189i
$451$	2.33934e12			2.66256
$452$	−1.26835e12			−1.42927
$453$	2.81419e11	+	4.87432e11i	0.313987	+	0.543841i
$454$	1.64874e10	+	2.85570e10i	0.0182138	+	0.0315473i
$455$	−9.23295e10	+	1.59919e11i	−0.100993	+	0.174924i
$456$	−2.09226e11	+	3.62389e11i	−0.226607	+	0.392495i
$457$	1.18196e12			1.26759			0.633797	−	0.773499i	$-0.281495\pi$
$457$	1.18196e12			1.26759			0.633797	+	0.773499i	$0.281495\pi$
$458$	−7.58649e9	+	1.31402e10i	−0.00805650	+	0.0139543i
$459$	2.49161e10	−	4.31560e10i	0.0262013	−	0.0453820i
$460$	−2.55985e11	+	4.43379e11i	−0.266565	+	0.461705i
$461$	−2.54171e11	−	4.40236e11i	−0.262102	−	0.453975i	0.704698	−	0.709507i	$-0.251083\pi$
$461$	−2.54171e11	−	4.40236e11i	−0.262102	−	0.453975i	−0.966800	+	0.255533i	$0.917749\pi$
$462$	−1.26774e11			−0.129462
$463$	−8.36324e11	−	1.44855e12i	−0.845785	−	1.46494i	−0.884938	−	0.465709i	$-0.845799\pi$
$463$	−8.36324e11	−	1.44855e12i	−0.845785	−	1.46494i	0.0391530	−	0.999233i	$-0.487534\pi$
$464$	6.93106e11	−	1.20050e12i	0.694175	−	1.20235i
$465$	−5.07318e11			−0.503202
$466$	3.85921e10	−	6.68435e10i	0.0379107	−	0.0656633i
$467$	−1.85505e11	−	3.21303e11i	−0.180480	−	0.312600i	0.761564	−	0.648089i	$-0.224432\pi$
$467$	−1.85505e11	−	3.21303e11i	−0.180480	−	0.312600i	−0.942044	+	0.335489i	$0.891098\pi$
$468$	−6.55671e11	−	1.13566e12i	−0.631800	−	1.09431i
$469$	−2.60895e11			−0.248994
$470$	1.75783e10	+	3.04464e10i	0.0166163	+	0.0287803i
$471$	9.79257e11			0.916859
$472$	1.07294e11			0.0995028
$473$	−7.23314e11	+	1.44240e12i	−0.664434	+	1.32498i
$474$	−4.95936e10			−0.0451256
$475$	−1.72777e12			−1.55727
$476$	−1.05224e11	−	1.82253e11i	−0.0939468	−	0.162721i
$477$	3.59297e11			0.317776
$478$	5.14222e10	+	8.90659e10i	0.0450532	+	0.0780344i
$479$	6.71825e11	+	1.16363e12i	0.583104	+	1.00997i	0.995109	+	0.0987844i	$0.0314954\pi$
$479$	6.71825e11	+	1.16363e12i	0.583104	+	1.00997i	−0.412005	+	0.911182i	$0.635171\pi$
$480$	6.41002e10	−	1.11025e11i	0.0551155	−	0.0954628i
$481$	−2.63545e11			−0.224493
$482$	−7.32253e10	+	1.26830e11i	−0.0617944	+	0.107031i
$483$	1.10104e12	+	1.90706e12i	0.920538	+	1.59442i
$484$	−1.43275e12			−1.18677
$485$	3.16120e11	+	5.47536e11i	0.259426	+	0.449340i
$486$	−8.18143e10	+	1.41706e11i	−0.0665221	+	0.115220i
$487$	−9.02452e11	+	1.56309e12i	−0.727015	+	1.25923i	0.231124	+	0.972924i	$0.425760\pi$
$487$	−9.02452e11	+	1.56309e12i	−0.727015	+	1.25923i	−0.958139	+	0.286303i	$0.907574\pi$
$488$	7.52821e10	−	1.30392e11i	0.0600901	−	0.104079i
$489$	1.20712e12			0.954684
$490$	9.47195e9	−	1.64059e10i	0.00742262	−	0.0128563i
$491$	−4.43915e11	+	7.68883e11i	−0.344693	+	0.597026i	−0.985298	−	0.170845i	$-0.945350\pi$
$491$	−4.43915e11	+	7.68883e11i	−0.344693	+	0.597026i	0.640605	+	0.767871i	$0.278684\pi$
$492$	1.68612e12	+	2.92044e12i	1.29731	+	2.24701i
$493$	2.73917e11	+	4.74438e11i	0.208837	+	0.361716i
$494$	−2.34726e11			−0.177333
$495$	−6.11652e11			−0.457911
$496$	−8.24192e11	−	1.42754e12i	−0.611450	−	1.05906i
$497$	1.42248e11	+	2.46381e11i	0.104578	+	0.181135i
$498$	8.53960e10	−	1.47910e11i	0.0622165	−	0.107762i
$499$	−7.54681e11	+	1.30715e12i	−0.544893	+	0.943782i	0.453721	+	0.891144i	$0.350096\pi$
$499$	−7.54681e11	+	1.30715e12i	−0.544893	+	0.943782i	−0.998614	+	0.0526378i	$0.983237\pi$
$500$	7.33631e11			0.524944
$501$	1.57975e11	−	2.73622e11i	0.112026	−	0.194035i
$502$	−3.59606e10	+	6.22855e10i	−0.0252732	+	0.0437744i
$503$	1.63681e11	−	2.83504e11i	0.114010	−	0.197471i	−0.803374	−	0.595475i	$-0.796964\pi$
$503$	1.63681e11	−	2.83504e11i	0.114010	−	0.197471i	0.917383	+	0.398004i	$0.130297\pi$
$504$	−9.70756e10	−	1.68140e11i	−0.0670151	−	0.116074i
$505$	−3.25211e11			−0.222512
$506$	−1.98015e11	−	3.42972e11i	−0.134283	−	0.232585i
$507$	3.12992e11	−	5.42118e11i	0.210377	−	0.364383i
$508$	1.92154e12			1.28016
$509$	−7.28055e11	+	1.26103e12i	−0.480766	+	0.832712i	−0.999756	−	0.0220686i	$-0.992975\pi$
$509$	−7.28055e11	+	1.26103e12i	−0.480766	+	0.832712i	0.518990	+	0.854780i	$0.326308\pi$
$510$	8.32222e9	+	1.44145e10i	0.00544720	+	0.00943483i
$511$	−3.28468e11	−	5.68924e11i	−0.213108	−	0.369114i
$512$	6.96256e11			0.447769
$513$	2.36257e11	+	4.09209e11i	0.150611	+	0.260865i
$514$	−2.97469e10			−0.0187979
$515$	−2.29634e11			−0.143848
$516$	−2.32204e12	+	1.36646e11i	−1.44193	+	0.0848540i
$517$	3.13662e12			1.93087
$518$	−1.94254e10			−0.0118546
$519$	3.79068e11	+	6.56565e11i	0.229332	+	0.397214i
$520$	9.61608e10			0.0576744
$521$	−1.19940e12	−	2.07742e12i	−0.713171	−	1.23525i	−0.963661	−	0.267128i	$-0.913925\pi$
$521$	−1.19940e12	−	2.07742e12i	−0.713171	−	1.23525i	0.250490	−	0.968119i	$-0.419408\pi$
$522$	1.25808e11	+	2.17905e11i	0.0741634	+	0.128455i
$523$	8.07674e10	−	1.39893e11i	0.0472040	−	0.0817597i	−0.841458	−	0.540322i	$-0.818302\pi$
$523$	8.07674e10	−	1.39893e11i	0.0472040	−	0.0817597i	0.888662	+	0.458563i	$0.151636\pi$
$524$	1.81778e12			1.05330
$525$	7.57833e11	−	1.31261e12i	0.435368	−	0.754080i
$526$	2.44897e10	+	4.24174e10i	0.0139491	+	0.0241606i
$527$	6.51445e11			0.367900
$528$	−1.87878e12	−	3.25414e12i	−1.05202	−	1.82215i
$529$	−2.53897e12	+	4.39763e12i	−1.40964	+	2.44156i
$530$	−6.55838e9	+	1.13594e10i	−0.00361040	+	0.00625339i
$531$	5.54242e11	−	9.59975e11i	0.302534	−	0.524004i
$532$	1.99548e12			1.08005
$533$	−1.89982e12	+	3.29058e12i	−1.01962	+	1.76604i
$534$	−1.16645e10	+	2.02035e10i	−0.00620770	+	0.0107520i
$535$	2.64766e11	+	4.58588e11i	0.139724	+	0.242009i
$536$	6.79303e10	+	1.17659e11i	0.0355485	+	0.0615719i
$537$	3.92912e12			2.03897
$538$	−4.89176e10			−0.0251736
$539$	−8.45074e11	−	1.46371e12i	−0.431266	−	0.746975i
$540$	−4.81851e10	−	8.34590e10i	−0.0243860	−	0.0422378i
$541$	1.65773e12	−	2.87126e12i	0.832003	−	1.44107i	−0.0644445	−	0.997921i	$-0.520528\pi$
$541$	1.65773e12	−	2.87126e12i	0.832003	−	1.44107i	0.896447	−	0.443150i	$-0.146139\pi$
$542$	5.77404e10	−	1.00009e11i	0.0287398	−	0.0497787i
$543$	−4.40326e12			−2.17358
$544$	−8.23107e10	+	1.42566e11i	−0.0402959	+	0.0697946i
$545$	1.78239e11	−	3.08718e11i	0.0865401	−	0.149892i
$546$	1.02955e11	−	1.78324e11i	0.0495772	−	0.0858702i
$547$	−1.99119e12	−	3.44884e12i	−0.950975	−	1.64714i	−0.743322	−	0.668934i	$-0.766751\pi$
$547$	−1.99119e12	−	3.44884e12i	−0.950975	−	1.64714i	−0.207653	−	0.978203i	$-0.566582\pi$
$548$	−3.09664e12			−1.46682
$549$	−7.77762e11	−	1.34712e12i	−0.365402	−	0.632896i
$550$	−1.36291e11	+	2.36063e11i	−0.0635091	+	0.110001i
$551$	−5.19461e12			−2.40088
$552$	5.73364e11	−	9.93096e11i	0.262848	−	0.455266i
$553$	2.37524e11	+	4.11403e11i	0.108005	+	0.187070i
$554$	1.03267e11	+	1.78863e11i	0.0465764	+	0.0806727i
$555$	−1.77202e11			−0.0792773
$556$	1.05655e12	+	1.82999e12i	0.468869	+	0.812106i
$557$	2.56276e12			1.12813			0.564066	−	0.825729i	$-0.309236\pi$
$557$	2.56276e12			1.12813			0.564066	+	0.825729i	$0.309236\pi$
$558$	2.99203e11			0.130651
$559$	−1.44151e12	−	2.18883e12i	−0.624400	−	0.948111i
$560$	−4.03424e11			−0.173347
$561$	1.48499e12			0.632983
$562$	2.28321e10	+	3.95463e10i	0.00965455	+	0.0167222i
$563$	−9.94302e11			−0.417091			−0.208545	−	0.978013i	$-0.566873\pi$
$563$	−9.94302e11			−0.417091			−0.208545	+	0.978013i	$0.566873\pi$
$564$	2.26076e12	+	3.91576e12i	0.940804	+	1.62952i
$565$	−4.80447e11	−	8.32158e11i	−0.198348	−	0.343548i
$566$	−3.20988e9	+	5.55968e9i	−0.00131467	+	0.00227707i
$567$	1.37209e12			0.557519
$568$	7.40752e10	−	1.28302e11i	0.0298611	−	0.0517209i
$569$	−1.71881e12	−	2.97707e12i	−0.687423	−	1.19065i	−0.972669	−	0.232196i	$-0.925409\pi$
$569$	−1.71881e12	−	2.97707e12i	−0.687423	−	1.19065i	0.285246	−	0.958454i	$-0.407925\pi$
$570$	−1.57824e11			−0.0626233
$571$	8.29269e11	+	1.43634e12i	0.326462	+	0.565449i	0.981807	−	0.189881i	$-0.0608101\pi$
$571$	8.29269e11	+	1.43634e12i	0.326462	+	0.565449i	−0.655345	+	0.755330i	$0.727477\pi$
$572$	2.13557e12	−	3.69892e12i	0.834128	−	1.44475i
$573$	1.50770e12	−	2.61141e12i	0.584276	−	1.01200i
$574$	−1.40032e11	+	2.42542e11i	−0.0538423	+	0.0932576i
$575$	4.73480e12			1.80633
$576$	1.40706e12	−	2.43709e12i	0.532611	−	0.922509i
$577$	2.52722e11	−	4.37728e11i	0.0949188	−	0.164404i	−0.814656	−	0.579945i	$-0.803074\pi$
$577$	2.52722e11	−	4.37728e11i	0.0949188	−	0.164404i	0.909575	+	0.415540i	$0.136408\pi$
$578$	1.13703e11	+	1.96940e11i	0.0423738	+	0.0733937i
$579$	2.39945e12	+	4.15596e12i	0.887273	+	1.53680i
$580$	1.05945e12			0.388737
$581$	−1.63598e12			−0.595643
$582$	−3.52501e11	−	6.10549e11i	−0.127352	−	0.220581i
$583$	5.85129e11	+	1.01347e12i	0.209770	+	0.363332i
$584$	−1.71049e11	+	2.96266e11i	−0.0608503	+	0.105396i
$585$	4.96733e11	−	8.60367e11i	0.175356	−	0.303726i
$586$	−2.23065e10			−0.00781434
$587$	−9.58705e11	+	1.66053e12i	−0.333283	+	0.577263i	−0.983154	−	0.182782i	$-0.941490\pi$
$587$	−9.58705e11	+	1.66053e12i	−0.333283	+	0.577263i	0.649870	+	0.760045i	$0.274823\pi$
$588$	1.21820e12	−	2.10999e12i	0.420263	−	0.727916i
$589$	−3.08853e12	+	5.34949e12i	−1.05738	+	1.83144i
$590$	2.02336e10	+	3.50456e10i	0.00687446	+	0.0119069i
$591$	1.54792e11			0.0521920
$592$	−2.87883e11	−	4.98628e11i	−0.0963314	−	0.166851i
$593$	1.84934e12	−	3.20316e12i	0.614146	−	1.06373i	−0.376388	−	0.926462i	$-0.622834\pi$
$593$	1.84934e12	−	3.20316e12i	0.614146	−	1.06373i	0.990534	−	0.137269i	$-0.0438325\pi$
$594$	7.45464e10			0.0245690
$595$	7.97169e10	−	1.38074e11i	0.0260750	−	0.0451632i
$596$	−1.70766e12	−	2.95775e12i	−0.554361	−	0.960182i
$597$	9.17443e11	+	1.58906e12i	0.295593	+	0.511983i
$598$	6.43245e11			0.205694
$599$	1.01096e11	+	1.75104e11i	0.0320860	+	0.0555745i	0.881622	−	0.471955i	$-0.156452\pi$
$599$	1.01096e11	+	1.75104e11i	0.0320860	+	0.0555745i	−0.849537	+	0.527530i	$0.823118\pi$
$600$	−7.89279e11			−0.248628
$601$	−1.84901e12			−0.578101			−0.289050	−	0.957314i	$-0.593340\pi$
$601$	−1.84901e12			−0.578101			−0.289050	+	0.957314i	$0.593340\pi$
$602$	−1.06251e11	−	1.61335e11i	−0.0329722	−	0.0500661i
$603$	1.40362e12			0.432335
$604$	−1.39770e12			−0.427313
$605$	−5.42721e11	−	9.40021e11i	−0.164694	−	0.285258i
$606$	3.62638e11			0.109231
$607$	−4.20263e11	−	7.27916e11i	−0.125653	−	0.217637i	0.796335	−	0.604856i	$-0.206769\pi$
$607$	−4.20263e11	−	7.27916e11i	−0.125653	−	0.217637i	−0.921988	+	0.387219i	$0.873436\pi$
$608$	−7.80477e11	−	1.35183e12i	−0.231630	−	0.401194i
$609$	2.27846e12	−	3.94640e12i	0.671217	−	1.16258i
$610$	5.67872e10			0.0166060
$611$	−2.54730e12	+	4.41205e12i	−0.739425	+	1.28072i
$612$	5.66103e11	+	9.80520e11i	0.163123	+	0.282537i
$613$	4.18815e11			0.119798			0.0598991	−	0.998204i	$-0.480922\pi$
$613$	4.18815e11			0.119798			0.0598991	+	0.998204i	$0.480922\pi$
$614$	−2.81183e11	−	4.87023e11i	−0.0798420	−	0.138290i
$615$	−1.27739e12	+	2.21251e12i	−0.360069	+	0.623659i
$616$	3.16183e11	−	5.47645e11i	0.0884760	−	0.153245i
$617$	3.34860e11	−	5.79994e11i	0.0930208	−	0.161117i	−0.815760	−	0.578390i	$-0.803681\pi$
$617$	3.34860e11	−	5.79994e11i	0.0930208	−	0.161117i	0.908781	+	0.417274i	$0.137014\pi$
$618$	2.56061e11			0.0706147
$619$	4.03888e11	−	6.99554e11i	0.110574	−	0.191520i	−0.805428	−	0.592694i	$-0.798064\pi$
$619$	4.03888e11	−	6.99554e11i	0.110574	−	0.191520i	0.916002	+	0.401174i	$0.131398\pi$
$620$	6.29912e11	−	1.09104e12i	0.171205	−	0.296537i
$621$	−6.47441e11	−	1.12140e12i	−0.174698	−	0.302586i
$622$	1.27594e11	+	2.20999e11i	0.0341801	+	0.0592017i
$623$	2.23464e11			0.0594308
$624$	6.10315e12			1.61147
$625$	−1.48504e12	−	2.57216e12i	−0.389293	−	0.674275i
$626$	−3.21400e11	−	5.56681e11i	−0.0836490	−	0.144884i
$627$	−7.04042e12	+	1.21944e13i	−1.81926	+	3.15105i
$628$	−1.21590e12	+	2.10599e12i	−0.311945	+	0.540304i
$629$	2.27544e11			0.0579611
$630$	3.66133e10	−	6.34160e10i	0.00925989	−	0.0160386i
$631$	3.84731e11	−	6.66374e11i	0.0966107	−	0.167335i	−0.813669	−	0.581328i	$-0.802533\pi$
$631$	3.84731e11	−	6.66374e11i	0.0966107	−	0.167335i	0.910280	+	0.413994i	$0.135866\pi$
$632$	1.23690e11	−	2.14237e11i	0.0308395	−	0.0534156i
$633$	2.72797e12	+	4.72498e12i	0.675340	+	1.16972i
$634$	1.79645e11			0.0441584
$635$	7.27875e11	+	1.26072e12i	0.177654	+	0.307706i
$636$	−8.43482e11	+	1.46095e12i	−0.204418	+	0.354062i
$637$	2.74520e12			0.660611
$638$	−4.09766e11	+	7.09735e11i	−0.0979134	+	0.169591i
$639$	−7.65293e11	−	1.32553e12i	−0.181583	−	0.314510i
$640$	2.11927e11	+	3.67069e11i	0.0499318	+	0.0864844i
$641$	−1.48332e12			−0.347035			−0.173517	−	0.984831i	$-0.555513\pi$
$641$	−1.48332e12			−0.347035			−0.173517	+	0.984831i	$0.555513\pi$
$642$	−2.95237e11	−	5.11365e11i	−0.0685903	−	0.118802i
$643$	1.00954e12			0.232904			0.116452	−	0.993196i	$-0.462848\pi$
$643$	1.00954e12			0.232904			0.116452	+	0.993196i	$0.462848\pi$
$644$	−5.46844e12			−1.25279
$645$	−9.69234e11	−	1.47172e12i	−0.220501	−	0.334816i
$646$	2.02661e11			0.0457851
$647$	−6.67837e12			−1.49831			−0.749154	−	0.662396i	$-0.769540\pi$
$647$	−6.67837e12			−1.49831			−0.749154	+	0.662396i	$0.769540\pi$
$648$	−3.57257e11	−	6.18787e11i	−0.0795963	−	0.137865i
$649$	3.61042e12			0.798835
$650$	−2.21369e11	−	3.83422e11i	−0.0486414	−	0.0842494i
$651$	−2.70938e12	−	4.69278e12i	−0.591228	−	1.02404i
$652$	−1.49882e12	+	2.59603e12i	−0.324814	+	0.562595i
$653$	−3.96154e12			−0.852620			−0.426310	−	0.904577i	$-0.640187\pi$
$653$	−3.96154e12			−0.852620			−0.426310	+	0.904577i	$0.640187\pi$
$654$	−1.98751e11	+	3.44247e11i	−0.0424825	+	0.0735818i
$655$	6.88572e11	+	1.19264e12i	0.146172	+	0.253177i
$656$	−8.30104e12			−1.75011
$657$	1.76716e12	+	3.06081e12i	0.370026	+	0.640903i
$658$	−1.87756e11	+	3.25204e11i	−0.0390462	+	0.0676299i
$659$	2.25747e12	−	3.91006e12i	0.466271	−	0.807605i	−0.532987	−	0.846124i	$-0.678930\pi$
$659$	2.25747e12	−	3.91006e12i	0.466271	−	0.807605i	0.999258	+	0.0385184i	$0.0122638\pi$
$660$	1.43591e12	−	2.48707e12i	0.294564	−	0.510200i
$661$	−2.96967e12			−0.605064			−0.302532	−	0.953139i	$-0.597832\pi$
$661$	−2.96967e12			−0.605064			−0.302532	+	0.953139i	$0.597832\pi$
$662$	−2.29448e11	+	3.97415e11i	−0.0464326	+	0.0804236i
$663$	−1.20599e12	+	2.08883e12i	−0.242400	+	0.419849i
$664$	4.25967e11	+	7.37796e11i	0.0850392	+	0.147292i
$665$	7.55883e11	+	1.30923e12i	0.149885	+	0.259608i
$666$	1.04509e11			0.0205835
$667$	1.42354e13			2.78485
$668$	3.92301e11	+	6.79485e11i	0.0762299	+	0.132034i
$669$	3.86684e12	+	6.69756e12i	0.746343	+	1.29270i
$670$	−2.56207e10	+	4.43764e10i	−0.00491196	+	0.00850777i
$671$	2.53324e12	−	4.38769e12i	0.482419	−	0.835574i
$672$	1.36933e12			0.259028
$673$	−1.26587e12	+	2.19255e12i	−0.237859	+	0.411984i	−0.960100	−	0.279658i	$-0.909779\pi$
$673$	−1.26587e12	+	2.19255e12i	−0.237859	+	0.411984i	0.722241	+	0.691642i	$0.243112\pi$
$674$	−1.25806e11	+	2.17903e11i	−0.0234818	+	0.0406717i
$675$	−4.45625e11	+	7.71846e11i	−0.0826234	+	0.143108i
$676$	7.77254e11	+	1.34624e12i	0.143154	+	0.247950i
$677$	8.15281e12			1.49162			0.745810	−	0.666159i	$-0.232063\pi$
$677$	8.15281e12			1.49162			0.745810	+	0.666159i	$0.232063\pi$
$678$	5.35739e11	+	9.27927e11i	0.0973687	+	0.168648i
$679$	−3.37653e12	+	5.84833e12i	−0.609617	+	1.05589i
$680$	−8.30247e10			−0.0148908
$681$	−1.60646e12	+	2.78246e12i	−0.286224	+	0.495755i
$682$	4.87264e11	+	8.43966e11i	0.0862451	+	0.149381i
$683$	−2.01766e11	−	3.49468e11i	−0.0354776	−	0.0614490i	0.847741	−	0.530410i	$-0.177962\pi$
$683$	−2.01766e11	−	3.49468e11i	−0.0354776	−	0.0614490i	−0.883219	+	0.468961i	$0.844629\pi$
$684$	−1.07357e13			−1.87533
$685$	−1.17300e12	−	2.03169e12i	−0.203559	−	0.352574i
$686$	5.50067e11			0.0948324
$687$	−1.47838e12			−0.253211
$688$	2.56665e12	−	5.11829e12i	0.436735	−	0.870918i
$689$	−1.90077e12			−0.321324
$690$	4.32503e11			0.0726387
$691$	3.73112e12	+	6.46250e12i	0.622571	+	1.07832i	0.989005	+	0.147880i	$0.0472450\pi$
$691$	3.73112e12	+	6.46250e12i	0.622571	+	1.07832i	−0.366435	+	0.930444i	$0.619422\pi$
$692$	−1.88268e12			−0.312104
$693$	−3.26658e12	−	5.65789e12i	−0.538015	−	0.931869i
$694$	1.01725e11	+	1.76192e11i	0.0166459	+	0.0288316i
$695$	−8.00434e11	+	1.38639e12i	−0.130135	+	0.225400i
$696$	−2.37300e12			−0.383316
$697$	1.64029e12	−	2.84107e12i	0.263253	−	0.455968i
$698$	−4.37648e11	−	7.58029e11i	−0.0697872	−	0.120875i
$699$	7.52047e12			1.19151
$700$	1.88193e12	+	3.25960e12i	0.296253	+	0.513124i
$701$	5.87178e12	−	1.01702e13i	0.918414	−	1.59074i	0.116589	−	0.993180i	$-0.462804\pi$
$701$	5.87178e12	−	1.01702e13i	0.918414	−	1.59074i	0.801825	−	0.597559i	$-0.203863\pi$
$702$	−6.05404e10	+	1.04859e11i	−0.00940867	+	0.0162963i
$703$	−1.07879e12	+	1.86853e12i	−0.166586	+	0.288536i
$704$	9.16579e12			1.40635
$705$	−1.71274e12	+	2.96656e12i	−0.261121	+	0.452274i
$706$	−3.65954e11	+	6.33850e11i	−0.0554377	+	0.0960209i
$707$	−1.73682e12	−	3.00826e12i	−0.261437	−	0.452823i
$708$	2.60227e12	+	4.50726e12i	0.389226	+	0.674160i
$709$	−4.28865e12			−0.637401			−0.318701	−	0.947855i	$-0.603246\pi$
$709$	−4.28865e12			−0.637401			−0.318701	+	0.947855i	$0.603246\pi$
$710$	5.58768e10			0.00825218
$711$	−1.27788e12	−	2.21335e12i	−0.187532	−	0.324815i
$712$	−5.81841e10	−	1.00778e11i	−0.00848486	−	0.0146962i
$713$	8.46384e12	−	1.46598e13i	1.22649	−	2.12435i
$714$	−8.88911e10	+	1.53964e11i	−0.0128002	+	0.0221706i
$715$	3.23580e12			0.463025
$716$	−4.87859e12	+	8.44997e12i	−0.693723	+	1.20156i
$717$	−5.01034e12	+	8.67817e12i	−0.707997	+	1.22629i
$718$	3.45555e11	−	5.98519e11i	0.0485241	−	0.0840462i
$719$	3.19600e12	+	5.53563e12i	0.445991	+	0.772480i	0.998121	−	0.0612788i	$-0.0195179\pi$
$719$	3.19600e12	+	5.53563e12i	0.445991	+	0.772480i	−0.552129	+	0.833758i	$0.686185\pi$
$720$	2.17042e12			0.300987
$721$	−1.22638e12	−	2.12415e12i	−0.169011	−	0.292736i
$722$	−6.22349e11	+	1.07794e12i	−0.0852348	+	0.147631i
$723$	−1.42695e13			−1.94216
$724$	5.46731e12	−	9.46966e12i	0.739521	−	1.28089i
$725$	−4.89901e12	−	8.48534e12i	−0.658548	−	1.14064i
$726$	6.05181e11	+	1.04820e12i	0.0808482	+	0.140033i
$727$	−2.07077e11			−0.0274934			−0.0137467	−	0.999906i	$-0.504376\pi$
$727$	−2.07077e11			−0.0274934			−0.0137467	+	0.999906i	$0.504376\pi$
$728$	5.13555e11	+	8.89504e11i	0.0677635	+	0.117370i
$729$	−9.36816e12			−1.22852
$730$	−1.29027e11			−0.0168161
$731$	1.24459e12	+	1.88983e12i	0.161212	+	0.244790i
$732$	7.30348e12			0.940221
$733$	−5.40052e12			−0.690983			−0.345492	−	0.938422i	$-0.612288\pi$
$733$	−5.40052e12			−0.690983			−0.345492	+	0.938422i	$0.612288\pi$
$734$	−5.14518e11	−	8.91171e11i	−0.0654287	−	0.113326i
$735$	1.84580e12			0.233288
$736$	2.13883e12	+	3.70456e12i	0.268674	+	0.465357i
$737$	2.28585e12	+	3.95920e12i	0.285393	+	0.494315i
$738$	7.53372e11	−	1.30488e12i	0.0934880	−	0.161926i
$739$	5.83514e12			0.719700			0.359850	−	0.933010i	$-0.382828\pi$
$739$	5.83514e12			0.719700			0.359850	+	0.933010i	$0.382828\pi$
$740$	2.20023e11	−	3.81090e11i	0.0269727	−	0.0467181i
$741$	−1.14353e13	−	1.98065e13i	−1.39337	−	2.41338i
$742$	−1.40102e11			−0.0169679
$743$	−2.13078e12	−	3.69061e12i	−0.256500	−	0.444272i	0.708802	−	0.705408i	$-0.249236\pi$
$743$	−2.13078e12	−	3.69061e12i	−0.256500	−	0.444272i	−0.965302	+	0.261136i	$0.915903\pi$
$744$	−1.41090e12	+	2.44375e12i	−0.168818	+	0.292401i
$745$	1.29371e12	−	2.24078e12i	0.153863	−	0.266499i
$746$	3.22255e11	−	5.58162e11i	0.0380956	−	0.0659835i
$747$	8.80158e12			1.03423
$748$	−1.84384e12	+	3.19363e12i	−0.215361	+	0.373016i
$749$	−2.82801e12	+	4.89826e12i	−0.328332	+	0.568688i
$750$	−3.09879e11	−	5.36727e11i	−0.0357616	−	0.0619409i
$751$	−4.55149e12	−	7.88341e12i	−0.522124	−	0.904345i	−0.999669	−	0.0257377i	$-0.991807\pi$
$751$	−4.55149e12	−	7.88341e12i	−0.522124	−	0.904345i	0.477545	−	0.878607i	$-0.341527\pi$
$752$	−1.11301e13			−1.26917
$753$	−7.00766e12			−0.794320
$754$	−6.65555e11	−	1.15277e12i	−0.0749916	−	0.129889i
$755$	−5.29444e11	−	9.17023e11i	−0.0593005	−	0.102711i
$756$	5.14674e11	−	8.91441e11i	0.0573039	−	0.0992532i
$757$	7.98896e12	−	1.38373e13i	0.884217	−	1.53151i	0.0376087	−	0.999293i	$-0.488026\pi$
$757$	7.98896e12	−	1.38373e13i	0.884217	−	1.53151i	0.846608	−	0.532216i	$-0.178641\pi$
$758$	−4.60311e11			−0.0506454
$759$	1.92937e13	−	3.34176e13i	2.11021	−	3.65500i
$760$	3.93624e11	−	6.81777e11i	0.0427977	−	0.0741278i
$761$	2.53345e12	−	4.38807e12i	0.273830	−	0.474288i	−0.696009	−	0.718033i	$-0.745043\pi$
$761$	2.53345e12	−	4.38807e12i	0.273830	−	0.474288i	0.969839	+	0.243745i	$0.0783760\pi$
$762$	−8.11643e11	−	1.40581e12i	−0.0872102	−	0.151053i
$763$	3.80760e12			0.406715
$764$	3.74407e12	+	6.48492e12i	0.397579	+	0.688627i
$765$	−4.28877e11	+	7.42836e11i	−0.0452748	+	0.0784182i
$766$	−1.43808e11			−0.0150922
$767$	−2.93208e12	+	5.07852e12i	−0.305912	+	0.529856i
$768$	6.42735e12	+	1.11325e13i	0.666663	+	1.15469i
$769$	−2.81335e12	−	4.87287e12i	−0.290105	−	0.502477i	0.683729	−	0.729736i	$-0.260357\pi$
$769$	−2.81335e12	−	4.87287e12i	−0.290105	−	0.502477i	−0.973834	+	0.227259i	$0.927024\pi$
$770$	2.38505e11			0.0244506
$771$	−1.44920e12	−	2.51009e12i	−0.147701	−	0.255826i
$772$	−1.19171e13			−1.20752
$773$	8.08358e12			0.814322			0.407161	−	0.913356i	$-0.366519\pi$
$773$	8.08358e12			0.814322			0.407161	+	0.913356i	$0.366519\pi$
$774$	5.71628e11	+	8.67980e11i	0.0572505	+	0.0869312i
$775$	−1.16511e13			−1.16014
$776$	3.51664e12			0.348137
$777$	−9.46361e11	−	1.63914e12i	−0.0931456	−	0.161333i
$778$	2.32484e11			0.0227502
$779$	1.55534e13	+	2.69393e13i	1.51324	+	2.62100i
$780$	2.33225e12	+	4.03958e12i	0.225606	+	0.390760i
$781$	2.49262e12	−	4.31735e12i	0.239733	−	0.415229i
$782$	−5.55375e11			−0.0531075
$783$	−1.33979e12	+	2.32059e12i	−0.127382	+	0.220633i
$784$	2.99871e12	+	5.19391e12i	0.283473	+	0.490989i
$785$	−1.84231e12			−0.173161
$786$	−7.67816e11	−	1.32990e12i	−0.0717556	−	0.124284i
$787$	−2.65865e12	+	4.60492e12i	−0.247045	+	0.427894i	−0.962705	−	0.270555i	$-0.912793\pi$
$787$	−2.65865e12	+	4.60492e12i	−0.247045	+	0.427894i	0.715660	+	0.698449i	$0.246126\pi$
$788$	−1.92197e11	+	3.32896e11i	−0.0177574	+	0.0307567i
$789$	−2.38616e12	+	4.13295e12i	−0.219206	+	0.379677i
$790$	9.33023e10			0.00852257
$791$	5.13174e12	−	8.88843e12i	0.466090	−	0.807292i
$792$	−1.70107e12	+	2.94633e12i	−0.153624	+	0.266084i
$793$	4.11457e12	+	7.12664e12i	0.369483	+	0.639964i
$794$	3.10107e11	+	5.37121e11i	0.0276898	+	0.0479601i
$795$	−1.27804e12			−0.113473
$796$	−4.55658e12			−0.402281
$797$	6.48717e12	+	1.12361e13i	0.569499	+	0.986400i	0.996616	+	0.0822041i	$0.0261959\pi$
$797$	6.48717e12	+	1.12361e13i	0.569499	+	0.986400i	−0.427117	+	0.904196i	$0.640471\pi$
$798$	−8.42873e11	−	1.45990e12i	−0.0735782	−	0.127441i
$799$	2.19932e12	−	3.80934e12i	0.190910	−	0.330666i
$800$	1.47213e12	−	2.54980e12i	0.127069	−	0.220091i
$801$	−1.20224e12			−0.103191
$802$	−1.73950e11	+	3.01290e11i	−0.0148470	+	0.0257158i
$803$	−5.75579e12	+	9.96931e12i	−0.488523	+	0.846146i
$804$	−3.29512e12	+	5.70731e12i	−0.278112	+	0.481703i
$805$	−2.07143e12	−	3.58782e12i	−0.173856	−	0.301127i
$806$	−1.58286e12			−0.132110
$807$	−2.38315e12	−	4.12774e12i	−0.197798	−	0.342595i
$808$	−9.04445e11	+	1.56654e12i	−0.0746502	+	0.129298i
$809$	8.82575e12			0.724408			0.362204	−	0.932099i	$-0.382024\pi$
$809$	8.82575e12			0.724408			0.362204	+	0.932099i	$0.382024\pi$
$810$	1.34744e11	−	2.33383e11i	0.0109983	−	0.0190496i
$811$	3.78052e12	+	6.54805e12i	0.306872	+	0.531518i	0.977676	−	0.210116i	$-0.0673842\pi$
$811$	3.78052e12	+	6.54805e12i	0.306872	+	0.531518i	−0.670804	+	0.741635i	$0.734051\pi$
$812$	5.65810e12	+	9.80012e12i	0.456739	+	0.791096i
$813$	1.12519e13			0.903272
$814$	1.70197e11	+	2.94789e11i	0.0135876	+	0.0235343i
$815$	−2.27100e12			−0.180305
$816$	−5.26943e12			−0.416062
$817$	−2.14194e13	+	1.26047e12i	−1.68193	+	0.0989771i
$818$	1.94664e12			0.152019
$819$	1.06114e13			0.824128
$820$	−3.17215e12	−	5.49433e12i	−0.245014	−	0.424378i
$821$	−2.45610e11			−0.0188670			−0.00943349	−	0.999956i	$-0.503003\pi$
$821$	−2.45610e11			−0.0188670			−0.00943349	+	0.999956i	$0.503003\pi$
$822$	1.30799e12	+	2.26551e12i	0.0999269	+	0.173078i
$823$	−2.75494e12	−	4.77169e12i	−0.209321	−	0.362554i	0.742180	−	0.670201i	$-0.233792\pi$
$823$	−2.75494e12	−	4.77169e12i	−0.209321	−	0.362554i	−0.951501	+	0.307646i	$0.900459\pi$
$824$	−6.38634e11	+	1.10615e12i	−0.0482591	+	0.0835873i
$825$	−2.65592e13			−1.99605
$826$	−2.16118e11	+	3.74328e11i	−0.0161541	+	0.0279796i
$827$	7.74698e12	+	1.34182e13i	0.575914	+	0.997513i	0.995942	+	0.0900013i	$0.0286871\pi$
$827$	7.74698e12	+	1.34182e13i	0.575914	+	0.997513i	−0.420027	+	0.907511i	$0.637980\pi$
$828$	2.94202e13			2.17525
$829$	9.05417e12	+	1.56823e13i	0.665815	+	1.15322i	0.979064	+	0.203554i	$0.0652491\pi$
$829$	9.05417e12	+	1.56823e13i	0.665815	+	1.15322i	−0.313249	+	0.949671i	$0.601418\pi$
$830$	−1.60659e11	+	2.78269e11i	−0.0117504	+	0.0203523i
$831$	−1.00618e13	+	1.74276e13i	−0.731934	+	1.26775i
$832$	−7.44369e12	+	1.28929e13i	−0.538559	+	0.932812i
$833$	−2.37019e12			−0.170561
$834$	8.92552e11	−	1.54595e12i	0.0638831	−	0.110649i
$835$	−2.97205e11	+	5.14774e11i	−0.0211576	+	0.0366461i
$836$	−1.74835e13	−	3.02823e13i	−1.23794	−	2.14418i
$837$	1.59318e12	+	2.75948e12i	0.112202	+	0.194340i
$838$	1.04293e12			0.0730560
$839$	−1.75638e13			−1.22374			−0.611870	−	0.790959i	$-0.709582\pi$
$839$	−1.75638e13			−1.22374			−0.611870	+	0.790959i	$0.709582\pi$
$840$	3.45302e11	+	5.98081e11i	0.0239300	+	0.0414480i
$841$	−7.47552e12	−	1.29480e13i	−0.515299	−	0.892524i
$842$	9.44811e11	−	1.63646e12i	0.0647799	−	0.112202i
$843$	−2.22465e12	+	3.85321e12i	−0.151718	+	0.262784i
$844$	−1.35487e13			−0.919089
$845$	−5.88844e11	+	1.01991e12i	−0.0397324	+	0.0688185i
$846$	1.01013e12	−	1.74960e12i	0.0677970	−	0.117428i
$847$	5.79690e12	−	1.00405e13i	0.387009	−	0.670319i
$848$	−2.07630e12	−	3.59626e12i	−0.137883	−	0.238820i
$849$	−6.25512e11			−0.0413191
$850$	1.91129e11	+	3.31045e11i	0.0125586	+	0.0217521i
$851$	2.95634e12	−	5.12053e12i	0.193229	−	0.334682i
$852$	7.18639e12			0.467232
$853$	3.92410e11	−	6.79674e11i	0.0253787	−	0.0439572i	−0.853057	−	0.521818i	$-0.825254\pi$
$853$	3.92410e11	−	6.79674e11i	0.0253787	−	0.0439572i	0.878436	+	0.477860i	$0.158588\pi$
$854$	3.03277e11	+	5.25291e11i	0.0195110	+	0.0337940i
$855$	−4.06665e12	−	7.04364e12i	−0.260249	−	0.450764i
$856$	2.94536e12			0.187502
$857$	−9.98059e11	−	1.72869e12i	−0.0632037	−	0.109472i	0.832692	−	0.553736i	$-0.186798\pi$
$857$	−9.98059e11	−	1.72869e12i	−0.0632037	−	0.109472i	−0.895896	+	0.444264i	$0.853465\pi$
$858$	−3.60819e12			−0.227299
$859$	1.50016e13			0.940088			0.470044	−	0.882643i	$-0.344238\pi$
$859$	1.50016e13			0.940088			0.470044	+	0.882643i	$0.344238\pi$
$860$	4.36854e12	−	2.57077e11i	0.272328	−	0.0160258i
$861$	−2.72881e13			−1.69223
$862$	−4.86253e11			−0.0299971
$863$	8.93303e12	+	1.54725e13i	0.548214	+	0.949534i	0.998397	+	0.0565981i	$0.0180254\pi$
$863$	8.93303e12	+	1.54725e13i	0.548214	+	0.949534i	−0.450183	+	0.892936i	$0.648641\pi$
$864$	−8.05202e11			−0.0491579
$865$	−7.13154e11	−	1.23522e12i	−0.0433123	−	0.0750191i
$866$	5.56215e11	+	9.63393e11i	0.0336056	+	0.0582067i
$867$	−1.10787e13	+	1.91889e13i	−0.665892	+	1.15336i
$868$	1.34564e13			0.804620
$869$	4.16215e12	−	7.20906e12i	0.247588	−	0.428834i
$870$	−4.47503e11	−	7.75099e11i	−0.0264825	−	0.0458691i
$871$	−7.42550e12			−0.437163
$872$	−9.91398e11	−	1.71715e12i	−0.0580663	−	0.100574i
$873$	1.81658e13	−	3.14640e13i	1.05850	−	1.83337i
$874$	2.63306e12	−	4.56059e12i	0.152637	−	0.264374i
$875$	−2.96827e12	+	5.14120e12i	−0.171186	+	0.296502i
$876$	−1.65943e13			−0.952117
$877$	6.79144e12	−	1.17631e13i	0.387671	−	0.671467i	−0.604464	−	0.796632i	$-0.706613\pi$
$877$	6.79144e12	−	1.17631e13i	0.387671	−	0.671467i	0.992136	+	0.125166i	$0.0399462\pi$
$878$	−1.14310e10	+	1.97991e10i	−0.000649172	+	0.00112440i
$879$	−1.08672e12	−	1.88226e12i	−0.0614000	−	0.106348i
$880$	3.53462e12	+	6.12214e12i	0.198687	+	0.344137i
$881$	2.29963e13			1.28607			0.643037	−	0.765835i	$-0.277674\pi$
$881$	2.29963e13			1.28607			0.643037	+	0.765835i	$0.277674\pi$
$882$	−1.08861e12			−0.0605706
$883$	1.00742e13	+	1.74491e13i	0.557684	+	0.965937i	0.997689	+	0.0679418i	$0.0216432\pi$
$883$	1.00742e13	+	1.74491e13i	0.557684	+	0.965937i	−0.440005	+	0.897995i	$0.645023\pi$
$884$	−2.99483e12	−	5.18720e12i	−0.164944	−	0.285692i
$885$	−1.97146e12	+	3.41468e12i	−0.108030	+	0.187113i
$886$	−5.21312e11	+	9.02939e11i	−0.0284214	+	0.0492274i
$887$	1.15027e13			0.623943			0.311972	−	0.950091i	$-0.399011\pi$
$887$	1.15027e13			0.623943			0.311972	+	0.950091i	$0.399011\pi$
$888$	−4.92815e11	+	8.53581e11i	−0.0265966	+	0.0460666i
$889$	−7.77456e12	+	1.34659e13i	−0.417463	+	0.723067i
$890$	2.19449e10	−	3.80096e10i	0.00117241	−	0.00203067i
$891$	−1.20217e13	−	2.08221e13i	−0.639020	−	1.10682i
$892$	−1.92051e13			−1.01572
$893$	2.08542e13	+	3.61205e13i	1.09739	+	1.90074i
$894$	−1.44260e12	+	2.49866e12i	−0.0755313	+	0.130824i
$895$	−7.39199e12			−0.385086
$896$	−2.26363e12	+	3.92073e12i	−0.117333	+	0.203227i
$897$	3.13374e13	+	5.42780e13i	1.61621	+	2.79935i
$898$	−1.45802e12	−	2.52537e12i	−0.0748206	−	0.129593i
$899$	−3.50296e13			−1.78861
$900$	−1.01248e13	−	1.75366e13i	−0.514392	−	0.890953i
$901$	1.64112e12			0.0829618
$902$	4.90759e12			0.246853
$903$	8.43737e12	−	1.68254e13i	0.422291	−	0.842115i
$904$	−5.34468e12			−0.266173
$905$	8.28401e12			0.410508
$906$	5.90375e11	+	1.02256e12i	0.0291106	+	0.0504210i
$907$	1.90342e12			0.0933905			0.0466952	−	0.998909i	$-0.485131\pi$
$907$	1.90342e12			0.0933905			0.0466952	+	0.998909i	$0.485131\pi$
$908$	−3.98932e12	−	6.90970e12i	−0.194766	−	0.337344i
$909$	9.34409e12	+	1.61844e13i	0.453941	+	0.786249i
$910$	−1.93694e11	+	3.35487e11i	−0.00936330	+	0.0162177i
$911$	−2.07837e13			−0.999745			−0.499873	−	0.866099i	$-0.666620\pi$
$911$	−2.07837e13			−0.999745			−0.499873	+	0.866099i	$0.666620\pi$
$912$	2.49826e13	−	4.32711e13i	1.19581	−	2.07120i
$913$	1.43337e13	+	2.48268e13i	0.682717	+	1.18250i
$914$	2.47958e12			0.117522
$915$	2.76654e12	+	4.79178e12i	0.130479	+	0.225997i
$916$	1.83564e12	−	3.17942e12i	0.0861504	−	0.149217i
$917$	−7.35476e12	+	1.27388e13i	−0.343484	+	0.594932i
$918$	5.22703e10	−	9.05348e10i	0.00242920	−	0.00420749i
$919$	−2.14314e13			−0.991130			−0.495565	−	0.868571i	$-0.665039\pi$
$919$	−2.14314e13			−0.991130			−0.495565	+	0.868571i	$0.665039\pi$
$920$	−1.07869e12	+	1.86835e12i	−0.0496423	+	0.0859830i
$921$	2.73971e13	−	4.74532e13i	1.25469	−	2.17319i
$922$	−5.33212e11	−	9.23550e11i	−0.0243002	−	0.0420893i
$923$	4.04860e12	+	7.01238e12i	0.183610	+	0.318023i
$924$	3.06744e13			1.38437
$925$	−4.06963e12			−0.182775
$926$	−1.75448e12	−	3.03885e12i	−0.0784151	−	0.135819i
$927$	6.59792e12	+	1.14279e13i	0.293459	+	0.508287i
$928$	4.42602e12	−	7.66609e12i	0.195906	−	0.339319i
$929$	7.92418e12	−	1.37251e13i	0.349047	−	0.604567i	−0.637034	−	0.770836i	$-0.719839\pi$
$929$	7.92418e12	−	1.37251e13i	0.349047	−	0.604567i	0.986080	+	0.166269i	$0.0531721\pi$
$930$	−1.06428e12			−0.0466532
$931$	1.12372e13	−	1.94633e13i	0.490211	−	0.849071i
$932$	−9.33781e12	+	1.61736e13i	−0.405390	+	0.702157i
$933$	−1.24322e13	+	2.15331e13i	−0.537130	+	0.930336i
$934$	−3.89161e11	−	6.74047e11i	−0.0167328	−	0.0289820i
$935$	−2.79377e12			−0.119547
$936$	−2.76293e12	−	4.78553e12i	−0.117660	−	0.203793i
$937$	−1.55957e12	+	2.70125e12i	−0.0660962	+	0.114482i	−0.897180	−	0.441666i	$-0.854388\pi$
$937$	−1.55957e12	+	2.70125e12i	−0.0660962	+	0.114482i	0.831084	+	0.556148i	$0.187721\pi$
$938$	−5.47319e11			−0.0230849
$939$	3.13157e13	−	5.42403e13i	1.31452	−	2.27681i
$940$	−4.25326e12	−	7.36686e12i	−0.177683	−	0.307756i
$941$	6.95764e12	+	1.20510e13i	0.289273	+	0.501036i	0.973637	−	0.228105i	$-0.0732530\pi$
$941$	6.95764e12	+	1.20510e13i	0.289273	+	0.501036i	−0.684363	+	0.729141i	$0.739920\pi$
$942$	2.05433e12			0.0850045
$943$	−4.26227e13	−	7.38247e13i	−1.75525	−	3.04018i
$944$	−1.28114e13			−0.525077
$945$	7.79828e11			0.0318094
$946$	−1.51741e12	+	3.02594e12i	−0.0616015	+	0.122843i
$947$	3.36988e13			1.36157			0.680785	−	0.732484i	$-0.261639\pi$
$947$	3.36988e13			1.36157			0.680785	+	0.732484i	$0.261639\pi$
$948$	1.19997e13			0.482541
$949$	−9.34874e12	−	1.61925e13i	−0.374158	−	0.648061i
$950$	−3.62460e12			−0.144379
$951$	8.75188e12	+	1.51587e13i	0.346968	+	0.600966i
$952$	−4.43401e11	−	7.67993e11i	−0.0174957	−	0.0303034i
$953$	−1.69299e13	+	2.93234e13i	−0.664869	+	1.15159i	0.314452	+	0.949273i	$0.398179\pi$
$953$	−1.69299e13	+	2.93234e13i	−0.664869	+	1.15159i	−0.979321	+	0.202314i	$0.935154\pi$
$954$	7.53751e11			0.0294619
$955$	−2.83649e12	+	4.91294e12i	−0.110348	+	0.191129i
$956$	−1.24422e13	−	2.15505e13i	−0.481766	−	0.834444i
$957$	−7.98513e13			−3.07736
$958$	1.40939e12	+	2.44113e12i	0.0540612	+	0.0936368i
$959$	1.25290e13	−	2.17009e13i	0.478336	−	0.828502i
$960$	−5.00496e12	+	8.66885e12i	−0.190187	+	0.329413i
$961$	−7.60751e12	+	1.31766e13i	−0.287731	+	0.498365i
$962$	−5.52878e11			−0.0208133
$963$	1.52147e13	−	2.63526e13i	0.570093	−	0.987429i
$964$	1.77177e13	−	3.06879e13i	0.660785	−	1.14451i
$965$	−4.51417e12	−	7.81877e12i	−0.167573	−	0.290245i
$966$	2.30982e12	+	4.00073e12i	0.0853456	+	0.147823i
$967$	−3.70603e13			−1.36298			−0.681490	−	0.731827i	$-0.738668\pi$
$967$	−3.70603e13			−1.36298			−0.681490	+	0.731827i	$0.738668\pi$
$968$	−6.03745e12			−0.221011
$969$	9.87317e12	+	1.71008e13i	0.359749	+	0.623103i
$970$	6.63173e11	+	1.14865e12i	0.0240521	+	0.0416595i
$971$	−2.25488e12	+	3.90557e12i	−0.0814024	+	0.140993i	−0.903853	−	0.427844i	$-0.859273\pi$
$971$	−2.25488e12	+	3.90557e12i	−0.0814024	+	0.140993i	0.822450	+	0.568837i	$0.192607\pi$
$972$	1.97959e13	−	3.42875e13i	0.711339	−	1.23208i
$973$	−1.70992e13			−0.611599
$974$	−1.89321e12	+	3.27913e12i	−0.0674036	+	0.116747i
$975$	2.15691e13	−	3.73588e13i	0.764385	−	1.32395i
$976$	−8.98907e12	+	1.55695e13i	−0.317096	+	0.549226i
$977$	5.17495e12	+	8.96328e12i	0.181711	+	0.314733i	0.942463	−	0.334310i	$-0.108503\pi$
$977$	5.17495e12	+	8.96328e12i	0.181711	+	0.314733i	−0.760752	+	0.649042i	$0.775170\pi$
$978$	2.53235e12			0.0885115
$979$	−1.95789e12	−	3.39117e12i	−0.0681187	−	0.117985i
$980$	−2.29185e12	+	3.96959e12i	−0.0793722	+	0.137477i
$981$	−2.04849e13			−0.706192
$982$	−9.31267e11	+	1.61300e12i	−0.0319575	+	0.0553520i
$983$	5.43424e12	+	9.41237e12i	0.185630	+	0.321520i	0.943789	−	0.330550i	$-0.107234\pi$
$983$	5.43424e12	+	9.41237e12i	0.185630	+	0.321520i	−0.758159	+	0.652070i	$0.773901\pi$
$984$	7.10511e12	+	1.23064e13i	0.241598	+	0.418459i
$985$	−2.91216e11			−0.00985715
$986$	5.74637e11	+	9.95300e11i	0.0193619	+	0.0335357i
$987$	−3.65882e13			−1.22720
$988$	5.67946e13			1.89627
$989$	5.86980e13	−	3.45422e12i	1.95092	−	0.114807i
$990$	−1.28316e12			−0.0424542
$991$	4.66036e13			1.53493			0.767465	−	0.641091i	$-0.221518\pi$
$991$	4.66036e13			1.53493			0.767465	+	0.641091i	$0.221518\pi$
$992$	−5.26311e12	−	9.11597e12i	−0.172560	−	0.298882i
$993$	−4.47127e13			−1.45935
$994$	2.98415e11	+	5.16870e11i	0.00969576	+	0.0167935i
$995$	−1.72602e12	−	2.98955e12i	−0.0558267	−	0.0966946i
$996$	−2.06625e13	+	3.57886e13i	−0.665298	+	1.15233i
$997$	5.75025e12			0.184314			0.0921571	−	0.995744i	$-0.470624\pi$
$997$	5.75025e12			0.184314			0.0921571	+	0.995744i	$0.470624\pi$
$998$	−1.58321e12	+	2.74220e12i	−0.0505185	+	0.0875006i
$999$	5.56485e11	+	9.63860e11i	0.0176770	+	0.0306175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.c.a.36.18	yes	64
43.6	even	3	inner	43.10.c.a.6.18	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.c.a.6.18	✓	64	43.6	even	3	inner
43.10.c.a.36.18	yes	64	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+2.09785 q^{2} +(102.202 + 177.020i) q^{3} -507.599 q^{4} +(-192.277 - 333.034i) q^{5} +(214.405 + 371.361i) q^{6} +(2053.75 - 3557.19i) q^{7} -2138.97 q^{8} +(-11049.2 + 19137.7i) q^{9} +O(q^{10})\)	\(q+2.09785 q^{2} +(102.202 + 177.020i) q^{3} -507.599 q^{4} +(-192.277 - 333.034i) q^{5} +(214.405 + 371.361i) q^{6} +(2053.75 - 3557.19i) q^{7} -2138.97 q^{8} +(-11049.2 + 19137.7i) q^{9} +(-403.369 - 698.655i) q^{10} -71976.0 q^{11} +(-51877.8 - 89855.0i) q^{12} +(58452.9 - 101243. i) q^{13} +(4308.45 - 7462.46i) q^{14} +(39302.4 - 68073.7i) q^{15} +255403. q^{16} +(-50468.0 + 87413.1i) q^{17} +(-23179.5 + 40148.0i) q^{18} +(-478542. - 828858. i) q^{19} +(97599.7 + 169048. i) q^{20} +839591. q^{21} -150995. q^{22} +(1.31140e6 + 2.27141e6i) q^{23} +(-218608. - 378639. i) q^{24} +(902621. - 1.56339e6i) q^{25} +(122626. - 212394. i) q^{26} -493701. q^{27} +(-1.04248e6 + 1.80563e6i) q^{28} +(2.71377e6 - 4.70039e6i) q^{29} +(82450.5 - 142808. i) q^{30} +(-3.22702e6 - 5.58936e6i) q^{31} +1.63095e6 q^{32} +(-7.35612e6 - 1.27412e7i) q^{33} +(-105874. + 183380. i) q^{34} -1.57955e6 q^{35} +(5.60854e6 - 9.71428e6i) q^{36} +(-1.12717e6 - 1.95231e6i) q^{37} +(-1.00391e6 - 1.73882e6i) q^{38} +2.38961e7 q^{39} +(411274. + 712348. i) q^{40} -3.25017e7 q^{41} +1.76134e6 q^{42} +(1.00494e7 - 2.00400e7i) q^{43} +3.65350e7 q^{44} +8.49800e6 q^{45} +(2.75113e6 + 4.76509e6i) q^{46} -4.35786e7 q^{47} +(2.61028e7 + 4.52115e7i) q^{48} +(1.17411e7 + 2.03361e7i) q^{49} +(1.89357e6 - 3.27975e6i) q^{50} -2.06318e7 q^{51} +(-2.96706e7 + 5.13911e7i) q^{52} +(-8.12950e6 - 1.40807e7i) q^{53} -1.03571e6 q^{54} +(1.38393e7 + 2.39704e7i) q^{55} +(-4.39290e6 + 7.60872e6i) q^{56} +(9.78162e7 - 1.69423e8i) q^{57} +(5.69308e6 - 9.86071e6i) q^{58} -5.01615e7 q^{59} +(-1.99498e7 + 3.45541e7i) q^{60} +(-3.51956e7 + 6.09605e7i) q^{61} +(-6.76981e6 - 1.17257e7i) q^{62} +(4.53843e7 + 7.86080e7i) q^{63} -1.27345e8 q^{64} -4.49566e7 q^{65} +(-1.54320e7 - 2.67291e7i) q^{66} +(-3.17585e7 - 5.50073e7i) q^{67} +(2.56175e7 - 4.43708e7i) q^{68} +(-2.68057e8 + 4.64288e8i) q^{69} -3.31367e6 q^{70} +(-3.46313e7 + 5.99832e7i) q^{71} +(2.36338e7 - 4.09349e7i) q^{72} +(7.99681e7 - 1.38509e8i) q^{73} +(-2.36463e6 - 4.09566e6i) q^{74} +3.69000e8 q^{75} +(2.42907e8 + 4.20728e8i) q^{76} +(-1.47821e8 + 2.56033e8i) q^{77} +5.01305e7 q^{78} +(-5.78269e7 + 1.00159e8i) q^{79} +(-4.91083e7 - 8.50580e7i) q^{80} +(1.67023e8 + 2.89292e8i) q^{81} -6.81837e7 q^{82} +(-1.99146e8 - 3.44931e8i) q^{83} -4.26176e8 q^{84} +3.88153e7 q^{85} +(2.10821e7 - 4.20410e7i) q^{86} +1.10941e9 q^{87} +1.53954e8 q^{88} +(2.72020e7 + 4.71152e7i) q^{89} +1.78275e7 q^{90} +(-2.40095e8 - 4.15857e8i) q^{91} +(-6.65666e8 - 1.15297e9i) q^{92} +(6.59618e8 - 1.14249e9i) q^{93} -9.14214e7 q^{94} +(-1.84025e8 + 3.18741e8i) q^{95} +(1.66687e8 + 2.88710e8i) q^{96} -1.64409e9 q^{97} +(2.46310e7 + 4.26621e7i) q^{98} +(7.95274e8 - 1.37746e9i) 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

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