LMFDB - Embedded newform 43.10.c.a.36.10

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			36.10
Character	$\chi$	$=$	43.36
Dual form			43.10.c.a.6.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-25.2231 q^{2} +(-62.6577 - 108.526i) q^{3} +124.205 q^{4} +(1186.15 + 2054.47i) q^{5} +(1580.42 + 2737.37i) q^{6} +(1704.14 - 2951.66i) q^{7} +9781.39 q^{8} +(1989.53 - 3445.96i) q^{9} +O(q^{10})$	\(q-25.2231 q^{2} +(-62.6577 - 108.526i) q^{3} +124.205 q^{4} +(1186.15 + 2054.47i) q^{5} +(1580.42 + 2737.37i) q^{6} +(1704.14 - 2951.66i) q^{7} +9781.39 q^{8} +(1989.53 - 3445.96i) q^{9} +(-29918.4 - 51820.2i) q^{10} -93392.8 q^{11} +(-7782.41 - 13479.5i) q^{12} +(-12909.2 + 22359.4i) q^{13} +(-42983.7 + 74449.9i) q^{14} +(148643. - 257457. i) q^{15} -310310. q^{16} +(312220. - 540781. i) q^{17} +(-50182.1 + 86917.9i) q^{18} +(120008. + 207860. i) q^{19} +(147326. + 255176. i) q^{20} -427110. q^{21} +2.35566e6 q^{22} +(1.04238e6 + 1.80546e6i) q^{23} +(-612879. - 1.06154e6i) q^{24} +(-1.83735e6 + 3.18238e6i) q^{25} +(325610. - 563974. i) q^{26} -2.96522e6 q^{27} +(211663. - 366611. i) q^{28} +(975944. - 1.69039e6i) q^{29} +(-3.74924e6 + 6.49387e6i) q^{30} +(147505. + 255487. i) q^{31} +2.81892e6 q^{32} +(5.85178e6 + 1.01356e7i) q^{33} +(-7.87517e6 + 1.36402e7i) q^{34} +8.08547e6 q^{35} +(247110. - 428007. i) q^{36} +(1.49862e6 + 2.59569e6i) q^{37} +(-3.02698e6 - 5.24289e6i) q^{38} +3.23545e6 q^{39} +(1.16022e7 + 2.00956e7i) q^{40} -1.70390e7 q^{41} +1.07730e7 q^{42} +(-1.68242e7 + 1.48168e7i) q^{43} -1.15999e7 q^{44} +9.43953e6 q^{45} +(-2.62921e7 - 4.55392e7i) q^{46} +2.92066e7 q^{47} +(1.94433e7 + 3.36768e7i) q^{48} +(1.43686e7 + 2.48872e7i) q^{49} +(4.63436e7 - 8.02695e7i) q^{50} -7.82520e7 q^{51} +(-1.60339e6 + 2.77716e6i) q^{52} +(4.36055e7 + 7.55270e7i) q^{53} +7.47921e7 q^{54} +(-1.10778e8 - 1.91873e8i) q^{55} +(1.66688e7 - 2.88713e7i) q^{56} +(1.50389e7 - 2.60481e7i) q^{57} +(-2.46164e7 + 4.26368e7i) q^{58} -8.12593e7 q^{59} +(1.84622e7 - 3.19775e7i) q^{60} +(-1.93975e7 + 3.35974e7i) q^{61} +(-3.72055e6 - 6.44417e6i) q^{62} +(-6.78087e6 - 1.17448e7i) q^{63} +8.77770e7 q^{64} -6.12491e7 q^{65} +(-1.47600e8 - 2.55651e8i) q^{66} +(1.31644e8 + 2.28014e8i) q^{67} +(3.87794e7 - 6.71679e7i) q^{68} +(1.30626e8 - 2.26251e8i) q^{69} -2.03941e8 q^{70} +(-6.08133e7 + 1.05332e8i) q^{71} +(1.94604e7 - 3.37063e7i) q^{72} +(-1.08595e8 + 1.88092e8i) q^{73} +(-3.77999e7 - 6.54713e7i) q^{74} +4.60496e8 q^{75} +(1.49057e7 + 2.58174e7i) q^{76} +(-1.59154e8 + 2.75663e8i) q^{77} -8.16080e7 q^{78} +(-2.06742e8 + 3.58088e8i) q^{79} +(-3.68075e8 - 6.37524e8i) q^{80} +(1.46634e8 + 2.53977e8i) q^{81} +4.29776e8 q^{82} +(-7.11550e7 - 1.23244e8i) q^{83} -5.30493e7 q^{84} +1.48136e9 q^{85} +(4.24359e8 - 3.73727e8i) q^{86} -2.44602e8 q^{87} -9.13512e8 q^{88} +(-2.01154e7 - 3.48410e7i) q^{89} -2.38094e8 q^{90} +(4.39982e7 + 7.62071e7i) q^{91} +(1.29469e8 + 2.24247e8i) q^{92} +(1.84847e7 - 3.20164e7i) q^{93} -7.36681e8 q^{94} +(-2.84696e8 + 4.93108e8i) q^{95} +(-1.76627e8 - 3.05926e8i) q^{96} +1.95291e8 q^{97} +(-3.62421e8 - 6.27732e8i) q^{98} +(-1.85808e8 + 3.21828e8i) 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 $

$2$	−25.2231			−1.11471			−0.557357	−	0.830273i	$-0.688185\pi$
$2$	−25.2231			−1.11471			−0.557357	+	0.830273i	$0.688185\pi$
$3$	−62.6577	−	108.526i	−0.446610	−	0.773552i	0.551553	−	0.834140i	$-0.314036\pi$
$3$	−62.6577	−	108.526i	−0.446610	−	0.773552i	−0.998163	+	0.0605884i	$0.980702\pi$
$4$	124.205			0.242588
$5$	1186.15	+	2054.47i	0.848741	+	1.47006i	0.882333	+	0.470626i	$0.155972\pi$
$5$	1186.15	+	2054.47i	0.848741	+	1.47006i	−0.0335918	+	0.999436i	$0.510695\pi$
$6$	1580.42	+	2737.37i	0.497843	+	0.862289i
$7$	1704.14	−	2951.66i	0.268265	−	0.464648i	−0.700149	−	0.713997i	$-0.746883\pi$
$7$	1704.14	−	2951.66i	0.268265	−	0.464648i	0.968414	+	0.249348i	$0.0802164\pi$
$8$	9781.39			0.844298
$9$	1989.53	−	3445.96i	0.101079	−	0.175073i
$10$	−29918.4	−	51820.2i	−0.946104	−	1.63870i
$11$	−93392.8			−1.92330			−0.961649	−	0.274284i	$-0.911559\pi$
$11$	−93392.8			−1.92330			−0.961649	+	0.274284i	$0.911559\pi$
$12$	−7782.41	−	13479.5i	−0.108342	−	0.187655i
$13$	−12909.2	+	22359.4i	−0.125359	+	0.217128i	−0.921873	−	0.387492i	$-0.873342\pi$
$13$	−12909.2	+	22359.4i	−0.125359	+	0.217128i	0.796514	+	0.604620i	$0.206675\pi$
$14$	−42983.7	+	74449.9i	−0.299039	+	0.517950i
$15$	148643.	−	257457.i	0.758113	−	1.31309i
$16$	−310310.			−1.18374
$17$	312220.	−	540781.i	0.906653	−	1.57037i	0.0879693	−	0.996123i	$-0.471962\pi$
$17$	312220.	−	540781.i	0.906653	−	1.57037i	0.818683	−	0.574245i	$-0.194704\pi$
$18$	−50182.1	+	86917.9i	−0.112674	+	0.195157i
$19$	120008.	+	207860.i	0.211261	+	0.365915i	0.952110	−	0.305757i	$-0.0989096\pi$
$19$	120008.	+	207860.i	0.211261	+	0.365915i	−0.740848	+	0.671672i	$0.765576\pi$
$20$	147326.	+	255176.i	0.205895	+	0.356620i
$21$	−427110.			−0.479239
$22$	2.35566e6			2.14393
$23$	1.04238e6	+	1.80546e6i	0.776696	+	1.34528i	0.933836	+	0.357701i	$0.116439\pi$
$23$	1.04238e6	+	1.80546e6i	0.776696	+	1.34528i	−0.157140	+	0.987576i	$0.550227\pi$
$24$	−612879.	−	1.06154e6i	−0.377072	−	0.653108i
$25$	−1.83735e6	+	3.18238e6i	−0.940722	+	1.62938i
$26$	325610.	−	563974.i	0.139739	−	0.242035i
$27$	−2.96522e6			−1.07379
$28$	211663.	−	366611.i	0.0650779	−	0.112718i
$29$	975944.	−	1.69039e6i	0.256232	−	0.443808i	−0.708997	−	0.705211i	$-0.750852\pi$
$29$	975944.	−	1.69039e6i	0.256232	−	0.443808i	0.965230	+	0.261404i	$0.0841854\pi$
$30$	−3.74924e6	+	6.49387e6i	−0.845079	+	1.46372i
$31$	147505.	+	255487.i	0.0286867	+	0.0496868i	0.880012	−	0.474951i	$-0.157534\pi$
$31$	147505.	+	255487.i	0.0286867	+	0.0496868i	−0.851326	+	0.524638i	$0.824201\pi$
$32$	2.81892e6			0.475234
$33$	5.85178e6	+	1.01356e7i	0.858964	+	1.48777i
$34$	−7.87517e6	+	1.36402e7i	−1.01066	+	1.75051i
$35$	8.08547e6			0.910749
$36$	247110.	−	428007.i	0.0245205	−	0.0424707i
$37$	1.49862e6	+	2.59569e6i	0.131457	+	0.227690i	0.924238	−	0.381816i	$-0.124701\pi$
$37$	1.49862e6	+	2.59569e6i	0.131457	+	0.227690i	−0.792781	+	0.609506i	$0.791368\pi$
$38$	−3.02698e6	−	5.24289e6i	−0.235496	−	0.407891i
$39$	3.23545e6			0.223946
$40$	1.16022e7	+	2.00956e7i	0.716590	+	1.24117i
$41$	−1.70390e7			−0.941708			−0.470854	−	0.882211i	$-0.656054\pi$
$41$	−1.70390e7			−0.941708			−0.470854	+	0.882211i	$0.656054\pi$
$42$	1.07730e7			0.534215
$43$	−1.68242e7	+	1.48168e7i	−0.750458	+	0.660918i
$43$	−1.68242e7	+	1.48168e7i	−0.750458	+	0.660918i
$44$	−1.15999e7			−0.466570
$45$	9.43953e6			0.343158
$46$	−2.62921e7	−	4.55392e7i	−0.865794	−	1.49960i
$47$	2.92066e7			0.873053			0.436527	−	0.899691i	$-0.356208\pi$
$47$	2.92066e7			0.873053			0.436527	+	0.899691i	$0.356208\pi$
$48$	1.94433e7	+	3.36768e7i	0.528670	+	0.915684i
$49$	1.43686e7	+	2.48872e7i	0.356068	+	0.616728i
$50$	4.63436e7	−	8.02695e7i	1.04864	−	1.81629i
$51$	−7.82520e7			−1.61968
$52$	−1.60339e6	+	2.77716e6i	−0.0304106	+	0.0526727i
$53$	4.36055e7	+	7.55270e7i	0.759102	+	1.31480i	0.943309	+	0.331916i	$0.107695\pi$
$53$	4.36055e7	+	7.55270e7i	0.759102	+	1.31480i	−0.184207	+	0.982888i	$0.558972\pi$
$54$	7.47921e7			1.19697
$55$	−1.10778e8	−	1.91873e8i	−1.63238	−	2.82737i
$56$	1.66688e7	−	2.88713e7i	0.226495	−	0.392302i
$57$	1.50389e7	−	2.60481e7i	0.188703	−	0.326843i
$58$	−2.46164e7	+	4.26368e7i	−0.285626	+	0.494719i
$59$	−8.12593e7			−0.873050			−0.436525	−	0.899692i	$-0.643791\pi$
$59$	−8.12593e7			−0.873050			−0.436525	+	0.899692i	$0.643791\pi$
$60$	1.84622e7	−	3.19775e7i	0.183909	−	0.318540i
$61$	−1.93975e7	+	3.35974e7i	−0.179375	+	0.310686i	−0.941667	−	0.336547i	$-0.890741\pi$
$61$	−1.93975e7	+	3.35974e7i	−0.179375	+	0.310686i	0.762292	+	0.647233i	$0.224074\pi$
$62$	−3.72055e6	−	6.44417e6i	−0.0319775	−	0.0553866i
$63$	−6.78087e6	−	1.17448e7i	−0.0542316	−	0.0939319i
$64$	8.77770e7			0.653990
$65$	−6.12491e7			−0.425588
$66$	−1.47600e8	−	2.55651e8i	−0.957500	−	1.65844i
$67$	1.31644e8	+	2.28014e8i	0.798114	+	1.38237i	0.920843	+	0.389934i	$0.127502\pi$
$67$	1.31644e8	+	2.28014e8i	0.798114	+	1.38237i	−0.122728	+	0.992440i	$0.539164\pi$
$68$	3.87794e7	−	6.71679e7i	0.219943	−	0.380953i
$69$	1.30626e8	−	2.26251e8i	0.693761	−	1.20163i
$70$	−2.03941e8			−1.01523
$71$	−6.08133e7	+	1.05332e8i	−0.284011	+	0.491922i	−0.972369	−	0.233449i	$-0.924999\pi$
$71$	−6.08133e7	+	1.05332e8i	−0.284011	+	0.491922i	0.688358	+	0.725371i	$0.258332\pi$
$72$	1.94604e7	−	3.37063e7i	0.0853404	−	0.147814i
$73$	−1.08595e8	+	1.88092e8i	−0.447565	+	0.775206i	−0.998227	−	0.0595229i	$-0.981042\pi$
$73$	−1.08595e8	+	1.88092e8i	−0.447565	+	0.775206i	0.550662	+	0.834728i	$0.314375\pi$
$74$	−3.77999e7	−	6.54713e7i	−0.146537	−	0.253810i
$75$	4.60496e8			1.68054
$76$	1.49057e7	+	2.58174e7i	0.0512495	+	0.0887668i
$77$	−1.59154e8	+	2.75663e8i	−0.515953	+	0.893657i
$78$	−8.16080e7			−0.249636
$79$	−2.06742e8	+	3.58088e8i	−0.597182	+	1.03435i	0.396053	+	0.918228i	$0.370380\pi$
$79$	−2.06742e8	+	3.58088e8i	−0.597182	+	1.03435i	−0.993235	+	0.116122i	$0.962954\pi$
$80$	−3.68075e8	−	6.37524e8i	−1.00469	−	1.74017i
$81$	1.46634e8	+	2.53977e8i	0.378488	+	0.655560i
$82$	4.29776e8			1.04974
$83$	−7.11550e7	−	1.23244e8i	−0.164571	−	0.285046i	0.771932	−	0.635706i	$-0.219291\pi$
$83$	−7.11550e7	−	1.23244e8i	−0.164571	−	0.285046i	−0.936503	+	0.350660i	$0.885957\pi$
$84$	−5.30493e7			−0.116258
$85$	1.48136e9			3.07805
$86$	4.24359e8	−	3.73727e8i	0.836546	−	0.736735i
$87$	−2.44602e8			−0.457744
$88$	−9.13512e8			−1.62384
$89$	−2.01154e7	−	3.48410e7i	−0.0339840	−	0.0588620i	0.848533	−	0.529142i	$-0.177486\pi$
$89$	−2.01154e7	−	3.48410e7i	−0.0339840	−	0.0588620i	−0.882517	+	0.470280i	$0.844153\pi$
$90$	−2.38094e8			−0.382523
$91$	4.39982e7	+	7.62071e7i	0.0672587	+	0.116495i
$92$	1.29469e8	+	2.24247e8i	0.188417	+	0.326349i
$93$	1.84847e7	−	3.20164e7i	0.0256235	−	0.0443813i
$94$	−7.36681e8			−0.973205
$95$	−2.84696e8	+	4.93108e8i	−0.358612	+	0.621135i
$96$	−1.76627e8	−	3.05926e8i	−0.212244	−	0.367618i
$97$	1.95291e8			0.223980			0.111990	−	0.993709i	$-0.464278\pi$
$97$	1.95291e8			0.223980			0.111990	+	0.993709i	$0.464278\pi$
$98$	−3.62421e8	−	6.27732e8i	−0.396914	−	0.687475i
$99$	−1.85808e8	+	3.21828e8i	−0.194404	+	0.336718i
$100$	−2.28208e8	+	3.95268e8i	−0.228208	+	0.395268i
$101$	−7.33837e8	+	1.27104e9i	−0.701703	+	1.21539i	0.266165	+	0.963928i	$0.414243\pi$
$101$	−7.33837e8	+	1.27104e9i	−0.701703	+	1.21539i	−0.967868	+	0.251458i	$0.919090\pi$
$102$	1.97376e9			1.80548
$103$	7.18726e8	−	1.24487e9i	0.629211	−	1.08982i	−0.358500	−	0.933530i	$-0.616712\pi$
$103$	7.18726e8	−	1.24487e9i	0.629211	−	1.08982i	0.987710	−	0.156295i	$-0.0499551\pi$
$104$	−1.26270e8	+	2.18706e8i	−0.105840	+	0.183320i
$105$	−5.06617e8	−	8.77486e8i	−0.406750	−	0.704512i
$106$	−1.09987e9	−	1.90503e9i	−0.846182	−	1.46563i
$107$	−2.15298e9			−1.58786			−0.793930	−	0.608010i	$-0.791968\pi$
$107$	−2.15298e9			−1.58786			−0.793930	+	0.608010i	$0.791968\pi$
$108$	−3.68296e8			−0.260489
$109$	7.86911e8	+	1.36297e9i	0.533957	+	0.924841i	0.999213	+	0.0396647i	$0.0126290\pi$
$109$	7.86911e8	+	1.36297e9i	0.533957	+	0.924841i	−0.465256	+	0.885176i	$0.654038\pi$
$110$	2.79417e9	+	4.83964e9i	1.81964	+	3.15171i
$111$	1.87800e8	−	3.25280e8i	0.117420	−	0.203378i
$112$	−5.28812e8	+	9.15929e8i	−0.317556	+	0.550023i
$113$	2.00079e9			1.15438			0.577189	−	0.816611i	$-0.304150\pi$
$113$	2.00079e9			1.15438			0.577189	+	0.816611i	$0.304150\pi$
$114$	−3.79327e8	+	6.57014e8i	−0.210350	+	0.364337i
$115$	−2.47284e9	+	4.28309e9i	−1.31843	+	2.28358i
$116$	1.21217e8	−	2.09955e8i	0.0621590	−	0.107663i
$117$	5.13665e7	+	8.89694e7i	0.0253421	+	0.0438939i
$118$	2.04961e9			0.973202
$119$	−1.06413e9	−	1.84313e9i	−0.486446	−	0.842549i
$120$	1.45394e9	−	2.51829e9i	0.640073	−	1.10864i
$121$	6.36427e9			2.69907
$122$	4.89265e8	−	8.47431e8i	0.199951	−	0.346326i
$123$	1.06762e9	+	1.84918e9i	0.420576	+	0.728460i
$124$	1.83209e7	+	3.17328e7i	0.00695906	+	0.0120534i
$125$	−4.08408e9			−1.49623
$126$	1.71035e8	+	2.96240e8i	0.0604528	+	0.104707i
$127$	−1.61138e9			−0.549642			−0.274821	−	0.961495i	$-0.588619\pi$
$127$	−1.61138e9			−0.549642			−0.274821	+	0.961495i	$0.588619\pi$
$128$	−3.65729e9			−1.20425
$129$	2.66218e9	+	8.97479e8i	0.846417	+	0.285345i
$130$	1.54489e9			0.474409
$131$	−4.03385e9			−1.19674			−0.598369	−	0.801221i	$-0.704184\pi$
$131$	−4.03385e9			−1.19674			−0.598369	+	0.801221i	$0.704184\pi$
$132$	7.26822e8	+	1.25889e9i	0.208375	+	0.360916i
$133$	8.18043e8			0.226696
$134$	−3.32048e9	−	5.75123e9i	−0.889670	−	1.54095i
$135$	−3.51720e9	−	6.09197e9i	−0.911370	−	1.57854i
$136$	3.05395e9	−	5.28959e9i	0.765485	−	1.32586i
$137$	−4.41945e9			−1.07183			−0.535915	−	0.844272i	$-0.680033\pi$
$137$	−4.41945e9			−1.07183			−0.535915	+	0.844272i	$0.680033\pi$
$138$	−3.29480e9	+	5.70677e9i	−0.773345	+	1.33947i
$139$	−1.34981e9	−	2.33793e9i	−0.306694	−	0.531209i	0.670943	−	0.741509i	$-0.265889\pi$
$139$	−1.34981e9	−	2.33793e9i	−0.306694	−	0.531209i	−0.977637	+	0.210300i	$0.932556\pi$
$140$	1.00426e9			0.220937
$141$	−1.83002e9	−	3.16968e9i	−0.389915	−	0.675352i
$142$	1.53390e9	−	2.65679e9i	0.316592	−	0.548353i
$143$	1.20563e9	−	2.08821e9i	0.241102	−	0.417601i
$144$	−6.17371e8	+	1.06932e9i	−0.119651	+	0.207241i
$145$	4.63047e9			0.869900
$146$	2.73910e9	−	4.74426e9i	0.498907	−	0.864133i
$147$	1.80061e9	−	3.11875e9i	0.318047	−	0.550874i
$148$	1.86137e8	+	3.22398e8i	0.0318900	+	0.0552351i
$149$	2.96172e9	+	5.12985e9i	0.492272	+	0.852641i	0.999960	−	0.00890010i	$-0.00283303\pi$
$149$	2.96172e9	+	5.12985e9i	0.492272	+	0.852641i	−0.507688	+	0.861541i	$0.669500\pi$
$150$	−1.16151e10			−1.87333
$151$	6.33963e9			0.992356			0.496178	−	0.868221i	$-0.334736\pi$
$151$	6.33963e9			0.992356			0.496178	+	0.868221i	$0.334736\pi$
$152$	1.17385e9	+	2.03316e9i	0.178367	+	0.308941i
$153$	−1.24234e9	−	2.15180e9i	−0.183286	−	0.317461i
$154$	4.01437e9	−	6.95309e9i	0.575141	−	0.996173i
$155$	−3.49928e8	+	6.06092e8i	−0.0486951	+	0.0843424i
$156$	4.01859e8			0.0543267
$157$	−1.17929e9	+	2.04258e9i	−0.154907	+	0.268307i	−0.933025	−	0.359811i	$-0.882841\pi$
$157$	−1.17929e9	+	2.04258e9i	−0.154907	+	0.268307i	0.778118	+	0.628118i	$0.216174\pi$
$158$	5.21468e9	−	9.03208e9i	0.665687	−	1.15300i
$159$	5.46444e9	−	9.46470e9i	0.678046	−	1.17441i
$160$	3.34366e9	+	5.79139e9i	0.403350	+	0.698623i
$161$	7.10545e9			0.833441
$162$	−3.69856e9	−	6.40610e9i	−0.421906	−	0.730762i
$163$	−1.94067e9	+	3.36134e9i	−0.215332	+	0.372965i	−0.953375	−	0.301788i	$-0.902417\pi$
$163$	−1.94067e9	+	3.36134e9i	−0.215332	+	0.372965i	0.738044	+	0.674753i	$0.235750\pi$
$164$	−2.11633e9			−0.228447
$165$	−1.38822e10	+	2.40447e10i	−1.45808	+	2.52546i
$166$	1.79475e9	+	3.10860e9i	0.183450	+	0.317745i
$167$	−3.18267e9	−	5.51255e9i	−0.316641	−	0.548439i	0.663144	−	0.748492i	$-0.269222\pi$
$167$	−3.18267e9	−	5.51255e9i	−0.316641	−	0.548439i	−0.979785	+	0.200053i	$0.935888\pi$
$168$	−4.17773e9			−0.404621
$169$	4.96895e9	+	8.60648e9i	0.468570	+	0.811588i
$170$	−3.73645e10			−3.43115
$171$	9.55039e8			0.0854159
$172$	−2.08965e9	+	1.84033e9i	−0.182052	+	0.160331i
$173$	4.93412e9			0.418796			0.209398	−	0.977831i	$-0.432850\pi$
$173$	4.93412e9			0.418796			0.209398	+	0.977831i	$0.432850\pi$
$174$	6.16961e9			0.510254
$175$	6.26219e9	+	1.08464e10i	0.504725	+	0.874210i
$176$	2.89807e10			2.27668
$177$	5.09152e9	+	8.81878e9i	0.389913	+	0.675350i
$178$	5.07374e8	+	8.78798e8i	0.0378825	+	0.0656144i
$179$	6.54204e9	−	1.13311e10i	0.476293	−	0.824964i	−0.523338	−	0.852125i	$-0.675313\pi$
$179$	6.54204e9	−	1.13311e10i	0.476293	−	0.824964i	0.999631	+	0.0271614i	$0.00864679\pi$
$180$	1.17244e9			0.0832461
$181$	3.04355e8	−	5.27158e8i	0.0210779	−	0.0365080i	−0.855294	−	0.518143i	$-0.826624\pi$
$181$	3.04355e8	−	5.27158e8i	0.0210779	−	0.0365080i	0.876372	+	0.481635i	$0.159957\pi$
$182$	−1.10977e9	−	1.92218e9i	−0.0749742	−	0.129859i
$183$	4.86160e9			0.320442
$184$	1.01959e10	+	1.76599e10i	0.655763	+	1.13581i
$185$	−3.55518e9	+	6.15776e9i	−0.223146	+	0.386500i
$186$	−4.66242e8	+	8.07554e8i	−0.0285629	+	0.0494724i
$187$	−2.91591e10	+	5.05051e10i	−1.74376	+	3.02029i
$188$	3.62761e9			0.211793
$189$	−5.05315e9	+	8.75231e9i	−0.288061	+	0.498936i
$190$	7.18092e9	−	1.24377e10i	0.399750	−	0.692388i
$191$	5.32663e9	+	9.22599e9i	0.289602	+	0.501606i	0.973715	−	0.227771i	$-0.0731436\pi$
$191$	5.32663e9	+	9.22599e9i	0.289602	+	0.501606i	−0.684112	+	0.729377i	$0.739810\pi$
$192$	−5.49990e9	−	9.52611e9i	−0.292078	−	0.505895i
$193$	−1.05047e10			−0.544972			−0.272486	−	0.962160i	$-0.587846\pi$
$193$	−1.05047e10			−0.544972			−0.272486	+	0.962160i	$0.587846\pi$
$194$	−4.92585e9			−0.249674
$195$	3.83773e9	+	6.64714e9i	0.190072	+	0.329215i
$196$	1.78466e9	+	3.09112e9i	0.0863779	+	0.149611i
$197$	7.83947e9	−	1.35784e10i	0.370842	−	0.642317i	−0.618854	−	0.785506i	$-0.712403\pi$
$197$	7.83947e9	−	1.35784e10i	0.370842	−	0.642317i	0.989695	+	0.143190i	$0.0457359\pi$
$198$	4.68665e9	−	8.11751e9i	0.216705	−	0.375344i
$199$	−1.87505e9			−0.0847566			−0.0423783	−	0.999102i	$-0.513493\pi$
$199$	−1.87505e9			−0.0847566			−0.0423783	+	0.999102i	$0.513493\pi$
$200$	−1.79718e10	+	3.11281e10i	−0.794249	+	1.37568i
$201$	1.64970e10	−	2.85737e10i	0.712892	−	1.23477i
$202$	1.85097e10	−	3.20597e10i	0.782199	−	1.35481i
$203$	−3.32629e9	−	5.76130e9i	−0.137476	−	0.238116i
$204$	−9.71931e9			−0.392916
$205$	−2.02108e10	−	3.50061e10i	−0.799266	−	1.38437i
$206$	−1.81285e10	+	3.13995e10i	−0.701390	+	1.21484i
$207$	8.29538e9			0.314029
$208$	4.00586e9	−	6.93835e9i	0.148392	−	0.257023i
$209$	−1.12079e10	−	1.94127e10i	−0.406318	−	0.703764i
$210$	1.27784e10	+	2.21329e10i	0.453410	+	0.785329i
$211$	−2.26499e10			−0.786675			−0.393338	−	0.919394i	$-0.628680\pi$
$211$	−2.26499e10			−0.786675			−0.393338	+	0.919394i	$0.628680\pi$
$212$	5.41604e9	+	9.38085e9i	0.184149	+	0.318956i
$213$	1.52417e10			0.507370
$214$	5.43047e10			1.77001
$215$	−5.03969e10	−	1.69899e10i	−1.60854	−	0.542271i
$216$	−2.90040e10			−0.906600
$217$	1.00548e9			0.0307825
$218$	−1.98483e10	−	3.43783e10i	−0.595210	−	1.03093i
$219$	2.72172e10			0.799549
$220$	−1.37592e10	−	2.38317e10i	−0.395997	−	0.685886i
$221$	8.06103e9	+	1.39621e10i	0.227314	+	0.393719i
$222$	−4.73691e9	+	8.20457e9i	−0.130890	+	0.226708i
$223$	5.09682e10			1.38015			0.690076	−	0.723736i	$-0.257577\pi$
$223$	5.09682e10			1.38015			0.690076	+	0.723736i	$0.257577\pi$
$224$	4.80382e9	−	8.32047e9i	0.127488	−	0.220817i
$225$	7.31091e9	+	1.26629e10i	0.190173	+	0.329390i
$226$	−5.04661e10			−1.28680
$227$	6.68868e9	+	1.15851e10i	0.167195	+	0.289591i	0.937433	−	0.348167i	$-0.113196\pi$
$227$	6.68868e9	+	1.15851e10i	0.167195	+	0.289591i	−0.770237	+	0.637757i	$0.779862\pi$
$228$	1.86791e9	−	3.23531e9i	0.0457771	−	0.0792883i
$229$	1.19855e10	−	2.07596e10i	0.288004	−	0.498837i	−0.685330	−	0.728233i	$-0.740342\pi$
$229$	1.19855e10	−	2.07596e10i	0.288004	−	0.498837i	0.973333	+	0.229396i	$0.0736752\pi$
$230$	6.23728e10	−	1.08033e11i	1.46967	−	2.54554i
$231$	3.98890e10			0.921720
$232$	9.54609e9	−	1.65343e10i	0.216336	−	0.374706i
$233$	−1.00808e10	+	1.74604e10i	−0.224074	+	0.388107i	−0.956041	−	0.293232i	$-0.905269\pi$
$233$	−1.00808e10	+	1.74604e10i	−0.224074	+	0.388107i	0.731967	+	0.681340i	$0.238602\pi$
$234$	−1.29562e9	−	2.24408e9i	−0.0282493	−	0.0489292i
$235$	3.46435e10	+	6.00042e10i	0.740996	+	1.28344i
$236$	−1.00928e10			−0.211792
$237$	5.18159e10			1.06683
$238$	2.68408e10	+	4.64896e10i	0.542249	+	0.939202i
$239$	−1.91625e10	−	3.31904e10i	−0.379893	−	0.657994i	0.611154	−	0.791512i	$-0.290706\pi$
$239$	−1.91625e10	−	3.31904e10i	−0.379893	−	0.657994i	−0.991046	+	0.133518i	$0.957372\pi$
$240$	−4.61254e10	+	7.98916e10i	−0.897408	+	1.55436i
$241$	7.58372e9	−	1.31354e10i	0.144812	−	0.250822i	−0.784491	−	0.620141i	$-0.787075\pi$
$241$	7.58372e9	−	1.31354e10i	0.144812	−	0.250822i	0.929303	+	0.369318i	$0.120409\pi$
$242$	−1.60527e11			−3.00870
$243$	−1.08067e10	+	1.87178e10i	−0.198823	+	0.344371i
$244$	−2.40927e9	+	4.17298e9i	−0.0435142	+	0.0753688i
$245$	−3.40867e10	+	5.90399e10i	−0.604419	+	1.04688i
$246$	−2.69288e10	−	4.66420e10i	−0.468823	−	0.812025i
$247$	−6.19685e9			−0.105934
$248$	1.44281e9	+	2.49902e9i	0.0242201	+	0.0419505i
$249$	−8.91682e9	+	1.54444e10i	−0.146999	+	0.254609i
$250$	1.03013e11			1.66787
$251$	−9.89874e9	+	1.71451e10i	−0.157416	+	0.272652i	−0.933936	−	0.357440i	$-0.883650\pi$
$251$	−9.89874e9	+	1.71451e10i	−0.157416	+	0.272652i	0.776520	+	0.630092i	$0.216983\pi$
$252$	−8.42219e8	−	1.45877e9i	−0.0131560	−	0.0227868i
$253$	−9.73509e10	−	1.68617e11i	−1.49382	−	2.58737i
$254$	4.06439e10			0.612694
$255$	−9.28187e10	−	1.60767e11i	−1.37469	−	2.38103i
$256$	4.73065e10			0.688400
$257$	−2.62034e9			−0.0374679			−0.0187339	−	0.999825i	$-0.505964\pi$
$257$	−2.62034e9			−0.0374679			−0.0187339	+	0.999825i	$0.505964\pi$
$258$	−6.71485e10	−	2.26372e10i	−0.943513	−	0.318078i
$259$	1.02154e10			0.141061
$260$	−7.60746e9			−0.103243
$261$	−3.88334e9	−	6.72614e9i	−0.0517992	−	0.0897188i
$262$	1.01746e11			1.33402
$263$	−7.63104e10	−	1.32173e11i	−0.983519	−	1.70351i	−0.648341	−	0.761350i	$-0.724537\pi$
$263$	−7.63104e10	−	1.32173e11i	−0.983519	−	1.70351i	−0.335178	−	0.942155i	$-0.608797\pi$
$264$	5.72385e10	+	9.91400e10i	0.725222	+	1.25612i
$265$	−1.03446e11	+	1.79173e11i	−1.28856	+	2.23185i
$266$	−2.06336e10			−0.252701
$267$	−2.52078e9	+	4.36611e9i	−0.0303552	+	0.0525768i
$268$	1.63509e10	+	2.83206e10i	0.193613	+	0.335348i
$269$	1.43068e11			1.66593			0.832966	−	0.553324i	$-0.186641\pi$
$269$	1.43068e11			1.66593			0.832966	+	0.553324i	$0.186641\pi$
$270$	8.87147e10	+	1.53658e11i	1.01592	+	1.75962i
$271$	−1.94503e10	+	3.36888e10i	−0.219060	+	0.379423i	−0.954521	−	0.298144i	$-0.903632\pi$
$271$	−1.94503e10	+	3.36888e10i	−0.219060	+	0.379423i	0.735461	+	0.677567i	$0.236966\pi$
$272$	−9.68851e10	+	1.67810e11i	−1.07324	+	1.85891i
$273$	5.51365e9	−	9.54992e9i	0.0600769	−	0.104056i
$274$	1.11472e11			1.19478
$275$	1.71595e11	−	2.97211e11i	1.80929	−	3.13378i
$276$	1.62245e10	−	2.81016e10i	0.168298	−	0.291501i
$277$	−2.21400e10	−	3.83476e10i	−0.225953	−	0.391363i	0.730652	−	0.682750i	$-0.239216\pi$
$277$	−2.21400e10	−	3.83476e10i	−0.225953	−	0.391363i	−0.956605	+	0.291388i	$0.905883\pi$
$278$	3.40463e10	+	5.89699e10i	0.341876	+	0.592146i
$279$	1.17386e9			0.0115984
$280$	7.90871e10			0.768944
$281$	4.88903e10	+	8.46805e10i	0.467783	+	0.810223i	0.999322	−	0.0368101i	$-0.0117197\pi$
$281$	4.88903e10	+	8.46805e10i	0.467783	+	0.810223i	−0.531540	+	0.847033i	$0.678386\pi$
$282$	4.61588e10	+	7.99493e10i	0.434643	+	0.752824i
$283$	−6.23304e10	+	1.07959e11i	−0.577645	+	1.00051i	0.418103	+	0.908399i	$0.362695\pi$
$283$	−6.23304e10	+	1.07959e11i	−0.577645	+	1.00051i	−0.995749	+	0.0921115i	$0.970638\pi$
$284$	−7.55332e9	+	1.30827e10i	−0.0688978	+	0.119335i
$285$	7.13536e10			0.640640
$286$	−3.04097e10	+	5.26711e10i	−0.268760	+	0.465506i
$287$	−2.90368e10	+	5.02932e10i	−0.252627	+	0.437563i
$288$	5.60831e9	−	9.71388e9i	0.0480359	−	0.0832006i
$289$	−1.35669e11	−	2.34986e11i	−1.14404	−	1.98153i
$290$	−1.16795e11			−0.969690
$291$	−1.22365e10	−	2.11942e10i	−0.100032	−	0.173260i
$292$	−1.34880e10	+	2.33620e10i	−0.108574	+	0.188056i
$293$	−1.53986e11			−1.22061			−0.610305	−	0.792166i	$-0.708953\pi$
$293$	−1.53986e11			−1.22061			−0.610305	+	0.792166i	$0.708953\pi$
$294$	−4.54170e10	+	7.86645e10i	−0.354532	+	0.614067i
$295$	−9.63859e10	−	1.66945e11i	−0.740993	−	1.28344i
$296$	1.46586e10	+	2.53894e10i	0.110989	+	0.192239i
$297$	2.76930e11			2.06522
$298$	−7.47037e10	−	1.29391e11i	−0.548743	−	0.950451i
$299$	−5.38253e10			−0.389463
$300$	5.71960e10			0.407680
$301$	1.50635e10	+	7.49092e10i	0.105773	+	0.526000i
$302$	−1.59905e11			−1.10619
$303$	1.83922e11			1.25355
$304$	−3.72398e10	−	6.45012e10i	−0.250078	−	0.433148i
$305$	−9.20334e10			−0.608970
$306$	3.13357e10	+	5.42751e10i	0.204312	+	0.353878i
$307$	−1.68828e10	−	2.92419e10i	−0.108473	−	0.187881i	0.806679	−	0.590990i	$-0.201263\pi$
$307$	−1.68828e10	−	2.92419e10i	−0.108473	−	0.187881i	−0.915152	+	0.403109i	$0.867929\pi$
$308$	−1.97678e10	+	3.42388e10i	−0.125164	+	0.216791i
$309$	−1.80135e11			−1.12405
$310$	8.82626e9	−	1.52875e10i	0.0542812	−	0.0940177i
$311$	5.89690e10	+	1.02137e11i	0.357439	+	0.619103i	0.987532	−	0.157417i	$-0.0503166\pi$
$311$	5.89690e10	+	1.02137e11i	0.357439	+	0.619103i	−0.630093	+	0.776520i	$0.716983\pi$
$312$	3.16472e10			0.189077
$313$	1.08757e11	+	1.88373e11i	0.640485	+	1.10935i	0.985325	+	0.170690i	$0.0545998\pi$
$313$	1.08757e11	+	1.88373e11i	0.640485	+	1.10935i	−0.344840	+	0.938661i	$0.612067\pi$
$314$	2.97452e10	−	5.15203e10i	0.172677	−	0.299085i
$315$	1.60863e10	−	2.78622e10i	0.0920572	−	0.159448i
$316$	−2.56784e10	+	4.44764e10i	−0.144869	+	0.250921i
$317$	−6.58228e9			−0.0366108			−0.0183054	−	0.999832i	$-0.505827\pi$
$317$	−6.58228e9			−0.0366108			−0.0183054	+	0.999832i	$0.505827\pi$
$318$	−1.37830e11	+	2.38729e11i	−0.755827	+	1.30913i
$319$	−9.11462e10	+	1.57870e11i	−0.492811	+	0.853574i
$320$	1.04117e11	+	1.80336e11i	0.555068	+	0.961405i
$321$	1.34900e11	+	2.33654e11i	0.709154	+	1.22829i
$322$	−1.79221e11			−0.929049
$323$	1.49876e11			0.766163
$324$	1.82127e10	+	3.15453e10i	0.0918167	+	0.159031i
$325$	−4.74374e10	−	8.21640e10i	−0.235855	−	0.408513i
$326$	4.89497e10	−	8.47834e10i	0.240033	−	0.415750i
$327$	9.86121e10	−	1.70801e11i	0.476942	−	0.826087i
$328$	−1.66665e11			−0.795082
$329$	4.97721e10	−	8.62078e10i	0.234210	−	0.405663i
$330$	3.50152e11	−	6.06481e11i	1.62534	−	2.81517i
$331$	−1.69730e9	+	2.93981e9i	−0.00777199	+	0.0134615i	−0.869885	−	0.493254i	$-0.835807\pi$
$331$	−1.69730e9	+	2.93981e9i	−0.00777199	+	0.0134615i	0.862113	+	0.506716i	$0.169141\pi$
$332$	−8.83783e9	−	1.53076e10i	−0.0399231	−	0.0691488i
$333$	1.19262e10			0.0531500
$334$	8.02768e10	+	1.39044e11i	0.352965	+	0.611353i
$335$	−3.12300e11	+	5.40919e11i	−1.35478	+	2.34656i
$336$	1.32536e11			0.567295
$337$	−2.93494e10	+	5.08347e10i	−0.123955	+	0.214697i	−0.921324	−	0.388795i	$-0.872891\pi$
$337$	−2.93494e10	+	5.08347e10i	−0.123955	+	0.214697i	0.797369	+	0.603492i	$0.206225\pi$
$338$	−1.25332e11	−	2.17082e11i	−0.522322	−	0.904689i
$339$	−1.25365e11	−	2.17138e11i	−0.515557	−	0.892971i
$340$	1.83993e11			0.746700
$341$	−1.37760e10	−	2.38606e10i	−0.0551730	−	0.0955625i
$342$	−2.40891e10			−0.0952144
$343$	2.35481e11			0.918612
$344$	−1.64564e11	+	1.44929e11i	−0.633610	+	0.558012i
$345$	6.19770e11			2.35529
$346$	−1.24454e11			−0.466838
$347$	2.89994e10	+	5.02285e10i	0.107376	+	0.185981i	0.914706	−	0.404119i	$-0.132422\pi$
$347$	2.89994e10	+	5.02285e10i	0.107376	+	0.185981i	−0.807331	+	0.590100i	$0.799088\pi$
$348$	−3.03808e10			−0.111043
$349$	8.83756e10	+	1.53071e11i	0.318873	+	0.552305i	0.980253	−	0.197746i	$-0.0633623\pi$
$349$	8.83756e10	+	1.53071e11i	0.318873	+	0.552305i	−0.661380	+	0.750051i	$0.730029\pi$
$350$	−1.57952e11	−	2.73581e11i	−0.562625	−	0.974494i
$351$	3.82786e10	−	6.63006e10i	0.134609	−	0.233150i
$352$	−2.63266e11			−0.914015
$353$	2.36169e11	−	4.09057e11i	0.809537	−	1.40216i	−0.103649	−	0.994614i	$-0.533052\pi$
$353$	2.36169e11	−	4.09057e11i	0.809537	−	1.40216i	0.913185	−	0.407545i	$-0.133615\pi$
$354$	−1.28424e11	−	2.22437e11i	−0.434642	−	0.752822i
$355$	−2.88535e11			−0.964208
$356$	−2.49844e9	−	4.32743e9i	−0.00824413	−	0.0142792i
$357$	−1.33352e11	+	2.30973e11i	−0.434504	+	0.752583i
$358$	−1.65010e11	+	2.85807e11i	−0.530931	+	0.919599i
$359$	3.51117e10	−	6.08152e10i	0.111565	−	0.193236i	−0.804837	−	0.593496i	$-0.797747\pi$
$359$	3.51117e10	−	6.08152e10i	0.111565	−	0.193236i	0.916401	+	0.400261i	$0.131080\pi$
$360$	9.23317e10			0.289727
$361$	1.32540e11	−	2.29566e11i	0.410737	−	0.711418i
$362$	−7.67678e9	+	1.32966e10i	−0.0234958	+	0.0406960i
$363$	−3.98771e11	−	6.90691e11i	−1.20543	−	2.08787i
$364$	5.46480e9	+	9.46532e9i	0.0163162	+	0.0282604i
$365$	−5.15240e11			−1.51947
$366$	−1.22625e11			−0.357202
$367$	4.54100e10	+	7.86524e10i	0.130663	+	0.226316i	0.923933	−	0.382556i	$-0.124956\pi$
$367$	4.54100e10	+	7.86524e10i	0.130663	+	0.226316i	−0.793269	+	0.608871i	$0.791623\pi$
$368$	−3.23461e11	−	5.60251e11i	−0.919406	−	1.59246i
$369$	−3.38995e10	+	5.87157e10i	−0.0951864	+	0.164868i
$370$	8.96728e10	−	1.55318e11i	0.248744	−	0.430838i
$371$	2.97240e11			0.814562
$372$	2.29590e9	−	3.97661e9i	0.00621597	−	0.0107664i
$373$	−2.20074e11	+	3.81179e11i	−0.588680	+	1.01962i	0.405726	+	0.913995i	$0.367019\pi$
$373$	−2.20074e11	+	3.81179e11i	−0.588680	+	1.01962i	−0.994406	+	0.105629i	$0.966315\pi$
$374$	7.35484e11	−	1.27390e12i	1.94380	−	3.36676i
$375$	2.55899e11	+	4.43230e11i	0.668233	+	1.15741i
$376$	2.85681e11			0.737117
$377$	2.51973e10	+	4.36431e10i	0.0642419	+	0.111270i
$378$	1.27456e11	−	2.20760e11i	0.321105	−	0.556171i
$379$	5.22477e11			1.30074			0.650370	−	0.759617i	$-0.274614\pi$
$379$	5.22477e11			1.30074			0.650370	+	0.759617i	$0.274614\pi$
$380$	−3.53607e10	+	6.12466e10i	−0.0869951	+	0.150680i
$381$	1.00965e11	+	1.74877e11i	0.245476	+	0.425177i
$382$	−1.34354e11	−	2.32708e11i	−0.322824	−	0.559147i
$383$	−6.74970e11			−1.60284			−0.801419	−	0.598103i	$-0.795921\pi$
$383$	−6.74970e11			−1.60284			−0.801419	+	0.598103i	$0.795921\pi$
$384$	2.29158e11	+	3.96912e11i	0.537828	+	0.931546i
$385$	−7.55125e11			−1.75164
$386$	2.64960e11			0.607488
$387$	1.75861e10	+	8.74541e10i	0.0398539	+	0.198190i
$388$	2.42562e10			0.0543350
$389$	−3.38255e11			−0.748982			−0.374491	−	0.927231i	$-0.622183\pi$
$389$	−3.38255e11			−0.748982			−0.374491	+	0.927231i	$0.622183\pi$
$390$	−9.67994e10	−	1.67662e11i	−0.211876	−	0.366980i
$391$	1.30181e12			2.81677
$392$	1.40545e11	+	2.43431e11i	0.300627	+	0.520702i
$393$	2.52752e11	+	4.37779e11i	0.534476	+	0.925739i
$394$	−1.97736e11	+	3.42488e11i	−0.413383	+	0.716000i
$395$	−9.80909e11			−2.02741
$396$	−2.30783e10	+	3.99728e10i	−0.0471602	+	0.0816838i
$397$	−2.17468e11	−	3.76666e11i	−0.439378	−	0.761024i	0.558264	−	0.829663i	$-0.311468\pi$
$397$	−2.17468e11	−	3.76666e11i	−0.439378	−	0.761024i	−0.997642	+	0.0686390i	$0.978134\pi$
$398$	4.72946e10			0.0944794
$399$	−5.12567e10	−	8.87792e10i	−0.101245	−	0.175361i
$400$	5.70147e11	−	9.87524e11i	1.11357	−	1.92876i
$401$	2.61885e10	−	4.53599e10i	0.0505780	−	0.0876036i	−0.839628	−	0.543162i	$-0.817227\pi$
$401$	2.61885e10	−	4.53599e10i	0.0505780	−	0.0876036i	0.890206	+	0.455558i	$0.150560\pi$
$402$	−4.16107e11	+	7.20718e11i	−0.794671	+	1.37641i
$403$	−7.61672e9			−0.0143845
$404$	−9.11464e10	+	1.57870e11i	−0.170225	+	0.294838i
$405$	−3.47860e11	+	6.02511e11i	−0.642476	+	1.11280i
$406$	8.38994e10	+	1.45318e11i	0.153247	+	0.265431i
$407$	−1.39961e11	−	2.42419e11i	−0.252831	−	0.437916i
$408$	−7.65413e11			−1.36749
$409$	−6.99100e11			−1.23533			−0.617667	−	0.786440i	$-0.711922\pi$
$409$	−6.99100e11			−1.23533			−0.617667	+	0.786440i	$0.711922\pi$
$410$	5.09779e11	+	8.82964e11i	0.890953	+	1.54318i
$411$	2.76913e11	+	4.79627e11i	0.478690	+	0.829116i
$412$	8.92696e10	−	1.54619e11i	0.152639	−	0.264379i
$413$	−1.38477e11	+	2.39850e11i	−0.234209	+	0.405661i
$414$	−2.09235e11			−0.350053
$415$	1.68801e11	−	2.92372e11i	0.279357	−	0.483860i
$416$	−3.63900e10	+	6.30293e10i	−0.0595747	+	0.103186i
$417$	−1.69151e11	+	2.92979e11i	−0.273945	+	0.474487i
$418$	2.82698e11	+	4.89648e11i	0.452929	+	0.784496i
$419$	4.82014e11			0.764005			0.382002	−	0.924161i	$-0.375235\pi$
$419$	4.82014e11			0.764005			0.382002	+	0.924161i	$0.375235\pi$
$420$	−6.29244e10	−	1.08988e11i	−0.0986728	−	0.170906i
$421$	1.77897e11	−	3.08127e11i	0.275994	−	0.478035i	−0.694392	−	0.719597i	$-0.744326\pi$
$421$	1.77897e11	−	3.08127e11i	0.275994	−	0.478035i	0.970385	+	0.241562i	$0.0776597\pi$
$422$	5.71301e11			0.876918
$423$	5.81074e10	−	1.00645e11i	0.0882469	−	0.152848i
$424$	4.26523e11	+	7.38759e11i	0.640908	+	1.11009i
$425$	1.14731e12	+	1.98721e12i	1.70582	+	2.95456i
$426$	−3.84442e11			−0.565572
$427$	6.61120e10	+	1.14509e11i	0.0962398	+	0.166692i
$428$	−2.67411e11			−0.385196
$429$	−3.02167e11			−0.430715
$430$	1.27117e12	+	4.28537e11i	1.79306	+	0.604478i
$431$	−2.09610e11			−0.292593			−0.146296	−	0.989241i	$-0.546735\pi$
$431$	−2.09610e11			−0.292593			−0.146296	+	0.989241i	$0.546735\pi$
$432$	9.20138e11			1.27109
$433$	4.42503e11	+	7.66438e11i	0.604952	+	1.04781i	0.992059	+	0.125773i	$0.0401411\pi$
$433$	4.42503e11	+	7.66438e11i	0.604952	+	1.04781i	−0.387107	+	0.922035i	$0.626526\pi$
$434$	−2.53613e10			−0.0343137
$435$	−2.90135e11	−	5.02528e11i	−0.388506	−	0.672912i
$436$	9.77385e10	+	1.69288e11i	0.129532	+	0.224356i
$437$	−2.50189e11	+	4.33339e11i	−0.328172	+	0.568410i
$438$	−6.86503e11			−0.891269
$439$	3.39709e10	−	5.88394e10i	0.0436533	−	0.0756097i	−0.843373	−	0.537328i	$-0.819434\pi$
$439$	3.39709e10	−	5.88394e10i	0.0436533	−	0.0756097i	0.887027	+	0.461719i	$0.152767\pi$
$440$	−1.08356e12	−	1.87679e12i	−1.37822	−	2.38714i
$441$	1.14347e11			0.143963
$442$	−2.03324e11	−	3.52168e11i	−0.253390	−	0.438884i
$443$	−2.61024e11	+	4.52108e11i	−0.322006	+	0.557731i	−0.980902	−	0.194503i	$-0.937691\pi$
$443$	−2.61024e11	+	4.52108e11i	−0.322006	+	0.557731i	0.658896	+	0.752234i	$0.271024\pi$
$444$	2.33258e10	−	4.04014e10i	0.0284848	−	0.0493371i
$445$	4.77199e10	−	8.26533e10i	0.0576872	−	0.0999172i
$446$	−1.28558e12			−1.53848
$447$	3.71149e11	−	6.42849e11i	0.439708	−	0.761596i
$448$	1.49584e11	−	2.59087e11i	0.175442	−	0.303875i
$449$	1.61677e11	+	2.80033e11i	0.187732	+	0.325162i	0.944494	−	0.328529i	$-0.106553\pi$
$449$	1.61677e11	+	2.80033e11i	0.187732	+	0.325162i	−0.756761	+	0.653691i	$0.773220\pi$
$450$	−1.84404e11	−	3.19397e11i	−0.211989	−	0.367176i
$451$	1.59132e12			1.81118
$452$	2.48508e11			0.280039
$453$	−3.97226e11	−	6.88016e11i	−0.443196	−	0.767638i
$454$	−1.68709e11	−	2.92213e11i	−0.186375	−	0.322811i
$455$	−1.04377e11	+	1.80786e11i	−0.114170	+	0.197749i
$456$	1.47101e11	−	2.54787e11i	0.159321	−	0.275953i
$457$	1.43190e12			1.53564			0.767821	−	0.640665i	$-0.221341\pi$
$457$	1.43190e12			1.53564			0.767821	+	0.640665i	$0.221341\pi$
$458$	−3.02313e11	+	5.23621e11i	−0.321042	+	0.556061i
$459$	−9.25802e11	+	1.60354e12i	−0.973556	+	1.68625i
$460$	−3.07140e11	+	5.31982e11i	−0.319835	+	0.553971i
$461$	−7.75088e11	−	1.34249e12i	−0.799276	−	1.38439i	−0.920088	−	0.391711i	$-0.871883\pi$
$461$	−7.75088e11	−	1.34249e12i	−0.799276	−	1.38439i	0.120812	−	0.992675i	$-0.461450\pi$
$462$	−1.00612e12			−1.02745
$463$	−3.99204e11	−	6.91442e11i	−0.403720	−	0.699264i	0.590451	−	0.807073i	$-0.298950\pi$
$463$	−3.99204e11	−	6.91442e11i	−0.403720	−	0.699264i	−0.994172	+	0.107809i	$0.965616\pi$
$464$	−3.02845e11	+	5.24544e11i	−0.303312	+	0.525352i
$465$	8.77026e10			0.0869910
$466$	2.54268e11	−	4.40405e11i	0.249778	−	0.432629i
$467$	−2.88270e11	−	4.99299e11i	−0.280462	−	0.485774i	0.691037	−	0.722820i	$-0.257154\pi$
$467$	−2.88270e11	−	4.99299e11i	−0.280462	−	0.485774i	−0.971499	+	0.237045i	$0.923821\pi$
$468$	6.37999e9	+	1.10505e10i	0.00614771	+	0.0106481i
$469$	8.97360e11			0.856424
$470$	−8.73816e11	−	1.51349e12i	−0.825999	−	1.43067i
$471$	2.95565e11			0.276732
$472$	−7.94829e11			−0.737114
$473$	1.57126e12	−	1.38379e12i	1.44335	−	1.27114i
$474$	−1.30696e12			−1.18921
$475$	−8.81987e11			−0.794952
$476$	−1.32171e11	−	2.28927e11i	−0.118006	−	0.204393i
$477$	3.47018e11			0.306916
$478$	4.83337e11	+	8.37165e11i	0.423472	+	0.733475i
$479$	−4.32876e11	−	7.49763e11i	−0.375711	−	0.650750i	0.614722	−	0.788744i	$-0.289268\pi$
$479$	−4.32876e11	−	7.49763e11i	−0.375711	−	0.650750i	−0.990433	+	0.137993i	$0.955935\pi$
$480$	4.19012e11	−	7.25750e11i	0.360281	−	0.624024i
$481$	−7.73841e10			−0.0659172
$482$	−1.91285e11	+	3.31315e11i	−0.161424	+	0.279595i
$483$	−4.45211e11	−	7.71128e11i	−0.372223	−	0.644710i
$484$	7.90476e11			0.654764
$485$	2.31645e11	+	4.01220e11i	0.190101	+	0.329265i
$486$	2.72579e11	−	4.72121e11i	0.221630	−	0.383875i
$487$	−2.98357e11	+	5.16769e11i	−0.240356	+	0.416309i	−0.960816	−	0.277188i	$-0.910598\pi$
$487$	−2.98357e11	+	5.16769e11i	−0.240356	+	0.416309i	0.720460	+	0.693497i	$0.243931\pi$
$488$	−1.89734e11	+	3.28629e11i	−0.151446	+	0.262311i
$489$	4.86392e11			0.384677
$490$	8.59773e11	−	1.48917e12i	0.673754	−	1.16698i
$491$	6.73336e11	−	1.16625e12i	0.522836	−	0.905578i	−0.476811	−	0.879006i	$-0.658207\pi$
$491$	6.73336e11	−	1.16625e12i	0.522836	−	0.905578i	0.999647	−	0.0265723i	$-0.00845923\pi$
$492$	1.32604e11	+	2.29678e11i	0.102027	+	0.176716i
$493$	−6.09419e11	−	1.05555e12i	−0.464628	−	0.804759i
$494$	1.56304e11			0.118086
$495$	−8.81584e11			−0.659994
$496$	−4.57724e10	−	7.92802e10i	−0.0339576	−	0.0588162i
$497$	2.07268e11	+	3.59000e11i	0.152381	+	0.263931i
$498$	2.24910e11	−	3.89555e11i	0.163861	−	0.283816i
$499$	7.49790e11	−	1.29867e12i	0.541361	−	0.937665i	−0.457465	−	0.889228i	$-0.651242\pi$
$499$	7.49790e11	−	1.29867e12i	0.541361	−	0.937665i	0.998826	−	0.0484375i	$-0.0154242\pi$
$500$	−5.07264e11			−0.362969
$501$	−3.98838e11	+	6.90807e11i	−0.282831	+	0.489877i
$502$	2.49677e11	−	4.32453e11i	0.175474	−	0.303929i
$503$	3.28076e11	−	5.68243e11i	0.228517	−	0.395802i	−0.728852	−	0.684671i	$-0.759946\pi$
$503$	3.28076e11	−	5.68243e11i	0.228517	−	0.395802i	0.957369	+	0.288869i	$0.0932791\pi$
$504$	−6.63263e10	−	1.14881e11i	−0.0457876	−	0.0793065i
$505$	−3.48177e12			−2.38226
$506$	2.45549e12	+	4.25304e12i	1.66518	+	2.88418i
$507$	6.22686e11	−	1.07852e12i	0.418537	−	0.724927i
$508$	−2.00141e11			−0.133337
$509$	−1.99995e11	+	3.46401e11i	−0.132065	+	0.228744i	−0.924473	−	0.381249i	$-0.875494\pi$
$509$	−1.99995e11	+	3.46401e11i	−0.132065	+	0.228744i	0.792407	+	0.609992i	$0.208828\pi$
$510$	2.34118e12	+	4.05504e12i	1.53239	+	2.65417i
$511$	3.70121e11	+	6.41069e11i	0.240132	+	0.415921i
$512$	6.79317e11			0.436876
$513$	−3.55851e11	−	6.16352e11i	−0.226851	−	0.392917i
$514$	6.60932e10			0.0417660
$515$	3.41007e12			2.13615
$516$	3.30657e11	+	1.11472e11i	0.205331	+	0.0692214i
$517$	−2.72769e12			−1.67914
$518$	−2.57665e11			−0.157243
$519$	−3.09161e11	−	5.35482e11i	−0.187039	−	0.323960i
$520$	−5.99101e11			−0.359323
$521$	7.96574e11	+	1.37971e12i	0.473649	+	0.820383i	0.999545	−	0.0301653i	$-0.00960338\pi$
$521$	7.96574e11	+	1.37971e12i	0.473649	+	0.820383i	−0.525896	+	0.850549i	$0.676270\pi$
$522$	9.79499e10	+	1.69654e11i	0.0577413	+	0.100011i
$523$	−6.44823e11	+	1.11687e12i	−0.376863	+	0.652745i	−0.990604	−	0.136762i	$-0.956330\pi$
$523$	−6.44823e11	+	1.11687e12i	−0.376863	+	0.652745i	0.613741	+	0.789507i	$0.289664\pi$
$524$	−5.01026e11			−0.290315
$525$	7.84749e11	−	1.35922e12i	0.450831	−	0.780862i
$526$	1.92479e12	+	3.33383e12i	1.09634	+	1.89892i
$527$	1.84217e11			0.104035
$528$	−1.81587e12	−	3.14517e12i	−1.01679	−	1.76113i
$529$	−1.27254e12	+	2.20410e12i	−0.706514	+	1.22372i
$530$	2.60922e12	−	4.51930e12i	1.43638	−	2.48788i
$531$	−1.61668e11	+	2.80017e11i	−0.0882466	+	0.152848i
$532$	1.01605e11			0.0549938
$533$	2.19960e11	−	3.80982e11i	0.118051	−	0.204471i
$534$	6.35818e10	−	1.10127e11i	0.0338374	−	0.0586081i
$535$	−2.55375e12	−	4.42323e12i	−1.34768	−	2.33425i
$536$	1.28766e12	+	2.23030e12i	0.673846	+	1.16714i
$537$	−1.63964e12			−0.850870
$538$	−3.60862e12			−1.85704
$539$	−1.34193e12	−	2.32428e12i	−0.684824	−	1.18615i
$540$	−4.36855e11	−	7.56654e11i	−0.221088	−	0.382935i
$541$	−2.93512e11	+	5.08377e11i	−0.147312	+	0.255152i	−0.930233	−	0.366969i	$-0.880395\pi$
$541$	−2.93512e11	+	5.08377e11i	−0.147312	+	0.255152i	0.782921	+	0.622121i	$0.213729\pi$
$542$	4.90596e11	−	8.49737e11i	0.244190	−	0.422949i
$543$	−7.62807e10			−0.0376544
$544$	8.80122e11	−	1.52442e12i	0.430872	−	0.746292i
$545$	−1.86679e12	+	3.23338e12i	−0.906382	+	1.56990i
$546$	−1.39071e11	+	2.40879e11i	−0.0669685	+	0.115993i
$547$	9.97254e11	+	1.72729e12i	0.476281	+	0.824942i	0.999631	−	0.0271756i	$-0.00865134\pi$
$547$	9.97254e11	+	1.72729e12i	0.476281	+	0.824942i	−0.523350	+	0.852118i	$0.675318\pi$
$548$	−5.48919e11			−0.260013
$549$	7.71837e10	+	1.33686e11i	0.0362618	+	0.0628073i
$550$	−4.32816e12	+	7.49659e12i	−2.01684	+	3.49327i
$551$	4.68486e11			0.216528
$552$	1.27771e12	−	2.21305e12i	0.585741	−	1.01453i
$553$	7.04634e11	+	1.22046e12i	0.320406	+	0.554959i
$554$	5.58440e11	+	9.67247e11i	0.251874	+	0.436258i
$555$	8.91038e11			0.398637
$556$	−1.67653e11	−	2.90383e11i	−0.0744003	−	0.128865i
$557$	2.37000e12			1.04328			0.521639	−	0.853166i	$-0.325321\pi$
$557$	2.37000e12			1.04328			0.521639	+	0.853166i	$0.325321\pi$
$558$	−2.96085e10			−0.0129289
$559$	−1.14109e11	−	5.67453e11i	−0.0494272	−	0.245797i
$560$	−2.50900e12			−1.07809
$561$	7.30818e12			3.11513
$562$	−1.23316e12	−	2.13590e12i	−0.521444	−	0.903168i
$563$	−1.65784e12			−0.695431			−0.347716	−	0.937600i	$-0.613043\pi$
$563$	−1.65784e12			−0.695431			−0.347716	+	0.937600i	$0.613043\pi$
$564$	−2.27298e11	−	3.93691e11i	−0.0945887	−	0.163832i
$565$	2.37324e12	+	4.11057e12i	0.979768	+	1.69701i
$566$	1.57217e12	−	2.72307e12i	0.643909	−	1.11528i
$567$	9.99538e11			0.406140
$568$	−5.94838e11	+	1.03029e12i	−0.239790	+	0.415329i
$569$	1.85829e11	+	3.21866e11i	0.0743206	+	0.128727i	0.900791	−	0.434254i	$-0.142988\pi$
$569$	1.85829e11	+	3.21866e11i	0.0743206	+	0.128727i	−0.826470	+	0.562981i	$0.809655\pi$
$570$	−1.79976e12			−0.714130
$571$	5.72075e11	+	9.90862e11i	0.225211	+	0.390078i	0.956383	−	0.292116i	$-0.0943594\pi$
$571$	5.72075e11	+	9.90862e11i	0.225211	+	0.390078i	−0.731171	+	0.682194i	$0.761026\pi$
$572$	1.49745e11	−	2.59366e11i	0.0584886	−	0.101305i
$573$	6.67508e11	−	1.15616e12i	0.258679	−	0.448045i
$574$	7.32398e11	−	1.26855e12i	0.281607	−	0.487758i
$575$	−7.66086e12			−2.92262
$576$	1.74635e11	−	3.02476e11i	0.0661043	−	0.114496i
$577$	1.01879e12	−	1.76460e12i	0.382644	−	0.662758i	−0.608796	−	0.793327i	$-0.708347\pi$
$577$	1.01879e12	−	1.76460e12i	0.382644	−	0.662758i	0.991439	+	0.130569i	$0.0416804\pi$
$578$	3.42199e12	+	5.92707e12i	1.27528	+	2.20884i
$579$	6.58198e11	+	1.14003e12i	0.243390	+	0.421564i
$580$	5.75129e11			0.211028
$581$	−4.85032e11			−0.176595
$582$	3.08642e11	+	5.34584e11i	0.111507	+	0.193136i
$583$	−4.07245e12	−	7.05368e12i	−1.45998	−	2.52876i
$584$	−1.06221e12	+	1.83980e12i	−0.377878	+	0.654504i
$585$	−1.21857e11	+	2.11062e11i	−0.0430178	+	0.0745091i
$586$	3.88401e12			1.36063
$587$	1.51023e12	−	2.61579e12i	0.525013	−	0.909350i	−0.474562	−	0.880222i	$-0.657394\pi$
$587$	1.51023e12	−	2.61579e12i	0.525013	−	0.909350i	0.999576	−	0.0291278i	$-0.00927298\pi$
$588$	2.23645e11	−	3.87365e11i	0.0771545	−	0.133636i
$589$	−3.54037e10	+	6.13211e10i	−0.0121208	+	0.0209938i
$590$	2.43115e12	+	4.21088e12i	0.825996	+	1.43067i
$591$	−1.96481e12			−0.662487
$592$	−4.65037e11	−	8.05468e11i	−0.155611	−	0.269526i
$593$	−3.93652e11	+	6.81826e11i	−0.130727	+	0.226427i	−0.923957	−	0.382496i	$-0.875065\pi$
$593$	−3.93652e11	+	6.81826e11i	−0.130727	+	0.226427i	0.793230	+	0.608922i	$0.208398\pi$
$594$	−6.98504e12			−2.30213
$595$	2.52445e12	−	4.37247e12i	0.825733	−	1.43021i
$596$	3.67861e11	+	6.37154e11i	0.119420	+	0.206841i
$597$	1.17486e11	+	2.03492e11i	0.0378532	+	0.0655636i
$598$	1.35764e12			0.434140
$599$	−1.53879e12	−	2.66526e12i	−0.488381	−	0.845900i	0.511530	−	0.859265i	$-0.329079\pi$
$599$	−1.53879e12	−	2.66526e12i	−0.488381	−	0.845900i	−0.999911	+	0.0133654i	$0.995746\pi$
$600$	4.50429e12			1.41888
$601$	1.31463e12			0.411025			0.205512	−	0.978655i	$-0.434114\pi$
$601$	1.31463e12			0.411025			0.205512	+	0.978655i	$0.434114\pi$
$602$	−3.79947e11	−	1.88944e12i	−0.117907	−	0.586340i
$603$	1.04764e12			0.322689
$604$	7.87415e11			0.240734
$605$	7.54899e12	+	1.30752e13i	2.29081	+	3.96781i
$606$	−4.63909e12			−1.39735
$607$	2.86279e11	+	4.95850e11i	0.0855935	+	0.148252i	0.905644	−	0.424039i	$-0.139388\pi$
$607$	2.86279e11	+	4.95850e11i	0.0855935	+	0.148252i	−0.820050	+	0.572291i	$0.806055\pi$
$608$	3.38293e11	+	5.85941e11i	0.100398	+	0.173895i
$609$	−4.16835e11	+	7.21980e11i	−0.122797	+	0.212690i
$610$	2.32137e12			0.678828
$611$	−3.77034e11	+	6.53042e11i	−0.109445	+	0.189564i
$612$	−1.54305e11	−	2.67265e11i	−0.0444631	−	0.0770123i
$613$	−4.57559e12			−1.30881			−0.654403	−	0.756146i	$-0.727080\pi$
$613$	−4.57559e12			−1.30881			−0.654403	+	0.756146i	$0.727080\pi$
$614$	4.25837e11	+	7.37572e11i	0.120917	+	0.209434i
$615$	−2.53272e12	+	4.38681e12i	−0.713921	+	1.23655i
$616$	−1.55675e12	+	2.69637e12i	−0.435618	+	0.754513i
$617$	2.69395e12	−	4.66606e12i	0.748352	−	1.29618i	−0.200260	−	0.979743i	$-0.564179\pi$
$617$	2.69395e12	−	4.66606e12i	0.748352	−	1.29618i	0.948612	−	0.316441i	$-0.102488\pi$
$618$	4.54356e12			1.25299
$619$	−3.18755e11	+	5.52101e11i	−0.0872669	+	0.151151i	−0.906355	−	0.422517i	$-0.861147\pi$
$619$	−3.18755e11	+	5.52101e11i	−0.0872669	+	0.151151i	0.819088	+	0.573668i	$0.194480\pi$
$620$	−4.34628e10	+	7.52798e10i	−0.0118129	+	0.0204605i
$621$	−3.09089e12	−	5.35357e12i	−0.834010	−	1.44455i
$622$	−1.48738e12	−	2.57622e12i	−0.398443	−	0.690123i
$623$	−1.37118e11			−0.0364669
$624$	−1.00399e12			−0.265094
$625$	−1.25577e12	−	2.17506e12i	−0.329193	−	0.570179i
$626$	−2.74320e12	−	4.75135e12i	−0.713957	−	1.23661i
$627$	−1.40452e12	+	2.43271e12i	−0.362932	+	0.628617i
$628$	−1.46473e11	+	2.53699e11i	−0.0375786	+	0.0650880i
$629$	1.87160e12			0.476744
$630$	−4.05746e11	+	7.02772e11i	−0.102617	+	0.177739i
$631$	−1.49381e12	+	2.58736e12i	−0.375115	+	0.649718i	−0.990344	−	0.138630i	$-0.955730\pi$
$631$	−1.49381e12	+	2.58736e12i	−0.375115	+	0.649718i	0.615229	+	0.788348i	$0.289063\pi$
$632$	−2.02222e12	+	3.50259e12i	−0.504199	+	0.873299i
$633$	1.41919e12	+	2.45811e12i	0.351337	+	0.608534i
$634$	1.66026e11			0.0408106
$635$	−1.91134e12	−	3.31053e12i	−0.466504	−	0.808008i
$636$	6.78713e11	−	1.17556e12i	0.164486	−	0.284898i
$637$	−7.41950e11			−0.178545
$638$	2.29899e12	−	3.98197e12i	0.549344	−	0.951491i
$639$	2.41979e11	+	4.19121e11i	0.0574149	+	0.0994455i
$640$	−4.33810e12	−	7.51381e12i	−1.02209	−	1.77032i
$641$	−9.41436e11			−0.220257			−0.110129	−	0.993917i	$-0.535126\pi$
$641$	−9.41436e11			−0.220257			−0.110129	+	0.993917i	$0.535126\pi$
$642$	−3.40261e12	−	5.89349e12i	−0.790505	−	1.36919i
$643$	−4.61925e12			−1.06567			−0.532835	−	0.846219i	$-0.678873\pi$
$643$	−4.61925e12			−1.06567			−0.532835	+	0.846219i	$0.678873\pi$
$644$	8.82534e11			0.202183
$645$	1.31391e12	+	6.53393e12i	0.298913	+	1.48647i
$646$	−3.78034e12			−0.854052
$647$	8.74488e12			1.96194			0.980968	−	0.194171i	$-0.0622017\pi$
$647$	8.74488e12			1.96194			0.980968	+	0.194171i	$0.0622017\pi$
$648$	1.43428e12	+	2.48425e12i	0.319556	+	0.553488i
$649$	7.58904e12			1.67914
$650$	1.19652e12	+	2.07243e12i	0.262911	+	0.455376i
$651$	−6.30010e10	−	1.09121e11i	−0.0137478	−	0.0238119i
$652$	−2.41041e11	+	4.17496e11i	−0.0522369	+	0.0904770i
$653$	1.25680e12			0.270493			0.135246	−	0.990812i	$-0.456817\pi$
$653$	1.25680e12			0.270493			0.135246	+	0.990812i	$0.456817\pi$
$654$	−2.48730e12	+	4.30813e12i	−0.531654	+	0.920851i
$655$	−4.78476e12	−	8.28745e12i	−1.01572	−	1.75928i
$656$	5.28737e12			1.11474
$657$	4.32105e11	+	7.48428e11i	0.0904784	+	0.156713i
$658$	−1.25541e12	+	2.17443e12i	−0.261077	+	0.452198i
$659$	−2.45352e12	+	4.24962e12i	−0.506763	+	0.877739i	0.493206	+	0.869912i	$0.335825\pi$
$659$	−2.45352e12	+	4.24962e12i	−0.506763	+	0.877739i	−0.999969	+	0.00782685i	$0.997509\pi$
$660$	−1.72424e12	+	2.98647e12i	−0.353712	+	0.612648i
$661$	−6.09536e11			−0.124192			−0.0620959	−	0.998070i	$-0.519778\pi$
$661$	−6.09536e11			−0.124192			−0.0620959	+	0.998070i	$0.519778\pi$
$662$	4.28111e10	−	7.41510e10i	0.00866355	−	0.0150057i
$663$	1.01017e12	−	1.74967e12i	0.203041	−	0.351678i
$664$	−6.95995e11	−	1.20550e12i	−0.138947	−	0.240664i
$665$	9.70323e11	+	1.68065e12i	0.192406	+	0.333257i
$666$	−3.00816e11			−0.0592470
$667$	4.06922e12			0.796059
$668$	−3.95304e11	−	6.84687e11i	−0.0768135	−	0.133045i
$669$	−3.19355e12	−	5.53139e12i	−0.616391	−	1.06762i
$670$	7.87717e12	−	1.36437e13i	1.51020	−	2.61574i
$671$	1.81159e12	−	3.13776e12i	0.344991	−	0.597542i
$672$	−1.20399e12			−0.227751
$673$	−5.13427e12	+	8.89282e12i	−0.964742	+	1.67098i	−0.254435	+	0.967090i	$0.581890\pi$
$673$	−5.13427e12	+	8.89282e12i	−0.964742	+	1.67098i	−0.710307	+	0.703892i	$0.751444\pi$
$674$	7.40284e11	−	1.28221e12i	0.138175	−	0.239326i
$675$	5.44814e12	−	9.43645e12i	1.01014	−	1.74961i
$676$	6.17170e11	+	1.06897e12i	0.113670	+	0.196882i
$677$	−5.48520e12			−1.00356			−0.501780	−	0.864995i	$-0.667321\pi$
$677$	−5.48520e12			−1.00356			−0.501780	+	0.864995i	$0.667321\pi$
$678$	3.16209e12	+	5.47690e12i	0.574699	+	0.995408i
$679$	3.32803e11	−	5.76432e11i	0.0600860	−	0.104072i
$680$	1.44898e13			2.59879
$681$	8.38194e11	−	1.45180e12i	0.149342	−	0.258668i
$682$	3.47472e11	+	6.01840e11i	0.0615022	+	0.106525i
$683$	1.41220e12	+	2.44600e12i	0.248315	+	0.430095i	0.963058	−	0.269292i	$-0.0867898\pi$
$683$	1.41220e12	+	2.44600e12i	0.248315	+	0.430095i	−0.714743	+	0.699387i	$0.753456\pi$
$684$	1.18621e11			0.0207209
$685$	−5.24214e12	−	9.07965e12i	−0.909706	−	1.57566i
$686$	−5.93956e12			−1.02399
$687$	−3.00394e12			−0.514501
$688$	5.22072e12	−	4.59782e12i	0.888346	−	0.782355i
$689$	−2.25165e12			−0.380640
$690$	−1.56325e13			−2.62548
$691$	−2.60585e12	−	4.51347e12i	−0.434809	−	0.753112i	0.562471	−	0.826817i	$-0.309851\pi$
$691$	−2.60585e12	−	4.51347e12i	−0.434809	−	0.753112i	−0.997280	+	0.0737054i	$0.976518\pi$
$692$	6.12844e11			0.101595
$693$	6.33284e11	+	1.09688e12i	0.104304	+	0.180659i
$694$	−7.31456e11	−	1.26692e12i	−0.119694	−	0.207315i
$695$	3.20215e12	−	5.54628e12i	0.520607	−	0.901717i
$696$	−2.39254e12			−0.386472
$697$	−5.31991e12	+	9.21436e12i	−0.853802	+	1.47883i
$698$	−2.22911e12	−	3.86093e12i	−0.355453	−	0.615662i
$699$	2.52655e12			0.400295
$700$	7.77797e11	+	1.34718e12i	0.122440	+	0.212073i
$701$	2.32315e12	−	4.02381e12i	0.363368	−	0.629371i	−0.625145	−	0.780508i	$-0.714960\pi$
$701$	2.32315e12	−	4.02381e12i	0.363368	−	0.629371i	0.988513	+	0.151137i	$0.0482936\pi$
$702$	−9.65506e11	+	1.67231e12i	−0.150051	+	0.259896i
$703$	−3.59694e11	+	6.23008e11i	−0.0555436	+	0.0962044i
$704$	−8.19774e12			−1.25782
$705$	4.34136e12	−	7.51945e12i	0.661873	−	1.14640i
$706$	−5.95691e12	+	1.03177e13i	−0.902402	+	1.56301i
$707$	2.50112e12	+	4.33207e12i	0.376485	+	0.652091i
$708$	6.32394e11	+	1.09534e12i	0.0945884	+	0.163832i
$709$	3.27619e11			0.0486923			0.0243462	−	0.999704i	$-0.492250\pi$
$709$	3.27619e11			0.0486923			0.0243462	+	0.999704i	$0.492250\pi$
$710$	7.27775e12			1.07482
$711$	8.22638e11	+	1.42485e12i	0.120725	+	0.209101i
$712$	−1.96757e11	−	3.40793e11i	−0.0286926	−	0.0496971i
$713$	−3.07514e11	+	5.32629e11i	−0.0445617	+	0.0771831i
$714$	3.36356e12	−	5.82586e12i	0.484348	−	0.838915i
$715$	5.72023e12			0.818533
$716$	8.12555e11	−	1.40739e12i	0.115543	−	0.200127i
$717$	−2.40135e12	+	4.15927e12i	−0.339328	+	0.587733i
$718$	−8.85625e11	+	1.53395e12i	−0.124363	+	0.215402i
$719$	2.14255e12	+	3.71100e12i	0.298986	+	0.517859i	0.975904	−	0.218199i	$-0.0700183\pi$
$719$	2.14255e12	+	3.71100e12i	0.298986	+	0.517859i	−0.676918	+	0.736058i	$0.736685\pi$
$720$	−2.92918e12			−0.406209
$721$	−2.44962e12	−	4.24287e12i	−0.337590	−	0.584724i
$722$	−3.34307e12	+	5.79036e12i	−0.457855	+	0.793028i
$723$	−1.90071e12			−0.258699
$724$	3.78025e10	−	6.54758e10i	0.00511325	−	0.00885641i
$725$	3.58630e12	+	6.21165e12i	0.482087	+	0.834999i
$726$	1.00582e13	+	1.74214e13i	1.34371	+	2.32738i
$727$	−7.89368e12			−1.04803			−0.524016	−	0.851708i	$-0.675567\pi$
$727$	−7.89368e12			−1.04803			−0.524016	+	0.851708i	$0.675567\pi$
$728$	4.30363e11	+	7.45411e11i	0.0567864	+	0.0983569i
$729$	8.48089e12			1.11216
$730$	1.29959e13			1.69377
$731$	2.75982e12	+	1.37243e13i	0.357481	+	1.77772i
$732$	6.03837e11			0.0777356
$733$	1.64619e12			0.210626			0.105313	−	0.994439i	$-0.466416\pi$
$733$	1.64619e12			0.210626			0.105313	+	0.994439i	$0.466416\pi$
$734$	−1.14538e12	−	1.98386e12i	−0.145652	−	0.252277i
$735$	8.54318e12			1.07976
$736$	2.93838e12	+	5.08943e12i	0.369112	+	0.639321i
$737$	−1.22946e13	−	2.12949e13i	−1.53501	−	2.65872i
$738$	8.55052e11	−	1.48099e12i	0.106106	−	0.183780i
$739$	2.50827e12			0.309367			0.154683	−	0.987964i	$-0.450564\pi$
$739$	2.50827e12			0.309367			0.154683	+	0.987964i	$0.450564\pi$
$740$	−4.41572e11	+	7.64826e11i	−0.0541326	+	0.0937605i
$741$	3.88280e11	+	6.72521e11i	0.0473111	+	0.0819453i
$742$	−7.49731e12			−0.908004
$743$	−2.67132e12	−	4.62686e12i	−0.321571	−	0.556977i	0.659242	−	0.751931i	$-0.270877\pi$
$743$	−2.67132e12	−	4.62686e12i	−0.321571	−	0.556977i	−0.980812	+	0.194954i	$0.937544\pi$
$744$	1.80806e11	−	3.13165e11i	0.0216339	−	0.0374710i
$745$	−7.02609e12	+	1.21695e13i	−0.835623	+	1.44734i
$746$	5.55095e12	−	9.61453e12i	0.656210	−	1.13659i
$747$	−5.66260e11			−0.0665385
$748$	−3.62172e12	+	6.27300e12i	−0.423017	+	0.732686i
$749$	−3.66897e12	+	6.35484e12i	−0.425967	+	0.737796i
$750$	−6.45457e12	−	1.11796e13i	−0.744889	−	1.29019i
$751$	7.18280e12	+	1.24410e13i	0.823975	+	1.42717i	0.902700	+	0.430270i	$0.141582\pi$
$751$	7.18280e12	+	1.24410e13i	0.823975	+	1.42717i	−0.0787249	+	0.996896i	$0.525085\pi$
$752$	−9.06311e12			−1.03347
$753$	2.48093e12			0.281214
$754$	−6.35555e11	−	1.10081e12i	−0.0716114	−	0.124035i
$755$	7.51975e12	+	1.30246e13i	0.842253	+	1.45882i
$756$	−6.27627e11	+	1.08708e12i	−0.0698801	+	0.121036i
$757$	−5.70193e12	+	9.87603e12i	−0.631089	+	1.09308i	0.356241	+	0.934394i	$0.384058\pi$
$757$	−5.70193e12	+	9.87603e12i	−0.631089	+	1.09308i	−0.987330	+	0.158683i	$0.949275\pi$
$758$	−1.31785e13			−1.44995
$759$	−1.21996e13	+	2.11303e13i	−1.33431	+	2.31109i
$760$	−2.78472e12	+	4.82328e12i	−0.302775	+	0.524422i
$761$	−2.76116e12	+	4.78247e12i	−0.298442	+	0.516918i	−0.975780	−	0.218755i	$-0.929800\pi$
$761$	−2.76116e12	+	4.78247e12i	−0.298442	+	0.516918i	0.677337	+	0.735673i	$0.263134\pi$
$762$	−2.54665e12	−	4.41093e12i	−0.273636	−	0.473951i
$763$	5.36402e12			0.572968
$764$	6.61595e11	+	1.14592e12i	0.0702542	+	0.121684i
$765$	2.94721e12	−	5.10472e12i	0.311125	−	0.538884i
$766$	1.70248e13			1.78671
$767$	1.04899e12	−	1.81691e12i	0.109444	−	0.189563i
$768$	−2.96411e12	−	5.13400e12i	−0.307446	−	0.532513i
$769$	−7.72881e12	−	1.33867e13i	−0.796974	−	1.38040i	−0.921578	−	0.388192i	$-0.873100\pi$
$769$	−7.72881e12	−	1.33867e13i	−0.796974	−	1.38040i	0.124605	−	0.992206i	$-0.460234\pi$
$770$	1.90466e13			1.95258
$771$	1.64185e11	+	2.84376e11i	0.0167335	+	0.0289833i
$772$	−1.30473e12			−0.132204
$773$	1.11394e13			1.12216			0.561080	−	0.827762i	$-0.310386\pi$
$773$	1.11394e13			1.12216			0.561080	+	0.827762i	$0.310386\pi$
$774$	−4.43576e11	−	2.20586e12i	−0.0444257	−	0.220925i
$775$	−1.08407e12			−0.107945
$776$	1.91022e12			0.189106
$777$	−6.40076e11	−	1.10864e12i	−0.0629995	−	0.109118i
$778$	8.53185e12			0.834901
$779$	−2.04482e12	−	3.54173e12i	−0.198946	−	0.344585i
$780$	4.76666e11	+	8.25609e11i	0.0461093	+	0.0798636i
$781$	5.67952e12	−	9.83722e12i	0.546238	−	0.946112i
$782$	−3.28357e13			−3.13990
$783$	−2.89389e12	+	5.01236e12i	−0.275140	+	0.476557i
$784$	−4.45873e12	−	7.72275e12i	−0.421492	−	0.730045i
$785$	−5.59524e12			−0.525903
$786$	−6.37519e12	−	1.10421e13i	−0.595788	−	1.03193i
$787$	−9.47207e12	+	1.64061e13i	−0.880153	+	1.52447i	−0.0289837	+	0.999580i	$0.509227\pi$
$787$	−9.47207e12	+	1.64061e13i	−0.880153	+	1.52447i	−0.851170	+	0.524891i	$0.824106\pi$
$788$	9.73703e11	−	1.68650e12i	0.0899619	−	0.155819i
$789$	−9.56286e12	+	1.65634e13i	−0.878499	+	1.52161i
$790$	2.47416e13			2.25998
$791$	3.40962e12	−	5.90564e12i	0.309679	−	0.536380i
$792$	−1.81746e12	+	3.14793e12i	−0.164135	+	0.284290i
$793$	−5.00812e11	−	8.67432e11i	−0.0449724	−	0.0778944i
$794$	5.48522e12	+	9.50068e12i	0.489781	+	0.848325i
$795$	2.59266e13			2.30194
$796$	−2.32891e11			−0.0205610
$797$	−4.08267e12	−	7.07139e12i	−0.358411	−	0.620787i	0.629284	−	0.777175i	$-0.283348\pi$
$797$	−4.08267e12	−	7.07139e12i	−0.358411	−	0.620787i	−0.987696	+	0.156389i	$0.950015\pi$
$798$	1.29285e12	+	2.23929e12i	0.112859	+	0.195478i
$799$	9.11889e12	−	1.57944e13i	0.791556	−	1.37102i
$800$	−5.17933e12	+	8.97085e12i	−0.447062	+	0.774335i
$801$	−1.60081e11			−0.0137402
$802$	−6.60556e11	+	1.14412e12i	−0.0563800	+	0.0976530i
$803$	1.01420e13	−	1.75664e13i	0.860801	−	1.49095i
$804$	2.04902e12	−	3.54901e12i	0.172939	−	0.299540i
$805$	8.42814e12	+	1.45980e13i	0.707376	+	1.22521i
$806$	1.92117e11			0.0160346
$807$	−8.96431e12	−	1.55266e13i	−0.744023	−	1.28868i
$808$	−7.17795e12	+	1.24326e13i	−0.592446	+	1.02615i
$809$	−1.59752e13			−1.31123			−0.655613	−	0.755097i	$-0.727590\pi$
$809$	−1.59752e13			−1.31123			−0.655613	+	0.755097i	$0.727590\pi$
$810$	8.77411e12	−	1.51972e13i	0.716177	−	1.24046i
$811$	−3.50066e12	−	6.06331e12i	−0.284155	−	0.492171i	0.688249	−	0.725475i	$-0.258380\pi$
$811$	−3.50066e12	−	6.06331e12i	−0.284155	−	0.492171i	−0.972404	+	0.233304i	$0.925046\pi$
$812$	−4.13143e11	−	7.15584e11i	−0.0333502	−	0.0577642i
$813$	4.87483e12			0.391338
$814$	3.53024e12	+	6.11455e12i	0.281835	+	0.488152i
$815$	−9.20771e12			−0.731042
$816$	2.42824e13			1.91728
$817$	−5.09888e12	−	1.71894e12i	−0.400383	−	0.134978i
$818$	1.76335e13			1.37705
$819$	3.50143e11			0.0271936
$820$	−2.51029e12	−	4.34795e12i	−0.193893	−	0.335832i
$821$	2.29669e13			1.76424			0.882121	−	0.471023i	$-0.156115\pi$
$821$	2.29669e13			1.76424			0.882121	+	0.471023i	$0.156115\pi$
$822$	−6.98460e12	−	1.20977e13i	−0.533603	−	0.924227i
$823$	1.08605e13	+	1.88110e13i	0.825187	+	1.42927i	0.901776	+	0.432203i	$0.142264\pi$
$823$	1.08605e13	+	1.88110e13i	0.825187	+	1.42927i	−0.0765892	+	0.997063i	$0.524403\pi$
$824$	7.03014e12	−	1.21766e13i	0.531241	−	0.920137i
$825$	−4.30070e13			−3.23219
$826$	3.49283e12	−	6.04975e12i	0.261076	−	0.452197i
$827$	−8.99029e12	−	1.55716e13i	−0.668342	−	1.15760i	−0.978368	−	0.206874i	$-0.933671\pi$
$827$	−8.99029e12	−	1.55716e13i	−0.668342	−	1.15760i	0.310025	−	0.950728i	$-0.399662\pi$
$828$	1.03033e12			0.0761798
$829$	−7.57529e12	−	1.31208e13i	−0.557063	−	0.964861i	−0.997740	−	0.0671952i	$-0.978595\pi$
$829$	−7.57529e12	−	1.31208e13i	−0.557063	−	0.964861i	0.440677	−	0.897666i	$-0.354738\pi$
$830$	−4.25769e12	+	7.37454e12i	−0.311403	+	0.539366i
$831$	−2.77448e12	+	4.80555e12i	−0.201826	+	0.349573i
$832$	−1.13313e12	+	1.96264e12i	−0.0819833	+	0.141999i
$833$	1.79447e13			1.29132
$834$	4.26652e12	−	7.38984e12i	0.305370	−	0.528917i
$835$	7.55026e12	−	1.30774e13i	0.537493	−	0.930965i
$836$	−1.39208e12	−	2.41116e12i	−0.0985681	−	0.170725i
$837$	−4.37386e11	−	7.57575e11i	−0.0308035	−	0.0533533i
$838$	−1.21579e13			−0.851647
$839$	−2.20384e13			−1.53550			−0.767751	−	0.640748i	$-0.778624\pi$
$839$	−2.20384e13			−1.53550			−0.767751	+	0.640748i	$0.778624\pi$
$840$	−4.95542e12	−	8.58303e12i	−0.343418	−	0.594818i
$841$	5.34864e12	+	9.26411e12i	0.368690	+	0.638590i
$842$	−4.48712e12	+	7.77191e12i	−0.307654	+	0.532873i
$843$	6.12670e12	−	1.06118e13i	0.417833	−	0.723708i
$844$	−2.81324e12			−0.190838
$845$	−1.17879e13	+	2.04172e13i	−0.795390	+	1.37766i
$846$	−1.46565e12	+	2.53858e12i	−0.0983701	+	0.170382i
$847$	1.08456e13	−	1.87851e13i	0.724067	−	1.25412i
$848$	−1.35312e13	−	2.34368e13i	−0.898579	−	1.55638i
$849$	1.56219e13			1.03193
$850$	−2.89388e13	−	5.01235e13i	−1.90150	−	3.29349i
$851$	−3.12427e12	+	5.41139e12i	−0.204205	+	0.353693i
$852$	1.89310e12			0.123082
$853$	−7.58605e12	+	1.31394e13i	−0.490620	+	0.849778i	−0.999942	−	0.0107977i	$-0.996563\pi$
$853$	−7.58605e12	+	1.31394e13i	−0.490620	+	0.849778i	0.509322	+	0.860576i	$0.329896\pi$
$854$	−1.66755e12	−	2.88828e12i	−0.107280	−	0.185814i
$855$	1.13282e12	+	1.96210e12i	0.0724960	+	0.125567i
$856$	−2.10591e13			−1.34063
$857$	−1.22465e13	−	2.12116e13i	−0.775529	−	1.34326i	−0.934496	−	0.355972i	$-0.884150\pi$
$857$	−1.22465e13	−	2.12116e13i	−0.775529	−	1.34326i	0.158967	−	0.987284i	$-0.449184\pi$
$858$	7.62160e12			0.480124
$859$	−1.16279e13			−0.728672			−0.364336	−	0.931268i	$-0.618704\pi$
$859$	−1.16279e13			−0.728672			−0.364336	+	0.931268i	$0.618704\pi$
$860$	−6.25956e12	−	2.11023e12i	−0.390212	−	0.131549i
$861$	7.27751e12			0.451304
$862$	5.28701e12			0.326157
$863$	1.26356e13	+	2.18855e13i	0.775439	+	1.34310i	0.934547	+	0.355839i	$0.115805\pi$
$863$	1.26356e13	+	2.18855e13i	0.775439	+	1.34310i	−0.159108	+	0.987261i	$0.550862\pi$
$864$	−8.35870e12			−0.510302
$865$	5.85261e12	+	1.01370e13i	0.355449	+	0.615656i
$866$	−1.11613e13	−	1.93320e13i	−0.674349	−	1.16801i
$867$	−1.70014e13	+	2.94473e13i	−1.02188	+	1.76995i
$868$	1.24886e11			0.00746748
$869$	1.93082e13	−	3.34428e13i	1.14856	−	1.98936i
$870$	7.31810e12	+	1.26753e13i	0.433073	+	0.750105i
$871$	−6.79769e12			−0.400202
$872$	7.69708e12	+	1.33317e13i	0.450819	+	0.780841i
$873$	3.88537e11	−	6.72966e11i	0.0226396	−	0.0392129i
$874$	6.31054e12	−	1.09302e13i	0.365818	−	0.633615i
$875$	−6.95984e12	+	1.20548e13i	−0.401387	+	0.695223i
$876$	3.38052e12			0.193961
$877$	8.14682e12	−	1.41107e13i	0.465040	−	0.805472i	−0.534164	−	0.845381i	$-0.679373\pi$
$877$	8.14682e12	−	1.41107e13i	0.465040	−	0.805472i	0.999203	+	0.0399087i	$0.0127067\pi$
$878$	−8.56852e11	+	1.48411e12i	−0.0486610	+	0.0842832i
$879$	9.64841e12	+	1.67115e13i	0.545137	+	0.944205i
$880$	3.43755e13	+	5.95402e13i	1.93231	+	3.34686i
$881$	−1.12004e13			−0.626387			−0.313193	−	0.949689i	$-0.601399\pi$
$881$	−1.12004e13			−0.626387			−0.313193	+	0.949689i	$0.601399\pi$
$882$	−2.88419e12			−0.160478
$883$	6.97507e12	+	1.20812e13i	0.386123	+	0.668784i	0.991924	−	0.126832i	$-0.0404808\pi$
$883$	6.97507e12	+	1.20812e13i	0.386123	+	0.668784i	−0.605801	+	0.795616i	$0.707147\pi$
$884$	1.00122e12	+	1.73417e12i	0.0551436	+	0.0955116i
$885$	−1.20786e13	+	2.09208e13i	−0.661871	+	1.14639i
$886$	6.58385e12	−	1.14036e13i	0.358945	−	0.621711i
$887$	2.21163e13			1.19965			0.599827	−	0.800130i	$-0.295236\pi$
$887$	2.21163e13			1.19965			0.599827	+	0.800130i	$0.295236\pi$
$888$	1.83695e12	−	3.18169e12i	0.0991376	−	0.171711i
$889$	−2.74601e12	+	4.75623e12i	−0.147450	+	0.255390i
$890$	−1.20365e12	+	2.08477e12i	−0.0643048	+	0.111379i
$891$	−1.36946e13	−	2.37197e13i	−0.727945	−	1.26084i
$892$	6.33051e12			0.334809
$893$	3.50503e12	+	6.07090e12i	0.184442	+	0.319464i
$894$	−9.36153e12	+	1.62146e13i	−0.490149	+	0.848963i
$895$	3.10394e13			1.61700
$896$	−6.23254e12	+	1.07951e13i	−0.323057	+	0.559551i
$897$	3.37257e12	+	5.84146e12i	0.173938	+	0.301269i
$898$	−4.07799e12	−	7.06329e12i	−0.209268	−	0.362463i
$899$	5.75828e11			0.0294018
$900$	9.08053e11	+	1.57279e12i	0.0461339	+	0.0799062i
$901$	5.44581e13			2.75297
$902$	−4.01380e13			−2.01895
$903$	7.18578e12	−	6.32842e12i	0.359649	−	0.316738i
$904$	1.95705e13			0.974639
$905$	1.44404e12			0.0715586
$906$	1.00193e13	+	1.73539e13i	0.494037	+	0.855698i
$907$	6.71398e12			0.329418			0.164709	−	0.986342i	$-0.447332\pi$
$907$	6.71398e12			0.329418			0.164709	+	0.986342i	$0.447332\pi$
$908$	8.30769e11	+	1.43893e12i	0.0405596	+	0.0702513i
$909$	2.91998e12	+	5.05755e12i	0.141854	+	0.245699i
$910$	2.63271e12	−	4.55999e12i	0.127267	−	0.220434i
$911$	−3.38766e11			−0.0162955			−0.00814774	−	0.999967i	$-0.502594\pi$
$911$	−3.38766e11			−0.0162955			−0.00814774	+	0.999967i	$0.502594\pi$
$912$	−4.66672e12	+	8.08299e12i	−0.223375	+	0.386897i
$913$	6.64537e12	+	1.15101e13i	0.316520	+	0.548228i
$914$	−3.61170e13			−1.71180
$915$	5.76660e12	+	9.98804e12i	0.271972	+	0.471070i
$916$	1.48867e12	−	2.57845e12i	0.0698663	−	0.121012i
$917$	−6.87425e12	+	1.19065e13i	−0.321043	+	0.556063i
$918$	2.33516e13	−	4.04461e13i	1.08524	−	1.87969i
$919$	8.51534e12			0.393806			0.196903	−	0.980423i	$-0.436912\pi$
$919$	8.51534e12			0.393806			0.196903	+	0.980423i	$0.436912\pi$
$920$	−2.41878e13	+	4.18946e13i	−1.11315	+	1.92802i
$921$	−2.11568e12	+	3.66446e12i	−0.0968905	+	0.167819i
$922$	1.95501e13	+	3.38618e13i	0.890965	+	1.54320i
$923$	−1.57010e12	−	2.71950e12i	−0.0712066	−	0.123333i
$924$	4.95442e12			0.223599
$925$	−1.10140e13			−0.494658
$926$	1.00692e13	+	1.74403e13i	0.450033	+	0.779480i
$927$	−2.85985e12	−	4.95341e12i	−0.127199	−	0.220316i
$928$	2.75110e12	−	4.76505e12i	0.121770	−	0.210912i
$929$	1.52796e13	−	2.64651e13i	0.673042	−	1.16574i	−0.303996	−	0.952673i	$-0.598321\pi$
$929$	1.52796e13	−	2.64651e13i	0.673042	−	1.16574i	0.977037	−	0.213069i	$-0.0683459\pi$
$930$	−2.21213e12			−0.0969701
$931$	−3.44871e12	+	5.97334e12i	−0.150447	+	0.260581i
$932$	−1.25208e12	+	2.16867e12i	−0.0543577	+	0.0941504i
$933$	7.38973e12	−	1.27994e13i	0.319272	−	0.552996i
$934$	7.27107e12	+	1.25939e13i	0.312635	+	0.541500i
$935$	−1.38349e14			−5.92001
$936$	5.02436e11	+	8.70244e11i	0.0213963	+	0.0370595i
$937$	2.36442e12	−	4.09530e12i	0.100207	−	0.173563i	−0.811563	−	0.584265i	$-0.801383\pi$
$937$	2.36442e12	−	4.09530e12i	0.100207	−	0.173563i	0.911770	+	0.410702i	$0.134716\pi$
$938$	−2.26342e13			−0.954669
$939$	1.36290e13	−	2.36060e13i	0.572094	−	0.990896i
$940$	4.30290e12	+	7.45284e12i	0.179757	+	0.311348i
$941$	−2.98549e12	−	5.17103e12i	−0.124126	−	0.214993i	0.797265	−	0.603630i	$-0.206279\pi$
$941$	−2.98549e12	−	5.17103e12i	−0.124126	−	0.214993i	−0.921391	+	0.388637i	$0.872946\pi$
$942$	−7.45507e12			−0.308477
$943$	−1.77611e13	−	3.07631e13i	−0.731421	−	1.26686i
$944$	2.52156e13			1.03346
$945$	−2.39752e13			−0.977955
$946$	−3.96320e13	+	3.49034e13i	−1.60893	+	1.41696i
$947$	2.13724e12			0.0863531			0.0431765	−	0.999067i	$-0.486252\pi$
$947$	2.13724e12			0.0863531			0.0431765	+	0.999067i	$0.486252\pi$
$948$	6.43581e12			0.258801
$949$	−2.80375e12	−	4.85623e12i	−0.112212	−	0.194358i
$950$	2.22465e13			0.886145
$951$	4.12430e11	+	7.14350e11i	0.0163508	+	0.0283204i
$952$	−1.04087e13	−	1.80284e13i	−0.410705	−	0.711363i
$953$	1.77976e13	−	3.08264e13i	0.698946	−	1.21061i	−0.269886	−	0.962892i	$-0.586986\pi$
$953$	1.77976e13	−	3.08264e13i	0.698946	−	1.21061i	0.968832	−	0.247718i	$-0.0796807\pi$
$954$	−8.75287e12			−0.342123
$955$	−1.26364e13	+	2.18868e13i	−0.491595	+	0.851467i
$956$	−2.38008e12	−	4.12242e12i	−0.0921576	−	0.159622i
$957$	2.28440e13			0.880378
$958$	1.09185e13	+	1.89114e13i	0.418810	+	0.725401i
$959$	−7.53136e12	+	1.30447e13i	−0.287534	+	0.498024i
$960$	1.30474e13	−	2.25988e13i	0.495798	−	0.858747i
$961$	1.31763e13	−	2.28220e13i	0.498354	−	0.863175i
$962$	1.95187e12			0.0734789
$963$	−4.28340e12	+	7.41907e12i	−0.160498	+	0.277991i
$964$	9.41938e11	−	1.63148e12i	0.0351298	−	0.0608466i
$965$	−1.24601e13	−	2.15816e13i	−0.462540	−	0.801143i
$966$	1.12296e13	+	1.94502e13i	0.414923	+	0.718667i
$967$	4.38101e13			1.61122			0.805611	−	0.592445i	$-0.201837\pi$
$967$	4.38101e13			1.61122			0.805611	+	0.592445i	$0.201837\pi$
$968$	6.22514e13			2.27882
$969$	−9.39089e12	−	1.62655e13i	−0.342176	−	0.592666i
$970$	−5.84280e12	−	1.01200e13i	−0.211908	−	0.367036i
$971$	3.28364e12	−	5.68742e12i	0.118541	−	0.205319i	−0.800649	−	0.599134i	$-0.795512\pi$
$971$	3.28364e12	−	5.68742e12i	0.118541	−	0.205319i	0.919190	+	0.393815i	$0.128845\pi$
$972$	−1.34225e12	+	2.32485e12i	−0.0482321	+	0.0835404i
$973$	−9.20103e12			−0.329100
$974$	7.52548e12	−	1.30345e13i	0.267929	−	0.464066i
$975$	−5.94464e12	+	1.02964e13i	−0.210671	+	0.364893i
$976$	6.01923e12	−	1.04256e13i	0.212333	−	0.367771i
$977$	−2.27383e13	−	3.93839e13i	−0.798423	−	1.38291i	−0.920643	−	0.390406i	$-0.872335\pi$
$977$	−2.27383e13	−	3.93839e13i	−0.798423	−	1.38291i	0.122220	−	0.992503i	$-0.460999\pi$
$978$	−1.22683e13			−0.428805
$979$	1.87864e12	+	3.25390e12i	0.0653614	+	0.113209i
$980$	−4.23375e12	+	7.33307e12i	−0.146625	+	0.253962i
$981$	6.26233e12			0.215886
$982$	−1.69836e13	+	2.94165e13i	−0.582813	+	1.00946i
$983$	−2.62267e12	−	4.54261e12i	−0.0895888	−	0.155172i	0.817749	−	0.575576i	$-0.195222\pi$
$983$	−2.62267e12	−	4.54261e12i	−0.0895888	−	0.155172i	−0.907337	+	0.420403i	$0.861889\pi$
$984$	1.04428e13	+	1.80875e13i	0.355092	+	0.615037i
$985$	3.71952e13			1.25899
$986$	1.53714e13	+	2.66241e13i	0.517927	+	0.897076i
$987$	−1.24744e13			−0.418402
$988$	−7.69681e11			−0.0256983
$989$	−4.42884e13	−	1.49306e13i	−1.47200	−	0.496241i
$990$	2.22363e13			0.735705
$991$	−1.30890e13			−0.431098			−0.215549	−	0.976493i	$-0.569154\pi$
$991$	−1.30890e13			−0.431098			−0.215549	+	0.976493i	$0.569154\pi$
$992$	4.15805e11	+	7.20196e11i	0.0136329	+	0.0236128i
$993$	4.25395e11			0.0138842
$994$	−5.22796e12	−	9.05508e12i	−0.169861	−	0.294208i
$995$	−2.22409e12	−	3.85224e12i	−0.0719364	−	0.124598i
$996$	−1.10752e12	+	1.91827e12i	−0.0356601	+	0.0617652i
$997$	−3.71973e11			−0.0119229			−0.00596147	−	0.999982i	$-0.501898\pi$
$997$	−3.71973e11			−0.0119229			−0.00596147	+	0.999982i	$0.501898\pi$
$998$	−1.89120e13	+	3.27566e13i	−0.603463	+	1.04523i
$999$	−4.44374e12	−	7.69679e12i	−0.141158	−	0.244492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.c.a.36.10	yes	64
43.6	even	3	inner	43.10.c.a.6.10	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.c.a.6.10	✓	64	43.6	even	3	inner
43.10.c.a.36.10	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)

\(f(q)\)	\(=\)	\(q-25.2231 q^{2} +(-62.6577 - 108.526i) q^{3} +124.205 q^{4} +(1186.15 + 2054.47i) q^{5} +(1580.42 + 2737.37i) q^{6} +(1704.14 - 2951.66i) q^{7} +9781.39 q^{8} +(1989.53 - 3445.96i) q^{9} +O(q^{10})\)	\(q-25.2231 q^{2} +(-62.6577 - 108.526i) q^{3} +124.205 q^{4} +(1186.15 + 2054.47i) q^{5} +(1580.42 + 2737.37i) q^{6} +(1704.14 - 2951.66i) q^{7} +9781.39 q^{8} +(1989.53 - 3445.96i) q^{9} +(-29918.4 - 51820.2i) q^{10} -93392.8 q^{11} +(-7782.41 - 13479.5i) q^{12} +(-12909.2 + 22359.4i) q^{13} +(-42983.7 + 74449.9i) q^{14} +(148643. - 257457. i) q^{15} -310310. q^{16} +(312220. - 540781. i) q^{17} +(-50182.1 + 86917.9i) q^{18} +(120008. + 207860. i) q^{19} +(147326. + 255176. i) q^{20} -427110. q^{21} +2.35566e6 q^{22} +(1.04238e6 + 1.80546e6i) q^{23} +(-612879. - 1.06154e6i) q^{24} +(-1.83735e6 + 3.18238e6i) q^{25} +(325610. - 563974. i) q^{26} -2.96522e6 q^{27} +(211663. - 366611. i) q^{28} +(975944. - 1.69039e6i) q^{29} +(-3.74924e6 + 6.49387e6i) q^{30} +(147505. + 255487. i) q^{31} +2.81892e6 q^{32} +(5.85178e6 + 1.01356e7i) q^{33} +(-7.87517e6 + 1.36402e7i) q^{34} +8.08547e6 q^{35} +(247110. - 428007. i) q^{36} +(1.49862e6 + 2.59569e6i) q^{37} +(-3.02698e6 - 5.24289e6i) q^{38} +3.23545e6 q^{39} +(1.16022e7 + 2.00956e7i) q^{40} -1.70390e7 q^{41} +1.07730e7 q^{42} +(-1.68242e7 + 1.48168e7i) q^{43} -1.15999e7 q^{44} +9.43953e6 q^{45} +(-2.62921e7 - 4.55392e7i) q^{46} +2.92066e7 q^{47} +(1.94433e7 + 3.36768e7i) q^{48} +(1.43686e7 + 2.48872e7i) q^{49} +(4.63436e7 - 8.02695e7i) q^{50} -7.82520e7 q^{51} +(-1.60339e6 + 2.77716e6i) q^{52} +(4.36055e7 + 7.55270e7i) q^{53} +7.47921e7 q^{54} +(-1.10778e8 - 1.91873e8i) q^{55} +(1.66688e7 - 2.88713e7i) q^{56} +(1.50389e7 - 2.60481e7i) q^{57} +(-2.46164e7 + 4.26368e7i) q^{58} -8.12593e7 q^{59} +(1.84622e7 - 3.19775e7i) q^{60} +(-1.93975e7 + 3.35974e7i) q^{61} +(-3.72055e6 - 6.44417e6i) q^{62} +(-6.78087e6 - 1.17448e7i) q^{63} +8.77770e7 q^{64} -6.12491e7 q^{65} +(-1.47600e8 - 2.55651e8i) q^{66} +(1.31644e8 + 2.28014e8i) q^{67} +(3.87794e7 - 6.71679e7i) q^{68} +(1.30626e8 - 2.26251e8i) q^{69} -2.03941e8 q^{70} +(-6.08133e7 + 1.05332e8i) q^{71} +(1.94604e7 - 3.37063e7i) q^{72} +(-1.08595e8 + 1.88092e8i) q^{73} +(-3.77999e7 - 6.54713e7i) q^{74} +4.60496e8 q^{75} +(1.49057e7 + 2.58174e7i) q^{76} +(-1.59154e8 + 2.75663e8i) q^{77} -8.16080e7 q^{78} +(-2.06742e8 + 3.58088e8i) q^{79} +(-3.68075e8 - 6.37524e8i) q^{80} +(1.46634e8 + 2.53977e8i) q^{81} +4.29776e8 q^{82} +(-7.11550e7 - 1.23244e8i) q^{83} -5.30493e7 q^{84} +1.48136e9 q^{85} +(4.24359e8 - 3.73727e8i) q^{86} -2.44602e8 q^{87} -9.13512e8 q^{88} +(-2.01154e7 - 3.48410e7i) q^{89} -2.38094e8 q^{90} +(4.39982e7 + 7.62071e7i) q^{91} +(1.29469e8 + 2.24247e8i) q^{92} +(1.84847e7 - 3.20164e7i) q^{93} -7.36681e8 q^{94} +(-2.84696e8 + 4.93108e8i) q^{95} +(-1.76627e8 - 3.05926e8i) q^{96} +1.95291e8 q^{97} +(-3.62421e8 - 6.27732e8i) q^{98} +(-1.85808e8 + 3.21828e8i) 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

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