LMFDB - Embedded newform 62.8.d.a.35.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,8,Mod(33,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.33"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	62.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,-80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$19.3678715800$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			35.4
Character	$\chi$	$=$	62.35
Dual form			62.8.d.a.39.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.47214 + 7.60845i) q^{2} +(-10.2355 + 31.5015i) q^{3} +(-51.7771 + 37.6183i) q^{4} +307.829 q^{5} -264.981 q^{6} +(767.579 - 557.679i) q^{7} +(-414.217 - 300.946i) q^{8} +(881.740 + 640.622i) q^{9} +(760.996 + 2342.11i) q^{10} +(5329.73 - 3872.27i) q^{11} +(-655.069 - 2016.10i) q^{12} +(2123.22 - 6534.59i) q^{13} +(6140.63 + 4461.43i) q^{14} +(-3150.78 + 9697.09i) q^{15} +(1265.73 - 3895.53i) q^{16} +(1486.65 + 1080.12i) q^{17} +(-2694.36 + 8292.38i) q^{18} +(4931.28 + 15176.9i) q^{19} +(-15938.5 + 11580.0i) q^{20} +(9711.20 + 29888.0i) q^{21} +(42637.8 + 30978.2i) q^{22} +(14369.2 + 10439.8i) q^{23} +(13720.0 - 9968.13i) q^{24} +16634.0 q^{25} +54967.0 q^{26} +(-87810.1 + 63797.8i) q^{27} +(-18764.1 + 57750.0i) q^{28} +(1929.06 + 5937.05i) q^{29} -81569.0 q^{30} +(-156877. + 53871.4i) q^{31} +32768.0 q^{32} +(67430.2 + 207529. i) q^{33} +(-4542.81 + 13981.3i) q^{34} +(236283. - 171670. i) q^{35} -69753.0 q^{36} +223976. q^{37} +(-103282. + 75038.9i) q^{38} +(184117. + 133769. i) q^{39} +(-127508. - 92640.1i) q^{40} +(36538.9 + 112455. i) q^{41} +(-203394. + 147774. i) q^{42} +(-5113.19 - 15736.8i) q^{43} +(-130290. + 400990. i) q^{44} +(271426. + 197202. i) q^{45} +(-43908.3 + 135136. i) q^{46} +(-27713.2 + 85292.6i) q^{47} +(109760. + 79745.0i) q^{48} +(23683.0 - 72888.9i) q^{49} +(41121.5 + 126559. i) q^{50} +(-49241.9 + 35776.3i) q^{51} +(135886. + 418214. i) q^{52} +(276000. + 200526. i) q^{53} +(-702481. - 510382. i) q^{54} +(1.64065e6 - 1.19200e6i) q^{55} -485775. q^{56} -528570. q^{57} +(-40402.9 + 29354.4i) q^{58} +(831651. - 2.55956e6i) q^{59} +(-201650. - 620614. i) q^{60} -2.41604e6 q^{61} +(-797700. - 1.06042e6i) q^{62} +1.03407e6 q^{63} +(81007.0 + 249314. i) q^{64} +(653589. - 2.01154e6i) q^{65} +(-1.41228e6 + 1.02608e6i) q^{66} +3.43836e6 q^{67} -117607. q^{68} +(-475945. + 345794. i) q^{69} +(1.89027e6 + 1.37336e6i) q^{70} +(-2.43611e6 - 1.76994e6i) q^{71} +(-172439. - 530712. i) q^{72} +(-3.05894e6 + 2.22245e6i) q^{73} +(553698. + 1.70411e6i) q^{74} +(-170257. + 523996. i) q^{75} +(-826257. - 600311. i) q^{76} +(1.93150e6 - 5.94455e6i) q^{77} +(-562613. + 1.73154e6i) q^{78} +(-475331. - 345348. i) q^{79} +(389630. - 1.19916e6i) q^{80} +(-374379. - 1.15222e6i) q^{81} +(-765280. + 556009. i) q^{82} +(-1.35755e6 - 4.17811e6i) q^{83} +(-1.62715e6 - 1.18219e6i) q^{84} +(457636. + 332492. i) q^{85} +(107092. - 77807.0i) q^{86} -206771. q^{87} -3.37301e6 q^{88} +(-549883. + 399514. i) q^{89} +(-829403. + 2.55264e6i) q^{90} +(-2.01447e6 - 6.19989e6i) q^{91} -1.13672e6 q^{92} +(-91319.1 - 5.49327e6i) q^{93} -717456. q^{94} +(1.51799e6 + 4.67191e6i) q^{95} +(-335395. + 1.03224e6i) q^{96} +(-5.01682e6 + 3.64493e6i) q^{97} +613119. q^{98} +7.18010e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) $ 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

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

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 $

$2$	2.47214	+	7.60845i	0.218508	+	0.672499i
$2$	2.47214	+	7.60845i	0.218508	+	0.672499i
$3$	−10.2355	+	31.5015i	−0.218868	+	0.673607i	0.779988	+	0.625794i	$0.215225\pi$
$3$	−10.2355	+	31.5015i	−0.218868	+	0.673607i	−0.998856	+	0.0478129i	$0.984775\pi$
$4$	−51.7771	+	37.6183i	−0.404508	+	0.293893i
$5$	307.829			1.10132			0.550662	−	0.834728i	$-0.314375\pi$
$5$	307.829			1.10132			0.550662	+	0.834728i	$0.314375\pi$
$6$	−264.981			−0.500824
$7$	767.579	−	557.679i	0.845824	−	0.614527i	−0.0781676	−	0.996940i	$-0.524907\pi$
$7$	767.579	−	557.679i	0.845824	−	0.614527i	0.923991	+	0.382413i	$0.124907\pi$
$8$	−414.217	−	300.946i	−0.286031	−	0.207813i
$9$	881.740	+	640.622i	0.403173	+	0.292923i
$10$	760.996	+	2342.11i	0.240648	+	0.740639i
$11$	5329.73	−	3872.27i	1.20734	−	0.877186i	0.212356	−	0.977192i	$-0.431886\pi$
$11$	5329.73	−	3872.27i	1.20734	−	0.877186i	0.994987	+	0.100007i	$0.0318864\pi$
$12$	−655.069	−	2016.10i	−0.109434	−	0.336804i
$13$	2123.22	−	6534.59i	0.268036	−	0.824929i	−0.722943	−	0.690908i	$-0.757211\pi$
$13$	2123.22	−	6534.59i	0.268036	−	0.824929i	0.990978	−	0.134021i	$-0.0427891\pi$
$14$	6140.63	+	4461.43i	0.598088	+	0.434536i
$15$	−3150.78	+	9697.09i	−0.241045	+	0.741860i
$16$	1265.73	−	3895.53i	0.0772542	−	0.237764i
$17$	1486.65	+	1080.12i	0.0733903	+	0.0533211i	0.623875	−	0.781524i	$-0.285557\pi$
$17$	1486.65	+	1080.12i	0.0733903	+	0.0533211i	−0.550485	+	0.834845i	$0.685557\pi$
$18$	−2694.36	+	8292.38i	−0.108893	+	0.335139i
$19$	4931.28	+	15176.9i	0.164939	+	0.507629i	0.999032	−	0.0439947i	$-0.0140085\pi$
$19$	4931.28	+	15176.9i	0.164939	+	0.507629i	−0.834093	+	0.551624i	$0.814008\pi$
$20$	−15938.5	+	11580.0i	−0.445495	+	0.323671i
$21$	9711.20	+	29888.0i	0.228826	+	0.704254i
$22$	42637.8	+	30978.2i	0.853720	+	0.620264i
$23$	14369.2	+	10439.8i	0.246255	+	0.178915i	0.704065	−	0.710135i	$-0.251366\pi$
$23$	14369.2	+	10439.8i	0.246255	+	0.178915i	−0.457811	+	0.889050i	$0.651366\pi$
$24$	13720.0	−	9968.13i	0.202588	−	0.147189i
$25$	16634.0			0.212915
$26$	54967.0			0.613332
$27$	−87810.1	+	63797.8i	−0.858561	+	0.623781i
$28$	−18764.1	+	57750.0i	−0.161538	+	0.497163i
$29$	1929.06	+	5937.05i	0.0146877	+	0.0452041i	0.958132	−	0.286328i	$-0.0924346\pi$
$29$	1929.06	+	5937.05i	0.0146877	+	0.0452041i	−0.943444	+	0.331532i	$0.892435\pi$
$30$	−81569.0			−0.551570
$31$	−156877.	+	53871.4i	−0.945789	+	0.324782i
$31$	−156877.	+	53871.4i	−0.945789	+	0.324782i
$32$	32768.0			0.176777
$33$	67430.2	+	207529.i	0.326630	+	1.00526i
$34$	−4542.81	+	13981.3i	−0.0198220	+	0.0610059i
$35$	236283.	−	171670.i	0.931526	−	0.676793i
$36$	−69753.0			−0.249175
$37$	223976.			0.726933			0.363467	−	0.931607i	$-0.381593\pi$
$37$	223976.			0.726933			0.363467	+	0.931607i	$0.381593\pi$
$38$	−103282.	+	75038.9i	−0.305339	+	0.221842i
$39$	184117.	+	133769.i	0.497014	+	0.361102i
$40$	−127508.	−	92640.1i	−0.315013	−	0.228870i
$41$	36538.9	+	112455.i	0.0827965	+	0.254821i	0.983882	−	0.178821i	$-0.0572282\pi$
$41$	36538.9	+	112455.i	0.0827965	+	0.254821i	−0.901085	+	0.433642i	$0.857228\pi$
$42$	−203394.	+	147774.i	−0.423609	+	0.307770i
$43$	−5113.19	−	15736.8i	−0.00980737	−	0.0301840i	0.946033	−	0.324070i	$-0.105051\pi$
$43$	−5113.19	−	15736.8i	−0.00980737	−	0.0301840i	−0.955840	+	0.293886i	$0.905051\pi$
$44$	−130290.	+	400990.i	−0.230582	+	0.709658i
$45$	271426.	+	197202.i	0.444025	+	0.322603i
$46$	−43908.3	+	135136.i	−0.0665111	+	0.204700i
$47$	−27713.2	+	85292.6i	−0.0389354	+	0.119831i	−0.968635	−	0.248488i	$-0.920066\pi$
$47$	−27713.2	+	85292.6i	−0.0389354	+	0.119831i	0.929700	+	0.368319i	$0.120066\pi$
$48$	109760.	+	79745.0i	0.143251	+	0.104078i
$49$	23683.0	−	72888.9i	0.0287575	−	0.0885065i
$50$	41121.5	+	126559.i	0.0465237	+	0.143185i
$51$	−49241.9	+	35776.3i	−0.0519803	+	0.0377659i
$52$	135886.	+	418214.i	0.134018	+	0.412465i
$53$	276000.	+	200526.i	0.254650	+	0.185014i	0.707785	−	0.706428i	$-0.249694\pi$
$53$	276000.	+	200526.i	0.254650	+	0.185014i	−0.453135	+	0.891442i	$0.649694\pi$
$54$	−702481.	−	510382.i	−0.607095	−	0.441080i
$55$	1.64065e6	−	1.19200e6i	1.32968	−	0.966066i
$56$	−485775.			−0.369639
$57$	−528570.			−0.378042
$58$	−40402.9	+	29354.4i	−0.0271903	+	0.0197549i
$59$	831651.	−	2.55956e6i	0.527180	−	1.62249i	−0.232784	−	0.972528i	$-0.574784\pi$
$59$	831651.	−	2.55956e6i	0.527180	−	1.62249i	0.759964	−	0.649965i	$-0.225216\pi$
$60$	−201650.	−	620614.i	−0.120522	−	0.370930i
$61$	−2.41604e6			−1.36286			−0.681428	−	0.731885i	$-0.738641\pi$
$61$	−2.41604e6			−1.36286			−0.681428	+	0.731885i	$0.738641\pi$
$62$	−797700.	−	1.06042e6i	−0.425078	−	0.565074i
$63$	1.03407e6			0.521022
$64$	81007.0	+	249314.i	0.0386271	+	0.118882i
$65$	653589.	−	2.01154e6i	0.295194	−	0.908515i
$66$	−1.41228e6	+	1.02608e6i	−0.604667	+	0.439316i
$67$	3.43836e6			1.39666			0.698329	−	0.715777i	$-0.253927\pi$
$67$	3.43836e6			1.39666			0.698329	+	0.715777i	$0.253927\pi$
$68$	−117607.			−0.0453577
$69$	−475945.	+	345794.i	−0.174416	+	0.126720i
$70$	1.89027e6	+	1.37336e6i	0.658689	+	0.478565i
$71$	−2.43611e6	−	1.76994e6i	−0.807780	−	0.586886i	0.105406	−	0.994429i	$-0.466386\pi$
$71$	−2.43611e6	−	1.76994e6i	−0.807780	−	0.586886i	−0.913186	+	0.407543i	$0.866386\pi$
$72$	−172439.	−	530712.i	−0.0544467	−	0.167570i
$73$	−3.05894e6	+	2.22245e6i	−0.920323	+	0.668654i	−0.943604	−	0.331075i	$-0.892589\pi$
$73$	−3.05894e6	+	2.22245e6i	−0.920323	+	0.668654i	0.0232811	+	0.999729i	$0.492589\pi$
$74$	553698.	+	1.70411e6i	0.158841	+	0.488862i
$75$	−170257.	+	523996.i	−0.0466004	+	0.143421i
$76$	−826257.	−	600311.i	−0.215907	−	0.156866i
$77$	1.93150e6	−	5.94455e6i	0.482145	−	1.48389i
$78$	−562613.	+	1.73154e6i	−0.134239	+	0.413145i
$79$	−475331.	−	345348.i	−0.108468	−	0.0788065i	0.532229	−	0.846600i	$-0.321354\pi$
$79$	−475331.	−	345348.i	−0.108468	−	0.0788065i	−0.640697	+	0.767794i	$0.721354\pi$
$80$	389630.	−	1.19916e6i	0.0850820	−	0.261855i
$81$	−374379.	−	1.15222e6i	−0.0782734	−	0.240901i
$82$	−765280.	+	556009.i	−0.153275	+	0.111361i
$83$	−1.35755e6	−	4.17811e6i	−0.260605	−	0.802060i	−0.992673	−	0.120829i	$-0.961445\pi$
$83$	−1.35755e6	−	4.17811e6i	−0.260605	−	0.802060i	0.732068	−	0.681231i	$-0.238555\pi$
$84$	−1.62715e6	−	1.18219e6i	−0.299537	−	0.217626i
$85$	457636.	+	332492.i	0.0808265	+	0.0587239i
$86$	107092.	−	77807.0i	0.0181557	−	0.0131909i
$87$	−206771.			−0.0336645
$88$	−3.37301e6			−0.527628
$89$	−549883.	+	399514.i	−0.0826810	+	0.0600712i	−0.628358	−	0.777924i	$-0.716273\pi$
$89$	−549883.	+	399514.i	−0.0826810	+	0.0600712i	0.545677	+	0.837996i	$0.316273\pi$
$90$	−829403.	+	2.55264e6i	−0.119927	+	0.369097i
$91$	−2.01447e6	−	6.19989e6i	−0.280230	−	0.862460i
$92$	−1.13672e6			−0.152194
$93$	−91319.1	−	5.49327e6i	−0.0117726	−	0.708175i
$94$	−717456.			−0.0890938
$95$	1.51799e6	+	4.67191e6i	0.181651	+	0.559064i
$96$	−335395.	+	1.03224e6i	−0.0386908	+	0.119078i
$97$	−5.01682e6	+	3.64493e6i	−0.558120	+	0.405498i	−0.830770	−	0.556615i	$-0.812100\pi$
$97$	−5.01682e6	+	3.64493e6i	−0.558120	+	0.405498i	0.272651	+	0.962113i	$0.412100\pi$
$98$	613119.			0.0658042
$99$	7.18010e6			0.743716
$100$	−861260.	+	625742.i	−0.0861260	+	0.0625742i
$101$	1.19538e7	+	8.68495e6i	1.15447	+	0.838769i	0.989068	−	0.147457i	$-0.0471090\pi$
$101$	1.19538e7	+	8.68495e6i	1.15447	+	0.838769i	0.165399	+	0.986227i	$0.447109\pi$
$102$	−393935.	−	286211.i	−0.0367556	−	0.0267045i
$103$	5.50920e6	+	1.69556e7i	0.496774	+	1.52891i	0.814174	+	0.580620i	$0.197190\pi$
$103$	5.50920e6	+	1.69556e7i	0.496774	+	1.52891i	−0.317401	+	0.948292i	$0.602810\pi$
$104$	−2.84603e6	+	2.06776e6i	−0.248098	+	0.180254i
$105$	2.98939e6	+	9.20040e6i	0.252011	+	0.775612i
$106$	−843382.	+	2.59566e6i	−0.0687786	+	0.211679i
$107$	7.51788e6	+	5.46206e6i	0.593269	+	0.431035i	0.843483	−	0.537155i	$-0.180501\pi$
$107$	7.51788e6	+	5.46206e6i	0.593269	+	0.431035i	−0.250214	+	0.968191i	$0.580501\pi$
$108$	2.14659e6	−	6.60653e6i	0.163971	−	0.504650i
$109$	−2.46479e6	+	7.58584e6i	−0.182300	+	0.561062i	−0.999891	−	0.0147369i	$-0.995309\pi$
$109$	−2.46479e6	+	7.58584e6i	−0.182300	+	0.561062i	0.817591	+	0.575799i	$0.195309\pi$
$110$	1.31252e7	+	9.53600e6i	0.940223	+	0.683112i
$111$	−2.29249e6	+	7.05557e6i	−0.159103	+	0.489668i
$112$	−1.20090e6	−	3.69600e6i	−0.0807690	−	0.248581i
$113$	−1.54448e7	+	1.12213e7i	−1.00695	+	0.731592i	−0.963567	−	0.267466i	$-0.913814\pi$
$113$	−1.54448e7	+	1.12213e7i	−1.00695	+	0.731592i	−0.0433829	+	0.999059i	$0.513814\pi$
$114$	−1.30670e6	−	4.02160e6i	−0.0826053	−	0.254233i
$115$	4.42326e6	+	3.21368e6i	0.271206	+	0.197043i
$116$	−323223.	−	234835.i	−0.0192265	−	0.0139688i
$117$	6.05833e6	−	4.40163e6i	0.349705	−	0.254076i
$118$	2.15302e7			1.20632
$119$	1.74348e6			0.0948425
$120$	4.22341e6	−	3.06848e6i	0.223115	−	0.162102i
$121$	7.38962e6	−	2.27429e7i	0.379204	−	1.16707i
$122$	−5.97278e6	−	1.83823e7i	−0.297795	−	0.916519i
$123$	−3.91650e6			−0.189771
$124$	6.09610e6	−	8.69075e6i	0.287128	−	0.409338i
$125$	−1.89287e7			−0.866836
$126$	2.55635e6	+	7.86764e6i	0.113848	+	0.350387i
$127$	1.04490e7	−	3.21588e7i	0.452650	−	1.39311i	−0.421222	−	0.906957i	$-0.638399\pi$
$127$	1.04490e7	−	3.21588e7i	0.452650	−	1.39311i	0.873872	−	0.486156i	$-0.161601\pi$
$128$	−1.69663e6	+	1.23268e6i	−0.0715077	+	0.0519534i
$129$	548069.			0.0224787
$130$	1.69205e7			0.675477
$131$	−1.63013e7	+	1.18436e7i	−0.633539	+	0.460293i	−0.857624	−	0.514277i	$-0.828060\pi$
$131$	−1.63013e7	+	1.18436e7i	−0.633539	+	0.460293i	0.224086	+	0.974569i	$0.428060\pi$
$132$	−1.12982e7	−	8.20863e6i	−0.427564	−	0.310643i
$133$	1.22490e7	+	8.89942e6i	0.451461	+	0.328005i
$134$	8.50010e6	+	2.61606e7i	0.305181	+	0.939250i
$135$	−2.70305e7	+	1.96388e7i	−0.945555	+	0.686986i
$136$	−290740.	−	894805.i	−0.00991102	−	0.0305030i
$137$	−8.81500e6	+	2.71298e7i	−0.292887	+	0.901414i	0.691036	+	0.722821i	$0.257155\pi$
$137$	−8.81500e6	+	2.71298e7i	−0.292887	+	0.901414i	−0.983923	+	0.178594i	$0.942845\pi$
$138$	−3.80756e6	−	2.76636e6i	−0.123330	−	0.0896048i
$139$	−1.59531e7	+	4.90987e7i	−0.503842	+	1.55067i	0.298866	+	0.954295i	$0.403392\pi$
$139$	−1.59531e7	+	4.90987e7i	−0.503842	+	1.55067i	−0.802708	+	0.596372i	$0.796608\pi$
$140$	−5.77614e6	+	1.77771e7i	−0.177906	+	0.547537i
$141$	−2.40319e6	−	1.74602e6i	−0.0721973	−	0.0524544i
$142$	7.44410e6	−	2.29106e7i	0.218174	−	0.671470i
$143$	−1.39876e7	−	4.30493e7i	−0.400005	−	1.23109i
$144$	3.61161e6	−	2.62399e6i	0.100793	−	0.0732307i
$145$	593823.	+	1.82760e6i	0.0161759	+	0.0497844i
$146$	−2.44715e7	−	1.77796e7i	−0.650767	−	0.472810i
$147$	2.05370e6	+	1.49210e6i	0.0533245	+	0.0387425i
$148$	−1.15968e7	+	8.42557e6i	−0.294051	+	0.213640i
$149$	−4.83631e7			−1.19774			−0.598869	−	0.800847i	$-0.704383\pi$
$149$	−4.83631e7			−1.19774			−0.598869	+	0.800847i	$0.704383\pi$
$150$	−4.40769e6			−0.106633
$151$	6.11531e7	−	4.44303e7i	1.44544	−	1.05017i	0.458565	−	0.888661i	$-0.348363\pi$
$151$	6.11531e7	−	4.44303e7i	1.44544	−	1.05017i	0.986871	−	0.161510i	$-0.0516365\pi$
$152$	2.52482e6	−	7.77059e6i	0.0583146	−	0.179474i
$153$	618896.	+	1.90476e6i	0.0139700	+	0.0429953i
$154$	5.00038e7			1.10327
$155$	−4.82915e7	+	1.65832e7i	−1.04162	+	0.357691i
$156$	−1.45652e7			−0.307172
$157$	−2.59723e7	−	7.99345e7i	−0.535626	−	1.64849i	−0.742292	−	0.670076i	$-0.766261\pi$
$157$	−2.59723e7	−	7.99345e7i	−0.535626	−	1.64849i	0.206666	−	0.978412i	$-0.433739\pi$
$158$	1.45248e6	−	4.47028e6i	0.0292962	−	0.0901643i
$159$	−9.14186e6	+	6.64195e6i	−0.180362	+	0.131040i
$160$	1.00870e7			0.194688
$161$	1.68515e7			0.318236
$162$	7.84110e6	−	5.69689e6i	0.144902	−	0.105277i
$163$	−6.33081e7	−	4.59961e7i	−1.14499	−	0.831886i	−0.157186	−	0.987569i	$-0.550242\pi$
$163$	−6.33081e7	−	4.59961e7i	−1.14499	−	0.831886i	−0.987807	+	0.155683i	$0.950242\pi$
$164$	−6.12224e6	−	4.44807e6i	−0.108382	−	0.0787441i
$165$	2.07570e7	+	6.38835e7i	0.359725	+	1.10712i
$166$	2.84329e7	−	2.06577e7i	0.482440	−	0.350513i
$167$	−2.67927e7	−	8.24596e7i	−0.445153	−	1.37004i	−0.882316	−	0.470658i	$-0.844016\pi$
$167$	−2.67927e7	−	8.24596e7i	−0.445153	−	1.37004i	0.437162	−	0.899383i	$-0.355984\pi$
$168$	4.97213e6	−	1.53026e7i	0.0809022	−	0.248991i
$169$	1.25718e7	+	9.13393e6i	0.200352	+	0.145564i
$170$	−1.39841e6	+	4.30386e6i	−0.0218305	+	0.0671873i
$171$	−5.37456e6	+	1.65412e7i	−0.0821971	+	0.252977i
$172$	856737.	+	622456.i	0.0128380	+	0.00932737i
$173$	1.73427e6	−	5.33752e6i	0.0254656	−	0.0783752i	−0.937516	−	0.347942i	$-0.886881\pi$
$173$	1.73427e6	−	5.33752e6i	0.0254656	−	0.0783752i	0.962982	+	0.269567i	$0.0868806\pi$
$174$	−511166.	−	1.57321e6i	−0.00735596	−	0.0226393i
$175$	1.27679e7	−	9.27642e6i	0.180089	−	0.130842i
$176$	−8.33853e6	−	2.56634e7i	−0.115291	−	0.354829i
$177$	7.21176e7	+	5.23965e7i	0.977540	+	0.710225i
$178$	−4.39907e6	−	3.19611e6i	−0.0584643	−	0.0424768i
$179$	6.50098e7	−	4.72324e7i	0.847215	−	0.615537i	−0.0771621	−	0.997019i	$-0.524586\pi$
$179$	6.50098e7	−	4.72324e7i	0.847215	−	0.615537i	0.924377	+	0.381481i	$0.124586\pi$
$180$	−2.14720e7			−0.274422
$181$	−2.34855e7			−0.294392			−0.147196	−	0.989107i	$-0.547025\pi$
$181$	−2.34855e7			−0.294392			−0.147196	+	0.989107i	$0.547025\pi$
$182$	4.21915e7	−	3.06539e7i	0.518771	−	0.376909i
$183$	2.47293e7	−	7.61089e7i	0.298286	−	0.918030i
$184$	−2.81013e6	−	8.64870e6i	−0.0332556	−	0.102350i
$185$	6.89463e7			0.800589
$186$	4.15695e7	−	1.42749e7i	0.473674	−	0.162659i
$187$	1.21060e7			0.135380
$188$	−1.77365e6	−	5.45873e6i	−0.0194677	−	0.0599155i
$189$	−3.18225e7	+	9.79397e7i	−0.342861	+	1.05522i
$190$	−3.17933e7	+	2.30992e7i	−0.336278	+	0.244320i
$191$	2.94864e7			0.306200			0.153100	−	0.988211i	$-0.451074\pi$
$191$	2.94864e7			0.306200			0.153100	+	0.988211i	$0.451074\pi$
$192$	−8.68290e6			−0.0885341
$193$	−8.82275e7	+	6.41010e7i	−0.883392	+	0.641822i	−0.934147	−	0.356889i	$-0.883837\pi$
$193$	−8.82275e7	+	6.41010e7i	−0.883392	+	0.641822i	0.0507546	+	0.998711i	$0.483837\pi$
$194$	−4.01345e7	−	2.91595e7i	−0.394650	−	0.286730i
$195$	5.66768e7	+	4.11781e7i	0.547374	+	0.397690i
$196$	1.51571e6	+	4.66489e6i	0.0143787	+	0.0442532i
$197$	−4.14186e7	+	3.00924e7i	−0.385979	+	0.280430i	−0.763806	−	0.645446i	$-0.776672\pi$
$197$	−4.14186e7	+	3.00924e7i	−0.385979	+	0.280430i	0.377827	+	0.925876i	$0.376672\pi$
$198$	1.77502e7	+	5.46294e7i	0.162508	+	0.500148i
$199$	6.15499e7	−	1.89431e8i	0.553658	−	1.70398i	−0.145804	−	0.989314i	$-0.546577\pi$
$199$	6.15499e7	−	1.89431e8i	0.553658	−	1.70398i	0.699462	−	0.714670i	$-0.253423\pi$
$200$	−6.89008e6	−	5.00593e6i	−0.0609003	−	0.0442466i
$201$	−3.51932e7	+	1.08314e8i	−0.305684	+	0.940799i
$202$	−3.65276e7	+	1.12420e8i	−0.311811	+	0.959655i
$203$	4.79168e6	+	3.48136e6i	0.0402023	+	0.0292087i
$204$	1.20376e6	−	3.70479e6i	0.00992736	−	0.0305533i
$205$	1.12477e7	+	3.46170e7i	0.0911858	+	0.280641i
$206$	−1.15386e8	+	8.38330e7i	−0.919642	+	0.668159i
$207$	5.98191e6	+	1.84104e7i	0.0468752	+	0.144267i
$208$	−2.27683e7	−	1.65421e7i	−0.175432	−	0.127459i
$209$	8.50516e7	+	6.17936e7i	0.644422	+	0.468200i
$210$	−6.26106e7	+	4.54893e7i	−0.466531	+	0.338955i
$211$	−1.42299e7			−0.104283			−0.0521416	−	0.998640i	$-0.516605\pi$
$211$	−1.42299e7			−0.104283			−0.0521416	+	0.998640i	$0.516605\pi$
$212$	−2.18339e7			−0.157382
$213$	8.06905e7	−	5.86251e7i	0.572128	−	0.415676i
$214$	−2.29726e7	+	7.07023e7i	−0.160237	+	0.493157i
$215$	−1.57399e6	−	4.84425e6i	−0.0108011	−	0.0332424i
$216$	5.55721e7			0.375205
$217$	−9.03728e7	+	1.28838e8i	−0.600383	+	0.855921i
$218$	−6.38098e7			−0.417148
$219$	−3.87008e7	−	1.19109e8i	−0.248981	−	0.766284i
$220$	−4.01070e7	+	1.23437e8i	−0.253945	+	0.781564i
$221$	1.02146e7	−	7.42135e6i	0.0636574	−	0.0462498i
$222$	−5.93493e7			−0.364066
$223$	1.54601e8			0.933567			0.466783	−	0.884372i	$-0.345413\pi$
$223$	1.54601e8			0.933567			0.466783	+	0.884372i	$0.345413\pi$
$224$	2.51520e7	−	1.82740e7i	0.149522	−	0.108634i
$225$	1.46669e7	+	1.06561e7i	0.0858417	+	0.0623677i
$226$	−1.23558e8	−	8.97705e7i	−0.712021	−	0.517314i
$227$	1.12139e7	+	3.45130e7i	0.0636308	+	0.195836i	0.977818	−	0.209457i	$-0.0671696\pi$
$227$	1.12139e7	+	3.45130e7i	0.0636308	+	0.195836i	−0.914187	+	0.405293i	$0.867170\pi$
$228$	2.73678e7	−	1.98839e7i	0.152921	−	0.111104i
$229$	−5.97835e7	−	1.83995e8i	−0.328971	−	1.01247i	−0.969616	−	0.244631i	$-0.921333\pi$
$229$	−5.97835e7	−	1.83995e8i	−0.328971	−	1.01247i	0.640645	−	0.767837i	$-0.278667\pi$
$230$	−1.35163e7	+	4.15988e7i	−0.0732503	+	0.225441i
$231$	1.67492e8	+	1.21690e8i	0.894033	+	0.649553i
$232$	987681.	−	3.03977e6i	0.00519289	−	0.0159821i
$233$	−1.07820e8	+	3.31836e8i	−0.558411	+	1.71861i	0.128348	+	0.991729i	$0.459033\pi$
$233$	−1.07820e8	+	3.31836e8i	−0.558411	+	1.71861i	−0.686760	+	0.726885i	$0.740967\pi$
$234$	4.84666e7	+	3.52131e7i	0.247279	+	0.179659i
$235$	−8.53095e6	+	2.62556e7i	−0.0428805	+	0.131973i
$236$	5.32256e7	+	1.63812e8i	0.263590	+	0.811247i
$237$	1.57442e7	−	1.14388e7i	0.0768248	−	0.0558165i
$238$	4.31012e6	+	1.32652e7i	0.0207238	+	0.0637814i
$239$	−2.31855e8	−	1.68452e8i	−1.09856	−	0.798151i	−0.117736	−	0.993045i	$-0.537564\pi$
$239$	−2.31855e8	−	1.68452e8i	−1.09856	−	0.798151i	−0.980824	+	0.194894i	$0.937564\pi$
$240$	3.37872e7	+	2.45479e7i	0.157766	+	0.114624i
$241$	3.02901e8	−	2.20070e8i	1.39393	−	1.01275i	0.398509	−	0.917165i	$-0.369528\pi$
$241$	3.02901e8	−	2.20070e8i	1.39393	−	1.01275i	0.995421	−	0.0955850i	$-0.0304722\pi$
$242$	1.91307e8			0.867713
$243$	−1.97247e8			−0.881836
$244$	1.25096e8	−	9.08873e7i	0.551287	−	0.400533i
$245$	7.29034e6	−	2.24374e7i	0.0316713	−	0.0974743i
$246$	−9.68212e6	−	2.97985e7i	−0.0414665	−	0.127621i
$247$	1.09645e8			0.462968
$248$	8.11936e7	+	2.48972e7i	0.338019	+	0.103650i
$249$	1.45512e8			0.597312
$250$	−4.67944e7	−	1.44018e8i	−0.189411	−	0.582946i
$251$	−4.79706e7	+	1.47638e8i	−0.191477	+	0.589306i	0.808522	+	0.588465i	$0.200268\pi$
$251$	−4.79706e7	+	1.47638e8i	−0.191477	+	0.589306i	−1.00000		0.000840915i	$0.999732\pi$
$252$	−5.35409e7	+	3.88998e7i	−0.210758	+	0.153125i
$253$	1.17010e8			0.454255
$254$	2.70510e8			1.03577
$255$	−1.51581e7	+	1.10130e7i	−0.0572472	+	0.0415925i
$256$	−1.35731e7	−	9.86140e6i	−0.0505636	−	0.0367366i
$257$	−3.55850e8	−	2.58540e8i	−1.30768	−	0.950084i	−0.307680	−	0.951490i	$-0.599552\pi$
$257$	−3.55850e8	−	2.58540e8i	−1.30768	−	0.950084i	−0.999999	+	0.00140590i	$0.999552\pi$
$258$	1.35490e6	+	4.16995e6i	0.00491177	+	0.0151169i
$259$	1.71919e8	−	1.24906e8i	0.614858	−	0.446720i
$260$	4.18297e7	+	1.28739e8i	0.147597	+	0.454257i
$261$	−2.10247e6	+	6.47074e6i	−0.00731961	+	0.0225274i
$262$	−1.30411e8	−	9.47488e7i	−0.447980	−	0.325476i
$263$	−1.44638e7	+	4.45149e7i	−0.0490271	+	0.150890i	−0.972573	−	0.232598i	$-0.925277\pi$
$263$	−1.44638e7	+	4.45149e7i	−0.0490271	+	0.150890i	0.923546	+	0.383488i	$0.125277\pi$
$264$	3.45243e7	−	1.06255e8i	0.115481	−	0.355414i
$265$	8.49610e7	+	6.17278e7i	0.280452	+	0.203761i
$266$	−3.74296e7	+	1.15197e8i	−0.121935	+	0.375278i
$267$	−6.95697e6	−	2.14114e7i	−0.0223682	−	0.0688422i
$268$	−1.78028e8	+	1.29345e8i	−0.564960	+	0.410467i
$269$	2.68360e7	+	8.25928e7i	0.0840592	+	0.258708i	0.984248	−	0.176792i	$-0.0565719\pi$
$269$	2.68360e7	+	8.25928e7i	0.0840592	+	0.258708i	−0.900189	+	0.435499i	$0.856572\pi$
$270$	−2.16244e8	−	1.57111e8i	−0.668608	−	0.485772i
$271$	−1.07087e8	−	7.78030e7i	−0.326846	−	0.237467i	0.412245	−	0.911073i	$-0.364745\pi$
$271$	−1.07087e8	−	7.78030e7i	−0.326846	−	0.237467i	−0.739091	+	0.673606i	$0.764745\pi$
$272$	6.08933e6	−	4.42416e6i	0.0183476	−	0.0133303i
$273$	2.15925e8			0.642293
$274$	−2.28208e8			−0.670198
$275$	8.86546e7	−	6.44114e7i	0.257062	−	0.186766i
$276$	1.16349e7	−	3.58085e7i	0.0333104	−	0.102519i
$277$	−9.11647e7	−	2.80576e8i	−0.257720	−	0.793180i	−0.993282	−	0.115722i	$-0.963082\pi$
$277$	−9.11647e7	−	2.80576e8i	−0.257720	−	0.793180i	0.735562	−	0.677457i	$-0.236918\pi$
$278$	−4.13004e8			−1.15291
$279$	−1.72836e8	−	5.29984e7i	−0.476453	−	0.146099i
$280$	−1.49536e8			−0.407092
$281$	9.77747e7	+	3.00919e8i	0.262878	+	0.809055i	0.992175	+	0.124858i	$0.0398474\pi$
$281$	9.77747e7	+	3.00919e8i	0.262878	+	0.809055i	−0.729297	+	0.684198i	$0.760153\pi$
$282$	7.34349e6	−	2.26009e7i	0.0194998	−	0.0600143i
$283$	1.18915e8	−	8.63972e7i	0.311879	−	0.226593i	−0.420823	−	0.907143i	$-0.638259\pi$
$283$	1.18915e8	−	8.63972e7i	0.311879	−	0.226593i	0.732702	+	0.680549i	$0.238259\pi$
$284$	1.92717e8			0.499235
$285$	−1.62709e8			−0.416347
$286$	2.92959e8	−	2.12847e8i	0.740502	−	0.538006i
$287$	9.07603e7	+	6.59412e7i	0.226626	+	0.164653i
$288$	2.88929e7	+	2.09919e7i	0.0712717	+	0.0517819i
$289$	−1.25758e8	−	3.87044e8i	−0.306474	−	0.943230i
$290$	−1.24372e7	+	9.03615e6i	−0.0299453	+	0.0217566i
$291$	−6.34714e7	−	1.95345e8i	−0.150992	−	0.464704i
$292$	7.47782e7	−	2.30144e8i	0.175766	−	0.540952i
$293$	9.00178e7	+	6.54017e7i	0.209070	+	0.151898i	0.687393	−	0.726286i	$-0.258755\pi$
$293$	9.00178e7	+	6.54017e7i	0.209070	+	0.151898i	−0.478323	+	0.878184i	$0.658755\pi$
$294$	−6.27556e6	+	1.93142e7i	−0.0144025	+	0.0443262i
$295$	2.56007e8	−	7.87907e8i	0.580596	−	1.78689i
$296$	−9.27744e7	−	6.74046e7i	−0.207925	−	0.151067i
$297$	−2.20961e8	+	6.80050e8i	−0.489406	+	1.50624i
$298$	−1.19560e8	−	3.67968e8i	−0.261715	−	0.805477i
$299$	9.87289e7	−	7.17307e7i	0.213597	−	0.155187i
$300$	−1.08964e7	−	3.35357e7i	−0.0233002	−	0.0717106i
$301$	−1.27009e7	−	9.22771e6i	−0.0268442	−	0.0195034i
$302$	4.89225e8	+	3.55442e8i	1.02208	+	0.742583i
$303$	−3.95942e8	+	2.87668e8i	−0.817677	+	0.594077i
$304$	6.53639e7			0.133438
$305$	−7.43729e8			−1.50095
$306$	−1.29623e7	+	9.41767e6i	−0.0258617	+	0.0187896i
$307$	1.00307e8	−	3.08713e8i	0.197855	−	0.608934i	−0.802077	−	0.597221i	$-0.796272\pi$
$307$	1.00307e8	−	3.08713e8i	0.197855	−	0.608934i	0.999931	−	0.0117128i	$-0.00372839\pi$
$308$	1.23616e8	+	3.80451e8i	0.241072	+	0.741945i
$309$	−5.90516e8			−1.13861
$310$	−2.45556e8	−	3.26427e8i	−0.468149	−	0.622330i
$311$	5.25444e8			0.990525			0.495262	−	0.868743i	$-0.335072\pi$
$311$	5.25444e8			0.990525			0.495262	+	0.868743i	$0.335072\pi$
$312$	−3.60072e7	−	1.10819e8i	−0.0671194	−	0.206572i
$313$	−1.93991e8	+	5.97044e8i	−0.357583	+	1.10053i	0.596913	+	0.802306i	$0.296394\pi$
$313$	−1.93991e8	+	5.97044e8i	−0.357583	+	1.10053i	−0.954496	+	0.298222i	$0.903606\pi$
$314$	5.43971e8	−	3.95218e8i	0.991567	−	0.720416i
$315$	3.18316e8			0.573815
$316$	3.76026e7			0.0670368
$317$	−6.26407e8	+	4.55112e8i	−1.10446	+	0.802436i	−0.981782	−	0.190010i	$-0.939148\pi$
$317$	−6.26407e8	+	4.55112e8i	−1.10446	+	0.802436i	−0.122677	+	0.992447i	$0.539148\pi$
$318$	−7.31348e7	−	5.31356e7i	−0.127535	−	0.0926596i
$319$	3.32713e7	+	2.41730e7i	0.0573855	+	0.0416930i
$320$	2.49363e7	+	7.67461e7i	0.0425410	+	0.130928i
$321$	−2.49012e8	+	1.80918e8i	−0.420197	+	0.305291i
$322$	4.16593e7	+	1.28214e8i	0.0695371	+	0.214013i
$323$	−9.06175e6	+	2.78892e7i	−0.0149625	+	0.0460497i
$324$	6.27288e7	+	4.55751e7i	0.102461	+	0.0744424i
$325$	3.53176e7	−	1.08696e8i	0.0570689	−	0.175640i
$326$	1.93452e8	−	5.95385e8i	0.309252	−	0.951780i
$327$	−2.13737e8	−	1.55289e8i	−0.338036	−	0.245597i
$328$	1.87079e7	−	5.75770e7i	0.0292730	−	0.0900930i
$329$	2.62938e7	+	8.09239e7i	0.0407068	+	0.125283i
$330$	−4.34740e8	+	3.15857e8i	−0.665934	+	0.483829i
$331$	−2.85233e8	−	8.77856e8i	−0.432316	−	1.33053i	−0.895812	−	0.444433i	$-0.853405\pi$
$331$	−2.85233e8	−	8.77856e8i	−0.432316	−	1.33053i	0.463496	−	0.886099i	$-0.346595\pi$
$332$	2.27463e8	+	1.65262e8i	0.341136	+	0.247850i
$333$	1.97488e8	+	1.43484e8i	0.293080	+	0.212935i
$334$	5.61155e8	−	4.07703e8i	0.824081	−	0.598730i
$335$	1.05843e9			1.53817
$336$	1.28721e8			0.185124
$337$	−2.03905e7	+	1.48145e7i	−0.0290217	+	0.0210855i	−0.602202	−	0.798344i	$-0.705710\pi$
$337$	−2.03905e7	+	1.48145e7i	−0.0290217	+	0.0210855i	0.573180	+	0.819430i	$0.305710\pi$
$338$	−3.84159e7	+	1.18232e8i	−0.0541131	+	0.166543i
$339$	−1.95403e8	−	6.01390e8i	−0.272416	−	0.838411i
$340$	−3.62028e7			−0.0499535
$341$	−6.27508e8	+	8.94592e8i	−0.856997	+	1.22176i
$342$	−1.39140e8			−0.188087
$343$	2.18984e8	+	6.73963e8i	0.293010	+	0.901792i
$344$	−2.61796e6	+	8.05724e6i	−0.00346743	+	0.0106717i
$345$	−1.46510e8	+	1.06446e8i	−0.192088	+	0.139560i
$346$	4.48976e7			0.0582716
$347$	−2.28160e8			−0.293147			−0.146574	−	0.989200i	$-0.546825\pi$
$347$	−2.28160e8			−0.293147			−0.146574	+	0.989200i	$0.546825\pi$
$348$	1.07060e7	−	7.77836e6i	0.0136176	−	0.00989375i
$349$	1.14554e9	+	8.32286e8i	1.44252	+	1.04805i	0.987508	+	0.157570i	$0.0503661\pi$
$349$	1.14554e9	+	8.32286e8i	1.44252	+	1.04805i	0.455015	+	0.890484i	$0.349634\pi$
$350$	1.02143e8	+	7.42114e7i	0.127342	+	0.0925193i
$351$	2.30453e8	+	7.09260e8i	0.284450	+	0.875448i
$352$	1.74644e8	−	1.26887e8i	0.213430	−	0.155066i
$353$	1.41240e8	+	4.34693e8i	0.170902	+	0.525983i	0.999423	−	0.0339761i	$-0.0108170\pi$
$353$	1.41240e8	+	4.34693e8i	0.170902	+	0.525983i	−0.828521	+	0.559959i	$0.810817\pi$
$354$	−2.20372e8	+	6.78234e8i	−0.264025	+	0.812584i
$355$	−7.49907e8	−	5.44839e8i	−0.889628	−	0.646352i
$356$	1.34424e7	−	4.13713e7i	0.0157907	−	0.0485987i
$357$	−1.78453e7	+	5.49223e7i	−0.0207580	+	0.0638866i
$358$	5.20079e8	+	3.77859e8i	0.599071	+	0.435251i
$359$	−2.43658e8	+	7.49903e8i	−0.277940	+	0.855410i	0.710487	+	0.703710i	$0.248475\pi$
$359$	−2.43658e8	+	7.49903e8i	−0.277940	+	0.855410i	−0.988427	+	0.151700i	$0.951525\pi$
$360$	−5.30818e7	−	1.63369e8i	−0.0599635	−	0.184549i
$361$	5.17136e8	−	3.75721e8i	0.578535	−	0.420330i
$362$	−5.80594e7	−	1.78689e8i	−0.0643269	−	0.197978i
$363$	6.40800e8	+	4.65568e8i	0.703152	+	0.510870i
$364$	3.37532e8	+	2.45231e8i	0.366826	+	0.266515i
$365$	−9.41631e8	+	6.84135e8i	−1.01357	+	0.736405i
$366$	6.40205e8			0.682552
$367$	−9.60750e8			−1.01456			−0.507282	−	0.861780i	$-0.669350\pi$
$367$	−9.60750e8			−1.01456			−0.507282	+	0.861780i	$0.669350\pi$
$368$	5.88562e7	−	4.27615e7i	0.0615637	−	0.0447286i
$369$	−3.98234e7	+	1.22564e8i	−0.0412616	+	0.126990i
$370$	1.70445e8	+	5.24575e8i	0.174935	+	0.538395i
$371$	3.23681e8			0.329085
$372$	2.11375e8	+	2.80990e8i	0.212889	+	0.283003i
$373$	−2.43151e8			−0.242603			−0.121301	−	0.992616i	$-0.538707\pi$
$373$	−2.43151e8			−0.242603			−0.121301	+	0.992616i	$0.538707\pi$
$374$	2.99276e7	+	9.21076e7i	0.0295816	+	0.0910427i
$375$	1.93744e8	−	5.96284e8i	0.189723	−	0.583907i
$376$	3.71478e7	−	2.69894e7i	0.0360392	−	0.0261840i
$377$	4.28920e7			0.0412270
$378$	−8.23839e8			−0.784551
$379$	−5.31194e8	+	3.85935e8i	−0.501205	+	0.364147i	−0.809477	−	0.587151i	$-0.800249\pi$
$379$	−5.31194e8	+	3.85935e8i	−0.501205	+	0.364147i	0.308272	+	0.951298i	$0.400249\pi$
$380$	−2.54346e8	−	1.84793e8i	−0.237784	−	0.172760i
$381$	9.06099e8	+	6.58319e8i	0.839341	+	0.609817i
$382$	7.28945e7	+	2.24346e8i	0.0669072	+	0.205919i
$383$	7.45168e8	−	5.41397e8i	0.677733	−	0.492402i	−0.194872	−	0.980829i	$-0.562429\pi$
$383$	7.45168e8	−	5.41397e8i	0.677733	−	0.492402i	0.872605	+	0.488427i	$0.162429\pi$
$384$	−2.14653e7	−	6.60634e7i	−0.0193454	−	0.0595390i
$385$	5.94573e8	−	1.82991e9i	0.530998	−	1.63424i
$386$	−7.05820e8	−	5.12808e8i	−0.624653	−	0.453837i
$387$	5.57282e6	−	1.71514e7i	0.00488750	−	0.0150422i
$388$	1.22640e8	−	3.77448e8i	0.106591	−	0.328054i
$389$	1.31469e9	+	9.55175e8i	1.13240	+	0.822734i	0.986042	−	0.166499i	$-0.0532462\pi$
$389$	1.31469e9	+	9.55175e8i	1.13240	+	0.822734i	0.146354	+	0.989232i	$0.453246\pi$
$390$	−1.73189e8	+	5.33020e8i	−0.147841	+	0.455006i
$391$	1.00858e7	+	3.10408e7i	0.00853277	+	0.0262612i
$392$	−3.17455e7	+	2.30645e7i	−0.0266184	+	0.0193394i
$393$	−2.06240e8	−	6.34741e8i	−0.171395	−	0.527500i
$394$	−3.31349e8	−	2.40739e8i	−0.272929	−	0.198294i
$395$	−1.46321e8	−	1.06308e8i	−0.119458	−	0.0867915i
$396$	−3.71764e8	+	2.70103e8i	−0.300839	+	0.218573i
$397$	9.68510e8			0.776850			0.388425	−	0.921480i	$-0.373019\pi$
$397$	9.68510e8			0.776850			0.388425	+	0.921480i	$0.373019\pi$
$398$	1.59344e9			1.26691
$399$	−4.05719e8	+	2.94772e8i	−0.319757	+	0.232317i
$400$	2.10542e7	−	6.47982e7i	0.0164486	−	0.0506236i
$401$	−2.69259e8	−	8.28693e8i	−0.208528	−	0.641783i	−0.999550	−	0.0299954i	$-0.990451\pi$
$401$	−2.69259e8	−	8.28693e8i	−0.208528	−	0.641783i	0.791022	−	0.611788i	$-0.209549\pi$
$402$	−9.11102e8			−0.699480
$403$	1.89430e7	+	1.13951e9i	0.0144172	+	0.867262i
$404$	−9.45646e8			−0.713500
$405$	−1.15245e8	−	3.54687e8i	−0.0862043	−	0.265310i
$406$	−1.46421e7	+	4.50636e7i	−0.0108583	+	0.0334184i
$407$	1.19373e9	−	8.67295e8i	0.877658	−	0.637656i
$408$	3.11635e7			0.0227162
$409$	8.48553e8			0.613264			0.306632	−	0.951828i	$-0.400798\pi$
$409$	8.48553e8			0.613264			0.306632	+	0.951828i	$0.400798\pi$
$410$	−2.35576e8	+	1.71156e8i	−0.168806	+	0.122645i
$411$	−7.64403e8	−	5.55372e8i	−0.543096	−	0.394582i
$412$	−9.23090e8	−	6.70664e8i	−0.650285	−	0.472460i
$413$	−7.89053e8	−	2.42846e9i	−0.551164	−	1.69631i
$414$	−1.25287e8	+	9.10261e7i	−0.0867768	+	0.0630471i
$415$	−4.17894e8	−	1.28615e9i	−0.287011	−	0.883328i
$416$	6.95736e7	−	2.14126e8i	0.0473825	−	0.145828i
$417$	−1.38340e9	−	1.00510e9i	−0.934266	−	0.678784i
$418$	−2.59895e8	+	7.99873e8i	−0.174053	+	0.535679i
$419$	−6.43214e8	+	1.97961e9i	−0.427176	+	1.31471i	0.473720	+	0.880676i	$0.342911\pi$
$419$	−6.43214e8	+	1.97961e9i	−0.427176	+	1.31471i	−0.900895	+	0.434036i	$0.857089\pi$
$420$	−5.00885e8	−	3.63914e8i	−0.329887	−	0.239677i
$421$	1.67691e8	−	5.16098e8i	0.109527	−	0.337090i	−0.881239	−	0.472670i	$-0.843290\pi$
$421$	1.67691e8	−	5.16098e8i	0.109527	−	0.337090i	0.990766	+	0.135581i	$0.0432901\pi$
$422$	−3.51783e7	−	1.08268e8i	−0.0227867	−	0.0701303i
$423$	−7.90762e7	+	5.74522e7i	−0.0507989	+	0.0369076i
$424$	−5.39764e7	−	1.66122e8i	−0.0343893	−	0.105839i
$425$	2.47290e7	+	1.79667e7i	0.0156259	+	0.0113529i
$426$	6.45524e8	+	4.69000e8i	0.404556	+	0.293927i
$427$	−1.85450e9	+	1.34737e9i	−1.15274	+	0.837512i
$428$	−5.94727e8			−0.366661
$429$	1.49929e9			0.916820
$430$	3.29661e7	−	2.39513e7i	0.0199953	−	0.0145274i
$431$	−5.90962e7	+	1.81879e8i	−0.0355541	+	0.109424i	−0.967259	−	0.253793i	$-0.918322\pi$
$431$	−5.90962e7	+	1.81879e8i	−0.0355541	+	0.109424i	0.931704	+	0.363217i	$0.118322\pi$
$432$	1.37382e8	+	4.22818e8i	0.0819853	+	0.252325i
$433$	7.95668e8			0.471004			0.235502	−	0.971874i	$-0.424327\pi$
$433$	7.95668e8			0.471004			0.235502	+	0.971874i	$0.424327\pi$
$434$	−1.20367e9	−	3.69093e8i	−0.706794	−	0.216731i
$435$	−6.36502e7			−0.0370755
$436$	−1.57747e8	−	4.85494e8i	−0.0911501	−	0.280531i
$437$	−8.75859e7	+	2.69562e8i	−0.0502053	+	0.154516i
$438$	8.10560e8	−	5.88907e8i	0.460920	−	0.334878i
$439$	−4.93987e8			−0.278669			−0.139335	−	0.990245i	$-0.544496\pi$
$439$	−4.93987e8			−0.278669			−0.139335	+	0.990245i	$0.544496\pi$
$440$	−1.03831e9			−0.581090
$441$	6.75765e7	−	4.90972e7i	0.0375198	−	0.0272597i
$442$	8.17169e7	+	5.93708e7i	0.0450126	+	0.0327036i
$443$	5.97618e8	+	4.34195e8i	0.326596	+	0.237286i	0.738985	−	0.673722i	$-0.235305\pi$
$443$	5.97618e8	+	4.34195e8i	0.326596	+	0.237286i	−0.412389	+	0.911008i	$0.635305\pi$
$444$	−1.46720e8	−	4.51556e8i	−0.0795514	−	0.244834i
$445$	−1.69270e8	+	1.22982e8i	−0.0910586	+	0.0661579i
$446$	3.82195e8	+	1.17627e9i	0.203992	+	0.627822i
$447$	4.95018e8	−	1.52351e9i	0.262147	−	0.806806i
$448$	2.01216e8	+	1.46192e8i	0.105728	+	0.0768159i
$449$	8.41722e8	−	2.59055e9i	0.438840	−	1.35061i	−0.450259	−	0.892898i	$-0.648668\pi$
$449$	8.41722e8	−	2.59055e9i	0.438840	−	1.35061i	0.889100	−	0.457714i	$-0.151332\pi$
$450$	−4.48179e7	+	1.37935e8i	−0.0231851	+	0.0713563i
$451$	6.30199e8	+	4.57867e8i	0.323489	+	0.235029i
$452$	3.77561e8	−	1.16201e9i	0.192310	−	0.591870i
$453$	7.73692e8	+	2.38118e9i	0.391043	+	1.20351i
$454$	−2.34868e8	+	1.70641e8i	−0.117795	+	0.0855833i
$455$	−6.20112e8	−	1.90851e9i	−0.308624	−	0.949848i
$456$	2.18943e8	+	1.59071e8i	0.108132	+	0.0785623i
$457$	−1.38634e9	−	1.00723e9i	−0.679457	−	0.493654i	0.193721	−	0.981057i	$-0.437945\pi$
$457$	−1.38634e9	−	1.00723e9i	−0.679457	−	0.493654i	−0.873177	+	0.487402i	$0.837945\pi$
$458$	1.25212e9	−	9.09720e8i	0.609001	−	0.442465i
$459$	−1.99452e8			−0.0962708
$460$	−3.49917e8			−0.167615
$461$	−1.87782e9	+	1.36431e9i	−0.892688	+	0.648576i	−0.936577	−	0.350461i	$-0.886025\pi$
$461$	−1.87782e9	+	1.36431e9i	−0.892688	+	0.648576i	0.0438896	+	0.999036i	$0.486025\pi$
$462$	−5.11811e8	+	1.57519e9i	−0.241470	+	0.743168i
$463$	−1.37524e8	−	4.23256e8i	−0.0643940	−	0.198184i	0.913683	−	0.406427i	$-0.133226\pi$
$463$	−1.37524e8	−	4.23256e8i	−0.0643940	−	0.198184i	−0.978077	+	0.208243i	$0.933226\pi$
$464$	2.55696e7			0.0118826
$465$	−2.81107e7	−	1.69099e9i	−0.0129654	−	0.779930i
$466$	−2.79131e9			−1.27778
$467$	−2.24795e8	−	6.91848e8i	−0.102136	−	0.314342i	0.886912	−	0.461939i	$-0.152846\pi$
$467$	−2.24795e8	−	6.91848e8i	−0.102136	−	0.314342i	−0.989048	+	0.147597i	$0.952846\pi$
$468$	−1.48101e8	+	4.55807e8i	−0.0667878	+	0.205552i
$469$	2.63922e9	−	1.91750e9i	1.18133	−	0.858284i
$470$	−2.20854e8			−0.0981212
$471$	2.78390e9			1.22767
$472$	−1.11477e9	+	8.09929e8i	−0.487966	+	0.354528i
$473$	−8.81891e7	−	6.40731e7i	−0.0383178	−	0.0278395i
$474$	1.25954e8	+	9.15107e7i	0.0543234	+	0.0394682i
$475$	8.20270e7	+	2.52453e8i	0.0351179	+	0.108082i
$476$	−9.02724e7	+	6.55867e7i	−0.0383646	+	0.0278735i
$477$	1.14899e8	+	3.53623e8i	0.0484733	+	0.149186i
$478$	7.08486e8	−	2.18049e9i	0.296711	−	0.913182i
$479$	−3.53341e9	−	2.56717e9i	−1.46899	−	1.06729i	−0.980904	−	0.194491i	$-0.937694\pi$
$479$	−3.53341e9	−	2.56717e9i	−1.46899	−	1.06729i	−0.488088	−	0.872794i	$-0.662306\pi$
$480$	−1.03245e8	+	3.17754e8i	−0.0426111	+	0.131144i
$481$	4.75549e8	−	1.46359e9i	0.194844	−	0.599669i
$482$	2.42321e9	+	1.76056e9i	0.985657	+	0.716122i
$483$	−1.72483e8	+	5.30849e8i	−0.0696518	+	0.214366i
$484$	4.72936e8	+	1.45555e9i	0.189602	+	0.583536i
$485$	−1.54432e9	+	1.12202e9i	−0.614671	+	0.446584i
$486$	−4.87621e8	−	1.50074e9i	−0.192688	−	0.593034i
$487$	2.33673e9	+	1.69773e9i	0.916762	+	0.666067i	0.942716	−	0.333596i	$-0.108262\pi$
$487$	2.33673e9	+	1.69773e9i	0.916762	+	0.666067i	−0.0259538	+	0.999663i	$0.508262\pi$
$488$	1.00076e9	+	7.27098e8i	0.389819	+	0.283220i
$489$	2.09693e9	−	1.52351e9i	0.810968	−	0.589202i
$490$	1.88736e8			0.0724718
$491$	1.98217e9			0.755710			0.377855	−	0.925865i	$-0.376662\pi$
$491$	1.98217e9			0.755710			0.377855	+	0.925865i	$0.376662\pi$
$492$	2.02785e8	−	1.47332e8i	0.0767640	−	0.0557723i
$493$	−3.54486e6	+	1.09100e7i	−0.00133240	+	0.00410071i
$494$	2.71058e8	+	8.34231e8i	0.101162	+	0.311345i
$495$	2.21025e9			0.819072
$496$	1.12927e7	+	6.79307e8i	0.00415538	+	0.249965i
$497$	−2.85697e9			−1.04390
$498$	3.59725e8	+	1.10712e9i	0.130517	+	0.401691i
$499$	−2.81380e8	+	8.66000e8i	−0.101378	+	0.312008i	−0.988863	−	0.148827i	$-0.952450\pi$
$499$	−2.81380e8	+	8.66000e8i	−0.101378	+	0.312008i	0.887486	+	0.460835i	$0.152450\pi$
$500$	9.80075e8	−	7.12066e8i	0.350642	−	0.254757i
$501$	2.87184e9			1.02030
$502$	−1.24189e9			−0.438147
$503$	−4.21491e9	+	3.06231e9i	−1.47673	+	1.07290i	−0.498134	+	0.867100i	$0.665981\pi$
$503$	−4.21491e9	+	3.06231e9i	−1.47673	+	1.07290i	−0.978593	+	0.205804i	$0.934019\pi$
$504$	−4.28328e8	−	3.11198e8i	−0.149028	−	0.108275i
$505$	3.67973e9	+	2.67348e9i	1.27144	+	0.923757i
$506$	2.89264e8	+	8.90262e8i	0.0992584	+	0.305486i
$507$	−4.16410e8	+	3.02540e8i	−0.141904	+	0.103099i
$508$	6.68737e8	+	2.05816e9i	0.226325	+	0.696557i
$509$	9.62859e8	−	2.96338e9i	0.323631	−	0.996035i	−0.648423	−	0.761280i	$-0.724571\pi$
$509$	9.62859e8	−	2.96338e9i	0.323631	−	0.996035i	0.972055	−	0.234755i	$-0.0754287\pi$
$510$	−1.21265e8	−	8.81040e7i	−0.0404799	−	0.0294104i
$511$	−1.10856e9	+	3.41181e9i	−0.367525	+	1.13113i
$512$	4.14756e7	−	1.27649e8i	0.0136568	−	0.0420312i
$513$	−1.40127e9	−	1.01808e9i	−0.458259	−	0.332945i
$514$	1.08738e9	−	3.34661e9i	0.353192	−	1.08701i
$515$	1.69590e9	+	5.21943e9i	0.547109	+	1.68383i
$516$	−2.83774e7	+	2.06174e7i	−0.00909282	+	0.00660632i
$517$	1.82572e8	+	5.61900e8i	0.0581056	+	0.178831i
$518$	1.37535e9	+	9.99251e8i	0.434770	+	0.315879i
$519$	1.50389e8	+	1.09264e8i	0.0472205	+	0.0343077i
$520$	−8.76093e8	+	6.36519e8i	−0.273236	+	0.198518i
$521$	−5.04052e9			−1.56150			−0.780752	−	0.624841i	$-0.785164\pi$
$521$	−5.04052e9			−1.56150			−0.780752	+	0.624841i	$0.785164\pi$
$522$	−5.44299e7			−0.0167491
$523$	−1.76663e9	+	1.28353e9i	−0.539996	+	0.392330i	−0.824083	−	0.566468i	$-0.808309\pi$
$523$	−1.76663e9	+	1.28353e9i	−0.539996	+	0.392330i	0.284088	+	0.958798i	$0.408309\pi$
$524$	3.98499e8	−	1.22645e9i	0.120995	−	0.372385i
$525$	1.61536e8	+	4.97157e8i	0.0487205	+	0.149946i
$526$	−3.74446e8			−0.112186
$527$	−2.91410e8	−	8.93577e7i	−0.0867294	−	0.0265947i
$528$	8.93783e8			0.264249
$529$	−9.54665e8	−	2.93816e9i	−0.280386	−	0.862939i
$530$	−2.59618e8	+	7.99021e8i	−0.0757476	+	0.233127i
$531$	2.37301e9	−	1.72409e9i	0.687810	−	0.499723i
$532$	−9.68998e8			−0.279018
$533$	8.12429e8			0.232402
$534$	1.45709e8	−	1.05864e8i	0.0414087	−	0.0300851i
$535$	2.31422e9	+	1.68138e9i	0.653382	+	0.474710i
$536$	−1.42423e9	−	1.03476e9i	−0.399487	−	0.290244i
$537$	8.22486e8	+	2.53135e9i	0.229202	+	0.705412i
$538$	−5.62061e8	+	4.08361e8i	−0.155613	+	0.113059i
$539$	−1.56022e8	−	4.80185e8i	−0.0429165	−	0.132083i
$540$	6.60784e8	−	2.03368e9i	0.180585	−	0.555783i
$541$	4.95407e9	+	3.59934e9i	1.34515	+	0.977311i	0.999237	+	0.0390449i	$0.0124315\pi$
$541$	4.95407e9	+	3.59934e9i	1.34515	+	0.977311i	0.345915	+	0.938266i	$0.387568\pi$
$542$	3.27228e8	−	1.00710e9i	0.0882780	−	0.271692i
$543$	2.40385e8	−	7.39830e8i	0.0644330	−	0.198304i
$544$	4.87146e7	+	3.53933e7i	0.0129737	+	0.00942594i
$545$	−7.58735e8	+	2.33515e9i	−0.200772	+	0.617911i
$546$	5.33795e8	+	1.64285e9i	0.140346	+	0.431941i
$547$	−4.20281e9	+	3.05352e9i	−1.09795	+	0.797710i	−0.980725	−	0.195395i	$-0.937401\pi$
$547$	−4.20281e9	+	3.05352e9i	−1.09795	+	0.797710i	−0.117229	+	0.993105i	$0.537401\pi$
$548$	−5.64160e8	−	1.73631e9i	−0.146444	−	0.450707i
$549$	−2.13032e9	−	1.54777e9i	−0.549467	−	0.399211i
$550$	7.09237e8	+	5.15291e8i	0.181770	+	0.132064i
$551$	−8.05935e7	+	5.85546e7i	−0.0205243	+	0.0149118i
$552$	3.01210e8			0.0762224
$553$	−5.57447e8			−0.140173
$554$	1.90938e9	−	1.38724e9i	0.477098	−	0.346632i
$555$	−7.05697e8	+	2.17191e9i	−0.175224	+	0.539283i
$556$	−1.02100e9	−	3.14232e9i	−0.251921	−	0.775333i
$557$	−5.34005e9			−1.30934			−0.654670	−	0.755915i	$-0.727192\pi$
$557$	−5.34005e9			−1.30934			−0.654670	+	0.755915i	$0.727192\pi$
$558$	−2.40386e7	−	1.44604e9i	−0.00585720	−	0.352338i
$559$	−1.13690e8			−0.0275284
$560$	−3.69673e8	−	1.13774e9i	−0.0889528	−	0.273769i
$561$	−1.23910e8	+	3.81356e8i	−0.0296303	+	0.0911928i
$562$	−2.04782e9	+	1.48783e9i	−0.486647	+	0.353570i
$563$	−9.28767e8			−0.219345			−0.109672	−	0.993968i	$-0.534980\pi$
$563$	−9.28767e8			−0.219345			−0.109672	+	0.993968i	$0.534980\pi$
$564$	1.90112e8			0.0446204
$565$	−4.75437e9	+	3.45425e9i	−1.10898	+	0.805720i
$566$	9.51324e8	+	6.91177e8i	0.220532	+	0.160226i
$567$	−9.29934e8	−	6.75637e8i	−0.214245	−	0.155658i
$568$	4.76422e8	+	1.46628e9i	0.109087	+	0.335735i
$569$	1.64431e9	−	1.19466e9i	0.374189	−	0.271864i	−0.384757	−	0.923018i	$-0.625715\pi$
$569$	1.64431e9	−	1.19466e9i	0.374189	−	0.271864i	0.758946	+	0.651154i	$0.225715\pi$
$570$	−4.02240e8	−	1.23797e9i	−0.0909752	−	0.279993i
$571$	−2.03406e9	+	6.26020e9i	−0.457234	+	1.40722i	0.411259	+	0.911518i	$0.365089\pi$
$571$	−2.03406e9	+	6.26020e9i	−0.457234	+	1.40722i	−0.868493	+	0.495702i	$0.834911\pi$
$572$	2.34367e9	+	1.70278e9i	0.523614	+	0.380428i
$573$	−3.01807e8	+	9.28867e8i	−0.0670175	+	0.206259i
$574$	−2.77339e8	+	8.53561e8i	−0.0612095	+	0.188384i
$575$	2.39017e8	+	1.73656e8i	0.0524314	+	0.0380936i
$576$	−8.82887e7	+	2.71725e8i	−0.0192498	+	0.0592448i
$577$	−9.57025e8	−	2.94542e9i	−0.207400	−	0.638310i	−0.999606	−	0.0280575i	$-0.991068\pi$
$577$	−9.57025e8	−	2.94542e9i	−0.207400	−	0.638310i	0.792207	−	0.610253i	$-0.208932\pi$
$578$	2.63391e9	−	1.91365e9i	0.567354	−	0.412207i
$579$	−1.11623e9	−	3.43540e9i	−0.238989	−	0.735534i
$580$	−9.94975e7	−	7.22892e7i	−0.0211746	−	0.0153842i
$581$	−3.37207e9	−	2.44995e9i	−0.713313	−	0.518253i
$582$	1.32936e9	−	9.65838e8i	0.279520	−	0.203083i
$583$	2.24750e9			0.469742
$584$	1.93590e9			0.402196
$585$	1.86493e9	−	1.35495e9i	0.385139	−	0.279820i
$586$	−2.75070e8	+	8.46578e8i	−0.0564679	+	0.173790i
$587$	−1.78227e9	−	5.48526e9i	−0.363697	−	1.11935i	−0.950793	−	0.309828i	$-0.899729\pi$
$587$	−1.78227e9	−	5.48526e9i	−0.363697	−	1.11935i	0.587095	−	0.809518i	$-0.300271\pi$
$588$	−1.62465e8			−0.0329564
$589$	−1.59121e9	−	2.11526e9i	−0.320866	−	0.426541i
$590$	6.62764e9			1.32855
$591$	−5.24017e8	−	1.61276e9i	−0.104421	−	0.321376i
$592$	2.83493e8	−	8.72503e8i	0.0561587	−	0.172839i
$593$	4.04833e9	−	2.94128e9i	0.797232	−	0.579223i	−0.112869	−	0.993610i	$-0.536004\pi$
$593$	4.04833e9	−	2.94128e9i	0.797232	−	0.579223i	0.910101	+	0.414387i	$0.136004\pi$
$594$	−5.72037e9			−1.11988
$595$	5.36695e8			0.104452
$596$	2.50410e9	−	1.81933e9i	0.484495	−	0.352007i
$597$	5.33737e9	+	3.87783e9i	1.02664	+	0.745896i
$598$	7.89831e8	+	5.73846e8i	0.151036	+	0.109734i
$599$	8.17398e8	+	2.51569e9i	0.155396	+	0.478260i	0.998201	−	0.0599597i	$-0.0190972\pi$
$599$	8.17398e8	+	2.51569e9i	0.155396	+	0.478260i	−0.842805	+	0.538219i	$0.819097\pi$
$600$	2.28218e8	−	1.65810e8i	0.0431340	−	0.0313387i
$601$	8.73511e8	+	2.68839e9i	0.164137	+	0.505163i	0.998972	−	0.0453384i	$-0.0144366\pi$
$601$	8.73511e8	+	2.68839e9i	0.164137	+	0.505163i	−0.834834	+	0.550501i	$0.814437\pi$
$602$	3.88104e7	−	1.19446e8i	0.00725037	−	0.0223143i
$603$	3.03174e9	+	2.20269e9i	0.563095	+	0.409113i
$604$	−1.49494e9	+	4.60094e9i	−0.276054	+	0.849606i
$605$	2.27474e9	−	7.00094e9i	0.417627	−	1.28532i
$606$	−3.16753e9	−	2.30135e9i	−0.578185	−	0.420076i
$607$	−7.53364e8	+	2.31862e9i	−0.136724	+	0.420793i	−0.995854	−	0.0909641i	$-0.971005\pi$
$607$	−7.53364e8	+	2.31862e9i	−0.136724	+	0.420793i	0.859130	+	0.511757i	$0.171005\pi$
$608$	1.61588e8	+	4.97318e8i	0.0291573	+	0.0897370i
$609$	−1.58713e8	+	1.15312e8i	−0.0284742	+	0.0206877i
$610$	−1.83860e9	−	5.65863e9i	−0.327969	−	1.00938i
$611$	4.98511e8	+	3.62190e8i	0.0884160	+	0.0642380i
$612$	−1.03699e8	−	7.53414e7i	−0.0182870	−	0.0132863i
$613$	1.60155e9	−	1.16359e9i	0.280821	−	0.204028i	−0.438455	−	0.898753i	$-0.644474\pi$
$613$	1.60155e9	−	1.16359e9i	0.280821	−	0.204028i	0.719275	+	0.694725i	$0.244474\pi$
$614$	2.59680e9			0.452740
$615$	−1.20561e9			−0.209000
$616$	−2.58905e9	+	1.88105e9i	−0.446280	+	0.324242i
$617$	1.34785e8	−	4.14825e8i	0.0231017	−	0.0710996i	−0.938841	−	0.344351i	$-0.888099\pi$
$617$	1.34785e8	−	4.14825e8i	0.0231017	−	0.0710996i	0.961943	+	0.273251i	$0.0880990\pi$
$618$	−1.45983e9	−	4.49291e9i	−0.248796	−	0.765717i
$619$	6.26909e9			1.06240			0.531199	−	0.847247i	$-0.321742\pi$
$619$	6.26909e9			1.06240			0.531199	+	0.847247i	$0.321742\pi$
$620$	1.87656e9	−	2.67527e9i	0.316222	−	0.450813i
$621$	−1.92780e9			−0.323028
$622$	1.29897e9	+	3.99782e9i	0.216438	+	0.666127i
$623$	−1.99279e8	+	6.13316e8i	−0.0330181	+	0.101619i
$624$	7.54145e8	−	5.47918e8i	0.124254	−	0.0902755i
$625$	−7.12636e9			−1.16758
$626$	−5.02215e9			−0.818238
$627$	−2.81713e9	+	2.04677e9i	−0.456427	+	0.331614i
$628$	4.35177e9	+	3.16175e9i	0.701144	+	0.509411i
$629$	3.32974e8	+	2.41920e8i	0.0533498	+	0.0387609i
$630$	7.86921e8	+	2.42189e9i	0.125383	+	0.385890i
$631$	6.63767e9	−	4.82255e9i	1.05175	−	0.764142i	0.0792069	−	0.996858i	$-0.474761\pi$
$631$	6.63767e9	−	4.82255e9i	1.05175	−	0.764142i	0.972545	+	0.232716i	$0.0747612\pi$
$632$	9.29588e7	+	2.86098e8i	0.0146481	+	0.0450822i
$633$	1.45650e8	−	4.48264e8i	0.0228243	−	0.0702459i
$634$	−5.01126e9	−	3.64089e9i	−0.780970	−	0.567408i
$635$	3.21652e9	−	9.89942e9i	0.498514	−	1.53427i
$636$	2.23480e8	−	6.87801e8i	0.0344460	−	0.106014i
$637$	−4.26015e8	−	3.09518e8i	−0.0653036	−	0.0474458i
$638$	−1.01668e8	+	3.12902e8i	−0.0154993	+	0.0477019i
$639$	−1.01416e9	−	3.12125e9i	−0.153763	−	0.473234i
$640$	−5.22273e8	+	3.79454e8i	−0.0787531	+	0.0572175i
$641$	−6.52021e8	−	2.00671e9i	−0.0977819	−	0.300942i	0.890187	−	0.455596i	$-0.150574\pi$
$641$	−6.52021e8	−	2.00671e9i	−0.0977819	−	0.300942i	−0.987969	+	0.154654i	$0.950574\pi$
$642$	−1.99210e9	−	1.44734e9i	−0.297124	−	0.215873i
$643$	4.44225e9	+	3.22748e9i	0.658968	+	0.478768i	0.866314	−	0.499499i	$-0.166483\pi$
$643$	4.44225e9	+	3.22748e9i	0.658968	+	0.478768i	−0.207346	+	0.978268i	$0.566483\pi$
$644$	−8.72524e8	+	6.33926e8i	−0.128729	+	0.0935272i
$645$	1.68712e8			0.0247563
$646$	−2.34595e8			−0.0342378
$647$	−2.92196e9	+	2.12293e9i	−0.424140	+	0.308156i	−0.779301	−	0.626649i	$-0.784426\pi$
$647$	−2.92196e9	+	2.12293e9i	−0.424140	+	0.308156i	0.355161	+	0.934805i	$0.384426\pi$
$648$	−1.91682e8	+	5.89937e8i	−0.0276738	+	0.0851712i
$649$	−5.47884e9	−	1.68621e10i	−0.786741	−	2.42134i
$650$	9.14321e8			0.130588
$651$	−3.13357e9	−	4.16559e9i	−0.445150	−	0.591757i
$652$	5.00820e9			0.707645
$653$	−2.34479e9	−	7.21652e9i	−0.329540	−	1.01422i	−0.969350	−	0.245685i	$-0.920987\pi$
$653$	−2.34479e9	−	7.21652e9i	−0.329540	−	1.01422i	0.639810	−	0.768533i	$-0.279013\pi$
$654$	6.53123e8	−	2.01010e9i	0.0913004	−	0.280994i
$655$	−5.01803e9	+	3.64581e9i	−0.697732	+	0.506932i
$656$	4.84321e8			0.0669838
$657$	−4.12094e9			−0.566914
$658$	−5.50704e8	+	4.00110e8i	−0.0753577	+	0.0547505i
$659$	−7.93127e9	−	5.76240e9i	−1.07955	−	0.784341i	−0.101948	−	0.994790i	$-0.532507\pi$
$659$	−7.93127e9	−	5.76240e9i	−1.07955	−	0.784341i	−0.977605	+	0.210449i	$0.932507\pi$
$660$	−3.47792e9	−	2.52686e9i	−0.470887	−	0.342119i
$661$	−3.70836e6	−	1.14131e7i	−0.000499432	−	0.00153709i	0.950806	−	0.309785i	$-0.100257\pi$
$661$	−3.70836e6	−	1.14131e7i	−0.000499432	−	0.00153709i	−0.951306	+	0.308248i	$0.900257\pi$
$662$	5.97399e9	−	4.34036e9i	0.800316	−	0.581464i
$663$	1.29232e8	+	3.97736e8i	0.0172216	+	0.0530027i
$664$	−6.95066e8	+	2.13919e9i	−0.0921378	+	0.283571i
$665$	3.77060e9	+	2.73950e9i	0.497205	+	0.361240i
$666$	−6.03470e8	+	1.85729e9i	−0.0791583	+	0.243624i
$667$	−3.42627e7	+	1.05450e8i	−0.00447075	+	0.0137596i
$668$	4.48924e9	+	3.26162e9i	0.582713	+	0.423366i
$669$	−1.58241e9	+	4.87016e9i	−0.204328	+	0.628858i
$670$	2.61658e9	+	8.05301e9i	0.336103	+	1.03442i
$671$	−1.28768e10	+	9.35557e9i	−1.64543	+	1.19548i
$672$	3.18216e8	+	9.79370e8i	0.0404511	+	0.124496i
$673$	8.39114e9	+	6.09652e9i	1.06113	+	0.770956i	0.974297	−	0.225267i	$-0.0723255\pi$
$673$	8.39114e9	+	6.09652e9i	1.06113	+	0.770956i	0.0868324	+	0.996223i	$0.472326\pi$
$674$	−1.63124e8	−	1.18516e8i	−0.0205214	−	0.0149097i
$675$	−1.46063e9	+	1.06121e9i	−0.182801	+	0.132812i
$676$	−9.94532e8			−0.123824
$677$	−7.24393e8			−0.0897251			−0.0448625	−	0.998993i	$-0.514285\pi$
$677$	−7.24393e8			−0.0897251			−0.0448625	+	0.998993i	$0.514285\pi$
$678$	4.09258e9	−	2.97344e9i	0.504305	−	0.366399i
$679$	−1.81810e9	+	5.59554e9i	−0.222882	+	0.685959i
$680$	−8.94982e7	−	2.75447e8i	−0.0109152	−	0.0335937i
$681$	−1.20199e9			−0.145843
$682$	−8.35774e9	−	2.56282e9i	−1.00889	−	0.309366i
$683$	4.73540e9			0.568702			0.284351	−	0.958720i	$-0.408222\pi$
$683$	4.73540e9			0.568702			0.284351	+	0.958720i	$0.408222\pi$
$684$	−3.43972e8	−	1.05864e9i	−0.0410986	−	0.126488i
$685$	−2.71352e9	+	8.35135e9i	−0.322564	+	0.992749i
$686$	−4.58646e9	+	3.33226e9i	−0.542429	+	0.394098i
$687$	6.40802e9			0.754007
$688$	−6.77751e7			−0.00793433
$689$	1.89636e9	−	1.37779e9i	0.220879	−	0.160478i
$690$	−1.17208e9	−	8.51566e8i	−0.135827	−	0.0986839i
$691$	6.33896e9	+	4.60552e9i	0.730878	+	0.531014i	0.889841	−	0.456271i	$-0.150815\pi$
$691$	6.33896e9	+	4.60552e9i	0.730878	+	0.531014i	−0.158963	+	0.987285i	$0.550815\pi$
$692$	1.10993e8	+	3.41602e8i	0.0127328	+	0.0391876i
$693$	5.51129e9	−	4.00419e9i	0.629053	−	0.457033i
$694$	−5.64042e8	−	1.73594e9i	−0.0640550	−	0.197141i
$695$	−4.91085e9	+	1.51140e10i	−0.554894	+	1.70779i
$696$	8.56480e7	+	6.22269e7i	0.00962908	+	0.00699593i
$697$	−6.71440e7	+	2.06648e8i	−0.00751091	+	0.0231162i
$698$	−3.50047e9	+	1.07733e10i	−0.389612	+	1.19910i
$699$	−9.34976e9	−	6.79300e9i	−1.03545	−	0.752300i
$700$	−3.12122e8	+	9.60612e8i	−0.0343939	+	0.105853i
$701$	3.16813e9	+	9.75050e9i	0.347368	+	1.06909i	0.960304	+	0.278956i	$0.0899885\pi$
$701$	3.16813e9	+	9.75050e9i	0.347368	+	1.06909i	−0.612936	+	0.790133i	$0.710012\pi$
$702$	−4.82666e9	+	3.50677e9i	−0.526583	+	0.382585i
$703$	1.10449e9	+	3.39926e9i	0.119899	+	0.369012i
$704$	1.39716e9	+	1.01509e9i	0.150918	+	0.109648i
$705$	−7.39772e8	−	5.37476e8i	−0.0795126	−	0.0577693i
$706$	−2.95818e9	+	2.14924e9i	−0.316379	+	0.229863i
$707$	1.40189e10			1.49192
$708$	−5.70510e9			−0.604153
$709$	1.26697e10	−	9.20507e9i	1.33507	−	0.969986i	0.335461	−	0.942054i	$-0.391108\pi$
$709$	1.26697e10	−	9.20507e9i	1.33507	−	0.969986i	0.999610	−	0.0279319i	$-0.00889214\pi$
$710$	2.29151e9	−	7.05255e9i	0.240280	−	0.739506i
$711$	−1.97881e8	−	6.09014e8i	−0.0206471	−	0.0635454i
$712$	3.48003e8			0.0361329
$713$	−2.81661e9	−	8.63683e8i	−0.291013	−	0.0892362i
$714$	−4.61990e8			−0.0474994
$715$	−4.30578e9	−	1.32518e10i	−0.440536	−	1.35583i
$716$	−1.58922e9	+	4.89111e9i	−0.161804	+	0.497980i
$717$	7.67965e9	−	5.57959e9i	0.778080	−	0.565308i
$718$	−6.30796e9			−0.635994
$719$	−1.54253e10			−1.54768			−0.773842	−	0.633378i	$-0.781668\pi$
$719$	−1.54253e10			−1.54768			−0.773842	+	0.633378i	$0.781668\pi$
$720$	1.11176e9	−	8.07740e8i	0.111006	−	0.0806507i
$721$	1.36845e10	+	9.94238e9i	1.35974	+	0.987909i
$722$	4.13709e9	+	3.00577e9i	0.409086	+	0.297218i
$723$	3.83222e9	+	1.17944e10i	0.377108	+	1.16062i
$724$	1.21601e9	−	8.83485e8i	0.119084	−	0.0865195i
$725$	3.20881e7	+	9.87569e7i	0.00312723	+	0.00962464i
$726$	−1.95811e9	+	6.02644e9i	−0.189915	+	0.584498i
$727$	7.00443e9	+	5.08901e9i	0.676086	+	0.491205i	0.872057	−	0.489404i	$-0.162786\pi$
$727$	7.00443e9	+	5.08901e9i	0.676086	+	0.491205i	−0.195971	+	0.980610i	$0.562786\pi$
$728$	−1.03141e9	+	3.17434e9i	−0.0990764	+	0.304926i
$729$	2.83768e9	−	8.73348e9i	0.271279	−	0.834912i
$730$	−7.53305e9	−	5.47308e9i	−0.716705	−	0.520717i
$731$	9.39603e6	−	2.89180e7i	0.000889679	−	0.00273815i
$732$	1.58267e9	+	4.87097e9i	0.149143	+	0.459015i
$733$	−5.01926e9	+	3.64670e9i	−0.470734	+	0.342008i	−0.797727	−	0.603018i	$-0.793965\pi$
$733$	−5.01926e9	+	3.64670e9i	−0.470734	+	0.342008i	0.326993	+	0.945027i	$0.393965\pi$
$734$	−2.37510e9	−	7.30982e9i	−0.221690	−	0.682292i
$735$	6.32190e8	+	4.59313e8i	0.0587276	+	0.0426681i
$736$	4.70849e8	+	3.42092e8i	0.0435321	+	0.0316279i
$737$	1.83255e10	−	1.33143e10i	1.68624	−	1.22513i
$738$	−1.03097e9			−0.0944167
$739$	2.48765e9			0.226743			0.113372	−	0.993553i	$-0.463835\pi$
$739$	2.48765e9			0.226743			0.113372	+	0.993553i	$0.463835\pi$
$740$	−3.56984e9	+	2.59364e9i	−0.323845	+	0.235287i
$741$	−1.12227e9	+	3.45399e9i	−0.101329	+	0.311858i
$742$	8.00183e8	+	2.46271e9i	0.0719078	+	0.221309i
$743$	1.54490e10			1.38178			0.690889	−	0.722961i	$-0.257219\pi$
$743$	1.54490e10			1.38178			0.690889	+	0.722961i	$0.257219\pi$
$744$	−1.61535e9	+	2.30289e9i	−0.143801	+	0.205006i
$745$	−1.48876e10			−1.31910
$746$	−6.01103e8	−	1.85001e9i	−0.0530107	−	0.163150i
$747$	1.47958e9	−	4.55369e9i	0.129872	−	0.399706i
$748$	−6.26811e8	+	4.55405e8i	−0.0547623	+	0.0397871i
$749$	8.81664e9			0.766684
$750$	5.01576e9			0.434133
$751$	1.09078e10	−	7.92495e9i	0.939715	−	0.682743i	−0.00863740	−	0.999963i	$-0.502749\pi$
$751$	1.09078e10	−	7.92495e9i	0.939715	−	0.682743i	0.948352	+	0.317220i	$0.102749\pi$
$752$	2.97182e8	+	2.15915e8i	0.0254836	+	0.0185149i
$753$	−4.15983e9	−	3.02229e9i	−0.355053	−	0.257961i
$754$	1.06035e8	+	3.26342e8i	0.00900843	+	0.0277251i
$755$	1.88247e10	−	1.36770e10i	1.59189	−	1.15658i
$756$	−2.03664e9	−	6.26814e9i	−0.171431	−	0.527609i
$757$	−2.73684e9	+	8.42312e9i	−0.229305	+	0.705728i	0.768521	+	0.639824i	$0.220993\pi$
$757$	−2.73684e9	+	8.42312e9i	−0.229305	+	0.705728i	−0.997826	+	0.0659034i	$0.979007\pi$
$758$	−4.24955e9	−	3.08748e9i	−0.354406	−	0.257491i
$759$	−1.19765e9	+	3.68598e9i	−0.0994221	+	0.305990i
$760$	7.77213e8	−	2.39202e9i	0.0642233	−	0.197659i
$761$	9.99529e9	+	7.26201e9i	0.822147	+	0.597325i	0.917327	−	0.398136i	$-0.130343\pi$
$761$	9.99529e9	+	7.26201e9i	0.822147	+	0.597325i	−0.0951799	+	0.995460i	$0.530343\pi$
$762$	−2.76879e9	+	8.52147e9i	−0.226698	+	0.697705i
$763$	2.33854e9	+	7.19729e9i	0.190594	+	0.586588i
$764$	−1.52672e9	+	1.10923e9i	−0.123861	+	0.0899900i
$765$	1.90514e8	+	5.86343e8i	0.0153855	+	0.0473518i
$766$	5.96135e9	+	4.33117e9i	0.479230	+	0.348181i
$767$	−1.49599e10	−	1.08690e10i	−1.19714	−	0.869772i
$768$	4.49575e8	−	3.26636e8i	0.0358128	−	0.0260195i
$769$	−2.04001e10			−1.61767			−0.808834	−	0.588037i	$-0.799901\pi$
$769$	−2.04001e10			−1.61767			−0.808834	+	0.588037i	$0.799901\pi$
$770$	1.53926e10			1.21505
$771$	1.17867e10	−	8.56353e9i	0.926193	−	0.672919i
$772$	2.15679e9	−	6.63793e9i	0.168713	−	0.519245i
$773$	7.33225e9	+	2.25663e10i	0.570964	+	1.75725i	0.649527	+	0.760338i	$0.274967\pi$
$773$	7.33225e9	+	2.25663e10i	0.570964	+	1.75725i	−0.0785632	+	0.996909i	$0.525033\pi$
$774$	1.44272e8			0.0111838
$775$	−2.60950e9	+	8.96097e8i	−0.201373	+	0.0691511i
$776$	3.17498e9			0.243907
$777$	2.17507e9	+	6.69418e9i	0.166341	+	0.511946i
$778$	−4.01732e9	+	1.23640e10i	−0.305850	+	0.941308i
$779$	−1.52654e9	+	1.10910e9i	−0.115698	+	0.0840598i
$780$	−4.48360e9			−0.338295
$781$	−1.98375e10			−1.49008
$782$	−2.11239e8	+	1.53474e8i	−0.0157961	+	0.0114766i
$783$	−5.48162e8	−	3.98263e8i	−0.0408078	−	0.0296486i
$784$	−2.53964e8	−	1.84516e8i	−0.0188220	−	0.0136750i
$785$	−7.99504e9	−	2.46062e10i	−0.589898	−	1.81552i
$786$	4.31954e9	−	3.13833e9i	0.317292	−	0.230526i
$787$	−1.41382e9	−	4.35130e9i	−0.103391	−	0.318205i	0.885958	−	0.463765i	$-0.153502\pi$
$787$	−1.41382e9	−	4.35130e9i	−0.103391	−	0.318205i	−0.989349	+	0.145560i	$0.953502\pi$
$788$	1.01251e9	−	3.11619e9i	0.0737155	−	0.226873i
$789$	−1.25424e9	−	9.11260e8i	−0.0909100	−	0.0660500i
$790$	4.47117e8	−	1.37608e9i	0.0322646	−	0.0993002i
$791$	−5.59722e9	+	1.72265e10i	−0.402119	+	1.23760i
$792$	−2.97412e9	−	2.16082e9i	−0.212726	−	0.154554i
$793$	−5.12978e9	+	1.57878e10i	−0.365294	+	1.12426i
$794$	2.39429e9	+	7.36886e9i	0.169748	+	0.522431i
$795$	−2.81413e9	+	2.04459e9i	−0.198637	+	0.144318i
$796$	3.93919e9	+	1.21236e10i	0.276829	+	0.851992i
$797$	1.53630e9	+	1.11619e9i	0.107491	+	0.0780966i	0.640232	−	0.768181i	$-0.278838\pi$
$797$	1.53630e9	+	1.11619e9i	0.107491	+	0.0780966i	−0.532741	+	0.846278i	$0.678838\pi$
$798$	−3.24575e9	−	2.35818e9i	−0.226103	−	0.164273i
$799$	−1.33326e8	+	9.68670e7i	−0.00924700	+	0.00671834i
$800$	5.45063e8			0.0376384
$801$	−7.40791e8			−0.0509310
$802$	5.63943e9	−	4.09728e9i	0.386033	−	0.280469i
$803$	−7.69737e9	+	2.36901e10i	−0.524612	+	1.61459i
$804$	−2.25237e9	−	6.93207e9i	−0.152842	−	0.470400i
$805$	5.18740e9			0.350481
$806$	−8.62308e9	+	2.96115e9i	−0.580082	+	0.199199i
$807$	−2.87648e9			−0.192665
$808$	−2.33777e9	−	7.19490e9i	−0.155905	−	0.479828i
$809$	−2.04792e9	+	6.30284e9i	−0.135985	+	0.418520i	−0.995742	−	0.0921840i	$-0.970615\pi$
$809$	−2.04792e9	+	6.30284e9i	−0.135985	+	0.418520i	0.859757	+	0.510704i	$0.170615\pi$
$810$	2.41372e9	−	1.75367e9i	0.159584	−	0.115945i
$811$	1.15329e9			0.0759214			0.0379607	−	0.999279i	$-0.487914\pi$
$811$	1.15329e9			0.0759214			0.0379607	+	0.999279i	$0.487914\pi$
$812$	−3.79062e8			−0.0248464
$813$	3.54699e9	−	2.57704e9i	0.231496	−	0.168192i
$814$	9.54983e9	+	6.93836e9i	0.620598	+	0.450891i
$815$	−1.94881e10	−	1.41589e10i	−1.26101	−	0.916177i
$816$	7.70405e7	+	2.37106e8i	0.00496368	+	0.0152766i
$817$	2.13622e8	−	1.55205e8i	0.0137047	−	0.00995701i
$818$	2.09774e9	+	6.45617e9i	0.134003	+	0.412419i
$819$	2.19555e9	−	6.75720e9i	0.139653	−	0.429807i
$820$	−1.88461e9	−	1.36925e9i	−0.119364	−	0.0867228i
$821$	−5.88306e9	+	1.81062e10i	−0.371024	+	1.14189i	0.575098	+	0.818085i	$0.304964\pi$
$821$	−5.88306e9	+	1.81062e10i	−0.371024	+	1.14189i	−0.946122	+	0.323810i	$0.895036\pi$
$822$	2.33581e9	−	7.18888e9i	0.146685	−	0.451450i
$823$	−1.31786e10	−	9.57481e9i	−0.824081	−	0.598730i	0.0937977	−	0.995591i	$-0.470099\pi$
$823$	−1.31786e10	−	9.57481e9i	−0.824081	−	0.598730i	−0.917879	+	0.396862i	$0.870099\pi$
$824$	2.82071e9	−	8.68126e9i	0.175636	−	0.540552i
$825$	1.12163e9	+	3.45203e9i	0.0695444	+	0.214036i
$826$	1.65261e10	−	1.20069e10i	1.02033	−	0.741314i
$827$	−9.83826e9	−	3.02791e10i	−0.604852	−	1.86154i	−0.497805	−	0.867289i	$-0.665861\pi$
$827$	−9.83826e9	−	3.02791e10i	−0.604852	−	1.86154i	−0.107047	−	0.994254i	$-0.534139\pi$
$828$	−1.00229e9	−	7.28209e8i	−0.0613605	−	0.0445810i
$829$	−2.23566e10	−	1.62430e10i	−1.36290	−	0.990207i	−0.998254	−	0.0590617i	$-0.981189\pi$
$829$	−2.23566e10	−	1.62430e10i	−1.36290	−	0.990207i	−0.364649	−	0.931145i	$-0.618811\pi$
$830$	8.75249e9	−	6.35906e9i	0.531323	−	0.386029i
$831$	9.77168e9			0.590698
$832$	1.80116e9			0.108423
$833$	1.13937e8	−	8.27801e7i	0.00682979	−	0.00496213i
$834$	4.22728e9	−	1.30102e10i	0.252337	−	0.776612i
$835$	−8.24760e9	−	2.53835e10i	−0.490258	−	1.50886i
$836$	−6.72829e9			−0.398275
$837$	1.03385e10	−	1.47389e10i	0.609425	−	0.868811i
$838$	−1.66519e10			−0.977483
$839$	−6.89845e9	−	2.12313e10i	−0.403260	−	1.24111i	−0.922340	−	0.386380i	$-0.873725\pi$
$839$	−6.89845e9	−	2.12313e10i	−0.403260	−	1.24111i	0.519080	−	0.854726i	$-0.326275\pi$
$840$	1.53057e9	−	4.71061e9i	0.0890995	−	0.274220i
$841$	1.39239e10	−	1.01163e10i	0.807189	−	0.586457i
$842$	4.34126e9			0.250625
$843$	−1.04802e10			−0.602521
$844$	7.36785e8	−	5.35305e8i	0.0421834	−	0.0306481i
$845$	3.86996e9	+	2.81169e9i	0.220652	+	0.160313i
$846$	−6.32609e8	−	4.59618e8i	−0.0359203	−	0.0260976i
$847$	−7.01112e9	−	2.15780e10i	−0.396457	−	1.22017i
$848$	1.13050e9	−	8.21354e8i	0.0636625	−	0.0462535i
$849$	1.50449e9	+	4.63033e9i	0.0843745	+	0.259678i
$850$	−7.55650e7	+	2.32565e8i	−0.00422041	+	0.0129891i
$851$	3.21835e9	+	2.33827e9i	0.179011	+	0.130059i
$852$	−1.97254e9	+	6.07087e9i	−0.109267	+	0.336289i
$853$	−8.64848e9	+	2.66173e10i	−0.477110	+	1.46839i	0.365981	+	0.930622i	$0.380733\pi$
$853$	−8.64848e9	+	2.66173e10i	−0.477110	+	1.46839i	−0.843091	+	0.537771i	$0.819267\pi$
$854$	−1.48360e10	−	1.07790e10i	−0.815107	−	0.592210i
$855$	−1.65445e9	+	5.09187e9i	−0.0905257	+	0.278609i
$856$	−1.47025e9	−	4.52495e9i	−0.0801183	−	0.246579i
$857$	−7.41638e9	+	5.38831e9i	−0.402494	+	0.292429i	−0.770556	−	0.637372i	$-0.780021\pi$
$857$	−7.41638e9	+	5.38831e9i	−0.402494	+	0.292429i	0.368062	+	0.929801i	$0.380021\pi$
$858$	3.70644e9	+	1.14072e10i	0.200332	+	0.616560i
$859$	−8.64374e9	−	6.28005e9i	−0.465292	−	0.338054i	0.330312	−	0.943872i	$-0.392846\pi$
$859$	−8.64374e9	−	6.28005e9i	−0.465292	−	0.338054i	−0.795604	+	0.605817i	$0.792846\pi$
$860$	2.63729e8	+	1.91610e8i	0.0141388	+	0.0102725i
$861$	−3.00622e9	+	2.18415e9i	−0.160513	+	0.116619i
$862$	−1.52992e9			−0.0813564
$863$	2.47844e10			1.31263			0.656313	−	0.754489i	$-0.272115\pi$
$863$	2.47844e10			1.31263			0.656313	+	0.754489i	$0.272115\pi$
$864$	−2.87736e9	+	2.09053e9i	−0.151774	+	0.110270i
$865$	5.33858e8	−	1.64305e9i	0.0280459	−	0.0863165i
$866$	1.96700e9	+	6.05380e9i	0.102918	+	0.316749i
$867$	1.34797e10			0.702444
$868$	−1.67410e8	−	1.00705e10i	−0.00868887	−	0.522676i
$869$	−3.87066e9			−0.200086
$870$	−1.57352e8	−	4.84279e8i	−0.00810130	−	0.0249332i
$871$	7.30040e9	−	2.24683e10i	0.374354	−	1.15214i
$872$	3.30389e9	−	2.40041e9i	0.168740	−	0.122597i
$873$	−6.75855e9			−0.343798
$874$	−2.26747e9			−0.114882
$875$	−1.45293e10	+	1.05562e10i	−0.733190	+	0.532694i
$876$	6.48448e9	+	4.71125e9i	0.325920	+	0.236795i
$877$	2.25801e10	+	1.64054e10i	1.13039	+	0.821276i	0.985751	−	0.168209i	$-0.0537983\pi$
$877$	2.25801e10	+	1.64054e10i	1.13039	+	0.821276i	0.144638	+	0.989485i	$0.453798\pi$
$878$	−1.22120e9	−	3.75847e9i	−0.0608915	−	0.187405i
$879$	−2.98163e9	+	2.16628e9i	−0.148079	+	0.107585i
$880$	−2.56685e9	−	7.89994e9i	−0.126973	−	0.390782i
$881$	−2.87386e9	+	8.84484e9i	−0.141596	+	0.435787i	−0.996558	−	0.0829039i	$-0.973581\pi$
$881$	−2.87386e9	+	8.84484e9i	−0.141596	+	0.435787i	0.854962	+	0.518691i	$0.173581\pi$
$882$	5.40612e8	+	3.92778e8i	0.0265305	+	0.0192755i
$883$	−1.22437e10	+	3.76823e10i	−0.598483	+	1.84194i	−0.0619168	+	0.998081i	$0.519721\pi$
$883$	−1.22437e10	+	3.76823e10i	−0.598483	+	1.84194i	−0.536566	+	0.843859i	$0.680279\pi$
$884$	−2.49705e8	+	7.68512e8i	−0.0121575	+	0.0374169i
$885$	2.21999e10	+	1.61292e10i	1.07659	+	0.782188i
$886$	−1.82616e9	+	5.62034e9i	−0.0882106	+	0.271484i
$887$	8.23579e9	+	2.53472e10i	0.396253	+	1.21954i	0.927981	+	0.372627i	$0.121543\pi$
$887$	8.23579e9	+	2.53472e10i	0.396253	+	1.21954i	−0.531728	+	0.846915i	$0.678457\pi$
$888$	3.07293e9	−	2.23262e9i	0.147268	−	0.106996i
$889$	−9.91382e9	−	3.05116e10i	−0.473244	−	1.45649i
$890$	−1.35416e9	−	9.83857e8i	−0.0643881	−	0.0467807i
$891$	−6.45705e9	−	4.69132e9i	−0.305817	−	0.222189i
$892$	−8.00479e9	+	5.81582e9i	−0.377636	+	0.274368i
$893$	−1.43114e9			−0.0672516
$894$	1.28153e10			0.599857
$895$	2.00119e10	−	1.45395e10i	0.933058	−	0.677906i
$896$	−6.14862e8	+	1.89235e9i	−0.0285561	+	0.0878868i
$897$	1.24909e9	+	3.84430e9i	0.0577857	+	0.177846i
$898$	2.17910e10			1.00417
$899$	−6.22464e8	−	8.27467e8i	−0.0285730	−	0.0379832i
$900$	−1.16027e9			−0.0530531
$901$	1.93725e8	+	5.96225e8i	0.00882367	+	0.0271565i
$902$	−1.92572e9	+	5.92675e9i	−0.0873715	+	0.268902i
$903$	4.20686e8	−	3.05646e8i	0.0190130	−	0.0138138i
$904$	9.77451e9			0.440053
$905$	−7.22954e9			−0.324221
$906$	−1.62044e10	+	1.17732e10i	−0.723910	+	0.525951i
$907$	3.08704e10	+	2.24286e10i	1.37378	+	0.998108i	0.997431	+	0.0716285i	$0.0228196\pi$
$907$	3.08704e10	+	2.24286e10i	1.37378	+	0.998108i	0.376346	+	0.926479i	$0.377180\pi$
$908$	−1.87894e9	−	1.36513e9i	−0.0832939	−	0.0605165i
$909$	4.97639e9	+	1.53157e10i	0.219756	+	0.676339i
$910$	1.29878e10	−	9.43619e9i	0.571335	−	0.415099i
$911$	−3.50555e9	−	1.07890e10i	−0.153618	−	0.472788i	0.844400	−	0.535713i	$-0.179957\pi$
$911$	−3.50555e9	−	1.07890e10i	−0.153618	−	0.472788i	−0.998018	+	0.0629251i	$0.979957\pi$
$912$	−6.69029e8	+	2.05906e9i	−0.0292054	+	0.0898849i
$913$	−2.34142e10	−	1.70114e10i	−1.01820	−	0.739762i
$914$	4.23627e9	−	1.30379e10i	0.183515	−	0.564801i
$915$	7.61241e9	−	2.34286e10i	0.328510	−	1.01105i
$916$	1.00170e10	+	7.27776e9i	0.430628	+	0.312870i
$917$	−5.90762e9	+	1.81818e10i	−0.253000	+	0.778653i
$918$	−4.93073e8	−	1.51752e9i	−0.0210359	−	0.0647420i
$919$	1.79971e10	−	1.30757e10i	0.764890	−	0.555725i	−0.135516	−	0.990775i	$-0.543269\pi$
$919$	1.79971e10	−	1.30757e10i	0.764890	−	0.555725i	0.900406	+	0.435050i	$0.143269\pi$
$920$	−8.65041e8	−	2.66232e9i	−0.0366252	−	0.112721i
$921$	8.69822e9	+	6.31963e9i	0.366878	+	0.266553i
$922$	−1.50225e10	−	1.09145e10i	−0.631226	−	0.458612i
$923$	−1.67382e10	+	1.21610e10i	−0.700654	+	0.509055i
$924$	−1.32501e10			−0.552543
$925$	3.72561e9			0.154775
$926$	2.88034e9	−	2.09269e9i	0.119208	−	0.0866097i
$927$	−6.00443e9	+	1.84797e10i	−0.247567	+	0.761933i
$928$	6.32116e7	+	1.94545e8i	0.00259644	+	0.00799103i
$929$	−2.78850e10			−1.14108			−0.570539	−	0.821271i	$-0.693266\pi$
$929$	−2.78850e10			−1.14108			−0.570539	+	0.821271i	$0.693266\pi$
$930$	1.27963e10	−	4.39424e9i	0.521669	−	0.179140i
$931$	1.22302e9			0.0496717
$932$	−6.90049e9	−	2.12375e10i	−0.279206	−	0.859307i
$933$	−5.37816e9	+	1.65523e10i	−0.216795	+	0.667225i
$934$	4.70817e9	−	3.42069e9i	0.189077	−	0.137372i
$935$	3.72657e9			0.149097
$936$	−3.83411e9			−0.152827
$937$	−2.19702e10	+	1.59623e10i	−0.872459	+	0.633878i	−0.931246	−	0.364392i	$-0.881277\pi$
$937$	−2.19702e10	+	1.59623e10i	−0.872459	+	0.633878i	0.0587868	+	0.998271i	$0.481277\pi$
$938$	2.11137e10	+	1.53400e10i	0.835324	+	0.606898i
$939$	−1.68222e10	−	1.22220e10i	−0.663060	−	0.481741i
$940$	−5.45981e8	−	1.68036e9i	−0.0214403	−	0.0659863i
$941$	3.90492e9	−	2.83709e9i	0.152774	−	0.110997i	−0.508772	−	0.860901i	$-0.669901\pi$
$941$	3.90492e9	−	2.83709e9i	0.152774	−	0.110997i	0.661546	+	0.749904i	$0.269901\pi$
$942$	6.88217e9	+	2.11811e10i	0.268255	+	0.825603i
$943$	−6.48978e8	+	1.99735e9i	−0.0252022	+	0.0775645i
$944$	−8.91818e9	−	6.47944e9i	−0.345044	−	0.250689i
$945$	−9.79591e9	+	3.01487e10i	−0.377601	+	1.16214i
$946$	2.69482e8	−	8.29380e8i	0.0103493	−	0.0318518i
$947$	3.68846e10	+	2.67982e10i	1.41130	+	1.02537i	0.993132	+	0.117003i	$0.0373288\pi$
$947$	3.68846e10	+	2.67982e10i	1.41130	+	1.02537i	0.418171	+	0.908368i	$0.362671\pi$
$948$	−3.84880e8	+	1.18454e9i	−0.0146722	+	0.0451565i
$949$	8.02800e9	+	2.47076e10i	0.304913	+	0.938425i
$950$	−1.71799e9	+	1.24820e9i	−0.0650114	+	0.0472335i
$951$	−7.92513e9	−	2.43911e10i	−0.298796	−	0.919599i
$952$	−7.22179e8	−	5.24694e8i	−0.0271279	−	0.0197095i
$953$	−2.86713e10	−	2.08309e10i	−1.07306	−	0.779620i	−0.0965964	−	0.995324i	$-0.530796\pi$
$953$	−2.86713e10	−	2.08309e10i	−1.07306	−	0.779620i	−0.976459	+	0.215703i	$0.930796\pi$
$954$	−2.40648e9	+	1.74841e9i	−0.0897353	+	0.0651965i
$955$	9.07679e9			0.337226
$956$	1.83417e10			0.678947
$957$	−1.10203e9	+	8.00673e8i	−0.0406446	+	0.0295300i
$958$	1.07971e10	−	3.32302e10i	0.396761	−	1.22111i
$959$	8.36349e9	+	2.57402e10i	0.306212	+	0.942425i
$960$	−2.67285e9			−0.0975047
$961$	2.17084e10	−	1.69024e10i	0.789033	−	0.614351i
$962$	1.23113e10			0.445851
$963$	3.12970e9	+	9.63223e9i	0.112930	+	0.347564i
$964$	−7.40466e9	+	2.27892e10i	−0.266217	+	0.819332i
$965$	−2.71590e10	+	1.97322e10i	−0.972901	+	0.706854i
$966$	−4.46534e9			−0.159380
$967$	3.09711e10			1.10145			0.550724	−	0.834687i	$-0.314352\pi$
$967$	3.09711e10			1.10145			0.550724	+	0.834687i	$0.314352\pi$
$968$	−9.90530e9	+	7.19662e9i	−0.350997	+	0.255014i
$969$	−7.85800e8	−	5.70917e8i	−0.0277446	−	0.0201577i
$970$	−1.23546e10	−	8.97614e9i	−0.434638	−	0.315783i
$971$	−2.34366e9	−	7.21305e9i	−0.0821538	−	0.252843i	0.901540	−	0.432696i	$-0.142438\pi$
$971$	−2.34366e9	−	7.21305e9i	−0.0821538	−	0.252843i	−0.983693	+	0.179853i	$0.942438\pi$
$972$	1.02129e10	−	7.42008e9i	0.356710	−	0.259165i
$973$	1.51360e10	+	4.65839e10i	0.526765	+	1.62122i
$974$	−7.14040e9	+	2.19759e10i	−0.247609	+	0.762062i
$975$	3.06261e9	+	2.22511e9i	0.105822	+	0.0768840i
$976$	−3.05806e9	+	9.41176e9i	−0.105286	+	0.324038i
$977$	1.33624e10	−	4.11254e10i	0.458411	−	1.41084i	−0.408673	−	0.912681i	$-0.634008\pi$
$977$	1.33624e10	−	4.11254e10i	0.458411	−	1.41084i	0.867084	−	0.498162i	$-0.165992\pi$
$978$	1.67755e10	+	1.21881e10i	0.573441	+	0.416629i
$979$	−1.38370e9	+	4.25860e9i	−0.0471306	+	0.145053i
$980$	4.66582e8	+	1.43599e9i	0.0158357	+	0.0487372i
$981$	−7.03296e9	+	5.10974e9i	−0.237846	+	0.172805i
$982$	4.90019e9	+	1.50812e10i	0.165129	+	0.508214i
$983$	−7.30452e9	−	5.30704e9i	−0.245275	−	0.178203i	0.458355	−	0.888769i	$-0.348439\pi$
$983$	−7.30452e9	−	5.30704e9i	−0.245275	−	0.178203i	−0.703630	+	0.710566i	$0.748439\pi$
$984$	1.62228e9	+	1.17865e9i	0.0542804	+	0.0394370i
$985$	−1.27499e10	+	9.26333e9i	−0.425088	+	0.308845i
$986$	−9.17712e7			−0.00304886
$987$	−2.81835e9			−0.0933008
$988$	−5.67711e9	+	4.12466e9i	−0.187274	+	0.136063i
$989$	9.08169e7	−	2.79506e8i	0.00298524	−	0.00918763i
$990$	5.46403e9	+	1.68165e10i	0.178974	+	0.550825i
$991$	2.38642e10			0.778913			0.389457	−	0.921045i	$-0.372663\pi$
$991$	2.38642e10			0.778913			0.389457	+	0.921045i	$0.372663\pi$
$992$	−5.14056e9	+	1.76526e9i	−0.167193	+	0.0574139i
$993$	3.05733e10			0.990876
$994$	−7.06281e9	−	2.17371e10i	−0.228100	−	0.702019i
$995$	1.89469e10	−	5.83125e10i	0.609757	−	1.87664i
$996$	−7.53419e9	+	5.47391e9i	−0.241618	+	0.175546i
$997$	4.56023e10			1.45731			0.728657	−	0.684878i	$-0.240145\pi$
$997$	4.56023e10			1.45731			0.728657	+	0.684878i	$0.240145\pi$
$998$	−7.28453e9			−0.231977
$999$	−1.96673e10	+	1.42891e10i	−0.624117	+	0.453448i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.8.d.a.35.4	✓	40
31.8	even	5	inner	62.8.d.a.39.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.8.d.a.35.4	✓	40	1.1	even	1	trivial
62.8.d.a.39.4	yes	40	31.8	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.47214 + 7.60845i) q^{2} +(-10.2355 + 31.5015i) q^{3} +(-51.7771 + 37.6183i) q^{4} +307.829 q^{5} -264.981 q^{6} +(767.579 - 557.679i) q^{7} +(-414.217 - 300.946i) q^{8} +(881.740 + 640.622i) q^{9} +(760.996 + 2342.11i) q^{10} +(5329.73 - 3872.27i) q^{11} +(-655.069 - 2016.10i) q^{12} +(2123.22 - 6534.59i) q^{13} +(6140.63 + 4461.43i) q^{14} +(-3150.78 + 9697.09i) q^{15} +(1265.73 - 3895.53i) q^{16} +(1486.65 + 1080.12i) q^{17} +(-2694.36 + 8292.38i) q^{18} +(4931.28 + 15176.9i) q^{19} +(-15938.5 + 11580.0i) q^{20} +(9711.20 + 29888.0i) q^{21} +(42637.8 + 30978.2i) q^{22} +(14369.2 + 10439.8i) q^{23} +(13720.0 - 9968.13i) q^{24} +16634.0 q^{25} +54967.0 q^{26} +(-87810.1 + 63797.8i) q^{27} +(-18764.1 + 57750.0i) q^{28} +(1929.06 + 5937.05i) q^{29} -81569.0 q^{30} +(-156877. + 53871.4i) q^{31} +32768.0 q^{32} +(67430.2 + 207529. i) q^{33} +(-4542.81 + 13981.3i) q^{34} +(236283. - 171670. i) q^{35} -69753.0 q^{36} +223976. q^{37} +(-103282. + 75038.9i) q^{38} +(184117. + 133769. i) q^{39} +(-127508. - 92640.1i) q^{40} +(36538.9 + 112455. i) q^{41} +(-203394. + 147774. i) q^{42} +(-5113.19 - 15736.8i) q^{43} +(-130290. + 400990. i) q^{44} +(271426. + 197202. i) q^{45} +(-43908.3 + 135136. i) q^{46} +(-27713.2 + 85292.6i) q^{47} +(109760. + 79745.0i) q^{48} +(23683.0 - 72888.9i) q^{49} +(41121.5 + 126559. i) q^{50} +(-49241.9 + 35776.3i) q^{51} +(135886. + 418214. i) q^{52} +(276000. + 200526. i) q^{53} +(-702481. - 510382. i) q^{54} +(1.64065e6 - 1.19200e6i) q^{55} -485775. q^{56} -528570. q^{57} +(-40402.9 + 29354.4i) q^{58} +(831651. - 2.55956e6i) q^{59} +(-201650. - 620614. i) q^{60} -2.41604e6 q^{61} +(-797700. - 1.06042e6i) q^{62} +1.03407e6 q^{63} +(81007.0 + 249314. i) q^{64} +(653589. - 2.01154e6i) q^{65} +(-1.41228e6 + 1.02608e6i) q^{66} +3.43836e6 q^{67} -117607. q^{68} +(-475945. + 345794. i) q^{69} +(1.89027e6 + 1.37336e6i) q^{70} +(-2.43611e6 - 1.76994e6i) q^{71} +(-172439. - 530712. i) q^{72} +(-3.05894e6 + 2.22245e6i) q^{73} +(553698. + 1.70411e6i) q^{74} +(-170257. + 523996. i) q^{75} +(-826257. - 600311. i) q^{76} +(1.93150e6 - 5.94455e6i) q^{77} +(-562613. + 1.73154e6i) q^{78} +(-475331. - 345348. i) q^{79} +(389630. - 1.19916e6i) q^{80} +(-374379. - 1.15222e6i) q^{81} +(-765280. + 556009. i) q^{82} +(-1.35755e6 - 4.17811e6i) q^{83} +(-1.62715e6 - 1.18219e6i) q^{84} +(457636. + 332492. i) q^{85} +(107092. - 77807.0i) q^{86} -206771. q^{87} -3.37301e6 q^{88} +(-549883. + 399514. i) q^{89} +(-829403. + 2.55264e6i) q^{90} +(-2.01447e6 - 6.19989e6i) q^{91} -1.13672e6 q^{92} +(-91319.1 - 5.49327e6i) q^{93} -717456. q^{94} +(1.51799e6 + 4.67191e6i) q^{95} +(-335395. + 1.03224e6i) q^{96} +(-5.01682e6 + 3.64493e6i) q^{97} +613119. q^{98} +7.18010e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) \) 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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