LMFDB - Embedded newform 48.7.i.a.5.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,7,Mod(5,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("48.5");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	48.i (of order $4$, 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:	$11.0425960138$
Analytic rank:	$0$
Dimension:	$92$
Relative dimension:	$46$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.12
Character	$\chi$	$=$	48.5
Dual form			48.7.i.a.29.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.52373 + 5.78692i) q^{2} +(-24.5429 + 11.2536i) q^{3} +(-2.97683 - 63.9307i) q^{4} +(35.5126 - 35.5126i) q^{5} +(70.4446 - 204.190i) q^{6} -8.76023i q^{7} +(386.405 + 335.909i) q^{8} +(475.711 - 552.395i) q^{9} +O(q^{10})$	\(q+(-5.52373 + 5.78692i) q^{2} +(-24.5429 + 11.2536i) q^{3} +(-2.97683 - 63.9307i) q^{4} +(35.5126 - 35.5126i) q^{5} +(70.4446 - 204.190i) q^{6} -8.76023i q^{7} +(386.405 + 335.909i) q^{8} +(475.711 - 552.395i) q^{9} +(9.34650 + 401.670i) q^{10} +(1403.30 - 1403.30i) q^{11} +(792.514 + 1535.55i) q^{12} +(-2698.89 + 2698.89i) q^{13} +(50.6947 + 48.3891i) q^{14} +(-471.937 + 1271.23i) q^{15} +(-4078.28 + 380.622i) q^{16} +4368.58i q^{17} +(568.966 + 5804.18i) q^{18} +(520.076 - 520.076i) q^{19} +(-2376.06 - 2164.63i) q^{20} +(98.5846 + 215.002i) q^{21} +(369.333 + 15872.3i) q^{22} +1260.33 q^{23} +(-13263.7 - 3895.73i) q^{24} +13102.7i q^{25} +(-710.317 - 30526.2i) q^{26} +(-5458.88 + 18910.9i) q^{27} +(-560.048 + 26.0777i) q^{28} +(20060.4 + 20060.4i) q^{29} +(-4749.65 - 9752.98i) q^{30} +42021.6 q^{31} +(20324.7 - 25703.1i) q^{32} +(-18648.9 + 50233.4i) q^{33} +(-25280.6 - 24130.8i) q^{34} +(-311.098 - 311.098i) q^{35} +(-36731.1 - 28768.2i) q^{36} +(-2874.51 - 2874.51i) q^{37} +(136.878 + 5882.40i) q^{38} +(35866.4 - 96611.1i) q^{39} +(25651.2 - 1793.23i) q^{40} +29404.4 q^{41} +(-1788.75 - 617.111i) q^{42} +(-3630.73 - 3630.73i) q^{43} +(-93891.5 - 85536.7i) q^{44} +(-2723.25 - 36510.7i) q^{45} +(-6961.73 + 7293.44i) q^{46} +131257. i q^{47} +(95809.5 - 55237.1i) q^{48} +117572. q^{49} +(-75824.3 - 72375.8i) q^{50} +(-49162.4 - 107218. i) q^{51} +(180576. + 164508. i) q^{52} +(52051.2 - 52051.2i) q^{53} +(-79282.3 - 136049. i) q^{54} -99669.7i q^{55} +(2942.64 - 3385.00i) q^{56} +(-6911.44 + 18617.0i) q^{57} +(-226896. + 5279.66i) q^{58} +(-63024.1 + 63024.1i) q^{59} +(82675.5 + 26387.0i) q^{60} +(-245985. + 245985. i) q^{61} +(-232116. + 243175. i) q^{62} +(-4839.11 - 4167.34i) q^{63} +(36473.8 + 259594. i) q^{64} +191689. i q^{65} +(-187685. - 385395. i) q^{66} +(6386.21 - 6386.21i) q^{67} +(279286. - 13004.5i) q^{68} +(-30932.2 + 14183.3i) q^{69} +(3518.72 - 81.8775i) q^{70} +297386. q^{71} +(369372. - 53652.5i) q^{72} +563014. i q^{73} +(32512.6 - 756.538i) q^{74} +(-147453. - 321579. i) q^{75} +(-34797.0 - 31700.7i) q^{76} +(-12293.2 - 12293.2i) q^{77} +(360965. + 741209. i) q^{78} +402177. q^{79} +(-131313. + 158347. i) q^{80} +(-78839.4 - 525561. i) q^{81} +(-162422. + 170161. i) q^{82} +(-521793. - 521793. i) q^{83} +(13451.7 - 6942.61i) q^{84} +(155139. + 155139. i) q^{85} +(41065.9 - 955.566i) q^{86} +(-718093. - 266588. i) q^{87} +(1.01363e6 - 70860.7i) q^{88} +1.13718e6 q^{89} +(226327. + 185916. i) q^{90} +(23642.9 + 23642.9i) q^{91} +(-3751.80 - 80574.0i) q^{92} +(-1.03133e6 + 472896. i) q^{93} +(-759576. - 725030. i) q^{94} -36938.5i q^{95} +(-209573. + 859556. i) q^{96} -1.47962e6 q^{97} +(-649437. + 680381. i) q^{98} +(-107611. - 1.44274e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6}+O(q^{10}) $ 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6	$ 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6} + 1496 q^{10} + 4288 q^{12} - 4 q^{13} - 4 q^{15} + 10352 q^{16} + 10020 q^{18} - 3940 q^{19} + 1456 q^{21} - 42088 q^{22} + 66376 q^{24} - 34322 q^{27} + 27000 q^{28} - 127836 q^{30} - 8 q^{31} - 4 q^{33} + 128424 q^{34} + 172420 q^{36} - 4 q^{37} - 164392 q^{40} + 221560 q^{42} - 195268 q^{43} - 31252 q^{45} + 150712 q^{46} - 188048 q^{48} - 1142884 q^{49} + 385056 q^{51} - 122368 q^{52} + 151912 q^{54} - 181960 q^{58} + 242304 q^{60} - 326500 q^{61} + 470592 q^{63} - 251752 q^{64} + 489172 q^{66} + 1207676 q^{67} - 1460 q^{69} + 346392 q^{70} - 903480 q^{72} + 1413778 q^{75} - 359992 q^{76} + 1478252 q^{78} + 860920 q^{79} - 4 q^{81} - 2412800 q^{82} - 730640 q^{84} + 434496 q^{85} + 1259360 q^{88} - 291792 q^{90} + 2320992 q^{91} - 1176260 q^{93} - 1412496 q^{94} + 1956200 q^{96} - 8 q^{97} - 4048228 q^{99}+O(q^{100}) $ 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6 + 1496 * q^10 + 4288 * q^12 - 4 * q^13 - 4 * q^15 + 10352 * q^16 + 10020 * q^18 - 3940 * q^19 + 1456 * q^21 - 42088 * q^22 + 66376 * q^24 - 34322 * q^27 + 27000 * q^28 - 127836 * q^30 - 8 * q^31 - 4 * q^33 + 128424 * q^34 + 172420 * q^36 - 4 * q^37 - 164392 * q^40 + 221560 * q^42 - 195268 * q^43 - 31252 * q^45 + 150712 * q^46 - 188048 * q^48 - 1142884 * q^49 + 385056 * q^51 - 122368 * q^52 + 151912 * q^54 - 181960 * q^58 + 242304 * q^60 - 326500 * q^61 + 470592 * q^63 - 251752 * q^64 + 489172 * q^66 + 1207676 * q^67 - 1460 * q^69 + 346392 * q^70 - 903480 * q^72 + 1413778 * q^75 - 359992 * q^76 + 1478252 * q^78 + 860920 * q^79 - 4 * q^81 - 2412800 * q^82 - 730640 * q^84 + 434496 * q^85 + 1259360 * q^88 - 291792 * q^90 + 2320992 * q^91 - 1176260 * q^93 - 1412496 * q^94 + 1956200 * q^96 - 8 * q^97 - 4048228 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−5.52373	+	5.78692i	−0.690466	+	0.723365i
$2$	−5.52373	+	5.78692i	−0.690466	+	0.723365i
$3$	−24.5429	+	11.2536i	−0.908997	+	0.416802i
$3$	−24.5429	+	11.2536i	−0.908997	+	0.416802i
$4$	−2.97683	−	63.9307i	−0.0465130	−	0.998918i
$5$	35.5126	−	35.5126i	0.284101	−	0.284101i	−0.550641	−	0.834742i	$-0.685617\pi$
$5$	35.5126	−	35.5126i	0.284101	−	0.284101i	0.834742	+	0.550641i	$0.185617\pi$
$6$	70.4446	−	204.190i	0.326132	−	0.945324i
$7$		−	8.76023i		−	0.0255400i	−0.999918	−	0.0127700i	$-0.995935\pi$
$7$		−	8.76023i		−	0.0255400i	0.999918	−	0.0127700i	$-0.00406493\pi$
$8$	386.405	+	335.909i	0.754697	+	0.656073i
$9$	475.711	−	552.395i	0.652553	−	0.757743i
$10$	9.34650	+	401.670i	0.00934650	+	0.401670i
$11$	1403.30	−	1403.30i	1.05432	−	1.05432i	0.0558841	−	0.998437i	$-0.482202\pi$
$11$	1403.30	−	1403.30i	1.05432	−	1.05432i	0.998437	−	0.0558841i	$-0.0177977\pi$
$12$	792.514	+	1535.55i	0.458631	+	0.888627i
$13$	−2698.89	+	2698.89i	−1.22844	+	1.22844i	−0.263893	+	0.964552i	$0.585007\pi$
$13$	−2698.89	+	2698.89i	−1.22844	+	1.22844i	−0.964552	+	0.263893i	$0.914993\pi$
$14$	50.6947	+	48.3891i	0.0184748	+	0.0176345i
$15$	−471.937	+	1271.23i	−0.139833	+	0.376660i
$16$	−4078.28	+	380.622i	−0.995673	+	0.0929253i
$17$			4368.58i			0.889187i	0.895732	+	0.444593i	$0.146652\pi$
$17$			4368.58i			0.889187i	−0.895732	+	0.444593i	$0.853348\pi$
$18$	568.966	+	5804.18i	0.0975594	+	0.995230i
$19$	520.076	−	520.076i	0.0758239	−	0.0758239i	−0.668178	−	0.744002i	$-0.732925\pi$
$19$	520.076	−	520.076i	0.0758239	−	0.0758239i	0.744002	+	0.668178i	$0.232925\pi$
$20$	−2376.06	−	2164.63i	−0.297008	−	0.270579i
$21$	98.5846	+	215.002i	0.0106451	+	0.0232158i
$22$	369.333	+	15872.3i	0.0346856	+	1.49063i
$23$	1260.33			0.103586			0.0517931	−	0.998658i	$-0.483506\pi$
$23$	1260.33			0.103586			0.0517931	+	0.998658i	$0.483506\pi$
$24$	−13263.7	−	3895.73i	−0.959470	−	0.281809i
$25$			13102.7i			0.838574i
$26$	−710.317	−	30526.2i	−0.0404141	−	1.73681i
$27$	−5458.88	+	18910.9i	−0.277340	+	0.960772i
$28$	−560.048	+	26.0777i	−0.0255124	+	0.00118794i
$29$	20060.4	+	20060.4i	0.822517	+	0.822517i	0.986468	−	0.163951i	$-0.0524240\pi$
$29$	20060.4	+	20060.4i	0.822517	+	0.822517i	−0.163951	+	0.986468i	$0.552424\pi$
$30$	−4749.65	−	9752.98i	−0.175913	−	0.361222i
$31$	42021.6			1.41055			0.705273	−	0.708936i	$-0.250825\pi$
$31$	42021.6			1.41055			0.705273	+	0.708936i	$0.250825\pi$
$32$	20324.7	−	25703.1i	0.620260	−	0.784397i
$33$	−18648.9	+	50233.4i	−0.518932	+	1.39782i
$34$	−25280.6	−	24130.8i	−0.643206	−	0.613953i
$35$	−311.098	−	311.098i	−0.00725594	−	0.00725594i
$36$	−36731.1	−	28768.2i	−0.787275	−	0.616601i
$37$	−2874.51	−	2874.51i	−0.0567491	−	0.0567491i	0.678163	−	0.734912i	$-0.262776\pi$
$37$	−2874.51	−	2874.51i	−0.0567491	−	0.0567491i	−0.734912	+	0.678163i	$0.762776\pi$
$38$	136.878	+	5882.40i	0.00249450	+	0.107202i
$39$	35866.4	−	96611.1i	0.604635	−	1.62867i
$40$	25651.2	−	1793.23i	0.400801	−	0.0280193i
$41$	29404.4			0.426639			0.213319	−	0.976983i	$-0.431573\pi$
$41$	29404.4			0.426639			0.213319	+	0.976983i	$0.431573\pi$
$42$	−1788.75	−	617.111i	−0.0241436	−	0.00832943i
$43$	−3630.73	−	3630.73i	−0.0456656	−	0.0456656i	0.683905	−	0.729571i	$-0.260280\pi$
$43$	−3630.73	−	3630.73i	−0.0456656	−	0.0456656i	−0.729571	+	0.683905i	$0.760280\pi$
$44$	−93891.5	−	85536.7i	−1.10222	−	1.00414i
$45$	−2723.25	−	36510.7i	−0.0298848	−	0.400666i
$46$	−6961.73	+	7293.44i	−0.0715227	+	0.0749305i
$47$			131257.i			1.26424i	0.774870	+	0.632121i	$0.217815\pi$
$47$			131257.i			1.26424i	−0.774870	+	0.632121i	$0.782185\pi$
$48$	95809.5	−	55237.1i	0.866333	−	0.499467i
$49$	117572.			0.999348
$50$	−75824.3	−	72375.8i	−0.606595	−	0.579007i
$51$	−49162.4	−	107218.i	−0.370615	−	0.808269i
$52$	180576.	+	164508.i	1.28425	+	1.16998i
$53$	52051.2	−	52051.2i	0.349626	−	0.349626i	−0.510345	−	0.859970i	$-0.670482\pi$
$53$	52051.2	−	52051.2i	0.349626	−	0.349626i	0.859970	+	0.510345i	$0.170482\pi$
$54$	−79282.3	−	136049.i	−0.503495	−	0.863998i
$55$		−	99669.7i		−	0.599067i
$56$	2942.64	−	3385.00i	0.0167561	−	0.0192750i
$57$	−6911.44	+	18617.0i	−0.0373202	+	0.100527i
$58$	−226896.	+	5279.66i	−1.16290	+	0.0270596i
$59$	−63024.1	+	63024.1i	−0.306867	+	0.306867i	−0.843693	−	0.536826i	$-0.819623\pi$
$59$	−63024.1	+	63024.1i	−0.306867	+	0.306867i	0.536826	+	0.843693i	$0.319623\pi$
$60$	82675.5	+	26387.0i	0.382757	+	0.122162i
$61$	−245985.	+	245985.i	−1.08372	+	1.08372i	−0.0875653	+	0.996159i	$0.527909\pi$
$61$	−245985.	+	245985.i	−1.08372	+	1.08372i	−0.996159	+	0.0875653i	$0.972091\pi$
$62$	−232116.	+	243175.i	−0.973934	+	1.02034i
$63$	−4839.11	−	4167.34i	−0.0193528	−	0.0166662i
$64$	36473.8	+	259594.i	0.139136	+	0.990273i
$65$			191689.i			0.698004i
$66$	−187685.	−	385395.i	−0.652827	−	1.34052i
$67$	6386.21	−	6386.21i	0.0212334	−	0.0212334i	−0.696410	−	0.717644i	$-0.745221\pi$
$67$	6386.21	−	6386.21i	0.0212334	−	0.0212334i	0.717644	+	0.696410i	$0.245221\pi$
$68$	279286.	−	13004.5i	0.888224	−	0.0413587i
$69$	−30932.2	+	14183.3i	−0.0941595	+	0.0431749i
$70$	3518.72	−	81.8775i	0.0102587	−	0.000238710i
$71$	297386.			0.830893			0.415446	−	0.909618i	$-0.363625\pi$
$71$	297386.			0.830893			0.415446	+	0.909618i	$0.363625\pi$
$72$	369372.	−	53652.5i	0.989615	−	0.143745i
$73$			563014.i			1.44727i	0.690182	+	0.723636i	$0.257531\pi$
$73$			563014.i			1.44727i	−0.690182	+	0.723636i	$0.742469\pi$
$74$	32512.6	−	756.538i	0.0802336	−	0.00186696i
$75$	−147453.	−	321579.i	−0.349519	−	0.762261i
$76$	−34797.0	−	31700.7i	−0.0792687	−	0.0722151i
$77$	−12293.2	−	12293.2i	−0.0269274	−	0.0269274i
$78$	360965.	+	741209.i	0.760643	+	1.56191i
$79$	402177.			0.815710			0.407855	−	0.913047i	$-0.366277\pi$
$79$	402177.			0.815710			0.407855	+	0.913047i	$0.366277\pi$
$80$	−131313.	+	158347.i	−0.256471	+	0.309271i
$81$	−78839.4	−	525561.i	−0.148350	−	0.988935i
$82$	−162422.	+	170161.i	−0.294580	+	0.308615i
$83$	−521793.	−	521793.i	−0.912566	−	0.912566i	0.0839077	−	0.996474i	$-0.473260\pi$
$83$	−521793.	−	521793.i	−0.912566	−	0.912566i	−0.996474	+	0.0839077i	$0.973260\pi$
$84$	13451.7	−	6942.61i	0.0226956	−	0.0117134i
$85$	155139.	+	155139.i	0.252619	+	0.252619i
$86$	41065.9	−	955.566i	0.0645634	−	0.00150233i
$87$	−718093.	−	266588.i	−1.09049	−	0.404839i
$88$	1.01363e6	−	70860.7i	1.48741	−	0.103982i
$89$	1.13718e6			1.61309			0.806547	−	0.591169i	$-0.201334\pi$
$89$	1.13718e6			1.61309			0.806547	+	0.591169i	$0.201334\pi$
$90$	226327.	+	185916.i	0.310462	+	0.255029i
$91$	23642.9	+	23642.9i	0.0313745	+	0.0313745i
$92$	−3751.80	−	80574.0i	−0.00481810	−	0.103474i
$93$	−1.03133e6	+	472896.i	−1.28218	+	0.587918i
$94$	−759576.	−	725030.i	−0.914508	−	0.872916i
$95$		−	36938.5i		−	0.0430833i
$96$	−209573.	+	859556.i	−0.236877	+	0.971540i
$97$	−1.47962e6			−1.62119			−0.810594	−	0.585608i	$-0.800856\pi$
$97$	−1.47962e6			−1.62119			−0.810594	+	0.585608i	$0.800856\pi$
$98$	−649437.	+	680381.i	−0.690016	+	0.722893i
$99$	−107611.	−	1.44274e6i	−0.110905	−	1.48691i
$100$	837666.	−	39004.6i	0.837666	−	0.0390046i
$101$	−588542.	+	588542.i	−0.571233	+	0.571233i	−0.932473	−	0.361240i	$-0.882354\pi$
$101$	−588542.	+	588542.i	−0.571233	+	0.571233i	0.361240	+	0.932473i	$0.382354\pi$
$102$	892019.	+	307742.i	0.840570	+	0.289993i
$103$		−	909100.i		−	0.831956i	−0.909375	−	0.415978i	$-0.863439\pi$
$103$		−	909100.i		−	0.831956i	0.909375	−	0.415978i	$-0.136561\pi$
$104$	−1.94945e6	+	136283.i	−1.73305	+	0.121155i
$105$	11136.3	+	4134.27i	0.00961992	+	0.00357134i
$106$	13699.3	+	588733.i	0.0115022	+	0.494311i
$107$	1.08840e6	−	1.08840e6i	0.888458	−	0.888458i	−0.105917	−	0.994375i	$-0.533778\pi$
$107$	1.08840e6	−	1.08840e6i	0.888458	−	0.888458i	0.994375	+	0.105917i	$0.0337778\pi$
$108$	1.22524e6	+	292696.i	0.972632	+	0.232351i
$109$	325470.	−	325470.i	0.251322	−	0.251322i	−0.570190	−	0.821513i	$-0.693131\pi$
$109$	325470.	−	325470.i	0.251322	−	0.251322i	0.821513	+	0.570190i	$0.193131\pi$
$110$	576781.	+	550549.i	0.433344	+	0.413635i
$111$	102898.	+	38200.2i	0.0752379	+	0.0279317i
$112$	3334.34	+	35726.7i	0.00237332	+	0.0254295i
$113$		−	1.29319e6i		−	0.896242i	−0.893973	−	0.448121i	$-0.852093\pi$
$113$		−	1.29319e6i		−	0.896242i	0.893973	−	0.448121i	$-0.147907\pi$
$114$	−69557.8	−	142831.i	−0.0469496	−	0.0964068i
$115$	44757.6	−	44757.6i	0.0294289	−	0.0294289i
$116$	1.22276e6	−	1.34219e6i	0.783369	−	0.859885i
$117$	206962.	+	2.77475e6i	0.129221	+	1.73247i
$118$	−16587.2	−	712843.i	−0.0100955	−	0.433858i
$119$	38269.7			0.0227099
$120$	−609376.	+	332681.i	−0.352648	+	0.192524i
$121$		−	2.16695e6i		−	1.22319i
$122$	−64740.3	−	2.78225e6i	−0.0356530	−	1.53220i
$123$	−721669.	+	330906.i	−0.387814	+	0.177824i
$124$	−125091.	−	2.68647e6i	−0.0656087	−	1.40902i
$125$	1.02020e6	+	1.02020e6i	0.522340	+	0.522340i
$126$	50846.0	−	4984.28i	0.0254182	−	0.00249167i
$127$	972886.			0.474953			0.237477	−	0.971393i	$-0.423680\pi$
$127$	972886.			0.474953			0.237477	+	0.971393i	$0.423680\pi$
$128$	−1.70372e6	−	1.22286e6i	−0.812398	−	0.583104i
$129$	129968.	+	48249.8i	0.0605433	+	0.0224764i
$130$	−1.10929e6	−	1.05884e6i	−0.504911	−	0.481948i
$131$	1.04387e6	+	1.04387e6i	0.464334	+	0.464334i	0.900073	−	0.435739i	$-0.143513\pi$
$131$	1.04387e6	+	1.04387e6i	0.464334	+	0.464334i	−0.435739	+	0.900073i	$0.643513\pi$
$132$	3.26697e6	+	1.04270e6i	1.42044	+	0.453354i
$133$	−4555.99	−	4555.99i	−0.00193655	−	0.00193655i
$134$	1680.78	+	72232.2i	0.000698547	+	0.0300204i
$135$	477715.	+	865433.i	0.194163	+	0.351748i
$136$	−1.46745e6	+	1.68804e6i	−0.583371	+	0.671067i
$137$	3.80446e6			1.47956			0.739778	−	0.672851i	$-0.234930\pi$
$137$	3.80446e6			1.47956			0.739778	+	0.672851i	$0.234930\pi$
$138$	88783.6	−	257347.i	0.0337828	−	0.0979225i
$139$	−772143.	−	772143.i	−0.287510	−	0.287510i	0.548585	−	0.836095i	$-0.315167\pi$
$139$	−772143.	−	772143.i	−0.287510	−	0.287510i	−0.836095	+	0.548585i	$0.815167\pi$
$140$	−18962.7	+	20814.8i	−0.00691059	+	0.00758558i
$141$	−1.47712e6	−	3.22144e6i	−0.526938	−	1.14919i
$142$	−1.64268e6	+	1.72095e6i	−0.573703	+	0.601038i
$143$			7.57472e6i			2.59035i
$144$	−1.72983e6	+	2.43389e6i	−0.579316	+	0.815103i
$145$	1.42479e6			0.467355
$146$	−3.25811e6	−	3.10993e6i	−1.04691	−	0.999293i
$147$	−2.88557e6	+	1.32312e6i	−0.908404	+	0.416530i
$148$	−175213.	+	192327.i	−0.0540481	+	0.0593272i
$149$	−3.66196e6	+	3.66196e6i	−1.10702	+	1.10702i	−0.113477	+	0.993541i	$0.536199\pi$
$149$	−3.66196e6	+	3.66196e6i	−1.10702	+	1.10702i	−0.993541	+	0.113477i	$0.963801\pi$
$150$	2.67544e6	+	923015.i	0.792724	+	0.273486i
$151$			4.82385e6i			1.40108i	0.713613	+	0.700540i	$0.247057\pi$
$151$			4.82385e6i			1.40108i	−0.713613	+	0.700540i	$0.752943\pi$
$152$	375659.	−	26261.6i	0.106970	−	0.00747809i
$153$	2.41318e6	+	2.07818e6i	0.673776	+	0.580241i
$154$	139045.	−	3235.44i	0.0380708	−	0.000885873i
$155$	1.49229e6	−	1.49229e6i	0.400737	−	0.400737i
$156$	−6.28319e6	−	2.00537e6i	−1.65503	−	0.528226i
$157$	1.37437e6	−	1.37437e6i	0.355144	−	0.355144i	−0.506875	−	0.862020i	$-0.669199\pi$
$157$	1.37437e6	−	1.37437e6i	0.355144	−	0.355144i	0.862020	+	0.506875i	$0.169199\pi$
$158$	−2.22152e6	+	2.32736e6i	−0.563220	+	0.590056i
$159$	−691723.	+	1.86325e6i	−0.172084	+	0.463533i
$160$	−191002.	−	1.63456e6i	−0.0466314	−	0.399064i
$161$		−	11040.8i		−	0.00264559i
$162$	3.47686e6	+	2.44682e6i	0.817791	+	0.575515i
$163$	−3.83173e6	+	3.83173e6i	−0.884773	+	0.884773i	−0.994015	−	0.109242i	$-0.965158\pi$
$163$	−3.83173e6	+	3.83173e6i	−0.884773	+	0.884773i	0.109242	+	0.994015i	$0.465158\pi$
$164$	−87531.8	−	1.87984e6i	−0.0198442	−	0.426177i
$165$	1.12165e6	+	2.44619e6i	0.249692	+	0.544550i
$166$	5.90182e6	−	137330.i	1.29021	−	0.0300221i
$167$	6.09191e6			1.30799			0.653995	−	0.756499i	$-0.273092\pi$
$167$	6.09191e6			1.30799			0.653995	+	0.756499i	$0.273092\pi$
$168$	−34127.5	+	116193.i	−0.00719742	+	0.0245049i
$169$		−	9.74124e6i		−	2.01815i
$170$	−1.75473e6	+	40830.9i	−0.357160	+	0.00831078i
$171$	−39881.6	−	534694.i	−0.00797598	−	0.106934i
$172$	−221307.	+	242923.i	−0.0434921	+	0.0477402i
$173$	−1.06601e6	−	1.06601e6i	−0.205885	−	0.205885i	0.596631	−	0.802516i	$-0.296506\pi$
$173$	−1.06601e6	−	1.06601e6i	−0.205885	−	0.205885i	−0.802516	+	0.596631i	$0.796506\pi$
$174$	5.50927e6	−	2.68298e6i	1.04579	−	0.509296i
$175$	114783.			0.0214172
$176$	−5.18893e6	+	6.25718e6i	−0.951786	+	1.14773i
$177$	837545.	−	2.25605e6i	0.151039	−	0.406844i
$178$	−6.28148e6	+	6.58078e6i	−1.11379	+	1.16686i
$179$	−5.33346e6	−	5.33346e6i	−0.929929	−	0.929929i	0.0677721	−	0.997701i	$-0.478411\pi$
$179$	−5.33346e6	−	5.33346e6i	−0.929929	−	0.929929i	−0.997701	+	0.0677721i	$0.978411\pi$
$180$	−2.32605e6	+	282786.i	−0.398842	+	0.0484886i
$181$	−4.30517e6	−	4.30517e6i	−0.726030	−	0.726030i	0.243796	−	0.969826i	$-0.421607\pi$
$181$	−4.30517e6	−	4.30517e6i	−0.726030	−	0.726030i	−0.969826	+	0.243796i	$0.921607\pi$
$182$	−267417.	+	6222.55i	−0.0443583	+	0.00103218i
$183$	3.26896e6	−	8.80541e6i	0.533404	−	1.43680i
$184$	486999.	+	423357.i	0.0781762	+	0.0679601i
$185$	−204163.			−0.0322449
$186$	2.96019e6	−	8.58038e6i	0.460024	−	1.33342i
$187$	6.13043e6	+	6.13043e6i	0.937489	+	0.937489i
$188$	8.39138e6	−	390731.i	1.26287	−	0.0588037i
$189$	165664.	+	47821.0i	0.0245381	+	0.00708327i
$190$	213760.	+	204038.i	0.0311649	+	0.0297475i
$191$			3.67002e6i			0.526706i	0.964700	+	0.263353i	$0.0848283\pi$
$191$			3.67002e6i			0.526706i	−0.964700	+	0.263353i	$0.915172\pi$
$192$	−3.81655e6	−	5.96074e6i	−0.539222	−	0.842163i
$193$	2.72506e6			0.379056			0.189528	−	0.981875i	$-0.439304\pi$
$193$	2.72506e6			0.379056			0.189528	+	0.981875i	$0.439304\pi$
$194$	8.17299e6	−	8.56241e6i	1.11938	−	1.17271i
$195$	−2.15720e6	−	4.70462e6i	−0.290929	−	0.634484i
$196$	−349993.	−	7.51648e6i	−0.0464826	−	0.998266i
$197$	1.38220e6	−	1.38220e6i	0.180790	−	0.180790i	−0.610910	−	0.791700i	$-0.709196\pi$
$197$	1.38220e6	−	1.38220e6i	0.180790	−	0.180790i	0.791700	+	0.610910i	$0.209196\pi$
$198$	8.94345e6	+	7.34658e6i	1.15215	+	0.946433i
$199$			5.91468e6i			0.750537i	0.926916	+	0.375268i	$0.122449\pi$
$199$			5.91468e6i			0.750537i	−0.926916	+	0.375268i	$0.877551\pi$
$200$	−4.40132e6	+	5.06296e6i	−0.550166	+	0.632869i
$201$	−84868.1	+	228604.i	−0.0104510	+	0.0281512i
$202$	−154897.	−	6.65679e6i	−0.0187927	−	0.807627i
$203$	175734.	−	175734.i	0.0210071	−	0.0210071i
$204$	−6.70815e6	+	3.46216e6i	−0.790155	+	0.407809i
$205$	1.04422e6	−	1.04422e6i	0.121208	−	0.121208i
$206$	5.26089e6	+	5.02162e6i	0.601807	+	0.574437i
$207$	599554.	−	696201.i	0.0675954	−	0.0784917i
$208$	9.97958e6	−	1.20341e7i	1.10898	−	1.33728i
$209$		−	1.45965e6i		−	0.159886i
$210$	−85438.4	+	41608.0i	−0.00922561	+	0.00449282i
$211$	−6.80072e6	+	6.80072e6i	−0.723948	+	0.723948i	−0.969407	−	0.245459i	$-0.921061\pi$
$211$	−6.80072e6	+	6.80072e6i	−0.723948	+	0.723948i	0.245459	+	0.969407i	$0.421061\pi$
$212$	−3.48262e6	−	3.17272e6i	−0.365509	−	0.332985i
$213$	−7.29872e6	+	3.34667e6i	−0.755279	+	0.346318i
$214$	286454.	+	1.23105e7i	0.0292290	+	1.25613i
$215$	−257873.			−0.0259472
$216$	−8.46168e6	+	5.47357e6i	−0.839644	+	0.543137i
$217$		−	368119.i		−	0.0360254i
$218$	85659.9	+	3.68127e6i	0.00826814	+	0.355327i
$219$	−6.33596e6	−	1.38180e7i	−0.603226	−	1.31557i
$220$	−6.37196e6	+	296700.i	−0.598418	+	0.0278644i
$221$	−1.17903e7	−	1.17903e7i	−1.09232	−	1.09232i
$222$	−789440.	+	384453.i	−0.0721540	+	0.0351386i
$223$	1.01285e7			0.913334			0.456667	−	0.889638i	$-0.349043\pi$
$223$	1.01285e7			0.913334			0.456667	+	0.889638i	$0.349043\pi$
$224$	−225165.	−	178049.i	−0.0200335	−	0.0158415i
$225$	7.23787e6	+	6.23310e6i	0.635424	+	0.547213i
$226$	7.48356e6	+	7.14320e6i	0.648310	+	0.618825i
$227$	−1.34275e7	−	1.34275e7i	−1.14794	−	1.14794i	−0.986958	−	0.160979i	$-0.948535\pi$
$227$	−1.34275e7	−	1.34275e7i	−1.14794	−	1.14794i	−0.160979	−	0.986958i	$-0.551465\pi$
$228$	1.21077e6	+	386434.i	0.102154	+	0.0326040i
$229$	322133.	+	322133.i	0.0268243	+	0.0268243i	0.720392	−	0.693567i	$-0.243962\pi$
$229$	322133.	+	322133.i	0.0268243	+	0.0268243i	−0.693567	+	0.720392i	$0.743962\pi$
$230$	11779.7	+	506238.i	0.000968168	+	0.0416075i
$231$	440056.	+	163368.i	0.0357003	+	0.0132536i
$232$	1.01296e6	+	1.44899e7i	0.0811203	+	1.16038i
$233$	−2.26971e6			−0.179433			−0.0897165	−	0.995967i	$-0.528596\pi$
$233$	−2.26971e6			−0.179433			−0.0897165	+	0.995967i	$0.528596\pi$
$234$	−1.72004e7	−	1.41293e7i	−1.34243	−	1.10274i
$235$	4.66129e6	+	4.66129e6i	0.359172	+	0.359172i
$236$	4.21679e6	+	3.84156e6i	0.320808	+	0.292262i
$237$	−9.87060e6	+	4.52596e6i	−0.741478	+	0.339989i
$238$	−211392.	+	221464.i	−0.0156804	+	0.0164275i
$239$		−	1.58624e6i		−	0.116192i	−0.998311	−	0.0580960i	$-0.981497\pi$
$239$		−	1.58624e6i		−	0.116192i	0.998311	−	0.0580960i	$-0.0185029\pi$
$240$	1.44083e6	−	5.36405e6i	0.104227	−	0.388025i
$241$	−1.86872e7			−1.33504			−0.667519	−	0.744593i	$-0.732644\pi$
$241$	−1.86872e7			−1.33504			−0.667519	+	0.744593i	$0.732644\pi$
$242$	1.25400e7	+	1.19696e7i	0.884810	+	0.844569i
$243$	7.84942e6	+	1.20116e7i	0.547040	+	0.837107i
$244$	1.64582e7	+	1.49937e7i	1.13296	+	1.03214i
$245$	4.17529e6	−	4.17529e6i	0.283915	−	0.283915i
$246$	2.07138e6	−	6.00408e6i	0.139141	−	0.403312i
$247$			2.80726e6i			0.186291i
$248$	1.62373e7	+	1.41154e7i	1.06453	+	0.925421i
$249$	1.86784e7	+	6.93426e6i	1.20988	+	0.449161i
$250$	−1.15391e7	+	268504.i	−0.738500	+	0.0171842i
$251$	9.85061e6	−	9.85061e6i	0.622934	−	0.622934i	−0.323347	−	0.946281i	$-0.604808\pi$
$251$	9.85061e6	−	9.85061e6i	0.622934	−	0.622934i	0.946281	+	0.323347i	$0.104808\pi$
$252$	−252016.	+	321773.i	−0.0157480	+	0.0201070i
$253$	1.76863e6	−	1.76863e6i	0.109213	−	0.109213i
$254$	−5.37396e6	+	5.63001e6i	−0.327939	+	0.343564i
$255$	−5.55346e6	−	2.06169e6i	−0.334921	−	0.124338i
$256$	1.64875e7	−	3.10456e6i	0.982730	−	0.185046i
$257$		−	1.77894e7i		−	1.04800i	−0.851718	−	0.524000i	$-0.824439\pi$
$257$		−	1.77894e7i		−	1.04800i	0.851718	−	0.524000i	$-0.175561\pi$
$258$	−997124.	+	485594.i	−0.0580618	+	0.0282757i
$259$	−25181.4	+	25181.4i	−0.00144937	+	0.00144937i
$260$	1.22548e7	−	570627.i	0.697248	−	0.0324662i
$261$	2.06242e7	−	1.53831e6i	1.15999	−	0.0865213i
$262$	−1.18068e7	+	274733.i	−0.656490	+	0.0152759i
$263$	−1.91346e7			−1.05184			−0.525922	−	0.850533i	$-0.676280\pi$
$263$	−1.91346e7			−1.05184			−0.525922	+	0.850533i	$0.676280\pi$
$264$	−2.40799e7	+	1.31461e7i	−1.30871	+	0.714472i
$265$		−	3.69694e6i		−	0.198658i
$266$	51531.2	−	1199.08i	0.00273795	−	6.37096e-5i
$267$	−2.79098e7	+	1.27974e7i	−1.46630	+	0.672341i
$268$	−427286.	−	389264.i	−0.0221980	−	0.0202228i
$269$	2.69478e7	+	2.69478e7i	1.38441	+	1.38441i	0.836599	+	0.547815i	$0.184540\pi$
$269$	2.69478e7	+	2.69478e7i	1.38441	+	1.38441i	0.547815	+	0.836599i	$0.315460\pi$
$270$	−7.64696e6	−	2.01592e6i	−0.388506	−	0.102419i
$271$	−2.46391e7			−1.23799			−0.618994	−	0.785395i	$-0.712460\pi$
$271$	−2.46391e7			−1.23799			−0.618994	+	0.785395i	$0.712460\pi$
$272$	−1.66278e6	−	1.78163e7i	−0.0826280	−	0.885339i
$273$	−846336.	−	314198.i	−0.0415963	−	0.0154424i
$274$	−2.10148e7	+	2.20161e7i	−1.02158	+	1.07026i
$275$	1.83871e7	+	1.83871e7i	0.884126	+	0.884126i
$276$	998831.	+	1.93530e6i	0.0475078	+	0.0920494i
$277$	5.31319e6	+	5.31319e6i	0.249986	+	0.249986i	0.820965	−	0.570979i	$-0.193436\pi$
$277$	5.31319e6	+	5.31319e6i	0.249986	+	0.249986i	−0.570979	+	0.820965i	$0.693436\pi$
$278$	8.73344e6	−	203219.i	0.406491	−	0.00945867i
$279$	1.99901e7	−	2.32125e7i	0.920455	−	1.06883i
$280$	−15709.1	−	224711.i	−0.000715613	−	0.0102365i
$281$	−4.08440e7			−1.84081			−0.920406	−	0.390965i	$-0.872141\pi$
$281$	−4.08440e7			−1.84081			−0.920406	+	0.390965i	$0.872141\pi$
$282$	2.68014e7	+	9.24637e6i	1.19512	+	0.412310i
$283$	1.44997e7	+	1.44997e7i	0.639735	+	0.639735i	0.950490	−	0.310755i	$-0.100582\pi$
$283$	1.44997e7	+	1.44997e7i	0.639735	+	0.639735i	−0.310755	+	0.950490i	$0.600582\pi$
$284$	−885267.	−	1.90121e7i	−0.0386473	−	0.829993i
$285$	415693.	+	906579.i	0.0179572	+	0.0391626i
$286$	−4.38343e7	−	4.18407e7i	−1.87377	−	1.78855i
$287$		−	257589.i		−	0.0108964i
$288$	−4.52960e6	−	2.34545e7i	−0.189619	−	0.981858i
$289$	5.05312e6			0.209347
$290$	−7.87016e6	+	8.24515e6i	−0.322693	+	0.338068i
$291$	3.63141e7	−	1.66511e7i	1.47366	−	0.675714i
$292$	3.59939e7	−	1.67600e6i	1.44571	−	0.0673170i
$293$	−1.83636e7	+	1.83636e7i	−0.730053	+	0.730053i	−0.970630	−	0.240577i	$-0.922663\pi$
$293$	−1.83636e7	+	1.83636e7i	−0.730053	+	0.730053i	0.240577	+	0.970630i	$0.422663\pi$
$294$	8.28233e6	−	2.40071e7i	0.325920	−	0.944708i
$295$			4.47629e6i			0.174362i
$296$	−145151.	−	2.07630e6i	−0.00559685	−	0.0800599i
$297$	1.88772e7	+	3.41981e7i	0.720557	+	1.30537i
$298$	−963785.	−	4.14191e7i	−0.0364193	−	1.56514i
$299$	−3.40150e6	+	3.40150e6i	−0.127250	+	0.127250i
$300$	−2.01198e7	+	1.03841e7i	−0.745179	+	0.384596i
$301$	−31806.0	+	31806.0i	−0.00116630	+	0.00116630i
$302$	−2.79152e7	−	2.66456e7i	−1.01349	−	0.967398i
$303$	7.82130e6	−	2.10678e7i	0.281158	−	0.757340i
$304$	−1.92306e6	+	2.31897e6i	−0.0684499	+	0.0825418i
$305$			1.74711e7i			0.615773i
$306$	−2.53560e7	+	2.48557e6i	−0.884945	+	0.0867485i
$307$	3.92489e7	−	3.92489e7i	1.35648	−	1.35648i	0.478260	−	0.878218i	$-0.341268\pi$
$307$	3.92489e7	−	3.92489e7i	1.35648	−	1.35648i	0.878218	−	0.478260i	$-0.158732\pi$
$308$	−749321.	+	822511.i	−0.0256458	+	0.0281507i
$309$	1.02307e7	+	2.23120e7i	0.346761	+	0.756246i
$310$	392754.	+	1.68788e7i	0.0131837	+	0.566574i
$311$	−5.73532e7			−1.90668			−0.953338	−	0.301906i	$-0.902377\pi$
$311$	−5.73532e7			−1.90668			−0.953338	+	0.301906i	$0.902377\pi$
$312$	4.63115e7	−	2.52832e7i	1.52484	−	0.832469i
$313$		−	4.18077e6i		−	0.136340i	−0.997674	−	0.0681699i	$-0.978284\pi$
$313$		−	4.18077e6i		−	0.136340i	0.997674	−	0.0681699i	$-0.0217160\pi$
$314$	361718.	+	1.55450e7i	0.0116837	+	0.502114i
$315$	−319842.	+	23856.3i	−0.0102330	+	0.000763259i
$316$	−1.19721e6	−	2.57115e7i	−0.0379411	−	0.814827i
$317$	1.69119e7	+	1.69119e7i	0.530902	+	0.530902i	0.920841	−	0.389939i	$-0.127504\pi$
$317$	1.69119e7	+	1.69119e7i	0.530902	+	0.530902i	−0.389939	+	0.920841i	$0.627504\pi$
$318$	−6.96161e6	−	1.42951e7i	−0.216485	−	0.444534i
$319$	5.63015e7			1.73439
$320$	1.05141e7	+	7.92358e6i	0.320866	+	0.241808i
$321$	−1.44640e7	+	3.89610e7i	−0.437295	+	1.17792i
$322$	63892.2	+	60986.4i	0.00191373	+	0.00182669i
$323$	2.27199e6	+	2.27199e6i	0.0674216	+	0.0674216i
$324$	−3.33648e7	+	6.60477e6i	−0.980964	+	0.194188i
$325$	−3.53628e7	−	3.53628e7i	−1.03014	−	1.03014i
$326$	−1.00847e6	−	4.33393e7i	−0.0291078	−	1.25092i
$327$	−4.32526e6	+	1.16507e7i	−0.123700	+	0.333203i
$328$	1.13620e7	+	9.87720e6i	0.321983	+	0.279906i
$329$	1.14985e6			0.0322888
$330$	−2.03516e7	−	7.02119e6i	−0.566312	−	0.195375i
$331$	−4.75932e7	−	4.75932e7i	−1.31238	−	1.31238i	−0.919654	−	0.392730i	$-0.871531\pi$
$331$	−4.75932e7	−	4.75932e7i	−1.31238	−	1.31238i	−0.392730	−	0.919654i	$-0.628469\pi$
$332$	−3.18053e7	+	3.49119e7i	−0.869132	+	0.954024i
$333$	−2.95530e6	+	220429.i	−0.0800330	+	0.00596949i
$334$	−3.36501e7	+	3.52534e7i	−0.903122	+	0.946153i
$335$		−	453582.i		−	0.0120648i
$336$	−483890.	−	839313.i	−0.0127564	−	0.0221262i
$337$	1.94384e6			0.0507892			0.0253946	−	0.999678i	$-0.491916\pi$
$337$	1.94384e6			0.0507892			0.0253946	+	0.999678i	$0.491916\pi$
$338$	5.63718e7	+	5.38080e7i	1.45986	+	1.39347i
$339$	1.45531e7	+	3.17386e7i	0.373555	+	0.814682i
$340$	9.45635e6	−	1.03800e7i	0.240595	−	0.264095i
$341$	5.89689e7	−	5.89689e7i	1.48717	−	1.48717i
$342$	3.31452e6	+	2.72271e6i	0.0828596	+	0.0680649i
$343$		−	2.06059e6i		−	0.0510634i
$344$	−183336.	−	2.62253e6i	−0.00450374	−	0.0644236i
$345$	−594797.	+	1.60217e6i	−0.0144848	+	0.0390168i
$346$	1.20573e7	−	280562.i	0.291086	−	0.00677330i
$347$	−519401.	+	519401.i	−0.0124312	+	0.0124312i	−0.713295	−	0.700864i	$-0.752798\pi$
$347$	−519401.	+	519401.i	−0.0124312	+	0.0124312i	0.700864	+	0.713295i	$0.252798\pi$
$348$	−1.49055e7	+	4.67018e7i	−0.353679	+	1.10814i
$349$	−2.09404e7	+	2.09404e7i	−0.492617	+	0.492617i	−0.909130	−	0.416513i	$-0.863252\pi$
$349$	−2.09404e7	+	2.09404e7i	−0.492617	+	0.492617i	0.416513	+	0.909130i	$0.363252\pi$
$350$	−634029.	+	664239.i	−0.0147879	+	0.0154924i
$351$	−3.63055e7	−	6.57714e7i	−0.839559	−	1.52095i
$352$	−7.54757e6	−	6.45909e7i	−0.173053	−	1.48096i
$353$		−	7.31762e6i		−	0.166359i	−0.996535	−	0.0831794i	$-0.973493\pi$
$353$		−	7.31762e6i		−	0.166359i	0.996535	−	0.0831794i	$-0.0265075\pi$
$354$	8.42918e6	+	1.73086e7i	0.190010	+	0.390168i
$355$	1.05609e7	−	1.05609e7i	0.236057	−	0.236057i
$356$	−3.38520e6	−	7.27009e7i	−0.0750299	−	1.61135i
$357$	−939251.	+	430674.i	−0.0206432	+	0.00946551i
$358$	6.03248e7	−	1.40370e6i	1.31476	−	0.0305933i
$359$	4.77083e7			1.03112			0.515561	−	0.856853i	$-0.327583\pi$
$359$	4.77083e7			1.03112			0.515561	+	0.856853i	$0.327583\pi$
$360$	1.12120e7	−	1.50227e7i	0.240312	−	0.321988i
$361$			4.65049e7i			0.988501i
$362$	4.86943e7	−	1.13307e6i	1.02648	−	0.0238853i
$363$	2.43861e7	+	5.31833e7i	0.509827	+	1.11187i
$364$	1.44113e6	−	1.58189e6i	0.0298812	−	0.0327999i
$365$	1.99941e7	+	1.99941e7i	0.411171	+	0.411171i
$366$	3.28993e7	+	6.75559e7i	0.671033	+	1.37791i
$367$	−5.52642e7			−1.11801			−0.559005	−	0.829165i	$-0.688817\pi$
$367$	−5.52642e7			−1.11801			−0.559005	+	0.829165i	$0.688817\pi$
$368$	−5.13998e6	+	479710.i	−0.103138	+	0.00962577i
$369$	1.39880e7	−	1.62428e7i	0.278404	−	0.323283i
$370$	1.12774e6	−	1.18147e6i	0.0222640	−	0.0233248i
$371$	−455981.	−	455981.i	−0.00892945	−	0.00892945i
$372$	3.33027e7	+	6.45261e7i	0.646920	+	1.25345i
$373$	−1.81247e7	−	1.81247e7i	−0.349256	−	0.349256i	0.510577	−	0.859832i	$-0.329432\pi$
$373$	−1.81247e7	−	1.81247e7i	−0.349256	−	0.349256i	−0.859832	+	0.510577i	$0.829432\pi$
$374$	−6.93391e7	+	1.61346e6i	−1.32545	+	0.0308420i
$375$	−3.65195e7	−	1.35577e7i	−0.692518	−	0.257093i
$376$	−4.40906e7	+	5.07185e7i	−0.829435	+	0.954120i
$377$	−1.08282e8			−2.02083
$378$	−1.19182e6	+	694531.i	−0.0220665	+	0.0128593i
$379$	5.42609e7	+	5.42609e7i	0.996710	+	0.996710i	0.999995	−	0.00328420i	$-0.00104539\pi$
$379$	5.42609e7	+	5.42609e7i	0.996710	+	0.996710i	−0.00328420	+	0.999995i	$0.501045\pi$
$380$	−2.36151e6	+	109960.i	−0.0430366	+	0.00200393i
$381$	−2.38775e7	+	1.09485e7i	−0.431731	+	0.197961i
$382$	−2.12381e7	−	2.02722e7i	−0.381000	−	0.363672i
$383$		−	4.40212e7i		−	0.783548i	−0.920061	−	0.391774i	$-0.871861\pi$
$383$		−	4.40212e7i		−	0.783548i	0.920061	−	0.391774i	$-0.128139\pi$
$384$	5.55759e7	+	1.08394e7i	0.981506	+	0.191431i
$385$	−873130.			−0.0153002
$386$	−1.50525e7	+	1.57697e7i	−0.261726	+	0.274196i
$387$	−3.73278e6	+	278419.i	−0.0644019	+	0.00480360i
$388$	4.40457e6	+	9.45929e7i	0.0754063	+	1.61943i
$389$	6.60291e7	−	6.60291e7i	1.12172	−	1.12172i	0.130242	−	0.991482i	$-0.458424\pi$
$389$	6.60291e7	−	6.60291e7i	1.12172	−	1.12172i	0.991482	−	0.130242i	$-0.0415756\pi$
$390$	3.91410e7	+	1.35035e7i	0.659840	+	0.227642i
$391$			5.50586e6i			0.0921074i
$392$	4.54305e7	+	3.94936e7i	0.754205	+	0.655645i
$393$	−3.73668e7	−	1.38722e7i	−0.615614	−	0.228543i
$394$	363780.	+	1.56336e7i	0.00594772	+	0.255606i
$395$	1.42823e7	−	1.42823e7i	0.231744	−	0.231744i
$396$	−9.19153e7	+	1.11745e7i	−1.48014	+	0.179945i
$397$	4.89603e7	−	4.89603e7i	0.782479	−	0.782479i	−0.197769	−	0.980249i	$-0.563370\pi$
$397$	4.89603e7	−	4.89603e7i	0.782479	−	0.782479i	0.980249	+	0.197769i	$0.0633697\pi$
$398$	−3.42278e7	−	3.26711e7i	−0.542912	−	0.518220i
$399$	163089.	+	60545.8i	0.00256747	+	0.000953159i
$400$	−4.98718e6	−	5.34365e7i	−0.0779247	−	0.834945i
$401$			2.69185e7i			0.417463i	0.977973	+	0.208732i	$0.0669335\pi$
$401$			2.69185e7i			0.417463i	−0.977973	+	0.208732i	$0.933067\pi$
$402$	−854126.	−	1.75387e6i	−0.0131475	−	0.0269973i
$403$	−1.13412e8	+	1.13412e8i	−1.73278	+	1.73278i
$404$	3.93779e7	+	3.58739e7i	0.597185	+	0.544045i
$405$	−2.14638e7	−	1.58642e7i	−0.323103	−	0.238811i
$406$	46251.0	+	1.98766e6i	0.000691104	+	0.0297005i
$407$	−8.06761e6			−0.119664
$408$	1.70188e7	−	5.79436e7i	0.250581	−	0.853148i
$409$		−	2.80471e7i		−	0.409938i	−0.978768	−	0.204969i	$-0.934291\pi$
$409$		−	2.80471e7i		−	0.409938i	0.978768	−	0.204969i	$-0.0657093\pi$
$410$	274828.	+	1.18109e7i	0.00398758	+	0.171368i
$411$	−9.33726e7	+	4.28141e7i	−1.34491	+	0.616682i
$412$	−5.81195e7	+	2.70624e6i	−0.831055	+	0.0386967i
$413$	552105.	+	552105.i	0.00783740	+	0.00783740i
$414$	717087.	+	7.31519e6i	0.0101058	+	0.103092i
$415$	−3.70604e7			−0.518521
$416$	1.45158e7	+	1.24224e8i	0.201633	+	1.72554i
$417$	2.76401e7	+	1.02612e7i	0.381181	+	0.141511i
$418$	8.44686e6	+	8.06270e6i	0.115656	+	0.110396i
$419$	2.23426e7	+	2.23426e7i	0.303732	+	0.303732i	0.842472	−	0.538740i	$-0.181099\pi$
$419$	2.23426e7	+	2.23426e7i	0.303732	+	0.303732i	−0.538740	+	0.842472i	$0.681099\pi$
$420$	231156.	−	724256.i	0.00312003	−	0.00977562i
$421$	2.71548e7	+	2.71548e7i	0.363915	+	0.363915i	0.865252	−	0.501337i	$-0.167158\pi$
$421$	2.71548e7	+	2.71548e7i	0.363915	+	0.363915i	−0.501337	+	0.865252i	$0.667158\pi$
$422$	−1.78987e6	−	7.69205e7i	−0.0238168	−	1.02354i
$423$	7.25059e7	+	6.24406e7i	0.957971	+	0.824984i
$424$	3.75973e7	−	2.62836e6i	0.493241	−	0.0344816i
$425$	−5.72402e7			−0.745649
$426$	2.09492e7	−	6.07232e7i	0.270981	−	0.785463i
$427$	2.15488e6	+	2.15488e6i	0.0276783	+	0.0276783i
$428$	−7.28221e7	−	6.63422e7i	−0.928821	−	0.846172i
$429$	−8.52433e7	−	1.85906e8i	−1.07966	−	2.35462i
$430$	1.42442e6	−	1.49229e6i	0.0179157	−	0.0187693i
$431$			1.06844e8i			1.33450i	0.744835	+	0.667249i	$0.232528\pi$
$431$			1.06844e8i			1.33450i	−0.744835	+	0.667249i	$0.767472\pi$
$432$	1.50649e7	−	7.92015e7i	0.186860	−	0.982387i
$433$	7.60826e7			0.937177			0.468588	−	0.883417i	$-0.344763\pi$
$433$	7.60826e7			0.937177			0.468588	+	0.883417i	$0.344763\pi$
$434$	2.13027e6	+	2.03339e6i	0.0260595	+	0.0248743i
$435$	−3.49685e7	+	1.60341e7i	−0.424825	+	0.194795i
$436$	−2.17764e7	−	1.98387e7i	−0.262740	−	0.239361i
$437$	655469.	−	655469.i	0.00785431	−	0.00785431i
$438$	1.14962e8	+	3.96612e7i	1.36814	+	0.472002i
$439$		−	3.24554e7i		−	0.383613i	−0.981433	−	0.191807i	$-0.938565\pi$
$439$		−	3.24554e7i		−	0.383613i	0.981433	−	0.191807i	$-0.0614347\pi$
$440$	3.34800e7	−	3.85129e7i	0.393032	−	0.452114i
$441$	5.59304e7	−	6.49463e7i	0.652127	−	0.757249i
$442$	1.33356e8	−	3.10308e6i	1.54435	−	0.0359357i
$443$	9.82510e7	−	9.82510e7i	1.13012	−	1.13012i	0.139968	−	0.990156i	$-0.455300\pi$
$443$	9.82510e7	−	9.82510e7i	1.13012	−	1.13012i	0.990156	−	0.139968i	$-0.0446998\pi$
$444$	2.13586e6	−	6.69204e6i	0.0244019	−	0.0764556i
$445$	4.03843e7	−	4.03843e7i	0.458281	−	0.458281i
$446$	−5.59470e7	+	5.86127e7i	−0.630626	+	0.660674i
$447$	4.86648e7	−	1.31086e8i	0.544869	−	1.46768i
$448$	2.27411e6	−	319519.i	0.0252916	−	0.00355355i
$449$		−	6.23022e7i		−	0.688278i	−0.938919	−	0.344139i	$-0.888171\pi$
$449$		−	6.23022e7i		−	0.688278i	0.938919	−	0.344139i	$-0.111829\pi$
$450$	−7.60505e7	+	7.45500e6i	−0.834573	+	0.0818107i
$451$	4.12632e7	−	4.12632e7i	0.449814	−	0.449814i
$452$	−8.26743e7	+	3.84959e6i	−0.895272	+	0.0416869i
$453$	−5.42859e7	−	1.18391e8i	−0.583972	−	1.27358i
$454$	1.51874e8	−	3.53397e6i	1.62299	−	0.0377655i
$455$	1.67924e6			0.0178270
$456$	−8.92423e6	+	4.87207e6i	−0.0941187	+	0.0513829i
$457$			2.47388e7i			0.259197i	0.991567	+	0.129598i	$0.0413688\pi$
$457$			2.47388e7i			0.259197i	−0.991567	+	0.129598i	$0.958631\pi$
$458$	−3.64353e6	+	84781.7i	−0.0379251	+	0.000882482i
$459$	−8.26136e7	−	2.38475e7i	−0.854306	−	0.246607i
$460$	−2.99463e6	−	2.72815e6i	−0.0307659	−	0.0280282i
$461$	1.02878e8	+	1.02878e8i	1.05007	+	1.05007i	0.998679	+	0.0513931i	$0.0163661\pi$
$461$	1.02878e8	+	1.02878e8i	1.05007	+	1.05007i	0.0513931	+	0.998679i	$0.483634\pi$
$462$	−3.37615e6	+	1.64417e6i	−0.0342370	+	0.0166732i
$463$	−2.43620e6			−0.0245454			−0.0122727	−	0.999925i	$-0.503907\pi$
$463$	−2.43620e6			−0.0245454			−0.0122727	+	0.999925i	$0.503907\pi$
$464$	−8.94472e7	−	7.41763e7i	−0.895391	−	0.742526i
$465$	−1.98315e7	+	5.34190e7i	−0.197241	+	0.531297i
$466$	1.25373e7	−	1.31346e7i	0.123892	−	0.129795i
$467$	3.59699e7	+	3.59699e7i	0.353174	+	0.353174i	0.861289	−	0.508115i	$-0.169658\pi$
$467$	3.59699e7	+	3.59699e7i	0.353174	+	0.353174i	−0.508115	+	0.861289i	$0.669658\pi$
$468$	1.76776e8	−	2.14912e7i	1.72459	−	0.209664i
$469$	−55944.7	−	55944.7i	−0.000542301	−	0.000542301i
$470$	−5.27222e7	+	1.22680e6i	−0.507808	+	0.0118162i
$471$	−1.82644e7	+	4.91978e7i	−0.174801	+	0.470850i
$472$	−4.55232e7	+	3.18245e6i	−0.432919	+	0.0302646i
$473$	−1.01900e7			−0.0962923
$474$	2.83312e7	−	8.21205e7i	0.266029	−	0.771110i
$475$	6.81441e6	+	6.81441e6i	0.0635840	+	0.0635840i
$476$	−113923.	−	2.44661e6i	−0.00105630	−	0.0226853i
$477$	−3.99150e6	−	5.35141e7i	−0.0367774	−	0.493075i
$478$	9.17946e6	+	8.76198e6i	0.0840492	+	0.0802266i
$479$			1.16905e8i			1.06371i	0.846834	+	0.531857i	$0.178506\pi$
$479$			1.16905e8i			1.06371i	−0.846834	+	0.531857i	$0.821494\pi$
$480$	2.30826e7	+	3.79675e7i	0.208718	+	0.343312i
$481$	1.55160e7			0.139426
$482$	1.03223e8	−	1.08141e8i	0.921798	−	0.965719i
$483$	124249.	+	270974.i	0.00110269	+	0.00240484i
$484$	−1.38535e8	+	6.45065e6i	−1.22186	+	0.0568941i
$485$	−5.25450e7	+	5.25450e7i	−0.460581	+	0.460581i
$486$	−1.12868e8	−	2.09247e7i	−0.983246	−	0.182284i
$487$			7.93846e7i			0.687305i	0.939097	+	0.343652i	$0.111664\pi$
$487$			7.93846e7i			0.687305i	−0.939097	+	0.343652i	$0.888336\pi$
$488$	−1.77678e8	+	1.24212e7i	−1.52889	+	0.106882i
$489$	5.09209e7	−	1.37163e8i	0.435482	−	1.17303i
$490$	1.09889e6	+	4.72253e7i	0.00934040	+	0.401408i
$491$	−1.01052e7	+	1.01052e7i	−0.0853691	+	0.0853691i	−0.748502	−	0.663133i	$-0.769226\pi$
$491$	−1.01052e7	+	1.01052e7i	−0.0853691	+	0.0853691i	0.663133	+	0.748502i	$0.269226\pi$
$492$	2.33034e7	+	4.51518e7i	0.195670	+	0.379123i
$493$	−8.76352e7	+	8.76352e7i	−0.731371	+	0.731371i
$494$	−1.62454e7	−	1.55066e7i	−0.134756	−	0.128628i
$495$	−5.50571e7	−	4.74140e7i	−0.453939	−	0.390923i
$496$	−1.71376e8	+	1.59943e7i	−1.40444	+	0.131075i
$497$		−	2.60517e6i		−	0.0212210i
$498$	−1.43302e8	+	6.97875e7i	−1.16029	+	0.565053i
$499$	6.67073e7	−	6.67073e7i	0.536873	−	0.536873i	−0.385736	−	0.922609i	$-0.626052\pi$
$499$	6.67073e7	−	6.67073e7i	0.536873	−	0.536873i	0.922609	+	0.385736i	$0.126052\pi$
$500$	6.21849e7	−	6.82588e7i	0.497479	−	0.546070i
$501$	−1.49513e8	+	6.85562e7i	−1.18896	+	0.545172i
$502$	2.59257e6	+	1.11417e8i	0.0204936	+	0.880723i
$503$	−4.41869e7			−0.347208			−0.173604	−	0.984816i	$-0.555541\pi$
$503$	−4.41869e7			−0.347208			−0.173604	+	0.984816i	$0.555541\pi$
$504$	−470008.	−	3.23578e6i	−0.00367125	−	0.0252748i
$505$			4.18013e7i			0.324575i
$506$	465482.	+	2.00043e7i	0.00359295	+	0.154409i
$507$	1.09625e8	+	2.39079e8i	0.841170	+	1.83450i
$508$	−2.89612e6	−	6.21973e7i	−0.0220915	−	0.474439i
$509$	1.56083e8	+	1.56083e8i	1.18360	+	1.18360i	0.978806	+	0.204789i	$0.0656510\pi$
$509$	1.56083e8	+	1.56083e8i	1.18360	+	1.18360i	0.204789	+	0.978806i	$0.434349\pi$
$510$	4.26066e7	−	2.07492e7i	0.321193	−	0.156419i
$511$	4.93213e6			0.0369634
$512$	−7.31065e7	+	1.12560e8i	−0.544686	+	0.838640i
$513$	6.99606e6	+	1.26741e7i	0.0518205	+	0.0938785i
$514$	1.02946e8	+	9.82637e7i	0.758086	+	0.723608i
$515$	−3.22845e7	−	3.22845e7i	−0.236359	−	0.236359i
$516$	2.69775e6	−	8.45256e6i	0.0196360	−	0.0615233i
$517$	1.84194e8	+	1.84194e8i	1.33292	+	1.33292i
$518$	−6627.45	−	284818.i	−4.76823e−5	−	0.00204917i
$519$	3.81596e7	+	1.41665e7i	0.272962	+	0.101335i
$520$	−6.43902e7	+	7.40697e7i	−0.457942	+	0.526782i
$521$	3.33563e7			0.235866			0.117933	−	0.993022i	$-0.462373\pi$
$521$	3.33563e7			0.235866			0.117933	+	0.993022i	$0.462373\pi$
$522$	−1.05020e8	+	1.27848e8i	−0.738349	+	0.898838i
$523$	−8.11980e7	−	8.11980e7i	−0.567597	−	0.567597i	0.363858	−	0.931455i	$-0.381460\pi$
$523$	−8.11980e7	−	8.11980e7i	−0.567597	−	0.567597i	−0.931455	+	0.363858i	$0.881460\pi$
$524$	6.36277e7	−	6.98425e7i	0.442234	−	0.485429i
$525$	−2.81711e6	+	1.29173e6i	−0.0194682	+	0.00892673i
$526$	1.05694e8	−	1.10730e8i	0.726263	−	0.760867i
$527$			1.83574e8i			1.25424i
$528$	5.69353e7	−	2.11964e8i	0.386794	−	1.43999i
$529$	−1.46447e8			−0.989270
$530$	2.13939e7	+	2.04209e7i	0.143702	+	0.137166i
$531$	4.83295e6	+	6.47954e7i	0.0322796	+	0.432774i
$532$	−277705.	+	304830.i	−0.00184438	+	0.00202452i
$533$	−7.93593e7	+	7.93593e7i	−0.524102	+	0.524102i
$534$	8.01083e7	−	2.32201e8i	0.526082	−	1.52490i
$535$		−	7.73037e7i		−	0.504823i
$536$	4.61285e6	−	322476.i	0.0299554	−	0.00209413i
$537$	1.90919e8	+	7.08778e7i	1.23290	+	0.457707i
$538$	−3.04797e8	+	7.09234e6i	−1.95733	+	0.0455452i
$539$	1.64989e8	−	1.64989e8i	1.05363	−	1.05363i
$540$	5.39057e7	−	3.31169e7i	0.342336	−	0.210314i
$541$	−4.90760e7	+	4.90760e7i	−0.309940	+	0.309940i	−0.844886	−	0.534946i	$-0.820332\pi$
$541$	−4.90760e7	+	4.90760e7i	−0.309940	+	0.309940i	0.534946	+	0.844886i	$0.320332\pi$
$542$	1.36100e8	−	1.42584e8i	0.854789	−	0.895517i
$543$	1.54110e8	+	5.72126e7i	0.962570	+	0.357349i
$544$	1.12286e8	+	8.87898e7i	0.697475	+	0.551527i
$545$		−	2.31165e7i		−	0.142802i
$546$	6.49317e6	−	3.16213e6i	0.0398913	−	0.0194269i
$547$	6.00315e7	−	6.00315e7i	0.366790	−	0.366790i	−0.499515	−	0.866305i	$-0.666489\pi$
$547$	6.00315e7	−	6.00315e7i	0.366790	−	0.366790i	0.866305	+	0.499515i	$0.166489\pi$
$548$	−1.13252e7	−	2.43222e8i	−0.0688186	−	1.47796i
$549$	1.88631e7	+	2.52898e8i	0.113998	+	1.52837i
$550$	−2.07970e8	+	4.83926e6i	−1.25000	+	0.0290865i
$551$	2.08659e7			0.124733
$552$	−1.67167e7	−	4.90992e6i	−0.0993878	−	0.0291915i
$553$		−	3.52316e6i		−	0.0208333i
$554$	−6.00956e7	+	1.39837e6i	−0.353438	+	0.00822418i
$555$	5.01075e6	−	2.29757e6i	0.0293105	−	0.0134397i
$556$	−4.70651e7	+	5.16622e7i	−0.273826	+	0.300572i
$557$	−1.21856e8	−	1.21856e8i	−0.705147	−	0.705147i	0.260363	−	0.965511i	$-0.416158\pi$
$557$	−1.21856e8	−	1.21856e8i	−0.705147	−	0.705147i	−0.965511	+	0.260363i	$0.916158\pi$
$558$	2.39089e7	+	2.43901e8i	0.137612	+	1.40382i
$559$	1.95979e7			0.112195
$560$	1.38716e6	+	1.15033e6i	0.00789880	+	0.00655028i
$561$	−2.19448e8	−	8.14690e7i	−1.24292	−	0.461428i
$562$	2.25611e8	−	2.36361e8i	1.27102	−	1.33158i
$563$	−9.47359e7	−	9.47359e7i	−0.530871	−	0.530871i	0.389960	−	0.920832i	$-0.372489\pi$
$563$	−9.47359e7	−	9.47359e7i	−0.530871	−	0.530871i	−0.920832	+	0.389960i	$0.872489\pi$
$564$	−2.01552e8	+	1.04023e8i	−1.12344	+	0.579820i
$565$	−4.59243e7	−	4.59243e7i	−0.254623	−	0.254623i
$566$	−1.64001e8	+	3.81616e6i	−0.904477	+	0.0210464i
$567$	−4.60403e6	+	690651.i	−0.0252574	+	0.00378887i
$568$	1.14911e8	+	9.98946e7i	0.627073	+	0.545126i
$569$	2.14348e8			1.16354			0.581771	−	0.813353i	$-0.302360\pi$
$569$	2.14348e8			1.16354			0.581771	+	0.813353i	$0.302360\pi$
$570$	−7.54247e6	−	2.60212e6i	−0.0407276	−	0.0140508i
$571$	−2.28582e8	−	2.28582e8i	−1.22782	−	1.22782i	−0.964788	−	0.263030i	$-0.915278\pi$
$571$	−2.28582e8	−	2.28582e8i	−1.22782	−	1.22782i	−0.263030	−	0.964788i	$-0.584722\pi$
$572$	4.84258e8	−	2.25487e7i	2.58755	−	0.120485i
$573$	−4.13011e7	−	9.00730e7i	−0.219532	−	0.478774i
$574$	1.49065e6	+	1.42285e6i	0.00788205	+	0.00752357i
$575$			1.65138e7i			0.0868646i
$576$	1.60749e8	+	1.03344e8i	0.841167	+	0.540776i
$577$	1.52721e8			0.795005			0.397503	−	0.917601i	$-0.369877\pi$
$577$	1.52721e8			0.795005			0.397503	+	0.917601i	$0.369877\pi$
$578$	−2.79121e7	+	2.92420e7i	−0.144547	+	0.151434i
$579$	−6.68809e7	+	3.06668e7i	−0.344561	+	0.157991i
$580$	−4.24136e6	−	9.10879e7i	−0.0217381	−	0.466849i
$581$	−4.57103e6	+	4.57103e6i	−0.0233070	+	0.0233070i
$582$	−1.04231e8	+	3.02123e8i	−0.528722	+	1.53255i
$583$		−	1.46087e8i		−	0.737235i
$584$	−1.89122e8	+	2.17551e8i	−0.949516	+	1.09225i
$585$	1.05888e8	+	9.11887e7i	0.528908	+	0.455484i
$586$	−4.83308e6	−	2.07704e8i	−0.0240177	−	1.03217i
$587$	−5.09896e6	+	5.09896e6i	−0.0252097	+	0.0252097i	−0.719599	−	0.694390i	$-0.755674\pi$
$587$	−5.09896e6	+	5.09896e6i	−0.0252097	+	0.0252097i	0.694390	+	0.719599i	$0.255674\pi$
$588$	9.31777e7	+	1.80538e8i	0.458332	+	0.888047i
$589$	2.18544e7	−	2.18544e7i	0.106953	−	0.106953i
$590$	−2.59039e7	−	2.47258e7i	−0.126128	−	0.120391i
$591$	−1.83685e7	+	4.94782e7i	−0.0889839	+	0.239691i
$592$	1.28172e7	+	1.06290e7i	0.0617770	+	0.0512301i
$593$		−	2.49004e8i		−	1.19410i	−0.802203	−	0.597051i	$-0.796339\pi$
$593$		−	2.49004e8i		−	1.19410i	0.802203	−	0.597051i	$-0.203661\pi$
$594$	−3.02174e8	−	7.96603e7i	−1.44178	−	0.380087i
$595$	1.35906e6	−	1.35906e6i	0.00645189	−	0.00645189i
$596$	2.45013e8	+	2.23211e8i	1.15731	+	1.05433i
$597$	−6.65617e7	−	1.45164e8i	−0.312825	−	0.682236i
$598$	−895236.	−	3.84732e7i	−0.00418634	−	0.179910i
$599$	−1.98437e7			−0.0923298			−0.0461649	−	0.998934i	$-0.514700\pi$
$599$	−1.98437e7			−0.0923298			−0.0461649	+	0.998934i	$0.514700\pi$
$600$	5.10447e7	−	1.73791e8i	0.236318	−	0.804587i
$601$		−	2.91626e7i		−	0.134339i	−0.997742	−	0.0671696i	$-0.978603\pi$
$601$		−	2.91626e7i		−	0.134339i	0.997742	−	0.0671696i	$-0.0213969\pi$
$602$	−8370.98	−	359747.i	−3.83696e−5	−	0.00164895i
$603$	−489721.	−	6.56570e6i	−0.00223356	−	0.0299453i
$604$	3.08392e8	−	1.43598e7i	1.39956	−	0.0651684i
$605$	−7.69540e7	−	7.69540e7i	−0.347508	−	0.347508i
$606$	7.87148e7	+	1.61634e8i	0.353703	+	0.726298i
$607$	2.88709e7			0.129091			0.0645453	−	0.997915i	$-0.479440\pi$
$607$	2.88709e7			0.129091			0.0645453	+	0.997915i	$0.479440\pi$
$608$	−2.79720e6	−	2.39380e7i	−0.0124455	−	0.106507i
$609$	−2.33537e6	+	6.29066e6i	−0.0103396	+	0.0278512i
$610$	−1.01104e8	−	9.65057e7i	−0.445429	−	0.425171i
$611$	−3.54250e8	−	3.54250e8i	−1.55305	−	1.55305i
$612$	1.25676e8	−	1.60463e8i	0.548274	−	0.700035i
$613$	1.49037e8	+	1.49037e8i	0.647011	+	0.647011i	0.952270	−	0.305258i	$-0.0987428\pi$
$613$	1.49037e8	+	1.49037e8i	0.647011	+	0.647011i	−0.305258	+	0.952270i	$0.598743\pi$
$614$	1.03299e7	+	4.43931e8i	0.0446262	+	1.91783i
$615$	−1.38770e7	+	3.73797e7i	−0.0596582	+	0.160698i
$616$	−620756.	−	8.87959e6i	−0.00265570	−	0.0379884i
$617$	−2.40640e8			−1.02450			−0.512251	−	0.858836i	$-0.671188\pi$
$617$	−2.40640e8			−1.02450			−0.512251	+	0.858836i	$0.671188\pi$
$618$	−1.85629e8	−	6.40412e7i	−0.786468	−	0.271328i
$619$	1.60962e7	+	1.60962e7i	0.0678659	+	0.0678659i	0.740225	−	0.672359i	$-0.234719\pi$
$619$	1.60962e7	+	1.60962e7i	0.0678659	+	0.0678659i	−0.672359	+	0.740225i	$0.734719\pi$
$620$	−9.98457e7	−	9.09611e7i	−0.418943	−	0.381664i
$621$	−6.88000e6	+	2.38340e7i	−0.0287286	+	0.0995226i
$622$	3.16804e8	−	3.31898e8i	1.31649	−	1.37922i
$623$		−	9.96198e6i		−	0.0411985i
$624$	−1.09501e8	+	4.07659e8i	−0.450674	+	1.67781i
$625$	−1.32270e8			−0.541779
$626$	2.41937e7	+	2.30934e7i	0.0986234	+	0.0941381i
$627$	1.64264e7	+	3.58240e7i	0.0666406	+	0.145336i
$628$	−9.19558e7	−	8.37733e7i	−0.371279	−	0.338241i
$629$	1.25575e7	−	1.25575e7i	0.0504605	−	0.0504605i
$630$	1.62867e6	−	1.98268e6i	0.00651344	−	0.00792921i
$631$		−	4.82983e8i		−	1.92240i	−0.275851	−	0.961200i	$-0.588960\pi$
$631$		−	4.82983e8i		−	1.92240i	0.275851	−	0.961200i	$-0.411040\pi$
$632$	1.55403e8	+	1.35095e8i	0.615614	+	0.535165i
$633$	9.03766e7	−	2.43442e8i	0.356324	−	0.959809i
$634$	−1.91284e8	+	4.45101e6i	−0.750606	+	0.0174659i
$635$	3.45497e7	−	3.45497e7i	0.134934	−	0.134934i
$636$	1.21178e8	+	3.86758e7i	0.471036	+	0.150338i
$637$	−3.17315e8	+	3.17315e8i	−1.22764	+	1.22764i
$638$	−3.10994e8	+	3.25812e8i	−1.19754	+	1.25460i
$639$	1.41470e8	−	1.64274e8i	0.542201	−	0.629604i
$640$	−1.03930e8	+	1.70767e7i	−0.396463	+	0.0651426i
$641$		−	1.51160e8i		−	0.573934i	−0.957940	−	0.286967i	$-0.907353\pi$
$641$		−	1.51160e8i		−	0.573934i	0.957940	−	0.286967i	$-0.0926470\pi$
$642$	−1.45568e8	−	2.98912e8i	−0.550126	−	1.12964i
$643$	7.97459e7	−	7.97459e7i	0.299968	−	0.299968i	−0.541033	−	0.841001i	$-0.681967\pi$
$643$	7.97459e7	−	7.97459e7i	0.299968	−	0.299968i	0.841001	+	0.541033i	$0.181967\pi$
$644$	−705847.	+	32866.6i	−0.00264273	+	0.000123054i
$645$	6.32896e6	−	2.90201e6i	0.0235860	−	0.0108148i
$646$	−2.56977e7	+	597962.i	−0.0953228	+	0.00221807i
$647$	−1.94699e8			−0.718872			−0.359436	−	0.933170i	$-0.617031\pi$
$647$	−1.94699e8			−0.718872			−0.359436	+	0.933170i	$0.617031\pi$
$648$	1.46077e8	−	2.29562e8i	0.536854	−	0.843675i
$649$			1.76884e8i			0.647073i
$650$	3.99976e8	−	9.30709e6i	1.45645	−	0.0338902i
$651$	4.14268e6	+	9.03471e6i	0.0150154	+	0.0327470i
$652$	2.56372e8	+	2.33559e8i	0.924969	+	0.842662i
$653$	−1.25905e8	−	1.25905e8i	−0.452173	−	0.452173i	0.443902	−	0.896075i	$-0.353594\pi$
$653$	−1.25905e8	−	1.25905e8i	−0.452173	−	0.452173i	−0.896075	+	0.443902i	$0.853594\pi$
$654$	−4.35301e7	−	8.93853e7i	−0.155617	−	0.319545i
$655$	7.41407e7			0.263835
$656$	−1.19919e8	+	1.11919e7i	−0.424793	+	0.0396455i
$657$	3.11006e8	+	2.67832e8i	1.09666	+	0.944421i
$658$	−6.35143e6	+	6.65406e6i	−0.0222943	+	0.0233566i
$659$	−1.70941e8	−	1.70941e8i	−0.597297	−	0.597297i	0.342295	−	0.939592i	$-0.388796\pi$
$659$	−1.70941e8	−	1.70941e8i	−0.597297	−	0.597297i	−0.939592	+	0.342295i	$0.888796\pi$
$660$	1.53048e8	−	7.89897e7i	0.532347	−	0.274750i
$661$	3.59011e7	+	3.59011e7i	0.124309	+	0.124309i	0.766524	−	0.642215i	$-0.221984\pi$
$661$	3.59011e7	+	3.59011e7i	0.124309	+	0.124309i	−0.642215	+	0.766524i	$0.721984\pi$
$662$	5.38310e8	−	1.25260e7i	1.85549	−	0.0431755i
$663$	4.22053e8	+	1.56685e8i	1.44819	+	0.537634i
$664$	−2.63483e7	−	3.76899e8i	−0.0900013	−	1.28742i
$665$	−323590.			−0.00110035
$666$	1.50487e7	−	1.83197e7i	0.0509420	−	0.0620148i
$667$	2.52827e7	+	2.52827e7i	0.0852014	+	0.0852014i
$668$	−1.81346e7	−	3.89460e8i	−0.0608385	−	1.30657i
$669$	−2.48583e8	+	1.13982e8i	−0.830218	+	0.380679i
$670$	2.62484e6	+	2.50546e6i	0.00872727	+	0.00833035i
$671$			6.90382e8i			2.28519i
$672$	7.52991e6	+	1.83591e6i	0.0248132	+	0.00604984i
$673$	−9.39363e7			−0.308168			−0.154084	−	0.988058i	$-0.549243\pi$
$673$	−9.39363e7			−0.308168			−0.154084	+	0.988058i	$0.549243\pi$
$674$	−1.07373e7	+	1.12488e7i	−0.0350682	+	0.0367391i
$675$	−2.47784e8	−	7.15261e7i	−0.805678	−	0.232570i
$676$	−6.22765e8	+	2.89980e7i	−2.01597	+	0.0938704i
$677$	2.42481e7	−	2.42481e7i	0.0781470	−	0.0781470i	−0.666953	−	0.745100i	$-0.732402\pi$
$677$	2.42481e7	−	2.42481e7i	0.0781470	−	0.0781470i	0.745100	+	0.666953i	$0.232402\pi$
$678$	−2.64056e8	−	9.10979e7i	−0.847239	−	0.292293i
$679$			1.29618e7i			0.0414052i
$680$	7.83387e6	+	1.12059e8i	0.0249144	+	0.356387i
$681$	4.80659e8	+	1.78442e8i	1.52193	+	0.565010i
$682$	1.55199e7	+	6.66977e8i	0.0489257	+	2.10260i
$683$	4.47794e7	−	4.47794e7i	0.140545	−	0.140545i	−0.633334	−	0.773879i	$-0.718314\pi$
$683$	4.47794e7	−	4.47794e7i	0.140545	−	0.140545i	0.773879	+	0.633334i	$0.218314\pi$
$684$	−3.40646e7	+	4.14135e6i	−0.106447	+	0.0129412i
$685$	1.35106e8	−	1.35106e8i	0.420343	−	0.420343i
$686$	1.19245e7	+	1.13822e7i	0.0369375	+	0.0352576i
$687$	−1.15313e7	−	4.28092e6i	−0.0355637	−	0.0132028i
$688$	1.61891e7	+	1.34252e7i	0.0497114	+	0.0412245i
$689$			2.80961e8i			0.858991i
$690$	−5.98613e6	−	1.22920e7i	−0.0182221	−	0.0374175i
$691$	−2.27256e8	+	2.27256e8i	−0.688781	+	0.688781i	−0.961962	−	0.273182i	$-0.911924\pi$
$691$	−2.27256e8	+	2.27256e8i	−0.688781	+	0.688781i	0.273182	+	0.961962i	$0.411924\pi$
$692$	−6.49776e7	+	7.13242e7i	−0.196085	+	0.215238i
$693$	−1.26388e7	+	942697.i	−0.0379756	+	0.00283252i
$694$	−136700.	−	5.87476e6i	−0.000408969	−	0.0175757i
$695$	−5.48416e7			−0.163364
$696$	−1.87925e8	−	3.44225e8i	−0.557388	−	1.02097i
$697$			1.28455e8i			0.379362i
$698$	−5.51127e6	−	2.36850e8i	−0.0162064	−	0.696476i
$699$	5.57053e7	−	2.55425e7i	0.163104	−	0.0747880i
$700$	−341689.	−	7.33815e6i	−0.000996178	−	0.0213940i
$701$	2.60867e8	+	2.60867e8i	0.757296	+	0.757296i	0.975830	−	0.218533i	$-0.0701272\pi$
$701$	2.60867e8	+	2.60867e8i	0.757296	+	0.757296i	−0.218533	+	0.975830i	$0.570127\pi$
$702$	5.81155e8	+	1.53206e8i	1.67989	+	0.442859i
$703$	−2.98993e6			−0.00860588
$704$	4.15473e8	+	3.13105e8i	1.19076	+	0.897372i
$705$	−1.66858e8	−	6.19452e7i	−0.476190	−	0.176783i
$706$	4.23465e7	+	4.04206e7i	0.120338	+	0.114865i
$707$	5.15577e6	+	5.15577e6i	0.0145893	+	0.0145893i
$708$	−1.46724e8	−	4.68290e7i	−0.413429	−	0.131952i
$709$	−2.65291e8	−	2.65291e8i	−0.744361	−	0.744361i	0.229053	−	0.973414i	$-0.426437\pi$
$709$	−2.65291e8	−	2.65291e8i	−0.744361	−	0.744361i	−0.973414	+	0.229053i	$0.926437\pi$
$710$	2.77951e6	+	1.19451e8i	0.00776594	+	0.333745i
$711$	1.91320e8	−	2.22161e8i	0.532294	−	0.618099i
$712$	4.39413e8	+	3.81990e8i	1.21740	+	1.05831i
$713$	5.29611e7			0.146113
$714$	2.69589e6	−	7.81430e6i	0.00740642	−	0.0214682i
$715$	2.68998e8	+	2.68998e8i	0.735920	+	0.735920i
$716$	−3.25095e8	+	3.56849e8i	−0.885668	+	0.972176i
$717$	1.78510e7	+	3.89311e7i	0.0484290	+	0.105618i
$718$	−2.63528e8	+	2.76084e8i	−0.711955	+	0.745878i
$719$		−	4.71644e8i		−	1.26890i	−0.772963	−	0.634451i	$-0.781226\pi$
$719$		−	4.71644e8i		−	1.26890i	0.772963	−	0.634451i	$-0.218774\pi$
$720$	2.50029e7	+	1.47864e8i	0.0669875	+	0.396155i
$721$	−7.96393e6			−0.0212482
$722$	−2.69120e8	−	2.56881e8i	−0.715047	−	0.682527i
$723$	4.58639e8	−	2.10299e8i	1.21355	−	0.556446i
$724$	−2.62417e8	+	2.88048e8i	−0.691474	+	0.759014i
$725$	−2.62845e8	+	2.62845e8i	−0.689741	+	0.689741i
$726$	−4.42470e8	−	1.52650e8i	−1.15631	−	0.398921i
$727$			2.80757e8i			0.730681i	0.930874	+	0.365340i	$0.119047\pi$
$727$			2.80757e8i			0.730681i	−0.930874	+	0.365340i	$0.880953\pi$
$728$	1.19387e6	+	1.70776e7i	0.00309429	+	0.0442623i
$729$	−3.27822e8	−	2.06464e8i	−0.846165	−	0.532921i
$730$	−2.26146e8	+	5.26221e6i	−0.581326	+	0.0135269i
$731$	1.58611e7	−	1.58611e7i	0.0406052	−	0.0406052i
$732$	−5.72668e8	−	1.82775e8i	−1.46006	−	0.465997i
$733$	2.02296e8	−	2.02296e8i	0.513659	−	0.513659i	−0.401986	−	0.915646i	$-0.631680\pi$
$733$	2.02296e8	−	2.02296e8i	0.513659	−	0.513659i	0.915646	+	0.401986i	$0.131680\pi$
$734$	3.05264e8	−	3.19809e8i	0.771948	−	0.808728i
$735$	−5.54867e7	+	1.49461e8i	−0.139742	+	0.376415i
$736$	2.56158e7	−	3.23945e7i	0.0642503	−	0.0812526i
$737$		−	1.79236e7i		−	0.0447736i
$738$	1.67301e7	+	1.70668e8i	0.0416226	+	0.424604i
$739$	−2.31444e8	+	2.31444e8i	−0.573473	+	0.573473i	−0.933097	−	0.359624i	$-0.882905\pi$
$739$	−2.31444e8	+	2.31444e8i	−0.573473	+	0.573473i	0.359624	+	0.933097i	$0.382905\pi$
$740$	607758.	+	1.30523e7i	0.00149981	+	0.0322100i
$741$	−3.15919e7	−	6.88984e7i	−0.0776464	−	0.169338i
$742$	5.15743e6	−	120009.i	0.0126247	−	0.000293766i
$743$	2.48518e8			0.605886			0.302943	−	0.953009i	$-0.402031\pi$
$743$	2.48518e8			0.605886			0.302943	+	0.953009i	$0.402031\pi$
$744$	−5.57362e8	−	1.63705e8i	−1.35338	−	0.397505i
$745$			2.60091e8i			0.629009i
$746$	2.05002e8	−	4.77020e6i	0.493789	−	0.0114900i
$747$	−5.36459e8	+	4.00133e7i	−1.28699	+	0.0959936i
$748$	3.73674e8	−	4.10172e8i	0.892869	−	0.980079i
$749$	−9.53463e6	−	9.53463e6i	−0.0226912	−	0.0226912i
$750$	2.80181e8	−	1.36446e8i	0.664132	−	0.323429i
$751$	3.65748e8			0.863500			0.431750	−	0.901993i	$-0.357896\pi$
$751$	3.65748e8			0.863500			0.431750	+	0.901993i	$0.357896\pi$
$752$	−4.99594e7	−	5.35304e8i	−0.117480	−	1.25877i
$753$	−1.30908e8	+	3.52618e8i	−0.306605	+	0.825885i
$754$	5.98118e8	−	6.26617e8i	1.39532	−	1.46180i
$755$	1.71307e8	+	1.71307e8i	0.398048	+	0.398048i
$756$	2.56408e6	−	1.07334e7i	0.00593426	−	0.0248411i
$757$	−3.31019e7	−	3.31019e7i	−0.0763072	−	0.0763072i	0.667923	−	0.744230i	$-0.267184\pi$
$757$	−3.31019e7	−	3.31019e7i	−0.0763072	−	0.0763072i	−0.744230	+	0.667923i	$0.767184\pi$
$758$	−6.13725e8	+	1.42808e7i	−1.40918	+	0.0327903i
$759$	−2.35038e7	+	6.33108e7i	−0.0537542	+	0.144795i
$760$	1.24080e7	−	1.42732e7i	0.0282658	−	0.0325148i
$761$	−5.84581e8			−1.32645			−0.663225	−	0.748420i	$-0.730813\pi$
$761$	−5.84581e8			−1.32645			−0.663225	+	0.748420i	$0.730813\pi$
$762$	6.85345e7	−	1.98654e8i	0.154897	−	0.448985i
$763$	−2.85119e6	−	2.85119e6i	−0.00641878	−	0.00641878i
$764$	2.34627e8	−	1.09250e7i	0.526136	−	0.0244987i
$765$	1.59500e8	−	1.18967e7i	0.356267	−	0.0265732i
$766$	2.54747e8	+	2.43161e8i	0.566791	+	0.541014i
$767$		−	3.40190e8i		−	0.753939i
$768$	−3.69713e8	+	2.61739e8i	−0.816171	+	0.577810i
$769$	5.60410e8			1.23233			0.616165	−	0.787617i	$-0.288685\pi$
$769$	5.60410e8			1.23233			0.616165	+	0.787617i	$0.288685\pi$
$770$	4.82293e6	−	5.05273e6i	0.0105643	−	0.0110676i
$771$	2.00195e8	+	4.36603e8i	0.436808	+	0.952629i
$772$	−8.11204e6	−	1.74215e8i	−0.0176310	−	0.378646i
$773$	1.28074e8	−	1.28074e8i	0.277283	−	0.277283i	−0.554740	−	0.832023i	$-0.687182\pi$
$773$	1.28074e8	−	1.28074e8i	0.277283	−	0.277283i	0.832023	+	0.554740i	$0.187182\pi$
$774$	1.90077e7	−	2.31392e7i	0.0409926	−	0.0499028i
$775$			5.50596e8i			1.18285i
$776$	−5.71731e8	−	4.97017e8i	−1.22351	−	1.06362i
$777$	334643.	−	901407.i	0.000713375	−	0.00192158i
$778$	1.73781e7	+	7.46831e8i	0.0369031	+	1.58593i
$779$	1.52925e7	−	1.52925e7i	0.0323494	−	0.0323494i
$780$	−2.94348e8	+	1.51916e8i	−0.620265	+	0.320126i
$781$	4.17322e8	−	4.17322e8i	0.876028	−	0.876028i
$782$	−3.18619e7	−	3.04129e7i	−0.0666273	−	0.0635970i
$783$	−4.88866e8	+	2.69852e8i	−1.01837	+	0.562135i
$784$	−4.79492e8	+	4.47506e7i	−0.995024	+	0.0928647i
$785$		−	9.76149e7i		−	0.201793i
$786$	2.86681e8	−	1.39612e8i	0.590381	−	0.287512i
$787$	1.03455e8	−	1.03455e8i	0.212239	−	0.212239i	−0.592979	−	0.805218i	$-0.702048\pi$
$787$	1.03455e8	−	1.03455e8i	0.212239	−	0.212239i	0.805218	+	0.592979i	$0.202048\pi$
$788$	−9.24799e7	−	8.42507e7i	−0.189003	−	0.172185i
$789$	4.69618e8	−	2.15334e8i	0.956124	−	0.438411i
$790$	3.75895e6	+	1.61542e8i	0.00762403	+	0.327646i
$791$	−1.13286e7			−0.0228901
$792$	4.43049e8	−	5.93631e8i	0.891819	−	1.19493i
$793$		−	1.32777e9i		−	2.66259i
$794$	1.28858e7	+	5.53773e8i	0.0257424	+	1.10629i
$795$	4.16041e7	+	9.07338e7i	0.0828009	+	0.180579i
$796$	3.78130e8	−	1.76070e7i	0.749724	−	0.0349097i
$797$	−3.45214e7	−	3.45214e7i	−0.0681888	−	0.0681888i	0.672190	−	0.740379i	$-0.265354\pi$
$797$	−3.45214e7	−	3.45214e7i	−0.0681888	−	0.0681888i	−0.740379	+	0.672190i	$0.765354\pi$
$798$	−1.25123e6	+	609343.i	−0.00246223	+	0.00119909i
$799$	−5.73408e8			−1.12415
$800$	3.36780e8	+	2.66308e8i	0.657774	+	0.520133i
$801$	5.40970e8	−	6.28174e8i	1.05263	−	1.22231i
$802$	−1.55775e8	−	1.48691e8i	−0.301978	−	0.288244i
$803$	7.90078e8	+	7.90078e8i	1.52589	+	1.52589i
$804$	1.48675e7	+	4.74517e6i	0.0286068	+	0.00913026i
$805$	−392087.	−	392087.i	−0.000751615	−	0.000751615i
$806$	−2.98486e7	−	1.28276e9i	−0.0570059	−	2.44985i
$807$	−9.64638e8	−	3.58117e8i	−1.83546	−	0.681403i
$808$	−4.25112e8	+	2.97189e7i	−0.805879	+	0.0563376i
$809$	4.49923e8			0.849754			0.424877	−	0.905251i	$-0.360317\pi$
$809$	4.49923e8			0.849754			0.424877	+	0.905251i	$0.360317\pi$
$810$	2.10365e8	−	3.65796e7i	0.395839	−	0.0688310i
$811$	2.67359e7	+	2.67359e7i	0.0501224	+	0.0501224i	0.731724	−	0.681601i	$-0.238716\pi$
$811$	2.67359e7	+	2.67359e7i	0.0501224	+	0.0501224i	−0.681601	+	0.731724i	$0.738716\pi$
$812$	−1.17579e7	−	1.07116e7i	−0.0219615	−	0.0200073i
$813$	6.04715e8	−	2.77280e8i	1.12533	−	0.515996i
$814$	4.45633e7	−	4.66866e7i	0.0826236	−	0.0865604i
$815$			2.72149e8i			0.502729i
$816$	2.41307e8	+	4.18551e8i	0.444120	+	0.770332i
$817$	−3.77651e6			−0.00692508
$818$	1.62306e8	+	1.54925e8i	0.296535	+	0.283048i
$819$	2.43074e7	−	1.81304e6i	0.0442474	−	0.00330031i
$820$	−6.98665e7	−	6.36496e7i	−0.126715	−	0.115439i
$821$	1.74491e8	−	1.74491e8i	0.315314	−	0.315314i	−0.531650	−	0.846964i	$-0.678428\pi$
$821$	1.74491e8	−	1.74491e8i	0.315314	−	0.315314i	0.846964	+	0.531650i	$0.178428\pi$
$822$	2.68004e8	−	7.76833e8i	0.482531	−	1.39866i
$823$			9.63324e8i			1.72812i	0.503392	+	0.864058i	$0.332085\pi$
$823$			9.63324e8i			1.72812i	−0.503392	+	0.864058i	$0.667915\pi$
$824$	3.05375e8	−	3.51281e8i	0.545824	−	0.627875i
$825$	−6.58194e8	−	2.44351e8i	−1.17217	−	0.435163i
$826$	−6.24467e6	+	145308.i	−0.0110808	+	0.000257839i
$827$	−4.26277e8	+	4.26277e8i	−0.753659	+	0.753659i	−0.975160	−	0.221501i	$-0.928904\pi$
$827$	−4.26277e8	+	4.26277e8i	−0.753659	+	0.753659i	0.221501	+	0.975160i	$0.428904\pi$
$828$	−4.62934e7	−	3.62574e7i	−0.0815508	−	0.0638713i
$829$	−2.43456e8	+	2.43456e8i	−0.427323	+	0.427323i	−0.887716	−	0.460392i	$-0.847709\pi$
$829$	−2.43456e8	+	2.43456e8i	−0.427323	+	0.427323i	0.460392	+	0.887716i	$0.347709\pi$
$830$	2.04712e8	−	2.14466e8i	0.358021	−	0.375080i
$831$	−1.90194e8	−	7.06084e7i	−0.331431	−	0.123042i
$832$	−7.99056e8	−	6.02178e8i	−1.38742	−	1.04557i
$833$			5.13623e8i			0.888607i
$834$	−2.12057e8	+	1.03271e8i	−0.365557	+	0.178024i
$835$	2.16340e8	−	2.16340e8i	0.371601	−	0.371601i
$836$	−9.33164e7	+	4.34513e6i	−0.159713	+	0.00743676i
$837$	−2.29391e8	+	7.94664e8i	−0.391200	+	1.35521i
$838$	−2.52709e8	+	5.88030e6i	−0.429426	+	0.00999235i
$839$	8.75681e7			0.148272			0.0741361	−	0.997248i	$-0.476380\pi$
$839$	8.75681e7			0.148272			0.0741361	+	0.997248i	$0.476380\pi$
$840$	2.91437e6	+	5.33828e6i	0.00491707	+	0.00900665i
$841$			2.10014e8i			0.353069i
$842$	−3.07138e8	+	7.14682e6i	−0.514514	+	0.0119723i
$843$	1.00243e9	−	4.59644e8i	1.67329	−	0.767253i
$844$	4.55019e8	+	4.14530e8i	0.756837	+	0.689491i
$845$	−3.45937e8	−	3.45937e8i	−0.573359	−	0.573359i
$846$	−7.61841e8	+	7.46810e7i	−1.25821	+	0.123339i
$847$	−1.89830e7			−0.0312402
$848$	−1.92467e8	+	2.32091e8i	−0.315624	+	0.380602i
$849$	−5.19040e8	−	1.92691e8i	−0.848160	−	0.314875i
$850$	3.16179e8	−	3.31244e8i	0.514845	−	0.539376i
$851$	−3.62284e6	−	3.62284e6i	−0.00587842	−	0.00587842i
$852$	2.35682e8	+	4.56650e8i	0.381073	+	0.738354i
$853$	−3.61419e8	−	3.61419e8i	−0.582323	−	0.582323i	0.353218	−	0.935541i	$-0.385087\pi$
$853$	−3.61419e8	−	3.61419e8i	−0.582323	−	0.582323i	−0.935541	+	0.353218i	$0.885087\pi$
$854$	−2.43731e7	+	567140.i	−0.0391325	+	0.000910578i
$855$	−2.04046e7	−	1.75720e7i	−0.0326461	−	0.0281141i
$856$	7.86167e8	−	5.49595e7i	1.25341	−	0.0876237i
$857$	−9.86616e7			−0.156749			−0.0783747	−	0.996924i	$-0.524973\pi$
$857$	−9.86616e7			−0.156749			−0.0783747	+	0.996924i	$0.524973\pi$
$858$	1.54668e9	+	5.33598e8i	2.44872	+	0.844797i
$859$	1.49790e8	+	1.49790e8i	0.236322	+	0.236322i	0.815325	−	0.579003i	$-0.196558\pi$
$859$	1.49790e8	+	1.49790e8i	0.236322	+	0.236322i	−0.579003	+	0.815325i	$0.696558\pi$
$860$	767645.	+	1.64860e7i	0.00120688	+	0.0259191i
$861$	2.89882e6	+	6.32199e6i	0.00454163	+	0.00990477i
$862$	−6.18297e8	−	5.90177e8i	−0.965329	−	0.921426i
$863$		−	1.10334e9i		−	1.71663i	−0.513123	−	0.858315i	$-0.671512\pi$
$863$		−	1.10334e9i		−	1.71663i	0.513123	−	0.858315i	$-0.328488\pi$
$864$	3.75118e8	+	5.24667e8i	0.581603	+	0.813472i
$865$	−7.57137e7			−0.116984
$866$	−4.20259e8	+	4.40284e8i	−0.647089	+	0.677920i
$867$	−1.24018e8	+	5.68660e7i	−0.190296	+	0.0872561i
$868$	−2.35341e7	+	1.09583e6i	−0.0359864	+	0.00167565i
$869$	5.64376e8	−	5.64376e8i	0.860021	−	0.860021i
$870$	1.00369e8	−	2.90928e8i	0.152420	−	0.441802i
$871$			3.44714e7i			0.0521680i
$872$	2.35092e8	−	1.64348e7i	0.354558	−	0.0247865i
$873$	−7.03869e8	+	8.17332e8i	−1.05791	+	1.22845i
$874$	172512.	+	7.41378e6i	0.000258395	+	0.0111047i
$875$	8.93715e6	−	8.93715e6i	0.0133406	−	0.0133406i
$876$	−8.64534e8	+	4.46196e8i	−1.28609	+	0.663764i
$877$	2.42919e8	−	2.42919e8i	0.360132	−	0.360132i	−0.503729	−	0.863862i	$-0.668039\pi$
$877$	2.42919e8	−	2.42919e8i	0.360132	−	0.360132i	0.863862	+	0.503729i	$0.168039\pi$
$878$	1.87817e8	+	1.79275e8i	0.277492	+	0.264872i
$879$	2.44039e8	−	6.57353e8i	0.359329	−	0.967903i
$880$	3.79365e7	+	4.06481e8i	0.0556685	+	0.596475i
$881$		−	2.63420e8i		−	0.385231i	−0.981274	−	0.192615i	$-0.938303\pi$
$881$		−	2.63420e8i		−	0.385231i	0.981274	−	0.192615i	$-0.0616969\pi$
$882$	6.68947e7	+	6.82411e8i	0.0974958	+	0.994581i
$883$	−4.37308e8	+	4.37308e8i	−0.635193	+	0.635193i	−0.949366	−	0.314173i	$-0.898273\pi$
$883$	−4.37308e8	+	4.37308e8i	−0.635193	+	0.635193i	0.314173	+	0.949366i	$0.398273\pi$
$884$	−7.18666e8	+	7.88861e8i	−1.04033	+	1.14194i
$885$	−5.03746e7	−	1.09861e8i	−0.0726745	−	0.158495i
$886$	2.58585e7	+	1.11128e9i	0.0371794	+	1.59780i
$887$	−3.07538e8			−0.440685			−0.220342	−	0.975423i	$-0.570717\pi$
$887$	−3.07538e8			−0.440685			−0.220342	+	0.975423i	$0.570717\pi$
$888$	2.69284e7	+	4.93250e7i	0.0384566	+	0.0704415i
$889$		−	8.52270e6i		−	0.0121303i
$890$	1.06287e7	+	4.56772e8i	0.0150768	+	0.647932i
$891$	−8.48156e8	−	6.26885e8i	−1.19906	−	0.886246i
$892$	−3.01508e7	−	6.47521e8i	−0.0424819	−	0.912345i
$893$	6.82639e7	+	6.82639e7i	0.0958598	+	0.0958598i
$894$	4.89770e8	+	1.00570e9i	0.685456	+	1.40752i
$895$	−3.78810e8			−0.528387
$896$	−1.07125e7	+	1.49250e7i	−0.0148925	+	0.0207487i
$897$	4.52035e7	−	1.21762e8i	0.0626318	−	0.168708i
$898$	3.60538e8	+	3.44140e8i	0.497876	+	0.475233i
$899$	8.42968e8	+	8.42968e8i	1.16020	+	1.16020i
$900$	3.76941e8	−	4.81277e8i	0.517066	−	0.660189i
$901$	2.27390e8	+	2.27390e8i	0.310882	+	0.310882i
$902$	1.08600e7	+	4.66714e8i	0.0147982	+	0.635961i
$903$	422680.	−	1.13855e6i	0.000574048	−	0.00154628i
$904$	4.34393e8	−	4.99693e8i	0.588000	−	0.676392i
$905$	−3.05775e8			−0.412531
$906$	9.84982e8	+	3.39814e8i	1.32447	+	0.456937i
$907$	3.89980e8	+	3.89980e8i	0.522662	+	0.522662i	0.918374	−	0.395713i	$-0.129502\pi$
$907$	3.89980e8	+	3.89980e8i	0.522662	+	0.522662i	−0.395713	+	0.918374i	$0.629502\pi$
$908$	−8.18459e8	+	8.98402e8i	−1.09330	+	1.20009i
$909$	4.51318e7	+	6.05084e8i	0.0600885	+	0.805608i
$910$	−9.27568e6	+	9.71764e6i	−0.0123090	+	0.0128955i
$911$		−	9.80416e8i		−	1.29675i	−0.761322	−	0.648373i	$-0.775450\pi$
$911$		−	9.80416e8i		−	1.29675i	0.761322	−	0.648373i	$-0.224550\pi$
$912$	2.11008e7	−	7.85557e7i	0.0278172	−	0.103560i
$913$	−1.46447e9			−1.92428
$914$	−1.43161e8	−	1.36650e8i	−0.187494	−	0.178967i
$915$	−1.96614e8	−	4.28792e8i	−0.256655	−	0.559736i
$916$	1.96353e7	−	2.15531e7i	0.0255476	−	0.0280430i
$917$	9.14450e6	−	9.14450e6i	0.0118591	−	0.0118591i
$918$	5.94339e8	−	3.46351e8i	0.768256	−	0.447701i
$919$			4.53857e6i			0.00584753i	0.999996	+	0.00292376i	$0.000930664\pi$
$919$			4.53857e6i			0.00584753i	−0.999996	+	0.00292376i	$0.999069\pi$
$920$	3.23291e7	−	2.26007e6i	0.0415174	−	0.00290241i
$921$	−5.21590e8	+	1.40498e9i	−0.667653	+	1.79842i
$922$	−1.16361e9	+	2.70762e7i	−1.48462	+	0.0345458i
$923$	−8.02612e8	+	8.02612e8i	−1.02071	+	1.02071i
$924$	9.13429e6	−	2.86194e7i	0.0115787	−	0.0362782i
$925$	3.76639e7	−	3.76639e7i	0.0475883	−	0.0475883i
$926$	1.34569e7	−	1.40981e7i	0.0169478	−	0.0177553i
$927$	−5.02183e8	−	4.32469e8i	−0.630409	−	0.542895i
$928$	9.23334e8	−	1.07893e8i	1.15535	−	0.135005i
$929$		−	3.05914e7i		−	0.0381551i	−0.999818	−	0.0190775i	$-0.993927\pi$
$929$		−	3.05914e7i		−	0.0381551i	0.999818	−	0.0190775i	$-0.00607294\pi$
$930$	−1.99588e8	−	4.09835e8i	−0.248133	−	0.509519i
$931$	6.11466e7	−	6.11466e7i	0.0757745	−	0.0757745i
$932$	6.75654e6	+	1.45104e8i	0.00834596	+	0.179239i
$933$	1.40762e9	−	6.45433e8i	1.73316	−	0.794706i
$934$	−4.06842e8	+	9.46685e6i	−0.499328	+	0.0116189i
$935$	4.35415e8			0.532682
$936$	−8.52093e8	+	1.14170e9i	−1.03910	+	1.39227i
$937$		−	1.16948e8i		−	0.142159i	−0.997471	−	0.0710796i	$-0.977356\pi$
$937$		−	1.16948e8i		−	0.142159i	0.997471	−	0.0710796i	$-0.0226444\pi$
$938$	632770.	−	14724.0i	0.000766722	−	1.78409e-5i
$939$	4.70489e7	+	1.02608e8i	0.0568267	+	0.123933i
$940$	2.84124e8	−	3.11875e8i	0.342077	−	0.375489i
$941$	6.71409e8	+	6.71409e8i	0.805784	+	0.805784i	0.983993	−	0.178209i	$-0.0570303\pi$
$941$	6.71409e8	+	6.71409e8i	0.805784	+	0.805784i	−0.178209	+	0.983993i	$0.557030\pi$
$942$	−1.83816e8	−	3.77450e8i	−0.219903	−	0.451551i
$943$	3.70593e7			0.0441938
$944$	2.33041e8	−	2.81018e8i	0.277024	−	0.334055i
$945$	7.58139e6	−	4.18489e6i	0.00898366	−	0.00495894i
$946$	5.62869e7	−	5.89688e7i	0.0664866	−	0.0696545i
$947$	−4.07175e8	−	4.07175e8i	−0.479437	−	0.479437i	0.425514	−	0.904952i	$-0.360093\pi$
$947$	−4.07175e8	−	4.07175e8i	−0.479437	−	0.479437i	−0.904952	+	0.425514i	$0.860093\pi$
$948$	3.18731e8	+	6.17562e8i	0.374110	+	0.724862i
$949$	−1.51951e9	−	1.51951e9i	−1.77789	−	1.77789i
$950$	−7.70754e7	+	1.79347e6i	−0.0898970	+	0.00209182i
$951$	−6.05388e8	−	2.24747e8i	−0.703869	−	0.261308i
$952$	1.47876e7	+	1.28552e7i	0.0171391	+	0.0148993i
$953$	7.19944e8			0.831803			0.415901	−	0.909410i	$-0.363466\pi$
$953$	7.19944e8			0.831803			0.415901	+	0.909410i	$0.363466\pi$
$954$	3.31730e8	+	2.72499e8i	0.382067	+	0.313848i
$955$	1.30332e8	+	1.30332e8i	0.149637	+	0.149637i
$956$	−1.01410e8	+	4.72198e6i	−0.116066	+	0.00540444i
$957$	−1.38180e9	+	6.33597e8i	−1.57656	+	0.722899i
$958$	−6.76517e8	−	6.45749e8i	−0.769453	−	0.734458i
$959$		−	3.33280e7i		−	0.0377879i
$960$	−3.47217e8	−	7.61455e7i	−0.392453	−	0.0860658i
$961$	8.78308e8			0.989638
$962$	−8.57062e7	+	8.97898e7i	−0.0962691	+	0.100856i
$963$	−8.34630e7	−	1.11899e9i	−0.0934577	−	1.25299i
$964$	5.56287e7	+	1.19469e9i	0.0620966	+	1.33359i
$965$	9.67738e7	−	9.67738e7i	0.107690	−	0.107690i
$966$	−2.25442e6	−	777765.i	−0.00250094	−	0.000862813i
$967$		−	1.15788e9i		−	1.28052i	−0.768159	−	0.640259i	$-0.778827\pi$
$967$		−	1.15788e9i		−	1.28052i	0.768159	−	0.640259i	$-0.221173\pi$
$968$	7.27899e8	−	8.37321e8i	0.802500	−	0.923136i
$969$	−8.13296e7	−	3.01932e7i	−0.0893876	−	0.0331846i
$970$	−1.38292e7	−	5.94317e8i	−0.0151524	−	0.651183i
$971$	5.23797e8	−	5.23797e8i	0.572143	−	0.572143i	−0.360583	−	0.932727i	$-0.617422\pi$
$971$	5.23797e8	−	5.23797e8i	0.572143	−	0.572143i	0.932727	+	0.360583i	$0.117422\pi$
$972$	7.44542e8	−	5.37576e8i	0.810756	−	0.585384i
$973$	−6.76415e6	+	6.76415e6i	−0.00734302	+	0.00734302i
$974$	−4.59392e8	−	4.38499e8i	−0.497172	−	0.474561i
$975$	1.26587e9	+	4.69947e8i	1.36576	+	0.507031i
$976$	9.09567e8	−	1.09682e9i	0.978329	−	1.17974i
$977$			1.40698e9i			1.50871i	0.656469	+	0.754353i	$0.272049\pi$
$977$			1.40698e9i			1.50871i	−0.656469	+	0.754353i	$0.727951\pi$
$978$	5.12476e8	+	1.05233e9i	0.547844	+	1.12495i
$979$	1.59581e9	−	1.59581e9i	1.70072	−	1.70072i
$980$	−2.79359e8	−	2.54500e8i	−0.296814	−	0.270402i
$981$	−2.49584e7	−	3.34617e8i	−0.0264368	−	0.354439i
$982$	−2.65957e6	−	1.14296e8i	−0.00280852	−	0.120697i
$983$	1.39123e8			0.146466			0.0732331	−	0.997315i	$-0.476668\pi$
$983$	1.39123e8			0.146466			0.0732331	+	0.997315i	$0.476668\pi$
$984$	−3.90011e8	−	1.14552e8i	−0.409347	−	0.120231i
$985$		−	9.81713e7i		−	0.102725i
$986$	−2.30646e7	−	9.91211e8i	−0.0240611	−	1.03404i
$987$	−2.82206e7	+	1.29400e7i	−0.0293504	+	0.0134580i
$988$	1.79470e8	−	8.35674e6i	0.186089	−	0.00866495i
$989$	−4.57593e6	−	4.57593e6i	−0.00473032	−	0.00473032i
$990$	5.78501e8	−	5.67087e7i	0.596209	−	0.0584446i
$991$	5.68730e8			0.584366			0.292183	−	0.956362i	$-0.405618\pi$
$991$	5.68730e8			0.584366			0.292183	+	0.956362i	$0.405618\pi$
$992$	8.54074e8	−	1.08008e9i	0.874904	−	1.10643i
$993$	1.70367e9	+	6.32479e8i	1.73996	+	0.645950i
$994$	1.50759e7	+	1.43902e7i	0.0153505	+	0.0146524i
$995$	2.10045e8	+	2.10045e8i	0.213228	+	0.213228i
$996$	3.87710e8	−	1.21477e9i	0.392400	−	1.22946i
$997$	8.13194e8	+	8.13194e8i	0.820557	+	0.820557i	0.986188	−	0.165631i	$-0.0529660\pi$
$997$	8.13194e8	+	8.13194e8i	0.820557	+	0.820557i	−0.165631	+	0.986188i	$0.552966\pi$
$998$	1.75566e7	+	7.54503e8i	0.0176624	+	0.759048i
$999$	7.00511e7	−	3.86679e7i	0.0702617	−	0.0387841i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.i.a.5.12	✓	92
3.2	odd	2	inner	48.7.i.a.5.35	yes	92
4.3	odd	2		192.7.i.a.113.39		92
12.11	even	2		192.7.i.a.113.31		92
16.3	odd	4		192.7.i.a.17.31		92
16.13	even	4	inner	48.7.i.a.29.35	yes	92
48.29	odd	4	inner	48.7.i.a.29.12	yes	92
48.35	even	4		192.7.i.a.17.39		92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.i.a.5.12	✓	92	1.1	even	1	trivial
48.7.i.a.5.35	yes	92	3.2	odd	2	inner
48.7.i.a.29.12	yes	92	48.29	odd	4	inner
48.7.i.a.29.35	yes	92	16.13	even	4	inner
192.7.i.a.17.31		92	16.3	odd	4
192.7.i.a.17.39		92	48.35	even	4
192.7.i.a.113.31		92	12.11	even	2
192.7.i.a.113.39		92	4.3	odd	2

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	48.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.52373 + 5.78692i) q^{2} +(-24.5429 + 11.2536i) q^{3} +(-2.97683 - 63.9307i) q^{4} +(35.5126 - 35.5126i) q^{5} +(70.4446 - 204.190i) q^{6} -8.76023i q^{7} +(386.405 + 335.909i) q^{8} +(475.711 - 552.395i) q^{9} +O(q^{10})\)	\(q+(-5.52373 + 5.78692i) q^{2} +(-24.5429 + 11.2536i) q^{3} +(-2.97683 - 63.9307i) q^{4} +(35.5126 - 35.5126i) q^{5} +(70.4446 - 204.190i) q^{6} -8.76023i q^{7} +(386.405 + 335.909i) q^{8} +(475.711 - 552.395i) q^{9} +(9.34650 + 401.670i) q^{10} +(1403.30 - 1403.30i) q^{11} +(792.514 + 1535.55i) q^{12} +(-2698.89 + 2698.89i) q^{13} +(50.6947 + 48.3891i) q^{14} +(-471.937 + 1271.23i) q^{15} +(-4078.28 + 380.622i) q^{16} +4368.58i q^{17} +(568.966 + 5804.18i) q^{18} +(520.076 - 520.076i) q^{19} +(-2376.06 - 2164.63i) q^{20} +(98.5846 + 215.002i) q^{21} +(369.333 + 15872.3i) q^{22} +1260.33 q^{23} +(-13263.7 - 3895.73i) q^{24} +13102.7i q^{25} +(-710.317 - 30526.2i) q^{26} +(-5458.88 + 18910.9i) q^{27} +(-560.048 + 26.0777i) q^{28} +(20060.4 + 20060.4i) q^{29} +(-4749.65 - 9752.98i) q^{30} +42021.6 q^{31} +(20324.7 - 25703.1i) q^{32} +(-18648.9 + 50233.4i) q^{33} +(-25280.6 - 24130.8i) q^{34} +(-311.098 - 311.098i) q^{35} +(-36731.1 - 28768.2i) q^{36} +(-2874.51 - 2874.51i) q^{37} +(136.878 + 5882.40i) q^{38} +(35866.4 - 96611.1i) q^{39} +(25651.2 - 1793.23i) q^{40} +29404.4 q^{41} +(-1788.75 - 617.111i) q^{42} +(-3630.73 - 3630.73i) q^{43} +(-93891.5 - 85536.7i) q^{44} +(-2723.25 - 36510.7i) q^{45} +(-6961.73 + 7293.44i) q^{46} +131257. i q^{47} +(95809.5 - 55237.1i) q^{48} +117572. q^{49} +(-75824.3 - 72375.8i) q^{50} +(-49162.4 - 107218. i) q^{51} +(180576. + 164508. i) q^{52} +(52051.2 - 52051.2i) q^{53} +(-79282.3 - 136049. i) q^{54} -99669.7i q^{55} +(2942.64 - 3385.00i) q^{56} +(-6911.44 + 18617.0i) q^{57} +(-226896. + 5279.66i) q^{58} +(-63024.1 + 63024.1i) q^{59} +(82675.5 + 26387.0i) q^{60} +(-245985. + 245985. i) q^{61} +(-232116. + 243175. i) q^{62} +(-4839.11 - 4167.34i) q^{63} +(36473.8 + 259594. i) q^{64} +191689. i q^{65} +(-187685. - 385395. i) q^{66} +(6386.21 - 6386.21i) q^{67} +(279286. - 13004.5i) q^{68} +(-30932.2 + 14183.3i) q^{69} +(3518.72 - 81.8775i) q^{70} +297386. q^{71} +(369372. - 53652.5i) q^{72} +563014. i q^{73} +(32512.6 - 756.538i) q^{74} +(-147453. - 321579. i) q^{75} +(-34797.0 - 31700.7i) q^{76} +(-12293.2 - 12293.2i) q^{77} +(360965. + 741209. i) q^{78} +402177. q^{79} +(-131313. + 158347. i) q^{80} +(-78839.4 - 525561. i) q^{81} +(-162422. + 170161. i) q^{82} +(-521793. - 521793. i) q^{83} +(13451.7 - 6942.61i) q^{84} +(155139. + 155139. i) q^{85} +(41065.9 - 955.566i) q^{86} +(-718093. - 266588. i) q^{87} +(1.01363e6 - 70860.7i) q^{88} +1.13718e6 q^{89} +(226327. + 185916. i) q^{90} +(23642.9 + 23642.9i) q^{91} +(-3751.80 - 80574.0i) q^{92} +(-1.03133e6 + 472896. i) q^{93} +(-759576. - 725030. i) q^{94} -36938.5i q^{95} +(-209573. + 859556. i) q^{96} -1.47962e6 q^{97} +(-649437. + 680381. i) q^{98} +(-107611. - 1.44274e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6}+O(q^{10}) \) 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6	\( 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6} + 1496 q^{10} + 4288 q^{12} - 4 q^{13} - 4 q^{15} + 10352 q^{16} + 10020 q^{18} - 3940 q^{19} + 1456 q^{21} - 42088 q^{22} + 66376 q^{24} - 34322 q^{27} + 27000 q^{28} - 127836 q^{30} - 8 q^{31} - 4 q^{33} + 128424 q^{34} + 172420 q^{36} - 4 q^{37} - 164392 q^{40} + 221560 q^{42} - 195268 q^{43} - 31252 q^{45} + 150712 q^{46} - 188048 q^{48} - 1142884 q^{49} + 385056 q^{51} - 122368 q^{52} + 151912 q^{54} - 181960 q^{58} + 242304 q^{60} - 326500 q^{61} + 470592 q^{63} - 251752 q^{64} + 489172 q^{66} + 1207676 q^{67} - 1460 q^{69} + 346392 q^{70} - 903480 q^{72} + 1413778 q^{75} - 359992 q^{76} + 1478252 q^{78} + 860920 q^{79} - 4 q^{81} - 2412800 q^{82} - 730640 q^{84} + 434496 q^{85} + 1259360 q^{88} - 291792 q^{90} + 2320992 q^{91} - 1176260 q^{93} - 1412496 q^{94} + 1956200 q^{96} - 8 q^{97} - 4048228 q^{99}+O(q^{100}) \) 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6 + 1496 * q^10 + 4288 * q^12 - 4 * q^13 - 4 * q^15 + 10352 * q^16 + 10020 * q^18 - 3940 * q^19 + 1456 * q^21 - 42088 * q^22 + 66376 * q^24 - 34322 * q^27 + 27000 * q^28 - 127836 * q^30 - 8 * q^31 - 4 * q^33 + 128424 * q^34 + 172420 * q^36 - 4 * q^37 - 164392 * q^40 + 221560 * q^42 - 195268 * q^43 - 31252 * q^45 + 150712 * q^46 - 188048 * q^48 - 1142884 * q^49 + 385056 * q^51 - 122368 * q^52 + 151912 * q^54 - 181960 * q^58 + 242304 * q^60 - 326500 * q^61 + 470592 * q^63 - 251752 * q^64 + 489172 * q^66 + 1207676 * q^67 - 1460 * q^69 + 346392 * q^70 - 903480 * q^72 + 1413778 * q^75 - 359992 * q^76 + 1478252 * q^78 + 860920 * q^79 - 4 * q^81 - 2412800 * q^82 - 730640 * q^84 + 434496 * q^85 + 1259360 * q^88 - 291792 * q^90 + 2320992 * q^91 - 1176260 * q^93 - 1412496 * q^94 + 1956200 * q^96 - 8 * q^97 - 4048228 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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