LMFDB - Embedded newform 38.8.c.b.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,8,Mod(7,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("38.7");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	38.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.8706309684$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 9740 x^{12} + 37173 x^{11} + 71393485 x^{10} + 196352446 x^{9} + 218671355941 x^{8} + \cdots + 66\!\cdots\!81 $ x^14 - x^13 + 9740x^12 + 37173x^11 + 71393485x^10 + 196352446x^9 + 218671355941x^8 - 33116965187x^7 + 501909199155445x^6 + 488917878843726x^5 + 115037439673768301x^4 + 1132246613431747493x^3 + 24536677825193566084x^2 + 126800218755690130647x + 666410398757822143881
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.2
Root			$28.5226 + 49.4026i$ of defining polynomial
Character	$\chi$	$=$	38.11
Dual form			38.8.c.b.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.00000 - 6.92820i) q^{2} +(-24.5226 + 42.4744i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(81.5095 - 141.179i) q^{5} +(196.181 + 339.795i) q^{6} -230.715 q^{7} -512.000 q^{8} +(-109.217 - 189.169i) q^{9} +O(q^{10})$	\(q+(4.00000 - 6.92820i) q^{2} +(-24.5226 + 42.4744i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(81.5095 - 141.179i) q^{5} +(196.181 + 339.795i) q^{6} -230.715 q^{7} -512.000 q^{8} +(-109.217 - 189.169i) q^{9} +(-652.076 - 1129.43i) q^{10} +7729.81 q^{11} +3138.89 q^{12} +(6132.77 + 10622.3i) q^{13} +(-922.858 + 1598.44i) q^{14} +(3997.65 + 6924.13i) q^{15} +(-2048.00 + 3547.24i) q^{16} +(9689.69 - 16783.0i) q^{17} -1747.47 q^{18} +(29279.7 + 6047.52i) q^{19} -10433.2 q^{20} +(5657.72 - 9799.47i) q^{21} +(30919.2 - 53553.7i) q^{22} +(-35215.8 - 60995.6i) q^{23} +(12555.6 - 21746.9i) q^{24} +(25774.9 + 44643.5i) q^{25} +98124.3 q^{26} -96548.8 q^{27} +(7382.87 + 12787.5i) q^{28} +(61059.0 + 105757. i) q^{29} +63962.4 q^{30} +26721.5 q^{31} +(16384.0 + 28377.9i) q^{32} +(-189555. + 328319. i) q^{33} +(-77517.6 - 134264. i) q^{34} +(-18805.4 + 32571.9i) q^{35} +(-6989.89 + 12106.8i) q^{36} +239066. q^{37} +(159017. - 178665. i) q^{38} -601566. q^{39} +(-41732.8 + 72283.4i) q^{40} +(-8691.35 + 15053.9i) q^{41} +(-45261.8 - 78395.7i) q^{42} +(-149564. + 259053. i) q^{43} +(-247354. - 428430. i) q^{44} -35608.9 q^{45} -563454. q^{46} +(-440470. - 762916. i) q^{47} +(-100445. - 173975. i) q^{48} -770314. q^{49} +412399. q^{50} +(475233. + 823128. i) q^{51} +(392497. - 679825. i) q^{52} +(-140441. - 243252. i) q^{53} +(-386195. + 668909. i) q^{54} +(630053. - 1.09128e6i) q^{55} +118126. q^{56} +(-974879. + 1.09534e6i) q^{57} +976945. q^{58} +(-160296. + 277641. i) q^{59} +(255850. - 443144. i) q^{60} +(1.38359e6 + 2.39645e6i) q^{61} +(106886. - 185132. i) q^{62} +(25198.0 + 43644.1i) q^{63} +262144. q^{64} +1.99951e6 q^{65} +(1.51644e6 + 2.62655e6i) q^{66} +(-736714. - 1.27603e6i) q^{67} -1.24028e6 q^{68} +3.45434e6 q^{69} +(150443. + 260576. i) q^{70} +(1.23505e6 - 2.13917e6i) q^{71} +(55919.1 + 96854.7i) q^{72} +(2.05033e6 - 3.55128e6i) q^{73} +(956265. - 1.65630e6i) q^{74} -2.52827e6 q^{75} +(-601762. - 1.81636e6i) q^{76} -1.78338e6 q^{77} +(-2.40626e6 + 4.16777e6i) q^{78} +(-2.59078e6 + 4.48736e6i) q^{79} +(333863. + 578267. i) q^{80} +(2.60649e6 - 4.51457e6i) q^{81} +(69530.8 + 120431. i) q^{82} +7.24258e6 q^{83} -724189. q^{84} +(-1.57960e6 - 2.73595e6i) q^{85} +(1.19651e6 + 2.07242e6i) q^{86} -5.98931e6 q^{87} -3.95766e6 q^{88} +(2.52576e6 + 4.37475e6i) q^{89} +(-142436. + 246706. i) q^{90} +(-1.41492e6 - 2.45071e6i) q^{91} +(-2.25381e6 + 3.90372e6i) q^{92} +(-655281. + 1.13498e6i) q^{93} -7.04752e6 q^{94} +(3.24035e6 - 3.64073e6i) q^{95} -1.60711e6 q^{96} +(1.60831e6 - 2.78568e6i) q^{97} +(-3.08126e6 + 5.33689e6i) q^{98} +(-844227. - 1.46224e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 56 q^{2} + 55 q^{3} - 448 q^{4} - 126 q^{5} - 440 q^{6} + 1928 q^{7} - 7168 q^{8} - 4602 q^{9}+O(q^{10}) $ 14 * q + 56 * q^2 + 55 * q^3 - 448 * q^4 - 126 * q^5 - 440 * q^6 + 1928 * q^7 - 7168 * q^8 - 4602 * q^9	\( 14 q + 56 q^{2} + 55 q^{3} - 448 q^{4} - 126 q^{5} - 440 q^{6} + 1928 q^{7} - 7168 q^{8} - 4602 q^{9} + 1008 q^{10} + 646 q^{11} - 7040 q^{12} - 1308 q^{13} + 7712 q^{14} + 8740 q^{15} - 28672 q^{16} + 10528 q^{17} - 73632 q^{18} - 87463 q^{19} + 16128 q^{20} - 30584 q^{21} + 2584 q^{22} - 113822 q^{23} - 28160 q^{24} - 50143 q^{25} - 20928 q^{26} - 319898 q^{27} - 61696 q^{28} + 167706 q^{29} + 139840 q^{30} + 201780 q^{31} + 229376 q^{32} + 377473 q^{33} - 84224 q^{34} - 33168 q^{35} - 294528 q^{36} + 380924 q^{37} - 384064 q^{38} + 1379564 q^{39} + 64512 q^{40} + 66301 q^{41} + 244672 q^{42} + 726564 q^{43} - 20672 q^{44} + 428936 q^{45} - 1821152 q^{46} - 2373788 q^{47} + 225280 q^{48} + 5898846 q^{49} - 802288 q^{50} + 3264054 q^{51} - 83712 q^{52} + 161792 q^{53} - 1279592 q^{54} - 53424 q^{55} - 987136 q^{56} - 4487994 q^{57} + 2683296 q^{58} - 1845767 q^{59} + 559360 q^{60} - 1600418 q^{61} + 807120 q^{62} - 3064040 q^{63} + 3670016 q^{64} + 6534852 q^{65} - 3019784 q^{66} - 8911929 q^{67} - 1347584 q^{68} - 8860208 q^{69} + 265344 q^{70} + 517154 q^{71} + 2356224 q^{72} - 9558049 q^{73} + 1523696 q^{74} - 24621450 q^{75} + 2525120 q^{76} - 9188192 q^{77} + 5518256 q^{78} + 7963520 q^{79} - 516096 q^{80} - 4125855 q^{81} - 530408 q^{82} + 30616886 q^{83} + 3914752 q^{84} + 6973266 q^{85} - 5812512 q^{86} + 25084136 q^{87} - 330752 q^{88} + 11829436 q^{89} + 1715744 q^{90} + 4017336 q^{91} - 7284608 q^{92} + 396810 q^{93} - 37980608 q^{94} + 7058892 q^{95} + 3604480 q^{96} - 8033723 q^{97} + 23595384 q^{98} + 24812606 q^{99}+O(q^{100}) \) 14 * q + 56 * q^2 + 55 * q^3 - 448 * q^4 - 126 * q^5 - 440 * q^6 + 1928 * q^7 - 7168 * q^8 - 4602 * q^9 + 1008 * q^10 + 646 * q^11 - 7040 * q^12 - 1308 * q^13 + 7712 * q^14 + 8740 * q^15 - 28672 * q^16 + 10528 * q^17 - 73632 * q^18 - 87463 * q^19 + 16128 * q^20 - 30584 * q^21 + 2584 * q^22 - 113822 * q^23 - 28160 * q^24 - 50143 * q^25 - 20928 * q^26 - 319898 * q^27 - 61696 * q^28 + 167706 * q^29 + 139840 * q^30 + 201780 * q^31 + 229376 * q^32 + 377473 * q^33 - 84224 * q^34 - 33168 * q^35 - 294528 * q^36 + 380924 * q^37 - 384064 * q^38 + 1379564 * q^39 + 64512 * q^40 + 66301 * q^41 + 244672 * q^42 + 726564 * q^43 - 20672 * q^44 + 428936 * q^45 - 1821152 * q^46 - 2373788 * q^47 + 225280 * q^48 + 5898846 * q^49 - 802288 * q^50 + 3264054 * q^51 - 83712 * q^52 + 161792 * q^53 - 1279592 * q^54 - 53424 * q^55 - 987136 * q^56 - 4487994 * q^57 + 2683296 * q^58 - 1845767 * q^59 + 559360 * q^60 - 1600418 * q^61 + 807120 * q^62 - 3064040 * q^63 + 3670016 * q^64 + 6534852 * q^65 - 3019784 * q^66 - 8911929 * q^67 - 1347584 * q^68 - 8860208 * q^69 + 265344 * q^70 + 517154 * q^71 + 2356224 * q^72 - 9558049 * q^73 + 1523696 * q^74 - 24621450 * q^75 + 2525120 * q^76 - 9188192 * q^77 + 5518256 * q^78 + 7963520 * q^79 - 516096 * q^80 - 4125855 * q^81 - 530408 * q^82 + 30616886 * q^83 + 3914752 * q^84 + 6973266 * q^85 - 5812512 * q^86 + 25084136 * q^87 - 330752 * q^88 + 11829436 * q^89 + 1715744 * q^90 + 4017336 * q^91 - 7284608 * q^92 + 396810 * q^93 - 37980608 * q^94 + 7058892 * q^95 + 3604480 * q^96 - 8033723 * q^97 + 23595384 * q^98 + 24812606 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	4.00000	−	6.92820i	0.353553	−	0.612372i
$2$	4.00000	−	6.92820i	0.353553	−	0.612372i
$3$	−24.5226	+	42.4744i	−0.524375	+	0.908245i	0.475222	+	0.879866i	$0.342368\pi$
$3$	−24.5226	+	42.4744i	−0.524375	+	0.908245i	−0.999597	+	0.0283789i	$0.990966\pi$
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	81.5095	−	141.179i	0.291617	−	0.505096i	−0.682575	−	0.730815i	$-0.739140\pi$
$5$	81.5095	−	141.179i	0.291617	−	0.505096i	0.974192	+	0.225720i	$0.0724734\pi$
$6$	196.181	+	339.795i	0.370789	+	0.642226i
$7$	−230.715			−0.254233			−0.127117	−	0.991888i	$-0.540572\pi$
$7$	−230.715			−0.254233			−0.127117	+	0.991888i	$0.540572\pi$
$8$	−512.000			−0.353553
$9$	−109.217	−	189.169i	−0.0499392	−	0.0864972i
$10$	−652.076	−	1129.43i	−0.206204	−	0.357157i
$11$	7729.81			1.75103			0.875517	−	0.483188i	$-0.160521\pi$
$11$	7729.81			1.75103			0.875517	+	0.483188i	$0.160521\pi$
$12$	3138.89			0.524375
$13$	6132.77	+	10622.3i	0.774203	+	1.34096i	0.935241	+	0.354011i	$0.115182\pi$
$13$	6132.77	+	10622.3i	0.774203	+	1.34096i	−0.161038	+	0.986948i	$0.551484\pi$
$14$	−922.858	+	1598.44i	−0.0898849	+	0.155685i
$15$	3997.65	+	6924.13i	0.305834	+	0.529719i
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	9689.69	−	16783.0i	0.478342	−	0.828513i	−0.521349	−	0.853343i	$-0.674571\pi$
$17$	9689.69	−	16783.0i	0.478342	−	0.828513i	0.999692	+	0.0248301i	$0.00790447\pi$
$18$	−1747.47			−0.0706247
$19$	29279.7	+	6047.52i	0.979329	+	0.202274i
$19$	29279.7	+	6047.52i	0.979329	+	0.202274i
$20$	−10433.2			−0.291617
$21$	5657.72	−	9799.47i	0.133314	−	0.230906i
$22$	30919.2	−	53553.7i	0.619084	−	1.07228i
$23$	−35215.8	−	60995.6i	−0.603519	−	1.04532i	−0.992284	−	0.123988i	$-0.960432\pi$
$23$	−35215.8	−	60995.6i	−0.603519	−	1.04532i	0.388765	−	0.921337i	$-0.372902\pi$
$24$	12555.6	−	21746.9i	0.185395	−	0.321113i
$25$	25774.9	+	44643.5i	0.329919	+	0.571436i
$26$	98124.3			1.09489
$27$	−96548.8			−0.944003
$28$	7382.87	+	12787.5i	0.0635583	+	0.110086i
$29$	61059.0	+	105757.i	0.464897	+	0.805226i	0.999197	−	0.0400695i	$-0.0127579\pi$
$29$	61059.0	+	105757.i	0.464897	+	0.805226i	−0.534300	+	0.845295i	$0.679425\pi$
$30$	63962.4			0.432514
$31$	26721.5			0.161100			0.0805499	−	0.996751i	$-0.474332\pi$
$31$	26721.5			0.161100			0.0805499	+	0.996751i	$0.474332\pi$
$32$	16384.0	+	28377.9i	0.0883883	+	0.153093i
$33$	−189555.	+	328319.i	−0.918199	+	1.59037i
$34$	−77517.6	−	134264.i	−0.338239	−	0.585847i
$35$	−18805.4	+	32571.9i	−0.0741387	+	0.128412i
$36$	−6989.89	+	12106.8i	−0.0249696	+	0.0432486i
$37$	239066.			0.775912			0.387956	−	0.921678i	$-0.373181\pi$
$37$	239066.			0.775912			0.387956	+	0.921678i	$0.373181\pi$
$38$	159017.	−	178665.i	0.470112	−	0.528200i
$39$	−601566.			−1.62389
$40$	−41732.8	+	72283.4i	−0.103102	+	0.178578i
$41$	−8691.35	+	15053.9i	−0.0196944	+	0.0341118i	−0.875705	−	0.482847i	$-0.839603\pi$
$41$	−8691.35	+	15053.9i	−0.0196944	+	0.0341118i	0.856010	+	0.516959i	$0.172936\pi$
$42$	−45261.8	−	78395.7i	−0.0942669	−	0.163275i
$43$	−149564.	+	259053.i	−0.286872	+	0.496877i	−0.973061	−	0.230546i	$-0.925949\pi$
$43$	−149564.	+	259053.i	−0.286872	+	0.496877i	0.686189	+	0.727423i	$0.259282\pi$
$44$	−247354.	−	428430.i	−0.437758	−	0.758220i
$45$	−35608.9			−0.0582525
$46$	−563454.			−0.853504
$47$	−440470.	−	762916.i	−0.618833	−	1.07185i	−0.989699	−	0.143164i	$-0.954272\pi$
$47$	−440470.	−	762916.i	−0.618833	−	1.07185i	0.370865	−	0.928687i	$-0.379061\pi$
$48$	−100445.	−	173975.i	−0.131094	−	0.227061i
$49$	−770314.			−0.935366
$50$	412399.			0.466576
$51$	475233.	+	823128.i	0.501662	+	0.868904i
$52$	392497.	−	679825.i	0.387102	−	0.670480i
$53$	−140441.	−	243252.i	−0.129577	−	0.224435i	0.793935	−	0.608002i	$-0.208029\pi$
$53$	−140441.	−	243252.i	−0.129577	−	0.224435i	−0.923513	+	0.383567i	$0.874695\pi$
$54$	−386195.	+	668909.i	−0.333756	+	0.578082i
$55$	630053.	−	1.09128e6i	0.510631	−	0.884439i
$56$	118126.			0.0898849
$57$	−974879.	+	1.09534e6i	−0.697250	+	0.783403i
$58$	976945.			0.657464
$59$	−160296.	+	277641.i	−0.101611	+	0.175996i	−0.912349	−	0.409414i	$-0.865733\pi$
$59$	−160296.	+	277641.i	−0.101611	+	0.175996i	0.810737	+	0.585410i	$0.199066\pi$
$60$	255850.	−	443144.i	0.152917	−	0.264860i
$61$	1.38359e6	+	2.39645e6i	0.780464	+	1.35180i	0.931672	+	0.363302i	$0.118351\pi$
$61$	1.38359e6	+	2.39645e6i	0.780464	+	1.35180i	−0.151207	+	0.988502i	$0.548316\pi$
$62$	106886.	−	185132.i	0.0569574	−	0.0986531i
$63$	25198.0	+	43644.1i	0.0126962	+	0.0219904i
$64$	262144.			0.125000
$65$	1.99951e6			0.903084
$66$	1.51644e6	+	2.62655e6i	0.649265	+	1.12456i
$67$	−736714.	−	1.27603e6i	−0.299252	−	0.518320i	0.676713	−	0.736247i	$-0.263404\pi$
$67$	−736714.	−	1.27603e6i	−0.299252	−	0.518320i	−0.975965	+	0.217927i	$0.930070\pi$
$68$	−1.24028e6			−0.478342
$69$	3.45434e6			1.26588
$70$	150443.	+	260576.i	0.0524240	+	0.0908010i
$71$	1.23505e6	−	2.13917e6i	0.409525	−	0.709319i	−0.585311	−	0.810809i	$-0.699028\pi$
$71$	1.23505e6	−	2.13917e6i	0.409525	−	0.709319i	0.994837	+	0.101490i	$0.0323610\pi$
$72$	55919.1	+	96854.7i	0.0176562	+	0.0305814i
$73$	2.05033e6	−	3.55128e6i	0.616871	−	1.06845i	−0.373182	−	0.927758i	$-0.621733\pi$
$73$	2.05033e6	−	3.55128e6i	0.616871	−	1.06845i	0.990053	−	0.140694i	$-0.0449335\pi$
$74$	956265.	−	1.65630e6i	0.274326	−	0.475147i
$75$	−2.52827e6			−0.692006
$76$	−601762.	−	1.81636e6i	−0.157245	−	0.474630i
$77$	−1.78338e6			−0.445170
$78$	−2.40626e6	+	4.16777e6i	−0.574133	+	0.994427i
$79$	−2.59078e6	+	4.48736e6i	−0.591202	+	1.02399i	0.402869	+	0.915258i	$0.368013\pi$
$79$	−2.59078e6	+	4.48736e6i	−0.591202	+	1.02399i	−0.994071	+	0.108734i	$0.965320\pi$
$80$	333863.	+	578267.i	0.0729043	+	0.126274i
$81$	2.60649e6	−	4.51457e6i	0.544951	−	0.943883i
$82$	69530.8	+	120431.i	0.0139261	+	0.0241207i
$83$	7.24258e6			1.39034			0.695169	−	0.718847i	$-0.255330\pi$
$83$	7.24258e6			1.39034			0.695169	+	0.718847i	$0.255330\pi$
$84$	−724189.			−0.133314
$85$	−1.57960e6	−	2.73595e6i	−0.278986	−	0.483217i
$86$	1.19651e6	+	2.07242e6i	0.202849	+	0.351345i
$87$	−5.98931e6			−0.975123
$88$	−3.95766e6			−0.619084
$89$	2.52576e6	+	4.37475e6i	0.379776	+	0.657791i	0.991029	−	0.133644i	$-0.0426678\pi$
$89$	2.52576e6	+	4.37475e6i	0.379776	+	0.657791i	−0.611254	+	0.791435i	$0.709335\pi$
$90$	−142436.	+	246706.i	−0.0205954	+	0.0356722i
$91$	−1.41492e6	−	2.45071e6i	−0.196828	−	0.340916i
$92$	−2.25381e6	+	3.90372e6i	−0.301759	+	0.522662i
$93$	−655281.	+	1.13498e6i	−0.0844768	+	0.146318i
$94$	−7.04752e6			−0.875163
$95$	3.24035e6	−	3.64073e6i	0.387757	−	0.435668i
$96$	−1.60711e6			−0.185395
$97$	1.60831e6	−	2.78568e6i	0.178924	−	0.309906i	−0.762588	−	0.646884i	$-0.776072\pi$
$97$	1.60831e6	−	2.78568e6i	0.178924	−	0.309906i	0.941512	+	0.336979i	$0.109405\pi$
$98$	−3.08126e6	+	5.33689e6i	−0.330702	+	0.572792i
$99$	−844227.	−	1.46224e6i	−0.0874452	−	0.151459i
$100$	1.64959e6	−	2.85718e6i	0.164959	−	0.285718i
$101$	−6.25823e6	−	1.08396e7i	−0.604403	−	1.04686i	−0.992145	−	0.125089i	$-0.960078\pi$
$101$	−6.25823e6	−	1.08396e7i	−0.604403	−	1.04686i	0.387742	−	0.921768i	$-0.373255\pi$
$102$	7.60373e6			0.709457
$103$	−8.22738e6			−0.741876			−0.370938	−	0.928658i	$-0.620964\pi$
$103$	−8.22738e6			−0.741876			−0.370938	+	0.928658i	$0.620964\pi$
$104$	−3.13998e6	−	5.43860e6i	−0.273722	−	0.474101i
$105$	−922316.	−	1.59750e6i	−0.0777530	−	0.134672i
$106$	−2.24706e6			−0.183250
$107$	5.49130e6			0.433343			0.216672	−	0.976245i	$-0.430480\pi$
$107$	5.49130e6			0.433343			0.216672	+	0.976245i	$0.430480\pi$
$108$	3.08956e6	+	5.35128e6i	0.236001	+	0.408765i
$109$	−1.12666e7	+	1.95142e7i	−0.833294	+	1.44331i	0.0621179	+	0.998069i	$0.480215\pi$
$109$	−1.12666e7	+	1.95142e7i	−0.833294	+	1.44331i	−0.895412	+	0.445239i	$0.853119\pi$
$110$	−5.04042e6	−	8.73026e6i	−0.361071	−	0.625393i
$111$	−5.86253e6	+	1.01542e7i	−0.406869	+	0.704718i
$112$	472504.	−	818400.i	0.0317791	−	0.0550431i
$113$	−3.77596e6			−0.246180			−0.123090	−	0.992396i	$-0.539280\pi$
$113$	−3.77596e6			−0.246180			−0.123090	+	0.992396i	$0.539280\pi$
$114$	3.68920e6	+	1.11355e7i	0.233219	+	0.703952i
$115$	−1.14817e7			−0.703985
$116$	3.90778e6	−	6.76847e6i	0.232449	−	0.402613i
$117$	1.33961e6	−	2.32027e6i	0.0773262	−	0.133933i
$118$	1.28237e6	+	2.22113e6i	0.0718499	+	0.124448i
$119$	−2.23555e6	+	3.87209e6i	−0.121610	+	0.210635i
$120$	−2.04680e6	−	3.54516e6i	−0.108129	−	0.187284i
$121$	4.02628e7			2.06612
$122$	2.21374e7			1.10374
$123$	−426269.	−	738320.i	−0.0206546	−	0.0357747i
$124$	−855088.	−	1.48106e6i	−0.0402749	−	0.0697582i
$125$	2.11395e7			0.968074
$126$	403167.			0.0179551
$127$	−2.49284e6	−	4.31772e6i	−0.107989	−	0.187043i	0.806966	−	0.590598i	$-0.201108\pi$
$127$	−2.49284e6	−	4.31772e6i	−0.107989	−	0.187043i	−0.914956	+	0.403554i	$0.867775\pi$
$128$	1.04858e6	−	1.81619e6i	0.0441942	−	0.0765466i
$129$	−7.33541e6	−	1.27053e7i	−0.300857	−	0.521100i
$130$	7.99806e6	−	1.38530e7i	0.319288	−	0.553023i
$131$	−1.52320e7	+	2.63826e7i	−0.591980	+	1.02534i	0.401985	+	0.915646i	$0.368320\pi$
$131$	−1.52320e7	+	2.63826e7i	−0.591980	+	1.02534i	−0.993965	+	0.109694i	$0.965013\pi$
$132$	2.42631e7			0.918199
$133$	−6.75525e6	−	1.39525e6i	−0.248978	−	0.0514247i
$134$	−1.17874e7			−0.423206
$135$	−7.86964e6	+	1.36306e7i	−0.275287	+	0.476812i
$136$	−4.96112e6	+	8.59292e6i	−0.169120	+	0.292924i
$137$	−1.55860e6	−	2.69957e6i	−0.0517859	−	0.0896958i	0.838970	−	0.544177i	$-0.183158\pi$
$137$	−1.55860e6	−	2.69957e6i	−0.0517859	−	0.0896958i	−0.890756	+	0.454481i	$0.849825\pi$
$138$	1.38174e7	−	2.39324e7i	0.447557	−	0.775191i
$139$	−2.68335e7	−	4.64770e7i	−0.847473	−	1.46787i	−0.883456	−	0.468514i	$-0.844790\pi$
$139$	−2.68335e7	−	4.64770e7i	−0.847473	−	1.46787i	0.0359829	−	0.999352i	$-0.488544\pi$
$140$	2.40709e6			0.0741387
$141$	4.32059e7			1.29800
$142$	−9.88041e6	−	1.71134e7i	−0.289578	−	0.501564i
$143$	4.74051e7	+	8.21081e7i	1.35566	+	2.34806i
$144$	894706.			0.0249696
$145$	1.99076e7			0.542288
$146$	−1.64027e7	−	2.84103e7i	−0.436194	−	0.755510i
$147$	1.88901e7	−	3.27186e7i	0.490483	−	0.849541i
$148$	−7.65012e6	−	1.32504e7i	−0.193978	−	0.335980i
$149$	−1.23980e7	+	2.14740e7i	−0.307043	+	0.531815i	−0.977714	−	0.209940i	$-0.932673\pi$
$149$	−1.23980e7	+	2.14740e7i	−0.307043	+	0.531815i	0.670671	+	0.741755i	$0.266006\pi$
$150$	−1.01131e7	+	1.75164e7i	−0.244661	+	0.423765i
$151$	−5.98949e7			−1.41570			−0.707849	−	0.706364i	$-0.750334\pi$
$151$	−5.98949e7			−1.41570			−0.707849	+	0.706364i	$0.750334\pi$
$152$	−1.49912e7	−	3.09633e6i	−0.346245	−	0.0715146i
$153$	−4.23312e6			−0.0955521
$154$	−7.13352e6	+	1.23556e7i	−0.157392	+	0.272610i
$155$	2.17806e6	−	3.77250e6i	0.0469794	−	0.0813708i
$156$	1.92501e7	+	3.33422e7i	0.405973	+	0.703166i
$157$	3.09147e7	−	5.35458e7i	0.637552	−	1.10427i	−0.348416	−	0.937340i	$-0.613280\pi$
$157$	3.09147e7	−	5.35458e7i	0.637552	−	1.10427i	0.985968	−	0.166933i	$-0.0533863\pi$
$158$	2.07262e7	+	3.58989e7i	0.418043	+	0.724071i
$159$	1.37760e7			0.271789
$160$	5.34180e6			0.103102
$161$	8.12481e6	+	1.40726e7i	0.153434	+	0.265756i
$162$	−2.08519e7	−	3.61165e7i	−0.385339	−	0.667426i
$163$	−7.63609e7			−1.38107			−0.690533	−	0.723301i	$-0.742624\pi$
$163$	−7.63609e7			−1.38107			−0.690533	+	0.723301i	$0.742624\pi$
$164$	1.11249e6			0.0196944
$165$	3.09011e7	+	5.35222e7i	0.535525	+	0.927556i
$166$	2.89703e7	−	5.01781e7i	0.491558	−	0.851404i
$167$	−1.49342e7	−	2.58667e7i	−0.248126	−	0.429768i	0.714880	−	0.699248i	$-0.246482\pi$
$167$	−1.49342e7	−	2.58667e7i	−0.248126	−	0.429768i	−0.963006	+	0.269480i	$0.913148\pi$
$168$	−2.89676e6	+	5.01733e6i	−0.0471335	+	0.0816375i
$169$	−4.38475e7	+	7.59461e7i	−0.698781	+	1.21032i
$170$	−2.52737e7			−0.394545
$171$	−2.05383e6	−	6.19931e6i	−0.0314108	−	0.0948106i
$172$	1.91442e7			0.286872
$173$	−2.38555e7	+	4.13189e7i	−0.350290	+	0.606719i	−0.986300	−	0.164961i	$-0.947250\pi$
$173$	−2.38555e7	+	4.13189e7i	−0.350290	+	0.606719i	0.636010	+	0.771680i	$0.280584\pi$
$174$	−2.39572e7	+	4.14951e7i	−0.344758	+	0.597138i
$175$	−5.94665e6	−	1.02999e7i	−0.0838763	−	0.145278i
$176$	−1.58306e7	+	2.74195e7i	−0.218879	+	0.379110i
$177$	−7.86176e6	−	1.36170e7i	−0.106565	−	0.184576i
$178$	4.04122e7			0.537084
$179$	1.59181e6			0.0207447			0.0103723	−	0.999946i	$-0.496698\pi$
$179$	1.59181e6			0.0207447			0.0103723	+	0.999946i	$0.496698\pi$
$180$	1.13948e6	+	1.97364e6i	0.0145631	+	0.0252241i
$181$	−2.61859e7	−	4.53553e7i	−0.328241	−	0.568530i	0.653922	−	0.756562i	$-0.273122\pi$
$181$	−2.61859e7	−	4.53553e7i	−0.328241	−	0.568530i	−0.982163	+	0.188032i	$0.939789\pi$
$182$	−2.26387e7			−0.278357
$183$	−1.35717e8			−1.63702
$184$	1.80305e7	+	3.12298e7i	0.213376	+	0.369578i
$185$	1.94862e7	−	3.37510e7i	0.226269	−	0.391910i
$186$	5.24225e6	+	9.07984e6i	0.0597341	+	0.103462i
$187$	7.48995e7	−	1.29730e8i	0.837593	−	1.45075i
$188$	−2.81901e7	+	4.88266e7i	−0.309417	+	0.535926i
$189$	2.22752e7			0.239997
$190$	−1.22623e7	−	3.70127e7i	−0.129699	−	0.391483i
$191$	−1.37877e8			−1.43178			−0.715888	−	0.698215i	$-0.753978\pi$
$191$	−1.37877e8			−1.43178			−0.715888	+	0.698215i	$0.753978\pi$
$192$	−6.42846e6	+	1.11344e7i	−0.0655469	+	0.113531i
$193$	7.38689e7	−	1.27945e8i	0.739624	−	1.28107i	−0.213041	−	0.977043i	$-0.568337\pi$
$193$	7.38689e7	−	1.27945e8i	0.739624	−	1.28107i	0.952665	−	0.304023i	$-0.0983299\pi$
$194$	−1.28665e7	−	2.22854e7i	−0.126518	−	0.219136i
$195$	−4.90333e7	+	8.49282e7i	−0.473555	+	0.820221i
$196$	2.46500e7	+	4.26951e7i	0.233841	+	0.405025i
$197$	7.86683e7			0.733108			0.366554	−	0.930397i	$-0.380538\pi$
$197$	7.86683e7			0.733108			0.366554	+	0.930397i	$0.380538\pi$
$198$	−1.35076e7			−0.123666
$199$	−4.71931e7	−	8.17409e7i	−0.424515	−	0.735281i	0.571860	−	0.820351i	$-0.306222\pi$
$199$	−4.71931e7	−	8.17409e7i	−0.424515	−	0.735281i	−0.996375	+	0.0850698i	$0.972889\pi$
$200$	−1.31968e7	−	2.28575e7i	−0.116644	−	0.202033i
$201$	7.22646e7			0.627682
$202$	−1.00132e8			−0.854755
$203$	−1.40872e7	−	2.43998e7i	−0.118192	−	0.204715i
$204$	3.04149e7	−	5.26802e7i	0.250831	−	0.434452i
$205$	1.41685e6	+	2.45406e6i	0.0114865	+	0.0198951i
$206$	−3.29095e7	+	5.70010e7i	−0.262293	+	0.454305i
$207$	−7.69234e6	+	1.33235e7i	−0.0602785	+	0.104405i
$208$	−5.02397e7			−0.387102
$209$	2.26326e8	+	4.67461e7i	1.71484	+	0.354188i
$210$	−1.47571e7			−0.109959
$211$	1.00743e8	−	1.74493e8i	0.738291	−	1.27876i	−0.214973	−	0.976620i	$-0.568966\pi$
$211$	1.00743e8	−	1.74493e8i	0.738291	−	1.27876i	0.953264	−	0.302138i	$-0.0977004\pi$
$212$	−8.98825e6	+	1.55681e7i	−0.0647887	+	0.112217i
$213$	6.05734e7	+	1.04916e8i	0.429490	+	0.743899i
$214$	2.19652e7	−	3.80448e7i	0.153210	−	0.265367i
$215$	2.43818e7	+	4.22305e7i	0.167313	+	0.289795i
$216$	4.94330e7			0.333756
$217$	−6.16504e6			−0.0409569
$218$	9.01324e7	+	1.56114e8i	0.589228	+	1.02057i
$219$	1.00559e8	+	1.74173e8i	0.646944	+	1.12054i
$220$	−8.06467e7			−0.510631
$221$	2.37699e8			1.48134
$222$	4.69002e7	+	8.12336e7i	0.287700	+	0.498311i
$223$	6.93940e6	−	1.20194e7i	0.0419040	−	0.0725798i	−0.844313	−	0.535851i	$-0.819991\pi$
$223$	6.93940e6	−	1.20194e7i	0.0419040	−	0.0725798i	0.886217	+	0.463271i	$0.153324\pi$
$224$	−3.78003e6	−	6.54720e6i	−0.0224712	−	0.0389213i
$225$	5.63012e6	−	9.75165e6i	0.0329518	−	0.0570741i
$226$	−1.51038e7	+	2.61606e7i	−0.0870378	+	0.150754i
$227$	2.92092e8			1.65741			0.828703	−	0.559689i	$-0.189079\pi$
$227$	2.92092e8			1.65741			0.828703	+	0.559689i	$0.189079\pi$
$228$	9.19058e7	+	1.89825e7i	0.513536	+	0.106067i
$229$	−1.68088e8			−0.924939			−0.462470	−	0.886635i	$-0.653037\pi$
$229$	−1.68088e8			−0.924939			−0.462470	+	0.886635i	$0.653037\pi$
$230$	−4.59268e7	+	7.95475e7i	−0.248896	+	0.431101i
$231$	4.37331e7	−	7.57480e7i	0.233436	−	0.404324i
$232$	−3.12622e7	−	5.41478e7i	−0.164366	−	0.284690i
$233$	−1.34474e8	+	2.32916e8i	−0.696455	+	1.20629i	0.273233	+	0.961948i	$0.411907\pi$
$233$	−1.34474e8	+	2.32916e8i	−0.696455	+	1.20629i	−0.969688	+	0.244347i	$0.921426\pi$
$234$	−1.07168e7	−	1.85621e7i	−0.0546779	−	0.0947048i
$235$	−1.43610e8			−0.721850
$236$	2.05179e7			0.101611
$237$	−1.27065e8	−	2.20084e8i	−0.620023	−	1.07391i
$238$	1.78844e7	+	3.09767e7i	0.0859916	+	0.148942i
$239$	−5.99654e7			−0.284124			−0.142062	−	0.989858i	$-0.545373\pi$
$239$	−5.99654e7			−0.284124			−0.142062	+	0.989858i	$0.545373\pi$
$240$	−3.27487e7			−0.152917
$241$	2.48802e7	+	4.30937e7i	0.114497	+	0.198314i	0.917579	−	0.397555i	$-0.130141\pi$
$241$	2.48802e7	+	4.30937e7i	0.114497	+	0.198314i	−0.803082	+	0.595869i	$0.796808\pi$
$242$	1.61051e8	−	2.78949e8i	0.730483	−	1.26523i
$243$	2.22596e7	+	3.85547e7i	0.0995165	+	0.172368i
$244$	8.85498e7	−	1.53373e8i	0.390232	−	0.675902i
$245$	−6.27879e7	+	1.08752e8i	−0.272769	+	0.472449i
$246$	−6.82031e6			−0.0292100
$247$	1.15327e8	+	3.48105e8i	0.486959	+	1.46984i
$248$	−1.36814e7			−0.0569574
$249$	−1.77607e8	+	3.07624e8i	−0.729059	+	1.26277i
$250$	8.45578e7	−	1.46458e8i	0.342266	−	0.592822i
$251$	−2.48699e8	−	4.30759e8i	−0.992696	−	1.71940i	−0.600829	−	0.799378i	$-0.705163\pi$
$251$	−2.48699e8	−	4.30759e8i	−0.992696	−	1.71940i	−0.391867	−	0.920022i	$-0.628171\pi$
$252$	1.61267e6	−	2.79323e6i	0.00634810	−	0.0109952i
$253$	−2.72212e8	−	4.71485e8i	−1.05678	−	1.83040i
$254$	−3.98854e7			−0.152720
$255$	1.54944e8			0.585173
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	−2.46505e8	−	4.26959e8i	−0.905858	−	1.56899i	−0.819762	−	0.572705i	$-0.805894\pi$
$257$	−2.46505e8	−	4.26959e8i	−0.905858	−	1.56899i	−0.0860960	−	0.996287i	$-0.527439\pi$
$258$	−1.17367e8			−0.425476
$259$	−5.51561e7			−0.197262
$260$	−6.39845e7	−	1.10824e8i	−0.225771	−	0.391047i
$261$	1.33374e7	−	2.31010e7i	0.0464332	−	0.0804246i
$262$	1.21856e8	+	2.11061e8i	0.418593	+	0.725025i
$263$	−1.39699e8	+	2.41965e8i	−0.473529	+	0.820177i	−0.999541	−	0.0303007i	$-0.990354\pi$
$263$	−1.39699e8	+	2.41965e8i	−0.473529	+	0.820177i	0.526012	+	0.850477i	$0.323687\pi$
$264$	9.70522e7	−	1.68099e8i	0.324632	−	0.562280i
$265$	−4.57892e7			−0.151148
$266$	−3.66876e7	+	4.12207e7i	−0.119518	+	0.134286i
$267$	−2.47753e8			−0.796580
$268$	−4.71497e7	+	8.16657e7i	−0.149626	+	0.259160i
$269$	1.01461e8	−	1.75736e8i	0.317810	−	0.550463i	−0.662221	−	0.749309i	$-0.730386\pi$
$269$	1.01461e8	−	1.75736e8i	0.317810	−	0.550463i	0.980031	+	0.198846i	$0.0637192\pi$
$270$	6.29571e7	+	1.09045e8i	0.194658	+	0.337157i
$271$	−2.79662e8	+	4.84388e8i	−0.853572	+	1.47843i	0.0243914	+	0.999702i	$0.492235\pi$
$271$	−2.79662e8	+	4.84388e8i	−0.853572	+	1.47843i	−0.877963	+	0.478728i	$0.841098\pi$
$272$	3.96890e7	+	6.87433e7i	0.119586	+	0.207128i
$273$	1.38790e8			0.412847
$274$	−2.49375e7			−0.0732363
$275$	1.99235e8	+	3.45085e8i	0.577699	+	1.00060i
$276$	−1.10539e8	−	1.91459e8i	−0.316470	−	0.548143i
$277$	−8.78459e7			−0.248337			−0.124169	−	0.992261i	$-0.539626\pi$
$277$	−8.78459e7			−0.248337			−0.124169	+	0.992261i	$0.539626\pi$
$278$	−4.29336e8			−1.19851
$279$	−2.91844e6	−	5.05489e6i	−0.00804519	−	0.0139347i
$280$	9.62838e6	−	1.66768e7i	0.0262120	−	0.0454005i
$281$	2.81723e8	+	4.87959e8i	0.757444	+	1.31193i	0.944150	+	0.329516i	$0.106886\pi$
$281$	2.81723e8	+	4.87959e8i	0.757444	+	1.31193i	−0.186706	+	0.982416i	$0.559781\pi$
$282$	1.72824e8	−	2.99339e8i	0.458914	−	0.794862i
$283$	−1.14113e8	+	1.97650e8i	−0.299283	+	0.518374i	−0.975972	−	0.217895i	$-0.930081\pi$
$283$	−1.14113e8	+	1.97650e8i	−0.299283	+	0.518374i	0.676689	+	0.736269i	$0.263414\pi$
$284$	−1.58087e8			−0.409525
$285$	7.51761e7	+	2.26912e8i	0.192363	+	0.580632i
$286$	7.58482e8			1.91719
$287$	2.00522e6	−	3.47314e6i	0.00500698	−	0.00867234i
$288$	3.57882e6	−	6.19870e6i	0.00882809	−	0.0152907i
$289$	1.73890e7	+	3.01186e7i	0.0423772	+	0.0733994i
$290$	7.96302e7	−	1.37924e8i	0.191728	−	0.332082i
$291$	7.88800e7	+	1.36624e8i	0.187647	+	0.325014i
$292$	−2.62443e8			−0.616871
$293$	−5.64984e8			−1.31220			−0.656099	−	0.754675i	$-0.727795\pi$
$293$	−5.64984e8			−1.31220			−0.656099	+	0.754675i	$0.727795\pi$
$294$	−1.51121e8	−	2.61749e8i	−0.346824	−	0.600716i
$295$	2.61313e7	+	4.52608e7i	0.0592631	+	0.102647i
$296$	−1.22402e8			−0.274326
$297$	−7.46303e8			−1.65298
$298$	9.91840e7	+	1.71792e8i	0.217112	+	0.376050i
$299$	4.31941e8	−	7.48144e8i	0.934492	−	1.61859i
$300$	8.09047e7	+	1.40131e8i	0.173001	+	0.299647i
$301$	3.45066e7	−	5.97673e7i	0.0729323	−	0.126322i
$302$	−2.39580e8	+	4.14964e8i	−0.500525	+	0.866935i
$303$	6.13873e8			1.26774
$304$	−8.14168e7	+	9.14767e7i	−0.166210	+	0.186747i
$305$	4.51103e8			0.910387
$306$	−1.69325e7	+	2.93279e7i	−0.0337828	+	0.0585135i
$307$	8.52062e7	−	1.47581e8i	0.168069	−	0.291104i	−0.769672	−	0.638439i	$-0.779580\pi$
$307$	8.52062e7	−	1.47581e8i	0.168069	−	0.291104i	0.937741	+	0.347336i	$0.112914\pi$
$308$	5.70682e7	+	9.88449e7i	0.111293	+	0.192764i
$309$	2.01757e8	−	3.49453e8i	0.389022	−	0.673805i
$310$	−1.74244e7	−	3.01800e7i	−0.0332195	−	0.0575378i
$311$	7.87734e8			1.48497			0.742486	−	0.669862i	$-0.233647\pi$
$311$	7.87734e8			1.48497			0.742486	+	0.669862i	$0.233647\pi$
$312$	3.08002e8			0.574133
$313$	−3.55295e8	−	6.15389e8i	−0.654914	−	1.13434i	−0.981915	−	0.189320i	$-0.939372\pi$
$313$	−3.55295e8	−	6.15389e8i	−0.654914	−	1.13434i	0.327002	−	0.945024i	$-0.393962\pi$
$314$	−2.47317e8	−	4.28366e8i	−0.450817	−	0.780839i
$315$	8.21549e6			0.0148097
$316$	3.31620e8			0.591202
$317$	−5.32543e7	−	9.22392e7i	−0.0938961	−	0.162633i	0.815251	−	0.579107i	$-0.196599\pi$
$317$	−5.32543e7	−	9.22392e7i	−0.0938961	−	0.162633i	−0.909147	+	0.416475i	$0.863265\pi$
$318$	5.51038e7	−	9.54426e7i	0.0960919	−	0.166436i
$319$	4.71975e8	+	8.17484e8i	0.814051	+	1.40998i
$320$	2.13672e7	−	3.70091e7i	0.0364521	−	0.0631370i
$321$	−1.34661e8	+	2.33240e8i	−0.227235	+	0.393582i
$322$	1.29997e8			0.216989
$323$	3.85207e8	−	4.32803e8i	0.636041	−	0.714631i
$324$	−3.33630e8			−0.544951
$325$	−3.16143e8	+	5.47576e8i	−0.510849	+	0.884816i
$326$	−3.05444e8	+	5.29044e8i	−0.488280	+	0.845727i
$327$	−5.52571e8	−	9.57080e8i	−0.873918	−	1.51367i
$328$	4.44997e6	−	7.70757e6i	0.00696304	−	0.0120603i
$329$	1.01623e8	+	1.76016e8i	0.157328	+	0.272500i
$330$	4.94417e8			0.757347
$331$	7.66542e8			1.16182			0.580909	−	0.813969i	$-0.302697\pi$
$331$	7.66542e8			1.16182			0.580909	+	0.813969i	$0.302697\pi$
$332$	−2.31763e8	−	4.01425e8i	−0.347584	−	0.602034i
$333$	−2.61101e7	−	4.52240e7i	−0.0387484	−	0.0671142i
$334$	−2.38946e8			−0.350904
$335$	−2.40197e8			−0.349068
$336$	2.31740e7	+	4.01386e7i	0.0333284	+	0.0577265i
$337$	−3.77594e8	+	6.54013e8i	−0.537429	+	0.930854i	0.461613	+	0.887082i	$0.347271\pi$
$337$	−3.77594e8	+	6.54013e8i	−0.537429	+	0.930854i	−0.999042	+	0.0437724i	$0.986062\pi$
$338$	3.50780e8	+	6.07569e8i	0.494113	+	0.855829i
$339$	9.25964e7	−	1.60382e8i	0.129091	−	0.223592i
$340$	−1.01095e8	+	1.75101e8i	−0.139493	+	0.241609i
$341$	2.06552e8			0.282091
$342$	−5.11654e7	−	1.05679e7i	−0.0691648	−	0.0142855i
$343$	3.67726e8			0.492034
$344$	7.65769e7	−	1.32635e8i	0.101425	−	0.175672i
$345$	2.81561e8	−	4.87678e8i	0.369153	−	0.639391i
$346$	1.90844e8	+	3.30552e8i	0.247692	+	0.429015i
$347$	−1.05284e8	+	1.82357e8i	−0.135272	+	0.234298i	−0.925701	−	0.378255i	$-0.876524\pi$
$347$	−1.05284e8	+	1.82357e8i	−0.135272	+	0.234298i	0.790429	+	0.612553i	$0.209858\pi$
$348$	1.91658e8	+	3.31961e8i	0.243781	+	0.422241i
$349$	4.47136e8			0.563055			0.281527	−	0.959553i	$-0.409159\pi$
$349$	4.47136e8			0.563055			0.281527	+	0.959553i	$0.409159\pi$
$350$	−9.51464e7			−0.118619
$351$	−5.92111e8	−	1.02557e9i	−0.730850	−	1.26587i
$352$	1.26645e8	+	2.19356e8i	0.154771	+	0.268071i
$353$	−2.80559e8			−0.339479			−0.169739	−	0.985489i	$-0.554293\pi$
$353$	−2.80559e8			−0.339479			−0.169739	+	0.985489i	$0.554293\pi$
$354$	−1.25788e8			−0.150705
$355$	−2.01337e8	−	3.48725e8i	−0.238849	−	0.413699i
$356$	1.61649e8	−	2.79984e8i	0.189888	−	0.328895i
$357$	−1.09643e8	−	1.89908e8i	−0.127539	−	0.220904i
$358$	6.36725e6	−	1.10284e7i	0.00733435	−	0.0127035i
$359$	4.62741e8	−	8.01491e8i	0.527846	−	0.914257i	−0.471627	−	0.881798i	$-0.656333\pi$
$359$	4.62741e8	−	8.01491e8i	0.527846	−	0.914257i	0.999473	−	0.0324585i	$-0.0103337\pi$
$360$	1.82317e7			0.0205954
$361$	8.20727e8	+	3.54139e8i	0.918171	+	0.396185i
$362$	−4.18975e8			−0.464203
$363$	−9.87349e8	+	1.71014e9i	−1.08342	+	1.87654i
$364$	−9.05549e7	+	1.56846e8i	−0.0984140	+	0.170458i
$365$	−3.34243e8	−	5.78926e8i	−0.359780	−	0.623158i
$366$	−5.42868e8	+	9.40275e8i	−0.578776	+	1.00247i
$367$	−4.62365e8	−	8.00840e8i	−0.488263	−	0.845696i	0.511646	−	0.859196i	$-0.329036\pi$
$367$	−4.62365e8	−	8.00840e8i	−0.488263	−	0.845696i	−0.999909	+	0.0135003i	$0.995703\pi$
$368$	2.88488e8			0.301759
$369$	3.79697e6			0.00393410
$370$	−1.55889e8	−	2.70008e8i	−0.159996	−	0.277122i
$371$	3.24019e7	+	5.61217e7i	0.0329429	+	0.0570587i
$372$	8.38760e7			0.0844768
$373$	4.29338e8			0.428369			0.214184	−	0.976793i	$-0.431291\pi$
$373$	4.29338e8			0.428369			0.214184	+	0.976793i	$0.431291\pi$
$374$	−5.99196e8	−	1.03784e9i	−0.592268	−	1.02584i
$375$	−5.18395e8	+	8.97886e8i	−0.507634	+	0.879248i
$376$	2.25521e8	+	3.90613e8i	0.218791	+	0.378957i
$377$	−7.48922e8	+	1.29717e9i	−0.719850	+	1.24682i
$378$	8.91008e7	−	1.54327e8i	0.0848517	−	0.146967i
$379$	3.62954e8			0.342463			0.171232	−	0.985231i	$-0.445225\pi$
$379$	3.62954e8			0.342463			0.171232	+	0.985231i	$0.445225\pi$
$380$	−3.05481e8	−	6.30950e7i	−0.285589	−	0.0589865i
$381$	2.44524e8			0.226508
$382$	−5.51508e8	+	9.55240e8i	−0.506209	+	0.876780i
$383$	7.02564e8	−	1.21688e9i	0.638985	−	1.10675i	−0.346671	−	0.937987i	$-0.612688\pi$
$383$	7.02564e8	−	1.21688e9i	0.638985	−	1.10675i	0.985656	−	0.168767i	$-0.0539786\pi$
$384$	5.14276e7	+	8.90753e7i	0.0463487	+	0.0802783i
$385$	−1.45362e8	+	2.51775e8i	−0.129819	+	0.224854i
$386$	−5.90951e8	−	1.02356e9i	−0.522993	−	0.905850i
$387$	6.53398e7			0.0573046
$388$	−2.05864e8			−0.178924
$389$	−8.10916e8	−	1.40455e9i	−0.698477	−	1.20980i	−0.968994	−	0.247083i	$-0.920528\pi$
$389$	−8.10916e8	−	1.40455e9i	−0.698477	−	1.20980i	0.270517	−	0.962715i	$-0.412805\pi$
$390$	3.92267e8	+	6.79426e8i	0.334854	+	0.579984i
$391$	−1.36492e9			−1.15475
$392$	3.94401e8			0.330702
$393$	−7.47057e8	−	1.29394e9i	−0.620840	−	1.07533i
$394$	3.14673e8	−	5.45030e8i	0.259193	−	0.448935i
$395$	4.22346e8	+	7.31525e8i	0.344809	+	0.597227i
$396$	−5.40305e7	+	9.35836e7i	−0.0437226	+	0.0757297i
$397$	−7.42517e8	+	1.28608e9i	−0.595579	+	1.03157i	0.397885	+	0.917435i	$0.369744\pi$
$397$	−7.42517e8	+	1.28608e9i	−0.595579	+	1.03157i	−0.993465	+	0.114139i	$0.963589\pi$
$398$	−7.55090e8			−0.600355
$399$	2.24919e8	−	2.52710e8i	0.177264	−	0.199167i
$400$	−2.11148e8			−0.164959
$401$	−5.86660e8	+	1.01613e9i	−0.454341	+	0.786941i	−0.998650	−	0.0519436i	$-0.983458\pi$
$401$	−5.86660e8	+	1.01613e9i	−0.454341	+	0.786941i	0.544309	+	0.838884i	$0.316792\pi$
$402$	2.89058e8	−	5.00664e8i	0.221919	−	0.384375i
$403$	1.63877e8	+	2.83843e8i	0.124724	+	0.216028i
$404$	−4.00527e8	+	6.93733e8i	−0.302202	+	0.523429i
$405$	−4.24906e8	−	7.35959e8i	−0.317834	−	0.550505i
$406$	−2.25395e8			−0.167149
$407$	1.84794e9			1.35865
$408$	−2.43319e8	−	4.21442e8i	−0.177364	−	0.307204i
$409$	6.36521e8	+	1.10249e9i	0.460025	+	0.796786i	0.998962	−	0.0455601i	$-0.0145073\pi$
$409$	6.36521e8	+	1.10249e9i	0.460025	+	0.796786i	−0.538937	+	0.842346i	$0.681174\pi$
$410$	2.26697e7			0.0162443
$411$	1.52883e8			0.108621
$412$	2.63276e8	+	4.56008e8i	0.185469	+	0.321242i
$413$	3.69827e7	−	6.40559e7i	0.0258329	−	0.0447439i
$414$	6.15387e7	+	1.06588e8i	0.0426233	+	0.0738257i
$415$	5.90339e8	−	1.02250e9i	0.405446	−	0.702253i
$416$	−2.00959e8	+	3.48071e8i	−0.136861	+	0.237050i
$417$	2.63211e9			1.77758
$418$	1.22917e9	−	1.38105e9i	0.823182	−	0.924895i
$419$	5.71209e8			0.379355			0.189678	−	0.981846i	$-0.439256\pi$
$419$	5.71209e8			0.379355			0.189678	+	0.981846i	$0.439256\pi$
$420$	−5.90282e7	+	1.02240e8i	−0.0388765	+	0.0673361i
$421$	−1.04855e9	+	1.81613e9i	−0.684857	+	1.18621i	0.288625	+	0.957442i	$0.406802\pi$
$421$	−1.04855e9	+	1.81613e9i	−0.684857	+	1.18621i	−0.973482	+	0.228765i	$0.926531\pi$
$422$	−8.05947e8	−	1.39594e9i	−0.522051	−	0.904219i
$423$	−9.62136e7	+	1.66647e8i	−0.0618081	+	0.107055i
$424$	7.19060e7	+	1.24545e8i	0.0458125	+	0.0793497i
$425$	9.99004e8			0.631257
$426$	9.69174e8			0.607391
$427$	−3.19214e8	−	5.52896e8i	−0.198420	−	0.343673i
$428$	−1.75722e8	−	3.04359e8i	−0.108336	−	0.187643i
$429$	−4.64999e9			−2.84349
$430$	3.90109e8			0.236617
$431$	8.99942e8	+	1.55874e9i	0.541432	+	0.937788i	0.998822	+	0.0485217i	$0.0154510\pi$
$431$	8.99942e8	+	1.55874e9i	0.541432	+	0.937788i	−0.457390	+	0.889266i	$0.651216\pi$
$432$	1.97732e8	−	3.42482e8i	0.118000	−	0.204383i
$433$	−7.16533e8	−	1.24107e9i	−0.424159	−	0.734665i	0.572183	−	0.820126i	$-0.306097\pi$
$433$	−7.16533e8	−	1.24107e9i	−0.424159	−	0.734665i	−0.996341	+	0.0854617i	$0.972763\pi$
$434$	−2.46602e7	+	4.27127e7i	−0.0144804	+	0.0250809i
$435$	−4.88185e8	+	8.45562e8i	−0.284362	+	0.492530i
$436$	1.44212e9			0.833294
$437$	−6.62236e8	−	1.99890e9i	−0.379602	−	1.14579i
$438$	1.60895e9			0.914917
$439$	−6.57259e8	+	1.13841e9i	−0.370775	+	0.642201i	−0.989685	−	0.143261i	$-0.954241\pi$
$439$	−6.57259e8	+	1.13841e9i	−0.370775	+	0.642201i	0.618910	+	0.785462i	$0.287575\pi$
$440$	−3.22587e8	+	5.58737e8i	−0.180535	+	0.312696i
$441$	8.41314e7	+	1.45720e8i	0.0467114	+	0.0809065i
$442$	9.50795e8	−	1.64682e9i	0.523732	−	0.907130i
$443$	8.24159e8	+	1.42749e9i	0.450400	+	0.780115i	0.998411	−	0.0563558i	$-0.0179481\pi$
$443$	8.24159e8	+	1.42749e9i	0.450400	+	0.780115i	−0.548011	+	0.836471i	$0.684615\pi$
$444$	7.50404e8			0.406869
$445$	8.23493e8			0.442996
$446$	−5.55152e7	−	9.61552e7i	−0.0296306	−	0.0513217i
$447$	−6.08063e8	−	1.05320e9i	−0.322012	−	0.557741i
$448$	−6.04804e7			−0.0317791
$449$	1.95177e9			1.01758			0.508788	−	0.860892i	$-0.330094\pi$
$449$	1.95177e9			1.01758			0.508788	+	0.860892i	$0.330094\pi$
$450$	−4.50410e7	−	7.80132e7i	−0.0233004	−	0.0403575i
$451$	−6.71825e7	+	1.16363e8i	−0.0344856	+	0.0597308i
$452$	1.20831e8	+	2.09285e8i	0.0615450	+	0.106599i
$453$	1.46878e9	−	2.54400e9i	0.742357	−	1.28580i
$454$	1.16837e9	−	2.02367e9i	0.585982	−	1.01495i
$455$	−4.61317e8			−0.229594
$456$	4.99138e8	−	5.60812e8i	0.246515	−	0.276975i
$457$	4.10061e8			0.200975			0.100487	−	0.994938i	$-0.467960\pi$
$457$	4.10061e8			0.200975			0.100487	+	0.994938i	$0.467960\pi$
$458$	−6.72353e8	+	1.16455e9i	−0.327015	+	0.566407i
$459$	−9.35528e8	+	1.62038e9i	−0.451557	+	0.782119i
$460$	3.67414e8	+	6.36380e8i	0.175996	+	0.304835i
$461$	2.31800e8	−	4.01489e8i	0.110194	−	0.190862i	−0.805654	−	0.592386i	$-0.798186\pi$
$461$	2.31800e8	−	4.01489e8i	0.110194	−	0.190862i	0.915849	+	0.401524i	$0.131519\pi$
$462$	−3.49865e8	−	6.05984e8i	−0.165064	−	0.285900i
$463$	2.80958e9			1.31555			0.657775	−	0.753215i	$-0.271498\pi$
$463$	2.80958e9			1.31555			0.657775	+	0.753215i	$0.271498\pi$
$464$	−5.00196e8			−0.232449
$465$	1.06823e8	+	1.85023e8i	0.0492697	+	0.0853377i
$466$	1.07579e9	+	1.86333e9i	0.492468	+	0.852979i
$467$	−2.87647e9			−1.30693			−0.653464	−	0.756958i	$-0.726685\pi$
$467$	−2.87647e9			−1.30693			−0.653464	+	0.756958i	$0.726685\pi$
$468$	−1.71470e8			−0.0773262
$469$	1.69971e8	+	2.94398e8i	0.0760798	+	0.131774i
$470$	−5.74439e8	+	9.94958e8i	−0.255212	+	0.442041i
$471$	1.51622e9	+	2.62616e9i	0.668633	+	1.15811i
$472$	8.20717e7	−	1.42152e8i	0.0359250	−	0.0622239i
$473$	−1.15610e9	+	2.00243e9i	−0.502322	+	0.870048i
$474$	−2.03305e9			−0.876845
$475$	4.84699e8	+	1.46302e9i	0.207513	+	0.626358i
$476$	2.86151e8			0.121610
$477$	−3.06772e7	+	5.31344e7i	−0.0129420	+	0.0224162i
$478$	−2.39862e8	+	4.15453e8i	−0.100453	+	0.173990i
$479$	−7.05341e8	−	1.22169e9i	−0.293241	−	0.507908i	0.681333	−	0.731973i	$-0.261400\pi$
$479$	−7.05341e8	−	1.22169e9i	−0.293241	−	0.507908i	−0.974574	+	0.224065i	$0.928067\pi$
$480$	−1.30995e8	+	2.26890e8i	−0.0540643	+	0.0936421i
$481$	1.46614e9	+	2.53943e9i	0.600713	+	1.04047i
$482$	3.98083e8			0.161923
$483$	−7.96966e8			−0.321829
$484$	−1.28841e9	−	2.23159e9i	−0.516529	−	0.894655i
$485$	−2.62185e8	−	4.54118e8i	−0.104355	−	0.180748i
$486$	3.56153e8			0.140738
$487$	−7.10520e8			−0.278757			−0.139378	−	0.990239i	$-0.544510\pi$
$487$	−7.10520e8			−0.278757			−0.139378	+	0.990239i	$0.544510\pi$
$488$	−7.08398e8	−	1.22698e9i	−0.275936	−	0.477935i
$489$	1.87257e9	−	3.24338e9i	0.724197	−	1.25435i
$490$	5.02303e8	+	8.70014e8i	0.192877	+	0.334072i
$491$	−5.55424e8	+	9.62023e8i	−0.211758	+	0.366775i	−0.952265	−	0.305273i	$-0.901252\pi$
$491$	−5.55424e8	+	9.62023e8i	−0.211758	+	0.366775i	0.740507	+	0.672049i	$0.234585\pi$
$492$	−2.72812e7	+	4.72525e7i	−0.0103273	+	0.0178874i
$493$	2.36657e9			0.889520
$494$	2.87305e9	+	5.93408e8i	1.07226	+	0.221467i
$495$	−2.75250e8			−0.102002
$496$	−5.47256e7	+	9.47876e7i	−0.0201375	+	0.0348791i
$497$	−2.84944e8	+	4.93538e8i	−0.104115	+	0.180332i
$498$	1.42086e9	+	2.46100e9i	0.515522	+	0.892911i
$499$	7.53339e8	−	1.30482e9i	0.271418	−	0.470110i	−0.697807	−	0.716286i	$-0.745841\pi$
$499$	7.53339e8	−	1.30482e9i	0.271418	−	0.470110i	0.969225	+	0.246176i	$0.0791741\pi$
$500$	−6.76462e8	−	1.17167e9i	−0.242019	−	0.419188i
$501$	1.46490e9			0.520446
$502$	−3.97919e9			−1.40388
$503$	−1.15921e9	−	2.00781e9i	−0.406138	−	0.703452i	0.588315	−	0.808632i	$-0.299792\pi$
$503$	−1.15921e9	−	2.00781e9i	−0.406138	−	0.703452i	−0.994453	+	0.105180i	$0.966458\pi$
$504$	−1.29014e7	−	2.23458e7i	−0.00448878	−	0.00777480i
$505$	−2.04042e9			−0.705017
$506$	−4.35539e9			−1.49451
$507$	−2.15051e9	−	3.72479e9i	−0.732847	−	1.26933i
$508$	−1.59542e8	+	2.76334e8i	−0.0539947	+	0.0935216i
$509$	1.60922e9	+	2.78725e9i	0.540882	+	0.936835i	0.998854	+	0.0478680i	$0.0152427\pi$
$509$	1.60922e9	+	2.78725e9i	0.540882	+	0.936835i	−0.457972	+	0.888967i	$0.651424\pi$
$510$	6.19776e8	−	1.07348e9i	0.206890	−	0.358344i
$511$	−4.73042e8	+	8.19333e8i	−0.156829	+	0.271636i
$512$	−1.34218e8			−0.0441942
$513$	−2.82692e9	−	5.83880e8i	−0.924490	−	0.190947i
$514$	−3.94408e9			−1.28108
$515$	−6.70610e8	+	1.16153e9i	−0.216344	+	0.374718i
$516$	−4.69466e8	+	8.13139e8i	−0.150429	+	0.260550i
$517$	−3.40475e9	−	5.89720e9i	−1.08360	−	1.87685i
$518$	−2.20624e8	+	3.82133e8i	−0.0697428	+	0.120798i
$519$	−1.17000e9	−	2.02650e9i	−0.367367	−	0.636298i
$520$	−1.02375e9			−0.319288
$521$	3.28859e9			1.01877			0.509387	−	0.860537i	$-0.329872\pi$
$521$	3.28859e9			1.01877			0.509387	+	0.860537i	$0.329872\pi$
$522$	−1.06699e8	−	1.84808e8i	−0.0328332	−	0.0568688i
$523$	−2.25584e9	−	3.90723e9i	−0.689528	−	1.19430i	−0.971991	−	0.235019i	$-0.924485\pi$
$523$	−2.25584e9	−	3.90723e9i	−0.689528	−	1.19430i	0.282463	−	0.959278i	$-0.408849\pi$
$524$	1.94970e9			0.591980
$525$	5.83310e8			0.175931
$526$	1.11759e9	+	1.93572e9i	0.334836	+	0.579952i
$527$	2.58923e8	−	4.48468e8i	0.0770608	−	0.133473i
$528$	−7.76418e8	−	1.34479e9i	−0.229550	−	0.397592i
$529$	−7.77899e8	+	1.34736e9i	−0.228469	+	0.395721i
$530$	−1.83157e8	+	3.17237e8i	−0.0534389	+	0.0925589i
$531$	7.00283e7			0.0202975
$532$	1.38835e8	+	4.19062e8i	0.0399769	+	0.120667i
$533$	−2.13208e8			−0.0609900
$534$	−9.91012e8	+	1.71648e9i	−0.281634	+	0.487804i
$535$	4.47593e8	−	7.75254e8i	0.126370	−	0.218880i
$536$	3.77198e8	+	6.53326e8i	0.105802	+	0.183254i
$537$	−3.90354e7	+	6.76113e7i	−0.0108780	+	0.0188412i
$538$	−8.11691e8	−	1.40589e9i	−0.224726	−	0.389236i
$539$	−5.95438e9			−1.63786
$540$	1.00731e9			0.275287
$541$	1.80142e9	+	3.12015e9i	0.489129	+	0.847197i	0.999922	−	0.0125071i	$-0.00398124\pi$
$541$	1.80142e9	+	3.12015e9i	0.489129	+	0.847197i	−0.510792	+	0.859704i	$0.670648\pi$
$542$	2.23729e9	+	3.87510e9i	0.603567	+	1.04541i
$543$	2.56859e9			0.688486
$544$	6.35024e8			0.169120
$545$	1.83666e9	+	3.18119e9i	0.486006	+	0.841786i
$546$	5.55160e8	−	9.61566e8i	0.145963	−	0.252816i
$547$	−1.81524e9	−	3.14409e9i	−0.474219	−	0.821372i	0.525345	−	0.850889i	$-0.323936\pi$
$547$	−1.81524e9	−	3.14409e9i	−0.474219	−	0.821372i	−0.999564	+	0.0295173i	$0.990603\pi$
$548$	−9.97502e7	+	1.72772e8i	−0.0258930	+	0.0448479i
$549$	3.02223e8	−	5.23466e8i	0.0779515	−	0.135016i
$550$	3.18776e9			0.816990
$551$	1.14822e9	+	3.46580e9i	0.292411	+	0.882617i
$552$	−1.76862e9			−0.447557
$553$	5.97731e8	−	1.03530e9i	0.150303	−	0.260332i
$554$	−3.51383e8	+	6.08614e8i	−0.0878005	+	0.152075i
$555$	9.55703e8	+	1.65533e9i	0.237300	+	0.411016i
$556$	−1.71735e9	+	2.97453e9i	−0.423737	+	0.733933i
$557$	−3.26746e9	−	5.65940e9i	−0.801156	−	1.38764i	−0.918856	−	0.394593i	$-0.870886\pi$
$557$	−3.26746e9	−	5.65940e9i	−0.801156	−	1.38764i	0.117700	−	0.993049i	$-0.462448\pi$
$558$	−4.66951e7			−0.0113776
$559$	−3.66897e9			−0.888389
$560$	−7.70270e7	−	1.33415e8i	−0.0185347	−	0.0321030i
$561$	3.67346e9	+	6.36262e9i	0.878427	+	1.52148i
$562$	4.50757e9			1.07119
$563$	2.12910e9			0.502824			0.251412	−	0.967880i	$-0.419105\pi$
$563$	2.12910e9			0.502824			0.251412	+	0.967880i	$0.419105\pi$
$564$	−1.38259e9	−	2.39471e9i	−0.324501	−	0.562052i
$565$	−3.07776e8	+	5.33084e8i	−0.0717903	+	0.124344i
$566$	9.12904e8	+	1.58120e9i	0.211625	+	0.366546i
$567$	−6.01354e8	+	1.04158e9i	−0.138545	+	0.239966i
$568$	−6.32346e8	+	1.09526e9i	−0.144789	+	0.250782i
$569$	4.65841e9			1.06009			0.530047	−	0.847968i	$-0.322174\pi$
$569$	4.65841e9			1.06009			0.530047	+	0.847968i	$0.322174\pi$
$570$	1.87280e9	+	3.86814e8i	0.423574	+	0.0874862i
$571$	3.20307e9			0.720012			0.360006	−	0.932950i	$-0.382775\pi$
$571$	3.20307e9			0.720012			0.360006	+	0.932950i	$0.382775\pi$
$572$	3.03393e9	−	5.25492e9i	0.677828	−	1.17403i
$573$	3.38110e9	−	5.85625e9i	0.750788	−	1.30040i
$574$	−1.60418e7	−	2.77852e7i	−0.00354047	−	0.00613227i
$575$	1.81537e9	−	3.14431e9i	0.398224	−	0.689745i
$576$	−2.86306e7	−	4.95896e7i	−0.00624240	−	0.0108122i
$577$	6.10939e9			1.32398			0.661992	−	0.749511i	$-0.269711\pi$
$577$	6.10939e9			1.32398			0.661992	+	0.749511i	$0.269711\pi$
$578$	2.78224e8			0.0599303
$579$	3.62292e9	+	6.27507e9i	0.775681	+	1.34352i
$580$	−6.37042e8	−	1.10339e9i	−0.135572	−	0.234818i
$581$	−1.67097e9			−0.353470
$582$	1.26208e9			0.265373
$583$	−1.08558e9	−	1.88029e9i	−0.226894	−	0.392993i
$584$	−1.04977e9	+	1.81826e9i	−0.218097	+	0.377755i
$585$	−2.18381e8	−	3.78247e8i	−0.0450993	−	0.0781142i
$586$	−2.25994e9	+	3.91432e9i	−0.463932	+	0.803554i
$587$	−1.08825e9	+	1.88490e9i	−0.222072	+	0.384640i	−0.955437	−	0.295195i	$-0.904615\pi$
$587$	−1.08825e9	+	1.88490e9i	−0.222072	+	0.384640i	0.733365	+	0.679835i	$0.237949\pi$
$588$	−2.41793e9			−0.490483
$589$	7.82397e8	+	1.61599e8i	0.157770	+	0.0325863i
$590$	4.18101e8			0.0838107
$591$	−1.92915e9	+	3.34139e9i	−0.384424	+	0.665841i
$592$	−4.89608e8	+	8.48025e8i	−0.0969890	+	0.167990i
$593$	3.14368e9	+	5.44501e9i	0.619080	+	1.07228i	0.989654	+	0.143475i	$0.0458278\pi$
$593$	3.14368e9	+	5.44501e9i	0.619080	+	1.07228i	−0.370574	+	0.928803i	$0.620839\pi$
$594$	−2.98521e9	+	5.17054e9i	−0.584417	+	1.01224i
$595$	3.64438e8	+	6.31224e8i	0.0709274	+	0.122850i
$596$	1.58694e9			0.307043
$597$	4.62919e9			0.890421
$598$	−3.45553e9	−	5.98516e9i	−0.660786	−	1.14451i
$599$	−4.01746e9	−	6.95845e9i	−0.763762	−	1.32287i	−0.940899	−	0.338688i	$-0.890017\pi$
$599$	−4.01746e9	−	6.95845e9i	−0.763762	−	1.32287i	0.177136	−	0.984186i	$-0.443317\pi$
$600$	1.29448e9			0.244661
$601$	−8.64757e9			−1.62493			−0.812463	−	0.583013i	$-0.801874\pi$
$601$	−8.64757e9			−1.62493			−0.812463	+	0.583013i	$0.801874\pi$
$602$	−2.76053e8	−	4.78138e8i	−0.0515709	−	0.0893235i
$603$	−1.60923e8	+	2.78728e8i	−0.0298888	+	0.0517689i
$604$	1.91664e9	+	3.31971e9i	0.353925	+	0.613015i
$605$	3.28180e9	−	5.68424e9i	0.602515	−	1.04359i
$606$	2.45549e9	−	4.25303e9i	0.448213	−	0.776327i
$607$	−6.05629e9			−1.09912			−0.549561	−	0.835454i	$-0.685205\pi$
$607$	−6.05629e9			−1.09912			−0.549561	+	0.835454i	$0.685205\pi$
$608$	3.08102e8	+	9.29979e8i	0.0555946	+	0.167807i
$609$	1.38182e9			0.247908
$610$	1.80441e9	−	3.12533e9i	0.321870	−	0.557496i
$611$	5.40260e9	−	9.35758e9i	0.958206	−	1.65966i
$612$	1.35460e8	+	2.34623e8i	0.0238880	+	0.0413753i
$613$	−1.43071e9	+	2.47807e9i	−0.250865	+	0.434511i	−0.963764	−	0.266755i	$-0.914048\pi$
$613$	−1.43071e9	+	2.47807e9i	−0.250865	+	0.434511i	0.712899	+	0.701267i	$0.247382\pi$
$614$	−6.81650e8	−	1.18065e9i	−0.118843	−	0.205841i
$615$	−1.38980e8			−0.0240929
$616$	9.13090e8			0.157392
$617$	2.12139e9	+	3.67436e9i	0.363599	+	0.629772i	0.988550	−	0.150892i	$-0.0482146\pi$
$617$	2.12139e9	+	3.67436e9i	0.363599	+	0.629772i	−0.624951	+	0.780664i	$0.714881\pi$
$618$	−1.61406e9	−	2.79563e9i	−0.275080	−	0.476452i
$619$	1.38696e9			0.235043			0.117522	−	0.993070i	$-0.462505\pi$
$619$	1.38696e9			0.235043			0.117522	+	0.993070i	$0.462505\pi$
$620$	−2.78791e8			−0.0469794
$621$	3.40005e9	+	5.88905e9i	0.569724	+	0.986790i
$622$	3.15094e9	−	5.45758e9i	0.525017	−	0.909356i
$623$	−5.82730e8	−	1.00932e9i	−0.0965515	−	0.167232i
$624$	1.23201e9	−	2.13390e9i	0.202987	−	0.351583i
$625$	−2.90600e8	+	5.03335e8i	−0.0476120	+	0.0824664i
$626$	−5.68472e9			−0.926188
$627$	−7.53563e9	+	8.46674e9i	−1.22091	+	1.37177i
$628$	−3.95708e9			−0.637552
$629$	2.31648e9	−	4.01226e9i	0.371151	−	0.642853i
$630$	3.28620e7	−	5.69186e7i	0.00523602	−	0.00906906i
$631$	−5.17212e9	−	8.95837e9i	−0.819531	−	1.41947i	−0.906028	−	0.423218i	$-0.860900\pi$
$631$	−5.17212e9	−	8.95837e9i	−0.819531	−	1.41947i	0.0864966	−	0.996252i	$-0.472433\pi$
$632$	1.32648e9	−	2.29753e9i	0.209021	−	0.362036i
$633$	4.94098e9	+	8.55803e9i	0.774284	+	1.34110i
$634$	−8.52069e8			−0.132789
$635$	−8.12760e8			−0.125966
$636$	−4.40831e8	−	7.63541e8i	−0.0679472	−	0.117688i
$637$	−4.72416e9	−	8.18248e9i	−0.724163	−	1.25429i
$638$	7.55160e9			1.15124
$639$	−5.39555e8			−0.0818055
$640$	−1.70938e8	−	2.96073e8i	−0.0257756	−	0.0446446i
$641$	−1.52468e9	+	2.64083e9i	−0.228652	+	0.396038i	−0.957409	−	0.288735i	$-0.906765\pi$
$641$	−1.52468e9	+	2.64083e9i	−0.228652	+	0.396038i	0.728757	+	0.684773i	$0.240099\pi$
$642$	1.07729e9	+	1.86592e9i	0.160679	+	0.278304i
$643$	−4.83364e8	+	8.37211e8i	−0.0717027	+	0.124193i	−0.899648	−	0.436617i	$-0.856177\pi$
$643$	−4.83364e8	+	8.37211e8i	−0.0717027	+	0.124193i	0.827945	+	0.560809i	$0.189510\pi$
$644$	5.19988e8	−	9.00645e8i	0.0767172	−	0.132878i
$645$	−2.39162e9			−0.350940
$646$	−1.45772e9	−	4.40000e9i	−0.212746	−	0.642154i
$647$	−8.64681e8			−0.125514			−0.0627568	−	0.998029i	$-0.519989\pi$
$647$	−8.64681e8			−0.125514			−0.0627568	+	0.998029i	$0.519989\pi$
$648$	−1.33452e9	+	2.31146e9i	−0.192669	+	0.333713i
$649$	−1.23906e9	+	2.14611e9i	−0.177924	+	0.308174i
$650$	2.52915e9	+	4.38061e9i	0.361225	+	0.625659i
$651$	1.51183e8	−	2.61856e8i	0.0214768	−	0.0371989i
$652$	2.44355e9	+	4.23235e9i	0.345266	+	0.598019i
$653$	−1.11384e10			−1.56541			−0.782703	−	0.622395i	$-0.786160\pi$
$653$	−1.11384e10			−1.56541			−0.782703	+	0.622395i	$0.786160\pi$
$654$	−8.84113e9			−1.23591
$655$	2.48310e9	+	4.30086e9i	0.345263	+	0.598013i
$656$	−3.55998e7	−	6.16606e7i	−0.00492361	−	0.00852794i
$657$	−8.95725e8			−0.123224
$658$	1.62597e9			0.222495
$659$	6.09197e9	+	1.05516e10i	0.829200	+	1.43622i	0.898667	+	0.438632i	$0.144537\pi$
$659$	6.09197e9	+	1.05516e10i	0.829200	+	1.43622i	−0.0694671	+	0.997584i	$0.522130\pi$
$660$	1.97767e9	−	3.42542e9i	0.267762	−	0.463778i
$661$	−4.38556e9	−	7.59602e9i	−0.590636	−	1.02301i	−0.994147	−	0.108037i	$-0.965543\pi$
$661$	−4.38556e9	−	7.59602e9i	−0.590636	−	1.02301i	0.403510	−	0.914975i	$-0.367790\pi$
$662$	3.06617e9	−	5.31076e9i	0.410765	−	0.711465i
$663$	−5.82899e9	+	1.00961e10i	−0.776777	+	1.34542i
$664$	−3.70820e9			−0.491558
$665$	−7.47596e8	+	8.39970e8i	−0.0985805	+	0.110761i
$666$	−4.17762e8			−0.0547985
$667$	4.30049e9	−	7.44867e9i	0.561148	−	0.971937i
$668$	−9.55786e8	+	1.65547e9i	−0.124063	+	0.214884i
$669$	3.40345e8	+	5.89494e8i	0.0439468	+	0.0761181i
$670$	−9.60787e8	+	1.66413e9i	−0.123414	+	0.213760i
$671$	1.06949e10	+	1.85241e10i	1.36662	+	2.36705i
$672$	3.70785e8			0.0471335
$673$	2.80629e9			0.354878			0.177439	−	0.984132i	$-0.443219\pi$
$673$	2.80629e9			0.354878			0.177439	+	0.984132i	$0.443219\pi$
$674$	3.02076e9	+	5.23210e9i	0.380020	+	0.658213i
$675$	−2.48854e9	−	4.31027e9i	−0.311445	−	0.539438i
$676$	5.61248e9			0.698781
$677$	−1.28316e10			−1.58936			−0.794679	−	0.607030i	$-0.792361\pi$
$677$	−1.28316e10			−1.58936			−0.794679	+	0.607030i	$0.792361\pi$
$678$	−7.40771e8	−	1.28305e9i	−0.0912810	−	0.158103i
$679$	−3.71061e8	+	6.42696e8i	−0.0454884	+	0.0787882i
$680$	8.08757e8	+	1.40081e9i	0.0986363	+	0.170843i
$681$	−7.16285e9	+	1.24064e10i	−0.869103	+	1.50533i
$682$	8.26208e8	−	1.43104e9i	0.0997342	−	0.172745i
$683$	−5.53294e9			−0.664482			−0.332241	−	0.943194i	$-0.607805\pi$
$683$	−5.53294e9			−0.664482			−0.332241	+	0.943194i	$0.607805\pi$
$684$	−2.77878e8	+	3.12213e8i	−0.0332015	+	0.0373039i
$685$	−5.08161e8			−0.0604066
$686$	1.47090e9	−	2.54768e9i	0.173960	−	0.301308i
$687$	4.12196e9	−	7.13945e9i	0.485015	−	0.840071i
$688$	−6.12615e8	−	1.06108e9i	−0.0717180	−	0.124219i
$689$	1.72259e9	−	2.98361e9i	0.200639	−	0.347516i
$690$	−2.25249e9	−	3.90143e9i	−0.261030	−	0.452118i
$691$	−4.58582e9			−0.528742			−0.264371	−	0.964421i	$-0.585164\pi$
$691$	−4.58582e9			−0.528742			−0.264371	+	0.964421i	$0.585164\pi$
$692$	3.05350e9			0.350290
$693$	1.94775e8	+	3.37361e8i	0.0222315	+	0.0385060i
$694$	8.42271e8	+	1.45886e9i	0.0956519	+	0.165674i
$695$	−8.74874e9			−0.988551
$696$	3.06653e9			0.344758
$697$	1.68433e8	+	2.91735e8i	0.0188414	+	0.0326342i
$698$	1.78854e9	−	3.09785e9i	0.199070	−	0.344799i
$699$	−6.59531e9	−	1.14234e10i	−0.730407	−	1.26510i
$700$	−3.80586e8	+	6.59194e8i	−0.0419381	+	0.0726390i
$701$	2.89045e9	−	5.00641e9i	0.316922	−	0.548925i	−0.662922	−	0.748688i	$-0.730684\pi$
$701$	2.89045e9	−	5.00641e9i	0.316922	−	0.548925i	0.979844	+	0.199763i	$0.0640173\pi$
$702$	−9.47378e9			−1.03358
$703$	6.99978e9	+	1.44576e9i	0.759873	+	0.156947i
$704$	2.02632e9			0.218879
$705$	3.52169e9	−	6.09974e9i	0.378520	−	0.655616i
$706$	−1.12224e9	+	1.94377e9i	−0.120024	+	0.207888i
$707$	1.44387e9	+	2.50085e9i	0.153659	+	0.266146i
$708$	−5.03153e8	+	8.71486e8i	−0.0532824	+	0.0922878i
$709$	−6.06605e9	−	1.05067e10i	−0.639211	−	1.10715i	−0.985606	−	0.169057i	$-0.945928\pi$
$709$	−6.06605e9	−	1.05067e10i	−0.639211	−	1.10715i	0.346395	−	0.938089i	$-0.387406\pi$
$710$	−3.22139e9			−0.337784
$711$	1.13183e9			0.118097
$712$	−1.29319e9	−	2.23987e9i	−0.134271	−	0.232564i
$713$	−9.41020e8	−	1.62989e9i	−0.0972267	−	0.168402i
$714$	−1.75429e9			−0.180367
$715$	1.54559e10			1.58133
$716$	−5.09380e7	−	8.82272e7i	−0.00518617	−	0.00898271i
$717$	1.47051e9	−	2.54700e9i	0.148988	−	0.258054i
$718$	−3.70193e9	−	6.41193e9i	−0.373244	−	0.646477i
$719$	1.66888e9	−	2.89059e9i	0.167446	−	0.290025i	−0.770075	−	0.637953i	$-0.779781\pi$
$719$	1.66888e9	−	2.89059e9i	0.167446	−	0.290025i	0.937521	+	0.347928i	$0.113115\pi$
$720$	7.29270e7	−	1.26313e8i	0.00728156	−	0.0126120i
$721$	1.89818e9			0.188609
$722$	5.73645e9	−	4.26961e9i	0.567235	−	0.422190i
$723$	−2.44051e9			−0.240157
$724$	−1.67590e9	+	2.90274e9i	−0.164121	+	0.284265i
$725$	−3.14758e9	+	5.45177e9i	−0.306757	+	0.531318i
$726$	7.89879e9	+	1.36811e10i	0.766094	+	1.32691i
$727$	−3.18862e9	+	5.52285e9i	−0.307774	+	0.533080i	−0.977875	−	0.209189i	$-0.932917\pi$
$727$	−3.18862e9	+	5.52285e9i	−0.307774	+	0.533080i	0.670101	+	0.742270i	$0.266251\pi$
$728$	7.24439e8	+	1.25476e9i	0.0695892	+	0.120532i
$729$	9.21731e9			0.881167
$730$	−5.34789e9			−0.508806
$731$	2.89846e9	+	5.02028e9i	0.274446	+	0.475354i
$732$	4.34294e9	+	7.52220e9i	0.409256	+	0.708853i
$733$	1.68252e10			1.57796			0.788980	−	0.614419i	$-0.210610\pi$
$733$	1.68252e10			1.57796			0.788980	+	0.614419i	$0.210610\pi$
$734$	−7.39784e9			−0.690508
$735$	−3.07944e9	−	5.33375e9i	−0.286066	−	0.495481i
$736$	1.15395e9	−	1.99870e9i	0.106688	−	0.184789i
$737$	−5.69466e9	−	9.86344e9i	−0.524000	−	0.907595i
$738$	1.51879e7	−	2.63062e7i	0.00139091	−	0.00240913i
$739$	1.01579e10	−	1.75941e10i	0.925870	−	1.60365i	0.135715	−	0.990748i	$-0.456667\pi$
$739$	1.01579e10	−	1.75941e10i	0.925870	−	1.60365i	0.790155	−	0.612907i	$-0.210000\pi$
$740$	−2.49423e9			−0.226269
$741$	−1.76137e10	−	3.63798e9i	−1.59033	−	0.328471i
$742$	5.18430e8			0.0465882
$743$	1.81151e9	−	3.13763e9i	0.162025	−	0.280635i	−0.773570	−	0.633711i	$-0.781531\pi$
$743$	1.81151e9	−	3.13763e9i	0.162025	−	0.280635i	0.935595	+	0.353076i	$0.114864\pi$
$744$	3.35504e8	−	5.81110e8i	0.0298670	−	0.0517312i
$745$	2.02111e9	+	3.50066e9i	0.179078	+	0.310173i
$746$	1.71735e9	−	2.97454e9i	0.151451	−	0.262321i
$747$	−7.91013e8	−	1.37008e9i	−0.0694323	−	0.120260i
$748$	−9.58713e9			−0.837593
$749$	−1.26692e9			−0.110170
$750$	4.14716e9	+	7.18309e9i	0.358952	+	0.621723i
$751$	1.00829e10	+	1.74641e10i	0.868653	+	1.50455i	0.863374	+	0.504564i	$0.168347\pi$
$751$	1.00829e10	+	1.74641e10i	0.868653	+	1.50455i	0.00527838	+	0.999986i	$0.498320\pi$
$752$	3.60833e9			0.309417
$753$	2.43950e10			2.08218
$754$	5.99138e9	+	1.03774e10i	0.509011	+	0.881632i
$755$	−4.88200e9	+	8.45588e9i	−0.412842	+	0.715063i
$756$	−7.12807e8	−	1.23462e9i	−0.0599992	−	0.103922i
$757$	−6.47674e9	+	1.12180e10i	−0.542651	+	0.939899i	0.456100	+	0.889929i	$0.349246\pi$
$757$	−6.47674e9	+	1.12180e10i	−0.542651	+	0.939899i	−0.998751	+	0.0499706i	$0.984087\pi$
$758$	1.45182e9	−	2.51462e9i	0.121079	−	0.209715i
$759$	2.67014e10			2.21660
$760$	−1.65906e9	+	1.86405e9i	−0.137093	+	0.154032i
$761$	−9.71611e9			−0.799183			−0.399592	−	0.916693i	$-0.630848\pi$
$761$	−9.71611e9			−0.799183			−0.399592	+	0.916693i	$0.630848\pi$
$762$	9.78095e8	−	1.69411e9i	0.0800827	−	0.138707i
$763$	2.59936e9	−	4.50222e9i	0.211851	−	0.366936i
$764$	4.41206e9	+	7.64192e9i	0.357944	+	0.619977i
$765$	−3.45039e8	+	5.97625e8i	−0.0278646	+	0.0482630i
$766$	−5.62052e9	−	9.73502e9i	−0.451830	−	0.782593i
$767$	−3.93224e9			−0.314671
$768$	8.22842e8			0.0655469
$769$	3.97105e9	+	6.87805e9i	0.314893	+	0.545410i	0.979415	−	0.201858i	$-0.0646981\pi$
$769$	3.97105e9	+	6.87805e9i	0.314893	+	0.545410i	−0.664522	+	0.747269i	$0.731365\pi$
$770$	1.16290e9	+	2.01420e9i	0.0917961	+	0.158996i
$771$	2.41798e10			1.90004
$772$	−9.45522e9			−0.739624
$773$	2.11168e9	+	3.65753e9i	0.164437	+	0.284813i	0.936455	−	0.350787i	$-0.114086\pi$
$773$	2.11168e9	+	3.65753e9i	0.164437	+	0.284813i	−0.772018	+	0.635600i	$0.780753\pi$
$774$	2.61359e8	−	4.52688e8i	0.0202602	−	0.0350918i
$775$	6.88745e8	+	1.19294e9i	0.0531499	+	0.0920583i
$776$	−8.23455e8	+	1.42627e9i	−0.0632592	+	0.109568i
$777$	1.35257e9	−	2.34272e9i	0.103440	−	0.179163i
$778$	−1.29747e10			−0.987796
$779$	−3.45518e8	+	3.88211e8i	−0.0261872	+	0.0294230i
$780$	6.27627e9			0.473555
$781$	9.54671e9	−	1.65354e10i	0.717093	−	1.24204i
$782$	−5.45969e9	+	9.45646e9i	−0.408267	+	0.707140i
$783$	−5.89517e9	−	1.02107e10i	−0.438865	−	0.760136i
$784$	1.57760e9	−	2.73249e9i	0.116921	−	0.202513i
$785$	−5.03967e9	−	8.72897e9i	−0.371842	−	0.644050i
$786$	−1.19529e10			−0.878000
$787$	1.40574e9			0.102800			0.0513999	−	0.998678i	$-0.483632\pi$
$787$	1.40574e9			0.102800			0.0513999	+	0.998678i	$0.483632\pi$
$788$	−2.51738e9	−	4.36024e9i	−0.183277	−	0.317445i
$789$	−6.85155e9	−	1.18672e10i	−0.496614	−	0.860161i
$790$	6.75754e9			0.487634
$791$	8.71169e8			0.0625871
$792$	4.32244e8	+	7.48669e8i	0.0309165	+	0.0535490i
$793$	−1.69705e10	+	2.93937e10i	−1.20848	+	2.09314i
$794$	5.94014e9	+	1.02886e10i	0.421138	+	0.729433i
$795$	1.12287e9	−	1.94487e9i	0.0792583	−	0.137279i
$796$	−3.02036e9	+	5.23142e9i	−0.212257	+	0.367641i
$797$	−4.98618e8			−0.0348870			−0.0174435	−	0.999848i	$-0.505553\pi$
$797$	−4.98618e8			−0.0348870			−0.0174435	+	0.999848i	$0.505553\pi$
$798$	−8.51151e8	−	2.56912e9i	−0.0592921	−	0.178968i
$799$	−1.70721e10			−1.18406
$800$	−8.44593e8	+	1.46288e9i	−0.0583220	+	0.101017i
$801$	5.51712e8	−	9.55593e8i	0.0379314	−	0.0656991i
$802$	4.69328e9	+	8.12901e9i	0.321267	+	0.556451i
$803$	1.58487e10	−	2.74507e10i	1.08016	−	1.87090i
$804$	−2.31247e9	−	4.00531e9i	−0.156920	−	0.271794i
$805$	2.64900e9			0.178976
$806$	2.62203e9			0.176386
$807$	4.97620e9	+	8.61902e9i	0.333304	+	0.577299i
$808$	3.20421e9	+	5.54986e9i	0.213689	+	0.370120i
$809$	−2.38275e10			−1.58219			−0.791097	−	0.611691i	$-0.790489\pi$
$809$	−2.38275e10			−1.58219			−0.791097	+	0.611691i	$0.790489\pi$
$810$	−6.79850e9			−0.449486
$811$	−3.54142e9	−	6.13392e9i	−0.233134	−	0.403799i	0.725595	−	0.688122i	$-0.241565\pi$
$811$	−3.54142e9	−	6.13392e9i	−0.233134	−	0.403799i	−0.958729	+	0.284323i	$0.908231\pi$
$812$	−9.01582e8	+	1.56159e9i	−0.0590961	+	0.102357i
$813$	−1.37161e10	−	2.37569e10i	−0.895184	−	1.55050i
$814$	7.39175e9	−	1.28029e10i	0.480354	−	0.831998i
$815$	−6.22413e9	+	1.07805e10i	−0.402742	+	0.697570i
$816$	−3.89311e9			−0.250831
$817$	−5.94582e9	+	6.68049e9i	−0.381447	+	0.428579i
$818$	1.01843e10			0.650573
$819$	−3.09067e8	+	5.35319e8i	−0.0196589	+	0.0340501i
$820$	9.06787e7	−	1.57060e8i	0.00574323	−	0.00994757i
$821$	−8.18363e9	−	1.41745e10i	−0.516113	−	0.893935i	−0.999825	−	0.0187073i	$-0.994045\pi$
$821$	−8.18363e9	−	1.41745e10i	−0.516113	−	0.893935i	0.483712	−	0.875227i	$-0.339288\pi$
$822$	6.11534e8	−	1.05921e9i	0.0384033	−	0.0665165i
$823$	8.14143e9	+	1.41014e10i	0.509098	+	0.881783i	0.999944	+	0.0105374i	$0.00335422\pi$
$823$	8.14143e9	+	1.41014e10i	0.509098	+	0.881783i	−0.490847	+	0.871246i	$0.663312\pi$
$824$	4.21242e9			0.262293
$825$	−1.95431e10			−1.21172
$826$	−2.95861e8	−	5.12447e8i	−0.0182666	−	0.0316387i
$827$	1.04062e10	+	1.80241e10i	0.639770	+	1.10811i	0.985483	+	0.169774i	$0.0543037\pi$
$827$	1.04062e10	+	1.80241e10i	0.639770	+	1.10811i	−0.345713	+	0.938340i	$0.612363\pi$
$828$	9.84619e8			0.0602785
$829$	2.43147e10			1.48227			0.741137	−	0.671354i	$-0.234287\pi$
$829$	2.43147e10			1.48227			0.741137	+	0.671354i	$0.234287\pi$
$830$	−4.72271e9	−	8.17998e9i	−0.286694	−	0.496568i
$831$	2.15421e9	−	3.73120e9i	0.130222	−	0.225551i
$832$	1.60767e9	+	2.78456e9i	0.0967754	+	0.167620i
$833$	−7.46410e9	+	1.29282e10i	−0.447425	+	0.774963i
$834$	1.05285e10	−	1.82358e10i	0.628468	−	1.08854i
$835$	−4.86910e9			−0.289432
$836$	−4.65151e9	−	1.40402e10i	−0.275342	−	0.831093i
$837$	−2.57993e9			−0.152079
$838$	2.28484e9	−	3.95745e9i	0.134122	−	0.232307i
$839$	−1.03810e10	+	1.79805e10i	−0.606839	+	1.05108i	0.384918	+	0.922951i	$0.374230\pi$
$839$	−1.03810e10	+	1.79805e10i	−0.606839	+	1.05108i	−0.991758	+	0.128126i	$0.959104\pi$
$840$	4.72226e8	+	8.17919e8i	0.0274898	+	0.0476138i
$841$	1.16853e9	−	2.02395e9i	0.0677411	−	0.117331i
$842$	8.38836e9	+	1.45291e10i	0.484267	+	0.838775i
$843$	−2.76344e10			−1.58874
$844$	−1.28951e10			−0.738291
$845$	7.14797e9	+	1.23806e10i	0.407553	+	0.705903i
$846$	7.69709e8	+	1.33318e9i	0.0437049	+	0.0756991i
$847$	−9.28921e9			−0.525275
$848$	1.15050e9			0.0647887
$849$	−5.59670e9	−	9.69377e9i	−0.313874	−	0.543645i
$850$	3.99602e9	−	6.92130e9i	0.223183	−	0.386564i
$851$	−8.41892e9	−	1.45820e10i	−0.468277	−	0.811080i
$852$	3.87670e9	−	6.71463e9i	0.214745	−	0.371949i
$853$	−1.26330e10	+	2.18809e10i	−0.696921	+	1.20710i	0.272608	+	0.962125i	$0.412114\pi$
$853$	−1.26330e10	+	2.18809e10i	−0.696921	+	1.20710i	−0.969529	+	0.244977i	$0.921220\pi$
$854$	−5.10743e9			−0.280608
$855$	−1.04262e9	−	2.15345e8i	−0.0570484	−	0.0117829i
$856$	−2.81155e9			−0.153210
$857$	8.67654e9	−	1.50282e10i	0.470884	−	0.815595i	−0.528562	−	0.848895i	$-0.677268\pi$
$857$	8.67654e9	−	1.50282e10i	0.470884	−	0.815595i	0.999445	+	0.0333002i	$0.0106017\pi$
$858$	−1.86000e10	+	3.22161e10i	−1.00533	+	1.74127i
$859$	−6.85846e9	−	1.18792e10i	−0.369190	−	0.639456i	0.620249	−	0.784405i	$-0.287032\pi$
$859$	−6.85846e9	−	1.18792e10i	−0.369190	−	0.639456i	−0.989439	+	0.144949i	$0.953698\pi$
$860$	1.56043e9	−	2.70275e9i	0.0836567	−	0.144898i
$861$	9.83465e7	+	1.70341e8i	0.00525107	+	0.00909512i
$862$	1.43991e10			0.765701
$863$	1.86127e9			0.0985760			0.0492880	−	0.998785i	$-0.484305\pi$
$863$	1.86127e9			0.0985760			0.0492880	+	0.998785i	$0.484305\pi$
$864$	−1.58185e9	−	2.73985e9i	−0.0834389	−	0.144520i
$865$	3.88890e9	+	6.73577e9i	0.204301	+	0.353859i
$866$	−1.14645e10			−0.599851
$867$	−1.70569e9			−0.0888862
$868$	1.97281e8	+	3.41701e8i	0.0102392	+	0.0177348i
$869$	−2.00262e10	+	3.46865e10i	−1.03521	+	1.79304i
$870$	3.90548e9	+	6.76449e9i	0.201075	+	0.348271i
$871$	9.03620e9	−	1.56512e10i	0.463364	−	0.802570i
$872$	5.76847e9	−	9.99129e9i	0.294614	−	0.510286i
$873$	−7.02620e8			−0.0357413
$874$	−1.64977e10	−	3.40749e9i	−0.835861	−	0.172641i
$875$	−4.87718e9			−0.246116
$876$	6.43578e9	−	1.11471e10i	0.323472	−	0.560270i
$877$	−2.13292e9	+	3.69432e9i	−0.106776	+	0.184942i	−0.914463	−	0.404671i	$-0.867386\pi$
$877$	−2.13292e9	+	3.69432e9i	−0.106776	+	0.184942i	0.807686	+	0.589613i	$0.200720\pi$
$878$	5.25807e9	+	9.10725e9i	0.262178	+	0.454105i
$879$	1.38549e10	−	2.39974e10i	0.688085	−	1.19180i
$880$	2.58070e9	+	4.46990e9i	0.127658	+	0.221110i
$881$	2.42375e10			1.19419			0.597094	−	0.802171i	$-0.296322\pi$
$881$	2.42375e10			1.19419			0.597094	+	0.802171i	$0.296322\pi$
$882$	1.34610e9			0.0660599
$883$	1.13925e10	+	1.97324e10i	0.556873	+	0.964532i	0.997755	+	0.0669671i	$0.0213323\pi$
$883$	1.13925e10	+	1.97324e10i	0.556873	+	0.964532i	−0.440882	+	0.897565i	$0.645334\pi$
$884$	−7.60636e9	−	1.31746e10i	−0.370334	−	0.641438i
$885$	−2.56323e9			−0.124304
$886$	1.31866e10			0.636962
$887$	4.69147e8	+	8.12586e8i	0.0225723	+	0.0390964i	0.877091	−	0.480324i	$-0.159481\pi$
$887$	4.69147e8	+	8.12586e8i	0.0225723	+	0.0390964i	−0.854519	+	0.519421i	$0.826148\pi$
$888$	3.00162e9	−	5.19895e9i	0.143850	−	0.249155i
$889$	5.75135e8	+	9.96162e8i	0.0274545	+	0.0475526i
$890$	3.29397e9	−	5.70533e9i	0.156623	−	0.271279i
$891$	2.01476e10	−	3.48967e10i	0.954228	−	1.65277i
$892$	−8.88243e8			−0.0419040
$893$	−8.28307e9	−	2.50017e10i	−0.389234	−	1.17487i
$894$	−9.72900e9			−0.455394
$895$	1.29748e8	−	2.24730e8i	0.00604950	−	0.0104780i
$896$	−2.41922e8	+	4.19021e8i	−0.0112356	+	0.0194607i
$897$	2.11847e10	+	3.66929e10i	0.980049	+	1.69750i
$898$	7.80709e9	−	1.35223e10i	0.359768	−	0.623136i
$899$	1.63159e9	+	2.82600e9i	0.0748948	+	0.129722i
$900$	−7.20655e8			−0.0329518
$901$	−5.44333e9			−0.247930
$902$	5.37460e8	+	9.30907e8i	0.0243850	+	0.0422361i
$903$	1.69239e9	+	2.93130e9i	0.0764878	+	0.132481i
$904$	1.93329e9			0.0870378
$905$	−8.53760e9			−0.382883
$906$	−1.17502e10	−	2.03520e10i	−0.524926	−	0.909198i
$907$	−1.77125e10	+	3.06789e10i	−0.788231	+	1.36526i	0.138818	+	0.990318i	$0.455670\pi$
$907$	−1.77125e10	+	3.06789e10i	−0.788231	+	1.36526i	−0.927050	+	0.374939i	$0.877664\pi$
$908$	−9.34694e9	−	1.61894e10i	−0.414351	−	0.717678i
$909$	−1.36701e9	+	2.36773e9i	−0.0603668	+	0.104558i
$910$	−1.84527e9	+	3.19610e9i	−0.0811736	+	0.140597i
$911$	−6.27911e9			−0.275159			−0.137580	−	0.990491i	$-0.543932\pi$
$911$	−6.27911e9			−0.275159			−0.137580	+	0.990491i	$0.543932\pi$
$912$	−1.88887e9	−	5.70138e9i	−0.0824555	−	0.248884i
$913$	5.59838e10			2.43453
$914$	1.64024e9	−	2.84099e9i	0.0710554	−	0.123072i
$915$	−1.10622e10	+	1.91603e10i	−0.477384	+	0.826854i
$916$	5.37882e9	+	9.31640e9i	0.231235	+	0.400510i
$917$	3.51424e9	−	6.08685e9i	0.150501	−	0.260675i
$918$	7.48422e9	+	1.29631e10i	0.319299	+	0.553042i
$919$	8.58450e9			0.364847			0.182423	−	0.983220i	$-0.441606\pi$
$919$	8.58450e9			0.364847			0.182423	+	0.983220i	$0.441606\pi$
$920$	5.87863e9			0.248896
$921$	4.17896e9	+	7.23817e9i	0.176262	+	0.305295i
$922$	−1.85440e9	−	3.21191e9i	−0.0779192	−	0.134960i
$923$	3.02971e10			1.26822
$924$	−5.59784e9			−0.233436
$925$	6.16191e9	+	1.06727e10i	0.255988	+	0.443384i
$926$	1.12383e10	−	1.94653e10i	0.465117	−	0.805606i
$927$	8.98570e8	+	1.55637e9i	0.0370487	+	0.0641702i
$928$	−2.00078e9	+	3.46546e9i	−0.0821830	+	0.142345i
$929$	5.78741e9	−	1.00241e10i	0.236826	−	0.410195i	−0.722976	−	0.690873i	$-0.757226\pi$
$929$	5.78741e9	−	1.00241e10i	0.236826	−	0.410195i	0.959802	+	0.280679i	$0.0905596\pi$
$930$	1.70917e9			0.0696779
$931$	−2.25545e10	−	4.65849e9i	−0.916031	−	0.189200i
$932$	1.72127e10			0.696455
$933$	−1.93173e10	+	3.34585e10i	−0.778683	+	1.34872i
$934$	−1.15059e10	+	1.99288e10i	−0.462068	+	0.800326i
$935$	−1.22100e10	−	2.11484e10i	−0.488513	−	0.846129i
$936$	−6.85878e8	+	1.18798e9i	−0.0273389	+	0.0473524i
$937$	−2.19499e9	−	3.80183e9i	−0.0871653	−	0.150975i	0.819147	−	0.573584i	$-0.194447\pi$
$937$	−2.19499e9	−	3.80183e9i	−0.0871653	−	0.150975i	−0.906312	+	0.422610i	$0.861114\pi$
$938$	2.71953e9			0.107593
$939$	3.48511e10			1.37368
$940$	4.59552e9	+	7.95967e9i	0.180462	+	0.312570i
$941$	−6.48248e9	−	1.12280e10i	−0.253617	−	0.439277i	0.710902	−	0.703291i	$-0.248287\pi$
$941$	−6.48248e9	−	1.12280e10i	−0.253617	−	0.439277i	−0.964519	+	0.264014i	$0.914953\pi$
$942$	2.42595e10			0.945590
$943$	1.22429e9			0.0475438
$944$	−6.56573e8	−	1.13722e9i	−0.0254028	−	0.0439989i
$945$	1.81564e9	−	3.14478e9i	0.0699872	−	0.121221i
$946$	9.24882e9	+	1.60194e10i	0.355195	+	0.615217i
$947$	−2.14907e10	+	3.72231e10i	−0.822293	+	1.42425i	0.0816780	+	0.996659i	$0.473972\pi$
$947$	−2.14907e10	+	3.72231e10i	−0.822293	+	1.42425i	−0.903971	+	0.427594i	$0.859361\pi$
$948$	−8.13218e9	+	1.40854e10i	−0.310012	+	0.536956i
$949$	5.02969e10			1.91034
$950$	1.20749e10	+	2.49399e9i	0.456931	+	0.0943760i
$951$	5.22374e9			0.196947
$952$	1.14460e9	−	1.98251e9i	0.0429958	−	0.0744709i
$953$	2.61962e10	−	4.53731e10i	0.980421	−	1.69814i	0.319680	−	0.947525i	$-0.396424\pi$
$953$	2.61962e10	−	4.53731e10i	0.980421	−	1.69814i	0.660741	−	0.750614i	$-0.270242\pi$
$954$	2.45417e8	+	4.25075e8i	0.00915137	+	0.0158506i
$955$	−1.12383e10	+	1.94653e10i	−0.417530	+	0.723184i
$956$	1.91889e9	+	3.32362e9i	0.0710310	+	0.123029i
$957$	−4.62962e10			−1.70747
$958$	−1.12855e10			−0.414705
$959$	3.59591e8	+	6.22830e8i	0.0131657	+	0.0228036i
$960$	1.04796e9	+	1.81512e9i	0.0382292	+	0.0662149i
$961$	−2.67986e10			−0.974047
$962$	2.34582e10			0.849537
$963$	−5.99743e8	−	1.03879e9i	−0.0216408	−	0.0374830i
$964$	1.59233e9	−	2.75800e9i	0.0572485	−	0.0991572i
$965$	−1.20420e10	−	2.08574e10i	−0.431374	−	0.747161i
$966$	−3.18786e9	+	5.52154e9i	−0.113784	+	0.197079i
$967$	1.46863e10	−	2.54375e10i	0.522301	−	0.904652i	−0.477362	−	0.878707i	$-0.658407\pi$
$967$	1.46863e10	−	2.54375e10i	0.522301	−	0.904652i	0.999663	−	0.0259453i	$-0.00825959\pi$
$968$	−2.06145e10			−0.730483
$969$	8.93679e9	+	2.69749e10i	0.315536	+	0.952416i
$970$	−4.19496e9			−0.147580
$971$	6.93087e8	−	1.20046e9i	0.0242952	−	0.0420805i	−0.853622	−	0.520893i	$-0.825599\pi$
$971$	6.93087e8	−	1.20046e9i	0.0242952	−	0.0420805i	0.877917	+	0.478812i	$0.158932\pi$
$972$	1.42461e9	−	2.46750e9i	0.0497583	−	0.0861838i
$973$	6.19089e9	+	1.07229e10i	0.215456	+	0.373180i
$974$	−2.84208e9	+	4.92263e9i	−0.0985553	+	0.170703i
$975$	−1.55053e10	−	2.68560e10i	−0.535753	−	0.927951i
$976$	−1.13344e10			−0.390232
$977$	−2.68223e10			−0.920164			−0.460082	−	0.887876i	$-0.652180\pi$
$977$	−2.68223e10			−0.920164			−0.460082	+	0.887876i	$0.652180\pi$
$978$	−1.49805e10	−	2.59471e10i	−0.512085	−	0.886957i
$979$	1.95236e10	+	3.38159e10i	0.665000	+	1.15181i
$980$	8.03685e9			0.272769
$981$	4.92200e9			0.166456
$982$	4.44339e9	+	7.69618e9i	0.149735	+	0.259349i
$983$	−8.08196e9	+	1.39984e10i	−0.271381	+	0.470046i	−0.969216	−	0.246213i	$-0.920814\pi$
$983$	−8.08196e9	+	1.39984e10i	−0.271381	+	0.470046i	0.697835	+	0.716259i	$0.254147\pi$
$984$	2.18250e8	+	3.78020e8i	0.00730249	+	0.0126483i
$985$	6.41221e9	−	1.11063e10i	0.213787	−	0.370289i
$986$	9.46629e9	−	1.63961e10i	0.314493	−	0.544718i
$987$	−9.96823e9			−0.329996
$988$	1.56034e10	−	1.75314e10i	0.514720	−	0.578320i
$989$	2.10681e10			0.692530
$990$	−1.10100e9	+	1.90699e9i	−0.0360632	+	0.0624632i
$991$	2.02875e10	−	3.51390e10i	0.662172	−	1.14692i	−0.317872	−	0.948134i	$-0.602968\pi$
$991$	2.02875e10	−	3.51390e10i	0.662172	−	1.14692i	0.980044	−	0.198782i	$-0.0636985\pi$
$992$	4.37805e8	+	7.58301e8i	0.0142393	+	0.0246633i
$993$	−1.87976e10	+	3.25584e10i	−0.609229	+	1.05522i
$994$	2.27956e9	+	3.94831e9i	0.0736203	+	0.127514i
$995$	−1.53867e10			−0.495183
$996$	2.27337e10			0.729059
$997$	−2.51988e10	−	4.36456e10i	−0.805279	−	1.39478i	−0.916102	−	0.400945i	$-0.868682\pi$
$997$	−2.51988e10	−	4.36456e10i	−0.805279	−	1.39478i	0.110823	−	0.993840i	$-0.464651\pi$
$998$	−6.02671e9	−	1.04386e10i	−0.191921	−	0.332418i
$999$	−2.30816e10			−0.732463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.8.c.b.11.2	yes	14
19.7	even	3	inner	38.8.c.b.7.2	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.8.c.b.7.2	✓	14	19.7	even	3	inner
38.8.c.b.11.2	yes	14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 - 6.92820i) q^{2} +(-24.5226 + 42.4744i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(81.5095 - 141.179i) q^{5} +(196.181 + 339.795i) q^{6} -230.715 q^{7} -512.000 q^{8} +(-109.217 - 189.169i) q^{9} +O(q^{10})\)	\(q+(4.00000 - 6.92820i) q^{2} +(-24.5226 + 42.4744i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(81.5095 - 141.179i) q^{5} +(196.181 + 339.795i) q^{6} -230.715 q^{7} -512.000 q^{8} +(-109.217 - 189.169i) q^{9} +(-652.076 - 1129.43i) q^{10} +7729.81 q^{11} +3138.89 q^{12} +(6132.77 + 10622.3i) q^{13} +(-922.858 + 1598.44i) q^{14} +(3997.65 + 6924.13i) q^{15} +(-2048.00 + 3547.24i) q^{16} +(9689.69 - 16783.0i) q^{17} -1747.47 q^{18} +(29279.7 + 6047.52i) q^{19} -10433.2 q^{20} +(5657.72 - 9799.47i) q^{21} +(30919.2 - 53553.7i) q^{22} +(-35215.8 - 60995.6i) q^{23} +(12555.6 - 21746.9i) q^{24} +(25774.9 + 44643.5i) q^{25} +98124.3 q^{26} -96548.8 q^{27} +(7382.87 + 12787.5i) q^{28} +(61059.0 + 105757. i) q^{29} +63962.4 q^{30} +26721.5 q^{31} +(16384.0 + 28377.9i) q^{32} +(-189555. + 328319. i) q^{33} +(-77517.6 - 134264. i) q^{34} +(-18805.4 + 32571.9i) q^{35} +(-6989.89 + 12106.8i) q^{36} +239066. q^{37} +(159017. - 178665. i) q^{38} -601566. q^{39} +(-41732.8 + 72283.4i) q^{40} +(-8691.35 + 15053.9i) q^{41} +(-45261.8 - 78395.7i) q^{42} +(-149564. + 259053. i) q^{43} +(-247354. - 428430. i) q^{44} -35608.9 q^{45} -563454. q^{46} +(-440470. - 762916. i) q^{47} +(-100445. - 173975. i) q^{48} -770314. q^{49} +412399. q^{50} +(475233. + 823128. i) q^{51} +(392497. - 679825. i) q^{52} +(-140441. - 243252. i) q^{53} +(-386195. + 668909. i) q^{54} +(630053. - 1.09128e6i) q^{55} +118126. q^{56} +(-974879. + 1.09534e6i) q^{57} +976945. q^{58} +(-160296. + 277641. i) q^{59} +(255850. - 443144. i) q^{60} +(1.38359e6 + 2.39645e6i) q^{61} +(106886. - 185132. i) q^{62} +(25198.0 + 43644.1i) q^{63} +262144. q^{64} +1.99951e6 q^{65} +(1.51644e6 + 2.62655e6i) q^{66} +(-736714. - 1.27603e6i) q^{67} -1.24028e6 q^{68} +3.45434e6 q^{69} +(150443. + 260576. i) q^{70} +(1.23505e6 - 2.13917e6i) q^{71} +(55919.1 + 96854.7i) q^{72} +(2.05033e6 - 3.55128e6i) q^{73} +(956265. - 1.65630e6i) q^{74} -2.52827e6 q^{75} +(-601762. - 1.81636e6i) q^{76} -1.78338e6 q^{77} +(-2.40626e6 + 4.16777e6i) q^{78} +(-2.59078e6 + 4.48736e6i) q^{79} +(333863. + 578267. i) q^{80} +(2.60649e6 - 4.51457e6i) q^{81} +(69530.8 + 120431. i) q^{82} +7.24258e6 q^{83} -724189. q^{84} +(-1.57960e6 - 2.73595e6i) q^{85} +(1.19651e6 + 2.07242e6i) q^{86} -5.98931e6 q^{87} -3.95766e6 q^{88} +(2.52576e6 + 4.37475e6i) q^{89} +(-142436. + 246706. i) q^{90} +(-1.41492e6 - 2.45071e6i) q^{91} +(-2.25381e6 + 3.90372e6i) q^{92} +(-655281. + 1.13498e6i) q^{93} -7.04752e6 q^{94} +(3.24035e6 - 3.64073e6i) q^{95} -1.60711e6 q^{96} +(1.60831e6 - 2.78568e6i) q^{97} +(-3.08126e6 + 5.33689e6i) q^{98} +(-844227. - 1.46224e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 56 q^{2} + 55 q^{3} - 448 q^{4} - 126 q^{5} - 440 q^{6} + 1928 q^{7} - 7168 q^{8} - 4602 q^{9}+O(q^{10}) \) 14 * q + 56 * q^2 + 55 * q^3 - 448 * q^4 - 126 * q^5 - 440 * q^6 + 1928 * q^7 - 7168 * q^8 - 4602 * q^9	\( 14 q + 56 q^{2} + 55 q^{3} - 448 q^{4} - 126 q^{5} - 440 q^{6} + 1928 q^{7} - 7168 q^{8} - 4602 q^{9} + 1008 q^{10} + 646 q^{11} - 7040 q^{12} - 1308 q^{13} + 7712 q^{14} + 8740 q^{15} - 28672 q^{16} + 10528 q^{17} - 73632 q^{18} - 87463 q^{19} + 16128 q^{20} - 30584 q^{21} + 2584 q^{22} - 113822 q^{23} - 28160 q^{24} - 50143 q^{25} - 20928 q^{26} - 319898 q^{27} - 61696 q^{28} + 167706 q^{29} + 139840 q^{30} + 201780 q^{31} + 229376 q^{32} + 377473 q^{33} - 84224 q^{34} - 33168 q^{35} - 294528 q^{36} + 380924 q^{37} - 384064 q^{38} + 1379564 q^{39} + 64512 q^{40} + 66301 q^{41} + 244672 q^{42} + 726564 q^{43} - 20672 q^{44} + 428936 q^{45} - 1821152 q^{46} - 2373788 q^{47} + 225280 q^{48} + 5898846 q^{49} - 802288 q^{50} + 3264054 q^{51} - 83712 q^{52} + 161792 q^{53} - 1279592 q^{54} - 53424 q^{55} - 987136 q^{56} - 4487994 q^{57} + 2683296 q^{58} - 1845767 q^{59} + 559360 q^{60} - 1600418 q^{61} + 807120 q^{62} - 3064040 q^{63} + 3670016 q^{64} + 6534852 q^{65} - 3019784 q^{66} - 8911929 q^{67} - 1347584 q^{68} - 8860208 q^{69} + 265344 q^{70} + 517154 q^{71} + 2356224 q^{72} - 9558049 q^{73} + 1523696 q^{74} - 24621450 q^{75} + 2525120 q^{76} - 9188192 q^{77} + 5518256 q^{78} + 7963520 q^{79} - 516096 q^{80} - 4125855 q^{81} - 530408 q^{82} + 30616886 q^{83} + 3914752 q^{84} + 6973266 q^{85} - 5812512 q^{86} + 25084136 q^{87} - 330752 q^{88} + 11829436 q^{89} + 1715744 q^{90} + 4017336 q^{91} - 7284608 q^{92} + 396810 q^{93} - 37980608 q^{94} + 7058892 q^{95} + 3604480 q^{96} - 8033723 q^{97} + 23595384 q^{98} + 24812606 q^{99}+O(q^{100}) \) 14 * q + 56 * q^2 + 55 * q^3 - 448 * q^4 - 126 * q^5 - 440 * q^6 + 1928 * q^7 - 7168 * q^8 - 4602 * q^9 + 1008 * q^10 + 646 * q^11 - 7040 * q^12 - 1308 * q^13 + 7712 * q^14 + 8740 * q^15 - 28672 * q^16 + 10528 * q^17 - 73632 * q^18 - 87463 * q^19 + 16128 * q^20 - 30584 * q^21 + 2584 * q^22 - 113822 * q^23 - 28160 * q^24 - 50143 * q^25 - 20928 * q^26 - 319898 * q^27 - 61696 * q^28 + 167706 * q^29 + 139840 * q^30 + 201780 * q^31 + 229376 * q^32 + 377473 * q^33 - 84224 * q^34 - 33168 * q^35 - 294528 * q^36 + 380924 * q^37 - 384064 * q^38 + 1379564 * q^39 + 64512 * q^40 + 66301 * q^41 + 244672 * q^42 + 726564 * q^43 - 20672 * q^44 + 428936 * q^45 - 1821152 * q^46 - 2373788 * q^47 + 225280 * q^48 + 5898846 * q^49 - 802288 * q^50 + 3264054 * q^51 - 83712 * q^52 + 161792 * q^53 - 1279592 * q^54 - 53424 * q^55 - 987136 * q^56 - 4487994 * q^57 + 2683296 * q^58 - 1845767 * q^59 + 559360 * q^60 - 1600418 * q^61 + 807120 * q^62 - 3064040 * q^63 + 3670016 * q^64 + 6534852 * q^65 - 3019784 * q^66 - 8911929 * q^67 - 1347584 * q^68 - 8860208 * q^69 + 265344 * q^70 + 517154 * q^71 + 2356224 * q^72 - 9558049 * q^73 + 1523696 * q^74 - 24621450 * q^75 + 2525120 * q^76 - 9188192 * q^77 + 5518256 * q^78 + 7963520 * q^79 - 516096 * q^80 - 4125855 * q^81 - 530408 * q^82 + 30616886 * q^83 + 3914752 * q^84 + 6973266 * q^85 - 5812512 * q^86 + 25084136 * q^87 - 330752 * q^88 + 11829436 * q^89 + 1715744 * q^90 + 4017336 * q^91 - 7284608 * q^92 + 396810 * q^93 - 37980608 * q^94 + 7058892 * q^95 + 3604480 * q^96 - 8033723 * q^97 + 23595384 * q^98 + 24812606 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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