LMFDB - Embedded newform 108.6.h.a.71.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,6,Mod(35,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("108.35");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	108.h (of order $6$, degree $2$, not 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:	$17.3214525398$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.19
Character	$\chi$	$=$	108.71
Dual form			108.6.h.a.35.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.01287 - 5.28662i) q^{2} +(-23.8967 - 21.2825i) q^{4} +(78.5398 + 45.3450i) q^{5} +(-69.6792 + 40.2293i) q^{7} +(-160.614 + 83.4942i) q^{8} +O(q^{10})$	\(q+(2.01287 - 5.28662i) q^{2} +(-23.8967 - 21.2825i) q^{4} +(78.5398 + 45.3450i) q^{5} +(-69.6792 + 40.2293i) q^{7} +(-160.614 + 83.4942i) q^{8} +(397.812 - 323.937i) q^{10} +(275.903 + 477.878i) q^{11} +(-307.186 + 532.062i) q^{13} +(72.4223 + 449.344i) q^{14} +(118.109 + 1017.17i) q^{16} +482.387i q^{17} +453.989i q^{19} +(-911.790 - 2755.12i) q^{20} +(3081.72 - 496.691i) q^{22} +(310.876 - 538.452i) q^{23} +(2549.83 + 4416.44i) q^{25} +(2194.49 + 2694.95i) q^{26} +(2521.29 + 521.599i) q^{28} +(7777.18 - 4490.16i) q^{29} +(-650.730 - 375.699i) q^{31} +(5615.11 + 1423.02i) q^{32} +(2550.20 + 970.980i) q^{34} -7296.79 q^{35} -4221.49 q^{37} +(2400.07 + 913.819i) q^{38} +(-16400.6 - 725.399i) q^{40} +(-11012.8 - 6358.24i) q^{41} +(13956.9 - 8058.04i) q^{43} +(3577.26 - 17291.6i) q^{44} +(-2220.84 - 2727.31i) q^{46} +(9570.02 + 16575.8i) q^{47} +(-5166.71 + 8949.00i) q^{49} +(28480.5 - 4590.30i) q^{50} +(18664.4 - 6176.86i) q^{52} +8422.39i q^{53} +50043.2i q^{55} +(7832.51 - 12279.2i) q^{56} +(-8083.35 - 50153.1i) q^{58} +(-2693.87 + 4665.91i) q^{59} +(-5910.89 - 10238.0i) q^{61} +(-3296.01 + 2683.93i) q^{62} +(18825.4 - 26820.6i) q^{64} +(-48252.7 + 27858.7i) q^{65} +(27131.6 + 15664.5i) q^{67} +(10266.4 - 11527.5i) q^{68} +(-14687.4 + 38575.3i) q^{70} -68895.9 q^{71} -23822.3 q^{73} +(-8497.30 + 22317.4i) q^{74} +(9662.03 - 10848.9i) q^{76} +(-38449.4 - 22198.8i) q^{77} +(-19337.5 + 11164.5i) q^{79} +(-36847.1 + 85243.6i) q^{80} +(-55780.9 + 45422.2i) q^{82} +(39320.2 + 68104.6i) q^{83} +(-21873.8 + 37886.6i) q^{85} +(-14506.4 - 90004.8i) q^{86} +(-84213.8 - 53717.4i) q^{88} -87925.1i q^{89} -49431.5i q^{91} +(-18888.5 + 6251.04i) q^{92} +(106893. - 17228.3i) q^{94} +(-20586.1 + 35656.2i) q^{95} +(-39159.6 - 67826.3i) q^{97} +(36910.1 + 45327.5i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) $ 56 * q + 3 * q^2 - q^4 + 6 * q^5	$ 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) $ 56 * q + 3 * q^2 - q^4 + 6 * q^5 - 68 * q^10 - 2 * q^13 + 1518 * q^14 - q^16 + 1242 * q^20 + 63 * q^22 + 12498 * q^25 - 2052 * q^28 + 11946 * q^29 + 7233 * q^32 + 6361 * q^34 - 8 * q^37 + 14877 * q^38 - 1526 * q^40 + 43536 * q^41 - 26880 * q^46 + 38414 * q^49 - 38631 * q^50 + 24988 * q^52 - 21186 * q^56 - 3314 * q^58 - 2 * q^61 - 106342 * q^64 - 35970 * q^65 - 31413 * q^68 + 10524 * q^70 + 53620 * q^73 + 20406 * q^74 + 26193 * q^76 - 26178 * q^77 - 151286 * q^82 + 6248 * q^85 - 279237 * q^86 - 122541 * q^88 - 435804 * q^92 + 63480 * q^94 - 58148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	2.01287	−	5.28662i	0.355828	−	0.934552i
$2$	2.01287	−	5.28662i	0.355828	−	0.934552i
$3$		0			0
$3$		0			0
$4$	−23.8967	−	21.2825i	−0.746773	−	0.665079i
$5$	78.5398	+	45.3450i	1.40496	+	0.811155i	0.994897	−	0.100901i	$-0.0321724\pi$
$5$	78.5398	+	45.3450i	1.40496	+	0.811155i	0.410066	+	0.912056i	$0.365506\pi$
$6$		0			0
$7$	−69.6792	+	40.2293i	−0.537475	+	0.310311i	−0.744055	−	0.668118i	$-0.767100\pi$
$7$	−69.6792	+	40.2293i	−0.537475	+	0.310311i	0.206580	+	0.978430i	$0.433767\pi$
$8$	−160.614	+	83.4942i	−0.887273	+	0.461245i
$9$		0			0
$10$	397.812	−	323.937i	1.25799	−	1.02438i
$11$	275.903	+	477.878i	0.687503	+	1.19079i	0.972643	+	0.232304i	$0.0746265\pi$
$11$	275.903	+	477.878i	0.687503	+	1.19079i	−0.285140	+	0.958486i	$0.592040\pi$
$12$		0			0
$13$	−307.186	+	532.062i	−0.504131	+	0.873180i	0.495858	+	0.868404i	$0.334854\pi$
$13$	−307.186	+	532.062i	−0.504131	+	0.873180i	−0.999989	+	0.00477646i	$0.998480\pi$
$14$	72.4223	+	449.344i	0.0987534	+	0.612715i
$15$		0			0
$16$	118.109	+	1017.17i	0.115341	+	0.993326i
$17$			482.387i			0.404830i	0.979300	+	0.202415i	$0.0648791\pi$
$17$			482.387i			0.404830i	−0.979300	+	0.202415i	$0.935121\pi$
$18$		0			0
$19$			453.989i			0.288510i	0.989541	+	0.144255i	$0.0460786\pi$
$19$			453.989i			0.288510i	−0.989541	+	0.144255i	$0.953921\pi$
$20$	−911.790	−	2755.12i	−0.509706	−	1.54016i
$21$		0			0
$22$	3081.72	−	496.691i	1.35749	−	0.218791i
$23$	310.876	−	538.452i	0.122537	−	0.212240i	−0.798231	−	0.602352i	$-0.794230\pi$
$23$	310.876	−	538.452i	0.122537	−	0.212240i	0.920767	+	0.390112i	$0.127564\pi$
$24$		0			0
$25$	2549.83	+	4416.44i	0.815946	+	1.41326i
$26$	2194.49	+	2694.95i	0.636648	+	0.781838i
$27$		0			0
$28$	2521.29	+	521.599i	0.607753	+	0.125731i
$29$	7777.18	−	4490.16i	1.71723	−	0.991440i	0.793332	−	0.608789i	$-0.208344\pi$
$29$	7777.18	−	4490.16i	1.71723	−	0.991440i	0.923893	−	0.382652i	$-0.124989\pi$
$30$		0			0
$31$	−650.730	−	375.699i	−0.121618	−	0.0702159i	0.437957	−	0.898996i	$-0.355702\pi$
$31$	−650.730	−	375.699i	−0.121618	−	0.0702159i	−0.559575	+	0.828780i	$0.689035\pi$
$32$	5615.11	+	1423.02i	0.969356	+	0.245661i
$33$		0			0
$34$	2550.20	+	970.980i	0.378335	+	0.144050i
$35$	−7296.79			−1.00684
$36$		0			0
$37$	−4221.49			−0.506946			−0.253473	−	0.967342i	$-0.581573\pi$
$37$	−4221.49			−0.506946			−0.253473	+	0.967342i	$0.581573\pi$
$38$	2400.07	+	913.819i	0.269628	+	0.102660i
$39$		0			0
$40$	−16400.6	−	725.399i	−1.62073	−	0.0716848i
$41$	−11012.8	−	6358.24i	−1.02315	−	0.590714i	−0.108133	−	0.994136i	$-0.534487\pi$
$41$	−11012.8	−	6358.24i	−1.02315	−	0.590714i	−0.915014	+	0.403422i	$0.867821\pi$
$42$		0			0
$43$	13956.9	−	8058.04i	1.15112	−	0.664597i	0.201957	−	0.979394i	$-0.435270\pi$
$43$	13956.9	−	8058.04i	1.15112	−	0.664597i	0.949159	+	0.314797i	$0.101937\pi$
$44$	3577.26	−	17291.6i	0.278560	−	1.34649i
$45$		0			0
$46$	−2220.84	−	2727.31i	−0.154747	−	0.190038i
$47$	9570.02	+	16575.8i	0.631929	+	1.09453i	0.987157	+	0.159753i	$0.0510697\pi$
$47$	9570.02	+	16575.8i	0.631929	+	1.09453i	−0.355228	+	0.934780i	$0.615597\pi$
$48$		0			0
$49$	−5166.71	+	8949.00i	−0.307414	+	0.532457i
$50$	28480.5	−	4590.30i	1.61110	−	0.259667i
$51$		0			0
$52$	18664.4	−	6176.86i	0.957205	−	0.316781i
$53$			8422.39i			0.411856i	0.978567	+	0.205928i	$0.0660213\pi$
$53$			8422.39i			0.411856i	−0.978567	+	0.205928i	$0.933979\pi$
$54$		0			0
$55$			50043.2i			2.23069i
$56$	7832.51	−	12279.2i	0.333757	−	0.523238i
$57$		0			0
$58$	−8083.35	−	50153.1i	−0.315516	−	1.95762i
$59$	−2693.87	+	4665.91i	−0.100750	+	0.174505i	−0.911994	−	0.410204i	$-0.865458\pi$
$59$	−2693.87	+	4665.91i	−0.100750	+	0.174505i	0.811244	+	0.584708i	$0.198791\pi$
$60$		0			0
$61$	−5910.89	−	10238.0i	−0.203390	−	0.352281i	0.746229	−	0.665689i	$-0.231862\pi$
$61$	−5910.89	−	10238.0i	−0.203390	−	0.352281i	−0.949618	+	0.313408i	$0.898529\pi$
$62$	−3296.01	+	2683.93i	−0.108895	+	0.0886731i
$63$		0			0
$64$	18825.4	−	26820.6i	0.574507	−	0.818500i
$65$	−48252.7	+	27858.7i	−1.41657	+	0.817857i
$66$		0			0
$67$	27131.6	+	15664.5i	0.738395	+	0.426313i	0.821486	−	0.570229i	$-0.193146\pi$
$67$	27131.6	+	15664.5i	0.738395	+	0.426313i	−0.0830902	+	0.996542i	$0.526479\pi$
$68$	10266.4	−	11527.5i	0.269244	−	0.302317i
$69$		0			0
$70$	−14687.4	+	38575.3i	−0.358262	+	0.940946i
$71$	−68895.9			−1.62199			−0.810994	−	0.585054i	$-0.801073\pi$
$71$	−68895.9			−1.62199			−0.810994	+	0.585054i	$0.801073\pi$
$72$		0			0
$73$	−23822.3			−0.523210			−0.261605	−	0.965175i	$-0.584252\pi$
$73$	−23822.3			−0.523210			−0.261605	+	0.965175i	$0.584252\pi$
$74$	−8497.30	+	22317.4i	−0.180385	+	0.473767i
$75$		0			0
$76$	9662.03	−	10848.9i	0.191882	−	0.215452i
$77$	−38449.4	−	22198.8i	−0.739031	−	0.426680i
$78$		0			0
$79$	−19337.5	+	11164.5i	−0.348604	+	0.201267i	−0.664070	−	0.747670i	$-0.731172\pi$
$79$	−19337.5	+	11164.5i	−0.348604	+	0.201267i	0.315466	+	0.948937i	$0.397839\pi$
$80$	−36847.1	+	85243.6i	−0.643692	+	1.48914i
$81$		0			0
$82$	−55780.9	+	45422.2i	−0.916117	+	0.745991i
$83$	39320.2	+	68104.6i	0.626499	+	1.08513i	0.988249	+	0.152853i	$0.0488461\pi$
$83$	39320.2	+	68104.6i	0.626499	+	1.08513i	−0.361750	+	0.932275i	$0.617821\pi$
$84$		0			0
$85$	−21873.8	+	37886.6i	−0.328380	+	0.568772i
$86$	−14506.4	−	90004.8i	−0.211501	−	1.31226i
$87$		0			0
$88$	−84213.8	−	53717.4i	−1.15925	−	0.739449i
$89$		−	87925.1i		−	1.17662i	−0.808634	−	0.588312i	$-0.799793\pi$
$89$		−	87925.1i		−	1.17662i	0.808634	−	0.588312i	$-0.200207\pi$
$90$		0			0
$91$		−	49431.5i		−	0.625750i
$92$	−18888.5	+	6251.04i	−0.232664	+	0.0769986i
$93$		0			0
$94$	106893.	−	17228.3i	1.24775	−	0.201105i
$95$	−20586.1	+	35656.2i	−0.234027	+	0.405346i
$96$		0			0
$97$	−39159.6	−	67826.3i	−0.422580	−	0.731929i	0.573611	−	0.819128i	$-0.305542\pi$
$97$	−39159.6	−	67826.3i	−0.422580	−	0.731929i	−0.996191	+	0.0871983i	$0.972209\pi$
$98$	36910.1	+	45327.5i	0.388222	+	0.476757i
$99$		0			0
$100$	33060.2	−	159805.i	0.330602	−	1.59805i
$101$	22486.3	−	12982.5i	0.219339	−	0.126635i	−0.386305	−	0.922371i	$-0.626249\pi$
$101$	22486.3	−	12982.5i	0.219339	−	0.126635i	0.605644	+	0.795736i	$0.292916\pi$
$102$		0			0
$103$	−21490.3	−	12407.4i	−0.199595	−	0.115236i	0.396872	−	0.917874i	$-0.370096\pi$
$103$	−21490.3	−	12407.4i	−0.199595	−	0.115236i	−0.596466	+	0.802638i	$0.703429\pi$
$104$	4914.16	−	111105.i	0.0445519	−	1.00728i
$105$		0			0
$106$	44526.0	+	16953.1i	0.384901	+	0.146550i
$107$	105956.			0.894680			0.447340	−	0.894364i	$-0.352371\pi$
$107$	105956.			0.894680			0.447340	+	0.894364i	$0.352371\pi$
$108$		0			0
$109$	−24092.4			−0.194229			−0.0971146	−	0.995273i	$-0.530961\pi$
$109$	−24092.4			−0.194229			−0.0971146	+	0.995273i	$0.530961\pi$
$110$	264560.	+	100730.i	2.08469	+	0.793740i
$111$		0			0
$112$	−49149.6	−	66123.9i	−0.370233	−	0.498096i
$113$	−7844.35	−	4528.94i	−0.0577911	−	0.0333657i	0.470826	−	0.882226i	$-0.343956\pi$
$113$	−7844.35	−	4528.94i	−0.0577911	−	0.0333657i	−0.528617	+	0.848860i	$0.677289\pi$
$114$		0			0
$115$	48832.2	−	28193.3i	0.344320	−	0.198793i
$116$	−281411.	−	58217.8i	−1.94176	−	0.401709i
$117$		0			0
$118$	19244.5	+	23633.3i	0.127234	+	0.156250i
$119$	−19406.1	−	33612.3i	−0.125623	−	0.217586i
$120$		0			0
$121$	−71719.4	+	124222.i	−0.445321	+	0.771318i
$122$	−66022.1	+	10641.0i	−0.401596	+	0.0647267i
$123$		0			0
$124$	7554.50	+	22827.1i	0.0441216	+	0.133321i
$125$			179082.i			1.02513i
$126$		0			0
$127$			195212.i			1.07398i	0.843587	+	0.536992i	$0.180439\pi$
$127$			195212.i			1.07398i	−0.843587	+	0.536992i	$0.819561\pi$
$128$	−103897.	−	153509.i	−0.560505	−	0.828151i
$129$		0			0
$130$	50152.2	+	311169.i	0.260275	+	1.61487i
$131$	126871.	−	219747.i	0.645929	−	1.11878i	−0.338157	−	0.941090i	$-0.609803\pi$
$131$	126871.	−	219747.i	0.645929	−	1.11878i	0.984086	−	0.177693i	$-0.0568632\pi$
$132$		0			0
$133$	−18263.7	−	31633.6i	−0.0895280	−	0.155067i
$134$	137424.	−	111904.i	0.661153	−	0.538375i
$135$		0			0
$136$	−40276.5	−	77477.9i	−0.186726	−	0.359195i
$137$	108349.	−	62555.1i	0.493199	−	0.284748i	−0.232702	−	0.972548i	$-0.574757\pi$
$137$	108349.	−	62555.1i	0.493199	−	0.284748i	0.725900	+	0.687800i	$0.241423\pi$
$138$		0			0
$139$	−155476.	−	89764.4i	−0.682539	−	0.394064i	0.118272	−	0.992981i	$-0.462265\pi$
$139$	−155476.	−	89764.4i	−0.682539	−	0.394064i	−0.800811	+	0.598917i	$0.795598\pi$
$140$	174369.	+	155294.i	0.751883	+	0.669629i
$141$		0			0
$142$	−138678.	+	364227.i	−0.577149	+	1.51583i
$143$	−339014.			−1.38637
$144$		0			0
$145$	814424.			3.21685
$146$	−47951.1	+	125939.i	−0.186173	+	0.488967i
$147$		0			0
$148$	100880.	+	89844.0i	0.378574	+	0.337159i
$149$	395679.	+	228445.i	1.46008	+	0.842978i	0.999014	−	0.0443874i	$-0.0141336\pi$
$149$	395679.	+	228445.i	1.46008	+	0.842978i	0.461067	+	0.887366i	$0.347467\pi$
$150$		0			0
$151$	189659.	−	109500.i	0.676909	−	0.390814i	−0.121780	−	0.992557i	$-0.538860\pi$
$151$	189659.	−	109500.i	0.676909	−	0.390814i	0.798690	+	0.601743i	$0.205527\pi$
$152$	−37905.4	−	72916.8i	−0.133074	−	0.255987i
$153$		0			0
$154$	−194750.	+	158584.i	−0.661722	+	0.538838i
$155$	−34072.1	−	59014.6i	−0.113912	−	0.197301i
$156$		0			0
$157$	113832.	−	197163.i	0.368566	−	0.638375i	−0.620776	−	0.783988i	$-0.713182\pi$
$157$	113832.	−	197163.i	0.368566	−	0.638375i	0.989342	+	0.145614i	$0.0465156\pi$
$158$	20098.8	+	124703.i	0.0640511	+	0.397405i
$159$		0			0
$160$	376483.	+	366381.i	1.16264	+	1.13144i
$161$			50025.3i			0.152098i
$162$		0			0
$163$		−	460735.i		−	1.35826i	−0.734020	−	0.679128i	$-0.762358\pi$
$163$		−	460735.i		−	1.35826i	0.734020	−	0.679128i	$-0.237642\pi$
$164$	127851.	+	386321.i	0.371187	+	1.12160i
$165$		0			0
$166$	439189.	−	70785.6i	1.23703	−	0.199377i
$167$	286572.	−	496357.i	0.795137	−	1.37722i	−0.127614	−	0.991824i	$-0.540732\pi$
$167$	286572.	−	496357.i	0.795137	−	1.37722i	0.922752	−	0.385395i	$-0.125935\pi$
$168$		0			0
$169$	−3080.17	−	5335.01i	−0.00829579	−	0.0143687i
$170$	156263.	+	191899.i	0.414699	+	0.509273i
$171$		0			0
$172$	−505021.	−	104478.i	−1.30163	−	0.269279i
$173$	283930.	−	163927.i	0.721268	−	0.416424i	−0.0939514	−	0.995577i	$-0.529950\pi$
$173$	283930.	−	163927.i	0.721268	−	0.416424i	0.815219	+	0.579153i	$0.196617\pi$
$174$		0			0
$175$	−355340.	−	205156.i	−0.877101	−	0.506394i
$176$	−453495.	+	337081.i	−1.10355	+	0.820261i
$177$		0			0
$178$	−464827.	−	176981.i	−1.09962	−	0.418676i
$179$	123110.			0.287185			0.143592	−	0.989637i	$-0.454135\pi$
$179$	123110.			0.287185			0.143592	+	0.989637i	$0.454135\pi$
$180$		0			0
$181$	−311888.			−0.707622			−0.353811	−	0.935317i	$-0.615114\pi$
$181$	−311888.			−0.707622			−0.353811	+	0.935317i	$0.615114\pi$
$182$	−261326.	−	99499.0i	−0.584795	−	0.222659i
$183$		0			0
$184$	−4973.19	+	112439.i	−0.0108290	+	0.244835i
$185$	−331555.	−	191423.i	−0.712240	−	0.411212i
$186$		0			0
$187$	−230522.	+	133092.i	−0.482068	+	0.278322i
$188$	124082.	−	599781.i	0.256043	−	1.23765i
$189$		0			0
$190$	147064.	+	180602.i	0.295544	+	0.362943i
$191$	97915.9	+	169595.i	0.194209	+	0.336380i	0.946641	−	0.322290i	$-0.104453\pi$
$191$	97915.9	+	169595.i	0.194209	+	0.336380i	−0.752432	+	0.658670i	$0.771119\pi$
$192$		0			0
$193$	−296774.	+	514028.i	−0.573499	+	0.993330i	0.422704	+	0.906268i	$0.361081\pi$
$193$	−296774.	+	514028.i	−0.573499	+	0.993330i	−0.996203	+	0.0870619i	$0.972252\pi$
$194$	−437395.	+	70496.5i	−0.834391	+	0.134482i
$195$		0			0
$196$	313925.	−	103891.i	0.583694	−	0.193170i
$197$			100175.i			0.183905i	0.995763	+	0.0919523i	$0.0293107\pi$
$197$			100175.i			0.183905i	−0.995763	+	0.0919523i	$0.970689\pi$
$198$		0			0
$199$			402805.i			0.721045i	0.932751	+	0.360522i	$0.117402\pi$
$199$			402805.i			0.721045i	−0.932751	+	0.360522i	$0.882598\pi$
$200$	−778285.	−	496444.i	−1.37583	−	0.877597i
$201$		0			0
$202$	−23371.6	−	145009.i	−0.0403004	−	0.250044i
$203$	−361272.	+	625741.i	−0.615310	+	1.06575i
$204$		0			0
$205$	−576628.	−	998750.i	−0.958322	−	1.65986i
$206$	−108850.	+	88636.5i	−0.178715	+	0.145527i
$207$		0			0
$208$	−577477.	−	249618.i	−0.925499	−	0.400053i
$209$	−216951.	+	125257.i	−0.343555	+	0.198352i
$210$		0			0
$211$	−538419.	−	310856.i	−0.832557	−	0.480677i	0.0221701	−	0.999754i	$-0.492942\pi$
$211$	−538419.	−	310856.i	−0.832557	−	0.480677i	−0.854728	+	0.519077i	$0.826276\pi$
$212$	179250.	−	201268.i	0.273917	−	0.307563i
$213$		0			0
$214$	213276.	−	560152.i	0.318352	−	0.836125i
$215$	1.46157e6			2.15637
$216$		0			0
$217$	60456.4			0.0871552
$218$	−48494.9	+	127368.i	−0.0691122	+	0.181517i
$219$		0			0
$220$	1.06505e6	−	1.19587e6i	1.48358	−	1.66582i
$221$	−256660.	−	148183.i	−0.353490	−	0.204088i
$222$		0			0
$223$	1.11763e6	−	645261.i	1.50499	−	0.868907i	0.505008	−	0.863115i	$-0.331490\pi$
$223$	1.11763e6	−	645261.i	1.50499	−	0.868907i	0.999983	−	0.00579252i	$-0.00184383\pi$
$224$	−448503.	+	126737.i	−0.597236	+	0.168765i
$225$		0			0
$226$	−39732.4	+	32354.0i	−0.0517456	+	0.0421363i
$227$	−435023.	−	753483.i	−0.560335	−	0.970529i	−0.997467	−	0.0711316i	$-0.977339\pi$
$227$	−435023.	−	753483.i	−0.560335	−	0.970529i	0.437132	−	0.899398i	$-0.355994\pi$
$228$		0			0
$229$	55144.9	−	95513.7i	0.0694891	−	0.120359i	−0.829187	−	0.558971i	$-0.811196\pi$
$229$	55144.9	−	95513.7i	0.0694891	−	0.120359i	0.898677	+	0.438612i	$0.144530\pi$
$230$	−50754.6	−	314907.i	−0.0632639	−	0.392521i
$231$		0			0
$232$	−874219.	+	1.37053e6i	−1.06635	+	1.67174i
$233$		−	352716.i		−	0.425633i	−0.977092	−	0.212817i	$-0.931736\pi$
$233$		−	352716.i		−	0.425633i	0.977092	−	0.212817i	$-0.0682637\pi$
$234$		0			0
$235$			1.73581e6i			2.05037i
$236$	163677.	−	54167.9i	0.191297	−	0.0633085i
$237$		0			0
$238$	−216758.	+	34935.6i	−0.248046	+	0.0399784i
$239$	−345720.	+	598804.i	−0.391498	+	0.678094i	−0.992647	−	0.121043i	$-0.961376\pi$
$239$	−345720.	+	598804.i	−0.391498	+	0.678094i	0.601150	+	0.799137i	$0.294710\pi$
$240$		0			0
$241$	−37478.3	−	64914.3i	−0.0415659	−	0.0719942i	0.844494	−	0.535565i	$-0.179901\pi$
$241$	−37478.3	−	64914.3i	−0.0415659	−	0.0719942i	−0.886060	+	0.463571i	$0.846568\pi$
$242$	512351.	+	629195.i	0.562379	+	0.690632i
$243$		0			0
$244$	−76638.6	+	370453.i	−0.0824087	+	0.398344i
$245$	−811584.	+	468568.i	−0.863810	+	0.498721i
$246$		0			0
$247$	−241550.	−	139459.i	−0.251921	−	0.145447i
$248$	135885.	+	6010.18i	0.140295	+	0.00620524i
$249$		0			0
$250$	946739.	+	360468.i	0.958033	+	0.364768i
$251$	−1.33103e6			−1.33353			−0.666767	−	0.745266i	$-0.732322\pi$
$251$	−1.33103e6			−1.33353			−0.666767	+	0.745266i	$0.732322\pi$
$252$		0			0
$253$	343086.			0.336978
$254$	1.03201e6	+	392936.i	1.00369	+	0.382153i
$255$		0			0
$256$	−1.02068e6	+	240273.i	−0.973393	+	0.229142i
$257$	185992.	+	107383.i	0.175656	+	0.101415i	0.585250	−	0.810853i	$-0.300996\pi$
$257$	185992.	+	107383.i	0.175656	+	0.101415i	−0.409594	+	0.912268i	$0.634330\pi$
$258$		0			0
$259$	294150.	−	169828.i	0.272471	−	0.157311i
$260$	1.74598e6	+	361206.i	1.60180	+	0.331377i
$261$		0			0
$262$	−906347.	−	1.11304e6i	−0.815720	−	1.00175i
$263$	−327806.	−	567776.i	−0.292232	−	0.506160i	0.682106	−	0.731254i	$-0.261064\pi$
$263$	−327806.	−	567776.i	−0.292232	−	0.506160i	−0.974337	+	0.225094i	$0.927731\pi$
$264$		0			0
$265$	−381913.	+	661492.i	−0.334079	+	0.578642i
$266$	−203997.	+	32878.9i	−0.176775	+	0.0284914i
$267$		0			0
$268$	−314979.	−	951759.i	−0.267882	−	0.809450i
$269$		−	424539.i		−	0.357715i	−0.983875	−	0.178857i	$-0.942760\pi$
$269$		−	424539.i		−	0.357715i	0.983875	−	0.178857i	$-0.0572401\pi$
$270$		0			0
$271$		−	276579.i		−	0.228769i	−0.993437	−	0.114384i	$-0.963510\pi$
$271$		−	276579.i		−	0.228769i	0.993437	−	0.114384i	$-0.0364895\pi$
$272$	−490667.	+	56974.2i	−0.402129	+	0.0466934i
$273$		0			0
$274$	−112614.	−	698713.i	−0.0906183	−	0.562241i
$275$	−1.40701e6	+	2.43702e6i	−1.12193	+	1.94324i
$276$		0			0
$277$	758444.	+	1.31366e6i	0.593915	+	1.02869i	0.993699	+	0.112081i	$0.0357517\pi$
$277$	758444.	+	1.31366e6i	0.593915	+	1.02869i	−0.399784	+	0.916609i	$0.630915\pi$
$278$	−787503.	+	641262.i	−0.611140	+	0.497649i
$279$		0			0
$280$	1.17196e6	−	609239.i	0.893344	−	0.464401i
$281$	−831581.	+	480113.i	−0.628259	+	0.362725i	−0.780077	−	0.625683i	$-0.784820\pi$
$281$	−831581.	+	480113.i	−0.628259	+	0.362725i	0.151819	+	0.988408i	$0.451487\pi$
$282$		0			0
$283$	780527.	+	450638.i	0.579325	+	0.334473i	0.760865	−	0.648910i	$-0.224775\pi$
$283$	780527.	+	450638.i	0.579325	+	0.334473i	−0.181540	+	0.983384i	$0.558108\pi$
$284$	1.64639e6	+	1.46628e6i	1.21126	+	1.07875i
$285$		0			0
$286$	−682390.	+	1.79224e6i	−0.493307	+	1.29563i
$287$	1.02315e6			0.733221
$288$		0			0
$289$	1.18716e6			0.836112
$290$	1.63933e6	−	4.30555e6i	1.14464	−	3.00631i
$291$		0			0
$292$	569275.	+	506998.i	0.390719	+	0.347976i
$293$	1.02663e6	+	592723.i	0.698623	+	0.403350i	0.806835	−	0.590778i	$-0.201179\pi$
$293$	1.02663e6	+	592723.i	0.698623	+	0.403350i	−0.108211	+	0.994128i	$0.534512\pi$
$294$		0			0
$295$	−423151.	+	244307.i	−0.283101	+	0.163448i
$296$	678029.	−	352470.i	0.449800	−	0.233826i
$297$		0			0
$298$	2.00415e6	−	1.63197e6i	1.30734	−	1.06457i
$299$	190993.	+	330810.i	0.123549	+	0.213994i
$300$		0			0
$301$	−648339.	+	1.12296e6i	−0.412464	+	0.714408i
$302$	−197125.	−	1.22306e6i	−0.124373	−	0.771669i
$303$		0			0
$304$	−461782.	+	53620.1i	−0.286585	+	0.0332770i
$305$		−	1.07212e6i		−	0.659922i
$306$		0			0
$307$			740939.i			0.448680i	0.974511	+	0.224340i	$0.0720226\pi$
$307$			740939.i			0.448680i	−0.974511	+	0.224340i	$0.927977\pi$
$308$	446370.	+	1.34878e6i	0.268113	+	0.810147i
$309$		0			0
$310$	−380571.	+	61337.9i	−0.224921	+	0.0362514i
$311$	1.37781e6	−	2.38644e6i	0.807771	−	1.39910i	−0.106633	−	0.994298i	$-0.534007\pi$
$311$	1.37781e6	−	2.38644e6i	0.807771	−	1.39910i	0.914404	−	0.404802i	$-0.132660\pi$
$312$		0			0
$313$	−1.36134e6	−	2.35791e6i	−0.785427	−	1.36040i	−0.928744	−	0.370722i	$-0.879110\pi$
$313$	−1.36134e6	−	2.35791e6i	−0.785427	−	1.36040i	0.143317	−	0.989677i	$-0.454223\pi$
$314$	−813196.	−	998648.i	−0.465448	−	0.571595i
$315$		0			0
$316$	699713.	+	144755.i	0.394187	+	0.0815486i
$317$	731344.	−	422242.i	0.408765	−	0.236001i	−0.281494	−	0.959563i	$-0.590830\pi$
$317$	731344.	−	422242.i	0.408765	−	0.236001i	0.690259	+	0.723562i	$0.257497\pi$
$318$		0			0
$319$	4.29149e6	+	2.47770e6i	2.36119	+	1.36324i
$320$	2.69472e6	−	1.25285e6i	1.47109	−	0.683947i
$321$		0			0
$322$	264465.	+	100694.i	0.142144	+	0.0541208i
$323$	−218998.			−0.116798
$324$		0			0
$325$	−3.13309e6			−1.64537
$326$	−2.43573e6	−	927397.i	−1.26936	−	0.483305i
$327$		0			0
$328$	2.29968e6	+	101715.i	1.18027	+	0.0522036i
$329$	−1.33366e6	−	769990.i	−0.679291	−	0.392189i
$330$		0			0
$331$	−1.52485e6	+	880372.i	−0.764992	+	0.441668i	−0.831085	−	0.556145i	$-0.812280\pi$
$331$	−1.52485e6	+	880372.i	−0.764992	+	0.441668i	0.0660935	+	0.997813i	$0.478946\pi$
$332$	509812.	−	2.46431e6i	0.253843	−	1.22702i
$333$		0			0
$334$	−2.04722e6	−	2.51410e6i	−1.00415	−	1.23315i
$335$	1.42061e6	+	2.46057e6i	0.691612	+	1.19791i
$336$		0			0
$337$	−1.23174e6	+	2.13344e6i	−0.590806	+	1.02331i	0.403318	+	0.915060i	$0.367857\pi$
$337$	−1.23174e6	+	2.13344e6i	−0.590806	+	1.02331i	−0.994124	+	0.108246i	$0.965477\pi$
$338$	−34404.1	+	5545.03i	−0.0163802	+	0.00264005i
$339$		0			0
$340$	1.32903e6	−	439836.i	0.623504	−	0.206345i
$341$		−	414626.i		−	0.193095i
$342$		0			0
$343$		−	2.18368e6i		−	1.00220i
$344$	−1.56887e6	+	2.45955e6i	−0.714812	+	1.12063i
$345$		0			0
$346$	−295108.	−	1.83100e6i	−0.132523	−	0.822237i
$347$	−473354.	+	819874.i	−0.211039	+	0.365530i	−0.952040	−	0.305974i	$-0.901018\pi$
$347$	−473354.	+	819874.i	−0.211039	+	0.365530i	0.741001	+	0.671504i	$0.234351\pi$
$348$		0			0
$349$	1.96690e6	+	3.40677e6i	0.864408	+	1.49720i	0.867633	+	0.497204i	$0.165640\pi$
$349$	1.96690e6	+	3.40677e6i	0.864408	+	1.49720i	−0.00322519	+	0.999995i	$0.501027\pi$
$350$	−1.79983e6	+	1.46560e6i	−0.785349	+	0.639507i
$351$		0			0
$352$	869195.	+	3.07595e6i	0.373904	+	1.32319i
$353$	3.34675e6	−	1.93225e6i	1.42951	−	0.825327i	0.432426	−	0.901669i	$-0.357658\pi$
$353$	3.34675e6	−	1.93225e6i	1.42951	−	0.825327i	0.997082	+	0.0763423i	$0.0243242\pi$
$354$		0			0
$355$	−5.41107e6	−	3.12408e6i	−2.27883	−	1.31568i
$356$	−1.87127e6	+	2.10112e6i	−0.782548	+	0.878672i
$357$		0			0
$358$	247804.	−	650837.i	0.102188	−	0.268389i
$359$	−1.23588e6			−0.506106			−0.253053	−	0.967452i	$-0.581435\pi$
$359$	−1.23588e6			−0.506106			−0.253053	+	0.967452i	$0.581435\pi$
$360$		0			0
$361$	2.26999e6			0.916762
$362$	−627788.	+	1.64883e6i	−0.251792	+	0.661310i
$363$		0			0
$364$	−1.05203e6	+	1.18125e6i	−0.416173	+	0.467293i
$365$	−1.87100e6	−	1.08022e6i	−0.735091	−	0.424405i
$366$		0			0
$367$	435715.	−	251560.i	0.168864	−	0.0974937i	−0.413186	−	0.910647i	$-0.635584\pi$
$367$	435715.	−	251560.i	0.168864	−	0.0974937i	0.582050	+	0.813153i	$0.302251\pi$
$368$	584413.	+	252616.i	0.224957	+	0.0972392i
$369$		0			0
$370$	−1.67936e6	+	1.36750e6i	−0.637734	+	0.519305i
$371$	−338827.	−	586865.i	−0.127804	−	0.221362i
$372$		0			0
$373$	2.28143e6	−	3.95156e6i	0.849055	−	1.47061i	−0.0329973	−	0.999455i	$-0.510505\pi$
$373$	2.28143e6	−	3.95156e6i	0.849055	−	1.47061i	0.882052	−	0.471151i	$-0.156161\pi$
$374$	239597.	+	1.48658e6i	0.0885732	+	0.549552i
$375$		0			0
$376$	−2.92105e6	−	1.86325e6i	−1.06554	−	0.679675i
$377$			5.51726e6i			1.99926i
$378$		0			0
$379$		−	3.52082e6i		−	1.25906i	−0.776977	−	0.629529i	$-0.783248\pi$
$379$		−	3.52082e6i		−	1.25906i	0.776977	−	0.629529i	$-0.216752\pi$
$380$	1.25079e6	−	413943.i	0.444352	−	0.147055i
$381$		0			0
$382$	1.09368e6	−	176272.i	0.383470	−	0.0618051i
$383$	598408.	−	1.03647e6i	0.208449	−	0.361045i	−0.742777	−	0.669539i	$-0.766492\pi$
$383$	598408.	−	1.03647e6i	0.208449	−	0.361045i	0.951226	+	0.308494i	$0.0998250\pi$
$384$		0			0
$385$	−2.01320e6	−	3.48697e6i	−0.692207	−	1.19894i
$386$	2.12011e6	+	2.60360e6i	0.724251	+	0.889419i
$387$		0			0
$388$	−507729.	+	2.45424e6i	−0.171219	+	0.827634i
$389$	−1.22413e6	+	706752.i	−0.410160	+	0.236806i	−0.690859	−	0.722990i	$-0.742767\pi$
$389$	−1.22413e6	+	706752.i	−0.410160	+	0.236806i	0.280698	+	0.959796i	$0.409434\pi$
$390$		0			0
$391$	259742.	+	149962.i	0.0859213	+	0.0496067i
$392$	82653.6	−	1.86872e6i	0.0271673	−	0.614227i
$393$		0			0
$394$	529586.	+	201638.i	0.171868	+	0.0654383i
$395$	−2.02502e6			−0.653035
$396$		0			0
$397$	1.97577e6			0.629160			0.314580	−	0.949231i	$-0.398136\pi$
$397$	1.97577e6			0.629160			0.314580	+	0.949231i	$0.398136\pi$
$398$	2.12948e6	+	810792.i	0.673854	+	0.256568i
$399$		0			0
$400$	−4.19109e6	+	3.11522e6i	−1.30972	+	0.973507i
$401$	650613.	+	375632.i	0.202052	+	0.116654i	0.597612	−	0.801785i	$-0.296116\pi$
$401$	650613.	+	375632.i	0.202052	+	0.116654i	−0.395561	+	0.918440i	$0.629450\pi$
$402$		0			0
$403$	399790.	−	230819.i	0.122622	−	0.0707960i
$404$	−813650.	−	168327.i	−0.248019	−	0.0513097i
$405$		0			0
$406$	2.58087e6	+	3.16944e6i	0.777052	+	0.954262i
$407$	−1.16472e6	−	2.01736e6i	−0.348527	−	0.603666i
$408$		0			0
$409$	1.22030e6	−	2.11362e6i	0.360710	−	0.624768i	−0.627368	−	0.778723i	$-0.715868\pi$
$409$	1.22030e6	−	2.11362e6i	0.360710	−	0.624768i	0.988078	+	0.153955i	$0.0492011\pi$
$410$	−6.44069e6	+	1.03807e6i	−1.89222	+	0.304976i
$411$		0			0
$412$	249487.	+	753864.i	0.0724109	+	0.218801i
$413$		−	433490.i		−	0.125056i
$414$		0			0
$415$			7.13189e6i			2.03275i
$416$	−2.48202e6	+	2.55045e6i	−0.703189	+	0.722577i
$417$		0			0
$418$	225492.	+	1.39906e6i	0.0631234	+	0.391649i
$419$	3.49913e6	−	6.06068e6i	0.973701	−	1.68650i	0.289543	−	0.957165i	$-0.406497\pi$
$419$	3.49913e6	−	6.06068e6i	0.973701	−	1.68650i	0.684158	−	0.729334i	$-0.260170\pi$
$420$		0			0
$421$	575740.	+	997211.i	0.158315	+	0.274209i	0.934261	−	0.356590i	$-0.116061\pi$
$421$	575740.	+	997211.i	0.158315	+	0.274209i	−0.775946	+	0.630799i	$0.782727\pi$
$422$	−2.72714e6	+	2.22071e6i	−0.745465	+	0.607030i
$423$		0			0
$424$	−703220.	−	1.35275e6i	−0.189966	−	0.365429i
$425$	−2.13043e6	+	1.23001e6i	−0.572131	+	0.330320i
$426$		0			0
$427$	823733.	+	475582.i	0.218633	+	0.126228i
$428$	−2.53201e6	−	2.25502e6i	−0.668123	−	0.595033i
$429$		0			0
$430$	2.94194e6	−	7.72675e6i	0.767295	−	2.01524i
$431$	−61287.6			−0.0158920			−0.00794601	−	0.999968i	$-0.502529\pi$
$431$	−61287.6			−0.0158920			−0.00794601	+	0.999968i	$0.502529\pi$
$432$		0			0
$433$	−6.42481e6			−1.64680			−0.823399	−	0.567462i	$-0.807925\pi$
$433$	−6.42481e6			−1.64680			−0.823399	+	0.567462i	$0.807925\pi$
$434$	121691.	−	319610.i	0.0310122	−	0.0814510i
$435$		0			0
$436$	575731.	+	512748.i	0.145045	+	0.129178i
$437$	244451.	+	141134.i	0.0612335	+	0.0353532i
$438$		0			0
$439$	−1.53160e6	+	884268.i	−0.379301	+	0.218989i	−0.677514	−	0.735510i	$-0.736943\pi$
$439$	−1.53160e6	+	884268.i	−0.379301	+	0.218989i	0.298213	+	0.954499i	$0.403609\pi$
$440$	−4.17832e6	−	8.03762e6i	−1.02889	−	1.97923i
$441$		0			0
$442$	−1.30001e6	+	1.05859e6i	−0.316512	+	0.257735i
$443$	3.28943e6	+	5.69747e6i	0.796364	+	1.37934i	0.921969	+	0.387263i	$0.126579\pi$
$443$	3.28943e6	+	5.69747e6i	0.796364	+	1.37934i	−0.125605	+	0.992080i	$0.540087\pi$
$444$		0			0
$445$	3.98696e6	−	6.90562e6i	0.954425	−	1.65311i
$446$	−1.16162e6	−	7.20729e6i	−0.276521	−	1.71567i
$447$		0			0
$448$	−232767.	+	2.62617e6i	−0.0547931	+	0.618199i
$449$			974339.i			0.228084i	0.993476	+	0.114042i	$0.0363798\pi$
$449$			974339.i			0.228084i	−0.993476	+	0.114042i	$0.963620\pi$
$450$		0			0
$451$		−	7.01703e6i		−	1.62447i
$452$	91067.2	+	275174.i	0.0209660	+	0.0633522i
$453$		0			0
$454$	−4.85902e6	+	783145.i	−1.10639	+	0.178321i
$455$	2.24147e6	−	3.88234e6i	0.507580	−	0.879155i
$456$		0			0
$457$	2.33316e6	+	4.04116e6i	0.522583	+	0.905140i	0.999655	+	0.0262754i	$0.00836468\pi$
$457$	2.33316e6	+	4.04116e6i	0.522583	+	0.905140i	−0.477072	+	0.878864i	$0.658302\pi$
$458$	−393946.	−	483787.i	−0.0877552	−	0.107768i
$459$		0			0
$460$	−1.76696e6	−	365545.i	−0.389342	−	0.0805463i
$461$	−2.23506e6	+	1.29041e6i	−0.489820	+	0.282798i	−0.724500	−	0.689275i	$-0.757929\pi$
$461$	−2.23506e6	+	1.29041e6i	−0.489820	+	0.282798i	0.234680	+	0.972073i	$0.424596\pi$
$462$		0			0
$463$	2.00581e6	+	1.15806e6i	0.434849	+	0.251060i	0.701410	−	0.712758i	$-0.252554\pi$
$463$	2.00581e6	+	1.15806e6i	0.434849	+	0.251060i	−0.266561	+	0.963818i	$0.585887\pi$
$464$	5.48579e6	+	7.38036e6i	1.18289	+	1.59141i
$465$		0			0
$466$	−1.86468e6	−	709970.i	−0.397776	−	0.151452i
$467$	26296.7			0.00557969			0.00278984	−	0.999996i	$-0.499112\pi$
$467$	26296.7			0.00557969			0.00278984	+	0.999996i	$0.499112\pi$
$468$		0			0
$469$	−2.52068e6			−0.529159
$470$	9.17656e6	+	3.49395e6i	1.91618	+	0.729578i
$471$		0			0
$472$	43094.7	−	974331.i	0.00890367	−	0.201304i
$473$	7.70152e6	+	4.44648e6i	1.58279	+	0.913825i
$474$		0			0
$475$	−2.00501e6	+	1.15760e6i	−0.407740	+	0.235409i
$476$	−251613.	+	1.21624e6i	−0.0508997	+	0.246037i
$477$		0			0
$478$	2.46976e6	+	3.03300e6i	0.494408	+	0.607159i
$479$	−3.17700e6	−	5.50272e6i	−0.632671	−	1.09582i	−0.987003	−	0.160699i	$-0.948625\pi$
$479$	−3.17700e6	−	5.50272e6i	−0.632671	−	1.09582i	0.354332	−	0.935120i	$-0.384708\pi$
$480$		0			0
$481$	1.29678e6	−	2.24610e6i	0.255567	−	0.442655i
$482$	−418616.	+	67469.7i	−0.0820726	+	0.0132279i
$483$		0			0
$484$	4.35761e6	−	1.44212e6i	0.845541	−	0.279827i
$485$		−	7.10276e6i		−	1.37111i
$486$		0			0
$487$		−	7.12992e6i		−	1.36227i	−0.732159	−	0.681134i	$-0.761487\pi$
$487$		−	7.12992e6i		−	1.36227i	0.732159	−	0.681134i	$-0.238513\pi$
$488$	1.80418e6	+	1.15083e6i	0.342950	+	0.218757i
$489$		0			0
$490$	843534.	+	5.23370e6i	0.158713	+	0.984734i
$491$	−4.12052e6	+	7.13694e6i	−0.771343	+	1.33601i	0.165483	+	0.986213i	$0.447082\pi$
$491$	−4.12052e6	+	7.13694e6i	−0.771343	+	1.33601i	−0.936827	+	0.349793i	$0.886252\pi$
$492$		0			0
$493$	2.16599e6	+	3.75161e6i	0.401365	+	0.695185i
$494$	−1.22348e6	+	996273.i	−0.225568	+	0.183680i
$495$		0			0
$496$	305291.	−	706273.i	0.0557199	−	0.128905i
$497$	4.80061e6	−	2.77164e6i	0.871778	−	0.503321i
$498$		0			0
$499$	−7.31706e6	−	4.22451e6i	−1.31548	−	0.759495i	−0.332485	−	0.943109i	$-0.607887\pi$
$499$	−7.31706e6	−	4.22451e6i	−1.31548	−	0.759495i	−0.982998	+	0.183614i	$0.941220\pi$
$500$	3.81132e6	−	4.27948e6i	0.681789	−	0.765536i
$501$		0			0
$502$	−2.67919e6	+	7.03666e6i	−0.474508	+	1.24626i
$503$	6.32200e6			1.11413			0.557063	−	0.830470i	$-0.311928\pi$
$503$	6.32200e6			1.11413			0.557063	+	0.830470i	$0.311928\pi$
$504$		0			0
$505$	2.35476e6			0.410883
$506$	690586.	−	1.81377e6i	0.119906	−	0.314923i
$507$		0			0
$508$	4.15461e6	−	4.66494e6i	0.714284	−	0.802023i
$509$	194691.	+	112405.i	0.0333082	+	0.0192305i	0.516562	−	0.856250i	$-0.327212\pi$
$509$	194691.	+	112405.i	0.0333082	+	0.0192305i	−0.483253	+	0.875481i	$0.660545\pi$
$510$		0			0
$511$	1.65992e6	−	958354.i	0.281212	−	0.162358i
$512$	−784254.	+	5.87957e6i	−0.132215	+	0.991221i
$513$		0			0
$514$	942070.	−	767124.i	0.157281	−	0.128073i
$515$	−1.12523e6	−	1.94895e6i	−0.186949	−	0.323805i
$516$		0			0
$517$	−5.28079e6	+	9.14660e6i	−0.868906	+	1.50499i
$518$	−305730.	−	1.89690e6i	−0.0500627	−	0.310614i
$519$		0			0
$520$	5.42399e6	−	8.50330e6i	0.879652	−	1.37905i
$521$		−	5.59008e6i		−	0.902243i	−0.892462	−	0.451122i	$-0.851024\pi$
$521$		−	5.59008e6i		−	0.902243i	0.892462	−	0.451122i	$-0.148976\pi$
$522$		0			0
$523$		−	193807.i		−	0.0309825i	−0.999880	−	0.0154912i	$-0.995069\pi$
$523$		−	193807.i		−	0.0309825i	0.999880	−	0.0154912i	$-0.00493121\pi$
$524$	−7.70859e6	+	2.55111e6i	−1.22644	+	0.405883i
$525$		0			0
$526$	−3.66145e6	+	590128.i	−0.577017	+	0.0929997i
$527$	181232.	−	313903.i	0.0284255	−	0.0492345i
$528$		0			0
$529$	3.02488e6	+	5.23925e6i	0.469969	+	0.814011i
$530$	2.72832e6	+	3.35052e6i	0.421896	+	0.518111i
$531$		0			0
$532$	−236800.	+	1.14464e6i	−0.0362747	+	0.175343i
$533$	6.76596e6	−	3.90633e6i	1.03160	−	0.595594i
$534$		0			0
$535$	8.32179e6	+	4.80459e6i	1.25699	+	0.725725i
$536$	−5.66560e6	−	250590.i	−0.851793	−	0.0376748i
$537$		0			0
$538$	−2.24438e6	−	854540.i	−0.334303	−	0.127285i
$539$	−5.70204e6			−0.845392
$540$		0			0
$541$	3.08637e6			0.453373			0.226686	−	0.973968i	$-0.427211\pi$
$541$	3.08637e6			0.453373			0.226686	+	0.973968i	$0.427211\pi$
$542$	−1.46217e6	−	556717.i	−0.213796	−	0.0814022i
$543$		0			0
$544$	−686447.	+	2.70865e6i	−0.0994511	+	0.392425i
$545$	−1.89222e6	−	1.09247e6i	−0.272885	−	0.157550i
$546$		0			0
$547$	−2.05052e6	+	1.18387e6i	−0.293018	+	0.169174i	−0.639302	−	0.768955i	$-0.720777\pi$
$547$	−2.05052e6	+	1.18387e6i	−0.293018	+	0.169174i	0.346284	+	0.938130i	$0.387443\pi$
$548$	−3.92051e6	−	811068.i	−0.557688	−	0.115373i
$549$		0			0
$550$	1.00515e7	+	1.23437e7i	1.41685	+	1.73996i
$551$	2.03848e6	+	3.53075e6i	0.286041	+	0.495437i
$552$		0			0
$553$	898281.	−	1.55587e6i	0.124911	−	0.216352i
$554$	8.47149e6	−	1.36538e6i	1.17270	−	0.189007i
$555$		0			0
$556$	1.80497e6	+	5.45401e6i	0.247618	+	0.748219i
$557$			1.20970e7i			1.65211i	0.563589	+	0.826056i	$0.309420\pi$
$557$			1.20970e7i			1.65211i	−0.563589	+	0.826056i	$0.690580\pi$
$558$		0			0
$559$			9.90128e6i			1.34018i
$560$	−861815.	−	7.42204e6i	−0.116130	−	1.00012i
$561$		0			0
$562$	864318.	+	5.36266e6i	0.115434	+	0.716208i
$563$	−2.49691e6	+	4.32478e6i	−0.331996	+	0.575033i	−0.982903	−	0.184124i	$-0.941055\pi$
$563$	−2.49691e6	+	4.32478e6i	−0.331996	+	0.575033i	0.650907	+	0.759157i	$0.274389\pi$
$564$		0			0
$565$	−410729.	−	711403.i	−0.0541295	−	0.0937551i
$566$	3.95345e6	−	3.21928e6i	0.518722	−	0.422394i
$567$		0			0
$568$	1.10656e7	−	5.75241e6i	1.43915	−	0.748134i
$569$	−5.38818e6	+	3.11087e6i	−0.697688	+	0.402810i	−0.806486	−	0.591253i	$-0.798633\pi$
$569$	−5.38818e6	+	3.11087e6i	−0.697688	+	0.402810i	0.108798	+	0.994064i	$0.465300\pi$
$570$		0			0
$571$	8.67863e6	+	5.01061e6i	1.11394	+	0.643132i	0.939846	−	0.341597i	$-0.110968\pi$
$571$	8.67863e6	+	5.01061e6i	1.11394	+	0.643132i	0.174091	+	0.984730i	$0.444301\pi$
$572$	8.10134e6	+	7.21508e6i	1.03530	+	0.922042i
$573$		0			0
$574$	2.05946e6	−	5.40901e6i	0.260900	−	0.685233i
$575$	3.17072e6			0.399934
$576$		0			0
$577$	−6.84784e6			−0.856276			−0.428138	−	0.903713i	$-0.640830\pi$
$577$	−6.84784e6			−0.856276			−0.428138	+	0.903713i	$0.640830\pi$
$578$	2.38959e6	−	6.27607e6i	0.297512	−	0.781390i
$579$		0			0
$580$	−1.94621e7	−	1.73330e7i	−2.40226	−	2.13946i
$581$	−5.47960e6	−	3.16365e6i	−0.673455	−	0.388819i
$582$		0			0
$583$	−4.02487e6	+	2.32376e6i	−0.490434	+	0.283152i
$584$	3.82618e6	−	1.98902e6i	0.464230	−	0.241328i
$585$		0			0
$586$	5.19996e6	−	4.23431e6i	0.625541	−	0.509376i
$587$	636726.	+	1.10284e6i	0.0762706	+	0.132105i	0.901638	−	0.432491i	$-0.142365\pi$
$587$	636726.	+	1.10284e6i	0.0762706	+	0.132105i	−0.825368	+	0.564596i	$0.809032\pi$
$588$		0			0
$589$	170563.	−	295424.i	0.0202580	−	0.0350879i
$590$	439810.	+	2.72880e6i	0.0520157	+	0.322731i
$591$		0			0
$592$	−498596.	−	4.29396e6i	−0.0584715	−	0.503563i
$593$			1.18555e6i			0.138447i	0.997601	+	0.0692233i	$0.0220521\pi$
$593$			1.18555e6i			0.138447i	−0.997601	+	0.0692233i	$0.977948\pi$
$594$		0			0
$595$		−	3.51987e6i		−	0.407600i
$596$	−4.59354e6	−	1.38801e7i	−0.529703	−	1.60058i
$597$		0			0
$598$	2.13331e6	−	343833.i	0.243950	−	0.0393183i
$599$	124447.	−	215548.i	0.0141715	−	0.0245458i	−0.858853	−	0.512223i	$-0.828822\pi$
$599$	124447.	−	215548.i	0.0141715	−	0.0245458i	0.873024	+	0.487677i	$0.162156\pi$
$600$		0			0
$601$	−2.20084e6	−	3.81197e6i	−0.248544	−	0.430491i	0.714578	−	0.699556i	$-0.246619\pi$
$601$	−2.20084e6	−	3.81197e6i	−0.248544	−	0.430491i	−0.963122	+	0.269065i	$0.913285\pi$
$602$	4.63163e6	+	5.68788e6i	0.520885	+	0.639675i
$603$		0			0
$604$	−6.86265e6	−	1.41973e6i	−0.765420	−	0.158349i
$605$	−1.12656e7	+	6.50422e6i	−1.25132	+	0.722449i
$606$		0			0
$607$	5.35875e6	+	3.09387e6i	0.590325	+	0.340824i	0.765226	−	0.643762i	$-0.222627\pi$
$607$	5.35875e6	+	3.09387e6i	0.590325	+	0.340824i	−0.174901	+	0.984586i	$0.555960\pi$
$608$	−646036.	+	2.54920e6i	−0.0708758	+	0.279669i
$609$		0			0
$610$	−5.66788e6	−	2.15803e6i	−0.616731	−	0.234819i
$611$	−1.17591e7			−1.27430
$612$		0			0
$613$	−1.13948e7			−1.22478			−0.612389	−	0.790557i	$-0.709791\pi$
$613$	−1.13948e7			−1.22478			−0.612389	+	0.790557i	$0.709791\pi$
$614$	3.91707e6	+	1.49141e6i	0.419314	+	0.159653i
$615$		0			0
$616$	8.02896e6	+	355121.i	0.852526	+	0.0377073i
$617$	−1.05792e7	−	6.10788e6i	−1.11876	−	0.645918i	−0.177678	−	0.984089i	$-0.556859\pi$
$617$	−1.05792e7	−	6.10788e6i	−1.11876	−	0.645918i	−0.941085	+	0.338170i	$0.890192\pi$
$618$		0			0
$619$	−1.02681e7	+	5.92826e6i	−1.07711	+	0.621872i	−0.930116	−	0.367265i	$-0.880294\pi$
$619$	−1.02681e7	+	5.92826e6i	−1.07711	+	0.621872i	−0.146997	+	0.989137i	$0.546961\pi$
$620$	−441767.	+	2.13540e6i	−0.0461545	+	0.223100i
$621$		0			0
$622$	−9.84284e6	−	1.20875e7i	−1.02010	−	1.25274i
$623$	3.53717e6	+	6.12655e6i	0.365120	+	0.632406i
$624$		0			0
$625$	−152246.	+	263699.i	−0.0155900	+	0.0270027i
$626$	−1.52056e7	+	2.45073e6i	−1.55084	+	0.249954i
$627$		0			0
$628$	−6.91633e6	+	2.28892e6i	−0.699804	+	0.231596i
$629$		−	2.03639e6i		−	0.205227i
$630$		0			0
$631$			2.84995e6i			0.284947i	0.989799	+	0.142474i	$0.0455056\pi$
$631$			2.84995e6i			0.284947i	−0.989799	+	0.142474i	$0.954494\pi$
$632$	2.17369e6	−	3.40774e6i	0.216474	−	0.339371i
$633$		0			0
$634$	−760135.	−	4.71626e6i	−0.0751048	−	0.465987i
$635$	−8.85189e6	+	1.53319e7i	−0.871168	+	1.50891i
$636$		0			0
$637$	−3.17428e6	−	5.49802e6i	−0.309954	−	0.536856i
$638$	2.17368e7	−	1.77002e7i	2.11419	−	1.72158i
$639$		0			0
$640$	−1.19920e6	−	1.67678e7i	−0.115729	−	1.61818i
$641$	−174871.	+	100962.i	−0.0168102	+	0.00970538i	−0.508382	−	0.861132i	$-0.669756\pi$
$641$	−174871.	+	100962.i	−0.0168102	+	0.00970538i	0.491571	+	0.870837i	$0.336423\pi$
$642$		0			0
$643$	3.06513e6	+	1.76965e6i	0.292362	+	0.168795i	0.639007	−	0.769201i	$-0.279346\pi$
$643$	3.06513e6	+	1.76965e6i	0.292362	+	0.168795i	−0.346644	+	0.937997i	$0.612679\pi$
$644$	1.06466e6	−	1.19544e6i	0.101157	−	0.113583i
$645$		0			0
$646$	−440814.	+	1.15776e6i	−0.0415599	+	0.109154i
$647$	1.88702e7			1.77221			0.886106	−	0.463482i	$-0.153400\pi$
$647$	1.88702e7			1.77221			0.886106	+	0.463482i	$0.153400\pi$
$648$		0			0
$649$	−2.97298e6			−0.277064
$650$	−6.30649e6	+	1.65635e7i	−0.585470	+	1.53769i
$651$		0			0
$652$	−9.80559e6	+	1.10101e7i	−0.903347	+	1.01431i
$653$	−7.69628e6	−	4.44345e6i	−0.706314	−	0.407790i	0.103381	−	0.994642i	$-0.467034\pi$
$653$	−7.69628e6	−	4.44345e6i	−0.706314	−	0.407790i	−0.809695	+	0.586851i	$0.800367\pi$
$654$		0			0
$655$	1.99289e7	−	1.15059e7i	1.81501	−	1.04790i
$656$	5.16668e6	−	1.19528e7i	0.468761	−	1.08445i
$657$		0			0
$658$	−6.75513e6	+	5.50068e6i	−0.608232	+	0.495281i
$659$	−3.43642e6	−	5.95205e6i	−0.308242	−	0.533892i	0.669736	−	0.742600i	$-0.266407\pi$
$659$	−3.43642e6	−	5.95205e6i	−0.308242	−	0.533892i	−0.977978	+	0.208708i	$0.933074\pi$
$660$		0			0
$661$	−219686.	+	380507.i	−0.0195568	+	0.0338734i	−0.875638	−	0.482968i	$-0.839559\pi$
$661$	−219686.	+	380507.i	−0.0195568	+	0.0338734i	0.856081	+	0.516841i	$0.172892\pi$
$662$	1.58488e6	+	9.83337e6i	0.140556	+	0.872082i
$663$		0			0
$664$	−1.20017e7	−	7.65551e6i	−1.05639	−	0.673835i
$665$		−	3.31266e6i		−	0.290484i
$666$		0			0
$667$		−	5.58352e6i		−	0.485952i
$668$	−1.74119e7	+	5.76234e6i	−1.50975	+	0.499641i
$669$		0			0
$670$	1.58676e7	−	2.55743e6i	1.36560	−	0.220098i
$671$	3.26167e6	−	5.64937e6i	0.279662	−	0.484388i
$672$		0			0
$673$	−4.79543e6	−	8.30592e6i	−0.408122	−	0.706887i	0.586558	−	0.809908i	$-0.300483\pi$
$673$	−4.79543e6	−	8.30592e6i	−0.408122	−	0.706887i	−0.994679	+	0.103020i	$0.967149\pi$
$674$	8.79935e6	+	1.08061e7i	0.746107	+	0.916259i
$675$		0			0
$676$	−39936.4	+	193043.i	−0.00336126	+	0.0162475i
$677$	4.71537e6	−	2.72242e6i	0.395407	−	0.228288i	−0.289093	−	0.957301i	$-0.593354\pi$
$677$	4.71537e6	−	2.72242e6i	0.395407	−	0.228288i	0.684500	+	0.729013i	$0.260020\pi$
$678$		0			0
$679$	5.45721e6	+	3.15072e6i	0.454252	+	0.262262i
$680$	349923.	−	7.91143e6i	0.0290202	−	0.656119i
$681$		0			0
$682$	−2.19197e6	−	834586.i	−0.180457	−	0.0687084i
$683$	−1.41906e7			−1.16399			−0.581995	−	0.813193i	$-0.697728\pi$
$683$	−1.41906e7			−1.16399			−0.581995	+	0.813193i	$0.697728\pi$
$684$		0			0
$685$	1.13462e7			0.923901
$686$	−1.15443e7	−	4.39545e6i	−0.936606	−	0.356610i
$687$		0			0
$688$	9.84480e6	+	1.32448e7i	0.792932	+	1.06678i
$689$	−4.48123e6	−	2.58724e6i	−0.359625	−	0.207629i
$690$		0			0
$691$	−1.74007e7	+	1.00463e7i	−1.38634	+	0.800406i	−0.992901	−	0.118943i	$-0.962049\pi$
$691$	−1.74007e7	+	1.00463e7i	−1.38634	+	0.800406i	−0.393443	+	0.919349i	$0.628716\pi$
$692$	−1.02738e7	−	2.12542e6i	−0.815578	−	0.168725i
$693$		0			0
$694$	3.38156e6	+	4.15274e6i	0.266513	+	0.327293i
$695$	−8.14072e6	−	1.41001e7i	−0.639295	−	1.10729i
$696$		0			0
$697$	3.06713e6	−	5.31243e6i	0.239139	−	0.414201i
$698$	2.19694e7	−	3.54089e6i	1.70679	−	0.275089i
$699$		0			0
$700$	4.12525e6	+	1.24651e7i	0.318203	+	0.961503i
$701$		−	1.36721e7i		−	1.05085i	−0.850841	−	0.525423i	$-0.823907\pi$
$701$		−	1.36721e7i		−	1.05085i	0.850841	−	0.525423i	$-0.176093\pi$
$702$		0			0
$703$		−	1.91651e6i		−	0.146259i
$704$	1.80110e7	+	1.59637e6i	1.36964	+	0.121396i
$705$		0			0
$706$	−3.47850e6	−	2.15824e7i	−0.262652	−	1.62962i
$707$	−1.04455e6	+	1.80922e6i	−0.0785927	+	0.136126i
$708$		0			0
$709$	−1.00757e6	−	1.74517e6i	−0.0752767	−	0.130383i	0.825930	−	0.563773i	$-0.190651\pi$
$709$	−1.00757e6	−	1.74517e6i	−0.0752767	−	0.130383i	−0.901207	+	0.433390i	$0.857317\pi$
$710$	−2.74076e7	+	2.23179e7i	−2.04045	+	1.66153i
$711$		0			0
$712$	7.34124e6	+	1.41220e7i	0.542712	+	1.04399i
$713$	−404592.	+	233591.i	−0.0298053	+	0.0172081i
$714$		0			0
$715$	−2.66261e7	−	1.53726e7i	−1.94779	−	1.12456i
$716$	−2.94193e6	−	2.62009e6i	−0.214462	−	0.191000i
$717$		0			0
$718$	−2.48767e6	+	6.53365e6i	−0.180087	+	0.472982i
$719$	1.07956e7			0.778796			0.389398	−	0.921070i	$-0.372683\pi$
$719$	1.07956e7			0.778796			0.389398	+	0.921070i	$0.372683\pi$
$720$		0			0
$721$	1.99657e6			0.143036
$722$	4.56919e6	−	1.20006e7i	0.326209	−	0.856761i
$723$		0			0
$724$	7.45310e6	+	6.63775e6i	0.528433	+	0.470625i
$725$	3.96610e7	+	2.28983e7i	2.80233	+	1.61792i
$726$		0			0
$727$	2.00659e7	−	1.15851e7i	1.40807	−	0.812947i	0.412864	−	0.910793i	$-0.364528\pi$
$727$	2.00659e7	−	1.15851e7i	1.40807	−	0.812947i	0.995202	+	0.0978454i	$0.0311951\pi$
$728$	4.12725e6	+	7.93938e6i	0.288624	+	0.555211i
$729$		0			0
$730$	−9.47678e6	+	7.71691e6i	−0.658194	+	0.535965i
$731$	3.88709e6	+	6.73265e6i	0.269049	+	0.466007i
$732$		0			0
$733$	−3.96332e6	+	6.86468e6i	−0.272458	+	0.471911i	−0.969491	−	0.245128i	$-0.921170\pi$
$733$	−3.96332e6	+	6.86468e6i	−0.272458	+	0.471911i	0.697033	+	0.717039i	$0.254503\pi$
$734$	−452868.	−	2.80982e6i	−0.0310264	−	0.192503i
$735$		0			0
$736$	2.51183e6	−	2.58109e6i	0.170921	−	0.175634i
$737$			1.72875e7i			1.17237i
$738$		0			0
$739$			2.45640e7i			1.65458i	0.561776	+	0.827289i	$0.310118\pi$
$739$			2.45640e7i			1.65458i	−0.561776	+	0.827289i	$0.689882\pi$
$740$	3.84912e6	+	1.16307e7i	0.258394	+	0.780778i
$741$		0			0
$742$	−3.78455e6	+	609968.i	−0.252350	+	0.0406722i
$743$	−2.79240e6	+	4.83658e6i	−0.185569	+	0.321415i	−0.943768	−	0.330608i	$-0.892746\pi$
$743$	−2.79240e6	+	4.83658e6i	−0.185569	+	0.321415i	0.758199	+	0.652023i	$0.226080\pi$
$744$		0			0
$745$	2.07177e7	+	3.58841e7i	1.36757	+	2.36871i
$746$	−1.62982e7	−	2.00150e7i	−1.07224	−	1.31677i
$747$		0			0
$748$	8.34126e6	+	1.72562e6i	0.545102	+	0.112770i
$749$	−7.38296e6	+	4.26255e6i	−0.480868	+	0.277629i
$750$		0			0
$751$	−1.13834e7	−	6.57223e6i	−0.736501	−	0.425219i	0.0842946	−	0.996441i	$-0.473136\pi$
$751$	−1.13834e7	−	6.57223e6i	−0.736501	−	0.425219i	−0.820796	+	0.571222i	$0.806470\pi$
$752$	−1.57300e7	+	1.16920e7i	−1.01434	+	0.753955i
$753$		0			0
$754$	2.91677e7	+	1.11055e7i	1.86841	+	0.711393i
$755$	1.98610e7			1.26804
$756$		0			0
$757$	1.33312e7			0.845528			0.422764	−	0.906240i	$-0.361060\pi$
$757$	1.33312e7			0.845528			0.422764	+	0.906240i	$0.361060\pi$
$758$	−1.86132e7	−	7.08694e6i	−1.17666	−	0.448008i
$759$		0			0
$760$	329323.	−	7.44569e6i	0.0206818	−	0.467596i
$761$	−9.74299e6	−	5.62512e6i	−0.609861	−	0.352103i	0.163050	−	0.986618i	$-0.447867\pi$
$761$	−9.74299e6	−	5.62512e6i	−0.609861	−	0.352103i	−0.772911	+	0.634515i	$0.781200\pi$
$762$		0			0
$763$	1.67874e6	−	969222.i	0.104393	−	0.0602715i
$764$	1.26954e6	−	6.13667e6i	0.0786891	−	0.380364i
$765$		0			0
$766$	−4.27493e6	−	5.24984e6i	−0.263243	−	0.323276i
$767$	−1.65504e6	−	2.86661e6i	−0.101583	−	0.175946i
$768$		0			0
$769$	−1.05229e7	+	1.82262e7i	−0.641680	+	1.11142i	0.343378	+	0.939197i	$0.388429\pi$
$769$	−1.05229e7	+	1.82262e7i	−0.641680	+	1.11142i	−0.985058	+	0.172225i	$0.944904\pi$
$770$	−2.24866e7	+	3.62424e6i	−1.36678	+	0.220288i
$771$		0			0
$772$	1.80317e7	−	5.96749e6i	1.08892	−	0.360370i
$773$		−	5.93037e6i		−	0.356971i	−0.983943	−	0.178486i	$-0.942880\pi$
$773$		−	5.93037e6i		−	0.356971i	0.983943	−	0.178486i	$-0.0571198\pi$
$774$		0			0
$775$		−	3.83188e6i		−	0.229170i
$776$	1.19527e7	+	7.62423e6i	0.712542	+	0.454508i
$777$		0			0
$778$	1.27232e6	+	7.89411e6i	0.0753612	+	0.467578i
$779$	2.88657e6	−	4.99969e6i	0.170427	−	0.295188i
$780$		0			0
$781$	−1.90086e7	−	3.29239e7i	−1.11512	−	1.93145i
$782$	1.31562e6	−	1.07131e6i	0.0769332	−	0.0626465i
$783$		0			0
$784$	−9.71285e6	−	4.19844e6i	−0.564360	−	0.243948i
$785$	1.78807e7	−	1.03234e7i	1.03564	−	0.597928i
$786$		0			0
$787$	−6.15888e6	−	3.55583e6i	−0.354458	−	0.204646i	0.312189	−	0.950020i	$-0.398938\pi$
$787$	−6.15888e6	−	3.55583e6i	−0.354458	−	0.204646i	−0.666647	+	0.745374i	$0.732271\pi$
$788$	2.13197e6	−	2.39385e6i	0.122311	−	0.137335i
$789$		0			0
$790$	−4.07609e6	+	1.07055e7i	−0.232368	+	0.610295i
$791$	728784.			0.0414150
$792$		0			0
$793$	7.26298e6			0.410140
$794$	3.97697e6	−	1.04452e7i	0.223872	−	0.587982i
$795$		0			0
$796$	8.57271e6	−	9.62573e6i	0.479552	−	0.538457i
$797$	2.88348e7	+	1.66478e7i	1.60795	+	0.928348i	0.989829	+	0.142261i	$0.0454371\pi$
$797$	2.88348e7	+	1.66478e7i	1.60795	+	0.928348i	0.618116	+	0.786087i	$0.287896\pi$
$798$		0			0
$799$	−7.99593e6	+	4.61645e6i	−0.443100	+	0.255824i
$800$	8.03290e6	+	2.84272e7i	0.443759	+	1.57040i
$801$		0			0
$802$	3.29542e6	−	2.68345e6i	0.180915	−	0.147319i
$803$	−6.57264e6	−	1.13841e7i	−0.359709	−	0.623034i
$804$		0			0
$805$	−2.26839e6	+	3.92897e6i	−0.123375	+	0.213692i
$806$	−415529.	−	2.57815e6i	−0.0225301	−	0.139788i
$807$		0			0
$808$	−2.52765e6	+	3.96264e6i	−0.136203	+	0.213529i
$809$		−	5.88004e6i		−	0.315871i	−0.987449	−	0.157935i	$-0.949516\pi$
$809$		−	5.88004e6i		−	0.315871i	0.987449	−	0.157935i	$-0.0504838\pi$
$810$		0			0
$811$		−	6.76658e6i		−	0.361258i	−0.983551	−	0.180629i	$-0.942187\pi$
$811$		−	6.76658e6i		−	0.361258i	0.983551	−	0.180629i	$-0.0578133\pi$
$812$	2.19506e7	−	7.26440e6i	1.16830	−	0.386643i
$813$		0			0
$814$	−1.30094e7	+	2.09678e6i	−0.688173	+	0.110915i
$815$	2.08920e7	−	3.61860e7i	1.10176	−	1.90830i
$816$		0			0
$817$	3.65826e6	+	6.33630e6i	0.191743	+	0.332109i
$818$	−8.71761e6	−	1.07057e7i	−0.455527	−	0.559412i
$819$		0			0
$820$	−7.47637e6	+	3.61390e7i	−0.388290	+	1.87690i
$821$	8.96822e6	−	5.17780e6i	0.464353	−	0.268094i	−0.249520	−	0.968370i	$-0.580273\pi$
$821$	8.96822e6	−	5.17780e6i	0.464353	−	0.268094i	0.713873	+	0.700275i	$0.246939\pi$
$822$		0			0
$823$	−1.37906e7	−	7.96198e6i	−0.709712	−	0.409752i	0.101242	−	0.994862i	$-0.467718\pi$
$823$	−1.37906e7	−	7.96198e6i	−0.709712	−	0.409752i	−0.810954	+	0.585109i	$0.801052\pi$
$824$	4.48758e6	+	198486.i	0.230247	+	0.0101838i
$825$		0			0
$826$	−2.29170e6	−	872556.i	−0.116871	−	0.0444983i
$827$	−4.35492e6			−0.221420			−0.110710	−	0.993853i	$-0.535312\pi$
$827$	−4.35492e6			−0.221420			−0.110710	+	0.993853i	$0.535312\pi$
$828$		0			0
$829$	1.45459e7			0.735112			0.367556	−	0.930001i	$-0.380195\pi$
$829$	1.45459e7			0.735112			0.367556	+	0.930001i	$0.380195\pi$
$830$	3.77036e7	+	1.43555e7i	1.89971	+	0.723310i
$831$		0			0
$832$	8.48731e6	+	1.82552e7i	0.425071	+	0.914279i
$833$	−4.31688e6	−	2.49235e6i	−0.215555	−	0.124451i
$834$		0			0
$835$	4.50146e7	−	2.59892e7i	2.23428	−	1.28996i
$836$	7.85021e6	+	1.62404e6i	0.388477	+	0.0803675i
$837$		0			0
$838$	−2.49972e7	−	3.06979e7i	−1.22965	−	1.51008i
$839$	6.07367e6	+	1.05199e7i	0.297884	+	0.515949i	0.975652	−	0.219326i	$-0.0703860\pi$
$839$	6.07367e6	+	1.05199e7i	0.297884	+	0.515949i	−0.677768	+	0.735276i	$0.737053\pi$
$840$		0			0
$841$	3.00675e7	−	5.20784e7i	1.46591	−	2.53903i
$842$	6.43076e6	−	1.03647e6i	0.312595	−	0.0503820i
$843$		0			0
$844$	6.25066e6	+	1.88874e7i	0.302043	+	0.912673i
$845$		−	558680.i		−	0.0269167i
$846$		0			0
$847$		−	1.15409e7i		−	0.552752i
$848$	−8.56696e6	+	994758.i	−0.409107	+	0.0475037i
$849$		0			0
$850$	2.21430e6	+	1.37386e7i	0.105121	+	0.652223i
$851$	−1.31236e6	+	2.27307e6i	−0.0621196	+	0.107594i
$852$		0			0
$853$	−6.85932e6	−	1.18807e7i	−0.322782	−	0.559074i	0.658279	−	0.752774i	$-0.271285\pi$
$853$	−6.85932e6	−	1.18807e7i	−0.322782	−	0.559074i	−0.981061	+	0.193700i	$0.937951\pi$
$854$	4.17229e6	−	3.39748e6i	0.195763	−	0.159409i
$855$		0			0
$856$	−1.70180e7	+	8.84675e6i	−0.793826	+	0.412667i
$857$	−4.68499e6	+	2.70488e6i	−0.217900	+	0.125804i	−0.604977	−	0.796243i	$-0.706818\pi$
$857$	−4.68499e6	+	2.70488e6i	−0.217900	+	0.125804i	0.387078	+	0.922047i	$0.373485\pi$
$858$		0			0
$859$	−2.58659e6	−	1.49337e6i	−0.119604	−	0.0690532i	0.439005	−	0.898485i	$-0.355331\pi$
$859$	−2.58659e6	−	1.49337e6i	−0.119604	−	0.0690532i	−0.558608	+	0.829432i	$0.688664\pi$
$860$	−3.49267e7	−	3.11058e7i	−1.61032	−	1.43415i
$861$		0			0
$862$	−123364.	+	324004.i	−0.00565482	+	0.0148519i
$863$	−2.98138e7			−1.36267			−0.681334	−	0.731973i	$-0.738600\pi$
$863$	−2.98138e7			−1.36267			−0.681334	+	0.731973i	$0.738600\pi$
$864$		0			0
$865$	2.97331e7			1.35114
$866$	−1.29323e7	+	3.39655e7i	−0.585977	+	1.53902i
$867$		0			0
$868$	−1.44471e6	−	1.28666e6i	−0.0650851	−	0.0579650i
$869$	−1.06706e7	−	6.16065e6i	−0.479333	−	0.276743i
$870$		0			0
$871$	−1.66689e7	+	9.62381e6i	−0.744496	+	0.429835i
$872$	3.86957e6	−	2.01158e6i	0.172334	−	0.0895872i
$873$		0			0
$874$	1.23817e6	−	1.00824e6i	0.0548279	−	0.0446462i
$875$	−7.20435e6	−	1.24783e7i	−0.318108	−	0.550979i
$876$		0			0
$877$	−1.54476e7	+	2.67561e7i	−0.678207	+	1.17469i	0.297313	+	0.954780i	$0.403910\pi$
$877$	−1.54476e7	+	2.67561e7i	−0.678207	+	1.17469i	−0.975520	+	0.219910i	$0.929424\pi$
$878$	1.59189e6	+	9.87689e6i	0.0696911	+	0.432398i
$879$		0			0
$880$	−5.09023e7	+	5.91055e6i	−2.21580	+	0.257289i
$881$			1.23151e7i			0.534563i	0.963618	+	0.267282i	$0.0861254\pi$
$881$			1.23151e7i			0.534563i	−0.963618	+	0.267282i	$0.913875\pi$
$882$		0			0
$883$		−	1.12796e7i		−	0.486845i	−0.969920	−	0.243422i	$-0.921730\pi$
$883$		−	1.12796e7i		−	0.486845i	0.969920	−	0.243422i	$-0.0782701\pi$
$884$	2.97963e6	+	9.00345e6i	0.128243	+	0.387506i
$885$		0			0
$886$	3.67415e7	−	5.92176e6i	1.57244	−	0.253435i
$887$	−5.21370e6	+	9.03039e6i	−0.222504	+	0.385388i	−0.955568	−	0.294772i	$-0.904756\pi$
$887$	−5.21370e6	+	9.03039e6i	−0.222504	+	0.385388i	0.733064	+	0.680160i	$0.238090\pi$
$888$		0			0
$889$	−7.85325e6	−	1.36022e7i	−0.333269	−	0.577239i
$890$	−2.84822e7	−	3.49776e7i	−1.20531	−	1.48018i
$891$		0			0
$892$	−4.04404e7	−	8.36624e6i	−1.70178	−	0.352061i
$893$	−7.52521e6	+	4.34468e6i	−0.315784	+	0.182318i
$894$		0			0
$895$	9.66904e6	+	5.58242e6i	0.403484	+	0.232951i
$896$	1.34151e7	+	6.51668e6i	0.558242	+	0.271179i
$897$		0			0
$898$	5.15096e6	+	1.96121e6i	0.213156	+	0.0811585i
$899$	−6.74779e6			−0.278460
$900$		0			0
$901$	−4.06285e6			−0.166732
$902$	−3.70964e7	−	1.41243e7i	−1.51815	−	0.578032i
$903$		0			0
$904$	1.63805e6	+	72451.0i	0.0666662	+	0.00294865i
$905$	−2.44956e7	−	1.41425e7i	−0.994183	−	0.573992i
$906$		0			0
$907$	−2.24643e7	+	1.29698e7i	−0.906723	+	0.523497i	−0.879375	−	0.476129i	$-0.842039\pi$
$907$	−2.24643e7	+	1.29698e7i	−0.906723	+	0.523497i	−0.0273474	+	0.999626i	$0.508706\pi$
$908$	−5.64036e6	+	2.72642e7i	−0.227035	+	1.09743i
$909$		0			0
$910$	−1.60127e7	−	1.96644e7i	−0.641004	−	0.787188i
$911$	5.68513e6	+	9.84694e6i	0.226958	+	0.393102i	0.956905	−	0.290401i	$-0.0937888\pi$
$911$	5.68513e6	+	9.84694e6i	0.226958	+	0.393102i	−0.729947	+	0.683503i	$0.760455\pi$
$912$		0			0
$913$	−2.16971e7	+	3.75805e7i	−0.861440	+	1.49206i
$914$	2.60604e7	−	4.20025e6i	1.03185	−	0.166307i
$915$		0			0
$916$	−3.35056e6	+	1.10885e6i	−0.131941	+	0.0436649i
$917$			2.04158e7i			0.801756i
$918$		0			0
$919$			4.39949e7i			1.71836i	0.511675	+	0.859179i	$0.329025\pi$
$919$			4.39949e7i			1.71836i	−0.511675	+	0.859179i	$0.670975\pi$
$920$	−5.48914e6	+	8.60543e6i	−0.213813	+	0.335199i
$921$		0			0
$922$	2.32304e6	+	1.44133e7i	0.0899975	+	0.558389i
$923$	2.11639e7	−	3.66569e7i	0.817694	−	1.41629i
$924$		0			0
$925$	−1.07641e7	−	1.86440e7i	−0.413641	−	0.716447i
$926$	1.01596e7	−	8.27297e6i	0.389360	−	0.317054i
$927$		0			0
$928$	5.00593e7	−	1.41456e7i	1.90816	−	0.539203i
$929$	2.15711e7	−	1.24541e7i	0.820037	−	0.473449i	−0.0303922	−	0.999538i	$-0.509676\pi$
$929$	2.15711e7	−	1.24541e7i	0.820037	−	0.473449i	0.850429	+	0.526089i	$0.176342\pi$
$930$		0			0
$931$	−4.06275e6	−	2.34563e6i	−0.153619	−	0.0886921i
$932$	−7.50669e6	+	8.42877e6i	−0.283080	+	0.317852i
$933$		0			0
$934$	52931.8	−	139021.i	0.00198541	−	0.00521451i
$935$	−2.41402e7			−0.903050
$936$		0			0
$937$	−3.28010e7			−1.22050			−0.610250	−	0.792209i	$-0.708931\pi$
$937$	−3.28010e7			−1.22050			−0.610250	+	0.792209i	$0.708931\pi$
$938$	−5.07379e6	+	1.33259e7i	−0.188289	+	0.494526i
$939$		0			0
$940$	3.69424e7	−	4.14802e7i	1.36366	−	1.53116i
$941$	−3.67890e7	−	2.12402e7i	−1.35439	−	0.781959i	−0.365531	−	0.930799i	$-0.619112\pi$
$941$	−3.67890e7	−	2.12402e7i	−1.35439	−	0.781959i	−0.988861	+	0.148841i	$0.952446\pi$
$942$		0			0
$943$	−6.84722e6	+	3.95325e6i	−0.250747	+	0.144769i
$944$	−5.06418e6	−	2.18902e6i	−0.184960	−	0.0799504i
$945$		0			0
$946$	3.90090e7	−	3.17649e7i	1.41722	−	1.15404i
$947$	2.36823e7	+	4.10190e7i	0.858123	+	1.48631i	0.873718	+	0.486433i	$0.161702\pi$
$947$	2.36823e7	+	4.10190e7i	0.858123	+	1.48631i	−0.0155950	+	0.999878i	$0.504964\pi$
$948$		0			0
$949$	7.31788e6	−	1.26749e7i	0.263766	−	0.456857i
$950$	2.08395e6	+	1.29298e7i	0.0749165	+	0.464819i
$951$		0			0
$952$	5.92332e6	+	3.77830e6i	0.211823	+	0.135115i
$953$			3.03620e7i			1.08293i	0.840725	+	0.541463i	$0.182129\pi$
$953$			3.03620e7i			1.08293i	−0.840725	+	0.541463i	$0.817871\pi$
$954$		0			0
$955$			1.77600e7i			0.630135i
$956$	2.10056e7	−	6.95168e6i	0.743346	−	0.246006i
$957$		0			0
$958$	−3.54857e7	+	5.71935e6i	−1.24922	+	0.201341i
$959$	−5.03310e6	+	8.71758e6i	−0.176721	+	0.306090i
$960$		0			0
$961$	−1.40323e7	−	2.43046e7i	−0.490139	−	0.848946i
$962$	−9.26401e6	−	1.13767e7i	−0.322746	−	0.396350i
$963$		0			0
$964$	−485930.	+	2.34887e6i	−0.0168415	+	0.0814079i
$965$	−4.66172e7	+	2.69144e7i	−1.61149	+	0.930394i
$966$		0			0
$967$	2.41777e7	+	1.39590e7i	0.831475	+	0.480052i	0.854357	−	0.519686i	$-0.173951\pi$
$967$	2.41777e7	+	1.39590e7i	0.831475	+	0.480052i	−0.0228826	+	0.999738i	$0.507284\pi$
$968$	1.14732e6	−	2.59398e7i	0.0393546	−	0.889772i
$969$		0			0
$970$	−3.75496e7	−	1.42969e7i	−1.28137	−	0.487879i
$971$	2.50332e7			0.852057			0.426028	−	0.904710i	$-0.359912\pi$
$971$	2.50332e7			0.852057			0.426028	+	0.904710i	$0.359912\pi$
$972$		0			0
$973$	1.44446e7			0.489130
$974$	−3.76932e7	−	1.43516e7i	−1.27311	−	0.484733i
$975$		0			0
$976$	9.71558e6	−	7.22155e6i	0.326471	−	0.242664i
$977$	2.16546e7	+	1.25023e7i	0.725793	+	0.419037i	0.816881	−	0.576806i	$-0.195701\pi$
$977$	2.16546e7	+	1.25023e7i	0.725793	+	0.419037i	−0.0910880	+	0.995843i	$0.529034\pi$
$978$		0			0
$979$	4.20175e7	−	2.42588e7i	1.40111	−	0.808933i
$980$	2.93665e7	+	6.07529e6i	0.976759	+	0.202070i
$981$		0			0
$982$	2.94363e7	+	3.61493e7i	0.974101	+	1.19625i
$983$	1.95719e7	+	3.38995e7i	0.646025	+	1.11895i	0.984064	+	0.177816i	$0.0569031\pi$
$983$	1.95719e7	+	3.38995e7i	0.646025	+	1.11895i	−0.338039	+	0.941132i	$0.609764\pi$
$984$		0			0
$985$	−4.54242e6	+	7.86770e6i	−0.149175	+	0.258379i
$986$	2.41932e7	−	3.89930e6i	0.792503	−	0.127730i
$987$		0			0
$988$	2.80422e6	+	8.47342e6i	0.0913946	+	0.276163i
$989$		−	1.00202e7i		−	0.325751i
$990$		0			0
$991$		−	1.82027e7i		−	0.588779i	−0.955686	−	0.294389i	$-0.904884\pi$
$991$		−	1.82027e7i		−	0.588779i	0.955686	−	0.294389i	$-0.0951163\pi$
$992$	−3.11929e6	−	3.03559e6i	−0.100641	−	0.0979409i
$993$		0			0
$994$	−4.98960e6	−	3.09580e7i	−0.160177	−	0.993817i
$995$	−1.82652e7	+	3.16362e7i	−0.584879	+	1.01304i
$996$		0			0
$997$	2.16083e7	+	3.74266e7i	0.688466	+	1.19246i	0.972334	+	0.233594i	$0.0750488\pi$
$997$	2.16083e7	+	3.74266e7i	0.688466	+	1.19246i	−0.283868	+	0.958863i	$0.591618\pi$
$998$	−3.70616e7	+	3.01792e7i	−1.17787	+	0.959138i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.h.a.71.19		56
3.2	odd	2		36.6.h.a.23.10	yes	56
4.3	odd	2	inner	108.6.h.a.71.28		56
9.2	odd	6	inner	108.6.h.a.35.28		56
9.7	even	3		36.6.h.a.11.1	✓	56
12.11	even	2		36.6.h.a.23.1	yes	56
36.7	odd	6		36.6.h.a.11.10	yes	56
36.11	even	6	inner	108.6.h.a.35.19		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.h.a.11.1	✓	56	9.7	even	3
36.6.h.a.11.10	yes	56	36.7	odd	6
36.6.h.a.23.1	yes	56	12.11	even	2
36.6.h.a.23.10	yes	56	3.2	odd	2
108.6.h.a.35.19		56	36.11	even	6	inner
108.6.h.a.35.28		56	9.2	odd	6	inner
108.6.h.a.71.19		56	1.1	even	1	trivial
108.6.h.a.71.28		56	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	108.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.01287 - 5.28662i) q^{2} +(-23.8967 - 21.2825i) q^{4} +(78.5398 + 45.3450i) q^{5} +(-69.6792 + 40.2293i) q^{7} +(-160.614 + 83.4942i) q^{8} +O(q^{10})\)	\(q+(2.01287 - 5.28662i) q^{2} +(-23.8967 - 21.2825i) q^{4} +(78.5398 + 45.3450i) q^{5} +(-69.6792 + 40.2293i) q^{7} +(-160.614 + 83.4942i) q^{8} +(397.812 - 323.937i) q^{10} +(275.903 + 477.878i) q^{11} +(-307.186 + 532.062i) q^{13} +(72.4223 + 449.344i) q^{14} +(118.109 + 1017.17i) q^{16} +482.387i q^{17} +453.989i q^{19} +(-911.790 - 2755.12i) q^{20} +(3081.72 - 496.691i) q^{22} +(310.876 - 538.452i) q^{23} +(2549.83 + 4416.44i) q^{25} +(2194.49 + 2694.95i) q^{26} +(2521.29 + 521.599i) q^{28} +(7777.18 - 4490.16i) q^{29} +(-650.730 - 375.699i) q^{31} +(5615.11 + 1423.02i) q^{32} +(2550.20 + 970.980i) q^{34} -7296.79 q^{35} -4221.49 q^{37} +(2400.07 + 913.819i) q^{38} +(-16400.6 - 725.399i) q^{40} +(-11012.8 - 6358.24i) q^{41} +(13956.9 - 8058.04i) q^{43} +(3577.26 - 17291.6i) q^{44} +(-2220.84 - 2727.31i) q^{46} +(9570.02 + 16575.8i) q^{47} +(-5166.71 + 8949.00i) q^{49} +(28480.5 - 4590.30i) q^{50} +(18664.4 - 6176.86i) q^{52} +8422.39i q^{53} +50043.2i q^{55} +(7832.51 - 12279.2i) q^{56} +(-8083.35 - 50153.1i) q^{58} +(-2693.87 + 4665.91i) q^{59} +(-5910.89 - 10238.0i) q^{61} +(-3296.01 + 2683.93i) q^{62} +(18825.4 - 26820.6i) q^{64} +(-48252.7 + 27858.7i) q^{65} +(27131.6 + 15664.5i) q^{67} +(10266.4 - 11527.5i) q^{68} +(-14687.4 + 38575.3i) q^{70} -68895.9 q^{71} -23822.3 q^{73} +(-8497.30 + 22317.4i) q^{74} +(9662.03 - 10848.9i) q^{76} +(-38449.4 - 22198.8i) q^{77} +(-19337.5 + 11164.5i) q^{79} +(-36847.1 + 85243.6i) q^{80} +(-55780.9 + 45422.2i) q^{82} +(39320.2 + 68104.6i) q^{83} +(-21873.8 + 37886.6i) q^{85} +(-14506.4 - 90004.8i) q^{86} +(-84213.8 - 53717.4i) q^{88} -87925.1i q^{89} -49431.5i q^{91} +(-18888.5 + 6251.04i) q^{92} +(106893. - 17228.3i) q^{94} +(-20586.1 + 35656.2i) q^{95} +(-39159.6 - 67826.3i) q^{97} +(36910.1 + 45327.5i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) 56 * q + 3 * q^2 - q^4 + 6 * q^5	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) \) 56 * q + 3 * q^2 - q^4 + 6 * q^5 - 68 * q^10 - 2 * q^13 + 1518 * q^14 - q^16 + 1242 * q^20 + 63 * q^22 + 12498 * q^25 - 2052 * q^28 + 11946 * q^29 + 7233 * q^32 + 6361 * q^34 - 8 * q^37 + 14877 * q^38 - 1526 * q^40 + 43536 * q^41 - 26880 * q^46 + 38414 * q^49 - 38631 * q^50 + 24988 * q^52 - 21186 * q^56 - 3314 * q^58 - 2 * q^61 - 106342 * q^64 - 35970 * q^65 - 31413 * q^68 + 10524 * q^70 + 53620 * q^73 + 20406 * q^74 + 26193 * q^76 - 26178 * q^77 - 151286 * q^82 + 6248 * q^85 - 279237 * q^86 - 122541 * q^88 - 435804 * q^92 + 63480 * q^94 - 58148 * q^97

Introduction

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