LMFDB - Embedded newform 108.6.h.a.35.11

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			35.11
Character	$\chi$	$=$	108.35
Dual form			108.6.h.a.71.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.78768 + 5.36696i) q^{2} +(-25.6084 - 19.1888i) q^{4} +(52.1793 - 30.1257i) q^{5} +(-185.316 - 106.992i) q^{7} +(148.765 - 103.136i) q^{8} +O(q^{10})$	\(q+(-1.78768 + 5.36696i) q^{2} +(-25.6084 - 19.1888i) q^{4} +(52.1793 - 30.1257i) q^{5} +(-185.316 - 106.992i) q^{7} +(148.765 - 103.136i) q^{8} +(68.4038 + 333.899i) q^{10} +(-185.570 + 321.417i) q^{11} +(402.759 + 697.599i) q^{13} +(905.506 - 803.314i) q^{14} +(287.583 + 982.788i) q^{16} +34.0704i q^{17} +1173.48i q^{19} +(-1914.31 - 229.783i) q^{20} +(-1393.29 - 1570.54i) q^{22} +(1980.40 + 3430.16i) q^{23} +(252.621 - 437.553i) q^{25} +(-4463.99 + 914.509i) q^{26} +(2692.60 + 6295.88i) q^{28} +(382.894 + 221.064i) q^{29} +(-1381.28 + 797.481i) q^{31} +(-5788.68 - 213.459i) q^{32} +(-182.854 - 60.9068i) q^{34} -12892.9 q^{35} -11057.6 q^{37} +(-6298.01 - 2097.80i) q^{38} +(4655.40 - 9863.22i) q^{40} +(7969.76 - 4601.35i) q^{41} +(1061.38 + 612.787i) q^{43} +(10919.8 - 4670.13i) q^{44} +(-21949.8 + 4496.72i) q^{46} +(1222.66 - 2117.71i) q^{47} +(14491.1 + 25099.3i) q^{49} +(1896.72 + 2138.01i) q^{50} +(3072.03 - 25592.9i) q^{52} +20212.4i q^{53} +22361.8i q^{55} +(-38603.2 + 3196.07i) q^{56} +(-1870.93 + 1659.78i) q^{58} +(-1704.67 - 2952.58i) q^{59} +(-19919.9 + 34502.3i) q^{61} +(-1810.77 - 8838.89i) q^{62} +(11493.9 - 30686.0i) q^{64} +(42031.4 + 24266.8i) q^{65} +(6088.22 - 3515.04i) q^{67} +(653.768 - 872.488i) q^{68} +(23048.3 - 69195.4i) q^{70} +25694.1 q^{71} +65431.6 q^{73} +(19767.4 - 59345.7i) q^{74} +(22517.6 - 30051.0i) q^{76} +(68778.2 - 39709.1i) q^{77} +(-41126.9 - 23744.6i) q^{79} +(44613.1 + 42617.5i) q^{80} +(10447.9 + 50999.1i) q^{82} +(6605.97 - 11441.9i) q^{83} +(1026.39 + 1777.77i) q^{85} +(-5186.20 + 4600.90i) q^{86} +(5543.37 + 66954.6i) q^{88} +85682.2i q^{89} -172368. i q^{91} +(15105.5 - 125842. i) q^{92} +(9179.93 + 10347.7i) q^{94} +(35352.0 + 61231.4i) q^{95} +(-27944.9 + 48402.0i) q^{97} +(-160612. + 32903.6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.78768	+	5.36696i	−0.316019	+	0.948753i
$2$	−1.78768	+	5.36696i	−0.316019	+	0.948753i
$3$		0			0
$3$		0			0
$4$	−25.6084	−	19.1888i	−0.800263	−	0.599649i
$5$	52.1793	−	30.1257i	0.933412	−	0.538906i	0.0455230	−	0.998963i	$-0.485505\pi$
$5$	52.1793	−	30.1257i	0.933412	−	0.538906i	0.887889	+	0.460058i	$0.152171\pi$
$6$		0			0
$7$	−185.316	−	106.992i	−1.42944	−	0.825290i	−0.432367	−	0.901698i	$-0.642321\pi$
$7$	−185.316	−	106.992i	−1.42944	−	0.825290i	−0.997077	+	0.0764081i	$0.975655\pi$
$8$	148.765	−	103.136i	0.821817	−	0.569751i
$9$		0			0
$10$	68.4038	+	333.899i	0.216312	+	1.05588i
$11$	−185.570	+	321.417i	−0.462410	+	0.800917i	−0.999080	−	0.0428745i	$-0.986348\pi$
$11$	−185.570	+	321.417i	−0.462410	+	0.800917i	0.536671	+	0.843792i	$0.319682\pi$
$12$		0			0
$13$	402.759	+	697.599i	0.660978	+	1.14485i	0.980359	+	0.197221i	$0.0631917\pi$
$13$	402.759	+	697.599i	0.660978	+	1.14485i	−0.319381	+	0.947626i	$0.603475\pi$
$14$	905.506	−	803.314i	1.23473	−	1.09538i
$15$		0			0
$16$	287.583	+	982.788i	0.280843	+	0.959754i
$17$			34.0704i			0.0285926i	0.999898	+	0.0142963i	$0.00455082\pi$
$17$			34.0704i			0.0285926i	−0.999898	+	0.0142963i	$0.995449\pi$
$18$		0			0
$19$			1173.48i			0.745747i	0.927882	+	0.372874i	$0.121627\pi$
$19$			1173.48i			0.745747i	−0.927882	+	0.372874i	$0.878373\pi$
$20$	−1914.31	−	229.783i	−1.07013	−	0.128453i
$21$		0			0
$22$	−1393.29	−	1570.54i	−0.613742	−	0.691818i
$23$	1980.40	+	3430.16i	0.780610	+	1.35206i	0.931587	+	0.363519i	$0.118425\pi$
$23$	1980.40	+	3430.16i	0.780610	+	1.35206i	−0.150977	+	0.988537i	$0.548242\pi$
$24$		0			0
$25$	252.621	−	437.553i	0.0808388	−	0.140017i
$26$	−4463.99	+	914.509i	−1.29506	+	0.265311i
$27$		0			0
$28$	2692.60	+	6295.88i	0.649048	+	1.51761i
$29$	382.894	+	221.064i	0.0845441	+	0.0488115i	0.541676	−	0.840587i	$-0.317790\pi$
$29$	382.894	+	221.064i	0.0845441	+	0.0488115i	−0.457132	+	0.889399i	$0.651123\pi$
$30$		0			0
$31$	−1381.28	+	797.481i	−0.258153	+	0.149045i	−0.623492	−	0.781830i	$-0.714286\pi$
$31$	−1381.28	+	797.481i	−0.258153	+	0.149045i	0.365339	+	0.930875i	$0.380953\pi$
$32$	−5788.68	−	213.459i	−0.999321	−	0.0368502i
$33$		0			0
$34$	−182.854	−	60.9068i	−0.0271274	−	0.00903583i
$35$	−12892.9			−1.77901
$36$		0			0
$37$	−11057.6			−1.32787			−0.663937	−	0.747788i	$-0.731116\pi$
$37$	−11057.6			−1.32787			−0.663937	+	0.747788i	$0.731116\pi$
$38$	−6298.01	−	2097.80i	−0.707530	−	0.235671i
$39$		0			0
$40$	4655.40	−	9863.22i	0.460052	−	0.974695i
$41$	7969.76	−	4601.35i	0.740433	−	0.427489i	−0.0817937	−	0.996649i	$-0.526065\pi$
$41$	7969.76	−	4601.35i	0.740433	−	0.427489i	0.822227	+	0.569160i	$0.192732\pi$
$42$		0			0
$43$	1061.38	+	612.787i	0.0875384	+	0.0505403i	0.543130	−	0.839648i	$-0.317239\pi$
$43$	1061.38	+	612.787i	0.0875384	+	0.0505403i	−0.455592	+	0.890189i	$0.650572\pi$
$44$	10919.8	−	4670.13i	0.850319	−	0.363661i
$45$		0			0
$46$	−21949.8	+	4496.72i	−1.52945	+	0.313330i
$47$	1222.66	−	2117.71i	0.0807348	−	0.139837i	−0.822831	−	0.568286i	$-0.807607\pi$
$47$	1222.66	−	2117.71i	0.0807348	−	0.139837i	0.903566	+	0.428449i	$0.140940\pi$
$48$		0			0
$49$	14491.1	+	25099.3i	0.862206	+	1.49338i
$50$	1896.72	+	2138.01i	0.107295	+	0.120944i
$51$		0			0
$52$	3072.03	−	25592.9i	0.157550	−	1.31253i
$53$			20212.4i			0.988390i	0.869351	+	0.494195i	$0.164537\pi$
$53$			20212.4i			0.988390i	−0.869351	+	0.494195i	$0.835463\pi$
$54$		0			0
$55$			22361.8i			0.996781i
$56$	−38603.2	+	3196.07i	−1.64495	+	0.136190i
$57$		0			0
$58$	−1870.93	+	1659.78i	−0.0730276	+	0.0647860i
$59$	−1704.67	−	2952.58i	−0.0637546	−	0.110426i	0.832386	−	0.554196i	$-0.186974\pi$
$59$	−1704.67	−	2952.58i	−0.0637546	−	0.110426i	−0.896141	+	0.443770i	$0.853641\pi$
$60$		0			0
$61$	−19919.9	+	34502.3i	−0.685430	+	1.18720i	0.287872	+	0.957669i	$0.407052\pi$
$61$	−19919.9	+	34502.3i	−0.685430	+	1.18720i	−0.973302	+	0.229530i	$0.926281\pi$
$62$	−1810.77	−	8838.89i	−0.0598251	−	0.292024i
$63$		0			0
$64$	11493.9	−	30686.0i	0.350767	−	0.936463i
$65$	42031.4	+	24266.8i	1.23393	+	0.712410i
$66$		0			0
$67$	6088.22	−	3515.04i	0.165693	−	0.0956627i	−0.414861	−	0.909885i	$-0.636170\pi$
$67$	6088.22	−	3515.04i	0.165693	−	0.0956627i	0.580553	+	0.814222i	$0.302836\pi$
$68$	653.768	−	872.488i	0.0171455	−	0.0228816i
$69$		0			0
$70$	23048.3	−	69195.4i	0.562203	−	1.68784i
$71$	25694.1			0.604905			0.302453	−	0.953164i	$-0.402195\pi$
$71$	25694.1			0.604905			0.302453	+	0.953164i	$0.402195\pi$
$72$		0			0
$73$	65431.6			1.43708			0.718540	−	0.695486i	$-0.244811\pi$
$73$	65431.6			1.43708			0.718540	+	0.695486i	$0.244811\pi$
$74$	19767.4	−	59345.7i	0.419634	−	1.25982i
$75$		0			0
$76$	22517.6	−	30051.0i	0.447186	−	0.596794i
$77$	68778.2	−	39709.1i	1.32198	−	0.763244i
$78$		0			0
$79$	−41126.9	−	23744.6i	−0.741409	−	0.428053i	0.0811725	−	0.996700i	$-0.474134\pi$
$79$	−41126.9	−	23744.6i	−0.741409	−	0.428053i	−0.822581	+	0.568647i	$0.807467\pi$
$80$	44613.1	+	42617.5i	0.779359	+	0.744498i
$81$		0			0
$82$	10447.9	+	50999.1i	0.171590	+	0.837583i
$83$	6605.97	−	11441.9i	0.105255	−	0.182306i	−0.808588	−	0.588376i	$-0.799768\pi$
$83$	6605.97	−	11441.9i	0.105255	−	0.182306i	0.913842	+	0.406069i	$0.133101\pi$
$84$		0			0
$85$	1026.39	+	1777.77i	0.0154087	+	0.0266887i
$86$	−5186.20	+	4600.90i	−0.0756141	+	0.0670806i
$87$		0			0
$88$	5543.37	+	66954.6i	0.0763075	+	0.921666i
$89$			85682.2i			1.14661i	0.819342	+	0.573305i	$0.194339\pi$
$89$			85682.2i			1.14661i	−0.819342	+	0.573305i	$0.805661\pi$
$90$		0			0
$91$		−	172368.i		−	2.18199i
$92$	15105.5	−	125842.i	0.186065	−	1.55009i
$93$		0			0
$94$	9179.93	+	10347.7i	0.107157	+	0.120789i
$95$	35352.0	+	61231.4i	0.401887	+	0.696089i
$96$		0			0
$97$	−27944.9	+	48402.0i	−0.301560	+	0.522317i	−0.976490	−	0.215565i	$-0.930841\pi$
$97$	−27944.9	+	48402.0i	−0.301560	+	0.522317i	0.674929	+	0.737882i	$0.264174\pi$
$98$	−160612.	+	32903.6i	−1.68933	+	0.346082i
$99$		0			0
$100$	−14865.3	+	6357.56i	−0.148653	+	0.0635756i
$101$	−79337.0	−	45805.2i	−0.773878	−	0.446799i	0.0603784	−	0.998176i	$-0.480769\pi$
$101$	−79337.0	−	45805.2i	−0.773878	−	0.446799i	−0.834256	+	0.551377i	$0.814103\pi$
$102$		0			0
$103$	−91488.4	+	52820.9i	−0.849715	+	0.490583i	−0.860555	−	0.509358i	$-0.829883\pi$
$103$	−91488.4	+	52820.9i	−0.849715	+	0.490583i	0.0108398	+	0.999941i	$0.496550\pi$
$104$	131864.	+	62239.2i	1.19548	+	0.564262i
$105$		0			0
$106$	−108479.	−	36133.2i	−0.937737	−	0.312350i
$107$	3806.62			0.0321426			0.0160713	−	0.999871i	$-0.494884\pi$
$107$	3806.62			0.0321426			0.0160713	+	0.999871i	$0.494884\pi$
$108$		0			0
$109$	−85149.1			−0.686458			−0.343229	−	0.939252i	$-0.611521\pi$
$109$	−85149.1			−0.686458			−0.343229	+	0.939252i	$0.611521\pi$
$110$	−120015.	−	39975.6i	−0.945699	−	0.315002i
$111$		0			0
$112$	51856.8	−	212895.i	0.390625	−	1.60369i
$113$	36754.5	−	21220.2i	0.270778	−	0.156334i	−0.358463	−	0.933544i	$-0.616699\pi$
$113$	36754.5	−	21220.2i	0.270778	−	0.156334i	0.629241	+	0.777210i	$0.283366\pi$
$114$		0			0
$115$	206672.	+	119322.i	1.45726	+	0.841350i
$116$	−5563.37	−	13008.3i	−0.0383877	−	0.0897588i
$117$		0			0
$118$	18893.8	−	3870.65i	0.124915	−	0.0255905i
$119$	3645.26	−	6313.77i	0.0235972	−	0.0408716i
$120$		0			0
$121$	11652.7	+	20183.1i	0.0723543	+	0.125321i
$122$	−149562.	−	168588.i	−0.909749	−	1.02548i
$123$		0			0
$124$	50675.0	+	6082.76i	0.295964	+	0.0355260i
$125$			157844.i			0.903553i
$126$		0			0
$127$			37078.8i			0.203994i	0.994785	+	0.101997i	$0.0325232\pi$
$127$			37078.8i			0.203994i	−0.994785	+	0.101997i	$0.967477\pi$
$128$	144143.	+	116544.i	0.777623	+	0.628731i
$129$		0			0
$130$	−205378.	+	182199.i	−1.06585	+	0.945559i
$131$	−83730.6	−	145026.i	−0.426291	−	0.738357i	0.570249	−	0.821472i	$-0.306847\pi$
$131$	−83730.6	−	145026.i	−0.426291	−	0.738357i	−0.996540	+	0.0831144i	$0.973513\pi$
$132$		0			0
$133$	125553.	−	217464.i	0.615457	−	1.06600i
$134$	7981.28	+	38959.0i	0.0383982	+	0.187433i
$135$		0			0
$136$	3513.88	+	5068.47i	0.0162907	+	0.0234979i
$137$	−298026.	−	172065.i	−1.35660	−	0.783234i	−0.367438	−	0.930048i	$-0.619765\pi$
$137$	−298026.	−	172065.i	−1.35660	−	0.783234i	−0.989164	+	0.146814i	$0.953098\pi$
$138$		0			0
$139$	−239133.	+	138064.i	−1.04979	+	0.606097i	−0.922591	−	0.385780i	$-0.873932\pi$
$139$	−239133.	+	138064.i	−1.04979	+	0.606097i	−0.127200	+	0.991877i	$0.540599\pi$
$140$	330166.	+	247398.i	1.42368	+	1.06678i
$141$		0			0
$142$	−45932.7	+	137899.i	−0.191162	+	0.573906i
$143$	−298961.			−1.22257
$144$		0			0
$145$	26638.8			0.105219
$146$	−116971.	+	351169.i	−0.454145	+	1.36343i
$147$		0			0
$148$	283168.	+	212182.i	1.06265	+	0.796258i
$149$	−33899.5	+	19571.9i	−0.125091	+	0.0722216i	−0.561240	−	0.827653i	$-0.689676\pi$
$149$	−33899.5	+	19571.9i	−0.125091	+	0.0722216i	0.436149	+	0.899875i	$0.356342\pi$
$150$		0			0
$151$	372275.	+	214933.i	1.32868	+	0.767115i	0.985096	−	0.172006i	$-0.0550247\pi$
$151$	372275.	+	214933.i	1.32868	+	0.767115i	0.343587	+	0.939121i	$0.388358\pi$
$152$	121028.	+	174572.i	0.424890	+	0.612868i
$153$		0			0
$154$	90163.9	+	440117.i	0.306359	+	1.49543i
$155$	−48049.4	+	83224.0i	−0.160642	+	0.278240i
$156$		0			0
$157$	−283488.	−	491016.i	−0.917881	−	1.58982i	−0.802628	−	0.596479i	$-0.796566\pi$
$157$	−283488.	−	491016.i	−0.917881	−	1.58982i	−0.115252	−	0.993336i	$-0.536768\pi$
$158$	200958.	−	178278.i	0.640416	−	0.568141i
$159$		0			0
$160$	−308480.	+	163250.i	−0.952637	+	0.504143i
$161$		−	847550.i		−	2.57692i
$162$		0			0
$163$		−	50545.5i		−	0.149009i	−0.997221	−	0.0745047i	$-0.976262\pi$
$163$		−	50545.5i		−	0.149009i	0.997221	−	0.0745047i	$-0.0237376\pi$
$164$	−292387.	−	35096.6i	−0.848885	−	0.101896i
$165$		0			0
$166$	49598.7	+	55908.3i	0.139701	+	0.157473i
$167$	155078.	+	268602.i	0.430287	+	0.745279i	0.996898	−	0.0787068i	$-0.0250791\pi$
$167$	155078.	+	268602.i	0.430287	+	0.745279i	−0.566611	+	0.823985i	$0.691746\pi$
$168$		0			0
$169$	−138783.	+	240380.i	−0.373784	+	0.647413i
$170$	−11376.1	+	2330.54i	−0.0301905	+	0.00618493i
$171$		0			0
$172$	−15421.6	−	36059.0i	−0.0397474	−	0.0929379i
$173$	140517.	+	81127.6i	0.356955	+	0.206088i	0.667744	−	0.744391i	$-0.267260\pi$
$173$	140517.	+	81127.6i	0.356955	+	0.206088i	−0.310789	+	0.950479i	$0.600593\pi$
$174$		0			0
$175$	−93629.4	+	54056.9i	−0.231109	+	0.133431i
$176$	−369252.	−	89942.1i	−0.898548	−	0.218867i
$177$		0			0
$178$	−459852.	−	153172.i	−1.08785	−	0.362351i
$179$	313216.			0.730653			0.365326	−	0.930880i	$-0.380957\pi$
$179$	313216.			0.730653			0.365326	+	0.930880i	$0.380957\pi$
$180$		0			0
$181$	241414.			0.547729			0.273865	−	0.961768i	$-0.411698\pi$
$181$	241414.			0.547729			0.273865	+	0.961768i	$0.411698\pi$
$182$	925092.	+	308138.i	2.07017	+	0.689552i
$183$		0			0
$184$	648387.	+	306036.i	1.41185	+	0.666389i
$185$	−576979.	+	333119.i	−1.23945	+	0.715599i
$186$		0			0
$187$	−10950.8	−	6322.45i	−0.0229003	−	0.0132215i
$188$	−71946.6	+	30769.9i	−0.148462	+	0.0634938i
$189$		0			0
$190$	−391824.	+	80270.5i	−0.787421	+	0.161314i
$191$	378078.	−	654851.i	0.749891	−	1.29885i	−0.197983	−	0.980205i	$-0.563439\pi$
$191$	378078.	−	654851.i	0.749891	−	1.29885i	0.947874	−	0.318644i	$-0.103227\pi$
$192$		0			0
$193$	−210750.	−	365029.i	−0.407262	−	0.705398i	0.587320	−	0.809355i	$-0.300183\pi$
$193$	−210750.	−	365029.i	−0.407262	−	0.705398i	−0.994582	+	0.103957i	$0.966850\pi$
$194$	−209815.	−	236506.i	−0.400251	−	0.451168i
$195$		0			0
$196$	110530.	−	920820.i	0.205514	−	1.71212i
$197$			796004.i			1.46133i	0.682734	+	0.730667i	$0.260791\pi$
$197$			796004.i			1.46133i	−0.682734	+	0.730667i	$0.739209\pi$
$198$		0			0
$199$		−	1.10972e6i		−	1.98646i	−0.116163	−	0.993230i	$-0.537060\pi$
$199$		−	1.10972e6i		−	1.98646i	0.116163	−	0.993230i	$-0.462940\pi$
$200$	−7546.32	−	91146.8i	−0.0133401	−	0.161126i
$201$		0			0
$202$	387664.	−	343913.i	0.668462	−	0.593022i
$203$	−47304.1	−	81933.1i	−0.0805673	−	0.139547i
$204$		0			0
$205$	277238.	−	480190.i	0.460753	−	0.798047i
$206$	−119936.	−	585441.i	−0.196916	−	0.961203i
$207$		0			0
$208$	−569765.	+	596445.i	−0.913141	+	0.955899i
$209$	−377177.	−	217763.i	−0.597282	−	0.344841i
$210$		0			0
$211$	179473.	−	103619.i	0.277520	−	0.160226i	−0.354780	−	0.934950i	$-0.615444\pi$
$211$	179473.	−	103619.i	0.277520	−	0.160226i	0.632300	+	0.774724i	$0.282111\pi$
$212$	387851.	−	517608.i	0.592687	−	0.790972i
$213$		0			0
$214$	−6805.01	+	20430.0i	−0.0101577	+	0.0304953i
$215$	73842.6			0.108946
$216$		0			0
$217$	341296.			0.492020
$218$	152219.	−	456991.i	0.216934	−	0.651278i
$219$		0			0
$220$	429095.	−	572650.i	0.597719	−	0.797688i
$221$	−23767.5	+	13722.1i	−0.0327342	+	0.0188991i
$222$		0			0
$223$	−557586.	−	321922.i	−0.750844	−	0.433500i	0.0751547	−	0.997172i	$-0.476055\pi$
$223$	−557586.	−	321922.i	−0.750844	−	0.433500i	−0.825999	+	0.563672i	$0.809388\pi$
$224$	1.04990e6	+	658901.i	1.39806	+	0.877404i
$225$		0			0
$226$	48182.8	+	235194.i	0.0627511	+	0.306306i
$227$	−596328.	+	1.03287e6i	−0.768105	+	1.33040i	0.170485	+	0.985360i	$0.445467\pi$
$227$	−596328.	+	1.03287e6i	−0.768105	+	1.33040i	−0.938589	+	0.345036i	$0.887867\pi$
$228$		0			0
$229$	538232.	+	932245.i	0.678236	+	1.17474i	0.975512	+	0.219947i	$0.0705886\pi$
$229$	538232.	+	932245.i	0.678236	+	1.17474i	−0.297276	+	0.954792i	$0.596078\pi$
$230$	−1.00986e6	+	895891.i	−1.25876	+	1.11670i
$231$		0			0
$232$	79760.7	−	6603.63i	0.0972902	−	0.00805495i
$233$		−	178167.i		−	0.214999i	−0.994205	−	0.107500i	$-0.965716\pi$
$233$		−	178167.i		−	0.214999i	0.994205	−	0.107500i	$-0.0342845\pi$
$234$		0			0
$235$		−	147334.i		−	0.174034i
$236$	−13002.4	+	108322.i	−0.0151964	+	0.126600i
$237$		0			0
$238$	27369.2	+	30850.9i	0.0313198	+	0.0353041i
$239$	−336873.	−	583482.i	−0.381480	−	0.660743i	0.609794	−	0.792560i	$-0.291252\pi$
$239$	−336873.	−	583482.i	−0.381480	−	0.660743i	−0.991274	+	0.131817i	$0.957919\pi$
$240$		0			0
$241$	−162984.	+	282297.i	−0.180760	+	0.313086i	−0.942140	−	0.335221i	$-0.891189\pi$
$241$	−162984.	+	282297.i	−0.180760	+	0.313086i	0.761379	+	0.648307i	$0.224522\pi$
$242$	−129153.	+	26458.8i	−0.141764	+	0.0290424i
$243$		0			0
$244$	1.17217e6	−	501311.i	1.26043	−	0.539055i
$245$	1.51227e6	+	873110.i	1.60959	+	0.929296i
$246$		0			0
$247$	−818619.	+	472630.i	−0.853767	+	0.492922i
$248$	−123236.	+	261096.i	−0.127236	+	0.269570i
$249$		0			0
$250$	−847143.	−	282174.i	−0.857249	−	0.285540i
$251$	1.32110e6			1.32358			0.661789	−	0.749690i	$-0.269797\pi$
$251$	1.32110e6			1.32358			0.661789	+	0.749690i	$0.269797\pi$
$252$		0			0
$253$	−1.47002e6			−1.44385
$254$	−199000.	−	66284.9i	−0.193540	−	0.0644660i
$255$		0			0
$256$	−883168.	+	565267.i	−0.842254	+	0.539080i
$257$	1.15605e6	−	667444.i	1.09180	−	0.630350i	0.157744	−	0.987480i	$-0.449578\pi$
$257$	1.15605e6	−	667444.i	1.09180	−	0.630350i	0.934055	+	0.357130i	$0.116245\pi$
$258$		0			0
$259$	2.04915e6	+	1.18308e6i	1.89812	+	1.09588i
$260$	−610708.	−	1.42797e6i	−0.560273	−	1.31004i
$261$		0			0
$262$	928030.	−	190120.i	0.835235	−	0.171109i
$263$	457251.	−	791982.i	0.407629	−	0.706035i	−0.586994	−	0.809591i	$-0.699689\pi$
$263$	457251.	−	791982.i	0.407629	−	0.706035i	0.994624	+	0.103556i	$0.0330222\pi$
$264$		0			0
$265$	608914.	+	1.05467e6i	0.532649	+	0.922575i
$266$	942672.	+	1.06259e6i	0.816877	+	0.920795i
$267$		0			0
$268$	−223359.	−	26810.8i	−0.189962	−	0.0228020i
$269$		−	1.86227e6i		−	1.56914i	−0.620038	−	0.784572i	$-0.712883\pi$
$269$		−	1.86227e6i		−	1.56914i	0.620038	−	0.784572i	$-0.287117\pi$
$270$		0			0
$271$			517756.i			0.428254i	0.976806	+	0.214127i	$0.0686907\pi$
$271$			517756.i			0.428254i	−0.976806	+	0.214127i	$0.931309\pi$
$272$	−33483.9	+	9798.07i	−0.0274419	+	0.00803005i
$273$		0			0
$274$	1.45624e6	−	1.29189e6i	1.17181	−	1.03956i
$275$	93758.1	+	162394.i	0.0747613	+	0.129490i
$276$		0			0
$277$	−311881.	+	540194.i	−0.244225	+	0.423010i	−0.961913	−	0.273354i	$-0.911867\pi$
$277$	−311881.	+	540194.i	−0.244225	+	0.423010i	0.717689	+	0.696364i	$0.245200\pi$
$278$	−313489.	−	1.53023e6i	−0.243282	−	1.18753i
$279$		0			0
$280$	−1.91800e6	+	1.32972e6i	−1.46202	+	1.01360i
$281$	1.53273e6	+	884922.i	1.15798	+	0.668558i	0.950818	−	0.309749i	$-0.100245\pi$
$281$	1.53273e6	+	884922.i	1.15798	+	0.668558i	0.207159	+	0.978307i	$0.433578\pi$
$282$		0			0
$283$	−1.28654e6	+	742782.i	−0.954895	+	0.551309i	−0.894598	−	0.446871i	$-0.852538\pi$
$283$	−1.28654e6	+	742782.i	−0.954895	+	0.551309i	−0.0602971	+	0.998180i	$0.519205\pi$
$284$	−657985.	−	493038.i	−0.484084	−	0.362731i
$285$		0			0
$286$	534445.	−	1.60451e6i	0.386356	−	1.15992i
$287$	−1.96923e6			−1.41121
$288$		0			0
$289$	1.41870e6			0.999182
$290$	−47621.6	+	142969.i	−0.0332513	+	0.0998271i
$291$		0			0
$292$	−1.67560e6	−	1.25555e6i	−1.15004	−	0.861742i
$293$	−1.40797e6	+	812891.i	−0.958129	+	0.553176i	−0.895597	−	0.444867i	$-0.853251\pi$
$293$	−1.40797e6	+	812891.i	−0.958129	+	0.553176i	−0.0625325	+	0.998043i	$0.519918\pi$
$294$		0			0
$295$	−177898.	−	102709.i	−0.119019	−	0.0687154i
$296$	−1.64498e6	+	1.14044e6i	−1.09127	+	0.756559i
$297$		0			0
$298$	−44440.1	−	216925.i	−0.0289891	−	0.141504i
$299$	−1.59525e6	+	2.76306e6i	−1.03193	+	1.78736i
$300$		0			0
$301$	−131127.	−	227118.i	−0.0834208	−	0.144489i
$302$	−1.81904e6	+	1.61375e6i	−1.14769	+	1.01817i
$303$		0			0
$304$	−1.15328e6	+	337473.i	−0.715734	+	0.209438i
$305$			2.40041e6i			1.47753i
$306$		0			0
$307$			29930.7i			0.0181247i	0.999959	+	0.00906235i	$0.00288467\pi$
$307$			29930.7i			0.0181247i	−0.999959	+	0.00906235i	$0.997115\pi$
$308$	−2.52327e6	−	302880.i	−1.51561	−	0.181926i
$309$		0			0
$310$	−360763.	−	406657.i	−0.213215	−	0.240339i
$311$	−828429.	−	1.43488e6i	−0.485685	−	0.841231i	0.514180	−	0.857682i	$-0.328096\pi$
$311$	−828429.	−	1.43488e6i	−0.485685	−	0.841231i	−0.999865	+	0.0164516i	$0.994763\pi$
$312$		0			0
$313$	−1.49316e6	+	2.58623e6i	−0.861482	+	1.49213i	0.00901652	+	0.999959i	$0.497130\pi$
$313$	−1.49316e6	+	2.58623e6i	−0.861482	+	1.49213i	−0.870498	+	0.492171i	$0.836203\pi$
$314$	3.14205e6	−	643692.i	1.79841	−	0.368429i
$315$		0			0
$316$	597565.	+	1.39724e6i	0.336641	+	0.787140i
$317$	−748156.	−	431948.i	−0.418162	−	0.241426i	0.276129	−	0.961121i	$-0.410948\pi$
$317$	−748156.	−	431948.i	−0.418162	−	0.241426i	−0.694290	+	0.719695i	$0.744282\pi$
$318$		0			0
$319$	−142107.	+	82045.8i	−0.0781880	+	0.0451419i
$320$	−324694.	−	1.94744e6i	−0.177256	−	1.06314i
$321$		0			0
$322$	4.54876e6	+	1.51514e6i	2.44486	+	0.814356i
$323$	−39980.9			−0.0213229
$324$		0			0
$325$	406982.			0.213731
$326$	271276.	+	90359.0i	0.141373	+	0.0470899i
$327$		0			0
$328$	711056.	−	1.50649e6i	0.364938	−	0.773181i
$329$	−453156.	+	261630.i	−0.230812	+	0.133259i
$330$		0			0
$331$	1828.81	+	1055.86i	0.000917484	+	0.000529710i	0.500459	−	0.865760i	$-0.333165\pi$
$331$	1828.81	+	1055.86i	0.000917484	+	0.000529710i	−0.499541	+	0.866290i	$0.666498\pi$
$332$	−388724.	+	166248.i	−0.193551	+	0.0827773i
$333$		0			0
$334$	−1.71881e6	+	352121.i	−0.843064	+	0.172713i
$335$	211786.	−	366824.i	0.103106	−	0.178586i
$336$		0			0
$337$	−1.24422e6	−	2.15505e6i	−0.596790	−	1.03367i	−0.993292	−	0.115637i	$-0.963109\pi$
$337$	−1.24422e6	−	2.15505e6i	−0.596790	−	1.03367i	0.396501	−	0.918034i	$-0.370224\pi$
$338$	−1.04201e6	−	1.17457e6i	−0.496112	−	0.559224i
$339$		0			0
$340$	7828.80	−	65221.1i	0.00367280	−	0.0305978i
$341$		−	591955.i		−	0.275679i
$342$		0			0
$343$		−	2.60530e6i		−	1.19570i
$344$	221096.	−	18305.2i	0.100736	−	0.00834024i
$345$		0			0
$346$	−686607.	+	609119.i	−0.308332	+	0.273534i
$347$	1.65555e6	+	2.86750e6i	0.738106	+	1.27844i	0.953347	+	0.301877i	$0.0976131\pi$
$347$	1.65555e6	+	2.86750e6i	0.738106	+	1.27844i	−0.215241	+	0.976561i	$0.569054\pi$
$348$		0			0
$349$	−131505.	+	227773.i	−0.0577934	+	0.100101i	−0.893475	−	0.449114i	$-0.851740\pi$
$349$	−131505.	+	227773.i	−0.0577934	+	0.100101i	0.835681	+	0.549215i	$0.185073\pi$
$350$	−122742.	−	599141.i	−0.0535580	−	0.261432i
$351$		0			0
$352$	1.14282e6	−	1.82097e6i	0.491610	−	0.783333i
$353$	−127875.	−	73828.9i	−0.0546198	−	0.0315347i	0.472441	−	0.881362i	$-0.343373\pi$
$353$	−127875.	−	73828.9i	−0.0546198	−	0.0315347i	−0.527061	+	0.849827i	$0.676706\pi$
$354$		0			0
$355$	1.34070e6	−	774054.i	0.564626	−	0.325987i
$356$	1.64413e6	−	2.19419e6i	0.687563	−	0.917590i
$357$		0			0
$358$	−559928.	+	1.68102e6i	−0.230900	+	0.693209i
$359$	1.46738e6			0.600905			0.300453	−	0.953797i	$-0.402862\pi$
$359$	1.46738e6			0.600905			0.300453	+	0.953797i	$0.402862\pi$
$360$		0			0
$361$	1.09904e6			0.443861
$362$	−431570.	+	1.29566e6i	−0.173093	+	0.519660i
$363$		0			0
$364$	−3.30753e6	+	4.41408e6i	−1.30843	+	1.74617i
$365$	3.41418e6	−	1.97118e6i	1.34139	−	0.774450i
$366$		0			0
$367$	−1.76458e6	−	1.01878e6i	−0.683874	−	0.394835i	0.117439	−	0.993080i	$-0.462532\pi$
$367$	−1.76458e6	−	1.01878e6i	−0.683874	−	0.394835i	−0.801313	+	0.598245i	$0.795865\pi$
$368$	−2.80159e6	+	2.93277e6i	−1.07841	+	1.12891i
$369$		0			0
$370$	−756383.	−	3.69213e6i	−0.287235	−	1.40208i
$371$	2.16257e6	−	3.74567e6i	0.815708	−	1.41285i
$372$		0			0
$373$	629011.	+	1.08948e6i	0.234092	+	0.405459i	0.959008	−	0.283378i	$-0.0914551\pi$
$373$	629011.	+	1.08948e6i	0.234092	+	0.405459i	−0.724917	+	0.688837i	$0.758122\pi$
$374$	53508.8	−	47470.0i	0.0197809	−	0.0175485i
$375$		0			0
$376$	−36523.4	−	441141.i	−0.0133230	−	0.160919i
$377$			356142.i			0.129053i
$378$		0			0
$379$			3.51959e6i			1.25862i	0.777154	+	0.629310i	$0.216662\pi$
$379$			3.51959e6i			1.25862i	−0.777154	+	0.629310i	$0.783338\pi$
$380$	269646.	−	2.24640e6i	0.0957933	−	0.798046i
$381$		0			0
$382$	2.83867e6	+	3.19979e6i	0.995307	+	1.12192i
$383$	1.45304e6	+	2.51675e6i	0.506153	+	0.876683i	0.999975	+	0.00711941i	$0.00226620\pi$
$383$	1.45304e6	+	2.51675e6i	0.506153	+	0.876683i	−0.493822	+	0.869563i	$0.664400\pi$
$384$		0			0
$385$	2.39253e6	−	4.14399e6i	0.822633	−	1.42484i
$386$	2.33585e6	−	478530.i	0.797951	−	0.163471i
$387$		0			0
$388$	1.64440e6	−	703272.i	0.554534	−	0.237161i
$389$	−3.99038e6	−	2.30384e6i	−1.33703	−	0.771932i	−0.350660	−	0.936503i	$-0.614043\pi$
$389$	−3.99038e6	−	2.30384e6i	−1.33703	−	0.771932i	−0.986365	+	0.164570i	$0.947376\pi$
$390$		0			0
$391$	−116867.	+	67473.0i	−0.0386589	+	0.0223197i
$392$	4.74441e6	+	2.23934e6i	1.55943	+	0.736046i
$393$		0			0
$394$	−4.27212e6	−	1.42300e6i	−1.38644	−	0.461810i
$395$	−2.86130e6			−0.922720
$396$		0			0
$397$	−1.37551e6			−0.438012			−0.219006	−	0.975723i	$-0.570281\pi$
$397$	−1.37551e6			−0.438012			−0.219006	+	0.975723i	$0.570281\pi$
$398$	5.95581e6	+	1.98382e6i	1.88466	+	0.627760i
$399$		0			0
$400$	502671.	+	122440.i	0.157085	+	0.0382626i
$401$	−93720.9	+	54109.8i	−0.0291055	+	0.0168041i	−0.514482	−	0.857501i	$-0.672016\pi$
$401$	−93720.9	+	54109.8i	−0.0291055	+	0.0168041i	0.485377	+	0.874305i	$0.338682\pi$
$402$		0			0
$403$	−1.11264e6	−	642385.i	−0.341266	−	0.197030i
$404$	1.15275e6	+	2.69538e6i	0.351384	+	0.821611i
$405$		0			0
$406$	524296.	−	107409.i	0.157856	−	0.0323390i
$407$	2.05197e6	−	3.55411e6i	0.614022	−	1.06352i
$408$		0			0
$409$	−903457.	−	1.56483e6i	−0.267054	−	0.462551i	0.701046	−	0.713116i	$-0.252717\pi$
$409$	−903457.	−	1.56483e6i	−0.267054	−	0.462551i	−0.968100	+	0.250565i	$0.919384\pi$
$410$	2.08155e6	+	2.34635e6i	0.611543	+	0.689339i
$411$		0			0
$412$	3.35644e6	+	402890.i	0.974173	+	0.116935i
$413$			729546.i			0.210464i
$414$		0			0
$415$		−	796039.i		−	0.226889i
$416$	−2.18254e6	−	4.12416e6i	−0.618341	−	1.16843i
$417$		0			0
$418$	1.84299e6	−	1.63500e6i	0.515921	−	0.457696i
$419$	−926212.	−	1.60425e6i	−0.257736	−	0.446412i	0.707899	−	0.706314i	$-0.249643\pi$
$419$	−926212.	−	1.60425e6i	−0.257736	−	0.446412i	−0.965635	+	0.259902i	$0.916310\pi$
$420$		0			0
$421$	1.85582e6	−	3.21437e6i	0.510305	−	0.883874i	−0.489624	−	0.871934i	$-0.662866\pi$
$421$	1.85582e6	−	3.21437e6i	0.510305	−	0.883874i	0.999929	−	0.0119403i	$-0.00380082\pi$
$422$	235278.	+	1.14846e6i	0.0643133	+	0.313932i
$423$		0			0
$424$	2.08463e6	+	3.00689e6i	0.563137	+	0.812276i
$425$	14907.6	+	8606.90i	0.00400346	+	0.00231140i
$426$		0			0
$427$	7.38295e6	−	4.26255e6i	1.95957	−	1.13136i
$428$	−97481.6	−	73044.4i	−0.0257225	−	0.0192742i
$429$		0			0
$430$	−132007.	+	396310.i	−0.0344290	+	0.103363i
$431$	277886.			0.0720565			0.0360283	−	0.999351i	$-0.488529\pi$
$431$	277886.			0.0720565			0.0360283	+	0.999351i	$0.488529\pi$
$432$		0			0
$433$	−2.49224e6			−0.638807			−0.319403	−	0.947619i	$-0.603482\pi$
$433$	−2.49224e6			−0.638807			−0.319403	+	0.947619i	$0.603482\pi$
$434$	−610127.	+	1.83172e6i	−0.155488	+	0.466805i
$435$		0			0
$436$	2.18053e6	+	1.63390e6i	0.549347	+	0.411633i
$437$	−4.02522e6	+	2.32396e6i	−1.00829	+	0.582138i
$438$		0			0
$439$	−1.04465e6	−	603126.i	−0.258707	−	0.149364i	0.365038	−	0.930993i	$-0.381056\pi$
$439$	−1.04465e6	−	603126.i	−0.258707	−	0.149364i	−0.623744	+	0.781628i	$0.714389\pi$
$440$	2.30631e6	+	3.32665e6i	0.567918	+	0.819172i
$441$		0			0
$442$	−31157.6	−	152090.i	−0.00758593	−	0.0370292i
$443$	−1.30812e6	+	2.26572e6i	−0.316692	+	0.548526i	−0.979796	−	0.200001i	$-0.935905\pi$
$443$	−1.30812e6	+	2.26572e6i	−0.316692	+	0.548526i	0.663104	+	0.748527i	$0.269239\pi$
$444$		0			0
$445$	2.58124e6	+	4.47084e6i	0.617914	+	1.07026i
$446$	2.72453e6	−	2.41705e6i	0.648566	−	0.575371i
$447$		0			0
$448$	−5.41316e6	+	4.45684e6i	−1.27425	+	1.04914i
$449$			348912.i			0.0816770i	0.999166	+	0.0408385i	$0.0130029\pi$
$449$			348912.i			0.0816770i	−0.999166	+	0.0408385i	$0.986997\pi$
$450$		0			0
$451$			3.41549e6i			0.790701i
$452$	−1.34841e6	−	161856.i	−0.310440	−	0.0372635i
$453$		0			0
$454$	−4.47733e6	−	5.04690e6i	−1.01948	−	1.14917i
$455$	−5.19272e6	−	8.99405e6i	−1.17589	−	2.03670i
$456$		0			0
$457$	1.71163e6	−	2.96463e6i	0.383371	−	0.664018i	−0.608171	−	0.793806i	$-0.708096\pi$
$457$	1.71163e6	−	2.96463e6i	0.383371	−	0.664018i	0.991542	+	0.129788i	$0.0414297\pi$
$458$	−5.96550e6	+	1.22211e6i	−1.32887	+	0.272238i
$459$		0			0
$460$	−3.00291e6	−	7.02144e6i	−0.661679	−	1.54715i
$461$	−4.70141e6	−	2.71436e6i	−1.03033	−	0.594861i	−0.113251	−	0.993566i	$-0.536126\pi$
$461$	−4.70141e6	−	2.71436e6i	−1.03033	−	0.594861i	−0.917079	+	0.398705i	$0.869460\pi$
$462$		0			0
$463$	−3.74259e6	+	2.16079e6i	−0.811373	+	0.468446i	−0.847432	−	0.530903i	$-0.821853\pi$
$463$	−3.74259e6	+	2.16079e6i	−0.811373	+	0.468446i	0.0360597	+	0.999350i	$0.488519\pi$
$464$	−107145.	+	439877.i	−0.0231034	+	0.0948499i
$465$		0			0
$466$	956214.	+	318505.i	0.203981	+	0.0679440i
$467$	3.41339e6			0.724258			0.362129	−	0.932128i	$-0.382050\pi$
$467$	3.41339e6			0.724258			0.362129	+	0.932128i	$0.382050\pi$
$468$		0			0
$469$	−1.50432e6			−0.315798
$470$	790736.	+	263386.i	0.165115	+	0.0549981i
$471$		0			0
$472$	−558113.	−	263427.i	−0.115310	−	0.0544258i
$473$	−393921.	+	227430.i	−0.0809572	+	0.0467407i
$474$		0			0
$475$	513459.	+	296446.i	0.104417	+	0.0602853i
$476$	−214503.	+	91737.8i	−0.0433926	+	0.0185580i
$477$		0			0
$478$	3.73374e6	−	764908.i	0.747437	−	0.153123i
$479$	−1.30808e6	+	2.26567e6i	−0.260493	+	0.451188i	−0.966373	−	0.257144i	$-0.917219\pi$
$479$	−1.30808e6	+	2.26567e6i	−0.260493	+	0.451188i	0.705880	+	0.708332i	$0.250552\pi$
$480$		0			0
$481$	−4.45356e6	−	7.71378e6i	−0.877696	−	1.52021i
$482$	−1.22371e6	−	1.37938e6i	−0.239917	−	0.270438i
$483$		0			0
$484$	88880.9	−	740460.i	0.0172463	−	0.143677i
$485$			3.36745e6i			0.650050i
$486$		0			0
$487$			8.58357e6i			1.64001i	0.572359	+	0.820003i	$0.306029\pi$
$487$			8.58357e6i			1.64001i	−0.572359	+	0.820003i	$0.693971\pi$
$488$	595049.	+	7.18719e6i	0.113111	+	1.36619i
$489$		0			0
$490$	−7.38940e6	+	6.55546e6i	−1.39033	+	1.23342i
$491$	4.45187e6	+	7.71087e6i	0.833372	+	1.44344i	0.895349	+	0.445366i	$0.146926\pi$
$491$	4.45187e6	+	7.71087e6i	0.833372	+	1.44344i	−0.0619764	+	0.998078i	$0.519740\pi$
$492$		0			0
$493$	−7531.72	+	13045.3i	−0.00139565	+	0.00241734i
$494$	−1.07316e6	−	5.23840e6i	−0.197855	−	0.965787i
$495$		0			0
$496$	−1.18099e6	−	1.12816e6i	−0.215546	−	0.205905i
$497$	−4.76152e6	−	2.74906e6i	−0.864678	−	0.499222i
$498$		0			0
$499$	9.00734e6	−	5.20039e6i	1.61937	−	0.934942i	0.632284	−	0.774737i	$-0.282118\pi$
$499$	9.00734e6	−	5.20039e6i	1.61937	−	0.934942i	0.987084	−	0.160205i	$-0.0512156\pi$
$500$	3.02884e6	−	4.04214e6i	0.541815	−	0.723081i
$501$		0			0
$502$	−2.36169e6	+	7.09026e6i	−0.418277	+	1.25575i
$503$	3.07909e6			0.542628			0.271314	−	0.962491i	$-0.412542\pi$
$503$	3.07909e6			0.542628			0.271314	+	0.962491i	$0.412542\pi$
$504$		0			0
$505$	−5.51967e6			−0.963129
$506$	2.62791e6	−	7.88952e6i	0.456284	−	1.36985i
$507$		0			0
$508$	711497.	−	949531.i	0.122325	−	0.163249i
$509$	8.39198e6	−	4.84511e6i	1.43572	−	0.828914i	0.438172	−	0.898891i	$-0.355626\pi$
$509$	8.39198e6	−	4.84511e6i	1.43572	−	0.828914i	0.997549	+	0.0699775i	$0.0222928\pi$
$510$		0			0
$511$	−1.21255e7	−	7.00067e6i	−2.05422	−	1.18601i
$512$	−1.45494e6	−	5.75044e6i	−0.245285	−	0.969451i
$513$		0			0
$514$	1.51550e6	+	7.39762e6i	0.253017	+	1.23505i
$515$	−3.18254e6	+	5.51232e6i	−0.528756	+	0.915832i
$516$		0			0
$517$	453779.	+	785968.i	0.0746651	+	0.129324i
$518$	−1.00127e7	+	8.88273e6i	−1.63956	+	1.45453i
$519$		0			0
$520$	8.75558e6	−	724901.i	1.41996	−	0.117563i
$521$		−	7.69134e6i		−	1.24139i	−0.784053	−	0.620694i	$-0.786851\pi$
$521$		−	7.69134e6i		−	1.24139i	0.784053	−	0.620694i	$-0.213149\pi$
$522$		0			0
$523$			1.02773e6i			0.164295i	0.996620	+	0.0821476i	$0.0261779\pi$
$523$			1.02773e6i			0.164295i	−0.996620	+	0.0821476i	$0.973822\pi$
$524$	−638653.	+	5.32057e6i	−0.101610	+	0.846505i
$525$		0			0
$526$	3.43312e6	+	3.86985e6i	0.541034	+	0.609860i
$527$	−27170.5	−	47060.6i	−0.00426158	−	0.00738127i
$528$		0			0
$529$	−4.62582e6	+	8.01216e6i	−0.718704	+	1.24483i
$530$	−6.74890e6	+	1.38261e6i	−1.04362	+	0.213800i
$531$		0			0
$532$	−7.38808e6	+	3.15971e6i	−1.13176	+	0.484025i
$533$	6.41979e6	+	3.70647e6i	0.978820	+	0.565122i
$534$		0			0
$535$	198627.	−	114677.i	0.0300023	−	0.0173218i
$536$	543186.	−	1.15083e6i	0.0816651	−	0.173021i
$537$		0			0
$538$	9.99474e6	+	3.32914e6i	1.48873	+	0.495880i
$539$	−1.07565e7			−1.59477
$540$		0			0
$541$	9.97892e6			1.46585			0.732926	−	0.680308i	$-0.238154\pi$
$541$	9.97892e6			1.46585			0.732926	+	0.680308i	$0.238154\pi$
$542$	−2.77877e6	−	925579.i	−0.406307	−	0.135337i
$543$		0			0
$544$	7272.63	−	197223.i	0.00105365	−	0.0285732i
$545$	−4.44302e6	+	2.56518e6i	−0.640748	+	0.369936i
$546$		0			0
$547$	6.89166e6	+	3.97890e6i	0.984817	+	0.568584i	0.903721	−	0.428122i	$-0.140825\pi$
$547$	6.89166e6	+	3.97890e6i	0.984817	+	0.568584i	0.0810959	+	0.996706i	$0.474158\pi$
$548$	4.33025e6	+	1.01251e7i	0.615973	+	1.44028i
$549$		0			0
$550$	−1.03917e6	+	212888.i	−0.146480	+	0.0300085i
$551$	−259414.	+	449318.i	−0.0364011	+	0.0630485i
$552$		0			0
$553$	5.08097e6	+	8.80049e6i	0.706535	+	1.22375i
$554$	−2.34165e6	−	2.63954e6i	−0.324152	−	0.365388i
$555$		0			0
$556$	8.77310e6	+	1.05308e6i	1.20355	+	0.144468i
$557$			968143.i			0.132221i	0.997812	+	0.0661107i	$0.0210590\pi$
$557$			968143.i			0.132221i	−0.997812	+	0.0661107i	$0.978941\pi$
$558$		0			0
$559$			987222.i			0.133624i
$560$	−3.70777e6	−	1.26709e7i	−0.499624	−	1.70741i
$561$		0			0
$562$	−7.48936e6	+	6.64414e6i	−1.00024	+	0.887356i
$563$	3.58742e6	+	6.21360e6i	0.476993	+	0.826176i	0.999652	−	0.0263657i	$-0.00839345\pi$
$563$	3.58742e6	+	6.21360e6i	0.476993	+	0.826176i	−0.522660	+	0.852541i	$0.675060\pi$
$564$		0			0
$565$	1.27855e6	−	2.21451e6i	0.168499	−	0.291848i
$566$	−1.68657e6	−	8.23263e6i	−0.221290	−	1.08018i
$567$		0			0
$568$	3.82238e6	−	2.64999e6i	0.497121	−	0.344646i
$569$	1.01785e7	+	5.87656e6i	1.31796	+	0.760926i	0.983400	−	0.181448i	$-0.0580785\pi$
$569$	1.01785e7	+	5.87656e6i	1.31796	+	0.760926i	0.334561	+	0.942374i	$0.391412\pi$
$570$		0			0
$571$	−9.11184e6	+	5.26072e6i	−1.16954	+	0.675235i	−0.953572	−	0.301165i	$-0.902625\pi$
$571$	−9.11184e6	+	5.26072e6i	−1.16954	+	0.675235i	−0.215970	+	0.976400i	$0.569291\pi$
$572$	7.65592e6	+	5.73669e6i	0.978379	+	0.733113i
$573$		0			0
$574$	3.52034e6	−	1.05688e7i	0.445970	−	1.33889i
$575$	2.00117e6			0.252414
$576$		0			0
$577$	1.46593e6			0.183305			0.0916526	−	0.995791i	$-0.470785\pi$
$577$	1.46593e6			0.183305			0.0916526	+	0.995791i	$0.470785\pi$
$578$	−2.53617e6	+	7.61408e6i	−0.315761	+	0.947977i
$579$		0			0
$580$	−682179.	−	511166.i	−0.0842031	−	0.0630946i
$581$	−2.44838e6	+	1.41357e6i	−0.300911	+	0.173731i
$582$		0			0
$583$	−6.49662e6	−	3.75082e6i	−0.791618	−	0.457041i
$584$	9.73392e6	−	6.74836e6i	1.18102	−	0.818778i
$585$		0			0
$586$	−1.84576e6	−	9.00970e6i	−0.222040	−	1.08384i
$587$	523994.	−	907585.i	0.0627670	−	0.108716i	−0.832934	−	0.553372i	$-0.813341\pi$
$587$	523994.	−	907585.i	0.0627670	−	0.108716i	0.895701	+	0.444656i	$0.146674\pi$
$588$		0			0
$589$	−935827.	−	1.62090e6i	−0.111150	−	0.192517i
$590$	869259.	−	771157.i	0.102806	−	0.0912038i
$591$		0			0
$592$	−3.17998e6	−	1.08673e7i	−0.372924	−	1.27443i
$593$			8.50755e6i			0.993500i	0.867894	+	0.496750i	$0.165473\pi$
$593$			8.50755e6i			0.993500i	−0.867894	+	0.496750i	$0.834527\pi$
$594$		0			0
$595$		−	439264.i		−	0.0508667i
$596$	1.24367e6	+	149284.i	0.143414	+	0.0172146i
$597$		0			0
$598$	−1.19774e7	−	1.35011e7i	−1.36965	−	1.54389i
$599$	−4.39728e6	−	7.61632e6i	−0.500746	−	0.867317i	−1.00000		0.000861327i	$-0.999726\pi$
$599$	−4.39728e6	−	7.61632e6i	−0.500746	−	0.867317i	0.499254	−	0.866456i	$-0.333608\pi$
$600$		0			0
$601$	−2.32237e6	+	4.02246e6i	−0.262268	+	0.454261i	−0.966844	−	0.255367i	$-0.917804\pi$
$601$	−2.32237e6	+	4.02246e6i	−0.262268	+	0.454261i	0.704576	+	0.709628i	$0.251137\pi$
$602$	1.45334e6	−	297737.i	0.163447	−	0.0334844i
$603$		0			0
$604$	−5.40908e6	−	1.26476e7i	−0.603297	−	1.41064i
$605$	1.21606e6	+	702095.i	0.135073	+	0.0779843i
$606$		0			0
$607$	1.45173e6	−	838155.i	0.159924	−	0.0923320i	−0.417902	−	0.908492i	$-0.637235\pi$
$607$	1.45173e6	−	838155.i	0.159924	−	0.0923320i	0.577826	+	0.816160i	$0.303901\pi$
$608$	250490.	−	6.79290e6i	0.0274809	−	0.745241i
$609$		0			0
$610$	−1.28829e7	−	4.29115e6i	−1.40181	−	0.466928i
$611$	1.96975e6			0.213456
$612$		0			0
$613$	615822.			0.0661918			0.0330959	−	0.999452i	$-0.489463\pi$
$613$	615822.			0.0661918			0.0330959	+	0.999452i	$0.489463\pi$
$614$	−160637.	−	53506.4i	−0.0171959	−	0.00572776i
$615$		0			0
$616$	6.13633e6	−	1.30008e7i	0.651564	−	1.38045i
$617$	3.65601e6	−	2.11080e6i	0.386629	−	0.223220i	−0.294070	−	0.955784i	$-0.595010\pi$
$617$	3.65601e6	−	2.11080e6i	0.386629	−	0.223220i	0.680698	+	0.732564i	$0.261676\pi$
$618$		0			0
$619$	1.47506e7	+	8.51629e6i	1.54733	+	0.893354i	0.998344	+	0.0575254i	$0.0183210\pi$
$619$	1.47506e7	+	8.51629e6i	1.54733	+	0.893354i	0.548991	+	0.835829i	$0.315012\pi$
$620$	2.82744e6	−	1.20923e6i	0.295402	−	0.126337i
$621$		0			0
$622$	9.18191e6	−	1.88104e6i	0.951606	−	0.194950i
$623$	9.16731e6	−	1.58782e7i	0.946285	−	1.63901i
$624$		0			0
$625$	5.54462e6	+	9.60356e6i	0.567769	+	0.983405i
$626$	−1.12109e7	−	1.26371e7i	−1.14342	−	1.28888i
$627$		0			0
$628$	−2.16230e6	+	1.80139e7i	−0.218785	+	1.82268i
$629$		−	376737.i		−	0.0379674i
$630$		0			0
$631$		−	1.01556e7i		−	1.01539i	−0.861538	−	0.507693i	$-0.830498\pi$
$631$		−	1.01556e7i		−	1.01539i	0.861538	−	0.507693i	$-0.169502\pi$
$632$	−8.56715e6	+	709300.i	−0.853186	+	0.0706378i
$633$		0			0
$634$	3.65571e6	−	3.24314e6i	0.361200	−	0.320437i
$635$	1.11703e6	+	1.93475e6i	0.109933	+	0.190410i
$636$		0			0
$637$	−1.16728e7	+	2.02180e7i	−1.13980	+	1.97419i
$638$	−186294.	−	909356.i	−0.0181195	−	0.0884468i
$639$		0			0
$640$	1.10323e7	+	1.73877e6i	1.06467	+	0.167800i
$641$	1.77251e7	+	1.02336e7i	1.70389	+	0.983744i	0.941735	+	0.336355i	$0.109194\pi$
$641$	1.77251e7	+	1.02336e7i	1.70389	+	0.983744i	0.762160	+	0.647389i	$0.224139\pi$
$642$		0			0
$643$	1.99881e6	−	1.15401e6i	0.190653	−	0.110074i	−0.401635	−	0.915800i	$-0.631558\pi$
$643$	1.99881e6	−	1.15401e6i	0.190653	−	0.110074i	0.592288	+	0.805726i	$0.298225\pi$
$644$	−1.62634e7	+	2.17044e7i	−1.54524	+	2.06221i
$645$		0			0
$646$	71472.8	−	214576.i	0.00673845	−	0.0202301i
$647$	4.18696e6			0.393222			0.196611	−	0.980482i	$-0.437006\pi$
$647$	4.18696e6			0.393222			0.196611	+	0.980482i	$0.437006\pi$
$648$		0			0
$649$	1.26535e6			0.117923
$650$	−727552.	+	2.18426e6i	−0.0675431	+	0.202778i
$651$		0			0
$652$	−969906.	+	1.29439e6i	−0.0893533	+	0.119247i
$653$	1.70167e6	−	982460.i	0.156168	−	0.0901638i	−0.419879	−	0.907580i	$-0.637928\pi$
$653$	1.70167e6	−	982460.i	0.156168	−	0.0901638i	0.576048	+	0.817416i	$0.304594\pi$
$654$		0			0
$655$	−8.73801e6	−	5.04489e6i	−0.795810	−	0.459461i
$656$	6.81412e6	+	6.50932e6i	0.618230	+	0.590576i
$657$		0			0
$658$	−594059.	−	2.89978e6i	−0.0534890	−	0.261096i
$659$	−2.30212e6	+	3.98739e6i	−0.206497	+	0.357664i	−0.950609	−	0.310391i	$-0.899540\pi$
$659$	−2.30212e6	+	3.98739e6i	−0.206497	+	0.357664i	0.744111	+	0.668056i	$0.232873\pi$
$660$		0			0
$661$	−2.73544e6	−	4.73792e6i	−0.243514	−	0.421778i	0.718199	−	0.695838i	$-0.244967\pi$
$661$	−2.73544e6	−	4.73792e6i	−0.243514	−	0.421778i	−0.961713	+	0.274060i	$0.911633\pi$
$662$	−8936.09	+	7927.60i	−0.000792506	+	0.000703067i
$663$		0			0
$664$	−197334.	−	2.38346e6i	−0.0173693	−	0.209791i
$665$		−	1.51295e7i		−	1.32669i
$666$		0			0
$667$			1.75118e6i			0.152411i
$668$	1.18285e6	−	9.85423e6i	0.102562	−	0.854440i
$669$		0			0
$670$	1.59013e6	+	1.79241e6i	0.136850	+	0.154259i
$671$	−7.39309e6	−	1.28052e7i	−0.633899	−	1.09795i
$672$		0			0
$673$	1.03102e7	−	1.78577e7i	0.877460	−	1.51981i	0.0233415	−	0.999728i	$-0.492569\pi$
$673$	1.03102e7	−	1.78577e7i	0.877460	−	1.51981i	0.854119	−	0.520078i	$-0.174097\pi$
$674$	1.37903e7	−	2.82513e6i	1.16930	−	0.239546i
$675$		0			0
$676$	8.16662e6	−	3.49267e6i	0.687346	−	0.293962i
$677$	−2.59618e6	−	1.49891e6i	−0.217702	−	0.125691i	0.387184	−	0.922003i	$-0.373448\pi$
$677$	−2.59618e6	−	1.49891e6i	−0.217702	−	0.125691i	−0.604886	+	0.796312i	$0.706781\pi$
$678$		0			0
$679$	1.03573e7	−	5.97977e6i	0.862126	−	0.497749i
$680$	336043.	+	158611.i	0.0278691	+	0.0131541i
$681$		0			0
$682$	3.17700e6	+	1.05822e6i	0.261551	+	0.0871198i
$683$	3.24667e6			0.266310			0.133155	−	0.991095i	$-0.457489\pi$
$683$	3.24667e6			0.266310			0.133155	+	0.991095i	$0.457489\pi$
$684$		0			0
$685$	−2.07344e7			−1.68836
$686$	1.39825e7	+	4.65743e6i	1.13442	+	0.377864i
$687$		0			0
$688$	−297005.	+	1.21934e6i	−0.0239217	+	0.0982092i
$689$	−1.41002e7	+	8.14073e6i	−1.13156	+	0.653304i
$690$		0			0
$691$	−1.27793e7	−	7.37815e6i	−1.01815	−	0.587831i	−0.104584	−	0.994516i	$-0.533351\pi$
$691$	−1.27793e7	−	7.37815e6i	−1.01815	−	0.587831i	−0.913568	+	0.406685i	$0.866685\pi$
$692$	−2.04169e6	−	4.77390e6i	−0.162078	−	0.378973i
$693$		0			0
$694$	−1.83493e7	+	3.75911e6i	−1.44618	+	0.296269i
$695$	−8.31854e6	+	1.44081e7i	−0.653259	+	1.13148i
$696$		0			0
$697$	156769.	+	271533.i	0.0122230	+	0.0211709i
$698$	−987361.	−	1.11297e6i	−0.0767074	−	0.0864656i
$699$		0			0
$700$	3.43499e6	+	412318.i	0.264960	+	0.0318044i
$701$			571089.i			0.0438944i	0.999759	+	0.0219472i	$0.00698656\pi$
$701$			571089.i			0.0438944i	−0.999759	+	0.0219472i	$0.993013\pi$
$702$		0			0
$703$		−	1.29759e7i		−	0.990259i
$704$	7.73009e6	+	9.38876e6i	0.587831	+	0.713965i
$705$		0			0
$706$	624836.	−	554319.i	0.0471796	−	0.0418551i
$707$	9.80159e6	+	1.69769e7i	0.737476	+	1.27735i
$708$		0			0
$709$	9.31781e6	−	1.61389e7i	0.696143	−	1.20576i	−0.273651	−	0.961829i	$-0.588231\pi$
$709$	9.31781e6	−	1.61389e7i	0.696143	−	1.20576i	0.969794	−	0.243926i	$-0.0784354\pi$
$710$	1.75757e6	+	8.57924e6i	0.130848	+	0.638709i
$711$		0			0
$712$	8.83692e6	+	1.27465e7i	0.653282	+	0.942303i
$713$	−5.47097e6	−	3.15867e6i	−0.403033	−	0.232691i
$714$		0			0
$715$	−1.55996e7	+	9.00642e6i	−1.14116	+	0.658851i
$716$	−8.02096e6	−	6.01022e6i	−0.584715	−	0.438135i
$717$		0			0
$718$	−2.62320e6	+	7.87535e6i	−0.189898	+	0.570110i
$719$	−7.72155e6			−0.557035			−0.278517	−	0.960431i	$-0.589843\pi$
$719$	−7.72155e6			−0.557035			−0.278517	+	0.960431i	$0.589843\pi$
$720$		0			0
$721$	2.26057e7			1.61949
$722$	−1.96474e6	+	5.89852e6i	−0.140269	+	0.421115i
$723$		0			0
$724$	−6.18223e6	−	4.63243e6i	−0.438328	−	0.328445i
$725$	193454.	−	111691.i	0.0136689	−	0.00789173i
$726$		0			0
$727$	1.28498e7	+	7.41886e6i	0.901700	+	0.520596i	0.877751	−	0.479117i	$-0.159043\pi$
$727$	1.28498e7	+	7.41886e6i	0.901700	+	0.520596i	0.0239484	+	0.999713i	$0.492376\pi$
$728$	−1.77774e7	−	2.56423e7i	−1.24319	−	1.79320i
$729$		0			0
$730$	4.47577e6	+	2.18476e7i	0.310857	+	1.51739i
$731$	−20877.9	+	36161.5i	−0.00144508	+	0.00250296i
$732$		0			0
$733$	−1.71343e6	−	2.96776e6i	−0.117790	−	0.204018i	0.801102	−	0.598528i	$-0.204248\pi$
$733$	−1.71343e6	−	2.96776e6i	−0.117790	−	0.204018i	−0.918891	+	0.394510i	$0.870914\pi$
$734$	8.62225e6	−	7.64917e6i	0.590718	−	0.524052i
$735$		0			0
$736$	−1.07317e7	−	2.02788e7i	−0.730256	−	1.37990i
$737$			2.60915e6i			0.176942i
$738$		0			0
$739$			1.26632e7i			0.852970i	0.904495	+	0.426485i	$0.140248\pi$
$739$			1.26632e7i			0.852970i	−0.904495	+	0.426485i	$0.859752\pi$
$740$	2.11677e7	+	2.54085e6i	1.42100	+	0.170569i
$741$		0			0
$742$	1.62369e7	+	1.83025e7i	1.08266	+	1.22039i
$743$	−6.02221e6	−	1.04308e7i	−0.400206	−	0.693178i	0.593544	−	0.804801i	$-0.297728\pi$
$743$	−6.02221e6	−	1.04308e7i	−0.400206	−	0.693178i	−0.993751	+	0.111624i	$0.964395\pi$
$744$		0			0
$745$	−1.17924e6	+	2.04250e6i	−0.0778413	+	0.134825i
$746$	−6.97165e6	+	1.42824e6i	−0.458658	+	0.0939623i
$747$		0			0
$748$	159113.	+	372040.i	0.0103980	+	0.0243129i
$749$	−705427.	−	407278.i	−0.0459460	−	0.0265269i
$750$		0			0
$751$	−1.01719e7	+	5.87273e6i	−0.658114	+	0.379962i	−0.791558	−	0.611094i	$-0.790730\pi$
$751$	−1.01719e7	+	5.87273e6i	−0.658114	+	0.379962i	0.133444	+	0.991056i	$0.457396\pi$
$752$	2.43287e6	+	592597.i	0.156883	+	0.0382133i
$753$		0			0
$754$	−1.91140e6	−	636666.i	−0.122440	−	0.0407834i
$755$	2.59001e7			1.65361
$756$		0			0
$757$	5.08821e6			0.322719			0.161360	−	0.986896i	$-0.448412\pi$
$757$	5.08821e6			0.322719			0.161360	+	0.986896i	$0.448412\pi$
$758$	−1.88895e7	−	6.29189e6i	−1.19412	−	0.397748i
$759$		0			0
$760$	1.15743e7	+	5.46301e6i	0.726876	+	0.343082i
$761$	6.60390e6	−	3.81276e6i	0.413370	−	0.238659i	−0.278867	−	0.960330i	$-0.589959\pi$
$761$	6.60390e6	−	3.81276e6i	0.413370	−	0.238659i	0.692237	+	0.721671i	$0.256625\pi$
$762$		0			0
$763$	1.57795e7	+	9.11027e6i	0.981252	+	0.566526i
$764$	−2.22478e7	+	9.51485e6i	−1.37896	+	0.589751i
$765$		0			0
$766$	−1.61048e7	+	3.29930e6i	−0.991709	+	0.203165i
$767$	1.37315e6	−	2.37836e6i	0.0842808	−	0.145979i
$768$		0			0
$769$	8.36212e6	+	1.44836e7i	0.509918	+	0.883205i	0.999934	+	0.0114909i	$0.00365776\pi$
$769$	8.36212e6	+	1.44836e7i	0.509918	+	0.883205i	−0.490016	+	0.871714i	$0.663009\pi$
$770$	1.79635e7	+	2.02487e7i	1.09186	+	1.23075i
$771$		0			0
$772$	−1.60749e6	+	1.33918e7i	−0.0970742	+	0.808718i
$773$		−	610007.i		−	0.0367186i	−0.999831	−	0.0183593i	$-0.994156\pi$
$773$		−	610007.i		−	0.0367186i	0.999831	−	0.0183593i	$-0.00584428\pi$
$774$		0			0
$775$			805843.i			0.0481943i
$776$	834773.	+	1.00826e7i	0.0497639	+	0.601064i
$777$		0			0
$778$	1.94981e7	−	1.72976e7i	1.15490	−	1.02456i
$779$	5.39958e6	+	9.35236e6i	0.318799	+	0.552176i
$780$		0			0
$781$	−4.76806e6	+	8.25853e6i	−0.279714	+	0.484479i
$782$	−153205.	−	747839.i	−0.00895893	−	0.0437312i
$783$		0			0
$784$	−2.04999e7	+	2.14598e7i	−1.19114	+	1.24691i
$785$	−2.95845e7	−	1.70806e7i	−1.71352	−	0.989302i
$786$		0			0
$787$	1.47383e7	−	8.50913e6i	0.848221	−	0.489721i	−0.0118291	−	0.999930i	$-0.503765\pi$
$787$	1.47383e7	−	8.50913e6i	0.848221	−	0.489721i	0.860050	+	0.510209i	$0.170432\pi$
$788$	1.52743e7	−	2.03844e7i	0.876287	−	1.16945i
$789$		0			0
$790$	5.11507e6	−	1.53564e7i	0.291597	−	0.875433i
$791$	−9.08157e6			−0.516083
$792$		0			0
$793$	−3.20917e7			−1.81222
$794$	2.45896e6	−	7.38228e6i	0.138420	−	0.415565i
$795$		0			0
$796$	−2.12941e7	+	2.84181e7i	−1.19118	+	1.58969i
$797$	−1.38609e7	+	8.00260e6i	−0.772941	+	0.446257i	−0.833923	−	0.551881i	$-0.813910\pi$
$797$	−1.38609e7	+	8.00260e6i	−0.772941	+	0.446257i	0.0609820	+	0.998139i	$0.480577\pi$
$798$		0			0
$799$	72151.1	+	41656.4i	0.00399830	+	0.00230842i
$800$	−1.55574e6	+	2.47893e6i	−0.0859436	+	0.136943i
$801$		0			0
$802$	−122862.	−	599727.i	−0.00674501	−	0.0329244i
$803$	−1.21422e7	+	2.10309e7i	−0.664519	+	1.15098i
$804$		0			0
$805$	−2.55331e7	−	4.42246e7i	−1.38872	−	2.40533i
$806$	5.43670e6	−	4.82313e6i	0.294780	−	0.261512i
$807$		0			0
$808$	−1.65267e7	+	1.36830e6i	−0.890550	+	0.0737313i
$809$		−	2.13263e7i		−	1.14563i	−0.819686	−	0.572813i	$-0.805852\pi$
$809$		−	2.13263e7i		−	1.14563i	0.819686	−	0.572813i	$-0.194148\pi$
$810$		0			0
$811$		−	8.01640e6i		−	0.427984i	−0.976835	−	0.213992i	$-0.931353\pi$
$811$		−	8.01640e6i		−	0.427984i	0.976835	−	0.213992i	$-0.0686466\pi$
$812$	−360811.	+	3.00589e6i	−0.0192039	+	0.159986i
$813$		0			0
$814$	1.54065e7	+	1.73664e7i	0.814972	+	0.918648i
$815$	−1.52272e6	−	2.63743e6i	−0.0803020	−	0.139087i
$816$		0			0
$817$	−719093.	+	1.24550e6i	−0.0376903	+	0.0652815i
$818$	1.00135e7	−	2.05140e6i	0.523241	−	0.107193i
$819$		0			0
$820$	−1.63139e7	+	6.97707e6i	−0.847272	+	0.362358i
$821$	−1.96434e6	−	1.13411e6i	−0.101709	−	0.0587215i	0.448283	−	0.893892i	$-0.352036\pi$
$821$	−1.96434e6	−	1.13411e6i	−0.101709	−	0.0587215i	−0.549992	+	0.835170i	$0.685369\pi$
$822$		0			0
$823$	−3.22738e7	+	1.86333e7i	−1.66093	+	0.958936i	−0.688652	+	0.725092i	$0.741797\pi$
$823$	−3.22738e7	+	1.86333e7i	−1.66093	+	0.958936i	−0.972274	+	0.233844i	$0.924870\pi$
$824$	−8.16252e6	+	1.72936e7i	−0.418800	+	0.887296i
$825$		0			0
$826$	−3.91544e6	−	1.30419e6i	−0.199678	−	0.0665107i
$827$	−3.20117e7			−1.62759			−0.813794	−	0.581153i	$-0.802602\pi$
$827$	−3.20117e7			−1.62759			−0.813794	+	0.581153i	$0.802602\pi$
$828$		0			0
$829$	1.94310e7			0.981994			0.490997	−	0.871161i	$-0.336633\pi$
$829$	1.94310e7			0.981994			0.490997	+	0.871161i	$0.336633\pi$
$830$	4.27231e6	+	1.42306e6i	0.215262	+	0.0717014i
$831$		0			0
$832$	2.60358e7	−	4.34093e6i	1.30396	−	0.217407i
$833$	−855143.	+	493717.i	−0.0426998	+	0.0246528i
$834$		0			0
$835$	1.61837e7	+	9.34366e6i	0.803270	+	0.463768i
$836$	5.48030e6	+	1.28141e7i	0.271199	+	0.634123i
$837$		0			0
$838$	1.02657e7	−	2.10307e6i	0.504984	−	0.103453i
$839$	4.00186e6	−	6.93143e6i	0.196272	−	0.339952i	−0.751045	−	0.660251i	$-0.770450\pi$
$839$	4.00186e6	−	6.93143e6i	0.196272	−	0.339952i	0.947317	+	0.320299i	$0.103783\pi$
$840$		0			0
$841$	−1.01578e7	−	1.75939e7i	−0.495235	−	0.857772i
$842$	1.39338e7	+	1.57063e7i	0.677312	+	0.763475i
$843$		0			0
$844$	−6.58435e6	−	790351.i	−0.318168	−	0.0381912i
$845$			1.67238e7i			0.805738i
$846$		0			0
$847$		−	4.98700e6i		−	0.238853i
$848$	−1.98645e7	+	5.81275e6i	−0.948611	+	0.277582i
$849$		0			0
$850$	−72842.8	+	64622.0i	−0.00345811	+	0.00306784i
$851$	−2.18985e7	−	3.79294e7i	−1.03655	−	1.79536i
$852$		0			0
$853$	7.09314e6	−	1.22857e7i	0.333784	−	0.578131i	−0.649466	−	0.760390i	$-0.725008\pi$
$853$	7.09314e6	−	1.22857e7i	0.333784	−	0.578131i	0.983251	+	0.182259i	$0.0583410\pi$
$854$	9.67858e6	+	4.72440e7i	0.454116	+	2.21667i
$855$		0			0
$856$	566291.	−	392600.i	0.0264153	−	0.0183133i
$857$	−3.07075e7	−	1.77290e7i	−1.42821	−	0.824578i	−0.431232	−	0.902241i	$-0.641921\pi$
$857$	−3.07075e7	−	1.77290e7i	−1.42821	−	0.824578i	−0.996980	+	0.0776628i	$0.975254\pi$
$858$		0			0
$859$	1.51108e7	−	8.72423e6i	0.698723	−	0.403408i	−0.108149	−	0.994135i	$-0.534492\pi$
$859$	1.51108e7	−	8.72423e6i	0.698723	−	0.403408i	0.806872	+	0.590727i	$0.201159\pi$
$860$	−1.89099e6	−	1.41695e6i	−0.0871854	−	0.0653293i
$861$		0			0
$862$	−496770.	+	1.49140e6i	−0.0227713	+	0.0683638i
$863$	7.28107e6			0.332788			0.166394	−	0.986059i	$-0.446788\pi$
$863$	7.28107e6			0.332788			0.166394	+	0.986059i	$0.446788\pi$
$864$		0			0
$865$	9.77612e6			0.444249
$866$	4.45531e6	−	1.33757e7i	0.201875	−	0.606069i
$867$		0			0
$868$	−8.74006e6	−	6.54905e6i	−0.393745	−	0.295039i
$869$	1.52639e7	−	8.81259e6i	0.685669	−	0.395871i
$870$		0			0
$871$	4.90417e6	+	2.83143e6i	0.219039	+	0.126462i
$872$	−1.26672e7	+	8.78194e6i	−0.564143	+	0.391110i
$873$		0			0
$874$	−5.27681e6	−	2.57577e7i	−0.233665	−	1.14059i
$875$	1.68881e7	−	2.92510e7i	0.745693	−	1.29158i
$876$		0			0
$877$	−432760.	−	749562.i	−0.0189998	−	0.0329085i	0.856369	−	0.516364i	$-0.172715\pi$
$877$	−432760.	−	749562.i	−0.0189998	−	0.0329085i	−0.875369	+	0.483455i	$0.839382\pi$
$878$	5.10444e6	−	4.52837e6i	0.223466	−	0.198247i
$879$		0			0
$880$	−2.19769e7	+	6.43088e6i	−0.956665	+	0.279939i
$881$			8.64368e6i			0.375197i	0.982246	+	0.187598i	$0.0600703\pi$
$881$			8.64368e6i			0.375197i	−0.982246	+	0.187598i	$0.939930\pi$
$882$		0			0
$883$		−	6.19117e6i		−	0.267221i	−0.991034	−	0.133611i	$-0.957343\pi$
$883$		−	6.19117e6i		−	0.267221i	0.991034	−	0.133611i	$-0.0426572\pi$
$884$	871958.	+	104665.i	0.0375288	+	0.00450476i
$885$		0			0
$886$	−9.82155e6	−	1.10710e7i	−0.420335	−	0.473807i
$887$	1.36675e7	+	2.36728e7i	0.583285	+	1.01028i	0.995087	+	0.0990058i	$0.0315662\pi$
$887$	1.36675e7	+	2.36728e7i	0.583285	+	1.01028i	−0.411802	+	0.911273i	$0.635100\pi$
$888$		0			0
$889$	3.96714e6	−	6.87129e6i	0.168354	−	0.291598i
$890$	−2.86092e7	+	5.86099e6i	−1.21068	+	0.248025i
$891$		0			0
$892$	8.10161e6	+	1.89433e7i	0.340925	+	0.797157i
$893$	2.48509e6	+	1.43477e6i	0.104283	+	0.0602077i
$894$		0			0
$895$	1.63434e7	−	9.43586e6i	0.682000	−	0.393753i
$896$	−1.42427e7	−	3.70196e7i	−0.592682	−	1.54050i
$897$		0			0
$898$	−1.87260e6	−	623742.i	−0.0774913	−	0.0258115i
$899$	−705176.			−0.0291004
$900$		0			0
$901$	−688644.			−0.0282607
$902$	−1.83308e7	−	6.10580e6i	−0.750180	−	0.249877i
$903$		0			0
$904$	3.27920e6	−	6.94753e6i	0.133459	−	0.282754i
$905$	1.25968e7	−	7.27278e6i	0.511257	−	0.295174i
$906$		0			0
$907$	−2.71438e6	−	1.56715e6i	−0.109560	−	0.0632545i	0.444219	−	0.895918i	$-0.353481\pi$
$907$	−2.71438e6	−	1.56715e6i	−0.109560	−	0.0632545i	−0.553779	+	0.832664i	$0.686815\pi$
$908$	3.50905e7	−	1.50074e7i	1.41246	−	0.604075i
$909$		0			0
$910$	5.75536e7	−	1.17906e7i	2.30393	−	0.471991i
$911$	2.15693e7	−	3.73592e7i	0.861074	−	1.49142i	−0.00981891	−	0.999952i	$-0.503126\pi$
$911$	2.15693e7	−	3.73592e7i	0.861074	−	1.49142i	0.870893	−	0.491472i	$-0.163541\pi$
$912$		0			0
$913$	2.45174e6	+	4.24655e6i	0.0973415	+	0.168600i
$914$	1.28512e7	+	1.44860e7i	0.508836	+	0.573567i
$915$		0			0
$916$	4.10535e6	−	3.42013e7i	0.161663	−	1.34680i
$917$			3.58340e7i			1.40725i
$918$		0			0
$919$		−	9.73606e6i		−	0.380272i	−0.981758	−	0.190136i	$-0.939107\pi$
$919$		−	9.73606e6i		−	0.380272i	0.981758	−	0.190136i	$-0.0608929\pi$
$920$	4.30520e7	−	3.56440e6i	1.67696	−	0.138841i
$921$		0			0
$922$	2.29725e7	−	2.03799e7i	0.889980	−	0.789540i
$923$	1.03485e7	+	1.79242e7i	0.399829	+	0.692524i
$924$		0			0
$925$	−2.79339e6	+	4.83829e6i	−0.107344	+	0.185925i
$926$	−4.90631e6	−	2.39491e7i	−0.188030	−	0.917830i
$927$		0			0
$928$	−2.16926e6	−	1.36140e6i	−0.0826879	−	0.0518938i
$929$	3.71782e7	+	2.14649e7i	1.41335	+	0.815997i	0.995702	−	0.0926123i	$-0.0295217\pi$
$929$	3.71782e7	+	2.14649e7i	1.41335	+	0.815997i	0.417647	+	0.908610i	$0.362855\pi$
$930$		0			0
$931$	−2.94535e7	+	1.70050e7i	−1.11369	+	0.642988i
$932$	−3.41880e6	+	4.56258e6i	−0.128924	+	0.172056i
$933$		0			0
$934$	−6.10203e6	+	1.83195e7i	−0.228880	+	0.687141i
$935$	−761874.			−0.0285006
$936$		0			0
$937$	−2.31461e7			−0.861250			−0.430625	−	0.902531i	$-0.641707\pi$
$937$	−2.31461e7			−0.861250			−0.430625	+	0.902531i	$0.641707\pi$
$938$	2.68924e6	−	8.07364e6i	0.0997983	−	0.299614i
$939$		0			0
$940$	−2.82716e6	+	3.77299e6i	−0.104359	+	0.139273i
$941$	1.44508e7	−	8.34315e6i	0.532006	−	0.307154i	−0.209827	−	0.977739i	$-0.567290\pi$
$941$	1.44508e7	−	8.34315e6i	0.532006	−	0.307154i	0.741833	+	0.670585i	$0.233957\pi$
$942$		0			0
$943$	3.15667e7	+	1.82250e7i	1.15598	+	0.667405i
$944$	2.41153e6	−	2.52445e6i	0.0880769	−	0.0922011i
$945$		0			0
$946$	−516405.	−	2.52073e6i	−0.0187613	−	0.0915794i
$947$	−4.97026e6	+	8.60874e6i	−0.180096	+	0.311936i	−0.941913	−	0.335857i	$-0.890974\pi$
$947$	−4.97026e6	+	8.60874e6i	−0.180096	+	0.311936i	0.761817	+	0.647792i	$0.224308\pi$
$948$		0			0
$949$	2.63532e7	+	4.56451e7i	0.949878	+	1.64524i
$950$	−2.50891e6	+	2.22577e6i	−0.0901937	+	0.0800148i
$951$		0			0
$952$	−108891.	−	1.31522e6i	−0.00389405	−	0.0470335i
$953$		−	1.33255e7i		−	0.475283i	−0.971353	−	0.237641i	$-0.923626\pi$
$953$		−	1.33255e7i		−	0.475283i	0.971353	−	0.237641i	$-0.0763743\pi$
$954$		0			0
$955$		−	4.55595e7i		−	1.61648i
$956$	−2.56949e6	+	2.14062e7i	−0.0909290	+	0.757522i
$957$		0			0
$958$	−9.82131e6	−	1.10707e7i	−0.345745	−	0.389728i
$959$	3.68192e7	+	6.37728e7i	1.29279	+	2.23918i
$960$		0			0
$961$	−1.30426e7	+	2.25905e7i	−0.455571	+	0.789073i
$962$	4.93610e7	−	1.01123e7i	1.71968	−	0.352299i
$963$		0			0
$964$	9.59070e6	−	4.10172e6i	0.332397	−	0.142159i
$965$	−2.19935e7	−	1.26980e7i	−0.760286	−	0.438951i
$966$		0			0
$967$	−4.52649e7	+	2.61337e7i	−1.55667	+	0.898742i	−0.559094	+	0.829104i	$0.688851\pi$
$967$	−4.52649e7	+	2.61337e7i	−1.55667	+	0.898742i	−0.997572	+	0.0696376i	$0.977816\pi$
$968$	3.81512e6	+	1.80072e6i	0.130864	+	0.0617672i
$969$		0			0
$970$	−1.80729e7	−	6.01991e6i	−0.616736	−	0.205428i
$971$	2.52629e7			0.859874			0.429937	−	0.902859i	$-0.358536\pi$
$971$	2.52629e7			0.859874			0.429937	+	0.902859i	$0.358536\pi$
$972$		0			0
$973$	5.90868e7			2.00082
$974$	−4.60676e7	−	1.53446e7i	−1.55596	−	0.518274i
$975$		0			0
$976$	−3.96371e7	−	9.65476e6i	−1.33192	−	0.324427i
$977$	−2.99055e7	+	1.72660e7i	−1.00234	+	0.578701i	−0.908940	−	0.416927i	$-0.863107\pi$
$977$	−2.99055e7	+	1.72660e7i	−1.00234	+	0.578701i	−0.0934002	+	0.995629i	$0.529774\pi$
$978$		0			0
$979$	−2.75397e7	−	1.59001e7i	−0.918339	−	0.530203i
$980$	−2.19730e7	−	5.13776e7i	−0.730843	−	1.70887i
$981$		0			0
$982$	−4.93424e7	+	1.01085e7i	−1.63283	+	0.334508i
$983$	−1.02022e7	+	1.76708e7i	−0.336753	+	0.583273i	−0.983820	−	0.179160i	$-0.942662\pi$
$983$	−1.02022e7	+	1.76708e7i	−0.336753	+	0.583273i	0.647067	+	0.762433i	$0.275995\pi$
$984$		0			0
$985$	2.39802e7	+	4.15349e7i	0.787521	+	1.36403i
$986$	−56549.4	−	63743.2i	−0.00185240	−	0.00208805i
$987$		0			0
$988$	3.00327e7	+	3.60497e6i	0.978819	+	0.117492i
$989$			4.85426e6i			0.157809i
$990$		0			0
$991$		−	2.57219e7i		−	0.831991i	−0.909367	−	0.415996i	$-0.863433\pi$
$991$		−	2.57219e7i		−	0.831991i	0.909367	−	0.415996i	$-0.136567\pi$
$992$	8.16601e6	−	4.32152e6i	0.263470	−	0.139430i
$993$		0			0
$994$	2.32662e7	−	2.06404e7i	0.746893	−	0.662602i
$995$	−3.34311e7	−	5.79043e7i	−1.07051	−	1.85419i
$996$		0			0
$997$	−4.80332e6	+	8.31959e6i	−0.153040	+	0.265072i	−0.932343	−	0.361574i	$-0.882240\pi$
$997$	−4.80332e6	+	8.31959e6i	−0.153040	+	0.265072i	0.779304	+	0.626646i	$0.215573\pi$
$998$	1.18081e7	+	5.76386e7i	0.375277	+	1.83184i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.h.a.35.11		56
3.2	odd	2		36.6.h.a.11.18	yes	56
4.3	odd	2	inner	108.6.h.a.35.20		56
9.4	even	3		36.6.h.a.23.9	yes	56
9.5	odd	6	inner	108.6.h.a.71.20		56
12.11	even	2		36.6.h.a.11.9	✓	56
36.23	even	6	inner	108.6.h.a.71.11		56
36.31	odd	6		36.6.h.a.23.18	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.h.a.11.9	✓	56	12.11	even	2
36.6.h.a.11.18	yes	56	3.2	odd	2
36.6.h.a.23.9	yes	56	9.4	even	3
36.6.h.a.23.18	yes	56	36.31	odd	6
108.6.h.a.35.11		56	1.1	even	1	trivial
108.6.h.a.35.20		56	4.3	odd	2	inner
108.6.h.a.71.11		56	36.23	even	6	inner
108.6.h.a.71.20		56	9.5	odd	6	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)

\(f(q)\)	\(=\)	\(q+(-1.78768 + 5.36696i) q^{2} +(-25.6084 - 19.1888i) q^{4} +(52.1793 - 30.1257i) q^{5} +(-185.316 - 106.992i) q^{7} +(148.765 - 103.136i) q^{8} +O(q^{10})\)	\(q+(-1.78768 + 5.36696i) q^{2} +(-25.6084 - 19.1888i) q^{4} +(52.1793 - 30.1257i) q^{5} +(-185.316 - 106.992i) q^{7} +(148.765 - 103.136i) q^{8} +(68.4038 + 333.899i) q^{10} +(-185.570 + 321.417i) q^{11} +(402.759 + 697.599i) q^{13} +(905.506 - 803.314i) q^{14} +(287.583 + 982.788i) q^{16} +34.0704i q^{17} +1173.48i q^{19} +(-1914.31 - 229.783i) q^{20} +(-1393.29 - 1570.54i) q^{22} +(1980.40 + 3430.16i) q^{23} +(252.621 - 437.553i) q^{25} +(-4463.99 + 914.509i) q^{26} +(2692.60 + 6295.88i) q^{28} +(382.894 + 221.064i) q^{29} +(-1381.28 + 797.481i) q^{31} +(-5788.68 - 213.459i) q^{32} +(-182.854 - 60.9068i) q^{34} -12892.9 q^{35} -11057.6 q^{37} +(-6298.01 - 2097.80i) q^{38} +(4655.40 - 9863.22i) q^{40} +(7969.76 - 4601.35i) q^{41} +(1061.38 + 612.787i) q^{43} +(10919.8 - 4670.13i) q^{44} +(-21949.8 + 4496.72i) q^{46} +(1222.66 - 2117.71i) q^{47} +(14491.1 + 25099.3i) q^{49} +(1896.72 + 2138.01i) q^{50} +(3072.03 - 25592.9i) q^{52} +20212.4i q^{53} +22361.8i q^{55} +(-38603.2 + 3196.07i) q^{56} +(-1870.93 + 1659.78i) q^{58} +(-1704.67 - 2952.58i) q^{59} +(-19919.9 + 34502.3i) q^{61} +(-1810.77 - 8838.89i) q^{62} +(11493.9 - 30686.0i) q^{64} +(42031.4 + 24266.8i) q^{65} +(6088.22 - 3515.04i) q^{67} +(653.768 - 872.488i) q^{68} +(23048.3 - 69195.4i) q^{70} +25694.1 q^{71} +65431.6 q^{73} +(19767.4 - 59345.7i) q^{74} +(22517.6 - 30051.0i) q^{76} +(68778.2 - 39709.1i) q^{77} +(-41126.9 - 23744.6i) q^{79} +(44613.1 + 42617.5i) q^{80} +(10447.9 + 50999.1i) q^{82} +(6605.97 - 11441.9i) q^{83} +(1026.39 + 1777.77i) q^{85} +(-5186.20 + 4600.90i) q^{86} +(5543.37 + 66954.6i) q^{88} +85682.2i q^{89} -172368. i q^{91} +(15105.5 - 125842. i) q^{92} +(9179.93 + 10347.7i) q^{94} +(35352.0 + 61231.4i) q^{95} +(-27944.9 + 48402.0i) q^{97} +(-160612. + 32903.6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) 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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