LMFDB - Embedded newform 108.6.h.a.71.11

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			71.11
Character	$\chi$	$=$	108.71
Dual form			108.6.h.a.35.11

$q$-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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

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

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 $

$2$	−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	0.887889	−	0.460058i	$-0.152171\pi$
$5$	52.1793	+	30.1257i	0.933412	+	0.538906i	0.0455230	+	0.998963i	$0.485505\pi$
$6$		0			0
$7$	−185.316	+	106.992i	−1.42944	+	0.825290i	−0.997077	−	0.0764081i	$-0.975655\pi$
$7$	−185.316	+	106.992i	−1.42944	+	0.825290i	−0.432367	+	0.901698i	$0.642321\pi$
$8$	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	0.536671	−	0.843792i	$-0.319682\pi$
$11$	−185.570	−	321.417i	−0.462410	−	0.800917i	−0.999080	+	0.0428745i	$0.986348\pi$
$12$		0			0
$13$	402.759	−	697.599i	0.660978	−	1.14485i	−0.319381	−	0.947626i	$-0.603475\pi$
$13$	402.759	−	697.599i	0.660978	−	1.14485i	0.980359	−	0.197221i	$-0.0631917\pi$
$14$	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	$-0.995449\pi$
$17$		−	34.0704i		−	0.0285926i	0.999898	−	0.0142963i	$-0.00455082\pi$
$18$		0			0
$19$		−	1173.48i		−	0.745747i	−0.927882	−	0.372874i	$-0.878373\pi$
$19$		−	1173.48i		−	0.745747i	0.927882	−	0.372874i	$-0.121627\pi$
$20$	−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	−0.150977	−	0.988537i	$-0.548242\pi$
$23$	1980.40	−	3430.16i	0.780610	−	1.35206i	0.931587	−	0.363519i	$-0.118425\pi$
$24$		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	−0.457132	−	0.889399i	$-0.651123\pi$
$29$	382.894	−	221.064i	0.0845441	−	0.0488115i	0.541676	+	0.840587i	$0.317790\pi$
$30$		0			0
$31$	−1381.28	−	797.481i	−0.258153	−	0.149045i	0.365339	−	0.930875i	$-0.380953\pi$
$31$	−1381.28	−	797.481i	−0.258153	−	0.149045i	−0.623492	+	0.781830i	$0.714286\pi$
$32$	−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	0.822227	−	0.569160i	$-0.192732\pi$
$41$	7969.76	+	4601.35i	0.740433	+	0.427489i	−0.0817937	+	0.996649i	$0.526065\pi$
$42$		0			0
$43$	1061.38	−	612.787i	0.0875384	−	0.0505403i	−0.455592	−	0.890189i	$-0.650572\pi$
$43$	1061.38	−	612.787i	0.0875384	−	0.0505403i	0.543130	+	0.839648i	$0.317239\pi$
$44$	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	0.903566	−	0.428449i	$-0.140940\pi$
$47$	1222.66	+	2117.71i	0.0807348	+	0.139837i	−0.822831	+	0.568286i	$0.807607\pi$
$48$		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	$-0.835463\pi$
$53$		−	20212.4i		−	0.988390i	0.869351	−	0.494195i	$-0.164537\pi$
$54$		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	−0.896141	−	0.443770i	$-0.853641\pi$
$59$	−1704.67	+	2952.58i	−0.0637546	+	0.110426i	0.832386	+	0.554196i	$0.186974\pi$
$60$		0			0
$61$	−19919.9	−	34502.3i	−0.685430	−	1.18720i	−0.973302	−	0.229530i	$-0.926281\pi$
$61$	−19919.9	−	34502.3i	−0.685430	−	1.18720i	0.287872	−	0.957669i	$-0.407052\pi$
$62$	−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	0.580553	−	0.814222i	$-0.302836\pi$
$67$	6088.22	+	3515.04i	0.165693	+	0.0956627i	−0.414861	+	0.909885i	$0.636170\pi$
$68$	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	−0.822581	−	0.568647i	$-0.807467\pi$
$79$	−41126.9	+	23744.6i	−0.741409	+	0.428053i	0.0811725	+	0.996700i	$0.474134\pi$
$80$	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	0.913842	−	0.406069i	$-0.133101\pi$
$83$	6605.97	+	11441.9i	0.105255	+	0.182306i	−0.808588	+	0.588376i	$0.799768\pi$
$84$		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	$-0.805661\pi$
$89$		−	85682.2i		−	1.14661i	0.819342	−	0.573305i	$-0.194339\pi$
$90$		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	0.674929	−	0.737882i	$-0.264174\pi$
$97$	−27944.9	−	48402.0i	−0.301560	−	0.522317i	−0.976490	+	0.215565i	$0.930841\pi$
$98$	−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	−0.834256	−	0.551377i	$-0.814103\pi$
$101$	−79337.0	+	45805.2i	−0.773878	+	0.446799i	0.0603784	+	0.998176i	$0.480769\pi$
$102$		0			0
$103$	−91488.4	−	52820.9i	−0.849715	−	0.490583i	0.0108398	−	0.999941i	$-0.496550\pi$
$103$	−91488.4	−	52820.9i	−0.849715	−	0.490583i	−0.860555	+	0.509358i	$0.829883\pi$
$104$	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	0.629241	−	0.777210i	$-0.283366\pi$
$113$	36754.5	+	21220.2i	0.270778	+	0.156334i	−0.358463	+	0.933544i	$0.616699\pi$
$114$		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	$-0.967477\pi$
$127$		−	37078.8i		−	0.203994i	0.994785	−	0.101997i	$-0.0325232\pi$
$128$	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	−0.996540	−	0.0831144i	$-0.973513\pi$
$131$	−83730.6	+	145026.i	−0.426291	+	0.738357i	0.570249	+	0.821472i	$0.306847\pi$
$132$		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	−0.989164	−	0.146814i	$-0.953098\pi$
$137$	−298026.	+	172065.i	−1.35660	+	0.783234i	−0.367438	+	0.930048i	$0.619765\pi$
$138$		0			0
$139$	−239133.	−	138064.i	−1.04979	−	0.606097i	−0.127200	−	0.991877i	$-0.540599\pi$
$139$	−239133.	−	138064.i	−1.04979	−	0.606097i	−0.922591	+	0.385780i	$0.873932\pi$
$140$	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	0.436149	−	0.899875i	$-0.356342\pi$
$149$	−33899.5	−	19571.9i	−0.125091	−	0.0722216i	−0.561240	+	0.827653i	$0.689676\pi$
$150$		0			0
$151$	372275.	−	214933.i	1.32868	−	0.767115i	0.343587	−	0.939121i	$-0.388358\pi$
$151$	372275.	−	214933.i	1.32868	−	0.767115i	0.985096	+	0.172006i	$0.0550247\pi$
$152$	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	−0.115252	+	0.993336i	$0.536768\pi$
$157$	−283488.	+	491016.i	−0.917881	+	1.58982i	−0.802628	+	0.596479i	$0.796566\pi$
$158$	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	$0.0237376\pi$
$163$			50545.5i			0.149009i	−0.997221	+	0.0745047i	$0.976262\pi$
$164$	−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	−0.566611	−	0.823985i	$-0.691746\pi$
$167$	155078.	−	268602.i	0.430287	−	0.745279i	0.996898	+	0.0787068i	$0.0250791\pi$
$168$		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	−0.310789	−	0.950479i	$-0.600593\pi$
$173$	140517.	−	81127.6i	0.356955	−	0.206088i	0.667744	+	0.744391i	$0.267260\pi$
$174$		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	0.947874	+	0.318644i	$0.103227\pi$
$191$	378078.	+	654851.i	0.749891	+	1.29885i	−0.197983	+	0.980205i	$0.563439\pi$
$192$		0			0
$193$	−210750.	+	365029.i	−0.407262	+	0.705398i	−0.994582	−	0.103957i	$-0.966850\pi$
$193$	−210750.	+	365029.i	−0.407262	+	0.705398i	0.587320	+	0.809355i	$0.300183\pi$
$194$	−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	$-0.739209\pi$
$197$		−	796004.i		−	1.46133i	0.682734	−	0.730667i	$-0.260791\pi$
$198$		0			0
$199$			1.10972e6i			1.98646i	0.116163	+	0.993230i	$0.462940\pi$
$199$			1.10972e6i			1.98646i	−0.116163	+	0.993230i	$0.537060\pi$
$200$	−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	0.632300	−	0.774724i	$-0.282111\pi$
$211$	179473.	+	103619.i	0.277520	+	0.160226i	−0.354780	+	0.934950i	$0.615444\pi$
$212$	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	−0.825999	−	0.563672i	$-0.809388\pi$
$223$	−557586.	+	321922.i	−0.750844	+	0.433500i	0.0751547	+	0.997172i	$0.476055\pi$
$224$	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	−0.938589	−	0.345036i	$-0.887867\pi$
$227$	−596328.	−	1.03287e6i	−0.768105	−	1.33040i	0.170485	−	0.985360i	$-0.445467\pi$
$228$		0			0
$229$	538232.	−	932245.i	0.678236	−	1.17474i	−0.297276	−	0.954792i	$-0.596078\pi$
$229$	538232.	−	932245.i	0.678236	−	1.17474i	0.975512	−	0.219947i	$-0.0705886\pi$
$230$	−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	$0.0342845\pi$
$233$			178167.i			0.214999i	−0.994205	+	0.107500i	$0.965716\pi$
$234$		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	−0.991274	−	0.131817i	$-0.957919\pi$
$239$	−336873.	+	583482.i	−0.381480	+	0.660743i	0.609794	+	0.792560i	$0.291252\pi$
$240$		0			0
$241$	−162984.	−	282297.i	−0.180760	−	0.313086i	0.761379	−	0.648307i	$-0.224522\pi$
$241$	−162984.	−	282297.i	−0.180760	−	0.313086i	−0.942140	+	0.335221i	$0.891189\pi$
$242$	−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	0.934055	−	0.357130i	$-0.116245\pi$
$257$	1.15605e6	+	667444.i	1.09180	+	0.630350i	0.157744	+	0.987480i	$0.449578\pi$
$258$		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	0.994624	−	0.103556i	$-0.0330222\pi$
$263$	457251.	+	791982.i	0.407629	+	0.706035i	−0.586994	+	0.809591i	$0.699689\pi$
$264$		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	$0.287117\pi$
$269$			1.86227e6i			1.56914i	−0.620038	+	0.784572i	$0.712883\pi$
$270$		0			0
$271$		−	517756.i		−	0.428254i	−0.976806	−	0.214127i	$-0.931309\pi$
$271$		−	517756.i		−	0.428254i	0.976806	−	0.214127i	$-0.0686907\pi$
$272$	−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	0.717689	−	0.696364i	$-0.245200\pi$
$277$	−311881.	−	540194.i	−0.244225	−	0.423010i	−0.961913	+	0.273354i	$0.911867\pi$
$278$	−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	0.207159	−	0.978307i	$-0.433578\pi$
$281$	1.53273e6	−	884922.i	1.15798	−	0.668558i	0.950818	+	0.309749i	$0.100245\pi$
$282$		0			0
$283$	−1.28654e6	−	742782.i	−0.954895	−	0.551309i	−0.0602971	−	0.998180i	$-0.519205\pi$
$283$	−1.28654e6	−	742782.i	−0.954895	−	0.551309i	−0.894598	+	0.446871i	$0.852538\pi$
$284$	−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	−0.0625325	−	0.998043i	$-0.519918\pi$
$293$	−1.40797e6	−	812891.i	−0.958129	−	0.553176i	−0.895597	+	0.444867i	$0.853251\pi$
$294$		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	$-0.997115\pi$
$307$		−	29930.7i		−	0.0181247i	0.999959	−	0.00906235i	$-0.00288467\pi$
$308$	−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	−0.999865	−	0.0164516i	$-0.994763\pi$
$311$	−828429.	+	1.43488e6i	−0.485685	+	0.841231i	0.514180	+	0.857682i	$0.328096\pi$
$312$		0			0
$313$	−1.49316e6	−	2.58623e6i	−0.861482	−	1.49213i	−0.870498	−	0.492171i	$-0.836203\pi$
$313$	−1.49316e6	−	2.58623e6i	−0.861482	−	1.49213i	0.00901652	−	0.999959i	$-0.497130\pi$
$314$	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	−0.694290	−	0.719695i	$-0.744282\pi$
$317$	−748156.	+	431948.i	−0.418162	+	0.241426i	0.276129	+	0.961121i	$0.410948\pi$
$318$		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	−0.499541	−	0.866290i	$-0.666498\pi$
$331$	1828.81	−	1055.86i	0.000917484	−	0.000529710i	0.500459	+	0.865760i	$0.333165\pi$
$332$	−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	0.396501	+	0.918034i	$0.370224\pi$
$337$	−1.24422e6	+	2.15505e6i	−0.596790	+	1.03367i	−0.993292	+	0.115637i	$0.963109\pi$
$338$	−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	−0.215241	−	0.976561i	$-0.569054\pi$
$347$	1.65555e6	−	2.86750e6i	0.738106	−	1.27844i	0.953347	−	0.301877i	$-0.0976131\pi$
$348$		0			0
$349$	−131505.	−	227773.i	−0.0577934	−	0.100101i	0.835681	−	0.549215i	$-0.185073\pi$
$349$	−131505.	−	227773.i	−0.0577934	−	0.100101i	−0.893475	+	0.449114i	$0.851740\pi$
$350$	−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	−0.527061	−	0.849827i	$-0.676706\pi$
$353$	−127875.	+	73828.9i	−0.0546198	+	0.0315347i	0.472441	+	0.881362i	$0.343373\pi$
$354$		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	−0.801313	−	0.598245i	$-0.795865\pi$
$367$	−1.76458e6	+	1.01878e6i	−0.683874	+	0.394835i	0.117439	+	0.993080i	$0.462532\pi$
$368$	−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	−0.724917	−	0.688837i	$-0.758122\pi$
$373$	629011.	−	1.08948e6i	0.234092	−	0.405459i	0.959008	+	0.283378i	$0.0914551\pi$
$374$	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	$-0.783338\pi$
$379$		−	3.51959e6i		−	1.25862i	0.777154	−	0.629310i	$-0.216662\pi$
$380$	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	−0.493822	−	0.869563i	$-0.664400\pi$
$383$	1.45304e6	−	2.51675e6i	0.506153	−	0.876683i	0.999975	−	0.00711941i	$-0.00226620\pi$
$384$		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	−0.986365	−	0.164570i	$-0.947376\pi$
$389$	−3.99038e6	+	2.30384e6i	−1.33703	+	0.771932i	−0.350660	+	0.936503i	$0.614043\pi$
$390$		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	0.485377	−	0.874305i	$-0.338682\pi$
$401$	−93720.9	−	54109.8i	−0.0291055	−	0.0168041i	−0.514482	+	0.857501i	$0.672016\pi$
$402$		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	−0.968100	−	0.250565i	$-0.919384\pi$
$409$	−903457.	+	1.56483e6i	−0.267054	+	0.462551i	0.701046	+	0.713116i	$0.252717\pi$
$410$	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	−0.965635	−	0.259902i	$-0.916310\pi$
$419$	−926212.	+	1.60425e6i	−0.257736	+	0.446412i	0.707899	+	0.706314i	$0.249643\pi$
$420$		0			0
$421$	1.85582e6	+	3.21437e6i	0.510305	+	0.883874i	0.999929	+	0.0119403i	$0.00380082\pi$
$421$	1.85582e6	+	3.21437e6i	0.510305	+	0.883874i	−0.489624	+	0.871934i	$0.662866\pi$
$422$	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	−0.623744	−	0.781628i	$-0.714389\pi$
$439$	−1.04465e6	+	603126.i	−0.258707	+	0.149364i	0.365038	+	0.930993i	$0.381056\pi$
$440$	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	0.663104	−	0.748527i	$-0.269239\pi$
$443$	−1.30812e6	−	2.26572e6i	−0.316692	−	0.548526i	−0.979796	+	0.200001i	$0.935905\pi$
$444$		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	$-0.986997\pi$
$449$		−	348912.i		−	0.0816770i	0.999166	−	0.0408385i	$-0.0130029\pi$
$450$		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	0.991542	−	0.129788i	$-0.0414297\pi$
$457$	1.71163e6	+	2.96463e6i	0.383371	+	0.664018i	−0.608171	+	0.793806i	$0.708096\pi$
$458$	−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	−0.917079	−	0.398705i	$-0.869460\pi$
$461$	−4.70141e6	+	2.71436e6i	−1.03033	+	0.594861i	−0.113251	+	0.993566i	$0.536126\pi$
$462$		0			0
$463$	−3.74259e6	−	2.16079e6i	−0.811373	−	0.468446i	0.0360597	−	0.999350i	$-0.488519\pi$
$463$	−3.74259e6	−	2.16079e6i	−0.811373	−	0.468446i	−0.847432	+	0.530903i	$0.821853\pi$
$464$	−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	0.705880	−	0.708332i	$-0.250552\pi$
$479$	−1.30808e6	−	2.26567e6i	−0.260493	−	0.451188i	−0.966373	+	0.257144i	$0.917219\pi$
$480$		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	$-0.693971\pi$
$487$		−	8.58357e6i		−	1.64001i	0.572359	−	0.820003i	$-0.306029\pi$
$488$	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	−0.0619764	−	0.998078i	$-0.519740\pi$
$491$	4.45187e6	−	7.71087e6i	0.833372	−	1.44344i	0.895349	−	0.445366i	$-0.146926\pi$
$492$		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	0.987084	+	0.160205i	$0.0512156\pi$
$499$	9.00734e6	+	5.20039e6i	1.61937	+	0.934942i	0.632284	+	0.774737i	$0.282118\pi$
$500$	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	0.997549	−	0.0699775i	$-0.0222928\pi$
$509$	8.39198e6	+	4.84511e6i	1.43572	+	0.828914i	0.438172	+	0.898891i	$0.355626\pi$
$510$		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	$0.213149\pi$
$521$			7.69134e6i			1.24139i	−0.784053	+	0.620694i	$0.786851\pi$
$522$		0			0
$523$		−	1.02773e6i		−	0.164295i	−0.996620	−	0.0821476i	$-0.973822\pi$
$523$		−	1.02773e6i		−	0.164295i	0.996620	−	0.0821476i	$-0.0261779\pi$
$524$	−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	0.0810959	−	0.996706i	$-0.474158\pi$
$547$	6.89166e6	−	3.97890e6i	0.984817	−	0.568584i	0.903721	+	0.428122i	$0.140825\pi$
$548$	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	$-0.978941\pi$
$557$		−	968143.i		−	0.132221i	0.997812	−	0.0661107i	$-0.0210590\pi$
$558$		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	−0.522660	−	0.852541i	$-0.675060\pi$
$563$	3.58742e6	−	6.21360e6i	0.476993	−	0.826176i	0.999652	+	0.0263657i	$0.00839345\pi$
$564$		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	0.334561	−	0.942374i	$-0.391412\pi$
$569$	1.01785e7	−	5.87656e6i	1.31796	−	0.760926i	0.983400	+	0.181448i	$0.0580785\pi$
$570$		0			0
$571$	−9.11184e6	−	5.26072e6i	−1.16954	−	0.675235i	−0.215970	−	0.976400i	$-0.569291\pi$
$571$	−9.11184e6	−	5.26072e6i	−1.16954	−	0.675235i	−0.953572	+	0.301165i	$0.902625\pi$
$572$	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	0.895701	−	0.444656i	$-0.146674\pi$
$587$	523994.	+	907585.i	0.0627670	+	0.108716i	−0.832934	+	0.553372i	$0.813341\pi$
$588$		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	$-0.834527\pi$
$593$		−	8.50755e6i		−	0.993500i	0.867894	−	0.496750i	$-0.165473\pi$
$594$		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	0.499254	+	0.866456i	$0.333608\pi$
$599$	−4.39728e6	+	7.61632e6i	−0.500746	+	0.867317i	−1.00000		0.000861327i	$0.999726\pi$
$600$		0			0
$601$	−2.32237e6	−	4.02246e6i	−0.262268	−	0.454261i	0.704576	−	0.709628i	$-0.251137\pi$
$601$	−2.32237e6	−	4.02246e6i	−0.262268	−	0.454261i	−0.966844	+	0.255367i	$0.917804\pi$
$602$	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	0.577826	−	0.816160i	$-0.303901\pi$
$607$	1.45173e6	+	838155.i	0.159924	+	0.0923320i	−0.417902	+	0.908492i	$0.637235\pi$
$608$	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	0.680698	−	0.732564i	$-0.261676\pi$
$617$	3.65601e6	+	2.11080e6i	0.386629	+	0.223220i	−0.294070	+	0.955784i	$0.595010\pi$
$618$		0			0
$619$	1.47506e7	−	8.51629e6i	1.54733	−	0.893354i	0.548991	−	0.835829i	$-0.315012\pi$
$619$	1.47506e7	−	8.51629e6i	1.54733	−	0.893354i	0.998344	−	0.0575254i	$-0.0183210\pi$
$620$	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	$0.169502\pi$
$631$			1.01556e7i			1.01539i	−0.861538	+	0.507693i	$0.830498\pi$
$632$	−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	0.762160	−	0.647389i	$-0.224139\pi$
$641$	1.77251e7	−	1.02336e7i	1.70389	−	0.983744i	0.941735	−	0.336355i	$-0.109194\pi$
$642$		0			0
$643$	1.99881e6	+	1.15401e6i	0.190653	+	0.110074i	0.592288	−	0.805726i	$-0.298225\pi$
$643$	1.99881e6	+	1.15401e6i	0.190653	+	0.110074i	−0.401635	+	0.915800i	$0.631558\pi$
$644$	−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	0.576048	−	0.817416i	$-0.304594\pi$
$653$	1.70167e6	+	982460.i	0.156168	+	0.0901638i	−0.419879	+	0.907580i	$0.637928\pi$
$654$		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	0.744111	−	0.668056i	$-0.232873\pi$
$659$	−2.30212e6	−	3.98739e6i	−0.206497	−	0.357664i	−0.950609	+	0.310391i	$0.899540\pi$
$660$		0			0
$661$	−2.73544e6	+	4.73792e6i	−0.243514	+	0.421778i	−0.961713	−	0.274060i	$-0.911633\pi$
$661$	−2.73544e6	+	4.73792e6i	−0.243514	+	0.421778i	0.718199	+	0.695838i	$0.244967\pi$
$662$	−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	0.854119	+	0.520078i	$0.174097\pi$
$673$	1.03102e7	+	1.78577e7i	0.877460	+	1.51981i	0.0233415	+	0.999728i	$0.492569\pi$
$674$	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	−0.604886	−	0.796312i	$-0.706781\pi$
$677$	−2.59618e6	+	1.49891e6i	−0.217702	+	0.125691i	0.387184	+	0.922003i	$0.373448\pi$
$678$		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	−0.913568	−	0.406685i	$-0.866685\pi$
$691$	−1.27793e7	+	7.37815e6i	−1.01815	+	0.587831i	−0.104584	+	0.994516i	$0.533351\pi$
$692$	−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	$-0.993013\pi$
$701$		−	571089.i		−	0.0438944i	0.999759	−	0.0219472i	$-0.00698656\pi$
$702$		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	0.969794	+	0.243926i	$0.0784354\pi$
$709$	9.31781e6	+	1.61389e7i	0.696143	+	1.20576i	−0.273651	+	0.961829i	$0.588231\pi$
$710$	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	0.0239484	−	0.999713i	$-0.492376\pi$
$727$	1.28498e7	−	7.41886e6i	0.901700	−	0.520596i	0.877751	+	0.479117i	$0.159043\pi$
$728$	−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	−0.918891	−	0.394510i	$-0.870914\pi$
$733$	−1.71343e6	+	2.96776e6i	−0.117790	+	0.204018i	0.801102	+	0.598528i	$0.204248\pi$
$734$	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	$-0.859752\pi$
$739$		−	1.26632e7i		−	0.852970i	0.904495	−	0.426485i	$-0.140248\pi$
$740$	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	−0.993751	−	0.111624i	$-0.964395\pi$
$743$	−6.02221e6	+	1.04308e7i	−0.400206	+	0.693178i	0.593544	+	0.804801i	$0.297728\pi$
$744$		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	0.133444	−	0.991056i	$-0.457396\pi$
$751$	−1.01719e7	−	5.87273e6i	−0.658114	−	0.379962i	−0.791558	+	0.611094i	$0.790730\pi$
$752$	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	0.692237	−	0.721671i	$-0.256625\pi$
$761$	6.60390e6	+	3.81276e6i	0.413370	+	0.238659i	−0.278867	+	0.960330i	$0.589959\pi$
$762$		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	−0.490016	−	0.871714i	$-0.663009\pi$
$769$	8.36212e6	−	1.44836e7i	0.509918	−	0.883205i	0.999934	−	0.0114909i	$-0.00365776\pi$
$770$	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	$0.00584428\pi$
$773$			610007.i			0.0367186i	−0.999831	+	0.0183593i	$0.994156\pi$
$774$		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	0.860050	−	0.510209i	$-0.170432\pi$
$787$	1.47383e7	+	8.50913e6i	0.848221	+	0.489721i	−0.0118291	+	0.999930i	$0.503765\pi$
$788$	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	0.0609820	−	0.998139i	$-0.480577\pi$
$797$	−1.38609e7	−	8.00260e6i	−0.772941	−	0.446257i	−0.833923	+	0.551881i	$0.813910\pi$
$798$		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	$0.194148\pi$
$809$			2.13263e7i			1.14563i	−0.819686	+	0.572813i	$0.805852\pi$
$810$		0			0
$811$			8.01640e6i			0.427984i	0.976835	+	0.213992i	$0.0686466\pi$
$811$			8.01640e6i			0.427984i	−0.976835	+	0.213992i	$0.931353\pi$
$812$	−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	−0.549992	−	0.835170i	$-0.685369\pi$
$821$	−1.96434e6	+	1.13411e6i	−0.101709	+	0.0587215i	0.448283	+	0.893892i	$0.352036\pi$
$822$		0			0
$823$	−3.22738e7	−	1.86333e7i	−1.66093	−	0.958936i	−0.972274	−	0.233844i	$-0.924870\pi$
$823$	−3.22738e7	−	1.86333e7i	−1.66093	−	0.958936i	−0.688652	−	0.725092i	$-0.741797\pi$
$824$	−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	0.947317	−	0.320299i	$-0.103783\pi$
$839$	4.00186e6	+	6.93143e6i	0.196272	+	0.339952i	−0.751045	+	0.660251i	$0.770450\pi$
$840$		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	0.983251	−	0.182259i	$-0.0583410\pi$
$853$	7.09314e6	+	1.22857e7i	0.333784	+	0.578131i	−0.649466	+	0.760390i	$0.725008\pi$
$854$	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	−0.996980	−	0.0776628i	$-0.975254\pi$
$857$	−3.07075e7	+	1.77290e7i	−1.42821	+	0.824578i	−0.431232	+	0.902241i	$0.641921\pi$
$858$		0			0
$859$	1.51108e7	+	8.72423e6i	0.698723	+	0.403408i	0.806872	−	0.590727i	$-0.201159\pi$
$859$	1.51108e7	+	8.72423e6i	0.698723	+	0.403408i	−0.108149	+	0.994135i	$0.534492\pi$
$860$	−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	−0.875369	−	0.483455i	$-0.839382\pi$
$877$	−432760.	+	749562.i	−0.0189998	+	0.0329085i	0.856369	+	0.516364i	$0.172715\pi$
$878$	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	$-0.939930\pi$
$881$		−	8.64368e6i		−	0.375197i	0.982246	−	0.187598i	$-0.0600703\pi$
$882$		0			0
$883$			6.19117e6i			0.267221i	0.991034	+	0.133611i	$0.0426572\pi$
$883$			6.19117e6i			0.267221i	−0.991034	+	0.133611i	$0.957343\pi$
$884$	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	−0.411802	−	0.911273i	$-0.635100\pi$
$887$	1.36675e7	−	2.36728e7i	0.583285	−	1.01028i	0.995087	−	0.0990058i	$-0.0315662\pi$
$888$		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	−0.553779	−	0.832664i	$-0.686815\pi$
$907$	−2.71438e6	+	1.56715e6i	−0.109560	+	0.0632545i	0.444219	+	0.895918i	$0.353481\pi$
$908$	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	0.870893	+	0.491472i	$0.163541\pi$
$911$	2.15693e7	+	3.73592e7i	0.861074	+	1.49142i	−0.00981891	+	0.999952i	$0.503126\pi$
$912$		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	$0.0608929\pi$
$919$			9.73606e6i			0.380272i	−0.981758	+	0.190136i	$0.939107\pi$
$920$	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	0.417647	−	0.908610i	$-0.362855\pi$
$929$	3.71782e7	−	2.14649e7i	1.41335	−	0.815997i	0.995702	+	0.0926123i	$0.0295217\pi$
$930$		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	0.741833	−	0.670585i	$-0.233957\pi$
$941$	1.44508e7	+	8.34315e6i	0.532006	+	0.307154i	−0.209827	+	0.977739i	$0.567290\pi$
$942$		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	0.761817	−	0.647792i	$-0.224308\pi$
$947$	−4.97026e6	−	8.60874e6i	−0.180096	−	0.311936i	−0.941913	+	0.335857i	$0.890974\pi$
$948$		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	$0.0763743\pi$
$953$			1.33255e7i			0.475283i	−0.971353	+	0.237641i	$0.923626\pi$
$954$		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	−0.997572	−	0.0696376i	$-0.977816\pi$
$967$	−4.52649e7	−	2.61337e7i	−1.55667	−	0.898742i	−0.559094	−	0.829104i	$-0.688851\pi$
$968$	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	−0.0934002	−	0.995629i	$-0.529774\pi$
$977$	−2.99055e7	−	1.72660e7i	−1.00234	−	0.578701i	−0.908940	+	0.416927i	$0.863107\pi$
$978$		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	0.647067	−	0.762433i	$-0.275995\pi$
$983$	−1.02022e7	−	1.76708e7i	−0.336753	−	0.583273i	−0.983820	+	0.179160i	$0.942662\pi$
$984$		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	$0.136567\pi$
$991$			2.57219e7i			0.831991i	−0.909367	+	0.415996i	$0.863433\pi$
$992$	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	0.779304	−	0.626646i	$-0.215573\pi$
$997$	−4.80332e6	−	8.31959e6i	−0.153040	−	0.265072i	−0.932343	+	0.361574i	$0.882240\pi$
$998$	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.71.11		56
3.2	odd	2		36.6.h.a.23.18	yes	56
4.3	odd	2	inner	108.6.h.a.71.20		56
9.2	odd	6	inner	108.6.h.a.35.20		56
9.7	even	3		36.6.h.a.11.9	✓	56
12.11	even	2		36.6.h.a.23.9	yes	56
36.7	odd	6		36.6.h.a.11.18	yes	56
36.11	even	6	inner	108.6.h.a.35.11		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.h.a.11.9	✓	56	9.7	even	3
36.6.h.a.11.18	yes	56	36.7	odd	6
36.6.h.a.23.9	yes	56	12.11	even	2
36.6.h.a.23.18	yes	56	3.2	odd	2
108.6.h.a.35.11		56	36.11	even	6	inner
108.6.h.a.35.20		56	9.2	odd	6	inner
108.6.h.a.71.11		56	1.1	even	1	trivial
108.6.h.a.71.20		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)

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