LMFDB - Embedded newform 700.5.o.c.649.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,5,Mod(549,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("700.549");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	700.o (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:	$72.3589741587$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			649.15
Character	$\chi$	$=$	700.649
Dual form			700.5.o.c.549.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.15197 + 5.45937i) q^{3} +(-32.2417 + 36.8981i) q^{7} +(20.6302 - 35.7325i) q^{9} +(14.1885 + 24.5752i) q^{11} +322.698 q^{13} +(-249.783 - 432.637i) q^{17} +(-160.504 - 92.6668i) q^{19} +(-303.066 - 59.7178i) q^{21} +(-349.914 - 202.023i) q^{23} +770.722 q^{27} -732.477 q^{29} +(-671.196 + 387.515i) q^{31} +(-89.4433 + 154.920i) q^{33} +(-630.104 - 363.791i) q^{37} +(1017.13 + 1761.73i) q^{39} -20.3416i q^{41} -1854.44i q^{43} +(-1893.08 + 3278.90i) q^{47} +(-321.943 - 2379.32i) q^{49} +(1574.62 - 2727.31i) q^{51} +(4690.29 - 2707.94i) q^{53} -1168.33i q^{57} +(4641.86 - 2679.98i) q^{59} +(-5830.99 - 3366.53i) q^{61} +(653.310 + 1913.29i) q^{63} +(5698.00 - 3289.74i) q^{67} -2547.08i q^{69} +3986.32 q^{71} +(-4398.75 - 7618.86i) q^{73} +(-1364.24 - 268.817i) q^{77} +(-2452.82 + 4248.41i) q^{79} +(758.248 + 1313.32i) q^{81} +4449.18 q^{83} +(-2308.75 - 3998.87i) q^{87} +(11675.4 + 6740.79i) q^{89} +(-10404.3 + 11906.9i) q^{91} +(-4231.18 - 2442.87i) q^{93} +7101.58 q^{97} +1170.84 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 684 q^{9} - 300 q^{11} + 540 q^{19} - 190 q^{21} - 528 q^{29} - 2334 q^{31} - 852 q^{39} + 4092 q^{49} - 3902 q^{51} + 9414 q^{59} - 23598 q^{61} + 32820 q^{71} - 4890 q^{79} - 23710 q^{81} - 37764 q^{89}+ \cdots + 168180 q^{99}+O(q^{100}) $ 44 * q - 684 * q^9 - 300 * q^11 + 540 * q^19 - 190 * q^21 - 528 * q^29 - 2334 * q^31 - 852 * q^39 + 4092 * q^49 - 3902 * q^51 + 9414 * q^59 - 23598 * q^61 + 32820 * q^71 - 4890 * q^79 - 23710 * q^81 - 37764 * q^89 + 6418 * q^91 + 168180 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	3.15197	+	5.45937i	0.350219	+	0.606597i	0.986288	−	0.165036i	$-0.0527739\pi$
$3$	3.15197	+	5.45937i	0.350219	+	0.606597i	−0.636069	+	0.771632i	$0.719441\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−32.2417	+	36.8981i	−0.657994	+	0.753023i
$7$	−32.2417	+	36.8981i	−0.657994	+	0.753023i
$8$		0			0
$9$	20.6302	−	35.7325i	0.254693	−	0.441142i
$10$		0			0
$11$	14.1885	+	24.5752i	0.117260	+	0.203100i	0.918681	−	0.395000i	$-0.129256\pi$
$11$	14.1885	+	24.5752i	0.117260	+	0.203100i	−0.801421	+	0.598101i	$0.795922\pi$
$12$		0			0
$13$	322.698			1.90945			0.954727	−	0.297485i	$-0.0961478\pi$
$13$	322.698			1.90945			0.954727	+	0.297485i	$0.0961478\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−249.783	−	432.637i	−0.864301	−	1.49701i	−0.867740	−	0.497018i	$-0.834428\pi$
$17$	−249.783	−	432.637i	−0.864301	−	1.49701i	0.00343955	−	0.999994i	$-0.498905\pi$
$18$		0			0
$19$	−160.504	−	92.6668i	−0.444608	−	0.256695i	0.260942	−	0.965354i	$-0.415967\pi$
$19$	−160.504	−	92.6668i	−0.444608	−	0.256695i	−0.705550	+	0.708660i	$0.749300\pi$
$20$		0			0
$21$	−303.066	−	59.7178i	−0.687223	−	0.135414i
$22$		0			0
$23$	−349.914	−	202.023i	−0.661463	−	0.381896i	0.131371	−	0.991333i	$-0.458062\pi$
$23$	−349.914	−	202.023i	−0.661463	−	0.381896i	−0.792834	+	0.609438i	$0.791395\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	770.722			1.05723
$28$		0			0
$29$	−732.477			−0.870960			−0.435480	−	0.900198i	$-0.643421\pi$
$29$	−732.477			−0.870960			−0.435480	+	0.900198i	$0.643421\pi$
$30$		0			0
$31$	−671.196	+	387.515i	−0.698435	+	0.403242i	−0.806764	−	0.590873i	$-0.798783\pi$
$31$	−671.196	+	387.515i	−0.698435	+	0.403242i	0.108329	+	0.994115i	$0.465450\pi$
$32$		0			0
$33$	−89.4433	+	154.920i	−0.0821334	+	0.142259i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−630.104	−	363.791i	−0.460266	−	0.265735i	0.251890	−	0.967756i	$-0.418948\pi$
$37$	−630.104	−	363.791i	−0.460266	−	0.265735i	−0.712156	+	0.702021i	$0.752281\pi$
$38$		0			0
$39$	1017.13	+	1761.73i	0.668727	+	1.15827i
$40$		0			0
$41$		−	20.3416i		−	0.0121009i	−0.999982	−	0.00605044i	$-0.998074\pi$
$41$		−	20.3416i		−	0.0121009i	0.999982	−	0.00605044i	$-0.00192593\pi$
$42$		0			0
$43$		−	1854.44i		−	1.00294i	−0.865174	−	0.501472i	$-0.832792\pi$
$43$		−	1854.44i		−	1.00294i	0.865174	−	0.501472i	$-0.167208\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1893.08	+	3278.90i	−0.856983	+	1.48434i	0.0178095	+	0.999841i	$0.494331\pi$
$47$	−1893.08	+	3278.90i	−0.856983	+	1.48434i	−0.874793	+	0.484497i	$0.839003\pi$
$48$		0			0
$49$	−321.943	−	2379.32i	−0.134087	−	0.990970i
$50$		0			0
$51$	1574.62	−	2727.31i	0.605389	−	1.04856i
$52$		0			0
$53$	4690.29	−	2707.94i	1.66974	−	0.964023i	0.701959	−	0.712217i	$-0.252309\pi$
$53$	4690.29	−	2707.94i	1.66974	−	0.964023i	0.967778	−	0.251806i	$-0.0810244\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	1168.33i		−	0.359597i
$58$		0			0
$59$	4641.86	−	2679.98i	1.33348	−	0.769888i	0.347653	−	0.937623i	$-0.386979\pi$
$59$	4641.86	−	2679.98i	1.33348	−	0.769888i	0.985832	+	0.167736i	$0.0536456\pi$
$60$		0			0
$61$	−5830.99	−	3366.53i	−1.56705	−	0.904737i	−0.996511	−	0.0834671i	$-0.973401\pi$
$61$	−5830.99	−	3366.53i	−1.56705	−	0.904737i	−0.570540	−	0.821270i	$-0.693266\pi$
$62$		0			0
$63$	653.310	+	1913.29i	0.164603	+	0.482059i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	5698.00	−	3289.74i	1.26933	−	0.732845i	0.294465	−	0.955662i	$-0.404859\pi$
$67$	5698.00	−	3289.74i	1.26933	−	0.732845i	0.974860	+	0.222817i	$0.0715253\pi$
$68$		0			0
$69$		−	2547.08i		−	0.534988i
$70$		0			0
$71$	3986.32			0.790780			0.395390	−	0.918513i	$-0.370609\pi$
$71$	3986.32			0.790780			0.395390	+	0.918513i	$0.370609\pi$
$72$		0			0
$73$	−4398.75	−	7618.86i	−0.825436	−	1.42970i	−0.901586	−	0.432601i	$-0.857596\pi$
$73$	−4398.75	−	7618.86i	−0.825436	−	1.42970i	0.0761494	−	0.997096i	$-0.475737\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1364.24	−	268.817i	−0.230096	−	0.0453394i
$78$		0			0
$79$	−2452.82	+	4248.41i	−0.393017	+	0.680725i	−0.992846	−	0.119403i	$-0.961902\pi$
$79$	−2452.82	+	4248.41i	−0.393017	+	0.680725i	0.599829	+	0.800128i	$0.295235\pi$
$80$		0			0
$81$	758.248	+	1313.32i	0.115569	+	0.200171i
$82$		0			0
$83$	4449.18			0.645838			0.322919	−	0.946427i	$-0.395336\pi$
$83$	4449.18			0.645838			0.322919	+	0.946427i	$0.395336\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2308.75	−	3998.87i	−0.305027	−	0.528322i
$88$		0			0
$89$	11675.4	+	6740.79i	1.47398	+	0.851003i	0.999571	−	0.0293012i	$-0.00932819\pi$
$89$	11675.4	+	6740.79i	1.47398	+	0.851003i	0.474410	+	0.880304i	$0.342662\pi$
$90$		0			0
$91$	−10404.3	+	11906.9i	−1.25641	+	1.43786i
$92$		0			0
$93$	−4231.18	−	2442.87i	−0.489210	−	0.282446i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	7101.58			0.754765			0.377382	−	0.926057i	$-0.376824\pi$
$97$	7101.58			0.754765			0.377382	+	0.926057i	$0.376824\pi$
$98$		0			0
$99$	1170.84			0.119462
$100$		0			0
$101$	−3123.73	+	1803.48i	−0.306218	+	0.176795i	−0.645233	−	0.763986i	$-0.723240\pi$
$101$	−3123.73	+	1803.48i	−0.306218	+	0.176795i	0.339015	+	0.940781i	$0.389906\pi$
$102$		0			0
$103$	1024.57	−	1774.60i	0.0965752	−	0.167273i	−0.813690	−	0.581299i	$-0.802545\pi$
$103$	1024.57	−	1774.60i	0.0965752	−	0.167273i	0.910265	+	0.414026i	$0.135878\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−11753.6	−	6785.97i	−1.02661	−	0.592713i	−0.110598	−	0.993865i	$-0.535276\pi$
$107$	−11753.6	−	6785.97i	−1.02661	−	0.592713i	−0.916011	+	0.401152i	$0.868610\pi$
$108$		0			0
$109$	4084.63	+	7074.79i	0.343795	+	0.595471i	0.985134	−	0.171787i	$-0.0549541\pi$
$109$	4084.63	+	7074.79i	0.343795	+	0.595471i	−0.641339	+	0.767258i	$0.721621\pi$
$110$		0			0
$111$		−	4586.63i		−	0.372261i
$112$		0			0
$113$		−	3805.54i		−	0.298029i	−0.988835	−	0.149015i	$-0.952390\pi$
$113$		−	3805.54i		−	0.298029i	0.988835	−	0.149015i	$-0.0476101\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	6657.31	−	11530.8i	0.486325	−	0.842340i
$118$		0			0
$119$	24016.9	+	4732.43i	1.69599	+	0.334188i
$120$		0			0
$121$	6917.87	−	11982.1i	0.472500	−	0.818394i
$122$		0			0
$123$	111.052	−	64.1160i	0.00734035	−	0.00423796i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	29755.4i		−	1.84484i	−0.386189	−	0.922420i	$-0.626209\pi$
$127$		−	29755.4i		−	1.84484i	0.386189	−	0.922420i	$-0.373791\pi$
$128$		0			0
$129$	10124.1	−	5845.15i	0.608383	−	0.351250i
$130$		0			0
$131$	−5204.68	−	3004.92i	−0.303285	−	0.175102i	0.340633	−	0.940196i	$-0.389359\pi$
$131$	−5204.68	−	3004.92i	−0.303285	−	0.175102i	−0.643918	+	0.765095i	$0.722692\pi$
$132$		0			0
$133$	8594.15	−	2934.54i	0.485847	−	0.165897i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2034.06	+	1174.37i	−0.108373	+	0.0625694i	−0.553207	−	0.833044i	$-0.686596\pi$
$137$	−2034.06	+	1174.37i	−0.108373	+	0.0625694i	0.444834	+	0.895613i	$0.353263\pi$
$138$		0			0
$139$			8981.94i			0.464880i	0.972611	+	0.232440i	$0.0746709\pi$
$139$			8981.94i			0.464880i	−0.972611	+	0.232440i	$0.925329\pi$
$140$		0			0
$141$	−23867.7			−1.20053
$142$		0			0
$143$	4578.59	+	7930.34i	0.223903	+	0.387811i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	11974.8	−	9257.14i	0.554159	−	0.428393i
$148$		0			0
$149$	8669.18	−	15015.5i	0.390486	−	0.676342i	−0.602028	−	0.798475i	$-0.705640\pi$
$149$	8669.18	−	15015.5i	0.390486	−	0.676342i	0.992514	+	0.122133i	$0.0389736\pi$
$150$		0			0
$151$	5355.10	+	9275.31i	0.234863	+	0.406794i	0.959233	−	0.282617i	$-0.0912026\pi$
$151$	5355.10	+	9275.31i	0.234863	+	0.406794i	−0.724370	+	0.689411i	$0.757869\pi$
$152$		0			0
$153$	−20612.3			−0.880527
$154$		0			0
$155$		0			0
$156$		0			0
$157$	4606.75	+	7979.12i	0.186894	+	0.323710i	0.944213	−	0.329335i	$-0.106825\pi$
$157$	4606.75	+	7979.12i	0.186894	+	0.323710i	−0.757319	+	0.653045i	$0.773491\pi$
$158$		0			0
$159$	29567.3	+	17070.7i	1.16955	+	0.675238i
$160$		0			0
$161$	18736.1	−	6397.60i	0.722815	−	0.246811i
$162$		0			0
$163$	−23594.3	−	13622.1i	−0.888037	−	0.512708i	−0.0147370	−	0.999891i	$-0.504691\pi$
$163$	−23594.3	−	13622.1i	−0.888037	−	0.512708i	−0.873300	+	0.487183i	$0.838024\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4063.60			−0.145706			−0.0728531	−	0.997343i	$-0.523210\pi$
$167$	−4063.60			−0.145706			−0.0728531	+	0.997343i	$0.523210\pi$
$168$		0			0
$169$	75572.7			2.64601
$170$		0			0
$171$	−6622.44	+	3823.46i	−0.226478	+	0.130757i
$172$		0			0
$173$	22916.1	−	39691.8i	0.765681	−	1.32620i	−0.174205	−	0.984709i	$-0.555736\pi$
$173$	22916.1	−	39691.8i	0.765681	−	1.32620i	0.939886	−	0.341488i	$-0.110931\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	29262.0	+	16894.4i	0.934023	+	0.539258i
$178$		0			0
$179$	10965.3	+	18992.5i	0.342228	+	0.592756i	0.984846	−	0.173431i	$-0.0554853\pi$
$179$	10965.3	+	18992.5i	0.342228	+	0.592756i	−0.642618	+	0.766186i	$0.722152\pi$
$180$		0			0
$181$		−	6943.49i		−	0.211944i	−0.994369	−	0.105972i	$-0.966205\pi$
$181$		−	6943.49i		−	0.211944i	0.994369	−	0.105972i	$-0.0337954\pi$
$182$		0			0
$183$		−	42444.8i		−	1.26742i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	7088.08	−	12276.9i	0.202696	−	0.351080i
$188$		0			0
$189$	−24849.4	+	28438.2i	−0.695652	+	0.796120i
$190$		0			0
$191$	−28099.2	+	48669.2i	−0.770242	+	1.33410i	0.167188	+	0.985925i	$0.446531\pi$
$191$	−28099.2	+	48669.2i	−0.770242	+	1.33410i	−0.937430	+	0.348173i	$0.886802\pi$
$192$		0			0
$193$	−34678.4	+	20021.6i	−0.930989	+	0.537507i	−0.887124	−	0.461531i	$-0.847300\pi$
$193$	−34678.4	+	20021.6i	−0.930989	+	0.537507i	−0.0438648	+	0.999037i	$0.513967\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	46320.3i		−	1.19355i	−0.802410	−	0.596773i	$-0.796449\pi$
$197$		−	46320.3i		−	1.19355i	0.802410	−	0.596773i	$-0.203551\pi$
$198$		0			0
$199$	14564.3	−	8408.71i	0.367776	−	0.212336i	−0.304710	−	0.952445i	$-0.598560\pi$
$199$	14564.3	−	8408.71i	0.367776	−	0.212336i	0.672487	+	0.740109i	$0.265226\pi$
$200$		0			0
$201$	35919.9	+	20738.3i	0.889083	+	0.513312i
$202$		0			0
$203$	23616.3	−	27027.0i	0.573087	−	0.655853i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−14437.6	+	8335.53i	−0.336940	+	0.194533i
$208$		0			0
$209$		−	5259.20i		−	0.120400i
$210$		0			0
$211$	7624.96			0.171267			0.0856333	−	0.996327i	$-0.472709\pi$
$211$	7624.96			0.171267			0.0856333	+	0.996327i	$0.472709\pi$
$212$		0			0
$213$	12564.8	+	21762.8i	0.276946	+	0.479685i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	7341.93	−	37260.0i	0.155916	−	0.791268i
$218$		0			0
$219$	27729.4	−	48028.8i	0.578167	−	1.00141i
$220$		0			0
$221$	−80604.3	−	139611.i	−1.65034	−	2.85847i
$222$		0			0
$223$	53858.4			1.08304			0.541519	−	0.840688i	$-0.317849\pi$
$223$	53858.4			1.08304			0.541519	+	0.840688i	$0.317849\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	563.521	+	976.047i	0.0109360	+	0.0189417i	0.871442	−	0.490499i	$-0.163186\pi$
$227$	563.521	+	976.047i	0.0109360	+	0.0189417i	−0.860506	+	0.509441i	$0.829852\pi$
$228$		0			0
$229$	−21593.5	−	12467.0i	−0.411768	−	0.237735i	0.279781	−	0.960064i	$-0.409738\pi$
$229$	−21593.5	−	12467.0i	−0.411768	−	0.237735i	−0.691549	+	0.722329i	$0.743072\pi$
$230$		0			0
$231$	−2832.46	−	8295.19i	−0.0530812	−	0.155454i
$232$		0			0
$233$	33282.2	+	19215.5i	0.613057	+	0.353948i	0.774161	−	0.632989i	$-0.218172\pi$
$233$	33282.2	+	19215.5i	0.613057	+	0.353948i	−0.161104	+	0.986937i	$0.551506\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−30924.8			−0.550568
$238$		0			0
$239$	−71148.4			−1.24557			−0.622786	−	0.782392i	$-0.713999\pi$
$239$	−71148.4			−1.24557			−0.622786	+	0.782392i	$0.713999\pi$
$240$		0			0
$241$	−52009.9	+	30027.9i	−0.895472	+	0.517001i	−0.875728	−	0.482804i	$-0.839618\pi$
$241$	−52009.9	+	30027.9i	−0.895472	+	0.517001i	−0.0197436	+	0.999805i	$0.506285\pi$
$242$		0			0
$243$	26434.3	−	45785.5i	0.447667	−	0.775382i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−51794.1	−	29903.4i	−0.848959	−	0.490147i
$248$		0			0
$249$	14023.7	+	24289.7i	0.226185	+	0.391763i
$250$		0			0
$251$		−	11274.6i		−	0.178958i	−0.995989	−	0.0894792i	$-0.971480\pi$
$251$		−	11274.6i		−	0.178958i	0.995989	−	0.0894792i	$-0.0285203\pi$
$252$		0			0
$253$		−	11465.6i		−	0.179125i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	33242.4	−	57577.5i	0.503299	−	0.871739i	−0.496694	−	0.867926i	$-0.665453\pi$
$257$	33242.4	−	57577.5i	0.503299	−	0.871739i	0.999993	−	0.00381315i	$-0.00121377\pi$
$258$		0			0
$259$	33738.8	−	11520.4i	0.502956	−	0.171739i
$260$		0			0
$261$	−15111.1	+	26173.2i	−0.221828	+	0.384217i
$262$		0			0
$263$	48524.1	−	28015.4i	0.701530	−	0.405029i	−0.106387	−	0.994325i	$-0.533928\pi$
$263$	48524.1	−	28015.4i	0.701530	−	0.405029i	0.807917	+	0.589296i	$0.200595\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			84987.1i			1.19215i
$268$		0			0
$269$	63570.6	−	36702.5i	0.878520	−	0.507214i	0.00834980	−	0.999965i	$-0.497342\pi$
$269$	63570.6	−	36702.5i	0.878520	−	0.507214i	0.870170	+	0.492751i	$0.164009\pi$
$270$		0			0
$271$	−12291.4	−	7096.42i	−0.167364	−	0.0966275i	0.413978	−	0.910287i	$-0.364139\pi$
$271$	−12291.4	−	7096.42i	−0.167364	−	0.0966275i	−0.581342	+	0.813659i	$0.697472\pi$
$272$		0			0
$273$	−97798.5	−	19270.8i	−1.31222	−	0.258568i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−85595.2	+	49418.4i	−1.11555	+	0.644065i	−0.940262	−	0.340452i	$-0.889420\pi$
$277$	−85595.2	+	49418.4i	−1.11555	+	0.644065i	−0.175291	+	0.984517i	$0.556087\pi$
$278$		0			0
$279$			31978.0i			0.410812i
$280$		0			0
$281$	58127.8			0.736158			0.368079	−	0.929795i	$-0.380016\pi$
$281$	58127.8			0.736158			0.368079	+	0.929795i	$0.380016\pi$
$282$		0			0
$283$	4444.83	+	7698.66i	0.0554986	+	0.0961263i	0.892440	−	0.451166i	$-0.148992\pi$
$283$	4444.83	+	7698.66i	0.0554986	+	0.0961263i	−0.836941	+	0.547293i	$0.815659\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	750.566	+	655.847i	0.00911224	+	0.00796231i
$288$		0			0
$289$	−83022.4	+	143799.i	−0.994031	+	1.72171i
$290$		0			0
$291$	22384.0	+	38770.2i	0.264333	+	0.457838i
$292$		0			0
$293$	−74609.7			−0.869081			−0.434540	−	0.900652i	$-0.643089\pi$
$293$	−74609.7			−0.869081			−0.434540	+	0.900652i	$0.643089\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	10935.4	+	18940.6i	0.123971	+	0.214724i
$298$		0			0
$299$	−112916.	−	65192.3i	−1.26303	−	0.729212i
$300$		0			0
$301$	68425.5	+	59790.5i	0.755240	+	0.659932i
$302$		0			0
$303$	−19691.8	−	11369.1i	−0.214486	−	0.123834i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	66333.5			0.703812			0.351906	−	0.936035i	$-0.385534\pi$
$307$	66333.5			0.703812			0.351906	+	0.936035i	$0.385534\pi$
$308$		0			0
$309$	12917.6			0.135290
$310$		0			0
$311$	−91239.5	+	52677.1i	−0.943327	+	0.544630i	−0.891002	−	0.454000i	$-0.849997\pi$
$311$	−91239.5	+	52677.1i	−0.943327	+	0.544630i	−0.0523251	+	0.998630i	$0.516663\pi$
$312$		0			0
$313$	3135.62	−	5431.06i	0.0320063	−	0.0554365i	−0.849579	−	0.527462i	$-0.823144\pi$
$313$	3135.62	−	5431.06i	0.0320063	−	0.0554365i	0.881585	+	0.472026i	$0.156477\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	95624.0	+	55208.6i	0.951587	+	0.549399i	0.893574	−	0.448917i	$-0.148190\pi$
$317$	95624.0	+	55208.6i	0.951587	+	0.549399i	0.0580134	+	0.998316i	$0.481523\pi$
$318$		0			0
$319$	−10392.7	−	18000.7i	−0.102129	−	0.176892i
$320$		0			0
$321$		−	85556.7i		−	0.830317i
$322$		0			0
$323$			92586.3i			0.887446i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−25749.3	+	44599.0i	−0.240807	+	0.417090i
$328$		0			0
$329$	−59949.4	−	175568.i	−0.553851	−	1.62201i
$330$		0			0
$331$	62929.9	−	108998.i	0.574382	−	0.994859i	−0.421726	−	0.906723i	$-0.638576\pi$
$331$	62929.9	−	108998.i	0.574382	−	0.994859i	0.996108	−	0.0881359i	$-0.0280910\pi$
$332$		0			0
$333$	−25998.3	+	15010.1i	−0.234453	+	0.135362i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			36428.0i			0.320756i	0.987056	+	0.160378i	$0.0512714\pi$
$337$			36428.0i			0.320756i	−0.987056	+	0.160378i	$0.948729\pi$
$338$		0			0
$339$	20775.8	−	11994.9i	0.180784	−	0.104375i
$340$		0			0
$341$	−19046.5	−	10996.5i	−0.163797	−	0.0945683i
$342$		0			0
$343$	98172.3	+	64834.2i	0.834451	+	0.551082i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	85231.1	−	49208.2i	0.707846	−	0.408675i	−0.102417	−	0.994742i	$-0.532658\pi$
$347$	85231.1	−	49208.2i	0.707846	−	0.408675i	0.810263	+	0.586066i	$0.199324\pi$
$348$		0			0
$349$		−	87986.1i		−	0.722376i	−0.932493	−	0.361188i	$-0.882371\pi$
$349$		−	87986.1i		−	0.722376i	0.932493	−	0.361188i	$-0.117629\pi$
$350$		0			0
$351$	248710.			2.01873
$352$		0			0
$353$	84730.1	+	146757.i	0.679968	+	1.17774i	0.974990	+	0.222248i	$0.0713396\pi$
$353$	84730.1	+	146757.i	0.679968	+	1.17774i	−0.295022	+	0.955490i	$0.595327\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	49864.5	+	146034.i	0.391250	+	1.14582i
$358$		0			0
$359$	−48155.7	+	83408.1i	−0.373644	+	0.647171i	−0.990123	−	0.140200i	$-0.955225\pi$
$359$	−48155.7	+	83408.1i	−0.373644	+	0.647171i	0.616479	+	0.787372i	$0.288559\pi$
$360$		0			0
$361$	−47986.2	−	83114.6i	−0.368216	−	0.637768i
$362$		0			0
$363$	87219.7			0.661914
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−4784.17	−	8286.43i	−0.0355201	−	0.0615227i	0.847719	−	0.530446i	$-0.177975\pi$
$367$	−4784.17	−	8286.43i	−0.0355201	−	0.0615227i	−0.883239	+	0.468923i	$0.844642\pi$
$368$		0			0
$369$	−726.855	−	419.650i	−0.00533821	−	0.00308201i
$370$		0			0
$371$	−51305.1	+	260372.i	−0.372746	+	1.89167i
$372$		0			0
$373$	−123404.	−	71247.2i	−0.886974	−	0.512095i	−0.0140223	−	0.999902i	$-0.504464\pi$
$373$	−123404.	−	71247.2i	−0.886974	−	0.512095i	−0.872951	+	0.487807i	$0.837797\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−236369.			−1.66306
$378$		0			0
$379$	−203100.			−1.41394			−0.706970	−	0.707243i	$-0.749939\pi$
$379$	−203100.			−1.41394			−0.706970	+	0.707243i	$0.749939\pi$
$380$		0			0
$381$	162446.	−	93788.2i	1.11907	−	0.646097i
$382$		0			0
$383$	−85906.7	+	148795.i	−0.585638	+	1.01435i	0.409158	+	0.912464i	$0.365823\pi$
$383$	−85906.7	+	148795.i	−0.585638	+	1.01435i	−0.994796	+	0.101891i	$0.967511\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−66263.9	−	38257.5i	−0.442441	−	0.255443i
$388$		0			0
$389$	21093.4	+	36534.9i	0.139395	+	0.241440i	0.927268	−	0.374399i	$-0.122151\pi$
$389$	21093.4	+	36534.9i	0.139395	+	0.241440i	−0.787873	+	0.615838i	$0.788818\pi$
$390$		0			0
$391$			201847.i			1.32029i
$392$		0			0
$393$		−	37885.7i		−	0.245296i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−123220.	+	213423.i	−0.781808	+	1.35413i	0.149080	+	0.988825i	$0.452369\pi$
$397$	−123220.	+	213423.i	−0.781808	+	1.35413i	−0.930888	+	0.365305i	$0.880965\pi$
$398$		0			0
$399$	43109.3	+	37669.0i	0.270785	+	0.236613i
$400$		0			0
$401$	48551.6	−	84093.8i	0.301936	−	0.522968i	−0.674639	−	0.738148i	$-0.735701\pi$
$401$	48551.6	−	84093.8i	0.301936	−	0.522968i	0.976574	+	0.215180i	$0.0690339\pi$
$402$		0			0
$403$	−216593.	+	125050.i	−1.33363	+	0.769971i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	20646.5i		−	0.124640i
$408$		0			0
$409$	−151468.	+	87449.9i	−0.905468	+	0.522772i	−0.878970	−	0.476877i	$-0.841769\pi$
$409$	−151468.	+	87449.9i	−0.905468	+	0.522772i	−0.0264978	+	0.999649i	$0.508436\pi$
$410$		0			0
$411$	−12822.6	−	7403.13i	−0.0759088	−	0.0438260i
$412$		0			0
$413$	−50775.4	+	257683.i	−0.297682	+	1.51073i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−49035.8	+	28310.8i	−0.281995	+	0.162810i
$418$		0			0
$419$			147615.i			0.840821i	0.907334	+	0.420411i	$0.138114\pi$
$419$			147615.i			0.840821i	−0.907334	+	0.420411i	$0.861886\pi$
$420$		0			0
$421$	−28665.0			−0.161729			−0.0808646	−	0.996725i	$-0.525768\pi$
$421$	−28665.0			−0.161729			−0.0808646	+	0.996725i	$0.525768\pi$
$422$		0			0
$423$	78109.0	+	135289.i	0.436536	+	0.756103i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	312220.	−	106610.i	1.71240	−	0.584713i
$428$		0			0
$429$	−28863.1	+	49992.4i	−0.156830	+	0.271637i
$430$		0			0
$431$	112765.	+	195314.i	0.607042	+	1.05143i	0.991725	+	0.128379i	$0.0409774\pi$
$431$	112765.	+	195314.i	0.607042	+	1.05143i	−0.384683	+	0.923049i	$0.625689\pi$
$432$		0			0
$433$	−65473.0			−0.349210			−0.174605	−	0.984639i	$-0.555865\pi$
$433$	−65473.0			−0.349210			−0.174605	+	0.984639i	$0.555865\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	37441.6	+	64850.8i	0.196061	+	0.339588i
$438$		0			0
$439$	−258048.	−	148984.i	−1.33897	−	0.773057i	−0.352319	−	0.935880i	$-0.614607\pi$
$439$	−258048.	−	148984.i	−1.33897	−	0.773057i	−0.986655	+	0.162823i	$0.947940\pi$
$440$		0			0
$441$	−91660.7	−	37581.9i	−0.471309	−	0.193242i
$442$		0			0
$443$	−269244.	−	155448.i	−1.37195	−	0.792095i	−0.380776	−	0.924667i	$-0.624343\pi$
$443$	−269244.	−	155448.i	−1.37195	−	0.792095i	−0.991173	+	0.132572i	$0.957677\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	109300.			0.547023
$448$		0			0
$449$	−217824.			−1.08047			−0.540235	−	0.841514i	$-0.681665\pi$
$449$	−217824.			−1.08047			−0.540235	+	0.841514i	$0.681665\pi$
$450$		0			0
$451$	499.897	−	288.616i	0.00245769	−	0.00141895i
$452$		0			0
$453$	−33758.3	+	58471.0i	−0.164507	+	0.284934i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−172454.	−	99566.6i	−0.825738	−	0.476740i	0.0266534	−	0.999645i	$-0.491515\pi$
$457$	−172454.	−	99566.6i	−0.825738	−	0.476740i	−0.852391	+	0.522905i	$0.824848\pi$
$458$		0			0
$459$	−192513.	−	333442.i	−0.913766	−	1.58269i
$460$		0			0
$461$		−	71484.4i		−	0.336364i	−0.985756	−	0.168182i	$-0.946210\pi$
$461$		−	71484.4i		−	0.336364i	0.985756	−	0.168182i	$-0.0537896\pi$
$462$		0			0
$463$			106595.i			0.497252i	0.968600	+	0.248626i	$0.0799790\pi$
$463$			106595.i			0.497252i	−0.968600	+	0.248626i	$0.920021\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−47671.0	+	82568.7i	−0.218585	+	0.378601i	−0.954376	−	0.298609i	$-0.903478\pi$
$467$	−47671.0	+	82568.7i	−0.218585	+	0.378601i	0.735790	+	0.677209i	$0.236811\pi$
$468$		0			0
$469$	−62328.0	+	316312.i	−0.283360	+	1.43804i
$470$		0			0
$471$	−29040.7	+	50299.9i	−0.130908	+	0.226738i
$472$		0			0
$473$	45573.3	−	26311.7i	0.203698	−	0.117605i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		−	223461.i		−	0.982121i
$478$		0			0
$479$	67483.3	−	38961.5i	0.294120	−	0.169811i	−0.345678	−	0.938353i	$-0.612351\pi$
$479$	67483.3	−	38961.5i	0.294120	−	0.169811i	0.639799	+	0.768543i	$0.279018\pi$
$480$		0			0
$481$	−203333.	−	117394.i	−0.878856	−	0.507408i
$482$		0			0
$483$	93982.4	+	82122.2i	0.402858	+	0.352019i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−205567.	+	118684.i	−0.866752	+	0.500419i	−0.866267	−	0.499581i	$-0.833487\pi$
$487$	−205567.	+	118684.i	−0.866752	+	0.500419i	−0.000484141		1.00000i	$0.500154\pi$
$488$		0			0
$489$		−	171746.i		−	0.718241i
$490$		0			0
$491$	257204.			1.06688			0.533439	−	0.845838i	$-0.320899\pi$
$491$	257204.			1.06688			0.533439	+	0.845838i	$0.320899\pi$
$492$		0			0
$493$	182960.	+	316896.i	0.752771	+	1.30384i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−128526.	+	147088.i	−0.520329	+	0.595476i
$498$		0			0
$499$	37144.5	−	64336.1i	0.149174	−	0.258377i	−0.781748	−	0.623594i	$-0.785672\pi$
$499$	37144.5	−	64336.1i	0.149174	−	0.258377i	0.930922	+	0.365217i	$0.119005\pi$
$500$		0			0
$501$	−12808.3	−	22184.7i	−0.0510291	−	0.0883849i
$502$		0			0
$503$	344439.			1.36137			0.680685	−	0.732576i	$-0.261682\pi$
$503$	344439.			1.36137			0.680685	+	0.732576i	$0.261682\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	238203.	+	412580.i	0.926683	+	1.60506i
$508$		0			0
$509$	−34030.4	−	19647.5i	−0.131350	−	0.0758352i	0.432885	−	0.901449i	$-0.357496\pi$
$509$	−34030.4	−	19647.5i	−0.131350	−	0.0758352i	−0.564235	+	0.825614i	$0.690829\pi$
$510$		0			0
$511$	422945.	+	83339.5i	1.61973	+	0.319160i
$512$		0			0
$513$	−123704.	−	71420.3i	−0.470054	−	0.271386i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−107439.			−0.401960
$518$		0			0
$519$	288923.			1.07262
$520$		0			0
$521$	−198381.	+	114535.i	−0.730844	+	0.421953i	−0.818731	−	0.574178i	$-0.805322\pi$
$521$	−198381.	+	114535.i	−0.730844	+	0.421953i	0.0878869	+	0.996130i	$0.471989\pi$
$522$		0			0
$523$	264310.	−	457799.i	0.966298	−	1.67368i	0.260211	−	0.965552i	$-0.416208\pi$
$523$	264310.	−	457799.i	0.966298	−	1.67368i	0.706087	−	0.708125i	$-0.250459\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	335307.	+	193589.i	1.20732	+	0.697044i
$528$		0			0
$529$	−58294.1	−	100968.i	−0.208311	−	0.360806i
$530$		0			0
$531$		−	221154.i		−	0.784341i
$532$		0			0
$533$		−	6564.18i		−	0.0231061i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−69124.7	+	119727.i	−0.239709	+	0.415188i
$538$		0			0
$539$	53904.2	−	41670.7i	0.185543	−	0.143434i
$540$		0			0
$541$	70992.7	−	122963.i	0.242560	−	0.420126i	−0.718883	−	0.695131i	$-0.755346\pi$
$541$	70992.7	−	122963.i	0.242560	−	0.420126i	0.961443	+	0.275005i	$0.0886795\pi$
$542$		0			0
$543$	37907.1	−	21885.7i	0.128565	−	0.0742268i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	115290.i		−	0.385315i	−0.981266	−	0.192658i	$-0.938289\pi$
$547$		−	115290.i		−	0.385315i	0.981266	−	0.192658i	$-0.0617107\pi$
$548$		0			0
$549$	−240589.	+	138904.i	−0.798235	+	0.460861i
$550$		0			0
$551$	117565.	+	67876.3i	0.387236	+	0.223571i
$552$		0			0
$553$	−77675.1	−	227480.i	−0.253999	−	0.743864i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−250583.	+	144674.i	−0.807683	+	0.466316i	−0.846150	−	0.532944i	$-0.821086\pi$
$557$	−250583.	+	144674.i	−0.807683	+	0.466316i	0.0384678	+	0.999260i	$0.487752\pi$
$558$		0			0
$559$		−	598425.i		−	1.91508i
$560$		0			0
$561$	89365.6			0.283952
$562$		0			0
$563$	14137.7	+	24487.2i	0.0446027	+	0.0772542i	0.887465	−	0.460875i	$-0.152464\pi$
$563$	14137.7	+	24487.2i	0.0446027	+	0.0772542i	−0.842862	+	0.538129i	$0.819131\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−72906.4	−	14365.9i	−0.226777	−	0.0446855i
$568$		0			0
$569$	−233552.	+	404525.i	−0.721373	+	1.24945i	0.239076	+	0.971001i	$0.423155\pi$
$569$	−233552.	+	404525.i	−0.721373	+	1.24945i	−0.960450	+	0.278454i	$0.910178\pi$
$570$		0			0
$571$	−215219.	−	372770.i	−0.660098	−	1.14332i	−0.980590	−	0.196071i	$-0.937182\pi$
$571$	−215219.	−	372770.i	−0.660098	−	1.14332i	0.320492	−	0.947251i	$-0.396152\pi$
$572$		0			0
$573$	−354271.			−1.07901
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−90598.5	−	156921.i	−0.272126	−	0.471335i	0.697280	−	0.716799i	$-0.254393\pi$
$577$	−90598.5	−	156921.i	−0.272126	−	0.471335i	−0.969406	+	0.245463i	$0.921060\pi$
$578$		0			0
$579$	−218611.	−	126215.i	−0.652100	−	0.376490i
$580$		0			0
$581$	−143449.	+	164166.i	−0.424957	+	0.486331i
$582$		0			0
$583$	133096.	+	76843.1i	0.391587	+	0.226083i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	332481.			0.964919			0.482460	−	0.875918i	$-0.339743\pi$
$587$	332481.			0.964919			0.482460	+	0.875918i	$0.339743\pi$
$588$		0			0
$589$	143639.			0.414040
$590$		0			0
$591$	252880.	−	146000.i	0.724001	−	0.418002i
$592$		0			0
$593$	171569.	−	297166.i	0.487898	−	0.845064i	−0.512005	−	0.858982i	$-0.671097\pi$
$593$	171569.	−	297166.i	0.487898	−	0.845064i	0.999903	+	0.0139186i	$0.00443057\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	91812.5	+	53008.0i	0.257604	+	0.148728i
$598$		0			0
$599$	171088.	+	296333.i	0.476832	+	0.825897i	0.999648	−	0.0265490i	$-0.00845181\pi$
$599$	171088.	+	296333.i	0.476832	+	0.825897i	−0.522816	+	0.852446i	$0.675118\pi$
$600$		0			0
$601$		−	227319.i		−	0.629341i	−0.949201	−	0.314670i	$-0.898106\pi$
$601$		−	227319.i		−	0.629341i	0.949201	−	0.314670i	$-0.101894\pi$
$602$		0			0
$603$		−	271472.i		−	0.746604i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	186230.	−	322559.i	0.505442	−	0.875451i	−0.494538	−	0.869156i	$-0.664663\pi$
$607$	186230.	−	322559.i	0.505442	−	0.875451i	0.999980	−	0.00629550i	$-0.00200393\pi$
$608$		0			0
$609$	221989.	+	43741.9i	0.598544	+	0.117941i
$610$		0			0
$611$	−610891.	+	1.05809e6i	−1.63637	+	2.83427i
$612$		0			0
$613$	−217492.	+	125569.i	−0.578791	+	0.334165i	−0.760653	−	0.649159i	$-0.775121\pi$
$613$	−217492.	+	125569.i	−0.578791	+	0.334165i	0.181862	+	0.983324i	$0.441788\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			297850.i			0.782398i	0.920306	+	0.391199i	$0.127940\pi$
$617$			297850.i			0.782398i	−0.920306	+	0.391199i	$0.872060\pi$
$618$		0			0
$619$	308493.	−	178108.i	0.805126	−	0.464839i	−0.0401347	−	0.999194i	$-0.512779\pi$
$619$	308493.	−	178108.i	0.805126	−	0.464839i	0.845260	+	0.534355i	$0.179445\pi$
$620$		0			0
$621$	−269686.	−	155703.i	−0.699319	−	0.403752i
$622$		0			0
$623$	−625158.	+	213465.i	−1.61070	+	0.549986i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	28711.9	−	16576.9i	0.0730344	−	0.0421664i
$628$		0			0
$629$			363475.i			0.918698i
$630$		0			0
$631$	−714986.			−1.79572			−0.897861	−	0.440279i	$-0.854879\pi$
$631$	−714986.			−1.79572			−0.897861	+	0.440279i	$0.854879\pi$
$632$		0			0
$633$	24033.7	+	41627.5i	0.0599808	+	0.103890i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−103890.	−	767800.i	−0.256033	−	1.89221i
$638$		0			0
$639$	82238.5	−	142441.i	0.201407	−	0.348846i
$640$		0			0
$641$	−219867.	−	380821.i	−0.535111	−	0.926839i	−0.999158	−	0.0410288i	$-0.986936\pi$
$641$	−219867.	−	380821.i	−0.535111	−	0.926839i	0.464047	−	0.885811i	$-0.346397\pi$
$642$		0			0
$643$	414727.			1.00309			0.501545	−	0.865131i	$-0.332765\pi$
$643$	414727.			1.00309			0.501545	+	0.865131i	$0.332765\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−320219.	−	554636.i	−0.764960	−	1.32495i	−0.940268	−	0.340436i	$-0.889425\pi$
$647$	−320219.	−	554636.i	−0.764960	−	1.32495i	0.175307	−	0.984514i	$-0.443908\pi$
$648$		0			0
$649$	131722.	+	76049.6i	0.312729	+	0.180554i
$650$		0			0
$651$	226558.	−	77360.2i	0.534586	−	0.182539i
$652$		0			0
$653$	−149250.	−	86169.4i	−0.350016	−	0.202082i	0.314676	−	0.949199i	$-0.398104\pi$
$653$	−149250.	−	86169.4i	−0.350016	−	0.202082i	−0.664692	+	0.747117i	$0.731437\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−362988.			−0.840933
$658$		0			0
$659$	−349413.			−0.804578			−0.402289	−	0.915513i	$-0.631785\pi$
$659$	−349413.			−0.804578			−0.402289	+	0.915513i	$0.631785\pi$
$660$		0			0
$661$	534419.	−	308547.i	1.22315	−	0.706185i	0.257560	−	0.966262i	$-0.417081\pi$
$661$	534419.	−	308547.i	1.22315	−	0.706185i	0.965588	+	0.260077i	$0.0837481\pi$
$662$		0			0
$663$	508125.	−	880098.i	1.15596	−	2.00218i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	256304.	+	147977.i	0.576107	+	0.332616i
$668$		0			0
$669$	169760.	+	294033.i	0.379300	+	0.656968i
$670$		0			0
$671$		−	191064.i		−	0.424358i
$672$		0			0
$673$			624802.i			1.37947i	0.724062	+	0.689735i	$0.242273\pi$
$673$			624802.i			1.37947i	−0.724062	+	0.689735i	$0.757727\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−92525.5	+	160259.i	−0.201876	+	0.349659i	−0.949133	−	0.314876i	$-0.898037\pi$
$677$	−92525.5	+	160259.i	−0.201876	+	0.349659i	0.747257	+	0.664535i	$0.231370\pi$
$678$		0			0
$679$	−228967.	+	262035.i	−0.496631	+	0.568355i
$680$		0			0
$681$	−3552.40	+	6152.94i	−0.00765998	+	0.0132675i
$682$		0			0
$683$	620426.	−	358203.i	1.32999	−	0.767870i	0.344692	−	0.938716i	$-0.387983\pi$
$683$	620426.	−	358203.i	1.32999	−	0.767870i	0.985298	+	0.170846i	$0.0546500\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	157183.i		−	0.333037i
$688$		0			0
$689$	1.51355e6	−	873846.i	3.18828	−	1.84076i
$690$		0			0
$691$	550552.	+	317861.i	1.15303	+	0.665704i	0.949625	−	0.313390i	$-0.101465\pi$
$691$	550552.	+	317861.i	1.15303	+	0.665704i	0.203409	+	0.979094i	$0.434798\pi$
$692$		0			0
$693$	−37750.0	+	43201.9i	−0.0786050	+	0.0899573i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−8800.51	+	5080.98i	−0.0181152	+	0.0104588i
$698$		0			0
$699$			242267.i			0.495838i
$700$		0			0
$701$	−54574.0			−0.111058			−0.0555290	−	0.998457i	$-0.517685\pi$
$701$	−54574.0			−0.111058			−0.0555290	+	0.998457i	$0.517685\pi$
$702$		0			0
$703$	67422.6	+	116779.i	0.136425	+	0.236296i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	34169.1	−	173407.i	0.0683589	−	0.346919i
$708$		0			0
$709$	−170368.	+	295086.i	−0.338919	+	0.587024i	−0.984230	−	0.176896i	$-0.943394\pi$
$709$	−170368.	+	295086.i	−0.338919	+	0.587024i	0.645311	+	0.763920i	$0.276728\pi$
$710$		0			0
$711$	101204.	+	175291.i	0.200198	+	0.346752i
$712$		0			0
$713$	313148.			0.615985
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−224257.	−	388425.i	−0.436223	−	0.755560i
$718$		0			0
$719$	−200103.	−	115530.i	−0.387076	−	0.223478i	0.293816	−	0.955862i	$-0.405075\pi$
$719$	−200103.	−	115530.i	−0.387076	−	0.223478i	−0.680892	+	0.732383i	$0.738408\pi$
$720$		0			0
$721$	32445.7	+	95020.7i	0.0624146	+	0.182788i
$722$		0			0
$723$	−327867.	−	189294.i	−0.627222	−	0.362127i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−149550.			−0.282955			−0.141477	−	0.989941i	$-0.545185\pi$
$727$	−149550.			−0.282955			−0.141477	+	0.989941i	$0.545185\pi$
$728$		0			0
$729$	456116.			0.858264
$730$		0			0
$731$	−802300.	+	463208.i	−1.50142	+	0.866845i
$732$		0			0
$733$	144720.	−	250662.i	0.269352	−	0.466532i	−0.699342	−	0.714787i	$-0.746524\pi$
$733$	144720.	−	250662.i	0.269352	−	0.466532i	0.968695	+	0.248255i	$0.0798571\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	161692.	+	93352.9i	0.297682	+	0.171867i
$738$		0			0
$739$	263530.	+	456448.i	0.482550	+	0.835800i	0.999799	−	0.0200341i	$-0.00637747\pi$
$739$	263530.	+	456448.i	0.482550	+	0.835800i	−0.517250	+	0.855835i	$0.673044\pi$
$740$		0			0
$741$		−	377018.i		−	0.686634i
$742$		0			0
$743$			464605.i			0.841602i	0.907153	+	0.420801i	$0.138251\pi$
$743$			464605.i			0.841602i	−0.907153	+	0.420801i	$0.861749\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	91787.3	−	158980.i	0.164491	−	0.284906i
$748$		0			0
$749$	629347.	−	214896.i	1.12183	−	0.383058i
$750$		0			0
$751$	−165782.	+	287143.i	−0.293940	+	0.509119i	−0.974738	−	0.223353i	$-0.928300\pi$
$751$	−165782.	+	287143.i	−0.293940	+	0.509119i	0.680798	+	0.732471i	$0.261633\pi$
$752$		0			0
$753$	61552.0	−	35537.1i	0.108556	−	0.0626746i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	202873.i		−	0.354025i	−0.984209	−	0.177012i	$-0.943357\pi$
$757$		−	202873.i		−	0.354025i	0.984209	−	0.177012i	$-0.0566432\pi$
$758$		0			0
$759$	62594.9	−	36139.2i	0.108656	−	0.0627328i
$760$		0			0
$761$	−611918.	−	353291.i	−1.05663	−	0.610046i	−0.132133	−	0.991232i	$-0.542183\pi$
$761$	−611918.	−	353291.i	−1.05663	−	0.610046i	−0.924499	+	0.381186i	$0.875516\pi$
$762$		0			0
$763$	−392742.	−	77388.2i	−0.674618	−	0.132931i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.49792e6	−	864823.i	2.54623	−	1.47006i
$768$		0			0
$769$			367720.i			0.621820i	0.950439	+	0.310910i	$0.100634\pi$
$769$			367720.i			0.621820i	−0.950439	+	0.310910i	$0.899366\pi$
$770$		0			0
$771$	419116.			0.705059
$772$		0			0
$773$	6593.12	+	11419.6i	0.0110340	+	0.0191114i	0.871490	−	0.490414i	$-0.163154\pi$
$773$	6593.12	+	11419.6i	0.0110340	+	0.0191114i	−0.860456	+	0.509525i	$0.829821\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	169238.	+	147881.i	0.280321	+	0.244946i
$778$		0			0
$779$	−1884.99	+	3264.90i	−0.00310623	+	0.00538015i
$780$		0			0
$781$	56559.8	+	97964.5i	0.0927270	+	0.160608i
$782$		0			0
$783$	−564536.			−0.920806
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−244709.	−	423849.i	−0.395094	−	0.684323i	0.598019	−	0.801482i	$-0.295955\pi$
$787$	−244709.	−	423849.i	−0.395094	−	0.684323i	−0.993113	+	0.117159i	$0.962621\pi$
$788$		0			0
$789$	305893.	+	176608.i	0.491378	+	0.283697i
$790$		0			0
$791$	140417.	+	122697.i	0.224423	+	0.196102i
$792$		0			0
$793$	−1.88165e6	−	1.08637e6i	−2.99221	−	1.72755i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	720256.			1.13389			0.566944	−	0.823756i	$-0.308126\pi$
$797$	720256.			1.13389			0.566944	+	0.823756i	$0.308126\pi$
$798$		0			0
$799$	1.89143e6			2.96276
$800$		0			0
$801$	481731.	−	278127.i	0.750826	−	0.433490i
$802$		0			0
$803$	124823.	−	216200.i	0.193581	−	0.335293i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	400745.	+	231370.i	0.615349	+	0.355272i
$808$		0			0
$809$	129195.	+	223772.i	0.197400	+	0.341908i	0.947685	−	0.319208i	$-0.103417\pi$
$809$	129195.	+	223772.i	0.197400	+	0.341908i	−0.750284	+	0.661115i	$0.770083\pi$
$810$		0			0
$811$			553771.i			0.841954i	0.907071	+	0.420977i	$0.138313\pi$
$811$			553771.i			0.841954i	−0.907071	+	0.420977i	$0.861687\pi$
$812$		0			0
$813$		−	89470.8i		−	0.135363i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−171845.	+	297645.i	−0.257451	+	0.445917i
$818$		0			0
$819$	210822.	+	617415.i	0.314302	+	0.920469i
$820$		0			0
$821$	−168896.	+	292536.i	−0.250572	+	0.434003i	−0.963683	−	0.267048i	$-0.913952\pi$
$821$	−168896.	+	292536.i	−0.250572	+	0.434003i	0.713112	+	0.701050i	$0.247285\pi$
$822$		0			0
$823$	820673.	−	473816.i	1.21163	−	0.699536i	0.248517	−	0.968628i	$-0.420057\pi$
$823$	820673.	−	473816.i	1.21163	−	0.699536i	0.963114	+	0.269092i	$0.0867236\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	163948.i		−	0.239715i	−0.992791	−	0.119857i	$-0.961756\pi$
$827$		−	163948.i		−	0.239715i	0.992791	−	0.119857i	$-0.0382437\pi$
$828$		0			0
$829$	−394627.	+	227838.i	−0.574219	+	0.331525i	−0.758833	−	0.651286i	$-0.774230\pi$
$829$	−394627.	+	227838.i	−0.574219	+	0.331525i	0.184614	+	0.982811i	$0.440897\pi$
$830$		0			0
$831$	−539587.	−	311531.i	−0.781375	−	0.451127i
$832$		0			0
$833$	−948964.	+	733597.i	−1.36760	+	1.05723i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−517306.	+	298666.i	−0.738408	+	0.426320i
$838$		0			0
$839$		−	1.16012e6i		−	1.64809i	−0.566526	−	0.824044i	$-0.691713\pi$
$839$		−	1.16012e6i		−	1.64809i	0.566526	−	0.824044i	$-0.308287\pi$
$840$		0			0
$841$	−170758.			−0.241429
$842$		0			0
$843$	183217.	+	317341.i	0.257816	+	0.446551i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	219073.	+	641580.i	0.305367	+	0.894302i
$848$		0			0
$849$	−28019.9	+	48531.9i	−0.0388733	+	0.0673305i
$850$		0			0
$851$	146988.	+	254591.i	0.202966	+	0.351547i
$852$		0			0
$853$	937108.			1.28793			0.643964	−	0.765056i	$-0.277289\pi$
$853$	937108.			1.28793			0.643964	+	0.765056i	$0.277289\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−335586.	−	581252.i	−0.456922	−	0.791412i	0.541875	−	0.840459i	$-0.317715\pi$
$857$	−335586.	−	581252.i	−0.456922	−	0.791412i	−0.998796	+	0.0490476i	$0.984381\pi$
$858$		0			0
$859$	−50992.8	−	29440.7i	−0.0691071	−	0.0398990i	0.465048	−	0.885285i	$-0.346037\pi$
$859$	−50992.8	−	29440.7i	−0.0691071	−	0.0398990i	−0.534155	+	0.845386i	$0.679370\pi$
$860$		0			0
$861$	−1214.75	+	6164.83i	−0.00163863	+	0.00831601i
$862$		0			0
$863$	638608.	+	368701.i	0.857458	+	0.495054i	0.863160	−	0.504930i	$-0.168482\pi$
$863$	638608.	+	368701.i	0.857458	+	0.495054i	−0.00570214	+	0.999984i	$0.501815\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1.04674e6			−1.39251
$868$		0			0
$869$	−139207.			−0.184341
$870$		0			0
$871$	1.83873e6	−	1.06159e6i	2.42372	−	1.39933i
$872$		0			0
$873$	146507.	−	253757.i	0.192234	−	0.332959i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−433203.	−	250110.i	−0.563238	−	0.325186i	0.191206	−	0.981550i	$-0.438760\pi$
$877$	−433203.	−	250110.i	−0.563238	−	0.325186i	−0.754444	+	0.656364i	$0.772093\pi$
$878$		0			0
$879$	−235168.	−	407322.i	−0.304368	−	0.527182i
$880$		0			0
$881$			92648.1i			0.119367i	0.998217	+	0.0596836i	$0.0190092\pi$
$881$			92648.1i			0.119367i	−0.998217	+	0.0596836i	$0.980991\pi$
$882$		0			0
$883$		−	1.16488e6i		−	1.49403i	−0.664810	−	0.747013i	$-0.731487\pi$
$883$		−	1.16488e6i		−	1.49403i	0.664810	−	0.747013i	$-0.268513\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−156053.	+	270292.i	−0.198347	+	0.343547i	−0.947993	−	0.318292i	$-0.896891\pi$
$887$	−156053.	+	270292.i	−0.198347	+	0.343547i	0.749646	+	0.661840i	$0.230224\pi$
$888$		0			0
$889$	1.09792e6	+	959366.i	1.38921	+	1.21389i
$890$		0			0
$891$	−21516.8	+	37268.1i	−0.0271033	+	0.0469442i
$892$		0			0
$893$	607691.	−	350851.i	0.762044	−	0.439966i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	821936.i		−	1.02154i
$898$		0			0
$899$	491636.	−	283846.i	0.608309	−	0.351207i
$900$		0			0
$901$	−2.34311e6	−	1.35279e6i	−2.88631	−	1.66641i
$902$		0			0
$903$	−110743.	+	562018.i	−0.135813	+	0.689247i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−461241.	+	266298.i	−0.560678	+	0.323708i	−0.753418	−	0.657542i	$-0.771596\pi$
$907$	−461241.	+	266298.i	−0.560678	+	0.323708i	0.192740	+	0.981250i	$0.438263\pi$
$908$		0			0
$909$			148825.i			0.180114i
$910$		0			0
$911$	−327869.			−0.395060			−0.197530	−	0.980297i	$-0.563292\pi$
$911$	−327869.			−0.395060			−0.197530	+	0.980297i	$0.563292\pi$
$912$		0			0
$913$	63127.0	+	109339.i	0.0757310	+	0.131170i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	278684.	−	95159.0i	0.331416	−	0.113165i
$918$		0			0
$919$	−504033.	+	873011.i	−0.596799	+	1.03369i	0.396491	+	0.918038i	$0.370228\pi$
$919$	−504033.	+	873011.i	−0.596799	+	1.03369i	−0.993290	+	0.115648i	$0.963106\pi$
$920$		0			0
$921$	209081.	+	362140.i	0.246488	+	0.426930i
$922$		0			0
$923$	1.28638e6			1.50996
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−42274.0	−	73220.6i	−0.0491941	−	0.0852067i
$928$		0			0
$929$	−280859.	−	162154.i	−0.325430	−	0.187887i	0.328380	−	0.944546i	$-0.393497\pi$
$929$	−280859.	−	162154.i	−0.325430	−	0.187887i	−0.653810	+	0.756659i	$0.726831\pi$
$930$		0			0
$931$	−168811.	+	411723.i	−0.194761	+	0.475013i
$932$		0			0
$933$	−575168.	−	332074.i	−0.660742	−	0.381479i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	651900.			0.742510			0.371255	−	0.928531i	$-0.378928\pi$
$937$	651900.			0.742510			0.371255	+	0.928531i	$0.378928\pi$
$938$		0			0
$939$	39533.6			0.0448368
$940$		0			0
$941$	430681.	−	248654.i	0.486380	−	0.280812i	−0.236691	−	0.971585i	$-0.576063\pi$
$941$	430681.	−	248654.i	0.486380	−	0.280812i	0.723072	+	0.690773i	$0.242730\pi$
$942$		0			0
$943$	−4109.46	+	7117.80i	−0.00462127	+	0.00800428i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	18192.0	+	10503.2i	0.0202853	+	0.0117117i	0.510108	−	0.860110i	$-0.329605\pi$
$947$	18192.0	+	10503.2i	0.0202853	+	0.0117117i	−0.489823	+	0.871822i	$0.662939\pi$
$948$		0			0
$949$	−1.41947e6	−	2.45859e6i	−1.57613	−	2.72994i
$950$		0			0
$951$			696063.i			0.769640i
$952$		0			0
$953$			935565.i			1.03012i	0.857154	+	0.515060i	$0.172231\pi$
$953$			935565.i			1.03012i	−0.857154	+	0.515060i	$0.827769\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	65515.2	−	113476.i	0.0715349	−	0.123902i
$958$		0			0
$959$	22249.7	−	112917.i	0.0241929	−	0.122778i
$960$		0			0
$961$	−161424.	+	279595.i	−0.174792	+	0.302749i
$962$		0			0
$963$	−484959.	+	279991.i	−0.522941	+	0.301920i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	602673.i		−	0.644509i	−0.946653	−	0.322255i	$-0.895559\pi$
$967$		−	602673.i		−	0.644509i	0.946653	−	0.322255i	$-0.104441\pi$
$968$		0			0
$969$	−505463.	+	291829.i	−0.538322	+	0.310800i
$970$		0			0
$971$	−1.27656e6	−	737020.i	−1.35395	−	0.781701i	−0.365147	−	0.930950i	$-0.618981\pi$
$971$	−1.27656e6	−	737020.i	−1.35395	−	0.781701i	−0.988800	+	0.149249i	$0.952315\pi$
$972$		0			0
$973$	−331417.	−	289593.i	−0.350065	−	0.305888i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	586613.	−	338681.i	0.614558	−	0.354815i	−0.160189	−	0.987086i	$-0.551211\pi$
$977$	586613.	−	338681.i	0.614558	−	0.354815i	0.774747	+	0.632271i	$0.217877\pi$
$978$		0			0
$979$			382566.i			0.399155i
$980$		0			0
$981$	337067.			0.350250
$982$		0			0
$983$	603535.	+	1.04535e6i	0.624590	+	1.08182i	0.988620	+	0.150435i	$0.0480674\pi$
$983$	603535.	+	1.04535e6i	0.624590	+	1.08182i	−0.364030	+	0.931387i	$0.618599\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	769535.	−	880672.i	0.789940	−	0.904024i
$988$		0			0
$989$	−374640.	+	648896.i	−0.383020	+	0.663410i
$990$		0			0
$991$	747522.	+	1.29475e6i	0.761161	+	1.31837i	0.942253	+	0.334903i	$0.108704\pi$
$991$	747522.	+	1.29475e6i	0.761161	+	1.31837i	−0.181092	+	0.983466i	$0.557963\pi$
$992$		0			0
$993$	793412.			0.804638
$994$		0			0
$995$		0			0
$996$		0			0
$997$	139754.	+	242061.i	0.140597	+	0.243520i	0.927721	−	0.373273i	$-0.121765\pi$
$997$	139754.	+	242061.i	0.140597	+	0.243520i	−0.787125	+	0.616794i	$0.788431\pi$
$998$		0			0
$999$	−485635.	−	280381.i	−0.486607	−	0.280943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.5.o.c.649.15		44
5.2	odd	4		700.5.s.c.201.8	yes	22
5.3	odd	4		700.5.s.d.201.4	yes	22
5.4	even	2	inner	700.5.o.c.649.8		44
7.3	odd	6	inner	700.5.o.c.549.8		44
35.3	even	12		700.5.s.d.101.4	yes	22
35.17	even	12		700.5.s.c.101.8	✓	22
35.24	odd	6	inner	700.5.o.c.549.15		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.5.o.c.549.8		44	7.3	odd	6	inner
700.5.o.c.549.15		44	35.24	odd	6	inner
700.5.o.c.649.8		44	5.4	even	2	inner
700.5.o.c.649.15		44	1.1	even	1	trivial
700.5.s.c.101.8	✓	22	35.17	even	12
700.5.s.c.201.8	yes	22	5.2	odd	4
700.5.s.d.101.4	yes	22	35.3	even	12
700.5.s.d.201.4	yes	22	5.3	odd	4

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	700.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.15197 + 5.45937i) q^{3} +(-32.2417 + 36.8981i) q^{7} +(20.6302 - 35.7325i) q^{9} +(14.1885 + 24.5752i) q^{11} +322.698 q^{13} +(-249.783 - 432.637i) q^{17} +(-160.504 - 92.6668i) q^{19} +(-303.066 - 59.7178i) q^{21} +(-349.914 - 202.023i) q^{23} +770.722 q^{27} -732.477 q^{29} +(-671.196 + 387.515i) q^{31} +(-89.4433 + 154.920i) q^{33} +(-630.104 - 363.791i) q^{37} +(1017.13 + 1761.73i) q^{39} -20.3416i q^{41} -1854.44i q^{43} +(-1893.08 + 3278.90i) q^{47} +(-321.943 - 2379.32i) q^{49} +(1574.62 - 2727.31i) q^{51} +(4690.29 - 2707.94i) q^{53} -1168.33i q^{57} +(4641.86 - 2679.98i) q^{59} +(-5830.99 - 3366.53i) q^{61} +(653.310 + 1913.29i) q^{63} +(5698.00 - 3289.74i) q^{67} -2547.08i q^{69} +3986.32 q^{71} +(-4398.75 - 7618.86i) q^{73} +(-1364.24 - 268.817i) q^{77} +(-2452.82 + 4248.41i) q^{79} +(758.248 + 1313.32i) q^{81} +4449.18 q^{83} +(-2308.75 - 3998.87i) q^{87} +(11675.4 + 6740.79i) q^{89} +(-10404.3 + 11906.9i) q^{91} +(-4231.18 - 2442.87i) q^{93} +7101.58 q^{97} +1170.84 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 684 q^{9} - 300 q^{11} + 540 q^{19} - 190 q^{21} - 528 q^{29} - 2334 q^{31} - 852 q^{39} + 4092 q^{49} - 3902 q^{51} + 9414 q^{59} - 23598 q^{61} + 32820 q^{71} - 4890 q^{79} - 23710 q^{81} - 37764 q^{89}+ \cdots + 168180 q^{99}+O(q^{100}) \) 44 * q - 684 * q^9 - 300 * q^11 + 540 * q^19 - 190 * q^21 - 528 * q^29 - 2334 * q^31 - 852 * q^39 + 4092 * q^49 - 3902 * q^51 + 9414 * q^59 - 23598 * q^61 + 32820 * q^71 - 4890 * q^79 - 23710 * q^81 - 37764 * q^89 + 6418 * q^91 + 168180 * q^99

Introduction

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