LMFDB - Embedded newform 700.5.s.d.201.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,5,Mod(101,700)]

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, 0, 1]))

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

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

chi := DirichletCharacter("700.101");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	700.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$72.3589741587$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			201.4
Character	$\chi$	$=$	700.201
Dual form			700.5.s.d.101.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.45937 + 3.15197i) q^{3} +(36.8981 + 32.2417i) q^{7} +(-20.6302 + 35.7325i) q^{9} +(14.1885 + 24.5752i) q^{11} +322.698i q^{13} +(-432.637 + 249.783i) q^{17} +(160.504 + 92.6668i) q^{19} +(-303.066 - 59.7178i) q^{21} +(202.023 - 349.914i) q^{23} -770.722i q^{27} +732.477 q^{29} +(-671.196 + 387.515i) q^{31} +(-154.920 - 89.4433i) q^{33} +(-363.791 + 630.104i) q^{37} +(-1017.13 - 1761.73i) q^{39} -20.3416i q^{41} +1854.44 q^{43} +(3278.90 + 1893.08i) q^{47} +(321.943 + 2379.32i) q^{49} +(1574.62 - 2727.31i) q^{51} +(2707.94 + 4690.29i) q^{53} -1168.33 q^{57} +(-4641.86 + 2679.98i) q^{59} +(-5830.99 - 3366.53i) q^{61} +(-1913.29 + 653.310i) q^{63} +(-3289.74 - 5698.00i) q^{67} +2547.08i q^{69} +3986.32 q^{71} +(7618.86 - 4398.75i) q^{73} +(-268.817 + 1364.24i) q^{77} +(2452.82 - 4248.41i) q^{79} +(758.248 + 1313.32i) q^{81} +4449.18i q^{83} +(-3998.87 + 2308.75i) q^{87} +(-11675.4 - 6740.79i) q^{89} +(-10404.3 + 11906.9i) q^{91} +(2442.87 - 4231.18i) q^{93} -7101.58i q^{97} -1170.84 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 9 q^{3} + 66 q^{7} + 342 q^{9} - 150 q^{11} - 432 q^{17} - 270 q^{19} - 95 q^{21} + 333 q^{23} + 264 q^{29} - 1167 q^{31} + 192 q^{33} + 930 q^{37} + 426 q^{39} + 4162 q^{43} - 6822 q^{47} - 2046 q^{49}+ \cdots - 84090 q^{99}+O(q^{100}) $ 22 * q + 9 * q^3 + 66 * q^7 + 342 * q^9 - 150 * q^11 - 432 * q^17 - 270 * q^19 - 95 * q^21 + 333 * q^23 + 264 * q^29 - 1167 * q^31 + 192 * q^33 + 930 * q^37 + 426 * q^39 + 4162 * q^43 - 6822 * q^47 - 2046 * q^49 - 1951 * q^51 + 1776 * q^53 + 13866 * q^57 - 4707 * q^59 - 11799 * q^61 + 13393 * q^63 - 4926 * q^67 + 16410 * q^71 - 3108 * q^73 + 12585 * q^77 + 2445 * q^79 - 11855 * q^81 - 38151 * q^87 + 18882 * q^89 + 3209 * q^91 + 5504 * q^93 - 84090 * 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
$3$	−5.45937	+	3.15197i	−0.606597	+	0.350219i	−0.771632	−	0.636069i	$-0.780559\pi$
$3$	−5.45937	+	3.15197i	−0.606597	+	0.350219i	0.165036	+	0.986288i	$0.447226\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	36.8981	+	32.2417i	0.753023	+	0.657994i
$7$	36.8981	+	32.2417i	0.753023	+	0.657994i
$8$		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
$13$			322.698i			1.90945i	0.297485	+	0.954727i	$0.403852\pi$
$13$			322.698i			1.90945i	−0.297485	+	0.954727i	$0.596148\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−432.637	+	249.783i	−1.49701	+	0.864301i	−0.999994	−	0.00343955i	$-0.998905\pi$
$17$	−432.637	+	249.783i	−1.49701	+	0.864301i	−0.497018	+	0.867740i	$0.665572\pi$
$18$		0			0
$19$	160.504	+	92.6668i	0.444608	+	0.256695i	0.705550	−	0.708660i	$-0.250700\pi$
$19$	160.504	+	92.6668i	0.444608	+	0.256695i	−0.260942	+	0.965354i	$0.584033\pi$
$20$		0			0
$21$	−303.066	−	59.7178i	−0.687223	−	0.135414i
$22$		0			0
$23$	202.023	−	349.914i	0.381896	−	0.661463i	−0.609438	−	0.792834i	$-0.708605\pi$
$23$	202.023	−	349.914i	0.381896	−	0.661463i	0.991333	+	0.131371i	$0.0419380\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	770.722i		−	1.05723i
$28$		0			0
$29$	732.477			0.870960			0.435480	−	0.900198i	$-0.356579\pi$
$29$	732.477			0.870960			0.435480	+	0.900198i	$0.356579\pi$
$30$		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
$33$	−154.920	−	89.4433i	−0.142259	−	0.0821334i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−363.791	+	630.104i	−0.265735	+	0.460266i	−0.967756	−	0.251890i	$-0.918948\pi$
$37$	−363.791	+	630.104i	−0.265735	+	0.460266i	0.702021	+	0.712156i	$0.252281\pi$
$38$		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
$43$	1854.44			1.00294			0.501472	−	0.865174i	$-0.332792\pi$
$43$	1854.44			1.00294			0.501472	+	0.865174i	$0.332792\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3278.90	+	1893.08i	1.48434	+	0.856983i	0.999841	−	0.0178095i	$-0.00566923\pi$
$47$	3278.90	+	1893.08i	1.48434	+	0.856983i	0.484497	+	0.874793i	$0.339003\pi$
$48$		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
$53$	2707.94	+	4690.29i	0.964023	+	1.66974i	0.712217	+	0.701959i	$0.247691\pi$
$53$	2707.94	+	4690.29i	0.964023	+	1.66974i	0.251806	+	0.967778i	$0.418976\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1168.33			−0.359597
$58$		0			0
$59$	−4641.86	+	2679.98i	−1.33348	+	0.769888i	−0.985832	−	0.167736i	$-0.946354\pi$
$59$	−4641.86	+	2679.98i	−1.33348	+	0.769888i	−0.347653	+	0.937623i	$0.613021\pi$
$60$		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
$63$	−1913.29	+	653.310i	−0.482059	+	0.164603i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−3289.74	−	5698.00i	−0.732845	−	1.26933i	−0.955662	−	0.294465i	$-0.904859\pi$
$67$	−3289.74	−	5698.00i	−0.732845	−	1.26933i	0.222817	−	0.974860i	$-0.428475\pi$
$68$		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
$73$	7618.86	−	4398.75i	1.42970	−	0.825436i	0.432601	−	0.901586i	$-0.357596\pi$
$73$	7618.86	−	4398.75i	1.42970	−	0.825436i	0.997096	+	0.0761494i	$0.0242626\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−268.817	+	1364.24i	−0.0453394	+	0.230096i
$78$		0			0
$79$	2452.82	−	4248.41i	0.393017	−	0.680725i	−0.599829	−	0.800128i	$-0.704765\pi$
$79$	2452.82	−	4248.41i	0.393017	−	0.680725i	0.992846	+	0.119403i	$0.0380981\pi$
$80$		0			0
$81$	758.248	+	1313.32i	0.115569	+	0.200171i
$82$		0			0
$83$			4449.18i			0.645838i	0.946427	+	0.322919i	$0.104664\pi$
$83$			4449.18i			0.645838i	−0.946427	+	0.322919i	$0.895336\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−3998.87	+	2308.75i	−0.528322	+	0.305027i
$88$		0			0
$89$	−11675.4	−	6740.79i	−1.47398	−	0.851003i	−0.474410	−	0.880304i	$-0.657338\pi$
$89$	−11675.4	−	6740.79i	−1.47398	−	0.851003i	−0.999571	+	0.0293012i	$0.990672\pi$
$90$		0			0
$91$	−10404.3	+	11906.9i	−1.25641	+	1.43786i
$92$		0			0
$93$	2442.87	−	4231.18i	0.282446	−	0.489210i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	7101.58i		−	0.754765i	−0.926057	−	0.377382i	$-0.876824\pi$
$97$		−	7101.58i		−	0.754765i	0.926057	−	0.377382i	$-0.123176\pi$
$98$		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
$103$	1774.60	+	1024.57i	0.167273	+	0.0965752i	0.581299	−	0.813690i	$-0.302545\pi$
$103$	1774.60	+	1024.57i	0.167273	+	0.0965752i	−0.414026	+	0.910265i	$0.635878\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6785.97	+	11753.6i	−0.592713	+	1.02661i	0.401152	+	0.916011i	$0.368610\pi$
$107$	−6785.97	+	11753.6i	−0.592713	+	1.02661i	−0.993865	+	0.110598i	$0.964724\pi$
$108$		0			0
$109$	−4084.63	−	7074.79i	−0.343795	−	0.595471i	0.641339	−	0.767258i	$-0.278379\pi$
$109$	−4084.63	−	7074.79i	−0.343795	−	0.595471i	−0.985134	+	0.171787i	$0.945046\pi$
$110$		0			0
$111$		−	4586.63i		−	0.372261i
$112$		0			0
$113$	3805.54			0.298029			0.149015	−	0.988835i	$-0.452390\pi$
$113$	3805.54			0.298029			0.149015	+	0.988835i	$0.452390\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−11530.8	−	6657.31i	−0.842340	−	0.486325i
$118$		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
$123$	64.1160	+	111.052i	0.00423796	+	0.00734035i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−29755.4			−1.84484			−0.922420	−	0.386189i	$-0.873791\pi$
$127$	−29755.4			−1.84484			−0.922420	+	0.386189i	$0.873791\pi$
$128$		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
$133$	2934.54	+	8594.15i	0.165897	+	0.485847i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1174.37	+	2034.06i	0.0625694	+	0.108373i	0.895613	−	0.444834i	$-0.146737\pi$
$137$	1174.37	+	2034.06i	0.0625694	+	0.108373i	−0.833044	+	0.553207i	$0.813404\pi$
$138$		0			0
$139$		−	8981.94i		−	0.464880i	−0.972611	−	0.232440i	$-0.925329\pi$
$139$		−	8981.94i		−	0.464880i	0.972611	−	0.232440i	$-0.0746709\pi$
$140$		0			0
$141$	−23867.7			−1.20053
$142$		0			0
$143$	−7930.34	+	4578.59i	−0.387811	+	0.223903i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−9257.14	−	11974.8i	−0.428393	−	0.554159i
$148$		0			0
$149$	−8669.18	+	15015.5i	−0.390486	+	0.676342i	−0.992514	−	0.122133i	$-0.961026\pi$
$149$	−8669.18	+	15015.5i	−0.390486	+	0.676342i	0.602028	+	0.798475i	$0.294360\pi$
$150$		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
$153$		−	20612.3i		−	0.880527i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	7979.12	−	4606.75i	0.323710	−	0.186894i	−0.329335	−	0.944213i	$-0.606825\pi$
$157$	7979.12	−	4606.75i	0.323710	−	0.186894i	0.653045	+	0.757319i	$0.273491\pi$
$158$		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
$163$	13622.1	−	23594.3i	0.512708	−	0.888037i	−0.487183	−	0.873300i	$-0.661976\pi$
$163$	13622.1	−	23594.3i	0.512708	−	0.888037i	0.999891	−	0.0147370i	$-0.00469111\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			4063.60i			0.145706i	0.997343	+	0.0728531i	$0.0232104\pi$
$167$			4063.60i			0.145706i	−0.997343	+	0.0728531i	$0.976790\pi$
$168$		0			0
$169$	−75572.7			−2.64601
$170$		0			0
$171$	−6622.44	+	3823.46i	−0.226478	+	0.130757i
$172$		0			0
$173$	39691.8	+	22916.1i	1.32620	+	0.765681i	0.984709	−	0.174205i	$-0.0557357\pi$
$173$	39691.8	+	22916.1i	1.32620	+	0.765681i	0.341488	+	0.939886i	$0.389069\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	16894.4	−	29262.0i	0.539258	−	0.934023i
$178$		0			0
$179$	−10965.3	−	18992.5i	−0.342228	−	0.592756i	0.642618	−	0.766186i	$-0.277848\pi$
$179$	−10965.3	−	18992.5i	−0.342228	−	0.592756i	−0.984846	+	0.173431i	$0.944515\pi$
$180$		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
$183$	42444.8			1.26742
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−12276.9	−	7088.08i	−0.351080	−	0.202696i
$188$		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
$193$	−20021.6	−	34678.4i	−0.537507	−	0.930989i	−0.999037	−	0.0438648i	$-0.986033\pi$
$193$	−20021.6	−	34678.4i	−0.537507	−	0.930989i	0.461531	−	0.887124i	$-0.347300\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−46320.3			−1.19355			−0.596773	−	0.802410i	$-0.703551\pi$
$197$	−46320.3			−1.19355			−0.596773	+	0.802410i	$0.703551\pi$
$198$		0			0
$199$	−14564.3	+	8408.71i	−0.367776	+	0.212336i	−0.672487	−	0.740109i	$-0.734774\pi$
$199$	−14564.3	+	8408.71i	−0.367776	+	0.212336i	0.304710	+	0.952445i	$0.401440\pi$
$200$		0			0
$201$	35919.9	+	20738.3i	0.889083	+	0.513312i
$202$		0			0
$203$	27027.0	+	23616.3i	0.655853	+	0.573087i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	8335.53	+	14437.6i	0.194533	+	0.336940i
$208$		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
$213$	−21762.8	+	12564.8i	−0.479685	+	0.276946i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−37260.0	−	7341.93i	−0.791268	−	0.155916i
$218$		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
$223$			53858.4i			1.08304i	0.840688	+	0.541519i	$0.182151\pi$
$223$			53858.4i			1.08304i	−0.840688	+	0.541519i	$0.817849\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	976.047	−	563.521i	0.0189417	−	0.0109360i	−0.490499	−	0.871442i	$-0.663186\pi$
$227$	976.047	−	563.521i	0.0189417	−	0.0109360i	0.509441	+	0.860506i	$0.329852\pi$
$228$		0			0
$229$	21593.5	+	12467.0i	0.411768	+	0.237735i	0.691549	−	0.722329i	$-0.256928\pi$
$229$	21593.5	+	12467.0i	0.411768	+	0.237735i	−0.279781	+	0.960064i	$0.590262\pi$
$230$		0			0
$231$	−2832.46	−	8295.19i	−0.0530812	−	0.155454i
$232$		0			0
$233$	−19215.5	+	33282.2i	−0.353948	+	0.613057i	−0.986937	−	0.161104i	$-0.948494\pi$
$233$	−19215.5	+	33282.2i	−0.353948	+	0.613057i	0.632989	+	0.774161i	$0.281828\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			30924.8i			0.550568i
$238$		0			0
$239$	71148.4			1.24557			0.622786	−	0.782392i	$-0.286001\pi$
$239$	71148.4			1.24557			0.622786	+	0.782392i	$0.286001\pi$
$240$		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
$243$	45785.5	+	26434.3i	0.775382	+	0.447667i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−29903.4	+	51794.1i	−0.490147	+	0.848959i
$248$		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
$253$	11465.6			0.179125
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−57577.5	−	33242.4i	−0.871739	−	0.503299i	−0.00381315	−	0.999993i	$-0.501214\pi$
$257$	−57577.5	−	33242.4i	−0.871739	−	0.503299i	−0.867926	+	0.496694i	$0.834547\pi$
$258$		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
$263$	28015.4	+	48524.1i	0.405029	+	0.701530i	0.994325	−	0.106387i	$-0.0339283\pi$
$263$	28015.4	+	48524.1i	0.405029	+	0.701530i	−0.589296	+	0.807917i	$0.700595\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	84987.1			1.19215
$268$		0			0
$269$	−63570.6	+	36702.5i	−0.878520	+	0.507214i	−0.870170	−	0.492751i	$-0.835991\pi$
$269$	−63570.6	+	36702.5i	−0.878520	+	0.507214i	−0.00834980	+	0.999965i	$0.502658\pi$
$270$		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
$273$	19270.8	−	97798.5i	0.258568	−	1.31222i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	49418.4	+	85595.2i	0.644065	+	1.11555i	0.984517	+	0.175291i	$0.0560865\pi$
$277$	49418.4	+	85595.2i	0.644065	+	1.11555i	−0.340452	+	0.940262i	$0.610580\pi$
$278$		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
$283$	−7698.66	+	4444.83i	−0.0961263	+	0.0554986i	−0.547293	−	0.836941i	$-0.684341\pi$
$283$	−7698.66	+	4444.83i	−0.0961263	+	0.0554986i	0.451166	+	0.892440i	$0.351008\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	655.847	−	750.566i	0.00796231	−	0.00911224i
$288$		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
$293$		−	74609.7i		−	0.869081i	−0.900652	−	0.434540i	$-0.856911\pi$
$293$		−	74609.7i		−	0.869081i	0.900652	−	0.434540i	$-0.143089\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	18940.6	−	10935.4i	0.214724	−	0.123971i
$298$		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
$303$	11369.1	−	19691.8i	0.123834	−	0.214486i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	66333.5i		−	0.703812i	−0.936035	−	0.351906i	$-0.885534\pi$
$307$		−	66333.5i		−	0.703812i	0.936035	−	0.351906i	$-0.114466\pi$
$308$		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
$313$	5431.06	+	3135.62i	0.0554365	+	0.0320063i	0.527462	−	0.849579i	$-0.323144\pi$
$313$	5431.06	+	3135.62i	0.0554365	+	0.0320063i	−0.472026	+	0.881585i	$0.656477\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	55208.6	−	95624.0i	0.549399	−	0.951587i	−0.448917	−	0.893574i	$-0.648190\pi$
$317$	55208.6	−	95624.0i	0.549399	−	0.951587i	0.998316	−	0.0580134i	$-0.0184766\pi$
$318$		0			0
$319$	10392.7	+	18000.7i	0.102129	+	0.176892i
$320$		0			0
$321$		−	85556.7i		−	0.830317i
$322$		0			0
$323$	−92586.3			−0.887446
$324$		0			0
$325$		0			0
$326$		0			0
$327$	44599.0	+	25749.3i	0.417090	+	0.240807i
$328$		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
$333$	−15010.1	−	25998.3i	−0.135362	−	0.234453i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	36428.0			0.320756			0.160378	−	0.987056i	$-0.448729\pi$
$337$	36428.0			0.320756			0.160378	+	0.987056i	$0.448729\pi$
$338$		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
$343$	−64834.2	+	98172.3i	−0.551082	+	0.834451i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−49208.2	−	85231.1i	−0.408675	−	0.707846i	0.586066	−	0.810263i	$-0.300676\pi$
$347$	−49208.2	−	85231.1i	−0.408675	−	0.707846i	−0.994742	+	0.102417i	$0.967342\pi$
$348$		0			0
$349$			87986.1i			0.722376i	0.932493	+	0.361188i	$0.117629\pi$
$349$			87986.1i			0.722376i	−0.932493	+	0.361188i	$0.882371\pi$
$350$		0			0
$351$	248710.			2.01873
$352$		0			0
$353$	−146757.	+	84730.1i	−1.17774	+	0.679968i	−0.955490	−	0.295022i	$-0.904673\pi$
$353$	−146757.	+	84730.1i	−1.17774	+	0.679968i	−0.222248	+	0.974990i	$0.571340\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	146034.	−	49864.5i	1.14582	−	0.391250i
$358$		0			0
$359$	48155.7	−	83408.1i	0.373644	−	0.647171i	−0.616479	−	0.787372i	$-0.711441\pi$
$359$	48155.7	−	83408.1i	0.373644	−	0.647171i	0.990123	+	0.140200i	$0.0447747\pi$
$360$		0			0
$361$	−47986.2	−	83114.6i	−0.368216	−	0.637768i
$362$		0			0
$363$			87219.7i			0.661914i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−8286.43	+	4784.17i	−0.0615227	+	0.0355201i	−0.530446	−	0.847719i	$-0.677975\pi$
$367$	−8286.43	+	4784.17i	−0.0615227	+	0.0355201i	0.468923	+	0.883239i	$0.344642\pi$
$368$		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
$373$	71247.2	−	123404.i	0.512095	−	0.886974i	−0.487807	−	0.872951i	$-0.662203\pi$
$373$	71247.2	−	123404.i	0.512095	−	0.886974i	0.999902	−	0.0140223i	$-0.00446359\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			236369.i			1.66306i
$378$		0			0
$379$	203100.			1.41394			0.706970	−	0.707243i	$-0.250061\pi$
$379$	203100.			1.41394			0.706970	+	0.707243i	$0.250061\pi$
$380$		0			0
$381$	162446.	−	93788.2i	1.11907	−	0.646097i
$382$		0			0
$383$	−148795.	−	85906.7i	−1.01435	−	0.585638i	−0.101891	−	0.994796i	$-0.532489\pi$
$383$	−148795.	−	85906.7i	−1.01435	−	0.585638i	−0.912464	+	0.409158i	$0.865823\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−38257.5	+	66263.9i	−0.255443	+	0.442441i
$388$		0			0
$389$	−21093.4	−	36534.9i	−0.139395	−	0.241440i	0.787873	−	0.615838i	$-0.211182\pi$
$389$	−21093.4	−	36534.9i	−0.139395	−	0.241440i	−0.927268	+	0.374399i	$0.877849\pi$
$390$		0			0
$391$			201847.i			1.32029i
$392$		0			0
$393$	37885.7			0.245296
$394$		0			0
$395$		0			0
$396$		0			0
$397$	213423.	+	123220.i	1.35413	+	0.781808i	0.988825	−	0.149080i	$-0.0476313\pi$
$397$	213423.	+	123220.i	1.35413	+	0.781808i	0.365305	+	0.930888i	$0.380965\pi$
$398$		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
$403$	−125050.	−	216593.i	−0.769971	−	1.33363i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−20646.5			−0.124640
$408$		0			0
$409$	151468.	−	87449.9i	0.905468	−	0.522772i	0.0264978	−	0.999649i	$-0.491564\pi$
$409$	151468.	−	87449.9i	0.905468	−	0.522772i	0.878970	+	0.476877i	$0.158231\pi$
$410$		0			0
$411$	−12822.6	−	7403.13i	−0.0759088	−	0.0438260i
$412$		0			0
$413$	−257683.	−	50775.4i	−1.51073	−	0.297682i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	28310.8	+	49035.8i	0.162810	+	0.281995i
$418$		0			0
$419$		−	147615.i		−	0.840821i	−0.907334	−	0.420411i	$-0.861886\pi$
$419$		−	147615.i		−	0.840821i	0.907334	−	0.420411i	$-0.138114\pi$
$420$		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
$423$	−135289.	+	78109.0i	−0.756103	+	0.436536i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−106610.	−	312220.i	−0.584713	−	1.71240i
$428$		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
$433$		−	65473.0i		−	0.349210i	−0.984639	−	0.174605i	$-0.944135\pi$
$433$		−	65473.0i		−	0.349210i	0.984639	−	0.174605i	$-0.0558648\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	64850.8	−	37441.6i	0.339588	−	0.196061i
$438$		0			0
$439$	258048.	+	148984.i	1.33897	+	0.773057i	0.986655	−	0.162823i	$-0.0520599\pi$
$439$	258048.	+	148984.i	1.33897	+	0.773057i	0.352319	+	0.935880i	$0.385393\pi$
$440$		0			0
$441$	−91660.7	−	37581.9i	−0.471309	−	0.193242i
$442$		0			0
$443$	155448.	−	269244.i	0.792095	−	1.37195i	−0.132572	−	0.991173i	$-0.542323\pi$
$443$	155448.	−	269244.i	0.792095	−	1.37195i	0.924667	−	0.380776i	$-0.124343\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	109300.i		−	0.547023i
$448$		0			0
$449$	217824.			1.08047			0.540235	−	0.841514i	$-0.318335\pi$
$449$	217824.			1.08047			0.540235	+	0.841514i	$0.318335\pi$
$450$		0			0
$451$	499.897	−	288.616i	0.00245769	−	0.00141895i
$452$		0			0
$453$	−58471.0	−	33758.3i	−0.284934	−	0.164507i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−99566.6	+	172454.i	−0.476740	+	0.825738i	−0.999645	−	0.0266534i	$-0.991515\pi$
$457$	−99566.6	+	172454.i	−0.476740	+	0.825738i	0.522905	+	0.852391i	$0.324848\pi$
$458$		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.			−0.497252			−0.248626	−	0.968600i	$-0.579979\pi$
$463$	−106595.			−0.497252			−0.248626	+	0.968600i	$0.579979\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	82568.7	+	47671.0i	0.378601	+	0.218585i	0.677209	−	0.735790i	$-0.263189\pi$
$467$	82568.7	+	47671.0i	0.378601	+	0.218585i	−0.298609	+	0.954376i	$0.596522\pi$
$468$		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
$473$	26311.7	+	45573.3i	0.117605	+	0.203698i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−223461.			−0.982121
$478$		0			0
$479$	−67483.3	+	38961.5i	−0.294120	+	0.169811i	−0.639799	−	0.768543i	$-0.720982\pi$
$479$	−67483.3	+	38961.5i	−0.294120	+	0.169811i	0.345678	+	0.938353i	$0.387649\pi$
$480$		0			0
$481$	−203333.	−	117394.i	−0.878856	−	0.507408i
$482$		0			0
$483$	−82122.2	+	93982.4i	−0.352019	+	0.402858i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	118684.	+	205567.i	0.500419	+	0.866752i	1.00000		0.000484141i	$0.000154107\pi$
$487$	118684.	+	205567.i	0.500419	+	0.866752i	−0.499581	+	0.866267i	$0.666513\pi$
$488$		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
$493$	−316896.	+	182960.i	−1.30384	+	0.752771i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	147088.	+	128526.i	0.595476	+	0.520329i
$498$		0			0
$499$	−37144.5	+	64336.1i	−0.149174	+	0.258377i	−0.930922	−	0.365217i	$-0.880995\pi$
$499$	−37144.5	+	64336.1i	−0.149174	+	0.258377i	0.781748	+	0.623594i	$0.214328\pi$
$500$		0			0
$501$	−12808.3	−	22184.7i	−0.0510291	−	0.0883849i
$502$		0			0
$503$			344439.i			1.36137i	0.732576	+	0.680685i	$0.238318\pi$
$503$			344439.i			1.36137i	−0.732576	+	0.680685i	$0.761682\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	412580.	−	238203.i	1.60506	−	0.926683i
$508$		0			0
$509$	34030.4	+	19647.5i	0.131350	+	0.0758352i	0.564235	−	0.825614i	$-0.309171\pi$
$509$	34030.4	+	19647.5i	0.131350	+	0.0758352i	−0.432885	+	0.901449i	$0.642504\pi$
$510$		0			0
$511$	422945.	+	83339.5i	1.61973	+	0.319160i
$512$		0			0
$513$	71420.3	−	123704.i	0.271386	−	0.470054i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			107439.i			0.401960i
$518$		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
$523$	457799.	+	264310.i	1.67368	+	0.966298i	0.965552	+	0.260211i	$0.0837921\pi$
$523$	457799.	+	264310.i	1.67368	+	0.966298i	0.708125	+	0.706087i	$0.249541\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	193589.	−	335307.i	0.697044	−	1.20732i
$528$		0			0
$529$	58294.1	+	100968.i	0.208311	+	0.360806i
$530$		0			0
$531$		−	221154.i		−	0.784341i
$532$		0			0
$533$	6564.18			0.0231061
$534$		0			0
$535$		0			0
$536$		0			0
$537$	119727.	+	69124.7i	0.415188	+	0.239709i
$538$		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
$543$	21885.7	+	37907.1i	0.0742268	+	0.128565i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−115290.			−0.385315			−0.192658	−	0.981266i	$-0.561711\pi$
$547$	−115290.			−0.385315			−0.192658	+	0.981266i	$0.561711\pi$
$548$		0			0
$549$	240589.	−	138904.i	0.798235	−	0.460861i
$550$		0			0
$551$	117565.	+	67876.3i	0.387236	+	0.223571i
$552$		0			0
$553$	227480.	−	77675.1i	0.743864	−	0.253999i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	144674.	+	250583.i	0.466316	+	0.807683i	0.999260	−	0.0384678i	$-0.0122477\pi$
$557$	144674.	+	250583.i	0.466316	+	0.807683i	−0.532944	+	0.846150i	$0.678914\pi$
$558$		0			0
$559$			598425.i			1.91508i
$560$		0			0
$561$	89365.6			0.283952
$562$		0			0
$563$	−24487.2	+	14137.7i	−0.0772542	+	0.0446027i	−0.538129	−	0.842862i	$-0.680869\pi$
$563$	−24487.2	+	14137.7i	−0.0772542	+	0.0446027i	0.460875	+	0.887465i	$0.347536\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−14365.9	+	72906.4i	−0.0446855	+	0.226777i
$568$		0			0
$569$	233552.	−	404525.i	0.721373	−	1.24945i	−0.239076	−	0.971001i	$-0.576845\pi$
$569$	233552.	−	404525.i	0.721373	−	1.24945i	0.960450	−	0.278454i	$-0.0898220\pi$
$570$		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.i		−	1.07901i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−156921.	+	90598.5i	−0.471335	+	0.272126i	−0.716799	−	0.697280i	$-0.754393\pi$
$577$	−156921.	+	90598.5i	−0.471335	+	0.272126i	0.245463	+	0.969406i	$0.421060\pi$
$578$		0			0
$579$	218611.	+	126215.i	0.652100	+	0.376490i
$580$		0			0
$581$	−143449.	+	164166.i	−0.424957	+	0.486331i
$582$		0			0
$583$	−76843.1	+	133096.i	−0.226083	+	0.391587i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	332481.i		−	0.964919i	−0.875918	−	0.482460i	$-0.839743\pi$
$587$		−	332481.i		−	0.964919i	0.875918	−	0.482460i	$-0.160257\pi$
$588$		0			0
$589$	−143639.			−0.414040
$590$		0			0
$591$	252880.	−	146000.i	0.724001	−	0.418002i
$592$		0			0
$593$	297166.	+	171569.i	0.845064	+	0.487898i	0.858982	−	0.512005i	$-0.171097\pi$
$593$	297166.	+	171569.i	0.845064	+	0.487898i	−0.0139186	+	0.999903i	$0.504431\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	53008.0	−	91812.5i	0.148728	−	0.257604i
$598$		0			0
$599$	−171088.	−	296333.i	−0.476832	−	0.825897i	0.522816	−	0.852446i	$-0.324882\pi$
$599$	−171088.	−	296333.i	−0.476832	−	0.825897i	−0.999648	+	0.0265490i	$0.991548\pi$
$600$		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.			0.746604
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−322559.	−	186230.i	−0.875451	−	0.505442i	−0.00629550	−	0.999980i	$-0.502004\pi$
$607$	−322559.	−	186230.i	−0.875451	−	0.505442i	−0.869156	+	0.494538i	$0.835337\pi$
$608$		0			0
$609$	−221989.	−	43741.9i	−0.598544	−	0.117941i
$610$		0			0
$611$	−610891.	+	1.05809e6i	−1.63637	+	2.83427i
$612$		0			0
$613$	−125569.	−	217492.i	−0.334165	−	0.578791i	0.649159	−	0.760653i	$-0.275121\pi$
$613$	−125569.	−	217492.i	−0.334165	−	0.578791i	−0.983324	+	0.181862i	$0.941788\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	297850.			0.782398			0.391199	−	0.920306i	$-0.372060\pi$
$617$	297850.			0.782398			0.391199	+	0.920306i	$0.372060\pi$
$618$		0			0
$619$	−308493.	+	178108.i	−0.805126	+	0.464839i	−0.845260	−	0.534355i	$-0.820555\pi$
$619$	−308493.	+	178108.i	−0.805126	+	0.464839i	0.0401347	+	0.999194i	$0.487221\pi$
$620$		0			0
$621$	−269686.	−	155703.i	−0.699319	−	0.403752i
$622$		0			0
$623$	−213465.	−	625158.i	−0.549986	−	1.61070i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−16576.9	−	28711.9i	−0.0421664	−	0.0730344i
$628$		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
$633$	−41627.5	+	24033.7i	−0.103890	+	0.0599808i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−767800.	+	103890.i	−1.89221	+	0.256033i
$638$		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.i			1.00309i	0.865131	+	0.501545i	$0.167235\pi$
$643$			414727.i			1.00309i	−0.865131	+	0.501545i	$0.832765\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−554636.	+	320219.i	−1.32495	+	0.764960i	−0.984514	−	0.175307i	$-0.943908\pi$
$647$	−554636.	+	320219.i	−1.32495	+	0.764960i	−0.340436	+	0.940268i	$0.610575\pi$
$648$		0			0
$649$	−131722.	−	76049.6i	−0.312729	−	0.180554i
$650$		0			0
$651$	226558.	−	77360.2i	0.534586	−	0.182539i
$652$		0			0
$653$	86169.4	−	149250.i	0.202082	−	0.350016i	−0.747117	−	0.664692i	$-0.768563\pi$
$653$	86169.4	−	149250.i	0.202082	−	0.350016i	0.949199	+	0.314676i	$0.101896\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			362988.i			0.840933i
$658$		0			0
$659$	349413.			0.804578			0.402289	−	0.915513i	$-0.368215\pi$
$659$	349413.			0.804578			0.402289	+	0.915513i	$0.368215\pi$
$660$		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
$663$	880098.	+	508125.i	2.00218	+	1.15596i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	147977.	−	256304.i	0.332616	−	0.576107i
$668$		0			0
$669$	−169760.	−	294033.i	−0.379300	−	0.656968i
$670$		0			0
$671$		−	191064.i		−	0.424358i
$672$		0			0
$673$	−624802.			−1.37947			−0.689735	−	0.724062i	$-0.742273\pi$
$673$	−624802.			−1.37947			−0.689735	+	0.724062i	$0.742273\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	160259.	+	92525.5i	0.349659	+	0.201876i	0.664535	−	0.747257i	$-0.268630\pi$
$677$	160259.	+	92525.5i	0.349659	+	0.201876i	−0.314876	+	0.949133i	$0.601963\pi$
$678$		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
$683$	358203.	+	620426.i	0.767870	+	1.32999i	0.938716	+	0.344692i	$0.112017\pi$
$683$	358203.	+	620426.i	0.767870	+	1.32999i	−0.170846	+	0.985298i	$0.554650\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−157183.			−0.333037
$688$		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
$693$	−43201.9	−	37750.0i	−0.0899573	−	0.0786050i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	5080.98	+	8800.51i	0.0104588	+	0.0181152i
$698$		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
$703$	−116779.	+	67422.6i	−0.236296	+	0.136425i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−173407.	−	34169.1i	−0.346919	−	0.0683589i
$708$		0			0
$709$	170368.	−	295086.i	0.338919	−	0.587024i	−0.645311	−	0.763920i	$-0.723272\pi$
$709$	170368.	−	295086.i	0.338919	−	0.587024i	0.984230	+	0.176896i	$0.0566055\pi$
$710$		0			0
$711$	101204.	+	175291.i	0.200198	+	0.346752i
$712$		0			0
$713$			313148.i			0.615985i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−388425.	+	224257.i	−0.755560	+	0.436223i
$718$		0			0
$719$	200103.	+	115530.i	0.387076	+	0.223478i	0.680892	−	0.732383i	$-0.261592\pi$
$719$	200103.	+	115530.i	0.387076	+	0.223478i	−0.293816	+	0.955862i	$0.594925\pi$
$720$		0			0
$721$	32445.7	+	95020.7i	0.0624146	+	0.182788i
$722$		0			0
$723$	189294.	−	327867.i	0.362127	−	0.627222i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			149550.i			0.282955i	0.989941	+	0.141477i	$0.0451853\pi$
$727$			149550.i			0.282955i	−0.989941	+	0.141477i	$0.954815\pi$
$728$		0			0
$729$	−456116.			−0.858264
$730$		0			0
$731$	−802300.	+	463208.i	−1.50142	+	0.866845i
$732$		0			0
$733$	250662.	+	144720.i	0.466532	+	0.269352i	0.714787	−	0.699342i	$-0.246524\pi$
$733$	250662.	+	144720.i	0.466532	+	0.269352i	−0.248255	+	0.968695i	$0.579857\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	93352.9	−	161692.i	0.171867	−	0.297682i
$738$		0			0
$739$	−263530.	−	456448.i	−0.482550	−	0.835800i	0.517250	−	0.855835i	$-0.326956\pi$
$739$	−263530.	−	456448.i	−0.482550	−	0.835800i	−0.999799	+	0.0200341i	$0.993623\pi$
$740$		0			0
$741$		−	377018.i		−	0.686634i
$742$		0			0
$743$	−464605.			−0.841602			−0.420801	−	0.907153i	$-0.638251\pi$
$743$	−464605.			−0.841602			−0.420801	+	0.907153i	$0.638251\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−158980.	−	91787.3i	−0.284906	−	0.164491i
$748$		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
$753$	35537.1	+	61552.0i	0.0626746	+	0.108556i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−202873.			−0.354025			−0.177012	−	0.984209i	$-0.556643\pi$
$757$	−202873.			−0.354025			−0.177012	+	0.984209i	$0.556643\pi$
$758$		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
$763$	77388.2	−	392742.i	0.132931	−	0.674618i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−864823.	−	1.49792e6i	−1.47006	−	2.54623i
$768$		0			0
$769$		−	367720.i		−	0.621820i	−0.950439	−	0.310910i	$-0.899366\pi$
$769$		−	367720.i		−	0.621820i	0.950439	−	0.310910i	$-0.100634\pi$
$770$		0			0
$771$	419116.			0.705059
$772$		0			0
$773$	−11419.6	+	6593.12i	−0.0191114	+	0.0110340i	−0.509525	−	0.860456i	$-0.670179\pi$
$773$	−11419.6	+	6593.12i	−0.0191114	+	0.0110340i	0.490414	+	0.871490i	$0.336846\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	147881.	−	169238.i	0.244946	−	0.280321i
$778$		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.i		−	0.920806i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−423849.	+	244709.i	−0.684323	+	0.395094i	−0.801482	−	0.598019i	$-0.795955\pi$
$787$	−423849.	+	244709.i	−0.684323	+	0.395094i	0.117159	+	0.993113i	$0.462621\pi$
$788$		0			0
$789$	−305893.	−	176608.i	−0.491378	−	0.283697i
$790$		0			0
$791$	140417.	+	122697.i	0.224423	+	0.196102i
$792$		0			0
$793$	1.08637e6	−	1.88165e6i	1.72755	−	2.99221i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	720256.i		−	1.13389i	−0.823756	−	0.566944i	$-0.808126\pi$
$797$		−	720256.i		−	1.13389i	0.823756	−	0.566944i	$-0.191874\pi$
$798$		0			0
$799$	−1.89143e6			−2.96276
$800$		0			0
$801$	481731.	−	278127.i	0.750826	−	0.433490i
$802$		0			0
$803$	216200.	+	124823.i	0.335293	+	0.193581i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	231370.	−	400745.i	0.355272	−	0.615349i
$808$		0			0
$809$	−129195.	−	223772.i	−0.197400	−	0.341908i	0.750284	−	0.661115i	$-0.229917\pi$
$809$	−129195.	−	223772.i	−0.197400	−	0.341908i	−0.947685	+	0.319208i	$0.896583\pi$
$810$		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
$813$	89470.8			0.135363
$814$		0			0
$815$		0			0
$816$		0			0
$817$	297645.	+	171845.i	0.445917	+	0.257451i
$818$		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
$823$	473816.	+	820673.i	0.699536	+	1.21163i	0.968628	+	0.248517i	$0.0799431\pi$
$823$	473816.	+	820673.i	0.699536	+	1.21163i	−0.269092	+	0.963114i	$0.586724\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−163948.			−0.239715			−0.119857	−	0.992791i	$-0.538244\pi$
$827$	−163948.			−0.239715			−0.119857	+	0.992791i	$0.538244\pi$
$828$		0			0
$829$	394627.	−	227838.i	0.574219	−	0.331525i	−0.184614	−	0.982811i	$-0.559103\pi$
$829$	394627.	−	227838.i	0.574219	−	0.331525i	0.758833	+	0.651286i	$0.225770\pi$
$830$		0			0
$831$	−539587.	−	311531.i	−0.781375	−	0.451127i
$832$		0			0
$833$	−733597.	−	948964.i	−1.05723	−	1.36760i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	298666.	+	517306.i	0.426320	+	0.738408i
$838$		0			0
$839$			1.16012e6i			1.64809i	0.566526	+	0.824044i	$0.308287\pi$
$839$			1.16012e6i			1.64809i	−0.566526	+	0.824044i	$0.691713\pi$
$840$		0			0
$841$	−170758.			−0.241429
$842$		0			0
$843$	−317341.	+	183217.i	−0.446551	+	0.257816i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	641580.	−	219073.i	0.894302	−	0.305367i
$848$		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.i			1.28793i	0.765056	+	0.643964i	$0.222711\pi$
$853$			937108.i			1.28793i	−0.765056	+	0.643964i	$0.777289\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−581252.	+	335586.i	−0.791412	+	0.456922i	−0.840459	−	0.541875i	$-0.817715\pi$
$857$	−581252.	+	335586.i	−0.791412	+	0.456922i	0.0490476	+	0.998796i	$0.484381\pi$
$858$		0			0
$859$	50992.8	+	29440.7i	0.0691071	+	0.0398990i	0.534155	−	0.845386i	$-0.320630\pi$
$859$	50992.8	+	29440.7i	0.0691071	+	0.0398990i	−0.465048	+	0.885285i	$0.653963\pi$
$860$		0			0
$861$	−1214.75	+	6164.83i	−0.00163863	+	0.00831601i
$862$		0			0
$863$	−368701.	+	638608.i	−0.495054	+	0.857458i	−0.999984	−	0.00570214i	$-0.998185\pi$
$863$	−368701.	+	638608.i	−0.495054	+	0.857458i	0.504930	+	0.863160i	$0.331518\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			1.04674e6i			1.39251i
$868$		0			0
$869$	139207.			0.184341
$870$		0			0
$871$	1.83873e6	−	1.06159e6i	2.42372	−	1.39933i
$872$		0			0
$873$	253757.	+	146507.i	0.332959	+	0.192234i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−250110.	+	433203.i	−0.325186	+	0.563238i	−0.981550	−	0.191206i	$-0.938760\pi$
$877$	−250110.	+	433203.i	−0.325186	+	0.563238i	0.656364	+	0.754444i	$0.272093\pi$
$878$		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
$883$	1.16488e6			1.49403			0.747013	−	0.664810i	$-0.231487\pi$
$883$	1.16488e6			1.49403			0.747013	+	0.664810i	$0.231487\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	270292.	+	156053.i	0.343547	+	0.198347i	0.661840	−	0.749646i	$-0.269776\pi$
$887$	270292.	+	156053.i	0.343547	+	0.198347i	−0.318292	+	0.947993i	$0.603109\pi$
$888$		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
$893$	350851.	+	607691.i	0.439966	+	0.762044i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−821936.			−1.02154
$898$		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
$903$	−562018.	−	110743.i	−0.689247	−	0.135813i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	266298.	+	461241.i	0.323708	+	0.560678i	0.981250	−	0.192740i	$-0.0617373\pi$
$907$	266298.	+	461241.i	0.323708	+	0.560678i	−0.657542	+	0.753418i	$0.728404\pi$
$908$		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
$913$	−109339.	+	63127.0i	−0.131170	+	0.0757310i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−95159.0	−	278684.i	−0.113165	−	0.331416i
$918$		0			0
$919$	504033.	−	873011.i	0.596799	−	1.03369i	−0.396491	−	0.918038i	$-0.629772\pi$
$919$	504033.	−	873011.i	0.596799	−	1.03369i	0.993290	−	0.115648i	$-0.0368943\pi$
$920$		0			0
$921$	209081.	+	362140.i	0.246488	+	0.426930i
$922$		0			0
$923$			1.28638e6i			1.50996i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−73220.6	+	42274.0i	−0.0852067	+	0.0491941i
$928$		0			0
$929$	280859.	+	162154.i	0.325430	+	0.187887i	0.653810	−	0.756659i	$-0.273169\pi$
$929$	280859.	+	162154.i	0.325430	+	0.187887i	−0.328380	+	0.944546i	$0.606503\pi$
$930$		0			0
$931$	−168811.	+	411723.i	−0.194761	+	0.475013i
$932$		0			0
$933$	332074.	−	575168.i	0.381479	−	0.660742i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	651900.i		−	0.742510i	−0.928531	−	0.371255i	$-0.878928\pi$
$937$		−	651900.i		−	0.742510i	0.928531	−	0.371255i	$-0.121072\pi$
$938$		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
$943$	−7117.80	−	4109.46i	−0.00800428	−	0.00462127i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	10503.2	−	18192.0i	0.0117117	−	0.0202853i	−0.860110	−	0.510108i	$-0.829605\pi$
$947$	10503.2	−	18192.0i	0.0117117	−	0.0202853i	0.871822	+	0.489823i	$0.162939\pi$
$948$		0			0
$949$	1.41947e6	+	2.45859e6i	1.57613	+	2.72994i
$950$		0			0
$951$			696063.i			0.769640i
$952$		0			0
$953$	−935565.			−1.03012			−0.515060	−	0.857154i	$-0.672231\pi$
$953$	−935565.			−1.03012			−0.515060	+	0.857154i	$0.672231\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−113476.	−	65515.2i	−0.123902	−	0.0715349i
$958$		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
$963$	−279991.	−	484959.i	−0.301920	−	0.522941i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−602673.			−0.644509			−0.322255	−	0.946653i	$-0.604441\pi$
$967$	−602673.			−0.644509			−0.322255	+	0.946653i	$0.604441\pi$
$968$		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
$973$	289593.	−	331417.i	0.305888	−	0.350065i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−338681.	−	586613.i	−0.354815	−	0.614558i	0.632271	−	0.774747i	$-0.282123\pi$
$977$	−338681.	−	586613.i	−0.354815	−	0.614558i	−0.987086	+	0.160189i	$0.948789\pi$
$978$		0			0
$979$		−	382566.i		−	0.399155i
$980$		0			0
$981$	337067.			0.350250
$982$		0			0
$983$	−1.04535e6	+	603535.i	−1.08182	+	0.624590i	−0.931387	−	0.364030i	$-0.881401\pi$
$983$	−1.04535e6	+	603535.i	−1.08182	+	0.624590i	−0.150435	+	0.988620i	$0.548067\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−880672.	−	769535.i	−0.904024	−	0.789940i
$988$		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.i			0.804638i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	242061.	−	139754.i	0.243520	−	0.140597i	−0.373273	−	0.927721i	$-0.621765\pi$
$997$	242061.	−	139754.i	0.243520	−	0.140597i	0.616794	+	0.787125i	$0.288431\pi$
$998$		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.s.d.201.4	yes	22
5.2	odd	4		700.5.o.c.649.15		44
5.3	odd	4		700.5.o.c.649.8		44
5.4	even	2		700.5.s.c.201.8	yes	22
7.3	odd	6	inner	700.5.s.d.101.4	yes	22
35.3	even	12		700.5.o.c.549.15		44
35.17	even	12		700.5.o.c.549.8		44
35.24	odd	6		700.5.s.c.101.8	✓	22

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	700.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.45937 + 3.15197i) q^{3} +(36.8981 + 32.2417i) q^{7} +(-20.6302 + 35.7325i) q^{9} +(14.1885 + 24.5752i) q^{11} +322.698i q^{13} +(-432.637 + 249.783i) q^{17} +(160.504 + 92.6668i) q^{19} +(-303.066 - 59.7178i) q^{21} +(202.023 - 349.914i) q^{23} -770.722i q^{27} +732.477 q^{29} +(-671.196 + 387.515i) q^{31} +(-154.920 - 89.4433i) q^{33} +(-363.791 + 630.104i) q^{37} +(-1017.13 - 1761.73i) q^{39} -20.3416i q^{41} +1854.44 q^{43} +(3278.90 + 1893.08i) q^{47} +(321.943 + 2379.32i) q^{49} +(1574.62 - 2727.31i) q^{51} +(2707.94 + 4690.29i) q^{53} -1168.33 q^{57} +(-4641.86 + 2679.98i) q^{59} +(-5830.99 - 3366.53i) q^{61} +(-1913.29 + 653.310i) q^{63} +(-3289.74 - 5698.00i) q^{67} +2547.08i q^{69} +3986.32 q^{71} +(7618.86 - 4398.75i) q^{73} +(-268.817 + 1364.24i) q^{77} +(2452.82 - 4248.41i) q^{79} +(758.248 + 1313.32i) q^{81} +4449.18i q^{83} +(-3998.87 + 2308.75i) q^{87} +(-11675.4 - 6740.79i) q^{89} +(-10404.3 + 11906.9i) q^{91} +(2442.87 - 4231.18i) q^{93} -7101.58i q^{97} -1170.84 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 9 q^{3} + 66 q^{7} + 342 q^{9} - 150 q^{11} - 432 q^{17} - 270 q^{19} - 95 q^{21} + 333 q^{23} + 264 q^{29} - 1167 q^{31} + 192 q^{33} + 930 q^{37} + 426 q^{39} + 4162 q^{43} - 6822 q^{47} - 2046 q^{49}+ \cdots - 84090 q^{99}+O(q^{100}) \) 22 * q + 9 * q^3 + 66 * q^7 + 342 * q^9 - 150 * q^11 - 432 * q^17 - 270 * q^19 - 95 * q^21 + 333 * q^23 + 264 * q^29 - 1167 * q^31 + 192 * q^33 + 930 * q^37 + 426 * q^39 + 4162 * q^43 - 6822 * q^47 - 2046 * q^49 - 1951 * q^51 + 1776 * q^53 + 13866 * q^57 - 4707 * q^59 - 11799 * q^61 + 13393 * q^63 - 4926 * q^67 + 16410 * q^71 - 3108 * q^73 + 12585 * q^77 + 2445 * q^79 - 11855 * q^81 - 38151 * q^87 + 18882 * q^89 + 3209 * q^91 + 5504 * q^93 - 84090 * q^99

Introduction

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