LMFDB - Embedded newform 289.4.b.f.288.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,4,Mod(288,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("289.288");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	289.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.0515519917$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			288.13
Character	$\chi$	$=$	289.288
Dual form			289.4.b.f.288.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.820352 q^{2} +0.130026i q^{3} -7.32702 q^{4} +8.70710i q^{5} +0.106667i q^{6} -11.4024i q^{7} -12.5736 q^{8} +26.9831 q^{9} +O(q^{10})$	\(q+0.820352 q^{2} +0.130026i q^{3} -7.32702 q^{4} +8.70710i q^{5} +0.106667i q^{6} -11.4024i q^{7} -12.5736 q^{8} +26.9831 q^{9} +7.14288i q^{10} +7.27316i q^{11} -0.952700i q^{12} -52.1470 q^{13} -9.35395i q^{14} -1.13214 q^{15} +48.3014 q^{16} +22.1356 q^{18} -84.1527 q^{19} -63.7971i q^{20} +1.48260 q^{21} +5.96655i q^{22} -157.541i q^{23} -1.63488i q^{24} +49.1864 q^{25} -42.7789 q^{26} +7.01918i q^{27} +83.5454i q^{28} -276.210i q^{29} -0.928757 q^{30} -235.134i q^{31} +140.213 q^{32} -0.945697 q^{33} +99.2815 q^{35} -197.706 q^{36} -352.809i q^{37} -69.0348 q^{38} -6.78044i q^{39} -109.479i q^{40} +90.2409i q^{41} +1.21625 q^{42} +167.386 q^{43} -53.2906i q^{44} +234.944i q^{45} -129.239i q^{46} -589.668 q^{47} +6.28042i q^{48} +212.986 q^{49} +40.3502 q^{50} +382.082 q^{52} -288.759 q^{53} +5.75820i q^{54} -63.3281 q^{55} +143.368i q^{56} -10.9420i q^{57} -226.589i q^{58} -519.269 q^{59} +8.29525 q^{60} +557.682i q^{61} -192.892i q^{62} -307.671i q^{63} -271.388 q^{64} -454.049i q^{65} -0.775804 q^{66} +304.306 q^{67} +20.4843 q^{69} +81.4458 q^{70} +316.681i q^{71} -339.273 q^{72} +66.6132i q^{73} -289.428i q^{74} +6.39549i q^{75} +616.588 q^{76} +82.9313 q^{77} -5.56234i q^{78} +118.819i q^{79} +420.565i q^{80} +727.631 q^{81} +74.0293i q^{82} +215.569 q^{83} -10.8630 q^{84} +137.316 q^{86} +35.9144 q^{87} -91.4495i q^{88} +931.329 q^{89} +192.737i q^{90} +594.599i q^{91} +1154.30i q^{92} +30.5734 q^{93} -483.735 q^{94} -732.725i q^{95} +18.2312i q^{96} +402.033i q^{97} +174.723 q^{98} +196.252i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 96 q^{4} + 102 q^{8} - 216 q^{9}+O(q^{10}) $ 24 * q + 96 * q^4 + 102 * q^8 - 216 * q^9	$ 24 q + 96 q^{4} + 102 q^{8} - 216 q^{9} - 144 q^{13} + 276 q^{15} + 384 q^{16} + 378 q^{18} + 132 q^{19} + 492 q^{21} - 888 q^{25} - 1056 q^{26} - 3780 q^{30} + 2706 q^{32} + 1932 q^{33} - 132 q^{35} + 1326 q^{36} - 120 q^{38} - 1608 q^{42} - 972 q^{43} - 1776 q^{47} + 1140 q^{49} + 870 q^{50} + 450 q^{52} - 2052 q^{53} + 1944 q^{55} + 1584 q^{59} - 2916 q^{60} - 3714 q^{64} + 1188 q^{66} + 1248 q^{67} - 3012 q^{69} + 3300 q^{70} + 2910 q^{72} - 1350 q^{76} + 2016 q^{77} + 5040 q^{81} - 1344 q^{83} - 1554 q^{84} + 5556 q^{86} - 1452 q^{87} - 1812 q^{89} - 264 q^{93} - 1470 q^{94} + 3822 q^{98}+O(q^{100}) $ 24 * q + 96 * q^4 + 102 * q^8 - 216 * q^9 - 144 * q^13 + 276 * q^15 + 384 * q^16 + 378 * q^18 + 132 * q^19 + 492 * q^21 - 888 * q^25 - 1056 * q^26 - 3780 * q^30 + 2706 * q^32 + 1932 * q^33 - 132 * q^35 + 1326 * q^36 - 120 * q^38 - 1608 * q^42 - 972 * q^43 - 1776 * q^47 + 1140 * q^49 + 870 * q^50 + 450 * q^52 - 2052 * q^53 + 1944 * q^55 + 1584 * q^59 - 2916 * q^60 - 3714 * q^64 + 1188 * q^66 + 1248 * q^67 - 3012 * q^69 + 3300 * q^70 + 2910 * q^72 - 1350 * q^76 + 2016 * q^77 + 5040 * q^81 - 1344 * q^83 - 1554 * q^84 + 5556 * q^86 - 1452 * q^87 - 1812 * q^89 - 264 * q^93 - 1470 * q^94 + 3822 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	0.820352	0.290038	0.145019	−	0.989429i	$-0.453676\pi$
$2$	0.820352	0.290038	0.145019	+	0.989429i	$0.453676\pi$
$3$	0.130026i	0.0250234i	0.999922	+	0.0125117i	$0.00398270\pi$
$3$	0.130026i	0.0250234i	−0.999922	+	0.0125117i	$0.996017\pi$
$4$	−7.32702	−0.915878
$5$	8.70710i	0.778787i	0.921072	+	0.389393i	$0.127315\pi$
$5$	8.70710i	0.778787i	−0.921072	+	0.389393i	$0.872685\pi$
$6$	0.106667i	0.00725775i
$7$	− 11.4024i	− 0.615670i	−0.951440	−	0.307835i	$-0.900396\pi$
$7$	− 11.4024i	− 0.615670i	0.951440	−	0.307835i	$-0.0996045\pi$
$8$	−12.5736	−0.555678
$9$	26.9831	0.999374
$10$	7.14288i	0.225878i
$11$	7.27316i	0.199358i	0.995020	+	0.0996792i	$0.0317816\pi$
$11$	7.27316i	0.199358i	−0.995020	+	0.0996792i	$0.968218\pi$
$12$	− 0.952700i	− 0.0229184i
$13$	−52.1470	−1.11254	−0.556268	−	0.831003i	$-0.687767\pi$
$13$	−52.1470	−1.11254	−0.556268	+	0.831003i	$0.687767\pi$
$14$	− 9.35395i	− 0.178568i
$15$	−1.13214	−0.0194879
$16$	48.3014	0.754710
$17$	0	0
$17$	0	0
$18$	22.1356	0.289857
$19$	−84.1527	−1.01610	−0.508051	−	0.861327i	$-0.669634\pi$
$19$	−84.1527	−1.01610	−0.508051	+	0.861327i	$0.669634\pi$
$20$	− 63.7971i	− 0.713273i
$21$	1.48260	0.0154062
$22$	5.96655i	0.0578215i
$23$	− 157.541i	− 1.42824i	−0.700024	−	0.714119i	$-0.746827\pi$
$23$	− 157.541i	− 1.42824i	0.700024	−	0.714119i	$-0.253173\pi$
$24$	− 1.63488i	− 0.0139050i
$25$	49.1864	0.393492
$26$	−42.7789	−0.322678
$27$	7.01918i	0.0500312i
$28$	83.5454i	0.563879i
$29$	− 276.210i	− 1.76865i	−0.466869	−	0.884326i	$-0.654618\pi$
$29$	− 276.210i	− 1.76865i	0.466869	−	0.884326i	$-0.345382\pi$
$30$	−0.928757	−0.00565224
$31$	− 235.134i	− 1.36230i	−0.732145	−	0.681149i	$-0.761480\pi$
$31$	− 235.134i	− 1.36230i	0.732145	−	0.681149i	$-0.238520\pi$
$32$	140.213	0.774572
$33$	−0.945697	−0.00498863
$34$	0	0
$35$	99.2815	0.479475
$36$	−197.706	−0.915304
$37$	− 352.809i	− 1.56761i	−0.621009	−	0.783803i	$-0.713277\pi$
$37$	− 352.809i	− 1.56761i	0.621009	−	0.783803i	$-0.286723\pi$
$38$	−69.0348	−0.294708
$39$	− 6.78044i	− 0.0278395i
$40$	− 109.479i	− 0.432754i
$41$	90.2409i	0.343738i	0.985120	+	0.171869i	$0.0549806\pi$
$41$	90.2409i	0.343738i	−0.985120	+	0.171869i	$0.945019\pi$
$42$	1.21625	0.00446838
$43$	167.386	0.593632	0.296816	−	0.954935i	$-0.404075\pi$
$43$	167.386	0.593632	0.296816	+	0.954935i	$0.404075\pi$
$44$	− 53.2906i	− 0.182588i
$45$	234.944i	0.778299i
$46$	− 129.239i	− 0.414244i
$47$	−589.668	−1.83004	−0.915021	−	0.403407i	$-0.867826\pi$
$47$	−589.668	−1.83004	−0.915021	+	0.403407i	$0.867826\pi$
$48$	6.28042i	0.0188854i
$49$	212.986	0.620950
$50$	40.3502	0.114128
$51$	0	0
$52$	382.082	1.01895
$53$	−288.759	−0.748378	−0.374189	−	0.927352i	$-0.622079\pi$
$53$	−288.759	−0.748378	−0.374189	+	0.927352i	$0.622079\pi$
$54$	5.75820i	0.0145109i
$55$	−63.3281	−0.155258
$56$	143.368i	0.342114i
$57$	− 10.9420i	− 0.0254264i
$58$	− 226.589i	− 0.512977i
$59$	−519.269	−1.14581	−0.572907	−	0.819620i	$-0.694184\pi$
$59$	−519.269	−1.14581	−0.572907	+	0.819620i	$0.694184\pi$
$60$	8.29525	0.0178485
$61$	557.682i	1.17056i	0.810833	+	0.585278i	$0.199015\pi$
$61$	557.682i	1.17056i	−0.810833	+	0.585278i	$0.800985\pi$
$62$	− 192.892i	− 0.395119i
$63$	− 307.671i	− 0.615284i
$64$	−271.388	−0.530055
$65$	− 454.049i	− 0.866428i
$66$	−0.775804	−0.00144689
$67$	304.306	0.554879	0.277440	−	0.960743i	$-0.410514\pi$
$67$	304.306	0.554879	0.277440	+	0.960743i	$0.410514\pi$
$68$	0	0
$69$	20.4843	0.0357394
$70$	81.4458	0.139066
$71$	316.681i	0.529340i	0.964339	+	0.264670i	$0.0852629\pi$
$71$	316.681i	0.529340i	−0.964339	+	0.264670i	$0.914737\pi$
$72$	−339.273	−0.555330
$73$	66.6132i	0.106801i	0.998573	+	0.0534006i	$0.0170060\pi$
$73$	66.6132i	0.106801i	−0.998573	+	0.0534006i	$0.982994\pi$
$74$	− 289.428i	− 0.454666i
$75$	6.39549i	0.00984651i
$76$	616.588	0.930626
$77$	82.9313	0.122739
$78$	− 5.56234i	− 0.00807451i
$79$	118.819i	0.169218i	0.996414	+	0.0846088i	$0.0269640\pi$
$79$	118.819i	0.169218i	−0.996414	+	0.0846088i	$0.973036\pi$
$80$	420.565i	0.587758i
$81$	727.631	0.998122
$82$	74.0293i	0.0996972i
$83$	215.569	0.285082	0.142541	−	0.989789i	$-0.454473\pi$
$83$	215.569	0.285082	0.142541	+	0.989789i	$0.454473\pi$
$84$	−10.8630	−0.0141102
$85$	0	0
$86$	137.316	0.172176
$87$	35.9144	0.0442577
$88$	− 91.4495i	− 0.110779i
$89$	931.329	1.10922	0.554610	−	0.832110i	$-0.312867\pi$
$89$	931.329	1.10922	0.554610	+	0.832110i	$0.312867\pi$
$90$	192.737i	0.225736i
$91$	594.599i	0.684955i
$92$	1154.30i	1.30809i
$93$	30.5734	0.0340894
$94$	−483.735	−0.530782
$95$	− 732.725i	− 0.791327i
$96$	18.2312i	0.0193825i
$97$	402.033i	0.420827i	0.977612	+	0.210414i	$0.0674811\pi$
$97$	402.033i	0.420827i	−0.977612	+	0.210414i	$0.932519\pi$
$98$	174.723	0.180099
$99$	196.252i	0.199233i
$100$	−360.390	−0.360390
$101$	−860.667	−0.847916	−0.423958	−	0.905682i	$-0.639360\pi$
$101$	−860.667	−0.847916	−0.423958	+	0.905682i	$0.639360\pi$
$102$	0	0
$103$	−1438.94	−1.37653	−0.688265	−	0.725460i	$-0.741627\pi$
$103$	−1438.94	−1.37653	−0.688265	+	0.725460i	$0.741627\pi$
$104$	655.673	0.618212
$105$	12.9091i	0.0119981i
$106$	−236.884	−0.217058
$107$	− 1903.37i	− 1.71968i	−0.510564	−	0.859840i	$-0.670563\pi$
$107$	− 1903.37i	− 1.71968i	0.510564	−	0.859840i	$-0.329437\pi$
$108$	− 51.4297i	− 0.0458224i
$109$	− 1327.80i	− 1.16679i	−0.812190	−	0.583393i	$-0.801725\pi$
$109$	− 1327.80i	− 1.16679i	0.812190	−	0.583393i	$-0.198275\pi$
$110$	−51.9514	−0.0450306
$111$	45.8742	0.0392269
$112$	− 550.751i	− 0.464652i
$113$	− 817.949i	− 0.680940i	−0.940255	−	0.340470i	$-0.889414\pi$
$113$	− 817.949i	− 0.680940i	0.940255	−	0.340470i	$-0.110586\pi$
$114$	− 8.97628i	− 0.00737461i
$115$	1371.72	1.11229
$116$	2023.80i	1.61987i
$117$	−1407.09	−1.11184
$118$	−425.983	−0.332330
$119$	0	0
$120$	14.2351	0.0108290
$121$	1278.10	0.960256
$122$	457.496i	0.339506i
$123$	−11.7336	−0.00860150
$124$	1722.83i	1.24770i
$125$	1516.66i	1.08523i
$126$	− 252.399i	− 0.178456i
$127$	−257.330	−0.179798	−0.0898989	−	0.995951i	$-0.528654\pi$
$127$	−257.330	−0.179798	−0.0898989	+	0.995951i	$0.528654\pi$
$128$	−1344.33	−0.928308
$129$	21.7645i	0.0148547i
$130$	− 372.480i	− 0.251297i
$131$	1120.49i	0.747309i	0.927568	+	0.373654i	$0.121895\pi$
$131$	1120.49i	0.747309i	−0.927568	+	0.373654i	$0.878105\pi$
$132$	6.92914	0.00456897
$133$	959.540i	0.625584i
$134$	249.638	0.160936
$135$	−61.1167	−0.0389636
$136$	0	0
$137$	−987.072	−0.615557	−0.307778	−	0.951458i	$-0.599586\pi$
$137$	−987.072	−0.615557	−0.307778	+	0.951458i	$0.599586\pi$
$138$	16.8043	0.0103658
$139$	1828.38i	1.11569i	0.829944	+	0.557847i	$0.188372\pi$
$139$	1828.38i	1.11569i	−0.829944	+	0.557847i	$0.811628\pi$
$140$	−727.438	−0.439141
$141$	− 76.6719i	− 0.0457939i
$142$	259.790i	0.153529i
$143$	− 379.274i	− 0.221793i
$144$	1303.32	0.754238
$145$	2404.99	1.37740
$146$	54.6462i	0.0309764i
$147$	27.6936i	0.0155383i
$148$	2585.04i	1.43574i
$149$	1317.50	0.724386	0.362193	−	0.932103i	$-0.382028\pi$
$149$	1317.50	0.724386	0.362193	+	0.932103i	$0.382028\pi$
$150$	5.24655i	0.00285586i
$151$	−1877.92	−1.01207	−0.506036	−	0.862512i	$-0.668890\pi$
$151$	−1877.92	−1.01207	−0.506036	+	0.862512i	$0.668890\pi$
$152$	1058.10	0.564625
$153$	0	0
$154$	68.0328	0.0355990
$155$	2047.33	1.06094
$156$	49.6804i	0.0254975i
$157$	1777.09	0.903356	0.451678	−	0.892181i	$-0.350826\pi$
$157$	1777.09	0.903356	0.451678	+	0.892181i	$0.350826\pi$
$158$	97.4734i	0.0490795i
$159$	− 37.5460i	− 0.0187270i
$160$	1220.84i	0.603227i
$161$	−1796.34	−0.879323
$162$	596.913	0.289493
$163$	575.788i	0.276682i	0.990385	+	0.138341i	$0.0441770\pi$
$163$	575.788i	0.276682i	−0.990385	+	0.138341i	$0.955823\pi$
$164$	− 661.197i	− 0.314822i
$165$	− 8.23427i	− 0.00388508i
$166$	176.842	0.0826845
$167$	− 2375.57i	− 1.10076i	−0.834914	−	0.550381i	$-0.814482\pi$
$167$	− 2375.57i	− 1.10076i	0.834914	−	0.550381i	$-0.185518\pi$
$168$	−18.6415	−0.00856086
$169$	522.307	0.237737
$170$	0	0
$171$	−2270.70	−1.01547
$172$	−1226.44	−0.543695
$173$	1860.47i	0.817625i	0.912618	+	0.408812i	$0.134057\pi$
$173$	1860.47i	0.817625i	−0.912618	+	0.408812i	$0.865943\pi$
$174$	29.4624	0.0128364
$175$	− 560.842i	− 0.242261i
$176$	351.304i	0.150458i
$177$	− 67.5182i	− 0.0286722i
$178$	764.017	0.321716
$179$	−2282.20	−0.952959	−0.476480	−	0.879185i	$-0.658087\pi$
$179$	−2282.20	−0.952959	−0.476480	+	0.879185i	$0.658087\pi$
$180$	− 1721.44i	− 0.712827i
$181$	− 358.388i	− 0.147176i	−0.997289	−	0.0735879i	$-0.976555\pi$
$181$	− 358.388i	− 0.147176i	0.997289	−	0.0735879i	$-0.0234449\pi$
$182$	487.780i	0.198663i
$183$	−72.5129	−0.0292913
$184$	1980.84i	0.793640i
$185$	3071.94	1.22083
$186$	25.0809	0.00988722
$187$	0	0
$188$	4320.51	1.67609
$189$	80.0353	0.0308027
$190$	− 601.093i	− 0.229515i
$191$	−60.9643	−0.0230954	−0.0115477	−	0.999933i	$-0.503676\pi$
$191$	−60.9643	−0.0230954	−0.0115477	+	0.999933i	$0.503676\pi$
$192$	− 35.2874i	− 0.0132638i
$193$	− 2006.00i	− 0.748161i	−0.927396	−	0.374080i	$-0.877958\pi$
$193$	− 2006.00i	− 0.748161i	0.927396	−	0.374080i	$-0.122042\pi$
$194$	329.808i	0.122056i
$195$	59.0379	0.0216810
$196$	−1560.55	−0.568715
$197$	3028.58i	1.09532i	0.836703	+	0.547658i	$0.184480\pi$
$197$	3028.58i	1.09532i	−0.836703	+	0.547658i	$0.815520\pi$
$198$	160.996i	0.0577853i
$199$	− 4651.35i	− 1.65691i	−0.560054	−	0.828456i	$-0.689220\pi$
$199$	− 4651.35i	− 1.65691i	0.560054	−	0.828456i	$-0.310780\pi$
$200$	−618.448	−0.218655
$201$	39.5676i	0.0138850i
$202$	−706.050	−0.245928
$203$	−3149.45	−1.08891
$204$	0	0
$205$	−785.736	−0.267699
$206$	−1180.43	−0.399246
$207$	− 4250.93i	− 1.42734i
$208$	−2518.77	−0.839642
$209$	− 612.056i	− 0.202568i
$210$	10.5900i	0.00347991i
$211$	− 569.094i	− 0.185678i	−0.995681	−	0.0928390i	$-0.970406\pi$
$211$	− 569.094i	− 0.185678i	0.995681	−	0.0928390i	$-0.0295942\pi$
$212$	2115.74	0.685423
$213$	−41.1766	−0.0132459
$214$	− 1561.43i	− 0.498773i
$215$	1457.45i	0.462313i
$216$	− 88.2560i	− 0.0278012i
$217$	−2681.08	−0.838726
$218$	− 1089.26i	− 0.338413i
$219$	−8.66141	−0.00267253
$220$	464.007	0.142197
$221$	0	0
$222$	37.6330	0.0113773
$223$	−2862.42	−0.859560	−0.429780	−	0.902934i	$-0.641409\pi$
$223$	−2862.42	−0.859560	−0.429780	+	0.902934i	$0.641409\pi$
$224$	− 1598.76i	− 0.476881i
$225$	1327.20	0.393245
$226$	− 671.006i	− 0.197498i
$227$	4241.22i	1.24009i	0.784568	+	0.620043i	$0.212885\pi$
$227$	4241.22i	1.24009i	−0.784568	+	0.620043i	$0.787115\pi$
$228$	80.1722i	0.0232874i
$229$	−3807.17	−1.09862	−0.549312	−	0.835618i	$-0.685110\pi$
$229$	−3807.17	−1.09862	−0.549312	+	0.835618i	$0.685110\pi$
$230$	1125.29	0.322607
$231$	10.7832i	0.00307135i
$232$	3472.94i	0.982801i
$233$	− 4705.00i	− 1.32290i	−0.749990	−	0.661449i	$-0.769942\pi$
$233$	− 4705.00i	− 1.32290i	0.749990	−	0.661449i	$-0.230058\pi$
$234$	−1154.31	−0.322476
$235$	− 5134.30i	− 1.42521i
$236$	3804.70	1.04943
$237$	−15.4495	−0.00423440
$238$	0	0
$239$	3807.70	1.03054	0.515272	−	0.857027i	$-0.327691\pi$
$239$	3807.70	1.03054	0.515272	+	0.857027i	$0.327691\pi$
$240$	−54.6842	−0.0147077
$241$	− 1561.48i	− 0.417361i	−0.977984	−	0.208681i	$-0.933083\pi$
$241$	− 1561.48i	− 0.417361i	0.977984	−	0.208681i	$-0.0669169\pi$
$242$	1048.49	0.278511
$243$	284.128i	0.0750076i
$244$	− 4086.15i	− 1.07209i
$245$	1854.49i	0.483588i
$246$	−9.62570	−0.00249476
$247$	4388.31	1.13045
$248$	2956.47i	0.756999i
$249$	28.0295i	0.00713372i
$250$	1244.19i	0.314759i
$251$	−3553.31	−0.893558	−0.446779	−	0.894644i	$-0.647429\pi$
$251$	−3553.31	−0.893558	−0.446779	+	0.894644i	$0.647429\pi$
$252$	2254.31i	0.563525i
$253$	1145.82	0.284731
$254$	−211.101	−0.0521482
$255$	0	0
$256$	1068.28	0.260810
$257$	−3889.35	−0.944013	−0.472006	−	0.881595i	$-0.656470\pi$
$257$	−3889.35	−0.944013	−0.472006	+	0.881595i	$0.656470\pi$
$258$	17.8545i	0.00430843i
$259$	−4022.86	−0.965128
$260$	3326.83i	0.793542i
$261$	− 7453.00i	− 1.76755i
$262$	919.194i	0.216748i
$263$	1083.25	0.253978	0.126989	−	0.991904i	$-0.459469\pi$
$263$	1083.25	0.253978	0.126989	+	0.991904i	$0.459469\pi$
$264$	11.8908	0.00277207
$265$	− 2514.25i	− 0.582827i
$266$	787.160i	0.181443i
$267$	121.097i	0.0277565i
$268$	−2229.66	−0.508202
$269$	− 5495.85i	− 1.24568i	−0.782350	−	0.622840i	$-0.785979\pi$
$269$	− 5495.85i	− 1.24568i	0.782350	−	0.622840i	$-0.214021\pi$
$270$	−50.1372	−0.0113009
$271$	8472.62	1.89917	0.949584	−	0.313512i	$-0.101506\pi$
$271$	8472.62	1.89917	0.949584	+	0.313512i	$0.101506\pi$
$272$	0	0
$273$	−77.3130	−0.0171399
$274$	−809.746	−0.178535
$275$	357.741i	0.0784458i
$276$	−150.089	−0.0327329
$277$	1846.59i	0.400546i	0.979740	+	0.200273i	$0.0641828\pi$
$277$	1846.59i	0.400546i	−0.979740	+	0.200273i	$0.935817\pi$
$278$	1499.92i	0.323594i
$279$	− 6344.63i	− 1.36145i
$280$	−1248.32	−0.266434
$281$	−2152.85	−0.457039	−0.228520	−	0.973539i	$-0.573389\pi$
$281$	−2152.85	−0.457039	−0.228520	+	0.973539i	$0.573389\pi$
$282$	− 62.8979i	− 0.0132820i
$283$	− 4239.37i	− 0.890474i	−0.895413	−	0.445237i	$-0.853119\pi$
$283$	− 4239.37i	− 0.890474i	0.895413	−	0.445237i	$-0.146881\pi$
$284$	− 2320.33i	− 0.484810i
$285$	95.2730	0.0198017
$286$	− 311.138i	− 0.0643285i
$287$	1028.96	0.211629
$288$	3783.37	0.774087
$289$	0	0
$290$	1972.94	0.399499
$291$	−52.2745	−0.0105305
$292$	− 488.076i	− 0.0978168i
$293$	1207.74	0.240809	0.120404	−	0.992725i	$-0.461581\pi$
$293$	1207.74	0.240809	0.120404	+	0.992725i	$0.461581\pi$
$294$	22.7185i	0.00450670i
$295$	− 4521.33i	− 0.892345i
$296$	4436.06i	0.871084i
$297$	−51.0516	−0.00997413
$298$	1080.81	0.210099
$299$	8215.26i	1.58897i
$300$	− 46.8599i	− 0.00901820i
$301$	− 1908.60i	− 0.365482i
$302$	−1540.55	−0.293540
$303$	− 111.909i	− 0.0212178i
$304$	−4064.70	−0.766863
$305$	−4855.80	−0.911613
$306$	0	0
$307$	−454.092	−0.0844183	−0.0422091	−	0.999109i	$-0.513440\pi$
$307$	−454.092	−0.0844183	−0.0422091	+	0.999109i	$0.513440\pi$
$308$	−607.639	−0.112414
$309$	− 187.098i	− 0.0344455i
$310$	1679.53	0.307713
$311$	− 1997.93i	− 0.364283i	−0.983272	−	0.182142i	$-0.941697\pi$
$311$	− 1997.93i	− 0.364283i	0.983272	−	0.182142i	$-0.0583030\pi$
$312$	85.2542i	0.0154698i
$313$	− 5409.58i	− 0.976892i	−0.872594	−	0.488446i	$-0.837564\pi$
$313$	− 5409.58i	− 0.976892i	0.872594	−	0.488446i	$-0.162436\pi$
$314$	1457.84	0.262008
$315$	2678.92	0.479175
$316$	− 870.590i	− 0.154983i
$317$	8125.30i	1.43963i	0.694166	+	0.719815i	$0.255773\pi$
$317$	8125.30i	1.43963i	−0.694166	+	0.719815i	$0.744227\pi$
$318$	− 30.8009i	− 0.00543154i
$319$	2008.92	0.352596
$320$	− 2363.00i	− 0.412799i
$321$	247.487	0.0430323
$322$	−1473.63	−0.255037
$323$	0	0
$324$	−5331.37	−0.914158
$325$	−2564.92	−0.437774
$326$	472.349i	0.0802484i
$327$	172.647	0.0291970
$328$	− 1134.65i	− 0.191008i
$329$	6723.61i	1.12670i
$330$	− 6.75500i	− 0.00112682i
$331$	1564.31	0.259765	0.129883	−	0.991529i	$-0.458540\pi$
$331$	1564.31	0.259765	0.129883	+	0.991529i	$0.458540\pi$
$332$	−1579.48	−0.261100
$333$	− 9519.88i	− 1.56663i
$334$	− 1948.81i	− 0.319263i
$335$	2649.62i	0.432133i
$336$	71.6117	0.0116272
$337$	10840.7i	1.75232i	0.482019	+	0.876161i	$0.339904\pi$
$337$	10840.7i	1.75232i	−0.482019	+	0.876161i	$0.660096\pi$
$338$	428.476	0.0689527
$339$	106.354	0.0170394
$340$	0	0
$341$	1710.17	0.271586
$342$	−1862.77	−0.294524
$343$	− 6339.56i	− 0.997971i
$344$	−2104.64	−0.329868
$345$	178.359i	0.0278334i
$346$	1526.24i	0.237142i
$347$	9680.61i	1.49764i	0.662771	+	0.748822i	$0.269380\pi$
$347$	9680.61i	1.49764i	−0.662771	+	0.748822i	$0.730620\pi$
$348$	−263.145	−0.0405347
$349$	−1152.28	−0.176735	−0.0883673	−	0.996088i	$-0.528165\pi$
$349$	−1152.28	−0.176735	−0.0883673	+	0.996088i	$0.528165\pi$
$350$	− 460.088i	− 0.0702649i
$351$	− 366.029i	− 0.0556615i
$352$	1019.79i	0.154417i
$353$	4545.98	0.685433	0.342717	−	0.939439i	$-0.388653\pi$
$353$	4545.98	0.685433	0.342717	+	0.939439i	$0.388653\pi$
$354$	− 55.3887i	− 0.00831603i
$355$	−2757.37	−0.412242
$356$	−6823.87	−1.01591
$357$	0	0
$358$	−1872.21	−0.276395
$359$	11499.9	1.69065	0.845326	−	0.534251i	$-0.179406\pi$
$359$	11499.9	1.69065	0.845326	+	0.534251i	$0.179406\pi$
$360$	− 2954.09i	− 0.432483i
$361$	222.670	0.0324639
$362$	− 294.005i	− 0.0426866i
$363$	166.186i	0.0240289i
$364$	− 4356.64i	− 0.627335i
$365$	−580.007	−0.0831753
$366$	−59.4861	−0.00849560
$367$	− 5586.57i	− 0.794596i	−0.917690	−	0.397298i	$-0.869948\pi$
$367$	− 5586.57i	− 0.794596i	0.917690	−	0.397298i	$-0.130052\pi$
$368$	− 7609.44i	− 1.07791i
$369$	2434.98i	0.343523i
$370$	2520.07	0.354088
$371$	3292.53i	0.460754i
$372$	−224.012	−0.0312217
$373$	−4644.89	−0.644781	−0.322391	−	0.946607i	$-0.604486\pi$
$373$	−4644.89	−0.644781	−0.322391	+	0.946607i	$0.604486\pi$
$374$	0	0
$375$	−197.204	−0.0271562
$376$	7414.22	1.01691
$377$	14403.5i	1.96769i
$378$	65.6571	0.00893396
$379$	− 5213.72i	− 0.706625i	−0.935505	−	0.353312i	$-0.885055\pi$
$379$	− 5213.72i	− 0.706625i	0.935505	−	0.353312i	$-0.114945\pi$
$380$	5368.70i	0.724759i
$381$	− 33.4594i	− 0.00449916i
$382$	−50.0121	−0.00669854
$383$	−8072.13	−1.07694	−0.538468	−	0.842646i	$-0.680997\pi$
$383$	−8072.13	−1.07694	−0.538468	+	0.842646i	$0.680997\pi$
$384$	− 174.798i	− 0.0232295i
$385$	722.091i	0.0955874i
$386$	− 1645.63i	− 0.216995i
$387$	4516.60	0.593260
$388$	− 2945.70i	− 0.385427i
$389$	5774.57	0.752654	0.376327	−	0.926487i	$-0.377187\pi$
$389$	5774.57	0.752654	0.376327	+	0.926487i	$0.377187\pi$
$390$	48.4319	0.00628832
$391$	0	0
$392$	−2677.99	−0.345048
$393$	−145.692	−0.0187002
$394$	2484.50i	0.317683i
$395$	−1034.57	−0.131784
$396$	− 1437.95i	− 0.182474i
$397$	1145.58i	0.144824i	0.997375	+	0.0724121i	$0.0230697\pi$
$397$	1145.58i	0.144824i	−0.997375	+	0.0724121i	$0.976930\pi$
$398$	− 3815.74i	− 0.480568i
$399$	−124.765	−0.0156542
$400$	2375.78	0.296972
$401$	9526.00i	1.18630i	0.805093	+	0.593149i	$0.202116\pi$
$401$	9526.00i	1.18630i	−0.805093	+	0.593149i	$0.797884\pi$
$402$	32.4593i	0.00402717i
$403$	12261.5i	1.51561i
$404$	6306.13	0.776588
$405$	6335.55i	0.777324i
$406$	−2583.66	−0.315824
$407$	2566.04	0.312515
$408$	0	0
$409$	−9232.68	−1.11620	−0.558101	−	0.829773i	$-0.688470\pi$
$409$	−9232.68	−1.11620	−0.558101	+	0.829773i	$0.688470\pi$
$410$	−644.580	−0.0776428
$411$	− 128.345i	− 0.0154033i
$412$	10543.1	1.26073
$413$	5920.90i	0.705444i
$414$	− 3487.26i	− 0.413984i
$415$	1876.98i	0.222018i
$416$	−7311.66	−0.861740
$417$	−237.736	−0.0279185
$418$	− 502.101i	− 0.0587526i
$419$	− 13347.0i	− 1.55619i	−0.628146	−	0.778096i	$-0.716186\pi$
$419$	− 13347.0i	− 1.55619i	0.628146	−	0.778096i	$-0.283814\pi$
$420$	− 94.5855i	− 0.0109888i
$421$	3111.03	0.360148	0.180074	−	0.983653i	$-0.442366\pi$
$421$	3111.03	0.360148	0.180074	+	0.983653i	$0.442366\pi$
$422$	− 466.858i	− 0.0538537i
$423$	−15911.1	−1.82890
$424$	3630.72	0.415857
$425$	0	0
$426$	−33.7793	−0.00384181
$427$	6358.90	0.720676
$428$	13946.0i	1.57502i
$429$	49.3152	0.00555003
$430$	1195.62i	0.134088i
$431$	13024.0i	1.45555i	0.685816	+	0.727775i	$0.259445\pi$
$431$	13024.0i	1.45555i	−0.685816	+	0.727775i	$0.740555\pi$
$432$	339.037i	0.0377590i
$433$	14809.7	1.64367	0.821834	−	0.569727i	$-0.192951\pi$
$433$	14809.7	1.64367	0.821834	+	0.569727i	$0.192951\pi$
$434$	−2199.43	−0.243263
$435$	312.710i	0.0344673i
$436$	9728.79i	1.06863i
$437$	13257.5i	1.45124i
$438$	−7.10541	−0.000775136 0
$439$	3350.47i	0.364257i	0.983275	+	0.182129i	$0.0582988\pi$
$439$	3350.47i	0.364257i	−0.983275	+	0.182129i	$0.941701\pi$
$440$	796.260	0.0862732
$441$	5747.02	0.620562
$442$	0	0
$443$	15215.7	1.63188	0.815938	−	0.578140i	$-0.196221\pi$
$443$	15215.7	1.63188	0.815938	+	0.578140i	$0.196221\pi$
$444$	−336.121	−0.0359270
$445$	8109.17i	0.863846i
$446$	−2348.19	−0.249305
$447$	171.308i	0.0181266i
$448$	3094.46i	0.326339i
$449$	9942.68i	1.04504i	0.852626	+	0.522521i	$0.175008\pi$
$449$	9942.68i	1.04504i	−0.852626	+	0.522521i	$0.824992\pi$
$450$	1088.77	0.114056
$451$	−656.337	−0.0685270
$452$	5993.13i	0.623658i
$453$	− 244.177i	− 0.0253255i
$454$	3479.29i	0.359672i
$455$	−5177.23	−0.533434
$456$	137.580i	0.0141289i
$457$	2203.40	0.225538	0.112769	−	0.993621i	$-0.464028\pi$
$457$	2203.40	0.225538	0.112769	+	0.993621i	$0.464028\pi$
$458$	−3123.22	−0.318643
$459$	0	0
$460$	−10050.6	−1.01872
$461$	904.355	0.0913667	0.0456833	−	0.998956i	$-0.485453\pi$
$461$	904.355	0.0913667	0.0456833	+	0.998956i	$0.485453\pi$
$462$	8.84600i	0 0.000890808i
$463$	−2104.09	−0.211200	−0.105600	−	0.994409i	$-0.533676\pi$
$463$	−2104.09	−0.211200	−0.105600	+	0.994409i	$0.533676\pi$
$464$	− 13341.3i	− 1.33482i
$465$	266.205i	0.0265483i
$466$	− 3859.76i	− 0.383691i
$467$	−6031.14	−0.597619	−0.298809	−	0.954313i	$-0.596589\pi$
$467$	−6031.14	−0.597619	−0.298809	+	0.954313i	$0.596589\pi$
$468$	10309.8	1.01831
$469$	− 3469.81i	− 0.341623i
$470$	− 4211.93i	− 0.413366i
$471$	231.067i	0.0226051i
$472$	6529.05	0.636704
$473$	1217.43i	0.118345i
$474$	−12.6740	−0.00122814
$475$	−4139.17	−0.399828
$476$	0	0
$477$	−7791.60	−0.747910
$478$	3123.66	0.298897
$479$	− 3474.22i	− 0.331401i	−0.986176	−	0.165700i	$-0.947012\pi$
$479$	− 3474.22i	− 0.331401i	0.986176	−	0.165700i	$-0.0529885\pi$
$480$	−158.741	−0.0150948
$481$	18397.9i	1.74402i
$482$	− 1280.97i	− 0.121051i
$483$	− 233.569i	− 0.0220037i
$484$	−9364.68	−0.879477
$485$	−3500.54	−0.327735
$486$	233.085i	0.0217551i
$487$	− 7067.88i	− 0.657651i	−0.944391	−	0.328826i	$-0.893347\pi$
$487$	− 7067.88i	− 0.657651i	0.944391	−	0.328826i	$-0.106653\pi$
$488$	− 7012.05i	− 0.650452i
$489$	−74.8671	−0.00692354
$490$	1521.33i	0.140259i
$491$	4962.67	0.456135	0.228067	−	0.973645i	$-0.426759\pi$
$491$	4962.67	0.456135	0.228067	+	0.973645i	$0.426759\pi$
$492$	85.9725	0.00787793
$493$	0	0
$494$	3599.96	0.327874
$495$	−1708.79	−0.155160
$496$	− 11357.3i	− 1.02814i
$497$	3610.91	0.325898
$498$	22.9940i	0.00206905i
$499$	− 5518.75i	− 0.495097i	−0.968876	−	0.247548i	$-0.920375\pi$
$499$	− 5518.75i	− 0.495097i	0.968876	−	0.247548i	$-0.0796249\pi$
$500$	− 11112.6i	− 0.993940i
$501$	308.885	0.0275448
$502$	−2914.96	−0.259166
$503$	− 19453.6i	− 1.72444i	−0.506533	−	0.862221i	$-0.669073\pi$
$503$	− 19453.6i	− 1.72444i	0.506533	−	0.862221i	$-0.330927\pi$
$504$	3868.52i	0.341900i
$505$	− 7493.91i	− 0.660346i
$506$	939.974	0.0825829
$507$	67.9133i	0.00594898i
$508$	1885.46	0.164673
$509$	−10475.2	−0.912190	−0.456095	−	0.889931i	$-0.650752\pi$
$509$	−10475.2	−0.912190	−0.456095	+	0.889931i	$0.650752\pi$
$510$	0	0
$511$	759.548	0.0657543
$512$	11631.0	1.00395
$513$	− 590.683i	− 0.0508368i
$514$	−3190.64	−0.273800
$515$	− 12529.0i	− 1.07202i
$516$	− 159.469i	− 0.0136051i
$517$	− 4288.75i	− 0.364834i
$518$	−3300.16	−0.279924
$519$	−241.909	−0.0204598
$520$	5709.01i	0.481455i
$521$	14527.2i	1.22159i	0.791789	+	0.610794i	$0.209150\pi$
$521$	14527.2i	1.22159i	−0.791789	+	0.610794i	$0.790850\pi$
$522$	− 6114.08i	− 0.512656i
$523$	−5114.00	−0.427571	−0.213785	−	0.976881i	$-0.568579\pi$
$523$	−5114.00	−0.427571	−0.213785	+	0.976881i	$0.568579\pi$
$524$	− 8209.84i	− 0.684443i
$525$	72.9238	0.00606220
$526$	888.650	0.0736634
$527$	0	0
$528$	−45.6785	−0.00376497
$529$	−12652.0	−1.03986
$530$	− 2062.57i	− 0.169042i
$531$	−14011.5	−1.14510
$532$	− 7030.57i	− 0.572958i
$533$	− 4705.79i	− 0.382421i
$534$	99.3417i	0.00805045i
$535$	16572.8	1.33926
$536$	−3826.21	−0.308334
$537$	− 296.744i	− 0.0238463i
$538$	− 4508.53i	− 0.361295i
$539$	1549.08i	0.123792i
$540$	447.803	0.0356859
$541$	10714.7i	0.851501i	0.904841	+	0.425751i	$0.139990\pi$
$541$	10714.7i	0.851501i	−0.904841	+	0.425751i	$0.860010\pi$
$542$	6950.53	0.550831
$543$	46.5996	0.00368284
$544$	0	0
$545$	11561.2	0.908677
$546$	−63.4239	−0.00497123
$547$	− 24157.2i	− 1.88827i	−0.329552	−	0.944137i	$-0.606898\pi$
$547$	− 24157.2i	− 1.88827i	0.329552	−	0.944137i	$-0.393102\pi$
$548$	7232.30	0.563775
$549$	15048.0i	1.16982i
$550$	293.474i	0.0227523i
$551$	23243.8i	1.79713i
$552$	−257.560	−0.0198596
$553$	1354.82	0.104182
$554$	1514.86i	0.116174i
$555$	399.431i	0.0305494i
$556$	− 13396.6i	− 1.02184i
$557$	−15028.7	−1.14325	−0.571623	−	0.820516i	$-0.693686\pi$
$557$	−15028.7	−1.14325	−0.571623	+	0.820516i	$0.693686\pi$
$558$	− 5204.83i	− 0.394871i
$559$	−8728.69	−0.660437
$560$	4795.44	0.361865
$561$	0	0
$562$	−1766.09	−0.132559
$563$	−22490.0	−1.68355	−0.841775	−	0.539828i	$-0.818489\pi$
$563$	−22490.0	−1.68355	−0.841775	+	0.539828i	$0.818489\pi$
$564$	561.777i	0.0419416i
$565$	7121.96	0.530307
$566$	− 3477.77i	− 0.258272i
$567$	− 8296.71i	− 0.614514i
$568$	− 3981.80i	− 0.294142i
$569$	−1395.28	−0.102800	−0.0514000	−	0.998678i	$-0.516368\pi$
$569$	−1395.28	−0.102800	−0.0514000	+	0.998678i	$0.516368\pi$
$570$	78.1574	0.00574325
$571$	6512.53i	0.477304i	0.971105	+	0.238652i	$0.0767056\pi$
$571$	6512.53i	0.477304i	−0.971105	+	0.238652i	$0.923294\pi$
$572$	2778.95i	0.203136i
$573$	− 7.92691i	0 0.000577926i
$574$	844.109	0.0613806
$575$	− 7748.86i	− 0.562000i
$576$	−7322.89	−0.529723
$577$	8371.03	0.603970	0.301985	−	0.953313i	$-0.402351\pi$
$577$	8371.03	0.603970	0.301985	+	0.953313i	$0.402351\pi$
$578$	0	0
$579$	260.831	0.0187215
$580$	−17621.4	−1.26153
$581$	− 2458.00i	− 0.175516i
$582$	−42.8835	−0.00305426
$583$	− 2100.19i	− 0.149195i
$584$	− 837.564i	− 0.0593470i
$585$	− 12251.6i	− 0.865886i
$586$	990.772	0.0698437
$587$	4015.43	0.282342	0.141171	−	0.989985i	$-0.454913\pi$
$587$	4015.43	0.282342	0.141171	+	0.989985i	$0.454913\pi$
$588$	− 202.912i	− 0.0142312i
$589$	19787.1i	1.38423i
$590$	− 3709.08i	− 0.258814i
$591$	−393.792	−0.0274085
$592$	− 17041.2i	− 1.18309i
$593$	20568.8	1.42438	0.712191	−	0.701985i	$-0.247703\pi$
$593$	20568.8	1.42438	0.712191	+	0.701985i	$0.247703\pi$
$594$	−41.8803	−0.00289288
$595$	0	0
$596$	−9653.32	−0.663449
$597$	604.794	0.0414616
$598$	6739.41i	0.460861i
$599$	−953.480	−0.0650386	−0.0325193	−	0.999471i	$-0.510353\pi$
$599$	−953.480	−0.0650386	−0.0325193	+	0.999471i	$0.510353\pi$
$600$	− 80.4141i	− 0.00547148i
$601$	− 23469.7i	− 1.59293i	−0.604685	−	0.796465i	$-0.706701\pi$
$601$	− 23469.7i	− 1.59293i	0.604685	−	0.796465i	$-0.293299\pi$
$602$	− 1565.72i	− 0.106004i
$603$	8211.12	0.554532
$604$	13759.6	0.926934
$605$	11128.6i	0.747835i
$606$	− 91.8045i	− 0.00615396i
$607$	− 16081.9i	− 1.07536i	−0.843150	−	0.537679i	$-0.819301\pi$
$607$	− 16081.9i	− 1.07536i	0.843150	−	0.537679i	$-0.180699\pi$
$608$	−11799.3	−0.787045
$609$	− 409.509i	− 0.0272482i
$610$	−3983.46	−0.264403
$611$	30749.4	2.03599
$612$	0	0
$613$	18724.7	1.23374	0.616871	−	0.787064i	$-0.288400\pi$
$613$	18724.7	1.23374	0.616871	+	0.787064i	$0.288400\pi$
$614$	−372.515	−0.0244845
$615$	− 102.166i	− 0.00669873i
$616$	−1042.74	−0.0682033
$617$	6794.64i	0.443342i	0.975122	+	0.221671i	$0.0711511\pi$
$617$	6794.64i	0.443342i	−0.975122	+	0.221671i	$0.928849\pi$
$618$	− 153.486i	− 0.00999050i
$619$	2590.60i	0.168215i	0.996457	+	0.0841075i	$0.0268039\pi$
$619$	2590.60i	0.168215i	−0.996457	+	0.0841075i	$0.973196\pi$
$620$	−15000.8	−0.971691
$621$	1105.81	0.0714564
$622$	− 1639.00i	− 0.105656i
$623$	− 10619.4i	− 0.682914i
$624$	− 327.505i	− 0.0210107i
$625$	−7057.39	−0.451673
$626$	− 4437.76i	− 0.283336i
$627$	79.5829	0.00506895
$628$	−13020.8	−0.827364
$629$	0	0
$630$	2197.66	0.138979
$631$	13517.4	0.852804	0.426402	−	0.904534i	$-0.359781\pi$
$631$	13517.4	0.852804	0.426402	+	0.904534i	$0.359781\pi$
$632$	− 1493.98i	− 0.0940304i
$633$	73.9968	0.00464630
$634$	6665.61i	0.417547i
$635$	− 2240.60i	− 0.140024i
$636$	275.100i	0.0171516i
$637$	−11106.6	−0.690830
$638$	1648.02	0.102266
$639$	8545.03i	0.529008i
$640$	− 11705.3i	− 0.722954i
$641$	6505.82i	0.400881i	0.979706	+	0.200440i	$0.0642373\pi$
$641$	6505.82i	0.400881i	−0.979706	+	0.200440i	$0.935763\pi$
$642$	203.026	0.0124810
$643$	− 22660.6i	− 1.38981i	−0.719102	−	0.694905i	$-0.755447\pi$
$643$	− 22660.6i	− 1.38981i	0.719102	−	0.694905i	$-0.244553\pi$
$644$	13161.8	0.805353
$645$	−189.506	−0.0115686
$646$	0	0
$647$	18446.3	1.12086	0.560432	−	0.828201i	$-0.310635\pi$
$647$	18446.3	1.12086	0.560432	+	0.828201i	$0.310635\pi$
$648$	−9148.90	−0.554634
$649$	− 3776.73i	− 0.228428i
$650$	−2104.14	−0.126971
$651$	− 348.609i	− 0.0209878i
$652$	− 4218.81i	− 0.253407i
$653$	− 4455.99i	− 0.267039i	−0.991046	−	0.133520i	$-0.957372\pi$
$653$	− 4455.99i	− 0.267039i	0.991046	−	0.133520i	$-0.0426279\pi$
$654$	141.631	0.00846824
$655$	−9756.19	−0.581994
$656$	4358.77i	0.259423i
$657$	1797.43i	0.106734i
$658$	5515.73i	0.326786i
$659$	−18134.3	−1.07194	−0.535972	−	0.844236i	$-0.680055\pi$
$659$	−18134.3	−1.07194	−0.535972	+	0.844236i	$0.680055\pi$
$660$	60.3327i	0.00355825i
$661$	15946.6	0.938351	0.469175	−	0.883105i	$-0.344551\pi$
$661$	15946.6	0.938351	0.469175	+	0.883105i	$0.344551\pi$
$662$	1283.29	0.0753418
$663$	0	0
$664$	−2710.47	−0.158413
$665$	−8354.80	−0.487196
$666$	− 7809.65i	− 0.454381i
$667$	−43514.3	−2.52606
$668$	17405.9i	1.00816i
$669$	− 372.188i	− 0.0215091i
$670$	2173.62i	0.125335i
$671$	−4056.12	−0.233360
$672$	207.879	0.0119332
$673$	− 17263.1i	− 0.988774i	−0.869242	−	0.494387i	$-0.835393\pi$
$673$	− 17263.1i	− 0.988774i	0.869242	−	0.494387i	$-0.164607\pi$
$674$	8893.21i	0.508240i
$675$	345.248i	0.0196868i
$676$	−3826.96	−0.217738
$677$	15848.6i	0.899719i	0.893099	+	0.449859i	$0.148526\pi$
$677$	15848.6i	0.899719i	−0.893099	+	0.449859i	$0.851474\pi$
$678$	87.2479	0.00494209
$679$	4584.13	0.259091
$680$	0	0
$681$	−551.466	−0.0310312
$682$	1402.94	0.0787702
$683$	119.390i	0.00668863i	0.999994	+	0.00334432i	$0.00106453\pi$
$683$	119.390i	0.00668863i	−0.999994	+	0.00334432i	$0.998935\pi$
$684$	16637.5	0.930043
$685$	− 8594.53i	− 0.479387i
$686$	− 5200.67i	− 0.289450i
$687$	− 495.029i	− 0.0274913i
$688$	8085.00	0.448020
$689$	15057.9	0.832598
$690$	146.317i	0.00807274i
$691$	18092.7i	0.996061i	0.867159	+	0.498031i	$0.165943\pi$
$691$	18092.7i	0.996061i	−0.867159	+	0.498031i	$0.834057\pi$
$692$	− 13631.7i	− 0.748844i
$693$	2237.74	0.122662
$694$	7941.51i	0.434374i
$695$	−15919.9	−0.868887
$696$	−451.571	−0.0245930
$697$	0	0
$698$	−945.278	−0.0512598
$699$	611.771	0.0331034
$700$	4109.30i	0.221881i
$701$	23710.0	1.27748	0.638741	−	0.769422i	$-0.279456\pi$
$701$	23710.0	1.27748	0.638741	+	0.769422i	$0.279456\pi$
$702$	− 300.273i	− 0.0161440i
$703$	29689.8i	1.59285i
$704$	− 1973.85i	− 0.105671i
$705$	667.590	0.0356637
$706$	3729.30	0.198802
$707$	9813.64i	0.522037i
$708$	494.707i	0.0262602i
$709$	− 11909.1i	− 0.630826i	−0.948954	−	0.315413i	$-0.897857\pi$
$709$	− 11909.1i	− 0.630826i	0.948954	−	0.315413i	$-0.102143\pi$
$710$	−2262.01	−0.119566
$711$	3206.10i	0.169112i
$712$	−11710.1	−0.616369
$713$	−37043.1	−1.94569
$714$	0	0
$715$	3302.37	0.172730
$716$	16721.7	0.872794
$717$	495.099i	0.0257877i
$718$	9434.00	0.490354
$719$	− 12905.7i	− 0.669406i	−0.942324	−	0.334703i	$-0.891364\pi$
$719$	− 12905.7i	− 0.669406i	0.942324	−	0.334703i	$-0.108636\pi$
$720$	11348.2i	0.587390i
$721$	16407.3i	0.847488i
$722$	182.668	0.00941576
$723$	203.033	0.0104438
$724$	2625.92i	0.134795i
$725$	− 13585.8i	− 0.695950i
$726$	136.331i	0.00696930i
$727$	13914.0	0.709824	0.354912	−	0.934900i	$-0.384511\pi$
$727$	13914.0	0.709824	0.354912	+	0.934900i	$0.384511\pi$
$728$	− 7476.22i	− 0.380614i
$729$	19609.1	0.996245
$730$	−475.810	−0.0241240
$731$	0	0
$732$	531.304	0.0268273
$733$	−26387.4	−1.32966	−0.664830	−	0.746995i	$-0.731496\pi$
$733$	−26387.4	−1.32966	−0.664830	+	0.746995i	$0.731496\pi$
$734$	− 4582.96i	− 0.230463i
$735$	−241.131	−0.0121010
$736$	− 22089.2i	− 1.10627i
$737$	2213.27i	0.110620i
$738$	1997.54i	0.0996347i
$739$	−4544.65	−0.226221	−0.113111	−	0.993582i	$-0.536081\pi$
$739$	−4544.65	−0.226221	−0.113111	+	0.993582i	$0.536081\pi$
$740$	−22508.2	−1.11813
$741$	570.592i	0.0282877i
$742$	2701.03i	0.133636i
$743$	13381.7i	0.660738i	0.943852	+	0.330369i	$0.107173\pi$
$743$	13381.7i	0.660738i	−0.943852	+	0.330369i	$0.892827\pi$
$744$	−384.416	−0.0189427
$745$	11471.6i	0.564142i
$746$	−3810.45	−0.187011
$747$	5816.72	0.284903
$748$	0	0
$749$	−21702.9	−1.05876
$750$	−161.777	−0.00787634
$751$	2582.21i	0.125468i	0.998030	+	0.0627338i	$0.0199819\pi$
$751$	2582.21i	0.125468i	−0.998030	+	0.0627338i	$0.980018\pi$
$752$	−28481.8	−1.38115
$753$	− 462.021i	− 0.0223599i
$754$	11816.0i	0.570705i
$755$	− 16351.2i	− 0.788188i
$756$	−586.420	−0.0282115
$757$	−26990.8	−1.29590	−0.647952	−	0.761681i	$-0.724374\pi$
$757$	−26990.8	−1.29590	−0.647952	+	0.761681i	$0.724374\pi$
$758$	− 4277.08i	− 0.204948i
$759$	148.986i	0.00712495i
$760$	9212.96i	0.439723i
$761$	29083.4	1.38538	0.692688	−	0.721237i	$-0.256426\pi$
$761$	29083.4	1.38538	0.692688	+	0.721237i	$0.256426\pi$
$762$	− 27.4485i	− 0.00130493i
$763$	−15140.0	−0.718355
$764$	446.686	0.0211526
$765$	0	0
$766$	−6621.98	−0.312352
$767$	27078.3	1.27476
$768$	138.903i	0.00652635i
$769$	30381.9	1.42471	0.712354	−	0.701820i	$-0.247629\pi$
$769$	30381.9	1.42471	0.712354	+	0.701820i	$0.247629\pi$
$770$	592.369i	0.0277240i
$771$	− 505.715i	− 0.0236224i
$772$	14698.0i	0.685224i
$773$	27193.1	1.26529	0.632644	−	0.774443i	$-0.281970\pi$
$773$	27193.1	1.26529	0.632644	+	0.774443i	$0.281970\pi$
$774$	3705.20	0.172068
$775$	− 11565.4i	− 0.536053i
$776$	− 5054.98i	− 0.233844i
$777$	− 523.074i	− 0.0241508i
$778$	4737.18	0.218298
$779$	− 7594.01i	− 0.349273i
$780$	−432.572	−0.0198571
$781$	−2303.27	−0.105528
$782$	0	0
$783$	1938.77	0.0884878
$784$	10287.5	0.468638
$785$	15473.3i	0.703522i
$786$	−119.519	−0.00542378
$787$	7711.24i	0.349271i	0.984633	+	0.174635i	$0.0558747\pi$
$787$	7711.24i	0.349271i	−0.984633	+	0.174635i	$0.944125\pi$
$788$	− 22190.4i	− 1.00318i
$789$	140.851i	0.00635541i
$790$	−848.710	−0.0382225
$791$	−9326.56	−0.419234
$792$	− 2467.59i	− 0.110710i
$793$	− 29081.5i	− 1.30229i
$794$	939.781i	0.0420045i
$795$	326.917	0.0145843
$796$	34080.5i	1.51753i
$797$	−5128.97	−0.227952	−0.113976	−	0.993484i	$-0.536359\pi$
$797$	−5128.97	−0.227952	−0.113976	+	0.993484i	$0.536359\pi$
$798$	−102.351	−0.00454033
$799$	0	0
$800$	6896.56	0.304788
$801$	25130.1	1.10853
$802$	7814.67i	0.344072i
$803$	−484.489	−0.0212917
$804$	− 289.912i	− 0.0127169i
$805$	− 15640.9i	− 0.684805i
$806$	10058.8i	0.439584i
$807$	714.600	0.0311712
$808$	10821.6	0.471168
$809$	− 15982.4i	− 0.694575i	−0.937759	−	0.347288i	$-0.887103\pi$
$809$	− 15982.4i	− 0.694575i	0.937759	−	0.347288i	$-0.112897\pi$
$810$	5197.38i	0.225454i
$811$	24954.3i	1.08047i	0.841513	+	0.540237i	$0.181666\pi$
$811$	24954.3i	1.08047i	−0.841513	+	0.540237i	$0.818334\pi$
$812$	23076.1	0.997305
$813$	1101.66i	0.0475237i
$814$	2105.05	0.0906414
$815$	−5013.44	−0.215476
$816$	0	0
$817$	−14086.0	−0.603191
$818$	−7574.05	−0.323741
$819$	16044.1i	0.684526i
$820$	5757.11	0.245179
$821$	22706.8i	0.965253i	0.875826	+	0.482627i	$0.160317\pi$
$821$	22706.8i	0.965253i	−0.875826	+	0.482627i	$0.839683\pi$
$822$	− 105.288i	− 0.00446755i
$823$	− 16780.0i	− 0.710708i	−0.934732	−	0.355354i	$-0.884360\pi$
$823$	− 16780.0i	− 0.710708i	0.934732	−	0.355354i	$-0.115640\pi$
$824$	18092.5	0.764907
$825$	−46.5155	−0.00196298
$826$	4857.22i	0.204606i
$827$	− 11724.6i	− 0.492992i	−0.969144	−	0.246496i	$-0.920721\pi$
$827$	− 11724.6i	− 0.492992i	0.969144	−	0.246496i	$-0.0792791\pi$
$828$	31146.7i	1.30727i
$829$	25050.0	1.04948	0.524742	−	0.851262i	$-0.324162\pi$
$829$	25050.0	1.04948	0.524742	+	0.851262i	$0.324162\pi$
$830$	1539.78i	0.0643936i
$831$	−240.104	−0.0100230
$832$	14152.1	0.589705
$833$	0	0
$834$	−195.028	−0.00809742
$835$	20684.3	0.857259
$836$	4484.55i	0.185528i
$837$	1650.45	0.0681574
$838$	− 10949.2i	− 0.451355i
$839$	32103.3i	1.32101i	0.750821	+	0.660505i	$0.229658\pi$
$839$	32103.3i	1.32101i	−0.750821	+	0.660505i	$0.770342\pi$
$840$	− 162.314i	− 0.00666709i
$841$	−51903.0	−2.12813
$842$	2552.14	0.104457
$843$	− 279.925i	− 0.0114367i
$844$	4169.77i	0.170058i
$845$	4547.78i	0.185146i
$846$	−13052.7	−0.530450
$847$	− 14573.4i	− 0.591201i
$848$	−13947.5	−0.564809
$849$	551.226	0.0222827
$850$	0	0
$851$	−55581.7	−2.23892
$852$	301.702	0.0121316
$853$	35039.8i	1.40649i	0.710946	+	0.703247i	$0.248267\pi$
$853$	35039.8i	1.40649i	−0.710946	+	0.703247i	$0.751733\pi$
$854$	5216.54	0.209024
$855$	− 19771.2i	− 0.790831i
$856$	23932.1i	0.955587i
$857$	− 9190.48i	− 0.366325i	−0.983083	−	0.183163i	$-0.941366\pi$
$857$	− 9190.48i	− 0.366325i	0.983083	−	0.183163i	$-0.0586335\pi$
$858$	40.4558	0.00160972
$859$	18161.5	0.721376	0.360688	−	0.932687i	$-0.382542\pi$
$859$	18161.5	0.721376	0.360688	+	0.932687i	$0.382542\pi$
$860$	− 10678.8i	− 0.423422i
$861$	133.791i	0.00529569i
$862$	10684.2i	0.422165i
$863$	7208.75	0.284344	0.142172	−	0.989842i	$-0.454591\pi$
$863$	7208.75	0.284344	0.142172	+	0.989842i	$0.454591\pi$
$864$	984.177i	0.0387528i
$865$	−16199.3	−0.636755
$866$	12149.2	0.476727
$867$	0	0
$868$	19644.3	0.768171
$869$	−864.190	−0.0337349
$870$	256.532i	0.00999684i
$871$	−15868.6	−0.617323
$872$	16695.1i	0.648357i
$873$	10848.1i	0.420564i
$874$	10875.8i	0.420914i
$875$	17293.5	0.668145
$876$	63.4624	0.00244771
$877$	28571.7i	1.10011i	0.835128	+	0.550055i	$0.185393\pi$
$877$	28571.7i	1.10011i	−0.835128	+	0.550055i	$0.814607\pi$
$878$	2748.56i	0.105649i
$879$	157.037i	0.00602585i
$880$	−3058.84	−0.117174
$881$	38157.7i	1.45921i	0.683868	+	0.729606i	$0.260296\pi$
$881$	38157.7i	1.45921i	−0.683868	+	0.729606i	$0.739704\pi$
$882$	4714.58	0.179987
$883$	−15653.9	−0.596598	−0.298299	−	0.954472i	$-0.596419\pi$
$883$	−15653.9	−0.596598	−0.298299	+	0.954472i	$0.596419\pi$
$884$	0	0
$885$	587.888	0.0223295
$886$	12482.2	0.473306
$887$	− 20787.1i	− 0.786879i	−0.919351	−	0.393439i	$-0.871285\pi$
$887$	− 20787.1i	− 0.786879i	0.919351	−	0.393439i	$-0.128715\pi$
$888$	−576.801	−0.0217975
$889$	2934.17i	0.110696i
$890$	6652.37i	0.250548i
$891$	5292.18i	0.198984i
$892$	20973.0	0.787252
$893$	49622.1	1.85951
$894$	140.533i	0.00525741i
$895$	− 19871.4i	− 0.742152i
$896$	15328.6i	0.571532i
$897$	−1068.19	−0.0397614
$898$	8156.50i	0.303102i
$899$	−64946.3	−2.40943
$900$	−9724.44	−0.360165
$901$	0	0
$902$	−538.427	−0.0198755
$903$	248.167	0.00914560
$904$	10284.5i	0.378383i
$905$	3120.52	0.114618
$906$	− 200.311i	− 0.00734536i
$907$	− 10127.0i	− 0.370739i	−0.982669	−	0.185370i	$-0.940652\pi$
$907$	− 10127.0i	− 0.370739i	0.982669	−	0.185370i	$-0.0593482\pi$
$908$	− 31075.5i	− 1.13577i
$909$	−23223.5	−0.847385
$910$	−4247.15	−0.154716
$911$	3789.48i	0.137817i	0.997623	+	0.0689084i	$0.0219516\pi$
$911$	3789.48i	0.137817i	−0.997623	+	0.0689084i	$0.978048\pi$
$912$	− 528.514i	− 0.0191895i
$913$	1567.87i	0.0568334i
$914$	1807.56	0.0654146
$915$	− 631.377i	− 0.0228117i
$916$	27895.2	1.00620
$917$	12776.2	0.460096
$918$	0	0
$919$	−3496.26	−0.125496	−0.0627481	−	0.998029i	$-0.519986\pi$
$919$	−3496.26	−0.125496	−0.0627481	+	0.998029i	$0.519986\pi$
$920$	−17247.4	−0.618076
$921$	− 59.0436i	− 0.00211243i
$922$	741.890	0.0264998
$923$	− 16514.0i	− 0.588909i
$924$	− 79.0086i	− 0.00281298i
$925$	− 17353.4i	− 0.616840i
$926$	−1726.10	−0.0612560
$927$	−38826.9	−1.37567
$928$	− 38728.1i	− 1.36995i
$929$	42446.8i	1.49907i	0.661967	+	0.749533i	$0.269722\pi$
$929$	42446.8i	1.49907i	−0.661967	+	0.749533i	$0.730278\pi$
$930$	218.382i	0.00770003i
$931$	−17923.3	−0.630949
$932$	34473.7i	1.21161i
$933$	259.782	0.00911562
$934$	−4947.66	−0.173332
$935$	0	0
$936$	17692.1	0.617824
$937$	22981.0	0.801235	0.400617	−	0.916245i	$-0.368796\pi$
$937$	22981.0	0.801235	0.400617	+	0.916245i	$0.368796\pi$
$938$	− 2846.47i	− 0.0990836i
$939$	703.383	0.0244452
$940$	37619.1i	1.30532i
$941$	5546.95i	0.192163i	0.995373	+	0.0960815i	$0.0306310\pi$
$941$	5546.95i	0.192163i	−0.995373	+	0.0960815i	$0.969369\pi$
$942$	189.556i	0.00655633i
$943$	14216.6	0.490940
$944$	−25081.4	−0.864758
$945$	696.875i	0.0239887i
$946$	998.720i	0.0343247i
$947$	− 19587.1i	− 0.672119i	−0.941841	−	0.336059i	$-0.890906\pi$
$947$	− 19587.1i	− 0.672119i	0.941841	−	0.336059i	$-0.109094\pi$
$948$	113.199	0.00387819
$949$	− 3473.68i	− 0.118820i
$950$	−3395.58	−0.115965
$951$	−1056.50	−0.0360244
$952$	0	0
$953$	−14441.2	−0.490866	−0.245433	−	0.969414i	$-0.578930\pi$
$953$	−14441.2	−0.490866	−0.245433	+	0.969414i	$0.578930\pi$
$954$	−6391.85	−0.216922
$955$	− 530.822i	− 0.0179864i
$956$	−27899.1	−0.943852
$957$	261.211i	0.00882315i
$958$	− 2850.08i	− 0.0961189i
$959$	11255.0i	0.378980i
$960$	307.250	0.0103297
$961$	−25496.8	−0.855857
$962$	15092.8i	0.505832i
$963$	− 51358.8i	− 1.71860i
$964$	11441.0i	0.382252i
$965$	17466.4	0.582657
$966$	− 191.609i	− 0.00638191i
$967$	52887.3	1.75878	0.879390	−	0.476103i	$-0.157951\pi$
$967$	52887.3	1.75878	0.879390	+	0.476103i	$0.157951\pi$
$968$	−16070.3	−0.533593
$969$	0	0
$970$	−2871.67	−0.0950556
$971$	13505.0	0.446340	0.223170	−	0.974780i	$-0.428360\pi$
$971$	13505.0	0.446340	0.223170	+	0.974780i	$0.428360\pi$
$972$	− 2081.82i	− 0.0686978i
$973$	20847.9	0.686899
$974$	− 5798.15i	− 0.190744i
$975$	− 333.506i	− 0.0109546i
$976$	26936.9i	0.883431i
$977$	−16575.1	−0.542770	−0.271385	−	0.962471i	$-0.587482\pi$
$977$	−16575.1	−0.542770	−0.271385	+	0.962471i	$0.587482\pi$
$978$	−61.4174	−0.00200809
$979$	6773.71i	0.221132i
$980$	− 13587.9i	− 0.442907i
$981$	− 35828.0i	− 1.16606i
$982$	4071.14	0.132297
$983$	− 41792.9i	− 1.35604i	−0.735043	−	0.678020i	$-0.762838\pi$
$983$	− 41792.9i	− 1.35604i	0.735043	−	0.678020i	$-0.237162\pi$
$984$	147.533	0.00477966
$985$	−26370.1	−0.853017
$986$	0	0
$987$	−874.241	−0.0281939
$988$	−32153.2	−1.03535
$989$	− 26370.1i	− 0.847848i
$990$	−1401.81	−0.0450024
$991$	− 47381.0i	− 1.51877i	−0.650639	−	0.759387i	$-0.725499\pi$
$991$	− 47381.0i	− 1.51877i	0.650639	−	0.759387i	$-0.274501\pi$
$992$	− 32968.7i	− 1.05520i
$993$	203.400i	0.00650022i
$994$	2962.22	0.0945230
$995$	40499.8	1.29038
$996$	− 205.373i	− 0.00653361i
$997$	27506.7i	0.873766i	0.899518	+	0.436883i	$0.143918\pi$
$997$	27506.7i	0.873766i	−0.899518	+	0.436883i	$0.856082\pi$
$998$	− 4527.32i	− 0.143597i
$999$	2476.43	0.0784292

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.b.f.288.13		24
17.4	even	4		289.4.a.h.1.6	✓	12
17.13	even	4		289.4.a.i.1.6	yes	12
17.16	even	2	inner	289.4.b.f.288.14		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.4.a.h.1.6	✓	12	17.4	even	4
289.4.a.i.1.6	yes	12	17.13	even	4
289.4.b.f.288.13		24	1.1	even	1	trivial
289.4.b.f.288.14		24	17.16	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	289.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+0.820352 q^{2} +0.130026i q^{3} -7.32702 q^{4} +8.70710i q^{5} +0.106667i q^{6} -11.4024i q^{7} -12.5736 q^{8} +26.9831 q^{9} +O(q^{10})\)	\(q+0.820352 q^{2} +0.130026i q^{3} -7.32702 q^{4} +8.70710i q^{5} +0.106667i q^{6} -11.4024i q^{7} -12.5736 q^{8} +26.9831 q^{9} +7.14288i q^{10} +7.27316i q^{11} -0.952700i q^{12} -52.1470 q^{13} -9.35395i q^{14} -1.13214 q^{15} +48.3014 q^{16} +22.1356 q^{18} -84.1527 q^{19} -63.7971i q^{20} +1.48260 q^{21} +5.96655i q^{22} -157.541i q^{23} -1.63488i q^{24} +49.1864 q^{25} -42.7789 q^{26} +7.01918i q^{27} +83.5454i q^{28} -276.210i q^{29} -0.928757 q^{30} -235.134i q^{31} +140.213 q^{32} -0.945697 q^{33} +99.2815 q^{35} -197.706 q^{36} -352.809i q^{37} -69.0348 q^{38} -6.78044i q^{39} -109.479i q^{40} +90.2409i q^{41} +1.21625 q^{42} +167.386 q^{43} -53.2906i q^{44} +234.944i q^{45} -129.239i q^{46} -589.668 q^{47} +6.28042i q^{48} +212.986 q^{49} +40.3502 q^{50} +382.082 q^{52} -288.759 q^{53} +5.75820i q^{54} -63.3281 q^{55} +143.368i q^{56} -10.9420i q^{57} -226.589i q^{58} -519.269 q^{59} +8.29525 q^{60} +557.682i q^{61} -192.892i q^{62} -307.671i q^{63} -271.388 q^{64} -454.049i q^{65} -0.775804 q^{66} +304.306 q^{67} +20.4843 q^{69} +81.4458 q^{70} +316.681i q^{71} -339.273 q^{72} +66.6132i q^{73} -289.428i q^{74} +6.39549i q^{75} +616.588 q^{76} +82.9313 q^{77} -5.56234i q^{78} +118.819i q^{79} +420.565i q^{80} +727.631 q^{81} +74.0293i q^{82} +215.569 q^{83} -10.8630 q^{84} +137.316 q^{86} +35.9144 q^{87} -91.4495i q^{88} +931.329 q^{89} +192.737i q^{90} +594.599i q^{91} +1154.30i q^{92} +30.5734 q^{93} -483.735 q^{94} -732.725i q^{95} +18.2312i q^{96} +402.033i q^{97} +174.723 q^{98} +196.252i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 96 q^{4} + 102 q^{8} - 216 q^{9}+O(q^{10}) \) 24 * q + 96 * q^4 + 102 * q^8 - 216 * q^9	\( 24 q + 96 q^{4} + 102 q^{8} - 216 q^{9} - 144 q^{13} + 276 q^{15} + 384 q^{16} + 378 q^{18} + 132 q^{19} + 492 q^{21} - 888 q^{25} - 1056 q^{26} - 3780 q^{30} + 2706 q^{32} + 1932 q^{33} - 132 q^{35} + 1326 q^{36} - 120 q^{38} - 1608 q^{42} - 972 q^{43} - 1776 q^{47} + 1140 q^{49} + 870 q^{50} + 450 q^{52} - 2052 q^{53} + 1944 q^{55} + 1584 q^{59} - 2916 q^{60} - 3714 q^{64} + 1188 q^{66} + 1248 q^{67} - 3012 q^{69} + 3300 q^{70} + 2910 q^{72} - 1350 q^{76} + 2016 q^{77} + 5040 q^{81} - 1344 q^{83} - 1554 q^{84} + 5556 q^{86} - 1452 q^{87} - 1812 q^{89} - 264 q^{93} - 1470 q^{94} + 3822 q^{98}+O(q^{100}) \) 24 * q + 96 * q^4 + 102 * q^8 - 216 * q^9 - 144 * q^13 + 276 * q^15 + 384 * q^16 + 378 * q^18 + 132 * q^19 + 492 * q^21 - 888 * q^25 - 1056 * q^26 - 3780 * q^30 + 2706 * q^32 + 1932 * q^33 - 132 * q^35 + 1326 * q^36 - 120 * q^38 - 1608 * q^42 - 972 * q^43 - 1776 * q^47 + 1140 * q^49 + 870 * q^50 + 450 * q^52 - 2052 * q^53 + 1944 * q^55 + 1584 * q^59 - 2916 * q^60 - 3714 * q^64 + 1188 * q^66 + 1248 * q^67 - 3012 * q^69 + 3300 * q^70 + 2910 * q^72 - 1350 * q^76 + 2016 * q^77 + 5040 * q^81 - 1344 * q^83 - 1554 * q^84 + 5556 * q^86 - 1452 * q^87 - 1812 * q^89 - 264 * q^93 - 1470 * q^94 + 3822 * q^98

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