LMFDB - Embedded newform 289.4.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,4,Mod(1,289)]

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([0]))

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

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	289.a (trivial)

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:	yes
Analytic conductor:	$17.0515519917$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.2555057.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 21x^{2} - 4x + 36 $ x^4 - x^3 - 21x^2 - 4x + 36
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.22501$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.22501 q^{2} +0.534684 q^{3} -6.49935 q^{4} +20.9528 q^{5} +0.654993 q^{6} -15.0235 q^{7} -17.7618 q^{8} -26.7141 q^{9} +O(q^{10})$	\(q+1.22501 q^{2} +0.534684 q^{3} -6.49935 q^{4} +20.9528 q^{5} +0.654993 q^{6} -15.0235 q^{7} -17.7618 q^{8} -26.7141 q^{9} +25.6674 q^{10} -45.4168 q^{11} -3.47510 q^{12} +3.14456 q^{13} -18.4039 q^{14} +11.2031 q^{15} +30.2364 q^{16} -32.7250 q^{18} -63.2180 q^{19} -136.180 q^{20} -8.03282 q^{21} -55.6360 q^{22} -114.551 q^{23} -9.49698 q^{24} +314.020 q^{25} +3.85211 q^{26} -28.7201 q^{27} +97.6429 q^{28} +96.6197 q^{29} +13.7239 q^{30} -194.578 q^{31} +179.135 q^{32} -24.2837 q^{33} -314.784 q^{35} +173.624 q^{36} -73.6682 q^{37} -77.4426 q^{38} +1.68135 q^{39} -372.161 q^{40} -341.047 q^{41} -9.84027 q^{42} -281.677 q^{43} +295.180 q^{44} -559.736 q^{45} -140.326 q^{46} +36.2294 q^{47} +16.1669 q^{48} -117.295 q^{49} +384.678 q^{50} -20.4376 q^{52} +191.274 q^{53} -35.1824 q^{54} -951.610 q^{55} +266.845 q^{56} -33.8017 q^{57} +118.360 q^{58} +104.171 q^{59} -72.8131 q^{60} +517.547 q^{61} -238.359 q^{62} +401.339 q^{63} -22.4497 q^{64} +65.8874 q^{65} -29.7477 q^{66} -560.893 q^{67} -61.2488 q^{69} -385.613 q^{70} -333.262 q^{71} +474.492 q^{72} -378.895 q^{73} -90.2443 q^{74} +167.902 q^{75} +410.876 q^{76} +682.319 q^{77} +2.05967 q^{78} +877.994 q^{79} +633.538 q^{80} +705.925 q^{81} -417.786 q^{82} +1195.27 q^{83} +52.2081 q^{84} -345.057 q^{86} +51.6611 q^{87} +806.687 q^{88} +783.884 q^{89} -685.682 q^{90} -47.2422 q^{91} +744.509 q^{92} -104.038 q^{93} +44.3813 q^{94} -1324.59 q^{95} +95.7804 q^{96} -1605.30 q^{97} -143.688 q^{98} +1213.27 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 2 q^{3} + 11 q^{4} - 14 q^{5} - 38 q^{6} - 36 q^{7} + 60 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q + q^2 + 2 * q^3 + 11 * q^4 - 14 * q^5 - 38 * q^6 - 36 * q^7 + 60 * q^8 + 6 * q^9	\( 4 q + q^{2} + 2 q^{3} + 11 q^{4} - 14 q^{5} - 38 q^{6} - 36 q^{7} + 60 q^{8} + 6 q^{9} + 7 q^{10} - 10 q^{11} + 29 q^{12} - 22 q^{13} - 73 q^{14} + 54 q^{15} + 63 q^{16} - 334 q^{18} + 22 q^{19} - 330 q^{20} - 352 q^{21} + 79 q^{22} - 380 q^{23} - 159 q^{24} + 378 q^{25} - 448 q^{26} + 494 q^{27} - 608 q^{28} + 78 q^{29} + 313 q^{30} - 362 q^{31} + 331 q^{32} + 94 q^{33} - 242 q^{35} + 141 q^{36} - 512 q^{37} - 524 q^{38} - 12 q^{39} - 1381 q^{40} - 840 q^{41} + 1455 q^{42} - 114 q^{43} + 1041 q^{44} - 648 q^{45} + 1051 q^{46} + 10 q^{47} - 998 q^{48} + 1006 q^{49} + 805 q^{50} - 1537 q^{52} + 50 q^{53} - 581 q^{54} - 1316 q^{55} - 411 q^{56} - 358 q^{57} + 376 q^{58} + 996 q^{59} - 217 q^{60} - 448 q^{61} + 73 q^{62} - 766 q^{63} - 150 q^{64} + 372 q^{65} - 1090 q^{66} - 868 q^{67} - 1128 q^{69} + 1052 q^{70} - 1116 q^{71} - 39 q^{72} - 540 q^{73} - 1630 q^{74} - 1070 q^{75} - 873 q^{76} - 894 q^{77} + 1245 q^{78} - 940 q^{79} - 307 q^{80} + 1080 q^{81} + 334 q^{82} + 850 q^{83} + 443 q^{84} + 2411 q^{86} - 384 q^{87} + 2252 q^{88} + 784 q^{89} + 2069 q^{90} + 2858 q^{91} + 1566 q^{92} - 1550 q^{93} + 1119 q^{94} - 2494 q^{95} + 2643 q^{96} + 518 q^{97} - 1877 q^{98} + 1406 q^{99}+O(q^{100}) \) 4 * q + q^2 + 2 * q^3 + 11 * q^4 - 14 * q^5 - 38 * q^6 - 36 * q^7 + 60 * q^8 + 6 * q^9 + 7 * q^10 - 10 * q^11 + 29 * q^12 - 22 * q^13 - 73 * q^14 + 54 * q^15 + 63 * q^16 - 334 * q^18 + 22 * q^19 - 330 * q^20 - 352 * q^21 + 79 * q^22 - 380 * q^23 - 159 * q^24 + 378 * q^25 - 448 * q^26 + 494 * q^27 - 608 * q^28 + 78 * q^29 + 313 * q^30 - 362 * q^31 + 331 * q^32 + 94 * q^33 - 242 * q^35 + 141 * q^36 - 512 * q^37 - 524 * q^38 - 12 * q^39 - 1381 * q^40 - 840 * q^41 + 1455 * q^42 - 114 * q^43 + 1041 * q^44 - 648 * q^45 + 1051 * q^46 + 10 * q^47 - 998 * q^48 + 1006 * q^49 + 805 * q^50 - 1537 * q^52 + 50 * q^53 - 581 * q^54 - 1316 * q^55 - 411 * q^56 - 358 * q^57 + 376 * q^58 + 996 * q^59 - 217 * q^60 - 448 * q^61 + 73 * q^62 - 766 * q^63 - 150 * q^64 + 372 * q^65 - 1090 * q^66 - 868 * q^67 - 1128 * q^69 + 1052 * q^70 - 1116 * q^71 - 39 * q^72 - 540 * q^73 - 1630 * q^74 - 1070 * q^75 - 873 * q^76 - 894 * q^77 + 1245 * q^78 - 940 * q^79 - 307 * q^80 + 1080 * q^81 + 334 * q^82 + 850 * q^83 + 443 * q^84 + 2411 * q^86 - 384 * q^87 + 2252 * q^88 + 784 * q^89 + 2069 * q^90 + 2858 * q^91 + 1566 * q^92 - 1550 * q^93 + 1119 * q^94 - 2494 * q^95 + 2643 * q^96 + 518 * q^97 - 1877 * q^98 + 1406 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.22501	0.433106	0.216553	−	0.976271i	$-0.430519\pi$
$2$	1.22501	0.433106	0.216553	+	0.976271i	$0.430519\pi$
$3$	0.534684	0.102900	0.0514500	−	0.998676i	$-0.483616\pi$
$3$	0.534684	0.102900	0.0514500	+	0.998676i	$0.483616\pi$
$4$	−6.49935	−0.812419
$5$	20.9528	1.87408	0.937038	−	0.349227i	$-0.113556\pi$
$5$	20.9528	1.87408	0.937038	+	0.349227i	$0.113556\pi$
$6$	0.654993	0.0445666
$7$	−15.0235	−0.811191	−0.405596	−	0.914053i	$-0.632936\pi$
$7$	−15.0235	−0.811191	−0.405596	+	0.914053i	$0.632936\pi$
$8$	−17.7618	−0.784970
$9$	−26.7141	−0.989412
$10$	25.6674	0.811674
$11$	−45.4168	−1.24488	−0.622440	−	0.782667i	$-0.713859\pi$
$11$	−45.4168	−1.24488	−0.622440	+	0.782667i	$0.713859\pi$
$12$	−3.47510	−0.0835979
$13$	3.14456	0.0670880	0.0335440	−	0.999437i	$-0.489321\pi$
$13$	3.14456	0.0670880	0.0335440	+	0.999437i	$0.489321\pi$
$14$	−18.4039	−0.351332
$15$	11.2031	0.192843
$16$	30.2364	0.472444
$17$	0	0
$17$	0	0
$18$	−32.7250	−0.428520
$19$	−63.2180	−0.763326	−0.381663	−	0.924302i	$-0.624649\pi$
$19$	−63.2180	−0.763326	−0.381663	+	0.924302i	$0.624649\pi$
$20$	−136.180	−1.52254
$21$	−8.03282	−0.0834716
$22$	−55.6360	−0.539166
$23$	−114.551	−1.03850	−0.519252	−	0.854621i	$-0.673789\pi$
$23$	−114.551	−1.03850	−0.519252	+	0.854621i	$0.673789\pi$
$24$	−9.49698	−0.0807734
$25$	314.020	2.51216
$26$	3.85211	0.0290562
$27$	−28.7201	−0.204711
$28$	97.6429	0.659027
$29$	96.6197	0.618684	0.309342	−	0.950951i	$-0.399891\pi$
$29$	96.6197	0.618684	0.309342	+	0.950951i	$0.399891\pi$
$30$	13.7239	0.0835213
$31$	−194.578	−1.12733	−0.563664	−	0.826004i	$-0.690609\pi$
$31$	−194.578	−1.12733	−0.563664	+	0.826004i	$0.690609\pi$
$32$	179.135	0.989588
$33$	−24.2837	−0.128098
$34$	0	0
$35$	−314.784	−1.52023
$36$	173.624	0.803817
$37$	−73.6682	−0.327324	−0.163662	−	0.986516i	$-0.552331\pi$
$37$	−73.6682	−0.327324	−0.163662	+	0.986516i	$0.552331\pi$
$38$	−77.4426	−0.330601
$39$	1.68135	0.00690336
$40$	−372.161	−1.47109
$41$	−341.047	−1.29909	−0.649545	−	0.760324i	$-0.725040\pi$
$41$	−341.047	−1.29909	−0.649545	+	0.760324i	$0.725040\pi$
$42$	−9.84027	−0.0361521
$43$	−281.677	−0.998962	−0.499481	−	0.866325i	$-0.666476\pi$
$43$	−281.677	−0.998962	−0.499481	+	0.866325i	$0.666476\pi$
$44$	295.180	1.01137
$45$	−559.736	−1.85423
$46$	−140.326	−0.449783
$47$	36.2294	0.112438	0.0562191	−	0.998418i	$-0.482095\pi$
$47$	36.2294	0.112438	0.0562191	+	0.998418i	$0.482095\pi$
$48$	16.1669	0.0486145
$49$	−117.295	−0.341968
$50$	384.678	1.08803
$51$	0	0
$52$	−20.4376	−0.0545036
$53$	191.274	0.495727	0.247863	−	0.968795i	$-0.420272\pi$
$53$	191.274	0.495727	0.247863	+	0.968795i	$0.420272\pi$
$54$	−35.1824	−0.0886614
$55$	−951.610	−2.33300
$56$	266.845	0.636761
$57$	−33.8017	−0.0785463
$58$	118.360	0.267956
$59$	104.171	0.229864	0.114932	−	0.993373i	$-0.463335\pi$
$59$	104.171	0.229864	0.114932	+	0.993373i	$0.463335\pi$
$60$	−72.8131	−0.156669
$61$	517.547	1.08631	0.543157	−	0.839631i	$-0.317229\pi$
$61$	517.547	1.08631	0.543157	+	0.839631i	$0.317229\pi$
$62$	−238.359	−0.488253
$63$	401.339	0.802602
$64$	−22.4497	−0.0438470
$65$	65.8874	0.125728
$66$	−29.7477	−0.0554802
$67$	−560.893	−1.02275	−0.511373	−	0.859359i	$-0.670863\pi$
$67$	−560.893	−1.02275	−0.511373	+	0.859359i	$0.670863\pi$
$68$	0	0
$69$	−61.2488	−0.106862
$70$	−385.613	−0.658423
$71$	−333.262	−0.557056	−0.278528	−	0.960428i	$-0.589846\pi$
$71$	−333.262	−0.557056	−0.278528	+	0.960428i	$0.589846\pi$
$72$	474.492	0.776658
$73$	−378.895	−0.607484	−0.303742	−	0.952754i	$-0.598236\pi$
$73$	−378.895	−0.607484	−0.303742	+	0.952754i	$0.598236\pi$
$74$	−90.2443	−0.141766
$75$	167.902	0.258502
$76$	410.876	0.620141
$77$	682.319	1.00984
$78$	2.05967	0.00298989
$79$	877.994	1.25041	0.625203	−	0.780462i	$-0.285016\pi$
$79$	877.994	1.25041	0.625203	+	0.780462i	$0.285016\pi$
$80$	633.538	0.885396
$81$	705.925	0.968347
$82$	−417.786	−0.562643
$83$	1195.27	1.58069	0.790346	−	0.612661i	$-0.209901\pi$
$83$	1195.27	1.58069	0.790346	+	0.612661i	$0.209901\pi$
$84$	52.2081	0.0678139
$85$	0	0
$86$	−345.057	−0.432656
$87$	51.6611	0.0636626
$88$	806.687	0.977194
$89$	783.884	0.933613	0.466806	−	0.884360i	$-0.345405\pi$
$89$	783.884	0.933613	0.466806	+	0.884360i	$0.345405\pi$
$90$	−685.682	−0.803080
$91$	−47.2422	−0.0544212
$92$	744.509	0.843701
$93$	−104.038	−0.116002
$94$	44.3813	0.0486977
$95$	−1324.59	−1.43053
$96$	95.7804	0.101829
$97$	−1605.30	−1.68034	−0.840172	−	0.542320i	$-0.817546\pi$
$97$	−1605.30	−1.68034	−0.840172	+	0.542320i	$0.817546\pi$
$98$	−143.688	−0.148109
$99$	1213.27	1.23170
$100$	−2040.93	−2.04093
$101$	118.682	0.116923	0.0584617	−	0.998290i	$-0.481380\pi$
$101$	118.682	0.116923	0.0584617	+	0.998290i	$0.481380\pi$
$102$	0	0
$103$	1399.63	1.33893	0.669466	−	0.742843i	$-0.266523\pi$
$103$	1399.63	1.33893	0.669466	+	0.742843i	$0.266523\pi$
$104$	−55.8532	−0.0526621
$105$	−168.310	−0.156432
$106$	234.312	0.214702
$107$	631.693	0.570730	0.285365	−	0.958419i	$-0.407885\pi$
$107$	631.693	0.570730	0.285365	+	0.958419i	$0.407885\pi$
$108$	186.662	0.166311
$109$	−1231.00	−1.08173	−0.540866	−	0.841109i	$-0.681904\pi$
$109$	−1231.00	−1.08173	−0.540866	+	0.841109i	$0.681904\pi$
$110$	−1165.73	−1.01044
$111$	−39.3892	−0.0336816
$112$	−454.256	−0.383242
$113$	343.826	0.286234	0.143117	−	0.989706i	$-0.454288\pi$
$113$	343.826	0.286234	0.143117	+	0.989706i	$0.454288\pi$
$114$	−41.4073	−0.0340189
$115$	−2400.17	−1.94624
$116$	−627.966	−0.502631
$117$	−84.0041	−0.0663776
$118$	127.611	0.0995555
$119$	0	0
$120$	−198.988	−0.151376
$121$	731.689	0.549729
$122$	634.000	0.470489
$123$	−182.353	−0.133676
$124$	1264.63	0.915862
$125$	3960.51	2.83391
$126$	491.644	0.347612
$127$	−2346.48	−1.63950	−0.819749	−	0.572723i	$-0.805887\pi$
$127$	−2346.48	−1.63950	−0.819749	+	0.572723i	$0.805887\pi$
$128$	−1460.58	−1.00858
$129$	−150.608	−0.102793
$130$	80.7126	0.0544536
$131$	−399.454	−0.266416	−0.133208	−	0.991088i	$-0.542528\pi$
$131$	−399.454	−0.266416	−0.133208	+	0.991088i	$0.542528\pi$
$132$	157.828	0.104069
$133$	949.754	0.619204
$134$	−687.099	−0.442958
$135$	−601.767	−0.383643
$136$	0	0
$137$	1431.60	0.892773	0.446387	−	0.894840i	$-0.352711\pi$
$137$	1431.60	0.892773	0.446387	+	0.894840i	$0.352711\pi$
$138$	−75.0303	−0.0462826
$139$	811.640	0.495269	0.247635	−	0.968854i	$-0.420347\pi$
$139$	811.640	0.495269	0.247635	+	0.968854i	$0.420347\pi$
$140$	2045.89	1.23507
$141$	19.3713	0.0115699
$142$	−408.250	−0.241264
$143$	−142.816	−0.0835166
$144$	−807.739	−0.467441
$145$	2024.46	1.15946
$146$	−464.150	−0.263105
$147$	−62.7159	−0.0351886
$148$	478.796	0.265924
$149$	1760.04	0.967704	0.483852	−	0.875150i	$-0.339237\pi$
$149$	1760.04	0.967704	0.483852	+	0.875150i	$0.339237\pi$
$150$	205.681	0.111959
$151$	1669.08	0.899523	0.449761	−	0.893149i	$-0.351509\pi$
$151$	1669.08	0.899523	0.449761	+	0.893149i	$0.351509\pi$
$152$	1122.87	0.599188
$153$	0	0
$154$	835.847	0.437367
$155$	−4076.95	−2.11270
$156$	−10.9277	−0.00560842
$157$	1167.18	0.593321	0.296661	−	0.954983i	$-0.404127\pi$
$157$	1167.18	0.593321	0.296661	+	0.954983i	$0.404127\pi$
$158$	1075.55	0.541558
$159$	102.271	0.0510103
$160$	3753.37	1.85456
$161$	1720.96	0.842426
$162$	864.764	0.419397
$163$	−2173.56	−1.04446	−0.522229	−	0.852805i	$-0.674899\pi$
$163$	−2173.56	−1.04446	−0.522229	+	0.852805i	$0.674899\pi$
$164$	2216.59	1.05540
$165$	−508.811	−0.240066
$166$	1464.21	0.684607
$167$	−1132.85	−0.524924	−0.262462	−	0.964942i	$-0.584534\pi$
$167$	−1132.85	−0.524924	−0.262462	+	0.964942i	$0.584534\pi$
$168$	142.678	0.0655227
$169$	−2187.11	−0.995499
$170$	0	0
$171$	1688.81	0.755244
$172$	1830.72	0.811575
$173$	−46.3472	−0.0203683	−0.0101841	−	0.999948i	$-0.503242\pi$
$173$	−46.3472	−0.0203683	−0.0101841	+	0.999948i	$0.503242\pi$
$174$	63.2853	0.0275727
$175$	−4717.68	−2.03785
$176$	−1373.24	−0.588136
$177$	55.6988	0.0236530
$178$	960.265	0.404353
$179$	−643.960	−0.268893	−0.134446	−	0.990921i	$-0.542926\pi$
$179$	−643.960	−0.268893	−0.134446	+	0.990921i	$0.542926\pi$
$180$	3637.92	1.50641
$181$	−371.082	−0.152388	−0.0761942	−	0.997093i	$-0.524277\pi$
$181$	−371.082	−0.152388	−0.0761942	+	0.997093i	$0.524277\pi$
$182$	−57.8722	−0.0235702
$183$	276.724	0.111782
$184$	2034.64	0.815194
$185$	−1543.56	−0.613430
$186$	−127.447	−0.0502412
$187$	0	0
$188$	−235.468	−0.0913470
$189$	431.476	0.166059
$190$	−1622.64	−0.619572
$191$	−1874.95	−0.710298	−0.355149	−	0.934810i	$-0.615570\pi$
$191$	−1874.95	−0.710298	−0.355149	+	0.934810i	$0.615570\pi$
$192$	−12.0035	−0.00451186
$193$	819.870	0.305780	0.152890	−	0.988243i	$-0.451142\pi$
$193$	819.870	0.305780	0.152890	+	0.988243i	$0.451142\pi$
$194$	−1966.51	−0.727767
$195$	35.2289	0.0129374
$196$	762.343	0.277822
$197$	−1067.82	−0.386189	−0.193094	−	0.981180i	$-0.561852\pi$
$197$	−1067.82	−0.386189	−0.193094	+	0.981180i	$0.561852\pi$
$198$	1486.27	0.533457
$199$	2378.01	0.847099	0.423550	−	0.905873i	$-0.360784\pi$
$199$	2378.01	0.847099	0.423550	+	0.905873i	$0.360784\pi$
$200$	−5577.58	−1.97197
$201$	−299.901	−0.105241
$202$	145.386	0.0506402
$203$	−1451.56	−0.501871
$204$	0	0
$205$	−7145.90	−2.43459
$206$	1714.56	0.579899
$207$	3060.14	1.02751
$208$	95.0802	0.0316953
$209$	2871.16	0.950250
$210$	−206.181	−0.0677518
$211$	−3536.41	−1.15382	−0.576910	−	0.816807i	$-0.695742\pi$
$211$	−3536.41	−1.15382	−0.576910	+	0.816807i	$0.695742\pi$
$212$	−1243.16	−0.402738
$213$	−178.190	−0.0573211
$214$	773.830	0.247187
$215$	−5901.93	−1.87213
$216$	510.122	0.160692
$217$	2923.23	0.914479
$218$	−1507.99	−0.468505
$219$	−202.589	−0.0625101
$220$	6184.85	1.89538
$221$	0	0
$222$	−48.2522	−0.0145877
$223$	4920.87	1.47769	0.738847	−	0.673873i	$-0.235371\pi$
$223$	4920.87	1.47769	0.738847	+	0.673873i	$0.235371\pi$
$224$	−2691.22	−0.802745
$225$	−8388.78	−2.48556
$226$	421.190	0.123970
$227$	−5114.37	−1.49538	−0.747692	−	0.664045i	$-0.768838\pi$
$227$	−5114.37	−1.49538	−0.747692	+	0.664045i	$0.768838\pi$
$228$	219.689	0.0638125
$229$	1829.79	0.528016	0.264008	−	0.964521i	$-0.414955\pi$
$229$	1829.79	0.528016	0.264008	+	0.964521i	$0.414955\pi$
$230$	−2940.23	−0.842927
$231$	364.825	0.103912
$232$	−1716.14	−0.485648
$233$	−5252.53	−1.47684	−0.738422	−	0.674338i	$-0.764429\pi$
$233$	−5252.53	−1.47684	−0.738422	+	0.674338i	$0.764429\pi$
$234$	−102.906	−0.0287486
$235$	759.108	0.210718
$236$	−677.047	−0.186746
$237$	469.450	0.128667
$238$	0	0
$239$	355.927	0.0963306	0.0481653	−	0.998839i	$-0.484663\pi$
$239$	355.927	0.0963306	0.0481653	+	0.998839i	$0.484663\pi$
$240$	338.743	0.0911073
$241$	2229.06	0.595794	0.297897	−	0.954598i	$-0.403715\pi$
$241$	2229.06	0.595794	0.297897	+	0.954598i	$0.403715\pi$
$242$	896.325	0.238091
$243$	1152.89	0.304353
$244$	−3363.72	−0.882542
$245$	−2457.66	−0.640875
$246$	−223.384	−0.0578960
$247$	−198.793	−0.0512100
$248$	3456.05	0.884918
$249$	639.089	0.162653
$250$	4851.66	1.22738
$251$	1388.08	0.349063	0.174531	−	0.984652i	$-0.444159\pi$
$251$	1388.08	0.349063	0.174531	+	0.984652i	$0.444159\pi$
$252$	−2608.44	−0.652049
$253$	5202.56	1.29281
$254$	−2874.46	−0.710077
$255$	0	0
$256$	−1609.62	−0.392975
$257$	−7401.42	−1.79645	−0.898225	−	0.439535i	$-0.855143\pi$
$257$	−7401.42	−1.79645	−0.898225	+	0.439535i	$0.855143\pi$
$258$	−184.497	−0.0445204
$259$	1106.75	0.265522
$260$	−428.225	−0.102144
$261$	−2581.11	−0.612133
$262$	−489.335	−0.115386
$263$	6738.57	1.57992	0.789959	−	0.613160i	$-0.210102\pi$
$263$	6738.57	1.57992	0.789959	+	0.613160i	$0.210102\pi$
$264$	431.323	0.100553
$265$	4007.73	0.929030
$266$	1163.46	0.268181
$267$	419.130	0.0960688
$268$	3645.44	0.830899
$269$	−3474.39	−0.787500	−0.393750	−	0.919218i	$-0.628822\pi$
$269$	−3474.39	−0.787500	−0.393750	+	0.919218i	$0.628822\pi$
$270$	−737.170	−0.166158
$271$	−1524.81	−0.341791	−0.170896	−	0.985289i	$-0.554666\pi$
$271$	−1524.81	−0.341791	−0.170896	+	0.985289i	$0.554666\pi$
$272$	0	0
$273$	−25.2597	−0.00559994
$274$	1753.72	0.386665
$275$	−14261.8	−3.12734
$276$	398.077	0.0868168
$277$	−5379.31	−1.16683	−0.583414	−	0.812175i	$-0.698283\pi$
$277$	−5379.31	−1.16683	−0.583414	+	0.812175i	$0.698283\pi$
$278$	994.267	0.214504
$279$	5197.97	1.11539
$280$	5591.14	1.19334
$281$	−5595.31	−1.18786	−0.593929	−	0.804517i	$-0.702424\pi$
$281$	−5595.31	−1.18786	−0.593929	+	0.804517i	$0.702424\pi$
$282$	23.7300	0.00501100
$283$	−3604.25	−0.757069	−0.378534	−	0.925587i	$-0.623572\pi$
$283$	−3604.25	−0.757069	−0.378534	+	0.925587i	$0.623572\pi$
$284$	2165.99	0.452563
$285$	−708.240	−0.147202
$286$	−174.951	−0.0361715
$287$	5123.72	1.05381
$288$	−4785.42	−0.979110
$289$	0	0
$290$	2479.98	0.502170
$291$	−858.328	−0.172907
$292$	2462.57	0.493531
$293$	3857.83	0.769204	0.384602	−	0.923083i	$-0.374339\pi$
$293$	3857.83	0.769204	0.384602	+	0.923083i	$0.374339\pi$
$294$	−76.8275	−0.0152404
$295$	2182.69	0.430783
$296$	1308.48	0.256939
$297$	1304.38	0.254840
$298$	2156.06	0.419119
$299$	−360.213	−0.0696712
$300$	−1091.25	−0.210012
$301$	4231.77	0.810349
$302$	2044.64	0.389589
$303$	63.4572	0.0120314
$304$	−1911.48	−0.360629
$305$	10844.1	2.03584
$306$	0	0
$307$	−4799.00	−0.892161	−0.446080	−	0.894993i	$-0.647180\pi$
$307$	−4799.00	−0.892161	−0.446080	+	0.894993i	$0.647180\pi$
$308$	−4434.63	−0.820411
$309$	748.362	0.137776
$310$	−4994.30	−0.915023
$311$	2633.07	0.480090	0.240045	−	0.970762i	$-0.422838\pi$
$311$	2633.07	0.480090	0.240045	+	0.970762i	$0.422838\pi$
$312$	−29.8638	−0.00541893
$313$	−3669.10	−0.662587	−0.331293	−	0.943528i	$-0.607485\pi$
$313$	−3669.10	−0.662587	−0.331293	+	0.943528i	$0.607485\pi$
$314$	1429.81	0.256971
$315$	8409.18	1.50414
$316$	−5706.39	−1.01585
$317$	3963.01	0.702161	0.351080	−	0.936345i	$-0.385814\pi$
$317$	3963.01	0.702161	0.351080	+	0.936345i	$0.385814\pi$
$318$	125.283	0.0220929
$319$	−4388.16	−0.770188
$320$	−470.384	−0.0821727
$321$	337.756	0.0587281
$322$	2108.19	0.364860
$323$	0	0
$324$	−4588.05	−0.786703
$325$	987.456	0.168536
$326$	−2662.64	−0.452361
$327$	−658.199	−0.111310
$328$	6057.63	1.01975
$329$	−544.291	−0.0912090
$330$	−623.298	−0.103974
$331$	−11619.0	−1.92942	−0.964710	−	0.263316i	$-0.915184\pi$
$331$	−11619.0	−1.92942	−0.964710	+	0.263316i	$0.915184\pi$
$332$	−7768.45	−1.28418
$333$	1967.98	0.323858
$334$	−1387.75	−0.227348
$335$	−11752.3	−1.91671
$336$	−242.883	−0.0394357
$337$	1616.09	0.261229	0.130615	−	0.991433i	$-0.458305\pi$
$337$	1616.09	0.261229	0.130615	+	0.991433i	$0.458305\pi$
$338$	−2679.23	−0.431157
$339$	183.838	0.0294535
$340$	0	0
$341$	8837.09	1.40339
$342$	2068.81	0.327101
$343$	6915.23	1.08859
$344$	5003.10	0.784155
$345$	−1283.33	−0.200268
$346$	−56.7757	−0.00882162
$347$	−6435.64	−0.995629	−0.497814	−	0.867284i	$-0.665864\pi$
$347$	−6435.64	−0.995629	−0.497814	+	0.867284i	$0.665864\pi$
$348$	−335.763	−0.0517207
$349$	−5582.36	−0.856210	−0.428105	−	0.903729i	$-0.640819\pi$
$349$	−5582.36	−0.856210	−0.428105	+	0.903729i	$0.640819\pi$
$350$	−5779.20	−0.882603
$351$	−90.3120	−0.0137336
$352$	−8135.73	−1.23192
$353$	−7725.05	−1.16477	−0.582384	−	0.812914i	$-0.697880\pi$
$353$	−7725.05	−1.16477	−0.582384	+	0.812914i	$0.697880\pi$
$354$	68.2316	0.0102443
$355$	−6982.78	−1.04397
$356$	−5094.74	−0.758485
$357$	0	0
$358$	−788.856	−0.116459
$359$	10767.6	1.58299	0.791494	−	0.611178i	$-0.209304\pi$
$359$	10767.6	1.58299	0.791494	+	0.611178i	$0.209304\pi$
$360$	9941.94	1.45552
$361$	−2862.49	−0.417333
$362$	−454.579	−0.0660004
$363$	391.222	0.0565671
$364$	307.044	0.0442128
$365$	−7938.92	−1.13847
$366$	338.990	0.0484134
$367$	3600.73	0.512143	0.256071	−	0.966658i	$-0.417572\pi$
$367$	3600.73	0.512143	0.256071	+	0.966658i	$0.417572\pi$
$368$	−3463.62	−0.490635
$369$	9110.78	1.28533
$370$	−1890.87	−0.265680
$371$	−2873.60	−0.402129
$372$	676.177	0.0942423
$373$	−7071.35	−0.981610	−0.490805	−	0.871269i	$-0.663297\pi$
$373$	−7071.35	−0.981610	−0.490805	+	0.871269i	$0.663297\pi$
$374$	0	0
$375$	2117.62	0.291609
$376$	−643.501	−0.0882607
$377$	303.827	0.0415063
$378$	528.562	0.0719214
$379$	4374.71	0.592912	0.296456	−	0.955046i	$-0.404195\pi$
$379$	4374.71	0.592912	0.296456	+	0.955046i	$0.404195\pi$
$380$	8609.00	1.16219
$381$	−1254.62	−0.168704
$382$	−2296.83	−0.307634
$383$	6532.97	0.871591	0.435795	−	0.900046i	$-0.356467\pi$
$383$	6532.97	0.871591	0.435795	+	0.900046i	$0.356467\pi$
$384$	−780.948	−0.103783
$385$	14296.5	1.89251
$386$	1004.35	0.132435
$387$	7524.75	0.988384
$388$	10433.4	1.36514
$389$	−2513.01	−0.327544	−0.163772	−	0.986498i	$-0.552366\pi$
$389$	−2513.01	−0.327544	−0.163772	+	0.986498i	$0.552366\pi$
$390$	43.1558	0.00560328
$391$	0	0
$392$	2083.38	0.268435
$393$	−213.582	−0.0274142
$394$	−1308.09	−0.167261
$395$	18396.4	2.34336
$396$	−7885.47	−1.00066
$397$	1967.83	0.248772	0.124386	−	0.992234i	$-0.460304\pi$
$397$	1967.83	0.248772	0.124386	+	0.992234i	$0.460304\pi$
$398$	2913.09	0.366884
$399$	507.818	0.0637161
$400$	9494.85	1.18686
$401$	−12269.2	−1.52792	−0.763958	−	0.645266i	$-0.776747\pi$
$401$	−12269.2	−1.52792	−0.763958	+	0.645266i	$0.776747\pi$
$402$	−367.381	−0.0455804
$403$	−611.861	−0.0756302
$404$	−771.354	−0.0949908
$405$	14791.1	1.81476
$406$	−1778.18	−0.217363
$407$	3345.78	0.407479
$408$	0	0
$409$	11894.5	1.43801	0.719004	−	0.695006i	$-0.244598\pi$
$409$	11894.5	1.43801	0.719004	+	0.695006i	$0.244598\pi$
$410$	−8753.80	−1.05444
$411$	765.454	0.0918664
$412$	−9096.71	−1.08777
$413$	−1565.02	−0.186464
$414$	3748.70	0.445020
$415$	25044.2	2.96234
$416$	563.299	0.0663895
$417$	433.971	0.0509632
$418$	3517.20	0.411559
$419$	137.704	0.0160555	0.00802776	−	0.999968i	$-0.497445\pi$
$419$	137.704	0.0160555	0.00802776	+	0.999968i	$0.497445\pi$
$420$	1093.91	0.127089
$421$	6240.45	0.722425	0.361213	−	0.932483i	$-0.382363\pi$
$421$	6240.45	0.722425	0.361213	+	0.932483i	$0.382363\pi$
$422$	−4332.13	−0.499727
$423$	−967.836	−0.111248
$424$	−3397.38	−0.389130
$425$	0	0
$426$	−218.285	−0.0248261
$427$	−7775.36	−0.881209
$428$	−4105.60	−0.463672
$429$	−76.3614	−0.00859386
$430$	−7229.91	−0.810831
$431$	10990.9	1.22834	0.614171	−	0.789173i	$-0.289491\pi$
$431$	10990.9	1.22834	0.614171	+	0.789173i	$0.289491\pi$
$432$	−868.392	−0.0967142
$433$	1643.15	0.182367	0.0911835	−	0.995834i	$-0.470935\pi$
$433$	1643.15	0.182367	0.0911835	+	0.995834i	$0.470935\pi$
$434$	3580.98	0.396066
$435$	1082.44	0.119309
$436$	8000.73	0.878820
$437$	7241.70	0.792717
$438$	−248.174	−0.0270735
$439$	−13532.5	−1.47124	−0.735618	−	0.677397i	$-0.763108\pi$
$439$	−13532.5	−1.47124	−0.735618	+	0.677397i	$0.763108\pi$
$440$	16902.4	1.83134
$441$	3133.44	0.338347
$442$	0	0
$443$	−7579.72	−0.812920	−0.406460	−	0.913669i	$-0.633237\pi$
$443$	−7579.72	−0.812920	−0.406460	+	0.913669i	$0.633237\pi$
$444$	256.005	0.0273636
$445$	16424.6	1.74966
$446$	6028.11	0.639998
$447$	941.064	0.0995768
$448$	337.272	0.0355683
$449$	8617.72	0.905781	0.452890	−	0.891566i	$-0.350393\pi$
$449$	8617.72	0.905781	0.452890	+	0.891566i	$0.350393\pi$
$450$	−10276.3	−1.07651
$451$	15489.3	1.61721
$452$	−2234.64	−0.232542
$453$	892.432	0.0925609
$454$	−6265.15	−0.647660
$455$	−989.857	−0.101990
$456$	600.380	0.0616565
$457$	−12066.5	−1.23512	−0.617558	−	0.786525i	$-0.711878\pi$
$457$	−12066.5	−1.23512	−0.617558	+	0.786525i	$0.711878\pi$
$458$	2241.50	0.228687
$459$	0	0
$460$	15599.6	1.58116
$461$	−8906.49	−0.899819	−0.449910	−	0.893074i	$-0.648544\pi$
$461$	−8906.49	−0.899819	−0.449910	+	0.893074i	$0.648544\pi$
$462$	446.914	0.0450050
$463$	−3044.63	−0.305607	−0.152803	−	0.988257i	$-0.548830\pi$
$463$	−3044.63	−0.305607	−0.152803	+	0.988257i	$0.548830\pi$
$464$	2921.43	0.292293
$465$	−2179.88	−0.217397
$466$	−6434.40	−0.639631
$467$	−2838.99	−0.281312	−0.140656	−	0.990058i	$-0.544921\pi$
$467$	−2838.99	−0.281312	−0.140656	+	0.990058i	$0.544921\pi$
$468$	545.972	0.0539265
$469$	8426.57	0.829643
$470$	929.914	0.0912632
$471$	624.075	0.0610528
$472$	−1850.28	−0.180436
$473$	12792.9	1.24359
$474$	575.080	0.0557264
$475$	−19851.7	−1.91760
$476$	0	0
$477$	−5109.72	−0.490478
$478$	436.014	0.0417214
$479$	−502.893	−0.0479703	−0.0239852	−	0.999712i	$-0.507635\pi$
$479$	−502.893	−0.0479703	−0.0239852	+	0.999712i	$0.507635\pi$
$480$	2006.87	0.190835
$481$	−231.654	−0.0219595
$482$	2730.62	0.258042
$483$	920.170	0.0866856
$484$	−4755.50	−0.446610
$485$	−33635.5	−3.14909
$486$	1412.30	0.131817
$487$	−6031.80	−0.561246	−0.280623	−	0.959818i	$-0.590541\pi$
$487$	−6031.80	−0.561246	−0.280623	+	0.959818i	$0.590541\pi$
$488$	−9192.59	−0.852724
$489$	−1162.17	−0.107475
$490$	−3010.66	−0.277567
$491$	−16555.8	−1.52169	−0.760846	−	0.648932i	$-0.775216\pi$
$491$	−16555.8	−1.52169	−0.760846	+	0.648932i	$0.775216\pi$
$492$	1185.17	0.108601
$493$	0	0
$494$	−243.523	−0.0221794
$495$	25421.4	2.30830
$496$	−5883.32	−0.532599
$497$	5006.76	0.451879
$498$	782.890	0.0704461
$499$	−5163.14	−0.463194	−0.231597	−	0.972812i	$-0.574395\pi$
$499$	−5163.14	−0.463194	−0.231597	+	0.972812i	$0.574395\pi$
$500$	−25740.7	−2.30232
$501$	−605.716	−0.0540147
$502$	1700.41	0.151181
$503$	−10736.0	−0.951683	−0.475842	−	0.879531i	$-0.657856\pi$
$503$	−10736.0	−0.951683	−0.475842	+	0.879531i	$0.657856\pi$
$504$	−7128.52	−0.630019
$505$	2486.71	0.219123
$506$	6373.18	0.559926
$507$	−1169.41	−0.102437
$508$	15250.6	1.33196
$509$	18206.2	1.58542	0.792709	−	0.609600i	$-0.208670\pi$
$509$	18206.2	1.58542	0.792709	+	0.609600i	$0.208670\pi$
$510$	0	0
$511$	5692.32	0.492786
$512$	9712.82	0.838379
$513$	1815.63	0.156261
$514$	−9066.81	−0.778054
$515$	29326.2	2.50926
$516$	978.856	0.0835111
$517$	−1645.42	−0.139972
$518$	1355.78	0.114999
$519$	−24.7811	−0.00209589
$520$	−1170.28	−0.0986927
$521$	−2147.80	−0.180608	−0.0903039	−	0.995914i	$-0.528784\pi$
$521$	−2147.80	−0.180608	−0.0903039	+	0.995914i	$0.528784\pi$
$522$	−3161.88	−0.265119
$523$	−21222.1	−1.77434	−0.887169	−	0.461444i	$-0.847331\pi$
$523$	−21222.1	−1.77434	−0.887169	+	0.461444i	$0.847331\pi$
$524$	2596.19	0.216441
$525$	−2522.47	−0.209694
$526$	8254.82	0.684272
$527$	0	0
$528$	−734.251	−0.0605192
$529$	955.000	0.0784910
$530$	4909.51	0.402368
$531$	−2782.85	−0.227430
$532$	−6172.78	−0.503053
$533$	−1072.44	−0.0871533
$534$	513.439	0.0416080
$535$	13235.7	1.06959
$536$	9962.50	0.802825
$537$	−344.315	−0.0276691
$538$	−4256.16	−0.341071
$539$	5327.17	0.425710
$540$	3911.09	0.311679
$541$	−5123.54	−0.407169	−0.203584	−	0.979057i	$-0.565259\pi$
$541$	−5123.54	−0.407169	−0.203584	+	0.979057i	$0.565259\pi$
$542$	−1867.90	−0.148032
$543$	−198.412	−0.0156808
$544$	0	0
$545$	−25793.0	−2.02725
$546$	−30.9433	−0.00242537
$547$	−17905.9	−1.39964	−0.699820	−	0.714319i	$-0.746736\pi$
$547$	−17905.9	−1.39964	−0.699820	+	0.714319i	$0.746736\pi$
$548$	−9304.48	−0.725306
$549$	−13825.8	−1.07481
$550$	−17470.8	−1.35447
$551$	−6108.10	−0.472258
$552$	1087.89	0.0838835
$553$	−13190.5	−1.01432
$554$	−6589.70	−0.505360
$555$	−825.315	−0.0631220
$556$	−5275.14	−0.402366
$557$	−416.095	−0.0316526	−0.0158263	−	0.999875i	$-0.505038\pi$
$557$	−416.095	−0.0316526	−0.0158263	+	0.999875i	$0.505038\pi$
$558$	6367.56	0.483083
$559$	−885.750	−0.0670183
$560$	−9517.94	−0.718226
$561$	0	0
$562$	−6854.31	−0.514469
$563$	−23092.3	−1.72864	−0.864321	−	0.502940i	$-0.832252\pi$
$563$	−23092.3	−1.72864	−0.864321	+	0.502940i	$0.832252\pi$
$564$	−125.901	−0.00939961
$565$	7204.12	0.536424
$566$	−4415.24	−0.327891
$567$	−10605.4	−0.785515
$568$	5919.35	0.437272
$569$	11328.2	0.834630	0.417315	−	0.908762i	$-0.362971\pi$
$569$	11328.2	0.834630	0.417315	+	0.908762i	$0.362971\pi$
$570$	−867.600	−0.0637540
$571$	15325.7	1.12323	0.561613	−	0.827400i	$-0.310181\pi$
$571$	15325.7	1.12323	0.561613	+	0.827400i	$0.310181\pi$
$572$	928.211	0.0678505
$573$	−1002.51	−0.0730896
$574$	6276.60	0.456412
$575$	−35971.4	−2.60889
$576$	599.723	0.0433828
$577$	9112.72	0.657482	0.328741	−	0.944420i	$-0.393376\pi$
$577$	9112.72	0.657482	0.328741	+	0.944420i	$0.393376\pi$
$578$	0	0
$579$	438.372	0.0314648
$580$	−13157.6	−0.941968
$581$	−17957.0	−1.28224
$582$	−1051.46	−0.0748873
$583$	−8687.06	−0.617121
$584$	6729.87	0.476856
$585$	−1760.12	−0.124397
$586$	4725.87	0.333147
$587$	13653.4	0.960025	0.480013	−	0.877262i	$-0.340632\pi$
$587$	13653.4	0.960025	0.480013	+	0.877262i	$0.340632\pi$
$588$	407.613	0.0285879
$589$	12300.8	0.860519
$590$	2673.81	0.186575
$591$	−570.947	−0.0397388
$592$	−2227.46	−0.154642
$593$	21660.3	1.49997	0.749986	−	0.661453i	$-0.230060\pi$
$593$	21660.3	1.49997	0.749986	+	0.661453i	$0.230060\pi$
$594$	1597.87	0.110373
$595$	0	0
$596$	−11439.1	−0.786181
$597$	1271.49	0.0871665
$598$	−441.265	−0.0301750
$599$	4638.62	0.316408	0.158204	−	0.987406i	$-0.449430\pi$
$599$	4638.62	0.316408	0.158204	+	0.987406i	$0.449430\pi$
$600$	−2982.24	−0.202916
$601$	18.6165	0.00126353	0.000631766	−	1.00000i	$-0.499799\pi$
$601$	18.6165	0.00126353	0.000631766		1.00000i	$0.499799\pi$
$602$	5183.96	0.350967
$603$	14983.8	1.01192
$604$	−10847.9	−0.730789
$605$	15330.9	1.03023
$606$	77.7357	0.00521088
$607$	21481.4	1.43641	0.718206	−	0.695831i	$-0.244964\pi$
$607$	21481.4	1.43641	0.718206	+	0.695831i	$0.244964\pi$
$608$	−11324.5	−0.755379
$609$	−776.129	−0.0516426
$610$	13284.1	0.881733
$611$	113.925	0.00754326
$612$	0	0
$613$	−4978.56	−0.328030	−0.164015	−	0.986458i	$-0.552445\pi$
$613$	−4978.56	−0.328030	−0.164015	+	0.986458i	$0.552445\pi$
$614$	−5878.82	−0.386400
$615$	−3820.80	−0.250520
$616$	−12119.2	−0.792691
$617$	320.723	0.0209268	0.0104634	−	0.999945i	$-0.496669\pi$
$617$	320.723	0.0209268	0.0104634	+	0.999945i	$0.496669\pi$
$618$	916.750	0.0596717
$619$	5305.17	0.344480	0.172240	−	0.985055i	$-0.444900\pi$
$619$	5305.17	0.344480	0.172240	+	0.985055i	$0.444900\pi$
$620$	26497.5	1.71640
$621$	3289.92	0.212593
$622$	3225.54	0.207930
$623$	−11776.7	−0.757339
$624$	50.8379	0.00326145
$625$	43731.2	2.79880
$626$	−4494.68	−0.286970
$627$	1535.16	0.0977808
$628$	−7585.94	−0.482025
$629$	0	0
$630$	10301.3	0.651451
$631$	19724.5	1.24440	0.622202	−	0.782857i	$-0.286238\pi$
$631$	19724.5	1.24440	0.622202	+	0.782857i	$0.286238\pi$
$632$	−15594.8	−0.981531
$633$	−1890.86	−0.118728
$634$	4854.73	0.304110
$635$	−49165.3	−3.07255
$636$	−664.697	−0.0414417
$637$	−368.842	−0.0229420
$638$	−5375.54	−0.333573
$639$	8902.81	0.551158
$640$	−30603.2	−1.89015
$641$	8160.70	0.502852	0.251426	−	0.967876i	$-0.419100\pi$
$641$	8160.70	0.502852	0.251426	+	0.967876i	$0.419100\pi$
$642$	413.755	0.0254355
$643$	31644.9	1.94083	0.970413	−	0.241449i	$-0.0776228\pi$
$643$	31644.9	1.94083	0.970413	+	0.241449i	$0.0776228\pi$
$644$	−11185.1	−0.684403
$645$	−3155.67	−0.192642
$646$	0	0
$647$	23434.3	1.42395	0.711976	−	0.702204i	$-0.247801\pi$
$647$	23434.3	1.42395	0.711976	+	0.702204i	$0.247801\pi$
$648$	−12538.5	−0.760123
$649$	−4731.14	−0.286153
$650$	1209.64	0.0729940
$651$	1563.01	0.0940999
$652$	14126.8	0.848538
$653$	−7603.42	−0.455658	−0.227829	−	0.973701i	$-0.573163\pi$
$653$	−7603.42	−0.455658	−0.227829	+	0.973701i	$0.573163\pi$
$654$	−806.300	−0.0482092
$655$	−8369.69	−0.499283
$656$	−10312.0	−0.613747
$657$	10121.8	0.601051
$658$	−666.762	−0.0395032
$659$	−11917.6	−0.704468	−0.352234	−	0.935912i	$-0.614578\pi$
$659$	−11917.6	−0.704468	−0.352234	+	0.935912i	$0.614578\pi$
$660$	3306.94	0.195034
$661$	−7319.30	−0.430693	−0.215346	−	0.976538i	$-0.569088\pi$
$661$	−7319.30	−0.430693	−0.215346	+	0.976538i	$0.569088\pi$
$662$	−14233.4	−0.835643
$663$	0	0
$664$	−21230.1	−1.24080
$665$	19900.0	1.16044
$666$	2410.80	0.140265
$667$	−11067.9	−0.642506
$668$	7362.77	0.426458
$669$	2631.11	0.152055
$670$	−14396.7	−0.830137
$671$	−23505.4	−1.35233
$672$	−1438.96	−0.0826025
$673$	20860.7	1.19483	0.597414	−	0.801933i	$-0.296195\pi$
$673$	20860.7	1.19483	0.597414	+	0.801933i	$0.296195\pi$
$674$	1979.73	0.113140
$675$	−9018.69	−0.514266
$676$	14214.8	0.808763
$677$	−9840.97	−0.558670	−0.279335	−	0.960194i	$-0.590114\pi$
$677$	−9840.97	−0.558670	−0.279335	+	0.960194i	$0.590114\pi$
$678$	225.204	0.0127565
$679$	24117.2	1.36308
$680$	0	0
$681$	−2734.57	−0.153875
$682$	10825.5	0.607816
$683$	16967.2	0.950560	0.475280	−	0.879835i	$-0.342347\pi$
$683$	16967.2	0.950560	0.475280	+	0.879835i	$0.342347\pi$
$684$	−10976.2	−0.613574
$685$	29996.1	1.67312
$686$	8471.22	0.471476
$687$	978.358	0.0543329
$688$	−8516.90	−0.471953
$689$	601.473	0.0332573
$690$	−1572.10	−0.0867372
$691$	−24669.3	−1.35813	−0.679064	−	0.734079i	$-0.737614\pi$
$691$	−24669.3	−1.35813	−0.679064	+	0.734079i	$0.737614\pi$
$692$	301.227	0.0165476
$693$	−18227.5	−0.999144
$694$	−7883.72	−0.431213
$695$	17006.1	0.928172
$696$	−917.595	−0.0499732
$697$	0	0
$698$	−6838.45	−0.370830
$699$	−2808.45	−0.151967
$700$	30661.8	1.65558
$701$	−28908.3	−1.55756	−0.778780	−	0.627297i	$-0.784161\pi$
$701$	−28908.3	−1.55756	−0.778780	+	0.627297i	$0.784161\pi$
$702$	−110.633	−0.00594812
$703$	4657.16	0.249855
$704$	1019.59	0.0545843
$705$	405.883	0.0216829
$706$	−9463.26	−0.504468
$707$	−1783.01	−0.0948473
$708$	−362.006	−0.0192162
$709$	−7775.90	−0.411890	−0.205945	−	0.978564i	$-0.566027\pi$
$709$	−7775.90	−0.411890	−0.205945	+	0.978564i	$0.566027\pi$
$710$	−8553.98	−0.452148
$711$	−23454.8	−1.23717
$712$	−13923.2	−0.732858
$713$	22289.1	1.17073
$714$	0	0
$715$	−2992.40	−0.156516
$716$	4185.32	0.218454
$717$	190.309	0.00991242
$718$	13190.4	0.685601
$719$	−30789.3	−1.59700	−0.798502	−	0.601992i	$-0.794374\pi$
$719$	−30789.3	−1.59700	−0.798502	+	0.601992i	$0.794374\pi$
$720$	−16924.4	−0.876021
$721$	−21027.4	−1.08613
$722$	−3506.57	−0.180750
$723$	1191.84	0.0613073
$724$	2411.79	0.123803
$725$	30340.6	1.55423
$726$	479.251	0.0244996
$727$	−25161.8	−1.28363	−0.641815	−	0.766860i	$-0.721818\pi$
$727$	−25161.8	−1.28363	−0.641815	+	0.766860i	$0.721818\pi$
$728$	839.109	0.0427190
$729$	−18443.5	−0.937029
$730$	−9725.25	−0.493079
$731$	0	0
$732$	−1798.53	−0.0908136
$733$	2453.96	0.123655	0.0618274	−	0.998087i	$-0.480307\pi$
$733$	2453.96	0.123655	0.0618274	+	0.998087i	$0.480307\pi$
$734$	4410.92	0.221812
$735$	−1314.07	−0.0659460
$736$	−20520.1	−1.02769
$737$	25474.0	1.27320
$738$	11160.8	0.556686
$739$	−28203.6	−1.40391	−0.701953	−	0.712224i	$-0.747688\pi$
$739$	−28203.6	−1.40391	−0.701953	+	0.712224i	$0.747688\pi$
$740$	10032.1	0.498362
$741$	−106.291	−0.00526951
$742$	−3520.19	−0.174165
$743$	−25185.5	−1.24356	−0.621781	−	0.783191i	$-0.713590\pi$
$743$	−25185.5	−1.24356	−0.621781	+	0.783191i	$0.713590\pi$
$744$	1847.90	0.0910581
$745$	36877.7	1.81355
$746$	−8662.47	−0.425141
$747$	−31930.4	−1.56395
$748$	0	0
$749$	−9490.23	−0.462971
$750$	2594.11	0.126298
$751$	−16814.8	−0.817020	−0.408510	−	0.912754i	$-0.633952\pi$
$751$	−16814.8	−0.817020	−0.408510	+	0.912754i	$0.633952\pi$
$752$	1095.45	0.0531208
$753$	742.184	0.0359186
$754$	372.190	0.0179766
$755$	34972.0	1.68577
$756$	−2804.31	−0.134910
$757$	31469.3	1.51093	0.755464	−	0.655191i	$-0.227412\pi$
$757$	31469.3	1.51093	0.755464	+	0.655191i	$0.227412\pi$
$758$	5359.06	0.256794
$759$	2781.73	0.133031
$760$	23527.2	1.12292
$761$	16621.7	0.791771	0.395885	−	0.918300i	$-0.370438\pi$
$761$	16621.7	0.791771	0.395885	+	0.918300i	$0.370438\pi$
$762$	−1536.93	−0.0730669
$763$	18494.0	0.877492
$764$	12186.0	0.577059
$765$	0	0
$766$	8002.95	0.377491
$767$	327.573	0.0154211
$768$	−860.641	−0.0404371
$769$	35810.5	1.67927	0.839635	−	0.543151i	$-0.182769\pi$
$769$	35810.5	1.67927	0.839635	+	0.543151i	$0.182769\pi$
$770$	17513.3	0.819658
$771$	−3957.42	−0.184855
$772$	−5328.63	−0.248422
$773$	29648.3	1.37953	0.689765	−	0.724033i	$-0.257714\pi$
$773$	29648.3	1.37953	0.689765	+	0.724033i	$0.257714\pi$
$774$	9217.89	0.428075
$775$	−61101.3	−2.83203
$776$	28513.1	1.31902
$777$	591.763	0.0273223
$778$	−3078.45	−0.141861
$779$	21560.3	0.991629
$780$	−228.965	−0.0105106
$781$	15135.7	0.693468
$782$	0	0
$783$	−2774.93	−0.126651
$784$	−3546.58	−0.161561
$785$	24455.8	1.11193
$786$	−261.640	−0.0118733
$787$	−12772.1	−0.578496	−0.289248	−	0.957254i	$-0.593405\pi$
$787$	−12772.1	−0.578496	−0.289248	+	0.957254i	$0.593405\pi$
$788$	6940.15	0.313747
$789$	3603.01	0.162574
$790$	22535.8	1.01492
$791$	−5165.46	−0.232190
$792$	−21549.9	−0.966847
$793$	1627.46	0.0728786
$794$	2410.61	0.107745
$795$	2142.87	0.0955972
$796$	−15455.5	−0.688200
$797$	−12572.8	−0.558785	−0.279392	−	0.960177i	$-0.590133\pi$
$797$	−12572.8	−0.558785	−0.279392	+	0.960177i	$0.590133\pi$
$798$	622.082	0.0275958
$799$	0	0
$800$	56251.9	2.48601
$801$	−20940.8	−0.923727
$802$	−15029.9	−0.661750
$803$	17208.2	0.756245
$804$	1949.16	0.0854995
$805$	36058.9	1.57877
$806$	−749.535	−0.0327559
$807$	−1857.70	−0.0810338
$808$	−2108.00	−0.0917813
$809$	14249.3	0.619259	0.309629	−	0.950857i	$-0.399795\pi$
$809$	14249.3	0.619259	0.309629	+	0.950857i	$0.399795\pi$
$810$	18119.2	0.785982
$811$	25534.0	1.10557	0.552786	−	0.833323i	$-0.313565\pi$
$811$	25534.0	1.10557	0.552786	+	0.833323i	$0.313565\pi$
$812$	9434.23	0.407730
$813$	−815.290	−0.0351703
$814$	4098.61	0.176482
$815$	−45542.3	−1.95739
$816$	0	0
$817$	17807.1	0.762533
$818$	14570.9	0.622810
$819$	1262.03	0.0538450
$820$	46443.7	1.97791
$821$	−34196.6	−1.45368	−0.726838	−	0.686809i	$-0.759011\pi$
$821$	−34196.6	−1.45368	−0.726838	+	0.686809i	$0.759011\pi$
$822$	937.689	0.0397879
$823$	35235.8	1.49240	0.746199	−	0.665723i	$-0.231877\pi$
$823$	35235.8	1.49240	0.746199	+	0.665723i	$0.231877\pi$
$824$	−24860.1	−1.05102
$825$	−7625.57	−0.321804
$826$	−1917.16	−0.0807586
$827$	−6761.12	−0.284289	−0.142145	−	0.989846i	$-0.545400\pi$
$827$	−6761.12	−0.284289	−0.142145	+	0.989846i	$0.545400\pi$
$828$	−19888.9	−0.834767
$829$	26249.2	1.09973	0.549863	−	0.835255i	$-0.314680\pi$
$829$	26249.2	1.09973	0.549863	+	0.835255i	$0.314680\pi$
$830$	30679.3	1.28301
$831$	−2876.23	−0.120067
$832$	−70.5944	−0.00294161
$833$	0	0
$834$	531.619	0.0220725
$835$	−23736.3	−0.983748
$836$	−18660.7	−0.772001
$837$	5588.28	0.230776
$838$	168.688	0.00695374
$839$	−8884.87	−0.365602	−0.182801	−	0.983150i	$-0.558516\pi$
$839$	−8884.87	−0.365602	−0.182801	+	0.983150i	$0.558516\pi$
$840$	2989.50	0.122795
$841$	−15053.6	−0.617230
$842$	7644.61	0.312887
$843$	−2991.73	−0.122231
$844$	22984.3	0.937386
$845$	−45826.1	−1.86564
$846$	−1185.61	−0.0481821
$847$	−10992.5	−0.445935
$848$	5783.44	0.234203
$849$	−1927.14	−0.0779024
$850$	0	0
$851$	8438.79	0.339927
$852$	1158.12	0.0465687
$853$	39637.2	1.59104	0.795518	−	0.605931i	$-0.207199\pi$
$853$	39637.2	1.59104	0.795518	+	0.605931i	$0.207199\pi$
$854$	−9524.89	−0.381657
$855$	35385.4	1.41538
$856$	−11220.0	−0.448006
$857$	−18348.8	−0.731367	−0.365684	−	0.930739i	$-0.619165\pi$
$857$	−18348.8	−0.731367	−0.365684	+	0.930739i	$0.619165\pi$
$858$	−93.5435	−0.00372205
$859$	3064.71	0.121730	0.0608652	−	0.998146i	$-0.480614\pi$
$859$	3064.71	0.121730	0.0608652	+	0.998146i	$0.480614\pi$
$860$	38358.7	1.52095
$861$	2739.57	0.108437
$862$	13464.0	0.532002
$863$	−19334.7	−0.762643	−0.381321	−	0.924443i	$-0.624531\pi$
$863$	−19334.7	−0.762643	−0.381321	+	0.924443i	$0.624531\pi$
$864$	−5144.76	−0.202579
$865$	−971.103	−0.0381717
$866$	2012.88	0.0789843
$867$	0	0
$868$	−18999.1	−0.742940
$869$	−39875.7	−1.55661
$870$	1326.00	0.0516733
$871$	−1763.76	−0.0686140
$872$	21864.9	0.849127
$873$	42884.1	1.66255
$874$	8871.15	0.343331
$875$	−59500.6	−2.29884
$876$	1316.70	0.0507844
$877$	−20294.5	−0.781409	−0.390704	−	0.920516i	$-0.627769\pi$
$877$	−20294.5	−0.781409	−0.390704	+	0.920516i	$0.627769\pi$
$878$	−16577.5	−0.637201
$879$	2062.72	0.0791511
$880$	−28773.3	−1.10221
$881$	−30744.7	−1.17573	−0.587863	−	0.808961i	$-0.700031\pi$
$881$	−30744.7	−1.17573	−0.587863	+	0.808961i	$0.700031\pi$
$882$	3838.49	0.146540
$883$	−9156.84	−0.348983	−0.174492	−	0.984659i	$-0.555828\pi$
$883$	−9156.84	−0.348983	−0.174492	+	0.984659i	$0.555828\pi$
$884$	0	0
$885$	1167.05	0.0443275
$886$	−9285.23	−0.352081
$887$	14045.4	0.531677	0.265838	−	0.964018i	$-0.414351\pi$
$887$	14045.4	0.531677	0.265838	+	0.964018i	$0.414351\pi$
$888$	699.625	0.0264391
$889$	35252.3	1.32995
$890$	20120.3	0.757789
$891$	−32060.9	−1.20548
$892$	−31982.5	−1.20051
$893$	−2290.35	−0.0858271
$894$	1152.81	0.0431273
$895$	−13492.8	−0.503926
$896$	21943.0	0.818150
$897$	−192.600	−0.00716917
$898$	10556.8	0.392299
$899$	−18800.0	−0.697459
$900$	54521.6	2.01932
$901$	0	0
$902$	18974.5	0.700424
$903$	2262.66	0.0833850
$904$	−6106.98	−0.224685
$905$	−7775.21	−0.285588
$906$	1093.24	0.0400887
$907$	28078.7	1.02794	0.513968	−	0.857810i	$-0.328175\pi$
$907$	28078.7	1.02794	0.513968	+	0.857810i	$0.328175\pi$
$908$	33240.1	1.21488
$909$	−3170.47	−0.115685
$910$	−1212.58	−0.0441723
$911$	−41942.5	−1.52538	−0.762688	−	0.646767i	$-0.776121\pi$
$911$	−41942.5	−1.52538	−0.762688	+	0.646767i	$0.776121\pi$
$912$	−1022.04	−0.0371087
$913$	−54285.2	−1.96777
$914$	−14781.6	−0.534937
$915$	5798.16	0.209488
$916$	−11892.4	−0.428970
$917$	6001.19	0.216114
$918$	0	0
$919$	18355.9	0.658873	0.329437	−	0.944178i	$-0.393141\pi$
$919$	18355.9	0.658873	0.329437	+	0.944178i	$0.393141\pi$
$920$	42631.5	1.52774
$921$	−2565.95	−0.0918034
$922$	−10910.5	−0.389717
$923$	−1047.96	−0.0373718
$924$	−2371.13	−0.0844203
$925$	−23133.3	−0.822291
$926$	−3729.70	−0.132360
$927$	−37389.9	−1.32475
$928$	17307.9	0.612242
$929$	−31074.3	−1.09743	−0.548717	−	0.836008i	$-0.684883\pi$
$929$	−31074.3	−1.09743	−0.548717	+	0.836008i	$0.684883\pi$
$930$	−2670.37	−0.0941559
$931$	7415.16	0.261033
$932$	34138.1	1.19982
$933$	1407.86	0.0494013
$934$	−3477.79	−0.121838
$935$	0	0
$936$	1492.07	0.0521045
$937$	12245.2	0.426930	0.213465	−	0.976951i	$-0.431525\pi$
$937$	12245.2	0.426930	0.213465	+	0.976951i	$0.431525\pi$
$938$	10322.6	0.359324
$939$	−1961.81	−0.0681802
$940$	−4933.71	−0.171191
$941$	−11112.2	−0.384960	−0.192480	−	0.981301i	$-0.561653\pi$
$941$	−11112.2	−0.384960	−0.192480	+	0.981301i	$0.561653\pi$
$942$	764.497	0.0264423
$943$	39067.4	1.34911
$944$	3149.77	0.108598
$945$	9040.63	0.311208
$946$	15671.4	0.538606
$947$	40553.8	1.39157	0.695787	−	0.718248i	$-0.255056\pi$
$947$	40553.8	1.39157	0.695787	+	0.718248i	$0.255056\pi$
$948$	−3051.12	−0.104531
$949$	−1191.46	−0.0407549
$950$	−24318.6	−0.830524
$951$	2118.96	0.0722524
$952$	0	0
$953$	−10668.5	−0.362631	−0.181316	−	0.983425i	$-0.558036\pi$
$953$	−10668.5	−0.362631	−0.181316	+	0.983425i	$0.558036\pi$
$954$	−6259.45	−0.212429
$955$	−39285.5	−1.33115
$956$	−2313.30	−0.0782608
$957$	−2346.28	−0.0792524
$958$	−616.049	−0.0207762
$959$	−21507.6	−0.724210
$960$	−251.507	−0.00845557
$961$	8069.41	0.270867
$962$	−283.778	−0.00951080
$963$	−16875.1	−0.564687
$964$	−14487.5	−0.484035
$965$	17178.6	0.573055
$966$	1127.22	0.0375441
$967$	12007.5	0.399311	0.199656	−	0.979866i	$-0.436018\pi$
$967$	12007.5	0.399311	0.199656	+	0.979866i	$0.436018\pi$
$968$	−12996.1	−0.431520
$969$	0	0
$970$	−41203.8	−1.36389
$971$	21024.0	0.694842	0.347421	−	0.937709i	$-0.387057\pi$
$971$	21024.0	0.694842	0.347421	+	0.937709i	$0.387057\pi$
$972$	−7493.03	−0.247263
$973$	−12193.7	−0.401758
$974$	−7389.01	−0.243079
$975$	527.977	0.0173424
$976$	15648.8	0.513222
$977$	21887.9	0.716740	0.358370	−	0.933580i	$-0.383333\pi$
$977$	21887.9	0.716740	0.358370	+	0.933580i	$0.383333\pi$
$978$	−1423.67	−0.0465480
$979$	−35601.5	−1.16224
$980$	15973.2	0.520659
$981$	32885.2	1.07028
$982$	−20281.0	−0.659054
$983$	38731.8	1.25672	0.628358	−	0.777924i	$-0.283727\pi$
$983$	38731.8	1.25672	0.628358	+	0.777924i	$0.283727\pi$
$984$	3238.92	0.104932
$985$	−22373.9	−0.723747
$986$	0	0
$987$	−291.024	−0.00938541
$988$	1292.02	0.0416040
$989$	32266.5	1.03743
$990$	31141.5	0.999739
$991$	−16776.8	−0.537771	−0.268886	−	0.963172i	$-0.586655\pi$
$991$	−16776.8	−0.537771	−0.268886	+	0.963172i	$0.586655\pi$
$992$	−34855.6	−1.11559
$993$	−6212.49	−0.198537
$994$	6133.33	0.195712
$995$	49826.0	1.58753
$996$	−4153.67	−0.132143
$997$	51595.5	1.63896	0.819482	−	0.573105i	$-0.194261\pi$
$997$	51595.5	1.63896	0.819482	+	0.573105i	$0.194261\pi$
$998$	−6324.90	−0.200612
$999$	2115.76	0.0670066

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.d.1.3	yes	4
17.4	even	4		289.4.b.d.288.3		8
17.13	even	4		289.4.b.d.288.4		8
17.16	even	2		289.4.a.c.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.4.a.c.1.3	✓	4	17.16	even	2
289.4.a.d.1.3	yes	4	1.1	even	1	trivial
289.4.b.d.288.3		8	17.4	even	4
289.4.b.d.288.4		8	17.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+1.22501 q^{2} +0.534684 q^{3} -6.49935 q^{4} +20.9528 q^{5} +0.654993 q^{6} -15.0235 q^{7} -17.7618 q^{8} -26.7141 q^{9} +O(q^{10})\)	\(q+1.22501 q^{2} +0.534684 q^{3} -6.49935 q^{4} +20.9528 q^{5} +0.654993 q^{6} -15.0235 q^{7} -17.7618 q^{8} -26.7141 q^{9} +25.6674 q^{10} -45.4168 q^{11} -3.47510 q^{12} +3.14456 q^{13} -18.4039 q^{14} +11.2031 q^{15} +30.2364 q^{16} -32.7250 q^{18} -63.2180 q^{19} -136.180 q^{20} -8.03282 q^{21} -55.6360 q^{22} -114.551 q^{23} -9.49698 q^{24} +314.020 q^{25} +3.85211 q^{26} -28.7201 q^{27} +97.6429 q^{28} +96.6197 q^{29} +13.7239 q^{30} -194.578 q^{31} +179.135 q^{32} -24.2837 q^{33} -314.784 q^{35} +173.624 q^{36} -73.6682 q^{37} -77.4426 q^{38} +1.68135 q^{39} -372.161 q^{40} -341.047 q^{41} -9.84027 q^{42} -281.677 q^{43} +295.180 q^{44} -559.736 q^{45} -140.326 q^{46} +36.2294 q^{47} +16.1669 q^{48} -117.295 q^{49} +384.678 q^{50} -20.4376 q^{52} +191.274 q^{53} -35.1824 q^{54} -951.610 q^{55} +266.845 q^{56} -33.8017 q^{57} +118.360 q^{58} +104.171 q^{59} -72.8131 q^{60} +517.547 q^{61} -238.359 q^{62} +401.339 q^{63} -22.4497 q^{64} +65.8874 q^{65} -29.7477 q^{66} -560.893 q^{67} -61.2488 q^{69} -385.613 q^{70} -333.262 q^{71} +474.492 q^{72} -378.895 q^{73} -90.2443 q^{74} +167.902 q^{75} +410.876 q^{76} +682.319 q^{77} +2.05967 q^{78} +877.994 q^{79} +633.538 q^{80} +705.925 q^{81} -417.786 q^{82} +1195.27 q^{83} +52.2081 q^{84} -345.057 q^{86} +51.6611 q^{87} +806.687 q^{88} +783.884 q^{89} -685.682 q^{90} -47.2422 q^{91} +744.509 q^{92} -104.038 q^{93} +44.3813 q^{94} -1324.59 q^{95} +95.7804 q^{96} -1605.30 q^{97} -143.688 q^{98} +1213.27 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 2 q^{3} + 11 q^{4} - 14 q^{5} - 38 q^{6} - 36 q^{7} + 60 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q + q^2 + 2 * q^3 + 11 * q^4 - 14 * q^5 - 38 * q^6 - 36 * q^7 + 60 * q^8 + 6 * q^9	\( 4 q + q^{2} + 2 q^{3} + 11 q^{4} - 14 q^{5} - 38 q^{6} - 36 q^{7} + 60 q^{8} + 6 q^{9} + 7 q^{10} - 10 q^{11} + 29 q^{12} - 22 q^{13} - 73 q^{14} + 54 q^{15} + 63 q^{16} - 334 q^{18} + 22 q^{19} - 330 q^{20} - 352 q^{21} + 79 q^{22} - 380 q^{23} - 159 q^{24} + 378 q^{25} - 448 q^{26} + 494 q^{27} - 608 q^{28} + 78 q^{29} + 313 q^{30} - 362 q^{31} + 331 q^{32} + 94 q^{33} - 242 q^{35} + 141 q^{36} - 512 q^{37} - 524 q^{38} - 12 q^{39} - 1381 q^{40} - 840 q^{41} + 1455 q^{42} - 114 q^{43} + 1041 q^{44} - 648 q^{45} + 1051 q^{46} + 10 q^{47} - 998 q^{48} + 1006 q^{49} + 805 q^{50} - 1537 q^{52} + 50 q^{53} - 581 q^{54} - 1316 q^{55} - 411 q^{56} - 358 q^{57} + 376 q^{58} + 996 q^{59} - 217 q^{60} - 448 q^{61} + 73 q^{62} - 766 q^{63} - 150 q^{64} + 372 q^{65} - 1090 q^{66} - 868 q^{67} - 1128 q^{69} + 1052 q^{70} - 1116 q^{71} - 39 q^{72} - 540 q^{73} - 1630 q^{74} - 1070 q^{75} - 873 q^{76} - 894 q^{77} + 1245 q^{78} - 940 q^{79} - 307 q^{80} + 1080 q^{81} + 334 q^{82} + 850 q^{83} + 443 q^{84} + 2411 q^{86} - 384 q^{87} + 2252 q^{88} + 784 q^{89} + 2069 q^{90} + 2858 q^{91} + 1566 q^{92} - 1550 q^{93} + 1119 q^{94} - 2494 q^{95} + 2643 q^{96} + 518 q^{97} - 1877 q^{98} + 1406 q^{99}+O(q^{100}) \) 4 * q + q^2 + 2 * q^3 + 11 * q^4 - 14 * q^5 - 38 * q^6 - 36 * q^7 + 60 * q^8 + 6 * q^9 + 7 * q^10 - 10 * q^11 + 29 * q^12 - 22 * q^13 - 73 * q^14 + 54 * q^15 + 63 * q^16 - 334 * q^18 + 22 * q^19 - 330 * q^20 - 352 * q^21 + 79 * q^22 - 380 * q^23 - 159 * q^24 + 378 * q^25 - 448 * q^26 + 494 * q^27 - 608 * q^28 + 78 * q^29 + 313 * q^30 - 362 * q^31 + 331 * q^32 + 94 * q^33 - 242 * q^35 + 141 * q^36 - 512 * q^37 - 524 * q^38 - 12 * q^39 - 1381 * q^40 - 840 * q^41 + 1455 * q^42 - 114 * q^43 + 1041 * q^44 - 648 * q^45 + 1051 * q^46 + 10 * q^47 - 998 * q^48 + 1006 * q^49 + 805 * q^50 - 1537 * q^52 + 50 * q^53 - 581 * q^54 - 1316 * q^55 - 411 * q^56 - 358 * q^57 + 376 * q^58 + 996 * q^59 - 217 * q^60 - 448 * q^61 + 73 * q^62 - 766 * q^63 - 150 * q^64 + 372 * q^65 - 1090 * q^66 - 868 * q^67 - 1128 * q^69 + 1052 * q^70 - 1116 * q^71 - 39 * q^72 - 540 * q^73 - 1630 * q^74 - 1070 * q^75 - 873 * q^76 - 894 * q^77 + 1245 * q^78 - 940 * q^79 - 307 * q^80 + 1080 * q^81 + 334 * q^82 + 850 * q^83 + 443 * q^84 + 2411 * q^86 - 384 * q^87 + 2252 * q^88 + 784 * q^89 + 2069 * q^90 + 2858 * q^91 + 1566 * q^92 - 1550 * q^93 + 1119 * q^94 - 2494 * q^95 + 2643 * q^96 + 518 * q^97 - 1877 * q^98 + 1406 * q^99

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