LMFDB - Embedded newform 289.4.a.h.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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 72 x^{10} - 17 x^{9} + 1872 x^{8} + 627 x^{7} - 20922 x^{6} - 5163 x^{5} + 93255 x^{4} + \cdots + 29352 $ x^12 - 72x^10 - 17x^9 + 1872x^8 + 627x^7 - 20922x^6 - 5163x^5 + 93255x^4 - 4607x^3 - 117822x^2 + 21960x + 29352
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 17^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.73276$ 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)

$f(q)$	$=$	$q-3.73276 q^{2} +3.65511 q^{3} +5.93351 q^{4} +14.5154 q^{5} -13.6437 q^{6} -12.9694 q^{7} +7.71372 q^{8} -13.6402 q^{9} +O(q^{10})$	\(q-3.73276 q^{2} +3.65511 q^{3} +5.93351 q^{4} +14.5154 q^{5} -13.6437 q^{6} -12.9694 q^{7} +7.71372 q^{8} -13.6402 q^{9} -54.1823 q^{10} +20.2490 q^{11} +21.6876 q^{12} -90.7856 q^{13} +48.4118 q^{14} +53.0552 q^{15} -76.2615 q^{16} +50.9155 q^{18} -127.359 q^{19} +86.1270 q^{20} -47.4047 q^{21} -75.5848 q^{22} +69.5078 q^{23} +28.1945 q^{24} +85.6954 q^{25} +338.881 q^{26} -148.544 q^{27} -76.9542 q^{28} +43.9568 q^{29} -198.042 q^{30} +218.817 q^{31} +222.956 q^{32} +74.0124 q^{33} -188.256 q^{35} -80.9340 q^{36} +41.5125 q^{37} +475.399 q^{38} -331.832 q^{39} +111.967 q^{40} -440.141 q^{41} +176.951 q^{42} -310.790 q^{43} +120.148 q^{44} -197.992 q^{45} -259.456 q^{46} +84.3763 q^{47} -278.744 q^{48} -174.794 q^{49} -319.880 q^{50} -538.677 q^{52} +47.6186 q^{53} +554.480 q^{54} +293.922 q^{55} -100.043 q^{56} -465.510 q^{57} -164.080 q^{58} -1.73428 q^{59} +314.804 q^{60} -159.400 q^{61} -816.792 q^{62} +176.905 q^{63} -222.151 q^{64} -1317.78 q^{65} -276.271 q^{66} +141.756 q^{67} +254.059 q^{69} +702.714 q^{70} -447.302 q^{71} -105.216 q^{72} -757.081 q^{73} -154.956 q^{74} +313.226 q^{75} -755.684 q^{76} -262.618 q^{77} +1238.65 q^{78} -529.801 q^{79} -1106.96 q^{80} -174.662 q^{81} +1642.94 q^{82} -762.097 q^{83} -281.276 q^{84} +1160.11 q^{86} +160.667 q^{87} +156.195 q^{88} -397.434 q^{89} +739.056 q^{90} +1177.44 q^{91} +412.425 q^{92} +799.801 q^{93} -314.957 q^{94} -1848.66 q^{95} +814.930 q^{96} +427.919 q^{97} +652.464 q^{98} -276.200 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) $ 12 * q - 18 * q^3 + 48 * q^4 - 30 * q^5 + 9 * q^6 - 24 * q^7 - 51 * q^8 + 108 * q^9	\( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9} - 60 q^{10} - 162 q^{11} - 216 q^{12} - 72 q^{13} - 267 q^{14} - 138 q^{15} + 192 q^{16} + 189 q^{18} - 66 q^{19} - 129 q^{20} + 246 q^{21} - 456 q^{22} - 282 q^{23} - 72 q^{24} + 444 q^{25} + 528 q^{26} - 1092 q^{27} - 120 q^{28} - 648 q^{29} - 1890 q^{30} - 504 q^{31} - 1353 q^{32} + 966 q^{33} - 66 q^{35} - 663 q^{36} + 30 q^{37} - 60 q^{38} - 1758 q^{39} + 450 q^{40} - 318 q^{41} + 804 q^{42} + 486 q^{43} - 2448 q^{44} - 486 q^{45} - 1617 q^{46} - 888 q^{47} - 1257 q^{48} - 570 q^{49} + 435 q^{50} + 225 q^{52} + 1026 q^{53} - 933 q^{54} + 972 q^{55} - 2661 q^{56} + 156 q^{57} - 201 q^{58} - 792 q^{59} + 1458 q^{60} - 1212 q^{61} - 2817 q^{62} - 2112 q^{63} - 1857 q^{64} - 2742 q^{65} - 594 q^{66} + 624 q^{67} - 1506 q^{69} - 1650 q^{70} - 2802 q^{71} + 1455 q^{72} - 726 q^{73} - 270 q^{74} + 264 q^{75} + 675 q^{76} - 1008 q^{77} + 3090 q^{78} + 444 q^{79} + 1143 q^{80} + 2520 q^{81} + 4950 q^{82} + 672 q^{83} - 777 q^{84} + 2778 q^{86} + 726 q^{87} + 3750 q^{88} - 906 q^{89} + 7755 q^{90} - 2280 q^{91} - 87 q^{92} + 132 q^{93} + 735 q^{94} - 966 q^{95} + 5046 q^{96} + 3246 q^{97} + 1911 q^{98} + 282 q^{99}+O(q^{100}) \) 12 * q - 18 * q^3 + 48 * q^4 - 30 * q^5 + 9 * q^6 - 24 * q^7 - 51 * q^8 + 108 * q^9 - 60 * q^10 - 162 * q^11 - 216 * q^12 - 72 * q^13 - 267 * q^14 - 138 * q^15 + 192 * q^16 + 189 * q^18 - 66 * q^19 - 129 * q^20 + 246 * q^21 - 456 * q^22 - 282 * q^23 - 72 * q^24 + 444 * q^25 + 528 * q^26 - 1092 * q^27 - 120 * q^28 - 648 * q^29 - 1890 * q^30 - 504 * q^31 - 1353 * q^32 + 966 * q^33 - 66 * q^35 - 663 * q^36 + 30 * q^37 - 60 * q^38 - 1758 * q^39 + 450 * q^40 - 318 * q^41 + 804 * q^42 + 486 * q^43 - 2448 * q^44 - 486 * q^45 - 1617 * q^46 - 888 * q^47 - 1257 * q^48 - 570 * q^49 + 435 * q^50 + 225 * q^52 + 1026 * q^53 - 933 * q^54 + 972 * q^55 - 2661 * q^56 + 156 * q^57 - 201 * q^58 - 792 * q^59 + 1458 * q^60 - 1212 * q^61 - 2817 * q^62 - 2112 * q^63 - 1857 * q^64 - 2742 * q^65 - 594 * q^66 + 624 * q^67 - 1506 * q^69 - 1650 * q^70 - 2802 * q^71 + 1455 * q^72 - 726 * q^73 - 270 * q^74 + 264 * q^75 + 675 * q^76 - 1008 * q^77 + 3090 * q^78 + 444 * q^79 + 1143 * q^80 + 2520 * q^81 + 4950 * q^82 + 672 * q^83 - 777 * q^84 + 2778 * q^86 + 726 * q^87 + 3750 * q^88 - 906 * q^89 + 7755 * q^90 - 2280 * q^91 - 87 * q^92 + 132 * q^93 + 735 * q^94 - 966 * q^95 + 5046 * q^96 + 3246 * q^97 + 1911 * q^98 + 282 * 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 $

$2$	−3.73276	−1.31973	−0.659865	−	0.751384i	$-0.729387\pi$
$2$	−3.73276	−1.31973	−0.659865	+	0.751384i	$0.729387\pi$
$3$	3.65511	0.703426	0.351713	−	0.936108i	$-0.385599\pi$
$3$	3.65511	0.703426	0.351713	+	0.936108i	$0.385599\pi$
$4$	5.93351	0.741689
$5$	14.5154	1.29829	0.649146	−	0.760664i	$-0.275126\pi$
$5$	14.5154	1.29829	0.649146	+	0.760664i	$0.275126\pi$
$6$	−13.6437	−0.928333
$7$	−12.9694	−0.700284	−0.350142	−	0.936697i	$-0.613867\pi$
$7$	−12.9694	−0.700284	−0.350142	+	0.936697i	$0.613867\pi$
$8$	7.71372	0.340901
$9$	−13.6402	−0.505191
$10$	−54.1823	−1.71340
$11$	20.2490	0.555028	0.277514	−	0.960722i	$-0.410489\pi$
$11$	20.2490	0.555028	0.277514	+	0.960722i	$0.410489\pi$
$12$	21.6876	0.521723
$13$	−90.7856	−1.93688	−0.968438	−	0.249253i	$-0.919815\pi$
$13$	−90.7856	−1.93688	−0.968438	+	0.249253i	$0.919815\pi$
$14$	48.4118	0.924186
$15$	53.0552	0.913253
$16$	−76.2615	−1.19159
$17$	0	0
$17$	0	0
$18$	50.9155	0.666716
$19$	−127.359	−1.53779	−0.768897	−	0.639373i	$-0.779194\pi$
$19$	−127.359	−1.53779	−0.768897	+	0.639373i	$0.779194\pi$
$20$	86.1270	0.962929
$21$	−47.4047	−0.492598
$22$	−75.5848	−0.732488
$23$	69.5078	0.630147	0.315073	−	0.949067i	$-0.397971\pi$
$23$	69.5078	0.630147	0.315073	+	0.949067i	$0.397971\pi$
$24$	28.1945	0.239799
$25$	85.6954	0.685563
$26$	338.881	2.55616
$27$	−148.544	−1.05879
$28$	−76.9542	−0.519392
$29$	43.9568	0.281468	0.140734	−	0.990047i	$-0.455054\pi$
$29$	43.9568	0.281468	0.140734	+	0.990047i	$0.455054\pi$
$30$	−198.042	−1.20525
$31$	218.817	1.26776	0.633882	−	0.773430i	$-0.281460\pi$
$31$	218.817	1.26776	0.633882	+	0.773430i	$0.281460\pi$
$32$	222.956	1.23167
$33$	74.0124	0.390422
$34$	0	0
$35$	−188.256	−0.909173
$36$	−80.9340	−0.374695
$37$	41.5125	0.184449	0.0922245	−	0.995738i	$-0.470602\pi$
$37$	41.5125	0.184449	0.0922245	+	0.995738i	$0.470602\pi$
$38$	475.399	2.02947
$39$	−331.832	−1.36245
$40$	111.967	0.442590
$41$	−440.141	−1.67655	−0.838274	−	0.545249i	$-0.816435\pi$
$41$	−440.141	−1.67655	−0.838274	+	0.545249i	$0.816435\pi$
$42$	176.951	0.650097
$43$	−310.790	−1.10221	−0.551106	−	0.834435i	$-0.685794\pi$
$43$	−310.790	−1.10221	−0.551106	+	0.834435i	$0.685794\pi$
$44$	120.148	0.411658
$45$	−197.992	−0.655886
$46$	−259.456	−0.831624
$47$	84.3763	0.261863	0.130931	−	0.991391i	$-0.458203\pi$
$47$	84.3763	0.261863	0.130931	+	0.991391i	$0.458203\pi$
$48$	−278.744	−0.838194
$49$	−174.794	−0.509603
$50$	−319.880	−0.904759
$51$	0	0
$52$	−538.677	−1.43656
$53$	47.6186	0.123414	0.0617068	−	0.998094i	$-0.480346\pi$
$53$	47.6186	0.123414	0.0617068	+	0.998094i	$0.480346\pi$
$54$	554.480	1.39732
$55$	293.922	0.720589
$56$	−100.043	−0.238728
$57$	−465.510	−1.08172
$58$	−164.080	−0.371462
$59$	−1.73428	−0.00382685	−0.00191342	−	0.999998i	$-0.500609\pi$
$59$	−1.73428	−0.00382685	−0.00191342	+	0.999998i	$0.500609\pi$
$60$	314.804	0.677350
$61$	−159.400	−0.334575	−0.167287	−	0.985908i	$-0.553501\pi$
$61$	−159.400	−0.334575	−0.167287	+	0.985908i	$0.553501\pi$
$62$	−816.792	−1.67311
$63$	176.905	0.353777
$64$	−222.151	−0.433888
$65$	−1317.78	−2.51463
$66$	−276.271	−0.515251
$67$	141.756	0.258482	0.129241	−	0.991613i	$-0.458746\pi$
$67$	141.756	0.258482	0.129241	+	0.991613i	$0.458746\pi$
$68$	0	0
$69$	254.059	0.443262
$70$	702.714	1.19986
$71$	−447.302	−0.747675	−0.373838	−	0.927494i	$-0.621958\pi$
$71$	−447.302	−0.747675	−0.373838	+	0.927494i	$0.621958\pi$
$72$	−105.216	−0.172220
$73$	−757.081	−1.21383	−0.606916	−	0.794766i	$-0.707593\pi$
$73$	−757.081	−1.21383	−0.606916	+	0.794766i	$0.707593\pi$
$74$	−154.956	−0.243423
$75$	313.226	0.482243
$76$	−755.684	−1.14056
$77$	−262.618	−0.388677
$78$	1238.65	1.79807
$79$	−529.801	−0.754523	−0.377261	−	0.926107i	$-0.623134\pi$
$79$	−529.801	−0.754523	−0.377261	+	0.926107i	$0.623134\pi$
$80$	−1106.96	−1.54703
$81$	−174.662	−0.239591
$82$	1642.94	2.21259
$83$	−762.097	−1.00784	−0.503922	−	0.863749i	$-0.668110\pi$
$83$	−762.097	−1.00784	−0.503922	+	0.863749i	$0.668110\pi$
$84$	−281.276	−0.365354
$85$	0	0
$86$	1160.11	1.45462
$87$	160.667	0.197992
$88$	156.195	0.189210
$89$	−397.434	−0.473348	−0.236674	−	0.971589i	$-0.576057\pi$
$89$	−397.434	−0.473348	−0.236674	+	0.971589i	$0.576057\pi$
$90$	739.056	0.865593
$91$	1177.44	1.35636
$92$	412.425	0.467373
$93$	799.801	0.891779
$94$	−314.957	−0.345588
$95$	−1848.66	−1.99651
$96$	814.930	0.866391
$97$	427.919	0.447924	0.223962	−	0.974598i	$-0.428101\pi$
$97$	427.919	0.447924	0.223962	+	0.974598i	$0.428101\pi$
$98$	652.464	0.672538
$99$	−276.200	−0.280395
$100$	508.474	0.508474
$101$	1591.35	1.56778	0.783889	−	0.620901i	$-0.213233\pi$
$101$	1591.35	1.56778	0.783889	+	0.620901i	$0.213233\pi$
$102$	0	0
$103$	−1094.59	−1.04712	−0.523558	−	0.851990i	$-0.675396\pi$
$103$	−1094.59	−1.04712	−0.523558	+	0.851990i	$0.675396\pi$
$104$	−700.295	−0.660284
$105$	−688.096	−0.639536
$106$	−177.749	−0.162873
$107$	1321.45	1.19392	0.596960	−	0.802271i	$-0.296375\pi$
$107$	1321.45	1.19392	0.596960	+	0.802271i	$0.296375\pi$
$108$	−881.389	−0.785293
$109$	1324.25	1.16367	0.581835	−	0.813307i	$-0.302335\pi$
$109$	1324.25	1.16367	0.581835	+	0.813307i	$0.302335\pi$
$110$	−1097.14	−0.950983
$111$	151.733	0.129746
$112$	989.069	0.834449
$113$	1621.26	1.34969	0.674847	−	0.737958i	$-0.264210\pi$
$113$	1621.26	1.34969	0.674847	+	0.737958i	$0.264210\pi$
$114$	1737.64	1.42758
$115$	1008.93	0.818115
$116$	260.818	0.208762
$117$	1238.33	0.978493
$118$	6.47365	0.00505041
$119$	0	0
$120$	409.253	0.311329
$121$	−920.977	−0.691944
$122$	595.001	0.441548
$123$	−1608.76	−1.17933
$124$	1298.35	0.940287
$125$	−570.520	−0.408231
$126$	−660.345	−0.466890
$127$	423.287	0.295753	0.147876	−	0.989006i	$-0.452756\pi$
$127$	423.287	0.295753	0.147876	+	0.989006i	$0.452756\pi$
$128$	−954.415	−0.659056
$129$	−1135.97	−0.775325
$130$	4918.98	3.31864
$131$	792.977	0.528876	0.264438	−	0.964403i	$-0.414814\pi$
$131$	792.977	0.528876	0.264438	+	0.964403i	$0.414814\pi$
$132$	439.153	0.289571
$133$	1651.77	1.07689
$134$	−529.143	−0.341127
$135$	−2156.17	−1.37462
$136$	0	0
$137$	809.512	0.504827	0.252414	−	0.967619i	$-0.418776\pi$
$137$	809.512	0.504827	0.252414	+	0.967619i	$0.418776\pi$
$138$	−948.341	−0.584986
$139$	−2842.04	−1.73424	−0.867119	−	0.498102i	$-0.834031\pi$
$139$	−2842.04	−1.73424	−0.867119	+	0.498102i	$0.834031\pi$
$140$	−1117.02	−0.674323
$141$	308.405	0.184201
$142$	1669.67	0.986730
$143$	−1838.32	−1.07502
$144$	1040.22	0.601979
$145$	638.048	0.365428
$146$	2826.00	1.60193
$147$	−638.891	−0.358468
$148$	246.315	0.136804
$149$	−1010.84	−0.555782	−0.277891	−	0.960613i	$-0.589635\pi$
$149$	−1010.84	−0.555782	−0.277891	+	0.960613i	$0.589635\pi$
$150$	−1169.20	−0.636431
$151$	1340.29	0.722327	0.361163	−	0.932503i	$-0.382380\pi$
$151$	1340.29	0.722327	0.361163	+	0.932503i	$0.382380\pi$
$152$	−982.409	−0.524236
$153$	0	0
$154$	980.292	0.512949
$155$	3176.21	1.64593
$156$	−1968.93	−1.01051
$157$	−947.372	−0.481583	−0.240792	−	0.970577i	$-0.577407\pi$
$157$	−947.372	−0.481583	−0.240792	+	0.970577i	$0.577407\pi$
$158$	1977.62	0.995766
$159$	174.051	0.0868123
$160$	3236.29	1.59907
$161$	−901.477	−0.441282
$162$	651.970	0.316195
$163$	−966.144	−0.464259	−0.232129	−	0.972685i	$-0.574569\pi$
$163$	−966.144	−0.464259	−0.232129	+	0.972685i	$0.574569\pi$
$164$	−2611.58	−1.24348
$165$	1074.32	0.506881
$166$	2844.73	1.33008
$167$	−1193.13	−0.552857	−0.276429	−	0.961034i	$-0.589151\pi$
$167$	−1193.13	−0.552857	−0.276429	+	0.961034i	$0.589151\pi$
$168$	−365.667	−0.167927
$169$	6045.03	2.75149
$170$	0	0
$171$	1737.19	0.776880
$172$	−1844.08	−0.817498
$173$	8.50924	0.00373957	0.00186978	−	0.999998i	$-0.499405\pi$
$173$	8.50924	0.00373957	0.00186978	+	0.999998i	$0.499405\pi$
$174$	−599.731	−0.261296
$175$	−1111.42	−0.480089
$176$	−1544.22	−0.661364
$177$	−6.33899	−0.00269191
$178$	1483.53	0.624691
$179$	−909.300	−0.379689	−0.189844	−	0.981814i	$-0.560798\pi$
$179$	−909.300	−0.379689	−0.189844	+	0.981814i	$0.560798\pi$
$180$	−1174.79	−0.486463
$181$	−2448.71	−1.00559	−0.502793	−	0.864407i	$-0.667694\pi$
$181$	−2448.71	−1.00559	−0.502793	+	0.864407i	$0.667694\pi$
$182$	−4395.10	−1.79003
$183$	−582.624	−0.235349
$184$	536.164	0.214818
$185$	602.568	0.239469
$186$	−2985.47	−1.17691
$187$	0	0
$188$	500.648	0.194221
$189$	1926.54	0.741454
$190$	6900.59	2.63485
$191$	845.418	0.320274	0.160137	−	0.987095i	$-0.448806\pi$
$191$	845.418	0.320274	0.160137	+	0.987095i	$0.448806\pi$
$192$	−811.986	−0.305208
$193$	7.70682	0.00287435	0.00143717	−	0.999999i	$-0.499543\pi$
$193$	7.70682	0.00287435	0.00143717	+	0.999999i	$0.499543\pi$
$194$	−1597.32	−0.591139
$195$	−4816.65	−1.76886
$196$	−1037.14	−0.377967
$197$	5024.07	1.81701	0.908503	−	0.417879i	$-0.137227\pi$
$197$	5024.07	1.81701	0.908503	+	0.417879i	$0.137227\pi$
$198$	1030.99	0.370046
$199$	−1210.87	−0.431339	−0.215669	−	0.976466i	$-0.569193\pi$
$199$	−1210.87	−0.431339	−0.215669	+	0.976466i	$0.569193\pi$
$200$	661.030	0.233709
$201$	518.135	0.181823
$202$	−5940.15	−2.06905
$203$	−570.095	−0.197107
$204$	0	0
$205$	−6388.80	−2.17665
$206$	4085.84	1.38191
$207$	−948.098	−0.318345
$208$	6923.45	2.30796
$209$	−2578.89	−0.853519
$210$	2568.50	0.844016
$211$	3047.09	0.994172	0.497086	−	0.867701i	$-0.334403\pi$
$211$	3047.09	0.994172	0.497086	+	0.867701i	$0.334403\pi$
$212$	282.545	0.0915344
$213$	−1634.94	−0.525934
$214$	−4932.66	−1.57565
$215$	−4511.23	−1.43099
$216$	−1145.83	−0.360943
$217$	−2837.93	−0.887795
$218$	−4943.10	−1.53573
$219$	−2767.22	−0.853841
$220$	1743.99	0.534453
$221$	0	0
$222$	−566.382	−0.171230
$223$	−2883.35	−0.865846	−0.432923	−	0.901431i	$-0.642518\pi$
$223$	−2883.35	−0.865846	−0.432923	+	0.901431i	$0.642518\pi$
$224$	−2891.62	−0.862520
$225$	−1168.90	−0.346340
$226$	−6051.78	−1.78123
$227$	−5402.18	−1.57954	−0.789770	−	0.613403i	$-0.789800\pi$
$227$	−5402.18	−1.57954	−0.789770	+	0.613403i	$0.789800\pi$
$228$	−2762.11	−0.802303
$229$	−1524.25	−0.439849	−0.219925	−	0.975517i	$-0.570581\pi$
$229$	−1524.25	−0.439849	−0.219925	+	0.975517i	$0.570581\pi$
$230$	−3766.10	−1.07969
$231$	−959.899	−0.273406
$232$	339.070	0.0959528
$233$	1685.79	0.473989	0.236995	−	0.971511i	$-0.423838\pi$
$233$	1685.79	0.473989	0.236995	+	0.971511i	$0.423838\pi$
$234$	−4622.39	−1.29135
$235$	1224.75	0.339975
$236$	−10.2904	−0.00283833
$237$	−1936.48	−0.530751
$238$	0	0
$239$	−4887.91	−1.32290	−0.661449	−	0.749990i	$-0.730058\pi$
$239$	−4887.91	−1.32290	−0.661449	+	0.749990i	$0.730058\pi$
$240$	−4046.07	−1.08822
$241$	3416.56	0.913195	0.456597	−	0.889673i	$-0.349068\pi$
$241$	3416.56	0.913195	0.456597	+	0.889673i	$0.349068\pi$
$242$	3437.79	0.913179
$243$	3372.29	0.890257
$244$	−945.800	−0.248150
$245$	−2537.19	−0.661614
$246$	6005.13	1.55640
$247$	11562.3	2.97852
$248$	1687.89	0.432183
$249$	−2785.55	−0.708944
$250$	2129.62	0.538755
$251$	2357.42	0.592825	0.296413	−	0.955060i	$-0.404210\pi$
$251$	2357.42	0.592825	0.296413	+	0.955060i	$0.404210\pi$
$252$	1049.67	0.262392
$253$	1407.47	0.349749
$254$	−1580.03	−0.390314
$255$	0	0
$256$	5339.81	1.30366
$257$	2033.64	0.493598	0.246799	−	0.969067i	$-0.420621\pi$
$257$	2033.64	0.493598	0.246799	+	0.969067i	$0.420621\pi$
$258$	4240.32	1.02322
$259$	−538.393	−0.129167
$260$	−7819.09	−1.86507
$261$	−599.578	−0.142195
$262$	−2960.00	−0.697974
$263$	5377.07	1.26070	0.630351	−	0.776310i	$-0.282911\pi$
$263$	5377.07	1.26070	0.630351	+	0.776310i	$0.282911\pi$
$264$	570.911	0.133095
$265$	691.200	0.160227
$266$	−6165.66	−1.42121
$267$	−1452.67	−0.332965
$268$	841.113	0.191713
$269$	−3012.15	−0.682728	−0.341364	−	0.939931i	$-0.610889\pi$
$269$	−3012.15	−0.682728	−0.341364	+	0.939931i	$0.610889\pi$
$270$	8048.48	1.81413
$271$	−1340.23	−0.300417	−0.150209	−	0.988654i	$-0.547995\pi$
$271$	−1340.23	−0.300417	−0.150209	+	0.988654i	$0.547995\pi$
$272$	0	0
$273$	4303.67	0.954102
$274$	−3021.72	−0.666236
$275$	1735.25	0.380507
$276$	1507.46	0.328762
$277$	4917.83	1.06673	0.533365	−	0.845885i	$-0.320927\pi$
$277$	4917.83	1.06673	0.533365	+	0.845885i	$0.320927\pi$
$278$	10608.7	2.28873
$279$	−2984.70	−0.640463
$280$	−1452.15	−0.309938
$281$	−697.896	−0.148160	−0.0740801	−	0.997252i	$-0.523602\pi$
$281$	−697.896	−0.148160	−0.0740801	+	0.997252i	$0.523602\pi$
$282$	−1151.20	−0.243096
$283$	5379.29	1.12991	0.564957	−	0.825121i	$-0.308893\pi$
$283$	5379.29	1.12991	0.564957	+	0.825121i	$0.308893\pi$
$284$	−2654.07	−0.554542
$285$	−6757.04	−1.40439
$286$	6862.01	1.41874
$287$	5708.38	1.17406
$288$	−3041.16	−0.622230
$289$	0	0
$290$	−2381.68	−0.482266
$291$	1564.09	0.315081
$292$	−4492.15	−0.900285
$293$	2876.89	0.573616	0.286808	−	0.957988i	$-0.407406\pi$
$293$	2876.89	0.573616	0.286808	+	0.957988i	$0.407406\pi$
$294$	2384.83	0.473081
$295$	−25.1737	−0.00496837
$296$	320.216	0.0628789
$297$	−3007.88	−0.587659
$298$	3773.24	0.733482
$299$	−6310.31	−1.22052
$300$	1858.53	0.357674
$301$	4030.78	0.771861
$302$	−5002.99	−0.953276
$303$	5816.58	1.10282
$304$	9712.57	1.83241
$305$	−2313.74	−0.434376
$306$	0	0
$307$	−3765.61	−0.700048	−0.350024	−	0.936741i	$-0.613827\pi$
$307$	−3765.61	−0.700048	−0.350024	+	0.936741i	$0.613827\pi$
$308$	−1558.25	−0.288277
$309$	−4000.84	−0.736570
$310$	−11856.0	−2.17218
$311$	−1043.69	−0.190297	−0.0951483	−	0.995463i	$-0.530333\pi$
$311$	−1043.69	−0.190297	−0.0951483	+	0.995463i	$0.530333\pi$
$312$	−2559.66	−0.464461
$313$	−801.837	−0.144800	−0.0724002	−	0.997376i	$-0.523066\pi$
$313$	−801.837	−0.144800	−0.0724002	+	0.997376i	$0.523066\pi$
$314$	3536.31	0.635560
$315$	2567.84	0.459306
$316$	−3143.58	−0.559621
$317$	806.122	0.142827	0.0714137	−	0.997447i	$-0.477249\pi$
$317$	806.122	0.142827	0.0714137	+	0.997447i	$0.477249\pi$
$318$	−649.692	−0.114569
$319$	890.082	0.156223
$320$	−3224.60	−0.563314
$321$	4830.05	0.839836
$322$	3365.00	0.582373
$323$	0	0
$324$	−1036.36	−0.177702
$325$	−7779.91	−1.32785
$326$	3606.38	0.612697
$327$	4840.27	0.818556
$328$	−3395.12	−0.571538
$329$	−1094.31	−0.183378
$330$	−4010.17	−0.668947
$331$	2607.01	0.432913	0.216457	−	0.976292i	$-0.430550\pi$
$331$	2607.01	0.432913	0.216457	+	0.976292i	$0.430550\pi$
$332$	−4521.91	−0.747506
$333$	−566.237	−0.0931820
$334$	4453.67	0.729623
$335$	2057.64	0.335585
$336$	3615.16	0.586973
$337$	1067.31	0.172523	0.0862614	−	0.996273i	$-0.472508\pi$
$337$	1067.31	0.172523	0.0862614	+	0.996273i	$0.472508\pi$
$338$	−22564.6	−3.63123
$339$	5925.89	0.949410
$340$	0	0
$341$	4430.83	0.703645
$342$	−6484.53	−1.02527
$343$	6715.49	1.05715
$344$	−2397.35	−0.375745
$345$	3687.75	0.575484
$346$	−31.7630	−0.00493522
$347$	11380.2	1.76058	0.880288	−	0.474439i	$-0.157349\pi$
$347$	11380.2	1.76058	0.880288	+	0.474439i	$0.157349\pi$
$348$	953.319	0.146848
$349$	−2447.03	−0.375320	−0.187660	−	0.982234i	$-0.560090\pi$
$349$	−2447.03	−0.375320	−0.187660	+	0.982234i	$0.560090\pi$
$350$	4148.67	0.633588
$351$	13485.7	2.05075
$352$	4514.65	0.683613
$353$	5229.05	0.788426	0.394213	−	0.919019i	$-0.371017\pi$
$353$	5229.05	0.788426	0.394213	+	0.919019i	$0.371017\pi$
$354$	23.6619	0.00355259
$355$	−6492.74	−0.970701
$356$	−2358.18	−0.351077
$357$	0	0
$358$	3394.20	0.501087
$359$	9108.24	1.33904	0.669519	−	0.742795i	$-0.266500\pi$
$359$	9108.24	1.33904	0.669519	+	0.742795i	$0.266500\pi$
$360$	−1527.25	−0.223592
$361$	9361.22	1.36481
$362$	9140.44	1.32710
$363$	−3366.27	−0.486731
$364$	6986.34	1.00600
$365$	−10989.3	−1.57591
$366$	2174.80	0.310597
$367$	1155.57	0.164360	0.0821801	−	0.996617i	$-0.473812\pi$
$367$	1155.57	0.164360	0.0821801	+	0.996617i	$0.473812\pi$
$368$	−5300.77	−0.750875
$369$	6003.59	0.846977
$370$	−2249.24	−0.316034
$371$	−617.586	−0.0864245
$372$	4745.62	0.661422
$373$	−9949.97	−1.38121	−0.690603	−	0.723234i	$-0.742655\pi$
$373$	−9949.97	−1.38121	−0.690603	+	0.723234i	$0.742655\pi$
$374$	0	0
$375$	−2085.31	−0.287160
$376$	650.855	0.0892694
$377$	−3990.64	−0.545169
$378$	−7191.30	−0.978520
$379$	−1443.78	−0.195678	−0.0978388	−	0.995202i	$-0.531193\pi$
$379$	−1443.78	−0.195678	−0.0978388	+	0.995202i	$0.531193\pi$
$380$	−10969.0	−1.48079
$381$	1547.16	0.208040
$382$	−3155.74	−0.422675
$383$	−8249.59	−1.10061	−0.550306	−	0.834963i	$-0.685489\pi$
$383$	−8249.59	−1.10061	−0.550306	+	0.834963i	$0.685489\pi$
$384$	−3488.49	−0.463598
$385$	−3812.00	−0.504617
$386$	−28.7677	−0.00379336
$387$	4239.23	0.556827
$388$	2539.06	0.332220
$389$	−9396.96	−1.22479	−0.612397	−	0.790551i	$-0.709794\pi$
$389$	−9396.96	−1.22479	−0.612397	+	0.790551i	$0.709794\pi$
$390$	17979.4	2.33442
$391$	0	0
$392$	−1348.31	−0.173724
$393$	2898.42	0.372025
$394$	−18753.6	−2.39796
$395$	−7690.25	−0.979591
$396$	−1638.83	−0.207966
$397$	11970.7	1.51333	0.756667	−	0.653800i	$-0.226826\pi$
$397$	11970.7	1.51333	0.756667	+	0.653800i	$0.226826\pi$
$398$	4519.90	0.569251
$399$	6037.40	0.757514
$400$	−6535.26	−0.816908
$401$	10710.9	1.33386	0.666928	−	0.745122i	$-0.267609\pi$
$401$	10710.9	1.33386	0.666928	+	0.745122i	$0.267609\pi$
$402$	−1934.08	−0.239958
$403$	−19865.4	−2.45550
$404$	9442.31	1.16280
$405$	−2535.27	−0.311059
$406$	2128.03	0.260129
$407$	840.587	0.102374
$408$	0	0
$409$	−1220.58	−0.147565	−0.0737824	−	0.997274i	$-0.523507\pi$
$409$	−1220.58	−0.147565	−0.0737824	+	0.997274i	$0.523507\pi$
$410$	23847.9	2.87259
$411$	2958.86	0.355109
$412$	−6494.75	−0.776634
$413$	22.4926	0.00267988
$414$	3539.02	0.420129
$415$	−11062.1	−1.30848
$416$	−20241.2	−2.38560
$417$	−10388.0	−1.21991
$418$	9626.37	1.12641
$419$	−10940.2	−1.27557	−0.637784	−	0.770215i	$-0.720149\pi$
$419$	−10940.2	−1.27557	−0.637784	+	0.770215i	$0.720149\pi$
$420$	−4082.82	−0.474337
$421$	−2304.87	−0.266823	−0.133411	−	0.991061i	$-0.542593\pi$
$421$	−2304.87	−0.266823	−0.133411	+	0.991061i	$0.542593\pi$
$422$	−11374.1	−1.31204
$423$	−1150.91	−0.132291
$424$	367.316	0.0420718
$425$	0	0
$426$	6102.83	0.694092
$427$	2067.32	0.234297
$428$	7840.84	0.885518
$429$	−6719.26	−0.756198
$430$	16839.4	1.88852
$431$	−5741.54	−0.641671	−0.320835	−	0.947135i	$-0.603964\pi$
$431$	−5741.54	−0.641671	−0.320835	+	0.947135i	$0.603964\pi$
$432$	11328.2	1.26164
$433$	4553.54	0.505379	0.252690	−	0.967547i	$-0.418685\pi$
$433$	4553.54	0.505379	0.252690	+	0.967547i	$0.418685\pi$
$434$	10593.3	1.17165
$435$	2332.14	0.257051
$436$	7857.44	0.863080
$437$	−8852.42	−0.969036
$438$	10329.4	1.12684
$439$	−10786.4	−1.17268	−0.586340	−	0.810065i	$-0.699432\pi$
$439$	−10786.4	−1.17268	−0.586340	+	0.810065i	$0.699432\pi$
$440$	2267.23	0.245650
$441$	2384.22	0.257447
$442$	0	0
$443$	13133.5	1.40856	0.704280	−	0.709922i	$-0.251270\pi$
$443$	13133.5	1.40856	0.704280	+	0.709922i	$0.251270\pi$
$444$	900.307	0.0962313
$445$	−5768.90	−0.614544
$446$	10762.9	1.14268
$447$	−3694.74	−0.390952
$448$	2881.17	0.303845
$449$	714.661	0.0751157	0.0375578	−	0.999294i	$-0.488042\pi$
$449$	714.661	0.0751157	0.0375578	+	0.999294i	$0.488042\pi$
$450$	4363.22	0.457076
$451$	−8912.42	−0.930531
$452$	9619.77	1.00105
$453$	4898.91	0.508104
$454$	20165.1	2.08457
$455$	17090.9	1.76096
$456$	−3590.81	−0.368761
$457$	−976.357	−0.0999388	−0.0499694	−	0.998751i	$-0.515912\pi$
$457$	−976.357	−0.0999388	−0.0499694	+	0.998751i	$0.515912\pi$
$458$	5689.67	0.580482
$459$	0	0
$460$	5986.50	0.606787
$461$	−17713.0	−1.78953	−0.894767	−	0.446533i	$-0.852659\pi$
$461$	−17713.0	−1.78953	−0.894767	+	0.446533i	$0.852659\pi$
$462$	3583.08	0.360822
$463$	−13597.7	−1.36488	−0.682441	−	0.730941i	$-0.739082\pi$
$463$	−13597.7	−1.36488	−0.682441	+	0.730941i	$0.739082\pi$
$464$	−3352.21	−0.335393
$465$	11609.4	1.15779
$466$	−6292.63	−0.625538
$467$	9115.78	0.903272	0.451636	−	0.892202i	$-0.350841\pi$
$467$	9115.78	0.903272	0.451636	+	0.892202i	$0.350841\pi$
$468$	7347.64	0.725737
$469$	−1838.50	−0.181011
$470$	−4571.71	−0.448675
$471$	−3462.75	−0.338758
$472$	−13.3777	−0.00130458
$473$	−6293.20	−0.611758
$474$	7228.43	0.700448
$475$	−10914.0	−1.05425
$476$	0	0
$477$	−649.525	−0.0623474
$478$	18245.4	1.74587
$479$	−11483.2	−1.09537	−0.547683	−	0.836686i	$-0.684490\pi$
$479$	−11483.2	−1.09537	−0.547683	+	0.836686i	$0.684490\pi$
$480$	11829.0	1.12483
$481$	−3768.74	−0.357255
$482$	−12753.2	−1.20517
$483$	−3295.00	−0.310409
$484$	−5464.63	−0.513207
$485$	6211.40	0.581536
$486$	−12588.0	−1.17490
$487$	4117.57	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$487$	4117.57	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$488$	−1229.57	−0.114057
$489$	−3531.36	−0.326572
$490$	9470.74	0.873152
$491$	−11870.1	−1.09102	−0.545509	−	0.838105i	$-0.683664\pi$
$491$	−11870.1	−1.09102	−0.545509	+	0.838105i	$0.683664\pi$
$492$	−9545.61	−0.874694
$493$	0	0
$494$	−43159.4	−3.93084
$495$	−4009.14	−0.364035
$496$	−16687.3	−1.51065
$497$	5801.25	0.523585
$498$	10397.8	0.935615
$499$	−16770.4	−1.50450	−0.752252	−	0.658875i	$-0.771033\pi$
$499$	−16770.4	−1.50450	−0.752252	+	0.658875i	$0.771033\pi$
$500$	−3385.19	−0.302780
$501$	−4361.02	−0.388895
$502$	−8799.69	−0.782369
$503$	14451.7	1.28105	0.640525	−	0.767938i	$-0.278717\pi$
$503$	14451.7	1.28105	0.640525	+	0.767938i	$0.278717\pi$
$504$	1364.60	0.120603
$505$	23099.1	2.03544
$506$	−5253.73	−0.461575
$507$	22095.2	1.93547
$508$	2511.57	0.219357
$509$	22279.2	1.94010	0.970049	−	0.242910i	$-0.0781019\pi$
$509$	22279.2	1.94010	0.970049	+	0.242910i	$0.0781019\pi$
$510$	0	0
$511$	9818.92	0.850026
$512$	−12296.9	−1.06143
$513$	18918.4	1.62820
$514$	−7591.08	−0.651417
$515$	−15888.3	−1.35946
$516$	−6740.31	−0.575049
$517$	1708.54	0.145341
$518$	2009.69	0.170465
$519$	31.1022	0.00263051
$520$	−10165.0	−0.857242
$521$	16004.3	1.34580	0.672898	−	0.739735i	$-0.265049\pi$
$521$	16004.3	1.34580	0.672898	+	0.739735i	$0.265049\pi$
$522$	2238.08	0.187659
$523$	−22158.6	−1.85264	−0.926319	−	0.376739i	$-0.877045\pi$
$523$	−22158.6	−1.85264	−0.926319	+	0.376739i	$0.877045\pi$
$524$	4705.14	0.392261
$525$	−4062.37	−0.337707
$526$	−20071.3	−1.66379
$527$	0	0
$528$	−5644.30	−0.465221
$529$	−7335.66	−0.602915
$530$	−2580.09	−0.211456
$531$	23.6559	0.00193329
$532$	9800.79	0.798718
$533$	39958.5	3.24727
$534$	5422.46	0.439424
$535$	19181.3	1.55006
$536$	1093.47	0.0881169
$537$	−3323.59	−0.267083
$538$	11243.6	0.901017
$539$	−3539.40	−0.282844
$540$	−12793.7	−1.01954
$541$	−3099.41	−0.246310	−0.123155	−	0.992387i	$-0.539301\pi$
$541$	−3099.41	−0.246310	−0.123155	+	0.992387i	$0.539301\pi$
$542$	5002.75	0.396470
$543$	−8950.30	−0.707355
$544$	0	0
$545$	19221.9	1.51078
$546$	−16064.6	−1.25916
$547$	21795.9	1.70370	0.851852	−	0.523783i	$-0.175480\pi$
$547$	21795.9	1.70370	0.851852	+	0.523783i	$0.175480\pi$
$548$	4803.25	0.374424
$549$	2174.24	0.169024
$550$	−6477.27	−0.502167
$551$	−5598.28	−0.432839
$552$	1959.74	0.151109
$553$	6871.22	0.528380
$554$	−18357.1	−1.40780
$555$	2202.45	0.168449
$556$	−16863.3	−1.28626
$557$	12689.7	0.965315	0.482658	−	0.875809i	$-0.339672\pi$
$557$	12689.7	0.965315	0.482658	+	0.875809i	$0.339672\pi$
$558$	11141.2	0.845239
$559$	28215.3	2.13485
$560$	14356.7	1.08336
$561$	0	0
$562$	2605.08	0.195532
$563$	−10849.0	−0.812129	−0.406065	−	0.913844i	$-0.633099\pi$
$563$	−10849.0	−0.812129	−0.406065	+	0.913844i	$0.633099\pi$
$564$	1829.92	0.136620
$565$	23533.2	1.75230
$566$	−20079.6	−1.49118
$567$	2265.26	0.167781
$568$	−3450.36	−0.254884
$569$	−5582.88	−0.411329	−0.205665	−	0.978623i	$-0.565936\pi$
$569$	−5582.88	−0.411329	−0.205665	+	0.978623i	$0.565936\pi$
$570$	25222.4	1.85342
$571$	−20899.4	−1.53172	−0.765859	−	0.643008i	$-0.777686\pi$
$571$	−20899.4	−1.53172	−0.765859	+	0.643008i	$0.777686\pi$
$572$	−10907.7	−0.797331
$573$	3090.10	0.225289
$574$	−21308.0	−1.54944
$575$	5956.50	0.432006
$576$	3030.17	0.219196
$577$	−7924.36	−0.571742	−0.285871	−	0.958268i	$-0.592283\pi$
$577$	−7924.36	−0.571742	−0.285871	+	0.958268i	$0.592283\pi$
$578$	0	0
$579$	28.1693	0.00202189
$580$	3785.86	0.271034
$581$	9883.97	0.705776
$582$	−5838.38	−0.415823
$583$	964.230	0.0684980
$584$	−5839.91	−0.413797
$585$	17974.8	1.27037
$586$	−10738.7	−0.757019
$587$	1139.92	0.0801529	0.0400764	−	0.999197i	$-0.487240\pi$
$587$	1139.92	0.0801529	0.0400764	+	0.999197i	$0.487240\pi$
$588$	−3790.86	−0.265872
$589$	−27868.2	−1.94956
$590$	93.9673	0.00655690
$591$	18363.5	1.27813
$592$	−3165.81	−0.219787
$593$	2645.81	0.183222	0.0916109	−	0.995795i	$-0.470798\pi$
$593$	2645.81	0.183222	0.0916109	+	0.995795i	$0.470798\pi$
$594$	11227.7	0.775552
$595$	0	0
$596$	−5997.84	−0.412217
$597$	−4425.87	−0.303415
$598$	23554.9	1.61075
$599$	−21822.7	−1.48856	−0.744282	−	0.667865i	$-0.767208\pi$
$599$	−21822.7	−1.48856	−0.744282	+	0.667865i	$0.767208\pi$
$600$	2416.14	0.164397
$601$	−10909.3	−0.740434	−0.370217	−	0.928945i	$-0.620717\pi$
$601$	−10909.3	−0.740434	−0.370217	+	0.928945i	$0.620717\pi$
$602$	−15045.9	−1.01865
$603$	−1933.58	−0.130583
$604$	7952.63	0.535741
$605$	−13368.3	−0.898345
$606$	−21711.9	−1.45542
$607$	−15308.1	−1.02362	−0.511808	−	0.859100i	$-0.671024\pi$
$607$	−15308.1	−1.02362	−0.511808	+	0.859100i	$0.671024\pi$
$608$	−28395.4	−1.89406
$609$	−2083.76	−0.138651
$610$	8636.65	0.573259
$611$	−7660.16	−0.507196
$612$	0	0
$613$	24096.7	1.58769	0.793847	−	0.608118i	$-0.208075\pi$
$613$	24096.7	1.58769	0.793847	+	0.608118i	$0.208075\pi$
$614$	14056.1	0.923875
$615$	−23351.8	−1.53111
$616$	−2025.76	−0.132501
$617$	−7030.91	−0.458758	−0.229379	−	0.973337i	$-0.573670\pi$
$617$	−7030.91	−0.458758	−0.229379	+	0.973337i	$0.573670\pi$
$618$	14934.2	0.972073
$619$	−19270.2	−1.25127	−0.625635	−	0.780116i	$-0.715160\pi$
$619$	−19270.2	−1.25127	−0.625635	+	0.780116i	$0.715160\pi$
$620$	18846.0	1.22077
$621$	−10325.0	−0.667194
$622$	3895.85	0.251140
$623$	5154.50	0.331478
$624$	25306.0	1.62348
$625$	−18993.2	−1.21557
$626$	2993.07	0.191097
$627$	−9426.12	−0.600388
$628$	−5621.24	−0.357185
$629$	0	0
$630$	−9585.14	−0.606160
$631$	−1474.23	−0.0930079	−0.0465040	−	0.998918i	$-0.514808\pi$
$631$	−1474.23	−0.0930079	−0.0465040	+	0.998918i	$0.514808\pi$
$632$	−4086.74	−0.257218
$633$	11137.5	0.699327
$634$	−3009.06	−0.188494
$635$	6144.15	0.383974
$636$	1032.73	0.0643877
$637$	15868.8	0.987038
$638$	−3322.46	−0.206172
$639$	6101.27	0.377719
$640$	−13853.7	−0.855648
$641$	−18747.7	−1.15521	−0.577604	−	0.816317i	$-0.696012\pi$
$641$	−18747.7	−1.15521	−0.577604	+	0.816317i	$0.696012\pi$
$642$	−18029.4	−1.10836
$643$	2324.44	0.142561	0.0712807	−	0.997456i	$-0.477291\pi$
$643$	2324.44	0.142561	0.0712807	+	0.997456i	$0.477291\pi$
$644$	−5348.92	−0.327294
$645$	−16489.1	−1.00660
$646$	0	0
$647$	−11883.3	−0.722071	−0.361036	−	0.932552i	$-0.617577\pi$
$647$	−11883.3	−0.722071	−0.361036	+	0.932552i	$0.617577\pi$
$648$	−1347.29	−0.0816768
$649$	−35.1175	−0.00212401
$650$	29040.5	1.75241
$651$	−10373.0	−0.624498
$652$	−5732.62	−0.344336
$653$	873.094	0.0523228	0.0261614	−	0.999658i	$-0.491672\pi$
$653$	873.094	0.0523228	0.0261614	+	0.999658i	$0.491672\pi$
$654$	−18067.6	−1.08027
$655$	11510.3	0.686636
$656$	33565.8	1.99775
$657$	10326.7	0.613217
$658$	4084.81	0.242010
$659$	−965.182	−0.0570534	−0.0285267	−	0.999593i	$-0.509082\pi$
$659$	−965.182	−0.0570534	−0.0285267	+	0.999593i	$0.509082\pi$
$660$	6374.47	0.375948
$661$	10564.2	0.621631	0.310815	−	0.950470i	$-0.399398\pi$
$661$	10564.2	0.621631	0.310815	+	0.950470i	$0.399398\pi$
$662$	−9731.35	−0.571329
$663$	0	0
$664$	−5878.60	−0.343575
$665$	23976.0	1.39812
$666$	2113.63	0.122975
$667$	3055.34	0.177366
$668$	−7079.45	−0.410048
$669$	−10539.0	−0.609059
$670$	−7680.69	−0.442882
$671$	−3227.69	−0.185698
$672$	−10569.2	−0.606719
$673$	24755.2	1.41789	0.708947	−	0.705262i	$-0.249171\pi$
$673$	24755.2	1.41789	0.708947	+	0.705262i	$0.249171\pi$
$674$	−3984.02	−0.227684
$675$	−12729.6	−0.725868
$676$	35868.2	2.04075
$677$	−34038.8	−1.93238	−0.966188	−	0.257840i	$-0.916989\pi$
$677$	−34038.8	−1.93238	−0.966188	+	0.257840i	$0.916989\pi$
$678$	−22119.9	−1.25297
$679$	−5549.87	−0.313674
$680$	0	0
$681$	−19745.6	−1.11109
$682$	−16539.2	−0.928622
$683$	23062.1	1.29202	0.646008	−	0.763330i	$-0.276437\pi$
$683$	23062.1	1.29202	0.646008	+	0.763330i	$0.276437\pi$
$684$	10307.6	0.576203
$685$	11750.4	0.655413
$686$	−25067.3	−1.39515
$687$	−5571.31	−0.309401
$688$	23701.4	1.31338
$689$	−4323.08	−0.239037
$690$	−13765.5	−0.759484
$691$	−14331.9	−0.789018	−0.394509	−	0.918892i	$-0.629085\pi$
$691$	−14331.9	−0.789018	−0.394509	+	0.918892i	$0.629085\pi$
$692$	50.4896	0.00277360
$693$	3582.16	0.196356
$694$	−42479.5	−2.32349
$695$	−41253.3	−2.25155
$696$	1239.34	0.0674958
$697$	0	0
$698$	9134.19	0.495321
$699$	6161.73	0.333417
$700$	−6594.62	−0.356076
$701$	28211.9	1.52004	0.760020	−	0.649900i	$-0.225189\pi$
$701$	28211.9	1.52004	0.760020	+	0.649900i	$0.225189\pi$
$702$	−50338.9	−2.70644
$703$	−5286.97	−0.283644
$704$	−4498.34	−0.240820
$705$	4476.61	0.239147
$706$	−19518.8	−1.04051
$707$	−20639.0	−1.09789
$708$	−37.6124	−0.00199656
$709$	5397.14	0.285887	0.142943	−	0.989731i	$-0.454343\pi$
$709$	5397.14	0.285887	0.142943	+	0.989731i	$0.454343\pi$
$710$	24235.8	1.28106
$711$	7226.57	0.381178
$712$	−3065.70	−0.161365
$713$	15209.5	0.798878
$714$	0	0
$715$	−26683.9	−1.39569
$716$	−5395.34	−0.281611
$717$	−17865.9	−0.930562
$718$	−33998.9	−1.76717
$719$	17858.0	0.926276	0.463138	−	0.886286i	$-0.346723\pi$
$719$	17858.0	0.926276	0.463138	+	0.886286i	$0.346723\pi$
$720$	15099.2	0.781545
$721$	14196.2	0.733279
$722$	−34943.2	−1.80118
$723$	12487.9	0.642366
$724$	−14529.4	−0.745831
$725$	3766.89	0.192964
$726$	12565.5	0.642354
$727$	27634.4	1.40977	0.704885	−	0.709322i	$-0.250999\pi$
$727$	27634.4	1.40977	0.704885	+	0.709322i	$0.250999\pi$
$728$	9082.43	0.462386
$729$	17042.0	0.865821
$730$	41020.4	2.07977
$731$	0	0
$732$	−3457.00	−0.174555
$733$	16773.4	0.845209	0.422605	−	0.906314i	$-0.361116\pi$
$733$	16773.4	0.845209	0.422605	+	0.906314i	$0.361116\pi$
$734$	−4313.46	−0.216911
$735$	−9273.72	−0.465396
$736$	15497.2	0.776134
$737$	2870.43	0.143465
$738$	−22410.0	−1.11778
$739$	−26618.2	−1.32499	−0.662495	−	0.749067i	$-0.730502\pi$
$739$	−26618.2	−1.32499	−0.662495	+	0.749067i	$0.730502\pi$
$740$	3575.34	0.177611
$741$	42261.6	2.09517
$742$	2305.30	0.114057
$743$	−3231.55	−0.159561	−0.0797806	−	0.996812i	$-0.525422\pi$
$743$	−3231.55	−0.159561	−0.0797806	+	0.996812i	$0.525422\pi$
$744$	6169.44	0.304009
$745$	−14672.7	−0.721567
$746$	37140.9	1.82282
$747$	10395.1	0.509154
$748$	0	0
$749$	−17138.5	−0.836083
$750$	7783.98	0.378974
$751$	6094.29	0.296117	0.148058	−	0.988979i	$-0.452698\pi$
$751$	6094.29	0.296117	0.148058	+	0.988979i	$0.452698\pi$
$752$	−6434.67	−0.312032
$753$	8616.63	0.417009
$754$	14896.1	0.719476
$755$	19454.8	0.937791
$756$	11431.1	0.549928
$757$	−4282.74	−0.205626	−0.102813	−	0.994701i	$-0.532784\pi$
$757$	−4282.74	−0.205626	−0.102813	+	0.994701i	$0.532784\pi$
$758$	5389.27	0.258242
$759$	5144.44	0.246023
$760$	−14260.0	−0.680612
$761$	−35191.9	−1.67636	−0.838178	−	0.545397i	$-0.816379\pi$
$761$	−35191.9	−1.67636	−0.838178	+	0.545397i	$0.816379\pi$
$762$	−5775.18	−0.274557
$763$	−17174.7	−0.814899
$764$	5016.29	0.237543
$765$	0	0
$766$	30793.8	1.45251
$767$	157.448	0.00741213
$768$	19517.6	0.917032
$769$	23142.5	1.08523	0.542614	−	0.839982i	$-0.317434\pi$
$769$	23142.5	1.08523	0.542614	+	0.839982i	$0.317434\pi$
$770$	14229.3	0.665958
$771$	7433.17	0.347210
$772$	45.7285	0.00213187
$773$	−4345.19	−0.202181	−0.101090	−	0.994877i	$-0.532233\pi$
$773$	−4345.19	−0.202181	−0.101090	+	0.994877i	$0.532233\pi$
$774$	−15824.0	−0.734862
$775$	18751.6	0.869133
$776$	3300.85	0.152698
$777$	−1967.89	−0.0908592
$778$	35076.6	1.61640
$779$	56055.7	2.57818
$780$	−28579.6	−1.31194
$781$	−9057.42	−0.414981
$782$	0	0
$783$	−6529.53	−0.298016
$784$	13330.0	0.607236
$785$	−13751.4	−0.625236
$786$	−10819.1	−0.490973
$787$	−15543.2	−0.704010	−0.352005	−	0.935998i	$-0.614500\pi$
$787$	−15543.2	−0.704010	−0.352005	+	0.935998i	$0.614500\pi$
$788$	29810.3	1.34765
$789$	19653.8	0.886811
$790$	28705.9	1.29280
$791$	−21026.8	−0.945169
$792$	−2130.53	−0.0955872
$793$	14471.2	0.648030
$794$	−44683.9	−1.99719
$795$	2526.41	0.112708
$796$	−7184.72	−0.319919
$797$	15559.4	0.691519	0.345759	−	0.938323i	$-0.387621\pi$
$797$	15559.4	0.691519	0.345759	+	0.938323i	$0.387621\pi$
$798$	−22536.2	−0.999714
$799$	0	0
$800$	19106.3	0.844389
$801$	5421.07	0.239131
$802$	−39981.2	−1.76033
$803$	−15330.2	−0.673711
$804$	3074.36	0.134856
$805$	−13085.3	−0.572913
$806$	74153.0	3.24060
$807$	−11009.7	−0.480249
$808$	12275.3	0.534458
$809$	−9433.22	−0.409956	−0.204978	−	0.978767i	$-0.565712\pi$
$809$	−9433.22	−0.409956	−0.204978	+	0.978767i	$0.565712\pi$
$810$	9463.57	0.410514
$811$	12596.0	0.545381	0.272691	−	0.962102i	$-0.412086\pi$
$811$	12596.0	0.545381	0.272691	+	0.962102i	$0.412086\pi$
$812$	−3382.66	−0.146192
$813$	−4898.68	−0.211321
$814$	−3137.71	−0.135107
$815$	−14023.9	−0.602744
$816$	0	0
$817$	39581.8	1.69497
$818$	4556.15	0.194746
$819$	−16060.4	−0.685223
$820$	−37908.0	−1.61440
$821$	24332.2	1.03435	0.517175	−	0.855880i	$-0.326984\pi$
$821$	24332.2	1.03435	0.517175	+	0.855880i	$0.326984\pi$
$822$	−11044.7	−0.468648
$823$	−40516.8	−1.71607	−0.858035	−	0.513591i	$-0.828315\pi$
$823$	−40516.8	−1.71607	−0.858035	+	0.513591i	$0.828315\pi$
$824$	−8443.35	−0.356964
$825$	6342.53	0.267659
$826$	−83.9596	−0.00353672
$827$	−3544.77	−0.149049	−0.0745247	−	0.997219i	$-0.523744\pi$
$827$	−3544.77	−0.149049	−0.0745247	+	0.997219i	$0.523744\pi$
$828$	−5625.55	−0.236113
$829$	−25265.7	−1.05852	−0.529260	−	0.848460i	$-0.677530\pi$
$829$	−25265.7	−1.05852	−0.529260	+	0.848460i	$0.677530\pi$
$830$	41292.2	1.72684
$831$	17975.2	0.750366
$832$	20168.1	0.840388
$833$	0	0
$834$	38775.9	1.60995
$835$	−17318.7	−0.717771
$836$	−15301.9	−0.633045
$837$	−32504.0	−1.34230
$838$	40837.1	1.68341
$839$	−32421.0	−1.33408	−0.667042	−	0.745021i	$-0.732440\pi$
$839$	−32421.0	−1.33408	−0.667042	+	0.745021i	$0.732440\pi$
$840$	−5307.78	−0.218019
$841$	−22456.8	−0.920776
$842$	8603.51	0.352134
$843$	−2550.89	−0.104220
$844$	18079.9	0.737366
$845$	87745.7	3.57224
$846$	4296.06	0.174588
$847$	11944.6	0.484557
$848$	−3631.47	−0.147058
$849$	19661.9	0.794811
$850$	0	0
$851$	2885.44	0.116230
$852$	−9700.91	−0.390080
$853$	31041.4	1.24600	0.623000	−	0.782222i	$-0.285913\pi$
$853$	31041.4	1.24600	0.623000	+	0.782222i	$0.285913\pi$
$854$	−7716.83	−0.309209
$855$	25216.0	1.00862
$856$	10193.3	0.407009
$857$	−6852.25	−0.273125	−0.136563	−	0.990631i	$-0.543606\pi$
$857$	−6852.25	−0.273125	−0.136563	+	0.990631i	$0.543606\pi$
$858$	25081.4	0.997978
$859$	31049.1	1.23327	0.616636	−	0.787248i	$-0.288495\pi$
$859$	31049.1	1.23327	0.616636	+	0.787248i	$0.288495\pi$
$860$	−26767.4	−1.06135
$861$	20864.8	0.825864
$862$	21431.8	0.846833
$863$	31789.3	1.25391	0.626953	−	0.779057i	$-0.284302\pi$
$863$	31789.3	1.25391	0.626953	+	0.779057i	$0.284302\pi$
$864$	−33118.9	−1.30408
$865$	123.515	0.00485505
$866$	−16997.3	−0.666964
$867$	0	0
$868$	−16838.9	−0.658467
$869$	−10728.0	−0.418781
$870$	−8705.31	−0.339239
$871$	−12869.4	−0.500648
$872$	10214.9	0.396697
$873$	−5836.89	−0.226287
$874$	33044.0	1.27887
$875$	7399.32	0.285877
$876$	−16419.3	−0.633284
$877$	−34579.2	−1.33142	−0.665711	−	0.746210i	$-0.731872\pi$
$877$	−34579.2	−1.33142	−0.665711	+	0.746210i	$0.731872\pi$
$878$	40263.0	1.54762
$879$	10515.3	0.403497
$880$	−22414.9	−0.858644
$881$	−14088.5	−0.538765	−0.269383	−	0.963033i	$-0.586820\pi$
$881$	−14088.5	−0.538765	−0.269383	+	0.963033i	$0.586820\pi$
$882$	−8899.71	−0.339761
$883$	4779.77	0.182165	0.0910827	−	0.995843i	$-0.470967\pi$
$883$	4779.77	0.182165	0.0910827	+	0.995843i	$0.470967\pi$
$884$	0	0
$885$	−92.0126	−0.00349488
$886$	−49024.3	−1.85892
$887$	−14254.5	−0.539594	−0.269797	−	0.962917i	$-0.586957\pi$
$887$	−14254.5	−0.539594	−0.269797	+	0.962917i	$0.586957\pi$
$888$	1170.42	0.0442307
$889$	−5489.79	−0.207111
$890$	21533.9	0.811032
$891$	−3536.73	−0.132980
$892$	−17108.4	−0.642188
$893$	−10746.1	−0.402691
$894$	13791.6	0.515951
$895$	−13198.8	−0.492947
$896$	12378.2	0.461526
$897$	−23064.9	−0.858544
$898$	−2667.66	−0.0991325
$899$	9618.49	0.356835
$900$	−6935.67	−0.256877
$901$	0	0
$902$	33268.0	1.22805
$903$	14732.9	0.542947
$904$	12506.0	0.460113
$905$	−35543.8	−1.30554
$906$	−18286.5	−0.670560
$907$	−36585.5	−1.33936	−0.669680	−	0.742650i	$-0.733569\pi$
$907$	−36585.5	−1.33936	−0.669680	+	0.742650i	$0.733569\pi$
$908$	−32053.9	−1.17153
$909$	−21706.3	−0.792028
$910$	−63796.3	−2.32399
$911$	−19721.3	−0.717230	−0.358615	−	0.933486i	$-0.616751\pi$
$911$	−19721.3	−0.717230	−0.358615	+	0.933486i	$0.616751\pi$
$912$	35500.5	1.28897
$913$	−15431.7	−0.559382
$914$	3644.51	0.131892
$915$	−8456.99	−0.305551
$916$	−9044.16	−0.326231
$917$	−10284.5	−0.370363
$918$	0	0
$919$	−28189.0	−1.01183	−0.505913	−	0.862585i	$-0.668844\pi$
$919$	−28189.0	−1.01183	−0.505913	+	0.862585i	$0.668844\pi$
$920$	7782.60	0.278897
$921$	−13763.7	−0.492432
$922$	66118.3	2.36170
$923$	40608.5	1.44815
$924$	−5695.57	−0.202782
$925$	3557.43	0.126451
$926$	50757.1	1.80128
$927$	14930.4	0.528994
$928$	9800.45	0.346676
$929$	30866.1	1.09008	0.545040	−	0.838410i	$-0.316515\pi$
$929$	30866.1	1.09008	0.545040	+	0.838410i	$0.316515\pi$
$930$	−43335.1	−1.52797
$931$	22261.5	0.783664
$932$	10002.6	0.351552
$933$	−3814.80	−0.133860
$934$	−34027.0	−1.19208
$935$	0	0
$936$	9552.13	0.333570
$937$	13990.7	0.487785	0.243893	−	0.969802i	$-0.421576\pi$
$937$	13990.7	0.487785	0.243893	+	0.969802i	$0.421576\pi$
$938$	6862.68	0.238885
$939$	−2930.80	−0.101856
$940$	7267.08	0.252155
$941$	4495.60	0.155741	0.0778706	−	0.996963i	$-0.475188\pi$
$941$	4495.60	0.155741	0.0778706	+	0.996963i	$0.475188\pi$
$942$	12925.6	0.447070
$943$	−30593.2	−1.05647
$944$	132.259	0.00456002
$945$	27964.3	0.962624
$946$	23491.0	0.807356
$947$	−29959.5	−1.02804	−0.514019	−	0.857779i	$-0.671844\pi$
$947$	−29959.5	−1.02804	−0.514019	+	0.857779i	$0.671844\pi$
$948$	−11490.1	−0.393652
$949$	68732.1	2.35104
$950$	40739.5	1.39133
$951$	2946.47	0.100469
$952$	0	0
$953$	−44526.8	−1.51350	−0.756750	−	0.653704i	$-0.773214\pi$
$953$	−44526.8	−1.51350	−0.756750	+	0.653704i	$0.773214\pi$
$954$	2424.52	0.0822818
$955$	12271.5	0.415809
$956$	−29002.5	−0.981178
$957$	3253.35	0.109891
$958$	42864.0	1.44559
$959$	−10498.9	−0.353522
$960$	−11786.3	−0.396250
$961$	18089.9	0.607227
$962$	14067.8	0.471480
$963$	−18024.8	−0.603158
$964$	20272.2	0.677306
$965$	111.867	0.00373174
$966$	12299.4	0.409656
$967$	31696.1	1.05406	0.527031	−	0.849846i	$-0.323305\pi$
$967$	31696.1	1.05406	0.527031	+	0.849846i	$0.323305\pi$
$968$	−7104.16	−0.235885
$969$	0	0
$970$	−23185.7	−0.767471
$971$	−47645.1	−1.57467	−0.787335	−	0.616525i	$-0.788540\pi$
$971$	−47645.1	−1.57467	−0.787335	+	0.616525i	$0.788540\pi$
$972$	20009.5	0.660293
$973$	36859.7	1.21446
$974$	−15369.9	−0.505629
$975$	−28436.4	−0.934046
$976$	12156.1	0.398675
$977$	47682.5	1.56141	0.780706	−	0.624898i	$-0.214860\pi$
$977$	47682.5	1.56141	0.780706	+	0.624898i	$0.214860\pi$
$978$	13181.7	0.430987
$979$	−8047.66	−0.262721
$980$	−15054.5	−0.490711
$981$	−18063.0	−0.587875
$982$	44308.2	1.43985
$983$	−42569.9	−1.38125	−0.690626	−	0.723212i	$-0.742665\pi$
$983$	−42569.9	−1.38125	−0.690626	+	0.723212i	$0.742665\pi$
$984$	−12409.6	−0.402035
$985$	72926.1	2.35900
$986$	0	0
$987$	−3999.84	−0.128993
$988$	68605.2	2.20913
$989$	−21602.4	−0.694555
$990$	14965.2	0.480428
$991$	−36264.9	−1.16245	−0.581227	−	0.813742i	$-0.697427\pi$
$991$	−36264.9	−1.16245	−0.581227	+	0.813742i	$0.697427\pi$
$992$	48786.7	1.56147
$993$	9528.92	0.304523
$994$	−21654.7	−0.690991
$995$	−17576.2	−0.560004
$996$	−16528.1	−0.525816
$997$	−37027.1	−1.17619	−0.588094	−	0.808792i	$-0.700122\pi$
$997$	−37027.1	−1.17619	−0.588094	+	0.808792i	$0.700122\pi$
$998$	62600.0	1.98554
$999$	−6166.44	−0.195293

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.h.1.3	✓	12
17.4	even	4		289.4.b.f.288.19		24
17.13	even	4		289.4.b.f.288.20		24
17.16	even	2		289.4.a.i.1.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.4.a.h.1.3	✓	12	1.1	even	1	trivial
289.4.a.i.1.3	yes	12	17.16	even	2
289.4.b.f.288.19		24	17.4	even	4
289.4.b.f.288.20		24	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)

\(f(q)\)	\(=\)	\(q-3.73276 q^{2} +3.65511 q^{3} +5.93351 q^{4} +14.5154 q^{5} -13.6437 q^{6} -12.9694 q^{7} +7.71372 q^{8} -13.6402 q^{9} +O(q^{10})\)	\(q-3.73276 q^{2} +3.65511 q^{3} +5.93351 q^{4} +14.5154 q^{5} -13.6437 q^{6} -12.9694 q^{7} +7.71372 q^{8} -13.6402 q^{9} -54.1823 q^{10} +20.2490 q^{11} +21.6876 q^{12} -90.7856 q^{13} +48.4118 q^{14} +53.0552 q^{15} -76.2615 q^{16} +50.9155 q^{18} -127.359 q^{19} +86.1270 q^{20} -47.4047 q^{21} -75.5848 q^{22} +69.5078 q^{23} +28.1945 q^{24} +85.6954 q^{25} +338.881 q^{26} -148.544 q^{27} -76.9542 q^{28} +43.9568 q^{29} -198.042 q^{30} +218.817 q^{31} +222.956 q^{32} +74.0124 q^{33} -188.256 q^{35} -80.9340 q^{36} +41.5125 q^{37} +475.399 q^{38} -331.832 q^{39} +111.967 q^{40} -440.141 q^{41} +176.951 q^{42} -310.790 q^{43} +120.148 q^{44} -197.992 q^{45} -259.456 q^{46} +84.3763 q^{47} -278.744 q^{48} -174.794 q^{49} -319.880 q^{50} -538.677 q^{52} +47.6186 q^{53} +554.480 q^{54} +293.922 q^{55} -100.043 q^{56} -465.510 q^{57} -164.080 q^{58} -1.73428 q^{59} +314.804 q^{60} -159.400 q^{61} -816.792 q^{62} +176.905 q^{63} -222.151 q^{64} -1317.78 q^{65} -276.271 q^{66} +141.756 q^{67} +254.059 q^{69} +702.714 q^{70} -447.302 q^{71} -105.216 q^{72} -757.081 q^{73} -154.956 q^{74} +313.226 q^{75} -755.684 q^{76} -262.618 q^{77} +1238.65 q^{78} -529.801 q^{79} -1106.96 q^{80} -174.662 q^{81} +1642.94 q^{82} -762.097 q^{83} -281.276 q^{84} +1160.11 q^{86} +160.667 q^{87} +156.195 q^{88} -397.434 q^{89} +739.056 q^{90} +1177.44 q^{91} +412.425 q^{92} +799.801 q^{93} -314.957 q^{94} -1848.66 q^{95} +814.930 q^{96} +427.919 q^{97} +652.464 q^{98} -276.200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) \) 12 * q - 18 * q^3 + 48 * q^4 - 30 * q^5 + 9 * q^6 - 24 * q^7 - 51 * q^8 + 108 * q^9	\( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9} - 60 q^{10} - 162 q^{11} - 216 q^{12} - 72 q^{13} - 267 q^{14} - 138 q^{15} + 192 q^{16} + 189 q^{18} - 66 q^{19} - 129 q^{20} + 246 q^{21} - 456 q^{22} - 282 q^{23} - 72 q^{24} + 444 q^{25} + 528 q^{26} - 1092 q^{27} - 120 q^{28} - 648 q^{29} - 1890 q^{30} - 504 q^{31} - 1353 q^{32} + 966 q^{33} - 66 q^{35} - 663 q^{36} + 30 q^{37} - 60 q^{38} - 1758 q^{39} + 450 q^{40} - 318 q^{41} + 804 q^{42} + 486 q^{43} - 2448 q^{44} - 486 q^{45} - 1617 q^{46} - 888 q^{47} - 1257 q^{48} - 570 q^{49} + 435 q^{50} + 225 q^{52} + 1026 q^{53} - 933 q^{54} + 972 q^{55} - 2661 q^{56} + 156 q^{57} - 201 q^{58} - 792 q^{59} + 1458 q^{60} - 1212 q^{61} - 2817 q^{62} - 2112 q^{63} - 1857 q^{64} - 2742 q^{65} - 594 q^{66} + 624 q^{67} - 1506 q^{69} - 1650 q^{70} - 2802 q^{71} + 1455 q^{72} - 726 q^{73} - 270 q^{74} + 264 q^{75} + 675 q^{76} - 1008 q^{77} + 3090 q^{78} + 444 q^{79} + 1143 q^{80} + 2520 q^{81} + 4950 q^{82} + 672 q^{83} - 777 q^{84} + 2778 q^{86} + 726 q^{87} + 3750 q^{88} - 906 q^{89} + 7755 q^{90} - 2280 q^{91} - 87 q^{92} + 132 q^{93} + 735 q^{94} - 966 q^{95} + 5046 q^{96} + 3246 q^{97} + 1911 q^{98} + 282 q^{99}+O(q^{100}) \) 12 * q - 18 * q^3 + 48 * q^4 - 30 * q^5 + 9 * q^6 - 24 * q^7 - 51 * q^8 + 108 * q^9 - 60 * q^10 - 162 * q^11 - 216 * q^12 - 72 * q^13 - 267 * q^14 - 138 * q^15 + 192 * q^16 + 189 * q^18 - 66 * q^19 - 129 * q^20 + 246 * q^21 - 456 * q^22 - 282 * q^23 - 72 * q^24 + 444 * q^25 + 528 * q^26 - 1092 * q^27 - 120 * q^28 - 648 * q^29 - 1890 * q^30 - 504 * q^31 - 1353 * q^32 + 966 * q^33 - 66 * q^35 - 663 * q^36 + 30 * q^37 - 60 * q^38 - 1758 * q^39 + 450 * q^40 - 318 * q^41 + 804 * q^42 + 486 * q^43 - 2448 * q^44 - 486 * q^45 - 1617 * q^46 - 888 * q^47 - 1257 * q^48 - 570 * q^49 + 435 * q^50 + 225 * q^52 + 1026 * q^53 - 933 * q^54 + 972 * q^55 - 2661 * q^56 + 156 * q^57 - 201 * q^58 - 792 * q^59 + 1458 * q^60 - 1212 * q^61 - 2817 * q^62 - 2112 * q^63 - 1857 * q^64 - 2742 * q^65 - 594 * q^66 + 624 * q^67 - 1506 * q^69 - 1650 * q^70 - 2802 * q^71 + 1455 * q^72 - 726 * q^73 - 270 * q^74 + 264 * q^75 + 675 * q^76 - 1008 * q^77 + 3090 * q^78 + 444 * q^79 + 1143 * q^80 + 2520 * q^81 + 4950 * q^82 + 672 * q^83 - 777 * q^84 + 2778 * q^86 + 726 * q^87 + 3750 * q^88 - 906 * q^89 + 7755 * q^90 - 2280 * q^91 - 87 * q^92 + 132 * q^93 + 735 * q^94 - 966 * q^95 + 5046 * q^96 + 3246 * q^97 + 1911 * q^98 + 282 * q^99

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