LMFDB - Embedded newform 289.4.a.h.1.2

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			1.2
Root			$4.98104$ 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)

$f(q)$	$=$	$q-4.98104 q^{2} -6.26206 q^{3} +16.8108 q^{4} -15.7477 q^{5} +31.1916 q^{6} -0.789949 q^{7} -43.8870 q^{8} +12.2134 q^{9} +O(q^{10})$	\(q-4.98104 q^{2} -6.26206 q^{3} +16.8108 q^{4} -15.7477 q^{5} +31.1916 q^{6} -0.789949 q^{7} -43.8870 q^{8} +12.2134 q^{9} +78.4401 q^{10} -45.3316 q^{11} -105.270 q^{12} +46.7491 q^{13} +3.93477 q^{14} +98.6131 q^{15} +84.1166 q^{16} -60.8354 q^{18} +100.512 q^{19} -264.732 q^{20} +4.94671 q^{21} +225.798 q^{22} +84.1579 q^{23} +274.823 q^{24} +122.991 q^{25} -232.859 q^{26} +92.5947 q^{27} -13.2797 q^{28} +101.693 q^{29} -491.196 q^{30} -7.36111 q^{31} -67.8926 q^{32} +283.869 q^{33} +12.4399 q^{35} +205.317 q^{36} +251.101 q^{37} -500.657 q^{38} -292.745 q^{39} +691.120 q^{40} -260.918 q^{41} -24.6398 q^{42} -401.442 q^{43} -762.060 q^{44} -192.333 q^{45} -419.194 q^{46} +304.102 q^{47} -526.743 q^{48} -342.376 q^{49} -612.622 q^{50} +785.889 q^{52} +398.236 q^{53} -461.218 q^{54} +713.869 q^{55} +34.6685 q^{56} -629.414 q^{57} -506.536 q^{58} -577.767 q^{59} +1657.77 q^{60} -126.259 q^{61} +36.6660 q^{62} -9.64795 q^{63} -334.757 q^{64} -736.191 q^{65} -1413.96 q^{66} -150.923 q^{67} -527.002 q^{69} -61.9637 q^{70} -434.653 q^{71} -536.008 q^{72} -493.829 q^{73} -1250.74 q^{74} -770.175 q^{75} +1689.69 q^{76} +35.8096 q^{77} +1458.18 q^{78} +72.2153 q^{79} -1324.64 q^{80} -909.595 q^{81} +1299.65 q^{82} +711.089 q^{83} +83.1581 q^{84} +1999.60 q^{86} -636.806 q^{87} +1989.47 q^{88} +1354.30 q^{89} +958.018 q^{90} -36.9294 q^{91} +1414.76 q^{92} +46.0957 q^{93} -1514.75 q^{94} -1582.84 q^{95} +425.147 q^{96} +1402.59 q^{97} +1705.39 q^{98} -553.651 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.98104	−1.76107	−0.880533	−	0.473986i	$-0.842815\pi$
$2$	−4.98104	−1.76107	−0.880533	+	0.473986i	$0.842815\pi$
$3$	−6.26206	−1.20513	−0.602567	−	0.798068i	$-0.705855\pi$
$3$	−6.26206	−1.20513	−0.602567	+	0.798068i	$0.705855\pi$
$4$	16.8108	2.10135
$5$	−15.7477	−1.40852	−0.704259	−	0.709943i	$-0.748721\pi$
$5$	−15.7477	−1.40852	−0.704259	+	0.709943i	$0.748721\pi$
$6$	31.1916	2.12232
$7$	−0.789949	−0.0426533	−0.0213266	−	0.999773i	$-0.506789\pi$
$7$	−0.789949	−0.0426533	−0.0213266	+	0.999773i	$0.506789\pi$
$8$	−43.8870	−1.93955
$9$	12.2134	0.452347
$10$	78.4401	2.48049
$11$	−45.3316	−1.24254	−0.621272	−	0.783595i	$-0.713384\pi$
$11$	−45.3316	−1.24254	−0.621272	+	0.783595i	$0.713384\pi$
$12$	−105.270	−2.53241
$13$	46.7491	0.997374	0.498687	−	0.866782i	$-0.333816\pi$
$13$	46.7491	0.997374	0.498687	+	0.866782i	$0.333816\pi$
$14$	3.93477	0.0751152
$15$	98.6131	1.69745
$16$	84.1166	1.31432
$17$	0	0
$17$	0	0
$18$	−60.8354	−0.796613
$19$	100.512	1.21364	0.606819	−	0.794840i	$-0.292445\pi$
$19$	100.512	1.21364	0.606819	+	0.794840i	$0.292445\pi$
$20$	−264.732	−2.95979
$21$	4.94671	0.0514029
$22$	225.798	2.18820
$23$	84.1579	0.762962	0.381481	−	0.924377i	$-0.375414\pi$
$23$	84.1579	0.762962	0.381481	+	0.924377i	$0.375414\pi$
$24$	274.823	2.33742
$25$	122.991	0.983925
$26$	−232.859	−1.75644
$27$	92.5947	0.659995
$28$	−13.2797	−0.0896294
$29$	101.693	0.651168	0.325584	−	0.945513i	$-0.394439\pi$
$29$	101.693	0.651168	0.325584	+	0.945513i	$0.394439\pi$
$30$	−491.196	−2.98933
$31$	−7.36111	−0.0426482	−0.0213241	−	0.999773i	$-0.506788\pi$
$31$	−7.36111	−0.0426482	−0.0213241	+	0.999773i	$0.506788\pi$
$32$	−67.8926	−0.375057
$33$	283.869	1.49743
$34$	0	0
$35$	12.4399	0.0600779
$36$	205.317	0.950540
$37$	251.101	1.11570	0.557848	−	0.829943i	$-0.311627\pi$
$37$	251.101	1.11570	0.557848	+	0.829943i	$0.311627\pi$
$38$	−500.657	−2.13730
$39$	−292.745	−1.20197
$40$	691.120	2.73189
$41$	−260.918	−0.993868	−0.496934	−	0.867788i	$-0.665541\pi$
$41$	−260.918	−0.993868	−0.496934	+	0.867788i	$0.665541\pi$
$42$	−24.6398	−0.0905238
$43$	−401.442	−1.42370	−0.711852	−	0.702329i	$-0.752144\pi$
$43$	−401.442	−1.42370	−0.711852	+	0.702329i	$0.752144\pi$
$44$	−762.060	−2.61102
$45$	−192.333	−0.637140
$46$	−419.194	−1.34363
$47$	304.102	0.943785	0.471892	−	0.881656i	$-0.343571\pi$
$47$	304.102	0.943785	0.471892	+	0.881656i	$0.343571\pi$
$48$	−526.743	−1.58393
$49$	−342.376	−0.998181
$50$	−612.622	−1.73276
$51$	0	0
$52$	785.889	2.09583
$53$	398.236	1.03211	0.516055	−	0.856555i	$-0.327400\pi$
$53$	398.236	1.03211	0.516055	+	0.856555i	$0.327400\pi$
$54$	−461.218	−1.16229
$55$	713.869	1.75015
$56$	34.6685	0.0827281
$57$	−629.414	−1.46260
$58$	−506.536	−1.14675
$59$	−577.767	−1.27490	−0.637448	−	0.770493i	$-0.720010\pi$
$59$	−577.767	−1.27490	−0.637448	+	0.770493i	$0.720010\pi$
$60$	1657.77	3.56694
$61$	−126.259	−0.265013	−0.132507	−	0.991182i	$-0.542303\pi$
$61$	−126.259	−0.265013	−0.132507	+	0.991182i	$0.542303\pi$
$62$	36.6660	0.0751063
$63$	−9.64795	−0.0192941
$64$	−334.757	−0.653822
$65$	−736.191	−1.40482
$66$	−1413.96	−2.63707
$67$	−150.923	−0.275198	−0.137599	−	0.990488i	$-0.543938\pi$
$67$	−150.923	−0.275198	−0.137599	+	0.990488i	$0.543938\pi$
$68$	0	0
$69$	−527.002	−0.919471
$70$	−61.9637	−0.105801
$71$	−434.653	−0.726533	−0.363267	−	0.931685i	$-0.618339\pi$
$71$	−434.653	−0.726533	−0.363267	+	0.931685i	$0.618339\pi$
$72$	−536.008	−0.877350
$73$	−493.829	−0.791757	−0.395879	−	0.918303i	$-0.629560\pi$
$73$	−493.829	−0.791757	−0.395879	+	0.918303i	$0.629560\pi$
$74$	−1250.74	−1.96481
$75$	−770.175	−1.18576
$76$	1689.69	2.55028
$77$	35.8096	0.0529985
$78$	1458.18	2.11674
$79$	72.2153	0.102846	0.0514232	−	0.998677i	$-0.483624\pi$
$79$	72.2153	0.102846	0.0514232	+	0.998677i	$0.483624\pi$
$80$	−1324.64	−1.85125
$81$	−909.595	−1.24773
$82$	1299.65	1.75027
$83$	711.089	0.940388	0.470194	−	0.882563i	$-0.344184\pi$
$83$	711.089	0.940388	0.470194	+	0.882563i	$0.344184\pi$
$84$	83.1581	0.108015
$85$	0	0
$86$	1999.60	2.50724
$87$	−636.806	−0.784745
$88$	1989.47	2.40997
$89$	1354.30	1.61298	0.806489	−	0.591250i	$-0.201365\pi$
$89$	1354.30	1.61298	0.806489	+	0.591250i	$0.201365\pi$
$90$	958.018	1.12204
$91$	−36.9294	−0.0425412
$92$	1414.76	1.60325
$93$	46.0957	0.0513968
$94$	−1514.75	−1.66207
$95$	−1582.84	−1.70943
$96$	425.147	0.451994
$97$	1402.59	1.46816	0.734079	−	0.679064i	$-0.237614\pi$
$97$	1402.59	1.46816	0.734079	+	0.679064i	$0.237614\pi$
$98$	1705.39	1.75786
$99$	−553.651	−0.562061
$100$	2067.57	2.06757
$101$	151.252	0.149012	0.0745058	−	0.997221i	$-0.476262\pi$
$101$	151.252	0.149012	0.0745058	+	0.997221i	$0.476262\pi$
$102$	0	0
$103$	−687.247	−0.657441	−0.328720	−	0.944427i	$-0.606617\pi$
$103$	−687.247	−0.657441	−0.328720	+	0.944427i	$0.606617\pi$
$104$	−2051.68	−1.93445
$105$	−77.8994	−0.0724019
$106$	−1983.63	−1.81761
$107$	456.959	0.412859	0.206430	−	0.978461i	$-0.433816\pi$
$107$	456.959	0.412859	0.206430	+	0.978461i	$0.433816\pi$
$108$	1556.59	1.38688
$109$	1281.43	1.12605	0.563023	−	0.826441i	$-0.309638\pi$
$109$	1281.43	1.12605	0.563023	+	0.826441i	$0.309638\pi$
$110$	−3555.81	−3.08212
$111$	−1572.41	−1.34456
$112$	−66.4479	−0.0560601
$113$	−1887.62	−1.57143	−0.785717	−	0.618586i	$-0.787706\pi$
$113$	−1887.62	−1.57143	−0.785717	+	0.618586i	$0.787706\pi$
$114$	3135.14	2.57573
$115$	−1325.29	−1.07465
$116$	1709.54	1.36833
$117$	570.964	0.451159
$118$	2877.88	2.24518
$119$	0	0
$120$	−4327.83	−3.29229
$121$	723.950	0.543914
$122$	628.902	0.466706
$123$	1633.89	1.19774
$124$	−123.746	−0.0896188
$125$	31.6426	0.0226416
$126$	48.0569	0.0339781
$127$	1920.56	1.34190	0.670952	−	0.741501i	$-0.265886\pi$
$127$	1920.56	1.34190	0.670952	+	0.741501i	$0.265886\pi$
$128$	2210.58	1.52648
$129$	2513.85	1.71575
$130$	3667.00	2.47398
$131$	−1656.13	−1.10456	−0.552279	−	0.833660i	$-0.686242\pi$
$131$	−1656.13	−1.10456	−0.552279	+	0.833660i	$0.686242\pi$
$132$	4772.06	3.14663
$133$	−79.3997	−0.0517656
$134$	751.757	0.484641
$135$	−1458.16	−0.929615
$136$	0	0
$137$	−2725.42	−1.69962	−0.849811	−	0.527088i	$-0.823284\pi$
$137$	−2725.42	−1.69962	−0.849811	+	0.527088i	$0.823284\pi$
$138$	2625.02	1.61925
$139$	−1231.94	−0.751739	−0.375870	−	0.926673i	$-0.622656\pi$
$139$	−1231.94	−0.751739	−0.375870	+	0.926673i	$0.622656\pi$
$140$	209.125	0.126245
$141$	−1904.31	−1.13739
$142$	2165.03	1.27947
$143$	−2119.21	−1.23928
$144$	1027.35	0.594530
$145$	−1601.43	−0.917183
$146$	2459.78	1.39434
$147$	2143.98	1.20294
$148$	4221.21	2.34447
$149$	2317.73	1.27434	0.637169	−	0.770724i	$-0.280106\pi$
$149$	2317.73	1.27434	0.637169	+	0.770724i	$0.280106\pi$
$150$	3836.27	2.08820
$151$	1155.92	0.622964	0.311482	−	0.950252i	$-0.399175\pi$
$151$	1155.92	0.622964	0.311482	+	0.950252i	$0.399175\pi$
$152$	−4411.19	−2.35391
$153$	0	0
$154$	−178.369	−0.0933339
$155$	115.921	0.0600708
$156$	−4921.28	−2.52576
$157$	−3226.75	−1.64027	−0.820137	−	0.572167i	$-0.806103\pi$
$157$	−3226.75	−1.64027	−0.820137	+	0.572167i	$0.806103\pi$
$158$	−359.708	−0.181119
$159$	−2493.77	−1.24383
$160$	1069.15	0.528275
$161$	−66.4805	−0.0325428
$162$	4530.73	2.19733
$163$	−982.257	−0.472002	−0.236001	−	0.971753i	$-0.575837\pi$
$163$	−982.257	−0.472002	−0.236001	+	0.971753i	$0.575837\pi$
$164$	−4386.25	−2.08847
$165$	−4470.29	−2.10916
$166$	−3541.97	−1.65608
$167$	−36.6005	−0.0169595	−0.00847974	−	0.999964i	$-0.502699\pi$
$167$	−36.6005	−0.0169595	−0.00847974	+	0.999964i	$0.502699\pi$
$168$	−217.096	−0.0996984
$169$	−11.5254	−0.00524596
$170$	0	0
$171$	1227.60	0.548986
$172$	−6748.56	−2.99170
$173$	2826.57	1.24220	0.621099	−	0.783732i	$-0.286686\pi$
$173$	2826.57	1.24220	0.621099	+	0.783732i	$0.286686\pi$
$174$	3171.96	1.38199
$175$	−97.1564	−0.0419676
$176$	−3813.14	−1.63310
$177$	3618.01	1.53642
$178$	−6745.80	−2.84056
$179$	−1168.77	−0.488032	−0.244016	−	0.969771i	$-0.578465\pi$
$179$	−1168.77	−0.488032	−0.244016	+	0.969771i	$0.578465\pi$
$180$	−3233.27	−1.33885
$181$	−2871.88	−1.17936	−0.589682	−	0.807635i	$-0.700747\pi$
$181$	−2871.88	−1.17936	−0.589682	+	0.807635i	$0.700747\pi$
$182$	183.947	0.0749179
$183$	790.642	0.319377
$184$	−3693.44	−1.47980
$185$	−3954.26	−1.57148
$186$	−229.605	−0.0905131
$187$	0	0
$188$	5112.20	1.98322
$189$	−73.1451	−0.0281509
$190$	7884.20	3.01042
$191$	−1626.96	−0.616350	−0.308175	−	0.951330i	$-0.599718\pi$
$191$	−1626.96	−0.616350	−0.308175	+	0.951330i	$0.599718\pi$
$192$	2096.27	0.787943
$193$	−796.367	−0.297014	−0.148507	−	0.988911i	$-0.547447\pi$
$193$	−796.367	−0.297014	−0.148507	+	0.988911i	$0.547447\pi$
$194$	−6986.36	−2.58552
$195$	4610.07	1.69300
$196$	−5755.61	−2.09753
$197$	−977.275	−0.353441	−0.176721	−	0.984261i	$-0.556549\pi$
$197$	−977.275	−0.353441	−0.176721	+	0.984261i	$0.556549\pi$
$198$	2757.76	0.989826
$199$	711.695	0.253521	0.126761	−	0.991933i	$-0.459542\pi$
$199$	711.695	0.253521	0.126761	+	0.991933i	$0.459542\pi$
$200$	−5397.69	−1.90837
$201$	945.092	0.331650
$202$	−753.395	−0.262419
$203$	−80.3322	−0.0277745
$204$	0	0
$205$	4108.87	1.39988
$206$	3423.21	1.15780
$207$	1027.85	0.345124
$208$	3932.37	1.31087
$209$	−4556.38	−1.50800
$210$	388.020	0.127504
$211$	3690.17	1.20399	0.601994	−	0.798501i	$-0.294373\pi$
$211$	3690.17	1.20399	0.601994	+	0.798501i	$0.294373\pi$
$212$	6694.66	2.16883
$213$	2721.82	0.875570
$214$	−2276.13	−0.727072
$215$	6321.79	2.00532
$216$	−4063.70	−1.28009
$217$	5.81490	0.00181909
$218$	−6382.87	−1.98304
$219$	3092.38	0.954173
$220$	12000.7	3.67767
$221$	0	0
$222$	7832.23	2.36786
$223$	−1726.16	−0.518351	−0.259176	−	0.965830i	$-0.583451\pi$
$223$	−1726.16	−0.518351	−0.259176	+	0.965830i	$0.583451\pi$
$224$	53.6317	0.0159974
$225$	1502.13	0.445076
$226$	9402.31	2.76740
$227$	2144.75	0.627100	0.313550	−	0.949572i	$-0.398482\pi$
$227$	2144.75	0.627100	0.313550	+	0.949572i	$0.398482\pi$
$228$	−10581.0	−3.07343
$229$	5082.23	1.46656	0.733282	−	0.679924i	$-0.237987\pi$
$229$	5082.23	1.46656	0.733282	+	0.679924i	$0.237987\pi$
$230$	6601.35	1.89252
$231$	−224.242	−0.0638703
$232$	−4462.99	−1.26297
$233$	3271.12	0.919735	0.459868	−	0.887987i	$-0.347897\pi$
$233$	3271.12	0.919735	0.459868	+	0.887987i	$0.347897\pi$
$234$	−2844.00	−0.794521
$235$	−4788.92	−1.32934
$236$	−9712.73	−2.67900
$237$	−452.217	−0.123944
$238$	0	0
$239$	−4905.70	−1.32771	−0.663857	−	0.747860i	$-0.731082\pi$
$239$	−4905.70	−1.32771	−0.663857	+	0.747860i	$0.731082\pi$
$240$	8295.00	2.23100
$241$	−494.108	−0.132068	−0.0660338	−	0.997817i	$-0.521035\pi$
$241$	−494.108	−0.132068	−0.0660338	+	0.997817i	$0.521035\pi$
$242$	−3606.03	−0.957869
$243$	3195.88	0.843686
$244$	−2122.52	−0.556886
$245$	5391.64	1.40596
$246$	−8138.46	−2.10931
$247$	4698.86	1.21045
$248$	323.057	0.0827183
$249$	−4452.88	−1.13329
$250$	−157.613	−0.0398734
$251$	−691.360	−0.173858	−0.0869288	−	0.996215i	$-0.527705\pi$
$251$	−691.360	−0.173858	−0.0869288	+	0.996215i	$0.527705\pi$
$252$	−162.190	−0.0405436
$253$	−3815.01	−0.948014
$254$	−9566.37	−2.36318
$255$	0	0
$256$	−8332.94	−2.03441
$257$	−2900.44	−0.703986	−0.351993	−	0.936003i	$-0.614496\pi$
$257$	−2900.44	−0.703986	−0.351993	+	0.936003i	$0.614496\pi$
$258$	−12521.6	−3.02156
$259$	−198.357	−0.0475880
$260$	−12376.0	−2.95202
$261$	1242.01	0.294554
$262$	8249.27	1.94520
$263$	−5458.82	−1.27987	−0.639934	−	0.768430i	$-0.721038\pi$
$263$	−5458.82	−1.27987	−0.639934	+	0.768430i	$0.721038\pi$
$264$	−12458.1	−2.90434
$265$	−6271.30	−1.45375
$266$	395.493	0.0911626
$267$	−8480.67	−1.94385
$268$	−2537.14	−0.578286
$269$	1028.77	0.233179	0.116590	−	0.993180i	$-0.462804\pi$
$269$	1028.77	0.233179	0.116590	+	0.993180i	$0.462804\pi$
$270$	7263.14	1.63711
$271$	−4117.13	−0.922869	−0.461435	−	0.887174i	$-0.652665\pi$
$271$	−4117.13	−0.922869	−0.461435	+	0.887174i	$0.652665\pi$
$272$	0	0
$273$	231.254	0.0512679
$274$	13575.4	2.99314
$275$	−5575.36	−1.22257
$276$	−8859.32	−1.93213
$277$	5787.84	1.25544	0.627721	−	0.778438i	$-0.283988\pi$
$277$	5787.84	1.25544	0.627721	+	0.778438i	$0.283988\pi$
$278$	6136.35	1.32386
$279$	−89.9040	−0.0192918
$280$	−545.950	−0.116524
$281$	2012.48	0.427240	0.213620	−	0.976917i	$-0.431475\pi$
$281$	2012.48	0.427240	0.213620	+	0.976917i	$0.431475\pi$
$282$	9485.43	2.00301
$283$	558.874	0.117391	0.0586954	−	0.998276i	$-0.481306\pi$
$283$	558.874	0.117391	0.0586954	+	0.998276i	$0.481306\pi$
$284$	−7306.87	−1.52670
$285$	9911.84	2.06009
$286$	10555.9	2.18245
$287$	206.112	0.0423917
$288$	−829.198	−0.169656
$289$	0	0
$290$	7976.79	1.61522
$291$	−8783.10	−1.76933
$292$	−8301.65	−1.66376
$293$	2860.10	0.570268	0.285134	−	0.958488i	$-0.407962\pi$
$293$	2860.10	0.570268	0.285134	+	0.958488i	$0.407962\pi$
$294$	−10679.3	−2.11846
$295$	9098.52	1.79572
$296$	−11020.1	−2.16395
$297$	−4197.46	−0.820072
$298$	−11544.7	−2.24419
$299$	3934.30	0.760958
$300$	−12947.3	−2.49170
$301$	317.119	0.0607257
$302$	−5757.70	−1.09708
$303$	−947.151	−0.179579
$304$	8454.76	1.59511
$305$	1988.29	0.373276
$306$	0	0
$307$	−4297.16	−0.798867	−0.399433	−	0.916762i	$-0.630793\pi$
$307$	−4297.16	−0.798867	−0.399433	+	0.916762i	$0.630793\pi$
$308$	601.989	0.111368
$309$	4303.58	0.792304
$310$	−577.406	−0.105789
$311$	−2989.87	−0.545145	−0.272572	−	0.962135i	$-0.587874\pi$
$311$	−2989.87	−0.545145	−0.272572	+	0.962135i	$0.587874\pi$
$312$	12847.7	2.33128
$313$	3932.78	0.710204	0.355102	−	0.934828i	$-0.384446\pi$
$313$	3932.78	0.710204	0.355102	+	0.934828i	$0.384446\pi$
$314$	16072.6	2.88863
$315$	151.933	0.0271761
$316$	1214.00	0.216116
$317$	10623.2	1.88221	0.941103	−	0.338120i	$-0.109791\pi$
$317$	10623.2	1.88221	0.941103	+	0.338120i	$0.109791\pi$
$318$	12421.6	2.19047
$319$	−4609.89	−0.809105
$320$	5271.65	0.920920
$321$	−2861.51	−0.497550
$322$	331.142	0.0573100
$323$	0	0
$324$	−15291.0	−2.62192
$325$	5749.70	0.981341
$326$	4892.67	0.831226
$327$	−8024.41	−1.35704
$328$	11450.9	1.92766
$329$	−240.225	−0.0402555
$330$	22266.7	3.71437
$331$	−7246.73	−1.20337	−0.601687	−	0.798732i	$-0.705504\pi$
$331$	−7246.73	−1.20337	−0.601687	+	0.798732i	$0.705504\pi$
$332$	11954.0	1.97608
$333$	3066.79	0.504682
$334$	182.309	0.0298667
$335$	2376.70	0.387621
$336$	416.100	0.0675599
$337$	−4128.94	−0.667411	−0.333706	−	0.942677i	$-0.608299\pi$
$337$	−4128.94	−0.667411	−0.333706	+	0.942677i	$0.608299\pi$
$338$	57.4084	0.00923847
$339$	11820.4	1.89379
$340$	0	0
$341$	333.691	0.0529923
$342$	−6114.71	−0.966800
$343$	541.412	0.0852289
$344$	17618.1	2.76135
$345$	8299.07	1.29509
$346$	−14079.3	−2.18759
$347$	−6293.09	−0.973575	−0.486788	−	0.873520i	$-0.661831\pi$
$347$	−6293.09	−0.973575	−0.486788	+	0.873520i	$0.661831\pi$
$348$	−10705.2	−1.64902
$349$	−6188.65	−0.949201	−0.474600	−	0.880201i	$-0.657407\pi$
$349$	−6188.65	−0.949201	−0.474600	+	0.880201i	$0.657407\pi$
$350$	483.940	0.0739077
$351$	4328.72	0.658261
$352$	3077.68	0.466025
$353$	−1116.16	−0.168292	−0.0841460	−	0.996453i	$-0.526816\pi$
$353$	−1116.16	−0.168292	−0.0841460	+	0.996453i	$0.526816\pi$
$354$	−18021.5	−2.70574
$355$	6844.80	1.02334
$356$	22766.8	3.38943
$357$	0	0
$358$	5821.68	0.859457
$359$	78.6313	0.0115599	0.00577995	−	0.999983i	$-0.498160\pi$
$359$	78.6313	0.0115599	0.00577995	+	0.999983i	$0.498160\pi$
$360$	8440.91	1.23576
$361$	3243.74	0.472917
$362$	14304.9	2.07694
$363$	−4533.42	−0.655490
$364$	−620.813	−0.0893940
$365$	7776.68	1.11520
$366$	−3938.22	−0.562443
$367$	−6974.49	−0.992004	−0.496002	−	0.868321i	$-0.665199\pi$
$367$	−6974.49	−0.992004	−0.496002	+	0.868321i	$0.665199\pi$
$368$	7079.07	1.00278
$369$	−3186.69	−0.449574
$370$	19696.4	2.76747
$371$	−314.586	−0.0440229
$372$	774.906	0.108003
$373$	32.5559	0.00451925	0.00225963	−	0.999997i	$-0.499281\pi$
$373$	32.5559	0.00451925	0.00225963	+	0.999997i	$0.499281\pi$
$374$	0	0
$375$	−198.148	−0.0272862
$376$	−13346.1	−1.83052
$377$	4754.04	0.649458
$378$	364.339	0.0495756
$379$	−5407.85	−0.732935	−0.366468	−	0.930431i	$-0.619433\pi$
$379$	−5407.85	−0.732935	−0.366468	+	0.930431i	$0.619433\pi$
$380$	−26608.8	−3.59212
$381$	−12026.6	−1.61717
$382$	8103.97	1.08543
$383$	2705.02	0.360889	0.180444	−	0.983585i	$-0.442246\pi$
$383$	2705.02	0.360889	0.180444	+	0.983585i	$0.442246\pi$
$384$	−13842.8	−1.83961
$385$	−563.920	−0.0746494
$386$	3966.74	0.523061
$387$	−4902.96	−0.644009
$388$	23578.6	3.08511
$389$	−392.912	−0.0512119	−0.0256059	−	0.999672i	$-0.508152\pi$
$389$	−392.912	−0.0512119	−0.0256059	+	0.999672i	$0.508152\pi$
$390$	−22963.0	−2.98147
$391$	0	0
$392$	15025.8	1.93602
$393$	10370.8	1.33114
$394$	4867.85	0.622433
$395$	−1137.23	−0.144861
$396$	−9307.32	−1.18109
$397$	11750.1	1.48544	0.742721	−	0.669601i	$-0.233535\pi$
$397$	11750.1	1.48544	0.742721	+	0.669601i	$0.233535\pi$
$398$	−3544.98	−0.446467
$399$	497.206	0.0623845
$400$	10345.6	1.29319
$401$	2918.07	0.363395	0.181697	−	0.983354i	$-0.441841\pi$
$401$	2918.07	0.363395	0.181697	+	0.983354i	$0.441841\pi$
$402$	−4707.54	−0.584057
$403$	−344.125	−0.0425362
$404$	2542.67	0.313125
$405$	14324.0	1.75745
$406$	400.138	0.0489126
$407$	−11382.8	−1.38630
$408$	0	0
$409$	5650.88	0.683174	0.341587	−	0.939850i	$-0.389036\pi$
$409$	5650.88	0.683174	0.341587	+	0.939850i	$0.389036\pi$
$410$	−20466.5	−2.46528
$411$	17066.7	2.04827
$412$	−11553.2	−1.38151
$413$	456.407	0.0543785
$414$	−5119.78	−0.607786
$415$	−11198.0	−1.32455
$416$	−3173.92	−0.374072
$417$	7714.48	0.905947
$418$	22695.5	2.65568
$419$	−14806.3	−1.72633	−0.863166	−	0.504920i	$-0.831522\pi$
$419$	−14806.3	−1.72633	−0.863166	+	0.504920i	$0.831522\pi$
$420$	−1309.55	−0.152142
$421$	3314.27	0.383676	0.191838	−	0.981427i	$-0.438555\pi$
$421$	3314.27	0.383676	0.191838	+	0.981427i	$0.438555\pi$
$422$	−18380.9	−2.12030
$423$	3714.12	0.426918
$424$	−17477.4	−2.00183
$425$	0	0
$426$	−13557.5	−1.54193
$427$	99.7383	0.0113037
$428$	7681.85	0.867561
$429$	13270.6	1.49350
$430$	−31489.1	−3.53149
$431$	−12204.2	−1.36394	−0.681969	−	0.731381i	$-0.738876\pi$
$431$	−12204.2	−1.36394	−0.681969	+	0.731381i	$0.738876\pi$
$432$	7788.75	0.867446
$433$	423.908	0.0470479	0.0235239	−	0.999723i	$-0.492511\pi$
$433$	423.908	0.0470479	0.0235239	+	0.999723i	$0.492511\pi$
$434$	−28.9643	−0.00320353
$435$	10028.2	1.10533
$436$	21541.9	2.36622
$437$	8458.91	0.925960
$438$	−15403.3	−1.68036
$439$	−14528.7	−1.57953	−0.789767	−	0.613407i	$-0.789799\pi$
$439$	−14528.7	−1.57953	−0.789767	+	0.613407i	$0.789799\pi$
$440$	−31329.5	−3.39449
$441$	−4181.57	−0.451524
$442$	0	0
$443$	15763.6	1.69063	0.845317	−	0.534265i	$-0.179411\pi$
$443$	15763.6	1.69063	0.845317	+	0.534265i	$0.179411\pi$
$444$	−26433.4	−2.82539
$445$	−21327.1	−2.27191
$446$	8598.09	0.912850
$447$	−14513.8	−1.53575
$448$	264.441	0.0278876
$449$	5204.32	0.547009	0.273504	−	0.961871i	$-0.411817\pi$
$449$	5204.32	0.547009	0.273504	+	0.961871i	$0.411817\pi$
$450$	−7482.18	−0.783808
$451$	11827.8	1.23492
$452$	−31732.4	−3.30213
$453$	−7238.45	−0.750755
$454$	−10683.1	−1.10436
$455$	581.554	0.0599201
$456$	27623.1	2.83678
$457$	−4156.78	−0.425484	−0.212742	−	0.977108i	$-0.568239\pi$
$457$	−4156.78	−0.425484	−0.212742	+	0.977108i	$0.568239\pi$
$458$	−25314.8	−2.58272
$459$	0	0
$460$	−22279.3	−2.25821
$461$	6715.13	0.678427	0.339214	−	0.940709i	$-0.389839\pi$
$461$	6715.13	0.678427	0.339214	+	0.940709i	$0.389839\pi$
$462$	1116.96	0.112480
$463$	−14587.2	−1.46420	−0.732098	−	0.681199i	$-0.761459\pi$
$463$	−14587.2	−1.46420	−0.732098	+	0.681199i	$0.761459\pi$
$464$	8554.05	0.855845
$465$	−725.902	−0.0723933
$466$	−16293.6	−1.61971
$467$	−7011.17	−0.694729	−0.347364	−	0.937730i	$-0.612923\pi$
$467$	−7011.17	−0.694729	−0.347364	+	0.937730i	$0.612923\pi$
$468$	9598.36	0.948043
$469$	119.222	0.0117381
$470$	23853.8	2.34105
$471$	20206.1	1.97675
$472$	25356.5	2.47272
$473$	18198.0	1.76902
$474$	2252.51	0.218273
$475$	12362.1	1.19413
$476$	0	0
$477$	4863.80	0.466872
$478$	24435.5	2.33819
$479$	−10914.1	−1.04108	−0.520540	−	0.853837i	$-0.674269\pi$
$479$	−10914.1	−1.04108	−0.520540	+	0.853837i	$0.674269\pi$
$480$	−6695.10	−0.636642
$481$	11738.7	1.11276
$482$	2461.18	0.232580
$483$	416.305	0.0392185
$484$	12170.2	1.14295
$485$	−22087.6	−2.06793
$486$	−15918.8	−1.48579
$487$	−8144.98	−0.757873	−0.378937	−	0.925423i	$-0.623710\pi$
$487$	−8144.98	−0.757873	−0.378937	+	0.925423i	$0.623710\pi$
$488$	5541.13	0.514007
$489$	6150.95	0.568826
$490$	−26856.0	−2.47598
$491$	3767.66	0.346297	0.173149	−	0.984896i	$-0.444606\pi$
$491$	3767.66	0.346297	0.173149	+	0.984896i	$0.444606\pi$
$492$	27466.9	2.51688
$493$	0	0
$494$	−23405.2	−2.13168
$495$	8718.75	0.791674
$496$	−619.192	−0.0560535
$497$	343.354	0.0309890
$498$	22180.0	1.99580
$499$	−12922.1	−1.15926	−0.579631	−	0.814879i	$-0.696803\pi$
$499$	−12922.1	−1.15926	−0.579631	+	0.814879i	$0.696803\pi$
$500$	531.938	0.0475780
$501$	229.194	0.0204384
$502$	3443.70	0.306175
$503$	−2856.34	−0.253196	−0.126598	−	0.991954i	$-0.540406\pi$
$503$	−2856.34	−0.253196	−0.126598	+	0.991954i	$0.540406\pi$
$504$	423.419	0.0374218
$505$	−2381.88	−0.209886
$506$	19002.7	1.66951
$507$	72.1726	0.00632208
$508$	32286.1	2.81981
$509$	−1841.34	−0.160346	−0.0801729	−	0.996781i	$-0.525547\pi$
$509$	−1841.34	−0.160346	−0.0801729	+	0.996781i	$0.525547\pi$
$510$	0	0
$511$	390.100	0.0337710
$512$	23822.1	2.05625
$513$	9306.92	0.800995
$514$	14447.2	1.23976
$515$	10822.6	0.926018
$516$	42259.9	3.60540
$517$	−13785.4	−1.17269
$518$	988.025	0.0838056
$519$	−17700.2	−1.49702
$520$	32309.2	2.72472
$521$	−15200.3	−1.27819	−0.639096	−	0.769127i	$-0.720691\pi$
$521$	−15200.3	−1.27819	−0.639096	+	0.769127i	$0.720691\pi$
$522$	−6186.52	−0.518729
$523$	−20391.5	−1.70489	−0.852444	−	0.522818i	$-0.824881\pi$
$523$	−20391.5	−1.70489	−0.852444	+	0.522818i	$0.824881\pi$
$524$	−27840.9	−2.32106
$525$	608.399	0.0505766
$526$	27190.6	2.25393
$527$	0	0
$528$	23878.1	1.96811
$529$	−5084.45	−0.417889
$530$	31237.6	2.56014
$531$	−7056.49	−0.576696
$532$	−1334.77	−0.108778
$533$	−12197.7	−0.991258
$534$	42242.6	3.42325
$535$	−7196.07	−0.581520
$536$	6623.58	0.533759
$537$	7318.89	0.588144
$538$	−5124.35	−0.410644
$539$	15520.4	1.24028
$540$	−24512.8	−1.95345
$541$	14367.0	1.14175	0.570874	−	0.821038i	$-0.306604\pi$
$541$	14367.0	1.14175	0.570874	+	0.821038i	$0.306604\pi$
$542$	20507.6	1.62523
$543$	17983.9	1.42129
$544$	0	0
$545$	−20179.6	−1.58606
$546$	−1151.89	−0.0902861
$547$	−18943.7	−1.48076	−0.740378	−	0.672190i	$-0.765354\pi$
$547$	−18943.7	−1.48076	−0.740378	+	0.672190i	$0.765354\pi$
$548$	−45816.4	−3.57150
$549$	−1542.05	−0.119878
$550$	27771.1	2.15303
$551$	10221.4	0.790283
$552$	23128.5	1.78336
$553$	−57.0465	−0.00438673
$554$	−28829.5	−2.21092
$555$	24761.8	1.89384
$556$	−20709.9	−1.57967
$557$	−23122.6	−1.75895	−0.879477	−	0.475941i	$-0.842108\pi$
$557$	−23122.6	−1.75895	−0.879477	+	0.475941i	$0.842108\pi$
$558$	447.816	0.0339741
$559$	−18767.0	−1.41997
$560$	1046.40	0.0789617
$561$	0	0
$562$	−10024.3	−0.752398
$563$	−13150.5	−0.984416	−0.492208	−	0.870478i	$-0.663810\pi$
$563$	−13150.5	−0.984416	−0.492208	+	0.870478i	$0.663810\pi$
$564$	−32012.9	−2.39005
$565$	29725.7	2.21340
$566$	−2783.77	−0.206733
$567$	718.534	0.0532197
$568$	19075.6	1.40915
$569$	−15690.7	−1.15605	−0.578023	−	0.816021i	$-0.696176\pi$
$569$	−15690.7	−1.15605	−0.578023	+	0.816021i	$0.696176\pi$
$570$	−49371.3	−3.62796
$571$	18135.9	1.32918	0.664592	−	0.747207i	$-0.268606\pi$
$571$	18135.9	1.32918	0.664592	+	0.747207i	$0.268606\pi$
$572$	−35625.6	−2.60416
$573$	10188.1	0.742785
$574$	−1026.65	−0.0746546
$575$	10350.6	0.750698
$576$	−4088.51	−0.295754
$577$	−15740.7	−1.13569	−0.567847	−	0.823134i	$-0.692223\pi$
$577$	−15740.7	−1.13569	−0.567847	+	0.823134i	$0.692223\pi$
$578$	0	0
$579$	4986.89	0.357942
$580$	−26921.3	−1.92732
$581$	−561.724	−0.0401106
$582$	43749.0	3.11590
$583$	−18052.6	−1.28244
$584$	21672.7	1.53565
$585$	−8991.38	−0.635466
$586$	−14246.3	−1.00428
$587$	−9153.33	−0.643609	−0.321804	−	0.946806i	$-0.604289\pi$
$587$	−9153.33	−0.643609	−0.321804	+	0.946806i	$0.604289\pi$
$588$	36042.0	2.52780
$589$	−739.883	−0.0517595
$590$	−45320.1	−3.16237
$591$	6119.75	0.425944
$592$	21121.7	1.46638
$593$	−3898.87	−0.269995	−0.134998	−	0.990846i	$-0.543103\pi$
$593$	−3898.87	−0.269995	−0.134998	+	0.990846i	$0.543103\pi$
$594$	20907.7	1.44420
$595$	0	0
$596$	38963.0	2.67783
$597$	−4456.68	−0.305527
$598$	−19596.9	−1.34010
$599$	−11841.6	−0.807740	−0.403870	−	0.914816i	$-0.632335\pi$
$599$	−11841.6	−0.807740	−0.403870	+	0.914816i	$0.632335\pi$
$600$	33800.6	2.29984
$601$	17152.8	1.16419	0.582093	−	0.813122i	$-0.302234\pi$
$601$	17152.8	1.16419	0.582093	+	0.813122i	$0.302234\pi$
$602$	−1579.58	−0.106942
$603$	−1843.29	−0.124485
$604$	19432.0	1.30907
$605$	−11400.6	−0.766114
$606$	4717.80	0.316250
$607$	−10576.6	−0.707234	−0.353617	−	0.935390i	$-0.615048\pi$
$607$	−10576.6	−0.707234	−0.353617	+	0.935390i	$0.615048\pi$
$608$	−6824.05	−0.455184
$609$	503.045	0.0334719
$610$	−9903.77	−0.657364
$611$	14216.5	0.941306
$612$	0	0
$613$	16518.7	1.08839	0.544196	−	0.838958i	$-0.316835\pi$
$613$	16518.7	1.08839	0.544196	+	0.838958i	$0.316835\pi$
$614$	21404.4	1.40686
$615$	−25730.0	−1.68705
$616$	−1571.58	−0.102793
$617$	14629.4	0.954547	0.477274	−	0.878755i	$-0.341625\pi$
$617$	14629.4	0.954547	0.477274	+	0.878755i	$0.341625\pi$
$618$	−21436.3	−1.39530
$619$	19584.0	1.27164	0.635822	−	0.771836i	$-0.280661\pi$
$619$	19584.0	1.27164	0.635822	+	0.771836i	$0.280661\pi$
$620$	1948.72	0.126230
$621$	7792.57	0.503551
$622$	14892.7	0.960035
$623$	−1069.82	−0.0687987
$624$	−24624.7	−1.57977
$625$	−15872.1	−1.01582
$626$	−19589.3	−1.25072
$627$	28532.3	1.81734
$628$	−54244.3	−3.44679
$629$	0	0
$630$	−756.786	−0.0478588
$631$	28856.7	1.82055	0.910276	−	0.414002i	$-0.135869\pi$
$631$	28856.7	1.82055	0.910276	+	0.414002i	$0.135869\pi$
$632$	−3169.31	−0.199476
$633$	−23108.0	−1.45097
$634$	−52914.7	−3.31469
$635$	−30244.4	−1.89010
$636$	−41922.3	−2.61372
$637$	−16005.8	−0.995559
$638$	22962.1	1.42489
$639$	−5308.58	−0.328645
$640$	−34811.6	−2.15008
$641$	−9419.79	−0.580436	−0.290218	−	0.956961i	$-0.593728\pi$
$641$	−9419.79	−0.580436	−0.290218	+	0.956961i	$0.593728\pi$
$642$	14253.3	0.876218
$643$	2848.83	0.174723	0.0873615	−	0.996177i	$-0.472156\pi$
$643$	2848.83	0.174723	0.0873615	+	0.996177i	$0.472156\pi$
$644$	−1117.59	−0.0683839
$645$	−39587.4	−2.41667
$646$	0	0
$647$	−6881.30	−0.418132	−0.209066	−	0.977901i	$-0.567042\pi$
$647$	−6881.30	−0.418132	−0.209066	+	0.977901i	$0.567042\pi$
$648$	39919.4	2.42003
$649$	26191.1	1.58411
$650$	−28639.5	−1.72821
$651$	−36.4133	−0.00219224
$652$	−16512.5	−0.991841
$653$	−10521.5	−0.630534	−0.315267	−	0.949003i	$-0.602094\pi$
$653$	−10521.5	−0.630534	−0.315267	+	0.949003i	$0.602094\pi$
$654$	39969.9	2.38983
$655$	26080.3	1.55579
$656$	−21947.6	−1.30626
$657$	−6031.32	−0.358149
$658$	1196.57	0.0708925
$659$	26606.5	1.57275	0.786374	−	0.617751i	$-0.211956\pi$
$659$	26606.5	1.57275	0.786374	+	0.617751i	$0.211956\pi$
$660$	−75149.1	−4.43208
$661$	−15511.7	−0.912758	−0.456379	−	0.889785i	$-0.650854\pi$
$661$	−15511.7	−0.912758	−0.456379	+	0.889785i	$0.650854\pi$
$662$	36096.3	2.11922
$663$	0	0
$664$	−31207.6	−1.82393
$665$	1250.36	0.0729128
$666$	−15275.8	−0.888777
$667$	8558.25	0.496817
$668$	−615.284	−0.0356378
$669$	10809.3	0.624683
$670$	−11838.5	−0.682626
$671$	5723.52	0.329291
$672$	−335.845	−0.0192790
$673$	5711.21	0.327119	0.163559	−	0.986533i	$-0.447702\pi$
$673$	5711.21	0.327119	0.163559	+	0.986533i	$0.447702\pi$
$674$	20566.4	1.17535
$675$	11388.3	0.649386
$676$	−193.751	−0.0110236
$677$	−398.222	−0.0226070	−0.0113035	−	0.999936i	$-0.503598\pi$
$677$	−398.222	−0.0226070	−0.0113035	+	0.999936i	$0.503598\pi$
$678$	−58877.8	−3.33509
$679$	−1107.97	−0.0626217
$680$	0	0
$681$	−13430.5	−0.755740
$682$	−1662.13	−0.0933228
$683$	6504.72	0.364416	0.182208	−	0.983260i	$-0.441676\pi$
$683$	6504.72	0.364416	0.182208	+	0.983260i	$0.441676\pi$
$684$	20636.9	1.15361
$685$	42919.1	2.39395
$686$	−2696.80	−0.150094
$687$	−31825.2	−1.76741
$688$	−33767.9	−1.87121
$689$	18617.1	1.02940
$690$	−41338.0	−2.28074
$691$	−7641.66	−0.420698	−0.210349	−	0.977626i	$-0.567460\pi$
$691$	−7641.66	−0.420698	−0.210349	+	0.977626i	$0.567460\pi$
$692$	47516.9	2.61029
$693$	437.357	0.0239737
$694$	31346.1	1.71453
$695$	19400.2	1.05884
$696$	27947.5	1.52205
$697$	0	0
$698$	30826.0	1.67160
$699$	−20484.0	−1.10840
$700$	−1633.28	−0.0881887
$701$	27948.0	1.50582	0.752912	−	0.658122i	$-0.228649\pi$
$701$	27948.0	1.50582	0.752912	+	0.658122i	$0.228649\pi$
$702$	−21561.5	−1.15924
$703$	25238.7	1.35405
$704$	15175.0	0.812402
$705$	29988.5	1.60203
$706$	5559.63	0.296373
$707$	−119.482	−0.00635583
$708$	60821.7	3.22856
$709$	−28431.5	−1.50602	−0.753010	−	0.658009i	$-0.771399\pi$
$709$	−28431.5	−1.50602	−0.753010	+	0.658009i	$0.771399\pi$
$710$	−34094.2	−1.80216
$711$	881.993	0.0465223
$712$	−59435.9	−3.12845
$713$	−619.495	−0.0325390
$714$	0	0
$715$	33372.7	1.74555
$716$	−19647.9	−1.02553
$717$	30719.8	1.60007
$718$	−391.666	−0.0203577
$719$	−21104.4	−1.09466	−0.547330	−	0.836917i	$-0.684356\pi$
$719$	−21104.4	−1.09466	−0.547330	+	0.836917i	$0.684356\pi$
$720$	−16178.4	−0.837406
$721$	542.890	0.0280420
$722$	−16157.2	−0.832838
$723$	3094.13	0.159159
$724$	−48278.5	−2.47826
$725$	12507.3	0.640701
$726$	22581.2	1.15436
$727$	−7655.66	−0.390554	−0.195277	−	0.980748i	$-0.562561\pi$
$727$	−7655.66	−0.390554	−0.195277	+	0.980748i	$0.562561\pi$
$728$	1620.72	0.0825108
$729$	4546.28	0.230975
$730$	−38736.0	−1.96395
$731$	0	0
$732$	13291.3	0.671122
$733$	1921.12	0.0968052	0.0484026	−	0.998828i	$-0.484587\pi$
$733$	1921.12	0.0968052	0.0484026	+	0.998828i	$0.484587\pi$
$734$	34740.2	1.74698
$735$	−33762.8	−1.69437
$736$	−5713.70	−0.286154
$737$	6841.60	0.341945
$738$	15873.1	0.791728
$739$	24081.6	1.19872	0.599362	−	0.800478i	$-0.295421\pi$
$739$	24081.6	1.19872	0.599362	+	0.800478i	$0.295421\pi$
$740$	−66474.4	−3.30222
$741$	−29424.5	−1.45875
$742$	1566.97	0.0775271
$743$	17540.0	0.866058	0.433029	−	0.901380i	$-0.357445\pi$
$743$	17540.0	0.866058	0.433029	+	0.901380i	$0.357445\pi$
$744$	−2023.00	−0.0996866
$745$	−36499.0	−1.79493
$746$	−162.163	−0.00795870
$747$	8684.80	0.425382
$748$	0	0
$749$	−360.975	−0.0176098
$750$	986.984	0.0480528
$751$	−21239.6	−1.03202	−0.516009	−	0.856583i	$-0.672583\pi$
$751$	−21239.6	−1.03202	−0.516009	+	0.856583i	$0.672583\pi$
$752$	25580.0	1.24044
$753$	4329.34	0.209522
$754$	−23680.1	−1.14374
$755$	−18203.1	−0.877457
$756$	−1229.63	−0.0591550
$757$	−22831.4	−1.09620	−0.548098	−	0.836414i	$-0.684648\pi$
$757$	−22831.4	−1.09620	−0.548098	+	0.836414i	$0.684648\pi$
$758$	26936.7	1.29075
$759$	23889.8	1.14248
$760$	69466.1	3.31553
$761$	−12398.1	−0.590579	−0.295289	−	0.955408i	$-0.595416\pi$
$761$	−12398.1	−0.590579	−0.295289	+	0.955408i	$0.595416\pi$
$762$	59905.2	2.84795
$763$	−1012.27	−0.0480295
$764$	−27350.6	−1.29517
$765$	0	0
$766$	−13473.8	−0.635548
$767$	−27010.1	−1.27155
$768$	52181.3	2.45173
$769$	−40338.4	−1.89160	−0.945800	−	0.324751i	$-0.894720\pi$
$769$	−40338.4	−1.89160	−0.945800	+	0.324751i	$0.894720\pi$
$770$	2808.91	0.131462
$771$	18162.7	0.848397
$772$	−13387.6	−0.624131
$773$	−6385.94	−0.297136	−0.148568	−	0.988902i	$-0.547466\pi$
$773$	−6385.94	−0.297136	−0.148568	+	0.988902i	$0.547466\pi$
$774$	24421.9	1.13414
$775$	−905.348	−0.0419626
$776$	−61555.4	−2.84756
$777$	1242.12	0.0573499
$778$	1957.11	0.0901874
$779$	−26225.5	−1.20620
$780$	77499.0	3.55758
$781$	19703.5	0.902749
$782$	0	0
$783$	9416.22	0.429768
$784$	−28799.5	−1.31193
$785$	50814.0	2.31036
$786$	−51657.4	−2.34422
$787$	−26132.8	−1.18365	−0.591826	−	0.806066i	$-0.701593\pi$
$787$	−26132.8	−1.18365	−0.591826	+	0.806066i	$0.701593\pi$
$788$	−16428.8	−0.742704
$789$	34183.4	1.54241
$790$	5664.58	0.255110
$791$	1491.12	0.0670268
$792$	24298.1	1.09015
$793$	−5902.49	−0.264317
$794$	−58527.8	−2.61596
$795$	39271.3	1.75196
$796$	11964.2	0.532737
$797$	8629.21	0.383516	0.191758	−	0.981442i	$-0.438581\pi$
$797$	8629.21	0.383516	0.191758	+	0.981442i	$0.438581\pi$
$798$	−2476.60	−0.109863
$799$	0	0
$800$	−8350.16	−0.369028
$801$	16540.5	0.729626
$802$	−14535.0	−0.639962
$803$	22386.0	0.983793
$804$	15887.7	0.696913
$805$	1046.92	0.0458372
$806$	1714.10	0.0749090
$807$	−6442.22	−0.281012
$808$	−6638.01	−0.289015
$809$	42653.7	1.85368	0.926839	−	0.375460i	$-0.122515\pi$
$809$	42653.7	1.85368	0.926839	+	0.375460i	$0.122515\pi$
$810$	−71348.7	−3.09498
$811$	−45388.0	−1.96521	−0.982607	−	0.185700i	$-0.940545\pi$
$811$	−45388.0	−1.96521	−0.982607	+	0.185700i	$0.940545\pi$
$812$	−1350.45	−0.0583639
$813$	25781.7	1.11218
$814$	56698.2	2.44136
$815$	15468.3	0.664824
$816$	0	0
$817$	−40349.9	−1.72786
$818$	−28147.3	−1.20311
$819$	−451.033	−0.0192434
$820$	69073.4	2.94164
$821$	16898.6	0.718349	0.359175	−	0.933270i	$-0.383058\pi$
$821$	16898.6	0.718349	0.359175	+	0.933270i	$0.383058\pi$
$822$	−85010.1	−3.60714
$823$	38258.3	1.62042	0.810208	−	0.586143i	$-0.199354\pi$
$823$	38258.3	1.62042	0.810208	+	0.586143i	$0.199354\pi$
$824$	30161.2	1.27514
$825$	34913.2	1.47336
$826$	−2273.38	−0.0957641
$827$	30489.3	1.28200	0.641001	−	0.767540i	$-0.278520\pi$
$827$	30489.3	1.28200	0.641001	+	0.767540i	$0.278520\pi$
$828$	17279.0	0.725226
$829$	44358.5	1.85843	0.929213	−	0.369545i	$-0.120486\pi$
$829$	44358.5	1.85843	0.929213	+	0.369545i	$0.120486\pi$
$830$	55777.9	2.33263
$831$	−36243.8	−1.51298
$832$	−15649.6	−0.652104
$833$	0	0
$834$	−38426.2	−1.59543
$835$	576.374	0.0238877
$836$	−76596.4	−3.16883
$837$	−681.600	−0.0281476
$838$	73750.6	3.04018
$839$	20819.6	0.856702	0.428351	−	0.903612i	$-0.359095\pi$
$839$	20819.6	0.856702	0.428351	+	0.903612i	$0.359095\pi$
$840$	3418.77	0.140427
$841$	−14047.6	−0.575980
$842$	−16508.5	−0.675678
$843$	−12602.3	−0.514882
$844$	62034.6	2.53000
$845$	181.498	0.00738903
$846$	−18500.2	−0.751831
$847$	−571.884	−0.0231997
$848$	33498.2	1.35653
$849$	−3499.70	−0.141472
$850$	0	0
$851$	21132.1	0.851233
$852$	45756.0	1.83988
$853$	−43406.9	−1.74235	−0.871175	−	0.490973i	$-0.836641\pi$
$853$	−43406.9	−1.74235	−0.871175	+	0.490973i	$0.836641\pi$
$854$	−496.801	−0.0199065
$855$	−19331.8	−0.773257
$856$	−20054.6	−0.800760
$857$	−7893.90	−0.314645	−0.157322	−	0.987547i	$-0.550286\pi$
$857$	−7893.90	−0.314645	−0.157322	+	0.987547i	$0.550286\pi$
$858$	−66101.5	−2.63015
$859$	−10441.9	−0.414751	−0.207376	−	0.978261i	$-0.566492\pi$
$859$	−10441.9	−0.414751	−0.207376	+	0.978261i	$0.566492\pi$
$860$	106274.	4.21387
$861$	−1290.69	−0.0510877
$862$	60789.9	2.40198
$863$	39784.6	1.56928	0.784638	−	0.619954i	$-0.212849\pi$
$863$	39784.6	1.56928	0.784638	+	0.619954i	$0.212849\pi$
$864$	−6286.50	−0.247536
$865$	−44512.1	−1.74966
$866$	−2111.51	−0.0828544
$867$	0	0
$868$	97.7532	0.00382253
$869$	−3273.63	−0.127791
$870$	−49951.1	−1.94655
$871$	−7055.53	−0.274475
$872$	−56238.2	−2.18402
$873$	17130.3	0.664117
$874$	−42134.2	−1.63068
$875$	−24.9961	−0.000965739 0
$876$	51985.4	2.00505
$877$	−11135.4	−0.428752	−0.214376	−	0.976751i	$-0.568772\pi$
$877$	−11135.4	−0.428752	−0.214376	+	0.976751i	$0.568772\pi$
$878$	72367.9	2.78166
$879$	−17910.1	−0.687250
$880$	60048.2	2.30025
$881$	18890.9	0.722416	0.361208	−	0.932485i	$-0.382364\pi$
$881$	18890.9	0.722416	0.361208	+	0.932485i	$0.382364\pi$
$882$	20828.6	0.795164
$883$	36453.6	1.38931	0.694656	−	0.719342i	$-0.255557\pi$
$883$	36453.6	1.38931	0.694656	+	0.719342i	$0.255557\pi$
$884$	0	0
$885$	−56975.5	−2.16408
$886$	−78519.2	−2.97732
$887$	−23100.3	−0.874446	−0.437223	−	0.899353i	$-0.644038\pi$
$887$	−23100.3	−0.874446	−0.437223	+	0.899353i	$0.644038\pi$
$888$	69008.2	2.60784
$889$	−1517.14	−0.0572366
$890$	106231.	4.00098
$891$	41233.3	1.55036
$892$	−29018.2	−1.08924
$893$	30566.0	1.14541
$894$	72293.8	2.70455
$895$	18405.4	0.687403
$896$	−1746.25	−0.0651093
$897$	−24636.8	−0.917057
$898$	−25922.9	−0.963318
$899$	−748.572	−0.0277712
$900$	25252.0	0.935260
$901$	0	0
$902$	−58915.0	−2.17478
$903$	−1985.82	−0.0731825
$904$	82841.8	3.04787
$905$	45225.5	1.66116
$906$	36055.1	1.32213
$907$	−25240.6	−0.924036	−0.462018	−	0.886871i	$-0.652874\pi$
$907$	−25240.6	−0.924036	−0.462018	+	0.886871i	$0.652874\pi$
$908$	36054.9	1.31776
$909$	1847.30	0.0674050
$910$	−2896.74	−0.105523
$911$	−12331.2	−0.448465	−0.224232	−	0.974536i	$-0.571987\pi$
$911$	−12331.2	−0.448465	−0.224232	+	0.974536i	$0.571987\pi$
$912$	−52944.2	−1.92232
$913$	−32234.8	−1.16847
$914$	20705.1	0.749304
$915$	−12450.8	−0.449848
$916$	85436.4	3.08177
$917$	1308.26	0.0471130
$918$	0	0
$919$	40235.8	1.44424	0.722121	−	0.691767i	$-0.243168\pi$
$919$	40235.8	1.44424	0.722121	+	0.691767i	$0.243168\pi$
$920$	58163.2	2.08433
$921$	26909.1	0.962741
$922$	−33448.4	−1.19475
$923$	−20319.6	−0.724625
$924$	−3769.69	−0.134214
$925$	30883.1	1.09776
$926$	72659.3	2.57855
$927$	−8393.60	−0.297392
$928$	−6904.19	−0.244225
$929$	−45692.0	−1.61368	−0.806838	−	0.590772i	$-0.798823\pi$
$929$	−45692.0	−1.61368	−0.806838	+	0.590772i	$0.798823\pi$
$930$	3615.75	0.127489
$931$	−34413.0	−1.21143
$932$	54990.2	1.93269
$933$	18722.7	0.656972
$934$	34923.0	1.22346
$935$	0	0
$936$	−25057.9	−0.875045
$937$	−3141.20	−0.109518	−0.0547590	−	0.998500i	$-0.517439\pi$
$937$	−3141.20	−0.109518	−0.0547590	+	0.998500i	$0.517439\pi$
$938$	−593.850	−0.0206715
$939$	−24627.3	−0.855891
$940$	−80505.5	−2.79341
$941$	24333.2	0.842975	0.421487	−	0.906834i	$-0.361508\pi$
$941$	24333.2	0.842975	0.421487	+	0.906834i	$0.361508\pi$
$942$	−100648.	−3.48119
$943$	−21958.3	−0.758284
$944$	−48599.8	−1.67562
$945$	1151.87	0.0396511
$946$	−90645.0	−3.11535
$947$	39879.6	1.36844	0.684220	−	0.729276i	$-0.260143\pi$
$947$	39879.6	1.36844	0.684220	+	0.729276i	$0.260143\pi$
$948$	−7602.12	−0.260449
$949$	−23086.0	−0.789678
$950$	−61576.1	−2.10294
$951$	−66523.2	−2.26831
$952$	0	0
$953$	−26021.7	−0.884496	−0.442248	−	0.896893i	$-0.645819\pi$
$953$	−26021.7	−0.884496	−0.442248	+	0.896893i	$0.645819\pi$
$954$	−24226.8	−0.822193
$955$	25621.0	0.868141
$956$	−82468.8	−2.78999
$957$	28867.4	0.975080
$958$	54363.6	1.83341
$959$	2152.94	0.0724944
$960$	−33011.4	−1.10983
$961$	−29736.8	−0.998181
$962$	−58471.1	−1.95965
$963$	5581.01	0.186756
$964$	−8306.36	−0.277520
$965$	12541.0	0.418350
$966$	−2073.63	−0.0690662
$967$	42806.0	1.42352	0.711762	−	0.702420i	$-0.247897\pi$
$967$	42806.0	1.42352	0.711762	+	0.702420i	$0.247897\pi$
$968$	−31772.0	−1.05495
$969$	0	0
$970$	110019.	3.64176
$971$	−19147.5	−0.632825	−0.316413	−	0.948622i	$-0.602478\pi$
$971$	−19147.5	−0.632825	−0.316413	+	0.948622i	$0.602478\pi$
$972$	53725.3	1.77288
$973$	973.170	0.0320641
$974$	40570.5	1.33466
$975$	−36004.9	−1.18265
$976$	−10620.5	−0.348313
$977$	8209.83	0.268839	0.134420	−	0.990925i	$-0.457083\pi$
$977$	8209.83	0.268839	0.134420	+	0.990925i	$0.457083\pi$
$978$	−30638.2	−1.00174
$979$	−61392.3	−2.00419
$980$	90637.8	2.95441
$981$	15650.6	0.509364
$982$	−18766.9	−0.609852
$983$	−35203.4	−1.14223	−0.571116	−	0.820870i	$-0.693489\pi$
$983$	−35203.4	−1.14223	−0.571116	+	0.820870i	$0.693489\pi$
$984$	−71706.3	−2.32308
$985$	15389.9	0.497829
$986$	0	0
$987$	1504.31	0.0485132
$988$	78991.6	2.54358
$989$	−33784.5	−1.08623
$990$	−43428.5	−1.39419
$991$	5669.58	0.181736	0.0908678	−	0.995863i	$-0.471036\pi$
$991$	5669.58	0.181736	0.0908678	+	0.995863i	$0.471036\pi$
$992$	499.765	0.0159955
$993$	45379.5	1.45023
$994$	−1710.26	−0.0545737
$995$	−11207.6	−0.357089
$996$	−74856.5	−2.38144
$997$	27125.7	0.861666	0.430833	−	0.902432i	$-0.358220\pi$
$997$	27125.7	0.861666	0.430833	+	0.902432i	$0.358220\pi$
$998$	64365.4	2.04153
$999$	23250.6	0.736353

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.h.1.2	✓	12
17.4	even	4		289.4.b.f.288.22		24
17.13	even	4		289.4.b.f.288.21		24
17.16	even	2		289.4.a.i.1.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.4.a.h.1.2	✓	12	1.1	even	1	trivial
289.4.a.i.1.2	yes	12	17.16	even	2
289.4.b.f.288.21		24	17.13	even	4
289.4.b.f.288.22		24	17.4	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)

\(f(q)\)	\(=\)	\(q-4.98104 q^{2} -6.26206 q^{3} +16.8108 q^{4} -15.7477 q^{5} +31.1916 q^{6} -0.789949 q^{7} -43.8870 q^{8} +12.2134 q^{9} +O(q^{10})\)	\(q-4.98104 q^{2} -6.26206 q^{3} +16.8108 q^{4} -15.7477 q^{5} +31.1916 q^{6} -0.789949 q^{7} -43.8870 q^{8} +12.2134 q^{9} +78.4401 q^{10} -45.3316 q^{11} -105.270 q^{12} +46.7491 q^{13} +3.93477 q^{14} +98.6131 q^{15} +84.1166 q^{16} -60.8354 q^{18} +100.512 q^{19} -264.732 q^{20} +4.94671 q^{21} +225.798 q^{22} +84.1579 q^{23} +274.823 q^{24} +122.991 q^{25} -232.859 q^{26} +92.5947 q^{27} -13.2797 q^{28} +101.693 q^{29} -491.196 q^{30} -7.36111 q^{31} -67.8926 q^{32} +283.869 q^{33} +12.4399 q^{35} +205.317 q^{36} +251.101 q^{37} -500.657 q^{38} -292.745 q^{39} +691.120 q^{40} -260.918 q^{41} -24.6398 q^{42} -401.442 q^{43} -762.060 q^{44} -192.333 q^{45} -419.194 q^{46} +304.102 q^{47} -526.743 q^{48} -342.376 q^{49} -612.622 q^{50} +785.889 q^{52} +398.236 q^{53} -461.218 q^{54} +713.869 q^{55} +34.6685 q^{56} -629.414 q^{57} -506.536 q^{58} -577.767 q^{59} +1657.77 q^{60} -126.259 q^{61} +36.6660 q^{62} -9.64795 q^{63} -334.757 q^{64} -736.191 q^{65} -1413.96 q^{66} -150.923 q^{67} -527.002 q^{69} -61.9637 q^{70} -434.653 q^{71} -536.008 q^{72} -493.829 q^{73} -1250.74 q^{74} -770.175 q^{75} +1689.69 q^{76} +35.8096 q^{77} +1458.18 q^{78} +72.2153 q^{79} -1324.64 q^{80} -909.595 q^{81} +1299.65 q^{82} +711.089 q^{83} +83.1581 q^{84} +1999.60 q^{86} -636.806 q^{87} +1989.47 q^{88} +1354.30 q^{89} +958.018 q^{90} -36.9294 q^{91} +1414.76 q^{92} +46.0957 q^{93} -1514.75 q^{94} -1582.84 q^{95} +425.147 q^{96} +1402.59 q^{97} +1705.39 q^{98} -553.651 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) \) 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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