LMFDB - Embedded newform 242.4.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [242,4,Mod(1,242)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(242, 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("242.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 242 = 2 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	242.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:	$14.2784622214$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.978025.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 99x^{2} + 100x + 2420 $ x^4 - 2x^3 - 99x^2 + 100*x + 2420
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 11 $
Twist minimal:	no (minimal twist has level 22)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$6.92695$ of defining polynomial
Character	$\chi$	$=$	242.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -4.30892 q^{3} +4.00000 q^{4} -8.06215 q^{5} +8.61784 q^{6} -26.0792 q^{7} -8.00000 q^{8} -8.43321 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -4.30892 q^{3} +4.00000 q^{4} -8.06215 q^{5} +8.61784 q^{6} -26.0792 q^{7} -8.00000 q^{8} -8.43321 q^{9} +16.1243 q^{10} -17.2357 q^{12} -3.26382 q^{13} +52.1583 q^{14} +34.7391 q^{15} +16.0000 q^{16} -20.8717 q^{17} +16.8664 q^{18} -125.970 q^{19} -32.2486 q^{20} +112.373 q^{21} +97.8394 q^{23} +34.4714 q^{24} -60.0018 q^{25} +6.52764 q^{26} +152.679 q^{27} -104.317 q^{28} -263.834 q^{29} -69.4783 q^{30} +199.364 q^{31} -32.0000 q^{32} +41.7433 q^{34} +210.254 q^{35} -33.7329 q^{36} +365.643 q^{37} +251.939 q^{38} +14.0635 q^{39} +64.4972 q^{40} +273.732 q^{41} -224.746 q^{42} +388.059 q^{43} +67.9898 q^{45} -195.679 q^{46} -51.8541 q^{47} -68.9427 q^{48} +337.122 q^{49} +120.004 q^{50} +89.9343 q^{51} -13.0553 q^{52} -412.524 q^{53} -305.358 q^{54} +208.633 q^{56} +542.793 q^{57} +527.669 q^{58} +26.2834 q^{59} +138.957 q^{60} +164.149 q^{61} -398.727 q^{62} +219.931 q^{63} +64.0000 q^{64} +26.3134 q^{65} +276.961 q^{67} -83.4866 q^{68} -421.582 q^{69} -420.508 q^{70} -516.930 q^{71} +67.4657 q^{72} -241.565 q^{73} -731.287 q^{74} +258.543 q^{75} -503.879 q^{76} -28.1271 q^{78} -273.120 q^{79} -128.994 q^{80} -430.184 q^{81} -547.465 q^{82} +72.5940 q^{83} +449.492 q^{84} +168.270 q^{85} -776.118 q^{86} +1136.84 q^{87} -1194.73 q^{89} -135.980 q^{90} +85.1177 q^{91} +391.358 q^{92} -859.041 q^{93} +103.708 q^{94} +1015.59 q^{95} +137.885 q^{96} +1463.63 q^{97} -674.244 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} + 4 q^{3} + 16 q^{4} + 25 q^{5} - 8 q^{6} - 3 q^{7} - 32 q^{8} + 102 q^{9}+O(q^{10}) $ 4 * q - 8 * q^2 + 4 * q^3 + 16 * q^4 + 25 * q^5 - 8 * q^6 - 3 * q^7 - 32 * q^8 + 102 * q^9	\( 4 q - 8 q^{2} + 4 q^{3} + 16 q^{4} + 25 q^{5} - 8 q^{6} - 3 q^{7} - 32 q^{8} + 102 q^{9} - 50 q^{10} + 16 q^{12} + 41 q^{13} + 6 q^{14} + 68 q^{15} + 64 q^{16} - 52 q^{17} - 204 q^{18} - 16 q^{19} + 100 q^{20} - 25 q^{21} + 314 q^{23} - 32 q^{24} - 21 q^{25} - 82 q^{26} + 286 q^{27} - 12 q^{28} - 561 q^{29} - 136 q^{30} + 199 q^{31} - 128 q^{32} + 104 q^{34} + 714 q^{35} + 408 q^{36} + 357 q^{37} + 32 q^{38} + 1038 q^{39} - 200 q^{40} - 32 q^{41} + 50 q^{42} + 721 q^{43} + 1326 q^{45} - 628 q^{46} + 403 q^{47} + 64 q^{48} + 823 q^{49} + 42 q^{50} + 174 q^{51} + 164 q^{52} - 133 q^{53} - 572 q^{54} + 24 q^{56} + 1031 q^{57} + 1122 q^{58} + 1016 q^{59} + 272 q^{60} + 919 q^{61} - 398 q^{62} + 1367 q^{63} + 256 q^{64} - 69 q^{65} + 289 q^{67} - 208 q^{68} - 1620 q^{69} - 1428 q^{70} - 1205 q^{71} - 816 q^{72} + 1234 q^{73} - 714 q^{74} - 911 q^{75} - 64 q^{76} - 2076 q^{78} + 603 q^{79} + 400 q^{80} - 1400 q^{81} + 64 q^{82} - 1514 q^{83} - 100 q^{84} - 717 q^{85} - 1442 q^{86} + 1061 q^{87} - 1101 q^{89} - 2652 q^{90} - 2306 q^{91} + 1256 q^{92} - 2298 q^{93} - 806 q^{94} + 1766 q^{95} - 128 q^{96} + 2116 q^{97} - 1646 q^{98}+O(q^{100}) \) 4 * q - 8 * q^2 + 4 * q^3 + 16 * q^4 + 25 * q^5 - 8 * q^6 - 3 * q^7 - 32 * q^8 + 102 * q^9 - 50 * q^10 + 16 * q^12 + 41 * q^13 + 6 * q^14 + 68 * q^15 + 64 * q^16 - 52 * q^17 - 204 * q^18 - 16 * q^19 + 100 * q^20 - 25 * q^21 + 314 * q^23 - 32 * q^24 - 21 * q^25 - 82 * q^26 + 286 * q^27 - 12 * q^28 - 561 * q^29 - 136 * q^30 + 199 * q^31 - 128 * q^32 + 104 * q^34 + 714 * q^35 + 408 * q^36 + 357 * q^37 + 32 * q^38 + 1038 * q^39 - 200 * q^40 - 32 * q^41 + 50 * q^42 + 721 * q^43 + 1326 * q^45 - 628 * q^46 + 403 * q^47 + 64 * q^48 + 823 * q^49 + 42 * q^50 + 174 * q^51 + 164 * q^52 - 133 * q^53 - 572 * q^54 + 24 * q^56 + 1031 * q^57 + 1122 * q^58 + 1016 * q^59 + 272 * q^60 + 919 * q^61 - 398 * q^62 + 1367 * q^63 + 256 * q^64 - 69 * q^65 + 289 * q^67 - 208 * q^68 - 1620 * q^69 - 1428 * q^70 - 1205 * q^71 - 816 * q^72 + 1234 * q^73 - 714 * q^74 - 911 * q^75 - 64 * q^76 - 2076 * q^78 + 603 * q^79 + 400 * q^80 - 1400 * q^81 + 64 * q^82 - 1514 * q^83 - 100 * q^84 - 717 * q^85 - 1442 * q^86 + 1061 * q^87 - 1101 * q^89 - 2652 * q^90 - 2306 * q^91 + 1256 * q^92 - 2298 * q^93 - 806 * q^94 + 1766 * q^95 - 128 * q^96 + 2116 * q^97 - 1646 * q^98

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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−4.30892	−0.829252	−0.414626	−	0.909992i	$-0.636088\pi$
$3$	−4.30892	−0.829252	−0.414626	+	0.909992i	$0.636088\pi$
$4$	4.00000	0.500000
$5$	−8.06215	−0.721100	−0.360550	−	0.932740i	$-0.617411\pi$
$5$	−8.06215	−0.721100	−0.360550	+	0.932740i	$0.617411\pi$
$6$	8.61784	0.586370
$7$	−26.0792	−1.40814	−0.704071	−	0.710130i	$-0.748636\pi$
$7$	−26.0792	−1.40814	−0.704071	+	0.710130i	$0.748636\pi$
$8$	−8.00000	−0.353553
$9$	−8.43321	−0.312341
$10$	16.1243	0.509895
$11$	0	0
$11$	0	0
$12$	−17.2357	−0.414626
$13$	−3.26382	−0.0696324	−0.0348162	−	0.999394i	$-0.511085\pi$
$13$	−3.26382	−0.0696324	−0.0348162	+	0.999394i	$0.511085\pi$
$14$	52.1583	0.995707
$15$	34.7391	0.597974
$16$	16.0000	0.250000
$17$	−20.8717	−0.297772	−0.148886	−	0.988854i	$-0.547569\pi$
$17$	−20.8717	−0.297772	−0.148886	+	0.988854i	$0.547569\pi$
$18$	16.8664	0.220859
$19$	−125.970	−1.52102	−0.760511	−	0.649325i	$-0.775052\pi$
$19$	−125.970	−1.52102	−0.760511	+	0.649325i	$0.775052\pi$
$20$	−32.2486	−0.360550
$21$	112.373	1.16770
$22$	0	0
$23$	97.8394	0.886997	0.443498	−	0.896275i	$-0.353737\pi$
$23$	97.8394	0.886997	0.443498	+	0.896275i	$0.353737\pi$
$24$	34.4714	0.293185
$25$	−60.0018	−0.480014
$26$	6.52764	0.0492375
$27$	152.679	1.08826
$28$	−104.317	−0.704071
$29$	−263.834	−1.68941	−0.844703	−	0.535235i	$-0.820223\pi$
$29$	−263.834	−1.68941	−0.844703	+	0.535235i	$0.820223\pi$
$30$	−69.4783	−0.422831
$31$	199.364	1.15506	0.577528	−	0.816371i	$-0.304017\pi$
$31$	199.364	1.15506	0.577528	+	0.816371i	$0.304017\pi$
$32$	−32.0000	−0.176777
$33$	0	0
$34$	41.7433	0.210557
$35$	210.254	1.01541
$36$	−33.7329	−0.156171
$37$	365.643	1.62463	0.812316	−	0.583217i	$-0.198206\pi$
$37$	365.643	1.62463	0.812316	+	0.583217i	$0.198206\pi$
$38$	251.939	1.07553
$39$	14.0635	0.0577428
$40$	64.4972	0.254947
$41$	273.732	1.04268	0.521339	−	0.853350i	$-0.325433\pi$
$41$	273.732	1.04268	0.521339	+	0.853350i	$0.325433\pi$
$42$	−224.746	−0.825692
$43$	388.059	1.37624	0.688121	−	0.725596i	$-0.258436\pi$
$43$	388.059	1.37624	0.688121	+	0.725596i	$0.258436\pi$
$44$	0	0
$45$	67.9898	0.225229
$46$	−195.679	−0.627201
$47$	−51.8541	−0.160930	−0.0804649	−	0.996757i	$-0.525641\pi$
$47$	−51.8541	−0.160930	−0.0804649	+	0.996757i	$0.525641\pi$
$48$	−68.9427	−0.207313
$49$	337.122	0.982863
$50$	120.004	0.339421
$51$	89.9343	0.246928
$52$	−13.0553	−0.0348162
$53$	−412.524	−1.06914	−0.534572	−	0.845123i	$-0.679527\pi$
$53$	−412.524	−1.06914	−0.534572	+	0.845123i	$0.679527\pi$
$54$	−305.358	−0.769517
$55$	0	0
$56$	208.633	0.497853
$57$	542.793	1.26131
$58$	527.669	1.19459
$59$	26.2834	0.0579967	0.0289984	−	0.999579i	$-0.490768\pi$
$59$	26.2834	0.0579967	0.0289984	+	0.999579i	$0.490768\pi$
$60$	138.957	0.298987
$61$	164.149	0.344543	0.172272	−	0.985050i	$-0.444889\pi$
$61$	164.149	0.344543	0.172272	+	0.985050i	$0.444889\pi$
$62$	−398.727	−0.816748
$63$	219.931	0.439821
$64$	64.0000	0.125000
$65$	26.3134	0.0502119
$66$	0	0
$67$	276.961	0.505017	0.252508	−	0.967595i	$-0.418744\pi$
$67$	276.961	0.505017	0.252508	+	0.967595i	$0.418744\pi$
$68$	−83.4866	−0.148886
$69$	−421.582	−0.735544
$70$	−420.508	−0.718004
$71$	−516.930	−0.864060	−0.432030	−	0.901859i	$-0.642203\pi$
$71$	−516.930	−0.864060	−0.432030	+	0.901859i	$0.642203\pi$
$72$	67.4657	0.110429
$73$	−241.565	−0.387302	−0.193651	−	0.981071i	$-0.562033\pi$
$73$	−241.565	−0.387302	−0.193651	+	0.981071i	$0.562033\pi$
$74$	−731.287	−1.14879
$75$	258.543	0.398053
$76$	−503.879	−0.760511
$77$	0	0
$78$	−28.1271	−0.0408303
$79$	−273.120	−0.388967	−0.194483	−	0.980906i	$-0.562303\pi$
$79$	−273.120	−0.388967	−0.194483	+	0.980906i	$0.562303\pi$
$80$	−128.994	−0.180275
$81$	−430.184	−0.590102
$82$	−547.465	−0.737285
$83$	72.5940	0.0960027	0.0480014	−	0.998847i	$-0.484715\pi$
$83$	72.5940	0.0960027	0.0480014	+	0.998847i	$0.484715\pi$
$84$	449.492	0.583852
$85$	168.270	0.214723
$86$	−776.118	−0.973151
$87$	1136.84	1.40094
$88$	0	0
$89$	−1194.73	−1.42294	−0.711470	−	0.702717i	$-0.751970\pi$
$89$	−1194.73	−1.42294	−0.711470	+	0.702717i	$0.751970\pi$
$90$	−135.980	−0.159261
$91$	85.1177	0.0980522
$92$	391.358	0.443498
$93$	−859.041	−0.957833
$94$	103.708	0.113795
$95$	1015.59	1.09681
$96$	137.885	0.146592
$97$	1463.63	1.53205	0.766026	−	0.642810i	$-0.222232\pi$
$97$	1463.63	1.53205	0.766026	+	0.642810i	$0.222232\pi$
$98$	−674.244	−0.694989
$99$	0	0
$100$	−240.007	−0.240007
$101$	−900.093	−0.886759	−0.443379	−	0.896334i	$-0.646221\pi$
$101$	−900.093	−0.886759	−0.443379	+	0.896334i	$0.646221\pi$
$102$	−179.869	−0.174604
$103$	−417.125	−0.399035	−0.199517	−	0.979894i	$-0.563937\pi$
$103$	−417.125	−0.399035	−0.199517	+	0.979894i	$0.563937\pi$
$104$	26.1106	0.0246188
$105$	−905.967	−0.842032
$106$	825.049	0.755998
$107$	1080.39	0.976120	0.488060	−	0.872810i	$-0.337705\pi$
$107$	1080.39	0.976120	0.488060	+	0.872810i	$0.337705\pi$
$108$	610.715	0.544131
$109$	−1472.08	−1.29358	−0.646789	−	0.762669i	$-0.723888\pi$
$109$	−1472.08	−1.29358	−0.646789	+	0.762669i	$0.723888\pi$
$110$	0	0
$111$	−1575.53	−1.34723
$112$	−417.266	−0.352035
$113$	−126.481	−0.105295	−0.0526473	−	0.998613i	$-0.516766\pi$
$113$	−126.481	−0.105295	−0.0526473	+	0.998613i	$0.516766\pi$
$114$	−1085.59	−0.891881
$115$	−788.796	−0.639614
$116$	−1055.34	−0.844703
$117$	27.5245	0.0217491
$118$	−52.5668	−0.0410099
$119$	544.315	0.419305
$120$	−277.913	−0.211416
$121$	0	0
$122$	−328.298	−0.243629
$123$	−1179.49	−0.864643
$124$	797.454	0.577528
$125$	1491.51	1.06724
$126$	−439.862	−0.311000
$127$	1063.54	0.743105	0.371552	−	0.928412i	$-0.378826\pi$
$127$	1063.54	0.743105	0.371552	+	0.928412i	$0.378826\pi$
$128$	−128.000	−0.0883883
$129$	−1672.11	−1.14125
$130$	−52.6268	−0.0355052
$131$	−1525.04	−1.01713	−0.508563	−	0.861025i	$-0.669823\pi$
$131$	−1525.04	−1.01713	−0.508563	+	0.861025i	$0.669823\pi$
$132$	0	0
$133$	3285.18	2.14182
$134$	−553.921	−0.357101
$135$	−1230.92	−0.784746
$136$	166.973	0.105278
$137$	−2078.83	−1.29640	−0.648199	−	0.761471i	$-0.724478\pi$
$137$	−2078.83	−1.29640	−0.648199	+	0.761471i	$0.724478\pi$
$138$	843.164	0.520108
$139$	1507.45	0.919855	0.459927	−	0.887957i	$-0.347875\pi$
$139$	1507.45	0.919855	0.459927	+	0.887957i	$0.347875\pi$
$140$	841.016	0.507706
$141$	223.435	0.133451
$142$	1033.86	0.610983
$143$	0	0
$144$	−134.931	−0.0780853
$145$	2127.07	1.21823
$146$	483.130	0.273864
$147$	−1452.63	−0.815041
$148$	1462.57	0.812316
$149$	−429.848	−0.236339	−0.118169	−	0.992993i	$-0.537703\pi$
$149$	−429.848	−0.236339	−0.118169	+	0.992993i	$0.537703\pi$
$150$	−517.086	−0.281466
$151$	891.682	0.480556	0.240278	−	0.970704i	$-0.422761\pi$
$151$	891.682	0.480556	0.240278	+	0.970704i	$0.422761\pi$
$152$	1007.76	0.537763
$153$	176.015	0.0930064
$154$	0	0
$155$	−1607.30	−0.832912
$156$	56.2541	0.0288714
$157$	541.031	0.275025	0.137513	−	0.990500i	$-0.456089\pi$
$157$	541.031	0.275025	0.137513	+	0.990500i	$0.456089\pi$
$158$	546.240	0.275041
$159$	1777.53	0.886589
$160$	257.989	0.127474
$161$	−2551.57	−1.24902
$162$	860.368	0.417265
$163$	−2927.59	−1.40679	−0.703395	−	0.710799i	$-0.748334\pi$
$163$	−2927.59	−1.40679	−0.703395	+	0.710799i	$0.748334\pi$
$164$	1094.93	0.521339
$165$	0	0
$166$	−145.188	−0.0678842
$167$	1740.23	0.806366	0.403183	−	0.915119i	$-0.367904\pi$
$167$	1740.23	0.806366	0.403183	+	0.915119i	$0.367904\pi$
$168$	−898.984	−0.412846
$169$	−2186.35	−0.995151
$170$	−336.541	−0.151832
$171$	1062.33	0.475078
$172$	1552.24	0.688121
$173$	−290.801	−0.127799	−0.0638995	−	0.997956i	$-0.520354\pi$
$173$	−290.801	−0.127799	−0.0638995	+	0.997956i	$0.520354\pi$
$174$	−2273.68	−0.990617
$175$	1564.80	0.675928
$176$	0	0
$177$	−113.253	−0.0480939
$178$	2389.47	1.00617
$179$	2600.32	1.08580	0.542898	−	0.839799i	$-0.317327\pi$
$179$	2600.32	1.08580	0.542898	+	0.839799i	$0.317327\pi$
$180$	271.959	0.112615
$181$	1855.83	0.762114	0.381057	−	0.924552i	$-0.375560\pi$
$181$	1855.83	0.762114	0.381057	+	0.924552i	$0.375560\pi$
$182$	−170.235	−0.0693334
$183$	−707.305	−0.285713
$184$	−782.715	−0.313601
$185$	−2947.87	−1.17152
$186$	1718.08	0.677290
$187$	0	0
$188$	−207.417	−0.0804649
$189$	−3981.73	−1.53243
$190$	−2031.17	−0.775562
$191$	1532.16	0.580434	0.290217	−	0.956961i	$-0.406273\pi$
$191$	1532.16	0.580434	0.290217	+	0.956961i	$0.406273\pi$
$192$	−275.771	−0.103656
$193$	1051.58	0.392197	0.196099	−	0.980584i	$-0.437173\pi$
$193$	1051.58	0.392197	0.196099	+	0.980584i	$0.437173\pi$
$194$	−2927.26	−1.08332
$195$	−113.382	−0.0416383
$196$	1348.49	0.491432
$197$	−1577.77	−0.570616	−0.285308	−	0.958436i	$-0.592096\pi$
$197$	−1577.77	−0.570616	−0.285308	+	0.958436i	$0.592096\pi$
$198$	0	0
$199$	3760.53	1.33958	0.669791	−	0.742550i	$-0.266384\pi$
$199$	3760.53	1.33958	0.669791	+	0.742550i	$0.266384\pi$
$200$	480.014	0.169711
$201$	−1193.40	−0.418786
$202$	1800.19	0.627033
$203$	6880.57	2.37892
$204$	359.737	0.123464
$205$	−2206.87	−0.751876
$206$	834.251	0.282160
$207$	−825.101	−0.277046
$208$	−52.2211	−0.0174081
$209$	0	0
$210$	1811.93	0.595407
$211$	1420.58	0.463492	0.231746	−	0.972776i	$-0.425556\pi$
$211$	1420.58	0.463492	0.231746	+	0.972776i	$0.425556\pi$
$212$	−1650.10	−0.534572
$213$	2227.41	0.716523
$214$	−2160.77	−0.690221
$215$	−3128.59	−0.992409
$216$	−1221.43	−0.384759
$217$	−5199.23	−1.62648
$218$	2944.16	0.914697
$219$	1040.88	0.321171
$220$	0	0
$221$	68.1213	0.0207346
$222$	3151.06	0.952635
$223$	5256.47	1.57847	0.789235	−	0.614091i	$-0.210477\pi$
$223$	5256.47	1.57847	0.789235	+	0.614091i	$0.210477\pi$
$224$	834.533	0.248927
$225$	506.008	0.149928
$226$	252.961	0.0744545
$227$	2786.28	0.814677	0.407338	−	0.913277i	$-0.366457\pi$
$227$	2786.28	0.814677	0.407338	+	0.913277i	$0.366457\pi$
$228$	2171.17	0.630655
$229$	4482.59	1.29353	0.646763	−	0.762691i	$-0.276122\pi$
$229$	4482.59	1.29353	0.646763	+	0.762691i	$0.276122\pi$
$230$	1577.59	0.452275
$231$	0	0
$232$	2110.67	0.597296
$233$	315.613	0.0887404	0.0443702	−	0.999015i	$-0.485872\pi$
$233$	315.613	0.0887404	0.0443702	+	0.999015i	$0.485872\pi$
$234$	−55.0490	−0.0153789
$235$	418.056	0.116047
$236$	105.134	0.0289984
$237$	1176.85	0.322551
$238$	−1088.63	−0.296493
$239$	806.382	0.218245	0.109122	−	0.994028i	$-0.465196\pi$
$239$	806.382	0.218245	0.109122	+	0.994028i	$0.465196\pi$
$240$	555.826	0.149493
$241$	−1009.91	−0.269935	−0.134967	−	0.990850i	$-0.543093\pi$
$241$	−1009.91	−0.269935	−0.134967	+	0.990850i	$0.543093\pi$
$242$	0	0
$243$	−2268.70	−0.598919
$244$	656.596	0.172272
$245$	−2717.93	−0.708743
$246$	2358.98	0.611395
$247$	411.142	0.105912
$248$	−1594.91	−0.408374
$249$	−312.802	−0.0796104
$250$	−2983.02	−0.754652
$251$	−3187.25	−0.801503	−0.400751	−	0.916187i	$-0.631251\pi$
$251$	−3187.25	−0.801503	−0.400751	+	0.916187i	$0.631251\pi$
$252$	879.724	0.219910
$253$	0	0
$254$	−2127.09	−0.525455
$255$	−725.064	−0.178060
$256$	256.000	0.0625000
$257$	2543.39	0.617325	0.308662	−	0.951172i	$-0.400119\pi$
$257$	2543.39	0.617325	0.308662	+	0.951172i	$0.400119\pi$
$258$	3344.23	0.806987
$259$	−9535.67	−2.28771
$260$	105.254	0.0251060
$261$	2224.97	0.527672
$262$	3050.09	0.719217
$263$	2992.29	0.701568	0.350784	−	0.936456i	$-0.385915\pi$
$263$	2992.29	0.701568	0.350784	+	0.936456i	$0.385915\pi$
$264$	0	0
$265$	3325.83	0.770960
$266$	−6570.36	−1.51449
$267$	5148.02	1.17998
$268$	1107.84	0.252508
$269$	−821.328	−0.186161	−0.0930804	−	0.995659i	$-0.529671\pi$
$269$	−821.328	−0.186161	−0.0930804	+	0.995659i	$0.529671\pi$
$270$	2461.84	0.554899
$271$	6439.74	1.44349	0.721746	−	0.692158i	$-0.243340\pi$
$271$	6439.74	1.44349	0.721746	+	0.692158i	$0.243340\pi$
$272$	−333.947	−0.0744430
$273$	−366.765	−0.0813100
$274$	4157.66	0.916692
$275$	0	0
$276$	−1686.33	−0.367772
$277$	514.466	0.111593	0.0557965	−	0.998442i	$-0.482230\pi$
$277$	514.466	0.111593	0.0557965	+	0.998442i	$0.482230\pi$
$278$	−3014.89	−0.650436
$279$	−1681.28	−0.360772
$280$	−1682.03	−0.359002
$281$	7758.68	1.64713	0.823566	−	0.567220i	$-0.191981\pi$
$281$	7758.68	1.64713	0.823566	+	0.567220i	$0.191981\pi$
$282$	−446.871	−0.0943644
$283$	−5847.37	−1.22823	−0.614116	−	0.789215i	$-0.710487\pi$
$283$	−5847.37	−1.22823	−0.614116	+	0.789215i	$0.710487\pi$
$284$	−2067.72	−0.432030
$285$	−4376.08	−0.909532
$286$	0	0
$287$	−7138.71	−1.46824
$288$	269.863	0.0552147
$289$	−4477.37	−0.911332
$290$	−4254.14	−0.861420
$291$	−6306.66	−1.27046
$292$	−966.259	−0.193651
$293$	−8074.49	−1.60996	−0.804978	−	0.593305i	$-0.797823\pi$
$293$	−8074.49	−1.60996	−0.804978	+	0.593305i	$0.797823\pi$
$294$	2905.26	0.576321
$295$	−211.901	−0.0418215
$296$	−2925.15	−0.574394
$297$	0	0
$298$	859.695	0.167117
$299$	−319.330	−0.0617637
$300$	1034.17	0.199026
$301$	−10120.2	−1.93794
$302$	−1783.36	−0.339805
$303$	3878.43	0.735346
$304$	−2015.51	−0.380256
$305$	−1323.39	−0.248450
$306$	−352.030	−0.0657655
$307$	−4210.64	−0.782781	−0.391391	−	0.920225i	$-0.628006\pi$
$307$	−4210.64	−0.782781	−0.391391	+	0.920225i	$0.628006\pi$
$308$	0	0
$309$	1797.36	0.330900
$310$	3214.60	0.588958
$311$	−1318.85	−0.240468	−0.120234	−	0.992746i	$-0.538364\pi$
$311$	−1318.85	−0.240468	−0.120234	+	0.992746i	$0.538364\pi$
$312$	−112.508	−0.0204152
$313$	−4206.15	−0.759571	−0.379785	−	0.925075i	$-0.624002\pi$
$313$	−4206.15	−0.759571	−0.379785	+	0.925075i	$0.624002\pi$
$314$	−1082.06	−0.194472
$315$	−1773.12	−0.317155
$316$	−1092.48	−0.194483
$317$	−2463.10	−0.436409	−0.218204	−	0.975903i	$-0.570020\pi$
$317$	−2463.10	−0.436409	−0.218204	+	0.975903i	$0.570020\pi$
$318$	−3555.07	−0.626913
$319$	0	0
$320$	−515.977	−0.0901376
$321$	−4655.30	−0.809450
$322$	5103.14	0.883189
$323$	2629.20	0.452918
$324$	−1720.74	−0.295051
$325$	195.835	0.0334245
$326$	5855.19	0.994751
$327$	6343.08	1.07270
$328$	−2189.86	−0.368642
$329$	1352.31	0.226612
$330$	0	0
$331$	−3332.42	−0.553373	−0.276687	−	0.960960i	$-0.589236\pi$
$331$	−3332.42	−0.553373	−0.276687	+	0.960960i	$0.589236\pi$
$332$	290.376	0.0480014
$333$	−3083.55	−0.507440
$334$	−3480.46	−0.570187
$335$	−2232.90	−0.364168
$336$	1797.97	0.291926
$337$	8323.48	1.34543	0.672714	−	0.739903i	$-0.265129\pi$
$337$	8323.48	1.34543	0.672714	+	0.739903i	$0.265129\pi$
$338$	4372.69	0.703678
$339$	544.995	0.0873158
$340$	673.082	0.107362
$341$	0	0
$342$	−2124.66	−0.335931
$343$	153.291	0.0241311
$344$	−3104.47	−0.486575
$345$	3398.86	0.530401
$346$	581.603	0.0903675
$347$	3622.50	0.560420	0.280210	−	0.959939i	$-0.409596\pi$
$347$	3622.50	0.560420	0.280210	+	0.959939i	$0.409596\pi$
$348$	4547.36	0.700472
$349$	2086.66	0.320047	0.160023	−	0.987113i	$-0.448843\pi$
$349$	2086.66	0.320047	0.160023	+	0.987113i	$0.448843\pi$
$350$	−3129.59	−0.477953
$351$	−498.316	−0.0757782
$352$	0	0
$353$	7582.15	1.14322	0.571611	−	0.820525i	$-0.306319\pi$
$353$	7582.15	1.14322	0.571611	+	0.820525i	$0.306319\pi$
$354$	226.506	0.0340075
$355$	4167.56	0.623074
$356$	−4778.94	−0.711470
$357$	−2345.41	−0.347709
$358$	−5200.65	−0.767773
$359$	4532.99	0.666413	0.333206	−	0.942854i	$-0.391869\pi$
$359$	4532.99	0.666413	0.333206	+	0.942854i	$0.391869\pi$
$360$	−543.919	−0.0796306
$361$	9009.36	1.31351
$362$	−3711.66	−0.538896
$363$	0	0
$364$	340.471	0.0490261
$365$	1947.53	0.279283
$366$	1414.61	0.202030
$367$	−2893.05	−0.411488	−0.205744	−	0.978606i	$-0.565961\pi$
$367$	−2893.05	−0.411488	−0.205744	+	0.978606i	$0.565961\pi$
$368$	1565.43	0.221749
$369$	−2308.44	−0.325672
$370$	5895.74	0.828392
$371$	10758.3	1.50550
$372$	−3436.17	−0.478916
$373$	−3389.46	−0.470508	−0.235254	−	0.971934i	$-0.575592\pi$
$373$	−3389.46	−0.470508	−0.235254	+	0.971934i	$0.575592\pi$
$374$	0	0
$375$	−6426.80	−0.885010
$376$	414.833	0.0568973
$377$	861.108	0.117637
$378$	7963.47	1.08359
$379$	8063.43	1.09285	0.546426	−	0.837508i	$-0.315988\pi$
$379$	8063.43	1.09285	0.546426	+	0.837508i	$0.315988\pi$
$380$	4062.34	0.548405
$381$	−4582.73	−0.616221
$382$	−3064.31	−0.410429
$383$	5254.51	0.701026	0.350513	−	0.936558i	$-0.386007\pi$
$383$	5254.51	0.701026	0.350513	+	0.936558i	$0.386007\pi$
$384$	551.542	0.0732962
$385$	0	0
$386$	−2103.15	−0.277325
$387$	−3272.58	−0.429857
$388$	5854.51	0.766026
$389$	−11334.5	−1.47733	−0.738666	−	0.674071i	$-0.764544\pi$
$389$	−11334.5	−1.47733	−0.738666	+	0.674071i	$0.764544\pi$
$390$	226.765	0.0294428
$391$	−2042.07	−0.264123
$392$	−2696.98	−0.347495
$393$	6571.29	0.843454
$394$	3155.54	0.403486
$395$	2201.93	0.280484
$396$	0	0
$397$	9896.10	1.25106	0.625530	−	0.780200i	$-0.284883\pi$
$397$	9896.10	1.25106	0.625530	+	0.780200i	$0.284883\pi$
$398$	−7521.05	−0.947227
$399$	−14155.6	−1.77610
$400$	−960.028	−0.120004
$401$	−14853.7	−1.84978	−0.924888	−	0.380239i	$-0.875842\pi$
$401$	−14853.7	−1.84978	−0.924888	+	0.380239i	$0.875842\pi$
$402$	2386.80	0.296127
$403$	−650.687	−0.0804293
$404$	−3600.37	−0.443379
$405$	3468.21	0.425523
$406$	−13761.1	−1.68215
$407$	0	0
$408$	−719.474	−0.0873022
$409$	8342.08	1.00853	0.504265	−	0.863549i	$-0.331763\pi$
$409$	8342.08	1.00853	0.504265	+	0.863549i	$0.331763\pi$
$410$	4413.74	0.531656
$411$	8957.52	1.07504
$412$	−1668.50	−0.199517
$413$	−685.449	−0.0816676
$414$	1650.20	0.195901
$415$	−585.263	−0.0692276
$416$	104.442	0.0123094
$417$	−6495.46	−0.762791
$418$	0	0
$419$	−13082.4	−1.52534	−0.762670	−	0.646788i	$-0.776112\pi$
$419$	−13082.4	−1.52534	−0.762670	+	0.646788i	$0.776112\pi$
$420$	−3623.87	−0.421016
$421$	−5555.51	−0.643133	−0.321567	−	0.946887i	$-0.604209\pi$
$421$	−5555.51	−0.643133	−0.321567	+	0.946887i	$0.604209\pi$
$422$	−2841.16	−0.327738
$423$	437.297	0.0502650
$424$	3300.20	0.377999
$425$	1252.34	0.142935
$426$	−4454.82	−0.506659
$427$	−4280.87	−0.485165
$428$	4321.55	0.488060
$429$	0	0
$430$	6257.18	0.701739
$431$	−359.818	−0.0402130	−0.0201065	−	0.999798i	$-0.506401\pi$
$431$	−359.818	−0.0402130	−0.0201065	+	0.999798i	$0.506401\pi$
$432$	2442.86	0.272065
$433$	14968.3	1.66127	0.830634	−	0.556819i	$-0.187978\pi$
$433$	14968.3	1.66127	0.830634	+	0.556819i	$0.187978\pi$
$434$	10398.5	1.15010
$435$	−9165.38	−1.01022
$436$	−5888.33	−0.646789
$437$	−12324.8	−1.34914
$438$	−2081.77	−0.227102
$439$	15893.9	1.72796	0.863979	−	0.503527i	$-0.167965\pi$
$439$	15893.9	1.72796	0.863979	+	0.503527i	$0.167965\pi$
$440$	0	0
$441$	−2843.02	−0.306989
$442$	−136.243	−0.0146615
$443$	−2628.46	−0.281900	−0.140950	−	0.990017i	$-0.545016\pi$
$443$	−2628.46	−0.281900	−0.140950	+	0.990017i	$0.545016\pi$
$444$	−6302.11	−0.673615
$445$	9632.13	1.02608
$446$	−10512.9	−1.11615
$447$	1852.18	0.195984
$448$	−1669.07	−0.176018
$449$	−1297.47	−0.136373	−0.0681865	−	0.997673i	$-0.521721\pi$
$449$	−1297.47	−0.136373	−0.0681865	+	0.997673i	$0.521721\pi$
$450$	−1012.02	−0.106015
$451$	0	0
$452$	−505.922	−0.0526473
$453$	−3842.18	−0.398502
$454$	−5572.55	−0.576063
$455$	−686.231	−0.0707055
$456$	−4342.35	−0.445941
$457$	2251.96	0.230508	0.115254	−	0.993336i	$-0.463232\pi$
$457$	2251.96	0.230508	0.115254	+	0.993336i	$0.463232\pi$
$458$	−8965.17	−0.914662
$459$	−3186.66	−0.324054
$460$	−3155.18	−0.319807
$461$	16772.0	1.69447	0.847233	−	0.531222i	$-0.178267\pi$
$461$	16772.0	1.69447	0.847233	+	0.531222i	$0.178267\pi$
$462$	0	0
$463$	7726.06	0.775509	0.387754	−	0.921763i	$-0.373251\pi$
$463$	7726.06	0.775509	0.387754	+	0.921763i	$0.373251\pi$
$464$	−4221.35	−0.422352
$465$	6925.72	0.690694
$466$	−631.227	−0.0627489
$467$	−7555.52	−0.748668	−0.374334	−	0.927294i	$-0.622129\pi$
$467$	−7555.52	−0.748668	−0.374334	+	0.927294i	$0.622129\pi$
$468$	110.098	0.0108745
$469$	−7222.90	−0.711135
$470$	−836.111	−0.0820573
$471$	−2331.26	−0.228065
$472$	−210.267	−0.0205049
$473$	0	0
$474$	−2353.70	−0.228078
$475$	7558.40	0.730112
$476$	2177.26	0.209652
$477$	3478.91	0.333938
$478$	−1612.76	−0.154322
$479$	13342.6	1.27273	0.636367	−	0.771387i	$-0.280437\pi$
$479$	13342.6	1.27273	0.636367	+	0.771387i	$0.280437\pi$
$480$	−1111.65	−0.105708
$481$	−1193.39	−0.113127
$482$	2019.83	0.190873
$483$	10994.5	1.03575
$484$	0	0
$485$	−11800.0	−1.10476
$486$	4537.40	0.423499
$487$	18820.1	1.75117	0.875584	−	0.483066i	$-0.160477\pi$
$487$	18820.1	1.75117	0.875584	+	0.483066i	$0.160477\pi$
$488$	−1313.19	−0.121814
$489$	12614.8	1.16658
$490$	5435.86	0.501157
$491$	3139.16	0.288530	0.144265	−	0.989539i	$-0.453918\pi$
$491$	3139.16	0.288530	0.144265	+	0.989539i	$0.453918\pi$
$492$	−4717.96	−0.432322
$493$	5506.66	0.503058
$494$	−822.285	−0.0748914
$495$	0	0
$496$	3189.82	0.288764
$497$	13481.1	1.21672
$498$	625.603	0.0562931
$499$	−5575.30	−0.500170	−0.250085	−	0.968224i	$-0.580459\pi$
$499$	−5575.30	−0.500170	−0.250085	+	0.968224i	$0.580459\pi$
$500$	5966.05	0.533619
$501$	−7498.52	−0.668681
$502$	6374.49	0.566748
$503$	2359.08	0.209117	0.104559	−	0.994519i	$-0.466657\pi$
$503$	2359.08	0.209117	0.104559	+	0.994519i	$0.466657\pi$
$504$	−1759.45	−0.155500
$505$	7256.68	0.639442
$506$	0	0
$507$	9420.79	0.825231
$508$	4254.18	0.371552
$509$	−7623.13	−0.663829	−0.331915	−	0.943309i	$-0.607695\pi$
$509$	−7623.13	−0.663829	−0.331915	+	0.943309i	$0.607695\pi$
$510$	1450.13	0.125907
$511$	6299.80	0.545376
$512$	−512.000	−0.0441942
$513$	−19232.9	−1.65527
$514$	−5086.78	−0.436514
$515$	3362.93	0.287744
$516$	−6688.46	−0.570626
$517$	0	0
$518$	19071.3	1.61766
$519$	1253.04	0.105978
$520$	−210.507	−0.0177526
$521$	20944.8	1.76125	0.880623	−	0.473818i	$-0.157125\pi$
$521$	20944.8	1.76125	0.880623	+	0.473818i	$0.157125\pi$
$522$	−4449.94	−0.373120
$523$	−5979.83	−0.499962	−0.249981	−	0.968251i	$-0.580424\pi$
$523$	−5979.83	−0.499962	−0.249981	+	0.968251i	$0.580424\pi$
$524$	−6100.17	−0.508563
$525$	−6742.58	−0.560515
$526$	−5984.58	−0.496084
$527$	−4161.05	−0.343943
$528$	0	0
$529$	−2594.45	−0.213237
$530$	−6651.67	−0.545151
$531$	−221.654	−0.0181148
$532$	13140.7	1.07091
$533$	−893.413	−0.0726042
$534$	−10296.0	−0.834369
$535$	−8710.23	−0.703881
$536$	−2215.68	−0.178550
$537$	−11204.6	−0.900398
$538$	1642.66	0.131636
$539$	0	0
$540$	−4923.68	−0.392373
$541$	−8452.29	−0.671705	−0.335852	−	0.941915i	$-0.609024\pi$
$541$	−8452.29	−0.671705	−0.335852	+	0.941915i	$0.609024\pi$
$542$	−12879.5	−1.02070
$543$	−7996.62	−0.631985
$544$	667.893	0.0526391
$545$	11868.1	0.932799
$546$	733.530	0.0574949
$547$	1216.63	0.0950995	0.0475498	−	0.998869i	$-0.484859\pi$
$547$	1216.63	0.0950995	0.0475498	+	0.998869i	$0.484859\pi$
$548$	−8315.33	−0.648199
$549$	−1384.30	−0.107615
$550$	0	0
$551$	33235.1	2.56963
$552$	3372.66	0.260054
$553$	7122.73	0.547720
$554$	−1028.93	−0.0789082
$555$	12702.1	0.971488
$556$	6029.78	0.459927
$557$	6620.02	0.503589	0.251795	−	0.967781i	$-0.418979\pi$
$557$	6620.02	0.503589	0.251795	+	0.967781i	$0.418979\pi$
$558$	3362.55	0.255104
$559$	−1266.55	−0.0958310
$560$	3364.06	0.253853
$561$	0	0
$562$	−15517.4	−1.16470
$563$	971.347	0.0727129	0.0363565	−	0.999339i	$-0.488425\pi$
$563$	971.347	0.0727129	0.0363565	+	0.999339i	$0.488425\pi$
$564$	893.741	0.0667257
$565$	1019.70	0.0759280
$566$	11694.7	0.868492
$567$	11218.8	0.830947
$568$	4135.44	0.305491
$569$	4202.74	0.309645	0.154823	−	0.987942i	$-0.450519\pi$
$569$	4202.74	0.309645	0.154823	+	0.987942i	$0.450519\pi$
$570$	8752.16	0.643136
$571$	−11418.5	−0.836862	−0.418431	−	0.908248i	$-0.637420\pi$
$571$	−11418.5	−0.836862	−0.418431	+	0.908248i	$0.637420\pi$
$572$	0	0
$573$	−6601.93	−0.481326
$574$	14277.4	1.03820
$575$	−5870.54	−0.425771
$576$	−539.726	−0.0390427
$577$	−1453.97	−0.104904	−0.0524518	−	0.998623i	$-0.516704\pi$
$577$	−1453.97	−0.104904	−0.0524518	+	0.998623i	$0.516704\pi$
$578$	8954.75	0.644409
$579$	−4531.15	−0.325230
$580$	8508.28	0.609116
$581$	−1893.19	−0.135185
$582$	12613.3	0.898348
$583$	0	0
$584$	1932.52	0.136932
$585$	−221.907	−0.0156833
$586$	16149.0	1.13841
$587$	9754.51	0.685880	0.342940	−	0.939357i	$-0.388577\pi$
$587$	9754.51	0.685880	0.342940	+	0.939357i	$0.388577\pi$
$588$	−5810.53	−0.407521
$589$	−25113.8	−1.75687
$590$	423.801	0.0295722
$591$	6798.48	0.473184
$592$	5850.29	0.406158
$593$	−22963.3	−1.59020	−0.795102	−	0.606476i	$-0.792583\pi$
$593$	−22963.3	−1.59020	−0.795102	+	0.606476i	$0.792583\pi$
$594$	0	0
$595$	−4388.35	−0.302361
$596$	−1719.39	−0.118169
$597$	−16203.8	−1.11085
$598$	638.660	0.0436735
$599$	9988.67	0.681345	0.340673	−	0.940182i	$-0.389345\pi$
$599$	9988.67	0.681345	0.340673	+	0.940182i	$0.389345\pi$
$600$	−2068.34	−0.140733
$601$	−473.946	−0.0321675	−0.0160837	−	0.999871i	$-0.505120\pi$
$601$	−473.946	−0.0321675	−0.0160837	+	0.999871i	$0.505120\pi$
$602$	20240.5	1.37033
$603$	−2335.67	−0.157738
$604$	3566.73	0.240278
$605$	0	0
$606$	−7756.86	−0.519968
$607$	−3994.04	−0.267073	−0.133536	−	0.991044i	$-0.542633\pi$
$607$	−3994.04	−0.267073	−0.133536	+	0.991044i	$0.542633\pi$
$608$	4031.03	0.268881
$609$	−29647.8	−1.97273
$610$	2646.79	0.175681
$611$	169.243	0.0112059
$612$	704.061	0.0465032
$613$	10552.2	0.695270	0.347635	−	0.937630i	$-0.386985\pi$
$613$	10552.2	0.695270	0.347635	+	0.937630i	$0.386985\pi$
$614$	8421.28	0.553510
$615$	9509.23	0.623494
$616$	0	0
$617$	−14598.0	−0.952500	−0.476250	−	0.879310i	$-0.658004\pi$
$617$	−14598.0	−0.952500	−0.476250	+	0.879310i	$0.658004\pi$
$618$	−3594.72	−0.233982
$619$	−13995.3	−0.908752	−0.454376	−	0.890810i	$-0.650138\pi$
$619$	−13995.3	−0.908752	−0.454376	+	0.890810i	$0.650138\pi$
$620$	−6429.19	−0.416456
$621$	14938.0	0.965285
$622$	2637.71	0.170036
$623$	31157.7	2.00370
$624$	225.017	0.0144357
$625$	−4524.57	−0.289572
$626$	8412.30	0.537097
$627$	0	0
$628$	2164.12	0.137513
$629$	−7631.59	−0.483770
$630$	3546.23	0.224262
$631$	−8163.63	−0.515038	−0.257519	−	0.966273i	$-0.582905\pi$
$631$	−8163.63	−0.515038	−0.257519	+	0.966273i	$0.582905\pi$
$632$	2184.96	0.137521
$633$	−6121.17	−0.384352
$634$	4926.20	0.308587
$635$	−8574.45	−0.535853
$636$	7110.14	0.443294
$637$	−1100.31	−0.0684391
$638$	0	0
$639$	4359.38	0.269882
$640$	1031.95	0.0637369
$641$	17660.4	1.08821	0.544105	−	0.839017i	$-0.316869\pi$
$641$	17660.4	1.08821	0.544105	+	0.839017i	$0.316869\pi$
$642$	9310.59	0.572367
$643$	−18030.1	−1.10581	−0.552907	−	0.833243i	$-0.686482\pi$
$643$	−18030.1	−1.10581	−0.552907	+	0.833243i	$0.686482\pi$
$644$	−10206.3	−0.624509
$645$	13480.8	0.822957
$646$	−5258.39	−0.320261
$647$	9871.78	0.599845	0.299922	−	0.953964i	$-0.403039\pi$
$647$	9871.78	0.599845	0.299922	+	0.953964i	$0.403039\pi$
$648$	3441.47	0.208632
$649$	0	0
$650$	−391.670	−0.0236347
$651$	22403.1	1.34876
$652$	−11710.4	−0.703395
$653$	9962.52	0.597034	0.298517	−	0.954404i	$-0.403508\pi$
$653$	9962.52	0.597034	0.298517	+	0.954404i	$0.403508\pi$
$654$	−12686.2	−0.758514
$655$	12295.1	0.733451
$656$	4379.72	0.260670
$657$	2037.17	0.120970
$658$	−2704.62	−0.160239
$659$	−15778.5	−0.932692	−0.466346	−	0.884602i	$-0.654430\pi$
$659$	−15778.5	−0.932692	−0.466346	+	0.884602i	$0.654430\pi$
$660$	0	0
$661$	9698.70	0.570704	0.285352	−	0.958423i	$-0.407889\pi$
$661$	9698.70	0.570704	0.285352	+	0.958423i	$0.407889\pi$
$662$	6664.85	0.391294
$663$	−293.529	−0.0171942
$664$	−580.752	−0.0339421
$665$	−26485.6	−1.54446
$666$	6167.10	0.358814
$667$	−25813.4	−1.49850
$668$	6960.93	0.403183
$669$	−22649.7	−1.30895
$670$	4465.79	0.257506
$671$	0	0
$672$	−3595.93	−0.206423
$673$	−27028.8	−1.54812	−0.774058	−	0.633115i	$-0.781776\pi$
$673$	−27028.8	−1.54812	−0.774058	+	0.633115i	$0.781776\pi$
$674$	−16647.0	−0.951361
$675$	−9161.00	−0.522381
$676$	−8745.39	−0.497576
$677$	3475.64	0.197311	0.0986555	−	0.995122i	$-0.468546\pi$
$677$	3475.64	0.197311	0.0986555	+	0.995122i	$0.468546\pi$
$678$	−1089.99	−0.0617416
$679$	−38170.2	−2.15735
$680$	−1346.16	−0.0759162
$681$	−12005.8	−0.675572
$682$	0	0
$683$	−2691.57	−0.150790	−0.0753952	−	0.997154i	$-0.524022\pi$
$683$	−2691.57	−0.150790	−0.0753952	+	0.997154i	$0.524022\pi$
$684$	4249.32	0.237539
$685$	16759.8	0.934833
$686$	−306.583	−0.0170632
$687$	−19315.1	−1.07266
$688$	6208.94	0.344061
$689$	1346.41	0.0744470
$690$	−6797.71	−0.375050
$691$	7178.64	0.395207	0.197604	−	0.980282i	$-0.436684\pi$
$691$	7178.64	0.395207	0.197604	+	0.980282i	$0.436684\pi$
$692$	−1163.21	−0.0638995
$693$	0	0
$694$	−7244.99	−0.396277
$695$	−12153.2	−0.663308
$696$	−9094.73	−0.495308
$697$	−5713.25	−0.310480
$698$	−4173.32	−0.226307
$699$	−1359.95	−0.0735882
$700$	6259.18	0.337964
$701$	4109.27	0.221405	0.110703	−	0.993854i	$-0.464690\pi$
$701$	4109.27	0.221405	0.110703	+	0.993854i	$0.464690\pi$
$702$	996.633	0.0535833
$703$	−46060.0	−2.47110
$704$	0	0
$705$	−1801.37	−0.0962319
$706$	−15164.3	−0.808380
$707$	23473.7	1.24868
$708$	−453.012	−0.0240469
$709$	−16036.5	−0.849456	−0.424728	−	0.905321i	$-0.639630\pi$
$709$	−16036.5	−0.849456	−0.424728	+	0.905321i	$0.639630\pi$
$710$	−8335.13	−0.440580
$711$	2303.28	0.121490
$712$	9557.88	0.503085
$713$	19505.6	1.02453
$714$	4690.82	0.245868
$715$	0	0
$716$	10401.3	0.542898
$717$	−3474.64	−0.180980
$718$	−9065.98	−0.471225
$719$	−36813.7	−1.90949	−0.954743	−	0.297432i	$-0.903870\pi$
$719$	−36813.7	−1.90949	−0.954743	+	0.297432i	$0.903870\pi$
$720$	1087.84	0.0563074
$721$	10878.3	0.561898
$722$	−18018.7	−0.928791
$723$	4351.64	0.223844
$724$	7423.31	0.381057
$725$	15830.5	0.810939
$726$	0	0
$727$	−21685.1	−1.10627	−0.553133	−	0.833093i	$-0.686568\pi$
$727$	−21685.1	−1.10627	−0.553133	+	0.833093i	$0.686568\pi$
$728$	−680.941	−0.0346667
$729$	21390.6	1.08676
$730$	−3895.06	−0.197483
$731$	−8099.44	−0.409806
$732$	−2829.22	−0.142856
$733$	24131.3	1.21598	0.607988	−	0.793946i	$-0.291977\pi$
$733$	24131.3	1.21598	0.607988	+	0.793946i	$0.291977\pi$
$734$	5786.11	0.290966
$735$	11711.3	0.587727
$736$	−3130.86	−0.156800
$737$	0	0
$738$	4616.89	0.230285
$739$	−36063.3	−1.79514	−0.897570	−	0.440872i	$-0.854669\pi$
$739$	−36063.3	−1.79514	−0.897570	+	0.440872i	$0.854669\pi$
$740$	−11791.5	−0.585762
$741$	−1771.58	−0.0878281
$742$	−21516.6	−1.06455
$743$	14060.8	0.694268	0.347134	−	0.937816i	$-0.387155\pi$
$743$	14060.8	0.694268	0.347134	+	0.937816i	$0.387155\pi$
$744$	6872.33	0.338645
$745$	3465.49	0.170424
$746$	6778.92	0.332699
$747$	−612.201	−0.0299856
$748$	0	0
$749$	−28175.6	−1.37452
$750$	12853.6	0.625796
$751$	−28942.9	−1.40632	−0.703158	−	0.711034i	$-0.748227\pi$
$751$	−28942.9	−1.40632	−0.703158	+	0.711034i	$0.748227\pi$
$752$	−829.666	−0.0402325
$753$	13733.6	0.664648
$754$	−1722.22	−0.0831822
$755$	−7188.87	−0.346529
$756$	−15926.9	−0.766213
$757$	−21622.7	−1.03817	−0.519083	−	0.854724i	$-0.673726\pi$
$757$	−21622.7	−1.03817	−0.519083	+	0.854724i	$0.673726\pi$
$758$	−16126.9	−0.772763
$759$	0	0
$760$	−8124.69	−0.387781
$761$	21593.7	1.02861	0.514305	−	0.857607i	$-0.328050\pi$
$761$	21593.7	1.02861	0.514305	+	0.857607i	$0.328050\pi$
$762$	9165.46	0.435734
$763$	38390.7	1.82154
$764$	6128.62	0.290217
$765$	−1419.06	−0.0670670
$766$	−10509.0	−0.495700
$767$	−85.7843	−0.00403845
$768$	−1103.08	−0.0518282
$769$	30161.8	1.41439	0.707194	−	0.707020i	$-0.249961\pi$
$769$	30161.8	1.41439	0.707194	+	0.707020i	$0.249961\pi$
$770$	0	0
$771$	−10959.3	−0.511918
$772$	4206.30	0.196099
$773$	31010.7	1.44292	0.721461	−	0.692455i	$-0.243471\pi$
$773$	31010.7	1.44292	0.721461	+	0.692455i	$0.243471\pi$
$774$	6545.17	0.303955
$775$	−11962.2	−0.554443
$776$	−11709.0	−0.541662
$777$	41088.4	1.89709
$778$	22669.0	1.04463
$779$	−34482.0	−1.58594
$780$	−453.529	−0.0208192
$781$	0	0
$782$	4084.14	0.186763
$783$	−40281.9	−1.83852
$784$	5393.95	0.245716
$785$	−4361.87	−0.198321
$786$	−13142.6	−0.596412
$787$	−19518.7	−0.884072	−0.442036	−	0.896997i	$-0.645744\pi$
$787$	−19518.7	−0.884072	−0.442036	+	0.896997i	$0.645744\pi$
$788$	−6311.07	−0.285308
$789$	−12893.5	−0.581777
$790$	−4403.86	−0.198332
$791$	3298.51	0.148270
$792$	0	0
$793$	−535.753	−0.0239913
$794$	−19792.2	−0.884633
$795$	−14330.7	−0.639320
$796$	15042.1	0.669791
$797$	21887.8	0.972781	0.486391	−	0.873741i	$-0.338313\pi$
$797$	21887.8	0.972781	0.486391	+	0.873741i	$0.338313\pi$
$798$	28311.2	1.25590
$799$	1082.28	0.0479204
$800$	1920.06	0.0848553
$801$	10075.5	0.444443
$802$	29707.5	1.30799
$803$	0	0
$804$	−4773.60	−0.209393
$805$	20571.1	0.900667
$806$	1301.37	0.0568721
$807$	3539.04	0.154374
$808$	7200.75	0.313517
$809$	−37165.5	−1.61517	−0.807584	−	0.589752i	$-0.799225\pi$
$809$	−37165.5	−1.61517	−0.807584	+	0.589752i	$0.799225\pi$
$810$	−6936.42	−0.300890
$811$	28558.8	1.23654	0.618272	−	0.785965i	$-0.287833\pi$
$811$	28558.8	1.23654	0.618272	+	0.785965i	$0.287833\pi$
$812$	27522.3	1.18946
$813$	−27748.3	−1.19702
$814$	0	0
$815$	23602.7	1.01444
$816$	1438.95	0.0617320
$817$	−48883.7	−2.09330
$818$	−16684.2	−0.713139
$819$	−717.815	−0.0306258
$820$	−8827.48	−0.375938
$821$	6293.15	0.267518	0.133759	−	0.991014i	$-0.457295\pi$
$821$	6293.15	0.267518	0.133759	+	0.991014i	$0.457295\pi$
$822$	−17915.0	−0.760168
$823$	14939.0	0.632733	0.316367	−	0.948637i	$-0.397537\pi$
$823$	14939.0	0.632733	0.316367	+	0.948637i	$0.397537\pi$
$824$	3337.00	0.141080
$825$	0	0
$826$	1370.90	0.0577477
$827$	34659.0	1.45733	0.728665	−	0.684870i	$-0.240141\pi$
$827$	34659.0	1.45733	0.728665	+	0.684870i	$0.240141\pi$
$828$	−3300.40	−0.138523
$829$	−29323.7	−1.22853	−0.614266	−	0.789099i	$-0.710548\pi$
$829$	−29323.7	−1.22853	−0.614266	+	0.789099i	$0.710548\pi$
$830$	1170.53	0.0489513
$831$	−2216.79	−0.0925387
$832$	−208.884	−0.00870405
$833$	−7036.30	−0.292669
$834$	12990.9	0.539375
$835$	−14030.0	−0.581471
$836$	0	0
$837$	30438.6	1.25700
$838$	26164.8	1.07858
$839$	5888.98	0.242324	0.121162	−	0.992633i	$-0.461338\pi$
$839$	5888.98	0.242324	0.121162	+	0.992633i	$0.461338\pi$
$840$	7247.74	0.297703
$841$	45219.5	1.85410
$842$	11111.0	0.454764
$843$	−33431.5	−1.36589
$844$	5682.32	0.231746
$845$	17626.7	0.717604
$846$	−874.594	−0.0355428
$847$	0	0
$848$	−6600.39	−0.267286
$849$	25195.8	1.01851
$850$	−2504.67	−0.101070
$851$	35774.3	1.44104
$852$	8909.63	0.358262
$853$	38138.0	1.53085	0.765427	−	0.643522i	$-0.222528\pi$
$853$	38138.0	1.53085	0.765427	+	0.643522i	$0.222528\pi$
$854$	8561.73	0.343064
$855$	−8564.66	−0.342579
$856$	−8643.09	−0.345111
$857$	12704.1	0.506377	0.253188	−	0.967417i	$-0.418521\pi$
$857$	12704.1	0.506377	0.253188	+	0.967417i	$0.418521\pi$
$858$	0	0
$859$	−11123.7	−0.441833	−0.220916	−	0.975293i	$-0.570905\pi$
$859$	−11123.7	−0.441833	−0.220916	+	0.975293i	$0.570905\pi$
$860$	−12514.4	−0.496205
$861$	30760.1	1.21754
$862$	719.636	0.0284349
$863$	−13680.5	−0.539617	−0.269808	−	0.962914i	$-0.586960\pi$
$863$	−13680.5	−0.539617	−0.269808	+	0.962914i	$0.586960\pi$
$864$	−4885.72	−0.192379
$865$	2344.48	0.0921559
$866$	−29936.5	−1.17469
$867$	19292.6	0.755724
$868$	−20796.9	−0.813242
$869$	0	0
$870$	18330.8	0.714334
$871$	−903.950	−0.0351655
$872$	11776.7	0.457349
$873$	−12343.1	−0.478523
$874$	24649.6	0.953988
$875$	−38897.4	−1.50282
$876$	4163.53	0.160585
$877$	45407.1	1.74833	0.874166	−	0.485627i	$-0.161409\pi$
$877$	45407.1	1.74833	0.874166	+	0.485627i	$0.161409\pi$
$878$	−31787.8	−1.22185
$879$	34792.3	1.33506
$880$	0	0
$881$	13620.9	0.520884	0.260442	−	0.965490i	$-0.416132\pi$
$881$	13620.9	0.520884	0.260442	+	0.965490i	$0.416132\pi$
$882$	5686.05	0.217074
$883$	−7945.73	−0.302826	−0.151413	−	0.988471i	$-0.548382\pi$
$883$	−7945.73	−0.302826	−0.151413	+	0.988471i	$0.548382\pi$
$884$	272.485	0.0103673
$885$	913.063	0.0346805
$886$	5256.91	0.199333
$887$	−41541.1	−1.57251	−0.786253	−	0.617904i	$-0.787982\pi$
$887$	−41541.1	−1.57251	−0.786253	+	0.617904i	$0.787982\pi$
$888$	12604.2	0.476318
$889$	−27736.3	−1.04640
$890$	−19264.3	−0.725550
$891$	0	0
$892$	21025.9	0.789235
$893$	6532.05	0.244778
$894$	−3704.36	−0.138582
$895$	−20964.2	−0.782968
$896$	3338.13	0.124463
$897$	1375.97	0.0512177
$898$	2594.94	0.0964303
$899$	−52598.9	−1.95136
$900$	2024.03	0.0749641
$901$	8610.07	0.318361
$902$	0	0
$903$	43607.3	1.60704
$904$	1011.84	0.0372273
$905$	−14962.0	−0.549561
$906$	7684.37	0.281784
$907$	43231.1	1.58265	0.791326	−	0.611394i	$-0.209391\pi$
$907$	43231.1	1.58265	0.791326	+	0.611394i	$0.209391\pi$
$908$	11145.1	0.407338
$909$	7590.68	0.276971
$910$	1372.46	0.0499963
$911$	−33500.8	−1.21837	−0.609183	−	0.793030i	$-0.708503\pi$
$911$	−33500.8	−1.21837	−0.609183	+	0.793030i	$0.708503\pi$
$912$	8684.69	0.315328
$913$	0	0
$914$	−4503.92	−0.162994
$915$	5702.40	0.206028
$916$	17930.3	0.646763
$917$	39771.8	1.43226
$918$	6373.32	0.229141
$919$	18900.5	0.678421	0.339211	−	0.940710i	$-0.389840\pi$
$919$	18900.5	0.678421	0.339211	+	0.940710i	$0.389840\pi$
$920$	6310.37	0.226138
$921$	18143.3	0.649123
$922$	−33544.0	−1.19817
$923$	1687.17	0.0601665
$924$	0	0
$925$	−21939.3	−0.779847
$926$	−15452.1	−0.548367
$927$	3517.71	0.124635
$928$	8442.70	0.298648
$929$	29149.2	1.02944	0.514722	−	0.857357i	$-0.327895\pi$
$929$	29149.2	1.02944	0.514722	+	0.857357i	$0.327895\pi$
$930$	−13851.4	−0.488394
$931$	−42467.2	−1.49496
$932$	1262.45	0.0443702
$933$	5682.84	0.199408
$934$	15111.0	0.529388
$935$	0	0
$936$	−220.196	−0.00768946
$937$	−32193.0	−1.12241	−0.561205	−	0.827677i	$-0.689662\pi$
$937$	−32193.0	−1.12241	−0.561205	+	0.827677i	$0.689662\pi$
$938$	14445.8	0.502849
$939$	18124.0	0.629875
$940$	1672.22	0.0580233
$941$	37395.9	1.29550	0.647752	−	0.761851i	$-0.275709\pi$
$941$	37395.9	1.29550	0.647752	+	0.761851i	$0.275709\pi$
$942$	4662.52	0.161267
$943$	26781.8	0.924852
$944$	420.534	0.0144992
$945$	32101.3	1.10503
$946$	0	0
$947$	3065.34	0.105185	0.0525925	−	0.998616i	$-0.483252\pi$
$947$	3065.34	0.105185	0.0525925	+	0.998616i	$0.483252\pi$
$948$	4707.40	0.161276
$949$	788.424	0.0269687
$950$	−15116.8	−0.516267
$951$	10613.3	0.361893
$952$	−4354.52	−0.148247
$953$	16385.4	0.556953	0.278476	−	0.960443i	$-0.410171\pi$
$953$	16385.4	0.556953	0.278476	+	0.960443i	$0.410171\pi$
$954$	−6957.81	−0.236129
$955$	−12352.5	−0.418551
$956$	3225.53	0.109122
$957$	0	0
$958$	−26685.2	−0.899958
$959$	54214.2	1.82551
$960$	2223.31	0.0747467
$961$	9954.82	0.334155
$962$	2386.79	0.0799929
$963$	−9111.13	−0.304883
$964$	−4039.65	−0.134967
$965$	−8477.95	−0.282813
$966$	−21989.0	−0.732386
$967$	16183.5	0.538187	0.269094	−	0.963114i	$-0.413276\pi$
$967$	16183.5	0.538187	0.269094	+	0.963114i	$0.413276\pi$
$968$	0	0
$969$	−11329.0	−0.375583
$970$	23600.0	0.781185
$971$	4694.04	0.155138	0.0775690	−	0.996987i	$-0.475284\pi$
$971$	4694.04	0.155138	0.0775690	+	0.996987i	$0.475284\pi$
$972$	−9074.80	−0.299459
$973$	−39312.9	−1.29529
$974$	−37640.1	−1.23826
$975$	−843.837	−0.0277174
$976$	2626.38	0.0861358
$977$	−7663.58	−0.250952	−0.125476	−	0.992097i	$-0.540046\pi$
$977$	−7663.58	−0.250952	−0.125476	+	0.992097i	$0.540046\pi$
$978$	−25229.5	−0.824899
$979$	0	0
$980$	−10871.7	−0.354372
$981$	12414.4	0.404038
$982$	−6278.33	−0.204022
$983$	37397.3	1.21342	0.606708	−	0.794925i	$-0.292490\pi$
$983$	37397.3	1.21342	0.606708	+	0.794925i	$0.292490\pi$
$984$	9435.93	0.305697
$985$	12720.2	0.411471
$986$	−11013.3	−0.355716
$987$	−5827.00	−0.187918
$988$	1644.57	0.0529562
$989$	37967.5	1.22072
$990$	0	0
$991$	15536.1	0.498002	0.249001	−	0.968503i	$-0.419898\pi$
$991$	15536.1	0.498002	0.249001	+	0.968503i	$0.419898\pi$
$992$	−6379.63	−0.204187
$993$	14359.1	0.458886
$994$	−26962.2	−0.860350
$995$	−30317.9	−0.965973
$996$	−1251.21	−0.0398052
$997$	−41167.8	−1.30772	−0.653860	−	0.756615i	$-0.726852\pi$
$997$	−41167.8	−1.30772	−0.653860	+	0.756615i	$0.726852\pi$
$998$	11150.6	0.353674
$999$	55826.0	1.76803

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.4.a.n.1.2		4
3.2	odd	2		2178.4.a.by.1.4		4
4.3	odd	2		1936.4.a.bn.1.3		4
11.2	odd	10		242.4.c.q.81.1		8
11.3	even	5		242.4.c.r.9.2		8
11.4	even	5		242.4.c.r.27.2		8
11.5	even	5		22.4.c.b.3.1	✓	8
11.6	odd	10		242.4.c.q.3.1		8
11.7	odd	10		242.4.c.n.27.2		8
11.8	odd	10		242.4.c.n.9.2		8
11.9	even	5		22.4.c.b.15.1	yes	8
11.10	odd	2		242.4.a.o.1.2		4
33.5	odd	10		198.4.f.d.91.1		8
33.20	odd	10		198.4.f.d.37.1		8
33.32	even	2		2178.4.a.bt.1.4		4
44.27	odd	10		176.4.m.b.113.2		8
44.31	odd	10		176.4.m.b.81.2		8
44.43	even	2		1936.4.a.bm.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.4.c.b.3.1	✓	8	11.5	even	5
22.4.c.b.15.1	yes	8	11.9	even	5
176.4.m.b.81.2		8	44.31	odd	10
176.4.m.b.113.2		8	44.27	odd	10
198.4.f.d.37.1		8	33.20	odd	10
198.4.f.d.91.1		8	33.5	odd	10
242.4.a.n.1.2		4	1.1	even	1	trivial
242.4.a.o.1.2		4	11.10	odd	2
242.4.c.n.9.2		8	11.8	odd	10
242.4.c.n.27.2		8	11.7	odd	10
242.4.c.q.3.1		8	11.6	odd	10
242.4.c.q.81.1		8	11.2	odd	10
242.4.c.r.9.2		8	11.3	even	5
242.4.c.r.27.2		8	11.4	even	5
1936.4.a.bm.1.3		4	44.43	even	2
1936.4.a.bn.1.3		4	4.3	odd	2
2178.4.a.bt.1.4		4	33.32	even	2
2178.4.a.by.1.4		4	3.2	odd	2

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:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	242.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -4.30892 q^{3} +4.00000 q^{4} -8.06215 q^{5} +8.61784 q^{6} -26.0792 q^{7} -8.00000 q^{8} -8.43321 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -4.30892 q^{3} +4.00000 q^{4} -8.06215 q^{5} +8.61784 q^{6} -26.0792 q^{7} -8.00000 q^{8} -8.43321 q^{9} +16.1243 q^{10} -17.2357 q^{12} -3.26382 q^{13} +52.1583 q^{14} +34.7391 q^{15} +16.0000 q^{16} -20.8717 q^{17} +16.8664 q^{18} -125.970 q^{19} -32.2486 q^{20} +112.373 q^{21} +97.8394 q^{23} +34.4714 q^{24} -60.0018 q^{25} +6.52764 q^{26} +152.679 q^{27} -104.317 q^{28} -263.834 q^{29} -69.4783 q^{30} +199.364 q^{31} -32.0000 q^{32} +41.7433 q^{34} +210.254 q^{35} -33.7329 q^{36} +365.643 q^{37} +251.939 q^{38} +14.0635 q^{39} +64.4972 q^{40} +273.732 q^{41} -224.746 q^{42} +388.059 q^{43} +67.9898 q^{45} -195.679 q^{46} -51.8541 q^{47} -68.9427 q^{48} +337.122 q^{49} +120.004 q^{50} +89.9343 q^{51} -13.0553 q^{52} -412.524 q^{53} -305.358 q^{54} +208.633 q^{56} +542.793 q^{57} +527.669 q^{58} +26.2834 q^{59} +138.957 q^{60} +164.149 q^{61} -398.727 q^{62} +219.931 q^{63} +64.0000 q^{64} +26.3134 q^{65} +276.961 q^{67} -83.4866 q^{68} -421.582 q^{69} -420.508 q^{70} -516.930 q^{71} +67.4657 q^{72} -241.565 q^{73} -731.287 q^{74} +258.543 q^{75} -503.879 q^{76} -28.1271 q^{78} -273.120 q^{79} -128.994 q^{80} -430.184 q^{81} -547.465 q^{82} +72.5940 q^{83} +449.492 q^{84} +168.270 q^{85} -776.118 q^{86} +1136.84 q^{87} -1194.73 q^{89} -135.980 q^{90} +85.1177 q^{91} +391.358 q^{92} -859.041 q^{93} +103.708 q^{94} +1015.59 q^{95} +137.885 q^{96} +1463.63 q^{97} -674.244 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} + 4 q^{3} + 16 q^{4} + 25 q^{5} - 8 q^{6} - 3 q^{7} - 32 q^{8} + 102 q^{9}+O(q^{10}) \) 4 * q - 8 * q^2 + 4 * q^3 + 16 * q^4 + 25 * q^5 - 8 * q^6 - 3 * q^7 - 32 * q^8 + 102 * q^9	\( 4 q - 8 q^{2} + 4 q^{3} + 16 q^{4} + 25 q^{5} - 8 q^{6} - 3 q^{7} - 32 q^{8} + 102 q^{9} - 50 q^{10} + 16 q^{12} + 41 q^{13} + 6 q^{14} + 68 q^{15} + 64 q^{16} - 52 q^{17} - 204 q^{18} - 16 q^{19} + 100 q^{20} - 25 q^{21} + 314 q^{23} - 32 q^{24} - 21 q^{25} - 82 q^{26} + 286 q^{27} - 12 q^{28} - 561 q^{29} - 136 q^{30} + 199 q^{31} - 128 q^{32} + 104 q^{34} + 714 q^{35} + 408 q^{36} + 357 q^{37} + 32 q^{38} + 1038 q^{39} - 200 q^{40} - 32 q^{41} + 50 q^{42} + 721 q^{43} + 1326 q^{45} - 628 q^{46} + 403 q^{47} + 64 q^{48} + 823 q^{49} + 42 q^{50} + 174 q^{51} + 164 q^{52} - 133 q^{53} - 572 q^{54} + 24 q^{56} + 1031 q^{57} + 1122 q^{58} + 1016 q^{59} + 272 q^{60} + 919 q^{61} - 398 q^{62} + 1367 q^{63} + 256 q^{64} - 69 q^{65} + 289 q^{67} - 208 q^{68} - 1620 q^{69} - 1428 q^{70} - 1205 q^{71} - 816 q^{72} + 1234 q^{73} - 714 q^{74} - 911 q^{75} - 64 q^{76} - 2076 q^{78} + 603 q^{79} + 400 q^{80} - 1400 q^{81} + 64 q^{82} - 1514 q^{83} - 100 q^{84} - 717 q^{85} - 1442 q^{86} + 1061 q^{87} - 1101 q^{89} - 2652 q^{90} - 2306 q^{91} + 1256 q^{92} - 2298 q^{93} - 806 q^{94} + 1766 q^{95} - 128 q^{96} + 2116 q^{97} - 1646 q^{98}+O(q^{100}) \) 4 * q - 8 * q^2 + 4 * q^3 + 16 * q^4 + 25 * q^5 - 8 * q^6 - 3 * q^7 - 32 * q^8 + 102 * q^9 - 50 * q^10 + 16 * q^12 + 41 * q^13 + 6 * q^14 + 68 * q^15 + 64 * q^16 - 52 * q^17 - 204 * q^18 - 16 * q^19 + 100 * q^20 - 25 * q^21 + 314 * q^23 - 32 * q^24 - 21 * q^25 - 82 * q^26 + 286 * q^27 - 12 * q^28 - 561 * q^29 - 136 * q^30 + 199 * q^31 - 128 * q^32 + 104 * q^34 + 714 * q^35 + 408 * q^36 + 357 * q^37 + 32 * q^38 + 1038 * q^39 - 200 * q^40 - 32 * q^41 + 50 * q^42 + 721 * q^43 + 1326 * q^45 - 628 * q^46 + 403 * q^47 + 64 * q^48 + 823 * q^49 + 42 * q^50 + 174 * q^51 + 164 * q^52 - 133 * q^53 - 572 * q^54 + 24 * q^56 + 1031 * q^57 + 1122 * q^58 + 1016 * q^59 + 272 * q^60 + 919 * q^61 - 398 * q^62 + 1367 * q^63 + 256 * q^64 - 69 * q^65 + 289 * q^67 - 208 * q^68 - 1620 * q^69 - 1428 * q^70 - 1205 * q^71 - 816 * q^72 + 1234 * q^73 - 714 * q^74 - 911 * q^75 - 64 * q^76 - 2076 * q^78 + 603 * q^79 + 400 * q^80 - 1400 * q^81 + 64 * q^82 - 1514 * q^83 - 100 * q^84 - 717 * q^85 - 1442 * q^86 + 1061 * q^87 - 1101 * q^89 - 2652 * q^90 - 2306 * q^91 + 1256 * q^92 - 2298 * q^93 - 806 * q^94 + 1766 * q^95 - 128 * q^96 + 2116 * q^97 - 1646 * q^98

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