LMFDB - Embedded newform 983.4.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,4,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, 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("983.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	983.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:	$57.9988775356$
Analytic rank:	$0$
Dimension:	$136$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.81837 q^{2} +2.07447 q^{3} +15.2167 q^{4} +4.44379 q^{5} -9.99556 q^{6} -32.3361 q^{7} -34.7726 q^{8} -22.6966 q^{9} +O(q^{10})$	\(q-4.81837 q^{2} +2.07447 q^{3} +15.2167 q^{4} +4.44379 q^{5} -9.99556 q^{6} -32.3361 q^{7} -34.7726 q^{8} -22.6966 q^{9} -21.4118 q^{10} -27.3550 q^{11} +31.5665 q^{12} +10.2416 q^{13} +155.807 q^{14} +9.21850 q^{15} +45.8139 q^{16} -108.332 q^{17} +109.360 q^{18} -104.490 q^{19} +67.6197 q^{20} -67.0803 q^{21} +131.806 q^{22} -107.662 q^{23} -72.1348 q^{24} -105.253 q^{25} -49.3478 q^{26} -103.094 q^{27} -492.048 q^{28} +19.4976 q^{29} -44.4181 q^{30} -264.988 q^{31} +57.4326 q^{32} -56.7471 q^{33} +521.983 q^{34} -143.695 q^{35} -345.367 q^{36} +202.813 q^{37} +503.469 q^{38} +21.2459 q^{39} -154.522 q^{40} +107.071 q^{41} +323.217 q^{42} +28.9091 q^{43} -416.252 q^{44} -100.859 q^{45} +518.756 q^{46} +311.693 q^{47} +95.0396 q^{48} +702.624 q^{49} +507.147 q^{50} -224.731 q^{51} +155.843 q^{52} -113.443 q^{53} +496.745 q^{54} -121.560 q^{55} +1124.41 q^{56} -216.760 q^{57} -93.9467 q^{58} -360.072 q^{59} +140.275 q^{60} +772.798 q^{61} +1276.81 q^{62} +733.919 q^{63} -643.243 q^{64} +45.5115 q^{65} +273.428 q^{66} -871.666 q^{67} -1648.45 q^{68} -223.342 q^{69} +692.375 q^{70} +370.859 q^{71} +789.220 q^{72} +203.492 q^{73} -977.228 q^{74} -218.344 q^{75} -1589.98 q^{76} +884.553 q^{77} -102.370 q^{78} -554.585 q^{79} +203.587 q^{80} +398.942 q^{81} -515.909 q^{82} -762.763 q^{83} -1020.74 q^{84} -481.404 q^{85} -139.295 q^{86} +40.4472 q^{87} +951.204 q^{88} -765.763 q^{89} +485.975 q^{90} -331.173 q^{91} -1638.26 q^{92} -549.709 q^{93} -1501.85 q^{94} -464.329 q^{95} +119.142 q^{96} +1068.66 q^{97} -3385.50 q^{98} +620.864 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9}+O(q^{10}) $ 136 * q + 17 * q^2 + 25 * q^3 + 601 * q^4 + 50 * q^5 + 61 * q^6 + 223 * q^7 + 207 * q^8 + 1443 * q^9	\( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9} + 257 q^{10} + 204 q^{11} + 296 q^{12} + 530 q^{13} + 103 q^{14} + 226 q^{15} + 2737 q^{16} + 664 q^{17} + 949 q^{18} + 421 q^{19} + 500 q^{20} + 684 q^{21} + 905 q^{22} + 617 q^{23} + 917 q^{24} + 5430 q^{25} + 572 q^{26} + 886 q^{27} + 2728 q^{28} + 688 q^{29} + 712 q^{30} + 1019 q^{31} + 2363 q^{32} + 1764 q^{33} + 1260 q^{34} + 834 q^{35} + 7190 q^{36} + 3303 q^{37} + 384 q^{38} + 1950 q^{39} + 2766 q^{40} + 1975 q^{41} + 448 q^{42} + 3021 q^{43} + 2038 q^{44} + 2266 q^{45} + 2742 q^{46} + 1293 q^{47} + 2589 q^{48} + 10447 q^{49} + 2191 q^{50} + 1032 q^{51} + 4983 q^{52} + 2415 q^{53} + 1878 q^{54} + 2612 q^{55} + 1540 q^{56} + 7908 q^{57} + 5743 q^{58} + 1059 q^{59} + 2611 q^{60} + 4312 q^{61} + 3258 q^{62} + 5605 q^{63} + 13735 q^{64} + 3554 q^{65} + 433 q^{66} + 5715 q^{67} + 5881 q^{68} + 1398 q^{69} + 4287 q^{70} + 2530 q^{71} + 9891 q^{72} + 14106 q^{73} + 2318 q^{74} + 2621 q^{75} + 4651 q^{76} + 4750 q^{77} + 6639 q^{78} + 4791 q^{79} + 4812 q^{80} + 19932 q^{81} + 5380 q^{82} + 4284 q^{83} + 9282 q^{84} + 12058 q^{85} + 2451 q^{86} + 6984 q^{87} + 11197 q^{88} + 5313 q^{89} + 5405 q^{90} + 6298 q^{91} + 6588 q^{92} + 5700 q^{93} + 4743 q^{94} + 5778 q^{95} + 9613 q^{96} + 15382 q^{97} + 6640 q^{98} + 8542 q^{99}+O(q^{100}) \) 136 * q + 17 * q^2 + 25 * q^3 + 601 * q^4 + 50 * q^5 + 61 * q^6 + 223 * q^7 + 207 * q^8 + 1443 * q^9 + 257 * q^10 + 204 * q^11 + 296 * q^12 + 530 * q^13 + 103 * q^14 + 226 * q^15 + 2737 * q^16 + 664 * q^17 + 949 * q^18 + 421 * q^19 + 500 * q^20 + 684 * q^21 + 905 * q^22 + 617 * q^23 + 917 * q^24 + 5430 * q^25 + 572 * q^26 + 886 * q^27 + 2728 * q^28 + 688 * q^29 + 712 * q^30 + 1019 * q^31 + 2363 * q^32 + 1764 * q^33 + 1260 * q^34 + 834 * q^35 + 7190 * q^36 + 3303 * q^37 + 384 * q^38 + 1950 * q^39 + 2766 * q^40 + 1975 * q^41 + 448 * q^42 + 3021 * q^43 + 2038 * q^44 + 2266 * q^45 + 2742 * q^46 + 1293 * q^47 + 2589 * q^48 + 10447 * q^49 + 2191 * q^50 + 1032 * q^51 + 4983 * q^52 + 2415 * q^53 + 1878 * q^54 + 2612 * q^55 + 1540 * q^56 + 7908 * q^57 + 5743 * q^58 + 1059 * q^59 + 2611 * q^60 + 4312 * q^61 + 3258 * q^62 + 5605 * q^63 + 13735 * q^64 + 3554 * q^65 + 433 * q^66 + 5715 * q^67 + 5881 * q^68 + 1398 * q^69 + 4287 * q^70 + 2530 * q^71 + 9891 * q^72 + 14106 * q^73 + 2318 * q^74 + 2621 * q^75 + 4651 * q^76 + 4750 * q^77 + 6639 * q^78 + 4791 * q^79 + 4812 * q^80 + 19932 * q^81 + 5380 * q^82 + 4284 * q^83 + 9282 * q^84 + 12058 * q^85 + 2451 * q^86 + 6984 * q^87 + 11197 * q^88 + 5313 * q^89 + 5405 * q^90 + 6298 * q^91 + 6588 * q^92 + 5700 * q^93 + 4743 * q^94 + 5778 * q^95 + 9613 * q^96 + 15382 * q^97 + 6640 * q^98 + 8542 * 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 $

$2$	−4.81837	−1.70355	−0.851775	−	0.523907i	$-0.824474\pi$
$2$	−4.81837	−1.70355	−0.851775	+	0.523907i	$0.824474\pi$
$3$	2.07447	0.399232	0.199616	−	0.979874i	$-0.436031\pi$
$3$	2.07447	0.399232	0.199616	+	0.979874i	$0.436031\pi$
$4$	15.2167	1.90209
$5$	4.44379	0.397464	0.198732	−	0.980054i	$-0.436318\pi$
$5$	4.44379	0.397464	0.198732	+	0.980054i	$0.436318\pi$
$6$	−9.99556	−0.680112
$7$	−32.3361	−1.74599	−0.872993	−	0.487733i	$-0.837824\pi$
$7$	−32.3361	−1.74599	−0.872993	+	0.487733i	$0.837824\pi$
$8$	−34.7726	−1.53675
$9$	−22.6966	−0.840614
$10$	−21.4118	−0.677101
$11$	−27.3550	−0.749803	−0.374902	−	0.927065i	$-0.622324\pi$
$11$	−27.3550	−0.749803	−0.374902	+	0.927065i	$0.622324\pi$
$12$	31.5665	0.759373
$13$	10.2416	0.218500	0.109250	−	0.994014i	$-0.465155\pi$
$13$	10.2416	0.218500	0.109250	+	0.994014i	$0.465155\pi$
$14$	155.807	2.97438
$15$	9.21850	0.158680
$16$	45.8139	0.715843
$17$	−108.332	−1.54555	−0.772775	−	0.634680i	$-0.781132\pi$
$17$	−108.332	−1.54555	−0.772775	+	0.634680i	$0.781132\pi$
$18$	109.360	1.43203
$19$	−104.490	−1.26166	−0.630830	−	0.775921i	$-0.717286\pi$
$19$	−104.490	−1.26166	−0.630830	+	0.775921i	$0.717286\pi$
$20$	67.6197	0.756011
$21$	−67.0803	−0.697053
$22$	131.806	1.27733
$23$	−107.662	−0.976048	−0.488024	−	0.872830i	$-0.662282\pi$
$23$	−107.662	−0.976048	−0.488024	+	0.872830i	$0.662282\pi$
$24$	−72.1348	−0.613519
$25$	−105.253	−0.842022
$26$	−49.3478	−0.372227
$27$	−103.094	−0.734832
$28$	−492.048	−3.32101
$29$	19.4976	0.124849	0.0624244	−	0.998050i	$-0.480117\pi$
$29$	19.4976	0.124849	0.0624244	+	0.998050i	$0.480117\pi$
$30$	−44.4181	−0.270320
$31$	−264.988	−1.53527	−0.767633	−	0.640890i	$-0.778565\pi$
$31$	−264.988	−1.53527	−0.767633	+	0.640890i	$0.778565\pi$
$32$	57.4326	0.317273
$33$	−56.7471	−0.299345
$34$	521.983	2.63292
$35$	−143.695	−0.693967
$36$	−345.367	−1.59892
$37$	202.813	0.901142	0.450571	−	0.892741i	$-0.351220\pi$
$37$	202.813	0.901142	0.450571	+	0.892741i	$0.351220\pi$
$38$	503.469	2.14930
$39$	21.2459	0.0872323
$40$	−154.522	−0.610803
$41$	107.071	0.407847	0.203923	−	0.978987i	$-0.434631\pi$
$41$	107.071	0.407847	0.203923	+	0.978987i	$0.434631\pi$
$42$	323.217	1.18747
$43$	28.9091	0.102526	0.0512628	−	0.998685i	$-0.483675\pi$
$43$	28.9091	0.102526	0.0512628	+	0.998685i	$0.483675\pi$
$44$	−416.252	−1.42619
$45$	−100.859	−0.334114
$46$	518.756	1.66275
$47$	311.693	0.967344	0.483672	−	0.875249i	$-0.339303\pi$
$47$	311.693	0.967344	0.483672	+	0.875249i	$0.339303\pi$
$48$	95.0396	0.285787
$49$	702.624	2.04847
$50$	507.147	1.43443
$51$	−224.731	−0.617032
$52$	155.843	0.415606
$53$	−113.443	−0.294012	−0.147006	−	0.989136i	$-0.546964\pi$
$53$	−113.443	−0.294012	−0.147006	+	0.989136i	$0.546964\pi$
$54$	496.745	1.25182
$55$	−121.560	−0.298020
$56$	1124.41	2.68314
$57$	−216.760	−0.503695
$58$	−93.9467	−0.212686
$59$	−360.072	−0.794532	−0.397266	−	0.917703i	$-0.630041\pi$
$59$	−360.072	−0.794532	−0.397266	+	0.917703i	$0.630041\pi$
$60$	140.275	0.301824
$61$	772.798	1.62208	0.811038	−	0.584993i	$-0.198903\pi$
$61$	772.798	1.62208	0.811038	+	0.584993i	$0.198903\pi$
$62$	1276.81	2.61540
$63$	733.919	1.46770
$64$	−643.243	−1.25633
$65$	45.5115	0.0868462
$66$	273.428	0.509950
$67$	−871.666	−1.58942	−0.794708	−	0.606991i	$-0.792376\pi$
$67$	−871.666	−1.58942	−0.794708	+	0.606991i	$0.792376\pi$
$68$	−1648.45	−2.93977
$69$	−223.342	−0.389670
$70$	692.375	1.18221
$71$	370.859	0.619900	0.309950	−	0.950753i	$-0.399688\pi$
$71$	370.859	0.619900	0.309950	+	0.950753i	$0.399688\pi$
$72$	789.220	1.29181
$73$	203.492	0.326259	0.163129	−	0.986605i	$-0.447841\pi$
$73$	203.492	0.326259	0.163129	+	0.986605i	$0.447841\pi$
$74$	−977.228	−1.53514
$75$	−218.344	−0.336162
$76$	−1589.98	−2.39979
$77$	884.553	1.30915
$78$	−102.370	−0.148605
$79$	−554.585	−0.789819	−0.394909	−	0.918720i	$-0.629224\pi$
$79$	−554.585	−0.789819	−0.394909	+	0.918720i	$0.629224\pi$
$80$	203.587	0.284522
$81$	398.942	0.547246
$82$	−515.909	−0.694788
$83$	−762.763	−1.00872	−0.504362	−	0.863492i	$-0.668272\pi$
$83$	−762.763	−1.00872	−0.504362	+	0.863492i	$0.668272\pi$
$84$	−1020.74	−1.32585
$85$	−481.404	−0.614301
$86$	−139.295	−0.174658
$87$	40.4472	0.0498436
$88$	951.204	1.15226
$89$	−765.763	−0.912030	−0.456015	−	0.889972i	$-0.650724\pi$
$89$	−765.763	−0.912030	−0.456015	+	0.889972i	$0.650724\pi$
$90$	485.975	0.569180
$91$	−331.173	−0.381499
$92$	−1638.26	−1.85653
$93$	−549.709	−0.612927
$94$	−1501.85	−1.64792
$95$	−464.329	−0.501465
$96$	119.142	0.126666
$97$	1068.66	1.11862	0.559309	−	0.828959i	$-0.311066\pi$
$97$	1068.66	1.11862	0.559309	+	0.828959i	$0.311066\pi$
$98$	−3385.50	−3.48967
$99$	620.864	0.630295
$100$	−1601.60	−1.60160
$101$	1397.07	1.37637	0.688186	−	0.725534i	$-0.258407\pi$
$101$	1397.07	1.37637	0.688186	+	0.725534i	$0.258407\pi$
$102$	1082.84	1.05115
$103$	1114.36	1.06603	0.533014	−	0.846106i	$-0.321059\pi$
$103$	1114.36	1.06603	0.533014	+	0.846106i	$0.321059\pi$
$104$	−356.127	−0.335780
$105$	−298.090	−0.277054
$106$	546.612	0.500864
$107$	1066.44	0.963519	0.481759	−	0.876303i	$-0.339998\pi$
$107$	1066.44	0.963519	0.481759	+	0.876303i	$0.339998\pi$
$108$	−1568.75	−1.39771
$109$	−1445.23	−1.26998	−0.634990	−	0.772521i	$-0.718996\pi$
$109$	−1445.23	−1.26998	−0.634990	+	0.772521i	$0.718996\pi$
$110$	585.720	0.507692
$111$	420.729	0.359764
$112$	−1481.44	−1.24985
$113$	−2216.57	−1.84529	−0.922644	−	0.385652i	$-0.873976\pi$
$113$	−2216.57	−1.84529	−0.922644	+	0.385652i	$0.873976\pi$
$114$	1044.43	0.858070
$115$	−478.428	−0.387945
$116$	296.689	0.237473
$117$	−232.449	−0.183675
$118$	1734.96	1.35353
$119$	3503.03	2.69851
$120$	−320.552	−0.243852
$121$	−582.705	−0.437795
$122$	−3723.63	−2.76329
$123$	222.116	0.162825
$124$	−4032.23	−2.92020
$125$	−1023.19	−0.732138
$126$	−3536.29	−2.50030
$127$	−1588.67	−1.11001	−0.555007	−	0.831846i	$-0.687284\pi$
$127$	−1588.67	−1.11001	−0.555007	+	0.831846i	$0.687284\pi$
$128$	2639.92	1.82296
$129$	59.9711	0.0409315
$130$	−219.291	−0.147947
$131$	−2257.90	−1.50590	−0.752952	−	0.658076i	$-0.771371\pi$
$131$	−2257.90	−1.50590	−0.752952	+	0.658076i	$0.771371\pi$
$132$	−863.502	−0.569380
$133$	3378.79	2.20284
$134$	4200.01	2.70765
$135$	−458.128	−0.292069
$136$	3766.98	2.37512
$137$	−1880.18	−1.17252	−0.586258	−	0.810124i	$-0.699400\pi$
$137$	−1880.18	−1.17252	−0.586258	+	0.810124i	$0.699400\pi$
$138$	1076.14	0.663822
$139$	771.727	0.470914	0.235457	−	0.971885i	$-0.424341\pi$
$139$	771.727	0.470914	0.235457	+	0.971885i	$0.424341\pi$
$140$	−2186.56	−1.31998
$141$	646.598	0.386194
$142$	−1786.94	−1.05603
$143$	−280.158	−0.163832
$144$	−1039.82	−0.601747
$145$	86.6433	0.0496230
$146$	−980.498	−0.555798
$147$	1457.57	0.817813
$148$	3086.14	1.71405
$149$	−97.7807	−0.0537618	−0.0268809	−	0.999639i	$-0.508557\pi$
$149$	−97.7807	−0.0537618	−0.0268809	+	0.999639i	$0.508557\pi$
$150$	1052.06	0.572669
$151$	2224.12	1.19865	0.599326	−	0.800505i	$-0.295435\pi$
$151$	2224.12	1.19865	0.599326	+	0.800505i	$0.295435\pi$
$152$	3633.38	1.93885
$153$	2458.76	1.29921
$154$	−4262.11	−2.23020
$155$	−1177.55	−0.610213
$156$	323.292	0.165923
$157$	2482.08	1.26173	0.630864	−	0.775894i	$-0.282701\pi$
$157$	2482.08	1.26173	0.630864	+	0.775894i	$0.282701\pi$
$158$	2672.20	1.34550
$159$	−235.335	−0.117379
$160$	255.218	0.126105
$161$	3481.38	1.70417
$162$	−1922.25	−0.932261
$163$	214.739	0.103188	0.0515940	−	0.998668i	$-0.483570\pi$
$163$	214.739	0.103188	0.0515940	+	0.998668i	$0.483570\pi$
$164$	1629.27	0.775759
$165$	−252.172	−0.118979
$166$	3675.27	1.71841
$167$	1540.39	0.713766	0.356883	−	0.934149i	$-0.383839\pi$
$167$	1540.39	0.713766	0.356883	+	0.934149i	$0.383839\pi$
$168$	2332.56	1.07119
$169$	−2092.11	−0.952258
$170$	2319.58	1.04649
$171$	2371.55	1.06057
$172$	439.901	0.195012
$173$	−1295.40	−0.569293	−0.284646	−	0.958633i	$-0.591876\pi$
$173$	−1295.40	−0.569293	−0.284646	+	0.958633i	$0.591876\pi$
$174$	−194.890	−0.0849112
$175$	3403.46	1.47016
$176$	−1253.24	−0.536741
$177$	−746.959	−0.317203
$178$	3689.73	1.55369
$179$	−2586.06	−1.07984	−0.539919	−	0.841717i	$-0.681545\pi$
$179$	−2586.06	−1.07984	−0.539919	+	0.841717i	$0.681545\pi$
$180$	−1534.74	−0.635514
$181$	2383.64	0.978867	0.489433	−	0.872041i	$-0.337204\pi$
$181$	2383.64	0.978867	0.489433	+	0.872041i	$0.337204\pi$
$182$	1595.71	0.649902
$183$	1603.15	0.647585
$184$	3743.70	1.49994
$185$	901.258	0.358172
$186$	2648.70	1.04415
$187$	2963.42	1.15886
$188$	4742.94	1.83997
$189$	3333.66	1.28301
$190$	2237.31	0.854271
$191$	−5223.74	−1.97894	−0.989468	−	0.144755i	$-0.953761\pi$
$191$	−5223.74	−1.97894	−0.989468	+	0.144755i	$0.953761\pi$
$192$	−1334.39	−0.501569
$193$	1263.89	0.471381	0.235691	−	0.971828i	$-0.424265\pi$
$193$	1263.89	0.471381	0.235691	+	0.971828i	$0.424265\pi$
$194$	−5149.20	−1.90562
$195$	94.4121	0.0346718
$196$	10691.6	3.89636
$197$	37.0378	0.0133951	0.00669755	−	0.999978i	$-0.497868\pi$
$197$	37.0378	0.0133951	0.00669755	+	0.999978i	$0.497868\pi$
$198$	−2991.55	−1.07374
$199$	−4577.49	−1.63060	−0.815301	−	0.579038i	$-0.803428\pi$
$199$	−4577.49	−1.63060	−0.815301	+	0.579038i	$0.803428\pi$
$200$	3659.92	1.29398
$201$	−1808.24	−0.634546
$202$	−6731.59	−2.34472
$203$	−630.477	−0.217984
$204$	−3419.66	−1.17365
$205$	475.802	0.162105
$206$	−5369.38	−1.81603
$207$	2443.56	0.820480
$208$	469.208	0.156412
$209$	2858.31	0.945997
$210$	1436.31	0.471975
$211$	−2767.98	−0.903109	−0.451554	−	0.892244i	$-0.649130\pi$
$211$	−2767.98	−0.903109	−0.451554	+	0.892244i	$0.649130\pi$
$212$	−1726.23	−0.559236
$213$	769.337	0.247484
$214$	−5138.50	−1.64140
$215$	128.466	0.0407503
$216$	3584.85	1.12925
$217$	8568.67	2.68055
$218$	6963.64	2.16347
$219$	422.137	0.130253
$220$	−1849.74	−0.566860
$221$	−1109.49	−0.337703
$222$	−2027.23	−0.612877
$223$	4380.21	1.31534	0.657669	−	0.753307i	$-0.271543\pi$
$223$	4380.21	1.31534	0.657669	+	0.753307i	$0.271543\pi$
$224$	−1857.15	−0.553955
$225$	2388.88	0.707815
$226$	10680.3	3.14354
$227$	−499.317	−0.145995	−0.0729974	−	0.997332i	$-0.523256\pi$
$227$	−499.317	−0.145995	−0.0729974	+	0.997332i	$0.523256\pi$
$228$	−3298.37	−0.958071
$229$	−6924.44	−1.99816	−0.999082	−	0.0428293i	$-0.986363\pi$
$229$	−6924.44	−1.99816	−0.999082	+	0.0428293i	$0.986363\pi$
$230$	2305.24	0.660883
$231$	1834.98	0.522653
$232$	−677.984	−0.191861
$233$	−4605.21	−1.29484	−0.647419	−	0.762134i	$-0.724152\pi$
$233$	−4605.21	−1.29484	−0.647419	+	0.762134i	$0.724152\pi$
$234$	1120.03	0.312899
$235$	1385.10	0.384485
$236$	−5479.10	−1.51127
$237$	−1150.47	−0.315321
$238$	−16878.9	−4.59704
$239$	589.412	0.159523	0.0797613	−	0.996814i	$-0.474584\pi$
$239$	589.412	0.159523	0.0797613	+	0.996814i	$0.474584\pi$
$240$	422.336	0.113590
$241$	5792.48	1.54824	0.774122	−	0.633037i	$-0.218192\pi$
$241$	5792.48	1.54824	0.774122	+	0.633037i	$0.218192\pi$
$242$	2807.69	0.745806
$243$	3611.13	0.953310
$244$	11759.4	3.08533
$245$	3122.31	0.814193
$246$	−1070.24	−0.277381
$247$	−1070.14	−0.275673
$248$	9214.32	2.35932
$249$	−1582.33	−0.402715
$250$	4930.13	1.24723
$251$	2452.59	0.616757	0.308378	−	0.951264i	$-0.400214\pi$
$251$	2452.59	0.616757	0.308378	+	0.951264i	$0.400214\pi$
$252$	11167.8	2.79169
$253$	2945.10	0.731844
$254$	7654.81	1.89097
$255$	−998.658	−0.245248
$256$	−7574.17	−1.84916
$257$	2042.82	0.495827	0.247914	−	0.968782i	$-0.420255\pi$
$257$	2042.82	0.495827	0.247914	+	0.968782i	$0.420255\pi$
$258$	−288.963	−0.0697289
$259$	−6558.18	−1.57338
$260$	692.533	0.165189
$261$	−442.529	−0.104950
$262$	10879.4	2.56538
$263$	5655.41	1.32596	0.662980	−	0.748637i	$-0.269291\pi$
$263$	5655.41	1.32596	0.662980	+	0.748637i	$0.269291\pi$
$264$	1973.24	0.460018
$265$	−504.118	−0.116859
$266$	−16280.2	−3.75265
$267$	−1588.55	−0.364112
$268$	−13263.9	−3.02321
$269$	1919.45	0.435060	0.217530	−	0.976054i	$-0.430200\pi$
$269$	1919.45	0.435060	0.217530	+	0.976054i	$0.430200\pi$
$270$	2207.43	0.497555
$271$	3950.16	0.885443	0.442722	−	0.896659i	$-0.354013\pi$
$271$	3950.16	0.885443	0.442722	+	0.896659i	$0.354013\pi$
$272$	−4963.11	−1.10637
$273$	−687.009	−0.152306
$274$	9059.41	1.99744
$275$	2879.19	0.631351
$276$	−3398.52	−0.741185
$277$	2534.50	0.549760	0.274880	−	0.961479i	$-0.411362\pi$
$277$	2534.50	0.549760	0.274880	+	0.961479i	$0.411362\pi$
$278$	−3718.46	−0.802225
$279$	6014.32	1.29057
$280$	4996.65	1.06645
$281$	−6717.41	−1.42608	−0.713038	−	0.701126i	$-0.752681\pi$
$281$	−6717.41	−1.42608	−0.713038	+	0.701126i	$0.752681\pi$
$282$	−3115.55	−0.657902
$283$	−5322.79	−1.11805	−0.559023	−	0.829152i	$-0.688824\pi$
$283$	−5322.79	−1.11805	−0.559023	+	0.829152i	$0.688824\pi$
$284$	5643.25	1.17910
$285$	−963.237	−0.200201
$286$	1349.91	0.279097
$287$	−3462.27	−0.712095
$288$	−1303.52	−0.266704
$289$	6822.79	1.38872
$290$	−417.479	−0.0845353
$291$	2216.90	0.446588
$292$	3096.47	0.620572
$293$	−1876.43	−0.374138	−0.187069	−	0.982347i	$-0.559899\pi$
$293$	−1876.43	−0.374138	−0.187069	+	0.982347i	$0.559899\pi$
$294$	−7023.12	−1.39319
$295$	−1600.08	−0.315798
$296$	−7052.34	−1.38483
$297$	2820.13	0.550979
$298$	471.143	0.0915859
$299$	−1102.63	−0.213267
$300$	−3322.47	−0.639409
$301$	−934.809	−0.179008
$302$	−10716.6	−2.04196
$303$	2898.18	0.549491
$304$	−4787.08	−0.903150
$305$	3434.15	0.644718
$306$	−11847.2	−2.21327
$307$	−1636.73	−0.304278	−0.152139	−	0.988359i	$-0.548616\pi$
$307$	−1636.73	−0.304278	−0.152139	+	0.988359i	$0.548616\pi$
$308$	13460.0	2.49011
$309$	2311.70	0.425592
$310$	5673.87	1.03953
$311$	4083.51	0.744548	0.372274	−	0.928123i	$-0.378578\pi$
$311$	4083.51	0.744548	0.372274	+	0.928123i	$0.378578\pi$
$312$	−738.775	−0.134054
$313$	−3583.62	−0.647151	−0.323575	−	0.946202i	$-0.604885\pi$
$313$	−3583.62	−0.647151	−0.323575	+	0.946202i	$0.604885\pi$
$314$	−11959.6	−2.14942
$315$	3261.38	0.583359
$316$	−8438.94	−1.50230
$317$	8569.46	1.51832	0.759162	−	0.650901i	$-0.225609\pi$
$317$	8569.46	1.51832	0.759162	+	0.650901i	$0.225609\pi$
$318$	1133.93	0.199961
$319$	−533.357	−0.0936121
$320$	−2858.44	−0.499348
$321$	2212.29	0.384667
$322$	−16774.6	−2.90313
$323$	11319.5	1.94996
$324$	6070.58	1.04091
$325$	−1077.96	−0.183982
$326$	−1034.69	−0.175786
$327$	−2998.08	−0.507016
$328$	−3723.15	−0.626758
$329$	−10079.0	−1.68897
$330$	1215.06	0.202687
$331$	7439.59	1.23540	0.617699	−	0.786415i	$-0.288065\pi$
$331$	7439.59	1.23540	0.617699	+	0.786415i	$0.288065\pi$
$332$	−11606.7	−1.91868
$333$	−4603.16	−0.757512
$334$	−7422.17	−1.21594
$335$	−3873.50	−0.631737
$336$	−3073.21	−0.498980
$337$	4045.38	0.653905	0.326952	−	0.945041i	$-0.393978\pi$
$337$	4045.38	0.653905	0.326952	+	0.945041i	$0.393978\pi$
$338$	10080.6	1.62222
$339$	−4598.21	−0.736698
$340$	−7325.37	−1.16845
$341$	7248.73	1.15115
$342$	−11427.0	−1.80673
$343$	−11628.8	−1.83061
$344$	−1005.25	−0.157556
$345$	−992.484	−0.154880
$346$	6241.73	0.969819
$347$	8302.78	1.28449	0.642243	−	0.766501i	$-0.278004\pi$
$347$	8302.78	1.28449	0.642243	+	0.766501i	$0.278004\pi$
$348$	615.472	0.0948069
$349$	9103.03	1.39620	0.698100	−	0.716000i	$-0.254029\pi$
$349$	9103.03	1.39620	0.698100	+	0.716000i	$0.254029\pi$
$350$	−16399.1	−2.50449
$351$	−1055.85	−0.160561
$352$	−1571.07	−0.237893
$353$	−9005.98	−1.35790	−0.678952	−	0.734183i	$-0.737566\pi$
$353$	−9005.98	−1.35790	−0.678952	+	0.734183i	$0.737566\pi$
$354$	3599.12	0.540371
$355$	1648.02	0.246388
$356$	−11652.4	−1.73476
$357$	7266.93	1.07733
$358$	12460.6	1.83956
$359$	−7892.95	−1.16037	−0.580186	−	0.814484i	$-0.697020\pi$
$359$	−7892.95	−1.16037	−0.580186	+	0.814484i	$0.697020\pi$
$360$	3507.12	0.513449
$361$	4059.06	0.591787
$362$	−11485.3	−1.66755
$363$	−1208.80	−0.174782
$364$	−5039.36	−0.725643
$365$	904.273	0.129676
$366$	−7724.55	−1.10319
$367$	−9008.05	−1.28124	−0.640622	−	0.767856i	$-0.721323\pi$
$367$	−9008.05	−1.28124	−0.640622	+	0.767856i	$0.721323\pi$
$368$	−4932.43	−0.698697
$369$	−2430.15	−0.342842
$370$	−4342.59	−0.610164
$371$	3668.32	0.513341
$372$	−8364.75	−1.16584
$373$	12636.6	1.75415	0.877073	−	0.480357i	$-0.159493\pi$
$373$	12636.6	1.75415	0.877073	+	0.480357i	$0.159493\pi$
$374$	−14278.8	−1.97417
$375$	−2122.59	−0.292293
$376$	−10838.4	−1.48656
$377$	199.687	0.0272795
$378$	−16062.8	−2.18567
$379$	5525.33	0.748858	0.374429	−	0.927256i	$-0.377839\pi$
$379$	5525.33	0.748858	0.374429	+	0.927256i	$0.377839\pi$
$380$	−7065.55	−0.953829
$381$	−3295.65	−0.443153
$382$	25169.9	3.37122
$383$	−6526.18	−0.870685	−0.435343	−	0.900265i	$-0.643373\pi$
$383$	−6526.18	−0.870685	−0.435343	+	0.900265i	$0.643373\pi$
$384$	5476.44	0.727782
$385$	3930.77	0.520339
$386$	−6089.87	−0.803022
$387$	−656.138	−0.0861845
$388$	16261.5	2.12771
$389$	−13618.5	−1.77503	−0.887513	−	0.460782i	$-0.847569\pi$
$389$	−13618.5	−1.77503	−0.887513	+	0.460782i	$0.847569\pi$
$390$	−454.912	−0.0590651
$391$	11663.2	1.50853
$392$	−24432.1	−3.14798
$393$	−4683.94	−0.601205
$394$	−178.462	−0.0228192
$395$	−2464.46	−0.313925
$396$	9447.49	1.19887
$397$	10254.0	1.29630	0.648152	−	0.761511i	$-0.275542\pi$
$397$	10254.0	1.29630	0.648152	+	0.761511i	$0.275542\pi$
$398$	22056.0	2.77781
$399$	7009.19	0.879444
$400$	−4822.04	−0.602755
$401$	−9085.04	−1.13138	−0.565692	−	0.824616i	$-0.691391\pi$
$401$	−9085.04	−1.13138	−0.565692	+	0.824616i	$0.691391\pi$
$402$	8712.79	1.08098
$403$	−2713.90	−0.335456
$404$	21258.8	2.61798
$405$	1772.81	0.217511
$406$	3037.87	0.371347
$407$	−5547.94	−0.675679
$408$	7814.49	0.948223
$409$	2130.89	0.257618	0.128809	−	0.991669i	$-0.458885\pi$
$409$	2130.89	0.257618	0.128809	+	0.991669i	$0.458885\pi$
$410$	−2292.59	−0.276153
$411$	−3900.38	−0.468106
$412$	16956.8	2.02768
$413$	11643.3	1.38724
$414$	−11774.0	−1.39773
$415$	−3389.56	−0.400932
$416$	588.201	0.0693244
$417$	1600.92	0.188004
$418$	−13772.4	−1.61155
$419$	−13799.4	−1.60894	−0.804470	−	0.593994i	$-0.797550\pi$
$419$	−13799.4	−1.60894	−0.804470	+	0.593994i	$0.797550\pi$
$420$	−4535.95	−0.526980
$421$	−5813.93	−0.673049	−0.336524	−	0.941675i	$-0.609251\pi$
$421$	−5813.93	−0.673049	−0.336524	+	0.941675i	$0.609251\pi$
$422$	13337.2	1.53849
$423$	−7074.37	−0.813163
$424$	3944.72	0.451822
$425$	11402.2	1.30139
$426$	−3706.95	−0.421601
$427$	−24989.3	−2.83212
$428$	16227.7	1.83270
$429$	−581.180	−0.0654071
$430$	−618.997	−0.0694202
$431$	−5252.94	−0.587065	−0.293533	−	0.955949i	$-0.594831\pi$
$431$	−5252.94	−0.587065	−0.293533	+	0.955949i	$0.594831\pi$
$432$	−4723.14	−0.526024
$433$	4175.69	0.463443	0.231722	−	0.972782i	$-0.425564\pi$
$433$	4175.69	0.463443	0.231722	+	0.972782i	$0.425564\pi$
$434$	−41287.0	−4.56645
$435$	179.739	0.0198111
$436$	−21991.6	−2.41561
$437$	11249.6	1.23144
$438$	−2034.01	−0.221892
$439$	−4503.74	−0.489639	−0.244820	−	0.969569i	$-0.578729\pi$
$439$	−4503.74	−0.489639	−0.244820	+	0.969569i	$0.578729\pi$
$440$	4226.95	0.457982
$441$	−15947.2	−1.72197
$442$	5345.94	0.575295
$443$	−120.416	−0.0129146	−0.00645728	−	0.999979i	$-0.502055\pi$
$443$	−120.416	−0.0129146	−0.00645728	+	0.999979i	$0.502055\pi$
$444$	6402.10	0.684303
$445$	−3402.89	−0.362500
$446$	−21105.5	−2.24075
$447$	−202.843	−0.0214634
$448$	20800.0	2.19354
$449$	−1668.66	−0.175387	−0.0876935	−	0.996148i	$-0.527950\pi$
$449$	−1668.66	−0.175387	−0.0876935	+	0.996148i	$0.527950\pi$
$450$	−11510.5	−1.20580
$451$	−2928.93	−0.305805
$452$	−33728.9	−3.50990
$453$	4613.87	0.478540
$454$	2405.89	0.248710
$455$	−1471.66	−0.151632
$456$	7537.33	0.774052
$457$	4754.98	0.486715	0.243358	−	0.969937i	$-0.421751\pi$
$457$	4754.98	0.486715	0.243358	+	0.969937i	$0.421751\pi$
$458$	33364.5	3.40398
$459$	11168.4	1.13572
$460$	−7280.08	−0.737904
$461$	−6440.49	−0.650680	−0.325340	−	0.945597i	$-0.605479\pi$
$461$	−6440.49	−0.650680	−0.325340	+	0.945597i	$0.605479\pi$
$462$	−8841.61	−0.890365
$463$	−3111.46	−0.312315	−0.156157	−	0.987732i	$-0.549911\pi$
$463$	−3111.46	−0.312315	−0.156157	+	0.987732i	$0.549911\pi$
$464$	893.263	0.0893722
$465$	−2442.79	−0.243617
$466$	22189.6	2.20582
$467$	−2035.57	−0.201702	−0.100851	−	0.994902i	$-0.532157\pi$
$467$	−2035.57	−0.201702	−0.100851	+	0.994902i	$0.532157\pi$
$468$	−3537.10	−0.349365
$469$	28186.3	2.77510
$470$	−6673.92	−0.654989
$471$	5148.99	0.503722
$472$	12520.7	1.22100
$473$	−790.809	−0.0768740
$474$	5543.39	0.537165
$475$	10997.8	1.06235
$476$	53304.5	5.13279
$477$	2574.77	0.247151
$478$	−2840.00	−0.271755
$479$	−18065.8	−1.72327	−0.861635	−	0.507528i	$-0.830559\pi$
$479$	−18065.8	−1.72327	−0.861635	+	0.507528i	$0.830559\pi$
$480$	529.443	0.0503451
$481$	2077.13	0.196900
$482$	−27910.3	−2.63751
$483$	7222.01	0.680357
$484$	−8866.84	−0.832724
$485$	4748.90	0.444611
$486$	−17399.8	−1.62401
$487$	4035.85	0.375527	0.187764	−	0.982214i	$-0.439876\pi$
$487$	4035.85	0.375527	0.187764	+	0.982214i	$0.439876\pi$
$488$	−26872.2	−2.49272
$489$	445.469	0.0411959
$490$	−15044.5	−1.38702
$491$	−8737.01	−0.803046	−0.401523	−	0.915849i	$-0.631519\pi$
$491$	−8737.01	−0.803046	−0.401523	+	0.915849i	$0.631519\pi$
$492$	3379.87	0.309708
$493$	−2112.21	−0.192960
$494$	5156.33	0.469624
$495$	2758.99	0.250520
$496$	−12140.1	−1.09901
$497$	−11992.2	−1.08234
$498$	7624.24	0.686045
$499$	5812.20	0.521423	0.260711	−	0.965417i	$-0.416043\pi$
$499$	5812.20	0.521423	0.260711	+	0.965417i	$0.416043\pi$
$500$	−15569.6	−1.39259
$501$	3195.49	0.284958
$502$	−11817.5	−1.05068
$503$	5003.87	0.443562	0.221781	−	0.975097i	$-0.428813\pi$
$503$	5003.87	0.443562	0.221781	+	0.975097i	$0.428813\pi$
$504$	−25520.3	−2.25548
$505$	6208.28	0.547059
$506$	−14190.6	−1.24673
$507$	−4340.02	−0.380172
$508$	−24174.3	−2.11134
$509$	1585.30	0.138049	0.0690246	−	0.997615i	$-0.478011\pi$
$509$	1585.30	0.138049	0.0690246	+	0.997615i	$0.478011\pi$
$510$	4811.90	0.417793
$511$	−6580.13	−0.569643
$512$	15375.8	1.32719
$513$	10772.2	0.927108
$514$	−9843.06	−0.844667
$515$	4951.97	0.423708
$516$	912.561	0.0778552
$517$	−8526.36	−0.725317
$518$	31599.7	2.68033
$519$	−2687.27	−0.227280
$520$	−1582.55	−0.133461
$521$	−10056.2	−0.845626	−0.422813	−	0.906217i	$-0.638957\pi$
$521$	−10056.2	−0.845626	−0.422813	+	0.906217i	$0.638957\pi$
$522$	2132.27	0.178787
$523$	11036.4	0.922731	0.461365	−	0.887210i	$-0.347360\pi$
$523$	11036.4	0.922731	0.461365	+	0.887210i	$0.347360\pi$
$524$	−34357.7	−2.86436
$525$	7060.38	0.586934
$526$	−27249.9	−2.25884
$527$	28706.6	2.37283
$528$	−2599.81	−0.214284
$529$	−575.860	−0.0473297
$530$	2429.03	0.199076
$531$	8172.41	0.667895
$532$	51413.9	4.18999
$533$	1096.58	0.0891147
$534$	7654.23	0.620282
$535$	4739.03	0.382965
$536$	30310.1	2.44253
$537$	−5364.70	−0.431106
$538$	−9248.62	−0.741146
$539$	−19220.3	−1.53595
$540$	−6971.19	−0.555541
$541$	3334.86	0.265022	0.132511	−	0.991182i	$-0.457696\pi$
$541$	3334.86	0.265022	0.132511	+	0.991182i	$0.457696\pi$
$542$	−19033.3	−1.50840
$543$	4944.80	0.390795
$544$	−6221.78	−0.490362
$545$	−6422.29	−0.504772
$546$	3310.26	0.259462
$547$	−19865.4	−1.55281	−0.776403	−	0.630237i	$-0.782958\pi$
$547$	−19865.4	−1.55281	−0.776403	+	0.630237i	$0.782958\pi$
$548$	−28610.1	−2.23023
$549$	−17539.9	−1.36354
$550$	−13873.0	−1.07554
$551$	−2037.30	−0.157517
$552$	7766.18	0.598824
$553$	17933.1	1.37901
$554$	−12212.2	−0.936544
$555$	1869.63	0.142994
$556$	11743.1	0.895718
$557$	−22426.0	−1.70596	−0.852981	−	0.521941i	$-0.825208\pi$
$557$	−22426.0	−1.70596	−0.852981	+	0.521941i	$0.825208\pi$
$558$	−28979.2	−2.19854
$559$	296.076	0.0224019
$560$	−6583.22	−0.496771
$561$	6147.51	0.462653
$562$	32367.0	2.42939
$563$	−13599.0	−1.01799	−0.508995	−	0.860769i	$-0.669983\pi$
$563$	−13599.0	−1.01799	−0.508995	+	0.860769i	$0.669983\pi$
$564$	9839.08	0.734575
$565$	−9849.98	−0.733437
$566$	25647.2	1.90465
$567$	−12900.2	−0.955483
$568$	−12895.8	−0.952630
$569$	−10223.3	−0.753220	−0.376610	−	0.926372i	$-0.622910\pi$
$569$	−10223.3	−0.753220	−0.376610	+	0.926372i	$0.622910\pi$
$570$	4641.23	0.341052
$571$	22415.8	1.64286	0.821428	−	0.570313i	$-0.193178\pi$
$571$	22415.8	1.64286	0.821428	+	0.570313i	$0.193178\pi$
$572$	−4263.08	−0.311623
$573$	−10836.5	−0.790054
$574$	16682.5	1.21309
$575$	11331.7	0.821854
$576$	14599.4	1.05609
$577$	−4178.53	−0.301481	−0.150740	−	0.988573i	$-0.548166\pi$
$577$	−4178.53	−0.301481	−0.150740	+	0.988573i	$0.548166\pi$
$578$	−32874.7	−2.36576
$579$	2621.89	0.188190
$580$	1318.42	0.0943872
$581$	24664.8	1.76122
$582$	−10681.9	−0.760786
$583$	3103.24	0.220451
$584$	−7075.94	−0.501377
$585$	−1032.95	−0.0730041
$586$	9041.34	0.637362
$587$	20517.8	1.44269	0.721345	−	0.692576i	$-0.243524\pi$
$587$	20517.8	1.44269	0.721345	+	0.692576i	$0.243524\pi$
$588$	22179.4	1.55555
$589$	27688.5	1.93698
$590$	7709.80	0.537978
$591$	76.8338	0.00534775
$592$	9291.66	0.645076
$593$	21010.1	1.45494	0.727471	−	0.686138i	$-0.240696\pi$
$593$	21010.1	1.45494	0.727471	+	0.686138i	$0.240696\pi$
$594$	−13588.4	−0.938621
$595$	15566.7	1.07256
$596$	−1487.90	−0.102259
$597$	−9495.86	−0.650988
$598$	5312.89	0.363311
$599$	−6321.07	−0.431172	−0.215586	−	0.976485i	$-0.569166\pi$
$599$	−6321.07	−0.431172	−0.215586	+	0.976485i	$0.569166\pi$
$600$	7592.38	0.516596
$601$	−16283.6	−1.10519	−0.552597	−	0.833449i	$-0.686363\pi$
$601$	−16283.6	−1.10519	−0.552597	+	0.833449i	$0.686363\pi$
$602$	4504.26	0.304950
$603$	19783.8	1.33609
$604$	33843.8	2.27994
$605$	−2589.42	−0.174008
$606$	−13964.5	−0.936086
$607$	−1917.29	−0.128205	−0.0641024	−	0.997943i	$-0.520418\pi$
$607$	−1917.29	−0.128205	−0.0641024	+	0.997943i	$0.520418\pi$
$608$	−6001.11	−0.400291
$609$	−1307.91	−0.0870263
$610$	−16547.0	−1.09831
$611$	3192.24	0.211365
$612$	37414.2	2.47121
$613$	17169.9	1.13130	0.565648	−	0.824647i	$-0.308626\pi$
$613$	17169.9	1.13130	0.565648	+	0.824647i	$0.308626\pi$
$614$	7886.38	0.518353
$615$	987.036	0.0647173
$616$	−30758.3	−2.01183
$617$	−6622.62	−0.432118	−0.216059	−	0.976380i	$-0.569320\pi$
$617$	−6622.62	−0.432118	−0.216059	+	0.976380i	$0.569320\pi$
$618$	−11138.6	−0.725018
$619$	−21011.1	−1.36431	−0.682154	−	0.731209i	$-0.738957\pi$
$619$	−21011.1	−1.36431	−0.682154	+	0.731209i	$0.738957\pi$
$620$	−17918.4	−1.16068
$621$	11099.3	0.717231
$622$	−19675.8	−1.26838
$623$	24761.8	1.59239
$624$	973.357	0.0624446
$625$	8609.74	0.551023
$626$	17267.2	1.10245
$627$	5929.47	0.377672
$628$	37769.0	2.39991
$629$	−21971.1	−1.39276
$630$	−15714.5	−0.993781
$631$	22937.0	1.44708	0.723540	−	0.690282i	$-0.242514\pi$
$631$	22937.0	1.44708	0.723540	+	0.690282i	$0.242514\pi$
$632$	19284.4	1.21375
$633$	−5742.10	−0.360550
$634$	−41290.8	−2.58654
$635$	−7059.72	−0.441191
$636$	−3581.01	−0.223265
$637$	7195.99	0.447591
$638$	2569.91	0.159473
$639$	−8417.24	−0.521097
$640$	11731.3	0.724560
$641$	−10911.6	−0.672359	−0.336179	−	0.941798i	$-0.609135\pi$
$641$	−10911.6	−0.672359	−0.336179	+	0.941798i	$0.609135\pi$
$642$	−10659.7	−0.655300
$643$	−16762.2	−1.02805	−0.514024	−	0.857776i	$-0.671846\pi$
$643$	−16762.2	−1.02805	−0.514024	+	0.857776i	$0.671846\pi$
$644$	52975.0	3.24147
$645$	266.499	0.0162688
$646$	−54541.8	−3.32185
$647$	3316.00	0.201492	0.100746	−	0.994912i	$-0.467877\pi$
$647$	3316.00	0.201492	0.100746	+	0.994912i	$0.467877\pi$
$648$	−13872.3	−0.840979
$649$	9849.76	0.595743
$650$	5193.99	0.313423
$651$	17775.5	1.07016
$652$	3267.61	0.196272
$653$	12886.1	0.772238	0.386119	−	0.922449i	$-0.373815\pi$
$653$	12886.1	0.772238	0.386119	+	0.922449i	$0.373815\pi$
$654$	14445.9	0.863728
$655$	−10033.6	−0.598543
$656$	4905.35	0.291954
$657$	−4618.56	−0.274258
$658$	48564.1	2.87724
$659$	21680.6	1.28158	0.640788	−	0.767718i	$-0.278608\pi$
$659$	21680.6	1.28158	0.640788	+	0.767718i	$0.278608\pi$
$660$	−3837.22	−0.226308
$661$	10287.5	0.605350	0.302675	−	0.953094i	$-0.402120\pi$
$661$	10287.5	0.605350	0.302675	+	0.953094i	$0.402120\pi$
$662$	−35846.7	−2.10456
$663$	−2301.60	−0.134822
$664$	26523.3	1.55015
$665$	15014.6	0.875551
$666$	22179.7	1.29046
$667$	−2099.16	−0.121859
$668$	23439.6	1.35764
$669$	9086.61	0.525125
$670$	18663.9	1.07620
$671$	−21139.9	−1.21624
$672$	−3852.60	−0.221156
$673$	−16862.3	−0.965813	−0.482907	−	0.875672i	$-0.660419\pi$
$673$	−16862.3	−0.965813	−0.482907	+	0.875672i	$0.660419\pi$
$674$	−19492.1	−1.11396
$675$	10850.9	0.618744
$676$	−31835.0	−1.81127
$677$	23330.0	1.32444	0.662218	−	0.749311i	$-0.269615\pi$
$677$	23330.0	1.32444	0.662218	+	0.749311i	$0.269615\pi$
$678$	22155.9	1.25500
$679$	−34556.3	−1.95309
$680$	16739.7	0.944026
$681$	−1035.82	−0.0582858
$682$	−34927.1	−1.96104
$683$	−34126.2	−1.91186	−0.955932	−	0.293588i	$-0.905151\pi$
$683$	−34126.2	−1.91186	−0.955932	+	0.293588i	$0.905151\pi$
$684$	36087.2	2.01729
$685$	−8355.13	−0.466034
$686$	56032.0	3.11853
$687$	−14364.5	−0.797731
$688$	1324.44	0.0733922
$689$	−1161.84	−0.0642418
$690$	4782.15	0.263846
$691$	10734.5	0.590968	0.295484	−	0.955348i	$-0.404519\pi$
$691$	10734.5	0.590968	0.295484	+	0.955348i	$0.404519\pi$
$692$	−19711.7	−1.08284
$693$	−20076.3	−1.10049
$694$	−40005.9	−2.18819
$695$	3429.39	0.187171
$696$	−1406.46	−0.0765971
$697$	−11599.2	−0.630347
$698$	−43861.8	−2.37850
$699$	−9553.37	−0.516941
$700$	51789.4	2.79637
$701$	23309.5	1.25590	0.627952	−	0.778252i	$-0.283893\pi$
$701$	23309.5	1.25590	0.627952	+	0.778252i	$0.283893\pi$
$702$	5087.46	0.273524
$703$	−21191.8	−1.13693
$704$	17595.9	0.942003
$705$	2873.35	0.153499
$706$	43394.1	2.31326
$707$	−45175.8	−2.40313
$708$	−11366.2	−0.603346
$709$	−15656.4	−0.829323	−0.414661	−	0.909976i	$-0.636100\pi$
$709$	−15656.4	−0.829323	−0.414661	+	0.909976i	$0.636100\pi$
$710$	−7940.77	−0.419735
$711$	12587.2	0.663933
$712$	26627.6	1.40156
$713$	28529.2	1.49849
$714$	−35014.8	−1.83529
$715$	−1244.96	−0.0651175
$716$	−39351.2	−2.05394
$717$	1222.72	0.0636865
$718$	38031.1	1.97675
$719$	−20137.0	−1.04448	−0.522242	−	0.852798i	$-0.674904\pi$
$719$	−20137.0	−1.04448	−0.522242	+	0.852798i	$0.674904\pi$
$720$	−4620.74	−0.239173
$721$	−36034.0	−1.86127
$722$	−19558.1	−1.00814
$723$	12016.3	0.618108
$724$	36271.2	1.86189
$725$	−2052.18	−0.105126
$726$	5824.47	0.297750
$727$	−18713.7	−0.954678	−0.477339	−	0.878719i	$-0.658399\pi$
$727$	−18713.7	−0.954678	−0.477339	+	0.878719i	$0.658399\pi$
$728$	11515.8	0.586267
$729$	−3280.26	−0.166654
$730$	−4357.12	−0.220910
$731$	−3131.78	−0.158458
$732$	24394.6	1.23176
$733$	−11326.6	−0.570749	−0.285375	−	0.958416i	$-0.592118\pi$
$733$	−11326.6	−0.570749	−0.285375	+	0.958416i	$0.592118\pi$
$734$	43404.1	2.18266
$735$	6477.14	0.325052
$736$	−6183.32	−0.309674
$737$	23844.4	1.19175
$738$	11709.4	0.584048
$739$	16332.6	0.812994	0.406497	−	0.913652i	$-0.366750\pi$
$739$	16332.6	0.812994	0.406497	+	0.913652i	$0.366750\pi$
$740$	13714.1	0.681273
$741$	−2219.97	−0.110058
$742$	−17675.3	−0.874502
$743$	10731.3	0.529871	0.264936	−	0.964266i	$-0.414649\pi$
$743$	10731.3	0.529871	0.264936	+	0.964266i	$0.414649\pi$
$744$	19114.8	0.941914
$745$	−434.516	−0.0213684
$746$	−60887.6	−2.98828
$747$	17312.1	0.847947
$748$	45093.3	2.20425
$749$	−34484.5	−1.68229
$750$	10227.4	0.497936
$751$	−5134.32	−0.249473	−0.124736	−	0.992190i	$-0.539808\pi$
$751$	−5134.32	−0.249473	−0.124736	+	0.992190i	$0.539808\pi$
$752$	14279.9	0.692466
$753$	5087.82	0.246229
$754$	−962.164	−0.0464721
$755$	9883.53	0.476422
$756$	50727.2	2.44039
$757$	1182.40	0.0567702	0.0283851	−	0.999597i	$-0.490964\pi$
$757$	1182.40	0.0567702	0.0283851	+	0.999597i	$0.490964\pi$
$758$	−26623.1	−1.27572
$759$	6109.51	0.292175
$760$	16146.0	0.770625
$761$	20318.0	0.967842	0.483921	−	0.875112i	$-0.339212\pi$
$761$	20318.0	0.967842	0.483921	+	0.875112i	$0.339212\pi$
$762$	15879.7	0.754934
$763$	46733.0	2.21737
$764$	−79488.0	−3.76410
$765$	10926.2	0.516390
$766$	31445.6	1.48326
$767$	−3687.71	−0.173606
$768$	−15712.4	−0.738245
$769$	−37125.9	−1.74095	−0.870476	−	0.492210i	$-0.836189\pi$
$769$	−37125.9	−1.74095	−0.870476	+	0.492210i	$0.836189\pi$
$770$	−18939.9	−0.886424
$771$	4237.77	0.197950
$772$	19232.2	0.896607
$773$	20199.8	0.939892	0.469946	−	0.882695i	$-0.344273\pi$
$773$	20199.8	0.939892	0.469946	+	0.882695i	$0.344273\pi$
$774$	3161.52	0.146820
$775$	27890.7	1.29273
$776$	−37160.1	−1.71904
$777$	−13604.7	−0.628144
$778$	65618.9	3.02385
$779$	−11187.8	−0.514564
$780$	1436.64	0.0659486
$781$	−10144.9	−0.464803
$782$	−56197.8	−2.56986
$783$	−2010.09	−0.0917429
$784$	32190.0	1.46638
$785$	11029.8	0.501492
$786$	22568.9	1.02418
$787$	26135.3	1.18377	0.591883	−	0.806024i	$-0.298385\pi$
$787$	26135.3	1.18377	0.591883	+	0.806024i	$0.298385\pi$
$788$	563.593	0.0254786
$789$	11732.0	0.529366
$790$	11874.7	0.534787
$791$	71675.3	3.22185
$792$	−21589.1	−0.968604
$793$	7914.68	0.354424
$794$	−49407.4	−2.20832
$795$	−1045.78	−0.0466540
$796$	−69654.2	−3.10154
$797$	−1793.71	−0.0797197	−0.0398599	−	0.999205i	$-0.512691\pi$
$797$	−1793.71	−0.0797197	−0.0398599	+	0.999205i	$0.512691\pi$
$798$	−33772.8	−1.49818
$799$	−33766.3	−1.49508
$800$	−6044.94	−0.267151
$801$	17380.2	0.766665
$802$	43775.1	1.92737
$803$	−5566.51	−0.244630
$804$	−27515.5	−1.20696
$805$	15470.5	0.677346
$806$	13076.6	0.571467
$807$	3981.84	0.173690
$808$	−48579.8	−2.11514
$809$	−30436.6	−1.32274	−0.661369	−	0.750061i	$-0.730024\pi$
$809$	−30436.6	−1.32274	−0.661369	+	0.750061i	$0.730024\pi$
$810$	−8542.07	−0.370541
$811$	22343.3	0.967424	0.483712	−	0.875227i	$-0.339288\pi$
$811$	22343.3	0.967424	0.483712	+	0.875227i	$0.339288\pi$
$812$	−9593.77	−0.414625
$813$	8194.49	0.353497
$814$	26732.0	1.15105
$815$	954.253	0.0410135
$816$	−10295.8	−0.441698
$817$	−3020.70	−0.129353
$818$	−10267.4	−0.438865
$819$	7516.50	0.320693
$820$	7240.12	0.308337
$821$	−7646.82	−0.325062	−0.162531	−	0.986703i	$-0.551966\pi$
$821$	−7646.82	−0.325062	−0.162531	+	0.986703i	$0.551966\pi$
$822$	18793.5	0.797442
$823$	18038.3	0.764004	0.382002	−	0.924161i	$-0.375235\pi$
$823$	18038.3	0.764004	0.382002	+	0.924161i	$0.375235\pi$
$824$	−38749.1	−1.63822
$825$	5972.78	0.252055
$826$	−56101.9	−2.36324
$827$	−27305.3	−1.14812	−0.574062	−	0.818812i	$-0.694633\pi$
$827$	−27305.3	−1.14812	−0.574062	+	0.818812i	$0.694633\pi$
$828$	37182.9	1.56062
$829$	4115.36	0.172416	0.0862078	−	0.996277i	$-0.472525\pi$
$829$	4115.36	0.172416	0.0862078	+	0.996277i	$0.472525\pi$
$830$	16332.1	0.683008
$831$	5257.75	0.219482
$832$	−6587.83	−0.274510
$833$	−76116.6	−3.16601
$834$	−7713.84	−0.320274
$835$	6845.17	0.283697
$836$	43494.0	1.79937
$837$	27318.7	1.12816
$838$	66490.7	2.74091
$839$	27440.0	1.12912	0.564561	−	0.825392i	$-0.309046\pi$
$839$	27440.0	1.12912	0.564561	+	0.825392i	$0.309046\pi$
$840$	10365.4	0.425762
$841$	−24008.8	−0.984413
$842$	28013.7	1.14657
$843$	−13935.1	−0.569335
$844$	−42119.5	−1.71779
$845$	−9296.89	−0.378489
$846$	34086.9	1.38526
$847$	18842.4	0.764384
$848$	−5197.28	−0.210466
$849$	−11042.0	−0.446360
$850$	−54940.1	−2.21698
$851$	−21835.3	−0.879558
$852$	11706.8	0.470736
$853$	−18033.9	−0.723880	−0.361940	−	0.932201i	$-0.617886\pi$
$853$	−18033.9	−0.723880	−0.361940	+	0.932201i	$0.617886\pi$
$854$	120408.	4.82466
$855$	10538.7	0.421539
$856$	−37082.9	−1.48069
$857$	−3999.71	−0.159425	−0.0797127	−	0.996818i	$-0.525400\pi$
$857$	−3999.71	−0.159425	−0.0797127	+	0.996818i	$0.525400\pi$
$858$	2800.34	0.111424
$859$	−43580.8	−1.73104	−0.865518	−	0.500879i	$-0.833010\pi$
$859$	−43580.8	−1.73104	−0.865518	+	0.500879i	$0.833010\pi$
$860$	1954.83	0.0775105
$861$	−7182.37	−0.284291
$862$	25310.6	1.00010
$863$	18620.4	0.734468	0.367234	−	0.930129i	$-0.380305\pi$
$863$	18620.4	0.734468	0.367234	+	0.930129i	$0.380305\pi$
$864$	−5920.96	−0.233143
$865$	−5756.49	−0.226274
$866$	−20120.0	−0.789499
$867$	14153.7	0.554422
$868$	130387.	5.09864
$869$	15170.7	0.592209
$870$	−866.048	−0.0337492
$871$	−8927.24	−0.347288
$872$	50254.4	1.95164
$873$	−24254.9	−0.940327
$874$	−54204.6	−2.09782
$875$	33086.1	1.27830
$876$	6423.53	0.247752
$877$	17147.7	0.660249	0.330124	−	0.943937i	$-0.392909\pi$
$877$	17147.7	0.660249	0.330124	+	0.943937i	$0.392909\pi$
$878$	21700.7	0.834125
$879$	−3892.60	−0.149368
$880$	−5569.13	−0.213336
$881$	194.738	0.00744710	0.00372355	−	0.999993i	$-0.498815\pi$
$881$	194.738	0.00744710	0.00372355	+	0.999993i	$0.498815\pi$
$882$	76839.3	2.93346
$883$	−10858.1	−0.413822	−0.206911	−	0.978360i	$-0.566341\pi$
$883$	−10858.1	−0.413822	−0.206911	+	0.978360i	$0.566341\pi$
$884$	−16882.8	−0.642340
$885$	−3319.33	−0.126077
$886$	580.210	0.0220006
$887$	28167.5	1.06626	0.533129	−	0.846034i	$-0.321016\pi$
$887$	28167.5	1.06626	0.533129	+	0.846034i	$0.321016\pi$
$888$	−14629.9	−0.552867
$889$	51371.5	1.93807
$890$	16396.4	0.617537
$891$	−10913.1	−0.410327
$892$	66652.2	2.50189
$893$	−32568.7	−1.22046
$894$	977.372	0.0365640
$895$	−11491.9	−0.429197
$896$	−85364.8	−3.18285
$897$	−2287.38	−0.0851430
$898$	8040.20	0.298781
$899$	−5166.63	−0.191676
$900$	36350.8	1.34633
$901$	12289.5	0.454410
$902$	14112.7	0.520954
$903$	−1939.23	−0.0714658
$904$	77076.1	2.83574
$905$	10592.4	0.389065
$906$	−22231.3	−0.815217
$907$	−26075.2	−0.954588	−0.477294	−	0.878744i	$-0.658382\pi$
$907$	−26075.2	−0.954588	−0.477294	+	0.878744i	$0.658382\pi$
$908$	−7597.95	−0.277695
$909$	−31708.7	−1.15700
$910$	7091.02	0.258313
$911$	4411.55	0.160440	0.0802202	−	0.996777i	$-0.474438\pi$
$911$	4411.55	0.160440	0.0802202	+	0.996777i	$0.474438\pi$
$912$	−9930.64	−0.360566
$913$	20865.4	0.756344
$914$	−22911.3	−0.829144
$915$	7124.04	0.257392
$916$	−105367.	−3.80068
$917$	73011.6	2.62929
$918$	−53813.3	−1.93475
$919$	14088.1	0.505684	0.252842	−	0.967508i	$-0.418635\pi$
$919$	14088.1	0.505684	0.252842	+	0.967508i	$0.418635\pi$
$920$	16636.2	0.596173
$921$	−3395.35	−0.121477
$922$	31032.6	1.10847
$923$	3798.19	0.135449
$924$	27922.3	0.994130
$925$	−21346.6	−0.758781
$926$	14992.2	0.532044
$927$	−25292.1	−0.896118
$928$	1119.80	0.0396112
$929$	−43269.9	−1.52814	−0.764069	−	0.645135i	$-0.776801\pi$
$929$	−43269.9	−1.52814	−0.764069	+	0.645135i	$0.776801\pi$
$930$	11770.3	0.415013
$931$	−73416.9	−2.58447
$932$	−70076.0	−2.46289
$933$	8471.11	0.297247
$934$	9808.12	0.343610
$935$	13168.8	0.460605
$936$	8082.87	0.282261
$937$	19983.3	0.696721	0.348360	−	0.937361i	$-0.386739\pi$
$937$	19983.3	0.696721	0.348360	+	0.937361i	$0.386739\pi$
$938$	−135812.	−4.72752
$939$	−7434.11	−0.258363
$940$	21076.6	0.731323
$941$	−13878.0	−0.480774	−0.240387	−	0.970677i	$-0.577274\pi$
$941$	−13878.0	−0.480774	−0.240387	+	0.970677i	$0.577274\pi$
$942$	−24809.7	−0.858116
$943$	−11527.5	−0.398078
$944$	−16496.3	−0.568760
$945$	14814.1	0.509949
$946$	3810.41	0.130959
$947$	20189.7	0.692796	0.346398	−	0.938088i	$-0.387405\pi$
$947$	20189.7	0.692796	0.346398	+	0.938088i	$0.387405\pi$
$948$	−17506.3	−0.599767
$949$	2084.08	0.0712877
$950$	−52991.5	−1.80976
$951$	17777.1	0.606163
$952$	−121810.	−4.14692
$953$	−4918.54	−0.167185	−0.0835924	−	0.996500i	$-0.526639\pi$
$953$	−4918.54	−0.167185	−0.0835924	+	0.996500i	$0.526639\pi$
$954$	−12406.2	−0.421034
$955$	−23213.2	−0.786556
$956$	8968.89	0.303425
$957$	−1106.43	−0.0373729
$958$	87047.6	2.93568
$959$	60797.8	2.04720
$960$	−5929.74	−0.199356
$961$	40427.5	1.35704
$962$	−10008.4	−0.335429
$963$	−24204.5	−0.809947
$964$	88142.4	2.94489
$965$	5616.45	0.187357
$966$	−34798.3	−1.15902
$967$	−7732.57	−0.257149	−0.128574	−	0.991700i	$-0.541040\pi$
$967$	−7732.57	−0.257149	−0.128574	+	0.991700i	$0.541040\pi$
$968$	20262.2	0.672781
$969$	23482.1	0.778485
$970$	−22882.0	−0.757418
$971$	8487.87	0.280524	0.140262	−	0.990114i	$-0.455206\pi$
$971$	8487.87	0.280524	0.140262	+	0.990114i	$0.455206\pi$
$972$	54949.4	1.81328
$973$	−24954.6	−0.822209
$974$	−19446.2	−0.639730
$975$	−2236.19	−0.0734515
$976$	35404.9	1.16115
$977$	−32413.5	−1.06141	−0.530707	−	0.847555i	$-0.678074\pi$
$977$	−32413.5	−1.06141	−0.530707	+	0.847555i	$0.678074\pi$
$978$	−2146.43	−0.0701793
$979$	20947.4	0.683843
$980$	47511.2	1.54866
$981$	32801.7	1.06756
$982$	42098.1	1.36803
$983$	−983.000	−0.0318950
$983$	−983.000	−0.0318950
$984$	−7723.56	−0.250222
$985$	164.588	0.00532408
$986$	10177.4	0.328717
$987$	−20908.5	−0.674290
$988$	−16284.0	−0.524354
$989$	−3112.42	−0.100070
$990$	−13293.8	−0.426773
$991$	−37769.5	−1.21068	−0.605342	−	0.795966i	$-0.706963\pi$
$991$	−37769.5	−1.21068	−0.605342	+	0.795966i	$0.706963\pi$
$992$	−15218.9	−0.487099
$993$	15433.2	0.493210
$994$	57782.6	1.84382
$995$	−20341.4	−0.648106
$996$	−24077.8	−0.765998
$997$	−40978.4	−1.30170	−0.650852	−	0.759205i	$-0.725588\pi$
$997$	−40978.4	−1.30170	−0.650852	+	0.759205i	$0.725588\pi$
$998$	−28005.3	−0.888270
$999$	−20908.8	−0.662187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.4.a.b.1.13	✓	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.4.a.b.1.13	✓	136	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-4.81837 q^{2} +2.07447 q^{3} +15.2167 q^{4} +4.44379 q^{5} -9.99556 q^{6} -32.3361 q^{7} -34.7726 q^{8} -22.6966 q^{9} +O(q^{10})\)	\(q-4.81837 q^{2} +2.07447 q^{3} +15.2167 q^{4} +4.44379 q^{5} -9.99556 q^{6} -32.3361 q^{7} -34.7726 q^{8} -22.6966 q^{9} -21.4118 q^{10} -27.3550 q^{11} +31.5665 q^{12} +10.2416 q^{13} +155.807 q^{14} +9.21850 q^{15} +45.8139 q^{16} -108.332 q^{17} +109.360 q^{18} -104.490 q^{19} +67.6197 q^{20} -67.0803 q^{21} +131.806 q^{22} -107.662 q^{23} -72.1348 q^{24} -105.253 q^{25} -49.3478 q^{26} -103.094 q^{27} -492.048 q^{28} +19.4976 q^{29} -44.4181 q^{30} -264.988 q^{31} +57.4326 q^{32} -56.7471 q^{33} +521.983 q^{34} -143.695 q^{35} -345.367 q^{36} +202.813 q^{37} +503.469 q^{38} +21.2459 q^{39} -154.522 q^{40} +107.071 q^{41} +323.217 q^{42} +28.9091 q^{43} -416.252 q^{44} -100.859 q^{45} +518.756 q^{46} +311.693 q^{47} +95.0396 q^{48} +702.624 q^{49} +507.147 q^{50} -224.731 q^{51} +155.843 q^{52} -113.443 q^{53} +496.745 q^{54} -121.560 q^{55} +1124.41 q^{56} -216.760 q^{57} -93.9467 q^{58} -360.072 q^{59} +140.275 q^{60} +772.798 q^{61} +1276.81 q^{62} +733.919 q^{63} -643.243 q^{64} +45.5115 q^{65} +273.428 q^{66} -871.666 q^{67} -1648.45 q^{68} -223.342 q^{69} +692.375 q^{70} +370.859 q^{71} +789.220 q^{72} +203.492 q^{73} -977.228 q^{74} -218.344 q^{75} -1589.98 q^{76} +884.553 q^{77} -102.370 q^{78} -554.585 q^{79} +203.587 q^{80} +398.942 q^{81} -515.909 q^{82} -762.763 q^{83} -1020.74 q^{84} -481.404 q^{85} -139.295 q^{86} +40.4472 q^{87} +951.204 q^{88} -765.763 q^{89} +485.975 q^{90} -331.173 q^{91} -1638.26 q^{92} -549.709 q^{93} -1501.85 q^{94} -464.329 q^{95} +119.142 q^{96} +1068.66 q^{97} -3385.50 q^{98} +620.864 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9}+O(q^{10}) \) 136 * q + 17 * q^2 + 25 * q^3 + 601 * q^4 + 50 * q^5 + 61 * q^6 + 223 * q^7 + 207 * q^8 + 1443 * q^9	\( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9} + 257 q^{10} + 204 q^{11} + 296 q^{12} + 530 q^{13} + 103 q^{14} + 226 q^{15} + 2737 q^{16} + 664 q^{17} + 949 q^{18} + 421 q^{19} + 500 q^{20} + 684 q^{21} + 905 q^{22} + 617 q^{23} + 917 q^{24} + 5430 q^{25} + 572 q^{26} + 886 q^{27} + 2728 q^{28} + 688 q^{29} + 712 q^{30} + 1019 q^{31} + 2363 q^{32} + 1764 q^{33} + 1260 q^{34} + 834 q^{35} + 7190 q^{36} + 3303 q^{37} + 384 q^{38} + 1950 q^{39} + 2766 q^{40} + 1975 q^{41} + 448 q^{42} + 3021 q^{43} + 2038 q^{44} + 2266 q^{45} + 2742 q^{46} + 1293 q^{47} + 2589 q^{48} + 10447 q^{49} + 2191 q^{50} + 1032 q^{51} + 4983 q^{52} + 2415 q^{53} + 1878 q^{54} + 2612 q^{55} + 1540 q^{56} + 7908 q^{57} + 5743 q^{58} + 1059 q^{59} + 2611 q^{60} + 4312 q^{61} + 3258 q^{62} + 5605 q^{63} + 13735 q^{64} + 3554 q^{65} + 433 q^{66} + 5715 q^{67} + 5881 q^{68} + 1398 q^{69} + 4287 q^{70} + 2530 q^{71} + 9891 q^{72} + 14106 q^{73} + 2318 q^{74} + 2621 q^{75} + 4651 q^{76} + 4750 q^{77} + 6639 q^{78} + 4791 q^{79} + 4812 q^{80} + 19932 q^{81} + 5380 q^{82} + 4284 q^{83} + 9282 q^{84} + 12058 q^{85} + 2451 q^{86} + 6984 q^{87} + 11197 q^{88} + 5313 q^{89} + 5405 q^{90} + 6298 q^{91} + 6588 q^{92} + 5700 q^{93} + 4743 q^{94} + 5778 q^{95} + 9613 q^{96} + 15382 q^{97} + 6640 q^{98} + 8542 q^{99}+O(q^{100}) \) 136 * q + 17 * q^2 + 25 * q^3 + 601 * q^4 + 50 * q^5 + 61 * q^6 + 223 * q^7 + 207 * q^8 + 1443 * q^9 + 257 * q^10 + 204 * q^11 + 296 * q^12 + 530 * q^13 + 103 * q^14 + 226 * q^15 + 2737 * q^16 + 664 * q^17 + 949 * q^18 + 421 * q^19 + 500 * q^20 + 684 * q^21 + 905 * q^22 + 617 * q^23 + 917 * q^24 + 5430 * q^25 + 572 * q^26 + 886 * q^27 + 2728 * q^28 + 688 * q^29 + 712 * q^30 + 1019 * q^31 + 2363 * q^32 + 1764 * q^33 + 1260 * q^34 + 834 * q^35 + 7190 * q^36 + 3303 * q^37 + 384 * q^38 + 1950 * q^39 + 2766 * q^40 + 1975 * q^41 + 448 * q^42 + 3021 * q^43 + 2038 * q^44 + 2266 * q^45 + 2742 * q^46 + 1293 * q^47 + 2589 * q^48 + 10447 * q^49 + 2191 * q^50 + 1032 * q^51 + 4983 * q^52 + 2415 * q^53 + 1878 * q^54 + 2612 * q^55 + 1540 * q^56 + 7908 * q^57 + 5743 * q^58 + 1059 * q^59 + 2611 * q^60 + 4312 * q^61 + 3258 * q^62 + 5605 * q^63 + 13735 * q^64 + 3554 * q^65 + 433 * q^66 + 5715 * q^67 + 5881 * q^68 + 1398 * q^69 + 4287 * q^70 + 2530 * q^71 + 9891 * q^72 + 14106 * q^73 + 2318 * q^74 + 2621 * q^75 + 4651 * q^76 + 4750 * q^77 + 6639 * q^78 + 4791 * q^79 + 4812 * q^80 + 19932 * q^81 + 5380 * q^82 + 4284 * q^83 + 9282 * q^84 + 12058 * q^85 + 2451 * q^86 + 6984 * q^87 + 11197 * q^88 + 5313 * q^89 + 5405 * q^90 + 6298 * q^91 + 6588 * q^92 + 5700 * q^93 + 4743 * q^94 + 5778 * q^95 + 9613 * q^96 + 15382 * q^97 + 6640 * q^98 + 8542 * q^99

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