LMFDB - Embedded newform 983.4.a.a.1.12

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:	$1$
Dimension:	$109$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-4.74560 q^{2} +9.89469 q^{3} +14.5207 q^{4} +10.6639 q^{5} -46.9563 q^{6} -4.53278 q^{7} -30.9447 q^{8} +70.9049 q^{9} +O(q^{10})$	\(q-4.74560 q^{2} +9.89469 q^{3} +14.5207 q^{4} +10.6639 q^{5} -46.9563 q^{6} -4.53278 q^{7} -30.9447 q^{8} +70.9049 q^{9} -50.6066 q^{10} -68.3080 q^{11} +143.678 q^{12} -5.07991 q^{13} +21.5107 q^{14} +105.516 q^{15} +30.6856 q^{16} -31.1856 q^{17} -336.487 q^{18} -157.168 q^{19} +154.847 q^{20} -44.8504 q^{21} +324.162 q^{22} -0.208252 q^{23} -306.189 q^{24} -11.2813 q^{25} +24.1072 q^{26} +434.426 q^{27} -65.8192 q^{28} -176.024 q^{29} -500.737 q^{30} +42.5920 q^{31} +101.936 q^{32} -675.887 q^{33} +147.994 q^{34} -48.3371 q^{35} +1029.59 q^{36} -26.6864 q^{37} +745.855 q^{38} -50.2641 q^{39} -329.992 q^{40} -8.33664 q^{41} +212.842 q^{42} +21.6906 q^{43} -991.881 q^{44} +756.123 q^{45} +0.988283 q^{46} -632.759 q^{47} +303.624 q^{48} -322.454 q^{49} +53.5364 q^{50} -308.572 q^{51} -73.7639 q^{52} +395.267 q^{53} -2061.61 q^{54} -728.430 q^{55} +140.266 q^{56} -1555.13 q^{57} +835.340 q^{58} -650.347 q^{59} +1532.17 q^{60} -647.768 q^{61} -202.125 q^{62} -321.396 q^{63} -729.234 q^{64} -54.1716 q^{65} +3207.49 q^{66} +85.3728 q^{67} -452.837 q^{68} -2.06059 q^{69} +229.388 q^{70} +643.680 q^{71} -2194.13 q^{72} +88.0743 q^{73} +126.643 q^{74} -111.625 q^{75} -2282.19 q^{76} +309.625 q^{77} +238.534 q^{78} -972.995 q^{79} +327.228 q^{80} +2384.08 q^{81} +39.5623 q^{82} +728.878 q^{83} -651.261 q^{84} -332.560 q^{85} -102.935 q^{86} -1741.70 q^{87} +2113.77 q^{88} +398.686 q^{89} -3588.26 q^{90} +23.0261 q^{91} -3.02397 q^{92} +421.435 q^{93} +3002.82 q^{94} -1676.02 q^{95} +1008.63 q^{96} +25.8849 q^{97} +1530.24 q^{98} -4843.38 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q - 19 q^{2} - 23 q^{3} + 385 q^{4} - 50 q^{5} - 83 q^{6} - 225 q^{7} - 225 q^{8} + 714 q^{9}+O(q^{10}) $ 109 * q - 19 * q^2 - 23 * q^3 + 385 * q^4 - 50 * q^5 - 83 * q^6 - 225 * q^7 - 225 * q^8 + 714 * q^9	\( 109 q - 19 q^{2} - 23 q^{3} + 385 q^{4} - 50 q^{5} - 83 q^{6} - 225 q^{7} - 225 q^{8} + 714 q^{9} - 243 q^{10} - 126 q^{11} - 280 q^{12} - 458 q^{13} - 177 q^{14} - 314 q^{15} + 1009 q^{16} - 594 q^{17} - 671 q^{18} - 491 q^{19} - 500 q^{20} - 660 q^{21} - 899 q^{22} - 487 q^{23} - 811 q^{24} + 705 q^{25} - 104 q^{26} - 842 q^{27} - 2648 q^{28} - 820 q^{29} - 728 q^{30} - 965 q^{31} - 1669 q^{32} - 2196 q^{33} - 508 q^{34} - 846 q^{35} + 1358 q^{36} - 3209 q^{37} - 1136 q^{38} - 1326 q^{39} - 3234 q^{40} - 1961 q^{41} - 2240 q^{42} - 2999 q^{43} - 1922 q^{44} - 2234 q^{45} - 2962 q^{46} - 1903 q^{47} - 2787 q^{48} + 1186 q^{49} - 2309 q^{50} - 2436 q^{51} - 4897 q^{52} - 1825 q^{53} - 3306 q^{54} - 2888 q^{55} - 1820 q^{56} - 6684 q^{57} - 4813 q^{58} - 1537 q^{59} - 3869 q^{60} - 2276 q^{61} - 1950 q^{62} - 6491 q^{63} - 89 q^{64} - 5546 q^{65} - 3527 q^{66} - 5005 q^{67} - 4183 q^{68} - 3018 q^{69} - 2993 q^{70} - 2014 q^{71} - 9549 q^{72} - 12904 q^{73} - 2714 q^{74} - 3379 q^{75} - 6293 q^{76} - 3258 q^{77} - 4593 q^{78} - 5005 q^{79} - 3988 q^{80} + 249 q^{81} - 5116 q^{82} - 2854 q^{83} - 4158 q^{84} - 11742 q^{85} - 2709 q^{86} - 2412 q^{87} - 10451 q^{88} - 2519 q^{89} - 8095 q^{90} - 2438 q^{91} - 6660 q^{92} - 10668 q^{93} - 4281 q^{94} - 4482 q^{95} - 6515 q^{96} - 16628 q^{97} - 5708 q^{98} - 6308 q^{99}+O(q^{100}) \) 109 * q - 19 * q^2 - 23 * q^3 + 385 * q^4 - 50 * q^5 - 83 * q^6 - 225 * q^7 - 225 * q^8 + 714 * q^9 - 243 * q^10 - 126 * q^11 - 280 * q^12 - 458 * q^13 - 177 * q^14 - 314 * q^15 + 1009 * q^16 - 594 * q^17 - 671 * q^18 - 491 * q^19 - 500 * q^20 - 660 * q^21 - 899 * q^22 - 487 * q^23 - 811 * q^24 + 705 * q^25 - 104 * q^26 - 842 * q^27 - 2648 * q^28 - 820 * q^29 - 728 * q^30 - 965 * q^31 - 1669 * q^32 - 2196 * q^33 - 508 * q^34 - 846 * q^35 + 1358 * q^36 - 3209 * q^37 - 1136 * q^38 - 1326 * q^39 - 3234 * q^40 - 1961 * q^41 - 2240 * q^42 - 2999 * q^43 - 1922 * q^44 - 2234 * q^45 - 2962 * q^46 - 1903 * q^47 - 2787 * q^48 + 1186 * q^49 - 2309 * q^50 - 2436 * q^51 - 4897 * q^52 - 1825 * q^53 - 3306 * q^54 - 2888 * q^55 - 1820 * q^56 - 6684 * q^57 - 4813 * q^58 - 1537 * q^59 - 3869 * q^60 - 2276 * q^61 - 1950 * q^62 - 6491 * q^63 - 89 * q^64 - 5546 * q^65 - 3527 * q^66 - 5005 * q^67 - 4183 * q^68 - 3018 * q^69 - 2993 * q^70 - 2014 * q^71 - 9549 * q^72 - 12904 * q^73 - 2714 * q^74 - 3379 * q^75 - 6293 * q^76 - 3258 * q^77 - 4593 * q^78 - 5005 * q^79 - 3988 * q^80 + 249 * q^81 - 5116 * q^82 - 2854 * q^83 - 4158 * q^84 - 11742 * q^85 - 2709 * q^86 - 2412 * q^87 - 10451 * q^88 - 2519 * q^89 - 8095 * q^90 - 2438 * q^91 - 6660 * q^92 - 10668 * q^93 - 4281 * q^94 - 4482 * q^95 - 6515 * q^96 - 16628 * q^97 - 5708 * q^98 - 6308 * 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 $

$2$	−4.74560	−1.67782	−0.838912	−	0.544268i	$-0.816808\pi$
$2$	−4.74560	−1.67782	−0.838912	+	0.544268i	$0.816808\pi$
$3$	9.89469	1.90423	0.952117	−	0.305733i	$-0.0989015\pi$
$3$	9.89469	1.90423	0.952117	+	0.305733i	$0.0989015\pi$
$4$	14.5207	1.81509
$5$	10.6639	0.953808	0.476904	−	0.878955i	$-0.341759\pi$
$5$	10.6639	0.953808	0.476904	+	0.878955i	$0.341759\pi$
$6$	−46.9563	−3.19497
$7$	−4.53278	−0.244747	−0.122373	−	0.992484i	$-0.539051\pi$
$7$	−4.53278	−0.244747	−0.122373	+	0.992484i	$0.539051\pi$
$8$	−30.9447	−1.36758
$9$	70.9049	2.62611
$10$	−50.6066	−1.60032
$11$	−68.3080	−1.87233	−0.936165	−	0.351560i	$-0.885651\pi$
$11$	−68.3080	−1.87233	−0.936165	+	0.351560i	$0.885651\pi$
$12$	143.678	3.45636
$13$	−5.07991	−0.108378	−0.0541890	−	0.998531i	$-0.517257\pi$
$13$	−5.07991	−0.108378	−0.0541890	+	0.998531i	$0.517257\pi$
$14$	21.5107	0.410642
$15$	105.516	1.81627
$16$	30.6856	0.479462
$17$	−31.1856	−0.444918	−0.222459	−	0.974942i	$-0.571408\pi$
$17$	−31.1856	−0.444918	−0.222459	+	0.974942i	$0.571408\pi$
$18$	−336.487	−4.40615
$19$	−157.168	−1.89772	−0.948861	−	0.315694i	$-0.897763\pi$
$19$	−157.168	−1.89772	−0.948861	+	0.315694i	$0.897763\pi$
$20$	154.847	1.73125
$21$	−44.8504	−0.466056
$22$	324.162	3.14144
$23$	−0.208252	−0.00188798	−0.000943992	−	1.00000i	$-0.500300\pi$
$23$	−0.208252	−0.00188798	−0.000943992		1.00000i	$0.500300\pi$
$24$	−306.189	−2.60419
$25$	−11.2813	−0.0902502
$26$	24.1072	0.181839
$27$	434.426	3.09649
$28$	−65.8192	−0.444238
$29$	−176.024	−1.12713	−0.563566	−	0.826071i	$-0.690571\pi$
$29$	−176.024	−1.12713	−0.563566	+	0.826071i	$0.690571\pi$
$30$	−500.737	−3.04739
$31$	42.5920	0.246766	0.123383	−	0.992359i	$-0.460626\pi$
$31$	42.5920	0.246766	0.123383	+	0.992359i	$0.460626\pi$
$32$	101.936	0.563124
$33$	−675.887	−3.56536
$34$	147.994	0.746494
$35$	−48.3371	−0.233442
$36$	1029.59	4.76662
$37$	−26.6864	−0.118573	−0.0592866	−	0.998241i	$-0.518883\pi$
$37$	−26.6864	−0.118573	−0.0592866	+	0.998241i	$0.518883\pi$
$38$	745.855	3.18404
$39$	−50.2641	−0.206377
$40$	−329.992	−1.30441
$41$	−8.33664	−0.0317552	−0.0158776	−	0.999874i	$-0.505054\pi$
$41$	−8.33664	−0.0317552	−0.0158776	+	0.999874i	$0.505054\pi$
$42$	212.842	0.781959
$43$	21.6906	0.0769253	0.0384626	−	0.999260i	$-0.487754\pi$
$43$	21.6906	0.0769253	0.0384626	+	0.999260i	$0.487754\pi$
$44$	−991.881	−3.39845
$45$	756.123	2.50480
$46$	0.988283	0.00316770
$47$	−632.759	−1.96378	−0.981888	−	0.189463i	$-0.939325\pi$
$47$	−632.759	−1.96378	−0.981888	+	0.189463i	$0.939325\pi$
$48$	303.624	0.913009
$49$	−322.454	−0.940099
$50$	53.5364	0.151424
$51$	−308.572	−0.847229
$52$	−73.7639	−0.196716
$53$	395.267	1.02442	0.512208	−	0.858861i	$-0.328828\pi$
$53$	395.267	1.02442	0.512208	+	0.858861i	$0.328828\pi$
$54$	−2061.61	−5.19537
$55$	−728.430	−1.78584
$56$	140.266	0.334710
$57$	−1555.13	−3.61371
$58$	835.340	1.89113
$59$	−650.347	−1.43505	−0.717525	−	0.696533i	$-0.754725\pi$
$59$	−650.347	−1.43505	−0.717525	+	0.696533i	$0.754725\pi$
$60$	1532.17	3.29670
$61$	−647.768	−1.35964	−0.679821	−	0.733378i	$-0.737943\pi$
$61$	−647.768	−1.35964	−0.679821	+	0.733378i	$0.737943\pi$
$62$	−202.125	−0.414030
$63$	−321.396	−0.642732
$64$	−729.234	−1.42429
$65$	−54.1716	−0.103372
$66$	3207.49	5.98204
$67$	85.3728	0.155671	0.0778354	−	0.996966i	$-0.475199\pi$
$67$	85.3728	0.155671	0.0778354	+	0.996966i	$0.475199\pi$
$68$	−452.837	−0.807567
$69$	−2.06059	−0.00359516
$70$	229.388	0.391674
$71$	643.680	1.07593	0.537963	−	0.842969i	$-0.319194\pi$
$71$	643.680	1.07593	0.537963	+	0.842969i	$0.319194\pi$
$72$	−2194.13	−3.59141
$73$	88.0743	0.141210	0.0706049	−	0.997504i	$-0.477507\pi$
$73$	88.0743	0.141210	0.0706049	+	0.997504i	$0.477507\pi$
$74$	126.643	0.198945
$75$	−111.625	−0.171858
$76$	−2282.19	−3.44454
$77$	309.625	0.458247
$78$	238.534	0.346264
$79$	−972.995	−1.38570	−0.692851	−	0.721081i	$-0.743646\pi$
$79$	−972.995	−1.38570	−0.692851	+	0.721081i	$0.743646\pi$
$80$	327.228	0.457315
$81$	2384.08	3.27034
$82$	39.5623	0.0532796
$83$	728.878	0.963913	0.481956	−	0.876195i	$-0.339926\pi$
$83$	728.878	0.963913	0.481956	+	0.876195i	$0.339926\pi$
$84$	−651.261	−0.845933
$85$	−332.560	−0.424367
$86$	−102.935	−0.129067
$87$	−1741.70	−2.14633
$88$	2113.77	2.56056
$89$	398.686	0.474838	0.237419	−	0.971407i	$-0.423699\pi$
$89$	398.686	0.474838	0.237419	+	0.971407i	$0.423699\pi$
$90$	−3588.26	−4.20262
$91$	23.0261	0.0265252
$92$	−3.02397	−0.00342686
$93$	421.435	0.469900
$94$	3002.82	3.29487
$95$	−1676.02	−1.81006
$96$	1008.63	1.07232
$97$	25.8849	0.0270949	0.0135475	−	0.999908i	$-0.495688\pi$
$97$	25.8849	0.0270949	0.0135475	+	0.999908i	$0.495688\pi$
$98$	1530.24	1.57732
$99$	−4843.38	−4.91694
$100$	−163.812	−0.163812
$101$	−952.632	−0.938519	−0.469260	−	0.883060i	$-0.655479\pi$
$101$	−952.632	−0.938519	−0.469260	+	0.883060i	$0.655479\pi$
$102$	1464.36	1.42150
$103$	881.371	0.843147	0.421573	−	0.906794i	$-0.361478\pi$
$103$	881.371	0.843147	0.421573	+	0.906794i	$0.361478\pi$
$104$	157.196	0.148215
$105$	−478.281	−0.444528
$106$	−1875.78	−1.71879
$107$	1086.36	0.981515	0.490758	−	0.871296i	$-0.336720\pi$
$107$	1086.36	0.981515	0.490758	+	0.871296i	$0.336720\pi$
$108$	6308.18	5.62041
$109$	764.306	0.671626	0.335813	−	0.941929i	$-0.390989\pi$
$109$	764.306	0.671626	0.335813	+	0.941929i	$0.390989\pi$
$110$	3456.84	2.99633
$111$	−264.053	−0.225791
$112$	−139.091	−0.117347
$113$	268.550	0.223567	0.111783	−	0.993733i	$-0.464344\pi$
$113$	268.550	0.223567	0.111783	+	0.993733i	$0.464344\pi$
$114$	7380.00	6.06316
$115$	−2.22078	−0.00180077
$116$	−2556.00	−2.04585
$117$	−360.191	−0.284612
$118$	3086.29	2.40776
$119$	141.357	0.108892
$120$	−3265.16	−2.48390
$121$	3334.98	2.50562
$122$	3074.05	2.28124
$123$	−82.4884	−0.0604694
$124$	618.466	0.447903
$125$	−1453.29	−1.03989
$126$	1525.22	1.07839
$127$	1670.43	1.16714	0.583571	−	0.812062i	$-0.301655\pi$
$127$	1670.43	1.16714	0.583571	+	0.812062i	$0.301655\pi$
$128$	2645.16	1.82657
$129$	214.622	0.146484
$130$	257.077	0.173440
$131$	1668.92	1.11309	0.556544	−	0.830818i	$-0.312127\pi$
$131$	1668.92	1.11309	0.556544	+	0.830818i	$0.312127\pi$
$132$	−9814.36	−6.47144
$133$	712.406	0.464462
$134$	−405.145	−0.261188
$135$	4632.67	2.95346
$136$	965.029	0.608460
$137$	1076.61	0.671392	0.335696	−	0.941970i	$-0.391028\pi$
$137$	1076.61	0.671392	0.335696	+	0.941970i	$0.391028\pi$
$138$	9.77875	0.00603205
$139$	1191.16	0.726857	0.363428	−	0.931622i	$-0.381606\pi$
$139$	1191.16	0.726857	0.363428	+	0.931622i	$0.381606\pi$
$140$	−701.889	−0.423718
$141$	−6260.96	−3.73949
$142$	−3054.65	−1.80521
$143$	346.998	0.202919
$144$	2175.76	1.25912
$145$	−1877.10	−1.07507
$146$	−417.965	−0.236925
$147$	−3190.58	−1.79017
$148$	−387.505	−0.215221
$149$	−978.597	−0.538052	−0.269026	−	0.963133i	$-0.586702\pi$
$149$	−978.597	−0.538052	−0.269026	+	0.963133i	$0.586702\pi$
$150$	529.726	0.288347
$151$	−1796.42	−0.968152	−0.484076	−	0.875026i	$-0.660844\pi$
$151$	−1796.42	−0.968152	−0.484076	+	0.875026i	$0.660844\pi$
$152$	4863.51	2.59528
$153$	−2211.21	−1.16840
$154$	−1469.36	−0.768858
$155$	454.197	0.235367
$156$	−729.872	−0.374593
$157$	1505.70	0.765402	0.382701	−	0.923872i	$-0.374994\pi$
$157$	1505.70	0.765402	0.382701	+	0.923872i	$0.374994\pi$
$158$	4617.45	2.32496
$159$	3911.04	1.95073
$160$	1087.04	0.537113
$161$	0.943962	0.000462078 0
$162$	−11313.9	−5.48705
$163$	2329.17	1.11923	0.559616	−	0.828752i	$-0.310948\pi$
$163$	2329.17	1.11923	0.559616	+	0.828752i	$0.310948\pi$
$164$	−121.054	−0.0576386
$165$	−7207.59	−3.40067
$166$	−3458.96	−1.61727
$167$	1548.04	0.717309	0.358654	−	0.933470i	$-0.383236\pi$
$167$	1548.04	0.717309	0.358654	+	0.933470i	$0.383236\pi$
$168$	1387.89	0.637367
$169$	−2171.19	−0.988254
$170$	1578.20	0.712012
$171$	−11144.0	−4.98363
$172$	314.963	0.139626
$173$	−1356.70	−0.596231	−0.298116	−	0.954530i	$-0.596358\pi$
$173$	−1356.70	−0.596231	−0.298116	+	0.954530i	$0.596358\pi$
$174$	8265.43	3.60115
$175$	51.1355	0.0220885
$176$	−2096.07	−0.897712
$177$	−6434.98	−2.73267
$178$	−1892.00	−0.796694
$179$	3837.91	1.60256	0.801282	−	0.598287i	$-0.204152\pi$
$179$	3837.91	1.60256	0.801282	+	0.598287i	$0.204152\pi$
$180$	10979.5	4.54645
$181$	−4280.00	−1.75762	−0.878811	−	0.477170i	$-0.841663\pi$
$181$	−4280.00	−1.75762	−0.878811	+	0.477170i	$0.841663\pi$
$182$	−109.273	−0.0445045
$183$	−6409.46	−2.58908
$184$	6.44432	0.00258196
$185$	−284.581	−0.113096
$186$	−1999.96	−0.788410
$187$	2130.22	0.833034
$188$	−9188.12	−3.56443
$189$	−1969.16	−0.757857
$190$	7953.72	3.03696
$191$	2842.31	1.07677	0.538384	−	0.842700i	$-0.319035\pi$
$191$	2842.31	1.07677	0.538384	+	0.842700i	$0.319035\pi$
$192$	−7215.55	−2.71217
$193$	−1694.43	−0.631957	−0.315978	−	0.948766i	$-0.602333\pi$
$193$	−1694.43	−0.631957	−0.315978	+	0.948766i	$0.602333\pi$
$194$	−122.839	−0.0454605
$195$	−536.012	−0.196844
$196$	−4682.26	−1.70636
$197$	75.3428	0.0272485	0.0136242	−	0.999907i	$-0.495663\pi$
$197$	75.3428	0.0272485	0.0136242	+	0.999907i	$0.495663\pi$
$198$	22984.7	8.24976
$199$	−1275.64	−0.454411	−0.227205	−	0.973847i	$-0.572959\pi$
$199$	−1275.64	−0.454411	−0.227205	+	0.973847i	$0.572959\pi$
$200$	349.096	0.123424
$201$	844.738	0.296434
$202$	4520.81	1.57467
$203$	797.878	0.275862
$204$	−4480.68	−1.53780
$205$	−88.9010	−0.0302884
$206$	−4182.64	−1.41465
$207$	−14.7661	−0.00495805
$208$	−155.880	−0.0519631
$209$	10735.8	3.55316
$210$	2269.73	0.745839
$211$	−1738.04	−0.567069	−0.283535	−	0.958962i	$-0.591507\pi$
$211$	−1738.04	−0.567069	−0.283535	+	0.958962i	$0.591507\pi$
$212$	5739.56	1.85941
$213$	6369.01	2.04881
$214$	−5155.42	−1.64681
$215$	231.306	0.0733720
$216$	−13443.2	−4.23469
$217$	−193.060	−0.0603952
$218$	−3627.09	−1.12687
$219$	871.468	0.268897
$220$	−10577.3	−3.24147
$221$	158.420	0.0482193
$222$	1253.09	0.378838
$223$	4315.38	1.29587	0.647936	−	0.761695i	$-0.275633\pi$
$223$	4315.38	1.29587	0.647936	+	0.761695i	$0.275633\pi$
$224$	−462.055	−0.137823
$225$	−799.898	−0.237007
$226$	−1274.43	−0.375105
$227$	−4019.80	−1.17535	−0.587673	−	0.809099i	$-0.699956\pi$
$227$	−4019.80	−1.17535	−0.587673	+	0.809099i	$0.699956\pi$
$228$	−22581.5	−6.55921
$229$	−3048.22	−0.879617	−0.439808	−	0.898092i	$-0.644954\pi$
$229$	−3048.22	−0.879617	−0.439808	+	0.898092i	$0.644954\pi$
$230$	10.5389	0.00302138
$231$	3063.64	0.872610
$232$	5447.02	1.54144
$233$	−2633.04	−0.740327	−0.370164	−	0.928967i	$-0.620698\pi$
$233$	−2633.04	−0.740327	−0.370164	+	0.928967i	$0.620698\pi$
$234$	1709.32	0.477529
$235$	−6747.68	−1.87307
$236$	−9443.51	−2.60475
$237$	−9627.49	−2.63870
$238$	−670.825	−0.182702
$239$	−186.099	−0.0503671	−0.0251835	−	0.999683i	$-0.508017\pi$
$239$	−186.099	−0.0503671	−0.0251835	+	0.999683i	$0.508017\pi$
$240$	3237.82	0.870835
$241$	−4693.94	−1.25462	−0.627310	−	0.778769i	$-0.715844\pi$
$241$	−4693.94	−1.25462	−0.627310	+	0.778769i	$0.715844\pi$
$242$	−15826.5	−4.20399
$243$	11860.2	3.13100
$244$	−9406.06	−2.46787
$245$	−3438.62	−0.896674
$246$	391.457	0.101457
$247$	798.397	0.205671
$248$	−1318.00	−0.337472
$249$	7212.02	1.83552
$250$	6896.73	1.74475
$251$	−1237.43	−0.311179	−0.155590	−	0.987822i	$-0.549728\pi$
$251$	−1237.43	−0.311179	−0.155590	+	0.987822i	$0.549728\pi$
$252$	−4666.91	−1.16662
$253$	14.2253	0.00353493
$254$	−7927.21	−1.95826
$255$	−3290.58	−0.808094
$256$	−6719.01	−1.64038
$257$	554.186	0.134510	0.0672552	−	0.997736i	$-0.478576\pi$
$257$	554.186	0.134510	0.0672552	+	0.997736i	$0.478576\pi$
$258$	−1018.51	−0.245774
$259$	120.963	0.0290205
$260$	−786.611	−0.187629
$261$	−12481.0	−2.95997
$262$	−7920.04	−1.86756
$263$	4838.81	1.13450	0.567251	−	0.823545i	$-0.308007\pi$
$263$	4838.81	1.13450	0.567251	+	0.823545i	$0.308007\pi$
$264$	20915.1	4.87590
$265$	4215.09	0.977097
$266$	−3380.79	−0.779285
$267$	3944.87	0.904203
$268$	1239.67	0.282557
$269$	4211.45	0.954561	0.477280	−	0.878751i	$-0.341623\pi$
$269$	4211.45	0.954561	0.477280	+	0.878751i	$0.341623\pi$
$270$	−21984.8	−4.95538
$271$	−4777.84	−1.07097	−0.535485	−	0.844545i	$-0.679871\pi$
$271$	−4777.84	−1.07097	−0.535485	+	0.844545i	$0.679871\pi$
$272$	−956.947	−0.213322
$273$	227.836	0.0505101
$274$	−5109.15	−1.12648
$275$	770.601	0.168978
$276$	−29.9213	−0.00652555
$277$	−4678.09	−1.01473	−0.507363	−	0.861732i	$-0.669380\pi$
$277$	−4678.09	−1.01473	−0.507363	+	0.861732i	$0.669380\pi$
$278$	−5652.78	−1.21954
$279$	3019.98	0.648035
$280$	1495.78	0.319249
$281$	7114.79	1.51044	0.755218	−	0.655473i	$-0.227531\pi$
$281$	7114.79	1.51044	0.755218	+	0.655473i	$0.227531\pi$
$282$	29712.0	6.27420
$283$	9110.81	1.91371	0.956857	−	0.290559i	$-0.0938411\pi$
$283$	9110.81	1.91371	0.956857	+	0.290559i	$0.0938411\pi$
$284$	9346.69	1.95290
$285$	−16583.7	−3.44678
$286$	−1646.72	−0.340463
$287$	37.7881	0.00777199
$288$	7227.79	1.47883
$289$	−3940.46	−0.802048
$290$	8907.98	1.80377
$291$	256.123	0.0515951
$292$	1278.90	0.256309
$293$	−4039.39	−0.805404	−0.402702	−	0.915331i	$-0.631929\pi$
$293$	−4039.39	−0.805404	−0.402702	+	0.915331i	$0.631929\pi$
$294$	15141.2	3.00359
$295$	−6935.23	−1.36876
$296$	825.803	0.162158
$297$	−29674.8	−5.79766
$298$	4644.03	0.902756
$299$	1.05790	0.000204616 0
$300$	−1620.87	−0.311937
$301$	−98.3187	−0.0188272
$302$	8525.11	1.62439
$303$	−9426.00	−1.78716
$304$	−4822.78	−0.909886
$305$	−6907.73	−1.29684
$306$	10493.5	1.96038
$307$	−8558.43	−1.59106	−0.795530	−	0.605914i	$-0.792807\pi$
$307$	−8558.43	−1.59106	−0.795530	+	0.605914i	$0.792807\pi$
$308$	4495.98	0.831760
$309$	8720.90	1.60555
$310$	−2155.44	−0.394905
$311$	9431.53	1.71966	0.859828	−	0.510584i	$-0.170571\pi$
$311$	9431.53	1.71966	0.859828	+	0.510584i	$0.170571\pi$
$312$	1555.41	0.282236
$313$	−1709.33	−0.308680	−0.154340	−	0.988018i	$-0.549325\pi$
$313$	−1709.33	−0.308680	−0.154340	+	0.988018i	$0.549325\pi$
$314$	−7145.46	−1.28421
$315$	−3427.34	−0.613043
$316$	−14128.6	−2.51517
$317$	−4851.28	−0.859543	−0.429771	−	0.902938i	$-0.641406\pi$
$317$	−4851.28	−0.859543	−0.429771	+	0.902938i	$0.641406\pi$
$318$	−18560.3	−3.27298
$319$	12023.9	2.11037
$320$	−7776.48	−1.35849
$321$	10749.2	1.86904
$322$	−4.47966	−0.000775286 0
$323$	4901.36	0.844331
$324$	34618.5	5.93596
$325$	57.3078	0.00978113
$326$	−11053.3	−1.87787
$327$	7562.57	1.27893
$328$	257.975	0.0434277
$329$	2868.16	0.480628
$330$	34204.3	5.70572
$331$	1818.17	0.301921	0.150960	−	0.988540i	$-0.451763\pi$
$331$	1818.17	0.301921	0.150960	+	0.988540i	$0.451763\pi$
$332$	10583.8	1.74959
$333$	−1892.20	−0.311386
$334$	−7346.36	−1.20352
$335$	910.407	0.148480
$336$	−1376.26	−0.223456
$337$	3535.26	0.571448	0.285724	−	0.958312i	$-0.407766\pi$
$337$	3535.26	0.571448	0.285724	+	0.958312i	$0.407766\pi$
$338$	10303.6	1.65812
$339$	2657.22	0.425723
$340$	−4829.01	−0.770264
$341$	−2909.37	−0.462028
$342$	52884.8	8.36164
$343$	3016.35	0.474833
$344$	−671.210	−0.105201
$345$	−21.9740	−0.00342910
$346$	6438.35	1.00037
$347$	9373.26	1.45010	0.725048	−	0.688699i	$-0.241818\pi$
$347$	9373.26	1.45010	0.725048	+	0.688699i	$0.241818\pi$
$348$	−25290.8	−3.89577
$349$	−3752.44	−0.575539	−0.287770	−	0.957700i	$-0.592914\pi$
$349$	−3752.44	−0.575539	−0.287770	+	0.957700i	$0.592914\pi$
$350$	−242.669	−0.0370605
$351$	−2206.84	−0.335592
$352$	−6963.07	−1.05435
$353$	−9050.04	−1.36455	−0.682273	−	0.731097i	$-0.739008\pi$
$353$	−9050.04	−1.36455	−0.682273	+	0.731097i	$0.739008\pi$
$354$	30537.9	4.58494
$355$	6864.13	1.02623
$356$	5789.20	0.861874
$357$	1398.69	0.207357
$358$	−18213.2	−2.68882
$359$	−551.377	−0.0810601	−0.0405301	−	0.999178i	$-0.512905\pi$
$359$	−551.377	−0.0810601	−0.0405301	+	0.999178i	$0.512905\pi$
$360$	−23398.0	−3.42551
$361$	17842.7	2.60135
$362$	20311.2	2.94898
$363$	32998.6	4.77129
$364$	334.356	0.0481456
$365$	939.215	0.134687
$366$	30416.8	4.34401
$367$	−1192.44	−0.169604	−0.0848020	−	0.996398i	$-0.527026\pi$
$367$	−1192.44	−0.169604	−0.0848020	+	0.996398i	$0.527026\pi$
$368$	−6.39035	−0.000905217 0
$369$	−591.109	−0.0833927
$370$	1350.51	0.189755
$371$	−1791.66	−0.250723
$372$	6119.54	0.852912
$373$	−14119.1	−1.95994	−0.979970	−	0.199145i	$-0.936184\pi$
$373$	−14119.1	−1.95994	−0.979970	+	0.199145i	$0.936184\pi$
$374$	−10109.2	−1.39768
$375$	−14379.9	−1.98019
$376$	19580.6	2.68561
$377$	894.186	0.122156
$378$	9344.83	1.27155
$379$	−9702.65	−1.31502	−0.657509	−	0.753447i	$-0.728390\pi$
$379$	−9702.65	−1.31502	−0.657509	+	0.753447i	$0.728390\pi$
$380$	−24337.0	−3.28543
$381$	16528.4	2.22251
$382$	−13488.5	−1.80663
$383$	3139.69	0.418879	0.209439	−	0.977822i	$-0.432836\pi$
$383$	3139.69	0.418879	0.209439	+	0.977822i	$0.432836\pi$
$384$	26173.1	3.47823
$385$	3301.81	0.437080
$386$	8041.08	1.06031
$387$	1537.97	0.202014
$388$	375.867	0.0491798
$389$	12214.7	1.59205	0.796025	−	0.605264i	$-0.206932\pi$
$389$	12214.7	1.59205	0.796025	+	0.605264i	$0.206932\pi$
$390$	2543.70	0.330270
$391$	6.49447	0.000839999 0
$392$	9978.25	1.28566
$393$	16513.5	2.11958
$394$	−357.547	−0.0457181
$395$	−10375.9	−1.32169
$396$	−70329.3	−8.92470
$397$	−5742.27	−0.725935	−0.362968	−	0.931802i	$-0.618236\pi$
$397$	−5742.27	−0.725935	−0.362968	+	0.931802i	$0.618236\pi$
$398$	6053.68	0.762421
$399$	7049.04	0.884444
$400$	−346.172	−0.0432716
$401$	−12719.8	−1.58403	−0.792015	−	0.610502i	$-0.790968\pi$
$401$	−12719.8	−1.58403	−0.792015	+	0.610502i	$0.790968\pi$
$402$	−4008.79	−0.497363
$403$	−216.363	−0.0267440
$404$	−13832.9	−1.70350
$405$	25423.6	3.11928
$406$	−3786.41	−0.462848
$407$	1822.89	0.222008
$408$	9548.67	1.15865
$409$	−8859.52	−1.07109	−0.535544	−	0.844507i	$-0.679893\pi$
$409$	−8859.52	−1.07109	−0.535544	+	0.844507i	$0.679893\pi$
$410$	421.889	0.0508185
$411$	10652.7	1.27849
$412$	12798.1	1.53039
$413$	2947.88	0.351224
$414$	70.0741	0.00831873
$415$	7772.68	0.919388
$416$	−517.828	−0.0610303
$417$	11786.2	1.38411
$418$	−50947.8	−5.96158
$419$	2972.21	0.346544	0.173272	−	0.984874i	$-0.444566\pi$
$419$	2972.21	0.346544	0.173272	+	0.984874i	$0.444566\pi$
$420$	−6944.98	−0.806858
$421$	−1522.46	−0.176247	−0.0881236	−	0.996110i	$-0.528087\pi$
$421$	−1522.46	−0.176247	−0.0881236	+	0.996110i	$0.528087\pi$
$422$	8248.04	0.951442
$423$	−44865.8	−5.15709
$424$	−12231.4	−1.40097
$425$	351.813	0.0401540
$426$	−30224.8	−3.43755
$427$	2936.19	0.332768
$428$	15774.7	1.78154
$429$	3433.44	0.386406
$430$	−1097.69	−0.123105
$431$	−5953.65	−0.665377	−0.332688	−	0.943037i	$-0.607956\pi$
$431$	−5953.65	−0.665377	−0.332688	+	0.943037i	$0.607956\pi$
$432$	13330.6	1.48465
$433$	1198.26	0.132990	0.0664948	−	0.997787i	$-0.478818\pi$
$433$	1198.26	0.132990	0.0664948	+	0.997787i	$0.478818\pi$
$434$	916.186	0.101333
$435$	−18573.4	−2.04718
$436$	11098.3	1.21906
$437$	32.7305	0.00358287
$438$	−4135.64	−0.451161
$439$	−13444.3	−1.46164	−0.730822	−	0.682568i	$-0.760863\pi$
$439$	−13444.3	−1.46164	−0.730822	+	0.682568i	$0.760863\pi$
$440$	22541.1	2.44228
$441$	−22863.6	−2.46880
$442$	−751.797	−0.0809035
$443$	6638.67	0.711992	0.355996	−	0.934487i	$-0.384142\pi$
$443$	6638.67	0.711992	0.355996	+	0.934487i	$0.384142\pi$
$444$	−3834.25	−0.409832
$445$	4251.54	0.452904
$446$	−20479.1	−2.17424
$447$	−9682.92	−1.02458
$448$	3305.46	0.348589
$449$	−18446.9	−1.93890	−0.969449	−	0.245294i	$-0.921115\pi$
$449$	−18446.9	−1.93890	−0.969449	+	0.245294i	$0.921115\pi$
$450$	3796.00	0.397656
$451$	569.459	0.0594563
$452$	3899.54	0.405794
$453$	−17775.1	−1.84359
$454$	19076.4	1.97202
$455$	245.548	0.0252999
$456$	48122.9	4.94202
$457$	5708.21	0.584286	0.292143	−	0.956375i	$-0.405632\pi$
$457$	5708.21	0.584286	0.292143	+	0.956375i	$0.405632\pi$
$458$	14465.7	1.47584
$459$	−13547.8	−1.37769
$460$	−32.2474	−0.00326857
$461$	6710.84	0.677994	0.338997	−	0.940787i	$-0.389912\pi$
$461$	6710.84	0.677994	0.338997	+	0.940787i	$0.389912\pi$
$462$	−14538.8	−1.46409
$463$	19332.8	1.94055	0.970274	−	0.242009i	$-0.0778064\pi$
$463$	19332.8	1.94055	0.970274	+	0.242009i	$0.0778064\pi$
$464$	−5401.40	−0.540418
$465$	4494.14	0.448195
$466$	12495.4	1.24214
$467$	8651.13	0.857231	0.428615	−	0.903487i	$-0.359002\pi$
$467$	8651.13	0.857231	0.428615	+	0.903487i	$0.359002\pi$
$468$	−5230.23	−0.516597
$469$	−386.976	−0.0381000
$470$	32021.8	3.14267
$471$	14898.5	1.45750
$472$	20124.8	1.96254
$473$	−1481.64	−0.144030
$474$	45688.2	4.42728
$475$	1773.05	0.171270
$476$	2052.61	0.197650
$477$	28026.4	2.69023
$478$	883.151	0.0845071
$479$	−6962.81	−0.664173	−0.332087	−	0.943249i	$-0.607753\pi$
$479$	−6962.81	−0.664173	−0.332087	+	0.943249i	$0.607753\pi$
$480$	10755.9	1.02279
$481$	135.564	0.0128507
$482$	22275.6	2.10503
$483$	9.34021	0.000879905 0
$484$	48426.4	4.54793
$485$	276.034	0.0258434
$486$	−56283.8	−5.25327
$487$	−17096.5	−1.59080	−0.795398	−	0.606087i	$-0.792738\pi$
$487$	−17096.5	−1.59080	−0.795398	+	0.606087i	$0.792738\pi$
$488$	20045.0	1.85942
$489$	23046.5	2.13128
$490$	16318.3	1.50446
$491$	−15334.4	−1.40943	−0.704716	−	0.709490i	$-0.748925\pi$
$491$	−15334.4	−1.40943	−0.704716	+	0.709490i	$0.748925\pi$
$492$	−1197.79	−0.109757
$493$	5489.41	0.501482
$494$	−3788.87	−0.345080
$495$	−51649.3	−4.68982
$496$	1306.96	0.118315
$497$	−2917.66	−0.263330
$498$	−34225.4	−3.07967
$499$	−7675.93	−0.688621	−0.344311	−	0.938856i	$-0.611887\pi$
$499$	−7675.93	−0.688621	−0.344311	+	0.938856i	$0.611887\pi$
$500$	−21102.8	−1.88749
$501$	15317.3	1.36592
$502$	5872.36	0.522104
$503$	−12257.1	−1.08651	−0.543256	−	0.839567i	$-0.682809\pi$
$503$	−12257.1	−1.08651	−0.543256	+	0.839567i	$0.682809\pi$
$504$	9945.52	0.878986
$505$	−10158.8	−0.895167
$506$	−67.5076	−0.00593099
$507$	−21483.3	−1.88187
$508$	24255.9	2.11847
$509$	14581.5	1.26977	0.634887	−	0.772605i	$-0.281047\pi$
$509$	14581.5	1.26977	0.634887	+	0.772605i	$0.281047\pi$
$510$	15615.8	1.35584
$511$	−399.221	−0.0345607
$512$	10724.4	0.925698
$513$	−68277.7	−5.87628
$514$	−2629.95	−0.225685
$515$	9398.86	0.804200
$516$	3116.47	0.265881
$517$	43222.5	3.67684
$518$	−574.044	−0.0486912
$519$	−13424.1	−1.13536
$520$	1676.33	0.141369
$521$	−19079.6	−1.60440	−0.802199	−	0.597057i	$-0.796337\pi$
$521$	−19079.6	−1.60440	−0.802199	+	0.597057i	$0.796337\pi$
$522$	59229.7	4.96631
$523$	11871.1	0.992518	0.496259	−	0.868175i	$-0.334707\pi$
$523$	11871.1	0.992518	0.496259	+	0.868175i	$0.334707\pi$
$524$	24234.0	2.02035
$525$	505.970	0.0420616
$526$	−22963.1	−1.90349
$527$	−1328.26	−0.109791
$528$	−20740.0	−1.70945
$529$	−12167.0	−0.999996
$530$	−20003.1	−1.63940
$531$	−46112.8	−3.76860
$532$	10344.6	0.843040
$533$	42.3494	0.00344156
$534$	−18720.8	−1.51709
$535$	11584.8	0.936177
$536$	−2641.84	−0.212892
$537$	37975.0	3.05166
$538$	−19985.9	−1.60158
$539$	22026.2	1.76018
$540$	67269.8	5.36080
$541$	−14848.0	−1.17997	−0.589987	−	0.807412i	$-0.700867\pi$
$541$	−14848.0	−1.17997	−0.589987	+	0.807412i	$0.700867\pi$
$542$	22673.7	1.79690
$543$	−42349.3	−3.34693
$544$	−3178.94	−0.250544
$545$	8150.48	0.640602
$546$	−1081.22	−0.0847471
$547$	−3087.93	−0.241371	−0.120686	−	0.992691i	$-0.538509\pi$
$547$	−3087.93	−0.241371	−0.120686	+	0.992691i	$0.538509\pi$
$548$	15633.1	1.21864
$549$	−45930.0	−3.57057
$550$	−3656.97	−0.283516
$551$	27665.3	2.13899
$552$	63.7645	0.00491666
$553$	4410.37	0.339146
$554$	22200.4	1.70253
$555$	−2815.84	−0.215362
$556$	17296.5	1.31931
$557$	1943.86	0.147870	0.0739352	−	0.997263i	$-0.476444\pi$
$557$	1943.86	0.147870	0.0739352	+	0.997263i	$0.476444\pi$
$558$	−14331.6	−1.08729
$559$	−110.186	−0.00833700
$560$	−1483.25	−0.111926
$561$	21077.9	1.58629
$562$	−33763.9	−2.53425
$563$	10478.3	0.784387	0.392193	−	0.919883i	$-0.371716\pi$
$563$	10478.3	0.784387	0.392193	+	0.919883i	$0.371716\pi$
$564$	−90913.7	−6.78751
$565$	2863.79	0.213240
$566$	−43236.2	−3.21087
$567$	−10806.5	−0.800406
$568$	−19918.5	−1.47141
$569$	10105.4	0.744537	0.372269	−	0.928125i	$-0.378580\pi$
$569$	10105.4	0.744537	0.372269	+	0.928125i	$0.378580\pi$
$570$	78699.6	5.78309
$571$	−13432.6	−0.984478	−0.492239	−	0.870460i	$-0.663821\pi$
$571$	−13432.6	−0.984478	−0.492239	+	0.870460i	$0.663821\pi$
$572$	5038.67	0.368317
$573$	28123.8	2.05042
$574$	−179.327	−0.0130400
$575$	2.34935	0.000170391 0
$576$	−51706.3	−3.74033
$577$	−12878.1	−0.929157	−0.464578	−	0.885532i	$-0.653794\pi$
$577$	−12878.1	−0.929157	−0.464578	+	0.885532i	$0.653794\pi$
$578$	18699.8	1.34569
$579$	−16765.9	−1.20339
$580$	−27256.9	−1.95135
$581$	−3303.84	−0.235915
$582$	−1215.46	−0.0865675
$583$	−26999.9	−1.91805
$584$	−2725.44	−0.193115
$585$	−3841.04	−0.271466
$586$	19169.3	1.35133
$587$	−27686.3	−1.94674	−0.973368	−	0.229247i	$-0.926374\pi$
$587$	−27686.3	−1.94674	−0.973368	+	0.229247i	$0.926374\pi$
$588$	−46329.6	−3.24932
$589$	−6694.08	−0.468293
$590$	32911.9	2.29654
$591$	745.493	0.0518875
$592$	−818.887	−0.0568514
$593$	6589.51	0.456322	0.228161	−	0.973623i	$-0.426729\pi$
$593$	6589.51	0.456322	0.228161	+	0.973623i	$0.426729\pi$
$594$	140825.	9.72745
$595$	1507.42	0.103862
$596$	−14209.9	−0.976613
$597$	−12622.1	−0.865305
$598$	−5.02039	−0.000343309 0
$599$	10152.5	0.692520	0.346260	−	0.938139i	$-0.387452\pi$
$599$	10152.5	0.692520	0.346260	+	0.938139i	$0.387452\pi$
$600$	3454.20	0.235028
$601$	−9894.16	−0.671532	−0.335766	−	0.941945i	$-0.608995\pi$
$601$	−9894.16	−0.671532	−0.335766	+	0.941945i	$0.608995\pi$
$602$	466.581	0.0315888
$603$	6053.35	0.408809
$604$	−26085.4	−1.75728
$605$	35563.9	2.38988
$606$	44732.0	2.99854
$607$	−20465.8	−1.36850	−0.684250	−	0.729248i	$-0.739870\pi$
$607$	−20465.8	−1.36850	−0.684250	+	0.729248i	$0.739870\pi$
$608$	−16021.1	−1.06865
$609$	7894.76	0.525307
$610$	32781.3	2.17586
$611$	3214.36	0.212830
$612$	−32108.4	−2.12076
$613$	25208.5	1.66095	0.830476	−	0.557055i	$-0.188069\pi$
$613$	25208.5	1.66095	0.830476	+	0.557055i	$0.188069\pi$
$614$	40614.9	2.66952
$615$	−879.648	−0.0576762
$616$	−9581.26	−0.626688
$617$	−21771.8	−1.42058	−0.710291	−	0.703909i	$-0.751436\pi$
$617$	−21771.8	−1.42058	−0.710291	+	0.703909i	$0.751436\pi$
$618$	−41385.9	−2.69383
$619$	−12251.2	−0.795507	−0.397754	−	0.917492i	$-0.630210\pi$
$619$	−12251.2	−0.795507	−0.397754	+	0.917492i	$0.630210\pi$
$620$	6595.26	0.427213
$621$	−90.4702	−0.00584613
$622$	−44758.3	−2.88528
$623$	−1807.15	−0.116215
$624$	−1542.38	−0.0989500
$625$	−14087.6	−0.901605
$626$	8111.79	0.517911
$627$	106227.	6.76606
$628$	21863.9	1.38927
$629$	832.230	0.0527554
$630$	16264.8	1.02858
$631$	12260.2	0.773486	0.386743	−	0.922188i	$-0.373600\pi$
$631$	12260.2	0.773486	0.386743	+	0.922188i	$0.373600\pi$
$632$	30109.1	1.89505
$633$	−17197.4	−1.07983
$634$	23022.2	1.44216
$635$	17813.3	1.11323
$636$	56791.2	3.54075
$637$	1638.04	0.101886
$638$	−57060.4	−3.54082
$639$	45640.1	2.82550
$640$	28207.7	1.74220
$641$	−27593.9	−1.70030	−0.850150	−	0.526541i	$-0.823489\pi$
$641$	−27593.9	−1.70030	−0.850150	+	0.526541i	$0.823489\pi$
$642$	−51011.3	−3.13591
$643$	17363.4	1.06493	0.532463	−	0.846453i	$-0.321267\pi$
$643$	17363.4	1.06493	0.532463	+	0.846453i	$0.321267\pi$
$644$	13.7070	0.000838714 0
$645$	2288.71	0.139717
$646$	−23259.9	−1.41664
$647$	5647.37	0.343154	0.171577	−	0.985171i	$-0.445114\pi$
$647$	5647.37	0.343154	0.171577	+	0.985171i	$0.445114\pi$
$648$	−73774.7	−4.47244
$649$	44423.9	2.68689
$650$	−271.960	−0.0164110
$651$	−1910.27	−0.115007
$652$	33821.3	2.03151
$653$	24858.4	1.48972	0.744858	−	0.667223i	$-0.232517\pi$
$653$	24858.4	1.48972	0.744858	+	0.667223i	$0.232517\pi$
$654$	−35888.9	−2.14582
$655$	17797.2	1.06167
$656$	−255.815	−0.0152254
$657$	6244.90	0.370832
$658$	−13611.1	−0.806409
$659$	33246.1	1.96523	0.982614	−	0.185662i	$-0.0594430\pi$
$659$	33246.1	1.96523	0.982614	+	0.185662i	$0.0594430\pi$
$660$	−104659.	−6.17252
$661$	11332.7	0.666854	0.333427	−	0.942776i	$-0.391795\pi$
$661$	11332.7	0.666854	0.333427	+	0.942776i	$0.391795\pi$
$662$	−8628.32	−0.506570
$663$	1567.52	0.0918209
$664$	−22554.9	−1.31822
$665$	7597.02	0.443007
$666$	8979.60	0.522451
$667$	36.6574	0.00212801
$668$	22478.6	1.30198
$669$	42699.4	2.46764
$670$	−4320.43	−0.249123
$671$	44247.7	2.54570
$672$	−4571.89	−0.262447
$673$	−9187.92	−0.526253	−0.263126	−	0.964761i	$-0.584754\pi$
$673$	−9187.92	−0.526253	−0.263126	+	0.964761i	$0.584754\pi$
$674$	−16776.9	−0.958789
$675$	−4900.88	−0.279459
$676$	−31527.3	−1.79377
$677$	−15815.1	−0.897819	−0.448910	−	0.893577i	$-0.648187\pi$
$677$	−15815.1	−0.897819	−0.448910	+	0.893577i	$0.648187\pi$
$678$	−12610.1	−0.714289
$679$	−117.330	−0.00663141
$680$	10291.0	0.580354
$681$	−39774.7	−2.23813
$682$	13806.7	0.775201
$683$	2954.61	0.165527	0.0827635	−	0.996569i	$-0.473625\pi$
$683$	2954.61	0.165527	0.0827635	+	0.996569i	$0.473625\pi$
$684$	−161818.	−9.04573
$685$	11480.8	0.640379
$686$	−14314.4	−0.796686
$687$	−30161.2	−1.67500
$688$	665.589	0.0368828
$689$	−2007.92	−0.111024
$690$	104.280	0.00575342
$691$	−2739.75	−0.150832	−0.0754160	−	0.997152i	$-0.524028\pi$
$691$	−2739.75	−0.150832	−0.0754160	+	0.997152i	$0.524028\pi$
$692$	−19700.3	−1.08221
$693$	21953.9	1.20341
$694$	−44481.8	−2.43300
$695$	12702.4	0.693282
$696$	53896.6	2.93527
$697$	259.983	0.0141285
$698$	17807.6	0.965653
$699$	−26053.1	−1.40976
$700$	742.524	0.0400925
$701$	13374.0	0.720584	0.360292	−	0.932840i	$-0.382677\pi$
$701$	13374.0	0.720584	0.360292	+	0.932840i	$0.382677\pi$
$702$	10472.8	0.563063
$703$	4194.23	0.225019
$704$	49812.5	2.66673
$705$	−66766.2	−3.56676
$706$	42947.9	2.28947
$707$	4318.07	0.229700
$708$	−93440.6	−4.96005
$709$	−5786.47	−0.306510	−0.153255	−	0.988187i	$-0.548976\pi$
$709$	−5786.47	−0.306510	−0.153255	+	0.988187i	$0.548976\pi$
$710$	−32574.4	−1.72183
$711$	−68990.2	−3.63901
$712$	−12337.2	−0.649378
$713$	−8.86988	−0.000465890 0
$714$	−6637.61	−0.347908
$715$	3700.36	0.193546
$716$	55729.3	2.90880
$717$	−1841.39	−0.0959108
$718$	2616.62	0.136005
$719$	17914.4	0.929201	0.464601	−	0.885520i	$-0.346198\pi$
$719$	17914.4	0.929201	0.464601	+	0.885520i	$0.346198\pi$
$720$	23202.1	1.20096
$721$	−3995.06	−0.206358
$722$	−84674.1	−4.36460
$723$	−46445.1	−2.38909
$724$	−62148.6	−3.19024
$725$	1985.78	0.101724
$726$	−156598.	−8.00538
$727$	31156.5	1.58945	0.794726	−	0.606968i	$-0.207614\pi$
$727$	31156.5	1.58945	0.794726	+	0.606968i	$0.207614\pi$
$728$	−712.536	−0.0362752
$729$	52983.1	2.69182
$730$	−4457.14	−0.225981
$731$	−676.434	−0.0342255
$732$	−93070.1	−4.69941
$733$	6586.43	0.331890	0.165945	−	0.986135i	$-0.446933\pi$
$733$	6586.43	0.331890	0.165945	+	0.986135i	$0.446933\pi$
$734$	5658.83	0.284566
$735$	−34024.0	−1.70748
$736$	−21.2285	−0.00106317
$737$	−5831.64	−0.291467
$738$	2805.17	0.139918
$739$	9772.80	0.486466	0.243233	−	0.969968i	$-0.421792\pi$
$739$	9772.80	0.486466	0.243233	+	0.969968i	$0.421792\pi$
$740$	−4132.32	−0.205280
$741$	7899.89	0.391646
$742$	8502.49	0.420669
$743$	13294.7	0.656440	0.328220	−	0.944601i	$-0.393551\pi$
$743$	13294.7	0.656440	0.328220	+	0.944601i	$0.393551\pi$
$744$	−13041.2	−0.642625
$745$	−10435.7	−0.513199
$746$	67003.5	3.28843
$747$	51681.0	2.53134
$748$	30932.4	1.51203
$749$	−4924.22	−0.240223
$750$	68241.0	3.32241
$751$	3770.43	0.183202	0.0916012	−	0.995796i	$-0.470802\pi$
$751$	3770.43	0.183202	0.0916012	+	0.995796i	$0.470802\pi$
$752$	−19416.6	−0.941556
$753$	−12244.0	−0.592558
$754$	−4243.45	−0.204957
$755$	−19156.9	−0.923431
$756$	−28593.6	−1.37558
$757$	−30569.7	−1.46773	−0.733867	−	0.679293i	$-0.762286\pi$
$757$	−30569.7	−1.46773	−0.733867	+	0.679293i	$0.762286\pi$
$758$	46044.9	2.20637
$759$	140.755	0.00673133
$760$	51864.0	2.47540
$761$	15797.5	0.752507	0.376254	−	0.926517i	$-0.377212\pi$
$761$	15797.5	0.752507	0.376254	+	0.926517i	$0.377212\pi$
$762$	−78437.3	−3.72898
$763$	−3464.43	−0.164378
$764$	41272.5	1.95443
$765$	−23580.1	−1.11443
$766$	−14899.7	−0.702804
$767$	3303.70	0.155528
$768$	−66482.5	−3.12367
$769$	−11901.9	−0.558118	−0.279059	−	0.960274i	$-0.590023\pi$
$769$	−11901.9	−0.558118	−0.279059	+	0.960274i	$0.590023\pi$
$770$	−15669.1	−0.733343
$771$	5483.50	0.256140
$772$	−24604.3	−1.14706
$773$	−1003.96	−0.0467142	−0.0233571	−	0.999727i	$-0.507435\pi$
$773$	−1003.96	−0.0467142	−0.0233571	+	0.999727i	$0.507435\pi$
$774$	−7298.60	−0.338944
$775$	−480.492	−0.0222707
$776$	−801.000	−0.0370544
$777$	1196.90	0.0552617
$778$	−57965.9	−2.67118
$779$	1310.25	0.0602626
$780$	−7783.28	−0.357290
$781$	−43968.5	−2.01449
$782$	−30.8202	−0.00140937
$783$	−76469.4	−3.49016
$784$	−9894.69	−0.450742
$785$	16056.7	0.730047
$786$	−78366.4	−3.55628
$787$	−28541.1	−1.29273	−0.646367	−	0.763027i	$-0.723712\pi$
$787$	−28541.1	−1.29273	−0.646367	+	0.763027i	$0.723712\pi$
$788$	1094.03	0.0494584
$789$	47878.5	2.16036
$790$	49240.0	2.21757
$791$	−1217.28	−0.0547173
$792$	149877.	6.72430
$793$	3290.60	0.147355
$794$	27250.5	1.21799
$795$	41707.0	1.86062
$796$	−18523.2	−0.824797
$797$	15695.2	0.697556	0.348778	−	0.937205i	$-0.386597\pi$
$797$	15695.2	0.697556	0.348778	+	0.937205i	$0.386597\pi$
$798$	−33451.9	−1.48394
$799$	19733.0	0.873720
$800$	−1149.97	−0.0508221
$801$	28268.8	1.24698
$802$	60363.0	2.65772
$803$	−6016.18	−0.264391
$804$	12266.2	0.538054
$805$	10.0663	0.000440734 0
$806$	1026.77	0.0448717
$807$	41671.0	1.81771
$808$	29478.9	1.28350
$809$	8659.19	0.376318	0.188159	−	0.982139i	$-0.439748\pi$
$809$	8659.19	0.376318	0.188159	+	0.982139i	$0.439748\pi$
$810$	−120650.	−5.23359
$811$	37800.8	1.63670	0.818351	−	0.574718i	$-0.194888\pi$
$811$	37800.8	1.63670	0.818351	+	0.574718i	$0.194888\pi$
$812$	11585.8	0.500715
$813$	−47275.2	−2.03938
$814$	−8650.72	−0.372491
$815$	24838.1	1.06753
$816$	−9468.70	−0.406214
$817$	−3409.06	−0.145983
$818$	42043.7	1.79710
$819$	1632.66	0.0696580
$820$	−1290.91	−0.0549761
$821$	−9437.46	−0.401181	−0.200590	−	0.979675i	$-0.564286\pi$
$821$	−9437.46	−0.401181	−0.200590	+	0.979675i	$0.564286\pi$
$822$	−50553.4	−2.14508
$823$	−16063.8	−0.680377	−0.340189	−	0.940357i	$-0.610491\pi$
$823$	−16063.8	−0.680377	−0.340189	+	0.940357i	$0.610491\pi$
$824$	−27273.8	−1.15307
$825$	7624.86	0.321774
$826$	−13989.5	−0.589292
$827$	19043.3	0.800725	0.400362	−	0.916357i	$-0.368884\pi$
$827$	19043.3	0.800725	0.400362	+	0.916357i	$0.368884\pi$
$828$	−214.415	−0.00899931
$829$	41.4443	0.00173633	0.000868167	−	1.00000i	$-0.499724\pi$
$829$	41.4443	0.00173633	0.000868167		1.00000i	$0.499724\pi$
$830$	−36886.0	−1.54257
$831$	−46288.3	−1.93228
$832$	3704.44	0.154361
$833$	10055.9	0.418267
$834$	−55932.5	−2.32228
$835$	16508.1	0.684175
$836$	155892.	6.44931
$837$	18503.1	0.764109
$838$	−14104.9	−0.581440
$839$	−31958.8	−1.31507	−0.657534	−	0.753425i	$-0.728400\pi$
$839$	−31958.8	−1.31507	−0.657534	+	0.753425i	$0.728400\pi$
$840$	14800.3	0.607926
$841$	6595.48	0.270429
$842$	7224.97	0.295711
$843$	70398.7	2.87623
$844$	−25237.6	−1.02928
$845$	−23153.4	−0.942605
$846$	212915.	8.65268
$847$	−15116.7	−0.613243
$848$	12129.0	0.491169
$849$	90148.6	3.64416
$850$	−1669.56	−0.0673712
$851$	5.55750	0.000223864 0
$852$	92482.7	3.71878
$853$	22739.3	0.912753	0.456376	−	0.889787i	$-0.349147\pi$
$853$	22739.3	0.912753	0.456376	+	0.889787i	$0.349147\pi$
$854$	−13934.0	−0.558326
$855$	−118838.	−4.75342
$856$	−33617.0	−1.34230
$857$	−7935.15	−0.316289	−0.158144	−	0.987416i	$-0.550551\pi$
$857$	−7935.15	−0.316289	−0.158144	+	0.987416i	$0.550551\pi$
$858$	−16293.7	−0.648321
$859$	−41604.6	−1.65254	−0.826270	−	0.563275i	$-0.809541\pi$
$859$	−41604.6	−1.65254	−0.826270	+	0.563275i	$0.809541\pi$
$860$	3358.74	0.133177
$861$	373.902	0.0147997
$862$	28253.7	1.11638
$863$	−33297.9	−1.31341	−0.656706	−	0.754146i	$-0.728051\pi$
$863$	−33297.9	−1.31341	−0.656706	+	0.754146i	$0.728051\pi$
$864$	44283.8	1.74371
$865$	−14467.7	−0.568690
$866$	−5686.44	−0.223133
$867$	−38989.6	−1.52729
$868$	−2803.37	−0.109623
$869$	66463.3	2.59449
$870$	88141.7	3.43481
$871$	−433.686	−0.0168713
$872$	−23651.2	−0.918500
$873$	1835.37	0.0711543
$874$	−155.326	−0.00601142
$875$	6587.44	0.254510
$876$	12654.3	0.488072
$877$	−20931.0	−0.805918	−0.402959	−	0.915218i	$-0.632018\pi$
$877$	−20931.0	−0.805918	−0.402959	+	0.915218i	$0.632018\pi$
$878$	63801.3	2.45238
$879$	−39968.5	−1.53368
$880$	−22352.3	−0.856245
$881$	−21406.2	−0.818609	−0.409305	−	0.912398i	$-0.634229\pi$
$881$	−21406.2	−0.818609	−0.409305	+	0.912398i	$0.634229\pi$
$882$	108501.	4.14221
$883$	14561.9	0.554980	0.277490	−	0.960728i	$-0.410497\pi$
$883$	14561.9	0.554980	0.277490	+	0.960728i	$0.410497\pi$
$884$	2300.37	0.0875224
$885$	−68622.0	−2.60645
$886$	−31504.5	−1.19460
$887$	4738.34	0.179366	0.0896831	−	0.995970i	$-0.471415\pi$
$887$	4738.34	0.179366	0.0896831	+	0.995970i	$0.471415\pi$
$888$	8171.06	0.308787
$889$	−7571.70	−0.285654
$890$	−20176.1	−0.759894
$891$	−162852.	−6.12316
$892$	62662.5	2.35212
$893$	99449.3	3.72670
$894$	45951.2	1.71906
$895$	40927.1	1.52854
$896$	−11989.9	−0.447048
$897$	10.4676	0.000389636 0
$898$	87541.8	3.25313
$899$	−7497.22	−0.278138
$900$	−11615.1	−0.430189
$901$	−12326.6	−0.455782
$902$	−2702.42	−0.0997571
$903$	−972.833	−0.0358515
$904$	−8310.20	−0.305745
$905$	−45641.4	−1.67643
$906$	84353.3	3.09321
$907$	−18817.7	−0.688901	−0.344450	−	0.938805i	$-0.611935\pi$
$907$	−18817.7	−0.688901	−0.344450	+	0.938805i	$0.611935\pi$
$908$	−58370.4	−2.13336
$909$	−67546.3	−2.46465
$910$	−1165.27	−0.0424488
$911$	−1352.52	−0.0491888	−0.0245944	−	0.999698i	$-0.507829\pi$
$911$	−1352.52	−0.0491888	−0.0245944	+	0.999698i	$0.507829\pi$
$912$	−47719.9	−1.73264
$913$	−49788.2	−1.80476
$914$	−27088.9	−0.980328
$915$	−68349.9	−2.46948
$916$	−44262.4	−1.59658
$917$	−7564.85	−0.272425
$918$	64292.5	2.31151
$919$	−888.511	−0.0318926	−0.0159463	−	0.999873i	$-0.505076\pi$
$919$	−888.511	−0.0318926	−0.0159463	+	0.999873i	$0.505076\pi$
$920$	68.7215	0.00246270
$921$	−84683.0	−3.02975
$922$	−31847.0	−1.13755
$923$	−3269.83	−0.116607
$924$	44486.3	1.58387
$925$	301.056	0.0107013
$926$	−91746.0	−3.25590
$927$	62493.6	2.21420
$928$	−17943.3	−0.634716
$929$	−4175.36	−0.147459	−0.0737294	−	0.997278i	$-0.523490\pi$
$929$	−4175.36	−0.147459	−0.0737294	+	0.997278i	$0.523490\pi$
$930$	−21327.4	−0.751992
$931$	50679.3	1.78405
$932$	−38233.6	−1.34376
$933$	93322.1	3.27463
$934$	−41054.8	−1.43828
$935$	22716.5	0.794555
$936$	11146.0	0.389229
$937$	42107.7	1.46809	0.734043	−	0.679103i	$-0.237631\pi$
$937$	42107.7	1.46809	0.734043	+	0.679103i	$0.237631\pi$
$938$	1836.43	0.0639250
$939$	−16913.3	−0.587800
$940$	−97981.2	−3.39978
$941$	13687.1	0.474161	0.237081	−	0.971490i	$-0.423809\pi$
$941$	13687.1	0.474161	0.237081	+	0.971490i	$0.423809\pi$
$942$	−70702.1	−2.44544
$943$	1.73612	5.99533e−5 0
$944$	−19956.3	−0.688052
$945$	−20998.9	−0.722850
$946$	7031.28	0.241656
$947$	−28637.4	−0.982673	−0.491337	−	0.870970i	$-0.663491\pi$
$947$	−28637.4	−0.982673	−0.491337	+	0.870970i	$0.663491\pi$
$948$	−139798.	−4.78948
$949$	−447.409	−0.0153040
$950$	−8414.19	−0.287360
$951$	−48001.9	−1.63677
$952$	−4374.26	−0.148919
$953$	11320.3	0.384786	0.192393	−	0.981318i	$-0.438375\pi$
$953$	11320.3	0.384786	0.192393	+	0.981318i	$0.438375\pi$
$954$	−133002.	−4.51373
$955$	30310.1	1.02703
$956$	−2702.29	−0.0914208
$957$	118972.	4.01863
$958$	33042.7	1.11437
$959$	−4880.02	−0.164321
$960$	−76945.9	−2.58689
$961$	−27976.9	−0.939107
$962$	−643.334	−0.0215612
$963$	77028.1	2.57757
$964$	−68159.5	−2.27725
$965$	−18069.2	−0.602766
$966$	−44.3249	−0.00147633
$967$	32716.2	1.08798	0.543992	−	0.839090i	$-0.316912\pi$
$967$	32716.2	1.08798	0.543992	+	0.839090i	$0.316912\pi$
$968$	−103200.	−3.42663
$969$	48497.5	1.60780
$970$	−1309.95	−0.0433606
$971$	−45441.9	−1.50185	−0.750926	−	0.660386i	$-0.770393\pi$
$971$	−45441.9	−1.50185	−0.750926	+	0.660386i	$0.770393\pi$
$972$	172219.	5.68305
$973$	−5399.27	−0.177896
$974$	81133.3	2.66907
$975$	567.043	0.0186256
$976$	−19877.1	−0.651897
$977$	−2927.38	−0.0958600	−0.0479300	−	0.998851i	$-0.515262\pi$
$977$	−2927.38	−0.0958600	−0.0479300	+	0.998851i	$0.515262\pi$
$978$	−109369.	−3.57591
$979$	−27233.4	−0.889054
$980$	−49931.2	−1.62754
$981$	54193.1	1.76376
$982$	72770.8	2.36478
$983$	983.000	0.0318950
$983$	983.000	0.0318950
$984$	2552.58	0.0826965
$985$	803.447	0.0259898
$986$	−26050.6	−0.841398
$987$	28379.5	0.915229
$988$	11593.3	0.373312
$989$	−4.51712	−0.000145234 0
$990$	245107.	7.86869
$991$	−42370.2	−1.35816	−0.679079	−	0.734065i	$-0.737621\pi$
$991$	−42370.2	−1.35816	−0.679079	+	0.734065i	$0.737621\pi$
$992$	4341.67	0.138960
$993$	17990.2	0.574928
$994$	13846.0	0.441820
$995$	−13603.3	−0.433421
$996$	104724.	3.33163
$997$	37554.7	1.19295	0.596474	−	0.802632i	$-0.296568\pi$
$997$	37554.7	1.19295	0.596474	+	0.802632i	$0.296568\pi$
$998$	36426.9	1.15538
$999$	−11593.2	−0.367161

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.4.a.a.1.12	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.4.a.a.1.12	✓	109	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)

\(f(q)\)	\(=\)	\(q-4.74560 q^{2} +9.89469 q^{3} +14.5207 q^{4} +10.6639 q^{5} -46.9563 q^{6} -4.53278 q^{7} -30.9447 q^{8} +70.9049 q^{9} +O(q^{10})\)	\(q-4.74560 q^{2} +9.89469 q^{3} +14.5207 q^{4} +10.6639 q^{5} -46.9563 q^{6} -4.53278 q^{7} -30.9447 q^{8} +70.9049 q^{9} -50.6066 q^{10} -68.3080 q^{11} +143.678 q^{12} -5.07991 q^{13} +21.5107 q^{14} +105.516 q^{15} +30.6856 q^{16} -31.1856 q^{17} -336.487 q^{18} -157.168 q^{19} +154.847 q^{20} -44.8504 q^{21} +324.162 q^{22} -0.208252 q^{23} -306.189 q^{24} -11.2813 q^{25} +24.1072 q^{26} +434.426 q^{27} -65.8192 q^{28} -176.024 q^{29} -500.737 q^{30} +42.5920 q^{31} +101.936 q^{32} -675.887 q^{33} +147.994 q^{34} -48.3371 q^{35} +1029.59 q^{36} -26.6864 q^{37} +745.855 q^{38} -50.2641 q^{39} -329.992 q^{40} -8.33664 q^{41} +212.842 q^{42} +21.6906 q^{43} -991.881 q^{44} +756.123 q^{45} +0.988283 q^{46} -632.759 q^{47} +303.624 q^{48} -322.454 q^{49} +53.5364 q^{50} -308.572 q^{51} -73.7639 q^{52} +395.267 q^{53} -2061.61 q^{54} -728.430 q^{55} +140.266 q^{56} -1555.13 q^{57} +835.340 q^{58} -650.347 q^{59} +1532.17 q^{60} -647.768 q^{61} -202.125 q^{62} -321.396 q^{63} -729.234 q^{64} -54.1716 q^{65} +3207.49 q^{66} +85.3728 q^{67} -452.837 q^{68} -2.06059 q^{69} +229.388 q^{70} +643.680 q^{71} -2194.13 q^{72} +88.0743 q^{73} +126.643 q^{74} -111.625 q^{75} -2282.19 q^{76} +309.625 q^{77} +238.534 q^{78} -972.995 q^{79} +327.228 q^{80} +2384.08 q^{81} +39.5623 q^{82} +728.878 q^{83} -651.261 q^{84} -332.560 q^{85} -102.935 q^{86} -1741.70 q^{87} +2113.77 q^{88} +398.686 q^{89} -3588.26 q^{90} +23.0261 q^{91} -3.02397 q^{92} +421.435 q^{93} +3002.82 q^{94} -1676.02 q^{95} +1008.63 q^{96} +25.8849 q^{97} +1530.24 q^{98} -4843.38 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q - 19 q^{2} - 23 q^{3} + 385 q^{4} - 50 q^{5} - 83 q^{6} - 225 q^{7} - 225 q^{8} + 714 q^{9}+O(q^{10}) \) 109 * q - 19 * q^2 - 23 * q^3 + 385 * q^4 - 50 * q^5 - 83 * q^6 - 225 * q^7 - 225 * q^8 + 714 * q^9	\( 109 q - 19 q^{2} - 23 q^{3} + 385 q^{4} - 50 q^{5} - 83 q^{6} - 225 q^{7} - 225 q^{8} + 714 q^{9} - 243 q^{10} - 126 q^{11} - 280 q^{12} - 458 q^{13} - 177 q^{14} - 314 q^{15} + 1009 q^{16} - 594 q^{17} - 671 q^{18} - 491 q^{19} - 500 q^{20} - 660 q^{21} - 899 q^{22} - 487 q^{23} - 811 q^{24} + 705 q^{25} - 104 q^{26} - 842 q^{27} - 2648 q^{28} - 820 q^{29} - 728 q^{30} - 965 q^{31} - 1669 q^{32} - 2196 q^{33} - 508 q^{34} - 846 q^{35} + 1358 q^{36} - 3209 q^{37} - 1136 q^{38} - 1326 q^{39} - 3234 q^{40} - 1961 q^{41} - 2240 q^{42} - 2999 q^{43} - 1922 q^{44} - 2234 q^{45} - 2962 q^{46} - 1903 q^{47} - 2787 q^{48} + 1186 q^{49} - 2309 q^{50} - 2436 q^{51} - 4897 q^{52} - 1825 q^{53} - 3306 q^{54} - 2888 q^{55} - 1820 q^{56} - 6684 q^{57} - 4813 q^{58} - 1537 q^{59} - 3869 q^{60} - 2276 q^{61} - 1950 q^{62} - 6491 q^{63} - 89 q^{64} - 5546 q^{65} - 3527 q^{66} - 5005 q^{67} - 4183 q^{68} - 3018 q^{69} - 2993 q^{70} - 2014 q^{71} - 9549 q^{72} - 12904 q^{73} - 2714 q^{74} - 3379 q^{75} - 6293 q^{76} - 3258 q^{77} - 4593 q^{78} - 5005 q^{79} - 3988 q^{80} + 249 q^{81} - 5116 q^{82} - 2854 q^{83} - 4158 q^{84} - 11742 q^{85} - 2709 q^{86} - 2412 q^{87} - 10451 q^{88} - 2519 q^{89} - 8095 q^{90} - 2438 q^{91} - 6660 q^{92} - 10668 q^{93} - 4281 q^{94} - 4482 q^{95} - 6515 q^{96} - 16628 q^{97} - 5708 q^{98} - 6308 q^{99}+O(q^{100}) \) 109 * q - 19 * q^2 - 23 * q^3 + 385 * q^4 - 50 * q^5 - 83 * q^6 - 225 * q^7 - 225 * q^8 + 714 * q^9 - 243 * q^10 - 126 * q^11 - 280 * q^12 - 458 * q^13 - 177 * q^14 - 314 * q^15 + 1009 * q^16 - 594 * q^17 - 671 * q^18 - 491 * q^19 - 500 * q^20 - 660 * q^21 - 899 * q^22 - 487 * q^23 - 811 * q^24 + 705 * q^25 - 104 * q^26 - 842 * q^27 - 2648 * q^28 - 820 * q^29 - 728 * q^30 - 965 * q^31 - 1669 * q^32 - 2196 * q^33 - 508 * q^34 - 846 * q^35 + 1358 * q^36 - 3209 * q^37 - 1136 * q^38 - 1326 * q^39 - 3234 * q^40 - 1961 * q^41 - 2240 * q^42 - 2999 * q^43 - 1922 * q^44 - 2234 * q^45 - 2962 * q^46 - 1903 * q^47 - 2787 * q^48 + 1186 * q^49 - 2309 * q^50 - 2436 * q^51 - 4897 * q^52 - 1825 * q^53 - 3306 * q^54 - 2888 * q^55 - 1820 * q^56 - 6684 * q^57 - 4813 * q^58 - 1537 * q^59 - 3869 * q^60 - 2276 * q^61 - 1950 * q^62 - 6491 * q^63 - 89 * q^64 - 5546 * q^65 - 3527 * q^66 - 5005 * q^67 - 4183 * q^68 - 3018 * q^69 - 2993 * q^70 - 2014 * q^71 - 9549 * q^72 - 12904 * q^73 - 2714 * q^74 - 3379 * q^75 - 6293 * q^76 - 3258 * q^77 - 4593 * q^78 - 5005 * q^79 - 3988 * q^80 + 249 * q^81 - 5116 * q^82 - 2854 * q^83 - 4158 * q^84 - 11742 * q^85 - 2709 * q^86 - 2412 * q^87 - 10451 * q^88 - 2519 * q^89 - 8095 * q^90 - 2438 * q^91 - 6660 * q^92 - 10668 * q^93 - 4281 * q^94 - 4482 * q^95 - 6515 * q^96 - 16628 * q^97 - 5708 * q^98 - 6308 * q^99

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