LMFDB - Embedded newform 983.4.a.b.1.3

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			1.3
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)

$f(q)$	$=$	$q-5.42093 q^{2} -6.60411 q^{3} +21.3865 q^{4} -7.49992 q^{5} +35.8004 q^{6} +7.21303 q^{7} -72.5672 q^{8} +16.6143 q^{9} +O(q^{10})$	\(q-5.42093 q^{2} -6.60411 q^{3} +21.3865 q^{4} -7.49992 q^{5} +35.8004 q^{6} +7.21303 q^{7} -72.5672 q^{8} +16.6143 q^{9} +40.6566 q^{10} -55.3574 q^{11} -141.239 q^{12} +35.7917 q^{13} -39.1013 q^{14} +49.5303 q^{15} +222.290 q^{16} -78.1906 q^{17} -90.0650 q^{18} -47.6350 q^{19} -160.397 q^{20} -47.6357 q^{21} +300.089 q^{22} -104.915 q^{23} +479.242 q^{24} -68.7511 q^{25} -194.024 q^{26} +68.5883 q^{27} +154.261 q^{28} +58.8176 q^{29} -268.501 q^{30} -270.014 q^{31} -624.481 q^{32} +365.587 q^{33} +423.866 q^{34} -54.0972 q^{35} +355.322 q^{36} +264.596 q^{37} +258.226 q^{38} -236.372 q^{39} +544.249 q^{40} +381.569 q^{41} +258.230 q^{42} +370.700 q^{43} -1183.90 q^{44} -124.606 q^{45} +568.737 q^{46} -634.224 q^{47} -1468.03 q^{48} -290.972 q^{49} +372.695 q^{50} +516.379 q^{51} +765.458 q^{52} -300.988 q^{53} -371.812 q^{54} +415.176 q^{55} -523.430 q^{56} +314.587 q^{57} -318.846 q^{58} -89.3894 q^{59} +1059.28 q^{60} -925.759 q^{61} +1463.73 q^{62} +119.839 q^{63} +1606.95 q^{64} -268.435 q^{65} -1981.82 q^{66} -246.900 q^{67} -1672.22 q^{68} +692.871 q^{69} +293.257 q^{70} -357.049 q^{71} -1205.65 q^{72} -725.334 q^{73} -1434.35 q^{74} +454.040 q^{75} -1018.75 q^{76} -399.295 q^{77} +1281.36 q^{78} -685.406 q^{79} -1667.16 q^{80} -901.551 q^{81} -2068.46 q^{82} -1112.76 q^{83} -1018.76 q^{84} +586.423 q^{85} -2009.54 q^{86} -388.438 q^{87} +4017.13 q^{88} +48.7358 q^{89} +675.481 q^{90} +258.167 q^{91} -2243.76 q^{92} +1783.20 q^{93} +3438.09 q^{94} +357.259 q^{95} +4124.14 q^{96} +305.095 q^{97} +1577.34 q^{98} -919.725 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.42093	−1.91659	−0.958294	−	0.285784i	$-0.907746\pi$
$2$	−5.42093	−1.91659	−0.958294	+	0.285784i	$0.907746\pi$
$3$	−6.60411	−1.27096	−0.635481	−	0.772116i	$-0.719198\pi$
$3$	−6.60411	−1.27096	−0.635481	+	0.772116i	$0.719198\pi$
$4$	21.3865	2.67331
$5$	−7.49992	−0.670814	−0.335407	−	0.942073i	$-0.608874\pi$
$5$	−7.49992	−0.670814	−0.335407	+	0.942073i	$0.608874\pi$
$6$	35.8004	2.43591
$7$	7.21303	0.389467	0.194734	−	0.980856i	$-0.437616\pi$
$7$	7.21303	0.389467	0.194734	+	0.980856i	$0.437616\pi$
$8$	−72.5672	−3.20705
$9$	16.6143	0.615345
$10$	40.6566	1.28567
$11$	−55.3574	−1.51735	−0.758677	−	0.651467i	$-0.774154\pi$
$11$	−55.3574	−1.51735	−0.758677	+	0.651467i	$0.774154\pi$
$12$	−141.239	−3.39768
$13$	35.7917	0.763602	0.381801	−	0.924245i	$-0.375304\pi$
$13$	35.7917	0.763602	0.381801	+	0.924245i	$0.375304\pi$
$14$	−39.1013	−0.746448
$15$	49.5303	0.852579
$16$	222.290	3.47328
$17$	−78.1906	−1.11553	−0.557765	−	0.829999i	$-0.688341\pi$
$17$	−78.1906	−1.11553	−0.557765	+	0.829999i	$0.688341\pi$
$18$	−90.0650	−1.17936
$19$	−47.6350	−0.575170	−0.287585	−	0.957755i	$-0.592852\pi$
$19$	−47.6350	−0.575170	−0.287585	+	0.957755i	$0.592852\pi$
$20$	−160.397	−1.79329
$21$	−47.6357	−0.494998
$22$	300.089	2.90814
$23$	−104.915	−0.951143	−0.475572	−	0.879677i	$-0.657759\pi$
$23$	−104.915	−0.951143	−0.475572	+	0.879677i	$0.657759\pi$
$24$	479.242	4.07604
$25$	−68.7511	−0.550009
$26$	−194.024	−1.46351
$27$	68.5883	0.488882
$28$	154.261	1.04117
$29$	58.8176	0.376626	0.188313	−	0.982109i	$-0.439698\pi$
$29$	58.8176	0.376626	0.188313	+	0.982109i	$0.439698\pi$
$30$	−268.501	−1.63404
$31$	−270.014	−1.56438	−0.782192	−	0.623037i	$-0.785899\pi$
$31$	−270.014	−1.56438	−0.782192	+	0.623037i	$0.785899\pi$
$32$	−624.481	−3.44980
$33$	365.587	1.92850
$34$	423.866	2.13801
$35$	−54.0972	−0.261260
$36$	355.322	1.64501
$37$	264.596	1.17566	0.587828	−	0.808986i	$-0.299983\pi$
$37$	264.596	1.17566	0.587828	+	0.808986i	$0.299983\pi$
$38$	258.226	1.10236
$39$	−236.372	−0.970509
$40$	544.249	2.15133
$41$	381.569	1.45344	0.726721	−	0.686933i	$-0.241043\pi$
$41$	381.569	1.45344	0.726721	+	0.686933i	$0.241043\pi$
$42$	258.230	0.948707
$43$	370.700	1.31468	0.657339	−	0.753595i	$-0.271682\pi$
$43$	370.700	1.31468	0.657339	+	0.753595i	$0.271682\pi$
$44$	−1183.90	−4.05636
$45$	−124.606	−0.412782
$46$	568.737	1.82295
$47$	−634.224	−1.96832	−0.984161	−	0.177276i	$-0.943271\pi$
$47$	−634.224	−1.96832	−0.984161	+	0.177276i	$0.943271\pi$
$48$	−1468.03	−4.41441
$49$	−290.972	−0.848315
$50$	372.695	1.05414
$51$	516.379	1.41780
$52$	765.458	2.04135
$53$	−300.988	−0.780073	−0.390036	−	0.920799i	$-0.627538\pi$
$53$	−300.988	−0.780073	−0.390036	+	0.920799i	$0.627538\pi$
$54$	−371.812	−0.936986
$55$	415.176	1.01786
$56$	−523.430	−1.24904
$57$	314.587	0.731019
$58$	−318.846	−0.721837
$59$	−89.3894	−0.197246	−0.0986230	−	0.995125i	$-0.531444\pi$
$59$	−89.3894	−0.197246	−0.0986230	+	0.995125i	$0.531444\pi$
$60$	1059.28	2.27921
$61$	−925.759	−1.94314	−0.971568	−	0.236760i	$-0.923914\pi$
$61$	−925.759	−1.94314	−0.971568	+	0.236760i	$0.923914\pi$
$62$	1463.73	2.99828
$63$	119.839	0.239656
$64$	1606.95	3.13857
$65$	−268.435	−0.512235
$66$	−1981.82	−3.69614
$67$	−246.900	−0.450203	−0.225102	−	0.974335i	$-0.572271\pi$
$67$	−246.900	−0.450203	−0.225102	+	0.974335i	$0.572271\pi$
$68$	−1672.22	−2.98216
$69$	692.871	1.20887
$70$	293.257	0.500728
$71$	−357.049	−0.596815	−0.298408	−	0.954439i	$-0.596455\pi$
$71$	−357.049	−0.596815	−0.298408	+	0.954439i	$0.596455\pi$
$72$	−1205.65	−1.97344
$73$	−725.334	−1.16293	−0.581465	−	0.813571i	$-0.697520\pi$
$73$	−725.334	−1.16293	−0.581465	+	0.813571i	$0.697520\pi$
$74$	−1434.35	−2.25325
$75$	454.040	0.699041
$76$	−1018.75	−1.53761
$77$	−399.295	−0.590959
$78$	1281.36	1.86007
$79$	−685.406	−0.976129	−0.488064	−	0.872808i	$-0.662297\pi$
$79$	−685.406	−0.976129	−0.488064	+	0.872808i	$0.662297\pi$
$80$	−1667.16	−2.32992
$81$	−901.551	−1.23670
$82$	−2068.46	−2.78565
$83$	−1112.76	−1.47158	−0.735789	−	0.677211i	$-0.763188\pi$
$83$	−1112.76	−1.47158	−0.735789	+	0.677211i	$0.763188\pi$
$84$	−1018.76	−1.32328
$85$	586.423	0.748312
$86$	−2009.54	−2.51970
$87$	−388.438	−0.478678
$88$	4017.13	4.86623
$89$	48.7358	0.0580448	0.0290224	−	0.999579i	$-0.490761\pi$
$89$	48.7358	0.0580448	0.0290224	+	0.999579i	$0.490761\pi$
$90$	675.481	0.791132
$91$	258.167	0.297398
$92$	−2243.76	−2.54270
$93$	1783.20	1.98827
$94$	3438.09	3.77246
$95$	357.259	0.385832
$96$	4124.14	4.38457
$97$	305.095	0.319358	0.159679	−	0.987169i	$-0.448954\pi$
$97$	305.095	0.319358	0.159679	+	0.987169i	$0.448954\pi$
$98$	1577.34	1.62587
$99$	−919.725	−0.933695
$100$	−1470.35	−1.47035
$101$	−699.780	−0.689413	−0.344706	−	0.938711i	$-0.612022\pi$
$101$	−699.780	−0.689413	−0.344706	+	0.938711i	$0.612022\pi$
$102$	−2799.26	−2.71733
$103$	−383.134	−0.366518	−0.183259	−	0.983065i	$-0.558665\pi$
$103$	−383.134	−0.366518	−0.183259	+	0.983065i	$0.558665\pi$
$104$	−2597.30	−2.44891
$105$	357.264	0.332051
$106$	1631.63	1.49508
$107$	−1433.97	−1.29558	−0.647789	−	0.761820i	$-0.724306\pi$
$107$	−1433.97	−1.29558	−0.647789	+	0.761820i	$0.724306\pi$
$108$	1466.86	1.30693
$109$	−1833.53	−1.61119	−0.805596	−	0.592465i	$-0.798155\pi$
$109$	−1833.53	−1.61119	−0.805596	+	0.592465i	$0.798155\pi$
$110$	−2250.64	−1.95082
$111$	−1747.42	−1.49421
$112$	1603.38	1.35273
$113$	1062.61	0.884616	0.442308	−	0.896863i	$-0.354160\pi$
$113$	1062.61	0.884616	0.442308	+	0.896863i	$0.354160\pi$
$114$	−1705.36	−1.40106
$115$	786.855	0.638040
$116$	1257.90	1.00684
$117$	594.654	0.469878
$118$	484.574	0.378039
$119$	−563.991	−0.434462
$120$	−3594.28	−2.73426
$121$	1733.44	1.30236
$122$	5018.48	3.72419
$123$	−2519.93	−1.84727
$124$	−5774.65	−4.18209
$125$	1453.12	1.03977
$126$	−649.642	−0.459323
$127$	1437.43	1.00434	0.502169	−	0.864770i	$-0.332536\pi$
$127$	1437.43	1.00434	0.502169	+	0.864770i	$0.332536\pi$
$128$	−3715.30	−2.56554
$129$	−2448.14	−1.67091
$130$	1455.17	0.981743
$131$	−1242.98	−0.829003	−0.414502	−	0.910049i	$-0.636044\pi$
$131$	−1242.98	−0.829003	−0.414502	+	0.910049i	$0.636044\pi$
$132$	7818.61	5.15548
$133$	−343.593	−0.224010
$134$	1338.43	0.862855
$135$	−514.407	−0.327949
$136$	5674.07	3.57756
$137$	2562.91	1.59828	0.799140	−	0.601145i	$-0.205289\pi$
$137$	2562.91	1.59828	0.799140	+	0.601145i	$0.205289\pi$
$138$	−3756.00	−2.31690
$139$	−2516.30	−1.53547	−0.767733	−	0.640770i	$-0.778615\pi$
$139$	−2516.30	−1.53547	−0.767733	+	0.640770i	$0.778615\pi$
$140$	−1156.95	−0.698429
$141$	4188.49	2.50166
$142$	1935.54	1.14385
$143$	−1981.33	−1.15865
$144$	3693.19	2.13726
$145$	−441.128	−0.252646
$146$	3931.99	2.22886
$147$	1921.61	1.07818
$148$	5658.77	3.14289
$149$	−833.150	−0.458083	−0.229041	−	0.973417i	$-0.573559\pi$
$149$	−833.150	−0.458083	−0.229041	+	0.973417i	$0.573559\pi$
$150$	−2461.32	−1.33977
$151$	−114.946	−0.0619483	−0.0309741	−	0.999520i	$-0.509861\pi$
$151$	−114.946	−0.0619483	−0.0309741	+	0.999520i	$0.509861\pi$
$152$	3456.74	1.84460
$153$	−1299.08	−0.686435
$154$	2164.55	1.13263
$155$	2025.08	1.04941
$156$	−5055.17	−2.59447
$157$	−3582.95	−1.82134	−0.910670	−	0.413135i	$-0.864434\pi$
$157$	−3582.95	−1.82134	−0.910670	+	0.413135i	$0.864434\pi$
$158$	3715.54	1.87084
$159$	1987.76	0.991443
$160$	4683.56	2.31417
$161$	−756.755	−0.370439
$162$	4887.25	2.37024
$163$	1270.98	0.610743	0.305372	−	0.952233i	$-0.401219\pi$
$163$	1270.98	0.610743	0.305372	+	0.952233i	$0.401219\pi$
$164$	8160.42	3.88550
$165$	−2741.87	−1.29366
$166$	6032.18	2.82041
$167$	−2120.47	−0.982556	−0.491278	−	0.871003i	$-0.663470\pi$
$167$	−2120.47	−0.982556	−0.491278	+	0.871003i	$0.663470\pi$
$168$	3456.79	1.58748
$169$	−915.955	−0.416912
$170$	−3178.96	−1.43421
$171$	−791.423	−0.353928
$172$	7927.97	3.51454
$173$	2854.22	1.25435	0.627173	−	0.778880i	$-0.284212\pi$
$173$	2854.22	1.25435	0.627173	+	0.778880i	$0.284212\pi$
$174$	2105.70	0.917428
$175$	−495.904	−0.214210
$176$	−12305.4	−5.27019
$177$	590.338	0.250692
$178$	−264.193	−0.111248
$179$	274.255	0.114518	0.0572592	−	0.998359i	$-0.481764\pi$
$179$	274.255	0.114518	0.0572592	+	0.998359i	$0.481764\pi$
$180$	−2664.89	−1.10349
$181$	−4139.21	−1.69981	−0.849903	−	0.526940i	$-0.823339\pi$
$181$	−4139.21	−1.69981	−0.849903	+	0.526940i	$0.823339\pi$
$182$	−1399.50	−0.569989
$183$	6113.82	2.46965
$184$	7613.39	3.05036
$185$	−1984.45	−0.788646
$186$	−9666.61	−3.81070
$187$	4328.43	1.69265
$188$	−13563.8	−5.26194
$189$	494.730	0.190404
$190$	−1936.68	−0.739481
$191$	−163.958	−0.0621131	−0.0310565	−	0.999518i	$-0.509887\pi$
$191$	−163.958	−0.0621131	−0.0310565	+	0.999518i	$0.509887\pi$
$192$	−10612.5	−3.98900
$193$	91.3010	0.0340518	0.0170259	−	0.999855i	$-0.494580\pi$
$193$	91.3010	0.0340518	0.0170259	+	0.999855i	$0.494580\pi$
$194$	−1653.90	−0.612078
$195$	1772.77	0.651031
$196$	−6222.87	−2.26781
$197$	−810.480	−0.293118	−0.146559	−	0.989202i	$-0.546820\pi$
$197$	−810.480	−0.293118	−0.146559	+	0.989202i	$0.546820\pi$
$198$	4985.76	1.78951
$199$	−474.794	−0.169132	−0.0845660	−	0.996418i	$-0.526950\pi$
$199$	−474.794	−0.169132	−0.0845660	+	0.996418i	$0.526950\pi$
$200$	4989.08	1.76391
$201$	1630.56	0.572191
$202$	3793.46	1.32132
$203$	424.253	0.146684
$204$	11043.5	3.79021
$205$	−2861.74	−0.974988
$206$	2076.94	0.702464
$207$	−1743.09	−0.585281
$208$	7956.13	2.65220
$209$	2636.95	0.872736
$210$	−1936.70	−0.636406
$211$	3018.51	0.984847	0.492424	−	0.870356i	$-0.336111\pi$
$211$	3018.51	0.984847	0.492424	+	0.870356i	$0.336111\pi$
$212$	−6437.07	−2.08538
$213$	2357.99	0.758530
$214$	7773.44	2.48309
$215$	−2780.22	−0.881904
$216$	−4977.26	−1.56787
$217$	−1947.62	−0.609276
$218$	9939.42	3.08799
$219$	4790.19	1.47804
$220$	8879.16	2.72106
$221$	−2798.57	−0.851821
$222$	9472.64	2.86379
$223$	−2256.91	−0.677730	−0.338865	−	0.940835i	$-0.610043\pi$
$223$	−2256.91	−0.677730	−0.338865	+	0.940835i	$0.610043\pi$
$224$	−4504.40	−1.34358
$225$	−1142.25	−0.338445
$226$	−5760.32	−1.69544
$227$	5226.46	1.52816	0.764080	−	0.645122i	$-0.223193\pi$
$227$	5226.46	1.52816	0.764080	+	0.645122i	$0.223193\pi$
$228$	6727.91	1.95424
$229$	1465.97	0.423032	0.211516	−	0.977375i	$-0.432160\pi$
$229$	1465.97	0.423032	0.211516	+	0.977375i	$0.432160\pi$
$230$	−4265.48	−1.22286
$231$	2636.99	0.751087
$232$	−4268.23	−1.20786
$233$	−668.448	−0.187946	−0.0939731	−	0.995575i	$-0.529957\pi$
$233$	−668.448	−0.187946	−0.0939731	+	0.995575i	$0.529957\pi$
$234$	−3223.58	−0.900564
$235$	4756.64	1.32038
$236$	−1911.73	−0.527300
$237$	4526.50	1.24062
$238$	3057.36	0.832685
$239$	−3180.69	−0.860845	−0.430423	−	0.902627i	$-0.641635\pi$
$239$	−3180.69	−0.860845	−0.430423	+	0.902627i	$0.641635\pi$
$240$	11010.1	2.96125
$241$	712.915	0.190551	0.0952757	−	0.995451i	$-0.469627\pi$
$241$	712.915	0.190551	0.0952757	+	0.995451i	$0.469627\pi$
$242$	−9396.87	−2.49609
$243$	4102.06	1.08291
$244$	−19798.7	−5.19461
$245$	2182.27	0.569062
$246$	13660.3	3.54045
$247$	−1704.94	−0.439201
$248$	19594.2	5.01706
$249$	7348.77	1.87032
$250$	−7877.26	−1.99281
$251$	5718.67	1.43808	0.719042	−	0.694966i	$-0.244581\pi$
$251$	5718.67	1.43808	0.719042	+	0.694966i	$0.244581\pi$
$252$	2562.95	0.640676
$253$	5807.82	1.44322
$254$	−7792.18	−1.92490
$255$	−3872.81	−0.951077
$256$	7284.82	1.77852
$257$	7309.98	1.77426	0.887128	−	0.461523i	$-0.152697\pi$
$257$	7309.98	1.77426	0.887128	+	0.461523i	$0.152697\pi$
$258$	13271.2	3.20244
$259$	1908.54	0.457879
$260$	−5740.88	−1.36936
$261$	977.214	0.231755
$262$	6738.09	1.58886
$263$	−958.362	−0.224696	−0.112348	−	0.993669i	$-0.535837\pi$
$263$	−958.362	−0.224696	−0.112348	+	0.993669i	$0.535837\pi$
$264$	−26529.6	−6.18479
$265$	2257.39	0.523283
$266$	1862.59	0.429334
$267$	−321.857	−0.0737727
$268$	−5280.32	−1.20353
$269$	−421.460	−0.0955275	−0.0477638	−	0.998859i	$-0.515209\pi$
$269$	−421.460	−0.0955275	−0.0477638	+	0.998859i	$0.515209\pi$
$270$	2788.57	0.628543
$271$	−46.1743	−0.0103501	−0.00517507	−	0.999987i	$-0.501647\pi$
$271$	−46.1743	−0.0103501	−0.00517507	+	0.999987i	$0.501647\pi$
$272$	−17381.0	−3.87455
$273$	−1704.96	−0.377981
$274$	−13893.4	−3.06324
$275$	3805.88	0.834558
$276$	14818.1	3.23168
$277$	−5140.34	−1.11499	−0.557497	−	0.830179i	$-0.688238\pi$
$277$	−5140.34	−1.11499	−0.557497	+	0.830179i	$0.688238\pi$
$278$	13640.7	2.94286
$279$	−4486.09	−0.962635
$280$	3925.68	0.837873
$281$	−7347.50	−1.55984	−0.779920	−	0.625879i	$-0.784740\pi$
$281$	−7347.50	−1.55984	−0.779920	+	0.625879i	$0.784740\pi$
$282$	−22705.5	−4.79466
$283$	−2467.78	−0.518353	−0.259177	−	0.965830i	$-0.583451\pi$
$283$	−2467.78	−0.518353	−0.259177	+	0.965830i	$0.583451\pi$
$284$	−7636.02	−1.59547
$285$	−2359.38	−0.490378
$286$	10740.7	2.22066
$287$	2752.27	0.566067
$288$	−10375.3	−2.12282
$289$	1200.77	0.244406
$290$	2391.32	0.484218
$291$	−2014.88	−0.405892
$292$	−15512.3	−3.10887
$293$	−2614.16	−0.521232	−0.260616	−	0.965443i	$-0.583926\pi$
$293$	−2614.16	−0.521232	−0.260616	+	0.965443i	$0.583926\pi$
$294$	−10416.9	−2.06642
$295$	670.414	0.132315
$296$	−19201.0	−3.77038
$297$	−3796.87	−0.741807
$298$	4516.45	0.877956
$299$	−3755.09	−0.726295
$300$	9710.33	1.86875
$301$	2673.87	0.512024
$302$	623.115	0.118729
$303$	4621.42	0.876217
$304$	−10588.8	−1.99773
$305$	6943.12	1.30348
$306$	7042.23	1.31561
$307$	5786.10	1.07567	0.537834	−	0.843050i	$-0.319243\pi$
$307$	5786.10	1.07567	0.537834	+	0.843050i	$0.319243\pi$
$308$	−8539.51	−1.57982
$309$	2530.26	0.465830
$310$	−10977.8	−2.01129
$311$	−8683.43	−1.58325	−0.791627	−	0.611005i	$-0.790766\pi$
$311$	−8683.43	−1.58325	−0.791627	+	0.611005i	$0.790766\pi$
$312$	17152.9	3.11247
$313$	9835.97	1.77624	0.888118	−	0.459615i	$-0.152013\pi$
$313$	9835.97	1.77624	0.888118	+	0.459615i	$0.152013\pi$
$314$	19422.9	3.49076
$315$	−898.787	−0.160765
$316$	−14658.4	−2.60950
$317$	6581.71	1.16614	0.583069	−	0.812423i	$-0.301852\pi$
$317$	6581.71	1.16614	0.583069	+	0.812423i	$0.301852\pi$
$318$	−10775.5	−1.90019
$319$	−3255.99	−0.571475
$320$	−12052.0	−2.10539
$321$	9470.09	1.64663
$322$	4102.32	0.709979
$323$	3724.61	0.641619
$324$	−19281.0	−3.30607
$325$	−2460.72	−0.419988
$326$	−6889.91	−1.17054
$327$	12108.8	2.04776
$328$	−27689.4	−4.66126
$329$	−4574.68	−0.766597
$330$	14863.5	2.47942
$331$	−8535.11	−1.41732	−0.708659	−	0.705552i	$-0.750699\pi$
$331$	−8535.11	−1.41732	−0.708659	+	0.705552i	$0.750699\pi$
$332$	−23798.0	−3.93398
$333$	4396.07	0.723433
$334$	11494.9	1.88316
$335$	1851.73	0.302003
$336$	−10588.9	−1.71927
$337$	2412.06	0.389891	0.194945	−	0.980814i	$-0.437547\pi$
$337$	2412.06	0.389891	0.194945	+	0.980814i	$0.437547\pi$
$338$	4965.33	0.799048
$339$	−7017.57	−1.12431
$340$	12541.5	2.00047
$341$	14947.3	2.37372
$342$	4290.25	0.678334
$343$	−4572.86	−0.719858
$344$	−26900.7	−4.21624
$345$	−5196.48	−0.810924
$346$	−15472.5	−2.40407
$347$	−5263.57	−0.814303	−0.407151	−	0.913361i	$-0.633478\pi$
$347$	−5263.57	−0.814303	−0.407151	+	0.913361i	$0.633478\pi$
$348$	−8307.33	−1.27965
$349$	−7834.07	−1.20157	−0.600785	−	0.799410i	$-0.705145\pi$
$349$	−7834.07	−1.20157	−0.600785	+	0.799410i	$0.705145\pi$
$350$	2688.26	0.410553
$351$	2454.89	0.373312
$352$	34569.6	5.23457
$353$	1922.01	0.289798	0.144899	−	0.989446i	$-0.453714\pi$
$353$	1922.01	0.289798	0.144899	+	0.989446i	$0.453714\pi$
$354$	−3200.18	−0.480474
$355$	2677.84	0.400352
$356$	1042.29	0.155172
$357$	3724.66	0.552185
$358$	−1486.72	−0.219485
$359$	2243.90	0.329884	0.164942	−	0.986303i	$-0.447256\pi$
$359$	2243.90	0.329884	0.164942	+	0.986303i	$0.447256\pi$
$360$	9042.31	1.32381
$361$	−4589.90	−0.669180
$362$	22438.3	3.25783
$363$	−11447.8	−1.65525
$364$	5521.28	0.795037
$365$	5439.95	0.780110
$366$	−33142.6	−4.73331
$367$	12456.2	1.77168	0.885841	−	0.463990i	$-0.153583\pi$
$367$	12456.2	1.77168	0.885841	+	0.463990i	$0.153583\pi$
$368$	−23321.6	−3.30359
$369$	6339.51	0.894367
$370$	10757.6	1.51151
$371$	−2171.03	−0.303813
$372$	38136.4	5.31527
$373$	−12099.7	−1.67962	−0.839811	−	0.542878i	$-0.817334\pi$
$373$	−12099.7	−1.67962	−0.839811	+	0.542878i	$0.817334\pi$
$374$	−23464.1	−3.24412
$375$	−9596.56	−1.32150
$376$	46023.9	6.31251
$377$	2105.18	0.287593
$378$	−2681.89	−0.364925
$379$	7738.71	1.04884	0.524420	−	0.851460i	$-0.324282\pi$
$379$	7738.71	1.04884	0.524420	+	0.851460i	$0.324282\pi$
$380$	7640.52	1.03145
$381$	−9492.92	−1.27647
$382$	888.806	0.119045
$383$	1984.55	0.264767	0.132384	−	0.991199i	$-0.457737\pi$
$383$	1984.55	0.264767	0.132384	+	0.991199i	$0.457737\pi$
$384$	24536.3	3.26071
$385$	2994.68	0.396423
$386$	−494.936	−0.0652632
$387$	6158.92	0.808980
$388$	6524.92	0.853744
$389$	1888.43	0.246137	0.123068	−	0.992398i	$-0.460727\pi$
$389$	1888.43	0.246137	0.123068	+	0.992398i	$0.460727\pi$
$390$	−9610.09	−1.24776
$391$	8203.37	1.06103
$392$	21115.0	2.72059
$393$	8208.76	1.05363
$394$	4393.55	0.561787
$395$	5140.49	0.654801
$396$	−19669.7	−2.49606
$397$	1401.65	0.177196	0.0885980	−	0.996067i	$-0.471761\pi$
$397$	1401.65	0.177196	0.0885980	+	0.996067i	$0.471761\pi$
$398$	2573.83	0.324156
$399$	2269.13	0.284708
$400$	−15282.7	−1.91034
$401$	−3885.47	−0.483868	−0.241934	−	0.970293i	$-0.577782\pi$
$401$	−3885.47	−0.483868	−0.241934	+	0.970293i	$0.577782\pi$
$402$	−8839.13	−1.09666
$403$	−9664.25	−1.19457
$404$	−14965.8	−1.84301
$405$	6761.57	0.829592
$406$	−2299.85	−0.281132
$407$	−14647.3	−1.78388
$408$	−37472.2	−4.54694
$409$	13920.6	1.68295	0.841477	−	0.540292i	$-0.181686\pi$
$409$	13920.6	1.68295	0.841477	+	0.540292i	$0.181686\pi$
$410$	15513.3	1.86865
$411$	−16925.8	−2.03135
$412$	−8193.89	−0.979816
$413$	−644.769	−0.0768208
$414$	9449.17	1.12174
$415$	8345.59	0.987154
$416$	−22351.2	−2.63428
$417$	16617.9	1.95152
$418$	−14294.7	−1.67268
$419$	−5713.62	−0.666178	−0.333089	−	0.942895i	$-0.608091\pi$
$419$	−5713.62	−0.666178	−0.333089	+	0.942895i	$0.608091\pi$
$420$	7640.62	0.887676
$421$	7048.21	0.815936	0.407968	−	0.912996i	$-0.366238\pi$
$421$	7048.21	0.815936	0.407968	+	0.912996i	$0.366238\pi$
$422$	−16363.1	−1.88755
$423$	−10537.2	−1.21120
$424$	21841.8	2.50173
$425$	5375.69	0.613551
$426$	−12782.5	−1.45379
$427$	−6677.53	−0.756788
$428$	−30667.5	−3.46348
$429$	13085.0	1.47261
$430$	15071.4	1.69025
$431$	9415.83	1.05231	0.526154	−	0.850389i	$-0.323634\pi$
$431$	9415.83	1.05231	0.526154	+	0.850389i	$0.323634\pi$
$432$	15246.5	1.69803
$433$	−1114.73	−0.123719	−0.0618595	−	0.998085i	$-0.519703\pi$
$433$	−1114.73	−0.123719	−0.0618595	+	0.998085i	$0.519703\pi$
$434$	10557.9	1.16773
$435$	2913.26	0.321103
$436$	−39212.7	−4.30722
$437$	4997.63	0.547069
$438$	−25967.3	−2.83280
$439$	−10830.9	−1.17752	−0.588762	−	0.808307i	$-0.700384\pi$
$439$	−10830.9	−1.17752	−0.588762	+	0.808307i	$0.700384\pi$
$440$	−30128.2	−3.26433
$441$	−4834.30	−0.522006
$442$	15170.9	1.63259
$443$	−12149.7	−1.30305	−0.651526	−	0.758627i	$-0.725871\pi$
$443$	−12149.7	−1.30305	−0.651526	+	0.758627i	$0.725871\pi$
$444$	−37371.2	−3.99450
$445$	−365.515	−0.0389372
$446$	12234.5	1.29893
$447$	5502.22	0.582206
$448$	11591.0	1.22237
$449$	−6288.16	−0.660927	−0.330464	−	0.943819i	$-0.607205\pi$
$449$	−6288.16	−0.660927	−0.330464	+	0.943819i	$0.607205\pi$
$450$	6192.07	0.648660
$451$	−21122.7	−2.20538
$452$	22725.4	2.36485
$453$	759.118	0.0787339
$454$	−28332.3	−2.92885
$455$	−1936.23	−0.199499
$456$	−22828.7	−2.34441
$457$	11305.6	1.15723	0.578613	−	0.815602i	$-0.303594\pi$
$457$	11305.6	1.15723	0.578613	+	0.815602i	$0.303594\pi$
$458$	−7946.94	−0.810777
$459$	−5362.96	−0.545363
$460$	16828.1	1.70568
$461$	12515.1	1.26440	0.632199	−	0.774806i	$-0.282152\pi$
$461$	12515.1	1.26440	0.632199	+	0.774806i	$0.282152\pi$
$462$	−14294.9	−1.43952
$463$	−2926.31	−0.293731	−0.146865	−	0.989156i	$-0.546918\pi$
$463$	−2926.31	−0.293731	−0.146865	+	0.989156i	$0.546918\pi$
$464$	13074.6	1.30813
$465$	−13373.9	−1.33376
$466$	3623.61	0.360216
$467$	5602.71	0.555166	0.277583	−	0.960702i	$-0.410467\pi$
$467$	5602.71	0.555166	0.277583	+	0.960702i	$0.410467\pi$
$468$	12717.6	1.25613
$469$	−1780.90	−0.175339
$470$	−25785.4	−2.53062
$471$	23662.2	2.31485
$472$	6486.74	0.632577
$473$	−20521.0	−1.99483
$474$	−24537.8	−2.37776
$475$	3274.96	0.316349
$476$	−12061.8	−1.16145
$477$	−5000.70	−0.480014
$478$	17242.3	1.64989
$479$	−3332.59	−0.317891	−0.158945	−	0.987287i	$-0.550809\pi$
$479$	−3332.59	−0.317891	−0.158945	+	0.987287i	$0.550809\pi$
$480$	−30930.7	−2.94123
$481$	9470.32	0.897733
$482$	−3864.66	−0.365209
$483$	4997.70	0.470814
$484$	37072.2	3.48161
$485$	−2288.19	−0.214230
$486$	−22237.0	−2.07549
$487$	11270.9	1.04873	0.524367	−	0.851492i	$-0.324302\pi$
$487$	11270.9	1.04873	0.524367	+	0.851492i	$0.324302\pi$
$488$	67179.8	6.23173
$489$	−8393.72	−0.776231
$490$	−11829.9	−1.09066
$491$	3170.04	0.291369	0.145684	−	0.989331i	$-0.453462\pi$
$491$	3170.04	0.291369	0.145684	+	0.989331i	$0.453462\pi$
$492$	−53892.4	−4.93832
$493$	−4598.98	−0.420138
$494$	9242.35	0.841767
$495$	6897.87	0.626335
$496$	−60021.4	−5.43355
$497$	−2575.40	−0.232440
$498$	−39837.2	−3.58463
$499$	10734.5	0.963014	0.481507	−	0.876442i	$-0.340090\pi$
$499$	10734.5	0.963014	0.481507	+	0.876442i	$0.340090\pi$
$500$	31077.1	2.77962
$501$	14003.8	1.24879
$502$	−31000.5	−2.75622
$503$	−9926.20	−0.879896	−0.439948	−	0.898023i	$-0.645003\pi$
$503$	−9926.20	−0.879896	−0.439948	+	0.898023i	$0.645003\pi$
$504$	−8696.42	−0.768590
$505$	5248.29	0.462467
$506$	−31483.8	−2.76606
$507$	6049.07	0.529879
$508$	30741.5	2.68491
$509$	−14790.9	−1.28801	−0.644003	−	0.765023i	$-0.722728\pi$
$509$	−14790.9	−1.28801	−0.644003	+	0.765023i	$0.722728\pi$
$510$	20994.2	1.82282
$511$	−5231.86	−0.452923
$512$	−9768.08	−0.843149
$513$	−3267.21	−0.281190
$514$	−39626.9	−3.40052
$515$	2873.48	0.245865
$516$	−52357.2	−4.46685
$517$	35109.0	2.98664
$518$	−10346.0	−0.877566
$519$	−18849.6	−1.59423
$520$	19479.6	1.64276
$521$	1844.17	0.155076	0.0775380	−	0.996989i	$-0.475294\pi$
$521$	1844.17	0.155076	0.0775380	+	0.996989i	$0.475294\pi$
$522$	−5297.41	−0.444179
$523$	12962.5	1.08377	0.541885	−	0.840452i	$-0.317711\pi$
$523$	12962.5	1.08377	0.541885	+	0.840452i	$0.317711\pi$
$524$	−26582.9	−2.21618
$525$	3275.01	0.272253
$526$	5195.21	0.430650
$527$	21112.5	1.74512
$528$	81266.2	6.69822
$529$	−1159.84	−0.0953266
$530$	−12237.1	−1.00292
$531$	−1485.14	−0.121374
$532$	−7348.25	−0.598848
$533$	13657.0	1.10985
$534$	1744.76	0.141392
$535$	10754.7	0.869092
$536$	17916.8	1.44382
$537$	−1811.21	−0.145549
$538$	2284.71	0.183087
$539$	16107.5	1.28719
$540$	−11001.4	−0.876710
$541$	17534.3	1.39345	0.696727	−	0.717336i	$-0.254639\pi$
$541$	17534.3	1.39345	0.696727	+	0.717336i	$0.254639\pi$
$542$	250.308	0.0198370
$543$	27335.8	2.16039
$544$	48828.5	3.84835
$545$	13751.3	1.08081
$546$	9242.47	0.724435
$547$	−3442.71	−0.269104	−0.134552	−	0.990907i	$-0.542959\pi$
$547$	−3442.71	−0.269104	−0.134552	+	0.990907i	$0.542959\pi$
$548$	54811.7	4.27270
$549$	−15380.8	−1.19570
$550$	−20631.4	−1.59950
$551$	−2801.78	−0.216624
$552$	−50279.7	−3.87690
$553$	−4943.85	−0.380170
$554$	27865.4	2.13698
$555$	13105.5	1.00234
$556$	−53814.8	−4.10478
$557$	−1332.67	−0.101377	−0.0506887	−	0.998715i	$-0.516142\pi$
$557$	−1332.67	−0.101377	−0.0506887	+	0.998715i	$0.516142\pi$
$558$	24318.8	1.84498
$559$	13268.0	1.00389
$560$	−12025.3	−0.907429
$561$	−28585.4	−2.15130
$562$	39830.3	2.98957
$563$	−13629.6	−1.02028	−0.510140	−	0.860091i	$-0.670407\pi$
$563$	−13629.6	−1.02028	−0.510140	+	0.860091i	$0.670407\pi$
$564$	89577.1	6.68772
$565$	−7969.47	−0.593413
$566$	13377.6	0.993470
$567$	−6502.92	−0.481652
$568$	25910.0	1.91402
$569$	24494.3	1.80466	0.902331	−	0.431044i	$-0.141855\pi$
$569$	24494.3	1.80466	0.902331	+	0.431044i	$0.141855\pi$
$570$	12790.0	0.939852
$571$	9781.43	0.716883	0.358441	−	0.933552i	$-0.383308\pi$
$571$	9781.43	0.716883	0.358441	+	0.933552i	$0.383308\pi$
$572$	−42373.8	−3.09744
$573$	1082.80	0.0789434
$574$	−14919.9	−1.08492
$575$	7213.03	0.523137
$576$	26698.3	1.93130
$577$	−4266.63	−0.307837	−0.153919	−	0.988084i	$-0.549189\pi$
$577$	−4266.63	−0.307837	−0.153919	+	0.988084i	$0.549189\pi$
$578$	−6509.26	−0.468425
$579$	−602.962	−0.0432785
$580$	−9434.17	−0.675401
$581$	−8026.35	−0.573131
$582$	10922.6	0.777928
$583$	16661.9	1.18365
$584$	52635.5	3.72957
$585$	−4459.86	−0.315201
$586$	14171.2	0.998987
$587$	−6427.20	−0.451923	−0.225962	−	0.974136i	$-0.572552\pi$
$587$	−6427.20	−0.451923	−0.225962	+	0.974136i	$0.572552\pi$
$588$	41096.6	2.88230
$589$	12862.1	0.899787
$590$	−3634.27	−0.253594
$591$	5352.50	0.372542
$592$	58817.0	4.08338
$593$	4258.41	0.294894	0.147447	−	0.989070i	$-0.452894\pi$
$593$	4258.41	0.294894	0.147447	+	0.989070i	$0.452894\pi$
$594$	20582.6	1.42174
$595$	4229.89	0.291443
$596$	−17818.2	−1.22460
$597$	3135.59	0.214960
$598$	20356.1	1.39201
$599$	−6791.37	−0.463252	−0.231626	−	0.972805i	$-0.574404\pi$
$599$	−6791.37	−0.463252	−0.231626	+	0.972805i	$0.574404\pi$
$600$	−32948.4	−2.24186
$601$	12588.1	0.854372	0.427186	−	0.904164i	$-0.359505\pi$
$601$	12588.1	0.854372	0.427186	+	0.904164i	$0.359505\pi$
$602$	−14494.9	−0.981339
$603$	−4102.07	−0.277030
$604$	−2458.30	−0.165607
$605$	−13000.7	−0.873641
$606$	−25052.4	−1.67935
$607$	−12292.2	−0.821950	−0.410975	−	0.911647i	$-0.634812\pi$
$607$	−12292.2	−0.821950	−0.410975	+	0.911647i	$0.634812\pi$
$608$	29747.2	1.98422
$609$	−2801.82	−0.186429
$610$	−37638.2	−2.49824
$611$	−22700.0	−1.50302
$612$	−27782.8	−1.83505
$613$	−3268.57	−0.215361	−0.107680	−	0.994186i	$-0.534342\pi$
$613$	−3268.57	−0.215361	−0.107680	+	0.994186i	$0.534342\pi$
$614$	−31366.1	−2.06161
$615$	18899.3	1.23917
$616$	28975.7	1.89523
$617$	−15578.6	−1.01649	−0.508244	−	0.861213i	$-0.669705\pi$
$617$	−15578.6	−1.01649	−0.508244	+	0.861213i	$0.669705\pi$
$618$	−13716.4	−0.892805
$619$	19311.1	1.25392	0.626961	−	0.779050i	$-0.284298\pi$
$619$	19311.1	1.25392	0.626961	+	0.779050i	$0.284298\pi$
$620$	43309.4	2.80540
$621$	−7195.94	−0.464997
$622$	47072.3	3.03445
$623$	351.533	0.0226065
$624$	−52543.2	−3.37085
$625$	−2304.39	−0.147481
$626$	−53320.1	−3.40431
$627$	−17414.7	−1.10921
$628$	−76626.7	−4.86901
$629$	−20688.9	−1.31148
$630$	4872.26	0.308120
$631$	11749.8	0.741285	0.370642	−	0.928776i	$-0.379138\pi$
$631$	11749.8	0.741285	0.370642	+	0.928776i	$0.379138\pi$
$632$	49738.0	3.13049
$633$	−19934.6	−1.25170
$634$	−35679.0	−2.23501
$635$	−10780.6	−0.673723
$636$	42511.1	2.65044
$637$	−10414.4	−0.647775
$638$	17650.5	1.09528
$639$	−5932.12	−0.367247
$640$	27864.5	1.72100
$641$	24259.9	1.49487	0.747433	−	0.664337i	$-0.231286\pi$
$641$	24259.9	1.49487	0.747433	+	0.664337i	$0.231286\pi$
$642$	−51336.7	−3.15591
$643$	−1187.33	−0.0728208	−0.0364104	−	0.999337i	$-0.511592\pi$
$643$	−1187.33	−0.0728208	−0.0364104	+	0.999337i	$0.511592\pi$
$644$	−16184.3	−0.990299
$645$	18360.9	1.12087
$646$	−20190.9	−1.22972
$647$	31495.4	1.91377	0.956886	−	0.290464i	$-0.0938097\pi$
$647$	31495.4	1.91377	0.956886	+	0.290464i	$0.0938097\pi$
$648$	65423.1	3.96614
$649$	4948.37	0.299292
$650$	13339.4	0.804944
$651$	12862.3	0.774367
$652$	27181.9	1.63271
$653$	−20819.1	−1.24765	−0.623823	−	0.781566i	$-0.714421\pi$
$653$	−20819.1	−1.24765	−0.623823	+	0.781566i	$0.714421\pi$
$654$	−65641.0	−3.92472
$655$	9322.24	0.556107
$656$	84819.0	5.04821
$657$	−12050.9	−0.715603
$658$	24799.0	1.46925
$659$	−9149.84	−0.540861	−0.270430	−	0.962740i	$-0.587166\pi$
$659$	−9149.84	−0.540861	−0.270430	+	0.962740i	$0.587166\pi$
$660$	−58639.0	−3.45836
$661$	2328.53	0.137018	0.0685092	−	0.997650i	$-0.478176\pi$
$661$	2328.53	0.137018	0.0685092	+	0.997650i	$0.478176\pi$
$662$	46268.2	2.71641
$663$	18482.1	1.08263
$664$	80749.7	4.71942
$665$	2576.92	0.150269
$666$	−23830.8	−1.38652
$667$	−6170.85	−0.358225
$668$	−45349.4	−2.62668
$669$	14904.9	0.861369
$670$	−10038.1	−0.578815
$671$	51247.6	2.94842
$672$	29747.6	1.70764
$673$	−5408.95	−0.309806	−0.154903	−	0.987930i	$-0.549507\pi$
$673$	−5408.95	−0.309806	−0.154903	+	0.987930i	$0.549507\pi$
$674$	−13075.6	−0.747260
$675$	−4715.52	−0.268890
$676$	−19589.1	−1.11453
$677$	−18216.0	−1.03412	−0.517059	−	0.855950i	$-0.672973\pi$
$677$	−18216.0	−1.03412	−0.517059	+	0.855950i	$0.672973\pi$
$678$	38041.8	2.15485
$679$	2200.66	0.124380
$680$	−42555.1	−2.39987
$681$	−34516.1	−1.94223
$682$	−81028.1	−4.54945
$683$	−24950.1	−1.39779	−0.698893	−	0.715227i	$-0.746323\pi$
$683$	−24950.1	−1.39779	−0.698893	+	0.715227i	$0.746323\pi$
$684$	−16925.8	−0.946159
$685$	−19221.6	−1.07215
$686$	24789.2	1.37967
$687$	−9681.45	−0.537657
$688$	82402.8	4.56625
$689$	−10772.9	−0.595665
$690$	28169.7	1.55421
$691$	−16822.8	−0.926147	−0.463074	−	0.886320i	$-0.653253\pi$
$691$	−16822.8	−0.926147	−0.463074	+	0.886320i	$0.653253\pi$
$692$	61041.7	3.35326
$693$	−6634.00	−0.363643
$694$	28533.4	1.56068
$695$	18872.1	1.03001
$696$	28187.9	1.53514
$697$	−29835.1	−1.62136
$698$	42468.0	2.30292
$699$	4414.50	0.238872
$700$	−10605.6	−0.572651
$701$	23812.0	1.28298	0.641489	−	0.767132i	$-0.278317\pi$
$701$	23812.0	1.28298	0.641489	+	0.767132i	$0.278317\pi$
$702$	−13307.8	−0.715485
$703$	−12604.0	−0.676202
$704$	−88956.4	−4.76232
$705$	−31413.4	−1.67815
$706$	−10419.1	−0.555423
$707$	−5047.53	−0.268504
$708$	12625.3	0.670178
$709$	19029.1	1.00797	0.503985	−	0.863712i	$-0.331867\pi$
$709$	19029.1	1.00797	0.503985	+	0.863712i	$0.331867\pi$
$710$	−14516.4	−0.767310
$711$	−11387.5	−0.600656
$712$	−3536.62	−0.186152
$713$	28328.5	1.48795
$714$	−20191.1	−1.05831
$715$	14859.9	0.777241
$716$	5865.36	0.306143
$717$	21005.7	1.09410
$718$	−12164.0	−0.632252
$719$	−35760.1	−1.85484	−0.927419	−	0.374025i	$-0.877977\pi$
$719$	−35760.1	−1.85484	−0.927419	+	0.374025i	$0.877977\pi$
$720$	−27698.7	−1.43371
$721$	−2763.56	−0.142747
$722$	24881.5	1.28254
$723$	−4708.17	−0.242184
$724$	−88523.1	−4.54411
$725$	−4043.78	−0.207148
$726$	62058.0	3.17243
$727$	−36629.5	−1.86866	−0.934328	−	0.356415i	$-0.883999\pi$
$727$	−36629.5	−1.86866	−0.934328	+	0.356415i	$0.883999\pi$
$728$	−18734.4	−0.953769
$729$	−2748.59	−0.139643
$730$	−29489.6	−1.49515
$731$	−28985.2	−1.46656
$732$	130753.	6.60215
$733$	9630.40	0.485276	0.242638	−	0.970117i	$-0.421987\pi$
$733$	9630.40	0.485276	0.242638	+	0.970117i	$0.421987\pi$
$734$	−67524.1	−3.39558
$735$	−14412.0	−0.723256
$736$	65517.4	3.28126
$737$	13667.7	0.683118
$738$	−34366.0	−1.71413
$739$	−10972.2	−0.546171	−0.273086	−	0.961990i	$-0.588044\pi$
$739$	−10972.2	−0.546171	−0.273086	+	0.961990i	$0.588044\pi$
$740$	−42440.4	−2.10830
$741$	11259.6	0.558208
$742$	11769.0	0.582284
$743$	−8151.83	−0.402506	−0.201253	−	0.979539i	$-0.564501\pi$
$743$	−8151.83	−0.402506	−0.201253	+	0.979539i	$0.564501\pi$
$744$	−129402.	−6.37649
$745$	6248.56	0.307288
$746$	65591.7	3.21915
$747$	−18487.7	−0.905527
$748$	92569.8	4.52498
$749$	−10343.3	−0.504585
$750$	52022.3	2.53278
$751$	5316.45	0.258322	0.129161	−	0.991624i	$-0.458772\pi$
$751$	5316.45	0.258322	0.129161	+	0.991624i	$0.458772\pi$
$752$	−140982.	−6.83654
$753$	−37766.7	−1.82775
$754$	−11412.0	−0.551197
$755$	862.088	0.0415558
$756$	10580.5	0.509008
$757$	−3362.20	−0.161428	−0.0807141	−	0.996737i	$-0.525720\pi$
$757$	−3362.20	−0.161428	−0.0807141	+	0.996737i	$0.525720\pi$
$758$	−41951.0	−2.01020
$759$	−38355.5	−1.83428
$760$	−25925.3	−1.23738
$761$	11005.1	0.524224	0.262112	−	0.965037i	$-0.415581\pi$
$761$	11005.1	0.524224	0.262112	+	0.965037i	$0.415581\pi$
$762$	51460.4	2.44648
$763$	−13225.3	−0.627506
$764$	−3506.49	−0.166048
$765$	9743.02	0.460470
$766$	−10758.1	−0.507450
$767$	−3199.40	−0.150617
$768$	−48109.8	−2.26043
$769$	6341.21	0.297360	0.148680	−	0.988885i	$-0.452498\pi$
$769$	6341.21	0.297360	0.148680	+	0.988885i	$0.452498\pi$
$770$	−16234.0	−0.759780
$771$	−48275.9	−2.25501
$772$	1952.61	0.0910309
$773$	−31939.2	−1.48612	−0.743062	−	0.669223i	$-0.766627\pi$
$773$	−31939.2	−1.48612	−0.743062	+	0.669223i	$0.766627\pi$
$774$	−33387.1	−1.55048
$775$	18563.8	0.860426
$776$	−22139.9	−1.02420
$777$	−12604.2	−0.581947
$778$	−10237.0	−0.471743
$779$	−18176.1	−0.835976
$780$	37913.4	1.74041
$781$	19765.3	0.905580
$782$	−44469.9	−2.03355
$783$	4034.20	0.184126
$784$	−64680.2	−2.94644
$785$	26871.8	1.22178
$786$	−44499.1	−2.01938
$787$	1040.57	0.0471315	0.0235657	−	0.999722i	$-0.492498\pi$
$787$	1040.57	0.0471315	0.0235657	+	0.999722i	$0.492498\pi$
$788$	−17333.3	−0.783596
$789$	6329.13	0.285581
$790$	−27866.2	−1.25498
$791$	7664.61	0.344529
$792$	66741.9	2.99441
$793$	−33134.5	−1.48378
$794$	−7598.25	−0.339612
$795$	−14908.0	−0.665073
$796$	−10154.2	−0.452142
$797$	−3420.34	−0.152013	−0.0760066	−	0.997107i	$-0.524217\pi$
$797$	−3420.34	−0.152013	−0.0760066	+	0.997107i	$0.524217\pi$
$798$	−12300.8	−0.545668
$799$	49590.4	2.19572
$800$	42933.8	1.89742
$801$	809.711	0.0357175
$802$	21062.9	0.927376
$803$	40152.6	1.76458
$804$	34871.8	1.52965
$805$	5675.61	0.248495
$806$	52389.2	2.28949
$807$	2783.37	0.121412
$808$	50781.1	2.21098
$809$	1096.77	0.0476641	0.0238321	−	0.999716i	$-0.492413\pi$
$809$	1096.77	0.0476641	0.0238321	+	0.999716i	$0.492413\pi$
$810$	−36654.0	−1.58999
$811$	−38079.6	−1.64878	−0.824388	−	0.566025i	$-0.808480\pi$
$811$	−38079.6	−1.64878	−0.824388	+	0.566025i	$0.808480\pi$
$812$	9073.29	0.392131
$813$	304.940	0.0131546
$814$	79402.1	3.41897
$815$	−9532.28	−0.409695
$816$	114786.	4.92440
$817$	−17658.3	−0.756164
$818$	−75462.5	−3.22553
$819$	4289.26	0.183002
$820$	−61202.6	−2.60645
$821$	−5414.65	−0.230174	−0.115087	−	0.993355i	$-0.536715\pi$
$821$	−5414.65	−0.230174	−0.115087	+	0.993355i	$0.536715\pi$
$822$	91753.3	3.89327
$823$	28910.3	1.22448	0.612242	−	0.790671i	$-0.290268\pi$
$823$	28910.3	1.22448	0.612242	+	0.790671i	$0.290268\pi$
$824$	27803.0	1.17544
$825$	−25134.5	−1.06069
$826$	3495.25	0.147234
$827$	−26868.4	−1.12975	−0.564876	−	0.825176i	$-0.691076\pi$
$827$	−26868.4	−1.12975	−0.564876	+	0.825176i	$0.691076\pi$
$828$	−37278.6	−1.56464
$829$	21055.9	0.882148	0.441074	−	0.897471i	$-0.354598\pi$
$829$	21055.9	0.882148	0.441074	+	0.897471i	$0.354598\pi$
$830$	−45240.9	−1.89197
$831$	33947.4	1.41711
$832$	57515.3	2.39662
$833$	22751.3	0.946321
$834$	−90084.6	−3.74026
$835$	15903.4	0.659112
$836$	56395.1	2.33309
$837$	−18519.8	−0.764800
$838$	30973.1	1.27679
$839$	20903.4	0.860151	0.430075	−	0.902793i	$-0.358487\pi$
$839$	20903.4	0.860151	0.430075	+	0.902793i	$0.358487\pi$
$840$	−25925.7	−1.06490
$841$	−20929.5	−0.858153
$842$	−38207.9	−1.56381
$843$	48523.7	1.98250
$844$	64555.3	2.63280
$845$	6869.60	0.279670
$846$	57121.4	2.32137
$847$	12503.4	0.507226
$848$	−66906.6	−2.70941
$849$	16297.5	0.658808
$850$	−29141.2	−1.17593
$851$	−27760.1	−1.11822
$852$	50429.1	2.02779
$853$	2619.13	0.105132	0.0525658	−	0.998617i	$-0.483260\pi$
$853$	2619.13	0.105132	0.0525658	+	0.998617i	$0.483260\pi$
$854$	36198.4	1.45045
$855$	5935.61	0.237420
$856$	104059.	4.15498
$857$	7376.25	0.294012	0.147006	−	0.989136i	$-0.453036\pi$
$857$	7376.25	0.294012	0.147006	+	0.989136i	$0.453036\pi$
$858$	−70932.6	−2.82238
$859$	−36401.2	−1.44586	−0.722930	−	0.690921i	$-0.757205\pi$
$859$	−36401.2	−1.44586	−0.722930	+	0.690921i	$0.757205\pi$
$860$	−59459.1	−2.35760
$861$	−18176.3	−0.719450
$862$	−51042.6	−2.01684
$863$	38184.4	1.50616	0.753079	−	0.657931i	$-0.228568\pi$
$863$	38184.4	1.50616	0.753079	+	0.657931i	$0.228568\pi$
$864$	−42832.1	−1.68655
$865$	−21406.4	−0.841433
$866$	6042.85	0.237118
$867$	−7929.99	−0.310630
$868$	−41652.7	−1.62878
$869$	37942.3	1.48113
$870$	−15792.6	−0.615423
$871$	−8836.97	−0.343776
$872$	133054.	5.16717
$873$	5068.95	0.196515
$874$	−27091.8	−1.04851
$875$	10481.4	0.404955
$876$	102445.	3.95126
$877$	−12198.2	−0.469675	−0.234837	−	0.972035i	$-0.575456\pi$
$877$	−12198.2	−0.469675	−0.234837	+	0.972035i	$0.575456\pi$
$878$	58713.8	2.25683
$879$	17264.2	0.662466
$880$	92289.5	3.53532
$881$	48457.4	1.85309	0.926545	−	0.376183i	$-0.122764\pi$
$881$	48457.4	1.85309	0.926545	+	0.376183i	$0.122764\pi$
$882$	26206.4	1.00047
$883$	−43190.5	−1.64607	−0.823033	−	0.567994i	$-0.807720\pi$
$883$	−43190.5	−1.64607	−0.823033	+	0.567994i	$0.807720\pi$
$884$	−59851.6	−2.27718
$885$	−4427.49	−0.168168
$886$	65862.9	2.49741
$887$	41921.5	1.58690	0.793452	−	0.608632i	$-0.208282\pi$
$887$	41921.5	1.58690	0.793452	+	0.608632i	$0.208282\pi$
$888$	126805.	4.79202
$889$	10368.2	0.391156
$890$	1981.43	0.0746266
$891$	49907.5	1.87650
$892$	−48267.3	−1.81178
$893$	30211.3	1.13212
$894$	−29827.1	−1.11585
$895$	−2056.89	−0.0768205
$896$	−26798.6	−0.999194
$897$	24799.0	0.923093
$898$	34087.7	1.26673
$899$	−15881.6	−0.589188
$900$	−24428.8	−0.904769
$901$	23534.4	0.870194
$902$	114505.	4.22681
$903$	−17658.5	−0.650763
$904$	−77110.4	−2.83701
$905$	31043.7	1.14025
$906$	−4115.12	−0.150901
$907$	19732.8	0.722399	0.361199	−	0.932489i	$-0.382367\pi$
$907$	19732.8	0.722399	0.361199	+	0.932489i	$0.382367\pi$
$908$	111776.	4.08524
$909$	−11626.4	−0.424226
$910$	10496.2	0.382357
$911$	−15825.4	−0.575542	−0.287771	−	0.957699i	$-0.592914\pi$
$911$	−15825.4	−0.575542	−0.287771	+	0.957699i	$0.592914\pi$
$912$	69929.6	2.53903
$913$	61599.3	2.23290
$914$	−61286.7	−2.21793
$915$	−45853.2	−1.65668
$916$	31352.0	1.13090
$917$	−8965.63	−0.322869
$918$	29072.2	1.04524
$919$	19746.2	0.708778	0.354389	−	0.935098i	$-0.384689\pi$
$919$	19746.2	0.708778	0.354389	+	0.935098i	$0.384689\pi$
$920$	−57099.9	−2.04622
$921$	−38212.1	−1.36713
$922$	−67843.7	−2.42333
$923$	−12779.4	−0.455729
$924$	56395.9	2.00789
$925$	−18191.3	−0.646621
$926$	15863.3	0.562961
$927$	−6365.51	−0.225535
$928$	−36730.5	−1.29929
$929$	47429.8	1.67505	0.837525	−	0.546399i	$-0.184002\pi$
$929$	47429.8	1.67505	0.837525	+	0.546399i	$0.184002\pi$
$930$	72498.9	2.55627
$931$	13860.5	0.487925
$932$	−14295.7	−0.502439
$933$	57346.3	2.01226
$934$	−30371.9	−1.06402
$935$	−32462.9	−1.13545
$936$	−43152.4	−1.50692
$937$	2077.72	0.0724398	0.0362199	−	0.999344i	$-0.488468\pi$
$937$	2077.72	0.0724398	0.0362199	+	0.999344i	$0.488468\pi$
$938$	9654.12	0.336053
$939$	−64957.9	−2.25753
$940$	101728.	3.52978
$941$	−1244.60	−0.0431166	−0.0215583	−	0.999768i	$-0.506863\pi$
$941$	−1244.60	−0.0431166	−0.0215583	+	0.999768i	$0.506863\pi$
$942$	−128271.	−4.43662
$943$	−40032.3	−1.38243
$944$	−19870.4	−0.685091
$945$	−3710.43	−0.127725
$946$	111243.	3.82327
$947$	−34160.9	−1.17221	−0.586104	−	0.810236i	$-0.699339\pi$
$947$	−34160.9	−1.17221	−0.586104	+	0.810236i	$0.699339\pi$
$948$	96805.9	3.31657
$949$	−25960.9	−0.888016
$950$	−17753.3	−0.606310
$951$	−43466.3	−1.48212
$952$	40927.3	1.39334
$953$	−2124.03	−0.0721973	−0.0360986	−	0.999348i	$-0.511493\pi$
$953$	−2124.03	−0.0721973	−0.0360986	+	0.999348i	$0.511493\pi$
$954$	27108.5	0.919988
$955$	1229.67	0.0416663
$956$	−68023.9	−2.30131
$957$	21502.9	0.726323
$958$	18065.7	0.609266
$959$	18486.4	0.622477
$960$	79592.6	2.67588
$961$	43116.5	1.44730
$962$	−51338.0	−1.72058
$963$	−23824.4	−0.797227
$964$	15246.7	0.509403
$965$	−684.751	−0.0228424
$966$	−27092.2	−0.902356
$967$	−40715.3	−1.35400	−0.677000	−	0.735983i	$-0.736720\pi$
$967$	−40715.3	−1.35400	−0.677000	+	0.735983i	$0.736720\pi$
$968$	−125791.	−4.17673
$969$	−24597.7	−0.815473
$970$	12404.1	0.410591
$971$	12402.1	0.409890	0.204945	−	0.978774i	$-0.434298\pi$
$971$	12402.1	0.409890	0.204945	+	0.978774i	$0.434298\pi$
$972$	87728.7	2.89496
$973$	−18150.2	−0.598013
$974$	−61098.8	−2.00999
$975$	16250.9	0.533789
$976$	−205787.	−6.74906
$977$	−29941.4	−0.980462	−0.490231	−	0.871593i	$-0.663088\pi$
$977$	−29941.4	−0.980462	−0.490231	+	0.871593i	$0.663088\pi$
$978$	45501.8	1.48772
$979$	−2697.89	−0.0880744
$980$	46671.1	1.52128
$981$	−30462.8	−0.991438
$982$	−17184.6	−0.558434
$983$	−983.000	−0.0318950
$983$	−983.000	−0.0318950
$984$	182864.	5.92428
$985$	6078.54	0.196628
$986$	24930.8	0.805231
$987$	30211.7	0.974315
$988$	−36462.6	−1.17412
$989$	−38892.0	−1.25045
$990$	−37392.9	−1.20043
$991$	−33167.1	−1.06315	−0.531577	−	0.847010i	$-0.678401\pi$
$991$	−33167.1	−1.06315	−0.531577	+	0.847010i	$0.678401\pi$
$992$	168618.	5.39682
$993$	56366.8	1.80136
$994$	13961.1	0.445492
$995$	3560.92	0.113456
$996$	157164.	4.99994
$997$	23612.2	0.750056	0.375028	−	0.927014i	$-0.377633\pi$
$997$	23612.2	0.750056	0.375028	+	0.927014i	$0.377633\pi$
$998$	−58191.2	−1.84570
$999$	18148.2	0.574757

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.4.a.b.1.3	✓	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.4.a.b.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-5.42093 q^{2} -6.60411 q^{3} +21.3865 q^{4} -7.49992 q^{5} +35.8004 q^{6} +7.21303 q^{7} -72.5672 q^{8} +16.6143 q^{9} +O(q^{10})\)	\(q-5.42093 q^{2} -6.60411 q^{3} +21.3865 q^{4} -7.49992 q^{5} +35.8004 q^{6} +7.21303 q^{7} -72.5672 q^{8} +16.6143 q^{9} +40.6566 q^{10} -55.3574 q^{11} -141.239 q^{12} +35.7917 q^{13} -39.1013 q^{14} +49.5303 q^{15} +222.290 q^{16} -78.1906 q^{17} -90.0650 q^{18} -47.6350 q^{19} -160.397 q^{20} -47.6357 q^{21} +300.089 q^{22} -104.915 q^{23} +479.242 q^{24} -68.7511 q^{25} -194.024 q^{26} +68.5883 q^{27} +154.261 q^{28} +58.8176 q^{29} -268.501 q^{30} -270.014 q^{31} -624.481 q^{32} +365.587 q^{33} +423.866 q^{34} -54.0972 q^{35} +355.322 q^{36} +264.596 q^{37} +258.226 q^{38} -236.372 q^{39} +544.249 q^{40} +381.569 q^{41} +258.230 q^{42} +370.700 q^{43} -1183.90 q^{44} -124.606 q^{45} +568.737 q^{46} -634.224 q^{47} -1468.03 q^{48} -290.972 q^{49} +372.695 q^{50} +516.379 q^{51} +765.458 q^{52} -300.988 q^{53} -371.812 q^{54} +415.176 q^{55} -523.430 q^{56} +314.587 q^{57} -318.846 q^{58} -89.3894 q^{59} +1059.28 q^{60} -925.759 q^{61} +1463.73 q^{62} +119.839 q^{63} +1606.95 q^{64} -268.435 q^{65} -1981.82 q^{66} -246.900 q^{67} -1672.22 q^{68} +692.871 q^{69} +293.257 q^{70} -357.049 q^{71} -1205.65 q^{72} -725.334 q^{73} -1434.35 q^{74} +454.040 q^{75} -1018.75 q^{76} -399.295 q^{77} +1281.36 q^{78} -685.406 q^{79} -1667.16 q^{80} -901.551 q^{81} -2068.46 q^{82} -1112.76 q^{83} -1018.76 q^{84} +586.423 q^{85} -2009.54 q^{86} -388.438 q^{87} +4017.13 q^{88} +48.7358 q^{89} +675.481 q^{90} +258.167 q^{91} -2243.76 q^{92} +1783.20 q^{93} +3438.09 q^{94} +357.259 q^{95} +4124.14 q^{96} +305.095 q^{97} +1577.34 q^{98} -919.725 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9}+O(q^{10}) \) 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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