LMFDB - Embedded newform 983.4.a.a.1.11

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			1.11
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)

$f(q)$	$=$	$q-4.76719 q^{2} +8.84156 q^{3} +14.7261 q^{4} -7.92466 q^{5} -42.1494 q^{6} -15.4085 q^{7} -32.0645 q^{8} +51.1732 q^{9} +O(q^{10})$	\(q-4.76719 q^{2} +8.84156 q^{3} +14.7261 q^{4} -7.92466 q^{5} -42.1494 q^{6} -15.4085 q^{7} -32.0645 q^{8} +51.1732 q^{9} +37.7783 q^{10} +54.2256 q^{11} +130.201 q^{12} -20.2775 q^{13} +73.4550 q^{14} -70.0663 q^{15} +35.0487 q^{16} -106.463 q^{17} -243.952 q^{18} +52.0147 q^{19} -116.699 q^{20} -136.235 q^{21} -258.503 q^{22} +30.1937 q^{23} -283.500 q^{24} -62.1998 q^{25} +96.6668 q^{26} +213.729 q^{27} -226.906 q^{28} -189.750 q^{29} +334.019 q^{30} +243.263 q^{31} +89.4320 q^{32} +479.439 q^{33} +507.528 q^{34} +122.107 q^{35} +753.580 q^{36} -131.983 q^{37} -247.964 q^{38} -179.285 q^{39} +254.100 q^{40} -412.958 q^{41} +649.457 q^{42} +20.7829 q^{43} +798.530 q^{44} -405.530 q^{45} -143.939 q^{46} +290.285 q^{47} +309.885 q^{48} -105.579 q^{49} +296.518 q^{50} -941.297 q^{51} -298.608 q^{52} +675.179 q^{53} -1018.88 q^{54} -429.719 q^{55} +494.064 q^{56} +459.891 q^{57} +904.576 q^{58} -518.720 q^{59} -1031.80 q^{60} -135.830 q^{61} -1159.68 q^{62} -788.500 q^{63} -706.729 q^{64} +160.692 q^{65} -2285.57 q^{66} -655.425 q^{67} -1567.78 q^{68} +266.959 q^{69} -582.106 q^{70} +331.218 q^{71} -1640.84 q^{72} -470.419 q^{73} +629.189 q^{74} -549.943 q^{75} +765.972 q^{76} -835.532 q^{77} +854.685 q^{78} +141.346 q^{79} -277.749 q^{80} +508.018 q^{81} +1968.65 q^{82} -981.431 q^{83} -2006.20 q^{84} +843.681 q^{85} -99.0759 q^{86} -1677.69 q^{87} -1738.71 q^{88} +679.280 q^{89} +1933.24 q^{90} +312.445 q^{91} +444.634 q^{92} +2150.82 q^{93} -1383.84 q^{94} -412.198 q^{95} +790.719 q^{96} +46.6609 q^{97} +503.317 q^{98} +2774.90 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.76719	−1.68546	−0.842728	−	0.538340i	$-0.819052\pi$
$2$	−4.76719	−1.68546	−0.842728	+	0.538340i	$0.819052\pi$
$3$	8.84156	1.70156	0.850779	−	0.525523i	$-0.176130\pi$
$3$	8.84156	1.70156	0.850779	+	0.525523i	$0.176130\pi$
$4$	14.7261	1.84076
$5$	−7.92466	−0.708803	−0.354401	−	0.935093i	$-0.615315\pi$
$5$	−7.92466	−0.708803	−0.354401	+	0.935093i	$0.615315\pi$
$6$	−42.1494	−2.86790
$7$	−15.4085	−0.831978	−0.415989	−	0.909370i	$-0.636565\pi$
$7$	−15.4085	−0.831978	−0.415989	+	0.909370i	$0.636565\pi$
$8$	−32.0645	−1.41706
$9$	51.1732	1.89530
$10$	37.7783	1.19466
$11$	54.2256	1.48633	0.743165	−	0.669108i	$-0.233324\pi$
$11$	54.2256	1.48633	0.743165	+	0.669108i	$0.233324\pi$
$12$	130.201	3.13216
$13$	−20.2775	−0.432613	−0.216307	−	0.976325i	$-0.569401\pi$
$13$	−20.2775	−0.432613	−0.216307	+	0.976325i	$0.569401\pi$
$14$	73.4550	1.40226
$15$	−70.0663	−1.20607
$16$	35.0487	0.547636
$17$	−106.463	−1.51888	−0.759442	−	0.650575i	$-0.774528\pi$
$17$	−106.463	−1.51888	−0.759442	+	0.650575i	$0.774528\pi$
$18$	−243.952	−3.19445
$19$	52.0147	0.628052	0.314026	−	0.949414i	$-0.398322\pi$
$19$	52.0147	0.628052	0.314026	+	0.949414i	$0.398322\pi$
$20$	−116.699	−1.30474
$21$	−136.235	−1.41566
$22$	−258.503	−2.50514
$23$	30.1937	0.273731	0.136866	−	0.990590i	$-0.456297\pi$
$23$	30.1937	0.273731	0.136866	+	0.990590i	$0.456297\pi$
$24$	−283.500	−2.41121
$25$	−62.1998	−0.497598
$26$	96.6668	0.729150
$27$	213.729	1.52341
$28$	−226.906	−1.53147
$29$	−189.750	−1.21503	−0.607513	−	0.794310i	$-0.707833\pi$
$29$	−189.750	−1.21503	−0.607513	+	0.794310i	$0.707833\pi$
$30$	334.019	2.03278
$31$	243.263	1.40940	0.704698	−	0.709507i	$-0.251082\pi$
$31$	243.263	1.40940	0.704698	+	0.709507i	$0.251082\pi$
$32$	89.4320	0.494047
$33$	479.439	2.52908
$34$	507.528	2.56001
$35$	122.107	0.589709
$36$	753.580	3.48880
$37$	−131.983	−0.586430	−0.293215	−	0.956047i	$-0.594725\pi$
$37$	−131.983	−0.586430	−0.293215	+	0.956047i	$0.594725\pi$
$38$	−247.964	−1.05855
$39$	−179.285	−0.736117
$40$	254.100	1.00442
$41$	−412.958	−1.57300	−0.786502	−	0.617587i	$-0.788110\pi$
$41$	−412.958	−1.57300	−0.786502	+	0.617587i	$0.788110\pi$
$42$	649.457	2.38603
$43$	20.7829	0.0737060	0.0368530	−	0.999321i	$-0.488267\pi$
$43$	20.7829	0.0737060	0.0368530	+	0.999321i	$0.488267\pi$
$44$	798.530	2.73598
$45$	−405.530	−1.34340
$46$	−143.939	−0.461361
$47$	290.285	0.900902	0.450451	−	0.892801i	$-0.351263\pi$
$47$	290.285	0.900902	0.450451	+	0.892801i	$0.351263\pi$
$48$	309.885	0.931834
$49$	−105.579	−0.307812
$50$	296.518	0.838680
$51$	−941.297	−2.58447
$52$	−298.608	−0.796337
$53$	675.179	1.74987	0.874933	−	0.484244i	$-0.160905\pi$
$53$	675.179	1.74987	0.874933	+	0.484244i	$0.160905\pi$
$54$	−1018.88	−2.56764
$55$	−429.719	−1.05351
$56$	494.064	1.17897
$57$	459.891	1.06867
$58$	904.576	2.04787
$59$	−518.720	−1.14460	−0.572302	−	0.820043i	$-0.693949\pi$
$59$	−518.720	−1.14460	−0.572302	+	0.820043i	$0.693949\pi$
$60$	−1031.80	−2.22008
$61$	−135.830	−0.285101	−0.142551	−	0.989787i	$-0.545530\pi$
$61$	−135.830	−0.285101	−0.142551	+	0.989787i	$0.545530\pi$
$62$	−1159.68	−2.37547
$63$	−788.500	−1.57685
$64$	−706.729	−1.38033
$65$	160.692	0.306638
$66$	−2285.57	−4.26265
$67$	−655.425	−1.19512	−0.597559	−	0.801825i	$-0.703863\pi$
$67$	−655.425	−1.19512	−0.597559	+	0.801825i	$0.703863\pi$
$68$	−1567.78	−2.79590
$69$	266.959	0.465770
$70$	−582.106	−0.993928
$71$	331.218	0.553638	0.276819	−	0.960922i	$-0.410720\pi$
$71$	331.218	0.553638	0.276819	+	0.960922i	$0.410720\pi$
$72$	−1640.84	−2.68576
$73$	−470.419	−0.754224	−0.377112	−	0.926168i	$-0.623083\pi$
$73$	−470.419	−0.754224	−0.377112	+	0.926168i	$0.623083\pi$
$74$	629.189	0.988401
$75$	−549.943	−0.846693
$76$	765.972	1.15609
$77$	−835.532	−1.23659
$78$	854.685	1.24069
$79$	141.346	0.201300	0.100650	−	0.994922i	$-0.467908\pi$
$79$	141.346	0.201300	0.100650	+	0.994922i	$0.467908\pi$
$80$	−277.749	−0.388166
$81$	508.018	0.696870
$82$	1968.65	2.65123
$83$	−981.431	−1.29790	−0.648952	−	0.760829i	$-0.724792\pi$
$83$	−981.431	−1.29790	−0.648952	+	0.760829i	$0.724792\pi$
$84$	−2006.20	−2.60589
$85$	843.681	1.07659
$86$	−99.0759	−0.124228
$87$	−1677.69	−2.06744
$88$	−1738.71	−2.10622
$89$	679.280	0.809028	0.404514	−	0.914532i	$-0.367441\pi$
$89$	679.280	0.809028	0.404514	+	0.914532i	$0.367441\pi$
$90$	1933.24	2.26423
$91$	312.445	0.359925
$92$	444.634	0.503873
$93$	2150.82	2.39817
$94$	−1383.84	−1.51843
$95$	−412.198	−0.445165
$96$	790.719	0.840650
$97$	46.6609	0.0488422	0.0244211	−	0.999702i	$-0.492226\pi$
$97$	46.6609	0.0488422	0.0244211	+	0.999702i	$0.492226\pi$
$98$	503.317	0.518803
$99$	2774.90	2.81704
$100$	−915.959	−0.915959
$101$	1795.60	1.76900	0.884500	−	0.466539i	$-0.154499\pi$
$101$	1795.60	1.76900	0.884500	+	0.466539i	$0.154499\pi$
$102$	4487.34	4.35601
$103$	143.287	0.137073	0.0685364	−	0.997649i	$-0.478167\pi$
$103$	143.287	0.137073	0.0685364	+	0.997649i	$0.478167\pi$
$104$	650.188	0.613040
$105$	1079.61	1.00342
$106$	−3218.70	−2.94932
$107$	−1209.27	−1.09257	−0.546285	−	0.837599i	$-0.683958\pi$
$107$	−1209.27	−1.09257	−0.546285	+	0.837599i	$0.683958\pi$
$108$	3147.38	2.80423
$109$	−2085.78	−1.83286	−0.916428	−	0.400200i	$-0.868941\pi$
$109$	−2085.78	−1.83286	−0.916428	+	0.400200i	$0.868941\pi$
$110$	2048.55	1.77565
$111$	−1166.94	−0.997845
$112$	−540.046	−0.455621
$113$	−206.254	−0.171705	−0.0858527	−	0.996308i	$-0.527361\pi$
$113$	−206.254	−0.171705	−0.0858527	+	0.996308i	$0.527361\pi$
$114$	−2192.39	−1.80119
$115$	−239.274	−0.194021
$116$	−2794.28	−2.23657
$117$	−1037.67	−0.819933
$118$	2472.84	1.92918
$119$	1640.43	1.26368
$120$	2246.64	1.70908
$121$	1609.41	1.20918
$122$	647.525	0.480526
$123$	−3651.19	−2.67656
$124$	3582.31	2.59436
$125$	1483.49	1.06150
$126$	3758.93	2.65771
$127$	−1694.37	−1.18387	−0.591935	−	0.805986i	$-0.701636\pi$
$127$	−1694.37	−1.18387	−0.591935	+	0.805986i	$0.701636\pi$
$128$	2653.65	1.83244
$129$	183.753	0.125415
$130$	−766.051	−0.516824
$131$	282.768	0.188592	0.0942962	−	0.995544i	$-0.469940\pi$
$131$	282.768	0.188592	0.0942962	+	0.995544i	$0.469940\pi$
$132$	7060.25	4.65542
$133$	−801.466	−0.522526
$134$	3124.53	2.01432
$135$	−1693.73	−1.07980
$136$	3413.67	2.15235
$137$	−2999.91	−1.87080	−0.935399	−	0.353595i	$-0.884959\pi$
$137$	−2999.91	−1.87080	−0.935399	+	0.353595i	$0.884959\pi$
$138$	−1272.64	−0.785034
$139$	905.239	0.552384	0.276192	−	0.961102i	$-0.410927\pi$
$139$	905.239	0.552384	0.276192	+	0.961102i	$0.410927\pi$
$140$	1798.15	1.08551
$141$	2566.57	1.53294
$142$	−1578.98	−0.933133
$143$	−1099.56	−0.643006
$144$	1793.55	1.03794
$145$	1503.71	0.861214
$146$	2242.57	1.27121
$147$	−933.487	−0.523760
$148$	−1943.59	−1.07948
$149$	1092.50	0.600677	0.300339	−	0.953833i	$-0.402900\pi$
$149$	1092.50	0.600677	0.300339	+	0.953833i	$0.402900\pi$
$150$	2621.68	1.42706
$151$	−2387.88	−1.28691	−0.643454	−	0.765485i	$-0.722499\pi$
$151$	−2387.88	−1.28691	−0.643454	+	0.765485i	$0.722499\pi$
$152$	−1667.82	−0.889989
$153$	−5448.04	−2.87874
$154$	3983.14	2.08422
$155$	−1927.77	−0.998984
$156$	−2640.16	−1.35501
$157$	−2628.34	−1.33608	−0.668040	−	0.744125i	$-0.732867\pi$
$157$	−2628.34	−1.33608	−0.668040	+	0.744125i	$0.732867\pi$
$158$	−673.824	−0.339282
$159$	5969.63	2.97750
$160$	−708.718	−0.350182
$161$	−465.238	−0.227738
$162$	−2421.82	−1.17454
$163$	−649.278	−0.311996	−0.155998	−	0.987757i	$-0.549859\pi$
$163$	−649.278	−0.311996	−0.155998	+	0.987757i	$0.549859\pi$
$164$	−6081.25	−2.89552
$165$	−3799.39	−1.79262
$166$	4678.66	2.18756
$167$	−2851.96	−1.32150	−0.660751	−	0.750605i	$-0.729762\pi$
$167$	−2851.96	−1.32150	−0.660751	+	0.750605i	$0.729762\pi$
$168$	4368.29	2.00608
$169$	−1785.82	−0.812846
$170$	−4021.99	−1.81454
$171$	2661.76	1.19035
$172$	306.050	0.135675
$173$	3378.89	1.48493	0.742464	−	0.669886i	$-0.233657\pi$
$173$	3378.89	1.48493	0.742464	+	0.669886i	$0.233657\pi$
$174$	7997.86	3.48458
$175$	958.403	0.413991
$176$	1900.53	0.813967
$177$	−4586.29	−1.94761
$178$	−3238.25	−1.36358
$179$	1890.09	0.789229	0.394615	−	0.918847i	$-0.370878\pi$
$179$	1890.09	0.789229	0.394615	+	0.918847i	$0.370878\pi$
$180$	−5971.86	−2.47287
$181$	2055.01	0.843912	0.421956	−	0.906616i	$-0.361344\pi$
$181$	2055.01	0.843912	0.421956	+	0.906616i	$0.361344\pi$
$182$	−1489.49	−0.606637
$183$	−1200.94	−0.485117
$184$	−968.144	−0.387894
$185$	1045.92	0.415663
$186$	−10253.4	−4.04201
$187$	−5773.01	−2.25756
$188$	4274.76	1.65834
$189$	−3293.23	−1.26744
$190$	1965.03	0.750306
$191$	−1391.57	−0.527176	−0.263588	−	0.964635i	$-0.584906\pi$
$191$	−1391.57	−0.527176	−0.263588	+	0.964635i	$0.584906\pi$
$192$	−6248.58	−2.34871
$193$	3041.47	1.13435	0.567175	−	0.823597i	$-0.308036\pi$
$193$	3041.47	1.13435	0.567175	+	0.823597i	$0.308036\pi$
$194$	−222.441	−0.0823214
$195$	1420.77	0.521762
$196$	−1554.77	−0.566608
$197$	−3158.39	−1.14226	−0.571131	−	0.820859i	$-0.693495\pi$
$197$	−3158.39	−1.14226	−0.571131	+	0.820859i	$0.693495\pi$
$198$	−13228.4	−4.74800
$199$	−589.596	−0.210027	−0.105013	−	0.994471i	$-0.533489\pi$
$199$	−589.596	−0.210027	−0.105013	+	0.994471i	$0.533489\pi$
$200$	1994.40	0.705128
$201$	−5794.98	−2.03356
$202$	−8559.97	−2.98157
$203$	2923.76	1.01088
$204$	−13861.6	−4.75739
$205$	3272.55	1.11495
$206$	−683.076	−0.231030
$207$	1545.11	0.518803
$208$	−710.700	−0.236914
$209$	2820.53	0.933492
$210$	−5146.72	−1.69123
$211$	1104.16	0.360253	0.180127	−	0.983643i	$-0.442349\pi$
$211$	1104.16	0.360253	0.180127	+	0.983643i	$0.442349\pi$
$212$	9942.73	3.22108
$213$	2928.48	0.942048
$214$	5764.84	1.84148
$215$	−164.697	−0.0522430
$216$	−6853.09	−2.15877
$217$	−3748.30	−1.17259
$218$	9943.29	3.08920
$219$	−4159.24	−1.28336
$220$	−6328.08	−1.93927
$221$	2158.80	0.657089
$222$	5563.01	1.68182
$223$	−5366.64	−1.61156	−0.805778	−	0.592218i	$-0.798252\pi$
$223$	−5366.64	−1.61156	−0.805778	+	0.592218i	$0.798252\pi$
$224$	−1378.01	−0.411036
$225$	−3182.96	−0.943100
$226$	983.250	0.289402
$227$	4855.03	1.41956	0.709778	−	0.704425i	$-0.248795\pi$
$227$	4855.03	1.41956	0.709778	+	0.704425i	$0.248795\pi$
$228$	6772.39	1.96716
$229$	−1975.61	−0.570097	−0.285048	−	0.958513i	$-0.592010\pi$
$229$	−1975.61	−0.570097	−0.285048	+	0.958513i	$0.592010\pi$
$230$	1140.67	0.327014
$231$	−7387.41	−2.10414
$232$	6084.24	1.72177
$233$	−1469.63	−0.413213	−0.206607	−	0.978424i	$-0.566242\pi$
$233$	−1469.63	−0.413213	−0.206607	+	0.978424i	$0.566242\pi$
$234$	4946.74	1.38196
$235$	−2300.41	−0.638562
$236$	−7638.71	−2.10694
$237$	1249.72	0.342524
$238$	−7820.23	−2.12987
$239$	2827.53	0.765264	0.382632	−	0.923901i	$-0.375018\pi$
$239$	2827.53	0.765264	0.382632	+	0.923901i	$0.375018\pi$
$240$	−2455.73	−0.660487
$241$	−5410.26	−1.44608	−0.723040	−	0.690806i	$-0.757256\pi$
$241$	−5410.26	−1.44608	−0.723040	+	0.690806i	$0.757256\pi$
$242$	−7672.38	−2.03801
$243$	−1279.00	−0.337645
$244$	−2000.24	−0.524803
$245$	836.681	0.218178
$246$	17405.9	4.51122
$247$	−1054.73	−0.271704
$248$	−7800.09	−1.99720
$249$	−8677.38	−2.20846
$250$	−7072.10	−1.78911
$251$	226.603	0.0569843	0.0284922	−	0.999594i	$-0.490929\pi$
$251$	226.603	0.0569843	0.0284922	+	0.999594i	$0.490929\pi$
$252$	−11611.5	−2.90260
$253$	1637.27	0.406855
$254$	8077.40	1.99536
$255$	7459.46	1.83188
$256$	−6996.63	−1.70816
$257$	1454.20	0.352959	0.176480	−	0.984304i	$-0.443529\pi$
$257$	1454.20	0.352959	0.176480	+	0.984304i	$0.443529\pi$
$258$	−875.985	−0.211382
$259$	2033.66	0.487897
$260$	2366.37	0.564446
$261$	−9710.13	−2.30284
$262$	−1348.01	−0.317864
$263$	5004.58	1.17337	0.586684	−	0.809816i	$-0.300433\pi$
$263$	5004.58	1.17337	0.586684	+	0.809816i	$0.300433\pi$
$264$	−15372.9	−3.58386
$265$	−5350.56	−1.24031
$266$	3820.74	0.880693
$267$	6005.89	1.37661
$268$	−9651.84	−2.19993
$269$	−4178.02	−0.946984	−0.473492	−	0.880798i	$-0.657007\pi$
$269$	−4178.02	−0.946984	−0.473492	+	0.880798i	$0.657007\pi$
$270$	8074.31	1.81995
$271$	−7936.04	−1.77889	−0.889446	−	0.457039i	$-0.848910\pi$
$271$	−7936.04	−1.77889	−0.889446	+	0.457039i	$0.848910\pi$
$272$	−3731.38	−0.831795
$273$	2762.50	0.612433
$274$	14301.1	3.15314
$275$	−3372.82	−0.739595
$276$	3931.26	0.857370
$277$	−1850.35	−0.401361	−0.200680	−	0.979657i	$-0.564315\pi$
$277$	−1850.35	−0.401361	−0.200680	+	0.979657i	$0.564315\pi$
$278$	−4315.44	−0.931019
$279$	12448.5	2.67123
$280$	−3915.29	−0.835654
$281$	1091.17	0.231650	0.115825	−	0.993270i	$-0.463049\pi$
$281$	1091.17	0.231650	0.115825	+	0.993270i	$0.463049\pi$
$282$	−12235.3	−2.58370
$283$	−6401.97	−1.34473	−0.672363	−	0.740222i	$-0.734721\pi$
$283$	−6401.97	−1.34473	−0.672363	+	0.740222i	$0.734721\pi$
$284$	4877.54	1.01912
$285$	−3644.48	−0.757474
$286$	5241.81	1.08376
$287$	6363.04	1.30871
$288$	4576.52	0.936369
$289$	6421.33	1.30701
$290$	−7168.45	−1.45154
$291$	412.555	0.0831079
$292$	−6927.42	−1.38834
$293$	−2211.58	−0.440961	−0.220481	−	0.975391i	$-0.570763\pi$
$293$	−2211.58	−0.440961	−0.220481	+	0.975391i	$0.570763\pi$
$294$	4450.11	0.882774
$295$	4110.68	0.811298
$296$	4231.97	0.831008
$297$	11589.6	2.26429
$298$	−5208.14	−1.01241
$299$	−612.253	−0.118420
$300$	−8098.51	−1.55856
$301$	−320.232	−0.0613218
$302$	11383.5	2.16903
$303$	15875.9	3.01006
$304$	1823.05	0.343944
$305$	1076.40	0.202081
$306$	25971.8	4.85200
$307$	−4738.62	−0.880936	−0.440468	−	0.897768i	$-0.645188\pi$
$307$	−4738.62	−0.880936	−0.440468	+	0.897768i	$0.645188\pi$
$308$	−12304.1	−2.27627
$309$	1266.88	0.233237
$310$	9190.06	1.68374
$311$	5455.34	0.994674	0.497337	−	0.867557i	$-0.334311\pi$
$311$	5455.34	0.994674	0.497337	+	0.867557i	$0.334311\pi$
$312$	5748.67	1.04312
$313$	−2708.30	−0.489081	−0.244540	−	0.969639i	$-0.578637\pi$
$313$	−2708.30	−0.489081	−0.244540	+	0.969639i	$0.578637\pi$
$314$	12529.8	2.25190
$315$	6248.59	1.11768
$316$	2081.48	0.370545
$317$	−2633.32	−0.466567	−0.233284	−	0.972409i	$-0.574947\pi$
$317$	−2633.32	−0.466567	−0.233284	+	0.972409i	$0.574947\pi$
$318$	−28458.4	−5.01844
$319$	−10289.3	−1.80593
$320$	5600.58	0.978382
$321$	−10691.9	−1.85907
$322$	2217.88	0.383843
$323$	−5537.63	−0.953938
$324$	7481.11	1.28277
$325$	1261.26	0.215268
$326$	3095.23	0.525856
$327$	−18441.5	−3.11871
$328$	13241.3	2.22905
$329$	−4472.84	−0.749531
$330$	18112.4	3.02138
$331$	−6722.11	−1.11626	−0.558128	−	0.829755i	$-0.688480\pi$
$331$	−6722.11	−1.11626	−0.558128	+	0.829755i	$0.688480\pi$
$332$	−14452.6	−2.38913
$333$	−6754.00	−1.11146
$334$	13595.8	2.22733
$335$	5194.02	0.847103
$336$	−4774.85	−0.775266
$337$	3116.16	0.503704	0.251852	−	0.967766i	$-0.418960\pi$
$337$	3116.16	0.503704	0.251852	+	0.967766i	$0.418960\pi$
$338$	8513.35	1.37002
$339$	−1823.60	−0.292167
$340$	12424.1	1.98174
$341$	13191.1	2.09483
$342$	−12689.1	−2.00628
$343$	6911.92	1.08807
$344$	−666.392	−0.104446
$345$	−2115.56	−0.330139
$346$	−16107.8	−2.50278
$347$	−9665.36	−1.49528	−0.747642	−	0.664102i	$-0.768814\pi$
$347$	−9665.36	−1.49528	−0.747642	+	0.664102i	$0.768814\pi$
$348$	−24705.8	−3.80566
$349$	4552.13	0.698194	0.349097	−	0.937087i	$-0.386488\pi$
$349$	4552.13	0.698194	0.349097	+	0.937087i	$0.386488\pi$
$350$	−4568.89	−0.697764
$351$	−4333.89	−0.659048
$352$	4849.50	0.734317
$353$	4469.50	0.673903	0.336951	−	0.941522i	$-0.390604\pi$
$353$	4469.50	0.673903	0.336951	+	0.941522i	$0.390604\pi$
$354$	21863.7	3.28261
$355$	−2624.79	−0.392421
$356$	10003.1	1.48923
$357$	14503.9	2.15022
$358$	−9010.42	−1.33021
$359$	−9836.34	−1.44608	−0.723039	−	0.690807i	$-0.757255\pi$
$359$	−9836.34	−1.44608	−0.723039	+	0.690807i	$0.757255\pi$
$360$	13003.1	1.90368
$361$	−4153.47	−0.605551
$362$	−9796.64	−1.42238
$363$	14229.7	2.05748
$364$	4601.09	0.662535
$365$	3727.91	0.534596
$366$	5725.13	0.817643
$367$	−354.669	−0.0504457	−0.0252229	−	0.999682i	$-0.508030\pi$
$367$	−354.669	−0.0504457	−0.0252229	+	0.999682i	$0.508030\pi$
$368$	1058.25	0.149905
$369$	−21132.4	−2.98132
$370$	−4986.11	−0.700582
$371$	−10403.5	−1.45585
$372$	31673.2	4.41445
$373$	1671.29	0.232001	0.116000	−	0.993249i	$-0.462993\pi$
$373$	1671.29	0.232001	0.116000	+	0.993249i	$0.462993\pi$
$374$	27521.0	3.80502
$375$	13116.4	1.80621
$376$	−9307.82	−1.27663
$377$	3847.67	0.525637
$378$	15699.4	2.13622
$379$	4822.46	0.653596	0.326798	−	0.945094i	$-0.394030\pi$
$379$	4822.46	0.653596	0.326798	+	0.945094i	$0.394030\pi$
$380$	−6070.07	−0.819442
$381$	−14980.9	−2.01442
$382$	6633.89	0.888532
$383$	−11862.4	−1.58262	−0.791309	−	0.611416i	$-0.790600\pi$
$383$	−11862.4	−1.58262	−0.791309	+	0.611416i	$0.790600\pi$
$384$	23462.4	3.11800
$385$	6621.31	0.876502
$386$	−14499.2	−1.91190
$387$	1063.53	0.139695
$388$	687.132	0.0899068
$389$	7874.08	1.02630	0.513152	−	0.858298i	$-0.328478\pi$
$389$	7874.08	1.02630	0.513152	+	0.858298i	$0.328478\pi$
$390$	−6773.08	−0.879406
$391$	−3214.50	−0.415766
$392$	3385.35	0.436189
$393$	2500.11	0.320901
$394$	15056.6	1.92523
$395$	−1120.12	−0.142682
$396$	40863.3	5.18550
$397$	3767.94	0.476341	0.238171	−	0.971223i	$-0.423452\pi$
$397$	3767.94	0.476341	0.238171	+	0.971223i	$0.423452\pi$
$398$	2810.72	0.353991
$399$	−7086.21	−0.889108
$400$	−2180.02	−0.272503
$401$	−5061.56	−0.630330	−0.315165	−	0.949037i	$-0.602060\pi$
$401$	−5061.56	−0.630330	−0.315165	+	0.949037i	$0.602060\pi$
$402$	27625.8	3.42748
$403$	−4932.77	−0.609724
$404$	26442.2	3.25631
$405$	−4025.87	−0.493943
$406$	−13938.1	−1.70379
$407$	−7156.87	−0.871628
$408$	30182.2	3.66236
$409$	−10666.1	−1.28950	−0.644749	−	0.764394i	$-0.723038\pi$
$409$	−10666.1	−1.28950	−0.644749	+	0.764394i	$0.723038\pi$
$410$	−15600.9	−1.87920
$411$	−26523.8	−3.18327
$412$	2110.06	0.252318
$413$	7992.68	0.952285
$414$	−7365.81	−0.874420
$415$	7777.50	0.919958
$416$	−1813.46	−0.213731
$417$	8003.73	0.939914
$418$	−13446.0	−1.57336
$419$	10366.3	1.20865	0.604325	−	0.796738i	$-0.293443\pi$
$419$	10366.3	1.20865	0.604325	+	0.796738i	$0.293443\pi$
$420$	15898.5	1.84706
$421$	7500.65	0.868312	0.434156	−	0.900838i	$-0.357047\pi$
$421$	7500.65	0.868312	0.434156	+	0.900838i	$0.357047\pi$
$422$	−5263.73	−0.607190
$423$	14854.8	1.70748
$424$	−21649.2	−2.47967
$425$	6621.97	0.755794
$426$	−13960.6	−1.58778
$427$	2092.92	0.237198
$428$	−17807.9	−2.01116
$429$	−9721.83	−1.09411
$430$	785.142	0.0880533
$431$	1865.10	0.208443	0.104222	−	0.994554i	$-0.466765\pi$
$431$	1865.10	0.208443	0.104222	+	0.994554i	$0.466765\pi$
$432$	7490.90	0.834274
$433$	−96.4709	−0.0107069	−0.00535346	−	0.999986i	$-0.501704\pi$
$433$	−96.4709	−0.0107069	−0.00535346	+	0.999986i	$0.501704\pi$
$434$	17868.9	1.97634
$435$	13295.1	1.46541
$436$	−30715.3	−3.37385
$437$	1570.51	0.171917
$438$	19827.9	2.16304
$439$	11395.9	1.23894	0.619470	−	0.785021i	$-0.287348\pi$
$439$	11395.9	1.23894	0.619470	+	0.785021i	$0.287348\pi$
$440$	13778.7	1.49290
$441$	−5402.84	−0.583397
$442$	−10291.4	−1.10749
$443$	−283.251	−0.0303785	−0.0151892	−	0.999885i	$-0.504835\pi$
$443$	−283.251	−0.0303785	−0.0151892	+	0.999885i	$0.504835\pi$
$444$	−17184.4	−1.83679
$445$	−5383.06	−0.573441
$446$	25583.8	2.71620
$447$	9659.38	1.02209
$448$	10889.6	1.14840
$449$	4189.03	0.440295	0.220148	−	0.975467i	$-0.429346\pi$
$449$	4189.03	0.440295	0.220148	+	0.975467i	$0.429346\pi$
$450$	15173.8	1.58955
$451$	−22392.9	−2.33800
$452$	−3037.31	−0.316068
$453$	−21112.6	−2.18975
$454$	−23144.8	−2.39260
$455$	−2476.02	−0.255116
$456$	−14746.2	−1.51437
$457$	−13350.2	−1.36651	−0.683255	−	0.730180i	$-0.739436\pi$
$457$	−13350.2	−1.36651	−0.683255	+	0.730180i	$0.739436\pi$
$458$	9418.11	0.960872
$459$	−22754.1	−2.31388
$460$	−3523.57	−0.357147
$461$	−2020.88	−0.204169	−0.102084	−	0.994776i	$-0.532551\pi$
$461$	−2020.88	−0.204169	−0.102084	+	0.994776i	$0.532551\pi$
$462$	35217.2	3.54643
$463$	−2016.51	−0.202409	−0.101204	−	0.994866i	$-0.532270\pi$
$463$	−2016.51	−0.202409	−0.101204	+	0.994866i	$0.532270\pi$
$464$	−6650.50	−0.665392
$465$	−17044.5	−1.69983
$466$	7006.00	0.696452
$467$	6715.44	0.665425	0.332713	−	0.943028i	$-0.392036\pi$
$467$	6715.44	0.665425	0.332713	+	0.943028i	$0.392036\pi$
$468$	−15280.7	−1.50930
$469$	10099.1	0.994313
$470$	10966.5	1.07627
$471$	−23238.7	−2.27342
$472$	16632.5	1.62197
$473$	1126.96	0.109551
$474$	−5957.66	−0.577309
$475$	−3235.30	−0.312518
$476$	24157.1	2.32613
$477$	34551.0	3.31653
$478$	−13479.4	−1.28982
$479$	13656.1	1.30264	0.651319	−	0.758804i	$-0.274216\pi$
$479$	13656.1	1.30264	0.651319	+	0.758804i	$0.274216\pi$
$480$	−6266.18	−0.595855
$481$	2676.29	0.253697
$482$	25791.7	2.43730
$483$	−4113.43	−0.387510
$484$	23700.3	2.22580
$485$	−369.772	−0.0346195
$486$	6097.23	0.569086
$487$	15826.0	1.47258	0.736288	−	0.676669i	$-0.236577\pi$
$487$	15826.0	1.47258	0.736288	+	0.676669i	$0.236577\pi$
$488$	4355.30	0.404007
$489$	−5740.63	−0.530880
$490$	−3988.62	−0.367729
$491$	6624.47	0.608876	0.304438	−	0.952532i	$-0.401531\pi$
$491$	6624.47	0.608876	0.304438	+	0.952532i	$0.401531\pi$
$492$	−53767.7	−4.92690
$493$	20201.4	1.84548
$494$	5028.09	0.457944
$495$	−21990.1	−1.99673
$496$	8526.04	0.771836
$497$	−5103.56	−0.460615
$498$	41366.7	3.72226
$499$	16091.9	1.44363	0.721814	−	0.692087i	$-0.243309\pi$
$499$	16091.9	1.44363	0.721814	+	0.692087i	$0.243309\pi$
$500$	21846.0	1.95397
$501$	−25215.7	−2.24862
$502$	−1080.26	−0.0960446
$503$	−6581.48	−0.583406	−0.291703	−	0.956509i	$-0.594222\pi$
$503$	−6581.48	−0.583406	−0.291703	+	0.956509i	$0.594222\pi$
$504$	25282.8	2.23450
$505$	−14229.5	−1.25387
$506$	−7805.17	−0.685735
$507$	−15789.5	−1.38310
$508$	−24951.5	−2.17922
$509$	−16931.5	−1.47441	−0.737205	−	0.675669i	$-0.763855\pi$
$509$	−16931.5	−1.47441	−0.737205	+	0.675669i	$0.763855\pi$
$510$	−35560.6	−3.08755
$511$	7248.43	0.627498
$512$	12125.0	1.04659
$513$	11117.0	0.956781
$514$	−6932.44	−0.594897
$515$	−1135.50	−0.0971576
$516$	2705.96	0.230859
$517$	15740.9	1.33904
$518$	−9694.83	−0.822329
$519$	29874.7	2.52669
$520$	−5152.52	−0.434525
$521$	6127.63	0.515271	0.257636	−	0.966242i	$-0.417057\pi$
$521$	6127.63	0.515271	0.257636	+	0.966242i	$0.417057\pi$
$522$	46290.0	3.88134
$523$	−14761.7	−1.23420	−0.617099	−	0.786886i	$-0.711692\pi$
$523$	−14761.7	−1.23420	−0.617099	+	0.786886i	$0.711692\pi$
$524$	4164.07	0.347153
$525$	8473.78	0.704430
$526$	−23857.8	−1.97766
$527$	−25898.4	−2.14071
$528$	16803.7	1.38501
$529$	−11255.3	−0.925071
$530$	25507.1	2.09049
$531$	−26544.6	−2.16937
$532$	−11802.4	−0.961844
$533$	8373.77	0.680503
$534$	−28631.2	−2.32021
$535$	9583.09	0.774417
$536$	21015.9	1.69356
$537$	16711.4	1.34292
$538$	19917.4	1.59610
$539$	−5725.11	−0.457510
$540$	−24941.9	−1.98765
$541$	21856.7	1.73696	0.868478	−	0.495727i	$-0.165098\pi$
$541$	21856.7	1.73696	0.868478	+	0.495727i	$0.165098\pi$
$542$	37832.6	2.99824
$543$	18169.5	1.43597
$544$	−9521.19	−0.750400
$545$	16529.1	1.29913
$546$	−13169.4	−1.03223
$547$	−1839.18	−0.143762	−0.0718808	−	0.997413i	$-0.522900\pi$
$547$	−1839.18	−0.143762	−0.0718808	+	0.997413i	$0.522900\pi$
$548$	−44176.8	−3.44369
$549$	−6950.83	−0.540354
$550$	16078.9	1.24655
$551$	−9869.81	−0.763100
$552$	−8559.90	−0.660024
$553$	−2177.93	−0.167477
$554$	8820.98	0.676476
$555$	9247.58	0.707276
$556$	13330.6	1.01681
$557$	13617.8	1.03591	0.517956	−	0.855407i	$-0.326693\pi$
$557$	13617.8	1.03591	0.517956	+	0.855407i	$0.326693\pi$
$558$	−59344.5	−4.50224
$559$	−421.425	−0.0318862
$560$	4279.68	0.322945
$561$	−51042.4	−3.84138
$562$	−5201.81	−0.390436
$563$	−4560.17	−0.341364	−0.170682	−	0.985326i	$-0.554597\pi$
$563$	−4560.17	−0.341364	−0.170682	+	0.985326i	$0.554597\pi$
$564$	37795.5	2.82177
$565$	1634.49	0.121705
$566$	30519.4	2.26648
$567$	−7827.77	−0.579781
$568$	−10620.3	−0.784540
$569$	19979.6	1.47204	0.736020	−	0.676960i	$-0.236703\pi$
$569$	19979.6	1.47204	0.736020	+	0.676960i	$0.236703\pi$
$570$	17373.9	1.27669
$571$	−4955.14	−0.363163	−0.181582	−	0.983376i	$-0.558122\pi$
$571$	−4955.14	−0.363163	−0.181582	+	0.983376i	$0.558122\pi$
$572$	−16192.2	−1.18362
$573$	−12303.7	−0.897022
$574$	−30333.8	−2.20577
$575$	−1878.04	−0.136208
$576$	−36165.6	−2.61614
$577$	−7753.51	−0.559416	−0.279708	−	0.960085i	$-0.590238\pi$
$577$	−7753.51	−0.559416	−0.279708	+	0.960085i	$0.590238\pi$
$578$	−30611.7	−2.20290
$579$	26891.3	1.93016
$580$	22143.7	1.58529
$581$	15122.3	1.07983
$582$	−1966.73	−0.140075
$583$	36612.0	2.60088
$584$	15083.7	1.06878
$585$	8223.14	0.581171
$586$	10543.0	0.743220
$587$	−20458.0	−1.43849	−0.719244	−	0.694758i	$-0.755511\pi$
$587$	−20458.0	−1.43849	−0.719244	+	0.694758i	$0.755511\pi$
$588$	−13746.6	−0.964116
$589$	12653.2	0.885174
$590$	−19596.4	−1.36741
$591$	−27925.1	−1.94363
$592$	−4625.84	−0.321150
$593$	17508.0	1.21242	0.606211	−	0.795304i	$-0.292689\pi$
$593$	17508.0	1.21242	0.606211	+	0.795304i	$0.292689\pi$
$594$	−55249.6	−3.81636
$595$	−12999.8	−0.895699
$596$	16088.2	1.10570
$597$	−5212.95	−0.357373
$598$	2918.72	0.199591
$599$	24529.0	1.67317	0.836584	−	0.547838i	$-0.184549\pi$
$599$	24529.0	1.67317	0.836584	+	0.547838i	$0.184549\pi$
$600$	17633.6	1.19982
$601$	15525.9	1.05377	0.526885	−	0.849937i	$-0.323360\pi$
$601$	15525.9	1.05377	0.526885	+	0.849937i	$0.323360\pi$
$602$	1526.61	0.103355
$603$	−33540.2	−2.26511
$604$	−35164.1	−2.36889
$605$	−12754.1	−0.857068
$606$	−75683.5	−5.07332
$607$	25597.3	1.71163	0.855816	−	0.517280i	$-0.173055\pi$
$607$	25597.3	1.71163	0.855816	+	0.517280i	$0.173055\pi$
$608$	4651.78	0.310287
$609$	25850.6	1.72006
$610$	−5131.41	−0.340598
$611$	−5886.26	−0.389742
$612$	−80228.3	−5.29908
$613$	−1223.74	−0.0806303	−0.0403152	−	0.999187i	$-0.512836\pi$
$613$	−1223.74	−0.0806303	−0.0403152	+	0.999187i	$0.512836\pi$
$614$	22589.9	1.48478
$615$	28934.5	1.89715
$616$	26790.9	1.75233
$617$	−7317.83	−0.477480	−0.238740	−	0.971084i	$-0.576734\pi$
$617$	−7317.83	−0.477480	−0.238740	+	0.971084i	$0.576734\pi$
$618$	−6039.46	−0.393111
$619$	−14593.4	−0.947591	−0.473795	−	0.880635i	$-0.657116\pi$
$619$	−14593.4	−0.947591	−0.473795	+	0.880635i	$0.657116\pi$
$620$	−28388.5	−1.83889
$621$	6453.25	0.417005
$622$	−26006.6	−1.67648
$623$	−10466.6	−0.673094
$624$	−6283.70	−0.403124
$625$	−3981.21	−0.254797
$626$	12911.0	0.824323
$627$	24937.8	1.58839
$628$	−38705.2	−2.45940
$629$	14051.3	0.890719
$630$	−29788.2	−1.88379
$631$	20978.7	1.32353	0.661767	−	0.749710i	$-0.269807\pi$
$631$	20978.7	1.32353	0.661767	+	0.749710i	$0.269807\pi$
$632$	−4532.19	−0.285255
$633$	9762.48	0.612992
$634$	12553.5	0.786378
$635$	13427.3	0.839130
$636$	87909.3	5.48086
$637$	2140.89	0.133164
$638$	49051.2	3.04381
$639$	16949.5	1.04931
$640$	−21029.3	−1.29884
$641$	15927.8	0.981450	0.490725	−	0.871315i	$-0.336732\pi$
$641$	15927.8	0.981450	0.490725	+	0.871315i	$0.336732\pi$
$642$	50970.2	3.13338
$643$	−2197.27	−0.134762	−0.0673810	−	0.997727i	$-0.521464\pi$
$643$	−2197.27	−0.134762	−0.0673810	+	0.997727i	$0.521464\pi$
$644$	−6851.13	−0.419211
$645$	−1456.18	−0.0888946
$646$	26398.9	1.60782
$647$	−2410.90	−0.146495	−0.0732474	−	0.997314i	$-0.523336\pi$
$647$	−2410.90	−0.146495	−0.0732474	+	0.997314i	$0.523336\pi$
$648$	−16289.3	−0.987508
$649$	−28127.9	−1.70126
$650$	−6012.65	−0.362824
$651$	−33140.8	−1.99523
$652$	−9561.32	−0.574310
$653$	21329.1	1.27821	0.639106	−	0.769118i	$-0.279304\pi$
$653$	21329.1	1.27821	0.639106	+	0.769118i	$0.279304\pi$
$654$	87914.2	5.25645
$655$	−2240.84	−0.133675
$656$	−14473.6	−0.861433
$657$	−24072.8	−1.42948
$658$	21322.9	1.26330
$659$	−11186.7	−0.661261	−0.330631	−	0.943760i	$-0.607261\pi$
$659$	−11186.7	−0.661261	−0.330631	+	0.943760i	$0.607261\pi$
$660$	−55950.1	−3.29978
$661$	448.054	0.0263650	0.0131825	−	0.999913i	$-0.495804\pi$
$661$	448.054	0.0263650	0.0131825	+	0.999913i	$0.495804\pi$
$662$	32045.6	1.88140
$663$	19087.2	1.11808
$664$	31469.0	1.83921
$665$	6351.34	0.370368
$666$	32197.6	1.87332
$667$	−5729.26	−0.332591
$668$	−41998.1	−2.43257
$669$	−47449.5	−2.74216
$670$	−24760.9	−1.42775
$671$	−7365.44	−0.423755
$672$	−12183.8	−0.699403
$673$	14527.8	0.832101	0.416050	−	0.909342i	$-0.363414\pi$
$673$	14527.8	0.832101	0.416050	+	0.909342i	$0.363414\pi$
$674$	−14855.3	−0.848970
$675$	−13293.9	−0.758047
$676$	−26298.1	−1.49625
$677$	−26612.0	−1.51076	−0.755379	−	0.655288i	$-0.772547\pi$
$677$	−26612.0	−1.51076	−0.755379	+	0.655288i	$0.772547\pi$
$678$	8693.46	0.492434
$679$	−718.972	−0.0406357
$680$	−27052.2	−1.52559
$681$	42926.0	2.41546
$682$	−62884.3	−3.53074
$683$	11734.3	0.657393	0.328696	−	0.944436i	$-0.393391\pi$
$683$	11734.3	0.657393	0.328696	+	0.944436i	$0.393391\pi$
$684$	39197.2	2.19114
$685$	23773.2	1.32603
$686$	−32950.4	−1.83390
$687$	−17467.5	−0.970053
$688$	728.412	0.0403640
$689$	−13691.0	−0.757016
$690$	10085.3	0.556434
$691$	−10274.1	−0.565625	−0.282813	−	0.959175i	$-0.591267\pi$
$691$	−10274.1	−0.565625	−0.282813	+	0.959175i	$0.591267\pi$
$692$	49757.8	2.73339
$693$	−42756.8	−2.34372
$694$	46076.6	2.52023
$695$	−7173.71	−0.391531
$696$	53794.2	2.92969
$697$	43964.7	2.38921
$698$	−21700.8	−1.17677
$699$	−12993.8	−0.703106
$700$	14113.5	0.762058
$701$	−27909.1	−1.50373	−0.751864	−	0.659318i	$-0.770845\pi$
$701$	−27909.1	−1.50373	−0.751864	+	0.659318i	$0.770845\pi$
$702$	20660.4	1.11080
$703$	−6865.06	−0.368308
$704$	−38322.8	−2.05163
$705$	−20339.2	−1.08655
$706$	−21307.0	−1.13583
$707$	−27667.5	−1.47177
$708$	−67538.1	−3.58508
$709$	18093.0	0.958389	0.479194	−	0.877709i	$-0.340929\pi$
$709$	18093.0	0.958389	0.479194	+	0.877709i	$0.340929\pi$
$710$	12512.9	0.661407
$711$	7233.14	0.381525
$712$	−21780.7	−1.14644
$713$	7344.99	0.385796
$714$	−69143.0	−3.62411
$715$	8713.64	0.455765
$716$	27833.6	1.45278
$717$	24999.8	1.30214
$718$	46891.7	2.43730
$719$	6026.71	0.312599	0.156299	−	0.987710i	$-0.450044\pi$
$719$	6026.71	0.312599	0.156299	+	0.987710i	$0.450044\pi$
$720$	−14213.3	−0.735692
$721$	−2207.83	−0.114042
$722$	19800.4	1.02063
$723$	−47835.1	−2.46059
$724$	30262.3	1.55344
$725$	11802.4	0.604595
$726$	−67835.8	−3.46780
$727$	−12576.3	−0.641580	−0.320790	−	0.947150i	$-0.603948\pi$
$727$	−12576.3	−0.641580	−0.320790	+	0.947150i	$0.603948\pi$
$728$	−10018.4	−0.510036
$729$	−25024.8	−1.27139
$730$	−17771.6	−0.901038
$731$	−2212.60	−0.111951
$732$	−17685.2	−0.892984
$733$	33384.9	1.68226	0.841132	−	0.540830i	$-0.181890\pi$
$733$	33384.9	1.68226	0.841132	+	0.540830i	$0.181890\pi$
$734$	1690.77	0.0850240
$735$	7397.57	0.371243
$736$	2700.28	0.135236
$737$	−35540.8	−1.77634
$738$	100742.	5.02488
$739$	30503.3	1.51838	0.759191	−	0.650868i	$-0.225595\pi$
$739$	30503.3	1.51838	0.759191	+	0.650868i	$0.225595\pi$
$740$	15402.3	0.765136
$741$	−9325.45	−0.462320
$742$	49595.2	2.45377
$743$	−12188.8	−0.601838	−0.300919	−	0.953650i	$-0.597293\pi$
$743$	−12188.8	−0.601838	−0.300919	+	0.953650i	$0.597293\pi$
$744$	−68964.9	−3.39836
$745$	−8657.67	−0.425762
$746$	−7967.37	−0.391027
$747$	−50222.9	−2.45992
$748$	−85013.8	−4.15563
$749$	18633.1	0.908995
$750$	−62528.4	−3.04428
$751$	34437.6	1.67330	0.836648	−	0.547740i	$-0.184512\pi$
$751$	34437.6	1.67330	0.836648	+	0.547740i	$0.184512\pi$
$752$	10174.1	0.493366
$753$	2003.53	0.0969622
$754$	−18342.6	−0.885937
$755$	18923.1	0.912164
$756$	−48496.3	−2.33306
$757$	−33719.3	−1.61895	−0.809477	−	0.587152i	$-0.800249\pi$
$757$	−33719.3	−1.61895	−0.809477	+	0.587152i	$0.800249\pi$
$758$	−22989.6	−1.10161
$759$	14476.0	0.692287
$760$	13216.9	0.630826
$761$	1254.28	0.0597472	0.0298736	−	0.999554i	$-0.490490\pi$
$761$	1254.28	0.0597472	0.0298736	+	0.999554i	$0.490490\pi$
$762$	71416.8	3.39522
$763$	32138.6	1.52490
$764$	−20492.4	−0.970405
$765$	43173.9	2.04046
$766$	56550.5	2.66743
$767$	10518.4	0.495171
$768$	−61861.1	−2.90654
$769$	29493.7	1.38305	0.691527	−	0.722350i	$-0.256938\pi$
$769$	29493.7	1.38305	0.691527	+	0.722350i	$0.256938\pi$
$770$	−31565.0	−1.47730
$771$	12857.4	0.600581
$772$	44788.9	2.08807
$773$	−16053.7	−0.746973	−0.373486	−	0.927636i	$-0.621838\pi$
$773$	−16053.7	−0.746973	−0.373486	+	0.927636i	$0.621838\pi$
$774$	−5070.03	−0.235450
$775$	−15130.9	−0.701313
$776$	−1496.16	−0.0692125
$777$	17980.7	0.830186
$778$	−37537.2	−1.72979
$779$	−21479.9	−0.987929
$780$	20922.4	0.960438
$781$	17960.5	0.822889
$782$	15324.1	0.700755
$783$	−40555.1	−1.85098
$784$	−3700.42	−0.168569
$785$	20828.7	0.947018
$786$	−11918.5	−0.540864
$787$	10884.6	0.493004	0.246502	−	0.969142i	$-0.420719\pi$
$787$	10884.6	0.493004	0.246502	+	0.969142i	$0.420719\pi$
$788$	−46510.6	−2.10263
$789$	44248.3	1.99655
$790$	5339.83	0.240484
$791$	3178.05	0.142855
$792$	−88975.5	−3.99193
$793$	2754.29	0.123339
$794$	−17962.5	−0.802852
$795$	−47307.3	−2.11046
$796$	−8682.44	−0.386609
$797$	22766.7	1.01184	0.505920	−	0.862580i	$-0.331153\pi$
$797$	22766.7	1.01184	0.505920	+	0.862580i	$0.331153\pi$
$798$	33781.3	1.49855
$799$	−30904.5	−1.36837
$800$	−5562.66	−0.245837
$801$	34760.9	1.53335
$802$	24129.4	1.06239
$803$	−25508.7	−1.12103
$804$	−85337.3	−3.74330
$805$	3686.85	0.161422
$806$	23515.4	1.02766
$807$	−36940.3	−1.61135
$808$	−57575.0	−2.50678
$809$	5534.71	0.240532	0.120266	−	0.992742i	$-0.461625\pi$
$809$	5534.71	0.240532	0.120266	+	0.992742i	$0.461625\pi$
$810$	19192.1	0.832519
$811$	−10860.3	−0.470232	−0.235116	−	0.971967i	$-0.575547\pi$
$811$	−10860.3	−0.470232	−0.235116	+	0.971967i	$0.575547\pi$
$812$	43055.5	1.86078
$813$	−70167.0	−3.02689
$814$	34118.1	1.46909
$815$	5145.31	0.221144
$816$	−32991.2	−1.41535
$817$	1081.01	0.0462912
$818$	50847.3	2.17339
$819$	15988.8	0.682167
$820$	48191.8	2.05236
$821$	−16470.7	−0.700161	−0.350081	−	0.936720i	$-0.613846\pi$
$821$	−16470.7	−0.700161	−0.350081	+	0.936720i	$0.613846\pi$
$822$	126444.	5.36526
$823$	20235.3	0.857059	0.428530	−	0.903528i	$-0.359032\pi$
$823$	20235.3	0.857059	0.428530	+	0.903528i	$0.359032\pi$
$824$	−4594.42	−0.194241
$825$	−29821.0	−1.25847
$826$	−38102.6	−1.60503
$827$	19053.4	0.801152	0.400576	−	0.916264i	$-0.368810\pi$
$827$	19053.4	0.801152	0.400576	+	0.916264i	$0.368810\pi$
$828$	22753.3	0.954992
$829$	−30335.7	−1.27093	−0.635465	−	0.772129i	$-0.719192\pi$
$829$	−30335.7	−1.27093	−0.635465	+	0.772129i	$0.719192\pi$
$830$	−37076.8	−1.55055
$831$	−16360.0	−0.682939
$832$	14330.7	0.597149
$833$	11240.3	0.467531
$834$	−38155.3	−1.58418
$835$	22600.8	0.936685
$836$	41535.3	1.71833
$837$	51992.2	2.14709
$838$	−49417.9	−2.03713
$839$	−13383.0	−0.550693	−0.275346	−	0.961345i	$-0.588793\pi$
$839$	−13383.0	−0.550693	−0.275346	+	0.961345i	$0.588793\pi$
$840$	−34617.2	−1.42191
$841$	11616.2	0.476290
$842$	−35757.0	−1.46350
$843$	9647.64	0.394166
$844$	16259.9	0.663139
$845$	14152.0	0.576147
$846$	−70815.6	−2.87788
$847$	−24798.6	−1.00601
$848$	23664.1	0.958289
$849$	−56603.4	−2.28813
$850$	−31568.2	−1.27386
$851$	−3985.06	−0.160524
$852$	43125.1	1.73408
$853$	11155.0	0.447759	0.223879	−	0.974617i	$-0.428128\pi$
$853$	11155.0	0.447759	0.223879	+	0.974617i	$0.428128\pi$
$854$	−9977.36	−0.399787
$855$	−21093.5	−0.843722
$856$	38774.7	1.54824
$857$	44575.1	1.77673	0.888365	−	0.459138i	$-0.151842\pi$
$857$	44575.1	1.77673	0.888365	+	0.459138i	$0.151842\pi$
$858$	46345.8	1.84408
$859$	2465.06	0.0979122	0.0489561	−	0.998801i	$-0.484411\pi$
$859$	2465.06	0.0979122	0.0489561	+	0.998801i	$0.484411\pi$
$860$	−2425.34	−0.0961669
$861$	56259.2	2.22684
$862$	−8891.30	−0.351321
$863$	−28651.9	−1.13015	−0.565077	−	0.825038i	$-0.691154\pi$
$863$	−28651.9	−1.13015	−0.565077	+	0.825038i	$0.691154\pi$
$864$	19114.2	0.752636
$865$	−26776.6	−1.05252
$866$	459.895	0.0180460
$867$	56774.6	2.22395
$868$	−55197.8	−2.15845
$869$	7664.59	0.299198
$870$	−63380.3	−2.46988
$871$	13290.4	0.517024
$872$	66879.3	2.59727
$873$	2387.79	0.0925708
$874$	−7486.93	−0.289759
$875$	−22858.4	−0.883147
$876$	−61249.2	−2.36235
$877$	37052.8	1.42666	0.713332	−	0.700826i	$-0.247185\pi$
$877$	37052.8	1.42666	0.713332	+	0.700826i	$0.247185\pi$
$878$	−54326.2	−2.08818
$879$	−19553.8	−0.750321
$880$	−15061.1	−0.576942
$881$	34659.6	1.32544	0.662719	−	0.748868i	$-0.269402\pi$
$881$	34659.6	1.32544	0.662719	+	0.748868i	$0.269402\pi$
$882$	25756.3	0.983289
$883$	−43727.5	−1.66653	−0.833265	−	0.552873i	$-0.813531\pi$
$883$	−43727.5	−1.66653	−0.833265	+	0.552873i	$0.813531\pi$
$884$	31790.7	1.20954
$885$	36344.8	1.38047
$886$	1350.31	0.0512016
$887$	−552.599	−0.0209182	−0.0104591	−	0.999945i	$-0.503329\pi$
$887$	−552.599	−0.0209182	−0.0104591	+	0.999945i	$0.503329\pi$
$888$	37417.2	1.41401
$889$	26107.7	0.984954
$890$	25662.0	0.966510
$891$	27547.6	1.03578
$892$	−79029.6	−2.96649
$893$	15099.1	0.565813
$894$	−46048.1	−1.72268
$895$	−14978.3	−0.559408
$896$	−40888.7	−1.52455
$897$	−5413.27	−0.201498
$898$	−19969.9	−0.742098
$899$	−46159.2	−1.71245
$900$	−46872.5	−1.73602
$901$	−71881.4	−2.65784
$902$	106751.	3.94060
$903$	−2831.35	−0.104343
$904$	6613.41	0.243317
$905$	−16285.3	−0.598167
$906$	100648.	3.69072
$907$	−14356.7	−0.525587	−0.262794	−	0.964852i	$-0.584644\pi$
$907$	−14356.7	−0.525587	−0.262794	+	0.964852i	$0.584644\pi$
$908$	71495.5	2.61306
$909$	91886.7	3.35279
$910$	11803.7	0.429986
$911$	34832.9	1.26681	0.633406	−	0.773820i	$-0.281657\pi$
$911$	34832.9	1.26681	0.633406	+	0.773820i	$0.281657\pi$
$912$	16118.6	0.585240
$913$	−53218.6	−1.92911
$914$	63642.8	2.30319
$915$	9517.08	0.343852
$916$	−29093.0	−1.04941
$917$	−4357.02	−0.156905
$918$	108473.	3.89995
$919$	−10802.4	−0.387745	−0.193872	−	0.981027i	$-0.562105\pi$
$919$	−10802.4	−0.387745	−0.193872	+	0.981027i	$0.562105\pi$
$920$	7672.21	0.274940
$921$	−41896.8	−1.49896
$922$	9633.93	0.344118
$923$	−6716.28	−0.239511
$924$	−108788.	−3.87321
$925$	8209.33	0.291807
$926$	9613.08	0.341151
$927$	7332.46	0.259794
$928$	−16969.8	−0.600280
$929$	−9359.62	−0.330548	−0.165274	−	0.986248i	$-0.552851\pi$
$929$	−9359.62	−0.330548	−0.165274	+	0.986248i	$0.552851\pi$
$930$	81254.5	2.86499
$931$	−5491.68	−0.193322
$932$	−21641.9	−0.760626
$933$	48233.7	1.69250
$934$	−32013.8	−1.12154
$935$	45749.1	1.60017
$936$	33272.2	1.16190
$937$	32215.2	1.12319	0.561593	−	0.827413i	$-0.310189\pi$
$937$	32215.2	1.12319	0.561593	+	0.827413i	$0.310189\pi$
$938$	−48144.3	−1.67587
$939$	−23945.6	−0.832199
$940$	−33876.0	−1.17544
$941$	−51372.5	−1.77970	−0.889850	−	0.456254i	$-0.849191\pi$
$941$	−51372.5	−1.77970	−0.889850	+	0.456254i	$0.849191\pi$
$942$	110783.	3.83175
$943$	−12468.7	−0.430580
$944$	−18180.5	−0.626826
$945$	26097.7	0.898368
$946$	−5372.45	−0.184644
$947$	53716.9	1.84326	0.921628	−	0.388074i	$-0.126859\pi$
$947$	53716.9	1.84326	0.921628	+	0.388074i	$0.126859\pi$
$948$	18403.5	0.630504
$949$	9538.93	0.326287
$950$	15423.3	0.526734
$951$	−23282.6	−0.793892
$952$	−52599.4	−1.79071
$953$	12846.6	0.436664	0.218332	−	0.975875i	$-0.429938\pi$
$953$	12846.6	0.436664	0.218332	+	0.975875i	$0.429938\pi$
$954$	−164711.	−5.58986
$955$	11027.7	0.373664
$956$	41638.5	1.40867
$957$	−90973.7	−3.07290
$958$	−65101.3	−2.19554
$959$	46223.9	1.55646
$960$	49517.9	1.66477
$961$	29385.8	0.986398
$962$	−12758.4	−0.427596
$963$	−61882.4	−2.07075
$964$	−79671.8	−2.66188
$965$	−24102.6	−0.804031
$966$	19609.5	0.653131
$967$	−42090.0	−1.39971	−0.699857	−	0.714283i	$-0.746753\pi$
$967$	−42090.0	−1.39971	−0.699857	+	0.714283i	$0.746753\pi$
$968$	−51605.0	−1.71348
$969$	−48961.3	−1.62318
$970$	1762.77	0.0583497
$971$	629.548	0.0208065	0.0104033	−	0.999946i	$-0.496688\pi$
$971$	629.548	0.0208065	0.0104033	+	0.999946i	$0.496688\pi$
$972$	−18834.6	−0.621524
$973$	−13948.3	−0.459572
$974$	−75445.5	−2.48196
$975$	11151.5	0.366291
$976$	−4760.65	−0.156132
$977$	20194.7	0.661294	0.330647	−	0.943754i	$-0.392733\pi$
$977$	20194.7	0.661294	0.330647	+	0.943754i	$0.392733\pi$
$978$	27366.7	0.894775
$979$	36834.3	1.20248
$980$	12321.0	0.401613
$981$	−106736.	−3.47382
$982$	−31580.1	−1.02623
$983$	983.000	0.0318950
$983$	983.000	0.0318950
$984$	117074.	3.79285
$985$	25029.1	0.809639
$986$	−96303.7	−3.11048
$987$	−39546.9	−1.27537
$988$	−15532.0	−0.500141
$989$	627.511	0.0201756
$990$	104831.	3.36540
$991$	20810.9	0.667082	0.333541	−	0.942736i	$-0.391756\pi$
$991$	20810.9	0.667082	0.333541	+	0.942736i	$0.391756\pi$
$992$	21755.5	0.696308
$993$	−59433.9	−1.89937
$994$	24329.6	0.776346
$995$	4672.35	0.148868
$996$	−127784.	−4.06524
$997$	−11894.2	−0.377825	−0.188913	−	0.981994i	$-0.560496\pi$
$997$	−11894.2	−0.377825	−0.188913	+	0.981994i	$0.560496\pi$
$998$	−76712.9	−2.43317
$999$	−28208.6	−0.893373

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.4.a.a.1.11	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.4.a.a.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-4.76719 q^{2} +8.84156 q^{3} +14.7261 q^{4} -7.92466 q^{5} -42.1494 q^{6} -15.4085 q^{7} -32.0645 q^{8} +51.1732 q^{9} +O(q^{10})\)	\(q-4.76719 q^{2} +8.84156 q^{3} +14.7261 q^{4} -7.92466 q^{5} -42.1494 q^{6} -15.4085 q^{7} -32.0645 q^{8} +51.1732 q^{9} +37.7783 q^{10} +54.2256 q^{11} +130.201 q^{12} -20.2775 q^{13} +73.4550 q^{14} -70.0663 q^{15} +35.0487 q^{16} -106.463 q^{17} -243.952 q^{18} +52.0147 q^{19} -116.699 q^{20} -136.235 q^{21} -258.503 q^{22} +30.1937 q^{23} -283.500 q^{24} -62.1998 q^{25} +96.6668 q^{26} +213.729 q^{27} -226.906 q^{28} -189.750 q^{29} +334.019 q^{30} +243.263 q^{31} +89.4320 q^{32} +479.439 q^{33} +507.528 q^{34} +122.107 q^{35} +753.580 q^{36} -131.983 q^{37} -247.964 q^{38} -179.285 q^{39} +254.100 q^{40} -412.958 q^{41} +649.457 q^{42} +20.7829 q^{43} +798.530 q^{44} -405.530 q^{45} -143.939 q^{46} +290.285 q^{47} +309.885 q^{48} -105.579 q^{49} +296.518 q^{50} -941.297 q^{51} -298.608 q^{52} +675.179 q^{53} -1018.88 q^{54} -429.719 q^{55} +494.064 q^{56} +459.891 q^{57} +904.576 q^{58} -518.720 q^{59} -1031.80 q^{60} -135.830 q^{61} -1159.68 q^{62} -788.500 q^{63} -706.729 q^{64} +160.692 q^{65} -2285.57 q^{66} -655.425 q^{67} -1567.78 q^{68} +266.959 q^{69} -582.106 q^{70} +331.218 q^{71} -1640.84 q^{72} -470.419 q^{73} +629.189 q^{74} -549.943 q^{75} +765.972 q^{76} -835.532 q^{77} +854.685 q^{78} +141.346 q^{79} -277.749 q^{80} +508.018 q^{81} +1968.65 q^{82} -981.431 q^{83} -2006.20 q^{84} +843.681 q^{85} -99.0759 q^{86} -1677.69 q^{87} -1738.71 q^{88} +679.280 q^{89} +1933.24 q^{90} +312.445 q^{91} +444.634 q^{92} +2150.82 q^{93} -1383.84 q^{94} -412.198 q^{95} +790.719 q^{96} +46.6609 q^{97} +503.317 q^{98} +2774.90 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q - 19 q^{2} - 23 q^{3} + 385 q^{4} - 50 q^{5} - 83 q^{6} - 225 q^{7} - 225 q^{8} + 714 q^{9}+O(q^{10}) \) 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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