LMFDB - Embedded newform 841.4.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,4,Mod(1,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, 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("841.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	841.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:	$49.6206063148$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.13458092.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 14x^{3} + 18x^{2} + 20x - 8 $ x^5 - x^4 - 14x^3 + 18x^2 + 20*x - 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.957567$ of defining polynomial
Character	$\chi$	$=$	841.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.84972 q^{2} -4.64574 q^{3} +0.120922 q^{4} +12.8729 q^{5} -13.2391 q^{6} +26.0540 q^{7} -22.4532 q^{8} -5.41713 q^{9} +O(q^{10})$	\(q+2.84972 q^{2} -4.64574 q^{3} +0.120922 q^{4} +12.8729 q^{5} -13.2391 q^{6} +26.0540 q^{7} -22.4532 q^{8} -5.41713 q^{9} +36.6841 q^{10} +62.8274 q^{11} -0.561770 q^{12} +22.3936 q^{13} +74.2465 q^{14} -59.8039 q^{15} -64.9528 q^{16} +57.9808 q^{17} -15.4373 q^{18} -71.3143 q^{19} +1.55661 q^{20} -121.040 q^{21} +179.041 q^{22} -49.5307 q^{23} +104.312 q^{24} +40.7104 q^{25} +63.8155 q^{26} +150.601 q^{27} +3.15048 q^{28} -170.425 q^{30} -62.9198 q^{31} -5.47182 q^{32} -291.880 q^{33} +165.229 q^{34} +335.389 q^{35} -0.655048 q^{36} -119.123 q^{37} -203.226 q^{38} -104.035 q^{39} -289.037 q^{40} +414.916 q^{41} -344.930 q^{42} +348.009 q^{43} +7.59719 q^{44} -69.7340 q^{45} -141.149 q^{46} -553.259 q^{47} +301.753 q^{48} +335.808 q^{49} +116.013 q^{50} -269.364 q^{51} +2.70787 q^{52} -107.308 q^{53} +429.172 q^{54} +808.768 q^{55} -584.994 q^{56} +331.308 q^{57} +136.881 q^{59} -7.23158 q^{60} +579.408 q^{61} -179.304 q^{62} -141.138 q^{63} +504.029 q^{64} +288.269 q^{65} -831.776 q^{66} +919.959 q^{67} +7.01113 q^{68} +230.106 q^{69} +955.765 q^{70} +781.802 q^{71} +121.632 q^{72} +133.237 q^{73} -339.467 q^{74} -189.130 q^{75} -8.62344 q^{76} +1636.90 q^{77} -296.470 q^{78} -868.196 q^{79} -836.127 q^{80} -553.392 q^{81} +1182.39 q^{82} -83.3560 q^{83} -14.6363 q^{84} +746.379 q^{85} +991.730 q^{86} -1410.68 q^{88} +357.919 q^{89} -198.722 q^{90} +583.442 q^{91} -5.98933 q^{92} +292.309 q^{93} -1576.64 q^{94} -918.019 q^{95} +25.4206 q^{96} +187.105 q^{97} +956.961 q^{98} -340.344 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 8 q^{3} + 26 q^{4} + 10 q^{5} + 34 q^{6} + 40 q^{7} + 84 q^{8} + 33 q^{9}+O(q^{10}) $ 5 * q - 8 * q^3 + 26 * q^4 + 10 * q^5 + 34 * q^6 + 40 * q^7 + 84 * q^8 + 33 * q^9	\( 5 q - 8 q^{3} + 26 q^{4} + 10 q^{5} + 34 q^{6} + 40 q^{7} + 84 q^{8} + 33 q^{9} + 64 q^{10} - 12 q^{11} + 224 q^{12} + 14 q^{13} + 192 q^{14} + 74 q^{15} + 146 q^{16} - 66 q^{17} + 108 q^{18} - 214 q^{19} + 6 q^{20} - 98 q^{22} + 164 q^{23} + 314 q^{24} + 207 q^{25} - 56 q^{26} - 362 q^{27} + 540 q^{28} - 234 q^{30} - 420 q^{31} + 652 q^{32} - 576 q^{33} + 204 q^{34} - 52 q^{35} - 260 q^{36} - 378 q^{37} - 496 q^{38} + 374 q^{39} + 80 q^{40} + 1158 q^{41} + 348 q^{42} + 204 q^{43} - 784 q^{44} - 1506 q^{45} - 580 q^{46} - 248 q^{47} + 1880 q^{48} - 283 q^{49} - 908 q^{50} + 228 q^{51} + 1482 q^{52} - 554 q^{53} + 918 q^{54} - 546 q^{55} + 608 q^{56} + 44 q^{57} + 440 q^{59} - 636 q^{60} - 618 q^{61} + 1250 q^{62} + 804 q^{63} + 2594 q^{64} - 1656 q^{65} - 2940 q^{66} + 1164 q^{67} - 356 q^{68} + 1968 q^{69} + 2184 q^{70} - 692 q^{71} + 2648 q^{72} + 1950 q^{73} - 1832 q^{74} - 3074 q^{75} - 1376 q^{76} + 1616 q^{77} - 1302 q^{78} - 272 q^{79} - 890 q^{80} + 1801 q^{81} + 92 q^{82} + 512 q^{83} + 3208 q^{84} + 1628 q^{85} + 2446 q^{86} - 6954 q^{88} - 866 q^{89} + 2200 q^{90} + 2580 q^{91} + 3468 q^{92} - 40 q^{93} - 5942 q^{94} - 2244 q^{95} + 7386 q^{96} - 1562 q^{97} + 3408 q^{98} + 238 q^{99}+O(q^{100}) \) 5 * q - 8 * q^3 + 26 * q^4 + 10 * q^5 + 34 * q^6 + 40 * q^7 + 84 * q^8 + 33 * q^9 + 64 * q^10 - 12 * q^11 + 224 * q^12 + 14 * q^13 + 192 * q^14 + 74 * q^15 + 146 * q^16 - 66 * q^17 + 108 * q^18 - 214 * q^19 + 6 * q^20 - 98 * q^22 + 164 * q^23 + 314 * q^24 + 207 * q^25 - 56 * q^26 - 362 * q^27 + 540 * q^28 - 234 * q^30 - 420 * q^31 + 652 * q^32 - 576 * q^33 + 204 * q^34 - 52 * q^35 - 260 * q^36 - 378 * q^37 - 496 * q^38 + 374 * q^39 + 80 * q^40 + 1158 * q^41 + 348 * q^42 + 204 * q^43 - 784 * q^44 - 1506 * q^45 - 580 * q^46 - 248 * q^47 + 1880 * q^48 - 283 * q^49 - 908 * q^50 + 228 * q^51 + 1482 * q^52 - 554 * q^53 + 918 * q^54 - 546 * q^55 + 608 * q^56 + 44 * q^57 + 440 * q^59 - 636 * q^60 - 618 * q^61 + 1250 * q^62 + 804 * q^63 + 2594 * q^64 - 1656 * q^65 - 2940 * q^66 + 1164 * q^67 - 356 * q^68 + 1968 * q^69 + 2184 * q^70 - 692 * q^71 + 2648 * q^72 + 1950 * q^73 - 1832 * q^74 - 3074 * q^75 - 1376 * q^76 + 1616 * q^77 - 1302 * q^78 - 272 * q^79 - 890 * q^80 + 1801 * q^81 + 92 * q^82 + 512 * q^83 + 3208 * q^84 + 1628 * q^85 + 2446 * q^86 - 6954 * q^88 - 866 * q^89 + 2200 * q^90 + 2580 * q^91 + 3468 * q^92 - 40 * q^93 - 5942 * q^94 - 2244 * q^95 + 7386 * q^96 - 1562 * q^97 + 3408 * q^98 + 238 * 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 $

$2$	2.84972	1.00753	0.503765	−	0.863841i	$-0.331948\pi$
$2$	2.84972	1.00753	0.503765	+	0.863841i	$0.331948\pi$
$3$	−4.64574	−0.894072	−0.447036	−	0.894516i	$-0.647520\pi$
$3$	−4.64574	−0.894072	−0.447036	+	0.894516i	$0.647520\pi$
$4$	0.120922	0.0151152
$5$	12.8729	1.15138	0.575692	−	0.817667i	$-0.304733\pi$
$5$	12.8729	1.15138	0.575692	+	0.817667i	$0.304733\pi$
$6$	−13.2391	−0.900804
$7$	26.0540	1.40678	0.703391	−	0.710804i	$-0.251669\pi$
$7$	26.0540	1.40678	0.703391	+	0.710804i	$0.251669\pi$
$8$	−22.4532	−0.992300
$9$	−5.41713	−0.200635
$10$	36.6841	1.16005
$11$	62.8274	1.72211	0.861053	−	0.508515i	$-0.169805\pi$
$11$	62.8274	1.72211	0.861053	+	0.508515i	$0.169805\pi$
$12$	−0.561770	−0.0135141
$13$	22.3936	0.477759	0.238879	−	0.971049i	$-0.423220\pi$
$13$	22.3936	0.477759	0.238879	+	0.971049i	$0.423220\pi$
$14$	74.2465	1.41737
$15$	−59.8039	−1.02942
$16$	−64.9528	−1.01489
$17$	57.9808	0.827201	0.413601	−	0.910458i	$-0.364271\pi$
$17$	57.9808	0.827201	0.413601	+	0.910458i	$0.364271\pi$
$18$	−15.4373	−0.202145
$19$	−71.3143	−0.861086	−0.430543	−	0.902570i	$-0.641678\pi$
$19$	−71.3143	−0.861086	−0.430543	+	0.902570i	$0.641678\pi$
$20$	1.55661	0.0174034
$21$	−121.040	−1.25776
$22$	179.041	1.73507
$23$	−49.5307	−0.449037	−0.224519	−	0.974470i	$-0.572081\pi$
$23$	−49.5307	−0.449037	−0.224519	+	0.974470i	$0.572081\pi$
$24$	104.312	0.887188
$25$	40.7104	0.325683
$26$	63.8155	0.481356
$27$	150.601	1.07345
$28$	3.15048	0.0212638
$29$	0	0
$29$	0	0
$30$	−170.425	−1.03717
$31$	−62.9198	−0.364540	−0.182270	−	0.983249i	$-0.558344\pi$
$31$	−62.9198	−0.364540	−0.182270	+	0.983249i	$0.558344\pi$
$32$	−5.47182	−0.0302278
$33$	−291.880	−1.53969
$34$	165.229	0.833429
$35$	335.389	1.61974
$36$	−0.655048	−0.00303263
$37$	−119.123	−0.529288	−0.264644	−	0.964346i	$-0.585254\pi$
$37$	−119.123	−0.529288	−0.264644	+	0.964346i	$0.585254\pi$
$38$	−203.226	−0.867569
$39$	−104.035	−0.427151
$40$	−289.037	−1.14252
$41$	414.916	1.58046	0.790231	−	0.612810i	$-0.209961\pi$
$41$	414.916	1.58046	0.790231	+	0.612810i	$0.209961\pi$
$42$	−344.930	−1.26723
$43$	348.009	1.23421	0.617103	−	0.786882i	$-0.288306\pi$
$43$	348.009	1.23421	0.617103	+	0.786882i	$0.288306\pi$
$44$	7.59719	0.0260300
$45$	−69.7340	−0.231007
$46$	−141.149	−0.452418
$47$	−553.259	−1.71705	−0.858523	−	0.512775i	$-0.828618\pi$
$47$	−553.259	−1.71705	−0.858523	+	0.512775i	$0.828618\pi$
$48$	301.753	0.907382
$49$	335.808	0.979033
$50$	116.013	0.328136
$51$	−269.364	−0.739578
$52$	2.70787	0.00722142
$53$	−107.308	−0.278111	−0.139055	−	0.990285i	$-0.544407\pi$
$53$	−107.308	−0.278111	−0.139055	+	0.990285i	$0.544407\pi$
$54$	429.172	1.08154
$55$	808.768	1.98280
$56$	−584.994	−1.39595
$57$	331.308	0.769873
$58$	0	0
$59$	136.881	0.302041	0.151020	−	0.988531i	$-0.451744\pi$
$59$	136.881	0.302041	0.151020	+	0.988531i	$0.451744\pi$
$60$	−7.23158	−0.0155599
$61$	579.408	1.21616	0.608078	−	0.793877i	$-0.291941\pi$
$61$	579.408	1.21616	0.608078	+	0.793877i	$0.291941\pi$
$62$	−179.304	−0.367285
$63$	−141.138	−0.282249
$64$	504.029	0.984431
$65$	288.269	0.550084
$66$	−831.776	−1.55128
$67$	919.959	1.67748	0.838738	−	0.544535i	$-0.183294\pi$
$67$	919.959	1.67748	0.838738	+	0.544535i	$0.183294\pi$
$68$	7.01113	0.0125033
$69$	230.106	0.401472
$70$	955.765	1.63194
$71$	781.802	1.30680	0.653400	−	0.757013i	$-0.273342\pi$
$71$	781.802	1.30680	0.653400	+	0.757013i	$0.273342\pi$
$72$	121.632	0.199090
$73$	133.237	0.213619	0.106810	−	0.994279i	$-0.465936\pi$
$73$	133.237	0.213619	0.106810	+	0.994279i	$0.465936\pi$
$74$	−339.467	−0.533273
$75$	−189.130	−0.291185
$76$	−8.62344	−0.0130155
$77$	1636.90	2.42263
$78$	−296.470	−0.430367
$79$	−868.196	−1.23645	−0.618225	−	0.786001i	$-0.712148\pi$
$79$	−868.196	−1.23645	−0.618225	+	0.786001i	$0.712148\pi$
$80$	−836.127	−1.16852
$81$	−553.392	−0.759111
$82$	1182.39	1.59236
$83$	−83.3560	−0.110235	−0.0551175	−	0.998480i	$-0.517553\pi$
$83$	−83.3560	−0.110235	−0.0551175	+	0.998480i	$0.517553\pi$
$84$	−14.6363	−0.0190114
$85$	746.379	0.952425
$86$	991.730	1.24350
$87$	0	0
$88$	−1410.68	−1.70885
$89$	357.919	0.426284	0.213142	−	0.977021i	$-0.431630\pi$
$89$	357.919	0.426284	0.213142	+	0.977021i	$0.431630\pi$
$90$	−198.722	−0.232747
$91$	583.442	0.672102
$92$	−5.98933	−0.00678729
$93$	292.309	0.325925
$94$	−1576.64	−1.72997
$95$	−918.019	−0.991440
$96$	25.4206	0.0270259
$97$	187.105	0.195852	0.0979260	−	0.995194i	$-0.468779\pi$
$97$	187.105	0.195852	0.0979260	+	0.995194i	$0.468779\pi$
$98$	956.961	0.986404
$99$	−340.344	−0.345514
$100$	4.92277	0.00492277
$101$	959.423	0.945209	0.472605	−	0.881275i	$-0.343314\pi$
$101$	959.423	0.945209	0.472605	+	0.881275i	$0.343314\pi$
$102$	−767.612	−0.745146
$103$	78.8738	0.0754531	0.0377265	−	0.999288i	$-0.487988\pi$
$103$	78.8738	0.0754531	0.0377265	+	0.999288i	$0.487988\pi$
$104$	−502.808	−0.474080
$105$	−1558.13	−1.44817
$106$	−305.797	−0.280205
$107$	713.851	0.644959	0.322479	−	0.946577i	$-0.395484\pi$
$107$	713.851	0.644959	0.322479	+	0.946577i	$0.395484\pi$
$108$	18.2110	0.0162255
$109$	536.561	0.471497	0.235749	−	0.971814i	$-0.424246\pi$
$109$	536.561	0.471497	0.235749	+	0.971814i	$0.424246\pi$
$110$	2304.76	1.99773
$111$	553.412	0.473222
$112$	−1692.28	−1.42772
$113$	−1946.36	−1.62034	−0.810170	−	0.586195i	$-0.800625\pi$
$113$	−1946.36	−1.62034	−0.810170	+	0.586195i	$0.800625\pi$
$114$	944.135	0.775670
$115$	−637.601	−0.517014
$116$	0	0
$117$	−121.309	−0.0958549
$118$	390.073	0.304315
$119$	1510.63	1.16369
$120$	1342.79	1.02149
$121$	2616.28	1.96565
$122$	1651.15	1.22531
$123$	−1927.59	−1.41305
$124$	−7.60837	−0.00551009
$125$	−1085.05	−0.776397
$126$	−402.203	−0.284374
$127$	1995.14	1.39402	0.697009	−	0.717062i	$-0.254514\pi$
$127$	1995.14	1.39402	0.697009	+	0.717062i	$0.254514\pi$
$128$	1480.12	1.02207
$129$	−1616.76	−1.10347
$130$	821.488	0.554225
$131$	−1544.84	−1.03033	−0.515164	−	0.857092i	$-0.672269\pi$
$131$	−1544.84	−1.03033	−0.515164	+	0.857092i	$0.672269\pi$
$132$	−35.2945	−0.0232727
$133$	−1858.02	−1.21136
$134$	2621.63	1.69011
$135$	1938.67	1.23596
$136$	−1301.85	−0.820832
$137$	1294.93	0.807543	0.403771	−	0.914860i	$-0.367699\pi$
$137$	1294.93	0.807543	0.403771	+	0.914860i	$0.367699\pi$
$138$	655.740	0.404495
$139$	1999.66	1.22021	0.610105	−	0.792320i	$-0.291127\pi$
$139$	1999.66	1.22021	0.610105	+	0.792320i	$0.291127\pi$
$140$	40.5557	0.0244828
$141$	2570.30	1.53516
$142$	2227.92	1.31664
$143$	1406.93	0.822752
$144$	351.858	0.203621
$145$	0	0
$146$	379.688	0.215228
$147$	−1560.08	−0.875326
$148$	−14.4045	−0.00800029
$149$	1187.63	0.652984	0.326492	−	0.945200i	$-0.394133\pi$
$149$	1187.63	0.652984	0.326492	+	0.945200i	$0.394133\pi$
$150$	−538.968	−0.293377
$151$	−2257.61	−1.21670	−0.608350	−	0.793669i	$-0.708168\pi$
$151$	−2257.61	−1.21670	−0.608350	+	0.793669i	$0.708168\pi$
$152$	1601.23	0.854456
$153$	−314.090	−0.165965
$154$	4664.72	2.44087
$155$	−809.958	−0.419725
$156$	−12.5800	−0.00645647
$157$	−1188.18	−0.603995	−0.301997	−	0.953309i	$-0.597653\pi$
$157$	−1188.18	−0.603995	−0.301997	+	0.953309i	$0.597653\pi$
$158$	−2474.12	−1.24576
$159$	498.524	0.248651
$160$	−70.4379	−0.0348038
$161$	−1290.47	−0.631697
$162$	−1577.01	−0.764827
$163$	2452.33	1.17841	0.589207	−	0.807982i	$-0.299440\pi$
$163$	2452.33	1.17841	0.589207	+	0.807982i	$0.299440\pi$
$164$	50.1722	0.0238890
$165$	−3757.32	−1.77277
$166$	−237.541	−0.111065
$167$	−2020.14	−0.936067	−0.468034	−	0.883711i	$-0.655037\pi$
$167$	−2020.14	−0.936067	−0.468034	+	0.883711i	$0.655037\pi$
$168$	2717.73	1.24808
$169$	−1695.53	−0.771746
$170$	2126.97	0.959597
$171$	386.319	0.172764
$172$	42.0818	0.0186553
$173$	2862.12	1.25782	0.628910	−	0.777478i	$-0.283501\pi$
$173$	2862.12	1.25782	0.628910	+	0.777478i	$0.283501\pi$
$174$	0	0
$175$	1060.67	0.458165
$176$	−4080.81	−1.74774
$177$	−635.914	−0.270046
$178$	1019.97	0.429494
$179$	−232.651	−0.0971460	−0.0485730	−	0.998820i	$-0.515467\pi$
$179$	−232.651	−0.0971460	−0.0485730	+	0.998820i	$0.515467\pi$
$180$	−8.43234	−0.00349172
$181$	−2607.67	−1.07086	−0.535432	−	0.844578i	$-0.679851\pi$
$181$	−2607.67	−1.07086	−0.535432	+	0.844578i	$0.679851\pi$
$182$	1662.65	0.677163
$183$	−2691.78	−1.08733
$184$	1112.12	0.445580
$185$	−1533.45	−0.609413
$186$	833.000	0.328379
$187$	3642.78	1.42453
$188$	−66.9010	−0.0259535
$189$	3923.76	1.51012
$190$	−2616.10	−0.998905
$191$	−1528.90	−0.579202	−0.289601	−	0.957147i	$-0.593523\pi$
$191$	−1528.90	−0.579202	−0.289601	+	0.957147i	$0.593523\pi$
$192$	−2341.59	−0.880153
$193$	−1017.58	−0.379518	−0.189759	−	0.981831i	$-0.560771\pi$
$193$	−1017.58	−0.379518	−0.189759	+	0.981831i	$0.560771\pi$
$194$	533.197	0.197327
$195$	−1339.22	−0.491815
$196$	40.6065	0.0147983
$197$	3290.20	1.18994	0.594968	−	0.803749i	$-0.297165\pi$
$197$	3290.20	1.18994	0.594968	+	0.803749i	$0.297165\pi$
$198$	−969.887	−0.348115
$199$	−29.9190	−0.0106578	−0.00532891	−	0.999986i	$-0.501696\pi$
$199$	−29.9190	−0.0106578	−0.00532891	+	0.999986i	$0.501696\pi$
$200$	−914.079	−0.323176
$201$	−4273.89	−1.49979
$202$	2734.09	0.952326
$203$	0	0
$204$	−32.5719	−0.0111789
$205$	5341.15	1.81972
$206$	224.769	0.0760212
$207$	268.314	0.0900924
$208$	−1454.53	−0.484871
$209$	−4480.49	−1.48288
$210$	−4440.23	−1.45907
$211$	−2267.20	−0.739717	−0.369859	−	0.929088i	$-0.620594\pi$
$211$	−2267.20	−0.739717	−0.369859	+	0.929088i	$0.620594\pi$
$212$	−12.9758	−0.00420370
$213$	−3632.05	−1.16837
$214$	2034.28	0.649815
$215$	4479.87	1.42105
$216$	−3381.48	−1.06519
$217$	−1639.31	−0.512828
$218$	1529.05	0.475047
$219$	−618.984	−0.190991
$220$	97.7975	0.0299705
$221$	1298.40	0.395203
$222$	1577.07	0.476785
$223$	4945.03	1.48495	0.742474	−	0.669875i	$-0.233652\pi$
$223$	4945.03	1.48495	0.742474	+	0.669875i	$0.233652\pi$
$224$	−142.562	−0.0425239
$225$	−220.534	−0.0653433
$226$	−5546.59	−1.63254
$227$	−3559.46	−1.04075	−0.520374	−	0.853938i	$-0.674208\pi$
$227$	−3559.46	−1.04075	−0.520374	+	0.853938i	$0.674208\pi$
$228$	40.0622	0.0116368
$229$	−6143.40	−1.77278	−0.886391	−	0.462937i	$-0.846796\pi$
$229$	−6143.40	−1.77278	−0.886391	+	0.462937i	$0.846796\pi$
$230$	−1816.99	−0.520907
$231$	−7604.61	−2.16600
$232$	0	0
$233$	−1087.06	−0.305648	−0.152824	−	0.988253i	$-0.548837\pi$
$233$	−1087.06	−0.305648	−0.152824	+	0.988253i	$0.548837\pi$
$234$	−345.697	−0.0965766
$235$	−7122.03	−1.97698
$236$	16.5519	0.00456540
$237$	4033.41	1.10548
$238$	4304.88	1.17245
$239$	1079.00	0.292027	0.146013	−	0.989283i	$-0.453356\pi$
$239$	1079.00	0.292027	0.146013	+	0.989283i	$0.453356\pi$
$240$	3884.43	1.04474
$241$	−989.224	−0.264405	−0.132202	−	0.991223i	$-0.542205\pi$
$241$	−989.224	−0.264405	−0.132202	+	0.991223i	$0.542205\pi$
$242$	7455.68	1.98045
$243$	−1495.33	−0.394754
$244$	70.0629	0.0183824
$245$	4322.81	1.12724
$246$	−5493.09	−1.42369
$247$	−1596.98	−0.411391
$248$	1412.75	0.361733
$249$	387.250	0.0985581
$250$	−3092.09	−0.782243
$251$	−900.246	−0.226386	−0.113193	−	0.993573i	$-0.536108\pi$
$251$	−900.246	−0.226386	−0.113193	+	0.993573i	$0.536108\pi$
$252$	−17.0666	−0.00426625
$253$	−3111.88	−0.773290
$254$	5685.61	1.40451
$255$	−3467.48	−0.851537
$256$	185.693	0.0453353
$257$	−3125.18	−0.758534	−0.379267	−	0.925287i	$-0.623824\pi$
$257$	−3125.18	−0.758534	−0.379267	+	0.925287i	$0.623824\pi$
$258$	−4607.31	−1.11178
$259$	−3103.62	−0.744592
$260$	34.8580	0.00831462
$261$	0	0
$262$	−4402.35	−1.03808
$263$	−2814.89	−0.659976	−0.329988	−	0.943985i	$-0.607045\pi$
$263$	−2814.89	−0.659976	−0.329988	+	0.943985i	$0.607045\pi$
$264$	6553.63	1.52783
$265$	−1381.36	−0.320212
$266$	−5294.84	−1.22048
$267$	−1662.80	−0.381129
$268$	111.243	0.0253554
$269$	−4409.28	−0.999400	−0.499700	−	0.866199i	$-0.666556\pi$
$269$	−4409.28	−0.999400	−0.499700	+	0.866199i	$0.666556\pi$
$270$	5524.68	1.24526
$271$	4417.97	0.990304	0.495152	−	0.868806i	$-0.335112\pi$
$271$	4417.97	0.990304	0.495152	+	0.868806i	$0.335112\pi$
$272$	−3766.01	−0.839515
$273$	−2710.52	−0.600908
$274$	3690.19	0.813623
$275$	2557.73	0.560862
$276$	27.8248	0.00606833
$277$	−887.577	−0.192525	−0.0962624	−	0.995356i	$-0.530689\pi$
$277$	−887.577	−0.192525	−0.0962624	+	0.995356i	$0.530689\pi$
$278$	5698.49	1.22940
$279$	340.845	0.0731393
$280$	−7530.55	−1.60727
$281$	−4286.58	−0.910021	−0.455010	−	0.890486i	$-0.650364\pi$
$281$	−4286.58	−0.910021	−0.455010	+	0.890486i	$0.650364\pi$
$282$	7324.64	1.54672
$283$	−1709.59	−0.359097	−0.179549	−	0.983749i	$-0.557464\pi$
$283$	−1709.59	−0.359097	−0.179549	+	0.983749i	$0.557464\pi$
$284$	94.5367	0.0197525
$285$	4264.88	0.886419
$286$	4009.36	0.828946
$287$	10810.2	2.22336
$288$	29.6416	0.00606474
$289$	−1551.22	−0.315738
$290$	0	0
$291$	−869.241	−0.175106
$292$	16.1112	0.00322890
$293$	−1145.01	−0.228301	−0.114151	−	0.993463i	$-0.536415\pi$
$293$	−1145.01	−0.228301	−0.114151	+	0.993463i	$0.536415\pi$
$294$	−4445.79	−0.881917
$295$	1762.05	0.347765
$296$	2674.68	0.525212
$297$	9461.90	1.84860
$298$	3384.42	0.657900
$299$	−1109.17	−0.214532
$300$	−22.8699	−0.00440131
$301$	9067.01	1.73626
$302$	−6433.56	−1.22586
$303$	−4457.23	−0.845086
$304$	4632.06	0.873905
$305$	7458.63	1.40026
$306$	−895.069	−0.167215
$307$	−1079.39	−0.200665	−0.100333	−	0.994954i	$-0.531991\pi$
$307$	−1079.39	−0.200665	−0.100333	+	0.994954i	$0.531991\pi$
$308$	197.937	0.0366185
$309$	−366.427	−0.0674605
$310$	−2308.16	−0.422885
$311$	−2313.90	−0.421895	−0.210947	−	0.977497i	$-0.567655\pi$
$311$	−2313.90	−0.421895	−0.210947	+	0.977497i	$0.567655\pi$
$312$	2335.91	0.423862
$313$	−7653.19	−1.38206	−0.691029	−	0.722827i	$-0.742842\pi$
$313$	−7653.19	−1.38206	−0.691029	+	0.722827i	$0.742842\pi$
$314$	−3385.99	−0.608542
$315$	−1816.85	−0.324977
$316$	−104.984	−0.0186892
$317$	3657.23	0.647982	0.323991	−	0.946060i	$-0.394975\pi$
$317$	3657.23	0.647982	0.323991	+	0.946060i	$0.394975\pi$
$318$	1420.65	0.250523
$319$	0	0
$320$	6488.29	1.13346
$321$	−3316.36	−0.576640
$322$	−3677.48	−0.636453
$323$	−4134.86	−0.712291
$324$	−66.9170	−0.0114741
$325$	911.653	0.155598
$326$	6988.47	1.18729
$327$	−2492.72	−0.421553
$328$	−9316.18	−1.56829
$329$	−14414.6	−2.41551
$330$	−10707.3	−1.78612
$331$	−3237.92	−0.537681	−0.268841	−	0.963185i	$-0.586640\pi$
$331$	−3237.92	−0.537681	−0.268841	+	0.963185i	$0.586640\pi$
$332$	−10.0795	−0.00166622
$333$	645.303	0.106193
$334$	−5756.84	−0.943115
$335$	11842.5	1.93142
$336$	7861.87	1.27649
$337$	7976.89	1.28940	0.644702	−	0.764434i	$-0.276982\pi$
$337$	7976.89	1.28940	0.644702	+	0.764434i	$0.276982\pi$
$338$	−4831.78	−0.777557
$339$	9042.29	1.44870
$340$	90.2533	0.0143961
$341$	−3953.09	−0.627777
$342$	1100.90	0.174064
$343$	−187.371	−0.0294959
$344$	−7813.92	−1.22470
$345$	2962.13	0.462248
$346$	8156.25	1.26729
$347$	−8355.93	−1.29271	−0.646354	−	0.763037i	$-0.723707\pi$
$347$	−8355.93	−1.29271	−0.646354	+	0.763037i	$0.723707\pi$
$348$	0	0
$349$	5544.56	0.850411	0.425205	−	0.905097i	$-0.360202\pi$
$349$	5544.56	0.850411	0.425205	+	0.905097i	$0.360202\pi$
$350$	3022.61	0.461615
$351$	3372.51	0.512852
$352$	−343.780	−0.0520555
$353$	−1682.79	−0.253727	−0.126864	−	0.991920i	$-0.540491\pi$
$353$	−1682.79	−0.253727	−0.126864	+	0.991920i	$0.540491\pi$
$354$	−1812.18	−0.272080
$355$	10064.0	1.50463
$356$	43.2801	0.00644337
$357$	−7017.99	−1.04042
$358$	−662.990	−0.0978774
$359$	−7143.13	−1.05014	−0.525069	−	0.851059i	$-0.675961\pi$
$359$	−7143.13	−1.05014	−0.525069	+	0.851059i	$0.675961\pi$
$360$	1565.75	0.229229
$361$	−1773.27	−0.258531
$362$	−7431.13	−1.07893
$363$	−12154.6	−1.75743
$364$	70.5507	0.0101590
$365$	1715.14	0.245958
$366$	−7670.81	−1.09552
$367$	4456.16	0.633814	0.316907	−	0.948457i	$-0.397356\pi$
$367$	4456.16	0.633814	0.316907	+	0.948457i	$0.397356\pi$
$368$	3217.15	0.455722
$369$	−2247.65	−0.317095
$370$	−4369.90	−0.614001
$371$	−2795.79	−0.391241
$372$	35.3465	0.00492642
$373$	2508.28	0.348187	0.174094	−	0.984729i	$-0.444300\pi$
$373$	2508.28	0.348187	0.174094	+	0.984729i	$0.444300\pi$
$374$	10380.9	1.43525
$375$	5040.85	0.694155
$376$	12422.4	1.70383
$377$	0	0
$378$	11181.6	1.52149
$379$	12733.9	1.72585	0.862926	−	0.505331i	$-0.168629\pi$
$379$	12733.9	1.72585	0.862926	+	0.505331i	$0.168629\pi$
$380$	−111.008	−0.0149858
$381$	−9268.91	−1.24635
$382$	−4356.95	−0.583563
$383$	−1027.19	−0.137042	−0.0685209	−	0.997650i	$-0.521828\pi$
$383$	−1027.19	−0.137042	−0.0685209	+	0.997650i	$0.521828\pi$
$384$	−6876.23	−0.913806
$385$	21071.6	2.78937
$386$	−2899.82	−0.382376
$387$	−1885.21	−0.247624
$388$	22.6250	0.00296034
$389$	−5153.35	−0.671684	−0.335842	−	0.941918i	$-0.609021\pi$
$389$	−5153.35	−0.671684	−0.335842	+	0.941918i	$0.609021\pi$
$390$	−3816.42	−0.495518
$391$	−2871.83	−0.371444
$392$	−7539.97	−0.971495
$393$	7176.90	0.921187
$394$	9376.17	1.19890
$395$	−11176.2	−1.42363
$396$	−41.1550	−0.00522251
$397$	6250.95	0.790242	0.395121	−	0.918629i	$-0.370703\pi$
$397$	6250.95	0.790242	0.395121	+	0.918629i	$0.370703\pi$
$398$	−85.2610	−0.0107381
$399$	8631.87	1.08304
$400$	−2644.25	−0.330532
$401$	11083.8	1.38029	0.690145	−	0.723671i	$-0.257547\pi$
$401$	11083.8	1.38029	0.690145	+	0.723671i	$0.257547\pi$
$402$	−12179.4	−1.51108
$403$	−1409.00	−0.174162
$404$	116.015	0.0142870
$405$	−7123.74	−0.874028
$406$	0	0
$407$	−7484.17	−0.911490
$408$	6048.07	0.733883
$409$	3375.43	0.408079	0.204039	−	0.978963i	$-0.434593\pi$
$409$	3375.43	0.408079	0.204039	+	0.978963i	$0.434593\pi$
$410$	15220.8	1.83342
$411$	−6015.91	−0.722002
$412$	9.53754	0.00114049
$413$	3566.29	0.424905
$414$	764.621	0.0907707
$415$	−1073.03	−0.126923
$416$	−122.534	−0.0144416
$417$	−9289.91	−1.09096
$418$	−12768.2	−1.49405
$419$	6486.50	0.756292	0.378146	−	0.925746i	$-0.376562\pi$
$419$	6486.50	0.756292	0.378146	+	0.925746i	$0.376562\pi$
$420$	−188.411	−0.0218894
$421$	10938.6	1.26631	0.633153	−	0.774026i	$-0.281760\pi$
$421$	10938.6	1.26631	0.633153	+	0.774026i	$0.281760\pi$
$422$	−6460.89	−0.745287
$423$	2997.08	0.344499
$424$	2409.40	0.275969
$425$	2360.42	0.269406
$426$	−10350.3	−1.17717
$427$	15095.9	1.71087
$428$	86.3200	0.00974867
$429$	−6536.23	−0.735600
$430$	12766.4	1.43174
$431$	4124.34	0.460934	0.230467	−	0.973080i	$-0.425975\pi$
$431$	4124.34	0.460934	0.230467	+	0.973080i	$0.425975\pi$
$432$	−9781.98	−1.08943
$433$	1561.41	0.173295	0.0866473	−	0.996239i	$-0.472385\pi$
$433$	1561.41	0.173295	0.0866473	+	0.996239i	$0.472385\pi$
$434$	−4671.58	−0.516689
$435$	0	0
$436$	64.8818	0.00712677
$437$	3532.25	0.386660
$438$	−1763.93	−0.192429
$439$	−15712.7	−1.70826	−0.854130	−	0.520060i	$-0.825909\pi$
$439$	−15712.7	−1.70826	−0.854130	+	0.520060i	$0.825909\pi$
$440$	−18159.4	−1.96754
$441$	−1819.12	−0.196428
$442$	3700.08	0.398178
$443$	−12763.5	−1.36888	−0.684439	−	0.729070i	$-0.739953\pi$
$443$	−12763.5	−1.36888	−0.684439	+	0.729070i	$0.739953\pi$
$444$	66.9195	0.00715284
$445$	4607.44	0.490817
$446$	14092.0	1.49613
$447$	−5517.42	−0.583815
$448$	13131.9	1.38488
$449$	−3117.88	−0.327710	−0.163855	−	0.986484i	$-0.552393\pi$
$449$	−3117.88	−0.327710	−0.163855	+	0.986484i	$0.552393\pi$
$450$	−628.460	−0.0658353
$451$	26068.1	2.72172
$452$	−235.357	−0.0244918
$453$	10488.3	1.08782
$454$	−10143.5	−1.04858
$455$	7510.56	0.773847
$456$	−7438.91	−0.763945
$457$	−8479.41	−0.867943	−0.433972	−	0.900927i	$-0.642888\pi$
$457$	−8479.41	−0.867943	−0.433972	+	0.900927i	$0.642888\pi$
$458$	−17507.0	−1.78613
$459$	8732.00	0.887962
$460$	−77.0997	−0.00781477
$461$	−9253.32	−0.934859	−0.467430	−	0.884030i	$-0.654820\pi$
$461$	−9253.32	−0.934859	−0.467430	+	0.884030i	$0.654820\pi$
$462$	−21671.0	−2.18231
$463$	521.395	0.0523354	0.0261677	−	0.999658i	$-0.491670\pi$
$463$	521.395	0.0523354	0.0261677	+	0.999658i	$0.491670\pi$
$464$	0	0
$465$	3762.85	0.375265
$466$	−3097.83	−0.307949
$467$	−4337.35	−0.429783	−0.214891	−	0.976638i	$-0.568940\pi$
$467$	−4337.35	−0.429783	−0.214891	+	0.976638i	$0.568940\pi$
$468$	−14.6689	−0.00144887
$469$	23968.6	2.35984
$470$	−20295.8	−1.99186
$471$	5519.98	0.540015
$472$	−3073.42	−0.299715
$473$	21864.5	2.12544
$474$	11494.1	1.11380
$475$	−2903.24	−0.280441
$476$	182.668	0.0175894
$477$	581.300	0.0557986
$478$	3074.84	0.294226
$479$	11258.1	1.07390	0.536949	−	0.843615i	$-0.319577\pi$
$479$	11258.1	1.07390	0.536949	+	0.843615i	$0.319577\pi$
$480$	327.236	0.0311171
$481$	−2667.58	−0.252872
$482$	−2819.02	−0.266395
$483$	5995.18	0.564783
$484$	316.365	0.0297112
$485$	2408.58	0.225501
$486$	−4261.26	−0.397726
$487$	4353.54	0.405088	0.202544	−	0.979273i	$-0.435079\pi$
$487$	4353.54	0.405088	0.202544	+	0.979273i	$0.435079\pi$
$488$	−13009.6	−1.20679
$489$	−11392.9	−1.05359
$490$	12318.8	1.13573
$491$	8458.77	0.777472	0.388736	−	0.921349i	$-0.372912\pi$
$491$	8458.77	0.777472	0.388736	+	0.921349i	$0.372912\pi$
$492$	−233.087	−0.0213585
$493$	0	0
$494$	−4550.96	−0.414489
$495$	−4381.20	−0.397819
$496$	4086.82	0.369967
$497$	20369.0	1.83838
$498$	1103.56	0.0993002
$499$	14850.9	1.33230	0.666149	−	0.745819i	$-0.267942\pi$
$499$	14850.9	1.33230	0.666149	+	0.745819i	$0.267942\pi$
$500$	−131.206	−0.0117354
$501$	9385.04	0.836912
$502$	−2565.45	−0.228091
$503$	1686.45	0.149493	0.0747464	−	0.997203i	$-0.476185\pi$
$503$	1686.45	0.149493	0.0747464	+	0.997203i	$0.476185\pi$
$504$	3168.99	0.280076
$505$	12350.5	1.08830
$506$	−8868.00	−0.779112
$507$	7876.97	0.689997
$508$	241.256	0.0210709
$509$	−11113.5	−0.967773	−0.483887	−	0.875131i	$-0.660775\pi$
$509$	−11113.5	−0.967773	−0.483887	+	0.875131i	$0.660775\pi$
$510$	−9881.36	−0.857949
$511$	3471.35	0.300516
$512$	−11311.8	−0.976395
$513$	−10740.0	−0.924336
$514$	−8905.90	−0.764246
$515$	1015.33	0.0868754
$516$	−195.501	−0.0166792
$517$	−34759.8	−2.95694
$518$	−8844.45	−0.750198
$519$	−13296.7	−1.12458
$520$	−6472.57	−0.545848
$521$	−15931.1	−1.33964	−0.669820	−	0.742523i	$-0.733629\pi$
$521$	−15931.1	−1.33964	−0.669820	+	0.742523i	$0.733629\pi$
$522$	0	0
$523$	−7960.43	−0.665555	−0.332778	−	0.943005i	$-0.607986\pi$
$523$	−7960.43	−0.665555	−0.332778	+	0.943005i	$0.607986\pi$
$524$	−186.804	−0.0155736
$525$	−4927.58	−0.409633
$526$	−8021.67	−0.664945
$527$	−3648.14	−0.301548
$528$	18958.4	1.56261
$529$	−9713.71	−0.798366
$530$	−3936.49	−0.322623
$531$	−741.503	−0.0605998
$532$	−224.675	−0.0183099
$533$	9291.45	0.755079
$534$	−4738.51	−0.383999
$535$	9189.30	0.742594
$536$	−20656.0	−1.66456
$537$	1080.83	0.0868555
$538$	−12565.2	−1.00692
$539$	21098.0	1.68600
$540$	234.427	0.0186817
$541$	−13818.9	−1.09819	−0.549096	−	0.835760i	$-0.685028\pi$
$541$	−13818.9	−1.09819	−0.549096	+	0.835760i	$0.685028\pi$
$542$	12590.0	0.997760
$543$	12114.5	0.957430
$544$	−317.261	−0.0250045
$545$	6907.07	0.542874
$546$	−7724.22	−0.605432
$547$	22093.3	1.72695	0.863474	−	0.504393i	$-0.168284\pi$
$547$	22093.3	1.72695	0.863474	+	0.504393i	$0.168284\pi$
$548$	156.585	0.0122062
$549$	−3138.73	−0.244003
$550$	7288.82	0.565084
$551$	0	0
$552$	−5166.62	−0.398381
$553$	−22619.9	−1.73942
$554$	−2529.35	−0.193974
$555$	7124.00	0.544859
$556$	241.802	0.0184437
$557$	−3110.34	−0.236606	−0.118303	−	0.992978i	$-0.537745\pi$
$557$	−3110.34	−0.236606	−0.118303	+	0.992978i	$0.537745\pi$
$558$	971.314	0.0736900
$559$	7793.17	0.589653
$560$	−21784.4	−1.64386
$561$	−16923.4	−1.27363
$562$	−12215.6	−0.916873
$563$	13284.6	0.994455	0.497227	−	0.867620i	$-0.334351\pi$
$563$	13284.6	0.994455	0.497227	+	0.867620i	$0.334351\pi$
$564$	310.804	0.0232043
$565$	−25055.2	−1.86563
$566$	−4871.86	−0.361801
$567$	−14418.1	−1.06790
$568$	−17553.9	−1.29674
$569$	6809.18	0.501680	0.250840	−	0.968029i	$-0.419293\pi$
$569$	6809.18	0.501680	0.250840	+	0.968029i	$0.419293\pi$
$570$	12153.7	0.893093
$571$	−13471.8	−0.987352	−0.493676	−	0.869646i	$-0.664347\pi$
$571$	−13471.8	−0.987352	−0.493676	+	0.869646i	$0.664347\pi$
$572$	170.128	0.0124361
$573$	7102.88	0.517849
$574$	30806.0	2.24010
$575$	−2016.41	−0.146244
$576$	−2730.39	−0.197511
$577$	−5331.06	−0.384636	−0.192318	−	0.981333i	$-0.561601\pi$
$577$	−5331.06	−0.384636	−0.192318	+	0.981333i	$0.561601\pi$
$578$	−4420.56	−0.318116
$579$	4727.41	0.339317
$580$	0	0
$581$	−2171.75	−0.155077
$582$	−2477.10	−0.176424
$583$	−6741.87	−0.478936
$584$	−2991.59	−0.211974
$585$	−1561.59	−0.110366
$586$	−3262.96	−0.230020
$587$	3333.96	0.234425	0.117212	−	0.993107i	$-0.462604\pi$
$587$	3333.96	0.234425	0.117212	+	0.993107i	$0.462604\pi$
$588$	−188.647	−0.0132307
$589$	4487.09	0.313900
$590$	5021.36	0.350383
$591$	−15285.4	−1.06389
$592$	7737.34	0.537167
$593$	−23405.3	−1.62081	−0.810404	−	0.585872i	$-0.800752\pi$
$593$	−23405.3	−1.62081	−0.810404	+	0.585872i	$0.800752\pi$
$594$	26963.8	1.86252
$595$	19446.1	1.33985
$596$	143.610	0.00986998
$597$	138.996	0.00952886
$598$	−3160.83	−0.216147
$599$	10352.1	0.706133	0.353067	−	0.935598i	$-0.385139\pi$
$599$	10352.1	0.706133	0.353067	+	0.935598i	$0.385139\pi$
$600$	4246.57	0.288943
$601$	−15171.1	−1.02969	−0.514843	−	0.857285i	$-0.672150\pi$
$601$	−15171.1	−1.02969	−0.514843	+	0.857285i	$0.672150\pi$
$602$	25838.5	1.74933
$603$	−4983.54	−0.336560
$604$	−272.994	−0.0183907
$605$	33679.0	2.26322
$606$	−12701.9	−0.851449
$607$	20823.0	1.39239	0.696193	−	0.717854i	$-0.254876\pi$
$607$	20823.0	1.39239	0.696193	+	0.717854i	$0.254876\pi$
$608$	390.219	0.0260287
$609$	0	0
$610$	21255.0	1.41081
$611$	−12389.5	−0.820334
$612$	−37.9802	−0.00250859
$613$	−19071.6	−1.25660	−0.628299	−	0.777972i	$-0.716249\pi$
$613$	−19071.6	−1.25660	−0.628299	+	0.777972i	$0.716249\pi$
$614$	−3075.97	−0.202176
$615$	−24813.6	−1.62696
$616$	−36753.7	−2.40397
$617$	−15200.4	−0.991806	−0.495903	−	0.868378i	$-0.665163\pi$
$617$	−15200.4	−0.991806	−0.495903	+	0.868378i	$0.665163\pi$
$618$	−1044.22	−0.0679684
$619$	−4358.76	−0.283026	−0.141513	−	0.989936i	$-0.545197\pi$
$619$	−4358.76	−0.283026	−0.141513	+	0.989936i	$0.545197\pi$
$620$	−97.9414	−0.00634423
$621$	−7459.39	−0.482021
$622$	−6593.98	−0.425071
$623$	9325.20	0.599689
$624$	6757.34	0.433510
$625$	−19056.5	−1.21961
$626$	−21809.5	−1.39246
$627$	20815.2	1.32580
$628$	−143.677	−0.00912950
$629$	−6906.83	−0.437827
$630$	−5177.51	−0.327423
$631$	−2580.66	−0.162812	−0.0814062	−	0.996681i	$-0.525941\pi$
$631$	−2580.66	−0.162812	−0.0814062	+	0.996681i	$0.525941\pi$
$632$	19493.8	1.22693
$633$	10532.8	0.661361
$634$	10422.1	0.652861
$635$	25683.2	1.60505
$636$	60.2823	0.00375841
$637$	7519.96	0.467742
$638$	0	0
$639$	−4235.12	−0.262189
$640$	19053.3	1.17680
$641$	−19858.9	−1.22368	−0.611840	−	0.790982i	$-0.709570\pi$
$641$	−19858.9	−1.22368	−0.611840	+	0.790982i	$0.709570\pi$
$642$	−9450.72	−0.580981
$643$	17371.9	1.06545	0.532723	−	0.846290i	$-0.321169\pi$
$643$	17371.9	1.06545	0.532723	+	0.846290i	$0.321169\pi$
$644$	−156.046	−0.00954823
$645$	−20812.3	−1.27052
$646$	−11783.2	−0.717654
$647$	3275.07	0.199005	0.0995024	−	0.995037i	$-0.468275\pi$
$647$	3275.07	0.199005	0.0995024	+	0.995037i	$0.468275\pi$
$648$	12425.4	0.753266
$649$	8599.88	0.520146
$650$	2597.96	0.156770
$651$	7615.80	0.458505
$652$	296.540	0.0178120
$653$	−20726.5	−1.24210	−0.621049	−	0.783772i	$-0.713293\pi$
$653$	−20726.5	−1.24210	−0.621049	+	0.783772i	$0.713293\pi$
$654$	−7103.56	−0.424727
$655$	−19886.4	−1.18630
$656$	−26949.9	−1.60399
$657$	−721.762	−0.0428594
$658$	−41077.6	−2.43370
$659$	18404.6	1.08792	0.543960	−	0.839111i	$-0.316924\pi$
$659$	18404.6	1.08792	0.543960	+	0.839111i	$0.316924\pi$
$660$	−454.341	−0.0267958
$661$	−7146.10	−0.420501	−0.210250	−	0.977648i	$-0.567428\pi$
$661$	−7146.10	−0.420501	−0.210250	+	0.977648i	$0.567428\pi$
$662$	−9227.19	−0.541729
$663$	−6032.02	−0.353340
$664$	1871.61	0.109386
$665$	−23918.0	−1.39474
$666$	1838.94	0.106993
$667$	0	0
$668$	−244.279	−0.0141488
$669$	−22973.3	−1.32765
$670$	33747.9	1.94596
$671$	36402.7	2.09435
$672$	662.308	0.0380195
$673$	−26819.0	−1.53610	−0.768051	−	0.640389i	$-0.778773\pi$
$673$	−26819.0	−1.53610	−0.768051	+	0.640389i	$0.778773\pi$
$674$	22731.9	1.29911
$675$	6131.05	0.349606
$676$	−205.026	−0.0116651
$677$	20093.1	1.14068	0.570340	−	0.821408i	$-0.306811\pi$
$677$	20093.1	1.14068	0.570340	+	0.821408i	$0.306811\pi$
$678$	25768.0	1.45961
$679$	4874.82	0.275521
$680$	−16758.6	−0.945092
$681$	16536.3	0.930505
$682$	−11265.2	−0.632503
$683$	−6876.22	−0.385229	−0.192614	−	0.981275i	$-0.561697\pi$
$683$	−6876.22	−0.385229	−0.192614	+	0.981275i	$0.561697\pi$
$684$	46.7143	0.00261135
$685$	16669.5	0.929791
$686$	−533.956	−0.0297180
$687$	28540.6	1.58500
$688$	−22604.1	−1.25258
$689$	−2403.01	−0.132870
$690$	8441.24	0.465728
$691$	17332.7	0.954224	0.477112	−	0.878842i	$-0.341684\pi$
$691$	17332.7	0.954224	0.477112	+	0.878842i	$0.341684\pi$
$692$	346.092	0.0190122
$693$	−8867.31	−0.486063
$694$	−23812.1	−1.30244
$695$	25741.4	1.40493
$696$	0	0
$697$	24057.1	1.30736
$698$	15800.5	0.856814
$699$	5050.21	0.273271
$700$	128.258	0.00692526
$701$	11127.5	0.599545	0.299772	−	0.954011i	$-0.403089\pi$
$701$	11127.5	0.599545	0.299772	+	0.954011i	$0.403089\pi$
$702$	9610.71	0.516714
$703$	8495.15	0.455762
$704$	31666.8	1.69530
$705$	33087.1	1.76756
$706$	−4795.48	−0.255638
$707$	24996.8	1.32970
$708$	−76.8957	−0.00408180
$709$	17432.0	0.923374	0.461687	−	0.887043i	$-0.347244\pi$
$709$	17432.0	0.923374	0.461687	+	0.887043i	$0.347244\pi$
$710$	28679.7	1.51596
$711$	4703.13	0.248075
$712$	−8036.42	−0.423002
$713$	3116.46	0.163692
$714$	−19999.3	−1.04826
$715$	18111.2	0.947302
$716$	−28.1325	−0.00146838
$717$	−5012.73	−0.261093
$718$	−20355.9	−1.05805
$719$	21082.7	1.09353	0.546767	−	0.837285i	$-0.315858\pi$
$719$	21082.7	1.09353	0.546767	+	0.837285i	$0.315858\pi$
$720$	4529.41	0.234446
$721$	2054.97	0.106146
$722$	−5053.32	−0.260478
$723$	4595.68	0.236397
$724$	−315.323	−0.0161863
$725$	0	0
$726$	−34637.1	−1.77067
$727$	25839.1	1.31818	0.659091	−	0.752063i	$-0.270941\pi$
$727$	25839.1	1.31818	0.659091	+	0.752063i	$0.270941\pi$
$728$	−13100.1	−0.666927
$729$	21888.5	1.11205
$730$	4887.67	0.247810
$731$	20177.9	1.02094
$732$	−325.494	−0.0164352
$733$	−1278.54	−0.0644256	−0.0322128	−	0.999481i	$-0.510255\pi$
$733$	−1278.54	−0.0644256	−0.0322128	+	0.999481i	$0.510255\pi$
$734$	12698.8	0.638586
$735$	−20082.6	−1.00784
$736$	271.023	0.0135734
$737$	57798.6	2.88879
$738$	−6405.19	−0.319483
$739$	−4224.54	−0.210287	−0.105144	−	0.994457i	$-0.533530\pi$
$739$	−4224.54	−0.210287	−0.105144	+	0.994457i	$0.533530\pi$
$740$	−185.427	−0.00921140
$741$	7419.17	0.367814
$742$	−7967.23	−0.394186
$743$	17992.3	0.888390	0.444195	−	0.895930i	$-0.353490\pi$
$743$	17992.3	0.888390	0.444195	+	0.895930i	$0.353490\pi$
$744$	−6563.27	−0.323416
$745$	15288.2	0.751835
$746$	7147.91	0.350809
$747$	451.550	0.0221170
$748$	440.491	0.0215320
$749$	18598.6	0.907316
$750$	14365.0	0.699381
$751$	10082.4	0.489895	0.244948	−	0.969536i	$-0.421229\pi$
$751$	10082.4	0.489895	0.244948	+	0.969536i	$0.421229\pi$
$752$	35935.7	1.74261
$753$	4182.30	0.202406
$754$	0	0
$755$	−29061.9	−1.40089
$756$	474.468	0.0228257
$757$	−10806.5	−0.518851	−0.259425	−	0.965763i	$-0.583533\pi$
$757$	−10806.5	−0.518851	−0.259425	+	0.965763i	$0.583533\pi$
$758$	36288.2	1.73885
$759$	14457.0	0.691377
$760$	20612.5	0.983806
$761$	−30710.4	−1.46288	−0.731439	−	0.681907i	$-0.761151\pi$
$761$	−30710.4	−1.46288	−0.731439	+	0.681907i	$0.761151\pi$
$762$	−26413.8	−1.25574
$763$	13979.5	0.663293
$764$	−184.877	−0.00875475
$765$	−4043.23	−0.191089
$766$	−2927.21	−0.138074
$767$	3065.26	0.144303
$768$	−862.682	−0.0405330
$769$	−10757.1	−0.504436	−0.252218	−	0.967670i	$-0.581160\pi$
$769$	−10757.1	−0.504436	−0.252218	+	0.967670i	$0.581160\pi$
$770$	60048.2	2.81037
$771$	14518.8	0.678185
$772$	−123.047	−0.00573649
$773$	18077.2	0.841125	0.420563	−	0.907263i	$-0.361833\pi$
$773$	18077.2	0.841125	0.420563	+	0.907263i	$0.361833\pi$
$774$	−5372.33	−0.249489
$775$	−2561.49	−0.118725
$776$	−4201.10	−0.194344
$777$	14418.6	0.665719
$778$	−14685.6	−0.676742
$779$	−29589.4	−1.36091
$780$	−161.941	−0.00743387
$781$	49118.6	2.25045
$782$	−8183.92	−0.374241
$783$	0	0
$784$	−21811.7	−0.993608
$785$	−15295.3	−0.695430
$786$	20452.2	0.928123
$787$	−31543.7	−1.42873	−0.714366	−	0.699773i	$-0.753285\pi$
$787$	−31543.7	−1.42873	−0.714366	+	0.699773i	$0.753285\pi$
$788$	397.857	0.0179861
$789$	13077.3	0.590066
$790$	−31848.9	−1.43435
$791$	−50710.4	−2.27946
$792$	7641.81	0.342854
$793$	12975.0	0.581030
$794$	17813.5	0.796192
$795$	6417.42	0.286293
$796$	−3.61786	−0.000161095 0
$797$	−18280.9	−0.812477	−0.406239	−	0.913767i	$-0.633160\pi$
$797$	−18280.9	−0.812477	−0.406239	+	0.913767i	$0.633160\pi$
$798$	24598.4	1.09120
$799$	−32078.4	−1.42034
$800$	−222.760	−0.00984470
$801$	−1938.89	−0.0855273
$802$	31585.6	1.39068
$803$	8370.93	0.367875
$804$	−516.805	−0.0226695
$805$	−16612.0	−0.727326
$806$	−4015.26	−0.175473
$807$	20484.4	0.893536
$808$	−21542.1	−0.937932
$809$	−21776.3	−0.946372	−0.473186	−	0.880963i	$-0.656896\pi$
$809$	−21776.3	−0.946372	−0.473186	+	0.880963i	$0.656896\pi$
$810$	−20300.7	−0.880609
$811$	17035.7	0.737612	0.368806	−	0.929506i	$-0.379767\pi$
$811$	17035.7	0.737612	0.368806	+	0.929506i	$0.379767\pi$
$812$	0	0
$813$	−20524.7	−0.885404
$814$	−21327.8	−0.918353
$815$	31568.5	1.35681
$816$	17495.9	0.750588
$817$	−24818.0	−1.06276
$818$	9619.03	0.411151
$819$	−3160.58	−0.134847
$820$	645.860	0.0275054
$821$	−45120.7	−1.91805	−0.959027	−	0.283314i	$-0.908566\pi$
$821$	−45120.7	−1.91805	−0.959027	+	0.283314i	$0.908566\pi$
$822$	−17143.7	−0.727438
$823$	−22261.7	−0.942883	−0.471442	−	0.881897i	$-0.656266\pi$
$823$	−22261.7	−0.942883	−0.471442	+	0.881897i	$0.656266\pi$
$824$	−1770.97	−0.0748721
$825$	−11882.5	−0.501451
$826$	10162.9	0.428104
$827$	−10280.4	−0.432266	−0.216133	−	0.976364i	$-0.569345\pi$
$827$	−10280.4	−0.432266	−0.216133	+	0.976364i	$0.569345\pi$
$828$	32.4450	0.00136176
$829$	−28509.2	−1.19441	−0.597206	−	0.802088i	$-0.703722\pi$
$829$	−28509.2	−1.19441	−0.597206	+	0.802088i	$0.703722\pi$
$830$	−3057.84	−0.127878
$831$	4123.45	0.172131
$832$	11287.0	0.470321
$833$	19470.4	0.809857
$834$	−26473.7	−1.09917
$835$	−26005.0	−1.07777
$836$	−541.788	−0.0224140
$837$	−9475.82	−0.391317
$838$	18484.7	0.761986
$839$	−4746.97	−0.195332	−0.0976661	−	0.995219i	$-0.531138\pi$
$839$	−4746.97	−0.195332	−0.0976661	+	0.995219i	$0.531138\pi$
$840$	34984.9	1.43702
$841$	0	0
$842$	31172.0	1.27584
$843$	19914.3	0.813625
$844$	−274.153	−0.0111810
$845$	−21826.3	−0.888576
$846$	8540.85	0.347093
$847$	68164.5	2.76524
$848$	6969.94	0.282251
$849$	7942.30	0.321059
$850$	6726.56	0.271434
$851$	5900.22	0.237670
$852$	−439.193	−0.0176602
$853$	−35313.3	−1.41747	−0.708736	−	0.705473i	$-0.750734\pi$
$853$	−35313.3	−1.41747	−0.708736	+	0.705473i	$0.750734\pi$
$854$	43019.0	1.72375
$855$	4973.03	0.198917
$856$	−16028.2	−0.639993
$857$	32142.8	1.28119	0.640594	−	0.767880i	$-0.278688\pi$
$857$	32142.8	1.28119	0.640594	+	0.767880i	$0.278688\pi$
$858$	−18626.4	−0.741138
$859$	−37568.2	−1.49221	−0.746107	−	0.665826i	$-0.768079\pi$
$859$	−37568.2	−1.49221	−0.746107	+	0.665826i	$0.768079\pi$
$860$	541.713	0.0214794
$861$	−50221.3	−1.98785
$862$	11753.2	0.464404
$863$	3416.95	0.134779	0.0673896	−	0.997727i	$-0.478533\pi$
$863$	3416.95	0.134779	0.0673896	+	0.997727i	$0.478533\pi$
$864$	−824.064	−0.0324482
$865$	36843.6	1.44823
$866$	4449.59	0.174599
$867$	7206.57	0.282293
$868$	−198.228	−0.00775149
$869$	−54546.5	−2.12930
$870$	0	0
$871$	20601.2	0.801429
$872$	−12047.5	−0.467867
$873$	−1013.57	−0.0392947
$874$	10065.9	0.389571
$875$	−28269.8	−1.09222
$876$	−74.8485	−0.00288687
$877$	−11891.0	−0.457847	−0.228923	−	0.973444i	$-0.573521\pi$
$877$	−11891.0	−0.457847	−0.228923	+	0.973444i	$0.573521\pi$
$878$	−44776.8	−1.72112
$879$	5319.42	0.204118
$880$	−52531.7	−2.01232
$881$	−20042.7	−0.766464	−0.383232	−	0.923652i	$-0.625189\pi$
$881$	−20042.7	−0.766464	−0.383232	+	0.923652i	$0.625189\pi$
$882$	−5183.98	−0.197907
$883$	−18042.8	−0.687641	−0.343821	−	0.939035i	$-0.611721\pi$
$883$	−18042.8	−0.687641	−0.343821	+	0.939035i	$0.611721\pi$
$884$	157.004	0.00597356
$885$	−8186.02	−0.310927
$886$	−36372.5	−1.37919
$887$	−2247.91	−0.0850929	−0.0425464	−	0.999094i	$-0.513547\pi$
$887$	−2247.91	−0.0850929	−0.0425464	+	0.999094i	$0.513547\pi$
$888$	−12425.9	−0.469578
$889$	51981.4	1.96108
$890$	13129.9	0.494512
$891$	−34768.2	−1.30727
$892$	597.960	0.0224453
$893$	39455.3	1.47852
$894$	−15723.1	−0.588211
$895$	−2994.88	−0.111852
$896$	38562.9	1.43783
$897$	5152.91	0.191807
$898$	−8885.09	−0.330177
$899$	0	0
$900$	−26.6673	−0.000987677 0
$901$	−6221.80	−0.230053
$902$	74286.7	2.74222
$903$	−42123.0	−1.55234
$904$	43702.1	1.60786
$905$	−33568.1	−1.23298
$906$	29888.6	1.09601
$907$	1798.34	0.0658354	0.0329177	−	0.999458i	$-0.489520\pi$
$907$	1798.34	0.0658354	0.0329177	+	0.999458i	$0.489520\pi$
$908$	−430.416	−0.0157311
$909$	−5197.32	−0.189642
$910$	21403.0	0.779674
$911$	−4602.02	−0.167367	−0.0836837	−	0.996492i	$-0.526669\pi$
$911$	−4602.02	−0.167367	−0.0836837	+	0.996492i	$0.526669\pi$
$912$	−21519.3	−0.781334
$913$	−5237.04	−0.189836
$914$	−24164.0	−0.874478
$915$	−34650.8	−1.25194
$916$	−742.869	−0.0267960
$917$	−40249.1	−1.44944
$918$	24883.8	0.894648
$919$	20622.0	0.740215	0.370107	−	0.928989i	$-0.379321\pi$
$919$	20622.0	0.740215	0.370107	+	0.928989i	$0.379321\pi$
$920$	14316.2	0.513033
$921$	5014.58	0.179409
$922$	−26369.4	−0.941898
$923$	17507.4	0.624335
$924$	−919.562	−0.0327396
$925$	−4849.53	−0.172380
$926$	1485.83	0.0527294
$927$	−427.270	−0.0151385
$928$	0	0
$929$	−24061.8	−0.849777	−0.424889	−	0.905246i	$-0.639687\pi$
$929$	−24061.8	−0.849777	−0.424889	+	0.905246i	$0.639687\pi$
$930$	10723.1	0.378090
$931$	−23947.9	−0.843032
$932$	−131.449	−0.00461992
$933$	10749.8	0.377204
$934$	−12360.2	−0.433019
$935$	46893.0	1.64018
$936$	2723.78	0.0951169
$937$	−6581.96	−0.229481	−0.114740	−	0.993396i	$-0.536604\pi$
$937$	−6581.96	−0.229481	−0.114740	+	0.993396i	$0.536604\pi$
$938$	68303.8	2.37761
$939$	35554.7	1.23566
$940$	−861.207	−0.0298824
$941$	23579.7	0.816873	0.408436	−	0.912787i	$-0.366074\pi$
$941$	23579.7	0.816873	0.408436	+	0.912787i	$0.366074\pi$
$942$	15730.4	0.544081
$943$	−20551.0	−0.709686
$944$	−8890.80	−0.306537
$945$	50510.0	1.73872
$946$	62307.8	2.14144
$947$	36368.6	1.24796	0.623982	−	0.781439i	$-0.285514\pi$
$947$	36368.6	1.24796	0.623982	+	0.781439i	$0.285514\pi$
$948$	487.726	0.0167095
$949$	2983.65	0.102058
$950$	−8273.42	−0.282553
$951$	−16990.5	−0.579343
$952$	−33918.5	−1.15473
$953$	44404.3	1.50933	0.754667	−	0.656108i	$-0.227798\pi$
$953$	44404.3	1.50933	0.754667	+	0.656108i	$0.227798\pi$
$954$	1656.55	0.0562187
$955$	−19681.4	−0.666884
$956$	130.474	0.00441404
$957$	0	0
$958$	32082.5	1.08198
$959$	33738.1	1.13604
$960$	−30142.9	−1.01339
$961$	−25832.1	−0.867111
$962$	−7601.88	−0.254776
$963$	−3867.02	−0.129401
$964$	−119.619	−0.00399653
$965$	−13099.2	−0.436971
$966$	17084.6	0.569035
$967$	−21928.3	−0.729230	−0.364615	−	0.931158i	$-0.618799\pi$
$967$	−21928.3	−0.729230	−0.364615	+	0.931158i	$0.618799\pi$
$968$	−58743.9	−1.95052
$969$	19209.5	0.636840
$970$	6863.77	0.227198
$971$	6352.95	0.209965	0.104982	−	0.994474i	$-0.466521\pi$
$971$	6352.95	0.209965	0.104982	+	0.994474i	$0.466521\pi$
$972$	−180.817	−0.00596678
$973$	52099.1	1.71657
$974$	12406.4	0.408138
$975$	−4235.30	−0.139116
$976$	−37634.1	−1.23426
$977$	12792.8	0.418913	0.209456	−	0.977818i	$-0.432831\pi$
$977$	12792.8	0.418913	0.209456	+	0.977818i	$0.432831\pi$
$978$	−32466.6	−1.06152
$979$	22487.1	0.734107
$980$	522.721	0.0170385
$981$	−2906.62	−0.0945986
$982$	24105.1	0.783326
$983$	−7536.73	−0.244542	−0.122271	−	0.992497i	$-0.539018\pi$
$983$	−7536.73	−0.244542	−0.122271	+	0.992497i	$0.539018\pi$
$984$	43280.5	1.40217
$985$	42354.3	1.37007
$986$	0	0
$987$	66966.4	2.15964
$988$	−193.110	−0.00621826
$989$	−17237.1	−0.554205
$990$	−12485.2	−0.400814
$991$	−28088.3	−0.900357	−0.450179	−	0.892938i	$-0.648640\pi$
$991$	−28088.3	−0.900357	−0.450179	+	0.892938i	$0.648640\pi$
$992$	344.286	0.0110192
$993$	15042.5	0.480726
$994$	58046.1	1.85222
$995$	−385.144	−0.0122712
$996$	46.8269	0.00148973
$997$	44951.9	1.42793	0.713963	−	0.700184i	$-0.246899\pi$
$997$	44951.9	1.42793	0.713963	+	0.700184i	$0.246899\pi$
$998$	42320.9	1.34233
$999$	−17940.0	−0.568166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.4.a.b.1.4		5
29.28	even	2		29.4.a.b.1.2	✓	5
87.86	odd	2		261.4.a.f.1.4		5
116.115	odd	2		464.4.a.l.1.2		5
145.144	even	2		725.4.a.c.1.4		5
203.202	odd	2		1421.4.a.e.1.2		5
232.115	odd	2		1856.4.a.bb.1.4		5
232.173	even	2		1856.4.a.y.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.4.a.b.1.2	✓	5	29.28	even	2
261.4.a.f.1.4		5	87.86	odd	2
464.4.a.l.1.2		5	116.115	odd	2
725.4.a.c.1.4		5	145.144	even	2
841.4.a.b.1.4		5	1.1	even	1	trivial
1421.4.a.e.1.2		5	203.202	odd	2
1856.4.a.y.1.2		5	232.173	even	2
1856.4.a.bb.1.4		5	232.115	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	841.a (trivial)

\(f(q)\)	\(=\)	\(q+2.84972 q^{2} -4.64574 q^{3} +0.120922 q^{4} +12.8729 q^{5} -13.2391 q^{6} +26.0540 q^{7} -22.4532 q^{8} -5.41713 q^{9} +O(q^{10})\)	\(q+2.84972 q^{2} -4.64574 q^{3} +0.120922 q^{4} +12.8729 q^{5} -13.2391 q^{6} +26.0540 q^{7} -22.4532 q^{8} -5.41713 q^{9} +36.6841 q^{10} +62.8274 q^{11} -0.561770 q^{12} +22.3936 q^{13} +74.2465 q^{14} -59.8039 q^{15} -64.9528 q^{16} +57.9808 q^{17} -15.4373 q^{18} -71.3143 q^{19} +1.55661 q^{20} -121.040 q^{21} +179.041 q^{22} -49.5307 q^{23} +104.312 q^{24} +40.7104 q^{25} +63.8155 q^{26} +150.601 q^{27} +3.15048 q^{28} -170.425 q^{30} -62.9198 q^{31} -5.47182 q^{32} -291.880 q^{33} +165.229 q^{34} +335.389 q^{35} -0.655048 q^{36} -119.123 q^{37} -203.226 q^{38} -104.035 q^{39} -289.037 q^{40} +414.916 q^{41} -344.930 q^{42} +348.009 q^{43} +7.59719 q^{44} -69.7340 q^{45} -141.149 q^{46} -553.259 q^{47} +301.753 q^{48} +335.808 q^{49} +116.013 q^{50} -269.364 q^{51} +2.70787 q^{52} -107.308 q^{53} +429.172 q^{54} +808.768 q^{55} -584.994 q^{56} +331.308 q^{57} +136.881 q^{59} -7.23158 q^{60} +579.408 q^{61} -179.304 q^{62} -141.138 q^{63} +504.029 q^{64} +288.269 q^{65} -831.776 q^{66} +919.959 q^{67} +7.01113 q^{68} +230.106 q^{69} +955.765 q^{70} +781.802 q^{71} +121.632 q^{72} +133.237 q^{73} -339.467 q^{74} -189.130 q^{75} -8.62344 q^{76} +1636.90 q^{77} -296.470 q^{78} -868.196 q^{79} -836.127 q^{80} -553.392 q^{81} +1182.39 q^{82} -83.3560 q^{83} -14.6363 q^{84} +746.379 q^{85} +991.730 q^{86} -1410.68 q^{88} +357.919 q^{89} -198.722 q^{90} +583.442 q^{91} -5.98933 q^{92} +292.309 q^{93} -1576.64 q^{94} -918.019 q^{95} +25.4206 q^{96} +187.105 q^{97} +956.961 q^{98} -340.344 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 8 q^{3} + 26 q^{4} + 10 q^{5} + 34 q^{6} + 40 q^{7} + 84 q^{8} + 33 q^{9}+O(q^{10}) \) 5 * q - 8 * q^3 + 26 * q^4 + 10 * q^5 + 34 * q^6 + 40 * q^7 + 84 * q^8 + 33 * q^9	\( 5 q - 8 q^{3} + 26 q^{4} + 10 q^{5} + 34 q^{6} + 40 q^{7} + 84 q^{8} + 33 q^{9} + 64 q^{10} - 12 q^{11} + 224 q^{12} + 14 q^{13} + 192 q^{14} + 74 q^{15} + 146 q^{16} - 66 q^{17} + 108 q^{18} - 214 q^{19} + 6 q^{20} - 98 q^{22} + 164 q^{23} + 314 q^{24} + 207 q^{25} - 56 q^{26} - 362 q^{27} + 540 q^{28} - 234 q^{30} - 420 q^{31} + 652 q^{32} - 576 q^{33} + 204 q^{34} - 52 q^{35} - 260 q^{36} - 378 q^{37} - 496 q^{38} + 374 q^{39} + 80 q^{40} + 1158 q^{41} + 348 q^{42} + 204 q^{43} - 784 q^{44} - 1506 q^{45} - 580 q^{46} - 248 q^{47} + 1880 q^{48} - 283 q^{49} - 908 q^{50} + 228 q^{51} + 1482 q^{52} - 554 q^{53} + 918 q^{54} - 546 q^{55} + 608 q^{56} + 44 q^{57} + 440 q^{59} - 636 q^{60} - 618 q^{61} + 1250 q^{62} + 804 q^{63} + 2594 q^{64} - 1656 q^{65} - 2940 q^{66} + 1164 q^{67} - 356 q^{68} + 1968 q^{69} + 2184 q^{70} - 692 q^{71} + 2648 q^{72} + 1950 q^{73} - 1832 q^{74} - 3074 q^{75} - 1376 q^{76} + 1616 q^{77} - 1302 q^{78} - 272 q^{79} - 890 q^{80} + 1801 q^{81} + 92 q^{82} + 512 q^{83} + 3208 q^{84} + 1628 q^{85} + 2446 q^{86} - 6954 q^{88} - 866 q^{89} + 2200 q^{90} + 2580 q^{91} + 3468 q^{92} - 40 q^{93} - 5942 q^{94} - 2244 q^{95} + 7386 q^{96} - 1562 q^{97} + 3408 q^{98} + 238 q^{99}+O(q^{100}) \) 5 * q - 8 * q^3 + 26 * q^4 + 10 * q^5 + 34 * q^6 + 40 * q^7 + 84 * q^8 + 33 * q^9 + 64 * q^10 - 12 * q^11 + 224 * q^12 + 14 * q^13 + 192 * q^14 + 74 * q^15 + 146 * q^16 - 66 * q^17 + 108 * q^18 - 214 * q^19 + 6 * q^20 - 98 * q^22 + 164 * q^23 + 314 * q^24 + 207 * q^25 - 56 * q^26 - 362 * q^27 + 540 * q^28 - 234 * q^30 - 420 * q^31 + 652 * q^32 - 576 * q^33 + 204 * q^34 - 52 * q^35 - 260 * q^36 - 378 * q^37 - 496 * q^38 + 374 * q^39 + 80 * q^40 + 1158 * q^41 + 348 * q^42 + 204 * q^43 - 784 * q^44 - 1506 * q^45 - 580 * q^46 - 248 * q^47 + 1880 * q^48 - 283 * q^49 - 908 * q^50 + 228 * q^51 + 1482 * q^52 - 554 * q^53 + 918 * q^54 - 546 * q^55 + 608 * q^56 + 44 * q^57 + 440 * q^59 - 636 * q^60 - 618 * q^61 + 1250 * q^62 + 804 * q^63 + 2594 * q^64 - 1656 * q^65 - 2940 * q^66 + 1164 * q^67 - 356 * q^68 + 1968 * q^69 + 2184 * q^70 - 692 * q^71 + 2648 * q^72 + 1950 * q^73 - 1832 * q^74 - 3074 * q^75 - 1376 * q^76 + 1616 * q^77 - 1302 * q^78 - 272 * q^79 - 890 * q^80 + 1801 * q^81 + 92 * q^82 + 512 * q^83 + 3208 * q^84 + 1628 * q^85 + 2446 * q^86 - 6954 * q^88 - 866 * q^89 + 2200 * q^90 + 2580 * q^91 + 3468 * q^92 - 40 * q^93 - 5942 * q^94 - 2244 * q^95 + 7386 * q^96 - 1562 * q^97 + 3408 * q^98 + 238 * q^99

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