LMFDB - Embedded newform 29.4.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,4,Mod(1,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, 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("29.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	29.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:	$1.71105539017$
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:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-3.68360$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.47236 q^{2} -1.90549 q^{3} +12.0020 q^{4} -6.52855 q^{5} -8.52204 q^{6} +5.22706 q^{7} +17.8986 q^{8} -23.3691 q^{9} +O(q^{10})$	\(q+4.47236 q^{2} -1.90549 q^{3} +12.0020 q^{4} -6.52855 q^{5} -8.52204 q^{6} +5.22706 q^{7} +17.8986 q^{8} -23.3691 q^{9} -29.1981 q^{10} -21.1299 q^{11} -22.8697 q^{12} +83.4615 q^{13} +23.3773 q^{14} +12.4401 q^{15} -15.9674 q^{16} +11.3273 q^{17} -104.515 q^{18} -7.68096 q^{19} -78.3559 q^{20} -9.96011 q^{21} -94.5005 q^{22} +153.169 q^{23} -34.1055 q^{24} -82.3780 q^{25} +373.270 q^{26} +95.9778 q^{27} +62.7354 q^{28} -29.0000 q^{29} +55.6366 q^{30} +270.530 q^{31} -214.601 q^{32} +40.2628 q^{33} +50.6597 q^{34} -34.1251 q^{35} -280.477 q^{36} -298.404 q^{37} -34.3520 q^{38} -159.035 q^{39} -116.852 q^{40} -184.710 q^{41} -44.5452 q^{42} +208.337 q^{43} -253.602 q^{44} +152.566 q^{45} +685.028 q^{46} -553.098 q^{47} +30.4258 q^{48} -315.678 q^{49} -368.424 q^{50} -21.5840 q^{51} +1001.71 q^{52} -321.465 q^{53} +429.248 q^{54} +137.948 q^{55} +93.5569 q^{56} +14.6360 q^{57} -129.699 q^{58} +104.930 q^{59} +149.306 q^{60} +464.230 q^{61} +1209.91 q^{62} -122.152 q^{63} -832.032 q^{64} -544.883 q^{65} +180.070 q^{66} +745.813 q^{67} +135.950 q^{68} -291.862 q^{69} -152.620 q^{70} -509.252 q^{71} -418.273 q^{72} -0.374979 q^{73} -1334.57 q^{74} +156.970 q^{75} -92.1871 q^{76} -110.447 q^{77} -711.262 q^{78} +610.912 q^{79} +104.244 q^{80} +448.081 q^{81} -826.092 q^{82} +791.431 q^{83} -119.542 q^{84} -73.9507 q^{85} +931.757 q^{86} +55.2592 q^{87} -378.194 q^{88} -342.011 q^{89} +682.333 q^{90} +436.258 q^{91} +1838.34 q^{92} -515.491 q^{93} -2473.65 q^{94} +50.1455 q^{95} +408.919 q^{96} +601.476 q^{97} -1411.83 q^{98} +493.787 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 5 q + 8 q^{3} + 26 q^{4} + 10 q^{5} + 34 q^{6} + 40 q^{7} - 84 q^{8} + 33 q^{9} - 64 q^{10} + 12 q^{11} - 224 q^{12} + 14 q^{13} - 192 q^{14} - 74 q^{15} + 146 q^{16} + 66 q^{17} - 108 q^{18} + 214 q^{19} + 6 q^{20} - 98 q^{22} + 164 q^{23} + 314 q^{24} + 207 q^{25} + 56 q^{26} + 362 q^{27} + 540 q^{28} - 145 q^{29} - 234 q^{30} + 420 q^{31} - 652 q^{32} - 576 q^{33} + 204 q^{34} - 52 q^{35} - 260 q^{36} + 378 q^{37} - 496 q^{38} - 374 q^{39} - 80 q^{40} - 1158 q^{41} + 348 q^{42} - 204 q^{43} + 784 q^{44} - 1506 q^{45} + 580 q^{46} + 248 q^{47} - 1880 q^{48} - 283 q^{49} + 908 q^{50} + 228 q^{51} + 1482 q^{52} - 554 q^{53} + 918 q^{54} + 546 q^{55} - 608 q^{56} + 44 q^{57} + 440 q^{59} + 636 q^{60} + 618 q^{61} + 1250 q^{62} + 804 q^{63} + 2594 q^{64} - 1656 q^{65} + 2940 q^{66} + 1164 q^{67} + 356 q^{68} - 1968 q^{69} - 2184 q^{70} - 692 q^{71} - 2648 q^{72} - 1950 q^{73} - 1832 q^{74} + 3074 q^{75} + 1376 q^{76} - 1616 q^{77} - 1302 q^{78} + 272 q^{79} - 890 q^{80} + 1801 q^{81} + 92 q^{82} + 512 q^{83} - 3208 q^{84} - 1628 q^{85} + 2446 q^{86} - 232 q^{87} - 6954 q^{88} + 866 q^{89} - 2200 q^{90} + 2580 q^{91} + 3468 q^{92} - 40 q^{93} - 5942 q^{94} + 2244 q^{95} + 7386 q^{96} + 1562 q^{97} - 3408 q^{98} - 238 q^{99}+O(q^{100}) \) 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 - 145 * q^29 - 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 - 232 * q^87 - 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 $

$2$	4.47236	1.58122	0.790610	−	0.612321i	$-0.209764\pi$
$2$	4.47236	1.58122	0.790610	+	0.612321i	$0.209764\pi$
$3$	−1.90549	−0.366712	−0.183356	−	0.983047i	$-0.558696\pi$
$3$	−1.90549	−0.366712	−0.183356	+	0.983047i	$0.558696\pi$
$4$	12.0020	1.50025
$5$	−6.52855	−0.583931	−0.291966	−	0.956429i	$-0.594309\pi$
$5$	−6.52855	−0.583931	−0.291966	+	0.956429i	$0.594309\pi$
$6$	−8.52204	−0.579851
$7$	5.22706	0.282235	0.141117	−	0.989993i	$-0.454930\pi$
$7$	5.22706	0.282235	0.141117	+	0.989993i	$0.454930\pi$
$8$	17.8986	0.791012
$9$	−23.3691	−0.865523
$10$	−29.1981	−0.923324
$11$	−21.1299	−0.579173	−0.289586	−	0.957152i	$-0.593518\pi$
$11$	−21.1299	−0.579173	−0.289586	+	0.957152i	$0.593518\pi$
$12$	−22.8697	−0.550161
$13$	83.4615	1.78062	0.890310	−	0.455355i	$-0.150488\pi$
$13$	83.4615	1.78062	0.890310	+	0.455355i	$0.150488\pi$
$14$	23.3773	0.446275
$15$	12.4401	0.214134
$16$	−15.9674	−0.249491
$17$	11.3273	0.161604	0.0808020	−	0.996730i	$-0.474252\pi$
$17$	11.3273	0.161604	0.0808020	+	0.996730i	$0.474252\pi$
$18$	−104.515	−1.36858
$19$	−7.68096	−0.0927438	−0.0463719	−	0.998924i	$-0.514766\pi$
$19$	−7.68096	−0.0927438	−0.0463719	+	0.998924i	$0.514766\pi$
$20$	−78.3559	−0.876046
$21$	−9.96011	−0.103499
$22$	−94.5005	−0.915799
$23$	153.169	1.38861	0.694303	−	0.719683i	$-0.255713\pi$
$23$	153.169	1.38861	0.694303	+	0.719683i	$0.255713\pi$
$24$	−34.1055	−0.290073
$25$	−82.3780	−0.659024
$26$	373.270	2.81555
$27$	95.9778	0.684109
$28$	62.7354	0.423424
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	55.6366	0.338593
$31$	270.530	1.56737	0.783687	−	0.621156i	$-0.213337\pi$
$31$	270.530	1.56737	0.783687	+	0.621156i	$0.213337\pi$
$32$	−214.601	−1.18551
$33$	40.2628	0.212389
$34$	50.6597	0.255531
$35$	−34.1251	−0.164806
$36$	−280.477	−1.29850
$37$	−298.404	−1.32587	−0.662936	−	0.748676i	$-0.730690\pi$
$37$	−298.404	−1.32587	−0.662936	+	0.748676i	$0.730690\pi$
$38$	−34.3520	−0.146648
$39$	−159.035	−0.652974
$40$	−116.852	−0.461897
$41$	−184.710	−0.703584	−0.351792	−	0.936078i	$-0.614427\pi$
$41$	−184.710	−0.703584	−0.351792	+	0.936078i	$0.614427\pi$
$42$	−44.5452	−0.163654
$43$	208.337	0.738861	0.369430	−	0.929258i	$-0.379553\pi$
$43$	208.337	0.738861	0.369430	+	0.929258i	$0.379553\pi$
$44$	−253.602	−0.868906
$45$	152.566	0.505406
$46$	685.028	2.19569
$47$	−553.098	−1.71654	−0.858272	−	0.513194i	$-0.828462\pi$
$47$	−553.098	−1.71654	−0.858272	+	0.513194i	$0.828462\pi$
$48$	30.4258	0.0914913
$49$	−315.678	−0.920344
$50$	−368.424	−1.04206
$51$	−21.5840	−0.0592620
$52$	1001.71	2.67138
$53$	−321.465	−0.833144	−0.416572	−	0.909103i	$-0.636769\pi$
$53$	−321.465	−0.833144	−0.416572	+	0.909103i	$0.636769\pi$
$54$	429.248	1.08173
$55$	137.948	0.338197
$56$	93.5569	0.223251
$57$	14.6360	0.0340102
$58$	−129.699	−0.293625
$59$	104.930	0.231538	0.115769	−	0.993276i	$-0.463067\pi$
$59$	104.930	0.231538	0.115769	+	0.993276i	$0.463067\pi$
$60$	149.306	0.321256
$61$	464.230	0.974403	0.487201	−	0.873290i	$-0.338018\pi$
$61$	464.230	0.974403	0.487201	+	0.873290i	$0.338018\pi$
$62$	1209.91	2.47836
$63$	−122.152	−0.244281
$64$	−832.032	−1.62506
$65$	−544.883	−1.03976
$66$	180.070	0.335834
$67$	745.813	1.35993	0.679967	−	0.733243i	$-0.261994\pi$
$67$	745.813	1.35993	0.679967	+	0.733243i	$0.261994\pi$
$68$	135.950	0.242447
$69$	−291.862	−0.509218
$70$	−152.620	−0.260594
$71$	−509.252	−0.851227	−0.425613	−	0.904905i	$-0.639942\pi$
$71$	−509.252	−0.851227	−0.425613	+	0.904905i	$0.639942\pi$
$72$	−418.273	−0.684639
$73$	−0.374979	−0.000601205 0	−0.000300603	−	1.00000i	$-0.500096\pi$
$73$	−0.374979	−0.000601205 0	−0.000300603		1.00000i	$0.500096\pi$
$74$	−1334.57	−2.09649
$75$	156.970	0.241672
$76$	−92.1871	−0.139139
$77$	−110.447	−0.163463
$78$	−711.262	−1.03249
$79$	610.912	0.870037	0.435018	−	0.900422i	$-0.356742\pi$
$79$	610.912	0.870037	0.435018	+	0.900422i	$0.356742\pi$
$80$	104.244	0.145686
$81$	448.081	0.614652
$82$	−826.092	−1.11252
$83$	791.431	1.04664	0.523319	−	0.852137i	$-0.324694\pi$
$83$	791.431	1.04664	0.523319	+	0.852137i	$0.324694\pi$
$84$	−119.542	−0.155274
$85$	−73.9507	−0.0943656
$86$	931.757	1.16830
$87$	55.2592	0.0680966
$88$	−378.194	−0.458132
$89$	−342.011	−0.407338	−0.203669	−	0.979040i	$-0.565287\pi$
$89$	−342.011	−0.407338	−0.203669	+	0.979040i	$0.565287\pi$
$90$	682.333	0.799157
$91$	436.258	0.502553
$92$	1838.34	2.08326
$93$	−515.491	−0.574774
$94$	−2473.65	−2.71423
$95$	50.1455	0.0541560
$96$	408.919	0.434741
$97$	601.476	0.629594	0.314797	−	0.949159i	$-0.398063\pi$
$97$	601.476	0.629594	0.314797	+	0.949159i	$0.398063\pi$
$98$	−1411.83	−1.45526
$99$	493.787	0.501287
$100$	−988.704	−0.988704
$101$	402.327	0.396367	0.198183	−	0.980165i	$-0.436496\pi$
$101$	402.327	0.396367	0.198183	+	0.980165i	$0.436496\pi$
$102$	−96.5314	−0.0937063
$103$	−1338.38	−1.28033	−0.640166	−	0.768236i	$-0.721134\pi$
$103$	−1338.38	−1.28033	−0.640166	+	0.768236i	$0.721134\pi$
$104$	1493.84	1.40849
$105$	65.0251	0.0604362
$106$	−1437.71	−1.31738
$107$	500.501	0.452199	0.226099	−	0.974104i	$-0.427403\pi$
$107$	500.501	0.452199	0.226099	+	0.974104i	$0.427403\pi$
$108$	1151.93	1.02634
$109$	1274.80	1.12022	0.560108	−	0.828420i	$-0.310760\pi$
$109$	1274.80	1.12022	0.560108	+	0.828420i	$0.310760\pi$
$110$	616.951	0.534764
$111$	568.605	0.486212
$112$	−83.4628	−0.0704151
$113$	335.278	0.279118	0.139559	−	0.990214i	$-0.455432\pi$
$113$	335.278	0.279118	0.139559	+	0.990214i	$0.455432\pi$
$114$	65.4574	0.0537776
$115$	−999.972	−0.810851
$116$	−348.059	−0.278590
$117$	−1950.42	−1.54117
$118$	469.287	0.366113
$119$	59.2083	0.0456103
$120$	222.660	0.169383
$121$	−884.528	−0.664559
$122$	2076.21	1.54074
$123$	351.964	0.258012
$124$	3246.91	2.35146
$125$	1353.88	0.968756
$126$	−546.307	−0.386261
$127$	755.312	0.527741	0.263870	−	0.964558i	$-0.415001\pi$
$127$	755.312	0.527741	0.263870	+	0.964558i	$0.415001\pi$
$128$	−2004.35	−1.38407
$129$	−396.983	−0.270949
$130$	−2436.91	−1.64409
$131$	−253.351	−0.168973	−0.0844863	−	0.996425i	$-0.526925\pi$
$131$	−253.351	−0.168973	−0.0844863	+	0.996425i	$0.526925\pi$
$132$	483.235	0.318638
$133$	−40.1488	−0.0261755
$134$	3335.55	2.15035
$135$	−626.596	−0.399473
$136$	202.742	0.127831
$137$	−2477.49	−1.54501	−0.772504	−	0.635010i	$-0.780996\pi$
$137$	−2477.49	−1.54501	−0.772504	+	0.635010i	$0.780996\pi$
$138$	−1305.31	−0.805185
$139$	423.114	0.258187	0.129094	−	0.991632i	$-0.458793\pi$
$139$	423.114	0.258187	0.129094	+	0.991632i	$0.458793\pi$
$140$	−409.571	−0.247251
$141$	1053.92	0.629477
$142$	−2277.56	−1.34598
$143$	−1763.53	−1.03129
$144$	373.145	0.215940
$145$	189.328	0.108433
$146$	−1.67704	−0.000950637 0
$147$	601.521	0.337501
$148$	−3581.45	−1.98914
$149$	−1263.82	−0.694873	−0.347437	−	0.937703i	$-0.612948\pi$
$149$	−1263.82	−0.694873	−0.347437	+	0.937703i	$0.612948\pi$
$150$	702.029	0.382136
$151$	3369.67	1.81603	0.908013	−	0.418943i	$-0.137599\pi$
$151$	3369.67	1.81603	0.908013	+	0.418943i	$0.137599\pi$
$152$	−137.478	−0.0733615
$153$	−264.708	−0.139872
$154$	−493.960	−0.258470
$155$	−1766.17	−0.915238
$156$	−1908.74	−0.979627
$157$	−3688.61	−1.87505	−0.937527	−	0.347914i	$-0.886890\pi$
$157$	−3688.61	−1.87505	−0.937527	+	0.347914i	$0.886890\pi$
$158$	2732.22	1.37572
$159$	612.548	0.305523
$160$	1401.03	0.692258
$161$	800.624	0.391913
$162$	2003.98	0.971900
$163$	−1975.81	−0.949432	−0.474716	−	0.880139i	$-0.657449\pi$
$163$	−1975.81	−0.949432	−0.474716	+	0.880139i	$0.657449\pi$
$164$	−2216.90	−1.05555
$165$	−262.857	−0.124021
$166$	3539.57	1.65496
$167$	−1608.44	−0.745297	−0.372649	−	0.927973i	$-0.621550\pi$
$167$	−1608.44	−0.745297	−0.372649	+	0.927973i	$0.621550\pi$
$168$	−178.272	−0.0818687
$169$	4768.82	2.17061
$170$	−330.734	−0.149213
$171$	179.497	0.0802719
$172$	2500.46	1.10848
$173$	4445.71	1.95376	0.976881	−	0.213784i	$-0.0685788\pi$
$173$	4445.71	1.95376	0.976881	+	0.213784i	$0.0685788\pi$
$174$	247.139	0.107676
$175$	−430.595	−0.186000
$176$	337.390	0.144498
$177$	−199.944	−0.0849078
$178$	−1529.60	−0.644091
$179$	1461.35	0.610203	0.305101	−	0.952320i	$-0.401310\pi$
$179$	1461.35	0.610203	0.305101	+	0.952320i	$0.401310\pi$
$180$	1831.11	0.758237
$181$	3789.62	1.55624	0.778122	−	0.628113i	$-0.216172\pi$
$181$	3789.62	1.55624	0.778122	+	0.628113i	$0.216172\pi$
$182$	1951.11	0.794646
$183$	−884.585	−0.357325
$184$	2741.50	1.09840
$185$	1948.14	0.774218
$186$	−2305.46	−0.908843
$187$	−239.344	−0.0935966
$188$	−6638.30	−2.57525
$189$	501.682	0.193079
$190$	224.269	0.0856326
$191$	−4782.10	−1.81163	−0.905813	−	0.423678i	$-0.860739\pi$
$191$	−4782.10	−1.81163	−0.905813	+	0.423678i	$0.860739\pi$
$192$	1585.43	0.595929
$193$	−3557.27	−1.32673	−0.663363	−	0.748298i	$-0.730871\pi$
$193$	−3557.27	−1.32673	−0.663363	+	0.748298i	$0.730871\pi$
$194$	2690.02	0.995527
$195$	1038.27	0.381292
$196$	−3788.78	−1.38075
$197$	−2290.24	−0.828290	−0.414145	−	0.910211i	$-0.635919\pi$
$197$	−2290.24	−0.828290	−0.414145	+	0.910211i	$0.635919\pi$
$198$	2208.39	0.792645
$199$	−2788.00	−0.993146	−0.496573	−	0.867995i	$-0.665409\pi$
$199$	−2788.00	−0.993146	−0.496573	+	0.867995i	$0.665409\pi$
$200$	−1474.45	−0.521296
$201$	−1421.14	−0.498703
$202$	1799.35	0.626742
$203$	−151.585	−0.0524097
$204$	−259.052	−0.0889081
$205$	1205.89	0.410845
$206$	−5985.71	−2.02449
$207$	−3579.42	−1.20187
$208$	−1332.67	−0.444249
$209$	162.298	0.0537147
$210$	290.816	0.0955628
$211$	628.449	0.205044	0.102522	−	0.994731i	$-0.467309\pi$
$211$	628.449	0.205044	0.102522	+	0.994731i	$0.467309\pi$
$212$	−3858.24	−1.24993
$213$	970.374	0.312155
$214$	2238.42	0.715025
$215$	−1360.14	−0.431444
$216$	1717.86	0.541138
$217$	1414.08	0.442367
$218$	5701.36	1.77131
$219$	0.714519	0.000220469 0
$220$	1655.65	0.507382
$221$	945.391	0.287755
$222$	2543.01	0.768808
$223$	136.439	0.0409714	0.0204857	−	0.999790i	$-0.493479\pi$
$223$	136.439	0.0409714	0.0204857	+	0.999790i	$0.493479\pi$
$224$	−1121.73	−0.334593
$225$	1925.10	0.570400
$226$	1499.49	0.441347
$227$	4180.45	1.22232	0.611159	−	0.791508i	$-0.290704\pi$
$227$	4180.45	1.22232	0.611159	+	0.791508i	$0.290704\pi$
$228$	175.662	0.0510240
$229$	−1352.95	−0.390417	−0.195209	−	0.980762i	$-0.562538\pi$
$229$	−1352.95	−0.390417	−0.195209	+	0.980762i	$0.562538\pi$
$230$	−4472.24	−1.28213
$231$	210.456	0.0599436
$232$	−519.058	−0.146887
$233$	2175.34	0.611635	0.305818	−	0.952090i	$-0.401070\pi$
$233$	2175.34	0.611635	0.305818	+	0.952090i	$0.401070\pi$
$234$	−8722.99	−2.43692
$235$	3610.93	1.00234
$236$	1259.38	0.347367
$237$	−1164.09	−0.319053
$238$	264.801	0.0721198
$239$	−4512.18	−1.22121	−0.610604	−	0.791936i	$-0.709073\pi$
$239$	−4512.18	−1.22121	−0.610604	+	0.791936i	$0.709073\pi$
$240$	−198.636	−0.0534246
$241$	1950.53	0.521346	0.260673	−	0.965427i	$-0.416056\pi$
$241$	1950.53	0.521346	0.260673	+	0.965427i	$0.416056\pi$
$242$	−3955.93	−1.05081
$243$	−3445.21	−0.909509
$244$	5571.70	1.46185
$245$	2060.92	0.537417
$246$	1574.11	0.407974
$247$	−641.064	−0.165141
$248$	4842.09	1.23981
$249$	−1508.06	−0.383814
$250$	6055.03	1.53182
$251$	27.4143	0.00689393	0.00344696	−	0.999994i	$-0.498903\pi$
$251$	27.4143	0.00689393	0.00344696	+	0.999994i	$0.498903\pi$
$252$	−1466.07	−0.366483
$253$	−3236.44	−0.804243
$254$	3378.03	0.834474
$255$	140.912	0.0346050
$256$	−2307.91	−0.563454
$257$	4458.31	1.08211	0.541053	−	0.840988i	$-0.318026\pi$
$257$	4458.31	1.08211	0.541053	+	0.840988i	$0.318026\pi$
$258$	−1775.45	−0.428429
$259$	−1559.77	−0.374207
$260$	−6539.70	−1.55990
$261$	677.704	0.160724
$262$	−1133.08	−0.267183
$263$	4641.08	1.08814	0.544071	−	0.839039i	$-0.316882\pi$
$263$	4641.08	1.08814	0.544071	+	0.839039i	$0.316882\pi$
$264$	720.645	0.168002
$265$	2098.70	0.486499
$266$	−179.560	−0.0413893
$267$	651.699	0.149376
$268$	8951.28	2.04025
$269$	−235.021	−0.0532694	−0.0266347	−	0.999645i	$-0.508479\pi$
$269$	−235.021	−0.0532694	−0.0266347	+	0.999645i	$0.508479\pi$
$270$	−2802.36	−0.631654
$271$	3816.09	0.855392	0.427696	−	0.903923i	$-0.359325\pi$
$271$	3816.09	0.855392	0.427696	+	0.903923i	$0.359325\pi$
$272$	−180.867	−0.0403188
$273$	−831.286	−0.184292
$274$	−11080.2	−2.44300
$275$	1740.64	0.381689
$276$	−3502.94	−0.763957
$277$	−2024.79	−0.439198	−0.219599	−	0.975590i	$-0.570475\pi$
$277$	−2024.79	−0.439198	−0.219599	+	0.975590i	$0.570475\pi$
$278$	1892.32	0.408251
$279$	−6322.04	−1.35660
$280$	−610.791	−0.130363
$281$	5451.81	1.15739	0.578697	−	0.815543i	$-0.303561\pi$
$281$	5451.81	1.15739	0.578697	+	0.815543i	$0.303561\pi$
$282$	4713.52	0.995341
$283$	5026.80	1.05587	0.527937	−	0.849284i	$-0.322966\pi$
$283$	5026.80	1.05587	0.527937	+	0.849284i	$0.322966\pi$
$284$	−6112.06	−1.27706
$285$	−95.5517	−0.0198596
$286$	−7887.16	−1.63069
$287$	−965.493	−0.198576
$288$	5015.03	1.02609
$289$	−4784.69	−0.973884
$290$	846.744	0.171457
$291$	−1146.11	−0.230880
$292$	−4.50051	−0.000901961 0
$293$	6160.34	1.22830	0.614148	−	0.789191i	$-0.289500\pi$
$293$	6160.34	1.22830	0.614148	+	0.789191i	$0.289500\pi$
$294$	2690.22	0.533662
$295$	−685.043	−0.135203
$296$	−5340.99	−1.04878
$297$	−2028.00	−0.396217
$298$	−5652.26	−1.09875
$299$	12783.7	2.47258
$300$	1883.96	0.362569
$301$	1088.99	0.208532
$302$	15070.4	2.87153
$303$	−766.629	−0.145352
$304$	122.645	0.0231388
$305$	−3030.75	−0.568984
$306$	−1183.87	−0.221168
$307$	−4329.54	−0.804885	−0.402443	−	0.915445i	$-0.631839\pi$
$307$	−4329.54	−0.804885	−0.402443	+	0.915445i	$0.631839\pi$
$308$	−1325.59	−0.245236
$309$	2550.26	0.469513
$310$	−7898.94	−1.44719
$311$	−6411.83	−1.16907	−0.584536	−	0.811368i	$-0.698724\pi$
$311$	−6411.83	−1.16907	−0.584536	+	0.811368i	$0.698724\pi$
$312$	−2846.50	−0.516510
$313$	−19.5263	−0.00352617	−0.00176309	−	0.999998i	$-0.500561\pi$
$313$	−19.5263	−0.00352617	−0.00176309	+	0.999998i	$0.500561\pi$
$314$	−16496.8	−2.96487
$315$	797.474	0.142643
$316$	7332.18	1.30528
$317$	−8198.11	−1.45253	−0.726265	−	0.687415i	$-0.758745\pi$
$317$	−8198.11	−1.45253	−0.726265	+	0.687415i	$0.758745\pi$
$318$	2739.54	0.483100
$319$	612.767	0.107550
$320$	5431.97	0.948926
$321$	−953.699	−0.165826
$322$	3580.68	0.619701
$323$	−87.0043	−0.0149878
$324$	5377.89	0.922135
$325$	−6875.39	−1.17347
$326$	−8836.54	−1.50126
$327$	−2429.11	−0.410796
$328$	−3306.05	−0.556543
$329$	−2891.08	−0.484469
$330$	−1175.59	−0.196104
$331$	2374.46	0.394297	0.197148	−	0.980374i	$-0.436832\pi$
$331$	2374.46	0.394297	0.197148	+	0.980374i	$0.436832\pi$
$332$	9498.79	1.57022
$333$	6973.43	1.14757
$334$	−7193.52	−1.17848
$335$	−4869.08	−0.794108
$336$	159.037	0.0258220
$337$	−4985.34	−0.805842	−0.402921	−	0.915235i	$-0.632005\pi$
$337$	−4985.34	−0.805842	−0.402921	+	0.915235i	$0.632005\pi$
$338$	21327.9	3.43221
$339$	−638.869	−0.102356
$340$	−887.559	−0.141572
$341$	−5716.26	−0.907780
$342$	802.777	0.126927
$343$	−3442.95	−0.541988
$344$	3728.92	0.584448
$345$	1905.44	0.297348
$346$	19882.8	3.08933
$347$	−2023.98	−0.313121	−0.156560	−	0.987668i	$-0.550041\pi$
$347$	−2023.98	−0.313121	−0.156560	+	0.987668i	$0.550041\pi$
$348$	663.223	0.102162
$349$	−2651.99	−0.406755	−0.203378	−	0.979100i	$-0.565192\pi$
$349$	−2651.99	−0.406755	−0.203378	+	0.979100i	$0.565192\pi$
$350$	−1925.78	−0.294106
$351$	8010.45	1.21814
$352$	4534.49	0.686616
$353$	−1729.22	−0.260729	−0.130364	−	0.991466i	$-0.541615\pi$
$353$	−1729.22	−0.260729	−0.130364	+	0.991466i	$0.541615\pi$
$354$	−894.220	−0.134258
$355$	3324.68	0.497058
$356$	−4104.83	−0.611111
$357$	−112.821	−0.0167258
$358$	6535.68	0.964864
$359$	6875.38	1.01078	0.505388	−	0.862892i	$-0.331349\pi$
$359$	6875.38	1.01078	0.505388	+	0.862892i	$0.331349\pi$
$360$	2730.72	0.399782
$361$	−6800.00	−0.991399
$362$	16948.6	2.46076
$363$	1685.46	0.243701
$364$	5235.99	0.753957
$365$	2.44807	0.000351063 0
$366$	−3956.19	−0.565009
$367$	−7435.15	−1.05753	−0.528763	−	0.848770i	$-0.677344\pi$
$367$	−7435.15	−1.05753	−0.528763	+	0.848770i	$0.677344\pi$
$368$	−2445.72	−0.346445
$369$	4316.52	0.608968
$370$	8712.80	1.22421
$371$	−1680.32	−0.235142
$372$	−6186.95	−0.862307
$373$	1397.48	0.193991	0.0969954	−	0.995285i	$-0.469077\pi$
$373$	1397.48	0.193991	0.0969954	+	0.995285i	$0.469077\pi$
$374$	−1070.43	−0.147997
$375$	−2579.80	−0.355254
$376$	−9899.65	−1.35781
$377$	−2420.38	−0.330653
$378$	2243.70	0.305301
$379$	7009.57	0.950020	0.475010	−	0.879980i	$-0.342444\pi$
$379$	7009.57	0.950020	0.475010	+	0.879980i	$0.342444\pi$
$380$	601.848	0.0812478
$381$	−1439.24	−0.193529
$382$	−21387.3	−2.86458
$383$	−11728.7	−1.56477	−0.782387	−	0.622792i	$-0.785998\pi$
$383$	−11728.7	−1.56477	−0.782387	+	0.622792i	$0.785998\pi$
$384$	3819.26	0.507554
$385$	721.060	0.0954510
$386$	−15909.4	−2.09784
$387$	−4868.64	−0.639501
$388$	7218.94	0.944552
$389$	−4367.15	−0.569212	−0.284606	−	0.958645i	$-0.591863\pi$
$389$	−4367.15	−0.569212	−0.284606	+	0.958645i	$0.591863\pi$
$390$	4643.51	0.602906
$391$	1734.99	0.224404
$392$	−5650.18	−0.728003
$393$	482.758	0.0619642
$394$	−10242.8	−1.30971
$395$	−3988.37	−0.508042
$396$	5926.44	0.752058
$397$	1632.74	0.206410	0.103205	−	0.994660i	$-0.467090\pi$
$397$	1632.74	0.206410	0.103205	+	0.994660i	$0.467090\pi$
$398$	−12469.0	−1.57038
$399$	76.5032	0.00959887
$400$	1315.37	0.164421
$401$	5028.65	0.626232	0.313116	−	0.949715i	$-0.398627\pi$
$401$	5028.65	0.626232	0.313116	+	0.949715i	$0.398627\pi$
$402$	−6355.85	−0.788559
$403$	22578.8	2.79090
$404$	4828.74	0.594651
$405$	−2925.32	−0.358915
$406$	−677.942	−0.0828712
$407$	6305.23	0.767908
$408$	−386.322	−0.0468770
$409$	−2497.21	−0.301904	−0.150952	−	0.988541i	$-0.548234\pi$
$409$	−2497.21	−0.301904	−0.150952	+	0.988541i	$0.548234\pi$
$410$	5393.19	0.649635
$411$	4720.82	0.566572
$412$	−16063.3	−1.92082
$413$	548.477	0.0653482
$414$	−16008.5	−1.90042
$415$	−5166.90	−0.611164
$416$	−17910.9	−2.11095
$417$	−806.239	−0.0946803
$418$	725.854	0.0849347
$419$	12909.4	1.50517	0.752585	−	0.658496i	$-0.228807\pi$
$419$	12909.4	1.50517	0.752585	+	0.658496i	$0.228807\pi$
$420$	780.433	0.0906696
$421$	−4019.30	−0.465293	−0.232647	−	0.972561i	$-0.574739\pi$
$421$	−4019.30	−0.465293	−0.232647	+	0.972561i	$0.574739\pi$
$422$	2810.65	0.324219
$423$	12925.4	1.48571
$424$	−5753.76	−0.659027
$425$	−933.118	−0.106501
$426$	4339.86	0.493585
$427$	2426.56	0.275010
$428$	6007.03	0.678413
$429$	3360.39	0.378185
$430$	−6083.02	−0.682208
$431$	8768.94	0.980012	0.490006	−	0.871719i	$-0.336995\pi$
$431$	8768.94	0.980012	0.490006	+	0.871719i	$0.336995\pi$
$432$	−1532.52	−0.170679
$433$	4496.26	0.499021	0.249511	−	0.968372i	$-0.419730\pi$
$433$	4496.26	0.499021	0.249511	+	0.968372i	$0.419730\pi$
$434$	6324.26	0.699480
$435$	−360.762	−0.0397638
$436$	15300.2	1.68061
$437$	−1176.48	−0.128785
$438$	3.19559	0.000348610 0
$439$	−7316.62	−0.795451	−0.397725	−	0.917504i	$-0.630200\pi$
$439$	−7316.62	−0.795451	−0.397725	+	0.917504i	$0.630200\pi$
$440$	2469.06	0.267518
$441$	7377.11	0.796578
$442$	4228.13	0.455004
$443$	−12801.1	−1.37291	−0.686454	−	0.727173i	$-0.740834\pi$
$443$	−12801.1	−1.37291	−0.686454	+	0.727173i	$0.740834\pi$
$444$	6824.41	0.729442
$445$	2232.84	0.237858
$446$	610.204	0.0647847
$447$	2408.19	0.254818
$448$	−4349.08	−0.458649
$449$	6412.22	0.673968	0.336984	−	0.941510i	$-0.390593\pi$
$449$	6412.22	0.673968	0.336984	+	0.941510i	$0.390593\pi$
$450$	8609.75	0.901928
$451$	3902.91	0.407496
$452$	4024.02	0.418748
$453$	−6420.87	−0.665957
$454$	18696.5	1.93275
$455$	−2848.14	−0.293456
$456$	261.963	0.0269025
$457$	−2153.32	−0.220412	−0.110206	−	0.993909i	$-0.535151\pi$
$457$	−2153.32	−0.220412	−0.110206	+	0.993909i	$0.535151\pi$
$458$	−6050.89	−0.617336
$459$	1087.17	0.110555
$460$	−12001.7	−1.21648
$461$	−1850.55	−0.186960	−0.0934800	−	0.995621i	$-0.529799\pi$
$461$	−1850.55	−0.186960	−0.0934800	+	0.995621i	$0.529799\pi$
$462$	941.235	0.0947840
$463$	1892.04	0.189914	0.0949572	−	0.995481i	$-0.469729\pi$
$463$	1892.04	0.189914	0.0949572	+	0.995481i	$0.469729\pi$
$464$	463.056	0.0463293
$465$	3365.41	0.335628
$466$	9728.89	0.967129
$467$	−3739.40	−0.370533	−0.185267	−	0.982688i	$-0.559315\pi$
$467$	−3739.40	−0.370533	−0.185267	+	0.982688i	$0.559315\pi$
$468$	−23409.0	−2.31214
$469$	3898.41	0.383821
$470$	16149.4	1.58493
$471$	7028.61	0.687604
$472$	1878.10	0.183150
$473$	−4402.13	−0.427928
$474$	−5206.21	−0.504492
$475$	632.742	0.0611204
$476$	710.621	0.0684270
$477$	7512.35	0.721105
$478$	−20180.1	−1.93100
$479$	−7260.30	−0.692550	−0.346275	−	0.938133i	$-0.612554\pi$
$479$	−7260.30	−0.692550	−0.346275	+	0.938133i	$0.612554\pi$
$480$	−2669.65	−0.253859
$481$	−24905.2	−2.36087
$482$	8723.46	0.824363
$483$	−1525.58	−0.143719
$484$	−10616.1	−0.997008
$485$	−3926.77	−0.367640
$486$	−15408.3	−1.43813
$487$	4756.40	0.442573	0.221287	−	0.975209i	$-0.428974\pi$
$487$	4756.40	0.442573	0.221287	+	0.975209i	$0.428974\pi$
$488$	8309.05	0.770764
$489$	3764.88	0.348168
$490$	9217.18	0.849775
$491$	−2007.83	−0.184546	−0.0922730	−	0.995734i	$-0.529413\pi$
$491$	−2007.83	−0.184546	−0.0922730	+	0.995734i	$0.529413\pi$
$492$	4224.28	0.387084
$493$	−328.491	−0.0300091
$494$	−2867.07	−0.261125
$495$	−3223.71	−0.292717
$496$	−4319.66	−0.391046
$497$	−2661.89	−0.240246
$498$	−6744.61	−0.606894
$499$	−8952.55	−0.803149	−0.401574	−	0.915826i	$-0.631537\pi$
$499$	−8952.55	−0.803149	−0.401574	+	0.915826i	$0.631537\pi$
$500$	16249.3	1.45338
$501$	3064.86	0.273309
$502$	122.607	0.0109008
$503$	20564.9	1.82295	0.911477	−	0.411351i	$-0.134943\pi$
$503$	20564.9	1.82295	0.911477	+	0.411351i	$0.134943\pi$
$504$	−2186.34	−0.193229
$505$	−2626.61	−0.231451
$506$	−14474.6	−1.27168
$507$	−9086.94	−0.795987
$508$	9065.28	0.791746
$509$	13321.9	1.16008	0.580041	−	0.814587i	$-0.303036\pi$
$509$	13321.9	1.16008	0.580041	+	0.814587i	$0.303036\pi$
$510$	630.211	0.0547180
$511$	−1.96004	−0.000169681 0
$512$	5712.97	0.493125
$513$	−737.201	−0.0634468
$514$	19939.2	1.71105
$515$	8737.66	0.747626
$516$	−4764.60	−0.406492
$517$	11686.9	0.994176
$518$	−6975.87	−0.591703
$519$	−8471.24	−0.716467
$520$	−9752.62	−0.822462
$521$	−13047.0	−1.09712	−0.548558	−	0.836113i	$-0.684823\pi$
$521$	−13047.0	−1.09712	−0.548558	+	0.836113i	$0.684823\pi$
$522$	3030.94	0.254139
$523$	−20207.4	−1.68950	−0.844750	−	0.535161i	$-0.820251\pi$
$523$	−20207.4	−1.68950	−0.844750	+	0.535161i	$0.820251\pi$
$524$	−3040.73	−0.253502
$525$	820.494	0.0682082
$526$	20756.6	1.72059
$527$	3064.36	0.253294
$528$	−642.893	−0.0529892
$529$	11293.8	0.928228
$530$	9386.16	0.769262
$531$	−2452.13	−0.200402
$532$	−481.868	−0.0392700
$533$	−15416.2	−1.25281
$534$	2914.63	0.236196
$535$	−3267.55	−0.264053
$536$	13349.0	1.07572
$537$	−2784.58	−0.223768
$538$	−1051.10	−0.0842306
$539$	6670.23	0.533038
$540$	−7520.43	−0.599310
$541$	−17866.0	−1.41981	−0.709906	−	0.704297i	$-0.751263\pi$
$541$	−17866.0	−1.41981	−0.709906	+	0.704297i	$0.751263\pi$
$542$	17067.0	1.35256
$543$	−7221.08	−0.570693
$544$	−2430.84	−0.191583
$545$	−8322.59	−0.654129
$546$	−3717.81	−0.291406
$547$	−8027.79	−0.627502	−0.313751	−	0.949505i	$-0.601586\pi$
$547$	−8027.79	−0.627502	−0.313751	+	0.949505i	$0.601586\pi$
$548$	−29734.9	−2.31790
$549$	−10848.6	−0.843367
$550$	7784.76	0.603534
$551$	222.748	0.0172221
$552$	−5223.91	−0.402797
$553$	3193.27	0.245555
$554$	−9055.59	−0.694468
$555$	−3712.16	−0.283915
$556$	5078.23	0.387347
$557$	17357.6	1.32040	0.660201	−	0.751089i	$-0.270471\pi$
$557$	17357.6	1.32040	0.660201	+	0.751089i	$0.270471\pi$
$558$	−28274.5	−2.14508
$559$	17388.1	1.31563
$560$	544.891	0.0411176
$561$	456.067	0.0343229
$562$	24382.5	1.83009
$563$	−6073.90	−0.454679	−0.227340	−	0.973816i	$-0.573003\pi$
$563$	−6073.90	−0.454679	−0.227340	+	0.973816i	$0.573003\pi$
$564$	12649.2	0.944375
$565$	−2188.88	−0.162986
$566$	22481.7	1.66957
$567$	2342.15	0.173476
$568$	−9114.87	−0.673330
$569$	5084.04	0.374577	0.187288	−	0.982305i	$-0.440030\pi$
$569$	5084.04	0.374577	0.187288	+	0.982305i	$0.440030\pi$
$570$	−427.342	−0.0314024
$571$	15552.3	1.13983	0.569914	−	0.821704i	$-0.306976\pi$
$571$	15552.3	1.13983	0.569914	+	0.821704i	$0.306976\pi$
$572$	−21166.0	−1.54719
$573$	9112.24	0.664344
$574$	−4318.03	−0.313992
$575$	−12617.8	−0.915125
$576$	19443.9	1.40653
$577$	−20714.3	−1.49454	−0.747269	−	0.664521i	$-0.768635\pi$
$577$	−20714.3	−1.49454	−0.747269	+	0.664521i	$0.768635\pi$
$578$	−21398.9	−1.53992
$579$	6778.34	0.486526
$580$	2272.32	0.162678
$581$	4136.86	0.295397
$582$	−5125.80	−0.365071
$583$	6792.52	0.482534
$584$	−6.71159	−0.000475561 0
$585$	12733.4	0.899936
$586$	27551.3	1.94221
$587$	−1015.03	−0.0713711	−0.0356856	−	0.999363i	$-0.511361\pi$
$587$	−1015.03	−0.0713711	−0.0356856	+	0.999363i	$0.511361\pi$
$588$	7219.47	0.506337
$589$	−2077.93	−0.145364
$590$	−3063.76	−0.213785
$591$	4364.03	0.303744
$592$	4764.74	0.330793
$593$	3831.39	0.265323	0.132661	−	0.991161i	$-0.457648\pi$
$593$	3831.39	0.265323	0.132661	+	0.991161i	$0.457648\pi$
$594$	−9069.95	−0.626506
$595$	−386.545	−0.0266333
$596$	−15168.4	−1.04249
$597$	5312.50	0.364198
$598$	57173.4	3.90969
$599$	−16703.5	−1.13938	−0.569688	−	0.821861i	$-0.692936\pi$
$599$	−16703.5	−1.13938	−0.569688	+	0.821861i	$0.692936\pi$
$600$	2809.54	0.191165
$601$	17781.6	1.20686	0.603432	−	0.797414i	$-0.293799\pi$
$601$	17781.6	1.20686	0.603432	+	0.797414i	$0.293799\pi$
$602$	4870.35	0.329735
$603$	−17429.0	−1.17705
$604$	40442.9	2.72450
$605$	5774.69	0.388057
$606$	−3428.65	−0.229834
$607$	7610.08	0.508869	0.254435	−	0.967090i	$-0.418111\pi$
$607$	7610.08	0.508869	0.254435	+	0.967090i	$0.418111\pi$
$608$	1648.34	0.109949
$609$	288.843	0.0192192
$610$	−13554.6	−0.899689
$611$	−46162.4	−3.05651
$612$	−3177.04	−0.209843
$613$	4207.29	0.277212	0.138606	−	0.990348i	$-0.455738\pi$
$613$	4207.29	0.277212	0.138606	+	0.990348i	$0.455738\pi$
$614$	−19363.3	−1.27270
$615$	−2297.81	−0.150661
$616$	−1976.85	−0.129301
$617$	28539.4	1.86216	0.931082	−	0.364810i	$-0.118866\pi$
$617$	28539.4	1.86216	0.931082	+	0.364810i	$0.118866\pi$
$618$	11405.7	0.742402
$619$	16799.9	1.09086	0.545432	−	0.838155i	$-0.316366\pi$
$619$	16799.9	1.09086	0.545432	+	0.838155i	$0.316366\pi$
$620$	−21197.6	−1.37309
$621$	14700.8	0.949958
$622$	−28676.0	−1.84856
$623$	−1787.71	−0.114965
$624$	2539.38	0.162911
$625$	1458.39	0.0933369
$626$	−87.3288	−0.00557565
$627$	−309.256	−0.0196978
$628$	−44270.9	−2.81306
$629$	−3380.10	−0.214266
$630$	3566.59	0.225550
$631$	−16207.1	−1.02249	−0.511247	−	0.859434i	$-0.670816\pi$
$631$	−16207.1	−1.02249	−0.511247	+	0.859434i	$0.670816\pi$
$632$	10934.4	0.688210
$633$	−1197.50	−0.0751919
$634$	−36664.9	−2.29677
$635$	−4931.09	−0.308164
$636$	7351.83	0.458363
$637$	−26346.9	−1.63878
$638$	2740.51	0.170060
$639$	11900.8	0.736756
$640$	13085.5	0.808202
$641$	10697.0	0.659133	0.329567	−	0.944132i	$-0.393097\pi$
$641$	10697.0	0.659133	0.329567	+	0.944132i	$0.393097\pi$
$642$	−4265.29	−0.262208
$643$	7901.34	0.484601	0.242300	−	0.970201i	$-0.422098\pi$
$643$	7901.34	0.484601	0.242300	+	0.970201i	$0.422098\pi$
$644$	9609.12	0.587969
$645$	2591.72	0.158216
$646$	−389.115	−0.0236989
$647$	−312.370	−0.0189807	−0.00949036	−	0.999955i	$-0.503021\pi$
$647$	−312.370	−0.0189807	−0.00949036	+	0.999955i	$0.503021\pi$
$648$	8020.01	0.486197
$649$	−2217.17	−0.134101
$650$	−30749.3	−1.85552
$651$	−2694.50	−0.162221
$652$	−23713.7	−1.42439
$653$	13732.3	0.822950	0.411475	−	0.911421i	$-0.365014\pi$
$653$	13732.3	0.822950	0.411475	+	0.911421i	$0.365014\pi$
$654$	−10863.9	−0.649559
$655$	1654.02	0.0986684
$656$	2949.35	0.175538
$657$	8.76293	0.000520357 0
$658$	−12929.9	−0.766051
$659$	19869.0	1.17449	0.587244	−	0.809410i	$-0.300213\pi$
$659$	19869.0	1.17449	0.587244	+	0.809410i	$0.300213\pi$
$660$	−3154.82	−0.186063
$661$	−11047.2	−0.650057	−0.325029	−	0.945704i	$-0.605374\pi$
$661$	−11047.2	−0.650057	−0.325029	+	0.945704i	$0.605374\pi$
$662$	10619.5	0.623470
$663$	−1801.43	−0.105523
$664$	14165.5	0.827902
$665$	262.114	0.0152847
$666$	31187.7	1.81456
$667$	−4441.90	−0.257858
$668$	−19304.5	−1.11814
$669$	−259.983	−0.0150247
$670$	−21776.3	−1.25566
$671$	−9809.12	−0.564347
$672$	2137.45	0.122699
$673$	−25673.8	−1.47051	−0.735253	−	0.677793i	$-0.762937\pi$
$673$	−25673.8	−1.47051	−0.735253	+	0.677793i	$0.762937\pi$
$674$	−22296.2	−1.27421
$675$	−7906.46	−0.450844
$676$	57235.6	3.25646
$677$	4268.79	0.242338	0.121169	−	0.992632i	$-0.461336\pi$
$677$	4268.79	0.242338	0.121169	+	0.992632i	$0.461336\pi$
$678$	−2857.25	−0.161847
$679$	3143.95	0.177693
$680$	−1323.61	−0.0746443
$681$	−7965.79	−0.448238
$682$	−25565.2	−1.43540
$683$	7370.85	0.412940	0.206470	−	0.978453i	$-0.433802\pi$
$683$	7370.85	0.412940	0.206470	+	0.978453i	$0.433802\pi$
$684$	2154.33	0.120428
$685$	16174.4	0.902178
$686$	−15398.1	−0.857001
$687$	2578.04	0.143171
$688$	−3326.60	−0.184339
$689$	−26830.0	−1.48351
$690$	8521.80	0.470173
$691$	2112.00	0.116272	0.0581361	−	0.998309i	$-0.481484\pi$
$691$	2112.00	0.116272	0.0581361	+	0.998309i	$0.481484\pi$
$692$	53357.5	2.93114
$693$	2581.05	0.141481
$694$	−9051.97	−0.495113
$695$	−2762.32	−0.150764
$696$	989.059	0.0538652
$697$	−2092.27	−0.113702
$698$	−11860.6	−0.643169
$699$	−4145.08	−0.224294
$700$	−5168.02	−0.279047
$701$	20945.5	1.12853	0.564266	−	0.825593i	$-0.309159\pi$
$701$	20945.5	1.12853	0.564266	+	0.825593i	$0.309159\pi$
$702$	35825.6	1.92614
$703$	2292.02	0.122966
$704$	17580.7	0.941192
$705$	−6880.58	−0.367571
$706$	−7733.71	−0.412269
$707$	2102.99	0.111868
$708$	−2399.73	−0.127383
$709$	7826.11	0.414550	0.207275	−	0.978283i	$-0.433541\pi$
$709$	7826.11	0.414550	0.207275	+	0.978283i	$0.433541\pi$
$710$	14869.2	0.785958
$711$	−14276.5	−0.753037
$712$	−6121.51	−0.322210
$713$	41436.8	2.17646
$714$	−504.576	−0.0264472
$715$	11513.3	0.602200
$716$	17539.1	0.915459
$717$	8597.91	0.447831
$718$	30749.2	1.59826
$719$	23373.7	1.21237	0.606183	−	0.795325i	$-0.292700\pi$
$719$	23373.7	1.21237	0.606183	+	0.795325i	$0.292700\pi$
$720$	−2436.09	−0.126094
$721$	−6995.78	−0.361354
$722$	−30412.1	−1.56762
$723$	−3716.71	−0.191184
$724$	45483.2	2.33476
$725$	2388.96	0.122378
$726$	7537.98	0.385345
$727$	31240.8	1.59375	0.796875	−	0.604145i	$-0.206485\pi$
$727$	31240.8	1.59375	0.796875	+	0.604145i	$0.206485\pi$
$728$	7808.40	0.397525
$729$	−5533.38	−0.281125
$730$	10.9487	0.000555107 0
$731$	2359.88	0.119403
$732$	−10616.8	−0.536078
$733$	−4426.59	−0.223056	−0.111528	−	0.993761i	$-0.535574\pi$
$733$	−4426.59	−0.223056	−0.111528	+	0.993761i	$0.535574\pi$
$734$	−33252.7	−1.67218
$735$	−3927.06	−0.197077
$736$	−32870.2	−1.64621
$737$	−15758.9	−0.787636
$738$	19305.0	0.962911
$739$	−32119.5	−1.59883	−0.799414	−	0.600781i	$-0.794856\pi$
$739$	−32119.5	−1.59883	−0.799414	+	0.600781i	$0.794856\pi$
$740$	23381.7	1.16152
$741$	1221.54	0.0605593
$742$	−7514.99	−0.371811
$743$	−19215.0	−0.948763	−0.474382	−	0.880319i	$-0.657328\pi$
$743$	−19215.0	−0.948763	−0.474382	+	0.880319i	$0.657328\pi$
$744$	−9226.55	−0.454653
$745$	8250.91	0.405758
$746$	6250.02	0.306742
$747$	−18495.0	−0.905888
$748$	−2872.61	−0.140419
$749$	2616.15	0.127626
$750$	−11537.8	−0.561735
$751$	3593.57	0.174609	0.0873045	−	0.996182i	$-0.472175\pi$
$751$	3593.57	0.174609	0.0873045	+	0.996182i	$0.472175\pi$
$752$	8831.55	0.428263
$753$	−52.2377	−0.00252808
$754$	−10824.8	−0.522835
$755$	−21999.1	−1.06043
$756$	6021.20	0.289668
$757$	−32956.7	−1.58234	−0.791169	−	0.611598i	$-0.790527\pi$
$757$	−32956.7	−1.58234	−0.791169	+	0.611598i	$0.790527\pi$
$758$	31349.4	1.50219
$759$	6167.01	0.294925
$760$	897.532	0.0428381
$761$	15689.7	0.747373	0.373687	−	0.927555i	$-0.378094\pi$
$761$	15689.7	0.747373	0.373687	+	0.927555i	$0.378094\pi$
$762$	−6436.80	−0.306011
$763$	6663.45	0.316164
$764$	−57394.9	−2.71790
$765$	1728.16	0.0816756
$766$	−52455.0	−2.47425
$767$	8757.64	0.412282
$768$	4397.69	0.206625
$769$	2134.77	0.100106	0.0500532	−	0.998747i	$-0.484061\pi$
$769$	2134.77	0.100106	0.0500532	+	0.998747i	$0.484061\pi$
$770$	3224.84	0.150929
$771$	−8495.25	−0.396821
$772$	−42694.5	−1.99043
$773$	14780.2	0.687721	0.343861	−	0.939021i	$-0.388265\pi$
$773$	14780.2	0.687721	0.343861	+	0.939021i	$0.388265\pi$
$774$	−21774.3	−1.01119
$775$	−22285.7	−1.03294
$776$	10765.6	0.498017
$777$	2972.13	0.137226
$778$	−19531.5	−0.900049
$779$	1418.75	0.0652530
$780$	12461.3	0.572035
$781$	10760.4	0.493007
$782$	7759.49	0.354832
$783$	−2783.36	−0.127036
$784$	5040.56	0.229618
$785$	24081.3	1.09490
$786$	2159.07	0.0979790
$787$	35525.7	1.60909	0.804545	−	0.593892i	$-0.202409\pi$
$787$	35525.7	1.60909	0.804545	+	0.593892i	$0.202409\pi$
$788$	−27487.6	−1.24265
$789$	−8843.53	−0.399034
$790$	−17837.4	−0.803326
$791$	1752.52	0.0787768
$792$	8838.07	0.396524
$793$	38745.3	1.73504
$794$	7302.21	0.326380
$795$	−3999.05	−0.178405
$796$	−33461.7	−1.48997
$797$	2190.00	0.0973321	0.0486660	−	0.998815i	$-0.484503\pi$
$797$	2190.00	0.0973321	0.0486660	+	0.998815i	$0.484503\pi$
$798$	342.150	0.0151779
$799$	−6265.09	−0.277400
$800$	17678.4	0.781281
$801$	7992.50	0.352561
$802$	22490.0	0.990210
$803$	7.92326	0.000348202 0
$804$	−17056.6	−0.748182
$805$	−5226.91	−0.228850
$806$	100981.	4.41302
$807$	447.830	0.0195345
$808$	7201.07	0.313531
$809$	21464.6	0.932824	0.466412	−	0.884568i	$-0.345546\pi$
$809$	21464.6	0.932824	0.466412	+	0.884568i	$0.345546\pi$
$810$	−13083.1	−0.567523
$811$	−32288.8	−1.39804	−0.699021	−	0.715101i	$-0.746380\pi$
$811$	−32288.8	−1.39804	−0.699021	+	0.715101i	$0.746380\pi$
$812$	−1819.33	−0.0786279
$813$	−7271.52	−0.313682
$814$	28199.3	1.21423
$815$	12899.2	0.554403
$816$	344.641	0.0147853
$817$	−1600.22	−0.0685248
$818$	−11168.4	−0.477377
$819$	−10195.0	−0.434971
$820$	14473.2	0.616371
$821$	−40334.4	−1.71459	−0.857296	−	0.514825i	$-0.827857\pi$
$821$	−40334.4	−1.71459	−0.857296	+	0.514825i	$0.827857\pi$
$822$	21113.2	0.895874
$823$	8188.53	0.346822	0.173411	−	0.984850i	$-0.444521\pi$
$823$	8188.53	0.346822	0.173411	+	0.984850i	$0.444521\pi$
$824$	−23955.0	−1.01276
$825$	−3316.77	−0.139970
$826$	2452.99	0.103330
$827$	−7630.74	−0.320855	−0.160427	−	0.987048i	$-0.551287\pi$
$827$	−7630.74	−0.320855	−0.160427	+	0.987048i	$0.551287\pi$
$828$	−42960.4	−1.80311
$829$	12637.7	0.529462	0.264731	−	0.964322i	$-0.414717\pi$
$829$	12637.7	0.529462	0.264731	+	0.964322i	$0.414717\pi$
$830$	−23108.3	−0.966385
$831$	3858.21	0.161059
$832$	−69442.7	−2.89362
$833$	−3575.77	−0.148731
$834$	−3605.79	−0.149710
$835$	10500.8	0.435203
$836$	1947.90	0.0805857
$837$	25964.8	1.07225
$838$	57735.6	2.38000
$839$	24059.1	0.990005	0.495002	−	0.868892i	$-0.335167\pi$
$839$	24059.1	0.990005	0.495002	+	0.868892i	$0.335167\pi$
$840$	1163.85	0.0478057
$841$	841.000	0.0344828
$842$	−17975.8	−0.735731
$843$	−10388.4	−0.424430
$844$	7542.67	0.307618
$845$	−31133.5	−1.26749
$846$	57807.1	2.34923
$847$	−4623.48	−0.187562
$848$	5132.97	0.207862
$849$	−9578.51	−0.387201
$850$	−4173.24	−0.168401
$851$	−45706.2	−1.84111
$852$	11646.5	0.468311
$853$	−18588.4	−0.746138	−0.373069	−	0.927804i	$-0.621695\pi$
$853$	−18588.4	−0.746138	−0.373069	+	0.927804i	$0.621695\pi$
$854$	10852.5	0.434852
$855$	−1171.86	−0.0468733
$856$	8958.25	0.357695
$857$	28616.2	1.14062	0.570310	−	0.821430i	$-0.306823\pi$
$857$	28616.2	1.14062	0.570310	+	0.821430i	$0.306823\pi$
$858$	15028.9	0.597993
$859$	−31968.9	−1.26981	−0.634904	−	0.772591i	$-0.718960\pi$
$859$	−31968.9	−1.26981	−0.634904	+	0.772591i	$0.718960\pi$
$860$	−16324.4	−0.647276
$861$	1839.74	0.0728200
$862$	39217.9	1.54961
$863$	15417.8	0.608145	0.304072	−	0.952649i	$-0.401654\pi$
$863$	15417.8	0.608145	0.304072	+	0.952649i	$0.401654\pi$
$864$	−20596.9	−0.811019
$865$	−29024.0	−1.14086
$866$	20108.9	0.789062
$867$	9117.18	0.357135
$868$	16971.8	0.663663
$869$	−12908.5	−0.503902
$870$	−1613.46	−0.0628752
$871$	62246.7	2.42153
$872$	22817.0	0.886104
$873$	−14056.0	−0.544928
$874$	−5261.67	−0.203637
$875$	7076.80	0.273417
$876$	8.57568	0.000330759 0
$877$	−41961.0	−1.61565	−0.807824	−	0.589424i	$-0.799355\pi$
$877$	−41961.0	−1.61565	−0.807824	+	0.589424i	$0.799355\pi$
$878$	−32722.6	−1.25778
$879$	−11738.5	−0.450430
$880$	−2202.67	−0.0843772
$881$	−22884.6	−0.875145	−0.437573	−	0.899183i	$-0.644162\pi$
$881$	−22884.6	−0.875145	−0.437573	+	0.899183i	$0.644162\pi$
$882$	32993.1	1.25956
$883$	29611.7	1.12855	0.564277	−	0.825585i	$-0.309155\pi$
$883$	29611.7	1.12855	0.564277	+	0.825585i	$0.309155\pi$
$884$	11346.6	0.431706
$885$	1305.34	0.0495803
$886$	−57251.1	−2.17087
$887$	27117.7	1.02652	0.513259	−	0.858234i	$-0.328438\pi$
$887$	27117.7	1.02652	0.513259	+	0.858234i	$0.328438\pi$
$888$	10177.2	0.384600
$889$	3948.06	0.148947
$890$	9986.06	0.376105
$891$	−9467.91	−0.355990
$892$	1637.54	0.0614675
$893$	4248.32	0.159199
$894$	10770.3	0.402923
$895$	−9540.48	−0.356316
$896$	−10476.8	−0.390633
$897$	−24359.2	−0.906724
$898$	28677.8	1.06569
$899$	−7845.36	−0.291054
$900$	23105.1	0.855746
$901$	−3641.32	−0.134639
$902$	17455.2	0.644341
$903$	−2075.05	−0.0764712
$904$	6001.00	0.220786
$905$	−24740.7	−0.908740
$906$	−28716.5	−1.05302
$907$	10010.9	0.366491	0.183245	−	0.983067i	$-0.441340\pi$
$907$	10010.9	0.366491	0.183245	+	0.983067i	$0.441340\pi$
$908$	50173.9	1.83379
$909$	−9402.02	−0.343064
$910$	−12737.9	−0.464019
$911$	40394.1	1.46906	0.734532	−	0.678575i	$-0.237402\pi$
$911$	40394.1	1.46906	0.734532	+	0.678575i	$0.237402\pi$
$912$	−233.699	−0.00848525
$913$	−16722.8	−0.606183
$914$	−9630.44	−0.348519
$915$	5775.06	0.208653
$916$	−16238.2	−0.585725
$917$	−1324.28	−0.0476899
$918$	4862.20	0.174811
$919$	2392.98	0.0858945	0.0429472	−	0.999077i	$-0.486325\pi$
$919$	2392.98	0.0858945	0.0429472	+	0.999077i	$0.486325\pi$
$920$	−17898.1	−0.641393
$921$	8249.89	0.295161
$922$	−8276.32	−0.295625
$923$	−42502.9	−1.51571
$924$	2525.90	0.0899307
$925$	24581.9	0.873781
$926$	8461.87	0.300296
$927$	31276.7	1.10816
$928$	6223.42	0.220144
$929$	−21920.3	−0.774148	−0.387074	−	0.922049i	$-0.626514\pi$
$929$	−21920.3	−0.774148	−0.387074	+	0.922049i	$0.626514\pi$
$930$	15051.3	0.530702
$931$	2424.71	0.0853562
$932$	26108.5	0.917608
$933$	12217.7	0.428712
$934$	−16724.0	−0.585894
$935$	1562.57	0.0546540
$936$	−34909.7	−1.21908
$937$	4891.90	0.170556	0.0852782	−	0.996357i	$-0.472822\pi$
$937$	4891.90	0.170556	0.0852782	+	0.996357i	$0.472822\pi$
$938$	17435.1	0.606905
$939$	37.2072	0.00129309
$940$	43338.5	1.50377
$941$	−40152.3	−1.39100	−0.695499	−	0.718527i	$-0.744817\pi$
$941$	−40152.3	−1.39100	−0.695499	+	0.718527i	$0.744817\pi$
$942$	31434.5	1.08725
$943$	−28291.9	−0.977001
$944$	−1675.47	−0.0577668
$945$	−3275.26	−0.112745
$946$	−19687.9	−0.676648
$947$	−16057.5	−0.551002	−0.275501	−	0.961301i	$-0.588844\pi$
$947$	−16057.5	−0.551002	−0.275501	+	0.961301i	$0.588844\pi$
$948$	−13971.4	−0.478660
$949$	−31.2963	−0.00107052
$950$	2829.85	0.0966448
$951$	15621.4	0.532659
$952$	1059.74	0.0360783
$953$	−21912.3	−0.744815	−0.372408	−	0.928069i	$-0.621468\pi$
$953$	−21912.3	−0.744815	−0.372408	+	0.928069i	$0.621468\pi$
$954$	33598.0	1.14023
$955$	31220.2	1.05787
$956$	−54155.4	−1.83212
$957$	−1167.62	−0.0394397
$958$	−32470.7	−1.09507
$959$	−12950.0	−0.436055
$960$	−10350.6	−0.347982
$961$	43395.3	1.45666
$962$	−111385.	−3.73306
$963$	−11696.3	−0.391388
$964$	23410.3	0.782152
$965$	23223.8	0.774717
$966$	−6822.95	−0.227251
$967$	17618.1	0.585895	0.292948	−	0.956129i	$-0.405364\pi$
$967$	17618.1	0.585895	0.292948	+	0.956129i	$0.405364\pi$
$968$	−15831.8	−0.525674
$969$	165.786	0.00549619
$970$	−17561.9	−0.581319
$971$	24152.9	0.798252	0.399126	−	0.916896i	$-0.369314\pi$
$971$	24152.9	0.798252	0.399126	+	0.916896i	$0.369314\pi$
$972$	−41349.6	−1.36449
$973$	2211.64	0.0728694
$974$	21272.4	0.699805
$975$	13101.0	0.430325
$976$	−7412.56	−0.243105
$977$	−43754.7	−1.43279	−0.716395	−	0.697695i	$-0.754209\pi$
$977$	−43754.7	−1.43279	−0.716395	+	0.697695i	$0.754209\pi$
$978$	16837.9	0.550529
$979$	7226.66	0.235919
$980$	24735.2	0.806263
$981$	−29790.9	−0.969572
$982$	−8979.74	−0.291808
$983$	−51651.4	−1.67591	−0.837957	−	0.545736i	$-0.816250\pi$
$983$	−51651.4	−1.67591	−0.837957	+	0.545736i	$0.816250\pi$
$984$	6299.64	0.204091
$985$	14952.0	0.483665
$986$	−1469.13	−0.0474510
$987$	5508.91	0.177660
$988$	−7694.08	−0.247754
$989$	31910.7	1.02599
$990$	−14417.6	−0.462850
$991$	23894.0	0.765911	0.382956	−	0.923767i	$-0.374906\pi$
$991$	23894.0	0.765911	0.382956	+	0.923767i	$0.374906\pi$
$992$	−58055.8	−1.85814
$993$	−4524.51	−0.144593
$994$	−11904.9	−0.379881
$995$	18201.6	0.579929
$996$	−18099.8	−0.575818
$997$	5951.47	0.189052	0.0945261	−	0.995522i	$-0.469866\pi$
$997$	5951.47	0.189052	0.0945261	+	0.995522i	$0.469866\pi$
$998$	−40039.1	−1.26995
$999$	−28640.1	−0.907040

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.4.a.b.1.5	✓	5
3.2	odd	2		261.4.a.f.1.1		5
4.3	odd	2		464.4.a.l.1.4		5
5.4	even	2		725.4.a.c.1.1		5
7.6	odd	2		1421.4.a.e.1.5		5
8.3	odd	2		1856.4.a.bb.1.2		5
8.5	even	2		1856.4.a.y.1.4		5
29.28	even	2		841.4.a.b.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.4.a.b.1.5	✓	5	1.1	even	1	trivial
261.4.a.f.1.1		5	3.2	odd	2
464.4.a.l.1.4		5	4.3	odd	2
725.4.a.c.1.1		5	5.4	even	2
841.4.a.b.1.1		5	29.28	even	2
1421.4.a.e.1.5		5	7.6	odd	2
1856.4.a.y.1.4		5	8.5	even	2
1856.4.a.bb.1.2		5	8.3	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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+4.47236 q^{2} -1.90549 q^{3} +12.0020 q^{4} -6.52855 q^{5} -8.52204 q^{6} +5.22706 q^{7} +17.8986 q^{8} -23.3691 q^{9} +O(q^{10})\)	\(q+4.47236 q^{2} -1.90549 q^{3} +12.0020 q^{4} -6.52855 q^{5} -8.52204 q^{6} +5.22706 q^{7} +17.8986 q^{8} -23.3691 q^{9} -29.1981 q^{10} -21.1299 q^{11} -22.8697 q^{12} +83.4615 q^{13} +23.3773 q^{14} +12.4401 q^{15} -15.9674 q^{16} +11.3273 q^{17} -104.515 q^{18} -7.68096 q^{19} -78.3559 q^{20} -9.96011 q^{21} -94.5005 q^{22} +153.169 q^{23} -34.1055 q^{24} -82.3780 q^{25} +373.270 q^{26} +95.9778 q^{27} +62.7354 q^{28} -29.0000 q^{29} +55.6366 q^{30} +270.530 q^{31} -214.601 q^{32} +40.2628 q^{33} +50.6597 q^{34} -34.1251 q^{35} -280.477 q^{36} -298.404 q^{37} -34.3520 q^{38} -159.035 q^{39} -116.852 q^{40} -184.710 q^{41} -44.5452 q^{42} +208.337 q^{43} -253.602 q^{44} +152.566 q^{45} +685.028 q^{46} -553.098 q^{47} +30.4258 q^{48} -315.678 q^{49} -368.424 q^{50} -21.5840 q^{51} +1001.71 q^{52} -321.465 q^{53} +429.248 q^{54} +137.948 q^{55} +93.5569 q^{56} +14.6360 q^{57} -129.699 q^{58} +104.930 q^{59} +149.306 q^{60} +464.230 q^{61} +1209.91 q^{62} -122.152 q^{63} -832.032 q^{64} -544.883 q^{65} +180.070 q^{66} +745.813 q^{67} +135.950 q^{68} -291.862 q^{69} -152.620 q^{70} -509.252 q^{71} -418.273 q^{72} -0.374979 q^{73} -1334.57 q^{74} +156.970 q^{75} -92.1871 q^{76} -110.447 q^{77} -711.262 q^{78} +610.912 q^{79} +104.244 q^{80} +448.081 q^{81} -826.092 q^{82} +791.431 q^{83} -119.542 q^{84} -73.9507 q^{85} +931.757 q^{86} +55.2592 q^{87} -378.194 q^{88} -342.011 q^{89} +682.333 q^{90} +436.258 q^{91} +1838.34 q^{92} -515.491 q^{93} -2473.65 q^{94} +50.1455 q^{95} +408.919 q^{96} +601.476 q^{97} -1411.83 q^{98} +493.787 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 8 q^{3} + 26 q^{4} + 10 q^{5} + 34 q^{6} + 40 q^{7} - 84 q^{8} + 33 q^{9}+O(q^{10}) \) 5 * q + 8 * q^3 + 26 * q^4 + 10 * q^5 + 34 * q^6 + 40 * q^7 - 84 * q^8 + 33 * q^9	\( 5 q + 8 q^{3} + 26 q^{4} + 10 q^{5} + 34 q^{6} + 40 q^{7} - 84 q^{8} + 33 q^{9} - 64 q^{10} + 12 q^{11} - 224 q^{12} + 14 q^{13} - 192 q^{14} - 74 q^{15} + 146 q^{16} + 66 q^{17} - 108 q^{18} + 214 q^{19} + 6 q^{20} - 98 q^{22} + 164 q^{23} + 314 q^{24} + 207 q^{25} + 56 q^{26} + 362 q^{27} + 540 q^{28} - 145 q^{29} - 234 q^{30} + 420 q^{31} - 652 q^{32} - 576 q^{33} + 204 q^{34} - 52 q^{35} - 260 q^{36} + 378 q^{37} - 496 q^{38} - 374 q^{39} - 80 q^{40} - 1158 q^{41} + 348 q^{42} - 204 q^{43} + 784 q^{44} - 1506 q^{45} + 580 q^{46} + 248 q^{47} - 1880 q^{48} - 283 q^{49} + 908 q^{50} + 228 q^{51} + 1482 q^{52} - 554 q^{53} + 918 q^{54} + 546 q^{55} - 608 q^{56} + 44 q^{57} + 440 q^{59} + 636 q^{60} + 618 q^{61} + 1250 q^{62} + 804 q^{63} + 2594 q^{64} - 1656 q^{65} + 2940 q^{66} + 1164 q^{67} + 356 q^{68} - 1968 q^{69} - 2184 q^{70} - 692 q^{71} - 2648 q^{72} - 1950 q^{73} - 1832 q^{74} + 3074 q^{75} + 1376 q^{76} - 1616 q^{77} - 1302 q^{78} + 272 q^{79} - 890 q^{80} + 1801 q^{81} + 92 q^{82} + 512 q^{83} - 3208 q^{84} - 1628 q^{85} + 2446 q^{86} - 232 q^{87} - 6954 q^{88} + 866 q^{89} - 2200 q^{90} + 2580 q^{91} + 3468 q^{92} - 40 q^{93} - 5942 q^{94} + 2244 q^{95} + 7386 q^{96} + 1562 q^{97} - 3408 q^{98} - 238 q^{99}+O(q^{100}) \) 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 - 145 * q^29 - 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 - 232 * q^87 - 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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