LMFDB - Embedded newform 2013.4.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,4,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2013.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:	$118.770844842$
Analytic rank:	$1$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.85102 q^{2} -3.00000 q^{3} +15.5324 q^{4} -6.76910 q^{5} +14.5530 q^{6} -14.4227 q^{7} -36.5396 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.85102 q^{2} -3.00000 q^{3} +15.5324 q^{4} -6.76910 q^{5} +14.5530 q^{6} -14.4227 q^{7} -36.5396 q^{8} +9.00000 q^{9} +32.8370 q^{10} +11.0000 q^{11} -46.5971 q^{12} +89.5149 q^{13} +69.9648 q^{14} +20.3073 q^{15} +52.9953 q^{16} +75.6637 q^{17} -43.6591 q^{18} -53.1971 q^{19} -105.140 q^{20} +43.2681 q^{21} -53.3612 q^{22} -60.1792 q^{23} +109.619 q^{24} -79.1792 q^{25} -434.238 q^{26} -27.0000 q^{27} -224.019 q^{28} +99.6268 q^{29} -98.5111 q^{30} -238.729 q^{31} +35.2357 q^{32} -33.0000 q^{33} -367.046 q^{34} +97.6288 q^{35} +139.791 q^{36} -17.6324 q^{37} +258.060 q^{38} -268.545 q^{39} +247.340 q^{40} +140.856 q^{41} -209.894 q^{42} +4.39867 q^{43} +170.856 q^{44} -60.9219 q^{45} +291.930 q^{46} -582.557 q^{47} -158.986 q^{48} -134.986 q^{49} +384.100 q^{50} -226.991 q^{51} +1390.38 q^{52} -2.72271 q^{53} +130.977 q^{54} -74.4601 q^{55} +527.000 q^{56} +159.591 q^{57} -483.291 q^{58} +518.109 q^{59} +315.420 q^{60} -61.0000 q^{61} +1158.08 q^{62} -129.804 q^{63} -594.891 q^{64} -605.936 q^{65} +160.084 q^{66} +347.266 q^{67} +1175.24 q^{68} +180.538 q^{69} -473.599 q^{70} +563.974 q^{71} -328.856 q^{72} +392.009 q^{73} +85.5352 q^{74} +237.538 q^{75} -826.276 q^{76} -158.650 q^{77} +1302.71 q^{78} +180.030 q^{79} -358.731 q^{80} +81.0000 q^{81} -683.294 q^{82} -139.672 q^{83} +672.056 q^{84} -512.176 q^{85} -21.3380 q^{86} -298.881 q^{87} -401.936 q^{88} +438.719 q^{89} +295.533 q^{90} -1291.05 q^{91} -934.725 q^{92} +716.186 q^{93} +2825.99 q^{94} +360.097 q^{95} -105.707 q^{96} -1452.37 q^{97} +654.817 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9}+O(q^{10}) $ 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9} - 45 q^{10} + 407 q^{11} - 474 q^{12} - 169 q^{13} + 102 q^{14} + 45 q^{15} + 598 q^{16} - 338 q^{17} - 36 q^{18} - 235 q^{19} - 550 q^{20} + 231 q^{21} - 44 q^{22} - 53 q^{23} + 207 q^{24} + 750 q^{25} - 75 q^{26} - 999 q^{27} - 1378 q^{28} - 30 q^{29} + 135 q^{30} - 506 q^{31} - 841 q^{32} - 1221 q^{33} - 316 q^{34} - 822 q^{35} + 1422 q^{36} - 830 q^{37} - 371 q^{38} + 507 q^{39} - 613 q^{40} + 16 q^{41} - 306 q^{42} - 1137 q^{43} + 1738 q^{44} - 135 q^{45} - 659 q^{46} - 489 q^{47} - 1794 q^{48} + 2214 q^{49} + 1066 q^{50} + 1014 q^{51} - 2342 q^{52} + 731 q^{53} + 108 q^{54} - 165 q^{55} + 3051 q^{56} + 705 q^{57} - 611 q^{58} - 425 q^{59} + 1650 q^{60} - 2257 q^{61} + 453 q^{62} - 693 q^{63} + 4919 q^{64} + 1346 q^{65} + 132 q^{66} - 1907 q^{67} - 3236 q^{68} + 159 q^{69} - 1050 q^{70} - 561 q^{71} - 621 q^{72} - 2397 q^{73} - 1840 q^{74} - 2250 q^{75} - 3868 q^{76} - 847 q^{77} + 225 q^{78} + 393 q^{79} - 4031 q^{80} + 2997 q^{81} - 1946 q^{82} - 4191 q^{83} + 4134 q^{84} - 2667 q^{85} + 2405 q^{86} + 90 q^{87} - 759 q^{88} + 1437 q^{89} - 405 q^{90} - 5192 q^{91} - 737 q^{92} + 1518 q^{93} - 1960 q^{94} + 1356 q^{95} + 2523 q^{96} - 2368 q^{97} - 3014 q^{98} + 3663 q^{99}+O(q^{100}) \) 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9 - 45 * q^10 + 407 * q^11 - 474 * q^12 - 169 * q^13 + 102 * q^14 + 45 * q^15 + 598 * q^16 - 338 * q^17 - 36 * q^18 - 235 * q^19 - 550 * q^20 + 231 * q^21 - 44 * q^22 - 53 * q^23 + 207 * q^24 + 750 * q^25 - 75 * q^26 - 999 * q^27 - 1378 * q^28 - 30 * q^29 + 135 * q^30 - 506 * q^31 - 841 * q^32 - 1221 * q^33 - 316 * q^34 - 822 * q^35 + 1422 * q^36 - 830 * q^37 - 371 * q^38 + 507 * q^39 - 613 * q^40 + 16 * q^41 - 306 * q^42 - 1137 * q^43 + 1738 * q^44 - 135 * q^45 - 659 * q^46 - 489 * q^47 - 1794 * q^48 + 2214 * q^49 + 1066 * q^50 + 1014 * q^51 - 2342 * q^52 + 731 * q^53 + 108 * q^54 - 165 * q^55 + 3051 * q^56 + 705 * q^57 - 611 * q^58 - 425 * q^59 + 1650 * q^60 - 2257 * q^61 + 453 * q^62 - 693 * q^63 + 4919 * q^64 + 1346 * q^65 + 132 * q^66 - 1907 * q^67 - 3236 * q^68 + 159 * q^69 - 1050 * q^70 - 561 * q^71 - 621 * q^72 - 2397 * q^73 - 1840 * q^74 - 2250 * q^75 - 3868 * q^76 - 847 * q^77 + 225 * q^78 + 393 * q^79 - 4031 * q^80 + 2997 * q^81 - 1946 * q^82 - 4191 * q^83 + 4134 * q^84 - 2667 * q^85 + 2405 * q^86 + 90 * q^87 - 759 * q^88 + 1437 * q^89 - 405 * q^90 - 5192 * q^91 - 737 * q^92 + 1518 * q^93 - 1960 * q^94 + 1356 * q^95 + 2523 * q^96 - 2368 * q^97 - 3014 * q^98 + 3663 * 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 $

$2$	−4.85102	−1.71509	−0.857547	−	0.514406i	$-0.828012\pi$
$2$	−4.85102	−1.71509	−0.857547	+	0.514406i	$0.828012\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	15.5324	1.94154
$5$	−6.76910	−0.605447	−0.302724	−	0.953078i	$-0.597896\pi$
$5$	−6.76910	−0.605447	−0.302724	+	0.953078i	$0.597896\pi$
$6$	14.5530	0.990210
$7$	−14.4227	−0.778753	−0.389376	−	0.921079i	$-0.627309\pi$
$7$	−14.4227	−0.778753	−0.389376	+	0.921079i	$0.627309\pi$
$8$	−36.5396	−1.61484
$9$	9.00000	0.333333
$10$	32.8370	1.03840
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−46.5971	−1.12095
$13$	89.5149	1.90977	0.954883	−	0.296982i	$-0.0959800\pi$
$13$	89.5149	1.90977	0.954883	+	0.296982i	$0.0959800\pi$
$14$	69.9648	1.33563
$15$	20.3073	0.349555
$16$	52.9953	0.828051
$17$	75.6637	1.07948	0.539740	−	0.841832i	$-0.318523\pi$
$17$	75.6637	1.07948	0.539740	+	0.841832i	$0.318523\pi$
$18$	−43.6591	−0.571698
$19$	−53.1971	−0.642329	−0.321164	−	0.947023i	$-0.604074\pi$
$19$	−53.1971	−0.642329	−0.321164	+	0.947023i	$0.604074\pi$
$20$	−105.140	−1.17550
$21$	43.2681	0.449613
$22$	−53.3612	−0.517120
$23$	−60.1792	−0.545575	−0.272788	−	0.962074i	$-0.587946\pi$
$23$	−60.1792	−0.545575	−0.272788	+	0.962074i	$0.587946\pi$
$24$	109.619	0.932327
$25$	−79.1792	−0.633434
$26$	−434.238	−3.27543
$27$	−27.0000	−0.192450
$28$	−224.019	−1.51198
$29$	99.6268	0.637939	0.318970	−	0.947765i	$-0.396663\pi$
$29$	99.6268	0.637939	0.318970	+	0.947765i	$0.396663\pi$
$30$	−98.5111	−0.599519
$31$	−238.729	−1.38313	−0.691563	−	0.722316i	$-0.743078\pi$
$31$	−238.729	−1.38313	−0.691563	+	0.722316i	$0.743078\pi$
$32$	35.2357	0.194652
$33$	−33.0000	−0.174078
$34$	−367.046	−1.85141
$35$	97.6288	0.471494
$36$	139.791	0.647182
$37$	−17.6324	−0.0783447	−0.0391724	−	0.999232i	$-0.512472\pi$
$37$	−17.6324	−0.0783447	−0.0391724	+	0.999232i	$0.512472\pi$
$38$	258.060	1.10165
$39$	−268.545	−1.10260
$40$	247.340	0.977698
$41$	140.856	0.536537	0.268268	−	0.963344i	$-0.413549\pi$
$41$	140.856	0.536537	0.268268	+	0.963344i	$0.413549\pi$
$42$	−209.894	−0.771128
$43$	4.39867	0.0155998	0.00779990	−	0.999970i	$-0.497517\pi$
$43$	4.39867	0.0155998	0.00779990	+	0.999970i	$0.497517\pi$
$44$	170.856	0.585398
$45$	−60.9219	−0.201816
$46$	291.930	0.935712
$47$	−582.557	−1.80797	−0.903985	−	0.427564i	$-0.859372\pi$
$47$	−582.557	−1.80797	−0.903985	+	0.427564i	$0.859372\pi$
$48$	−158.986	−0.478076
$49$	−134.986	−0.393544
$50$	384.100	1.08640
$51$	−226.991	−0.623238
$52$	1390.38	3.70790
$53$	−2.72271	−0.00705646	−0.00352823	−	0.999994i	$-0.501123\pi$
$53$	−2.72271	−0.00705646	−0.00352823	+	0.999994i	$0.501123\pi$
$54$	130.977	0.330070
$55$	−74.4601	−0.182549
$56$	527.000	1.25756
$57$	159.591	0.370849
$58$	−483.291	−1.09413
$59$	518.109	1.14326	0.571628	−	0.820513i	$-0.306312\pi$
$59$	518.109	1.14326	0.571628	+	0.820513i	$0.306312\pi$
$60$	315.420	0.678677
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	1158.08	2.37219
$63$	−129.804	−0.259584
$64$	−594.891	−1.16190
$65$	−605.936	−1.15626
$66$	160.084	0.298559
$67$	347.266	0.633213	0.316606	−	0.948557i	$-0.397457\pi$
$67$	347.266	0.633213	0.316606	+	0.948557i	$0.397457\pi$
$68$	1175.24	2.09586
$69$	180.538	0.314988
$70$	−473.599	−0.808655
$71$	563.974	0.942695	0.471348	−	0.881948i	$-0.343768\pi$
$71$	563.974	0.942695	0.471348	+	0.881948i	$0.343768\pi$
$72$	−328.856	−0.538279
$73$	392.009	0.628509	0.314255	−	0.949339i	$-0.398245\pi$
$73$	392.009	0.628509	0.314255	+	0.949339i	$0.398245\pi$
$74$	85.5352	0.134369
$75$	237.538	0.365713
$76$	−826.276	−1.24711
$77$	−158.650	−0.234803
$78$	1302.71	1.89107
$79$	180.030	0.256392	0.128196	−	0.991749i	$-0.459081\pi$
$79$	180.030	0.256392	0.128196	+	0.991749i	$0.459081\pi$
$80$	−358.731	−0.501341
$81$	81.0000	0.111111
$82$	−683.294	−0.920210
$83$	−139.672	−0.184710	−0.0923552	−	0.995726i	$-0.529440\pi$
$83$	−139.672	−0.184710	−0.0923552	+	0.995726i	$0.529440\pi$
$84$	672.056	0.872944
$85$	−512.176	−0.653568
$86$	−21.3380	−0.0267551
$87$	−298.881	−0.368314
$88$	−401.936	−0.486892
$89$	438.719	0.522518	0.261259	−	0.965269i	$-0.415862\pi$
$89$	438.719	0.522518	0.261259	+	0.965269i	$0.415862\pi$
$90$	295.533	0.346133
$91$	−1291.05	−1.48724
$92$	−934.725	−1.05926
$93$	716.186	0.798548
$94$	2825.99	3.10084
$95$	360.097	0.388896
$96$	−105.707	−0.112382
$97$	−1452.37	−1.52027	−0.760135	−	0.649765i	$-0.774867\pi$
$97$	−1452.37	−1.52027	−0.760135	+	0.649765i	$0.774867\pi$
$98$	654.817	0.674965
$99$	99.0000	0.100504
$100$	−1229.84	−1.22984
$101$	−469.246	−0.462294	−0.231147	−	0.972919i	$-0.574248\pi$
$101$	−469.246	−0.462294	−0.231147	+	0.972919i	$0.574248\pi$
$102$	1101.14	1.06891
$103$	−1654.60	−1.58284	−0.791421	−	0.611271i	$-0.790658\pi$
$103$	−1654.60	−1.58284	−0.791421	+	0.611271i	$0.790658\pi$
$104$	−3270.84	−3.08396
$105$	−292.886	−0.272217
$106$	13.2079	0.0121025
$107$	824.888	0.745280	0.372640	−	0.927976i	$-0.378453\pi$
$107$	824.888	0.745280	0.372640	+	0.927976i	$0.378453\pi$
$108$	−419.374	−0.373650
$109$	−313.903	−0.275839	−0.137919	−	0.990443i	$-0.544041\pi$
$109$	−313.903	−0.275839	−0.137919	+	0.990443i	$0.544041\pi$
$110$	361.207	0.313089
$111$	52.8973	0.0452323
$112$	−764.335	−0.644847
$113$	786.171	0.654485	0.327242	−	0.944940i	$-0.393881\pi$
$113$	786.171	0.654485	0.327242	+	0.944940i	$0.393881\pi$
$114$	−774.180	−0.636040
$115$	407.359	0.330317
$116$	1547.44	1.23859
$117$	805.634	0.636589
$118$	−2513.36	−1.96079
$119$	−1091.28	−0.840648
$120$	−742.021	−0.564474
$121$	121.000	0.0909091
$122$	295.912	0.219595
$123$	−422.568	−0.309770
$124$	−3708.02	−2.68540
$125$	1382.11	0.988958
$126$	629.683	0.445211
$127$	−610.233	−0.426373	−0.213187	−	0.977011i	$-0.568384\pi$
$127$	−610.233	−0.426373	−0.213187	+	0.977011i	$0.568384\pi$
$128$	2603.94	1.79811
$129$	−13.1960	−0.00900655
$130$	2939.40	1.98310
$131$	−1004.93	−0.670236	−0.335118	−	0.942176i	$-0.608776\pi$
$131$	−1004.93	−0.670236	−0.335118	+	0.942176i	$0.608776\pi$
$132$	−512.568	−0.337980
$133$	767.246	0.500215
$134$	−1684.59	−1.08602
$135$	182.766	0.116518
$136$	−2764.72	−1.74318
$137$	568.775	0.354699	0.177349	−	0.984148i	$-0.443248\pi$
$137$	568.775	0.354699	0.177349	+	0.984148i	$0.443248\pi$
$138$	−875.791	−0.540234
$139$	−2065.27	−1.26024	−0.630122	−	0.776496i	$-0.716995\pi$
$139$	−2065.27	−1.26024	−0.630122	+	0.776496i	$0.716995\pi$
$140$	1516.41	0.915426
$141$	1747.67	1.04383
$142$	−2735.85	−1.61681
$143$	984.664	0.575816
$144$	476.958	0.276017
$145$	−674.384	−0.386238
$146$	−1901.64	−1.07795
$147$	404.957	0.227213
$148$	−273.873	−0.152110
$149$	2681.34	1.47425	0.737127	−	0.675755i	$-0.236182\pi$
$149$	2681.34	1.47425	0.737127	+	0.675755i	$0.236182\pi$
$150$	−1152.30	−0.627232
$151$	3131.20	1.68751	0.843753	−	0.536732i	$-0.180342\pi$
$151$	3131.20	1.68751	0.843753	+	0.536732i	$0.180342\pi$
$152$	1943.80	1.03726
$153$	680.974	0.359827
$154$	769.612	0.402709
$155$	1615.98	0.837410
$156$	−4171.13	−2.14076
$157$	2399.59	1.21980	0.609898	−	0.792480i	$-0.291210\pi$
$157$	2399.59	1.21980	0.609898	+	0.792480i	$0.291210\pi$
$158$	−873.327	−0.439735
$159$	8.16812	0.00407405
$160$	−238.514	−0.117851
$161$	867.947	0.424868
$162$	−392.932	−0.190566
$163$	2788.69	1.34004	0.670022	−	0.742341i	$-0.266285\pi$
$163$	2788.69	1.34004	0.670022	+	0.742341i	$0.266285\pi$
$164$	2187.82	1.04171
$165$	223.380	0.105395
$166$	677.550	0.316795
$167$	−3335.14	−1.54539	−0.772697	−	0.634774i	$-0.781093\pi$
$167$	−3335.14	−1.54539	−0.772697	+	0.634774i	$0.781093\pi$
$168$	−1581.00	−0.726052
$169$	5815.91	2.64721
$170$	2484.57	1.12093
$171$	−478.774	−0.214110
$172$	68.3218	0.0302877
$173$	1664.71	0.731592	0.365796	−	0.930695i	$-0.380797\pi$
$173$	1664.71	0.731592	0.365796	+	0.930695i	$0.380797\pi$
$174$	1449.87	0.631694
$175$	1141.98	0.493288
$176$	582.948	0.249667
$177$	−1554.33	−0.660059
$178$	−2128.23	−0.896168
$179$	1131.10	0.472302	0.236151	−	0.971716i	$-0.424114\pi$
$179$	1131.10	0.472302	0.236151	+	0.971716i	$0.424114\pi$
$180$	−946.261	−0.391834
$181$	4355.99	1.78883	0.894415	−	0.447238i	$-0.147592\pi$
$181$	4355.99	1.78883	0.894415	+	0.447238i	$0.147592\pi$
$182$	6262.89	2.55075
$183$	183.000	0.0739221
$184$	2198.92	0.881015
$185$	119.356	0.0474336
$186$	−3474.23	−1.36959
$187$	832.301	0.325475
$188$	−9048.48	−3.51026
$189$	389.413	0.149871
$190$	−1746.83	−0.666993
$191$	−3421.08	−1.29602	−0.648012	−	0.761630i	$-0.724399\pi$
$191$	−3421.08	−1.29602	−0.648012	+	0.761630i	$0.724399\pi$
$192$	1784.67	0.670822
$193$	94.3531	0.0351901	0.0175950	−	0.999845i	$-0.494399\pi$
$193$	94.3531	0.0351901	0.0175950	+	0.999845i	$0.494399\pi$
$194$	7045.49	2.60741
$195$	1817.81	0.667568
$196$	−2096.65	−0.764083
$197$	−169.396	−0.0612637	−0.0306319	−	0.999531i	$-0.509752\pi$
$197$	−169.396	−0.0612637	−0.0306319	+	0.999531i	$0.509752\pi$
$198$	−480.251	−0.172373
$199$	−1067.55	−0.380286	−0.190143	−	0.981756i	$-0.560895\pi$
$199$	−1067.55	−0.380286	−0.190143	+	0.981756i	$0.560895\pi$
$200$	2893.18	1.02289
$201$	−1041.80	−0.365586
$202$	2276.32	0.792877
$203$	−1436.89	−0.496797
$204$	−3525.71	−1.21004
$205$	−953.468	−0.324844
$206$	8026.50	2.71472
$207$	−541.613	−0.181858
$208$	4743.87	1.58138
$209$	−585.168	−0.193669
$210$	1420.80	0.466877
$211$	−1153.05	−0.376205	−0.188102	−	0.982149i	$-0.560234\pi$
$211$	−1153.05	−0.376205	−0.188102	+	0.982149i	$0.560234\pi$
$212$	−42.2900	−0.0137004
$213$	−1691.92	−0.544265
$214$	−4001.55	−1.27822
$215$	−29.7751	−0.00944485
$216$	986.569	0.310776
$217$	3443.11	1.07711
$218$	1522.75	0.473089
$219$	−1176.03	−0.362870
$220$	−1156.54	−0.354427
$221$	6773.03	2.06155
$222$	−256.606	−0.0775777
$223$	−5261.13	−1.57987	−0.789936	−	0.613189i	$-0.789886\pi$
$223$	−5261.13	−1.57987	−0.789936	+	0.613189i	$0.789886\pi$
$224$	−508.194	−0.151586
$225$	−712.613	−0.211145
$226$	−3813.73	−1.12250
$227$	−2589.02	−0.757002	−0.378501	−	0.925601i	$-0.623560\pi$
$227$	−2589.02	−0.757002	−0.378501	+	0.925601i	$0.623560\pi$
$228$	2478.83	0.720020
$229$	3695.89	1.06651	0.533256	−	0.845954i	$-0.320968\pi$
$229$	3695.89	1.06651	0.533256	+	0.845954i	$0.320968\pi$
$230$	−1976.11	−0.566524
$231$	475.949	0.135563
$232$	−3640.32	−1.03017
$233$	4469.96	1.25681	0.628405	−	0.777886i	$-0.283708\pi$
$233$	4469.96	1.25681	0.628405	+	0.777886i	$0.283708\pi$
$234$	−3908.14	−1.09181
$235$	3943.39	1.09463
$236$	8047.46	2.21968
$237$	−540.089	−0.148028
$238$	5293.80	1.44179
$239$	3088.73	0.835956	0.417978	−	0.908457i	$-0.362739\pi$
$239$	3088.73	0.835956	0.417978	+	0.908457i	$0.362739\pi$
$240$	1076.19	0.289450
$241$	−5769.42	−1.54208	−0.771040	−	0.636787i	$-0.780263\pi$
$241$	−5769.42	−1.54208	−0.771040	+	0.636787i	$0.780263\pi$
$242$	−586.973	−0.155918
$243$	−243.000	−0.0641500
$244$	−947.474	−0.248589
$245$	913.732	0.238270
$246$	2049.88	0.531284
$247$	−4761.93	−1.22670
$248$	8723.05	2.23352
$249$	419.015	0.106643
$250$	−6704.64	−1.69615
$251$	1087.64	0.273512	0.136756	−	0.990605i	$-0.456332\pi$
$251$	1087.64	0.273512	0.136756	+	0.990605i	$0.456332\pi$
$252$	−2016.17	−0.503994
$253$	−661.971	−0.164497
$254$	2960.25	0.731270
$255$	1536.53	0.377338
$256$	−7872.63	−1.92203
$257$	−3980.32	−0.966091	−0.483045	−	0.875595i	$-0.660469\pi$
$257$	−3980.32	−0.966091	−0.483045	+	0.875595i	$0.660469\pi$
$258$	64.0141	0.0154471
$259$	254.307	0.0610112
$260$	−9411.61	−2.24494
$261$	896.642	0.212646
$262$	4874.92	1.14952
$263$	1000.22	0.234510	0.117255	−	0.993102i	$-0.462591\pi$
$263$	1000.22	0.234510	0.117255	+	0.993102i	$0.462591\pi$
$264$	1205.81	0.281107
$265$	18.4303	0.00427231
$266$	−3721.92	−0.857916
$267$	−1316.16	−0.301676
$268$	5393.85	1.22941
$269$	7983.78	1.80959	0.904795	−	0.425848i	$-0.140024\pi$
$269$	7983.78	1.80959	0.904795	+	0.425848i	$0.140024\pi$
$270$	−886.600	−0.199840
$271$	−1994.36	−0.447044	−0.223522	−	0.974699i	$-0.571755\pi$
$271$	−1994.36	−0.447044	−0.223522	+	0.974699i	$0.571755\pi$
$272$	4009.82	0.893865
$273$	3873.14	0.858656
$274$	−2759.14	−0.608341
$275$	−870.972	−0.190987
$276$	2804.17	0.611563
$277$	−4952.35	−1.07422	−0.537108	−	0.843513i	$-0.680483\pi$
$277$	−4952.35	−1.07422	−0.537108	+	0.843513i	$0.680483\pi$
$278$	10018.7	2.16144
$279$	−2148.56	−0.461042
$280$	−3567.32	−0.761385
$281$	−1259.91	−0.267474	−0.133737	−	0.991017i	$-0.542698\pi$
$281$	−1259.91	−0.267474	−0.133737	+	0.991017i	$0.542698\pi$
$282$	−8477.97	−1.79027
$283$	−12.0652	−0.00253427	−0.00126714	−	0.999999i	$-0.500403\pi$
$283$	−12.0652	−0.00253427	−0.00126714	+	0.999999i	$0.500403\pi$
$284$	8759.84	1.83028
$285$	−1080.29	−0.224529
$286$	−4776.62	−0.987579
$287$	−2031.52	−0.417829
$288$	317.121	0.0648839
$289$	812.003	0.165276
$290$	3271.45	0.662435
$291$	4357.12	0.877729
$292$	6088.83	1.22028
$293$	−3782.66	−0.754216	−0.377108	−	0.926169i	$-0.623081\pi$
$293$	−3782.66	−0.754216	−0.377108	+	0.926169i	$0.623081\pi$
$294$	−1964.45	−0.389691
$295$	−3507.14	−0.692181
$296$	644.282	0.126514
$297$	−297.000	−0.0580259
$298$	−13007.2	−2.52848
$299$	−5386.93	−1.04192
$300$	3689.52	0.710049
$301$	−63.4408	−0.0121484
$302$	−15189.5	−2.89423
$303$	1407.74	0.266906
$304$	−2819.20	−0.531881
$305$	412.915	0.0775196
$306$	−3303.41	−0.617136
$307$	−5683.63	−1.05662	−0.528309	−	0.849052i	$-0.677174\pi$
$307$	−5683.63	−1.05662	−0.528309	+	0.849052i	$0.677174\pi$
$308$	−2464.20	−0.455880
$309$	4963.81	0.913854
$310$	−7839.14	−1.43624
$311$	7654.68	1.39568	0.697841	−	0.716253i	$-0.254144\pi$
$311$	7654.68	1.39568	0.697841	+	0.716253i	$0.254144\pi$
$312$	9812.51	1.78053
$313$	1150.94	0.207843	0.103922	−	0.994585i	$-0.466861\pi$
$313$	1150.94	0.207843	0.103922	+	0.994585i	$0.466861\pi$
$314$	−11640.4	−2.09206
$315$	878.659	0.157165
$316$	2796.29	0.497796
$317$	−1256.91	−0.222698	−0.111349	−	0.993781i	$-0.535517\pi$
$317$	−1256.91	−0.222698	−0.111349	+	0.993781i	$0.535517\pi$
$318$	−39.6237	−0.00698737
$319$	1095.90	0.192346
$320$	4026.88	0.703467
$321$	−2474.66	−0.430288
$322$	−4210.42	−0.728689
$323$	−4025.09	−0.693381
$324$	1258.12	0.215727
$325$	−7087.72	−1.20971
$326$	−13528.0	−2.29830
$327$	941.708	0.159255
$328$	−5146.82	−0.866419
$329$	8402.04	1.40796
$330$	−1083.62	−0.180762
$331$	−10290.8	−1.70887	−0.854433	−	0.519562i	$-0.826095\pi$
$331$	−10290.8	−1.70887	−0.854433	+	0.519562i	$0.826095\pi$
$332$	−2169.43	−0.358623
$333$	−158.692	−0.0261149
$334$	16178.8	2.65050
$335$	−2350.68	−0.383377
$336$	2293.01	0.372303
$337$	−7738.39	−1.25085	−0.625426	−	0.780284i	$-0.715075\pi$
$337$	−7738.39	−1.25085	−0.625426	+	0.780284i	$0.715075\pi$
$338$	−28213.1	−4.54021
$339$	−2358.51	−0.377867
$340$	−7955.30	−1.26893
$341$	−2626.01	−0.417028
$342$	2322.54	0.367218
$343$	6893.84	1.08523
$344$	−160.726	−0.0251911
$345$	−1222.08	−0.190709
$346$	−8075.52	−1.25475
$347$	5699.79	0.881789	0.440895	−	0.897559i	$-0.354661\pi$
$347$	5699.79	0.881789	0.440895	+	0.897559i	$0.354661\pi$
$348$	−4642.32	−0.715099
$349$	−63.3211	−0.00971203	−0.00485602	−	0.999988i	$-0.501546\pi$
$349$	−63.3211	−0.00971203	−0.00485602	+	0.999988i	$0.501546\pi$
$350$	−5539.76	−0.846036
$351$	−2416.90	−0.367535
$352$	387.593	0.0586897
$353$	−573.483	−0.0864686	−0.0432343	−	0.999065i	$-0.513766\pi$
$353$	−573.483	−0.0864686	−0.0432343	+	0.999065i	$0.513766\pi$
$354$	7540.07	1.13206
$355$	−3817.60	−0.570752
$356$	6814.34	1.01449
$357$	3273.83	0.485348
$358$	−5486.97	−0.810043
$359$	165.272	0.0242973	0.0121486	−	0.999926i	$-0.496133\pi$
$359$	165.272	0.0242973	0.0121486	+	0.999926i	$0.496133\pi$
$360$	2226.06	0.325899
$361$	−4029.07	−0.587414
$362$	−21131.0	−3.06801
$363$	−363.000	−0.0524864
$364$	−20053.0	−2.88754
$365$	−2653.55	−0.380529
$366$	−887.736	−0.126783
$367$	10335.2	1.47001	0.735003	−	0.678064i	$-0.237181\pi$
$367$	10335.2	1.47001	0.735003	+	0.678064i	$0.237181\pi$
$368$	−3189.21	−0.451764
$369$	1267.70	0.178846
$370$	−578.997	−0.0813530
$371$	39.2688	0.00549524
$372$	11124.1	1.55042
$373$	1096.05	0.152149	0.0760743	−	0.997102i	$-0.475761\pi$
$373$	1096.05	0.152149	0.0760743	+	0.997102i	$0.475761\pi$
$374$	−4037.51	−0.558221
$375$	−4146.33	−0.570975
$376$	21286.4	2.91958
$377$	8918.09	1.21832
$378$	−1889.05	−0.257043
$379$	10241.5	1.38804	0.694022	−	0.719954i	$-0.255837\pi$
$379$	10241.5	1.38804	0.694022	+	0.719954i	$0.255837\pi$
$380$	5593.15	0.755059
$381$	1830.70	0.246167
$382$	16595.7	2.22280
$383$	6383.67	0.851672	0.425836	−	0.904800i	$-0.359980\pi$
$383$	6383.67	0.851672	0.425836	+	0.904800i	$0.359980\pi$
$384$	−7811.83	−1.03814
$385$	1073.92	0.142161
$386$	−457.709	−0.0603543
$387$	39.5881	0.00519993
$388$	−22558.8	−2.95167
$389$	−12963.7	−1.68968	−0.844838	−	0.535023i	$-0.820303\pi$
$389$	−12963.7	−1.68968	−0.844838	+	0.535023i	$0.820303\pi$
$390$	−8818.21	−1.14494
$391$	−4553.38	−0.588937
$392$	4932.32	0.635510
$393$	3014.78	0.386961
$394$	821.742	0.105073
$395$	−1218.64	−0.155232
$396$	1537.70	0.195133
$397$	12021.0	1.51969	0.759846	−	0.650103i	$-0.225274\pi$
$397$	12021.0	1.51969	0.759846	+	0.650103i	$0.225274\pi$
$398$	5178.72	0.652225
$399$	−2301.74	−0.288800
$400$	−4196.13	−0.524516
$401$	−9169.08	−1.14185	−0.570925	−	0.821002i	$-0.693415\pi$
$401$	−9169.08	−1.14185	−0.570925	+	0.821002i	$0.693415\pi$
$402$	5053.77	0.627013
$403$	−21369.8	−2.64145
$404$	−7288.49	−0.897565
$405$	−548.297	−0.0672719
$406$	6970.37	0.852053
$407$	−193.957	−0.0236218
$408$	8294.17	1.00643
$409$	−7536.91	−0.911189	−0.455595	−	0.890187i	$-0.650573\pi$
$409$	−7536.91	−0.911189	−0.455595	+	0.890187i	$0.650573\pi$
$410$	4625.29	0.557139
$411$	−1706.32	−0.204785
$412$	−25699.9	−3.07316
$413$	−7472.54	−0.890314
$414$	2627.37	0.311904
$415$	945.452	0.111832
$416$	3154.12	0.371739
$417$	6195.81	0.727602
$418$	2838.66	0.332161
$419$	−9937.89	−1.15871	−0.579353	−	0.815077i	$-0.696695\pi$
$419$	−9937.89	−1.15871	−0.579353	+	0.815077i	$0.696695\pi$
$420$	−4549.22	−0.528521
$421$	1578.19	0.182699	0.0913497	−	0.995819i	$-0.470882\pi$
$421$	1578.19	0.182699	0.0913497	+	0.995819i	$0.470882\pi$
$422$	5593.46	0.645226
$423$	−5243.01	−0.602657
$424$	99.4866	0.0113950
$425$	−5991.00	−0.683779
$426$	8207.54	0.933466
$427$	879.785	0.0997091
$428$	12812.5	1.44699
$429$	−2953.99	−0.332448
$430$	144.439	0.0161988
$431$	−1903.94	−0.212783	−0.106391	−	0.994324i	$-0.533930\pi$
$431$	−1903.94	−0.212783	−0.106391	+	0.994324i	$0.533930\pi$
$432$	−1430.87	−0.159359
$433$	−13270.4	−1.47283	−0.736414	−	0.676531i	$-0.763483\pi$
$433$	−13270.4	−1.47283	−0.736414	+	0.676531i	$0.763483\pi$
$434$	−16702.6	−1.84735
$435$	2023.15	0.222995
$436$	−4875.65	−0.535553
$437$	3201.36	0.350439
$438$	5704.93	0.622356
$439$	3277.91	0.356369	0.178185	−	0.983997i	$-0.442978\pi$
$439$	3277.91	0.356369	0.178185	+	0.983997i	$0.442978\pi$
$440$	2720.74	0.294787
$441$	−1214.87	−0.131181
$442$	−32856.1	−3.53576
$443$	−6709.86	−0.719628	−0.359814	−	0.933024i	$-0.617160\pi$
$443$	−6709.86	−0.719628	−0.359814	+	0.933024i	$0.617160\pi$
$444$	821.620	0.0878206
$445$	−2969.73	−0.316357
$446$	25521.8	2.70963
$447$	−8044.01	−0.851160
$448$	8579.94	0.904831
$449$	−12572.2	−1.32142	−0.660710	−	0.750641i	$-0.729745\pi$
$449$	−12572.2	−1.32142	−0.660710	+	0.750641i	$0.729745\pi$
$450$	3456.90	0.362133
$451$	1549.42	0.161772
$452$	12211.1	1.27071
$453$	−9393.59	−0.974282
$454$	12559.4	1.29833
$455$	8739.23	0.900443
$456$	−5831.40	−0.598860
$457$	−10365.9	−1.06105	−0.530523	−	0.847671i	$-0.678004\pi$
$457$	−10365.9	−1.06105	−0.530523	+	0.847671i	$0.678004\pi$
$458$	−17928.8	−1.82917
$459$	−2042.92	−0.207746
$460$	6327.25	0.641325
$461$	11540.6	1.16594	0.582970	−	0.812494i	$-0.301891\pi$
$461$	11540.6	1.16594	0.582970	+	0.812494i	$0.301891\pi$
$462$	−2308.84	−0.232504
$463$	−15568.1	−1.56266	−0.781329	−	0.624120i	$-0.785458\pi$
$463$	−15568.1	−1.56266	−0.781329	+	0.624120i	$0.785458\pi$
$464$	5279.75	0.528247
$465$	−4847.94	−0.483479
$466$	−21683.8	−2.15555
$467$	4970.21	0.492492	0.246246	−	0.969207i	$-0.420803\pi$
$467$	4970.21	0.492492	0.246246	+	0.969207i	$0.420803\pi$
$468$	12513.4	1.23597
$469$	−5008.51	−0.493116
$470$	−19129.4	−1.87739
$471$	−7198.76	−0.704249
$472$	−18931.5	−1.84617
$473$	48.3854	0.00470352
$474$	2619.98	0.253881
$475$	4212.10	0.406873
$476$	−16950.1	−1.63216
$477$	−24.5044	−0.00235215
$478$	−14983.5	−1.43374
$479$	−2932.62	−0.279738	−0.139869	−	0.990170i	$-0.544668\pi$
$479$	−2932.62	−0.279738	−0.139869	+	0.990170i	$0.544668\pi$
$480$	715.543	0.0680415
$481$	−1578.37	−0.149620
$482$	27987.6	2.64481
$483$	−2603.84	−0.245298
$484$	1879.42	0.176504
$485$	9831.27	0.920444
$486$	1178.80	0.110023
$487$	−7853.38	−0.730741	−0.365370	−	0.930862i	$-0.619058\pi$
$487$	−7853.38	−0.730741	−0.365370	+	0.930862i	$0.619058\pi$
$488$	2228.92	0.206759
$489$	−8366.08	−0.773675
$490$	−4432.53	−0.408655
$491$	11861.6	1.09024	0.545119	−	0.838359i	$-0.316485\pi$
$491$	11861.6	1.09024	0.545119	+	0.838359i	$0.316485\pi$
$492$	−6563.47	−0.601431
$493$	7538.14	0.688643
$494$	23100.2	2.10390
$495$	−670.141	−0.0608497
$496$	−12651.5	−1.14530
$497$	−8134.02	−0.734126
$498$	−2032.65	−0.182902
$499$	15023.0	1.34774	0.673868	−	0.738852i	$-0.264632\pi$
$499$	15023.0	1.34774	0.673868	+	0.738852i	$0.264632\pi$
$500$	21467.4	1.92011
$501$	10005.4	0.892234
$502$	−5276.18	−0.469098
$503$	−5350.56	−0.474294	−0.237147	−	0.971474i	$-0.576212\pi$
$503$	−5350.56	−0.474294	−0.237147	+	0.971474i	$0.576212\pi$
$504$	4743.00	0.419186
$505$	3176.37	0.279895
$506$	3211.23	0.282128
$507$	−17447.7	−1.52837
$508$	−9478.36	−0.827823
$509$	−3719.49	−0.323897	−0.161948	−	0.986799i	$-0.551778\pi$
$509$	−3719.49	−0.323897	−0.161948	+	0.986799i	$0.551778\pi$
$510$	−7453.72	−0.647169
$511$	−5653.83	−0.489453
$512$	17358.7	1.49835
$513$	1436.32	0.123616
$514$	19308.6	1.65694
$515$	11200.2	0.958327
$516$	−204.965	−0.0174866
$517$	−6408.12	−0.545124
$518$	−1233.65	−0.104640
$519$	−4994.12	−0.422385
$520$	22140.6	1.86718
$521$	−2441.73	−0.205324	−0.102662	−	0.994716i	$-0.532736\pi$
$521$	−2441.73	−0.205324	−0.102662	+	0.994716i	$0.532736\pi$
$522$	−4349.62	−0.364708
$523$	−14390.3	−1.20314	−0.601572	−	0.798819i	$-0.705459\pi$
$523$	−14390.3	−1.20314	−0.601572	+	0.798819i	$0.705459\pi$
$524$	−15608.9	−1.30129
$525$	−3425.94	−0.284800
$526$	−4852.08	−0.402206
$527$	−18063.1	−1.49306
$528$	−1748.84	−0.144145
$529$	−8545.46	−0.702348
$530$	−89.4056	−0.00732742
$531$	4662.98	0.381085
$532$	11917.1	0.971191
$533$	12608.7	1.02466
$534$	6384.70	0.517403
$535$	−5583.75	−0.451228
$536$	−12688.9	−1.02254
$537$	−3393.29	−0.272684
$538$	−38729.4	−3.10361
$539$	−1484.84	−0.118658
$540$	2838.78	0.226226
$541$	11933.1	0.948324	0.474162	−	0.880438i	$-0.342751\pi$
$541$	11933.1	0.948324	0.474162	+	0.880438i	$0.342751\pi$
$542$	9674.69	0.766722
$543$	−13068.0	−1.03278
$544$	2666.07	0.210123
$545$	2124.84	0.167006
$546$	−18788.7	−1.47268
$547$	2214.40	0.173091	0.0865456	−	0.996248i	$-0.472417\pi$
$547$	2214.40	0.173091	0.0865456	+	0.996248i	$0.472417\pi$
$548$	8834.41	0.688663
$549$	−549.000	−0.0426790
$550$	4225.10	0.327561
$551$	−5299.86	−0.409767
$552$	−6596.77	−0.508654
$553$	−2596.52	−0.199666
$554$	24023.9	1.84238
$555$	−358.067	−0.0273858
$556$	−32078.5	−2.44682
$557$	5738.55	0.436536	0.218268	−	0.975889i	$-0.429959\pi$
$557$	5738.55	0.436536	0.218268	+	0.975889i	$0.429959\pi$
$558$	10422.7	0.790730
$559$	393.747	0.0297920
$560$	5173.87	0.390421
$561$	−2496.90	−0.187913
$562$	6111.87	0.458743
$563$	−8048.90	−0.602524	−0.301262	−	0.953541i	$-0.597408\pi$
$563$	−8048.90	−0.602524	−0.301262	+	0.953541i	$0.597408\pi$
$564$	27145.4	2.02665
$565$	−5321.67	−0.396256
$566$	58.5282	0.00434651
$567$	−1168.24	−0.0865281
$568$	−20607.4	−1.52230
$569$	1319.92	0.0972478	0.0486239	−	0.998817i	$-0.484516\pi$
$569$	1319.92	0.0972478	0.0486239	+	0.998817i	$0.484516\pi$
$570$	5240.50	0.385089
$571$	18524.4	1.35766	0.678830	−	0.734295i	$-0.262487\pi$
$571$	18524.4	1.35766	0.678830	+	0.734295i	$0.262487\pi$
$572$	15294.2	1.11797
$573$	10263.2	0.748260
$574$	9854.95	0.716616
$575$	4764.94	0.345586
$576$	−5354.02	−0.387299
$577$	−24001.1	−1.73168	−0.865839	−	0.500322i	$-0.833215\pi$
$577$	−24001.1	−1.73168	−0.865839	+	0.500322i	$0.833215\pi$
$578$	−3939.04	−0.283464
$579$	−283.059	−0.0203170
$580$	−10474.8	−0.749899
$581$	2014.44	0.143844
$582$	−21136.5	−1.50539
$583$	−29.9498	−0.00212760
$584$	−14323.9	−1.01494
$585$	−5453.42	−0.385421
$586$	18349.7	1.29355
$587$	−647.341	−0.0455173	−0.0227586	−	0.999741i	$-0.507245\pi$
$587$	−647.341	−0.0455173	−0.0227586	+	0.999741i	$0.507245\pi$
$588$	6289.94	0.441144
$589$	12699.7	0.888422
$590$	17013.2	1.18715
$591$	508.187	0.0353706
$592$	−934.436	−0.0648735
$593$	−22123.5	−1.53205	−0.766024	−	0.642812i	$-0.777768\pi$
$593$	−22123.5	−1.53205	−0.766024	+	0.642812i	$0.777768\pi$
$594$	1440.75	0.0995198
$595$	7386.96	0.508968
$596$	41647.5	2.86233
$597$	3202.66	0.219558
$598$	26132.1	1.78699
$599$	3702.50	0.252555	0.126277	−	0.991995i	$-0.459697\pi$
$599$	3702.50	0.252555	0.126277	+	0.991995i	$0.459697\pi$
$600$	−8679.53	−0.590567
$601$	8868.69	0.601933	0.300966	−	0.953635i	$-0.402691\pi$
$601$	8868.69	0.601933	0.300966	+	0.953635i	$0.402691\pi$
$602$	307.752	0.0208356
$603$	3125.39	0.211071
$604$	48634.9	3.27637
$605$	−819.062	−0.0550406
$606$	−6828.96	−0.457768
$607$	−2955.12	−0.197603	−0.0988013	−	0.995107i	$-0.531501\pi$
$607$	−2955.12	−0.197603	−0.0988013	+	0.995107i	$0.531501\pi$
$608$	−1874.44	−0.125030
$609$	4310.67	0.286826
$610$	−2003.06	−0.132953
$611$	−52147.5	−3.45280
$612$	10577.1	0.698619
$613$	23008.2	1.51597	0.757987	−	0.652270i	$-0.226183\pi$
$613$	23008.2	1.51597	0.757987	+	0.652270i	$0.226183\pi$
$614$	27571.4	1.81220
$615$	2860.41	0.187549
$616$	5797.00	0.379168
$617$	−18401.6	−1.20068	−0.600341	−	0.799744i	$-0.704968\pi$
$617$	−18401.6	−1.20068	−0.600341	+	0.799744i	$0.704968\pi$
$618$	−24079.5	−1.56735
$619$	14748.2	0.957640	0.478820	−	0.877913i	$-0.341065\pi$
$619$	14748.2	0.957640	0.478820	+	0.877913i	$0.341065\pi$
$620$	25100.0	1.62587
$621$	1624.84	0.104996
$622$	−37133.0	−2.39372
$623$	−6327.51	−0.406913
$624$	−14231.6	−0.913013
$625$	541.755	0.0346723
$626$	−5583.23	−0.356471
$627$	1755.50	0.111815
$628$	37271.2	2.36829
$629$	−1334.14	−0.0845715
$630$	−4262.39	−0.269552
$631$	−12234.6	−0.771874	−0.385937	−	0.922525i	$-0.626122\pi$
$631$	−12234.6	−0.771874	−0.385937	+	0.922525i	$0.626122\pi$
$632$	−6578.22	−0.414031
$633$	3459.15	0.217202
$634$	6097.30	0.381947
$635$	4130.73	0.258147
$636$	126.870	0.00790995
$637$	−12083.2	−0.751577
$638$	−5316.21	−0.329891
$639$	5075.76	0.314232
$640$	−17626.4	−1.08866
$641$	−4640.13	−0.285919	−0.142960	−	0.989729i	$-0.545662\pi$
$641$	−4640.13	−0.285919	−0.142960	+	0.989729i	$0.545662\pi$
$642$	12004.6	0.737983
$643$	−19655.5	−1.20550	−0.602750	−	0.797930i	$-0.705928\pi$
$643$	−19655.5	−1.20550	−0.602750	+	0.797930i	$0.705928\pi$
$644$	13481.3	0.824901
$645$	89.3252	0.00545299
$646$	19525.8	1.18921
$647$	−715.713	−0.0434893	−0.0217446	−	0.999764i	$-0.506922\pi$
$647$	−715.713	−0.0434893	−0.0217446	+	0.999764i	$0.506922\pi$
$648$	−2959.71	−0.179426
$649$	5699.20	0.344705
$650$	34382.6	2.07477
$651$	−10329.3	−0.621872
$652$	43315.0	2.60176
$653$	−21192.2	−1.27000	−0.635002	−	0.772510i	$-0.719001\pi$
$653$	−21192.2	−1.27000	−0.635002	+	0.772510i	$0.719001\pi$
$654$	−4568.24	−0.273138
$655$	6802.46	0.405793
$656$	7464.70	0.444280
$657$	3528.08	0.209503
$658$	−40758.4	−2.41479
$659$	12672.3	0.749079	0.374540	−	0.927211i	$-0.377801\pi$
$659$	12672.3	0.749079	0.374540	+	0.927211i	$0.377801\pi$
$660$	3469.62	0.204629
$661$	−7475.22	−0.439867	−0.219934	−	0.975515i	$-0.570584\pi$
$661$	−7475.22	−0.439867	−0.219934	+	0.975515i	$0.570584\pi$
$662$	49920.9	2.93086
$663$	−20319.1	−1.19024
$664$	5103.55	0.298277
$665$	−5193.57	−0.302854
$666$	769.817	0.0447895
$667$	−5995.46	−0.348044
$668$	−51802.6	−3.00045
$669$	15783.4	0.912140
$670$	11403.2	0.657527
$671$	−671.000	−0.0386046
$672$	1524.58	0.0875180
$673$	22662.0	1.29800	0.649002	−	0.760787i	$-0.275187\pi$
$673$	22662.0	1.29800	0.649002	+	0.760787i	$0.275187\pi$
$674$	37539.0	2.14533
$675$	2137.84	0.121904
$676$	90334.9	5.13967
$677$	−8323.56	−0.472527	−0.236263	−	0.971689i	$-0.575923\pi$
$677$	−8323.56	−0.472527	−0.236263	+	0.971689i	$0.575923\pi$
$678$	11441.2	0.648077
$679$	20947.2	1.18392
$680$	18714.7	1.05541
$681$	7767.07	0.437055
$682$	12738.8	0.715242
$683$	11779.8	0.659942	0.329971	−	0.943991i	$-0.392961\pi$
$683$	11779.8	0.659942	0.329971	+	0.943991i	$0.392961\pi$
$684$	−7436.49	−0.415703
$685$	−3850.10	−0.214751
$686$	−33442.2	−1.86126
$687$	−11087.7	−0.615751
$688$	233.109	0.0129174
$689$	−243.723	−0.0134762
$690$	5928.32	0.327083
$691$	−8956.12	−0.493063	−0.246532	−	0.969135i	$-0.579291\pi$
$691$	−8956.12	−0.493063	−0.246532	+	0.969135i	$0.579291\pi$
$692$	25856.8	1.42042
$693$	−1427.85	−0.0782676
$694$	−27649.8	−1.51235
$695$	13980.0	0.763011
$696$	10921.0	0.594768
$697$	10657.7	0.579180
$698$	307.172	0.0166570
$699$	−13409.9	−0.725620
$700$	17737.6	0.957742
$701$	23215.5	1.25084	0.625419	−	0.780289i	$-0.284928\pi$
$701$	23215.5	1.25084	0.625419	+	0.780289i	$0.284928\pi$
$702$	11724.4	0.630356
$703$	937.994	0.0503231
$704$	−6543.81	−0.350325
$705$	−11830.2	−0.631985
$706$	2781.97	0.148302
$707$	6767.79	0.360013
$708$	−24142.4	−1.28153
$709$	−7770.17	−0.411587	−0.205793	−	0.978595i	$-0.565977\pi$
$709$	−7770.17	−0.411587	−0.205793	+	0.978595i	$0.565977\pi$
$710$	18519.2	0.978893
$711$	1620.27	0.0854639
$712$	−16030.6	−0.843782
$713$	14366.5	0.754600
$714$	−15881.4	−0.832417
$715$	−6665.29	−0.348626
$716$	17568.6	0.916996
$717$	−9266.19	−0.482639
$718$	−801.738	−0.0416721
$719$	16936.2	0.878462	0.439231	−	0.898374i	$-0.355251\pi$
$719$	16936.2	0.878462	0.439231	+	0.898374i	$0.355251\pi$
$720$	−3228.58	−0.167114
$721$	23863.8	1.23264
$722$	19545.1	1.00747
$723$	17308.3	0.890320
$724$	67658.8	3.47309
$725$	−7888.38	−0.404092
$726$	1760.92	0.0900190
$727$	−25682.6	−1.31020	−0.655099	−	0.755543i	$-0.727373\pi$
$727$	−25682.6	−1.31020	−0.655099	+	0.755543i	$0.727373\pi$
$728$	47174.3	2.40164
$729$	729.000	0.0370370
$730$	12872.4	0.652643
$731$	332.820	0.0168397
$732$	2842.42	0.143523
$733$	−24212.0	−1.22004	−0.610020	−	0.792386i	$-0.708839\pi$
$733$	−24212.0	−1.22004	−0.610020	+	0.792386i	$0.708839\pi$
$734$	−50136.1	−2.52120
$735$	−2741.20	−0.137565
$736$	−2120.46	−0.106197
$737$	3819.92	0.190921
$738$	−6149.65	−0.306737
$739$	189.266	0.00942120	0.00471060	−	0.999989i	$-0.498501\pi$
$739$	189.266	0.00942120	0.00471060	+	0.999989i	$0.498501\pi$
$740$	1853.88	0.0920944
$741$	14285.8	0.708235
$742$	−190.493	−0.00942485
$743$	−34616.4	−1.70922	−0.854612	−	0.519268i	$-0.826205\pi$
$743$	−34616.4	−1.70922	−0.854612	+	0.519268i	$0.826205\pi$
$744$	−26169.1	−1.28953
$745$	−18150.3	−0.892582
$746$	−5316.97	−0.260949
$747$	−1257.04	−0.0615701
$748$	12927.6	0.631925
$749$	−11897.1	−0.580389
$750$	20113.9	0.979275
$751$	−16270.6	−0.790576	−0.395288	−	0.918557i	$-0.629355\pi$
$751$	−16270.6	−0.790576	−0.395288	+	0.918557i	$0.629355\pi$
$752$	−30872.8	−1.49709
$753$	−3262.93	−0.157912
$754$	−43261.8	−2.08952
$755$	−21195.4	−1.02170
$756$	6048.50	0.290981
$757$	−30106.0	−1.44547	−0.722736	−	0.691125i	$-0.757116\pi$
$757$	−30106.0	−1.44547	−0.722736	+	0.691125i	$0.757116\pi$
$758$	−49681.5	−2.38062
$759$	1985.91	0.0949725
$760$	−13157.8	−0.628004
$761$	−1343.58	−0.0640012	−0.0320006	−	0.999488i	$-0.510188\pi$
$761$	−1343.58	−0.0640012	−0.0320006	+	0.999488i	$0.510188\pi$
$762$	−8880.75	−0.422199
$763$	4527.32	0.214810
$764$	−53137.4	−2.51629
$765$	−4609.58	−0.217856
$766$	−30967.3	−1.46070
$767$	46378.5	2.18335
$768$	23617.9	1.10968
$769$	−731.717	−0.0343126	−0.0171563	−	0.999853i	$-0.505461\pi$
$769$	−731.717	−0.0343126	−0.0171563	+	0.999853i	$0.505461\pi$
$770$	−5209.59	−0.243819
$771$	11940.9	0.557773
$772$	1465.53	0.0683231
$773$	267.749	0.0124583	0.00622915	−	0.999981i	$-0.498017\pi$
$773$	267.749	0.0124583	0.00622915	+	0.999981i	$0.498017\pi$
$774$	−192.042	−0.00891837
$775$	18902.3	0.876119
$776$	53069.2	2.45499
$777$	−762.922	−0.0352248
$778$	62886.9	2.89795
$779$	−7493.13	−0.344633
$780$	28234.8	1.29611
$781$	6203.71	0.284233
$782$	22088.5	1.01008
$783$	−2689.92	−0.122771
$784$	−7153.60	−0.325875
$785$	−16243.1	−0.738522
$786$	−14624.8	−0.663674
$787$	−1027.15	−0.0465233	−0.0232617	−	0.999729i	$-0.507405\pi$
$787$	−1027.15	−0.0465233	−0.0232617	+	0.999729i	$0.507405\pi$
$788$	−2631.12	−0.118946
$789$	−3000.66	−0.135394
$790$	5911.64	0.266237
$791$	−11338.7	−0.509682
$792$	−3617.42	−0.162297
$793$	−5460.41	−0.244521
$794$	−58314.2	−2.60641
$795$	−55.2908	−0.00246662
$796$	−16581.6	−0.738342
$797$	33037.4	1.46831	0.734155	−	0.678981i	$-0.237578\pi$
$797$	33037.4	1.46831	0.734155	+	0.678981i	$0.237578\pi$
$798$	11165.8	0.495318
$799$	−44078.4	−1.95167
$800$	−2789.94	−0.123299
$801$	3948.47	0.174173
$802$	44479.4	1.95838
$803$	4312.10	0.189503
$804$	−16181.6	−0.709801
$805$	−5875.22	−0.257235
$806$	103665.	4.53033
$807$	−23951.3	−1.04477
$808$	17146.1	0.746530
$809$	26456.6	1.14977	0.574885	−	0.818234i	$-0.305047\pi$
$809$	26456.6	1.14977	0.574885	+	0.818234i	$0.305047\pi$
$810$	2659.80	0.115378
$811$	21269.7	0.920937	0.460469	−	0.887676i	$-0.347681\pi$
$811$	21269.7	0.920937	0.460469	+	0.887676i	$0.347681\pi$
$812$	−22318.3	−0.964554
$813$	5983.09	0.258101
$814$	940.888	0.0405136
$815$	−18877.0	−0.811326
$816$	−12029.5	−0.516073
$817$	−233.997	−0.0100202
$818$	36561.7	1.56277
$819$	−11619.4	−0.495745
$820$	−14809.6	−0.630700
$821$	−38211.5	−1.62435	−0.812175	−	0.583414i	$-0.801717\pi$
$821$	−38211.5	−1.62435	−0.812175	+	0.583414i	$0.801717\pi$
$822$	8277.41	0.351226
$823$	31459.2	1.33244	0.666220	−	0.745755i	$-0.267911\pi$
$823$	31459.2	1.33244	0.666220	+	0.745755i	$0.267911\pi$
$824$	60458.5	2.55603
$825$	2612.91	0.110267
$826$	36249.4	1.52697
$827$	−41985.3	−1.76538	−0.882691	−	0.469954i	$-0.844271\pi$
$827$	−41985.3	−1.76538	−0.882691	+	0.469954i	$0.844271\pi$
$828$	−8412.52	−0.353086
$829$	7734.39	0.324037	0.162018	−	0.986788i	$-0.448200\pi$
$829$	7734.39	0.324037	0.162018	+	0.986788i	$0.448200\pi$
$830$	−4586.40	−0.191803
$831$	14857.1	0.620199
$832$	−53251.6	−2.21895
$833$	−10213.5	−0.424823
$834$	−30056.0	−1.24791
$835$	22575.9	0.935655
$836$	−9089.04	−0.376018
$837$	6445.67	0.266183
$838$	48208.9	1.98729
$839$	10876.0	0.447533	0.223767	−	0.974643i	$-0.428165\pi$
$839$	10876.0	0.447533	0.223767	+	0.974643i	$0.428165\pi$
$840$	10701.9	0.439586
$841$	−14463.5	−0.593033
$842$	−7655.84	−0.313347
$843$	3779.74	0.154426
$844$	−17909.6	−0.730418
$845$	−39368.5	−1.60274
$846$	25433.9	1.03361
$847$	−1745.15	−0.0707957
$848$	−144.291	−0.00584311
$849$	36.1955	0.00146316
$850$	29062.4	1.17274
$851$	1061.11	0.0427429
$852$	−26279.5	−1.05672
$853$	−3012.66	−0.120928	−0.0604640	−	0.998170i	$-0.519258\pi$
$853$	−3012.66	−0.120928	−0.0604640	+	0.998170i	$0.519258\pi$
$854$	−4267.85	−0.171010
$855$	3240.87	0.129632
$856$	−30141.1	−1.20351
$857$	13231.9	0.527413	0.263707	−	0.964603i	$-0.415055\pi$
$857$	13231.9	0.527413	0.263707	+	0.964603i	$0.415055\pi$
$858$	14329.9	0.570179
$859$	38715.8	1.53780	0.768898	−	0.639372i	$-0.220806\pi$
$859$	38715.8	1.53780	0.768898	+	0.639372i	$0.220806\pi$
$860$	−462.477	−0.0183376
$861$	6094.57	0.241234
$862$	9236.03	0.364942
$863$	−35963.1	−1.41854	−0.709270	−	0.704937i	$-0.750975\pi$
$863$	−35963.1	−1.41854	−0.709270	+	0.704937i	$0.750975\pi$
$864$	−951.364	−0.0374607
$865$	−11268.6	−0.442940
$866$	64374.9	2.52604
$867$	−2436.01	−0.0954224
$868$	53479.6	2.09126
$869$	1980.33	0.0773050
$870$	−9814.35	−0.382457
$871$	31085.4	1.20929
$872$	11469.9	0.445434
$873$	−13071.4	−0.506757
$874$	−15529.8	−0.601035
$875$	−19933.8	−0.770154
$876$	−18266.5	−0.704529
$877$	−47185.0	−1.81679	−0.908394	−	0.418115i	$-0.862691\pi$
$877$	−47185.0	−1.81679	−0.908394	+	0.418115i	$0.862691\pi$
$878$	−15901.2	−0.611206
$879$	11348.0	0.435447
$880$	−3946.04	−0.151160
$881$	−2080.81	−0.0795734	−0.0397867	−	0.999208i	$-0.512668\pi$
$881$	−2080.81	−0.0795734	−0.0397867	+	0.999208i	$0.512668\pi$
$882$	5893.36	0.224988
$883$	13414.3	0.511241	0.255620	−	0.966777i	$-0.417720\pi$
$883$	13414.3	0.511241	0.255620	+	0.966777i	$0.417720\pi$
$884$	105201.	4.00260
$885$	10521.4	0.399631
$886$	32549.6	1.23423
$887$	−30666.1	−1.16084	−0.580420	−	0.814317i	$-0.697112\pi$
$887$	−30666.1	−1.16084	−0.580420	+	0.814317i	$0.697112\pi$
$888$	−1932.85	−0.0730429
$889$	8801.21	0.332039
$890$	14406.2	0.542582
$891$	891.000	0.0335013
$892$	−81717.8	−3.06739
$893$	30990.3	1.16131
$894$	39021.6	1.45982
$895$	−7656.51	−0.285954
$896$	−37555.9	−1.40028
$897$	16160.8	0.601554
$898$	60987.8	2.26636
$899$	−23783.8	−0.882351
$900$	−11068.6	−0.409947
$901$	−206.010	−0.00761731
$902$	−7516.24	−0.277454
$903$	190.322	0.00701387
$904$	−28726.4	−1.05689
$905$	−29486.2	−1.08304
$906$	45568.5	1.67098
$907$	−5645.91	−0.206692	−0.103346	−	0.994645i	$-0.532955\pi$
$907$	−5645.91	−0.206692	−0.103346	+	0.994645i	$0.532955\pi$
$908$	−40213.6	−1.46975
$909$	−4223.21	−0.154098
$910$	−42394.1	−1.54434
$911$	−293.746	−0.0106830	−0.00534152	−	0.999986i	$-0.501700\pi$
$911$	−293.746	−0.0106830	−0.00534152	+	0.999986i	$0.501700\pi$
$912$	8457.59	0.307082
$913$	−1536.39	−0.0556923
$914$	50285.3	1.81979
$915$	−1238.75	−0.0447559
$916$	57405.9	2.07068
$917$	14493.8	0.521948
$918$	9910.24	0.356304
$919$	32840.1	1.17878	0.589388	−	0.807850i	$-0.299369\pi$
$919$	32840.1	1.17878	0.589388	+	0.807850i	$0.299369\pi$
$920$	−14884.7	−0.533408
$921$	17050.9	0.610039
$922$	−55983.5	−1.99969
$923$	50484.0	1.80033
$924$	7392.61	0.263203
$925$	1396.12	0.0496262
$926$	75521.0	2.68010
$927$	−14891.4	−0.527614
$928$	3510.42	0.124176
$929$	−27261.7	−0.962785	−0.481393	−	0.876505i	$-0.659869\pi$
$929$	−27261.7	−0.962785	−0.481393	+	0.876505i	$0.659869\pi$
$930$	23517.4	0.829211
$931$	7180.84	0.252785
$932$	69429.0	2.44015
$933$	−22964.0	−0.805797
$934$	−24110.5	−0.844669
$935$	−5633.93	−0.197058
$936$	−29437.5	−1.02799
$937$	39873.5	1.39019	0.695096	−	0.718917i	$-0.255362\pi$
$937$	39873.5	1.39019	0.695096	+	0.718917i	$0.255362\pi$
$938$	24296.4	0.845740
$939$	−3452.82	−0.119998
$940$	61250.1	2.12527
$941$	36458.6	1.26304	0.631518	−	0.775361i	$-0.282432\pi$
$941$	36458.6	1.26304	0.631518	+	0.775361i	$0.282432\pi$
$942$	34921.3	1.20785
$943$	−8476.60	−0.292721
$944$	27457.4	0.946675
$945$	−2635.98	−0.0907390
$946$	−234.718	−0.00806697
$947$	−4472.64	−0.153476	−0.0767378	−	0.997051i	$-0.524450\pi$
$947$	−4472.64	−0.153476	−0.0767378	+	0.997051i	$0.524450\pi$
$948$	−8388.86	−0.287402
$949$	35090.6	1.20031
$950$	−20433.0	−0.697825
$951$	3770.73	0.128575
$952$	39874.8	1.35751
$953$	−13545.9	−0.460436	−0.230218	−	0.973139i	$-0.573944\pi$
$953$	−13545.9	−0.460436	−0.230218	+	0.973139i	$0.573944\pi$
$954$	118.871	0.00403416
$955$	23157.6	0.784674
$956$	47975.3	1.62305
$957$	−3287.69	−0.111051
$958$	14226.2	0.479777
$959$	−8203.27	−0.276223
$960$	−12080.6	−0.406147
$961$	27200.3	0.913039
$962$	7656.68	0.256612
$963$	7423.99	0.248427
$964$	−89612.7	−2.99402
$965$	−638.686	−0.0213057
$966$	12631.3	0.420709
$967$	−8577.75	−0.285255	−0.142628	−	0.989776i	$-0.545555\pi$
$967$	−8577.75	−0.285255	−0.142628	+	0.989776i	$0.545555\pi$
$968$	−4421.29	−0.146803
$969$	12075.3	0.400324
$970$	−47691.7	−1.57865
$971$	41531.0	1.37260	0.686299	−	0.727320i	$-0.259234\pi$
$971$	41531.0	1.37260	0.686299	+	0.727320i	$0.259234\pi$
$972$	−3774.36	−0.124550
$973$	29786.8	0.981419
$974$	38096.9	1.25329
$975$	21263.2	0.698427
$976$	−3232.71	−0.106021
$977$	18314.0	0.599709	0.299855	−	0.953985i	$-0.403062\pi$
$977$	18314.0	0.599709	0.299855	+	0.953985i	$0.403062\pi$
$978$	40584.0	1.32693
$979$	4825.91	0.157545
$980$	14192.4	0.462612
$981$	−2825.12	−0.0919462
$982$	−57540.8	−1.86986
$983$	−33886.0	−1.09949	−0.549744	−	0.835333i	$-0.685275\pi$
$983$	−33886.0	−1.09949	−0.549744	+	0.835333i	$0.685275\pi$
$984$	15440.5	0.500227
$985$	1146.66	0.0370919
$986$	−36567.6	−1.18109
$987$	−25206.1	−0.812887
$988$	−73964.0	−2.38169
$989$	−264.709	−0.00851086
$990$	3250.87	0.104363
$991$	1106.52	0.0354690	0.0177345	−	0.999843i	$-0.494355\pi$
$991$	1106.52	0.0354690	0.0177345	+	0.999843i	$0.494355\pi$
$992$	−8411.77	−0.269228
$993$	30872.5	0.986614
$994$	39458.3	1.25910
$995$	7226.38	0.230243
$996$	6508.29	0.207051
$997$	−53735.4	−1.70694	−0.853468	−	0.521145i	$-0.825505\pi$
$997$	−53735.4	−1.70694	−0.853468	+	0.521145i	$0.825505\pi$
$998$	−72876.7	−2.31149
$999$	476.076	0.0150774

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.d.1.5	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.d.1.5	✓	37	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-4.85102 q^{2} -3.00000 q^{3} +15.5324 q^{4} -6.76910 q^{5} +14.5530 q^{6} -14.4227 q^{7} -36.5396 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.85102 q^{2} -3.00000 q^{3} +15.5324 q^{4} -6.76910 q^{5} +14.5530 q^{6} -14.4227 q^{7} -36.5396 q^{8} +9.00000 q^{9} +32.8370 q^{10} +11.0000 q^{11} -46.5971 q^{12} +89.5149 q^{13} +69.9648 q^{14} +20.3073 q^{15} +52.9953 q^{16} +75.6637 q^{17} -43.6591 q^{18} -53.1971 q^{19} -105.140 q^{20} +43.2681 q^{21} -53.3612 q^{22} -60.1792 q^{23} +109.619 q^{24} -79.1792 q^{25} -434.238 q^{26} -27.0000 q^{27} -224.019 q^{28} +99.6268 q^{29} -98.5111 q^{30} -238.729 q^{31} +35.2357 q^{32} -33.0000 q^{33} -367.046 q^{34} +97.6288 q^{35} +139.791 q^{36} -17.6324 q^{37} +258.060 q^{38} -268.545 q^{39} +247.340 q^{40} +140.856 q^{41} -209.894 q^{42} +4.39867 q^{43} +170.856 q^{44} -60.9219 q^{45} +291.930 q^{46} -582.557 q^{47} -158.986 q^{48} -134.986 q^{49} +384.100 q^{50} -226.991 q^{51} +1390.38 q^{52} -2.72271 q^{53} +130.977 q^{54} -74.4601 q^{55} +527.000 q^{56} +159.591 q^{57} -483.291 q^{58} +518.109 q^{59} +315.420 q^{60} -61.0000 q^{61} +1158.08 q^{62} -129.804 q^{63} -594.891 q^{64} -605.936 q^{65} +160.084 q^{66} +347.266 q^{67} +1175.24 q^{68} +180.538 q^{69} -473.599 q^{70} +563.974 q^{71} -328.856 q^{72} +392.009 q^{73} +85.5352 q^{74} +237.538 q^{75} -826.276 q^{76} -158.650 q^{77} +1302.71 q^{78} +180.030 q^{79} -358.731 q^{80} +81.0000 q^{81} -683.294 q^{82} -139.672 q^{83} +672.056 q^{84} -512.176 q^{85} -21.3380 q^{86} -298.881 q^{87} -401.936 q^{88} +438.719 q^{89} +295.533 q^{90} -1291.05 q^{91} -934.725 q^{92} +716.186 q^{93} +2825.99 q^{94} +360.097 q^{95} -105.707 q^{96} -1452.37 q^{97} +654.817 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9}+O(q^{10}) \) 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9} - 45 q^{10} + 407 q^{11} - 474 q^{12} - 169 q^{13} + 102 q^{14} + 45 q^{15} + 598 q^{16} - 338 q^{17} - 36 q^{18} - 235 q^{19} - 550 q^{20} + 231 q^{21} - 44 q^{22} - 53 q^{23} + 207 q^{24} + 750 q^{25} - 75 q^{26} - 999 q^{27} - 1378 q^{28} - 30 q^{29} + 135 q^{30} - 506 q^{31} - 841 q^{32} - 1221 q^{33} - 316 q^{34} - 822 q^{35} + 1422 q^{36} - 830 q^{37} - 371 q^{38} + 507 q^{39} - 613 q^{40} + 16 q^{41} - 306 q^{42} - 1137 q^{43} + 1738 q^{44} - 135 q^{45} - 659 q^{46} - 489 q^{47} - 1794 q^{48} + 2214 q^{49} + 1066 q^{50} + 1014 q^{51} - 2342 q^{52} + 731 q^{53} + 108 q^{54} - 165 q^{55} + 3051 q^{56} + 705 q^{57} - 611 q^{58} - 425 q^{59} + 1650 q^{60} - 2257 q^{61} + 453 q^{62} - 693 q^{63} + 4919 q^{64} + 1346 q^{65} + 132 q^{66} - 1907 q^{67} - 3236 q^{68} + 159 q^{69} - 1050 q^{70} - 561 q^{71} - 621 q^{72} - 2397 q^{73} - 1840 q^{74} - 2250 q^{75} - 3868 q^{76} - 847 q^{77} + 225 q^{78} + 393 q^{79} - 4031 q^{80} + 2997 q^{81} - 1946 q^{82} - 4191 q^{83} + 4134 q^{84} - 2667 q^{85} + 2405 q^{86} + 90 q^{87} - 759 q^{88} + 1437 q^{89} - 405 q^{90} - 5192 q^{91} - 737 q^{92} + 1518 q^{93} - 1960 q^{94} + 1356 q^{95} + 2523 q^{96} - 2368 q^{97} - 3014 q^{98} + 3663 q^{99}+O(q^{100}) \) 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9 - 45 * q^10 + 407 * q^11 - 474 * q^12 - 169 * q^13 + 102 * q^14 + 45 * q^15 + 598 * q^16 - 338 * q^17 - 36 * q^18 - 235 * q^19 - 550 * q^20 + 231 * q^21 - 44 * q^22 - 53 * q^23 + 207 * q^24 + 750 * q^25 - 75 * q^26 - 999 * q^27 - 1378 * q^28 - 30 * q^29 + 135 * q^30 - 506 * q^31 - 841 * q^32 - 1221 * q^33 - 316 * q^34 - 822 * q^35 + 1422 * q^36 - 830 * q^37 - 371 * q^38 + 507 * q^39 - 613 * q^40 + 16 * q^41 - 306 * q^42 - 1137 * q^43 + 1738 * q^44 - 135 * q^45 - 659 * q^46 - 489 * q^47 - 1794 * q^48 + 2214 * q^49 + 1066 * q^50 + 1014 * q^51 - 2342 * q^52 + 731 * q^53 + 108 * q^54 - 165 * q^55 + 3051 * q^56 + 705 * q^57 - 611 * q^58 - 425 * q^59 + 1650 * q^60 - 2257 * q^61 + 453 * q^62 - 693 * q^63 + 4919 * q^64 + 1346 * q^65 + 132 * q^66 - 1907 * q^67 - 3236 * q^68 + 159 * q^69 - 1050 * q^70 - 561 * q^71 - 621 * q^72 - 2397 * q^73 - 1840 * q^74 - 2250 * q^75 - 3868 * q^76 - 847 * q^77 + 225 * q^78 + 393 * q^79 - 4031 * q^80 + 2997 * q^81 - 1946 * q^82 - 4191 * q^83 + 4134 * q^84 - 2667 * q^85 + 2405 * q^86 + 90 * q^87 - 759 * q^88 + 1437 * q^89 - 405 * q^90 - 5192 * q^91 - 737 * q^92 + 1518 * q^93 - 1960 * q^94 + 1356 * q^95 + 2523 * q^96 - 2368 * q^97 - 3014 * q^98 + 3663 * q^99

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