LMFDB - Embedded newform 1849.4.a.k.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, 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("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.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:	$109.094531601$
Analytic rank:	$1$
Dimension:	$60$
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.22240 q^{2} +5.78517 q^{3} +9.82864 q^{4} +5.96613 q^{5} -24.4273 q^{6} -8.16125 q^{7} -7.72124 q^{8} +6.46824 q^{9} +O(q^{10})$	\(q-4.22240 q^{2} +5.78517 q^{3} +9.82864 q^{4} +5.96613 q^{5} -24.4273 q^{6} -8.16125 q^{7} -7.72124 q^{8} +6.46824 q^{9} -25.1914 q^{10} +6.81167 q^{11} +56.8604 q^{12} +54.2426 q^{13} +34.4600 q^{14} +34.5151 q^{15} -46.0270 q^{16} -7.26696 q^{17} -27.3115 q^{18} +112.159 q^{19} +58.6390 q^{20} -47.2142 q^{21} -28.7616 q^{22} -126.806 q^{23} -44.6687 q^{24} -89.4052 q^{25} -229.034 q^{26} -118.780 q^{27} -80.2140 q^{28} -216.188 q^{29} -145.737 q^{30} +190.895 q^{31} +256.114 q^{32} +39.4067 q^{33} +30.6840 q^{34} -48.6911 q^{35} +63.5740 q^{36} -268.358 q^{37} -473.578 q^{38} +313.803 q^{39} -46.0660 q^{40} -291.142 q^{41} +199.357 q^{42} +66.9495 q^{44} +38.5904 q^{45} +535.424 q^{46} +100.565 q^{47} -266.274 q^{48} -276.394 q^{49} +377.504 q^{50} -42.0406 q^{51} +533.131 q^{52} +407.945 q^{53} +501.536 q^{54} +40.6394 q^{55} +63.0150 q^{56} +648.856 q^{57} +912.831 q^{58} -94.5619 q^{59} +339.237 q^{60} +424.628 q^{61} -806.036 q^{62} -52.7889 q^{63} -713.200 q^{64} +323.618 q^{65} -166.391 q^{66} -62.4531 q^{67} -71.4243 q^{68} -733.594 q^{69} +205.593 q^{70} -660.446 q^{71} -49.9429 q^{72} -1078.33 q^{73} +1133.12 q^{74} -517.225 q^{75} +1102.37 q^{76} -55.5918 q^{77} -1325.00 q^{78} +109.716 q^{79} -274.603 q^{80} -861.804 q^{81} +1229.32 q^{82} -174.460 q^{83} -464.052 q^{84} -43.3556 q^{85} -1250.68 q^{87} -52.5946 q^{88} +271.903 q^{89} -162.944 q^{90} -442.687 q^{91} -1246.33 q^{92} +1104.36 q^{93} -424.624 q^{94} +669.153 q^{95} +1481.66 q^{96} -1077.56 q^{97} +1167.05 q^{98} +44.0595 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 15 q^{2} - 37 q^{3} + 213 q^{4} - 51 q^{5} + 22 q^{6} - 54 q^{7} - 204 q^{8} + 387 q^{9}+O(q^{10}) $ 60 * q - 15 * q^2 - 37 * q^3 + 213 * q^4 - 51 * q^5 + 22 * q^6 - 54 * q^7 - 204 * q^8 + 387 * q^9	\( 60 q - 15 q^{2} - 37 q^{3} + 213 q^{4} - 51 q^{5} + 22 q^{6} - 54 q^{7} - 204 q^{8} + 387 q^{9} + 27 q^{10} + 43 q^{11} - 432 q^{12} + 13 q^{13} + 96 q^{14} + 65 q^{15} + 717 q^{16} - 138 q^{17} - 625 q^{18} - 610 q^{19} - 345 q^{20} + 611 q^{21} - 118 q^{22} - 243 q^{23} + 258 q^{24} + 899 q^{25} - 1071 q^{26} - 1609 q^{27} - 46 q^{28} - 773 q^{29} - 375 q^{30} - 97 q^{31} - 1967 q^{32} - 500 q^{33} - 217 q^{34} + 247 q^{35} + 175 q^{36} - 228 q^{37} + 1253 q^{38} - 1493 q^{39} + 2220 q^{40} - 951 q^{41} - 2643 q^{42} - 1378 q^{44} - 1086 q^{45} + 565 q^{46} - 2 q^{47} - 2303 q^{48} + 1264 q^{49} - 3273 q^{50} - 3076 q^{51} - 2825 q^{52} - 39 q^{53} + 5201 q^{54} - 1306 q^{55} + 3683 q^{56} + 1342 q^{57} + 2588 q^{58} - 1065 q^{59} + 2803 q^{60} - 2999 q^{61} - 5569 q^{62} - 2377 q^{63} + 2082 q^{64} - 5578 q^{65} + 3338 q^{66} + 961 q^{67} - 3754 q^{68} - 1817 q^{69} - 2738 q^{70} - 8003 q^{71} - 1412 q^{72} + 1011 q^{73} - 1413 q^{74} - 7457 q^{75} - 5516 q^{76} - 4052 q^{77} + 1091 q^{78} - 4422 q^{79} - 1610 q^{80} + 2108 q^{81} - 4676 q^{82} - 297 q^{83} - 54 q^{84} - 4333 q^{85} + 1377 q^{87} - 3652 q^{88} - 2480 q^{89} - 1414 q^{90} - 4551 q^{91} - 3286 q^{92} - 4 q^{93} - 4609 q^{94} - 835 q^{95} + 5864 q^{96} + 3785 q^{97} - 753 q^{98} + 5072 q^{99}+O(q^{100}) \) 60 * q - 15 * q^2 - 37 * q^3 + 213 * q^4 - 51 * q^5 + 22 * q^6 - 54 * q^7 - 204 * q^8 + 387 * q^9 + 27 * q^10 + 43 * q^11 - 432 * q^12 + 13 * q^13 + 96 * q^14 + 65 * q^15 + 717 * q^16 - 138 * q^17 - 625 * q^18 - 610 * q^19 - 345 * q^20 + 611 * q^21 - 118 * q^22 - 243 * q^23 + 258 * q^24 + 899 * q^25 - 1071 * q^26 - 1609 * q^27 - 46 * q^28 - 773 * q^29 - 375 * q^30 - 97 * q^31 - 1967 * q^32 - 500 * q^33 - 217 * q^34 + 247 * q^35 + 175 * q^36 - 228 * q^37 + 1253 * q^38 - 1493 * q^39 + 2220 * q^40 - 951 * q^41 - 2643 * q^42 - 1378 * q^44 - 1086 * q^45 + 565 * q^46 - 2 * q^47 - 2303 * q^48 + 1264 * q^49 - 3273 * q^50 - 3076 * q^51 - 2825 * q^52 - 39 * q^53 + 5201 * q^54 - 1306 * q^55 + 3683 * q^56 + 1342 * q^57 + 2588 * q^58 - 1065 * q^59 + 2803 * q^60 - 2999 * q^61 - 5569 * q^62 - 2377 * q^63 + 2082 * q^64 - 5578 * q^65 + 3338 * q^66 + 961 * q^67 - 3754 * q^68 - 1817 * q^69 - 2738 * q^70 - 8003 * q^71 - 1412 * q^72 + 1011 * q^73 - 1413 * q^74 - 7457 * q^75 - 5516 * q^76 - 4052 * q^77 + 1091 * q^78 - 4422 * q^79 - 1610 * q^80 + 2108 * q^81 - 4676 * q^82 - 297 * q^83 - 54 * q^84 - 4333 * q^85 + 1377 * q^87 - 3652 * q^88 - 2480 * q^89 - 1414 * q^90 - 4551 * q^91 - 3286 * q^92 - 4 * q^93 - 4609 * q^94 - 835 * q^95 + 5864 * q^96 + 3785 * q^97 - 753 * q^98 + 5072 * 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 $

$2$	−4.22240	−1.49284	−0.746421	−	0.665474i	$-0.768230\pi$
$2$	−4.22240	−1.49284	−0.746421	+	0.665474i	$0.768230\pi$
$3$	5.78517	1.11336	0.556679	−	0.830728i	$-0.312075\pi$
$3$	5.78517	1.11336	0.556679	+	0.830728i	$0.312075\pi$
$4$	9.82864	1.22858
$5$	5.96613	0.533627	0.266814	−	0.963748i	$-0.414029\pi$
$5$	5.96613	0.533627	0.266814	+	0.963748i	$0.414029\pi$
$6$	−24.4273	−1.66207
$7$	−8.16125	−0.440666	−0.220333	−	0.975425i	$-0.570714\pi$
$7$	−8.16125	−0.440666	−0.220333	+	0.975425i	$0.570714\pi$
$8$	−7.72124	−0.341234
$9$	6.46824	0.239564
$10$	−25.1914	−0.796622
$11$	6.81167	0.186709	0.0933544	−	0.995633i	$-0.470241\pi$
$11$	6.81167	0.186709	0.0933544	+	0.995633i	$0.470241\pi$
$12$	56.8604	1.36785
$13$	54.2426	1.15724	0.578622	−	0.815596i	$-0.303591\pi$
$13$	54.2426	1.15724	0.578622	+	0.815596i	$0.303591\pi$
$14$	34.4600	0.657845
$15$	34.5151	0.594118
$16$	−46.0270	−0.719171
$17$	−7.26696	−0.103676	−0.0518381	−	0.998656i	$-0.516508\pi$
$17$	−7.26696	−0.103676	−0.0518381	+	0.998656i	$0.516508\pi$
$18$	−27.3115	−0.357632
$19$	112.159	1.35426	0.677130	−	0.735864i	$-0.263224\pi$
$19$	112.159	1.35426	0.677130	+	0.735864i	$0.263224\pi$
$20$	58.6390	0.655604
$21$	−47.2142	−0.490619
$22$	−28.7616	−0.278727
$23$	−126.806	−1.14960	−0.574801	−	0.818293i	$-0.694920\pi$
$23$	−126.806	−1.14960	−0.574801	+	0.818293i	$0.694920\pi$
$24$	−44.6687	−0.379915
$25$	−89.4052	−0.715242
$26$	−229.034	−1.72758
$27$	−118.780	−0.846636
$28$	−80.2140	−0.541393
$29$	−216.188	−1.38431	−0.692156	−	0.721748i	$-0.743339\pi$
$29$	−216.188	−1.38431	−0.692156	+	0.721748i	$0.743339\pi$
$30$	−145.737	−0.886925
$31$	190.895	1.10599	0.552997	−	0.833183i	$-0.313484\pi$
$31$	190.895	1.10599	0.552997	+	0.833183i	$0.313484\pi$
$32$	256.114	1.41484
$33$	39.4067	0.207874
$34$	30.6840	0.154772
$35$	−48.6911	−0.235151
$36$	63.5740	0.294324
$37$	−268.358	−1.19237	−0.596187	−	0.802846i	$-0.703318\pi$
$37$	−268.358	−1.19237	−0.596187	+	0.802846i	$0.703318\pi$
$38$	−473.578	−2.02170
$39$	313.803	1.28843
$40$	−46.0660	−0.182092
$41$	−291.142	−1.10899	−0.554497	−	0.832185i	$-0.687089\pi$
$41$	−291.142	−1.10899	−0.554497	+	0.832185i	$0.687089\pi$
$42$	199.357	0.732416
$43$	0	0
$43$	0	0
$44$	66.9495	0.229387
$45$	38.5904	0.127838
$46$	535.424	1.71617
$47$	100.565	0.312103	0.156052	−	0.987749i	$-0.450123\pi$
$47$	100.565	0.312103	0.156052	+	0.987749i	$0.450123\pi$
$48$	−266.274	−0.800695
$49$	−276.394	−0.805814
$50$	377.504	1.06774
$51$	−42.0406	−0.115429
$52$	533.131	1.42177
$53$	407.945	1.05728	0.528638	−	0.848848i	$-0.322703\pi$
$53$	407.945	1.05728	0.528638	+	0.848848i	$0.322703\pi$
$54$	501.536	1.26390
$55$	40.6394	0.0996329
$56$	63.0150	0.150370
$57$	648.856	1.50777
$58$	912.831	2.06656
$59$	−94.5619	−0.208660	−0.104330	−	0.994543i	$-0.533270\pi$
$59$	−94.5619	−0.208660	−0.104330	+	0.994543i	$0.533270\pi$
$60$	339.237	0.729921
$61$	424.628	0.891279	0.445640	−	0.895212i	$-0.352976\pi$
$61$	424.628	0.891279	0.445640	+	0.895212i	$0.352976\pi$
$62$	−806.036	−1.65108
$63$	−52.7889	−0.105568
$64$	−713.200	−1.39297
$65$	323.618	0.617537
$66$	−166.391	−0.310323
$67$	−62.4531	−0.113879	−0.0569393	−	0.998378i	$-0.518134\pi$
$67$	−62.4531	−0.113879	−0.0569393	+	0.998378i	$0.518134\pi$
$68$	−71.4243	−0.127375
$69$	−733.594	−1.27992
$70$	205.593	0.351044
$71$	−660.446	−1.10395	−0.551975	−	0.833861i	$-0.686126\pi$
$71$	−660.446	−1.10395	−0.551975	+	0.833861i	$0.686126\pi$
$72$	−49.9429	−0.0817475
$73$	−1078.33	−1.72889	−0.864447	−	0.502724i	$-0.832331\pi$
$73$	−1078.33	−1.72889	−0.864447	+	0.502724i	$0.832331\pi$
$74$	1133.12	1.78003
$75$	−517.225	−0.796320
$76$	1102.37	1.66382
$77$	−55.5918	−0.0822762
$78$	−1325.00	−1.92342
$79$	109.716	0.156254	0.0781270	−	0.996943i	$-0.475106\pi$
$79$	109.716	0.156254	0.0781270	+	0.996943i	$0.475106\pi$
$80$	−274.603	−0.383769
$81$	−861.804	−1.18217
$82$	1229.32	1.65555
$83$	−174.460	−0.230717	−0.115358	−	0.993324i	$-0.536802\pi$
$83$	−174.460	−0.230717	−0.115358	+	0.993324i	$0.536802\pi$
$84$	−464.052	−0.602764
$85$	−43.3556	−0.0553245
$86$	0	0
$87$	−1250.68	−1.54123
$88$	−52.5946	−0.0637114
$89$	271.903	0.323839	0.161919	−	0.986804i	$-0.448232\pi$
$89$	271.903	0.323839	0.161919	+	0.986804i	$0.448232\pi$
$90$	−162.944	−0.190842
$91$	−442.687	−0.509958
$92$	−1246.33	−1.41238
$93$	1104.36	1.23137
$94$	−424.624	−0.465921
$95$	669.153	0.722670
$96$	1481.66	1.57523
$97$	−1077.56	−1.12793	−0.563967	−	0.825798i	$-0.690725\pi$
$97$	−1077.56	−1.12793	−0.563967	+	0.825798i	$0.690725\pi$
$98$	1167.05	1.20295
$99$	44.0595	0.0447288
$100$	−878.732	−0.878732
$101$	195.269	0.192376	0.0961881	−	0.995363i	$-0.469335\pi$
$101$	195.269	0.192376	0.0961881	+	0.995363i	$0.469335\pi$
$102$	177.512	0.172317
$103$	1567.70	1.49971	0.749853	−	0.661604i	$-0.230124\pi$
$103$	1567.70	1.49971	0.749853	+	0.661604i	$0.230124\pi$
$104$	−418.820	−0.394891
$105$	−281.686	−0.261807
$106$	−1722.51	−1.57835
$107$	1268.82	1.14637	0.573186	−	0.819426i	$-0.305707\pi$
$107$	1268.82	1.14637	0.573186	+	0.819426i	$0.305707\pi$
$108$	−1167.44	−1.04016
$109$	349.083	0.306753	0.153376	−	0.988168i	$-0.450985\pi$
$109$	349.083	0.306753	0.153376	+	0.988168i	$0.450985\pi$
$110$	−171.596	−0.148736
$111$	−1552.50	−1.32754
$112$	375.637	0.316914
$113$	−1793.37	−1.49298	−0.746488	−	0.665399i	$-0.768261\pi$
$113$	−1793.37	−1.49298	−0.746488	+	0.665399i	$0.768261\pi$
$114$	−2739.73	−2.25087
$115$	−756.540	−0.613459
$116$	−2124.83	−1.70074
$117$	350.854	0.277235
$118$	399.278	0.311496
$119$	59.3074	0.0456866
$120$	−266.500	−0.202733
$121$	−1284.60	−0.965140
$122$	−1792.95	−1.33054
$123$	−1684.31	−1.23471
$124$	1876.24	1.35880
$125$	−1279.17	−0.915300
$126$	222.896	0.157596
$127$	1398.79	0.977341	0.488671	−	0.872468i	$-0.337482\pi$
$127$	1398.79	0.977341	0.488671	+	0.872468i	$0.337482\pi$
$128$	962.500	0.664639
$129$	0	0
$130$	−1366.45	−0.921886
$131$	−2179.32	−1.45350	−0.726749	−	0.686903i	$-0.758970\pi$
$131$	−2179.32	−1.45350	−0.726749	+	0.686903i	$0.758970\pi$
$132$	387.314	0.255389
$133$	−915.353	−0.596776
$134$	263.702	0.170003
$135$	−708.656	−0.451788
$136$	56.1100	0.0353779
$137$	−666.773	−0.415812	−0.207906	−	0.978149i	$-0.566665\pi$
$137$	−666.773	−0.415812	−0.207906	+	0.978149i	$0.566665\pi$
$138$	3097.52	1.91072
$139$	2354.85	1.43695	0.718473	−	0.695555i	$-0.244841\pi$
$139$	2354.85	1.43695	0.718473	+	0.695555i	$0.244841\pi$
$140$	−478.567	−0.288902
$141$	581.784	0.347483
$142$	2788.66	1.64802
$143$	369.483	0.216068
$144$	−297.713	−0.172288
$145$	−1289.81	−0.738707
$146$	4553.15	2.58097
$147$	−1598.99	−0.897158
$148$	−2637.60	−1.46493
$149$	−1474.35	−0.810628	−0.405314	−	0.914177i	$-0.632838\pi$
$149$	−1474.35	−0.810628	−0.405314	+	0.914177i	$0.632838\pi$
$150$	2183.93	1.18878
$151$	−2501.40	−1.34809	−0.674043	−	0.738692i	$-0.735444\pi$
$151$	−2501.40	−1.34809	−0.674043	+	0.738692i	$0.735444\pi$
$152$	−866.003	−0.462119
$153$	−47.0044	−0.0248371
$154$	234.730	0.122825
$155$	1138.91	0.590189
$156$	3084.25	1.58294
$157$	−2869.96	−1.45890	−0.729452	−	0.684032i	$-0.760225\pi$
$157$	−2869.96	−1.45890	−0.729452	+	0.684032i	$0.760225\pi$
$158$	−463.267	−0.233263
$159$	2360.03	1.17713
$160$	1528.01	0.754999
$161$	1034.89	0.506590
$162$	3638.88	1.76480
$163$	171.422	0.0823729	0.0411864	−	0.999151i	$-0.486886\pi$
$163$	171.422	0.0823729	0.0411864	+	0.999151i	$0.486886\pi$
$164$	−2861.53	−1.36249
$165$	235.106	0.110927
$166$	736.640	0.344424
$167$	2140.87	0.992009	0.496005	−	0.868320i	$-0.334800\pi$
$167$	2140.87	0.992009	0.496005	+	0.868320i	$0.334800\pi$
$168$	364.553	0.167416
$169$	745.257	0.339216
$170$	183.065	0.0825907
$171$	725.468	0.324432
$172$	0	0
$173$	−2420.61	−1.06379	−0.531895	−	0.846810i	$-0.678520\pi$
$173$	−2420.61	−1.06379	−0.531895	+	0.846810i	$0.678520\pi$
$174$	5280.88	2.30082
$175$	729.658	0.315183
$176$	−313.521	−0.134276
$177$	−547.057	−0.232313
$178$	−1148.08	−0.483440
$179$	3181.70	1.32855	0.664277	−	0.747486i	$-0.268740\pi$
$179$	3181.70	1.32855	0.664277	+	0.747486i	$0.268740\pi$
$180$	379.291	0.157059
$181$	−1101.49	−0.452337	−0.226168	−	0.974088i	$-0.572620\pi$
$181$	−1101.49	−0.452337	−0.226168	+	0.974088i	$0.572620\pi$
$182$	1869.20	0.761288
$183$	2456.55	0.992312
$184$	979.098	0.392283
$185$	−1601.06	−0.636283
$186$	−4663.06	−1.83824
$187$	−49.5002	−0.0193573
$188$	988.413	0.383444
$189$	969.391	0.373084
$190$	−2825.43	−1.07883
$191$	2595.56	0.983288	0.491644	−	0.870796i	$-0.336396\pi$
$191$	2595.56	0.983288	0.491644	+	0.870796i	$0.336396\pi$
$192$	−4125.98	−1.55087
$193$	4985.56	1.85942	0.929711	−	0.368291i	$-0.120057\pi$
$193$	4985.56	1.85942	0.929711	+	0.368291i	$0.120057\pi$
$194$	4549.88	1.68383
$195$	1872.19	0.687540
$196$	−2716.58	−0.990006
$197$	4091.66	1.47979	0.739896	−	0.672722i	$-0.234875\pi$
$197$	4091.66	1.47979	0.739896	+	0.672722i	$0.234875\pi$
$198$	−186.037	−0.0667731
$199$	1164.23	0.414723	0.207361	−	0.978264i	$-0.433512\pi$
$199$	1164.23	0.414723	0.207361	+	0.978264i	$0.433512\pi$
$200$	690.320	0.244065
$201$	−361.302	−0.126788
$202$	−824.503	−0.287187
$203$	1764.36	0.610019
$204$	−413.202	−0.141813
$205$	−1736.99	−0.591790
$206$	−6619.44	−2.23883
$207$	−820.210	−0.275404
$208$	−2496.62	−0.832257
$209$	763.987	0.252852
$210$	1189.39	0.390837
$211$	1089.48	0.355464	0.177732	−	0.984079i	$-0.443124\pi$
$211$	1089.48	0.355464	0.177732	+	0.984079i	$0.443124\pi$
$212$	4009.55	1.29895
$213$	−3820.79	−1.22909
$214$	−5357.47	−1.71135
$215$	0	0
$216$	917.128	0.288901
$217$	−1557.94	−0.487374
$218$	−1473.97	−0.457934
$219$	−6238.34	−1.92488
$220$	399.430	0.122407
$221$	−394.179	−0.119979
$222$	6555.27	1.98181
$223$	−5506.20	−1.65346	−0.826732	−	0.562596i	$-0.809803\pi$
$223$	−5506.20	−1.65346	−0.826732	+	0.562596i	$0.809803\pi$
$224$	−2090.21	−0.623473
$225$	−578.295	−0.171347
$226$	7572.33	2.22878
$227$	−4678.14	−1.36784	−0.683919	−	0.729558i	$-0.739726\pi$
$227$	−4678.14	−1.36784	−0.683919	+	0.729558i	$0.739726\pi$
$228$	6377.38	1.85242
$229$	1750.71	0.505198	0.252599	−	0.967571i	$-0.418715\pi$
$229$	1750.71	0.505198	0.252599	+	0.967571i	$0.418715\pi$
$230$	3194.41	0.915798
$231$	−321.608	−0.0916028
$232$	1669.24	0.472374
$233$	2931.36	0.824206	0.412103	−	0.911137i	$-0.364794\pi$
$233$	2931.36	0.824206	0.412103	+	0.911137i	$0.364794\pi$
$234$	−1481.45	−0.413868
$235$	599.982	0.166547
$236$	−929.415	−0.256355
$237$	634.729	0.173967
$238$	−250.420	−0.0682029
$239$	−3022.48	−0.818025	−0.409013	−	0.912529i	$-0.634127\pi$
$239$	−3022.48	−0.818025	−0.409013	+	0.912529i	$0.634127\pi$
$240$	−1588.63	−0.427272
$241$	518.530	0.138595	0.0692977	−	0.997596i	$-0.477924\pi$
$241$	518.530	0.138595	0.0692977	+	0.997596i	$0.477924\pi$
$242$	5424.10	1.44080
$243$	−1778.63	−0.469545
$244$	4173.51	1.09501
$245$	−1649.00	−0.430004
$246$	7111.82	1.84322
$247$	6083.77	1.56721
$248$	−1473.95	−0.377403
$249$	−1009.28	−0.256870
$250$	5401.17	1.36640
$251$	3597.24	0.904604	0.452302	−	0.891865i	$-0.350603\pi$
$251$	3597.24	0.904604	0.452302	+	0.891865i	$0.350603\pi$
$252$	−518.843	−0.129699
$253$	−863.760	−0.214641
$254$	−5906.24	−1.45902
$255$	−250.820	−0.0615959
$256$	1641.54	0.400767
$257$	−4221.69	−1.02468	−0.512338	−	0.858784i	$-0.671221\pi$
$257$	−4221.69	−1.02468	−0.512338	+	0.858784i	$0.671221\pi$
$258$	0	0
$259$	2190.14	0.525438
$260$	3180.73	0.758694
$261$	−1398.35	−0.331632
$262$	9201.96	2.16984
$263$	5477.80	1.28432	0.642159	−	0.766571i	$-0.278039\pi$
$263$	5477.80	1.28432	0.642159	+	0.766571i	$0.278039\pi$
$264$	−304.269	−0.0709335
$265$	2433.86	0.564191
$266$	3864.99	0.890893
$267$	1573.01	0.360548
$268$	−613.829	−0.139909
$269$	1933.34	0.438207	0.219103	−	0.975702i	$-0.429687\pi$
$269$	1933.34	0.438207	0.219103	+	0.975702i	$0.429687\pi$
$270$	2992.23	0.674449
$271$	−5288.42	−1.18542	−0.592710	−	0.805416i	$-0.701942\pi$
$271$	−5288.42	−1.18542	−0.592710	+	0.805416i	$0.701942\pi$
$272$	334.476	0.0745610
$273$	−2561.02	−0.567766
$274$	2815.38	0.620742
$275$	−608.999	−0.133542
$276$	−7210.23	−1.57248
$277$	7445.26	1.61495	0.807477	−	0.589900i	$-0.200833\pi$
$277$	7445.26	1.61495	0.807477	+	0.589900i	$0.200833\pi$
$278$	−9943.10	−2.14513
$279$	1234.76	0.264957
$280$	375.956	0.0802416
$281$	−6495.08	−1.37888	−0.689438	−	0.724344i	$-0.742143\pi$
$281$	−6495.08	−1.37888	−0.689438	+	0.724344i	$0.742143\pi$
$282$	−2456.52	−0.518737
$283$	−5240.39	−1.10074	−0.550369	−	0.834921i	$-0.685513\pi$
$283$	−5240.39	−1.10074	−0.550369	+	0.834921i	$0.685513\pi$
$284$	−6491.28	−1.35629
$285$	3871.16	0.804590
$286$	−1560.10	−0.322555
$287$	2376.08	0.488696
$288$	1656.61	0.338946
$289$	−4860.19	−0.989251
$290$	5446.07	1.10277
$291$	−6233.86	−1.25579
$292$	−10598.5	−2.12408
$293$	−2750.86	−0.548487	−0.274244	−	0.961660i	$-0.588427\pi$
$293$	−2750.86	−0.548487	−0.274244	+	0.961660i	$0.588427\pi$
$294$	6751.56	1.33932
$295$	−564.169	−0.111346
$296$	2072.06	0.406878
$297$	−809.089	−0.158074
$298$	6225.30	1.21014
$299$	−6878.27	−1.33037
$300$	−5083.62	−0.978343
$301$	0	0
$302$	10561.9	2.01248
$303$	1129.67	0.214183
$304$	−5162.31	−0.973944
$305$	2533.39	0.475611
$306$	198.471	0.0370780
$307$	−3367.36	−0.626012	−0.313006	−	0.949751i	$-0.601336\pi$
$307$	−3367.36	−0.626012	−0.313006	+	0.949751i	$0.601336\pi$
$308$	−546.391	−0.101083
$309$	9069.40	1.66971
$310$	−4808.92	−0.881059
$311$	−4609.09	−0.840377	−0.420189	−	0.907437i	$-0.638036\pi$
$311$	−4609.09	−0.840377	−0.420189	+	0.907437i	$0.638036\pi$
$312$	−2422.95	−0.439655
$313$	−2043.66	−0.369056	−0.184528	−	0.982827i	$-0.559076\pi$
$313$	−2043.66	−0.369056	−0.184528	+	0.982827i	$0.559076\pi$
$314$	12118.1	2.17792
$315$	−314.946	−0.0563339
$316$	1078.36	0.191971
$317$	−1110.69	−0.196790	−0.0983951	−	0.995147i	$-0.531371\pi$
$317$	−1110.69	−0.196790	−0.0983951	+	0.995147i	$0.531371\pi$
$318$	−9965.01	−1.75726
$319$	−1472.60	−0.258463
$320$	−4255.04	−0.743326
$321$	7340.36	1.27632
$322$	−4369.73	−0.756260
$323$	−815.051	−0.140405
$324$	−8470.36	−1.45239
$325$	−4849.57	−0.827710
$326$	−723.810	−0.122970
$327$	2019.50	0.341525
$328$	2247.98	0.378427
$329$	−820.733	−0.137533
$330$	−992.710	−0.165597
$331$	470.487	0.0781277	0.0390639	−	0.999237i	$-0.487562\pi$
$331$	470.487	0.0781277	0.0390639	+	0.999237i	$0.487562\pi$
$332$	−1714.71	−0.283454
$333$	−1735.81	−0.285650
$334$	−9039.61	−1.48091
$335$	−372.604	−0.0607687
$336$	2173.13	0.352839
$337$	−2826.46	−0.456876	−0.228438	−	0.973558i	$-0.573362\pi$
$337$	−2826.46	−0.456876	−0.228438	+	0.973558i	$0.573362\pi$
$338$	−3146.77	−0.506396
$339$	−10375.0	−1.66221
$340$	−426.127	−0.0679705
$341$	1300.32	0.206499
$342$	−3063.22	−0.484327
$343$	5055.03	0.795760
$344$	0	0
$345$	−4376.72	−0.682999
$346$	10220.8	1.58807
$347$	−5033.17	−0.778659	−0.389330	−	0.921098i	$-0.627293\pi$
$347$	−5033.17	−0.778659	−0.389330	+	0.921098i	$0.627293\pi$
$348$	−12292.5	−1.89353
$349$	−3757.02	−0.576242	−0.288121	−	0.957594i	$-0.593031\pi$
$349$	−3757.02	−0.576242	−0.288121	+	0.957594i	$0.593031\pi$
$350$	−3080.91	−0.470518
$351$	−6442.92	−0.979766
$352$	1744.57	0.264164
$353$	−5147.53	−0.776135	−0.388067	−	0.921631i	$-0.626857\pi$
$353$	−5147.53	−0.776135	−0.388067	+	0.921631i	$0.626857\pi$
$354$	2309.89	0.346806
$355$	−3940.31	−0.589098
$356$	2672.43	0.397862
$357$	343.104	0.0508655
$358$	−13434.4	−1.98332
$359$	4721.78	0.694167	0.347084	−	0.937834i	$-0.387172\pi$
$359$	4721.78	0.694167	0.347084	+	0.937834i	$0.387172\pi$
$360$	−297.966	−0.0436227
$361$	5720.53	0.834018
$362$	4650.92	0.675267
$363$	−7431.64	−1.07455
$364$	−4351.01	−0.626525
$365$	−6433.47	−0.922585
$366$	−10372.5	−1.48137
$367$	−13053.3	−1.85661	−0.928305	−	0.371818i	$-0.878734\pi$
$367$	−13053.3	−1.85661	−0.928305	+	0.371818i	$0.878734\pi$
$368$	5836.49	0.826760
$369$	−1883.18	−0.265676
$370$	6760.32	0.949871
$371$	−3329.34	−0.465905
$372$	10854.4	1.51283
$373$	2181.02	0.302759	0.151380	−	0.988476i	$-0.451628\pi$
$373$	2181.02	0.302759	0.151380	+	0.988476i	$0.451628\pi$
$374$	209.009	0.0288974
$375$	−7400.22	−1.01906
$376$	−776.484	−0.106500
$377$	−11726.6	−1.60199
$378$	−4093.16	−0.556956
$379$	11270.2	1.52748	0.763738	−	0.645527i	$-0.223362\pi$
$379$	11270.2	1.52748	0.763738	+	0.645527i	$0.223362\pi$
$380$	6576.86	0.887857
$381$	8092.23	1.08813
$382$	−10959.5	−1.46789
$383$	−4639.61	−0.618990	−0.309495	−	0.950901i	$-0.600160\pi$
$383$	−4639.61	−0.618990	−0.309495	+	0.950901i	$0.600160\pi$
$384$	5568.23	0.739981
$385$	−331.668	−0.0439048
$386$	−21051.0	−2.77582
$387$	0	0
$388$	−10590.9	−1.38576
$389$	−10730.6	−1.39862	−0.699311	−	0.714818i	$-0.746510\pi$
$389$	−10730.6	−1.39862	−0.699311	+	0.714818i	$0.746510\pi$
$390$	−7905.13	−1.02639
$391$	921.492	0.119186
$392$	2134.11	0.274971
$393$	−12607.8	−1.61826
$394$	−17276.6	−2.20910
$395$	654.583	0.0833814
$396$	433.045	0.0549529
$397$	6006.13	0.759292	0.379646	−	0.925132i	$-0.376046\pi$
$397$	6006.13	0.759292	0.379646	+	0.925132i	$0.376046\pi$
$398$	−4915.83	−0.619116
$399$	−5295.48	−0.664425
$400$	4115.05	0.514381
$401$	9005.22	1.12144	0.560722	−	0.828004i	$-0.310524\pi$
$401$	9005.22	1.12144	0.560722	+	0.828004i	$0.310524\pi$
$402$	1525.56	0.189274
$403$	10354.7	1.27991
$404$	1919.23	0.236350
$405$	−5141.64	−0.630840
$406$	−7449.84	−0.910663
$407$	−1827.97	−0.222627
$408$	324.606	0.0393882
$409$	8554.09	1.03416	0.517082	−	0.855936i	$-0.327018\pi$
$409$	8554.09	1.03416	0.517082	+	0.855936i	$0.327018\pi$
$410$	7334.28	0.883449
$411$	−3857.40	−0.462947
$412$	15408.3	1.84251
$413$	771.743	0.0919492
$414$	3463.25	0.411134
$415$	−1040.85	−0.123117
$416$	13892.3	1.63732
$417$	13623.2	1.59983
$418$	−3225.86	−0.377469
$419$	−8666.95	−1.01052	−0.505260	−	0.862967i	$-0.668604\pi$
$419$	−8666.95	−1.01052	−0.505260	+	0.862967i	$0.668604\pi$
$420$	−2768.59	−0.321651
$421$	11262.0	1.30375	0.651873	−	0.758328i	$-0.273983\pi$
$421$	11262.0	1.30375	0.651873	+	0.758328i	$0.273983\pi$
$422$	−4600.22	−0.530652
$423$	650.476	0.0747689
$424$	−3149.85	−0.360778
$425$	649.704	0.0741536
$426$	16132.9	1.83484
$427$	−3465.49	−0.392756
$428$	12470.8	1.40841
$429$	2137.52	0.240561
$430$	0	0
$431$	−3790.39	−0.423611	−0.211806	−	0.977312i	$-0.567934\pi$
$431$	−3790.39	−0.423611	−0.211806	+	0.977312i	$0.567934\pi$
$432$	5467.07	0.608877
$433$	−12645.7	−1.40350	−0.701748	−	0.712425i	$-0.747597\pi$
$433$	−12645.7	−1.40350	−0.701748	+	0.712425i	$0.747597\pi$
$434$	6578.26	0.727573
$435$	−7461.75	−0.822445
$436$	3431.01	0.376870
$437$	−14222.3	−1.55686
$438$	26340.7	2.87354
$439$	4602.58	0.500385	0.250193	−	0.968196i	$-0.419506\pi$
$439$	4602.58	0.500385	0.250193	+	0.968196i	$0.419506\pi$
$440$	−313.786	−0.0339981
$441$	−1787.78	−0.193044
$442$	1664.38	0.179110
$443$	−17560.0	−1.88329	−0.941646	−	0.336604i	$-0.890722\pi$
$443$	−17560.0	−1.88329	−0.941646	+	0.336604i	$0.890722\pi$
$444$	−15259.0	−1.63099
$445$	1622.21	0.172809
$446$	23249.4	2.46836
$447$	−8529.38	−0.902519
$448$	5820.60	0.613834
$449$	−13165.1	−1.38374	−0.691872	−	0.722020i	$-0.743214\pi$
$449$	−13165.1	−1.38374	−0.691872	+	0.722020i	$0.743214\pi$
$450$	2441.79	0.255794
$451$	−1983.17	−0.207059
$452$	−17626.4	−1.83424
$453$	−14471.0	−1.50090
$454$	19753.0	2.04197
$455$	−2641.13	−0.272128
$456$	−5009.98	−0.514504
$457$	10102.1	1.03404	0.517021	−	0.855972i	$-0.327041\pi$
$457$	10102.1	1.03404	0.517021	+	0.855972i	$0.327041\pi$
$458$	−7392.20	−0.754181
$459$	863.168	0.0877761
$460$	−7435.76	−0.753683
$461$	−4433.26	−0.447890	−0.223945	−	0.974602i	$-0.571894\pi$
$461$	−4433.26	−0.447890	−0.223945	+	0.974602i	$0.571894\pi$
$462$	1357.96	0.136749
$463$	−4562.27	−0.457941	−0.228971	−	0.973433i	$-0.573536\pi$
$463$	−4562.27	−0.457941	−0.228971	+	0.973433i	$0.573536\pi$
$464$	9950.46	0.995558
$465$	6588.78	0.657091
$466$	−12377.4	−1.23041
$467$	14160.0	1.40310	0.701551	−	0.712619i	$-0.252491\pi$
$467$	14160.0	1.40310	0.701551	+	0.712619i	$0.252491\pi$
$468$	3448.42	0.340605
$469$	509.695	0.0501824
$470$	−2533.36	−0.248628
$471$	−16603.2	−1.62428
$472$	730.136	0.0712017
$473$	0	0
$474$	−2680.08	−0.259705
$475$	−10027.6	−0.968623
$476$	582.911	0.0561296
$477$	2638.69	0.253286
$478$	12762.1	1.22118
$479$	−2837.36	−0.270652	−0.135326	−	0.990801i	$-0.543208\pi$
$479$	−2837.36	−0.270652	−0.135326	+	0.990801i	$0.543208\pi$
$480$	8839.81	0.840584
$481$	−14556.4	−1.37987
$482$	−2189.44	−0.206901
$483$	5987.04	0.564016
$484$	−12625.9	−1.18575
$485$	−6428.86	−0.601896
$486$	7510.10	0.700957
$487$	−15768.3	−1.46721	−0.733606	−	0.679576i	$-0.762164\pi$
$487$	−15768.3	−1.46721	−0.733606	+	0.679576i	$0.762164\pi$
$488$	−3278.66	−0.304135
$489$	991.704	0.0917104
$490$	6962.75	0.641929
$491$	684.661	0.0629293	0.0314647	−	0.999505i	$-0.489983\pi$
$491$	684.661	0.0629293	0.0314647	+	0.999505i	$0.489983\pi$
$492$	−16554.5	−1.51694
$493$	1571.03	0.143520
$494$	−25688.1	−2.33960
$495$	262.865	0.0238685
$496$	−8786.34	−0.795400
$497$	5390.06	0.486473
$498$	4261.59	0.383467
$499$	−8202.71	−0.735879	−0.367939	−	0.929850i	$-0.619937\pi$
$499$	−8202.71	−0.735879	−0.367939	+	0.929850i	$0.619937\pi$
$500$	−12572.5	−1.12452
$501$	12385.3	1.10446
$502$	−15189.0	−1.35043
$503$	−19176.1	−1.69984	−0.849921	−	0.526910i	$-0.823350\pi$
$503$	−19176.1	−1.69984	−0.849921	+	0.526910i	$0.823350\pi$
$504$	407.596	0.0360234
$505$	1165.00	0.102657
$506$	3647.14	0.320425
$507$	4311.44	0.377668
$508$	13748.2	1.20074
$509$	2417.36	0.210506	0.105253	−	0.994445i	$-0.466435\pi$
$509$	2417.36	0.210506	0.105253	+	0.994445i	$0.466435\pi$
$510$	1059.06	0.0919530
$511$	8800.53	0.761864
$512$	−14631.2	−1.26292
$513$	−13322.2	−1.14657
$514$	17825.7	1.52968
$515$	9353.09	0.800284
$516$	0	0
$517$	685.013	0.0582724
$518$	−9247.63	−0.784397
$519$	−14003.7	−1.18438
$520$	−2498.74	−0.210725
$521$	1208.49	0.101621	0.0508107	−	0.998708i	$-0.483819\pi$
$521$	1208.49	0.101621	0.0508107	+	0.998708i	$0.483819\pi$
$522$	5904.41	0.495075
$523$	−9179.22	−0.767456	−0.383728	−	0.923446i	$-0.625360\pi$
$523$	−9179.22	−0.767456	−0.383728	+	0.923446i	$0.625360\pi$
$524$	−21419.8	−1.78574
$525$	4221.20	0.350911
$526$	−23129.5	−1.91729
$527$	−1387.23	−0.114665
$528$	−1813.77	−0.149497
$529$	3912.71	0.321584
$530$	−10276.7	−0.842249
$531$	−611.649	−0.0499874
$532$	−8996.68	−0.733187
$533$	−15792.3	−1.28338
$534$	−6641.85	−0.538242
$535$	7569.97	0.611735
$536$	482.216	0.0388592
$537$	18406.7	1.47916
$538$	−8163.32	−0.654174
$539$	−1882.71	−0.150452
$540$	−6965.13	−0.555058
$541$	2982.95	0.237056	0.118528	−	0.992951i	$-0.462182\pi$
$541$	2982.95	0.237056	0.118528	+	0.992951i	$0.462182\pi$
$542$	22329.8	1.76964
$543$	−6372.30	−0.503612
$544$	−1861.17	−0.146686
$545$	2082.67	0.163692
$546$	10813.7	0.847585
$547$	4300.60	0.336161	0.168081	−	0.985773i	$-0.446243\pi$
$547$	4300.60	0.336161	0.168081	+	0.985773i	$0.446243\pi$
$548$	−6553.47	−0.510858
$549$	2746.60	0.213519
$550$	2571.44	0.199357
$551$	−24247.3	−1.87472
$552$	5664.25	0.436751
$553$	−895.423	−0.0688558
$554$	−31436.8	−2.41087
$555$	−9262.42	−0.708410
$556$	23144.9	1.76540
$557$	−17070.7	−1.29858	−0.649291	−	0.760540i	$-0.724934\pi$
$557$	−17070.7	−1.29858	−0.649291	+	0.760540i	$0.724934\pi$
$558$	−5213.64	−0.395539
$559$	0	0
$560$	2241.10	0.169114
$561$	−286.367	−0.0215516
$562$	27424.8	2.05845
$563$	17789.7	1.33170	0.665848	−	0.746088i	$-0.268070\pi$
$563$	17789.7	1.33170	0.665848	+	0.746088i	$0.268070\pi$
$564$	5718.14	0.426910
$565$	−10699.5	−0.796692
$566$	22127.0	1.64323
$567$	7033.40	0.520943
$568$	5099.46	0.376705
$569$	−23237.4	−1.71206	−0.856029	−	0.516929i	$-0.827075\pi$
$569$	−23237.4	−1.71206	−0.856029	+	0.516929i	$0.827075\pi$
$570$	−16345.6	−1.20113
$571$	−4403.95	−0.322766	−0.161383	−	0.986892i	$-0.551595\pi$
$571$	−4403.95	−0.322766	−0.161383	+	0.986892i	$0.551595\pi$
$572$	3631.51	0.265457
$573$	15015.8	1.09475
$574$	−10032.8	−0.729547
$575$	11337.1	0.822243
$576$	−4613.15	−0.333706
$577$	5047.14	0.364151	0.182076	−	0.983285i	$-0.441718\pi$
$577$	5047.14	0.364151	0.182076	+	0.983285i	$0.441718\pi$
$578$	20521.7	1.47680
$579$	28842.3	2.07020
$580$	−12677.0	−0.907560
$581$	1423.81	0.101669
$582$	26321.9	1.87470
$583$	2778.79	0.197403
$584$	8326.07	0.589957
$585$	2093.24	0.147940
$586$	11615.2	0.818806
$587$	−15568.1	−1.09466	−0.547329	−	0.836917i	$-0.684355\pi$
$587$	−15568.1	−1.09466	−0.547329	+	0.836917i	$0.684355\pi$
$588$	−15715.9	−1.10223
$589$	21410.5	1.49780
$590$	2382.15	0.166223
$591$	23671.0	1.64754
$592$	12351.7	0.857521
$593$	−21956.1	−1.52045	−0.760226	−	0.649659i	$-0.774912\pi$
$593$	−21956.1	−1.52045	−0.760226	+	0.649659i	$0.774912\pi$
$594$	3416.30	0.235980
$595$	353.836	0.0243796
$596$	−14490.9	−0.995922
$597$	6735.25	0.461735
$598$	29042.8	1.98603
$599$	−17432.3	−1.18909	−0.594544	−	0.804063i	$-0.702667\pi$
$599$	−17432.3	−1.18909	−0.594544	+	0.804063i	$0.702667\pi$
$600$	3993.62	0.271731
$601$	19590.9	1.32967	0.664834	−	0.746992i	$-0.268502\pi$
$601$	19590.9	1.32967	0.664834	+	0.746992i	$0.268502\pi$
$602$	0	0
$603$	−403.962	−0.0272813
$604$	−24585.4	−1.65623
$605$	−7664.10	−0.515025
$606$	−4769.90	−0.319742
$607$	1458.40	0.0975199	0.0487599	−	0.998811i	$-0.484473\pi$
$607$	1458.40	0.0975199	0.0487599	+	0.998811i	$0.484473\pi$
$608$	28725.4	1.91607
$609$	10207.1	0.679169
$610$	−10697.0	−0.710012
$611$	5454.88	0.361180
$612$	−461.990	−0.0305144
$613$	24725.4	1.62912	0.814559	−	0.580081i	$-0.196979\pi$
$613$	24725.4	1.62912	0.814559	+	0.580081i	$0.196979\pi$
$614$	14218.3	0.934537
$615$	−10048.8	−0.658874
$616$	429.237	0.0280754
$617$	11981.8	0.781795	0.390897	−	0.920434i	$-0.372165\pi$
$617$	11981.8	0.781795	0.390897	+	0.920434i	$0.372165\pi$
$618$	−38294.6	−2.49261
$619$	15026.5	0.975711	0.487855	−	0.872925i	$-0.337779\pi$
$619$	15026.5	0.975711	0.487855	+	0.872925i	$0.337779\pi$
$620$	11193.9	0.725094
$621$	15062.0	0.973295
$622$	19461.4	1.25455
$623$	−2219.07	−0.142705
$624$	−14443.4	−0.926600
$625$	3543.95	0.226813
$626$	8629.14	0.550942
$627$	4419.80	0.281515
$628$	−28207.8	−1.79238
$629$	1950.15	0.123621
$630$	1329.83	0.0840977
$631$	4910.46	0.309798	0.154899	−	0.987930i	$-0.450495\pi$
$631$	4910.46	0.309798	0.154899	+	0.987930i	$0.450495\pi$
$632$	−847.148	−0.0533192
$633$	6302.84	0.395759
$634$	4689.77	0.293777
$635$	8345.36	0.521536
$636$	23195.9	1.44619
$637$	−14992.3	−0.932524
$638$	6217.90	0.385845
$639$	−4271.92	−0.264467
$640$	5742.40	0.354669
$641$	−9059.47	−0.558233	−0.279117	−	0.960257i	$-0.590042\pi$
$641$	−9059.47	−0.558233	−0.279117	+	0.960257i	$0.590042\pi$
$642$	−30993.9	−1.90535
$643$	13265.5	0.813590	0.406795	−	0.913519i	$-0.366646\pi$
$643$	13265.5	0.813590	0.406795	+	0.913519i	$0.366646\pi$
$644$	10171.6	0.622387
$645$	0	0
$646$	3441.47	0.209602
$647$	9438.51	0.573518	0.286759	−	0.958003i	$-0.407422\pi$
$647$	9438.51	0.573518	0.286759	+	0.958003i	$0.407422\pi$
$648$	6654.20	0.403398
$649$	−644.125	−0.0389586
$650$	20476.8	1.23564
$651$	−9012.98	−0.542622
$652$	1684.84	0.101202
$653$	−18429.2	−1.10443	−0.552213	−	0.833703i	$-0.686217\pi$
$653$	−18429.2	−1.10443	−0.552213	+	0.833703i	$0.686217\pi$
$654$	−8527.15	−0.509844
$655$	−13002.1	−0.775626
$656$	13400.4	0.797557
$657$	−6974.91	−0.414182
$658$	3465.46	0.205316
$659$	7088.36	0.419003	0.209502	−	0.977808i	$-0.432816\pi$
$659$	7088.36	0.419003	0.209502	+	0.977808i	$0.432816\pi$
$660$	2310.77	0.136283
$661$	−14938.1	−0.879009	−0.439505	−	0.898240i	$-0.644846\pi$
$661$	−14938.1	−0.879009	−0.439505	+	0.898240i	$0.644846\pi$
$662$	−1986.58	−0.116632
$663$	−2280.39	−0.133579
$664$	1347.05	0.0787284
$665$	−5461.12	−0.318456
$666$	7329.26	0.426431
$667$	27413.9	1.59141
$668$	21041.9	1.21876
$669$	−31854.3	−1.84090
$670$	1573.28	0.0907181
$671$	2892.43	0.166410
$672$	−12092.2	−0.694149
$673$	12905.6	0.739187	0.369594	−	0.929193i	$-0.379497\pi$
$673$	12905.6	0.739187	0.369594	+	0.929193i	$0.379497\pi$
$674$	11934.4	0.682044
$675$	10619.5	0.605550
$676$	7324.86	0.416754
$677$	7622.42	0.432723	0.216361	−	0.976313i	$-0.430581\pi$
$677$	7622.42	0.432723	0.216361	+	0.976313i	$0.430581\pi$
$678$	43807.2	2.48143
$679$	8794.22	0.497042
$680$	334.760	0.0188786
$681$	−27063.9	−1.52289
$682$	−5490.46	−0.308271
$683$	12736.9	0.713564	0.356782	−	0.934188i	$-0.383874\pi$
$683$	12736.9	0.713564	0.356782	+	0.934188i	$0.383874\pi$
$684$	7130.37	0.398591
$685$	−3978.05	−0.221889
$686$	−21344.3	−1.18795
$687$	10128.2	0.562466
$688$	0	0
$689$	22128.0	1.22353
$690$	18480.2	1.01961
$691$	21879.4	1.20453	0.602266	−	0.798296i	$-0.294265\pi$
$691$	21879.4	1.20453	0.602266	+	0.798296i	$0.294265\pi$
$692$	−23791.3	−1.30695
$693$	−359.581	−0.0197105
$694$	21252.1	1.16242
$695$	14049.3	0.766793
$696$	9656.83	0.525921
$697$	2115.72	0.114976
$698$	15863.6	0.860239
$699$	16958.4	0.917636
$700$	7171.55	0.387227
$701$	−30693.0	−1.65372	−0.826860	−	0.562407i	$-0.809875\pi$
$701$	−30693.0	−1.65372	−0.826860	+	0.562407i	$0.809875\pi$
$702$	27204.6	1.46264
$703$	−30098.7	−1.61478
$704$	−4858.08	−0.260079
$705$	3471.00	0.185426
$706$	21734.9	1.15865
$707$	−1593.64	−0.0847736
$708$	−5376.83	−0.285415
$709$	12534.2	0.663936	0.331968	−	0.943291i	$-0.392287\pi$
$709$	12534.2	0.663936	0.331968	+	0.943291i	$0.392287\pi$
$710$	16637.5	0.879431
$711$	709.673	0.0374329
$712$	−2099.43	−0.110505
$713$	−24206.6	−1.27145
$714$	−1448.72	−0.0759342
$715$	2204.38	0.115300
$716$	31271.8	1.63223
$717$	−17485.6	−0.910755
$718$	−19937.2	−1.03628
$719$	33228.6	1.72353	0.861766	−	0.507306i	$-0.169359\pi$
$719$	33228.6	1.72353	0.861766	+	0.507306i	$0.169359\pi$
$720$	−1776.20	−0.0919375
$721$	−12794.4	−0.660869
$722$	−24154.4	−1.24506
$723$	2999.79	0.154306
$724$	−10826.1	−0.555732
$725$	19328.3	0.990118
$726$	31379.3	1.60413
$727$	9593.77	0.489426	0.244713	−	0.969595i	$-0.421306\pi$
$727$	9593.77	0.489426	0.244713	+	0.969595i	$0.421306\pi$
$728$	3418.09	0.174015
$729$	12979.0	0.659402
$730$	27164.7	1.37727
$731$	0	0
$732$	24144.5	1.21913
$733$	−3239.52	−0.163239	−0.0816197	−	0.996664i	$-0.526009\pi$
$733$	−3239.52	−0.163239	−0.0816197	+	0.996664i	$0.526009\pi$
$734$	55116.2	2.77163
$735$	−9539.78	−0.478748
$736$	−32476.7	−1.62651
$737$	−425.410	−0.0212621
$738$	7951.53	0.396612
$739$	−7750.57	−0.385804	−0.192902	−	0.981218i	$-0.561790\pi$
$739$	−7750.57	−0.385804	−0.192902	+	0.981218i	$0.561790\pi$
$740$	−15736.3	−0.781725
$741$	35195.6	1.74486
$742$	14057.8	0.695523
$743$	−29284.0	−1.44593	−0.722966	−	0.690884i	$-0.757222\pi$
$743$	−29284.0	−1.44593	−0.722966	+	0.690884i	$0.757222\pi$
$744$	−8527.06	−0.420184
$745$	−8796.18	−0.432573
$746$	−9209.15	−0.451972
$747$	−1128.45	−0.0552715
$748$	−486.519	−0.0237820
$749$	−10355.2	−0.505167
$750$	31246.7	1.52129
$751$	17359.2	0.843470	0.421735	−	0.906719i	$-0.361421\pi$
$751$	17359.2	0.843470	0.421735	+	0.906719i	$0.361421\pi$
$752$	−4628.68	−0.224456
$753$	20810.6	1.00715
$754$	49514.3	2.39152
$755$	−14923.7	−0.719376
$756$	9527.80	0.458363
$757$	27728.6	1.33133	0.665663	−	0.746253i	$-0.268149\pi$
$757$	27728.6	1.33133	0.665663	+	0.746253i	$0.268149\pi$
$758$	−47587.4	−2.28028
$759$	−4997.00	−0.238972
$760$	−5166.69	−0.246599
$761$	−15035.9	−0.716228	−0.358114	−	0.933678i	$-0.616580\pi$
$761$	−15035.9	−0.716228	−0.358114	+	0.933678i	$0.616580\pi$
$762$	−34168.6	−1.62441
$763$	−2848.95	−0.135175
$764$	25510.8	1.20805
$765$	−280.435	−0.0132538
$766$	19590.3	0.924054
$767$	−5129.28	−0.241470
$768$	9496.60	0.446196
$769$	−3084.97	−0.144664	−0.0723321	−	0.997381i	$-0.523044\pi$
$769$	−3084.97	−0.144664	−0.0723321	+	0.997381i	$0.523044\pi$
$770$	1400.43	0.0655430
$771$	−24423.2	−1.14083
$772$	49001.3	2.28445
$773$	−14704.3	−0.684187	−0.342094	−	0.939666i	$-0.611136\pi$
$773$	−14704.3	−0.684187	−0.342094	+	0.939666i	$0.611136\pi$
$774$	0	0
$775$	−17067.1	−0.791054
$776$	8320.09	0.384889
$777$	12670.3	0.585001
$778$	45308.9	2.08792
$779$	−32654.1	−1.50187
$780$	18401.1	0.844698
$781$	−4498.74	−0.206117
$782$	−3890.91	−0.177927
$783$	25678.7	1.17201
$784$	12721.6	0.579518
$785$	−17122.6	−0.778511
$786$	53235.0	2.41581
$787$	−8325.51	−0.377093	−0.188547	−	0.982064i	$-0.560378\pi$
$787$	−8325.51	−0.377093	−0.188547	+	0.982064i	$0.560378\pi$
$788$	40215.5	1.81804
$789$	31690.0	1.42990
$790$	−2763.91	−0.124475
$791$	14636.1	0.657903
$792$	−340.195	−0.0152630
$793$	23032.9	1.03143
$794$	−25360.2	−1.13350
$795$	14080.3	0.628146
$796$	11442.8	0.509520
$797$	43883.8	1.95037	0.975184	−	0.221396i	$-0.0710613\pi$
$797$	43883.8	1.95037	0.975184	+	0.221396i	$0.0710613\pi$
$798$	22359.6	0.991882
$799$	−730.799	−0.0323577
$800$	−22897.9	−1.01196
$801$	1758.73	0.0775802
$802$	−38023.6	−1.67414
$803$	−7345.25	−0.322800
$804$	−3551.11	−0.155769
$805$	6174.31	0.270330
$806$	−43721.5	−1.91070
$807$	11184.7	0.487881
$808$	−1507.72	−0.0656453
$809$	−25790.5	−1.12082	−0.560411	−	0.828215i	$-0.689357\pi$
$809$	−25790.5	−1.12082	−0.560411	+	0.828215i	$0.689357\pi$
$810$	21710.0	0.941745
$811$	−22564.2	−0.976988	−0.488494	−	0.872567i	$-0.662454\pi$
$811$	−22564.2	−0.976988	−0.488494	+	0.872567i	$0.662454\pi$
$812$	17341.3	0.749457
$813$	−30594.4	−1.31979
$814$	7718.41	0.332347
$815$	1022.72	0.0439564
$816$	1935.00	0.0830130
$817$	0	0
$818$	−36118.8	−1.54384
$819$	−2863.41	−0.122168
$820$	−17072.3	−0.727061
$821$	−37053.2	−1.57511	−0.787555	−	0.616245i	$-0.788653\pi$
$821$	−37053.2	−1.57511	−0.787555	+	0.616245i	$0.788653\pi$
$822$	16287.5	0.691107
$823$	−12707.3	−0.538213	−0.269106	−	0.963110i	$-0.586728\pi$
$823$	−12707.3	−0.538213	−0.269106	+	0.963110i	$0.586728\pi$
$824$	−12104.6	−0.511751
$825$	−3523.17	−0.148680
$826$	−3258.61	−0.137266
$827$	−2446.56	−0.102872	−0.0514361	−	0.998676i	$-0.516380\pi$
$827$	−2446.56	−0.102872	−0.0514361	+	0.998676i	$0.516380\pi$
$828$	−8061.55	−0.338355
$829$	−1431.69	−0.0599816	−0.0299908	−	0.999550i	$-0.509548\pi$
$829$	−1431.69	−0.0599816	−0.0299908	+	0.999550i	$0.509548\pi$
$830$	4394.89	0.183794
$831$	43072.1	1.79802
$832$	−38685.8	−1.61201
$833$	2008.54	0.0835437
$834$	−57522.5	−2.38830
$835$	12772.7	0.529363
$836$	7508.95	0.310649
$837$	−22674.5	−0.936375
$838$	36595.3	1.50855
$839$	−5075.00	−0.208830	−0.104415	−	0.994534i	$-0.533297\pi$
$839$	−5075.00	−0.208830	−0.104415	+	0.994534i	$0.533297\pi$
$840$	2174.97	0.0893376
$841$	22348.1	0.916320
$842$	−47552.7	−1.94629
$843$	−37575.2	−1.53518
$844$	10708.1	0.436716
$845$	4446.30	0.181015
$846$	−2746.57	−0.111618
$847$	10483.9	0.425304
$848$	−18776.5	−0.760362
$849$	−30316.6	−1.22552
$850$	−2743.31	−0.110700
$851$	34029.4	1.37075
$852$	−37553.2	−1.51004
$853$	6707.22	0.269227	0.134614	−	0.990898i	$-0.457021\pi$
$853$	6707.22	0.269227	0.134614	+	0.990898i	$0.457021\pi$
$854$	14632.7	0.586324
$855$	4328.24	0.173126
$856$	−9796.89	−0.391181
$857$	29804.9	1.18800	0.594000	−	0.804465i	$-0.297548\pi$
$857$	29804.9	1.18800	0.594000	+	0.804465i	$0.297548\pi$
$858$	−9025.47	−0.359119
$859$	4787.80	0.190172	0.0950860	−	0.995469i	$-0.469687\pi$
$859$	4787.80	0.190172	0.0950860	+	0.995469i	$0.469687\pi$
$860$	0	0
$861$	13746.1	0.544093
$862$	16004.5	0.632385
$863$	−3901.24	−0.153881	−0.0769407	−	0.997036i	$-0.524515\pi$
$863$	−3901.24	−0.153881	−0.0769407	+	0.997036i	$0.524515\pi$
$864$	−30421.2	−1.19786
$865$	−14441.7	−0.567668
$866$	53395.2	2.09520
$867$	−28117.1	−1.10139
$868$	−15312.5	−0.598778
$869$	747.353	0.0291740
$870$	31506.5	1.22778
$871$	−3387.62	−0.131785
$872$	−2695.35	−0.104674
$873$	−6969.91	−0.270213
$874$	60052.4	2.32415
$875$	10439.6	0.403341
$876$	−61314.4	−2.36486
$877$	22020.6	0.847872	0.423936	−	0.905692i	$-0.360648\pi$
$877$	22020.6	0.847872	0.423936	+	0.905692i	$0.360648\pi$
$878$	−19433.9	−0.746997
$879$	−15914.2	−0.610662
$880$	−1870.51	−0.0716531
$881$	41408.9	1.58354	0.791771	−	0.610819i	$-0.209160\pi$
$881$	41408.9	1.58354	0.791771	+	0.610819i	$0.209160\pi$
$882$	7548.73	0.288185
$883$	−21537.6	−0.820837	−0.410419	−	0.911897i	$-0.634617\pi$
$883$	−21537.6	−0.820837	−0.410419	+	0.911897i	$0.634617\pi$
$884$	−3874.24	−0.147404
$885$	−3263.82	−0.123968
$886$	74145.1	2.81146
$887$	−36095.7	−1.36637	−0.683187	−	0.730243i	$-0.739407\pi$
$887$	−36095.7	−1.36637	−0.683187	+	0.730243i	$0.739407\pi$
$888$	11987.2	0.453001
$889$	−11415.9	−0.430681
$890$	−6849.61	−0.257977
$891$	−5870.33	−0.220722
$892$	−54118.5	−2.03141
$893$	11279.2	0.422669
$894$	36014.5	1.34732
$895$	18982.4	0.708953
$896$	−7855.20	−0.292884
$897$	−39792.0	−1.48118
$898$	55588.4	2.06571
$899$	−41269.3	−1.53104
$900$	−5683.85	−0.210513
$901$	−2964.52	−0.109614
$902$	8373.72	0.309107
$903$	0	0
$904$	13847.1	0.509454
$905$	−6571.62	−0.241379
$906$	61102.5	2.24061
$907$	10483.5	0.383793	0.191896	−	0.981415i	$-0.438536\pi$
$907$	10483.5	0.383793	0.191896	+	0.981415i	$0.438536\pi$
$908$	−45979.8	−1.68050
$909$	1263.05	0.0460865
$910$	11151.9	0.406244
$911$	37654.2	1.36942	0.684709	−	0.728816i	$-0.259929\pi$
$911$	37654.2	1.36942	0.684709	+	0.728816i	$0.259929\pi$
$912$	−29864.9	−1.08435
$913$	−1188.37	−0.0430768
$914$	−42655.2	−1.54366
$915$	14656.1	0.529525
$916$	17207.1	0.620676
$917$	17786.0	0.640507
$918$	−3644.64	−0.131036
$919$	−24156.5	−0.867082	−0.433541	−	0.901134i	$-0.642736\pi$
$919$	−24156.5	−0.867082	−0.433541	+	0.901134i	$0.642736\pi$
$920$	5841.43	0.209333
$921$	−19480.8	−0.696974
$922$	18719.0	0.668630
$923$	−35824.3	−1.27754
$924$	−3160.97	−0.112541
$925$	23992.6	0.852836
$926$	19263.7	0.683634
$927$	10140.2	0.359276
$928$	−55368.7	−1.95859
$929$	13915.9	0.491460	0.245730	−	0.969338i	$-0.420972\pi$
$929$	13915.9	0.491460	0.245730	+	0.969338i	$0.420972\pi$
$930$	−27820.4	−0.980934
$931$	−30999.9	−1.09128
$932$	28811.3	1.01260
$933$	−26664.4	−0.935640
$934$	−59789.3	−2.09461
$935$	−295.325	−0.0103296
$936$	−2709.03	−0.0946019
$937$	29481.0	1.02786	0.513928	−	0.857833i	$-0.328190\pi$
$937$	29481.0	1.02786	0.513928	+	0.857833i	$0.328190\pi$
$938$	−2152.14	−0.0749144
$939$	−11822.9	−0.410891
$940$	5897.01	0.204616
$941$	−29335.1	−1.01625	−0.508127	−	0.861282i	$-0.669662\pi$
$941$	−29335.1	−1.01625	−0.508127	+	0.861282i	$0.669662\pi$
$942$	70105.5	2.42480
$943$	36918.5	1.27490
$944$	4352.40	0.150062
$945$	5783.52	0.199088
$946$	0	0
$947$	23752.5	0.815049	0.407524	−	0.913194i	$-0.366392\pi$
$947$	23752.5	0.815049	0.407524	+	0.913194i	$0.366392\pi$
$948$	6238.52	0.213732
$949$	−58491.5	−2.00075
$950$	42340.3	1.44600
$951$	−6425.53	−0.219098
$952$	−457.927	−0.0155898
$953$	−23020.3	−0.782476	−0.391238	−	0.920289i	$-0.627953\pi$
$953$	−23020.3	−0.782476	−0.391238	+	0.920289i	$0.627953\pi$
$954$	−11141.6	−0.378116
$955$	15485.4	0.524709
$956$	−29706.9	−1.00501
$957$	−8519.25	−0.287762
$958$	11980.5	0.404041
$959$	5441.69	0.183234
$960$	−24616.2	−0.827587
$961$	6650.07	0.223224
$962$	61463.1	2.05993
$963$	8207.05	0.274630
$964$	5096.45	0.170275
$965$	29744.5	0.992238
$966$	−25279.7	−0.841987
$967$	4478.31	0.148927	0.0744637	−	0.997224i	$-0.476276\pi$
$967$	4478.31	0.148927	0.0744637	+	0.997224i	$0.476276\pi$
$968$	9918.72	0.329338
$969$	−4715.21	−0.156320
$970$	27145.2	0.898536
$971$	20973.3	0.693166	0.346583	−	0.938019i	$-0.387342\pi$
$971$	20973.3	0.693166	0.346583	+	0.938019i	$0.387342\pi$
$972$	−17481.6	−0.576873
$973$	−19218.5	−0.633213
$974$	66580.2	2.19032
$975$	−28055.6	−0.921537
$976$	−19544.3	−0.640982
$977$	9003.96	0.294843	0.147422	−	0.989074i	$-0.452903\pi$
$977$	9003.96	0.294843	0.147422	+	0.989074i	$0.452903\pi$
$978$	−4187.37	−0.136909
$979$	1852.11	0.0604635
$980$	−16207.5	−0.528294
$981$	2257.95	0.0734871
$982$	−2890.91	−0.0939436
$983$	−40233.0	−1.30543	−0.652713	−	0.757605i	$-0.726369\pi$
$983$	−40233.0	−1.30543	−0.652713	+	0.757605i	$0.726369\pi$
$984$	13005.0	0.421324
$985$	24411.4	0.789657
$986$	−6633.50	−0.214253
$987$	−4748.08	−0.153124
$988$	59795.1	1.92544
$989$	0	0
$990$	−1109.92	−0.0356319
$991$	12184.3	0.390564	0.195282	−	0.980747i	$-0.437438\pi$
$991$	12184.3	0.390564	0.195282	+	0.980747i	$0.437438\pi$
$992$	48891.0	1.56481
$993$	2721.85	0.0869841
$994$	−22759.0	−0.726228
$995$	6945.93	0.221307
$996$	−9919.87	−0.315585
$997$	33658.7	1.06919	0.534595	−	0.845108i	$-0.320464\pi$
$997$	33658.7	1.06919	0.534595	+	0.845108i	$0.320464\pi$
$998$	34635.1	1.09855
$999$	31875.5	1.00951

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.k.1.10		60
43.19	odd	42		43.4.g.a.17.2	✓	120
43.34	odd	42		43.4.g.a.38.2	yes	120
43.42	odd	2		1849.4.a.l.1.51		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.g.a.17.2	✓	120	43.19	odd	42
43.4.g.a.38.2	yes	120	43.34	odd	42
1849.4.a.k.1.10		60	1.1	even	1	trivial
1849.4.a.l.1.51		60	43.42	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-4.22240 q^{2} +5.78517 q^{3} +9.82864 q^{4} +5.96613 q^{5} -24.4273 q^{6} -8.16125 q^{7} -7.72124 q^{8} +6.46824 q^{9} +O(q^{10})\)	\(q-4.22240 q^{2} +5.78517 q^{3} +9.82864 q^{4} +5.96613 q^{5} -24.4273 q^{6} -8.16125 q^{7} -7.72124 q^{8} +6.46824 q^{9} -25.1914 q^{10} +6.81167 q^{11} +56.8604 q^{12} +54.2426 q^{13} +34.4600 q^{14} +34.5151 q^{15} -46.0270 q^{16} -7.26696 q^{17} -27.3115 q^{18} +112.159 q^{19} +58.6390 q^{20} -47.2142 q^{21} -28.7616 q^{22} -126.806 q^{23} -44.6687 q^{24} -89.4052 q^{25} -229.034 q^{26} -118.780 q^{27} -80.2140 q^{28} -216.188 q^{29} -145.737 q^{30} +190.895 q^{31} +256.114 q^{32} +39.4067 q^{33} +30.6840 q^{34} -48.6911 q^{35} +63.5740 q^{36} -268.358 q^{37} -473.578 q^{38} +313.803 q^{39} -46.0660 q^{40} -291.142 q^{41} +199.357 q^{42} +66.9495 q^{44} +38.5904 q^{45} +535.424 q^{46} +100.565 q^{47} -266.274 q^{48} -276.394 q^{49} +377.504 q^{50} -42.0406 q^{51} +533.131 q^{52} +407.945 q^{53} +501.536 q^{54} +40.6394 q^{55} +63.0150 q^{56} +648.856 q^{57} +912.831 q^{58} -94.5619 q^{59} +339.237 q^{60} +424.628 q^{61} -806.036 q^{62} -52.7889 q^{63} -713.200 q^{64} +323.618 q^{65} -166.391 q^{66} -62.4531 q^{67} -71.4243 q^{68} -733.594 q^{69} +205.593 q^{70} -660.446 q^{71} -49.9429 q^{72} -1078.33 q^{73} +1133.12 q^{74} -517.225 q^{75} +1102.37 q^{76} -55.5918 q^{77} -1325.00 q^{78} +109.716 q^{79} -274.603 q^{80} -861.804 q^{81} +1229.32 q^{82} -174.460 q^{83} -464.052 q^{84} -43.3556 q^{85} -1250.68 q^{87} -52.5946 q^{88} +271.903 q^{89} -162.944 q^{90} -442.687 q^{91} -1246.33 q^{92} +1104.36 q^{93} -424.624 q^{94} +669.153 q^{95} +1481.66 q^{96} -1077.56 q^{97} +1167.05 q^{98} +44.0595 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 15 q^{2} - 37 q^{3} + 213 q^{4} - 51 q^{5} + 22 q^{6} - 54 q^{7} - 204 q^{8} + 387 q^{9}+O(q^{10}) \) 60 * q - 15 * q^2 - 37 * q^3 + 213 * q^4 - 51 * q^5 + 22 * q^6 - 54 * q^7 - 204 * q^8 + 387 * q^9	\( 60 q - 15 q^{2} - 37 q^{3} + 213 q^{4} - 51 q^{5} + 22 q^{6} - 54 q^{7} - 204 q^{8} + 387 q^{9} + 27 q^{10} + 43 q^{11} - 432 q^{12} + 13 q^{13} + 96 q^{14} + 65 q^{15} + 717 q^{16} - 138 q^{17} - 625 q^{18} - 610 q^{19} - 345 q^{20} + 611 q^{21} - 118 q^{22} - 243 q^{23} + 258 q^{24} + 899 q^{25} - 1071 q^{26} - 1609 q^{27} - 46 q^{28} - 773 q^{29} - 375 q^{30} - 97 q^{31} - 1967 q^{32} - 500 q^{33} - 217 q^{34} + 247 q^{35} + 175 q^{36} - 228 q^{37} + 1253 q^{38} - 1493 q^{39} + 2220 q^{40} - 951 q^{41} - 2643 q^{42} - 1378 q^{44} - 1086 q^{45} + 565 q^{46} - 2 q^{47} - 2303 q^{48} + 1264 q^{49} - 3273 q^{50} - 3076 q^{51} - 2825 q^{52} - 39 q^{53} + 5201 q^{54} - 1306 q^{55} + 3683 q^{56} + 1342 q^{57} + 2588 q^{58} - 1065 q^{59} + 2803 q^{60} - 2999 q^{61} - 5569 q^{62} - 2377 q^{63} + 2082 q^{64} - 5578 q^{65} + 3338 q^{66} + 961 q^{67} - 3754 q^{68} - 1817 q^{69} - 2738 q^{70} - 8003 q^{71} - 1412 q^{72} + 1011 q^{73} - 1413 q^{74} - 7457 q^{75} - 5516 q^{76} - 4052 q^{77} + 1091 q^{78} - 4422 q^{79} - 1610 q^{80} + 2108 q^{81} - 4676 q^{82} - 297 q^{83} - 54 q^{84} - 4333 q^{85} + 1377 q^{87} - 3652 q^{88} - 2480 q^{89} - 1414 q^{90} - 4551 q^{91} - 3286 q^{92} - 4 q^{93} - 4609 q^{94} - 835 q^{95} + 5864 q^{96} + 3785 q^{97} - 753 q^{98} + 5072 q^{99}+O(q^{100}) \) 60 * q - 15 * q^2 - 37 * q^3 + 213 * q^4 - 51 * q^5 + 22 * q^6 - 54 * q^7 - 204 * q^8 + 387 * q^9 + 27 * q^10 + 43 * q^11 - 432 * q^12 + 13 * q^13 + 96 * q^14 + 65 * q^15 + 717 * q^16 - 138 * q^17 - 625 * q^18 - 610 * q^19 - 345 * q^20 + 611 * q^21 - 118 * q^22 - 243 * q^23 + 258 * q^24 + 899 * q^25 - 1071 * q^26 - 1609 * q^27 - 46 * q^28 - 773 * q^29 - 375 * q^30 - 97 * q^31 - 1967 * q^32 - 500 * q^33 - 217 * q^34 + 247 * q^35 + 175 * q^36 - 228 * q^37 + 1253 * q^38 - 1493 * q^39 + 2220 * q^40 - 951 * q^41 - 2643 * q^42 - 1378 * q^44 - 1086 * q^45 + 565 * q^46 - 2 * q^47 - 2303 * q^48 + 1264 * q^49 - 3273 * q^50 - 3076 * q^51 - 2825 * q^52 - 39 * q^53 + 5201 * q^54 - 1306 * q^55 + 3683 * q^56 + 1342 * q^57 + 2588 * q^58 - 1065 * q^59 + 2803 * q^60 - 2999 * q^61 - 5569 * q^62 - 2377 * q^63 + 2082 * q^64 - 5578 * q^65 + 3338 * q^66 + 961 * q^67 - 3754 * q^68 - 1817 * q^69 - 2738 * q^70 - 8003 * q^71 - 1412 * q^72 + 1011 * q^73 - 1413 * q^74 - 7457 * q^75 - 5516 * q^76 - 4052 * q^77 + 1091 * q^78 - 4422 * q^79 - 1610 * q^80 + 2108 * q^81 - 4676 * q^82 - 297 * q^83 - 54 * q^84 - 4333 * q^85 + 1377 * q^87 - 3652 * q^88 - 2480 * q^89 - 1414 * q^90 - 4551 * q^91 - 3286 * q^92 - 4 * q^93 - 4609 * q^94 - 835 * q^95 + 5864 * q^96 + 3785 * q^97 - 753 * q^98 + 5072 * q^99

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