LMFDB - Embedded newform 1441.4.a.b.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,4,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1441.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1441.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:	$85.0217523183$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.07584 q^{2} +3.89949 q^{3} +8.61251 q^{4} -19.2550 q^{5} -15.8937 q^{6} -31.3149 q^{7} -2.49649 q^{8} -11.7940 q^{9} +O(q^{10})$	\(q-4.07584 q^{2} +3.89949 q^{3} +8.61251 q^{4} -19.2550 q^{5} -15.8937 q^{6} -31.3149 q^{7} -2.49649 q^{8} -11.7940 q^{9} +78.4803 q^{10} +11.0000 q^{11} +33.5844 q^{12} -43.5339 q^{13} +127.635 q^{14} -75.0846 q^{15} -58.7248 q^{16} +66.7189 q^{17} +48.0704 q^{18} +52.0415 q^{19} -165.834 q^{20} -122.112 q^{21} -44.8343 q^{22} +100.295 q^{23} -9.73503 q^{24} +245.754 q^{25} +177.437 q^{26} -151.277 q^{27} -269.700 q^{28} -211.618 q^{29} +306.033 q^{30} -59.1375 q^{31} +259.325 q^{32} +42.8944 q^{33} -271.936 q^{34} +602.967 q^{35} -101.576 q^{36} -65.1445 q^{37} -212.113 q^{38} -169.760 q^{39} +48.0698 q^{40} +293.178 q^{41} +497.710 q^{42} +460.848 q^{43} +94.7376 q^{44} +227.093 q^{45} -408.789 q^{46} -77.6401 q^{47} -228.997 q^{48} +637.622 q^{49} -1001.66 q^{50} +260.170 q^{51} -374.936 q^{52} +216.903 q^{53} +616.580 q^{54} -211.805 q^{55} +78.1772 q^{56} +202.935 q^{57} +862.521 q^{58} +169.502 q^{59} -646.667 q^{60} +545.629 q^{61} +241.035 q^{62} +369.327 q^{63} -587.170 q^{64} +838.244 q^{65} -174.831 q^{66} -166.110 q^{67} +574.617 q^{68} +391.101 q^{69} -2457.60 q^{70} +802.871 q^{71} +29.4435 q^{72} -142.065 q^{73} +265.519 q^{74} +958.316 q^{75} +448.208 q^{76} -344.464 q^{77} +691.916 q^{78} -603.534 q^{79} +1130.74 q^{80} -271.465 q^{81} -1194.95 q^{82} -1349.99 q^{83} -1051.69 q^{84} -1284.67 q^{85} -1878.34 q^{86} -825.201 q^{87} -27.4614 q^{88} -294.878 q^{89} -925.594 q^{90} +1363.26 q^{91} +863.796 q^{92} -230.606 q^{93} +316.449 q^{94} -1002.06 q^{95} +1011.24 q^{96} +253.207 q^{97} -2598.85 q^{98} -129.734 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9}+O(q^{10}) $ 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9	\( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9} - 178 q^{10} + 869 q^{11} - 144 q^{12} - 242 q^{13} - 342 q^{14} - 524 q^{15} + 928 q^{16} - 260 q^{17} - 611 q^{18} - 543 q^{19} - 578 q^{20} - 710 q^{21} - 220 q^{22} - 908 q^{23} - 1322 q^{24} + 1701 q^{25} - 844 q^{26} - 732 q^{27} - 1068 q^{28} - 1747 q^{29} - 973 q^{30} - 1248 q^{31} - 2069 q^{32} - 132 q^{33} - 76 q^{34} - 1630 q^{35} + 2155 q^{36} - 535 q^{37} + 1155 q^{38} - 2514 q^{39} - 298 q^{40} - 2087 q^{41} - 5 q^{42} - 1008 q^{43} + 3168 q^{44} - 1160 q^{45} - 1640 q^{46} - 1960 q^{47} + 3412 q^{48} + 3670 q^{49} - 2394 q^{50} - 2994 q^{51} - 2601 q^{52} - 2466 q^{53} + 1296 q^{54} - 440 q^{55} - 5195 q^{56} - 3776 q^{57} + 1068 q^{58} - 2310 q^{59} + 1599 q^{60} - 3404 q^{61} + 1534 q^{62} - 3409 q^{63} + 2568 q^{64} - 3906 q^{65} - 1221 q^{66} - 2405 q^{67} - 3145 q^{68} - 2420 q^{69} + 455 q^{70} - 8978 q^{71} - 7262 q^{72} - 1868 q^{73} - 2790 q^{74} - 1196 q^{75} - 5483 q^{76} - 1111 q^{77} + 349 q^{78} - 9130 q^{79} - 1697 q^{80} + 4171 q^{81} - 241 q^{82} - 4639 q^{83} - 1659 q^{84} - 7634 q^{85} - 5656 q^{86} - 4412 q^{87} - 2838 q^{88} - 6561 q^{89} - 6756 q^{90} - 2742 q^{91} - 5386 q^{92} - 3234 q^{93} - 5295 q^{94} - 7930 q^{95} - 12593 q^{96} - 4520 q^{97} - 3213 q^{98} + 6435 q^{99}+O(q^{100}) \) 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9 - 178 * q^10 + 869 * q^11 - 144 * q^12 - 242 * q^13 - 342 * q^14 - 524 * q^15 + 928 * q^16 - 260 * q^17 - 611 * q^18 - 543 * q^19 - 578 * q^20 - 710 * q^21 - 220 * q^22 - 908 * q^23 - 1322 * q^24 + 1701 * q^25 - 844 * q^26 - 732 * q^27 - 1068 * q^28 - 1747 * q^29 - 973 * q^30 - 1248 * q^31 - 2069 * q^32 - 132 * q^33 - 76 * q^34 - 1630 * q^35 + 2155 * q^36 - 535 * q^37 + 1155 * q^38 - 2514 * q^39 - 298 * q^40 - 2087 * q^41 - 5 * q^42 - 1008 * q^43 + 3168 * q^44 - 1160 * q^45 - 1640 * q^46 - 1960 * q^47 + 3412 * q^48 + 3670 * q^49 - 2394 * q^50 - 2994 * q^51 - 2601 * q^52 - 2466 * q^53 + 1296 * q^54 - 440 * q^55 - 5195 * q^56 - 3776 * q^57 + 1068 * q^58 - 2310 * q^59 + 1599 * q^60 - 3404 * q^61 + 1534 * q^62 - 3409 * q^63 + 2568 * q^64 - 3906 * q^65 - 1221 * q^66 - 2405 * q^67 - 3145 * q^68 - 2420 * q^69 + 455 * q^70 - 8978 * q^71 - 7262 * q^72 - 1868 * q^73 - 2790 * q^74 - 1196 * q^75 - 5483 * q^76 - 1111 * q^77 + 349 * q^78 - 9130 * q^79 - 1697 * q^80 + 4171 * q^81 - 241 * q^82 - 4639 * q^83 - 1659 * q^84 - 7634 * q^85 - 5656 * q^86 - 4412 * q^87 - 2838 * q^88 - 6561 * q^89 - 6756 * q^90 - 2742 * q^91 - 5386 * q^92 - 3234 * q^93 - 5295 * q^94 - 7930 * q^95 - 12593 * q^96 - 4520 * q^97 - 3213 * q^98 + 6435 * 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 $

$2$	−4.07584	−1.44103	−0.720514	−	0.693440i	$-0.756094\pi$
$2$	−4.07584	−1.44103	−0.720514	+	0.693440i	$0.756094\pi$
$3$	3.89949	0.750457	0.375229	−	0.926932i	$-0.377564\pi$
$3$	3.89949	0.750457	0.375229	+	0.926932i	$0.377564\pi$
$4$	8.61251	1.07656
$5$	−19.2550	−1.72222	−0.861109	−	0.508421i	$-0.830229\pi$
$5$	−19.2550	−1.72222	−0.861109	+	0.508421i	$0.830229\pi$
$6$	−15.8937	−1.08143
$7$	−31.3149	−1.69085	−0.845423	−	0.534098i	$-0.820651\pi$
$7$	−31.3149	−1.69085	−0.845423	+	0.534098i	$0.820651\pi$
$8$	−2.49649	−0.110330
$9$	−11.7940	−0.436814
$10$	78.4803	2.48176
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	33.5844	0.807915
$13$	−43.5339	−0.928780	−0.464390	−	0.885631i	$-0.653726\pi$
$13$	−43.5339	−0.928780	−0.464390	+	0.885631i	$0.653726\pi$
$14$	127.635	2.43656
$15$	−75.0846	−1.29245
$16$	−58.7248	−0.917575
$17$	66.7189	0.951866	0.475933	−	0.879482i	$-0.342110\pi$
$17$	66.7189	0.951866	0.475933	+	0.879482i	$0.342110\pi$
$18$	48.0704	0.629461
$19$	52.0415	0.628375	0.314188	−	0.949361i	$-0.398268\pi$
$19$	52.0415	0.628375	0.314188	+	0.949361i	$0.398268\pi$
$20$	−165.834	−1.85408
$21$	−122.112	−1.26891
$22$	−44.8343	−0.434486
$23$	100.295	0.909263	0.454632	−	0.890680i	$-0.349771\pi$
$23$	100.295	0.909263	0.454632	+	0.890680i	$0.349771\pi$
$24$	−9.73503	−0.0827981
$25$	245.754	1.96603
$26$	177.437	1.33840
$27$	−151.277	−1.07827
$28$	−269.700	−1.82030
$29$	−211.618	−1.35505	−0.677525	−	0.735500i	$-0.736947\pi$
$29$	−211.618	−1.35505	−0.677525	+	0.735500i	$0.736947\pi$
$30$	306.033	1.86246
$31$	−59.1375	−0.342626	−0.171313	−	0.985217i	$-0.554801\pi$
$31$	−59.1375	−0.342626	−0.171313	+	0.985217i	$0.554801\pi$
$32$	259.325	1.43258
$33$	42.8944	0.226271
$34$	−271.936	−1.37167
$35$	602.967	2.91200
$36$	−101.576	−0.470258
$37$	−65.1445	−0.289451	−0.144726	−	0.989472i	$-0.546230\pi$
$37$	−65.1445	−0.289451	−0.144726	+	0.989472i	$0.546230\pi$
$38$	−212.113	−0.905507
$39$	−169.760	−0.697009
$40$	48.0698	0.190013
$41$	293.178	1.11675	0.558375	−	0.829589i	$-0.311425\pi$
$41$	293.178	1.11675	0.558375	+	0.829589i	$0.311425\pi$
$42$	497.710	1.82853
$43$	460.848	1.63439	0.817194	−	0.576363i	$-0.195529\pi$
$43$	460.848	1.63439	0.817194	+	0.576363i	$0.195529\pi$
$44$	94.7376	0.324596
$45$	227.093	0.752288
$46$	−408.789	−1.31027
$47$	−77.6401	−0.240957	−0.120478	−	0.992716i	$-0.538443\pi$
$47$	−77.6401	−0.240957	−0.120478	+	0.992716i	$0.538443\pi$
$48$	−228.997	−0.688601
$49$	637.622	1.85896
$50$	−1001.66	−2.83311
$51$	260.170	0.714335
$52$	−374.936	−0.999890
$53$	216.903	0.562150	0.281075	−	0.959686i	$-0.409309\pi$
$53$	216.903	0.562150	0.281075	+	0.959686i	$0.409309\pi$
$54$	616.580	1.55381
$55$	−211.805	−0.519268
$56$	78.1772	0.186551
$57$	202.935	0.471569
$58$	862.521	1.95266
$59$	169.502	0.374021	0.187011	−	0.982358i	$-0.440120\pi$
$59$	169.502	0.374021	0.187011	+	0.982358i	$0.440120\pi$
$60$	−646.667	−1.39140
$61$	545.629	1.14526	0.572629	−	0.819815i	$-0.305924\pi$
$61$	545.629	1.14526	0.572629	+	0.819815i	$0.305924\pi$
$62$	241.035	0.493734
$63$	369.327	0.738585
$64$	−587.170	−1.14682
$65$	838.244	1.59956
$66$	−174.831	−0.326064
$67$	−166.110	−0.302889	−0.151444	−	0.988466i	$-0.548392\pi$
$67$	−166.110	−0.302889	−0.151444	+	0.988466i	$0.548392\pi$
$68$	574.617	1.02474
$69$	391.101	0.682363
$70$	−2457.60	−4.19628
$71$	802.871	1.34202	0.671009	−	0.741449i	$-0.265861\pi$
$71$	802.871	1.34202	0.671009	+	0.741449i	$0.265861\pi$
$72$	29.4435	0.0481937
$73$	−142.065	−0.227774	−0.113887	−	0.993494i	$-0.536330\pi$
$73$	−142.065	−0.227774	−0.113887	+	0.993494i	$0.536330\pi$
$74$	265.519	0.417107
$75$	958.316	1.47542
$76$	448.208	0.676486
$77$	−344.464	−0.509809
$78$	691.916	1.00441
$79$	−603.534	−0.859530	−0.429765	−	0.902941i	$-0.641404\pi$
$79$	−603.534	−0.859530	−0.429765	+	0.902941i	$0.641404\pi$
$80$	1130.74	1.58026
$81$	−271.465	−0.372380
$82$	−1194.95	−1.60927
$83$	−1349.99	−1.78531	−0.892656	−	0.450739i	$-0.851161\pi$
$83$	−1349.99	−1.78531	−0.892656	+	0.450739i	$0.851161\pi$
$84$	−1051.69	−1.36606
$85$	−1284.67	−1.63932
$86$	−1878.34	−2.35520
$87$	−825.201	−1.01691
$88$	−27.4614	−0.0332658
$89$	−294.878	−0.351202	−0.175601	−	0.984461i	$-0.556187\pi$
$89$	−294.878	−0.351202	−0.175601	+	0.984461i	$0.556187\pi$
$90$	−925.594	−1.08407
$91$	1363.26	1.57042
$92$	863.796	0.978880
$93$	−230.606	−0.257126
$94$	316.449	0.347226
$95$	−1002.06	−1.08220
$96$	1011.24	1.07509
$97$	253.207	0.265044	0.132522	−	0.991180i	$-0.457693\pi$
$97$	253.207	0.265044	0.132522	+	0.991180i	$0.457693\pi$
$98$	−2598.85	−2.67881
$99$	−129.734	−0.131704
$100$	2116.56	2.11656
$101$	−879.524	−0.866494	−0.433247	−	0.901275i	$-0.642632\pi$
$101$	−879.524	−0.866494	−0.433247	+	0.901275i	$0.642632\pi$
$102$	−1060.41	−1.02938
$103$	347.550	0.332477	0.166238	−	0.986086i	$-0.446838\pi$
$103$	347.550	0.332477	0.166238	+	0.986086i	$0.446838\pi$
$104$	108.682	0.102472
$105$	2351.27	2.18533
$106$	−884.063	−0.810074
$107$	1467.46	1.32584	0.662918	−	0.748692i	$-0.269318\pi$
$107$	1467.46	1.32584	0.662918	+	0.748692i	$0.269318\pi$
$108$	−1302.87	−1.16082
$109$	−933.686	−0.820467	−0.410233	−	0.911981i	$-0.634553\pi$
$109$	−933.686	−0.820467	−0.410233	+	0.911981i	$0.634553\pi$
$110$	863.283	0.748280
$111$	−254.030	−0.217221
$112$	1838.96	1.55148
$113$	−532.943	−0.443673	−0.221837	−	0.975084i	$-0.571205\pi$
$113$	−532.943	−0.443673	−0.221837	+	0.975084i	$0.571205\pi$
$114$	−827.132	−0.679544
$115$	−1931.19	−1.56595
$116$	−1822.56	−1.45880
$117$	513.438	0.405704
$118$	−690.863	−0.538975
$119$	−2089.30	−1.60946
$120$	187.448	0.142596
$121$	121.000	0.0909091
$122$	−2223.90	−1.65035
$123$	1143.25	0.838073
$124$	−509.322	−0.368859
$125$	−2325.12	−1.66372
$126$	−1505.32	−1.06432
$127$	−159.518	−0.111456	−0.0557280	−	0.998446i	$-0.517748\pi$
$127$	−159.518	−0.111456	−0.0557280	+	0.998446i	$0.517748\pi$
$128$	318.614	0.220014
$129$	1797.07	1.22654
$130$	−3416.55	−2.30501
$131$	−131.000	−0.0873704
$131$	−131.000	−0.0873704
$132$	369.428	0.243596
$133$	−1629.67	−1.06249
$134$	677.038	0.436471
$135$	2912.83	1.85701
$136$	−166.563	−0.105020
$137$	−135.120	−0.0842633	−0.0421317	−	0.999112i	$-0.513415\pi$
$137$	−135.120	−0.0842633	−0.0421317	+	0.999112i	$0.513415\pi$
$138$	−1594.07	−0.983305
$139$	1654.03	1.00930	0.504652	−	0.863323i	$-0.331621\pi$
$139$	1654.03	1.00930	0.504652	+	0.863323i	$0.331621\pi$
$140$	5193.06	3.13496
$141$	−302.757	−0.180828
$142$	−3272.38	−1.93389
$143$	−478.873	−0.280038
$144$	692.598	0.400809
$145$	4074.69	2.33369
$146$	579.036	0.328229
$147$	2486.40	1.39507
$148$	−561.057	−0.311612
$149$	885.705	0.486978	0.243489	−	0.969904i	$-0.421708\pi$
$149$	885.705	0.486978	0.243489	+	0.969904i	$0.421708\pi$
$150$	−3905.94	−2.12613
$151$	689.652	0.371676	0.185838	−	0.982580i	$-0.440500\pi$
$151$	689.652	0.371676	0.185838	+	0.982580i	$0.440500\pi$
$152$	−129.921	−0.0693288
$153$	−786.882	−0.415788
$154$	1403.98	0.734649
$155$	1138.69	0.590076
$156$	−1462.06	−0.750375
$157$	−347.736	−0.176767	−0.0883834	−	0.996087i	$-0.528170\pi$
$157$	−347.736	−0.176767	−0.0883834	+	0.996087i	$0.528170\pi$
$158$	2459.91	1.23861
$159$	845.812	0.421869
$160$	−4993.29	−2.46722
$161$	−3140.74	−1.53742
$162$	1106.45	0.536610
$163$	875.647	0.420773	0.210386	−	0.977618i	$-0.432528\pi$
$163$	875.647	0.420773	0.210386	+	0.977618i	$0.432528\pi$
$164$	2525.00	1.20225
$165$	−825.930	−0.389688
$166$	5502.36	2.57269
$167$	−1691.44	−0.783757	−0.391878	−	0.920017i	$-0.628175\pi$
$167$	−1691.44	−0.783757	−0.391878	+	0.920017i	$0.628175\pi$
$168$	304.851	0.139999
$169$	−301.798	−0.137368
$170$	5236.12	2.36231
$171$	−613.776	−0.274483
$172$	3969.06	1.75952
$173$	596.859	0.262303	0.131151	−	0.991362i	$-0.458133\pi$
$173$	596.859	0.262303	0.131151	+	0.991362i	$0.458133\pi$
$174$	3363.39	1.46539
$175$	−7695.76	−3.32426
$176$	−645.972	−0.276659
$177$	660.971	0.280687
$178$	1201.88	0.506093
$179$	903.522	0.377276	0.188638	−	0.982047i	$-0.439593\pi$
$179$	903.522	0.377276	0.188638	+	0.982047i	$0.439593\pi$
$180$	1955.84	0.809886
$181$	2341.84	0.961701	0.480851	−	0.876803i	$-0.340328\pi$
$181$	2341.84	0.961701	0.480851	+	0.876803i	$0.340328\pi$
$182$	−5556.43	−2.26302
$183$	2127.68	0.859467
$184$	−250.386	−0.100319
$185$	1254.36	0.498498
$186$	939.914	0.370526
$187$	733.908	0.286998
$188$	−668.676	−0.259406
$189$	4737.21	1.82318
$190$	4084.23	1.55948
$191$	2491.98	0.944049	0.472025	−	0.881585i	$-0.343523\pi$
$191$	2491.98	0.944049	0.472025	+	0.881585i	$0.343523\pi$
$192$	−2289.66	−0.860637
$193$	−4174.24	−1.55683	−0.778416	−	0.627749i	$-0.783976\pi$
$193$	−4174.24	−1.55683	−0.778416	+	0.627749i	$0.783976\pi$
$194$	−1032.03	−0.381935
$195$	3268.73	1.20040
$196$	5491.53	2.00129
$197$	327.981	0.118617	0.0593087	−	0.998240i	$-0.481110\pi$
$197$	327.981	0.118617	0.0593087	+	0.998240i	$0.481110\pi$
$198$	528.774	0.189790
$199$	267.566	0.0953130	0.0476565	−	0.998864i	$-0.484825\pi$
$199$	267.566	0.0953130	0.0476565	+	0.998864i	$0.484825\pi$
$200$	−613.522	−0.216913
$201$	−647.744	−0.227305
$202$	3584.80	1.24864
$203$	6626.79	2.29118
$204$	2240.72	0.769027
$205$	−5645.14	−1.92328
$206$	−1416.56	−0.479108
$207$	−1182.88	−0.397179
$208$	2556.52	0.852225
$209$	572.456	0.189462
$210$	−9583.39	−3.14913
$211$	−1035.78	−0.337942	−0.168971	−	0.985621i	$-0.554044\pi$
$211$	−1035.78	−0.337942	−0.168971	+	0.985621i	$0.554044\pi$
$212$	1868.08	0.605190
$213$	3130.79	1.00713
$214$	−5981.13	−1.91057
$215$	−8873.61	−2.81477
$216$	377.660	0.118965
$217$	1851.88	0.579327
$218$	3805.56	1.18232
$219$	−553.982	−0.170934
$220$	−1824.17	−0.559025
$221$	−2904.54	−0.884074
$222$	1035.39	0.313021
$223$	6226.51	1.86977	0.934883	−	0.354955i	$-0.115504\pi$
$223$	6226.51	1.86977	0.934883	+	0.354955i	$0.115504\pi$
$224$	−8120.73	−2.42227
$225$	−2898.42	−0.858790
$226$	2172.19	0.639346
$227$	−5066.67	−1.48144	−0.740720	−	0.671814i	$-0.765515\pi$
$227$	−5066.67	−1.48144	−0.740720	+	0.671814i	$0.765515\pi$
$228$	1747.78	0.507674
$229$	−4958.54	−1.43087	−0.715435	−	0.698679i	$-0.753771\pi$
$229$	−4958.54	−1.43087	−0.715435	+	0.698679i	$0.753771\pi$
$230$	7871.22	2.25658
$231$	−1343.23	−0.382590
$232$	528.301	0.149503
$233$	4601.16	1.29370	0.646850	−	0.762617i	$-0.276086\pi$
$233$	4601.16	1.29370	0.646850	+	0.762617i	$0.276086\pi$
$234$	−2092.69	−0.584631
$235$	1494.96	0.414980
$236$	1459.84	0.402658
$237$	−2353.48	−0.645041
$238$	8515.65	2.31928
$239$	−3335.99	−0.902875	−0.451438	−	0.892303i	$-0.649089\pi$
$239$	−3335.99	−0.902875	−0.451438	+	0.892303i	$0.649089\pi$
$240$	4409.33	1.18592
$241$	4011.49	1.07221	0.536106	−	0.844151i	$-0.319895\pi$
$241$	4011.49	1.07221	0.536106	+	0.844151i	$0.319895\pi$
$242$	−493.177	−0.131003
$243$	3025.90	0.798812
$244$	4699.24	1.23294
$245$	−12277.4	−3.20153
$246$	−4659.69	−1.20769
$247$	−2265.57	−0.583622
$248$	147.636	0.0378020
$249$	−5264.28	−1.33980
$250$	9476.81	2.39746
$251$	−6712.69	−1.68805	−0.844026	−	0.536302i	$-0.819821\pi$
$251$	−6712.69	−1.68805	−0.844026	+	0.536302i	$0.819821\pi$
$252$	3180.83	0.795133
$253$	1103.25	0.274153
$254$	650.170	0.160611
$255$	−5009.56	−1.23024
$256$	3398.74	0.829770
$257$	−7122.64	−1.72879	−0.864393	−	0.502817i	$-0.832297\pi$
$257$	−7122.64	−1.72879	−0.864393	+	0.502817i	$0.832297\pi$
$258$	−7324.59	−1.76748
$259$	2039.99	0.489417
$260$	7219.39	1.72203
$261$	2495.81	0.591904
$262$	533.936	0.125903
$263$	−5460.23	−1.28020	−0.640099	−	0.768292i	$-0.721107\pi$
$263$	−5460.23	−1.28020	−0.640099	+	0.768292i	$0.721107\pi$
$264$	−107.085	−0.0249646
$265$	−4176.46	−0.968144
$266$	6642.29	1.53107
$267$	−1149.87	−0.263562
$268$	−1430.62	−0.326079
$269$	6766.02	1.53357	0.766787	−	0.641901i	$-0.221854\pi$
$269$	6766.02	1.53357	0.766787	+	0.641901i	$0.221854\pi$
$270$	−11872.2	−2.67601
$271$	3116.17	0.698502	0.349251	−	0.937029i	$-0.386436\pi$
$271$	3116.17	0.698502	0.349251	+	0.937029i	$0.386436\pi$
$272$	−3918.05	−0.873408
$273$	5316.02	1.17854
$274$	550.728	0.121426
$275$	2703.29	0.592781
$276$	3368.36	0.734607
$277$	3607.64	0.782535	0.391268	−	0.920277i	$-0.372037\pi$
$277$	3607.64	0.782535	0.391268	+	0.920277i	$0.372037\pi$
$278$	−6741.59	−1.45444
$279$	697.466	0.149664
$280$	−1505.30	−0.321282
$281$	−2984.65	−0.633627	−0.316814	−	0.948488i	$-0.602613\pi$
$281$	−2984.65	−0.633627	−0.316814	+	0.948488i	$0.602613\pi$
$282$	1233.99	0.260578
$283$	855.760	0.179751	0.0898757	−	0.995953i	$-0.471353\pi$
$283$	855.760	0.179751	0.0898757	+	0.995953i	$0.471353\pi$
$284$	6914.74	1.44477
$285$	−3907.51	−0.812144
$286$	1951.81	0.403542
$287$	−9180.84	−1.88825
$288$	−3058.47	−0.625771
$289$	−461.582	−0.0939512
$290$	−16607.8	−3.36291
$291$	987.376	0.198904
$292$	−1223.54	−0.245213
$293$	−1000.06	−0.199400	−0.0997001	−	0.995018i	$-0.531788\pi$
$293$	−1000.06	−0.199400	−0.0997001	+	0.995018i	$0.531788\pi$
$294$	−10134.2	−2.01033
$295$	−3263.75	−0.644146
$296$	162.632	0.0319352
$297$	−1664.04	−0.325110
$298$	−3610.00	−0.701750
$299$	−4366.26	−0.844505
$300$	8253.50	1.58839
$301$	−14431.4	−2.76350
$302$	−2810.91	−0.535595
$303$	−3429.69	−0.650266
$304$	−3056.12	−0.576581
$305$	−10506.1	−1.97238
$306$	3207.21	0.599163
$307$	−1123.24	−0.208816	−0.104408	−	0.994535i	$-0.533295\pi$
$307$	−1123.24	−0.208816	−0.104408	+	0.994535i	$0.533295\pi$
$308$	−2966.70	−0.548842
$309$	1355.27	0.249510
$310$	−4641.12	−0.850317
$311$	−10508.3	−1.91598	−0.957990	−	0.286800i	$-0.907408\pi$
$311$	−10508.3	−1.91598	−0.957990	+	0.286800i	$0.907408\pi$
$312$	423.804	0.0769012
$313$	10404.5	1.87890	0.939450	−	0.342687i	$-0.111337\pi$
$313$	10404.5	1.87890	0.939450	+	0.342687i	$0.111337\pi$
$314$	1417.32	0.254726
$315$	−7111.38	−1.27200
$316$	−5197.94	−0.925339
$317$	−6430.25	−1.13930	−0.569651	−	0.821886i	$-0.692922\pi$
$317$	−6430.25	−1.13930	−0.569651	+	0.821886i	$0.692922\pi$
$318$	−3447.40	−0.607926
$319$	−2327.80	−0.408563
$320$	11305.9	1.97507
$321$	5722.34	0.994983
$322$	12801.2	2.21547
$323$	3472.15	0.598129
$324$	−2337.99	−0.400890
$325$	−10698.6	−1.82601
$326$	−3569.00	−0.606346
$327$	−3640.90	−0.615725
$328$	−731.915	−0.123211
$329$	2431.29	0.407421
$330$	3366.36	0.561552
$331$	3774.86	0.626844	0.313422	−	0.949614i	$-0.398525\pi$
$331$	3774.86	0.626844	0.313422	+	0.949614i	$0.398525\pi$
$332$	−11626.8	−1.92200
$333$	768.313	0.126436
$334$	6894.04	1.12942
$335$	3198.44	0.521640
$336$	7171.01	1.16432
$337$	4521.14	0.730808	0.365404	−	0.930849i	$-0.380931\pi$
$337$	4521.14	0.730808	0.365404	+	0.930849i	$0.380931\pi$
$338$	1230.08	0.197952
$339$	−2078.21	−0.332958
$340$	−11064.2	−1.76483
$341$	−650.512	−0.103306
$342$	2501.65	0.395538
$343$	−9226.07	−1.45236
$344$	−1150.50	−0.180322
$345$	−7530.65	−1.17518
$346$	−2432.70	−0.377986
$347$	363.461	0.0562294	0.0281147	−	0.999605i	$-0.491050\pi$
$347$	363.461	0.0562294	0.0281147	+	0.999605i	$0.491050\pi$
$348$	−7107.05	−1.09476
$349$	−3941.07	−0.604472	−0.302236	−	0.953233i	$-0.597733\pi$
$349$	−3941.07	−0.604472	−0.302236	+	0.953233i	$0.597733\pi$
$350$	31366.7	4.79035
$351$	6585.67	1.00147
$352$	2852.57	0.431940
$353$	6640.86	1.00130	0.500648	−	0.865651i	$-0.333095\pi$
$353$	6640.86	1.00130	0.500648	+	0.865651i	$0.333095\pi$
$354$	−2694.01	−0.404478
$355$	−15459.3	−2.31125
$356$	−2539.64	−0.378092
$357$	−8147.19	−1.20783
$358$	−3682.62	−0.543666
$359$	−167.952	−0.0246913	−0.0123456	−	0.999924i	$-0.503930\pi$
$359$	−167.952	−0.0246913	−0.0123456	+	0.999924i	$0.503930\pi$
$360$	−566.934	−0.0830001
$361$	−4150.69	−0.605144
$362$	−9544.99	−1.38584
$363$	471.838	0.0682234
$364$	11741.1	1.69066
$365$	2735.46	0.392276
$366$	−8672.08	−1.23852
$367$	−32.5684	−0.00463231	−0.00231615	−	0.999997i	$-0.500737\pi$
$367$	−32.5684	−0.00463231	−0.00231615	+	0.999997i	$0.500737\pi$
$368$	−5889.83	−0.834317
$369$	−3457.73	−0.487812
$370$	−5112.56	−0.718349
$371$	−6792.30	−0.950508
$372$	−1986.10	−0.276813
$373$	−10321.2	−1.43274	−0.716370	−	0.697720i	$-0.754198\pi$
$373$	−10321.2	−1.43274	−0.716370	+	0.697720i	$0.754198\pi$
$374$	−2991.30	−0.413573
$375$	−9066.77	−1.24855
$376$	193.828	0.0265848
$377$	9212.55	1.25854
$378$	−19308.1	−2.62726
$379$	8139.12	1.10311	0.551555	−	0.834139i	$-0.314035\pi$
$379$	8139.12	1.10311	0.551555	+	0.834139i	$0.314035\pi$
$380$	−8630.22	−1.16506
$381$	−622.038	−0.0836430
$382$	−10156.9	−1.36040
$383$	10381.0	1.38497	0.692487	−	0.721431i	$-0.256515\pi$
$383$	10381.0	1.38497	0.692487	+	0.721431i	$0.256515\pi$
$384$	1242.43	0.165111
$385$	6632.64	0.878002
$386$	17013.6	2.24344
$387$	−5435.23	−0.713923
$388$	2180.74	0.285336
$389$	−13833.6	−1.80306	−0.901530	−	0.432717i	$-0.857555\pi$
$389$	−13833.6	−1.80306	−0.901530	+	0.432717i	$0.857555\pi$
$390$	−13322.8	−1.72981
$391$	6691.61	0.865497
$392$	−1591.82	−0.205099
$393$	−510.833	−0.0655678
$394$	−1336.80	−0.170931
$395$	11621.0	1.48030
$396$	−1117.33	−0.141788
$397$	12995.9	1.64294	0.821468	−	0.570255i	$-0.193156\pi$
$397$	12995.9	1.64294	0.821468	+	0.570255i	$0.193156\pi$
$398$	−1090.56	−0.137349
$399$	−6354.89	−0.797350
$400$	−14431.8	−1.80398
$401$	−3264.79	−0.406573	−0.203287	−	0.979119i	$-0.565162\pi$
$401$	−3264.79	−0.406573	−0.203287	+	0.979119i	$0.565162\pi$
$402$	2640.10	0.327553
$403$	2574.49	0.318224
$404$	−7574.90	−0.932835
$405$	5227.05	0.641319
$406$	−27009.7	−3.30165
$407$	−716.589	−0.0872728
$408$	−649.511	−0.0788127
$409$	−2260.29	−0.273262	−0.136631	−	0.990622i	$-0.543628\pi$
$409$	−2260.29	−0.273262	−0.136631	+	0.990622i	$0.543628\pi$
$410$	23008.7	2.77151
$411$	−526.899	−0.0632360
$412$	2993.28	0.357932
$413$	−5307.93	−0.632412
$414$	4821.25	0.572346
$415$	25994.1	3.07470
$416$	−11289.4	−1.33055
$417$	6449.89	0.757440
$418$	−2333.24	−0.273021
$419$	−5944.73	−0.693124	−0.346562	−	0.938027i	$-0.612651\pi$
$419$	−5944.73	−0.693124	−0.346562	+	0.938027i	$0.612651\pi$
$420$	20250.3	2.35265
$421$	7683.14	0.889438	0.444719	−	0.895670i	$-0.353304\pi$
$421$	7683.14	0.889438	0.444719	+	0.895670i	$0.353304\pi$
$422$	4221.66	0.486984
$423$	915.686	0.105253
$424$	−541.496	−0.0620221
$425$	16396.5	1.87140
$426$	−12760.6	−1.45130
$427$	−17086.3	−1.93645
$428$	12638.5	1.42735
$429$	−1867.36	−0.210156
$430$	36167.5	4.05616
$431$	−11524.7	−1.28799	−0.643996	−	0.765029i	$-0.722725\pi$
$431$	−11524.7	−1.28799	−0.643996	+	0.765029i	$0.722725\pi$
$432$	8883.69	0.989391
$433$	13356.1	1.48234	0.741168	−	0.671320i	$-0.234272\pi$
$433$	13356.1	1.48234	0.741168	+	0.671320i	$0.234272\pi$
$434$	−7547.99	−0.834827
$435$	15889.2	1.75133
$436$	−8041.38	−0.883284
$437$	5219.52	0.571359
$438$	2257.95	0.246321
$439$	7186.37	0.781291	0.390645	−	0.920541i	$-0.372252\pi$
$439$	7186.37	0.781291	0.390645	+	0.920541i	$0.372252\pi$
$440$	528.768	0.0572909
$441$	−7520.10	−0.812018
$442$	11838.4	1.27398
$443$	9547.82	1.02400	0.511998	−	0.858986i	$-0.328905\pi$
$443$	9547.82	1.02400	0.511998	+	0.858986i	$0.328905\pi$
$444$	−2187.84	−0.233852
$445$	5677.87	0.604847
$446$	−25378.3	−2.69439
$447$	3453.80	0.365456
$448$	18387.2	1.93909
$449$	−3568.11	−0.375032	−0.187516	−	0.982262i	$-0.560044\pi$
$449$	−3568.11	−0.375032	−0.187516	+	0.982262i	$0.560044\pi$
$450$	11813.5	1.23754
$451$	3224.96	0.336713
$452$	−4589.98	−0.477642
$453$	2689.29	0.278927
$454$	20651.0	2.13480
$455$	−26249.5	−2.70461
$456$	−506.625	−0.0520283
$457$	−16423.8	−1.68112	−0.840561	−	0.541716i	$-0.817775\pi$
$457$	−16423.8	−1.68112	−0.840561	+	0.541716i	$0.817775\pi$
$458$	20210.2	2.06192
$459$	−10093.0	−1.02637
$460$	−16632.4	−1.68584
$461$	8024.55	0.810717	0.405358	−	0.914158i	$-0.367147\pi$
$461$	8024.55	0.810717	0.405358	+	0.914158i	$0.367147\pi$
$462$	5474.81	0.551323
$463$	8311.02	0.834224	0.417112	−	0.908855i	$-0.363042\pi$
$463$	8311.02	0.834224	0.417112	+	0.908855i	$0.363042\pi$
$464$	12427.2	1.24336
$465$	4440.31	0.442827
$466$	−18753.6	−1.86426
$467$	16810.5	1.66573	0.832866	−	0.553475i	$-0.186698\pi$
$467$	16810.5	1.66573	0.832866	+	0.553475i	$0.186698\pi$
$468$	4421.99	0.436766
$469$	5201.71	0.512138
$470$	−6093.22	−0.597998
$471$	−1355.99	−0.132656
$472$	−423.159	−0.0412658
$473$	5069.33	0.492786
$474$	9592.40	0.929522
$475$	12789.4	1.23541
$476$	−17994.1	−1.73268
$477$	−2558.15	−0.245555
$478$	13597.0	1.30107
$479$	−14668.1	−1.39917	−0.699587	−	0.714548i	$-0.746633\pi$
$479$	−14668.1	−1.39917	−0.699587	+	0.714548i	$0.746633\pi$
$480$	−19471.3	−1.85154
$481$	2835.99	0.268836
$482$	−16350.2	−1.54509
$483$	−12247.3	−1.15377
$484$	1042.11	0.0978694
$485$	−4875.49	−0.456463
$486$	−12333.1	−1.15111
$487$	−17768.0	−1.65327	−0.826637	−	0.562735i	$-0.809749\pi$
$487$	−17768.0	−1.65327	−0.826637	+	0.562735i	$0.809749\pi$
$488$	−1362.16	−0.126356
$489$	3414.58	0.315772
$490$	50040.8	4.61349
$491$	−8026.08	−0.737702	−0.368851	−	0.929489i	$-0.620249\pi$
$491$	−8026.08	−0.737702	−0.368851	+	0.929489i	$0.620249\pi$
$492$	9846.21	0.902238
$493$	−14118.9	−1.28983
$494$	9234.11	0.841016
$495$	2498.02	0.226823
$496$	3472.83	0.314385
$497$	−25141.8	−2.26914
$498$	21456.4	1.93069
$499$	9375.57	0.841099	0.420549	−	0.907270i	$-0.361837\pi$
$499$	9375.57	0.841099	0.420549	+	0.907270i	$0.361837\pi$
$500$	−20025.1	−1.79110
$501$	−6595.75	−0.588176
$502$	27359.9	2.43253
$503$	−10832.5	−0.960237	−0.480119	−	0.877204i	$-0.659406\pi$
$503$	−10832.5	−0.960237	−0.480119	+	0.877204i	$0.659406\pi$
$504$	−922.020	−0.0814882
$505$	16935.2	1.49229
$506$	−4496.68	−0.395063
$507$	−1176.86	−0.103089
$508$	−1373.85	−0.119989
$509$	−5620.26	−0.489418	−0.244709	−	0.969597i	$-0.578692\pi$
$509$	−5620.26	−0.489418	−0.244709	+	0.969597i	$0.578692\pi$
$510$	20418.2	1.77281
$511$	4448.76	0.385130
$512$	−16401.6	−1.41574
$513$	−7872.66	−0.677557
$514$	29030.8	2.49123
$515$	−6692.06	−0.572597
$516$	15477.3	1.32045
$517$	−854.042	−0.0726513
$518$	−8314.69	−0.705264
$519$	2327.45	0.196847
$520$	−2092.67	−0.176480
$521$	−20238.4	−1.70185	−0.850923	−	0.525291i	$-0.823957\pi$
$521$	−20238.4	−1.70185	−0.850923	+	0.525291i	$0.823957\pi$
$522$	−10172.5	−0.852951
$523$	23733.5	1.98431	0.992154	−	0.125024i	$-0.0399008\pi$
$523$	23733.5	1.98431	0.992154	+	0.125024i	$0.0399008\pi$
$524$	−1128.24	−0.0940598
$525$	−30009.5	−2.49471
$526$	22255.1	1.84480
$527$	−3945.59	−0.326134
$528$	−2518.96	−0.207621
$529$	−2107.81	−0.173240
$530$	17022.6	1.39512
$531$	−1999.10	−0.163378
$532$	−14035.6	−1.14383
$533$	−12763.2	−1.03721
$534$	4686.71	0.379801
$535$	−28255.9	−2.28338
$536$	414.691	0.0334178
$537$	3523.28	0.283130
$538$	−27577.2	−2.20992
$539$	7013.85	0.560497
$540$	25086.8	1.99919
$541$	−24380.4	−1.93751	−0.968755	−	0.248019i	$-0.920221\pi$
$541$	−24380.4	−1.93751	−0.968755	+	0.248019i	$0.920221\pi$
$542$	−12701.0	−1.00656
$543$	9132.00	0.721716
$544$	17301.9	1.36363
$545$	17978.1	1.41302
$546$	−21667.3	−1.69830
$547$	11206.6	0.875975	0.437987	−	0.898981i	$-0.355691\pi$
$547$	11206.6	0.875975	0.437987	+	0.898981i	$0.355691\pi$
$548$	−1163.72	−0.0907148
$549$	−6435.14	−0.500264
$550$	−11018.2	−0.854214
$551$	−11012.9	−0.851479
$552$	−976.379	−0.0752853
$553$	18899.6	1.45333
$554$	−14704.2	−1.12766
$555$	4891.35	0.374101
$556$	14245.4	1.08658
$557$	8025.53	0.610507	0.305254	−	0.952271i	$-0.401259\pi$
$557$	8025.53	0.610507	0.305254	+	0.952271i	$0.401259\pi$
$558$	−2842.76	−0.215670
$559$	−20062.5	−1.51799
$560$	−35409.1	−2.67198
$561$	2861.87	0.215380
$562$	12165.0	0.913075
$563$	17307.1	1.29557	0.647785	−	0.761823i	$-0.275695\pi$
$563$	17307.1	1.29557	0.647785	+	0.761823i	$0.275695\pi$
$564$	−2607.50	−0.194673
$565$	10261.8	0.764102
$566$	−3487.95	−0.259027
$567$	8500.89	0.629637
$568$	−2004.36	−0.148065
$569$	−20111.3	−1.48174	−0.740869	−	0.671650i	$-0.765586\pi$
$569$	−20111.3	−1.48174	−0.740869	+	0.671650i	$0.765586\pi$
$570$	15926.4	1.17032
$571$	−8584.41	−0.629153	−0.314576	−	0.949232i	$-0.601862\pi$
$571$	−8584.41	−0.629153	−0.314576	+	0.949232i	$0.601862\pi$
$572$	−4124.30	−0.301478
$573$	9717.45	0.708469
$574$	37419.7	2.72102
$575$	24648.0	1.78764
$576$	6925.07	0.500945
$577$	−6884.70	−0.496731	−0.248366	−	0.968666i	$-0.579893\pi$
$577$	−6884.70	−0.496731	−0.248366	+	0.968666i	$0.579893\pi$
$578$	1881.34	0.135386
$579$	−16277.4	−1.16834
$580$	35093.3	2.51236
$581$	42274.9	3.01869
$582$	−4024.39	−0.286626
$583$	2385.93	0.169494
$584$	354.664	0.0251303
$585$	−9886.23	−0.698710
$586$	4076.10	0.287341
$587$	7403.04	0.520539	0.260269	−	0.965536i	$-0.416189\pi$
$587$	7403.04	0.520539	0.260269	+	0.965536i	$0.416189\pi$
$588$	21414.2	1.50188
$589$	−3077.60	−0.215298
$590$	13302.6	0.928233
$591$	1278.96	0.0890174
$592$	3825.60	0.265593
$593$	−14853.9	−1.02863	−0.514313	−	0.857603i	$-0.671953\pi$
$593$	−14853.9	−1.02863	−0.514313	+	0.857603i	$0.671953\pi$
$594$	6782.38	0.468493
$595$	40229.4	2.77184
$596$	7628.14	0.524263
$597$	1043.37	0.0715283
$598$	17796.2	1.21696
$599$	18546.0	1.26506	0.632529	−	0.774536i	$-0.282017\pi$
$599$	18546.0	1.26506	0.632529	+	0.774536i	$0.282017\pi$
$600$	−2392.42	−0.162784
$601$	−10822.8	−0.734563	−0.367282	−	0.930110i	$-0.619711\pi$
$601$	−10822.8	−0.734563	−0.367282	+	0.930110i	$0.619711\pi$
$602$	58820.1	3.98228
$603$	1959.09	0.132306
$604$	5939.63	0.400133
$605$	−2329.85	−0.156565
$606$	13978.9	0.937053
$607$	9017.98	0.603012	0.301506	−	0.953464i	$-0.402511\pi$
$607$	9017.98	0.603012	0.301506	+	0.953464i	$0.402511\pi$
$608$	13495.6	0.900199
$609$	25841.1	1.71943
$610$	42821.2	2.84226
$611$	3379.98	0.223796
$612$	−6777.02	−0.447622
$613$	−9392.45	−0.618854	−0.309427	−	0.950923i	$-0.600137\pi$
$613$	−9392.45	−0.618854	−0.309427	+	0.950923i	$0.600137\pi$
$614$	4578.13	0.300909
$615$	−22013.2	−1.44334
$616$	859.949	0.0562473
$617$	−1817.29	−0.118576	−0.0592879	−	0.998241i	$-0.518883\pi$
$617$	−1817.29	−0.118576	−0.0592879	+	0.998241i	$0.518883\pi$
$618$	−5523.86	−0.359550
$619$	26057.4	1.69198	0.845989	−	0.533201i	$-0.179011\pi$
$619$	26057.4	1.69198	0.845989	+	0.533201i	$0.179011\pi$
$620$	9806.98	0.635254
$621$	−15172.4	−0.980429
$622$	42830.1	2.76098
$623$	9234.07	0.593829
$624$	9969.12	0.639558
$625$	14050.8	0.899251
$626$	−42407.0	−2.70755
$627$	2232.29	0.142183
$628$	−2994.88	−0.190301
$629$	−4346.37	−0.275519
$630$	28984.9	1.83299
$631$	19837.7	1.25155	0.625774	−	0.780004i	$-0.284783\pi$
$631$	19837.7	1.25155	0.625774	+	0.780004i	$0.284783\pi$
$632$	1506.71	0.0948321
$633$	−4039.00	−0.253611
$634$	26208.7	1.64177
$635$	3071.51	0.191951
$636$	7284.56	0.454169
$637$	−27758.2	−1.72656
$638$	9487.73	0.588751
$639$	−9469.04	−0.586212
$640$	−6134.90	−0.378911
$641$	−5767.00	−0.355355	−0.177678	−	0.984089i	$-0.556858\pi$
$641$	−5767.00	−0.355355	−0.177678	+	0.984089i	$0.556858\pi$
$642$	−23323.4	−1.43380
$643$	25240.9	1.54806	0.774031	−	0.633148i	$-0.218238\pi$
$643$	25240.9	1.54806	0.774031	+	0.633148i	$0.218238\pi$
$644$	−27049.7	−1.65513
$645$	−34602.6	−2.11236
$646$	−14152.0	−0.861921
$647$	−25976.5	−1.57843	−0.789213	−	0.614119i	$-0.789511\pi$
$647$	−25976.5	−1.57843	−0.789213	+	0.614119i	$0.789511\pi$
$648$	677.708	0.0410847
$649$	1864.52	0.112772
$650$	43606.0	2.63133
$651$	7221.40	0.434760
$652$	7541.52	0.452989
$653$	7276.10	0.436043	0.218021	−	0.975944i	$-0.430040\pi$
$653$	7276.10	0.436043	0.218021	+	0.975944i	$0.430040\pi$
$654$	14839.7	0.887278
$655$	2522.40	0.150471
$656$	−17216.8	−1.02470
$657$	1675.51	0.0994947
$658$	−9909.57	−0.587105
$659$	2235.61	0.132150	0.0660752	−	0.997815i	$-0.478952\pi$
$659$	2235.61	0.132150	0.0660752	+	0.997815i	$0.478952\pi$
$660$	−7113.33	−0.419524
$661$	−16710.5	−0.983305	−0.491652	−	0.870792i	$-0.663607\pi$
$661$	−16710.5	−0.983305	−0.491652	+	0.870792i	$0.663607\pi$
$662$	−15385.8	−0.903299
$663$	−11326.2	−0.663460
$664$	3370.24	0.196974
$665$	31379.3	1.82983
$666$	−3131.52	−0.182198
$667$	−21224.3	−1.23210
$668$	−14567.5	−0.843764
$669$	24280.2	1.40318
$670$	−13036.3	−0.751698
$671$	6001.92	0.345308
$672$	−31666.7	−1.81781
$673$	−31357.7	−1.79606	−0.898031	−	0.439932i	$-0.855003\pi$
$673$	−31357.7	−1.79606	−0.898031	+	0.439932i	$0.855003\pi$
$674$	−18427.5	−1.05312
$675$	−37176.9	−2.11991
$676$	−2599.24	−0.147886
$677$	−14428.6	−0.819108	−0.409554	−	0.912286i	$-0.634316\pi$
$677$	−14428.6	−0.819108	−0.409554	+	0.912286i	$0.634316\pi$
$678$	8470.45	0.479802
$679$	−7929.14	−0.448148
$680$	3207.17	0.180866
$681$	−19757.4	−1.11176
$682$	2651.39	0.148866
$683$	25625.0	1.43560	0.717800	−	0.696250i	$-0.245149\pi$
$683$	25625.0	1.43560	0.717800	+	0.696250i	$0.245149\pi$
$684$	−5286.15	−0.295498
$685$	2601.73	0.145120
$686$	37604.0	2.09290
$687$	−19335.8	−1.07381
$688$	−27063.2	−1.49967
$689$	−9442.64	−0.522113
$690$	30693.7	1.69346
$691$	17550.8	0.966226	0.483113	−	0.875558i	$-0.339506\pi$
$691$	17550.8	0.966226	0.483113	+	0.875558i	$0.339506\pi$
$692$	5140.45	0.282385
$693$	4062.60	0.222692
$694$	−1481.41	−0.0810281
$695$	−31848.4	−1.73824
$696$	2060.10	0.112195
$697$	19560.5	1.06300
$698$	16063.2	0.871061
$699$	17942.2	0.970866
$700$	−66279.8	−3.57877
$701$	25042.0	1.34925	0.674623	−	0.738162i	$-0.264306\pi$
$701$	25042.0	1.34925	0.674623	+	0.738162i	$0.264306\pi$
$702$	−26842.2	−1.44315
$703$	−3390.22	−0.181884
$704$	−6458.87	−0.345778
$705$	5829.58	0.311425
$706$	−27067.1	−1.44290
$707$	27542.2	1.46511
$708$	5692.62	0.302177
$709$	24072.0	1.27509	0.637547	−	0.770412i	$-0.279949\pi$
$709$	24072.0	1.27509	0.637547	+	0.770412i	$0.279949\pi$
$710$	63009.6	3.33057
$711$	7118.06	0.375455
$712$	736.159	0.0387482
$713$	−5931.22	−0.311537
$714$	33206.7	1.74052
$715$	9220.69	0.482286
$716$	7781.59	0.406162
$717$	−13008.7	−0.677569
$718$	684.546	0.0355808
$719$	−9972.23	−0.517248	−0.258624	−	0.965978i	$-0.583269\pi$
$719$	−9972.23	−0.517248	−0.258624	+	0.965978i	$0.583269\pi$
$720$	−13336.0	−0.690281
$721$	−10883.5	−0.562167
$722$	16917.5	0.872030
$723$	15642.8	0.804649
$724$	20169.2	1.03533
$725$	−52005.9	−2.66407
$726$	−1923.14	−0.0983119
$727$	−9464.97	−0.482856	−0.241428	−	0.970419i	$-0.577616\pi$
$727$	−9464.97	−0.482856	−0.241428	+	0.970419i	$0.577616\pi$
$728$	−3403.36	−0.173265
$729$	19129.0	0.971854
$730$	−11149.3	−0.565281
$731$	30747.3	1.55572
$732$	18324.6	0.925270
$733$	−20898.0	−1.05305	−0.526526	−	0.850159i	$-0.676506\pi$
$733$	−20898.0	−1.05305	−0.526526	+	0.850159i	$0.676506\pi$
$734$	132.744	0.00667529
$735$	−47875.6	−2.40261
$736$	26009.1	1.30259
$737$	−1827.21	−0.0913244
$738$	14093.2	0.702950
$739$	−14710.4	−0.732247	−0.366123	−	0.930566i	$-0.619315\pi$
$739$	−14710.4	−0.732247	−0.366123	+	0.930566i	$0.619315\pi$
$740$	10803.1	0.536664
$741$	−8834.56	−0.437984
$742$	27684.3	1.36971
$743$	16981.7	0.838491	0.419246	−	0.907873i	$-0.362295\pi$
$743$	16981.7	0.838491	0.419246	+	0.907873i	$0.362295\pi$
$744$	575.705	0.0283688
$745$	−17054.2	−0.838682
$746$	42067.7	2.06462
$747$	15921.8	0.779849
$748$	6320.79	0.308972
$749$	−45953.3	−2.24178
$750$	36954.7	1.79919
$751$	−33228.9	−1.61457	−0.807285	−	0.590162i	$-0.799064\pi$
$751$	−33228.9	−1.61457	−0.807285	+	0.590162i	$0.799064\pi$
$752$	4559.40	0.221096
$753$	−26176.1	−1.26681
$754$	−37548.9	−1.81360
$755$	−13279.2	−0.640106
$756$	40799.3	1.96277
$757$	27680.1	1.32900	0.664499	−	0.747289i	$-0.268645\pi$
$757$	27680.1	1.32900	0.664499	+	0.747289i	$0.268645\pi$
$758$	−33173.8	−1.58961
$759$	4302.11	0.205740
$760$	2501.62	0.119399
$761$	38083.4	1.81409	0.907046	−	0.421032i	$-0.138332\pi$
$761$	38083.4	1.81409	0.907046	+	0.421032i	$0.138332\pi$
$762$	2535.33	0.120532
$763$	29238.3	1.38728
$764$	21462.2	1.01633
$765$	15151.4	0.716078
$766$	−42311.4	−1.99579
$767$	−7379.08	−0.347383
$768$	13253.4	0.622707
$769$	−4120.47	−0.193222	−0.0966112	−	0.995322i	$-0.530800\pi$
$769$	−4120.47	−0.193222	−0.0966112	+	0.995322i	$0.530800\pi$
$770$	−27033.6	−1.26523
$771$	−27774.7	−1.29738
$772$	−35950.7	−1.67603
$773$	1636.34	0.0761385	0.0380692	−	0.999275i	$-0.487879\pi$
$773$	1636.34	0.0761385	0.0380692	+	0.999275i	$0.487879\pi$
$774$	22153.1	1.02878
$775$	−14533.3	−0.673614
$776$	−632.127	−0.0292423
$777$	7954.93	0.367287
$778$	56383.5	2.59826
$779$	15257.4	0.701738
$780$	28151.9	1.29231
$781$	8831.58	0.404634
$782$	−27274.0	−1.24721
$783$	32012.8	1.46111
$784$	−37444.2	−1.70573
$785$	6695.65	0.304431
$786$	2082.08	0.0944850
$787$	−13216.9	−0.598642	−0.299321	−	0.954152i	$-0.596760\pi$
$787$	−13216.9	−0.598642	−0.299321	+	0.954152i	$0.596760\pi$
$788$	2824.73	0.127699
$789$	−21292.1	−0.960734
$790$	−47365.5	−2.13315
$791$	16689.1	0.750183
$792$	323.879	0.0145310
$793$	−23753.4	−1.06369
$794$	−52969.3	−2.36752
$795$	−16286.1	−0.726551
$796$	2304.42	0.102610
$797$	28001.9	1.24452	0.622258	−	0.782812i	$-0.286216\pi$
$797$	28001.9	1.24452	0.622258	+	0.782812i	$0.286216\pi$
$798$	25901.6	1.14900
$799$	−5180.07	−0.229359
$800$	63730.1	2.81650
$801$	3477.78	0.153410
$802$	13306.8	0.585884
$803$	−1562.72	−0.0686764
$804$	−5578.70	−0.244708
$805$	60474.9	2.64778
$806$	−10493.2	−0.458570
$807$	26384.0	1.15088
$808$	2195.72	0.0956004
$809$	18052.7	0.784547	0.392273	−	0.919849i	$-0.371689\pi$
$809$	18052.7	0.784547	0.392273	+	0.919849i	$0.371689\pi$
$810$	−21304.6	−0.924159
$811$	−17960.2	−0.777644	−0.388822	−	0.921313i	$-0.627118\pi$
$811$	−17960.2	−0.777644	−0.388822	+	0.921313i	$0.627118\pi$
$812$	57073.2	2.46660
$813$	12151.5	0.524196
$814$	2920.71	0.125763
$815$	−16860.6	−0.724662
$816$	−15278.4	−0.655455
$817$	23983.2	1.02701
$818$	9212.60	0.393779
$819$	−16078.3	−0.685982
$820$	−48618.8	−2.07054
$821$	11392.4	0.484282	0.242141	−	0.970241i	$-0.422150\pi$
$821$	11392.4	0.484282	0.242141	+	0.970241i	$0.422150\pi$
$822$	2147.56	0.0911249
$823$	39727.8	1.68265	0.841327	−	0.540527i	$-0.181775\pi$
$823$	39727.8	1.68265	0.841327	+	0.540527i	$0.181775\pi$
$824$	−867.654	−0.0366822
$825$	10541.5	0.444857
$826$	21634.3	0.911324
$827$	−10314.0	−0.433680	−0.216840	−	0.976207i	$-0.569575\pi$
$827$	−10314.0	−0.433680	−0.216840	+	0.976207i	$0.569575\pi$
$828$	−10187.6	−0.427588
$829$	44550.6	1.86647	0.933236	−	0.359265i	$-0.116973\pi$
$829$	44550.6	1.86647	0.933236	+	0.359265i	$0.116973\pi$
$830$	−105948.	−4.43072
$831$	14068.0	0.587259
$832$	25561.8	1.06514
$833$	42541.5	1.76948
$834$	−26288.7	−1.09149
$835$	32568.6	1.34980
$836$	4930.28	0.203968
$837$	8946.12	0.369442
$838$	24229.8	0.998811
$839$	−40866.1	−1.68159	−0.840795	−	0.541353i	$-0.817912\pi$
$839$	−40866.1	−1.68159	−0.840795	+	0.541353i	$0.817912\pi$
$840$	−5869.90	−0.241108
$841$	20393.1	0.836158
$842$	−31315.3	−1.28171
$843$	−11638.6	−0.475510
$844$	−8920.62	−0.363816
$845$	5811.12	0.236578
$846$	−3732.19	−0.151673
$847$	−3789.10	−0.153713
$848$	−12737.6	−0.515814
$849$	3337.03	0.134896
$850$	−66829.4	−2.69674
$851$	−6533.70	−0.263187
$852$	26963.9	1.08424
$853$	−16296.9	−0.654155	−0.327078	−	0.944997i	$-0.606064\pi$
$853$	−16296.9	−0.654155	−0.327078	+	0.944997i	$0.606064\pi$
$854$	69641.2	2.79048
$855$	11818.2	0.472719
$856$	−3663.49	−0.146280
$857$	28761.5	1.14641	0.573206	−	0.819412i	$-0.305700\pi$
$857$	28761.5	1.14641	0.573206	+	0.819412i	$0.305700\pi$
$858$	7611.07	0.302841
$859$	−29356.7	−1.16605	−0.583025	−	0.812454i	$-0.698131\pi$
$859$	−29356.7	−1.16605	−0.583025	+	0.812454i	$0.698131\pi$
$860$	−76424.1	−3.03028
$861$	−35800.6	−1.41705
$862$	46972.8	1.85603
$863$	−1110.87	−0.0438175	−0.0219088	−	0.999760i	$-0.506974\pi$
$863$	−1110.87	−0.0438175	−0.0219088	+	0.999760i	$0.506974\pi$
$864$	−39229.8	−1.54471
$865$	−11492.5	−0.451742
$866$	−54437.2	−2.13609
$867$	−1799.93	−0.0705063
$868$	15949.4	0.623683
$869$	−6638.87	−0.259158
$870$	−64762.0	−2.52372
$871$	7231.41	0.281317
$872$	2330.93	0.0905222
$873$	−2986.31	−0.115775
$874$	−21274.0	−0.823344
$875$	72810.8	2.81309
$876$	−4771.18	−0.184022
$877$	−49590.4	−1.90940	−0.954702	−	0.297563i	$-0.903826\pi$
$877$	−49590.4	−1.90940	−0.954702	+	0.297563i	$0.903826\pi$
$878$	−29290.5	−1.12586
$879$	−3899.73	−0.149641
$880$	12438.2	0.476467
$881$	20077.0	0.767776	0.383888	−	0.923380i	$-0.374585\pi$
$881$	20077.0	0.767776	0.383888	+	0.923380i	$0.374585\pi$
$882$	30650.8	1.17014
$883$	8752.63	0.333578	0.166789	−	0.985993i	$-0.446660\pi$
$883$	8752.63	0.333578	0.166789	+	0.985993i	$0.446660\pi$
$884$	−25015.3	−0.951761
$885$	−12727.0	−0.483404
$886$	−38915.4	−1.47561
$887$	−29125.6	−1.10253	−0.551263	−	0.834331i	$-0.685854\pi$
$887$	−29125.6	−1.10253	−0.551263	+	0.834331i	$0.685854\pi$
$888$	634.183	0.0239660
$889$	4995.28	0.188455
$890$	−23142.1	−0.871601
$891$	−2986.11	−0.112277
$892$	53625.9	2.01292
$893$	−4040.51	−0.151411
$894$	−14077.1	−0.526633
$895$	−17397.3	−0.649752
$896$	−9977.35	−0.372009
$897$	−17026.2	−0.633765
$898$	14543.1	0.540432
$899$	12514.5	0.464275
$900$	−24962.6	−0.924542
$901$	14471.5	0.535091
$902$	−13144.4	−0.485212
$903$	−56275.1	−2.07389
$904$	1330.49	0.0489506
$905$	−45092.2	−1.65626
$906$	−10961.1	−0.401942
$907$	9671.92	0.354080	0.177040	−	0.984204i	$-0.443348\pi$
$907$	9671.92	0.354080	0.177040	+	0.984204i	$0.443348\pi$
$908$	−43636.7	−1.59486
$909$	10373.1	0.378496
$910$	106989.	3.89742
$911$	14453.0	0.525632	0.262816	−	0.964846i	$-0.415349\pi$
$911$	14453.0	0.525632	0.262816	+	0.964846i	$0.415349\pi$
$912$	−11917.3	−0.432700
$913$	−14849.9	−0.538292
$914$	66940.9	2.42255
$915$	−40968.4	−1.48019
$916$	−42705.4	−1.54042
$917$	4102.25	0.147730
$918$	41137.6	1.47902
$919$	47951.6	1.72119	0.860597	−	0.509287i	$-0.170091\pi$
$919$	47951.6	1.72119	0.860597	+	0.509287i	$0.170091\pi$
$920$	4821.18	0.172771
$921$	−4380.05	−0.156707
$922$	−32706.8	−1.16827
$923$	−34952.1	−1.24644
$924$	−11568.6	−0.411882
$925$	−16009.5	−0.569070
$926$	−33874.4	−1.20214
$927$	−4098.99	−0.145230
$928$	−54877.8	−1.94122
$929$	−16572.4	−0.585277	−0.292639	−	0.956223i	$-0.594533\pi$
$929$	−16572.4	−0.585277	−0.292639	+	0.956223i	$0.594533\pi$
$930$	−18098.0	−0.638126
$931$	33182.8	1.16812
$932$	39627.5	1.39275
$933$	−40977.0	−1.43786
$934$	−68516.9	−2.40037
$935$	−14131.4	−0.494274
$936$	−1281.79	−0.0447614
$937$	−12646.4	−0.440918	−0.220459	−	0.975396i	$-0.570756\pi$
$937$	−12646.4	−0.440918	−0.220459	+	0.975396i	$0.570756\pi$
$938$	−21201.4	−0.738005
$939$	40572.1	1.41003
$940$	12875.3	0.446753
$941$	24994.8	0.865894	0.432947	−	0.901419i	$-0.357474\pi$
$941$	24994.8	0.865894	0.432947	+	0.901419i	$0.357474\pi$
$942$	5526.82	0.191161
$943$	29404.4	1.01542
$944$	−9953.96	−0.343192
$945$	−91214.9	−3.13992
$946$	−20661.8	−0.710119
$947$	−5582.09	−0.191545	−0.0957727	−	0.995403i	$-0.530532\pi$
$947$	−5582.09	−0.191545	−0.0957727	+	0.995403i	$0.530532\pi$
$948$	−20269.3	−0.694427
$949$	6184.66	0.211552
$950$	−52127.6	−1.78026
$951$	−25074.7	−0.854998
$952$	5215.90	0.177572
$953$	−14061.1	−0.477948	−0.238974	−	0.971026i	$-0.576811\pi$
$953$	−14061.1	−0.477948	−0.238974	+	0.971026i	$0.576811\pi$
$954$	10426.6	0.353851
$955$	−47983.0	−1.62586
$956$	−28731.2	−0.972003
$957$	−9077.21	−0.306609
$958$	59785.0	2.01625
$959$	4231.27	0.142476
$960$	44087.4	1.48220
$961$	−26293.8	−0.882608
$962$	−11559.1	−0.387401
$963$	−17307.2	−0.579144
$964$	34549.0	1.15430
$965$	80374.9	2.68120
$966$	49918.1	1.66262
$967$	−12144.4	−0.403866	−0.201933	−	0.979399i	$-0.564722\pi$
$967$	−12144.4	−0.403866	−0.201933	+	0.979399i	$0.564722\pi$
$968$	−302.075	−0.0100300
$969$	13539.6	0.448870
$970$	19871.7	0.657776
$971$	57306.6	1.89398	0.946991	−	0.321260i	$-0.104106\pi$
$971$	57306.6	1.89398	0.946991	+	0.321260i	$0.104106\pi$
$972$	26060.6	0.859972
$973$	−51795.9	−1.70658
$974$	72419.6	2.38242
$975$	−41719.2	−1.37034
$976$	−32042.0	−1.05086
$977$	−12405.4	−0.406228	−0.203114	−	0.979155i	$-0.565106\pi$
$977$	−12405.4	−0.406228	−0.203114	+	0.979155i	$0.565106\pi$
$978$	−13917.3	−0.455036
$979$	−3243.66	−0.105891
$980$	−105739.	−3.44665
$981$	11011.9	0.358391
$982$	32713.0	1.06305
$983$	−27415.2	−0.889532	−0.444766	−	0.895647i	$-0.646713\pi$
$983$	−27415.2	−0.889532	−0.444766	+	0.895647i	$0.646713\pi$
$984$	−2854.10	−0.0924647
$985$	−6315.26	−0.204285
$986$	57546.5	1.85868
$987$	9480.80	0.305752
$988$	−19512.2	−0.628306
$989$	46221.0	1.48609
$990$	−10181.5	−0.326859
$991$	−25309.3	−0.811279	−0.405639	−	0.914033i	$-0.632951\pi$
$991$	−25309.3	−0.811279	−0.405639	+	0.914033i	$0.632951\pi$
$992$	−15335.8	−0.490839
$993$	14720.0	0.470419
$994$	102474.	3.26990
$995$	−5151.99	−0.164150
$996$	−45338.7	−1.44238
$997$	−28140.7	−0.893908	−0.446954	−	0.894557i	$-0.647491\pi$
$997$	−28140.7	−0.893908	−0.446954	+	0.894557i	$0.647491\pi$
$998$	−38213.4	−1.21205
$999$	9854.85	0.312106

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.b.1.15	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.b.1.15	✓	79	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-4.07584 q^{2} +3.89949 q^{3} +8.61251 q^{4} -19.2550 q^{5} -15.8937 q^{6} -31.3149 q^{7} -2.49649 q^{8} -11.7940 q^{9} +O(q^{10})\)	\(q-4.07584 q^{2} +3.89949 q^{3} +8.61251 q^{4} -19.2550 q^{5} -15.8937 q^{6} -31.3149 q^{7} -2.49649 q^{8} -11.7940 q^{9} +78.4803 q^{10} +11.0000 q^{11} +33.5844 q^{12} -43.5339 q^{13} +127.635 q^{14} -75.0846 q^{15} -58.7248 q^{16} +66.7189 q^{17} +48.0704 q^{18} +52.0415 q^{19} -165.834 q^{20} -122.112 q^{21} -44.8343 q^{22} +100.295 q^{23} -9.73503 q^{24} +245.754 q^{25} +177.437 q^{26} -151.277 q^{27} -269.700 q^{28} -211.618 q^{29} +306.033 q^{30} -59.1375 q^{31} +259.325 q^{32} +42.8944 q^{33} -271.936 q^{34} +602.967 q^{35} -101.576 q^{36} -65.1445 q^{37} -212.113 q^{38} -169.760 q^{39} +48.0698 q^{40} +293.178 q^{41} +497.710 q^{42} +460.848 q^{43} +94.7376 q^{44} +227.093 q^{45} -408.789 q^{46} -77.6401 q^{47} -228.997 q^{48} +637.622 q^{49} -1001.66 q^{50} +260.170 q^{51} -374.936 q^{52} +216.903 q^{53} +616.580 q^{54} -211.805 q^{55} +78.1772 q^{56} +202.935 q^{57} +862.521 q^{58} +169.502 q^{59} -646.667 q^{60} +545.629 q^{61} +241.035 q^{62} +369.327 q^{63} -587.170 q^{64} +838.244 q^{65} -174.831 q^{66} -166.110 q^{67} +574.617 q^{68} +391.101 q^{69} -2457.60 q^{70} +802.871 q^{71} +29.4435 q^{72} -142.065 q^{73} +265.519 q^{74} +958.316 q^{75} +448.208 q^{76} -344.464 q^{77} +691.916 q^{78} -603.534 q^{79} +1130.74 q^{80} -271.465 q^{81} -1194.95 q^{82} -1349.99 q^{83} -1051.69 q^{84} -1284.67 q^{85} -1878.34 q^{86} -825.201 q^{87} -27.4614 q^{88} -294.878 q^{89} -925.594 q^{90} +1363.26 q^{91} +863.796 q^{92} -230.606 q^{93} +316.449 q^{94} -1002.06 q^{95} +1011.24 q^{96} +253.207 q^{97} -2598.85 q^{98} -129.734 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9}+O(q^{10}) \) 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9	\( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9} - 178 q^{10} + 869 q^{11} - 144 q^{12} - 242 q^{13} - 342 q^{14} - 524 q^{15} + 928 q^{16} - 260 q^{17} - 611 q^{18} - 543 q^{19} - 578 q^{20} - 710 q^{21} - 220 q^{22} - 908 q^{23} - 1322 q^{24} + 1701 q^{25} - 844 q^{26} - 732 q^{27} - 1068 q^{28} - 1747 q^{29} - 973 q^{30} - 1248 q^{31} - 2069 q^{32} - 132 q^{33} - 76 q^{34} - 1630 q^{35} + 2155 q^{36} - 535 q^{37} + 1155 q^{38} - 2514 q^{39} - 298 q^{40} - 2087 q^{41} - 5 q^{42} - 1008 q^{43} + 3168 q^{44} - 1160 q^{45} - 1640 q^{46} - 1960 q^{47} + 3412 q^{48} + 3670 q^{49} - 2394 q^{50} - 2994 q^{51} - 2601 q^{52} - 2466 q^{53} + 1296 q^{54} - 440 q^{55} - 5195 q^{56} - 3776 q^{57} + 1068 q^{58} - 2310 q^{59} + 1599 q^{60} - 3404 q^{61} + 1534 q^{62} - 3409 q^{63} + 2568 q^{64} - 3906 q^{65} - 1221 q^{66} - 2405 q^{67} - 3145 q^{68} - 2420 q^{69} + 455 q^{70} - 8978 q^{71} - 7262 q^{72} - 1868 q^{73} - 2790 q^{74} - 1196 q^{75} - 5483 q^{76} - 1111 q^{77} + 349 q^{78} - 9130 q^{79} - 1697 q^{80} + 4171 q^{81} - 241 q^{82} - 4639 q^{83} - 1659 q^{84} - 7634 q^{85} - 5656 q^{86} - 4412 q^{87} - 2838 q^{88} - 6561 q^{89} - 6756 q^{90} - 2742 q^{91} - 5386 q^{92} - 3234 q^{93} - 5295 q^{94} - 7930 q^{95} - 12593 q^{96} - 4520 q^{97} - 3213 q^{98} + 6435 q^{99}+O(q^{100}) \) 79 * q - 20 * q^2 - 12 * q^3 + 288 * q^4 - 40 * q^5 - 111 * q^6 - 101 * q^7 - 258 * q^8 + 585 * q^9 - 178 * q^10 + 869 * q^11 - 144 * q^12 - 242 * q^13 - 342 * q^14 - 524 * q^15 + 928 * q^16 - 260 * q^17 - 611 * q^18 - 543 * q^19 - 578 * q^20 - 710 * q^21 - 220 * q^22 - 908 * q^23 - 1322 * q^24 + 1701 * q^25 - 844 * q^26 - 732 * q^27 - 1068 * q^28 - 1747 * q^29 - 973 * q^30 - 1248 * q^31 - 2069 * q^32 - 132 * q^33 - 76 * q^34 - 1630 * q^35 + 2155 * q^36 - 535 * q^37 + 1155 * q^38 - 2514 * q^39 - 298 * q^40 - 2087 * q^41 - 5 * q^42 - 1008 * q^43 + 3168 * q^44 - 1160 * q^45 - 1640 * q^46 - 1960 * q^47 + 3412 * q^48 + 3670 * q^49 - 2394 * q^50 - 2994 * q^51 - 2601 * q^52 - 2466 * q^53 + 1296 * q^54 - 440 * q^55 - 5195 * q^56 - 3776 * q^57 + 1068 * q^58 - 2310 * q^59 + 1599 * q^60 - 3404 * q^61 + 1534 * q^62 - 3409 * q^63 + 2568 * q^64 - 3906 * q^65 - 1221 * q^66 - 2405 * q^67 - 3145 * q^68 - 2420 * q^69 + 455 * q^70 - 8978 * q^71 - 7262 * q^72 - 1868 * q^73 - 2790 * q^74 - 1196 * q^75 - 5483 * q^76 - 1111 * q^77 + 349 * q^78 - 9130 * q^79 - 1697 * q^80 + 4171 * q^81 - 241 * q^82 - 4639 * q^83 - 1659 * q^84 - 7634 * q^85 - 5656 * q^86 - 4412 * q^87 - 2838 * q^88 - 6561 * q^89 - 6756 * q^90 - 2742 * q^91 - 5386 * q^92 - 3234 * q^93 - 5295 * q^94 - 7930 * q^95 - 12593 * q^96 - 4520 * q^97 - 3213 * q^98 + 6435 * q^99

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