LMFDB - Embedded newform 1441.4.a.b.1.2

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			1.2
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)

$f(q)$	$=$	$q-5.43622 q^{2} +10.0127 q^{3} +21.5525 q^{4} +2.58286 q^{5} -54.4312 q^{6} -19.3873 q^{7} -73.6746 q^{8} +73.2537 q^{9} +O(q^{10})$	\(q-5.43622 q^{2} +10.0127 q^{3} +21.5525 q^{4} +2.58286 q^{5} -54.4312 q^{6} -19.3873 q^{7} -73.6746 q^{8} +73.2537 q^{9} -14.0410 q^{10} +11.0000 q^{11} +215.799 q^{12} +16.3735 q^{13} +105.393 q^{14} +25.8614 q^{15} +228.091 q^{16} -88.8345 q^{17} -398.224 q^{18} +27.4450 q^{19} +55.6673 q^{20} -194.118 q^{21} -59.7985 q^{22} +34.5936 q^{23} -737.680 q^{24} -118.329 q^{25} -89.0100 q^{26} +463.124 q^{27} -417.844 q^{28} -241.778 q^{29} -140.588 q^{30} -329.511 q^{31} -650.559 q^{32} +110.139 q^{33} +482.924 q^{34} -50.0747 q^{35} +1578.80 q^{36} -142.338 q^{37} -149.197 q^{38} +163.943 q^{39} -190.291 q^{40} +206.420 q^{41} +1055.27 q^{42} +278.349 q^{43} +237.078 q^{44} +189.204 q^{45} -188.058 q^{46} -270.587 q^{47} +2283.80 q^{48} +32.8655 q^{49} +643.262 q^{50} -889.471 q^{51} +352.890 q^{52} -443.962 q^{53} -2517.64 q^{54} +28.4115 q^{55} +1428.35 q^{56} +274.798 q^{57} +1314.36 q^{58} +207.536 q^{59} +557.378 q^{60} -179.065 q^{61} +1791.29 q^{62} -1420.19 q^{63} +1711.85 q^{64} +42.2906 q^{65} -598.743 q^{66} +1030.73 q^{67} -1914.61 q^{68} +346.374 q^{69} +272.217 q^{70} -721.547 q^{71} -5396.94 q^{72} -1149.26 q^{73} +773.779 q^{74} -1184.79 q^{75} +591.509 q^{76} -213.260 q^{77} -891.229 q^{78} +172.930 q^{79} +589.129 q^{80} +2659.26 q^{81} -1122.15 q^{82} -208.475 q^{83} -4183.74 q^{84} -229.447 q^{85} -1513.17 q^{86} -2420.85 q^{87} -810.420 q^{88} -1461.88 q^{89} -1028.56 q^{90} -317.437 q^{91} +745.579 q^{92} -3299.28 q^{93} +1470.97 q^{94} +70.8867 q^{95} -6513.83 q^{96} +410.112 q^{97} -178.664 q^{98} +805.791 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.43622	−1.92200	−0.960998	−	0.276556i	$-0.910807\pi$
$2$	−5.43622	−1.92200	−0.960998	+	0.276556i	$0.910807\pi$
$3$	10.0127	1.92694	0.963470	−	0.267815i	$-0.0863015\pi$
$3$	10.0127	1.92694	0.963470	+	0.267815i	$0.0863015\pi$
$4$	21.5525	2.69407
$5$	2.58286	0.231018	0.115509	−	0.993306i	$-0.463150\pi$
$5$	2.58286	0.231018	0.115509	+	0.993306i	$0.463150\pi$
$6$	−54.4312	−3.70357
$7$	−19.3873	−1.04681	−0.523407	−	0.852083i	$-0.675339\pi$
$7$	−19.3873	−1.04681	−0.523407	+	0.852083i	$0.675339\pi$
$8$	−73.6746	−3.25599
$9$	73.2537	2.71310
$10$	−14.0410	−0.444016
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	215.799	5.19131
$13$	16.3735	0.349323	0.174661	−	0.984629i	$-0.444117\pi$
$13$	16.3735	0.349323	0.174661	+	0.984629i	$0.444117\pi$
$14$	105.393	2.01197
$15$	25.8614	0.445159
$16$	228.091	3.56393
$17$	−88.8345	−1.26738	−0.633692	−	0.773586i	$-0.718461\pi$
$17$	−88.8345	−1.26738	−0.633692	+	0.773586i	$0.718461\pi$
$18$	−398.224	−5.21457
$19$	27.4450	0.331385	0.165693	−	0.986177i	$-0.447014\pi$
$19$	27.4450	0.331385	0.165693	+	0.986177i	$0.447014\pi$
$20$	55.6673	0.622379
$21$	−194.118	−2.01715
$22$	−59.7985	−0.579503
$23$	34.5936	0.313620	0.156810	−	0.987629i	$-0.449879\pi$
$23$	34.5936	0.313620	0.156810	+	0.987629i	$0.449879\pi$
$24$	−737.680	−6.27409
$25$	−118.329	−0.946630
$26$	−89.0100	−0.671396
$27$	463.124	3.30104
$28$	−417.844	−2.82018
$29$	−241.778	−1.54818	−0.774088	−	0.633078i	$-0.781791\pi$
$29$	−241.778	−1.54818	−0.774088	+	0.633078i	$0.781791\pi$
$30$	−140.588	−0.855593
$31$	−329.511	−1.90909	−0.954546	−	0.298064i	$-0.903659\pi$
$31$	−329.511	−1.90909	−0.954546	+	0.298064i	$0.903659\pi$
$32$	−650.559	−3.59386
$33$	110.139	0.580995
$34$	482.924	2.43591
$35$	−50.0747	−0.241833
$36$	1578.80	7.30927
$37$	−142.338	−0.632437	−0.316218	−	0.948686i	$-0.602413\pi$
$37$	−142.338	−0.632437	−0.316218	+	0.948686i	$0.602413\pi$
$38$	−149.197	−0.636921
$39$	163.943	0.673124
$40$	−190.291	−0.752193
$41$	206.420	0.786278	0.393139	−	0.919479i	$-0.371389\pi$
$41$	206.420	0.786278	0.393139	+	0.919479i	$0.371389\pi$
$42$	1055.27	3.87695
$43$	278.349	0.987158	0.493579	−	0.869701i	$-0.335688\pi$
$43$	278.349	0.987158	0.493579	+	0.869701i	$0.335688\pi$
$44$	237.078	0.812292
$45$	189.204	0.626776
$46$	−188.058	−0.602776
$47$	−270.587	−0.839771	−0.419885	−	0.907577i	$-0.637930\pi$
$47$	−270.587	−0.839771	−0.419885	+	0.907577i	$0.637930\pi$
$48$	2283.80	6.86748
$49$	32.8655	0.0958178
$50$	643.262	1.81942
$51$	−889.471	−2.44217
$52$	352.890	0.941098
$53$	−443.962	−1.15062	−0.575311	−	0.817935i	$-0.695119\pi$
$53$	−443.962	−1.15062	−0.575311	+	0.817935i	$0.695119\pi$
$54$	−2517.64	−6.34459
$55$	28.4115	0.0696547
$56$	1428.35	3.40841
$57$	274.798	0.638559
$58$	1314.36	2.97559
$59$	207.536	0.457948	0.228974	−	0.973433i	$-0.426463\pi$
$59$	207.536	0.457948	0.228974	+	0.973433i	$0.426463\pi$
$60$	557.378	1.19929
$61$	−179.065	−0.375851	−0.187925	−	0.982183i	$-0.560176\pi$
$61$	−179.065	−0.375851	−0.187925	+	0.982183i	$0.560176\pi$
$62$	1791.29	3.66927
$63$	−1420.19	−2.84011
$64$	1711.85	3.34346
$65$	42.2906	0.0807000
$66$	−598.743	−1.11667
$67$	1030.73	1.87946	0.939731	−	0.341915i	$-0.111075\pi$
$67$	1030.73	1.87946	0.939731	+	0.341915i	$0.111075\pi$
$68$	−1914.61	−3.41442
$69$	346.374	0.604327
$70$	272.217	0.464802
$71$	−721.547	−1.20608	−0.603042	−	0.797710i	$-0.706045\pi$
$71$	−721.547	−1.20608	−0.603042	+	0.797710i	$0.706045\pi$
$72$	−5396.94	−8.83382
$73$	−1149.26	−1.84261	−0.921305	−	0.388840i	$-0.872876\pi$
$73$	−1149.26	−1.84261	−0.921305	+	0.388840i	$0.872876\pi$
$74$	773.779	1.21554
$75$	−1184.79	−1.82410
$76$	591.509	0.892773
$77$	−213.260	−0.315626
$78$	−891.229	−1.29374
$79$	172.930	0.246280	0.123140	−	0.992389i	$-0.460704\pi$
$79$	172.930	0.246280	0.123140	+	0.992389i	$0.460704\pi$
$80$	589.129	0.823333
$81$	2659.26	3.64782
$82$	−1122.15	−1.51122
$83$	−208.475	−0.275700	−0.137850	−	0.990453i	$-0.544019\pi$
$83$	−208.475	−0.275700	−0.137850	+	0.990453i	$0.544019\pi$
$84$	−4183.74	−5.43433
$85$	−229.447	−0.292789
$86$	−1513.17	−1.89731
$87$	−2420.85	−2.98324
$88$	−810.420	−0.981717
$89$	−1461.88	−1.74112	−0.870558	−	0.492067i	$-0.836242\pi$
$89$	−1461.88	−1.74112	−0.870558	+	0.492067i	$0.836242\pi$
$90$	−1028.56	−1.20466
$91$	−317.437	−0.365675
$92$	745.579	0.844913
$93$	−3299.28	−3.67871
$94$	1470.97	1.61404
$95$	70.8867	0.0765561
$96$	−6513.83	−6.92516
$97$	410.112	0.429284	0.214642	−	0.976693i	$-0.431141\pi$
$97$	410.112	0.429284	0.214642	+	0.976693i	$0.431141\pi$
$98$	−178.664	−0.184161
$99$	805.791	0.818031
$100$	−2550.29	−2.55029
$101$	−248.129	−0.244453	−0.122226	−	0.992502i	$-0.539003\pi$
$101$	−248.129	−0.244453	−0.122226	+	0.992502i	$0.539003\pi$
$102$	4835.36	4.69385
$103$	1441.61	1.37909	0.689544	−	0.724244i	$-0.257811\pi$
$103$	1441.61	1.37909	0.689544	+	0.724244i	$0.257811\pi$
$104$	−1206.31	−1.13739
$105$	−501.381	−0.465998
$106$	2413.48	2.21149
$107$	1957.87	1.76892	0.884460	−	0.466616i	$-0.154527\pi$
$107$	1957.87	1.76892	0.884460	+	0.466616i	$0.154527\pi$
$108$	9981.49	8.89323
$109$	−1398.84	−1.22921	−0.614607	−	0.788834i	$-0.710685\pi$
$109$	−1398.84	−1.22921	−0.614607	+	0.788834i	$0.710685\pi$
$110$	−154.451	−0.133876
$111$	−1425.18	−1.21867
$112$	−4422.06	−3.73077
$113$	−1427.21	−1.18814	−0.594072	−	0.804412i	$-0.702480\pi$
$113$	−1427.21	−1.18814	−0.594072	+	0.804412i	$0.702480\pi$
$114$	−1493.86	−1.22731
$115$	89.3505	0.0724520
$116$	−5210.93	−4.17089
$117$	1199.42	0.947747
$118$	−1128.21	−0.880173
$119$	1722.26	1.32671
$120$	−1905.33	−1.44943
$121$	121.000	0.0909091
$122$	973.436	0.722384
$123$	2066.82	1.51511
$124$	−7101.79	−5.14322
$125$	−628.485	−0.449708
$126$	7720.46	5.45868
$127$	434.200	0.303378	0.151689	−	0.988428i	$-0.451529\pi$
$127$	434.200	0.303378	0.151689	+	0.988428i	$0.451529\pi$
$128$	−4101.54	−2.83225
$129$	2787.02	1.90220
$130$	−229.901	−0.155105
$131$	−131.000	−0.0873704
$131$	−131.000	−0.0873704
$132$	2373.78	1.56524
$133$	−532.083	−0.346898
$134$	−5603.29	−3.61232
$135$	1196.19	0.762602
$136$	6544.84	4.12659
$137$	−852.000	−0.531323	−0.265661	−	0.964066i	$-0.585590\pi$
$137$	−852.000	−0.531323	−0.265661	+	0.964066i	$0.585590\pi$
$138$	−1882.97	−1.16151
$139$	−426.498	−0.260253	−0.130126	−	0.991497i	$-0.541538\pi$
$139$	−426.498	−0.260253	−0.130126	+	0.991497i	$0.541538\pi$
$140$	−1079.24	−0.651515
$141$	−2709.30	−1.61819
$142$	3922.49	2.31809
$143$	180.109	0.105325
$144$	16708.5	9.66929
$145$	−624.481	−0.357657
$146$	6247.63	3.54149
$147$	329.072	0.184635
$148$	−3067.74	−1.70383
$149$	−344.367	−0.189340	−0.0946699	−	0.995509i	$-0.530180\pi$
$149$	−344.367	−0.189340	−0.0946699	+	0.995509i	$0.530180\pi$
$150$	6440.77	3.50591
$151$	2756.32	1.48547	0.742735	−	0.669585i	$-0.233528\pi$
$151$	2756.32	1.48547	0.742735	+	0.669585i	$0.233528\pi$
$152$	−2022.00	−1.07899
$153$	−6507.46	−3.43854
$154$	1159.33	0.606632
$155$	−851.081	−0.441035
$156$	3533.38	1.81344
$157$	296.633	0.150789	0.0753946	−	0.997154i	$-0.475978\pi$
$157$	296.633	0.150789	0.0753946	+	0.997154i	$0.475978\pi$
$158$	−940.087	−0.473350
$159$	−4445.25	−2.21718
$160$	−1680.30	−0.830249
$161$	−670.674	−0.328301
$162$	−14456.3	−7.01108
$163$	2412.02	1.15904	0.579522	−	0.814957i	$-0.303239\pi$
$163$	2412.02	1.15904	0.579522	+	0.814957i	$0.303239\pi$
$164$	4448.87	2.11828
$165$	284.475	0.134220
$166$	1133.32	0.529894
$167$	2843.91	1.31778	0.658888	−	0.752241i	$-0.271027\pi$
$167$	2843.91	1.31778	0.658888	+	0.752241i	$0.271027\pi$
$168$	14301.6	6.56781
$169$	−1928.91	−0.877974
$170$	1247.33	0.562739
$171$	2010.45	0.899081
$172$	5999.12	2.65947
$173$	−1843.46	−0.810150	−0.405075	−	0.914284i	$-0.632755\pi$
$173$	−1843.46	−0.810150	−0.405075	+	0.914284i	$0.632755\pi$
$174$	13160.3	5.73378
$175$	2294.07	0.990945
$176$	2509.00	1.07456
$177$	2077.99	0.882438
$178$	7947.12	3.34642
$179$	−235.610	−0.0983815	−0.0491907	−	0.998789i	$-0.515664\pi$
$179$	−235.610	−0.0983815	−0.0491907	+	0.998789i	$0.515664\pi$
$180$	4077.83	1.68858
$181$	2195.42	0.901573	0.450786	−	0.892632i	$-0.351144\pi$
$181$	2195.42	0.901573	0.450786	+	0.892632i	$0.351144\pi$
$182$	1725.66	0.702827
$183$	−1792.92	−0.724242
$184$	−2548.67	−1.02114
$185$	−367.639	−0.146105
$186$	17935.6	7.07046
$187$	−977.179	−0.382131
$188$	−5831.84	−2.26240
$189$	−8978.69	−3.45558
$190$	−385.356	−0.147140
$191$	−4476.46	−1.69584	−0.847920	−	0.530124i	$-0.822145\pi$
$191$	−4476.46	−1.69584	−0.847920	+	0.530124i	$0.822145\pi$
$192$	17140.2	6.44265
$193$	−2252.96	−0.840266	−0.420133	−	0.907463i	$-0.638017\pi$
$193$	−2252.96	−0.840266	−0.420133	+	0.907463i	$0.638017\pi$
$194$	−2229.46	−0.825083
$195$	423.442	0.155504
$196$	708.335	0.258140
$197$	−2513.12	−0.908896	−0.454448	−	0.890773i	$-0.650163\pi$
$197$	−2513.12	−0.908896	−0.454448	+	0.890773i	$0.650163\pi$
$198$	−4380.46	−1.57225
$199$	−3344.52	−1.19139	−0.595696	−	0.803210i	$-0.703124\pi$
$199$	−3344.52	−1.19139	−0.595696	+	0.803210i	$0.703124\pi$
$200$	8717.83	3.08222
$201$	10320.4	3.62161
$202$	1348.88	0.469837
$203$	4687.42	1.62065
$204$	−19170.3	−6.57938
$205$	533.155	0.181645
$206$	−7836.92	−2.65060
$207$	2534.11	0.850882
$208$	3734.65	1.24496
$209$	301.895	0.0999164
$210$	2725.62	0.895646
$211$	3069.88	1.00161	0.500804	−	0.865561i	$-0.333038\pi$
$211$	3069.88	1.00161	0.500804	+	0.865561i	$0.333038\pi$
$212$	−9568.51	−3.09985
$213$	−7224.62	−2.32405
$214$	−10643.4	−3.39986
$215$	718.937	0.228052
$216$	−34120.4	−10.7482
$217$	6388.30	1.99846
$218$	7604.39	2.36254
$219$	−11507.2	−3.55060
$220$	612.340	0.187654
$221$	−1454.53	−0.442726
$222$	7747.60	2.34227
$223$	562.167	0.168814	0.0844070	−	0.996431i	$-0.473100\pi$
$223$	562.167	0.168814	0.0844070	+	0.996431i	$0.473100\pi$
$224$	12612.5	3.76210
$225$	−8668.03	−2.56830
$226$	7758.61	2.28361
$227$	−3745.07	−1.09502	−0.547509	−	0.836800i	$-0.684424\pi$
$227$	−3745.07	−1.09502	−0.547509	+	0.836800i	$0.684424\pi$
$228$	5922.59	1.72032
$229$	−94.5060	−0.0272713	−0.0136357	−	0.999907i	$-0.504341\pi$
$229$	−94.5060	−0.0272713	−0.0136357	+	0.999907i	$0.504341\pi$
$230$	−485.729	−0.139252
$231$	−2135.30	−0.608193
$232$	17812.9	5.04084
$233$	−764.254	−0.214884	−0.107442	−	0.994211i	$-0.534266\pi$
$233$	−764.254	−0.214884	−0.107442	+	0.994211i	$0.534266\pi$
$234$	−6520.32	−1.82157
$235$	−698.891	−0.194003
$236$	4472.93	1.23374
$237$	1731.49	0.474568
$238$	−9362.57	−2.54994
$239$	−2754.03	−0.745369	−0.372685	−	0.927958i	$-0.621563\pi$
$239$	−2754.03	−0.745369	−0.372685	+	0.927958i	$0.621563\pi$
$240$	5898.76	1.58651
$241$	−3242.02	−0.866543	−0.433271	−	0.901264i	$-0.642641\pi$
$241$	−3242.02	−0.866543	−0.433271	+	0.901264i	$0.642641\pi$
$242$	−657.783	−0.174727
$243$	14122.0	3.72808
$244$	−3859.30	−1.01257
$245$	84.8872	0.0221357
$246$	−11235.7	−2.91204
$247$	449.371	0.115760
$248$	24276.6	6.21598
$249$	−2087.39	−0.531257
$250$	3416.59	0.864336
$251$	−2852.80	−0.717398	−0.358699	−	0.933453i	$-0.616780\pi$
$251$	−2852.80	−0.717398	−0.358699	+	0.933453i	$0.616780\pi$
$252$	−30608.7	−7.65144
$253$	380.529	0.0945600
$254$	−2360.41	−0.583092
$255$	−2297.38	−0.564187
$256$	8602.08	2.10012
$257$	6063.63	1.47175	0.735873	−	0.677120i	$-0.236772\pi$
$257$	6063.63	1.47175	0.735873	+	0.677120i	$0.236772\pi$
$258$	−15150.9	−3.65601
$259$	2759.54	0.662043
$260$	911.468	0.217411
$261$	−17711.2	−4.20036
$262$	712.145	0.167926
$263$	3423.03	0.802559	0.401279	−	0.915956i	$-0.368566\pi$
$263$	3423.03	0.802559	0.401279	+	0.915956i	$0.368566\pi$
$264$	−8114.48	−1.89171
$265$	−1146.70	−0.265815
$266$	2892.52	0.666737
$267$	−14637.4	−3.35503
$268$	22214.9	5.06339
$269$	3825.62	0.867109	0.433554	−	0.901127i	$-0.357259\pi$
$269$	3825.62	0.867109	0.433554	+	0.901127i	$0.357259\pi$
$270$	−6502.73	−1.46572
$271$	−7489.14	−1.67872	−0.839360	−	0.543576i	$-0.817070\pi$
$271$	−7489.14	−1.67872	−0.839360	+	0.543576i	$0.817070\pi$
$272$	−20262.4	−4.51686
$273$	−3178.40	−0.704635
$274$	4631.66	1.02120
$275$	−1301.62	−0.285420
$276$	7465.24	1.62810
$277$	4911.19	1.06529	0.532644	−	0.846340i	$-0.321199\pi$
$277$	4911.19	1.06529	0.532644	+	0.846340i	$0.321199\pi$
$278$	2318.54	0.500204
$279$	−24137.9	−5.17956
$280$	3689.23	0.787406
$281$	2056.14	0.436509	0.218255	−	0.975892i	$-0.429964\pi$
$281$	2056.14	0.436509	0.218255	+	0.975892i	$0.429964\pi$
$282$	14728.4	3.11015
$283$	−606.850	−0.127468	−0.0637341	−	0.997967i	$-0.520301\pi$
$283$	−606.850	−0.127468	−0.0637341	+	0.997967i	$0.520301\pi$
$284$	−15551.2	−3.24927
$285$	709.766	0.147519
$286$	−979.110	−0.202434
$287$	−4001.92	−0.823086
$288$	−47655.8	−9.75051
$289$	2978.56	0.606262
$290$	3394.82	0.687415
$291$	4106.32	0.827206
$292$	−24769.4	−4.96412
$293$	2375.51	0.473647	0.236824	−	0.971553i	$-0.423894\pi$
$293$	2375.51	0.473647	0.236824	+	0.971553i	$0.423894\pi$
$294$	−1788.91	−0.354868
$295$	536.038	0.105794
$296$	10486.7	2.05921
$297$	5094.36	0.995302
$298$	1872.06	0.363910
$299$	566.418	0.109555
$300$	−25535.2	−4.91425
$301$	−5396.42	−1.03337
$302$	−14984.0	−2.85507
$303$	−2484.43	−0.471046
$304$	6259.97	1.18103
$305$	−462.500	−0.0868285
$306$	35376.0	6.60886
$307$	3524.68	0.655258	0.327629	−	0.944806i	$-0.393750\pi$
$307$	3524.68	0.655258	0.327629	+	0.944806i	$0.393750\pi$
$308$	−4596.29	−0.850317
$309$	14434.4	2.65742
$310$	4626.67	0.847668
$311$	8460.74	1.54265	0.771325	−	0.636441i	$-0.219594\pi$
$311$	8460.74	1.54265	0.771325	+	0.636441i	$0.219594\pi$
$312$	−12078.4	−2.19168
$313$	7209.23	1.30188	0.650942	−	0.759127i	$-0.274374\pi$
$313$	7209.23	1.30188	0.650942	+	0.759127i	$0.274374\pi$
$314$	−1612.56	−0.289816
$315$	−3668.15	−0.656118
$316$	3727.08	0.663496
$317$	−5062.00	−0.896878	−0.448439	−	0.893814i	$-0.648020\pi$
$317$	−5062.00	−0.896878	−0.448439	+	0.893814i	$0.648020\pi$
$318$	24165.4	4.26141
$319$	−2659.56	−0.466793
$320$	4421.48	0.772401
$321$	19603.5	3.40860
$322$	3645.94	0.630994
$323$	−2438.06	−0.419992
$324$	57313.7	9.82746
$325$	−1937.46	−0.330679
$326$	−13112.3	−2.22768
$327$	−14006.1	−2.36862
$328$	−15207.9	−2.56011
$329$	5245.94	0.879083
$330$	−1546.47	−0.257971
$331$	−1116.14	−0.185343	−0.0926713	−	0.995697i	$-0.529541\pi$
$331$	−1116.14	−0.185343	−0.0926713	+	0.995697i	$0.529541\pi$
$332$	−4493.16	−0.742754
$333$	−10426.8	−1.71586
$334$	−15460.1	−2.53276
$335$	2662.24	0.434190
$336$	−44276.7	−7.18896
$337$	4733.00	0.765053	0.382526	−	0.923945i	$-0.375054\pi$
$337$	4733.00	0.765053	0.382526	+	0.923945i	$0.375054\pi$
$338$	10486.0	1.68746
$339$	−14290.1	−2.28948
$340$	−4945.17	−0.788793
$341$	−3624.62	−0.575613
$342$	−10929.3	−1.72803
$343$	6012.66	0.946510
$344$	−20507.2	−3.21417
$345$	894.638	0.139611
$346$	10021.5	1.55710
$347$	10788.0	1.66897	0.834483	−	0.551033i	$-0.185766\pi$
$347$	10788.0	1.66897	0.834483	+	0.551033i	$0.185766\pi$
$348$	−52175.4	−8.03705
$349$	−90.4766	−0.0138771	−0.00693854	−	0.999976i	$-0.502209\pi$
$349$	−90.4766	−0.0138771	−0.00693854	+	0.999976i	$0.502209\pi$
$350$	−12471.1	−1.90459
$351$	7582.96	1.15313
$352$	−7156.14	−1.08359
$353$	−7711.53	−1.16273	−0.581365	−	0.813643i	$-0.697481\pi$
$353$	−7711.53	−1.16273	−0.581365	+	0.813643i	$0.697481\pi$
$354$	−11296.4	−1.69604
$355$	−1863.66	−0.278628
$356$	−31507.3	−4.69068
$357$	17244.4	2.55650
$358$	1280.83	0.189089
$359$	−10837.4	−1.59325	−0.796624	−	0.604475i	$-0.793383\pi$
$359$	−10837.4	−1.59325	−0.796624	+	0.604475i	$0.793383\pi$
$360$	−13939.6	−2.04078
$361$	−6105.77	−0.890184
$362$	−11934.8	−1.73282
$363$	1211.53	0.175176
$364$	−6841.58	−0.985154
$365$	−2968.38	−0.425677
$366$	9746.71	1.39199
$367$	5136.69	0.730608	0.365304	−	0.930888i	$-0.380965\pi$
$367$	5136.69	0.730608	0.365304	+	0.930888i	$0.380965\pi$
$368$	7890.49	1.11772
$369$	15121.0	2.13325
$370$	1998.57	0.280812
$371$	8607.21	1.20449
$372$	−71107.9	−9.91068
$373$	6053.66	0.840340	0.420170	−	0.907445i	$-0.361970\pi$
$373$	6053.66	0.840340	0.420170	+	0.907445i	$0.361970\pi$
$374$	5312.16	0.734453
$375$	−6292.82	−0.866560
$376$	19935.4	2.73428
$377$	−3958.76	−0.540813
$378$	48810.2	6.64160
$379$	−3239.55	−0.439062	−0.219531	−	0.975606i	$-0.570453\pi$
$379$	−3239.55	−0.439062	−0.219531	+	0.975606i	$0.570453\pi$
$380$	1527.79	0.206247
$381$	4347.51	0.584592
$382$	24335.1	3.25940
$383$	−889.837	−0.118717	−0.0593584	−	0.998237i	$-0.518905\pi$
$383$	−889.837	−0.118717	−0.0593584	+	0.998237i	$0.518905\pi$
$384$	−41067.4	−5.45759
$385$	−550.821	−0.0729154
$386$	12247.6	1.61499
$387$	20390.1	2.67826
$388$	8838.96	1.15652
$389$	−1779.64	−0.231957	−0.115979	−	0.993252i	$-0.537000\pi$
$389$	−1779.64	−0.231957	−0.115979	+	0.993252i	$0.537000\pi$
$390$	−2301.92	−0.298878
$391$	−3073.10	−0.397477
$392$	−2421.35	−0.311982
$393$	−1311.66	−0.168358
$394$	13661.9	1.74689
$395$	446.655	0.0568953
$396$	17366.8	2.20383
$397$	−8758.10	−1.10719	−0.553597	−	0.832785i	$-0.686745\pi$
$397$	−8758.10	−1.10719	−0.553597	+	0.832785i	$0.686745\pi$
$398$	18181.6	2.28985
$399$	−5327.58	−0.668452
$400$	−26989.8	−3.37372
$401$	−6560.73	−0.817026	−0.408513	−	0.912753i	$-0.633953\pi$
$401$	−6560.73	−0.817026	−0.408513	+	0.912753i	$0.633953\pi$
$402$	−56103.9	−6.96072
$403$	−5395.24	−0.666889
$404$	−5347.81	−0.658572
$405$	6868.50	0.842713
$406$	−25481.8	−3.11488
$407$	−1565.71	−0.190687
$408$	65531.4	7.95169
$409$	8435.56	1.01983	0.509916	−	0.860224i	$-0.329676\pi$
$409$	8435.56	1.01983	0.509916	+	0.860224i	$0.329676\pi$
$410$	−2898.35	−0.349120
$411$	−8530.80	−1.02383
$412$	31070.4	3.71536
$413$	−4023.56	−0.479385
$414$	−13776.0	−1.63539
$415$	−538.462	−0.0636918
$416$	−10651.9	−1.25542
$417$	−4270.39	−0.501491
$418$	−1641.17	−0.192039
$419$	−9228.19	−1.07596	−0.537979	−	0.842958i	$-0.680812\pi$
$419$	−9228.19	−1.07596	−0.537979	+	0.842958i	$0.680812\pi$
$420$	−10806.0	−1.25543
$421$	−440.214	−0.0509613	−0.0254807	−	0.999675i	$-0.508112\pi$
$421$	−440.214	−0.0509613	−0.0254807	+	0.999675i	$0.508112\pi$
$422$	−16688.6	−1.92509
$423$	−19821.5	−2.27838
$424$	32708.8	3.74641
$425$	10511.7	1.19974
$426$	39274.7	4.46682
$427$	3471.57	0.393446
$428$	42197.1	4.76559
$429$	1803.37	0.202954
$430$	−3908.31	−0.438314
$431$	−8354.27	−0.933668	−0.466834	−	0.884345i	$-0.654605\pi$
$431$	−8354.27	−0.933668	−0.466834	+	0.884345i	$0.654605\pi$
$432$	105634.	11.7647
$433$	8734.55	0.969413	0.484707	−	0.874677i	$-0.338926\pi$
$433$	8734.55	0.969413	0.484707	+	0.874677i	$0.338926\pi$
$434$	−34728.3	−3.84104
$435$	−6252.72	−0.689184
$436$	−30148.5	−3.31158
$437$	949.421	0.103929
$438$	62555.5	6.82424
$439$	−8750.48	−0.951338	−0.475669	−	0.879624i	$-0.657794\pi$
$439$	−8750.48	−0.951338	−0.475669	+	0.879624i	$0.657794\pi$
$440$	−2093.21	−0.226795
$441$	2407.52	0.259963
$442$	7907.16	0.850917
$443$	7832.06	0.839983	0.419992	−	0.907528i	$-0.362033\pi$
$443$	7832.06	0.839983	0.419992	+	0.907528i	$0.362033\pi$
$444$	−30716.3	−3.28317
$445$	−3775.85	−0.402230
$446$	−3056.07	−0.324460
$447$	−3448.04	−0.364847
$448$	−33188.1	−3.49998
$449$	−5795.11	−0.609105	−0.304553	−	0.952496i	$-0.598507\pi$
$449$	−5795.11	−0.609105	−0.304553	+	0.952496i	$0.598507\pi$
$450$	47121.3	4.93627
$451$	2270.62	0.237072
$452$	−30759.9	−3.20094
$453$	27598.1	2.86241
$454$	20359.0	2.10462
$455$	−819.898	−0.0844778
$456$	−20245.6	−2.07914
$457$	−8657.72	−0.886195	−0.443097	−	0.896473i	$-0.646120\pi$
$457$	−8657.72	−0.886195	−0.443097	+	0.896473i	$0.646120\pi$
$458$	513.756	0.0524154
$459$	−41141.3	−4.18369
$460$	1925.73	0.195190
$461$	4828.35	0.487806	0.243903	−	0.969800i	$-0.421572\pi$
$461$	4828.35	0.487806	0.243903	+	0.969800i	$0.421572\pi$
$462$	11608.0	1.16894
$463$	2812.71	0.282327	0.141164	−	0.989986i	$-0.454916\pi$
$463$	2812.71	0.282327	0.141164	+	0.989986i	$0.454916\pi$
$464$	−55147.5	−5.51758
$465$	−8521.60	−0.849849
$466$	4154.66	0.413006
$467$	−14060.9	−1.39327	−0.696637	−	0.717424i	$-0.745321\pi$
$467$	−14060.9	−1.39327	−0.696637	+	0.717424i	$0.745321\pi$
$468$	25850.5	2.55329
$469$	−19983.1	−1.96745
$470$	3799.33	0.372872
$471$	2970.09	0.290562
$472$	−15290.1	−1.49107
$473$	3061.84	0.297639
$474$	−9412.79	−0.912117
$475$	−3247.54	−0.313699
$476$	37119.0	3.57426
$477$	−32521.9	−3.12175
$478$	14971.5	1.43260
$479$	−1838.56	−0.175378	−0.0876891	−	0.996148i	$-0.527948\pi$
$479$	−1838.56	−0.175378	−0.0876891	+	0.996148i	$0.527948\pi$
$480$	−16824.4	−1.59984
$481$	−2330.57	−0.220924
$482$	17624.3	1.66549
$483$	−6715.24	−0.632617
$484$	2607.86	0.244915
$485$	1059.26	0.0991726
$486$	−76770.1	−7.16535
$487$	−1222.31	−0.113733	−0.0568666	−	0.998382i	$-0.518111\pi$
$487$	−1222.31	−0.113733	−0.0568666	+	0.998382i	$0.518111\pi$
$488$	13192.5	1.22377
$489$	24150.8	2.23341
$490$	−461.466	−0.0425447
$491$	15595.3	1.43341	0.716706	−	0.697376i	$-0.245649\pi$
$491$	15595.3	1.43341	0.716706	+	0.697376i	$0.245649\pi$
$492$	44545.1	4.08181
$493$	21478.2	1.96213
$494$	−2442.88	−0.222491
$495$	2081.25	0.188980
$496$	−75158.5	−6.80386
$497$	13988.8	1.26254
$498$	11347.5	1.02107
$499$	11242.1	1.00855	0.504274	−	0.863544i	$-0.331760\pi$
$499$	11242.1	1.00855	0.504274	+	0.863544i	$0.331760\pi$
$500$	−13545.5	−1.21154
$501$	28475.2	2.53928
$502$	15508.4	1.37884
$503$	−3946.15	−0.349801	−0.174901	−	0.984586i	$-0.555960\pi$
$503$	−3946.15	−0.349801	−0.174901	+	0.984586i	$0.555960\pi$
$504$	104632.	9.24736
$505$	−640.883	−0.0564731
$506$	−2068.64	−0.181744
$507$	−19313.5	−1.69180
$508$	9358.11	0.817321
$509$	3225.12	0.280846	0.140423	−	0.990092i	$-0.455154\pi$
$509$	3225.12	0.280846	0.140423	+	0.990092i	$0.455154\pi$
$510$	12489.1	1.08437
$511$	22281.0	1.92887
$512$	−13950.5	−1.20416
$513$	12710.4	1.09392
$514$	−32963.2	−2.82869
$515$	3723.48	0.318595
$516$	60067.3	5.12464
$517$	−2976.46	−0.253200
$518$	−15001.5	−1.27244
$519$	−18458.0	−1.56111
$520$	−3115.74	−0.262758
$521$	−22697.5	−1.90862	−0.954312	−	0.298811i	$-0.903410\pi$
$521$	−22697.5	−1.90862	−0.954312	+	0.298811i	$0.903410\pi$
$522$	96281.8	8.07307
$523$	−6523.57	−0.545423	−0.272711	−	0.962096i	$-0.587920\pi$
$523$	−6523.57	−0.545423	−0.272711	+	0.962096i	$0.587920\pi$
$524$	−2823.38	−0.235382
$525$	22969.8	1.90949
$526$	−18608.3	−1.54251
$527$	29271.9	2.41955
$528$	25121.9	2.07062
$529$	−10970.3	−0.901643
$530$	6233.69	0.510895
$531$	15202.8	1.24246
$532$	−11467.7	−0.934567
$533$	3379.82	0.274665
$534$	79572.0	6.44834
$535$	5056.91	0.408653
$536$	−75938.7	−6.11950
$537$	−2359.08	−0.189575
$538$	−20796.9	−1.66658
$539$	361.521	0.0288902
$540$	25780.8	2.05450
$541$	−3733.48	−0.296700	−0.148350	−	0.988935i	$-0.547396\pi$
$541$	−3733.48	−0.296700	−0.148350	+	0.988935i	$0.547396\pi$
$542$	40712.7	3.22649
$543$	21982.1	1.73728
$544$	57792.0	4.55480
$545$	−3613.01	−0.283971
$546$	17278.5	1.35431
$547$	−1000.51	−0.0782063	−0.0391031	−	0.999235i	$-0.512450\pi$
$547$	−1000.51	−0.0782063	−0.0391031	+	0.999235i	$0.512450\pi$
$548$	−18362.7	−1.43142
$549$	−13117.2	−1.01972
$550$	7075.88	0.548576
$551$	−6635.61	−0.513042
$552$	−25519.0	−1.96768
$553$	−3352.64	−0.257810
$554$	−26698.3	−2.04748
$555$	−3681.05	−0.281535
$556$	−9192.12	−0.701138
$557$	−23116.1	−1.75845	−0.879227	−	0.476403i	$-0.841940\pi$
$557$	−23116.1	−1.75845	−0.879227	+	0.476403i	$0.841940\pi$
$558$	131219.	9.95509
$559$	4557.55	0.344837
$560$	−11421.6	−0.861876
$561$	−9784.18	−0.736343
$562$	−11177.6	−0.838969
$563$	−17735.8	−1.32767	−0.663834	−	0.747880i	$-0.731072\pi$
$563$	−17735.8	−1.32767	−0.663834	+	0.747880i	$0.731072\pi$
$564$	−58392.4	−4.35951
$565$	−3686.28	−0.274483
$566$	3298.97	0.244993
$567$	−51555.7	−3.81858
$568$	53159.7	3.92699
$569$	−2688.27	−0.198064	−0.0990319	−	0.995084i	$-0.531575\pi$
$569$	−2688.27	−0.198064	−0.0990319	+	0.995084i	$0.531575\pi$
$570$	−3858.45	−0.283531
$571$	−4519.84	−0.331260	−0.165630	−	0.986188i	$-0.552966\pi$
$571$	−4519.84	−0.331260	−0.165630	+	0.986188i	$0.552966\pi$
$572$	3881.80	0.283752
$573$	−44821.4	−3.26778
$574$	21755.3	1.58197
$575$	−4093.42	−0.296882
$576$	125400.	9.07115
$577$	17159.3	1.23804	0.619020	−	0.785375i	$-0.287530\pi$
$577$	17159.3	1.23804	0.619020	+	0.785375i	$0.287530\pi$
$578$	−16192.1	−1.16523
$579$	−22558.1	−1.61914
$580$	−13459.1	−0.963552
$581$	4041.75	0.288606
$582$	−22322.9	−1.58989
$583$	−4883.59	−0.346925
$584$	84671.2	5.99952
$585$	3097.94	0.218947
$586$	−12913.8	−0.910347
$587$	−20923.0	−1.47118	−0.735590	−	0.677427i	$-0.763095\pi$
$587$	−20923.0	−1.47118	−0.735590	+	0.677427i	$0.763095\pi$
$588$	7092.33	0.497420
$589$	−9043.42	−0.632645
$590$	−2914.02	−0.203336
$591$	−25163.1	−1.75139
$592$	−32466.0	−2.25396
$593$	−19653.7	−1.36101	−0.680506	−	0.732742i	$-0.738240\pi$
$593$	−19653.7	−1.36101	−0.680506	+	0.732742i	$0.738240\pi$
$594$	−27694.1	−1.91297
$595$	4448.36	0.306495
$596$	−7421.98	−0.510094
$597$	−33487.6	−2.29574
$598$	−3079.17	−0.210563
$599$	−4968.87	−0.338936	−0.169468	−	0.985536i	$-0.554205\pi$
$599$	−4968.87	−0.338936	−0.169468	+	0.985536i	$0.554205\pi$
$600$	87288.8	5.93925
$601$	25026.3	1.69857	0.849286	−	0.527933i	$-0.177033\pi$
$601$	25026.3	1.69857	0.849286	+	0.527933i	$0.177033\pi$
$602$	29336.1	1.98613
$603$	75505.0	5.09917
$604$	59405.7	4.00196
$605$	312.527	0.0210017
$606$	13505.9	0.905349
$607$	−2286.32	−0.152881	−0.0764405	−	0.997074i	$-0.524356\pi$
$607$	−2286.32	−0.152881	−0.0764405	+	0.997074i	$0.524356\pi$
$608$	−17854.6	−1.19095
$609$	46933.6	3.12290
$610$	2514.25	0.166884
$611$	−4430.46	−0.293351
$612$	−140252.	−9.26365
$613$	3939.38	0.259560	0.129780	−	0.991543i	$-0.458573\pi$
$613$	3939.38	0.259560	0.129780	+	0.991543i	$0.458573\pi$
$614$	−19161.0	−1.25940
$615$	5338.31	0.350018
$616$	15711.8	1.02767
$617$	7090.54	0.462649	0.231324	−	0.972877i	$-0.425694\pi$
$617$	7090.54	0.462649	0.231324	+	0.972877i	$0.425694\pi$
$618$	−78468.5	−5.10755
$619$	−7110.90	−0.461730	−0.230865	−	0.972986i	$-0.574156\pi$
$619$	−7110.90	−0.461730	−0.230865	+	0.972986i	$0.574156\pi$
$620$	−18343.0	−1.18818
$621$	16021.1	1.03527
$622$	−45994.5	−2.96497
$623$	28341.9	1.82262
$624$	37393.9	2.39896
$625$	13167.8	0.842740
$626$	−39191.0	−2.50222
$627$	3022.78	0.192533
$628$	6393.20	0.406236
$629$	12644.5	0.801540
$630$	19940.9	1.26106
$631$	−23279.5	−1.46869	−0.734343	−	0.678779i	$-0.762510\pi$
$631$	−23279.5	−1.46869	−0.734343	+	0.678779i	$0.762510\pi$
$632$	−12740.6	−0.801886
$633$	30737.7	1.93004
$634$	27518.2	1.72379
$635$	1121.48	0.0700860
$636$	−95806.5	−5.97323
$637$	538.124	0.0334713
$638$	14458.0	0.897173
$639$	−52856.0	−3.27223
$640$	−10593.7	−0.654303
$641$	26817.6	1.65247	0.826233	−	0.563328i	$-0.190479\pi$
$641$	26817.6	1.65247	0.826233	+	0.563328i	$0.190479\pi$
$642$	−106569.	−6.55132
$643$	−7744.80	−0.475000	−0.237500	−	0.971388i	$-0.576328\pi$
$643$	−7744.80	−0.475000	−0.237500	+	0.971388i	$0.576328\pi$
$644$	−14454.7	−0.884466
$645$	7198.49	0.439442
$646$	13253.9	0.807223
$647$	3697.53	0.224675	0.112338	−	0.993670i	$-0.464166\pi$
$647$	3697.53	0.224675	0.112338	+	0.993670i	$0.464166\pi$
$648$	−195920.	−11.8772
$649$	2282.90	0.138076
$650$	10532.5	0.635564
$651$	63964.0	3.85092
$652$	51985.2	3.12254
$653$	−22121.2	−1.32568	−0.662840	−	0.748761i	$-0.730649\pi$
$653$	−22121.2	−1.32568	−0.662840	+	0.748761i	$0.730649\pi$
$654$	76140.3	4.55248
$655$	−338.355	−0.0201842
$656$	47082.6	2.80224
$657$	−84187.5	−4.99919
$658$	−28518.1	−1.68959
$659$	−20497.0	−1.21161	−0.605804	−	0.795614i	$-0.707148\pi$
$659$	−20497.0	−1.21161	−0.605804	+	0.795614i	$0.707148\pi$
$660$	6131.16	0.361599
$661$	22486.6	1.32319	0.661594	−	0.749862i	$-0.269880\pi$
$661$	22486.6	1.32319	0.661594	+	0.749862i	$0.269880\pi$
$662$	6067.57	0.356228
$663$	−14563.8	−0.853106
$664$	15359.3	0.897675
$665$	−1374.30	−0.0801399
$666$	56682.2	3.29788
$667$	−8363.97	−0.485539
$668$	61293.5	3.55018
$669$	5628.80	0.325294
$670$	−14472.5	−0.834512
$671$	−1969.71	−0.113323
$672$	126285.	7.24935
$673$	−9206.47	−0.527315	−0.263658	−	0.964616i	$-0.584929\pi$
$673$	−9206.47	−0.527315	−0.263658	+	0.964616i	$0.584929\pi$
$674$	−25729.6	−1.47043
$675$	−54800.9	−3.12487
$676$	−41572.9	−2.36532
$677$	4232.61	0.240284	0.120142	−	0.992757i	$-0.461665\pi$
$677$	4232.61	0.240284	0.120142	+	0.992757i	$0.461665\pi$
$678$	77684.4	4.40037
$679$	−7950.95	−0.449381
$680$	16904.4	0.953317
$681$	−37498.2	−2.11003
$682$	19704.2	1.10633
$683$	−7373.55	−0.413091	−0.206546	−	0.978437i	$-0.566222\pi$
$683$	−7373.55	−0.413091	−0.206546	+	0.978437i	$0.566222\pi$
$684$	43330.3	2.42218
$685$	−2200.60	−0.122745
$686$	−32686.1	−1.81919
$687$	−946.258	−0.0525502
$688$	63488.9	3.51816
$689$	−7269.22	−0.401938
$690$	−4863.45	−0.268331
$691$	9558.10	0.526205	0.263102	−	0.964768i	$-0.415254\pi$
$691$	9558.10	0.526205	0.263102	+	0.964768i	$0.415254\pi$
$692$	−39731.3	−2.18260
$693$	−15622.1	−0.856325
$694$	−58646.1	−3.20775
$695$	−1101.59	−0.0601232
$696$	178355.	9.71340
$697$	−18337.2	−0.996515
$698$	491.851	0.0266717
$699$	−7652.23	−0.414069
$700$	49443.0	2.66967
$701$	468.291	0.0252313	0.0126156	−	0.999920i	$-0.495984\pi$
$701$	468.291	0.0252313	0.0126156	+	0.999920i	$0.495984\pi$
$702$	−41222.7	−2.21631
$703$	−3906.46	−0.209580
$704$	18830.4	1.00809
$705$	−6997.77	−0.373831
$706$	41921.6	2.23476
$707$	4810.54	0.255897
$708$	44786.0	2.37735
$709$	31945.1	1.69214	0.846069	−	0.533074i	$-0.178963\pi$
$709$	31945.1	1.69214	0.846069	+	0.533074i	$0.178963\pi$
$710$	10131.3	0.535521
$711$	12667.8	0.668184
$712$	107704.	5.66905
$713$	−11398.9	−0.598729
$714$	−93744.4	−4.91358
$715$	465.196	0.0243320
$716$	−5077.98	−0.265046
$717$	−27575.2	−1.43628
$718$	58914.6	3.06222
$719$	37630.4	1.95185	0.975924	−	0.218113i	$-0.0699901\pi$
$719$	37630.4	1.95185	0.975924	+	0.218113i	$0.0699901\pi$
$720$	43155.9	2.23378
$721$	−27948.9	−1.44365
$722$	33192.3	1.71093
$723$	−32461.3	−1.66978
$724$	47317.0	2.42890
$725$	28609.3	1.46555
$726$	−6586.17	−0.336688
$727$	23144.6	1.18072	0.590362	−	0.807138i	$-0.298985\pi$
$727$	23144.6	1.18072	0.590362	+	0.807138i	$0.298985\pi$
$728$	23387.1	1.19063
$729$	69598.6	3.53598
$730$	16136.8	0.818149
$731$	−24727.0	−1.25111
$732$	−38641.9	−1.95116
$733$	4943.14	0.249085	0.124542	−	0.992214i	$-0.460254\pi$
$733$	4943.14	0.249085	0.124542	+	0.992214i	$0.460254\pi$
$734$	−27924.2	−1.40423
$735$	849.948	0.0426542
$736$	−22505.1	−1.12711
$737$	11338.1	0.566679
$738$	−82201.3	−4.10010
$739$	35033.6	1.74388	0.871942	−	0.489609i	$-0.162861\pi$
$739$	35033.6	1.74388	0.871942	+	0.489609i	$0.162861\pi$
$740$	−7923.55	−0.393615
$741$	4499.41	0.223063
$742$	−46790.7	−2.31502
$743$	−14578.5	−0.719829	−0.359914	−	0.932985i	$-0.617194\pi$
$743$	−14578.5	−0.719829	−0.359914	+	0.932985i	$0.617194\pi$
$744$	243073.	11.9778
$745$	−889.453	−0.0437410
$746$	−32909.1	−1.61513
$747$	−15271.6	−0.748002
$748$	−21060.7	−1.02949
$749$	−37957.7	−1.85173
$750$	34209.2	1.66552
$751$	927.298	0.0450567	0.0225283	−	0.999746i	$-0.492828\pi$
$751$	927.298	0.0450567	0.0225283	+	0.999746i	$0.492828\pi$
$752$	−61718.6	−2.99288
$753$	−28564.1	−1.38238
$754$	21520.7	1.03944
$755$	7119.20	0.343171
$756$	−193514.	−9.30955
$757$	−211.111	−0.0101360	−0.00506800	−	0.999987i	$-0.501613\pi$
$757$	−211.111	−0.0101360	−0.00506800	+	0.999987i	$0.501613\pi$
$758$	17610.9	0.843875
$759$	3810.12	0.182211
$760$	−5222.55	−0.249266
$761$	−29964.5	−1.42735	−0.713675	−	0.700477i	$-0.752971\pi$
$761$	−29964.5	−1.42735	−0.713675	+	0.700477i	$0.752971\pi$
$762$	−23634.0	−1.12358
$763$	27119.6	1.28676
$764$	−96479.1	−4.56871
$765$	−16807.9	−0.794366
$766$	4837.35	0.228173
$767$	3398.09	0.159971
$768$	86129.9	4.04680
$769$	26895.7	1.26123	0.630613	−	0.776098i	$-0.282804\pi$
$769$	26895.7	1.26123	0.630613	+	0.776098i	$0.282804\pi$
$770$	2994.39	0.140143
$771$	60713.2	2.83597
$772$	−48556.9	−2.26373
$773$	16840.4	0.783581	0.391790	−	0.920055i	$-0.371856\pi$
$773$	16840.4	0.783581	0.391790	+	0.920055i	$0.371856\pi$
$774$	−110845.	−5.14760
$775$	38990.6	1.80720
$776$	−30214.8	−1.39774
$777$	27630.3	1.27572
$778$	9674.53	0.445821
$779$	5665.20	0.260561
$780$	9126.24	0.418938
$781$	−7937.02	−0.363648
$782$	16706.1	0.763948
$783$	−111973.	−5.11060
$784$	7496.34	0.341488
$785$	766.163	0.0348351
$786$	7130.48	0.323583
$787$	−21465.1	−0.972232	−0.486116	−	0.873894i	$-0.661587\pi$
$787$	−21465.1	−0.972232	−0.486116	+	0.873894i	$0.661587\pi$
$788$	−54164.1	−2.44863
$789$	34273.7	1.54648
$790$	−2428.12	−0.109353
$791$	27669.6	1.24376
$792$	−59366.3	−2.66350
$793$	−2931.92	−0.131293
$794$	47611.0	2.12802
$795$	−11481.5	−0.512209
$796$	−72082.9	−3.20969
$797$	3297.95	0.146574	0.0732870	−	0.997311i	$-0.476651\pi$
$797$	3297.95	0.146574	0.0732870	+	0.997311i	$0.476651\pi$
$798$	28961.9	1.28476
$799$	24037.5	1.06431
$800$	76979.8	3.40206
$801$	−107088.	−4.72382
$802$	35665.6	1.57032
$803$	−12641.8	−0.555568
$804$	222430.	9.75686
$805$	−1732.26	−0.0758437
$806$	29329.8	1.28176
$807$	38304.7	1.67087
$808$	18280.8	0.795936
$809$	2756.75	0.119805	0.0599025	−	0.998204i	$-0.480921\pi$
$809$	2756.75	0.119805	0.0599025	+	0.998204i	$0.480921\pi$
$810$	−37338.7	−1.61969
$811$	19446.1	0.841978	0.420989	−	0.907066i	$-0.361683\pi$
$811$	19446.1	0.841978	0.420989	+	0.907066i	$0.361683\pi$
$812$	101026.	4.36614
$813$	−74986.4	−3.23479
$814$	8511.57	0.366499
$815$	6229.93	0.267760
$816$	−202881.	−8.70373
$817$	7639.29	0.327130
$818$	−45857.6	−1.96011
$819$	−23253.5	−0.992114
$820$	11490.8	0.489363
$821$	−24856.2	−1.05662	−0.528312	−	0.849051i	$-0.677175\pi$
$821$	−24856.2	−1.05662	−0.528312	+	0.849051i	$0.677175\pi$
$822$	46375.3	1.96779
$823$	12649.4	0.535760	0.267880	−	0.963452i	$-0.413677\pi$
$823$	12649.4	0.535760	0.267880	+	0.963452i	$0.413677\pi$
$824$	−106210.	−4.49029
$825$	−13032.7	−0.549987
$826$	21872.9	0.921377
$827$	2142.04	0.0900677	0.0450339	−	0.998985i	$-0.485660\pi$
$827$	2142.04	0.0900677	0.0450339	+	0.998985i	$0.485660\pi$
$828$	54616.4	2.29233
$829$	−29029.8	−1.21622	−0.608109	−	0.793853i	$-0.708072\pi$
$829$	−29029.8	−1.21622	−0.608109	+	0.793853i	$0.708072\pi$
$830$	2927.20	0.122415
$831$	49174.1	2.05275
$832$	28029.0	1.16795
$833$	−2919.59	−0.121438
$834$	23214.8	0.963864
$835$	7345.44	0.304431
$836$	6506.60	0.269181
$837$	−152604.	−6.30200
$838$	50166.5	2.06799
$839$	−33085.5	−1.36143	−0.680715	−	0.732548i	$-0.738331\pi$
$839$	−33085.5	−1.36143	−0.680715	+	0.732548i	$0.738331\pi$
$840$	36939.1	1.51728
$841$	34067.7	1.39685
$842$	2393.10	0.0979474
$843$	20587.5	0.841127
$844$	66163.7	2.69840
$845$	−4982.11	−0.202828
$846$	107754.	4.37904
$847$	−2345.86	−0.0951648
$848$	−101264.	−4.10073
$849$	−6076.20	−0.245624
$850$	−57143.8	−2.30590
$851$	−4923.97	−0.198345
$852$	−155709.	−6.26115
$853$	−1846.25	−0.0741084	−0.0370542	−	0.999313i	$-0.511797\pi$
$853$	−1846.25	−0.0741084	−0.0370542	+	0.999313i	$0.511797\pi$
$854$	−18872.3	−0.756201
$855$	5192.72	0.207704
$856$	−144245.	−5.75958
$857$	−29967.3	−1.19447	−0.597236	−	0.802065i	$-0.703735\pi$
$857$	−29967.3	−1.19447	−0.597236	+	0.802065i	$0.703735\pi$
$858$	−9803.52	−0.390078
$859$	29843.0	1.18537	0.592684	−	0.805435i	$-0.298068\pi$
$859$	29843.0	1.18537	0.592684	+	0.805435i	$0.298068\pi$
$860$	15494.9	0.614387
$861$	−40069.9	−1.58604
$862$	45415.7	1.79451
$863$	3463.99	0.136634	0.0683172	−	0.997664i	$-0.478237\pi$
$863$	3463.99	0.136634	0.0683172	+	0.997664i	$0.478237\pi$
$864$	−301289.	−11.8635
$865$	−4761.41	−0.187159
$866$	−47483.0	−1.86321
$867$	29823.4	1.16823
$868$	137684.	5.38399
$869$	1902.23	0.0742563
$870$	33991.2	1.32461
$871$	16876.7	0.656538
$872$	103059.	4.00230
$873$	30042.2	1.16469
$874$	−5161.26	−0.199751
$875$	12184.6	0.470760
$876$	−248008.	−9.56556
$877$	−15921.3	−0.613027	−0.306514	−	0.951866i	$-0.599162\pi$
$877$	−15921.3	−0.613027	−0.306514	+	0.951866i	$0.599162\pi$
$878$	47569.6	1.82847
$879$	23785.2	0.912690
$880$	6480.42	0.248244
$881$	33688.0	1.28828	0.644141	−	0.764907i	$-0.277215\pi$
$881$	33688.0	1.28828	0.644141	+	0.764907i	$0.277215\pi$
$882$	−13087.8	−0.499649
$883$	−16558.6	−0.631077	−0.315539	−	0.948913i	$-0.602185\pi$
$883$	−16558.6	−0.631077	−0.315539	+	0.948913i	$0.602185\pi$
$884$	−31348.8	−1.19273
$885$	5367.17	0.203859
$886$	−42576.9	−1.61444
$887$	−33758.4	−1.27790	−0.638950	−	0.769249i	$-0.720631\pi$
$887$	−33758.4	−1.27790	−0.638950	+	0.769249i	$0.720631\pi$
$888$	105000.	3.96797
$889$	−8417.95	−0.317580
$890$	20526.3	0.773084
$891$	29251.8	1.09986
$892$	12116.1	0.454796
$893$	−7426.27	−0.278287
$894$	18744.3	0.701234
$895$	−608.548	−0.0227279
$896$	79517.6	2.96484
$897$	5671.36	0.211105
$898$	31503.5	1.17070
$899$	79668.5	2.95561
$900$	−186818.	−6.91918
$901$	39439.2	1.45828
$902$	−12343.6	−0.455651
$903$	−54032.6	−1.99124
$904$	105149.	3.86858
$905$	5670.49	0.208280
$906$	−150030.	−5.50155
$907$	−4820.11	−0.176460	−0.0882299	−	0.996100i	$-0.528121\pi$
$907$	−4820.11	−0.176460	−0.0882299	+	0.996100i	$0.528121\pi$
$908$	−80715.7	−2.95005
$909$	−18176.4	−0.663226
$910$	4457.15	0.162366
$911$	20300.2	0.738283	0.369141	−	0.929373i	$-0.379652\pi$
$911$	20300.2	0.738283	0.369141	+	0.929373i	$0.379652\pi$
$912$	62679.0	2.27578
$913$	−2293.22	−0.0831266
$914$	47065.3	1.70326
$915$	−4630.87	−0.167313
$916$	−2036.84	−0.0734707
$917$	2539.73	0.0914605
$918$	223654.	8.04103
$919$	−38397.1	−1.37824	−0.689121	−	0.724646i	$-0.742003\pi$
$919$	−38397.1	−1.37824	−0.689121	+	0.724646i	$0.742003\pi$
$920$	−6582.86	−0.235903
$921$	35291.5	1.26264
$922$	−26248.0	−0.937561
$923$	−11814.3	−0.421312
$924$	−46021.1	−1.63851
$925$	16842.6	0.598684
$926$	−15290.5	−0.542632
$927$	105603.	3.74161
$928$	157291.	5.56393
$929$	27353.2	0.966018	0.483009	−	0.875615i	$-0.339544\pi$
$929$	27353.2	0.966018	0.483009	+	0.875615i	$0.339544\pi$
$930$	46325.3	1.63341
$931$	901.994	0.0317526
$932$	−16471.6	−0.578912
$933$	84714.6	2.97260
$934$	76438.0	2.67787
$935$	−2523.92	−0.0882792
$936$	−88366.8	−3.08585
$937$	−46782.2	−1.63107	−0.815533	−	0.578711i	$-0.803556\pi$
$937$	−46782.2	−1.63107	−0.815533	+	0.578711i	$0.803556\pi$
$938$	108632.	3.78142
$939$	72183.7	2.50865
$940$	−15062.9	−0.522656
$941$	9883.16	0.342382	0.171191	−	0.985238i	$-0.445238\pi$
$941$	9883.16	0.342382	0.171191	+	0.985238i	$0.445238\pi$
$942$	−16146.1	−0.558459
$943$	7140.80	0.246592
$944$	47337.2	1.63209
$945$	−23190.8	−0.798302
$946$	−16644.8	−0.572062
$947$	14273.4	0.489781	0.244891	−	0.969551i	$-0.421248\pi$
$947$	14273.4	0.489781	0.244891	+	0.969551i	$0.421248\pi$
$948$	37318.1	1.27852
$949$	−18817.4	−0.643666
$950$	17654.3	0.602928
$951$	−50684.2	−1.72823
$952$	−126887.	−4.31976
$953$	52280.8	1.77706	0.888531	−	0.458816i	$-0.151726\pi$
$953$	52280.8	1.77706	0.888531	+	0.458816i	$0.151726\pi$
$954$	176796.	5.99999
$955$	−11562.1	−0.391770
$956$	−59356.3	−2.00807
$957$	−26629.3	−0.899482
$958$	9994.84	0.337076
$959$	16517.9	0.556196
$960$	44270.9	1.48837
$961$	78786.2	2.64463
$962$	12669.5	0.424616
$963$	143421.	4.79926
$964$	−69873.7	−2.33452
$965$	−5819.08	−0.194117
$966$	36505.6	1.21589
$967$	46115.0	1.53357	0.766783	−	0.641907i	$-0.221856\pi$
$967$	46115.0	1.53357	0.766783	+	0.641907i	$0.221856\pi$
$968$	−8914.62	−0.295999
$969$	−24411.5	−0.809300
$970$	−5758.40	−0.190609
$971$	43055.8	1.42299	0.711497	−	0.702689i	$-0.248018\pi$
$971$	43055.8	1.42299	0.711497	+	0.702689i	$0.248018\pi$
$972$	304364.	10.0437
$973$	8268.63	0.272436
$974$	6644.74	0.218595
$975$	−19399.1	−0.637200
$976$	−40843.1	−1.33950
$977$	12791.9	0.418882	0.209441	−	0.977821i	$-0.432836\pi$
$977$	12791.9	0.418882	0.209441	+	0.977821i	$0.432836\pi$
$978$	−131289.	−4.29260
$979$	−16080.7	−0.524966
$980$	1829.53	0.0596350
$981$	−102470.	−3.33498
$982$	−84779.4	−2.75501
$983$	39904.5	1.29477	0.647383	−	0.762164i	$-0.275863\pi$
$983$	39904.5	1.29477	0.647383	+	0.762164i	$0.275863\pi$
$984$	−152272.	−4.93318
$985$	−6491.05	−0.209972
$986$	−116761.	−3.77121
$987$	52526.0	1.69394
$988$	9685.08	0.311866
$989$	9629.08	0.309592
$990$	−11314.1	−0.363219
$991$	−36765.5	−1.17850	−0.589250	−	0.807950i	$-0.700577\pi$
$991$	−36765.5	−1.17850	−0.589250	+	0.807950i	$0.700577\pi$
$992$	214366.	6.86101
$993$	−11175.5	−0.357144
$994$	−76046.4	−2.42660
$995$	−8638.45	−0.275233
$996$	−44988.6	−1.43124
$997$	−288.228	−0.00915573	−0.00457787	−	0.999990i	$-0.501457\pi$
$997$	−288.228	−0.00915573	−0.00457787	+	0.999990i	$0.501457\pi$
$998$	−61114.6	−1.93843
$999$	−65919.9	−2.08770

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.b.1.2	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.b.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-5.43622 q^{2} +10.0127 q^{3} +21.5525 q^{4} +2.58286 q^{5} -54.4312 q^{6} -19.3873 q^{7} -73.6746 q^{8} +73.2537 q^{9} +O(q^{10})\)	\(q-5.43622 q^{2} +10.0127 q^{3} +21.5525 q^{4} +2.58286 q^{5} -54.4312 q^{6} -19.3873 q^{7} -73.6746 q^{8} +73.2537 q^{9} -14.0410 q^{10} +11.0000 q^{11} +215.799 q^{12} +16.3735 q^{13} +105.393 q^{14} +25.8614 q^{15} +228.091 q^{16} -88.8345 q^{17} -398.224 q^{18} +27.4450 q^{19} +55.6673 q^{20} -194.118 q^{21} -59.7985 q^{22} +34.5936 q^{23} -737.680 q^{24} -118.329 q^{25} -89.0100 q^{26} +463.124 q^{27} -417.844 q^{28} -241.778 q^{29} -140.588 q^{30} -329.511 q^{31} -650.559 q^{32} +110.139 q^{33} +482.924 q^{34} -50.0747 q^{35} +1578.80 q^{36} -142.338 q^{37} -149.197 q^{38} +163.943 q^{39} -190.291 q^{40} +206.420 q^{41} +1055.27 q^{42} +278.349 q^{43} +237.078 q^{44} +189.204 q^{45} -188.058 q^{46} -270.587 q^{47} +2283.80 q^{48} +32.8655 q^{49} +643.262 q^{50} -889.471 q^{51} +352.890 q^{52} -443.962 q^{53} -2517.64 q^{54} +28.4115 q^{55} +1428.35 q^{56} +274.798 q^{57} +1314.36 q^{58} +207.536 q^{59} +557.378 q^{60} -179.065 q^{61} +1791.29 q^{62} -1420.19 q^{63} +1711.85 q^{64} +42.2906 q^{65} -598.743 q^{66} +1030.73 q^{67} -1914.61 q^{68} +346.374 q^{69} +272.217 q^{70} -721.547 q^{71} -5396.94 q^{72} -1149.26 q^{73} +773.779 q^{74} -1184.79 q^{75} +591.509 q^{76} -213.260 q^{77} -891.229 q^{78} +172.930 q^{79} +589.129 q^{80} +2659.26 q^{81} -1122.15 q^{82} -208.475 q^{83} -4183.74 q^{84} -229.447 q^{85} -1513.17 q^{86} -2420.85 q^{87} -810.420 q^{88} -1461.88 q^{89} -1028.56 q^{90} -317.437 q^{91} +745.579 q^{92} -3299.28 q^{93} +1470.97 q^{94} +70.8867 q^{95} -6513.83 q^{96} +410.112 q^{97} -178.664 q^{98} +805.791 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 20 q^{2} - 12 q^{3} + 288 q^{4} - 40 q^{5} - 111 q^{6} - 101 q^{7} - 258 q^{8} + 585 q^{9}+O(q^{10}) \) 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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