LMFDB - Embedded newform 1441.4.a.a.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:	$77$
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)

$f(q)$	$=$	$q-5.40673 q^{2} -0.868288 q^{3} +21.2327 q^{4} -21.2610 q^{5} +4.69460 q^{6} -2.80805 q^{7} -71.5459 q^{8} -26.2461 q^{9} +O(q^{10})$	\(q-5.40673 q^{2} -0.868288 q^{3} +21.2327 q^{4} -21.2610 q^{5} +4.69460 q^{6} -2.80805 q^{7} -71.5459 q^{8} -26.2461 q^{9} +114.953 q^{10} -11.0000 q^{11} -18.4361 q^{12} -14.9796 q^{13} +15.1824 q^{14} +18.4607 q^{15} +216.968 q^{16} -78.1011 q^{17} +141.905 q^{18} +0.324401 q^{19} -451.430 q^{20} +2.43820 q^{21} +59.4740 q^{22} -87.7172 q^{23} +62.1224 q^{24} +327.032 q^{25} +80.9909 q^{26} +46.2329 q^{27} -59.6227 q^{28} -7.07797 q^{29} -99.8121 q^{30} -152.344 q^{31} -600.718 q^{32} +9.55116 q^{33} +422.272 q^{34} +59.7022 q^{35} -557.276 q^{36} +140.222 q^{37} -1.75395 q^{38} +13.0066 q^{39} +1521.14 q^{40} +432.714 q^{41} -13.1827 q^{42} +63.0286 q^{43} -233.560 q^{44} +558.019 q^{45} +474.263 q^{46} +353.504 q^{47} -188.390 q^{48} -335.115 q^{49} -1768.18 q^{50} +67.8142 q^{51} -318.059 q^{52} +391.412 q^{53} -249.969 q^{54} +233.872 q^{55} +200.905 q^{56} -0.281673 q^{57} +38.2687 q^{58} -435.556 q^{59} +391.971 q^{60} -134.849 q^{61} +823.681 q^{62} +73.7004 q^{63} +1512.18 q^{64} +318.483 q^{65} -51.6406 q^{66} +205.619 q^{67} -1658.30 q^{68} +76.1637 q^{69} -322.794 q^{70} -1018.32 q^{71} +1877.80 q^{72} +515.303 q^{73} -758.145 q^{74} -283.958 q^{75} +6.88793 q^{76} +30.8886 q^{77} -70.3234 q^{78} +273.851 q^{79} -4612.96 q^{80} +668.501 q^{81} -2339.57 q^{82} -1017.78 q^{83} +51.7696 q^{84} +1660.51 q^{85} -340.779 q^{86} +6.14571 q^{87} +787.005 q^{88} +796.369 q^{89} -3017.06 q^{90} +42.0636 q^{91} -1862.48 q^{92} +132.278 q^{93} -1911.30 q^{94} -6.89711 q^{95} +521.596 q^{96} +1877.18 q^{97} +1811.88 q^{98} +288.707 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9}+O(q^{10}) $ 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9	\( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9} + 2 q^{10} - 847 q^{11} - 88 q^{12} - 20 q^{13} - 282 q^{14} - 330 q^{15} + 936 q^{16} - 56 q^{17} - 343 q^{18} - 157 q^{19} - 450 q^{20} - 122 q^{21} + 154 q^{22} - 764 q^{23} - 346 q^{24} + 1413 q^{25} - 408 q^{26} - 358 q^{27} - 228 q^{28} - 557 q^{29} - 267 q^{30} - 780 q^{31} - 1739 q^{32} + 110 q^{33} - 1104 q^{34} - 1254 q^{35} + 375 q^{36} - 541 q^{37} - 2133 q^{38} - 1458 q^{39} - 554 q^{40} - 1723 q^{41} - 5 q^{42} - 688 q^{43} - 3256 q^{44} - 1588 q^{45} + 276 q^{46} - 3086 q^{47} - 4280 q^{48} + 2452 q^{49} - 2234 q^{50} - 1570 q^{51} - 715 q^{52} - 1230 q^{53} - 5166 q^{54} + 462 q^{55} - 3203 q^{56} + 1024 q^{57} - 3016 q^{58} - 5408 q^{59} - 8221 q^{60} + 566 q^{61} - 3642 q^{62} - 3035 q^{63} + 1084 q^{64} - 1794 q^{65} + 143 q^{66} - 1925 q^{67} - 1105 q^{68} - 3710 q^{69} - 5875 q^{70} - 9614 q^{71} - 2198 q^{72} - 384 q^{73} - 2378 q^{74} - 3888 q^{75} - 2809 q^{76} + 649 q^{77} - 1731 q^{78} - 1086 q^{79} - 4357 q^{80} + 2329 q^{81} - 3167 q^{82} - 3045 q^{83} - 5359 q^{84} + 2582 q^{85} - 6468 q^{86} - 4432 q^{87} + 1650 q^{88} - 2831 q^{89} + 512 q^{90} - 6002 q^{91} - 7134 q^{92} - 4428 q^{93} + 1697 q^{94} - 10434 q^{95} + 195 q^{96} - 2506 q^{97} - 3435 q^{98} - 5951 q^{99}+O(q^{100}) \) 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9 + 2 * q^10 - 847 * q^11 - 88 * q^12 - 20 * q^13 - 282 * q^14 - 330 * q^15 + 936 * q^16 - 56 * q^17 - 343 * q^18 - 157 * q^19 - 450 * q^20 - 122 * q^21 + 154 * q^22 - 764 * q^23 - 346 * q^24 + 1413 * q^25 - 408 * q^26 - 358 * q^27 - 228 * q^28 - 557 * q^29 - 267 * q^30 - 780 * q^31 - 1739 * q^32 + 110 * q^33 - 1104 * q^34 - 1254 * q^35 + 375 * q^36 - 541 * q^37 - 2133 * q^38 - 1458 * q^39 - 554 * q^40 - 1723 * q^41 - 5 * q^42 - 688 * q^43 - 3256 * q^44 - 1588 * q^45 + 276 * q^46 - 3086 * q^47 - 4280 * q^48 + 2452 * q^49 - 2234 * q^50 - 1570 * q^51 - 715 * q^52 - 1230 * q^53 - 5166 * q^54 + 462 * q^55 - 3203 * q^56 + 1024 * q^57 - 3016 * q^58 - 5408 * q^59 - 8221 * q^60 + 566 * q^61 - 3642 * q^62 - 3035 * q^63 + 1084 * q^64 - 1794 * q^65 + 143 * q^66 - 1925 * q^67 - 1105 * q^68 - 3710 * q^69 - 5875 * q^70 - 9614 * q^71 - 2198 * q^72 - 384 * q^73 - 2378 * q^74 - 3888 * q^75 - 2809 * q^76 + 649 * q^77 - 1731 * q^78 - 1086 * q^79 - 4357 * q^80 + 2329 * q^81 - 3167 * q^82 - 3045 * q^83 - 5359 * q^84 + 2582 * q^85 - 6468 * q^86 - 4432 * q^87 + 1650 * q^88 - 2831 * q^89 + 512 * q^90 - 6002 * q^91 - 7134 * q^92 - 4428 * q^93 + 1697 * q^94 - 10434 * q^95 + 195 * q^96 - 2506 * q^97 - 3435 * q^98 - 5951 * 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 $

$2$	−5.40673	−1.91157	−0.955784	−	0.294069i	$-0.904990\pi$
$2$	−5.40673	−1.91157	−0.955784	+	0.294069i	$0.904990\pi$
$3$	−0.868288	−0.167102	−0.0835510	−	0.996504i	$-0.526626\pi$
$3$	−0.868288	−0.167102	−0.0835510	+	0.996504i	$0.526626\pi$
$4$	21.2327	2.65409
$5$	−21.2610	−1.90165	−0.950823	−	0.309735i	$-0.899760\pi$
$5$	−21.2610	−1.90165	−0.950823	+	0.309735i	$0.899760\pi$
$6$	4.69460	0.319427
$7$	−2.80805	−0.151621	−0.0758103	−	0.997122i	$-0.524154\pi$
$7$	−2.80805	−0.151621	−0.0758103	+	0.997122i	$0.524154\pi$
$8$	−71.5459	−3.16191
$9$	−26.2461	−0.972077
$10$	114.953	3.63513
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−18.4361	−0.443504
$13$	−14.9796	−0.319585	−0.159792	−	0.987151i	$-0.551083\pi$
$13$	−14.9796	−0.319585	−0.159792	+	0.987151i	$0.551083\pi$
$14$	15.1824	0.289833
$15$	18.4607	0.317769
$16$	216.968	3.39012
$17$	−78.1011	−1.11425	−0.557126	−	0.830428i	$-0.688096\pi$
$17$	−78.1011	−1.11425	−0.557126	+	0.830428i	$0.688096\pi$
$18$	141.905	1.85819
$19$	0.324401	0.00391698	0.00195849	−	0.999998i	$-0.499377\pi$
$19$	0.324401	0.00391698	0.00195849	+	0.999998i	$0.499377\pi$
$20$	−451.430	−5.04715
$21$	2.43820	0.0253361
$22$	59.4740	0.576360
$23$	−87.7172	−0.795230	−0.397615	−	0.917552i	$-0.630162\pi$
$23$	−87.7172	−0.795230	−0.397615	+	0.917552i	$0.630162\pi$
$24$	62.1224	0.528362
$25$	327.032	2.61626
$26$	80.9909	0.610909
$27$	46.2329	0.329538
$28$	−59.6227	−0.402415
$29$	−7.07797	−0.0453223	−0.0226611	−	0.999743i	$-0.507214\pi$
$29$	−7.07797	−0.0453223	−0.0226611	+	0.999743i	$0.507214\pi$
$30$	−99.8121	−0.607437
$31$	−152.344	−0.882636	−0.441318	−	0.897351i	$-0.645489\pi$
$31$	−152.344	−0.882636	−0.441318	+	0.897351i	$0.645489\pi$
$32$	−600.718	−3.31853
$33$	9.55116	0.0503832
$34$	422.272	2.12997
$35$	59.7022	0.288329
$36$	−557.276	−2.57998
$37$	140.222	0.623038	0.311519	−	0.950240i	$-0.399162\pi$
$37$	140.222	0.623038	0.311519	+	0.950240i	$0.399162\pi$
$38$	−1.75395	−0.00748758
$39$	13.0066	0.0534033
$40$	1521.14	6.01284
$41$	432.714	1.64826	0.824129	−	0.566402i	$-0.191665\pi$
$41$	432.714	1.64826	0.824129	+	0.566402i	$0.191665\pi$
$42$	−13.1827	−0.0484317
$43$	63.0286	0.223530	0.111765	−	0.993735i	$-0.464350\pi$
$43$	63.0286	0.223530	0.111765	+	0.993735i	$0.464350\pi$
$44$	−233.560	−0.800239
$45$	558.019	1.84855
$46$	474.263	1.52014
$47$	353.504	1.09710	0.548552	−	0.836116i	$-0.315179\pi$
$47$	353.504	1.09710	0.548552	+	0.836116i	$0.315179\pi$
$48$	−188.390	−0.566496
$49$	−335.115	−0.977011
$50$	−1768.18	−5.00115
$51$	67.8142	0.186194
$52$	−318.059	−0.848208
$53$	391.412	1.01443	0.507213	−	0.861820i	$-0.330676\pi$
$53$	391.412	1.01443	0.507213	+	0.861820i	$0.330676\pi$
$54$	−249.969	−0.629934
$55$	233.872	0.573368
$56$	200.905	0.479411
$57$	−0.281673	−0.000654536 0
$58$	38.2687	0.0866367
$59$	−435.556	−0.961094	−0.480547	−	0.876969i	$-0.659562\pi$
$59$	−435.556	−0.961094	−0.480547	+	0.876969i	$0.659562\pi$
$60$	391.971	0.843388
$61$	−134.849	−0.283043	−0.141521	−	0.989935i	$-0.545199\pi$
$61$	−134.849	−0.283043	−0.141521	+	0.989935i	$0.545199\pi$
$62$	823.681	1.68722
$63$	73.7004	0.147387
$64$	1512.18	2.95348
$65$	318.483	0.607737
$66$	−51.6406	−0.0963108
$67$	205.619	0.374931	0.187465	−	0.982271i	$-0.439973\pi$
$67$	205.619	0.374931	0.187465	+	0.982271i	$0.439973\pi$
$68$	−1658.30	−2.95733
$69$	76.1637	0.132885
$70$	−322.794	−0.551160
$71$	−1018.32	−1.70214	−0.851070	−	0.525052i	$-0.824046\pi$
$71$	−1018.32	−1.70214	−0.851070	+	0.525052i	$0.824046\pi$
$72$	1877.80	3.07362
$73$	515.303	0.826188	0.413094	−	0.910688i	$-0.364448\pi$
$73$	515.303	0.826188	0.413094	+	0.910688i	$0.364448\pi$
$74$	−758.145	−1.19098
$75$	−283.958	−0.437182
$76$	6.88793	0.0103960
$77$	30.8886	0.0457154
$78$	−70.3234	−0.102084
$79$	273.851	0.390008	0.195004	−	0.980802i	$-0.437528\pi$
$79$	273.851	0.390008	0.195004	+	0.980802i	$0.437528\pi$
$80$	−4612.96	−6.44680
$81$	668.501	0.917010
$82$	−2339.57	−3.15076
$83$	−1017.78	−1.34597	−0.672986	−	0.739655i	$-0.734989\pi$
$83$	−1017.78	−1.34597	−0.672986	+	0.739655i	$0.734989\pi$
$84$	51.7696	0.0672444
$85$	1660.51	2.11891
$86$	−340.779	−0.427292
$87$	6.14571	0.00757345
$88$	787.005	0.953352
$89$	796.369	0.948482	0.474241	−	0.880395i	$-0.342722\pi$
$89$	796.369	0.948482	0.474241	+	0.880395i	$0.342722\pi$
$90$	−3017.06	−3.53362
$91$	42.0636	0.0484557
$92$	−1862.48	−2.11061
$93$	132.278	0.147490
$94$	−1911.30	−2.09719
$95$	−6.89711	−0.00744872
$96$	521.596	0.554533
$97$	1877.18	1.96494	0.982470	−	0.186422i	$-0.0596893\pi$
$97$	1877.18	1.96494	0.982470	+	0.186422i	$0.0596893\pi$
$98$	1811.88	1.86762
$99$	288.707	0.293092
$100$	6943.79	6.94379
$101$	−1179.19	−1.16172	−0.580860	−	0.814003i	$-0.697284\pi$
$101$	−1179.19	−1.16172	−0.580860	+	0.814003i	$0.697284\pi$
$102$	−366.653	−0.355922
$103$	1309.19	1.25241	0.626206	−	0.779658i	$-0.284607\pi$
$103$	1309.19	1.25241	0.626206	+	0.779658i	$0.284607\pi$
$104$	1071.73	1.01050
$105$	−51.8387	−0.0481803
$106$	−2116.26	−1.93915
$107$	1162.93	1.05069	0.525347	−	0.850888i	$-0.323935\pi$
$107$	1162.93	1.05069	0.525347	+	0.850888i	$0.323935\pi$
$108$	981.652	0.874625
$109$	−1246.61	−1.09545	−0.547724	−	0.836659i	$-0.684506\pi$
$109$	−1246.61	−1.09545	−0.547724	+	0.836659i	$0.684506\pi$
$110$	−1264.48	−1.09603
$111$	−121.753	−0.104111
$112$	−609.257	−0.514012
$113$	89.6892	0.0746659	0.0373330	−	0.999303i	$-0.488114\pi$
$113$	89.6892	0.0746659	0.0373330	+	0.999303i	$0.488114\pi$
$114$	1.52293	0.00125119
$115$	1864.96	1.51225
$116$	−150.285	−0.120290
$117$	393.157	0.310661
$118$	2354.93	1.83720
$119$	219.312	0.168944
$120$	−1320.79	−1.00476
$121$	121.000	0.0909091
$122$	729.090	0.541055
$123$	−375.720	−0.275427
$124$	−3234.67	−2.34260
$125$	−4295.42	−3.07355
$126$	−398.478	−0.281740
$127$	−1148.28	−0.802310	−0.401155	−	0.916010i	$-0.631391\pi$
$127$	−1148.28	−0.802310	−0.401155	+	0.916010i	$0.631391\pi$
$128$	−3370.21	−2.32725
$129$	−54.7269	−0.0373522
$130$	−1721.95	−1.16173
$131$	131.000	0.0873704
$131$	131.000	0.0873704
$132$	202.797	0.133722
$133$	−0.910936	−0.000593896 0
$134$	−1111.73	−0.716706
$135$	−982.960	−0.626665
$136$	5587.81	3.52317
$137$	−650.518	−0.405675	−0.202838	−	0.979212i	$-0.565016\pi$
$137$	−650.518	−0.405675	−0.202838	+	0.979212i	$0.565016\pi$
$138$	−411.797	−0.254018
$139$	2706.35	1.65143	0.825717	−	0.564084i	$-0.190771\pi$
$139$	2706.35	1.65143	0.825717	+	0.564084i	$0.190771\pi$
$140$	1267.64	0.765252
$141$	−306.944	−0.183328
$142$	5505.76	3.25376
$143$	164.776	0.0963585
$144$	−5694.55	−3.29546
$145$	150.485	0.0861870
$146$	−2786.11	−1.57931
$147$	290.976	0.163261
$148$	2977.31	1.65360
$149$	2554.28	1.40439	0.702196	−	0.711983i	$-0.252203\pi$
$149$	2554.28	1.40439	0.702196	+	0.711983i	$0.252203\pi$
$150$	1535.28	0.835703
$151$	−569.750	−0.307057	−0.153529	−	0.988144i	$-0.549064\pi$
$151$	−569.750	−0.307057	−0.153529	+	0.988144i	$0.549064\pi$
$152$	−23.2096	−0.0123852
$153$	2049.85	1.08314
$154$	−167.006	−0.0873880
$155$	3238.99	1.67846
$156$	276.167	0.141737
$157$	1304.35	0.663049	0.331525	−	0.943447i	$-0.392437\pi$
$157$	1304.35	0.663049	0.331525	+	0.943447i	$0.392437\pi$
$158$	−1480.64	−0.745527
$159$	−339.858	−0.169513
$160$	12771.9	6.31067
$161$	246.315	0.120573
$162$	−3614.40	−1.75293
$163$	−268.563	−0.129052	−0.0645260	−	0.997916i	$-0.520554\pi$
$163$	−268.563	−0.129052	−0.0645260	+	0.997916i	$0.520554\pi$
$164$	9187.71	4.37463
$165$	−203.068	−0.0958109
$166$	5502.85	2.57292
$167$	1599.25	0.741039	0.370520	−	0.928825i	$-0.379180\pi$
$167$	1599.25	0.741039	0.370520	+	0.928825i	$0.379180\pi$
$168$	−174.443	−0.0801106
$169$	−1972.61	−0.897865
$170$	−8977.94	−4.05045
$171$	−8.51425	−0.00380761
$172$	1338.27	0.593268
$173$	2550.62	1.12092	0.560462	−	0.828180i	$-0.310623\pi$
$173$	2550.62	1.12092	0.560462	+	0.828180i	$0.310623\pi$
$174$	−33.2282	−0.0144772
$175$	−918.324	−0.396679
$176$	−2386.64	−1.02216
$177$	378.188	0.160601
$178$	−4305.75	−1.81309
$179$	2754.66	1.15024	0.575121	−	0.818068i	$-0.304955\pi$
$179$	2754.66	1.15024	0.575121	+	0.818068i	$0.304955\pi$
$180$	11848.3	4.90621
$181$	3416.10	1.40285	0.701427	−	0.712741i	$-0.252547\pi$
$181$	3416.10	1.40285	0.701427	+	0.712741i	$0.252547\pi$
$182$	−227.427	−0.0926264
$183$	117.087	0.0472970
$184$	6275.80	2.51445
$185$	−2981.27	−1.18480
$186$	−715.192	−0.281938
$187$	859.112	0.335960
$188$	7505.87	2.91182
$189$	−129.824	−0.0499648
$190$	37.2908	0.0142387
$191$	1346.58	0.510133	0.255066	−	0.966924i	$-0.417903\pi$
$191$	1346.58	0.510133	0.255066	+	0.966924i	$0.417903\pi$
$192$	−1313.01	−0.493532
$193$	2171.07	0.809725	0.404863	−	0.914377i	$-0.367319\pi$
$193$	2171.07	0.809725	0.404863	+	0.914377i	$0.367319\pi$
$194$	−10149.4	−3.75612
$195$	−276.535	−0.101554
$196$	−7115.41	−2.59308
$197$	−1508.45	−0.545545	−0.272773	−	0.962078i	$-0.587941\pi$
$197$	−1508.45	−0.545545	−0.272773	+	0.962078i	$0.587941\pi$
$198$	−1560.96	−0.560266
$199$	−2521.24	−0.898119	−0.449060	−	0.893502i	$-0.648241\pi$
$199$	−2521.24	−0.898119	−0.449060	+	0.893502i	$0.648241\pi$
$200$	−23397.8	−8.27238
$201$	−178.537	−0.0626517
$202$	6375.56	2.22071
$203$	19.8753	0.00687180
$204$	1439.88	0.494176
$205$	−9199.95	−3.13440
$206$	−7078.45	−2.39407
$207$	2302.23	0.773025
$208$	−3250.10	−1.08343
$209$	−3.56841	−0.00118102
$210$	280.278	0.0921000
$211$	2502.94	0.816634	0.408317	−	0.912840i	$-0.366116\pi$
$211$	2502.94	0.816634	0.408317	+	0.912840i	$0.366116\pi$
$212$	8310.76	2.69238
$213$	884.192	0.284431
$214$	−6287.63	−2.00847
$215$	−1340.05	−0.425074
$216$	−3307.78	−1.04197
$217$	427.789	0.133826
$218$	6740.10	2.09403
$219$	−447.431	−0.138058
$220$	4965.74	1.52177
$221$	1169.93	0.356098
$222$	658.287	0.199015
$223$	−5251.33	−1.57693	−0.788464	−	0.615081i	$-0.789123\pi$
$223$	−5251.33	−1.57693	−0.788464	+	0.615081i	$0.789123\pi$
$224$	1686.85	0.503158
$225$	−8583.31	−2.54320
$226$	−484.925	−0.142729
$227$	2621.57	0.766519	0.383259	−	0.923641i	$-0.374802\pi$
$227$	2621.57	0.766519	0.383259	+	0.923641i	$0.374802\pi$
$228$	−5.98070	−0.00173720
$229$	−3944.14	−1.13815	−0.569074	−	0.822286i	$-0.692698\pi$
$229$	−3944.14	−1.13815	−0.569074	+	0.822286i	$0.692698\pi$
$230$	−10083.3	−2.89076
$231$	−26.8202	−0.00763913
$232$	506.400	0.143305
$233$	−1494.04	−0.420078	−0.210039	−	0.977693i	$-0.567359\pi$
$233$	−1494.04	−0.420078	−0.210039	+	0.977693i	$0.567359\pi$
$234$	−2125.69	−0.593850
$235$	−7515.88	−2.08631
$236$	−9248.04	−2.55083
$237$	−237.781	−0.0651711
$238$	−1185.76	−0.322948
$239$	613.492	0.166040	0.0830198	−	0.996548i	$-0.473544\pi$
$239$	613.492	0.166040	0.0830198	+	0.996548i	$0.473544\pi$
$240$	4005.37	1.07727
$241$	−5557.74	−1.48550	−0.742751	−	0.669568i	$-0.766479\pi$
$241$	−5557.74	−1.48550	−0.742751	+	0.669568i	$0.766479\pi$
$242$	−654.215	−0.173779
$243$	−1828.74	−0.482772
$244$	−2863.21	−0.751221
$245$	7124.89	1.85793
$246$	2031.42	0.526498
$247$	−4.85941	−0.00125181
$248$	10899.6	2.79082
$249$	883.724	0.224915
$250$	23224.2	5.87530
$251$	−3591.31	−0.903113	−0.451556	−	0.892243i	$-0.649131\pi$
$251$	−3591.31	−0.903113	−0.451556	+	0.892243i	$0.649131\pi$
$252$	1564.86	0.391179
$253$	964.889	0.239771
$254$	6208.44	1.53367
$255$	−1441.80	−0.354075
$256$	6124.39	1.49521
$257$	6313.02	1.53228	0.766139	−	0.642675i	$-0.222176\pi$
$257$	6313.02	1.53228	0.766139	+	0.642675i	$0.222176\pi$
$258$	295.894	0.0714014
$259$	−393.752	−0.0944655
$260$	6762.27	1.61299
$261$	185.769	0.0440568
$262$	−708.282	−0.167014
$263$	−4468.13	−1.04759	−0.523796	−	0.851844i	$-0.675484\pi$
$263$	−4468.13	−1.04759	−0.523796	+	0.851844i	$0.675484\pi$
$264$	−683.347	−0.159307
$265$	−8321.84	−1.92908
$266$	4.92518	0.00113527
$267$	−691.477	−0.158493
$268$	4365.86	0.995102
$269$	−2375.34	−0.538391	−0.269196	−	0.963086i	$-0.586758\pi$
$269$	−2375.34	−0.538391	−0.269196	+	0.963086i	$0.586758\pi$
$270$	5314.60	1.19791
$271$	5445.95	1.22073	0.610365	−	0.792120i	$-0.291023\pi$
$271$	5445.95	1.22073	0.610365	+	0.792120i	$0.291023\pi$
$272$	−16945.4	−3.77745
$273$	−36.5233	−0.00809704
$274$	3517.17	0.775476
$275$	−3597.35	−0.788831
$276$	1617.16	0.352688
$277$	2742.30	0.594834	0.297417	−	0.954748i	$-0.403875\pi$
$277$	2742.30	0.594834	0.297417	+	0.954748i	$0.403875\pi$
$278$	−14632.5	−3.15683
$279$	3998.42	0.857991
$280$	−4271.45	−0.911671
$281$	−6910.93	−1.46716	−0.733579	−	0.679604i	$-0.762151\pi$
$281$	−6910.93	−1.46716	−0.733579	+	0.679604i	$0.762151\pi$
$282$	1659.56	0.350445
$283$	−5128.94	−1.07733	−0.538664	−	0.842520i	$-0.681071\pi$
$283$	−5128.94	−1.07733	−0.538664	+	0.842520i	$0.681071\pi$
$284$	−21621.7	−4.51764
$285$	5.98867	0.00124470
$286$	−890.900	−0.184196
$287$	−1215.08	−0.249910
$288$	15766.5	3.22587
$289$	1186.78	0.241559
$290$	−813.633	−0.164752
$291$	−1629.94	−0.328345
$292$	10941.3	2.19278
$293$	−2367.60	−0.472071	−0.236035	−	0.971744i	$-0.575848\pi$
$293$	−2367.60	−0.472071	−0.236035	+	0.971744i	$0.575848\pi$
$294$	−1573.23	−0.312084
$295$	9260.37	1.82766
$296$	−10032.3	−1.96999
$297$	−508.562	−0.0993595
$298$	−13810.3	−2.68459
$299$	1313.97	0.254144
$300$	−6029.21	−1.16032
$301$	−176.988	−0.0338917
$302$	3080.49	0.586961
$303$	1023.88	0.194126
$304$	70.3845	0.0132790
$305$	2867.02	0.538247
$306$	−11083.0	−2.07050
$307$	−6238.94	−1.15985	−0.579927	−	0.814669i	$-0.696919\pi$
$307$	−6238.94	−1.15985	−0.579927	+	0.814669i	$0.696919\pi$
$308$	655.850	0.121333
$309$	−1136.75	−0.209281
$310$	−17512.3	−3.20849
$311$	−5497.45	−1.00235	−0.501177	−	0.865345i	$-0.667099\pi$
$311$	−5497.45	−1.00235	−0.501177	+	0.865345i	$0.667099\pi$
$312$	−930.572	−0.168857
$313$	−6971.77	−1.25900	−0.629501	−	0.776999i	$-0.716741\pi$
$313$	−6971.77	−1.25900	−0.629501	+	0.776999i	$0.716741\pi$
$314$	−7052.29	−1.26746
$315$	−1566.95	−0.280278
$316$	5814.61	1.03512
$317$	−3093.12	−0.548034	−0.274017	−	0.961725i	$-0.588352\pi$
$317$	−3093.12	−0.548034	−0.274017	+	0.961725i	$0.588352\pi$
$318$	1837.52	0.324035
$319$	77.8577	0.0136652
$320$	−32150.6	−5.61647
$321$	−1009.75	−0.175573
$322$	−1331.76	−0.230484
$323$	−25.3361	−0.00436451
$324$	14194.1	2.43383
$325$	−4898.82	−0.836117
$326$	1452.05	0.246692
$327$	1082.42	0.183052
$328$	−30958.9	−5.21165
$329$	−992.660	−0.166344
$330$	1097.93	0.183149
$331$	−3279.14	−0.544526	−0.272263	−	0.962223i	$-0.587772\pi$
$331$	−3279.14	−0.544526	−0.272263	+	0.962223i	$0.587772\pi$
$332$	−21610.2	−3.57233
$333$	−3680.29	−0.605641
$334$	−8646.71	−1.41655
$335$	−4371.68	−0.712986
$336$	529.010	0.0858924
$337$	6398.08	1.03420	0.517100	−	0.855925i	$-0.327011\pi$
$337$	6398.08	1.03420	0.517100	+	0.855925i	$0.327011\pi$
$338$	10665.4	1.71633
$339$	−77.8760	−0.0124768
$340$	35257.2	5.62380
$341$	1675.78	0.266125
$342$	46.0343	0.00727851
$343$	1904.18	0.299756
$344$	−4509.44	−0.706781
$345$	−1619.32	−0.252699
$346$	−13790.5	−2.14272
$347$	5407.71	0.836603	0.418301	−	0.908308i	$-0.362626\pi$
$347$	5407.71	0.836603	0.418301	+	0.908308i	$0.362626\pi$
$348$	130.490	0.0201006
$349$	2239.74	0.343526	0.171763	−	0.985138i	$-0.445054\pi$
$349$	2239.74	0.343526	0.171763	+	0.985138i	$0.445054\pi$
$350$	4965.13	0.758278
$351$	−692.552	−0.105315
$352$	6607.90	1.00057
$353$	−225.054	−0.0339332	−0.0169666	−	0.999856i	$-0.505401\pi$
$353$	−225.054	−0.0339332	−0.0169666	+	0.999856i	$0.505401\pi$
$354$	−2044.76	−0.306999
$355$	21650.5	3.23687
$356$	16909.1	2.51736
$357$	−190.426	−0.0282308
$358$	−14893.7	−2.19877
$359$	8249.25	1.21275	0.606377	−	0.795177i	$-0.292622\pi$
$359$	8249.25	1.21275	0.606377	+	0.795177i	$0.292622\pi$
$360$	−39924.0	−5.84494
$361$	−6858.89	−0.999985
$362$	−18469.9	−2.68165
$363$	−105.063	−0.0151911
$364$	893.127	0.128606
$365$	−10955.9	−1.57112
$366$	−633.060	−0.0904114
$367$	−8720.10	−1.24029	−0.620144	−	0.784488i	$-0.712926\pi$
$367$	−8720.10	−1.24029	−0.620144	+	0.784488i	$0.712926\pi$
$368$	−19031.8	−2.69592
$369$	−11357.0	−1.60223
$370$	16118.9	2.26482
$371$	−1099.11	−0.153808
$372$	2808.63	0.391453
$373$	6907.33	0.958841	0.479421	−	0.877585i	$-0.340847\pi$
$373$	6907.33	0.958841	0.479421	+	0.877585i	$0.340847\pi$
$374$	−4644.99	−0.642210
$375$	3729.66	0.513596
$376$	−25291.8	−3.46895
$377$	106.025	0.0144843
$378$	701.926	0.0955111
$379$	887.067	0.120226	0.0601129	−	0.998192i	$-0.480854\pi$
$379$	887.067	0.120226	0.0601129	+	0.998192i	$0.480854\pi$
$380$	−146.445	−0.0197696
$381$	997.037	0.134068
$382$	−7280.61	−0.975153
$383$	2574.76	0.343509	0.171754	−	0.985140i	$-0.445056\pi$
$383$	2574.76	0.343509	0.171754	+	0.985140i	$0.445056\pi$
$384$	2926.31	0.388888
$385$	−656.724	−0.0869344
$386$	−11738.4	−1.54785
$387$	−1654.25	−0.217288
$388$	39857.8	5.21513
$389$	4056.96	0.528781	0.264391	−	0.964416i	$-0.414829\pi$
$389$	4056.96	0.528781	0.264391	+	0.964416i	$0.414829\pi$
$390$	1495.15	0.194128
$391$	6850.81	0.886087
$392$	23976.1	3.08922
$393$	−113.746	−0.0145998
$394$	8155.77	1.04285
$395$	−5822.36	−0.741657
$396$	6130.04	0.777894
$397$	−15057.6	−1.90357	−0.951786	−	0.306763i	$-0.900754\pi$
$397$	−15057.6	−1.90357	−0.951786	+	0.306763i	$0.900754\pi$
$398$	13631.6	1.71682
$399$	0.790954	9.92412e−5 0
$400$	70955.4	8.86942
$401$	−6572.49	−0.818490	−0.409245	−	0.912424i	$-0.634208\pi$
$401$	−6572.49	−0.818490	−0.409245	+	0.912424i	$0.634208\pi$
$402$	965.299	0.119763
$403$	2282.05	0.282077
$404$	−25037.4	−3.08332
$405$	−14213.0	−1.74383
$406$	−107.461	−0.0131359
$407$	−1542.45	−0.187853
$408$	−4851.83	−0.588729
$409$	−4490.21	−0.542852	−0.271426	−	0.962459i	$-0.587495\pi$
$409$	−4490.21	−0.542852	−0.271426	+	0.962459i	$0.587495\pi$
$410$	49741.7	5.99163
$411$	564.836	0.0677891
$412$	27797.7	3.32402
$413$	1223.06	0.145722
$414$	−12447.5	−1.47769
$415$	21639.0	2.55956
$416$	8998.54	1.06055
$417$	−2349.89	−0.275958
$418$	19.2934	0.00225759
$419$	3242.38	0.378045	0.189022	−	0.981973i	$-0.439468\pi$
$419$	3242.38	0.378045	0.189022	+	0.981973i	$0.439468\pi$
$420$	−1100.68	−0.127875
$421$	352.135	0.0407648	0.0203824	−	0.999792i	$-0.493512\pi$
$421$	352.135	0.0407648	0.0203824	+	0.999792i	$0.493512\pi$
$422$	−13532.7	−1.56105
$423$	−9278.11	−1.06647
$424$	−28004.0	−3.20753
$425$	−25541.6	−2.91517
$426$	−4780.59	−0.543709
$427$	378.662	0.0429151
$428$	24692.1	2.78864
$429$	−143.073	−0.0161017
$430$	7245.31	0.812558
$431$	13063.7	1.45999	0.729993	−	0.683454i	$-0.239523\pi$
$431$	13063.7	1.45999	0.729993	+	0.683454i	$0.239523\pi$
$432$	10031.0	1.11717
$433$	8159.76	0.905620	0.452810	−	0.891607i	$-0.350422\pi$
$433$	8159.76	0.905620	0.452810	+	0.891607i	$0.350422\pi$
$434$	−2312.94	−0.255817
$435$	−130.664	−0.0144020
$436$	−26469.0	−2.90742
$437$	−28.4555	−0.00311490
$438$	2419.14	0.263907
$439$	12601.2	1.36998	0.684992	−	0.728550i	$-0.259806\pi$
$439$	12601.2	1.36998	0.684992	+	0.728550i	$0.259806\pi$
$440$	−16732.6	−1.81294
$441$	8795.45	0.949730
$442$	−6325.48	−0.680707
$443$	7250.14	0.777573	0.388786	−	0.921328i	$-0.372894\pi$
$443$	7250.14	0.777573	0.388786	+	0.921328i	$0.372894\pi$
$444$	−2585.16	−0.276320
$445$	−16931.6	−1.80368
$446$	28392.5	3.01441
$447$	−2217.85	−0.234677
$448$	−4246.29	−0.447808
$449$	−5949.70	−0.625353	−0.312676	−	0.949860i	$-0.601226\pi$
$449$	−5949.70	−0.625353	−0.312676	+	0.949860i	$0.601226\pi$
$450$	46407.7	4.86151
$451$	−4759.85	−0.496968
$452$	1904.35	0.198170
$453$	494.707	0.0513099
$454$	−14174.1	−1.46525
$455$	−894.317	−0.0921456
$456$	20.1526	0.00206959
$457$	9585.27	0.981137	0.490569	−	0.871403i	$-0.336789\pi$
$457$	9585.27	0.981137	0.490569	+	0.871403i	$0.336789\pi$
$458$	21324.9	2.17565
$459$	−3610.84	−0.367189
$460$	39598.2	4.01364
$461$	−3928.06	−0.396850	−0.198425	−	0.980116i	$-0.563583\pi$
$461$	−3928.06	−0.396850	−0.198425	+	0.980116i	$0.563583\pi$
$462$	145.010	0.0146027
$463$	−9702.54	−0.973899	−0.486949	−	0.873430i	$-0.661890\pi$
$463$	−9702.54	−0.973899	−0.486949	+	0.873430i	$0.661890\pi$
$464$	−1535.69	−0.153648
$465$	−2812.37	−0.280474
$466$	8077.90	0.803007
$467$	−6111.57	−0.605589	−0.302794	−	0.953056i	$-0.597920\pi$
$467$	−6111.57	−0.605589	−0.302794	+	0.953056i	$0.597920\pi$
$468$	8347.80	0.824524
$469$	−577.390	−0.0568473
$470$	40636.3	3.98811
$471$	−1132.55	−0.110797
$472$	31162.2	3.03889
$473$	−693.315	−0.0673967
$474$	1285.62	0.124579
$475$	106.090	0.0102478
$476$	4656.60	0.448393
$477$	−10273.0	−0.986101
$478$	−3316.99	−0.317396
$479$	−11630.5	−1.10942	−0.554709	−	0.832044i	$-0.687170\pi$
$479$	−11630.5	−1.10942	−0.554709	+	0.832044i	$0.687170\pi$
$480$	−11089.7	−1.05453
$481$	−2100.48	−0.199114
$482$	30049.2	2.83964
$483$	−213.872	−0.0201480
$484$	2569.16	0.241281
$485$	−39910.9	−3.73662
$486$	9887.50	0.922852
$487$	6318.06	0.587883	0.293941	−	0.955823i	$-0.405033\pi$
$487$	6318.06	0.587883	0.293941	+	0.955823i	$0.405033\pi$
$488$	9647.87	0.894956
$489$	233.190	0.0215648
$490$	−38522.4	−3.55156
$491$	17696.8	1.62657	0.813286	−	0.581864i	$-0.197677\pi$
$491$	17696.8	1.62657	0.813286	+	0.581864i	$0.197677\pi$
$492$	−7977.57	−0.731010
$493$	552.797	0.0505005
$494$	26.2735	0.00239292
$495$	−6138.21	−0.557358
$496$	−33053.6	−2.99224
$497$	2859.49	0.258080
$498$	−4778.06	−0.429940
$499$	−20654.8	−1.85298	−0.926489	−	0.376321i	$-0.877189\pi$
$499$	−20654.8	−1.85298	−0.926489	+	0.376321i	$0.877189\pi$
$500$	−91203.5	−8.15749
$501$	−1388.61	−0.123829
$502$	19417.2	1.72636
$503$	3012.60	0.267048	0.133524	−	0.991046i	$-0.457371\pi$
$503$	3012.60	0.267048	0.133524	+	0.991046i	$0.457371\pi$
$504$	−5272.96	−0.466025
$505$	25070.8	2.20918
$506$	−5216.89	−0.458338
$507$	1712.79	0.150035
$508$	−24381.1	−2.12941
$509$	7708.88	0.671297	0.335649	−	0.941987i	$-0.391045\pi$
$509$	7708.88	0.671297	0.335649	+	0.941987i	$0.391045\pi$
$510$	7795.43	0.676838
$511$	−1447.00	−0.125267
$512$	−6151.21	−0.530953
$513$	14.9980	0.00129080
$514$	−34132.8	−2.92905
$515$	−27834.8	−2.38164
$516$	−1162.00	−0.0991363
$517$	−3888.55	−0.330790
$518$	2128.91	0.180577
$519$	−2214.67	−0.187309
$520$	−22786.1	−1.92161
$521$	−1774.26	−0.149197	−0.0745985	−	0.997214i	$-0.523768\pi$
$521$	−1774.26	−0.149197	−0.0745985	+	0.997214i	$0.523768\pi$
$522$	−1004.40	−0.0842175
$523$	16813.1	1.40571	0.702853	−	0.711335i	$-0.251909\pi$
$523$	16813.1	1.40571	0.702853	+	0.711335i	$0.251909\pi$
$524$	2781.49	0.231889
$525$	797.369	0.0662858
$526$	24158.0	2.00254
$527$	11898.2	0.983480
$528$	2072.29	0.170805
$529$	−4472.70	−0.367609
$530$	44993.9	3.68757
$531$	11431.6	0.934257
$532$	−19.3417	−0.00157625
$533$	−6481.90	−0.526758
$534$	3738.63	0.302971
$535$	−24725.0	−1.99805
$536$	−14711.2	−1.18550
$537$	−2391.84	−0.192208
$538$	12842.8	1.02917
$539$	3686.26	0.294580
$540$	−20870.9	−1.66323
$541$	7097.21	0.564016	0.282008	−	0.959412i	$-0.409000\pi$
$541$	7097.21	0.564016	0.282008	+	0.959412i	$0.409000\pi$
$542$	−29444.8	−2.33351
$543$	−2966.16	−0.234420
$544$	46916.7	3.69768
$545$	26504.3	2.08316
$546$	197.472	0.0154781
$547$	−2198.49	−0.171848	−0.0859238	−	0.996302i	$-0.527384\pi$
$547$	−2198.49	−0.171848	−0.0859238	+	0.996302i	$0.527384\pi$
$548$	−13812.3	−1.07670
$549$	3539.25	0.275139
$550$	19449.9	1.50790
$551$	−2.29610	−0.000177527 0
$552$	−5449.20	−0.420169
$553$	−768.988	−0.0591333
$554$	−14826.9	−1.13707
$555$	2588.60	0.197982
$556$	57463.2	4.38306
$557$	−5266.55	−0.400630	−0.200315	−	0.979732i	$-0.564197\pi$
$557$	−5266.55	−0.400630	−0.200315	+	0.979732i	$0.564197\pi$
$558$	−21618.4	−1.64011
$559$	−944.146	−0.0714367
$560$	12953.4	0.977469
$561$	−745.956	−0.0561396
$562$	37365.5	2.80457
$563$	−24173.3	−1.80956	−0.904781	−	0.425877i	$-0.859966\pi$
$563$	−24173.3	−1.80956	−0.904781	+	0.425877i	$0.859966\pi$
$564$	−6517.25	−0.486571
$565$	−1906.89	−0.141988
$566$	27730.8	2.05939
$567$	−1877.19	−0.139038
$568$	72856.4	5.38202
$569$	−7865.80	−0.579528	−0.289764	−	0.957098i	$-0.593577\pi$
$569$	−7865.80	−0.579528	−0.289764	+	0.957098i	$0.593577\pi$
$570$	−32.3791	−0.00237932
$571$	−13532.9	−0.991829	−0.495915	−	0.868371i	$-0.665167\pi$
$571$	−13532.9	−0.991829	−0.495915	+	0.868371i	$0.665167\pi$
$572$	3498.65	0.255744
$573$	−1169.22	−0.0852442
$574$	6569.63	0.477720
$575$	−28686.3	−2.08053
$576$	−39688.8	−2.87101
$577$	659.396	0.0475754	0.0237877	−	0.999717i	$-0.492427\pi$
$577$	659.396	0.0475754	0.0237877	+	0.999717i	$0.492427\pi$
$578$	−6416.61	−0.461757
$579$	−1885.11	−0.135307
$580$	3195.21	0.228748
$581$	2857.98	0.204077
$582$	8812.62	0.627655
$583$	−4305.54	−0.305861
$584$	−36867.8	−2.61233
$585$	−8358.93	−0.590768
$586$	12801.0	0.902396
$587$	14348.5	1.00890	0.504452	−	0.863440i	$-0.331695\pi$
$587$	14348.5	1.00890	0.504452	+	0.863440i	$0.331695\pi$
$588$	6178.22	0.433309
$589$	−49.4204	−0.00345727
$590$	−50068.3	−3.49370
$591$	1309.77	0.0911617
$592$	30423.7	2.11217
$593$	19685.4	1.36321	0.681605	−	0.731721i	$-0.261282\pi$
$593$	19685.4	1.36321	0.681605	+	0.731721i	$0.261282\pi$
$594$	2749.66	0.189932
$595$	−4662.81	−0.321271
$596$	54234.3	3.72739
$597$	2189.16	0.150078
$598$	−7104.29	−0.485813
$599$	327.191	0.0223183	0.0111591	−	0.999938i	$-0.496448\pi$
$599$	327.191	0.0223183	0.0111591	+	0.999938i	$0.496448\pi$
$600$	20316.0	1.38233
$601$	23024.7	1.56273	0.781363	−	0.624076i	$-0.214525\pi$
$601$	23024.7	1.56273	0.781363	+	0.624076i	$0.214525\pi$
$602$	956.925	0.0647863
$603$	−5396.70	−0.364462
$604$	−12097.4	−0.814958
$605$	−2572.59	−0.172877
$606$	−5535.82	−0.371085
$607$	−22830.5	−1.52662	−0.763312	−	0.646030i	$-0.776428\pi$
$607$	−22830.5	−1.52662	−0.763312	+	0.646030i	$0.776428\pi$
$608$	−194.874	−0.0129986
$609$	−17.2575	−0.00114829
$610$	−15501.2	−1.02890
$611$	−5295.37	−0.350618
$612$	43523.9	2.87475
$613$	23115.4	1.52304	0.761519	−	0.648142i	$-0.224454\pi$
$613$	23115.4	1.52304	0.761519	+	0.648142i	$0.224454\pi$
$614$	33732.3	2.21714
$615$	7988.20	0.523765
$616$	−2209.95	−0.144548
$617$	−20881.4	−1.36249	−0.681243	−	0.732058i	$-0.738560\pi$
$617$	−20881.4	−1.36249	−0.681243	+	0.732058i	$0.738560\pi$
$618$	6146.13	0.400054
$619$	−22654.0	−1.47099	−0.735493	−	0.677532i	$-0.763049\pi$
$619$	−22654.0	−1.47099	−0.735493	+	0.677532i	$0.763049\pi$
$620$	68772.6	4.45480
$621$	−4055.42	−0.262059
$622$	29723.2	1.91607
$623$	−2236.25	−0.143810
$624$	2822.02	0.181043
$625$	50446.0	3.22855
$626$	37694.5	2.40667
$627$	3.09841	0.000197350 0
$628$	27695.0	1.75979
$629$	−10951.5	−0.694222
$630$	8472.07	0.535770
$631$	−11795.1	−0.744146	−0.372073	−	0.928203i	$-0.621353\pi$
$631$	−11795.1	−0.744146	−0.372073	+	0.928203i	$0.621353\pi$
$632$	−19592.9	−1.23317
$633$	−2173.28	−0.136461
$634$	16723.7	1.04760
$635$	24413.6	1.52571
$636$	−7216.13	−0.449903
$637$	5019.90	0.312238
$638$	−420.956	−0.0261219
$639$	26726.8	1.65461
$640$	71654.3	4.42560
$641$	−21475.8	−1.32331	−0.661657	−	0.749807i	$-0.730147\pi$
$641$	−21475.8	−1.32331	−0.661657	+	0.749807i	$0.730147\pi$
$642$	5459.47	0.335620
$643$	28612.9	1.75487	0.877436	−	0.479693i	$-0.159252\pi$
$643$	28612.9	1.75487	0.877436	+	0.479693i	$0.159252\pi$
$644$	5229.93	0.320013
$645$	1163.55	0.0710307
$646$	136.985	0.00834306
$647$	8124.36	0.493665	0.246833	−	0.969058i	$-0.420610\pi$
$647$	8124.36	0.493665	0.246833	+	0.969058i	$0.420610\pi$
$648$	−47828.5	−2.89951
$649$	4791.11	0.289781
$650$	26486.6	1.59829
$651$	−371.444	−0.0223626
$652$	−5702.33	−0.342516
$653$	2493.03	0.149402	0.0747012	−	0.997206i	$-0.476200\pi$
$653$	2493.03	0.149402	0.0747012	+	0.997206i	$0.476200\pi$
$654$	−5852.35	−0.349916
$655$	−2785.20	−0.166148
$656$	93884.9	5.58779
$657$	−13524.7	−0.803118
$658$	5367.04	0.317977
$659$	−5288.11	−0.312588	−0.156294	−	0.987711i	$-0.549955\pi$
$659$	−5288.11	−0.312588	−0.156294	+	0.987711i	$0.549955\pi$
$660$	−4311.69	−0.254291
$661$	−12744.6	−0.749937	−0.374968	−	0.927038i	$-0.622346\pi$
$661$	−12744.6	−0.749937	−0.374968	+	0.927038i	$0.622346\pi$
$662$	17729.5	1.04090
$663$	−1015.83	−0.0595048
$664$	72817.9	4.25584
$665$	19.3674	0.00112938
$666$	19898.3	1.15772
$667$	620.860	0.0360416
$668$	33956.4	1.96679
$669$	4559.66	0.263508
$670$	23636.5	1.36292
$671$	1483.33	0.0853405
$672$	−1464.67	−0.0840787
$673$	11616.4	0.665351	0.332675	−	0.943041i	$-0.392049\pi$
$673$	11616.4	0.665351	0.332675	+	0.943041i	$0.392049\pi$
$674$	−34592.7	−1.97694
$675$	15119.6	0.862156
$676$	−41883.9	−2.38302
$677$	−7574.78	−0.430019	−0.215009	−	0.976612i	$-0.568978\pi$
$677$	−7574.78	−0.430019	−0.215009	+	0.976612i	$0.568978\pi$
$678$	421.055	0.0238503
$679$	−5271.23	−0.297925
$680$	−118803.	−6.69982
$681$	−2276.28	−0.128087
$682$	−9060.49	−0.508716
$683$	1991.26	0.111557	0.0557784	−	0.998443i	$-0.482236\pi$
$683$	1991.26	0.111557	0.0557784	+	0.998443i	$0.482236\pi$
$684$	−180.781	−0.0101058
$685$	13830.7	0.771450
$686$	−10295.4	−0.573004
$687$	3424.65	0.190187
$688$	13675.2	0.757792
$689$	−5863.22	−0.324196
$690$	8755.23	0.483052
$691$	14851.1	0.817600	0.408800	−	0.912624i	$-0.365947\pi$
$691$	14851.1	0.817600	0.408800	+	0.912624i	$0.365947\pi$
$692$	54156.6	2.97504
$693$	−810.704	−0.0444388
$694$	−29238.1	−1.59922
$695$	−57539.8	−3.14044
$696$	−439.701	−0.0239466
$697$	−33795.4	−1.83658
$698$	−12109.7	−0.656673
$699$	1297.26	0.0701958
$700$	−19498.5	−1.05282
$701$	16409.7	0.884146	0.442073	−	0.896979i	$-0.354243\pi$
$701$	16409.7	0.884146	0.442073	+	0.896979i	$0.354243\pi$
$702$	3744.44	0.201318
$703$	45.4883	0.00244043
$704$	−16634.0	−0.890507
$705$	6525.94	0.348626
$706$	1216.81	0.0648656
$707$	3311.23	0.176141
$708$	8029.96	0.426249
$709$	−6202.96	−0.328571	−0.164286	−	0.986413i	$-0.552532\pi$
$709$	−6202.96	−0.328571	−0.164286	+	0.986413i	$0.552532\pi$
$710$	−117058.	−6.18749
$711$	−7187.51	−0.379118
$712$	−56976.9	−2.99902
$713$	13363.2	0.701899
$714$	1029.58	0.0539652
$715$	−3503.31	−0.183240
$716$	58489.1	3.05285
$717$	−532.687	−0.0277456
$718$	−44601.5	−2.31826
$719$	19814.8	1.02777	0.513885	−	0.857859i	$-0.328206\pi$
$719$	19814.8	1.02777	0.513885	+	0.857859i	$0.328206\pi$
$720$	121072.	6.26679
$721$	−3676.28	−0.189892
$722$	37084.2	1.91154
$723$	4825.72	0.248230
$724$	72533.2	3.72331
$725$	−2314.72	−0.118575
$726$	568.046	0.0290388
$727$	−1054.25	−0.0537827	−0.0268914	−	0.999638i	$-0.508561\pi$
$727$	−1054.25	−0.0537827	−0.0268914	+	0.999638i	$0.508561\pi$
$728$	−3009.48	−0.153213
$729$	−16461.6	−0.836338
$730$	59235.6	3.00330
$731$	−4922.60	−0.249068
$732$	2486.09	0.125531
$733$	−5076.48	−0.255803	−0.127902	−	0.991787i	$-0.540824\pi$
$733$	−5076.48	−0.255803	−0.127902	+	0.991787i	$0.540824\pi$
$734$	47147.3	2.37090
$735$	−6186.46	−0.310464
$736$	52693.3	2.63900
$737$	−2261.81	−0.113046
$738$	61404.5	3.06278
$739$	15368.7	0.765014	0.382507	−	0.923953i	$-0.375061\pi$
$739$	15368.7	0.765014	0.382507	+	0.923953i	$0.375061\pi$
$740$	−63300.6	−3.14456
$741$	4.21937	0.000209180 0
$742$	5942.58	0.294015
$743$	−22102.2	−1.09132	−0.545661	−	0.838006i	$-0.683721\pi$
$743$	−22102.2	−1.09132	−0.545661	+	0.838006i	$0.683721\pi$
$744$	−9463.96	−0.466352
$745$	−54306.6	−2.67066
$746$	−37346.1	−1.83289
$747$	26712.7	1.30839
$748$	18241.3	0.891669
$749$	−3265.56	−0.159307
$750$	−20165.2	−0.981774
$751$	−11628.2	−0.565004	−0.282502	−	0.959267i	$-0.591164\pi$
$751$	−11628.2	−0.565004	−0.282502	+	0.959267i	$0.591164\pi$
$752$	76699.0	3.71932
$753$	3118.29	0.150912
$754$	−573.251	−0.0276878
$755$	12113.5	0.583914
$756$	−2756.53	−0.132611
$757$	−25314.0	−1.21539	−0.607697	−	0.794169i	$-0.707907\pi$
$757$	−25314.0	−1.21539	−0.607697	+	0.794169i	$0.707907\pi$
$758$	−4796.13	−0.229820
$759$	−837.801	−0.0400662
$760$	493.460	0.0235522
$761$	24102.7	1.14813	0.574063	−	0.818811i	$-0.305366\pi$
$761$	24102.7	1.14813	0.574063	+	0.818811i	$0.305366\pi$
$762$	−5390.71	−0.256279
$763$	3500.56	0.166093
$764$	28591.7	1.35394
$765$	−43581.9	−2.05975
$766$	−13921.0	−0.656641
$767$	6524.47	0.307151
$768$	−5317.73	−0.249853
$769$	13719.0	0.643330	0.321665	−	0.946853i	$-0.395757\pi$
$769$	13719.0	0.643330	0.321665	+	0.946853i	$0.395757\pi$
$770$	3550.73	0.166181
$771$	−5481.51	−0.256047
$772$	46097.8	2.14909
$773$	25605.8	1.19143	0.595717	−	0.803195i	$-0.296868\pi$
$773$	25605.8	1.19143	0.595717	+	0.803195i	$0.296868\pi$
$774$	8944.10	0.415361
$775$	−49821.3	−2.30920
$776$	−134305.	−6.21297
$777$	341.890	0.0157854
$778$	−21934.9	−1.01080
$779$	140.373	0.00645620
$780$	−5871.59	−0.269534
$781$	11201.5	0.513215
$782$	−37040.5	−1.69382
$783$	−327.235	−0.0149354
$784$	−72709.1	−3.31218
$785$	−27731.9	−1.26089
$786$	614.992	0.0279085
$787$	8145.74	0.368951	0.184475	−	0.982837i	$-0.440941\pi$
$787$	8145.74	0.368951	0.184475	+	0.982837i	$0.440941\pi$
$788$	−32028.5	−1.44793
$789$	3879.62	0.175055
$790$	31479.9	1.41773
$791$	−251.852	−0.0113209
$792$	−20655.8	−0.926732
$793$	2019.98	0.0904561
$794$	81412.3	3.63881
$795$	7225.75	0.322353
$796$	−53532.8	−2.38369
$797$	−9263.10	−0.411688	−0.205844	−	0.978585i	$-0.565994\pi$
$797$	−9263.10	−0.411688	−0.205844	+	0.978585i	$0.565994\pi$
$798$	−4.27648	−0.000189706 0
$799$	−27609.1	−1.22245
$800$	−196454.	−8.68213
$801$	−20901.6	−0.921998
$802$	35535.7	1.56460
$803$	−5668.34	−0.249105
$804$	−3790.82	−0.166284
$805$	−5236.91	−0.229288
$806$	−12338.4	−0.539210
$807$	2062.48	0.0899663
$808$	84366.2	3.67326
$809$	15146.4	0.658245	0.329122	−	0.944287i	$-0.393247\pi$
$809$	15146.4	0.658245	0.329122	+	0.944287i	$0.393247\pi$
$810$	76846.0	3.33345
$811$	−21951.0	−0.950438	−0.475219	−	0.879868i	$-0.657631\pi$
$811$	−21951.0	−0.950438	−0.475219	+	0.879868i	$0.657631\pi$
$812$	422.008	0.0182384
$813$	−4728.65	−0.203987
$814$	8339.59	0.359094
$815$	5709.93	0.245411
$816$	14713.5	0.631219
$817$	20.4465	0.000875562 0
$818$	24277.3	1.03770
$819$	−1104.01	−0.0471027
$820$	−195340.	−8.31900
$821$	−20341.1	−0.864690	−0.432345	−	0.901708i	$-0.642314\pi$
$821$	−20341.1	−0.864690	−0.432345	+	0.901708i	$0.642314\pi$
$822$	−3053.92	−0.129584
$823$	−11161.8	−0.472751	−0.236376	−	0.971662i	$-0.575960\pi$
$823$	−11161.8	−0.472751	−0.236376	+	0.971662i	$0.575960\pi$
$824$	−93667.3	−3.96002
$825$	3123.54	0.131815
$826$	−6612.78	−0.278557
$827$	−32613.5	−1.37132	−0.685661	−	0.727921i	$-0.740487\pi$
$827$	−32613.5	−1.37132	−0.685661	+	0.727921i	$0.740487\pi$
$828$	48882.7	2.05168
$829$	−46829.6	−1.96195	−0.980976	−	0.194128i	$-0.937812\pi$
$829$	−46829.6	−1.96195	−0.980976	+	0.194128i	$0.937812\pi$
$830$	−116996.	−4.89278
$831$	−2381.11	−0.0993979
$832$	−22651.9	−0.943887
$833$	26172.8	1.08864
$834$	12705.2	0.527513
$835$	−34001.7	−1.40919
$836$	−75.7672	−0.00313452
$837$	−7043.29	−0.290862
$838$	−17530.7	−0.722658
$839$	23671.0	0.974031	0.487016	−	0.873393i	$-0.338085\pi$
$839$	23671.0	0.974031	0.487016	+	0.873393i	$0.338085\pi$
$840$	3708.84	0.152342
$841$	−24338.9	−0.997946
$842$	−1903.90	−0.0779248
$843$	6000.67	0.245165
$844$	53144.4	2.16742
$845$	41939.8	1.70742
$846$	50164.2	2.03863
$847$	−339.775	−0.0137837
$848$	84923.8	3.43903
$849$	4453.40	0.180024
$850$	138096.	5.57255
$851$	−12299.9	−0.495459
$852$	18773.8	0.754907
$853$	14275.7	0.573027	0.286514	−	0.958076i	$-0.407504\pi$
$853$	14275.7	0.573027	0.286514	+	0.958076i	$0.407504\pi$
$854$	−2047.32	−0.0820351
$855$	181.022	0.00724073
$856$	−83202.6	−3.32220
$857$	40630.4	1.61949	0.809747	−	0.586779i	$-0.199604\pi$
$857$	40630.4	1.61949	0.809747	+	0.586779i	$0.199604\pi$
$858$	773.557	0.0307795
$859$	−7589.49	−0.301455	−0.150728	−	0.988575i	$-0.548162\pi$
$859$	−7589.49	−0.301455	−0.150728	+	0.988575i	$0.548162\pi$
$860$	−28453.0	−1.12819
$861$	1055.04	0.0417605
$862$	−70631.7	−2.79086
$863$	21374.7	0.843109	0.421555	−	0.906803i	$-0.361485\pi$
$863$	21374.7	0.843109	0.421555	+	0.906803i	$0.361485\pi$
$864$	−27772.9	−1.09358
$865$	−54228.8	−2.13160
$866$	−44117.7	−1.73115
$867$	−1030.47	−0.0403651
$868$	9083.14	0.355187
$869$	−3012.36	−0.117592
$870$	706.467	0.0275304
$871$	−3080.10	−0.119822
$872$	89190.1	3.46371
$873$	−49268.7	−1.91007
$874$	153.851	0.00595435
$875$	12061.8	0.466014
$876$	−9500.20	−0.366418
$877$	5099.64	0.196354	0.0981770	−	0.995169i	$-0.468699\pi$
$877$	5099.64	0.196354	0.0981770	+	0.995169i	$0.468699\pi$
$878$	−68131.4	−2.61882
$879$	2055.76	0.0788840
$880$	50742.5	1.94378
$881$	51499.4	1.96942	0.984709	−	0.174205i	$-0.0557355\pi$
$881$	51499.4	1.96942	0.984709	+	0.174205i	$0.0557355\pi$
$882$	−47554.6	−1.81547
$883$	43362.2	1.65261	0.826305	−	0.563223i	$-0.190439\pi$
$883$	43362.2	1.65261	0.826305	+	0.563223i	$0.190439\pi$
$884$	24840.7	0.945119
$885$	−8040.67	−0.305406
$886$	−39199.6	−1.48638
$887$	46049.8	1.74318	0.871589	−	0.490236i	$-0.163090\pi$
$887$	46049.8	1.74318	0.871589	+	0.490236i	$0.163090\pi$
$888$	8710.95	0.329190
$889$	3224.43	0.121647
$890$	91544.8	3.44785
$891$	−7353.51	−0.276489
$892$	−111500.	−4.18532
$893$	114.677	0.00429734
$894$	11991.3	0.448601
$895$	−58567.0	−2.18735
$896$	9463.74	0.352859
$897$	−1140.91	−0.0424679
$898$	32168.4	1.19540
$899$	1078.28	0.0400031
$900$	−182247.	−6.74990
$901$	−30569.7	−1.13033
$902$	25735.3	0.949989
$903$	153.676	0.00566337
$904$	−6416.89	−0.236087
$905$	−72629.8	−2.66773
$906$	−2674.75	−0.0980823
$907$	31069.2	1.13741	0.568707	−	0.822540i	$-0.307444\pi$
$907$	31069.2	1.13741	0.568707	+	0.822540i	$0.307444\pi$
$908$	55663.2	2.03441
$909$	30949.1	1.12928
$910$	4835.33	0.176143
$911$	−15974.1	−0.580949	−0.290474	−	0.956883i	$-0.593813\pi$
$911$	−15974.1	−0.580949	−0.290474	+	0.956883i	$0.593813\pi$
$912$	−61.1140	−0.00221895
$913$	11195.6	0.405826
$914$	−51825.0	−1.87551
$915$	−2489.40	−0.0899421
$916$	−83744.9	−3.02075
$917$	−367.855	−0.0132472
$918$	19522.8	0.701906
$919$	33881.1	1.21614	0.608071	−	0.793883i	$-0.291944\pi$
$919$	33881.1	1.21614	0.608071	+	0.793883i	$0.291944\pi$
$920$	−133430.	−4.78159
$921$	5417.19	0.193814
$922$	21238.0	0.758607
$923$	15254.0	0.543978
$924$	−569.466	−0.0202750
$925$	45857.2	1.63003
$926$	52459.0	1.86167
$927$	−34361.1	−1.21744
$928$	4251.87	0.150403
$929$	−52474.7	−1.85322	−0.926609	−	0.376027i	$-0.877290\pi$
$929$	−52474.7	−1.85322	−0.926609	+	0.376027i	$0.877290\pi$
$930$	15205.7	0.536146
$931$	−108.712	−0.00382694
$932$	−31722.7	−1.11493
$933$	4773.37	0.167495
$934$	33043.6	1.15762
$935$	−18265.6	−0.638877
$936$	−28128.8	−0.982283
$937$	−20616.2	−0.718784	−0.359392	−	0.933187i	$-0.617016\pi$
$937$	−20616.2	−0.718784	−0.359392	+	0.933187i	$0.617016\pi$
$938$	3121.79	0.108667
$939$	6053.50	0.210382
$940$	−159583.	−5.53725
$941$	35637.2	1.23458	0.617290	−	0.786736i	$-0.288231\pi$
$941$	35637.2	1.23458	0.617290	+	0.786736i	$0.288231\pi$
$942$	6123.42	0.211796
$943$	−37956.4	−1.31074
$944$	−94501.5	−3.25822
$945$	2760.20	0.0950153
$946$	3748.57	0.128833
$947$	−12351.9	−0.423845	−0.211923	−	0.977286i	$-0.567972\pi$
$947$	−12351.9	−0.423845	−0.211923	+	0.977286i	$0.567972\pi$
$948$	−5048.75	−0.172970
$949$	−7719.06	−0.264037
$950$	−573.598	−0.0195894
$951$	2685.71	0.0915776
$952$	−15690.9	−0.534185
$953$	54885.5	1.86560	0.932800	−	0.360394i	$-0.117358\pi$
$953$	54885.5	1.86560	0.932800	+	0.360394i	$0.117358\pi$
$954$	55543.6	1.88500
$955$	−28629.8	−0.970092
$956$	13026.1	0.440685
$957$	−67.6029	−0.00228348
$958$	62883.0	2.12073
$959$	1826.69	0.0615087
$960$	27915.9	0.938524
$961$	−6582.41	−0.220953
$962$	11356.7	0.380619
$963$	−30522.3	−1.02136
$964$	−118006.	−3.94266
$965$	−46159.2	−1.53981
$966$	1156.35	0.0385144
$967$	−6857.15	−0.228036	−0.114018	−	0.993479i	$-0.536372\pi$
$967$	−6857.15	−0.228036	−0.114018	+	0.993479i	$0.536372\pi$
$968$	−8657.06	−0.287447
$969$	21.9990	0.000729319 0
$970$	215787.	7.14280
$971$	−10679.4	−0.352955	−0.176478	−	0.984305i	$-0.556470\pi$
$971$	−10679.4	−0.352955	−0.176478	+	0.984305i	$0.556470\pi$
$972$	−38829.2	−1.28132
$973$	−7599.57	−0.250392
$974$	−34160.1	−1.12378
$975$	4253.59	0.139717
$976$	−29257.8	−0.959548
$977$	−14691.0	−0.481070	−0.240535	−	0.970640i	$-0.577323\pi$
$977$	−14691.0	−0.481070	−0.240535	+	0.970640i	$0.577323\pi$
$978$	−1260.80	−0.0412227
$979$	−8760.06	−0.285978
$980$	151281.	4.93112
$981$	32718.7	1.06486
$982$	−95682.0	−3.10930
$983$	24491.1	0.794655	0.397328	−	0.917677i	$-0.369938\pi$
$983$	24491.1	0.794655	0.397328	+	0.917677i	$0.369938\pi$
$984$	26881.2	0.870877
$985$	32071.2	1.03743
$986$	−2988.83	−0.0965351
$987$	861.914	0.0277964
$988$	−103.179	−0.00332242
$989$	−5528.69	−0.177757
$990$	33187.7	1.06543
$991$	56934.5	1.82501	0.912505	−	0.409066i	$-0.134145\pi$
$991$	56934.5	1.82501	0.912505	+	0.409066i	$0.134145\pi$
$992$	91515.6	2.92906
$993$	2847.24	0.0909914
$994$	−15460.5	−0.493337
$995$	53604.1	1.70790
$996$	18763.9	0.596944
$997$	−28198.3	−0.895737	−0.447869	−	0.894099i	$-0.647817\pi$
$997$	−28198.3	−0.895737	−0.447869	+	0.894099i	$0.647817\pi$
$998$	111675.	3.54210
$999$	6482.89	0.205315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.a.1.2	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.a.1.2	✓	77	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)

\(f(q)\)	\(=\)	\(q-5.40673 q^{2} -0.868288 q^{3} +21.2327 q^{4} -21.2610 q^{5} +4.69460 q^{6} -2.80805 q^{7} -71.5459 q^{8} -26.2461 q^{9} +O(q^{10})\)	\(q-5.40673 q^{2} -0.868288 q^{3} +21.2327 q^{4} -21.2610 q^{5} +4.69460 q^{6} -2.80805 q^{7} -71.5459 q^{8} -26.2461 q^{9} +114.953 q^{10} -11.0000 q^{11} -18.4361 q^{12} -14.9796 q^{13} +15.1824 q^{14} +18.4607 q^{15} +216.968 q^{16} -78.1011 q^{17} +141.905 q^{18} +0.324401 q^{19} -451.430 q^{20} +2.43820 q^{21} +59.4740 q^{22} -87.7172 q^{23} +62.1224 q^{24} +327.032 q^{25} +80.9909 q^{26} +46.2329 q^{27} -59.6227 q^{28} -7.07797 q^{29} -99.8121 q^{30} -152.344 q^{31} -600.718 q^{32} +9.55116 q^{33} +422.272 q^{34} +59.7022 q^{35} -557.276 q^{36} +140.222 q^{37} -1.75395 q^{38} +13.0066 q^{39} +1521.14 q^{40} +432.714 q^{41} -13.1827 q^{42} +63.0286 q^{43} -233.560 q^{44} +558.019 q^{45} +474.263 q^{46} +353.504 q^{47} -188.390 q^{48} -335.115 q^{49} -1768.18 q^{50} +67.8142 q^{51} -318.059 q^{52} +391.412 q^{53} -249.969 q^{54} +233.872 q^{55} +200.905 q^{56} -0.281673 q^{57} +38.2687 q^{58} -435.556 q^{59} +391.971 q^{60} -134.849 q^{61} +823.681 q^{62} +73.7004 q^{63} +1512.18 q^{64} +318.483 q^{65} -51.6406 q^{66} +205.619 q^{67} -1658.30 q^{68} +76.1637 q^{69} -322.794 q^{70} -1018.32 q^{71} +1877.80 q^{72} +515.303 q^{73} -758.145 q^{74} -283.958 q^{75} +6.88793 q^{76} +30.8886 q^{77} -70.3234 q^{78} +273.851 q^{79} -4612.96 q^{80} +668.501 q^{81} -2339.57 q^{82} -1017.78 q^{83} +51.7696 q^{84} +1660.51 q^{85} -340.779 q^{86} +6.14571 q^{87} +787.005 q^{88} +796.369 q^{89} -3017.06 q^{90} +42.0636 q^{91} -1862.48 q^{92} +132.278 q^{93} -1911.30 q^{94} -6.89711 q^{95} +521.596 q^{96} +1877.18 q^{97} +1811.88 q^{98} +288.707 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9}+O(q^{10}) \) 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9	\( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9} + 2 q^{10} - 847 q^{11} - 88 q^{12} - 20 q^{13} - 282 q^{14} - 330 q^{15} + 936 q^{16} - 56 q^{17} - 343 q^{18} - 157 q^{19} - 450 q^{20} - 122 q^{21} + 154 q^{22} - 764 q^{23} - 346 q^{24} + 1413 q^{25} - 408 q^{26} - 358 q^{27} - 228 q^{28} - 557 q^{29} - 267 q^{30} - 780 q^{31} - 1739 q^{32} + 110 q^{33} - 1104 q^{34} - 1254 q^{35} + 375 q^{36} - 541 q^{37} - 2133 q^{38} - 1458 q^{39} - 554 q^{40} - 1723 q^{41} - 5 q^{42} - 688 q^{43} - 3256 q^{44} - 1588 q^{45} + 276 q^{46} - 3086 q^{47} - 4280 q^{48} + 2452 q^{49} - 2234 q^{50} - 1570 q^{51} - 715 q^{52} - 1230 q^{53} - 5166 q^{54} + 462 q^{55} - 3203 q^{56} + 1024 q^{57} - 3016 q^{58} - 5408 q^{59} - 8221 q^{60} + 566 q^{61} - 3642 q^{62} - 3035 q^{63} + 1084 q^{64} - 1794 q^{65} + 143 q^{66} - 1925 q^{67} - 1105 q^{68} - 3710 q^{69} - 5875 q^{70} - 9614 q^{71} - 2198 q^{72} - 384 q^{73} - 2378 q^{74} - 3888 q^{75} - 2809 q^{76} + 649 q^{77} - 1731 q^{78} - 1086 q^{79} - 4357 q^{80} + 2329 q^{81} - 3167 q^{82} - 3045 q^{83} - 5359 q^{84} + 2582 q^{85} - 6468 q^{86} - 4432 q^{87} + 1650 q^{88} - 2831 q^{89} + 512 q^{90} - 6002 q^{91} - 7134 q^{92} - 4428 q^{93} + 1697 q^{94} - 10434 q^{95} + 195 q^{96} - 2506 q^{97} - 3435 q^{98} - 5951 q^{99}+O(q^{100}) \) 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9 + 2 * q^10 - 847 * q^11 - 88 * q^12 - 20 * q^13 - 282 * q^14 - 330 * q^15 + 936 * q^16 - 56 * q^17 - 343 * q^18 - 157 * q^19 - 450 * q^20 - 122 * q^21 + 154 * q^22 - 764 * q^23 - 346 * q^24 + 1413 * q^25 - 408 * q^26 - 358 * q^27 - 228 * q^28 - 557 * q^29 - 267 * q^30 - 780 * q^31 - 1739 * q^32 + 110 * q^33 - 1104 * q^34 - 1254 * q^35 + 375 * q^36 - 541 * q^37 - 2133 * q^38 - 1458 * q^39 - 554 * q^40 - 1723 * q^41 - 5 * q^42 - 688 * q^43 - 3256 * q^44 - 1588 * q^45 + 276 * q^46 - 3086 * q^47 - 4280 * q^48 + 2452 * q^49 - 2234 * q^50 - 1570 * q^51 - 715 * q^52 - 1230 * q^53 - 5166 * q^54 + 462 * q^55 - 3203 * q^56 + 1024 * q^57 - 3016 * q^58 - 5408 * q^59 - 8221 * q^60 + 566 * q^61 - 3642 * q^62 - 3035 * q^63 + 1084 * q^64 - 1794 * q^65 + 143 * q^66 - 1925 * q^67 - 1105 * q^68 - 3710 * q^69 - 5875 * q^70 - 9614 * q^71 - 2198 * q^72 - 384 * q^73 - 2378 * q^74 - 3888 * q^75 - 2809 * q^76 + 649 * q^77 - 1731 * q^78 - 1086 * q^79 - 4357 * q^80 + 2329 * q^81 - 3167 * q^82 - 3045 * q^83 - 5359 * q^84 + 2582 * q^85 - 6468 * q^86 - 4432 * q^87 + 1650 * q^88 - 2831 * q^89 + 512 * q^90 - 6002 * q^91 - 7134 * q^92 - 4428 * q^93 + 1697 * q^94 - 10434 * q^95 + 195 * q^96 - 2506 * q^97 - 3435 * q^98 - 5951 * q^99

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