LMFDB - Embedded newform 966.4.a.m.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,4,Mod(1,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("966.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	966.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:	$56.9958450655$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 351x^{3} - 663x^{2} + 18451x - 19243 $ x^5 - x^4 - 351x^3 - 663x^2 + 18451*x - 19243
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-11.8868$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +1.32009 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +1.32009 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -2.64018 q^{10} +64.4402 q^{11} -12.0000 q^{12} +49.6970 q^{13} +14.0000 q^{14} -3.96026 q^{15} +16.0000 q^{16} +4.18938 q^{17} -18.0000 q^{18} +98.3525 q^{19} +5.28035 q^{20} +21.0000 q^{21} -128.880 q^{22} -23.0000 q^{23} +24.0000 q^{24} -123.257 q^{25} -99.3940 q^{26} -27.0000 q^{27} -28.0000 q^{28} +4.52857 q^{29} +7.92053 q^{30} +215.412 q^{31} -32.0000 q^{32} -193.321 q^{33} -8.37875 q^{34} -9.24062 q^{35} +36.0000 q^{36} -181.747 q^{37} -196.705 q^{38} -149.091 q^{39} -10.5607 q^{40} +48.0909 q^{41} -42.0000 q^{42} +58.4393 q^{43} +257.761 q^{44} +11.8808 q^{45} +46.0000 q^{46} -178.330 q^{47} -48.0000 q^{48} +49.0000 q^{49} +246.515 q^{50} -12.5681 q^{51} +198.788 q^{52} -54.2750 q^{53} +54.0000 q^{54} +85.0667 q^{55} +56.0000 q^{56} -295.057 q^{57} -9.05713 q^{58} +278.903 q^{59} -15.8411 q^{60} +151.982 q^{61} -430.825 q^{62} -63.0000 q^{63} +64.0000 q^{64} +65.6044 q^{65} +386.641 q^{66} -786.112 q^{67} +16.7575 q^{68} +69.0000 q^{69} +18.4812 q^{70} +788.157 q^{71} -72.0000 q^{72} +244.133 q^{73} +363.494 q^{74} +369.772 q^{75} +393.410 q^{76} -451.081 q^{77} +298.182 q^{78} -271.610 q^{79} +21.1214 q^{80} +81.0000 q^{81} -96.1818 q^{82} -557.327 q^{83} +84.0000 q^{84} +5.53035 q^{85} -116.879 q^{86} -13.5857 q^{87} -515.521 q^{88} -98.1740 q^{89} -23.7616 q^{90} -347.879 q^{91} -92.0000 q^{92} -646.237 q^{93} +356.659 q^{94} +129.834 q^{95} +96.0000 q^{96} -471.995 q^{97} -98.0000 q^{98} +579.962 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 + 10 * q^5 + 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9} - 20 q^{10} + 4 q^{11} - 60 q^{12} + 24 q^{13} + 70 q^{14} - 30 q^{15} + 80 q^{16} + 28 q^{17} - 90 q^{18} - 160 q^{19} + 40 q^{20} + 105 q^{21} - 8 q^{22} - 115 q^{23} + 120 q^{24} + 219 q^{25} - 48 q^{26} - 135 q^{27} - 140 q^{28} + 79 q^{29} + 60 q^{30} - 162 q^{31} - 160 q^{32} - 12 q^{33} - 56 q^{34} - 70 q^{35} + 180 q^{36} + 301 q^{37} + 320 q^{38} - 72 q^{39} - 80 q^{40} + 251 q^{41} - 210 q^{42} - 380 q^{43} + 16 q^{44} + 90 q^{45} + 230 q^{46} - 505 q^{47} - 240 q^{48} + 245 q^{49} - 438 q^{50} - 84 q^{51} + 96 q^{52} + 93 q^{53} + 270 q^{54} - 503 q^{55} + 280 q^{56} + 480 q^{57} - 158 q^{58} + 637 q^{59} - 120 q^{60} - 679 q^{61} + 324 q^{62} - 315 q^{63} + 320 q^{64} + 961 q^{65} + 24 q^{66} - 1483 q^{67} + 112 q^{68} + 345 q^{69} + 140 q^{70} + 95 q^{71} - 360 q^{72} - 1310 q^{73} - 602 q^{74} - 657 q^{75} - 640 q^{76} - 28 q^{77} + 144 q^{78} + 494 q^{79} + 160 q^{80} + 405 q^{81} - 502 q^{82} - 482 q^{83} + 420 q^{84} - 291 q^{85} + 760 q^{86} - 237 q^{87} - 32 q^{88} + 661 q^{89} - 180 q^{90} - 168 q^{91} - 460 q^{92} + 486 q^{93} + 1010 q^{94} - 629 q^{95} + 480 q^{96} - 1905 q^{97} - 490 q^{98} + 36 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 + 10 * q^5 + 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9 - 20 * q^10 + 4 * q^11 - 60 * q^12 + 24 * q^13 + 70 * q^14 - 30 * q^15 + 80 * q^16 + 28 * q^17 - 90 * q^18 - 160 * q^19 + 40 * q^20 + 105 * q^21 - 8 * q^22 - 115 * q^23 + 120 * q^24 + 219 * q^25 - 48 * q^26 - 135 * q^27 - 140 * q^28 + 79 * q^29 + 60 * q^30 - 162 * q^31 - 160 * q^32 - 12 * q^33 - 56 * q^34 - 70 * q^35 + 180 * q^36 + 301 * q^37 + 320 * q^38 - 72 * q^39 - 80 * q^40 + 251 * q^41 - 210 * q^42 - 380 * q^43 + 16 * q^44 + 90 * q^45 + 230 * q^46 - 505 * q^47 - 240 * q^48 + 245 * q^49 - 438 * q^50 - 84 * q^51 + 96 * q^52 + 93 * q^53 + 270 * q^54 - 503 * q^55 + 280 * q^56 + 480 * q^57 - 158 * q^58 + 637 * q^59 - 120 * q^60 - 679 * q^61 + 324 * q^62 - 315 * q^63 + 320 * q^64 + 961 * q^65 + 24 * q^66 - 1483 * q^67 + 112 * q^68 + 345 * q^69 + 140 * q^70 + 95 * q^71 - 360 * q^72 - 1310 * q^73 - 602 * q^74 - 657 * q^75 - 640 * q^76 - 28 * q^77 + 144 * q^78 + 494 * q^79 + 160 * q^80 + 405 * q^81 - 502 * q^82 - 482 * q^83 + 420 * q^84 - 291 * q^85 + 760 * q^86 - 237 * q^87 - 32 * q^88 + 661 * q^89 - 180 * q^90 - 168 * q^91 - 460 * q^92 + 486 * q^93 + 1010 * q^94 - 629 * q^95 + 480 * q^96 - 1905 * q^97 - 490 * q^98 + 36 * 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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	1.32009	0.118072	0.0590361	−	0.998256i	$-0.481197\pi$
$5$	1.32009	0.118072	0.0590361	+	0.998256i	$0.481197\pi$
$6$	6.00000	0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−2.64018	−0.0834897
$11$	64.4402	1.76631	0.883157	−	0.469078i	$-0.155414\pi$
$11$	64.4402	1.76631	0.883157	+	0.469078i	$0.155414\pi$
$12$	−12.0000	−0.288675
$13$	49.6970	1.06027	0.530133	−	0.847914i	$-0.322142\pi$
$13$	49.6970	1.06027	0.530133	+	0.847914i	$0.322142\pi$
$14$	14.0000	0.267261
$15$	−3.96026	−0.0681691
$16$	16.0000	0.250000
$17$	4.18938	0.0597690	0.0298845	−	0.999553i	$-0.490486\pi$
$17$	4.18938	0.0597690	0.0298845	+	0.999553i	$0.490486\pi$
$18$	−18.0000	−0.235702
$19$	98.3525	1.18756	0.593779	−	0.804628i	$-0.297635\pi$
$19$	98.3525	1.18756	0.593779	+	0.804628i	$0.297635\pi$
$20$	5.28035	0.0590361
$21$	21.0000	0.218218
$22$	−128.880	−1.24897
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	24.0000	0.204124
$25$	−123.257	−0.986059
$26$	−99.3940	−0.749721
$27$	−27.0000	−0.192450
$28$	−28.0000	−0.188982
$29$	4.52857	0.0289977	0.0144989	−	0.999895i	$-0.495385\pi$
$29$	4.52857	0.0289977	0.0144989	+	0.999895i	$0.495385\pi$
$30$	7.92053	0.0482028
$31$	215.412	1.24804	0.624020	−	0.781409i	$-0.285499\pi$
$31$	215.412	1.24804	0.624020	+	0.781409i	$0.285499\pi$
$32$	−32.0000	−0.176777
$33$	−193.321	−1.01978
$34$	−8.37875	−0.0422631
$35$	−9.24062	−0.0446271
$36$	36.0000	0.166667
$37$	−181.747	−0.807542	−0.403771	−	0.914860i	$-0.632301\pi$
$37$	−181.747	−0.807542	−0.403771	+	0.914860i	$0.632301\pi$
$38$	−196.705	−0.839730
$39$	−149.091	−0.612145
$40$	−10.5607	−0.0417449
$41$	48.0909	0.183184	0.0915919	−	0.995797i	$-0.470804\pi$
$41$	48.0909	0.183184	0.0915919	+	0.995797i	$0.470804\pi$
$42$	−42.0000	−0.154303
$43$	58.4393	0.207254	0.103627	−	0.994616i	$-0.466955\pi$
$43$	58.4393	0.207254	0.103627	+	0.994616i	$0.466955\pi$
$44$	257.761	0.883157
$45$	11.8808	0.0393574
$46$	46.0000	0.147442
$47$	−178.330	−0.553448	−0.276724	−	0.960949i	$-0.589249\pi$
$47$	−178.330	−0.553448	−0.276724	+	0.960949i	$0.589249\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	246.515	0.697249
$51$	−12.5681	−0.0345076
$52$	198.788	0.530133
$53$	−54.2750	−0.140665	−0.0703325	−	0.997524i	$-0.522406\pi$
$53$	−54.2750	−0.140665	−0.0703325	+	0.997524i	$0.522406\pi$
$54$	54.0000	0.136083
$55$	85.0667	0.208553
$56$	56.0000	0.133631
$57$	−295.057	−0.685637
$58$	−9.05713	−0.0205045
$59$	278.903	0.615426	0.307713	−	0.951479i	$-0.400436\pi$
$59$	278.903	0.615426	0.307713	+	0.951479i	$0.400436\pi$
$60$	−15.8411	−0.0340845
$61$	151.982	0.319005	0.159503	−	0.987197i	$-0.449011\pi$
$61$	151.982	0.319005	0.159503	+	0.987197i	$0.449011\pi$
$62$	−430.825	−0.882497
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	65.6044	0.125188
$66$	386.641	0.721094
$67$	−786.112	−1.43342	−0.716708	−	0.697373i	$-0.754352\pi$
$67$	−786.112	−1.43342	−0.716708	+	0.697373i	$0.754352\pi$
$68$	16.7575	0.0298845
$69$	69.0000	0.120386
$70$	18.4812	0.0315561
$71$	788.157	1.31742	0.658711	−	0.752396i	$-0.271102\pi$
$71$	788.157	1.31742	0.658711	+	0.752396i	$0.271102\pi$
$72$	−72.0000	−0.117851
$73$	244.133	0.391420	0.195710	−	0.980662i	$-0.437299\pi$
$73$	244.133	0.391420	0.195710	+	0.980662i	$0.437299\pi$
$74$	363.494	0.571018
$75$	369.772	0.569301
$76$	393.410	0.593779
$77$	−451.081	−0.667604
$78$	298.182	0.432852
$79$	−271.610	−0.386817	−0.193408	−	0.981118i	$-0.561954\pi$
$79$	−271.610	−0.386817	−0.193408	+	0.981118i	$0.561954\pi$
$80$	21.1214	0.0295181
$81$	81.0000	0.111111
$82$	−96.1818	−0.129531
$83$	−557.327	−0.737043	−0.368521	−	0.929619i	$-0.620136\pi$
$83$	−557.327	−0.737043	−0.368521	+	0.929619i	$0.620136\pi$
$84$	84.0000	0.109109
$85$	5.53035	0.00705706
$86$	−116.879	−0.146550
$87$	−13.5857	−0.0167418
$88$	−515.521	−0.624486
$89$	−98.1740	−0.116926	−0.0584630	−	0.998290i	$-0.518620\pi$
$89$	−98.1740	−0.116926	−0.0584630	+	0.998290i	$0.518620\pi$
$90$	−23.7616	−0.0278299
$91$	−347.879	−0.400743
$92$	−92.0000	−0.104257
$93$	−646.237	−0.720556
$94$	356.659	0.391347
$95$	129.834	0.140218
$96$	96.0000	0.102062
$97$	−471.995	−0.494060	−0.247030	−	0.969008i	$-0.579455\pi$
$97$	−471.995	−0.494060	−0.247030	+	0.969008i	$0.579455\pi$
$98$	−98.0000	−0.101015
$99$	579.962	0.588771
$100$	−493.029	−0.493029
$101$	573.054	0.564564	0.282282	−	0.959331i	$-0.408909\pi$
$101$	573.054	0.564564	0.282282	+	0.959331i	$0.408909\pi$
$102$	25.1363	0.0244006
$103$	−1020.62	−0.976352	−0.488176	−	0.872745i	$-0.662338\pi$
$103$	−1020.62	−0.976352	−0.488176	+	0.872745i	$0.662338\pi$
$104$	−397.576	−0.374861
$105$	27.7219	0.0257655
$106$	108.550	0.0994652
$107$	767.973	0.693857	0.346929	−	0.937891i	$-0.387225\pi$
$107$	767.973	0.693857	0.346929	+	0.937891i	$0.387225\pi$
$108$	−108.000	−0.0962250
$109$	−391.544	−0.344065	−0.172033	−	0.985091i	$-0.555033\pi$
$109$	−391.544	−0.344065	−0.172033	+	0.985091i	$0.555033\pi$
$110$	−170.133	−0.147469
$111$	545.241	0.466234
$112$	−112.000	−0.0944911
$113$	1626.94	1.35442	0.677211	−	0.735789i	$-0.263188\pi$
$113$	1626.94	1.35442	0.677211	+	0.735789i	$0.263188\pi$
$114$	590.115	0.484819
$115$	−30.3620	−0.0246198
$116$	18.1143	0.0144989
$117$	447.273	0.353422
$118$	−557.807	−0.435172
$119$	−29.3256	−0.0225906
$120$	31.6821	0.0241014
$121$	2821.54	2.11986
$122$	−303.964	−0.225571
$123$	−144.273	−0.105761
$124$	861.650	0.624020
$125$	−327.722	−0.234498
$126$	126.000	0.0890871
$127$	−109.756	−0.0766870	−0.0383435	−	0.999265i	$-0.512208\pi$
$127$	−109.756	−0.0766870	−0.0383435	+	0.999265i	$0.512208\pi$
$128$	−128.000	−0.0883883
$129$	−175.318	−0.119658
$130$	−131.209	−0.0885213
$131$	−940.188	−0.627058	−0.313529	−	0.949579i	$-0.601511\pi$
$131$	−940.188	−0.627058	−0.313529	+	0.949579i	$0.601511\pi$
$132$	−773.282	−0.509891
$133$	−688.467	−0.448855
$134$	1572.22	1.01358
$135$	−35.6424	−0.0227230
$136$	−33.5150	−0.0211315
$137$	3072.89	1.91631	0.958156	−	0.286246i	$-0.0924073\pi$
$137$	3072.89	1.91631	0.958156	+	0.286246i	$0.0924073\pi$
$138$	−138.000	−0.0851257
$139$	−2424.58	−1.47950	−0.739748	−	0.672885i	$-0.765055\pi$
$139$	−2424.58	−1.47950	−0.739748	+	0.672885i	$0.765055\pi$
$140$	−36.9625	−0.0223136
$141$	534.989	0.319533
$142$	−1576.31	−0.931559
$143$	3202.48	1.87276
$144$	144.000	0.0833333
$145$	5.97810	0.00342382
$146$	−488.267	−0.276776
$147$	−147.000	−0.0824786
$148$	−726.989	−0.403771
$149$	1085.32	0.596733	0.298367	−	0.954451i	$-0.403558\pi$
$149$	1085.32	0.596733	0.298367	+	0.954451i	$0.403558\pi$
$150$	−739.544	−0.402557
$151$	−457.345	−0.246478	−0.123239	−	0.992377i	$-0.539328\pi$
$151$	−457.345	−0.246478	−0.123239	+	0.992377i	$0.539328\pi$
$152$	−786.820	−0.419865
$153$	37.7044	0.0199230
$154$	902.163	0.472067
$155$	284.363	0.147359
$156$	−596.364	−0.306073
$157$	2146.20	1.09099	0.545495	−	0.838114i	$-0.316342\pi$
$157$	2146.20	1.09099	0.545495	+	0.838114i	$0.316342\pi$
$158$	543.220	0.273521
$159$	162.825	0.0812130
$160$	−42.2428	−0.0208724
$161$	161.000	0.0788110
$162$	−162.000	−0.0785674
$163$	2029.78	0.975368	0.487684	−	0.873020i	$-0.337842\pi$
$163$	2029.78	0.975368	0.487684	+	0.873020i	$0.337842\pi$
$164$	192.364	0.0915919
$165$	−255.200	−0.120408
$166$	1114.65	0.521168
$167$	2279.37	1.05619	0.528093	−	0.849186i	$-0.322907\pi$
$167$	2279.37	1.05619	0.528093	+	0.849186i	$0.322907\pi$
$168$	−168.000	−0.0771517
$169$	272.790	0.124165
$170$	−11.0607	−0.00499010
$171$	885.172	0.395853
$172$	233.757	0.103627
$173$	1755.72	0.771589	0.385794	−	0.922585i	$-0.373927\pi$
$173$	1755.72	0.771589	0.385794	+	0.922585i	$0.373927\pi$
$174$	27.1714	0.0118383
$175$	862.802	0.372695
$176$	1031.04	0.441578
$177$	−836.710	−0.355316
$178$	196.348	0.0826792
$179$	3606.36	1.50588	0.752939	−	0.658091i	$-0.228636\pi$
$179$	3606.36	1.50588	0.752939	+	0.658091i	$0.228636\pi$
$180$	47.5232	0.0196787
$181$	−799.117	−0.328165	−0.164083	−	0.986447i	$-0.552466\pi$
$181$	−799.117	−0.328165	−0.164083	+	0.986447i	$0.552466\pi$
$182$	695.758	0.283368
$183$	−455.947	−0.184178
$184$	184.000	0.0737210
$185$	−239.922	−0.0953483
$186$	1292.47	0.509510
$187$	269.964	0.105571
$188$	−713.318	−0.276724
$189$	189.000	0.0727393
$190$	−259.668	−0.0991489
$191$	3519.29	1.33323	0.666616	−	0.745402i	$-0.267742\pi$
$191$	3519.29	1.33323	0.666616	+	0.745402i	$0.267742\pi$
$192$	−192.000	−0.0721688
$193$	3430.06	1.27928	0.639640	−	0.768675i	$-0.279083\pi$
$193$	3430.06	1.27928	0.639640	+	0.768675i	$0.279083\pi$
$194$	943.990	0.349353
$195$	−196.813	−0.0722774
$196$	196.000	0.0714286
$197$	3300.61	1.19370	0.596850	−	0.802353i	$-0.296419\pi$
$197$	3300.61	1.19370	0.596850	+	0.802353i	$0.296419\pi$
$198$	−1159.92	−0.416324
$199$	2302.94	0.820356	0.410178	−	0.912005i	$-0.365467\pi$
$199$	2302.94	0.820356	0.410178	+	0.912005i	$0.365467\pi$
$200$	986.059	0.348624
$201$	2358.34	0.827583
$202$	−1146.11	−0.399207
$203$	−31.7000	−0.0109601
$204$	−50.2725	−0.0172538
$205$	63.4842	0.0216289
$206$	2041.23	0.690385
$207$	−207.000	−0.0695048
$208$	795.152	0.265067
$209$	6337.85	2.09760
$210$	−55.4437	−0.0182189
$211$	−1154.09	−0.376544	−0.188272	−	0.982117i	$-0.560289\pi$
$211$	−1154.09	−0.376544	−0.188272	+	0.982117i	$0.560289\pi$
$212$	−217.100	−0.0703325
$213$	−2364.47	−0.760614
$214$	−1535.95	−0.490631
$215$	77.1450	0.0244709
$216$	216.000	0.0680414
$217$	−1507.89	−0.471714
$218$	783.088	0.243291
$219$	−732.400	−0.225986
$220$	340.267	0.104276
$221$	208.199	0.0633711
$222$	−1090.48	−0.329678
$223$	−1900.87	−0.570815	−0.285407	−	0.958406i	$-0.592129\pi$
$223$	−1900.87	−0.570815	−0.285407	+	0.958406i	$0.592129\pi$
$224$	224.000	0.0668153
$225$	−1109.32	−0.328686
$226$	−3253.88	−0.957721
$227$	−4795.12	−1.40204	−0.701020	−	0.713142i	$-0.747272\pi$
$227$	−4795.12	−1.40204	−0.701020	+	0.713142i	$0.747272\pi$
$228$	−1180.23	−0.342818
$229$	758.647	0.218920	0.109460	−	0.993991i	$-0.465088\pi$
$229$	758.647	0.218920	0.109460	+	0.993991i	$0.465088\pi$
$230$	60.7241	0.0174088
$231$	1353.24	0.385441
$232$	−36.2285	−0.0102522
$233$	−275.301	−0.0774058	−0.0387029	−	0.999251i	$-0.512323\pi$
$233$	−275.301	−0.0774058	−0.0387029	+	0.999251i	$0.512323\pi$
$234$	−894.546	−0.249907
$235$	−235.411	−0.0653468
$236$	1115.61	0.307713
$237$	814.830	0.223329
$238$	58.6513	0.0159739
$239$	−4853.13	−1.31348	−0.656742	−	0.754115i	$-0.728066\pi$
$239$	−4853.13	−1.31348	−0.656742	+	0.754115i	$0.728066\pi$
$240$	−63.3642	−0.0170423
$241$	−236.715	−0.0632703	−0.0316352	−	0.999499i	$-0.510071\pi$
$241$	−236.715	−0.0632703	−0.0316352	+	0.999499i	$0.510071\pi$
$242$	−5643.07	−1.49897
$243$	−243.000	−0.0641500
$244$	607.929	0.159503
$245$	64.6843	0.0168675
$246$	288.545	0.0747845
$247$	4887.82	1.25913
$248$	−1723.30	−0.441248
$249$	1671.98	0.425532
$250$	655.443	0.165815
$251$	363.718	0.0914649	0.0457324	−	0.998954i	$-0.485438\pi$
$251$	363.718	0.0914649	0.0457324	+	0.998954i	$0.485438\pi$
$252$	−252.000	−0.0629941
$253$	−1482.12	−0.368302
$254$	219.511	0.0542259
$255$	−16.5910	−0.00407440
$256$	256.000	0.0625000
$257$	−6206.34	−1.50638	−0.753192	−	0.657800i	$-0.771487\pi$
$257$	−6206.34	−1.50638	−0.753192	+	0.657800i	$0.771487\pi$
$258$	350.636	0.0846109
$259$	1272.23	0.305222
$260$	262.418	0.0625940
$261$	40.7571	0.00966590
$262$	1880.38	0.443397
$263$	−470.117	−0.110223	−0.0551115	−	0.998480i	$-0.517551\pi$
$263$	−470.117	−0.110223	−0.0551115	+	0.998480i	$0.517551\pi$
$264$	1546.56	0.360547
$265$	−71.6478	−0.0166086
$266$	1376.93	0.317388
$267$	294.522	0.0675073
$268$	−3144.45	−0.716708
$269$	539.902	0.122373	0.0611866	−	0.998126i	$-0.480512\pi$
$269$	539.902	0.122373	0.0611866	+	0.998126i	$0.480512\pi$
$270$	71.2848	0.0160676
$271$	6303.85	1.41303	0.706516	−	0.707697i	$-0.250266\pi$
$271$	6303.85	1.41303	0.706516	+	0.707697i	$0.250266\pi$
$272$	67.0300	0.0149422
$273$	1043.64	0.231369
$274$	−6145.78	−1.35504
$275$	−7942.73	−1.74169
$276$	276.000	0.0601929
$277$	−2631.75	−0.570854	−0.285427	−	0.958401i	$-0.592135\pi$
$277$	−2631.75	−0.570854	−0.285427	+	0.958401i	$0.592135\pi$
$278$	4849.15	1.04616
$279$	1938.71	0.416013
$280$	73.9249	0.0157781
$281$	7037.97	1.49413	0.747064	−	0.664752i	$-0.231463\pi$
$281$	7037.97	1.49413	0.747064	+	0.664752i	$0.231463\pi$
$282$	−1069.98	−0.225944
$283$	845.902	0.177681	0.0888404	−	0.996046i	$-0.471684\pi$
$283$	845.902	0.177681	0.0888404	+	0.996046i	$0.471684\pi$
$284$	3152.63	0.658711
$285$	−389.502	−0.0809547
$286$	−6404.96	−1.32424
$287$	−336.636	−0.0692370
$288$	−288.000	−0.0589256
$289$	−4895.45	−0.996428
$290$	−11.9562	−0.00242101
$291$	1415.98	0.285246
$292$	976.533	0.195710
$293$	4035.41	0.804612	0.402306	−	0.915505i	$-0.368209\pi$
$293$	4035.41	0.804612	0.402306	+	0.915505i	$0.368209\pi$
$294$	294.000	0.0583212
$295$	368.177	0.0726647
$296$	1453.98	0.285509
$297$	−1739.88	−0.339927
$298$	−2170.65	−0.421954
$299$	−1143.03	−0.221081
$300$	1479.09	0.284651
$301$	−409.075	−0.0783345
$302$	914.690	0.174286
$303$	−1719.16	−0.325951
$304$	1573.64	0.296890
$305$	200.630	0.0376657
$306$	−75.4088	−0.0140877
$307$	−8115.36	−1.50869	−0.754345	−	0.656478i	$-0.772046\pi$
$307$	−8115.36	−1.50869	−0.754345	+	0.656478i	$0.772046\pi$
$308$	−1804.33	−0.333802
$309$	3061.85	0.563697
$310$	−568.727	−0.104198
$311$	−3967.19	−0.723340	−0.361670	−	0.932306i	$-0.617793\pi$
$311$	−3967.19	−0.723340	−0.361670	+	0.932306i	$0.617793\pi$
$312$	1192.73	0.216426
$313$	3727.82	0.673192	0.336596	−	0.941649i	$-0.390724\pi$
$313$	3727.82	0.673192	0.336596	+	0.941649i	$0.390724\pi$
$314$	−4292.40	−0.771446
$315$	−83.1656	−0.0148757
$316$	−1086.44	−0.193408
$317$	3634.46	0.643948	0.321974	−	0.946749i	$-0.395654\pi$
$317$	3634.46	0.643948	0.321974	+	0.946749i	$0.395654\pi$
$318$	−325.650	−0.0574263
$319$	291.822	0.0512190
$320$	84.4856	0.0147590
$321$	−2303.92	−0.400599
$322$	−322.000	−0.0557278
$323$	412.035	0.0709792
$324$	324.000	0.0555556
$325$	−6125.52	−1.04549
$326$	−4059.57	−0.689689
$327$	1174.63	0.198646
$328$	−384.727	−0.0647653
$329$	1248.31	0.209184
$330$	510.400	0.0851413
$331$	6897.03	1.14530	0.572651	−	0.819799i	$-0.305915\pi$
$331$	6897.03	1.14530	0.572651	+	0.819799i	$0.305915\pi$
$332$	−2229.31	−0.368521
$333$	−1635.72	−0.269181
$334$	−4558.75	−0.746837
$335$	−1037.74	−0.169247
$336$	336.000	0.0545545
$337$	4212.94	0.680990	0.340495	−	0.940246i	$-0.389405\pi$
$337$	4212.94	0.680990	0.340495	+	0.940246i	$0.389405\pi$
$338$	−545.579	−0.0877976
$339$	−4880.82	−0.781976
$340$	22.1214	0.00352853
$341$	13881.2	2.20443
$342$	−1770.34	−0.279910
$343$	−343.000	−0.0539949
$344$	−467.514	−0.0732752
$345$	91.0861	0.0142142
$346$	−3511.44	−0.545595
$347$	−7267.35	−1.12430	−0.562150	−	0.827035i	$-0.690026\pi$
$347$	−7267.35	−1.12430	−0.562150	+	0.827035i	$0.690026\pi$
$348$	−54.3428	−0.00837092
$349$	−10426.0	−1.59911	−0.799555	−	0.600592i	$-0.794932\pi$
$349$	−10426.0	−1.59911	−0.799555	+	0.600592i	$0.794932\pi$
$350$	−1725.60	−0.263535
$351$	−1341.82	−0.204048
$352$	−2062.09	−0.312243
$353$	11400.4	1.71893	0.859465	−	0.511194i	$-0.170797\pi$
$353$	11400.4	1.71893	0.859465	+	0.511194i	$0.170797\pi$
$354$	1673.42	0.251246
$355$	1040.44	0.155551
$356$	−392.696	−0.0584630
$357$	87.9769	0.0130427
$358$	−7212.72	−1.06482
$359$	4721.56	0.694135	0.347067	−	0.937840i	$-0.387178\pi$
$359$	4721.56	0.694135	0.347067	+	0.937840i	$0.387178\pi$
$360$	−95.0463	−0.0139150
$361$	2814.21	0.410294
$362$	1598.23	0.232048
$363$	−8464.61	−1.22390
$364$	−1391.52	−0.200371
$365$	322.277	0.0462158
$366$	911.893	0.130233
$367$	−4227.00	−0.601220	−0.300610	−	0.953747i	$-0.597190\pi$
$367$	−4227.00	−0.601220	−0.300610	+	0.953747i	$0.597190\pi$
$368$	−368.000	−0.0521286
$369$	432.818	0.0610613
$370$	479.844	0.0674214
$371$	379.925	0.0531664
$372$	−2584.95	−0.360278
$373$	−4755.63	−0.660154	−0.330077	−	0.943954i	$-0.607075\pi$
$373$	−4755.63	−0.660154	−0.330077	+	0.943954i	$0.607075\pi$
$374$	−539.928	−0.0746498
$375$	983.165	0.135388
$376$	1426.64	0.195673
$377$	225.056	0.0307453
$378$	−378.000	−0.0514344
$379$	−4677.74	−0.633983	−0.316992	−	0.948428i	$-0.602673\pi$
$379$	−4677.74	−0.633983	−0.316992	+	0.948428i	$0.602673\pi$
$380$	519.336	0.0701088
$381$	329.267	0.0442752
$382$	−7038.59	−0.942737
$383$	11024.4	1.47082	0.735408	−	0.677625i	$-0.236991\pi$
$383$	11024.4	1.47082	0.735408	+	0.677625i	$0.236991\pi$
$384$	384.000	0.0510310
$385$	−595.467	−0.0788255
$386$	−6860.12	−0.904588
$387$	525.953	0.0690845
$388$	−1887.98	−0.247030
$389$	8450.89	1.10148	0.550742	−	0.834676i	$-0.314345\pi$
$389$	8450.89	1.10148	0.550742	+	0.834676i	$0.314345\pi$
$390$	393.626	0.0511078
$391$	−96.3557	−0.0124627
$392$	−392.000	−0.0505076
$393$	2820.56	0.362032
$394$	−6601.22	−0.844073
$395$	−358.549	−0.0456723
$396$	2319.85	0.294386
$397$	−2871.53	−0.363017	−0.181509	−	0.983389i	$-0.558098\pi$
$397$	−2871.53	−0.363017	−0.181509	+	0.983389i	$0.558098\pi$
$398$	−4605.87	−0.580079
$399$	2065.40	0.259146
$400$	−1972.12	−0.246515
$401$	−8506.36	−1.05932	−0.529660	−	0.848210i	$-0.677681\pi$
$401$	−8506.36	−1.05932	−0.529660	+	0.848210i	$0.677681\pi$
$402$	−4716.67	−0.585190
$403$	10705.3	1.32325
$404$	2292.21	0.282282
$405$	106.927	0.0131191
$406$	63.3999	0.00774996
$407$	−11711.8	−1.42637
$408$	100.545	0.0122003
$409$	10411.5	1.25872	0.629359	−	0.777115i	$-0.283318\pi$
$409$	10411.5	1.25872	0.629359	+	0.777115i	$0.283318\pi$
$410$	−126.968	−0.0152940
$411$	−9218.67	−1.10638
$412$	−4082.46	−0.488176
$413$	−1952.32	−0.232609
$414$	414.000	0.0491473
$415$	−735.720	−0.0870243
$416$	−1590.30	−0.187430
$417$	7273.73	0.854187
$418$	−12675.7	−1.48323
$419$	−7981.20	−0.930566	−0.465283	−	0.885162i	$-0.654047\pi$
$419$	−7981.20	−0.930566	−0.465283	+	0.885162i	$0.654047\pi$
$420$	110.887	0.0128827
$421$	9347.17	1.08207	0.541037	−	0.840999i	$-0.318032\pi$
$421$	9347.17	1.08207	0.541037	+	0.840999i	$0.318032\pi$
$422$	2308.18	0.266257
$423$	−1604.97	−0.184483
$424$	434.200	0.0497326
$425$	−516.371	−0.0589358
$426$	4728.94	0.537836
$427$	−1063.88	−0.120573
$428$	3071.89	0.346929
$429$	−9607.45	−1.08124
$430$	−154.290	−0.0173035
$431$	−58.4868	−0.00653645	−0.00326822	−	0.999995i	$-0.501040\pi$
$431$	−58.4868	−0.00653645	−0.00326822	+	0.999995i	$0.501040\pi$
$432$	−432.000	−0.0481125
$433$	−10719.3	−1.18969	−0.594844	−	0.803841i	$-0.702786\pi$
$433$	−10719.3	−1.18969	−0.594844	+	0.803841i	$0.702786\pi$
$434$	3015.77	0.333552
$435$	−17.9343	−0.00197675
$436$	−1566.18	−0.172033
$437$	−2262.11	−0.247623
$438$	1464.80	0.159796
$439$	−6982.84	−0.759163	−0.379582	−	0.925158i	$-0.623932\pi$
$439$	−6982.84	−0.759163	−0.379582	+	0.925158i	$0.623932\pi$
$440$	−680.534	−0.0737345
$441$	441.000	0.0476190
$442$	−416.399	−0.0448101
$443$	−1339.35	−0.143644	−0.0718222	−	0.997417i	$-0.522881\pi$
$443$	−1339.35	−0.143644	−0.0718222	+	0.997417i	$0.522881\pi$
$444$	2180.97	0.233117
$445$	−129.598	−0.0138057
$446$	3801.74	0.403627
$447$	−3255.97	−0.344524
$448$	−448.000	−0.0472456
$449$	6645.51	0.698488	0.349244	−	0.937032i	$-0.386438\pi$
$449$	6645.51	0.698488	0.349244	+	0.937032i	$0.386438\pi$
$450$	2218.63	0.232416
$451$	3098.99	0.323560
$452$	6507.76	0.677211
$453$	1372.03	0.142304
$454$	9590.23	0.991392
$455$	−459.231	−0.0473166
$456$	2360.46	0.242409
$457$	−10413.9	−1.06596	−0.532979	−	0.846128i	$-0.678928\pi$
$457$	−10413.9	−1.06596	−0.532979	+	0.846128i	$0.678928\pi$
$458$	−1517.29	−0.154800
$459$	−113.113	−0.0115025
$460$	−121.448	−0.0123099
$461$	−11343.1	−1.14599	−0.572994	−	0.819560i	$-0.694218\pi$
$461$	−11343.1	−1.14599	−0.572994	+	0.819560i	$0.694218\pi$
$462$	−2706.49	−0.272548
$463$	−11385.2	−1.14280	−0.571399	−	0.820673i	$-0.693599\pi$
$463$	−11385.2	−1.14280	−0.571399	+	0.820673i	$0.693599\pi$
$464$	72.4570	0.00724943
$465$	−853.090	−0.0850776
$466$	550.602	0.0547342
$467$	5768.99	0.571643	0.285821	−	0.958283i	$-0.407734\pi$
$467$	5768.99	0.571643	0.285821	+	0.958283i	$0.407734\pi$
$468$	1789.09	0.176711
$469$	5502.78	0.541780
$470$	470.822	0.0462072
$471$	−6438.60	−0.629883
$472$	−2231.23	−0.217586
$473$	3765.84	0.366075
$474$	−1629.66	−0.157917
$475$	−12122.7	−1.17100
$476$	−117.303	−0.0112953
$477$	−488.475	−0.0468884
$478$	9706.25	0.928773
$479$	7271.68	0.693636	0.346818	−	0.937932i	$-0.387262\pi$
$479$	7271.68	0.693636	0.346818	+	0.937932i	$0.387262\pi$
$480$	126.728	0.0120507
$481$	−9032.28	−0.856209
$482$	473.430	0.0447389
$483$	−483.000	−0.0455016
$484$	11286.1	1.05993
$485$	−623.075	−0.0583348
$486$	486.000	0.0453609
$487$	19893.5	1.85105	0.925525	−	0.378686i	$-0.123624\pi$
$487$	19893.5	1.85105	0.925525	+	0.378686i	$0.123624\pi$
$488$	−1215.86	−0.112785
$489$	−6089.35	−0.563129
$490$	−129.369	−0.0119271
$491$	−16272.8	−1.49568	−0.747840	−	0.663879i	$-0.768909\pi$
$491$	−16272.8	−1.49568	−0.747840	+	0.663879i	$0.768909\pi$
$492$	−577.091	−0.0528806
$493$	18.9719	0.00173316
$494$	−9775.64	−0.890338
$495$	765.600	0.0695175
$496$	3446.60	0.312010
$497$	−5517.10	−0.497939
$498$	−3343.96	−0.300896
$499$	3349.75	0.300512	0.150256	−	0.988647i	$-0.451990\pi$
$499$	3349.75	0.300512	0.150256	+	0.988647i	$0.451990\pi$
$500$	−1310.89	−0.117249
$501$	−6838.12	−0.609790
$502$	−727.436	−0.0646754
$503$	−5070.47	−0.449466	−0.224733	−	0.974420i	$-0.572151\pi$
$503$	−5070.47	−0.449466	−0.224733	+	0.974420i	$0.572151\pi$
$504$	504.000	0.0445435
$505$	756.481	0.0666593
$506$	2964.25	0.260429
$507$	−818.369	−0.0716864
$508$	−439.023	−0.0383435
$509$	5396.50	0.469933	0.234966	−	0.972004i	$-0.424502\pi$
$509$	5396.50	0.469933	0.234966	+	0.972004i	$0.424502\pi$
$510$	33.1821	0.00288103
$511$	−1708.93	−0.147943
$512$	−512.000	−0.0441942
$513$	−2655.52	−0.228546
$514$	12412.7	1.06517
$515$	−1347.30	−0.115280
$516$	−701.271	−0.0598290
$517$	−11491.6	−0.977562
$518$	−2544.46	−0.215825
$519$	−5267.16	−0.445477
$520$	−524.835	−0.0442607
$521$	−1966.79	−0.165387	−0.0826937	−	0.996575i	$-0.526352\pi$
$521$	−1966.79	−0.165387	−0.0826937	+	0.996575i	$0.526352\pi$
$522$	−81.5142	−0.00683482
$523$	−10824.3	−0.904997	−0.452498	−	0.891765i	$-0.649467\pi$
$523$	−10824.3	−0.904997	−0.452498	+	0.891765i	$0.649467\pi$
$524$	−3760.75	−0.313529
$525$	−2588.40	−0.215176
$526$	940.234	0.0779394
$527$	902.444	0.0745940
$528$	−3093.13	−0.254945
$529$	529.000	0.0434783
$530$	143.296	0.0117441
$531$	2510.13	0.205142
$532$	−2753.87	−0.224427
$533$	2389.97	0.194224
$534$	−589.044	−0.0477349
$535$	1013.79	0.0819253
$536$	6288.90	0.506789
$537$	−10819.1	−0.869419
$538$	−1079.80	−0.0865310
$539$	3157.57	0.252330
$540$	−142.570	−0.0113615
$541$	20837.7	1.65598	0.827988	−	0.560746i	$-0.189485\pi$
$541$	20837.7	1.65598	0.827988	+	0.560746i	$0.189485\pi$
$542$	−12607.7	−0.999164
$543$	2397.35	0.189466
$544$	−134.060	−0.0105658
$545$	−516.873	−0.0406246
$546$	−2087.27	−0.163603
$547$	−3961.09	−0.309623	−0.154812	−	0.987944i	$-0.549477\pi$
$547$	−3961.09	−0.309623	−0.154812	+	0.987944i	$0.549477\pi$
$548$	12291.6	0.958156
$549$	1367.84	0.106335
$550$	15885.5	1.23156
$551$	445.396	0.0344365
$552$	−552.000	−0.0425628
$553$	1901.27	0.146203
$554$	5263.50	0.403654
$555$	719.767	0.0550494
$556$	−9698.30	−0.739748
$557$	23969.4	1.82337	0.911684	−	0.410892i	$-0.134783\pi$
$557$	23969.4	1.82337	0.911684	+	0.410892i	$0.134783\pi$
$558$	−3877.42	−0.294166
$559$	2904.25	0.219744
$560$	−147.850	−0.0111568
$561$	−809.893	−0.0609513
$562$	−14075.9	−1.05651
$563$	18626.2	1.39432	0.697158	−	0.716917i	$-0.254447\pi$
$563$	18626.2	1.39432	0.697158	+	0.716917i	$0.254447\pi$
$564$	2139.96	0.159767
$565$	2147.71	0.159920
$566$	−1691.80	−0.125639
$567$	−567.000	−0.0419961
$568$	−6305.26	−0.465779
$569$	−12481.6	−0.919604	−0.459802	−	0.888022i	$-0.652080\pi$
$569$	−12481.6	−0.919604	−0.459802	+	0.888022i	$0.652080\pi$
$570$	779.004	0.0572436
$571$	−1957.23	−0.143446	−0.0717229	−	0.997425i	$-0.522850\pi$
$571$	−1957.23	−0.143446	−0.0717229	+	0.997425i	$0.522850\pi$
$572$	12809.9	0.936381
$573$	−10557.9	−0.769741
$574$	673.273	0.0489580
$575$	2834.92	0.205608
$576$	576.000	0.0416667
$577$	1351.24	0.0974916	0.0487458	−	0.998811i	$-0.484478\pi$
$577$	1351.24	0.0974916	0.0487458	+	0.998811i	$0.484478\pi$
$578$	9790.90	0.704581
$579$	−10290.2	−0.738593
$580$	23.9124	0.00171191
$581$	3901.29	0.278576
$582$	−2831.97	−0.201699
$583$	−3497.49	−0.248459
$584$	−1953.07	−0.138388
$585$	590.440	0.0417293
$586$	−8070.83	−0.568947
$587$	−7715.19	−0.542487	−0.271244	−	0.962511i	$-0.587435\pi$
$587$	−7715.19	−0.542487	−0.271244	+	0.962511i	$0.587435\pi$
$588$	−588.000	−0.0412393
$589$	21186.3	1.48212
$590$	−736.354	−0.0513817
$591$	−9901.83	−0.689183
$592$	−2907.95	−0.201885
$593$	−4037.63	−0.279605	−0.139802	−	0.990179i	$-0.544647\pi$
$593$	−4037.63	−0.279605	−0.139802	+	0.990179i	$0.544647\pi$
$594$	3479.77	0.240365
$595$	−38.7124	−0.00266732
$596$	4341.30	0.298367
$597$	−6908.81	−0.473633
$598$	2286.06	0.156328
$599$	9342.69	0.637282	0.318641	−	0.947875i	$-0.396774\pi$
$599$	9342.69	0.637282	0.318641	+	0.947875i	$0.396774\pi$
$600$	−2958.18	−0.201278
$601$	−16985.7	−1.15284	−0.576422	−	0.817152i	$-0.695552\pi$
$601$	−16985.7	−1.15284	−0.576422	+	0.817152i	$0.695552\pi$
$602$	818.150	0.0553909
$603$	−7075.01	−0.477805
$604$	−1829.38	−0.123239
$605$	3724.68	0.250297
$606$	3438.32	0.230482
$607$	25384.2	1.69739	0.848693	−	0.528885i	$-0.177390\pi$
$607$	25384.2	1.69739	0.848693	+	0.528885i	$0.177390\pi$
$608$	−3147.28	−0.209933
$609$	95.0999	0.00632782
$610$	−401.260	−0.0266337
$611$	−8862.44	−0.586802
$612$	150.818	0.00996150
$613$	−2266.44	−0.149332	−0.0746661	−	0.997209i	$-0.523789\pi$
$613$	−2266.44	−0.149332	−0.0746661	+	0.997209i	$0.523789\pi$
$614$	16230.7	1.06681
$615$	−190.453	−0.0124875
$616$	3608.65	0.236034
$617$	−1099.45	−0.0717378	−0.0358689	−	0.999357i	$-0.511420\pi$
$617$	−1099.45	−0.0717378	−0.0358689	+	0.999357i	$0.511420\pi$
$618$	−6123.70	−0.398594
$619$	−2805.62	−0.182177	−0.0910883	−	0.995843i	$-0.529035\pi$
$619$	−2805.62	−0.182177	−0.0910883	+	0.995843i	$0.529035\pi$
$620$	1137.45	0.0736794
$621$	621.000	0.0401286
$622$	7934.38	0.511478
$623$	687.218	0.0441939
$624$	−2385.45	−0.153036
$625$	14974.5	0.958371
$626$	−7455.64	−0.476018
$627$	−19013.6	−1.21105
$628$	8584.80	0.545495
$629$	−761.407	−0.0482660
$630$	166.331	0.0105187
$631$	185.699	0.0117156	0.00585780	−	0.999983i	$-0.498135\pi$
$631$	185.699	0.0117156	0.00585780	+	0.999983i	$0.498135\pi$
$632$	2172.88	0.136760
$633$	3462.27	0.217398
$634$	−7268.92	−0.455340
$635$	−144.887	−0.00905461
$636$	651.300	0.0406065
$637$	2435.15	0.151467
$638$	−583.643	−0.0362173
$639$	7093.41	0.439141
$640$	−168.971	−0.0104362
$641$	16123.9	0.993532	0.496766	−	0.867885i	$-0.334521\pi$
$641$	16123.9	0.993532	0.496766	+	0.867885i	$0.334521\pi$
$642$	4607.84	0.283266
$643$	−1837.05	−0.112669	−0.0563345	−	0.998412i	$-0.517941\pi$
$643$	−1837.05	−0.112669	−0.0563345	+	0.998412i	$0.517941\pi$
$644$	644.000	0.0394055
$645$	−231.435	−0.0141283
$646$	−824.071	−0.0501898
$647$	3630.22	0.220585	0.110293	−	0.993899i	$-0.464821\pi$
$647$	3630.22	0.220585	0.110293	+	0.993899i	$0.464821\pi$
$648$	−648.000	−0.0392837
$649$	17972.6	1.08703
$650$	12251.0	0.739270
$651$	4523.66	0.272344
$652$	8119.14	0.487684
$653$	4925.91	0.295200	0.147600	−	0.989047i	$-0.452845\pi$
$653$	4925.91	0.295200	0.147600	+	0.989047i	$0.452845\pi$
$654$	−2349.26	−0.140464
$655$	−1241.13	−0.0740382
$656$	769.455	0.0457960
$657$	2197.20	0.130473
$658$	−2496.61	−0.147915
$659$	−13887.7	−0.820924	−0.410462	−	0.911878i	$-0.634633\pi$
$659$	−13887.7	−0.820924	−0.410462	+	0.911878i	$0.634633\pi$
$660$	−1020.80	−0.0602040
$661$	−8936.52	−0.525855	−0.262928	−	0.964816i	$-0.584688\pi$
$661$	−8936.52	−0.525855	−0.262928	+	0.964816i	$0.584688\pi$
$662$	−13794.1	−0.809851
$663$	−624.598	−0.0365873
$664$	4458.61	0.260584
$665$	−908.837	−0.0529973
$666$	3271.45	0.190339
$667$	−104.157	−0.00604644
$668$	9117.49	0.528093
$669$	5702.61	0.329560
$670$	2075.47	0.119675
$671$	9793.76	0.563463
$672$	−672.000	−0.0385758
$673$	−3717.03	−0.212899	−0.106449	−	0.994318i	$-0.533948\pi$
$673$	−3717.03	−0.212899	−0.106449	+	0.994318i	$0.533948\pi$
$674$	−8425.88	−0.481532
$675$	3327.95	0.189767
$676$	1091.16	0.0620823
$677$	−22961.7	−1.30353	−0.651764	−	0.758422i	$-0.725971\pi$
$677$	−22961.7	−1.30353	−0.651764	+	0.758422i	$0.725971\pi$
$678$	9761.65	0.552941
$679$	3303.96	0.186737
$680$	−44.2428	−0.00249505
$681$	14385.3	0.809468
$682$	−27762.4	−1.55877
$683$	−15542.6	−0.870748	−0.435374	−	0.900250i	$-0.643384\pi$
$683$	−15542.6	−0.870748	−0.435374	+	0.900250i	$0.643384\pi$
$684$	3540.69	0.197926
$685$	4056.49	0.226263
$686$	686.000	0.0381802
$687$	−2275.94	−0.126394
$688$	935.028	0.0518134
$689$	−2697.30	−0.149142
$690$	−182.172	−0.0100510
$691$	2140.29	0.117830	0.0589151	−	0.998263i	$-0.481236\pi$
$691$	2140.29	0.117830	0.0589151	+	0.998263i	$0.481236\pi$
$692$	7022.87	0.385794
$693$	−4059.73	−0.222535
$694$	14534.7	0.795000
$695$	−3200.65	−0.174687
$696$	108.686	0.00591913
$697$	201.471	0.0109487
$698$	20852.0	1.13074
$699$	825.902	0.0446903
$700$	3451.21	0.186348
$701$	10755.5	0.579502	0.289751	−	0.957102i	$-0.406427\pi$
$701$	10755.5	0.579502	0.289751	+	0.957102i	$0.406427\pi$
$702$	2683.64	0.144284
$703$	−17875.3	−0.959003
$704$	4124.17	0.220789
$705$	706.232	0.0377280
$706$	−22800.8	−1.21547
$707$	−4011.37	−0.213385
$708$	−3346.84	−0.177658
$709$	−27548.4	−1.45924	−0.729622	−	0.683851i	$-0.760304\pi$
$709$	−27548.4	−1.45924	−0.729622	+	0.683851i	$0.760304\pi$
$710$	−2080.87	−0.109991
$711$	−2444.49	−0.128939
$712$	785.392	0.0413396
$713$	−4954.49	−0.260234
$714$	−175.954	−0.00922256
$715$	4227.56	0.221121
$716$	14425.4	0.752939
$717$	14559.4	0.758340
$718$	−9443.12	−0.490827
$719$	884.291	0.0458672	0.0229336	−	0.999737i	$-0.492699\pi$
$719$	884.291	0.0458672	0.0229336	+	0.999737i	$0.492699\pi$
$720$	190.093	0.00983936
$721$	7144.31	0.369027
$722$	−5628.42	−0.290122
$723$	710.145	0.0365291
$724$	−3196.47	−0.164083
$725$	−558.179	−0.0285934
$726$	16929.2	0.865430
$727$	−4136.68	−0.211033	−0.105516	−	0.994418i	$-0.533650\pi$
$727$	−4136.68	−0.211033	−0.105516	+	0.994418i	$0.533650\pi$
$728$	2783.03	0.141684
$729$	729.000	0.0370370
$730$	−644.555	−0.0326795
$731$	244.824	0.0123873
$732$	−1823.79	−0.0920889
$733$	18081.7	0.911137	0.455568	−	0.890201i	$-0.349436\pi$
$733$	18081.7	0.911137	0.455568	+	0.890201i	$0.349436\pi$
$734$	8454.01	0.425127
$735$	−194.053	−0.00973844
$736$	736.000	0.0368605
$737$	−50657.2	−2.53186
$738$	−865.636	−0.0431769
$739$	21757.2	1.08302	0.541509	−	0.840695i	$-0.317853\pi$
$739$	21757.2	1.08302	0.541509	+	0.840695i	$0.317853\pi$
$740$	−959.689	−0.0476741
$741$	−14663.5	−0.726958
$742$	−759.850	−0.0375943
$743$	−29549.5	−1.45904	−0.729520	−	0.683959i	$-0.760257\pi$
$743$	−29549.5	−1.45904	−0.729520	+	0.683959i	$0.760257\pi$
$744$	5169.90	0.254755
$745$	1432.72	0.0704577
$746$	9511.26	0.466799
$747$	−5015.94	−0.245681
$748$	1079.86	0.0527854
$749$	−5375.81	−0.262253
$750$	−1966.33	−0.0957336
$751$	−12046.1	−0.585309	−0.292655	−	0.956218i	$-0.594539\pi$
$751$	−12046.1	−0.585309	−0.292655	+	0.956218i	$0.594539\pi$
$752$	−2853.27	−0.138362
$753$	−1091.15	−0.0528073
$754$	−450.112	−0.0217402
$755$	−603.736	−0.0291022
$756$	756.000	0.0363696
$757$	10608.7	0.509352	0.254676	−	0.967026i	$-0.418031\pi$
$757$	10608.7	0.509352	0.254676	+	0.967026i	$0.418031\pi$
$758$	9355.49	0.448294
$759$	4446.37	0.212639
$760$	−1038.67	−0.0495744
$761$	36246.3	1.72658	0.863290	−	0.504708i	$-0.168400\pi$
$761$	36246.3	1.72658	0.863290	+	0.504708i	$0.168400\pi$
$762$	−658.534	−0.0313073
$763$	2740.81	0.130044
$764$	14077.2	0.666616
$765$	49.7731	0.00235235
$766$	−22048.9	−1.04002
$767$	13860.6	0.652515
$768$	−768.000	−0.0360844
$769$	11694.1	0.548373	0.274187	−	0.961676i	$-0.411591\pi$
$769$	11694.1	0.548373	0.274187	+	0.961676i	$0.411591\pi$
$770$	1190.93	0.0557380
$771$	18619.0	0.869712
$772$	13720.2	0.639640
$773$	23735.6	1.10441	0.552206	−	0.833708i	$-0.313786\pi$
$773$	23735.6	1.10441	0.552206	+	0.833708i	$0.313786\pi$
$774$	−1051.91	−0.0488501
$775$	−26551.2	−1.23064
$776$	3775.96	0.174677
$777$	−3816.69	−0.176220
$778$	−16901.8	−0.778867
$779$	4729.86	0.217542
$780$	−787.253	−0.0361387
$781$	50789.0	2.32698
$782$	192.711	0.00881246
$783$	−122.271	−0.00558061
$784$	784.000	0.0357143
$785$	2833.17	0.128816
$786$	−5641.13	−0.255995
$787$	15529.4	0.703385	0.351693	−	0.936116i	$-0.385606\pi$
$787$	15529.4	0.703385	0.351693	+	0.936116i	$0.385606\pi$
$788$	13202.4	0.596850
$789$	1410.35	0.0636373
$790$	717.098	0.0322952
$791$	−11388.6	−0.511924
$792$	−4639.69	−0.208162
$793$	7553.06	0.338231
$794$	5743.06	0.256692
$795$	214.943	0.00958901
$796$	9211.75	0.410178
$797$	−1741.11	−0.0773816	−0.0386908	−	0.999251i	$-0.512319\pi$
$797$	−1741.11	−0.0773816	−0.0386908	+	0.999251i	$0.512319\pi$
$798$	−4130.80	−0.183244
$799$	−747.090	−0.0330790
$800$	3944.24	0.174312
$801$	−883.566	−0.0389754
$802$	17012.7	0.749052
$803$	15732.0	0.691370
$804$	9433.34	0.413792
$805$	212.534	0.00930540
$806$	−21410.7	−0.935682
$807$	−1619.71	−0.0706522
$808$	−4584.43	−0.199604
$809$	21360.3	0.928292	0.464146	−	0.885759i	$-0.346361\pi$
$809$	21360.3	0.928292	0.464146	+	0.885759i	$0.346361\pi$
$810$	−213.854	−0.00927663
$811$	15318.2	0.663249	0.331624	−	0.943411i	$-0.392403\pi$
$811$	15318.2	0.663249	0.331624	+	0.943411i	$0.392403\pi$
$812$	−126.800	−0.00548005
$813$	−18911.6	−0.815814
$814$	23423.6	1.00860
$815$	2679.49	0.115164
$816$	−201.090	−0.00862691
$817$	5747.65	0.246126
$818$	−20823.0	−0.890048
$819$	−3130.91	−0.133581
$820$	253.937	0.0108145
$821$	8133.72	0.345760	0.172880	−	0.984943i	$-0.444693\pi$
$821$	8133.72	0.345760	0.172880	+	0.984943i	$0.444693\pi$
$822$	18437.3	0.782331
$823$	6099.29	0.258333	0.129166	−	0.991623i	$-0.458770\pi$
$823$	6099.29	0.258333	0.129166	+	0.991623i	$0.458770\pi$
$824$	8164.93	0.345193
$825$	23828.2	1.00556
$826$	3904.65	0.164479
$827$	3831.74	0.161116	0.0805579	−	0.996750i	$-0.474330\pi$
$827$	3831.74	0.161116	0.0805579	+	0.996750i	$0.474330\pi$
$828$	−828.000	−0.0347524
$829$	−32721.0	−1.37087	−0.685434	−	0.728135i	$-0.740387\pi$
$829$	−32721.0	−1.37087	−0.685434	+	0.728135i	$0.740387\pi$
$830$	1471.44	0.0615355
$831$	7895.25	0.329582
$832$	3180.61	0.132533
$833$	205.279	0.00853843
$834$	−14547.5	−0.604001
$835$	3008.97	0.124706
$836$	25351.4	1.04880
$837$	−5816.14	−0.240185
$838$	15962.4	0.658010
$839$	16329.1	0.671923	0.335962	−	0.941876i	$-0.390939\pi$
$839$	16329.1	0.671923	0.335962	+	0.941876i	$0.390939\pi$
$840$	−221.775	−0.00910947
$841$	−24368.5	−0.999159
$842$	−18694.3	−0.765142
$843$	−21113.9	−0.862635
$844$	−4616.36	−0.188272
$845$	360.106	0.0146604
$846$	3209.93	0.130449
$847$	−19750.8	−0.801233
$848$	−868.400	−0.0351663
$849$	−2537.71	−0.102584
$850$	1032.74	0.0416739
$851$	4180.18	0.168384
$852$	−9457.88	−0.380307
$853$	2202.40	0.0884041	0.0442020	−	0.999023i	$-0.485925\pi$
$853$	2202.40	0.0884041	0.0442020	+	0.999023i	$0.485925\pi$
$854$	2127.75	0.0852578
$855$	1168.51	0.0467392
$856$	−6143.78	−0.245316
$857$	−37826.0	−1.50771	−0.753857	−	0.657038i	$-0.771809\pi$
$857$	−37826.0	−1.50771	−0.753857	+	0.657038i	$0.771809\pi$
$858$	19214.9	0.764552
$859$	37600.5	1.49350	0.746748	−	0.665108i	$-0.231614\pi$
$859$	37600.5	1.49350	0.746748	+	0.665108i	$0.231614\pi$
$860$	308.580	0.0122355
$861$	1009.91	0.0399740
$862$	116.974	0.00462197
$863$	24679.4	0.973460	0.486730	−	0.873552i	$-0.338190\pi$
$863$	24679.4	0.973460	0.486730	+	0.873552i	$0.338190\pi$
$864$	864.000	0.0340207
$865$	2317.70	0.0911032
$866$	21438.5	0.841237
$867$	14686.3	0.575288
$868$	−6031.55	−0.235857
$869$	−17502.6	−0.683239
$870$	35.8686	0.00139777
$871$	−39067.4	−1.51980
$872$	3132.35	0.121645
$873$	−4247.95	−0.164687
$874$	4524.21	0.175096
$875$	2294.05	0.0886321
$876$	−2929.60	−0.112993
$877$	47933.0	1.84559	0.922796	−	0.385290i	$-0.125899\pi$
$877$	47933.0	1.84559	0.922796	+	0.385290i	$0.125899\pi$
$878$	13965.7	0.536809
$879$	−12106.2	−0.464543
$880$	1361.07	0.0521382
$881$	−16010.3	−0.612259	−0.306130	−	0.951990i	$-0.599034\pi$
$881$	−16010.3	−0.612259	−0.306130	+	0.951990i	$0.599034\pi$
$882$	−882.000	−0.0336718
$883$	−24000.6	−0.914705	−0.457353	−	0.889285i	$-0.651202\pi$
$883$	−24000.6	−0.914705	−0.457353	+	0.889285i	$0.651202\pi$
$884$	832.797	0.0316855
$885$	−1104.53	−0.0419530
$886$	2678.70	0.101572
$887$	−32307.0	−1.22296	−0.611479	−	0.791261i	$-0.709425\pi$
$887$	−32307.0	−1.22296	−0.611479	+	0.791261i	$0.709425\pi$
$888$	−4361.93	−0.164839
$889$	768.290	0.0289850
$890$	259.197	0.00976212
$891$	5219.65	0.196257
$892$	−7603.48	−0.285407
$893$	−17539.2	−0.657251
$894$	6511.95	0.243615
$895$	4760.71	0.177802
$896$	896.000	0.0334077
$897$	3429.09	0.127641
$898$	−13291.0	−0.493905
$899$	975.509	0.0361903
$900$	−4437.27	−0.164343
$901$	−227.379	−0.00840741
$902$	−6197.97	−0.228792
$903$	1227.22	0.0452264
$904$	−13015.5	−0.478861
$905$	−1054.90	−0.0387472
$906$	−2744.07	−0.100624
$907$	41072.9	1.50364	0.751821	−	0.659367i	$-0.229176\pi$
$907$	41072.9	1.50364	0.751821	+	0.659367i	$0.229176\pi$
$908$	−19180.5	−0.701020
$909$	5157.48	0.188188
$910$	918.461	0.0334579
$911$	−15590.1	−0.566984	−0.283492	−	0.958975i	$-0.591493\pi$
$911$	−15590.1	−0.566984	−0.283492	+	0.958975i	$0.591493\pi$
$912$	−4720.92	−0.171409
$913$	−35914.2	−1.30185
$914$	20827.8	0.753746
$915$	−601.890	−0.0217463
$916$	3034.59	0.109460
$917$	6581.32	0.237006
$918$	226.226	0.00813353
$919$	−10020.8	−0.359689	−0.179845	−	0.983695i	$-0.557560\pi$
$919$	−10020.8	−0.359689	−0.179845	+	0.983695i	$0.557560\pi$
$920$	242.896	0.00870440
$921$	24346.1	0.871043
$922$	22686.2	0.810335
$923$	39169.0	1.39682
$924$	5412.98	0.192721
$925$	22401.7	0.796284
$926$	22770.4	0.808080
$927$	−9185.55	−0.325451
$928$	−144.914	−0.00512612
$929$	−20010.9	−0.706712	−0.353356	−	0.935489i	$-0.614960\pi$
$929$	−20010.9	−0.706712	−0.353356	+	0.935489i	$0.614960\pi$
$930$	1706.18	0.0601590
$931$	4819.27	0.169651
$932$	−1101.20	−0.0387029
$933$	11901.6	0.417620
$934$	−11538.0	−0.404213
$935$	356.377	0.0124650
$936$	−3578.18	−0.124954
$937$	26554.5	0.925826	0.462913	−	0.886404i	$-0.346804\pi$
$937$	26554.5	0.925826	0.462913	+	0.886404i	$0.346804\pi$
$938$	−11005.6	−0.383097
$939$	−11183.5	−0.388667
$940$	−941.643	−0.0326734
$941$	42238.9	1.46328	0.731641	−	0.681691i	$-0.238755\pi$
$941$	42238.9	1.46328	0.731641	+	0.681691i	$0.238755\pi$
$942$	12877.2	0.445395
$943$	−1106.09	−0.0381965
$944$	4462.45	0.153856
$945$	249.497	0.00858849
$946$	−7531.67	−0.258854
$947$	24891.7	0.854141	0.427071	−	0.904218i	$-0.359546\pi$
$947$	24891.7	0.854141	0.427071	+	0.904218i	$0.359546\pi$
$948$	3259.32	0.111664
$949$	12132.7	0.415009
$950$	24245.3	0.828024
$951$	−10903.4	−0.371784
$952$	234.605	0.00798697
$953$	−25956.5	−0.882280	−0.441140	−	0.897438i	$-0.645426\pi$
$953$	−25956.5	−0.882280	−0.441140	+	0.897438i	$0.645426\pi$
$954$	976.951	0.0331551
$955$	4645.78	0.157418
$956$	−19412.5	−0.656742
$957$	−875.465	−0.0295713
$958$	−14543.4	−0.490475
$959$	−21510.2	−0.724298
$960$	−253.457	−0.00852113
$961$	16611.5	0.557602
$962$	18064.6	0.605431
$963$	6911.76	0.231286
$964$	−946.860	−0.0316352
$965$	4527.98	0.151047
$966$	966.000	0.0321745
$967$	−3892.91	−0.129460	−0.0647298	−	0.997903i	$-0.520619\pi$
$967$	−3892.91	−0.129460	−0.0647298	+	0.997903i	$0.520619\pi$
$968$	−22572.3	−0.749485
$969$	−1236.11	−0.0409798
$970$	1246.15	0.0412489
$971$	54465.6	1.80009	0.900044	−	0.435800i	$-0.143534\pi$
$971$	54465.6	1.80009	0.900044	+	0.435800i	$0.143534\pi$
$972$	−972.000	−0.0320750
$973$	16972.0	0.559197
$974$	−39787.0	−1.30889
$975$	18376.6	0.603611
$976$	2431.72	0.0797513
$977$	41365.1	1.35454	0.677270	−	0.735735i	$-0.263163\pi$
$977$	41365.1	1.35454	0.677270	+	0.735735i	$0.263163\pi$
$978$	12178.7	0.398192
$979$	−6326.35	−0.206528
$980$	258.737	0.00843373
$981$	−3523.90	−0.114688
$982$	32545.5	1.05761
$983$	−39193.0	−1.27168	−0.635840	−	0.771821i	$-0.719346\pi$
$983$	−39193.0	−1.27168	−0.635840	+	0.771821i	$0.719346\pi$
$984$	1154.18	0.0373923
$985$	4357.10	0.140943
$986$	−37.9437	−0.00122553
$987$	−3744.92	−0.120772
$988$	19551.3	0.629564
$989$	−1344.10	−0.0432154
$990$	−1531.20	−0.0491563
$991$	−22273.1	−0.713955	−0.356977	−	0.934113i	$-0.616193\pi$
$991$	−22273.1	−0.713955	−0.356977	+	0.934113i	$0.616193\pi$
$992$	−6893.20	−0.220624
$993$	−20691.1	−0.661241
$994$	11034.2	0.352096
$995$	3040.08	0.0968613
$996$	6687.92	0.212766
$997$	52161.1	1.65693	0.828465	−	0.560041i	$-0.189215\pi$
$997$	52161.1	1.65693	0.828465	+	0.560041i	$0.189215\pi$
$998$	−6699.49	−0.212494
$999$	4907.17	0.155411

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.m.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.m.1.3	✓	5	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +1.32009 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +1.32009 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -2.64018 q^{10} +64.4402 q^{11} -12.0000 q^{12} +49.6970 q^{13} +14.0000 q^{14} -3.96026 q^{15} +16.0000 q^{16} +4.18938 q^{17} -18.0000 q^{18} +98.3525 q^{19} +5.28035 q^{20} +21.0000 q^{21} -128.880 q^{22} -23.0000 q^{23} +24.0000 q^{24} -123.257 q^{25} -99.3940 q^{26} -27.0000 q^{27} -28.0000 q^{28} +4.52857 q^{29} +7.92053 q^{30} +215.412 q^{31} -32.0000 q^{32} -193.321 q^{33} -8.37875 q^{34} -9.24062 q^{35} +36.0000 q^{36} -181.747 q^{37} -196.705 q^{38} -149.091 q^{39} -10.5607 q^{40} +48.0909 q^{41} -42.0000 q^{42} +58.4393 q^{43} +257.761 q^{44} +11.8808 q^{45} +46.0000 q^{46} -178.330 q^{47} -48.0000 q^{48} +49.0000 q^{49} +246.515 q^{50} -12.5681 q^{51} +198.788 q^{52} -54.2750 q^{53} +54.0000 q^{54} +85.0667 q^{55} +56.0000 q^{56} -295.057 q^{57} -9.05713 q^{58} +278.903 q^{59} -15.8411 q^{60} +151.982 q^{61} -430.825 q^{62} -63.0000 q^{63} +64.0000 q^{64} +65.6044 q^{65} +386.641 q^{66} -786.112 q^{67} +16.7575 q^{68} +69.0000 q^{69} +18.4812 q^{70} +788.157 q^{71} -72.0000 q^{72} +244.133 q^{73} +363.494 q^{74} +369.772 q^{75} +393.410 q^{76} -451.081 q^{77} +298.182 q^{78} -271.610 q^{79} +21.1214 q^{80} +81.0000 q^{81} -96.1818 q^{82} -557.327 q^{83} +84.0000 q^{84} +5.53035 q^{85} -116.879 q^{86} -13.5857 q^{87} -515.521 q^{88} -98.1740 q^{89} -23.7616 q^{90} -347.879 q^{91} -92.0000 q^{92} -646.237 q^{93} +356.659 q^{94} +129.834 q^{95} +96.0000 q^{96} -471.995 q^{97} -98.0000 q^{98} +579.962 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 + 10 * q^5 + 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9} - 20 q^{10} + 4 q^{11} - 60 q^{12} + 24 q^{13} + 70 q^{14} - 30 q^{15} + 80 q^{16} + 28 q^{17} - 90 q^{18} - 160 q^{19} + 40 q^{20} + 105 q^{21} - 8 q^{22} - 115 q^{23} + 120 q^{24} + 219 q^{25} - 48 q^{26} - 135 q^{27} - 140 q^{28} + 79 q^{29} + 60 q^{30} - 162 q^{31} - 160 q^{32} - 12 q^{33} - 56 q^{34} - 70 q^{35} + 180 q^{36} + 301 q^{37} + 320 q^{38} - 72 q^{39} - 80 q^{40} + 251 q^{41} - 210 q^{42} - 380 q^{43} + 16 q^{44} + 90 q^{45} + 230 q^{46} - 505 q^{47} - 240 q^{48} + 245 q^{49} - 438 q^{50} - 84 q^{51} + 96 q^{52} + 93 q^{53} + 270 q^{54} - 503 q^{55} + 280 q^{56} + 480 q^{57} - 158 q^{58} + 637 q^{59} - 120 q^{60} - 679 q^{61} + 324 q^{62} - 315 q^{63} + 320 q^{64} + 961 q^{65} + 24 q^{66} - 1483 q^{67} + 112 q^{68} + 345 q^{69} + 140 q^{70} + 95 q^{71} - 360 q^{72} - 1310 q^{73} - 602 q^{74} - 657 q^{75} - 640 q^{76} - 28 q^{77} + 144 q^{78} + 494 q^{79} + 160 q^{80} + 405 q^{81} - 502 q^{82} - 482 q^{83} + 420 q^{84} - 291 q^{85} + 760 q^{86} - 237 q^{87} - 32 q^{88} + 661 q^{89} - 180 q^{90} - 168 q^{91} - 460 q^{92} + 486 q^{93} + 1010 q^{94} - 629 q^{95} + 480 q^{96} - 1905 q^{97} - 490 q^{98} + 36 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 + 10 * q^5 + 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9 - 20 * q^10 + 4 * q^11 - 60 * q^12 + 24 * q^13 + 70 * q^14 - 30 * q^15 + 80 * q^16 + 28 * q^17 - 90 * q^18 - 160 * q^19 + 40 * q^20 + 105 * q^21 - 8 * q^22 - 115 * q^23 + 120 * q^24 + 219 * q^25 - 48 * q^26 - 135 * q^27 - 140 * q^28 + 79 * q^29 + 60 * q^30 - 162 * q^31 - 160 * q^32 - 12 * q^33 - 56 * q^34 - 70 * q^35 + 180 * q^36 + 301 * q^37 + 320 * q^38 - 72 * q^39 - 80 * q^40 + 251 * q^41 - 210 * q^42 - 380 * q^43 + 16 * q^44 + 90 * q^45 + 230 * q^46 - 505 * q^47 - 240 * q^48 + 245 * q^49 - 438 * q^50 - 84 * q^51 + 96 * q^52 + 93 * q^53 + 270 * q^54 - 503 * q^55 + 280 * q^56 + 480 * q^57 - 158 * q^58 + 637 * q^59 - 120 * q^60 - 679 * q^61 + 324 * q^62 - 315 * q^63 + 320 * q^64 + 961 * q^65 + 24 * q^66 - 1483 * q^67 + 112 * q^68 + 345 * q^69 + 140 * q^70 + 95 * q^71 - 360 * q^72 - 1310 * q^73 - 602 * q^74 - 657 * q^75 - 640 * q^76 - 28 * q^77 + 144 * q^78 + 494 * q^79 + 160 * q^80 + 405 * q^81 - 502 * q^82 - 482 * q^83 + 420 * q^84 - 291 * q^85 + 760 * q^86 - 237 * q^87 - 32 * q^88 + 661 * q^89 - 180 * q^90 - 168 * q^91 - 460 * q^92 + 486 * q^93 + 1010 * q^94 - 629 * q^95 + 480 * q^96 - 1905 * q^97 - 490 * q^98 + 36 * q^99

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