LMFDB - Embedded newform 2166.4.a.s.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2166,4,Mod(1,2166)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2166, 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("2166.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2166 = 2 \cdot 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2166.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:	$127.798137072$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.1524.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 7x + 1 $ x^3 - x^2 - 7*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	no (minimal twist has level 114)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.13264$ of defining polynomial
Character	$\chi$	$=$	2166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -12.9884 q^{5} +6.00000 q^{6} -25.6033 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -12.9884 q^{5} +6.00000 q^{6} -25.6033 q^{7} -8.00000 q^{8} +9.00000 q^{9} +25.9768 q^{10} +26.7726 q^{11} -12.0000 q^{12} -8.59165 q^{13} +51.2065 q^{14} +38.9652 q^{15} +16.0000 q^{16} +8.16936 q^{17} -18.0000 q^{18} -51.9536 q^{20} +76.8098 q^{21} -53.5452 q^{22} +156.900 q^{23} +24.0000 q^{24} +43.6984 q^{25} +17.1833 q^{26} -27.0000 q^{27} -102.413 q^{28} -207.357 q^{29} -77.9304 q^{30} +94.5197 q^{31} -32.0000 q^{32} -80.3178 q^{33} -16.3387 q^{34} +332.545 q^{35} +36.0000 q^{36} +197.387 q^{37} +25.7749 q^{39} +103.907 q^{40} -376.738 q^{41} -153.620 q^{42} -508.244 q^{43} +107.090 q^{44} -116.896 q^{45} -313.800 q^{46} -366.487 q^{47} -48.0000 q^{48} +312.527 q^{49} -87.3968 q^{50} -24.5081 q^{51} -34.3666 q^{52} -203.329 q^{53} +54.0000 q^{54} -347.733 q^{55} +204.826 q^{56} +414.715 q^{58} +592.204 q^{59} +155.861 q^{60} -509.060 q^{61} -189.039 q^{62} -230.429 q^{63} +64.0000 q^{64} +111.592 q^{65} +160.636 q^{66} -250.719 q^{67} +32.6774 q^{68} -470.701 q^{69} -665.090 q^{70} -115.436 q^{71} -72.0000 q^{72} -832.671 q^{73} -394.775 q^{74} -131.095 q^{75} -685.466 q^{77} -51.5499 q^{78} +369.429 q^{79} -207.814 q^{80} +81.0000 q^{81} +753.476 q^{82} -1288.29 q^{83} +307.239 q^{84} -106.107 q^{85} +1016.49 q^{86} +622.072 q^{87} -214.181 q^{88} +61.0743 q^{89} +233.791 q^{90} +219.974 q^{91} +627.601 q^{92} -283.559 q^{93} +732.975 q^{94} +96.0000 q^{96} +247.510 q^{97} -625.053 q^{98} +240.954 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 6 q^{2} - 9 q^{3} + 12 q^{4} + 2 q^{5} + 18 q^{6} - 17 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q - 6 * q^2 - 9 * q^3 + 12 * q^4 + 2 * q^5 + 18 * q^6 - 17 * q^7 - 24 * q^8 + 27 * q^9	\( 3 q - 6 q^{2} - 9 q^{3} + 12 q^{4} + 2 q^{5} + 18 q^{6} - 17 q^{7} - 24 q^{8} + 27 q^{9} - 4 q^{10} - 52 q^{11} - 36 q^{12} + 75 q^{13} + 34 q^{14} - 6 q^{15} + 48 q^{16} - 48 q^{17} - 54 q^{18} + 8 q^{20} + 51 q^{21} + 104 q^{22} - 238 q^{23} + 72 q^{24} + 229 q^{25} - 150 q^{26} - 81 q^{27} - 68 q^{28} - 8 q^{29} + 12 q^{30} + 107 q^{31} - 96 q^{32} + 156 q^{33} + 96 q^{34} - 294 q^{35} + 108 q^{36} + 305 q^{37} - 225 q^{39} - 16 q^{40} + 16 q^{41} - 102 q^{42} - 331 q^{43} - 208 q^{44} + 18 q^{45} + 476 q^{46} - 766 q^{47} - 144 q^{48} + 1142 q^{49} - 458 q^{50} + 144 q^{51} + 300 q^{52} - 118 q^{53} + 162 q^{54} - 1400 q^{55} + 136 q^{56} + 16 q^{58} + 936 q^{59} - 24 q^{60} - 399 q^{61} - 214 q^{62} - 153 q^{63} + 192 q^{64} + 370 q^{65} - 312 q^{66} + 61 q^{67} - 192 q^{68} + 714 q^{69} + 588 q^{70} + 974 q^{71} - 216 q^{72} + 91 q^{73} - 610 q^{74} - 687 q^{75} - 36 q^{77} + 450 q^{78} - 321 q^{79} + 32 q^{80} + 243 q^{81} - 32 q^{82} - 2148 q^{83} + 204 q^{84} - 1680 q^{85} + 662 q^{86} + 24 q^{87} + 416 q^{88} + 1116 q^{89} - 36 q^{90} + 1367 q^{91} - 952 q^{92} - 321 q^{93} + 1532 q^{94} + 288 q^{96} + 1382 q^{97} - 2284 q^{98} - 468 q^{99}+O(q^{100}) \) 3 * q - 6 * q^2 - 9 * q^3 + 12 * q^4 + 2 * q^5 + 18 * q^6 - 17 * q^7 - 24 * q^8 + 27 * q^9 - 4 * q^10 - 52 * q^11 - 36 * q^12 + 75 * q^13 + 34 * q^14 - 6 * q^15 + 48 * q^16 - 48 * q^17 - 54 * q^18 + 8 * q^20 + 51 * q^21 + 104 * q^22 - 238 * q^23 + 72 * q^24 + 229 * q^25 - 150 * q^26 - 81 * q^27 - 68 * q^28 - 8 * q^29 + 12 * q^30 + 107 * q^31 - 96 * q^32 + 156 * q^33 + 96 * q^34 - 294 * q^35 + 108 * q^36 + 305 * q^37 - 225 * q^39 - 16 * q^40 + 16 * q^41 - 102 * q^42 - 331 * q^43 - 208 * q^44 + 18 * q^45 + 476 * q^46 - 766 * q^47 - 144 * q^48 + 1142 * q^49 - 458 * q^50 + 144 * q^51 + 300 * q^52 - 118 * q^53 + 162 * q^54 - 1400 * q^55 + 136 * q^56 + 16 * q^58 + 936 * q^59 - 24 * q^60 - 399 * q^61 - 214 * q^62 - 153 * q^63 + 192 * q^64 + 370 * q^65 - 312 * q^66 + 61 * q^67 - 192 * q^68 + 714 * q^69 + 588 * q^70 + 974 * q^71 - 216 * q^72 + 91 * q^73 - 610 * q^74 - 687 * q^75 - 36 * q^77 + 450 * q^78 - 321 * q^79 + 32 * q^80 + 243 * q^81 - 32 * q^82 - 2148 * q^83 + 204 * q^84 - 1680 * q^85 + 662 * q^86 + 24 * q^87 + 416 * q^88 + 1116 * q^89 - 36 * q^90 + 1367 * q^91 - 952 * q^92 - 321 * q^93 + 1532 * q^94 + 288 * q^96 + 1382 * q^97 - 2284 * q^98 - 468 * 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
$5$	−12.9884	−1.16172	−0.580859	−	0.814004i	$-0.697283\pi$
$5$	−12.9884	−1.16172	−0.580859	+	0.814004i	$0.697283\pi$
$6$	6.00000	0.408248
$7$	−25.6033	−1.38245	−0.691223	−	0.722642i	$-0.742928\pi$
$7$	−25.6033	−1.38245	−0.691223	+	0.722642i	$0.742928\pi$
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	25.9768	0.821458
$11$	26.7726	0.733841	0.366920	−	0.930252i	$-0.380412\pi$
$11$	26.7726	0.733841	0.366920	+	0.930252i	$0.380412\pi$
$12$	−12.0000	−0.288675
$13$	−8.59165	−0.183300	−0.0916498	−	0.995791i	$-0.529214\pi$
$13$	−8.59165	−0.183300	−0.0916498	+	0.995791i	$0.529214\pi$
$14$	51.2065	0.977537
$15$	38.9652	0.670718
$16$	16.0000	0.250000
$17$	8.16936	0.116551	0.0582753	−	0.998301i	$-0.481440\pi$
$17$	8.16936	0.116551	0.0582753	+	0.998301i	$0.481440\pi$
$18$	−18.0000	−0.235702
$19$	0	0
$19$	0	0
$20$	−51.9536	−0.580859
$21$	76.8098	0.798155
$22$	−53.5452	−0.518904
$23$	156.900	1.42243	0.711217	−	0.702973i	$-0.248145\pi$
$23$	156.900	1.42243	0.711217	+	0.702973i	$0.248145\pi$
$24$	24.0000	0.204124
$25$	43.6984	0.349587
$26$	17.1833	0.129612
$27$	−27.0000	−0.192450
$28$	−102.413	−0.691223
$29$	−207.357	−1.32777	−0.663884	−	0.747835i	$-0.731093\pi$
$29$	−207.357	−1.32777	−0.663884	+	0.747835i	$0.731093\pi$
$30$	−77.9304	−0.474269
$31$	94.5197	0.547621	0.273810	−	0.961784i	$-0.411716\pi$
$31$	94.5197	0.547621	0.273810	+	0.961784i	$0.411716\pi$
$32$	−32.0000	−0.176777
$33$	−80.3178	−0.423683
$34$	−16.3387	−0.0824138
$35$	332.545	1.60601
$36$	36.0000	0.166667
$37$	197.387	0.877035	0.438517	−	0.898723i	$-0.355504\pi$
$37$	197.387	0.877035	0.438517	+	0.898723i	$0.355504\pi$
$38$	0	0
$39$	25.7749	0.105828
$40$	103.907	0.410729
$41$	−376.738	−1.43504	−0.717519	−	0.696539i	$-0.754722\pi$
$41$	−376.738	−1.43504	−0.717519	+	0.696539i	$0.754722\pi$
$42$	−153.620	−0.564381
$43$	−508.244	−1.80248	−0.901238	−	0.433325i	$-0.857340\pi$
$43$	−508.244	−1.80248	−0.901238	+	0.433325i	$0.857340\pi$
$44$	107.090	0.366920
$45$	−116.896	−0.387239
$46$	−313.800	−1.00581
$47$	−366.487	−1.13740	−0.568699	−	0.822546i	$-0.692553\pi$
$47$	−366.487	−1.13740	−0.568699	+	0.822546i	$0.692553\pi$
$48$	−48.0000	−0.144338
$49$	312.527	0.911156
$50$	−87.3968	−0.247196
$51$	−24.5081	−0.0672906
$52$	−34.3666	−0.0916498
$53$	−203.329	−0.526970	−0.263485	−	0.964663i	$-0.584872\pi$
$53$	−203.329	−0.526970	−0.263485	+	0.964663i	$0.584872\pi$
$54$	54.0000	0.136083
$55$	−347.733	−0.852516
$56$	204.826	0.488768
$57$	0	0
$58$	414.715	0.938874
$59$	592.204	1.30675	0.653376	−	0.757033i	$-0.273352\pi$
$59$	592.204	1.30675	0.653376	+	0.757033i	$0.273352\pi$
$60$	155.861	0.335359
$61$	−509.060	−1.06850	−0.534250	−	0.845327i	$-0.679406\pi$
$61$	−509.060	−1.06850	−0.534250	+	0.845327i	$0.679406\pi$
$62$	−189.039	−0.387226
$63$	−230.429	−0.460815
$64$	64.0000	0.125000
$65$	111.592	0.212942
$66$	160.636	0.299589
$67$	−250.719	−0.457167	−0.228584	−	0.973524i	$-0.573409\pi$
$67$	−250.719	−0.457167	−0.228584	+	0.973524i	$0.573409\pi$
$68$	32.6774	0.0582753
$69$	−470.701	−0.821242
$70$	−665.090	−1.13562
$71$	−115.436	−0.192954	−0.0964771	−	0.995335i	$-0.530757\pi$
$71$	−115.436	−0.192954	−0.0964771	+	0.995335i	$0.530757\pi$
$72$	−72.0000	−0.117851
$73$	−832.671	−1.33502	−0.667512	−	0.744599i	$-0.732641\pi$
$73$	−832.671	−1.33502	−0.667512	+	0.744599i	$0.732641\pi$
$74$	−394.775	−0.620157
$75$	−131.095	−0.201834
$76$	0	0
$77$	−685.466	−1.01449
$78$	−51.5499	−0.0748318
$79$	369.429	0.526127	0.263064	−	0.964778i	$-0.415267\pi$
$79$	369.429	0.526127	0.263064	+	0.964778i	$0.415267\pi$
$80$	−207.814	−0.290429
$81$	81.0000	0.111111
$82$	753.476	1.01473
$83$	−1288.29	−1.70371	−0.851854	−	0.523780i	$-0.824521\pi$
$83$	−1288.29	−1.70371	−0.851854	+	0.523780i	$0.824521\pi$
$84$	307.239	0.399078
$85$	−106.107	−0.135399
$86$	1016.49	1.27454
$87$	622.072	0.766588
$88$	−214.181	−0.259452
$89$	61.0743	0.0727401	0.0363700	−	0.999338i	$-0.488421\pi$
$89$	61.0743	0.0727401	0.0363700	+	0.999338i	$0.488421\pi$
$90$	233.791	0.273819
$91$	219.974	0.253402
$92$	627.601	0.711217
$93$	−283.559	−0.316169
$94$	732.975	0.804261
$95$	0	0
$96$	96.0000	0.102062
$97$	247.510	0.259081	0.129541	−	0.991574i	$-0.458650\pi$
$97$	247.510	0.259081	0.129541	+	0.991574i	$0.458650\pi$
$98$	−625.053	−0.644285
$99$	240.954	0.244614
$100$	174.794	0.174794
$101$	−846.012	−0.833478	−0.416739	−	0.909026i	$-0.636827\pi$
$101$	−846.012	−0.833478	−0.416739	+	0.909026i	$0.636827\pi$
$102$	49.0162	0.0475816
$103$	−1422.55	−1.36085	−0.680427	−	0.732816i	$-0.738206\pi$
$103$	−1422.55	−1.36085	−0.680427	+	0.732816i	$0.738206\pi$
$104$	68.7332	0.0648062
$105$	−997.636	−0.927231
$106$	406.659	0.372624
$107$	286.239	0.258615	0.129307	−	0.991605i	$-0.458725\pi$
$107$	286.239	0.258615	0.129307	+	0.991605i	$0.458725\pi$
$108$	−108.000	−0.0962250
$109$	−32.2854	−0.0283705	−0.0141852	−	0.999899i	$-0.504515\pi$
$109$	−32.2854	−0.0283705	−0.0141852	+	0.999899i	$0.504515\pi$
$110$	695.467	0.602820
$111$	−592.162	−0.506356
$112$	−409.652	−0.345611
$113$	−297.098	−0.247333	−0.123666	−	0.992324i	$-0.539465\pi$
$113$	−297.098	−0.247333	−0.123666	+	0.992324i	$0.539465\pi$
$114$	0	0
$115$	−2037.88	−1.65247
$116$	−829.429	−0.663884
$117$	−77.3248	−0.0610999
$118$	−1184.41	−0.924014
$119$	−209.162	−0.161125
$120$	−311.721	−0.237135
$121$	−614.227	−0.461478
$122$	1018.12	0.755543
$123$	1130.21	0.828520
$124$	378.079	0.273810
$125$	1055.98	0.755596
$126$	460.859	0.325846
$127$	2667.19	1.86358	0.931792	−	0.362994i	$-0.118245\pi$
$127$	2667.19	1.86358	0.931792	+	0.362994i	$0.118245\pi$
$128$	−128.000	−0.0883883
$129$	1524.73	1.04066
$130$	−223.183	−0.150573
$131$	822.276	0.548417	0.274208	−	0.961670i	$-0.411584\pi$
$131$	822.276	0.548417	0.274208	+	0.961670i	$0.411584\pi$
$132$	−321.271	−0.211842
$133$	0	0
$134$	501.438	0.323266
$135$	350.687	0.223573
$136$	−65.3549	−0.0412069
$137$	−2445.22	−1.52489	−0.762443	−	0.647055i	$-0.776000\pi$
$137$	−2445.22	−1.52489	−0.762443	+	0.647055i	$0.776000\pi$
$138$	941.401	0.580706
$139$	1504.34	0.917961	0.458980	−	0.888446i	$-0.348215\pi$
$139$	1504.34	0.917961	0.458980	+	0.888446i	$0.348215\pi$
$140$	1330.18	0.803006
$141$	1099.46	0.656677
$142$	230.872	0.136439
$143$	−230.021	−0.134513
$144$	144.000	0.0833333
$145$	2693.24	1.54249
$146$	1665.34	0.944004
$147$	−937.580	−0.526056
$148$	789.550	0.438517
$149$	−720.747	−0.396281	−0.198141	−	0.980174i	$-0.563490\pi$
$149$	−720.747	−0.396281	−0.198141	+	0.980174i	$0.563490\pi$
$150$	262.191	0.142718
$151$	1801.25	0.970752	0.485376	−	0.874306i	$-0.338683\pi$
$151$	1801.25	0.970752	0.485376	+	0.874306i	$0.338683\pi$
$152$	0	0
$153$	73.5243	0.0388502
$154$	1370.93	0.717356
$155$	−1227.66	−0.636180
$156$	103.100	0.0529140
$157$	3829.11	1.94647	0.973236	−	0.229808i	$-0.0738097\pi$
$157$	3829.11	1.94647	0.973236	+	0.229808i	$0.0738097\pi$
$158$	−738.859	−0.372028
$159$	609.988	0.304247
$160$	415.629	0.205365
$161$	−4017.16	−1.96644
$162$	−162.000	−0.0785674
$163$	−956.496	−0.459623	−0.229812	−	0.973235i	$-0.573811\pi$
$163$	−956.496	−0.459623	−0.229812	+	0.973235i	$0.573811\pi$
$164$	−1506.95	−0.717519
$165$	1043.20	0.492200
$166$	2576.57	1.20470
$167$	−2779.77	−1.28805	−0.644027	−	0.765003i	$-0.722737\pi$
$167$	−2779.77	−1.28805	−0.644027	+	0.765003i	$0.722737\pi$
$168$	−614.478	−0.282191
$169$	−2123.18	−0.966401
$170$	212.214	0.0957415
$171$	0	0
$172$	−2032.97	−0.901238
$173$	−309.552	−0.136039	−0.0680196	−	0.997684i	$-0.521668\pi$
$173$	−309.552	−0.136039	−0.0680196	+	0.997684i	$0.521668\pi$
$174$	−1244.14	−0.542059
$175$	−1118.82	−0.483286
$176$	428.362	0.183460
$177$	−1776.61	−0.754454
$178$	−122.149	−0.0514350
$179$	4650.29	1.94178	0.970890	−	0.239524i	$-0.0769913\pi$
$179$	4650.29	1.94178	0.970890	+	0.239524i	$0.0769913\pi$
$180$	−467.582	−0.193620
$181$	−269.728	−0.110767	−0.0553833	−	0.998465i	$-0.517638\pi$
$181$	−269.728	−0.110767	−0.0553833	+	0.998465i	$0.517638\pi$
$182$	−439.948	−0.179182
$183$	1527.18	0.616899
$184$	−1255.20	−0.502906
$185$	−2563.75	−1.01887
$186$	567.118	0.223565
$187$	218.715	0.0855296
$188$	−1465.95	−0.568699
$189$	691.288	0.266052
$190$	0	0
$191$	−1949.96	−0.738715	−0.369357	−	0.929287i	$-0.620422\pi$
$191$	−1949.96	−0.738715	−0.369357	+	0.929287i	$0.620422\pi$
$192$	−192.000	−0.0721688
$193$	2931.30	1.09326	0.546631	−	0.837374i	$-0.315910\pi$
$193$	2931.30	1.09326	0.546631	+	0.837374i	$0.315910\pi$
$194$	−495.021	−0.183198
$195$	−334.775	−0.122942
$196$	1250.11	0.455578
$197$	−1236.48	−0.447186	−0.223593	−	0.974683i	$-0.571779\pi$
$197$	−1236.48	−0.447186	−0.223593	+	0.974683i	$0.571779\pi$
$198$	−481.907	−0.172968
$199$	−4509.01	−1.60621	−0.803103	−	0.595840i	$-0.796819\pi$
$199$	−4509.01	−1.60621	−0.803103	+	0.595840i	$0.796819\pi$
$200$	−349.587	−0.123598
$201$	752.157	0.263946
$202$	1692.02	0.589358
$203$	5309.02	1.83557
$204$	−98.0323	−0.0336453
$205$	4893.22	1.66711
$206$	2845.10	0.962269
$207$	1412.10	0.474144
$208$	−137.466	−0.0458249
$209$	0	0
$210$	1995.27	0.655651
$211$	−1.90470	−0.000621444 0	−0.000310722	−	1.00000i	$-0.500099\pi$
$211$	−1.90470	−0.000621444 0	−0.000310722		1.00000i	$0.500099\pi$
$212$	−813.317	−0.263485
$213$	346.308	0.111402
$214$	−572.479	−0.182868
$215$	6601.27	2.09397
$216$	216.000	0.0680414
$217$	−2420.01	−0.757056
$218$	64.5708	0.0200610
$219$	2498.01	0.770776
$220$	−1390.93	−0.426258
$221$	−70.1883	−0.0213637
$222$	1184.32	0.358048
$223$	−4660.23	−1.39943	−0.699713	−	0.714424i	$-0.746689\pi$
$223$	−4660.23	−1.39943	−0.699713	+	0.714424i	$0.746689\pi$
$224$	819.304	0.244384
$225$	393.286	0.116529
$226$	594.195	0.174891
$227$	−4045.15	−1.18276	−0.591380	−	0.806393i	$-0.701416\pi$
$227$	−4045.15	−1.18276	−0.591380	+	0.806393i	$0.701416\pi$
$228$	0	0
$229$	5062.73	1.46094	0.730468	−	0.682947i	$-0.239302\pi$
$229$	5062.73	1.46094	0.730468	+	0.682947i	$0.239302\pi$
$230$	4075.76	1.16847
$231$	2056.40	0.585719
$232$	1658.86	0.469437
$233$	433.089	0.121771	0.0608854	−	0.998145i	$-0.480608\pi$
$233$	433.089	0.121771	0.0608854	+	0.998145i	$0.480608\pi$
$234$	154.650	0.0432041
$235$	4760.08	1.32133
$236$	2368.82	0.653376
$237$	−1108.29	−0.303760
$238$	418.325	0.113933
$239$	−4165.22	−1.12730	−0.563652	−	0.826012i	$-0.690604\pi$
$239$	−4165.22	−1.12730	−0.563652	+	0.826012i	$0.690604\pi$
$240$	623.443	0.167679
$241$	4169.42	1.11442	0.557212	−	0.830370i	$-0.311871\pi$
$241$	4169.42	1.11442	0.557212	+	0.830370i	$0.311871\pi$
$242$	1228.45	0.326314
$243$	−243.000	−0.0641500
$244$	−2036.24	−0.534250
$245$	−4059.22	−1.05851
$246$	−2260.43	−0.585852
$247$	0	0
$248$	−756.158	−0.193613
$249$	3864.86	0.983636
$250$	−2111.95	−0.534287
$251$	−7132.25	−1.79356	−0.896780	−	0.442477i	$-0.854100\pi$
$251$	−7132.25	−1.79356	−0.896780	+	0.442477i	$0.854100\pi$
$252$	−921.717	−0.230408
$253$	4200.63	1.04384
$254$	−5334.38	−1.31775
$255$	318.321	0.0781726
$256$	256.000	0.0625000
$257$	−1077.52	−0.261532	−0.130766	−	0.991413i	$-0.541744\pi$
$257$	−1077.52	−0.261532	−0.130766	+	0.991413i	$0.541744\pi$
$258$	−3049.46	−0.735857
$259$	−5053.76	−1.21245
$260$	446.367	0.106471
$261$	−1866.22	−0.442590
$262$	−1644.55	−0.387789
$263$	2489.16	0.583606	0.291803	−	0.956478i	$-0.405745\pi$
$263$	2489.16	0.583606	0.291803	+	0.956478i	$0.405745\pi$
$264$	642.543	0.149795
$265$	2640.92	0.612191
$266$	0	0
$267$	−183.223	−0.0419965
$268$	−1002.88	−0.228584
$269$	−6181.28	−1.40104	−0.700519	−	0.713634i	$-0.747048\pi$
$269$	−6181.28	−1.40104	−0.700519	+	0.713634i	$0.747048\pi$
$270$	−701.373	−0.158090
$271$	6032.71	1.35226	0.676128	−	0.736784i	$-0.263657\pi$
$271$	6032.71	1.35226	0.676128	+	0.736784i	$0.263657\pi$
$272$	130.710	0.0291377
$273$	−659.923	−0.146302
$274$	4890.45	1.07826
$275$	1169.92	0.256541
$276$	−1882.80	−0.410621
$277$	912.717	0.197978	0.0989889	−	0.995089i	$-0.468439\pi$
$277$	912.717	0.197978	0.0989889	+	0.995089i	$0.468439\pi$
$278$	−3008.68	−0.649096
$279$	850.677	0.182540
$280$	−2660.36	−0.567811
$281$	−334.886	−0.0710948	−0.0355474	−	0.999368i	$-0.511317\pi$
$281$	−334.886	−0.0710948	−0.0355474	+	0.999368i	$0.511317\pi$
$282$	−2198.92	−0.464340
$283$	−2776.94	−0.583293	−0.291646	−	0.956526i	$-0.594203\pi$
$283$	−2776.94	−0.583293	−0.291646	+	0.956526i	$0.594203\pi$
$284$	−461.744	−0.0964771
$285$	0	0
$286$	460.042	0.0951149
$287$	9645.72	1.98386
$288$	−288.000	−0.0589256
$289$	−4846.26	−0.986416
$290$	−5386.48	−1.09071
$291$	−742.531	−0.149581
$292$	−3330.68	−0.667512
$293$	−3067.85	−0.611692	−0.305846	−	0.952081i	$-0.598939\pi$
$293$	−3067.85	−0.611692	−0.305846	+	0.952081i	$0.598939\pi$
$294$	1875.16	0.371978
$295$	−7691.78	−1.51808
$296$	−1579.10	−0.310079
$297$	−722.861	−0.141228
$298$	1441.49	0.280213
$299$	−1348.03	−0.260731
$300$	−524.381	−0.100917
$301$	13012.7	2.49182
$302$	−3602.50	−0.686425
$303$	2538.04	0.481209
$304$	0	0
$305$	6611.88	1.24129
$306$	−147.049	−0.0274713
$307$	−7487.81	−1.39203	−0.696013	−	0.718029i	$-0.745044\pi$
$307$	−7487.81	−1.39203	−0.696013	+	0.718029i	$0.745044\pi$
$308$	−2741.86	−0.507247
$309$	4267.65	0.785690
$310$	2455.32	0.449847
$311$	−6681.88	−1.21831	−0.609156	−	0.793051i	$-0.708492\pi$
$311$	−6681.88	−1.21831	−0.609156	+	0.793051i	$0.708492\pi$
$312$	−206.200	−0.0374159
$313$	8162.02	1.47394	0.736972	−	0.675923i	$-0.236255\pi$
$313$	8162.02	1.47394	0.736972	+	0.675923i	$0.236255\pi$
$314$	−7658.22	−1.37636
$315$	2992.91	0.535337
$316$	1477.72	0.263064
$317$	−2839.54	−0.503106	−0.251553	−	0.967844i	$-0.580941\pi$
$317$	−2839.54	−0.503106	−0.251553	+	0.967844i	$0.580941\pi$
$318$	−1219.98	−0.215135
$319$	−5551.50	−0.974371
$320$	−831.257	−0.145215
$321$	−858.718	−0.149311
$322$	8034.31	1.39048
$323$	0	0
$324$	324.000	0.0555556
$325$	−375.442	−0.0640792
$326$	1912.99	0.325003
$327$	96.8562	0.0163797
$328$	3013.90	0.507363
$329$	9383.27	1.57239
$330$	−2086.40	−0.348038
$331$	11056.2	1.83597	0.917984	−	0.396617i	$-0.129816\pi$
$331$	11056.2	1.83597	0.917984	+	0.396617i	$0.129816\pi$
$332$	−5153.14	−0.851854
$333$	1776.49	0.292345
$334$	5559.54	0.910791
$335$	3256.44	0.531099
$336$	1228.96	0.199539
$337$	−5050.33	−0.816347	−0.408174	−	0.912904i	$-0.633834\pi$
$337$	−5050.33	−0.816347	−0.408174	+	0.912904i	$0.633834\pi$
$338$	4246.37	0.683349
$339$	891.293	0.142798
$340$	−424.428	−0.0676995
$341$	2530.54	0.401866
$342$	0	0
$343$	780.217	0.122822
$344$	4065.95	0.637271
$345$	6113.65	0.954051
$346$	619.104	0.0961943
$347$	−6014.85	−0.930531	−0.465265	−	0.885171i	$-0.654041\pi$
$347$	−6014.85	−0.930531	−0.465265	+	0.885171i	$0.654041\pi$
$348$	2488.29	0.383294
$349$	−2514.51	−0.385669	−0.192834	−	0.981231i	$-0.561768\pi$
$349$	−2514.51	−0.385669	−0.192834	+	0.981231i	$0.561768\pi$
$350$	2237.64	0.341735
$351$	231.975	0.0352760
$352$	−856.724	−0.129726
$353$	4578.03	0.690266	0.345133	−	0.938554i	$-0.387834\pi$
$353$	4578.03	0.690266	0.345133	+	0.938554i	$0.387834\pi$
$354$	3553.23	0.533480
$355$	1499.33	0.224158
$356$	244.297	0.0363700
$357$	627.487	0.0930255
$358$	−9300.57	−1.37305
$359$	7972.44	1.17206	0.586029	−	0.810290i	$-0.300690\pi$
$359$	7972.44	1.17206	0.586029	+	0.810290i	$0.300690\pi$
$360$	935.164	0.136910
$361$	0	0
$362$	539.456	0.0783238
$363$	1842.68	0.266434
$364$	879.897	0.126701
$365$	10815.1	1.55092
$366$	−3054.36	−0.436213
$367$	5465.50	0.777376	0.388688	−	0.921369i	$-0.372928\pi$
$367$	5465.50	0.777376	0.388688	+	0.921369i	$0.372928\pi$
$368$	2510.40	0.355608
$369$	−3390.64	−0.478346
$370$	5127.49	0.720447
$371$	5205.89	0.728508
$372$	−1134.24	−0.158084
$373$	9245.54	1.28342	0.641710	−	0.766947i	$-0.278225\pi$
$373$	9245.54	1.28342	0.641710	+	0.766947i	$0.278225\pi$
$374$	−437.430	−0.0604786
$375$	−3167.93	−0.436243
$376$	2931.90	0.402131
$377$	1781.54	0.243379
$378$	−1382.58	−0.188127
$379$	6098.42	0.826530	0.413265	−	0.910611i	$-0.364388\pi$
$379$	6098.42	0.826530	0.413265	+	0.910611i	$0.364388\pi$
$380$	0	0
$381$	−8001.58	−1.07594
$382$	3899.93	0.522350
$383$	4529.81	0.604341	0.302170	−	0.953254i	$-0.402289\pi$
$383$	4529.81	0.604341	0.302170	+	0.953254i	$0.402289\pi$
$384$	384.000	0.0510310
$385$	8903.10	1.17856
$386$	−5862.60	−0.773053
$387$	−4574.19	−0.600825
$388$	990.042	0.129541
$389$	−5558.92	−0.724546	−0.362273	−	0.932072i	$-0.617999\pi$
$389$	−5558.92	−0.724546	−0.362273	+	0.932072i	$0.617999\pi$
$390$	669.550	0.0869334
$391$	1281.77	0.165786
$392$	−2500.21	−0.322142
$393$	−2466.83	−0.316629
$394$	2472.96	0.316208
$395$	−4798.29	−0.611211
$396$	963.814	0.122307
$397$	9391.66	1.18729	0.593645	−	0.804727i	$-0.297689\pi$
$397$	9391.66	1.18729	0.593645	+	0.804727i	$0.297689\pi$
$398$	9018.01	1.13576
$399$	0	0
$400$	699.175	0.0873968
$401$	9532.13	1.18706	0.593531	−	0.804811i	$-0.297733\pi$
$401$	9532.13	1.18706	0.593531	+	0.804811i	$0.297733\pi$
$402$	−1504.31	−0.186638
$403$	−812.080	−0.100379
$404$	−3384.05	−0.416739
$405$	−1052.06	−0.129080
$406$	−10618.0	−1.29794
$407$	5284.58	0.643604
$408$	196.065	0.0237908
$409$	6579.49	0.795439	0.397720	−	0.917507i	$-0.369802\pi$
$409$	6579.49	0.795439	0.397720	+	0.917507i	$0.369802\pi$
$410$	−9786.44	−1.17882
$411$	7335.67	0.880394
$412$	−5690.20	−0.680427
$413$	−15162.4	−1.80652
$414$	−2824.20	−0.335271
$415$	16732.8	1.97923
$416$	274.933	0.0324031
$417$	−4513.02	−0.529985
$418$	0	0
$419$	4136.42	0.482285	0.241143	−	0.970490i	$-0.422478\pi$
$419$	4136.42	0.482285	0.241143	+	0.970490i	$0.422478\pi$
$420$	−3990.54	−0.463616
$421$	7792.46	0.902093	0.451047	−	0.892500i	$-0.351051\pi$
$421$	7792.46	0.902093	0.451047	+	0.892500i	$0.351051\pi$
$422$	3.80939	0.000439428 0
$423$	−3298.39	−0.379132
$424$	1626.63	0.186312
$425$	356.988	0.0407446
$426$	−692.617	−0.0787732
$427$	13033.6	1.47714
$428$	1144.96	0.129307
$429$	690.063	0.0776610
$430$	−13202.5	−1.48066
$431$	−7350.59	−0.821498	−0.410749	−	0.911749i	$-0.634733\pi$
$431$	−7350.59	−0.821498	−0.410749	+	0.911749i	$0.634733\pi$
$432$	−432.000	−0.0481125
$433$	10692.6	1.18673	0.593365	−	0.804933i	$-0.297799\pi$
$433$	10692.6	1.18673	0.593365	+	0.804933i	$0.297799\pi$
$434$	4840.02	0.535319
$435$	−8079.72	−0.890558
$436$	−129.142	−0.0141852
$437$	0	0
$438$	−4996.02	−0.545021
$439$	−9619.66	−1.04583	−0.522917	−	0.852384i	$-0.675156\pi$
$439$	−9619.66	−1.04583	−0.522917	+	0.852384i	$0.675156\pi$
$440$	2781.87	0.301410
$441$	2812.74	0.303719
$442$	140.377	0.0151064
$443$	12604.5	1.35182	0.675909	−	0.736985i	$-0.263751\pi$
$443$	12604.5	1.35182	0.675909	+	0.736985i	$0.263751\pi$
$444$	−2368.65	−0.253178
$445$	−793.258	−0.0845034
$446$	9320.45	0.989543
$447$	2162.24	0.228793
$448$	−1638.61	−0.172806
$449$	14957.9	1.57218	0.786088	−	0.618114i	$-0.212103\pi$
$449$	14957.9	1.57218	0.786088	+	0.618114i	$0.212103\pi$
$450$	−786.572	−0.0823985
$451$	−10086.3	−1.05309
$452$	−1188.39	−0.123666
$453$	−5403.75	−0.560464
$454$	8090.31	0.836337
$455$	−2857.11	−0.294381
$456$	0	0
$457$	−2003.50	−0.205076	−0.102538	−	0.994729i	$-0.532696\pi$
$457$	−2003.50	−0.205076	−0.102538	+	0.994729i	$0.532696\pi$
$458$	−10125.5	−1.03304
$459$	−220.573	−0.0224302
$460$	−8151.53	−0.826233
$461$	−1134.66	−0.114634	−0.0573170	−	0.998356i	$-0.518255\pi$
$461$	−1134.66	−0.114634	−0.0573170	+	0.998356i	$0.518255\pi$
$462$	−4112.80	−0.414166
$463$	−2934.33	−0.294536	−0.147268	−	0.989097i	$-0.547048\pi$
$463$	−2934.33	−0.294536	−0.147268	+	0.989097i	$0.547048\pi$
$464$	−3317.72	−0.331942
$465$	3682.98	0.367299
$466$	−866.178	−0.0861050
$467$	−930.578	−0.0922098	−0.0461049	−	0.998937i	$-0.514681\pi$
$467$	−930.578	−0.0922098	−0.0461049	+	0.998937i	$0.514681\pi$
$468$	−309.299	−0.0305499
$469$	6419.23	0.632009
$470$	−9520.16	−0.934324
$471$	−11487.3	−1.12380
$472$	−4737.63	−0.462007
$473$	−13607.0	−1.32273
$474$	2216.58	0.214791
$475$	0	0
$476$	−836.649	−0.0805625
$477$	−1829.96	−0.175657
$478$	8330.45	0.797125
$479$	15599.2	1.48799	0.743994	−	0.668187i	$-0.232929\pi$
$479$	15599.2	1.48799	0.743994	+	0.668187i	$0.232929\pi$
$480$	−1246.89	−0.118567
$481$	−1695.88	−0.160760
$482$	−8338.84	−0.788016
$483$	12051.5	1.13532
$484$	−2456.91	−0.230739
$485$	−3214.76	−0.300979
$486$	486.000	0.0453609
$487$	13580.1	1.26360	0.631799	−	0.775132i	$-0.282317\pi$
$487$	13580.1	1.26360	0.631799	+	0.775132i	$0.282317\pi$
$488$	4072.48	0.377772
$489$	2869.49	0.265364
$490$	8118.44	0.748477
$491$	796.977	0.0732527	0.0366264	−	0.999329i	$-0.488339\pi$
$491$	796.977	0.0732527	0.0366264	+	0.999329i	$0.488339\pi$
$492$	4520.85	0.414260
$493$	−1693.98	−0.154752
$494$	0	0
$495$	−3129.60	−0.284172
$496$	1512.32	0.136905
$497$	2955.54	0.266749
$498$	−7729.71	−0.695535
$499$	8901.33	0.798553	0.399277	−	0.916830i	$-0.369261\pi$
$499$	8901.33	0.798553	0.399277	+	0.916830i	$0.369261\pi$
$500$	4223.91	0.377798
$501$	8339.30	0.743658
$502$	14264.5	1.26824
$503$	−20225.1	−1.79283	−0.896416	−	0.443214i	$-0.853838\pi$
$503$	−20225.1	−1.79283	−0.896416	+	0.443214i	$0.853838\pi$
$504$	1843.43	0.162923
$505$	10988.3	0.968266
$506$	−8401.26	−0.738106
$507$	6369.55	0.557952
$508$	10668.8	0.931792
$509$	21066.4	1.83448	0.917240	−	0.398335i	$-0.130412\pi$
$509$	21066.4	1.83448	0.917240	+	0.398335i	$0.130412\pi$
$510$	−636.641	−0.0552764
$511$	21319.1	1.84560
$512$	−512.000	−0.0441942
$513$	0	0
$514$	2155.03	0.184931
$515$	18476.6	1.58093
$516$	6098.92	0.520330
$517$	−9811.82	−0.834668
$518$	10107.5	0.857334
$519$	928.656	0.0785423
$520$	−892.734	−0.0752865
$521$	−1660.93	−0.139668	−0.0698338	−	0.997559i	$-0.522247\pi$
$521$	−1660.93	−0.139668	−0.0698338	+	0.997559i	$0.522247\pi$
$522$	3732.43	0.312958
$523$	22315.8	1.86578	0.932889	−	0.360165i	$-0.117280\pi$
$523$	22315.8	1.86578	0.932889	+	0.360165i	$0.117280\pi$
$524$	3289.10	0.274208
$525$	3356.47	0.279025
$526$	−4978.32	−0.412672
$527$	772.166	0.0638255
$528$	−1285.09	−0.105921
$529$	12450.7	1.02332
$530$	−5281.84	−0.432884
$531$	5329.84	0.435584
$532$	0	0
$533$	3236.80	0.263042
$534$	366.446	0.0296960
$535$	−3717.79	−0.300437
$536$	2005.75	0.161633
$537$	−13950.9	−1.12109
$538$	12362.6	0.990683
$539$	8367.16	0.668644
$540$	1402.75	0.111786
$541$	−11379.8	−0.904357	−0.452178	−	0.891927i	$-0.649353\pi$
$541$	−11379.8	−0.904357	−0.452178	+	0.891927i	$0.649353\pi$
$542$	−12065.4	−0.956189
$543$	809.185	0.0639511
$544$	−261.420	−0.0206034
$545$	419.336	0.0329585
$546$	1319.85	0.103451
$547$	−16531.0	−1.29216	−0.646081	−	0.763269i	$-0.723593\pi$
$547$	−16531.0	−1.29216	−0.646081	+	0.763269i	$0.723593\pi$
$548$	−9780.89	−0.762443
$549$	−4581.54	−0.356167
$550$	−2339.84	−0.181402
$551$	0	0
$552$	3765.61	0.290353
$553$	−9458.59	−0.727342
$554$	−1825.43	−0.139991
$555$	7691.24	0.588243
$556$	6017.36	0.458980
$557$	−7325.32	−0.557242	−0.278621	−	0.960401i	$-0.589877\pi$
$557$	−7325.32	−0.557242	−0.278621	+	0.960401i	$0.589877\pi$
$558$	−1701.35	−0.129075
$559$	4366.65	0.330393
$560$	5320.72	0.401503
$561$	−656.146	−0.0493805
$562$	669.773	0.0502716
$563$	10864.0	0.813258	0.406629	−	0.913593i	$-0.366704\pi$
$563$	10864.0	0.813258	0.406629	+	0.913593i	$0.366704\pi$
$564$	4397.85	0.328338
$565$	3858.82	0.287331
$566$	5553.87	0.412450
$567$	−2073.86	−0.153605
$568$	923.489	0.0682196
$569$	−19930.0	−1.46838	−0.734192	−	0.678941i	$-0.762439\pi$
$569$	−19930.0	−1.46838	−0.734192	+	0.678941i	$0.762439\pi$
$570$	0	0
$571$	1218.32	0.0892906	0.0446453	−	0.999003i	$-0.485784\pi$
$571$	1218.32	0.0892906	0.0446453	+	0.999003i	$0.485784\pi$
$572$	−920.084	−0.0672564
$573$	5849.89	0.426497
$574$	−19291.4	−1.40280
$575$	6856.29	0.497265
$576$	576.000	0.0416667
$577$	−9186.43	−0.662801	−0.331400	−	0.943490i	$-0.607521\pi$
$577$	−9186.43	−0.662801	−0.331400	+	0.943490i	$0.607521\pi$
$578$	9692.52	0.697501
$579$	−8793.90	−0.631195
$580$	10773.0	0.771246
$581$	32984.3	2.35528
$582$	1485.06	0.105769
$583$	−5443.66	−0.386712
$584$	6661.36	0.472002
$585$	1004.33	0.0709808
$586$	6135.70	0.432531
$587$	544.891	0.0383136	0.0191568	−	0.999816i	$-0.493902\pi$
$587$	544.891	0.0383136	0.0191568	+	0.999816i	$0.493902\pi$
$588$	−3750.32	−0.263028
$589$	0	0
$590$	15383.6	1.07344
$591$	3709.44	0.258183
$592$	3158.20	0.219259
$593$	12123.5	0.839551	0.419776	−	0.907628i	$-0.362109\pi$
$593$	12123.5	0.839551	0.419776	+	0.907628i	$0.362109\pi$
$594$	1445.72	0.0998631
$595$	2716.68	0.187182
$596$	−2882.99	−0.198141
$597$	13527.0	0.927344
$598$	2696.06	0.184365
$599$	−25305.2	−1.72612	−0.863058	−	0.505104i	$-0.831454\pi$
$599$	−25305.2	−1.72612	−0.863058	+	0.505104i	$0.831454\pi$
$600$	1048.76	0.0713592
$601$	−15329.1	−1.04041	−0.520206	−	0.854041i	$-0.674145\pi$
$601$	−15329.1	−1.04041	−0.520206	+	0.854041i	$0.674145\pi$
$602$	−26025.4	−1.76199
$603$	−2256.47	−0.152389
$604$	7204.99	0.485376
$605$	7977.82	0.536107
$606$	−5076.07	−0.340266
$607$	−1137.90	−0.0760891	−0.0380446	−	0.999276i	$-0.512113\pi$
$607$	−1137.90	−0.0760891	−0.0380446	+	0.999276i	$0.512113\pi$
$608$	0	0
$609$	−15927.1	−1.05977
$610$	−13223.8	−0.877728
$611$	3148.73	0.208484
$612$	294.097	0.0194251
$613$	−12853.8	−0.846916	−0.423458	−	0.905916i	$-0.639184\pi$
$613$	−12853.8	−0.846916	−0.423458	+	0.905916i	$0.639184\pi$
$614$	14975.6	0.984311
$615$	−14679.7	−0.962506
$616$	5483.73	0.358678
$617$	−18031.2	−1.17651	−0.588257	−	0.808674i	$-0.700186\pi$
$617$	−18031.2	−1.17651	−0.588257	+	0.808674i	$0.700186\pi$
$618$	−8535.30	−0.555567
$619$	−28147.3	−1.82768	−0.913841	−	0.406071i	$-0.866898\pi$
$619$	−28147.3	−1.82768	−0.913841	+	0.406071i	$0.866898\pi$
$620$	−4910.64	−0.318090
$621$	−4236.31	−0.273747
$622$	13363.8	0.861476
$623$	−1563.70	−0.100559
$624$	412.399	0.0264570
$625$	−19177.8	−1.22738
$626$	−16324.0	−1.04224
$627$	0	0
$628$	15316.4	0.973236
$629$	1612.53	0.102219
$630$	−5985.81	−0.378541
$631$	1024.56	0.0646386	0.0323193	−	0.999478i	$-0.489711\pi$
$631$	1024.56	0.0646386	0.0323193	+	0.999478i	$0.489711\pi$
$632$	−2955.43	−0.186014
$633$	5.71409	0.000358791 0
$634$	5679.08	0.355749
$635$	−34642.5	−2.16496
$636$	2439.95	0.152123
$637$	−2685.12	−0.167015
$638$	11103.0	0.688984
$639$	−1038.92	−0.0643180
$640$	1662.51	0.102682
$641$	17477.0	1.07691	0.538454	−	0.842655i	$-0.319009\pi$
$641$	17477.0	1.07691	0.538454	+	0.842655i	$0.319009\pi$
$642$	1717.44	0.105579
$643$	−13432.5	−0.823833	−0.411917	−	0.911222i	$-0.635141\pi$
$643$	−13432.5	−0.823833	−0.411917	+	0.911222i	$0.635141\pi$
$644$	−16068.6	−0.983218
$645$	−19803.8	−1.20895
$646$	0	0
$647$	−2658.09	−0.161515	−0.0807575	−	0.996734i	$-0.525734\pi$
$647$	−2658.09	−0.161515	−0.0807575	+	0.996734i	$0.525734\pi$
$648$	−648.000	−0.0392837
$649$	15854.9	0.958948
$650$	750.883	0.0453109
$651$	7260.04	0.437086
$652$	−3825.99	−0.229812
$653$	−9989.77	−0.598668	−0.299334	−	0.954148i	$-0.596764\pi$
$653$	−9989.77	−0.598668	−0.299334	+	0.954148i	$0.596764\pi$
$654$	−193.712	−0.0115822
$655$	−10680.0	−0.637105
$656$	−6027.81	−0.358760
$657$	−7494.03	−0.445008
$658$	−18766.5	−1.11185
$659$	20064.6	1.18605	0.593025	−	0.805184i	$-0.297934\pi$
$659$	20064.6	1.18605	0.593025	+	0.805184i	$0.297934\pi$
$660$	4172.80	0.246100
$661$	23719.1	1.39571	0.697855	−	0.716239i	$-0.254138\pi$
$661$	23719.1	1.39571	0.697855	+	0.716239i	$0.254138\pi$
$662$	−22112.5	−1.29823
$663$	210.565	0.0123343
$664$	10306.3	0.602351
$665$	0	0
$666$	−3552.97	−0.206719
$667$	−32534.4	−1.88866
$668$	−11119.1	−0.644027
$669$	13980.7	0.807959
$670$	−6512.88	−0.375544
$671$	−13628.9	−0.784109
$672$	−2457.91	−0.141095
$673$	−10144.0	−0.581014	−0.290507	−	0.956873i	$-0.593824\pi$
$673$	−10144.0	−0.581014	−0.290507	+	0.956873i	$0.593824\pi$
$674$	10100.7	0.577245
$675$	−1179.86	−0.0672781
$676$	−8492.73	−0.483201
$677$	−16883.4	−0.958469	−0.479234	−	0.877687i	$-0.659086\pi$
$677$	−16883.4	−0.958469	−0.479234	+	0.877687i	$0.659086\pi$
$678$	−1782.59	−0.100973
$679$	−6337.07	−0.358166
$680$	848.855	0.0478708
$681$	12135.5	0.682866
$682$	−5061.08	−0.284162
$683$	−16610.2	−0.930560	−0.465280	−	0.885164i	$-0.654046\pi$
$683$	−16610.2	−0.930560	−0.465280	+	0.885164i	$0.654046\pi$
$684$	0	0
$685$	31759.5	1.77149
$686$	−1560.43	−0.0868479
$687$	−15188.2	−0.843472
$688$	−8131.90	−0.450619
$689$	1746.93	0.0965935
$690$	−12227.3	−0.674616
$691$	24812.1	1.36598	0.682992	−	0.730426i	$-0.260678\pi$
$691$	24812.1	1.36598	0.682992	+	0.730426i	$0.260678\pi$
$692$	−1238.21	−0.0680196
$693$	−6169.19	−0.338165
$694$	12029.7	0.657984
$695$	−19539.0	−1.06641
$696$	−4976.58	−0.271030
$697$	−3077.71	−0.167255
$698$	5029.01	0.272709
$699$	−1299.27	−0.0703044
$700$	−4475.29	−0.241643
$701$	13067.2	0.704051	0.352025	−	0.935990i	$-0.385493\pi$
$701$	13067.2	0.704051	0.352025	+	0.935990i	$0.385493\pi$
$702$	−463.949	−0.0249439
$703$	0	0
$704$	1713.45	0.0917301
$705$	−14280.2	−0.762873
$706$	−9156.05	−0.488091
$707$	21660.7	1.15224
$708$	−7106.45	−0.377227
$709$	10445.2	0.553284	0.276642	−	0.960973i	$-0.410778\pi$
$709$	10445.2	0.553284	0.276642	+	0.960973i	$0.410778\pi$
$710$	−2998.66	−0.158504
$711$	3324.86	0.175376
$712$	−488.595	−0.0257175
$713$	14830.2	0.778954
$714$	−1254.97	−0.0657790
$715$	2987.60	0.156266
$716$	18601.1	0.970890
$717$	12495.7	0.650850
$718$	−15944.9	−0.828771
$719$	648.001	0.0336111	0.0168055	−	0.999859i	$-0.494650\pi$
$719$	648.001	0.0336111	0.0168055	+	0.999859i	$0.494650\pi$
$720$	−1870.33	−0.0968098
$721$	36421.9	1.88131
$722$	0	0
$723$	−12508.3	−0.643413
$724$	−1078.91	−0.0553833
$725$	−9061.19	−0.464171
$726$	−3685.36	−0.188398
$727$	16873.2	0.860789	0.430394	−	0.902641i	$-0.358375\pi$
$727$	16873.2	0.860789	0.430394	+	0.902641i	$0.358375\pi$
$728$	−1759.79	−0.0895911
$729$	729.000	0.0370370
$730$	−21630.1	−1.09667
$731$	−4152.03	−0.210080
$732$	6108.72	0.308449
$733$	−23662.1	−1.19233	−0.596166	−	0.802861i	$-0.703310\pi$
$733$	−23662.1	−1.19233	−0.596166	+	0.802861i	$0.703310\pi$
$734$	−10931.0	−0.549688
$735$	12177.7	0.611129
$736$	−5020.81	−0.251453
$737$	−6712.41	−0.335488
$738$	6781.28	0.338242
$739$	17277.3	0.860021	0.430011	−	0.902824i	$-0.358510\pi$
$739$	17277.3	0.860021	0.430011	+	0.902824i	$0.358510\pi$
$740$	−10255.0	−0.509433
$741$	0	0
$742$	−10411.8	−0.515133
$743$	25798.5	1.27383	0.636915	−	0.770934i	$-0.280210\pi$
$743$	25798.5	1.27383	0.636915	+	0.770934i	$0.280210\pi$
$744$	2268.47	0.111783
$745$	9361.35	0.460367
$746$	−18491.1	−0.907516
$747$	−11594.6	−0.567902
$748$	874.861	0.0427648
$749$	−7328.66	−0.357521
$750$	6335.86	0.308471
$751$	15156.5	0.736444	0.368222	−	0.929738i	$-0.379967\pi$
$751$	15156.5	0.736444	0.368222	+	0.929738i	$0.379967\pi$
$752$	−5863.80	−0.284349
$753$	21396.7	1.03551
$754$	−3563.08	−0.172095
$755$	−23395.3	−1.12774
$756$	2765.15	0.133026
$757$	7454.91	0.357931	0.178965	−	0.983855i	$-0.442725\pi$
$757$	7454.91	0.357931	0.178965	+	0.983855i	$0.442725\pi$
$758$	−12196.8	−0.584445
$759$	−12601.9	−0.602661
$760$	0	0
$761$	23295.2	1.10966	0.554830	−	0.831964i	$-0.312783\pi$
$761$	23295.2	1.10966	0.554830	+	0.831964i	$0.312783\pi$
$762$	16003.2	0.760805
$763$	826.611	0.0392206
$764$	−7799.86	−0.369357
$765$	−954.962	−0.0451330
$766$	−9059.62	−0.427333
$767$	−5088.01	−0.239527
$768$	−768.000	−0.0360844
$769$	−37973.8	−1.78072	−0.890358	−	0.455260i	$-0.849546\pi$
$769$	−37973.8	−1.78072	−0.890358	+	0.455260i	$0.849546\pi$
$770$	−17806.2	−0.833365
$771$	3232.55	0.150995
$772$	11725.2	0.546631
$773$	8339.37	0.388029	0.194014	−	0.980999i	$-0.437849\pi$
$773$	8339.37	0.388029	0.194014	+	0.980999i	$0.437849\pi$
$774$	9148.39	0.424847
$775$	4130.36	0.191441
$776$	−1980.08	−0.0915990
$777$	15161.3	0.700010
$778$	11117.8	0.512332
$779$	0	0
$780$	−1339.10	−0.0614712
$781$	−3090.53	−0.141598
$782$	−2563.55	−0.117228
$783$	5598.65	0.255529
$784$	5000.43	0.227789
$785$	−49734.0	−2.26125
$786$	4933.66	0.223890
$787$	−42901.7	−1.94318	−0.971588	−	0.236680i	$-0.923941\pi$
$787$	−42901.7	−1.94318	−0.971588	+	0.236680i	$0.923941\pi$
$788$	−4945.92	−0.223593
$789$	−7467.49	−0.336945
$790$	9596.59	0.432192
$791$	7606.67	0.341924
$792$	−1927.63	−0.0864840
$793$	4373.67	0.195856
$794$	−18783.3	−0.839540
$795$	−7922.77	−0.353449
$796$	−18036.0	−0.803103
$797$	5540.21	0.246229	0.123114	−	0.992392i	$-0.460712\pi$
$797$	5540.21	0.246229	0.123114	+	0.992392i	$0.460712\pi$
$798$	0	0
$799$	−2993.97	−0.132564
$800$	−1398.35	−0.0617989
$801$	549.669	0.0242467
$802$	−19064.3	−0.839379
$803$	−22292.8	−0.979695
$804$	3008.63	0.131973
$805$	52176.4	2.28444
$806$	1624.16	0.0709784
$807$	18543.8	0.808890
$808$	6768.09	0.294679
$809$	20817.8	0.904715	0.452357	−	0.891837i	$-0.350583\pi$
$809$	20817.8	0.904715	0.452357	+	0.891837i	$0.350583\pi$
$810$	2104.12	0.0912731
$811$	−20667.9	−0.894882	−0.447441	−	0.894313i	$-0.647665\pi$
$811$	−20667.9	−0.894882	−0.447441	+	0.894313i	$0.647665\pi$
$812$	21236.1	0.917784
$813$	−18098.1	−0.780725
$814$	−10569.2	−0.455097
$815$	12423.4	0.533952
$816$	−392.129	−0.0168226
$817$	0	0
$818$	−13159.0	−0.562461
$819$	1979.77	0.0844673
$820$	19572.9	0.833554
$821$	−7501.01	−0.318864	−0.159432	−	0.987209i	$-0.550966\pi$
$821$	−7501.01	−0.318864	−0.159432	+	0.987209i	$0.550966\pi$
$822$	−14671.3	−0.622532
$823$	−362.296	−0.0153449	−0.00767244	−	0.999971i	$-0.502442\pi$
$823$	−362.296	−0.0153449	−0.00767244	+	0.999971i	$0.502442\pi$
$824$	11380.4	0.481135
$825$	−3509.76	−0.148114
$826$	30324.7	1.27740
$827$	−8779.02	−0.369137	−0.184568	−	0.982820i	$-0.559089\pi$
$827$	−8779.02	−0.369137	−0.184568	+	0.982820i	$0.559089\pi$
$828$	5648.41	0.237072
$829$	11789.0	0.493909	0.246954	−	0.969027i	$-0.420570\pi$
$829$	11789.0	0.493909	0.246954	+	0.969027i	$0.420570\pi$
$830$	−33465.5	−1.39952
$831$	−2738.15	−0.114303
$832$	−549.866	−0.0229125
$833$	2553.14	0.106196
$834$	9026.05	0.374756
$835$	36104.7	1.49635
$836$	0	0
$837$	−2552.03	−0.105390
$838$	−8272.85	−0.341027
$839$	−10761.2	−0.442811	−0.221405	−	0.975182i	$-0.571064\pi$
$839$	−10761.2	−0.442811	−0.221405	+	0.975182i	$0.571064\pi$
$840$	7981.08	0.327826
$841$	18608.1	0.762969
$842$	−15584.9	−0.637876
$843$	1004.66	0.0410466
$844$	−7.61879	−0.000310722 0
$845$	27576.7	1.12269
$846$	6596.77	0.268087
$847$	15726.2	0.637968
$848$	−3253.27	−0.131743
$849$	8330.81	0.336764
$850$	−713.976	−0.0288108
$851$	30970.1	1.24752
$852$	1385.23	0.0557011
$853$	4890.26	0.196294	0.0981472	−	0.995172i	$-0.468708\pi$
$853$	4890.26	0.196294	0.0981472	+	0.995172i	$0.468708\pi$
$854$	−26067.2	−1.04450
$855$	0	0
$856$	−2289.91	−0.0914342
$857$	−30324.4	−1.20871	−0.604353	−	0.796717i	$-0.706568\pi$
$857$	−30324.4	−1.20871	−0.604353	+	0.796717i	$0.706568\pi$
$858$	−1380.13	−0.0549146
$859$	−15071.6	−0.598644	−0.299322	−	0.954152i	$-0.596760\pi$
$859$	−15071.6	−0.598644	−0.299322	+	0.954152i	$0.596760\pi$
$860$	26405.1	1.04698
$861$	−28937.1	−1.14538
$862$	14701.2	0.580887
$863$	283.180	0.0111698	0.00558490	−	0.999984i	$-0.498222\pi$
$863$	283.180	0.0111698	0.00558490	+	0.999984i	$0.498222\pi$
$864$	864.000	0.0340207
$865$	4020.58	0.158039
$866$	−21385.2	−0.839145
$867$	14538.8	0.569508
$868$	−9680.05	−0.378528
$869$	9890.59	0.386094
$870$	16159.4	0.629720
$871$	2154.09	0.0837986
$872$	258.283	0.0100305
$873$	2227.59	0.0863604
$874$	0	0
$875$	−27036.4	−1.04457
$876$	9992.05	0.385388
$877$	−2201.83	−0.0847782	−0.0423891	−	0.999101i	$-0.513497\pi$
$877$	−2201.83	−0.0847782	−0.0423891	+	0.999101i	$0.513497\pi$
$878$	19239.3	0.739516
$879$	9203.55	0.353160
$880$	−5563.73	−0.213129
$881$	21218.9	0.811443	0.405722	−	0.913997i	$-0.367020\pi$
$881$	21218.9	0.811443	0.405722	+	0.913997i	$0.367020\pi$
$882$	−5625.48	−0.214762
$883$	−8730.23	−0.332724	−0.166362	−	0.986065i	$-0.553202\pi$
$883$	−8730.23	−0.332724	−0.166362	+	0.986065i	$0.553202\pi$
$884$	−280.753	−0.0106818
$885$	23075.3	0.876463
$886$	−25208.9	−0.955880
$887$	−11548.0	−0.437139	−0.218570	−	0.975821i	$-0.570139\pi$
$887$	−11548.0	−0.437139	−0.218570	+	0.975821i	$0.570139\pi$
$888$	4737.30	0.179024
$889$	−68288.8	−2.57630
$890$	1586.52	0.0597529
$891$	2168.58	0.0815379
$892$	−18640.9	−0.699713
$893$	0	0
$894$	−4324.48	−0.161781
$895$	−60399.8	−2.25580
$896$	3277.22	0.122192
$897$	4044.10	0.150533
$898$	−29915.8	−1.11170
$899$	−19599.4	−0.727113
$900$	1573.14	0.0582646
$901$	−1661.07	−0.0614188
$902$	20172.5	0.744647
$903$	−39038.1	−1.43866
$904$	2376.78	0.0874453
$905$	3503.34	0.128679
$906$	10807.5	0.396308
$907$	−7282.96	−0.266622	−0.133311	−	0.991074i	$-0.542561\pi$
$907$	−7282.96	−0.266622	−0.133311	+	0.991074i	$0.542561\pi$
$908$	−16180.6	−0.591380
$909$	−7614.11	−0.277826
$910$	5714.22	0.208159
$911$	32720.6	1.18999	0.594995	−	0.803729i	$-0.297154\pi$
$911$	32720.6	1.18999	0.594995	+	0.803729i	$0.297154\pi$
$912$	0	0
$913$	−34490.8	−1.25025
$914$	4007.00	0.145011
$915$	−19835.6	−0.716662
$916$	20250.9	0.730468
$917$	−21052.9	−0.758156
$918$	441.146	0.0158605
$919$	1970.84	0.0707421	0.0353710	−	0.999374i	$-0.488739\pi$
$919$	1970.84	0.0707421	0.0353710	+	0.999374i	$0.488739\pi$
$920$	16303.1	0.584235
$921$	22463.4	0.803686
$922$	2269.31	0.0810585
$923$	991.786	0.0353684
$924$	8225.59	0.292859
$925$	8625.52	0.306600
$926$	5868.67	0.208268
$927$	−12802.9	−0.453618
$928$	6635.43	0.234719
$929$	10757.5	0.379916	0.189958	−	0.981792i	$-0.439165\pi$
$929$	10757.5	0.379916	0.189958	+	0.981792i	$0.439165\pi$
$930$	−7365.95	−0.259720
$931$	0	0
$932$	1732.36	0.0608854
$933$	20045.7	0.703392
$934$	1861.16	0.0652022
$935$	−2840.76	−0.0993613
$936$	618.599	0.0216021
$937$	32578.3	1.13585	0.567923	−	0.823082i	$-0.307747\pi$
$937$	32578.3	1.13585	0.567923	+	0.823082i	$0.307747\pi$
$938$	−12838.5	−0.446898
$939$	−24486.1	−0.850982
$940$	19040.3	0.660667
$941$	45845.4	1.58822	0.794112	−	0.607772i	$-0.207936\pi$
$941$	45845.4	1.58822	0.794112	+	0.607772i	$0.207936\pi$
$942$	22974.7	0.794644
$943$	−59110.3	−2.04125
$944$	9475.27	0.326688
$945$	−8978.72	−0.309077
$946$	27214.0	0.935311
$947$	−28244.0	−0.969172	−0.484586	−	0.874744i	$-0.661030\pi$
$947$	−28244.0	−0.969172	−0.484586	+	0.874744i	$0.661030\pi$
$948$	−4433.15	−0.151880
$949$	7154.01	0.244709
$950$	0	0
$951$	8518.62	0.290468
$952$	1673.30	0.0569663
$953$	−44693.4	−1.51916	−0.759582	−	0.650412i	$-0.774596\pi$
$953$	−44693.4	−1.51916	−0.759582	+	0.650412i	$0.774596\pi$
$954$	3659.93	0.124208
$955$	25326.9	0.858178
$956$	−16660.9	−0.563652
$957$	16654.5	0.562553
$958$	−31198.4	−1.05217
$959$	62605.7	2.10807
$960$	2493.77	0.0838397
$961$	−20857.0	−0.700112
$962$	3391.77	0.113675
$963$	2576.15	0.0862050
$964$	16677.7	0.557212
$965$	−38072.9	−1.27006
$966$	−24102.9	−0.802794
$967$	45581.0	1.51581	0.757905	−	0.652365i	$-0.226223\pi$
$967$	45581.0	1.51581	0.757905	+	0.652365i	$0.226223\pi$
$968$	4913.82	0.163157
$969$	0	0
$970$	6429.53	0.212824
$971$	−4735.96	−0.156523	−0.0782616	−	0.996933i	$-0.524937\pi$
$971$	−4735.96	−0.156523	−0.0782616	+	0.996933i	$0.524937\pi$
$972$	−972.000	−0.0320750
$973$	−38516.0	−1.26903
$974$	−27160.2	−0.893498
$975$	1126.32	0.0369962
$976$	−8144.96	−0.267125
$977$	−57565.1	−1.88503	−0.942514	−	0.334167i	$-0.891545\pi$
$977$	−57565.1	−1.88503	−0.942514	+	0.334167i	$0.891545\pi$
$978$	−5738.98	−0.187640
$979$	1635.12	0.0533796
$980$	−16236.9	−0.529253
$981$	−290.569	−0.00945682
$982$	−1593.95	−0.0517975
$983$	34628.3	1.12357	0.561786	−	0.827282i	$-0.310114\pi$
$983$	34628.3	1.12357	0.561786	+	0.827282i	$0.310114\pi$
$984$	−9041.71	−0.292926
$985$	16059.9	0.519503
$986$	3387.95	0.109426
$987$	−28149.8	−0.907820
$988$	0	0
$989$	−79743.5	−2.56390
$990$	6259.20	0.200940
$991$	31575.5	1.01214	0.506069	−	0.862493i	$-0.331098\pi$
$991$	31575.5	1.01214	0.506069	+	0.862493i	$0.331098\pi$
$992$	−3024.63	−0.0968066
$993$	−33168.7	−1.06000
$994$	−5911.08	−0.188620
$995$	58564.8	1.86596
$996$	15459.4	0.491818
$997$	38723.3	1.23007	0.615035	−	0.788500i	$-0.289142\pi$
$997$	38723.3	1.23007	0.615035	+	0.788500i	$0.289142\pi$
$998$	−17802.7	−0.564662
$999$	−5329.46	−0.168785

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.4.a.s.1.1		3
19.7	even	3		114.4.e.e.49.3	yes	6
19.11	even	3		114.4.e.e.7.3	✓	6
19.18	odd	2		2166.4.a.w.1.1		3
57.11	odd	6		342.4.g.g.235.1		6
57.26	odd	6		342.4.g.g.163.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.e.e.7.3	✓	6	19.11	even	3
114.4.e.e.49.3	yes	6	19.7	even	3
342.4.g.g.163.1		6	57.26	odd	6
342.4.g.g.235.1		6	57.11	odd	6
2166.4.a.s.1.1		3	1.1	even	1	trivial
2166.4.a.w.1.1		3	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2166.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -12.9884 q^{5} +6.00000 q^{6} -25.6033 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -12.9884 q^{5} +6.00000 q^{6} -25.6033 q^{7} -8.00000 q^{8} +9.00000 q^{9} +25.9768 q^{10} +26.7726 q^{11} -12.0000 q^{12} -8.59165 q^{13} +51.2065 q^{14} +38.9652 q^{15} +16.0000 q^{16} +8.16936 q^{17} -18.0000 q^{18} -51.9536 q^{20} +76.8098 q^{21} -53.5452 q^{22} +156.900 q^{23} +24.0000 q^{24} +43.6984 q^{25} +17.1833 q^{26} -27.0000 q^{27} -102.413 q^{28} -207.357 q^{29} -77.9304 q^{30} +94.5197 q^{31} -32.0000 q^{32} -80.3178 q^{33} -16.3387 q^{34} +332.545 q^{35} +36.0000 q^{36} +197.387 q^{37} +25.7749 q^{39} +103.907 q^{40} -376.738 q^{41} -153.620 q^{42} -508.244 q^{43} +107.090 q^{44} -116.896 q^{45} -313.800 q^{46} -366.487 q^{47} -48.0000 q^{48} +312.527 q^{49} -87.3968 q^{50} -24.5081 q^{51} -34.3666 q^{52} -203.329 q^{53} +54.0000 q^{54} -347.733 q^{55} +204.826 q^{56} +414.715 q^{58} +592.204 q^{59} +155.861 q^{60} -509.060 q^{61} -189.039 q^{62} -230.429 q^{63} +64.0000 q^{64} +111.592 q^{65} +160.636 q^{66} -250.719 q^{67} +32.6774 q^{68} -470.701 q^{69} -665.090 q^{70} -115.436 q^{71} -72.0000 q^{72} -832.671 q^{73} -394.775 q^{74} -131.095 q^{75} -685.466 q^{77} -51.5499 q^{78} +369.429 q^{79} -207.814 q^{80} +81.0000 q^{81} +753.476 q^{82} -1288.29 q^{83} +307.239 q^{84} -106.107 q^{85} +1016.49 q^{86} +622.072 q^{87} -214.181 q^{88} +61.0743 q^{89} +233.791 q^{90} +219.974 q^{91} +627.601 q^{92} -283.559 q^{93} +732.975 q^{94} +96.0000 q^{96} +247.510 q^{97} -625.053 q^{98} +240.954 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 6 q^{2} - 9 q^{3} + 12 q^{4} + 2 q^{5} + 18 q^{6} - 17 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q - 6 * q^2 - 9 * q^3 + 12 * q^4 + 2 * q^5 + 18 * q^6 - 17 * q^7 - 24 * q^8 + 27 * q^9	\( 3 q - 6 q^{2} - 9 q^{3} + 12 q^{4} + 2 q^{5} + 18 q^{6} - 17 q^{7} - 24 q^{8} + 27 q^{9} - 4 q^{10} - 52 q^{11} - 36 q^{12} + 75 q^{13} + 34 q^{14} - 6 q^{15} + 48 q^{16} - 48 q^{17} - 54 q^{18} + 8 q^{20} + 51 q^{21} + 104 q^{22} - 238 q^{23} + 72 q^{24} + 229 q^{25} - 150 q^{26} - 81 q^{27} - 68 q^{28} - 8 q^{29} + 12 q^{30} + 107 q^{31} - 96 q^{32} + 156 q^{33} + 96 q^{34} - 294 q^{35} + 108 q^{36} + 305 q^{37} - 225 q^{39} - 16 q^{40} + 16 q^{41} - 102 q^{42} - 331 q^{43} - 208 q^{44} + 18 q^{45} + 476 q^{46} - 766 q^{47} - 144 q^{48} + 1142 q^{49} - 458 q^{50} + 144 q^{51} + 300 q^{52} - 118 q^{53} + 162 q^{54} - 1400 q^{55} + 136 q^{56} + 16 q^{58} + 936 q^{59} - 24 q^{60} - 399 q^{61} - 214 q^{62} - 153 q^{63} + 192 q^{64} + 370 q^{65} - 312 q^{66} + 61 q^{67} - 192 q^{68} + 714 q^{69} + 588 q^{70} + 974 q^{71} - 216 q^{72} + 91 q^{73} - 610 q^{74} - 687 q^{75} - 36 q^{77} + 450 q^{78} - 321 q^{79} + 32 q^{80} + 243 q^{81} - 32 q^{82} - 2148 q^{83} + 204 q^{84} - 1680 q^{85} + 662 q^{86} + 24 q^{87} + 416 q^{88} + 1116 q^{89} - 36 q^{90} + 1367 q^{91} - 952 q^{92} - 321 q^{93} + 1532 q^{94} + 288 q^{96} + 1382 q^{97} - 2284 q^{98} - 468 q^{99}+O(q^{100}) \) 3 * q - 6 * q^2 - 9 * q^3 + 12 * q^4 + 2 * q^5 + 18 * q^6 - 17 * q^7 - 24 * q^8 + 27 * q^9 - 4 * q^10 - 52 * q^11 - 36 * q^12 + 75 * q^13 + 34 * q^14 - 6 * q^15 + 48 * q^16 - 48 * q^17 - 54 * q^18 + 8 * q^20 + 51 * q^21 + 104 * q^22 - 238 * q^23 + 72 * q^24 + 229 * q^25 - 150 * q^26 - 81 * q^27 - 68 * q^28 - 8 * q^29 + 12 * q^30 + 107 * q^31 - 96 * q^32 + 156 * q^33 + 96 * q^34 - 294 * q^35 + 108 * q^36 + 305 * q^37 - 225 * q^39 - 16 * q^40 + 16 * q^41 - 102 * q^42 - 331 * q^43 - 208 * q^44 + 18 * q^45 + 476 * q^46 - 766 * q^47 - 144 * q^48 + 1142 * q^49 - 458 * q^50 + 144 * q^51 + 300 * q^52 - 118 * q^53 + 162 * q^54 - 1400 * q^55 + 136 * q^56 + 16 * q^58 + 936 * q^59 - 24 * q^60 - 399 * q^61 - 214 * q^62 - 153 * q^63 + 192 * q^64 + 370 * q^65 - 312 * q^66 + 61 * q^67 - 192 * q^68 + 714 * q^69 + 588 * q^70 + 974 * q^71 - 216 * q^72 + 91 * q^73 - 610 * q^74 - 687 * q^75 - 36 * q^77 + 450 * q^78 - 321 * q^79 + 32 * q^80 + 243 * q^81 - 32 * q^82 - 2148 * q^83 + 204 * q^84 - 1680 * q^85 + 662 * q^86 + 24 * q^87 + 416 * q^88 + 1116 * q^89 - 36 * q^90 + 1367 * q^91 - 952 * q^92 - 321 * q^93 + 1532 * q^94 + 288 * q^96 + 1382 * q^97 - 2284 * q^98 - 468 * q^99

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