LMFDB - Embedded newform 2166.4.a.p.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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ 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)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -12.0902 q^{5} +6.00000 q^{6} -0.673762 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -12.0902 q^{5} +6.00000 q^{6} -0.673762 q^{7} +8.00000 q^{8} +9.00000 q^{9} -24.1803 q^{10} +15.9443 q^{11} +12.0000 q^{12} +3.90983 q^{13} -1.34752 q^{14} -36.2705 q^{15} +16.0000 q^{16} -44.0132 q^{17} +18.0000 q^{18} -48.3607 q^{20} -2.02129 q^{21} +31.8885 q^{22} -9.11146 q^{23} +24.0000 q^{24} +21.1722 q^{25} +7.81966 q^{26} +27.0000 q^{27} -2.69505 q^{28} -161.151 q^{29} -72.5410 q^{30} +60.5035 q^{31} +32.0000 q^{32} +47.8328 q^{33} -88.0263 q^{34} +8.14590 q^{35} +36.0000 q^{36} +104.885 q^{37} +11.7295 q^{39} -96.7214 q^{40} +249.353 q^{41} -4.04257 q^{42} -6.90481 q^{43} +63.7771 q^{44} -108.812 q^{45} -18.2229 q^{46} +145.257 q^{47} +48.0000 q^{48} -342.546 q^{49} +42.3444 q^{50} -132.039 q^{51} +15.6393 q^{52} -754.187 q^{53} +54.0000 q^{54} -192.769 q^{55} -5.39010 q^{56} -322.302 q^{58} -704.046 q^{59} -145.082 q^{60} -32.5085 q^{61} +121.007 q^{62} -6.06386 q^{63} +64.0000 q^{64} -47.2705 q^{65} +95.6656 q^{66} +77.7264 q^{67} -176.053 q^{68} -27.3344 q^{69} +16.2918 q^{70} +44.4183 q^{71} +72.0000 q^{72} +280.735 q^{73} +209.771 q^{74} +63.5166 q^{75} -10.7426 q^{77} +23.4590 q^{78} +779.508 q^{79} -193.443 q^{80} +81.0000 q^{81} +498.705 q^{82} -274.023 q^{83} -8.08514 q^{84} +532.127 q^{85} -13.8096 q^{86} -483.453 q^{87} +127.554 q^{88} -1005.91 q^{89} -217.623 q^{90} -2.63430 q^{91} -36.4458 q^{92} +181.510 q^{93} +290.515 q^{94} +96.0000 q^{96} -832.600 q^{97} -685.092 q^{98} +143.498 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} + 6 q^{3} + 8 q^{4} - 13 q^{5} + 12 q^{6} - 17 q^{7} + 16 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + 4 * q^2 + 6 * q^3 + 8 * q^4 - 13 * q^5 + 12 * q^6 - 17 * q^7 + 16 * q^8 + 18 * q^9	\( 2 q + 4 q^{2} + 6 q^{3} + 8 q^{4} - 13 q^{5} + 12 q^{6} - 17 q^{7} + 16 q^{8} + 18 q^{9} - 26 q^{10} + 14 q^{11} + 24 q^{12} + 19 q^{13} - 34 q^{14} - 39 q^{15} + 32 q^{16} - 12 q^{17} + 36 q^{18} - 52 q^{20} - 51 q^{21} + 28 q^{22} - 54 q^{23} + 48 q^{24} - 103 q^{25} + 38 q^{26} + 54 q^{27} - 68 q^{28} - 130 q^{29} - 78 q^{30} - 239 q^{31} + 64 q^{32} + 42 q^{33} - 24 q^{34} + 23 q^{35} + 72 q^{36} - 148 q^{37} + 57 q^{39} - 104 q^{40} + 331 q^{41} - 102 q^{42} - 224 q^{43} + 56 q^{44} - 117 q^{45} - 108 q^{46} + 333 q^{47} + 96 q^{48} - 419 q^{49} - 206 q^{50} - 36 q^{51} + 76 q^{52} - 766 q^{53} + 108 q^{54} - 191 q^{55} - 136 q^{56} - 260 q^{58} - 460 q^{59} - 156 q^{60} + 494 q^{61} - 478 q^{62} - 153 q^{63} + 128 q^{64} - 61 q^{65} + 84 q^{66} - 133 q^{67} - 48 q^{68} - 162 q^{69} + 46 q^{70} - 459 q^{71} + 144 q^{72} + 396 q^{73} - 296 q^{74} - 309 q^{75} + 21 q^{77} + 114 q^{78} + 1000 q^{79} - 208 q^{80} + 162 q^{81} + 662 q^{82} - 74 q^{83} - 204 q^{84} + 503 q^{85} - 448 q^{86} - 390 q^{87} + 112 q^{88} - 1180 q^{89} - 234 q^{90} - 249 q^{91} - 216 q^{92} - 717 q^{93} + 666 q^{94} + 192 q^{96} - 1938 q^{97} - 838 q^{98} + 126 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 + 6 * q^3 + 8 * q^4 - 13 * q^5 + 12 * q^6 - 17 * q^7 + 16 * q^8 + 18 * q^9 - 26 * q^10 + 14 * q^11 + 24 * q^12 + 19 * q^13 - 34 * q^14 - 39 * q^15 + 32 * q^16 - 12 * q^17 + 36 * q^18 - 52 * q^20 - 51 * q^21 + 28 * q^22 - 54 * q^23 + 48 * q^24 - 103 * q^25 + 38 * q^26 + 54 * q^27 - 68 * q^28 - 130 * q^29 - 78 * q^30 - 239 * q^31 + 64 * q^32 + 42 * q^33 - 24 * q^34 + 23 * q^35 + 72 * q^36 - 148 * q^37 + 57 * q^39 - 104 * q^40 + 331 * q^41 - 102 * q^42 - 224 * q^43 + 56 * q^44 - 117 * q^45 - 108 * q^46 + 333 * q^47 + 96 * q^48 - 419 * q^49 - 206 * q^50 - 36 * q^51 + 76 * q^52 - 766 * q^53 + 108 * q^54 - 191 * q^55 - 136 * q^56 - 260 * q^58 - 460 * q^59 - 156 * q^60 + 494 * q^61 - 478 * q^62 - 153 * q^63 + 128 * q^64 - 61 * q^65 + 84 * q^66 - 133 * q^67 - 48 * q^68 - 162 * q^69 + 46 * q^70 - 459 * q^71 + 144 * q^72 + 396 * q^73 - 296 * q^74 - 309 * q^75 + 21 * q^77 + 114 * q^78 + 1000 * q^79 - 208 * q^80 + 162 * q^81 + 662 * q^82 - 74 * q^83 - 204 * q^84 + 503 * q^85 - 448 * q^86 - 390 * q^87 + 112 * q^88 - 1180 * q^89 - 234 * q^90 - 249 * q^91 - 216 * q^92 - 717 * q^93 + 666 * q^94 + 192 * q^96 - 1938 * q^97 - 838 * q^98 + 126 * 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
$5$	−12.0902	−1.08138	−0.540689	−	0.841223i	$-0.681836\pi$
$5$	−12.0902	−1.08138	−0.540689	+	0.841223i	$0.681836\pi$
$6$	6.00000	0.408248
$7$	−0.673762	−0.0363797	−0.0181899	−	0.999835i	$-0.505790\pi$
$7$	−0.673762	−0.0363797	−0.0181899	+	0.999835i	$0.505790\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−24.1803	−0.764649
$11$	15.9443	0.437034	0.218517	−	0.975833i	$-0.429878\pi$
$11$	15.9443	0.437034	0.218517	+	0.975833i	$0.429878\pi$
$12$	12.0000	0.288675
$13$	3.90983	0.0834147	0.0417074	−	0.999130i	$-0.486720\pi$
$13$	3.90983	0.0834147	0.0417074	+	0.999130i	$0.486720\pi$
$14$	−1.34752	−0.0257244
$15$	−36.2705	−0.624334
$16$	16.0000	0.250000
$17$	−44.0132	−0.627927	−0.313963	−	0.949435i	$-0.601657\pi$
$17$	−44.0132	−0.627927	−0.313963	+	0.949435i	$0.601657\pi$
$18$	18.0000	0.235702
$19$	0	0
$19$	0	0
$20$	−48.3607	−0.540689
$21$	−2.02129	−0.0210038
$22$	31.8885	0.309030
$23$	−9.11146	−0.0826030	−0.0413015	−	0.999147i	$-0.513150\pi$
$23$	−9.11146	−0.0826030	−0.0413015	+	0.999147i	$0.513150\pi$
$24$	24.0000	0.204124
$25$	21.1722	0.169378
$26$	7.81966	0.0589831
$27$	27.0000	0.192450
$28$	−2.69505	−0.0181899
$29$	−161.151	−1.03190	−0.515948	−	0.856620i	$-0.672560\pi$
$29$	−161.151	−1.03190	−0.515948	+	0.856620i	$0.672560\pi$
$30$	−72.5410	−0.441471
$31$	60.5035	0.350540	0.175270	−	0.984520i	$-0.443920\pi$
$31$	60.5035	0.350540	0.175270	+	0.984520i	$0.443920\pi$
$32$	32.0000	0.176777
$33$	47.8328	0.252322
$34$	−88.0263	−0.444011
$35$	8.14590	0.0393402
$36$	36.0000	0.166667
$37$	104.885	0.466029	0.233014	−	0.972473i	$-0.425141\pi$
$37$	104.885	0.466029	0.233014	+	0.972473i	$0.425141\pi$
$38$	0	0
$39$	11.7295	0.0481595
$40$	−96.7214	−0.382325
$41$	249.353	0.949813	0.474906	−	0.880036i	$-0.342482\pi$
$41$	249.353	0.949813	0.474906	+	0.880036i	$0.342482\pi$
$42$	−4.04257	−0.0148520
$43$	−6.90481	−0.0244877	−0.0122439	−	0.999925i	$-0.503897\pi$
$43$	−6.90481	−0.0244877	−0.0122439	+	0.999925i	$0.503897\pi$
$44$	63.7771	0.218517
$45$	−108.812	−0.360459
$46$	−18.2229	−0.0584092
$47$	145.257	0.450808	0.225404	−	0.974265i	$-0.427630\pi$
$47$	145.257	0.450808	0.225404	+	0.974265i	$0.427630\pi$
$48$	48.0000	0.144338
$49$	−342.546	−0.998677
$50$	42.3444	0.119768
$51$	−132.039	−0.362534
$52$	15.6393	0.0417074
$53$	−754.187	−1.95463	−0.977317	−	0.211782i	$-0.932073\pi$
$53$	−754.187	−1.95463	−0.977317	+	0.211782i	$0.932073\pi$
$54$	54.0000	0.136083
$55$	−192.769	−0.472599
$56$	−5.39010	−0.0128622
$57$	0	0
$58$	−322.302	−0.729660
$59$	−704.046	−1.55354	−0.776771	−	0.629783i	$-0.783144\pi$
$59$	−704.046	−1.55354	−0.776771	+	0.629783i	$0.783144\pi$
$60$	−145.082	−0.312167
$61$	−32.5085	−0.0682342	−0.0341171	−	0.999418i	$-0.510862\pi$
$61$	−32.5085	−0.0682342	−0.0341171	+	0.999418i	$0.510862\pi$
$62$	121.007	0.247869
$63$	−6.06386	−0.0121266
$64$	64.0000	0.125000
$65$	−47.2705	−0.0902028
$66$	95.6656	0.178419
$67$	77.7264	0.141728	0.0708641	−	0.997486i	$-0.477424\pi$
$67$	77.7264	0.141728	0.0708641	+	0.997486i	$0.477424\pi$
$68$	−176.053	−0.313963
$69$	−27.3344	−0.0476909
$70$	16.2918	0.0278177
$71$	44.4183	0.0742463	0.0371231	−	0.999311i	$-0.488181\pi$
$71$	44.4183	0.0742463	0.0371231	+	0.999311i	$0.488181\pi$
$72$	72.0000	0.117851
$73$	280.735	0.450103	0.225051	−	0.974347i	$-0.427745\pi$
$73$	280.735	0.450103	0.225051	+	0.974347i	$0.427745\pi$
$74$	209.771	0.329532
$75$	63.5166	0.0977902
$76$	0	0
$77$	−10.7426	−0.0158992
$78$	23.4590	0.0340539
$79$	779.508	1.11015	0.555073	−	0.831802i	$-0.312690\pi$
$79$	779.508	1.11015	0.555073	+	0.831802i	$0.312690\pi$
$80$	−193.443	−0.270344
$81$	81.0000	0.111111
$82$	498.705	0.671619
$83$	−274.023	−0.362385	−0.181192	−	0.983448i	$-0.557996\pi$
$83$	−274.023	−0.362385	−0.181192	+	0.983448i	$0.557996\pi$
$84$	−8.08514	−0.0105019
$85$	532.127	0.679026
$86$	−13.8096	−0.0173154
$87$	−483.453	−0.595765
$88$	127.554	0.154515
$89$	−1005.91	−1.19805	−0.599023	−	0.800732i	$-0.704444\pi$
$89$	−1005.91	−1.19805	−0.599023	+	0.800732i	$0.704444\pi$
$90$	−217.623	−0.254883
$91$	−2.63430	−0.00303461
$92$	−36.4458	−0.0413015
$93$	181.510	0.202384
$94$	290.515	0.318769
$95$	0	0
$96$	96.0000	0.102062
$97$	−832.600	−0.871523	−0.435761	−	0.900062i	$-0.643521\pi$
$97$	−832.600	−0.871523	−0.435761	+	0.900062i	$0.643521\pi$
$98$	−685.092	−0.706171
$99$	143.498	0.145678
$100$	84.6888	0.0846888
$101$	910.371	0.896885	0.448442	−	0.893812i	$-0.351979\pi$
$101$	910.371	0.896885	0.448442	+	0.893812i	$0.351979\pi$
$102$	−264.079	−0.256350
$103$	−1272.16	−1.21699	−0.608493	−	0.793559i	$-0.708226\pi$
$103$	−1272.16	−1.21699	−0.608493	+	0.793559i	$0.708226\pi$
$104$	31.2786	0.0294916
$105$	24.4377	0.0227131
$106$	−1508.37	−1.38213
$107$	783.565	0.707945	0.353972	−	0.935256i	$-0.384831\pi$
$107$	783.565	0.707945	0.353972	+	0.935256i	$0.384831\pi$
$108$	108.000	0.0962250
$109$	−2013.17	−1.76905	−0.884524	−	0.466494i	$-0.845517\pi$
$109$	−2013.17	−1.76905	−0.884524	+	0.466494i	$0.845517\pi$
$110$	−385.538	−0.334178
$111$	314.656	0.269062
$112$	−10.7802	−0.00909493
$113$	−10.6506	−0.00886655	−0.00443327	−	0.999990i	$-0.501411\pi$
$113$	−10.6506	−0.00886655	−0.00443327	+	0.999990i	$0.501411\pi$
$114$	0	0
$115$	110.159	0.0893251
$116$	−644.604	−0.515948
$117$	35.1885	0.0278049
$118$	−1408.09	−1.09852
$119$	29.6544	0.0228438
$120$	−290.164	−0.220735
$121$	−1076.78	−0.809001
$122$	−65.0170	−0.0482489
$123$	748.058	0.548375
$124$	242.014	0.175270
$125$	1255.30	0.898216
$126$	−12.1277	−0.00857479
$127$	−932.541	−0.651572	−0.325786	−	0.945444i	$-0.605629\pi$
$127$	−932.541	−0.651572	−0.325786	+	0.945444i	$0.605629\pi$
$128$	128.000	0.0883883
$129$	−20.7144	−0.0141380
$130$	−94.5410	−0.0637830
$131$	208.795	0.139256	0.0696278	−	0.997573i	$-0.477819\pi$
$131$	208.795	0.139256	0.0696278	+	0.997573i	$0.477819\pi$
$132$	191.331	0.126161
$133$	0	0
$134$	155.453	0.100217
$135$	−326.435	−0.208111
$136$	−352.105	−0.222006
$137$	−368.275	−0.229663	−0.114832	−	0.993385i	$-0.536633\pi$
$137$	−368.275	−0.229663	−0.114832	+	0.993385i	$0.536633\pi$
$138$	−54.6687	−0.0337226
$139$	−1722.46	−1.05106	−0.525528	−	0.850776i	$-0.676132\pi$
$139$	−1722.46	−1.05106	−0.525528	+	0.850776i	$0.676132\pi$
$140$	32.5836	0.0196701
$141$	435.772	0.260274
$142$	88.8367	0.0525000
$143$	62.3394	0.0364551
$144$	144.000	0.0833333
$145$	1948.34	1.11587
$146$	561.469	0.318271
$147$	−1027.64	−0.576586
$148$	419.542	0.233014
$149$	−2688.05	−1.47795	−0.738973	−	0.673736i	$-0.764689\pi$
$149$	−2688.05	−1.47795	−0.738973	+	0.673736i	$0.764689\pi$
$150$	127.033	0.0691481
$151$	2474.74	1.33372	0.666860	−	0.745183i	$-0.267638\pi$
$151$	2474.74	1.33372	0.666860	+	0.745183i	$0.267638\pi$
$152$	0	0
$153$	−396.118	−0.209309
$154$	−21.4853	−0.0112424
$155$	−731.497	−0.379066
$156$	46.9180	0.0240798
$157$	−1209.81	−0.614991	−0.307495	−	0.951550i	$-0.599491\pi$
$157$	−1209.81	−0.614991	−0.307495	+	0.951550i	$0.599491\pi$
$158$	1559.02	0.784992
$159$	−2262.56	−1.12851
$160$	−386.885	−0.191162
$161$	6.13895	0.00300508
$162$	162.000	0.0785674
$163$	2745.03	1.31906	0.659531	−	0.751678i	$-0.270755\pi$
$163$	2745.03	1.31906	0.659531	+	0.751678i	$0.270755\pi$
$164$	997.410	0.474906
$165$	−578.307	−0.272855
$166$	−548.046	−0.256245
$167$	−3241.89	−1.50218	−0.751092	−	0.660197i	$-0.770473\pi$
$167$	−3241.89	−1.50218	−0.751092	+	0.660197i	$0.770473\pi$
$168$	−16.1703	−0.00742598
$169$	−2181.71	−0.993042
$170$	1064.25	0.480144
$171$	0	0
$172$	−27.6192	−0.0122439
$173$	−2461.28	−1.08166	−0.540832	−	0.841130i	$-0.681891\pi$
$173$	−2461.28	−1.08166	−0.540832	+	0.841130i	$0.681891\pi$
$174$	−966.906	−0.421270
$175$	−14.2650	−0.00616191
$176$	255.108	0.109259
$177$	−2112.14	−0.896938
$178$	−2011.82	−0.847147
$179$	−2964.26	−1.23776	−0.618880	−	0.785485i	$-0.712413\pi$
$179$	−2964.26	−1.23776	−0.618880	+	0.785485i	$0.712413\pi$
$180$	−435.246	−0.180230
$181$	4403.67	1.80841	0.904204	−	0.427100i	$-0.140465\pi$
$181$	4403.67	1.80841	0.904204	+	0.427100i	$0.140465\pi$
$182$	−5.26859	−0.00214579
$183$	−97.5255	−0.0393950
$184$	−72.8916	−0.0292046
$185$	−1268.08	−0.503953
$186$	363.021	0.143107
$187$	−701.758	−0.274426
$188$	581.029	0.225404
$189$	−18.1916	−0.00700128
$190$	0	0
$191$	−2167.97	−0.821302	−0.410651	−	0.911793i	$-0.634698\pi$
$191$	−2167.97	−0.821302	−0.410651	+	0.911793i	$0.634698\pi$
$192$	192.000	0.0721688
$193$	−3122.55	−1.16459	−0.582296	−	0.812977i	$-0.697845\pi$
$193$	−3122.55	−1.16459	−0.582296	+	0.812977i	$0.697845\pi$
$194$	−1665.20	−0.616260
$195$	−141.812	−0.0520786
$196$	−1370.18	−0.499338
$197$	202.429	0.0732106	0.0366053	−	0.999330i	$-0.488346\pi$
$197$	202.429	0.0732106	0.0366053	+	0.999330i	$0.488346\pi$
$198$	286.997	0.103010
$199$	−1649.25	−0.587497	−0.293749	−	0.955883i	$-0.594903\pi$
$199$	−1649.25	−0.587497	−0.293749	+	0.955883i	$0.594903\pi$
$200$	169.378	0.0598841
$201$	233.179	0.0818268
$202$	1820.74	0.634193
$203$	108.577	0.0375401
$204$	−528.158	−0.181267
$205$	−3014.71	−1.02711
$206$	−2544.32	−0.860540
$207$	−82.0031	−0.0275343
$208$	62.5573	0.0208537
$209$	0	0
$210$	48.8754	0.0160606
$211$	1629.35	0.531608	0.265804	−	0.964027i	$-0.414363\pi$
$211$	1629.35	0.531608	0.265804	+	0.964027i	$0.414363\pi$
$212$	−3016.75	−0.977317
$213$	133.255	0.0428661
$214$	1567.13	0.500593
$215$	83.4803	0.0264805
$216$	216.000	0.0680414
$217$	−40.7649	−0.0127526
$218$	−4026.33	−1.25091
$219$	842.204	0.259867
$220$	−771.076	−0.236300
$221$	−172.084	−0.0523784
$222$	629.313	0.190255
$223$	−481.492	−0.144588	−0.0722939	−	0.997383i	$-0.523032\pi$
$223$	−481.492	−0.144588	−0.0722939	+	0.997383i	$0.523032\pi$
$224$	−21.5604	−0.00643109
$225$	190.550	0.0564592
$226$	−21.3011	−0.00626960
$227$	2786.59	0.814768	0.407384	−	0.913257i	$-0.366441\pi$
$227$	2786.59	0.814768	0.407384	+	0.913257i	$0.366441\pi$
$228$	0	0
$229$	1437.72	0.414878	0.207439	−	0.978248i	$-0.433487\pi$
$229$	1437.72	0.414878	0.207439	+	0.978248i	$0.433487\pi$
$230$	220.318	0.0631624
$231$	−32.2279	−0.00917941
$232$	−1289.21	−0.364830
$233$	−2782.74	−0.782419	−0.391209	−	0.920302i	$-0.627943\pi$
$233$	−2782.74	−0.782419	−0.391209	+	0.920302i	$0.627943\pi$
$234$	70.3769	0.0196610
$235$	−1756.19	−0.487493
$236$	−2816.19	−0.776771
$237$	2338.53	0.640943
$238$	59.3088	0.0161530
$239$	4530.56	1.22618	0.613091	−	0.790013i	$-0.289926\pi$
$239$	4530.56	1.22618	0.613091	+	0.790013i	$0.289926\pi$
$240$	−580.328	−0.156083
$241$	−2457.27	−0.656792	−0.328396	−	0.944540i	$-0.606508\pi$
$241$	−2457.27	−0.656792	−0.328396	+	0.944540i	$0.606508\pi$
$242$	−2153.56	−0.572050
$243$	243.000	0.0641500
$244$	−130.034	−0.0341171
$245$	4141.44	1.07995
$246$	1496.12	0.387759
$247$	0	0
$248$	484.028	0.123935
$249$	−822.070	−0.209223
$250$	2510.59	0.635135
$251$	−3211.61	−0.807631	−0.403815	−	0.914841i	$-0.632316\pi$
$251$	−3211.61	−0.807631	−0.403815	+	0.914841i	$0.632316\pi$
$252$	−24.2554	−0.00606329
$253$	−145.276	−0.0361004
$254$	−1865.08	−0.460731
$255$	1596.38	0.392036
$256$	256.000	0.0625000
$257$	1670.69	0.405504	0.202752	−	0.979230i	$-0.435011\pi$
$257$	1670.69	0.405504	0.202752	+	0.979230i	$0.435011\pi$
$258$	−41.4288	−0.00999708
$259$	−70.6678	−0.0169540
$260$	−189.082	−0.0451014
$261$	−1450.36	−0.343965
$262$	417.590	0.0984686
$263$	−7731.93	−1.81282	−0.906409	−	0.422402i	$-0.861187\pi$
$263$	−7731.93	−1.81282	−0.906409	+	0.422402i	$0.861187\pi$
$264$	382.663	0.0892093
$265$	9118.25	2.11370
$266$	0	0
$267$	−3017.73	−0.691692
$268$	310.906	0.0708641
$269$	1024.48	0.232207	0.116104	−	0.993237i	$-0.462960\pi$
$269$	1024.48	0.232207	0.116104	+	0.993237i	$0.462960\pi$
$270$	−652.869	−0.147157
$271$	1067.86	0.239366	0.119683	−	0.992812i	$-0.461812\pi$
$271$	1067.86	0.239366	0.119683	+	0.992812i	$0.461812\pi$
$272$	−704.210	−0.156982
$273$	−7.90289	−0.00175203
$274$	−736.550	−0.162396
$275$	337.575	0.0740239
$276$	−109.337	−0.0238454
$277$	311.065	0.0674733	0.0337367	−	0.999431i	$-0.489259\pi$
$277$	311.065	0.0674733	0.0337367	+	0.999431i	$0.489259\pi$
$278$	−3444.91	−0.743209
$279$	544.531	0.116847
$280$	65.1672	0.0139089
$281$	−7346.75	−1.55968	−0.779840	−	0.625979i	$-0.784700\pi$
$281$	−7346.75	−1.55968	−0.779840	+	0.625979i	$0.784700\pi$
$282$	871.544	0.184041
$283$	4046.95	0.850056	0.425028	−	0.905180i	$-0.360264\pi$
$283$	4046.95	0.850056	0.425028	+	0.905180i	$0.360264\pi$
$284$	177.673	0.0371231
$285$	0	0
$286$	124.679	0.0257777
$287$	−168.004	−0.0345539
$288$	288.000	0.0589256
$289$	−2975.84	−0.605708
$290$	3896.68	0.789039
$291$	−2497.80	−0.503174
$292$	1122.94	0.225051
$293$	−3641.56	−0.726083	−0.363041	−	0.931773i	$-0.618262\pi$
$293$	−3641.56	−0.726083	−0.363041	+	0.931773i	$0.618262\pi$
$294$	−2055.28	−0.407708
$295$	8512.04	1.67997
$296$	839.084	0.164766
$297$	430.495	0.0841073
$298$	−5376.10	−1.04506
$299$	−35.6242	−0.00689031
$300$	254.067	0.0488951
$301$	4.65220	0.000890858 0
$302$	4949.49	0.943082
$303$	2731.11	0.517817
$304$	0	0
$305$	393.033	0.0737869
$306$	−792.237	−0.148004
$307$	4685.42	0.871045	0.435523	−	0.900178i	$-0.356564\pi$
$307$	4685.42	0.871045	0.435523	+	0.900178i	$0.356564\pi$
$308$	−42.9706	−0.00794960
$309$	−3816.48	−0.702628
$310$	−1462.99	−0.268040
$311$	−2413.55	−0.440065	−0.220032	−	0.975493i	$-0.570616\pi$
$311$	−2413.55	−0.440065	−0.220032	+	0.975493i	$0.570616\pi$
$312$	93.8359	0.0170270
$313$	−5062.23	−0.914167	−0.457084	−	0.889424i	$-0.651106\pi$
$313$	−5062.23	−0.914167	−0.457084	+	0.889424i	$0.651106\pi$
$314$	−2419.63	−0.434864
$315$	73.3131	0.0131134
$316$	3118.03	0.555073
$317$	5704.03	1.01063	0.505316	−	0.862935i	$-0.331376\pi$
$317$	5704.03	1.01063	0.505316	+	0.862935i	$0.331376\pi$
$318$	−4525.12	−0.797976
$319$	−2569.43	−0.450974
$320$	−773.771	−0.135172
$321$	2350.69	0.408732
$322$	12.2779	0.00212491
$323$	0	0
$324$	324.000	0.0555556
$325$	82.7797	0.0141286
$326$	5490.05	0.932717
$327$	−6039.50	−1.02136
$328$	1994.82	0.335810
$329$	−97.8689	−0.0164003
$330$	−1156.61	−0.192938
$331$	8367.55	1.38949	0.694747	−	0.719254i	$-0.255516\pi$
$331$	8367.55	1.38949	0.694747	+	0.719254i	$0.255516\pi$
$332$	−1096.09	−0.181192
$333$	943.969	0.155343
$334$	−6483.78	−1.06221
$335$	−939.725	−0.153262
$336$	−32.3406	−0.00525096
$337$	263.413	0.0425787	0.0212894	−	0.999773i	$-0.493223\pi$
$337$	263.413	0.0425787	0.0212894	+	0.999773i	$0.493223\pi$
$338$	−4363.43	−0.702187
$339$	−31.9517	−0.00511910
$340$	2128.51	0.339513
$341$	964.684	0.153198
$342$	0	0
$343$	461.895	0.0727113
$344$	−55.2384	−0.00865772
$345$	330.477	0.0515719
$346$	−4922.57	−0.764853
$347$	4021.50	0.622148	0.311074	−	0.950386i	$-0.399311\pi$
$347$	4021.50	0.622148	0.311074	+	0.950386i	$0.399311\pi$
$348$	−1933.81	−0.297883
$349$	453.400	0.0695414	0.0347707	−	0.999395i	$-0.488930\pi$
$349$	453.400	0.0695414	0.0347707	+	0.999395i	$0.488930\pi$
$350$	−28.5301	−0.00435713
$351$	105.565	0.0160532
$352$	510.217	0.0772575
$353$	−4547.61	−0.685680	−0.342840	−	0.939394i	$-0.611389\pi$
$353$	−4547.61	−0.685680	−0.342840	+	0.939394i	$0.611389\pi$
$354$	−4224.28	−0.634231
$355$	−537.025	−0.0802883
$356$	−4023.63	−0.599023
$357$	88.9632	0.0131889
$358$	−5928.52	−0.875229
$359$	8396.86	1.23445	0.617227	−	0.786785i	$-0.288256\pi$
$359$	8396.86	1.23445	0.617227	+	0.786785i	$0.288256\pi$
$360$	−870.492	−0.127442
$361$	0	0
$362$	8807.33	1.27874
$363$	−3230.34	−0.467077
$364$	−10.5372	−0.00151730
$365$	−3394.13	−0.486731
$366$	−195.051	−0.0278565
$367$	−5422.59	−0.771273	−0.385636	−	0.922651i	$-0.626018\pi$
$367$	−5422.59	−0.771273	−0.385636	+	0.922651i	$0.626018\pi$
$368$	−145.783	−0.0206508
$369$	2244.17	0.316604
$370$	−2536.17	−0.356349
$371$	508.143	0.0711091
$372$	726.042	0.101192
$373$	7439.39	1.03270	0.516350	−	0.856378i	$-0.327290\pi$
$373$	7439.39	1.03270	0.516350	+	0.856378i	$0.327290\pi$
$374$	−1403.52	−0.194048
$375$	3765.89	0.518586
$376$	1162.06	0.159385
$377$	−630.073	−0.0860753
$378$	−36.3832	−0.00495065
$379$	12741.8	1.72692	0.863461	−	0.504415i	$-0.168292\pi$
$379$	12741.8	1.72692	0.863461	+	0.504415i	$0.168292\pi$
$380$	0	0
$381$	−2797.62	−0.376185
$382$	−4335.93	−0.580748
$383$	10550.9	1.40764	0.703822	−	0.710376i	$-0.251475\pi$
$383$	10550.9	1.40764	0.703822	+	0.710376i	$0.251475\pi$
$384$	384.000	0.0510310
$385$	129.880	0.0171930
$386$	−6245.10	−0.823490
$387$	−62.1432	−0.00816258
$388$	−3330.40	−0.435761
$389$	6581.54	0.857834	0.428917	−	0.903344i	$-0.358895\pi$
$389$	6581.54	0.857834	0.428917	+	0.903344i	$0.358895\pi$
$390$	−283.623	−0.0368252
$391$	401.024	0.0518687
$392$	−2740.37	−0.353085
$393$	626.384	0.0803993
$394$	404.859	0.0517677
$395$	−9424.39	−1.20049
$396$	573.994	0.0728391
$397$	2148.76	0.271646	0.135823	−	0.990733i	$-0.456632\pi$
$397$	2148.76	0.271646	0.135823	+	0.990733i	$0.456632\pi$
$398$	−3298.49	−0.415423
$399$	0	0
$400$	338.755	0.0423444
$401$	2532.20	0.315342	0.157671	−	0.987492i	$-0.449602\pi$
$401$	2532.20	0.315342	0.157671	+	0.987492i	$0.449602\pi$
$402$	466.358	0.0578603
$403$	236.558	0.0292402
$404$	3641.49	0.448442
$405$	−979.304	−0.120153
$406$	217.155	0.0265449
$407$	1672.32	0.203671
$408$	−1056.32	−0.128175
$409$	8046.03	0.972740	0.486370	−	0.873753i	$-0.338321\pi$
$409$	8046.03	0.972740	0.486370	+	0.873753i	$0.338321\pi$
$410$	−6029.43	−0.726274
$411$	−1104.83	−0.132596
$412$	−5088.64	−0.608493
$413$	474.360	0.0565175
$414$	−164.006	−0.0194697
$415$	3312.99	0.391875
$416$	125.115	0.0147458
$417$	−5167.37	−0.606828
$418$	0	0
$419$	−10432.9	−1.21642	−0.608210	−	0.793776i	$-0.708112\pi$
$419$	−10432.9	−1.21642	−0.608210	+	0.793776i	$0.708112\pi$
$420$	97.7508	0.0113565
$421$	4591.58	0.531544	0.265772	−	0.964036i	$-0.414373\pi$
$421$	4591.58	0.531544	0.265772	+	0.964036i	$0.414373\pi$
$422$	3258.71	0.375904
$423$	1307.32	0.150269
$424$	−6033.50	−0.691067
$425$	−931.856	−0.106357
$426$	266.510	0.0303109
$427$	21.9030	0.00248234
$428$	3134.26	0.353972
$429$	187.018	0.0210474
$430$	166.961	0.0187245
$431$	14117.1	1.57772	0.788861	−	0.614571i	$-0.210671\pi$
$431$	14117.1	1.57772	0.788861	+	0.614571i	$0.210671\pi$
$432$	432.000	0.0481125
$433$	−13929.0	−1.54592	−0.772962	−	0.634452i	$-0.781226\pi$
$433$	−13929.0	−1.54592	−0.772962	+	0.634452i	$0.781226\pi$
$434$	−81.5299	−0.00901742
$435$	5845.03	0.644247
$436$	−8052.66	−0.884524
$437$	0	0
$438$	1684.41	0.183754
$439$	5222.03	0.567731	0.283866	−	0.958864i	$-0.408383\pi$
$439$	5222.03	0.567731	0.283866	+	0.958864i	$0.408383\pi$
$440$	−1542.15	−0.167089
$441$	−3082.91	−0.332892
$442$	−344.168	−0.0370371
$443$	−10163.4	−1.09002	−0.545010	−	0.838430i	$-0.683474\pi$
$443$	−10163.4	−1.09002	−0.545010	+	0.838430i	$0.683474\pi$
$444$	1258.63	0.134531
$445$	12161.6	1.29554
$446$	−962.984	−0.102239
$447$	−8064.16	−0.853292
$448$	−43.1208	−0.00454747
$449$	17851.6	1.87632	0.938161	−	0.346199i	$-0.112528\pi$
$449$	17851.6	1.87632	0.938161	+	0.346199i	$0.112528\pi$
$450$	381.100	0.0399227
$451$	3975.74	0.415101
$452$	−42.6022	−0.00443327
$453$	7424.23	0.770024
$454$	5573.18	0.576128
$455$	31.8491	0.00328156
$456$	0	0
$457$	−5037.95	−0.515679	−0.257839	−	0.966188i	$-0.583011\pi$
$457$	−5037.95	−0.515679	−0.257839	+	0.966188i	$0.583011\pi$
$458$	2875.44	0.293363
$459$	−1188.36	−0.120845
$460$	440.636	0.0446625
$461$	−11181.4	−1.12965	−0.564825	−	0.825211i	$-0.691056\pi$
$461$	−11181.4	−1.12965	−0.564825	+	0.825211i	$0.691056\pi$
$462$	−64.4559	−0.00649082
$463$	18455.1	1.85244	0.926222	−	0.376978i	$-0.123037\pi$
$463$	18455.1	1.85244	0.926222	+	0.376978i	$0.123037\pi$
$464$	−2578.41	−0.257974
$465$	−2194.49	−0.218854
$466$	−5565.48	−0.553253
$467$	6412.78	0.635435	0.317718	−	0.948185i	$-0.397084\pi$
$467$	6412.78	0.635435	0.317718	+	0.948185i	$0.397084\pi$
$468$	140.754	0.0139025
$469$	−52.3691	−0.00515603
$470$	−3512.37	−0.344710
$471$	−3629.44	−0.355065
$472$	−5632.37	−0.549260
$473$	−110.092	−0.0107020
$474$	4677.05	0.453215
$475$	0	0
$476$	118.618	0.0114219
$477$	−6787.69	−0.651545
$478$	9061.11	0.867041
$479$	−8519.67	−0.812680	−0.406340	−	0.913722i	$-0.633195\pi$
$479$	−8519.67	−0.812680	−0.406340	+	0.913722i	$0.633195\pi$
$480$	−1160.66	−0.110368
$481$	410.084	0.0388737
$482$	−4914.55	−0.464422
$483$	18.4169	0.00173498
$484$	−4307.12	−0.404500
$485$	10066.3	0.942445
$486$	486.000	0.0453609
$487$	12746.8	1.18607	0.593033	−	0.805178i	$-0.297930\pi$
$487$	12746.8	1.18607	0.593033	+	0.805178i	$0.297930\pi$
$488$	−260.068	−0.0241244
$489$	8235.08	0.761560
$490$	8282.88	0.763637
$491$	−5187.09	−0.476762	−0.238381	−	0.971172i	$-0.576617\pi$
$491$	−5187.09	−0.476762	−0.238381	+	0.971172i	$0.576617\pi$
$492$	2992.23	0.274187
$493$	7092.76	0.647955
$494$	0	0
$495$	−1734.92	−0.157533
$496$	968.056	0.0876350
$497$	−29.9274	−0.00270106
$498$	−1644.14	−0.147943
$499$	−10704.5	−0.960315	−0.480158	−	0.877182i	$-0.659421\pi$
$499$	−10704.5	−0.960315	−0.480158	+	0.877182i	$0.659421\pi$
$500$	5021.18	0.449108
$501$	−9725.67	−0.867287
$502$	−6423.23	−0.571081
$503$	13720.9	1.21627	0.608137	−	0.793832i	$-0.291917\pi$
$503$	13720.9	1.21627	0.608137	+	0.793832i	$0.291917\pi$
$504$	−48.5109	−0.00428739
$505$	−11006.5	−0.969871
$506$	−290.551	−0.0255268
$507$	−6545.14	−0.573333
$508$	−3730.16	−0.325786
$509$	−6427.78	−0.559737	−0.279869	−	0.960038i	$-0.590291\pi$
$509$	−6427.78	−0.559737	−0.279869	+	0.960038i	$0.590291\pi$
$510$	3192.76	0.277211
$511$	−189.148	−0.0163746
$512$	512.000	0.0441942
$513$	0	0
$514$	3341.37	0.286735
$515$	15380.6	1.31602
$516$	−82.8577	−0.00706900
$517$	2316.02	0.197018
$518$	−141.336	−0.0119883
$519$	−7383.85	−0.624500
$520$	−378.164	−0.0318915
$521$	−2296.27	−0.193093	−0.0965464	−	0.995328i	$-0.530780\pi$
$521$	−2296.27	−0.193093	−0.0965464	+	0.995328i	$0.530780\pi$
$522$	−2900.72	−0.243220
$523$	−672.621	−0.0562364	−0.0281182	−	0.999605i	$-0.508951\pi$
$523$	−672.621	−0.0562364	−0.0281182	+	0.999605i	$0.508951\pi$
$524$	835.179	0.0696278
$525$	−42.7951	−0.00355758
$526$	−15463.9	−1.28186
$527$	−2662.95	−0.220114
$528$	765.325	0.0630805
$529$	−12084.0	−0.993177
$530$	18236.5	1.49461
$531$	−6336.42	−0.517848
$532$	0	0
$533$	974.926	0.0792284
$534$	−6035.45	−0.489100
$535$	−9473.43	−0.765556
$536$	621.811	0.0501085
$537$	−8892.78	−0.714622
$538$	2048.96	0.164195
$539$	−5461.65	−0.436456
$540$	−1305.74	−0.104056
$541$	−18524.3	−1.47213	−0.736065	−	0.676911i	$-0.763318\pi$
$541$	−18524.3	−1.47213	−0.736065	+	0.676911i	$0.763318\pi$
$542$	2135.73	0.169257
$543$	13211.0	1.04409
$544$	−1408.42	−0.111003
$545$	24339.5	1.91301
$546$	−15.8058	−0.00123887
$547$	6149.10	0.480652	0.240326	−	0.970692i	$-0.422746\pi$
$547$	6149.10	0.480652	0.240326	+	0.970692i	$0.422746\pi$
$548$	−1473.10	−0.114832
$549$	−292.576	−0.0227447
$550$	675.151	0.0523428
$551$	0	0
$552$	−218.675	−0.0168613
$553$	−525.203	−0.0403868
$554$	622.131	0.0477109
$555$	−3804.25	−0.290957
$556$	−6889.82	−0.525528
$557$	−1151.85	−0.0876218	−0.0438109	−	0.999040i	$-0.513950\pi$
$557$	−1151.85	−0.0876218	−0.0438109	+	0.999040i	$0.513950\pi$
$558$	1089.06	0.0826231
$559$	−26.9966	−0.00204264
$560$	130.334	0.00983506
$561$	−2105.27	−0.158440
$562$	−14693.5	−1.10286
$563$	3182.72	0.238252	0.119126	−	0.992879i	$-0.461991\pi$
$563$	3182.72	0.238252	0.119126	+	0.992879i	$0.461991\pi$
$564$	1743.09	0.130137
$565$	128.767	0.00958809
$566$	8093.89	0.601081
$567$	−54.5747	−0.00404219
$568$	355.347	0.0262500
$569$	−20679.8	−1.52363	−0.761814	−	0.647796i	$-0.775691\pi$
$569$	−20679.8	−1.52363	−0.761814	+	0.647796i	$0.775691\pi$
$570$	0	0
$571$	−2820.58	−0.206721	−0.103360	−	0.994644i	$-0.532960\pi$
$571$	−2820.58	−0.206721	−0.103360	+	0.994644i	$0.532960\pi$
$572$	249.358	0.0182276
$573$	−6503.90	−0.474179
$574$	−336.009	−0.0244333
$575$	−192.910	−0.0139911
$576$	576.000	0.0416667
$577$	11208.6	0.808700	0.404350	−	0.914604i	$-0.367498\pi$
$577$	11208.6	0.808700	0.404350	+	0.914604i	$0.367498\pi$
$578$	−5951.68	−0.428300
$579$	−9367.65	−0.672377
$580$	7793.37	0.557934
$581$	184.626	0.0131835
$582$	−4995.60	−0.355798
$583$	−12025.0	−0.854242
$584$	2245.88	0.159135
$585$	−425.435	−0.0300676
$586$	−7283.12	−0.513418
$587$	−209.871	−0.0147569	−0.00737846	−	0.999973i	$-0.502349\pi$
$587$	−209.871	−0.0147569	−0.00737846	+	0.999973i	$0.502349\pi$
$588$	−4110.55	−0.288293
$589$	0	0
$590$	17024.1	1.18792
$591$	607.288	0.0422682
$592$	1678.17	0.116507
$593$	9737.59	0.674325	0.337163	−	0.941446i	$-0.390533\pi$
$593$	9737.59	0.674325	0.337163	+	0.941446i	$0.390533\pi$
$594$	860.991	0.0594729
$595$	−358.527	−0.0247028
$596$	−10752.2	−0.738973
$597$	−4947.74	−0.339192
$598$	−71.2485	−0.00487219
$599$	3772.44	0.257325	0.128662	−	0.991688i	$-0.458932\pi$
$599$	3772.44	0.257325	0.128662	+	0.991688i	$0.458932\pi$
$600$	508.133	0.0345741
$601$	12419.2	0.842910	0.421455	−	0.906849i	$-0.361520\pi$
$601$	12419.2	0.842910	0.421455	+	0.906849i	$0.361520\pi$
$602$	9.30439	0.000629931 0
$603$	699.537	0.0472427
$604$	9898.97	0.666860
$605$	13018.5	0.874836
$606$	5462.23	0.366152
$607$	−3934.15	−0.263068	−0.131534	−	0.991312i	$-0.541990\pi$
$607$	−3934.15	−0.263068	−0.131534	+	0.991312i	$0.541990\pi$
$608$	0	0
$609$	325.732	0.0216738
$610$	786.067	0.0521753
$611$	567.932	0.0376040
$612$	−1584.47	−0.104654
$613$	−22886.6	−1.50796	−0.753980	−	0.656897i	$-0.771868\pi$
$613$	−22886.6	−1.50796	−0.753980	+	0.656897i	$0.771868\pi$
$614$	9370.84	0.615922
$615$	−9044.14	−0.593000
$616$	−85.9412	−0.00562121
$617$	5961.78	0.388999	0.194500	−	0.980903i	$-0.437692\pi$
$617$	5961.78	0.388999	0.194500	+	0.980903i	$0.437692\pi$
$618$	−7632.96	−0.496833
$619$	15162.2	0.984526	0.492263	−	0.870447i	$-0.336170\pi$
$619$	15162.2	0.984526	0.492263	+	0.870447i	$0.336170\pi$
$620$	−2925.99	−0.189533
$621$	−246.009	−0.0158970
$622$	−4827.11	−0.311173
$623$	677.743	0.0435846
$624$	187.672	0.0120399
$625$	−17823.3	−1.14069
$626$	−10124.5	−0.646414
$627$	0	0
$628$	−4839.25	−0.307495
$629$	−4616.34	−0.292632
$630$	146.626	0.00927258
$631$	19490.7	1.22966	0.614829	−	0.788661i	$-0.289225\pi$
$631$	19490.7	1.22966	0.614829	+	0.788661i	$0.289225\pi$
$632$	6236.07	0.392496
$633$	4888.06	0.306924
$634$	11408.1	0.714624
$635$	11274.6	0.704595
$636$	−9050.25	−0.564254
$637$	−1339.30	−0.0833044
$638$	−5138.87	−0.318887
$639$	399.765	0.0247488
$640$	−1547.54	−0.0955812
$641$	−7848.89	−0.483639	−0.241819	−	0.970321i	$-0.577744\pi$
$641$	−7848.89	−0.483639	−0.241819	+	0.970321i	$0.577744\pi$
$642$	4701.39	0.289017
$643$	−15640.8	−0.959272	−0.479636	−	0.877468i	$-0.659231\pi$
$643$	−15640.8	−0.959272	−0.479636	+	0.877468i	$0.659231\pi$
$644$	24.5558	0.00150254
$645$	250.441	0.0152885
$646$	0	0
$647$	5621.52	0.341584	0.170792	−	0.985307i	$-0.445367\pi$
$647$	5621.52	0.341584	0.170792	+	0.985307i	$0.445367\pi$
$648$	648.000	0.0392837
$649$	−11225.5	−0.678952
$650$	165.559	0.00999043
$651$	−122.295	−0.00736269
$652$	10980.1	0.659531
$653$	−21586.7	−1.29365	−0.646824	−	0.762640i	$-0.723903\pi$
$653$	−21586.7	−1.29365	−0.646824	+	0.762640i	$0.723903\pi$
$654$	−12079.0	−0.722211
$655$	−2524.36	−0.150588
$656$	3989.64	0.237453
$657$	2526.61	0.150034
$658$	−195.738	−0.0115967
$659$	6062.41	0.358358	0.179179	−	0.983816i	$-0.442656\pi$
$659$	6062.41	0.358358	0.179179	+	0.983816i	$0.442656\pi$
$660$	−2313.23	−0.136428
$661$	−5076.16	−0.298698	−0.149349	−	0.988785i	$-0.547718\pi$
$661$	−5076.16	−0.298698	−0.149349	+	0.988785i	$0.547718\pi$
$662$	16735.1	0.982520
$663$	−516.252	−0.0302407
$664$	−2192.19	−0.128122
$665$	0	0
$666$	1887.94	0.109844
$667$	1468.32	0.0852377
$668$	−12967.6	−0.751092
$669$	−1444.48	−0.0834778
$670$	−1879.45	−0.108372
$671$	−518.324	−0.0298207
$672$	−64.6812	−0.00371299
$673$	15406.8	0.882450	0.441225	−	0.897397i	$-0.354544\pi$
$673$	15406.8	0.882450	0.441225	+	0.897397i	$0.354544\pi$
$674$	526.826	0.0301077
$675$	571.650	0.0325967
$676$	−8726.85	−0.496521
$677$	−7518.29	−0.426811	−0.213406	−	0.976964i	$-0.568456\pi$
$677$	−7518.29	−0.426811	−0.213406	+	0.976964i	$0.568456\pi$
$678$	−63.9033	−0.00361975
$679$	560.974	0.0317058
$680$	4257.01	0.240072
$681$	8359.77	0.470407
$682$	1929.37	0.108327
$683$	−18762.7	−1.05115	−0.525574	−	0.850748i	$-0.676149\pi$
$683$	−18762.7	−1.05115	−0.525574	+	0.850748i	$0.676149\pi$
$684$	0	0
$685$	4452.51	0.248353
$686$	923.790	0.0514147
$687$	4313.16	0.239530
$688$	−110.477	−0.00612194
$689$	−2948.74	−0.163045
$690$	660.954	0.0364668
$691$	30372.1	1.67208	0.836042	−	0.548666i	$-0.184864\pi$
$691$	30372.1	1.67208	0.836042	+	0.548666i	$0.184864\pi$
$692$	−9845.14	−0.540832
$693$	−96.6838	−0.00529973
$694$	8042.99	0.439925
$695$	20824.8	1.13659
$696$	−3867.62	−0.210635
$697$	−10974.8	−0.596413
$698$	906.800	0.0491732
$699$	−8348.23	−0.451730
$700$	−57.0601	−0.00308096
$701$	−23215.5	−1.25084	−0.625420	−	0.780288i	$-0.715072\pi$
$701$	−23215.5	−1.25084	−0.625420	+	0.780288i	$0.715072\pi$
$702$	211.131	0.0113513
$703$	0	0
$704$	1020.43	0.0546293
$705$	−5268.56	−0.281454
$706$	−9095.22	−0.484849
$707$	−613.374	−0.0326284
$708$	−8448.56	−0.448469
$709$	−2093.79	−0.110908	−0.0554540	−	0.998461i	$-0.517661\pi$
$709$	−2093.79	−0.110908	−0.0554540	+	0.998461i	$0.517661\pi$
$710$	−1074.05	−0.0567724
$711$	7015.58	0.370049
$712$	−8047.27	−0.423573
$713$	−551.275	−0.0289557
$714$	177.926	0.00932595
$715$	−753.694	−0.0394218
$716$	−11857.0	−0.618880
$717$	13591.7	0.707936
$718$	16793.7	0.872891
$719$	10026.4	0.520059	0.260030	−	0.965601i	$-0.416268\pi$
$719$	10026.4	0.520059	0.260030	+	0.965601i	$0.416268\pi$
$720$	−1740.98	−0.0901148
$721$	857.133	0.0442737
$722$	0	0
$723$	−7371.82	−0.379199
$724$	17614.7	0.904204
$725$	−3411.92	−0.174780
$726$	−6460.68	−0.330273
$727$	31486.5	1.60628	0.803142	−	0.595787i	$-0.203160\pi$
$727$	31486.5	1.60628	0.803142	+	0.595787i	$0.203160\pi$
$728$	−21.0744	−0.00107290
$729$	729.000	0.0370370
$730$	−6788.26	−0.344171
$731$	303.902	0.0153765
$732$	−390.102	−0.0196975
$733$	−14789.2	−0.745227	−0.372614	−	0.927987i	$-0.621538\pi$
$733$	−14789.2	−0.745227	−0.372614	+	0.927987i	$0.621538\pi$
$734$	−10845.2	−0.545372
$735$	12424.3	0.623507
$736$	−291.567	−0.0146023
$737$	1239.29	0.0619401
$738$	4488.35	0.223873
$739$	−34580.3	−1.72132	−0.860660	−	0.509179i	$-0.829949\pi$
$739$	−34580.3	−1.72132	−0.860660	+	0.509179i	$0.829949\pi$
$740$	−5072.33	−0.251976
$741$	0	0
$742$	1016.29	0.0502817
$743$	14656.3	0.723670	0.361835	−	0.932242i	$-0.382150\pi$
$743$	14656.3	0.723670	0.361835	+	0.932242i	$0.382150\pi$
$744$	1452.08	0.0715537
$745$	32499.0	1.59822
$746$	14878.8	0.730229
$747$	−2466.21	−0.120795
$748$	−2807.03	−0.137213
$749$	−527.936	−0.0257548
$750$	7531.77	0.366695
$751$	−15707.7	−0.763224	−0.381612	−	0.924323i	$-0.624631\pi$
$751$	−15707.7	−0.763224	−0.381612	+	0.924323i	$0.624631\pi$
$752$	2324.12	0.112702
$753$	−9634.84	−0.466286
$754$	−1260.15	−0.0608644
$755$	−29920.1	−1.44226
$756$	−72.7663	−0.00350064
$757$	−3495.32	−0.167820	−0.0839099	−	0.996473i	$-0.526741\pi$
$757$	−3495.32	−0.167820	−0.0839099	+	0.996473i	$0.526741\pi$
$758$	25483.7	1.22112
$759$	−435.827	−0.0208426
$760$	0	0
$761$	−9634.36	−0.458929	−0.229465	−	0.973317i	$-0.573698\pi$
$761$	−9634.36	−0.458929	−0.229465	+	0.973317i	$0.573698\pi$
$762$	−5595.25	−0.266003
$763$	1356.39	0.0643575
$764$	−8671.87	−0.410651
$765$	4789.14	0.226342
$766$	21101.9	0.995354
$767$	−2752.70	−0.129588
$768$	768.000	0.0360844
$769$	3390.81	0.159006	0.0795031	−	0.996835i	$-0.474667\pi$
$769$	3390.81	0.159006	0.0795031	+	0.996835i	$0.474667\pi$
$770$	259.761	0.0121573
$771$	5012.06	0.234118
$772$	−12490.2	−0.582296
$773$	34473.8	1.60406	0.802028	−	0.597286i	$-0.203754\pi$
$773$	34473.8	1.60406	0.802028	+	0.597286i	$0.203754\pi$
$774$	−124.286	−0.00577182
$775$	1280.99	0.0593737
$776$	−6660.80	−0.308130
$777$	−212.003	−0.00978840
$778$	13163.1	0.606580
$779$	0	0
$780$	−567.246	−0.0260393
$781$	708.218	0.0324482
$782$	802.048	0.0366767
$783$	−4351.07	−0.198588
$784$	−5480.74	−0.249669
$785$	14626.8	0.665037
$786$	1252.77	0.0568509
$787$	30099.5	1.36332	0.681658	−	0.731671i	$-0.261259\pi$
$787$	30099.5	1.36332	0.681658	+	0.731671i	$0.261259\pi$
$788$	809.717	0.0366053
$789$	−23195.8	−1.04663
$790$	−18848.8	−0.848873
$791$	7.17594	0.000322563 0
$792$	1147.99	0.0515050
$793$	−127.103	−0.00569174
$794$	4297.53	0.192083
$795$	27354.8	1.22034
$796$	−6596.98	−0.293749
$797$	2712.41	0.120550	0.0602752	−	0.998182i	$-0.480802\pi$
$797$	2712.41	0.120550	0.0602752	+	0.998182i	$0.480802\pi$
$798$	0	0
$799$	−6393.23	−0.283074
$800$	677.511	0.0299420
$801$	−9053.18	−0.399349
$802$	5064.40	0.222980
$803$	4476.11	0.196710
$804$	932.717	0.0409134
$805$	−74.2210	−0.00324962
$806$	473.117	0.0206760
$807$	3073.45	0.134065
$808$	7282.97	0.317097
$809$	25242.2	1.09699	0.548497	−	0.836153i	$-0.315200\pi$
$809$	25242.2	1.09699	0.548497	+	0.836153i	$0.315200\pi$
$810$	−1958.61	−0.0849611
$811$	−29503.8	−1.27746	−0.638728	−	0.769432i	$-0.720539\pi$
$811$	−29503.8	−1.27746	−0.638728	+	0.769432i	$0.720539\pi$
$812$	434.310	0.0187700
$813$	3203.59	0.138198
$814$	3344.64	0.144017
$815$	−33187.8	−1.42640
$816$	−2112.63	−0.0906334
$817$	0	0
$818$	16092.1	0.687831
$819$	−23.7087	−0.00101154
$820$	−12058.9	−0.513553
$821$	401.572	0.0170706	0.00853530	−	0.999964i	$-0.497283\pi$
$821$	401.572	0.0170706	0.00853530	+	0.999964i	$0.497283\pi$
$822$	−2209.65	−0.0937596
$823$	21122.7	0.894642	0.447321	−	0.894374i	$-0.352378\pi$
$823$	21122.7	0.894642	0.447321	+	0.894374i	$0.352378\pi$
$824$	−10177.3	−0.430270
$825$	1012.73	0.0427377
$826$	948.720	0.0399639
$827$	−43088.6	−1.81177	−0.905887	−	0.423519i	$-0.860795\pi$
$827$	−43088.6	−1.81177	−0.905887	+	0.423519i	$0.860795\pi$
$828$	−328.012	−0.0137672
$829$	33228.8	1.39214	0.696070	−	0.717974i	$-0.254930\pi$
$829$	33228.8	1.39214	0.696070	+	0.717974i	$0.254930\pi$
$830$	6625.97	0.277097
$831$	933.196	0.0389557
$832$	250.229	0.0104268
$833$	15076.5	0.627096
$834$	−10334.7	−0.429092
$835$	39195.0	1.62443
$836$	0	0
$837$	1633.59	0.0674615
$838$	−20865.8	−0.860139
$839$	35600.4	1.46491	0.732456	−	0.680814i	$-0.238374\pi$
$839$	35600.4	1.46491	0.732456	+	0.680814i	$0.238374\pi$
$840$	195.502	0.00803029
$841$	1580.62	0.0648087
$842$	9183.16	0.375858
$843$	−22040.2	−0.900482
$844$	6517.41	0.265804
$845$	26377.3	1.07385
$846$	2614.63	0.106256
$847$	725.494	0.0294312
$848$	−12067.0	−0.488658
$849$	12140.8	0.490780
$850$	−1863.71	−0.0752056
$851$	−955.659	−0.0384954
$852$	533.020	0.0214331
$853$	−8614.63	−0.345791	−0.172895	−	0.984940i	$-0.555312\pi$
$853$	−8614.63	−0.345791	−0.172895	+	0.984940i	$0.555312\pi$
$854$	43.8060	0.00175528
$855$	0	0
$856$	6268.52	0.250296
$857$	−26698.4	−1.06418	−0.532088	−	0.846689i	$-0.678593\pi$
$857$	−26698.4	−1.06418	−0.532088	+	0.846689i	$0.678593\pi$
$858$	374.036	0.0148827
$859$	45356.8	1.80158	0.900788	−	0.434260i	$-0.142990\pi$
$859$	45356.8	1.80158	0.900788	+	0.434260i	$0.142990\pi$
$860$	333.921	0.0132402
$861$	−504.013	−0.0199497
$862$	28234.3	1.11562
$863$	−20943.6	−0.826104	−0.413052	−	0.910707i	$-0.635537\pi$
$863$	−20943.6	−0.826104	−0.413052	+	0.910707i	$0.635537\pi$
$864$	864.000	0.0340207
$865$	29757.4	1.16969
$866$	−27858.0	−1.09313
$867$	−8927.53	−0.349706
$868$	−163.060	−0.00637628
$869$	12428.7	0.485172
$870$	11690.1	0.455552
$871$	303.897	0.0118222
$872$	−16105.3	−0.625453
$873$	−7493.40	−0.290508
$874$	0	0
$875$	−845.771	−0.0326769
$876$	3368.81	0.129933
$877$	−9561.82	−0.368164	−0.184082	−	0.982911i	$-0.558931\pi$
$877$	−9561.82	−0.368164	−0.184082	+	0.982911i	$0.558931\pi$
$878$	10444.1	0.401447
$879$	−10924.7	−0.419204
$880$	−3084.30	−0.118150
$881$	41424.3	1.58413	0.792065	−	0.610436i	$-0.209006\pi$
$881$	41424.3	1.58413	0.792065	+	0.610436i	$0.209006\pi$
$882$	−6165.83	−0.235390
$883$	37078.3	1.41312	0.706559	−	0.707654i	$-0.250246\pi$
$883$	37078.3	1.41312	0.706559	+	0.707654i	$0.250246\pi$
$884$	−688.336	−0.0261892
$885$	25536.1	0.969929
$886$	−20326.8	−0.770760
$887$	6509.98	0.246430	0.123215	−	0.992380i	$-0.460679\pi$
$887$	6509.98	0.246430	0.123215	+	0.992380i	$0.460679\pi$
$888$	2517.25	0.0951277
$889$	628.311	0.0237040
$890$	24323.2	0.916085
$891$	1291.49	0.0485594
$892$	−1925.97	−0.0722939
$893$	0	0
$894$	−16128.3	−0.603369
$895$	35838.4	1.33849
$896$	−86.2415	−0.00321554
$897$	−106.873	−0.00397812
$898$	35703.2	1.32676
$899$	−9750.19	−0.361721
$900$	762.200	0.0282296
$901$	33194.2	1.22737
$902$	7951.49	0.293521
$903$	13.9566	0.000514337 0
$904$	−85.2045	−0.00313480
$905$	−53241.1	−1.95557
$906$	14848.5	0.544489
$907$	52647.2	1.92737	0.963683	−	0.267048i	$-0.0860482\pi$
$907$	52647.2	1.92737	0.963683	+	0.267048i	$0.0860482\pi$
$908$	11146.4	0.407384
$909$	8193.34	0.298962
$910$	63.6982	0.00232041
$911$	16500.2	0.600084	0.300042	−	0.953926i	$-0.402999\pi$
$911$	16500.2	0.600084	0.300042	+	0.953926i	$0.402999\pi$
$912$	0	0
$913$	−4369.10	−0.158375
$914$	−10075.9	−0.364640
$915$	1179.10	0.0426009
$916$	5750.88	0.207439
$917$	−140.678	−0.00506608
$918$	−2376.71	−0.0854500
$919$	8761.75	0.314498	0.157249	−	0.987559i	$-0.449738\pi$
$919$	8761.75	0.314498	0.157249	+	0.987559i	$0.449738\pi$
$920$	881.272	0.0315812
$921$	14056.3	0.502898
$922$	−22362.8	−0.798783
$923$	173.668	0.00619323
$924$	−128.912	−0.00458970
$925$	2220.66	0.0789348
$926$	36910.2	1.30988
$927$	−11449.4	−0.405662
$928$	−5156.83	−0.182415
$929$	−27264.8	−0.962893	−0.481446	−	0.876476i	$-0.659888\pi$
$929$	−27264.8	−0.962893	−0.481446	+	0.876476i	$0.659888\pi$
$930$	−4388.98	−0.154753
$931$	0	0
$932$	−11131.0	−0.391209
$933$	−7240.66	−0.254071
$934$	12825.6	0.449321
$935$	8484.37	0.296758
$936$	281.508	0.00983052
$937$	23381.2	0.815186	0.407593	−	0.913164i	$-0.366368\pi$
$937$	23381.2	0.815186	0.407593	+	0.913164i	$0.366368\pi$
$938$	−104.738	−0.00364587
$939$	−15186.7	−0.527795
$940$	−7024.74	−0.243747
$941$	−39198.4	−1.35795	−0.678975	−	0.734161i	$-0.737576\pi$
$941$	−39198.4	−1.35795	−0.678975	+	0.734161i	$0.737576\pi$
$942$	−7258.88	−0.251069
$943$	−2271.96	−0.0784574
$944$	−11264.7	−0.388386
$945$	219.939	0.00757103
$946$	−220.184	−0.00756745
$947$	18505.7	0.635010	0.317505	−	0.948257i	$-0.397155\pi$
$947$	18505.7	0.635010	0.317505	+	0.948257i	$0.397155\pi$
$948$	9354.10	0.320472
$949$	1097.62	0.0375452
$950$	0	0
$951$	17112.1	0.583488
$952$	237.235	0.00807651
$953$	−14696.2	−0.499535	−0.249768	−	0.968306i	$-0.580354\pi$
$953$	−14696.2	−0.499535	−0.249768	+	0.968306i	$0.580354\pi$
$954$	−13575.4	−0.460712
$955$	26211.1	0.888137
$956$	18122.2	0.613091
$957$	−7708.30	−0.260370
$958$	−17039.3	−0.574651
$959$	248.130	0.00835509
$960$	−2321.31	−0.0780417
$961$	−26130.3	−0.877122
$962$	820.168	0.0274878
$963$	7052.08	0.235982
$964$	−9829.09	−0.328396
$965$	37752.2	1.25936
$966$	36.8337	0.00122682
$967$	−53986.4	−1.79533	−0.897666	−	0.440676i	$-0.854739\pi$
$967$	−53986.4	−1.79533	−0.897666	+	0.440676i	$0.854739\pi$
$968$	−8614.24	−0.286025
$969$	0	0
$970$	20132.5	0.666409
$971$	−29949.9	−0.989845	−0.494922	−	0.868937i	$-0.664804\pi$
$971$	−29949.9	−0.989845	−0.494922	+	0.868937i	$0.664804\pi$
$972$	972.000	0.0320750
$973$	1160.53	0.0382371
$974$	25493.7	0.838675
$975$	248.339	0.00815715
$976$	−520.136	−0.0170586
$977$	−10119.4	−0.331371	−0.165685	−	0.986179i	$-0.552984\pi$
$977$	−10119.4	−0.331371	−0.165685	+	0.986179i	$0.552984\pi$
$978$	16470.2	0.538505
$979$	−16038.5	−0.523587
$980$	16565.8	0.539973
$981$	−18118.5	−0.589683
$982$	−10374.2	−0.337122
$983$	21988.0	0.713438	0.356719	−	0.934212i	$-0.383895\pi$
$983$	21988.0	0.713438	0.356719	+	0.934212i	$0.383895\pi$
$984$	5984.46	0.193880
$985$	−2447.40	−0.0791683
$986$	14185.5	0.458173
$987$	−293.607	−0.00946870
$988$	0	0
$989$	62.9128	0.00202276
$990$	−3469.84	−0.111393
$991$	2492.80	0.0799056	0.0399528	−	0.999202i	$-0.487279\pi$
$991$	2492.80	0.0799056	0.0399528	+	0.999202i	$0.487279\pi$
$992$	1936.11	0.0619673
$993$	25102.7	0.802224
$994$	−59.8548	−0.00190994
$995$	19939.7	0.635306
$996$	−3288.28	−0.104612
$997$	45403.2	1.44226	0.721130	−	0.692799i	$-0.243623\pi$
$997$	45403.2	1.44226	0.721130	+	0.692799i	$0.243623\pi$
$998$	−21408.9	−0.679045
$999$	2831.91	0.0896873

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.4.a.p.1.1	yes	2
19.18	odd	2		2166.4.a.j.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2166.4.a.j.1.1	✓	2	19.18	odd	2
2166.4.a.p.1.1	yes	2	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:	\( N \)	\(=\)	\( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2166.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -12.0902 q^{5} +6.00000 q^{6} -0.673762 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -12.0902 q^{5} +6.00000 q^{6} -0.673762 q^{7} +8.00000 q^{8} +9.00000 q^{9} -24.1803 q^{10} +15.9443 q^{11} +12.0000 q^{12} +3.90983 q^{13} -1.34752 q^{14} -36.2705 q^{15} +16.0000 q^{16} -44.0132 q^{17} +18.0000 q^{18} -48.3607 q^{20} -2.02129 q^{21} +31.8885 q^{22} -9.11146 q^{23} +24.0000 q^{24} +21.1722 q^{25} +7.81966 q^{26} +27.0000 q^{27} -2.69505 q^{28} -161.151 q^{29} -72.5410 q^{30} +60.5035 q^{31} +32.0000 q^{32} +47.8328 q^{33} -88.0263 q^{34} +8.14590 q^{35} +36.0000 q^{36} +104.885 q^{37} +11.7295 q^{39} -96.7214 q^{40} +249.353 q^{41} -4.04257 q^{42} -6.90481 q^{43} +63.7771 q^{44} -108.812 q^{45} -18.2229 q^{46} +145.257 q^{47} +48.0000 q^{48} -342.546 q^{49} +42.3444 q^{50} -132.039 q^{51} +15.6393 q^{52} -754.187 q^{53} +54.0000 q^{54} -192.769 q^{55} -5.39010 q^{56} -322.302 q^{58} -704.046 q^{59} -145.082 q^{60} -32.5085 q^{61} +121.007 q^{62} -6.06386 q^{63} +64.0000 q^{64} -47.2705 q^{65} +95.6656 q^{66} +77.7264 q^{67} -176.053 q^{68} -27.3344 q^{69} +16.2918 q^{70} +44.4183 q^{71} +72.0000 q^{72} +280.735 q^{73} +209.771 q^{74} +63.5166 q^{75} -10.7426 q^{77} +23.4590 q^{78} +779.508 q^{79} -193.443 q^{80} +81.0000 q^{81} +498.705 q^{82} -274.023 q^{83} -8.08514 q^{84} +532.127 q^{85} -13.8096 q^{86} -483.453 q^{87} +127.554 q^{88} -1005.91 q^{89} -217.623 q^{90} -2.63430 q^{91} -36.4458 q^{92} +181.510 q^{93} +290.515 q^{94} +96.0000 q^{96} -832.600 q^{97} -685.092 q^{98} +143.498 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} + 6 q^{3} + 8 q^{4} - 13 q^{5} + 12 q^{6} - 17 q^{7} + 16 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + 4 * q^2 + 6 * q^3 + 8 * q^4 - 13 * q^5 + 12 * q^6 - 17 * q^7 + 16 * q^8 + 18 * q^9	\( 2 q + 4 q^{2} + 6 q^{3} + 8 q^{4} - 13 q^{5} + 12 q^{6} - 17 q^{7} + 16 q^{8} + 18 q^{9} - 26 q^{10} + 14 q^{11} + 24 q^{12} + 19 q^{13} - 34 q^{14} - 39 q^{15} + 32 q^{16} - 12 q^{17} + 36 q^{18} - 52 q^{20} - 51 q^{21} + 28 q^{22} - 54 q^{23} + 48 q^{24} - 103 q^{25} + 38 q^{26} + 54 q^{27} - 68 q^{28} - 130 q^{29} - 78 q^{30} - 239 q^{31} + 64 q^{32} + 42 q^{33} - 24 q^{34} + 23 q^{35} + 72 q^{36} - 148 q^{37} + 57 q^{39} - 104 q^{40} + 331 q^{41} - 102 q^{42} - 224 q^{43} + 56 q^{44} - 117 q^{45} - 108 q^{46} + 333 q^{47} + 96 q^{48} - 419 q^{49} - 206 q^{50} - 36 q^{51} + 76 q^{52} - 766 q^{53} + 108 q^{54} - 191 q^{55} - 136 q^{56} - 260 q^{58} - 460 q^{59} - 156 q^{60} + 494 q^{61} - 478 q^{62} - 153 q^{63} + 128 q^{64} - 61 q^{65} + 84 q^{66} - 133 q^{67} - 48 q^{68} - 162 q^{69} + 46 q^{70} - 459 q^{71} + 144 q^{72} + 396 q^{73} - 296 q^{74} - 309 q^{75} + 21 q^{77} + 114 q^{78} + 1000 q^{79} - 208 q^{80} + 162 q^{81} + 662 q^{82} - 74 q^{83} - 204 q^{84} + 503 q^{85} - 448 q^{86} - 390 q^{87} + 112 q^{88} - 1180 q^{89} - 234 q^{90} - 249 q^{91} - 216 q^{92} - 717 q^{93} + 666 q^{94} + 192 q^{96} - 1938 q^{97} - 838 q^{98} + 126 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 + 6 * q^3 + 8 * q^4 - 13 * q^5 + 12 * q^6 - 17 * q^7 + 16 * q^8 + 18 * q^9 - 26 * q^10 + 14 * q^11 + 24 * q^12 + 19 * q^13 - 34 * q^14 - 39 * q^15 + 32 * q^16 - 12 * q^17 + 36 * q^18 - 52 * q^20 - 51 * q^21 + 28 * q^22 - 54 * q^23 + 48 * q^24 - 103 * q^25 + 38 * q^26 + 54 * q^27 - 68 * q^28 - 130 * q^29 - 78 * q^30 - 239 * q^31 + 64 * q^32 + 42 * q^33 - 24 * q^34 + 23 * q^35 + 72 * q^36 - 148 * q^37 + 57 * q^39 - 104 * q^40 + 331 * q^41 - 102 * q^42 - 224 * q^43 + 56 * q^44 - 117 * q^45 - 108 * q^46 + 333 * q^47 + 96 * q^48 - 419 * q^49 - 206 * q^50 - 36 * q^51 + 76 * q^52 - 766 * q^53 + 108 * q^54 - 191 * q^55 - 136 * q^56 - 260 * q^58 - 460 * q^59 - 156 * q^60 + 494 * q^61 - 478 * q^62 - 153 * q^63 + 128 * q^64 - 61 * q^65 + 84 * q^66 - 133 * q^67 - 48 * q^68 - 162 * q^69 + 46 * q^70 - 459 * q^71 + 144 * q^72 + 396 * q^73 - 296 * q^74 - 309 * q^75 + 21 * q^77 + 114 * q^78 + 1000 * q^79 - 208 * q^80 + 162 * q^81 + 662 * q^82 - 74 * q^83 - 204 * q^84 + 503 * q^85 - 448 * q^86 - 390 * q^87 + 112 * q^88 - 1180 * q^89 - 234 * q^90 - 249 * q^91 - 216 * q^92 - 717 * q^93 + 666 * q^94 + 192 * q^96 - 1938 * q^97 - 838 * q^98 + 126 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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