LMFDB - Embedded newform 2166.4.a.bf.1.4

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:	$6$
Coefficient field:	6.6.11196169353.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 87x^{4} + 179x^{3} + 2574x^{2} - 2664x - 25992 $ x^6 - 3x^5 - 87x^4 + 179x^3 + 2574x^2 - 2664*x - 25992
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$5.78019$ 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)

$f(q)$	$=$	$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +6.58796 q^{5} -6.00000 q^{6} -12.5977 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +6.58796 q^{5} -6.00000 q^{6} -12.5977 q^{7} +8.00000 q^{8} +9.00000 q^{9} +13.1759 q^{10} -47.3817 q^{11} -12.0000 q^{12} +79.8267 q^{13} -25.1954 q^{14} -19.7639 q^{15} +16.0000 q^{16} +80.7757 q^{17} +18.0000 q^{18} +26.3518 q^{20} +37.7932 q^{21} -94.7635 q^{22} -214.127 q^{23} -24.0000 q^{24} -81.5988 q^{25} +159.653 q^{26} -27.0000 q^{27} -50.3909 q^{28} -72.7336 q^{29} -39.5278 q^{30} -213.372 q^{31} +32.0000 q^{32} +142.145 q^{33} +161.551 q^{34} -82.9933 q^{35} +36.0000 q^{36} +1.68978 q^{37} -239.480 q^{39} +52.7037 q^{40} +483.283 q^{41} +75.5863 q^{42} +350.794 q^{43} -189.527 q^{44} +59.2916 q^{45} -428.254 q^{46} +137.357 q^{47} -48.0000 q^{48} -184.297 q^{49} -163.198 q^{50} -242.327 q^{51} +319.307 q^{52} -97.2800 q^{53} -54.0000 q^{54} -312.149 q^{55} -100.782 q^{56} -145.467 q^{58} -830.473 q^{59} -79.0555 q^{60} -30.2378 q^{61} -426.745 q^{62} -113.380 q^{63} +64.0000 q^{64} +525.895 q^{65} +284.290 q^{66} +333.755 q^{67} +323.103 q^{68} +642.380 q^{69} -165.987 q^{70} +444.310 q^{71} +72.0000 q^{72} +198.544 q^{73} +3.37956 q^{74} +244.796 q^{75} +596.902 q^{77} -478.960 q^{78} -1007.87 q^{79} +105.407 q^{80} +81.0000 q^{81} +966.566 q^{82} +389.127 q^{83} +151.173 q^{84} +532.147 q^{85} +701.589 q^{86} +218.201 q^{87} -379.054 q^{88} -216.215 q^{89} +118.583 q^{90} -1005.63 q^{91} -856.507 q^{92} +640.117 q^{93} +274.714 q^{94} -96.0000 q^{96} -1395.60 q^{97} -368.595 q^{98} -426.436 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{2} - 18 q^{3} + 24 q^{4} + 27 q^{5} - 36 q^{6} - 42 q^{7} + 48 q^{8} + 54 q^{9}+O(q^{10}) $ 6 * q + 12 * q^2 - 18 * q^3 + 24 * q^4 + 27 * q^5 - 36 * q^6 - 42 * q^7 + 48 * q^8 + 54 * q^9	\( 6 q + 12 q^{2} - 18 q^{3} + 24 q^{4} + 27 q^{5} - 36 q^{6} - 42 q^{7} + 48 q^{8} + 54 q^{9} + 54 q^{10} - 57 q^{11} - 72 q^{12} + 21 q^{13} - 84 q^{14} - 81 q^{15} + 96 q^{16} - 45 q^{17} + 108 q^{18} + 108 q^{20} + 126 q^{21} - 114 q^{22} + 138 q^{23} - 144 q^{24} - 135 q^{25} + 42 q^{26} - 162 q^{27} - 168 q^{28} - 177 q^{29} - 162 q^{30} - 99 q^{31} + 192 q^{32} + 171 q^{33} - 90 q^{34} - 594 q^{35} + 216 q^{36} - 615 q^{37} - 63 q^{39} + 216 q^{40} - 171 q^{41} + 252 q^{42} + 456 q^{43} - 228 q^{44} + 243 q^{45} + 276 q^{46} + 228 q^{47} - 288 q^{48} + 168 q^{49} - 270 q^{50} + 135 q^{51} + 84 q^{52} - 357 q^{53} - 324 q^{54} - 1356 q^{55} - 336 q^{56} - 354 q^{58} - 741 q^{59} - 324 q^{60} - 66 q^{61} - 198 q^{62} - 378 q^{63} + 384 q^{64} + 843 q^{65} + 342 q^{66} + 966 q^{67} - 180 q^{68} - 414 q^{69} - 1188 q^{70} - 1338 q^{71} + 432 q^{72} + 1293 q^{73} - 1230 q^{74} + 405 q^{75} + 1299 q^{77} - 126 q^{78} - 1404 q^{79} + 432 q^{80} + 486 q^{81} - 342 q^{82} - 1440 q^{83} + 504 q^{84} - 1209 q^{85} + 912 q^{86} + 531 q^{87} - 456 q^{88} - 2991 q^{89} + 486 q^{90} - 4632 q^{91} + 552 q^{92} + 297 q^{93} + 456 q^{94} - 576 q^{96} - 2802 q^{97} + 336 q^{98} - 513 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 - 18 * q^3 + 24 * q^4 + 27 * q^5 - 36 * q^6 - 42 * q^7 + 48 * q^8 + 54 * q^9 + 54 * q^10 - 57 * q^11 - 72 * q^12 + 21 * q^13 - 84 * q^14 - 81 * q^15 + 96 * q^16 - 45 * q^17 + 108 * q^18 + 108 * q^20 + 126 * q^21 - 114 * q^22 + 138 * q^23 - 144 * q^24 - 135 * q^25 + 42 * q^26 - 162 * q^27 - 168 * q^28 - 177 * q^29 - 162 * q^30 - 99 * q^31 + 192 * q^32 + 171 * q^33 - 90 * q^34 - 594 * q^35 + 216 * q^36 - 615 * q^37 - 63 * q^39 + 216 * q^40 - 171 * q^41 + 252 * q^42 + 456 * q^43 - 228 * q^44 + 243 * q^45 + 276 * q^46 + 228 * q^47 - 288 * q^48 + 168 * q^49 - 270 * q^50 + 135 * q^51 + 84 * q^52 - 357 * q^53 - 324 * q^54 - 1356 * q^55 - 336 * q^56 - 354 * q^58 - 741 * q^59 - 324 * q^60 - 66 * q^61 - 198 * q^62 - 378 * q^63 + 384 * q^64 + 843 * q^65 + 342 * q^66 + 966 * q^67 - 180 * q^68 - 414 * q^69 - 1188 * q^70 - 1338 * q^71 + 432 * q^72 + 1293 * q^73 - 1230 * q^74 + 405 * q^75 + 1299 * q^77 - 126 * q^78 - 1404 * q^79 + 432 * q^80 + 486 * q^81 - 342 * q^82 - 1440 * q^83 + 504 * q^84 - 1209 * q^85 + 912 * q^86 + 531 * q^87 - 456 * q^88 - 2991 * q^89 + 486 * q^90 - 4632 * q^91 + 552 * q^92 + 297 * q^93 + 456 * q^94 - 576 * q^96 - 2802 * q^97 + 336 * q^98 - 513 * 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
$5$	6.58796	0.589245	0.294622	−	0.955614i	$-0.404806\pi$
$5$	6.58796	0.589245	0.294622	+	0.955614i	$0.404806\pi$
$6$	−6.00000	−0.408248
$7$	−12.5977	−0.680213	−0.340107	−	0.940387i	$-0.610463\pi$
$7$	−12.5977	−0.680213	−0.340107	+	0.940387i	$0.610463\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	13.1759	0.416659
$11$	−47.3817	−1.29874	−0.649370	−	0.760473i	$-0.724967\pi$
$11$	−47.3817	−1.29874	−0.649370	+	0.760473i	$0.724967\pi$
$12$	−12.0000	−0.288675
$13$	79.8267	1.70307	0.851536	−	0.524296i	$-0.175672\pi$
$13$	79.8267	1.70307	0.851536	+	0.524296i	$0.175672\pi$
$14$	−25.1954	−0.480983
$15$	−19.7639	−0.340201
$16$	16.0000	0.250000
$17$	80.7757	1.15241	0.576205	−	0.817305i	$-0.304533\pi$
$17$	80.7757	1.15241	0.576205	+	0.817305i	$0.304533\pi$
$18$	18.0000	0.235702
$19$	0	0
$19$	0	0
$20$	26.3518	0.294622
$21$	37.7932	0.392721
$22$	−94.7635	−0.918347
$23$	−214.127	−1.94124	−0.970620	−	0.240617i	$-0.922650\pi$
$23$	−214.127	−1.94124	−0.970620	+	0.240617i	$0.922650\pi$
$24$	−24.0000	−0.204124
$25$	−81.5988	−0.652790
$26$	159.653	1.20425
$27$	−27.0000	−0.192450
$28$	−50.3909	−0.340107
$29$	−72.7336	−0.465734	−0.232867	−	0.972509i	$-0.574811\pi$
$29$	−72.7336	−0.465734	−0.232867	+	0.972509i	$0.574811\pi$
$30$	−39.5278	−0.240558
$31$	−213.372	−1.23622	−0.618110	−	0.786092i	$-0.712101\pi$
$31$	−213.372	−1.23622	−0.618110	+	0.786092i	$0.712101\pi$
$32$	32.0000	0.176777
$33$	142.145	0.749827
$34$	161.551	0.814878
$35$	−82.9933	−0.400812
$36$	36.0000	0.166667
$37$	1.68978	0.00750807	0.00375403	−	0.999993i	$-0.498805\pi$
$37$	1.68978	0.00750807	0.00375403	+	0.999993i	$0.498805\pi$
$38$	0	0
$39$	−239.480	−0.983269
$40$	52.7037	0.208330
$41$	483.283	1.84088	0.920440	−	0.390883i	$-0.127830\pi$
$41$	483.283	1.84088	0.920440	+	0.390883i	$0.127830\pi$
$42$	75.5863	0.277696
$43$	350.794	1.24408	0.622042	−	0.782984i	$-0.286303\pi$
$43$	350.794	1.24408	0.622042	+	0.782984i	$0.286303\pi$
$44$	−189.527	−0.649370
$45$	59.2916	0.196415
$46$	−428.254	−1.37266
$47$	137.357	0.426289	0.213145	−	0.977021i	$-0.431629\pi$
$47$	137.357	0.426289	0.213145	+	0.977021i	$0.431629\pi$
$48$	−48.0000	−0.144338
$49$	−184.297	−0.537310
$50$	−163.198	−0.461592
$51$	−242.327	−0.665345
$52$	319.307	0.851536
$53$	−97.2800	−0.252121	−0.126061	−	0.992023i	$-0.540233\pi$
$53$	−97.2800	−0.252121	−0.126061	+	0.992023i	$0.540233\pi$
$54$	−54.0000	−0.136083
$55$	−312.149	−0.765276
$56$	−100.782	−0.240492
$57$	0	0
$58$	−145.467	−0.329324
$59$	−830.473	−1.83252	−0.916258	−	0.400589i	$-0.868806\pi$
$59$	−830.473	−1.83252	−0.916258	+	0.400589i	$0.868806\pi$
$60$	−79.0555	−0.170100
$61$	−30.2378	−0.0634680	−0.0317340	−	0.999496i	$-0.510103\pi$
$61$	−30.2378	−0.0634680	−0.0317340	+	0.999496i	$0.510103\pi$
$62$	−426.745	−0.874140
$63$	−113.380	−0.226738
$64$	64.0000	0.125000
$65$	525.895	1.00353
$66$	284.290	0.530208
$67$	333.755	0.608577	0.304289	−	0.952580i	$-0.401581\pi$
$67$	333.755	0.608577	0.304289	+	0.952580i	$0.401581\pi$
$68$	323.103	0.576205
$69$	642.380	1.12078
$70$	−165.987	−0.283417
$71$	444.310	0.742674	0.371337	−	0.928498i	$-0.378899\pi$
$71$	444.310	0.742674	0.371337	+	0.928498i	$0.378899\pi$
$72$	72.0000	0.117851
$73$	198.544	0.318326	0.159163	−	0.987252i	$-0.449120\pi$
$73$	198.544	0.318326	0.159163	+	0.987252i	$0.449120\pi$
$74$	3.37956	0.00530900
$75$	244.796	0.376889
$76$	0	0
$77$	596.902	0.883419
$78$	−478.960	−0.695276
$79$	−1007.87	−1.43537	−0.717685	−	0.696368i	$-0.754798\pi$
$79$	−1007.87	−1.43537	−0.717685	+	0.696368i	$0.754798\pi$
$80$	105.407	0.147311
$81$	81.0000	0.111111
$82$	966.566	1.30170
$83$	389.127	0.514605	0.257302	−	0.966331i	$-0.417166\pi$
$83$	389.127	0.514605	0.257302	+	0.966331i	$0.417166\pi$
$84$	151.173	0.196361
$85$	532.147	0.679052
$86$	701.589	0.879701
$87$	218.201	0.268892
$88$	−379.054	−0.459174
$89$	−216.215	−0.257514	−0.128757	−	0.991676i	$-0.541099\pi$
$89$	−216.215	−0.257514	−0.128757	+	0.991676i	$0.541099\pi$
$90$	118.583	0.138886
$91$	−1005.63	−1.15845
$92$	−856.507	−0.970620
$93$	640.117	0.713732
$94$	274.714	0.301432
$95$	0	0
$96$	−96.0000	−0.102062
$97$	−1395.60	−1.46084	−0.730419	−	0.682999i	$-0.760675\pi$
$97$	−1395.60	−1.46084	−0.730419	+	0.682999i	$0.760675\pi$
$98$	−368.595	−0.379936
$99$	−426.436	−0.432913
$100$	−326.395	−0.326395
$101$	879.974	0.866938	0.433469	−	0.901169i	$-0.357289\pi$
$101$	879.974	0.866938	0.433469	+	0.901169i	$0.357289\pi$
$102$	−484.654	−0.470470
$103$	−1303.73	−1.24719	−0.623594	−	0.781748i	$-0.714328\pi$
$103$	−1303.73	−1.24719	−0.623594	+	0.781748i	$0.714328\pi$
$104$	638.613	0.602127
$105$	248.980	0.231409
$106$	−194.560	−0.178277
$107$	−967.722	−0.874329	−0.437165	−	0.899382i	$-0.644017\pi$
$107$	−967.722	−0.874329	−0.437165	+	0.899382i	$0.644017\pi$
$108$	−108.000	−0.0962250
$109$	−1139.30	−1.00115	−0.500576	−	0.865693i	$-0.666878\pi$
$109$	−1139.30	−1.00115	−0.500576	+	0.865693i	$0.666878\pi$
$110$	−624.298	−0.541131
$111$	−5.06935	−0.00433478
$112$	−201.564	−0.170053
$113$	−142.311	−0.118473	−0.0592366	−	0.998244i	$-0.518867\pi$
$113$	−142.311	−0.118473	−0.0592366	+	0.998244i	$0.518867\pi$
$114$	0	0
$115$	−1410.66	−1.14387
$116$	−290.934	−0.232867
$117$	718.440	0.567691
$118$	−1660.95	−1.29578
$119$	−1017.59	−0.783885
$120$	−158.111	−0.120279
$121$	914.029	0.686723
$122$	−60.4755	−0.0448786
$123$	−1449.85	−1.06283
$124$	−853.490	−0.618110
$125$	−1361.06	−0.973898
$126$	−226.759	−0.160328
$127$	67.9598	0.0474839	0.0237420	−	0.999718i	$-0.492442\pi$
$127$	67.9598	0.0474839	0.0237420	+	0.999718i	$0.492442\pi$
$128$	128.000	0.0883883
$129$	−1052.38	−0.718273
$130$	1051.79	0.709600
$131$	−857.942	−0.572204	−0.286102	−	0.958199i	$-0.592360\pi$
$131$	−857.942	−0.572204	−0.286102	+	0.958199i	$0.592360\pi$
$132$	568.581	0.374914
$133$	0	0
$134$	667.510	0.430329
$135$	−177.875	−0.113400
$136$	646.206	0.407439
$137$	414.565	0.258530	0.129265	−	0.991610i	$-0.458738\pi$
$137$	414.565	0.258530	0.129265	+	0.991610i	$0.458738\pi$
$138$	1284.76	0.792508
$139$	89.1829	0.0544201	0.0272100	−	0.999630i	$-0.491338\pi$
$139$	89.1829	0.0544201	0.0272100	+	0.999630i	$0.491338\pi$
$140$	−331.973	−0.200406
$141$	−412.071	−0.246118
$142$	888.620	0.525150
$143$	−3782.33	−2.21185
$144$	144.000	0.0833333
$145$	−479.166	−0.274431
$146$	397.087	0.225090
$147$	552.892	0.310216
$148$	6.75913	0.00375403
$149$	2030.35	1.11633	0.558163	−	0.829731i	$-0.311506\pi$
$149$	2030.35	1.11633	0.558163	+	0.829731i	$0.311506\pi$
$150$	489.593	0.266501
$151$	2663.48	1.43544	0.717720	−	0.696332i	$-0.245186\pi$
$151$	2663.48	1.43544	0.717720	+	0.696332i	$0.245186\pi$
$152$	0	0
$153$	726.981	0.384137
$154$	1193.80	0.624672
$155$	−1405.69	−0.728437
$156$	−957.920	−0.491635
$157$	−3759.77	−1.91123	−0.955613	−	0.294624i	$-0.904806\pi$
$157$	−3759.77	−1.91123	−0.955613	+	0.294624i	$0.904806\pi$
$158$	−2015.74	−1.01496
$159$	291.840	0.145562
$160$	210.815	0.104165
$161$	2697.51	1.32046
$162$	162.000	0.0785674
$163$	−3741.65	−1.79797	−0.898984	−	0.437982i	$-0.855693\pi$
$163$	−3741.65	−1.79797	−0.898984	+	0.437982i	$0.855693\pi$
$164$	1933.13	0.920440
$165$	936.447	0.441832
$166$	778.253	0.363881
$167$	−2579.79	−1.19539	−0.597695	−	0.801724i	$-0.703917\pi$
$167$	−2579.79	−1.19539	−0.597695	+	0.801724i	$0.703917\pi$
$168$	302.345	0.138848
$169$	4175.30	1.90045
$170$	1064.29	0.480163
$171$	0	0
$172$	1403.18	0.622042
$173$	−2563.10	−1.12641	−0.563205	−	0.826317i	$-0.690432\pi$
$173$	−2563.10	−1.12641	−0.563205	+	0.826317i	$0.690432\pi$
$174$	436.402	0.190135
$175$	1027.96	0.444037
$176$	−758.108	−0.324685
$177$	2491.42	1.05800
$178$	−432.430	−0.182090
$179$	156.665	0.0654172	0.0327086	−	0.999465i	$-0.489587\pi$
$179$	156.665	0.0654172	0.0327086	+	0.999465i	$0.489587\pi$
$180$	237.167	0.0982075
$181$	184.864	0.0759162	0.0379581	−	0.999279i	$-0.487915\pi$
$181$	184.864	0.0759162	0.0379581	+	0.999279i	$0.487915\pi$
$182$	−2011.27	−0.819149
$183$	90.7133	0.0366433
$184$	−1713.01	−0.686332
$185$	11.1322	0.00442409
$186$	1280.23	0.504685
$187$	−3827.29	−1.49668
$188$	549.429	0.213145
$189$	340.139	0.130907
$190$	0	0
$191$	112.926	0.0427804	0.0213902	−	0.999771i	$-0.493191\pi$
$191$	112.926	0.0427804	0.0213902	+	0.999771i	$0.493191\pi$
$192$	−192.000	−0.0721688
$193$	−1808.33	−0.674437	−0.337218	−	0.941426i	$-0.609486\pi$
$193$	−1808.33	−0.674437	−0.337218	+	0.941426i	$0.609486\pi$
$194$	−2791.19	−1.03297
$195$	−1577.68	−0.579386
$196$	−737.189	−0.268655
$197$	−703.801	−0.254537	−0.127268	−	0.991868i	$-0.540621\pi$
$197$	−703.801	−0.254537	−0.127268	+	0.991868i	$0.540621\pi$
$198$	−852.871	−0.306116
$199$	1791.47	0.638159	0.319080	−	0.947728i	$-0.396626\pi$
$199$	1791.47	0.638159	0.319080	+	0.947728i	$0.396626\pi$
$200$	−652.790	−0.230796
$201$	−1001.27	−0.351362
$202$	1759.95	0.613017
$203$	916.278	0.316798
$204$	−969.308	−0.332672
$205$	3183.85	1.08473
$206$	−2607.46	−0.881896
$207$	−1927.14	−0.647080
$208$	1277.23	0.425768
$209$	0	0
$210$	497.960	0.163631
$211$	614.011	0.200333	0.100166	−	0.994971i	$-0.468062\pi$
$211$	614.011	0.200333	0.100166	+	0.994971i	$0.468062\pi$
$212$	−389.120	−0.126061
$213$	−1332.93	−0.428783
$214$	−1935.44	−0.618244
$215$	2311.02	0.733071
$216$	−216.000	−0.0680414
$217$	2688.01	0.840893
$218$	−2278.61	−0.707921
$219$	−595.631	−0.183785
$220$	−1248.60	−0.382638
$221$	6448.06	1.96264
$222$	−10.1387	−0.00306515
$223$	4195.80	1.25996	0.629981	−	0.776611i	$-0.283063\pi$
$223$	4195.80	1.25996	0.629981	+	0.776611i	$0.283063\pi$
$224$	−403.127	−0.120246
$225$	−734.389	−0.217597
$226$	−284.622	−0.0837732
$227$	−3228.38	−0.943943	−0.471972	−	0.881614i	$-0.656458\pi$
$227$	−3228.38	−0.943943	−0.471972	+	0.881614i	$0.656458\pi$
$228$	0	0
$229$	1911.99	0.551738	0.275869	−	0.961195i	$-0.411034\pi$
$229$	1911.99	0.551738	0.275869	+	0.961195i	$0.411034\pi$
$230$	−2821.32	−0.808836
$231$	−1790.71	−0.510042
$232$	−581.869	−0.164662
$233$	812.982	0.228585	0.114292	−	0.993447i	$-0.463540\pi$
$233$	812.982	0.228585	0.114292	+	0.993447i	$0.463540\pi$
$234$	1436.88	0.401418
$235$	904.903	0.251189
$236$	−3321.89	−0.916258
$237$	3023.61	0.828711
$238$	−2035.18	−0.554291
$239$	1113.48	0.301360	0.150680	−	0.988583i	$-0.451854\pi$
$239$	1113.48	0.301360	0.150680	+	0.988583i	$0.451854\pi$
$240$	−316.222	−0.0850502
$241$	−4988.43	−1.33333	−0.666666	−	0.745357i	$-0.732279\pi$
$241$	−4988.43	−1.33333	−0.666666	+	0.745357i	$0.732279\pi$
$242$	1828.06	0.485587
$243$	−243.000	−0.0641500
$244$	−120.951	−0.0317340
$245$	−1214.14	−0.316607
$246$	−2899.70	−0.751536
$247$	0	0
$248$	−1706.98	−0.437070
$249$	−1167.38	−0.297107
$250$	−2722.13	−0.688650
$251$	−6337.61	−1.59373	−0.796866	−	0.604156i	$-0.793510\pi$
$251$	−6337.61	−1.59373	−0.796866	+	0.604156i	$0.793510\pi$
$252$	−453.518	−0.113369
$253$	10145.7	2.52116
$254$	135.920	0.0335762
$255$	−1596.44	−0.392051
$256$	256.000	0.0625000
$257$	−2282.49	−0.553998	−0.276999	−	0.960870i	$-0.589340\pi$
$257$	−2282.49	−0.553998	−0.276999	+	0.960870i	$0.589340\pi$
$258$	−2104.77	−0.507895
$259$	−21.2874	−0.00510709
$260$	2103.58	0.501763
$261$	−654.602	−0.155245
$262$	−1715.88	−0.404610
$263$	−4602.08	−1.07900	−0.539498	−	0.841987i	$-0.681386\pi$
$263$	−4602.08	−1.07900	−0.539498	+	0.841987i	$0.681386\pi$
$264$	1137.16	0.265104
$265$	−640.876	−0.148561
$266$	0	0
$267$	648.645	0.148676
$268$	1335.02	0.304289
$269$	−5088.65	−1.15338	−0.576692	−	0.816962i	$-0.695657\pi$
$269$	−5088.65	−1.15338	−0.576692	+	0.816962i	$0.695657\pi$
$270$	−355.750	−0.0801861
$271$	2289.68	0.513241	0.256620	−	0.966512i	$-0.417391\pi$
$271$	2289.68	0.513241	0.256620	+	0.966512i	$0.417391\pi$
$272$	1292.41	0.288103
$273$	3016.90	0.668833
$274$	829.129	0.182809
$275$	3866.29	0.847804
$276$	2569.52	0.560388
$277$	−4061.46	−0.880974	−0.440487	−	0.897759i	$-0.645194\pi$
$277$	−4061.46	−0.880974	−0.440487	+	0.897759i	$0.645194\pi$
$278$	178.366	0.0384808
$279$	−1920.35	−0.412073
$280$	−663.946	−0.141709
$281$	1359.26	0.288565	0.144282	−	0.989537i	$-0.453913\pi$
$281$	1359.26	0.288565	0.144282	+	0.989537i	$0.453913\pi$
$282$	−824.143	−0.174032
$283$	−8052.33	−1.69138	−0.845691	−	0.533673i	$-0.820811\pi$
$283$	−8052.33	−1.69138	−0.845691	+	0.533673i	$0.820811\pi$
$284$	1777.24	0.371337
$285$	0	0
$286$	−7564.65	−1.56401
$287$	−6088.27	−1.25219
$288$	288.000	0.0589256
$289$	1611.71	0.328051
$290$	−958.332	−0.194052
$291$	4186.79	0.843416
$292$	794.175	0.159163
$293$	−258.910	−0.0516235	−0.0258118	−	0.999667i	$-0.508217\pi$
$293$	−258.910	−0.0516235	−0.0258118	+	0.999667i	$0.508217\pi$
$294$	1105.78	0.219356
$295$	−5471.13	−1.07980
$296$	13.5183	0.00265450
$297$	1279.31	0.249942
$298$	4060.70	0.789362
$299$	−17093.0	−3.30607
$300$	979.186	0.188444
$301$	−4419.21	−0.846243
$302$	5326.97	1.01501
$303$	−2639.92	−0.500527
$304$	0	0
$305$	−199.205	−0.0373982
$306$	1453.96	0.271626
$307$	7561.70	1.40576	0.702881	−	0.711307i	$-0.251897\pi$
$307$	7561.70	1.40576	0.702881	+	0.711307i	$0.251897\pi$
$308$	2387.61	0.441710
$309$	3911.19	0.720065
$310$	−2811.38	−0.515082
$311$	4343.33	0.791921	0.395961	−	0.918268i	$-0.370412\pi$
$311$	4343.33	0.791921	0.395961	+	0.918268i	$0.370412\pi$
$312$	−1915.84	−0.347638
$313$	−5718.59	−1.03270	−0.516348	−	0.856379i	$-0.672709\pi$
$313$	−5718.59	−1.03270	−0.516348	+	0.856379i	$0.672709\pi$
$314$	−7519.55	−1.35144
$315$	−746.940	−0.133604
$316$	−4031.48	−0.717685
$317$	−4729.36	−0.837942	−0.418971	−	0.908000i	$-0.637609\pi$
$317$	−4729.36	−0.837942	−0.418971	+	0.908000i	$0.637609\pi$
$318$	583.680	0.102928
$319$	3446.24	0.604867
$320$	421.629	0.0736556
$321$	2903.17	0.504794
$322$	5395.02	0.933704
$323$	0	0
$324$	324.000	0.0555556
$325$	−6513.76	−1.11175
$326$	−7483.30	−1.27136
$327$	3417.91	0.578015
$328$	3866.26	0.650850
$329$	−1730.39	−0.289968
$330$	1872.89	0.312422
$331$	5587.10	0.927778	0.463889	−	0.885893i	$-0.346454\pi$
$331$	5587.10	0.927778	0.463889	+	0.885893i	$0.346454\pi$
$332$	1556.51	0.257302
$333$	15.2080	0.00250269
$334$	−5159.58	−0.845268
$335$	2198.77	0.358601
$336$	604.691	0.0981803
$337$	−5294.39	−0.855798	−0.427899	−	0.903826i	$-0.640746\pi$
$337$	−5294.39	−0.855798	−0.427899	+	0.903826i	$0.640746\pi$
$338$	8350.59	1.34382
$339$	426.932	0.0684006
$340$	2128.59	0.339526
$341$	10110.0	1.60553
$342$	0	0
$343$	6642.75	1.04570
$344$	2806.35	0.439850
$345$	4231.98	0.660411
$346$	−5126.20	−0.796493
$347$	−8296.34	−1.28349	−0.641745	−	0.766918i	$-0.721789\pi$
$347$	−8296.34	−1.28349	−0.641745	+	0.766918i	$0.721789\pi$
$348$	872.803	0.134446
$349$	−4028.66	−0.617906	−0.308953	−	0.951077i	$-0.599979\pi$
$349$	−4028.66	−0.617906	−0.308953	+	0.951077i	$0.599979\pi$
$350$	2055.92	0.313981
$351$	−2155.32	−0.327756
$352$	−1516.22	−0.229587
$353$	−5394.55	−0.813380	−0.406690	−	0.913566i	$-0.633317\pi$
$353$	−5394.55	−0.813380	−0.406690	+	0.913566i	$0.633317\pi$
$354$	4982.84	0.748121
$355$	2927.09	0.437617
$356$	−864.860	−0.128757
$357$	3052.77	0.452576
$358$	313.330	0.0462569
$359$	−1679.42	−0.246898	−0.123449	−	0.992351i	$-0.539396\pi$
$359$	−1679.42	−0.246898	−0.123449	+	0.992351i	$0.539396\pi$
$360$	474.333	0.0694432
$361$	0	0
$362$	369.728	0.0536809
$363$	−2742.09	−0.396480
$364$	−4022.54	−0.579226
$365$	1308.00	0.187572
$366$	181.427	0.0259107
$367$	−1774.40	−0.252378	−0.126189	−	0.992006i	$-0.540275\pi$
$367$	−1774.40	−0.252378	−0.126189	+	0.992006i	$0.540275\pi$
$368$	−3426.03	−0.485310
$369$	4349.55	0.613627
$370$	22.2644	0.00312830
$371$	1225.51	0.171496
$372$	2560.47	0.356866
$373$	449.416	0.0623858	0.0311929	−	0.999513i	$-0.490069\pi$
$373$	449.416	0.0623858	0.0311929	+	0.999513i	$0.490069\pi$
$374$	−7654.59	−1.05831
$375$	4083.19	0.562281
$376$	1098.86	0.150716
$377$	−5806.08	−0.793179
$378$	680.277	0.0925653
$379$	−2407.32	−0.326268	−0.163134	−	0.986604i	$-0.552160\pi$
$379$	−2407.32	−0.326268	−0.163134	+	0.986604i	$0.552160\pi$
$380$	0	0
$381$	−203.879	−0.0274148
$382$	225.852	0.0302503
$383$	−2487.74	−0.331900	−0.165950	−	0.986134i	$-0.553069\pi$
$383$	−2487.74	−0.331900	−0.165950	+	0.986134i	$0.553069\pi$
$384$	−384.000	−0.0510310
$385$	3932.37	0.520550
$386$	−3616.66	−0.476899
$387$	3157.15	0.414695
$388$	−5582.39	−0.730419
$389$	14271.9	1.86019	0.930096	−	0.367317i	$-0.119723\pi$
$389$	14271.9	1.86019	0.930096	+	0.367317i	$0.119723\pi$
$390$	−3155.37	−0.409688
$391$	−17296.2	−2.23711
$392$	−1474.38	−0.189968
$393$	2573.83	0.330362
$394$	−1407.60	−0.179985
$395$	−6639.81	−0.845784
$396$	−1705.74	−0.216457
$397$	12551.5	1.58676	0.793380	−	0.608727i	$-0.208319\pi$
$397$	12551.5	1.58676	0.793380	+	0.608727i	$0.208319\pi$
$398$	3582.93	0.451247
$399$	0	0
$400$	−1305.58	−0.163198
$401$	2186.10	0.272240	0.136120	−	0.990692i	$-0.456537\pi$
$401$	2186.10	0.272240	0.136120	+	0.990692i	$0.456537\pi$
$402$	−2002.53	−0.248451
$403$	−17032.8	−2.10537
$404$	3519.90	0.433469
$405$	533.625	0.0654717
$406$	1832.56	0.224010
$407$	−80.0648	−0.00975102
$408$	−1938.62	−0.235235
$409$	−10695.5	−1.29305	−0.646525	−	0.762893i	$-0.723778\pi$
$409$	−10695.5	−1.29305	−0.646525	+	0.762893i	$0.723778\pi$
$410$	6367.70	0.767020
$411$	−1243.69	−0.149263
$412$	−5214.92	−0.623594
$413$	10462.1	1.24650
$414$	−3854.28	−0.457555
$415$	2563.55	0.303228
$416$	2554.45	0.301063
$417$	−267.549	−0.0314194
$418$	0	0
$419$	9079.35	1.05860	0.529302	−	0.848433i	$-0.322454\pi$
$419$	9079.35	1.05860	0.529302	+	0.848433i	$0.322454\pi$
$420$	995.920	0.115705
$421$	−12595.0	−1.45806	−0.729028	−	0.684484i	$-0.760028\pi$
$421$	−12595.0	−1.45806	−0.729028	+	0.684484i	$0.760028\pi$
$422$	1228.02	0.141657
$423$	1236.21	0.142096
$424$	−778.240	−0.0891383
$425$	−6591.20	−0.752283
$426$	−2665.86	−0.303195
$427$	380.927	0.0431718
$428$	−3870.89	−0.437165
$429$	11347.0	1.27701
$430$	4622.04	0.518359
$431$	8359.44	0.934246	0.467123	−	0.884192i	$-0.345291\pi$
$431$	8359.44	0.934246	0.467123	+	0.884192i	$0.345291\pi$
$432$	−432.000	−0.0481125
$433$	−4433.35	−0.492040	−0.246020	−	0.969265i	$-0.579123\pi$
$433$	−4433.35	−0.492040	−0.246020	+	0.969265i	$0.579123\pi$
$434$	5376.02	0.594601
$435$	1437.50	0.158443
$436$	−4557.22	−0.500576
$437$	0	0
$438$	−1191.26	−0.129956
$439$	4030.76	0.438218	0.219109	−	0.975700i	$-0.429685\pi$
$439$	4030.76	0.438218	0.219109	+	0.975700i	$0.429685\pi$
$440$	−2497.19	−0.270566
$441$	−1658.68	−0.179103
$442$	12896.1	1.38780
$443$	9444.72	1.01294	0.506470	−	0.862258i	$-0.330950\pi$
$443$	9444.72	1.01294	0.506470	+	0.862258i	$0.330950\pi$
$444$	−20.2774	−0.00216739
$445$	−1424.42	−0.151739
$446$	8391.60	0.890927
$447$	−6091.05	−0.644511
$448$	−806.254	−0.0850266
$449$	−18865.8	−1.98292	−0.991462	−	0.130398i	$-0.958375\pi$
$449$	−18865.8	−1.98292	−0.991462	+	0.130398i	$0.958375\pi$
$450$	−1468.78	−0.153864
$451$	−22898.8	−2.39082
$452$	−569.243	−0.0592366
$453$	−7990.45	−0.828751
$454$	−6456.76	−0.667469
$455$	−6625.08	−0.682612
$456$	0	0
$457$	−955.450	−0.0977988	−0.0488994	−	0.998804i	$-0.515571\pi$
$457$	−955.450	−0.0977988	−0.0488994	+	0.998804i	$0.515571\pi$
$458$	3823.98	0.390138
$459$	−2180.94	−0.221782
$460$	−5642.64	−0.571933
$461$	2951.19	0.298158	0.149079	−	0.988825i	$-0.452369\pi$
$461$	2951.19	0.298158	0.149079	+	0.988825i	$0.452369\pi$
$462$	−3581.41	−0.360654
$463$	5176.02	0.519547	0.259774	−	0.965670i	$-0.416352\pi$
$463$	5176.02	0.519547	0.259774	+	0.965670i	$0.416352\pi$
$464$	−1163.74	−0.116434
$465$	4217.07	0.420563
$466$	1625.96	0.161634
$467$	19387.6	1.92109	0.960545	−	0.278125i	$-0.0897129\pi$
$467$	19387.6	1.92109	0.960545	+	0.278125i	$0.0897129\pi$
$468$	2873.76	0.283845
$469$	−4204.56	−0.413962
$470$	1809.81	0.177617
$471$	11279.3	1.10345
$472$	−6643.79	−0.647892
$473$	−16621.2	−1.61574
$474$	6047.22	0.585987
$475$	0	0
$476$	−4070.36	−0.391943
$477$	−875.520	−0.0840404
$478$	2226.96	0.213093
$479$	11356.7	1.08330	0.541652	−	0.840603i	$-0.317799\pi$
$479$	11356.7	1.08330	0.541652	+	0.840603i	$0.317799\pi$
$480$	−632.444	−0.0601396
$481$	134.890	0.0127868
$482$	−9976.86	−0.942808
$483$	−8092.53	−0.762366
$484$	3656.11	0.343362
$485$	−9194.13	−0.860792
$486$	−486.000	−0.0453609
$487$	−5906.93	−0.549627	−0.274814	−	0.961498i	$-0.588616\pi$
$487$	−5906.93	−0.549627	−0.274814	+	0.961498i	$0.588616\pi$
$488$	−241.902	−0.0224393
$489$	11225.0	1.03806
$490$	−2428.29	−0.223875
$491$	−2724.86	−0.250451	−0.125225	−	0.992128i	$-0.539965\pi$
$491$	−2724.86	−0.250451	−0.125225	+	0.992128i	$0.539965\pi$
$492$	−5799.40	−0.531417
$493$	−5875.11	−0.536717
$494$	0	0
$495$	−2809.34	−0.255092
$496$	−3413.96	−0.309055
$497$	−5597.29	−0.505177
$498$	−2334.76	−0.210087
$499$	−11694.6	−1.04914	−0.524571	−	0.851366i	$-0.675774\pi$
$499$	−11694.6	−1.04914	−0.524571	+	0.851366i	$0.675774\pi$
$500$	−5444.26	−0.486949
$501$	7739.37	0.690159
$502$	−12675.2	−1.12694
$503$	119.452	0.0105886	0.00529432	−	0.999986i	$-0.498315\pi$
$503$	119.452	0.0105886	0.00529432	+	0.999986i	$0.498315\pi$
$504$	−907.036	−0.0801639
$505$	5797.23	0.510839
$506$	20291.4	1.78273
$507$	−12525.9	−1.09723
$508$	271.839	0.0237420
$509$	−13365.8	−1.16391	−0.581955	−	0.813221i	$-0.697712\pi$
$509$	−13365.8	−1.16391	−0.581955	+	0.813221i	$0.697712\pi$
$510$	−3192.88	−0.277222
$511$	−2501.20	−0.216529
$512$	512.000	0.0441942
$513$	0	0
$514$	−4564.97	−0.391736
$515$	−8588.93	−0.734900
$516$	−4209.53	−0.359136
$517$	−6508.22	−0.553639
$518$	−42.5748	−0.00361125
$519$	7689.31	0.650333
$520$	4207.16	0.354800
$521$	6324.11	0.531793	0.265897	−	0.964002i	$-0.414332\pi$
$521$	6324.11	0.531793	0.265897	+	0.964002i	$0.414332\pi$
$522$	−1309.20	−0.109775
$523$	−197.840	−0.0165410	−0.00827050	−	0.999966i	$-0.502633\pi$
$523$	−197.840	−0.0165410	−0.00827050	+	0.999966i	$0.502633\pi$
$524$	−3431.77	−0.286102
$525$	−3083.88	−0.256365
$526$	−9204.15	−0.762966
$527$	−17235.3	−1.42463
$528$	2274.32	0.187457
$529$	33683.3	2.76841
$530$	−1281.75	−0.105049
$531$	−7474.26	−0.610839
$532$	0	0
$533$	38578.9	3.13515
$534$	1297.29	0.105130
$535$	−6375.31	−0.515194
$536$	2670.04	0.215165
$537$	−469.994	−0.0377686
$538$	−10177.3	−0.815566
$539$	8732.33	0.697826
$540$	−711.500	−0.0567001
$541$	−13878.1	−1.10290	−0.551449	−	0.834209i	$-0.685925\pi$
$541$	−13878.1	−1.10290	−0.551449	+	0.834209i	$0.685925\pi$
$542$	4579.36	0.362916
$543$	−554.592	−0.0438303
$544$	2584.82	0.203719
$545$	−7505.69	−0.589924
$546$	6033.81	0.472936
$547$	22613.9	1.76764	0.883820	−	0.467827i	$-0.154963\pi$
$547$	22613.9	1.76764	0.883820	+	0.467827i	$0.154963\pi$
$548$	1658.26	0.129265
$549$	−272.140	−0.0211560
$550$	7732.58	0.599488
$551$	0	0
$552$	5139.04	0.396254
$553$	12696.9	0.976358
$554$	−8122.93	−0.622943
$555$	−33.3966	−0.00255425
$556$	356.731	0.0272100
$557$	6273.28	0.477213	0.238606	−	0.971116i	$-0.423309\pi$
$557$	6273.28	0.477213	0.238606	+	0.971116i	$0.423309\pi$
$558$	−3840.70	−0.291380
$559$	28002.7	2.11877
$560$	−1327.89	−0.100203
$561$	11481.9	0.864109
$562$	2718.52	0.204046
$563$	13056.6	0.977391	0.488696	−	0.872454i	$-0.337473\pi$
$563$	13056.6	0.977391	0.488696	+	0.872454i	$0.337473\pi$
$564$	−1648.29	−0.123059
$565$	−937.538	−0.0698098
$566$	−16104.7	−1.19599
$567$	−1020.42	−0.0755792
$568$	3554.48	0.262575
$569$	3616.03	0.266418	0.133209	−	0.991088i	$-0.457472\pi$
$569$	3616.03	0.266418	0.133209	+	0.991088i	$0.457472\pi$
$570$	0	0
$571$	−88.6661	−0.00649836	−0.00324918	−	0.999995i	$-0.501034\pi$
$571$	−88.6661	−0.00649836	−0.00324918	+	0.999995i	$0.501034\pi$
$572$	−15129.3	−1.10592
$573$	−338.779	−0.0246993
$574$	−12176.5	−0.885433
$575$	17472.5	1.26722
$576$	576.000	0.0416667
$577$	25383.4	1.83141	0.915705	−	0.401851i	$-0.131633\pi$
$577$	25383.4	1.83141	0.915705	+	0.401851i	$0.131633\pi$
$578$	3223.43	0.231967
$579$	5424.98	0.389386
$580$	−1916.66	−0.137216
$581$	−4902.11	−0.350041
$582$	8373.58	0.596385
$583$	4609.29	0.327440
$584$	1588.35	0.112545
$585$	4733.05	0.334509
$586$	−517.820	−0.0365033
$587$	20722.2	1.45707	0.728533	−	0.685011i	$-0.240203\pi$
$587$	20722.2	1.45707	0.728533	+	0.685011i	$0.240203\pi$
$588$	2211.57	0.155108
$589$	0	0
$590$	−10942.3	−0.763534
$591$	2111.40	0.146957
$592$	27.0365	0.00187702
$593$	18386.2	1.27324	0.636619	−	0.771178i	$-0.280332\pi$
$593$	18386.2	1.27324	0.636619	+	0.771178i	$0.280332\pi$
$594$	2558.61	0.176736
$595$	−6703.84	−0.461900
$596$	8121.39	0.558163
$597$	−5374.40	−0.368441
$598$	−34186.1	−2.33775
$599$	−10726.5	−0.731675	−0.365837	−	0.930679i	$-0.619217\pi$
$599$	−10726.5	−0.731675	−0.365837	+	0.930679i	$0.619217\pi$
$600$	1958.37	0.133250
$601$	−15183.9	−1.03055	−0.515277	−	0.857024i	$-0.672311\pi$
$601$	−15183.9	−1.03055	−0.515277	+	0.857024i	$0.672311\pi$
$602$	−8838.42	−0.598384
$603$	3003.80	0.202859
$604$	10653.9	0.717720
$605$	6021.58	0.404648
$606$	−5279.84	−0.353926
$607$	13289.7	0.888656	0.444328	−	0.895864i	$-0.353442\pi$
$607$	13289.7	0.888656	0.444328	+	0.895864i	$0.353442\pi$
$608$	0	0
$609$	−2748.83	−0.182904
$610$	−398.410	−0.0264445
$611$	10964.8	0.726001
$612$	2907.93	0.192068
$613$	−12282.5	−0.809276	−0.404638	−	0.914477i	$-0.632603\pi$
$613$	−12282.5	−0.809276	−0.404638	+	0.914477i	$0.632603\pi$
$614$	15123.4	0.994024
$615$	−9551.54	−0.626269
$616$	4775.22	0.312336
$617$	3854.71	0.251515	0.125758	−	0.992061i	$-0.459864\pi$
$617$	3854.71	0.251515	0.125758	+	0.992061i	$0.459864\pi$
$618$	7822.39	0.509163
$619$	−13146.4	−0.853635	−0.426817	−	0.904338i	$-0.640365\pi$
$619$	−13146.4	−0.853635	−0.426817	+	0.904338i	$0.640365\pi$
$620$	−5622.76	−0.364218
$621$	5781.42	0.373592
$622$	8686.65	0.559973
$623$	2723.82	0.175164
$624$	−3831.68	−0.245817
$625$	1233.21	0.0789256
$626$	−11437.2	−0.730227
$627$	0	0
$628$	−15039.1	−0.955613
$629$	136.493	0.00865238
$630$	−1493.88	−0.0944723
$631$	8730.01	0.550771	0.275385	−	0.961334i	$-0.411195\pi$
$631$	8730.01	0.550771	0.275385	+	0.961334i	$0.411195\pi$
$632$	−8062.96	−0.507480
$633$	−1842.03	−0.115662
$634$	−9458.73	−0.592514
$635$	447.716	0.0279797
$636$	1167.36	0.0727812
$637$	−14711.8	−0.915078
$638$	6892.49	0.427706
$639$	3998.79	0.247558
$640$	843.259	0.0520824
$641$	1950.05	0.120160	0.0600798	−	0.998194i	$-0.480864\pi$
$641$	1950.05	0.120160	0.0600798	+	0.998194i	$0.480864\pi$
$642$	5806.33	0.356943
$643$	−4548.84	−0.278987	−0.139493	−	0.990223i	$-0.544547\pi$
$643$	−4548.84	−0.278987	−0.139493	+	0.990223i	$0.544547\pi$
$644$	10790.0	0.660229
$645$	−6933.06	−0.423239
$646$	0	0
$647$	4085.71	0.248262	0.124131	−	0.992266i	$-0.460386\pi$
$647$	4085.71	0.248262	0.124131	+	0.992266i	$0.460386\pi$
$648$	648.000	0.0392837
$649$	39349.3	2.37996
$650$	−13027.5	−0.786125
$651$	−8064.02	−0.485490
$652$	−14966.6	−0.898984
$653$	14191.6	0.850474	0.425237	−	0.905082i	$-0.360191\pi$
$653$	14191.6	0.850474	0.425237	+	0.905082i	$0.360191\pi$
$654$	6835.82	0.408719
$655$	−5652.09	−0.337169
$656$	7732.53	0.460220
$657$	1786.89	0.106109
$658$	−3460.78	−0.205038
$659$	7383.20	0.436432	0.218216	−	0.975901i	$-0.429976\pi$
$659$	7383.20	0.436432	0.218216	+	0.975901i	$0.429976\pi$
$660$	3745.79	0.220916
$661$	−23191.5	−1.36467	−0.682334	−	0.731041i	$-0.739035\pi$
$661$	−23191.5	−1.36467	−0.682334	+	0.731041i	$0.739035\pi$
$662$	11174.2	0.656038
$663$	−19344.2	−1.13313
$664$	3113.01	0.181940
$665$	0	0
$666$	30.4161	0.00176967
$667$	15574.2	0.904102
$668$	−10319.2	−0.597695
$669$	−12587.4	−0.727439
$670$	4397.53	0.253569
$671$	1432.72	0.0824284
$672$	1209.38	0.0694240
$673$	17227.4	0.986726	0.493363	−	0.869824i	$-0.335767\pi$
$673$	17227.4	0.986726	0.493363	+	0.869824i	$0.335767\pi$
$674$	−10588.8	−0.605141
$675$	2203.17	0.125630
$676$	16701.2	0.950227
$677$	398.443	0.0226195	0.0113098	−	0.999936i	$-0.496400\pi$
$677$	398.443	0.0226195	0.0113098	+	0.999936i	$0.496400\pi$
$678$	853.865	0.0483665
$679$	17581.3	0.993682
$680$	4257.18	0.240081
$681$	9685.14	0.544986
$682$	20219.9	1.13528
$683$	10488.7	0.587611	0.293806	−	0.955865i	$-0.405078\pi$
$683$	10488.7	0.587611	0.293806	+	0.955865i	$0.405078\pi$
$684$	0	0
$685$	2731.14	0.152338
$686$	13285.5	0.739421
$687$	−5735.98	−0.318546
$688$	5612.71	0.311021
$689$	−7765.54	−0.429381
$690$	8463.95	0.466981
$691$	2612.01	0.143800	0.0718999	−	0.997412i	$-0.477094\pi$
$691$	2612.01	0.143800	0.0718999	+	0.997412i	$0.477094\pi$
$692$	−10252.4	−0.563205
$693$	5372.12	0.294473
$694$	−16592.7	−0.907564
$695$	587.533	0.0320668
$696$	1745.61	0.0950676
$697$	39037.5	2.12145
$698$	−8057.32	−0.436926
$699$	−2438.95	−0.131973
$700$	4111.84	0.222018
$701$	−27074.2	−1.45874	−0.729372	−	0.684118i	$-0.760187\pi$
$701$	−27074.2	−1.45874	−0.729372	+	0.684118i	$0.760187\pi$
$702$	−4310.64	−0.231759
$703$	0	0
$704$	−3032.43	−0.162342
$705$	−2714.71	−0.145024
$706$	−10789.1	−0.575146
$707$	−11085.7	−0.589702
$708$	9965.68	0.529002
$709$	3039.21	0.160987	0.0804937	−	0.996755i	$-0.474350\pi$
$709$	3039.21	0.160987	0.0804937	+	0.996755i	$0.474350\pi$
$710$	5854.19	0.309442
$711$	−9070.83	−0.478457
$712$	−1729.72	−0.0910450
$713$	45688.8	2.39980
$714$	6105.54	0.320020
$715$	−24917.8	−1.30332
$716$	626.659	0.0327086
$717$	−3340.44	−0.173990
$718$	−3358.84	−0.174583
$719$	13750.5	0.713220	0.356610	−	0.934253i	$-0.383932\pi$
$719$	13750.5	0.713220	0.356610	+	0.934253i	$0.383932\pi$
$720$	948.666	0.0491037
$721$	16424.0	0.848354
$722$	0	0
$723$	14965.3	0.769799
$724$	739.456	0.0379581
$725$	5934.97	0.304027
$726$	−5484.17	−0.280354
$727$	18138.1	0.925315	0.462657	−	0.886537i	$-0.346896\pi$
$727$	18138.1	0.925315	0.462657	+	0.886537i	$0.346896\pi$
$728$	−8045.08	−0.409575
$729$	729.000	0.0370370
$730$	2616.00	0.132633
$731$	28335.7	1.43370
$732$	362.853	0.0183216
$733$	−23212.7	−1.16969	−0.584845	−	0.811145i	$-0.698845\pi$
$733$	−23212.7	−1.16969	−0.584845	+	0.811145i	$0.698845\pi$
$734$	−3548.80	−0.178458
$735$	3642.43	0.182793
$736$	−6852.06	−0.343166
$737$	−15813.9	−0.790383
$738$	8699.09	0.433900
$739$	17007.3	0.846583	0.423291	−	0.905994i	$-0.360875\pi$
$739$	17007.3	0.846583	0.423291	+	0.905994i	$0.360875\pi$
$740$	44.5289	0.00221204
$741$	0	0
$742$	2451.01	0.121266
$743$	23348.7	1.15287	0.576435	−	0.817143i	$-0.304443\pi$
$743$	23348.7	1.15287	0.576435	+	0.817143i	$0.304443\pi$
$744$	5120.94	0.252342
$745$	13375.9	0.657790
$746$	898.833	0.0441134
$747$	3502.14	0.171535
$748$	−15309.2	−0.748341
$749$	12191.1	0.594730
$750$	8166.39	0.397592
$751$	34272.3	1.66526	0.832631	−	0.553828i	$-0.186833\pi$
$751$	34272.3	1.66526	0.832631	+	0.553828i	$0.186833\pi$
$752$	2197.71	0.106572
$753$	19012.8	0.920141
$754$	−11612.2	−0.560862
$755$	17546.9	0.845825
$756$	1360.55	0.0654535
$757$	−16389.2	−0.786888	−0.393444	−	0.919349i	$-0.628716\pi$
$757$	−16389.2	−0.786888	−0.393444	+	0.919349i	$0.628716\pi$
$758$	−4814.63	−0.230706
$759$	−30437.1	−1.45560
$760$	0	0
$761$	−2424.65	−0.115497	−0.0577487	−	0.998331i	$-0.518392\pi$
$761$	−2424.65	−0.115497	−0.0577487	+	0.998331i	$0.518392\pi$
$762$	−407.759	−0.0193852
$763$	14352.6	0.680997
$764$	451.705	0.0213902
$765$	4789.32	0.226351
$766$	−4975.48	−0.234689
$767$	−66293.9	−3.12091
$768$	−768.000	−0.0360844
$769$	−30209.5	−1.41662	−0.708310	−	0.705901i	$-0.750542\pi$
$769$	−30209.5	−1.41662	−0.708310	+	0.705901i	$0.750542\pi$
$770$	7864.73	0.368085
$771$	6847.46	0.319851
$772$	−7233.31	−0.337218
$773$	−11314.5	−0.526461	−0.263230	−	0.964733i	$-0.584788\pi$
$773$	−11314.5	−0.526461	−0.263230	+	0.964733i	$0.584788\pi$
$774$	6314.30	0.293234
$775$	17410.9	0.806993
$776$	−11164.8	−0.516484
$777$	63.8622	0.00294858
$778$	28543.8	1.31535
$779$	0	0
$780$	−6310.74	−0.289693
$781$	−21052.2	−0.964540
$782$	−34592.5	−1.58187
$783$	1963.81	0.0896306
$784$	−2948.76	−0.134328
$785$	−24769.2	−1.12618
$786$	5147.65	0.233601
$787$	708.118	0.0320733	0.0160366	−	0.999871i	$-0.494895\pi$
$787$	708.118	0.0320733	0.0160366	+	0.999871i	$0.494895\pi$
$788$	−2815.20	−0.127268
$789$	13806.2	0.622959
$790$	−13279.6	−0.598060
$791$	1792.79	0.0805871
$792$	−3411.48	−0.153058
$793$	−2413.78	−0.108091
$794$	25103.1	1.12201
$795$	1922.63	0.0857719
$796$	7165.87	0.319080
$797$	−30267.6	−1.34521	−0.672606	−	0.740001i	$-0.734825\pi$
$797$	−30267.6	−1.34521	−0.672606	+	0.740001i	$0.734825\pi$
$798$	0	0
$799$	11095.1	0.491261
$800$	−2611.16	−0.115398
$801$	−1945.94	−0.0858380
$802$	4372.19	0.192503
$803$	−9407.35	−0.413422
$804$	−4005.06	−0.175681
$805$	17771.1	0.778073
$806$	−34065.6	−1.48872
$807$	15265.9	0.665907
$808$	7039.79	0.306509
$809$	20443.6	0.888455	0.444228	−	0.895914i	$-0.353478\pi$
$809$	20443.6	0.888455	0.444228	+	0.895914i	$0.353478\pi$
$810$	1067.25	0.0462955
$811$	34243.7	1.48269	0.741344	−	0.671125i	$-0.234189\pi$
$811$	34243.7	1.48269	0.741344	+	0.671125i	$0.234189\pi$
$812$	3665.11	0.158399
$813$	−6869.05	−0.296320
$814$	−160.130	−0.00689501
$815$	−24649.8	−1.05944
$816$	−3877.23	−0.166336
$817$	0	0
$818$	−21391.0	−0.914325
$819$	−9050.71	−0.386151
$820$	12735.4	0.542365
$821$	45253.6	1.92370	0.961851	−	0.273572i	$-0.0882052\pi$
$821$	45253.6	1.92370	0.961851	+	0.273572i	$0.0882052\pi$
$822$	−2487.39	−0.105545
$823$	4925.73	0.208627	0.104314	−	0.994544i	$-0.466735\pi$
$823$	4925.73	0.208627	0.104314	+	0.994544i	$0.466735\pi$
$824$	−10429.8	−0.440948
$825$	−11598.9	−0.489480
$826$	20924.2	0.881410
$827$	28813.8	1.21155	0.605776	−	0.795635i	$-0.292863\pi$
$827$	28813.8	1.21155	0.605776	+	0.795635i	$0.292863\pi$
$828$	−7708.57	−0.323540
$829$	23406.5	0.980629	0.490315	−	0.871546i	$-0.336882\pi$
$829$	23406.5	0.980629	0.490315	+	0.871546i	$0.336882\pi$
$830$	5127.10	0.214415
$831$	12184.4	0.508630
$832$	5108.91	0.212884
$833$	−14886.7	−0.619202
$834$	−535.097	−0.0222169
$835$	−16995.5	−0.704377
$836$	0	0
$837$	5761.06	0.237911
$838$	18158.7	0.748547
$839$	20529.7	0.844771	0.422386	−	0.906416i	$-0.361193\pi$
$839$	20529.7	0.844771	0.422386	+	0.906416i	$0.361193\pi$
$840$	1991.84	0.0818154
$841$	−19098.8	−0.783092
$842$	−25189.9	−1.03100
$843$	−4077.78	−0.166603
$844$	2456.04	0.100166
$845$	27506.7	1.11983
$846$	2472.43	0.100477
$847$	−11514.7	−0.467118
$848$	−1556.48	−0.0630303
$849$	24157.0	0.976520
$850$	−13182.4	−0.531944
$851$	−361.828	−0.0145750
$852$	−5331.72	−0.214392
$853$	35793.6	1.43675	0.718377	−	0.695654i	$-0.244885\pi$
$853$	35793.6	1.43675	0.718377	+	0.695654i	$0.244885\pi$
$854$	761.854	0.0305270
$855$	0	0
$856$	−7741.78	−0.309122
$857$	−2463.56	−0.0981954	−0.0490977	−	0.998794i	$-0.515635\pi$
$857$	−2463.56	−0.0981954	−0.0490977	+	0.998794i	$0.515635\pi$
$858$	22694.0	0.902982
$859$	15462.9	0.614188	0.307094	−	0.951679i	$-0.400643\pi$
$859$	15462.9	0.614188	0.307094	+	0.951679i	$0.400643\pi$
$860$	9244.08	0.366535
$861$	18264.8	0.722953
$862$	16718.9	0.660612
$863$	−9776.04	−0.385609	−0.192804	−	0.981237i	$-0.561758\pi$
$863$	−9776.04	−0.385609	−0.192804	+	0.981237i	$0.561758\pi$
$864$	−864.000	−0.0340207
$865$	−16885.6	−0.663732
$866$	−8866.71	−0.347925
$867$	−4835.14	−0.189400
$868$	10752.0	0.420447
$869$	47754.6	1.86417
$870$	2875.00	0.112036
$871$	26642.6	1.03645
$872$	−9114.43	−0.353961
$873$	−12560.4	−0.486946
$874$	0	0
$875$	17146.3	0.662459
$876$	−2382.52	−0.0918927
$877$	19851.8	0.764365	0.382183	−	0.924087i	$-0.375173\pi$
$877$	19851.8	0.764365	0.382183	+	0.924087i	$0.375173\pi$
$878$	8061.52	0.309867
$879$	776.730	0.0298049
$880$	−4994.38	−0.191319
$881$	−21993.6	−0.841071	−0.420535	−	0.907276i	$-0.638158\pi$
$881$	−21993.6	−0.841071	−0.420535	+	0.907276i	$0.638158\pi$
$882$	−3317.35	−0.126645
$883$	−26602.5	−1.01387	−0.506934	−	0.861985i	$-0.669221\pi$
$883$	−26602.5	−1.01387	−0.506934	+	0.861985i	$0.669221\pi$
$884$	25792.2	0.981319
$885$	16413.4	0.623423
$886$	18889.4	0.716256
$887$	−28269.4	−1.07012	−0.535059	−	0.844815i	$-0.679711\pi$
$887$	−28269.4	−1.07012	−0.535059	+	0.844815i	$0.679711\pi$
$888$	−40.5548	−0.00153258
$889$	−856.139	−0.0322992
$890$	−2848.83	−0.107296
$891$	−3837.92	−0.144304
$892$	16783.2	0.629981
$893$	0	0
$894$	−12182.1	−0.455738
$895$	1032.10	0.0385467
$896$	−1612.51	−0.0601229
$897$	51279.1	1.90876
$898$	−37731.6	−1.40214
$899$	15519.3	0.575750
$900$	−2937.56	−0.108798
$901$	−7857.86	−0.290547
$902$	−45797.6	−1.69057
$903$	13257.6	0.488578
$904$	−1138.49	−0.0418866
$905$	1217.88	0.0447333
$906$	−15980.9	−0.586016
$907$	−45291.9	−1.65810	−0.829048	−	0.559177i	$-0.811117\pi$
$907$	−45291.9	−1.65810	−0.829048	+	0.559177i	$0.811117\pi$
$908$	−12913.5	−0.471972
$909$	7919.77	0.288979
$910$	−13250.2	−0.482680
$911$	−7522.61	−0.273584	−0.136792	−	0.990600i	$-0.543679\pi$
$911$	−7522.61	−0.273584	−0.136792	+	0.990600i	$0.543679\pi$
$912$	0	0
$913$	−18437.5	−0.668337
$914$	−1910.90	−0.0691542
$915$	597.615	0.0215919
$916$	7647.97	0.275869
$917$	10808.1	0.389221
$918$	−4361.89	−0.156823
$919$	−2692.69	−0.0966525	−0.0483262	−	0.998832i	$-0.515389\pi$
$919$	−2692.69	−0.0966525	−0.0483262	+	0.998832i	$0.515389\pi$
$920$	−11285.3	−0.404418
$921$	−22685.1	−0.811617
$922$	5902.39	0.210829
$923$	35467.8	1.26483
$924$	−7162.82	−0.255021
$925$	−137.884	−0.00490119
$926$	10352.0	0.367375
$927$	−11733.6	−0.415730
$928$	−2327.47	−0.0823309
$929$	43724.1	1.54418	0.772089	−	0.635514i	$-0.219212\pi$
$929$	43724.1	1.54418	0.772089	+	0.635514i	$0.219212\pi$
$930$	8434.13	0.297383
$931$	0	0
$932$	3251.93	0.114292
$933$	−13030.0	−0.457216
$934$	38775.1	1.35842
$935$	−25214.1	−0.881912
$936$	5747.52	0.200709
$937$	−55693.8	−1.94177	−0.970885	−	0.239546i	$-0.923001\pi$
$937$	−55693.8	−1.94177	−0.970885	+	0.239546i	$0.923001\pi$
$938$	−8409.11	−0.292716
$939$	17155.8	0.596228
$940$	3619.61	0.125594
$941$	−19583.1	−0.678418	−0.339209	−	0.940711i	$-0.610159\pi$
$941$	−19583.1	−0.678418	−0.339209	+	0.940711i	$0.610159\pi$
$942$	22558.6	0.780255
$943$	−103484.	−3.57359
$944$	−13287.6	−0.458129
$945$	2240.82	0.0771363
$946$	−33242.5	−1.14250
$947$	−21808.2	−0.748333	−0.374166	−	0.927362i	$-0.622071\pi$
$947$	−21808.2	−0.748333	−0.374166	+	0.927362i	$0.622071\pi$
$948$	12094.4	0.414356
$949$	15849.1	0.542132
$950$	0	0
$951$	14188.1	0.483786
$952$	−8140.72	−0.277145
$953$	30879.4	1.04961	0.524807	−	0.851221i	$-0.324137\pi$
$953$	30879.4	1.04961	0.524807	+	0.851221i	$0.324137\pi$
$954$	−1751.04	−0.0594256
$955$	743.953	0.0252081
$956$	4453.91	0.150680
$957$	−10338.7	−0.349220
$958$	22713.5	0.766012
$959$	−5222.57	−0.175856
$960$	−1264.89	−0.0425251
$961$	15736.8	0.528240
$962$	269.779	0.00904162
$963$	−8709.50	−0.291443
$964$	−19953.7	−0.666666
$965$	−11913.2	−0.397408
$966$	−16185.1	−0.539074
$967$	−31929.1	−1.06181	−0.530905	−	0.847431i	$-0.678148\pi$
$967$	−31929.1	−1.06181	−0.530905	+	0.847431i	$0.678148\pi$
$968$	7312.23	0.242793
$969$	0	0
$970$	−18388.3	−0.608672
$971$	−41092.4	−1.35810	−0.679052	−	0.734090i	$-0.737609\pi$
$971$	−41092.4	−1.35810	−0.679052	+	0.734090i	$0.737609\pi$
$972$	−972.000	−0.0320750
$973$	−1123.50	−0.0370173
$974$	−11813.9	−0.388645
$975$	19541.3	0.641869
$976$	−483.804	−0.0158670
$977$	37178.6	1.21745	0.608724	−	0.793382i	$-0.291682\pi$
$977$	37178.6	1.21745	0.608724	+	0.793382i	$0.291682\pi$
$978$	22449.9	0.734017
$979$	10244.6	0.334444
$980$	−4856.57	−0.158304
$981$	−10253.7	−0.333717
$982$	−5449.72	−0.177095
$983$	−6909.63	−0.224194	−0.112097	−	0.993697i	$-0.535757\pi$
$983$	−6909.63	−0.224194	−0.112097	+	0.993697i	$0.535757\pi$
$984$	−11598.8	−0.375768
$985$	−4636.61	−0.149985
$986$	−11750.2	−0.379516
$987$	5191.16	0.167413
$988$	0	0
$989$	−75114.5	−2.41507
$990$	−5618.68	−0.180377
$991$	12005.6	0.384835	0.192418	−	0.981313i	$-0.438367\pi$
$991$	12005.6	0.384835	0.192418	+	0.981313i	$0.438367\pi$
$992$	−6827.92	−0.218535
$993$	−16761.3	−0.535653
$994$	−11194.6	−0.357214
$995$	11802.1	0.376032
$996$	−4669.52	−0.148554
$997$	−8587.35	−0.272782	−0.136391	−	0.990655i	$-0.543550\pi$
$997$	−8587.35	−0.272782	−0.136391	+	0.990655i	$0.543550\pi$
$998$	−23389.2	−0.741856
$999$	−45.6241	−0.00144493

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.4.a.bf.1.4		6
19.9	even	9		114.4.i.a.43.2	✓	12
19.17	even	9		114.4.i.a.61.2	yes	12
19.18	odd	2		2166.4.a.bd.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.i.a.43.2	✓	12	19.9	even	9
114.4.i.a.61.2	yes	12	19.17	even	9
2166.4.a.bd.1.4		6	19.18	odd	2
2166.4.a.bf.1.4		6	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)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +6.58796 q^{5} -6.00000 q^{6} -12.5977 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +6.58796 q^{5} -6.00000 q^{6} -12.5977 q^{7} +8.00000 q^{8} +9.00000 q^{9} +13.1759 q^{10} -47.3817 q^{11} -12.0000 q^{12} +79.8267 q^{13} -25.1954 q^{14} -19.7639 q^{15} +16.0000 q^{16} +80.7757 q^{17} +18.0000 q^{18} +26.3518 q^{20} +37.7932 q^{21} -94.7635 q^{22} -214.127 q^{23} -24.0000 q^{24} -81.5988 q^{25} +159.653 q^{26} -27.0000 q^{27} -50.3909 q^{28} -72.7336 q^{29} -39.5278 q^{30} -213.372 q^{31} +32.0000 q^{32} +142.145 q^{33} +161.551 q^{34} -82.9933 q^{35} +36.0000 q^{36} +1.68978 q^{37} -239.480 q^{39} +52.7037 q^{40} +483.283 q^{41} +75.5863 q^{42} +350.794 q^{43} -189.527 q^{44} +59.2916 q^{45} -428.254 q^{46} +137.357 q^{47} -48.0000 q^{48} -184.297 q^{49} -163.198 q^{50} -242.327 q^{51} +319.307 q^{52} -97.2800 q^{53} -54.0000 q^{54} -312.149 q^{55} -100.782 q^{56} -145.467 q^{58} -830.473 q^{59} -79.0555 q^{60} -30.2378 q^{61} -426.745 q^{62} -113.380 q^{63} +64.0000 q^{64} +525.895 q^{65} +284.290 q^{66} +333.755 q^{67} +323.103 q^{68} +642.380 q^{69} -165.987 q^{70} +444.310 q^{71} +72.0000 q^{72} +198.544 q^{73} +3.37956 q^{74} +244.796 q^{75} +596.902 q^{77} -478.960 q^{78} -1007.87 q^{79} +105.407 q^{80} +81.0000 q^{81} +966.566 q^{82} +389.127 q^{83} +151.173 q^{84} +532.147 q^{85} +701.589 q^{86} +218.201 q^{87} -379.054 q^{88} -216.215 q^{89} +118.583 q^{90} -1005.63 q^{91} -856.507 q^{92} +640.117 q^{93} +274.714 q^{94} -96.0000 q^{96} -1395.60 q^{97} -368.595 q^{98} -426.436 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{2} - 18 q^{3} + 24 q^{4} + 27 q^{5} - 36 q^{6} - 42 q^{7} + 48 q^{8} + 54 q^{9}+O(q^{10}) \) 6 * q + 12 * q^2 - 18 * q^3 + 24 * q^4 + 27 * q^5 - 36 * q^6 - 42 * q^7 + 48 * q^8 + 54 * q^9	\( 6 q + 12 q^{2} - 18 q^{3} + 24 q^{4} + 27 q^{5} - 36 q^{6} - 42 q^{7} + 48 q^{8} + 54 q^{9} + 54 q^{10} - 57 q^{11} - 72 q^{12} + 21 q^{13} - 84 q^{14} - 81 q^{15} + 96 q^{16} - 45 q^{17} + 108 q^{18} + 108 q^{20} + 126 q^{21} - 114 q^{22} + 138 q^{23} - 144 q^{24} - 135 q^{25} + 42 q^{26} - 162 q^{27} - 168 q^{28} - 177 q^{29} - 162 q^{30} - 99 q^{31} + 192 q^{32} + 171 q^{33} - 90 q^{34} - 594 q^{35} + 216 q^{36} - 615 q^{37} - 63 q^{39} + 216 q^{40} - 171 q^{41} + 252 q^{42} + 456 q^{43} - 228 q^{44} + 243 q^{45} + 276 q^{46} + 228 q^{47} - 288 q^{48} + 168 q^{49} - 270 q^{50} + 135 q^{51} + 84 q^{52} - 357 q^{53} - 324 q^{54} - 1356 q^{55} - 336 q^{56} - 354 q^{58} - 741 q^{59} - 324 q^{60} - 66 q^{61} - 198 q^{62} - 378 q^{63} + 384 q^{64} + 843 q^{65} + 342 q^{66} + 966 q^{67} - 180 q^{68} - 414 q^{69} - 1188 q^{70} - 1338 q^{71} + 432 q^{72} + 1293 q^{73} - 1230 q^{74} + 405 q^{75} + 1299 q^{77} - 126 q^{78} - 1404 q^{79} + 432 q^{80} + 486 q^{81} - 342 q^{82} - 1440 q^{83} + 504 q^{84} - 1209 q^{85} + 912 q^{86} + 531 q^{87} - 456 q^{88} - 2991 q^{89} + 486 q^{90} - 4632 q^{91} + 552 q^{92} + 297 q^{93} + 456 q^{94} - 576 q^{96} - 2802 q^{97} + 336 q^{98} - 513 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 - 18 * q^3 + 24 * q^4 + 27 * q^5 - 36 * q^6 - 42 * q^7 + 48 * q^8 + 54 * q^9 + 54 * q^10 - 57 * q^11 - 72 * q^12 + 21 * q^13 - 84 * q^14 - 81 * q^15 + 96 * q^16 - 45 * q^17 + 108 * q^18 + 108 * q^20 + 126 * q^21 - 114 * q^22 + 138 * q^23 - 144 * q^24 - 135 * q^25 + 42 * q^26 - 162 * q^27 - 168 * q^28 - 177 * q^29 - 162 * q^30 - 99 * q^31 + 192 * q^32 + 171 * q^33 - 90 * q^34 - 594 * q^35 + 216 * q^36 - 615 * q^37 - 63 * q^39 + 216 * q^40 - 171 * q^41 + 252 * q^42 + 456 * q^43 - 228 * q^44 + 243 * q^45 + 276 * q^46 + 228 * q^47 - 288 * q^48 + 168 * q^49 - 270 * q^50 + 135 * q^51 + 84 * q^52 - 357 * q^53 - 324 * q^54 - 1356 * q^55 - 336 * q^56 - 354 * q^58 - 741 * q^59 - 324 * q^60 - 66 * q^61 - 198 * q^62 - 378 * q^63 + 384 * q^64 + 843 * q^65 + 342 * q^66 + 966 * q^67 - 180 * q^68 - 414 * q^69 - 1188 * q^70 - 1338 * q^71 + 432 * q^72 + 1293 * q^73 - 1230 * q^74 + 405 * q^75 + 1299 * q^77 - 126 * q^78 - 1404 * q^79 + 432 * q^80 + 486 * q^81 - 342 * q^82 - 1440 * q^83 + 504 * q^84 - 1209 * q^85 + 912 * q^86 + 531 * q^87 - 456 * q^88 - 2991 * q^89 + 486 * q^90 - 4632 * q^91 + 552 * q^92 + 297 * q^93 + 456 * q^94 - 576 * q^96 - 2802 * q^97 + 336 * q^98 - 513 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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