LMFDB - Embedded newform 2166.4.a.w.1.3

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:	$3$
Coefficient field:	3.3.1524.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 7x + 1 $ x^3 - x^2 - 7*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	no (minimal twist has level 114)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.140435$ 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)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +20.2020 q^{5} +6.00000 q^{6} -22.8872 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +20.2020 q^{5} +6.00000 q^{6} -22.8872 q^{7} +8.00000 q^{8} +9.00000 q^{9} +40.4040 q^{10} -57.5614 q^{11} +12.0000 q^{12} -27.3148 q^{13} -45.7744 q^{14} +60.6059 q^{15} +16.0000 q^{16} -73.4486 q^{17} +18.0000 q^{18} +80.8079 q^{20} -68.6616 q^{21} -115.123 q^{22} -188.584 q^{23} +24.0000 q^{24} +283.120 q^{25} -54.6296 q^{26} +27.0000 q^{27} -91.5488 q^{28} +7.15594 q^{29} +121.212 q^{30} +117.144 q^{31} +32.0000 q^{32} -172.684 q^{33} -146.897 q^{34} -462.367 q^{35} +36.0000 q^{36} +332.600 q^{37} -81.9443 q^{39} +161.616 q^{40} +42.7158 q^{41} -137.323 q^{42} +47.2469 q^{43} -230.245 q^{44} +181.818 q^{45} -377.168 q^{46} -507.995 q^{47} +48.0000 q^{48} +180.824 q^{49} +566.240 q^{50} -220.346 q^{51} -109.259 q^{52} -492.609 q^{53} +54.0000 q^{54} -1162.85 q^{55} -183.098 q^{56} +14.3119 q^{58} -460.041 q^{59} +242.424 q^{60} +450.745 q^{61} +234.287 q^{62} -205.985 q^{63} +64.0000 q^{64} -551.813 q^{65} -345.368 q^{66} -522.465 q^{67} -293.794 q^{68} -565.751 q^{69} -924.734 q^{70} -931.419 q^{71} +72.0000 q^{72} +350.123 q^{73} +665.199 q^{74} +849.360 q^{75} +1317.42 q^{77} -163.889 q^{78} -194.868 q^{79} +323.232 q^{80} +81.0000 q^{81} +85.4317 q^{82} -286.083 q^{83} -274.646 q^{84} -1483.81 q^{85} +94.4937 q^{86} +21.4678 q^{87} -460.491 q^{88} -839.690 q^{89} +363.636 q^{90} +625.159 q^{91} -754.335 q^{92} +351.431 q^{93} -1015.99 q^{94} +96.0000 q^{96} -605.516 q^{97} +361.648 q^{98} -518.052 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 6 q^{2} + 9 q^{3} + 12 q^{4} + 2 q^{5} + 18 q^{6} - 17 q^{7} + 24 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q + 6 * q^2 + 9 * q^3 + 12 * q^4 + 2 * q^5 + 18 * q^6 - 17 * q^7 + 24 * q^8 + 27 * q^9	\( 3 q + 6 q^{2} + 9 q^{3} + 12 q^{4} + 2 q^{5} + 18 q^{6} - 17 q^{7} + 24 q^{8} + 27 q^{9} + 4 q^{10} - 52 q^{11} + 36 q^{12} - 75 q^{13} - 34 q^{14} + 6 q^{15} + 48 q^{16} - 48 q^{17} + 54 q^{18} + 8 q^{20} - 51 q^{21} - 104 q^{22} - 238 q^{23} + 72 q^{24} + 229 q^{25} - 150 q^{26} + 81 q^{27} - 68 q^{28} + 8 q^{29} + 12 q^{30} - 107 q^{31} + 96 q^{32} - 156 q^{33} - 96 q^{34} - 294 q^{35} + 108 q^{36} - 305 q^{37} - 225 q^{39} + 16 q^{40} - 16 q^{41} - 102 q^{42} - 331 q^{43} - 208 q^{44} + 18 q^{45} - 476 q^{46} - 766 q^{47} + 144 q^{48} + 1142 q^{49} + 458 q^{50} - 144 q^{51} - 300 q^{52} + 118 q^{53} + 162 q^{54} - 1400 q^{55} - 136 q^{56} + 16 q^{58} - 936 q^{59} + 24 q^{60} - 399 q^{61} - 214 q^{62} - 153 q^{63} + 192 q^{64} - 370 q^{65} - 312 q^{66} - 61 q^{67} - 192 q^{68} - 714 q^{69} - 588 q^{70} - 974 q^{71} + 216 q^{72} + 91 q^{73} - 610 q^{74} + 687 q^{75} - 36 q^{77} - 450 q^{78} + 321 q^{79} + 32 q^{80} + 243 q^{81} - 32 q^{82} - 2148 q^{83} - 204 q^{84} - 1680 q^{85} - 662 q^{86} + 24 q^{87} - 416 q^{88} - 1116 q^{89} + 36 q^{90} - 1367 q^{91} - 952 q^{92} - 321 q^{93} - 1532 q^{94} + 288 q^{96} - 1382 q^{97} + 2284 q^{98} - 468 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 + 9 * q^3 + 12 * q^4 + 2 * q^5 + 18 * q^6 - 17 * q^7 + 24 * q^8 + 27 * q^9 + 4 * q^10 - 52 * q^11 + 36 * q^12 - 75 * q^13 - 34 * q^14 + 6 * q^15 + 48 * q^16 - 48 * q^17 + 54 * q^18 + 8 * q^20 - 51 * q^21 - 104 * q^22 - 238 * q^23 + 72 * q^24 + 229 * q^25 - 150 * q^26 + 81 * q^27 - 68 * q^28 + 8 * q^29 + 12 * q^30 - 107 * q^31 + 96 * q^32 - 156 * q^33 - 96 * q^34 - 294 * q^35 + 108 * q^36 - 305 * q^37 - 225 * q^39 + 16 * q^40 - 16 * q^41 - 102 * q^42 - 331 * q^43 - 208 * q^44 + 18 * q^45 - 476 * q^46 - 766 * q^47 + 144 * q^48 + 1142 * q^49 + 458 * q^50 - 144 * q^51 - 300 * q^52 + 118 * q^53 + 162 * q^54 - 1400 * q^55 - 136 * q^56 + 16 * q^58 - 936 * q^59 + 24 * q^60 - 399 * q^61 - 214 * q^62 - 153 * q^63 + 192 * q^64 - 370 * q^65 - 312 * q^66 - 61 * q^67 - 192 * q^68 - 714 * q^69 - 588 * q^70 - 974 * q^71 + 216 * q^72 + 91 * q^73 - 610 * q^74 + 687 * q^75 - 36 * q^77 - 450 * q^78 + 321 * q^79 + 32 * q^80 + 243 * q^81 - 32 * q^82 - 2148 * q^83 - 204 * q^84 - 1680 * q^85 - 662 * q^86 + 24 * q^87 - 416 * q^88 - 1116 * q^89 + 36 * q^90 - 1367 * q^91 - 952 * q^92 - 321 * q^93 - 1532 * q^94 + 288 * q^96 - 1382 * q^97 + 2284 * q^98 - 468 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	20.2020	1.80692	0.903460	−	0.428672i	$-0.141018\pi$
$5$	20.2020	1.80692	0.903460	+	0.428672i	$0.141018\pi$
$6$	6.00000	0.408248
$7$	−22.8872	−1.23579	−0.617897	−	0.786259i	$-0.712015\pi$
$7$	−22.8872	−1.23579	−0.617897	+	0.786259i	$0.712015\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	40.4040	1.27769
$11$	−57.5614	−1.57776	−0.788882	−	0.614545i	$-0.789340\pi$
$11$	−57.5614	−1.57776	−0.788882	+	0.614545i	$0.789340\pi$
$12$	12.0000	0.288675
$13$	−27.3148	−0.582750	−0.291375	−	0.956609i	$-0.594113\pi$
$13$	−27.3148	−0.582750	−0.291375	+	0.956609i	$0.594113\pi$
$14$	−45.7744	−0.873838
$15$	60.6059	1.04323
$16$	16.0000	0.250000
$17$	−73.4486	−1.04788	−0.523938	−	0.851756i	$-0.675538\pi$
$17$	−73.4486	−1.04788	−0.523938	+	0.851756i	$0.675538\pi$
$18$	18.0000	0.235702
$19$	0	0
$19$	0	0
$20$	80.8079	0.903460
$21$	−68.6616	−0.713485
$22$	−115.123	−1.11565
$23$	−188.584	−1.70967	−0.854836	−	0.518899i	$-0.826342\pi$
$23$	−188.584	−1.70967	−0.854836	+	0.518899i	$0.826342\pi$
$24$	24.0000	0.204124
$25$	283.120	2.26496
$26$	−54.6296	−0.412067
$27$	27.0000	0.192450
$28$	−91.5488	−0.617897
$29$	7.15594	0.0458215	0.0229108	−	0.999738i	$-0.492707\pi$
$29$	7.15594	0.0458215	0.0229108	+	0.999738i	$0.492707\pi$
$30$	121.212	0.737672
$31$	117.144	0.678698	0.339349	−	0.940661i	$-0.389793\pi$
$31$	117.144	0.678698	0.339349	+	0.940661i	$0.389793\pi$
$32$	32.0000	0.176777
$33$	−172.684	−0.910922
$34$	−146.897	−0.740960
$35$	−462.367	−2.23298
$36$	36.0000	0.166667
$37$	332.600	1.47781	0.738906	−	0.673809i	$-0.235343\pi$
$37$	332.600	1.47781	0.738906	+	0.673809i	$0.235343\pi$
$38$	0	0
$39$	−81.9443	−0.336451
$40$	161.616	0.638843
$41$	42.7158	0.162710	0.0813548	−	0.996685i	$-0.474075\pi$
$41$	42.7158	0.162710	0.0813548	+	0.996685i	$0.474075\pi$
$42$	−137.323	−0.504510
$43$	47.2469	0.167560	0.0837800	−	0.996484i	$-0.473301\pi$
$43$	47.2469	0.167560	0.0837800	+	0.996484i	$0.473301\pi$
$44$	−230.245	−0.788882
$45$	181.818	0.602307
$46$	−377.168	−1.20892
$47$	−507.995	−1.57657	−0.788284	−	0.615312i	$-0.789030\pi$
$47$	−507.995	−1.57657	−0.788284	+	0.615312i	$0.789030\pi$
$48$	48.0000	0.144338
$49$	180.824	0.527184
$50$	566.240	1.60157
$51$	−220.346	−0.604991
$52$	−109.259	−0.291375
$53$	−492.609	−1.27670	−0.638350	−	0.769746i	$-0.720383\pi$
$53$	−492.609	−1.27670	−0.638350	+	0.769746i	$0.720383\pi$
$54$	54.0000	0.136083
$55$	−1162.85	−2.85089
$56$	−183.098	−0.436919
$57$	0	0
$58$	14.3119	0.0324007
$59$	−460.041	−1.01512	−0.507561	−	0.861616i	$-0.669453\pi$
$59$	−460.041	−1.01512	−0.507561	+	0.861616i	$0.669453\pi$
$60$	242.424	0.521613
$61$	450.745	0.946097	0.473049	−	0.881036i	$-0.343153\pi$
$61$	450.745	0.946097	0.473049	+	0.881036i	$0.343153\pi$
$62$	234.287	0.479912
$63$	−205.985	−0.411931
$64$	64.0000	0.125000
$65$	−551.813	−1.05298
$66$	−345.368	−0.644119
$67$	−522.465	−0.952675	−0.476337	−	0.879263i	$-0.658036\pi$
$67$	−522.465	−0.952675	−0.476337	+	0.879263i	$0.658036\pi$
$68$	−293.794	−0.523938
$69$	−565.751	−0.987079
$70$	−924.734	−1.57895
$71$	−931.419	−1.55689	−0.778444	−	0.627714i	$-0.783991\pi$
$71$	−931.419	−1.55689	−0.778444	+	0.627714i	$0.783991\pi$
$72$	72.0000	0.117851
$73$	350.123	0.561354	0.280677	−	0.959802i	$-0.409441\pi$
$73$	350.123	0.561354	0.280677	+	0.959802i	$0.409441\pi$
$74$	665.199	1.04497
$75$	849.360	1.30768
$76$	0	0
$77$	1317.42	1.94979
$78$	−163.889	−0.237907
$79$	−194.868	−0.277524	−0.138762	−	0.990326i	$-0.544312\pi$
$79$	−194.868	−0.277524	−0.138762	+	0.990326i	$0.544312\pi$
$80$	323.232	0.451730
$81$	81.0000	0.111111
$82$	85.4317	0.115053
$83$	−286.083	−0.378333	−0.189167	−	0.981945i	$-0.560579\pi$
$83$	−286.083	−0.378333	−0.189167	+	0.981945i	$0.560579\pi$
$84$	−274.646	−0.356743
$85$	−1483.81	−1.89343
$86$	94.4937	0.118483
$87$	21.4678	0.0264551
$88$	−460.491	−0.557824
$89$	−839.690	−1.00008	−0.500039	−	0.866003i	$-0.666681\pi$
$89$	−839.690	−1.00008	−0.500039	+	0.866003i	$0.666681\pi$
$90$	363.636	0.425895
$91$	625.159	0.720159
$92$	−754.335	−0.854836
$93$	351.431	0.391846
$94$	−1015.99	−1.11480
$95$	0	0
$96$	96.0000	0.102062
$97$	−605.516	−0.633823	−0.316911	−	0.948455i	$-0.602646\pi$
$97$	−605.516	−0.633823	−0.316911	+	0.948455i	$0.602646\pi$
$98$	361.648	0.372776
$99$	−518.052	−0.525921
$100$	1132.48	1.13248
$101$	47.2760	0.0465756	0.0232878	−	0.999729i	$-0.492587\pi$
$101$	47.2760	0.0465756	0.0232878	+	0.999729i	$0.492587\pi$
$102$	−440.691	−0.427794
$103$	430.750	0.412069	0.206034	−	0.978545i	$-0.433944\pi$
$103$	430.750	0.412069	0.206034	+	0.978545i	$0.433944\pi$
$104$	−218.518	−0.206033
$105$	−1387.10	−1.28921
$106$	−985.219	−0.902763
$107$	−1055.78	−0.953893	−0.476946	−	0.878932i	$-0.658256\pi$
$107$	−1055.78	−0.953893	−0.476946	+	0.878932i	$0.658256\pi$
$108$	108.000	0.0962250
$109$	282.571	0.248307	0.124153	−	0.992263i	$-0.460379\pi$
$109$	282.571	0.248307	0.124153	+	0.992263i	$0.460379\pi$
$110$	−2325.71	−2.01589
$111$	997.799	0.853215
$112$	−366.195	−0.308948
$113$	841.860	0.700846	0.350423	−	0.936592i	$-0.386038\pi$
$113$	841.860	0.700846	0.350423	+	0.936592i	$0.386038\pi$
$114$	0	0
$115$	−3809.77	−3.08924
$116$	28.6238	0.0229108
$117$	−245.833	−0.194250
$118$	−920.081	−0.717799
$119$	1681.03	1.29496
$120$	484.848	0.368836
$121$	1982.31	1.48934
$122$	901.489	0.668992
$123$	128.148	0.0939404
$124$	468.575	0.339349
$125$	3194.34	2.28568
$126$	−411.970	−0.291279
$127$	955.393	0.667539	0.333769	−	0.942655i	$-0.391679\pi$
$127$	955.393	0.667539	0.333769	+	0.942655i	$0.391679\pi$
$128$	128.000	0.0883883
$129$	141.741	0.0967408
$130$	−1103.63	−0.744572
$131$	−1639.11	−1.09320	−0.546601	−	0.837393i	$-0.684079\pi$
$131$	−1639.11	−1.09320	−0.546601	+	0.837393i	$0.684079\pi$
$132$	−690.736	−0.455461
$133$	0	0
$134$	−1044.93	−0.673643
$135$	545.454	0.347742
$136$	−587.588	−0.370480
$137$	−847.711	−0.528649	−0.264324	−	0.964434i	$-0.585149\pi$
$137$	−847.711	−0.528649	−0.264324	+	0.964434i	$0.585149\pi$
$138$	−1131.50	−0.697970
$139$	1167.60	0.712481	0.356240	−	0.934394i	$-0.384058\pi$
$139$	1167.60	0.712481	0.356240	+	0.934394i	$0.384058\pi$
$140$	−1849.47	−1.11649
$141$	−1523.98	−0.910231
$142$	−1862.84	−1.10089
$143$	1572.28	0.919442
$144$	144.000	0.0833333
$145$	144.564	0.0827959
$146$	700.247	0.396937
$147$	542.473	0.304370
$148$	1330.40	0.738906
$149$	−1721.57	−0.946552	−0.473276	−	0.880914i	$-0.656929\pi$
$149$	−1721.57	−0.946552	−0.473276	+	0.880914i	$0.656929\pi$
$150$	1698.72	0.924666
$151$	−2327.14	−1.25417	−0.627085	−	0.778951i	$-0.715752\pi$
$151$	−2327.14	−1.25417	−0.627085	+	0.778951i	$0.715752\pi$
$152$	0	0
$153$	−661.037	−0.349292
$154$	2634.84	1.37871
$155$	2366.53	1.22635
$156$	−327.777	−0.168226
$157$	−954.679	−0.485297	−0.242649	−	0.970114i	$-0.578016\pi$
$157$	−954.679	−0.485297	−0.242649	+	0.970114i	$0.578016\pi$
$158$	−389.736	−0.196239
$159$	−1477.83	−0.737103
$160$	646.463	0.319421
$161$	4316.16	2.11280
$162$	162.000	0.0785674
$163$	1826.52	0.877696	0.438848	−	0.898561i	$-0.355387\pi$
$163$	1826.52	0.877696	0.438848	+	0.898561i	$0.355387\pi$
$164$	170.863	0.0813548
$165$	−3488.56	−1.64596
$166$	−572.166	−0.267522
$167$	−1465.61	−0.679116	−0.339558	−	0.940585i	$-0.610278\pi$
$167$	−1465.61	−0.679116	−0.339558	+	0.940585i	$0.610278\pi$
$168$	−549.293	−0.252255
$169$	−1450.90	−0.660402
$170$	−2967.61	−1.33886
$171$	0	0
$172$	188.987	0.0837800
$173$	−4162.86	−1.82946	−0.914730	−	0.404065i	$-0.867597\pi$
$173$	−4162.86	−1.82946	−0.914730	+	0.404065i	$0.867597\pi$
$174$	42.9356	0.0187066
$175$	−6479.83	−2.79902
$176$	−920.982	−0.394441
$177$	−1380.12	−0.586081
$178$	−1679.38	−0.707162
$179$	2637.74	1.10142	0.550710	−	0.834697i	$-0.314357\pi$
$179$	2637.74	1.10142	0.550710	+	0.834697i	$0.314357\pi$
$180$	727.271	0.301153
$181$	779.832	0.320246	0.160123	−	0.987097i	$-0.448811\pi$
$181$	779.832	0.320246	0.160123	+	0.987097i	$0.448811\pi$
$182$	1250.32	0.509229
$183$	1352.23	0.546230
$184$	−1508.67	−0.604460
$185$	6719.17	2.67029
$186$	702.862	0.277077
$187$	4227.80	1.65330
$188$	−2031.98	−0.788284
$189$	−617.955	−0.237828
$190$	0	0
$191$	3961.70	1.50083	0.750415	−	0.660967i	$-0.229854\pi$
$191$	3961.70	1.50083	0.750415	+	0.660967i	$0.229854\pi$
$192$	192.000	0.0721688
$193$	364.405	0.135909	0.0679545	−	0.997688i	$-0.478353\pi$
$193$	364.405	0.135909	0.0679545	+	0.997688i	$0.478353\pi$
$194$	−1211.03	−0.448180
$195$	−1655.44	−0.607940
$196$	723.297	0.263592
$197$	2309.32	0.835190	0.417595	−	0.908633i	$-0.362873\pi$
$197$	2309.32	0.835190	0.417595	+	0.908633i	$0.362873\pi$
$198$	−1036.10	−0.371882
$199$	3676.55	1.30967	0.654833	−	0.755774i	$-0.272739\pi$
$199$	3676.55	1.30967	0.654833	+	0.755774i	$0.272739\pi$
$200$	2264.96	0.800785
$201$	−1567.39	−0.550027
$202$	94.5519	0.0329339
$203$	−163.780	−0.0566259
$204$	−881.383	−0.302496
$205$	862.945	0.294003
$206$	861.501	0.291377
$207$	−1697.25	−0.569890
$208$	−437.036	−0.145688
$209$	0	0
$210$	−2774.20	−0.911610
$211$	−1342.60	−0.438051	−0.219025	−	0.975719i	$-0.570288\pi$
$211$	−1342.60	−0.438051	−0.219025	+	0.975719i	$0.570288\pi$
$212$	−1970.44	−0.638350
$213$	−2794.26	−0.898870
$214$	−2111.57	−0.674504
$215$	954.480	0.302767
$216$	216.000	0.0680414
$217$	−2681.09	−0.838730
$218$	565.143	0.175579
$219$	1050.37	0.324098
$220$	−4651.41	−1.42545
$221$	2006.23	0.610650
$222$	1995.60	0.603314
$223$	2239.58	0.672528	0.336264	−	0.941768i	$-0.390837\pi$
$223$	2239.58	0.672528	0.336264	+	0.941768i	$0.390837\pi$
$224$	−732.391	−0.218459
$225$	2548.08	0.754987
$226$	1683.72	0.495573
$227$	6233.41	1.82258	0.911291	−	0.411763i	$-0.135087\pi$
$227$	6233.41	1.82258	0.911291	+	0.411763i	$0.135087\pi$
$228$	0	0
$229$	−2291.74	−0.661320	−0.330660	−	0.943750i	$-0.607271\pi$
$229$	−2291.74	−0.661320	−0.330660	+	0.943750i	$0.607271\pi$
$230$	−7619.53	−2.18442
$231$	3952.26	1.12571
$232$	57.2475	0.0162004
$233$	1599.07	0.449609	0.224804	−	0.974404i	$-0.427826\pi$
$233$	1599.07	0.449609	0.224804	+	0.974404i	$0.427826\pi$
$234$	−491.666	−0.137356
$235$	−10262.5	−2.84873
$236$	−1840.16	−0.507561
$237$	−584.604	−0.160228
$238$	3362.06	0.915673
$239$	−2443.37	−0.661291	−0.330646	−	0.943755i	$-0.607266\pi$
$239$	−2443.37	−0.661291	−0.330646	+	0.943755i	$0.607266\pi$
$240$	969.695	0.260806
$241$	996.491	0.266347	0.133173	−	0.991093i	$-0.457483\pi$
$241$	996.491	0.266347	0.133173	+	0.991093i	$0.457483\pi$
$242$	3964.62	1.05312
$243$	243.000	0.0641500
$244$	1802.98	0.473049
$245$	3653.01	0.952580
$246$	256.295	0.0664259
$247$	0	0
$248$	937.150	0.239956
$249$	−858.248	−0.218431
$250$	6388.68	1.61622
$251$	759.890	0.191091	0.0955455	−	0.995425i	$-0.469540\pi$
$251$	759.890	0.191091	0.0955455	+	0.995425i	$0.469540\pi$
$252$	−823.939	−0.205966
$253$	10855.1	2.69746
$254$	1910.79	0.472021
$255$	−4451.42	−1.09317
$256$	256.000	0.0625000
$257$	4773.20	1.15854	0.579268	−	0.815137i	$-0.303338\pi$
$257$	4773.20	1.15854	0.579268	+	0.815137i	$0.303338\pi$
$258$	283.481	0.0684061
$259$	−7612.27	−1.82627
$260$	−2207.25	−0.526492
$261$	64.4035	0.0152738
$262$	−3278.22	−0.773011
$263$	4356.43	1.02140	0.510702	−	0.859758i	$-0.329386\pi$
$263$	4356.43	1.02140	0.510702	+	0.859758i	$0.329386\pi$
$264$	−1381.47	−0.322060
$265$	−9951.69	−2.30690
$266$	0	0
$267$	−2519.07	−0.577396
$268$	−2089.86	−0.476337
$269$	140.715	0.0318941	0.0159471	−	0.999873i	$-0.494924\pi$
$269$	140.715	0.0318941	0.0159471	+	0.999873i	$0.494924\pi$
$270$	1090.91	0.245891
$271$	1523.06	0.341399	0.170700	−	0.985323i	$-0.445397\pi$
$271$	1523.06	0.341399	0.170700	+	0.985323i	$0.445397\pi$
$272$	−1175.18	−0.261969
$273$	1875.48	0.415784
$274$	−1695.42	−0.373811
$275$	−16296.8	−3.57357
$276$	−2263.01	−0.493540
$277$	2217.54	0.481008	0.240504	−	0.970648i	$-0.422687\pi$
$277$	2217.54	0.481008	0.240504	+	0.970648i	$0.422687\pi$
$278$	2335.21	0.503800
$279$	1054.29	0.226233
$280$	−3698.94	−0.789477
$281$	−170.520	−0.0362005	−0.0181003	−	0.999836i	$-0.505762\pi$
$281$	−170.520	−0.0362005	−0.0181003	+	0.999836i	$0.505762\pi$
$282$	−3047.97	−0.643631
$283$	2176.30	0.457130	0.228565	−	0.973529i	$-0.426597\pi$
$283$	2176.30	0.457130	0.228565	+	0.973529i	$0.426597\pi$
$284$	−3725.68	−0.778444
$285$	0	0
$286$	3144.55	0.650144
$287$	−977.646	−0.201075
$288$	288.000	0.0589256
$289$	481.691	0.0980441
$290$	289.128	0.0585455
$291$	−1816.55	−0.365938
$292$	1400.49	0.280677
$293$	9879.00	1.96975	0.984876	−	0.173261i	$-0.0554306\pi$
$293$	9879.00	1.96975	0.984876	+	0.173261i	$0.0554306\pi$
$294$	1084.95	0.215222
$295$	−9293.73	−1.83424
$296$	2660.80	0.522485
$297$	−1554.16	−0.303641
$298$	−3443.13	−0.669313
$299$	5151.12	0.996312
$300$	3397.44	0.653838
$301$	−1081.35	−0.207069
$302$	−4654.27	−0.886832
$303$	141.828	0.0268904
$304$	0	0
$305$	9105.94	1.70952
$306$	−1322.07	−0.246987
$307$	1343.71	0.249803	0.124902	−	0.992169i	$-0.460138\pi$
$307$	1343.71	0.249803	0.124902	+	0.992169i	$0.460138\pi$
$308$	5269.67	0.974895
$309$	1292.25	0.237908
$310$	4733.07	0.867162
$311$	88.3559	0.0161100	0.00805499	−	0.999968i	$-0.497436\pi$
$311$	88.3559	0.0161100	0.00805499	+	0.999968i	$0.497436\pi$
$312$	−655.555	−0.118953
$313$	−1892.46	−0.341751	−0.170876	−	0.985293i	$-0.554660\pi$
$313$	−1892.46	−0.341751	−0.170876	+	0.985293i	$0.554660\pi$
$314$	−1909.36	−0.343157
$315$	−4161.30	−0.744326
$316$	−779.472	−0.138762
$317$	−8378.86	−1.48455	−0.742277	−	0.670093i	$-0.766254\pi$
$317$	−8378.86	−1.48455	−0.742277	+	0.670093i	$0.766254\pi$
$318$	−2955.66	−0.521211
$319$	−411.906	−0.0722956
$320$	1292.93	0.225865
$321$	−3167.35	−0.550730
$322$	8632.31	1.49398
$323$	0	0
$324$	324.000	0.0555556
$325$	−7733.36	−1.31991
$326$	3653.05	0.620625
$327$	847.714	0.143360
$328$	341.727	0.0575265
$329$	11626.6	1.94831
$330$	−6977.12	−1.16387
$331$	−4833.50	−0.802639	−0.401319	−	0.915938i	$-0.631448\pi$
$331$	−4833.50	−0.802639	−0.401319	+	0.915938i	$0.631448\pi$
$332$	−1144.33	−0.189167
$333$	2993.40	0.492604
$334$	−2931.22	−0.480208
$335$	−10554.8	−1.72141
$336$	−1098.59	−0.178371
$337$	2625.77	0.424436	0.212218	−	0.977222i	$-0.431931\pi$
$337$	2625.77	0.424436	0.212218	+	0.977222i	$0.431931\pi$
$338$	−2901.81	−0.466975
$339$	2525.58	0.404633
$340$	−5935.23	−0.946714
$341$	−6742.95	−1.07082
$342$	0	0
$343$	3711.75	0.584302
$344$	377.975	0.0592414
$345$	−11429.3	−1.78357
$346$	−8325.73	−1.29362
$347$	8041.49	1.24406	0.622031	−	0.782992i	$-0.286308\pi$
$347$	8041.49	1.24406	0.622031	+	0.782992i	$0.286308\pi$
$348$	85.8713	0.0132275
$349$	8603.95	1.31965	0.659826	−	0.751418i	$-0.270630\pi$
$349$	8603.95	1.31965	0.659826	+	0.751418i	$0.270630\pi$
$350$	−12959.7	−1.97921
$351$	−737.499	−0.112150
$352$	−1841.96	−0.278912
$353$	−10359.4	−1.56198	−0.780988	−	0.624547i	$-0.785284\pi$
$353$	−10359.4	−1.56198	−0.780988	+	0.624547i	$0.785284\pi$
$354$	−2760.24	−0.414422
$355$	−18816.5	−2.81317
$356$	−3358.76	−0.500039
$357$	5043.10	0.747644
$358$	5275.49	0.778821
$359$	−3544.68	−0.521117	−0.260558	−	0.965458i	$-0.583907\pi$
$359$	−3544.68	−0.521117	−0.260558	+	0.965458i	$0.583907\pi$
$360$	1454.54	0.212948
$361$	0	0
$362$	1559.66	0.226448
$363$	5946.93	0.859870
$364$	2500.64	0.360079
$365$	7073.18	1.01432
$366$	2704.47	0.386243
$367$	330.253	0.0469729	0.0234864	−	0.999724i	$-0.492523\pi$
$367$	330.253	0.0469729	0.0234864	+	0.999724i	$0.492523\pi$
$368$	−3017.34	−0.427418
$369$	384.443	0.0542365
$370$	13438.3	1.88818
$371$	11274.5	1.57774
$372$	1405.72	0.195923
$373$	12016.2	1.66802	0.834012	−	0.551747i	$-0.186039\pi$
$373$	12016.2	1.66802	0.834012	+	0.551747i	$0.186039\pi$
$374$	8455.60	1.16906
$375$	9583.02	1.31964
$376$	−4063.96	−0.557401
$377$	−195.463	−0.0267025
$378$	−1235.91	−0.168170
$379$	−5463.94	−0.740538	−0.370269	−	0.928925i	$-0.620734\pi$
$379$	−5463.94	−0.740538	−0.370269	+	0.928925i	$0.620734\pi$
$380$	0	0
$381$	2866.18	0.385404
$382$	7923.40	1.06125
$383$	−7380.58	−0.984673	−0.492337	−	0.870405i	$-0.663857\pi$
$383$	−7380.58	−0.984673	−0.492337	+	0.870405i	$0.663857\pi$
$384$	384.000	0.0510310
$385$	26614.5	3.52311
$386$	728.809	0.0961021
$387$	425.222	0.0558533
$388$	−2422.06	−0.316911
$389$	2035.83	0.265349	0.132675	−	0.991160i	$-0.457643\pi$
$389$	2035.83	0.265349	0.132675	+	0.991160i	$0.457643\pi$
$390$	−3310.88	−0.429879
$391$	13851.2	1.79152
$392$	1446.59	0.186388
$393$	−4917.32	−0.631161
$394$	4618.64	0.590568
$395$	−3936.72	−0.501463
$396$	−2072.21	−0.262961
$397$	13314.3	1.68318	0.841592	−	0.540114i	$-0.181619\pi$
$397$	13314.3	1.68318	0.841592	+	0.540114i	$0.181619\pi$
$398$	7353.09	0.926074
$399$	0	0
$400$	4529.92	0.566240
$401$	−13204.3	−1.64437	−0.822186	−	0.569219i	$-0.807246\pi$
$401$	−13204.3	−1.64437	−0.822186	+	0.569219i	$0.807246\pi$
$402$	−3134.79	−0.388928
$403$	−3199.75	−0.395511
$404$	189.104	0.0232878
$405$	1636.36	0.200769
$406$	−327.559	−0.0400406
$407$	−19144.9	−2.33164
$408$	−1762.77	−0.213897
$409$	−2761.86	−0.333900	−0.166950	−	0.985965i	$-0.553392\pi$
$409$	−2761.86	−0.333900	−0.166950	+	0.985965i	$0.553392\pi$
$410$	1725.89	0.207892
$411$	−2543.13	−0.305215
$412$	1723.00	0.206034
$413$	10529.0	1.25448
$414$	−3394.51	−0.402973
$415$	−5779.44	−0.683618
$416$	−874.073	−0.103017
$417$	3502.81	0.411351
$418$	0	0
$419$	−15182.0	−1.77015	−0.885073	−	0.465453i	$-0.845891\pi$
$419$	−15182.0	−1.77015	−0.885073	+	0.465453i	$0.845891\pi$
$420$	−5548.40	−0.644606
$421$	−15980.4	−1.84996	−0.924982	−	0.380011i	$-0.875920\pi$
$421$	−15980.4	−1.84996	−0.924982	+	0.380011i	$0.875920\pi$
$422$	−2685.21	−0.309749
$423$	−4571.95	−0.525522
$424$	−3940.88	−0.451382
$425$	−20794.8	−2.37340
$426$	−5588.51	−0.635597
$427$	−10316.3	−1.16918
$428$	−4223.14	−0.476946
$429$	4716.83	0.530840
$430$	1908.96	0.214089
$431$	−4762.00	−0.532198	−0.266099	−	0.963946i	$-0.585735\pi$
$431$	−4762.00	−0.532198	−0.266099	+	0.963946i	$0.585735\pi$
$432$	432.000	0.0481125
$433$	−9974.90	−1.10707	−0.553537	−	0.832825i	$-0.686722\pi$
$433$	−9974.90	−1.10707	−0.553537	+	0.832825i	$0.686722\pi$
$434$	−5362.18	−0.593072
$435$	433.693	0.0478022
$436$	1130.29	0.124153
$437$	0	0
$438$	2100.74	0.229172
$439$	8956.89	0.973779	0.486890	−	0.873464i	$-0.338131\pi$
$439$	8956.89	0.973779	0.486890	+	0.873464i	$0.338131\pi$
$440$	−9302.83	−1.00794
$441$	1627.42	0.175728
$442$	4012.46	0.431795
$443$	11368.1	1.21922	0.609612	−	0.792700i	$-0.291325\pi$
$443$	11368.1	1.21922	0.609612	+	0.792700i	$0.291325\pi$
$444$	3991.19	0.426607
$445$	−16963.4	−1.80706
$446$	4479.17	0.475549
$447$	−5164.70	−0.546492
$448$	−1464.78	−0.154474
$449$	−7630.20	−0.801985	−0.400993	−	0.916081i	$-0.631335\pi$
$449$	−7630.20	−0.801985	−0.400993	+	0.916081i	$0.631335\pi$
$450$	5096.16	0.533856
$451$	−2458.78	−0.256717
$452$	3367.44	0.350423
$453$	−6981.41	−0.724095
$454$	12466.8	1.28876
$455$	12629.4	1.30127
$456$	0	0
$457$	−1500.40	−0.153579	−0.0767896	−	0.997047i	$-0.524467\pi$
$457$	−1500.40	−0.153579	−0.0767896	+	0.997047i	$0.524467\pi$
$458$	−4583.47	−0.467624
$459$	−1983.11	−0.201664
$460$	−15239.1	−1.54462
$461$	−14495.8	−1.46450	−0.732252	−	0.681034i	$-0.761531\pi$
$461$	−14495.8	−1.46450	−0.732252	+	0.681034i	$0.761531\pi$
$462$	7904.51	0.795998
$463$	−12265.2	−1.23113	−0.615566	−	0.788086i	$-0.711072\pi$
$463$	−12265.2	−1.23113	−0.615566	+	0.788086i	$0.711072\pi$
$464$	114.495	0.0114554
$465$	7099.60	0.708035
$466$	3198.15	0.317921
$467$	−1890.82	−0.187360	−0.0936798	−	0.995602i	$-0.529863\pi$
$467$	−1890.82	−0.187360	−0.0936798	+	0.995602i	$0.529863\pi$
$468$	−983.332	−0.0971251
$469$	11957.8	1.17731
$470$	−20525.0	−2.01436
$471$	−2864.04	−0.280187
$472$	−3680.32	−0.358900
$473$	−2719.59	−0.264370
$474$	−1169.21	−0.113299
$475$	0	0
$476$	6724.13	0.647479
$477$	−4433.49	−0.425567
$478$	−4886.74	−0.467603
$479$	−11662.9	−1.11251	−0.556254	−	0.831013i	$-0.687762\pi$
$479$	−11662.9	−1.11251	−0.556254	+	0.831013i	$0.687762\pi$
$480$	1939.39	0.184418
$481$	−9084.88	−0.861195
$482$	1992.98	0.188336
$483$	12948.5	1.21983
$484$	7929.24	0.744669
$485$	−12232.6	−1.14527
$486$	486.000	0.0453609
$487$	−13286.6	−1.23629	−0.618147	−	0.786063i	$-0.712116\pi$
$487$	−13286.6	−1.23629	−0.618147	+	0.786063i	$0.712116\pi$
$488$	3605.96	0.334496
$489$	5479.57	0.506738
$490$	7306.02	0.673576
$491$	4037.71	0.371119	0.185559	−	0.982633i	$-0.440590\pi$
$491$	4037.71	0.371119	0.185559	+	0.982633i	$0.440590\pi$
$492$	512.590	0.0469702
$493$	−525.594	−0.0480153
$494$	0	0
$495$	−10465.7	−0.950298
$496$	1874.30	0.169674
$497$	21317.6	1.92399
$498$	−1716.50	−0.154454
$499$	3544.83	0.318013	0.159006	−	0.987278i	$-0.449171\pi$
$499$	3544.83	0.318013	0.159006	+	0.987278i	$0.449171\pi$
$500$	12777.4	1.14284
$501$	−4396.83	−0.392088
$502$	1519.78	0.135122
$503$	−12958.4	−1.14868	−0.574339	−	0.818617i	$-0.694741\pi$
$503$	−12958.4	−1.14868	−0.574339	+	0.818617i	$0.694741\pi$
$504$	−1647.88	−0.145640
$505$	955.068	0.0841584
$506$	21710.3	1.90739
$507$	−4352.71	−0.381283
$508$	3821.57	0.333769
$509$	8236.28	0.717224	0.358612	−	0.933487i	$-0.383250\pi$
$509$	8236.28	0.717224	0.358612	+	0.933487i	$0.383250\pi$
$510$	−8902.84	−0.772989
$511$	−8013.34	−0.693717
$512$	512.000	0.0441942
$513$	0	0
$514$	9546.39	0.819209
$515$	8702.01	0.744575
$516$	566.962	0.0483704
$517$	29240.9	2.48745
$518$	−15224.5	−1.29137
$519$	−12488.6	−1.05624
$520$	−4414.50	−0.372286
$521$	−7427.58	−0.624584	−0.312292	−	0.949986i	$-0.601097\pi$
$521$	−7427.58	−0.624584	−0.312292	+	0.949986i	$0.601097\pi$
$522$	128.807	0.0108002
$523$	4604.88	0.385005	0.192502	−	0.981297i	$-0.438340\pi$
$523$	4604.88	0.385005	0.192502	+	0.981297i	$0.438340\pi$
$524$	−6556.43	−0.546601
$525$	−19439.5	−1.61602
$526$	8712.87	0.722241
$527$	−8604.04	−0.711191
$528$	−2762.94	−0.227731
$529$	23396.8	1.92298
$530$	−19903.4	−1.63122
$531$	−4140.36	−0.338374
$532$	0	0
$533$	−1166.77	−0.0948191
$534$	−5038.14	−0.408280
$535$	−21328.9	−1.72361
$536$	−4179.72	−0.336821
$537$	7913.23	0.635905
$538$	281.429	0.0225525
$539$	−10408.5	−0.831772
$540$	2181.81	0.173871
$541$	9030.87	0.717685	0.358842	−	0.933398i	$-0.383172\pi$
$541$	9030.87	0.717685	0.358842	+	0.933398i	$0.383172\pi$
$542$	3046.12	0.241406
$543$	2339.50	0.184894
$544$	−2350.35	−0.185240
$545$	5708.50	0.448670
$546$	3750.95	0.294004
$547$	−12875.6	−1.00644	−0.503218	−	0.864159i	$-0.667851\pi$
$547$	−12875.6	−1.00644	−0.503218	+	0.864159i	$0.667851\pi$
$548$	−3390.85	−0.264324
$549$	4056.70	0.315366
$550$	−32593.6	−2.52690
$551$	0	0
$552$	−4526.01	−0.348985
$553$	4459.98	0.342962
$554$	4435.09	0.340124
$555$	20157.5	1.54169
$556$	4670.41	0.356240
$557$	−4891.20	−0.372077	−0.186038	−	0.982542i	$-0.559565\pi$
$557$	−4891.20	−0.372077	−0.186038	+	0.982542i	$0.559565\pi$
$558$	2108.59	0.159971
$559$	−1290.54	−0.0976456
$560$	−7397.87	−0.558245
$561$	12683.4	0.954534
$562$	−341.039	−0.0255976
$563$	−2367.05	−0.177192	−0.0885961	−	0.996068i	$-0.528238\pi$
$563$	−2367.05	−0.177192	−0.0885961	+	0.996068i	$0.528238\pi$
$564$	−6095.94	−0.455116
$565$	17007.2	1.26637
$566$	4352.61	0.323240
$567$	−1853.86	−0.137310
$568$	−7451.35	−0.550443
$569$	675.013	0.0497329	0.0248665	−	0.999691i	$-0.492084\pi$
$569$	675.013	0.0497329	0.0248665	+	0.999691i	$0.492084\pi$
$570$	0	0
$571$	17245.3	1.26391	0.631955	−	0.775005i	$-0.282253\pi$
$571$	17245.3	1.26391	0.631955	+	0.775005i	$0.282253\pi$
$572$	6289.10	0.459721
$573$	11885.1	0.866504
$574$	−1955.29	−0.142182
$575$	−53391.9	−3.87234
$576$	576.000	0.0416667
$577$	24732.5	1.78445	0.892226	−	0.451589i	$-0.149143\pi$
$577$	24732.5	1.78445	0.892226	+	0.451589i	$0.149143\pi$
$578$	963.382	0.0693277
$579$	1093.21	0.0784671
$580$	578.257	0.0413979
$581$	6547.64	0.467542
$582$	−3633.09	−0.258757
$583$	28355.3	2.01433
$584$	2800.99	0.198469
$585$	−4966.31	−0.350995
$586$	19758.0	1.39282
$587$	13718.5	0.964607	0.482304	−	0.876004i	$-0.339800\pi$
$587$	13718.5	0.964607	0.482304	+	0.876004i	$0.339800\pi$
$588$	2169.89	0.152185
$589$	0	0
$590$	−18587.5	−1.29701
$591$	6927.97	0.482197
$592$	5321.59	0.369453
$593$	7164.95	0.496170	0.248085	−	0.968738i	$-0.420199\pi$
$593$	7164.95	0.496170	0.248085	+	0.968738i	$0.420199\pi$
$594$	−3108.31	−0.214706
$595$	33960.2	2.33989
$596$	−6886.26	−0.473276
$597$	11029.6	0.756136
$598$	10302.2	0.704499
$599$	1507.84	0.102852	0.0514262	−	0.998677i	$-0.483623\pi$
$599$	1507.84	0.102852	0.0514262	+	0.998677i	$0.483623\pi$
$600$	6794.88	0.462333
$601$	−8574.64	−0.581975	−0.290987	−	0.956727i	$-0.593984\pi$
$601$	−8574.64	−0.581975	−0.290987	+	0.956727i	$0.593984\pi$
$602$	−2162.70	−0.146420
$603$	−4702.18	−0.317558
$604$	−9308.54	−0.627085
$605$	40046.6	2.69112
$606$	283.656	0.0190144
$607$	−504.688	−0.0337474	−0.0168737	−	0.999858i	$-0.505371\pi$
$607$	−504.688	−0.0337474	−0.0168737	+	0.999858i	$0.505371\pi$
$608$	0	0
$609$	−491.339	−0.0326930
$610$	18211.9	1.20882
$611$	13875.8	0.918745
$612$	−2644.15	−0.174646
$613$	14944.4	0.984666	0.492333	−	0.870407i	$-0.336144\pi$
$613$	14944.4	0.984666	0.492333	+	0.870407i	$0.336144\pi$
$614$	2687.42	0.176637
$615$	2588.83	0.169743
$616$	10539.3	0.689355
$617$	−3482.10	−0.227203	−0.113601	−	0.993526i	$-0.536239\pi$
$617$	−3482.10	−0.227203	−0.113601	+	0.993526i	$0.536239\pi$
$618$	2584.50	0.168226
$619$	3577.83	0.232319	0.116159	−	0.993231i	$-0.462942\pi$
$619$	3577.83	0.232319	0.116159	+	0.993231i	$0.462942\pi$
$620$	9466.14	0.613176
$621$	−5091.76	−0.329026
$622$	176.712	0.0113915
$623$	19218.2	1.23589
$624$	−1311.11	−0.0841128
$625$	29142.0	1.86509
$626$	−3784.92	−0.241655
$627$	0	0
$628$	−3818.72	−0.242649
$629$	−24429.0	−1.54856
$630$	−8322.61	−0.526318
$631$	3649.43	0.230240	0.115120	−	0.993352i	$-0.463275\pi$
$631$	3649.43	0.230240	0.115120	+	0.993352i	$0.463275\pi$
$632$	−1558.94	−0.0981194
$633$	−4027.81	−0.252909
$634$	−16757.7	−1.04974
$635$	19300.8	1.20619
$636$	−5911.31	−0.368552
$637$	−4939.17	−0.307217
$638$	−823.811	−0.0511207
$639$	−8382.77	−0.518963
$640$	2585.85	0.159711
$641$	14669.2	0.903898	0.451949	−	0.892044i	$-0.350729\pi$
$641$	14669.2	0.903898	0.451949	+	0.892044i	$0.350729\pi$
$642$	−6334.71	−0.389425
$643$	7008.11	0.429818	0.214909	−	0.976634i	$-0.431055\pi$
$643$	7008.11	0.429818	0.214909	+	0.976634i	$0.431055\pi$
$644$	17264.6	1.05640
$645$	2863.44	0.174803
$646$	0	0
$647$	9659.76	0.586962	0.293481	−	0.955965i	$-0.405186\pi$
$647$	9659.76	0.586962	0.293481	+	0.955965i	$0.405186\pi$
$648$	648.000	0.0392837
$649$	26480.6	1.60162
$650$	−15466.7	−0.933315
$651$	−8043.28	−0.484241
$652$	7306.10	0.438848
$653$	6799.09	0.407456	0.203728	−	0.979027i	$-0.434694\pi$
$653$	6799.09	0.407456	0.203728	+	0.979027i	$0.434694\pi$
$654$	1695.43	0.101371
$655$	−33113.2	−1.97533
$656$	683.454	0.0406774
$657$	3151.11	0.187118
$658$	23253.2	1.37766
$659$	19348.2	1.14370	0.571851	−	0.820357i	$-0.306225\pi$
$659$	19348.2	1.14370	0.571851	+	0.820357i	$0.306225\pi$
$660$	−13954.2	−0.822982
$661$	−5128.00	−0.301749	−0.150875	−	0.988553i	$-0.548209\pi$
$661$	−5128.00	−0.301749	−0.150875	+	0.988553i	$0.548209\pi$
$662$	−9667.01	−0.567551
$663$	6018.69	0.352559
$664$	−2288.66	−0.133761
$665$	0	0
$666$	5986.79	0.348324
$667$	−1349.49	−0.0783398
$668$	−5862.45	−0.339558
$669$	6718.75	0.388284
$670$	−21109.6	−1.21722
$671$	−25945.5	−1.49272
$672$	−2197.17	−0.126128
$673$	23921.1	1.37012	0.685061	−	0.728486i	$-0.259776\pi$
$673$	23921.1	1.37012	0.685061	+	0.728486i	$0.259776\pi$
$674$	5251.55	0.300122
$675$	7644.24	0.435892
$676$	−5803.61	−0.330201
$677$	766.891	0.0435362	0.0217681	−	0.999763i	$-0.493070\pi$
$677$	766.891	0.0435362	0.0217681	+	0.999763i	$0.493070\pi$
$678$	5051.16	0.286119
$679$	13858.6	0.783274
$680$	−11870.5	−0.669428
$681$	18700.2	1.05227
$682$	−13485.9	−0.757187
$683$	6573.45	0.368267	0.184133	−	0.982901i	$-0.441052\pi$
$683$	6573.45	0.368267	0.184133	+	0.982901i	$0.441052\pi$
$684$	0	0
$685$	−17125.5	−0.955226
$686$	7423.50	0.413164
$687$	−6875.21	−0.381813
$688$	755.950	0.0418900
$689$	13455.5	0.743998
$690$	−22858.6	−1.26118
$691$	−12816.9	−0.705613	−0.352806	−	0.935696i	$-0.614773\pi$
$691$	−12816.9	−0.705613	−0.352806	+	0.935696i	$0.614773\pi$
$692$	−16651.5	−0.914730
$693$	11856.8	0.649930
$694$	16083.0	0.879685
$695$	23587.9	1.28740
$696$	171.743	0.00935328
$697$	−3137.42	−0.170500
$698$	17207.9	0.933135
$699$	4797.22	0.259582
$700$	−25919.3	−1.39951
$701$	−31041.6	−1.67250	−0.836251	−	0.548347i	$-0.815257\pi$
$701$	−31041.6	−1.67250	−0.836251	+	0.548347i	$0.815257\pi$
$702$	−1475.00	−0.0793023
$703$	0	0
$704$	−3683.93	−0.197220
$705$	−30787.5	−1.64472
$706$	−20718.9	−1.10448
$707$	−1082.01	−0.0575578
$708$	−5520.49	−0.293040
$709$	−13641.0	−0.722564	−0.361282	−	0.932457i	$-0.617661\pi$
$709$	−13641.0	−0.722564	−0.361282	+	0.932457i	$0.617661\pi$
$710$	−37633.0	−1.98921
$711$	−1753.81	−0.0925079
$712$	−6717.52	−0.353581
$713$	−22091.4	−1.16035
$714$	10086.2	0.528664
$715$	31763.1	1.66136
$716$	10551.0	0.550710
$717$	−7330.11	−0.381797
$718$	−7089.35	−0.368485
$719$	27533.8	1.42815	0.714073	−	0.700071i	$-0.246848\pi$
$719$	27533.8	1.42815	0.714073	+	0.700071i	$0.246848\pi$
$720$	2909.09	0.150577
$721$	−9858.67	−0.509232
$722$	0	0
$723$	2989.47	0.153775
$724$	3119.33	0.160123
$725$	2025.99	0.103784
$726$	11893.9	0.608020
$727$	20867.3	1.06455	0.532273	−	0.846573i	$-0.321338\pi$
$727$	20867.3	1.06455	0.532273	+	0.846573i	$0.321338\pi$
$728$	5001.27	0.254615
$729$	729.000	0.0370370
$730$	14146.4	0.717234
$731$	−3470.21	−0.175582
$732$	5408.94	0.273115
$733$	−18422.0	−0.928282	−0.464141	−	0.885761i	$-0.653637\pi$
$733$	−18422.0	−0.928282	−0.464141	+	0.885761i	$0.653637\pi$
$734$	660.505	0.0332148
$735$	10959.0	0.549972
$736$	−6034.68	−0.302230
$737$	30073.8	1.50310
$738$	768.885	0.0383510
$739$	−15508.0	−0.771949	−0.385975	−	0.922509i	$-0.626135\pi$
$739$	−15508.0	−0.771949	−0.385975	+	0.922509i	$0.626135\pi$
$740$	26876.7	1.33514
$741$	0	0
$742$	22548.9	1.11563
$743$	11877.0	0.586441	0.293221	−	0.956045i	$-0.405273\pi$
$743$	11877.0	0.586441	0.293221	+	0.956045i	$0.405273\pi$
$744$	2811.45	0.138539
$745$	−34779.0	−1.71034
$746$	24032.3	1.17947
$747$	−2574.75	−0.126111
$748$	16911.2	0.826650
$749$	24164.0	1.17881
$750$	19166.0	0.933126
$751$	−26834.2	−1.30385	−0.651927	−	0.758281i	$-0.726039\pi$
$751$	−26834.2	−1.30385	−0.651927	+	0.758281i	$0.726039\pi$
$752$	−8127.92	−0.394142
$753$	2279.67	0.110326
$754$	−390.926	−0.0188815
$755$	−47012.8	−2.26618
$756$	−2471.82	−0.118914
$757$	−39104.9	−1.87753	−0.938767	−	0.344552i	$-0.888031\pi$
$757$	−39104.9	−1.87753	−0.938767	+	0.344552i	$0.888031\pi$
$758$	−10927.9	−0.523639
$759$	32565.4	1.55738
$760$	0	0
$761$	13627.0	0.649117	0.324559	−	0.945866i	$-0.394784\pi$
$761$	13627.0	0.649117	0.324559	+	0.945866i	$0.394784\pi$
$762$	5732.36	0.272522
$763$	−6467.27	−0.306856
$764$	15846.8	0.750415
$765$	−13354.3	−0.631143
$766$	−14761.2	−0.696269
$767$	12565.9	0.591563
$768$	768.000	0.0360844
$769$	23166.4	1.08635	0.543173	−	0.839621i	$-0.317223\pi$
$769$	23166.4	1.08635	0.543173	+	0.839621i	$0.317223\pi$
$770$	53228.9	2.49122
$771$	14319.6	0.668881
$772$	1457.62	0.0679545
$773$	−32201.6	−1.49833	−0.749167	−	0.662381i	$-0.769546\pi$
$773$	−32201.6	−1.49833	−0.749167	+	0.662381i	$0.769546\pi$
$774$	850.443	0.0394943
$775$	33165.7	1.53722
$776$	−4844.12	−0.224090
$777$	−22836.8	−1.05440
$778$	4071.67	0.187630
$779$	0	0
$780$	−6621.75	−0.303970
$781$	53613.7	2.45640
$782$	27702.4	1.26680
$783$	193.210	0.00881836
$784$	2893.19	0.131796
$785$	−19286.4	−0.876893
$786$	−9834.65	−0.446298
$787$	36081.7	1.63427	0.817137	−	0.576443i	$-0.195560\pi$
$787$	36081.7	1.63427	0.817137	+	0.576443i	$0.195560\pi$
$788$	9237.29	0.417595
$789$	13069.3	0.589708
$790$	−7873.44	−0.354588
$791$	−19267.8	−0.866100
$792$	−4144.42	−0.185941
$793$	−12312.0	−0.551339
$794$	26628.5	1.19019
$795$	−29855.1	−1.33189
$796$	14706.2	0.654833
$797$	39094.9	1.73753	0.868765	−	0.495224i	$-0.164914\pi$
$797$	39094.9	1.73753	0.868765	+	0.495224i	$0.164914\pi$
$798$	0	0
$799$	37311.5	1.65205
$800$	9059.84	0.400392
$801$	−7557.21	−0.333359
$802$	−26408.7	−1.16275
$803$	−20153.6	−0.885684
$804$	−6269.58	−0.275014
$805$	87194.9	3.81766
$806$	−6399.51	−0.279669
$807$	422.144	0.0184141
$808$	378.208	0.0164670
$809$	7261.33	0.315568	0.157784	−	0.987474i	$-0.449565\pi$
$809$	7261.33	0.315568	0.157784	+	0.987474i	$0.449565\pi$
$810$	3272.72	0.141965
$811$	−34133.3	−1.47791	−0.738953	−	0.673757i	$-0.764679\pi$
$811$	−34133.3	−1.47791	−0.738953	+	0.673757i	$0.764679\pi$
$812$	−655.118	−0.0283130
$813$	4569.18	0.197107
$814$	−38289.8	−1.64872
$815$	36899.4	1.58593
$816$	−3525.53	−0.151248
$817$	0	0
$818$	−5523.72	−0.236103
$819$	5626.43	0.240053
$820$	3451.78	0.147002
$821$	13880.3	0.590043	0.295022	−	0.955491i	$-0.404673\pi$
$821$	13880.3	0.590043	0.295022	+	0.955491i	$0.404673\pi$
$822$	−5086.27	−0.215820
$823$	13016.1	0.551291	0.275646	−	0.961259i	$-0.411108\pi$
$823$	13016.1	0.551291	0.275646	+	0.961259i	$0.411108\pi$
$824$	3446.00	0.145688
$825$	−48890.3	−2.06320
$826$	21058.1	0.887051
$827$	19864.1	0.835238	0.417619	−	0.908622i	$-0.362865\pi$
$827$	19864.1	0.835238	0.417619	+	0.908622i	$0.362865\pi$
$828$	−6789.02	−0.284945
$829$	−11325.6	−0.474494	−0.237247	−	0.971449i	$-0.576245\pi$
$829$	−11325.6	−0.474494	−0.237247	+	0.971449i	$0.576245\pi$
$830$	−11558.9	−0.483391
$831$	6652.63	0.277710
$832$	−1748.15	−0.0728438
$833$	−13281.3	−0.552424
$834$	7005.62	0.290869
$835$	−29608.3	−1.22711
$836$	0	0
$837$	3162.88	0.130615
$838$	−30364.1	−1.25168
$839$	−4507.99	−0.185498	−0.0927491	−	0.995690i	$-0.529565\pi$
$839$	−4507.99	−0.185498	−0.0927491	+	0.995690i	$0.529565\pi$
$840$	−11096.8	−0.455805
$841$	−24337.8	−0.997900
$842$	−31960.7	−1.30812
$843$	−511.559	−0.0209004
$844$	−5370.42	−0.219025
$845$	−29311.1	−1.19329
$846$	−9143.91	−0.371600
$847$	−45369.5	−1.84051
$848$	−7881.75	−0.319175
$849$	6528.91	0.263924
$850$	−41589.5	−1.67825
$851$	−62722.9	−2.52657
$852$	−11177.0	−0.449435
$853$	−31512.5	−1.26491	−0.632454	−	0.774598i	$-0.717952\pi$
$853$	−31512.5	−1.26491	−0.632454	+	0.774598i	$0.717952\pi$
$854$	−20632.6	−0.826736
$855$	0	0
$856$	−8446.28	−0.337252
$857$	6340.51	0.252728	0.126364	−	0.991984i	$-0.459669\pi$
$857$	6340.51	0.252728	0.126364	+	0.991984i	$0.459669\pi$
$858$	9433.65	0.375361
$859$	−20206.0	−0.802582	−0.401291	−	0.915951i	$-0.631438\pi$
$859$	−20206.0	−0.802582	−0.401291	+	0.915951i	$0.631438\pi$
$860$	3817.92	0.151384
$861$	−2932.94	−0.116091
$862$	−9524.00	−0.376321
$863$	34553.8	1.36295	0.681474	−	0.731842i	$-0.261339\pi$
$863$	34553.8	1.36295	0.681474	+	0.731842i	$0.261339\pi$
$864$	864.000	0.0340207
$865$	−84098.1	−3.30569
$866$	−19949.8	−0.782820
$867$	1445.07	0.0566058
$868$	−10724.4	−0.419365
$869$	11216.9	0.437867
$870$	867.385	0.0338013
$871$	14271.0	0.555172
$872$	2260.57	0.0877896
$873$	−5449.64	−0.211274
$874$	0	0
$875$	−73109.5	−2.82463
$876$	4201.48	0.162049
$877$	−30588.2	−1.17775	−0.588877	−	0.808223i	$-0.700430\pi$
$877$	−30588.2	−1.17775	−0.588877	+	0.808223i	$0.700430\pi$
$878$	17913.8	0.688566
$879$	29637.0	1.13724
$880$	−18605.7	−0.712723
$881$	48445.7	1.85264	0.926321	−	0.376735i	$-0.122953\pi$
$881$	48445.7	1.85264	0.926321	+	0.376735i	$0.122953\pi$
$882$	3254.84	0.124259
$883$	10270.4	0.391422	0.195711	−	0.980662i	$-0.437299\pi$
$883$	10270.4	0.391422	0.195711	+	0.980662i	$0.437299\pi$
$884$	8024.92	0.305325
$885$	−27881.2	−1.05900
$886$	22736.2	0.862121
$887$	−27630.3	−1.04592	−0.522962	−	0.852356i	$-0.675173\pi$
$887$	−27630.3	−1.04592	−0.522962	+	0.852356i	$0.675173\pi$
$888$	7982.39	0.301657
$889$	−21866.3	−0.824940
$890$	−33926.8	−1.27779
$891$	−4662.47	−0.175307
$892$	8958.34	0.336264
$893$	0	0
$894$	−10329.4	−0.386428
$895$	53287.6	1.99018
$896$	−2929.56	−0.109230
$897$	15453.4	0.575221
$898$	−15260.4	−0.567089
$899$	838.273	0.0310990
$900$	10192.3	0.377493
$901$	36181.5	1.33782
$902$	−4917.56	−0.181527
$903$	−3244.05	−0.119552
$904$	6734.88	0.247786
$905$	15754.2	0.578658
$906$	−13962.8	−0.512013
$907$	−40746.5	−1.49169	−0.745847	−	0.666118i	$-0.767955\pi$
$907$	−40746.5	−1.49169	−0.745847	+	0.666118i	$0.767955\pi$
$908$	24933.6	0.911291
$909$	425.484	0.0155252
$910$	25258.9	0.920137
$911$	−13335.5	−0.484989	−0.242494	−	0.970153i	$-0.577966\pi$
$911$	−13335.5	−0.484989	−0.242494	+	0.970153i	$0.577966\pi$
$912$	0	0
$913$	16467.3	0.596921
$914$	−3000.80	−0.108597
$915$	27317.8	0.986993
$916$	−9166.94	−0.330660
$917$	37514.6	1.35097
$918$	−3966.22	−0.142598
$919$	16604.5	0.596009	0.298005	−	0.954564i	$-0.403679\pi$
$919$	16604.5	0.596009	0.298005	+	0.954564i	$0.403679\pi$
$920$	−30478.1	−1.09221
$921$	4031.13	0.144224
$922$	−28991.6	−1.03556
$923$	25441.5	0.907277
$924$	15809.0	0.562856
$925$	94165.6	3.34719
$926$	−24530.5	−0.870541
$927$	3876.75	0.137356
$928$	228.990	0.00810018
$929$	−16679.4	−0.589056	−0.294528	−	0.955643i	$-0.595162\pi$
$929$	−16679.4	−0.589056	−0.294528	+	0.955643i	$0.595162\pi$
$930$	14199.2	0.500656
$931$	0	0
$932$	6396.29	0.224804
$933$	265.068	0.00930110
$934$	−3781.65	−0.132483
$935$	85409.9	2.98738
$936$	−1966.66	−0.0686778
$937$	6867.24	0.239427	0.119713	−	0.992808i	$-0.461802\pi$
$937$	6867.24	0.239427	0.119713	+	0.992808i	$0.461802\pi$
$938$	23915.5	0.832483
$939$	−5677.38	−0.197310
$940$	−41050.0	−1.42437
$941$	−48163.9	−1.66854	−0.834272	−	0.551353i	$-0.814112\pi$
$941$	−48163.9	−1.66854	−0.834272	+	0.551353i	$0.814112\pi$
$942$	−5728.07	−0.198122
$943$	−8055.52	−0.278180
$944$	−7360.65	−0.253780
$945$	−12483.9	−0.429737
$946$	−5439.19	−0.186938
$947$	−45311.2	−1.55482	−0.777412	−	0.628992i	$-0.783468\pi$
$947$	−45311.2	−1.55482	−0.777412	+	0.628992i	$0.783468\pi$
$948$	−2338.42	−0.0801142
$949$	−9563.54	−0.327129
$950$	0	0
$951$	−25136.6	−0.857108
$952$	13448.3	0.457837
$953$	−6964.61	−0.236732	−0.118366	−	0.992970i	$-0.537766\pi$
$953$	−6964.61	−0.236732	−0.118366	+	0.992970i	$0.537766\pi$
$954$	−8866.97	−0.300921
$955$	80034.1	2.71188
$956$	−9773.49	−0.330646
$957$	−1235.72	−0.0417399
$958$	−23325.8	−0.786661
$959$	19401.7	0.653300
$960$	3878.78	0.130403
$961$	−16068.4	−0.539369
$962$	−18169.8	−0.608957
$963$	−9502.06	−0.317964
$964$	3985.96	0.133173
$965$	7361.70	0.245577
$966$	25896.9	0.862547
$967$	46299.5	1.53970	0.769851	−	0.638224i	$-0.220331\pi$
$967$	46299.5	1.53970	0.769851	+	0.638224i	$0.220331\pi$
$968$	15858.5	0.526561
$969$	0	0
$970$	−24465.2	−0.809826
$971$	−44402.3	−1.46750	−0.733748	−	0.679422i	$-0.762231\pi$
$971$	−44402.3	−1.46750	−0.733748	+	0.679422i	$0.762231\pi$
$972$	972.000	0.0320750
$973$	−26723.2	−0.880478
$974$	−26573.3	−0.874192
$975$	−23200.1	−0.762049
$976$	7211.92	0.236524
$977$	−36365.1	−1.19081	−0.595405	−	0.803426i	$-0.703008\pi$
$977$	−36365.1	−1.19081	−0.595405	+	0.803426i	$0.703008\pi$
$978$	10959.1	0.358318
$979$	48333.7	1.57789
$980$	14612.0	0.476290
$981$	2543.14	0.0827689
$982$	8075.42	0.262421
$983$	−3682.23	−0.119476	−0.0597381	−	0.998214i	$-0.519027\pi$
$983$	−3682.23	−0.119476	−0.0597381	+	0.998214i	$0.519027\pi$
$984$	1025.18	0.0332130
$985$	46652.9	1.50912
$986$	−1051.19	−0.0339519
$987$	34879.7	1.12486
$988$	0	0
$989$	−8909.99	−0.286472
$990$	−20931.4	−0.671962
$991$	4412.76	0.141449	0.0707246	−	0.997496i	$-0.477469\pi$
$991$	4412.76	0.141449	0.0707246	+	0.997496i	$0.477469\pi$
$992$	3748.60	0.119978
$993$	−14500.5	−0.463404
$994$	42635.2	1.36047
$995$	74273.5	2.36646
$996$	−3432.99	−0.109215
$997$	−24825.9	−0.788610	−0.394305	−	0.918980i	$-0.629015\pi$
$997$	−24825.9	−0.788610	−0.394305	+	0.918980i	$0.629015\pi$
$998$	7089.66	0.224869
$999$	8980.19	0.284405

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.4.a.w.1.3		3
19.8	odd	6		114.4.e.e.7.1	✓	6
19.12	odd	6		114.4.e.e.49.1	yes	6
19.18	odd	2		2166.4.a.s.1.3		3
57.8	even	6		342.4.g.g.235.3		6
57.50	even	6		342.4.g.g.163.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.e.e.7.1	✓	6	19.8	odd	6
114.4.e.e.49.1	yes	6	19.12	odd	6
342.4.g.g.163.3		6	57.50	even	6
342.4.g.g.235.3		6	57.8	even	6
2166.4.a.s.1.3		3	19.18	odd	2
2166.4.a.w.1.3		3	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)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +20.2020 q^{5} +6.00000 q^{6} -22.8872 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +20.2020 q^{5} +6.00000 q^{6} -22.8872 q^{7} +8.00000 q^{8} +9.00000 q^{9} +40.4040 q^{10} -57.5614 q^{11} +12.0000 q^{12} -27.3148 q^{13} -45.7744 q^{14} +60.6059 q^{15} +16.0000 q^{16} -73.4486 q^{17} +18.0000 q^{18} +80.8079 q^{20} -68.6616 q^{21} -115.123 q^{22} -188.584 q^{23} +24.0000 q^{24} +283.120 q^{25} -54.6296 q^{26} +27.0000 q^{27} -91.5488 q^{28} +7.15594 q^{29} +121.212 q^{30} +117.144 q^{31} +32.0000 q^{32} -172.684 q^{33} -146.897 q^{34} -462.367 q^{35} +36.0000 q^{36} +332.600 q^{37} -81.9443 q^{39} +161.616 q^{40} +42.7158 q^{41} -137.323 q^{42} +47.2469 q^{43} -230.245 q^{44} +181.818 q^{45} -377.168 q^{46} -507.995 q^{47} +48.0000 q^{48} +180.824 q^{49} +566.240 q^{50} -220.346 q^{51} -109.259 q^{52} -492.609 q^{53} +54.0000 q^{54} -1162.85 q^{55} -183.098 q^{56} +14.3119 q^{58} -460.041 q^{59} +242.424 q^{60} +450.745 q^{61} +234.287 q^{62} -205.985 q^{63} +64.0000 q^{64} -551.813 q^{65} -345.368 q^{66} -522.465 q^{67} -293.794 q^{68} -565.751 q^{69} -924.734 q^{70} -931.419 q^{71} +72.0000 q^{72} +350.123 q^{73} +665.199 q^{74} +849.360 q^{75} +1317.42 q^{77} -163.889 q^{78} -194.868 q^{79} +323.232 q^{80} +81.0000 q^{81} +85.4317 q^{82} -286.083 q^{83} -274.646 q^{84} -1483.81 q^{85} +94.4937 q^{86} +21.4678 q^{87} -460.491 q^{88} -839.690 q^{89} +363.636 q^{90} +625.159 q^{91} -754.335 q^{92} +351.431 q^{93} -1015.99 q^{94} +96.0000 q^{96} -605.516 q^{97} +361.648 q^{98} -518.052 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6 q^{2} + 9 q^{3} + 12 q^{4} + 2 q^{5} + 18 q^{6} - 17 q^{7} + 24 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q + 6 * q^2 + 9 * q^3 + 12 * q^4 + 2 * q^5 + 18 * q^6 - 17 * q^7 + 24 * q^8 + 27 * q^9	\( 3 q + 6 q^{2} + 9 q^{3} + 12 q^{4} + 2 q^{5} + 18 q^{6} - 17 q^{7} + 24 q^{8} + 27 q^{9} + 4 q^{10} - 52 q^{11} + 36 q^{12} - 75 q^{13} - 34 q^{14} + 6 q^{15} + 48 q^{16} - 48 q^{17} + 54 q^{18} + 8 q^{20} - 51 q^{21} - 104 q^{22} - 238 q^{23} + 72 q^{24} + 229 q^{25} - 150 q^{26} + 81 q^{27} - 68 q^{28} + 8 q^{29} + 12 q^{30} - 107 q^{31} + 96 q^{32} - 156 q^{33} - 96 q^{34} - 294 q^{35} + 108 q^{36} - 305 q^{37} - 225 q^{39} + 16 q^{40} - 16 q^{41} - 102 q^{42} - 331 q^{43} - 208 q^{44} + 18 q^{45} - 476 q^{46} - 766 q^{47} + 144 q^{48} + 1142 q^{49} + 458 q^{50} - 144 q^{51} - 300 q^{52} + 118 q^{53} + 162 q^{54} - 1400 q^{55} - 136 q^{56} + 16 q^{58} - 936 q^{59} + 24 q^{60} - 399 q^{61} - 214 q^{62} - 153 q^{63} + 192 q^{64} - 370 q^{65} - 312 q^{66} - 61 q^{67} - 192 q^{68} - 714 q^{69} - 588 q^{70} - 974 q^{71} + 216 q^{72} + 91 q^{73} - 610 q^{74} + 687 q^{75} - 36 q^{77} - 450 q^{78} + 321 q^{79} + 32 q^{80} + 243 q^{81} - 32 q^{82} - 2148 q^{83} - 204 q^{84} - 1680 q^{85} - 662 q^{86} + 24 q^{87} - 416 q^{88} - 1116 q^{89} + 36 q^{90} - 1367 q^{91} - 952 q^{92} - 321 q^{93} - 1532 q^{94} + 288 q^{96} - 1382 q^{97} + 2284 q^{98} - 468 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 + 9 * q^3 + 12 * q^4 + 2 * q^5 + 18 * q^6 - 17 * q^7 + 24 * q^8 + 27 * q^9 + 4 * q^10 - 52 * q^11 + 36 * q^12 - 75 * q^13 - 34 * q^14 + 6 * q^15 + 48 * q^16 - 48 * q^17 + 54 * q^18 + 8 * q^20 - 51 * q^21 - 104 * q^22 - 238 * q^23 + 72 * q^24 + 229 * q^25 - 150 * q^26 + 81 * q^27 - 68 * q^28 + 8 * q^29 + 12 * q^30 - 107 * q^31 + 96 * q^32 - 156 * q^33 - 96 * q^34 - 294 * q^35 + 108 * q^36 - 305 * q^37 - 225 * q^39 + 16 * q^40 - 16 * q^41 - 102 * q^42 - 331 * q^43 - 208 * q^44 + 18 * q^45 - 476 * q^46 - 766 * q^47 + 144 * q^48 + 1142 * q^49 + 458 * q^50 - 144 * q^51 - 300 * q^52 + 118 * q^53 + 162 * q^54 - 1400 * q^55 - 136 * q^56 + 16 * q^58 - 936 * q^59 + 24 * q^60 - 399 * q^61 - 214 * q^62 - 153 * q^63 + 192 * q^64 - 370 * q^65 - 312 * q^66 - 61 * q^67 - 192 * q^68 - 714 * q^69 - 588 * q^70 - 974 * q^71 + 216 * q^72 + 91 * q^73 - 610 * q^74 + 687 * q^75 - 36 * q^77 - 450 * q^78 + 321 * q^79 + 32 * q^80 + 243 * q^81 - 32 * q^82 - 2148 * q^83 - 204 * q^84 - 1680 * q^85 - 662 * q^86 + 24 * q^87 - 416 * q^88 - 1116 * q^89 + 36 * q^90 - 1367 * q^91 - 952 * q^92 - 321 * q^93 - 1532 * q^94 + 288 * q^96 - 1382 * q^97 + 2284 * q^98 - 468 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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