LMFDB - Embedded newform 2166.4.a.u.1.2

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:	3.3.14457.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 32x - 3 $ x^3 - x^2 - 32*x - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
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			1.2
Root			$-0.0940524$ 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)

$f(q)$	$=$	$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +4.18810 q^{5} -6.00000 q^{6} +3.18810 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +4.18810 q^{5} -6.00000 q^{6} +3.18810 q^{7} +8.00000 q^{8} +9.00000 q^{9} +8.37621 q^{10} +69.4003 q^{11} -12.0000 q^{12} -8.12863 q^{13} +6.37621 q^{14} -12.5643 q^{15} +16.0000 q^{16} -106.084 q^{17} +18.0000 q^{18} +16.7524 q^{20} -9.56431 q^{21} +138.801 q^{22} -176.494 q^{23} -24.0000 q^{24} -107.460 q^{25} -16.2573 q^{26} -27.0000 q^{27} +12.7524 q^{28} -66.2219 q^{29} -25.1286 q^{30} -140.915 q^{31} +32.0000 q^{32} -208.201 q^{33} -212.167 q^{34} +13.3521 q^{35} +36.0000 q^{36} -156.003 q^{37} +24.3859 q^{39} +33.5048 q^{40} -414.563 q^{41} -19.1286 q^{42} +115.850 q^{43} +277.601 q^{44} +37.6929 q^{45} -352.987 q^{46} +620.283 q^{47} -48.0000 q^{48} -332.836 q^{49} -214.920 q^{50} +318.251 q^{51} -32.5145 q^{52} -371.986 q^{53} -54.0000 q^{54} +290.656 q^{55} +25.5048 q^{56} -132.444 q^{58} +91.6929 q^{59} -50.2573 q^{60} +218.621 q^{61} -281.830 q^{62} +28.6929 q^{63} +64.0000 q^{64} -34.0436 q^{65} -416.402 q^{66} -145.342 q^{67} -424.334 q^{68} +529.481 q^{69} +26.7042 q^{70} +887.829 q^{71} +72.0000 q^{72} +199.016 q^{73} -312.006 q^{74} +322.379 q^{75} +221.255 q^{77} +48.7718 q^{78} -389.558 q^{79} +67.0097 q^{80} +81.0000 q^{81} -829.125 q^{82} +380.039 q^{83} -38.2573 q^{84} -444.289 q^{85} +231.701 q^{86} +198.666 q^{87} +555.202 q^{88} -425.799 q^{89} +75.3859 q^{90} -25.9149 q^{91} -705.974 q^{92} +422.744 q^{93} +1240.57 q^{94} -96.0000 q^{96} +419.846 q^{97} -665.672 q^{98} +624.603 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 10 q^{5} - 18 q^{6} + 7 q^{7} + 24 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 10 * q^5 - 18 * q^6 + 7 * q^7 + 24 * q^8 + 27 * q^9	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 10 q^{5} - 18 q^{6} + 7 q^{7} + 24 q^{8} + 27 q^{9} + 20 q^{10} - 44 q^{11} - 36 q^{12} - 9 q^{13} + 14 q^{14} - 30 q^{15} + 48 q^{16} - 84 q^{17} + 54 q^{18} + 40 q^{20} - 21 q^{21} - 88 q^{22} - 2 q^{23} - 72 q^{24} - 83 q^{25} - 18 q^{26} - 81 q^{27} + 28 q^{28} + 92 q^{29} - 60 q^{30} - 109 q^{31} + 96 q^{32} + 132 q^{33} - 168 q^{34} + 282 q^{35} + 108 q^{36} + 245 q^{37} + 27 q^{39} + 80 q^{40} - 688 q^{41} - 42 q^{42} - 103 q^{43} - 176 q^{44} + 90 q^{45} - 4 q^{46} + 322 q^{47} - 144 q^{48} - 754 q^{49} - 166 q^{50} + 252 q^{51} - 36 q^{52} - 1322 q^{53} - 162 q^{54} - 248 q^{55} + 56 q^{56} + 184 q^{58} + 252 q^{59} - 120 q^{60} - 435 q^{61} - 218 q^{62} + 63 q^{63} + 192 q^{64} - 1582 q^{65} + 264 q^{66} - 719 q^{67} - 336 q^{68} + 6 q^{69} + 564 q^{70} - 62 q^{71} + 216 q^{72} - 581 q^{73} + 490 q^{74} + 249 q^{75} - 204 q^{77} + 54 q^{78} - 489 q^{79} + 160 q^{80} + 243 q^{81} - 1376 q^{82} + 2496 q^{83} - 84 q^{84} + 1632 q^{85} - 206 q^{86} - 276 q^{87} - 352 q^{88} + 1584 q^{89} + 180 q^{90} - 1573 q^{91} - 8 q^{92} + 327 q^{93} + 644 q^{94} - 288 q^{96} + 974 q^{97} - 1508 q^{98} - 396 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 10 * q^5 - 18 * q^6 + 7 * q^7 + 24 * q^8 + 27 * q^9 + 20 * q^10 - 44 * q^11 - 36 * q^12 - 9 * q^13 + 14 * q^14 - 30 * q^15 + 48 * q^16 - 84 * q^17 + 54 * q^18 + 40 * q^20 - 21 * q^21 - 88 * q^22 - 2 * q^23 - 72 * q^24 - 83 * q^25 - 18 * q^26 - 81 * q^27 + 28 * q^28 + 92 * q^29 - 60 * q^30 - 109 * q^31 + 96 * q^32 + 132 * q^33 - 168 * q^34 + 282 * q^35 + 108 * q^36 + 245 * q^37 + 27 * q^39 + 80 * q^40 - 688 * q^41 - 42 * q^42 - 103 * q^43 - 176 * q^44 + 90 * q^45 - 4 * q^46 + 322 * q^47 - 144 * q^48 - 754 * q^49 - 166 * q^50 + 252 * q^51 - 36 * q^52 - 1322 * q^53 - 162 * q^54 - 248 * q^55 + 56 * q^56 + 184 * q^58 + 252 * q^59 - 120 * q^60 - 435 * q^61 - 218 * q^62 + 63 * q^63 + 192 * q^64 - 1582 * q^65 + 264 * q^66 - 719 * q^67 - 336 * q^68 + 6 * q^69 + 564 * q^70 - 62 * q^71 + 216 * q^72 - 581 * q^73 + 490 * q^74 + 249 * q^75 - 204 * q^77 + 54 * q^78 - 489 * q^79 + 160 * q^80 + 243 * q^81 - 1376 * q^82 + 2496 * q^83 - 84 * q^84 + 1632 * q^85 - 206 * q^86 - 276 * q^87 - 352 * q^88 + 1584 * q^89 + 180 * q^90 - 1573 * q^91 - 8 * q^92 + 327 * q^93 + 644 * q^94 - 288 * q^96 + 974 * q^97 - 1508 * q^98 - 396 * 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
$5$	4.18810	0.374595	0.187298	−	0.982303i	$-0.440027\pi$
$5$	4.18810	0.374595	0.187298	+	0.982303i	$0.440027\pi$
$6$	−6.00000	−0.408248
$7$	3.18810	0.172141	0.0860707	−	0.996289i	$-0.472569\pi$
$7$	3.18810	0.172141	0.0860707	+	0.996289i	$0.472569\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	8.37621	0.264879
$11$	69.4003	1.90227	0.951135	−	0.308774i	$-0.0999187\pi$
$11$	69.4003	1.90227	0.951135	+	0.308774i	$0.0999187\pi$
$12$	−12.0000	−0.288675
$13$	−8.12863	−0.173421	−0.0867106	−	0.996234i	$-0.527636\pi$
$13$	−8.12863	−0.173421	−0.0867106	+	0.996234i	$0.527636\pi$
$14$	6.37621	0.121722
$15$	−12.5643	−0.216273
$16$	16.0000	0.250000
$17$	−106.084	−1.51347	−0.756737	−	0.653720i	$-0.773207\pi$
$17$	−106.084	−1.51347	−0.756737	+	0.653720i	$0.773207\pi$
$18$	18.0000	0.235702
$19$	0	0
$19$	0	0
$20$	16.7524	0.187298
$21$	−9.56431	−0.0993859
$22$	138.801	1.34511
$23$	−176.494	−1.60006	−0.800031	−	0.599958i	$-0.795184\pi$
$23$	−176.494	−1.60006	−0.800031	+	0.599958i	$0.795184\pi$
$24$	−24.0000	−0.204124
$25$	−107.460	−0.859678
$26$	−16.2573	−0.122627
$27$	−27.0000	−0.192450
$28$	12.7524	0.0860707
$29$	−66.2219	−0.424038	−0.212019	−	0.977266i	$-0.568004\pi$
$29$	−66.2219	−0.424038	−0.212019	+	0.977266i	$0.568004\pi$
$30$	−25.1286	−0.152928
$31$	−140.915	−0.816421	−0.408210	−	0.912888i	$-0.633847\pi$
$31$	−140.915	−0.816421	−0.408210	+	0.912888i	$0.633847\pi$
$32$	32.0000	0.176777
$33$	−208.201	−1.09828
$34$	−212.167	−1.07019
$35$	13.3521	0.0644834
$36$	36.0000	0.166667
$37$	−156.003	−0.693156	−0.346578	−	0.938021i	$-0.612656\pi$
$37$	−156.003	−0.693156	−0.346578	+	0.938021i	$0.612656\pi$
$38$	0	0
$39$	24.3859	0.100125
$40$	33.5048	0.132440
$41$	−414.563	−1.57912	−0.789559	−	0.613675i	$-0.789691\pi$
$41$	−414.563	−1.57912	−0.789559	+	0.613675i	$0.789691\pi$
$42$	−19.1286	−0.0702765
$43$	115.850	0.410861	0.205430	−	0.978672i	$-0.434141\pi$
$43$	115.850	0.410861	0.205430	+	0.978672i	$0.434141\pi$
$44$	277.601	0.951135
$45$	37.6929	0.124865
$46$	−352.987	−1.13142
$47$	620.283	1.92505	0.962527	−	0.271185i	$-0.0874156\pi$
$47$	620.283	1.92505	0.962527	+	0.271185i	$0.0874156\pi$
$48$	−48.0000	−0.144338
$49$	−332.836	−0.970367
$50$	−214.920	−0.607884
$51$	318.251	0.873804
$52$	−32.5145	−0.0867106
$53$	−371.986	−0.964078	−0.482039	−	0.876150i	$-0.660104\pi$
$53$	−371.986	−0.964078	−0.482039	+	0.876150i	$0.660104\pi$
$54$	−54.0000	−0.136083
$55$	290.656	0.712582
$56$	25.5048	0.0608612
$57$	0	0
$58$	−132.444	−0.299840
$59$	91.6929	0.202329	0.101164	−	0.994870i	$-0.467743\pi$
$59$	91.6929	0.202329	0.101164	+	0.994870i	$0.467743\pi$
$60$	−50.2573	−0.108136
$61$	218.621	0.458877	0.229438	−	0.973323i	$-0.426311\pi$
$61$	218.621	0.458877	0.229438	+	0.973323i	$0.426311\pi$
$62$	−281.830	−0.577297
$63$	28.6929	0.0573805
$64$	64.0000	0.125000
$65$	−34.0436	−0.0649628
$66$	−416.402	−0.776599
$67$	−145.342	−0.265021	−0.132510	−	0.991182i	$-0.542304\pi$
$67$	−145.342	−0.265021	−0.132510	+	0.991182i	$0.542304\pi$
$68$	−424.334	−0.756737
$69$	529.481	0.923797
$70$	26.7042	0.0455967
$71$	887.829	1.48403	0.742014	−	0.670385i	$-0.233871\pi$
$71$	887.829	1.48403	0.742014	+	0.670385i	$0.233871\pi$
$72$	72.0000	0.117851
$73$	199.016	0.319083	0.159542	−	0.987191i	$-0.448998\pi$
$73$	199.016	0.319083	0.159542	+	0.987191i	$0.448998\pi$
$74$	−312.006	−0.490135
$75$	322.379	0.496335
$76$	0	0
$77$	221.255	0.327460
$78$	48.7718	0.0707989
$79$	−389.558	−0.554793	−0.277397	−	0.960755i	$-0.589472\pi$
$79$	−389.558	−0.554793	−0.277397	+	0.960755i	$0.589472\pi$
$80$	67.0097	0.0936489
$81$	81.0000	0.111111
$82$	−829.125	−1.11660
$83$	380.039	0.502586	0.251293	−	0.967911i	$-0.419144\pi$
$83$	380.039	0.502586	0.251293	+	0.967911i	$0.419144\pi$
$84$	−38.2573	−0.0496930
$85$	−444.289	−0.566940
$86$	231.701	0.290523
$87$	198.666	0.244818
$88$	555.202	0.672554
$89$	−425.799	−0.507130	−0.253565	−	0.967318i	$-0.581603\pi$
$89$	−425.799	−0.507130	−0.253565	+	0.967318i	$0.581603\pi$
$90$	75.3859	0.0882930
$91$	−25.9149	−0.0298530
$92$	−705.974	−0.800031
$93$	422.744	0.471361
$94$	1240.57	1.36122
$95$	0	0
$96$	−96.0000	−0.102062
$97$	419.846	0.439473	0.219736	−	0.975559i	$-0.429480\pi$
$97$	419.846	0.439473	0.219736	+	0.975559i	$0.429480\pi$
$98$	−665.672	−0.686153
$99$	624.603	0.634090
$100$	−429.839	−0.429839
$101$	−1241.71	−1.22331	−0.611657	−	0.791123i	$-0.709497\pi$
$101$	−1241.71	−1.22331	−0.611657	+	0.791123i	$0.709497\pi$
$102$	636.501	0.617873
$103$	−593.606	−0.567862	−0.283931	−	0.958845i	$-0.591639\pi$
$103$	−593.606	−0.567862	−0.283931	+	0.958845i	$0.591639\pi$
$104$	−65.0290	−0.0613137
$105$	−40.0564	−0.0372295
$106$	−743.971	−0.681706
$107$	−1778.56	−1.60691	−0.803457	−	0.595363i	$-0.797008\pi$
$107$	−1778.56	−1.60691	−0.803457	+	0.595363i	$0.797008\pi$
$108$	−108.000	−0.0962250
$109$	−1069.99	−0.940243	−0.470121	−	0.882602i	$-0.655790\pi$
$109$	−1069.99	−0.940243	−0.470121	+	0.882602i	$0.655790\pi$
$110$	581.311	0.503872
$111$	468.009	0.400194
$112$	51.0097	0.0430354
$113$	583.197	0.485510	0.242755	−	0.970088i	$-0.421949\pi$
$113$	583.197	0.485510	0.242755	+	0.970088i	$0.421949\pi$
$114$	0	0
$115$	−739.173	−0.599376
$116$	−264.887	−0.212019
$117$	−73.1577	−0.0578071
$118$	183.386	0.143068
$119$	−338.206	−0.260532
$120$	−100.515	−0.0764640
$121$	3485.40	2.61863
$122$	437.241	0.324475
$123$	1243.69	0.911704
$124$	−563.659	−0.408210
$125$	−973.566	−0.696627
$126$	57.3859	0.0405741
$127$	1659.35	1.15940	0.579700	−	0.814830i	$-0.303170\pi$
$127$	1659.35	1.15940	0.579700	+	0.814830i	$0.303170\pi$
$128$	128.000	0.0883883
$129$	−347.551	−0.237211
$130$	−68.0871	−0.0459356
$131$	597.546	0.398533	0.199267	−	0.979945i	$-0.436144\pi$
$131$	597.546	0.398533	0.199267	+	0.979945i	$0.436144\pi$
$132$	−832.804	−0.549138
$133$	0	0
$134$	−290.685	−0.187398
$135$	−113.079	−0.0720909
$136$	−848.669	−0.535094
$137$	−1777.31	−1.10836	−0.554182	−	0.832396i	$-0.686969\pi$
$137$	−1777.31	−1.10836	−0.554182	+	0.832396i	$0.686969\pi$
$138$	1058.96	0.653223
$139$	163.567	0.0998099	0.0499050	−	0.998754i	$-0.484108\pi$
$139$	163.567	0.0998099	0.0499050	+	0.998754i	$0.484108\pi$
$140$	53.4085	0.0322417
$141$	−1860.85	−1.11143
$142$	1775.66	1.04937
$143$	−564.129	−0.329894
$144$	144.000	0.0833333
$145$	−277.344	−0.158843
$146$	398.032	0.225626
$147$	998.508	0.560242
$148$	−624.012	−0.346578
$149$	−1119.80	−0.615688	−0.307844	−	0.951437i	$-0.599607\pi$
$149$	−1119.80	−0.615688	−0.307844	+	0.951437i	$0.599607\pi$
$150$	644.759	0.350962
$151$	−2807.15	−1.51286	−0.756432	−	0.654073i	$-0.773059\pi$
$151$	−2807.15	−1.51286	−0.756432	+	0.654073i	$0.773059\pi$
$152$	0	0
$153$	−954.752	−0.504491
$154$	442.511	0.231549
$155$	−590.166	−0.305828
$156$	97.5436	0.0500624
$157$	1003.94	0.510339	0.255170	−	0.966896i	$-0.417869\pi$
$157$	1003.94	0.510339	0.255170	+	0.966896i	$0.417869\pi$
$158$	−779.116	−0.392298
$159$	1115.96	0.556611
$160$	134.019	0.0662198
$161$	−562.680	−0.275437
$162$	162.000	0.0785674
$163$	1271.99	0.611225	0.305612	−	0.952156i	$-0.401139\pi$
$163$	1271.99	0.611225	0.305612	+	0.952156i	$0.401139\pi$
$164$	−1658.25	−0.789559
$165$	−871.967	−0.411409
$166$	760.077	0.355382
$167$	−2984.98	−1.38314	−0.691572	−	0.722307i	$-0.743082\pi$
$167$	−2984.98	−1.38314	−0.691572	+	0.722307i	$0.743082\pi$
$168$	−76.5145	−0.0351382
$169$	−2130.93	−0.969925
$170$	−888.578	−0.400887
$171$	0	0
$172$	463.402	0.205430
$173$	56.7747	0.0249509	0.0124754	−	0.999922i	$-0.496029\pi$
$173$	56.7747	0.0249509	0.0124754	+	0.999922i	$0.496029\pi$
$174$	397.331	0.173113
$175$	−342.593	−0.147986
$176$	1110.40	0.475568
$177$	−275.079	−0.116815
$178$	−851.598	−0.358595
$179$	−4640.98	−1.93790	−0.968948	−	0.247266i	$-0.920468\pi$
$179$	−4640.98	−1.93790	−0.968948	+	0.247266i	$0.920468\pi$
$180$	150.772	0.0624326
$181$	3775.41	1.55041	0.775204	−	0.631711i	$-0.217647\pi$
$181$	3775.41	1.55041	0.775204	+	0.631711i	$0.217647\pi$
$182$	−51.8298	−0.0211093
$183$	−655.862	−0.264933
$184$	−1411.95	−0.565708
$185$	−653.357	−0.259653
$186$	845.489	0.333302
$187$	−7362.23	−2.87904
$188$	2481.13	0.962527
$189$	−86.0788	−0.0331286
$190$	0	0
$191$	−2762.53	−1.04654	−0.523271	−	0.852166i	$-0.675288\pi$
$191$	−2762.53	−1.04654	−0.523271	+	0.852166i	$0.675288\pi$
$192$	−192.000	−0.0721688
$193$	2061.51	0.768866	0.384433	−	0.923153i	$-0.374397\pi$
$193$	2061.51	0.768866	0.384433	+	0.923153i	$0.374397\pi$
$194$	839.691	0.310754
$195$	102.131	0.0375063
$196$	−1331.34	−0.485184
$197$	2094.82	0.757614	0.378807	−	0.925476i	$-0.376334\pi$
$197$	2094.82	0.757614	0.378807	+	0.925476i	$0.376334\pi$
$198$	1249.21	0.448370
$199$	−1717.36	−0.611762	−0.305881	−	0.952070i	$-0.598951\pi$
$199$	−1717.36	−0.611762	−0.305881	+	0.952070i	$0.598951\pi$
$200$	−859.678	−0.303942
$201$	436.027	0.153010
$202$	−2483.42	−0.865014
$203$	−211.122	−0.0729945
$204$	1273.00	0.436902
$205$	−1736.23	−0.591530
$206$	−1187.21	−0.401539
$207$	−1588.44	−0.533354
$208$	−130.058	−0.0433553
$209$	0	0
$210$	−80.1127	−0.0263252
$211$	−2291.05	−0.747500	−0.373750	−	0.927529i	$-0.621928\pi$
$211$	−2291.05	−0.747500	−0.373750	+	0.927529i	$0.621928\pi$
$212$	−1487.94	−0.482039
$213$	−2663.49	−0.856804
$214$	−3557.12	−1.13626
$215$	485.194	0.153907
$216$	−216.000	−0.0680414
$217$	−449.251	−0.140540
$218$	−2139.98	−0.664852
$219$	−597.048	−0.184223
$220$	1162.62	0.356291
$221$	862.314	0.262468
$222$	936.019	0.282980
$223$	3256.19	0.977805	0.488902	−	0.872338i	$-0.337397\pi$
$223$	3256.19	0.977805	0.488902	+	0.872338i	$0.337397\pi$
$224$	102.019	0.0304306
$225$	−967.138	−0.286559
$226$	1166.39	0.343307
$227$	−998.044	−0.291817	−0.145909	−	0.989298i	$-0.546611\pi$
$227$	−998.044	−0.291817	−0.145909	+	0.989298i	$0.546611\pi$
$228$	0	0
$229$	−1028.59	−0.296816	−0.148408	−	0.988926i	$-0.547415\pi$
$229$	−1028.59	−0.296816	−0.148408	+	0.988926i	$0.547415\pi$
$230$	−1478.35	−0.423823
$231$	−663.766	−0.189059
$232$	−529.775	−0.149920
$233$	−125.486	−0.0352827	−0.0176414	−	0.999844i	$-0.505616\pi$
$233$	−125.486	−0.0352827	−0.0176414	+	0.999844i	$0.505616\pi$
$234$	−146.315	−0.0408758
$235$	2597.81	0.721117
$236$	366.772	0.101164
$237$	1168.67	0.320310
$238$	−676.411	−0.184224
$239$	3591.03	0.971901	0.485950	−	0.873986i	$-0.338474\pi$
$239$	3591.03	0.971901	0.485950	+	0.873986i	$0.338474\pi$
$240$	−201.029	−0.0540682
$241$	−3691.84	−0.986773	−0.493386	−	0.869810i	$-0.664241\pi$
$241$	−3691.84	−0.986773	−0.493386	+	0.869810i	$0.664241\pi$
$242$	6970.80	1.85165
$243$	−243.000	−0.0641500
$244$	874.482	0.229438
$245$	−1393.95	−0.363495
$246$	2487.38	0.644672
$247$	0	0
$248$	−1127.32	−0.288648
$249$	−1140.12	−0.290168
$250$	−1947.13	−0.492590
$251$	7294.88	1.83446	0.917228	−	0.398362i	$-0.130421\pi$
$251$	7294.88	1.83446	0.917228	+	0.398362i	$0.130421\pi$
$252$	114.772	0.0286902
$253$	−12248.7	−3.04375
$254$	3318.71	0.819820
$255$	1332.87	0.327323
$256$	256.000	0.0625000
$257$	2303.20	0.559026	0.279513	−	0.960142i	$-0.409827\pi$
$257$	2303.20	0.559026	0.279513	+	0.960142i	$0.409827\pi$
$258$	−695.102	−0.167733
$259$	−497.354	−0.119321
$260$	−136.174	−0.0324814
$261$	−595.997	−0.141346
$262$	1195.09	0.281806
$263$	7138.38	1.67365	0.836827	−	0.547467i	$-0.184408\pi$
$263$	7138.38	1.67365	0.836827	+	0.547467i	$0.184408\pi$
$264$	−1665.61	−0.388299
$265$	−1557.91	−0.361139
$266$	0	0
$267$	1277.40	0.292792
$268$	−581.370	−0.132510
$269$	−5446.66	−1.23453	−0.617265	−	0.786755i	$-0.711759\pi$
$269$	−5446.66	−1.23453	−0.617265	+	0.786755i	$0.711759\pi$
$270$	−226.158	−0.0509760
$271$	−3403.68	−0.762947	−0.381474	−	0.924380i	$-0.624583\pi$
$271$	−3403.68	−0.762947	−0.381474	+	0.924380i	$0.624583\pi$
$272$	−1697.34	−0.378368
$273$	77.7448	0.0172356
$274$	−3554.62	−0.783731
$275$	−7457.74	−1.63534
$276$	2117.92	0.461898
$277$	−5131.93	−1.11317	−0.556584	−	0.830791i	$-0.687888\pi$
$277$	−5131.93	−1.11317	−0.556584	+	0.830791i	$0.687888\pi$
$278$	327.134	0.0705763
$279$	−1268.23	−0.272140
$280$	106.817	0.0227983
$281$	3366.68	0.714731	0.357365	−	0.933965i	$-0.383675\pi$
$281$	3366.68	0.714731	0.357365	+	0.933965i	$0.383675\pi$
$282$	−3721.70	−0.785900
$283$	6685.76	1.40434	0.702168	−	0.712011i	$-0.252215\pi$
$283$	6685.76	1.40434	0.702168	+	0.712011i	$0.252215\pi$
$284$	3551.32	0.742014
$285$	0	0
$286$	−1128.26	−0.233270
$287$	−1321.67	−0.271832
$288$	288.000	0.0589256
$289$	6340.72	1.29060
$290$	−554.688	−0.112319
$291$	−1259.54	−0.253730
$292$	796.065	0.159542
$293$	−5625.93	−1.12174	−0.560871	−	0.827903i	$-0.689534\pi$
$293$	−5625.93	−1.12174	−0.560871	+	0.827903i	$0.689534\pi$
$294$	1997.02	0.396151
$295$	384.020	0.0757915
$296$	−1248.02	−0.245067
$297$	−1873.81	−0.366092
$298$	−2239.60	−0.435357
$299$	1434.65	0.277485
$300$	1289.52	0.248168
$301$	369.343	0.0707262
$302$	−5614.29	−1.06976
$303$	3725.13	0.706281
$304$	0	0
$305$	915.606	0.171893
$306$	−1909.50	−0.356729
$307$	5603.54	1.04173	0.520865	−	0.853639i	$-0.325610\pi$
$307$	5603.54	1.04173	0.520865	+	0.853639i	$0.325610\pi$
$308$	885.022	0.163730
$309$	1780.82	0.327855
$310$	−1180.33	−0.216253
$311$	6668.20	1.21582	0.607908	−	0.794008i	$-0.292009\pi$
$311$	6668.20	1.21582	0.607908	+	0.794008i	$0.292009\pi$
$312$	195.087	0.0353995
$313$	4491.40	0.811083	0.405541	−	0.914077i	$-0.367083\pi$
$313$	4491.40	0.811083	0.405541	+	0.914077i	$0.367083\pi$
$314$	2007.88	0.360865
$315$	120.169	0.0214945
$316$	−1558.23	−0.277397
$317$	−1266.05	−0.224316	−0.112158	−	0.993690i	$-0.535776\pi$
$317$	−1266.05	−0.224316	−0.112158	+	0.993690i	$0.535776\pi$
$318$	2231.91	0.393583
$319$	−4595.82	−0.806635
$320$	268.039	0.0468244
$321$	5335.68	0.927752
$322$	−1125.36	−0.194764
$323$	0	0
$324$	324.000	0.0555556
$325$	873.501	0.149086
$326$	2543.97	0.432201
$327$	3209.97	0.542849
$328$	−3316.50	−0.558302
$329$	1977.53	0.331382
$330$	−1743.93	−0.290910
$331$	−5068.09	−0.841594	−0.420797	−	0.907155i	$-0.638249\pi$
$331$	−5068.09	−0.841594	−0.420797	+	0.907155i	$0.638249\pi$
$332$	1520.15	0.251293
$333$	−1404.03	−0.231052
$334$	−5969.97	−0.978031
$335$	−608.709	−0.0992757
$336$	−153.029	−0.0248465
$337$	10744.1	1.73670	0.868352	−	0.495948i	$-0.165179\pi$
$337$	10744.1	1.73670	0.868352	+	0.495948i	$0.165179\pi$
$338$	−4261.85	−0.685841
$339$	−1749.59	−0.280309
$340$	−1777.16	−0.283470
$341$	−9779.53	−1.55305
$342$	0	0
$343$	−2154.64	−0.339182
$344$	926.803	0.145261
$345$	2217.52	0.346050
$346$	113.549	0.0176429
$347$	−4851.34	−0.750528	−0.375264	−	0.926918i	$-0.622448\pi$
$347$	−4851.34	−0.750528	−0.375264	+	0.926918i	$0.622448\pi$
$348$	794.662	0.122409
$349$	−7611.35	−1.16741	−0.583705	−	0.811966i	$-0.698398\pi$
$349$	−7611.35	−1.16741	−0.583705	+	0.811966i	$0.698398\pi$
$350$	−685.186	−0.104642
$351$	219.473	0.0333749
$352$	2220.81	0.336277
$353$	5567.64	0.839477	0.419739	−	0.907645i	$-0.362122\pi$
$353$	5567.64	0.839477	0.419739	+	0.907645i	$0.362122\pi$
$354$	−550.158	−0.0826004
$355$	3718.32	0.555910
$356$	−1703.20	−0.253565
$357$	1014.62	0.150418
$358$	−9281.96	−1.37030
$359$	4341.31	0.638233	0.319116	−	0.947716i	$-0.396614\pi$
$359$	4341.31	0.638233	0.319116	+	0.947716i	$0.396614\pi$
$360$	301.544	0.0441465
$361$	0	0
$362$	7550.82	1.09630
$363$	−10456.2	−1.51187
$364$	−103.660	−0.0149265
$365$	833.500	0.119527
$366$	−1311.72	−0.187336
$367$	−8964.48	−1.27505	−0.637524	−	0.770431i	$-0.720041\pi$
$367$	−8964.48	−1.27505	−0.637524	+	0.770431i	$0.720041\pi$
$368$	−2823.90	−0.400016
$369$	−3731.06	−0.526372
$370$	−1306.71	−0.183602
$371$	−1185.93	−0.165958
$372$	1690.98	0.235680
$373$	5048.11	0.700755	0.350377	−	0.936609i	$-0.386053\pi$
$373$	5048.11	0.700755	0.350377	+	0.936609i	$0.386053\pi$
$374$	−14724.5	−2.03579
$375$	2920.70	0.402198
$376$	4962.26	0.680609
$377$	538.293	0.0735371
$378$	−172.158	−0.0234255
$379$	−9290.41	−1.25915	−0.629573	−	0.776941i	$-0.716770\pi$
$379$	−9290.41	−1.25915	−0.629573	+	0.776941i	$0.716770\pi$
$380$	0	0
$381$	−4978.06	−0.669380
$382$	−5525.06	−0.740017
$383$	4162.26	0.555304	0.277652	−	0.960682i	$-0.410444\pi$
$383$	4162.26	0.555304	0.277652	+	0.960682i	$0.410444\pi$
$384$	−384.000	−0.0510310
$385$	926.641	0.122665
$386$	4123.03	0.543670
$387$	1042.65	0.136954
$388$	1679.38	0.219736
$389$	4185.23	0.545500	0.272750	−	0.962085i	$-0.412067\pi$
$389$	4185.23	0.545500	0.272750	+	0.962085i	$0.412067\pi$
$390$	204.261	0.0265210
$391$	18723.1	2.42165
$392$	−2662.69	−0.343077
$393$	−1792.64	−0.230093
$394$	4189.64	0.535714
$395$	−1631.51	−0.207823
$396$	2498.41	0.317045
$397$	−4529.76	−0.572650	−0.286325	−	0.958133i	$-0.592434\pi$
$397$	−4529.76	−0.572650	−0.286325	+	0.958133i	$0.592434\pi$
$398$	−3434.72	−0.432581
$399$	0	0
$400$	−1719.36	−0.214920
$401$	−9497.05	−1.18269	−0.591347	−	0.806417i	$-0.701404\pi$
$401$	−9497.05	−1.18269	−0.591347	+	0.806417i	$0.701404\pi$
$402$	872.055	0.108194
$403$	1145.44	0.141585
$404$	−4966.84	−0.611657
$405$	339.236	0.0416217
$406$	−422.245	−0.0516149
$407$	−10826.7	−1.31857
$408$	2546.01	0.308936
$409$	−5354.44	−0.647335	−0.323667	−	0.946171i	$-0.604916\pi$
$409$	−5354.44	−0.647335	−0.323667	+	0.946171i	$0.604916\pi$
$410$	−3472.46	−0.418275
$411$	5331.93	0.639914
$412$	−2374.43	−0.283931
$413$	292.327	0.0348292
$414$	−3176.88	−0.377138
$415$	1591.64	0.188267
$416$	−260.116	−0.0306568
$417$	−490.701	−0.0576253
$418$	0	0
$419$	14506.1	1.69134	0.845668	−	0.533709i	$-0.179202\pi$
$419$	14506.1	1.69134	0.845668	+	0.533709i	$0.179202\pi$
$420$	−160.225	−0.0186148
$421$	−1263.45	−0.146263	−0.0731315	−	0.997322i	$-0.523299\pi$
$421$	−1263.45	−0.146263	−0.0731315	+	0.997322i	$0.523299\pi$
$422$	−4582.10	−0.528562
$423$	5582.55	0.641685
$424$	−2975.88	−0.340853
$425$	11399.7	1.30110
$426$	−5326.98	−0.605852
$427$	696.985	0.0789918
$428$	−7114.24	−0.803457
$429$	1692.39	0.190464
$430$	970.387	0.108828
$431$	−8187.62	−0.915043	−0.457522	−	0.889198i	$-0.651263\pi$
$431$	−8187.62	−0.915043	−0.457522	+	0.889198i	$0.651263\pi$
$432$	−432.000	−0.0481125
$433$	−9242.94	−1.02584	−0.512919	−	0.858437i	$-0.671436\pi$
$433$	−9242.94	−1.02584	−0.512919	+	0.858437i	$0.671436\pi$
$434$	−898.502	−0.0993767
$435$	832.032	0.0917078
$436$	−4279.96	−0.470121
$437$	0	0
$438$	−1194.10	−0.130265
$439$	−2043.05	−0.222117	−0.111059	−	0.993814i	$-0.535424\pi$
$439$	−2043.05	−0.222117	−0.111059	+	0.993814i	$0.535424\pi$
$440$	2325.25	0.251936
$441$	−2995.52	−0.323456
$442$	1724.63	0.185593
$443$	−9669.13	−1.03701	−0.518504	−	0.855075i	$-0.673511\pi$
$443$	−9669.13	−1.03701	−0.518504	+	0.855075i	$0.673511\pi$
$444$	1872.04	0.200097
$445$	−1783.29	−0.189969
$446$	6512.38	0.691412
$447$	3359.40	0.355467
$448$	204.039	0.0215177
$449$	−13227.2	−1.39027	−0.695134	−	0.718881i	$-0.744655\pi$
$449$	−13227.2	−1.39027	−0.695134	+	0.718881i	$0.744655\pi$
$450$	−1934.28	−0.202628
$451$	−28770.8	−3.00391
$452$	2332.79	0.242755
$453$	8421.44	0.873452
$454$	−1996.09	−0.206346
$455$	−108.534	−0.0111828
$456$	0	0
$457$	−5380.98	−0.550791	−0.275396	−	0.961331i	$-0.588809\pi$
$457$	−5380.98	−0.550791	−0.275396	+	0.961331i	$0.588809\pi$
$458$	−2057.17	−0.209880
$459$	2864.26	0.291268
$460$	−2956.69	−0.299688
$461$	−2844.67	−0.287396	−0.143698	−	0.989622i	$-0.545899\pi$
$461$	−2844.67	−0.287396	−0.143698	+	0.989622i	$0.545899\pi$
$462$	−1327.53	−0.133685
$463$	6625.39	0.665028	0.332514	−	0.943098i	$-0.392103\pi$
$463$	6625.39	0.665028	0.332514	+	0.943098i	$0.392103\pi$
$464$	−1059.55	−0.106009
$465$	1770.50	0.176570
$466$	−250.972	−0.0249487
$467$	−18635.1	−1.84653	−0.923264	−	0.384167i	$-0.874489\pi$
$467$	−18635.1	−1.84653	−0.923264	+	0.384167i	$0.874489\pi$
$468$	−292.631	−0.0289035
$469$	−463.367	−0.0456211
$470$	5195.62	0.509906
$471$	−3011.83	−0.294645
$472$	733.544	0.0715341
$473$	8040.05	0.781569
$474$	2337.35	0.226493
$475$	0	0
$476$	−1352.82	−0.130266
$477$	−3347.87	−0.321359
$478$	7182.05	0.687237
$479$	1556.62	0.148484	0.0742420	−	0.997240i	$-0.476346\pi$
$479$	1556.62	0.148484	0.0742420	+	0.997240i	$0.476346\pi$
$480$	−402.058	−0.0382320
$481$	1268.09	0.120208
$482$	−7383.68	−0.697754
$483$	1688.04	0.159024
$484$	13941.6	1.30932
$485$	1758.36	0.164625
$486$	−486.000	−0.0453609
$487$	19339.5	1.79950	0.899751	−	0.436405i	$-0.143748\pi$
$487$	19339.5	1.79950	0.899751	+	0.436405i	$0.143748\pi$
$488$	1748.96	0.162238
$489$	−3815.96	−0.352891
$490$	−2787.90	−0.257030
$491$	−6838.25	−0.628525	−0.314262	−	0.949336i	$-0.601757\pi$
$491$	−6838.25	−0.628525	−0.314262	+	0.949336i	$0.601757\pi$
$492$	4974.75	0.455852
$493$	7025.05	0.641770
$494$	0	0
$495$	2615.90	0.237527
$496$	−2254.64	−0.204105
$497$	2830.49	0.255463
$498$	−2280.23	−0.205180
$499$	−18115.0	−1.62513	−0.812563	−	0.582874i	$-0.801928\pi$
$499$	−18115.0	−1.62513	−0.812563	+	0.582874i	$0.801928\pi$
$500$	−3894.26	−0.348314
$501$	8954.95	0.798559
$502$	14589.8	1.29716
$503$	−5831.85	−0.516957	−0.258478	−	0.966017i	$-0.583221\pi$
$503$	−5831.85	−0.516957	−0.258478	+	0.966017i	$0.583221\pi$
$504$	229.544	0.0202871
$505$	−5200.41	−0.458248
$506$	−24497.4	−2.15226
$507$	6392.78	0.559987
$508$	6637.41	0.579700
$509$	9914.65	0.863377	0.431689	−	0.902023i	$-0.357918\pi$
$509$	9914.65	0.863377	0.431689	+	0.902023i	$0.357918\pi$
$510$	2665.73	0.231452
$511$	634.484	0.0549275
$512$	512.000	0.0441942
$513$	0	0
$514$	4606.40	0.395291
$515$	−2486.09	−0.212718
$516$	−1390.20	−0.118605
$517$	43047.8	3.66197
$518$	−994.709	−0.0843726
$519$	−170.324	−0.0144054
$520$	−272.348	−0.0229678
$521$	−5851.91	−0.492086	−0.246043	−	0.969259i	$-0.579131\pi$
$521$	−5851.91	−0.492086	−0.246043	+	0.969259i	$0.579131\pi$
$522$	−1191.99	−0.0999466
$523$	6894.09	0.576401	0.288200	−	0.957570i	$-0.406943\pi$
$523$	6894.09	0.576401	0.288200	+	0.957570i	$0.406943\pi$
$524$	2390.19	0.199267
$525$	1027.78	0.0854399
$526$	14276.8	1.18345
$527$	14948.7	1.23563
$528$	−3331.21	−0.274569
$529$	18983.0	1.56020
$530$	−3115.83	−0.255364
$531$	825.236	0.0674430
$532$	0	0
$533$	3369.83	0.273853
$534$	2554.79	0.207035
$535$	−7448.79	−0.601943
$536$	−1162.74	−0.0936991
$537$	13922.9	1.11884
$538$	−10893.3	−0.872945
$539$	−23098.9	−1.84590
$540$	−452.315	−0.0360455
$541$	−5624.99	−0.447019	−0.223509	−	0.974702i	$-0.571751\pi$
$541$	−5624.99	−0.447019	−0.223509	+	0.974702i	$0.571751\pi$
$542$	−6807.36	−0.539485
$543$	−11326.2	−0.895129
$544$	−3394.67	−0.267547
$545$	−4481.23	−0.352211
$546$	155.490	0.0121874
$547$	3596.14	0.281096	0.140548	−	0.990074i	$-0.455114\pi$
$547$	3596.14	0.281096	0.140548	+	0.990074i	$0.455114\pi$
$548$	−7109.24	−0.554182
$549$	1967.59	0.152959
$550$	−14915.5	−1.15636
$551$	0	0
$552$	4235.85	0.326611
$553$	−1241.95	−0.0955029
$554$	−10263.9	−0.787129
$555$	1960.07	0.149911
$556$	654.269	0.0499050
$557$	18381.5	1.39829	0.699145	−	0.714980i	$-0.253564\pi$
$557$	18381.5	1.39829	0.699145	+	0.714980i	$0.253564\pi$
$558$	−2536.47	−0.192432
$559$	−941.705	−0.0712520
$560$	213.634	0.0161209
$561$	22086.7	1.66221
$562$	6733.36	0.505391
$563$	5578.33	0.417582	0.208791	−	0.977960i	$-0.433047\pi$
$563$	5578.33	0.417582	0.208791	+	0.977960i	$0.433047\pi$
$564$	−7443.39	−0.555715
$565$	2442.49	0.181870
$566$	13371.5	0.993016
$567$	258.236	0.0191268
$568$	7102.63	0.524683
$569$	16981.3	1.25113	0.625564	−	0.780173i	$-0.284869\pi$
$569$	16981.3	1.25113	0.625564	+	0.780173i	$0.284869\pi$
$570$	0	0
$571$	−19520.5	−1.43066	−0.715332	−	0.698785i	$-0.753724\pi$
$571$	−19520.5	−1.43066	−0.715332	+	0.698785i	$0.753724\pi$
$572$	−2256.52	−0.164947
$573$	8287.59	0.604221
$574$	−2643.34	−0.192214
$575$	18966.0	1.37554
$576$	576.000	0.0416667
$577$	6371.35	0.459693	0.229846	−	0.973227i	$-0.426178\pi$
$577$	6371.35	0.459693	0.229846	+	0.973227i	$0.426178\pi$
$578$	12681.4	0.912593
$579$	−6184.54	−0.443905
$580$	−1109.38	−0.0794213
$581$	1211.60	0.0865159
$582$	−2519.07	−0.179414
$583$	−25815.9	−1.83394
$584$	1592.13	0.112813
$585$	−306.392	−0.0216543
$586$	−11251.9	−0.793191
$587$	10759.0	0.756513	0.378257	−	0.925701i	$-0.376524\pi$
$587$	10759.0	0.756513	0.378257	+	0.925701i	$0.376524\pi$
$588$	3994.03	0.280121
$589$	0	0
$590$	768.039	0.0535927
$591$	−6284.47	−0.437408
$592$	−2496.05	−0.173289
$593$	3611.76	0.250113	0.125057	−	0.992150i	$-0.460089\pi$
$593$	3611.76	0.250113	0.125057	+	0.992150i	$0.460089\pi$
$594$	−3747.62	−0.258866
$595$	−1416.44	−0.0975939
$596$	−4479.19	−0.307844
$597$	5152.09	0.353201
$598$	2869.30	0.196211
$599$	−9180.23	−0.626201	−0.313100	−	0.949720i	$-0.601368\pi$
$599$	−9180.23	−0.626201	−0.313100	+	0.949720i	$0.601368\pi$
$600$	2579.03	0.175481
$601$	12700.4	0.862000	0.431000	−	0.902352i	$-0.358161\pi$
$601$	12700.4	0.862000	0.431000	+	0.902352i	$0.358161\pi$
$602$	738.686	0.0500110
$603$	−1308.08	−0.0883403
$604$	−11228.6	−0.756432
$605$	14597.2	0.980928
$606$	7450.26	0.499416
$607$	−24227.5	−1.62004	−0.810019	−	0.586404i	$-0.800543\pi$
$607$	−24227.5	−1.62004	−0.810019	+	0.586404i	$0.800543\pi$
$608$	0	0
$609$	633.367	0.0421434
$610$	1831.21	0.121547
$611$	−5042.05	−0.333845
$612$	−3819.01	−0.252246
$613$	−16213.5	−1.06828	−0.534141	−	0.845396i	$-0.679365\pi$
$613$	−16213.5	−1.06828	−0.534141	+	0.845396i	$0.679365\pi$
$614$	11207.1	0.736614
$615$	5208.70	0.341520
$616$	1770.04	0.115774
$617$	−21515.3	−1.40385	−0.701924	−	0.712252i	$-0.747675\pi$
$617$	−21515.3	−1.40385	−0.701924	+	0.712252i	$0.747675\pi$
$618$	3561.64	0.231829
$619$	−15878.5	−1.03103	−0.515516	−	0.856880i	$-0.672400\pi$
$619$	−15878.5	−1.03103	−0.515516	+	0.856880i	$0.672400\pi$
$620$	−2360.66	−0.152914
$621$	4765.33	0.307932
$622$	13336.4	0.859712
$623$	−1357.49	−0.0872982
$624$	390.174	0.0250312
$625$	9355.08	0.598725
$626$	8982.80	0.573522
$627$	0	0
$628$	4015.77	0.255170
$629$	16549.4	1.04907
$630$	240.338	0.0151989
$631$	5559.75	0.350761	0.175380	−	0.984501i	$-0.443884\pi$
$631$	5559.75	0.350761	0.175380	+	0.984501i	$0.443884\pi$
$632$	−3116.46	−0.196149
$633$	6873.16	0.431569
$634$	−2532.09	−0.158616
$635$	6949.55	0.434306
$636$	4463.83	0.278305
$637$	2705.50	0.168282
$638$	−9191.64	−0.570377
$639$	7990.46	0.494676
$640$	536.077	0.0331099
$641$	−20486.9	−1.26238	−0.631190	−	0.775628i	$-0.717433\pi$
$641$	−20486.9	−1.26238	−0.631190	+	0.775628i	$0.717433\pi$
$642$	10671.4	0.656020
$643$	−4102.30	−0.251600	−0.125800	−	0.992056i	$-0.540150\pi$
$643$	−4102.30	−0.251600	−0.125800	+	0.992056i	$0.540150\pi$
$644$	−2250.72	−0.137719
$645$	−1455.58	−0.0888580
$646$	0	0
$647$	22860.4	1.38908	0.694539	−	0.719455i	$-0.255608\pi$
$647$	22860.4	1.38908	0.694539	+	0.719455i	$0.255608\pi$
$648$	648.000	0.0392837
$649$	6363.52	0.384884
$650$	1747.00	0.105420
$651$	1347.75	0.0811408
$652$	5087.94	0.305612
$653$	26388.5	1.58141	0.790706	−	0.612197i	$-0.209714\pi$
$653$	26388.5	1.58141	0.790706	+	0.612197i	$0.209714\pi$
$654$	6419.94	0.383853
$655$	2502.59	0.149289
$656$	−6633.00	−0.394779
$657$	1791.15	0.106361
$658$	3955.05	0.234322
$659$	3223.29	0.190534	0.0952668	−	0.995452i	$-0.469630\pi$
$659$	3223.29	0.190534	0.0952668	+	0.995452i	$0.469630\pi$
$660$	−3487.87	−0.205705
$661$	−27480.2	−1.61703	−0.808513	−	0.588478i	$-0.799727\pi$
$661$	−27480.2	−1.61703	−0.808513	+	0.588478i	$0.799727\pi$
$662$	−10136.2	−0.595097
$663$	−2586.94	−0.151536
$664$	3040.31	0.177691
$665$	0	0
$666$	−2808.06	−0.163378
$667$	11687.7	0.678487
$668$	−11939.9	−0.691572
$669$	−9768.56	−0.564536
$670$	−1217.42	−0.0701985
$671$	15172.3	0.872908
$672$	−306.058	−0.0175691
$673$	−2165.00	−0.124004	−0.0620020	−	0.998076i	$-0.519749\pi$
$673$	−2165.00	−0.124004	−0.0620020	+	0.998076i	$0.519749\pi$
$674$	21488.2	1.22804
$675$	2901.41	0.165445
$676$	−8523.70	−0.484963
$677$	11999.0	0.681179	0.340589	−	0.940212i	$-0.389373\pi$
$677$	11999.0	0.681179	0.340589	+	0.940212i	$0.389373\pi$
$678$	−3499.18	−0.198209
$679$	1338.51	0.0756515
$680$	−3554.31	−0.200444
$681$	2994.13	0.168481
$682$	−19559.1	−1.09817
$683$	5234.35	0.293246	0.146623	−	0.989192i	$-0.453160\pi$
$683$	5234.35	0.293246	0.146623	+	0.989192i	$0.453160\pi$
$684$	0	0
$685$	−7443.56	−0.415188
$686$	−4309.27	−0.239838
$687$	3085.76	0.171367
$688$	1853.61	0.102715
$689$	3023.73	0.167192
$690$	4435.04	0.244694
$691$	−5160.63	−0.284109	−0.142055	−	0.989859i	$-0.545371\pi$
$691$	−5160.63	−0.284109	−0.142055	+	0.989859i	$0.545371\pi$
$692$	227.099	0.0124754
$693$	1991.30	0.109153
$694$	−9702.67	−0.530704
$695$	685.036	0.0373884
$696$	1589.32	0.0865563
$697$	43978.3	2.38995
$698$	−15222.7	−0.825484
$699$	376.459	0.0203705
$700$	−1370.37	−0.0739931
$701$	−3315.03	−0.178612	−0.0893059	−	0.996004i	$-0.528465\pi$
$701$	−3315.03	−0.178612	−0.0893059	+	0.996004i	$0.528465\pi$
$702$	438.946	0.0235996
$703$	0	0
$704$	4441.62	0.237784
$705$	−7793.43	−0.416337
$706$	11135.3	0.593600
$707$	−3958.70	−0.210583
$708$	−1100.32	−0.0584073
$709$	−18333.2	−0.971111	−0.485555	−	0.874206i	$-0.661383\pi$
$709$	−18333.2	−0.971111	−0.485555	+	0.874206i	$0.661383\pi$
$710$	7436.64	0.393088
$711$	−3506.02	−0.184931
$712$	−3406.39	−0.179298
$713$	24870.6	1.30632
$714$	2029.23	0.106362
$715$	−2362.63	−0.123577
$716$	−18563.9	−0.968948
$717$	−10773.1	−0.561127
$718$	8682.62	0.451299
$719$	9747.00	0.505566	0.252783	−	0.967523i	$-0.418654\pi$
$719$	9747.00	0.505566	0.252783	+	0.967523i	$0.418654\pi$
$720$	603.087	0.0312163
$721$	−1892.48	−0.0977526
$722$	0	0
$723$	11075.5	0.569713
$724$	15101.6	0.775204
$725$	7116.19	0.364536
$726$	−20912.4	−1.06905
$727$	32723.6	1.66939	0.834697	−	0.550709i	$-0.185643\pi$
$727$	32723.6	1.66939	0.834697	+	0.550709i	$0.185643\pi$
$728$	−207.319	−0.0105546
$729$	729.000	0.0370370
$730$	1667.00	0.0845185
$731$	−12289.8	−0.621827
$732$	−2623.45	−0.132466
$733$	36938.2	1.86131	0.930657	−	0.365894i	$-0.119237\pi$
$733$	36938.2	1.86131	0.930657	+	0.365894i	$0.119237\pi$
$734$	−17929.0	−0.901594
$735$	4181.86	0.209864
$736$	−5647.79	−0.282854
$737$	−10086.8	−0.504142
$738$	−7462.13	−0.372202
$739$	−9987.19	−0.497138	−0.248569	−	0.968614i	$-0.579960\pi$
$739$	−9987.19	−0.497138	−0.248569	+	0.968614i	$0.579960\pi$
$740$	−2613.43	−0.129826
$741$	0	0
$742$	−2371.86	−0.117350
$743$	21739.8	1.07343	0.536713	−	0.843765i	$-0.319666\pi$
$743$	21739.8	1.07343	0.536713	+	0.843765i	$0.319666\pi$
$744$	3381.96	0.166651
$745$	−4689.83	−0.230634
$746$	10096.2	0.495508
$747$	3420.35	0.167529
$748$	−29448.9	−1.43952
$749$	−5670.23	−0.276617
$750$	5841.40	0.284397
$751$	−38067.4	−1.84967	−0.924833	−	0.380374i	$-0.875795\pi$
$751$	−38067.4	−1.84967	−0.924833	+	0.380374i	$0.875795\pi$
$752$	9924.53	0.481264
$753$	−21884.6	−1.05912
$754$	1076.59	0.0519986
$755$	−11756.6	−0.566712
$756$	−344.315	−0.0165643
$757$	−11365.2	−0.545675	−0.272838	−	0.962060i	$-0.587962\pi$
$757$	−11365.2	−0.545675	−0.272838	+	0.962060i	$0.587962\pi$
$758$	−18580.8	−0.890351
$759$	36746.1	1.75731
$760$	0	0
$761$	24549.3	1.16940	0.584699	−	0.811250i	$-0.301213\pi$
$761$	24549.3	1.16940	0.584699	+	0.811250i	$0.301213\pi$
$762$	−9956.12	−0.473323
$763$	−3411.24	−0.161855
$764$	−11050.1	−0.523271
$765$	−3998.60	−0.188980
$766$	8324.51	0.392659
$767$	−745.338	−0.0350881
$768$	−768.000	−0.0360844
$769$	14222.5	0.666941	0.333471	−	0.942760i	$-0.391780\pi$
$769$	14222.5	0.666941	0.333471	+	0.942760i	$0.391780\pi$
$770$	1853.28	0.0867372
$771$	−6909.60	−0.322754
$772$	8246.06	0.384433
$773$	16082.6	0.748319	0.374159	−	0.927364i	$-0.377931\pi$
$773$	16082.6	0.748319	0.374159	+	0.927364i	$0.377931\pi$
$774$	2085.31	0.0968409
$775$	15142.7	0.701859
$776$	3358.77	0.155377
$777$	1492.06	0.0688899
$778$	8370.46	0.385727
$779$	0	0
$780$	408.523	0.0187531
$781$	61615.6	2.82302
$782$	37446.1	1.71237
$783$	1787.99	0.0816061
$784$	−5325.38	−0.242592
$785$	4204.61	0.191171
$786$	−3585.28	−0.162701
$787$	30058.0	1.36144	0.680720	−	0.732544i	$-0.261667\pi$
$787$	30058.0	1.36144	0.680720	+	0.732544i	$0.261667\pi$
$788$	8379.29	0.378807
$789$	−21415.1	−0.966285
$790$	−3263.02	−0.146953
$791$	1859.29	0.0835764
$792$	4996.82	0.224185
$793$	−1777.09	−0.0795790
$794$	−9059.52	−0.404925
$795$	4673.74	0.208504
$796$	−6869.45	−0.305881
$797$	−20008.2	−0.889243	−0.444621	−	0.895719i	$-0.646662\pi$
$797$	−20008.2	−0.889243	−0.444621	+	0.895719i	$0.646662\pi$
$798$	0	0
$799$	−65801.8	−2.91352
$800$	−3438.71	−0.151971
$801$	−3832.19	−0.169043
$802$	−18994.1	−0.836291
$803$	13811.8	0.606983
$804$	1744.11	0.0765050
$805$	−2356.56	−0.103178
$806$	2290.89	0.100116
$807$	16340.0	0.712757
$808$	−9933.68	−0.432507
$809$	35302.3	1.53419	0.767097	−	0.641532i	$-0.221701\pi$
$809$	35302.3	1.53419	0.767097	+	0.641532i	$0.221701\pi$
$810$	678.473	0.0294310
$811$	10980.8	0.475446	0.237723	−	0.971333i	$-0.423599\pi$
$811$	10980.8	0.475446	0.237723	+	0.971333i	$0.423599\pi$
$812$	−844.489	−0.0364972
$813$	10211.0	0.440488
$814$	−21653.3	−0.932369
$815$	5327.21	0.228962
$816$	5092.01	0.218451
$817$	0	0
$818$	−10708.9	−0.457735
$819$	−233.234	−0.00995100
$820$	−6944.93	−0.295765
$821$	−5626.68	−0.239187	−0.119594	−	0.992823i	$-0.538159\pi$
$821$	−5626.68	−0.239187	−0.119594	+	0.992823i	$0.538159\pi$
$822$	10663.9	0.452487
$823$	28766.3	1.21838	0.609191	−	0.793023i	$-0.291494\pi$
$823$	28766.3	1.21838	0.609191	+	0.793023i	$0.291494\pi$
$824$	−4748.85	−0.200769
$825$	22373.2	0.944164
$826$	584.653	0.0246280
$827$	44482.4	1.87038	0.935191	−	0.354145i	$-0.115228\pi$
$827$	44482.4	1.87038	0.935191	+	0.354145i	$0.115228\pi$
$828$	−6353.77	−0.266677
$829$	23302.5	0.976271	0.488136	−	0.872768i	$-0.337677\pi$
$829$	23302.5	0.976271	0.488136	+	0.872768i	$0.337677\pi$
$830$	3183.28	0.133125
$831$	15395.8	0.642688
$832$	−520.232	−0.0216777
$833$	35308.4	1.46862
$834$	−981.403	−0.0407472
$835$	−12501.4	−0.518120
$836$	0	0
$837$	3804.70	0.157120
$838$	29012.2	1.19596
$839$	−27683.7	−1.13915	−0.569575	−	0.821939i	$-0.692892\pi$
$839$	−27683.7	−1.13915	−0.569575	+	0.821939i	$0.692892\pi$
$840$	−320.451	−0.0131626
$841$	−20003.7	−0.820192
$842$	−2526.90	−0.103424
$843$	−10100.0	−0.412650
$844$	−9164.21	−0.373750
$845$	−8924.54	−0.363330
$846$	11165.1	0.453740
$847$	11111.8	0.450776
$848$	−5951.77	−0.241020
$849$	−20057.3	−0.810794
$850$	22799.4	0.920017
$851$	27533.5	1.10909
$852$	−10654.0	−0.428402
$853$	−30609.5	−1.22866	−0.614331	−	0.789049i	$-0.710574\pi$
$853$	−30609.5	−1.22866	−0.614331	+	0.789049i	$0.710574\pi$
$854$	1393.97	0.0558556
$855$	0	0
$856$	−14228.5	−0.568130
$857$	10918.3	0.435194	0.217597	−	0.976039i	$-0.430178\pi$
$857$	10918.3	0.435194	0.217597	+	0.976039i	$0.430178\pi$
$858$	3384.78	0.134679
$859$	14639.5	0.581482	0.290741	−	0.956802i	$-0.406098\pi$
$859$	14639.5	0.581482	0.290741	+	0.956802i	$0.406098\pi$
$860$	1940.77	0.0769533
$861$	3965.01	0.156942
$862$	−16375.2	−0.647033
$863$	−22775.2	−0.898353	−0.449176	−	0.893443i	$-0.648283\pi$
$863$	−22775.2	−0.898353	−0.449176	+	0.893443i	$0.648283\pi$
$864$	−864.000	−0.0340207
$865$	237.778	0.00934648
$866$	−18485.9	−0.725377
$867$	−19022.2	−0.745129
$868$	−1797.00	−0.0702700
$869$	−27035.4	−1.05537
$870$	1664.06	0.0648472
$871$	1181.43	0.0459603
$872$	−8559.92	−0.332426
$873$	3778.61	0.146491
$874$	0	0
$875$	−3103.83	−0.119918
$876$	−2388.19	−0.0921114
$877$	805.908	0.0310303	0.0155152	−	0.999880i	$-0.495061\pi$
$877$	805.908	0.0310303	0.0155152	+	0.999880i	$0.495061\pi$
$878$	−4086.10	−0.157061
$879$	16877.8	0.647638
$880$	4650.49	0.178146
$881$	−901.690	−0.0344821	−0.0172410	−	0.999851i	$-0.505488\pi$
$881$	−901.690	−0.0344821	−0.0172410	+	0.999851i	$0.505488\pi$
$882$	−5991.05	−0.228718
$883$	−25406.3	−0.968279	−0.484140	−	0.874991i	$-0.660867\pi$
$883$	−25406.3	−0.968279	−0.484140	+	0.874991i	$0.660867\pi$
$884$	3449.26	0.131234
$885$	−1152.06	−0.0437582
$886$	−19338.3	−0.733275
$887$	28560.5	1.08114	0.540568	−	0.841300i	$-0.318209\pi$
$887$	28560.5	1.08114	0.540568	+	0.841300i	$0.318209\pi$
$888$	3744.07	0.141490
$889$	5290.19	0.199581
$890$	−3566.58	−0.134328
$891$	5621.42	0.211363
$892$	13024.8	0.488902
$893$	0	0
$894$	6718.79	0.251353
$895$	−19436.9	−0.725927
$896$	408.077	0.0152153
$897$	−4303.95	−0.160206
$898$	−26454.4	−0.983067
$899$	9331.64	0.346193
$900$	−3868.55	−0.143280
$901$	39461.6	1.45911
$902$	−57541.6	−2.12408
$903$	−1108.03	−0.0408338
$904$	4665.58	0.171654
$905$	15811.8	0.580776
$906$	16842.9	0.617624
$907$	−40905.4	−1.49751	−0.748755	−	0.662847i	$-0.769348\pi$
$907$	−40905.4	−1.49751	−0.748755	+	0.662847i	$0.769348\pi$
$908$	−3992.18	−0.145909
$909$	−11175.4	−0.407772
$910$	−217.069	−0.00790743
$911$	30047.9	1.09279	0.546395	−	0.837527i	$-0.316000\pi$
$911$	30047.9	1.09279	0.546395	+	0.837527i	$0.316000\pi$
$912$	0	0
$913$	26374.8	0.956055
$914$	−10762.0	−0.389468
$915$	−2746.82	−0.0992426
$916$	−4114.34	−0.148408
$917$	1905.04	0.0686041
$918$	5728.51	0.205958
$919$	−49600.1	−1.78036	−0.890182	−	0.455605i	$-0.849423\pi$
$919$	−49600.1	−1.78036	−0.890182	+	0.455605i	$0.849423\pi$
$920$	−5913.39	−0.211912
$921$	−16810.6	−0.601443
$922$	−5689.33	−0.203219
$923$	−7216.84	−0.257362
$924$	−2655.07	−0.0945295
$925$	16764.1	0.595891
$926$	13250.8	0.470246
$927$	−5342.46	−0.189287
$928$	−2119.10	−0.0749600
$929$	27556.8	0.973205	0.486603	−	0.873623i	$-0.338236\pi$
$929$	27556.8	0.973205	0.486603	+	0.873623i	$0.338236\pi$
$930$	3541.00	0.124854
$931$	0	0
$932$	−501.945	−0.0176414
$933$	−20004.6	−0.701952
$934$	−37270.1	−1.30569
$935$	−30833.8	−1.07847
$936$	−585.261	−0.0204379
$937$	−26880.8	−0.937202	−0.468601	−	0.883410i	$-0.655242\pi$
$937$	−26880.8	−0.937202	−0.468601	+	0.883410i	$0.655242\pi$
$938$	−926.734	−0.0322590
$939$	−13474.2	−0.468279
$940$	10391.2	0.360558
$941$	−6411.34	−0.222108	−0.111054	−	0.993814i	$-0.535423\pi$
$941$	−6411.34	−0.222108	−0.111054	+	0.993814i	$0.535423\pi$
$942$	−6023.65	−0.208345
$943$	73167.6	2.52669
$944$	1467.09	0.0505822
$945$	−360.507	−0.0124098
$946$	16080.1	0.552653
$947$	−1989.83	−0.0682796	−0.0341398	−	0.999417i	$-0.510869\pi$
$947$	−1989.83	−0.0682796	−0.0341398	+	0.999417i	$0.510869\pi$
$948$	4674.69	0.160155
$949$	−1617.73	−0.0553358
$950$	0	0
$951$	3798.14	0.129509
$952$	−2705.64	−0.0921118
$953$	−38266.4	−1.30070	−0.650351	−	0.759633i	$-0.725378\pi$
$953$	−38266.4	−1.30070	−0.650351	+	0.759633i	$0.725378\pi$
$954$	−6695.74	−0.227235
$955$	−11569.8	−0.392030
$956$	14364.1	0.485950
$957$	13787.5	0.465711
$958$	3113.24	0.104994
$959$	−5666.25	−0.190795
$960$	−804.116	−0.0270341
$961$	−9934.01	−0.333457
$962$	2536.18	0.0849998
$963$	−16007.0	−0.535638
$964$	−14767.4	−0.493386
$965$	8633.84	0.288014
$966$	3376.08	0.112447
$967$	220.116	0.00732002	0.00366001	−	0.999993i	$-0.498835\pi$
$967$	220.116	0.00732002	0.00366001	+	0.999993i	$0.498835\pi$
$968$	27883.2	0.925827
$969$	0	0
$970$	3516.72	0.116407
$971$	2175.36	0.0718955	0.0359478	−	0.999354i	$-0.488555\pi$
$971$	2175.36	0.0718955	0.0359478	+	0.999354i	$0.488555\pi$
$972$	−972.000	−0.0320750
$973$	521.469	0.0171814
$974$	38679.0	1.27244
$975$	−2620.50	−0.0860751
$976$	3497.93	0.114719
$977$	13707.7	0.448872	0.224436	−	0.974489i	$-0.427946\pi$
$977$	13707.7	0.448872	0.224436	+	0.974489i	$0.427946\pi$
$978$	−7631.91	−0.249531
$979$	−29550.6	−0.964699
$980$	−5575.81	−0.181748
$981$	−9629.91	−0.313414
$982$	−13676.5	−0.444434
$983$	−18885.7	−0.612779	−0.306389	−	0.951906i	$-0.599121\pi$
$983$	−18885.7	−0.612779	−0.306389	+	0.951906i	$0.599121\pi$
$984$	9949.50	0.322336
$985$	8773.33	0.283799
$986$	14050.1	0.453800
$987$	−5932.58	−0.191323
$988$	0	0
$989$	−20446.8	−0.657403
$990$	5231.80	0.167957
$991$	−40655.0	−1.30318	−0.651589	−	0.758572i	$-0.725897\pi$
$991$	−40655.0	−1.30318	−0.651589	+	0.758572i	$0.725897\pi$
$992$	−4509.27	−0.144324
$993$	15204.3	0.485894
$994$	5660.99	0.180639
$995$	−7192.49	−0.229163
$996$	−4560.46	−0.145084
$997$	−16433.3	−0.522014	−0.261007	−	0.965337i	$-0.584055\pi$
$997$	−16433.3	−0.522014	−0.261007	+	0.965337i	$0.584055\pi$
$998$	−36229.9	−1.14914
$999$	4212.08	0.133398

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.4.a.u.1.2		3
19.7	even	3		114.4.e.d.49.2	yes	6
19.11	even	3		114.4.e.d.7.2	✓	6
19.18	odd	2		2166.4.a.t.1.2		3
57.11	odd	6		342.4.g.h.235.2		6
57.26	odd	6		342.4.g.h.163.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.e.d.7.2	✓	6	19.11	even	3
114.4.e.d.49.2	yes	6	19.7	even	3
342.4.g.h.163.2		6	57.26	odd	6
342.4.g.h.235.2		6	57.11	odd	6
2166.4.a.t.1.2		3	19.18	odd	2
2166.4.a.u.1.2		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)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +4.18810 q^{5} -6.00000 q^{6} +3.18810 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +4.18810 q^{5} -6.00000 q^{6} +3.18810 q^{7} +8.00000 q^{8} +9.00000 q^{9} +8.37621 q^{10} +69.4003 q^{11} -12.0000 q^{12} -8.12863 q^{13} +6.37621 q^{14} -12.5643 q^{15} +16.0000 q^{16} -106.084 q^{17} +18.0000 q^{18} +16.7524 q^{20} -9.56431 q^{21} +138.801 q^{22} -176.494 q^{23} -24.0000 q^{24} -107.460 q^{25} -16.2573 q^{26} -27.0000 q^{27} +12.7524 q^{28} -66.2219 q^{29} -25.1286 q^{30} -140.915 q^{31} +32.0000 q^{32} -208.201 q^{33} -212.167 q^{34} +13.3521 q^{35} +36.0000 q^{36} -156.003 q^{37} +24.3859 q^{39} +33.5048 q^{40} -414.563 q^{41} -19.1286 q^{42} +115.850 q^{43} +277.601 q^{44} +37.6929 q^{45} -352.987 q^{46} +620.283 q^{47} -48.0000 q^{48} -332.836 q^{49} -214.920 q^{50} +318.251 q^{51} -32.5145 q^{52} -371.986 q^{53} -54.0000 q^{54} +290.656 q^{55} +25.5048 q^{56} -132.444 q^{58} +91.6929 q^{59} -50.2573 q^{60} +218.621 q^{61} -281.830 q^{62} +28.6929 q^{63} +64.0000 q^{64} -34.0436 q^{65} -416.402 q^{66} -145.342 q^{67} -424.334 q^{68} +529.481 q^{69} +26.7042 q^{70} +887.829 q^{71} +72.0000 q^{72} +199.016 q^{73} -312.006 q^{74} +322.379 q^{75} +221.255 q^{77} +48.7718 q^{78} -389.558 q^{79} +67.0097 q^{80} +81.0000 q^{81} -829.125 q^{82} +380.039 q^{83} -38.2573 q^{84} -444.289 q^{85} +231.701 q^{86} +198.666 q^{87} +555.202 q^{88} -425.799 q^{89} +75.3859 q^{90} -25.9149 q^{91} -705.974 q^{92} +422.744 q^{93} +1240.57 q^{94} -96.0000 q^{96} +419.846 q^{97} -665.672 q^{98} +624.603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 10 q^{5} - 18 q^{6} + 7 q^{7} + 24 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 10 * q^5 - 18 * q^6 + 7 * q^7 + 24 * q^8 + 27 * q^9	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 10 q^{5} - 18 q^{6} + 7 q^{7} + 24 q^{8} + 27 q^{9} + 20 q^{10} - 44 q^{11} - 36 q^{12} - 9 q^{13} + 14 q^{14} - 30 q^{15} + 48 q^{16} - 84 q^{17} + 54 q^{18} + 40 q^{20} - 21 q^{21} - 88 q^{22} - 2 q^{23} - 72 q^{24} - 83 q^{25} - 18 q^{26} - 81 q^{27} + 28 q^{28} + 92 q^{29} - 60 q^{30} - 109 q^{31} + 96 q^{32} + 132 q^{33} - 168 q^{34} + 282 q^{35} + 108 q^{36} + 245 q^{37} + 27 q^{39} + 80 q^{40} - 688 q^{41} - 42 q^{42} - 103 q^{43} - 176 q^{44} + 90 q^{45} - 4 q^{46} + 322 q^{47} - 144 q^{48} - 754 q^{49} - 166 q^{50} + 252 q^{51} - 36 q^{52} - 1322 q^{53} - 162 q^{54} - 248 q^{55} + 56 q^{56} + 184 q^{58} + 252 q^{59} - 120 q^{60} - 435 q^{61} - 218 q^{62} + 63 q^{63} + 192 q^{64} - 1582 q^{65} + 264 q^{66} - 719 q^{67} - 336 q^{68} + 6 q^{69} + 564 q^{70} - 62 q^{71} + 216 q^{72} - 581 q^{73} + 490 q^{74} + 249 q^{75} - 204 q^{77} + 54 q^{78} - 489 q^{79} + 160 q^{80} + 243 q^{81} - 1376 q^{82} + 2496 q^{83} - 84 q^{84} + 1632 q^{85} - 206 q^{86} - 276 q^{87} - 352 q^{88} + 1584 q^{89} + 180 q^{90} - 1573 q^{91} - 8 q^{92} + 327 q^{93} + 644 q^{94} - 288 q^{96} + 974 q^{97} - 1508 q^{98} - 396 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 10 * q^5 - 18 * q^6 + 7 * q^7 + 24 * q^8 + 27 * q^9 + 20 * q^10 - 44 * q^11 - 36 * q^12 - 9 * q^13 + 14 * q^14 - 30 * q^15 + 48 * q^16 - 84 * q^17 + 54 * q^18 + 40 * q^20 - 21 * q^21 - 88 * q^22 - 2 * q^23 - 72 * q^24 - 83 * q^25 - 18 * q^26 - 81 * q^27 + 28 * q^28 + 92 * q^29 - 60 * q^30 - 109 * q^31 + 96 * q^32 + 132 * q^33 - 168 * q^34 + 282 * q^35 + 108 * q^36 + 245 * q^37 + 27 * q^39 + 80 * q^40 - 688 * q^41 - 42 * q^42 - 103 * q^43 - 176 * q^44 + 90 * q^45 - 4 * q^46 + 322 * q^47 - 144 * q^48 - 754 * q^49 - 166 * q^50 + 252 * q^51 - 36 * q^52 - 1322 * q^53 - 162 * q^54 - 248 * q^55 + 56 * q^56 + 184 * q^58 + 252 * q^59 - 120 * q^60 - 435 * q^61 - 218 * q^62 + 63 * q^63 + 192 * q^64 - 1582 * q^65 + 264 * q^66 - 719 * q^67 - 336 * q^68 + 6 * q^69 + 564 * q^70 - 62 * q^71 + 216 * q^72 - 581 * q^73 + 490 * q^74 + 249 * q^75 - 204 * q^77 + 54 * q^78 - 489 * q^79 + 160 * q^80 + 243 * q^81 - 1376 * q^82 + 2496 * q^83 - 84 * q^84 + 1632 * q^85 - 206 * q^86 - 276 * q^87 - 352 * q^88 + 1584 * q^89 + 180 * q^90 - 1573 * q^91 - 8 * q^92 + 327 * q^93 + 644 * q^94 - 288 * q^96 + 974 * q^97 - 1508 * q^98 - 396 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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