LMFDB - Embedded newform 1859.4.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, 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("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.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:	$109.684550701$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.297133.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 19x^{2} - 2x + 52 $ x^4 - 19x^2 - 2x + 52
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.90566$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.90566 q^{2} -6.07897 q^{3} -4.36845 q^{4} -8.17977 q^{5} -11.5845 q^{6} -17.8958 q^{7} -23.5701 q^{8} +9.95391 q^{9} +O(q^{10})$	\(q+1.90566 q^{2} -6.07897 q^{3} -4.36845 q^{4} -8.17977 q^{5} -11.5845 q^{6} -17.8958 q^{7} -23.5701 q^{8} +9.95391 q^{9} -15.5879 q^{10} +11.0000 q^{11} +26.5557 q^{12} -34.1034 q^{14} +49.7246 q^{15} -9.96909 q^{16} -63.0295 q^{17} +18.9688 q^{18} +98.2318 q^{19} +35.7329 q^{20} +108.788 q^{21} +20.9623 q^{22} -1.03008 q^{23} +143.282 q^{24} -58.0913 q^{25} +103.623 q^{27} +78.1770 q^{28} -44.6518 q^{29} +94.7584 q^{30} -112.558 q^{31} +169.563 q^{32} -66.8687 q^{33} -120.113 q^{34} +146.384 q^{35} -43.4831 q^{36} +241.182 q^{37} +187.197 q^{38} +192.798 q^{40} +404.826 q^{41} +207.314 q^{42} +20.2537 q^{43} -48.0529 q^{44} -81.4207 q^{45} -1.96299 q^{46} +49.8584 q^{47} +60.6018 q^{48} -22.7394 q^{49} -110.702 q^{50} +383.155 q^{51} +158.607 q^{53} +197.470 q^{54} -89.9775 q^{55} +421.806 q^{56} -597.148 q^{57} -85.0913 q^{58} +503.222 q^{59} -217.219 q^{60} -10.6787 q^{61} -214.498 q^{62} -178.133 q^{63} +402.883 q^{64} -127.429 q^{66} +584.100 q^{67} +275.341 q^{68} +6.26184 q^{69} +278.958 q^{70} -382.259 q^{71} -234.615 q^{72} +855.289 q^{73} +459.611 q^{74} +353.135 q^{75} -429.120 q^{76} -196.854 q^{77} -239.095 q^{79} +81.5449 q^{80} -898.675 q^{81} +771.462 q^{82} -1174.35 q^{83} -475.236 q^{84} +515.567 q^{85} +38.5967 q^{86} +271.437 q^{87} -259.271 q^{88} -1304.02 q^{89} -155.160 q^{90} +4.49986 q^{92} +684.237 q^{93} +95.0134 q^{94} -803.514 q^{95} -1030.77 q^{96} +1318.09 q^{97} -43.3337 q^{98} +109.493 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 6 q^{4} + 6 q^{5} + 13 q^{6} + 17 q^{7} - 6 q^{8} - 44 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 + 6 * q^4 + 6 * q^5 + 13 * q^6 + 17 * q^7 - 6 * q^8 - 44 * q^9	\( 4 q - 4 q^{3} + 6 q^{4} + 6 q^{5} + 13 q^{6} + 17 q^{7} - 6 q^{8} - 44 q^{9} - 82 q^{10} + 44 q^{11} + 17 q^{12} - 40 q^{14} - 9 q^{15} - 142 q^{16} - 41 q^{17} + 75 q^{18} + 41 q^{19} + 174 q^{20} + 179 q^{21} - 136 q^{23} + 171 q^{24} - 162 q^{25} + 11 q^{27} + 56 q^{28} - 207 q^{29} + 305 q^{30} + 348 q^{31} + 2 q^{32} - 44 q^{33} - 197 q^{34} + 136 q^{35} - 153 q^{36} + 333 q^{37} - 110 q^{38} + 142 q^{40} + 198 q^{41} + 317 q^{42} - 252 q^{43} + 66 q^{44} - 303 q^{45} - 345 q^{46} - 561 q^{47} + q^{48} - 431 q^{49} - 958 q^{50} + 375 q^{51} + 343 q^{53} - 803 q^{54} + 66 q^{55} + 888 q^{56} - 797 q^{57} - 753 q^{58} + 541 q^{59} - 669 q^{60} - 801 q^{61} + 50 q^{62} - 895 q^{63} - 214 q^{64} + 143 q^{66} + 863 q^{67} + 221 q^{68} - 238 q^{69} + 184 q^{70} - 781 q^{71} - 711 q^{72} + 1306 q^{73} + 1347 q^{74} - 779 q^{75} - 1160 q^{76} + 187 q^{77} - 278 q^{79} - 874 q^{80} - 596 q^{81} + 1675 q^{82} - 437 q^{83} - 439 q^{84} + 615 q^{85} - 234 q^{86} - 818 q^{87} - 66 q^{88} - 2552 q^{89} + 899 q^{90} - 1391 q^{92} + 876 q^{93} - 415 q^{94} - 940 q^{95} - 3077 q^{96} + 2504 q^{97} + 144 q^{98} - 484 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 6 * q^4 + 6 * q^5 + 13 * q^6 + 17 * q^7 - 6 * q^8 - 44 * q^9 - 82 * q^10 + 44 * q^11 + 17 * q^12 - 40 * q^14 - 9 * q^15 - 142 * q^16 - 41 * q^17 + 75 * q^18 + 41 * q^19 + 174 * q^20 + 179 * q^21 - 136 * q^23 + 171 * q^24 - 162 * q^25 + 11 * q^27 + 56 * q^28 - 207 * q^29 + 305 * q^30 + 348 * q^31 + 2 * q^32 - 44 * q^33 - 197 * q^34 + 136 * q^35 - 153 * q^36 + 333 * q^37 - 110 * q^38 + 142 * q^40 + 198 * q^41 + 317 * q^42 - 252 * q^43 + 66 * q^44 - 303 * q^45 - 345 * q^46 - 561 * q^47 + q^48 - 431 * q^49 - 958 * q^50 + 375 * q^51 + 343 * q^53 - 803 * q^54 + 66 * q^55 + 888 * q^56 - 797 * q^57 - 753 * q^58 + 541 * q^59 - 669 * q^60 - 801 * q^61 + 50 * q^62 - 895 * q^63 - 214 * q^64 + 143 * q^66 + 863 * q^67 + 221 * q^68 - 238 * q^69 + 184 * q^70 - 781 * q^71 - 711 * q^72 + 1306 * q^73 + 1347 * q^74 - 779 * q^75 - 1160 * q^76 + 187 * q^77 - 278 * q^79 - 874 * q^80 - 596 * q^81 + 1675 * q^82 - 437 * q^83 - 439 * q^84 + 615 * q^85 - 234 * q^86 - 818 * q^87 - 66 * q^88 - 2552 * q^89 + 899 * q^90 - 1391 * q^92 + 876 * q^93 - 415 * q^94 - 940 * q^95 - 3077 * q^96 + 2504 * q^97 + 144 * q^98 - 484 * 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 $

$2$	1.90566	0.673754	0.336877	−	0.941549i	$-0.390629\pi$
$2$	1.90566	0.673754	0.336877	+	0.941549i	$0.390629\pi$
$3$	−6.07897	−1.16990	−0.584949	−	0.811070i	$-0.698886\pi$
$3$	−6.07897	−1.16990	−0.584949	+	0.811070i	$0.698886\pi$
$4$	−4.36845	−0.546056
$5$	−8.17977	−0.731621	−0.365811	−	0.930689i	$-0.619208\pi$
$5$	−8.17977	−0.731621	−0.365811	+	0.930689i	$0.619208\pi$
$6$	−11.5845	−0.788224
$7$	−17.8958	−0.966284	−0.483142	−	0.875542i	$-0.660504\pi$
$7$	−17.8958	−0.966284	−0.483142	+	0.875542i	$0.660504\pi$
$8$	−23.5701	−1.04166
$9$	9.95391	0.368663
$10$	−15.5879	−0.492933
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	26.5557	0.638830
$13$	0	0
$13$	0	0
$14$	−34.1034	−0.651037
$15$	49.7246	0.855923
$16$	−9.96909	−0.155767
$17$	−63.0295	−0.899229	−0.449615	−	0.893223i	$-0.648439\pi$
$17$	−63.0295	−0.899229	−0.449615	+	0.893223i	$0.648439\pi$
$18$	18.9688	0.248388
$19$	98.2318	1.18610	0.593051	−	0.805165i	$-0.297923\pi$
$19$	98.2318	1.18610	0.593051	+	0.805165i	$0.297923\pi$
$20$	35.7329	0.399506
$21$	108.788	1.13045
$22$	20.9623	0.203144
$23$	−1.03008	−0.00933857	−0.00466928	−	0.999989i	$-0.501486\pi$
$23$	−1.03008	−0.00933857	−0.00466928	+	0.999989i	$0.501486\pi$
$24$	143.282	1.21864
$25$	−58.0913	−0.464730
$26$	0	0
$27$	103.623	0.738600
$28$	78.1770	0.527645
$29$	−44.6518	−0.285918	−0.142959	−	0.989729i	$-0.545662\pi$
$29$	−44.6518	−0.285918	−0.142959	+	0.989729i	$0.545662\pi$
$30$	94.7584	0.576681
$31$	−112.558	−0.652130	−0.326065	−	0.945347i	$-0.605723\pi$
$31$	−112.558	−0.652130	−0.326065	+	0.945347i	$0.605723\pi$
$32$	169.563	0.936712
$33$	−66.8687	−0.352738
$34$	−120.113	−0.605859
$35$	146.384	0.706954
$36$	−43.4831	−0.201311
$37$	241.182	1.07162	0.535811	−	0.844338i	$-0.320006\pi$
$37$	241.182	1.07162	0.535811	+	0.844338i	$0.320006\pi$
$38$	187.197	0.799140
$39$	0	0
$40$	192.798	0.762101
$41$	404.826	1.54203	0.771015	−	0.636817i	$-0.219749\pi$
$41$	404.826	1.54203	0.771015	+	0.636817i	$0.219749\pi$
$42$	207.314	0.761648
$43$	20.2537	0.0718292	0.0359146	−	0.999355i	$-0.488566\pi$
$43$	20.2537	0.0718292	0.0359146	+	0.999355i	$0.488566\pi$
$44$	−48.0529	−0.164642
$45$	−81.4207	−0.269722
$46$	−1.96299	−0.00629190
$47$	49.8584	0.154736	0.0773681	−	0.997003i	$-0.475348\pi$
$47$	49.8584	0.154736	0.0773681	+	0.997003i	$0.475348\pi$
$48$	60.6018	0.182232
$49$	−22.7394	−0.0662958
$50$	−110.702	−0.313114
$51$	383.155	1.05201
$52$	0	0
$53$	158.607	0.411062	0.205531	−	0.978651i	$-0.434108\pi$
$53$	158.607	0.411062	0.205531	+	0.978651i	$0.434108\pi$
$54$	197.470	0.497635
$55$	−89.9775	−0.220592
$56$	421.806	1.00654
$57$	−597.148	−1.38762
$58$	−85.0913	−0.192638
$59$	503.222	1.11040	0.555202	−	0.831715i	$-0.312641\pi$
$59$	503.222	1.11040	0.555202	+	0.831715i	$0.312641\pi$
$60$	−217.219	−0.467382
$61$	−10.6787	−0.0224143	−0.0112071	−	0.999937i	$-0.503567\pi$
$61$	−10.6787	−0.0224143	−0.0112071	+	0.999937i	$0.503567\pi$
$62$	−214.498	−0.439375
$63$	−178.133	−0.356233
$64$	402.883	0.786880
$65$	0	0
$66$	−127.429	−0.237658
$67$	584.100	1.06506	0.532531	−	0.846411i	$-0.321241\pi$
$67$	584.100	1.06506	0.532531	+	0.846411i	$0.321241\pi$
$68$	275.341	0.491030
$69$	6.26184	0.0109252
$70$	278.958	0.476313
$71$	−382.259	−0.638955	−0.319477	−	0.947594i	$-0.603507\pi$
$71$	−382.259	−0.638955	−0.319477	+	0.947594i	$0.603507\pi$
$72$	−234.615	−0.384022
$73$	855.289	1.37129	0.685644	−	0.727937i	$-0.259521\pi$
$73$	855.289	1.37129	0.685644	+	0.727937i	$0.259521\pi$
$74$	459.611	0.722010
$75$	353.135	0.543688
$76$	−429.120	−0.647678
$77$	−196.854	−0.291346
$78$	0	0
$79$	−239.095	−0.340510	−0.170255	−	0.985400i	$-0.554459\pi$
$79$	−239.095	−0.340510	−0.170255	+	0.985400i	$0.554459\pi$
$80$	81.5449	0.113962
$81$	−898.675	−1.23275
$82$	771.462	1.03895
$83$	−1174.35	−1.55303	−0.776515	−	0.630099i	$-0.783014\pi$
$83$	−1174.35	−1.55303	−0.776515	+	0.630099i	$0.783014\pi$
$84$	−475.236	−0.617291
$85$	515.567	0.657895
$86$	38.5967	0.0483952
$87$	271.437	0.334495
$88$	−259.271	−0.314073
$89$	−1304.02	−1.55310	−0.776550	−	0.630055i	$-0.783032\pi$
$89$	−1304.02	−1.55310	−0.776550	+	0.630055i	$0.783032\pi$
$90$	−155.160	−0.181726
$91$	0	0
$92$	4.49986	0.00509938
$93$	684.237	0.762926
$94$	95.0134	0.104254
$95$	−803.514	−0.867777
$96$	−1030.77	−1.09586
$97$	1318.09	1.37971	0.689856	−	0.723947i	$-0.257674\pi$
$97$	1318.09	1.37971	0.689856	+	0.723947i	$0.257674\pi$
$98$	−43.3337	−0.0446670
$99$	109.493	0.111156
$100$	253.769	0.253769
$101$	−343.633	−0.338542	−0.169271	−	0.985570i	$-0.554141\pi$
$101$	−343.633	−0.338542	−0.169271	+	0.985570i	$0.554141\pi$
$102$	730.164	0.708794
$103$	−1339.84	−1.28173	−0.640867	−	0.767652i	$-0.721425\pi$
$103$	−1339.84	−1.28173	−0.640867	+	0.767652i	$0.721425\pi$
$104$	0	0
$105$	−889.863	−0.827064
$106$	302.251	0.276955
$107$	−468.216	−0.423029	−0.211515	−	0.977375i	$-0.567840\pi$
$107$	−468.216	−0.423029	−0.211515	+	0.977375i	$0.567840\pi$
$108$	−452.670	−0.403317
$109$	608.385	0.534612	0.267306	−	0.963612i	$-0.413867\pi$
$109$	608.385	0.534612	0.267306	+	0.963612i	$0.413867\pi$
$110$	−171.467	−0.148625
$111$	−1466.14	−1.25369
$112$	178.405	0.150515
$113$	655.151	0.545411	0.272705	−	0.962098i	$-0.412082\pi$
$113$	655.151	0.545411	0.272705	+	0.962098i	$0.412082\pi$
$114$	−1137.96	−0.934913
$115$	8.42584	0.00683229
$116$	195.059	0.156127
$117$	0	0
$118$	958.971	0.748139
$119$	1127.97	0.868911
$120$	−1172.01	−0.891581
$121$	121.000	0.0909091
$122$	−20.3500	−0.0151017
$123$	−2460.93	−1.80402
$124$	491.704	0.356099
$125$	1497.65	1.07163
$126$	−339.462	−0.240014
$127$	−2187.23	−1.52823	−0.764115	−	0.645080i	$-0.776824\pi$
$127$	−2187.23	−1.52823	−0.764115	+	0.645080i	$0.776824\pi$
$128$	−588.745	−0.406549
$129$	−123.121	−0.0840328
$130$	0	0
$131$	1780.78	1.18769	0.593846	−	0.804579i	$-0.297609\pi$
$131$	1780.78	1.18769	0.593846	+	0.804579i	$0.297609\pi$
$132$	292.112	0.192615
$133$	−1757.94	−1.14611
$134$	1113.10	0.717589
$135$	−847.610	−0.540376
$136$	1485.61	0.936692
$137$	1428.10	0.890591	0.445295	−	0.895384i	$-0.353099\pi$
$137$	1428.10	0.890591	0.445295	+	0.895384i	$0.353099\pi$
$138$	11.9330	0.00736088
$139$	194.903	0.118931	0.0594657	−	0.998230i	$-0.481060\pi$
$139$	194.903	0.118931	0.0594657	+	0.998230i	$0.481060\pi$
$140$	−639.470	−0.386036
$141$	−303.088	−0.181026
$142$	−728.457	−0.430498
$143$	0	0
$144$	−99.2314	−0.0574256
$145$	365.242	0.209184
$146$	1629.89	0.923911
$147$	138.232	0.0775593
$148$	−1053.59	−0.585166
$149$	108.973	0.0599153	0.0299577	−	0.999551i	$-0.490463\pi$
$149$	108.973	0.0599153	0.0299577	+	0.999551i	$0.490463\pi$
$150$	672.957	0.366312
$151$	−3080.51	−1.66019	−0.830093	−	0.557625i	$-0.811713\pi$
$151$	−3080.51	−1.66019	−0.830093	+	0.557625i	$0.811713\pi$
$152$	−2315.33	−1.23552
$153$	−627.390	−0.331513
$154$	−375.138	−0.196295
$155$	920.699	0.477112
$156$	0	0
$157$	−2482.97	−1.26218	−0.631091	−	0.775709i	$-0.717393\pi$
$157$	−2482.97	−1.26218	−0.631091	+	0.775709i	$0.717393\pi$
$158$	−455.635	−0.229420
$159$	−964.165	−0.480901
$160$	−1386.99	−0.685319
$161$	18.4342	0.00902371
$162$	−1712.57	−0.830570
$163$	−2199.24	−1.05680	−0.528399	−	0.848996i	$-0.677207\pi$
$163$	−2199.24	−1.05680	−0.528399	+	0.848996i	$0.677207\pi$
$164$	−1768.46	−0.842034
$165$	546.971	0.258070
$166$	−2237.91	−1.04636
$167$	−3336.22	−1.54589	−0.772947	−	0.634471i	$-0.781218\pi$
$167$	−3336.22	−1.54589	−0.772947	+	0.634471i	$0.781218\pi$
$168$	−2564.15	−1.17755
$169$	0	0
$170$	982.497	0.443259
$171$	977.790	0.437272
$172$	−88.4770	−0.0392227
$173$	3710.65	1.63072	0.815362	−	0.578951i	$-0.196538\pi$
$173$	3710.65	1.63072	0.815362	+	0.578951i	$0.196538\pi$
$174$	517.268	0.225368
$175$	1039.59	0.449061
$176$	−109.660	−0.0469655
$177$	−3059.07	−1.29906
$178$	−2485.03	−1.04641
$179$	1076.45	0.449486	0.224743	−	0.974418i	$-0.427846\pi$
$179$	1076.45	0.449486	0.224743	+	0.974418i	$0.427846\pi$
$180$	355.682	0.147283
$181$	−43.5599	−0.0178883	−0.00894415	−	0.999960i	$-0.502847\pi$
$181$	−43.5599	−0.0178883	−0.00894415	+	0.999960i	$0.502847\pi$
$182$	0	0
$183$	64.9156	0.0262224
$184$	24.2791	0.00972762
$185$	−1972.81	−0.784022
$186$	1303.93	0.514024
$187$	−693.325	−0.271128
$188$	−217.804	−0.0844946
$189$	−1854.41	−0.713697
$190$	−1531.23	−0.584668
$191$	2424.96	0.918659	0.459329	−	0.888266i	$-0.348090\pi$
$191$	2424.96	0.918659	0.459329	+	0.888266i	$0.348090\pi$
$192$	−2449.11	−0.920571
$193$	567.924	0.211814	0.105907	−	0.994376i	$-0.466225\pi$
$193$	567.924	0.211814	0.105907	+	0.994376i	$0.466225\pi$
$194$	2511.84	0.929586
$195$	0	0
$196$	99.3361	0.0362012
$197$	375.227	0.135704	0.0678522	−	0.997695i	$-0.478385\pi$
$197$	375.227	0.135704	0.0678522	+	0.997695i	$0.478385\pi$
$198$	208.657	0.0748919
$199$	−433.113	−0.154284	−0.0771421	−	0.997020i	$-0.524580\pi$
$199$	−433.113	−0.154284	−0.0771421	+	0.997020i	$0.524580\pi$
$200$	1369.22	0.484091
$201$	−3550.73	−1.24601
$202$	−654.849	−0.228094
$203$	799.081	0.276278
$204$	−1673.79	−0.574455
$205$	−3311.39	−1.12818
$206$	−2553.29	−0.863573
$207$	−10.2533	−0.00344279
$208$	0	0
$209$	1080.55	0.357623
$210$	−1695.78	−0.557238
$211$	5038.14	1.64379	0.821896	−	0.569637i	$-0.192916\pi$
$211$	5038.14	1.64379	0.821896	+	0.569637i	$0.192916\pi$
$212$	−692.865	−0.224463
$213$	2323.74	0.747513
$214$	−892.262	−0.285018
$215$	−165.670	−0.0525517
$216$	−2442.40	−0.769371
$217$	2014.32	0.630142
$218$	1159.38	0.360197
$219$	−5199.28	−1.60427
$220$	393.062	0.120456
$221$	0	0
$222$	−2793.96	−0.844678
$223$	6296.47	1.89078	0.945388	−	0.325948i	$-0.105683\pi$
$223$	6296.47	1.89078	0.945388	+	0.325948i	$0.105683\pi$
$224$	−3034.47	−0.905130
$225$	−578.235	−0.171329
$226$	1248.50	0.367473
$227$	5319.98	1.55550	0.777752	−	0.628572i	$-0.216360\pi$
$227$	5319.98	1.55550	0.777752	+	0.628572i	$0.216360\pi$
$228$	2608.61	0.757717
$229$	−3151.09	−0.909302	−0.454651	−	0.890670i	$-0.650236\pi$
$229$	−3151.09	−0.909302	−0.454651	+	0.890670i	$0.650236\pi$
$230$	16.0568	0.00460328
$231$	1196.67	0.340845
$232$	1052.45	0.297830
$233$	−3880.07	−1.09095	−0.545475	−	0.838127i	$-0.683651\pi$
$233$	−3880.07	−1.09095	−0.545475	+	0.838127i	$0.683651\pi$
$234$	0	0
$235$	−407.831	−0.113208
$236$	−2198.30	−0.606343
$237$	1453.45	0.398363
$238$	2149.52	0.585432
$239$	−982.401	−0.265884	−0.132942	−	0.991124i	$-0.542442\pi$
$239$	−982.401	−0.265884	−0.132942	+	0.991124i	$0.542442\pi$
$240$	−495.709	−0.133325
$241$	−2038.57	−0.544879	−0.272440	−	0.962173i	$-0.587830\pi$
$241$	−2038.57	−0.544879	−0.272440	+	0.962173i	$0.587830\pi$
$242$	230.585	0.0612503
$243$	2665.21	0.703593
$244$	46.6494	0.0122394
$245$	186.004	0.0485034
$246$	−4689.70	−1.21546
$247$	0	0
$248$	2653.00	0.679298
$249$	7138.83	1.81689
$250$	2854.01	0.722013
$251$	1729.17	0.434837	0.217419	−	0.976078i	$-0.430236\pi$
$251$	1729.17	0.434837	0.217419	+	0.976078i	$0.430236\pi$
$252$	778.166	0.194523
$253$	−11.3309	−0.00281568
$254$	−4168.12	−1.02965
$255$	−3134.12	−0.769671
$256$	−4345.01	−1.06079
$257$	3014.48	0.731666	0.365833	−	0.930680i	$-0.380784\pi$
$257$	3014.48	0.731666	0.365833	+	0.930680i	$0.380784\pi$
$258$	−234.628	−0.0566174
$259$	−4316.15	−1.03549
$260$	0	0
$261$	−444.460	−0.105408
$262$	3393.57	0.800212
$263$	−3244.21	−0.760633	−0.380316	−	0.924856i	$-0.624185\pi$
$263$	−3244.21	−0.760633	−0.380316	+	0.924856i	$0.624185\pi$
$264$	1576.10	0.367433
$265$	−1297.37	−0.300742
$266$	−3350.04	−0.772196
$267$	7927.11	1.81697
$268$	−2551.61	−0.581583
$269$	−5058.83	−1.14663	−0.573313	−	0.819336i	$-0.694342\pi$
$269$	−5058.83	−1.14663	−0.573313	+	0.819336i	$0.694342\pi$
$270$	−1615.26	−0.364080
$271$	492.449	0.110384	0.0551921	−	0.998476i	$-0.482423\pi$
$271$	492.449	0.110384	0.0551921	+	0.998476i	$0.482423\pi$
$272$	628.347	0.140070
$273$	0	0
$274$	2721.48	0.600039
$275$	−639.004	−0.140121
$276$	−27.3545	−0.00596576
$277$	4933.09	1.07004	0.535019	−	0.844840i	$-0.320305\pi$
$277$	4933.09	1.07004	0.535019	+	0.844840i	$0.320305\pi$
$278$	371.420	0.0801305
$279$	−1120.39	−0.240416
$280$	−3450.28	−0.736406
$281$	−2355.72	−0.500109	−0.250055	−	0.968232i	$-0.580449\pi$
$281$	−2355.72	−0.500109	−0.250055	+	0.968232i	$0.580449\pi$
$282$	−577.584	−0.121967
$283$	7298.80	1.53310	0.766552	−	0.642182i	$-0.221971\pi$
$283$	7298.80	1.53310	0.766552	+	0.642182i	$0.221971\pi$
$284$	1669.88	0.348905
$285$	4884.54	1.01521
$286$	0	0
$287$	−7244.70	−1.49004
$288$	1687.81	0.345331
$289$	−940.281	−0.191386
$290$	696.027	0.140938
$291$	−8012.65	−1.61412
$292$	−3736.29	−0.748800
$293$	4500.05	0.897255	0.448628	−	0.893719i	$-0.351913\pi$
$293$	4500.05	0.897255	0.448628	+	0.893719i	$0.351913\pi$
$294$	263.425	0.0522559
$295$	−4116.24	−0.812396
$296$	−5684.68	−1.11627
$297$	1139.85	0.222696
$298$	207.665	0.0403682
$299$	0	0
$300$	−1542.65	−0.296884
$301$	−362.456	−0.0694073
$302$	−5870.41	−1.11856
$303$	2088.94	0.396060
$304$	−979.282	−0.184755
$305$	87.3495	0.0163987
$306$	−1195.59	−0.223358
$307$	−5508.96	−1.02415	−0.512074	−	0.858942i	$-0.671122\pi$
$307$	−5508.96	−1.02415	−0.512074	+	0.858942i	$0.671122\pi$
$308$	859.947	0.159091
$309$	8144.86	1.49950
$310$	1754.54	0.321456
$311$	−8167.75	−1.48923	−0.744615	−	0.667494i	$-0.767367\pi$
$311$	−8167.75	−1.48923	−0.744615	+	0.667494i	$0.767367\pi$
$312$	0	0
$313$	−9337.31	−1.68619	−0.843093	−	0.537768i	$-0.819268\pi$
$313$	−9337.31	−1.68619	−0.843093	+	0.537768i	$0.819268\pi$
$314$	−4731.70	−0.850400
$315$	1457.09	0.260628
$316$	1044.48	0.185938
$317$	4742.42	0.840255	0.420127	−	0.907465i	$-0.361985\pi$
$317$	4742.42	0.840255	0.420127	+	0.907465i	$0.361985\pi$
$318$	−1837.37	−0.324009
$319$	−491.170	−0.0862076
$320$	−3295.49	−0.575698
$321$	2846.27	0.494902
$322$	35.1293	0.00607976
$323$	−6191.50	−1.06658
$324$	3925.82	0.673151
$325$	0	0
$326$	−4191.01	−0.712021
$327$	−3698.35	−0.625442
$328$	−9541.79	−1.60627
$329$	−892.258	−0.149519
$330$	1042.34	0.173876
$331$	7291.81	1.21086	0.605429	−	0.795899i	$-0.293002\pi$
$331$	7291.81	1.21086	0.605429	+	0.795899i	$0.293002\pi$
$332$	5130.08	0.848041
$333$	2400.70	0.395068
$334$	−6357.70	−1.04155
$335$	−4777.80	−0.779222
$336$	−1084.52	−0.176087
$337$	1874.32	0.302970	0.151485	−	0.988460i	$-0.451595\pi$
$337$	1874.32	0.302970	0.151485	+	0.988460i	$0.451595\pi$
$338$	0	0
$339$	−3982.64	−0.638075
$340$	−2252.23	−0.359248
$341$	−1238.14	−0.196624
$342$	1863.34	0.294614
$343$	6545.21	1.03034
$344$	−477.381	−0.0748216
$345$	−51.2205	−0.00799309
$346$	7071.24	1.09871
$347$	8098.35	1.25286	0.626430	−	0.779478i	$-0.284515\pi$
$347$	8098.35	1.25286	0.626430	+	0.779478i	$0.284515\pi$
$348$	−1185.76	−0.182653
$349$	3019.17	0.463073	0.231536	−	0.972826i	$-0.425625\pi$
$349$	3019.17	0.463073	0.231536	+	0.972826i	$0.425625\pi$
$350$	1981.11	0.302557
$351$	0	0
$352$	1865.19	0.282429
$353$	−1824.97	−0.275165	−0.137582	−	0.990490i	$-0.543933\pi$
$353$	−1824.97	−0.275165	−0.137582	+	0.990490i	$0.543933\pi$
$354$	−5829.56	−0.875247
$355$	3126.79	0.467473
$356$	5696.55	0.848080
$357$	−6856.87	−1.01654
$358$	2051.36	0.302843
$359$	8234.36	1.21057	0.605283	−	0.796011i	$-0.293060\pi$
$359$	8234.36	1.21057	0.605283	+	0.796011i	$0.293060\pi$
$360$	1919.09	0.280959
$361$	2790.49	0.406836
$362$	−83.0105	−0.0120523
$363$	−735.556	−0.106354
$364$	0	0
$365$	−6996.07	−1.00326
$366$	123.707	0.0176675
$367$	−3466.69	−0.493079	−0.246539	−	0.969133i	$-0.579293\pi$
$367$	−3466.69	−0.493079	−0.246539	+	0.969133i	$0.579293\pi$
$368$	10.2690	0.00145464
$369$	4029.60	0.568490
$370$	−3759.52	−0.528238
$371$	−2838.40	−0.397203
$372$	−2989.05	−0.416600
$373$	−7862.05	−1.09137	−0.545686	−	0.837990i	$-0.683731\pi$
$373$	−7862.05	−1.09137	−0.545686	+	0.837990i	$0.683731\pi$
$374$	−1321.24	−0.182673
$375$	−9104.15	−1.25370
$376$	−1175.17	−0.161183
$377$	0	0
$378$	−3533.89	−0.480856
$379$	2683.26	0.363667	0.181833	−	0.983329i	$-0.441797\pi$
$379$	2683.26	0.363667	0.181833	+	0.983329i	$0.441797\pi$
$380$	3510.11	0.473855
$381$	13296.1	1.78787
$382$	4621.15	0.618950
$383$	−9051.88	−1.20765	−0.603824	−	0.797117i	$-0.706357\pi$
$383$	−9051.88	−1.20765	−0.603824	+	0.797117i	$0.706357\pi$
$384$	3578.97	0.475621
$385$	1610.22	0.213155
$386$	1082.27	0.142710
$387$	201.603	0.0264808
$388$	−5758.02	−0.753400
$389$	4894.15	0.637901	0.318950	−	0.947771i	$-0.396670\pi$
$389$	4894.15	0.637901	0.318950	+	0.947771i	$0.396670\pi$
$390$	0	0
$391$	64.9256	0.00839752
$392$	535.971	0.0690577
$393$	−10825.3	−1.38948
$394$	715.055	0.0914314
$395$	1955.75	0.249125
$396$	−478.314	−0.0606975
$397$	−12303.9	−1.55545	−0.777724	−	0.628606i	$-0.783626\pi$
$397$	−12303.9	−1.55545	−0.777724	+	0.628606i	$0.783626\pi$
$398$	−825.367	−0.103950
$399$	10686.5	1.34083
$400$	579.117	0.0723897
$401$	−14161.8	−1.76361	−0.881807	−	0.471611i	$-0.843673\pi$
$401$	−14161.8	−1.76361	−0.881807	+	0.471611i	$0.843673\pi$
$402$	−6766.49	−0.839507
$403$	0	0
$404$	1501.14	0.184863
$405$	7350.96	0.901907
$406$	1522.78	0.186143
$407$	2653.00	0.323106
$408$	−9030.99	−1.09584
$409$	1881.80	0.227504	0.113752	−	0.993509i	$-0.463713\pi$
$409$	1881.80	0.227504	0.113752	+	0.993509i	$0.463713\pi$
$410$	−6310.39	−0.760117
$411$	−8681.39	−1.04190
$412$	5853.03	0.699898
$413$	−9005.57	−1.07297
$414$	−19.5394	−0.00231959
$415$	9605.90	1.13623
$416$	0	0
$417$	−1184.81	−0.139138
$418$	2059.16	0.240950
$419$	13660.8	1.59277	0.796387	−	0.604788i	$-0.206742\pi$
$419$	13660.8	1.59277	0.796387	+	0.604788i	$0.206742\pi$
$420$	3887.32	0.451623
$421$	−6429.60	−0.744322	−0.372161	−	0.928168i	$-0.621383\pi$
$421$	−6429.60	−0.744322	−0.372161	+	0.928168i	$0.621383\pi$
$422$	9601.01	1.10751
$423$	496.286	0.0570456
$424$	−3738.37	−0.428187
$425$	3661.47	0.417899
$426$	4428.27	0.503639
$427$	191.104	0.0216585
$428$	2045.38	0.230998
$429$	0	0
$430$	−315.712	−0.0354069
$431$	−13024.6	−1.45562	−0.727810	−	0.685779i	$-0.759462\pi$
$431$	−13024.6	−1.45562	−0.727810	+	0.685779i	$0.759462\pi$
$432$	−1033.02	−0.115050
$433$	12477.5	1.38482	0.692412	−	0.721503i	$-0.256548\pi$
$433$	12477.5	1.38482	0.692412	+	0.721503i	$0.256548\pi$
$434$	3838.61	0.424561
$435$	−2220.29	−0.244724
$436$	−2657.70	−0.291928
$437$	−101.187	−0.0110765
$438$	−9908.08	−1.08088
$439$	−11630.3	−1.26442	−0.632211	−	0.774796i	$-0.717853\pi$
$439$	−11630.3	−1.26442	−0.632211	+	0.774796i	$0.717853\pi$
$440$	2120.78	0.229782
$441$	−226.346	−0.0244408
$442$	0	0
$443$	−5078.52	−0.544668	−0.272334	−	0.962203i	$-0.587796\pi$
$443$	−5078.52	−0.544668	−0.272334	+	0.962203i	$0.587796\pi$
$444$	6404.74	0.684585
$445$	10666.6	1.13628
$446$	11999.0	1.27392
$447$	−662.442	−0.0700949
$448$	−7209.92	−0.760350
$449$	−4836.02	−0.508298	−0.254149	−	0.967165i	$-0.581795\pi$
$449$	−4836.02	−0.508298	−0.254149	+	0.967165i	$0.581795\pi$
$450$	−1101.92	−0.115434
$451$	4453.09	0.464939
$452$	−2861.99	−0.297825
$453$	18726.3	1.94225
$454$	10138.1	1.04803
$455$	0	0
$456$	14074.8	1.44543
$457$	6271.68	0.641962	0.320981	−	0.947086i	$-0.395987\pi$
$457$	6271.68	0.641962	0.320981	+	0.947086i	$0.395987\pi$
$458$	−6004.92	−0.612645
$459$	−6531.29	−0.664171
$460$	−36.8078	−0.00373081
$461$	16911.2	1.70854	0.854268	−	0.519833i	$-0.174006\pi$
$461$	16911.2	1.70854	0.854268	+	0.519833i	$0.174006\pi$
$462$	2280.45	0.229645
$463$	14840.3	1.48961	0.744803	−	0.667285i	$-0.232544\pi$
$463$	14840.3	1.48961	0.744803	+	0.667285i	$0.232544\pi$
$464$	445.138	0.0445366
$465$	−5596.91	−0.558173
$466$	−7394.10	−0.735032
$467$	9041.77	0.895938	0.447969	−	0.894049i	$-0.352147\pi$
$467$	9041.77	0.895938	0.447969	+	0.894049i	$0.352147\pi$
$468$	0	0
$469$	−10452.9	−1.02915
$470$	−777.188	−0.0762745
$471$	15093.9	1.47663
$472$	−11861.0	−1.15667
$473$	222.790	0.0216573
$474$	2769.79	0.268398
$475$	−5706.41	−0.551217
$476$	−4927.46	−0.474474
$477$	1578.76	0.151543
$478$	−1872.13	−0.179140
$479$	−6443.06	−0.614595	−0.307297	−	0.951614i	$-0.599425\pi$
$479$	−6443.06	−0.614595	−0.307297	+	0.951614i	$0.599425\pi$
$480$	8431.46	0.801753
$481$	0	0
$482$	−3884.83	−0.367114
$483$	−112.061	−0.0105568
$484$	−528.582	−0.0496414
$485$	−10781.7	−1.00943
$486$	5078.99	0.474049
$487$	7030.37	0.654161	0.327081	−	0.944996i	$-0.393935\pi$
$487$	7030.37	0.654161	0.327081	+	0.944996i	$0.393935\pi$
$488$	251.698	0.0233481
$489$	13369.1	1.23635
$490$	354.460	0.0326793
$491$	−10723.3	−0.985612	−0.492806	−	0.870139i	$-0.664029\pi$
$491$	−10723.3	−0.985612	−0.492806	+	0.870139i	$0.664029\pi$
$492$	10750.4	0.985095
$493$	2814.38	0.257106
$494$	0	0
$495$	−895.628	−0.0813242
$496$	1122.10	0.101580
$497$	6840.84	0.617412
$498$	13604.2	1.22413
$499$	14132.5	1.26785	0.633924	−	0.773396i	$-0.281443\pi$
$499$	14132.5	1.26785	0.633924	+	0.773396i	$0.281443\pi$
$500$	−6542.39	−0.585169
$501$	20280.8	1.80854
$502$	3295.21	0.292973
$503$	−510.757	−0.0452754	−0.0226377	−	0.999744i	$-0.507206\pi$
$503$	−510.757	−0.0452754	−0.0226377	+	0.999744i	$0.507206\pi$
$504$	4198.62	0.371074
$505$	2810.84	0.247685
$506$	−21.5929	−0.00189708
$507$	0	0
$508$	9554.79	0.834499
$509$	−414.759	−0.0361176	−0.0180588	−	0.999837i	$-0.505749\pi$
$509$	−414.759	−0.0361176	−0.0180588	+	0.999837i	$0.505749\pi$
$510$	−5972.57	−0.518569
$511$	−15306.1	−1.32505
$512$	−3570.17	−0.308165
$513$	10179.0	0.876054
$514$	5744.59	0.492963
$515$	10959.6	0.937743
$516$	537.849	0.0458866
$517$	548.443	0.0466547
$518$	−8225.12	−0.697666
$519$	−22556.9	−1.90778
$520$	0	0
$521$	−842.000	−0.0708036	−0.0354018	−	0.999373i	$-0.511271\pi$
$521$	−842.000	−0.0708036	−0.0354018	+	0.999373i	$0.511271\pi$
$522$	−846.991	−0.0710187
$523$	17885.7	1.49539	0.747694	−	0.664044i	$-0.231161\pi$
$523$	17885.7	1.49539	0.747694	+	0.664044i	$0.231161\pi$
$524$	−7779.25	−0.648546
$525$	−6319.65	−0.525356
$526$	−6182.37	−0.512479
$527$	7094.48	0.586414
$528$	666.620	0.0549449
$529$	−12165.9	−0.999913
$530$	−2472.34	−0.202626
$531$	5009.02	0.409365
$532$	7679.46	0.625840
$533$	0	0
$534$	15106.4	1.22419
$535$	3829.90	0.309497
$536$	−13767.3	−1.10943
$537$	−6543.74	−0.525853
$538$	−9640.43	−0.772543
$539$	−250.134	−0.0199889
$540$	3702.74	0.295075
$541$	−21676.2	−1.72261	−0.861307	−	0.508085i	$-0.830354\pi$
$541$	−21676.2	−1.72261	−0.861307	+	0.508085i	$0.830354\pi$
$542$	938.442	0.0743718
$543$	264.799	0.0209275
$544$	−10687.5	−0.842319
$545$	−4976.45	−0.391133
$546$	0	0
$547$	8965.81	0.700823	0.350411	−	0.936596i	$-0.386042\pi$
$547$	8965.81	0.700823	0.350411	+	0.936596i	$0.386042\pi$
$548$	−6238.59	−0.486312
$549$	−106.295	−0.00826331
$550$	−1217.73	−0.0944074
$551$	−4386.23	−0.339128
$552$	−147.592	−0.0113803
$553$	4278.81	0.329030
$554$	9400.80	0.720942
$555$	11992.7	0.917226
$556$	−851.424	−0.0649432
$557$	7114.16	0.541179	0.270590	−	0.962695i	$-0.412781\pi$
$557$	7114.16	0.541179	0.270590	+	0.962695i	$0.412781\pi$
$558$	−2135.09	−0.161981
$559$	0	0
$560$	−1459.31	−0.110120
$561$	4214.70	0.317192
$562$	−4489.22	−0.336950
$563$	−1274.40	−0.0953989	−0.0476994	−	0.998862i	$-0.515189\pi$
$563$	−1274.40	−0.0953989	−0.0476994	+	0.998862i	$0.515189\pi$
$564$	1324.02	0.0988502
$565$	−5358.99	−0.399034
$566$	13909.1	1.03293
$567$	16082.5	1.19119
$568$	9009.88	0.665574
$569$	−21642.0	−1.59452	−0.797258	−	0.603639i	$-0.793717\pi$
$569$	−21642.0	−1.59452	−0.797258	+	0.603639i	$0.793717\pi$
$570$	9308.29	0.684002
$571$	10297.2	0.754685	0.377343	−	0.926074i	$-0.376838\pi$
$571$	10297.2	0.754685	0.377343	+	0.926074i	$0.376838\pi$
$572$	0	0
$573$	−14741.3	−1.07474
$574$	−13806.0	−1.00392
$575$	59.8388	0.00433992
$576$	4010.26	0.290094
$577$	−7683.88	−0.554392	−0.277196	−	0.960813i	$-0.589405\pi$
$577$	−7683.88	−0.554392	−0.277196	+	0.960813i	$0.589405\pi$
$578$	−1791.86	−0.128947
$579$	−3452.39	−0.247801
$580$	−1595.54	−0.114226
$581$	21015.9	1.50067
$582$	−15269.4	−1.08752
$583$	1744.67	0.123940
$584$	−20159.3	−1.42842
$585$	0	0
$586$	8575.58	0.604529
$587$	−4302.01	−0.302493	−0.151246	−	0.988496i	$-0.548329\pi$
$587$	−4302.01	−0.302493	−0.151246	+	0.988496i	$0.548329\pi$
$588$	−603.861	−0.0423517
$589$	−11056.8	−0.773492
$590$	−7844.17	−0.547355
$591$	−2280.99	−0.158761
$592$	−2404.36	−0.166923
$593$	−15901.1	−1.10115	−0.550573	−	0.834787i	$-0.685591\pi$
$593$	−15901.1	−1.10115	−0.550573	+	0.834787i	$0.685591\pi$
$594$	2172.17	0.150042
$595$	−9226.50	−0.635714
$596$	−476.041	−0.0327171
$597$	2632.88	0.180497
$598$	0	0
$599$	−34.4945	−0.00235294	−0.00117647	−	0.999999i	$-0.500374\pi$
$599$	−34.4945	−0.00235294	−0.00117647	+	0.999999i	$0.500374\pi$
$600$	−8323.44	−0.566338
$601$	24633.6	1.67193	0.835963	−	0.548786i	$-0.184910\pi$
$601$	24633.6	1.67193	0.835963	+	0.548786i	$0.184910\pi$
$602$	−690.719	−0.0467635
$603$	5814.08	0.392649
$604$	13457.0	0.906554
$605$	−989.753	−0.0665110
$606$	3980.81	0.266847
$607$	6643.27	0.444221	0.222110	−	0.975022i	$-0.428705\pi$
$607$	6643.27	0.444221	0.222110	+	0.975022i	$0.428705\pi$
$608$	16656.5	1.11104
$609$	−4857.59	−0.323218
$610$	166.459	0.0110487
$611$	0	0
$612$	2740.72	0.181025
$613$	5204.50	0.342916	0.171458	−	0.985191i	$-0.445152\pi$
$613$	5204.50	0.342916	0.171458	+	0.985191i	$0.445152\pi$
$614$	−10498.2	−0.690023
$615$	20129.8	1.31986
$616$	4639.87	0.303483
$617$	28450.1	1.85633	0.928167	−	0.372163i	$-0.121384\pi$
$617$	28450.1	1.85633	0.928167	+	0.372163i	$0.121384\pi$
$618$	15521.4	1.01029
$619$	8558.14	0.555704	0.277852	−	0.960624i	$-0.410378\pi$
$619$	8558.14	0.555704	0.277852	+	0.960624i	$0.410378\pi$
$620$	−4022.03	−0.260530
$621$	−106.740	−0.00689747
$622$	−15565.0	−1.00337
$623$	23336.5	1.50074
$624$	0	0
$625$	−4988.99	−0.319295
$626$	−17793.8	−1.13607
$627$	−6568.63	−0.418383
$628$	10846.7	0.689222
$629$	−15201.6	−0.963635
$630$	2776.72	0.175599
$631$	3685.17	0.232495	0.116247	−	0.993220i	$-0.462913\pi$
$631$	3685.17	0.232495	0.116247	+	0.993220i	$0.462913\pi$
$632$	5635.50	0.354696
$633$	−30626.7	−1.92307
$634$	9037.45	0.566125
$635$	17891.0	1.11809
$636$	4211.90	0.262599
$637$	0	0
$638$	−936.004	−0.0580827
$639$	−3804.97	−0.235559
$640$	4815.80	0.297440
$641$	−9088.70	−0.560034	−0.280017	−	0.959995i	$-0.590340\pi$
$641$	−9088.70	−0.560034	−0.280017	+	0.959995i	$0.590340\pi$
$642$	5424.04	0.333442
$643$	−1140.66	−0.0699583	−0.0349791	−	0.999388i	$-0.511136\pi$
$643$	−1140.66	−0.0699583	−0.0349791	+	0.999388i	$0.511136\pi$
$644$	−80.5287	−0.00492745
$645$	1007.11	0.0614802
$646$	−11798.9	−0.718610
$647$	26897.5	1.63439	0.817194	−	0.576363i	$-0.195529\pi$
$647$	26897.5	1.63439	0.817194	+	0.576363i	$0.195529\pi$
$648$	21181.9	1.28411
$649$	5535.44	0.334800
$650$	0	0
$651$	−12245.0	−0.737203
$652$	9607.27	0.577070
$653$	26384.2	1.58116	0.790578	−	0.612361i	$-0.209780\pi$
$653$	26384.2	1.58116	0.790578	+	0.612361i	$0.209780\pi$
$654$	−7047.82	−0.421394
$655$	−14566.4	−0.868940
$656$	−4035.75	−0.240197
$657$	8513.47	0.505544
$658$	−1700.34	−0.100739
$659$	−2309.69	−0.136529	−0.0682645	−	0.997667i	$-0.521746\pi$
$659$	−2309.69	−0.136529	−0.0682645	+	0.997667i	$0.521746\pi$
$660$	−2389.41	−0.140921
$661$	−4616.62	−0.271658	−0.135829	−	0.990732i	$-0.543370\pi$
$661$	−4616.62	−0.271658	−0.135829	+	0.990732i	$0.543370\pi$
$662$	13895.7	0.815820
$663$	0	0
$664$	27679.5	1.61773
$665$	14379.5	0.838519
$666$	4574.93	0.266178
$667$	45.9950	0.00267007
$668$	14574.1	0.844144
$669$	−38276.1	−2.21202
$670$	−9104.89	−0.525004
$671$	−117.466	−0.00675815
$672$	18446.5	1.05891
$673$	−22090.3	−1.26526	−0.632629	−	0.774455i	$-0.718024\pi$
$673$	−22090.3	−1.26526	−0.632629	+	0.774455i	$0.718024\pi$
$674$	3571.83	0.204127
$675$	−6019.58	−0.343250
$676$	0	0
$677$	9502.09	0.539432	0.269716	−	0.962940i	$-0.413070\pi$
$677$	9502.09	0.539432	0.269716	+	0.962940i	$0.413070\pi$
$678$	−7589.58	−0.429906
$679$	−23588.4	−1.33319
$680$	−12152.0	−0.685304
$681$	−32340.0	−1.81978
$682$	−2359.47	−0.132476
$683$	−7260.63	−0.406764	−0.203382	−	0.979099i	$-0.565193\pi$
$683$	−7260.63	−0.406764	−0.203382	+	0.979099i	$0.565193\pi$
$684$	−4271.43	−0.238775
$685$	−11681.5	−0.651575
$686$	12473.0	0.694198
$687$	19155.4	1.06379
$688$	−201.911	−0.0111886
$689$	0	0
$690$	−97.6090	−0.00538538
$691$	7896.26	0.434715	0.217357	−	0.976092i	$-0.430256\pi$
$691$	7896.26	0.434715	0.217357	+	0.976092i	$0.430256\pi$
$692$	−16209.8	−0.890467
$693$	−1959.47	−0.107408
$694$	15432.7	0.844119
$695$	−1594.26	−0.0870128
$696$	−6397.80	−0.348431
$697$	−25516.0	−1.38664
$698$	5753.52	0.311997
$699$	23586.8	1.27630
$700$	−4541.40	−0.245213
$701$	830.884	0.0447675	0.0223838	−	0.999749i	$-0.492874\pi$
$701$	830.884	0.0447675	0.0223838	+	0.999749i	$0.492874\pi$
$702$	0	0
$703$	23691.7	1.27105
$704$	4431.71	0.237253
$705$	2479.19	0.132442
$706$	−3477.77	−0.185393
$707$	6149.60	0.327128
$708$	13363.4	0.709360
$709$	1716.43	0.0909197	0.0454598	−	0.998966i	$-0.485525\pi$
$709$	1716.43	0.0909197	0.0454598	+	0.998966i	$0.485525\pi$
$710$	5958.61	0.314962
$711$	−2379.93	−0.125534
$712$	30735.9	1.61780
$713$	115.944	0.00608996
$714$	−13066.9	−0.684896
$715$	0	0
$716$	−4702.44	−0.245445
$717$	5971.99	0.311057
$718$	15691.9	0.815623
$719$	−26896.3	−1.39508	−0.697541	−	0.716545i	$-0.745722\pi$
$719$	−26896.3	−1.39508	−0.697541	+	0.716545i	$0.745722\pi$
$720$	811.690	0.0420138
$721$	23977.6	1.23852
$722$	5317.73	0.274107
$723$	12392.4	0.637454
$724$	190.289	0.00976801
$725$	2593.88	0.132875
$726$	−1401.72	−0.0716567
$727$	−27454.0	−1.40057	−0.700283	−	0.713865i	$-0.746943\pi$
$727$	−27454.0	−1.40057	−0.700283	+	0.713865i	$0.746943\pi$
$728$	0	0
$729$	8062.50	0.409618
$730$	−13332.2	−0.675953
$731$	−1276.58	−0.0645909
$732$	−283.581	−0.0143189
$733$	−29826.9	−1.50298	−0.751489	−	0.659746i	$-0.770664\pi$
$733$	−29826.9	−1.50298	−0.751489	+	0.659746i	$0.770664\pi$
$734$	−6606.35	−0.332214
$735$	−1130.71	−0.0567441
$736$	−174.664	−0.00874755
$737$	6425.10	0.321128
$738$	7679.06	0.383022
$739$	−1442.27	−0.0717925	−0.0358963	−	0.999356i	$-0.511429\pi$
$739$	−1442.27	−0.0717925	−0.0358963	+	0.999356i	$0.511429\pi$
$740$	8618.13	0.428120
$741$	0	0
$742$	−5409.03	−0.267617
$743$	−15264.5	−0.753699	−0.376850	−	0.926274i	$-0.622993\pi$
$743$	−15264.5	−0.753699	−0.376850	+	0.926274i	$0.622993\pi$
$744$	−16127.5	−0.794710
$745$	−891.371	−0.0438353
$746$	−14982.4	−0.735316
$747$	−11689.3	−0.572545
$748$	3028.75	0.148051
$749$	8379.11	0.408766
$750$	−17349.4	−0.844682
$751$	26481.1	1.28670	0.643348	−	0.765574i	$-0.277545\pi$
$751$	26481.1	1.28670	0.643348	+	0.765574i	$0.277545\pi$
$752$	−497.043	−0.0241028
$753$	−10511.6	−0.508715
$754$	0	0
$755$	25197.8	1.21463
$756$	8100.91	0.389719
$757$	−33036.1	−1.58615	−0.793077	−	0.609122i	$-0.791522\pi$
$757$	−33036.1	−1.58615	−0.793077	+	0.609122i	$0.791522\pi$
$758$	5113.38	0.245022
$759$	68.8803	0.00329407
$760$	18938.9	0.903929
$761$	−23216.1	−1.10589	−0.552947	−	0.833217i	$-0.686497\pi$
$761$	−23216.1	−1.10589	−0.552947	+	0.833217i	$0.686497\pi$
$762$	25337.9	1.20459
$763$	−10887.5	−0.516587
$764$	−10593.3	−0.501639
$765$	5131.91	0.242542
$766$	−17249.8	−0.813658
$767$	0	0
$768$	26413.2	1.24102
$769$	−38370.0	−1.79930	−0.899648	−	0.436617i	$-0.856177\pi$
$769$	−38370.0	−1.79930	−0.899648	+	0.436617i	$0.856177\pi$
$770$	3068.54	0.143614
$771$	−18325.0	−0.855975
$772$	−2480.95	−0.115662
$773$	−33177.4	−1.54374	−0.771869	−	0.635781i	$-0.780678\pi$
$773$	−33177.4	−1.54374	−0.771869	+	0.635781i	$0.780678\pi$
$774$	384.188	0.0178415
$775$	6538.64	0.303064
$776$	−31067.6	−1.43719
$777$	26237.7	1.21142
$778$	9326.60	0.429788
$779$	39766.8	1.82900
$780$	0	0
$781$	−4204.85	−0.192652
$782$	123.726	0.00565786
$783$	−4626.94	−0.211179
$784$	226.692	0.0103267
$785$	20310.1	0.923439
$786$	−20629.4	−0.936167
$787$	236.801	0.0107256	0.00536280	−	0.999986i	$-0.498293\pi$
$787$	236.801	0.0107256	0.00536280	+	0.999986i	$0.498293\pi$
$788$	−1639.16	−0.0741022
$789$	19721.4	0.889863
$790$	3726.99	0.167849
$791$	−11724.5	−0.527022
$792$	−2580.76	−0.115787
$793$	0	0
$794$	−23447.0	−1.04799
$795$	7886.65	0.351837
$796$	1892.03	0.0842478
$797$	−29409.5	−1.30708	−0.653538	−	0.756894i	$-0.726716\pi$
$797$	−29409.5	−1.30708	−0.653538	+	0.756894i	$0.726716\pi$
$798$	20364.8	0.903391
$799$	−3142.55	−0.139143
$800$	−9850.14	−0.435319
$801$	−12980.1	−0.572571
$802$	−26987.7	−1.18824
$803$	9408.18	0.413459
$804$	15511.2	0.680394
$805$	−150.787	−0.00660194
$806$	0	0
$807$	30752.5	1.34144
$808$	8099.46	0.352646
$809$	−5969.71	−0.259436	−0.129718	−	0.991551i	$-0.541407\pi$
$809$	−5969.71	−0.259436	−0.129718	+	0.991551i	$0.541407\pi$
$810$	14008.5	0.607663
$811$	−18152.2	−0.785957	−0.392978	−	0.919548i	$-0.628555\pi$
$811$	−18152.2	−0.785957	−0.392978	+	0.919548i	$0.628555\pi$
$812$	−3490.74	−0.150863
$813$	−2993.58	−0.129138
$814$	5055.72	0.217694
$815$	17989.3	0.773175
$816$	−3819.70	−0.163868
$817$	1989.55	0.0851966
$818$	3586.07	0.153281
$819$	0	0
$820$	14465.6	0.616050
$821$	4858.68	0.206540	0.103270	−	0.994653i	$-0.467069\pi$
$821$	4858.68	0.206540	0.103270	+	0.994653i	$0.467069\pi$
$822$	−16543.8	−0.701985
$823$	−27983.7	−1.18524	−0.592619	−	0.805483i	$-0.701906\pi$
$823$	−27983.7	−1.18524	−0.592619	+	0.805483i	$0.701906\pi$
$824$	31580.2	1.33513
$825$	3884.49	0.163928
$826$	−17161.6	−0.722915
$827$	3348.15	0.140782	0.0703910	−	0.997519i	$-0.477575\pi$
$827$	3348.15	0.140782	0.0703910	+	0.997519i	$0.477575\pi$
$828$	44.7912	0.00187995
$829$	45885.7	1.92241	0.961204	−	0.275839i	$-0.0889557\pi$
$829$	45885.7	1.92241	0.961204	+	0.275839i	$0.0889557\pi$
$830$	18305.6	0.765539
$831$	−29988.1	−1.25184
$832$	0	0
$833$	1433.26	0.0596151
$834$	−2257.85	−0.0937446
$835$	27289.5	1.13101
$836$	−4720.32	−0.195282
$837$	−11663.6	−0.481663
$838$	26032.8	1.07314
$839$	−3957.88	−0.162862	−0.0814310	−	0.996679i	$-0.525949\pi$
$839$	−3957.88	−0.162862	−0.0814310	+	0.996679i	$0.525949\pi$
$840$	20974.2	0.861521
$841$	−22395.2	−0.918251
$842$	−12252.7	−0.501490
$843$	14320.4	0.585077
$844$	−22008.9	−0.897602
$845$	0	0
$846$	945.755	0.0384347
$847$	−2165.39	−0.0878440
$848$	−1581.16	−0.0640299
$849$	−44369.2	−1.79358
$850$	6977.52	0.281561
$851$	−248.437	−0.0100074
$852$	−10151.1	−0.408184
$853$	16588.4	0.665856	0.332928	−	0.942952i	$-0.391963\pi$
$853$	16588.4	0.665856	0.332928	+	0.942952i	$0.391963\pi$
$854$	364.181	0.0145925
$855$	−7998.10	−0.319917
$856$	11035.9	0.440653
$857$	−17024.1	−0.678569	−0.339285	−	0.940684i	$-0.610185\pi$
$857$	−17024.1	−0.678569	−0.339285	+	0.940684i	$0.610185\pi$
$858$	0	0
$859$	−25726.8	−1.02187	−0.510936	−	0.859619i	$-0.670701\pi$
$859$	−25726.8	−1.02187	−0.510936	+	0.859619i	$0.670701\pi$
$860$	723.722	0.0286962
$861$	44040.3	1.74319
$862$	−24820.5	−0.980729
$863$	42723.2	1.68518	0.842592	−	0.538553i	$-0.181029\pi$
$863$	42723.2	1.68518	0.842592	+	0.538553i	$0.181029\pi$
$864$	17570.6	0.691856
$865$	−30352.3	−1.19307
$866$	23777.8	0.933030
$867$	5715.94	0.223903
$868$	−8799.45	−0.344093
$869$	−2630.05	−0.102668
$870$	−4231.13	−0.164884
$871$	0	0
$872$	−14339.7	−0.556884
$873$	13120.2	0.508649
$874$	−192.828	−0.00746282
$875$	−26801.6	−1.03550
$876$	22712.8	0.876020
$877$	−34745.7	−1.33783	−0.668917	−	0.743337i	$-0.733242\pi$
$877$	−34745.7	−1.33783	−0.668917	+	0.743337i	$0.733242\pi$
$878$	−22163.3	−0.851910
$879$	−27355.7	−1.04970
$880$	896.994	0.0343610
$881$	−30116.8	−1.15171	−0.575857	−	0.817550i	$-0.695332\pi$
$881$	−30116.8	−1.15171	−0.575857	+	0.817550i	$0.695332\pi$
$882$	−431.340	−0.0164671
$883$	−31521.1	−1.20133	−0.600663	−	0.799502i	$-0.705097\pi$
$883$	−31521.1	−1.20133	−0.600663	+	0.799502i	$0.705097\pi$
$884$	0	0
$885$	25022.5	0.950421
$886$	−9677.96	−0.366972
$887$	−1535.53	−0.0581265	−0.0290633	−	0.999578i	$-0.509252\pi$
$887$	−1535.53	−0.0581265	−0.0290633	+	0.999578i	$0.509252\pi$
$888$	34557.0	1.30592
$889$	39142.3	1.47670
$890$	20326.9	0.765574
$891$	−9885.43	−0.371688
$892$	−27505.8	−1.03247
$893$	4897.69	0.183533
$894$	−1262.39	−0.0472267
$895$	−8805.16	−0.328854
$896$	10536.1	0.392841
$897$	0	0
$898$	−9215.82	−0.342468
$899$	5025.92	0.186456
$900$	2525.99	0.0935552
$901$	−9996.89	−0.369639
$902$	8486.08	0.313255
$903$	2203.36	0.0811996
$904$	−15442.0	−0.568133
$905$	356.310	0.0130875
$906$	35686.1	1.30860
$907$	40866.4	1.49608	0.748042	−	0.663652i	$-0.230994\pi$
$907$	40866.4	1.49608	0.748042	+	0.663652i	$0.230994\pi$
$908$	−23240.0	−0.849392
$909$	−3420.49	−0.124808
$910$	0	0
$911$	−17409.1	−0.633138	−0.316569	−	0.948569i	$-0.602531\pi$
$911$	−17409.1	−0.633138	−0.316569	+	0.948569i	$0.602531\pi$
$912$	5953.03	0.216145
$913$	−12917.8	−0.468256
$914$	11951.7	0.432524
$915$	−530.995	−0.0191849
$916$	13765.4	0.496530
$917$	−31868.6	−1.14765
$918$	−12446.4	−0.447488
$919$	12166.0	0.436691	0.218346	−	0.975871i	$-0.429934\pi$
$919$	12166.0	0.436691	0.218346	+	0.975871i	$0.429934\pi$
$920$	−198.598	−0.00711693
$921$	33488.8	1.19815
$922$	32227.1	1.15113
$923$	0	0
$924$	−5227.59	−0.186120
$925$	−14010.6	−0.498016
$926$	28280.6	1.00363
$927$	−13336.7	−0.472528
$928$	−7571.29	−0.267823
$929$	−41230.8	−1.45612	−0.728061	−	0.685512i	$-0.759578\pi$
$929$	−41230.8	−1.45612	−0.728061	+	0.685512i	$0.759578\pi$
$930$	−10665.8	−0.376071
$931$	−2233.74	−0.0786335
$932$	16949.9	0.595720
$933$	49651.5	1.74225
$934$	17230.6	0.603642
$935$	5671.24	0.198363
$936$	0	0
$937$	−17006.9	−0.592948	−0.296474	−	0.955041i	$-0.595811\pi$
$937$	−17006.9	−0.592948	−0.296474	+	0.955041i	$0.595811\pi$
$938$	−19919.8	−0.693395
$939$	56761.3	1.97267
$940$	1781.59	0.0618181
$941$	−41242.9	−1.42878	−0.714390	−	0.699748i	$-0.753296\pi$
$941$	−41242.9	−1.42878	−0.714390	+	0.699748i	$0.753296\pi$
$942$	28763.9	0.994882
$943$	−417.004	−0.0144003
$944$	−5016.66	−0.172964
$945$	15168.7	0.522156
$946$	424.563	0.0145917
$947$	49389.7	1.69477	0.847386	−	0.530977i	$-0.178175\pi$
$947$	49389.7	1.69477	0.847386	+	0.530977i	$0.178175\pi$
$948$	−6349.34	−0.217528
$949$	0	0
$950$	−10874.5	−0.371385
$951$	−28829.0	−0.983013
$952$	−26586.2	−0.905110
$953$	−7876.36	−0.267723	−0.133862	−	0.991000i	$-0.542738\pi$
$953$	−7876.36	−0.267723	−0.133862	+	0.991000i	$0.542738\pi$
$954$	3008.58	0.102103
$955$	−19835.6	−0.672110
$956$	4291.57	0.145187
$957$	2985.81	0.100854
$958$	−12278.3	−0.414086
$959$	−25557.1	−0.860563
$960$	20033.2	0.673509
$961$	−17121.7	−0.574727
$962$	0	0
$963$	−4660.58	−0.155955
$964$	8905.39	0.297535
$965$	−4645.49	−0.154967
$966$	−213.550	−0.00711270
$967$	34345.4	1.14217	0.571083	−	0.820892i	$-0.306523\pi$
$967$	34345.4	1.14217	0.571083	+	0.820892i	$0.306523\pi$
$968$	−2851.98	−0.0946964
$969$	37638.0	1.24779
$970$	−20546.3	−0.680105
$971$	−37218.0	−1.23005	−0.615027	−	0.788506i	$-0.710855\pi$
$971$	−37218.0	−1.23005	−0.615027	+	0.788506i	$0.710855\pi$
$972$	−11642.8	−0.384201
$973$	−3487.95	−0.114922
$974$	13397.5	0.440744
$975$	0	0
$976$	106.457	0.00349140
$977$	50248.8	1.64545	0.822724	−	0.568441i	$-0.192453\pi$
$977$	50248.8	1.64545	0.822724	+	0.568441i	$0.192453\pi$
$978$	25477.1	0.832992
$979$	−14344.2	−0.468278
$980$	−812.547	−0.0264856
$981$	6055.80	0.197092
$982$	−20435.0	−0.664060
$983$	45358.8	1.47174	0.735870	−	0.677122i	$-0.236773\pi$
$983$	45358.8	1.47174	0.735870	+	0.677122i	$0.236773\pi$
$984$	58004.3	1.87918
$985$	−3069.27	−0.0992843
$986$	5363.26	0.173226
$987$	5424.01	0.174922
$988$	0	0
$989$	−20.8629	−0.000670781 0
$990$	−1706.77	−0.0547925
$991$	−6009.88	−0.192644	−0.0963220	−	0.995350i	$-0.530708\pi$
$991$	−6009.88	−0.192644	−0.0963220	+	0.995350i	$0.530708\pi$
$992$	−19085.7	−0.610858
$993$	−44326.7	−1.41658
$994$	13036.3	0.415983
$995$	3542.77	0.112878
$996$	−31185.6	−0.992122
$997$	−54371.0	−1.72713	−0.863564	−	0.504239i	$-0.831773\pi$
$997$	−54371.0	−1.72713	−0.863564	+	0.504239i	$0.831773\pi$
$998$	26931.7	0.854217
$999$	24991.9	0.791501

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.b.1.3		4
13.12	even	2		143.4.a.a.1.2	✓	4
39.38	odd	2		1287.4.a.b.1.3		4
52.51	odd	2		2288.4.a.i.1.4		4
143.142	odd	2		1573.4.a.c.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.a.a.1.2	✓	4	13.12	even	2
1287.4.a.b.1.3		4	39.38	odd	2
1573.4.a.c.1.3		4	143.142	odd	2
1859.4.a.b.1.3		4	1.1	even	1	trivial
2288.4.a.i.1.4		4	52.51	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+1.90566 q^{2} -6.07897 q^{3} -4.36845 q^{4} -8.17977 q^{5} -11.5845 q^{6} -17.8958 q^{7} -23.5701 q^{8} +9.95391 q^{9} +O(q^{10})\)	\(q+1.90566 q^{2} -6.07897 q^{3} -4.36845 q^{4} -8.17977 q^{5} -11.5845 q^{6} -17.8958 q^{7} -23.5701 q^{8} +9.95391 q^{9} -15.5879 q^{10} +11.0000 q^{11} +26.5557 q^{12} -34.1034 q^{14} +49.7246 q^{15} -9.96909 q^{16} -63.0295 q^{17} +18.9688 q^{18} +98.2318 q^{19} +35.7329 q^{20} +108.788 q^{21} +20.9623 q^{22} -1.03008 q^{23} +143.282 q^{24} -58.0913 q^{25} +103.623 q^{27} +78.1770 q^{28} -44.6518 q^{29} +94.7584 q^{30} -112.558 q^{31} +169.563 q^{32} -66.8687 q^{33} -120.113 q^{34} +146.384 q^{35} -43.4831 q^{36} +241.182 q^{37} +187.197 q^{38} +192.798 q^{40} +404.826 q^{41} +207.314 q^{42} +20.2537 q^{43} -48.0529 q^{44} -81.4207 q^{45} -1.96299 q^{46} +49.8584 q^{47} +60.6018 q^{48} -22.7394 q^{49} -110.702 q^{50} +383.155 q^{51} +158.607 q^{53} +197.470 q^{54} -89.9775 q^{55} +421.806 q^{56} -597.148 q^{57} -85.0913 q^{58} +503.222 q^{59} -217.219 q^{60} -10.6787 q^{61} -214.498 q^{62} -178.133 q^{63} +402.883 q^{64} -127.429 q^{66} +584.100 q^{67} +275.341 q^{68} +6.26184 q^{69} +278.958 q^{70} -382.259 q^{71} -234.615 q^{72} +855.289 q^{73} +459.611 q^{74} +353.135 q^{75} -429.120 q^{76} -196.854 q^{77} -239.095 q^{79} +81.5449 q^{80} -898.675 q^{81} +771.462 q^{82} -1174.35 q^{83} -475.236 q^{84} +515.567 q^{85} +38.5967 q^{86} +271.437 q^{87} -259.271 q^{88} -1304.02 q^{89} -155.160 q^{90} +4.49986 q^{92} +684.237 q^{93} +95.0134 q^{94} -803.514 q^{95} -1030.77 q^{96} +1318.09 q^{97} -43.3337 q^{98} +109.493 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 6 q^{4} + 6 q^{5} + 13 q^{6} + 17 q^{7} - 6 q^{8} - 44 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 + 6 * q^4 + 6 * q^5 + 13 * q^6 + 17 * q^7 - 6 * q^8 - 44 * q^9	\( 4 q - 4 q^{3} + 6 q^{4} + 6 q^{5} + 13 q^{6} + 17 q^{7} - 6 q^{8} - 44 q^{9} - 82 q^{10} + 44 q^{11} + 17 q^{12} - 40 q^{14} - 9 q^{15} - 142 q^{16} - 41 q^{17} + 75 q^{18} + 41 q^{19} + 174 q^{20} + 179 q^{21} - 136 q^{23} + 171 q^{24} - 162 q^{25} + 11 q^{27} + 56 q^{28} - 207 q^{29} + 305 q^{30} + 348 q^{31} + 2 q^{32} - 44 q^{33} - 197 q^{34} + 136 q^{35} - 153 q^{36} + 333 q^{37} - 110 q^{38} + 142 q^{40} + 198 q^{41} + 317 q^{42} - 252 q^{43} + 66 q^{44} - 303 q^{45} - 345 q^{46} - 561 q^{47} + q^{48} - 431 q^{49} - 958 q^{50} + 375 q^{51} + 343 q^{53} - 803 q^{54} + 66 q^{55} + 888 q^{56} - 797 q^{57} - 753 q^{58} + 541 q^{59} - 669 q^{60} - 801 q^{61} + 50 q^{62} - 895 q^{63} - 214 q^{64} + 143 q^{66} + 863 q^{67} + 221 q^{68} - 238 q^{69} + 184 q^{70} - 781 q^{71} - 711 q^{72} + 1306 q^{73} + 1347 q^{74} - 779 q^{75} - 1160 q^{76} + 187 q^{77} - 278 q^{79} - 874 q^{80} - 596 q^{81} + 1675 q^{82} - 437 q^{83} - 439 q^{84} + 615 q^{85} - 234 q^{86} - 818 q^{87} - 66 q^{88} - 2552 q^{89} + 899 q^{90} - 1391 q^{92} + 876 q^{93} - 415 q^{94} - 940 q^{95} - 3077 q^{96} + 2504 q^{97} + 144 q^{98} - 484 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 6 * q^4 + 6 * q^5 + 13 * q^6 + 17 * q^7 - 6 * q^8 - 44 * q^9 - 82 * q^10 + 44 * q^11 + 17 * q^12 - 40 * q^14 - 9 * q^15 - 142 * q^16 - 41 * q^17 + 75 * q^18 + 41 * q^19 + 174 * q^20 + 179 * q^21 - 136 * q^23 + 171 * q^24 - 162 * q^25 + 11 * q^27 + 56 * q^28 - 207 * q^29 + 305 * q^30 + 348 * q^31 + 2 * q^32 - 44 * q^33 - 197 * q^34 + 136 * q^35 - 153 * q^36 + 333 * q^37 - 110 * q^38 + 142 * q^40 + 198 * q^41 + 317 * q^42 - 252 * q^43 + 66 * q^44 - 303 * q^45 - 345 * q^46 - 561 * q^47 + q^48 - 431 * q^49 - 958 * q^50 + 375 * q^51 + 343 * q^53 - 803 * q^54 + 66 * q^55 + 888 * q^56 - 797 * q^57 - 753 * q^58 + 541 * q^59 - 669 * q^60 - 801 * q^61 + 50 * q^62 - 895 * q^63 - 214 * q^64 + 143 * q^66 + 863 * q^67 + 221 * q^68 - 238 * q^69 + 184 * q^70 - 781 * q^71 - 711 * q^72 + 1306 * q^73 + 1347 * q^74 - 779 * q^75 - 1160 * q^76 + 187 * q^77 - 278 * q^79 - 874 * q^80 - 596 * q^81 + 1675 * q^82 - 437 * q^83 - 439 * q^84 + 615 * q^85 - 234 * q^86 - 818 * q^87 - 66 * q^88 - 2552 * q^89 + 899 * q^90 - 1391 * q^92 + 876 * q^93 - 415 * q^94 - 940 * q^95 - 3077 * q^96 + 2504 * q^97 + 144 * q^98 - 484 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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