LMFDB - Embedded newform 1183.2.a.c.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1183,2,Mod(1,1183)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1183.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1183, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,-3,-3,3,-3,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$9.44630255912$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	1183.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.61803 q^{2} -2.61803 q^{3} +4.85410 q^{4} -2.61803 q^{5} +6.85410 q^{6} -1.00000 q^{7} -7.47214 q^{8} +3.85410 q^{9} +6.85410 q^{10} -1.85410 q^{11} -12.7082 q^{12} +2.61803 q^{14} +6.85410 q^{15} +9.85410 q^{16} -1.47214 q^{17} -10.0902 q^{18} +1.85410 q^{19} -12.7082 q^{20} +2.61803 q^{21} +4.85410 q^{22} -4.47214 q^{23} +19.5623 q^{24} +1.85410 q^{25} -2.23607 q^{27} -4.85410 q^{28} +7.09017 q^{29} -17.9443 q^{30} +4.70820 q^{31} -10.8541 q^{32} +4.85410 q^{33} +3.85410 q^{34} +2.61803 q^{35} +18.7082 q^{36} -4.00000 q^{37} -4.85410 q^{38} +19.5623 q^{40} -0.763932 q^{41} -6.85410 q^{42} +12.5623 q^{43} -9.00000 q^{44} -10.0902 q^{45} +11.7082 q^{46} +2.23607 q^{47} -25.7984 q^{48} +1.00000 q^{49} -4.85410 q^{50} +3.85410 q^{51} +3.76393 q^{53} +5.85410 q^{54} +4.85410 q^{55} +7.47214 q^{56} -4.85410 q^{57} -18.5623 q^{58} +2.23607 q^{59} +33.2705 q^{60} -6.00000 q^{61} -12.3262 q^{62} -3.85410 q^{63} +8.70820 q^{64} -12.7082 q^{66} +12.7082 q^{67} -7.14590 q^{68} +11.7082 q^{69} -6.85410 q^{70} +14.1803 q^{71} -28.7984 q^{72} +2.00000 q^{73} +10.4721 q^{74} -4.85410 q^{75} +9.00000 q^{76} +1.85410 q^{77} +4.00000 q^{79} -25.7984 q^{80} -5.70820 q^{81} +2.00000 q^{82} -6.70820 q^{83} +12.7082 q^{84} +3.85410 q^{85} -32.8885 q^{86} -18.5623 q^{87} +13.8541 q^{88} -4.90983 q^{89} +26.4164 q^{90} -21.7082 q^{92} -12.3262 q^{93} -5.85410 q^{94} -4.85410 q^{95} +28.4164 q^{96} -18.8541 q^{97} -2.61803 q^{98} -7.14590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 7 q^{6} - 2 q^{7} - 6 q^{8} + q^{9} + 7 q^{10} + 3 q^{11} - 12 q^{12} + 3 q^{14} + 7 q^{15} + 13 q^{16} + 6 q^{17} - 9 q^{18} - 3 q^{19} - 12 q^{20} + 3 q^{21}+ \cdots - 21 q^{99}+O(q^{100}) $ 2 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 7 * q^6 - 2 * q^7 - 6 * q^8 + q^9 + 7 * q^10 + 3 * q^11 - 12 * q^12 + 3 * q^14 + 7 * q^15 + 13 * q^16 + 6 * q^17 - 9 * q^18 - 3 * q^19 - 12 * q^20 + 3 * q^21 + 3 * q^22 + 19 * q^24 - 3 * q^25 - 3 * q^28 + 3 * q^29 - 18 * q^30 - 4 * q^31 - 15 * q^32 + 3 * q^33 + q^34 + 3 * q^35 + 24 * q^36 - 8 * q^37 - 3 * q^38 + 19 * q^40 - 6 * q^41 - 7 * q^42 + 5 * q^43 - 18 * q^44 - 9 * q^45 + 10 * q^46 - 27 * q^48 + 2 * q^49 - 3 * q^50 + q^51 + 12 * q^53 + 5 * q^54 + 3 * q^55 + 6 * q^56 - 3 * q^57 - 17 * q^58 + 33 * q^60 - 12 * q^61 - 9 * q^62 - q^63 + 4 * q^64 - 12 * q^66 + 12 * q^67 - 21 * q^68 + 10 * q^69 - 7 * q^70 + 6 * q^71 - 33 * q^72 + 4 * q^73 + 12 * q^74 - 3 * q^75 + 18 * q^76 - 3 * q^77 + 8 * q^79 - 27 * q^80 + 2 * q^81 + 4 * q^82 + 12 * q^84 + q^85 - 30 * q^86 - 17 * q^87 + 21 * q^88 - 21 * q^89 + 26 * q^90 - 30 * q^92 - 9 * q^93 - 5 * q^94 - 3 * q^95 + 30 * q^96 - 31 * q^97 - 3 * q^98 - 21 * q^99

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 $

$2$	−2.61803	−1.85123	−0.925615	−	0.378467i	$-0.876451\pi$
$2$	−2.61803	−1.85123	−0.925615	+	0.378467i	$0.876451\pi$
$3$	−2.61803	−1.51152	−0.755761	−	0.654847i	$-0.772733\pi$
$3$	−2.61803	−1.51152	−0.755761	+	0.654847i	$0.772733\pi$
$4$	4.85410	2.42705
$5$	−2.61803	−1.17082	−0.585410	−	0.810737i	$-0.699067\pi$
$5$	−2.61803	−1.17082	−0.585410	+	0.810737i	$0.699067\pi$
$6$	6.85410	2.79818
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−7.47214	−2.64180
$9$	3.85410	1.28470
$10$	6.85410	2.16746
$11$	−1.85410	−0.559033	−0.279516	−	0.960141i	$-0.590174\pi$
$11$	−1.85410	−0.559033	−0.279516	+	0.960141i	$0.590174\pi$
$12$	−12.7082	−3.66854
$13$	0	0
$13$	0	0
$14$	2.61803	0.699699
$15$	6.85410	1.76972
$16$	9.85410	2.46353
$17$	−1.47214	−0.357045	−0.178523	−	0.983936i	$-0.557132\pi$
$17$	−1.47214	−0.357045	−0.178523	+	0.983936i	$0.557132\pi$
$18$	−10.0902	−2.37828
$19$	1.85410	0.425360	0.212680	−	0.977122i	$-0.431781\pi$
$19$	1.85410	0.425360	0.212680	+	0.977122i	$0.431781\pi$
$20$	−12.7082	−2.84164
$21$	2.61803	0.571302
$22$	4.85410	1.03490
$23$	−4.47214	−0.932505	−0.466252	−	0.884652i	$-0.654396\pi$
$23$	−4.47214	−0.932505	−0.466252	+	0.884652i	$0.654396\pi$
$24$	19.5623	3.99314
$25$	1.85410	0.370820
$26$	0	0
$27$	−2.23607	−0.430331
$28$	−4.85410	−0.917339
$29$	7.09017	1.31661	0.658306	−	0.752751i	$-0.271273\pi$
$29$	7.09017	1.31661	0.658306	+	0.752751i	$0.271273\pi$
$30$	−17.9443	−3.27616
$31$	4.70820	0.845618	0.422809	−	0.906219i	$-0.361044\pi$
$31$	4.70820	0.845618	0.422809	+	0.906219i	$0.361044\pi$
$32$	−10.8541	−1.91875
$33$	4.85410	0.844991
$34$	3.85410	0.660973
$35$	2.61803	0.442529
$36$	18.7082	3.11803
$37$	−4.00000	−0.657596	−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000	−0.657596	−0.328798	+	0.944400i	$0.606644\pi$
$38$	−4.85410	−0.787439
$39$	0	0
$40$	19.5623	3.09307
$41$	−0.763932	−0.119306	−0.0596531	−	0.998219i	$-0.518999\pi$
$41$	−0.763932	−0.119306	−0.0596531	+	0.998219i	$0.518999\pi$
$42$	−6.85410	−1.05761
$43$	12.5623	1.91573	0.957867	−	0.287213i	$-0.0927286\pi$
$43$	12.5623	1.91573	0.957867	+	0.287213i	$0.0927286\pi$
$44$	−9.00000	−1.35680
$45$	−10.0902	−1.50415
$46$	11.7082	1.72628
$47$	2.23607	0.326164	0.163082	−	0.986613i	$-0.447856\pi$
$47$	2.23607	0.326164	0.163082	+	0.986613i	$0.447856\pi$
$48$	−25.7984	−3.72367
$49$	1.00000	0.142857
$50$	−4.85410	−0.686474
$51$	3.85410	0.539682
$52$	0	0
$53$	3.76393	0.517016	0.258508	−	0.966009i	$-0.416769\pi$
$53$	3.76393	0.517016	0.258508	+	0.966009i	$0.416769\pi$
$54$	5.85410	0.796642
$55$	4.85410	0.654527
$56$	7.47214	0.998506
$57$	−4.85410	−0.642942
$58$	−18.5623	−2.43735
$59$	2.23607	0.291111	0.145556	−	0.989350i	$-0.453503\pi$
$59$	2.23607	0.291111	0.145556	+	0.989350i	$0.453503\pi$
$60$	33.2705	4.29520
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	−12.3262	−1.56543
$63$	−3.85410	−0.485571
$64$	8.70820	1.08853
$65$	0	0
$66$	−12.7082	−1.56427
$67$	12.7082	1.55255	0.776277	−	0.630392i	$-0.217106\pi$
$67$	12.7082	1.55255	0.776277	+	0.630392i	$0.217106\pi$
$68$	−7.14590	−0.866567
$69$	11.7082	1.40950
$70$	−6.85410	−0.819222
$71$	14.1803	1.68290	0.841448	−	0.540338i	$-0.181703\pi$
$71$	14.1803	1.68290	0.841448	+	0.540338i	$0.181703\pi$
$72$	−28.7984	−3.39392
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	10.4721	1.21736
$75$	−4.85410	−0.560503
$76$	9.00000	1.03237
$77$	1.85410	0.211295
$78$	0	0
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	−25.7984	−2.88435
$81$	−5.70820	−0.634245
$82$	2.00000	0.220863
$83$	−6.70820	−0.736321	−0.368161	−	0.929762i	$-0.620012\pi$
$83$	−6.70820	−0.736321	−0.368161	+	0.929762i	$0.620012\pi$
$84$	12.7082	1.38658
$85$	3.85410	0.418036
$86$	−32.8885	−3.54646
$87$	−18.5623	−1.99009
$88$	13.8541	1.47685
$89$	−4.90983	−0.520441	−0.260220	−	0.965549i	$-0.583795\pi$
$89$	−4.90983	−0.520441	−0.260220	+	0.965549i	$0.583795\pi$
$90$	26.4164	2.78453
$91$	0	0
$92$	−21.7082	−2.26324
$93$	−12.3262	−1.27817
$94$	−5.85410	−0.603805
$95$	−4.85410	−0.498020
$96$	28.4164	2.90024
$97$	−18.8541	−1.91434	−0.957172	−	0.289520i	$-0.906504\pi$
$97$	−18.8541	−1.91434	−0.957172	+	0.289520i	$0.906504\pi$
$98$	−2.61803	−0.264461
$99$	−7.14590	−0.718190
$100$	9.00000	0.900000
$101$	−11.5623	−1.15049	−0.575246	−	0.817980i	$-0.695094\pi$
$101$	−11.5623	−1.15049	−0.575246	+	0.817980i	$0.695094\pi$
$102$	−10.0902	−0.999076
$103$	−8.70820	−0.858045	−0.429022	−	0.903294i	$-0.641142\pi$
$103$	−8.70820	−0.858045	−0.429022	+	0.903294i	$0.641142\pi$
$104$	0	0
$105$	−6.85410	−0.668892
$106$	−9.85410	−0.957115
$107$	−3.38197	−0.326947	−0.163473	−	0.986548i	$-0.552270\pi$
$107$	−3.38197	−0.326947	−0.163473	+	0.986548i	$0.552270\pi$
$108$	−10.8541	−1.04444
$109$	2.70820	0.259399	0.129699	−	0.991553i	$-0.458599\pi$
$109$	2.70820	0.259399	0.129699	+	0.991553i	$0.458599\pi$
$110$	−12.7082	−1.21168
$111$	10.4721	0.993971
$112$	−9.85410	−0.931125
$113$	1.47214	0.138487	0.0692435	−	0.997600i	$-0.477941\pi$
$113$	1.47214	0.138487	0.0692435	+	0.997600i	$0.477941\pi$
$114$	12.7082	1.19023
$115$	11.7082	1.09180
$116$	34.4164	3.19548
$117$	0	0
$118$	−5.85410	−0.538914
$119$	1.47214	0.134950
$120$	−51.2148	−4.67525
$121$	−7.56231	−0.687482
$122$	15.7082	1.42215
$123$	2.00000	0.180334
$124$	22.8541	2.05236
$125$	8.23607	0.736656
$126$	10.0902	0.898904
$127$	−20.8541	−1.85050	−0.925251	−	0.379355i	$-0.876146\pi$
$127$	−20.8541	−1.85050	−0.925251	+	0.379355i	$0.876146\pi$
$128$	−1.09017	−0.0963583
$129$	−32.8885	−2.89567
$130$	0	0
$131$	−15.3262	−1.33906	−0.669530	−	0.742785i	$-0.733504\pi$
$131$	−15.3262	−1.33906	−0.669530	+	0.742785i	$0.733504\pi$
$132$	23.5623	2.05084
$133$	−1.85410	−0.160771
$134$	−33.2705	−2.87413
$135$	5.85410	0.503841
$136$	11.0000	0.943242
$137$	2.61803	0.223674	0.111837	−	0.993727i	$-0.464327\pi$
$137$	2.61803	0.223674	0.111837	+	0.993727i	$0.464327\pi$
$138$	−30.6525	−2.60931
$139$	4.56231	0.386970	0.193485	−	0.981103i	$-0.438021\pi$
$139$	4.56231	0.386970	0.193485	+	0.981103i	$0.438021\pi$
$140$	12.7082	1.07404
$141$	−5.85410	−0.493004
$142$	−37.1246	−3.11543
$143$	0	0
$144$	37.9787	3.16489
$145$	−18.5623	−1.54152
$146$	−5.23607	−0.433340
$147$	−2.61803	−0.215932
$148$	−19.4164	−1.59602
$149$	−1.85410	−0.151894	−0.0759470	−	0.997112i	$-0.524198\pi$
$149$	−1.85410	−0.151894	−0.0759470	+	0.997112i	$0.524198\pi$
$150$	12.7082	1.03762
$151$	1.29180	0.105125	0.0525624	−	0.998618i	$-0.483261\pi$
$151$	1.29180	0.105125	0.0525624	+	0.998618i	$0.483261\pi$
$152$	−13.8541	−1.12372
$153$	−5.67376	−0.458696
$154$	−4.85410	−0.391155
$155$	−12.3262	−0.990067
$156$	0	0
$157$	14.8541	1.18549	0.592743	−	0.805392i	$-0.298045\pi$
$157$	14.8541	1.18549	0.592743	+	0.805392i	$0.298045\pi$
$158$	−10.4721	−0.833118
$159$	−9.85410	−0.781481
$160$	28.4164	2.24651
$161$	4.47214	0.352454
$162$	14.9443	1.17413
$163$	3.70820	0.290449	0.145224	−	0.989399i	$-0.453610\pi$
$163$	3.70820	0.290449	0.145224	+	0.989399i	$0.453610\pi$
$164$	−3.70820	−0.289562
$165$	−12.7082	−0.989332
$166$	17.5623	1.36310
$167$	−14.2361	−1.10162	−0.550810	−	0.834631i	$-0.685681\pi$
$167$	−14.2361	−1.10162	−0.550810	+	0.834631i	$0.685681\pi$
$168$	−19.5623	−1.50926
$169$	0	0
$170$	−10.0902	−0.773881
$171$	7.14590	0.546460
$172$	60.9787	4.64958
$173$	−9.00000	−0.684257	−0.342129	−	0.939653i	$-0.611148\pi$
$173$	−9.00000	−0.684257	−0.342129	+	0.939653i	$0.611148\pi$
$174$	48.5967	3.68411
$175$	−1.85410	−0.140157
$176$	−18.2705	−1.37719
$177$	−5.85410	−0.440021
$178$	12.8541	0.963456
$179$	−9.00000	−0.672692	−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000	−0.672692	−0.336346	+	0.941739i	$0.609191\pi$
$180$	−48.9787	−3.65066
$181$	9.70820	0.721605	0.360803	−	0.932642i	$-0.382503\pi$
$181$	9.70820	0.721605	0.360803	+	0.932642i	$0.382503\pi$
$182$	0	0
$183$	15.7082	1.16118
$184$	33.4164	2.46349
$185$	10.4721	0.769927
$186$	32.2705	2.36619
$187$	2.72949	0.199600
$188$	10.8541	0.791617
$189$	2.23607	0.162650
$190$	12.7082	0.921950
$191$	21.3820	1.54714	0.773572	−	0.633708i	$-0.218468\pi$
$191$	21.3820	1.54714	0.773572	+	0.633708i	$0.218468\pi$
$192$	−22.7984	−1.64533
$193$	6.00000	0.431889	0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000	0.431889	0.215945	+	0.976406i	$0.430717\pi$
$194$	49.3607	3.54389
$195$	0	0
$196$	4.85410	0.346722
$197$	16.7984	1.19683	0.598417	−	0.801185i	$-0.295797\pi$
$197$	16.7984	1.19683	0.598417	+	0.801185i	$0.295797\pi$
$198$	18.7082	1.32953
$199$	−24.4164	−1.73083	−0.865417	−	0.501053i	$-0.832946\pi$
$199$	−24.4164	−1.73083	−0.865417	+	0.501053i	$0.832946\pi$
$200$	−13.8541	−0.979633
$201$	−33.2705	−2.34672
$202$	30.2705	2.12983
$203$	−7.09017	−0.497632
$204$	18.7082	1.30984
$205$	2.00000	0.139686
$206$	22.7984	1.58844
$207$	−17.2361	−1.19799
$208$	0	0
$209$	−3.43769	−0.237790
$210$	17.9443	1.23827
$211$	4.70820	0.324126	0.162063	−	0.986780i	$-0.448185\pi$
$211$	4.70820	0.324126	0.162063	+	0.986780i	$0.448185\pi$
$212$	18.2705	1.25482
$213$	−37.1246	−2.54374
$214$	8.85410	0.605254
$215$	−32.8885	−2.24298
$216$	16.7082	1.13685
$217$	−4.70820	−0.319614
$218$	−7.09017	−0.480207
$219$	−5.23607	−0.353821
$220$	23.5623	1.58857
$221$	0	0
$222$	−27.4164	−1.84007
$223$	−20.2705	−1.35741	−0.678707	−	0.734409i	$-0.737459\pi$
$223$	−20.2705	−1.35741	−0.678707	+	0.734409i	$0.737459\pi$
$224$	10.8541	0.725220
$225$	7.14590	0.476393
$226$	−3.85410	−0.256371
$227$	−1.47214	−0.0977091	−0.0488545	−	0.998806i	$-0.515557\pi$
$227$	−1.47214	−0.0977091	−0.0488545	+	0.998806i	$0.515557\pi$
$228$	−23.5623	−1.56045
$229$	13.1246	0.867299	0.433649	−	0.901082i	$-0.357226\pi$
$229$	13.1246	0.867299	0.433649	+	0.901082i	$0.357226\pi$
$230$	−30.6525	−2.02116
$231$	−4.85410	−0.319376
$232$	−52.9787	−3.47822
$233$	2.61803	0.171513	0.0857566	−	0.996316i	$-0.472669\pi$
$233$	2.61803	0.171513	0.0857566	+	0.996316i	$0.472669\pi$
$234$	0	0
$235$	−5.85410	−0.381880
$236$	10.8541	0.706542
$237$	−10.4721	−0.680238
$238$	−3.85410	−0.249824
$239$	24.7082	1.59824	0.799120	−	0.601171i	$-0.205299\pi$
$239$	24.7082	1.59824	0.799120	+	0.601171i	$0.205299\pi$
$240$	67.5410	4.35975
$241$	−24.5623	−1.58220	−0.791099	−	0.611689i	$-0.790491\pi$
$241$	−24.5623	−1.58220	−0.791099	+	0.611689i	$0.790491\pi$
$242$	19.7984	1.27269
$243$	21.6525	1.38901
$244$	−29.1246	−1.86451
$245$	−2.61803	−0.167260
$246$	−5.23607	−0.333840
$247$	0	0
$248$	−35.1803	−2.23395
$249$	17.5623	1.11297
$250$	−21.5623	−1.36372
$251$	0.763932	0.0482190	0.0241095	−	0.999709i	$-0.492325\pi$
$251$	0.763932	0.0482190	0.0241095	+	0.999709i	$0.492325\pi$
$252$	−18.7082	−1.17851
$253$	8.29180	0.521301
$254$	54.5967	3.42570
$255$	−10.0902	−0.631871
$256$	−14.5623	−0.910144
$257$	16.7426	1.04438	0.522189	−	0.852830i	$-0.325116\pi$
$257$	16.7426	1.04438	0.522189	+	0.852830i	$0.325116\pi$
$258$	86.1033	5.36056
$259$	4.00000	0.248548
$260$	0	0
$261$	27.3262	1.69145
$262$	40.1246	2.47891
$263$	9.00000	0.554964	0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000	0.554964	0.277482	+	0.960731i	$0.410500\pi$
$264$	−36.2705	−2.23230
$265$	−9.85410	−0.605333
$266$	4.85410	0.297624
$267$	12.8541	0.786658
$268$	61.6869	3.76813
$269$	−28.7426	−1.75247	−0.876235	−	0.481884i	$-0.839953\pi$
$269$	−28.7426	−1.75247	−0.876235	+	0.481884i	$0.839953\pi$
$270$	−15.3262	−0.932725
$271$	8.41641	0.511260	0.255630	−	0.966775i	$-0.417717\pi$
$271$	8.41641	0.511260	0.255630	+	0.966775i	$0.417717\pi$
$272$	−14.5066	−0.879590
$273$	0	0
$274$	−6.85410	−0.414071
$275$	−3.43769	−0.207301
$276$	56.8328	3.42093
$277$	−5.00000	−0.300421	−0.150210	−	0.988654i	$-0.547995\pi$
$277$	−5.00000	−0.300421	−0.150210	+	0.988654i	$0.547995\pi$
$278$	−11.9443	−0.716370
$279$	18.1459	1.08637
$280$	−19.5623	−1.16907
$281$	−20.1803	−1.20386	−0.601929	−	0.798550i	$-0.705601\pi$
$281$	−20.1803	−1.20386	−0.601929	+	0.798550i	$0.705601\pi$
$282$	15.3262	0.912664
$283$	13.4164	0.797523	0.398761	−	0.917055i	$-0.369440\pi$
$283$	13.4164	0.797523	0.398761	+	0.917055i	$0.369440\pi$
$284$	68.8328	4.08448
$285$	12.7082	0.752769
$286$	0	0
$287$	0.763932	0.0450935
$288$	−41.8328	−2.46502
$289$	−14.8328	−0.872519
$290$	48.5967	2.85370
$291$	49.3607	2.89357
$292$	9.70820	0.568130
$293$	6.76393	0.395153	0.197577	−	0.980287i	$-0.436693\pi$
$293$	6.76393	0.395153	0.197577	+	0.980287i	$0.436693\pi$
$294$	6.85410	0.399739
$295$	−5.85410	−0.340839
$296$	29.8885	1.73724
$297$	4.14590	0.240569
$298$	4.85410	0.281191
$299$	0	0
$300$	−23.5623	−1.36037
$301$	−12.5623	−0.724079
$302$	−3.38197	−0.194610
$303$	30.2705	1.73900
$304$	18.2705	1.04789
$305$	15.7082	0.899449
$306$	14.8541	0.849152
$307$	4.85410	0.277038	0.138519	−	0.990360i	$-0.455766\pi$
$307$	4.85410	0.277038	0.138519	+	0.990360i	$0.455766\pi$
$308$	9.00000	0.512823
$309$	22.7984	1.29695
$310$	32.2705	1.83284
$311$	3.32624	0.188614	0.0943068	−	0.995543i	$-0.469937\pi$
$311$	3.32624	0.188614	0.0943068	+	0.995543i	$0.469937\pi$
$312$	0	0
$313$	25.1246	1.42013	0.710064	−	0.704138i	$-0.248666\pi$
$313$	25.1246	1.42013	0.710064	+	0.704138i	$0.248666\pi$
$314$	−38.8885	−2.19461
$315$	10.0902	0.568517
$316$	19.4164	1.09226
$317$	−26.2361	−1.47356	−0.736782	−	0.676130i	$-0.763656\pi$
$317$	−26.2361	−1.47356	−0.736782	+	0.676130i	$0.763656\pi$
$318$	25.7984	1.44670
$319$	−13.1459	−0.736029
$320$	−22.7984	−1.27447
$321$	8.85410	0.494188
$322$	−11.7082	−0.652473
$323$	−2.72949	−0.151873
$324$	−27.7082	−1.53934
$325$	0	0
$326$	−9.70820	−0.537688
$327$	−7.09017	−0.392087
$328$	5.70820	0.315183
$329$	−2.23607	−0.123278
$330$	33.2705	1.83148
$331$	10.1459	0.557669	0.278834	−	0.960339i	$-0.410052\pi$
$331$	10.1459	0.557669	0.278834	+	0.960339i	$0.410052\pi$
$332$	−32.5623	−1.78709
$333$	−15.4164	−0.844814
$334$	37.2705	2.03935
$335$	−33.2705	−1.81776
$336$	25.7984	1.40742
$337$	−11.5623	−0.629839	−0.314919	−	0.949118i	$-0.601978\pi$
$337$	−11.5623	−0.629839	−0.314919	+	0.949118i	$0.601978\pi$
$338$	0	0
$339$	−3.85410	−0.209326
$340$	18.7082	1.01459
$341$	−8.72949	−0.472728
$342$	−18.7082	−1.01162
$343$	−1.00000	−0.0539949
$344$	−93.8673	−5.06098
$345$	−30.6525	−1.65027
$346$	23.5623	1.26672
$347$	30.7639	1.65149	0.825747	−	0.564040i	$-0.190754\pi$
$347$	30.7639	1.65149	0.825747	+	0.564040i	$0.190754\pi$
$348$	−90.1033	−4.83005
$349$	−20.7082	−1.10848	−0.554242	−	0.832355i	$-0.686992\pi$
$349$	−20.7082	−1.10848	−0.554242	+	0.832355i	$0.686992\pi$
$350$	4.85410	0.259463
$351$	0	0
$352$	20.1246	1.07265
$353$	−22.1459	−1.17871	−0.589354	−	0.807875i	$-0.700618\pi$
$353$	−22.1459	−1.17871	−0.589354	+	0.807875i	$0.700618\pi$
$354$	15.3262	0.814580
$355$	−37.1246	−1.97037
$356$	−23.8328	−1.26314
$357$	−3.85410	−0.203981
$358$	23.5623	1.24531
$359$	22.0902	1.16587	0.582937	−	0.812517i	$-0.301903\pi$
$359$	22.0902	1.16587	0.582937	+	0.812517i	$0.301903\pi$
$360$	75.3951	3.97367
$361$	−15.5623	−0.819069
$362$	−25.4164	−1.33586
$363$	19.7984	1.03915
$364$	0	0
$365$	−5.23607	−0.274068
$366$	−41.1246	−2.14962
$367$	−1.41641	−0.0739359	−0.0369679	−	0.999316i	$-0.511770\pi$
$367$	−1.41641	−0.0739359	−0.0369679	+	0.999316i	$0.511770\pi$
$368$	−44.0689	−2.29725
$369$	−2.94427	−0.153273
$370$	−27.4164	−1.42531
$371$	−3.76393	−0.195414
$372$	−59.8328	−3.10219
$373$	−20.5623	−1.06468	−0.532338	−	0.846532i	$-0.678686\pi$
$373$	−20.5623	−1.06468	−0.532338	+	0.846532i	$0.678686\pi$
$374$	−7.14590	−0.369506
$375$	−21.5623	−1.11347
$376$	−16.7082	−0.861660
$377$	0	0
$378$	−5.85410	−0.301103
$379$	6.14590	0.315694	0.157847	−	0.987464i	$-0.449545\pi$
$379$	6.14590	0.315694	0.157847	+	0.987464i	$0.449545\pi$
$380$	−23.5623	−1.20872
$381$	54.5967	2.79708
$382$	−55.9787	−2.86412
$383$	21.9787	1.12306	0.561530	−	0.827456i	$-0.310213\pi$
$383$	21.9787	1.12306	0.561530	+	0.827456i	$0.310213\pi$
$384$	2.85410	0.145648
$385$	−4.85410	−0.247388
$386$	−15.7082	−0.799527
$387$	48.4164	2.46114
$388$	−91.5197	−4.64621
$389$	−11.8885	−0.602773	−0.301387	−	0.953502i	$-0.597449\pi$
$389$	−11.8885	−0.602773	−0.301387	+	0.953502i	$0.597449\pi$
$390$	0	0
$391$	6.58359	0.332947
$392$	−7.47214	−0.377400
$393$	40.1246	2.02402
$394$	−43.9787	−2.21562
$395$	−10.4721	−0.526910
$396$	−34.6869	−1.74308
$397$	−1.41641	−0.0710875	−0.0355437	−	0.999368i	$-0.511316\pi$
$397$	−1.41641	−0.0710875	−0.0355437	+	0.999368i	$0.511316\pi$
$398$	63.9230	3.20417
$399$	4.85410	0.243009
$400$	18.2705	0.913525
$401$	−35.4508	−1.77033	−0.885165	−	0.465276i	$-0.845955\pi$
$401$	−35.4508	−1.77033	−0.885165	+	0.465276i	$0.845955\pi$
$402$	87.1033	4.34432
$403$	0	0
$404$	−56.1246	−2.79230
$405$	14.9443	0.742587
$406$	18.5623	0.921232
$407$	7.41641	0.367618
$408$	−28.7984	−1.42573
$409$	−14.4377	−0.713898	−0.356949	−	0.934124i	$-0.616183\pi$
$409$	−14.4377	−0.713898	−0.356949	+	0.934124i	$0.616183\pi$
$410$	−5.23607	−0.258591
$411$	−6.85410	−0.338088
$412$	−42.2705	−2.08252
$413$	−2.23607	−0.110030
$414$	45.1246	2.21775
$415$	17.5623	0.862100
$416$	0	0
$417$	−11.9443	−0.584914
$418$	9.00000	0.440204
$419$	−11.9443	−0.583516	−0.291758	−	0.956492i	$-0.594240\pi$
$419$	−11.9443	−0.583516	−0.291758	+	0.956492i	$0.594240\pi$
$420$	−33.2705	−1.62343
$421$	−1.41641	−0.0690315	−0.0345157	−	0.999404i	$-0.510989\pi$
$421$	−1.41641	−0.0690315	−0.0345157	+	0.999404i	$0.510989\pi$
$422$	−12.3262	−0.600032
$423$	8.61803	0.419023
$424$	−28.1246	−1.36585
$425$	−2.72949	−0.132400
$426$	97.1935	4.70904
$427$	6.00000	0.290360
$428$	−16.4164	−0.793517
$429$	0	0
$430$	86.1033	4.15227
$431$	−7.79837	−0.375634	−0.187817	−	0.982204i	$-0.560141\pi$
$431$	−7.79837	−0.375634	−0.187817	+	0.982204i	$0.560141\pi$
$432$	−22.0344	−1.06013
$433$	1.00000	0.0480569	0.0240285	−	0.999711i	$-0.492351\pi$
$433$	1.00000	0.0480569	0.0240285	+	0.999711i	$0.492351\pi$
$434$	12.3262	0.591678
$435$	48.5967	2.33004
$436$	13.1459	0.629574
$437$	−8.29180	−0.396650
$438$	13.7082	0.655003
$439$	14.8541	0.708948	0.354474	−	0.935066i	$-0.384660\pi$
$439$	14.8541	0.708948	0.354474	+	0.935066i	$0.384660\pi$
$440$	−36.2705	−1.72913
$441$	3.85410	0.183529
$442$	0	0
$443$	−5.23607	−0.248773	−0.124387	−	0.992234i	$-0.539696\pi$
$443$	−5.23607	−0.248773	−0.124387	+	0.992234i	$0.539696\pi$
$444$	50.8328	2.41242
$445$	12.8541	0.609343
$446$	53.0689	2.51288
$447$	4.85410	0.229591
$448$	−8.70820	−0.411424
$449$	−19.5279	−0.921577	−0.460788	−	0.887510i	$-0.652433\pi$
$449$	−19.5279	−0.921577	−0.460788	+	0.887510i	$0.652433\pi$
$450$	−18.7082	−0.881913
$451$	1.41641	0.0666960
$452$	7.14590	0.336115
$453$	−3.38197	−0.158899
$454$	3.85410	0.180882
$455$	0	0
$456$	36.2705	1.69852
$457$	−15.4164	−0.721149	−0.360575	−	0.932730i	$-0.617419\pi$
$457$	−15.4164	−0.721149	−0.360575	+	0.932730i	$0.617419\pi$
$458$	−34.3607	−1.60557
$459$	3.29180	0.153648
$460$	56.8328	2.64984
$461$	12.2148	0.568899	0.284450	−	0.958691i	$-0.408189\pi$
$461$	12.2148	0.568899	0.284450	+	0.958691i	$0.408189\pi$
$462$	12.7082	0.591239
$463$	−6.70820	−0.311757	−0.155878	−	0.987776i	$-0.549821\pi$
$463$	−6.70820	−0.311757	−0.155878	+	0.987776i	$0.549821\pi$
$464$	69.8673	3.24351
$465$	32.2705	1.49651
$466$	−6.85410	−0.317510
$467$	2.34752	0.108630	0.0543152	−	0.998524i	$-0.482702\pi$
$467$	2.34752	0.108630	0.0543152	+	0.998524i	$0.482702\pi$
$468$	0	0
$469$	−12.7082	−0.586810
$470$	15.3262	0.706947
$471$	−38.8885	−1.79189
$472$	−16.7082	−0.769057
$473$	−23.2918	−1.07096
$474$	27.4164	1.25928
$475$	3.43769	0.157732
$476$	7.14590	0.327532
$477$	14.5066	0.664211
$478$	−64.6869	−2.95871
$479$	−24.9787	−1.14131	−0.570653	−	0.821191i	$-0.693310\pi$
$479$	−24.9787	−1.14131	−0.570653	+	0.821191i	$0.693310\pi$
$480$	−74.3951	−3.39566
$481$	0	0
$482$	64.3050	2.92901
$483$	−11.7082	−0.532742
$484$	−36.7082	−1.66855
$485$	49.3607	2.24135
$486$	−56.6869	−2.57137
$487$	−29.9787	−1.35847	−0.679233	−	0.733923i	$-0.737687\pi$
$487$	−29.9787	−1.35847	−0.679233	+	0.733923i	$0.737687\pi$
$488$	44.8328	2.02949
$489$	−9.70820	−0.439020
$490$	6.85410	0.309637
$491$	12.3820	0.558790	0.279395	−	0.960176i	$-0.409866\pi$
$491$	12.3820	0.558790	0.279395	+	0.960176i	$0.409866\pi$
$492$	9.70820	0.437680
$493$	−10.4377	−0.470090
$494$	0	0
$495$	18.7082	0.840871
$496$	46.3951	2.08320
$497$	−14.1803	−0.636075
$498$	−45.9787	−2.06036
$499$	−14.8541	−0.664961	−0.332480	−	0.943110i	$-0.607886\pi$
$499$	−14.8541	−0.664961	−0.332480	+	0.943110i	$0.607886\pi$
$500$	39.9787	1.78790
$501$	37.2705	1.66512
$502$	−2.00000	−0.0892644
$503$	26.6180	1.18684	0.593420	−	0.804893i	$-0.297777\pi$
$503$	26.6180	1.18684	0.593420	+	0.804893i	$0.297777\pi$
$504$	28.7984	1.28278
$505$	30.2705	1.34702
$506$	−21.7082	−0.965047
$507$	0	0
$508$	−101.228	−4.49126
$509$	18.5967	0.824286	0.412143	−	0.911119i	$-0.364780\pi$
$509$	18.5967	0.824286	0.412143	+	0.911119i	$0.364780\pi$
$510$	26.4164	1.16974
$511$	−2.00000	−0.0884748
$512$	40.3050	1.78124
$513$	−4.14590	−0.183046
$514$	−43.8328	−1.93338
$515$	22.7984	1.00462
$516$	−159.644	−7.02795
$517$	−4.14590	−0.182336
$518$	−10.4721	−0.460119
$519$	23.5623	1.03427
$520$	0	0
$521$	18.6525	0.817180	0.408590	−	0.912718i	$-0.366021\pi$
$521$	18.6525	0.817180	0.408590	+	0.912718i	$0.366021\pi$
$522$	−71.5410	−3.13127
$523$	1.12461	0.0491758	0.0245879	−	0.999698i	$-0.492173\pi$
$523$	1.12461	0.0491758	0.0245879	+	0.999698i	$0.492173\pi$
$524$	−74.3951	−3.24997
$525$	4.85410	0.211850
$526$	−23.5623	−1.02737
$527$	−6.93112	−0.301924
$528$	47.8328	2.08166
$529$	−3.00000	−0.130435
$530$	25.7984	1.12061
$531$	8.61803	0.373991
$532$	−9.00000	−0.390199
$533$	0	0
$534$	−33.6525	−1.45629
$535$	8.85410	0.382796
$536$	−94.9574	−4.10154
$537$	23.5623	1.01679
$538$	75.2492	3.24422
$539$	−1.85410	−0.0798618
$540$	28.4164	1.22285
$541$	−35.2705	−1.51640	−0.758199	−	0.652023i	$-0.773920\pi$
$541$	−35.2705	−1.51640	−0.758199	+	0.652023i	$0.773920\pi$
$542$	−22.0344	−0.946460
$543$	−25.4164	−1.09072
$544$	15.9787	0.685082
$545$	−7.09017	−0.303710
$546$	0	0
$547$	−3.00000	−0.128271	−0.0641354	−	0.997941i	$-0.520429\pi$
$547$	−3.00000	−0.128271	−0.0641354	+	0.997941i	$0.520429\pi$
$548$	12.7082	0.542868
$549$	−23.1246	−0.986934
$550$	9.00000	0.383761
$551$	13.1459	0.560034
$552$	−87.4853	−3.72362
$553$	−4.00000	−0.170097
$554$	13.0902	0.556148
$555$	−27.4164	−1.16376
$556$	22.1459	0.939195
$557$	27.9787	1.18550	0.592748	−	0.805388i	$-0.298043\pi$
$557$	27.9787	1.18550	0.592748	+	0.805388i	$0.298043\pi$
$558$	−47.5066	−2.01111
$559$	0	0
$560$	25.7984	1.09018
$561$	−7.14590	−0.301700
$562$	52.8328	2.22862
$563$	−21.0557	−0.887393	−0.443697	−	0.896177i	$-0.646333\pi$
$563$	−21.0557	−0.887393	−0.443697	+	0.896177i	$0.646333\pi$
$564$	−28.4164	−1.19655
$565$	−3.85410	−0.162143
$566$	−35.1246	−1.47640
$567$	5.70820	0.239722
$568$	−105.957	−4.44587
$569$	14.9443	0.626496	0.313248	−	0.949671i	$-0.398583\pi$
$569$	14.9443	0.626496	0.313248	+	0.949671i	$0.398583\pi$
$570$	−33.2705	−1.39355
$571$	24.6869	1.03312	0.516558	−	0.856252i	$-0.327213\pi$
$571$	24.6869	1.03312	0.516558	+	0.856252i	$0.327213\pi$
$572$	0	0
$573$	−55.9787	−2.33854
$574$	−2.00000	−0.0834784
$575$	−8.29180	−0.345792
$576$	33.5623	1.39843
$577$	43.8328	1.82478	0.912392	−	0.409318i	$-0.134233\pi$
$577$	43.8328	1.82478	0.912392	+	0.409318i	$0.134233\pi$
$578$	38.8328	1.61523
$579$	−15.7082	−0.652811
$580$	−90.1033	−3.74134
$581$	6.70820	0.278303
$582$	−129.228	−5.35667
$583$	−6.97871	−0.289029
$584$	−14.9443	−0.618398
$585$	0	0
$586$	−17.7082	−0.731519
$587$	19.9098	0.821767	0.410883	−	0.911688i	$-0.365220\pi$
$587$	19.9098	0.821767	0.410883	+	0.911688i	$0.365220\pi$
$588$	−12.7082	−0.524077
$589$	8.72949	0.359692
$590$	15.3262	0.630971
$591$	−43.9787	−1.80904
$592$	−39.4164	−1.62000
$593$	−43.7984	−1.79858	−0.899292	−	0.437349i	$-0.855917\pi$
$593$	−43.7984	−1.79858	−0.899292	+	0.437349i	$0.855917\pi$
$594$	−10.8541	−0.445349
$595$	−3.85410	−0.158003
$596$	−9.00000	−0.368654
$597$	63.9230	2.61619
$598$	0	0
$599$	29.5066	1.20561	0.602803	−	0.797890i	$-0.294050\pi$
$599$	29.5066	1.20561	0.602803	+	0.797890i	$0.294050\pi$
$600$	36.2705	1.48074
$601$	40.3951	1.64775	0.823876	−	0.566771i	$-0.191807\pi$
$601$	40.3951	1.64775	0.823876	+	0.566771i	$0.191807\pi$
$602$	32.8885	1.34044
$603$	48.9787	1.99457
$604$	6.27051	0.255143
$605$	19.7984	0.804918
$606$	−79.2492	−3.21928
$607$	−23.0000	−0.933541	−0.466771	−	0.884378i	$-0.654583\pi$
$607$	−23.0000	−0.933541	−0.466771	+	0.884378i	$0.654583\pi$
$608$	−20.1246	−0.816161
$609$	18.5623	0.752183
$610$	−41.1246	−1.66509
$611$	0	0
$612$	−27.5410	−1.11328
$613$	−34.5623	−1.39596	−0.697979	−	0.716118i	$-0.745917\pi$
$613$	−34.5623	−1.39596	−0.697979	+	0.716118i	$0.745917\pi$
$614$	−12.7082	−0.512861
$615$	−5.23607	−0.211139
$616$	−13.8541	−0.558198
$617$	−0.0557281	−0.00224353	−0.00112176	−	0.999999i	$-0.500357\pi$
$617$	−0.0557281	−0.00224353	−0.00112176	+	0.999999i	$0.500357\pi$
$618$	−59.6869	−2.40096
$619$	−9.41641	−0.378477	−0.189239	−	0.981931i	$-0.560602\pi$
$619$	−9.41641	−0.378477	−0.189239	+	0.981931i	$0.560602\pi$
$620$	−59.8328	−2.40294
$621$	10.0000	0.401286
$622$	−8.70820	−0.349167
$623$	4.90983	0.196708
$624$	0	0
$625$	−30.8328	−1.23331
$626$	−65.7771	−2.62898
$627$	9.00000	0.359425
$628$	72.1033	2.87724
$629$	5.88854	0.234792
$630$	−26.4164	−1.05245
$631$	−34.3951	−1.36925	−0.684624	−	0.728896i	$-0.740034\pi$
$631$	−34.3951	−1.36925	−0.684624	+	0.728896i	$0.740034\pi$
$632$	−29.8885	−1.18890
$633$	−12.3262	−0.489924
$634$	68.6869	2.72791
$635$	54.5967	2.16661
$636$	−47.8328	−1.89669
$637$	0	0
$638$	34.4164	1.36256
$639$	54.6525	2.16202
$640$	2.85410	0.112818
$641$	−47.5066	−1.87640	−0.938199	−	0.346098i	$-0.887507\pi$
$641$	−47.5066	−1.87640	−0.938199	+	0.346098i	$0.887507\pi$
$642$	−23.1803	−0.914855
$643$	7.00000	0.276053	0.138027	−	0.990429i	$-0.455924\pi$
$643$	7.00000	0.276053	0.138027	+	0.990429i	$0.455924\pi$
$644$	21.7082	0.855423
$645$	86.1033	3.39032
$646$	7.14590	0.281152
$647$	24.7639	0.973571	0.486785	−	0.873522i	$-0.338169\pi$
$647$	24.7639	0.973571	0.486785	+	0.873522i	$0.338169\pi$
$648$	42.6525	1.67555
$649$	−4.14590	−0.162741
$650$	0	0
$651$	12.3262	0.483103
$652$	18.0000	0.704934
$653$	−0.381966	−0.0149475	−0.00747374	−	0.999972i	$-0.502379\pi$
$653$	−0.381966	−0.0149475	−0.00747374	+	0.999972i	$0.502379\pi$
$654$	18.5623	0.725844
$655$	40.1246	1.56780
$656$	−7.52786	−0.293914
$657$	7.70820	0.300726
$658$	5.85410	0.228217
$659$	−23.8885	−0.930566	−0.465283	−	0.885162i	$-0.654047\pi$
$659$	−23.8885	−0.930566	−0.465283	+	0.885162i	$0.654047\pi$
$660$	−61.6869	−2.40116
$661$	48.5410	1.88803	0.944013	−	0.329907i	$-0.107017\pi$
$661$	48.5410	1.88803	0.944013	+	0.329907i	$0.107017\pi$
$662$	−26.5623	−1.03237
$663$	0	0
$664$	50.1246	1.94521
$665$	4.85410	0.188234
$666$	40.3607	1.56394
$667$	−31.7082	−1.22775
$668$	−69.1033	−2.67369
$669$	53.0689	2.05176
$670$	87.1033	3.36510
$671$	11.1246	0.429461
$672$	−28.4164	−1.09619
$673$	−39.2492	−1.51295	−0.756473	−	0.654025i	$-0.773079\pi$
$673$	−39.2492	−1.51295	−0.756473	+	0.654025i	$0.773079\pi$
$674$	30.2705	1.16598
$675$	−4.14590	−0.159576
$676$	0	0
$677$	43.7426	1.68117	0.840583	−	0.541682i	$-0.182212\pi$
$677$	43.7426	1.68117	0.840583	+	0.541682i	$0.182212\pi$
$678$	10.0902	0.387511
$679$	18.8541	0.723554
$680$	−28.7984	−1.10437
$681$	3.85410	0.147690
$682$	22.8541	0.875129
$683$	−1.47214	−0.0563297	−0.0281649	−	0.999603i	$-0.508966\pi$
$683$	−1.47214	−0.0563297	−0.0281649	+	0.999603i	$0.508966\pi$
$684$	34.6869	1.32629
$685$	−6.85410	−0.261882
$686$	2.61803	0.0999570
$687$	−34.3607	−1.31094
$688$	123.790	4.71946
$689$	0	0
$690$	80.2492	3.05504
$691$	5.85410	0.222701	0.111350	−	0.993781i	$-0.464482\pi$
$691$	5.85410	0.222701	0.111350	+	0.993781i	$0.464482\pi$
$692$	−43.6869	−1.66073
$693$	7.14590	0.271450
$694$	−80.5410	−3.05730
$695$	−11.9443	−0.453072
$696$	138.700	5.25741
$697$	1.12461	0.0425977
$698$	54.2148	2.05206
$699$	−6.85410	−0.259246
$700$	−9.00000	−0.340168
$701$	11.2361	0.424380	0.212190	−	0.977228i	$-0.431940\pi$
$701$	11.2361	0.424380	0.212190	+	0.977228i	$0.431940\pi$
$702$	0	0
$703$	−7.41641	−0.279715
$704$	−16.1459	−0.608521
$705$	15.3262	0.577220
$706$	57.9787	2.18206
$707$	11.5623	0.434845
$708$	−28.4164	−1.06795
$709$	−23.5623	−0.884901	−0.442450	−	0.896793i	$-0.645891\pi$
$709$	−23.5623	−0.884901	−0.442450	+	0.896793i	$0.645891\pi$
$710$	97.1935	3.64761
$711$	15.4164	0.578160
$712$	36.6869	1.37490
$713$	−21.0557	−0.788543
$714$	10.0902	0.377615
$715$	0	0
$716$	−43.6869	−1.63266
$717$	−64.6869	−2.41578
$718$	−57.8328	−2.15830
$719$	8.12461	0.302997	0.151498	−	0.988457i	$-0.451590\pi$
$719$	8.12461	0.302997	0.151498	+	0.988457i	$0.451590\pi$
$720$	−99.4296	−3.70552
$721$	8.70820	0.324310
$722$	40.7426	1.51628
$723$	64.3050	2.39153
$724$	47.1246	1.75137
$725$	13.1459	0.488226
$726$	−51.8328	−1.92370
$727$	−30.7082	−1.13890	−0.569452	−	0.822025i	$-0.692845\pi$
$727$	−30.7082	−1.13890	−0.569452	+	0.822025i	$0.692845\pi$
$728$	0	0
$729$	−39.5623	−1.46527
$730$	13.7082	0.507363
$731$	−18.4934	−0.684004
$732$	76.2492	2.81825
$733$	32.2705	1.19194	0.595969	−	0.803007i	$-0.296768\pi$
$733$	32.2705	1.19194	0.595969	+	0.803007i	$0.296768\pi$
$734$	3.70820	0.136872
$735$	6.85410	0.252817
$736$	48.5410	1.78925
$737$	−23.5623	−0.867929
$738$	7.70820	0.283743
$739$	6.87539	0.252915	0.126458	−	0.991972i	$-0.459639\pi$
$739$	6.87539	0.252915	0.126458	+	0.991972i	$0.459639\pi$
$740$	50.8328	1.86865
$741$	0	0
$742$	9.85410	0.361755
$743$	−39.3262	−1.44274	−0.721370	−	0.692550i	$-0.756487\pi$
$743$	−39.3262	−1.44274	−0.721370	+	0.692550i	$0.756487\pi$
$744$	92.1033	3.37667
$745$	4.85410	0.177841
$746$	53.8328	1.97096
$747$	−25.8541	−0.945952
$748$	13.2492	0.484440
$749$	3.38197	0.123574
$750$	56.4508	2.06129
$751$	22.7082	0.828634	0.414317	−	0.910133i	$-0.364020\pi$
$751$	22.7082	0.828634	0.414317	+	0.910133i	$0.364020\pi$
$752$	22.0344	0.803513
$753$	−2.00000	−0.0728841
$754$	0	0
$755$	−3.38197	−0.123082
$756$	10.8541	0.394760
$757$	28.0000	1.01768	0.508839	−	0.860862i	$-0.330075\pi$
$757$	28.0000	1.01768	0.508839	+	0.860862i	$0.330075\pi$
$758$	−16.0902	−0.584421
$759$	−21.7082	−0.787958
$760$	36.2705	1.31567
$761$	28.8541	1.04596	0.522980	−	0.852345i	$-0.324820\pi$
$761$	28.8541	1.04596	0.522980	+	0.852345i	$0.324820\pi$
$762$	−142.936	−5.17803
$763$	−2.70820	−0.0980436
$764$	103.790	3.75500
$765$	14.8541	0.537051
$766$	−57.5410	−2.07904
$767$	0	0
$768$	38.1246	1.37570
$769$	18.4164	0.664113	0.332056	−	0.943260i	$-0.392258\pi$
$769$	18.4164	0.664113	0.332056	+	0.943260i	$0.392258\pi$
$770$	12.7082	0.457972
$771$	−43.8328	−1.57860
$772$	29.1246	1.04822
$773$	−25.3607	−0.912160	−0.456080	−	0.889939i	$-0.650747\pi$
$773$	−25.3607	−0.912160	−0.456080	+	0.889939i	$0.650747\pi$
$774$	−126.756	−4.55614
$775$	8.72949	0.313573
$776$	140.880	5.05731
$777$	−10.4721	−0.375686
$778$	31.1246	1.11587
$779$	−1.41641	−0.0507481
$780$	0	0
$781$	−26.2918	−0.940794
$782$	−17.2361	−0.616361
$783$	−15.8541	−0.566579
$784$	9.85410	0.351932
$785$	−38.8885	−1.38799
$786$	−105.048	−3.74692
$787$	−2.58359	−0.0920951	−0.0460476	−	0.998939i	$-0.514663\pi$
$787$	−2.58359	−0.0920951	−0.0460476	+	0.998939i	$0.514663\pi$
$788$	81.5410	2.90478
$789$	−23.5623	−0.838840
$790$	27.4164	0.975432
$791$	−1.47214	−0.0523431
$792$	53.3951	1.89731
$793$	0	0
$794$	3.70820	0.131599
$795$	25.7984	0.914974
$796$	−118.520	−4.20082
$797$	−8.18034	−0.289763	−0.144881	−	0.989449i	$-0.546280\pi$
$797$	−8.18034	−0.289763	−0.144881	+	0.989449i	$0.546280\pi$
$798$	−12.7082	−0.449866
$799$	−3.29180	−0.116455
$800$	−20.1246	−0.711512
$801$	−18.9230	−0.668611
$802$	92.8115	3.27729
$803$	−3.70820	−0.130860
$804$	−161.498	−5.69561
$805$	−11.7082	−0.412660
$806$	0	0
$807$	75.2492	2.64890
$808$	86.3951	3.03937
$809$	−4.41641	−0.155273	−0.0776363	−	0.996982i	$-0.524737\pi$
$809$	−4.41641	−0.155273	−0.0776363	+	0.996982i	$0.524737\pi$
$810$	−39.1246	−1.37470
$811$	−39.2705	−1.37897	−0.689487	−	0.724298i	$-0.742164\pi$
$811$	−39.2705	−1.37897	−0.689487	+	0.724298i	$0.742164\pi$
$812$	−34.4164	−1.20778
$813$	−22.0344	−0.772782
$814$	−19.4164	−0.680545
$815$	−9.70820	−0.340064
$816$	37.9787	1.32952
$817$	23.2918	0.814877
$818$	37.7984	1.32159
$819$	0	0
$820$	9.70820	0.339025
$821$	7.36068	0.256889	0.128445	−	0.991717i	$-0.459002\pi$
$821$	7.36068	0.256889	0.128445	+	0.991717i	$0.459002\pi$
$822$	17.9443	0.625878
$823$	−38.4164	−1.33911	−0.669556	−	0.742762i	$-0.733516\pi$
$823$	−38.4164	−1.33911	−0.669556	+	0.742762i	$0.733516\pi$
$824$	65.0689	2.26678
$825$	9.00000	0.313340
$826$	5.85410	0.203690
$827$	−15.9787	−0.555634	−0.277817	−	0.960634i	$-0.589611\pi$
$827$	−15.9787	−0.555634	−0.277817	+	0.960634i	$0.589611\pi$
$828$	−83.6656	−2.90758
$829$	7.56231	0.262650	0.131325	−	0.991339i	$-0.458077\pi$
$829$	7.56231	0.262650	0.131325	+	0.991339i	$0.458077\pi$
$830$	−45.9787	−1.59594
$831$	13.0902	0.454093
$832$	0	0
$833$	−1.47214	−0.0510065
$834$	31.2705	1.08281
$835$	37.2705	1.28980
$836$	−16.6869	−0.577129
$837$	−10.5279	−0.363896
$838$	31.2705	1.08022
$839$	−13.7426	−0.474449	−0.237224	−	0.971455i	$-0.576238\pi$
$839$	−13.7426	−0.474449	−0.237224	+	0.971455i	$0.576238\pi$
$840$	51.2148	1.76708
$841$	21.2705	0.733466
$842$	3.70820	0.127793
$843$	52.8328	1.81966
$844$	22.8541	0.786671
$845$	0	0
$846$	−22.5623	−0.775708
$847$	7.56231	0.259844
$848$	37.0902	1.27368
$849$	−35.1246	−1.20547
$850$	7.14590	0.245102
$851$	17.8885	0.613211
$852$	−180.207	−6.17378
$853$	−14.1246	−0.483617	−0.241809	−	0.970324i	$-0.577741\pi$
$853$	−14.1246	−0.483617	−0.241809	+	0.970324i	$0.577741\pi$
$854$	−15.7082	−0.537524
$855$	−18.7082	−0.639807
$856$	25.2705	0.863728
$857$	−26.4508	−0.903544	−0.451772	−	0.892133i	$-0.649208\pi$
$857$	−26.4508	−0.903544	−0.451772	+	0.892133i	$0.649208\pi$
$858$	0	0
$859$	−44.2492	−1.50976	−0.754882	−	0.655861i	$-0.772306\pi$
$859$	−44.2492	−1.50976	−0.754882	+	0.655861i	$0.772306\pi$
$860$	−159.644	−5.44383
$861$	−2.00000	−0.0681598
$862$	20.4164	0.695386
$863$	−11.8885	−0.404691	−0.202345	−	0.979314i	$-0.564856\pi$
$863$	−11.8885	−0.404691	−0.202345	+	0.979314i	$0.564856\pi$
$864$	24.2705	0.825700
$865$	23.5623	0.801142
$866$	−2.61803	−0.0889644
$867$	38.8328	1.31883
$868$	−22.8541	−0.775719
$869$	−7.41641	−0.251584
$870$	−127.228	−4.31343
$871$	0	0
$872$	−20.2361	−0.685280
$873$	−72.6656	−2.45936
$874$	21.7082	0.734291
$875$	−8.23607	−0.278430
$876$	−25.4164	−0.858741
$877$	−0.708204	−0.0239143	−0.0119572	−	0.999929i	$-0.503806\pi$
$877$	−0.708204	−0.0239143	−0.0119572	+	0.999929i	$0.503806\pi$
$878$	−38.8885	−1.31242
$879$	−17.7082	−0.597283
$880$	47.8328	1.61244
$881$	−36.5967	−1.23298	−0.616488	−	0.787364i	$-0.711445\pi$
$881$	−36.5967	−1.23298	−0.616488	+	0.787364i	$0.711445\pi$
$882$	−10.0902	−0.339754
$883$	29.0000	0.975928	0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000	0.975928	0.487964	+	0.872864i	$0.337740\pi$
$884$	0	0
$885$	15.3262	0.515186
$886$	13.7082	0.460536
$887$	54.6525	1.83505	0.917525	−	0.397677i	$-0.130184\pi$
$887$	54.6525	1.83505	0.917525	+	0.397677i	$0.130184\pi$
$888$	−78.2492	−2.62587
$889$	20.8541	0.699424
$890$	−33.6525	−1.12803
$891$	10.5836	0.354564
$892$	−98.3951	−3.29451
$893$	4.14590	0.138737
$894$	−12.7082	−0.425026
$895$	23.5623	0.787601
$896$	1.09017	0.0364200
$897$	0	0
$898$	51.1246	1.70605
$899$	33.3820	1.11335
$900$	34.6869	1.15623
$901$	−5.54102	−0.184598
$902$	−3.70820	−0.123470
$903$	32.8885	1.09446
$904$	−11.0000	−0.365855
$905$	−25.4164	−0.844870
$906$	8.85410	0.294158
$907$	−24.0000	−0.796907	−0.398453	−	0.917189i	$-0.630453\pi$
$907$	−24.0000	−0.796907	−0.398453	+	0.917189i	$0.630453\pi$
$908$	−7.14590	−0.237145
$909$	−44.5623	−1.47804
$910$	0	0
$911$	−22.6869	−0.751651	−0.375826	−	0.926690i	$-0.622641\pi$
$911$	−22.6869	−0.751651	−0.375826	+	0.926690i	$0.622641\pi$
$912$	−47.8328	−1.58390
$913$	12.4377	0.411628
$914$	40.3607	1.33501
$915$	−41.1246	−1.35954
$916$	63.7082	2.10498
$917$	15.3262	0.506117
$918$	−8.61803	−0.284438
$919$	−30.0000	−0.989609	−0.494804	−	0.869004i	$-0.664760\pi$
$919$	−30.0000	−0.989609	−0.494804	+	0.869004i	$0.664760\pi$
$920$	−87.4853	−2.88430
$921$	−12.7082	−0.418750
$922$	−31.9787	−1.05316
$923$	0	0
$924$	−23.5623	−0.775143
$925$	−7.41641	−0.243850
$926$	17.5623	0.577133
$927$	−33.5623	−1.10233
$928$	−76.9574	−2.52625
$929$	−11.0689	−0.363158	−0.181579	−	0.983376i	$-0.558121\pi$
$929$	−11.0689	−0.363158	−0.181579	+	0.983376i	$0.558121\pi$
$930$	−84.4853	−2.77038
$931$	1.85410	0.0607657
$932$	12.7082	0.416271
$933$	−8.70820	−0.285094
$934$	−6.14590	−0.201100
$935$	−7.14590	−0.233696
$936$	0	0
$937$	−15.8754	−0.518626	−0.259313	−	0.965793i	$-0.583496\pi$
$937$	−15.8754	−0.518626	−0.259313	+	0.965793i	$0.583496\pi$
$938$	33.2705	1.08632
$939$	−65.7771	−2.14655
$940$	−28.4164	−0.926841
$941$	−20.3475	−0.663310	−0.331655	−	0.943401i	$-0.607607\pi$
$941$	−20.3475	−0.663310	−0.331655	+	0.943401i	$0.607607\pi$
$942$	101.812	3.31720
$943$	3.41641	0.111254
$944$	22.0344	0.717160
$945$	−5.85410	−0.190434
$946$	60.9787	1.98259
$947$	36.8673	1.19802	0.599012	−	0.800740i	$-0.295560\pi$
$947$	36.8673	1.19802	0.599012	+	0.800740i	$0.295560\pi$
$948$	−50.8328	−1.65097
$949$	0	0
$950$	−9.00000	−0.291999
$951$	68.6869	2.22733
$952$	−11.0000	−0.356512
$953$	26.7771	0.867395	0.433697	−	0.901059i	$-0.357209\pi$
$953$	26.7771	0.867395	0.433697	+	0.901059i	$0.357209\pi$
$954$	−37.9787	−1.22961
$955$	−55.9787	−1.81143
$956$	119.936	3.87901
$957$	34.4164	1.11252
$958$	65.3951	2.11282
$959$	−2.61803	−0.0845407
$960$	59.6869	1.92639
$961$	−8.83282	−0.284930
$962$	0	0
$963$	−13.0344	−0.420029
$964$	−119.228	−3.84007
$965$	−15.7082	−0.505665
$966$	30.6525	0.986227
$967$	39.0000	1.25416	0.627078	−	0.778957i	$-0.284251\pi$
$967$	39.0000	1.25416	0.627078	+	0.778957i	$0.284251\pi$
$968$	56.5066	1.81619
$969$	7.14590	0.229559
$970$	−129.228	−4.14926
$971$	31.5836	1.01357	0.506783	−	0.862074i	$-0.330835\pi$
$971$	31.5836	1.01357	0.506783	+	0.862074i	$0.330835\pi$
$972$	105.103	3.37119
$973$	−4.56231	−0.146261
$974$	78.4853	2.51483
$975$	0	0
$976$	−59.1246	−1.89253
$977$	22.5279	0.720730	0.360365	−	0.932811i	$-0.382652\pi$
$977$	22.5279	0.720730	0.360365	+	0.932811i	$0.382652\pi$
$978$	25.4164	0.812727
$979$	9.10333	0.290944
$980$	−12.7082	−0.405949
$981$	10.4377	0.333250
$982$	−32.4164	−1.03445
$983$	−18.3820	−0.586294	−0.293147	−	0.956067i	$-0.594702\pi$
$983$	−18.3820	−0.586294	−0.293147	+	0.956067i	$0.594702\pi$
$984$	−14.9443	−0.476406
$985$	−43.9787	−1.40128
$986$	27.3262	0.870245
$987$	5.85410	0.186338
$988$	0	0
$989$	−56.1803	−1.78643
$990$	−48.9787	−1.55665
$991$	−16.1459	−0.512891	−0.256446	−	0.966559i	$-0.582551\pi$
$991$	−16.1459	−0.512891	−0.256446	+	0.966559i	$0.582551\pi$
$992$	−51.1033	−1.62253
$993$	−26.5623	−0.842929
$994$	37.1246	1.17752
$995$	63.9230	2.02649
$996$	85.2492	2.70123
$997$	49.0000	1.55185	0.775923	−	0.630828i	$-0.217285\pi$
$997$	49.0000	1.55185	0.775923	+	0.630828i	$0.217285\pi$
$998$	38.8885	1.23100
$999$	8.94427	0.282984

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.c.1.1		2
7.6	odd	2		8281.2.a.n.1.1		2
13.4	even	6		91.2.f.a.29.1	yes	4
13.5	odd	4		1183.2.c.c.337.4		4
13.8	odd	4		1183.2.c.c.337.1		4
13.10	even	6		91.2.f.a.22.1	✓	4
13.12	even	2		1183.2.a.g.1.2		2
39.17	odd	6		819.2.o.c.757.2		4
39.23	odd	6		819.2.o.c.568.2		4
52.23	odd	6		1456.2.s.h.113.1		4
52.43	odd	6		1456.2.s.h.1121.1		4
91.4	even	6		637.2.h.g.471.2		4
91.10	odd	6		637.2.g.c.373.1		4
91.17	odd	6		637.2.h.f.471.2		4
91.23	even	6		637.2.h.g.165.2		4
91.30	even	6		637.2.g.b.263.1		4
91.62	odd	6		637.2.f.c.295.1		4
91.69	odd	6		637.2.f.c.393.1		4
91.75	odd	6		637.2.h.f.165.2		4
91.82	odd	6		637.2.g.c.263.1		4
91.88	even	6		637.2.g.b.373.1		4
91.90	odd	2		8281.2.a.bb.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.a.22.1	✓	4	13.10	even	6
91.2.f.a.29.1	yes	4	13.4	even	6
637.2.f.c.295.1		4	91.62	odd	6
637.2.f.c.393.1		4	91.69	odd	6
637.2.g.b.263.1		4	91.30	even	6
637.2.g.b.373.1		4	91.88	even	6
637.2.g.c.263.1		4	91.82	odd	6
637.2.g.c.373.1		4	91.10	odd	6
637.2.h.f.165.2		4	91.75	odd	6
637.2.h.f.471.2		4	91.17	odd	6
637.2.h.g.165.2		4	91.23	even	6
637.2.h.g.471.2		4	91.4	even	6
819.2.o.c.568.2		4	39.23	odd	6
819.2.o.c.757.2		4	39.17	odd	6
1183.2.a.c.1.1		2	1.1	even	1	trivial
1183.2.a.g.1.2		2	13.12	even	2
1183.2.c.c.337.1		4	13.8	odd	4
1183.2.c.c.337.4		4	13.5	odd	4
1456.2.s.h.113.1		4	52.23	odd	6
1456.2.s.h.1121.1		4	52.43	odd	6
8281.2.a.n.1.1		2	7.6	odd	2
8281.2.a.bb.1.2		2	91.90	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61803 q^{2} -2.61803 q^{3} +4.85410 q^{4} -2.61803 q^{5} +6.85410 q^{6} -1.00000 q^{7} -7.47214 q^{8} +3.85410 q^{9} +6.85410 q^{10} -1.85410 q^{11} -12.7082 q^{12} +2.61803 q^{14} +6.85410 q^{15} +9.85410 q^{16} -1.47214 q^{17} -10.0902 q^{18} +1.85410 q^{19} -12.7082 q^{20} +2.61803 q^{21} +4.85410 q^{22} -4.47214 q^{23} +19.5623 q^{24} +1.85410 q^{25} -2.23607 q^{27} -4.85410 q^{28} +7.09017 q^{29} -17.9443 q^{30} +4.70820 q^{31} -10.8541 q^{32} +4.85410 q^{33} +3.85410 q^{34} +2.61803 q^{35} +18.7082 q^{36} -4.00000 q^{37} -4.85410 q^{38} +19.5623 q^{40} -0.763932 q^{41} -6.85410 q^{42} +12.5623 q^{43} -9.00000 q^{44} -10.0902 q^{45} +11.7082 q^{46} +2.23607 q^{47} -25.7984 q^{48} +1.00000 q^{49} -4.85410 q^{50} +3.85410 q^{51} +3.76393 q^{53} +5.85410 q^{54} +4.85410 q^{55} +7.47214 q^{56} -4.85410 q^{57} -18.5623 q^{58} +2.23607 q^{59} +33.2705 q^{60} -6.00000 q^{61} -12.3262 q^{62} -3.85410 q^{63} +8.70820 q^{64} -12.7082 q^{66} +12.7082 q^{67} -7.14590 q^{68} +11.7082 q^{69} -6.85410 q^{70} +14.1803 q^{71} -28.7984 q^{72} +2.00000 q^{73} +10.4721 q^{74} -4.85410 q^{75} +9.00000 q^{76} +1.85410 q^{77} +4.00000 q^{79} -25.7984 q^{80} -5.70820 q^{81} +2.00000 q^{82} -6.70820 q^{83} +12.7082 q^{84} +3.85410 q^{85} -32.8885 q^{86} -18.5623 q^{87} +13.8541 q^{88} -4.90983 q^{89} +26.4164 q^{90} -21.7082 q^{92} -12.3262 q^{93} -5.85410 q^{94} -4.85410 q^{95} +28.4164 q^{96} -18.8541 q^{97} -2.61803 q^{98} -7.14590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 7 q^{6} - 2 q^{7} - 6 q^{8} + q^{9} + 7 q^{10} + 3 q^{11} - 12 q^{12} + 3 q^{14} + 7 q^{15} + 13 q^{16} + 6 q^{17} - 9 q^{18} - 3 q^{19} - 12 q^{20} + 3 q^{21}+ \cdots - 21 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 7 * q^6 - 2 * q^7 - 6 * q^8 + q^9 + 7 * q^10 + 3 * q^11 - 12 * q^12 + 3 * q^14 + 7 * q^15 + 13 * q^16 + 6 * q^17 - 9 * q^18 - 3 * q^19 - 12 * q^20 + 3 * q^21 + 3 * q^22 + 19 * q^24 - 3 * q^25 - 3 * q^28 + 3 * q^29 - 18 * q^30 - 4 * q^31 - 15 * q^32 + 3 * q^33 + q^34 + 3 * q^35 + 24 * q^36 - 8 * q^37 - 3 * q^38 + 19 * q^40 - 6 * q^41 - 7 * q^42 + 5 * q^43 - 18 * q^44 - 9 * q^45 + 10 * q^46 - 27 * q^48 + 2 * q^49 - 3 * q^50 + q^51 + 12 * q^53 + 5 * q^54 + 3 * q^55 + 6 * q^56 - 3 * q^57 - 17 * q^58 + 33 * q^60 - 12 * q^61 - 9 * q^62 - q^63 + 4 * q^64 - 12 * q^66 + 12 * q^67 - 21 * q^68 + 10 * q^69 - 7 * q^70 + 6 * q^71 - 33 * q^72 + 4 * q^73 + 12 * q^74 - 3 * q^75 + 18 * q^76 - 3 * q^77 + 8 * q^79 - 27 * q^80 + 2 * q^81 + 4 * q^82 + 12 * q^84 + q^85 - 30 * q^86 - 17 * q^87 + 21 * q^88 - 21 * q^89 + 26 * q^90 - 30 * q^92 - 9 * q^93 - 5 * q^94 - 3 * q^95 + 30 * q^96 - 31 * q^97 - 3 * q^98 - 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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