LMFDB - Embedded newform 2107.4.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2107,4,Mod(1,2107)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2107, 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("2107.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2107 = 7^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2107.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:	$124.317024382$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 32x^{4} - 16x^{3} + 251x^{2} + 276x + 60 $ x^6 - 32x^4 - 16x^3 + 251x^2 + 276x + 60
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-3.17112$ of defining polynomial
Character	$\chi$	$=$	2107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.17112 q^{2} -2.46717 q^{3} +9.39827 q^{4} +7.54340 q^{5} -10.2909 q^{6} +5.83236 q^{8} -20.9131 q^{9} +O(q^{10})$	\(q+4.17112 q^{2} -2.46717 q^{3} +9.39827 q^{4} +7.54340 q^{5} -10.2909 q^{6} +5.83236 q^{8} -20.9131 q^{9} +31.4645 q^{10} +26.9150 q^{11} -23.1872 q^{12} +15.6529 q^{13} -18.6109 q^{15} -50.8587 q^{16} -27.2420 q^{17} -87.2309 q^{18} -38.3104 q^{19} +70.8949 q^{20} +112.266 q^{22} +82.5575 q^{23} -14.3894 q^{24} -68.0971 q^{25} +65.2903 q^{26} +118.210 q^{27} -34.2852 q^{29} -77.6283 q^{30} -119.055 q^{31} -258.797 q^{32} -66.4040 q^{33} -113.630 q^{34} -196.547 q^{36} +378.527 q^{37} -159.797 q^{38} -38.6185 q^{39} +43.9958 q^{40} -385.478 q^{41} -43.0000 q^{43} +252.955 q^{44} -157.756 q^{45} +344.358 q^{46} -271.022 q^{47} +125.477 q^{48} -284.041 q^{50} +67.2108 q^{51} +147.110 q^{52} -329.363 q^{53} +493.068 q^{54} +203.031 q^{55} +94.5184 q^{57} -143.008 q^{58} +173.956 q^{59} -174.910 q^{60} -54.5012 q^{61} -496.592 q^{62} -672.604 q^{64} +118.076 q^{65} -276.979 q^{66} -906.954 q^{67} -256.028 q^{68} -203.684 q^{69} -621.376 q^{71} -121.972 q^{72} +1025.87 q^{73} +1578.88 q^{74} +168.007 q^{75} -360.052 q^{76} -161.082 q^{78} -737.945 q^{79} -383.647 q^{80} +273.009 q^{81} -1607.88 q^{82} -558.465 q^{83} -205.498 q^{85} -179.358 q^{86} +84.5875 q^{87} +156.978 q^{88} -1631.31 q^{89} -658.018 q^{90} +775.898 q^{92} +293.729 q^{93} -1130.47 q^{94} -288.991 q^{95} +638.496 q^{96} +406.607 q^{97} -562.875 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 7 q^{3} + 22 q^{4} - 43 q^{5} + 3 q^{6} + 54 q^{8} + 81 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 7 * q^3 + 22 * q^4 - 43 * q^5 + 3 * q^6 + 54 * q^8 + 81 * q^9	\( 6 q + 6 q^{2} - 7 q^{3} + 22 q^{4} - 43 q^{5} + 3 q^{6} + 54 q^{8} + 81 q^{9} - 57 q^{10} - 28 q^{11} + 157 q^{12} - 56 q^{13} - 124 q^{15} - 54 q^{16} - 19 q^{17} - 81 q^{18} + 75 q^{19} - 135 q^{20} - 504 q^{22} + 131 q^{23} + 567 q^{24} + 105 q^{25} - 44 q^{26} - 238 q^{27} + 515 q^{29} - 396 q^{30} - 237 q^{31} + 558 q^{32} - 540 q^{33} + 107 q^{34} + 73 q^{36} + 269 q^{37} - 527 q^{38} + 290 q^{39} - 613 q^{40} - 471 q^{41} - 258 q^{43} - 428 q^{44} - 334 q^{45} - 67 q^{46} - 415 q^{47} + 989 q^{48} + 1335 q^{50} - 1241 q^{51} + 8 q^{52} + 450 q^{53} - 402 q^{54} + 1732 q^{55} - 1000 q^{57} - 1055 q^{58} - 356 q^{59} - 2732 q^{60} + 1328 q^{61} - 1603 q^{62} + 466 q^{64} - 62 q^{65} - 156 q^{66} - 632 q^{67} - 571 q^{68} + 1130 q^{69} - 144 q^{71} + 567 q^{72} - 864 q^{73} + 1207 q^{74} + 2494 q^{75} - 1005 q^{76} + 2222 q^{78} - 1613 q^{79} - 2399 q^{80} - 102 q^{81} - 1673 q^{82} + 682 q^{83} + 84 q^{85} - 258 q^{86} - 449 q^{87} - 608 q^{88} - 3378 q^{89} - 930 q^{90} + 3491 q^{92} + 1879 q^{93} - 3197 q^{94} - 79 q^{95} + 591 q^{96} + 55 q^{97} - 1612 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 7 * q^3 + 22 * q^4 - 43 * q^5 + 3 * q^6 + 54 * q^8 + 81 * q^9 - 57 * q^10 - 28 * q^11 + 157 * q^12 - 56 * q^13 - 124 * q^15 - 54 * q^16 - 19 * q^17 - 81 * q^18 + 75 * q^19 - 135 * q^20 - 504 * q^22 + 131 * q^23 + 567 * q^24 + 105 * q^25 - 44 * q^26 - 238 * q^27 + 515 * q^29 - 396 * q^30 - 237 * q^31 + 558 * q^32 - 540 * q^33 + 107 * q^34 + 73 * q^36 + 269 * q^37 - 527 * q^38 + 290 * q^39 - 613 * q^40 - 471 * q^41 - 258 * q^43 - 428 * q^44 - 334 * q^45 - 67 * q^46 - 415 * q^47 + 989 * q^48 + 1335 * q^50 - 1241 * q^51 + 8 * q^52 + 450 * q^53 - 402 * q^54 + 1732 * q^55 - 1000 * q^57 - 1055 * q^58 - 356 * q^59 - 2732 * q^60 + 1328 * q^61 - 1603 * q^62 + 466 * q^64 - 62 * q^65 - 156 * q^66 - 632 * q^67 - 571 * q^68 + 1130 * q^69 - 144 * q^71 + 567 * q^72 - 864 * q^73 + 1207 * q^74 + 2494 * q^75 - 1005 * q^76 + 2222 * q^78 - 1613 * q^79 - 2399 * q^80 - 102 * q^81 - 1673 * q^82 + 682 * q^83 + 84 * q^85 - 258 * q^86 - 449 * q^87 - 608 * q^88 - 3378 * q^89 - 930 * q^90 + 3491 * q^92 + 1879 * q^93 - 3197 * q^94 - 79 * q^95 + 591 * q^96 + 55 * q^97 - 1612 * 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 $

$2$	4.17112	1.47471	0.737357	−	0.675503i	$-0.236073\pi$
$2$	4.17112	1.47471	0.737357	+	0.675503i	$0.236073\pi$
$3$	−2.46717	−0.474808	−0.237404	−	0.971411i	$-0.576296\pi$
$3$	−2.46717	−0.474808	−0.237404	+	0.971411i	$0.576296\pi$
$4$	9.39827	1.17478
$5$	7.54340	0.674702	0.337351	−	0.941379i	$-0.390469\pi$
$5$	7.54340	0.674702	0.337351	+	0.941379i	$0.390469\pi$
$6$	−10.2909	−0.700206
$7$	0	0
$7$	0	0
$8$	5.83236	0.257756
$9$	−20.9131	−0.774558
$10$	31.4645	0.994994
$11$	26.9150	0.737744	0.368872	−	0.929480i	$-0.379744\pi$
$11$	26.9150	0.737744	0.368872	+	0.929480i	$0.379744\pi$
$12$	−23.1872	−0.557796
$13$	15.6529	0.333949	0.166975	−	0.985961i	$-0.446600\pi$
$13$	15.6529	0.333949	0.166975	+	0.985961i	$0.446600\pi$
$14$	0	0
$15$	−18.6109	−0.320354
$16$	−50.8587	−0.794667
$17$	−27.2420	−0.388657	−0.194328	−	0.980937i	$-0.562253\pi$
$17$	−27.2420	−0.388657	−0.194328	+	0.980937i	$0.562253\pi$
$18$	−87.2309	−1.14225
$19$	−38.3104	−0.462580	−0.231290	−	0.972885i	$-0.574295\pi$
$19$	−38.3104	−0.462580	−0.231290	+	0.972885i	$0.574295\pi$
$20$	70.8949	0.792629
$21$	0	0
$22$	112.266	1.08796
$23$	82.5575	0.748453	0.374227	−	0.927337i	$-0.377908\pi$
$23$	82.5575	0.748453	0.374227	+	0.927337i	$0.377908\pi$
$24$	−14.3894	−0.122385
$25$	−68.0971	−0.544777
$26$	65.2903	0.492480
$27$	118.210	0.842574
$28$	0	0
$29$	−34.2852	−0.219538	−0.109769	−	0.993957i	$-0.535011\pi$
$29$	−34.2852	−0.219538	−0.109769	+	0.993957i	$0.535011\pi$
$30$	−77.6283	−0.472431
$31$	−119.055	−0.689770	−0.344885	−	0.938645i	$-0.612082\pi$
$31$	−119.055	−0.689770	−0.344885	+	0.938645i	$0.612082\pi$
$32$	−258.797	−1.42966
$33$	−66.4040	−0.350286
$34$	−113.630	−0.573158
$35$	0	0
$36$	−196.547	−0.909938
$37$	378.527	1.68188	0.840939	−	0.541129i	$-0.182003\pi$
$37$	378.527	1.68188	0.840939	+	0.541129i	$0.182003\pi$
$38$	−159.797	−0.682173
$39$	−38.6185	−0.158562
$40$	43.9958	0.173909
$41$	−385.478	−1.46833	−0.734166	−	0.678970i	$-0.762427\pi$
$41$	−385.478	−1.46833	−0.734166	+	0.678970i	$0.762427\pi$
$42$	0	0
$43$	−43.0000	−0.152499
$43$	−43.0000	−0.152499
$44$	252.955	0.866689
$45$	−157.756	−0.522596
$46$	344.358	1.10376
$47$	−271.022	−0.841120	−0.420560	−	0.907265i	$-0.638166\pi$
$47$	−271.022	−0.841120	−0.420560	+	0.907265i	$0.638166\pi$
$48$	125.477	0.377314
$49$	0	0
$50$	−284.041	−0.803390
$51$	67.2108	0.184537
$52$	147.110	0.392318
$53$	−329.363	−0.853612	−0.426806	−	0.904343i	$-0.640361\pi$
$53$	−329.363	−0.853612	−0.426806	+	0.904343i	$0.640361\pi$
$54$	493.068	1.24256
$55$	203.031	0.497757
$56$	0	0
$57$	94.5184	0.219636
$58$	−143.008	−0.323756
$59$	173.956	0.383849	0.191924	−	0.981410i	$-0.438527\pi$
$59$	173.956	0.383849	0.191924	+	0.981410i	$0.438527\pi$
$60$	−174.910	−0.376346
$61$	−54.5012	−0.114396	−0.0571981	−	0.998363i	$-0.518217\pi$
$61$	−54.5012	−0.114396	−0.0571981	+	0.998363i	$0.518217\pi$
$62$	−496.592	−1.01721
$63$	0	0
$64$	−672.604	−1.31368
$65$	118.076	0.225316
$66$	−276.979	−0.516572
$67$	−906.954	−1.65376	−0.826881	−	0.562377i	$-0.809887\pi$
$67$	−906.954	−1.65376	−0.826881	+	0.562377i	$0.809887\pi$
$68$	−256.028	−0.456588
$69$	−203.684	−0.355371
$70$	0	0
$71$	−621.376	−1.03864	−0.519322	−	0.854579i	$-0.673816\pi$
$71$	−621.376	−1.03864	−0.519322	+	0.854579i	$0.673816\pi$
$72$	−121.972	−0.199647
$73$	1025.87	1.64477	0.822387	−	0.568928i	$-0.192642\pi$
$73$	1025.87	1.64477	0.822387	+	0.568928i	$0.192642\pi$
$74$	1578.88	2.48029
$75$	168.007	0.258664
$76$	−360.052	−0.543431
$77$	0	0
$78$	−161.082	−0.233833
$79$	−737.945	−1.05095	−0.525476	−	0.850808i	$-0.676113\pi$
$79$	−737.945	−1.05095	−0.525476	+	0.850808i	$0.676113\pi$
$80$	−383.647	−0.536164
$81$	273.009	0.374497
$82$	−1607.88	−2.16537
$83$	−558.465	−0.738548	−0.369274	−	0.929321i	$-0.620394\pi$
$83$	−558.465	−0.738548	−0.369274	+	0.929321i	$0.620394\pi$
$84$	0	0
$85$	−205.498	−0.262228
$86$	−179.358	−0.224892
$87$	84.5875	0.104238
$88$	156.978	0.190158
$89$	−1631.31	−1.94291	−0.971453	−	0.237231i	$-0.923760\pi$
$89$	−1631.31	−1.94291	−0.971453	+	0.237231i	$0.923760\pi$
$90$	−658.018	−0.770680
$91$	0	0
$92$	775.898	0.879271
$93$	293.729	0.327508
$94$	−1130.47	−1.24041
$95$	−288.991	−0.312104
$96$	638.496	0.678815
$97$	406.607	0.425616	0.212808	−	0.977094i	$-0.431739\pi$
$97$	406.607	0.425616	0.212808	+	0.977094i	$0.431739\pi$
$98$	0	0
$99$	−562.875	−0.571425
$100$	−639.995	−0.639995
$101$	−1000.43	−0.985606	−0.492803	−	0.870141i	$-0.664028\pi$
$101$	−1000.43	−0.985606	−0.492803	+	0.870141i	$0.664028\pi$
$102$	280.345	0.272140
$103$	1659.81	1.58783	0.793913	−	0.608031i	$-0.208040\pi$
$103$	1659.81	1.58783	0.793913	+	0.608031i	$0.208040\pi$
$104$	91.2935	0.0860775
$105$	0	0
$106$	−1373.81	−1.25883
$107$	−151.590	−0.136961	−0.0684803	−	0.997652i	$-0.521815\pi$
$107$	−151.590	−0.136961	−0.0684803	+	0.997652i	$0.521815\pi$
$108$	1110.97	0.989842
$109$	1092.76	0.960254	0.480127	−	0.877199i	$-0.340591\pi$
$109$	1092.76	0.960254	0.480127	+	0.877199i	$0.340591\pi$
$110$	846.866	0.734050
$111$	−933.892	−0.798569
$112$	0	0
$113$	−970.442	−0.807889	−0.403945	−	0.914783i	$-0.632361\pi$
$113$	−970.442	−0.807889	−0.403945	+	0.914783i	$0.632361\pi$
$114$	394.248	0.323901
$115$	622.764	0.504983
$116$	−322.222	−0.257910
$117$	−327.351	−0.258663
$118$	725.590	0.566068
$119$	0	0
$120$	−108.545	−0.0825732
$121$	−606.582	−0.455734
$122$	−227.331	−0.168702
$123$	951.042	0.697175
$124$	−1118.91	−0.810331
$125$	−1456.61	−1.04226
$126$	0	0
$127$	2115.78	1.47831	0.739155	−	0.673535i	$-0.235225\pi$
$127$	2115.78	1.47831	0.739155	+	0.673535i	$0.235225\pi$
$128$	−735.139	−0.507638
$129$	106.088	0.0724075
$130$	492.511	0.332277
$131$	1695.44	1.13077	0.565386	−	0.824826i	$-0.308727\pi$
$131$	1695.44	1.13077	0.565386	+	0.824826i	$0.308727\pi$
$132$	−624.083	−0.411511
$133$	0	0
$134$	−3783.02	−2.43883
$135$	891.704	0.568486
$136$	−158.885	−0.100179
$137$	1613.51	1.00622	0.503108	−	0.864224i	$-0.332190\pi$
$137$	1613.51	1.00622	0.503108	+	0.864224i	$0.332190\pi$
$138$	−849.590	−0.524071
$139$	−2072.45	−1.26463	−0.632313	−	0.774713i	$-0.717894\pi$
$139$	−2072.45	−1.26463	−0.632313	+	0.774713i	$0.717894\pi$
$140$	0	0
$141$	668.658	0.399370
$142$	−2591.84	−1.53170
$143$	421.299	0.246369
$144$	1063.61	0.615515
$145$	−258.627	−0.148123
$146$	4279.01	2.42557
$147$	0	0
$148$	3557.50	1.97584
$149$	−811.396	−0.446122	−0.223061	−	0.974805i	$-0.571605\pi$
$149$	−811.396	−0.446122	−0.223061	+	0.974805i	$0.571605\pi$
$150$	700.779	0.381456
$151$	−944.326	−0.508928	−0.254464	−	0.967082i	$-0.581899\pi$
$151$	−944.326	−0.508928	−0.254464	+	0.967082i	$0.581899\pi$
$152$	−223.440	−0.119233
$153$	569.714	0.301037
$154$	0	0
$155$	−898.078	−0.465390
$156$	−362.947	−0.186276
$157$	−2138.58	−1.08712	−0.543558	−	0.839372i	$-0.682923\pi$
$157$	−2138.58	−1.08712	−0.543558	+	0.839372i	$0.682923\pi$
$158$	−3078.06	−1.54986
$159$	812.595	0.405302
$160$	−1952.21	−0.964597
$161$	0	0
$162$	1138.75	0.552277
$163$	−2184.57	−1.04975	−0.524873	−	0.851180i	$-0.675887\pi$
$163$	−2184.57	−1.04975	−0.524873	+	0.851180i	$0.675887\pi$
$164$	−3622.83	−1.72497
$165$	−500.912	−0.236339
$166$	−2329.43	−1.08915
$167$	−3334.42	−1.54506	−0.772531	−	0.634978i	$-0.781009\pi$
$167$	−3334.42	−1.54506	−0.772531	+	0.634978i	$0.781009\pi$
$168$	0	0
$169$	−1951.99	−0.888478
$170$	−857.156	−0.386711
$171$	801.188	0.358295
$172$	−404.126	−0.179153
$173$	−1169.82	−0.514105	−0.257052	−	0.966397i	$-0.582751\pi$
$173$	−1169.82	−0.514105	−0.257052	+	0.966397i	$0.582751\pi$
$174$	352.825	0.153722
$175$	0	0
$176$	−1368.86	−0.586260
$177$	−429.178	−0.182254
$178$	−6804.40	−2.86523
$179$	206.597	0.0862669	0.0431334	−	0.999069i	$-0.486266\pi$
$179$	206.597	0.0862669	0.0431334	+	0.999069i	$0.486266\pi$
$180$	−1482.63	−0.613937
$181$	−652.242	−0.267849	−0.133925	−	0.990992i	$-0.542758\pi$
$181$	−652.242	−0.267849	−0.133925	+	0.990992i	$0.542758\pi$
$182$	0	0
$183$	134.464	0.0543162
$184$	481.505	0.192919
$185$	2855.38	1.13477
$186$	1225.18	0.482981
$187$	−733.220	−0.286729
$188$	−2547.14	−0.988134
$189$	0	0
$190$	−1205.42	−0.460264
$191$	−1128.21	−0.427404	−0.213702	−	0.976899i	$-0.568552\pi$
$191$	−1128.21	−0.427404	−0.213702	+	0.976899i	$0.568552\pi$
$192$	1659.43	0.623745
$193$	355.606	0.132627	0.0663136	−	0.997799i	$-0.478876\pi$
$193$	355.606	0.132627	0.0663136	+	0.997799i	$0.478876\pi$
$194$	1696.01	0.627662
$195$	−291.315	−0.106982
$196$	0	0
$197$	4347.00	1.57214	0.786068	−	0.618140i	$-0.212114\pi$
$197$	4347.00	1.57214	0.786068	+	0.618140i	$0.212114\pi$
$198$	−2347.82	−0.842689
$199$	−430.375	−0.153309	−0.0766545	−	0.997058i	$-0.524424\pi$
$199$	−430.375	−0.153309	−0.0766545	+	0.997058i	$0.524424\pi$
$200$	−397.167	−0.140420
$201$	2237.61	0.785219
$202$	−4172.91	−1.45349
$203$	0	0
$204$	631.665	0.216791
$205$	−2907.82	−0.990687
$206$	6923.28	2.34159
$207$	−1726.53	−0.579720
$208$	−796.087	−0.265378
$209$	−1031.13	−0.341265
$210$	0	0
$211$	103.702	0.0338347	0.0169174	−	0.999857i	$-0.494615\pi$
$211$	103.702	0.0338347	0.0169174	+	0.999857i	$0.494615\pi$
$212$	−3095.44	−1.00281
$213$	1533.04	0.493156
$214$	−632.302	−0.201978
$215$	−324.366	−0.102891
$216$	689.442	0.217179
$217$	0	0
$218$	4558.05	1.41610
$219$	−2530.99	−0.780951
$220$	1908.14	0.584757
$221$	−426.418	−0.129792
$222$	−3895.38	−1.17766
$223$	−4447.94	−1.33568	−0.667839	−	0.744306i	$-0.732781\pi$
$223$	−4447.94	−1.33568	−0.667839	+	0.744306i	$0.732781\pi$
$224$	0	0
$225$	1424.12	0.421961
$226$	−4047.83	−1.19141
$227$	−509.808	−0.149062	−0.0745311	−	0.997219i	$-0.523746\pi$
$227$	−509.808	−0.149062	−0.0745311	+	0.997219i	$0.523746\pi$
$228$	888.310	0.258025
$229$	4754.86	1.37210	0.686049	−	0.727556i	$-0.259344\pi$
$229$	4754.86	1.37210	0.686049	+	0.727556i	$0.259344\pi$
$230$	2597.63	0.744706
$231$	0	0
$232$	−199.964	−0.0565873
$233$	893.223	0.251146	0.125573	−	0.992084i	$-0.459923\pi$
$233$	893.223	0.251146	0.125573	+	0.992084i	$0.459923\pi$
$234$	−1365.42	−0.381454
$235$	−2044.43	−0.567506
$236$	1634.88	0.450939
$237$	1820.64	0.499000
$238$	0	0
$239$	−3883.75	−1.05112	−0.525562	−	0.850755i	$-0.676145\pi$
$239$	−3883.75	−1.05112	−0.525562	+	0.850755i	$0.676145\pi$
$240$	946.524	0.254575
$241$	3118.83	0.833616	0.416808	−	0.908995i	$-0.363149\pi$
$241$	3118.83	0.833616	0.416808	+	0.908995i	$0.363149\pi$
$242$	−2530.13	−0.672078
$243$	−3865.22	−1.02039
$244$	−512.217	−0.134391
$245$	0	0
$246$	3966.91	1.02813
$247$	−599.670	−0.154478
$248$	−694.370	−0.177793
$249$	1377.83	0.350668
$250$	−6075.70	−1.53704
$251$	−5196.19	−1.30669	−0.653347	−	0.757058i	$-0.726636\pi$
$251$	−5196.19	−1.30669	−0.653347	+	0.757058i	$0.726636\pi$
$252$	0	0
$253$	2222.04	0.552167
$254$	8825.19	2.18009
$255$	506.998	0.124508
$256$	2314.47	0.565057
$257$	2441.32	0.592550	0.296275	−	0.955103i	$-0.404256\pi$
$257$	2441.32	0.592550	0.296275	+	0.955103i	$0.404256\pi$
$258$	442.508	0.106780
$259$	0	0
$260$	1109.71	0.264698
$261$	717.008	0.170045
$262$	7071.89	1.66757
$263$	5831.01	1.36713	0.683566	−	0.729889i	$-0.260428\pi$
$263$	5831.01	1.36713	0.683566	+	0.729889i	$0.260428\pi$
$264$	−387.292	−0.0902885
$265$	−2484.52	−0.575934
$266$	0	0
$267$	4024.73	0.922507
$268$	−8523.80	−1.94281
$269$	2605.41	0.590538	0.295269	−	0.955414i	$-0.404591\pi$
$269$	2605.41	0.590538	0.295269	+	0.955414i	$0.404591\pi$
$270$	3719.41	0.838355
$271$	−1793.84	−0.402097	−0.201049	−	0.979581i	$-0.564435\pi$
$271$	−1793.84	−0.402097	−0.201049	+	0.979581i	$0.564435\pi$
$272$	1385.49	0.308853
$273$	0	0
$274$	6730.16	1.48388
$275$	−1832.83	−0.401906
$276$	−1914.27	−0.417485
$277$	−825.071	−0.178967	−0.0894833	−	0.995988i	$-0.528522\pi$
$277$	−825.071	−0.178967	−0.0894833	+	0.995988i	$0.528522\pi$
$278$	−8644.45	−1.86496
$279$	2489.80	0.534267
$280$	0	0
$281$	−5114.69	−1.08582	−0.542912	−	0.839789i	$-0.682678\pi$
$281$	−5114.69	−1.08582	−0.542912	+	0.839789i	$0.682678\pi$
$282$	2789.06	0.588957
$283$	3703.40	0.777895	0.388947	−	0.921260i	$-0.372839\pi$
$283$	3703.40	0.777895	0.388947	+	0.921260i	$0.372839\pi$
$284$	−5839.86	−1.22018
$285$	712.990	0.148189
$286$	1757.29	0.363324
$287$	0	0
$288$	5412.23	1.10736
$289$	−4170.87	−0.848946
$290$	−1078.77	−0.218439
$291$	−1003.17	−0.202085
$292$	9641.37	1.93225
$293$	−749.193	−0.149380	−0.0746899	−	0.997207i	$-0.523797\pi$
$293$	−749.193	−0.149380	−0.0746899	+	0.997207i	$0.523797\pi$
$294$	0	0
$295$	1312.22	0.258984
$296$	2207.71	0.433515
$297$	3181.62	0.621603
$298$	−3384.43	−0.657902
$299$	1292.27	0.249946
$300$	1578.98	0.303874
$301$	0	0
$302$	−3938.90	−0.750524
$303$	2468.23	0.467973
$304$	1948.42	0.367597
$305$	−411.125	−0.0771834
$306$	2376.35	0.443944
$307$	4761.00	0.885097	0.442548	−	0.896745i	$-0.354075\pi$
$307$	4761.00	0.885097	0.442548	+	0.896745i	$0.354075\pi$
$308$	0	0
$309$	−4095.04	−0.753912
$310$	−3745.99	−0.686317
$311$	5995.99	1.09325	0.546626	−	0.837377i	$-0.315912\pi$
$311$	5995.99	1.09325	0.546626	+	0.837377i	$0.315912\pi$
$312$	−225.237	−0.0408703
$313$	−398.261	−0.0719203	−0.0359602	−	0.999353i	$-0.511449\pi$
$313$	−398.261	−0.0719203	−0.0359602	+	0.999353i	$0.511449\pi$
$314$	−8920.27	−1.60318
$315$	0	0
$316$	−6935.40	−1.23464
$317$	4657.19	0.825154	0.412577	−	0.910923i	$-0.364629\pi$
$317$	4657.19	0.825154	0.412577	+	0.910923i	$0.364629\pi$
$318$	3389.43	0.597704
$319$	−922.786	−0.161963
$320$	−5073.72	−0.886342
$321$	374.000	0.0650300
$322$	0	0
$323$	1043.65	0.179785
$324$	2565.81	0.439954
$325$	−1065.92	−0.181928
$326$	−9112.11	−1.54808
$327$	−2696.03	−0.455936
$328$	−2248.25	−0.378472
$329$	0	0
$330$	−2089.37	−0.348533
$331$	10013.6	1.66282	0.831412	−	0.555656i	$-0.187533\pi$
$331$	10013.6	1.66282	0.831412	+	0.555656i	$0.187533\pi$
$332$	−5248.60	−0.867634
$333$	−7916.16	−1.30271
$334$	−13908.3	−2.27852
$335$	−6841.52	−1.11580
$336$	0	0
$337$	−3872.11	−0.625897	−0.312949	−	0.949770i	$-0.601317\pi$
$337$	−3872.11	−0.625897	−0.312949	+	0.949770i	$0.601317\pi$
$338$	−8141.97	−1.31025
$339$	2394.25	0.383592
$340$	−1931.32	−0.308061
$341$	−3204.36	−0.508874
$342$	3341.85	0.528382
$343$	0	0
$344$	−250.791	−0.0393075
$345$	−1536.47	−0.239770
$346$	−4879.48	−0.758158
$347$	10290.8	1.59204	0.796022	−	0.605267i	$-0.206934\pi$
$347$	10290.8	1.59204	0.796022	+	0.605267i	$0.206934\pi$
$348$	794.976	0.122457
$349$	−700.572	−0.107452	−0.0537260	−	0.998556i	$-0.517110\pi$
$349$	−700.572	−0.107452	−0.0537260	+	0.998556i	$0.517110\pi$
$350$	0	0
$351$	1850.33	0.281377
$352$	−6965.52	−1.05473
$353$	−3608.33	−0.544057	−0.272028	−	0.962289i	$-0.587694\pi$
$353$	−3608.33	−0.544057	−0.272028	+	0.962289i	$0.587694\pi$
$354$	−1790.16	−0.268773
$355$	−4687.29	−0.700776
$356$	−15331.5	−2.28250
$357$	0	0
$358$	861.741	0.127219
$359$	−12085.9	−1.77680	−0.888399	−	0.459072i	$-0.848182\pi$
$359$	−12085.9	−1.77680	−0.888399	+	0.459072i	$0.848182\pi$
$360$	−920.087	−0.134702
$361$	−5391.31	−0.786020
$362$	−2720.58	−0.395001
$363$	1496.54	0.216386
$364$	0	0
$365$	7738.52	1.10973
$366$	560.866	0.0801009
$367$	−968.974	−0.137820	−0.0689101	−	0.997623i	$-0.521952\pi$
$367$	−968.974	−0.137820	−0.0689101	+	0.997623i	$0.521952\pi$
$368$	−4198.77	−0.594771
$369$	8061.53	1.13731
$370$	11910.2	1.67346
$371$	0	0
$372$	2760.54	0.384751
$373$	13006.0	1.80543	0.902713	−	0.430243i	$-0.141572\pi$
$373$	13006.0	1.80543	0.902713	+	0.430243i	$0.141572\pi$
$374$	−3058.35	−0.422844
$375$	3593.71	0.494875
$376$	−1580.70	−0.216804
$377$	−536.664	−0.0733146
$378$	0	0
$379$	1901.08	0.257657	0.128828	−	0.991667i	$-0.458878\pi$
$379$	1901.08	0.257657	0.128828	+	0.991667i	$0.458878\pi$
$380$	−2716.01	−0.366654
$381$	−5220.00	−0.701913
$382$	−4705.89	−0.630299
$383$	9501.65	1.26765	0.633827	−	0.773475i	$-0.281483\pi$
$383$	9501.65	1.26765	0.633827	+	0.773475i	$0.281483\pi$
$384$	1813.71	0.241031
$385$	0	0
$386$	1483.27	0.195587
$387$	899.262	0.118119
$388$	3821.40	0.500006
$389$	4640.26	0.604808	0.302404	−	0.953180i	$-0.402211\pi$
$389$	4640.26	0.604808	0.302404	+	0.953180i	$0.402211\pi$
$390$	−1215.11	−0.157768
$391$	−2249.03	−0.290891
$392$	0	0
$393$	−4182.94	−0.536899
$394$	18131.9	2.31845
$395$	−5566.61	−0.709080
$396$	−5290.05	−0.671301
$397$	−4633.90	−0.585815	−0.292908	−	0.956141i	$-0.594623\pi$
$397$	−4633.90	−0.585815	−0.292908	+	0.956141i	$0.594623\pi$
$398$	−1795.15	−0.226087
$399$	0	0
$400$	3463.33	0.432916
$401$	−11801.3	−1.46965	−0.734823	−	0.678258i	$-0.762735\pi$
$401$	−11801.3	−1.46965	−0.734823	+	0.678258i	$0.762735\pi$
$402$	9333.35	1.15797
$403$	−1863.56	−0.230348
$404$	−9402.29	−1.15787
$405$	2059.41	0.252674
$406$	0	0
$407$	10188.1	1.24080
$408$	391.998	0.0475656
$409$	−5588.72	−0.675658	−0.337829	−	0.941207i	$-0.609693\pi$
$409$	−5588.72	−0.675658	−0.337829	+	0.941207i	$0.609693\pi$
$410$	−12128.9	−1.46098
$411$	−3980.81	−0.477759
$412$	15599.4	1.86535
$413$	0	0
$414$	−7201.57	−0.854922
$415$	−4212.72	−0.498300
$416$	−4050.93	−0.477435
$417$	5113.09	0.600454
$418$	−4300.95	−0.503269
$419$	6908.94	0.805547	0.402773	−	0.915300i	$-0.368046\pi$
$419$	6908.94	0.805547	0.402773	+	0.915300i	$0.368046\pi$
$420$	0	0
$421$	16499.6	1.91007	0.955036	−	0.296491i	$-0.0958165\pi$
$421$	16499.6	1.91007	0.955036	+	0.296491i	$0.0958165\pi$
$422$	432.553	0.0498966
$423$	5667.90	0.651496
$424$	−1920.96	−0.220024
$425$	1855.10	0.211731
$426$	6394.51	0.727265
$427$	0	0
$428$	−1424.69	−0.160899
$429$	−1039.42	−0.116978
$430$	−1352.97	−0.151735
$431$	−7101.67	−0.793679	−0.396839	−	0.917888i	$-0.629893\pi$
$431$	−7101.67	−0.793679	−0.396839	+	0.917888i	$0.629893\pi$
$432$	−6011.99	−0.669565
$433$	8935.72	0.991739	0.495870	−	0.868397i	$-0.334849\pi$
$433$	8935.72	0.991739	0.495870	+	0.868397i	$0.334849\pi$
$434$	0	0
$435$	638.077	0.0703298
$436$	10270.1	1.12809
$437$	−3162.81	−0.346219
$438$	−10557.1	−1.15168
$439$	−17789.3	−1.93403	−0.967015	−	0.254720i	$-0.918017\pi$
$439$	−17789.3	−1.93403	−0.967015	+	0.254720i	$0.918017\pi$
$440$	1184.15	0.128300
$441$	0	0
$442$	−1778.64	−0.191406
$443$	2744.62	0.294359	0.147180	−	0.989110i	$-0.452980\pi$
$443$	2744.62	0.294359	0.147180	+	0.989110i	$0.452980\pi$
$444$	−8776.97	−0.938146
$445$	−12305.6	−1.31088
$446$	−18552.9	−1.96974
$447$	2001.85	0.211822
$448$	0	0
$449$	−12051.9	−1.26673	−0.633366	−	0.773853i	$-0.718327\pi$
$449$	−12051.9	−1.26673	−0.633366	+	0.773853i	$0.718327\pi$
$450$	5940.17	0.622272
$451$	−10375.2	−1.08325
$452$	−9120.47	−0.949095
$453$	2329.81	0.241643
$454$	−2126.47	−0.219824
$455$	0	0
$456$	551.265	0.0566126
$457$	130.425	0.0133502	0.00667509	−	0.999978i	$-0.497875\pi$
$457$	130.425	0.0133502	0.00667509	+	0.999978i	$0.497875\pi$
$458$	19833.1	2.02345
$459$	−3220.28	−0.327472
$460$	5852.91	0.593246
$461$	981.122	0.0991223	0.0495612	−	0.998771i	$-0.484218\pi$
$461$	981.122	0.0991223	0.0495612	+	0.998771i	$0.484218\pi$
$462$	0	0
$463$	6359.89	0.638378	0.319189	−	0.947691i	$-0.396589\pi$
$463$	6359.89	0.638378	0.319189	+	0.947691i	$0.396589\pi$
$464$	1743.70	0.174460
$465$	2215.71	0.220970
$466$	3725.75	0.370369
$467$	14159.9	1.40309	0.701546	−	0.712624i	$-0.252494\pi$
$467$	14159.9	1.40309	0.701546	+	0.712624i	$0.252494\pi$
$468$	−3076.53	−0.303873
$469$	0	0
$470$	−8527.57	−0.836909
$471$	5276.24	0.516170
$472$	1014.57	0.0989395
$473$	−1157.35	−0.112505
$474$	7594.10	0.735883
$475$	2608.83	0.252003
$476$	0	0
$477$	6887.98	0.661172
$478$	−16199.6	−1.55011
$479$	20583.3	1.96342	0.981709	−	0.190390i	$-0.0609751\pi$
$479$	20583.3	1.96342	0.981709	+	0.190390i	$0.0609751\pi$
$480$	4816.43	0.457998
$481$	5925.06	0.561662
$482$	13009.0	1.22935
$483$	0	0
$484$	−5700.82	−0.535389
$485$	3067.20	0.287164
$486$	−16122.3	−1.50478
$487$	−17672.3	−1.64437	−0.822186	−	0.569218i	$-0.807246\pi$
$487$	−17672.3	−1.64437	−0.822186	+	0.569218i	$0.807246\pi$
$488$	−317.871	−0.0294863
$489$	5389.71	0.498428
$490$	0	0
$491$	−3484.50	−0.320271	−0.160136	−	0.987095i	$-0.551193\pi$
$491$	−3484.50	−0.320271	−0.160136	+	0.987095i	$0.551193\pi$
$492$	8938.15	0.819030
$493$	933.998	0.0853249
$494$	−2501.30	−0.227811
$495$	−4245.99	−0.385542
$496$	6054.97	0.548137
$497$	0	0
$498$	5747.09	0.517135
$499$	1393.45	0.125009	0.0625046	−	0.998045i	$-0.480091\pi$
$499$	1393.45	0.125009	0.0625046	+	0.998045i	$0.480091\pi$
$500$	−13689.6	−1.22444
$501$	8226.59	0.733607
$502$	−21673.9	−1.92700
$503$	−3191.15	−0.282875	−0.141438	−	0.989947i	$-0.545172\pi$
$503$	−3191.15	−0.282875	−0.141438	+	0.989947i	$0.545172\pi$
$504$	0	0
$505$	−7546.63	−0.664991
$506$	9268.39	0.814289
$507$	4815.89	0.421856
$508$	19884.7	1.73670
$509$	−10831.8	−0.943247	−0.471624	−	0.881800i	$-0.656332\pi$
$509$	−10831.8	−0.943247	−0.471624	+	0.881800i	$0.656332\pi$
$510$	2114.75	0.183613
$511$	0	0
$512$	15535.1	1.34094
$513$	−4528.67	−0.389757
$514$	10183.0	0.873842
$515$	12520.6	1.07131
$516$	997.048	0.0850631
$517$	−7294.56	−0.620531
$518$	0	0
$519$	2886.16	0.244101
$520$	688.664	0.0580767
$521$	−14277.5	−1.20059	−0.600296	−	0.799778i	$-0.704951\pi$
$521$	−14277.5	−1.20059	−0.600296	+	0.799778i	$0.704951\pi$
$522$	2990.73	0.250768
$523$	−4181.28	−0.349588	−0.174794	−	0.984605i	$-0.555926\pi$
$523$	−4181.28	−0.349588	−0.174794	+	0.984605i	$0.555926\pi$
$524$	15934.2	1.32841
$525$	0	0
$526$	24321.9	2.01613
$527$	3243.29	0.268084
$528$	3377.22	0.278361
$529$	−5351.26	−0.439817
$530$	−10363.2	−0.849339
$531$	−3637.94	−0.297313
$532$	0	0
$533$	−6033.87	−0.490348
$534$	16787.6	1.36043
$535$	−1143.51	−0.0924077
$536$	−5289.68	−0.426267
$537$	−509.710	−0.0409602
$538$	10867.5	0.870875
$539$	0	0
$540$	8380.48	0.667849
$541$	5123.26	0.407146	0.203573	−	0.979060i	$-0.434745\pi$
$541$	5123.26	0.407146	0.203573	+	0.979060i	$0.434745\pi$
$542$	−7482.35	−0.592979
$543$	1609.19	0.127177
$544$	7050.15	0.555648
$545$	8243.14	0.647885
$546$	0	0
$547$	−15435.6	−1.20654	−0.603271	−	0.797537i	$-0.706136\pi$
$547$	−15435.6	−1.20654	−0.603271	+	0.797537i	$0.706136\pi$
$548$	15164.2	1.18209
$549$	1139.79	0.0886064
$550$	−7644.98	−0.592696
$551$	1313.48	0.101554
$552$	−1187.96	−0.0915992
$553$	0	0
$554$	−3441.47	−0.263925
$555$	−7044.73	−0.538796
$556$	−19477.5	−1.48566
$557$	−978.643	−0.0744460	−0.0372230	−	0.999307i	$-0.511851\pi$
$557$	−978.643	−0.0744460	−0.0372230	+	0.999307i	$0.511851\pi$
$558$	10385.3	0.787891
$559$	−673.076	−0.0509268
$560$	0	0
$561$	1808.98	0.136141
$562$	−21334.0	−1.60128
$563$	24362.4	1.82371	0.911857	−	0.410507i	$-0.134648\pi$
$563$	24362.4	1.82371	0.911857	+	0.410507i	$0.134648\pi$
$564$	6284.23	0.469174
$565$	−7320.43	−0.545085
$566$	15447.3	1.14717
$567$	0	0
$568$	−3624.09	−0.267717
$569$	−12733.1	−0.938135	−0.469067	−	0.883162i	$-0.655410\pi$
$569$	−12733.1	−0.938135	−0.469067	+	0.883162i	$0.655410\pi$
$570$	2973.97	0.218537
$571$	−6363.95	−0.466415	−0.233208	−	0.972427i	$-0.574922\pi$
$571$	−6363.95	−0.466415	−0.233208	+	0.972427i	$0.574922\pi$
$572$	3959.48	0.289430
$573$	2783.48	0.202935
$574$	0	0
$575$	−5621.93	−0.407740
$576$	14066.2	1.01752
$577$	11981.3	0.864449	0.432225	−	0.901766i	$-0.357729\pi$
$577$	11981.3	0.864449	0.432225	+	0.901766i	$0.357729\pi$
$578$	−17397.2	−1.25195
$579$	−877.340	−0.0629724
$580$	−2430.65	−0.174012
$581$	0	0
$582$	−4184.35	−0.298018
$583$	−8864.80	−0.629747
$584$	5983.22	0.423951
$585$	−2469.34	−0.174521
$586$	−3124.97	−0.220293
$587$	−17927.4	−1.26055	−0.630276	−	0.776371i	$-0.717058\pi$
$587$	−17927.4	−1.26055	−0.630276	+	0.776371i	$0.717058\pi$
$588$	0	0
$589$	4561.04	0.319074
$590$	5473.42	0.381927
$591$	−10724.8	−0.746462
$592$	−19251.4	−1.33653
$593$	−19927.7	−1.37999	−0.689993	−	0.723816i	$-0.742387\pi$
$593$	−19927.7	−1.37999	−0.689993	+	0.723816i	$0.742387\pi$
$594$	13270.9	0.916688
$595$	0	0
$596$	−7625.72	−0.524097
$597$	1061.81	0.0727923
$598$	5390.20	0.368598
$599$	−4155.72	−0.283469	−0.141735	−	0.989905i	$-0.545268\pi$
$599$	−4155.72	−0.283469	−0.141735	+	0.989905i	$0.545268\pi$
$600$	979.879	0.0666723
$601$	4104.20	0.278559	0.139279	−	0.990253i	$-0.455521\pi$
$601$	4104.20	0.278559	0.139279	+	0.990253i	$0.455521\pi$
$602$	0	0
$603$	18967.2	1.28093
$604$	−8875.03	−0.597880
$605$	−4575.69	−0.307485
$606$	10295.3	0.690127
$607$	−5870.16	−0.392525	−0.196262	−	0.980551i	$-0.562880\pi$
$607$	−5870.16	−0.392525	−0.196262	+	0.980551i	$0.562880\pi$
$608$	9914.61	0.661333
$609$	0	0
$610$	−1714.85	−0.113823
$611$	−4242.29	−0.280891
$612$	5354.33	0.353653
$613$	29802.4	1.96363	0.981817	−	0.189830i	$-0.0607936\pi$
$613$	29802.4	1.96363	0.981817	+	0.189830i	$0.0607936\pi$
$614$	19858.7	1.30527
$615$	7174.09	0.470386
$616$	0	0
$617$	27394.8	1.78748	0.893738	−	0.448588i	$-0.148073\pi$
$617$	27394.8	1.78748	0.893738	+	0.448588i	$0.148073\pi$
$618$	−17080.9	−1.11181
$619$	25129.8	1.63174	0.815872	−	0.578232i	$-0.196257\pi$
$619$	25129.8	1.63174	0.815872	+	0.578232i	$0.196257\pi$
$620$	−8440.38	−0.546732
$621$	9759.11	0.630627
$622$	25010.0	1.61223
$623$	0	0
$624$	1964.08	0.126004
$625$	−2475.65	−0.158442
$626$	−1661.20	−0.106062
$627$	2543.96	0.162035
$628$	−20098.9	−1.27713
$629$	−10311.9	−0.653673
$630$	0	0
$631$	−1190.63	−0.0751160	−0.0375580	−	0.999294i	$-0.511958\pi$
$631$	−1190.63	−0.0751160	−0.0375580	+	0.999294i	$0.511958\pi$
$632$	−4303.96	−0.270890
$633$	−255.850	−0.0160650
$634$	19425.7	1.21687
$635$	15960.2	0.997420
$636$	7636.98	0.476142
$637$	0	0
$638$	−3849.06	−0.238849
$639$	12994.9	0.804490
$640$	−5545.45	−0.342505
$641$	28828.0	1.77635	0.888174	−	0.459508i	$-0.151974\pi$
$641$	28828.0	1.77635	0.888174	+	0.459508i	$0.151974\pi$
$642$	1560.00	0.0959007
$643$	−16853.2	−1.03363	−0.516816	−	0.856096i	$-0.672883\pi$
$643$	−16853.2	−1.03363	−0.516816	+	0.856096i	$0.672883\pi$
$644$	0	0
$645$	800.268	0.0488535
$646$	4353.21	0.265131
$647$	20234.3	1.22951	0.614754	−	0.788719i	$-0.289255\pi$
$647$	20234.3	1.22951	0.614754	+	0.788719i	$0.289255\pi$
$648$	1592.28	0.0965291
$649$	4682.02	0.283182
$650$	−4446.08	−0.268292
$651$	0	0
$652$	−20531.2	−1.23323
$653$	24965.3	1.49612	0.748062	−	0.663629i	$-0.230985\pi$
$653$	24965.3	1.49612	0.748062	+	0.663629i	$0.230985\pi$
$654$	−11245.5	−0.672375
$655$	12789.4	0.762935
$656$	19604.9	1.16683
$657$	−21454.0	−1.27397
$658$	0	0
$659$	9033.00	0.533954	0.266977	−	0.963703i	$-0.413975\pi$
$659$	9033.00	0.533954	0.266977	+	0.963703i	$0.413975\pi$
$660$	−4707.71	−0.277647
$661$	19710.5	1.15983	0.579915	−	0.814677i	$-0.303086\pi$
$661$	19710.5	1.15983	0.579915	+	0.814677i	$0.303086\pi$
$662$	41767.8	2.45219
$663$	1052.05	0.0616261
$664$	−3257.17	−0.190365
$665$	0	0
$666$	−33019.3	−1.92113
$667$	−2830.50	−0.164314
$668$	−31337.8	−1.81511
$669$	10973.8	0.634190
$670$	−28536.8	−1.64548
$671$	−1466.90	−0.0843951
$672$	0	0
$673$	19293.1	1.10504	0.552521	−	0.833499i	$-0.313666\pi$
$673$	19293.1	1.10504	0.552521	+	0.833499i	$0.313666\pi$
$674$	−16151.1	−0.923020
$675$	−8049.74	−0.459014
$676$	−18345.3	−1.04377
$677$	16029.1	0.909968	0.454984	−	0.890500i	$-0.349645\pi$
$677$	16029.1	0.909968	0.454984	+	0.890500i	$0.349645\pi$
$678$	9986.70	0.565689
$679$	0	0
$680$	−1198.54	−0.0675908
$681$	1257.78	0.0707759
$682$	−13365.8	−0.750443
$683$	−4293.48	−0.240535	−0.120267	−	0.992742i	$-0.538375\pi$
$683$	−4293.48	−0.240535	−0.120267	+	0.992742i	$0.538375\pi$
$684$	7529.78	0.420919
$685$	12171.4	0.678896
$686$	0	0
$687$	−11731.1	−0.651482
$688$	2186.92	0.121186
$689$	−5155.49	−0.285063
$690$	−6408.80	−0.353592
$691$	19631.7	1.08079	0.540393	−	0.841413i	$-0.318276\pi$
$691$	19631.7	1.08079	0.540393	+	0.841413i	$0.318276\pi$
$692$	−10994.3	−0.603962
$693$	0	0
$694$	42924.2	2.34781
$695$	−15633.3	−0.853246
$696$	493.345	0.0268681
$697$	10501.2	0.570677
$698$	−2922.17	−0.158461
$699$	−2203.74	−0.119246
$700$	0	0
$701$	−13399.7	−0.721967	−0.360983	−	0.932572i	$-0.617559\pi$
$701$	−13399.7	−0.721967	−0.360983	+	0.932572i	$0.617559\pi$
$702$	7717.95	0.414951
$703$	−14501.5	−0.778003
$704$	−18103.1	−0.969158
$705$	5043.96	0.269456
$706$	−15050.8	−0.802329
$707$	0	0
$708$	−4033.53	−0.214109
$709$	−510.833	−0.0270589	−0.0135294	−	0.999908i	$-0.504307\pi$
$709$	−510.833	−0.0270589	−0.0135294	+	0.999908i	$0.504307\pi$
$710$	−19551.3	−1.03344
$711$	15432.7	0.814023
$712$	−9514.40	−0.500796
$713$	−9828.87	−0.516261
$714$	0	0
$715$	3178.03	0.166226
$716$	1941.65	0.101345
$717$	9581.88	0.499082
$718$	−50411.9	−2.62027
$719$	29685.4	1.53975	0.769875	−	0.638195i	$-0.220319\pi$
$719$	29685.4	1.53975	0.769875	+	0.638195i	$0.220319\pi$
$720$	8023.24	0.415290
$721$	0	0
$722$	−22487.8	−1.15916
$723$	−7694.69	−0.395807
$724$	−6129.94	−0.314665
$725$	2334.72	0.119599
$726$	6242.26	0.319108
$727$	10575.9	0.539529	0.269765	−	0.962926i	$-0.413054\pi$
$727$	10575.9	0.539529	0.269765	+	0.962926i	$0.413054\pi$
$728$	0	0
$729$	2164.94	0.109990
$730$	32278.3	1.63654
$731$	1171.41	0.0592696
$732$	1263.73	0.0638098
$733$	4428.93	0.223173	0.111587	−	0.993755i	$-0.464407\pi$
$733$	4428.93	0.223173	0.111587	+	0.993755i	$0.464407\pi$
$734$	−4041.71	−0.203246
$735$	0	0
$736$	−21365.6	−1.07004
$737$	−24410.7	−1.22005
$738$	33625.6	1.67720
$739$	20131.6	1.00210	0.501052	−	0.865417i	$-0.332947\pi$
$739$	20131.6	1.00210	0.501052	+	0.865417i	$0.332947\pi$
$740$	26835.7	1.33311
$741$	1479.49	0.0733474
$742$	0	0
$743$	−7362.63	−0.363538	−0.181769	−	0.983341i	$-0.558182\pi$
$743$	−7362.63	−0.363538	−0.181769	+	0.983341i	$0.558182\pi$
$744$	1713.13	0.0844173
$745$	−6120.69	−0.300999
$746$	54249.5	2.66249
$747$	11679.2	0.572048
$748$	−6891.00	−0.336845
$749$	0	0
$750$	14989.8	0.729800
$751$	−7494.93	−0.364173	−0.182087	−	0.983283i	$-0.558285\pi$
$751$	−7494.93	−0.364173	−0.182087	+	0.983283i	$0.558285\pi$
$752$	13783.8	0.668410
$753$	12819.9	0.620429
$754$	−2238.49	−0.108118
$755$	−7123.43	−0.343375
$756$	0	0
$757$	26060.4	1.25123	0.625615	−	0.780132i	$-0.284848\pi$
$757$	26060.4	1.25123	0.625615	+	0.780132i	$0.284848\pi$
$758$	7929.64	0.379971
$759$	−5482.15	−0.262173
$760$	−1685.50	−0.0804467
$761$	23064.0	1.09865	0.549323	−	0.835610i	$-0.314886\pi$
$761$	23064.0	1.09865	0.549323	+	0.835610i	$0.314886\pi$
$762$	−21773.3	−1.03512
$763$	0	0
$764$	−10603.2	−0.502108
$765$	4297.58	0.203110
$766$	39632.6	1.86943
$767$	2722.91	0.128186
$768$	−5710.21	−0.268293
$769$	−19455.7	−0.912341	−0.456171	−	0.889892i	$-0.650779\pi$
$769$	−19455.7	−0.912341	−0.456171	+	0.889892i	$0.650779\pi$
$770$	0	0
$771$	−6023.16	−0.281347
$772$	3342.08	0.155808
$773$	14025.4	0.652599	0.326300	−	0.945266i	$-0.394198\pi$
$773$	14025.4	0.652599	0.326300	+	0.945266i	$0.394198\pi$
$774$	3750.93	0.174192
$775$	8107.28	0.375771
$776$	2371.48	0.109705
$777$	0	0
$778$	19355.1	0.891920
$779$	14767.8	0.679220
$780$	−2737.85	−0.125681
$781$	−16724.3	−0.766253
$782$	−9381.00	−0.428982
$783$	−4052.85	−0.184977
$784$	0	0
$785$	−16132.1	−0.733479
$786$	−17447.6	−0.791774
$787$	41219.6	1.86699	0.933495	−	0.358589i	$-0.116742\pi$
$787$	41219.6	1.86699	0.933495	+	0.358589i	$0.116742\pi$
$788$	40854.3	1.84692
$789$	−14386.1	−0.649124
$790$	−23219.0	−1.04569
$791$	0	0
$792$	−3282.89	−0.147288
$793$	−853.104	−0.0382025
$794$	−19328.6	−0.863910
$795$	6129.73	0.273458
$796$	−4044.78	−0.180105
$797$	−10289.5	−0.457305	−0.228653	−	0.973508i	$-0.573432\pi$
$797$	−10289.5	−0.457305	−0.228653	+	0.973508i	$0.573432\pi$
$798$	0	0
$799$	7383.19	0.326907
$800$	17623.3	0.778847
$801$	34115.7	1.50489
$802$	−49224.6	−2.16731
$803$	27611.2	1.21342
$804$	21029.7	0.922462
$805$	0	0
$806$	−7773.12	−0.339698
$807$	−6428.00	−0.280392
$808$	−5834.85	−0.254046
$809$	−20063.0	−0.871912	−0.435956	−	0.899968i	$-0.643590\pi$
$809$	−20063.0	−0.871912	−0.435956	+	0.899968i	$0.643590\pi$
$810$	8590.07	0.372623
$811$	−26523.6	−1.14842	−0.574210	−	0.818708i	$-0.694691\pi$
$811$	−26523.6	−1.14842	−0.574210	+	0.818708i	$0.694691\pi$
$812$	0	0
$813$	4425.73	0.190919
$814$	42495.7	1.82982
$815$	−16479.1	−0.708267
$816$	−3418.25	−0.146646
$817$	1647.35	0.0705427
$818$	−23311.2	−0.996403
$819$	0	0
$820$	−27328.5	−1.16384
$821$	−9204.45	−0.391276	−0.195638	−	0.980676i	$-0.562678\pi$
$821$	−9204.45	−0.391276	−0.195638	+	0.980676i	$0.562678\pi$
$822$	−16604.5	−0.704558
$823$	15569.2	0.659427	0.329713	−	0.944081i	$-0.393048\pi$
$823$	15569.2	0.659427	0.329713	+	0.944081i	$0.393048\pi$
$824$	9680.62	0.409272
$825$	4521.92	0.190828
$826$	0	0
$827$	−11786.2	−0.495582	−0.247791	−	0.968814i	$-0.579705\pi$
$827$	−11786.2	−0.495582	−0.247791	+	0.968814i	$0.579705\pi$
$828$	−16226.4	−0.681046
$829$	33661.5	1.41027	0.705133	−	0.709075i	$-0.250887\pi$
$829$	33661.5	1.41027	0.705133	+	0.709075i	$0.250887\pi$
$830$	−17571.8	−0.734850
$831$	2035.59	0.0849747
$832$	−10528.2	−0.438702
$833$	0	0
$834$	21327.3	0.885498
$835$	−25152.9	−1.04246
$836$	−9690.79	−0.400913
$837$	−14073.4	−0.581182
$838$	28818.1	1.18795
$839$	2686.31	0.110538	0.0552691	−	0.998471i	$-0.482398\pi$
$839$	2686.31	0.110538	0.0552691	+	0.998471i	$0.482398\pi$
$840$	0	0
$841$	−23213.5	−0.951803
$842$	68821.8	2.81681
$843$	12618.8	0.515558
$844$	974.618	0.0397485
$845$	−14724.6	−0.599458
$846$	23641.5	0.960771
$847$	0	0
$848$	16750.9	0.678337
$849$	−9136.93	−0.369350
$850$	7737.86	0.312243
$851$	31250.3	1.25881
$852$	14407.9	0.579352
$853$	−7920.78	−0.317940	−0.158970	−	0.987283i	$-0.550817\pi$
$853$	−7920.78	−0.317940	−0.158970	+	0.987283i	$0.550817\pi$
$854$	0	0
$855$	6043.68	0.241742
$856$	−884.129	−0.0353025
$857$	−36678.1	−1.46196	−0.730980	−	0.682398i	$-0.760937\pi$
$857$	−36678.1	−1.46196	−0.730980	+	0.682398i	$0.760937\pi$
$858$	−4335.54	−0.172509
$859$	−31205.9	−1.23950	−0.619750	−	0.784799i	$-0.712766\pi$
$859$	−31205.9	−1.23950	−0.619750	+	0.784799i	$0.712766\pi$
$860$	−3048.48	−0.120875
$861$	0	0
$862$	−29622.0	−1.17045
$863$	38340.4	1.51231	0.756155	−	0.654392i	$-0.227076\pi$
$863$	38340.4	1.51231	0.756155	+	0.654392i	$0.227076\pi$
$864$	−30592.3	−1.20460
$865$	−8824.46	−0.346868
$866$	37272.0	1.46253
$867$	10290.3	0.403086
$868$	0	0
$869$	−19861.8	−0.775334
$870$	2661.50	0.103716
$871$	−14196.5	−0.552273
$872$	6373.38	0.247511
$873$	−8503.40	−0.329664
$874$	−13192.5	−0.510575
$875$	0	0
$876$	−23786.9	−0.917449
$877$	−38409.6	−1.47890	−0.739452	−	0.673210i	$-0.764915\pi$
$877$	−38409.6	−1.47890	−0.739452	+	0.673210i	$0.764915\pi$
$878$	−74201.5	−2.85214
$879$	1848.39	0.0709267
$880$	−10325.9	−0.395551
$881$	−41203.4	−1.57568	−0.787842	−	0.615877i	$-0.788802\pi$
$881$	−41203.4	−1.57568	−0.787842	+	0.615877i	$0.788802\pi$
$882$	0	0
$883$	30194.6	1.15077	0.575384	−	0.817883i	$-0.304852\pi$
$883$	30194.6	1.15077	0.575384	+	0.817883i	$0.304852\pi$
$884$	−4007.59	−0.152477
$885$	−3237.47	−0.122967
$886$	11448.2	0.434096
$887$	13570.8	0.513712	0.256856	−	0.966450i	$-0.417313\pi$
$887$	13570.8	0.513712	0.256856	+	0.966450i	$0.417313\pi$
$888$	−5446.80	−0.205836
$889$	0	0
$890$	−51328.3	−1.93318
$891$	7348.03	0.276283
$892$	−41803.0	−1.56913
$893$	10383.0	0.389085
$894$	8349.98	0.312377
$895$	1558.44	0.0582045
$896$	0	0
$897$	−3188.25	−0.118676
$898$	−50269.8	−1.86807
$899$	4081.82	0.151431
$900$	13384.2	0.495713
$901$	8972.51	0.331762
$902$	−43276.1	−1.59749
$903$	0	0
$904$	−5659.96	−0.208239
$905$	−4920.12	−0.180719
$906$	9717.94	0.356354
$907$	21966.6	0.804176	0.402088	−	0.915601i	$-0.368285\pi$
$907$	21966.6	0.804176	0.402088	+	0.915601i	$0.368285\pi$
$908$	−4791.31	−0.175116
$909$	20922.0	0.763409
$910$	0	0
$911$	27091.0	0.985252	0.492626	−	0.870241i	$-0.336037\pi$
$911$	27091.0	0.985252	0.492626	+	0.870241i	$0.336037\pi$
$912$	−4807.08	−0.174538
$913$	−15031.1	−0.544859
$914$	544.020	0.0196877
$915$	1014.32	0.0366473
$916$	44687.5	1.61192
$917$	0	0
$918$	−13432.2	−0.482928
$919$	−24533.7	−0.880622	−0.440311	−	0.897845i	$-0.645132\pi$
$919$	−24533.7	−0.880622	−0.440311	+	0.897845i	$0.645132\pi$
$920$	3632.19	0.130163
$921$	−11746.2	−0.420251
$922$	4092.38	0.146177
$923$	−9726.35	−0.346855
$924$	0	0
$925$	−25776.6	−0.916248
$926$	26527.9	0.941426
$927$	−34711.8	−1.22986
$928$	8872.89	0.313865
$929$	−9220.40	−0.325631	−0.162816	−	0.986657i	$-0.552058\pi$
$929$	−9220.40	−0.325631	−0.162816	+	0.986657i	$0.552058\pi$
$930$	9242.02	0.325868
$931$	0	0
$932$	8394.76	0.295042
$933$	−14793.1	−0.519084
$934$	59062.9	2.06916
$935$	−5530.97	−0.193457
$936$	−1909.23	−0.0666720
$937$	−22526.6	−0.785392	−0.392696	−	0.919668i	$-0.628458\pi$
$937$	−22526.6	−0.785392	−0.392696	+	0.919668i	$0.628458\pi$
$938$	0	0
$939$	982.580	0.0341483
$940$	−19214.1	−0.666697
$941$	776.782	0.0269100	0.0134550	−	0.999909i	$-0.495717\pi$
$941$	776.782	0.0269100	0.0134550	+	0.999909i	$0.495717\pi$
$942$	22007.8	0.761204
$943$	−31824.1	−1.09898
$944$	−8847.15	−0.305032
$945$	0	0
$946$	−4827.43	−0.165913
$947$	−45677.6	−1.56739	−0.783697	−	0.621143i	$-0.786669\pi$
$947$	−45677.6	−1.56739	−0.783697	+	0.621143i	$0.786669\pi$
$948$	17110.8	0.586217
$949$	16057.8	0.549271
$950$	10881.7	0.371632
$951$	−11490.1	−0.391790
$952$	0	0
$953$	−41584.5	−1.41349	−0.706743	−	0.707470i	$-0.749836\pi$
$953$	−41584.5	−1.41349	−0.706743	+	0.707470i	$0.749836\pi$
$954$	28730.6	0.975040
$955$	−8510.52	−0.288371
$956$	−36500.5	−1.23484
$957$	2276.67	0.0769012
$958$	85855.7	2.89548
$959$	0	0
$960$	12517.7	0.420842
$961$	−15617.0	−0.524217
$962$	24714.2	0.828292
$963$	3170.22	0.106084
$964$	29311.6	0.979318
$965$	2682.48	0.0894839
$966$	0	0
$967$	5961.61	0.198255	0.0991274	−	0.995075i	$-0.468395\pi$
$967$	5961.61	0.198255	0.0991274	+	0.995075i	$0.468395\pi$
$968$	−3537.80	−0.117468
$969$	−2574.87	−0.0853631
$970$	12793.7	0.423485
$971$	25246.9	0.834410	0.417205	−	0.908812i	$-0.363010\pi$
$971$	25246.9	0.834410	0.417205	+	0.908812i	$0.363010\pi$
$972$	−36326.4	−1.19874
$973$	0	0
$974$	−73713.5	−2.42498
$975$	2629.81	0.0863807
$976$	2771.86	0.0909068
$977$	44505.1	1.45736	0.728682	−	0.684852i	$-0.240133\pi$
$977$	44505.1	1.45736	0.728682	+	0.684852i	$0.240133\pi$
$978$	22481.1	0.735039
$979$	−43906.8	−1.43337
$980$	0	0
$981$	−22853.0	−0.743772
$982$	−14534.3	−0.472308
$983$	−14970.7	−0.485750	−0.242875	−	0.970058i	$-0.578090\pi$
$983$	−14970.7	−0.485750	−0.242875	+	0.970058i	$0.578090\pi$
$984$	5546.82	0.179701
$985$	32791.1	1.06072
$986$	3895.82	0.125830
$987$	0	0
$988$	−5635.86	−0.181478
$989$	−3549.97	−0.114138
$990$	−17710.6	−0.568564
$991$	−10815.1	−0.346674	−0.173337	−	0.984863i	$-0.555455\pi$
$991$	−10815.1	−0.346674	−0.173337	+	0.984863i	$0.555455\pi$
$992$	30811.0	0.986139
$993$	−24705.2	−0.789522
$994$	0	0
$995$	−3246.49	−0.103438
$996$	12949.2	0.411959
$997$	39556.1	1.25652	0.628262	−	0.778002i	$-0.283767\pi$
$997$	39556.1	1.25652	0.628262	+	0.778002i	$0.283767\pi$
$998$	5812.27	0.184353
$999$	44745.6	1.41711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2107.4.a.c.1.5		6
7.6	odd	2		43.4.a.b.1.5	✓	6
21.20	even	2		387.4.a.h.1.2		6
28.27	even	2		688.4.a.i.1.3		6
35.34	odd	2		1075.4.a.b.1.2		6
301.300	even	2		1849.4.a.c.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.a.b.1.5	✓	6	7.6	odd	2
387.4.a.h.1.2		6	21.20	even	2
688.4.a.i.1.3		6	28.27	even	2
1075.4.a.b.1.2		6	35.34	odd	2
1849.4.a.c.1.2		6	301.300	even	2
2107.4.a.c.1.5		6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2107 = 7^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2107.a (trivial)

\(f(q)\)	\(=\)	\(q+4.17112 q^{2} -2.46717 q^{3} +9.39827 q^{4} +7.54340 q^{5} -10.2909 q^{6} +5.83236 q^{8} -20.9131 q^{9} +O(q^{10})\)	\(q+4.17112 q^{2} -2.46717 q^{3} +9.39827 q^{4} +7.54340 q^{5} -10.2909 q^{6} +5.83236 q^{8} -20.9131 q^{9} +31.4645 q^{10} +26.9150 q^{11} -23.1872 q^{12} +15.6529 q^{13} -18.6109 q^{15} -50.8587 q^{16} -27.2420 q^{17} -87.2309 q^{18} -38.3104 q^{19} +70.8949 q^{20} +112.266 q^{22} +82.5575 q^{23} -14.3894 q^{24} -68.0971 q^{25} +65.2903 q^{26} +118.210 q^{27} -34.2852 q^{29} -77.6283 q^{30} -119.055 q^{31} -258.797 q^{32} -66.4040 q^{33} -113.630 q^{34} -196.547 q^{36} +378.527 q^{37} -159.797 q^{38} -38.6185 q^{39} +43.9958 q^{40} -385.478 q^{41} -43.0000 q^{43} +252.955 q^{44} -157.756 q^{45} +344.358 q^{46} -271.022 q^{47} +125.477 q^{48} -284.041 q^{50} +67.2108 q^{51} +147.110 q^{52} -329.363 q^{53} +493.068 q^{54} +203.031 q^{55} +94.5184 q^{57} -143.008 q^{58} +173.956 q^{59} -174.910 q^{60} -54.5012 q^{61} -496.592 q^{62} -672.604 q^{64} +118.076 q^{65} -276.979 q^{66} -906.954 q^{67} -256.028 q^{68} -203.684 q^{69} -621.376 q^{71} -121.972 q^{72} +1025.87 q^{73} +1578.88 q^{74} +168.007 q^{75} -360.052 q^{76} -161.082 q^{78} -737.945 q^{79} -383.647 q^{80} +273.009 q^{81} -1607.88 q^{82} -558.465 q^{83} -205.498 q^{85} -179.358 q^{86} +84.5875 q^{87} +156.978 q^{88} -1631.31 q^{89} -658.018 q^{90} +775.898 q^{92} +293.729 q^{93} -1130.47 q^{94} -288.991 q^{95} +638.496 q^{96} +406.607 q^{97} -562.875 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 7 q^{3} + 22 q^{4} - 43 q^{5} + 3 q^{6} + 54 q^{8} + 81 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 7 * q^3 + 22 * q^4 - 43 * q^5 + 3 * q^6 + 54 * q^8 + 81 * q^9	\( 6 q + 6 q^{2} - 7 q^{3} + 22 q^{4} - 43 q^{5} + 3 q^{6} + 54 q^{8} + 81 q^{9} - 57 q^{10} - 28 q^{11} + 157 q^{12} - 56 q^{13} - 124 q^{15} - 54 q^{16} - 19 q^{17} - 81 q^{18} + 75 q^{19} - 135 q^{20} - 504 q^{22} + 131 q^{23} + 567 q^{24} + 105 q^{25} - 44 q^{26} - 238 q^{27} + 515 q^{29} - 396 q^{30} - 237 q^{31} + 558 q^{32} - 540 q^{33} + 107 q^{34} + 73 q^{36} + 269 q^{37} - 527 q^{38} + 290 q^{39} - 613 q^{40} - 471 q^{41} - 258 q^{43} - 428 q^{44} - 334 q^{45} - 67 q^{46} - 415 q^{47} + 989 q^{48} + 1335 q^{50} - 1241 q^{51} + 8 q^{52} + 450 q^{53} - 402 q^{54} + 1732 q^{55} - 1000 q^{57} - 1055 q^{58} - 356 q^{59} - 2732 q^{60} + 1328 q^{61} - 1603 q^{62} + 466 q^{64} - 62 q^{65} - 156 q^{66} - 632 q^{67} - 571 q^{68} + 1130 q^{69} - 144 q^{71} + 567 q^{72} - 864 q^{73} + 1207 q^{74} + 2494 q^{75} - 1005 q^{76} + 2222 q^{78} - 1613 q^{79} - 2399 q^{80} - 102 q^{81} - 1673 q^{82} + 682 q^{83} + 84 q^{85} - 258 q^{86} - 449 q^{87} - 608 q^{88} - 3378 q^{89} - 930 q^{90} + 3491 q^{92} + 1879 q^{93} - 3197 q^{94} - 79 q^{95} + 591 q^{96} + 55 q^{97} - 1612 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 7 * q^3 + 22 * q^4 - 43 * q^5 + 3 * q^6 + 54 * q^8 + 81 * q^9 - 57 * q^10 - 28 * q^11 + 157 * q^12 - 56 * q^13 - 124 * q^15 - 54 * q^16 - 19 * q^17 - 81 * q^18 + 75 * q^19 - 135 * q^20 - 504 * q^22 + 131 * q^23 + 567 * q^24 + 105 * q^25 - 44 * q^26 - 238 * q^27 + 515 * q^29 - 396 * q^30 - 237 * q^31 + 558 * q^32 - 540 * q^33 + 107 * q^34 + 73 * q^36 + 269 * q^37 - 527 * q^38 + 290 * q^39 - 613 * q^40 - 471 * q^41 - 258 * q^43 - 428 * q^44 - 334 * q^45 - 67 * q^46 - 415 * q^47 + 989 * q^48 + 1335 * q^50 - 1241 * q^51 + 8 * q^52 + 450 * q^53 - 402 * q^54 + 1732 * q^55 - 1000 * q^57 - 1055 * q^58 - 356 * q^59 - 2732 * q^60 + 1328 * q^61 - 1603 * q^62 + 466 * q^64 - 62 * q^65 - 156 * q^66 - 632 * q^67 - 571 * q^68 + 1130 * q^69 - 144 * q^71 + 567 * q^72 - 864 * q^73 + 1207 * q^74 + 2494 * q^75 - 1005 * q^76 + 2222 * q^78 - 1613 * q^79 - 2399 * q^80 - 102 * q^81 - 1673 * q^82 + 682 * q^83 + 84 * q^85 - 258 * q^86 - 449 * q^87 - 608 * q^88 - 3378 * q^89 - 930 * q^90 + 3491 * q^92 + 1879 * q^93 - 3197 * q^94 - 79 * q^95 + 591 * q^96 + 55 * q^97 - 1612 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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