LMFDB - Embedded newform 2303.4.a.n.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2303,4,Mod(1,2303)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2303, 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("2303.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2303 = 7^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2303.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:	$135.881398743$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	2303.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.80432 q^{2} -7.12022 q^{3} +6.47285 q^{4} -5.10593 q^{5} +27.0876 q^{6} +5.80976 q^{8} +23.6975 q^{9} +O(q^{10})$	\(q-3.80432 q^{2} -7.12022 q^{3} +6.47285 q^{4} -5.10593 q^{5} +27.0876 q^{6} +5.80976 q^{8} +23.6975 q^{9} +19.4246 q^{10} -7.98916 q^{11} -46.0881 q^{12} +41.6226 q^{13} +36.3554 q^{15} -73.8850 q^{16} -89.7848 q^{17} -90.1530 q^{18} -88.5695 q^{19} -33.0499 q^{20} +30.3933 q^{22} -111.964 q^{23} -41.3668 q^{24} -98.9295 q^{25} -158.346 q^{26} +23.5144 q^{27} -56.0551 q^{29} -138.307 q^{30} +172.373 q^{31} +234.604 q^{32} +56.8846 q^{33} +341.570 q^{34} +153.391 q^{36} +374.067 q^{37} +336.947 q^{38} -296.362 q^{39} -29.6642 q^{40} -8.60036 q^{41} -64.4162 q^{43} -51.7127 q^{44} -120.998 q^{45} +425.948 q^{46} -47.0000 q^{47} +526.077 q^{48} +376.359 q^{50} +639.287 q^{51} +269.417 q^{52} -536.809 q^{53} -89.4562 q^{54} +40.7921 q^{55} +630.634 q^{57} +213.251 q^{58} +891.755 q^{59} +235.323 q^{60} +9.19196 q^{61} -655.763 q^{62} -301.429 q^{64} -212.522 q^{65} -216.407 q^{66} +171.702 q^{67} -581.164 q^{68} +797.211 q^{69} +120.126 q^{71} +137.677 q^{72} -755.659 q^{73} -1423.07 q^{74} +704.399 q^{75} -573.297 q^{76} +1127.45 q^{78} -1167.49 q^{79} +377.252 q^{80} -807.261 q^{81} +32.7185 q^{82} -1361.37 q^{83} +458.435 q^{85} +245.060 q^{86} +399.124 q^{87} -46.4151 q^{88} +55.1461 q^{89} +460.315 q^{90} -724.729 q^{92} -1227.33 q^{93} +178.803 q^{94} +452.230 q^{95} -1670.43 q^{96} +1111.00 q^{97} -189.323 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9}+O(q^{10}) $ 68 * q - 2 * q^2 + 24 * q^3 + 254 * q^4 + 40 * q^5 + 48 * q^6 - 66 * q^8 + 576 * q^9	\( 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9} + 200 q^{10} - 20 q^{11} + 288 q^{12} + 520 q^{13} + 88 q^{15} + 1062 q^{16} + 784 q^{17} - 2 q^{18} + 532 q^{19} + 400 q^{20} - 4 q^{22} - 268 q^{23} + 576 q^{24} + 1864 q^{25} + 312 q^{26} + 864 q^{27} + 200 q^{29} + 792 q^{30} + 936 q^{31} + 30 q^{32} + 2112 q^{33} + 1088 q^{34} + 2130 q^{36} - 356 q^{37} + 1192 q^{38} - 488 q^{39} + 2400 q^{40} + 1476 q^{41} - 92 q^{43} + 192 q^{44} + 1848 q^{45} - 424 q^{46} - 3196 q^{47} + 2688 q^{48} - 1338 q^{50} - 148 q^{51} + 4980 q^{52} - 80 q^{53} + 4944 q^{54} + 2200 q^{55} + 2244 q^{57} - 356 q^{58} + 560 q^{59} - 736 q^{60} + 3944 q^{61} + 1488 q^{62} + 3778 q^{64} + 2004 q^{65} - 1000 q^{66} + 2768 q^{67} + 8192 q^{68} + 2208 q^{69} - 2448 q^{71} - 5234 q^{72} + 9532 q^{73} - 2000 q^{74} + 11136 q^{75} + 6384 q^{76} - 3460 q^{78} - 1520 q^{79} + 616 q^{80} + 6976 q^{81} + 4976 q^{82} + 3320 q^{83} + 3244 q^{85} - 2892 q^{86} + 2360 q^{87} - 2868 q^{88} + 8152 q^{89} + 5400 q^{90} - 4684 q^{92} + 2840 q^{93} + 94 q^{94} - 4256 q^{95} + 5376 q^{96} + 13968 q^{97} + 2380 q^{99}+O(q^{100}) \) 68 * q - 2 * q^2 + 24 * q^3 + 254 * q^4 + 40 * q^5 + 48 * q^6 - 66 * q^8 + 576 * q^9 + 200 * q^10 - 20 * q^11 + 288 * q^12 + 520 * q^13 + 88 * q^15 + 1062 * q^16 + 784 * q^17 - 2 * q^18 + 532 * q^19 + 400 * q^20 - 4 * q^22 - 268 * q^23 + 576 * q^24 + 1864 * q^25 + 312 * q^26 + 864 * q^27 + 200 * q^29 + 792 * q^30 + 936 * q^31 + 30 * q^32 + 2112 * q^33 + 1088 * q^34 + 2130 * q^36 - 356 * q^37 + 1192 * q^38 - 488 * q^39 + 2400 * q^40 + 1476 * q^41 - 92 * q^43 + 192 * q^44 + 1848 * q^45 - 424 * q^46 - 3196 * q^47 + 2688 * q^48 - 1338 * q^50 - 148 * q^51 + 4980 * q^52 - 80 * q^53 + 4944 * q^54 + 2200 * q^55 + 2244 * q^57 - 356 * q^58 + 560 * q^59 - 736 * q^60 + 3944 * q^61 + 1488 * q^62 + 3778 * q^64 + 2004 * q^65 - 1000 * q^66 + 2768 * q^67 + 8192 * q^68 + 2208 * q^69 - 2448 * q^71 - 5234 * q^72 + 9532 * q^73 - 2000 * q^74 + 11136 * q^75 + 6384 * q^76 - 3460 * q^78 - 1520 * q^79 + 616 * q^80 + 6976 * q^81 + 4976 * q^82 + 3320 * q^83 + 3244 * q^85 - 2892 * q^86 + 2360 * q^87 - 2868 * q^88 + 8152 * q^89 + 5400 * q^90 - 4684 * q^92 + 2840 * q^93 + 94 * q^94 - 4256 * q^95 + 5376 * q^96 + 13968 * q^97 + 2380 * 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 $

$2$	−3.80432	−1.34503	−0.672515	−	0.740083i	$-0.734786\pi$
$2$	−3.80432	−1.34503	−0.672515	+	0.740083i	$0.734786\pi$
$3$	−7.12022	−1.37029	−0.685143	−	0.728408i	$-0.740260\pi$
$3$	−7.12022	−1.37029	−0.685143	+	0.728408i	$0.740260\pi$
$4$	6.47285	0.809107
$5$	−5.10593	−0.456688	−0.228344	−	0.973580i	$-0.573331\pi$
$5$	−5.10593	−0.456688	−0.228344	+	0.973580i	$0.573331\pi$
$6$	27.0876	1.84308
$7$	0	0
$7$	0	0
$8$	5.80976	0.256757
$9$	23.6975	0.877686
$10$	19.4246	0.614260
$11$	−7.98916	−0.218984	−0.109492	−	0.993988i	$-0.534922\pi$
$11$	−7.98916	−0.218984	−0.109492	+	0.993988i	$0.534922\pi$
$12$	−46.0881	−1.10871
$13$	41.6226	0.888001	0.444001	−	0.896026i	$-0.353559\pi$
$13$	41.6226	0.888001	0.444001	+	0.896026i	$0.353559\pi$
$14$	0	0
$15$	36.3554	0.625794
$16$	−73.8850	−1.15445
$17$	−89.7848	−1.28094	−0.640471	−	0.767982i	$-0.721261\pi$
$17$	−89.7848	−1.28094	−0.640471	+	0.767982i	$0.721261\pi$
$18$	−90.1530	−1.18051
$19$	−88.5695	−1.06943	−0.534717	−	0.845031i	$-0.679582\pi$
$19$	−88.5695	−1.06943	−0.534717	+	0.845031i	$0.679582\pi$
$20$	−33.0499	−0.369510
$21$	0	0
$22$	30.3933	0.294540
$23$	−111.964	−1.01505	−0.507526	−	0.861636i	$-0.669440\pi$
$23$	−111.964	−1.01505	−0.507526	+	0.861636i	$0.669440\pi$
$24$	−41.3668	−0.351831
$25$	−98.9295	−0.791436
$26$	−158.346	−1.19439
$27$	23.5144	0.167605
$28$	0	0
$29$	−56.0551	−0.358937	−0.179468	−	0.983764i	$-0.557438\pi$
$29$	−56.0551	−0.358937	−0.179468	+	0.983764i	$0.557438\pi$
$30$	−138.307	−0.841712
$31$	172.373	0.998682	0.499341	−	0.866406i	$-0.333576\pi$
$31$	172.373	0.998682	0.499341	+	0.866406i	$0.333576\pi$
$32$	234.604	1.29602
$33$	56.8846	0.300071
$34$	341.570	1.72291
$35$	0	0
$36$	153.391	0.710142
$37$	374.067	1.66206	0.831029	−	0.556229i	$-0.187752\pi$
$37$	374.067	1.66206	0.831029	+	0.556229i	$0.187752\pi$
$38$	336.947	1.43842
$39$	−296.362	−1.21682
$40$	−29.6642	−0.117258
$41$	−8.60036	−0.0327598	−0.0163799	−	0.999866i	$-0.505214\pi$
$41$	−8.60036	−0.0327598	−0.0163799	+	0.999866i	$0.505214\pi$
$42$	0	0
$43$	−64.4162	−0.228451	−0.114225	−	0.993455i	$-0.536439\pi$
$43$	−64.4162	−0.228451	−0.114225	+	0.993455i	$0.536439\pi$
$44$	−51.7127	−0.177181
$45$	−120.998	−0.400829
$46$	425.948	1.36528
$47$	−47.0000	−0.145865
$47$	−47.0000	−0.145865
$48$	526.077	1.58193
$49$	0	0
$50$	376.359	1.06451
$51$	639.287	1.75526
$52$	269.417	0.718488
$53$	−536.809	−1.39125	−0.695627	−	0.718404i	$-0.744873\pi$
$53$	−536.809	−1.39125	−0.695627	+	0.718404i	$0.744873\pi$
$54$	−89.4562	−0.225434
$55$	40.7921	0.100007
$56$	0	0
$57$	630.634	1.46543
$58$	213.251	0.482781
$59$	891.755	1.96774	0.983870	−	0.178886i	$-0.0572492\pi$
$59$	891.755	1.96774	0.983870	+	0.178886i	$0.0572492\pi$
$60$	235.323	0.506334
$61$	9.19196	0.0192936	0.00964680	−	0.999953i	$-0.496929\pi$
$61$	9.19196	0.0192936	0.00964680	+	0.999953i	$0.496929\pi$
$62$	−655.763	−1.34326
$63$	0	0
$64$	−301.429	−0.588729
$65$	−212.522	−0.405540
$66$	−216.407	−0.403604
$67$	171.702	0.313086	0.156543	−	0.987671i	$-0.449965\pi$
$67$	171.702	0.313086	0.156543	+	0.987671i	$0.449965\pi$
$68$	−581.164	−1.03642
$69$	797.211	1.39091
$70$	0	0
$71$	120.126	0.200793	0.100396	−	0.994948i	$-0.467989\pi$
$71$	120.126	0.200793	0.100396	+	0.994948i	$0.467989\pi$
$72$	137.677	0.225352
$73$	−755.659	−1.21155	−0.605776	−	0.795636i	$-0.707137\pi$
$73$	−755.659	−1.21155	−0.605776	+	0.795636i	$0.707137\pi$
$74$	−1423.07	−2.23552
$75$	704.399	1.08449
$76$	−573.297	−0.865286
$77$	0	0
$78$	1127.45	1.63666
$79$	−1167.49	−1.66270	−0.831350	−	0.555749i	$-0.812431\pi$
$79$	−1167.49	−1.66270	−0.831350	+	0.555749i	$0.812431\pi$
$80$	377.252	0.527225
$81$	−807.261	−1.10735
$82$	32.7185	0.0440629
$83$	−1361.37	−1.80036	−0.900180	−	0.435518i	$-0.856565\pi$
$83$	−1361.37	−1.80036	−0.900180	+	0.435518i	$0.856565\pi$
$84$	0	0
$85$	458.435	0.584991
$86$	245.060	0.307273
$87$	399.124	0.491846
$88$	−46.4151	−0.0562258
$89$	55.1461	0.0656794	0.0328397	−	0.999461i	$-0.489545\pi$
$89$	55.1461	0.0656794	0.0328397	+	0.999461i	$0.489545\pi$
$90$	460.315	0.539127
$91$	0	0
$92$	−724.729	−0.821285
$93$	−1227.33	−1.36848
$94$	178.803	0.196193
$95$	452.230	0.488398
$96$	−1670.43	−1.77592
$97$	1111.00	1.16293	0.581467	−	0.813570i	$-0.302479\pi$
$97$	1111.00	1.16293	0.581467	+	0.813570i	$0.302479\pi$
$98$	0	0
$99$	−189.323	−0.192199
$100$	−640.356	−0.640356
$101$	−182.437	−0.179734	−0.0898670	−	0.995954i	$-0.528644\pi$
$101$	−182.437	−0.179734	−0.0898670	+	0.995954i	$0.528644\pi$
$102$	−2432.05	−2.36088
$103$	−512.150	−0.489938	−0.244969	−	0.969531i	$-0.578778\pi$
$103$	−512.150	−0.489938	−0.244969	+	0.969531i	$0.578778\pi$
$104$	241.817	0.228001
$105$	0	0
$106$	2042.19	1.87128
$107$	−1594.12	−1.44027	−0.720137	−	0.693832i	$-0.755921\pi$
$107$	−1594.12	−1.44027	−0.720137	+	0.693832i	$0.755921\pi$
$108$	152.205	0.135611
$109$	−81.2743	−0.0714189	−0.0357095	−	0.999362i	$-0.511369\pi$
$109$	−81.2743	−0.0714189	−0.0357095	+	0.999362i	$0.511369\pi$
$110$	−155.186	−0.134513
$111$	−2663.44	−2.27750
$112$	0	0
$113$	−233.315	−0.194234	−0.0971171	−	0.995273i	$-0.530962\pi$
$113$	−233.315	−0.194234	−0.0971171	+	0.995273i	$0.530962\pi$
$114$	−2399.13	−1.97105
$115$	571.683	0.463562
$116$	−362.836	−0.290418
$117$	986.351	0.779386
$118$	−3392.52	−2.64667
$119$	0	0
$120$	211.216	0.160677
$121$	−1267.17	−0.952046
$122$	−34.9692	−0.0259505
$123$	61.2364	0.0448903
$124$	1115.75	0.808040
$125$	1143.37	0.818128
$126$	0	0
$127$	1803.29	1.25997	0.629984	−	0.776608i	$-0.283061\pi$
$127$	1803.29	1.25997	0.629984	+	0.776608i	$0.283061\pi$
$128$	−730.100	−0.504159
$129$	458.657	0.313043
$130$	808.501	0.545464
$131$	−17.9678	−0.0119836	−0.00599179	−	0.999982i	$-0.501907\pi$
$131$	−17.9678	−0.0119836	−0.00599179	+	0.999982i	$0.501907\pi$
$132$	368.206	0.242789
$133$	0	0
$134$	−653.211	−0.421110
$135$	−120.063	−0.0765434
$136$	−521.628	−0.328891
$137$	−2598.76	−1.62064	−0.810319	−	0.585989i	$-0.800706\pi$
$137$	−2598.76	−1.62064	−0.810319	+	0.585989i	$0.800706\pi$
$138$	−3032.85	−1.87082
$139$	388.135	0.236843	0.118422	−	0.992963i	$-0.462217\pi$
$139$	388.135	0.236843	0.118422	+	0.992963i	$0.462217\pi$
$140$	0	0
$141$	334.650	0.199877
$142$	−456.996	−0.270072
$143$	−332.529	−0.194458
$144$	−1750.89	−1.01325
$145$	286.213	0.163922
$146$	2874.77	1.62957
$147$	0	0
$148$	2421.28	1.34478
$149$	1469.46	0.807937	0.403968	−	0.914773i	$-0.367631\pi$
$149$	1469.46	0.807937	0.403968	+	0.914773i	$0.367631\pi$
$150$	−2679.76	−1.45868
$151$	−2208.14	−1.19004	−0.595021	−	0.803710i	$-0.702856\pi$
$151$	−2208.14	−1.19004	−0.595021	+	0.803710i	$0.702856\pi$
$152$	−514.567	−0.274585
$153$	−2127.68	−1.12426
$154$	0	0
$155$	−880.126	−0.456086
$156$	−1918.31	−0.984534
$157$	1794.34	0.912129	0.456064	−	0.889947i	$-0.349259\pi$
$157$	1794.34	0.912129	0.456064	+	0.889947i	$0.349259\pi$
$158$	4441.52	2.23638
$159$	3822.20	1.90642
$160$	−1197.87	−0.591876
$161$	0	0
$162$	3071.08	1.48942
$163$	2674.45	1.28515	0.642574	−	0.766223i	$-0.277866\pi$
$163$	2674.45	1.28515	0.642574	+	0.766223i	$0.277866\pi$
$164$	−55.6688	−0.0265061
$165$	−290.449	−0.137039
$166$	5179.09	2.42154
$167$	1301.38	0.603018	0.301509	−	0.953463i	$-0.402510\pi$
$167$	1301.38	0.603018	0.301509	+	0.953463i	$0.402510\pi$
$168$	0	0
$169$	−464.563	−0.211453
$170$	−1744.03	−0.786831
$171$	−2098.88	−0.938627
$172$	−416.957	−0.184841
$173$	−194.337	−0.0854058	−0.0427029	−	0.999088i	$-0.513597\pi$
$173$	−194.337	−0.0854058	−0.0427029	+	0.999088i	$0.513597\pi$
$174$	−1518.40	−0.661548
$175$	0	0
$176$	590.279	0.252807
$177$	−6349.49	−2.69637
$178$	−209.793	−0.0883408
$179$	−2746.19	−1.14670	−0.573352	−	0.819309i	$-0.694357\pi$
$179$	−2746.19	−1.14670	−0.573352	+	0.819309i	$0.694357\pi$
$180$	−783.202	−0.324313
$181$	−1255.66	−0.515649	−0.257825	−	0.966192i	$-0.583006\pi$
$181$	−1255.66	−0.515649	−0.257825	+	0.966192i	$0.583006\pi$
$182$	0	0
$183$	−65.4488	−0.0264378
$184$	−650.486	−0.260622
$185$	−1909.96	−0.759043
$186$	4669.17	1.84065
$187$	717.306	0.280506
$188$	−304.224	−0.118020
$189$	0	0
$190$	−1720.43	−0.656910
$191$	−2700.64	−1.02310	−0.511549	−	0.859254i	$-0.670928\pi$
$191$	−2700.64	−1.02310	−0.511549	+	0.859254i	$0.670928\pi$
$192$	2146.24	0.806728
$193$	−3367.44	−1.25593	−0.627963	−	0.778243i	$-0.716111\pi$
$193$	−3367.44	−1.25593	−0.627963	+	0.778243i	$0.716111\pi$
$194$	−4226.58	−1.56418
$195$	1513.20	0.555706
$196$	0	0
$197$	−1003.69	−0.362994	−0.181497	−	0.983392i	$-0.558094\pi$
$197$	−1003.69	−0.362994	−0.181497	+	0.983392i	$0.558094\pi$
$198$	720.247	0.258514
$199$	−4820.75	−1.71726	−0.858628	−	0.512599i	$-0.828683\pi$
$199$	−4820.75	−1.71726	−0.858628	+	0.512599i	$0.828683\pi$
$200$	−574.756	−0.203207
$201$	−1222.56	−0.429018
$202$	694.048	0.241748
$203$	0	0
$204$	4138.01	1.42019
$205$	43.9128	0.0149610
$206$	1948.38	0.658982
$207$	−2653.28	−0.890897
$208$	−3075.28	−1.02516
$209$	707.596	0.234189
$210$	0	0
$211$	−3462.33	−1.12965	−0.564826	−	0.825210i	$-0.691057\pi$
$211$	−3462.33	−1.12965	−0.564826	+	0.825210i	$0.691057\pi$
$212$	−3474.69	−1.12567
$213$	−855.321	−0.275144
$214$	6064.54	1.93721
$215$	328.905	0.104331
$216$	136.613	0.0430339
$217$	0	0
$218$	309.193	0.0960606
$219$	5380.46	1.66017
$220$	264.041	0.0809167
$221$	−3737.07	−1.13748
$222$	10132.6	3.06330
$223$	−4238.79	−1.27287	−0.636435	−	0.771330i	$-0.719592\pi$
$223$	−4238.79	−1.27287	−0.636435	+	0.771330i	$0.719592\pi$
$224$	0	0
$225$	−2344.38	−0.694632
$226$	887.607	0.261251
$227$	−2169.48	−0.634332	−0.317166	−	0.948370i	$-0.602731\pi$
$227$	−2169.48	−0.634332	−0.317166	+	0.948370i	$0.602731\pi$
$228$	4082.00	1.18569
$229$	908.578	0.262186	0.131093	−	0.991370i	$-0.458151\pi$
$229$	908.578	0.262186	0.131093	+	0.991370i	$0.458151\pi$
$230$	−2174.86	−0.623506
$231$	0	0
$232$	−325.666	−0.0921597
$233$	−1778.77	−0.500133	−0.250067	−	0.968229i	$-0.580453\pi$
$233$	−1778.77	−0.500133	−0.250067	+	0.968229i	$0.580453\pi$
$234$	−3752.40	−1.04830
$235$	239.979	0.0666148
$236$	5772.20	1.59211
$237$	8312.81	2.27838
$238$	0	0
$239$	1348.06	0.364848	0.182424	−	0.983220i	$-0.441606\pi$
$239$	1348.06	0.364848	0.182424	+	0.983220i	$0.441606\pi$
$240$	−2686.12	−0.722450
$241$	−2032.83	−0.543344	−0.271672	−	0.962390i	$-0.587577\pi$
$241$	−2032.83	−0.543344	−0.271672	+	0.962390i	$0.587577\pi$
$242$	4820.73	1.28053
$243$	5112.98	1.34979
$244$	59.4982	0.0156106
$245$	0	0
$246$	−232.963	−0.0603788
$247$	−3686.49	−0.949659
$248$	1001.45	0.256419
$249$	9693.26	2.46701
$250$	−4349.74	−1.10041
$251$	−2295.00	−0.577128	−0.288564	−	0.957461i	$-0.593178\pi$
$251$	−2295.00	−0.577128	−0.288564	+	0.957461i	$0.593178\pi$
$252$	0	0
$253$	894.502	0.222280
$254$	−6860.29	−1.69470
$255$	−3264.16	−0.801606
$256$	5188.97	1.26684
$257$	−1567.01	−0.380339	−0.190170	−	0.981751i	$-0.560904\pi$
$257$	−1567.01	−0.380339	−0.190170	+	0.981751i	$0.560904\pi$
$258$	−1744.88	−0.421052
$259$	0	0
$260$	−1375.62	−0.328125
$261$	−1328.37	−0.315034
$262$	68.3551	0.0161183
$263$	−812.777	−0.190563	−0.0952813	−	0.995450i	$-0.530375\pi$
$263$	−812.777	−0.190563	−0.0952813	+	0.995450i	$0.530375\pi$
$264$	330.486	0.0770454
$265$	2740.91	0.635369
$266$	0	0
$267$	−392.652	−0.0899997
$268$	1111.40	0.253320
$269$	−572.380	−0.129735	−0.0648673	−	0.997894i	$-0.520662\pi$
$269$	−572.380	−0.129735	−0.0648673	+	0.997894i	$0.520662\pi$
$270$	456.757	0.102953
$271$	−3064.96	−0.687023	−0.343511	−	0.939148i	$-0.611616\pi$
$271$	−3064.96	−0.687023	−0.343511	+	0.939148i	$0.611616\pi$
$272$	6633.75	1.47879
$273$	0	0
$274$	9886.53	2.17981
$275$	790.364	0.173312
$276$	5160.23	1.12540
$277$	4882.21	1.05900	0.529501	−	0.848310i	$-0.322379\pi$
$277$	4882.21	1.05900	0.529501	+	0.848310i	$0.322379\pi$
$278$	−1476.59	−0.318561
$279$	4084.82	0.876529
$280$	0	0
$281$	8532.29	1.81136	0.905682	−	0.423957i	$-0.139359\pi$
$281$	8532.29	1.81136	0.905682	+	0.423957i	$0.139359\pi$
$282$	−1273.12	−0.268840
$283$	6537.64	1.37322	0.686612	−	0.727024i	$-0.259097\pi$
$283$	6537.64	1.37322	0.686612	+	0.727024i	$0.259097\pi$
$284$	777.556	0.162463
$285$	−3219.98	−0.669245
$286$	1265.05	0.261552
$287$	0	0
$288$	5559.54	1.13750
$289$	3148.31	0.640812
$290$	−1088.85	−0.220480
$291$	−7910.54	−1.59355
$292$	−4891.27	−0.980274
$293$	−3439.26	−0.685746	−0.342873	−	0.939382i	$-0.611400\pi$
$293$	−3439.26	−0.685746	−0.342873	+	0.939382i	$0.611400\pi$
$294$	0	0
$295$	−4553.24	−0.898644
$296$	2173.24	0.426746
$297$	−187.860	−0.0367029
$298$	−5590.28	−1.08670
$299$	−4660.24	−0.901368
$300$	4559.47	0.877471
$301$	0	0
$302$	8400.49	1.60064
$303$	1298.99	0.246287
$304$	6543.96	1.23461
$305$	−46.9335	−0.00881116
$306$	8094.37	1.51217
$307$	−8763.21	−1.62913	−0.814565	−	0.580073i	$-0.803024\pi$
$307$	−8763.21	−1.62913	−0.814565	+	0.580073i	$0.803024\pi$
$308$	0	0
$309$	3646.62	0.671356
$310$	3348.28	0.613450
$311$	1380.58	0.251722	0.125861	−	0.992048i	$-0.459831\pi$
$311$	1380.58	0.251722	0.125861	+	0.992048i	$0.459831\pi$
$312$	−1721.79	−0.312427
$313$	4565.25	0.824420	0.412210	−	0.911089i	$-0.364757\pi$
$313$	4565.25	0.824420	0.412210	+	0.911089i	$0.364757\pi$
$314$	−6826.26	−1.22684
$315$	0	0
$316$	−7557.01	−1.34530
$317$	−1474.99	−0.261337	−0.130668	−	0.991426i	$-0.541712\pi$
$317$	−1474.99	−0.261337	−0.130668	+	0.991426i	$0.541712\pi$
$318$	−14540.9	−2.56419
$319$	447.833	0.0786014
$320$	1539.08	0.268866
$321$	11350.5	1.97359
$322$	0	0
$323$	7952.20	1.36988
$324$	−5225.28	−0.895967
$325$	−4117.70	−0.702796
$326$	−10174.5	−1.72856
$327$	578.691	0.0978644
$328$	−49.9660	−0.00841131
$329$	0	0
$330$	1104.96	0.184321
$331$	−6096.63	−1.01239	−0.506195	−	0.862419i	$-0.668949\pi$
$331$	−6096.63	−1.01239	−0.506195	+	0.862419i	$0.668949\pi$
$332$	−8811.95	−1.45668
$333$	8864.45	1.45877
$334$	−4950.87	−0.811077
$335$	−876.700	−0.142983
$336$	0	0
$337$	−600.209	−0.0970192	−0.0485096	−	0.998823i	$-0.515447\pi$
$337$	−600.209	−0.0970192	−0.0485096	+	0.998823i	$0.515447\pi$
$338$	1767.35	0.284411
$339$	1661.26	0.266157
$340$	2967.38	0.473320
$341$	−1377.12	−0.218695
$342$	7984.80	1.26248
$343$	0	0
$344$	−374.243	−0.0586564
$345$	−4070.51	−0.635214
$346$	739.322	0.114873
$347$	1637.56	0.253339	0.126670	−	0.991945i	$-0.459571\pi$
$347$	1637.56	0.253339	0.126670	+	0.991945i	$0.459571\pi$
$348$	2583.47	0.397956
$349$	8711.32	1.33612	0.668061	−	0.744107i	$-0.267125\pi$
$349$	8711.32	1.33612	0.668061	+	0.744107i	$0.267125\pi$
$350$	0	0
$351$	978.728	0.148834
$352$	−1874.29	−0.283807
$353$	−2346.53	−0.353806	−0.176903	−	0.984228i	$-0.556608\pi$
$353$	−2346.53	−0.353806	−0.176903	+	0.984228i	$0.556608\pi$
$354$	24155.5	3.62670
$355$	−613.353	−0.0916998
$356$	356.952	0.0531417
$357$	0	0
$358$	10447.4	1.54235
$359$	3601.99	0.529542	0.264771	−	0.964311i	$-0.414704\pi$
$359$	3601.99	0.529542	0.264771	+	0.964311i	$0.414704\pi$
$360$	−702.969	−0.102916
$361$	985.557	0.143688
$362$	4776.93	0.693564
$363$	9022.55	1.30458
$364$	0	0
$365$	3858.34	0.553301
$366$	248.988	0.0355596
$367$	10927.9	1.55431	0.777156	−	0.629308i	$-0.216662\pi$
$367$	10927.9	1.55431	0.777156	+	0.629308i	$0.216662\pi$
$368$	8272.49	1.17183
$369$	−203.807	−0.0287528
$370$	7266.09	1.02094
$371$	0	0
$372$	−7944.36	−1.10725
$373$	3279.21	0.455204	0.227602	−	0.973754i	$-0.426912\pi$
$373$	3279.21	0.455204	0.227602	+	0.973754i	$0.426912\pi$
$374$	−2728.86	−0.377289
$375$	−8141.03	−1.12107
$376$	−273.059	−0.0374519
$377$	−2333.16	−0.318736
$378$	0	0
$379$	−13349.6	−1.80930	−0.904651	−	0.426154i	$-0.859868\pi$
$379$	−13349.6	−1.80930	−0.904651	+	0.426154i	$0.859868\pi$
$380$	2927.22	0.395166
$381$	−12839.8	−1.72652
$382$	10274.1	1.37610
$383$	−14973.9	−1.99773	−0.998865	−	0.0476261i	$-0.984834\pi$
$383$	−14973.9	−1.99773	−0.998865	+	0.0476261i	$0.984834\pi$
$384$	5198.47	0.690842
$385$	0	0
$386$	12810.8	1.68926
$387$	−1526.50	−0.200508
$388$	7191.31	0.940937
$389$	−10266.3	−1.33811	−0.669054	−	0.743214i	$-0.733301\pi$
$389$	−10266.3	−1.33811	−0.669054	+	0.743214i	$0.733301\pi$
$390$	−5756.71	−0.747442
$391$	10052.7	1.30022
$392$	0	0
$393$	127.934	0.0164210
$394$	3818.35	0.488238
$395$	5961.14	0.759336
$396$	−1225.46	−0.155510
$397$	−690.920	−0.0873458	−0.0436729	−	0.999046i	$-0.513906\pi$
$397$	−690.920	−0.0873458	−0.0436729	+	0.999046i	$0.513906\pi$
$398$	18339.7	2.30976
$399$	0	0
$400$	7309.40	0.913675
$401$	3076.13	0.383079	0.191540	−	0.981485i	$-0.438652\pi$
$401$	3076.13	0.383079	0.191540	+	0.981485i	$0.438652\pi$
$402$	4651.00	0.577042
$403$	7174.61	0.886831
$404$	−1180.89	−0.145424
$405$	4121.82	0.505715
$406$	0	0
$407$	−2988.48	−0.363964
$408$	3714.11	0.450676
$409$	2345.60	0.283576	0.141788	−	0.989897i	$-0.454715\pi$
$409$	2345.60	0.283576	0.141788	+	0.989897i	$0.454715\pi$
$410$	−167.058	−0.0201230
$411$	18503.8	2.22074
$412$	−3315.07	−0.396412
$413$	0	0
$414$	10093.9	1.19828
$415$	6951.07	0.822203
$416$	9764.82	1.15087
$417$	−2763.61	−0.324543
$418$	−2691.92	−0.314991
$419$	−1509.34	−0.175981	−0.0879904	−	0.996121i	$-0.528044\pi$
$419$	−1509.34	−0.175981	−0.0879904	+	0.996121i	$0.528044\pi$
$420$	0	0
$421$	−10566.4	−1.22322	−0.611608	−	0.791161i	$-0.709477\pi$
$421$	−10566.4	−1.22322	−0.611608	+	0.791161i	$0.709477\pi$
$422$	13171.8	1.51942
$423$	−1113.78	−0.128024
$424$	−3118.73	−0.357215
$425$	8882.36	1.01378
$426$	3253.91	0.370077
$427$	0	0
$428$	−10318.5	−1.16533
$429$	2367.68	0.266463
$430$	−1251.26	−0.140328
$431$	2265.18	0.253156	0.126578	−	0.991957i	$-0.459601\pi$
$431$	2265.18	0.253156	0.126578	+	0.991957i	$0.459601\pi$
$432$	−1737.36	−0.193492
$433$	12889.7	1.43057	0.715285	−	0.698832i	$-0.246297\pi$
$433$	12889.7	1.43057	0.715285	+	0.698832i	$0.246297\pi$
$434$	0	0
$435$	−2037.90	−0.224621
$436$	−526.076	−0.0577855
$437$	9916.63	1.08553
$438$	−20469.0	−2.23298
$439$	12304.3	1.33771	0.668854	−	0.743394i	$-0.266785\pi$
$439$	12304.3	1.33771	0.668854	+	0.743394i	$0.266785\pi$
$440$	236.992	0.0256777
$441$	0	0
$442$	14217.0	1.52994
$443$	−4239.51	−0.454685	−0.227342	−	0.973815i	$-0.573004\pi$
$443$	−4239.51	−0.454685	−0.227342	+	0.973815i	$0.573004\pi$
$444$	−17240.0	−1.84274
$445$	−281.572	−0.0299950
$446$	16125.7	1.71205
$447$	−10462.9	−1.10711
$448$	0	0
$449$	−12146.2	−1.27665	−0.638324	−	0.769768i	$-0.720372\pi$
$449$	−12146.2	−1.27665	−0.638324	+	0.769768i	$0.720372\pi$
$450$	8918.78	0.934301
$451$	68.7097	0.00717386
$452$	−1510.22	−0.157156
$453$	15722.5	1.63070
$454$	8253.39	0.853196
$455$	0	0
$456$	3663.83	0.376260
$457$	−10052.7	−1.02899	−0.514493	−	0.857495i	$-0.672020\pi$
$457$	−10052.7	−1.02899	−0.514493	+	0.857495i	$0.672020\pi$
$458$	−3456.52	−0.352648
$459$	−2111.23	−0.214693
$460$	3700.42	0.375071
$461$	−13755.0	−1.38966	−0.694831	−	0.719173i	$-0.744521\pi$
$461$	−13755.0	−1.38966	−0.694831	+	0.719173i	$0.744521\pi$
$462$	0	0
$463$	5532.44	0.555323	0.277661	−	0.960679i	$-0.410441\pi$
$463$	5532.44	0.555323	0.277661	+	0.960679i	$0.410441\pi$
$464$	4141.63	0.414376
$465$	6266.69	0.624969
$466$	6767.01	0.672695
$467$	1839.63	0.182287	0.0911434	−	0.995838i	$-0.470948\pi$
$467$	1839.63	0.182287	0.0911434	+	0.995838i	$0.470948\pi$
$468$	6384.51	0.630607
$469$	0	0
$470$	−912.956	−0.0895990
$471$	−12776.1	−1.24988
$472$	5180.88	0.505232
$473$	514.632	0.0500270
$474$	−31624.6	−3.06448
$475$	8762.13	0.846388
$476$	0	0
$477$	−12721.0	−1.22108
$478$	−5128.44	−0.490731
$479$	−5007.50	−0.477658	−0.238829	−	0.971062i	$-0.576764\pi$
$479$	−5007.50	−0.477658	−0.238829	+	0.971062i	$0.576764\pi$
$480$	8529.12	0.811040
$481$	15569.6	1.47591
$482$	7733.52	0.730814
$483$	0	0
$484$	−8202.23	−0.770307
$485$	−5672.67	−0.531098
$486$	−19451.4	−1.81550
$487$	−5318.95	−0.494917	−0.247459	−	0.968898i	$-0.579595\pi$
$487$	−5318.95	−0.494917	−0.247459	+	0.968898i	$0.579595\pi$
$488$	53.4031	0.00495378
$489$	−19042.7	−1.76102
$490$	0	0
$491$	−14572.9	−1.33944	−0.669721	−	0.742613i	$-0.733586\pi$
$491$	−14572.9	−1.33944	−0.669721	+	0.742613i	$0.733586\pi$
$492$	396.374	0.0363210
$493$	5032.89	0.459777
$494$	14024.6	1.27732
$495$	966.672	0.0877751
$496$	−12735.8	−1.15293
$497$	0	0
$498$	−36876.3	−3.31820
$499$	9015.07	0.808757	0.404379	−	0.914592i	$-0.367488\pi$
$499$	9015.07	0.808757	0.404379	+	0.914592i	$0.367488\pi$
$500$	7400.86	0.661953
$501$	−9266.12	−0.826307
$502$	8730.92	0.776255
$503$	−2422.01	−0.214696	−0.107348	−	0.994222i	$-0.534236\pi$
$503$	−2422.01	−0.214696	−0.107348	+	0.994222i	$0.534236\pi$
$504$	0	0
$505$	931.509	0.0820824
$506$	−3402.97	−0.298974
$507$	3307.79	0.289752
$508$	11672.4	1.01945
$509$	5175.58	0.450694	0.225347	−	0.974279i	$-0.427648\pi$
$509$	5175.58	0.450694	0.225347	+	0.974279i	$0.427648\pi$
$510$	12417.9	1.07818
$511$	0	0
$512$	−13899.7	−1.19978
$513$	−2082.66	−0.179243
$514$	5961.40	0.511568
$515$	2615.00	0.223749
$516$	2968.82	0.253285
$517$	375.491	0.0319421
$518$	0	0
$519$	1383.72	0.117030
$520$	−1234.70	−0.104125
$521$	12827.4	1.07866	0.539329	−	0.842095i	$-0.318678\pi$
$521$	12827.4	1.07866	0.539329	+	0.842095i	$0.318678\pi$
$522$	5053.53	0.423730
$523$	13239.8	1.10695	0.553474	−	0.832866i	$-0.313302\pi$
$523$	13239.8	1.10695	0.553474	+	0.832866i	$0.313302\pi$
$524$	−116.303	−0.00969600
$525$	0	0
$526$	3092.06	0.256312
$527$	−15476.5	−1.27925
$528$	−4202.92	−0.346418
$529$	369.030	0.0303304
$530$	−10427.3	−0.854591
$531$	21132.4	1.72706
$532$	0	0
$533$	−357.969	−0.0290907
$534$	1493.77	0.121052
$535$	8139.46	0.657756
$536$	997.549	0.0803872
$537$	19553.5	1.57131
$538$	2177.52	0.174497
$539$	0	0
$540$	−777.148	−0.0619317
$541$	1483.45	0.117890	0.0589449	−	0.998261i	$-0.481226\pi$
$541$	1483.45	0.117890	0.0589449	+	0.998261i	$0.481226\pi$
$542$	11660.1	0.924067
$543$	8940.58	0.706587
$544$	−21063.9	−1.66012
$545$	414.981	0.0326162
$546$	0	0
$547$	−14473.5	−1.13134	−0.565671	−	0.824631i	$-0.691383\pi$
$547$	−14473.5	−1.13134	−0.565671	+	0.824631i	$0.691383\pi$
$548$	−16821.4	−1.31127
$549$	217.827	0.0169337
$550$	−3006.80	−0.233110
$551$	4964.77	0.383859
$552$	4631.60	0.357127
$553$	0	0
$554$	−18573.5	−1.42439
$555$	13599.3	1.04011
$556$	2512.34	0.191631
$557$	18910.5	1.43853	0.719267	−	0.694734i	$-0.244478\pi$
$557$	18910.5	1.43853	0.719267	+	0.694734i	$0.244478\pi$
$558$	−15540.0	−1.17896
$559$	−2681.17	−0.202865
$560$	0	0
$561$	−5107.37	−0.384373
$562$	−32459.6	−2.43634
$563$	25527.9	1.91096	0.955481	−	0.295053i	$-0.0953375\pi$
$563$	25527.9	1.91096	0.955481	+	0.295053i	$0.0953375\pi$
$564$	2166.14	0.161722
$565$	1191.29	0.0887045
$566$	−24871.3	−1.84703
$567$	0	0
$568$	697.901	0.0515551
$569$	−8490.10	−0.625525	−0.312762	−	0.949831i	$-0.601254\pi$
$569$	−8490.10	−0.625525	−0.312762	+	0.949831i	$0.601254\pi$
$570$	12249.8	0.900155
$571$	11294.5	0.827779	0.413890	−	0.910327i	$-0.364170\pi$
$571$	11294.5	0.827779	0.413890	+	0.910327i	$0.364170\pi$
$572$	−2152.41	−0.157337
$573$	19229.2	1.40194
$574$	0	0
$575$	11076.6	0.803348
$576$	−7143.13	−0.516719
$577$	3110.96	0.224456	0.112228	−	0.993682i	$-0.464201\pi$
$577$	3110.96	0.224456	0.112228	+	0.993682i	$0.464201\pi$
$578$	−11977.2	−0.861912
$579$	23976.9	1.72098
$580$	1852.62	0.132631
$581$	0	0
$582$	30094.2	2.14338
$583$	4288.66	0.304662
$584$	−4390.20	−0.311075
$585$	−5036.24	−0.355937
$586$	13084.0	0.922349
$587$	−21803.7	−1.53311	−0.766553	−	0.642181i	$-0.778030\pi$
$587$	−21803.7	−1.53311	−0.766553	+	0.642181i	$0.778030\pi$
$588$	0	0
$589$	−15267.0	−1.06802
$590$	17322.0	1.20870
$591$	7146.48	0.497406
$592$	−27637.9	−1.91877
$593$	25928.2	1.79552	0.897759	−	0.440488i	$-0.145195\pi$
$593$	25928.2	1.79552	0.897759	+	0.440488i	$0.145195\pi$
$594$	714.680	0.0493665
$595$	0	0
$596$	9511.58	0.653707
$597$	34324.8	2.35313
$598$	17729.1	1.21237
$599$	−1450.64	−0.0989511	−0.0494755	−	0.998775i	$-0.515755\pi$
$599$	−1450.64	−0.0989511	−0.0494755	+	0.998775i	$0.515755\pi$
$600$	4092.39	0.278452
$601$	2726.95	0.185082	0.0925411	−	0.995709i	$-0.470501\pi$
$601$	2726.95	0.185082	0.0925411	+	0.995709i	$0.470501\pi$
$602$	0	0
$603$	4068.92	0.274791
$604$	−14293.0	−0.962870
$605$	6470.10	0.434788
$606$	−4941.77	−0.331264
$607$	−9309.86	−0.622530	−0.311265	−	0.950323i	$-0.600753\pi$
$607$	−9309.86	−0.622530	−0.311265	+	0.950323i	$0.600753\pi$
$608$	−20778.8	−1.38600
$609$	0	0
$610$	178.550	0.0118513
$611$	−1956.26	−0.129528
$612$	−13772.1	−0.909650
$613$	−2704.23	−0.178177	−0.0890887	−	0.996024i	$-0.528395\pi$
$613$	−2704.23	−0.178177	−0.0890887	+	0.996024i	$0.528395\pi$
$614$	33338.1	2.19123
$615$	−312.669	−0.0205009
$616$	0	0
$617$	8772.51	0.572395	0.286198	−	0.958171i	$-0.407609\pi$
$617$	8772.51	0.572395	0.286198	+	0.958171i	$0.407609\pi$
$618$	−13872.9	−0.902994
$619$	28504.5	1.85088	0.925438	−	0.378900i	$-0.123698\pi$
$619$	28504.5	1.85088	0.925438	+	0.378900i	$0.123698\pi$
$620$	−5696.92	−0.369023
$621$	−2632.77	−0.170128
$622$	−5252.17	−0.338573
$623$	0	0
$624$	21896.7	1.40476
$625$	6528.22	0.417806
$626$	−17367.7	−1.10887
$627$	−5038.24	−0.320906
$628$	11614.5	0.738009
$629$	−33585.5	−2.12900
$630$	0	0
$631$	10894.2	0.687306	0.343653	−	0.939097i	$-0.388336\pi$
$631$	10894.2	0.687306	0.343653	+	0.939097i	$0.388336\pi$
$632$	−6782.85	−0.426911
$633$	24652.5	1.54795
$634$	5611.34	0.351506
$635$	−9207.47	−0.575413
$636$	24740.5	1.54249
$637$	0	0
$638$	−1703.70	−0.105721
$639$	2846.68	0.176233
$640$	3727.84	0.230243
$641$	−17761.5	−1.09444	−0.547220	−	0.836989i	$-0.684314\pi$
$641$	−17761.5	−1.09444	−0.547220	+	0.836989i	$0.684314\pi$
$642$	−43180.8	−2.65453
$643$	11104.8	0.681074	0.340537	−	0.940231i	$-0.389391\pi$
$643$	11104.8	0.681074	0.340537	+	0.940231i	$0.389391\pi$
$644$	0	0
$645$	−2341.87	−0.142963
$646$	−30252.7	−1.84253
$647$	−4538.14	−0.275754	−0.137877	−	0.990449i	$-0.544028\pi$
$647$	−4538.14	−0.275754	−0.137877	+	0.990449i	$0.544028\pi$
$648$	−4689.99	−0.284321
$649$	−7124.38	−0.430903
$650$	15665.0	0.945282
$651$	0	0
$652$	17311.3	1.03982
$653$	15649.1	0.937818	0.468909	−	0.883246i	$-0.344647\pi$
$653$	15649.1	0.937818	0.468909	+	0.883246i	$0.344647\pi$
$654$	−2201.52	−0.131631
$655$	91.7421	0.00547277
$656$	635.437	0.0378196
$657$	−17907.3	−1.06336
$658$	0	0
$659$	−29437.9	−1.74012	−0.870059	−	0.492948i	$-0.835919\pi$
$659$	−29437.9	−1.74012	−0.870059	+	0.492948i	$0.835919\pi$
$660$	−1880.03	−0.110879
$661$	26849.4	1.57991	0.789954	−	0.613166i	$-0.210104\pi$
$661$	26849.4	1.57991	0.789954	+	0.613166i	$0.210104\pi$
$662$	23193.5	1.36170
$663$	26608.8	1.55867
$664$	−7909.24	−0.462256
$665$	0	0
$666$	−33723.2	−1.96208
$667$	6276.17	0.364339
$668$	8423.65	0.487906
$669$	30181.1	1.74420
$670$	3335.25	0.192316
$671$	−73.4361	−0.00422499
$672$	0	0
$673$	31109.7	1.78186	0.890931	−	0.454139i	$-0.150053\pi$
$673$	31109.7	1.78186	0.890931	+	0.454139i	$0.150053\pi$
$674$	2283.39	0.130494
$675$	−2326.26	−0.132649
$676$	−3007.05	−0.171088
$677$	−3421.45	−0.194235	−0.0971176	−	0.995273i	$-0.530962\pi$
$677$	−3421.45	−0.194235	−0.0971176	+	0.995273i	$0.530962\pi$
$678$	−6319.95	−0.357989
$679$	0	0
$680$	2663.40	0.150201
$681$	15447.2	0.869217
$682$	5239.00	0.294152
$683$	−26195.4	−1.46755	−0.733777	−	0.679391i	$-0.762244\pi$
$683$	−26195.4	−1.46755	−0.733777	+	0.679391i	$0.762244\pi$
$684$	−13585.7	−0.759449
$685$	13269.1	0.740126
$686$	0	0
$687$	−6469.28	−0.359270
$688$	4759.39	0.263736
$689$	−22343.4	−1.23543
$690$	15485.5	0.854381
$691$	−26763.4	−1.47341	−0.736706	−	0.676213i	$-0.763620\pi$
$691$	−26763.4	−1.47341	−0.736706	+	0.676213i	$0.763620\pi$
$692$	−1257.92	−0.0691024
$693$	0	0
$694$	−6229.80	−0.340749
$695$	−1981.79	−0.108164
$696$	2318.82	0.126285
$697$	772.181	0.0419634
$698$	−33140.7	−1.79712
$699$	12665.2	0.685326
$700$	0	0
$701$	−13903.4	−0.749106	−0.374553	−	0.927205i	$-0.622204\pi$
$701$	−13903.4	−0.749106	−0.374553	+	0.927205i	$0.622204\pi$
$702$	−3723.39	−0.200186
$703$	−33130.9	−1.77746
$704$	2408.17	0.128922
$705$	−1708.70	−0.0912814
$706$	8926.97	0.475880
$707$	0	0
$708$	−41099.3	−2.18165
$709$	2604.97	0.137985	0.0689927	−	0.997617i	$-0.478021\pi$
$709$	2604.97	0.137985	0.0689927	+	0.997617i	$0.478021\pi$
$710$	2333.39	0.123339
$711$	−27666.7	−1.45933
$712$	320.385	0.0168637
$713$	−19299.7	−1.01371
$714$	0	0
$715$	1697.87	0.0888068
$716$	−17775.7	−0.927806
$717$	−9598.47	−0.499946
$718$	−13703.1	−0.712251
$719$	14864.3	0.770993	0.385497	−	0.922709i	$-0.374030\pi$
$719$	14864.3	0.770993	0.385497	+	0.922709i	$0.374030\pi$
$720$	8939.93	0.462738
$721$	0	0
$722$	−3749.37	−0.193265
$723$	14474.2	0.744537
$724$	−8127.70	−0.417215
$725$	5545.50	0.284075
$726$	−34324.7	−1.75469
$727$	−16147.3	−0.823755	−0.411878	−	0.911239i	$-0.635127\pi$
$727$	−16147.3	−0.823755	−0.411878	+	0.911239i	$0.635127\pi$
$728$	0	0
$729$	−14609.5	−0.742241
$730$	−14678.4	−0.744207
$731$	5783.60	0.292632
$732$	−423.640	−0.0213910
$733$	21017.2	1.05906	0.529529	−	0.848292i	$-0.322369\pi$
$733$	21017.2	1.05906	0.529529	+	0.848292i	$0.322369\pi$
$734$	−41573.3	−2.09060
$735$	0	0
$736$	−26267.3	−1.31552
$737$	−1371.76	−0.0685609
$738$	775.348	0.0386734
$739$	−455.687	−0.0226829	−0.0113415	−	0.999936i	$-0.503610\pi$
$739$	−455.687	−0.0226829	−0.0113415	+	0.999936i	$0.503610\pi$
$740$	−12362.9	−0.614147
$741$	26248.6	1.30130
$742$	0	0
$743$	4593.46	0.226807	0.113404	−	0.993549i	$-0.463825\pi$
$743$	4593.46	0.226807	0.113404	+	0.993549i	$0.463825\pi$
$744$	−7130.52	−0.351368
$745$	−7502.94	−0.368975
$746$	−12475.2	−0.612263
$747$	−32261.1	−1.58015
$748$	4643.01	0.226959
$749$	0	0
$750$	30971.1	1.50787
$751$	−15135.3	−0.735413	−0.367707	−	0.929942i	$-0.619857\pi$
$751$	−15135.3	−0.735413	−0.367707	+	0.929942i	$0.619857\pi$
$752$	3472.60	0.168394
$753$	16340.9	0.790831
$754$	8876.07	0.428710
$755$	11274.6	0.543478
$756$	0	0
$757$	11670.9	0.560353	0.280176	−	0.959949i	$-0.409607\pi$
$757$	11670.9	0.560353	0.280176	+	0.959949i	$0.409607\pi$
$758$	50786.3	2.43356
$759$	−6369.05	−0.304588
$760$	2627.35	0.125400
$761$	−19527.7	−0.930195	−0.465097	−	0.885260i	$-0.653981\pi$
$761$	−19527.7	−0.930195	−0.465097	+	0.885260i	$0.653981\pi$
$762$	48846.8	2.32222
$763$	0	0
$764$	−17480.9	−0.827795
$765$	10863.8	0.513439
$766$	56965.5	2.68701
$767$	37117.1	1.74736
$768$	−36946.6	−1.73593
$769$	−13367.8	−0.626862	−0.313431	−	0.949611i	$-0.601478\pi$
$769$	−13367.8	−0.626862	−0.313431	+	0.949611i	$0.601478\pi$
$770$	0	0
$771$	11157.4	0.521174
$772$	−21797.0	−1.01618
$773$	8502.64	0.395626	0.197813	−	0.980240i	$-0.436616\pi$
$773$	8502.64	0.395626	0.197813	+	0.980240i	$0.436616\pi$
$774$	5807.31	0.269689
$775$	−17052.8	−0.790393
$776$	6454.62	0.298592
$777$	0	0
$778$	39056.4	1.79980
$779$	761.729	0.0350344
$780$	9794.74	0.449625
$781$	−959.704	−0.0439704
$782$	−38243.7	−1.74884
$783$	−1318.10	−0.0601597
$784$	0	0
$785$	−9161.79	−0.416559
$786$	−486.703	−0.0220867
$787$	7085.32	0.320920	0.160460	−	0.987042i	$-0.448702\pi$
$787$	7085.32	0.320920	0.160460	+	0.987042i	$0.448702\pi$
$788$	−6496.72	−0.293701
$789$	5787.15	0.261125
$790$	−22678.1	−1.02133
$791$	0	0
$792$	−1099.92	−0.0493486
$793$	382.593	0.0171327
$794$	2628.48	0.117483
$795$	−19515.9	−0.870638
$796$	−31204.0	−1.38944
$797$	−11566.9	−0.514078	−0.257039	−	0.966401i	$-0.582747\pi$
$797$	−11566.9	−0.514078	−0.257039	+	0.966401i	$0.582747\pi$
$798$	0	0
$799$	4219.89	0.186845
$800$	−23209.3	−1.02571
$801$	1306.82	0.0576459
$802$	−11702.6	−0.515253
$803$	6037.09	0.265310
$804$	−7913.44	−0.347121
$805$	0	0
$806$	−27294.5	−1.19281
$807$	4075.47	0.177774
$808$	−1059.91	−0.0461480
$809$	−1026.48	−0.0446095	−0.0223048	−	0.999751i	$-0.507100\pi$
$809$	−1026.48	−0.0446095	−0.0223048	+	0.999751i	$0.507100\pi$
$810$	−15680.7	−0.680203
$811$	17879.7	0.774156	0.387078	−	0.922047i	$-0.373484\pi$
$811$	17879.7	0.774156	0.387078	+	0.922047i	$0.373484\pi$
$812$	0	0
$813$	21823.2	0.941418
$814$	11369.1	0.489543
$815$	−13655.6	−0.586912
$816$	−47233.8	−2.02636
$817$	5705.31	0.244313
$818$	−8923.42	−0.381418
$819$	0	0
$820$	284.241	0.0121050
$821$	6030.81	0.256366	0.128183	−	0.991751i	$-0.459085\pi$
$821$	6030.81	0.256366	0.128183	+	0.991751i	$0.459085\pi$
$822$	−70394.3	−2.98696
$823$	43887.8	1.85885	0.929424	−	0.369013i	$-0.120304\pi$
$823$	43887.8	1.85885	0.929424	+	0.369013i	$0.120304\pi$
$824$	−2975.47	−0.125795
$825$	−5627.56	−0.237487
$826$	0	0
$827$	14962.9	0.629156	0.314578	−	0.949232i	$-0.398137\pi$
$827$	14962.9	0.629156	0.314578	+	0.949232i	$0.398137\pi$
$828$	−17174.3	−0.720831
$829$	45713.1	1.91518	0.957588	−	0.288140i	$-0.0930367\pi$
$829$	45713.1	1.91518	0.957588	+	0.288140i	$0.0930367\pi$
$830$	−26444.1	−1.10589
$831$	−34762.4	−1.45114
$832$	−12546.3	−0.522792
$833$	0	0
$834$	10513.7	0.436520
$835$	−6644.77	−0.275391
$836$	4580.17	0.189484
$837$	4053.25	0.167384
$838$	5742.01	0.236700
$839$	−25273.3	−1.03997	−0.519983	−	0.854176i	$-0.674062\pi$
$839$	−25273.3	−1.03997	−0.519983	+	0.854176i	$0.674062\pi$
$840$	0	0
$841$	−21246.8	−0.871164
$842$	40197.9	1.64526
$843$	−60751.8	−2.48209
$844$	−22411.1	−0.914008
$845$	2372.03	0.0965683
$846$	4237.19	0.172196
$847$	0	0
$848$	39662.1	1.60614
$849$	−46549.4	−1.88171
$850$	−33791.4	−1.36357
$851$	−41882.1	−1.68708
$852$	−5536.37	−0.222621
$853$	−30606.5	−1.22854	−0.614272	−	0.789095i	$-0.710550\pi$
$853$	−30606.5	−1.22854	−0.614272	+	0.789095i	$0.710550\pi$
$854$	0	0
$855$	10716.7	0.428660
$856$	−9261.44	−0.369801
$857$	32461.9	1.29391	0.646954	−	0.762529i	$-0.276043\pi$
$857$	32461.9	1.29391	0.646954	+	0.762529i	$0.276043\pi$
$858$	−9007.42	−0.358401
$859$	−36809.7	−1.46208	−0.731042	−	0.682333i	$-0.760965\pi$
$859$	−36809.7	−1.46208	−0.731042	+	0.682333i	$0.760965\pi$
$860$	2128.95	0.0844147
$861$	0	0
$862$	−8617.48	−0.340502
$863$	21277.6	0.839278	0.419639	−	0.907691i	$-0.362157\pi$
$863$	21277.6	0.839278	0.419639	+	0.907691i	$0.362157\pi$
$864$	5516.57	0.217219
$865$	992.273	0.0390038
$866$	−49036.4	−1.92416
$867$	−22416.7	−0.878097
$868$	0	0
$869$	9327.30	0.364105
$870$	7752.83	0.302121
$871$	7146.69	0.278021
$872$	−472.184	−0.0183373
$873$	26327.9	1.02069
$874$	−37726.0	−1.46007
$875$	0	0
$876$	34826.9	1.34326
$877$	25251.8	0.972283	0.486141	−	0.873880i	$-0.338404\pi$
$877$	25251.8	0.972283	0.486141	+	0.873880i	$0.338404\pi$
$878$	−46809.6	−1.79926
$879$	24488.3	0.939669
$880$	−3013.93	−0.115454
$881$	−28158.6	−1.07683	−0.538415	−	0.842680i	$-0.680977\pi$
$881$	−28158.6	−1.07683	−0.538415	+	0.842680i	$0.680977\pi$
$882$	0	0
$883$	20903.3	0.796661	0.398330	−	0.917242i	$-0.369590\pi$
$883$	20903.3	0.796661	0.398330	+	0.917242i	$0.369590\pi$
$884$	−24189.5	−0.920341
$885$	32420.1	1.23140
$886$	16128.5	0.611564
$887$	14134.4	0.535046	0.267523	−	0.963552i	$-0.413795\pi$
$887$	14134.4	0.535046	0.267523	+	0.963552i	$0.413795\pi$
$888$	−15473.9	−0.584764
$889$	0	0
$890$	1071.19	0.0403442
$891$	6449.34	0.242493
$892$	−27437.0	−1.02989
$893$	4162.77	0.155993
$894$	39804.0	1.48909
$895$	14021.9	0.523686
$896$	0	0
$897$	33182.0	1.23513
$898$	46208.0	1.71713
$899$	−9662.39	−0.358464
$900$	−15174.8	−0.562031
$901$	48197.3	1.78211
$902$	−261.394	−0.00964906
$903$	0	0
$904$	−1355.51	−0.0498711
$905$	6411.32	0.235491
$906$	−59813.3	−2.19334
$907$	−12469.2	−0.456487	−0.228243	−	0.973604i	$-0.573298\pi$
$907$	−12469.2	−0.456487	−0.228243	+	0.973604i	$0.573298\pi$
$908$	−14042.7	−0.513242
$909$	−4323.30	−0.157750
$910$	0	0
$911$	17220.7	0.626285	0.313143	−	0.949706i	$-0.398618\pi$
$911$	17220.7	0.626285	0.313143	+	0.949706i	$0.398618\pi$
$912$	−46594.4	−1.69177
$913$	10876.2	0.394250
$914$	38243.8	1.38402
$915$	334.177	0.0120738
$916$	5881.09	0.212136
$917$	0	0
$918$	8031.81	0.288768
$919$	42333.1	1.51952	0.759760	−	0.650203i	$-0.225316\pi$
$919$	42333.1	1.51952	0.759760	+	0.650203i	$0.225316\pi$
$920$	3321.34	0.119023
$921$	62396.0	2.23237
$922$	52328.5	1.86914
$923$	4999.94	0.178304
$924$	0	0
$925$	−37006.2	−1.31541
$926$	−21047.2	−0.746926
$927$	−12136.7	−0.430012
$928$	−13150.8	−0.465188
$929$	5367.99	0.189578	0.0947890	−	0.995497i	$-0.469782\pi$
$929$	5367.99	0.189578	0.0947890	+	0.995497i	$0.469782\pi$
$930$	−23840.5	−0.840603
$931$	0	0
$932$	−11513.7	−0.404661
$933$	−9830.03	−0.344931
$934$	−6998.55	−0.245181
$935$	−3662.51	−0.128104
$936$	5730.46	0.200113
$937$	−17531.9	−0.611251	−0.305625	−	0.952152i	$-0.598866\pi$
$937$	−17531.9	−0.611251	−0.305625	+	0.952152i	$0.598866\pi$
$938$	0	0
$939$	−32505.6	−1.12969
$940$	1553.35	0.0538985
$941$	−49792.8	−1.72497	−0.862487	−	0.506080i	$-0.831094\pi$
$941$	−49792.8	−1.72497	−0.862487	+	0.506080i	$0.831094\pi$
$942$	48604.4	1.68112
$943$	962.934	0.0332529
$944$	−65887.3	−2.27166
$945$	0	0
$946$	−1957.82	−0.0672879
$947$	38626.9	1.32545	0.662727	−	0.748861i	$-0.269399\pi$
$947$	38626.9	1.32545	0.662727	+	0.748861i	$0.269399\pi$
$948$	53807.6	1.84345
$949$	−31452.5	−1.07586
$950$	−33334.0	−1.13842
$951$	10502.3	0.358106
$952$	0	0
$953$	15720.9	0.534366	0.267183	−	0.963646i	$-0.413907\pi$
$953$	15720.9	0.534366	0.267183	+	0.963646i	$0.413907\pi$
$954$	48394.9	1.64239
$955$	13789.3	0.467237
$956$	8725.78	0.295201
$957$	−3188.67	−0.107706
$958$	19050.1	0.642465
$959$	0	0
$960$	−10958.6	−0.368423
$961$	−78.4839	−0.00263448
$962$	−59231.8	−1.98514
$963$	−37776.7	−1.26411
$964$	−13158.2	−0.439623
$965$	17193.9	0.573567
$966$	0	0
$967$	−34863.2	−1.15939	−0.579693	−	0.814835i	$-0.696828\pi$
$967$	−34863.2	−1.15939	−0.579693	+	0.814835i	$0.696828\pi$
$968$	−7361.97	−0.244445
$969$	−56621.4	−1.87713
$970$	21580.7	0.714343
$971$	−27616.0	−0.912709	−0.456354	−	0.889798i	$-0.650845\pi$
$971$	−27616.0	−0.912709	−0.456354	+	0.889798i	$0.650845\pi$
$972$	33095.6	1.09212
$973$	0	0
$974$	20235.0	0.665679
$975$	29318.9	0.963032
$976$	−679.148	−0.0222736
$977$	22729.4	0.744298	0.372149	−	0.928173i	$-0.378621\pi$
$977$	22729.4	0.744298	0.372149	+	0.928173i	$0.378621\pi$
$978$	72444.5	2.36863
$979$	−440.571	−0.0143827
$980$	0	0
$981$	−1926.00	−0.0626834
$982$	55440.0	1.80159
$983$	38566.7	1.25136	0.625680	−	0.780080i	$-0.284821\pi$
$983$	38566.7	1.25136	0.625680	+	0.780080i	$0.284821\pi$
$984$	355.769	0.0115259
$985$	5124.76	0.165775
$986$	−19146.7	−0.618414
$987$	0	0
$988$	−23862.1	−0.768375
$989$	7212.32	0.231889
$990$	−3677.53	−0.118060
$991$	−50445.1	−1.61700	−0.808498	−	0.588500i	$-0.799719\pi$
$991$	−50445.1	−1.61700	−0.808498	+	0.588500i	$0.799719\pi$
$992$	40439.5	1.29431
$993$	43409.4	1.38727
$994$	0	0
$995$	24614.4	0.784251
$996$	62743.0	1.99607
$997$	33878.9	1.07618	0.538092	−	0.842886i	$-0.319145\pi$
$997$	33878.9	1.07618	0.538092	+	0.842886i	$0.319145\pi$
$998$	−34296.2	−1.08780
$999$	8795.94	0.278570

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.n.1.13	yes	68
7.6	odd	2		2303.4.a.m.1.13	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.m.1.13	✓	68	7.6	odd	2
2303.4.a.n.1.13	yes	68	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:	\( N \)	\(=\)	\( 2303 = 7^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2303.a (trivial)

\(f(q)\)	\(=\)	\(q-3.80432 q^{2} -7.12022 q^{3} +6.47285 q^{4} -5.10593 q^{5} +27.0876 q^{6} +5.80976 q^{8} +23.6975 q^{9} +O(q^{10})\)	\(q-3.80432 q^{2} -7.12022 q^{3} +6.47285 q^{4} -5.10593 q^{5} +27.0876 q^{6} +5.80976 q^{8} +23.6975 q^{9} +19.4246 q^{10} -7.98916 q^{11} -46.0881 q^{12} +41.6226 q^{13} +36.3554 q^{15} -73.8850 q^{16} -89.7848 q^{17} -90.1530 q^{18} -88.5695 q^{19} -33.0499 q^{20} +30.3933 q^{22} -111.964 q^{23} -41.3668 q^{24} -98.9295 q^{25} -158.346 q^{26} +23.5144 q^{27} -56.0551 q^{29} -138.307 q^{30} +172.373 q^{31} +234.604 q^{32} +56.8846 q^{33} +341.570 q^{34} +153.391 q^{36} +374.067 q^{37} +336.947 q^{38} -296.362 q^{39} -29.6642 q^{40} -8.60036 q^{41} -64.4162 q^{43} -51.7127 q^{44} -120.998 q^{45} +425.948 q^{46} -47.0000 q^{47} +526.077 q^{48} +376.359 q^{50} +639.287 q^{51} +269.417 q^{52} -536.809 q^{53} -89.4562 q^{54} +40.7921 q^{55} +630.634 q^{57} +213.251 q^{58} +891.755 q^{59} +235.323 q^{60} +9.19196 q^{61} -655.763 q^{62} -301.429 q^{64} -212.522 q^{65} -216.407 q^{66} +171.702 q^{67} -581.164 q^{68} +797.211 q^{69} +120.126 q^{71} +137.677 q^{72} -755.659 q^{73} -1423.07 q^{74} +704.399 q^{75} -573.297 q^{76} +1127.45 q^{78} -1167.49 q^{79} +377.252 q^{80} -807.261 q^{81} +32.7185 q^{82} -1361.37 q^{83} +458.435 q^{85} +245.060 q^{86} +399.124 q^{87} -46.4151 q^{88} +55.1461 q^{89} +460.315 q^{90} -724.729 q^{92} -1227.33 q^{93} +178.803 q^{94} +452.230 q^{95} -1670.43 q^{96} +1111.00 q^{97} -189.323 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9}+O(q^{10}) \) 68 * q - 2 * q^2 + 24 * q^3 + 254 * q^4 + 40 * q^5 + 48 * q^6 - 66 * q^8 + 576 * q^9	\( 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9} + 200 q^{10} - 20 q^{11} + 288 q^{12} + 520 q^{13} + 88 q^{15} + 1062 q^{16} + 784 q^{17} - 2 q^{18} + 532 q^{19} + 400 q^{20} - 4 q^{22} - 268 q^{23} + 576 q^{24} + 1864 q^{25} + 312 q^{26} + 864 q^{27} + 200 q^{29} + 792 q^{30} + 936 q^{31} + 30 q^{32} + 2112 q^{33} + 1088 q^{34} + 2130 q^{36} - 356 q^{37} + 1192 q^{38} - 488 q^{39} + 2400 q^{40} + 1476 q^{41} - 92 q^{43} + 192 q^{44} + 1848 q^{45} - 424 q^{46} - 3196 q^{47} + 2688 q^{48} - 1338 q^{50} - 148 q^{51} + 4980 q^{52} - 80 q^{53} + 4944 q^{54} + 2200 q^{55} + 2244 q^{57} - 356 q^{58} + 560 q^{59} - 736 q^{60} + 3944 q^{61} + 1488 q^{62} + 3778 q^{64} + 2004 q^{65} - 1000 q^{66} + 2768 q^{67} + 8192 q^{68} + 2208 q^{69} - 2448 q^{71} - 5234 q^{72} + 9532 q^{73} - 2000 q^{74} + 11136 q^{75} + 6384 q^{76} - 3460 q^{78} - 1520 q^{79} + 616 q^{80} + 6976 q^{81} + 4976 q^{82} + 3320 q^{83} + 3244 q^{85} - 2892 q^{86} + 2360 q^{87} - 2868 q^{88} + 8152 q^{89} + 5400 q^{90} - 4684 q^{92} + 2840 q^{93} + 94 q^{94} - 4256 q^{95} + 5376 q^{96} + 13968 q^{97} + 2380 q^{99}+O(q^{100}) \) 68 * q - 2 * q^2 + 24 * q^3 + 254 * q^4 + 40 * q^5 + 48 * q^6 - 66 * q^8 + 576 * q^9 + 200 * q^10 - 20 * q^11 + 288 * q^12 + 520 * q^13 + 88 * q^15 + 1062 * q^16 + 784 * q^17 - 2 * q^18 + 532 * q^19 + 400 * q^20 - 4 * q^22 - 268 * q^23 + 576 * q^24 + 1864 * q^25 + 312 * q^26 + 864 * q^27 + 200 * q^29 + 792 * q^30 + 936 * q^31 + 30 * q^32 + 2112 * q^33 + 1088 * q^34 + 2130 * q^36 - 356 * q^37 + 1192 * q^38 - 488 * q^39 + 2400 * q^40 + 1476 * q^41 - 92 * q^43 + 192 * q^44 + 1848 * q^45 - 424 * q^46 - 3196 * q^47 + 2688 * q^48 - 1338 * q^50 - 148 * q^51 + 4980 * q^52 - 80 * q^53 + 4944 * q^54 + 2200 * q^55 + 2244 * q^57 - 356 * q^58 + 560 * q^59 - 736 * q^60 + 3944 * q^61 + 1488 * q^62 + 3778 * q^64 + 2004 * q^65 - 1000 * q^66 + 2768 * q^67 + 8192 * q^68 + 2208 * q^69 - 2448 * q^71 - 5234 * q^72 + 9532 * q^73 - 2000 * q^74 + 11136 * q^75 + 6384 * q^76 - 3460 * q^78 - 1520 * q^79 + 616 * q^80 + 6976 * q^81 + 4976 * q^82 + 3320 * q^83 + 3244 * q^85 - 2892 * q^86 + 2360 * q^87 - 2868 * q^88 + 8152 * q^89 + 5400 * q^90 - 4684 * q^92 + 2840 * q^93 + 94 * q^94 - 4256 * q^95 + 5376 * q^96 + 13968 * q^97 + 2380 * q^99

Introduction

L-functions

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