LMFDB - Embedded newform 2303.4.a.h.1.19

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:	$35$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q+0.529428 q^{2} -9.49502 q^{3} -7.71971 q^{4} -20.1615 q^{5} -5.02693 q^{6} -8.32246 q^{8} +63.1555 q^{9} +O(q^{10})$	\(q+0.529428 q^{2} -9.49502 q^{3} -7.71971 q^{4} -20.1615 q^{5} -5.02693 q^{6} -8.32246 q^{8} +63.1555 q^{9} -10.6741 q^{10} -60.5544 q^{11} +73.2988 q^{12} +52.1790 q^{13} +191.434 q^{15} +57.3515 q^{16} +80.2246 q^{17} +33.4363 q^{18} +161.493 q^{19} +155.641 q^{20} -32.0592 q^{22} -85.6488 q^{23} +79.0219 q^{24} +281.487 q^{25} +27.6250 q^{26} -343.297 q^{27} -155.622 q^{29} +101.351 q^{30} -278.915 q^{31} +96.9432 q^{32} +574.965 q^{33} +42.4732 q^{34} -487.542 q^{36} -16.7593 q^{37} +85.4991 q^{38} -495.441 q^{39} +167.793 q^{40} +50.9646 q^{41} -66.2906 q^{43} +467.462 q^{44} -1273.31 q^{45} -45.3449 q^{46} +47.0000 q^{47} -544.554 q^{48} +149.027 q^{50} -761.734 q^{51} -402.807 q^{52} -241.544 q^{53} -181.751 q^{54} +1220.87 q^{55} -1533.38 q^{57} -82.3906 q^{58} +195.863 q^{59} -1477.82 q^{60} +478.375 q^{61} -147.666 q^{62} -407.488 q^{64} -1052.01 q^{65} +304.403 q^{66} +115.053 q^{67} -619.310 q^{68} +813.237 q^{69} +492.226 q^{71} -525.609 q^{72} +174.986 q^{73} -8.87286 q^{74} -2672.73 q^{75} -1246.68 q^{76} -262.300 q^{78} -824.543 q^{79} -1156.29 q^{80} +1554.42 q^{81} +26.9821 q^{82} -181.830 q^{83} -1617.45 q^{85} -35.0961 q^{86} +1477.63 q^{87} +503.961 q^{88} +1578.71 q^{89} -674.127 q^{90} +661.184 q^{92} +2648.31 q^{93} +24.8831 q^{94} -3255.95 q^{95} -920.478 q^{96} +444.038 q^{97} -3824.34 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9}+O(q^{10}) $ 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9} + 100 q^{10} + 40 q^{11} + 144 q^{12} + 328 q^{13} + 20 q^{15} + 643 q^{16} + 152 q^{17} + 51 q^{18} + 266 q^{19} + 1064 q^{20} - 168 q^{22} - 134 q^{23} + 288 q^{24} + 1137 q^{25} + 156 q^{26} + 672 q^{27} + 248 q^{29} - 216 q^{30} + 276 q^{31} + 347 q^{32} + 1056 q^{33} + 908 q^{34} + 909 q^{36} - 418 q^{37} + 164 q^{38} - 548 q^{39} + 1200 q^{40} + 918 q^{41} + 608 q^{43} + 1288 q^{44} + 876 q^{45} - 972 q^{46} + 1645 q^{47} + 1252 q^{48} - 367 q^{50} - 464 q^{51} + 3798 q^{52} - 218 q^{53} - 744 q^{54} + 1004 q^{55} - 436 q^{57} - 1270 q^{58} + 3760 q^{59} - 424 q^{60} + 956 q^{61} + 84 q^{62} + 2189 q^{64} - 596 q^{65} + 5500 q^{66} - 476 q^{67} + 256 q^{68} + 444 q^{69} + 852 q^{71} - 883 q^{72} + 6250 q^{73} + 1366 q^{74} - 2568 q^{75} + 1742 q^{76} - 1460 q^{78} + 632 q^{79} + 10124 q^{80} + 1267 q^{81} + 792 q^{82} + 796 q^{83} - 1228 q^{85} - 2864 q^{86} + 8360 q^{87} - 50 q^{88} + 908 q^{89} - 1858 q^{90} + 1696 q^{92} + 644 q^{93} + 235 q^{94} + 1320 q^{95} + 2688 q^{96} + 6184 q^{97} - 1812 q^{99}+O(q^{100}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9 + 100 * q^10 + 40 * q^11 + 144 * q^12 + 328 * q^13 + 20 * q^15 + 643 * q^16 + 152 * q^17 + 51 * q^18 + 266 * q^19 + 1064 * q^20 - 168 * q^22 - 134 * q^23 + 288 * q^24 + 1137 * q^25 + 156 * q^26 + 672 * q^27 + 248 * q^29 - 216 * q^30 + 276 * q^31 + 347 * q^32 + 1056 * q^33 + 908 * q^34 + 909 * q^36 - 418 * q^37 + 164 * q^38 - 548 * q^39 + 1200 * q^40 + 918 * q^41 + 608 * q^43 + 1288 * q^44 + 876 * q^45 - 972 * q^46 + 1645 * q^47 + 1252 * q^48 - 367 * q^50 - 464 * q^51 + 3798 * q^52 - 218 * q^53 - 744 * q^54 + 1004 * q^55 - 436 * q^57 - 1270 * q^58 + 3760 * q^59 - 424 * q^60 + 956 * q^61 + 84 * q^62 + 2189 * q^64 - 596 * q^65 + 5500 * q^66 - 476 * q^67 + 256 * q^68 + 444 * q^69 + 852 * q^71 - 883 * q^72 + 6250 * q^73 + 1366 * q^74 - 2568 * q^75 + 1742 * q^76 - 1460 * q^78 + 632 * q^79 + 10124 * q^80 + 1267 * q^81 + 792 * q^82 + 796 * q^83 - 1228 * q^85 - 2864 * q^86 + 8360 * q^87 - 50 * q^88 + 908 * q^89 - 1858 * q^90 + 1696 * q^92 + 644 * q^93 + 235 * q^94 + 1320 * q^95 + 2688 * q^96 + 6184 * q^97 - 1812 * 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 $

$2$	0.529428	0.187181	0.0935906	−	0.995611i	$-0.470166\pi$
$2$	0.529428	0.187181	0.0935906	+	0.995611i	$0.470166\pi$
$3$	−9.49502	−1.82732	−0.913659	−	0.406481i	$-0.866756\pi$
$3$	−9.49502	−1.82732	−0.913659	+	0.406481i	$0.866756\pi$
$4$	−7.71971	−0.964963
$5$	−20.1615	−1.80330	−0.901651	−	0.432464i	$-0.857644\pi$
$5$	−20.1615	−1.80330	−0.901651	+	0.432464i	$0.857644\pi$
$6$	−5.02693	−0.342040
$7$	0	0
$7$	0	0
$8$	−8.32246	−0.367804
$9$	63.1555	2.33909
$10$	−10.6741	−0.337544
$11$	−60.5544	−1.65980	−0.829902	−	0.557910i	$-0.811604\pi$
$11$	−60.5544	−1.65980	−0.829902	+	0.557910i	$0.811604\pi$
$12$	73.2988	1.76329
$13$	52.1790	1.11322	0.556610	−	0.830774i	$-0.312102\pi$
$13$	52.1790	1.11322	0.556610	+	0.830774i	$0.312102\pi$
$14$	0	0
$15$	191.434	3.29521
$16$	57.3515	0.896117
$17$	80.2246	1.14455	0.572274	−	0.820062i	$-0.306061\pi$
$17$	80.2246	1.14455	0.572274	+	0.820062i	$0.306061\pi$
$18$	33.4363	0.437834
$19$	161.493	1.94995	0.974976	−	0.222311i	$-0.0713602\pi$
$19$	161.493	1.94995	0.974976	+	0.222311i	$0.0713602\pi$
$20$	155.641	1.74012
$21$	0	0
$22$	−32.0592	−0.310684
$23$	−85.6488	−0.776479	−0.388239	−	0.921559i	$-0.626917\pi$
$23$	−85.6488	−0.776479	−0.388239	+	0.921559i	$0.626917\pi$
$24$	79.0219	0.672095
$25$	281.487	2.25190
$26$	27.6250	0.208374
$27$	−343.297	−2.44695
$28$	0	0
$29$	−155.622	−0.996492	−0.498246	−	0.867036i	$-0.666022\pi$
$29$	−155.622	−0.996492	−0.498246	+	0.867036i	$0.666022\pi$
$30$	101.351	0.616801
$31$	−278.915	−1.61596	−0.807979	−	0.589212i	$-0.799438\pi$
$31$	−278.915	−1.61596	−0.807979	+	0.589212i	$0.799438\pi$
$32$	96.9432	0.535540
$33$	574.965	3.03299
$34$	42.4732	0.214238
$35$	0	0
$36$	−487.542	−2.25714
$37$	−16.7593	−0.0744653	−0.0372327	−	0.999307i	$-0.511854\pi$
$37$	−16.7593	−0.0744653	−0.0372327	+	0.999307i	$0.511854\pi$
$38$	85.4991	0.364994
$39$	−495.441	−2.03421
$40$	167.793	0.663262
$41$	50.9646	0.194130	0.0970650	−	0.995278i	$-0.469055\pi$
$41$	50.9646	0.194130	0.0970650	+	0.995278i	$0.469055\pi$
$42$	0	0
$43$	−66.2906	−0.235098	−0.117549	−	0.993067i	$-0.537504\pi$
$43$	−66.2906	−0.235098	−0.117549	+	0.993067i	$0.537504\pi$
$44$	467.462	1.60165
$45$	−1273.31	−4.21809
$46$	−45.3449	−0.145342
$47$	47.0000	0.145865
$47$	47.0000	0.145865
$48$	−544.554	−1.63749
$49$	0	0
$50$	149.027	0.421513
$51$	−761.734	−2.09145
$52$	−402.807	−1.07422
$53$	−241.544	−0.626012	−0.313006	−	0.949751i	$-0.601336\pi$
$53$	−241.544	−0.626012	−0.313006	+	0.949751i	$0.601336\pi$
$54$	−181.751	−0.458022
$55$	1220.87	2.99313
$56$	0	0
$57$	−1533.38	−3.56318
$58$	−82.3906	−0.186525
$59$	195.863	0.432189	0.216094	−	0.976372i	$-0.430668\pi$
$59$	195.863	0.432189	0.216094	+	0.976372i	$0.430668\pi$
$60$	−1477.82	−3.17975
$61$	478.375	1.00409	0.502046	−	0.864841i	$-0.332581\pi$
$61$	478.375	1.00409	0.502046	+	0.864841i	$0.332581\pi$
$62$	−147.666	−0.302477
$63$	0	0
$64$	−407.488	−0.795874
$65$	−1052.01	−2.00747
$66$	304.403	0.567718
$67$	115.053	0.209791	0.104896	−	0.994483i	$-0.466549\pi$
$67$	115.053	0.209791	0.104896	+	0.994483i	$0.466549\pi$
$68$	−619.310	−1.10445
$69$	813.237	1.41887
$70$	0	0
$71$	492.226	0.822767	0.411383	−	0.911462i	$-0.365046\pi$
$71$	492.226	0.822767	0.411383	+	0.911462i	$0.365046\pi$
$72$	−525.609	−0.860327
$73$	174.986	0.280556	0.140278	−	0.990112i	$-0.455200\pi$
$73$	174.986	0.280556	0.140278	+	0.990112i	$0.455200\pi$
$74$	−8.87286	−0.0139385
$75$	−2672.73	−4.11494
$76$	−1246.68	−1.88163
$77$	0	0
$78$	−262.300	−0.380765
$79$	−824.543	−1.17428	−0.587141	−	0.809485i	$-0.699747\pi$
$79$	−824.543	−1.17428	−0.587141	+	0.809485i	$0.699747\pi$
$80$	−1156.29	−1.61597
$81$	1554.42	2.13226
$82$	26.9821	0.0363375
$83$	−181.830	−0.240463	−0.120232	−	0.992746i	$-0.538364\pi$
$83$	−181.830	−0.240463	−0.120232	+	0.992746i	$0.538364\pi$
$84$	0	0
$85$	−1617.45	−2.06397
$86$	−35.0961	−0.0440059
$87$	1477.63	1.82091
$88$	503.961	0.610482
$89$	1578.71	1.88025	0.940126	−	0.340827i	$-0.110707\pi$
$89$	1578.71	1.88025	0.940126	+	0.340827i	$0.110707\pi$
$90$	−674.127	−0.789547
$91$	0	0
$92$	661.184	0.749273
$93$	2648.31	2.95287
$94$	24.8831	0.0273032
$95$	−3255.95	−3.51635
$96$	−920.478	−0.978603
$97$	444.038	0.464796	0.232398	−	0.972621i	$-0.425343\pi$
$97$	444.038	0.464796	0.232398	+	0.972621i	$0.425343\pi$
$98$	0	0
$99$	−3824.34	−3.88243
$100$	−2173.00	−2.17300
$101$	−262.323	−0.258436	−0.129218	−	0.991616i	$-0.541247\pi$
$101$	−262.323	−0.258436	−0.129218	+	0.991616i	$0.541247\pi$
$102$	−403.284	−0.391481
$103$	−152.600	−0.145982	−0.0729908	−	0.997333i	$-0.523254\pi$
$103$	−152.600	−0.145982	−0.0729908	+	0.997333i	$0.523254\pi$
$104$	−434.258	−0.409447
$105$	0	0
$106$	−127.880	−0.117178
$107$	34.2354	0.0309314	0.0154657	−	0.999880i	$-0.495077\pi$
$107$	34.2354	0.0309314	0.0154657	+	0.999880i	$0.495077\pi$
$108$	2650.15	2.36121
$109$	557.778	0.490142	0.245071	−	0.969505i	$-0.421189\pi$
$109$	557.778	0.490142	0.245071	+	0.969505i	$0.421189\pi$
$110$	646.363	0.560257
$111$	159.130	0.136072
$112$	0	0
$113$	1618.29	1.34722	0.673609	−	0.739088i	$-0.264743\pi$
$113$	1618.29	1.34722	0.673609	+	0.739088i	$0.264743\pi$
$114$	−811.816	−0.666960
$115$	1726.81	1.40023
$116$	1201.36	0.961578
$117$	3295.39	2.60392
$118$	103.695	0.0808976
$119$	0	0
$120$	−1593.20	−1.21199
$121$	2335.83	1.75495
$122$	253.265	0.187947
$123$	−483.910	−0.354737
$124$	2153.14	1.55934
$125$	−3155.03	−2.25755
$126$	0	0
$127$	316.262	0.220974	0.110487	−	0.993878i	$-0.464759\pi$
$127$	316.262	0.220974	0.110487	+	0.993878i	$0.464759\pi$
$128$	−991.281	−0.684513
$129$	629.430	0.429599
$130$	−556.963	−0.375761
$131$	−1362.84	−0.908949	−0.454474	−	0.890760i	$-0.650173\pi$
$131$	−1362.84	−0.908949	−0.454474	+	0.890760i	$0.650173\pi$
$132$	−4438.56	−2.92672
$133$	0	0
$134$	60.9125	0.0392690
$135$	6921.39	4.41258
$136$	−667.666	−0.420970
$137$	−955.157	−0.595654	−0.297827	−	0.954620i	$-0.596262\pi$
$137$	−955.157	−0.595654	−0.297827	+	0.954620i	$0.596262\pi$
$138$	430.551	0.265586
$139$	30.5061	0.0186150	0.00930752	−	0.999957i	$-0.497037\pi$
$139$	30.5061	0.0186150	0.00930752	+	0.999957i	$0.497037\pi$
$140$	0	0
$141$	−446.266	−0.266542
$142$	260.598	0.154006
$143$	−3159.67	−1.84773
$144$	3622.06	2.09610
$145$	3137.58	1.79698
$146$	92.6427	0.0525148
$147$	0	0
$148$	129.377	0.0718563
$149$	−1702.26	−0.935935	−0.467968	−	0.883746i	$-0.655014\pi$
$149$	−1702.26	−0.935935	−0.467968	+	0.883746i	$0.655014\pi$
$150$	−1415.02	−0.770238
$151$	−1371.71	−0.739261	−0.369631	−	0.929179i	$-0.620516\pi$
$151$	−1371.71	−0.739261	−0.369631	+	0.929179i	$0.620516\pi$
$152$	−1344.02	−0.717200
$153$	5066.62	2.67720
$154$	0	0
$155$	5623.36	2.91406
$156$	3824.66	1.96293
$157$	−2289.99	−1.16408	−0.582041	−	0.813160i	$-0.697746\pi$
$157$	−2289.99	−1.16408	−0.582041	+	0.813160i	$0.697746\pi$
$158$	−436.536	−0.219804
$159$	2293.47	1.14392
$160$	−1954.52	−0.965741
$161$	0	0
$162$	822.952	0.399118
$163$	707.527	0.339986	0.169993	−	0.985445i	$-0.445625\pi$
$163$	707.527	0.339986	0.169993	+	0.985445i	$0.445625\pi$
$164$	−393.432	−0.187328
$165$	−11592.2	−5.46940
$166$	−96.2660	−0.0450102
$167$	−2505.55	−1.16099	−0.580495	−	0.814264i	$-0.697141\pi$
$167$	−2505.55	−1.16099	−0.580495	+	0.814264i	$0.697141\pi$
$168$	0	0
$169$	525.650	0.239258
$170$	−856.324	−0.386336
$171$	10199.2	4.56111
$172$	511.744	0.226861
$173$	−3436.46	−1.51023	−0.755114	−	0.655593i	$-0.772419\pi$
$173$	−3436.46	−1.51023	−0.755114	+	0.655593i	$0.772419\pi$
$174$	782.301	0.340840
$175$	0	0
$176$	−3472.89	−1.48738
$177$	−1859.72	−0.789746
$178$	835.811	0.351948
$179$	−242.626	−0.101311	−0.0506557	−	0.998716i	$-0.516131\pi$
$179$	−242.626	−0.101311	−0.0506557	+	0.998716i	$0.516131\pi$
$180$	9829.59	4.07030
$181$	−671.350	−0.275697	−0.137848	−	0.990453i	$-0.544019\pi$
$181$	−671.350	−0.275697	−0.137848	+	0.990453i	$0.544019\pi$
$182$	0	0
$183$	−4542.18	−1.83480
$184$	712.809	0.285592
$185$	337.894	0.134283
$186$	1402.09	0.552721
$187$	−4857.95	−1.89973
$188$	−362.826	−0.140754
$189$	0	0
$190$	−1723.79	−0.658195
$191$	536.791	0.203355	0.101677	−	0.994817i	$-0.467579\pi$
$191$	536.791	0.203355	0.101677	+	0.994817i	$0.467579\pi$
$192$	3869.10	1.45432
$193$	−1306.81	−0.487389	−0.243695	−	0.969852i	$-0.578359\pi$
$193$	−1306.81	−0.487389	−0.243695	+	0.969852i	$0.578359\pi$
$194$	235.086	0.0870010
$195$	9988.85	3.66829
$196$	0	0
$197$	−1248.04	−0.451368	−0.225684	−	0.974201i	$-0.572462\pi$
$197$	−1248.04	−0.451368	−0.225684	+	0.974201i	$0.572462\pi$
$198$	−2024.71	−0.726718
$199$	−1946.89	−0.693526	−0.346763	−	0.937953i	$-0.612719\pi$
$199$	−1946.89	−0.693526	−0.346763	+	0.937953i	$0.612719\pi$
$200$	−2342.67	−0.828258
$201$	−1092.44	−0.383355
$202$	−138.881	−0.0483744
$203$	0	0
$204$	5880.36	2.01818
$205$	−1027.52	−0.350075
$206$	−80.7907	−0.0273250
$207$	−5409.19	−1.81625
$208$	2992.54	0.997575
$209$	−9779.12	−3.23654
$210$	0	0
$211$	−4382.86	−1.42999	−0.714996	−	0.699128i	$-0.753572\pi$
$211$	−4382.86	−1.42999	−0.714996	+	0.699128i	$0.753572\pi$
$212$	1864.65	0.604079
$213$	−4673.70	−1.50346
$214$	18.1252	0.00578978
$215$	1336.52	0.423953
$216$	2857.07	0.899997
$217$	0	0
$218$	295.303	0.0917453
$219$	−1661.50	−0.512665
$220$	−9424.75	−2.88826
$221$	4186.04	1.27413
$222$	84.2481	0.0254701
$223$	3213.95	0.965120	0.482560	−	0.875863i	$-0.339707\pi$
$223$	3213.95	0.965120	0.482560	+	0.875863i	$0.339707\pi$
$224$	0	0
$225$	17777.5	5.26740
$226$	856.767	0.252174
$227$	−5168.70	−1.51127	−0.755636	−	0.654992i	$-0.772672\pi$
$227$	−5168.70	−1.51127	−0.755636	+	0.654992i	$0.772672\pi$
$228$	11837.3	3.43834
$229$	4683.38	1.35147	0.675734	−	0.737146i	$-0.263827\pi$
$229$	4683.38	1.35147	0.675734	+	0.737146i	$0.263827\pi$
$230$	914.223	0.262096
$231$	0	0
$232$	1295.16	0.366514
$233$	5953.32	1.67388	0.836941	−	0.547292i	$-0.184341\pi$
$233$	5953.32	1.67388	0.836941	+	0.547292i	$0.184341\pi$
$234$	1744.67	0.487405
$235$	−947.592	−0.263039
$236$	−1512.00	−0.417046
$237$	7829.05	2.14579
$238$	0	0
$239$	−2276.62	−0.616161	−0.308081	−	0.951360i	$-0.599687\pi$
$239$	−2276.62	−0.616161	−0.308081	+	0.951360i	$0.599687\pi$
$240$	10979.0	2.95289
$241$	1417.50	0.378875	0.189438	−	0.981893i	$-0.439333\pi$
$241$	1417.50	0.378875	0.189438	+	0.981893i	$0.439333\pi$
$242$	1236.66	0.328493
$243$	−5490.19	−1.44937
$244$	−3692.92	−0.968913
$245$	0	0
$246$	−256.196	−0.0664002
$247$	8426.56	2.17072
$248$	2321.26	0.594356
$249$	1726.48	0.439403
$250$	−1670.36	−0.422571
$251$	4388.24	1.10352	0.551759	−	0.834004i	$-0.313957\pi$
$251$	4388.24	1.10352	0.551759	+	0.834004i	$0.313957\pi$
$252$	0	0
$253$	5186.41	1.28880
$254$	167.438	0.0413622
$255$	15357.7	3.77152
$256$	2735.09	0.667746
$257$	−6338.60	−1.53849	−0.769243	−	0.638956i	$-0.779366\pi$
$257$	−6338.60	−1.53849	−0.769243	+	0.638956i	$0.779366\pi$
$258$	333.238	0.0804128
$259$	0	0
$260$	8121.20	1.93714
$261$	−9828.38	−2.33089
$262$	−721.528	−0.170138
$263$	−1678.89	−0.393631	−0.196816	−	0.980440i	$-0.563060\pi$
$263$	−1678.89	−0.393631	−0.196816	+	0.980440i	$0.563060\pi$
$264$	−4785.12	−1.11555
$265$	4869.90	1.12889
$266$	0	0
$267$	−14989.8	−3.43582
$268$	−888.179	−0.202441
$269$	−2882.84	−0.653419	−0.326710	−	0.945125i	$-0.605940\pi$
$269$	−2882.84	−0.653419	−0.326710	+	0.945125i	$0.605940\pi$
$270$	3664.38	0.825953
$271$	6873.34	1.54069	0.770343	−	0.637630i	$-0.220085\pi$
$271$	6873.34	1.54069	0.770343	+	0.637630i	$0.220085\pi$
$272$	4601.00	1.02565
$273$	0	0
$274$	−505.687	−0.111495
$275$	−17045.3	−3.73771
$276$	−6277.95	−1.36916
$277$	3736.51	0.810487	0.405244	−	0.914209i	$-0.367187\pi$
$277$	3736.51	0.810487	0.405244	+	0.914209i	$0.367187\pi$
$278$	16.1508	0.00348438
$279$	−17615.0	−3.77987
$280$	0	0
$281$	−173.244	−0.0367788	−0.0183894	−	0.999831i	$-0.505854\pi$
$281$	−173.244	−0.0367788	−0.0183894	+	0.999831i	$0.505854\pi$
$282$	−236.266	−0.0498916
$283$	5931.09	1.24582	0.622909	−	0.782294i	$-0.285951\pi$
$283$	5931.09	1.24582	0.622909	+	0.782294i	$0.285951\pi$
$284$	−3799.84	−0.793940
$285$	30915.3	6.42549
$286$	−1672.82	−0.345859
$287$	0	0
$288$	6122.49	1.25268
$289$	1522.98	0.309991
$290$	1661.12	0.336360
$291$	−4216.15	−0.849330
$292$	−1350.84	−0.270726
$293$	4984.32	0.993812	0.496906	−	0.867804i	$-0.334469\pi$
$293$	4984.32	0.993812	0.496906	+	0.867804i	$0.334469\pi$
$294$	0	0
$295$	−3948.89	−0.779367
$296$	139.479	0.0273887
$297$	20788.1	4.06145
$298$	−901.223	−0.175189
$299$	−4469.07	−0.864391
$300$	20632.7	3.97076
$301$	0	0
$302$	−726.224	−0.138376
$303$	2490.76	0.472245
$304$	9261.88	1.74739
$305$	−9644.78	−1.81068
$306$	2682.41	0.501122
$307$	−10471.7	−1.94675	−0.973373	−	0.229228i	$-0.926380\pi$
$307$	−10471.7	−1.94675	−0.973373	+	0.229228i	$0.926380\pi$
$308$	0	0
$309$	1448.94	0.266755
$310$	2977.17	0.545457
$311$	5660.58	1.03210	0.516048	−	0.856559i	$-0.327402\pi$
$311$	5660.58	1.03210	0.516048	+	0.856559i	$0.327402\pi$
$312$	4123.29	0.748189
$313$	4895.30	0.884021	0.442010	−	0.897010i	$-0.354265\pi$
$313$	4895.30	0.884021	0.442010	+	0.897010i	$0.354265\pi$
$314$	−1212.38	−0.217894
$315$	0	0
$316$	6365.23	1.13314
$317$	−9027.16	−1.59942	−0.799709	−	0.600387i	$-0.795013\pi$
$317$	−9027.16	−1.59942	−0.799709	+	0.600387i	$0.795013\pi$
$318$	1214.23	0.214121
$319$	9423.59	1.65398
$320$	8215.57	1.43520
$321$	−325.066	−0.0565216
$322$	0	0
$323$	12955.7	2.23181
$324$	−11999.6	−2.05755
$325$	14687.7	2.50686
$326$	374.585	0.0636391
$327$	−5296.12	−0.895645
$328$	−424.151	−0.0714018
$329$	0	0
$330$	−6137.23	−1.02377
$331$	−7931.77	−1.31713	−0.658564	−	0.752524i	$-0.728836\pi$
$331$	−7931.77	−1.31713	−0.658564	+	0.752524i	$0.728836\pi$
$332$	1403.68	0.232038
$333$	−1058.44	−0.174181
$334$	−1326.51	−0.217316
$335$	−2319.65	−0.378317
$336$	0	0
$337$	8934.74	1.44423	0.722116	−	0.691772i	$-0.243170\pi$
$337$	8934.74	1.44423	0.722116	+	0.691772i	$0.243170\pi$
$338$	278.294	0.0447846
$339$	−15365.7	−2.46180
$340$	12486.2	1.99165
$341$	16889.5	2.68217
$342$	5399.73	0.853755
$343$	0	0
$344$	551.700	0.0864700
$345$	−16396.1	−2.55866
$346$	−1819.36	−0.282686
$347$	−431.991	−0.0668315	−0.0334157	−	0.999442i	$-0.510639\pi$
$347$	−431.991	−0.0668315	−0.0334157	+	0.999442i	$0.510639\pi$
$348$	−11406.9	−1.75711
$349$	−5721.17	−0.877500	−0.438750	−	0.898609i	$-0.644579\pi$
$349$	−5721.17	−0.877500	−0.438750	+	0.898609i	$0.644579\pi$
$350$	0	0
$351$	−17912.9	−2.72399
$352$	−5870.33	−0.888892
$353$	3655.11	0.551110	0.275555	−	0.961285i	$-0.411138\pi$
$353$	3655.11	0.551110	0.275555	+	0.961285i	$0.411138\pi$
$354$	−984.588	−0.147826
$355$	−9924.03	−1.48370
$356$	−12187.1	−1.81437
$357$	0	0
$358$	−128.453	−0.0189636
$359$	−5856.57	−0.860998	−0.430499	−	0.902591i	$-0.641662\pi$
$359$	−5856.57	−0.860998	−0.430499	+	0.902591i	$0.641662\pi$
$360$	10597.1	1.55143
$361$	19221.0	2.80231
$362$	−355.432	−0.0516052
$363$	−22178.8	−3.20685
$364$	0	0
$365$	−3527.99	−0.505927
$366$	−2404.76	−0.343439
$367$	2496.55	0.355092	0.177546	−	0.984112i	$-0.443184\pi$
$367$	2496.55	0.355092	0.177546	+	0.984112i	$0.443184\pi$
$368$	−4912.09	−0.695816
$369$	3218.69	0.454088
$370$	178.891	0.0251353
$371$	0	0
$372$	−20444.2	−2.84941
$373$	−908.874	−0.126165	−0.0630827	−	0.998008i	$-0.520093\pi$
$373$	−908.874	−0.126165	−0.0630827	+	0.998008i	$0.520093\pi$
$374$	−2571.94	−0.355593
$375$	29957.0	4.12527
$376$	−391.155	−0.0536497
$377$	−8120.20	−1.10931
$378$	0	0
$379$	10837.4	1.46882	0.734409	−	0.678707i	$-0.237459\pi$
$379$	10837.4	1.46882	0.734409	+	0.678707i	$0.237459\pi$
$380$	25135.0	3.39315
$381$	−3002.92	−0.403790
$382$	284.192	0.0380642
$383$	−11990.4	−1.59969	−0.799845	−	0.600207i	$-0.795085\pi$
$383$	−11990.4	−1.59969	−0.799845	+	0.600207i	$0.795085\pi$
$384$	9412.23	1.25082
$385$	0	0
$386$	−691.861	−0.0912301
$387$	−4186.61	−0.549916
$388$	−3427.84	−0.448511
$389$	−12006.1	−1.56487	−0.782433	−	0.622734i	$-0.786022\pi$
$389$	−12006.1	−1.56487	−0.782433	+	0.622734i	$0.786022\pi$
$390$	5288.38	0.686635
$391$	−6871.14	−0.888717
$392$	0	0
$393$	12940.2	1.66094
$394$	−660.750	−0.0844875
$395$	16624.0	2.11759
$396$	29522.8	3.74640
$397$	−6462.96	−0.817045	−0.408522	−	0.912748i	$-0.633956\pi$
$397$	−6462.96	−0.817045	−0.408522	+	0.912748i	$0.633956\pi$
$398$	−1030.74	−0.129815
$399$	0	0
$400$	16143.7	2.01797
$401$	−2450.78	−0.305202	−0.152601	−	0.988288i	$-0.548765\pi$
$401$	−2450.78	−0.305202	−0.152601	+	0.988288i	$0.548765\pi$
$402$	−578.366	−0.0717569
$403$	−14553.5	−1.79892
$404$	2025.05	0.249382
$405$	−31339.4	−3.84510
$406$	0	0
$407$	1014.85	0.123598
$408$	6339.50	0.769245
$409$	−3464.26	−0.418819	−0.209409	−	0.977828i	$-0.567154\pi$
$409$	−3464.26	−0.418819	−0.209409	+	0.977828i	$0.567154\pi$
$410$	−544.000	−0.0655275
$411$	9069.24	1.08845
$412$	1178.03	0.140867
$413$	0	0
$414$	−2863.78	−0.339969
$415$	3665.97	0.433628
$416$	5058.40	0.596174
$417$	−289.656	−0.0340156
$418$	−5177.34	−0.605819
$419$	9779.99	1.14030	0.570148	−	0.821542i	$-0.306886\pi$
$419$	9779.99	1.14030	0.570148	+	0.821542i	$0.306886\pi$
$420$	0	0
$421$	6714.02	0.777247	0.388624	−	0.921397i	$-0.372951\pi$
$421$	6714.02	0.777247	0.388624	+	0.921397i	$0.372951\pi$
$422$	−2320.41	−0.267668
$423$	2968.31	0.341192
$424$	2010.24	0.230250
$425$	22582.2	2.57741
$426$	−2474.39	−0.281419
$427$	0	0
$428$	−264.287	−0.0298477
$429$	30001.1	3.37638
$430$	707.591	0.0793560
$431$	7504.23	0.838668	0.419334	−	0.907832i	$-0.362264\pi$
$431$	7504.23	0.838668	0.419334	+	0.907832i	$0.362264\pi$
$432$	−19688.6	−2.19275
$433$	−541.083	−0.0600526	−0.0300263	−	0.999549i	$-0.509559\pi$
$433$	−541.083	−0.0600526	−0.0300263	+	0.999549i	$0.509559\pi$
$434$	0	0
$435$	−29791.4	−3.28365
$436$	−4305.88	−0.472969
$437$	−13831.7	−1.51410
$438$	−879.644	−0.0959613
$439$	−3439.07	−0.373891	−0.186945	−	0.982370i	$-0.559859\pi$
$439$	−3439.07	−0.373891	−0.186945	+	0.982370i	$0.559859\pi$
$440$	−10160.6	−1.10088
$441$	0	0
$442$	2216.21	0.238494
$443$	−1053.47	−0.112984	−0.0564921	−	0.998403i	$-0.517992\pi$
$443$	−1053.47	−0.112984	−0.0564921	+	0.998403i	$0.517992\pi$
$444$	−1228.44	−0.131304
$445$	−31829.1	−3.39066
$446$	1701.55	0.180652
$447$	16163.0	1.71025
$448$	0	0
$449$	13533.0	1.42241	0.711206	−	0.702984i	$-0.248149\pi$
$449$	13533.0	1.42241	0.711206	+	0.702984i	$0.248149\pi$
$450$	9411.89	0.985958
$451$	−3086.13	−0.322218
$452$	−12492.7	−1.30002
$453$	13024.5	1.35087
$454$	−2736.45	−0.282881
$455$	0	0
$456$	12761.5	1.31055
$457$	−15839.8	−1.62135	−0.810673	−	0.585499i	$-0.800899\pi$
$457$	−15839.8	−1.62135	−0.810673	+	0.585499i	$0.800899\pi$
$458$	2479.51	0.252969
$459$	−27540.9	−2.80065
$460$	−13330.5	−1.35117
$461$	−5480.20	−0.553663	−0.276831	−	0.960919i	$-0.589284\pi$
$461$	−5480.20	−0.553663	−0.276831	+	0.960919i	$0.589284\pi$
$462$	0	0
$463$	−10325.4	−1.03642	−0.518209	−	0.855254i	$-0.673401\pi$
$463$	−10325.4	−1.03642	−0.518209	+	0.855254i	$0.673401\pi$
$464$	−8925.15	−0.892974
$465$	−53393.9	−5.32491
$466$	3151.85	0.313319
$467$	−10156.7	−1.00642	−0.503210	−	0.864164i	$-0.667848\pi$
$467$	−10156.7	−1.00642	−0.503210	+	0.864164i	$0.667848\pi$
$468$	−25439.4	−2.51269
$469$	0	0
$470$	−501.682	−0.0492359
$471$	21743.5	2.12715
$472$	−1630.06	−0.158961
$473$	4014.18	0.390216
$474$	4144.92	0.401651
$475$	45458.3	4.39109
$476$	0	0
$477$	−15254.8	−1.46430
$478$	−1205.31	−0.115334
$479$	−15994.4	−1.52569	−0.762844	−	0.646583i	$-0.776198\pi$
$479$	−15994.4	−1.52569	−0.762844	+	0.646583i	$0.776198\pi$
$480$	18558.2	1.76472
$481$	−874.485	−0.0828963
$482$	750.463	0.0709183
$483$	0	0
$484$	−18032.0	−1.69346
$485$	−8952.48	−0.838167
$486$	−2906.66	−0.271294
$487$	10191.2	0.948272	0.474136	−	0.880451i	$-0.342760\pi$
$487$	10191.2	0.948272	0.474136	+	0.880451i	$0.342760\pi$
$488$	−3981.26	−0.369309
$489$	−6717.99	−0.621263
$490$	0	0
$491$	−10624.2	−0.976500	−0.488250	−	0.872704i	$-0.662365\pi$
$491$	−10624.2	−0.976500	−0.488250	+	0.872704i	$0.662365\pi$
$492$	3735.64	0.342309
$493$	−12484.7	−1.14053
$494$	4461.26	0.406319
$495$	77104.6	7.00120
$496$	−15996.2	−1.44809
$497$	0	0
$498$	914.048	0.0822479
$499$	4167.04	0.373832	0.186916	−	0.982376i	$-0.440151\pi$
$499$	4167.04	0.373832	0.186916	+	0.982376i	$0.440151\pi$
$500$	24355.9	2.17846
$501$	23790.3	2.12150
$502$	2323.26	0.206558
$503$	10168.2	0.901346	0.450673	−	0.892689i	$-0.351184\pi$
$503$	10168.2	0.901346	0.450673	+	0.892689i	$0.351184\pi$
$504$	0	0
$505$	5288.83	0.466039
$506$	2745.83	0.241239
$507$	−4991.06	−0.437200
$508$	−2441.45	−0.213232
$509$	22319.1	1.94357	0.971785	−	0.235867i	$-0.0757929\pi$
$509$	22319.1	1.94357	0.971785	+	0.235867i	$0.0757929\pi$
$510$	8130.82	0.705958
$511$	0	0
$512$	9378.28	0.809503
$513$	−55440.1	−4.77143
$514$	−3355.83	−0.287976
$515$	3076.65	0.263249
$516$	−4859.02	−0.414547
$517$	−2846.06	−0.242107
$518$	0	0
$519$	32629.3	2.75967
$520$	8755.30	0.738356
$521$	−9119.51	−0.766858	−0.383429	−	0.923570i	$-0.625257\pi$
$521$	−9119.51	−0.766858	−0.383429	+	0.923570i	$0.625257\pi$
$522$	−5203.42	−0.436298
$523$	−14800.1	−1.23741	−0.618703	−	0.785625i	$-0.712342\pi$
$523$	−14800.1	−1.23741	−0.618703	+	0.785625i	$0.712342\pi$
$524$	10520.8	0.877102
$525$	0	0
$526$	−888.854	−0.0736804
$527$	−22375.9	−1.84954
$528$	32975.1	2.71791
$529$	−4831.28	−0.397081
$530$	2578.26	0.211307
$531$	12369.8	1.01093
$532$	0	0
$533$	2659.28	0.216109
$534$	−7936.05	−0.643121
$535$	−690.239	−0.0557787
$536$	−957.527	−0.0771621
$537$	2303.74	0.185128
$538$	−1526.26	−0.122308
$539$	0	0
$540$	−53431.1	−4.25798
$541$	4325.45	0.343744	0.171872	−	0.985119i	$-0.445018\pi$
$541$	4325.45	0.343744	0.171872	+	0.985119i	$0.445018\pi$
$542$	3638.94	0.288387
$543$	6374.49	0.503785
$544$	7777.23	0.612952
$545$	−11245.7	−0.883874
$546$	0	0
$547$	22479.9	1.75717	0.878585	−	0.477586i	$-0.158488\pi$
$547$	22479.9	1.75717	0.878585	+	0.477586i	$0.158488\pi$
$548$	7373.53	0.574784
$549$	30212.0	2.34867
$550$	−9024.26	−0.699629
$551$	−25131.9	−1.94311
$552$	−6768.13	−0.521868
$553$	0	0
$554$	1978.21	0.151708
$555$	−3208.31	−0.245379
$556$	−235.498	−0.0179628
$557$	8538.75	0.649548	0.324774	−	0.945792i	$-0.394712\pi$
$557$	8538.75	0.649548	0.324774	+	0.945792i	$0.394712\pi$
$558$	−9325.89	−0.707521
$559$	−3458.98	−0.261716
$560$	0	0
$561$	46126.4	3.47140
$562$	−91.7201	−0.00688430
$563$	2793.46	0.209113	0.104556	−	0.994519i	$-0.466658\pi$
$563$	2793.46	0.209113	0.104556	+	0.994519i	$0.466658\pi$
$564$	3445.04	0.257203
$565$	−32627.2	−2.42944
$566$	3140.09	0.233194
$567$	0	0
$568$	−4096.53	−0.302617
$569$	−5529.64	−0.407407	−0.203704	−	0.979033i	$-0.565298\pi$
$569$	−5529.64	−0.407407	−0.203704	+	0.979033i	$0.565298\pi$
$570$	16367.4	1.20273
$571$	−3185.91	−0.233496	−0.116748	−	0.993162i	$-0.537247\pi$
$571$	−3185.91	−0.233496	−0.116748	+	0.993162i	$0.537247\pi$
$572$	24391.7	1.78299
$573$	−5096.84	−0.371594
$574$	0	0
$575$	−24109.1	−1.74855
$576$	−25735.1	−1.86162
$577$	13779.7	0.994203	0.497102	−	0.867692i	$-0.334398\pi$
$577$	13779.7	0.994203	0.497102	+	0.867692i	$0.334398\pi$
$578$	806.311	0.0580244
$579$	12408.2	0.890615
$580$	−24221.2	−1.73402
$581$	0	0
$582$	−2232.15	−0.158979
$583$	14626.6	1.03906
$584$	−1456.32	−0.103190
$585$	−66440.1	−4.69566
$586$	2638.84	0.186023
$587$	21914.4	1.54089	0.770447	−	0.637504i	$-0.220033\pi$
$587$	21914.4	1.54089	0.770447	+	0.637504i	$0.220033\pi$
$588$	0	0
$589$	−45042.9	−3.15104
$590$	−2090.65	−0.145883
$591$	11850.2	0.824792
$592$	−961.173	−0.0667297
$593$	17488.9	1.21110	0.605552	−	0.795806i	$-0.292952\pi$
$593$	17488.9	1.21110	0.605552	+	0.795806i	$0.292952\pi$
$594$	11005.8	0.760227
$595$	0	0
$596$	13140.9	0.903143
$597$	18485.8	1.26729
$598$	−2366.05	−0.161798
$599$	−24663.5	−1.68235	−0.841173	−	0.540766i	$-0.818134\pi$
$599$	−24663.5	−1.68235	−0.841173	+	0.540766i	$0.818134\pi$
$600$	22243.7	1.51349
$601$	19843.9	1.34684	0.673421	−	0.739260i	$-0.264824\pi$
$601$	19843.9	1.34684	0.673421	+	0.739260i	$0.264824\pi$
$602$	0	0
$603$	7266.25	0.490721
$604$	10589.2	0.713360
$605$	−47094.0	−3.16470
$606$	1318.68	0.0883955
$607$	9928.19	0.663876	0.331938	−	0.943301i	$-0.392297\pi$
$607$	9928.19	0.663876	0.331938	+	0.943301i	$0.392297\pi$
$608$	15655.7	1.04428
$609$	0	0
$610$	−5106.22	−0.338926
$611$	2452.41	0.162380
$612$	−39112.8	−2.58340
$613$	−28366.5	−1.86903	−0.934513	−	0.355929i	$-0.884165\pi$
$613$	−28366.5	−1.86903	−0.934513	+	0.355929i	$0.884165\pi$
$614$	−5544.01	−0.364394
$615$	9756.37	0.639699
$616$	0	0
$617$	−2910.34	−0.189896	−0.0949479	−	0.995482i	$-0.530268\pi$
$617$	−2910.34	−0.189896	−0.0949479	+	0.995482i	$0.530268\pi$
$618$	767.110	0.0499315
$619$	26300.9	1.70779	0.853897	−	0.520442i	$-0.174233\pi$
$619$	26300.9	1.70779	0.853897	+	0.520442i	$0.174233\pi$
$620$	−43410.7	−2.81196
$621$	29403.0	1.90000
$622$	2996.87	0.193189
$623$	0	0
$624$	−28414.3	−1.82289
$625$	28424.2	1.81915
$626$	2591.71	0.165472
$627$	92853.0	5.91418
$628$	17678.0	1.12330
$629$	−1344.51	−0.0852292
$630$	0	0
$631$	8910.75	0.562173	0.281087	−	0.959682i	$-0.409305\pi$
$631$	8910.75	0.562173	0.281087	+	0.959682i	$0.409305\pi$
$632$	6862.22	0.431906
$633$	41615.4	2.61305
$634$	−4779.23	−0.299381
$635$	−6376.33	−0.398483
$636$	−17704.9	−1.10384
$637$	0	0
$638$	4989.12	0.309594
$639$	31086.8	1.92453
$640$	19985.7	1.23438
$641$	2194.51	0.135223	0.0676116	−	0.997712i	$-0.478462\pi$
$641$	2194.51	0.135223	0.0676116	+	0.997712i	$0.478462\pi$
$642$	−172.099	−0.0105798
$643$	−20410.3	−1.25179	−0.625896	−	0.779907i	$-0.715266\pi$
$643$	−20410.3	−1.25179	−0.625896	+	0.779907i	$0.715266\pi$
$644$	0	0
$645$	−12690.3	−0.774697
$646$	6859.13	0.417753
$647$	8073.60	0.490581	0.245291	−	0.969450i	$-0.421117\pi$
$647$	8073.60	0.490581	0.245291	+	0.969450i	$0.421117\pi$
$648$	−12936.6	−0.784253
$649$	−11860.3	−0.717348
$650$	7776.10	0.469237
$651$	0	0
$652$	−5461.90	−0.328074
$653$	−12020.3	−0.720351	−0.360176	−	0.932885i	$-0.617283\pi$
$653$	−12020.3	−0.720351	−0.360176	+	0.932885i	$0.617283\pi$
$654$	−2803.91	−0.167648
$655$	27477.0	1.63911
$656$	2922.90	0.173963
$657$	11051.3	0.656246
$658$	0	0
$659$	10626.5	0.628148	0.314074	−	0.949398i	$-0.398306\pi$
$659$	10626.5	0.628148	0.314074	+	0.949398i	$0.398306\pi$
$660$	89488.2	5.27777
$661$	25190.8	1.48231	0.741157	−	0.671332i	$-0.234278\pi$
$661$	25190.8	1.48231	0.741157	+	0.671332i	$0.234278\pi$
$662$	−4199.30	−0.246542
$663$	−39746.5	−2.32825
$664$	1513.27	0.0884434
$665$	0	0
$666$	−560.370	−0.0326034
$667$	13328.8	0.773755
$668$	19342.1	1.12031
$669$	−30516.5	−1.76358
$670$	−1228.09	−0.0708138
$671$	−28967.7	−1.66660
$672$	0	0
$673$	−4778.89	−0.273719	−0.136859	−	0.990590i	$-0.543701\pi$
$673$	−4778.89	−0.273719	−0.136859	+	0.990590i	$0.543701\pi$
$674$	4730.30	0.270333
$675$	−96633.8	−5.51028
$676$	−4057.86	−0.230875
$677$	−26428.7	−1.50035	−0.750174	−	0.661240i	$-0.770030\pi$
$677$	−26428.7	−1.50035	−0.750174	+	0.661240i	$0.770030\pi$
$678$	−8135.03	−0.460802
$679$	0	0
$680$	13461.2	0.759135
$681$	49076.9	2.76157
$682$	8941.80	0.502052
$683$	−10706.7	−0.599827	−0.299914	−	0.953966i	$-0.596958\pi$
$683$	−10706.7	−0.599827	−0.299914	+	0.953966i	$0.596958\pi$
$684$	−78734.7	−4.40131
$685$	19257.4	1.07414
$686$	0	0
$687$	−44468.8	−2.46956
$688$	−3801.86	−0.210675
$689$	−12603.5	−0.696889
$690$	−8680.57	−0.478933
$691$	−2284.66	−0.125778	−0.0628889	−	0.998021i	$-0.520031\pi$
$691$	−2284.66	−0.125778	−0.0628889	+	0.998021i	$0.520031\pi$
$692$	26528.5	1.45732
$693$	0	0
$694$	−228.709	−0.0125096
$695$	−615.049	−0.0335685
$696$	−12297.5	−0.669737
$697$	4088.61	0.222191
$698$	−3028.95	−0.164251
$699$	−56526.9	−3.05872
$700$	0	0
$701$	−16612.7	−0.895084	−0.447542	−	0.894263i	$-0.647701\pi$
$701$	−16612.7	−0.895084	−0.447542	+	0.894263i	$0.647701\pi$
$702$	−9483.60	−0.509879
$703$	−2706.52	−0.145204
$704$	24675.2	1.32099
$705$	8997.41	0.480655
$706$	1935.12	0.103157
$707$	0	0
$708$	14356.5	0.762076
$709$	18332.1	0.971053	0.485527	−	0.874222i	$-0.338628\pi$
$709$	18332.1	0.971053	0.485527	+	0.874222i	$0.338628\pi$
$710$	−5254.06	−0.277720
$711$	−52074.4	−2.74675
$712$	−13138.7	−0.691565
$713$	23888.8	1.25476
$714$	0	0
$715$	63703.8	3.33201
$716$	1873.00	0.0977617
$717$	21616.6	1.12592
$718$	−3100.64	−0.161163
$719$	10757.3	0.557969	0.278985	−	0.960296i	$-0.410002\pi$
$719$	10757.3	0.557969	0.278985	+	0.960296i	$0.410002\pi$
$720$	−73026.3	−3.77990
$721$	0	0
$722$	10176.2	0.524540
$723$	−13459.2	−0.692326
$724$	5182.63	0.266037
$725$	−43805.6	−2.24400
$726$	−11742.1	−0.600261
$727$	12627.4	0.644185	0.322093	−	0.946708i	$-0.395614\pi$
$727$	12627.4	0.644185	0.322093	+	0.946708i	$0.395614\pi$
$728$	0	0
$729$	10160.3	0.516196
$730$	−1867.82	−0.0947001
$731$	−5318.13	−0.269081
$732$	35064.3	1.77051
$733$	20447.2	1.03034	0.515168	−	0.857090i	$-0.327730\pi$
$733$	20447.2	1.03034	0.515168	+	0.857090i	$0.327730\pi$
$734$	1321.74	0.0664666
$735$	0	0
$736$	−8303.07	−0.415836
$737$	−6966.99	−0.348212
$738$	1704.07	0.0849967
$739$	−18353.5	−0.913592	−0.456796	−	0.889571i	$-0.651003\pi$
$739$	−18353.5	−0.913592	−0.456796	+	0.889571i	$0.651003\pi$
$740$	−2608.44	−0.129579
$741$	−80010.3	−3.96660
$742$	0	0
$743$	14588.9	0.720341	0.360171	−	0.932886i	$-0.382719\pi$
$743$	14588.9	0.720341	0.360171	+	0.932886i	$0.382719\pi$
$744$	−22040.4	−1.08608
$745$	34320.1	1.68777
$746$	−481.183	−0.0236158
$747$	−11483.6	−0.562466
$748$	37502.0	1.83316
$749$	0	0
$750$	15860.1	0.772172
$751$	−13126.9	−0.637824	−0.318912	−	0.947784i	$-0.603317\pi$
$751$	−13126.9	−0.637824	−0.318912	+	0.947784i	$0.603317\pi$
$752$	2695.52	0.130712
$753$	−41666.4	−2.01648
$754$	−4299.06	−0.207643
$755$	27655.8	1.33311
$756$	0	0
$757$	−37077.4	−1.78019	−0.890093	−	0.455779i	$-0.849361\pi$
$757$	−37077.4	−1.78019	−0.890093	+	0.455779i	$0.849361\pi$
$758$	5737.65	0.274935
$759$	−49245.1	−2.35505
$760$	27097.5	1.29333
$761$	−15015.8	−0.715271	−0.357635	−	0.933861i	$-0.616417\pi$
$761$	−15015.8	−0.715271	−0.357635	+	0.933861i	$0.616417\pi$
$762$	−1589.83	−0.0755820
$763$	0	0
$764$	−4143.87	−0.196230
$765$	−102151.	−4.82781
$766$	−6348.06	−0.299432
$767$	10219.9	0.481121
$768$	−25969.7	−1.22018
$769$	−11385.8	−0.533918	−0.266959	−	0.963708i	$-0.586019\pi$
$769$	−11385.8	−0.533918	−0.266959	+	0.963708i	$0.586019\pi$
$770$	0	0
$771$	60185.1	2.81130
$772$	10088.2	0.470313
$773$	−9020.85	−0.419738	−0.209869	−	0.977730i	$-0.567304\pi$
$773$	−9020.85	−0.419738	−0.209869	+	0.977730i	$0.567304\pi$
$774$	−2216.51	−0.102934
$775$	−78511.1	−3.63897
$776$	−3695.48	−0.170954
$777$	0	0
$778$	−6356.37	−0.292914
$779$	8230.44	0.378544
$780$	−77111.0	−3.53976
$781$	−29806.4	−1.36563
$782$	−3637.78	−0.166351
$783$	53424.5	2.43836
$784$	0	0
$785$	46169.6	2.09919
$786$	6850.93	0.310896
$787$	−24152.8	−1.09397	−0.546985	−	0.837143i	$-0.684224\pi$
$787$	−24152.8	−1.09397	−0.546985	+	0.837143i	$0.684224\pi$
$788$	9634.53	0.435553
$789$	15941.1	0.719290
$790$	8801.24	0.396372
$791$	0	0
$792$	31827.9	1.42797
$793$	24961.1	1.11778
$794$	−3421.67	−0.152935
$795$	−46239.8	−2.06284
$796$	15029.4	0.669227
$797$	17364.7	0.771755	0.385877	−	0.922550i	$-0.373899\pi$
$797$	17364.7	0.771755	0.385877	+	0.922550i	$0.373899\pi$
$798$	0	0
$799$	3770.56	0.166950
$800$	27288.3	1.20598
$801$	99703.9	4.39808
$802$	−1297.51	−0.0571281
$803$	−10596.2	−0.465668
$804$	8433.28	0.369924
$805$	0	0
$806$	−7705.05	−0.336723
$807$	27372.6	1.19401
$808$	2183.17	0.0950540
$809$	−15678.2	−0.681356	−0.340678	−	0.940180i	$-0.610657\pi$
$809$	−15678.2	−0.681356	−0.340678	+	0.940180i	$0.610657\pi$
$810$	−16592.0	−0.719731
$811$	−9696.81	−0.419854	−0.209927	−	0.977717i	$-0.567323\pi$
$811$	−9696.81	−0.419854	−0.209927	+	0.977717i	$0.567323\pi$
$812$	0	0
$813$	−65262.5	−2.81532
$814$	537.291	0.0231352
$815$	−14264.8	−0.613098
$816$	−43686.6	−1.87419
$817$	−10705.5	−0.458430
$818$	−1834.08	−0.0783949
$819$	0	0
$820$	7932.19	0.337810
$821$	−30080.2	−1.27869	−0.639346	−	0.768919i	$-0.720795\pi$
$821$	−30080.2	−1.27869	−0.639346	+	0.768919i	$0.720795\pi$
$822$	4801.51	0.203737
$823$	−6381.87	−0.270301	−0.135151	−	0.990825i	$-0.543152\pi$
$823$	−6381.87	−0.270301	−0.135151	+	0.990825i	$0.543152\pi$
$824$	1270.01	0.0536927
$825$	161846.	6.82998
$826$	0	0
$827$	20498.6	0.861920	0.430960	−	0.902371i	$-0.358175\pi$
$827$	20498.6	0.861920	0.430960	+	0.902371i	$0.358175\pi$
$828$	41757.4	1.75262
$829$	−27716.0	−1.16118	−0.580588	−	0.814198i	$-0.697177\pi$
$829$	−27716.0	−1.16118	−0.580588	+	0.814198i	$0.697177\pi$
$830$	1940.87	0.0811670
$831$	−35478.2	−1.48102
$832$	−21262.3	−0.885983
$833$	0	0
$834$	−153.352	−0.00636708
$835$	50515.8	2.09362
$836$	75491.9	3.12314
$837$	95750.8	3.95416
$838$	5177.80	0.213442
$839$	−47411.1	−1.95091	−0.975456	−	0.220196i	$-0.929330\pi$
$839$	−47411.1	−1.95091	−0.975456	+	0.220196i	$0.929330\pi$
$840$	0	0
$841$	−170.816	−0.00700383
$842$	3554.59	0.145486
$843$	1644.95	0.0672066
$844$	33834.4	1.37989
$845$	−10597.9	−0.431454
$846$	1571.51	0.0638646
$847$	0	0
$848$	−13852.9	−0.560980
$849$	−56315.8	−2.27651
$850$	11955.7	0.482442
$851$	1435.42	0.0578207
$852$	36079.6	1.45078
$853$	−682.718	−0.0274042	−0.0137021	−	0.999906i	$-0.504362\pi$
$853$	−682.718	−0.0274042	−0.0137021	+	0.999906i	$0.504362\pi$
$854$	0	0
$855$	−205631.	−8.22507
$856$	−284.923	−0.0113767
$857$	5912.38	0.235663	0.117831	−	0.993034i	$-0.462406\pi$
$857$	5912.38	0.235663	0.117831	+	0.993034i	$0.462406\pi$
$858$	15883.4	0.631995
$859$	−29052.7	−1.15398	−0.576988	−	0.816753i	$-0.695772\pi$
$859$	−29052.7	−1.15398	−0.576988	+	0.816753i	$0.695772\pi$
$860$	−10317.5	−0.409099
$861$	0	0
$862$	3972.95	0.156983
$863$	5724.27	0.225790	0.112895	−	0.993607i	$-0.463988\pi$
$863$	5724.27	0.225790	0.112895	+	0.993607i	$0.463988\pi$
$864$	−33280.3	−1.31044
$865$	69284.4	2.72340
$866$	−286.464	−0.0112407
$867$	−14460.8	−0.566452
$868$	0	0
$869$	49929.7	1.94908
$870$	−15772.4	−0.614637
$871$	6003.37	0.233544
$872$	−4642.08	−0.180276
$873$	28043.4	1.08720
$874$	−7322.89	−0.283410
$875$	0	0
$876$	12826.3	0.494703
$877$	−26166.8	−1.00751	−0.503757	−	0.863845i	$-0.668049\pi$
$877$	−26166.8	−1.00751	−0.503757	+	0.863845i	$0.668049\pi$
$878$	−1820.74	−0.0699853
$879$	−47326.2	−1.81601
$880$	70018.7	2.68219
$881$	−17773.7	−0.679697	−0.339848	−	0.940480i	$-0.610376\pi$
$881$	−17773.7	−0.679697	−0.339848	+	0.940480i	$0.610376\pi$
$882$	0	0
$883$	29517.4	1.12496	0.562481	−	0.826810i	$-0.309847\pi$
$883$	29517.4	1.12496	0.562481	+	0.826810i	$0.309847\pi$
$884$	−32315.0	−1.22949
$885$	37494.8	1.42415
$886$	−557.738	−0.0211485
$887$	11426.1	0.432528	0.216264	−	0.976335i	$-0.430613\pi$
$887$	11426.1	0.432528	0.216264	+	0.976335i	$0.430613\pi$
$888$	−1324.35	−0.0500478
$889$	0	0
$890$	−16851.2	−0.634668
$891$	−94126.7	−3.53913
$892$	−24810.7	−0.931305
$893$	7590.18	0.284430
$894$	8557.14	0.320127
$895$	4891.71	0.182695
$896$	0	0
$897$	42433.9	1.57952
$898$	7164.77	0.266249
$899$	43405.3	1.61029
$900$	−137237.	−5.08285
$901$	−19377.8	−0.716501
$902$	−1633.88	−0.0603131
$903$	0	0
$904$	−13468.1	−0.495513
$905$	13535.5	0.497164
$906$	6895.51	0.252857
$907$	14877.2	0.544643	0.272321	−	0.962206i	$-0.412209\pi$
$907$	14877.2	0.544643	0.272321	+	0.962206i	$0.412209\pi$
$908$	39900.8	1.45832
$909$	−16567.1	−0.604506
$910$	0	0
$911$	24185.5	0.879584	0.439792	−	0.898100i	$-0.355052\pi$
$911$	24185.5	0.879584	0.439792	+	0.898100i	$0.355052\pi$
$912$	−87941.7	−3.19303
$913$	11010.6	0.399122
$914$	−8386.05	−0.303486
$915$	91577.4	3.30869
$916$	−36154.3	−1.30412
$917$	0	0
$918$	−14580.9	−0.524229
$919$	11330.9	0.406718	0.203359	−	0.979104i	$-0.434814\pi$
$919$	11330.9	0.406718	0.203359	+	0.979104i	$0.434814\pi$
$920$	−14371.3	−0.515009
$921$	99428.9	3.55732
$922$	−2901.37	−0.103635
$923$	25683.9	0.915920
$924$	0	0
$925$	−4717.54	−0.167688
$926$	−5466.55	−0.193998
$927$	−9637.52	−0.341465
$928$	−15086.5	−0.533662
$929$	26454.7	0.934285	0.467143	−	0.884182i	$-0.345283\pi$
$929$	26454.7	0.934285	0.467143	+	0.884182i	$0.345283\pi$
$930$	−28268.3	−0.996723
$931$	0	0
$932$	−45957.9	−1.61524
$933$	−53747.3	−1.88597
$934$	−5377.27	−0.188383
$935$	97943.7	3.42578
$936$	−27425.7	−0.957733
$937$	20872.9	0.727735	0.363867	−	0.931451i	$-0.381456\pi$
$937$	20872.9	0.727735	0.363867	+	0.931451i	$0.381456\pi$
$938$	0	0
$939$	−46481.0	−1.61539
$940$	7315.13	0.253823
$941$	−36433.7	−1.26217	−0.631086	−	0.775713i	$-0.717390\pi$
$941$	−36433.7	−1.26217	−0.631086	+	0.775713i	$0.717390\pi$
$942$	11511.6	0.398162
$943$	−4365.06	−0.150738
$944$	11233.0	0.387292
$945$	0	0
$946$	2125.22	0.0730412
$947$	13099.1	0.449486	0.224743	−	0.974418i	$-0.427846\pi$
$947$	13099.1	0.449486	0.224743	+	0.974418i	$0.427846\pi$
$948$	−60438.0	−2.07061
$949$	9130.61	0.312321
$950$	24066.9	0.821930
$951$	85713.1	2.92265
$952$	0	0
$953$	−11694.6	−0.397507	−0.198754	−	0.980049i	$-0.563689\pi$
$953$	−11694.6	−0.397507	−0.198754	+	0.980049i	$0.563689\pi$
$954$	−8076.34	−0.274089
$955$	−10822.5	−0.366711
$956$	17574.9	0.594573
$957$	−89477.2	−3.02235
$958$	−8467.91	−0.285580
$959$	0	0
$960$	−78007.1	−2.62257
$961$	48002.8	1.61132
$962$	−462.977	−0.0155166
$963$	2162.15	0.0723515
$964$	−10942.7	−0.365601
$965$	26347.3	0.878910
$966$	0	0
$967$	39070.0	1.29928	0.649641	−	0.760241i	$-0.274919\pi$
$967$	39070.0	1.29928	0.649641	+	0.760241i	$0.274919\pi$
$968$	−19439.9	−0.645477
$969$	−123015.	−4.07823
$970$	−4739.70	−0.156889
$971$	2185.66	0.0722359	0.0361179	−	0.999348i	$-0.488501\pi$
$971$	2185.66	0.0722359	0.0361179	+	0.999348i	$0.488501\pi$
$972$	42382.7	1.39859
$973$	0	0
$974$	5395.53	0.177499
$975$	−139460.	−4.58083
$976$	27435.5	0.899785
$977$	31137.0	1.01961	0.509806	−	0.860290i	$-0.329717\pi$
$977$	31137.0	1.01961	0.509806	+	0.860290i	$0.329717\pi$
$978$	−3556.69	−0.116289
$979$	−95597.6	−3.12085
$980$	0	0
$981$	35226.7	1.14649
$982$	−5624.73	−0.182782
$983$	−11132.3	−0.361204	−0.180602	−	0.983556i	$-0.557805\pi$
$983$	−11132.3	−0.361204	−0.180602	+	0.983556i	$0.557805\pi$
$984$	4027.32	0.130474
$985$	25162.5	0.813952
$986$	−6609.76	−0.213486
$987$	0	0
$988$	−65050.5	−2.09467
$989$	5677.71	0.182549
$990$	40821.3	1.31049
$991$	34247.6	1.09779	0.548895	−	0.835891i	$-0.315049\pi$
$991$	34247.6	1.09779	0.548895	+	0.835891i	$0.315049\pi$
$992$	−27038.9	−0.865410
$993$	75312.4	2.40681
$994$	0	0
$995$	39252.4	1.25064
$996$	−13327.9	−0.424008
$997$	29256.9	0.929364	0.464682	−	0.885478i	$-0.346169\pi$
$997$	29256.9	0.929364	0.464682	+	0.885478i	$0.346169\pi$
$998$	2206.15	0.0699744
$999$	5753.43	0.182213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.h.1.19	yes	35
7.6	odd	2		2303.4.a.g.1.19	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.g.1.19	✓	35	7.6	odd	2
2303.4.a.h.1.19	yes	35	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)

\(f(q)\)	\(=\)	\(q+0.529428 q^{2} -9.49502 q^{3} -7.71971 q^{4} -20.1615 q^{5} -5.02693 q^{6} -8.32246 q^{8} +63.1555 q^{9} +O(q^{10})\)	\(q+0.529428 q^{2} -9.49502 q^{3} -7.71971 q^{4} -20.1615 q^{5} -5.02693 q^{6} -8.32246 q^{8} +63.1555 q^{9} -10.6741 q^{10} -60.5544 q^{11} +73.2988 q^{12} +52.1790 q^{13} +191.434 q^{15} +57.3515 q^{16} +80.2246 q^{17} +33.4363 q^{18} +161.493 q^{19} +155.641 q^{20} -32.0592 q^{22} -85.6488 q^{23} +79.0219 q^{24} +281.487 q^{25} +27.6250 q^{26} -343.297 q^{27} -155.622 q^{29} +101.351 q^{30} -278.915 q^{31} +96.9432 q^{32} +574.965 q^{33} +42.4732 q^{34} -487.542 q^{36} -16.7593 q^{37} +85.4991 q^{38} -495.441 q^{39} +167.793 q^{40} +50.9646 q^{41} -66.2906 q^{43} +467.462 q^{44} -1273.31 q^{45} -45.3449 q^{46} +47.0000 q^{47} -544.554 q^{48} +149.027 q^{50} -761.734 q^{51} -402.807 q^{52} -241.544 q^{53} -181.751 q^{54} +1220.87 q^{55} -1533.38 q^{57} -82.3906 q^{58} +195.863 q^{59} -1477.82 q^{60} +478.375 q^{61} -147.666 q^{62} -407.488 q^{64} -1052.01 q^{65} +304.403 q^{66} +115.053 q^{67} -619.310 q^{68} +813.237 q^{69} +492.226 q^{71} -525.609 q^{72} +174.986 q^{73} -8.87286 q^{74} -2672.73 q^{75} -1246.68 q^{76} -262.300 q^{78} -824.543 q^{79} -1156.29 q^{80} +1554.42 q^{81} +26.9821 q^{82} -181.830 q^{83} -1617.45 q^{85} -35.0961 q^{86} +1477.63 q^{87} +503.961 q^{88} +1578.71 q^{89} -674.127 q^{90} +661.184 q^{92} +2648.31 q^{93} +24.8831 q^{94} -3255.95 q^{95} -920.478 q^{96} +444.038 q^{97} -3824.34 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9}+O(q^{10}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9} + 100 q^{10} + 40 q^{11} + 144 q^{12} + 328 q^{13} + 20 q^{15} + 643 q^{16} + 152 q^{17} + 51 q^{18} + 266 q^{19} + 1064 q^{20} - 168 q^{22} - 134 q^{23} + 288 q^{24} + 1137 q^{25} + 156 q^{26} + 672 q^{27} + 248 q^{29} - 216 q^{30} + 276 q^{31} + 347 q^{32} + 1056 q^{33} + 908 q^{34} + 909 q^{36} - 418 q^{37} + 164 q^{38} - 548 q^{39} + 1200 q^{40} + 918 q^{41} + 608 q^{43} + 1288 q^{44} + 876 q^{45} - 972 q^{46} + 1645 q^{47} + 1252 q^{48} - 367 q^{50} - 464 q^{51} + 3798 q^{52} - 218 q^{53} - 744 q^{54} + 1004 q^{55} - 436 q^{57} - 1270 q^{58} + 3760 q^{59} - 424 q^{60} + 956 q^{61} + 84 q^{62} + 2189 q^{64} - 596 q^{65} + 5500 q^{66} - 476 q^{67} + 256 q^{68} + 444 q^{69} + 852 q^{71} - 883 q^{72} + 6250 q^{73} + 1366 q^{74} - 2568 q^{75} + 1742 q^{76} - 1460 q^{78} + 632 q^{79} + 10124 q^{80} + 1267 q^{81} + 792 q^{82} + 796 q^{83} - 1228 q^{85} - 2864 q^{86} + 8360 q^{87} - 50 q^{88} + 908 q^{89} - 1858 q^{90} + 1696 q^{92} + 644 q^{93} + 235 q^{94} + 1320 q^{95} + 2688 q^{96} + 6184 q^{97} - 1812 q^{99}+O(q^{100}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9 + 100 * q^10 + 40 * q^11 + 144 * q^12 + 328 * q^13 + 20 * q^15 + 643 * q^16 + 152 * q^17 + 51 * q^18 + 266 * q^19 + 1064 * q^20 - 168 * q^22 - 134 * q^23 + 288 * q^24 + 1137 * q^25 + 156 * q^26 + 672 * q^27 + 248 * q^29 - 216 * q^30 + 276 * q^31 + 347 * q^32 + 1056 * q^33 + 908 * q^34 + 909 * q^36 - 418 * q^37 + 164 * q^38 - 548 * q^39 + 1200 * q^40 + 918 * q^41 + 608 * q^43 + 1288 * q^44 + 876 * q^45 - 972 * q^46 + 1645 * q^47 + 1252 * q^48 - 367 * q^50 - 464 * q^51 + 3798 * q^52 - 218 * q^53 - 744 * q^54 + 1004 * q^55 - 436 * q^57 - 1270 * q^58 + 3760 * q^59 - 424 * q^60 + 956 * q^61 + 84 * q^62 + 2189 * q^64 - 596 * q^65 + 5500 * q^66 - 476 * q^67 + 256 * q^68 + 444 * q^69 + 852 * q^71 - 883 * q^72 + 6250 * q^73 + 1366 * q^74 - 2568 * q^75 + 1742 * q^76 - 1460 * q^78 + 632 * q^79 + 10124 * q^80 + 1267 * q^81 + 792 * q^82 + 796 * q^83 - 1228 * q^85 - 2864 * q^86 + 8360 * q^87 - 50 * q^88 + 908 * q^89 - 1858 * q^90 + 1696 * q^92 + 644 * q^93 + 235 * q^94 + 1320 * q^95 + 2688 * q^96 + 6184 * q^97 - 1812 * q^99

Introduction

L-functions

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Database

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