LMFDB - Embedded newform 2303.4.a.h.1.14

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			1.14
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)

$f(q)$	$=$	$q-1.17274 q^{2} +3.53925 q^{3} -6.62469 q^{4} -19.8836 q^{5} -4.15061 q^{6} +17.1509 q^{8} -14.4737 q^{9} +O(q^{10})$	\(q-1.17274 q^{2} +3.53925 q^{3} -6.62469 q^{4} -19.8836 q^{5} -4.15061 q^{6} +17.1509 q^{8} -14.4737 q^{9} +23.3182 q^{10} +59.6624 q^{11} -23.4464 q^{12} +72.3372 q^{13} -70.3730 q^{15} +32.8840 q^{16} -26.0904 q^{17} +16.9739 q^{18} +37.9840 q^{19} +131.723 q^{20} -69.9684 q^{22} +79.9645 q^{23} +60.7014 q^{24} +270.358 q^{25} -84.8326 q^{26} -146.786 q^{27} -41.6796 q^{29} +82.5291 q^{30} +117.640 q^{31} -175.772 q^{32} +211.160 q^{33} +30.5971 q^{34} +95.8838 q^{36} -382.614 q^{37} -44.5453 q^{38} +256.019 q^{39} -341.022 q^{40} -281.599 q^{41} -308.226 q^{43} -395.245 q^{44} +287.790 q^{45} -93.7774 q^{46} +47.0000 q^{47} +116.385 q^{48} -317.058 q^{50} -92.3403 q^{51} -479.211 q^{52} +391.360 q^{53} +172.141 q^{54} -1186.30 q^{55} +134.435 q^{57} +48.8792 q^{58} +725.622 q^{59} +466.199 q^{60} +456.298 q^{61} -137.961 q^{62} -56.9376 q^{64} -1438.32 q^{65} -247.636 q^{66} -1012.03 q^{67} +172.840 q^{68} +283.014 q^{69} +591.250 q^{71} -248.238 q^{72} +136.532 q^{73} +448.706 q^{74} +956.863 q^{75} -251.632 q^{76} -300.244 q^{78} -313.120 q^{79} -653.851 q^{80} -128.721 q^{81} +330.242 q^{82} -737.457 q^{83} +518.770 q^{85} +361.468 q^{86} -147.514 q^{87} +1023.27 q^{88} -877.943 q^{89} -337.502 q^{90} -529.740 q^{92} +416.358 q^{93} -55.1187 q^{94} -755.260 q^{95} -622.100 q^{96} +1475.87 q^{97} -863.537 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.17274	−0.414625	−0.207313	−	0.978275i	$-0.566472\pi$
$2$	−1.17274	−0.414625	−0.207313	+	0.978275i	$0.566472\pi$
$3$	3.53925	0.681129	0.340564	−	0.940221i	$-0.389382\pi$
$3$	3.53925	0.681129	0.340564	+	0.940221i	$0.389382\pi$
$4$	−6.62469	−0.828086
$5$	−19.8836	−1.77844	−0.889222	−	0.457477i	$-0.848753\pi$
$5$	−19.8836	−1.77844	−0.889222	+	0.457477i	$0.848753\pi$
$6$	−4.15061	−0.282413
$7$	0	0
$7$	0	0
$8$	17.1509	0.757971
$9$	−14.4737	−0.536063
$10$	23.3182	0.737388
$11$	59.6624	1.63535	0.817677	−	0.575677i	$-0.195262\pi$
$11$	59.6624	1.63535	0.817677	+	0.575677i	$0.195262\pi$
$12$	−23.4464	−0.564033
$13$	72.3372	1.54329	0.771644	−	0.636055i	$-0.219435\pi$
$13$	72.3372	1.54329	0.771644	+	0.636055i	$0.219435\pi$
$14$	0	0
$15$	−70.3730	−1.21135
$16$	32.8840	0.513812
$17$	−26.0904	−0.372226	−0.186113	−	0.982528i	$-0.559589\pi$
$17$	−26.0904	−0.372226	−0.186113	+	0.982528i	$0.559589\pi$
$18$	16.9739	0.222266
$19$	37.9840	0.458639	0.229319	−	0.973351i	$-0.426350\pi$
$19$	37.9840	0.458639	0.229319	+	0.973351i	$0.426350\pi$
$20$	131.723	1.47270
$21$	0	0
$22$	−69.9684	−0.678059
$23$	79.9645	0.724946	0.362473	−	0.931994i	$-0.381932\pi$
$23$	79.9645	0.724946	0.362473	+	0.931994i	$0.381932\pi$
$24$	60.7014	0.516276
$25$	270.358	2.16286
$26$	−84.8326	−0.639886
$27$	−146.786	−1.04626
$28$	0	0
$29$	−41.6796	−0.266886	−0.133443	−	0.991056i	$-0.542603\pi$
$29$	−41.6796	−0.266886	−0.133443	+	0.991056i	$0.542603\pi$
$30$	82.5291	0.502256
$31$	117.640	0.681574	0.340787	−	0.940140i	$-0.389306\pi$
$31$	117.640	0.681574	0.340787	+	0.940140i	$0.389306\pi$
$32$	−175.772	−0.971010
$33$	211.160	1.11389
$34$	30.5971	0.154334
$35$	0	0
$36$	95.8838	0.443907
$37$	−382.614	−1.70004	−0.850019	−	0.526752i	$-0.823410\pi$
$37$	−382.614	−1.70004	−0.850019	+	0.526752i	$0.823410\pi$
$38$	−44.5453	−0.190163
$39$	256.019	1.05118
$40$	−341.022	−1.34801
$41$	−281.599	−1.07264	−0.536322	−	0.844013i	$-0.680187\pi$
$41$	−281.599	−1.07264	−0.536322	+	0.844013i	$0.680187\pi$
$42$	0	0
$43$	−308.226	−1.09312	−0.546558	−	0.837421i	$-0.684062\pi$
$43$	−308.226	−1.09312	−0.546558	+	0.837421i	$0.684062\pi$
$44$	−395.245	−1.35421
$45$	287.790	0.953358
$46$	−93.7774	−0.300581
$47$	47.0000	0.145865
$47$	47.0000	0.145865
$48$	116.385	0.349972
$49$	0	0
$50$	−317.058	−0.896777
$51$	−92.3403	−0.253534
$52$	−479.211	−1.27797
$53$	391.360	1.01429	0.507145	−	0.861860i	$-0.330701\pi$
$53$	391.360	1.01429	0.507145	+	0.861860i	$0.330701\pi$
$54$	172.141	0.433805
$55$	−1186.30	−2.90838
$56$	0	0
$57$	134.435	0.312392
$58$	48.8792	0.110658
$59$	725.622	1.60115	0.800575	−	0.599232i	$-0.204527\pi$
$59$	725.622	1.60115	0.800575	+	0.599232i	$0.204527\pi$
$60$	466.199	1.00310
$61$	456.298	0.957753	0.478877	−	0.877882i	$-0.341044\pi$
$61$	456.298	0.957753	0.478877	+	0.877882i	$0.341044\pi$
$62$	−137.961	−0.282598
$63$	0	0
$64$	−56.9376	−0.111206
$65$	−1438.32	−2.74465
$66$	−247.636	−0.461846
$67$	−1012.03	−1.84535	−0.922676	−	0.385577i	$-0.874002\pi$
$67$	−1012.03	−1.84535	−0.922676	+	0.385577i	$0.874002\pi$
$68$	172.840	0.308235
$69$	283.014	0.493782
$70$	0	0
$71$	591.250	0.988289	0.494144	−	0.869380i	$-0.335481\pi$
$71$	591.250	0.988289	0.494144	+	0.869380i	$0.335481\pi$
$72$	−248.238	−0.406320
$73$	136.532	0.218903	0.109451	−	0.993992i	$-0.465091\pi$
$73$	136.532	0.218903	0.109451	+	0.993992i	$0.465091\pi$
$74$	448.706	0.704879
$75$	956.863	1.47319
$76$	−251.632	−0.379792
$77$	0	0
$78$	−300.244	−0.435845
$79$	−313.120	−0.445934	−0.222967	−	0.974826i	$-0.571574\pi$
$79$	−313.120	−0.445934	−0.222967	+	0.974826i	$0.571574\pi$
$80$	−653.851	−0.913785
$81$	−128.721	−0.176573
$82$	330.242	0.444746
$83$	−737.457	−0.975258	−0.487629	−	0.873051i	$-0.662138\pi$
$83$	−737.457	−0.975258	−0.487629	+	0.873051i	$0.662138\pi$
$84$	0	0
$85$	518.770	0.661983
$86$	361.468	0.453234
$87$	−147.514	−0.181784
$88$	1023.27	1.23955
$89$	−877.943	−1.04564	−0.522819	−	0.852444i	$-0.675120\pi$
$89$	−877.943	−1.04564	−0.522819	+	0.852444i	$0.675120\pi$
$90$	−337.502	−0.395287
$91$	0	0
$92$	−529.740	−0.600318
$93$	416.358	0.464240
$94$	−55.1187	−0.0604793
$95$	−755.260	−0.815663
$96$	−622.100	−0.661383
$97$	1475.87	1.54487	0.772433	−	0.635097i	$-0.219040\pi$
$97$	1475.87	1.54487	0.772433	+	0.635097i	$0.219040\pi$
$98$	0	0
$99$	−863.537	−0.876654
$100$	−1791.03	−1.79103
$101$	−1303.09	−1.28378	−0.641891	−	0.766796i	$-0.721850\pi$
$101$	−1303.09	−1.28378	−0.641891	+	0.766796i	$0.721850\pi$
$102$	108.291	0.105122
$103$	935.248	0.894686	0.447343	−	0.894362i	$-0.352370\pi$
$103$	935.248	0.894686	0.447343	+	0.894362i	$0.352370\pi$
$104$	1240.65	1.16977
$105$	0	0
$106$	−458.963	−0.420551
$107$	−120.504	−0.108874	−0.0544372	−	0.998517i	$-0.517336\pi$
$107$	−120.504	−0.108874	−0.0544372	+	0.998517i	$0.517336\pi$
$108$	972.410	0.866391
$109$	429.978	0.377839	0.188919	−	0.981993i	$-0.439501\pi$
$109$	429.978	0.377839	0.188919	+	0.981993i	$0.439501\pi$
$110$	1391.22	1.20589
$111$	−1354.17	−1.15794
$112$	0	0
$113$	370.092	0.308101	0.154050	−	0.988063i	$-0.450768\pi$
$113$	370.092	0.308101	0.154050	+	0.988063i	$0.450768\pi$
$114$	−157.657	−0.129526
$115$	−1589.98	−1.28928
$116$	276.114	0.221005
$117$	−1046.99	−0.827300
$118$	−850.964	−0.663878
$119$	0	0
$120$	−1206.96	−0.918167
$121$	2228.60	1.67438
$122$	−535.118	−0.397109
$123$	−996.650	−0.730609
$124$	−779.329	−0.564402
$125$	−2890.23	−2.06808
$126$	0	0
$127$	240.057	0.167729	0.0838645	−	0.996477i	$-0.473274\pi$
$127$	240.057	0.167729	0.0838645	+	0.996477i	$0.473274\pi$
$128$	1472.95	1.01712
$129$	−1090.89	−0.744553
$130$	1686.78	1.13800
$131$	−504.056	−0.336180	−0.168090	−	0.985772i	$-0.553760\pi$
$131$	−504.056	−0.336180	−0.168090	+	0.985772i	$0.553760\pi$
$132$	−1398.87	−0.922394
$133$	0	0
$134$	1186.84	0.765130
$135$	2918.63	1.86071
$136$	−447.474	−0.282136
$137$	2142.73	1.33625	0.668123	−	0.744051i	$-0.267098\pi$
$137$	2142.73	1.33625	0.668123	+	0.744051i	$0.267098\pi$
$138$	−331.902	−0.204734
$139$	−571.695	−0.348853	−0.174426	−	0.984670i	$-0.555807\pi$
$139$	−571.695	−0.348853	−0.174426	+	0.984670i	$0.555807\pi$
$140$	0	0
$141$	166.345	0.0993529
$142$	−693.382	−0.409770
$143$	4315.81	2.52382
$144$	−475.953	−0.275436
$145$	828.740	0.474642
$146$	−160.117	−0.0907627
$147$	0	0
$148$	2534.70	1.40778
$149$	−2736.02	−1.50432	−0.752160	−	0.658981i	$-0.770988\pi$
$149$	−2736.02	−1.50432	−0.752160	+	0.658981i	$0.770988\pi$
$150$	−1122.15	−0.610821
$151$	323.943	0.174583	0.0872917	−	0.996183i	$-0.472179\pi$
$151$	323.943	0.174583	0.0872917	+	0.996183i	$0.472179\pi$
$152$	651.461	0.347635
$153$	377.624	0.199537
$154$	0	0
$155$	−2339.11	−1.21214
$156$	−1696.05	−0.870465
$157$	−1198.49	−0.609236	−0.304618	−	0.952475i	$-0.598529\pi$
$157$	−1198.49	−0.609236	−0.304618	+	0.952475i	$0.598529\pi$
$158$	367.208	0.184896
$159$	1385.12	0.690863
$160$	3494.97	1.72689
$161$	0	0
$162$	150.956	0.0732115
$163$	1439.89	0.691905	0.345953	−	0.938252i	$-0.387556\pi$
$163$	1439.89	0.691905	0.345953	+	0.938252i	$0.387556\pi$
$164$	1865.51	0.888242
$165$	−4198.62	−1.98098
$166$	864.844	0.404367
$167$	2304.52	1.06784	0.533920	−	0.845535i	$-0.320718\pi$
$167$	2304.52	1.06784	0.533920	+	0.845535i	$0.320718\pi$
$168$	0	0
$169$	3035.67	1.38174
$170$	−608.381	−0.274475
$171$	−549.770	−0.245860
$172$	2041.90	0.905194
$173$	1494.65	0.656857	0.328429	−	0.944529i	$-0.393481\pi$
$173$	1494.65	0.656857	0.328429	+	0.944529i	$0.393481\pi$
$174$	172.996	0.0753722
$175$	0	0
$176$	1961.94	0.840264
$177$	2568.16	1.09059
$178$	1029.60	0.433548
$179$	−1847.52	−0.771455	−0.385728	−	0.922613i	$-0.626050\pi$
$179$	−1847.52	−0.771455	−0.385728	+	0.922613i	$0.626050\pi$
$180$	−1906.52	−0.789463
$181$	−124.892	−0.0512882	−0.0256441	−	0.999671i	$-0.508164\pi$
$181$	−124.892	−0.0512882	−0.0256441	+	0.999671i	$0.508164\pi$
$182$	0	0
$183$	1614.95	0.652354
$184$	1371.47	0.549488
$185$	7607.75	3.02342
$186$	−488.279	−0.192486
$187$	−1556.61	−0.608721
$188$	−311.360	−0.120789
$189$	0	0
$190$	885.721	0.338195
$191$	−3868.87	−1.46566	−0.732831	−	0.680411i	$-0.761801\pi$
$191$	−3868.87	−1.46566	−0.732831	+	0.680411i	$0.761801\pi$
$192$	−201.516	−0.0757458
$193$	4783.33	1.78400	0.892000	−	0.452036i	$-0.149302\pi$
$193$	4783.33	1.78400	0.892000	+	0.452036i	$0.149302\pi$
$194$	−1730.81	−0.640540
$195$	−5090.59	−1.86946
$196$	0	0
$197$	−3355.87	−1.21368	−0.606842	−	0.794822i	$-0.707564\pi$
$197$	−3355.87	−1.21368	−0.606842	+	0.794822i	$0.707564\pi$
$198$	1012.70	0.363483
$199$	4120.77	1.46791	0.733953	−	0.679200i	$-0.237673\pi$
$199$	4120.77	1.46791	0.733953	+	0.679200i	$0.237673\pi$
$200$	4636.88	1.63938
$201$	−3581.81	−1.25692
$202$	1528.18	0.532289
$203$	0	0
$204$	611.725	0.209948
$205$	5599.21	1.90764
$206$	−1096.80	−0.370960
$207$	−1157.38	−0.388617
$208$	2378.73	0.792959
$209$	2266.22	0.750037
$210$	0	0
$211$	5065.75	1.65280	0.826399	−	0.563085i	$-0.190386\pi$
$211$	5065.75	1.65280	0.826399	+	0.563085i	$0.190386\pi$
$212$	−2592.64	−0.839920
$213$	2092.58	0.673152
$214$	141.320	0.0451421
$215$	6128.64	1.94405
$216$	−2517.51	−0.793032
$217$	0	0
$218$	−504.252	−0.156662
$219$	483.222	0.149101
$220$	7858.89	2.40839
$221$	−1887.30	−0.574451
$222$	1588.08	0.480113
$223$	−3545.63	−1.06472	−0.532361	−	0.846518i	$-0.678695\pi$
$223$	−3545.63	−1.06472	−0.532361	+	0.846518i	$0.678695\pi$
$224$	0	0
$225$	−3913.08	−1.15943
$226$	−434.021	−0.127746
$227$	−359.178	−0.105020	−0.0525099	−	0.998620i	$-0.516722\pi$
$227$	−359.178	−0.105020	−0.0525099	+	0.998620i	$0.516722\pi$
$228$	−890.590	−0.258688
$229$	−2563.53	−0.739750	−0.369875	−	0.929082i	$-0.620599\pi$
$229$	−2563.53	−0.739750	−0.369875	+	0.929082i	$0.620599\pi$
$230$	1864.63	0.534566
$231$	0	0
$232$	−714.843	−0.202292
$233$	−93.6929	−0.0263435	−0.0131717	−	0.999913i	$-0.504193\pi$
$233$	−93.6929	−0.0263435	−0.0131717	+	0.999913i	$0.504193\pi$
$234$	1227.84	0.343020
$235$	−934.529	−0.259413
$236$	−4807.02	−1.32589
$237$	−1108.21	−0.303738
$238$	0	0
$239$	5555.51	1.50358	0.751791	−	0.659402i	$-0.229190\pi$
$239$	5555.51	1.50358	0.751791	+	0.659402i	$0.229190\pi$
$240$	−2314.14	−0.622405
$241$	5907.09	1.57888	0.789438	−	0.613830i	$-0.210372\pi$
$241$	5907.09	1.57888	0.789438	+	0.613830i	$0.210372\pi$
$242$	−2613.57	−0.694242
$243$	3507.64	0.925989
$244$	−3022.83	−0.793102
$245$	0	0
$246$	1168.81	0.302929
$247$	2747.66	0.707811
$248$	2017.64	0.516613
$249$	−2610.04	−0.664276
$250$	3389.48	0.857479
$251$	1872.14	0.470791	0.235395	−	0.971900i	$-0.424361\pi$
$251$	1872.14	0.470791	0.235395	+	0.971900i	$0.424361\pi$
$252$	0	0
$253$	4770.88	1.18554
$254$	−281.524	−0.0695447
$255$	1836.06	0.450895
$256$	−1271.88	−0.310517
$257$	7346.21	1.78305	0.891526	−	0.452970i	$-0.149636\pi$
$257$	7346.21	1.78305	0.891526	+	0.452970i	$0.149636\pi$
$258$	1279.33	0.308711
$259$	0	0
$260$	9528.45	2.27280
$261$	603.258	0.143068
$262$	591.126	0.139389
$263$	−4555.29	−1.06803	−0.534013	−	0.845476i	$-0.679317\pi$
$263$	−4555.29	−1.06803	−0.534013	+	0.845476i	$0.679317\pi$
$264$	3621.59	0.844294
$265$	−7781.64	−1.80386
$266$	0	0
$267$	−3107.26	−0.712214
$268$	6704.35	1.52811
$269$	−2888.18	−0.654631	−0.327315	−	0.944915i	$-0.606144\pi$
$269$	−2888.18	−0.654631	−0.327315	+	0.944915i	$0.606144\pi$
$270$	−3422.79	−0.771497
$271$	5220.45	1.17018	0.585091	−	0.810967i	$-0.301059\pi$
$271$	5220.45	1.17018	0.585091	+	0.810967i	$0.301059\pi$
$272$	−857.954	−0.191254
$273$	0	0
$274$	−2512.86	−0.554041
$275$	16130.2	3.53704
$276$	−1874.88	−0.408894
$277$	−1251.68	−0.271503	−0.135751	−	0.990743i	$-0.543345\pi$
$277$	−1251.68	−0.271503	−0.135751	+	0.990743i	$0.543345\pi$
$278$	670.448	0.144643
$279$	−1702.69	−0.365367
$280$	0	0
$281$	−3345.20	−0.710170	−0.355085	−	0.934834i	$-0.615548\pi$
$281$	−3345.20	−0.710170	−0.355085	+	0.934834i	$0.615548\pi$
$282$	−195.079	−0.0411942
$283$	−1529.83	−0.321338	−0.160669	−	0.987008i	$-0.551365\pi$
$283$	−1529.83	−0.321338	−0.160669	+	0.987008i	$0.551365\pi$
$284$	−3916.85	−0.818388
$285$	−2673.05	−0.555572
$286$	−5061.32	−1.04644
$287$	0	0
$288$	2544.07	0.520523
$289$	−4232.29	−0.861448
$290$	−971.894	−0.196799
$291$	5223.47	1.05225
$292$	−904.484	−0.181270
$293$	9540.13	1.90219	0.951093	−	0.308906i	$-0.0999629\pi$
$293$	9540.13	1.90219	0.951093	+	0.308906i	$0.0999629\pi$
$294$	0	0
$295$	−14428.0	−2.84756
$296$	−6562.19	−1.28858
$297$	−8757.60	−1.71100
$298$	3208.64	0.623729
$299$	5784.41	1.11880
$300$	−6338.92	−1.21992
$301$	0	0
$302$	−379.900	−0.0723867
$303$	−4611.95	−0.874422
$304$	1249.07	0.235654
$305$	−9072.84	−1.70331
$306$	−442.854	−0.0827330
$307$	−8808.52	−1.63755	−0.818777	−	0.574112i	$-0.805348\pi$
$307$	−8808.52	−1.63755	−0.818777	+	0.574112i	$0.805348\pi$
$308$	0	0
$309$	3310.08	0.609397
$310$	2743.16	0.502585
$311$	−6295.37	−1.14784	−0.573919	−	0.818912i	$-0.694578\pi$
$311$	−6295.37	−1.14784	−0.573919	+	0.818912i	$0.694578\pi$
$312$	4390.97	0.796762
$313$	2157.25	0.389568	0.194784	−	0.980846i	$-0.437599\pi$
$313$	2157.25	0.389568	0.194784	+	0.980846i	$0.437599\pi$
$314$	1405.52	0.252605
$315$	0	0
$316$	2074.32	0.369271
$317$	−8776.82	−1.55506	−0.777532	−	0.628843i	$-0.783529\pi$
$317$	−8776.82	−1.55506	−0.777532	+	0.628843i	$0.783529\pi$
$318$	−1624.38	−0.286449
$319$	−2486.70	−0.436453
$320$	1132.13	0.197774
$321$	−426.494	−0.0741575
$322$	0	0
$323$	−991.017	−0.170717
$324$	852.739	0.146217
$325$	19556.9	3.33791
$326$	−1688.61	−0.286881
$327$	1521.80	0.257357
$328$	−4829.69	−0.813033
$329$	0	0
$330$	4923.89	0.821367
$331$	−2286.46	−0.379684	−0.189842	−	0.981815i	$-0.560798\pi$
$331$	−2286.46	−0.379684	−0.189842	+	0.981815i	$0.560798\pi$
$332$	4885.42	0.807597
$333$	5537.85	0.911328
$334$	−2702.60	−0.442753
$335$	20122.7	3.28185
$336$	0	0
$337$	−8908.98	−1.44007	−0.720034	−	0.693938i	$-0.755874\pi$
$337$	−8908.98	−1.44007	−0.720034	+	0.693938i	$0.755874\pi$
$338$	−3560.05	−0.572902
$339$	1309.85	0.209856
$340$	−3436.69	−0.548178
$341$	7018.70	1.11462
$342$	644.736	0.101940
$343$	0	0
$344$	−5286.36	−0.828551
$345$	−5627.35	−0.878163
$346$	−1752.84	−0.272350
$347$	152.863	0.0236487	0.0118243	−	0.999930i	$-0.496236\pi$
$347$	152.863	0.0236487	0.0118243	+	0.999930i	$0.496236\pi$
$348$	977.236	0.150533
$349$	2095.18	0.321354	0.160677	−	0.987007i	$-0.448632\pi$
$349$	2095.18	0.321354	0.160677	+	0.987007i	$0.448632\pi$
$350$	0	0
$351$	−10618.1	−1.61468
$352$	−10487.0	−1.58795
$353$	−1878.25	−0.283199	−0.141599	−	0.989924i	$-0.545224\pi$
$353$	−1878.25	−0.283199	−0.141599	+	0.989924i	$0.545224\pi$
$354$	−3011.77	−0.452186
$355$	−11756.2	−1.75762
$356$	5816.10	0.865878
$357$	0	0
$358$	2166.66	0.319865
$359$	4208.65	0.618730	0.309365	−	0.950943i	$-0.399884\pi$
$359$	4208.65	0.618730	0.309365	+	0.950943i	$0.399884\pi$
$360$	4935.86	0.722618
$361$	−5416.21	−0.789650
$362$	146.466	0.0212654
$363$	7887.58	1.14047
$364$	0	0
$365$	−2714.76	−0.389306
$366$	−1893.92	−0.270482
$367$	9524.10	1.35464	0.677321	−	0.735687i	$-0.263141\pi$
$367$	9524.10	1.35464	0.677321	+	0.735687i	$0.263141\pi$
$368$	2629.55	0.372486
$369$	4075.79	0.575005
$370$	−8921.89	−1.25359
$371$	0	0
$372$	−2758.24	−0.384431
$373$	−3623.90	−0.503051	−0.251526	−	0.967851i	$-0.580932\pi$
$373$	−3623.90	−0.503051	−0.251526	+	0.967851i	$0.580932\pi$
$374$	1825.50	0.252391
$375$	−10229.2	−1.40863
$376$	806.093	0.110561
$377$	−3014.98	−0.411882
$378$	0	0
$379$	−13408.8	−1.81732	−0.908661	−	0.417536i	$-0.862894\pi$
$379$	−13408.8	−1.81732	−0.908661	+	0.417536i	$0.862894\pi$
$380$	5003.36	0.675439
$381$	849.621	0.114245
$382$	4537.17	0.607700
$383$	−3796.67	−0.506529	−0.253265	−	0.967397i	$-0.581504\pi$
$383$	−3796.67	−0.506529	−0.253265	+	0.967397i	$0.581504\pi$
$384$	5213.12	0.692789
$385$	0	0
$386$	−5609.60	−0.739692
$387$	4461.17	0.585980
$388$	−9777.18	−1.27928
$389$	12777.4	1.66540	0.832700	−	0.553724i	$-0.186794\pi$
$389$	12777.4	1.66540	0.832700	+	0.553724i	$0.186794\pi$
$390$	5969.92	0.775125
$391$	−2086.30	−0.269844
$392$	0	0
$393$	−1783.98	−0.228982
$394$	3935.56	0.503225
$395$	6225.96	0.793068
$396$	5720.66	0.725944
$397$	13217.9	1.67100	0.835499	−	0.549491i	$-0.185178\pi$
$397$	13217.9	1.67100	0.835499	+	0.549491i	$0.185178\pi$
$398$	−4832.58	−0.608631
$399$	0	0
$400$	8890.43	1.11130
$401$	−4030.34	−0.501909	−0.250954	−	0.967999i	$-0.580744\pi$
$401$	−4030.34	−0.501909	−0.250954	+	0.967999i	$0.580744\pi$
$402$	4200.52	0.521152
$403$	8509.76	1.05186
$404$	8632.55	1.06308
$405$	2559.44	0.314024
$406$	0	0
$407$	−22827.7	−2.78016
$408$	−1583.72	−0.192171
$409$	7367.12	0.890662	0.445331	−	0.895366i	$-0.353086\pi$
$409$	7367.12	0.890662	0.445331	+	0.895366i	$0.353086\pi$
$410$	−6566.40	−0.790955
$411$	7583.65	0.910155
$412$	−6195.72	−0.740877
$413$	0	0
$414$	1357.31	0.161131
$415$	14663.3	1.73444
$416$	−12714.8	−1.49855
$417$	−2023.37	−0.237614
$418$	−2657.68	−0.310984
$419$	6393.47	0.745445	0.372722	−	0.927943i	$-0.378424\pi$
$419$	6393.47	0.745445	0.372722	+	0.927943i	$0.378424\pi$
$420$	0	0
$421$	−251.739	−0.0291426	−0.0145713	−	0.999894i	$-0.504638\pi$
$421$	−251.739	−0.0291426	−0.0145713	+	0.999894i	$0.504638\pi$
$422$	−5940.79	−0.685292
$423$	−680.265	−0.0781929
$424$	6712.18	0.768803
$425$	−7053.72	−0.805073
$426$	−2454.05	−0.279106
$427$	0	0
$428$	798.301	0.0901574
$429$	15274.7	1.71905
$430$	−7187.29	−0.806051
$431$	5799.29	0.648125	0.324063	−	0.946036i	$-0.394951\pi$
$431$	5799.29	0.648125	0.324063	+	0.946036i	$0.394951\pi$
$432$	−4826.90	−0.537579
$433$	2314.53	0.256881	0.128440	−	0.991717i	$-0.459003\pi$
$433$	2314.53	0.256881	0.128440	+	0.991717i	$0.459003\pi$
$434$	0	0
$435$	2933.12	0.323292
$436$	−2848.47	−0.312883
$437$	3037.38	0.332488
$438$	−566.693	−0.0618211
$439$	1284.41	0.139640	0.0698198	−	0.997560i	$-0.477758\pi$
$439$	1284.41	0.139640	0.0698198	+	0.997560i	$0.477758\pi$
$440$	−20346.2	−2.20447
$441$	0	0
$442$	2213.31	0.238182
$443$	7034.88	0.754486	0.377243	−	0.926114i	$-0.376872\pi$
$443$	7034.88	0.754486	0.377243	+	0.926114i	$0.376872\pi$
$444$	8970.93	0.958878
$445$	17456.7	1.85961
$446$	4158.09	0.441461
$447$	−9683.46	−1.02464
$448$	0	0
$449$	9347.99	0.982537	0.491268	−	0.871008i	$-0.336533\pi$
$449$	9347.99	0.982537	0.491268	+	0.871008i	$0.336533\pi$
$450$	4589.01	0.480729
$451$	−16800.9	−1.75415
$452$	−2451.75	−0.255134
$453$	1146.51	0.118914
$454$	421.222	0.0435439
$455$	0	0
$456$	2305.68	0.236784
$457$	−9097.60	−0.931220	−0.465610	−	0.884990i	$-0.654165\pi$
$457$	−9097.60	−0.931220	−0.465610	+	0.884990i	$0.654165\pi$
$458$	3006.35	0.306719
$459$	3829.69	0.389444
$460$	10533.1	1.06763
$461$	−101.740	−0.0102787	−0.00513936	−	0.999987i	$-0.501636\pi$
$461$	−101.740	−0.0102787	−0.00513936	+	0.999987i	$0.501636\pi$
$462$	0	0
$463$	3518.66	0.353187	0.176594	−	0.984284i	$-0.443492\pi$
$463$	3518.66	0.353187	0.176594	+	0.984284i	$0.443492\pi$
$464$	−1370.59	−0.137129
$465$	−8278.70	−0.825624
$466$	109.877	0.0109227
$467$	19715.7	1.95361	0.976804	−	0.214133i	$-0.0686927\pi$
$467$	19715.7	1.95361	0.976804	+	0.214133i	$0.0686927\pi$
$468$	6935.97	0.685075
$469$	0	0
$470$	1095.96	0.107559
$471$	−4241.76	−0.414968
$472$	12445.1	1.21363
$473$	−18389.5	−1.78763
$474$	1299.64	0.125938
$475$	10269.3	0.991972
$476$	0	0
$477$	−5664.43	−0.543724
$478$	−6515.16	−0.623423
$479$	−4492.27	−0.428512	−0.214256	−	0.976778i	$-0.568733\pi$
$479$	−4492.27	−0.428512	−0.214256	+	0.976778i	$0.568733\pi$
$480$	12369.6	1.17623
$481$	−27677.2	−2.62365
$482$	−6927.47	−0.654642
$483$	0	0
$484$	−14763.8	−1.38653
$485$	−29345.6	−2.74746
$486$	−4113.54	−0.383938
$487$	−5662.97	−0.526928	−0.263464	−	0.964669i	$-0.584865\pi$
$487$	−5662.97	−0.526928	−0.263464	+	0.964669i	$0.584865\pi$
$488$	7825.93	0.725949
$489$	5096.11	0.471277
$490$	0	0
$491$	4109.39	0.377707	0.188854	−	0.982005i	$-0.439523\pi$
$491$	4109.39	0.377707	0.188854	+	0.982005i	$0.439523\pi$
$492$	6602.49	0.605007
$493$	1087.43	0.0993419
$494$	−3222.28	−0.293477
$495$	17170.2	1.55908
$496$	3868.48	0.350201
$497$	0	0
$498$	3060.90	0.275426
$499$	−6236.26	−0.559466	−0.279733	−	0.960078i	$-0.590246\pi$
$499$	−6236.26	−0.559466	−0.279733	+	0.960078i	$0.590246\pi$
$500$	19146.9	1.71255
$501$	8156.28	0.727336
$502$	−2195.53	−0.195202
$503$	5445.35	0.482696	0.241348	−	0.970439i	$-0.422410\pi$
$503$	5445.35	0.482696	0.241348	+	0.970439i	$0.422410\pi$
$504$	0	0
$505$	25910.1	2.28313
$506$	−5594.99	−0.491556
$507$	10744.0	0.941140
$508$	−1590.30	−0.138894
$509$	−3473.93	−0.302513	−0.151256	−	0.988495i	$-0.548332\pi$
$509$	−3473.93	−0.302513	−0.151256	+	0.988495i	$0.548332\pi$
$510$	−2153.21	−0.186953
$511$	0	0
$512$	−10292.0	−0.888371
$513$	−5575.52	−0.479854
$514$	−8615.18	−0.739298
$515$	−18596.1	−1.59115
$516$	7226.79	0.616554
$517$	2804.13	0.238541
$518$	0	0
$519$	5289.95	0.447405
$520$	−24668.6	−2.08036
$521$	14961.3	1.25809	0.629045	−	0.777369i	$-0.283446\pi$
$521$	14961.3	1.25809	0.629045	+	0.777369i	$0.283446\pi$
$522$	−707.463	−0.0593196
$523$	6714.71	0.561403	0.280702	−	0.959795i	$-0.409433\pi$
$523$	6714.71	0.561403	0.280702	+	0.959795i	$0.409433\pi$
$524$	3339.21	0.278386
$525$	0	0
$526$	5342.16	0.442831
$527$	−3069.27	−0.253700
$528$	6943.78	0.572328
$529$	−5772.67	−0.474453
$530$	9125.83	0.747926
$531$	−10502.4	−0.858318
$532$	0	0
$533$	−20370.1	−1.65540
$534$	3644.00	0.295302
$535$	2396.05	0.193627
$536$	−17357.2	−1.39872
$537$	−6538.85	−0.525460
$538$	3387.08	0.271427
$539$	0	0
$540$	−19335.0	−1.54083
$541$	22651.8	1.80014	0.900071	−	0.435744i	$-0.143515\pi$
$541$	22651.8	1.80014	0.900071	+	0.435744i	$0.143515\pi$
$542$	−6122.21	−0.485187
$543$	−442.025	−0.0349339
$544$	4585.94	0.361435
$545$	−8549.51	−0.671965
$546$	0	0
$547$	15854.4	1.23928	0.619639	−	0.784887i	$-0.287279\pi$
$547$	15854.4	1.23928	0.619639	+	0.784887i	$0.287279\pi$
$548$	−14194.9	−1.10653
$549$	−6604.32	−0.513417
$550$	−18916.5	−1.46655
$551$	−1583.16	−0.122404
$552$	4853.96	0.374272
$553$	0	0
$554$	1467.89	0.112572
$555$	26925.7	2.05934
$556$	3787.30	0.288880
$557$	2135.77	0.162469	0.0812346	−	0.996695i	$-0.474114\pi$
$557$	2135.77	0.162469	0.0812346	+	0.996695i	$0.474114\pi$
$558$	1996.81	0.151490
$559$	−22296.2	−1.68699
$560$	0	0
$561$	−5509.24	−0.414618
$562$	3923.04	0.294454
$563$	−8840.05	−0.661747	−0.330873	−	0.943675i	$-0.607343\pi$
$563$	−8840.05	−0.661747	−0.330873	+	0.943675i	$0.607343\pi$
$564$	−1101.98	−0.0822727
$565$	−7358.77	−0.547939
$566$	1794.09	0.133235
$567$	0	0
$568$	10140.5	0.749094
$569$	−18986.8	−1.39889	−0.699446	−	0.714685i	$-0.746570\pi$
$569$	−18986.8	−1.39889	−0.699446	+	0.714685i	$0.746570\pi$
$570$	3134.79	0.230354
$571$	24945.4	1.82825	0.914125	−	0.405432i	$-0.132879\pi$
$571$	24945.4	1.82825	0.914125	+	0.405432i	$0.132879\pi$
$572$	−28590.9	−2.08994
$573$	−13692.9	−0.998304
$574$	0	0
$575$	21619.0	1.56796
$576$	824.099	0.0596136
$577$	−4629.51	−0.334019	−0.167009	−	0.985955i	$-0.553411\pi$
$577$	−4629.51	−0.334019	−0.167009	+	0.985955i	$0.553411\pi$
$578$	4963.37	0.357178
$579$	16929.4	1.21513
$580$	−5490.14	−0.393044
$581$	0	0
$582$	−6125.76	−0.436291
$583$	23349.5	1.65872
$584$	2341.66	0.165922
$585$	20817.9	1.47131
$586$	−11188.1	−0.788694
$587$	−4761.95	−0.334833	−0.167416	−	0.985886i	$-0.553542\pi$
$587$	−4761.95	−0.334833	−0.167416	+	0.985886i	$0.553542\pi$
$588$	0	0
$589$	4468.45	0.312596
$590$	16920.2	1.18067
$591$	−11877.3	−0.826676
$592$	−12581.9	−0.873500
$593$	9837.13	0.681218	0.340609	−	0.940205i	$-0.389367\pi$
$593$	9837.13	0.681218	0.340609	+	0.940205i	$0.389367\pi$
$594$	10270.4	0.709424
$595$	0	0
$596$	18125.3	1.24571
$597$	14584.4	0.999834
$598$	−6783.60	−0.463883
$599$	−4442.28	−0.303016	−0.151508	−	0.988456i	$-0.548413\pi$
$599$	−4442.28	−0.303016	−0.151508	+	0.988456i	$0.548413\pi$
$600$	16411.1	1.11663
$601$	2713.35	0.184160	0.0920799	−	0.995752i	$-0.470648\pi$
$601$	2713.35	0.184160	0.0920799	+	0.995752i	$0.470648\pi$
$602$	0	0
$603$	14647.8	0.989225
$604$	−2146.02	−0.144570
$605$	−44312.7	−2.97779
$606$	5408.61	0.362557
$607$	15166.5	1.01415	0.507076	−	0.861902i	$-0.330727\pi$
$607$	15166.5	1.01415	0.507076	+	0.861902i	$0.330727\pi$
$608$	−6676.52	−0.445343
$609$	0	0
$610$	10640.1	0.706236
$611$	3399.85	0.225112
$612$	−2501.64	−0.165233
$613$	8769.66	0.577819	0.288910	−	0.957356i	$-0.406707\pi$
$613$	8769.66	0.577819	0.288910	+	0.957356i	$0.406707\pi$
$614$	10330.1	0.678971
$615$	19817.0	1.29935
$616$	0	0
$617$	22488.7	1.46736	0.733680	−	0.679495i	$-0.237801\pi$
$617$	22488.7	1.46736	0.733680	+	0.679495i	$0.237801\pi$
$618$	−3881.85	−0.252671
$619$	12350.1	0.801926	0.400963	−	0.916094i	$-0.368676\pi$
$619$	12350.1	0.801926	0.400963	+	0.916094i	$0.368676\pi$
$620$	15495.9	1.00376
$621$	−11737.7	−0.758480
$622$	7382.82	0.475923
$623$	0	0
$624$	8418.93	0.540107
$625$	23673.5	1.51510
$626$	−2529.89	−0.161525
$627$	8020.72	0.510872
$628$	7939.63	0.504500
$629$	9982.54	0.632798
$630$	0	0
$631$	−9945.46	−0.627453	−0.313726	−	0.949513i	$-0.601577\pi$
$631$	−9945.46	−0.627453	−0.313726	+	0.949513i	$0.601577\pi$
$632$	−5370.30	−0.338005
$633$	17928.9	1.12577
$634$	10292.9	0.644769
$635$	−4773.19	−0.298297
$636$	−9175.99	−0.572094
$637$	0	0
$638$	2916.25	0.180965
$639$	−8557.59	−0.529785
$640$	−29287.5	−1.80889
$641$	−22309.2	−1.37466	−0.687332	−	0.726343i	$-0.741218\pi$
$641$	−22309.2	−1.37466	−0.687332	+	0.726343i	$0.741218\pi$
$642$	500.165	0.0307476
$643$	16781.3	1.02922	0.514612	−	0.857423i	$-0.327936\pi$
$643$	16781.3	1.02922	0.514612	+	0.857423i	$0.327936\pi$
$644$	0	0
$645$	21690.8	1.32415
$646$	1162.20	0.0707837
$647$	9657.77	0.586841	0.293421	−	0.955983i	$-0.405206\pi$
$647$	9657.77	0.586841	0.293421	+	0.955983i	$0.405206\pi$
$648$	−2207.69	−0.133837
$649$	43292.3	2.61845
$650$	−22935.1	−1.38398
$651$	0	0
$652$	−9538.79	−0.572957
$653$	−14704.4	−0.881208	−0.440604	−	0.897702i	$-0.645236\pi$
$653$	−14704.4	−0.881208	−0.440604	+	0.897702i	$0.645236\pi$
$654$	−1784.67	−0.106707
$655$	10022.5	0.597877
$656$	−9260.10	−0.551137
$657$	−1976.13	−0.117346
$658$	0	0
$659$	11595.5	0.685427	0.342714	−	0.939440i	$-0.388654\pi$
$659$	11595.5	0.685427	0.342714	+	0.939440i	$0.388654\pi$
$660$	27814.6	1.64043
$661$	2612.96	0.153755	0.0768777	−	0.997041i	$-0.475505\pi$
$661$	2612.96	0.153755	0.0768777	+	0.997041i	$0.475505\pi$
$662$	2681.42	0.157427
$663$	−6679.64	−0.391275
$664$	−12648.1	−0.739217
$665$	0	0
$666$	−6494.44	−0.377860
$667$	−3332.89	−0.193478
$668$	−15266.7	−0.884263
$669$	−12548.9	−0.725213
$670$	−23598.7	−1.36074
$671$	27223.8	1.56627
$672$	0	0
$673$	−837.721	−0.0479818	−0.0239909	−	0.999712i	$-0.507637\pi$
$673$	−837.721	−0.0479818	−0.0239909	+	0.999712i	$0.507637\pi$
$674$	10447.9	0.597089
$675$	−39684.7	−2.26291
$676$	−20110.4	−1.14420
$677$	12655.0	0.718419	0.359210	−	0.933257i	$-0.383046\pi$
$677$	12655.0	0.718419	0.359210	+	0.933257i	$0.383046\pi$
$678$	−1536.11	−0.0870117
$679$	0	0
$680$	8897.39	0.501763
$681$	−1271.22	−0.0715320
$682$	−8231.09	−0.462148
$683$	14639.1	0.820129	0.410064	−	0.912057i	$-0.365506\pi$
$683$	14639.1	0.820129	0.410064	+	0.912057i	$0.365506\pi$
$684$	3642.05	0.203593
$685$	−42605.1	−2.37644
$686$	0	0
$687$	−9072.97	−0.503865
$688$	−10135.7	−0.561656
$689$	28309.9	1.56534
$690$	6599.40	0.364109
$691$	−323.160	−0.0177910	−0.00889550	−	0.999960i	$-0.502832\pi$
$691$	−323.160	−0.0177910	−0.00889550	+	0.999960i	$0.502832\pi$
$692$	−9901.60	−0.543934
$693$	0	0
$694$	−179.268	−0.00980535
$695$	11367.4	0.620415
$696$	−2530.01	−0.137787
$697$	7347.02	0.399266
$698$	−2457.10	−0.133242
$699$	−331.603	−0.0179433
$700$	0	0
$701$	−2291.66	−0.123473	−0.0617367	−	0.998092i	$-0.519664\pi$
$701$	−2291.66	−0.123473	−0.0617367	+	0.998092i	$0.519664\pi$
$702$	12452.2	0.669485
$703$	−14533.2	−0.779703
$704$	−3397.04	−0.181862
$705$	−3307.53	−0.176693
$706$	2202.69	0.117421
$707$	0	0
$708$	−17013.2	−0.903102
$709$	27226.6	1.44220	0.721098	−	0.692833i	$-0.243638\pi$
$709$	27226.6	1.44220	0.721098	+	0.692833i	$0.243638\pi$
$710$	13786.9	0.728752
$711$	4532.01	0.239049
$712$	−15057.5	−0.792563
$713$	9407.05	0.494105
$714$	0	0
$715$	−85813.9	−4.48847
$716$	12239.3	0.638831
$717$	19662.3	1.02413
$718$	−4935.64	−0.256541
$719$	−6461.73	−0.335163	−0.167581	−	0.985858i	$-0.553596\pi$
$719$	−6461.73	−0.335163	−0.167581	+	0.985858i	$0.553596\pi$
$720$	9463.66	0.489847
$721$	0	0
$722$	6351.80	0.327409
$723$	20906.7	1.07542
$724$	827.372	0.0424711
$725$	−11268.4	−0.577238
$726$	−9250.07	−0.472868
$727$	34102.3	1.73973	0.869866	−	0.493289i	$-0.164205\pi$
$727$	34102.3	1.73973	0.869866	+	0.493289i	$0.164205\pi$
$728$	0	0
$729$	15889.9	0.807290
$730$	3183.70	0.161416
$731$	8041.72	0.406886
$732$	−10698.6	−0.540205
$733$	854.692	0.0430679	0.0215339	−	0.999768i	$-0.493145\pi$
$733$	854.692	0.0430679	0.0215339	+	0.999768i	$0.493145\pi$
$734$	−11169.3	−0.561669
$735$	0	0
$736$	−14055.5	−0.703930
$737$	−60379.9	−3.01780
$738$	−4779.83	−0.238412
$739$	−13680.5	−0.680984	−0.340492	−	0.940247i	$-0.610594\pi$
$739$	−13680.5	−0.680984	−0.340492	+	0.940247i	$0.610594\pi$
$740$	−50398.9	−2.50365
$741$	9724.65	0.482111
$742$	0	0
$743$	33700.8	1.66401	0.832007	−	0.554766i	$-0.187192\pi$
$743$	33700.8	1.66401	0.832007	+	0.554766i	$0.187192\pi$
$744$	7140.92	0.351880
$745$	54402.0	2.67535
$746$	4249.88	0.208578
$747$	10673.7	0.522800
$748$	10312.1	0.504073
$749$	0	0
$750$	11996.2	0.584054
$751$	17874.3	0.868498	0.434249	−	0.900793i	$-0.357014\pi$
$751$	17874.3	0.868498	0.434249	+	0.900793i	$0.357014\pi$
$752$	1545.55	0.0749472
$753$	6625.98	0.320669
$754$	3535.78	0.170777
$755$	−6441.15	−0.310487
$756$	0	0
$757$	27476.7	1.31923	0.659616	−	0.751603i	$-0.270719\pi$
$757$	27476.7	1.31923	0.659616	+	0.751603i	$0.270719\pi$
$758$	15725.0	0.753507
$759$	16885.3	0.807508
$760$	−12953.4	−0.618249
$761$	−8913.17	−0.424576	−0.212288	−	0.977207i	$-0.568091\pi$
$761$	−8913.17	−0.424576	−0.212288	+	0.977207i	$0.568091\pi$
$762$	−996.382	−0.0473689
$763$	0	0
$764$	25630.0	1.21369
$765$	−7508.53	−0.354865
$766$	4452.50	0.210020
$767$	52489.5	2.47104
$768$	−4501.49	−0.211502
$769$	28916.2	1.35598	0.677988	−	0.735073i	$-0.262852\pi$
$769$	28916.2	1.35598	0.677988	+	0.735073i	$0.262852\pi$
$770$	0	0
$771$	26000.1	1.21449
$772$	−31688.1	−1.47730
$773$	6144.75	0.285914	0.142957	−	0.989729i	$-0.454339\pi$
$773$	6144.75	0.285914	0.142957	+	0.989729i	$0.454339\pi$
$774$	−5231.79	−0.242962
$775$	31804.9	1.47415
$776$	25312.5	1.17096
$777$	0	0
$778$	−14984.6	−0.690517
$779$	−10696.3	−0.491956
$780$	33723.5	1.54807
$781$	35275.4	1.61620
$782$	2446.69	0.111884
$783$	6117.97	0.279232
$784$	0	0
$785$	23830.3	1.08349
$786$	2092.14	0.0949418
$787$	31986.4	1.44878	0.724390	−	0.689390i	$-0.242121\pi$
$787$	31986.4	1.44878	0.724390	+	0.689390i	$0.242121\pi$
$788$	22231.6	1.00504
$789$	−16122.3	−0.727464
$790$	−7301.41	−0.328826
$791$	0	0
$792$	−14810.4	−0.664478
$793$	33007.3	1.47809
$794$	−15501.1	−0.692839
$795$	−27541.2	−1.22866
$796$	−27298.8	−1.21555
$797$	−39054.4	−1.73573	−0.867867	−	0.496797i	$-0.834509\pi$
$797$	−39054.4	−1.73573	−0.867867	+	0.496797i	$0.834509\pi$
$798$	0	0
$799$	−1226.25	−0.0542947
$800$	−47521.2	−2.10016
$801$	12707.1	0.560528
$802$	4726.53	0.208104
$803$	8145.85	0.357984
$804$	23728.4	1.04084
$805$	0	0
$806$	−9979.72	−0.436130
$807$	−10222.0	−0.445888
$808$	−22349.2	−0.973070
$809$	−22764.5	−0.989316	−0.494658	−	0.869088i	$-0.664707\pi$
$809$	−22764.5	−0.989316	−0.494658	+	0.869088i	$0.664707\pi$
$810$	−3001.56	−0.130202
$811$	39599.3	1.71458	0.857288	−	0.514838i	$-0.172148\pi$
$811$	39599.3	1.71458	0.857288	+	0.514838i	$0.172148\pi$
$812$	0	0
$813$	18476.5	0.797045
$814$	26770.9	1.15273
$815$	−28630.1	−1.23051
$816$	−3036.51	−0.130269
$817$	−11707.7	−0.501346
$818$	−8639.70	−0.369291
$819$	0	0
$820$	−37093.0	−1.57969
$821$	−37027.7	−1.57403	−0.787013	−	0.616936i	$-0.788374\pi$
$821$	−37027.7	−1.57403	−0.787013	+	0.616936i	$0.788374\pi$
$822$	−8893.63	−0.377373
$823$	24559.6	1.04021	0.520106	−	0.854102i	$-0.325892\pi$
$823$	24559.6	1.04021	0.520106	+	0.854102i	$0.325892\pi$
$824$	16040.4	0.678146
$825$	57088.7	2.40918
$826$	0	0
$827$	32026.0	1.34662	0.673310	−	0.739361i	$-0.264872\pi$
$827$	32026.0	1.34662	0.673310	+	0.739361i	$0.264872\pi$
$828$	7667.30	0.321808
$829$	32123.1	1.34582	0.672908	−	0.739726i	$-0.265045\pi$
$829$	32123.1	1.34582	0.672908	+	0.739726i	$0.265045\pi$
$830$	−17196.2	−0.719143
$831$	−4430.01	−0.184928
$832$	−4118.71	−0.171623
$833$	0	0
$834$	2372.88	0.0985207
$835$	−45822.2	−1.89909
$836$	−15013.0	−0.621095
$837$	−17267.9	−0.713102
$838$	−7497.86	−0.309080
$839$	17549.7	0.722149	0.361075	−	0.932537i	$-0.382410\pi$
$839$	17549.7	0.722149	0.361075	+	0.932537i	$0.382410\pi$
$840$	0	0
$841$	−22651.8	−0.928772
$842$	295.224	0.0120833
$843$	−11839.5	−0.483717
$844$	−33559.0	−1.36866
$845$	−60360.1	−2.45734
$846$	797.772	0.0324208
$847$	0	0
$848$	12869.5	0.521155
$849$	−5414.44	−0.218873
$850$	8272.17	0.333804
$851$	−30595.6	−1.23244
$852$	−13862.7	−0.557428
$853$	417.945	0.0167763	0.00838813	−	0.999965i	$-0.497330\pi$
$853$	417.945	0.0167763	0.00838813	+	0.999965i	$0.497330\pi$
$854$	0	0
$855$	10931.4	0.437247
$856$	−2066.76	−0.0825236
$857$	6791.78	0.270715	0.135358	−	0.990797i	$-0.456782\pi$
$857$	6791.78	0.270715	0.135358	+	0.990797i	$0.456782\pi$
$858$	−17913.3	−0.712761
$859$	−13441.7	−0.533905	−0.266952	−	0.963710i	$-0.586017\pi$
$859$	−13441.7	−0.533905	−0.266952	+	0.963710i	$0.586017\pi$
$860$	−40600.3	−1.60984
$861$	0	0
$862$	−6801.05	−0.268729
$863$	−35621.6	−1.40507	−0.702534	−	0.711650i	$-0.747948\pi$
$863$	−35621.6	−1.40507	−0.702534	+	0.711650i	$0.747948\pi$
$864$	25800.8	1.01593
$865$	−29719.1	−1.16818
$866$	−2714.34	−0.106509
$867$	−14979.1	−0.586757
$868$	0	0
$869$	−18681.5	−0.729260
$870$	−3439.78	−0.134045
$871$	−73207.1	−2.84791
$872$	7374.52	0.286391
$873$	−21361.3	−0.828146
$874$	−3562.05	−0.137858
$875$	0	0
$876$	−3201.20	−0.123468
$877$	−30920.7	−1.19055	−0.595277	−	0.803520i	$-0.702958\pi$
$877$	−30920.7	−1.19055	−0.595277	+	0.803520i	$0.702958\pi$
$878$	−1506.28	−0.0578981
$879$	33764.9	1.29563
$880$	−39010.4	−1.49436
$881$	11625.1	0.444563	0.222282	−	0.974982i	$-0.428650\pi$
$881$	11625.1	0.444563	0.222282	+	0.974982i	$0.428650\pi$
$882$	0	0
$883$	17129.2	0.652825	0.326412	−	0.945227i	$-0.394160\pi$
$883$	17129.2	0.652825	0.326412	+	0.945227i	$0.394160\pi$
$884$	12502.8	0.475695
$885$	−51064.2	−1.93955
$886$	−8250.07	−0.312829
$887$	28053.0	1.06192	0.530962	−	0.847396i	$-0.321831\pi$
$887$	28053.0	1.06192	0.530962	+	0.847396i	$0.321831\pi$
$888$	−23225.2	−0.877688
$889$	0	0
$890$	−20472.1	−0.771041
$891$	−7679.83	−0.288759
$892$	23488.7	0.881681
$893$	1785.25	0.0668993
$894$	11356.2	0.424840
$895$	36735.4	1.37199
$896$	0	0
$897$	20472.5	0.762047
$898$	−10962.7	−0.407385
$899$	−4903.19	−0.181903
$900$	25922.9	0.960108
$901$	−10210.7	−0.377545
$902$	19703.0	0.727317
$903$	0	0
$904$	6347.43	0.233531
$905$	2483.31	0.0912132
$906$	−1344.56	−0.0493047
$907$	43900.8	1.60717	0.803585	−	0.595191i	$-0.202923\pi$
$907$	43900.8	1.60717	0.803585	+	0.595191i	$0.202923\pi$
$908$	2379.44	0.0869654
$909$	18860.5	0.688189
$910$	0	0
$911$	16538.5	0.601477	0.300739	−	0.953707i	$-0.402767\pi$
$911$	16538.5	0.601477	0.300739	+	0.953707i	$0.402767\pi$
$912$	4420.76	0.160511
$913$	−43998.5	−1.59489
$914$	10669.1	0.386108
$915$	−32111.1	−1.16017
$916$	16982.6	0.612576
$917$	0	0
$918$	−4491.23	−0.161473
$919$	16243.6	0.583055	0.291528	−	0.956562i	$-0.405836\pi$
$919$	16243.6	0.583055	0.291528	+	0.956562i	$0.405836\pi$
$920$	−27269.7	−0.977233
$921$	−31175.6	−1.11539
$922$	119.314	0.00426182
$923$	42769.4	1.52521
$924$	0	0
$925$	−103443.	−3.67694
$926$	−4126.46	−0.146440
$927$	−13536.5	−0.479609
$928$	7326.08	0.259149
$929$	−37780.4	−1.33427	−0.667134	−	0.744937i	$-0.732479\pi$
$929$	−37780.4	−1.33427	−0.667134	+	0.744937i	$0.732479\pi$
$930$	9708.74	0.342325
$931$	0	0
$932$	620.686	0.0218146
$933$	−22280.9	−0.781826
$934$	−23121.4	−0.810016
$935$	30951.1	1.08258
$936$	−17956.8	−0.627069
$937$	38269.3	1.33426	0.667131	−	0.744941i	$-0.267522\pi$
$937$	38269.3	1.33426	0.667131	+	0.744941i	$0.267522\pi$
$938$	0	0
$939$	7635.04	0.265346
$940$	6190.96	0.214816
$941$	−37786.0	−1.30902	−0.654510	−	0.756053i	$-0.727125\pi$
$941$	−37786.0	−1.30902	−0.654510	+	0.756053i	$0.727125\pi$
$942$	4974.47	0.172056
$943$	−22518.0	−0.777609
$944$	23861.3	0.822690
$945$	0	0
$946$	21566.1	0.741198
$947$	−25836.1	−0.886548	−0.443274	−	0.896386i	$-0.646183\pi$
$947$	−25836.1	−0.886548	−0.443274	+	0.896386i	$0.646183\pi$
$948$	7341.55	0.251521
$949$	9876.37	0.337830
$950$	−12043.2	−0.411297
$951$	−31063.4	−1.05920
$952$	0	0
$953$	−30233.4	−1.02766	−0.513828	−	0.857893i	$-0.671773\pi$
$953$	−30233.4	−1.02766	−0.513828	+	0.857893i	$0.671773\pi$
$954$	6642.89	0.225442
$955$	76927.0	2.60660
$956$	−36803.5	−1.24509
$957$	−8801.06	−0.297281
$958$	5268.26	0.177672
$959$	0	0
$960$	4006.87	0.134710
$961$	−15951.8	−0.535456
$962$	32458.2	1.08783
$963$	1744.14	0.0583636
$964$	−39132.6	−1.30745
$965$	−95109.9	−3.17274
$966$	0	0
$967$	−25472.9	−0.847109	−0.423555	−	0.905871i	$-0.639218\pi$
$967$	−25472.9	−0.847109	−0.423555	+	0.905871i	$0.639218\pi$
$968$	38222.6	1.26913
$969$	−3507.46	−0.116280
$970$	34414.7	1.13916
$971$	40795.5	1.34829	0.674145	−	0.738599i	$-0.264512\pi$
$971$	40795.5	1.34829	0.674145	+	0.738599i	$0.264512\pi$
$972$	−23237.0	−0.766798
$973$	0	0
$974$	6641.18	0.218478
$975$	69216.8	2.27355
$976$	15004.9	0.492105
$977$	−15791.6	−0.517112	−0.258556	−	0.965996i	$-0.583247\pi$
$977$	−15791.6	−0.517112	−0.258556	+	0.965996i	$0.583247\pi$
$978$	−5976.40	−0.195403
$979$	−52380.2	−1.70999
$980$	0	0
$981$	−6223.38	−0.202546
$982$	−4819.24	−0.156607
$983$	−4830.09	−0.156720	−0.0783601	−	0.996925i	$-0.524968\pi$
$983$	−4830.09	−0.156720	−0.0783601	+	0.996925i	$0.524968\pi$
$984$	−17093.5	−0.553780
$985$	66726.8	2.15847
$986$	−1275.28	−0.0411897
$987$	0	0
$988$	−18202.4	−0.586129
$989$	−24647.1	−0.792451
$990$	−20136.2	−0.646434
$991$	27586.7	0.884277	0.442139	−	0.896947i	$-0.354220\pi$
$991$	27586.7	0.884277	0.442139	+	0.896947i	$0.354220\pi$
$992$	−20677.8	−0.661816
$993$	−8092.36	−0.258614
$994$	0	0
$995$	−81935.7	−2.61059
$996$	17290.7	0.550078
$997$	−46244.7	−1.46899	−0.734495	−	0.678614i	$-0.762581\pi$
$997$	−46244.7	−1.46899	−0.734495	+	0.678614i	$0.762581\pi$
$998$	7313.50	0.231969
$999$	56162.3	1.77868

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.h.1.14	yes	35
7.6	odd	2		2303.4.a.g.1.14	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.g.1.14	✓	35	7.6	odd	2
2303.4.a.h.1.14	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)

\(f(q)\)	\(=\)	\(q-1.17274 q^{2} +3.53925 q^{3} -6.62469 q^{4} -19.8836 q^{5} -4.15061 q^{6} +17.1509 q^{8} -14.4737 q^{9} +O(q^{10})\)	\(q-1.17274 q^{2} +3.53925 q^{3} -6.62469 q^{4} -19.8836 q^{5} -4.15061 q^{6} +17.1509 q^{8} -14.4737 q^{9} +23.3182 q^{10} +59.6624 q^{11} -23.4464 q^{12} +72.3372 q^{13} -70.3730 q^{15} +32.8840 q^{16} -26.0904 q^{17} +16.9739 q^{18} +37.9840 q^{19} +131.723 q^{20} -69.9684 q^{22} +79.9645 q^{23} +60.7014 q^{24} +270.358 q^{25} -84.8326 q^{26} -146.786 q^{27} -41.6796 q^{29} +82.5291 q^{30} +117.640 q^{31} -175.772 q^{32} +211.160 q^{33} +30.5971 q^{34} +95.8838 q^{36} -382.614 q^{37} -44.5453 q^{38} +256.019 q^{39} -341.022 q^{40} -281.599 q^{41} -308.226 q^{43} -395.245 q^{44} +287.790 q^{45} -93.7774 q^{46} +47.0000 q^{47} +116.385 q^{48} -317.058 q^{50} -92.3403 q^{51} -479.211 q^{52} +391.360 q^{53} +172.141 q^{54} -1186.30 q^{55} +134.435 q^{57} +48.8792 q^{58} +725.622 q^{59} +466.199 q^{60} +456.298 q^{61} -137.961 q^{62} -56.9376 q^{64} -1438.32 q^{65} -247.636 q^{66} -1012.03 q^{67} +172.840 q^{68} +283.014 q^{69} +591.250 q^{71} -248.238 q^{72} +136.532 q^{73} +448.706 q^{74} +956.863 q^{75} -251.632 q^{76} -300.244 q^{78} -313.120 q^{79} -653.851 q^{80} -128.721 q^{81} +330.242 q^{82} -737.457 q^{83} +518.770 q^{85} +361.468 q^{86} -147.514 q^{87} +1023.27 q^{88} -877.943 q^{89} -337.502 q^{90} -529.740 q^{92} +416.358 q^{93} -55.1187 q^{94} -755.260 q^{95} -622.100 q^{96} +1475.87 q^{97} -863.537 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9}+O(q^{10}) \) 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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