LMFDB - Embedded newform 2303.4.a.n.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2303, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2303.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2303 = 7^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2303.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$135.881398743$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-5.07646 q^{2} +5.02841 q^{3} +17.7704 q^{4} +1.46556 q^{5} -25.5265 q^{6} -49.5992 q^{8} -1.71512 q^{9} +O(q^{10})$	\(q-5.07646 q^{2} +5.02841 q^{3} +17.7704 q^{4} +1.46556 q^{5} -25.5265 q^{6} -49.5992 q^{8} -1.71512 q^{9} -7.43986 q^{10} +27.0052 q^{11} +89.3570 q^{12} -84.3300 q^{13} +7.36944 q^{15} +109.625 q^{16} +83.9638 q^{17} +8.70672 q^{18} -87.1095 q^{19} +26.0436 q^{20} -137.091 q^{22} +49.7968 q^{23} -249.405 q^{24} -122.852 q^{25} +428.098 q^{26} -144.391 q^{27} +103.187 q^{29} -37.4106 q^{30} +230.822 q^{31} -159.712 q^{32} +135.793 q^{33} -426.239 q^{34} -30.4783 q^{36} +67.2519 q^{37} +442.208 q^{38} -424.046 q^{39} -72.6906 q^{40} -92.4762 q^{41} -227.516 q^{43} +479.893 q^{44} -2.51361 q^{45} -252.792 q^{46} -47.0000 q^{47} +551.238 q^{48} +623.654 q^{50} +422.204 q^{51} -1498.58 q^{52} +173.972 q^{53} +732.996 q^{54} +39.5777 q^{55} -438.022 q^{57} -523.823 q^{58} -287.714 q^{59} +130.958 q^{60} +402.328 q^{61} -1171.76 q^{62} -66.2270 q^{64} -123.591 q^{65} -689.348 q^{66} -699.292 q^{67} +1492.07 q^{68} +250.399 q^{69} +336.120 q^{71} +85.0683 q^{72} +684.233 q^{73} -341.401 q^{74} -617.751 q^{75} -1547.97 q^{76} +2152.65 q^{78} -986.826 q^{79} +160.662 q^{80} -679.750 q^{81} +469.452 q^{82} -107.589 q^{83} +123.054 q^{85} +1154.98 q^{86} +518.865 q^{87} -1339.43 q^{88} -1508.19 q^{89} +12.7602 q^{90} +884.911 q^{92} +1160.67 q^{93} +238.594 q^{94} -127.664 q^{95} -803.096 q^{96} +1783.50 q^{97} -46.3170 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9}+O(q^{10}) $ 68 * q - 2 * q^2 + 24 * q^3 + 254 * q^4 + 40 * q^5 + 48 * q^6 - 66 * q^8 + 576 * q^9	\( 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9} + 200 q^{10} - 20 q^{11} + 288 q^{12} + 520 q^{13} + 88 q^{15} + 1062 q^{16} + 784 q^{17} - 2 q^{18} + 532 q^{19} + 400 q^{20} - 4 q^{22} - 268 q^{23} + 576 q^{24} + 1864 q^{25} + 312 q^{26} + 864 q^{27} + 200 q^{29} + 792 q^{30} + 936 q^{31} + 30 q^{32} + 2112 q^{33} + 1088 q^{34} + 2130 q^{36} - 356 q^{37} + 1192 q^{38} - 488 q^{39} + 2400 q^{40} + 1476 q^{41} - 92 q^{43} + 192 q^{44} + 1848 q^{45} - 424 q^{46} - 3196 q^{47} + 2688 q^{48} - 1338 q^{50} - 148 q^{51} + 4980 q^{52} - 80 q^{53} + 4944 q^{54} + 2200 q^{55} + 2244 q^{57} - 356 q^{58} + 560 q^{59} - 736 q^{60} + 3944 q^{61} + 1488 q^{62} + 3778 q^{64} + 2004 q^{65} - 1000 q^{66} + 2768 q^{67} + 8192 q^{68} + 2208 q^{69} - 2448 q^{71} - 5234 q^{72} + 9532 q^{73} - 2000 q^{74} + 11136 q^{75} + 6384 q^{76} - 3460 q^{78} - 1520 q^{79} + 616 q^{80} + 6976 q^{81} + 4976 q^{82} + 3320 q^{83} + 3244 q^{85} - 2892 q^{86} + 2360 q^{87} - 2868 q^{88} + 8152 q^{89} + 5400 q^{90} - 4684 q^{92} + 2840 q^{93} + 94 q^{94} - 4256 q^{95} + 5376 q^{96} + 13968 q^{97} + 2380 q^{99}+O(q^{100}) \) 68 * q - 2 * q^2 + 24 * q^3 + 254 * q^4 + 40 * q^5 + 48 * q^6 - 66 * q^8 + 576 * q^9 + 200 * q^10 - 20 * q^11 + 288 * q^12 + 520 * q^13 + 88 * q^15 + 1062 * q^16 + 784 * q^17 - 2 * q^18 + 532 * q^19 + 400 * q^20 - 4 * q^22 - 268 * q^23 + 576 * q^24 + 1864 * q^25 + 312 * q^26 + 864 * q^27 + 200 * q^29 + 792 * q^30 + 936 * q^31 + 30 * q^32 + 2112 * q^33 + 1088 * q^34 + 2130 * q^36 - 356 * q^37 + 1192 * q^38 - 488 * q^39 + 2400 * q^40 + 1476 * q^41 - 92 * q^43 + 192 * q^44 + 1848 * q^45 - 424 * q^46 - 3196 * q^47 + 2688 * q^48 - 1338 * q^50 - 148 * q^51 + 4980 * q^52 - 80 * q^53 + 4944 * q^54 + 2200 * q^55 + 2244 * q^57 - 356 * q^58 + 560 * q^59 - 736 * q^60 + 3944 * q^61 + 1488 * q^62 + 3778 * q^64 + 2004 * q^65 - 1000 * q^66 + 2768 * q^67 + 8192 * q^68 + 2208 * q^69 - 2448 * q^71 - 5234 * q^72 + 9532 * q^73 - 2000 * q^74 + 11136 * q^75 + 6384 * q^76 - 3460 * q^78 - 1520 * q^79 + 616 * q^80 + 6976 * q^81 + 4976 * q^82 + 3320 * q^83 + 3244 * q^85 - 2892 * q^86 + 2360 * q^87 - 2868 * q^88 + 8152 * q^89 + 5400 * q^90 - 4684 * q^92 + 2840 * q^93 + 94 * q^94 - 4256 * q^95 + 5376 * q^96 + 13968 * q^97 + 2380 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−5.07646	−1.79480	−0.897400	−	0.441219i	$-0.854546\pi$
$2$	−5.07646	−1.79480	−0.897400	+	0.441219i	$0.854546\pi$
$3$	5.02841	0.967718	0.483859	−	0.875146i	$-0.339235\pi$
$3$	5.02841	0.967718	0.483859	+	0.875146i	$0.339235\pi$
$4$	17.7704	2.22130
$5$	1.46556	0.131084	0.0655419	−	0.997850i	$-0.479122\pi$
$5$	1.46556	0.131084	0.0655419	+	0.997850i	$0.479122\pi$
$6$	−25.5265	−1.73686
$7$	0	0
$7$	0	0
$8$	−49.5992	−2.19199
$9$	−1.71512	−0.0635228
$10$	−7.43986	−0.235269
$11$	27.0052	0.740215	0.370107	−	0.928989i	$-0.379321\pi$
$11$	27.0052	0.740215	0.370107	+	0.928989i	$0.379321\pi$
$12$	89.3570	2.14959
$13$	−84.3300	−1.79915	−0.899575	−	0.436767i	$-0.856123\pi$
$13$	−84.3300	−1.79915	−0.899575	+	0.436767i	$0.856123\pi$
$14$	0	0
$15$	7.36944	0.126852
$16$	109.625	1.71289
$17$	83.9638	1.19790	0.598948	−	0.800788i	$-0.295586\pi$
$17$	83.9638	1.19790	0.598948	+	0.800788i	$0.295586\pi$
$18$	8.70672	0.114011
$19$	−87.1095	−1.05180	−0.525902	−	0.850545i	$-0.676272\pi$
$19$	−87.1095	−1.05180	−0.525902	+	0.850545i	$0.676272\pi$
$20$	26.0436	0.291177
$21$	0	0
$22$	−137.091	−1.32854
$23$	49.7968	0.451450	0.225725	−	0.974191i	$-0.427525\pi$
$23$	49.7968	0.451450	0.225725	+	0.974191i	$0.427525\pi$
$24$	−249.405	−2.12123
$25$	−122.852	−0.982817
$26$	428.098	3.22911
$27$	−144.391	−1.02919
$28$	0	0
$29$	103.187	0.660734	0.330367	−	0.943853i	$-0.392827\pi$
$29$	103.187	0.660734	0.330367	+	0.943853i	$0.392827\pi$
$30$	−37.4106	−0.227674
$31$	230.822	1.33732	0.668659	−	0.743569i	$-0.266869\pi$
$31$	230.822	1.33732	0.668659	+	0.743569i	$0.266869\pi$
$32$	−159.712	−0.882292
$33$	135.793	0.716319
$34$	−426.239	−2.14998
$35$	0	0
$36$	−30.4783	−0.141103
$37$	67.2519	0.298815	0.149407	−	0.988776i	$-0.452263\pi$
$37$	67.2519	0.298815	0.149407	+	0.988776i	$0.452263\pi$
$38$	442.208	1.88778
$39$	−424.046	−1.74107
$40$	−72.6906	−0.287335
$41$	−92.4762	−0.352253	−0.176126	−	0.984368i	$-0.556357\pi$
$41$	−92.4762	−0.352253	−0.176126	+	0.984368i	$0.556357\pi$
$42$	0	0
$43$	−227.516	−0.806880	−0.403440	−	0.915006i	$-0.632186\pi$
$43$	−227.516	−0.806880	−0.403440	+	0.915006i	$0.632186\pi$
$44$	479.893	1.64424
$45$	−2.51361	−0.00832681
$46$	−252.792	−0.810263
$47$	−47.0000	−0.145865
$47$	−47.0000	−0.145865
$48$	551.238	1.65759
$49$	0	0
$50$	623.654	1.76396
$51$	422.204	1.15922
$52$	−1498.58	−3.99646
$53$	173.972	0.450884	0.225442	−	0.974257i	$-0.427617\pi$
$53$	173.972	0.450884	0.225442	+	0.974257i	$0.427617\pi$
$54$	732.996	1.84719
$55$	39.5777	0.0970301
$56$	0	0
$57$	−438.022	−1.01785
$58$	−523.823	−1.18589
$59$	−287.714	−0.634866	−0.317433	−	0.948281i	$-0.602821\pi$
$59$	−287.714	−0.634866	−0.317433	+	0.948281i	$0.602821\pi$
$60$	130.958	0.281777
$61$	402.328	0.844472	0.422236	−	0.906486i	$-0.361245\pi$
$61$	402.328	0.844472	0.422236	+	0.906486i	$0.361245\pi$
$62$	−1171.76	−2.40022
$63$	0	0
$64$	−66.2270	−0.129350
$65$	−123.591	−0.235839
$66$	−689.348	−1.28565
$67$	−699.292	−1.27511	−0.637553	−	0.770406i	$-0.720053\pi$
$67$	−699.292	−1.27511	−0.637553	+	0.770406i	$0.720053\pi$
$68$	1492.07	2.66089
$69$	250.399	0.436876
$70$	0	0
$71$	336.120	0.561833	0.280917	−	0.959732i	$-0.409362\pi$
$71$	336.120	0.561833	0.280917	+	0.959732i	$0.409362\pi$
$72$	85.0683	0.139242
$73$	684.233	1.09703	0.548516	−	0.836140i	$-0.315193\pi$
$73$	684.233	1.09703	0.548516	+	0.836140i	$0.315193\pi$
$74$	−341.401	−0.536312
$75$	−617.751	−0.951089
$76$	−1547.97	−2.33638
$77$	0	0
$78$	2152.65	3.12487
$79$	−986.826	−1.40540	−0.702700	−	0.711486i	$-0.748022\pi$
$79$	−986.826	−1.40540	−0.702700	+	0.711486i	$0.748022\pi$
$80$	160.662	0.224531
$81$	−679.750	−0.932442
$82$	469.452	0.632223
$83$	−107.589	−0.142282	−0.0711411	−	0.997466i	$-0.522664\pi$
$83$	−107.589	−0.142282	−0.0711411	+	0.997466i	$0.522664\pi$
$84$	0	0
$85$	123.054	0.157025
$86$	1154.98	1.44819
$87$	518.865	0.639404
$88$	−1339.43	−1.62255
$89$	−1508.19	−1.79627	−0.898135	−	0.439720i	$-0.855078\pi$
$89$	−1508.19	−1.79627	−0.898135	+	0.439720i	$0.855078\pi$
$90$	12.7602	0.0149449
$91$	0	0
$92$	884.911	1.00281
$93$	1160.67	1.29415
$94$	238.594	0.261798
$95$	−127.664	−0.137874
$96$	−803.096	−0.853809
$97$	1783.50	1.86687	0.933436	−	0.358744i	$-0.116795\pi$
$97$	1783.50	1.86687	0.933436	+	0.358744i	$0.116795\pi$
$98$	0	0
$99$	−46.3170	−0.0470205
$100$	−2183.14	−2.18314
$101$	991.190	0.976506	0.488253	−	0.872702i	$-0.337634\pi$
$101$	991.190	0.976506	0.488253	+	0.872702i	$0.337634\pi$
$102$	−2143.30	−2.08057
$103$	1321.67	1.26435	0.632176	−	0.774825i	$-0.282162\pi$
$103$	1321.67	1.26435	0.632176	+	0.774825i	$0.282162\pi$
$104$	4182.70	3.94373
$105$	0	0
$106$	−883.161	−0.809247
$107$	−734.714	−0.663808	−0.331904	−	0.943313i	$-0.607691\pi$
$107$	−734.714	−0.663808	−0.331904	+	0.943313i	$0.607691\pi$
$108$	−2565.90	−2.28614
$109$	1088.66	0.956652	0.478326	−	0.878182i	$-0.341244\pi$
$109$	1088.66	0.956652	0.478326	+	0.878182i	$0.341244\pi$
$110$	−200.915	−0.174150
$111$	338.170	0.289168
$112$	0	0
$113$	1672.24	1.39213	0.696067	−	0.717977i	$-0.254932\pi$
$113$	1672.24	1.39213	0.696067	+	0.717977i	$0.254932\pi$
$114$	2223.60	1.82684
$115$	72.9803	0.0591778
$116$	1833.67	1.46769
$117$	144.636	0.114287
$118$	1460.57	1.13946
$119$	0	0
$120$	−365.518	−0.278059
$121$	−601.721	−0.452082
$122$	−2042.40	−1.51566
$123$	−465.008	−0.340881
$124$	4101.80	2.97059
$125$	−363.242	−0.259915
$126$	0	0
$127$	1604.00	1.12073	0.560363	−	0.828247i	$-0.310662\pi$
$127$	1604.00	1.12073	0.560363	+	0.828247i	$0.310662\pi$
$128$	1613.89	1.11445
$129$	−1144.04	−0.780832
$130$	627.403	0.423284
$131$	1565.90	1.04438	0.522188	−	0.852830i	$-0.325116\pi$
$131$	1565.90	1.04438	0.522188	+	0.852830i	$0.325116\pi$
$132$	2413.10	1.59116
$133$	0	0
$134$	3549.93	2.28856
$135$	−211.614	−0.134910
$136$	−4164.54	−2.62578
$137$	−2402.41	−1.49819	−0.749095	−	0.662462i	$-0.769512\pi$
$137$	−2402.41	−1.49819	−0.749095	+	0.662462i	$0.769512\pi$
$138$	−1271.14	−0.784105
$139$	59.2423	0.0361501	0.0180751	−	0.999837i	$-0.494246\pi$
$139$	59.2423	0.0361501	0.0180751	+	0.999837i	$0.494246\pi$
$140$	0	0
$141$	−236.335	−0.141156
$142$	−1706.30	−1.00838
$143$	−2277.35	−1.33176
$144$	−188.019	−0.108807
$145$	151.226	0.0866115
$146$	−3473.48	−1.96895
$147$	0	0
$148$	1195.09	0.663758
$149$	2379.99	1.30857	0.654283	−	0.756250i	$-0.272970\pi$
$149$	2379.99	1.30857	0.654283	+	0.756250i	$0.272970\pi$
$150$	3135.99	1.70701
$151$	2233.14	1.20351	0.601756	−	0.798680i	$-0.294468\pi$
$151$	2233.14	1.20351	0.601756	+	0.798680i	$0.294468\pi$
$152$	4320.56	2.30555
$153$	−144.008	−0.0760937
$154$	0	0
$155$	338.284	0.175301
$156$	−7535.48	−3.86744
$157$	916.274	0.465775	0.232887	−	0.972504i	$-0.425183\pi$
$157$	916.274	0.465775	0.232887	+	0.972504i	$0.425183\pi$
$158$	5009.58	2.52241
$159$	874.801	0.436329
$160$	−234.067	−0.115654
$161$	0	0
$162$	3450.72	1.67355
$163$	−222.676	−0.107002	−0.0535011	−	0.998568i	$-0.517038\pi$
$163$	−222.676	−0.107002	−0.0535011	+	0.998568i	$0.517038\pi$
$164$	−1643.34	−0.782460
$165$	199.013	0.0938978
$166$	546.171	0.255368
$167$	1178.70	0.546169	0.273085	−	0.961990i	$-0.411956\pi$
$167$	1178.70	0.546169	0.273085	+	0.961990i	$0.411956\pi$
$168$	0	0
$169$	4914.55	2.23694
$170$	−624.679	−0.281828
$171$	149.403	0.0668136
$172$	−4043.06	−1.79233
$173$	469.104	0.206158	0.103079	−	0.994673i	$-0.467131\pi$
$173$	469.104	0.206158	0.103079	+	0.994673i	$0.467131\pi$
$174$	−2634.00	−1.14760
$175$	0	0
$176$	2960.43	1.26790
$177$	−1446.74	−0.614371
$178$	7656.27	3.22394
$179$	2366.26	0.988057	0.494029	−	0.869446i	$-0.335524\pi$
$179$	2366.26	0.988057	0.494029	+	0.869446i	$0.335524\pi$
$180$	−44.6679	−0.0184964
$181$	−1175.59	−0.482770	−0.241385	−	0.970429i	$-0.577602\pi$
$181$	−1175.59	−0.482770	−0.241385	+	0.970429i	$0.577602\pi$
$182$	0	0
$183$	2023.07	0.817210
$184$	−2469.88	−0.989577
$185$	98.5617	0.0391697
$186$	−5892.08	−2.32273
$187$	2267.46	0.886700
$188$	−835.210	−0.324010
$189$	0	0
$190$	648.082	0.247457
$191$	−2973.11	−1.12632	−0.563159	−	0.826349i	$-0.690414\pi$
$191$	−2973.11	−1.12632	−0.563159	+	0.826349i	$0.690414\pi$
$192$	−333.016	−0.125174
$193$	4814.64	1.79568	0.897839	−	0.440325i	$-0.145137\pi$
$193$	4814.64	1.79568	0.897839	+	0.440325i	$0.145137\pi$
$194$	−9053.84	−3.35066
$195$	−621.465	−0.228226
$196$	0	0
$197$	165.199	0.0597460	0.0298730	−	0.999554i	$-0.490490\pi$
$197$	165.199	0.0597460	0.0298730	+	0.999554i	$0.490490\pi$
$198$	235.126	0.0843924
$199$	−2218.58	−0.790307	−0.395154	−	0.918615i	$-0.629309\pi$
$199$	−2218.58	−0.790307	−0.395154	+	0.918615i	$0.629309\pi$
$200$	6093.36	2.15433
$201$	−3516.33	−1.23394
$202$	−5031.74	−1.75263
$203$	0	0
$204$	7502.75	2.57499
$205$	−135.529	−0.0461746
$206$	−6709.41	−2.26926
$207$	−85.4074	−0.0286774
$208$	−9244.66	−3.08174
$209$	−2352.41	−0.778562
$210$	0	0
$211$	−209.672	−0.0684095	−0.0342048	−	0.999415i	$-0.510890\pi$
$211$	−209.672	−0.0684095	−0.0342048	+	0.999415i	$0.510890\pi$
$212$	3091.55	1.00155
$213$	1690.15	0.543696
$214$	3729.74	1.19140
$215$	−333.438	−0.105769
$216$	7161.69	2.25598
$217$	0	0
$218$	−5526.56	−1.71700
$219$	3440.60	1.06162
$220$	703.313	0.215533
$221$	−7080.67	−2.15519
$222$	−1716.71	−0.518999
$223$	−4381.10	−1.31561	−0.657804	−	0.753189i	$-0.728514\pi$
$223$	−4381.10	−1.31561	−0.657804	+	0.753189i	$0.728514\pi$
$224$	0	0
$225$	210.706	0.0624313
$226$	−8489.06	−2.49860
$227$	−1801.27	−0.526671	−0.263335	−	0.964704i	$-0.584823\pi$
$227$	−1801.27	−0.526671	−0.263335	+	0.964704i	$0.584823\pi$
$228$	−7783.84	−2.26095
$229$	3284.31	0.947743	0.473872	−	0.880594i	$-0.342856\pi$
$229$	3284.31	0.947743	0.473872	+	0.880594i	$0.342856\pi$
$230$	−370.481	−0.106212
$231$	0	0
$232$	−5117.98	−1.44833
$233$	2039.58	0.573466	0.286733	−	0.958011i	$-0.407431\pi$
$233$	2039.58	0.573466	0.286733	+	0.958011i	$0.407431\pi$
$234$	−734.238	−0.205122
$235$	−68.8813	−0.0191205
$236$	−5112.79	−1.41023
$237$	−4962.16	−1.36003
$238$	0	0
$239$	69.6411	0.0188482	0.00942408	−	0.999956i	$-0.497000\pi$
$239$	69.6411	0.0188482	0.00942408	+	0.999956i	$0.497000\pi$
$240$	807.872	0.217283
$241$	−4652.16	−1.24345	−0.621726	−	0.783235i	$-0.713568\pi$
$241$	−4652.16	−1.24345	−0.621726	+	0.783235i	$0.713568\pi$
$242$	3054.61	0.811396
$243$	480.504	0.126849
$244$	7149.54	1.87583
$245$	0	0
$246$	2360.59	0.611813
$247$	7345.95	1.89235
$248$	−11448.6	−2.93139
$249$	−541.001	−0.137689
$250$	1843.98	0.466495
$251$	−2805.33	−0.705462	−0.352731	−	0.935725i	$-0.614747\pi$
$251$	−2805.33	−0.705462	−0.352731	+	0.935725i	$0.614747\pi$
$252$	0	0
$253$	1344.77	0.334170
$254$	−8142.66	−2.01148
$255$	618.766	0.151955
$256$	−7663.05	−1.87086
$257$	−6729.84	−1.63345	−0.816723	−	0.577030i	$-0.804212\pi$
$257$	−6729.84	−1.63345	−0.816723	+	0.577030i	$0.804212\pi$
$258$	5807.69	1.40144
$259$	0	0
$260$	−2196.26	−0.523870
$261$	−176.977	−0.0419717
$262$	−7949.22	−1.87445
$263$	4064.88	0.953047	0.476523	−	0.879162i	$-0.341897\pi$
$263$	4064.88	0.953047	0.476523	+	0.879162i	$0.341897\pi$
$264$	−6735.22	−1.57017
$265$	254.966	0.0591036
$266$	0	0
$267$	−7583.80	−1.73828
$268$	−12426.7	−2.83240
$269$	2681.54	0.607793	0.303897	−	0.952705i	$-0.401712\pi$
$269$	2681.54	0.607793	0.303897	+	0.952705i	$0.401712\pi$
$270$	1074.25	0.242136
$271$	−3672.49	−0.823202	−0.411601	−	0.911364i	$-0.635030\pi$
$271$	−3672.49	−0.823202	−0.411601	+	0.911364i	$0.635030\pi$
$272$	9204.51	2.05186
$273$	0	0
$274$	12195.8	2.68895
$275$	−3317.64	−0.727496
$276$	4449.69	0.970435
$277$	656.371	0.142374	0.0711868	−	0.997463i	$-0.477321\pi$
$277$	656.371	0.142374	0.0711868	+	0.997463i	$0.477321\pi$
$278$	−300.741	−0.0648822
$279$	−395.886	−0.0849502
$280$	0	0
$281$	−49.5220	−0.0105133	−0.00525664	−	0.999986i	$-0.501673\pi$
$281$	−49.5220	−0.0105133	−0.00525664	+	0.999986i	$0.501673\pi$
$282$	1199.75	0.253347
$283$	4515.48	0.948471	0.474236	−	0.880398i	$-0.342724\pi$
$283$	4515.48	0.948471	0.474236	+	0.880398i	$0.342724\pi$
$284$	5973.00	1.24800
$285$	−641.948	−0.133424
$286$	11560.9	2.39024
$287$	0	0
$288$	273.924	0.0560457
$289$	2136.93	0.434953
$290$	−767.694	−0.155450
$291$	8968.14	1.80660
$292$	12159.1	2.43684
$293$	1870.46	0.372947	0.186473	−	0.982460i	$-0.440294\pi$
$293$	1870.46	0.372947	0.186473	+	0.982460i	$0.440294\pi$
$294$	0	0
$295$	−421.662	−0.0832206
$296$	−3335.64	−0.655000
$297$	−3899.31	−0.761822
$298$	−12081.9	−2.34861
$299$	−4199.37	−0.812227
$300$	−10977.7	−2.11266
$301$	0	0
$302$	−11336.4	−2.16006
$303$	4984.11	0.944982
$304$	−9549.35	−1.80162
$305$	589.636	0.110696
$306$	731.049	0.136573
$307$	6990.45	1.29956	0.649782	−	0.760120i	$-0.274860\pi$
$307$	6990.45	1.29956	0.649782	+	0.760120i	$0.274860\pi$
$308$	0	0
$309$	6645.91	1.22354
$310$	−1717.28	−0.314629
$311$	5704.11	1.04003	0.520017	−	0.854156i	$-0.325926\pi$
$311$	5704.11	1.04003	0.520017	+	0.854156i	$0.325926\pi$
$312$	21032.3	3.81641
$313$	5705.14	1.03027	0.515134	−	0.857110i	$-0.327742\pi$
$313$	5705.14	1.03027	0.515134	+	0.857110i	$0.327742\pi$
$314$	−4651.43	−0.835972
$315$	0	0
$316$	−17536.3	−3.12182
$317$	−418.743	−0.0741924	−0.0370962	−	0.999312i	$-0.511811\pi$
$317$	−418.743	−0.0741924	−0.0370962	+	0.999312i	$0.511811\pi$
$318$	−4440.89	−0.783122
$319$	2786.57	0.489085
$320$	−97.0596	−0.0169556
$321$	−3694.44	−0.642378
$322$	0	0
$323$	−7314.05	−1.25995
$324$	−12079.5	−2.07124
$325$	10360.1	1.76823
$326$	1130.41	0.192047
$327$	5474.25	0.925769
$328$	4586.74	0.772136
$329$	0	0
$330$	−1010.28	−0.168528
$331$	3048.43	0.506215	0.253107	−	0.967438i	$-0.418547\pi$
$331$	3048.43	0.506215	0.253107	+	0.967438i	$0.418547\pi$
$332$	−1911.90	−0.316052
$333$	−115.345	−0.0189815
$334$	−5983.60	−0.980264
$335$	−1024.85	−0.167146
$336$	0	0
$337$	−5206.00	−0.841510	−0.420755	−	0.907174i	$-0.638235\pi$
$337$	−5206.00	−0.841510	−0.420755	+	0.907174i	$0.638235\pi$
$338$	−24948.5	−4.01486
$339$	8408.71	1.34719
$340$	2186.72	0.348799
$341$	6233.39	0.989903
$342$	−758.438	−0.119917
$343$	0	0
$344$	11284.6	1.76868
$345$	366.975	0.0572674
$346$	−2381.39	−0.370012
$347$	−10607.4	−1.64102	−0.820509	−	0.571633i	$-0.806310\pi$
$347$	−10607.4	−1.64102	−0.820509	+	0.571633i	$0.806310\pi$
$348$	9220.45	1.42031
$349$	2342.44	0.359277	0.179639	−	0.983733i	$-0.442507\pi$
$349$	2342.44	0.359277	0.179639	+	0.983733i	$0.442507\pi$
$350$	0	0
$351$	12176.5	1.85167
$352$	−4313.05	−0.653086
$353$	4450.82	0.671086	0.335543	−	0.942025i	$-0.391080\pi$
$353$	4450.82	0.671086	0.335543	+	0.942025i	$0.391080\pi$
$354$	7344.32	1.10267
$355$	492.605	0.0736472
$356$	−26801.2	−3.99006
$357$	0	0
$358$	−12012.2	−1.77336
$359$	1554.84	0.228584	0.114292	−	0.993447i	$-0.463540\pi$
$359$	1554.84	0.228584	0.114292	+	0.993447i	$0.463540\pi$
$360$	124.673	0.0182523
$361$	729.064	0.106293
$362$	5967.86	0.866474
$363$	−3025.70	−0.437487
$364$	0	0
$365$	1002.78	0.143803
$366$	−10270.0	−1.46673
$367$	2251.61	0.320254	0.160127	−	0.987096i	$-0.448810\pi$
$367$	2251.61	0.320254	0.160127	+	0.987096i	$0.448810\pi$
$368$	5458.96	0.773283
$369$	158.607	0.0223761
$370$	−500.344	−0.0703018
$371$	0	0
$372$	20625.5	2.87469
$373$	−3319.85	−0.460845	−0.230423	−	0.973091i	$-0.574011\pi$
$373$	−3319.85	−0.460845	−0.230423	+	0.973091i	$0.574011\pi$
$374$	−11510.7	−1.59145
$375$	−1826.53	−0.251524
$376$	2331.16	0.319735
$377$	−8701.74	−1.18876
$378$	0	0
$379$	−2757.83	−0.373774	−0.186887	−	0.982381i	$-0.559840\pi$
$379$	−2757.83	−0.373774	−0.186887	+	0.982381i	$0.559840\pi$
$380$	−2268.65	−0.306261
$381$	8065.58	1.08455
$382$	15092.9	2.02151
$383$	12672.5	1.69069	0.845345	−	0.534220i	$-0.179395\pi$
$383$	12672.5	1.69069	0.845345	+	0.534220i	$0.179395\pi$
$384$	8115.31	1.07847
$385$	0	0
$386$	−24441.3	−3.22288
$387$	390.216	0.0512553
$388$	31693.5	4.14689
$389$	−2055.72	−0.267941	−0.133970	−	0.990985i	$-0.542773\pi$
$389$	−2055.72	−0.267941	−0.133970	+	0.990985i	$0.542773\pi$
$390$	3154.84	0.409619
$391$	4181.13	0.540790
$392$	0	0
$393$	7873.98	1.01066
$394$	−838.627	−0.107232
$395$	−1446.25	−0.184225
$396$	−823.073	−0.104447
$397$	174.673	0.0220821	0.0110410	−	0.999939i	$-0.496485\pi$
$397$	174.673	0.0220821	0.0110410	+	0.999939i	$0.496485\pi$
$398$	11262.5	1.41844
$399$	0	0
$400$	−13467.6	−1.68345
$401$	−5699.47	−0.709771	−0.354885	−	0.934910i	$-0.615480\pi$
$401$	−5699.47	−0.709771	−0.354885	+	0.934910i	$0.615480\pi$
$402$	17850.5	2.21468
$403$	−19465.2	−2.40603
$404$	17613.9	2.16912
$405$	−996.215	−0.122228
$406$	0	0
$407$	1816.15	0.221187
$408$	−20941.0	−2.54101
$409$	66.6772	0.00806106	0.00403053	−	0.999992i	$-0.498717\pi$
$409$	66.6772	0.00806106	0.00403053	+	0.999992i	$0.498717\pi$
$410$	688.010	0.0828741
$411$	−12080.3	−1.44983
$412$	23486.7	2.80851
$413$	0	0
$414$	433.567	0.0514702
$415$	−157.678	−0.0186509
$416$	13468.5	1.58737
$417$	297.895	0.0349831
$418$	11941.9	1.39736
$419$	2049.10	0.238915	0.119457	−	0.992839i	$-0.461885\pi$
$419$	2049.10	0.238915	0.119457	+	0.992839i	$0.461885\pi$
$420$	0	0
$421$	13427.4	1.55442	0.777212	−	0.629239i	$-0.216633\pi$
$421$	13427.4	1.55442	0.777212	+	0.629239i	$0.216633\pi$
$422$	1064.39	0.122781
$423$	80.6105	0.00926576
$424$	−8628.86	−0.988336
$425$	−10315.1	−1.17731
$426$	−8579.98	−0.975825
$427$	0	0
$428$	−13056.2	−1.47452
$429$	−11451.4	−1.28876
$430$	1692.69	0.189834
$431$	15111.9	1.68890	0.844451	−	0.535633i	$-0.179927\pi$
$431$	15111.9	1.68890	0.844451	+	0.535633i	$0.179927\pi$
$432$	−15828.9	−1.76288
$433$	−1573.89	−0.174680	−0.0873399	−	0.996179i	$-0.527837\pi$
$433$	−1573.89	−0.174680	−0.0873399	+	0.996179i	$0.527837\pi$
$434$	0	0
$435$	760.428	0.0838155
$436$	19346.0	2.12502
$437$	−4337.78	−0.474838
$438$	−17466.1	−1.90539
$439$	2071.25	0.225183	0.112591	−	0.993641i	$-0.464085\pi$
$439$	2071.25	0.225183	0.112591	+	0.993641i	$0.464085\pi$
$440$	−1963.02	−0.212690
$441$	0	0
$442$	35944.7	3.86814
$443$	8902.07	0.954740	0.477370	−	0.878702i	$-0.341590\pi$
$443$	8902.07	0.954740	0.477370	+	0.878702i	$0.341590\pi$
$444$	6009.42	0.642330
$445$	−2210.35	−0.235462
$446$	22240.5	2.36125
$447$	11967.6	1.26632
$448$	0	0
$449$	−3600.46	−0.378433	−0.189216	−	0.981935i	$-0.560595\pi$
$449$	−3600.46	−0.378433	−0.189216	+	0.981935i	$0.560595\pi$
$450$	−1069.64	−0.112052
$451$	−2497.34	−0.260743
$452$	29716.4	3.09235
$453$	11229.1	1.16466
$454$	9144.06	0.945268
$455$	0	0
$456$	21725.5	2.23112
$457$	12345.5	1.26368	0.631838	−	0.775101i	$-0.282301\pi$
$457$	12345.5	1.26368	0.631838	+	0.775101i	$0.282301\pi$
$458$	−16672.7	−1.70101
$459$	−12123.6	−1.23286
$460$	1296.89	0.131452
$461$	12044.3	1.21683	0.608415	−	0.793619i	$-0.291806\pi$
$461$	12044.3	1.21683	0.608415	+	0.793619i	$0.291806\pi$
$462$	0	0
$463$	−15962.5	−1.60224	−0.801122	−	0.598502i	$-0.795763\pi$
$463$	−15962.5	−1.60224	−0.801122	+	0.598502i	$0.795763\pi$
$464$	11311.8	1.13176
$465$	1701.03	0.169641
$466$	−10353.9	−1.02926
$467$	14030.6	1.39028	0.695139	−	0.718875i	$-0.255343\pi$
$467$	14030.6	1.39028	0.695139	+	0.718875i	$0.255343\pi$
$468$	2570.24	0.253866
$469$	0	0
$470$	349.673	0.0343175
$471$	4607.40	0.450738
$472$	14270.4	1.39162
$473$	−6144.11	−0.597265
$474$	25190.2	2.44098
$475$	10701.6	1.03373
$476$	0	0
$477$	−298.382	−0.0286414
$478$	−353.530	−0.0338287
$479$	−17372.0	−1.65709	−0.828547	−	0.559919i	$-0.810832\pi$
$479$	−17372.0	−1.65709	−0.828547	+	0.559919i	$0.810832\pi$
$480$	−1176.99	−0.111920
$481$	−5671.35	−0.537612
$482$	23616.5	2.23175
$483$	0	0
$484$	−10692.8	−1.00421
$485$	2613.82	0.244716
$486$	−2439.26	−0.227669
$487$	7538.20	0.701414	0.350707	−	0.936485i	$-0.385941\pi$
$487$	7538.20	0.701414	0.350707	+	0.936485i	$0.385941\pi$
$488$	−19955.1	−1.85108
$489$	−1119.71	−0.103548
$490$	0	0
$491$	−6806.05	−0.625565	−0.312783	−	0.949825i	$-0.601261\pi$
$491$	−6806.05	−0.625565	−0.312783	+	0.949825i	$0.601261\pi$
$492$	−8263.39	−0.757200
$493$	8663.95	0.791490
$494$	−37291.4	−3.39639
$495$	−67.8804	−0.00616363
$496$	25303.8	2.29067
$497$	0	0
$498$	2746.37	0.247124
$499$	17697.0	1.58763	0.793814	−	0.608160i	$-0.208092\pi$
$499$	17697.0	1.58763	0.793814	+	0.608160i	$0.208092\pi$
$500$	−6454.97	−0.577350
$501$	5926.96	0.528537
$502$	14241.1	1.26616
$503$	6244.47	0.553533	0.276766	−	0.960937i	$-0.410737\pi$
$503$	6244.47	0.553533	0.276766	+	0.960937i	$0.410737\pi$
$504$	0	0
$505$	1452.65	0.128004
$506$	−6826.68	−0.599769
$507$	24712.4	2.16472
$508$	28503.8	2.48947
$509$	−20082.2	−1.74878	−0.874389	−	0.485226i	$-0.838737\pi$
$509$	−20082.2	−1.74878	−0.874389	+	0.485226i	$0.838737\pi$
$510$	−3141.14	−0.272729
$511$	0	0
$512$	25990.0	2.24337
$513$	12577.9	1.08251
$514$	34163.7	2.93171
$515$	1936.99	0.165736
$516$	−20330.1	−1.73447
$517$	−1269.24	−0.107971
$518$	0	0
$519$	2358.85	0.199503
$520$	6130.00	0.516958
$521$	14545.7	1.22315	0.611573	−	0.791188i	$-0.290537\pi$
$521$	14545.7	1.22315	0.611573	+	0.791188i	$0.290537\pi$
$522$	898.417	0.0753308
$523$	22484.9	1.87991	0.939957	−	0.341293i	$-0.110865\pi$
$523$	22484.9	1.87991	0.939957	+	0.341293i	$0.110865\pi$
$524$	27826.7	2.31988
$525$	0	0
$526$	−20635.2	−1.71053
$527$	19380.7	1.60197
$528$	14886.3	1.22697
$529$	−9687.27	−0.796193
$530$	−1294.33	−0.106079
$531$	493.462	0.0403285
$532$	0	0
$533$	7798.52	0.633755
$534$	38498.9	3.11987
$535$	−1076.77	−0.0870144
$536$	34684.3	2.79503
$537$	11898.5	0.956160
$538$	−13612.7	−1.09087
$539$	0	0
$540$	−3760.47	−0.299676
$541$	−74.7106	−0.00593727	−0.00296863	−	0.999996i	$-0.500945\pi$
$541$	−74.7106	−0.00593727	−0.00296863	+	0.999996i	$0.500945\pi$
$542$	18643.2	1.47748
$543$	−5911.37	−0.467185
$544$	−13410.0	−1.05689
$545$	1595.50	0.125402
$546$	0	0
$547$	12317.8	0.962833	0.481416	−	0.876492i	$-0.340122\pi$
$547$	12317.8	0.962833	0.481416	+	0.876492i	$0.340122\pi$
$548$	−42691.9	−3.32794
$549$	−690.039	−0.0536432
$550$	16841.9	1.30571
$551$	−8988.54	−0.694963
$552$	−12419.6	−0.957631
$553$	0	0
$554$	−3332.04	−0.255532
$555$	495.608	0.0379052
$556$	1052.76	0.0803004
$557$	−3153.95	−0.239923	−0.119962	−	0.992779i	$-0.538277\pi$
$557$	−3153.95	−0.239923	−0.119962	+	0.992779i	$0.538277\pi$
$558$	2009.70	0.152469
$559$	19186.4	1.45170
$560$	0	0
$561$	11401.7	0.858075
$562$	251.396	0.0188692
$563$	3039.61	0.227539	0.113769	−	0.993507i	$-0.463707\pi$
$563$	3039.61	0.227539	0.113769	+	0.993507i	$0.463707\pi$
$564$	−4199.78	−0.313551
$565$	2450.77	0.182486
$566$	−22922.6	−1.70232
$567$	0	0
$568$	−16671.3	−1.23154
$569$	24351.2	1.79412	0.897062	−	0.441905i	$-0.145697\pi$
$569$	24351.2	1.79412	0.897062	+	0.441905i	$0.145697\pi$
$570$	3258.82	0.239468
$571$	6636.54	0.486394	0.243197	−	0.969977i	$-0.421804\pi$
$571$	6636.54	0.486394	0.243197	+	0.969977i	$0.421804\pi$
$572$	−40469.4	−2.95824
$573$	−14950.0	−1.08996
$574$	0	0
$575$	−6117.65	−0.443693
$576$	113.587	0.00821665
$577$	14784.4	1.06669	0.533347	−	0.845897i	$-0.320934\pi$
$577$	14784.4	1.06669	0.533347	+	0.845897i	$0.320934\pi$
$578$	−10848.0	−0.780654
$579$	24210.0	1.73771
$580$	2687.36	0.192390
$581$	0	0
$582$	−45526.4	−3.24249
$583$	4698.14	0.333751
$584$	−33937.4	−2.40469
$585$	211.973	0.0149812
$586$	−9495.31	−0.669364
$587$	18363.2	1.29119	0.645597	−	0.763679i	$-0.276609\pi$
$587$	18363.2	1.29119	0.645597	+	0.763679i	$0.276609\pi$
$588$	0	0
$589$	−20106.8	−1.40660
$590$	2140.55	0.149364
$591$	830.689	0.0578172
$592$	7372.47	0.511835
$593$	−2708.49	−0.187562	−0.0937810	−	0.995593i	$-0.529895\pi$
$593$	−2708.49	−0.187562	−0.0937810	+	0.995593i	$0.529895\pi$
$594$	19794.7	1.36732
$595$	0	0
$596$	42293.4	2.90672
$597$	−11155.9	−0.764794
$598$	21317.9	1.45778
$599$	−18245.5	−1.24456	−0.622281	−	0.782794i	$-0.713794\pi$
$599$	−18245.5	−1.24456	−0.622281	+	0.782794i	$0.713794\pi$
$600$	30639.9	2.08478
$601$	16099.2	1.09268	0.546341	−	0.837563i	$-0.316020\pi$
$601$	16099.2	1.09268	0.546341	+	0.837563i	$0.316020\pi$
$602$	0	0
$603$	1199.37	0.0809983
$604$	39683.8	2.67336
$605$	−881.858	−0.0592606
$606$	−25301.6	−1.69605
$607$	13587.4	0.908560	0.454280	−	0.890859i	$-0.349897\pi$
$607$	13587.4	0.908560	0.454280	+	0.890859i	$0.349897\pi$
$608$	13912.4	0.927999
$609$	0	0
$610$	−2993.26	−0.198678
$611$	3963.51	0.262433
$612$	−2559.08	−0.169027
$613$	−17686.0	−1.16530	−0.582651	−	0.812723i	$-0.697985\pi$
$613$	−17686.0	−1.16530	−0.582651	+	0.812723i	$0.697985\pi$
$614$	−35486.8	−2.33246
$615$	−681.497	−0.0446839
$616$	0	0
$617$	−25127.0	−1.63951	−0.819753	−	0.572718i	$-0.805889\pi$
$617$	−25127.0	−1.63951	−0.819753	+	0.572718i	$0.805889\pi$
$618$	−33737.7	−2.19600
$619$	−7442.38	−0.483254	−0.241627	−	0.970369i	$-0.577681\pi$
$619$	−7442.38	−0.483254	−0.241627	+	0.970369i	$0.577681\pi$
$620$	6011.44	0.389396
$621$	−7190.23	−0.464628
$622$	−28956.7	−1.86665
$623$	0	0
$624$	−46485.9	−2.98225
$625$	14824.2	0.948746
$626$	−28961.9	−1.84912
$627$	−11828.9	−0.753428
$628$	16282.6	1.03463
$629$	5646.72	0.357949
$630$	0	0
$631$	−729.980	−0.0460540	−0.0230270	−	0.999735i	$-0.507330\pi$
$631$	−729.980	−0.0460540	−0.0230270	+	0.999735i	$0.507330\pi$
$632$	48945.8	3.08063
$633$	−1054.32	−0.0662011
$634$	2125.73	0.133160
$635$	2350.76	0.146909
$636$	15545.6	0.969219
$637$	0	0
$638$	−14145.9	−0.877810
$639$	−576.485	−0.0356892
$640$	2365.26	0.146086
$641$	4347.69	0.267899	0.133950	−	0.990988i	$-0.457234\pi$
$641$	4347.69	0.267899	0.133950	+	0.990988i	$0.457234\pi$
$642$	18754.7	1.15294
$643$	−6782.91	−0.416006	−0.208003	−	0.978128i	$-0.566696\pi$
$643$	−6782.91	−0.416006	−0.208003	+	0.978128i	$0.566696\pi$
$644$	0	0
$645$	−1676.66	−0.102354
$646$	37129.5	2.26136
$647$	−11984.2	−0.728206	−0.364103	−	0.931359i	$-0.618624\pi$
$647$	−11984.2	−0.728206	−0.364103	+	0.931359i	$0.618624\pi$
$648$	33715.1	2.04391
$649$	−7769.75	−0.469938
$650$	−52592.7	−3.17363
$651$	0	0
$652$	−3957.05	−0.237684
$653$	−12863.4	−0.770878	−0.385439	−	0.922733i	$-0.625950\pi$
$653$	−12863.4	−0.770878	−0.385439	+	0.922733i	$0.625950\pi$
$654$	−27789.8	−1.66157
$655$	2294.92	0.136901
$656$	−10137.7	−0.603369
$657$	−1173.54	−0.0696866
$658$	0	0
$659$	20202.1	1.19417	0.597087	−	0.802177i	$-0.296325\pi$
$659$	20202.1	1.19417	0.597087	+	0.802177i	$0.296325\pi$
$660$	3536.54	0.208575
$661$	25907.8	1.52450	0.762251	−	0.647282i	$-0.224094\pi$
$661$	25907.8	1.52450	0.762251	+	0.647282i	$0.224094\pi$
$662$	−15475.2	−0.908554
$663$	−35604.5	−2.08562
$664$	5336.33	0.311882
$665$	0	0
$666$	585.543	0.0340681
$667$	5138.37	0.298289
$668$	20945.9	1.21321
$669$	−22030.0	−1.27314
$670$	5202.63	0.299993
$671$	10864.9	0.625091
$672$	0	0
$673$	−17941.3	−1.02762	−0.513808	−	0.857905i	$-0.671766\pi$
$673$	−17941.3	−1.02762	−0.513808	+	0.857905i	$0.671766\pi$
$674$	26428.1	1.51034
$675$	17738.8	1.01151
$676$	87333.7	4.96892
$677$	−30911.3	−1.75483	−0.877414	−	0.479735i	$-0.840733\pi$
$677$	−30911.3	−1.75483	−0.877414	+	0.479735i	$0.840733\pi$
$678$	−42686.4	−2.41794
$679$	0	0
$680$	−6103.38	−0.344197
$681$	−9057.50	−0.509669
$682$	−31643.5	−1.77668
$683$	−28272.0	−1.58389	−0.791946	−	0.610591i	$-0.790932\pi$
$683$	−28272.0	−1.58389	−0.791946	+	0.610591i	$0.790932\pi$
$684$	2654.95	0.148413
$685$	−3520.88	−0.196388
$686$	0	0
$687$	16514.8	0.917148
$688$	−24941.4	−1.38209
$689$	−14671.1	−0.811208
$690$	−1862.93	−0.102783
$691$	−19023.1	−1.04729	−0.523643	−	0.851938i	$-0.675427\pi$
$691$	−19023.1	−1.04729	−0.523643	+	0.851938i	$0.675427\pi$
$692$	8336.18	0.457939
$693$	0	0
$694$	53847.9	2.94530
$695$	86.8232	0.00473869
$696$	−25735.3	−1.40157
$697$	−7764.66	−0.421962
$698$	−11891.3	−0.644830
$699$	10255.9	0.554953
$700$	0	0
$701$	−1383.86	−0.0745615	−0.0372807	−	0.999305i	$-0.511870\pi$
$701$	−1383.86	−0.0745615	−0.0372807	+	0.999305i	$0.511870\pi$
$702$	−61813.6	−3.32337
$703$	−5858.28	−0.314295
$704$	−1788.47	−0.0957465
$705$	−346.363	−0.0185033
$706$	−22594.4	−1.20446
$707$	0	0
$708$	−25709.2	−1.36471
$709$	10967.7	0.580962	0.290481	−	0.956881i	$-0.406185\pi$
$709$	10967.7	0.580962	0.290481	+	0.956881i	$0.406185\pi$
$710$	−2500.69	−0.132182
$711$	1692.52	0.0892750
$712$	74805.1	3.93741
$713$	11494.2	0.603733
$714$	0	0
$715$	−3337.59	−0.174572
$716$	42049.4	2.19478
$717$	350.184	0.0182397
$718$	−7893.10	−0.410262
$719$	22478.1	1.16591	0.582956	−	0.812504i	$-0.301896\pi$
$719$	22478.1	1.16591	0.582956	+	0.812504i	$0.301896\pi$
$720$	−275.553	−0.0142629
$721$	0	0
$722$	−3701.06	−0.190775
$723$	−23392.9	−1.20331
$724$	−20890.8	−1.07238
$725$	−12676.7	−0.649381
$726$	15359.8	0.785202
$727$	4388.63	0.223886	0.111943	−	0.993715i	$-0.464293\pi$
$727$	4388.63	0.223886	0.111943	+	0.993715i	$0.464293\pi$
$728$	0	0
$729$	20769.4	1.05520
$730$	−5090.59	−0.258098
$731$	−19103.1	−0.966558
$732$	35950.8	1.81527
$733$	22335.0	1.12546	0.562731	−	0.826640i	$-0.309751\pi$
$733$	22335.0	1.12546	0.562731	+	0.826640i	$0.309751\pi$
$734$	−11430.2	−0.574792
$735$	0	0
$736$	−7953.15	−0.398311
$737$	−18884.5	−0.943853
$738$	−805.164	−0.0401606
$739$	21968.2	1.09352	0.546761	−	0.837288i	$-0.315860\pi$
$739$	21968.2	1.09352	0.546761	+	0.837288i	$0.315860\pi$
$740$	1751.48	0.0870078
$741$	36938.4	1.83126
$742$	0	0
$743$	39791.5	1.96475	0.982374	−	0.186925i	$-0.0598523\pi$
$743$	39791.5	1.96475	0.982374	+	0.186925i	$0.0598523\pi$
$744$	−57568.1	−2.83676
$745$	3488.02	0.171532
$746$	16853.1	0.827124
$747$	184.528	0.00903817
$748$	40293.7	1.96963
$749$	0	0
$750$	9272.30	0.451436
$751$	−26854.5	−1.30484	−0.652421	−	0.757857i	$-0.726247\pi$
$751$	−26854.5	−1.30484	−0.652421	+	0.757857i	$0.726247\pi$
$752$	−5152.36	−0.249850
$753$	−14106.3	−0.682687
$754$	44174.0	2.13358
$755$	3272.80	0.157761
$756$	0	0
$757$	−28118.6	−1.35005	−0.675026	−	0.737794i	$-0.735868\pi$
$757$	−28118.6	−1.35005	−0.675026	+	0.737794i	$0.735868\pi$
$758$	14000.0	0.670849
$759$	6762.06	0.323383
$760$	6332.04	0.302220
$761$	34720.3	1.65389	0.826945	−	0.562283i	$-0.190077\pi$
$761$	34720.3	1.65389	0.826945	+	0.562283i	$0.190077\pi$
$762$	−40944.6	−1.94654
$763$	0	0
$764$	−52833.4	−2.50189
$765$	−211.052	−0.00997464
$766$	−64331.4	−3.03445
$767$	24262.9	1.14222
$768$	−38532.9	−1.81047
$769$	17833.5	0.836270	0.418135	−	0.908385i	$-0.362684\pi$
$769$	17833.5	0.836270	0.418135	+	0.908385i	$0.362684\pi$
$770$	0	0
$771$	−33840.4	−1.58071
$772$	85558.3	3.98874
$773$	25195.5	1.17234	0.586170	−	0.810188i	$-0.300635\pi$
$773$	25195.5	1.17234	0.586170	+	0.810188i	$0.300635\pi$
$774$	−1980.92	−0.0919930
$775$	−28357.0	−1.31434
$776$	−88459.9	−4.09217
$777$	0	0
$778$	10435.8	0.480900
$779$	8055.55	0.370501
$780$	−11043.7	−0.506959
$781$	9076.99	0.415877
$782$	−21225.4	−0.970610
$783$	−14899.3	−0.680021
$784$	0	0
$785$	1342.85	0.0610555
$786$	−39971.9	−1.81393
$787$	−1666.75	−0.0754931	−0.0377466	−	0.999287i	$-0.512018\pi$
$787$	−1666.75	−0.0754931	−0.0377466	+	0.999287i	$0.512018\pi$
$788$	2935.66	0.132714
$789$	20439.9	0.922280
$790$	7341.85	0.330647
$791$	0	0
$792$	2297.29	0.103069
$793$	−33928.3	−1.51933
$794$	−886.719	−0.0396328
$795$	1282.07	0.0571956
$796$	−39425.2	−1.75551
$797$	35690.7	1.58623	0.793117	−	0.609069i	$-0.208457\pi$
$797$	35690.7	1.58623	0.793117	+	0.609069i	$0.208457\pi$
$798$	0	0
$799$	−3946.30	−0.174731
$800$	19620.9	0.867132
$801$	2586.72	0.114104
$802$	28933.1	1.27390
$803$	18477.8	0.812040
$804$	−62486.6	−2.74096
$805$	0	0
$806$	98814.4	4.31835
$807$	13483.9	0.588172
$808$	−49162.2	−2.14050
$809$	−15577.1	−0.676959	−0.338480	−	0.940974i	$-0.609913\pi$
$809$	−15577.1	−0.676959	−0.338480	+	0.940974i	$0.609913\pi$
$810$	5057.24	0.219375
$811$	−26606.7	−1.15202	−0.576009	−	0.817443i	$-0.695391\pi$
$811$	−26606.7	−1.15202	−0.576009	+	0.817443i	$0.695391\pi$
$812$	0	0
$813$	−18466.8	−0.796627
$814$	−9219.60	−0.396986
$815$	−326.346	−0.0140262
$816$	46284.0	1.98562
$817$	19818.8	0.848680
$818$	−338.484	−0.0144680
$819$	0	0
$820$	−2408.42	−0.102568
$821$	6664.51	0.283305	0.141652	−	0.989916i	$-0.454759\pi$
$821$	6664.51	0.283305	0.141652	+	0.989916i	$0.454759\pi$
$822$	61325.2	2.60215
$823$	19484.9	0.825274	0.412637	−	0.910895i	$-0.364608\pi$
$823$	19484.9	0.825274	0.412637	+	0.910895i	$0.364608\pi$
$824$	−65553.9	−2.77145
$825$	−16682.5	−0.704011
$826$	0	0
$827$	−4836.52	−0.203364	−0.101682	−	0.994817i	$-0.532422\pi$
$827$	−4836.52	−0.203364	−0.101682	+	0.994817i	$0.532422\pi$
$828$	−1517.73	−0.0637012
$829$	−24300.8	−1.01810	−0.509049	−	0.860738i	$-0.670003\pi$
$829$	−24300.8	−1.01810	−0.509049	+	0.860738i	$0.670003\pi$
$830$	800.447	0.0334746
$831$	3300.50	0.137777
$832$	5584.92	0.232719
$833$	0	0
$834$	−1512.25	−0.0627877
$835$	1727.45	0.0715939
$836$	−41803.3	−1.72942
$837$	−33328.7	−1.37635
$838$	−10402.2	−0.428804
$839$	−19542.6	−0.804153	−0.402076	−	0.915606i	$-0.631711\pi$
$839$	−19542.6	−0.804153	−0.402076	+	0.915606i	$0.631711\pi$
$840$	0	0
$841$	−13741.5	−0.563430
$842$	−68163.8	−2.78988
$843$	−249.017	−0.0101739
$844$	−3725.96	−0.151958
$845$	7202.58	0.293226
$846$	−409.216	−0.0166302
$847$	0	0
$848$	19071.6	0.772314
$849$	22705.7	0.917852
$850$	52364.4	2.11304
$851$	3348.93	0.134900
$852$	30034.7	1.20771
$853$	11797.4	0.473547	0.236773	−	0.971565i	$-0.423910\pi$
$853$	11797.4	0.473547	0.236773	+	0.971565i	$0.423910\pi$
$854$	0	0
$855$	218.959	0.00875817
$856$	36441.2	1.45506
$857$	21668.0	0.863668	0.431834	−	0.901953i	$-0.357867\pi$
$857$	21668.0	0.863668	0.431834	+	0.901953i	$0.357867\pi$
$858$	58132.7	2.31307
$859$	−37235.9	−1.47902	−0.739508	−	0.673148i	$-0.764942\pi$
$859$	−37235.9	−1.47902	−0.739508	+	0.673148i	$0.764942\pi$
$860$	−5925.34	−0.234945
$861$	0	0
$862$	−76715.2	−3.03124
$863$	29664.7	1.17010	0.585050	−	0.810997i	$-0.301075\pi$
$863$	29664.7	1.17010	0.585050	+	0.810997i	$0.301075\pi$
$864$	23061.0	0.908046
$865$	687.500	0.0270239
$866$	7989.79	0.313515
$867$	10745.3	0.420912
$868$	0	0
$869$	−26649.4	−1.04030
$870$	−3860.28	−0.150432
$871$	58971.3	2.29411
$872$	−53996.8	−2.09698
$873$	−3058.90	−0.118589
$874$	22020.5	0.852238
$875$	0	0
$876$	61140.9	2.35817
$877$	−36204.0	−1.39398	−0.696991	−	0.717080i	$-0.745478\pi$
$877$	−36204.0	−1.39398	−0.696991	+	0.717080i	$0.745478\pi$
$878$	−10514.6	−0.404158
$879$	9405.43	0.360907
$880$	4338.69	0.166202
$881$	481.298	0.0184056	0.00920280	−	0.999958i	$-0.497071\pi$
$881$	481.298	0.0184056	0.00920280	+	0.999958i	$0.497071\pi$
$882$	0	0
$883$	1147.45	0.0437313	0.0218657	−	0.999761i	$-0.493039\pi$
$883$	1147.45	0.0437313	0.0218657	+	0.999761i	$0.493039\pi$
$884$	−125827.	−4.78734
$885$	−2120.29	−0.0805341
$886$	−45191.0	−1.71357
$887$	1968.25	0.0745066	0.0372533	−	0.999306i	$-0.488139\pi$
$887$	1968.25	0.0745066	0.0372533	+	0.999306i	$0.488139\pi$
$888$	−16772.9	−0.633855
$889$	0	0
$890$	11220.7	0.422606
$891$	−18356.8	−0.690208
$892$	−77854.1	−2.92236
$893$	4094.15	0.153421
$894$	−60752.8	−2.27279
$895$	3467.89	0.129518
$896$	0	0
$897$	−21116.1	−0.786006
$898$	18277.6	0.679210
$899$	23817.8	0.883611
$900$	3744.33	0.138679
$901$	14607.3	0.540112
$902$	12677.6	0.467981
$903$	0	0
$904$	−82941.7	−3.05155
$905$	−1722.91	−0.0632832
$906$	−57004.2	−2.09033
$907$	−14449.2	−0.528974	−0.264487	−	0.964389i	$-0.585203\pi$
$907$	−14449.2	−0.528974	−0.264487	+	0.964389i	$0.585203\pi$
$908$	−32009.3	−1.16990
$909$	−1700.01	−0.0620304
$910$	0	0
$911$	−41457.6	−1.50774	−0.753871	−	0.657023i	$-0.771816\pi$
$911$	−41457.6	−1.50774	−0.753871	+	0.657023i	$0.771816\pi$
$912$	−48018.0	−1.74346
$913$	−2905.46	−0.105319
$914$	−62671.6	−2.26804
$915$	2964.93	0.107123
$916$	58363.6	2.10523
$917$	0	0
$918$	61545.2	2.21274
$919$	−54466.9	−1.95506	−0.977529	−	0.210801i	$-0.932393\pi$
$919$	−54466.9	−1.95506	−0.977529	+	0.210801i	$0.932393\pi$
$920$	−3619.76	−0.129717
$921$	35150.9	1.25761
$922$	−61142.3	−2.18397
$923$	−28345.0	−1.01082
$924$	0	0
$925$	−8262.04	−0.293680
$926$	81032.8	2.87570
$927$	−2266.82	−0.0803152
$928$	−16480.1	−0.582960
$929$	2050.57	0.0724186	0.0362093	−	0.999344i	$-0.488472\pi$
$929$	2050.57	0.0724186	0.0362093	+	0.999344i	$0.488472\pi$
$930$	−8635.19	−0.304472
$931$	0	0
$932$	36244.3	1.27384
$933$	28682.6	1.00646
$934$	−71225.9	−2.49527
$935$	3323.10	0.116232
$936$	−7173.82	−0.250517
$937$	35025.8	1.22118	0.610589	−	0.791947i	$-0.290933\pi$
$937$	35025.8	1.22118	0.610589	+	0.791947i	$0.290933\pi$
$938$	0	0
$939$	28687.8	0.997008
$940$	−1224.05	−0.0424725
$941$	−26586.1	−0.921022	−0.460511	−	0.887654i	$-0.652334\pi$
$941$	−26586.1	−0.921022	−0.460511	+	0.887654i	$0.652334\pi$
$942$	−23389.3	−0.808985
$943$	−4605.02	−0.159025
$944$	−31540.5	−1.08745
$945$	0	0
$946$	31190.3	1.07197
$947$	51489.1	1.76681	0.883405	−	0.468610i	$-0.155245\pi$
$947$	51489.1	1.76681	0.883405	+	0.468610i	$0.155245\pi$
$948$	−88179.8	−3.02104
$949$	−57701.4	−1.97373
$950$	−54326.2	−1.85534
$951$	−2105.61	−0.0717972
$952$	0	0
$953$	43405.3	1.47538	0.737689	−	0.675141i	$-0.235917\pi$
$953$	43405.3	1.47538	0.737689	+	0.675141i	$0.235917\pi$
$954$	1514.72	0.0514056
$955$	−4357.27	−0.147642
$956$	1237.55	0.0418675
$957$	14012.0	0.473296
$958$	88188.4	2.97415
$959$	0	0
$960$	−488.055	−0.0164082
$961$	23487.8	0.788418
$962$	28790.4	0.964906
$963$	1260.12	0.0421669
$964$	−82670.8	−2.76208
$965$	7056.15	0.235384
$966$	0	0
$967$	−49132.2	−1.63390	−0.816952	−	0.576705i	$-0.804338\pi$
$967$	−49132.2	−1.63390	−0.816952	+	0.576705i	$0.804338\pi$
$968$	29844.9	0.990961
$969$	−36778.0	−1.21928
$970$	−13269.0	−0.439217
$971$	35687.1	1.17946	0.589729	−	0.807601i	$-0.299235\pi$
$971$	35687.1	1.17946	0.589729	+	0.807601i	$0.299235\pi$
$972$	8538.76	0.281771
$973$	0	0
$974$	−38267.4	−1.25890
$975$	52094.9	1.71115
$976$	44105.1	1.44648
$977$	18509.9	0.606126	0.303063	−	0.952971i	$-0.401991\pi$
$977$	18509.9	0.606126	0.303063	+	0.952971i	$0.401991\pi$
$978$	5684.15	0.185848
$979$	−40729.0	−1.32963
$980$	0	0
$981$	−1867.19	−0.0607693
$982$	34550.6	1.12276
$983$	2570.41	0.0834013	0.0417006	−	0.999130i	$-0.486722\pi$
$983$	2570.41	0.0834013	0.0417006	+	0.999130i	$0.486722\pi$
$984$	23064.0	0.747209
$985$	242.109	0.00783173
$986$	−43982.2	−1.42057
$987$	0	0
$988$	130541.	4.20349
$989$	−11329.6	−0.364266
$990$	344.592	0.0110625
$991$	55794.1	1.78845	0.894227	−	0.447614i	$-0.147726\pi$
$991$	55794.1	1.78845	0.894227	+	0.447614i	$0.147726\pi$
$992$	−36865.0	−1.17990
$993$	15328.8	0.489873
$994$	0	0
$995$	−3251.47	−0.103596
$996$	−9613.83	−0.305849
$997$	−56729.2	−1.80204	−0.901019	−	0.433779i	$-0.857180\pi$
$997$	−56729.2	−1.80204	−0.901019	+	0.433779i	$0.857180\pi$
$998$	−89838.1	−2.84947
$999$	−9710.59	−0.307537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.n.1.4	yes	68
7.6	odd	2		2303.4.a.m.1.4	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.m.1.4	✓	68	7.6	odd	2
2303.4.a.n.1.4	yes	68	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2303 = 7^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2303.a (trivial)

\(f(q)\)	\(=\)	\(q-5.07646 q^{2} +5.02841 q^{3} +17.7704 q^{4} +1.46556 q^{5} -25.5265 q^{6} -49.5992 q^{8} -1.71512 q^{9} +O(q^{10})\)	\(q-5.07646 q^{2} +5.02841 q^{3} +17.7704 q^{4} +1.46556 q^{5} -25.5265 q^{6} -49.5992 q^{8} -1.71512 q^{9} -7.43986 q^{10} +27.0052 q^{11} +89.3570 q^{12} -84.3300 q^{13} +7.36944 q^{15} +109.625 q^{16} +83.9638 q^{17} +8.70672 q^{18} -87.1095 q^{19} +26.0436 q^{20} -137.091 q^{22} +49.7968 q^{23} -249.405 q^{24} -122.852 q^{25} +428.098 q^{26} -144.391 q^{27} +103.187 q^{29} -37.4106 q^{30} +230.822 q^{31} -159.712 q^{32} +135.793 q^{33} -426.239 q^{34} -30.4783 q^{36} +67.2519 q^{37} +442.208 q^{38} -424.046 q^{39} -72.6906 q^{40} -92.4762 q^{41} -227.516 q^{43} +479.893 q^{44} -2.51361 q^{45} -252.792 q^{46} -47.0000 q^{47} +551.238 q^{48} +623.654 q^{50} +422.204 q^{51} -1498.58 q^{52} +173.972 q^{53} +732.996 q^{54} +39.5777 q^{55} -438.022 q^{57} -523.823 q^{58} -287.714 q^{59} +130.958 q^{60} +402.328 q^{61} -1171.76 q^{62} -66.2270 q^{64} -123.591 q^{65} -689.348 q^{66} -699.292 q^{67} +1492.07 q^{68} +250.399 q^{69} +336.120 q^{71} +85.0683 q^{72} +684.233 q^{73} -341.401 q^{74} -617.751 q^{75} -1547.97 q^{76} +2152.65 q^{78} -986.826 q^{79} +160.662 q^{80} -679.750 q^{81} +469.452 q^{82} -107.589 q^{83} +123.054 q^{85} +1154.98 q^{86} +518.865 q^{87} -1339.43 q^{88} -1508.19 q^{89} +12.7602 q^{90} +884.911 q^{92} +1160.67 q^{93} +238.594 q^{94} -127.664 q^{95} -803.096 q^{96} +1783.50 q^{97} -46.3170 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9}+O(q^{10}) \) 68 * q - 2 * q^2 + 24 * q^3 + 254 * q^4 + 40 * q^5 + 48 * q^6 - 66 * q^8 + 576 * q^9	\( 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9} + 200 q^{10} - 20 q^{11} + 288 q^{12} + 520 q^{13} + 88 q^{15} + 1062 q^{16} + 784 q^{17} - 2 q^{18} + 532 q^{19} + 400 q^{20} - 4 q^{22} - 268 q^{23} + 576 q^{24} + 1864 q^{25} + 312 q^{26} + 864 q^{27} + 200 q^{29} + 792 q^{30} + 936 q^{31} + 30 q^{32} + 2112 q^{33} + 1088 q^{34} + 2130 q^{36} - 356 q^{37} + 1192 q^{38} - 488 q^{39} + 2400 q^{40} + 1476 q^{41} - 92 q^{43} + 192 q^{44} + 1848 q^{45} - 424 q^{46} - 3196 q^{47} + 2688 q^{48} - 1338 q^{50} - 148 q^{51} + 4980 q^{52} - 80 q^{53} + 4944 q^{54} + 2200 q^{55} + 2244 q^{57} - 356 q^{58} + 560 q^{59} - 736 q^{60} + 3944 q^{61} + 1488 q^{62} + 3778 q^{64} + 2004 q^{65} - 1000 q^{66} + 2768 q^{67} + 8192 q^{68} + 2208 q^{69} - 2448 q^{71} - 5234 q^{72} + 9532 q^{73} - 2000 q^{74} + 11136 q^{75} + 6384 q^{76} - 3460 q^{78} - 1520 q^{79} + 616 q^{80} + 6976 q^{81} + 4976 q^{82} + 3320 q^{83} + 3244 q^{85} - 2892 q^{86} + 2360 q^{87} - 2868 q^{88} + 8152 q^{89} + 5400 q^{90} - 4684 q^{92} + 2840 q^{93} + 94 q^{94} - 4256 q^{95} + 5376 q^{96} + 13968 q^{97} + 2380 q^{99}+O(q^{100}) \) 68 * q - 2 * q^2 + 24 * q^3 + 254 * q^4 + 40 * q^5 + 48 * q^6 - 66 * q^8 + 576 * q^9 + 200 * q^10 - 20 * q^11 + 288 * q^12 + 520 * q^13 + 88 * q^15 + 1062 * q^16 + 784 * q^17 - 2 * q^18 + 532 * q^19 + 400 * q^20 - 4 * q^22 - 268 * q^23 + 576 * q^24 + 1864 * q^25 + 312 * q^26 + 864 * q^27 + 200 * q^29 + 792 * q^30 + 936 * q^31 + 30 * q^32 + 2112 * q^33 + 1088 * q^34 + 2130 * q^36 - 356 * q^37 + 1192 * q^38 - 488 * q^39 + 2400 * q^40 + 1476 * q^41 - 92 * q^43 + 192 * q^44 + 1848 * q^45 - 424 * q^46 - 3196 * q^47 + 2688 * q^48 - 1338 * q^50 - 148 * q^51 + 4980 * q^52 - 80 * q^53 + 4944 * q^54 + 2200 * q^55 + 2244 * q^57 - 356 * q^58 + 560 * q^59 - 736 * q^60 + 3944 * q^61 + 1488 * q^62 + 3778 * q^64 + 2004 * q^65 - 1000 * q^66 + 2768 * q^67 + 8192 * q^68 + 2208 * q^69 - 2448 * q^71 - 5234 * q^72 + 9532 * q^73 - 2000 * q^74 + 11136 * q^75 + 6384 * q^76 - 3460 * q^78 - 1520 * q^79 + 616 * q^80 + 6976 * q^81 + 4976 * q^82 + 3320 * q^83 + 3244 * q^85 - 2892 * q^86 + 2360 * q^87 - 2868 * q^88 + 8152 * q^89 + 5400 * q^90 - 4684 * q^92 + 2840 * q^93 + 94 * q^94 - 4256 * q^95 + 5376 * q^96 + 13968 * q^97 + 2380 * q^99

Introduction

L-functions

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Database

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