LMFDB - Embedded newform 2303.4.a.n.1.16

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			1.16
Character	$\chi$	$=$	2303.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.62360 q^{2} +1.56421 q^{3} +5.13048 q^{4} -17.7675 q^{5} -5.66806 q^{6} +10.3980 q^{8} -24.5533 q^{9} +O(q^{10})$	\(q-3.62360 q^{2} +1.56421 q^{3} +5.13048 q^{4} -17.7675 q^{5} -5.66806 q^{6} +10.3980 q^{8} -24.5533 q^{9} +64.3823 q^{10} +34.0020 q^{11} +8.02514 q^{12} +28.8758 q^{13} -27.7920 q^{15} -78.7220 q^{16} +50.2303 q^{17} +88.9712 q^{18} +103.137 q^{19} -91.1559 q^{20} -123.210 q^{22} +217.914 q^{23} +16.2646 q^{24} +190.684 q^{25} -104.634 q^{26} -80.6399 q^{27} -67.3685 q^{29} +100.707 q^{30} +79.9936 q^{31} +202.073 q^{32} +53.1861 q^{33} -182.015 q^{34} -125.970 q^{36} +277.041 q^{37} -373.727 q^{38} +45.1677 q^{39} -184.746 q^{40} -10.7967 q^{41} -47.4780 q^{43} +174.447 q^{44} +436.250 q^{45} -789.633 q^{46} -47.0000 q^{47} -123.137 q^{48} -690.963 q^{50} +78.5706 q^{51} +148.147 q^{52} -145.910 q^{53} +292.207 q^{54} -604.130 q^{55} +161.327 q^{57} +244.117 q^{58} +446.620 q^{59} -142.587 q^{60} +659.543 q^{61} -289.865 q^{62} -102.457 q^{64} -513.051 q^{65} -192.725 q^{66} +711.388 q^{67} +257.706 q^{68} +340.862 q^{69} -1052.67 q^{71} -255.304 q^{72} -702.486 q^{73} -1003.89 q^{74} +298.269 q^{75} +529.142 q^{76} -163.670 q^{78} -991.101 q^{79} +1398.69 q^{80} +536.801 q^{81} +39.1230 q^{82} +760.385 q^{83} -892.467 q^{85} +172.041 q^{86} -105.378 q^{87} +353.552 q^{88} -1161.20 q^{89} -1580.80 q^{90} +1118.00 q^{92} +125.126 q^{93} +170.309 q^{94} -1832.48 q^{95} +316.084 q^{96} -49.9378 q^{97} -834.859 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9}+O(q^{10}) $ 68 * q - 2 * q^2 + 24 * q^3 + 254 * q^4 + 40 * q^5 + 48 * q^6 - 66 * q^8 + 576 * q^9	\( 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9} + 200 q^{10} - 20 q^{11} + 288 q^{12} + 520 q^{13} + 88 q^{15} + 1062 q^{16} + 784 q^{17} - 2 q^{18} + 532 q^{19} + 400 q^{20} - 4 q^{22} - 268 q^{23} + 576 q^{24} + 1864 q^{25} + 312 q^{26} + 864 q^{27} + 200 q^{29} + 792 q^{30} + 936 q^{31} + 30 q^{32} + 2112 q^{33} + 1088 q^{34} + 2130 q^{36} - 356 q^{37} + 1192 q^{38} - 488 q^{39} + 2400 q^{40} + 1476 q^{41} - 92 q^{43} + 192 q^{44} + 1848 q^{45} - 424 q^{46} - 3196 q^{47} + 2688 q^{48} - 1338 q^{50} - 148 q^{51} + 4980 q^{52} - 80 q^{53} + 4944 q^{54} + 2200 q^{55} + 2244 q^{57} - 356 q^{58} + 560 q^{59} - 736 q^{60} + 3944 q^{61} + 1488 q^{62} + 3778 q^{64} + 2004 q^{65} - 1000 q^{66} + 2768 q^{67} + 8192 q^{68} + 2208 q^{69} - 2448 q^{71} - 5234 q^{72} + 9532 q^{73} - 2000 q^{74} + 11136 q^{75} + 6384 q^{76} - 3460 q^{78} - 1520 q^{79} + 616 q^{80} + 6976 q^{81} + 4976 q^{82} + 3320 q^{83} + 3244 q^{85} - 2892 q^{86} + 2360 q^{87} - 2868 q^{88} + 8152 q^{89} + 5400 q^{90} - 4684 q^{92} + 2840 q^{93} + 94 q^{94} - 4256 q^{95} + 5376 q^{96} + 13968 q^{97} + 2380 q^{99}+O(q^{100}) \) 68 * q - 2 * q^2 + 24 * q^3 + 254 * q^4 + 40 * q^5 + 48 * q^6 - 66 * q^8 + 576 * q^9 + 200 * q^10 - 20 * q^11 + 288 * q^12 + 520 * q^13 + 88 * q^15 + 1062 * q^16 + 784 * q^17 - 2 * q^18 + 532 * q^19 + 400 * q^20 - 4 * q^22 - 268 * q^23 + 576 * q^24 + 1864 * q^25 + 312 * q^26 + 864 * q^27 + 200 * q^29 + 792 * q^30 + 936 * q^31 + 30 * q^32 + 2112 * q^33 + 1088 * q^34 + 2130 * q^36 - 356 * q^37 + 1192 * q^38 - 488 * q^39 + 2400 * q^40 + 1476 * q^41 - 92 * q^43 + 192 * q^44 + 1848 * q^45 - 424 * q^46 - 3196 * q^47 + 2688 * q^48 - 1338 * q^50 - 148 * q^51 + 4980 * q^52 - 80 * q^53 + 4944 * q^54 + 2200 * q^55 + 2244 * q^57 - 356 * q^58 + 560 * q^59 - 736 * q^60 + 3944 * q^61 + 1488 * q^62 + 3778 * q^64 + 2004 * q^65 - 1000 * q^66 + 2768 * q^67 + 8192 * q^68 + 2208 * q^69 - 2448 * q^71 - 5234 * q^72 + 9532 * q^73 - 2000 * q^74 + 11136 * q^75 + 6384 * q^76 - 3460 * q^78 - 1520 * q^79 + 616 * q^80 + 6976 * q^81 + 4976 * q^82 + 3320 * q^83 + 3244 * q^85 - 2892 * q^86 + 2360 * q^87 - 2868 * q^88 + 8152 * q^89 + 5400 * q^90 - 4684 * q^92 + 2840 * q^93 + 94 * q^94 - 4256 * q^95 + 5376 * q^96 + 13968 * q^97 + 2380 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.62360	−1.28114	−0.640568	−	0.767901i	$-0.721301\pi$
$2$	−3.62360	−1.28114	−0.640568	+	0.767901i	$0.721301\pi$
$3$	1.56421	0.301032	0.150516	−	0.988608i	$-0.451907\pi$
$3$	1.56421	0.301032	0.150516	+	0.988608i	$0.451907\pi$
$4$	5.13048	0.641311
$5$	−17.7675	−1.58917	−0.794587	−	0.607150i	$-0.792313\pi$
$5$	−17.7675	−1.58917	−0.794587	+	0.607150i	$0.792313\pi$
$6$	−5.66806	−0.385663
$7$	0	0
$7$	0	0
$8$	10.3980	0.459530
$9$	−24.5533	−0.909380
$10$	64.3823	2.03595
$11$	34.0020	0.931998	0.465999	−	0.884785i	$-0.345695\pi$
$11$	34.0020	0.931998	0.465999	+	0.884785i	$0.345695\pi$
$12$	8.02514	0.193055
$13$	28.8758	0.616054	0.308027	−	0.951378i	$-0.400331\pi$
$13$	28.8758	0.616054	0.308027	+	0.951378i	$0.400331\pi$
$14$	0	0
$15$	−27.7920	−0.478392
$16$	−78.7220	−1.23003
$17$	50.2303	0.716626	0.358313	−	0.933602i	$-0.383352\pi$
$17$	50.2303	0.716626	0.358313	+	0.933602i	$0.383352\pi$
$18$	88.9712	1.16504
$19$	103.137	1.24533	0.622664	−	0.782490i	$-0.286051\pi$
$19$	103.137	1.24533	0.622664	+	0.782490i	$0.286051\pi$
$20$	−91.1559	−1.01915
$21$	0	0
$22$	−123.210	−1.19402
$23$	217.914	1.97557	0.987786	−	0.155814i	$-0.0498000\pi$
$23$	217.914	1.97557	0.987786	+	0.155814i	$0.0498000\pi$
$24$	16.2646	0.138333
$25$	190.684	1.52547
$26$	−104.634	−0.789249
$27$	−80.6399	−0.574784
$28$	0	0
$29$	−67.3685	−0.431380	−0.215690	−	0.976462i	$-0.569200\pi$
$29$	−67.3685	−0.431380	−0.215690	+	0.976462i	$0.569200\pi$
$30$	100.707	0.612885
$31$	79.9936	0.463460	0.231730	−	0.972780i	$-0.425561\pi$
$31$	79.9936	0.463460	0.231730	+	0.972780i	$0.425561\pi$
$32$	202.073	1.11631
$33$	53.1861	0.280561
$34$	−182.015	−0.918096
$35$	0	0
$36$	−125.970	−0.583195
$37$	277.041	1.23095	0.615477	−	0.788155i	$-0.288963\pi$
$37$	277.041	1.23095	0.615477	+	0.788155i	$0.288963\pi$
$38$	−373.727	−1.59543
$39$	45.1677	0.185452
$40$	−184.746	−0.730273
$41$	−10.7967	−0.0411259	−0.0205630	−	0.999789i	$-0.506546\pi$
$41$	−10.7967	−0.0411259	−0.0205630	+	0.999789i	$0.506546\pi$
$42$	0	0
$43$	−47.4780	−0.168380	−0.0841898	−	0.996450i	$-0.526830\pi$
$43$	−47.4780	−0.168380	−0.0841898	+	0.996450i	$0.526830\pi$
$44$	174.447	0.597701
$45$	436.250	1.44516
$46$	−789.633	−2.53098
$47$	−47.0000	−0.145865
$47$	−47.0000	−0.145865
$48$	−123.137	−0.370278
$49$	0	0
$50$	−690.963	−1.95434
$51$	78.5706	0.215727
$52$	148.147	0.395082
$53$	−145.910	−0.378156	−0.189078	−	0.981962i	$-0.560550\pi$
$53$	−145.910	−0.378156	−0.189078	+	0.981962i	$0.560550\pi$
$54$	292.207	0.736376
$55$	−604.130	−1.48111
$56$	0	0
$57$	161.327	0.374883
$58$	244.117	0.552656
$59$	446.620	0.985509	0.492754	−	0.870168i	$-0.335990\pi$
$59$	446.620	0.985509	0.492754	+	0.870168i	$0.335990\pi$
$60$	−142.587	−0.306798
$61$	659.543	1.38436	0.692179	−	0.721726i	$-0.256651\pi$
$61$	659.543	1.38436	0.692179	+	0.721726i	$0.256651\pi$
$62$	−289.865	−0.593756
$63$	0	0
$64$	−102.457	−0.200111
$65$	−513.051	−0.979017
$66$	−192.725	−0.359437
$67$	711.388	1.29716	0.648581	−	0.761145i	$-0.275363\pi$
$67$	711.388	1.29716	0.648581	+	0.761145i	$0.275363\pi$
$68$	257.706	0.459580
$69$	340.862	0.594710
$70$	0	0
$71$	−1052.67	−1.75956	−0.879779	−	0.475383i	$-0.842309\pi$
$71$	−1052.67	−1.75956	−0.879779	+	0.475383i	$0.842309\pi$
$72$	−255.304	−0.417887
$73$	−702.486	−1.12630	−0.563149	−	0.826356i	$-0.690410\pi$
$73$	−702.486	−1.12630	−0.563149	+	0.826356i	$0.690410\pi$
$74$	−1003.89	−1.57702
$75$	298.269	0.459216
$76$	529.142	0.798641
$77$	0	0
$78$	−163.670	−0.237589
$79$	−991.101	−1.41149	−0.705744	−	0.708467i	$-0.749387\pi$
$79$	−991.101	−1.41149	−0.705744	+	0.708467i	$0.749387\pi$
$80$	1398.69	1.95473
$81$	536.801	0.736352
$82$	39.1230	0.0526879
$83$	760.385	1.00558	0.502790	−	0.864409i	$-0.332307\pi$
$83$	760.385	1.00558	0.502790	+	0.864409i	$0.332307\pi$
$84$	0	0
$85$	−892.467	−1.13884
$86$	172.041	0.215717
$87$	−105.378	−0.129859
$88$	353.552	0.428281
$89$	−1161.20	−1.38300	−0.691502	−	0.722375i	$-0.743050\pi$
$89$	−1161.20	−1.38300	−0.691502	+	0.722375i	$0.743050\pi$
$90$	−1580.80	−1.85145
$91$	0	0
$92$	1118.00	1.26696
$93$	125.126	0.139516
$94$	170.309	0.186873
$95$	−1832.48	−1.97904
$96$	316.084	0.336044
$97$	−49.9378	−0.0522723	−0.0261361	−	0.999658i	$-0.508320\pi$
$97$	−49.9378	−0.0522723	−0.0261361	+	0.999658i	$0.508320\pi$
$98$	0	0
$99$	−834.859	−0.847541
$100$	978.302	0.978302
$101$	1149.16	1.13213	0.566066	−	0.824360i	$-0.308465\pi$
$101$	1149.16	1.13213	0.566066	+	0.824360i	$0.308465\pi$
$102$	−284.708	−0.276376
$103$	−1545.99	−1.47894	−0.739468	−	0.673191i	$-0.764923\pi$
$103$	−1545.99	−1.47894	−0.739468	+	0.673191i	$0.764923\pi$
$104$	300.250	0.283095
$105$	0	0
$106$	528.719	0.484469
$107$	−38.3170	−0.0346191	−0.0173095	−	0.999850i	$-0.505510\pi$
$107$	−38.3170	−0.0346191	−0.0173095	+	0.999850i	$0.505510\pi$
$108$	−413.722	−0.368615
$109$	1538.18	1.35166	0.675830	−	0.737058i	$-0.263785\pi$
$109$	1538.18	1.35166	0.675830	+	0.737058i	$0.263785\pi$
$110$	2189.13	1.89750
$111$	433.350	0.370556
$112$	0	0
$113$	−1321.48	−1.10012	−0.550062	−	0.835124i	$-0.685396\pi$
$113$	−1321.48	−1.10012	−0.550062	+	0.835124i	$0.685396\pi$
$114$	−584.586	−0.480276
$115$	−3871.78	−3.13953
$116$	−345.633	−0.276648
$117$	−708.995	−0.560227
$118$	−1618.37	−1.26257
$119$	0	0
$120$	−288.981	−0.219835
$121$	−174.865	−0.131379
$122$	−2389.92	−1.77355
$123$	−16.8883	−0.0123802
$124$	410.406	0.297222
$125$	−1167.04	−0.835069
$126$	0	0
$127$	154.727	0.108109	0.0540543	−	0.998538i	$-0.482786\pi$
$127$	154.727	0.108109	0.0540543	+	0.998538i	$0.482786\pi$
$128$	−1245.32	−0.859938
$129$	−74.2653	−0.0506876
$130$	1859.09	1.25425
$131$	2192.46	1.46226	0.731129	−	0.682239i	$-0.238994\pi$
$131$	2192.46	1.46226	0.731129	+	0.682239i	$0.238994\pi$
$132$	272.871	0.179927
$133$	0	0
$134$	−2577.79	−1.66184
$135$	1432.77	0.913431
$136$	522.294	0.329311
$137$	−432.499	−0.269714	−0.134857	−	0.990865i	$-0.543058\pi$
$137$	−432.499	−0.269714	−0.134857	+	0.990865i	$0.543058\pi$
$138$	−1235.15	−0.761904
$139$	3053.87	1.86350	0.931748	−	0.363105i	$-0.118283\pi$
$139$	3053.87	1.86350	0.931748	+	0.363105i	$0.118283\pi$
$140$	0	0
$141$	−73.5177	−0.0439100
$142$	3814.45	2.25423
$143$	981.834	0.574161
$144$	1932.88	1.11857
$145$	1196.97	0.685537
$146$	2545.53	1.44294
$147$	0	0
$148$	1421.36	0.789424
$149$	1058.33	0.581893	0.290947	−	0.956739i	$-0.406030\pi$
$149$	1058.33	0.581893	0.290947	+	0.956739i	$0.406030\pi$
$150$	−1080.81	−0.588318
$151$	−369.036	−0.198886	−0.0994428	−	0.995043i	$-0.531706\pi$
$151$	−369.036	−0.198886	−0.0994428	+	0.995043i	$0.531706\pi$
$152$	1072.41	0.572265
$153$	−1233.32	−0.651685
$154$	0	0
$155$	−1421.29	−0.736519
$156$	231.732	0.118932
$157$	457.474	0.232550	0.116275	−	0.993217i	$-0.462905\pi$
$157$	457.474	0.232550	0.116275	+	0.993217i	$0.462905\pi$
$158$	3591.35	1.80831
$159$	−228.233	−0.113837
$160$	−3590.34	−1.77401
$161$	0	0
$162$	−1945.15	−0.943367
$163$	−1432.85	−0.688524	−0.344262	−	0.938874i	$-0.611871\pi$
$163$	−1432.85	−0.688524	−0.344262	+	0.938874i	$0.611871\pi$
$164$	−55.3923	−0.0263745
$165$	−944.984	−0.445860
$166$	−2755.33	−1.28829
$167$	−679.964	−0.315073	−0.157537	−	0.987513i	$-0.550355\pi$
$167$	−679.964	−0.315073	−0.157537	+	0.987513i	$0.550355\pi$
$168$	0	0
$169$	−1363.19	−0.620477
$170$	3233.95	1.45901
$171$	−2532.35	−1.13248
$172$	−243.585	−0.107984
$173$	−2144.85	−0.942602	−0.471301	−	0.881972i	$-0.656215\pi$
$173$	−2144.85	−0.942602	−0.471301	+	0.881972i	$0.656215\pi$
$174$	381.849	0.166367
$175$	0	0
$176$	−2676.70	−1.14639
$177$	698.606	0.296669
$178$	4207.74	1.77182
$179$	2889.59	1.20658	0.603292	−	0.797521i	$-0.293855\pi$
$179$	2889.59	1.20658	0.603292	+	0.797521i	$0.293855\pi$
$180$	2238.17	0.926798
$181$	1569.82	0.644660	0.322330	−	0.946627i	$-0.395534\pi$
$181$	1569.82	0.644660	0.322330	+	0.946627i	$0.395534\pi$
$182$	0	0
$183$	1031.66	0.416736
$184$	2265.86	0.907835
$185$	−4922.33	−1.95620
$186$	−453.408	−0.178739
$187$	1707.93	0.667894
$188$	−241.133	−0.0935448
$189$	0	0
$190$	6640.19	2.53542
$191$	4244.97	1.60814	0.804072	−	0.594532i	$-0.202663\pi$
$191$	4244.97	1.60814	0.804072	+	0.594532i	$0.202663\pi$
$192$	−160.264	−0.0602399
$193$	844.547	0.314984	0.157492	−	0.987520i	$-0.449659\pi$
$193$	844.547	0.314984	0.157492	+	0.987520i	$0.449659\pi$
$194$	180.955	0.0669679
$195$	−802.517	−0.294715
$196$	0	0
$197$	1338.45	0.484064	0.242032	−	0.970268i	$-0.422186\pi$
$197$	1338.45	0.484064	0.242032	+	0.970268i	$0.422186\pi$
$198$	3025.20	1.08582
$199$	175.151	0.0623926	0.0311963	−	0.999513i	$-0.490068\pi$
$199$	175.151	0.0623926	0.0311963	+	0.999513i	$0.490068\pi$
$200$	1982.73	0.701001
$201$	1112.76	0.390487
$202$	−4164.08	−1.45041
$203$	0	0
$204$	403.105	0.138348
$205$	191.831	0.0653562
$206$	5602.04	1.89472
$207$	−5350.49	−1.79655
$208$	−2273.16	−0.757766
$209$	3506.86	1.16064
$210$	0	0
$211$	−258.317	−0.0842810	−0.0421405	−	0.999112i	$-0.513418\pi$
$211$	−258.317	−0.0842810	−0.0421405	+	0.999112i	$0.513418\pi$
$212$	−748.588	−0.242515
$213$	−1646.59	−0.529683
$214$	138.845	0.0443517
$215$	843.565	0.267584
$216$	−838.492	−0.264130
$217$	0	0
$218$	−5573.75	−1.73166
$219$	−1098.83	−0.339051
$220$	−3099.48	−0.949850
$221$	1450.44	0.441480
$222$	−1570.29	−0.474733
$223$	3492.54	1.04878	0.524390	−	0.851478i	$-0.324293\pi$
$223$	3492.54	1.04878	0.524390	+	0.851478i	$0.324293\pi$
$224$	0	0
$225$	−4681.92	−1.38724
$226$	4788.50	1.40941
$227$	−3080.06	−0.900576	−0.450288	−	0.892883i	$-0.648679\pi$
$227$	−3080.06	−0.900576	−0.450288	+	0.892883i	$0.648679\pi$
$228$	827.687	0.240416
$229$	−5733.19	−1.65441	−0.827205	−	0.561900i	$-0.810071\pi$
$229$	−5733.19	−1.65441	−0.827205	+	0.561900i	$0.810071\pi$
$230$	14029.8	4.02216
$231$	0	0
$232$	−700.496	−0.198232
$233$	−2537.83	−0.713558	−0.356779	−	0.934189i	$-0.616125\pi$
$233$	−2537.83	−0.713558	−0.356779	+	0.934189i	$0.616125\pi$
$234$	2569.11	0.717727
$235$	835.073	0.231805
$236$	2291.38	0.632017
$237$	−1550.29	−0.424903
$238$	0	0
$239$	−4379.92	−1.18541	−0.592706	−	0.805419i	$-0.701940\pi$
$239$	−4379.92	−1.18541	−0.592706	+	0.805419i	$0.701940\pi$
$240$	2187.84	0.588437
$241$	168.596	0.0450633	0.0225316	−	0.999746i	$-0.492827\pi$
$241$	168.596	0.0450633	0.0225316	+	0.999746i	$0.492827\pi$
$242$	633.642	0.168314
$243$	3016.94	0.796449
$244$	3383.78	0.887804
$245$	0	0
$246$	61.1964	0.0158607
$247$	2978.16	0.767189
$248$	831.771	0.212974
$249$	1189.40	0.302711
$250$	4228.90	1.06984
$251$	69.3734	0.0174455	0.00872273	−	0.999962i	$-0.497223\pi$
$251$	69.3734	0.0174455	0.00872273	+	0.999962i	$0.497223\pi$
$252$	0	0
$253$	7409.50	1.84123
$254$	−560.669	−0.138502
$255$	−1396.00	−0.342828
$256$	5332.21	1.30181
$257$	−4953.96	−1.20241	−0.601206	−	0.799094i	$-0.705313\pi$
$257$	−4953.96	−1.20241	−0.601206	+	0.799094i	$0.705313\pi$
$258$	269.108	0.0649377
$259$	0	0
$260$	−2632.20	−0.627854
$261$	1654.12	0.392288
$262$	−7944.59	−1.87335
$263$	750.692	0.176006	0.0880031	−	0.996120i	$-0.471951\pi$
$263$	750.692	0.176006	0.0880031	+	0.996120i	$0.471951\pi$
$264$	553.028	0.128926
$265$	2592.45	0.600955
$266$	0	0
$267$	−1816.36	−0.416328
$268$	3649.77	0.831884
$269$	−3301.13	−0.748228	−0.374114	−	0.927383i	$-0.622053\pi$
$269$	−3301.13	−0.748228	−0.374114	+	0.927383i	$0.622053\pi$
$270$	−5191.79	−1.17023
$271$	−631.727	−0.141604	−0.0708020	−	0.997490i	$-0.522556\pi$
$271$	−631.727	−0.141604	−0.0708020	+	0.997490i	$0.522556\pi$
$272$	−3954.23	−0.881472
$273$	0	0
$274$	1567.20	0.345541
$275$	6483.64	1.42174
$276$	1748.79	0.381394
$277$	5225.90	1.13355	0.566776	−	0.823872i	$-0.308190\pi$
$277$	5225.90	1.13355	0.566776	+	0.823872i	$0.308190\pi$
$278$	−11066.0	−2.38739
$279$	−1964.10	−0.421461
$280$	0	0
$281$	−4661.78	−0.989674	−0.494837	−	0.868986i	$-0.664772\pi$
$281$	−4661.78	−0.989674	−0.494837	+	0.868986i	$0.664772\pi$
$282$	266.399	0.0562547
$283$	2885.48	0.606092	0.303046	−	0.952976i	$-0.401996\pi$
$283$	2885.48	0.606092	0.303046	+	0.952976i	$0.401996\pi$
$284$	−5400.69	−1.12842
$285$	−2866.38	−0.595754
$286$	−3557.77	−0.735579
$287$	0	0
$288$	−4961.56	−1.01515
$289$	−2389.92	−0.486447
$290$	−4337.34	−0.878267
$291$	−78.1130	−0.0157356
$292$	−3604.09	−0.722307
$293$	8650.85	1.72487	0.862437	−	0.506165i	$-0.168937\pi$
$293$	8650.85	1.72487	0.862437	+	0.506165i	$0.168937\pi$
$294$	0	0
$295$	−7935.33	−1.56614
$296$	2880.67	0.565660
$297$	−2741.92	−0.535698
$298$	−3834.98	−0.745484
$299$	6292.43	1.21706
$300$	1530.27	0.294500
$301$	0	0
$302$	1337.24	0.254800
$303$	1797.52	0.340807
$304$	−8119.14	−1.53179
$305$	−11718.4	−2.19999
$306$	4469.05	0.834898
$307$	1676.84	0.311734	0.155867	−	0.987778i	$-0.450183\pi$
$307$	1676.84	0.311734	0.155867	+	0.987778i	$0.450183\pi$
$308$	0	0
$309$	−2418.24	−0.445207
$310$	5150.17	0.943581
$311$	−3163.80	−0.576857	−0.288428	−	0.957501i	$-0.593133\pi$
$311$	−3163.80	−0.576857	−0.288428	+	0.957501i	$0.593133\pi$
$312$	469.653	0.0852206
$313$	8809.38	1.59085	0.795425	−	0.606053i	$-0.207248\pi$
$313$	8809.38	1.59085	0.795425	+	0.606053i	$0.207248\pi$
$314$	−1657.70	−0.297929
$315$	0	0
$316$	−5084.83	−0.905202
$317$	−9026.46	−1.59929	−0.799647	−	0.600470i	$-0.794980\pi$
$317$	−9026.46	−1.59929	−0.799647	+	0.600470i	$0.794980\pi$
$318$	827.026	0.145841
$319$	−2290.66	−0.402045
$320$	1820.41	0.318012
$321$	−59.9356	−0.0104214
$322$	0	0
$323$	5180.60	0.892434
$324$	2754.05	0.472230
$325$	5506.16	0.939774
$326$	5192.07	0.882093
$327$	2406.03	0.406892
$328$	−112.264	−0.0188986
$329$	0	0
$330$	3424.25	0.571208
$331$	6522.32	1.08308	0.541539	−	0.840675i	$-0.317842\pi$
$331$	6522.32	1.08308	0.541539	+	0.840675i	$0.317842\pi$
$332$	3901.15	0.644889
$333$	−6802.27	−1.11941
$334$	2463.92	0.403652
$335$	−12639.6	−2.06142
$336$	0	0
$337$	−544.680	−0.0880434	−0.0440217	−	0.999031i	$-0.514017\pi$
$337$	−544.680	−0.0880434	−0.0440217	+	0.999031i	$0.514017\pi$
$338$	4939.65	0.794916
$339$	−2067.06	−0.331172
$340$	−4578.79	−0.730352
$341$	2719.94	0.431944
$342$	9176.21	1.45086
$343$	0	0
$344$	−493.675	−0.0773755
$345$	−6056.27	−0.945097
$346$	7772.09	1.20760
$347$	−8230.72	−1.27334	−0.636669	−	0.771137i	$-0.719688\pi$
$347$	−8230.72	−1.27334	−0.636669	+	0.771137i	$0.719688\pi$
$348$	−540.641	−0.0832799
$349$	3497.84	0.536491	0.268245	−	0.963351i	$-0.413556\pi$
$349$	3497.84	0.536491	0.268245	+	0.963351i	$0.413556\pi$
$350$	0	0
$351$	−2328.54	−0.354098
$352$	6870.89	1.04040
$353$	6572.10	0.990928	0.495464	−	0.868629i	$-0.334998\pi$
$353$	6572.10	0.990928	0.495464	+	0.868629i	$0.334998\pi$
$354$	−2531.47	−0.380074
$355$	18703.3	2.79624
$356$	−5957.53	−0.886935
$357$	0	0
$358$	−10470.7	−1.54580
$359$	−10382.6	−1.52639	−0.763193	−	0.646171i	$-0.776369\pi$
$359$	−10382.6	−1.52639	−0.763193	+	0.646171i	$0.776369\pi$
$360$	4536.12	0.664096
$361$	3778.21	0.550839
$362$	−5688.39	−0.825897
$363$	−273.525	−0.0395492
$364$	0	0
$365$	12481.4	1.78988
$366$	−3738.33	−0.533895
$367$	−10421.9	−1.48234	−0.741171	−	0.671317i	$-0.765729\pi$
$367$	−10421.9	−1.48234	−0.741171	+	0.671317i	$0.765729\pi$
$368$	−17154.6	−2.43002
$369$	265.094	0.0373991
$370$	17836.6	2.50616
$371$	0	0
$372$	641.959	0.0894732
$373$	−7396.55	−1.02675	−0.513377	−	0.858163i	$-0.671606\pi$
$373$	−7396.55	−1.02675	−0.513377	+	0.858163i	$0.671606\pi$
$374$	−6188.86	−0.855664
$375$	−1825.50	−0.251382
$376$	−488.705	−0.0670293
$377$	−1945.32	−0.265753
$378$	0	0
$379$	11400.8	1.54517	0.772587	−	0.634909i	$-0.218963\pi$
$379$	11400.8	1.54517	0.772587	+	0.634909i	$0.218963\pi$
$380$	−9401.53	−1.26918
$381$	242.025	0.0325441
$382$	−15382.1	−2.06025
$383$	7745.85	1.03341	0.516703	−	0.856165i	$-0.327159\pi$
$383$	7745.85	1.03341	0.516703	+	0.856165i	$0.327159\pi$
$384$	−1947.94	−0.258868
$385$	0	0
$386$	−3060.30	−0.403537
$387$	1165.74	0.153121
$388$	−256.205	−0.0335228
$389$	−2937.86	−0.382918	−0.191459	−	0.981501i	$-0.561322\pi$
$389$	−2937.86	−0.382918	−0.191459	+	0.981501i	$0.561322\pi$
$390$	2908.00	0.377570
$391$	10945.9	1.41575
$392$	0	0
$393$	3429.45	0.440186
$394$	−4850.01	−0.620153
$395$	17609.4	2.24310
$396$	−4283.23	−0.543537
$397$	−609.470	−0.0770489	−0.0385245	−	0.999258i	$-0.512266\pi$
$397$	−609.470	−0.0770489	−0.0385245	+	0.999258i	$0.512266\pi$
$398$	−634.678	−0.0799335
$399$	0	0
$400$	−15011.0	−1.87638
$401$	−7295.65	−0.908547	−0.454274	−	0.890862i	$-0.650101\pi$
$401$	−7295.65	−0.908547	−0.454274	+	0.890862i	$0.650101\pi$
$402$	−4032.19	−0.500267
$403$	2309.88	0.285517
$404$	5895.72	0.726048
$405$	−9537.61	−1.17019
$406$	0	0
$407$	9419.95	1.14725
$408$	816.975	0.0991331
$409$	10571.4	1.27804	0.639022	−	0.769189i	$-0.279339\pi$
$409$	10571.4	1.27804	0.639022	+	0.769189i	$0.279339\pi$
$410$	−695.117	−0.0837302
$411$	−676.518	−0.0811926
$412$	−7931.66	−0.948458
$413$	0	0
$414$	19388.1	2.30162
$415$	−13510.2	−1.59804
$416$	5835.03	0.687706
$417$	4776.89	0.560971
$418$	−12707.5	−1.48694
$419$	11528.1	1.34412	0.672059	−	0.740497i	$-0.265410\pi$
$419$	11528.1	1.34412	0.672059	+	0.740497i	$0.265410\pi$
$420$	0	0
$421$	−2937.11	−0.340015	−0.170007	−	0.985443i	$-0.554379\pi$
$421$	−2937.11	−0.340015	−0.170007	+	0.985443i	$0.554379\pi$
$422$	936.038	0.107975
$423$	1154.00	0.132647
$424$	−1517.17	−0.173774
$425$	9578.13	1.09319
$426$	5966.58	0.678596
$427$	0	0
$428$	−196.585	−0.0222016
$429$	1535.79	0.172841
$430$	−3056.74	−0.342812
$431$	9128.65	1.02021	0.510106	−	0.860111i	$-0.329606\pi$
$431$	9128.65	1.02021	0.510106	+	0.860111i	$0.329606\pi$
$432$	6348.14	0.707002
$433$	3452.20	0.383146	0.191573	−	0.981478i	$-0.438641\pi$
$433$	3452.20	0.383146	0.191573	+	0.981478i	$0.438641\pi$
$434$	0	0
$435$	1872.31	0.206368
$436$	7891.61	0.866834
$437$	22474.9	2.46023
$438$	3981.73	0.434371
$439$	13522.5	1.47014	0.735072	−	0.677989i	$-0.237148\pi$
$439$	13522.5	1.47014	0.735072	+	0.677989i	$0.237148\pi$
$440$	−6281.73	−0.680613
$441$	0	0
$442$	−5255.82	−0.565596
$443$	11188.0	1.19991	0.599955	−	0.800034i	$-0.295185\pi$
$443$	11188.0	1.19991	0.599955	+	0.800034i	$0.295185\pi$
$444$	2223.29	0.237642
$445$	20631.7	2.19783
$446$	−12655.6	−1.34363
$447$	1655.45	0.175168
$448$	0	0
$449$	−18560.3	−1.95082	−0.975408	−	0.220405i	$-0.929262\pi$
$449$	−18560.3	−1.95082	−0.975408	+	0.220405i	$0.929262\pi$
$450$	16965.4	1.77724
$451$	−367.109	−0.0383293
$452$	−6779.81	−0.705521
$453$	−577.248	−0.0598708
$454$	11160.9	1.15376
$455$	0	0
$456$	1677.48	0.172270
$457$	11762.6	1.20401	0.602004	−	0.798493i	$-0.294369\pi$
$457$	11762.6	1.20401	0.602004	+	0.798493i	$0.294369\pi$
$458$	20774.8	2.11953
$459$	−4050.57	−0.411905
$460$	−19864.1	−2.01341
$461$	−9940.90	−1.00432	−0.502162	−	0.864773i	$-0.667462\pi$
$461$	−9940.90	−1.00432	−0.502162	+	0.864773i	$0.667462\pi$
$462$	0	0
$463$	17407.9	1.74733	0.873667	−	0.486524i	$-0.161735\pi$
$463$	17407.9	1.74733	0.873667	+	0.486524i	$0.161735\pi$
$464$	5303.38	0.530611
$465$	−2223.18	−0.221715
$466$	9196.09	0.914165
$467$	−9233.93	−0.914979	−0.457490	−	0.889215i	$-0.651251\pi$
$467$	−9233.93	−0.914979	−0.457490	+	0.889215i	$0.651251\pi$
$468$	−3637.49	−0.359280
$469$	0	0
$470$	−3025.97	−0.296974
$471$	715.584	0.0700050
$472$	4643.95	0.452871
$473$	−1614.35	−0.156930
$474$	5617.62	0.544358
$475$	19666.6	1.89971
$476$	0	0
$477$	3582.56	0.343887
$478$	15871.1	1.51867
$479$	15969.4	1.52330	0.761649	−	0.647990i	$-0.224390\pi$
$479$	15969.4	1.52330	0.761649	+	0.647990i	$0.224390\pi$
$480$	−5616.03	−0.534032
$481$	7999.78	0.758334
$482$	−610.926	−0.0577322
$483$	0	0
$484$	−897.143	−0.0842546
$485$	887.270	0.0830698
$486$	−10932.2	−1.02036
$487$	−16806.7	−1.56382	−0.781912	−	0.623389i	$-0.785756\pi$
$487$	−16806.7	−1.56382	−0.781912	+	0.623389i	$0.785756\pi$
$488$	6857.92	0.636154
$489$	−2241.27	−0.207267
$490$	0	0
$491$	618.762	0.0568724	0.0284362	−	0.999596i	$-0.490947\pi$
$491$	618.762	0.0568724	0.0284362	+	0.999596i	$0.490947\pi$
$492$	−86.6450	−0.00793955
$493$	−3383.94	−0.309138
$494$	−10791.7	−0.982873
$495$	14833.4	1.34689
$496$	−6297.25	−0.570071
$497$	0	0
$498$	−4309.91	−0.387815
$499$	6455.19	0.579107	0.289553	−	0.957162i	$-0.406493\pi$
$499$	6455.19	0.579107	0.289553	+	0.957162i	$0.406493\pi$
$500$	−5987.50	−0.535538
$501$	−1063.60	−0.0948470
$502$	−251.382	−0.0223500
$503$	8610.63	0.763279	0.381639	−	0.924311i	$-0.375360\pi$
$503$	8610.63	0.763279	0.381639	+	0.924311i	$0.375360\pi$
$504$	0	0
$505$	−20417.6	−1.79915
$506$	−26849.1	−2.35887
$507$	−2132.31	−0.186783
$508$	793.824	0.0693312
$509$	2990.09	0.260380	0.130190	−	0.991489i	$-0.458441\pi$
$509$	2990.09	0.260380	0.130190	+	0.991489i	$0.458441\pi$
$510$	5058.56	0.439209
$511$	0	0
$512$	−9359.22	−0.807857
$513$	−8316.95	−0.715794
$514$	17951.2	1.54045
$515$	27468.3	2.35029
$516$	−381.017	−0.0325065
$517$	−1598.09	−0.135946
$518$	0	0
$519$	−3354.99	−0.283753
$520$	−5334.69	−0.449888
$521$	5982.91	0.503102	0.251551	−	0.967844i	$-0.419059\pi$
$521$	5982.91	0.503102	0.251551	+	0.967844i	$0.419059\pi$
$522$	−5993.86	−0.502575
$523$	14990.3	1.25331	0.626655	−	0.779297i	$-0.284424\pi$
$523$	14990.3	1.25331	0.626655	+	0.779297i	$0.284424\pi$
$524$	11248.4	0.937761
$525$	0	0
$526$	−2720.21	−0.225488
$527$	4018.10	0.332128
$528$	−4186.92	−0.345099
$529$	35319.4	2.90289
$530$	−9394.02	−0.769906
$531$	−10966.0	−0.896202
$532$	0	0
$533$	−311.763	−0.0253358
$534$	6581.77	0.533373
$535$	680.797	0.0550157
$536$	7397.00	0.596085
$537$	4519.92	0.363220
$538$	11962.0	0.958583
$539$	0	0
$540$	7350.81	0.585793
$541$	3218.97	0.255812	0.127906	−	0.991786i	$-0.459174\pi$
$541$	3218.97	0.255812	0.127906	+	0.991786i	$0.459174\pi$
$542$	2289.13	0.181414
$543$	2455.52	0.194063
$544$	10150.2	0.799975
$545$	−27329.6	−2.14802
$546$	0	0
$547$	16865.6	1.31832	0.659159	−	0.752004i	$-0.270913\pi$
$547$	16865.6	1.31832	0.659159	+	0.752004i	$0.270913\pi$
$548$	−2218.93	−0.172971
$549$	−16193.9	−1.25891
$550$	−23494.1	−1.82144
$551$	−6948.17	−0.537209
$552$	3544.28	0.273287
$553$	0	0
$554$	−18936.6	−1.45224
$555$	−7699.54	−0.588878
$556$	15667.8	1.19508
$557$	−96.5698	−0.00734613	−0.00367307	−	0.999993i	$-0.501169\pi$
$557$	−96.5698	−0.00734613	−0.00367307	+	0.999993i	$0.501169\pi$
$558$	7117.12	0.539950
$559$	−1370.96	−0.103731
$560$	0	0
$561$	2671.55	0.201057
$562$	16892.4	1.26791
$563$	7386.36	0.552927	0.276463	−	0.961024i	$-0.410838\pi$
$563$	7386.36	0.552927	0.276463	+	0.961024i	$0.410838\pi$
$564$	−377.181	−0.0281599
$565$	23479.3	1.74829
$566$	−10455.8	−0.776486
$567$	0	0
$568$	−10945.6	−0.808570
$569$	−12396.4	−0.913330	−0.456665	−	0.889639i	$-0.650956\pi$
$569$	−12396.4	−0.913330	−0.456665	+	0.889639i	$0.650956\pi$
$570$	10386.6	0.763242
$571$	−12596.4	−0.923191	−0.461595	−	0.887091i	$-0.652723\pi$
$571$	−12596.4	−0.923191	−0.461595	+	0.887091i	$0.652723\pi$
$572$	5037.28	0.368216
$573$	6640.01	0.484102
$574$	0	0
$575$	41552.7	3.01368
$576$	2515.65	0.181977
$577$	−2131.37	−0.153778	−0.0768891	−	0.997040i	$-0.524499\pi$
$577$	−2131.37	−0.153778	−0.0768891	+	0.997040i	$0.524499\pi$
$578$	8660.10	0.623205
$579$	1321.05	0.0948200
$580$	6141.04	0.439642
$581$	0	0
$582$	283.050	0.0201595
$583$	−4961.22	−0.352441
$584$	−7304.43	−0.517568
$585$	12597.1	0.890298
$586$	−31347.2	−2.20980
$587$	−12587.4	−0.885073	−0.442537	−	0.896750i	$-0.645921\pi$
$587$	−12587.4	−0.885073	−0.442537	+	0.896750i	$0.645921\pi$
$588$	0	0
$589$	8250.28	0.577160
$590$	28754.5	2.00645
$591$	2093.61	0.145719
$592$	−21809.2	−1.51411
$593$	−25862.1	−1.79094	−0.895472	−	0.445118i	$-0.853162\pi$
$593$	−25862.1	−1.79094	−0.895472	+	0.445118i	$0.853162\pi$
$594$	9935.61	0.686302
$595$	0	0
$596$	5429.76	0.373174
$597$	273.973	0.0187822
$598$	−22801.3	−1.55922
$599$	−7864.50	−0.536452	−0.268226	−	0.963356i	$-0.586437\pi$
$599$	−7864.50	−0.536452	−0.268226	+	0.963356i	$0.586437\pi$
$600$	3101.40	0.211023
$601$	8069.34	0.547679	0.273840	−	0.961775i	$-0.411706\pi$
$601$	8069.34	0.547679	0.273840	+	0.961775i	$0.411706\pi$
$602$	0	0
$603$	−17466.9	−1.17961
$604$	−1893.33	−0.127547
$605$	3106.92	0.208784
$606$	−6513.48	−0.436621
$607$	−1370.45	−0.0916391	−0.0458195	−	0.998950i	$-0.514590\pi$
$607$	−1370.45	−0.0916391	−0.0458195	+	0.998950i	$0.514590\pi$
$608$	20841.2	1.39017
$609$	0	0
$610$	42462.9	2.81848
$611$	−1357.16	−0.0898607
$612$	−6327.52	−0.417933
$613$	−18971.4	−1.25000	−0.624998	−	0.780626i	$-0.714900\pi$
$613$	−18971.4	−1.25000	−0.624998	+	0.780626i	$0.714900\pi$
$614$	−6076.20	−0.399373
$615$	300.062	0.0196743
$616$	0	0
$617$	−5562.78	−0.362965	−0.181482	−	0.983394i	$-0.558090\pi$
$617$	−5562.78	−0.362965	−0.181482	+	0.983394i	$0.558090\pi$
$618$	8762.74	0.570371
$619$	12188.2	0.791416	0.395708	−	0.918376i	$-0.370499\pi$
$619$	12188.2	0.791416	0.395708	+	0.918376i	$0.370499\pi$
$620$	−7291.89	−0.472337
$621$	−17572.6	−1.13553
$622$	11464.3	0.739032
$623$	0	0
$624$	−3555.69	−0.228111
$625$	−3100.06	−0.198404
$626$	−31921.7	−2.03809
$627$	5485.45	0.349390
$628$	2347.06	0.149137
$629$	13915.9	0.882134
$630$	0	0
$631$	28405.9	1.79211	0.896054	−	0.443946i	$-0.146422\pi$
$631$	28405.9	1.79211	0.896054	+	0.443946i	$0.146422\pi$
$632$	−10305.4	−0.648621
$633$	−404.061	−0.0253712
$634$	32708.3	2.04891
$635$	−2749.11	−0.171803
$636$	−1170.95	−0.0730048
$637$	0	0
$638$	8300.45	0.515075
$639$	25846.4	1.60011
$640$	22126.3	1.36659
$641$	13923.2	0.857933	0.428967	−	0.903320i	$-0.358878\pi$
$641$	13923.2	0.857933	0.428967	+	0.903320i	$0.358878\pi$
$642$	217.183	0.0133513
$643$	7050.47	0.432416	0.216208	−	0.976347i	$-0.430631\pi$
$643$	7050.47	0.432416	0.216208	+	0.976347i	$0.430631\pi$
$644$	0	0
$645$	1319.51	0.0805514
$646$	−18772.4	−1.14333
$647$	5117.85	0.310979	0.155489	−	0.987838i	$-0.450305\pi$
$647$	5117.85	0.310979	0.155489	+	0.987838i	$0.450305\pi$
$648$	5581.64	0.338376
$649$	15186.0	0.918493
$650$	−19952.1	−1.20398
$651$	0	0
$652$	−7351.21	−0.441558
$653$	−14856.2	−0.890305	−0.445153	−	0.895455i	$-0.646851\pi$
$653$	−14856.2	−0.890305	−0.445153	+	0.895455i	$0.646851\pi$
$654$	−8718.49	−0.521285
$655$	−38954.5	−2.32378
$656$	849.938	0.0505862
$657$	17248.3	1.02423
$658$	0	0
$659$	−17461.1	−1.03215	−0.516077	−	0.856542i	$-0.672608\pi$
$659$	−17461.1	−1.03215	−0.516077	+	0.856542i	$0.672608\pi$
$660$	−4848.23	−0.285935
$661$	13890.6	0.817371	0.408686	−	0.912675i	$-0.365987\pi$
$661$	13890.6	0.817371	0.408686	+	0.912675i	$0.365987\pi$
$662$	−23634.3	−1.38757
$663$	2268.79	0.132900
$664$	7906.47	0.462094
$665$	0	0
$666$	24648.7	1.43411
$667$	−14680.5	−0.852222
$668$	−3488.55	−0.202060
$669$	5463.05	0.315716
$670$	45800.8	2.64096
$671$	22425.8	1.29022
$672$	0	0
$673$	22823.2	1.30724	0.653618	−	0.756825i	$-0.273250\pi$
$673$	22823.2	1.30724	0.653618	+	0.756825i	$0.273250\pi$
$674$	1973.70	0.112796
$675$	−15376.8	−0.876817
$676$	−6993.82	−0.397919
$677$	−30321.1	−1.72132	−0.860662	−	0.509177i	$-0.829950\pi$
$677$	−30321.1	−1.72132	−0.860662	+	0.509177i	$0.829950\pi$
$678$	7490.20	0.424276
$679$	0	0
$680$	−9279.86	−0.523333
$681$	−4817.85	−0.271102
$682$	−9855.98	−0.553380
$683$	−4784.62	−0.268050	−0.134025	−	0.990978i	$-0.542790\pi$
$683$	−4784.62	−0.268050	−0.134025	+	0.990978i	$0.542790\pi$
$684$	−12992.2	−0.726268
$685$	7684.43	0.428623
$686$	0	0
$687$	−8967.90	−0.498030
$688$	3737.56	0.207112
$689$	−4213.26	−0.232964
$690$	21945.5	1.21080
$691$	16051.1	0.883666	0.441833	−	0.897097i	$-0.354328\pi$
$691$	16051.1	0.883666	0.441833	+	0.897097i	$0.354328\pi$
$692$	−11004.1	−0.604501
$693$	0	0
$694$	29824.9	1.63132
$695$	−54259.7	−2.96142
$696$	−1095.72	−0.0596741
$697$	−542.322	−0.0294719
$698$	−12674.8	−0.687318
$699$	−3969.69	−0.214803
$700$	0	0
$701$	11327.4	0.610316	0.305158	−	0.952302i	$-0.401291\pi$
$701$	11327.4	0.610316	0.305158	+	0.952302i	$0.401291\pi$
$702$	8437.70	0.453648
$703$	28573.2	1.53294
$704$	−3483.74	−0.186504
$705$	1306.23	0.0697806
$706$	−23814.7	−1.26951
$707$	0	0
$708$	3584.19	0.190257
$709$	7277.08	0.385467	0.192734	−	0.981251i	$-0.438265\pi$
$709$	7277.08	0.385467	0.192734	+	0.981251i	$0.438265\pi$
$710$	−67773.2	−3.58237
$711$	24334.8	1.28358
$712$	−12074.2	−0.635532
$713$	17431.7	0.915600
$714$	0	0
$715$	−17444.7	−0.912442
$716$	14825.0	0.773795
$717$	−6851.10	−0.356847
$718$	37622.4	1.95551
$719$	16205.5	0.840559	0.420280	−	0.907395i	$-0.361932\pi$
$719$	16205.5	0.840559	0.420280	+	0.907395i	$0.361932\pi$
$720$	−34342.5	−1.77760
$721$	0	0
$722$	−13690.7	−0.705700
$723$	263.719	0.0135655
$724$	8053.91	0.413427
$725$	−12846.1	−0.658058
$726$	991.146	0.0506679
$727$	20860.3	1.06419	0.532095	−	0.846684i	$-0.321405\pi$
$727$	20860.3	1.06419	0.532095	+	0.846684i	$0.321405\pi$
$728$	0	0
$729$	−9774.49	−0.496596
$730$	−45227.7	−2.29308
$731$	−2384.83	−0.120665
$732$	5292.92	0.267257
$733$	−7470.20	−0.376423	−0.188212	−	0.982129i	$-0.560269\pi$
$733$	−7470.20	−0.376423	−0.188212	+	0.982129i	$0.560269\pi$
$734$	37764.8	1.89908
$735$	0	0
$736$	44034.6	2.20535
$737$	24188.6	1.20895
$738$	−960.596	−0.0479133
$739$	−34217.2	−1.70325	−0.851623	−	0.524154i	$-0.824382\pi$
$739$	−34217.2	−1.70325	−0.851623	+	0.524154i	$0.824382\pi$
$740$	−25253.9	−1.25453
$741$	4658.45	0.230948
$742$	0	0
$743$	−17494.3	−0.863802	−0.431901	−	0.901921i	$-0.642157\pi$
$743$	−17494.3	−0.863802	−0.431901	+	0.901921i	$0.642157\pi$
$744$	1301.06	0.0641119
$745$	−18803.9	−0.924729
$746$	26802.2	1.31541
$747$	−18669.9	−0.914454
$748$	8762.51	0.428328
$749$	0	0
$750$	6614.88	0.322055
$751$	21653.0	1.05210	0.526052	−	0.850452i	$-0.323672\pi$
$751$	21653.0	1.05210	0.526052	+	0.850452i	$0.323672\pi$
$752$	3699.93	0.179419
$753$	108.514	0.00525163
$754$	7049.06	0.340466
$755$	6556.85	0.316064
$756$	0	0
$757$	−38091.6	−1.82888	−0.914440	−	0.404722i	$-0.867368\pi$
$757$	−38091.6	−1.82888	−0.914440	+	0.404722i	$0.867368\pi$
$758$	−41312.0	−1.97958
$759$	11590.0	0.554269
$760$	−19054.1	−0.909429
$761$	691.162	0.0329233	0.0164616	−	0.999864i	$-0.494760\pi$
$761$	691.162	0.0329233	0.0164616	+	0.999864i	$0.494760\pi$
$762$	−877.001	−0.0416935
$763$	0	0
$764$	21778.8	1.03132
$765$	21913.0	1.03564
$766$	−28067.9	−1.32393
$767$	12896.5	0.607127
$768$	8340.68	0.391886
$769$	37493.1	1.75817	0.879087	−	0.476662i	$-0.158153\pi$
$769$	37493.1	1.75817	0.879087	+	0.476662i	$0.158153\pi$
$770$	0	0
$771$	−7749.02	−0.361964
$772$	4332.94	0.202002
$773$	32774.4	1.52499	0.762493	−	0.646997i	$-0.223975\pi$
$773$	32774.4	1.52499	0.762493	+	0.646997i	$0.223975\pi$
$774$	−4224.17	−0.196169
$775$	15253.5	0.706996
$776$	−519.252	−0.0240207
$777$	0	0
$778$	10645.6	0.490571
$779$	−1113.54	−0.0512152
$780$	−4117.30	−0.189004
$781$	−35792.8	−1.63991
$782$	−39663.5	−1.81376
$783$	5432.59	0.247950
$784$	0	0
$785$	−8128.17	−0.369563
$786$	−12427.0	−0.563938
$787$	7837.30	0.354980	0.177490	−	0.984123i	$-0.443202\pi$
$787$	7837.30	0.354980	0.177490	+	0.984123i	$0.443202\pi$
$788$	6866.90	0.310436
$789$	1174.24	0.0529834
$790$	−63809.4	−2.87372
$791$	0	0
$792$	−8680.85	−0.389470
$793$	19044.8	0.852840
$794$	2208.48	0.0987102
$795$	4055.13	0.180907
$796$	898.610	0.0400131
$797$	−26703.7	−1.18682	−0.593410	−	0.804901i	$-0.702219\pi$
$797$	−26703.7	−1.18682	−0.593410	+	0.804901i	$0.702219\pi$
$798$	0	0
$799$	−2360.82	−0.104531
$800$	38532.2	1.70290
$801$	28511.3	1.25768
$802$	26436.5	1.16397
$803$	−23885.9	−1.04971
$804$	5708.99	0.250423
$805$	0	0
$806$	−8370.07	−0.365786
$807$	−5163.65	−0.225240
$808$	11948.9	0.520248
$809$	15204.6	0.660775	0.330387	−	0.943845i	$-0.392821\pi$
$809$	15204.6	0.660775	0.330387	+	0.943845i	$0.392821\pi$
$810$	34560.5	1.49917
$811$	−25148.8	−1.08889	−0.544447	−	0.838796i	$-0.683260\pi$
$811$	−25148.8	−1.08889	−0.544447	+	0.838796i	$0.683260\pi$
$812$	0	0
$813$	−988.152	−0.0426273
$814$	−34134.1	−1.46978
$815$	25458.1	1.09418
$816$	−6185.23	−0.265351
$817$	−4896.73	−0.209688
$818$	−38306.4	−1.63735
$819$	0	0
$820$	984.184	0.0419136
$821$	−144.629	−0.00614810	−0.00307405	−	0.999995i	$-0.500979\pi$
$821$	−144.629	−0.00614810	−0.00307405	+	0.999995i	$0.500979\pi$
$822$	2451.43	0.104019
$823$	−1012.14	−0.0428685	−0.0214343	−	0.999770i	$-0.506823\pi$
$823$	−1012.14	−0.0428685	−0.0214343	+	0.999770i	$0.506823\pi$
$824$	−16075.1	−0.679616
$825$	10141.8	0.427988
$826$	0	0
$827$	13057.2	0.549025	0.274513	−	0.961584i	$-0.411484\pi$
$827$	13057.2	0.549025	0.274513	+	0.961584i	$0.411484\pi$
$828$	−27450.6	−1.15214
$829$	32562.6	1.36423	0.682113	−	0.731246i	$-0.261061\pi$
$829$	32562.6	1.36423	0.682113	+	0.731246i	$0.261061\pi$
$830$	48955.4	2.04731
$831$	8174.39	0.341235
$832$	−2958.53	−0.123279
$833$	0	0
$834$	−17309.5	−0.718681
$835$	12081.3	0.500706
$836$	17991.9	0.744333
$837$	−6450.67	−0.266389
$838$	−41773.3	−1.72200
$839$	−24150.5	−0.993763	−0.496881	−	0.867818i	$-0.665522\pi$
$839$	−24150.5	−0.993763	−0.496881	+	0.867818i	$0.665522\pi$
$840$	0	0
$841$	−19850.5	−0.813911
$842$	10642.9	0.435605
$843$	−7291.99	−0.297923
$844$	−1325.29	−0.0540503
$845$	24220.5	0.986047
$846$	−4181.65	−0.169939
$847$	0	0
$848$	11486.3	0.465144
$849$	4513.48	0.182453
$850$	−34707.3	−1.40053
$851$	60371.1	2.43184
$852$	−8447.80	−0.339691
$853$	4268.02	0.171318	0.0856589	−	0.996325i	$-0.472700\pi$
$853$	4268.02	0.171318	0.0856589	+	0.996325i	$0.472700\pi$
$854$	0	0
$855$	44993.5	1.79970
$856$	−398.419	−0.0159085
$857$	25465.9	1.01505	0.507525	−	0.861637i	$-0.330560\pi$
$857$	25465.9	1.01505	0.507525	+	0.861637i	$0.330560\pi$
$858$	−5565.09	−0.221433
$859$	−13236.6	−0.525759	−0.262879	−	0.964829i	$-0.584672\pi$
$859$	−13236.6	−0.525759	−0.262879	+	0.964829i	$0.584672\pi$
$860$	4327.90	0.171605
$861$	0	0
$862$	−33078.6	−1.30703
$863$	25116.4	0.990699	0.495350	−	0.868694i	$-0.335040\pi$
$863$	25116.4	0.990699	0.495350	+	0.868694i	$0.335040\pi$
$864$	−16295.2	−0.641636
$865$	38108.7	1.49796
$866$	−12509.4	−0.490863
$867$	−3738.32	−0.146436
$868$	0	0
$869$	−33699.4	−1.31550
$870$	−6784.50	−0.264386
$871$	20541.9	0.799122
$872$	15994.0	0.621128
$873$	1226.14	0.0475354
$874$	−81440.2	−3.15190
$875$	0	0
$876$	−5637.54	−0.217437
$877$	−15895.6	−0.612037	−0.306018	−	0.952026i	$-0.598997\pi$
$877$	−15895.6	−0.612037	−0.306018	+	0.952026i	$0.598997\pi$
$878$	−49000.1	−1.88346
$879$	13531.7	0.519241
$880$	47558.4	1.82181
$881$	26880.0	1.02794	0.513968	−	0.857809i	$-0.328175\pi$
$881$	26880.0	1.02794	0.513968	+	0.857809i	$0.328175\pi$
$882$	0	0
$883$	24059.3	0.916942	0.458471	−	0.888709i	$-0.348397\pi$
$883$	24059.3	0.916942	0.458471	+	0.888709i	$0.348397\pi$
$884$	7441.46	0.283126
$885$	−12412.5	−0.471459
$886$	−40541.0	−1.53725
$887$	−10880.0	−0.411854	−0.205927	−	0.978567i	$-0.566021\pi$
$887$	−10880.0	−0.411854	−0.205927	+	0.978567i	$0.566021\pi$
$888$	4505.96	0.170282
$889$	0	0
$890$	−74761.0	−2.81572
$891$	18252.3	0.686279
$892$	17918.4	0.672593
$893$	−4847.43	−0.181650
$894$	−5998.70	−0.224414
$895$	−51340.9	−1.91747
$896$	0	0
$897$	9842.66	0.366373
$898$	67255.3	2.49926
$899$	−5389.05	−0.199927
$900$	−24020.5	−0.889649
$901$	−7329.10	−0.270996
$902$	1330.26	0.0491050
$903$	0	0
$904$	−13740.7	−0.505540
$905$	−27891.7	−1.02448
$906$	2091.72	0.0767027
$907$	36548.8	1.33802	0.669009	−	0.743255i	$-0.266719\pi$
$907$	36548.8	1.33802	0.669009	+	0.743255i	$0.266719\pi$
$908$	−15802.2	−0.577549
$909$	−28215.5	−1.02954
$910$	0	0
$911$	−11382.9	−0.413977	−0.206988	−	0.978343i	$-0.566366\pi$
$911$	−11382.9	−0.413977	−0.206988	+	0.978343i	$0.566366\pi$
$912$	−12700.0	−0.461118
$913$	25854.6	0.937199
$914$	−42623.0	−1.54250
$915$	−18330.1	−0.662265
$916$	−29414.1	−1.06099
$917$	0	0
$918$	14677.6	0.527706
$919$	−23783.2	−0.853684	−0.426842	−	0.904326i	$-0.640374\pi$
$919$	−23783.2	−0.853684	−0.426842	+	0.904326i	$0.640374\pi$
$920$	−40258.7	−1.44271
$921$	2622.92	0.0938417
$922$	36021.8	1.28668
$923$	−30396.6	−1.08398
$924$	0	0
$925$	52827.4	1.87779
$926$	−63079.4	−2.23857
$927$	37959.0	1.34492
$928$	−13613.4	−0.481553
$929$	−49635.5	−1.75295	−0.876474	−	0.481449i	$-0.840111\pi$
$929$	−49635.5	−1.75295	−0.876474	+	0.481449i	$0.840111\pi$
$930$	8055.93	0.284048
$931$	0	0
$932$	−13020.3	−0.457612
$933$	−4948.83	−0.173652
$934$	33460.1	1.17221
$935$	−30345.7	−1.06140
$936$	−7372.11	−0.257441
$937$	−32802.3	−1.14366	−0.571828	−	0.820374i	$-0.693765\pi$
$937$	−32802.3	−1.14366	−0.571828	+	0.820374i	$0.693765\pi$
$938$	0	0
$939$	13779.7	0.478896
$940$	4284.33	0.148659
$941$	−49647.4	−1.71994	−0.859968	−	0.510347i	$-0.829517\pi$
$941$	−49647.4	−1.71994	−0.859968	+	0.510347i	$0.829517\pi$
$942$	−2592.99	−0.0896860
$943$	−2352.75	−0.0812472
$944$	−35158.9	−1.21221
$945$	0	0
$946$	5849.74	0.201048
$947$	−36887.7	−1.26577	−0.632887	−	0.774244i	$-0.718130\pi$
$947$	−36887.7	−1.26577	−0.632887	+	0.774244i	$0.718130\pi$
$948$	−7953.72	−0.272495
$949$	−20284.8	−0.693860
$950$	−71263.8	−2.43379
$951$	−14119.2	−0.481438
$952$	0	0
$953$	−39254.5	−1.33429	−0.667146	−	0.744927i	$-0.732484\pi$
$953$	−39254.5	−1.33429	−0.667146	+	0.744927i	$0.732484\pi$
$954$	−12981.8	−0.440567
$955$	−75422.6	−2.55562
$956$	−22471.1	−0.760217
$957$	−3583.07	−0.121028
$958$	−57866.7	−1.95155
$959$	0	0
$960$	2847.49	0.0957316
$961$	−23392.0	−0.785205
$962$	−28988.0	−0.971530
$963$	940.806	0.0314819
$964$	864.981	0.0288995
$965$	−15005.5	−0.500564
$966$	0	0
$967$	22161.3	0.736979	0.368490	−	0.929632i	$-0.379875\pi$
$967$	22161.3	0.736979	0.368490	+	0.929632i	$0.379875\pi$
$968$	−1818.24	−0.0603725
$969$	8103.52	0.268651
$970$	−3215.11	−0.106424
$971$	889.974	0.0294136	0.0147068	−	0.999892i	$-0.495319\pi$
$971$	889.974	0.0294136	0.0147068	+	0.999892i	$0.495319\pi$
$972$	15478.4	0.510771
$973$	0	0
$974$	60900.6	2.00347
$975$	8612.76	0.282902
$976$	−51920.6	−1.70280
$977$	−55858.7	−1.82915	−0.914573	−	0.404420i	$-0.867473\pi$
$977$	−55858.7	−1.82915	−0.914573	+	0.404420i	$0.867473\pi$
$978$	8121.47	0.265538
$979$	−39483.2	−1.28896
$980$	0	0
$981$	−37767.3	−1.22917
$982$	−2242.15	−0.0728613
$983$	12033.8	0.390457	0.195229	−	0.980758i	$-0.437455\pi$
$983$	12033.8	0.390457	0.195229	+	0.980758i	$0.437455\pi$
$984$	−175.604	−0.00568907
$985$	−23780.9	−0.769263
$986$	12262.0	0.396048
$987$	0	0
$988$	15279.4	0.492006
$989$	−10346.1	−0.332646
$990$	−53750.2	−1.72555
$991$	3599.57	0.115382	0.0576912	−	0.998334i	$-0.481626\pi$
$991$	3599.57	0.115382	0.0576912	+	0.998334i	$0.481626\pi$
$992$	16164.6	0.517364
$993$	10202.3	0.326041
$994$	0	0
$995$	−3112.00	−0.0991528
$996$	6102.20	0.194132
$997$	18374.5	0.583677	0.291838	−	0.956468i	$-0.405733\pi$
$997$	18374.5	0.583677	0.291838	+	0.956468i	$0.405733\pi$
$998$	−23391.0	−0.741915
$999$	−22340.6	−0.707532

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.n.1.16	yes	68
7.6	odd	2		2303.4.a.m.1.16	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.m.1.16	✓	68	7.6	odd	2
2303.4.a.n.1.16	yes	68	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-3.62360 q^{2} +1.56421 q^{3} +5.13048 q^{4} -17.7675 q^{5} -5.66806 q^{6} +10.3980 q^{8} -24.5533 q^{9} +O(q^{10})\)	\(q-3.62360 q^{2} +1.56421 q^{3} +5.13048 q^{4} -17.7675 q^{5} -5.66806 q^{6} +10.3980 q^{8} -24.5533 q^{9} +64.3823 q^{10} +34.0020 q^{11} +8.02514 q^{12} +28.8758 q^{13} -27.7920 q^{15} -78.7220 q^{16} +50.2303 q^{17} +88.9712 q^{18} +103.137 q^{19} -91.1559 q^{20} -123.210 q^{22} +217.914 q^{23} +16.2646 q^{24} +190.684 q^{25} -104.634 q^{26} -80.6399 q^{27} -67.3685 q^{29} +100.707 q^{30} +79.9936 q^{31} +202.073 q^{32} +53.1861 q^{33} -182.015 q^{34} -125.970 q^{36} +277.041 q^{37} -373.727 q^{38} +45.1677 q^{39} -184.746 q^{40} -10.7967 q^{41} -47.4780 q^{43} +174.447 q^{44} +436.250 q^{45} -789.633 q^{46} -47.0000 q^{47} -123.137 q^{48} -690.963 q^{50} +78.5706 q^{51} +148.147 q^{52} -145.910 q^{53} +292.207 q^{54} -604.130 q^{55} +161.327 q^{57} +244.117 q^{58} +446.620 q^{59} -142.587 q^{60} +659.543 q^{61} -289.865 q^{62} -102.457 q^{64} -513.051 q^{65} -192.725 q^{66} +711.388 q^{67} +257.706 q^{68} +340.862 q^{69} -1052.67 q^{71} -255.304 q^{72} -702.486 q^{73} -1003.89 q^{74} +298.269 q^{75} +529.142 q^{76} -163.670 q^{78} -991.101 q^{79} +1398.69 q^{80} +536.801 q^{81} +39.1230 q^{82} +760.385 q^{83} -892.467 q^{85} +172.041 q^{86} -105.378 q^{87} +353.552 q^{88} -1161.20 q^{89} -1580.80 q^{90} +1118.00 q^{92} +125.126 q^{93} +170.309 q^{94} -1832.48 q^{95} +316.084 q^{96} -49.9378 q^{97} -834.859 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9}+O(q^{10}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more