LMFDB - Embedded newform 2303.4.a.n.1.17

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			1.17
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)

$f(q)$	$=$	$q-3.26875 q^{2} -5.67634 q^{3} +2.68473 q^{4} -2.63434 q^{5} +18.5546 q^{6} +17.3743 q^{8} +5.22089 q^{9} +O(q^{10})$	\(q-3.26875 q^{2} -5.67634 q^{3} +2.68473 q^{4} -2.63434 q^{5} +18.5546 q^{6} +17.3743 q^{8} +5.22089 q^{9} +8.61100 q^{10} +12.3610 q^{11} -15.2394 q^{12} -40.0263 q^{13} +14.9534 q^{15} -78.2701 q^{16} +37.9479 q^{17} -17.0658 q^{18} +2.76992 q^{19} -7.07249 q^{20} -40.4049 q^{22} +173.948 q^{23} -98.6225 q^{24} -118.060 q^{25} +130.836 q^{26} +123.626 q^{27} -29.7471 q^{29} -48.8790 q^{30} +33.8856 q^{31} +116.851 q^{32} -70.1651 q^{33} -124.042 q^{34} +14.0167 q^{36} -376.094 q^{37} -9.05418 q^{38} +227.203 q^{39} -45.7698 q^{40} +376.964 q^{41} +557.306 q^{43} +33.1859 q^{44} -13.7536 q^{45} -568.594 q^{46} -47.0000 q^{47} +444.288 q^{48} +385.909 q^{50} -215.406 q^{51} -107.460 q^{52} -349.584 q^{53} -404.102 q^{54} -32.5630 q^{55} -15.7230 q^{57} +97.2358 q^{58} +708.894 q^{59} +40.1459 q^{60} -95.4907 q^{61} -110.763 q^{62} +244.204 q^{64} +105.443 q^{65} +229.352 q^{66} -512.396 q^{67} +101.880 q^{68} -987.392 q^{69} +366.345 q^{71} +90.7093 q^{72} +492.629 q^{73} +1229.36 q^{74} +670.151 q^{75} +7.43649 q^{76} -742.670 q^{78} +756.796 q^{79} +206.190 q^{80} -842.706 q^{81} -1232.20 q^{82} +1214.95 q^{83} -99.9678 q^{85} -1821.69 q^{86} +168.855 q^{87} +214.763 q^{88} -1049.13 q^{89} +44.9571 q^{90} +467.005 q^{92} -192.346 q^{93} +153.631 q^{94} -7.29692 q^{95} -663.286 q^{96} -1350.59 q^{97} +64.5353 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.26875	−1.15568	−0.577839	−	0.816151i	$-0.696104\pi$
$2$	−3.26875	−1.15568	−0.577839	+	0.816151i	$0.696104\pi$
$3$	−5.67634	−1.09241	−0.546207	−	0.837651i	$-0.683929\pi$
$3$	−5.67634	−1.09241	−0.546207	+	0.837651i	$0.683929\pi$
$4$	2.68473	0.335591
$5$	−2.63434	−0.235623	−0.117811	−	0.993036i	$-0.537588\pi$
$5$	−2.63434	−0.235623	−0.117811	+	0.993036i	$0.537588\pi$
$6$	18.5546	1.26248
$7$	0	0
$7$	0	0
$8$	17.3743	0.767843
$9$	5.22089	0.193366
$10$	8.61100	0.272304
$11$	12.3610	0.338816	0.169408	−	0.985546i	$-0.445814\pi$
$11$	12.3610	0.338816	0.169408	+	0.985546i	$0.445814\pi$
$12$	−15.2394	−0.366604
$13$	−40.0263	−0.853945	−0.426973	−	0.904265i	$-0.640420\pi$
$13$	−40.0263	−0.853945	−0.426973	+	0.904265i	$0.640420\pi$
$14$	0	0
$15$	14.9534	0.257397
$16$	−78.2701	−1.22297
$17$	37.9479	0.541396	0.270698	−	0.962664i	$-0.412746\pi$
$17$	37.9479	0.541396	0.270698	+	0.962664i	$0.412746\pi$
$18$	−17.0658	−0.223469
$19$	2.76992	0.0334455	0.0167227	−	0.999860i	$-0.494677\pi$
$19$	2.76992	0.0334455	0.0167227	+	0.999860i	$0.494677\pi$
$20$	−7.07249	−0.0790728
$21$	0	0
$22$	−40.4049	−0.391562
$23$	173.948	1.57699	0.788495	−	0.615041i	$-0.210861\pi$
$23$	173.948	1.57699	0.788495	+	0.615041i	$0.210861\pi$
$24$	−98.6225	−0.838801
$25$	−118.060	−0.944482
$26$	130.836	0.986886
$27$	123.626	0.881177
$28$	0	0
$29$	−29.7471	−0.190479	−0.0952396	−	0.995454i	$-0.530362\pi$
$29$	−29.7471	−0.190479	−0.0952396	+	0.995454i	$0.530362\pi$
$30$	−48.8790	−0.297468
$31$	33.8856	0.196324	0.0981618	−	0.995170i	$-0.468704\pi$
$31$	33.8856	0.196324	0.0981618	+	0.995170i	$0.468704\pi$
$32$	116.851	0.645516
$33$	−70.1651	−0.370127
$34$	−124.042	−0.625679
$35$	0	0
$36$	14.0167	0.0648920
$37$	−376.094	−1.67107	−0.835534	−	0.549439i	$-0.814841\pi$
$37$	−376.094	−1.67107	−0.835534	+	0.549439i	$0.814841\pi$
$38$	−9.05418	−0.0386522
$39$	227.203	0.932861
$40$	−45.7698	−0.180921
$41$	376.964	1.43590	0.717950	−	0.696094i	$-0.245080\pi$
$41$	376.964	1.43590	0.717950	+	0.696094i	$0.245080\pi$
$42$	0	0
$43$	557.306	1.97647	0.988237	−	0.152933i	$-0.0488718\pi$
$43$	557.306	1.97647	0.988237	+	0.152933i	$0.0488718\pi$
$44$	33.1859	0.113704
$45$	−13.7536	−0.0455615
$46$	−568.594	−1.82249
$47$	−47.0000	−0.145865
$47$	−47.0000	−0.145865
$48$	444.288	1.33599
$49$	0	0
$50$	385.909	1.09152
$51$	−215.406	−0.591428
$52$	−107.460	−0.286576
$53$	−349.584	−0.906020	−0.453010	−	0.891506i	$-0.649650\pi$
$53$	−349.584	−0.906020	−0.453010	+	0.891506i	$0.649650\pi$
$54$	−404.102	−1.01836
$55$	−32.5630	−0.0798326
$56$	0	0
$57$	−15.7230	−0.0365363
$58$	97.2358	0.220133
$59$	708.894	1.56424	0.782120	−	0.623128i	$-0.214138\pi$
$59$	708.894	1.56424	0.782120	+	0.623128i	$0.214138\pi$
$60$	40.1459	0.0863802
$61$	−95.4907	−0.200432	−0.100216	−	0.994966i	$-0.531953\pi$
$61$	−95.4907	−0.200432	−0.100216	+	0.994966i	$0.531953\pi$
$62$	−110.763	−0.226887
$63$	0	0
$64$	244.204	0.476961
$65$	105.443	0.201209
$66$	229.352	0.427747
$67$	−512.396	−0.934315	−0.467157	−	0.884174i	$-0.654722\pi$
$67$	−512.396	−0.934315	−0.467157	+	0.884174i	$0.654722\pi$
$68$	101.880	0.181688
$69$	−987.392	−1.72272
$70$	0	0
$71$	366.345	0.612354	0.306177	−	0.951975i	$-0.400950\pi$
$71$	366.345	0.612354	0.306177	+	0.951975i	$0.400950\pi$
$72$	90.7093	0.148475
$73$	492.629	0.789834	0.394917	−	0.918717i	$-0.370773\pi$
$73$	492.629	0.789834	0.394917	+	0.918717i	$0.370773\pi$
$74$	1229.36	1.93122
$75$	670.151	1.03176
$76$	7.43649	0.0112240
$77$	0	0
$78$	−742.670	−1.07809
$79$	756.796	1.07780	0.538900	−	0.842370i	$-0.318840\pi$
$79$	756.796	1.07780	0.538900	+	0.842370i	$0.318840\pi$
$80$	206.190	0.288159
$81$	−842.706	−1.15598
$82$	−1232.20	−1.65944
$83$	1214.95	1.60672	0.803360	−	0.595493i	$-0.203043\pi$
$83$	1214.95	1.60672	0.803360	+	0.595493i	$0.203043\pi$
$84$	0	0
$85$	−99.9678	−0.127565
$86$	−1821.69	−2.28417
$87$	168.855	0.208082
$88$	214.763	0.260157
$89$	−1049.13	−1.24952	−0.624762	−	0.780815i	$-0.714804\pi$
$89$	−1049.13	−1.24952	−0.624762	+	0.780815i	$0.714804\pi$
$90$	44.9571	0.0526544
$91$	0	0
$92$	467.005	0.529224
$93$	−192.346	−0.214466
$94$	153.631	0.168573
$95$	−7.29692	−0.00788050
$96$	−663.286	−0.705171
$97$	−1350.59	−1.41372	−0.706862	−	0.707352i	$-0.749890\pi$
$97$	−1350.59	−1.41372	−0.706862	+	0.707352i	$0.749890\pi$
$98$	0	0
$99$	64.5353	0.0655155
$100$	−316.960	−0.316960
$101$	−2.07604	−0.00204528	−0.00102264	−	0.999999i	$-0.500326\pi$
$101$	−2.07604	−0.00204528	−0.00102264	+	0.999999i	$0.500326\pi$
$102$	704.107	0.683500
$103$	−577.511	−0.552464	−0.276232	−	0.961091i	$-0.589086\pi$
$103$	−577.511	−0.552464	−0.276232	+	0.961091i	$0.589086\pi$
$104$	−695.428	−0.655696
$105$	0	0
$106$	1142.70	1.04707
$107$	−615.999	−0.556550	−0.278275	−	0.960501i	$-0.589763\pi$
$107$	−615.999	−0.556550	−0.278275	+	0.960501i	$0.589763\pi$
$108$	331.902	0.295715
$109$	−1370.30	−1.20414	−0.602069	−	0.798444i	$-0.705657\pi$
$109$	−1370.30	−1.20414	−0.602069	+	0.798444i	$0.705657\pi$
$110$	106.440	0.0922608
$111$	2134.84	1.82550
$112$	0	0
$113$	1507.05	1.25461	0.627307	−	0.778772i	$-0.284157\pi$
$113$	1507.05	1.25461	0.627307	+	0.778772i	$0.284157\pi$
$114$	51.3947	0.0422241
$115$	−458.239	−0.371574
$116$	−79.8629	−0.0639231
$117$	−208.973	−0.165124
$118$	−2317.20	−1.80776
$119$	0	0
$120$	259.805	0.197640
$121$	−1178.21	−0.885204
$122$	312.135	0.231635
$123$	−2139.78	−1.56860
$124$	90.9736	0.0658844
$125$	640.303	0.458164
$126$	0	0
$127$	−560.670	−0.391743	−0.195872	−	0.980630i	$-0.562754\pi$
$127$	−560.670	−0.391743	−0.195872	+	0.980630i	$0.562754\pi$
$128$	−1733.05	−1.19673
$129$	−3163.46	−2.15913
$130$	−344.666	−0.232532
$131$	2458.88	1.63995	0.819975	−	0.572399i	$-0.193987\pi$
$131$	2458.88	1.63995	0.819975	+	0.572399i	$0.193987\pi$
$132$	−188.374	−0.124211
$133$	0	0
$134$	1674.89	1.07977
$135$	−325.672	−0.207625
$136$	659.319	0.415707
$137$	−608.963	−0.379761	−0.189880	−	0.981807i	$-0.560810\pi$
$137$	−608.963	−0.379761	−0.189880	+	0.981807i	$0.560810\pi$
$138$	3227.54	1.99091
$139$	−2625.11	−1.60186	−0.800932	−	0.598755i	$-0.795662\pi$
$139$	−2625.11	−1.60186	−0.800932	+	0.598755i	$0.795662\pi$
$140$	0	0
$141$	266.788	0.159345
$142$	−1197.49	−0.707684
$143$	−494.764	−0.289330
$144$	−408.639	−0.236481
$145$	78.3639	0.0448812
$146$	−1610.28	−0.912793
$147$	0	0
$148$	−1009.71	−0.560795
$149$	−316.339	−0.173929	−0.0869647	−	0.996211i	$-0.527717\pi$
$149$	−316.339	−0.173929	−0.0869647	+	0.996211i	$0.527717\pi$
$150$	−2190.56	−1.19239
$151$	−3397.80	−1.83118	−0.915592	−	0.402109i	$-0.868277\pi$
$151$	−3397.80	−1.83118	−0.915592	+	0.402109i	$0.868277\pi$
$152$	48.1254	0.0256808
$153$	198.122	0.104688
$154$	0	0
$155$	−89.2661	−0.0462582
$156$	609.978	0.313060
$157$	−3426.19	−1.74165	−0.870827	−	0.491590i	$-0.836416\pi$
$157$	−3426.19	−1.74165	−0.870827	+	0.491590i	$0.836416\pi$
$158$	−2473.78	−1.24559
$159$	1984.36	0.989748
$160$	−307.825	−0.152098
$161$	0	0
$162$	2754.60	1.33594
$163$	−3248.00	−1.56076	−0.780378	−	0.625307i	$-0.784974\pi$
$163$	−3248.00	−1.56076	−0.780378	+	0.625307i	$0.784974\pi$
$164$	1012.05	0.481876
$165$	184.839	0.0872102
$166$	−3971.36	−1.85685
$167$	1649.51	0.764329	0.382165	−	0.924094i	$-0.375179\pi$
$167$	1649.51	0.764329	0.382165	+	0.924094i	$0.375179\pi$
$168$	0	0
$169$	−594.898	−0.270777
$170$	326.770	0.147424
$171$	14.4615	0.00646722
$172$	1496.22	0.663287
$173$	−2617.78	−1.15044	−0.575221	−	0.817998i	$-0.695084\pi$
$173$	−2617.78	−1.15044	−0.575221	+	0.817998i	$0.695084\pi$
$174$	−551.944	−0.240476
$175$	0	0
$176$	−967.494	−0.414361
$177$	−4023.93	−1.70880
$178$	3429.35	1.44405
$179$	3766.31	1.57267	0.786333	−	0.617803i	$-0.211977\pi$
$179$	3766.31	1.57267	0.786333	+	0.617803i	$0.211977\pi$
$180$	−36.9247	−0.0152900
$181$	−15.7671	−0.00647491	−0.00323745	−	0.999995i	$-0.501031\pi$
$181$	−15.7671	−0.00647491	−0.00323745	+	0.999995i	$0.501031\pi$
$182$	0	0
$183$	542.038	0.218954
$184$	3022.23	1.21088
$185$	990.760	0.393741
$186$	628.732	0.247854
$187$	469.073	0.183433
$188$	−126.182	−0.0489510
$189$	0	0
$190$	23.8518	0.00910732
$191$	−4032.85	−1.52779	−0.763893	−	0.645343i	$-0.776714\pi$
$191$	−4032.85	−1.52779	−0.763893	+	0.645343i	$0.776714\pi$
$192$	−1386.19	−0.521038
$193$	3949.93	1.47317	0.736585	−	0.676345i	$-0.236437\pi$
$193$	3949.93	1.47317	0.736585	+	0.676345i	$0.236437\pi$
$194$	4414.73	1.63381
$195$	−598.530	−0.219803
$196$	0	0
$197$	−1704.20	−0.616343	−0.308171	−	0.951331i	$-0.599717\pi$
$197$	−1704.20	−0.616343	−0.308171	+	0.951331i	$0.599717\pi$
$198$	−210.950	−0.0757149
$199$	4510.93	1.60689	0.803446	−	0.595378i	$-0.202998\pi$
$199$	4510.93	1.60689	0.803446	+	0.595378i	$0.202998\pi$
$200$	−2051.21	−0.725213
$201$	2908.53	1.02066
$202$	6.78605	0.00236369
$203$	0	0
$204$	−578.306	−0.198478
$205$	−993.052	−0.338331
$206$	1887.74	0.638471
$207$	908.166	0.304937
$208$	3132.86	1.04435
$209$	34.2389	0.0113318
$210$	0	0
$211$	1875.32	0.611861	0.305930	−	0.952054i	$-0.401033\pi$
$211$	1875.32	0.611861	0.305930	+	0.952054i	$0.401033\pi$
$212$	−938.538	−0.304052
$213$	−2079.50	−0.668943
$214$	2013.55	0.643192
$215$	−1468.13	−0.465702
$216$	2147.91	0.676605
$217$	0	0
$218$	4479.17	1.39160
$219$	−2796.33	−0.862825
$220$	−87.4228	−0.0267911
$221$	−1518.91	−0.462322
$222$	−6978.26	−2.10968
$223$	4289.05	1.28796	0.643982	−	0.765041i	$-0.277281\pi$
$223$	4289.05	1.28796	0.643982	+	0.765041i	$0.277281\pi$
$224$	0	0
$225$	−616.380	−0.182631
$226$	−4926.17	−1.44993
$227$	−4363.42	−1.27582	−0.637908	−	0.770112i	$-0.720200\pi$
$227$	−4363.42	−1.27582	−0.637908	+	0.770112i	$0.720200\pi$
$228$	−42.2121	−0.0122612
$229$	3777.06	1.08993	0.544967	−	0.838457i	$-0.316542\pi$
$229$	3777.06	1.08993	0.544967	+	0.838457i	$0.316542\pi$
$230$	1497.87	0.429420
$231$	0	0
$232$	−516.835	−0.146258
$233$	5963.12	1.67664	0.838320	−	0.545178i	$-0.183538\pi$
$233$	5963.12	1.67664	0.838320	+	0.545178i	$0.183538\pi$
$234$	683.080	0.190830
$235$	123.814	0.0343691
$236$	1903.19	0.524945
$237$	−4295.83	−1.17740
$238$	0	0
$239$	−3896.96	−1.05470	−0.527351	−	0.849648i	$-0.676815\pi$
$239$	−3896.96	−1.05470	−0.527351	+	0.849648i	$0.676815\pi$
$240$	−1170.41	−0.314789
$241$	−2422.59	−0.647522	−0.323761	−	0.946139i	$-0.604947\pi$
$241$	−2422.59	−0.647522	−0.323761	+	0.946139i	$0.604947\pi$
$242$	3851.26	1.02301
$243$	1445.60	0.381626
$244$	−256.367	−0.0672631
$245$	0	0
$246$	6994.41	1.81279
$247$	−110.870	−0.0285606
$248$	588.738	0.150746
$249$	−6896.46	−1.75520
$250$	−2092.99	−0.529490
$251$	303.935	0.0764311	0.0382156	−	0.999270i	$-0.487833\pi$
$251$	303.935	0.0764311	0.0382156	+	0.999270i	$0.487833\pi$
$252$	0	0
$253$	2150.17	0.534309
$254$	1832.69	0.452729
$255$	567.451	0.139354
$256$	3711.27	0.906073
$257$	1217.16	0.295426	0.147713	−	0.989030i	$-0.452809\pi$
$257$	1217.16	0.295426	0.147713	+	0.989030i	$0.452809\pi$
$258$	10340.6	2.49525
$259$	0	0
$260$	283.085	0.0675239
$261$	−155.306	−0.0368322
$262$	−8037.47	−1.89525
$263$	−3845.65	−0.901646	−0.450823	−	0.892613i	$-0.648869\pi$
$263$	−3845.65	−0.901646	−0.450823	+	0.892613i	$0.648869\pi$
$264$	−1219.07	−0.284199
$265$	920.923	0.213479
$266$	0	0
$267$	5955.23	1.36500
$268$	−1375.64	−0.313548
$269$	2742.30	0.621565	0.310783	−	0.950481i	$-0.399409\pi$
$269$	2742.30	0.621565	0.310783	+	0.950481i	$0.399409\pi$
$270$	1064.54	0.239948
$271$	2633.82	0.590380	0.295190	−	0.955439i	$-0.404617\pi$
$271$	2633.82	0.590380	0.295190	+	0.955439i	$0.404617\pi$
$272$	−2970.19	−0.662110
$273$	0	0
$274$	1990.55	0.438881
$275$	−1459.34	−0.320005
$276$	−2650.88	−0.578131
$277$	3244.10	0.703679	0.351840	−	0.936060i	$-0.385556\pi$
$277$	3244.10	0.703679	0.351840	+	0.936060i	$0.385556\pi$
$278$	8580.84	1.85124
$279$	176.913	0.0379623
$280$	0	0
$281$	749.180	0.159047	0.0795237	−	0.996833i	$-0.474660\pi$
$281$	749.180	0.159047	0.0795237	+	0.996833i	$0.474660\pi$
$282$	−872.064	−0.184151
$283$	−2673.78	−0.561624	−0.280812	−	0.959763i	$-0.590604\pi$
$283$	−2673.78	−0.561624	−0.280812	+	0.959763i	$0.590604\pi$
$284$	983.537	0.205501
$285$	41.4198	0.00860876
$286$	1617.26	0.334372
$287$	0	0
$288$	610.066	0.124821
$289$	−3472.95	−0.706891
$290$	−256.152	−0.0518682
$291$	7666.39	1.54437
$292$	1322.58	0.265061
$293$	−6688.16	−1.33354	−0.666769	−	0.745264i	$-0.732323\pi$
$293$	−6688.16	−1.33354	−0.666769	+	0.745264i	$0.732323\pi$
$294$	0	0
$295$	−1867.47	−0.368570
$296$	−6534.37	−1.28312
$297$	1528.13	0.298557
$298$	1034.03	0.201006
$299$	−6962.51	−1.34666
$300$	1799.17	0.346251
$301$	0	0
$302$	11106.5	2.11626
$303$	11.7843	0.00223429
$304$	−216.802	−0.0409028
$305$	251.555	0.0472262
$306$	−647.611	−0.120985
$307$	5351.39	0.994853	0.497427	−	0.867506i	$-0.334278\pi$
$307$	5351.39	0.994853	0.497427	+	0.867506i	$0.334278\pi$
$308$	0	0
$309$	3278.15	0.603519
$310$	291.789	0.0534596
$311$	−5242.75	−0.955914	−0.477957	−	0.878383i	$-0.658623\pi$
$311$	−5242.75	−0.955914	−0.477957	+	0.878383i	$0.658623\pi$
$312$	3947.49	0.716290
$313$	−7370.88	−1.33108	−0.665538	−	0.746364i	$-0.731798\pi$
$313$	−7370.88	−1.33108	−0.665538	+	0.746364i	$0.731798\pi$
$314$	11199.4	2.01279
$315$	0	0
$316$	2031.79	0.361700
$317$	−2507.78	−0.444325	−0.222163	−	0.975010i	$-0.571312\pi$
$317$	−2507.78	−0.444325	−0.222163	+	0.975010i	$0.571312\pi$
$318$	−6486.37	−1.14383
$319$	−367.703	−0.0645373
$320$	−643.316	−0.112383
$321$	3496.62	0.607982
$322$	0	0
$323$	105.113	0.0181072
$324$	−2262.44	−0.387935
$325$	4725.51	0.806536
$326$	10616.9	1.80373
$327$	7778.30	1.31542
$328$	6549.49	1.10255
$329$	0	0
$330$	−604.192	−0.100787
$331$	6670.89	1.10775	0.553875	−	0.832600i	$-0.313148\pi$
$331$	6670.89	1.10775	0.553875	+	0.832600i	$0.313148\pi$
$332$	3261.81	0.539201
$333$	−1963.55	−0.323128
$334$	−5391.84	−0.883318
$335$	1349.82	0.220146
$336$	0	0
$337$	10602.2	1.71376	0.856878	−	0.515519i	$-0.172401\pi$
$337$	10602.2	1.71376	0.856878	+	0.515519i	$0.172401\pi$
$338$	1944.57	0.312931
$339$	−8554.53	−1.37056
$340$	−268.386	−0.0428097
$341$	418.859	0.0665175
$342$	−47.2709	−0.00747403
$343$	0	0
$344$	9682.80	1.51762
$345$	2601.13	0.405913
$346$	8556.88	1.32954
$347$	2690.54	0.416241	0.208121	−	0.978103i	$-0.433265\pi$
$347$	2690.54	0.416241	0.208121	+	0.978103i	$0.433265\pi$
$348$	453.329	0.0698304
$349$	−3999.27	−0.613398	−0.306699	−	0.951806i	$-0.599225\pi$
$349$	−3999.27	−0.613398	−0.306699	+	0.951806i	$0.599225\pi$
$350$	0	0
$351$	−4948.28	−0.752477
$352$	1444.39	0.218711
$353$	8340.21	1.25752	0.628760	−	0.777599i	$-0.283563\pi$
$353$	8340.21	1.25752	0.628760	+	0.777599i	$0.283563\pi$
$354$	13153.2	1.97482
$355$	−965.077	−0.144284
$356$	−2816.63	−0.419329
$357$	0	0
$358$	−12311.1	−1.81750
$359$	6074.83	0.893085	0.446543	−	0.894762i	$-0.352655\pi$
$359$	6074.83	0.893085	0.446543	+	0.894762i	$0.352655\pi$
$360$	−238.959	−0.0349840
$361$	−6851.33	−0.998881
$362$	51.5387	0.00748291
$363$	6687.91	0.967008
$364$	0	0
$365$	−1297.75	−0.186103
$366$	−1771.79	−0.253041
$367$	5273.71	0.750097	0.375049	−	0.927005i	$-0.377626\pi$
$367$	5273.71	0.750097	0.375049	+	0.927005i	$0.377626\pi$
$368$	−13615.0	−1.92861
$369$	1968.09	0.277655
$370$	−3238.55	−0.455038
$371$	0	0
$372$	−516.397	−0.0719730
$373$	−10502.1	−1.45785	−0.728924	−	0.684595i	$-0.759979\pi$
$373$	−10502.1	−1.45785	−0.728924	+	0.684595i	$0.759979\pi$
$374$	−1533.28	−0.211990
$375$	−3634.58	−0.500504
$376$	−816.592	−0.112001
$377$	1190.66	0.162659
$378$	0	0
$379$	3131.95	0.424479	0.212240	−	0.977218i	$-0.431924\pi$
$379$	3131.95	0.424479	0.212240	+	0.977218i	$0.431924\pi$
$380$	−19.5902	−0.00264463
$381$	3182.56	0.427946
$382$	13182.4	1.76563
$383$	10493.9	1.40004	0.700020	−	0.714124i	$-0.253175\pi$
$383$	10493.9	1.40004	0.700020	+	0.714124i	$0.253175\pi$
$384$	9837.38	1.30732
$385$	0	0
$386$	−12911.3	−1.70251
$387$	2909.63	0.382183
$388$	−3625.96	−0.474433
$389$	−11414.7	−1.48779	−0.743893	−	0.668299i	$-0.767023\pi$
$389$	−11414.7	−1.48779	−0.743893	+	0.668299i	$0.767023\pi$
$390$	1956.44	0.254022
$391$	6600.98	0.853775
$392$	0	0
$393$	−13957.5	−1.79150
$394$	5570.62	0.712293
$395$	−1993.66	−0.253954
$396$	173.260	0.0219864
$397$	10729.7	1.35644	0.678221	−	0.734858i	$-0.262751\pi$
$397$	10729.7	1.35644	0.678221	+	0.734858i	$0.262751\pi$
$398$	−14745.1	−1.85705
$399$	0	0
$400$	9240.58	1.15507
$401$	1380.98	0.171977	0.0859886	−	0.996296i	$-0.472595\pi$
$401$	1380.98	0.171977	0.0859886	+	0.996296i	$0.472595\pi$
$402$	−9507.27	−1.17955
$403$	−1356.31	−0.167650
$404$	−5.57360	−0.000686378 0
$405$	2219.98	0.272374
$406$	0	0
$407$	−4648.89	−0.566184
$408$	−3742.52	−0.454123
$409$	13314.8	1.60971	0.804856	−	0.593470i	$-0.202242\pi$
$409$	13314.8	1.60971	0.804856	+	0.593470i	$0.202242\pi$
$410$	3246.04	0.391001
$411$	3456.68	0.414856
$412$	−1550.46	−0.185402
$413$	0	0
$414$	−2968.57	−0.352409
$415$	−3200.59	−0.378580
$416$	−4677.11	−0.551236
$417$	14901.0	1.74990
$418$	−111.919	−0.0130960
$419$	16156.0	1.88370	0.941851	−	0.336032i	$-0.109085\pi$
$419$	16156.0	1.88370	0.941851	+	0.336032i	$0.109085\pi$
$420$	0	0
$421$	1843.19	0.213376	0.106688	−	0.994293i	$-0.465975\pi$
$421$	1843.19	0.213376	0.106688	+	0.994293i	$0.465975\pi$
$422$	−6129.96	−0.707114
$423$	−245.382	−0.0282054
$424$	−6073.77	−0.695680
$425$	−4480.14	−0.511338
$426$	6797.36	0.773083
$427$	0	0
$428$	−1653.79	−0.186773
$429$	2808.45	0.316068
$430$	4798.96	0.538201
$431$	−4989.08	−0.557577	−0.278789	−	0.960353i	$-0.589933\pi$
$431$	−4989.08	−0.557577	−0.278789	+	0.960353i	$0.589933\pi$
$432$	−9676.19	−1.07765
$433$	7029.72	0.780200	0.390100	−	0.920772i	$-0.372440\pi$
$433$	7029.72	0.780200	0.390100	+	0.920772i	$0.372440\pi$
$434$	0	0
$435$	−444.821	−0.0490288
$436$	−3678.89	−0.404098
$437$	481.824	0.0527431
$438$	9140.51	0.997147
$439$	989.884	0.107619	0.0538093	−	0.998551i	$-0.482864\pi$
$439$	989.884	0.107619	0.0538093	+	0.998551i	$0.482864\pi$
$440$	−565.759	−0.0612989
$441$	0	0
$442$	4964.95	0.534296
$443$	10685.3	1.14599	0.572995	−	0.819559i	$-0.305781\pi$
$443$	10685.3	1.14599	0.572995	+	0.819559i	$0.305781\pi$
$444$	5731.47	0.612620
$445$	2763.77	0.294416
$446$	−14019.8	−1.48847
$447$	1795.65	0.190003
$448$	0	0
$449$	−8849.12	−0.930102	−0.465051	−	0.885284i	$-0.653964\pi$
$449$	−8849.12	−0.930102	−0.465051	+	0.885284i	$0.653964\pi$
$450$	2014.79	0.211063
$451$	4659.65	0.486506
$452$	4046.02	0.421037
$453$	19287.1	2.00041
$454$	14262.9	1.47443
$455$	0	0
$456$	−273.177	−0.0280541
$457$	−2228.19	−0.228075	−0.114038	−	0.993476i	$-0.536378\pi$
$457$	−2228.19	−0.228075	−0.114038	+	0.993476i	$0.536378\pi$
$458$	−12346.3	−1.25961
$459$	4691.34	0.477065
$460$	−1230.25	−0.124697
$461$	−10724.7	−1.08351	−0.541756	−	0.840536i	$-0.682240\pi$
$461$	−10724.7	−1.08351	−0.541756	+	0.840536i	$0.682240\pi$
$462$	0	0
$463$	−18635.6	−1.87056	−0.935280	−	0.353909i	$-0.884852\pi$
$463$	−18635.6	−1.87056	−0.935280	+	0.353909i	$0.884852\pi$
$464$	2328.31	0.232950
$465$	506.705	0.0505331
$466$	−19492.0	−1.93766
$467$	8034.98	0.796177	0.398089	−	0.917347i	$-0.369674\pi$
$467$	8034.98	0.796177	0.398089	+	0.917347i	$0.369674\pi$
$468$	−561.035	−0.0554142
$469$	0	0
$470$	−404.717	−0.0397196
$471$	19448.2	1.90260
$472$	12316.5	1.20109
$473$	6888.84	0.669660
$474$	14042.0	1.36070
$475$	−327.018	−0.0315886
$476$	0	0
$477$	−1825.14	−0.175194
$478$	12738.2	1.21889
$479$	1360.51	0.129777	0.0648885	−	0.997893i	$-0.479331\pi$
$479$	1360.51	0.129777	0.0648885	+	0.997893i	$0.479331\pi$
$480$	1747.32	0.166154
$481$	15053.6	1.42700
$482$	7918.84	0.748326
$483$	0	0
$484$	−3163.16	−0.297067
$485$	3557.90	0.333105
$486$	−4725.29	−0.441036
$487$	10656.7	0.991581	0.495790	−	0.868442i	$-0.334878\pi$
$487$	10656.7	0.991581	0.495790	+	0.868442i	$0.334878\pi$
$488$	−1659.08	−0.153900
$489$	18436.8	1.70499
$490$	0	0
$491$	7216.66	0.663306	0.331653	−	0.943401i	$-0.392394\pi$
$491$	7216.66	0.663306	0.331653	+	0.943401i	$0.392394\pi$
$492$	−5744.73	−0.526407
$493$	−1128.84	−0.103125
$494$	362.405	0.0330068
$495$	−170.008	−0.0154369
$496$	−2652.23	−0.240098
$497$	0	0
$498$	22542.8	2.02845
$499$	−17262.8	−1.54868	−0.774340	−	0.632770i	$-0.781918\pi$
$499$	−17262.8	−1.54868	−0.774340	+	0.632770i	$0.781918\pi$
$500$	1719.04	0.153756
$501$	−9363.19	−0.834963
$502$	−993.488	−0.0883298
$503$	−9840.60	−0.872307	−0.436154	−	0.899872i	$-0.643660\pi$
$503$	−9840.60	−0.872307	−0.436154	+	0.899872i	$0.643660\pi$
$504$	0	0
$505$	5.46899	0.000481914 0
$506$	−7028.38	−0.617489
$507$	3376.85	0.295801
$508$	−1505.25	−0.131466
$509$	16629.0	1.44807	0.724033	−	0.689765i	$-0.242286\pi$
$509$	16629.0	1.44807	0.724033	+	0.689765i	$0.242286\pi$
$510$	−1854.86	−0.161048
$511$	0	0
$512$	1733.17	0.149601
$513$	342.434	0.0294714
$514$	−3978.60	−0.341417
$515$	1521.36	0.130173
$516$	−8493.03	−0.724583
$517$	−580.966	−0.0494214
$518$	0	0
$519$	14859.4	1.25676
$520$	1831.99	0.154497
$521$	18311.3	1.53980	0.769898	−	0.638167i	$-0.220307\pi$
$521$	18311.3	1.53980	0.769898	+	0.638167i	$0.220307\pi$
$522$	507.657	0.0425662
$523$	1319.51	0.110322	0.0551608	−	0.998477i	$-0.482433\pi$
$523$	1319.51	0.110322	0.0551608	+	0.998477i	$0.482433\pi$
$524$	6601.43	0.550353
$525$	0	0
$526$	12570.5	1.04201
$527$	1285.89	0.106289
$528$	5491.83	0.452654
$529$	18091.1	1.48690
$530$	−3010.27	−0.246712
$531$	3701.06	0.302471
$532$	0	0
$533$	−15088.5	−1.22618
$534$	−19466.2	−1.57750
$535$	1622.75	0.131136
$536$	−8902.51	−0.717407
$537$	−21378.9	−1.71800
$538$	−8963.90	−0.718329
$539$	0	0
$540$	−874.342	−0.0696772
$541$	−12640.5	−1.00455	−0.502273	−	0.864709i	$-0.667503\pi$
$541$	−12640.5	−1.00455	−0.502273	+	0.864709i	$0.667503\pi$
$542$	−8609.29	−0.682289
$543$	89.4994	0.00707327
$544$	4434.25	0.349480
$545$	3609.84	0.283722
$546$	0	0
$547$	−1331.48	−0.104077	−0.0520385	−	0.998645i	$-0.516572\pi$
$547$	−1331.48	−0.104077	−0.0520385	+	0.998645i	$0.516572\pi$
$548$	−1634.90	−0.127444
$549$	−498.547	−0.0387567
$550$	4770.22	0.369823
$551$	−82.3971	−0.00637066
$552$	−17155.2	−1.32278
$553$	0	0
$554$	−10604.2	−0.813227
$555$	−5623.89	−0.430128
$556$	−7047.71	−0.537571
$557$	1134.97	0.0863382	0.0431691	−	0.999068i	$-0.486255\pi$
$557$	1134.97	0.0863382	0.0431691	+	0.999068i	$0.486255\pi$
$558$	−578.284	−0.0438722
$559$	−22306.9	−1.68780
$560$	0	0
$561$	−2662.62	−0.200385
$562$	−2448.88	−0.183808
$563$	−3308.38	−0.247658	−0.123829	−	0.992304i	$-0.539517\pi$
$563$	−3308.38	−0.247658	−0.123829	+	0.992304i	$0.539517\pi$
$564$	716.254	0.0534747
$565$	−3970.08	−0.295615
$566$	8739.92	0.649057
$567$	0	0
$568$	6364.98	0.470191
$569$	7883.08	0.580801	0.290401	−	0.956905i	$-0.406211\pi$
$569$	7883.08	0.580801	0.290401	+	0.956905i	$0.406211\pi$
$570$	−135.391	−0.00994896
$571$	−19031.0	−1.39479	−0.697393	−	0.716689i	$-0.745657\pi$
$571$	−19031.0	−1.39479	−0.697393	+	0.716689i	$0.745657\pi$
$572$	−1328.31	−0.0970966
$573$	22891.9	1.66897
$574$	0	0
$575$	−20536.4	−1.48944
$576$	1274.96	0.0922281
$577$	4901.02	0.353609	0.176804	−	0.984246i	$-0.443424\pi$
$577$	4901.02	0.353609	0.176804	+	0.984246i	$0.443424\pi$
$578$	11352.2	0.816938
$579$	−22421.1	−1.60931
$580$	210.386	0.0150617
$581$	0	0
$582$	−25059.5	−1.78479
$583$	−4321.20	−0.306974
$584$	8559.08	0.606468
$585$	550.505	0.0389070
$586$	21861.9	1.54114
$587$	−8435.44	−0.593131	−0.296566	−	0.955012i	$-0.595841\pi$
$587$	−8435.44	−0.593131	−0.296566	+	0.955012i	$0.595841\pi$
$588$	0	0
$589$	93.8604	0.00656613
$590$	6104.29	0.425948
$591$	9673.65	0.673301
$592$	29436.9	2.04366
$593$	23375.3	1.61873	0.809367	−	0.587303i	$-0.199810\pi$
$593$	23375.3	1.61873	0.809367	+	0.587303i	$0.199810\pi$
$594$	−4995.09	−0.345035
$595$	0	0
$596$	−849.284	−0.0583692
$597$	−25605.6	−1.75539
$598$	22758.7	1.55631
$599$	−9583.91	−0.653736	−0.326868	−	0.945070i	$-0.605993\pi$
$599$	−9583.91	−0.653736	−0.326868	+	0.945070i	$0.605993\pi$
$600$	11643.4	0.792233
$601$	3485.11	0.236540	0.118270	−	0.992981i	$-0.462265\pi$
$601$	3485.11	0.236540	0.118270	+	0.992981i	$0.462265\pi$
$602$	0	0
$603$	−2675.16	−0.180665
$604$	−9122.16	−0.614529
$605$	3103.80	0.208574
$606$	−38.5199	−0.00258212
$607$	21948.1	1.46762	0.733810	−	0.679355i	$-0.237740\pi$
$607$	21948.1	1.46762	0.733810	+	0.679355i	$0.237740\pi$
$608$	323.668	0.0215896
$609$	0	0
$610$	−822.271	−0.0545783
$611$	1881.23	0.124561
$612$	531.904	0.0351322
$613$	15565.3	1.02557	0.512787	−	0.858516i	$-0.328613\pi$
$613$	15565.3	1.02557	0.512787	+	0.858516i	$0.328613\pi$
$614$	−17492.4	−1.14973
$615$	5636.91	0.369597
$616$	0	0
$617$	3827.83	0.249761	0.124881	−	0.992172i	$-0.460145\pi$
$617$	3827.83	0.249761	0.124881	+	0.992172i	$0.460145\pi$
$618$	−10715.5	−0.697474
$619$	16878.8	1.09599	0.547994	−	0.836483i	$-0.315392\pi$
$619$	16878.8	1.09599	0.547994	+	0.836483i	$0.315392\pi$
$620$	−239.655	−0.0155239
$621$	21504.5	1.38961
$622$	17137.3	1.10473
$623$	0	0
$624$	−17783.2	−1.14086
$625$	13070.8	0.836528
$626$	24093.6	1.53829
$627$	−194.352	−0.0123791
$628$	−9198.39	−0.584483
$629$	−14272.0	−0.904708
$630$	0	0
$631$	−21498.7	−1.35634	−0.678169	−	0.734906i	$-0.737226\pi$
$631$	−21498.7	−1.35634	−0.678169	+	0.734906i	$0.737226\pi$
$632$	13148.8	0.827581
$633$	−10645.0	−0.668404
$634$	8197.32	0.513497
$635$	1477.00	0.0923036
$636$	5327.46	0.332150
$637$	0	0
$638$	1201.93	0.0745844
$639$	1912.65	0.118409
$640$	4565.44	0.281976
$641$	−8686.24	−0.535236	−0.267618	−	0.963525i	$-0.586236\pi$
$641$	−8686.24	−0.535236	−0.267618	+	0.963525i	$0.586236\pi$
$642$	−11429.6	−0.702632
$643$	−4941.09	−0.303044	−0.151522	−	0.988454i	$-0.548417\pi$
$643$	−4941.09	−0.303044	−0.151522	+	0.988454i	$0.548417\pi$
$644$	0	0
$645$	8333.63	0.508739
$646$	−343.588	−0.0209261
$647$	20943.2	1.27258	0.636292	−	0.771449i	$-0.280468\pi$
$647$	20943.2	1.27258	0.636292	+	0.771449i	$0.280468\pi$
$648$	−14641.4	−0.887607
$649$	8762.62	0.529989
$650$	−15446.5	−0.932096
$651$	0	0
$652$	−8720.01	−0.523776
$653$	−11331.9	−0.679100	−0.339550	−	0.940588i	$-0.610275\pi$
$653$	−11331.9	−0.679100	−0.339550	+	0.940588i	$0.610275\pi$
$654$	−25425.3	−1.52020
$655$	−6477.53	−0.386409
$656$	−29505.0	−1.75606
$657$	2571.96	0.152727
$658$	0	0
$659$	−1702.63	−0.100645	−0.0503224	−	0.998733i	$-0.516025\pi$
$659$	−1702.63	−0.100645	−0.0503224	+	0.998733i	$0.516025\pi$
$660$	496.242	0.0292670
$661$	1099.36	0.0646901	0.0323451	−	0.999477i	$-0.489702\pi$
$661$	1099.36	0.0646901	0.0323451	+	0.999477i	$0.489702\pi$
$662$	−21805.5	−1.28020
$663$	8621.88	0.505047
$664$	21108.9	1.23371
$665$	0	0
$666$	6418.34	0.373432
$667$	−5174.46	−0.300384
$668$	4428.49	0.256502
$669$	−24346.1	−1.40699
$670$	−4412.24	−0.254417
$671$	−1180.36	−0.0679094
$672$	0	0
$673$	8658.75	0.495944	0.247972	−	0.968767i	$-0.420236\pi$
$673$	8658.75	0.495944	0.247972	+	0.968767i	$0.420236\pi$
$674$	−34655.8	−1.98055
$675$	−14595.3	−0.832256
$676$	−1597.14	−0.0908705
$677$	−897.808	−0.0509683	−0.0254842	−	0.999675i	$-0.508113\pi$
$677$	−897.808	−0.0509683	−0.0254842	+	0.999675i	$0.508113\pi$
$678$	27962.6	1.58392
$679$	0	0
$680$	−1736.87	−0.0979498
$681$	24768.3	1.39372
$682$	−1369.14	−0.0768728
$683$	13191.6	0.739039	0.369519	−	0.929223i	$-0.379522\pi$
$683$	13191.6	0.739039	0.369519	+	0.929223i	$0.379522\pi$
$684$	38.8251	0.00217034
$685$	1604.22	0.0894802
$686$	0	0
$687$	−21439.9	−1.19066
$688$	−43620.4	−2.41717
$689$	13992.5	0.773691
$690$	−8502.43	−0.469104
$691$	18692.4	1.02908	0.514539	−	0.857467i	$-0.327963\pi$
$691$	18692.4	1.02908	0.514539	+	0.857467i	$0.327963\pi$
$692$	−7028.04	−0.386078
$693$	0	0
$694$	−8794.70	−0.481041
$695$	6915.44	0.377435
$696$	2933.73	0.159774
$697$	14305.0	0.777390
$698$	13072.6	0.708891
$699$	−33848.7	−1.83158
$700$	0	0
$701$	−2786.14	−0.150116	−0.0750579	−	0.997179i	$-0.523914\pi$
$701$	−2786.14	−0.150116	−0.0750579	+	0.997179i	$0.523914\pi$
$702$	16174.7	0.869621
$703$	−1041.75	−0.0558896
$704$	3018.60	0.161602
$705$	−702.811	−0.0375452
$706$	−27262.1	−1.45329
$707$	0	0
$708$	−10803.2	−0.573457
$709$	23493.8	1.24447	0.622235	−	0.782830i	$-0.286225\pi$
$709$	23493.8	1.24447	0.622235	+	0.782830i	$0.286225\pi$
$710$	3154.60	0.166746
$711$	3951.15	0.208410
$712$	−18227.9	−0.959438
$713$	5894.34	0.309600
$714$	0	0
$715$	1303.38	0.0681727
$716$	10111.5	0.527773
$717$	22120.5	1.15217
$718$	−19857.1	−1.03212
$719$	−30377.9	−1.57567	−0.787835	−	0.615887i	$-0.788798\pi$
$719$	−30377.9	−1.57567	−0.787835	+	0.615887i	$0.788798\pi$
$720$	1076.50	0.0557203
$721$	0	0
$722$	22395.3	1.15439
$723$	13751.5	0.707361
$724$	−42.3304	−0.00217292
$725$	3511.95	0.179904
$726$	−21861.1	−1.11755
$727$	7731.08	0.394401	0.197201	−	0.980363i	$-0.436815\pi$
$727$	7731.08	0.394401	0.197201	+	0.980363i	$0.436815\pi$
$728$	0	0
$729$	14547.4	0.739083
$730$	4242.03	0.215075
$731$	21148.6	1.07005
$732$	1455.23	0.0734791
$733$	−29493.6	−1.48618	−0.743091	−	0.669190i	$-0.766641\pi$
$733$	−29493.6	−1.48618	−0.743091	+	0.669190i	$0.766641\pi$
$734$	−17238.5	−0.866870
$735$	0	0
$736$	20326.0	1.01797
$737$	−6333.71	−0.316561
$738$	−6433.19	−0.320880
$739$	−17233.1	−0.857823	−0.428912	−	0.903346i	$-0.641103\pi$
$739$	−17233.1	−0.857823	−0.428912	+	0.903346i	$0.641103\pi$
$740$	2659.92	0.132136
$741$	629.334	0.0312000
$742$	0	0
$743$	13428.0	0.663021	0.331510	−	0.943452i	$-0.392442\pi$
$743$	13428.0	0.663021	0.331510	+	0.943452i	$0.392442\pi$
$744$	−3341.88	−0.164676
$745$	833.344	0.0409817
$746$	34328.7	1.68480
$747$	6343.11	0.310686
$748$	1259.33	0.0615586
$749$	0	0
$750$	11880.5	0.578421
$751$	11598.7	0.563570	0.281785	−	0.959478i	$-0.409074\pi$
$751$	11598.7	0.563570	0.281785	+	0.959478i	$0.409074\pi$
$752$	3678.69	0.178388
$753$	−1725.24	−0.0834944
$754$	−3891.99	−0.187981
$755$	8950.95	0.431468
$756$	0	0
$757$	−6302.37	−0.302594	−0.151297	−	0.988488i	$-0.548345\pi$
$757$	−6302.37	−0.302594	−0.151297	+	0.988488i	$0.548345\pi$
$758$	−10237.6	−0.490561
$759$	−12205.1	−0.583686
$760$	−126.779	−0.00605099
$761$	−6763.49	−0.322176	−0.161088	−	0.986940i	$-0.551500\pi$
$761$	−6763.49	−0.322176	−0.161088	+	0.986940i	$0.551500\pi$
$762$	−10403.0	−0.494567
$763$	0	0
$764$	−10827.1	−0.512711
$765$	−521.921	−0.0246668
$766$	−34302.1	−1.61799
$767$	−28374.4	−1.33578
$768$	−21066.5	−0.989806
$769$	−20013.8	−0.938512	−0.469256	−	0.883062i	$-0.655478\pi$
$769$	−20013.8	−0.938512	−0.469256	+	0.883062i	$0.655478\pi$
$770$	0	0
$771$	−6909.03	−0.322727
$772$	10604.5	0.494383
$773$	−1087.18	−0.0505863	−0.0252932	−	0.999680i	$-0.508052\pi$
$773$	−1087.18	−0.0505863	−0.0252932	+	0.999680i	$0.508052\pi$
$774$	−9510.86	−0.441681
$775$	−4000.54	−0.185424
$776$	−23465.5	−1.08552
$777$	0	0
$778$	37311.8	1.71940
$779$	1044.16	0.0480244
$780$	−1606.89	−0.0737640
$781$	4528.38	0.207475
$782$	−21577.0	−0.986689
$783$	−3677.51	−0.167846
$784$	0	0
$785$	9025.74	0.410373
$786$	45623.4	2.07040
$787$	22354.5	1.01252	0.506259	−	0.862381i	$-0.331028\pi$
$787$	22354.5	1.01252	0.506259	+	0.862381i	$0.331028\pi$
$788$	−4575.33	−0.206839
$789$	21829.2	0.984970
$790$	6516.77	0.293489
$791$	0	0
$792$	1121.25	0.0503056
$793$	3822.14	0.171158
$794$	−35072.7	−1.56761
$795$	−5227.47	−0.233207
$796$	12110.6	0.539259
$797$	−27030.5	−1.20134	−0.600671	−	0.799496i	$-0.705100\pi$
$797$	−27030.5	−1.20134	−0.600671	+	0.799496i	$0.705100\pi$
$798$	0	0
$799$	−1783.55	−0.0789707
$800$	−13795.5	−0.609679
$801$	−5477.40	−0.241616
$802$	−4514.08	−0.198750
$803$	6089.37	0.267608
$804$	7808.63	0.342524
$805$	0	0
$806$	4433.45	0.193749
$807$	−15566.3	−0.679006
$808$	−36.0697	−0.00157045
$809$	15614.0	0.678566	0.339283	−	0.940684i	$-0.389816\pi$
$809$	15614.0	0.678566	0.339283	+	0.940684i	$0.389816\pi$
$810$	−7256.54	−0.314777
$811$	33410.8	1.44662	0.723311	−	0.690522i	$-0.242619\pi$
$811$	33410.8	1.44662	0.723311	+	0.690522i	$0.242619\pi$
$812$	0	0
$813$	−14950.5	−0.644939
$814$	15196.1	0.654326
$815$	8556.35	0.367750
$816$	16859.8	0.723298
$817$	1543.69	0.0661040
$818$	−43522.6	−1.86031
$819$	0	0
$820$	−2666.08	−0.113541
$821$	−32420.6	−1.37818	−0.689090	−	0.724676i	$-0.741989\pi$
$821$	−32420.6	−1.37818	−0.689090	+	0.724676i	$0.741989\pi$
$822$	−11299.0	−0.479439
$823$	23449.0	0.993171	0.496586	−	0.867988i	$-0.334587\pi$
$823$	23449.0	0.993171	0.496586	+	0.867988i	$0.334587\pi$
$824$	−10033.8	−0.424206
$825$	8283.71	0.349578
$826$	0	0
$827$	2349.07	0.0987727	0.0493864	−	0.998780i	$-0.484273\pi$
$827$	2349.07	0.0987727	0.0493864	+	0.998780i	$0.484273\pi$
$828$	2438.18	0.102334
$829$	−33971.5	−1.42326	−0.711628	−	0.702557i	$-0.752042\pi$
$829$	−33971.5	−1.42326	−0.711628	+	0.702557i	$0.752042\pi$
$830$	10461.9	0.437516
$831$	−18414.6	−0.768709
$832$	−9774.57	−0.407298
$833$	0	0
$834$	−48707.8	−2.02232
$835$	−4345.37	−0.180093
$836$	91.9222	0.00380287
$837$	4189.13	0.172996
$838$	−52809.8	−2.17695
$839$	8038.36	0.330769	0.165384	−	0.986229i	$-0.447114\pi$
$839$	8038.36	0.330769	0.165384	+	0.986229i	$0.447114\pi$
$840$	0	0
$841$	−23504.1	−0.963718
$842$	−6024.91	−0.246594
$843$	−4252.60	−0.173745
$844$	5034.73	0.205335
$845$	1567.16	0.0638013
$846$	802.092	0.0325963
$847$	0	0
$848$	27361.9	1.10803
$849$	15177.3	0.613526
$850$	14644.5	0.590942
$851$	−65421.0	−2.63526
$852$	−5582.89	−0.224492
$853$	4780.94	0.191906	0.0959532	−	0.995386i	$-0.469410\pi$
$853$	4780.94	0.191906	0.0959532	+	0.995386i	$0.469410\pi$
$854$	0	0
$855$	−38.0964	−0.00152382
$856$	−10702.5	−0.427343
$857$	5822.21	0.232069	0.116034	−	0.993245i	$-0.462982\pi$
$857$	5822.21	0.232069	0.116034	+	0.993245i	$0.462982\pi$
$858$	−9180.12	−0.365273
$859$	−469.130	−0.0186339	−0.00931694	−	0.999957i	$-0.502966\pi$
$859$	−469.130	−0.0186339	−0.00931694	+	0.999957i	$0.502966\pi$
$860$	−3941.54	−0.156285
$861$	0	0
$862$	16308.1	0.644379
$863$	49068.4	1.93547	0.967733	−	0.251977i	$-0.0810807\pi$
$863$	49068.4	1.93547	0.967733	+	0.251977i	$0.0810807\pi$
$864$	14445.8	0.568814
$865$	6896.13	0.271070
$866$	−22978.4	−0.901660
$867$	19713.7	0.772217
$868$	0	0
$869$	9354.73	0.365176
$870$	1454.01	0.0566615
$871$	20509.3	0.797854
$872$	−23808.0	−0.924588
$873$	−7051.26	−0.273367
$874$	−1574.96	−0.0609541
$875$	0	0
$876$	−7507.39	−0.289556
$877$	13367.1	0.514680	0.257340	−	0.966321i	$-0.417154\pi$
$877$	13367.1	0.514680	0.257340	+	0.966321i	$0.417154\pi$
$878$	−3235.68	−0.124372
$879$	37964.3	1.45677
$880$	2548.71	0.0976329
$881$	−29582.1	−1.13127	−0.565634	−	0.824657i	$-0.691368\pi$
$881$	−29582.1	−1.13127	−0.565634	+	0.824657i	$0.691368\pi$
$882$	0	0
$883$	−30194.5	−1.15077	−0.575383	−	0.817884i	$-0.695147\pi$
$883$	−30194.5	−1.15077	−0.575383	+	0.817884i	$0.695147\pi$
$884$	−4077.87	−0.155151
$885$	10600.4	0.402631
$886$	−34927.6	−1.32440
$887$	−19402.1	−0.734454	−0.367227	−	0.930131i	$-0.619693\pi$
$887$	−19402.1	−0.734454	−0.367227	+	0.930131i	$0.619693\pi$
$888$	37091.3	1.40169
$889$	0	0
$890$	−9034.07	−0.340250
$891$	−10416.7	−0.391663
$892$	11514.9	0.432229
$893$	−130.186	−0.00487852
$894$	−5869.52	−0.219582
$895$	−9921.74	−0.370556
$896$	0	0
$897$	39521.6	1.47111
$898$	28925.6	1.07490
$899$	−1008.00	−0.0373955
$900$	−1654.81	−0.0612893
$901$	−13266.0	−0.490515
$902$	−15231.2	−0.562244
$903$	0	0
$904$	26183.9	0.963345
$905$	41.5359	0.00152563
$906$	−63044.6	−2.31183
$907$	13713.2	0.502027	0.251014	−	0.967984i	$-0.419236\pi$
$907$	13713.2	0.502027	0.251014	+	0.967984i	$0.419236\pi$
$908$	−11714.6	−0.428153
$909$	−10.8388	−0.000395488 0
$910$	0	0
$911$	15868.3	0.577104	0.288552	−	0.957464i	$-0.406826\pi$
$911$	15868.3	0.577104	0.288552	+	0.957464i	$0.406826\pi$
$912$	1230.64	0.0446827
$913$	15017.9	0.544382
$914$	7283.40	0.263581
$915$	−1427.91	−0.0515906
$916$	10140.4	0.365772
$917$	0	0
$918$	−15334.8	−0.551334
$919$	15430.2	0.553858	0.276929	−	0.960890i	$-0.410683\pi$
$919$	15430.2	0.553858	0.276929	+	0.960890i	$0.410683\pi$
$920$	−7961.59	−0.285311
$921$	−30376.3	−1.08679
$922$	35056.4	1.25219
$923$	−14663.4	−0.522917
$924$	0	0
$925$	44401.8	1.57829
$926$	60915.1	2.16176
$927$	−3015.12	−0.106828
$928$	−3475.97	−0.122957
$929$	38415.6	1.35670	0.678350	−	0.734739i	$-0.262695\pi$
$929$	38415.6	1.35670	0.678350	+	0.734739i	$0.262695\pi$
$930$	−1656.29	−0.0584000
$931$	0	0
$932$	16009.4	0.562666
$933$	29759.7	1.04425
$934$	−26264.4	−0.920124
$935$	−1235.70	−0.0432210
$936$	−3630.75	−0.126789
$937$	−21559.0	−0.751656	−0.375828	−	0.926689i	$-0.622642\pi$
$937$	−21559.0	−0.751656	−0.375828	+	0.926689i	$0.622642\pi$
$938$	0	0
$939$	41839.6	1.45408
$940$	332.407	0.0115340
$941$	−29500.9	−1.02200	−0.511001	−	0.859580i	$-0.670725\pi$
$941$	−29500.9	−1.02200	−0.511001	+	0.859580i	$0.670725\pi$
$942$	−63571.4	−2.19880
$943$	65572.4	2.26440
$944$	−55485.2	−1.91302
$945$	0	0
$946$	−22517.9	−0.773912
$947$	18814.1	0.645591	0.322795	−	0.946469i	$-0.395377\pi$
$947$	18814.1	0.645591	0.322795	+	0.946469i	$0.395377\pi$
$948$	−11533.2	−0.395126
$949$	−19718.1	−0.674475
$950$	1068.94	0.0365063
$951$	14235.0	0.485387
$952$	0	0
$953$	−13353.0	−0.453878	−0.226939	−	0.973909i	$-0.572872\pi$
$953$	−13353.0	−0.453878	−0.226939	+	0.973909i	$0.572872\pi$
$954$	5965.92	0.202467
$955$	10623.9	0.359981
$956$	−10462.3	−0.353948
$957$	2087.21	0.0705014
$958$	−4447.16	−0.149980
$959$	0	0
$960$	3651.68	0.122768
$961$	−28642.8	−0.961457
$962$	−49206.6	−1.64915
$963$	−3216.06	−0.107618
$964$	−6504.00	−0.217303
$965$	−10405.4	−0.347112
$966$	0	0
$967$	40719.6	1.35414	0.677071	−	0.735918i	$-0.263249\pi$
$967$	40719.6	1.35414	0.677071	+	0.735918i	$0.263249\pi$
$968$	−20470.5	−0.679697
$969$	−596.657	−0.0197806
$970$	−11629.9	−0.384962
$971$	−36913.0	−1.21997	−0.609987	−	0.792411i	$-0.708826\pi$
$971$	−36913.0	−1.21997	−0.609987	+	0.792411i	$0.708826\pi$
$972$	3881.04	0.128070
$973$	0	0
$974$	−34834.0	−1.14595
$975$	−26823.6	−0.881070
$976$	7474.07	0.245122
$977$	31308.8	1.02524	0.512619	−	0.858616i	$-0.328675\pi$
$977$	31308.8	1.02524	0.512619	+	0.858616i	$0.328675\pi$
$978$	−60265.3	−1.97042
$979$	−12968.3	−0.423359
$980$	0	0
$981$	−7154.19	−0.232840
$982$	−23589.5	−0.766568
$983$	−10452.6	−0.339150	−0.169575	−	0.985517i	$-0.554240\pi$
$983$	−10452.6	−0.339150	−0.169575	+	0.985517i	$0.554240\pi$
$984$	−37177.2	−1.20444
$985$	4489.45	0.145224
$986$	3689.90	0.119179
$987$	0	0
$988$	−297.655	−0.00958468
$989$	96942.5	3.11688
$990$	555.713	0.0178401
$991$	14507.5	0.465032	0.232516	−	0.972593i	$-0.425304\pi$
$991$	14507.5	0.465032	0.232516	+	0.972593i	$0.425304\pi$
$992$	3959.56	0.126730
$993$	−37866.3	−1.21012
$994$	0	0
$995$	−11883.3	−0.378620
$996$	−18515.1	−0.589031
$997$	34160.2	1.08512	0.542560	−	0.840017i	$-0.317455\pi$
$997$	34160.2	1.08512	0.542560	+	0.840017i	$0.317455\pi$
$998$	56427.9	1.78977
$999$	−46494.9	−1.47251

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.n.1.17	yes	68
7.6	odd	2		2303.4.a.m.1.17	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.m.1.17	✓	68	7.6	odd	2
2303.4.a.n.1.17	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)

\(f(q)\)	\(=\)	\(q-3.26875 q^{2} -5.67634 q^{3} +2.68473 q^{4} -2.63434 q^{5} +18.5546 q^{6} +17.3743 q^{8} +5.22089 q^{9} +O(q^{10})\)	\(q-3.26875 q^{2} -5.67634 q^{3} +2.68473 q^{4} -2.63434 q^{5} +18.5546 q^{6} +17.3743 q^{8} +5.22089 q^{9} +8.61100 q^{10} +12.3610 q^{11} -15.2394 q^{12} -40.0263 q^{13} +14.9534 q^{15} -78.2701 q^{16} +37.9479 q^{17} -17.0658 q^{18} +2.76992 q^{19} -7.07249 q^{20} -40.4049 q^{22} +173.948 q^{23} -98.6225 q^{24} -118.060 q^{25} +130.836 q^{26} +123.626 q^{27} -29.7471 q^{29} -48.8790 q^{30} +33.8856 q^{31} +116.851 q^{32} -70.1651 q^{33} -124.042 q^{34} +14.0167 q^{36} -376.094 q^{37} -9.05418 q^{38} +227.203 q^{39} -45.7698 q^{40} +376.964 q^{41} +557.306 q^{43} +33.1859 q^{44} -13.7536 q^{45} -568.594 q^{46} -47.0000 q^{47} +444.288 q^{48} +385.909 q^{50} -215.406 q^{51} -107.460 q^{52} -349.584 q^{53} -404.102 q^{54} -32.5630 q^{55} -15.7230 q^{57} +97.2358 q^{58} +708.894 q^{59} +40.1459 q^{60} -95.4907 q^{61} -110.763 q^{62} +244.204 q^{64} +105.443 q^{65} +229.352 q^{66} -512.396 q^{67} +101.880 q^{68} -987.392 q^{69} +366.345 q^{71} +90.7093 q^{72} +492.629 q^{73} +1229.36 q^{74} +670.151 q^{75} +7.43649 q^{76} -742.670 q^{78} +756.796 q^{79} +206.190 q^{80} -842.706 q^{81} -1232.20 q^{82} +1214.95 q^{83} -99.9678 q^{85} -1821.69 q^{86} +168.855 q^{87} +214.763 q^{88} -1049.13 q^{89} +44.9571 q^{90} +467.005 q^{92} -192.346 q^{93} +153.631 q^{94} -7.29692 q^{95} -663.286 q^{96} -1350.59 q^{97} +64.5353 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 2 q^{2} + 24 q^{3} + 254 q^{4} + 40 q^{5} + 48 q^{6} - 66 q^{8} + 576 q^{9}+O(q^{10}) \) 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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Varieties

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Database

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