LMFDB - Embedded newform 2401.4.a.c.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2401,4,Mod(1,2401)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2401, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2401.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2401 = 7^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2401.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:	$141.663585924$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	no (minimal twist has level 49)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	2401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.275911 q^{2} -3.60983 q^{3} -7.92387 q^{4} +3.79895 q^{5} +0.995991 q^{6} +4.39357 q^{8} -13.9691 q^{9} +O(q^{10})$	\(q-0.275911 q^{2} -3.60983 q^{3} -7.92387 q^{4} +3.79895 q^{5} +0.995991 q^{6} +4.39357 q^{8} -13.9691 q^{9} -1.04817 q^{10} -55.4747 q^{11} +28.6038 q^{12} -48.3590 q^{13} -13.7136 q^{15} +62.1787 q^{16} -57.3770 q^{17} +3.85424 q^{18} +112.013 q^{19} -30.1024 q^{20} +15.3061 q^{22} +120.665 q^{23} -15.8600 q^{24} -110.568 q^{25} +13.3428 q^{26} +147.892 q^{27} +171.162 q^{29} +3.78372 q^{30} +75.8179 q^{31} -52.3044 q^{32} +200.254 q^{33} +15.8310 q^{34} +110.690 q^{36} -397.782 q^{37} -30.9056 q^{38} +174.568 q^{39} +16.6910 q^{40} +86.5608 q^{41} +47.3604 q^{43} +439.575 q^{44} -53.0681 q^{45} -33.2928 q^{46} +416.664 q^{47} -224.455 q^{48} +30.5069 q^{50} +207.121 q^{51} +383.191 q^{52} -315.587 q^{53} -40.8049 q^{54} -210.746 q^{55} -404.347 q^{57} -47.2255 q^{58} +689.606 q^{59} +108.665 q^{60} -245.883 q^{61} -20.9190 q^{62} -482.999 q^{64} -183.714 q^{65} -55.2523 q^{66} +367.091 q^{67} +454.648 q^{68} -435.580 q^{69} +91.8333 q^{71} -61.3745 q^{72} +55.3278 q^{73} +109.753 q^{74} +399.131 q^{75} -887.577 q^{76} -48.1651 q^{78} +436.724 q^{79} +236.214 q^{80} -156.696 q^{81} -23.8831 q^{82} +1298.85 q^{83} -217.973 q^{85} -13.0673 q^{86} -617.865 q^{87} -243.732 q^{88} +77.1808 q^{89} +14.6421 q^{90} -956.134 q^{92} -273.690 q^{93} -114.962 q^{94} +425.532 q^{95} +188.810 q^{96} -1261.25 q^{97} +774.935 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) $ 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9} - 78 q^{10} + q^{11} + 91 q^{12} - 77 q^{13} - 161 q^{15} + 461 q^{16} - 211 q^{17} + 8 q^{18} - 314 q^{19} - 476 q^{20} - 61 q^{22} - 69 q^{23} - 330 q^{24} + 606 q^{25} - 504 q^{26} + 50 q^{27} + 57 q^{29} + 42 q^{30} - 638 q^{31} - 1600 q^{32} - 1574 q^{33} - 1343 q^{34} + 782 q^{36} + 71 q^{37} - 1359 q^{38} - 84 q^{39} + 155 q^{40} - 1393 q^{41} - 125 q^{43} + 52 q^{44} - 1129 q^{45} - 1454 q^{46} - 1483 q^{47} + 974 q^{48} + 3074 q^{50} - 2044 q^{51} - 3899 q^{52} + 2213 q^{53} - 1142 q^{54} - 1604 q^{55} + 98 q^{57} + 2403 q^{58} - 2073 q^{59} - 1519 q^{60} - 2575 q^{61} - 1742 q^{62} + 1358 q^{64} + 1876 q^{65} + 48 q^{66} + 176 q^{67} - 3038 q^{68} + 638 q^{69} - 1259 q^{71} - 3799 q^{72} + 307 q^{73} + 3845 q^{74} - 131 q^{75} - 1974 q^{76} - 6041 q^{78} + 22 q^{79} + 804 q^{80} + 795 q^{81} - 8043 q^{82} - 6349 q^{83} + 3094 q^{85} + 1745 q^{86} - 9508 q^{87} + 1299 q^{88} - 2253 q^{89} - 11156 q^{90} + 1284 q^{92} - 3430 q^{93} - 2738 q^{94} - 3290 q^{95} - 3031 q^{96} + 770 q^{97} + 5384 q^{99}+O(q^{100}) \) 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9 - 78 * q^10 + q^11 + 91 * q^12 - 77 * q^13 - 161 * q^15 + 461 * q^16 - 211 * q^17 + 8 * q^18 - 314 * q^19 - 476 * q^20 - 61 * q^22 - 69 * q^23 - 330 * q^24 + 606 * q^25 - 504 * q^26 + 50 * q^27 + 57 * q^29 + 42 * q^30 - 638 * q^31 - 1600 * q^32 - 1574 * q^33 - 1343 * q^34 + 782 * q^36 + 71 * q^37 - 1359 * q^38 - 84 * q^39 + 155 * q^40 - 1393 * q^41 - 125 * q^43 + 52 * q^44 - 1129 * q^45 - 1454 * q^46 - 1483 * q^47 + 974 * q^48 + 3074 * q^50 - 2044 * q^51 - 3899 * q^52 + 2213 * q^53 - 1142 * q^54 - 1604 * q^55 + 98 * q^57 + 2403 * q^58 - 2073 * q^59 - 1519 * q^60 - 2575 * q^61 - 1742 * q^62 + 1358 * q^64 + 1876 * q^65 + 48 * q^66 + 176 * q^67 - 3038 * q^68 + 638 * q^69 - 1259 * q^71 - 3799 * q^72 + 307 * q^73 + 3845 * q^74 - 131 * q^75 - 1974 * q^76 - 6041 * q^78 + 22 * q^79 + 804 * q^80 + 795 * q^81 - 8043 * q^82 - 6349 * q^83 + 3094 * q^85 + 1745 * q^86 - 9508 * q^87 + 1299 * q^88 - 2253 * q^89 - 11156 * q^90 + 1284 * q^92 - 3430 * q^93 - 2738 * q^94 - 3290 * q^95 - 3031 * q^96 + 770 * q^97 + 5384 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.275911	−0.0975493	−0.0487746	−	0.998810i	$-0.515532\pi$
$2$	−0.275911	−0.0975493	−0.0487746	+	0.998810i	$0.515532\pi$
$3$	−3.60983	−0.694712	−0.347356	−	0.937733i	$-0.612920\pi$
$3$	−3.60983	−0.694712	−0.347356	+	0.937733i	$0.612920\pi$
$4$	−7.92387	−0.990484
$5$	3.79895	0.339789	0.169894	−	0.985462i	$-0.445657\pi$
$5$	3.79895	0.339789	0.169894	+	0.985462i	$0.445657\pi$
$6$	0.995991	0.0677686
$7$	0	0
$7$	0	0
$8$	4.39357	0.194170
$9$	−13.9691	−0.517376
$10$	−1.04817	−0.0331461
$11$	−55.4747	−1.52057	−0.760284	−	0.649590i	$-0.774940\pi$
$11$	−55.4747	−1.52057	−0.760284	+	0.649590i	$0.774940\pi$
$12$	28.6038	0.688101
$13$	−48.3590	−1.03172	−0.515861	−	0.856673i	$-0.672528\pi$
$13$	−48.3590	−1.03172	−0.515861	+	0.856673i	$0.672528\pi$
$14$	0	0
$15$	−13.7136	−0.236055
$16$	62.1787	0.971543
$17$	−57.3770	−0.818587	−0.409293	−	0.912403i	$-0.634225\pi$
$17$	−57.3770	−0.818587	−0.409293	+	0.912403i	$0.634225\pi$
$18$	3.85424	0.0504696
$19$	112.013	1.35250	0.676251	−	0.736671i	$-0.263604\pi$
$19$	112.013	1.35250	0.676251	+	0.736671i	$0.263604\pi$
$20$	−30.1024	−0.336555
$21$	0	0
$22$	15.3061	0.148330
$23$	120.665	1.09393	0.546965	−	0.837156i	$-0.315783\pi$
$23$	120.665	1.09393	0.546965	+	0.837156i	$0.315783\pi$
$24$	−15.8600	−0.134892
$25$	−110.568	−0.884544
$26$	13.3428	0.100644
$27$	147.892	1.05414
$28$	0	0
$29$	171.162	1.09600	0.548000	−	0.836478i	$-0.315389\pi$
$29$	171.162	1.09600	0.548000	+	0.836478i	$0.315389\pi$
$30$	3.78372	0.0230270
$31$	75.8179	0.439268	0.219634	−	0.975582i	$-0.429514\pi$
$31$	75.8179	0.439268	0.219634	+	0.975582i	$0.429514\pi$
$32$	−52.3044	−0.288944
$33$	200.254	1.05636
$34$	15.8310	0.0798526
$35$	0	0
$36$	110.690	0.512453
$37$	−397.782	−1.76743	−0.883717	−	0.468022i	$-0.844967\pi$
$37$	−397.782	−1.76743	−0.883717	+	0.468022i	$0.844967\pi$
$38$	−30.9056	−0.131936
$39$	174.568	0.716749
$40$	16.6910	0.0659769
$41$	86.5608	0.329720	0.164860	−	0.986317i	$-0.447283\pi$
$41$	86.5608	0.329720	0.164860	+	0.986317i	$0.447283\pi$
$42$	0	0
$43$	47.3604	0.167963	0.0839814	−	0.996467i	$-0.473236\pi$
$43$	47.3604	0.167963	0.0839814	+	0.996467i	$0.473236\pi$
$44$	439.575	1.50610
$45$	−53.0681	−0.175798
$46$	−33.2928	−0.106712
$47$	416.664	1.29312	0.646561	−	0.762863i	$-0.276207\pi$
$47$	416.664	1.29312	0.646561	+	0.762863i	$0.276207\pi$
$48$	−224.455	−0.674942
$49$	0	0
$50$	30.5069	0.0862866
$51$	207.121	0.568682
$52$	383.191	1.02190
$53$	−315.587	−0.817911	−0.408955	−	0.912554i	$-0.634107\pi$
$53$	−315.587	−0.817911	−0.408955	+	0.912554i	$0.634107\pi$
$54$	−40.8049	−0.102830
$55$	−210.746	−0.516672
$56$	0	0
$57$	−404.347	−0.939599
$58$	−47.2255	−0.106914
$59$	689.606	1.52168	0.760839	−	0.648941i	$-0.224788\pi$
$59$	689.606	1.52168	0.760839	+	0.648941i	$0.224788\pi$
$60$	108.665	0.233809
$61$	−245.883	−0.516099	−0.258050	−	0.966132i	$-0.583080\pi$
$61$	−245.883	−0.516099	−0.258050	+	0.966132i	$0.583080\pi$
$62$	−20.9190	−0.0428503
$63$	0	0
$64$	−482.999	−0.943357
$65$	−183.714	−0.350567
$66$	−55.2523	−0.103047
$67$	367.091	0.669363	0.334682	−	0.942331i	$-0.391371\pi$
$67$	367.091	0.669363	0.334682	+	0.942331i	$0.391371\pi$
$68$	454.648	0.810797
$69$	−435.580	−0.759966
$70$	0	0
$71$	91.8333	0.153502	0.0767508	−	0.997050i	$-0.475545\pi$
$71$	91.8333	0.153502	0.0767508	+	0.997050i	$0.475545\pi$
$72$	−61.3745	−0.100459
$73$	55.3278	0.0887072	0.0443536	−	0.999016i	$-0.485877\pi$
$73$	55.3278	0.0887072	0.0443536	+	0.999016i	$0.485877\pi$
$74$	109.753	0.172412
$75$	399.131	0.614503
$76$	−887.577	−1.33963
$77$	0	0
$78$	−48.1651	−0.0699183
$79$	436.724	0.621965	0.310983	−	0.950416i	$-0.399342\pi$
$79$	436.724	0.621965	0.310983	+	0.950416i	$0.399342\pi$
$80$	236.214	0.330119
$81$	−156.696	−0.214946
$82$	−23.8831	−0.0321640
$83$	1298.85	1.71768	0.858839	−	0.512246i	$-0.171186\pi$
$83$	1298.85	1.71768	0.858839	+	0.512246i	$0.171186\pi$
$84$	0	0
$85$	−217.973	−0.278147
$86$	−13.0673	−0.0163846
$87$	−617.865	−0.761404
$88$	−243.732	−0.295249
$89$	77.1808	0.0919230	0.0459615	−	0.998943i	$-0.485365\pi$
$89$	77.1808	0.0919230	0.0459615	+	0.998943i	$0.485365\pi$
$90$	14.6421	0.0171490
$91$	0	0
$92$	−956.134	−1.08352
$93$	−273.690	−0.305164
$94$	−114.962	−0.126143
$95$	425.532	0.459565
$96$	188.810	0.200732
$97$	−1261.25	−1.32021	−0.660103	−	0.751175i	$-0.729488\pi$
$97$	−1261.25	−1.32021	−0.660103	+	0.751175i	$0.729488\pi$
$98$	0	0
$99$	774.935	0.786706
$100$	876.126	0.876126
$101$	−1457.72	−1.43613	−0.718065	−	0.695977i	$-0.754972\pi$
$101$	−1457.72	−1.43613	−0.718065	+	0.695977i	$0.754972\pi$
$102$	−57.1470	−0.0554745
$103$	−106.986	−0.102346	−0.0511731	−	0.998690i	$-0.516296\pi$
$103$	−106.986	−0.102346	−0.0511731	+	0.998690i	$0.516296\pi$
$104$	−212.469	−0.200330
$105$	0	0
$106$	87.0741	0.0797866
$107$	674.731	0.609614	0.304807	−	0.952414i	$-0.401408\pi$
$107$	674.731	0.609614	0.304807	+	0.952414i	$0.401408\pi$
$108$	−1171.87	−1.04411
$109$	93.0313	0.0817503	0.0408751	−	0.999164i	$-0.486985\pi$
$109$	93.0313	0.0817503	0.0408751	+	0.999164i	$0.486985\pi$
$110$	58.1471	0.0504010
$111$	1435.93	1.22786
$112$	0	0
$113$	308.689	0.256982	0.128491	−	0.991711i	$-0.458987\pi$
$113$	308.689	0.256982	0.128491	+	0.991711i	$0.458987\pi$
$114$	111.564	0.0916572
$115$	458.400	0.371705
$116$	−1356.27	−1.08557
$117$	675.534	0.533788
$118$	−190.270	−0.148439
$119$	0	0
$120$	−60.2515	−0.0458349
$121$	1746.44	1.31213
$122$	67.8418	0.0503451
$123$	−312.469	−0.229060
$124$	−600.772	−0.435088
$125$	−894.911	−0.640347
$126$	0	0
$127$	1149.96	0.803482	0.401741	−	0.915753i	$-0.368405\pi$
$127$	1149.96	0.803482	0.401741	+	0.915753i	$0.368405\pi$
$128$	551.700	0.380967
$129$	−170.963	−0.116686
$130$	50.6886	0.0341976
$131$	−2301.06	−1.53469	−0.767345	−	0.641234i	$-0.778423\pi$
$131$	−2301.06	−1.53469	−0.767345	+	0.641234i	$0.778423\pi$
$132$	−1586.79	−1.04630
$133$	0	0
$134$	−101.285	−0.0652959
$135$	561.833	0.358184
$136$	−252.090	−0.158945
$137$	−578.326	−0.360655	−0.180328	−	0.983607i	$-0.557716\pi$
$137$	−578.326	−0.360655	−0.180328	+	0.983607i	$0.557716\pi$
$138$	120.181	0.0741341
$139$	71.8186	0.0438243	0.0219121	−	0.999760i	$-0.493025\pi$
$139$	71.8186	0.0438243	0.0219121	+	0.999760i	$0.493025\pi$
$140$	0	0
$141$	−1504.09	−0.898346
$142$	−25.3378	−0.0149740
$143$	2682.70	1.56880
$144$	−868.584	−0.502653
$145$	650.236	0.372408
$146$	−15.2655	−0.00865333
$147$	0	0
$148$	3151.98	1.75061
$149$	986.558	0.542429	0.271215	−	0.962519i	$-0.412575\pi$
$149$	986.558	0.542429	0.271215	+	0.962519i	$0.412575\pi$
$150$	−110.125	−0.0599443
$151$	2785.06	1.50096	0.750480	−	0.660894i	$-0.229823\pi$
$151$	2785.06	1.50096	0.750480	+	0.660894i	$0.229823\pi$
$152$	492.137	0.262616
$153$	801.508	0.423517
$154$	0	0
$155$	288.029	0.149258
$156$	−1383.25	−0.709928
$157$	2388.22	1.21402	0.607010	−	0.794694i	$-0.292369\pi$
$157$	2388.22	1.21402	0.607010	+	0.794694i	$0.292369\pi$
$158$	−120.497	−0.0606723
$159$	1139.22	0.568212
$160$	−198.702	−0.0981798
$161$	0	0
$162$	43.2341	0.0209679
$163$	−141.913	−0.0681934	−0.0340967	−	0.999419i	$-0.510855\pi$
$163$	−141.913	−0.0681934	−0.0340967	+	0.999419i	$0.510855\pi$
$164$	−685.897	−0.326583
$165$	760.756	0.358938
$166$	−358.367	−0.167558
$167$	−1208.28	−0.559877	−0.279938	−	0.960018i	$-0.590314\pi$
$167$	−1208.28	−0.559877	−0.279938	+	0.960018i	$0.590314\pi$
$168$	0	0
$169$	141.594	0.0644488
$170$	60.1411	0.0271330
$171$	−1564.73	−0.699752
$172$	−375.278	−0.166364
$173$	3771.68	1.65755	0.828774	−	0.559583i	$-0.189039\pi$
$173$	3771.68	1.65755	0.828774	+	0.559583i	$0.189039\pi$
$174$	170.476	0.0742744
$175$	0	0
$176$	−3449.35	−1.47730
$177$	−2489.36	−1.05713
$178$	−21.2950	−0.00896703
$179$	90.0444	0.0375991	0.0187995	−	0.999823i	$-0.494016\pi$
$179$	90.0444	0.0375991	0.0187995	+	0.999823i	$0.494016\pi$
$180$	420.505	0.174126
$181$	−3449.45	−1.41655	−0.708276	−	0.705936i	$-0.750527\pi$
$181$	−3449.45	−1.41655	−0.708276	+	0.705936i	$0.750527\pi$
$182$	0	0
$183$	887.594	0.358540
$184$	530.150	0.212409
$185$	−1511.16	−0.600554
$186$	75.5140	0.0297686
$187$	3182.98	1.24472
$188$	−3301.59	−1.28082
$189$	0	0
$190$	−117.409	−0.0448302
$191$	977.848	0.370443	0.185221	−	0.982697i	$-0.440700\pi$
$191$	977.848	0.370443	0.185221	+	0.982697i	$0.440700\pi$
$192$	1743.54	0.655361
$193$	484.265	0.180612	0.0903061	−	0.995914i	$-0.471215\pi$
$193$	484.265	0.180612	0.0903061	+	0.995914i	$0.471215\pi$
$194$	347.991	0.128785
$195$	663.174	0.243543
$196$	0	0
$197$	1683.13	0.608721	0.304360	−	0.952557i	$-0.401557\pi$
$197$	1683.13	0.608721	0.304360	+	0.952557i	$0.401557\pi$
$198$	−213.813	−0.0767426
$199$	−3142.38	−1.11938	−0.559692	−	0.828700i	$-0.689081\pi$
$199$	−3142.38	−1.11938	−0.559692	+	0.828700i	$0.689081\pi$
$200$	−485.788	−0.171752
$201$	−1325.14	−0.465014
$202$	402.202	0.140093
$203$	0	0
$204$	−1641.20	−0.563270
$205$	328.840	0.112035
$206$	29.5187	0.00998381
$207$	−1685.59	−0.565973
$208$	−3006.90	−1.00236
$209$	−6213.89	−2.05657
$210$	0	0
$211$	2555.93	0.833922	0.416961	−	0.908924i	$-0.363095\pi$
$211$	2555.93	0.833922	0.416961	+	0.908924i	$0.363095\pi$
$212$	2500.67	0.810128
$213$	−331.502	−0.106639
$214$	−186.166	−0.0594675
$215$	179.920	0.0570718
$216$	649.772	0.204682
$217$	0	0
$218$	−25.6684	−0.00797468
$219$	−199.724	−0.0616259
$220$	1669.92	0.511755
$221$	2774.70	0.844553
$222$	−396.188	−0.119777
$223$	1411.44	0.423843	0.211922	−	0.977287i	$-0.432028\pi$
$223$	1411.44	0.423843	0.211922	+	0.977287i	$0.432028\pi$
$224$	0	0
$225$	1544.54	0.457642
$226$	−85.1706	−0.0250684
$227$	3830.05	1.11986	0.559932	−	0.828539i	$-0.310827\pi$
$227$	3830.05	1.11986	0.559932	+	0.828539i	$0.310827\pi$
$228$	3204.00	0.930658
$229$	2056.10	0.593322	0.296661	−	0.954983i	$-0.404127\pi$
$229$	2056.10	0.593322	0.296661	+	0.954983i	$0.404127\pi$
$230$	−126.478	−0.0362595
$231$	0	0
$232$	752.013	0.212811
$233$	1842.62	0.518086	0.259043	−	0.965866i	$-0.416593\pi$
$233$	1842.62	0.518086	0.259043	+	0.965866i	$0.416593\pi$
$234$	−186.387	−0.0520706
$235$	1582.89	0.439388
$236$	−5464.35	−1.50720
$237$	−1576.50	−0.432086
$238$	0	0
$239$	−5634.35	−1.52492	−0.762459	−	0.647036i	$-0.776008\pi$
$239$	−5634.35	−1.52492	−0.762459	+	0.647036i	$0.776008\pi$
$240$	−852.692	−0.229338
$241$	4296.70	1.14844	0.574221	−	0.818700i	$-0.305305\pi$
$241$	4296.70	1.14844	0.574221	+	0.818700i	$0.305305\pi$
$242$	−481.863	−0.127997
$243$	−3427.43	−0.904813
$244$	1948.34	0.511188
$245$	0	0
$246$	86.2138	0.0223447
$247$	−5416.84	−1.39540
$248$	333.112	0.0852928
$249$	−4688.62	−1.19329
$250$	246.916	0.0624653
$251$	−7249.50	−1.82305	−0.911523	−	0.411250i	$-0.865092\pi$
$251$	−7249.50	−1.82305	−0.911523	+	0.411250i	$0.865092\pi$
$252$	0	0
$253$	−6693.85	−1.66340
$254$	−317.286	−0.0783791
$255$	786.844	0.193232
$256$	3711.77	0.906194
$257$	158.310	0.0384246	0.0192123	−	0.999815i	$-0.493884\pi$
$257$	158.310	0.0384246	0.0192123	+	0.999815i	$0.493884\pi$
$258$	47.1706	0.0113826
$259$	0	0
$260$	1455.72	0.347231
$261$	−2390.99	−0.567044
$262$	634.888	0.149708
$263$	−515.650	−0.120899	−0.0604493	−	0.998171i	$-0.519253\pi$
$263$	−515.650	−0.120899	−0.0604493	+	0.998171i	$0.519253\pi$
$264$	879.831	0.205113
$265$	−1198.90	−0.277917
$266$	0	0
$267$	−278.609	−0.0638600
$268$	−2908.78	−0.662994
$269$	570.737	0.129362	0.0646811	−	0.997906i	$-0.479397\pi$
$269$	570.737	0.129362	0.0646811	+	0.997906i	$0.479397\pi$
$270$	−155.016	−0.0349406
$271$	−7464.77	−1.67326	−0.836628	−	0.547772i	$-0.815476\pi$
$271$	−7464.77	−1.67326	−0.836628	+	0.547772i	$0.815476\pi$
$272$	−3567.63	−0.795292
$273$	0	0
$274$	159.567	0.0351817
$275$	6133.73	1.34501
$276$	3451.48	0.752734
$277$	−5823.49	−1.26318	−0.631588	−	0.775304i	$-0.717596\pi$
$277$	−5823.49	−1.26318	−0.631588	+	0.775304i	$0.717596\pi$
$278$	−19.8155	−0.00427503
$279$	−1059.11	−0.227267
$280$	0	0
$281$	8712.00	1.84952	0.924758	−	0.380555i	$-0.124267\pi$
$281$	8712.00	1.84952	0.924758	+	0.380555i	$0.124267\pi$
$282$	414.994	0.0876330
$283$	−2714.33	−0.570141	−0.285071	−	0.958506i	$-0.592017\pi$
$283$	−2714.33	−0.570141	−0.285071	+	0.958506i	$0.592017\pi$
$284$	−727.675	−0.152041
$285$	−1536.10	−0.319265
$286$	−740.187	−0.153036
$287$	0	0
$288$	730.648	0.149492
$289$	−1620.88	−0.329916
$290$	−179.407	−0.0363282
$291$	4552.88	0.917163
$292$	−438.410	−0.0878631
$293$	−5752.13	−1.14691	−0.573453	−	0.819239i	$-0.694396\pi$
$293$	−5752.13	−1.14691	−0.573453	+	0.819239i	$0.694396\pi$
$294$	0	0
$295$	2619.78	0.517049
$296$	−1747.69	−0.343183
$297$	−8204.24	−1.60289
$298$	−272.202	−0.0529136
$299$	−5835.24	−1.12863
$300$	−3162.67	−0.608655
$301$	0	0
$302$	−768.428	−0.146418
$303$	5262.13	0.997695
$304$	6964.83	1.31401
$305$	−934.097	−0.175365
$306$	−221.145	−0.0413138
$307$	−6249.19	−1.16176	−0.580879	−	0.813990i	$-0.697291\pi$
$307$	−6249.19	−1.16176	−0.580879	+	0.813990i	$0.697291\pi$
$308$	0	0
$309$	386.202	0.0711012
$310$	−79.4703	−0.0145600
$311$	−9034.12	−1.64720	−0.823598	−	0.567174i	$-0.808037\pi$
$311$	−9034.12	−1.64720	−0.823598	+	0.567174i	$0.808037\pi$
$312$	766.976	0.139171
$313$	−7433.40	−1.34237	−0.671183	−	0.741292i	$-0.734213\pi$
$313$	−7433.40	−1.34237	−0.671183	+	0.741292i	$0.734213\pi$
$314$	−658.937	−0.118427
$315$	0	0
$316$	−3460.54	−0.616047
$317$	−9996.32	−1.77113	−0.885567	−	0.464512i	$-0.846230\pi$
$317$	−9996.32	−1.77113	−0.885567	+	0.464512i	$0.846230\pi$
$318$	−314.322	−0.0554287
$319$	−9495.17	−1.66654
$320$	−1834.89	−0.320542
$321$	−2435.66	−0.423506
$322$	0	0
$323$	−6426.97	−1.10714
$324$	1241.64	0.212901
$325$	5346.96	0.912603
$326$	39.1555	0.00665221
$327$	−335.827	−0.0567929
$328$	380.311	0.0640218
$329$	0	0
$330$	−209.901	−0.0350141
$331$	911.706	0.151395	0.0756977	−	0.997131i	$-0.475882\pi$
$331$	911.706	0.151395	0.0756977	+	0.997131i	$0.475882\pi$
$332$	−10291.9	−1.70133
$333$	5556.68	0.914427
$334$	333.378	0.0546156
$335$	1394.56	0.227442
$336$	0	0
$337$	−5131.39	−0.829450	−0.414725	−	0.909947i	$-0.636122\pi$
$337$	−5131.39	−0.829450	−0.414725	+	0.909947i	$0.636122\pi$
$338$	−39.0673	−0.00628693
$339$	−1114.31	−0.178528
$340$	1727.19	0.275500
$341$	−4205.98	−0.667937
$342$	431.725	0.0682603
$343$	0	0
$344$	208.081	0.0326134
$345$	−1654.75	−0.258228
$346$	−1040.65	−0.161693
$347$	7160.27	1.10773	0.553866	−	0.832606i	$-0.313152\pi$
$347$	7160.27	1.10773	0.553866	+	0.832606i	$0.313152\pi$
$348$	4895.89	0.754158
$349$	−584.903	−0.0897110	−0.0448555	−	0.998993i	$-0.514283\pi$
$349$	−584.903	−0.0897110	−0.0448555	+	0.998993i	$0.514283\pi$
$350$	0	0
$351$	−7151.89	−1.08758
$352$	2901.57	0.439359
$353$	5835.10	0.879805	0.439903	−	0.898045i	$-0.355013\pi$
$353$	5835.10	0.879805	0.439903	+	0.898045i	$0.355013\pi$
$354$	686.841	0.103122
$355$	348.870	0.0521581
$356$	−611.571	−0.0910483
$357$	0	0
$358$	−24.8442	−0.00366776
$359$	4.10989	0.000604211 0	0.000302105	−	1.00000i	$-0.499904\pi$
$359$	4.10989	0.000604211 0	0.000302105		1.00000i	$0.499904\pi$
$360$	−233.159	−0.0341348
$361$	5687.90	0.829261
$362$	951.742	0.138184
$363$	−6304.36	−0.911552
$364$	0	0
$365$	210.188	0.0301417
$366$	−244.897	−0.0349753
$367$	−8104.12	−1.15268	−0.576338	−	0.817212i	$-0.695519\pi$
$367$	−8104.12	−1.15268	−0.576338	+	0.817212i	$0.695519\pi$
$368$	7502.80	1.06280
$369$	−1209.18	−0.170589
$370$	416.945	0.0585836
$371$	0	0
$372$	2168.68	0.302261
$373$	−9756.61	−1.35437	−0.677183	−	0.735815i	$-0.736799\pi$
$373$	−9756.61	−1.35437	−0.677183	+	0.735815i	$0.736799\pi$
$374$	−878.218	−0.121421
$375$	3230.48	0.444856
$376$	1830.64	0.251086
$377$	−8277.23	−1.13077
$378$	0	0
$379$	14051.0	1.90436	0.952178	−	0.305545i	$-0.0988387\pi$
$379$	14051.0	1.90436	0.952178	+	0.305545i	$0.0988387\pi$
$380$	−3371.86	−0.455192
$381$	−4151.15	−0.558188
$382$	−269.799	−0.0361364
$383$	−9007.97	−1.20179	−0.600895	−	0.799328i	$-0.705189\pi$
$383$	−9007.97	−1.20179	−0.600895	+	0.799328i	$0.705189\pi$
$384$	−1991.54	−0.264662
$385$	0	0
$386$	−133.614	−0.0176186
$387$	−661.585	−0.0868999
$388$	9993.95	1.30764
$389$	−11262.0	−1.46788	−0.733939	−	0.679216i	$-0.762320\pi$
$389$	−11262.0	−1.46788	−0.733939	+	0.679216i	$0.762320\pi$
$390$	−182.977	−0.0237575
$391$	−6923.40	−0.895476
$392$	0	0
$393$	8306.43	1.06617
$394$	−464.394	−0.0593803
$395$	1659.09	0.211337
$396$	−6140.48	−0.779219
$397$	7389.85	0.934222	0.467111	−	0.884199i	$-0.345295\pi$
$397$	7389.85	0.934222	0.467111	+	0.884199i	$0.345295\pi$
$398$	867.018	0.109195
$399$	0	0
$400$	−6874.98	−0.859372
$401$	−8571.69	−1.06746	−0.533728	−	0.845656i	$-0.679209\pi$
$401$	−8571.69	−1.06746	−0.533728	+	0.845656i	$0.679209\pi$
$402$	365.620	0.0453618
$403$	−3666.48	−0.453202
$404$	11550.8	1.42246
$405$	−595.280	−0.0730363
$406$	0	0
$407$	22066.9	2.68750
$408$	910.002	0.110421
$409$	6193.87	0.748819	0.374409	−	0.927263i	$-0.377845\pi$
$409$	6193.87	0.748819	0.374409	+	0.927263i	$0.377845\pi$
$410$	−90.7307	−0.0109289
$411$	2087.66	0.250551
$412$	847.745	0.101372
$413$	0	0
$414$	465.072	0.0552102
$415$	4934.27	0.583647
$416$	2529.39	0.298109
$417$	−259.253	−0.0304452
$418$	1714.48	0.200617
$419$	3273.63	0.381688	0.190844	−	0.981620i	$-0.438877\pi$
$419$	3273.63	0.381688	0.190844	+	0.981620i	$0.438877\pi$
$420$	0	0
$421$	−9308.11	−1.07755	−0.538776	−	0.842449i	$-0.681113\pi$
$421$	−9308.11	−1.07755	−0.538776	+	0.842449i	$0.681113\pi$
$422$	−705.209	−0.0813484
$423$	−5820.44	−0.669030
$424$	−1386.56	−0.158814
$425$	6344.06	0.724076
$426$	91.4652	0.0104026
$427$	0	0
$428$	−5346.49	−0.603813
$429$	−9684.09	−1.08987
$430$	−49.6419	−0.00556732
$431$	−15421.4	−1.72349	−0.861744	−	0.507343i	$-0.830628\pi$
$431$	−15421.4	−1.72349	−0.861744	+	0.507343i	$0.830628\pi$
$432$	9195.71	1.02414
$433$	−6988.28	−0.775602	−0.387801	−	0.921743i	$-0.626765\pi$
$433$	−6988.28	−0.775602	−0.387801	+	0.921743i	$0.626765\pi$
$434$	0	0
$435$	−2347.24	−0.258716
$436$	−737.168	−0.0809724
$437$	13516.0	1.47954
$438$	55.1060	0.00601157
$439$	5651.84	0.614460	0.307230	−	0.951635i	$-0.400598\pi$
$439$	5651.84	0.614460	0.307230	+	0.951635i	$0.400598\pi$
$440$	−925.927	−0.100322
$441$	0	0
$442$	−765.570	−0.0823856
$443$	8161.51	0.875316	0.437658	−	0.899141i	$-0.355808\pi$
$443$	8161.51	0.875316	0.437658	+	0.899141i	$0.355808\pi$
$444$	−11378.1	−1.21617
$445$	293.206	0.0312344
$446$	−389.432	−0.0413456
$447$	−3561.30	−0.376832
$448$	0	0
$449$	3184.25	0.334686	0.167343	−	0.985899i	$-0.446481\pi$
$449$	3184.25	0.334686	0.167343	+	0.985899i	$0.446481\pi$
$450$	−426.156	−0.0446426
$451$	−4801.94	−0.501362
$452$	−2446.01	−0.254537
$453$	−10053.6	−1.04273
$454$	−1056.75	−0.109242
$455$	0	0
$456$	−1776.53	−0.182442
$457$	−4229.99	−0.432977	−0.216488	−	0.976285i	$-0.569460\pi$
$457$	−4229.99	−0.432977	−0.216488	+	0.976285i	$0.569460\pi$
$458$	−567.300	−0.0578781
$459$	−8485.58	−0.862904
$460$	−3632.31	−0.368168
$461$	−6397.19	−0.646305	−0.323153	−	0.946347i	$-0.604743\pi$
$461$	−6397.19	−0.646305	−0.323153	+	0.946347i	$0.604743\pi$
$462$	0	0
$463$	4935.42	0.495396	0.247698	−	0.968837i	$-0.420326\pi$
$463$	4935.42	0.495396	0.247698	+	0.968837i	$0.420326\pi$
$464$	10642.6	1.06481
$465$	−1039.73	−0.103691
$466$	−508.399	−0.0505389
$467$	11990.1	1.18808	0.594042	−	0.804434i	$-0.297531\pi$
$467$	11990.1	1.18808	0.594042	+	0.804434i	$0.297531\pi$
$468$	−5352.85	−0.528708
$469$	0	0
$470$	−436.736	−0.0428620
$471$	−8621.08	−0.843393
$472$	3029.83	0.295465
$473$	−2627.31	−0.255399
$474$	434.973	0.0421497
$475$	−12385.0	−1.19635
$476$	0	0
$477$	4408.49	0.423167
$478$	1554.58	0.148755
$479$	−9819.93	−0.936710	−0.468355	−	0.883540i	$-0.655153\pi$
$479$	−9819.93	−0.936710	−0.468355	+	0.883540i	$0.655153\pi$
$480$	717.279	0.0682066
$481$	19236.4	1.82350
$482$	−1185.51	−0.112030
$483$	0	0
$484$	−13838.6	−1.29964
$485$	−4791.41	−0.448591
$486$	945.665	0.0882638
$487$	2094.88	0.194924	0.0974620	−	0.995239i	$-0.468928\pi$
$487$	2094.88	0.194924	0.0974620	+	0.995239i	$0.468928\pi$
$488$	−1080.30	−0.100211
$489$	512.283	0.0473747
$490$	0	0
$491$	14911.0	1.37051	0.685256	−	0.728302i	$-0.259690\pi$
$491$	14911.0	1.37051	0.685256	+	0.728302i	$0.259690\pi$
$492$	2475.97	0.226881
$493$	−9820.77	−0.897171
$494$	1494.56	0.136121
$495$	2943.94	0.267314
$496$	4714.26	0.426768
$497$	0	0
$498$	1293.64	0.116405
$499$	−15683.6	−1.40700	−0.703502	−	0.710694i	$-0.748381\pi$
$499$	−15683.6	−1.40700	−0.703502	+	0.710694i	$0.748381\pi$
$500$	7091.16	0.634253
$501$	4361.68	0.388953
$502$	2000.22	0.177837
$503$	2946.35	0.261176	0.130588	−	0.991437i	$-0.458314\pi$
$503$	2946.35	0.261176	0.130588	+	0.991437i	$0.458314\pi$
$504$	0	0
$505$	−5537.83	−0.487980
$506$	1846.91	0.162263
$507$	−511.130	−0.0447733
$508$	−9112.11	−0.795836
$509$	−518.395	−0.0451423	−0.0225712	−	0.999745i	$-0.507185\pi$
$509$	−518.395	−0.0451423	−0.0225712	+	0.999745i	$0.507185\pi$
$510$	−217.099	−0.0188496
$511$	0	0
$512$	−5437.72	−0.469366
$513$	16565.8	1.42572
$514$	−43.6796	−0.00374830
$515$	−406.436	−0.0347761
$516$	1354.69	0.115575
$517$	−23114.3	−1.96628
$518$	0	0
$519$	−13615.1	−1.15152
$520$	−807.159	−0.0680697
$521$	9518.96	0.800448	0.400224	−	0.916417i	$-0.368932\pi$
$521$	9518.96	0.800448	0.400224	+	0.916417i	$0.368932\pi$
$522$	659.700	0.0553147
$523$	74.0594	0.00619195	0.00309598	−	0.999995i	$-0.499015\pi$
$523$	74.0594	0.00619195	0.00309598	+	0.999995i	$0.499015\pi$
$524$	18233.3	1.52009
$525$	0	0
$526$	142.273	0.0117936
$527$	−4350.21	−0.359579
$528$	12451.6	1.02630
$529$	2393.03	0.196682
$530$	330.790	0.0271106
$531$	−9633.20	−0.787280
$532$	0	0
$533$	−4185.99	−0.340179
$534$	76.8714	0.00622950
$535$	2563.27	0.207140
$536$	1612.84	0.129970
$537$	−325.045	−0.0261205
$538$	−157.473	−0.0126192
$539$	0	0
$540$	−4451.89	−0.354776
$541$	10717.6	0.851727	0.425864	−	0.904787i	$-0.359970\pi$
$541$	10717.6	0.851727	0.425864	+	0.904787i	$0.359970\pi$
$542$	2059.61	0.163225
$543$	12451.9	0.984095
$544$	3001.07	0.236525
$545$	353.421	0.0277778
$546$	0	0
$547$	457.932	0.0357948	0.0178974	−	0.999840i	$-0.494303\pi$
$547$	457.932	0.0357948	0.0178974	+	0.999840i	$0.494303\pi$
$548$	4582.59	0.357223
$549$	3434.77	0.267017
$550$	−1692.36	−0.131205
$551$	19172.4	1.48234
$552$	−1913.75	−0.147563
$553$	0	0
$554$	1606.77	0.123222
$555$	5455.01	0.417212
$556$	−569.082	−0.0434073
$557$	8614.08	0.655279	0.327639	−	0.944803i	$-0.393747\pi$
$557$	8614.08	0.655279	0.327639	+	0.944803i	$0.393747\pi$
$558$	292.221	0.0221697
$559$	−2290.30	−0.173291
$560$	0	0
$561$	−11490.0	−0.864720
$562$	−2403.74	−0.180419
$563$	9480.10	0.709660	0.354830	−	0.934931i	$-0.384539\pi$
$563$	9480.10	0.709660	0.354830	+	0.934931i	$0.384539\pi$
$564$	11918.2	0.889798
$565$	1172.69	0.0873196
$566$	748.913	0.0556169
$567$	0	0
$568$	403.476	0.0298054
$569$	13190.6	0.971842	0.485921	−	0.874003i	$-0.338484\pi$
$569$	13190.6	0.971842	0.485921	+	0.874003i	$0.338484\pi$
$570$	423.826	0.0311441
$571$	15748.2	1.15419	0.577093	−	0.816678i	$-0.304187\pi$
$571$	15748.2	1.15419	0.577093	+	0.816678i	$0.304187\pi$
$572$	−21257.4	−1.55387
$573$	−3529.86	−0.257351
$574$	0	0
$575$	−13341.7	−0.967628
$576$	6747.08	0.488070
$577$	−13511.1	−0.974829	−0.487414	−	0.873171i	$-0.662060\pi$
$577$	−13511.1	−0.974829	−0.487414	+	0.873171i	$0.662060\pi$
$578$	447.217	0.0321830
$579$	−1748.11	−0.125473
$580$	−5152.39	−0.368864
$581$	0	0
$582$	−1256.19	−0.0894686
$583$	17507.1	1.24369
$584$	243.087	0.0172243
$585$	2566.32	0.181375
$586$	1587.08	0.111880
$587$	−14319.0	−1.00683	−0.503416	−	0.864044i	$-0.667924\pi$
$587$	−14319.0	−1.00683	−0.503416	+	0.864044i	$0.667924\pi$
$588$	0	0
$589$	8492.59	0.594111
$590$	−722.826	−0.0504378
$591$	−6075.80	−0.422885
$592$	−24733.6	−1.71714
$593$	−8383.18	−0.580533	−0.290266	−	0.956946i	$-0.593744\pi$
$593$	−8383.18	−0.580533	−0.290266	+	0.956946i	$0.593744\pi$
$594$	2263.64	0.156361
$595$	0	0
$596$	−7817.36	−0.537268
$597$	11343.5	0.777649
$598$	1610.01	0.110097
$599$	4015.29	0.273890	0.136945	−	0.990579i	$-0.456272\pi$
$599$	4015.29	0.273890	0.136945	+	0.990579i	$0.456272\pi$
$600$	1753.61	0.119318
$601$	23345.3	1.58448	0.792241	−	0.610208i	$-0.208914\pi$
$601$	23345.3	1.58448	0.792241	+	0.610208i	$0.208914\pi$
$602$	0	0
$603$	−5127.95	−0.346312
$604$	−22068.5	−1.48668
$605$	6634.66	0.445847
$606$	−1451.88	−0.0973245
$607$	14674.0	0.981217	0.490608	−	0.871380i	$-0.336775\pi$
$607$	14674.0	0.981217	0.490608	+	0.871380i	$0.336775\pi$
$608$	−5858.77	−0.390797
$609$	0	0
$610$	257.728	0.0171067
$611$	−20149.5	−1.33414
$612$	−6351.05	−0.419487
$613$	−3031.39	−0.199734	−0.0998669	−	0.995001i	$-0.531842\pi$
$613$	−3031.39	−0.199734	−0.0998669	+	0.995001i	$0.531842\pi$
$614$	1724.22	0.113329
$615$	−1187.06	−0.0778321
$616$	0	0
$617$	29900.8	1.95099	0.975495	−	0.220022i	$-0.0706129\pi$
$617$	29900.8	1.95099	0.975495	+	0.220022i	$0.0706129\pi$
$618$	−106.557	−0.00693587
$619$	−18888.3	−1.22647	−0.613235	−	0.789901i	$-0.710132\pi$
$619$	−18888.3	−1.22647	−0.613235	+	0.789901i	$0.710132\pi$
$620$	−2282.30	−0.147838
$621$	17845.3	1.15315
$622$	2492.61	0.160683
$623$	0	0
$624$	10854.4	0.696352
$625$	10421.3	0.666961
$626$	2050.96	0.130947
$627$	22431.1	1.42872
$628$	−18924.0	−1.20247
$629$	22823.6	1.44680
$630$	0	0
$631$	4453.95	0.280997	0.140498	−	0.990081i	$-0.455130\pi$
$631$	4453.95	0.280997	0.140498	+	0.990081i	$0.455130\pi$
$632$	1918.78	0.120767
$633$	−9226.46	−0.579335
$634$	2758.09	0.172773
$635$	4368.63	0.273014
$636$	−9027.00	−0.562805
$637$	0	0
$638$	2619.82	0.162570
$639$	−1282.83	−0.0794180
$640$	2095.88	0.129448
$641$	15724.7	0.968935	0.484468	−	0.874809i	$-0.339013\pi$
$641$	15724.7	0.968935	0.484468	+	0.874809i	$0.339013\pi$
$642$	672.027	0.0413127
$643$	−3717.07	−0.227973	−0.113987	−	0.993482i	$-0.536362\pi$
$643$	−3717.07	−0.227973	−0.113987	+	0.993482i	$0.536362\pi$
$644$	0	0
$645$	−649.480	−0.0396485
$646$	1773.27	0.108001
$647$	−5300.85	−0.322099	−0.161049	−	0.986946i	$-0.551488\pi$
$647$	−5300.85	−0.322099	−0.161049	+	0.986946i	$0.551488\pi$
$648$	−688.455	−0.0417362
$649$	−38255.7	−2.31382
$650$	−1475.28	−0.0890237
$651$	0	0
$652$	1124.50	0.0675445
$653$	1519.58	0.0910656	0.0455328	−	0.998963i	$-0.485501\pi$
$653$	1519.58	0.0910656	0.0455328	+	0.998963i	$0.485501\pi$
$654$	92.6583	0.00554010
$655$	−8741.62	−0.521471
$656$	5382.24	0.320337
$657$	−772.882	−0.0458950
$658$	0	0
$659$	17799.0	1.05213	0.526064	−	0.850445i	$-0.323667\pi$
$659$	17799.0	1.05213	0.526064	+	0.850445i	$0.323667\pi$
$660$	−6028.13	−0.355522
$661$	−8348.41	−0.491249	−0.245625	−	0.969365i	$-0.578993\pi$
$661$	−8348.41	−0.491249	−0.245625	+	0.969365i	$0.578993\pi$
$662$	−251.550	−0.0147685
$663$	−10016.2	−0.586721
$664$	5706.59	0.333522
$665$	0	0
$666$	−1533.15	−0.0892017
$667$	20653.3	1.19895
$668$	9574.25	0.554549
$669$	−5095.05	−0.294449
$670$	−384.775	−0.0221868
$671$	13640.3	0.784764
$672$	0	0
$673$	−3226.28	−0.184790	−0.0923952	−	0.995722i	$-0.529452\pi$
$673$	−3226.28	−0.184790	−0.0923952	+	0.995722i	$0.529452\pi$
$674$	1415.81	0.0809122
$675$	−16352.1	−0.932432
$676$	−1121.97	−0.0638355
$677$	910.375	0.0516817	0.0258409	−	0.999666i	$-0.491774\pi$
$677$	910.375	0.0516817	0.0258409	+	0.999666i	$0.491774\pi$
$678$	307.451	0.0174153
$679$	0	0
$680$	−957.679	−0.0540078
$681$	−13825.8	−0.777982
$682$	1160.48	0.0651568
$683$	−797.000	−0.0446506	−0.0223253	−	0.999751i	$-0.507107\pi$
$683$	−797.000	−0.0446506	−0.0223253	+	0.999751i	$0.507107\pi$
$684$	12398.7	0.693093
$685$	−2197.03	−0.122547
$686$	0	0
$687$	−7422.15	−0.412187
$688$	2944.81	0.163183
$689$	15261.5	0.843856
$690$	456.563	0.0251899
$691$	−18295.1	−1.00720	−0.503602	−	0.863936i	$-0.667992\pi$
$691$	−18295.1	−1.00720	−0.503602	+	0.863936i	$0.667992\pi$
$692$	−29886.3	−1.64178
$693$	0	0
$694$	−1975.60	−0.108059
$695$	272.835	0.0148910
$696$	−2714.64	−0.147842
$697$	−4966.60	−0.269905
$698$	161.381	0.00875124
$699$	−6651.54	−0.359920
$700$	0	0
$701$	−14832.1	−0.799146	−0.399573	−	0.916701i	$-0.630842\pi$
$701$	−14832.1	−0.799146	−0.399573	+	0.916701i	$0.630842\pi$
$702$	1973.29	0.106092
$703$	−44556.8	−2.39046
$704$	26794.2	1.43444
$705$	−5713.95	−0.305248
$706$	−1609.97	−0.0858244
$707$	0	0
$708$	19725.4	1.04707
$709$	19508.0	1.03334	0.516671	−	0.856184i	$-0.327171\pi$
$709$	19508.0	1.03334	0.516671	+	0.856184i	$0.327171\pi$
$710$	−96.2572	−0.00508798
$711$	−6100.66	−0.321790
$712$	339.100	0.0178487
$713$	9148.57	0.480528
$714$	0	0
$715$	10191.5	0.533061
$716$	−713.500	−0.0372413
$717$	20339.0	1.05938
$718$	−1.13396	−5.89403e−5 0
$719$	−8817.37	−0.457347	−0.228674	−	0.973503i	$-0.573439\pi$
$719$	−8817.37	−0.457347	−0.228674	+	0.973503i	$0.573439\pi$
$720$	−3299.71	−0.170796
$721$	0	0
$722$	−1569.36	−0.0808939
$723$	−15510.3	−0.797836
$724$	27333.0	1.40307
$725$	−18925.0	−0.969460
$726$	1739.44	0.0889212
$727$	20099.7	1.02539	0.512695	−	0.858571i	$-0.328647\pi$
$727$	20099.7	1.02539	0.512695	+	0.858571i	$0.328647\pi$
$728$	0	0
$729$	16603.2	0.843530
$730$	−57.9931	−0.00294030
$731$	−2717.40	−0.137492
$732$	−7033.18	−0.355128
$733$	4637.44	0.233680	0.116840	−	0.993151i	$-0.462723\pi$
$733$	4637.44	0.233680	0.116840	+	0.993151i	$0.462723\pi$
$734$	2236.02	0.112443
$735$	0	0
$736$	−6311.31	−0.316084
$737$	−20364.3	−1.01781
$738$	333.626	0.0166409
$739$	−7790.32	−0.387783	−0.193891	−	0.981023i	$-0.562111\pi$
$739$	−7790.32	−0.387783	−0.193891	+	0.981023i	$0.562111\pi$
$740$	11974.2	0.594839
$741$	19553.8	0.969404
$742$	0	0
$743$	10646.9	0.525704	0.262852	−	0.964836i	$-0.415337\pi$
$743$	10646.9	0.525704	0.262852	+	0.964836i	$0.415337\pi$
$744$	−1202.48	−0.0592539
$745$	3747.89	0.184311
$746$	2691.96	0.132117
$747$	−18143.8	−0.888685
$748$	−25221.5	−1.23287
$749$	0	0
$750$	−891.324	−0.0433954
$751$	33502.7	1.62787	0.813936	−	0.580955i	$-0.197321\pi$
$751$	33502.7	1.62787	0.813936	+	0.580955i	$0.197321\pi$
$752$	25907.7	1.25632
$753$	26169.4	1.26649
$754$	2283.78	0.110305
$755$	10580.3	0.510009
$756$	0	0
$757$	−19875.5	−0.954276	−0.477138	−	0.878828i	$-0.658326\pi$
$757$	−19875.5	−0.954276	−0.477138	+	0.878828i	$0.658326\pi$
$758$	−3876.82	−0.185768
$759$	24163.7	1.15558
$760$	1869.61	0.0892338
$761$	−18075.3	−0.861012	−0.430506	−	0.902588i	$-0.641665\pi$
$761$	−18075.3	−0.861012	−0.430506	+	0.902588i	$0.641665\pi$
$762$	1145.35	0.0544508
$763$	0	0
$764$	−7748.34	−0.366918
$765$	3044.89	0.143906
$766$	2485.40	0.117234
$767$	−33348.6	−1.56995
$768$	−13398.8	−0.629543
$769$	−9921.68	−0.465260	−0.232630	−	0.972565i	$-0.574733\pi$
$769$	−9921.68	−0.465260	−0.232630	+	0.972565i	$0.574733\pi$
$770$	0	0
$771$	−571.473	−0.0266940
$772$	−3837.26	−0.178894
$773$	28694.0	1.33512	0.667562	−	0.744554i	$-0.267338\pi$
$773$	28694.0	1.33512	0.667562	+	0.744554i	$0.267338\pi$
$774$	182.539	0.00847702
$775$	−8383.04	−0.388552
$776$	−5541.37	−0.256345
$777$	0	0
$778$	3107.30	0.143190
$779$	9695.93	0.445947
$780$	−5254.91	−0.241226
$781$	−5094.43	−0.233410
$782$	1910.24	0.0873531
$783$	25313.4	1.15534
$784$	0	0
$785$	9072.75	0.412510
$786$	−2291.84	−0.104004
$787$	−6494.44	−0.294157	−0.147079	−	0.989125i	$-0.546987\pi$
$787$	−6494.44	−0.294157	−0.147079	+	0.989125i	$0.546987\pi$
$788$	−13336.9	−0.602928
$789$	1861.41	0.0839897
$790$	−457.762	−0.0206157
$791$	0	0
$792$	3404.73	0.152755
$793$	11890.6	0.532471
$794$	−2038.94	−0.0911327
$795$	4327.83	0.193072
$796$	24899.8	1.10873
$797$	−14609.3	−0.649295	−0.324647	−	0.945835i	$-0.605246\pi$
$797$	−14609.3	−0.649295	−0.324647	+	0.945835i	$0.605246\pi$
$798$	0	0
$799$	−23907.0	−1.05853
$800$	5783.19	0.255583
$801$	−1078.15	−0.0475588
$802$	2365.02	0.104130
$803$	−3069.29	−0.134885
$804$	10500.2	0.460589
$805$	0	0
$806$	1011.62	0.0442095
$807$	−2060.26	−0.0898695
$808$	−6404.62	−0.278854
$809$	−23854.5	−1.03669	−0.518344	−	0.855172i	$-0.673451\pi$
$809$	−23854.5	−1.03669	−0.518344	+	0.855172i	$0.673451\pi$
$810$	164.244	0.00712464
$811$	42798.0	1.85307	0.926535	−	0.376208i	$-0.122772\pi$
$811$	42798.0	1.85307	0.926535	+	0.376208i	$0.122772\pi$
$812$	0	0
$813$	26946.5	1.16243
$814$	−6088.49	−0.262164
$815$	−539.122	−0.0231713
$816$	12878.5	0.552499
$817$	5304.98	0.227170
$818$	−1708.96	−0.0730468
$819$	0	0
$820$	−2605.69	−0.110969
$821$	21196.0	0.901031	0.450515	−	0.892769i	$-0.351240\pi$
$821$	21196.0	0.901031	0.450515	+	0.892769i	$0.351240\pi$
$822$	−576.008	−0.0244411
$823$	1732.61	0.0733841	0.0366920	−	0.999327i	$-0.488318\pi$
$823$	1732.61	0.0733841	0.0366920	+	0.999327i	$0.488318\pi$
$824$	−470.052	−0.0198726
$825$	−22141.7	−0.934394
$826$	0	0
$827$	−14266.2	−0.599858	−0.299929	−	0.953962i	$-0.596963\pi$
$827$	−14266.2	−0.599858	−0.299929	+	0.953962i	$0.596963\pi$
$828$	13356.4	0.560587
$829$	−35517.2	−1.48801	−0.744007	−	0.668172i	$-0.767077\pi$
$829$	−35517.2	−1.48801	−0.744007	+	0.668172i	$0.767077\pi$
$830$	−1361.42	−0.0569344
$831$	21021.8	0.877543
$832$	23357.3	0.973281
$833$	0	0
$834$	71.5307	0.00296991
$835$	−4590.19	−0.190240
$836$	49238.1	2.03700
$837$	11212.8	0.463049
$838$	−903.232	−0.0372334
$839$	23982.0	0.986832	0.493416	−	0.869793i	$-0.335748\pi$
$839$	23982.0	0.986832	0.493416	+	0.869793i	$0.335748\pi$
$840$	0	0
$841$	4907.44	0.201215
$842$	2568.21	0.105114
$843$	−31448.8	−1.28488
$844$	−20252.9	−0.825986
$845$	537.909	0.0218990
$846$	1605.92	0.0652634
$847$	0	0
$848$	−19622.8	−0.794635
$849$	9798.25	0.396084
$850$	−1750.40	−0.0706331
$851$	−47998.4	−1.93345
$852$	2626.78	0.105625
$853$	17846.5	0.716355	0.358178	−	0.933653i	$-0.383398\pi$
$853$	17846.5	0.716355	0.358178	+	0.933653i	$0.383398\pi$
$854$	0	0
$855$	−5944.32	−0.237768
$856$	2964.48	0.118369
$857$	−31230.1	−1.24481	−0.622403	−	0.782697i	$-0.713844\pi$
$857$	−31230.1	−1.24481	−0.622403	+	0.782697i	$0.713844\pi$
$858$	2671.95	0.106316
$859$	22761.8	0.904103	0.452051	−	0.891992i	$-0.350692\pi$
$859$	22761.8	0.904103	0.452051	+	0.891992i	$0.350692\pi$
$860$	−1425.66	−0.0565287
$861$	0	0
$862$	4254.94	0.168125
$863$	7962.22	0.314064	0.157032	−	0.987594i	$-0.449807\pi$
$863$	7962.22	0.314064	0.157032	+	0.987594i	$0.449807\pi$
$864$	−7735.38	−0.304587
$865$	14328.4	0.563216
$866$	1928.14	0.0756594
$867$	5851.08	0.229196
$868$	0	0
$869$	−24227.1	−0.945741
$870$	647.630	0.0252376
$871$	−17752.2	−0.690596
$872$	408.740	0.0158735
$873$	17618.5	0.683043
$874$	−3729.22	−0.144328
$875$	0	0
$876$	1582.59	0.0610395
$877$	8822.82	0.339710	0.169855	−	0.985469i	$-0.445670\pi$
$877$	8822.82	0.339710	0.169855	+	0.985469i	$0.445670\pi$
$878$	−1559.41	−0.0599401
$879$	20764.2	0.796769
$880$	−13103.9	−0.501969
$881$	41551.2	1.58898	0.794492	−	0.607274i	$-0.207737\pi$
$881$	41551.2	1.58898	0.794492	+	0.607274i	$0.207737\pi$
$882$	0	0
$883$	−42731.1	−1.62856	−0.814279	−	0.580474i	$-0.802867\pi$
$883$	−42731.1	−1.62856	−0.814279	+	0.580474i	$0.802867\pi$
$884$	−21986.3	−0.836517
$885$	−9456.95	−0.359200
$886$	−2251.85	−0.0853865
$887$	−19140.3	−0.724541	−0.362271	−	0.932073i	$-0.617998\pi$
$887$	−19140.3	−0.724541	−0.362271	+	0.932073i	$0.617998\pi$
$888$	6308.84	0.238413
$889$	0	0
$890$	−80.8988	−0.00304689
$891$	8692.66	0.326841
$892$	−11184.1	−0.419810
$893$	46671.8	1.74895
$894$	982.603	0.0367597
$895$	342.074	0.0127757
$896$	0	0
$897$	21064.2	0.784073
$898$	−878.569	−0.0326483
$899$	12977.2	0.481437
$900$	−12238.7	−0.453287
$901$	18107.5	0.669531
$902$	1324.91	0.0489075
$903$	0	0
$904$	1356.25	0.0498983
$905$	−13104.3	−0.481328
$906$	2773.89	0.101718
$907$	3121.68	0.114282	0.0571409	−	0.998366i	$-0.481802\pi$
$907$	3121.68	0.114282	0.0571409	+	0.998366i	$0.481802\pi$
$908$	−30348.8	−1.10921
$909$	20363.2	0.743018
$910$	0	0
$911$	−21526.7	−0.782887	−0.391443	−	0.920202i	$-0.628024\pi$
$911$	−21526.7	−0.782887	−0.391443	+	0.920202i	$0.628024\pi$
$912$	−25141.8	−0.912861
$913$	−72053.3	−2.61185
$914$	1167.10	0.0422366
$915$	3371.93	0.121828
$916$	−16292.2	−0.587676
$917$	0	0
$918$	2341.26	0.0841757
$919$	25773.2	0.925113	0.462556	−	0.886590i	$-0.346932\pi$
$919$	25773.2	0.925113	0.462556	+	0.886590i	$0.346932\pi$
$920$	2014.02	0.0721740
$921$	22558.5	0.807087
$922$	1765.05	0.0630466
$923$	−4440.97	−0.158371
$924$	0	0
$925$	43982.0	1.56337
$926$	−1361.74	−0.0483255
$927$	1494.51	0.0529515
$928$	−8952.52	−0.316682
$929$	−49763.1	−1.75745	−0.878726	−	0.477326i	$-0.841606\pi$
$929$	−49763.1	−1.75745	−0.878726	+	0.477326i	$0.841606\pi$
$930$	286.874	0.0101150
$931$	0	0
$932$	−14600.7	−0.513156
$933$	32611.6	1.14433
$934$	−3308.20	−0.115897
$935$	12092.0	0.422941
$936$	2968.01	0.103646
$937$	3394.03	0.118333	0.0591666	−	0.998248i	$-0.481156\pi$
$937$	3394.03	0.118333	0.0591666	+	0.998248i	$0.481156\pi$
$938$	0	0
$939$	26833.3	0.932557
$940$	−12542.6	−0.435207
$941$	15261.9	0.528717	0.264358	−	0.964425i	$-0.414840\pi$
$941$	15261.9	0.528717	0.264358	+	0.964425i	$0.414840\pi$
$942$	2378.65	0.0822724
$943$	10444.9	0.360691
$944$	42878.8	1.47838
$945$	0	0
$946$	724.903	0.0249140
$947$	−48775.5	−1.67370	−0.836849	−	0.547434i	$-0.815605\pi$
$947$	−48775.5	−1.67370	−0.836849	+	0.547434i	$0.815605\pi$
$948$	12492.0	0.427975
$949$	−2675.60	−0.0915211
$950$	3417.17	0.116703
$951$	36085.0	1.23043
$952$	0	0
$953$	4020.92	0.136674	0.0683369	−	0.997662i	$-0.478231\pi$
$953$	4020.92	0.136674	0.0683369	+	0.997662i	$0.478231\pi$
$954$	−1216.35	−0.0412797
$955$	3714.80	0.125872
$956$	44645.9	1.51041
$957$	34275.9	1.15777
$958$	2709.43	0.0913754
$959$	0	0
$960$	6623.63	0.222684
$961$	−24042.6	−0.807044
$962$	−5307.53	−0.177881
$963$	−9425.42	−0.315400
$964$	−34046.5	−1.13751
$965$	1839.70	0.0613700
$966$	0	0
$967$	−54950.2	−1.82738	−0.913692	−	0.406408i	$-0.866781\pi$
$967$	−54950.2	−1.82738	−0.913692	+	0.406408i	$0.866781\pi$
$968$	7673.13	0.254777
$969$	23200.3	0.769143
$970$	1322.00	0.0437597
$971$	−36170.1	−1.19542	−0.597710	−	0.801712i	$-0.703923\pi$
$971$	−36170.1	−1.19542	−0.597710	+	0.801712i	$0.703923\pi$
$972$	27158.5	0.896203
$973$	0	0
$974$	−578.000	−0.0190147
$975$	−19301.6	−0.633996
$976$	−15288.7	−0.501413
$977$	23972.6	0.785006	0.392503	−	0.919751i	$-0.371609\pi$
$977$	23972.6	0.785006	0.392503	+	0.919751i	$0.371609\pi$
$978$	−141.345	−0.00462137
$979$	−4281.58	−0.139775
$980$	0	0
$981$	−1299.57	−0.0422956
$982$	−4114.10	−0.133693
$983$	16418.6	0.532728	0.266364	−	0.963872i	$-0.414178\pi$
$983$	16418.6	0.532728	0.266364	+	0.963872i	$0.414178\pi$
$984$	−1372.86	−0.0444767
$985$	6394.13	0.206836
$986$	2709.66	0.0875184
$987$	0	0
$988$	42922.3	1.38213
$989$	5714.74	0.183739
$990$	−812.265	−0.0260763
$991$	−37562.8	−1.20406	−0.602028	−	0.798475i	$-0.705641\pi$
$991$	−37562.8	−1.20406	−0.602028	+	0.798475i	$0.705641\pi$
$992$	−3965.61	−0.126924
$993$	−3291.10	−0.105176
$994$	0	0
$995$	−11937.8	−0.380354
$996$	37152.0	1.18194
$997$	49788.3	1.58156	0.790778	−	0.612103i	$-0.209676\pi$
$997$	49788.3	1.58156	0.790778	+	0.612103i	$0.209676\pi$
$998$	4327.28	0.137252
$999$	−58828.7	−1.86312

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2401.4.a.c.1.19		39
7.6	odd	2		2401.4.a.d.1.19		39
49.6	odd	14		49.4.e.a.36.7	yes	78
49.41	odd	14		49.4.e.a.15.7	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.15.7	✓	78	49.41	odd	14
49.4.e.a.36.7	yes	78	49.6	odd	14
2401.4.a.c.1.19		39	1.1	even	1	trivial
2401.4.a.d.1.19		39	7.6	odd	2

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:	\( N \)	\(=\)	\( 2401 = 7^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2401.a (trivial)

\(f(q)\)	\(=\)	\(q-0.275911 q^{2} -3.60983 q^{3} -7.92387 q^{4} +3.79895 q^{5} +0.995991 q^{6} +4.39357 q^{8} -13.9691 q^{9} +O(q^{10})\)	\(q-0.275911 q^{2} -3.60983 q^{3} -7.92387 q^{4} +3.79895 q^{5} +0.995991 q^{6} +4.39357 q^{8} -13.9691 q^{9} -1.04817 q^{10} -55.4747 q^{11} +28.6038 q^{12} -48.3590 q^{13} -13.7136 q^{15} +62.1787 q^{16} -57.3770 q^{17} +3.85424 q^{18} +112.013 q^{19} -30.1024 q^{20} +15.3061 q^{22} +120.665 q^{23} -15.8600 q^{24} -110.568 q^{25} +13.3428 q^{26} +147.892 q^{27} +171.162 q^{29} +3.78372 q^{30} +75.8179 q^{31} -52.3044 q^{32} +200.254 q^{33} +15.8310 q^{34} +110.690 q^{36} -397.782 q^{37} -30.9056 q^{38} +174.568 q^{39} +16.6910 q^{40} +86.5608 q^{41} +47.3604 q^{43} +439.575 q^{44} -53.0681 q^{45} -33.2928 q^{46} +416.664 q^{47} -224.455 q^{48} +30.5069 q^{50} +207.121 q^{51} +383.191 q^{52} -315.587 q^{53} -40.8049 q^{54} -210.746 q^{55} -404.347 q^{57} -47.2255 q^{58} +689.606 q^{59} +108.665 q^{60} -245.883 q^{61} -20.9190 q^{62} -482.999 q^{64} -183.714 q^{65} -55.2523 q^{66} +367.091 q^{67} +454.648 q^{68} -435.580 q^{69} +91.8333 q^{71} -61.3745 q^{72} +55.3278 q^{73} +109.753 q^{74} +399.131 q^{75} -887.577 q^{76} -48.1651 q^{78} +436.724 q^{79} +236.214 q^{80} -156.696 q^{81} -23.8831 q^{82} +1298.85 q^{83} -217.973 q^{85} -13.0673 q^{86} -617.865 q^{87} -243.732 q^{88} +77.1808 q^{89} +14.6421 q^{90} -956.134 q^{92} -273.690 q^{93} -114.962 q^{94} +425.532 q^{95} +188.810 q^{96} -1261.25 q^{97} +774.935 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) \) 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9} - 78 q^{10} + q^{11} + 91 q^{12} - 77 q^{13} - 161 q^{15} + 461 q^{16} - 211 q^{17} + 8 q^{18} - 314 q^{19} - 476 q^{20} - 61 q^{22} - 69 q^{23} - 330 q^{24} + 606 q^{25} - 504 q^{26} + 50 q^{27} + 57 q^{29} + 42 q^{30} - 638 q^{31} - 1600 q^{32} - 1574 q^{33} - 1343 q^{34} + 782 q^{36} + 71 q^{37} - 1359 q^{38} - 84 q^{39} + 155 q^{40} - 1393 q^{41} - 125 q^{43} + 52 q^{44} - 1129 q^{45} - 1454 q^{46} - 1483 q^{47} + 974 q^{48} + 3074 q^{50} - 2044 q^{51} - 3899 q^{52} + 2213 q^{53} - 1142 q^{54} - 1604 q^{55} + 98 q^{57} + 2403 q^{58} - 2073 q^{59} - 1519 q^{60} - 2575 q^{61} - 1742 q^{62} + 1358 q^{64} + 1876 q^{65} + 48 q^{66} + 176 q^{67} - 3038 q^{68} + 638 q^{69} - 1259 q^{71} - 3799 q^{72} + 307 q^{73} + 3845 q^{74} - 131 q^{75} - 1974 q^{76} - 6041 q^{78} + 22 q^{79} + 804 q^{80} + 795 q^{81} - 8043 q^{82} - 6349 q^{83} + 3094 q^{85} + 1745 q^{86} - 9508 q^{87} + 1299 q^{88} - 2253 q^{89} - 11156 q^{90} + 1284 q^{92} - 3430 q^{93} - 2738 q^{94} - 3290 q^{95} - 3031 q^{96} + 770 q^{97} + 5384 q^{99}+O(q^{100}) \) 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9 - 78 * q^10 + q^11 + 91 * q^12 - 77 * q^13 - 161 * q^15 + 461 * q^16 - 211 * q^17 + 8 * q^18 - 314 * q^19 - 476 * q^20 - 61 * q^22 - 69 * q^23 - 330 * q^24 + 606 * q^25 - 504 * q^26 + 50 * q^27 + 57 * q^29 + 42 * q^30 - 638 * q^31 - 1600 * q^32 - 1574 * q^33 - 1343 * q^34 + 782 * q^36 + 71 * q^37 - 1359 * q^38 - 84 * q^39 + 155 * q^40 - 1393 * q^41 - 125 * q^43 + 52 * q^44 - 1129 * q^45 - 1454 * q^46 - 1483 * q^47 + 974 * q^48 + 3074 * q^50 - 2044 * q^51 - 3899 * q^52 + 2213 * q^53 - 1142 * q^54 - 1604 * q^55 + 98 * q^57 + 2403 * q^58 - 2073 * q^59 - 1519 * q^60 - 2575 * q^61 - 1742 * q^62 + 1358 * q^64 + 1876 * q^65 + 48 * q^66 + 176 * q^67 - 3038 * q^68 + 638 * q^69 - 1259 * q^71 - 3799 * q^72 + 307 * q^73 + 3845 * q^74 - 131 * q^75 - 1974 * q^76 - 6041 * q^78 + 22 * q^79 + 804 * q^80 + 795 * q^81 - 8043 * q^82 - 6349 * q^83 + 3094 * q^85 + 1745 * q^86 - 9508 * q^87 + 1299 * q^88 - 2253 * q^89 - 11156 * q^90 + 1284 * q^92 - 3430 * q^93 - 2738 * q^94 - 3290 * q^95 - 3031 * q^96 + 770 * q^97 + 5384 * q^99

Introduction

L-functions

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