LMFDB - Embedded newform 2401.4.a.d.1.9

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:	$0$
Dimension:	$39$
Twist minimal:	no (minimal twist has level 49)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-3.57033 q^{2} -9.05210 q^{3} +4.74728 q^{4} +15.7342 q^{5} +32.3190 q^{6} +11.6133 q^{8} +54.9406 q^{9} +O(q^{10})$	\(q-3.57033 q^{2} -9.05210 q^{3} +4.74728 q^{4} +15.7342 q^{5} +32.3190 q^{6} +11.6133 q^{8} +54.9406 q^{9} -56.1764 q^{10} +33.4349 q^{11} -42.9729 q^{12} -58.2042 q^{13} -142.428 q^{15} -79.4416 q^{16} -5.45990 q^{17} -196.156 q^{18} +30.1574 q^{19} +74.6947 q^{20} -119.374 q^{22} -121.066 q^{23} -105.125 q^{24} +122.565 q^{25} +207.809 q^{26} -252.921 q^{27} -169.051 q^{29} +508.514 q^{30} -98.7312 q^{31} +190.727 q^{32} -302.656 q^{33} +19.4937 q^{34} +260.819 q^{36} -374.320 q^{37} -107.672 q^{38} +526.871 q^{39} +182.726 q^{40} -8.20760 q^{41} -415.395 q^{43} +158.725 q^{44} +864.446 q^{45} +432.247 q^{46} -89.0617 q^{47} +719.113 q^{48} -437.598 q^{50} +49.4236 q^{51} -276.312 q^{52} +12.4428 q^{53} +903.013 q^{54} +526.071 q^{55} -272.988 q^{57} +603.568 q^{58} +427.574 q^{59} -676.145 q^{60} +342.910 q^{61} +352.503 q^{62} -45.4254 q^{64} -915.797 q^{65} +1080.58 q^{66} +286.141 q^{67} -25.9197 q^{68} +1095.90 q^{69} -57.1851 q^{71} +638.040 q^{72} +397.212 q^{73} +1336.45 q^{74} -1109.47 q^{75} +143.166 q^{76} -1881.10 q^{78} +1157.33 q^{79} -1249.95 q^{80} +806.072 q^{81} +29.3039 q^{82} -539.941 q^{83} -85.9072 q^{85} +1483.10 q^{86} +1530.26 q^{87} +388.288 q^{88} +624.657 q^{89} -3086.36 q^{90} -574.736 q^{92} +893.725 q^{93} +317.980 q^{94} +474.502 q^{95} -1726.48 q^{96} +147.308 q^{97} +1836.93 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.57033	−1.26230	−0.631152	−	0.775659i	$-0.717418\pi$
$2$	−3.57033	−1.26230	−0.631152	+	0.775659i	$0.717418\pi$
$3$	−9.05210	−1.74208	−0.871039	−	0.491214i	$-0.836553\pi$
$3$	−9.05210	−1.74208	−0.871039	+	0.491214i	$0.836553\pi$
$4$	4.74728	0.593411
$5$	15.7342	1.40731	0.703655	−	0.710542i	$-0.251550\pi$
$5$	15.7342	1.40731	0.703655	+	0.710542i	$0.251550\pi$
$6$	32.3190	2.19903
$7$	0	0
$7$	0	0
$8$	11.6133	0.513239
$9$	54.9406	2.03484
$10$	−56.1764	−1.77645
$11$	33.4349	0.916454	0.458227	−	0.888835i	$-0.348485\pi$
$11$	33.4349	0.916454	0.458227	+	0.888835i	$0.348485\pi$
$12$	−42.9729	−1.03377
$13$	−58.2042	−1.24177	−0.620883	−	0.783904i	$-0.713226\pi$
$13$	−58.2042	−1.24177	−0.620883	+	0.783904i	$0.713226\pi$
$14$	0	0
$15$	−142.428	−2.45164
$16$	−79.4416	−1.24127
$17$	−5.45990	−0.0778953	−0.0389477	−	0.999241i	$-0.512401\pi$
$17$	−5.45990	−0.0778953	−0.0389477	+	0.999241i	$0.512401\pi$
$18$	−196.156	−2.56858
$19$	30.1574	0.364136	0.182068	−	0.983286i	$-0.441721\pi$
$19$	30.1574	0.364136	0.182068	+	0.983286i	$0.441721\pi$
$20$	74.6947	0.835113
$21$	0	0
$22$	−119.374	−1.15684
$23$	−121.066	−1.09757	−0.548784	−	0.835964i	$-0.684909\pi$
$23$	−121.066	−1.09757	−0.548784	+	0.835964i	$0.684909\pi$
$24$	−105.125	−0.894103
$25$	122.565	0.980521
$26$	207.809	1.56748
$27$	−252.921	−1.80277
$28$	0	0
$29$	−169.051	−1.08248	−0.541240	−	0.840868i	$-0.682045\pi$
$29$	−169.051	−1.08248	−0.541240	+	0.840868i	$0.682045\pi$
$30$	508.514	3.09472
$31$	−98.7312	−0.572021	−0.286010	−	0.958227i	$-0.592329\pi$
$31$	−98.7312	−0.572021	−0.286010	+	0.958227i	$0.592329\pi$
$32$	190.727	1.05363
$33$	−302.656	−1.59653
$34$	19.4937	0.0983276
$35$	0	0
$36$	260.819	1.20749
$37$	−374.320	−1.66318	−0.831592	−	0.555388i	$-0.812570\pi$
$37$	−374.320	−1.66318	−0.831592	+	0.555388i	$0.812570\pi$
$38$	−107.672	−0.459650
$39$	526.871	2.16325
$40$	182.726	0.722287
$41$	−8.20760	−0.0312637	−0.0156318	−	0.999878i	$-0.504976\pi$
$41$	−8.20760	−0.0312637	−0.0156318	+	0.999878i	$0.504976\pi$
$42$	0	0
$43$	−415.395	−1.47319	−0.736594	−	0.676335i	$-0.763567\pi$
$43$	−415.395	−1.47319	−0.736594	+	0.676335i	$0.763567\pi$
$44$	158.725	0.543833
$45$	864.446	2.86365
$46$	432.247	1.38546
$47$	−89.0617	−0.276404	−0.138202	−	0.990404i	$-0.544132\pi$
$47$	−89.0617	−0.276404	−0.138202	+	0.990404i	$0.544132\pi$
$48$	719.113	2.16240
$49$	0	0
$50$	−437.598	−1.23772
$51$	49.4236	0.135700
$52$	−276.312	−0.736877
$53$	12.4428	0.0322480	0.0161240	−	0.999870i	$-0.494867\pi$
$53$	12.4428	0.0322480	0.0161240	+	0.999870i	$0.494867\pi$
$54$	903.013	2.27564
$55$	526.071	1.28973
$56$	0	0
$57$	−272.988	−0.634353
$58$	603.568	1.36642
$59$	427.574	0.943482	0.471741	−	0.881737i	$-0.343626\pi$
$59$	427.574	0.943482	0.471741	+	0.881737i	$0.343626\pi$
$60$	−676.145	−1.45483
$61$	342.910	0.719757	0.359879	−	0.932999i	$-0.382818\pi$
$61$	342.910	0.719757	0.359879	+	0.932999i	$0.382818\pi$
$62$	352.503	0.722064
$63$	0	0
$64$	−45.4254	−0.0887216
$65$	−915.797	−1.74755
$66$	1080.58	2.01531
$67$	286.141	0.521757	0.260878	−	0.965372i	$-0.415988\pi$
$67$	286.141	0.521757	0.260878	+	0.965372i	$0.415988\pi$
$68$	−25.9197	−0.0462239
$69$	1095.90	1.91205
$70$	0	0
$71$	−57.1851	−0.0955863	−0.0477931	−	0.998857i	$-0.515219\pi$
$71$	−57.1851	−0.0955863	−0.0477931	+	0.998857i	$0.515219\pi$
$72$	638.040	1.04436
$73$	397.212	0.636851	0.318425	−	0.947948i	$-0.396846\pi$
$73$	397.212	0.636851	0.318425	+	0.947948i	$0.396846\pi$
$74$	1336.45	2.09944
$75$	−1109.47	−1.70814
$76$	143.166	0.216082
$77$	0	0
$78$	−1881.10	−2.73068
$79$	1157.33	1.64823	0.824116	−	0.566421i	$-0.191672\pi$
$79$	1157.33	1.64823	0.824116	+	0.566421i	$0.191672\pi$
$80$	−1249.95	−1.74686
$81$	806.072	1.10572
$82$	29.3039	0.0394643
$83$	−539.941	−0.714050	−0.357025	−	0.934095i	$-0.616209\pi$
$83$	−539.941	−0.714050	−0.357025	+	0.934095i	$0.616209\pi$
$84$	0	0
$85$	−85.9072	−0.109623
$86$	1483.10	1.85961
$87$	1530.26	1.88577
$88$	388.288	0.470360
$89$	624.657	0.743972	0.371986	−	0.928238i	$-0.378677\pi$
$89$	624.657	0.743972	0.371986	+	0.928238i	$0.378677\pi$
$90$	−3086.36	−3.61479
$91$	0	0
$92$	−574.736	−0.651308
$93$	893.725	0.996505
$94$	317.980	0.348906
$95$	474.502	0.512452
$96$	−1726.48	−1.83550
$97$	147.308	0.154194	0.0770970	−	0.997024i	$-0.475435\pi$
$97$	147.308	0.154194	0.0770970	+	0.997024i	$0.475435\pi$
$98$	0	0
$99$	1836.93	1.86483
$100$	581.852	0.581852
$101$	−593.756	−0.584960	−0.292480	−	0.956272i	$-0.594480\pi$
$101$	−593.756	−0.584960	−0.292480	+	0.956272i	$0.594480\pi$
$102$	−176.459	−0.171294
$103$	−1863.22	−1.78241	−0.891206	−	0.453600i	$-0.850140\pi$
$103$	−1863.22	−1.78241	−0.891206	+	0.453600i	$0.850140\pi$
$104$	−675.942	−0.637323
$105$	0	0
$106$	−44.4248	−0.0407068
$107$	230.126	0.207917	0.103959	−	0.994582i	$-0.466849\pi$
$107$	230.126	0.207917	0.103959	+	0.994582i	$0.466849\pi$
$108$	−1200.69	−1.06978
$109$	−0.700065	−0.000615175 0	−0.000307587	−	1.00000i	$-0.500098\pi$
$109$	−0.700065	−0.000615175 0	−0.000307587		1.00000i	$0.500098\pi$
$110$	−1878.25	−1.62804
$111$	3388.38	2.89739
$112$	0	0
$113$	−934.188	−0.777708	−0.388854	−	0.921299i	$-0.627129\pi$
$113$	−934.188	−0.777708	−0.388854	+	0.921299i	$0.627129\pi$
$114$	974.657	0.800746
$115$	−1904.88	−1.54462
$116$	−802.532	−0.642355
$117$	−3197.77	−2.52679
$118$	−1526.58	−1.19096
$119$	0	0
$120$	−1654.05	−1.25828
$121$	−213.110	−0.160113
$122$	−1224.30	−0.908552
$123$	74.2960	0.0544638
$124$	−468.705	−0.339443
$125$	−38.3108	−0.0274130
$126$	0	0
$127$	1447.87	1.01163	0.505816	−	0.862641i	$-0.331191\pi$
$127$	1447.87	1.01163	0.505816	+	0.862641i	$0.331191\pi$
$128$	−1363.63	−0.941632
$129$	3760.20	2.56641
$130$	3269.70	2.20594
$131$	−1260.85	−0.840925	−0.420463	−	0.907310i	$-0.638132\pi$
$131$	−1260.85	−0.840925	−0.420463	+	0.907310i	$0.638132\pi$
$132$	−1436.79	−0.947400
$133$	0	0
$134$	−1021.62	−0.658615
$135$	−3979.51	−2.53705
$136$	−63.4074	−0.0399789
$137$	−192.057	−0.119771	−0.0598853	−	0.998205i	$-0.519073\pi$
$137$	−192.057	−0.119771	−0.0598853	+	0.998205i	$0.519073\pi$
$138$	−3912.74	−2.41359
$139$	−188.714	−0.115155	−0.0575774	−	0.998341i	$-0.518338\pi$
$139$	−188.714	−0.115155	−0.0575774	+	0.998341i	$0.518338\pi$
$140$	0	0
$141$	806.196	0.481517
$142$	204.170	0.120659
$143$	−1946.05	−1.13802
$144$	−4364.57	−2.52579
$145$	−2659.88	−1.52339
$146$	−1418.18	−0.803899
$147$	0	0
$148$	−1777.00	−0.986950
$149$	−3277.65	−1.80212	−0.901058	−	0.433699i	$-0.857208\pi$
$149$	−3277.65	−1.80212	−0.901058	+	0.433699i	$0.857208\pi$
$150$	3961.19	2.15620
$151$	−1952.70	−1.05237	−0.526187	−	0.850369i	$-0.676379\pi$
$151$	−1952.70	−1.05237	−0.526187	+	0.850369i	$0.676379\pi$
$152$	350.226	0.186889
$153$	−299.970	−0.158504
$154$	0	0
$155$	−1553.46	−0.805010
$156$	2501.21	1.28370
$157$	354.446	0.180178	0.0900888	−	0.995934i	$-0.471285\pi$
$157$	354.446	0.180178	0.0900888	+	0.995934i	$0.471285\pi$
$158$	−4132.07	−2.08057
$159$	−112.633	−0.0561786
$160$	3000.93	1.48278
$161$	0	0
$162$	−2877.95	−1.39576
$163$	1179.57	0.566817	0.283408	−	0.958999i	$-0.408535\pi$
$163$	1179.57	0.566817	0.283408	+	0.958999i	$0.408535\pi$
$164$	−38.9638	−0.0185522
$165$	−4762.05	−2.24682
$166$	1927.77	0.901348
$167$	3764.36	1.74428	0.872140	−	0.489256i	$-0.162732\pi$
$167$	3764.36	1.74428	0.872140	+	0.489256i	$0.162732\pi$
$168$	0	0
$169$	1190.73	0.541981
$170$	306.717	0.138377
$171$	1656.86	0.740956
$172$	−1972.00	−0.874206
$173$	2932.66	1.28882	0.644411	−	0.764679i	$-0.277103\pi$
$173$	2932.66	1.28882	0.644411	+	0.764679i	$0.277103\pi$
$174$	−5463.56	−2.38041
$175$	0	0
$176$	−2656.12	−1.13757
$177$	−3870.45	−1.64362
$178$	−2230.23	−0.939118
$179$	−617.174	−0.257708	−0.128854	−	0.991664i	$-0.541130\pi$
$179$	−617.174	−0.257708	−0.128854	+	0.991664i	$0.541130\pi$
$180$	4103.77	1.69932
$181$	3489.72	1.43309	0.716544	−	0.697542i	$-0.245723\pi$
$181$	3489.72	1.43309	0.716544	+	0.697542i	$0.245723\pi$
$182$	0	0
$183$	−3104.06	−1.25387
$184$	−1405.98	−0.563315
$185$	−5889.62	−2.34061
$186$	−3190.90	−1.25789
$187$	−182.551	−0.0713875
$188$	−422.801	−0.164021
$189$	0	0
$190$	−1694.13	−0.646870
$191$	2043.44	0.774128	0.387064	−	0.922053i	$-0.373489\pi$
$191$	2043.44	0.774128	0.387064	+	0.922053i	$0.373489\pi$
$192$	411.196	0.154560
$193$	5150.60	1.92098	0.960489	−	0.278319i	$-0.0897773\pi$
$193$	5150.60	1.92098	0.960489	+	0.278319i	$0.0897773\pi$
$194$	−525.937	−0.194640
$195$	8289.89	3.04437
$196$	0	0
$197$	−4426.06	−1.60073	−0.800365	−	0.599513i	$-0.795361\pi$
$197$	−4426.06	−1.60073	−0.800365	+	0.599513i	$0.795361\pi$
$198$	−6558.46	−2.35399
$199$	4352.49	1.55045	0.775226	−	0.631684i	$-0.217636\pi$
$199$	4352.49	1.55045	0.775226	+	0.631684i	$0.217636\pi$
$200$	1423.38	0.503242
$201$	−2590.18	−0.908941
$202$	2119.91	0.738397
$203$	0	0
$204$	234.628	0.0805257
$205$	−129.140	−0.0439977
$206$	6652.31	2.24994
$207$	−6651.45	−2.23337
$208$	4623.84	1.54137
$209$	1008.31	0.333713
$210$	0	0
$211$	4201.16	1.37071	0.685354	−	0.728210i	$-0.259647\pi$
$211$	4201.16	1.37071	0.685354	+	0.728210i	$0.259647\pi$
$212$	59.0693	0.0191363
$213$	517.646	0.166519
$214$	−821.627	−0.262455
$215$	−6535.90	−2.07323
$216$	−2937.24	−0.925250
$217$	0	0
$218$	2.49946	0.000776537 0
$219$	−3595.60	−1.10944
$220$	2497.41	0.765342
$221$	317.789	0.0967277
$222$	−12097.7	−3.65739
$223$	−524.091	−0.157380	−0.0786900	−	0.996899i	$-0.525074\pi$
$223$	−524.091	−0.157380	−0.0786900	+	0.996899i	$0.525074\pi$
$224$	0	0
$225$	6733.80	1.99520
$226$	3335.36	0.981704
$227$	5501.25	1.60851	0.804253	−	0.594287i	$-0.202566\pi$
$227$	5501.25	1.60851	0.804253	+	0.594287i	$0.202566\pi$
$228$	−1295.95	−0.376432
$229$	4777.44	1.37861	0.689306	−	0.724470i	$-0.257916\pi$
$229$	4777.44	1.37861	0.689306	+	0.724470i	$0.257916\pi$
$230$	6801.06	1.94978
$231$	0	0
$232$	−1963.23	−0.555571
$233$	−1483.72	−0.417175	−0.208587	−	0.978004i	$-0.566887\pi$
$233$	−1483.72	−0.417175	−0.208587	+	0.978004i	$0.566887\pi$
$234$	11417.1	3.18958
$235$	−1401.31	−0.388986
$236$	2029.82	0.559872
$237$	−10476.3	−2.87135
$238$	0	0
$239$	296.412	0.0802231	0.0401115	−	0.999195i	$-0.487229\pi$
$239$	296.412	0.0802231	0.0401115	+	0.999195i	$0.487229\pi$
$240$	11314.7	3.04316
$241$	−2661.86	−0.711476	−0.355738	−	0.934586i	$-0.615770\pi$
$241$	−2661.86	−0.711476	−0.355738	+	0.934586i	$0.615770\pi$
$242$	760.874	0.202111
$243$	−467.780	−0.123490
$244$	1627.89	0.427111
$245$	0	0
$246$	−265.262	−0.0687499
$247$	−1755.29	−0.452171
$248$	−1146.59	−0.293584
$249$	4887.60	1.24393
$250$	136.782	0.0346035
$251$	−4220.16	−1.06125	−0.530625	−	0.847607i	$-0.678043\pi$
$251$	−4220.16	−1.06125	−0.530625	+	0.847607i	$0.678043\pi$
$252$	0	0
$253$	−4047.83	−1.00587
$254$	−5169.37	−1.27699
$255$	777.641	0.190972
$256$	5232.02	1.27735
$257$	3005.41	0.729464	0.364732	−	0.931112i	$-0.381161\pi$
$257$	3005.41	0.729464	0.364732	+	0.931112i	$0.381161\pi$
$258$	−13425.2	−3.23959
$259$	0	0
$260$	−4347.55	−1.03701
$261$	−9287.75	−2.20267
$262$	4501.67	1.06150
$263$	−2239.53	−0.525078	−0.262539	−	0.964921i	$-0.584560\pi$
$263$	−2239.53	−0.525078	−0.262539	+	0.964921i	$0.584560\pi$
$264$	−3514.83	−0.819404
$265$	195.777	0.0453830
$266$	0	0
$267$	−5654.46	−1.29606
$268$	1358.39	0.309616
$269$	3679.12	0.833904	0.416952	−	0.908928i	$-0.363098\pi$
$269$	3679.12	0.833904	0.416952	+	0.908928i	$0.363098\pi$
$270$	14208.2	3.20253
$271$	3652.63	0.818751	0.409376	−	0.912366i	$-0.365747\pi$
$271$	3652.63	0.818751	0.409376	+	0.912366i	$0.365747\pi$
$272$	433.743	0.0966895
$273$	0	0
$274$	685.709	0.151187
$275$	4097.95	0.898602
$276$	5202.57	1.13463
$277$	551.737	0.119678	0.0598388	−	0.998208i	$-0.480941\pi$
$277$	551.737	0.119678	0.0598388	+	0.998208i	$0.480941\pi$
$278$	673.773	0.145360
$279$	−5424.35	−1.16397
$280$	0	0
$281$	597.604	0.126869	0.0634343	−	0.997986i	$-0.479795\pi$
$281$	597.604	0.126869	0.0634343	+	0.997986i	$0.479795\pi$
$282$	−2878.39	−0.607821
$283$	1120.91	0.235445	0.117723	−	0.993047i	$-0.462441\pi$
$283$	1120.91	0.235445	0.117723	+	0.993047i	$0.462441\pi$
$284$	−271.474	−0.0567219
$285$	−4295.24	−0.892731
$286$	6948.05	1.43653
$287$	0	0
$288$	10478.6	2.14396
$289$	−4883.19	−0.993932
$290$	9496.65	1.92297
$291$	−1333.44	−0.268618
$292$	1885.68	0.377914
$293$	−4458.67	−0.889005	−0.444502	−	0.895778i	$-0.646619\pi$
$293$	−4458.67	−0.889005	−0.444502	+	0.895778i	$0.646619\pi$
$294$	0	0
$295$	6727.54	1.32777
$296$	−4347.08	−0.853611
$297$	−8456.38	−1.65215
$298$	11702.3	2.27482
$299$	7046.57	1.36292
$300$	−5266.98	−1.01363
$301$	0	0
$302$	6971.79	1.32841
$303$	5374.74	1.01905
$304$	−2395.75	−0.451992
$305$	5395.42	1.01292
$306$	1070.99	0.200081
$307$	−4282.26	−0.796097	−0.398048	−	0.917364i	$-0.630312\pi$
$307$	−4282.26	−0.796097	−0.398048	+	0.917364i	$0.630312\pi$
$308$	0	0
$309$	16866.0	3.10510
$310$	5546.36	1.01617
$311$	2991.35	0.545414	0.272707	−	0.962097i	$-0.412081\pi$
$311$	2991.35	0.545414	0.272707	+	0.962097i	$0.412081\pi$
$312$	6118.70	1.11027
$313$	3715.35	0.670940	0.335470	−	0.942051i	$-0.391105\pi$
$313$	3715.35	0.670940	0.335470	+	0.942051i	$0.391105\pi$
$314$	−1265.49	−0.227439
$315$	0	0
$316$	5494.20	0.978078
$317$	−3217.96	−0.570154	−0.285077	−	0.958505i	$-0.592019\pi$
$317$	−3217.96	−0.570154	−0.285077	+	0.958505i	$0.592019\pi$
$318$	402.138	0.0709144
$319$	−5652.19	−0.992043
$320$	−714.733	−0.124859
$321$	−2083.13	−0.362208
$322$	0	0
$323$	−164.656	−0.0283645
$324$	3826.65	0.656148
$325$	−7133.81	−1.21758
$326$	−4211.46	−0.715495
$327$	6.33706	0.00107168
$328$	−95.3171	−0.0160458
$329$	0	0
$330$	17002.1	2.83617
$331$	2969.05	0.493032	0.246516	−	0.969139i	$-0.420714\pi$
$331$	2969.05	0.493032	0.246516	+	0.969139i	$0.420714\pi$
$332$	−2563.25	−0.423725
$333$	−20565.3	−3.38431
$334$	−13440.0	−2.20181
$335$	4502.20	0.734273
$336$	0	0
$337$	−5535.92	−0.894838	−0.447419	−	0.894324i	$-0.647657\pi$
$337$	−5535.92	−0.894838	−0.447419	+	0.894324i	$0.647657\pi$
$338$	−4251.31	−0.684145
$339$	8456.37	1.35483
$340$	−407.826	−0.0650514
$341$	−3301.06	−0.524231
$342$	−5915.56	−0.935312
$343$	0	0
$344$	−4824.09	−0.756098
$345$	17243.2	2.69085
$346$	−10470.6	−1.62688
$347$	5908.94	0.914146	0.457073	−	0.889429i	$-0.348898\pi$
$347$	5908.94	0.914146	0.457073	+	0.889429i	$0.348898\pi$
$348$	7264.60	1.11903
$349$	−7089.91	−1.08743	−0.543717	−	0.839269i	$-0.682983\pi$
$349$	−7089.91	−1.08743	−0.543717	+	0.839269i	$0.682983\pi$
$350$	0	0
$351$	14721.1	2.23861
$352$	6376.92	0.965599
$353$	−3735.91	−0.563294	−0.281647	−	0.959518i	$-0.590881\pi$
$353$	−3735.91	−0.563294	−0.281647	+	0.959518i	$0.590881\pi$
$354$	13818.8	2.07475
$355$	−899.762	−0.134519
$356$	2965.42	0.441481
$357$	0	0
$358$	2203.52	0.325306
$359$	−6143.56	−0.903189	−0.451594	−	0.892223i	$-0.649145\pi$
$359$	−6143.56	−0.903189	−0.451594	+	0.892223i	$0.649145\pi$
$360$	10039.1	1.46974
$361$	−5949.53	−0.867405
$362$	−12459.5	−1.80899
$363$	1929.09	0.278929
$364$	0	0
$365$	6249.81	0.896246
$366$	11082.5	1.58277
$367$	7746.50	1.10181	0.550904	−	0.834568i	$-0.314283\pi$
$367$	7746.50	1.10181	0.550904	+	0.834568i	$0.314283\pi$
$368$	9617.69	1.36238
$369$	−450.930	−0.0636165
$370$	21027.9	2.95457
$371$	0	0
$372$	4242.77	0.591337
$373$	8451.96	1.17326	0.586630	−	0.809855i	$-0.300454\pi$
$373$	8451.96	1.17326	0.586630	+	0.809855i	$0.300454\pi$
$374$	651.768	0.0901127
$375$	346.793	0.0477555
$376$	−1034.30	−0.141861
$377$	9839.47	1.34419
$378$	0	0
$379$	−884.442	−0.119870	−0.0599350	−	0.998202i	$-0.519089\pi$
$379$	−884.442	−0.119870	−0.0599350	+	0.998202i	$0.519089\pi$
$380$	2252.60	0.304094
$381$	−13106.2	−1.76234
$382$	−7295.78	−0.977184
$383$	10090.8	1.34626	0.673130	−	0.739524i	$-0.264950\pi$
$383$	10090.8	1.34626	0.673130	+	0.739524i	$0.264950\pi$
$384$	12343.7	1.64040
$385$	0	0
$386$	−18389.4	−2.42486
$387$	−22822.0	−2.99770
$388$	699.311	0.0915003
$389$	−12217.3	−1.59239	−0.796197	−	0.605037i	$-0.793158\pi$
$389$	−12217.3	−1.59239	−0.796197	+	0.605037i	$0.793158\pi$
$390$	−29597.7	−3.84291
$391$	661.010	0.0854954
$392$	0	0
$393$	11413.4	1.46496
$394$	15802.5	2.02061
$395$	18209.7	2.31957
$396$	8720.43	1.10661
$397$	−4402.84	−0.556605	−0.278303	−	0.960493i	$-0.589772\pi$
$397$	−4402.84	−0.556605	−0.278303	+	0.960493i	$0.589772\pi$
$398$	−15539.8	−1.95714
$399$	0	0
$400$	−9736.77	−1.21710
$401$	2205.42	0.274647	0.137324	−	0.990526i	$-0.456150\pi$
$401$	2205.42	0.274647	0.137324	+	0.990526i	$0.456150\pi$
$402$	9247.80	1.14736
$403$	5746.57	0.710316
$404$	−2818.73	−0.347121
$405$	12682.9	1.55610
$406$	0	0
$407$	−12515.3	−1.52423
$408$	573.970	0.0696464
$409$	13478.3	1.62948	0.814741	−	0.579826i	$-0.196879\pi$
$409$	13478.3	1.62948	0.814741	+	0.579826i	$0.196879\pi$
$410$	461.073	0.0555385
$411$	1738.52	0.208650
$412$	−8845.23	−1.05770
$413$	0	0
$414$	23747.9	2.81919
$415$	−8495.53	−1.00489
$416$	−11101.1	−1.30836
$417$	1708.26	0.200609
$418$	−3600.00	−0.421248
$419$	9113.61	1.06260	0.531300	−	0.847184i	$-0.321704\pi$
$419$	9113.61	1.06260	0.531300	+	0.847184i	$0.321704\pi$
$420$	0	0
$421$	−4084.96	−0.472895	−0.236448	−	0.971644i	$-0.575983\pi$
$421$	−4084.96	−0.472895	−0.236448	+	0.971644i	$0.575983\pi$
$422$	−14999.5	−1.73025
$423$	−4893.10	−0.562437
$424$	144.501	0.0165510
$425$	−669.193	−0.0763780
$426$	−1848.17	−0.210197
$427$	0	0
$428$	1092.47	0.123380
$429$	17615.9	1.98252
$430$	23335.4	2.61705
$431$	13099.8	1.46402	0.732011	−	0.681293i	$-0.238582\pi$
$431$	13099.8	1.46402	0.732011	+	0.681293i	$0.238582\pi$
$432$	20092.4	2.23773
$433$	1469.20	0.163061	0.0815303	−	0.996671i	$-0.474019\pi$
$433$	1469.20	0.163061	0.0815303	+	0.996671i	$0.474019\pi$
$434$	0	0
$435$	24077.5	2.65386
$436$	−3.32341	−0.000365051 0
$437$	−3651.04	−0.399663
$438$	12837.5	1.40045
$439$	−3633.33	−0.395010	−0.197505	−	0.980302i	$-0.563284\pi$
$439$	−3633.33	−0.395010	−0.197505	+	0.980302i	$0.563284\pi$
$440$	6109.41	0.661942
$441$	0	0
$442$	−1134.61	−0.122100
$443$	−2425.80	−0.260165	−0.130083	−	0.991503i	$-0.541524\pi$
$443$	−2425.80	−0.260165	−0.130083	+	0.991503i	$0.541524\pi$
$444$	16085.6	1.71934
$445$	9828.48	1.04700
$446$	1871.18	0.198661
$447$	29669.6	3.13943
$448$	0	0
$449$	6523.46	0.685659	0.342830	−	0.939398i	$-0.388615\pi$
$449$	6523.46	0.685659	0.342830	+	0.939398i	$0.388615\pi$
$450$	−24041.9	−2.51855
$451$	−274.420	−0.0286517
$452$	−4434.86	−0.461500
$453$	17676.0	1.83332
$454$	−19641.3	−2.03042
$455$	0	0
$456$	−3170.28	−0.325575
$457$	−3857.27	−0.394826	−0.197413	−	0.980320i	$-0.563254\pi$
$457$	−3857.27	−0.394826	−0.197413	+	0.980320i	$0.563254\pi$
$458$	−17057.1	−1.74023
$459$	1380.92	0.140427
$460$	−9043.01	−0.916593
$461$	−12782.5	−1.29141	−0.645704	−	0.763588i	$-0.723436\pi$
$461$	−12782.5	−1.29141	−0.645704	+	0.763588i	$0.723436\pi$
$462$	0	0
$463$	−16260.6	−1.63217	−0.816084	−	0.577933i	$-0.803860\pi$
$463$	−16260.6	−1.63217	−0.816084	+	0.577933i	$0.803860\pi$
$464$	13429.7	1.34366
$465$	14062.0	1.40239
$466$	5297.38	0.526601
$467$	6051.48	0.599634	0.299817	−	0.953997i	$-0.403074\pi$
$467$	6051.48	0.599634	0.299817	+	0.953997i	$0.403074\pi$
$468$	−15180.7	−1.49942
$469$	0	0
$470$	5003.16	0.491018
$471$	−3208.48	−0.313883
$472$	4965.54	0.484232
$473$	−13888.7	−1.35011
$474$	37403.9	3.62451
$475$	3696.24	0.357043
$476$	0	0
$477$	683.613	0.0656195
$478$	−1058.29	−0.101266
$479$	6373.71	0.607980	0.303990	−	0.952675i	$-0.401681\pi$
$479$	6373.71	0.607980	0.303990	+	0.952675i	$0.401681\pi$
$480$	−27164.8	−2.58312
$481$	21787.0	2.06528
$482$	9503.75	0.898099
$483$	0	0
$484$	−1011.69	−0.0950126
$485$	2317.77	0.216999
$486$	1670.13	0.155882
$487$	16775.9	1.56096	0.780480	−	0.625180i	$-0.214975\pi$
$487$	16775.9	1.56096	0.780480	+	0.625180i	$0.214975\pi$
$488$	3982.31	0.369408
$489$	−10677.6	−0.987440
$490$	0	0
$491$	20005.9	1.83881	0.919404	−	0.393314i	$-0.128672\pi$
$491$	20005.9	1.83881	0.919404	+	0.393314i	$0.128672\pi$
$492$	352.704	0.0323194
$493$	923.000	0.0843202
$494$	6266.96	0.570777
$495$	28902.6	2.62440
$496$	7843.36	0.710035
$497$	0	0
$498$	−17450.4	−1.57022
$499$	16434.6	1.47438	0.737189	−	0.675687i	$-0.236153\pi$
$499$	16434.6	1.47438	0.737189	+	0.675687i	$0.236153\pi$
$500$	−181.872	−0.0162671
$501$	−34075.4	−3.03867
$502$	15067.4	1.33962
$503$	−13761.0	−1.21982	−0.609912	−	0.792469i	$-0.708795\pi$
$503$	−13761.0	−1.21982	−0.609912	+	0.792469i	$0.708795\pi$
$504$	0	0
$505$	−9342.28	−0.823220
$506$	14452.1	1.26971
$507$	−10778.6	−0.944173
$508$	6873.43	0.600314
$509$	1983.85	0.172756	0.0863778	−	0.996262i	$-0.472471\pi$
$509$	1983.85	0.172756	0.0863778	+	0.996262i	$0.472471\pi$
$510$	−2776.44	−0.241064
$511$	0	0
$512$	−7771.01	−0.670768
$513$	−7627.44	−0.656451
$514$	−10730.3	−0.920805
$515$	−29316.3	−2.50840
$516$	17850.7	1.52293
$517$	−2977.76	−0.253311
$518$	0	0
$519$	−26546.8	−2.24523
$520$	−10635.4	−0.896911
$521$	6683.75	0.562035	0.281018	−	0.959703i	$-0.409328\pi$
$521$	6683.75	0.562035	0.281018	+	0.959703i	$0.409328\pi$
$522$	33160.4	2.78044
$523$	−1301.86	−0.108845	−0.0544227	−	0.998518i	$-0.517332\pi$
$523$	−1301.86	−0.108845	−0.0544227	+	0.998518i	$0.517332\pi$
$524$	−5985.63	−0.499014
$525$	0	0
$526$	7995.88	0.662808
$527$	539.062	0.0445577
$528$	24043.5	1.98174
$529$	2490.04	0.204655
$530$	−698.989	−0.0572871
$531$	23491.2	1.91983
$532$	0	0
$533$	477.717	0.0388222
$534$	20188.3	1.63602
$535$	3620.85	0.292604
$536$	3323.04	0.267786
$537$	5586.72	0.448947
$538$	−13135.7	−1.05264
$539$	0	0
$540$	−18891.9	−1.50551
$541$	4070.73	0.323501	0.161751	−	0.986832i	$-0.448286\pi$
$541$	4070.73	0.323501	0.161751	+	0.986832i	$0.448286\pi$
$542$	−13041.1	−1.03351
$543$	−31589.3	−2.49655
$544$	−1041.35	−0.0820725
$545$	−11.0150	−0.000865741 0
$546$	0	0
$547$	−5842.19	−0.456661	−0.228331	−	0.973584i	$-0.573327\pi$
$547$	−5842.19	−0.456661	−0.228331	+	0.973584i	$0.573327\pi$
$548$	−911.751	−0.0710732
$549$	18839.7	1.46459
$550$	−14631.0	−1.13431
$551$	−5098.13	−0.394170
$552$	12727.0	0.981339
$553$	0	0
$554$	−1969.89	−0.151069
$555$	53313.5	4.07753
$556$	−895.880	−0.0683341
$557$	−20828.1	−1.58440	−0.792202	−	0.610258i	$-0.791066\pi$
$557$	−20828.1	−1.58440	−0.792202	+	0.610258i	$0.791066\pi$
$558$	19366.7	1.46928
$559$	24177.7	1.82935
$560$	0	0
$561$	1652.47	0.124363
$562$	−2133.65	−0.160147
$563$	9297.26	0.695973	0.347987	−	0.937500i	$-0.386865\pi$
$563$	9297.26	0.695973	0.347987	+	0.937500i	$0.386865\pi$
$564$	3827.24	0.285737
$565$	−14698.7	−1.09448
$566$	−4002.02	−0.297204
$567$	0	0
$568$	−664.107	−0.0490586
$569$	22042.2	1.62400	0.812002	−	0.583654i	$-0.198378\pi$
$569$	22042.2	1.62400	0.812002	+	0.583654i	$0.198378\pi$
$570$	15335.5	1.12690
$571$	−1800.08	−0.131928	−0.0659641	−	0.997822i	$-0.521012\pi$
$571$	−1800.08	−0.131928	−0.0659641	+	0.997822i	$0.521012\pi$
$572$	−9238.46	−0.675313
$573$	−18497.5	−1.34859
$574$	0	0
$575$	−14838.5	−1.07619
$576$	−2495.70	−0.180534
$577$	−26384.5	−1.90364	−0.951821	−	0.306655i	$-0.900790\pi$
$577$	−26384.5	−1.90364	−0.951821	+	0.306655i	$0.900790\pi$
$578$	17434.6	1.25464
$579$	−46623.8	−3.34649
$580$	−12627.2	−0.903993
$581$	0	0
$582$	4760.84	0.339077
$583$	416.022	0.0295538
$584$	4612.93	0.326857
$585$	−50314.4	−3.55598
$586$	15918.9	1.12219
$587$	−7714.83	−0.542462	−0.271231	−	0.962514i	$-0.587431\pi$
$587$	−7714.83	−0.542462	−0.271231	+	0.962514i	$0.587431\pi$
$588$	0	0
$589$	−2977.47	−0.208293
$590$	−24019.6	−1.67605
$591$	40065.2	2.78860
$592$	29736.5	2.06447
$593$	−16086.7	−1.11400	−0.556998	−	0.830514i	$-0.688047\pi$
$593$	−16086.7	−1.11400	−0.556998	+	0.830514i	$0.688047\pi$
$594$	30192.1	2.08552
$595$	0	0
$596$	−15559.9	−1.06939
$597$	−39399.2	−2.70101
$598$	−25158.6	−1.72042
$599$	6392.53	0.436046	0.218023	−	0.975944i	$-0.430039\pi$
$599$	6392.53	0.436046	0.218023	+	0.975944i	$0.430039\pi$
$600$	−12884.6	−0.876687
$601$	−2990.17	−0.202948	−0.101474	−	0.994838i	$-0.532356\pi$
$601$	−2990.17	−0.202948	−0.101474	+	0.994838i	$0.532356\pi$
$602$	0	0
$603$	15720.8	1.06169
$604$	−9270.02	−0.624490
$605$	−3353.12	−0.225328
$606$	−19189.6	−1.28635
$607$	4184.97	0.279840	0.139920	−	0.990163i	$-0.455316\pi$
$607$	4184.97	0.279840	0.139920	+	0.990163i	$0.455316\pi$
$608$	5751.82	0.383663
$609$	0	0
$610$	−19263.5	−1.27861
$611$	5183.77	0.343229
$612$	−1424.04	−0.0940581
$613$	17371.7	1.14460	0.572299	−	0.820045i	$-0.306052\pi$
$613$	17371.7	1.14460	0.572299	+	0.820045i	$0.306052\pi$
$614$	15289.1	1.00492
$615$	1168.99	0.0766474
$616$	0	0
$617$	−14811.1	−0.966405	−0.483202	−	0.875509i	$-0.660526\pi$
$617$	−14811.1	−0.966405	−0.483202	+	0.875509i	$0.660526\pi$
$618$	−60217.4	−3.91958
$619$	−994.347	−0.0645657	−0.0322829	−	0.999479i	$-0.510278\pi$
$619$	−994.347	−0.0645657	−0.0322829	+	0.999479i	$0.510278\pi$
$620$	−7374.70	−0.477702
$621$	30620.2	1.97866
$622$	−10680.1	−0.688478
$623$	0	0
$624$	−41855.4	−2.68519
$625$	−15923.4	−1.01910
$626$	−13265.1	−0.846930
$627$	−9127.31	−0.581355
$628$	1682.66	0.106919
$629$	2043.75	0.129554
$630$	0	0
$631$	−22236.5	−1.40289	−0.701443	−	0.712725i	$-0.747461\pi$
$631$	−22236.5	−1.40289	−0.701443	+	0.712725i	$0.747461\pi$
$632$	13440.5	0.845937
$633$	−38029.3	−2.38788
$634$	11489.2	0.719707
$635$	22781.0	1.42368
$636$	−534.702	−0.0333370
$637$	0	0
$638$	20180.2	1.25226
$639$	−3141.78	−0.194502
$640$	−21455.6	−1.32517
$641$	−5824.34	−0.358889	−0.179444	−	0.983768i	$-0.557430\pi$
$641$	−5824.34	−0.358889	−0.179444	+	0.983768i	$0.557430\pi$
$642$	7437.46	0.457217
$643$	−3182.80	−0.195206	−0.0976029	−	0.995225i	$-0.531118\pi$
$643$	−3182.80	−0.195206	−0.0976029	+	0.995225i	$0.531118\pi$
$644$	0	0
$645$	59163.7	3.61173
$646$	587.878	0.0358046
$647$	23020.5	1.39881	0.699405	−	0.714726i	$-0.253449\pi$
$647$	23020.5	1.39881	0.699405	+	0.714726i	$0.253449\pi$
$648$	9361.14	0.567501
$649$	14295.9	0.864658
$650$	25470.1	1.53695
$651$	0	0
$652$	5599.76	0.336355
$653$	−4902.87	−0.293819	−0.146910	−	0.989150i	$-0.546933\pi$
$653$	−4902.87	−0.293819	−0.146910	+	0.989150i	$0.546933\pi$
$654$	−22.6254	−0.00135279
$655$	−19838.5	−1.18344
$656$	652.024	0.0388068
$657$	21823.0	1.29589
$658$	0	0
$659$	−9050.77	−0.535004	−0.267502	−	0.963557i	$-0.586198\pi$
$659$	−9050.77	−0.535004	−0.267502	+	0.963557i	$0.586198\pi$
$660$	−22606.8	−1.33329
$661$	−23731.2	−1.39642	−0.698211	−	0.715892i	$-0.746020\pi$
$661$	−23731.2	−1.39642	−0.698211	+	0.715892i	$0.746020\pi$
$662$	−10600.5	−0.622357
$663$	−2876.66	−0.168507
$664$	−6270.48	−0.366479
$665$	0	0
$666$	73425.1	4.27202
$667$	20466.3	1.18810
$668$	17870.5	1.03507
$669$	4744.13	0.274168
$670$	−16074.4	−0.926876
$671$	11465.2	0.659624
$672$	0	0
$673$	9470.05	0.542413	0.271206	−	0.962521i	$-0.412577\pi$
$673$	9470.05	0.542413	0.271206	+	0.962521i	$0.412577\pi$
$674$	19765.1	1.12956
$675$	−30999.3	−1.76765
$676$	5652.75	0.321617
$677$	26650.1	1.51292	0.756459	−	0.654041i	$-0.226928\pi$
$677$	26650.1	1.51292	0.756459	+	0.654041i	$0.226928\pi$
$678$	−30192.1	−1.71020
$679$	0	0
$680$	−997.664	−0.0562628
$681$	−49797.9	−2.80214
$682$	11785.9	0.661738
$683$	20278.9	1.13609	0.568045	−	0.822997i	$-0.307700\pi$
$683$	20278.9	1.13609	0.568045	+	0.822997i	$0.307700\pi$
$684$	7865.61	0.439691
$685$	−3021.87	−0.168554
$686$	0	0
$687$	−43245.9	−2.40165
$688$	32999.6	1.82863
$689$	−724.222	−0.0400445
$690$	−61563.9	−3.39666
$691$	1153.80	0.0635206	0.0317603	−	0.999496i	$-0.489889\pi$
$691$	1153.80	0.0635206	0.0317603	+	0.999496i	$0.489889\pi$
$692$	13922.2	0.764800
$693$	0	0
$694$	−21096.9	−1.15393
$695$	−2969.27	−0.162059
$696$	17771.4	0.967849
$697$	44.8127	0.00243530
$698$	25313.4	1.37267
$699$	13430.8	0.726751
$700$	0	0
$701$	−13298.1	−0.716493	−0.358247	−	0.933627i	$-0.616625\pi$
$701$	−13298.1	−0.716493	−0.358247	+	0.933627i	$0.616625\pi$
$702$	−52559.2	−2.82581
$703$	−11288.5	−0.605624
$704$	−1518.79	−0.0813092
$705$	12684.8	0.677644
$706$	13338.5	0.711048
$707$	0	0
$708$	−18374.1	−0.975341
$709$	16084.4	0.851993	0.425996	−	0.904725i	$-0.359924\pi$
$709$	16084.4	0.851993	0.425996	+	0.904725i	$0.359924\pi$
$710$	3212.45	0.169804
$711$	63584.7	3.35388
$712$	7254.31	0.381835
$713$	11953.0	0.627832
$714$	0	0
$715$	−30619.6	−1.60155
$716$	−2929.90	−0.152927
$717$	−2683.16	−0.139755
$718$	21934.6	1.14010
$719$	20047.4	1.03983	0.519917	−	0.854217i	$-0.325963\pi$
$719$	20047.4	1.03983	0.519917	+	0.854217i	$0.325963\pi$
$720$	−68673.0	−3.55457
$721$	0	0
$722$	21241.8	1.09493
$723$	24095.5	1.23945
$724$	16566.7	0.850409
$725$	−20719.7	−1.06139
$726$	−6887.51	−0.352093
$727$	−8839.43	−0.450944	−0.225472	−	0.974250i	$-0.572392\pi$
$727$	−8839.43	−0.450944	−0.225472	+	0.974250i	$0.572392\pi$
$728$	0	0
$729$	−17529.6	−0.890594
$730$	−22313.9	−1.13133
$731$	2268.01	0.114754
$732$	−14735.9	−0.744062
$733$	652.185	0.0328636	0.0164318	−	0.999865i	$-0.494769\pi$
$733$	652.185	0.0328636	0.0164318	+	0.999865i	$0.494769\pi$
$734$	−27657.6	−1.39082
$735$	0	0
$736$	−23090.6	−1.15643
$737$	9567.09	0.478166
$738$	1609.97	0.0803034
$739$	2514.37	0.125159	0.0625796	−	0.998040i	$-0.480067\pi$
$739$	2514.37	0.125159	0.0625796	+	0.998040i	$0.480067\pi$
$740$	−27959.7	−1.38895
$741$	15889.0	0.787717
$742$	0	0
$743$	−33049.2	−1.63184	−0.815919	−	0.578166i	$-0.803769\pi$
$743$	−33049.2	−1.63184	−0.815919	+	0.578166i	$0.803769\pi$
$744$	10379.1	0.511445
$745$	−51571.1	−2.53613
$746$	−30176.3	−1.48101
$747$	−29664.6	−1.45298
$748$	−866.622	−0.0423621
$749$	0	0
$750$	−1238.17	−0.0602820
$751$	−23623.7	−1.14786	−0.573930	−	0.818904i	$-0.694582\pi$
$751$	−23623.7	−1.14786	−0.573930	+	0.818904i	$0.694582\pi$
$752$	7075.20	0.343093
$753$	38201.3	1.84878
$754$	−35130.2	−1.69677
$755$	−30724.2	−1.48102
$756$	0	0
$757$	18319.8	0.879584	0.439792	−	0.898100i	$-0.355052\pi$
$757$	18319.8	0.879584	0.439792	+	0.898100i	$0.355052\pi$
$758$	3157.75	0.151312
$759$	36641.4	1.75230
$760$	5510.53	0.263010
$761$	−6334.09	−0.301722	−0.150861	−	0.988555i	$-0.548205\pi$
$761$	−6334.09	−0.301722	−0.150861	+	0.988555i	$0.548205\pi$
$762$	46793.6	2.22461
$763$	0	0
$764$	9700.81	0.459376
$765$	−4719.79	−0.223065
$766$	−36027.6	−1.69939
$767$	−24886.6	−1.17158
$768$	−47360.8	−2.22524
$769$	3468.39	0.162644	0.0813221	−	0.996688i	$-0.474086\pi$
$769$	3468.39	0.162644	0.0813221	+	0.996688i	$0.474086\pi$
$770$	0	0
$771$	−27205.3	−1.27078
$772$	24451.4	1.13993
$773$	35906.2	1.67071	0.835353	−	0.549714i	$-0.185263\pi$
$773$	35906.2	1.67071	0.835353	+	0.549714i	$0.185263\pi$
$774$	81482.3	3.78400
$775$	−12101.0	−0.560878
$776$	1710.72	0.0791384
$777$	0	0
$778$	43619.8	2.01009
$779$	−247.520	−0.0113842
$780$	39354.5	1.80656
$781$	−1911.98	−0.0876004
$782$	−2360.03	−0.107921
$783$	42756.5	1.95146
$784$	0	0
$785$	5576.93	0.253566
$786$	−40749.6	−1.84922
$787$	−39103.9	−1.77116	−0.885580	−	0.464487i	$-0.846239\pi$
$787$	−39103.9	−1.77116	−0.885580	+	0.464487i	$0.846239\pi$
$788$	−21011.8	−0.949890
$789$	20272.5	0.914726
$790$	−65014.9	−2.92801
$791$	0	0
$792$	21332.8	0.957106
$793$	−19958.8	−0.893769
$794$	15719.6	0.702605
$795$	−1772.19	−0.0790607
$796$	20662.5	0.920054
$797$	19145.5	0.850903	0.425452	−	0.904981i	$-0.360115\pi$
$797$	19145.5	0.850903	0.425452	+	0.904981i	$0.360115\pi$
$798$	0	0
$799$	486.268	0.0215306
$800$	23376.4	1.03310
$801$	34319.0	1.51386
$802$	−7874.10	−0.346688
$803$	13280.7	0.583644
$804$	−12296.3	−0.539375
$805$	0	0
$806$	−20517.2	−0.896634
$807$	−33303.8	−1.45273
$808$	−6895.46	−0.300224
$809$	−27091.2	−1.17735	−0.588675	−	0.808370i	$-0.700350\pi$
$809$	−27091.2	−1.17735	−0.588675	+	0.808370i	$0.700350\pi$
$810$	−45282.2	−1.96426
$811$	−16236.9	−0.703025	−0.351513	−	0.936183i	$-0.614333\pi$
$811$	−16236.9	−0.703025	−0.351513	+	0.936183i	$0.614333\pi$
$812$	0	0
$813$	−33064.0	−1.42633
$814$	44683.9	1.92404
$815$	18559.6	0.797687
$816$	−3926.29	−0.168441
$817$	−12527.2	−0.536440
$818$	−48121.9	−2.05690
$819$	0	0
$820$	−613.064	−0.0261087
$821$	−8059.42	−0.342601	−0.171301	−	0.985219i	$-0.554797\pi$
$821$	−8059.42	−0.342601	−0.171301	+	0.985219i	$0.554797\pi$
$822$	−6207.11	−0.263379
$823$	29296.3	1.24083	0.620417	−	0.784272i	$-0.286963\pi$
$823$	29296.3	1.24083	0.620417	+	0.784272i	$0.286963\pi$
$824$	−21638.1	−0.914803
$825$	−37095.1	−1.56544
$826$	0	0
$827$	15296.2	0.643171	0.321585	−	0.946881i	$-0.395784\pi$
$827$	15296.2	0.643171	0.321585	+	0.946881i	$0.395784\pi$
$828$	−31576.3	−1.32531
$829$	20509.1	0.859241	0.429621	−	0.903010i	$-0.358647\pi$
$829$	20509.1	0.859241	0.429621	+	0.903010i	$0.358647\pi$
$830$	30331.9	1.26848
$831$	−4994.38	−0.208488
$832$	2643.95	0.110171
$833$	0	0
$834$	−6099.06	−0.253229
$835$	59229.2	2.45474
$836$	4786.72	0.198029
$837$	24971.2	1.03122
$838$	−32538.6	−1.34132
$839$	−3957.65	−0.162853	−0.0814263	−	0.996679i	$-0.525948\pi$
$839$	−3957.65	−0.162853	−0.0814263	+	0.996679i	$0.525948\pi$
$840$	0	0
$841$	4189.15	0.171764
$842$	14584.7	0.596938
$843$	−5409.57	−0.221015
$844$	19944.1	0.813393
$845$	18735.2	0.762735
$846$	17470.0	0.709966
$847$	0	0
$848$	−988.473	−0.0400286
$849$	−10146.6	−0.410164
$850$	2389.24	0.0964122
$851$	45317.5	1.82546
$852$	2457.41	0.0988140
$853$	−12448.9	−0.499697	−0.249849	−	0.968285i	$-0.580381\pi$
$853$	−12448.9	−0.499697	−0.249849	+	0.968285i	$0.580381\pi$
$854$	0	0
$855$	26069.4	1.04276
$856$	2672.52	0.106711
$857$	7452.00	0.297031	0.148516	−	0.988910i	$-0.452551\pi$
$857$	7452.00	0.297031	0.148516	+	0.988910i	$0.452551\pi$
$858$	−62894.5	−2.50254
$859$	−31526.7	−1.25224	−0.626122	−	0.779725i	$-0.715359\pi$
$859$	−31526.7	−1.25224	−0.626122	+	0.779725i	$0.715359\pi$
$860$	−31027.8	−1.23028
$861$	0	0
$862$	−46770.6	−1.84804
$863$	7037.95	0.277607	0.138803	−	0.990320i	$-0.455674\pi$
$863$	7037.95	0.277607	0.138803	+	0.990320i	$0.455674\pi$
$864$	−48238.8	−1.89944
$865$	46143.1	1.81377
$866$	−5245.54	−0.205832
$867$	44203.1	1.73151
$868$	0	0
$869$	38695.3	1.51053
$870$	−85964.7	−3.34997
$871$	−16654.6	−0.647899
$872$	−8.13005	−0.000315732 0
$873$	8093.16	0.313760
$874$	13035.4	0.504497
$875$	0	0
$876$	−17069.3	−0.658356
$877$	19331.9	0.744346	0.372173	−	0.928163i	$-0.378613\pi$
$877$	19331.9	0.744346	0.372173	+	0.928163i	$0.378613\pi$
$878$	12972.2	0.498623
$879$	40360.4	1.54872
$880$	−41791.9	−1.60091
$881$	47384.8	1.81207	0.906036	−	0.423201i	$-0.139094\pi$
$881$	47384.8	1.81207	0.906036	+	0.423201i	$0.139094\pi$
$882$	0	0
$883$	−8680.62	−0.330834	−0.165417	−	0.986224i	$-0.552897\pi$
$883$	−8680.62	−0.330834	−0.165417	+	0.986224i	$0.552897\pi$
$884$	1508.64	0.0573993
$885$	−60898.4	−2.31308
$886$	8660.92	0.328408
$887$	39192.5	1.48360	0.741801	−	0.670620i	$-0.233972\pi$
$887$	39192.5	1.48360	0.741801	+	0.670620i	$0.233972\pi$
$888$	39350.2	1.48706
$889$	0	0
$890$	−35090.9	−1.32163
$891$	26950.9	1.01334
$892$	−2488.01	−0.0933909
$893$	−2685.87	−0.100648
$894$	−105930.	−3.96291
$895$	−9710.74	−0.362675
$896$	0	0
$897$	−63786.3	−2.37432
$898$	−23290.9	−0.865510
$899$	16690.6	0.619201
$900$	31967.3	1.18397
$901$	−67.9363	−0.00251197
$902$	979.771	0.0361672
$903$	0	0
$904$	−10849.0	−0.399150
$905$	54908.0	2.01680
$906$	−63109.3	−2.31420
$907$	9670.59	0.354032	0.177016	−	0.984208i	$-0.443356\pi$
$907$	9670.59	0.354032	0.177016	+	0.984208i	$0.443356\pi$
$908$	26116.0	0.954504
$909$	−32621.3	−1.19030
$910$	0	0
$911$	51397.9	1.86925	0.934627	−	0.355630i	$-0.115734\pi$
$911$	51397.9	1.86925	0.934627	+	0.355630i	$0.115734\pi$
$912$	21686.6	0.787406
$913$	−18052.8	−0.654394
$914$	13771.7	0.498390
$915$	−48839.9	−1.76459
$916$	22679.9	0.818083
$917$	0	0
$918$	−4930.36	−0.177262
$919$	16443.5	0.590228	0.295114	−	0.955462i	$-0.404642\pi$
$919$	16443.5	0.590228	0.295114	+	0.955462i	$0.404642\pi$
$920$	−22121.9	−0.792759
$921$	38763.5	1.38686
$922$	45637.7	1.63015
$923$	3328.42	0.118696
$924$	0	0
$925$	−45878.5	−1.63079
$926$	58055.8	2.06029
$927$	−102366.	−3.62692
$928$	−32242.5	−1.14053
$929$	55223.0	1.95028	0.975139	−	0.221593i	$-0.0711257\pi$
$929$	55223.0	1.95028	0.975139	+	0.221593i	$0.0711257\pi$
$930$	−50206.2	−1.77024
$931$	0	0
$932$	−7043.64	−0.247556
$933$	−27078.0	−0.950154
$934$	−21605.8	−0.756920
$935$	−2872.30	−0.100464
$936$	−37136.6	−1.29685
$937$	24930.8	0.869216	0.434608	−	0.900620i	$-0.356887\pi$
$937$	24930.8	0.869216	0.434608	+	0.900620i	$0.356887\pi$
$938$	0	0
$939$	−33631.8	−1.16883
$940$	−6652.44	−0.230828
$941$	13779.5	0.477364	0.238682	−	0.971098i	$-0.423285\pi$
$941$	13779.5	0.477364	0.238682	+	0.971098i	$0.423285\pi$
$942$	11455.4	0.396216
$943$	993.663	0.0343140
$944$	−33967.2	−1.17112
$945$	0	0
$946$	49587.2	1.70425
$947$	3174.72	0.108938	0.0544691	−	0.998515i	$-0.482653\pi$
$947$	3174.72	0.108938	0.0544691	+	0.998515i	$0.482653\pi$
$948$	−49734.0	−1.70389
$949$	−23119.4	−0.790819
$950$	−13196.8	−0.450696
$951$	29129.3	0.993252
$952$	0	0
$953$	−29455.4	−1.00121	−0.500606	−	0.865675i	$-0.666889\pi$
$953$	−29455.4	−1.00121	−0.500606	+	0.865675i	$0.666889\pi$
$954$	−2440.73	−0.0828317
$955$	32152.0	1.08944
$956$	1407.15	0.0476052
$957$	51164.2	1.72822
$958$	−22756.3	−0.767455
$959$	0	0
$960$	6469.84	0.217514
$961$	−20043.2	−0.672792
$962$	−77786.8	−2.60701
$963$	12643.3	0.423078
$964$	−12636.6	−0.422198
$965$	81040.7	2.70341
$966$	0	0
$967$	−41062.1	−1.36553	−0.682766	−	0.730637i	$-0.739223\pi$
$967$	−41062.1	−1.36553	−0.682766	+	0.730637i	$0.739223\pi$
$968$	−2474.91	−0.0821761
$969$	1490.49	0.0494131
$970$	−8275.20	−0.273918
$971$	−33782.3	−1.11651	−0.558253	−	0.829671i	$-0.688528\pi$
$971$	−33782.3	−1.11651	−0.558253	+	0.829671i	$0.688528\pi$
$972$	−2220.68	−0.0732803
$973$	0	0
$974$	−59895.5	−1.97041
$975$	64576.0	2.12111
$976$	−27241.3	−0.893416
$977$	−21387.9	−0.700367	−0.350183	−	0.936681i	$-0.613881\pi$
$977$	−21387.9	−0.700367	−0.350183	+	0.936681i	$0.613881\pi$
$978$	38122.6	1.24645
$979$	20885.3	0.681816
$980$	0	0
$981$	−38.4620	−0.00125178
$982$	−71427.8	−2.32113
$983$	20322.8	0.659405	0.329703	−	0.944085i	$-0.393051\pi$
$983$	20322.8	0.659405	0.329703	+	0.944085i	$0.393051\pi$
$984$	862.821	0.0279530
$985$	−69640.5	−2.25272
$986$	−3295.42	−0.106438
$987$	0	0
$988$	−8332.85	−0.268323
$989$	50290.3	1.61692
$990$	−103192.	−3.31279
$991$	50990.0	1.63446	0.817230	−	0.576311i	$-0.195508\pi$
$991$	50990.0	1.63446	0.817230	+	0.576311i	$0.195508\pi$
$992$	−18830.7	−0.602696
$993$	−26876.1	−0.858901
$994$	0	0
$995$	68483.0	2.18197
$996$	23202.8	0.738162
$997$	30493.6	0.968648	0.484324	−	0.874889i	$-0.339066\pi$
$997$	30493.6	0.968648	0.484324	+	0.874889i	$0.339066\pi$
$998$	−58677.1	−1.86111
$999$	94673.3	2.99833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2401.4.a.d.1.9		39
7.6	odd	2		2401.4.a.c.1.9		39
49.15	even	7		49.4.e.a.29.11	yes	78
49.36	even	7		49.4.e.a.22.11	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.22.11	✓	78	49.36	even	7
49.4.e.a.29.11	yes	78	49.15	even	7
2401.4.a.c.1.9		39	7.6	odd	2
2401.4.a.d.1.9		39	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:	\( N \)	\(=\)	\( 2401 = 7^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2401.a (trivial)

\(f(q)\)	\(=\)	\(q-3.57033 q^{2} -9.05210 q^{3} +4.74728 q^{4} +15.7342 q^{5} +32.3190 q^{6} +11.6133 q^{8} +54.9406 q^{9} +O(q^{10})\)	\(q-3.57033 q^{2} -9.05210 q^{3} +4.74728 q^{4} +15.7342 q^{5} +32.3190 q^{6} +11.6133 q^{8} +54.9406 q^{9} -56.1764 q^{10} +33.4349 q^{11} -42.9729 q^{12} -58.2042 q^{13} -142.428 q^{15} -79.4416 q^{16} -5.45990 q^{17} -196.156 q^{18} +30.1574 q^{19} +74.6947 q^{20} -119.374 q^{22} -121.066 q^{23} -105.125 q^{24} +122.565 q^{25} +207.809 q^{26} -252.921 q^{27} -169.051 q^{29} +508.514 q^{30} -98.7312 q^{31} +190.727 q^{32} -302.656 q^{33} +19.4937 q^{34} +260.819 q^{36} -374.320 q^{37} -107.672 q^{38} +526.871 q^{39} +182.726 q^{40} -8.20760 q^{41} -415.395 q^{43} +158.725 q^{44} +864.446 q^{45} +432.247 q^{46} -89.0617 q^{47} +719.113 q^{48} -437.598 q^{50} +49.4236 q^{51} -276.312 q^{52} +12.4428 q^{53} +903.013 q^{54} +526.071 q^{55} -272.988 q^{57} +603.568 q^{58} +427.574 q^{59} -676.145 q^{60} +342.910 q^{61} +352.503 q^{62} -45.4254 q^{64} -915.797 q^{65} +1080.58 q^{66} +286.141 q^{67} -25.9197 q^{68} +1095.90 q^{69} -57.1851 q^{71} +638.040 q^{72} +397.212 q^{73} +1336.45 q^{74} -1109.47 q^{75} +143.166 q^{76} -1881.10 q^{78} +1157.33 q^{79} -1249.95 q^{80} +806.072 q^{81} +29.3039 q^{82} -539.941 q^{83} -85.9072 q^{85} +1483.10 q^{86} +1530.26 q^{87} +388.288 q^{88} +624.657 q^{89} -3086.36 q^{90} -574.736 q^{92} +893.725 q^{93} +317.980 q^{94} +474.502 q^{95} -1726.48 q^{96} +147.308 q^{97} +1836.93 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + q^{2} + q^{3} + 145 q^{4} + 27 q^{5} + 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) \) 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

Modular forms

Varieties

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Database

Properties

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