LMFDB - Embedded newform 2401.4.a.c.1.10

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			1.10
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)

$f(q)$	$=$	$q-2.58597 q^{2} -3.61260 q^{3} -1.31274 q^{4} -3.92216 q^{5} +9.34209 q^{6} +24.0825 q^{8} -13.9491 q^{9} +O(q^{10})$	\(q-2.58597 q^{2} -3.61260 q^{3} -1.31274 q^{4} -3.92216 q^{5} +9.34209 q^{6} +24.0825 q^{8} -13.9491 q^{9} +10.1426 q^{10} +51.3433 q^{11} +4.74239 q^{12} +80.0934 q^{13} +14.1692 q^{15} -51.7748 q^{16} -12.9305 q^{17} +36.0721 q^{18} +124.338 q^{19} +5.14876 q^{20} -132.772 q^{22} -172.326 q^{23} -87.0004 q^{24} -109.617 q^{25} -207.119 q^{26} +147.933 q^{27} -151.493 q^{29} -36.6412 q^{30} -122.844 q^{31} -58.7716 q^{32} -185.483 q^{33} +33.4380 q^{34} +18.3115 q^{36} -100.407 q^{37} -321.536 q^{38} -289.345 q^{39} -94.4554 q^{40} -299.767 q^{41} +360.899 q^{43} -67.4002 q^{44} +54.7107 q^{45} +445.630 q^{46} -328.666 q^{47} +187.042 q^{48} +283.466 q^{50} +46.7127 q^{51} -105.142 q^{52} +213.751 q^{53} -382.550 q^{54} -201.376 q^{55} -449.185 q^{57} +391.757 q^{58} +438.890 q^{59} -18.6004 q^{60} -201.636 q^{61} +317.672 q^{62} +566.181 q^{64} -314.139 q^{65} +479.653 q^{66} +177.725 q^{67} +16.9744 q^{68} +622.544 q^{69} +162.124 q^{71} -335.930 q^{72} +199.627 q^{73} +259.650 q^{74} +396.001 q^{75} -163.224 q^{76} +748.239 q^{78} +676.194 q^{79} +203.069 q^{80} -157.796 q^{81} +775.189 q^{82} -122.420 q^{83} +50.7155 q^{85} -933.274 q^{86} +547.283 q^{87} +1236.47 q^{88} +240.004 q^{89} -141.480 q^{90} +226.219 q^{92} +443.787 q^{93} +849.921 q^{94} -487.675 q^{95} +212.318 q^{96} +559.285 q^{97} -716.194 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.58597	−0.914280	−0.457140	−	0.889395i	$-0.651126\pi$
$2$	−2.58597	−0.914280	−0.457140	+	0.889395i	$0.651126\pi$
$3$	−3.61260	−0.695245	−0.347623	−	0.937635i	$-0.613011\pi$
$3$	−3.61260	−0.695245	−0.347623	+	0.937635i	$0.613011\pi$
$4$	−1.31274	−0.164092
$5$	−3.92216	−0.350809	−0.175404	−	0.984496i	$-0.556123\pi$
$5$	−3.92216	−0.350809	−0.175404	+	0.984496i	$0.556123\pi$
$6$	9.34209	0.635649
$7$	0	0
$7$	0	0
$8$	24.0825	1.06431
$9$	−13.9491	−0.516634
$10$	10.1426	0.320737
$11$	51.3433	1.40733	0.703663	−	0.710534i	$-0.251547\pi$
$11$	51.3433	1.40733	0.703663	+	0.710534i	$0.251547\pi$
$12$	4.74239	0.114084
$13$	80.0934	1.70876	0.854381	−	0.519648i	$-0.173937\pi$
$13$	80.0934	1.70876	0.854381	+	0.519648i	$0.173937\pi$
$14$	0	0
$15$	14.1692	0.243898
$16$	−51.7748	−0.808982
$17$	−12.9305	−0.184477	−0.0922385	−	0.995737i	$-0.529402\pi$
$17$	−12.9305	−0.184477	−0.0922385	+	0.995737i	$0.529402\pi$
$18$	36.0721	0.472348
$19$	124.338	1.50133	0.750663	−	0.660685i	$-0.229734\pi$
$19$	124.338	1.50133	0.750663	+	0.660685i	$0.229734\pi$
$20$	5.14876	0.0575649
$21$	0	0
$22$	−132.772	−1.28669
$23$	−172.326	−1.56228	−0.781140	−	0.624356i	$-0.785361\pi$
$23$	−172.326	−1.56228	−0.781140	+	0.624356i	$0.785361\pi$
$24$	−87.0004	−0.739954
$25$	−109.617	−0.876933
$26$	−207.119	−1.56229
$27$	147.933	1.05443
$28$	0	0
$29$	−151.493	−0.970052	−0.485026	−	0.874500i	$-0.661190\pi$
$29$	−151.493	−0.970052	−0.485026	+	0.874500i	$0.661190\pi$
$30$	−36.6412	−0.222991
$31$	−122.844	−0.711726	−0.355863	−	0.934538i	$-0.615813\pi$
$31$	−122.844	−0.711726	−0.355863	+	0.934538i	$0.615813\pi$
$32$	−58.7716	−0.324670
$33$	−185.483	−0.978436
$34$	33.4380	0.168664
$35$	0	0
$36$	18.3115	0.0847756
$37$	−100.407	−0.446129	−0.223065	−	0.974804i	$-0.571606\pi$
$37$	−100.407	−0.446129	−0.223065	+	0.974804i	$0.571606\pi$
$38$	−321.536	−1.37263
$39$	−289.345	−1.18801
$40$	−94.4554	−0.373368
$41$	−299.767	−1.14185	−0.570923	−	0.821004i	$-0.693414\pi$
$41$	−299.767	−1.14185	−0.570923	+	0.821004i	$0.693414\pi$
$42$	0	0
$43$	360.899	1.27992	0.639959	−	0.768409i	$-0.278951\pi$
$43$	360.899	1.27992	0.639959	+	0.768409i	$0.278951\pi$
$44$	−67.4002	−0.230931
$45$	54.7107	0.181240
$46$	445.630	1.42836
$47$	−328.666	−1.02002	−0.510009	−	0.860169i	$-0.670358\pi$
$47$	−328.666	−1.02002	−0.510009	+	0.860169i	$0.670358\pi$
$48$	187.042	0.562441
$49$	0	0
$50$	283.466	0.801763
$51$	46.7127	0.128257
$52$	−105.142	−0.280394
$53$	213.751	0.553981	0.276990	−	0.960873i	$-0.410663\pi$
$53$	213.751	0.553981	0.276990	+	0.960873i	$0.410663\pi$
$54$	−382.550	−0.964047
$55$	−201.376	−0.493702
$56$	0	0
$57$	−449.185	−1.04379
$58$	391.757	0.886899
$59$	438.890	0.968450	0.484225	−	0.874943i	$-0.339102\pi$
$59$	438.890	0.968450	0.484225	+	0.874943i	$0.339102\pi$
$60$	−18.6004	−0.0400217
$61$	−201.636	−0.423227	−0.211613	−	0.977353i	$-0.567872\pi$
$61$	−201.636	−0.423227	−0.211613	+	0.977353i	$0.567872\pi$
$62$	317.672	0.650716
$63$	0	0
$64$	566.181	1.10582
$65$	−314.139	−0.599448
$66$	479.653	0.894565
$67$	177.725	0.324068	0.162034	−	0.986785i	$-0.448195\pi$
$67$	177.725	0.324068	0.162034	+	0.986785i	$0.448195\pi$
$68$	16.9744	0.0302712
$69$	622.544	1.08617
$70$	0	0
$71$	162.124	0.270995	0.135497	−	0.990778i	$-0.456737\pi$
$71$	162.124	0.270995	0.135497	+	0.990778i	$0.456737\pi$
$72$	−335.930	−0.549857
$73$	199.627	0.320063	0.160032	−	0.987112i	$-0.448840\pi$
$73$	199.627	0.320063	0.160032	+	0.987112i	$0.448840\pi$
$74$	259.650	0.407887
$75$	396.001	0.609684
$76$	−163.224	−0.246356
$77$	0	0
$78$	748.239	1.08617
$79$	676.194	0.963010	0.481505	−	0.876443i	$-0.340090\pi$
$79$	676.194	0.963010	0.481505	+	0.876443i	$0.340090\pi$
$80$	203.069	0.283798
$81$	−157.796	−0.216455
$82$	775.189	1.04397
$83$	−122.420	−0.161896	−0.0809481	−	0.996718i	$-0.525795\pi$
$83$	−122.420	−0.161896	−0.0809481	+	0.996718i	$0.525795\pi$
$84$	0	0
$85$	50.7155	0.0647161
$86$	−933.274	−1.17020
$87$	547.283	0.674424
$88$	1236.47	1.49783
$89$	240.004	0.285847	0.142923	−	0.989734i	$-0.454350\pi$
$89$	240.004	0.285847	0.142923	+	0.989734i	$0.454350\pi$
$90$	−141.480	−0.165704
$91$	0	0
$92$	226.219	0.256358
$93$	443.787	0.494824
$94$	849.921	0.932582
$95$	−487.675	−0.526678
$96$	212.318	0.225726
$97$	559.285	0.585431	0.292716	−	0.956200i	$-0.405441\pi$
$97$	559.285	0.585431	0.292716	+	0.956200i	$0.405441\pi$
$98$	0	0
$99$	−716.194	−0.727072
$100$	143.898	0.143898
$101$	−1223.70	−1.20557	−0.602785	−	0.797904i	$-0.705942\pi$
$101$	−1223.70	−1.20557	−0.602785	+	0.797904i	$0.705942\pi$
$102$	−120.798	−0.117263
$103$	−953.687	−0.912326	−0.456163	−	0.889896i	$-0.650777\pi$
$103$	−953.687	−0.912326	−0.456163	+	0.889896i	$0.650777\pi$
$104$	1928.85	1.81865
$105$	0	0
$106$	−552.755	−0.506494
$107$	529.047	0.477990	0.238995	−	0.971021i	$-0.423182\pi$
$107$	529.047	0.477990	0.238995	+	0.971021i	$0.423182\pi$
$108$	−194.197	−0.173024
$109$	853.149	0.749695	0.374848	−	0.927086i	$-0.377695\pi$
$109$	853.149	0.749695	0.374848	+	0.927086i	$0.377695\pi$
$110$	520.754	0.451382
$111$	362.730	0.310169
$112$	0	0
$113$	−473.731	−0.394380	−0.197190	−	0.980365i	$-0.563182\pi$
$113$	−473.731	−0.394380	−0.197190	+	0.980365i	$0.563182\pi$
$114$	1161.58	0.954316
$115$	675.889	0.548061
$116$	198.870	0.159178
$117$	−1117.23	−0.882805
$118$	−1134.96	−0.885435
$119$	0	0
$120$	341.229	0.259582
$121$	1305.13	0.980565
$122$	521.425	0.386948
$123$	1082.94	0.793863
$124$	161.262	0.116789
$125$	920.204	0.658444
$126$	0	0
$127$	−2755.56	−1.92533	−0.962663	−	0.270704i	$-0.912743\pi$
$127$	−2755.56	−1.92533	−0.962663	+	0.270704i	$0.912743\pi$
$128$	−993.955	−0.686360
$129$	−1303.78	−0.889857
$130$	812.355	0.548063
$131$	−1652.23	−1.10196	−0.550978	−	0.834520i	$-0.685745\pi$
$131$	−1652.23	−1.10196	−0.550978	+	0.834520i	$0.685745\pi$
$132$	243.490	0.160554
$133$	0	0
$134$	−459.592	−0.296289
$135$	−580.216	−0.369904
$136$	−311.399	−0.196340
$137$	−405.943	−0.253154	−0.126577	−	0.991957i	$-0.540399\pi$
$137$	−405.943	−0.253154	−0.126577	+	0.991957i	$0.540399\pi$
$138$	−1609.88	−0.993061
$139$	1437.06	0.876906	0.438453	−	0.898754i	$-0.355527\pi$
$139$	1437.06	0.876906	0.438453	+	0.898754i	$0.355527\pi$
$140$	0	0
$141$	1187.34	0.709162
$142$	−419.249	−0.247765
$143$	4112.26	2.40478
$144$	722.213	0.417948
$145$	594.179	0.340303
$146$	−516.231	−0.292627
$147$	0	0
$148$	131.808	0.0732064
$149$	−3455.43	−1.89986	−0.949932	−	0.312457i	$-0.898848\pi$
$149$	−3455.43	−1.89986	−0.949932	+	0.312457i	$0.898848\pi$
$150$	−1024.05	−0.557422
$151$	760.474	0.409844	0.204922	−	0.978778i	$-0.434306\pi$
$151$	760.474	0.409844	0.204922	+	0.978778i	$0.434306\pi$
$152$	2994.38	1.59787
$153$	180.369	0.0953071
$154$	0	0
$155$	481.815	0.249679
$156$	379.834	0.194943
$157$	−2810.45	−1.42865	−0.714327	−	0.699812i	$-0.753267\pi$
$157$	−2810.45	−1.42865	−0.714327	+	0.699812i	$0.753267\pi$
$158$	−1748.62	−0.880461
$159$	−772.198	−0.385153
$160$	230.512	0.113897
$161$	0	0
$162$	408.055	0.197900
$163$	3456.72	1.66105	0.830526	−	0.556980i	$-0.188040\pi$
$163$	3456.72	1.66105	0.830526	+	0.556980i	$0.188040\pi$
$164$	393.515	0.187368
$165$	727.493	0.343244
$166$	316.576	0.148018
$167$	3102.87	1.43777	0.718885	−	0.695129i	$-0.244653\pi$
$167$	3102.87	1.43777	0.718885	+	0.695129i	$0.244653\pi$
$168$	0	0
$169$	4217.95	1.91987
$170$	−131.149	−0.0591686
$171$	−1734.41	−0.775636
$172$	−473.765	−0.210025
$173$	−2735.26	−1.20207	−0.601035	−	0.799223i	$-0.705245\pi$
$173$	−2735.26	−1.20207	−0.601035	+	0.799223i	$0.705245\pi$
$174$	−1415.26	−0.616612
$175$	0	0
$176$	−2658.29	−1.13850
$177$	−1585.53	−0.673310
$178$	−620.644	−0.261344
$179$	1812.00	0.756622	0.378311	−	0.925678i	$-0.376505\pi$
$179$	1812.00	0.756622	0.378311	+	0.925678i	$0.376505\pi$
$180$	−71.8208	−0.0297400
$181$	−2383.51	−0.978814	−0.489407	−	0.872056i	$-0.662787\pi$
$181$	−2383.51	−0.978814	−0.489407	+	0.872056i	$0.662787\pi$
$182$	0	0
$183$	728.430	0.294246
$184$	−4150.04	−1.66274
$185$	393.812	0.156506
$186$	−1147.62	−0.452407
$187$	−663.895	−0.259619
$188$	431.452	0.167377
$189$	0	0
$190$	1261.12	0.481531
$191$	523.168	0.198194	0.0990972	−	0.995078i	$-0.468405\pi$
$191$	523.168	0.198194	0.0990972	+	0.995078i	$0.468405\pi$
$192$	−2045.38	−0.768817
$193$	1284.41	0.479035	0.239518	−	0.970892i	$-0.423011\pi$
$193$	1284.41	0.479035	0.239518	+	0.970892i	$0.423011\pi$
$194$	−1446.30	−0.535248
$195$	1134.86	0.416763
$196$	0	0
$197$	−956.560	−0.345950	−0.172975	−	0.984926i	$-0.555338\pi$
$197$	−956.560	−0.345950	−0.172975	+	0.984926i	$0.555338\pi$
$198$	1852.06	0.664748
$199$	−2577.22	−0.918061	−0.459031	−	0.888420i	$-0.651803\pi$
$199$	−2577.22	−0.918061	−0.459031	+	0.888420i	$0.651803\pi$
$200$	−2639.84	−0.933326
$201$	−642.049	−0.225307
$202$	3164.45	1.10223
$203$	0	0
$204$	−61.3216	−0.0210459
$205$	1175.73	0.400569
$206$	2466.21	0.834122
$207$	2403.80	0.807127
$208$	−4146.82	−1.38236
$209$	6383.94	2.11285
$210$	0	0
$211$	3067.54	1.00084	0.500422	−	0.865782i	$-0.333178\pi$
$211$	3067.54	1.00084	0.500422	+	0.865782i	$0.333178\pi$
$212$	−280.599	−0.0909039
$213$	−585.690	−0.188408
$214$	−1368.10	−0.437016
$215$	−1415.50	−0.449006
$216$	3562.59	1.12224
$217$	0	0
$218$	−2206.22	−0.685432
$219$	−721.174	−0.222522
$220$	264.354	0.0810126
$221$	−1035.65	−0.315227
$222$	−938.010	−0.283582
$223$	−394.692	−0.118523	−0.0592613	−	0.998243i	$-0.518875\pi$
$223$	−394.692	−0.118523	−0.0592613	+	0.998243i	$0.518875\pi$
$224$	0	0
$225$	1529.06	0.453054
$226$	1225.06	0.360573
$227$	−418.716	−0.122428	−0.0612141	−	0.998125i	$-0.519497\pi$
$227$	−418.716	−0.122428	−0.0612141	+	0.998125i	$0.519497\pi$
$228$	589.662	0.171278
$229$	−361.133	−0.104211	−0.0521056	−	0.998642i	$-0.516593\pi$
$229$	−361.133	−0.104211	−0.0521056	+	0.998642i	$0.516593\pi$
$230$	−1747.83	−0.501081
$231$	0	0
$232$	−3648.33	−1.03243
$233$	797.508	0.224234	0.112117	−	0.993695i	$-0.464237\pi$
$233$	797.508	0.224234	0.112117	+	0.993695i	$0.464237\pi$
$234$	2889.13	0.807131
$235$	1289.08	0.357831
$236$	−576.147	−0.158915
$237$	−2442.82	−0.669528
$238$	0	0
$239$	−107.794	−0.0291740	−0.0145870	−	0.999894i	$-0.504643\pi$
$239$	−107.794	−0.0291740	−0.0145870	+	0.999894i	$0.504643\pi$
$240$	−733.607	−0.197309
$241$	−58.7219	−0.0156955	−0.00784774	−	0.999969i	$-0.502498\pi$
$241$	−58.7219	−0.0156955	−0.00784774	+	0.999969i	$0.502498\pi$
$242$	−3375.04	−0.896511
$243$	−3424.13	−0.903943
$244$	264.695	0.0694482
$245$	0	0
$246$	−2800.45	−0.725813
$247$	9958.68	2.56541
$248$	−2958.40	−0.757494
$249$	442.256	0.112558
$250$	−2379.62	−0.602002
$251$	4771.85	1.19999	0.599993	−	0.800006i	$-0.295170\pi$
$251$	4771.85	1.19999	0.599993	+	0.800006i	$0.295170\pi$
$252$	0	0
$253$	−8847.78	−2.19864
$254$	7125.80	1.76029
$255$	−183.215	−0.0449936
$256$	−1959.10	−0.478296
$257$	−64.6635	−0.0156949	−0.00784747	−	0.999969i	$-0.502498\pi$
$257$	−64.6635	−0.0156949	−0.00784747	+	0.999969i	$0.502498\pi$
$258$	3371.55	0.813579
$259$	0	0
$260$	412.382	0.0983647
$261$	2113.19	0.501162
$262$	4272.63	1.00750
$263$	998.845	0.234188	0.117094	−	0.993121i	$-0.462642\pi$
$263$	998.845	0.234188	0.117094	+	0.993121i	$0.462642\pi$
$264$	−4466.89	−1.04136
$265$	−838.366	−0.194341
$266$	0	0
$267$	−867.037	−0.198733
$268$	−233.306	−0.0531771
$269$	692.571	0.156977	0.0784885	−	0.996915i	$-0.474991\pi$
$269$	692.571	0.156977	0.0784885	+	0.996915i	$0.474991\pi$
$270$	1500.42	0.338196
$271$	−1162.00	−0.260467	−0.130234	−	0.991483i	$-0.541573\pi$
$271$	−1162.00	−0.260467	−0.130234	+	0.991483i	$0.541573\pi$
$272$	669.475	0.149238
$273$	0	0
$274$	1049.76	0.231453
$275$	−5628.08	−1.23413
$276$	−817.237	−0.178232
$277$	−2197.86	−0.476738	−0.238369	−	0.971175i	$-0.576613\pi$
$277$	−2197.86	−0.476738	−0.238369	+	0.971175i	$0.576613\pi$
$278$	−3716.20	−0.801737
$279$	1713.57	0.367702
$280$	0	0
$281$	3450.91	0.732613	0.366306	−	0.930494i	$-0.380622\pi$
$281$	3450.91	0.732613	0.366306	+	0.930494i	$0.380622\pi$
$282$	−3070.42	−0.648373
$283$	−4624.35	−0.971339	−0.485669	−	0.874143i	$-0.661424\pi$
$283$	−4624.35	−0.971339	−0.485669	+	0.874143i	$0.661424\pi$
$284$	−212.827	−0.0444681
$285$	1761.77	0.366170
$286$	−10634.2	−2.19865
$287$	0	0
$288$	819.813	0.167736
$289$	−4745.80	−0.965968
$290$	−1536.53	−0.311132
$291$	−2020.47	−0.407018
$292$	−262.058	−0.0525199
$293$	−1790.83	−0.357070	−0.178535	−	0.983934i	$-0.557136\pi$
$293$	−1790.83	−0.357070	−0.178535	+	0.983934i	$0.557136\pi$
$294$	0	0
$295$	−1721.39	−0.339741
$296$	−2418.05	−0.474818
$297$	7595.35	1.48393
$298$	8935.65	1.73701
$299$	−13802.2	−2.66956
$300$	−519.846	−0.100044
$301$	0	0
$302$	−1966.57	−0.374712
$303$	4420.73	0.838166
$304$	−6437.60	−1.21454
$305$	790.848	0.148472
$306$	−466.430	−0.0871374
$307$	8893.09	1.65327	0.826637	−	0.562735i	$-0.190251\pi$
$307$	8893.09	1.65327	0.826637	+	0.562735i	$0.190251\pi$
$308$	0	0
$309$	3445.29	0.634290
$310$	−1245.96	−0.228277
$311$	3672.65	0.669636	0.334818	−	0.942283i	$-0.391325\pi$
$311$	3672.65	0.669636	0.334818	+	0.942283i	$0.391325\pi$
$312$	−6968.16	−1.26440
$313$	−3380.52	−0.610474	−0.305237	−	0.952276i	$-0.598736\pi$
$313$	−3380.52	−0.610474	−0.305237	+	0.952276i	$0.598736\pi$
$314$	7267.76	1.30619
$315$	0	0
$316$	−887.665	−0.158022
$317$	2923.83	0.518039	0.259020	−	0.965872i	$-0.416601\pi$
$317$	2923.83	0.518039	0.259020	+	0.965872i	$0.416601\pi$
$318$	1996.88	0.352137
$319$	−7778.14	−1.36518
$320$	−2220.65	−0.387932
$321$	−1911.24	−0.332320
$322$	0	0
$323$	−1607.76	−0.276960
$324$	207.144	0.0355186
$325$	−8779.57	−1.49847
$326$	−8939.00	−1.51867
$327$	−3082.08	−0.521222
$328$	−7219.13	−1.21527
$329$	0	0
$330$	−1881.28	−0.313821
$331$	−3256.68	−0.540796	−0.270398	−	0.962749i	$-0.587155\pi$
$331$	−3256.68	−0.540796	−0.270398	+	0.962749i	$0.587155\pi$
$332$	160.706	0.0265659
$333$	1400.59	0.230486
$334$	−8023.95	−1.31452
$335$	−697.066	−0.113686
$336$	0	0
$337$	3866.38	0.624971	0.312486	−	0.949923i	$-0.398838\pi$
$337$	3866.38	0.624971	0.312486	+	0.949923i	$0.398838\pi$
$338$	−10907.5	−1.75529
$339$	1711.40	0.274191
$340$	−66.5761	−0.0106194
$341$	−6307.23	−1.00163
$342$	4485.14	0.709149
$343$	0	0
$344$	8691.34	1.36223
$345$	−2441.72	−0.381037
$346$	7073.32	1.09903
$347$	−7028.14	−1.08729	−0.543646	−	0.839315i	$-0.682957\pi$
$347$	−7028.14	−1.08729	−0.543646	+	0.839315i	$0.682957\pi$
$348$	−718.439	−0.110668
$349$	−3941.16	−0.604486	−0.302243	−	0.953231i	$-0.597735\pi$
$349$	−3941.16	−0.604486	−0.302243	+	0.953231i	$0.597735\pi$
$350$	0	0
$351$	11848.4	1.80177
$352$	−3017.53	−0.456917
$353$	8846.83	1.33391	0.666954	−	0.745099i	$-0.267598\pi$
$353$	8846.83	1.33391	0.666954	+	0.745099i	$0.267598\pi$
$354$	4100.15	0.615594
$355$	−635.877	−0.0950672
$356$	−315.062	−0.0469052
$357$	0	0
$358$	−4685.79	−0.691765
$359$	9589.95	1.40986	0.704928	−	0.709279i	$-0.250979\pi$
$359$	9589.95	1.40986	0.704928	+	0.709279i	$0.250979\pi$
$360$	1317.57	0.192895
$361$	8601.04	1.25398
$362$	6163.71	0.894910
$363$	−4714.92	−0.681733
$364$	0	0
$365$	−782.970	−0.112281
$366$	−1883.70	−0.269024
$367$	1600.15	0.227594	0.113797	−	0.993504i	$-0.463699\pi$
$367$	1600.15	0.227594	0.113797	+	0.993504i	$0.463699\pi$
$368$	8922.14	1.26386
$369$	4181.48	0.589917
$370$	−1018.39	−0.143090
$371$	0	0
$372$	−582.576	−0.0811967
$373$	−13079.2	−1.81559	−0.907797	−	0.419409i	$-0.862237\pi$
$373$	−13079.2	−1.81559	−0.907797	+	0.419409i	$0.862237\pi$
$374$	1716.81	0.237365
$375$	−3324.33	−0.457780
$376$	−7915.09	−1.08561
$377$	−12133.6	−1.65759
$378$	0	0
$379$	3566.44	0.483366	0.241683	−	0.970355i	$-0.422301\pi$
$379$	3566.44	0.483366	0.241683	+	0.970355i	$0.422301\pi$
$380$	640.189	0.0864237
$381$	9954.73	1.33857
$382$	−1352.90	−0.181205
$383$	4310.05	0.575022	0.287511	−	0.957777i	$-0.407172\pi$
$383$	4310.05	0.575022	0.287511	+	0.957777i	$0.407172\pi$
$384$	3590.76	0.477188
$385$	0	0
$386$	−3321.45	−0.437972
$387$	−5034.22	−0.661250
$388$	−734.195	−0.0960647
$389$	4608.47	0.600665	0.300332	−	0.953835i	$-0.402902\pi$
$389$	4608.47	0.600665	0.300332	+	0.953835i	$0.402902\pi$
$390$	−2934.71	−0.381038
$391$	2228.26	0.288205
$392$	0	0
$393$	5968.85	0.766129
$394$	2473.64	0.316295
$395$	−2652.14	−0.337832
$396$	940.174	0.119307
$397$	8698.90	1.09971	0.549855	−	0.835260i	$-0.314683\pi$
$397$	8698.90	1.09971	0.549855	+	0.835260i	$0.314683\pi$
$398$	6664.62	0.839365
$399$	0	0
$400$	5675.38	0.709423
$401$	6939.73	0.864224	0.432112	−	0.901820i	$-0.357769\pi$
$401$	6939.73	0.864224	0.432112	+	0.901820i	$0.357769\pi$
$402$	1660.32	0.205994
$403$	−9839.01	−1.21617
$404$	1606.39	0.197825
$405$	618.899	0.0759342
$406$	0	0
$407$	−5155.22	−0.627849
$408$	1124.96	0.136504
$409$	−12106.5	−1.46363	−0.731816	−	0.681502i	$-0.761327\pi$
$409$	−12106.5	−1.46363	−0.731816	+	0.681502i	$0.761327\pi$
$410$	−3040.41	−0.366232
$411$	1466.51	0.176004
$412$	1251.94	0.149706
$413$	0	0
$414$	−6216.15	−0.737940
$415$	480.152	0.0567946
$416$	−4707.22	−0.554784
$417$	−5191.52	−0.609664
$418$	−16508.7	−1.93174
$419$	−8565.92	−0.998741	−0.499371	−	0.866388i	$-0.666435\pi$
$419$	−8565.92	−0.998741	−0.499371	+	0.866388i	$0.666435\pi$
$420$	0	0
$421$	7393.23	0.855876	0.427938	−	0.903808i	$-0.359240\pi$
$421$	7393.23	0.855876	0.427938	+	0.903808i	$0.359240\pi$
$422$	−7932.57	−0.915051
$423$	4584.60	0.526976
$424$	5147.66	0.589605
$425$	1417.40	0.161774
$426$	1514.58	0.172257
$427$	0	0
$428$	−694.500	−0.0784344
$429$	−14855.9	−1.67191
$430$	3660.45	0.410518
$431$	−12060.4	−1.34786	−0.673929	−	0.738796i	$-0.735395\pi$
$431$	−12060.4	−1.34786	−0.673929	+	0.738796i	$0.735395\pi$
$432$	−7659.19	−0.853017
$433$	−14079.2	−1.56260	−0.781299	−	0.624157i	$-0.785442\pi$
$433$	−14079.2	−1.56260	−0.781299	+	0.624157i	$0.785442\pi$
$434$	0	0
$435$	−2146.53	−0.236594
$436$	−1119.96	−0.123019
$437$	−21426.7	−2.34549
$438$	1864.94	0.203448
$439$	6001.68	0.652493	0.326246	−	0.945285i	$-0.394216\pi$
$439$	6001.68	0.652493	0.326246	+	0.945285i	$0.394216\pi$
$440$	−4849.65	−0.525450
$441$	0	0
$442$	2678.16	0.288206
$443$	1197.60	0.128442	0.0642210	−	0.997936i	$-0.479544\pi$
$443$	1197.60	0.128442	0.0642210	+	0.997936i	$0.479544\pi$
$444$	−476.169	−0.0508964
$445$	−941.333	−0.100277
$446$	1020.66	0.108363
$447$	12483.1	1.32087
$448$	0	0
$449$	−1892.15	−0.198878	−0.0994389	−	0.995044i	$-0.531705\pi$
$449$	−1892.15	−0.198878	−0.0994389	+	0.995044i	$0.531705\pi$
$450$	−3954.10	−0.414218
$451$	−15391.0	−1.60695
$452$	621.885	0.0647146
$453$	−2747.29	−0.284942
$454$	1082.79	0.111934
$455$	0	0
$456$	−10817.5	−1.11091
$457$	1531.45	0.156758	0.0783788	−	0.996924i	$-0.475026\pi$
$457$	1531.45	0.156758	0.0783788	+	0.996924i	$0.475026\pi$
$458$	933.881	0.0952782
$459$	−1912.85	−0.194519
$460$	−887.265	−0.0899325
$461$	−12142.9	−1.22679	−0.613396	−	0.789775i	$-0.710197\pi$
$461$	−12142.9	−1.22679	−0.613396	+	0.789775i	$0.710197\pi$
$462$	0	0
$463$	−856.307	−0.0859524	−0.0429762	−	0.999076i	$-0.513684\pi$
$463$	−856.307	−0.0859524	−0.0429762	+	0.999076i	$0.513684\pi$
$464$	7843.51	0.784754
$465$	−1740.60	−0.173588
$466$	−2062.34	−0.205013
$467$	9702.22	0.961382	0.480691	−	0.876890i	$-0.340386\pi$
$467$	9702.22	0.961382	0.480691	+	0.876890i	$0.340386\pi$
$468$	1466.63	0.144861
$469$	0	0
$470$	−3333.53	−0.327158
$471$	10153.0	0.993264
$472$	10569.6	1.03073
$473$	18529.7	1.80126
$474$	6317.07	0.612136
$475$	−13629.6	−1.31656
$476$	0	0
$477$	−2981.64	−0.286206
$478$	278.751	0.0266732
$479$	−18040.1	−1.72082	−0.860412	−	0.509599i	$-0.829794\pi$
$479$	−18040.1	−1.72082	−0.860412	+	0.509599i	$0.829794\pi$
$480$	−832.746	−0.0791865
$481$	−8041.92	−0.762329
$482$	151.853	0.0143501
$483$	0	0
$484$	−1713.30	−0.160903
$485$	−2193.61	−0.205374
$486$	8854.72	0.826457
$487$	−7676.00	−0.714236	−0.357118	−	0.934059i	$-0.616241\pi$
$487$	−7676.00	−0.714236	−0.357118	+	0.934059i	$0.616241\pi$
$488$	−4855.90	−0.450443
$489$	−12487.8	−1.15484
$490$	0	0
$491$	−14946.2	−1.37376	−0.686878	−	0.726773i	$-0.741019\pi$
$491$	−14946.2	−1.37376	−0.686878	+	0.726773i	$0.741019\pi$
$492$	−1421.61	−0.130267
$493$	1958.88	0.178952
$494$	−25752.9	−2.34550
$495$	2809.03	0.255063
$496$	6360.24	0.575773
$497$	0	0
$498$	−1143.66	−0.102909
$499$	8577.15	0.769471	0.384736	−	0.923027i	$-0.374293\pi$
$499$	8577.15	0.769471	0.384736	+	0.923027i	$0.374293\pi$
$500$	−1207.99	−0.108046
$501$	−11209.4	−0.999602
$502$	−12339.9	−1.09712
$503$	−17736.9	−1.57226	−0.786132	−	0.618059i	$-0.787919\pi$
$503$	−17736.9	−1.57226	−0.786132	+	0.618059i	$0.787919\pi$
$504$	0	0
$505$	4799.54	0.422924
$506$	22880.1	2.01017
$507$	−15237.7	−1.33478
$508$	3617.33	0.315931
$509$	−16898.8	−1.47157	−0.735784	−	0.677217i	$-0.763186\pi$
$509$	−16898.8	−1.47157	−0.735784	+	0.677217i	$0.763186\pi$
$510$	473.789	0.0411367
$511$	0	0
$512$	13017.8	1.12366
$513$	18393.7	1.58305
$514$	167.218	0.0143496
$515$	3740.51	0.320052
$516$	1711.52	0.146019
$517$	−16874.8	−1.43550
$518$	0	0
$519$	9881.41	0.835733
$520$	−7565.25	−0.637996
$521$	14509.6	1.22011	0.610055	−	0.792359i	$-0.291147\pi$
$521$	14509.6	1.22011	0.610055	+	0.792359i	$0.291147\pi$
$522$	−5464.66	−0.458202
$523$	13740.6	1.14882	0.574410	−	0.818568i	$-0.305231\pi$
$523$	13740.6	1.14882	0.574410	+	0.818568i	$0.305231\pi$
$524$	2168.95	0.180822
$525$	0	0
$526$	−2582.99	−0.214113
$527$	1588.44	0.131297
$528$	9603.33	0.791537
$529$	17529.2	1.44072
$530$	2167.99	0.177682
$531$	−6122.13	−0.500334
$532$	0	0
$533$	−24009.3	−1.95114
$534$	2242.14	0.181698
$535$	−2075.01	−0.167683
$536$	4280.06	0.344908
$537$	−6546.04	−0.526038
$538$	−1790.97	−0.143521
$539$	0	0
$540$	761.671	0.0606983
$541$	8373.79	0.665467	0.332733	−	0.943021i	$-0.392029\pi$
$541$	8373.79	0.665467	0.332733	+	0.943021i	$0.392029\pi$
$542$	3004.91	0.238140
$543$	8610.69	0.680515
$544$	759.947	0.0598942
$545$	−3346.18	−0.263000
$546$	0	0
$547$	10007.9	0.782279	0.391140	−	0.920331i	$-0.372081\pi$
$547$	10007.9	0.782279	0.391140	+	0.920331i	$0.372081\pi$
$548$	532.897	0.0415405
$549$	2812.64	0.218653
$550$	14554.1	1.12834
$551$	−18836.4	−1.45636
$552$	14992.4	1.15601
$553$	0	0
$554$	5683.60	0.435872
$555$	−1422.68	−0.108810
$556$	−1886.48	−0.143893
$557$	−880.557	−0.0669846	−0.0334923	−	0.999439i	$-0.510663\pi$
$557$	−880.557	−0.0669846	−0.0334923	+	0.999439i	$0.510663\pi$
$558$	−4431.25	−0.336182
$559$	28905.6	2.18708
$560$	0	0
$561$	2398.39	0.180499
$562$	−8923.97	−0.669813
$563$	11111.6	0.831790	0.415895	−	0.909413i	$-0.363468\pi$
$563$	11111.6	0.831790	0.415895	+	0.909413i	$0.363468\pi$
$564$	−1558.66	−0.116368
$565$	1858.05	0.138352
$566$	11958.4	0.888075
$567$	0	0
$568$	3904.36	0.288421
$569$	1846.90	0.136074	0.0680371	−	0.997683i	$-0.478326\pi$
$569$	1846.90	0.136074	0.0680371	+	0.997683i	$0.478326\pi$
$570$	−4555.90	−0.334782
$571$	−5256.81	−0.385272	−0.192636	−	0.981270i	$-0.561704\pi$
$571$	−5256.81	−0.385272	−0.192636	+	0.981270i	$0.561704\pi$
$572$	−5398.31	−0.394606
$573$	−1890.00	−0.137794
$574$	0	0
$575$	18889.8	1.37002
$576$	−7897.72	−0.571305
$577$	−9739.69	−0.702718	−0.351359	−	0.936241i	$-0.614280\pi$
$577$	−9739.69	−0.702718	−0.351359	+	0.936241i	$0.614280\pi$
$578$	12272.5	0.883165
$579$	−4640.06	−0.333047
$580$	−780.001	−0.0558410
$581$	0	0
$582$	5224.89	0.372128
$583$	10974.7	0.779632
$584$	4807.53	0.340645
$585$	4381.96	0.309695
$586$	4631.04	0.326462
$587$	−48.2902	−0.00339549	−0.00169774	−	0.999999i	$-0.500540\pi$
$587$	−48.2902	−0.00339549	−0.00169774	+	0.999999i	$0.500540\pi$
$588$	0	0
$589$	−15274.3	−1.06853
$590$	4451.48	0.310618
$591$	3455.67	0.240520
$592$	5198.55	0.360911
$593$	−23317.7	−1.61474	−0.807370	−	0.590045i	$-0.799110\pi$
$593$	−23317.7	−1.61474	−0.807370	+	0.590045i	$0.799110\pi$
$594$	−19641.4	−1.35673
$595$	0	0
$596$	4536.07	0.311753
$597$	9310.46	0.638278
$598$	35692.0	2.44073
$599$	2184.16	0.148985	0.0744927	−	0.997222i	$-0.476266\pi$
$599$	2184.16	0.148985	0.0744927	+	0.997222i	$0.476266\pi$
$600$	9536.70	0.648890
$601$	−1550.78	−0.105254	−0.0526270	−	0.998614i	$-0.516759\pi$
$601$	−1550.78	−0.105254	−0.0526270	+	0.998614i	$0.516759\pi$
$602$	0	0
$603$	−2479.11	−0.167425
$604$	−998.302	−0.0672522
$605$	−5118.93	−0.343991
$606$	−11431.9	−0.766319
$607$	−12160.6	−0.813150	−0.406575	−	0.913617i	$-0.633277\pi$
$607$	−12160.6	−0.813150	−0.406575	+	0.913617i	$0.633277\pi$
$608$	−7307.57	−0.487436
$609$	0	0
$610$	−2045.11	−0.135745
$611$	−26323.9	−1.74297
$612$	−236.777	−0.0156392
$613$	10788.4	0.710833	0.355417	−	0.934708i	$-0.384339\pi$
$613$	10788.4	0.710833	0.355417	+	0.934708i	$0.384339\pi$
$614$	−22997.3	−1.51156
$615$	−4247.45	−0.278494
$616$	0	0
$617$	15685.3	1.02344	0.511722	−	0.859151i	$-0.329008\pi$
$617$	15685.3	1.02344	0.511722	+	0.859151i	$0.329008\pi$
$618$	−8909.43	−0.579919
$619$	18459.4	1.19862	0.599309	−	0.800518i	$-0.295442\pi$
$619$	18459.4	1.19862	0.599309	+	0.800518i	$0.295442\pi$
$620$	−632.497	−0.0409704
$621$	−25492.6	−1.64732
$622$	−9497.37	−0.612234
$623$	0	0
$624$	14980.8	0.961077
$625$	10092.9	0.645945
$626$	8741.94	0.558144
$627$	−23062.6	−1.46895
$628$	3689.39	0.234431
$629$	1298.31	0.0823006
$630$	0	0
$631$	−13387.9	−0.844633	−0.422317	−	0.906448i	$-0.638783\pi$
$631$	−13387.9	−0.844633	−0.422317	+	0.906448i	$0.638783\pi$
$632$	16284.4	1.02494
$633$	−11081.8	−0.695832
$634$	−7560.94	−0.473633
$635$	10807.7	0.675421
$636$	1013.69	0.0632005
$637$	0	0
$638$	20114.1	1.24816
$639$	−2261.49	−0.140005
$640$	3898.45	0.240781
$641$	29546.7	1.82063	0.910314	−	0.413917i	$-0.135840\pi$
$641$	29546.7	1.82063	0.910314	+	0.413917i	$0.135840\pi$
$642$	4942.40	0.303834
$643$	6012.43	0.368751	0.184376	−	0.982856i	$-0.440974\pi$
$643$	6012.43	0.368751	0.184376	+	0.982856i	$0.440974\pi$
$644$	0	0
$645$	5113.64	0.312170
$646$	4157.62	0.253219
$647$	−10333.3	−0.627887	−0.313944	−	0.949442i	$-0.601650\pi$
$647$	−10333.3	−0.627887	−0.313944	+	0.949442i	$0.601650\pi$
$648$	−3800.11	−0.230374
$649$	22534.0	1.36292
$650$	22703.7	1.37002
$651$	0	0
$652$	−4537.77	−0.272566
$653$	−2885.54	−0.172925	−0.0864625	−	0.996255i	$-0.527556\pi$
$653$	−2885.54	−0.172925	−0.0864625	+	0.996255i	$0.527556\pi$
$654$	7970.19	0.476543
$655$	6480.32	0.386576
$656$	15520.4	0.923732
$657$	−2784.63	−0.165356
$658$	0	0
$659$	−26029.2	−1.53863	−0.769313	−	0.638872i	$-0.779401\pi$
$659$	−26029.2	−1.53863	−0.769313	+	0.638872i	$0.779401\pi$
$660$	−955.007	−0.0563236
$661$	−21383.1	−1.25825	−0.629127	−	0.777303i	$-0.716587\pi$
$661$	−21383.1	−1.25825	−0.629127	+	0.777303i	$0.716587\pi$
$662$	8421.70	0.494439
$663$	3741.38	0.219160
$664$	−2948.19	−0.172307
$665$	0	0
$666$	−3621.88	−0.210728
$667$	26106.1	1.51549
$668$	−4073.26	−0.235927
$669$	1425.86	0.0824023
$670$	1802.59	0.103941
$671$	−10352.6	−0.595618
$672$	0	0
$673$	−30339.8	−1.73776	−0.868880	−	0.495024i	$-0.835159\pi$
$673$	−30339.8	−1.73776	−0.868880	+	0.495024i	$0.835159\pi$
$674$	−9998.36	−0.571399
$675$	−16215.9	−0.924667
$676$	−5537.05	−0.315035
$677$	5672.68	0.322037	0.161018	−	0.986951i	$-0.448522\pi$
$677$	5672.68	0.322037	0.161018	+	0.986951i	$0.448522\pi$
$678$	−4425.64	−0.250687
$679$	0	0
$680$	1221.36	0.0688777
$681$	1512.65	0.0851176
$682$	16310.3	0.915770
$683$	3941.68	0.220826	0.110413	−	0.993886i	$-0.464783\pi$
$683$	3941.68	0.220826	0.110413	+	0.993886i	$0.464783\pi$
$684$	2276.83	0.127276
$685$	1592.17	0.0888085
$686$	0	0
$687$	1304.63	0.0724523
$688$	−18685.5	−1.03543
$689$	17120.1	0.946621
$690$	6314.22	0.348374
$691$	−10.4327	−0.000574356 0	−0.000287178	−	1.00000i	$-0.500091\pi$
$691$	−10.4327	−0.000574356 0	−0.000287178		1.00000i	$0.500091\pi$
$692$	3590.68	0.197250
$693$	0	0
$694$	18174.6	0.994089
$695$	−5636.38	−0.307626
$696$	13179.9	0.717794
$697$	3876.13	0.210644
$698$	10191.7	0.552670
$699$	−2881.08	−0.155897
$700$	0	0
$701$	−11880.7	−0.640123	−0.320062	−	0.947397i	$-0.603704\pi$
$701$	−11880.7	−0.640123	−0.320062	+	0.947397i	$0.603704\pi$
$702$	−30639.7	−1.64733
$703$	−12484.4	−0.669786
$704$	29069.6	1.55625
$705$	−4656.93	−0.248780
$706$	−22877.7	−1.21957
$707$	0	0
$708$	2081.39	0.110485
$709$	2109.47	0.111739	0.0558695	−	0.998438i	$-0.482207\pi$
$709$	2109.47	0.111739	0.0558695	+	0.998438i	$0.482207\pi$
$710$	1644.36	0.0869181
$711$	−9432.31	−0.497524
$712$	5779.89	0.304228
$713$	21169.3	1.11191
$714$	0	0
$715$	−16128.9	−0.843619
$716$	−2378.68	−0.124156
$717$	389.415	0.0202831
$718$	−24799.4	−1.28900
$719$	−23675.4	−1.22801	−0.614007	−	0.789301i	$-0.710443\pi$
$719$	−23675.4	−1.22801	−0.614007	+	0.789301i	$0.710443\pi$
$720$	−2832.64	−0.146620
$721$	0	0
$722$	−22242.1	−1.14649
$723$	212.139	0.0109122
$724$	3128.93	0.160616
$725$	16606.1	0.850671
$726$	12192.7	0.623295
$727$	−26252.8	−1.33929	−0.669645	−	0.742681i	$-0.733554\pi$
$727$	−26252.8	−1.33929	−0.669645	+	0.742681i	$0.733554\pi$
$728$	0	0
$729$	16630.5	0.844917
$730$	2024.74	0.102656
$731$	−4666.60	−0.236116
$732$	−956.237	−0.0482835
$733$	−9378.55	−0.472585	−0.236292	−	0.971682i	$-0.575932\pi$
$733$	−9378.55	−0.472585	−0.236292	+	0.971682i	$0.575932\pi$
$734$	−4137.95	−0.208085
$735$	0	0
$736$	10127.9	0.507226
$737$	9124.99	0.456069
$738$	−10813.2	−0.539349
$739$	−4332.70	−0.215671	−0.107836	−	0.994169i	$-0.534392\pi$
$739$	−4332.70	−0.215671	−0.107836	+	0.994169i	$0.534392\pi$
$740$	−516.971	−0.0256814
$741$	−35976.7	−1.78359
$742$	0	0
$743$	−32056.2	−1.58281	−0.791406	−	0.611291i	$-0.790651\pi$
$743$	−32056.2	−1.58281	−0.791406	+	0.611291i	$0.790651\pi$
$744$	10687.5	0.526644
$745$	13552.7	0.666488
$746$	33822.5	1.65996
$747$	1707.66	0.0836411
$748$	871.519	0.0426015
$749$	0	0
$750$	8596.63	0.418539
$751$	−19162.7	−0.931103	−0.465552	−	0.885021i	$-0.654144\pi$
$751$	−19162.7	−0.931103	−0.465552	+	0.885021i	$0.654144\pi$
$752$	17016.6	0.825175
$753$	−17238.8	−0.834284
$754$	31377.1	1.51550
$755$	−2982.70	−0.143777
$756$	0	0
$757$	−25743.6	−1.23602	−0.618010	−	0.786171i	$-0.712061\pi$
$757$	−25743.6	−1.23602	−0.618010	+	0.786171i	$0.712061\pi$
$758$	−9222.71	−0.441931
$759$	31963.5	1.52859
$760$	−11744.4	−0.560547
$761$	−6462.31	−0.307830	−0.153915	−	0.988084i	$-0.549188\pi$
$761$	−6462.31	−0.307830	−0.153915	+	0.988084i	$0.549188\pi$
$762$	−25742.7	−1.22383
$763$	0	0
$764$	−686.783	−0.0325222
$765$	−707.437	−0.0334346
$766$	−11145.7	−0.525731
$767$	35152.1	1.65485
$768$	7077.45	0.332533
$769$	33983.8	1.59361	0.796806	−	0.604235i	$-0.206521\pi$
$769$	33983.8	1.59361	0.796806	+	0.604235i	$0.206521\pi$
$770$	0	0
$771$	233.603	0.0109118
$772$	−1686.09	−0.0786060
$773$	−33623.0	−1.56447	−0.782236	−	0.622982i	$-0.785921\pi$
$773$	−33623.0	−1.56447	−0.782236	+	0.622982i	$0.785921\pi$
$774$	13018.4	0.604567
$775$	13465.8	0.624136
$776$	13469.0	0.623078
$777$	0	0
$778$	−11917.4	−0.549176
$779$	−37272.5	−1.71428
$780$	−1489.77	−0.0683876
$781$	8324.00	0.381378
$782$	−5762.23	−0.263500
$783$	−22410.8	−1.02285
$784$	0	0
$785$	11023.0	0.501184
$786$	−15435.3	−0.700457
$787$	−33460.2	−1.51554	−0.757769	−	0.652523i	$-0.773710\pi$
$787$	−33460.2	−1.51554	−0.757769	+	0.652523i	$0.773710\pi$
$788$	1255.71	0.0567676
$789$	−3608.43	−0.162818
$790$	6858.37	0.308873
$791$	0	0
$792$	−17247.7	−0.773828
$793$	−16149.7	−0.723194
$794$	−22495.1	−1.00544
$795$	3028.68	0.135115
$796$	3383.21	0.150647
$797$	−38922.2	−1.72985	−0.864927	−	0.501898i	$-0.832635\pi$
$797$	−38922.2	−1.72985	−0.864927	+	0.501898i	$0.832635\pi$
$798$	0	0
$799$	4249.82	0.188170
$800$	6442.35	0.284714
$801$	−3347.84	−0.147678
$802$	−17946.0	−0.790142
$803$	10249.5	0.450433
$804$	842.842	0.0369711
$805$	0	0
$806$	25443.4	1.11192
$807$	−2501.98	−0.109137
$808$	−29469.7	−1.28309
$809$	−32214.4	−1.40000	−0.699999	−	0.714143i	$-0.746816\pi$
$809$	−32214.4	−1.40000	−0.699999	+	0.714143i	$0.746816\pi$
$810$	−1600.46	−0.0694251
$811$	−7596.60	−0.328918	−0.164459	−	0.986384i	$-0.552588\pi$
$811$	−7596.60	−0.328918	−0.164459	+	0.986384i	$0.552588\pi$
$812$	0	0
$813$	4197.85	0.181088
$814$	13331.3	0.574030
$815$	−13557.8	−0.582711
$816$	−2418.54	−0.103757
$817$	44873.6	1.92158
$818$	31307.0	1.33817
$819$	0	0
$820$	−1543.43	−0.0657303
$821$	−8772.51	−0.372915	−0.186457	−	0.982463i	$-0.559701\pi$
$821$	−8772.51	−0.372915	−0.186457	+	0.982463i	$0.559701\pi$
$822$	−3792.36	−0.160917
$823$	−17175.9	−0.727476	−0.363738	−	0.931501i	$-0.618500\pi$
$823$	−17175.9	−0.727476	−0.363738	+	0.931501i	$0.618500\pi$
$824$	−22967.2	−0.970994
$825$	20332.0	0.858023
$826$	0	0
$827$	16632.3	0.699348	0.349674	−	0.936871i	$-0.386292\pi$
$827$	16632.3	0.699348	0.349674	+	0.936871i	$0.386292\pi$
$828$	−3155.55	−0.132443
$829$	17198.4	0.720539	0.360269	−	0.932848i	$-0.382685\pi$
$829$	17198.4	0.720539	0.360269	+	0.932848i	$0.382685\pi$
$830$	−1241.66	−0.0519262
$831$	7939.98	0.331450
$832$	45347.3	1.88958
$833$	0	0
$834$	13425.1	0.557404
$835$	−12170.0	−0.504382
$836$	−8380.44	−0.346703
$837$	−18172.7	−0.750467
$838$	22151.3	0.913129
$839$	−23416.1	−0.963546	−0.481773	−	0.876296i	$-0.660007\pi$
$839$	−23416.1	−0.963546	−0.481773	+	0.876296i	$0.660007\pi$
$840$	0	0
$841$	−1438.93	−0.0589990
$842$	−19118.7	−0.782510
$843$	−12466.8	−0.509345
$844$	−4026.87	−0.164231
$845$	−16543.5	−0.673505
$846$	−11855.7	−0.481804
$847$	0	0
$848$	−11066.9	−0.448160
$849$	16705.9	0.675318
$850$	−3665.36	−0.147907
$851$	17302.7	0.696979
$852$	768.858	0.0309162
$853$	−27982.9	−1.12323	−0.561616	−	0.827398i	$-0.689820\pi$
$853$	−27982.9	−1.12323	−0.561616	+	0.827398i	$0.689820\pi$
$854$	0	0
$855$	6802.64	0.272100
$856$	12740.8	0.508727
$857$	927.306	0.0369617	0.0184808	−	0.999829i	$-0.494117\pi$
$857$	927.306	0.0369617	0.0184808	+	0.999829i	$0.494117\pi$
$858$	38417.1	1.52860
$859$	40138.1	1.59429	0.797145	−	0.603788i	$-0.206343\pi$
$859$	40138.1	1.59429	0.797145	+	0.603788i	$0.206343\pi$
$860$	1858.18	0.0736784
$861$	0	0
$862$	31187.8	1.23232
$863$	29854.6	1.17759	0.588797	−	0.808281i	$-0.299602\pi$
$863$	29854.6	1.17759	0.588797	+	0.808281i	$0.299602\pi$
$864$	−8694.25	−0.342343
$865$	10728.1	0.421696
$866$	36408.5	1.42865
$867$	17144.7	0.671585
$868$	0	0
$869$	34718.0	1.35527
$870$	5550.87	0.216313
$871$	14234.6	0.553755
$872$	20545.9	0.797905
$873$	−7801.54	−0.302454
$874$	55409.0	2.14444
$875$	0	0
$876$	946.712	0.0365142
$877$	47393.2	1.82481	0.912404	−	0.409291i	$-0.134224\pi$
$877$	47393.2	1.82481	0.912404	+	0.409291i	$0.134224\pi$
$878$	−15520.2	−0.596561
$879$	6469.56	0.248251
$880$	10426.2	0.399396
$881$	6643.82	0.254070	0.127035	−	0.991898i	$-0.459454\pi$
$881$	6643.82	0.254070	0.127035	+	0.991898i	$0.459454\pi$
$882$	0	0
$883$	−43050.8	−1.64074	−0.820371	−	0.571831i	$-0.806233\pi$
$883$	−43050.8	−1.64074	−0.820371	+	0.571831i	$0.806233\pi$
$884$	1359.53	0.0517263
$885$	6218.71	0.236203
$886$	−3096.97	−0.117432
$887$	38745.3	1.46667	0.733336	−	0.679866i	$-0.237962\pi$
$887$	38745.3	1.46667	0.733336	+	0.679866i	$0.237962\pi$
$888$	8735.44	0.330115
$889$	0	0
$890$	2434.26	0.0916816
$891$	−8101.74	−0.304622
$892$	518.127	0.0194486
$893$	−40865.8	−1.53138
$894$	−32280.9	−1.20765
$895$	−7106.96	−0.265430
$896$	0	0
$897$	49861.7	1.85600
$898$	4893.05	0.181830
$899$	18610.0	0.690411
$900$	−2007.25	−0.0743426
$901$	−2763.91	−0.102197
$902$	39800.7	1.46920
$903$	0	0
$904$	−11408.6	−0.419741
$905$	9348.52	0.343376
$906$	7104.41	0.260517
$907$	17132.0	0.627188	0.313594	−	0.949557i	$-0.398467\pi$
$907$	17132.0	0.627188	0.313594	+	0.949557i	$0.398467\pi$
$908$	549.665	0.0200895
$909$	17069.5	0.622838
$910$	0	0
$911$	−42536.9	−1.54699	−0.773496	−	0.633801i	$-0.781494\pi$
$911$	−42536.9	−1.54699	−0.773496	+	0.633801i	$0.781494\pi$
$912$	23256.5	0.844406
$913$	−6285.47	−0.227841
$914$	−3960.29	−0.143320
$915$	−2857.02	−0.103224
$916$	474.073	0.0171002
$917$	0	0
$918$	4946.57	0.177844
$919$	39746.1	1.42666	0.713331	−	0.700827i	$-0.247186\pi$
$919$	39746.1	1.42666	0.713331	+	0.700827i	$0.247186\pi$
$920$	16277.1	0.583305
$921$	−32127.2	−1.14943
$922$	31401.2	1.12163
$923$	12985.1	0.463065
$924$	0	0
$925$	11006.3	0.391226
$926$	2214.39	0.0785845
$927$	13303.1	0.471339
$928$	8903.48	0.314947
$929$	−33269.7	−1.17496	−0.587482	−	0.809237i	$-0.699881\pi$
$929$	−33269.7	−1.17496	−0.587482	+	0.809237i	$0.699881\pi$
$930$	4501.16	0.158708
$931$	0	0
$932$	−1046.92	−0.0367950
$933$	−13267.8	−0.465561
$934$	−25089.7	−0.878972
$935$	2603.90	0.0910766
$936$	−26905.7	−0.939574
$937$	38567.7	1.34467	0.672333	−	0.740249i	$-0.265292\pi$
$937$	38567.7	1.34467	0.672333	+	0.740249i	$0.265292\pi$
$938$	0	0
$939$	12212.5	0.424429
$940$	−1692.22	−0.0587172
$941$	−10595.2	−0.367050	−0.183525	−	0.983015i	$-0.558751\pi$
$941$	−10595.2	−0.367050	−0.183525	+	0.983015i	$0.558751\pi$
$942$	−26255.5	−0.908122
$943$	51657.5	1.78388
$944$	−22723.4	−0.783458
$945$	0	0
$946$	−47917.4	−1.64686
$947$	−32160.6	−1.10357	−0.551784	−	0.833987i	$-0.686053\pi$
$947$	−32160.6	−1.10357	−0.551784	+	0.833987i	$0.686053\pi$
$948$	3206.78	0.109864
$949$	15988.8	0.546912
$950$	35245.7	1.20371
$951$	−10562.6	−0.360164
$952$	0	0
$953$	10013.8	0.340377	0.170189	−	0.985411i	$-0.445562\pi$
$953$	10013.8	0.340377	0.170189	+	0.985411i	$0.445562\pi$
$954$	7710.45	0.261672
$955$	−2051.95	−0.0695283
$956$	141.505	0.00478722
$957$	28099.3	0.949134
$958$	46651.3	1.57331
$959$	0	0
$960$	8022.32	0.269708
$961$	−14700.3	−0.493447
$962$	20796.2	0.696982
$963$	−7379.74	−0.246946
$964$	77.0864	0.00257550
$965$	−5037.66	−0.168050
$966$	0	0
$967$	48083.4	1.59903	0.799513	−	0.600648i	$-0.205091\pi$
$967$	48083.4	1.59903	0.799513	+	0.600648i	$0.205091\pi$
$968$	31430.8	1.04362
$969$	5808.19	0.192555
$970$	5672.61	0.187770
$971$	35110.9	1.16042	0.580208	−	0.814468i	$-0.302971\pi$
$971$	35110.9	1.16042	0.580208	+	0.814468i	$0.302971\pi$
$972$	4494.99	0.148330
$973$	0	0
$974$	19849.9	0.653012
$975$	31717.1	1.04180
$976$	10439.7	0.342383
$977$	15675.1	0.513295	0.256648	−	0.966505i	$-0.417382\pi$
$977$	15675.1	0.513295	0.256648	+	0.966505i	$0.417382\pi$
$978$	32293.0	1.05585
$979$	12322.6	0.402279
$980$	0	0
$981$	−11900.7	−0.387318
$982$	38650.6	1.25600
$983$	14689.3	0.476618	0.238309	−	0.971189i	$-0.423407\pi$
$983$	14689.3	0.476618	0.238309	+	0.971189i	$0.423407\pi$
$984$	26079.8	0.844913
$985$	3751.78	0.121362
$986$	−5065.61	−0.163612
$987$	0	0
$988$	−13073.1	−0.420963
$989$	−62192.2	−1.99959
$990$	−7264.07	−0.233199
$991$	10933.4	0.350465	0.175233	−	0.984527i	$-0.443932\pi$
$991$	10933.4	0.350465	0.175233	+	0.984527i	$0.443932\pi$
$992$	7219.76	0.231076
$993$	11765.1	0.375986
$994$	0	0
$995$	10108.3	0.322064
$996$	−580.566	−0.0184698
$997$	20408.7	0.648296	0.324148	−	0.946006i	$-0.394922\pi$
$997$	20408.7	0.648296	0.324148	+	0.946006i	$0.394922\pi$
$998$	−22180.3	−0.703512
$999$	−14853.5	−0.470413

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2401.4.a.c.1.10		39
7.6	odd	2		2401.4.a.d.1.10		39
49.20	odd	14		49.4.e.a.8.4	✓	78
49.27	odd	14		49.4.e.a.43.4	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.8.4	✓	78	49.20	odd	14
49.4.e.a.43.4	yes	78	49.27	odd	14
2401.4.a.c.1.10		39	1.1	even	1	trivial
2401.4.a.d.1.10		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)

\(f(q)\)	\(=\)	\(q-2.58597 q^{2} -3.61260 q^{3} -1.31274 q^{4} -3.92216 q^{5} +9.34209 q^{6} +24.0825 q^{8} -13.9491 q^{9} +O(q^{10})\)	\(q-2.58597 q^{2} -3.61260 q^{3} -1.31274 q^{4} -3.92216 q^{5} +9.34209 q^{6} +24.0825 q^{8} -13.9491 q^{9} +10.1426 q^{10} +51.3433 q^{11} +4.74239 q^{12} +80.0934 q^{13} +14.1692 q^{15} -51.7748 q^{16} -12.9305 q^{17} +36.0721 q^{18} +124.338 q^{19} +5.14876 q^{20} -132.772 q^{22} -172.326 q^{23} -87.0004 q^{24} -109.617 q^{25} -207.119 q^{26} +147.933 q^{27} -151.493 q^{29} -36.6412 q^{30} -122.844 q^{31} -58.7716 q^{32} -185.483 q^{33} +33.4380 q^{34} +18.3115 q^{36} -100.407 q^{37} -321.536 q^{38} -289.345 q^{39} -94.4554 q^{40} -299.767 q^{41} +360.899 q^{43} -67.4002 q^{44} +54.7107 q^{45} +445.630 q^{46} -328.666 q^{47} +187.042 q^{48} +283.466 q^{50} +46.7127 q^{51} -105.142 q^{52} +213.751 q^{53} -382.550 q^{54} -201.376 q^{55} -449.185 q^{57} +391.757 q^{58} +438.890 q^{59} -18.6004 q^{60} -201.636 q^{61} +317.672 q^{62} +566.181 q^{64} -314.139 q^{65} +479.653 q^{66} +177.725 q^{67} +16.9744 q^{68} +622.544 q^{69} +162.124 q^{71} -335.930 q^{72} +199.627 q^{73} +259.650 q^{74} +396.001 q^{75} -163.224 q^{76} +748.239 q^{78} +676.194 q^{79} +203.069 q^{80} -157.796 q^{81} +775.189 q^{82} -122.420 q^{83} +50.7155 q^{85} -933.274 q^{86} +547.283 q^{87} +1236.47 q^{88} +240.004 q^{89} -141.480 q^{90} +226.219 q^{92} +443.787 q^{93} +849.921 q^{94} -487.675 q^{95} +212.318 q^{96} +559.285 q^{97} -716.194 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) \) 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

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Database

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