LMFDB - Embedded newform 2401.4.a.d.1.13

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			1.13
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)

$f(q)$	$=$	$q-2.11024 q^{2} -5.68890 q^{3} -3.54689 q^{4} -12.6417 q^{5} +12.0050 q^{6} +24.3667 q^{8} +5.36363 q^{9} +O(q^{10})$	\(q-2.11024 q^{2} -5.68890 q^{3} -3.54689 q^{4} -12.6417 q^{5} +12.0050 q^{6} +24.3667 q^{8} +5.36363 q^{9} +26.6769 q^{10} -10.0089 q^{11} +20.1779 q^{12} +12.8371 q^{13} +71.9172 q^{15} -23.0445 q^{16} -50.2235 q^{17} -11.3185 q^{18} -42.4412 q^{19} +44.8385 q^{20} +21.1211 q^{22} +50.9366 q^{23} -138.620 q^{24} +34.8114 q^{25} -27.0894 q^{26} +123.087 q^{27} -177.055 q^{29} -151.762 q^{30} +261.107 q^{31} -146.304 q^{32} +56.9395 q^{33} +105.984 q^{34} -19.0242 q^{36} -88.0904 q^{37} +89.5611 q^{38} -73.0292 q^{39} -308.035 q^{40} +408.680 q^{41} +479.476 q^{43} +35.5003 q^{44} -67.8052 q^{45} -107.488 q^{46} +424.333 q^{47} +131.098 q^{48} -73.4605 q^{50} +285.717 q^{51} -45.5319 q^{52} +336.898 q^{53} -259.744 q^{54} +126.529 q^{55} +241.444 q^{57} +373.629 q^{58} -642.691 q^{59} -255.082 q^{60} -500.725 q^{61} -550.999 q^{62} +493.093 q^{64} -162.283 q^{65} -120.156 q^{66} -1028.35 q^{67} +178.137 q^{68} -289.773 q^{69} -796.583 q^{71} +130.694 q^{72} -296.735 q^{73} +185.892 q^{74} -198.039 q^{75} +150.534 q^{76} +154.109 q^{78} -1173.27 q^{79} +291.320 q^{80} -845.050 q^{81} -862.412 q^{82} -508.597 q^{83} +634.909 q^{85} -1011.81 q^{86} +1007.25 q^{87} -243.883 q^{88} +897.274 q^{89} +143.085 q^{90} -180.666 q^{92} -1485.42 q^{93} -895.445 q^{94} +536.527 q^{95} +832.311 q^{96} +185.840 q^{97} -53.6839 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.11024	−0.746082	−0.373041	−	0.927815i	$-0.621685\pi$
$2$	−2.11024	−0.746082	−0.373041	+	0.927815i	$0.621685\pi$
$3$	−5.68890	−1.09483	−0.547415	−	0.836861i	$-0.684388\pi$
$3$	−5.68890	−1.09483	−0.547415	+	0.836861i	$0.684388\pi$
$4$	−3.54689	−0.443361
$5$	−12.6417	−1.13070	−0.565352	−	0.824850i	$-0.691260\pi$
$5$	−12.6417	−1.13070	−0.565352	+	0.824850i	$0.691260\pi$
$6$	12.0050	0.816834
$7$	0	0
$7$	0	0
$8$	24.3667	1.07687
$9$	5.36363	0.198653
$10$	26.6769	0.843598
$11$	−10.0089	−0.274344	−0.137172	−	0.990547i	$-0.543801\pi$
$11$	−10.0089	−0.274344	−0.137172	+	0.990547i	$0.543801\pi$
$12$	20.1779	0.485405
$13$	12.8371	0.273875	0.136938	−	0.990580i	$-0.456274\pi$
$13$	12.8371	0.273875	0.136938	+	0.990580i	$0.456274\pi$
$14$	0	0
$15$	71.9172	1.23793
$16$	−23.0445	−0.360070
$17$	−50.2235	−0.716529	−0.358265	−	0.933620i	$-0.616631\pi$
$17$	−50.2235	−0.716529	−0.358265	+	0.933620i	$0.616631\pi$
$18$	−11.3185	−0.148212
$19$	−42.4412	−0.512457	−0.256228	−	0.966616i	$-0.582480\pi$
$19$	−42.4412	−0.512457	−0.256228	+	0.966616i	$0.582480\pi$
$20$	44.8385	0.501310
$21$	0	0
$22$	21.1211	0.204683
$23$	50.9366	0.461783	0.230891	−	0.972980i	$-0.425836\pi$
$23$	50.9366	0.461783	0.230891	+	0.972980i	$0.425836\pi$
$24$	−138.620	−1.17899
$25$	34.8114	0.278492
$26$	−27.0894	−0.204334
$27$	123.087	0.877339
$28$	0	0
$29$	−177.055	−1.13374	−0.566868	−	0.823809i	$-0.691845\pi$
$29$	−177.055	−1.13374	−0.566868	+	0.823809i	$0.691845\pi$
$30$	−151.762	−0.923597
$31$	261.107	1.51278	0.756392	−	0.654119i	$-0.226960\pi$
$31$	261.107	1.51278	0.756392	+	0.654119i	$0.226960\pi$
$32$	−146.304	−0.808224
$33$	56.9395	0.300360
$34$	105.984	0.534590
$35$	0	0
$36$	−19.0242	−0.0880750
$37$	−88.0904	−0.391404	−0.195702	−	0.980663i	$-0.562699\pi$
$37$	−88.0904	−0.391404	−0.195702	+	0.980663i	$0.562699\pi$
$38$	89.5611	0.382335
$39$	−73.0292	−0.299847
$40$	−308.035	−1.21762
$41$	408.680	1.55671	0.778354	−	0.627826i	$-0.216055\pi$
$41$	408.680	1.55671	0.778354	+	0.627826i	$0.216055\pi$
$42$	0	0
$43$	479.476	1.70045	0.850225	−	0.526419i	$-0.176466\pi$
$43$	479.476	1.70045	0.850225	+	0.526419i	$0.176466\pi$
$44$	35.5003	0.121634
$45$	−67.8052	−0.224618
$46$	−107.488	−0.344528
$47$	424.333	1.31692	0.658461	−	0.752615i	$-0.271208\pi$
$47$	424.333	1.31692	0.658461	+	0.752615i	$0.271208\pi$
$48$	131.098	0.394215
$49$	0	0
$50$	−73.4605	−0.207778
$51$	285.717	0.784478
$52$	−45.5319	−0.121426
$53$	336.898	0.873141	0.436570	−	0.899670i	$-0.356193\pi$
$53$	336.898	0.873141	0.436570	+	0.899670i	$0.356193\pi$
$54$	−259.744	−0.654567
$55$	126.529	0.310202
$56$	0	0
$57$	241.444	0.561053
$58$	373.629	0.845860
$59$	−642.691	−1.41816	−0.709078	−	0.705130i	$-0.750889\pi$
$59$	−642.691	−1.41816	−0.709078	+	0.705130i	$0.750889\pi$
$60$	−255.082	−0.548849
$61$	−500.725	−1.05100	−0.525502	−	0.850792i	$-0.676122\pi$
$61$	−500.725	−1.05100	−0.525502	+	0.850792i	$0.676122\pi$
$62$	−550.999	−1.12866
$63$	0	0
$64$	493.093	0.963072
$65$	−162.283	−0.309672
$66$	−120.156	−0.224094
$67$	−1028.35	−1.87512	−0.937560	−	0.347824i	$-0.886921\pi$
$67$	−1028.35	−1.87512	−0.937560	+	0.347824i	$0.886921\pi$
$68$	178.137	0.317681
$69$	−289.773	−0.505574
$70$	0	0
$71$	−796.583	−1.33151	−0.665753	−	0.746172i	$-0.731890\pi$
$71$	−796.583	−1.33151	−0.665753	+	0.746172i	$0.731890\pi$
$72$	130.694	0.213923
$73$	−296.735	−0.475756	−0.237878	−	0.971295i	$-0.576452\pi$
$73$	−296.735	−0.475756	−0.237878	+	0.971295i	$0.576452\pi$
$74$	185.892	0.292020
$75$	−198.039	−0.304901
$76$	150.534	0.227203
$77$	0	0
$78$	154.109	0.223711
$79$	−1173.27	−1.67093	−0.835463	−	0.549547i	$-0.814801\pi$
$79$	−1173.27	−1.67093	−0.835463	+	0.549547i	$0.814801\pi$
$80$	291.320	0.407133
$81$	−845.050	−1.15919
$82$	−862.412	−1.16143
$83$	−508.597	−0.672600	−0.336300	−	0.941755i	$-0.609176\pi$
$83$	−508.597	−0.672600	−0.336300	+	0.941755i	$0.609176\pi$
$84$	0	0
$85$	634.909	0.810183
$86$	−1011.81	−1.26868
$87$	1007.25	1.24125
$88$	−243.883	−0.295432
$89$	897.274	1.06866	0.534331	−	0.845276i	$-0.320564\pi$
$89$	897.274	1.06866	0.534331	+	0.845276i	$0.320564\pi$
$90$	143.085	0.167583
$91$	0	0
$92$	−180.666	−0.204737
$93$	−1485.42	−1.65624
$94$	−895.445	−0.982533
$95$	536.527	0.579437
$96$	832.311	0.884868
$97$	185.840	0.194528	0.0972639	−	0.995259i	$-0.468991\pi$
$97$	185.840	0.194528	0.0972639	+	0.995259i	$0.468991\pi$
$98$	0	0
$99$	−53.6839	−0.0544993
$100$	−123.472	−0.123472
$101$	−310.730	−0.306127	−0.153063	−	0.988216i	$-0.548914\pi$
$101$	−310.730	−0.306127	−0.153063	+	0.988216i	$0.548914\pi$
$102$	−602.931	−0.585285
$103$	147.361	0.140970	0.0704849	−	0.997513i	$-0.477545\pi$
$103$	147.361	0.140970	0.0704849	+	0.997513i	$0.477545\pi$
$104$	312.799	0.294927
$105$	0	0
$106$	−710.935	−0.651435
$107$	−1194.18	−1.07894	−0.539468	−	0.842006i	$-0.681375\pi$
$107$	−1194.18	−1.07894	−0.539468	+	0.842006i	$0.681375\pi$
$108$	−436.577	−0.388978
$109$	−416.520	−0.366012	−0.183006	−	0.983112i	$-0.558583\pi$
$109$	−416.520	−0.366012	−0.183006	+	0.983112i	$0.558583\pi$
$110$	−267.006	−0.231436
$111$	501.138	0.428521
$112$	0	0
$113$	908.912	0.756666	0.378333	−	0.925670i	$-0.376497\pi$
$113$	908.912	0.756666	0.378333	+	0.925670i	$0.376497\pi$
$114$	−509.504	−0.418592
$115$	−643.922	−0.522140
$116$	627.995	0.502654
$117$	68.8537	0.0544062
$118$	1356.23	1.05806
$119$	0	0
$120$	1752.38	1.33308
$121$	−1230.82	−0.924735
$122$	1056.65	0.784136
$123$	−2324.94	−1.70433
$124$	−926.119	−0.670709
$125$	1140.13	0.815813
$126$	0	0
$127$	−2710.31	−1.89371	−0.946853	−	0.321666i	$-0.895757\pi$
$127$	−2710.31	−1.89371	−0.946853	+	0.321666i	$0.895757\pi$
$128$	129.890	0.0896933
$129$	−2727.69	−1.86170
$130$	342.455	0.231041
$131$	−2675.67	−1.78454	−0.892269	−	0.451505i	$-0.850887\pi$
$131$	−2675.67	−1.78454	−0.892269	+	0.451505i	$0.850887\pi$
$132$	−201.958	−0.133168
$133$	0	0
$134$	2170.07	1.39899
$135$	−1556.03	−0.992010
$136$	−1223.78	−0.771606
$137$	1006.12	0.627432	0.313716	−	0.949517i	$-0.398426\pi$
$137$	1006.12	0.627432	0.313716	+	0.949517i	$0.398426\pi$
$138$	611.491	0.377200
$139$	−1228.73	−0.749779	−0.374889	−	0.927070i	$-0.622319\pi$
$139$	−1228.73	−0.749779	−0.374889	+	0.927070i	$0.622319\pi$
$140$	0	0
$141$	−2413.99	−1.44181
$142$	1680.98	0.993414
$143$	−128.485	−0.0751361
$144$	−123.602	−0.0715290
$145$	2238.27	1.28192
$146$	626.182	0.354954
$147$	0	0
$148$	312.447	0.173533
$149$	−1509.91	−0.830177	−0.415089	−	0.909781i	$-0.636249\pi$
$149$	−1509.91	−0.830177	−0.415089	+	0.909781i	$0.636249\pi$
$150$	417.910	0.227481
$151$	1507.32	0.812344	0.406172	−	0.913797i	$-0.366863\pi$
$151$	1507.32	0.812344	0.406172	+	0.913797i	$0.366863\pi$
$152$	−1034.15	−0.551847
$153$	−269.381	−0.142341
$154$	0	0
$155$	−3300.83	−1.71051
$156$	259.027	0.132941
$157$	−1504.47	−0.764775	−0.382387	−	0.924002i	$-0.624898\pi$
$157$	−1504.47	−0.764775	−0.382387	+	0.924002i	$0.624898\pi$
$158$	2475.88	1.24665
$159$	−1916.58	−0.955941
$160$	1849.53	0.913863
$161$	0	0
$162$	1783.26	0.864851
$163$	300.373	0.144338	0.0721688	−	0.997392i	$-0.477008\pi$
$163$	300.373	0.144338	0.0721688	+	0.997392i	$0.477008\pi$
$164$	−1449.54	−0.690184
$165$	−719.809	−0.339619
$166$	1073.26	0.501815
$167$	292.022	0.135313	0.0676566	−	0.997709i	$-0.478448\pi$
$167$	292.022	0.135313	0.0676566	+	0.997709i	$0.478448\pi$
$168$	0	0
$169$	−2032.21	−0.924992
$170$	−1339.81	−0.604463
$171$	−227.639	−0.101801
$172$	−1700.65	−0.753914
$173$	469.067	0.206142	0.103071	−	0.994674i	$-0.467133\pi$
$173$	469.067	0.206142	0.103071	+	0.994674i	$0.467133\pi$
$174$	−2125.54	−0.926073
$175$	0	0
$176$	230.649	0.0987831
$177$	3656.21	1.55264
$178$	−1893.46	−0.797309
$179$	1454.08	0.607169	0.303585	−	0.952805i	$-0.401817\pi$
$179$	1454.08	0.607169	0.303585	+	0.952805i	$0.401817\pi$
$180$	240.497	0.0995868
$181$	2755.70	1.13165	0.565827	−	0.824524i	$-0.308557\pi$
$181$	2755.70	1.13165	0.565827	+	0.824524i	$0.308557\pi$
$182$	0	0
$183$	2848.58	1.15067
$184$	1241.16	0.497278
$185$	1113.61	0.442563
$186$	3134.58	1.23569
$187$	502.681	0.196576
$188$	−1505.06	−0.583872
$189$	0	0
$190$	−1132.20	−0.432308
$191$	583.799	0.221164	0.110582	−	0.993867i	$-0.464729\pi$
$191$	583.799	0.221164	0.110582	+	0.993867i	$0.464729\pi$
$192$	−2805.16	−1.05440
$193$	3955.96	1.47542	0.737711	−	0.675116i	$-0.235907\pi$
$193$	3955.96	1.47542	0.737711	+	0.675116i	$0.235907\pi$
$194$	−392.167	−0.145134
$195$	923.210	0.339038
$196$	0	0
$197$	−1611.23	−0.582718	−0.291359	−	0.956614i	$-0.594107\pi$
$197$	−1611.23	−0.582718	−0.291359	+	0.956614i	$0.594107\pi$
$198$	113.286	0.0406610
$199$	2468.03	0.879167	0.439584	−	0.898202i	$-0.355126\pi$
$199$	2468.03	0.879167	0.439584	+	0.898202i	$0.355126\pi$
$200$	848.240	0.299898
$201$	5850.19	2.05294
$202$	655.715	0.228396
$203$	0	0
$204$	−1013.41	−0.347807
$205$	−5166.39	−1.76018
$206$	−310.967	−0.105175
$207$	273.205	0.0917346
$208$	−295.825	−0.0986143
$209$	424.788	0.140590
$210$	0	0
$211$	717.224	0.234008	0.117004	−	0.993131i	$-0.462671\pi$
$211$	717.224	0.234008	0.117004	+	0.993131i	$0.462671\pi$
$212$	−1194.94	−0.387117
$213$	4531.68	1.45777
$214$	2520.02	0.804976
$215$	−6061.37	−1.92271
$216$	2999.23	0.944777
$217$	0	0
$218$	878.956	0.273075
$219$	1688.10	0.520873
$220$	−448.783	−0.137532
$221$	−644.726	−0.196240
$222$	−1057.52	−0.319712
$223$	2606.20	0.782618	0.391309	−	0.920259i	$-0.372022\pi$
$223$	2606.20	0.782618	0.391309	+	0.920259i	$0.372022\pi$
$224$	0	0
$225$	186.716	0.0553232
$226$	−1918.02	−0.564535
$227$	−3734.91	−1.09205	−0.546024	−	0.837770i	$-0.683859\pi$
$227$	−3734.91	−1.09205	−0.546024	+	0.837770i	$0.683859\pi$
$228$	−856.374	−0.248749
$229$	1482.24	0.427725	0.213862	−	0.976864i	$-0.431396\pi$
$229$	1482.24	0.427725	0.213862	+	0.976864i	$0.431396\pi$
$230$	1358.83	0.389559
$231$	0	0
$232$	−4314.25	−1.22088
$233$	4548.93	1.27902	0.639508	−	0.768785i	$-0.279138\pi$
$233$	4548.93	1.27902	0.639508	+	0.768785i	$0.279138\pi$
$234$	−145.298	−0.0405915
$235$	−5364.27	−1.48905
$236$	2279.55	0.628755
$237$	6674.62	1.82938
$238$	0	0
$239$	170.647	0.0461852	0.0230926	−	0.999733i	$-0.492649\pi$
$239$	170.647	0.0461852	0.0230926	+	0.999733i	$0.492649\pi$
$240$	−1657.29	−0.445741
$241$	−5551.66	−1.48388	−0.741938	−	0.670469i	$-0.766093\pi$
$241$	−5551.66	−1.48388	−0.741938	+	0.670469i	$0.766093\pi$
$242$	2597.33	0.689929
$243$	1484.05	0.391777
$244$	1776.02	0.465974
$245$	0	0
$246$	4906.18	1.27157
$247$	−544.823	−0.140349
$248$	6362.33	1.62907
$249$	2893.36	0.736383
$250$	−2405.95	−0.608663
$251$	3414.09	0.858546	0.429273	−	0.903175i	$-0.358770\pi$
$251$	3414.09	0.858546	0.429273	+	0.903175i	$0.358770\pi$
$252$	0	0
$253$	−509.817	−0.126687
$254$	5719.39	1.41286
$255$	−3611.94	−0.887012
$256$	−4218.84	−1.02999
$257$	2872.39	0.697177	0.348589	−	0.937276i	$-0.386661\pi$
$257$	2872.39	0.697177	0.348589	+	0.937276i	$0.386661\pi$
$258$	5756.08	1.38899
$259$	0	0
$260$	575.598	0.137297
$261$	−949.659	−0.225220
$262$	5646.31	1.33141
$263$	−3715.72	−0.871182	−0.435591	−	0.900145i	$-0.643461\pi$
$263$	−3715.72	−0.871182	−0.435591	+	0.900145i	$0.643461\pi$
$264$	1387.43	0.323448
$265$	−4258.94	−0.987264
$266$	0	0
$267$	−5104.50	−1.17000
$268$	3647.44	0.831355
$269$	−6037.35	−1.36842	−0.684208	−	0.729287i	$-0.739852\pi$
$269$	−6037.35	−1.36842	−0.684208	+	0.729287i	$0.739852\pi$
$270$	3283.59	0.740122
$271$	−11.8979	−0.00266696	−0.00133348	−	0.999999i	$-0.500424\pi$
$271$	−11.8979	−0.00266696	−0.00133348	+	0.999999i	$0.500424\pi$
$272$	1157.38	0.258001
$273$	0	0
$274$	−2123.14	−0.468116
$275$	−348.423	−0.0764025
$276$	1027.79	0.224152
$277$	−1100.81	−0.238778	−0.119389	−	0.992848i	$-0.538094\pi$
$277$	−1100.81	−0.238778	−0.119389	+	0.992848i	$0.538094\pi$
$278$	2592.91	0.559397
$279$	1400.48	0.300519
$280$	0	0
$281$	2894.16	0.614417	0.307208	−	0.951642i	$-0.400605\pi$
$281$	2894.16	0.614417	0.307208	+	0.951642i	$0.400605\pi$
$282$	5094.10	1.07571
$283$	1872.66	0.393350	0.196675	−	0.980469i	$-0.436986\pi$
$283$	1872.66	0.393350	0.196675	+	0.980469i	$0.436986\pi$
$284$	2825.39	0.590338
$285$	−3052.25	−0.634385
$286$	271.134	0.0560577
$287$	0	0
$288$	−784.722	−0.160556
$289$	−2390.60	−0.486586
$290$	−4723.29	−0.956418
$291$	−1057.23	−0.212975
$292$	1052.49	0.210932
$293$	2375.66	0.473677	0.236839	−	0.971549i	$-0.423889\pi$
$293$	2375.66	0.473677	0.236839	+	0.971549i	$0.423889\pi$
$294$	0	0
$295$	8124.67	1.60351
$296$	−2146.47	−0.421490
$297$	−1231.96	−0.240693
$298$	3186.27	0.619381
$299$	653.879	0.126471
$300$	702.422	0.135181
$301$	0	0
$302$	−3180.81	−0.606076
$303$	1767.71	0.335157
$304$	978.035	0.184520
$305$	6329.99	1.18837
$306$	568.458	0.106198
$307$	−3387.12	−0.629685	−0.314843	−	0.949144i	$-0.601952\pi$
$307$	−3387.12	−0.629685	−0.314843	+	0.949144i	$0.601952\pi$
$308$	0	0
$309$	−838.321	−0.154338
$310$	6965.54	1.27618
$311$	−7430.10	−1.35473	−0.677367	−	0.735645i	$-0.736879\pi$
$311$	−7430.10	−1.35473	−0.677367	+	0.735645i	$0.736879\pi$
$312$	−1779.48	−0.322895
$313$	3669.26	0.662616	0.331308	−	0.943523i	$-0.392510\pi$
$313$	3669.26	0.662616	0.331308	+	0.943523i	$0.392510\pi$
$314$	3174.79	0.570585
$315$	0	0
$316$	4161.46	0.740824
$317$	−36.1403	−0.00640328	−0.00320164	−	0.999995i	$-0.501019\pi$
$317$	−36.1403	−0.00640328	−0.00320164	+	0.999995i	$0.501019\pi$
$318$	4044.44	0.713211
$319$	1772.12	0.311034
$320$	−6233.51	−1.08895
$321$	6793.60	1.18125
$322$	0	0
$323$	2131.55	0.367190
$324$	2997.30	0.513940
$325$	446.879	0.0762720
$326$	−633.859	−0.107688
$327$	2369.54	0.400721
$328$	9958.17	1.67637
$329$	0	0
$330$	1518.97	0.253383
$331$	−4932.92	−0.819148	−0.409574	−	0.912277i	$-0.634323\pi$
$331$	−4932.92	−0.819148	−0.409574	+	0.912277i	$0.634323\pi$
$332$	1803.94	0.298205
$333$	−472.484	−0.0777537
$334$	−616.236	−0.100955
$335$	13000.1	2.12021
$336$	0	0
$337$	−12305.8	−1.98914	−0.994570	−	0.104074i	$-0.966812\pi$
$337$	−12305.8	−1.98914	−0.994570	+	0.104074i	$0.966812\pi$
$338$	4288.45	0.690120
$339$	−5170.72	−0.828421
$340$	−2251.95	−0.359203
$341$	−2613.39	−0.415023
$342$	480.373	0.0759520
$343$	0	0
$344$	11683.2	1.83116
$345$	3663.21	0.571654
$346$	−989.843	−0.153799
$347$	−5498.02	−0.850573	−0.425287	−	0.905059i	$-0.639827\pi$
$347$	−5498.02	−0.850573	−0.425287	+	0.905059i	$0.639827\pi$
$348$	−3572.60	−0.550321
$349$	7661.39	1.17509	0.587543	−	0.809193i	$-0.300095\pi$
$349$	7661.39	1.17509	0.587543	+	0.809193i	$0.300095\pi$
$350$	0	0
$351$	1580.09	0.240282
$352$	1464.34	0.221732
$353$	−620.074	−0.0934935	−0.0467468	−	0.998907i	$-0.514885\pi$
$353$	−620.074	−0.0934935	−0.0467468	+	0.998907i	$0.514885\pi$
$354$	−7715.47	−1.15840
$355$	10070.1	1.50554
$356$	−3182.53	−0.473803
$357$	0	0
$358$	−3068.46	−0.452998
$359$	−8298.50	−1.21999	−0.609997	−	0.792403i	$-0.708830\pi$
$359$	−8298.50	−1.21999	−0.609997	+	0.792403i	$0.708830\pi$
$360$	−1652.19	−0.241883
$361$	−5057.75	−0.737388
$362$	−5815.18	−0.844307
$363$	7002.03	1.01243
$364$	0	0
$365$	3751.22	0.537940
$366$	−6011.18	−0.858495
$367$	3561.51	0.506565	0.253282	−	0.967392i	$-0.418490\pi$
$367$	3561.51	0.506565	0.253282	+	0.967392i	$0.418490\pi$
$368$	−1173.81	−0.166274
$369$	2192.01	0.309245
$370$	−2349.98	−0.330188
$371$	0	0
$372$	5268.60	0.734313
$373$	−5272.91	−0.731959	−0.365979	−	0.930623i	$-0.619266\pi$
$373$	−5272.91	−0.731959	−0.365979	+	0.930623i	$0.619266\pi$
$374$	−1060.78	−0.146662
$375$	−6486.11	−0.893176
$376$	10339.6	1.41815
$377$	−2272.88	−0.310502
$378$	0	0
$379$	4074.65	0.552244	0.276122	−	0.961123i	$-0.410951\pi$
$379$	4074.65	0.552244	0.276122	+	0.961123i	$0.410951\pi$
$380$	−1903.00	−0.256900
$381$	15418.7	2.07329
$382$	−1231.96	−0.165006
$383$	248.518	0.0331558	0.0165779	−	0.999863i	$-0.494723\pi$
$383$	248.518	0.0331558	0.0165779	+	0.999863i	$0.494723\pi$
$384$	−738.931	−0.0981989
$385$	0	0
$386$	−8348.03	−1.10079
$387$	2571.73	0.337800
$388$	−659.154	−0.0862460
$389$	−8731.10	−1.13801	−0.569003	−	0.822335i	$-0.692671\pi$
$389$	−8731.10	−1.13801	−0.569003	+	0.822335i	$0.692671\pi$
$390$	−1948.20	−0.252950
$391$	−2558.21	−0.330881
$392$	0	0
$393$	15221.6	1.95377
$394$	3400.08	0.434756
$395$	14832.1	1.88932
$396$	190.411	0.0241629
$397$	8208.17	1.03767	0.518836	−	0.854873i	$-0.326365\pi$
$397$	8208.17	1.03767	0.518836	+	0.854873i	$0.326365\pi$
$398$	−5208.14	−0.655931
$399$	0	0
$400$	−802.211	−0.100276
$401$	8255.65	1.02810	0.514049	−	0.857761i	$-0.328145\pi$
$401$	8255.65	1.02810	0.514049	+	0.857761i	$0.328145\pi$
$402$	−12345.3	−1.53166
$403$	3351.87	0.414314
$404$	1102.12	0.135725
$405$	10682.8	1.31070
$406$	0	0
$407$	881.684	0.107380
$408$	6961.98	0.844778
$409$	2289.15	0.276751	0.138375	−	0.990380i	$-0.455812\pi$
$409$	2289.15	0.276751	0.138375	+	0.990380i	$0.455812\pi$
$410$	10902.3	1.31324
$411$	−5723.69	−0.686932
$412$	−522.672	−0.0625005
$413$	0	0
$414$	−576.528	−0.0684416
$415$	6429.51	0.760512
$416$	−1878.13	−0.221353
$417$	6990.11	0.820880
$418$	−896.405	−0.104891
$419$	5890.09	0.686753	0.343377	−	0.939198i	$-0.388429\pi$
$419$	5890.09	0.686753	0.343377	+	0.939198i	$0.388429\pi$
$420$	0	0
$421$	−7601.77	−0.880018	−0.440009	−	0.897993i	$-0.645025\pi$
$421$	−7601.77	−0.880018	−0.440009	+	0.897993i	$0.645025\pi$
$422$	−1513.52	−0.174590
$423$	2275.97	0.261611
$424$	8209.09	0.940256
$425$	−1748.35	−0.199547
$426$	−9562.94	−1.08762
$427$	0	0
$428$	4235.64	0.478358
$429$	730.940	0.0822613
$430$	12790.9	1.43450
$431$	8456.60	0.945105	0.472552	−	0.881303i	$-0.343333\pi$
$431$	8456.60	0.945105	0.472552	+	0.881303i	$0.343333\pi$
$432$	−2836.48	−0.315903
$433$	−15308.9	−1.69907	−0.849536	−	0.527531i	$-0.823118\pi$
$433$	−15308.9	−1.69907	−0.849536	+	0.527531i	$0.823118\pi$
$434$	0	0
$435$	−12733.3	−1.40348
$436$	1477.35	0.162276
$437$	−2161.81	−0.236644
$438$	−3562.29	−0.388614
$439$	−12467.3	−1.35542	−0.677712	−	0.735327i	$-0.737029\pi$
$439$	−12467.3	−1.35542	−0.677712	+	0.735327i	$0.737029\pi$
$440$	3083.09	0.334046
$441$	0	0
$442$	1360.53	0.146411
$443$	6760.71	0.725081	0.362541	−	0.931968i	$-0.381909\pi$
$443$	6760.71	0.725081	0.362541	+	0.931968i	$0.381909\pi$
$444$	−1777.48	−0.189990
$445$	−11343.0	−1.20834
$446$	−5499.70	−0.583898
$447$	8589.72	0.908903
$448$	0	0
$449$	−13211.5	−1.38861	−0.694306	−	0.719680i	$-0.744289\pi$
$449$	−13211.5	−1.38861	−0.694306	+	0.719680i	$0.744289\pi$
$450$	−394.015	−0.0412757
$451$	−4090.42	−0.427074
$452$	−3223.81	−0.335476
$453$	−8575.00	−0.889379
$454$	7881.56	0.814757
$455$	0	0
$456$	5883.19	0.604179
$457$	11863.1	1.21430	0.607148	−	0.794589i	$-0.292313\pi$
$457$	11863.1	1.21430	0.607148	+	0.794589i	$0.292313\pi$
$458$	−3127.87	−0.319118
$459$	−6181.88	−0.628639
$460$	2283.92	0.231496
$461$	−1832.05	−0.185091	−0.0925456	−	0.995708i	$-0.529500\pi$
$461$	−1832.05	−0.185091	−0.0925456	+	0.995708i	$0.529500\pi$
$462$	0	0
$463$	−2277.23	−0.228579	−0.114289	−	0.993448i	$-0.536459\pi$
$463$	−2277.23	−0.228579	−0.114289	+	0.993448i	$0.536459\pi$
$464$	4080.15	0.408224
$465$	18778.1	1.87272
$466$	−9599.34	−0.954251
$467$	12037.0	1.19274	0.596368	−	0.802711i	$-0.296610\pi$
$467$	12037.0	1.19274	0.596368	+	0.802711i	$0.296610\pi$
$468$	−244.216	−0.0241216
$469$	0	0
$470$	11319.9	1.11095
$471$	8558.78	0.837298
$472$	−15660.2	−1.52716
$473$	−4799.01	−0.466509
$474$	−14085.0	−1.36487
$475$	−1477.44	−0.142715
$476$	0	0
$477$	1807.00	0.173452
$478$	−360.107	−0.0344580
$479$	7092.00	0.676496	0.338248	−	0.941057i	$-0.390166\pi$
$479$	7092.00	0.676496	0.338248	+	0.941057i	$0.390166\pi$
$480$	−10521.8	−1.00052
$481$	−1130.83	−0.107196
$482$	11715.3	1.10709
$483$	0	0
$484$	4365.59	0.409992
$485$	−2349.32	−0.219953
$486$	−3131.70	−0.292298
$487$	12604.1	1.17279	0.586394	−	0.810026i	$-0.300547\pi$
$487$	12604.1	1.17279	0.586394	+	0.810026i	$0.300547\pi$
$488$	−12201.0	−1.13179
$489$	−1708.79	−0.158025
$490$	0	0
$491$	−13353.9	−1.22740	−0.613699	−	0.789540i	$-0.710319\pi$
$491$	−13353.9	−1.22740	−0.613699	+	0.789540i	$0.710319\pi$
$492$	8246.30	0.755634
$493$	8892.34	0.812355
$494$	1149.71	0.104712
$495$	678.653	0.0616226
$496$	−6017.09	−0.544708
$497$	0	0
$498$	−6105.69	−0.549402
$499$	−2844.01	−0.255141	−0.127570	−	0.991830i	$-0.540718\pi$
$499$	−2844.01	−0.255141	−0.127570	+	0.991830i	$0.540718\pi$
$500$	−4043.92	−0.361699
$501$	−1661.28	−0.148145
$502$	−7204.54	−0.640546
$503$	−10539.7	−0.934276	−0.467138	−	0.884184i	$-0.654715\pi$
$503$	−10539.7	−0.934276	−0.467138	+	0.884184i	$0.654715\pi$
$504$	0	0
$505$	3928.14	0.346139
$506$	1075.84	0.0945193
$507$	11561.0	1.01271
$508$	9613.15	0.839596
$509$	10661.0	0.928367	0.464184	−	0.885739i	$-0.346348\pi$
$509$	10661.0	0.928367	0.464184	+	0.885739i	$0.346348\pi$
$510$	7622.05	0.661784
$511$	0	0
$512$	7863.65	0.678765
$513$	−5223.97	−0.449598
$514$	−6061.42	−0.520152
$515$	−1862.88	−0.159395
$516$	9674.82	0.825407
$517$	−4247.09	−0.361290
$518$	0	0
$519$	−2668.48	−0.225690
$520$	−3954.29	−0.333475
$521$	−259.834	−0.0218494	−0.0109247	−	0.999940i	$-0.503478\pi$
$521$	−259.834	−0.0218494	−0.0109247	+	0.999940i	$0.503478\pi$
$522$	2004.01	0.168033
$523$	8262.04	0.690772	0.345386	−	0.938461i	$-0.387748\pi$
$523$	8262.04	0.690772	0.345386	+	0.938461i	$0.387748\pi$
$524$	9490.30	0.791194
$525$	0	0
$526$	7841.05	0.649974
$527$	−13113.7	−1.08395
$528$	−1312.14	−0.108151
$529$	−9572.47	−0.786757
$530$	8987.39	0.736580
$531$	−3447.16	−0.281721
$532$	0	0
$533$	5246.27	0.426344
$534$	10771.7	0.872918
$535$	15096.5	1.21996
$536$	−25057.5	−2.01925
$537$	−8272.14	−0.664747
$538$	12740.3	1.02095
$539$	0	0
$540$	5519.05	0.439819
$541$	−1510.93	−0.120074	−0.0600369	−	0.998196i	$-0.519122\pi$
$541$	−1510.93	−0.120074	−0.0600369	+	0.998196i	$0.519122\pi$
$542$	25.1074	0.00198977
$543$	−15676.9	−1.23897
$544$	7347.92	0.579117
$545$	5265.50	0.413852
$546$	0	0
$547$	−24353.1	−1.90359	−0.951795	−	0.306734i	$-0.900764\pi$
$547$	−24353.1	−1.90359	−0.951795	+	0.306734i	$0.900764\pi$
$548$	−3568.58	−0.278179
$549$	−2685.70	−0.208785
$550$	735.256	0.0570026
$551$	7514.44	0.580991
$552$	−7060.82	−0.544435
$553$	0	0
$554$	2322.98	0.178148
$555$	−6335.21	−0.484531
$556$	4358.16	0.332423
$557$	3899.76	0.296658	0.148329	−	0.988938i	$-0.452611\pi$
$557$	3899.76	0.296658	0.148329	+	0.988938i	$0.452611\pi$
$558$	−2955.36	−0.224212
$559$	6155.10	0.465712
$560$	0	0
$561$	−2859.70	−0.215217
$562$	−6107.37	−0.458406
$563$	8850.81	0.662553	0.331276	−	0.943534i	$-0.392521\pi$
$563$	8850.81	0.662553	0.331276	+	0.943534i	$0.392521\pi$
$564$	8562.16	0.639241
$565$	−11490.2	−0.855565
$566$	−3951.76	−0.293471
$567$	0	0
$568$	−19410.1	−1.43385
$569$	4961.33	0.365536	0.182768	−	0.983156i	$-0.441494\pi$
$569$	4961.33	0.365536	0.182768	+	0.983156i	$0.441494\pi$
$570$	6440.98	0.473303
$571$	15405.7	1.12909	0.564544	−	0.825403i	$-0.309052\pi$
$571$	15405.7	1.12909	0.564544	+	0.825403i	$0.309052\pi$
$572$	455.722	0.0333124
$573$	−3321.18	−0.242137
$574$	0	0
$575$	1773.17	0.128603
$576$	2644.77	0.191317
$577$	−8507.85	−0.613841	−0.306921	−	0.951735i	$-0.599299\pi$
$577$	−8507.85	−0.613841	−0.306921	+	0.951735i	$0.599299\pi$
$578$	5044.73	0.363033
$579$	−22505.1	−1.61534
$580$	−7938.90	−0.568353
$581$	0	0
$582$	2231.00	0.158897
$583$	−3371.96	−0.239541
$584$	−7230.46	−0.512326
$585$	−870.424	−0.0615173
$586$	−5013.21	−0.353402
$587$	15021.4	1.05622	0.528109	−	0.849177i	$-0.322901\pi$
$587$	15021.4	1.05622	0.528109	+	0.849177i	$0.322901\pi$
$588$	0	0
$589$	−11081.7	−0.775236
$590$	−17145.0	−1.19635
$591$	9166.14	0.637977
$592$	2030.00	0.140933
$593$	−15336.5	−1.06205	−0.531023	−	0.847358i	$-0.678192\pi$
$593$	−15336.5	−1.06205	−0.531023	+	0.847358i	$0.678192\pi$
$594$	2599.74	0.179577
$595$	0	0
$596$	5355.47	0.368068
$597$	−14040.4	−0.962539
$598$	−1379.84	−0.0943578
$599$	24938.9	1.70113	0.850564	−	0.525871i	$-0.176261\pi$
$599$	24938.9	1.70113	0.850564	+	0.525871i	$0.176261\pi$
$600$	−4825.56	−0.328338
$601$	29218.2	1.98309	0.991545	−	0.129766i	$-0.0414226\pi$
$601$	29218.2	1.98309	0.991545	+	0.129766i	$0.0414226\pi$
$602$	0	0
$603$	−5515.69	−0.372498
$604$	−5346.30	−0.360162
$605$	15559.6	1.04560
$606$	−3730.30	−0.250054
$607$	19730.9	1.31936	0.659682	−	0.751545i	$-0.270691\pi$
$607$	19730.9	1.31936	0.659682	+	0.751545i	$0.270691\pi$
$608$	6209.33	0.414180
$609$	0	0
$610$	−13357.8	−0.886625
$611$	5447.22	0.360673
$612$	955.463	0.0631083
$613$	5601.87	0.369098	0.184549	−	0.982823i	$-0.440918\pi$
$613$	5601.87	0.369098	0.184549	+	0.982823i	$0.440918\pi$
$614$	7147.64	0.469797
$615$	29391.1	1.92709
$616$	0	0
$617$	−6214.02	−0.405457	−0.202729	−	0.979235i	$-0.564981\pi$
$617$	−6214.02	−0.405457	−0.202729	+	0.979235i	$0.564981\pi$
$618$	1769.06	0.115149
$619$	15396.6	0.999745	0.499873	−	0.866099i	$-0.333380\pi$
$619$	15396.6	0.999745	0.499873	+	0.866099i	$0.333380\pi$
$620$	11707.7	0.758374
$621$	6269.64	0.405140
$622$	15679.3	1.01074
$623$	0	0
$624$	1682.92	0.107966
$625$	−18764.6	−1.20093
$626$	−7743.02	−0.494366
$627$	−2416.58	−0.153922
$628$	5336.18	0.339071
$629$	4424.21	0.280453
$630$	0	0
$631$	−16725.6	−1.05521	−0.527604	−	0.849490i	$-0.676909\pi$
$631$	−16725.6	−1.05521	−0.527604	+	0.849490i	$0.676909\pi$
$632$	−28588.7	−1.79936
$633$	−4080.22	−0.256199
$634$	76.2646	0.00477737
$635$	34262.7	2.14122
$636$	6797.89	0.423827
$637$	0	0
$638$	−3739.60	−0.232057
$639$	−4272.58	−0.264508
$640$	−1642.02	−0.101417
$641$	14477.0	0.892057	0.446028	−	0.895019i	$-0.352838\pi$
$641$	14477.0	0.892057	0.446028	+	0.895019i	$0.352838\pi$
$642$	−14336.1	−0.881312
$643$	−3953.95	−0.242502	−0.121251	−	0.992622i	$-0.538691\pi$
$643$	−3953.95	−0.242502	−0.121251	+	0.992622i	$0.538691\pi$
$644$	0	0
$645$	34482.5	2.10504
$646$	−4498.08	−0.273954
$647$	24134.3	1.46649	0.733244	−	0.679966i	$-0.238005\pi$
$647$	24134.3	1.46649	0.733244	+	0.679966i	$0.238005\pi$
$648$	−20591.1	−1.24829
$649$	6432.60	0.389063
$650$	−943.022	−0.0569052
$651$	0	0
$652$	−1065.39	−0.0639937
$653$	−23338.9	−1.39865	−0.699326	−	0.714803i	$-0.746517\pi$
$653$	−23338.9	−1.39865	−0.699326	+	0.714803i	$0.746517\pi$
$654$	−5000.30	−0.298971
$655$	33824.9	2.01778
$656$	−9417.81	−0.560524
$657$	−1591.58	−0.0945105
$658$	0	0
$659$	−1319.35	−0.0779885	−0.0389943	−	0.999239i	$-0.512415\pi$
$659$	−1319.35	−0.0779885	−0.0389943	+	0.999239i	$0.512415\pi$
$660$	2553.08	0.150574
$661$	−13576.1	−0.798862	−0.399431	−	0.916763i	$-0.630792\pi$
$661$	−13576.1	−0.798862	−0.399431	+	0.916763i	$0.630792\pi$
$662$	10409.6	0.611152
$663$	3667.79	0.214849
$664$	−12392.8	−0.724301
$665$	0	0
$666$	997.055	0.0580107
$667$	−9018.59	−0.523540
$668$	−1035.77	−0.0599926
$669$	−14826.4	−0.856834
$670$	−27433.2	−1.58185
$671$	5011.69	0.288337
$672$	0	0
$673$	−19574.5	−1.12116	−0.560580	−	0.828101i	$-0.689422\pi$
$673$	−19574.5	−1.12116	−0.560580	+	0.828101i	$0.689422\pi$
$674$	25968.2	1.48406
$675$	4284.84	0.244331
$676$	7208.01	0.410106
$677$	5326.66	0.302393	0.151196	−	0.988504i	$-0.451687\pi$
$677$	5326.66	0.302393	0.151196	+	0.988504i	$0.451687\pi$
$678$	10911.4	0.618070
$679$	0	0
$680$	15470.6	0.872458
$681$	21247.6	1.19561
$682$	5514.88	0.309642
$683$	29615.4	1.65915	0.829575	−	0.558395i	$-0.188583\pi$
$683$	29615.4	1.65915	0.829575	+	0.558395i	$0.188583\pi$
$684$	807.410	0.0451346
$685$	−12719.0	−0.709440
$686$	0	0
$687$	−8432.30	−0.468286
$688$	−11049.3	−0.612281
$689$	4324.80	0.239132
$690$	−7730.26	−0.426501
$691$	−22053.0	−1.21409	−0.607045	−	0.794667i	$-0.707645\pi$
$691$	−22053.0	−1.21409	−0.607045	+	0.794667i	$0.707645\pi$
$692$	−1663.73	−0.0913951
$693$	0	0
$694$	11602.1	0.634598
$695$	15533.1	0.847778
$696$	24543.4	1.33666
$697$	−20525.3	−1.11543
$698$	−16167.4	−0.876711
$699$	−25878.4	−1.40030
$700$	0	0
$701$	28160.5	1.51727	0.758635	−	0.651516i	$-0.225867\pi$
$701$	28160.5	1.51727	0.758635	+	0.651516i	$0.225867\pi$
$702$	−3334.36	−0.179270
$703$	3738.66	0.200578
$704$	−4935.30	−0.264213
$705$	30516.8	1.63026
$706$	1308.50	0.0697539
$707$	0	0
$708$	−12968.2	−0.688380
$709$	−5639.27	−0.298713	−0.149356	−	0.988783i	$-0.547720\pi$
$709$	−5639.27	−0.298713	−0.149356	+	0.988783i	$0.547720\pi$
$710$	−21250.4	−1.12326
$711$	−6292.99	−0.331935
$712$	21863.6	1.15081
$713$	13299.9	0.698577
$714$	0	0
$715$	1624.26	0.0849567
$716$	−5157.47	−0.269195
$717$	−970.797	−0.0505649
$718$	17511.8	0.910217
$719$	−14592.5	−0.756898	−0.378449	−	0.925622i	$-0.623543\pi$
$719$	−14592.5	−0.756898	−0.378449	+	0.925622i	$0.623543\pi$
$720$	1562.54	0.0808781
$721$	0	0
$722$	10673.1	0.550152
$723$	31582.9	1.62459
$724$	−9774.14	−0.501731
$725$	−6163.55	−0.315736
$726$	−14776.0	−0.755355
$727$	−4920.88	−0.251039	−0.125520	−	0.992091i	$-0.540060\pi$
$727$	−4920.88	−0.251039	−0.125520	+	0.992091i	$0.540060\pi$
$728$	0	0
$729$	14373.7	0.730260
$730$	−7915.98	−0.401347
$731$	−24081.0	−1.21842
$732$	−10103.6	−0.510163
$733$	20148.1	1.01526	0.507630	−	0.861575i	$-0.330522\pi$
$733$	20148.1	1.01526	0.507630	+	0.861575i	$0.330522\pi$
$734$	−7515.64	−0.377939
$735$	0	0
$736$	−7452.23	−0.373224
$737$	10292.6	0.514428
$738$	−4625.66	−0.230722
$739$	7469.08	0.371793	0.185896	−	0.982569i	$-0.440481\pi$
$739$	7469.08	0.371793	0.185896	+	0.982569i	$0.440481\pi$
$740$	−3949.84	−0.196215
$741$	3099.45	0.153659
$742$	0	0
$743$	−9936.10	−0.490606	−0.245303	−	0.969447i	$-0.578887\pi$
$743$	−9936.10	−0.490606	−0.245303	+	0.969447i	$0.578887\pi$
$744$	−36194.7	−1.78355
$745$	19087.7	0.938685
$746$	11127.1	0.546102
$747$	−2727.93	−0.133614
$748$	−1782.95	−0.0871540
$749$	0	0
$750$	13687.2	0.666383
$751$	−7257.79	−0.352651	−0.176325	−	0.984332i	$-0.556421\pi$
$751$	−7257.79	−0.352651	−0.176325	+	0.984332i	$0.556421\pi$
$752$	−9778.54	−0.474184
$753$	−19422.4	−0.939963
$754$	4796.33	0.231660
$755$	−19055.0	−0.918521
$756$	0	0
$757$	10026.2	0.481386	0.240693	−	0.970601i	$-0.422625\pi$
$757$	10026.2	0.481386	0.240693	+	0.970601i	$0.422625\pi$
$758$	−8598.48	−0.412020
$759$	2900.30	0.138701
$760$	13073.4	0.623976
$761$	−6355.38	−0.302736	−0.151368	−	0.988477i	$-0.548368\pi$
$761$	−6355.38	−0.302736	−0.151368	+	0.988477i	$0.548368\pi$
$762$	−32537.1	−1.54684
$763$	0	0
$764$	−2070.67	−0.0980553
$765$	3405.42	0.160945
$766$	−524.433	−0.0247370
$767$	−8250.31	−0.388398
$768$	24000.6	1.12766
$769$	−26720.1	−1.25299	−0.626496	−	0.779424i	$-0.715512\pi$
$769$	−26720.1	−1.25299	−0.626496	+	0.779424i	$0.715512\pi$
$770$	0	0
$771$	−16340.7	−0.763291
$772$	−14031.4	−0.654145
$773$	−13231.3	−0.615650	−0.307825	−	0.951443i	$-0.599601\pi$
$773$	−13231.3	−0.615650	−0.307825	+	0.951443i	$0.599601\pi$
$774$	−5426.97	−0.252026
$775$	9089.53	0.421297
$776$	4528.31	0.209480
$777$	0	0
$778$	18424.7	0.849047
$779$	−17344.8	−0.797745
$780$	−3274.52	−0.150316
$781$	7972.89	0.365291
$782$	5398.45	0.246864
$783$	−21793.2	−0.994670
$784$	0	0
$785$	19019.0	0.864734
$786$	−32121.3	−1.45767
$787$	5816.34	0.263444	0.131722	−	0.991287i	$-0.457949\pi$
$787$	5816.34	0.263444	0.131722	+	0.991287i	$0.457949\pi$
$788$	5714.86	0.258355
$789$	21138.4	0.953797
$790$	−31299.2	−1.40959
$791$	0	0
$792$	−1308.10	−0.0586885
$793$	−6427.87	−0.287844
$794$	−17321.2	−0.774190
$795$	24228.7	1.08089
$796$	−8753.84	−0.389788
$797$	−9903.73	−0.440161	−0.220080	−	0.975482i	$-0.570632\pi$
$797$	−9903.73	−0.440161	−0.220080	+	0.975482i	$0.570632\pi$
$798$	0	0
$799$	−21311.5	−0.943614
$800$	−5093.06	−0.225084
$801$	4812.65	0.212293
$802$	−17421.4	−0.767046
$803$	2969.98	0.130521
$804$	−20750.0	−0.910192
$805$	0	0
$806$	−7073.25	−0.309113
$807$	34345.9	1.49818
$808$	−7571.46	−0.329657
$809$	29403.4	1.27784	0.638918	−	0.769274i	$-0.279382\pi$
$809$	29403.4	1.27784	0.638918	+	0.769274i	$0.279382\pi$
$810$	−22543.3	−0.977891
$811$	−27551.5	−1.19293	−0.596464	−	0.802640i	$-0.703428\pi$
$811$	−27551.5	−1.19293	−0.596464	+	0.802640i	$0.703428\pi$
$812$	0	0
$813$	67.6860	0.00291987
$814$	−1860.57	−0.0801140
$815$	−3797.21	−0.163203
$816$	−6584.20	−0.282467
$817$	−20349.5	−0.871407
$818$	−4830.65	−0.206479
$819$	0	0
$820$	18324.6	0.780393
$821$	−28990.6	−1.23237	−0.616187	−	0.787600i	$-0.711323\pi$
$821$	−28990.6	−1.23237	−0.616187	+	0.787600i	$0.711323\pi$
$822$	12078.4	0.512508
$823$	20510.6	0.868718	0.434359	−	0.900740i	$-0.356975\pi$
$823$	20510.6	0.868718	0.434359	+	0.900740i	$0.356975\pi$
$824$	3590.70	0.151806
$825$	1982.14	0.0836478
$826$	0	0
$827$	37073.4	1.55885	0.779425	−	0.626495i	$-0.215511\pi$
$827$	37073.4	1.55885	0.779425	+	0.626495i	$0.215511\pi$
$828$	−969.027	−0.0406715
$829$	37891.3	1.58748	0.793739	−	0.608258i	$-0.208131\pi$
$829$	37891.3	1.58748	0.793739	+	0.608258i	$0.208131\pi$
$830$	−13567.8	−0.567405
$831$	6262.42	0.261421
$832$	6329.90	0.263762
$833$	0	0
$834$	−14750.8	−0.612444
$835$	−3691.64	−0.152999
$836$	−1506.68	−0.0623319
$837$	32139.0	1.32722
$838$	−12429.5	−0.512374
$839$	15467.0	0.636449	0.318224	−	0.948015i	$-0.396913\pi$
$839$	15467.0	0.636449	0.318224	+	0.948015i	$0.396913\pi$
$840$	0	0
$841$	6959.57	0.285357
$842$	16041.6	0.656566
$843$	−16464.6	−0.672682
$844$	−2543.91	−0.103750
$845$	25690.5	1.04589
$846$	−4802.84	−0.195183
$847$	0	0
$848$	−7763.63	−0.314392
$849$	−10653.4	−0.430651
$850$	3689.45	0.148879
$851$	−4487.02	−0.180744
$852$	−16073.4	−0.646320
$853$	−28436.9	−1.14146	−0.570728	−	0.821139i	$-0.693339\pi$
$853$	−28436.9	−1.14146	−0.570728	+	0.821139i	$0.693339\pi$
$854$	0	0
$855$	2877.73	0.115107
$856$	−29098.4	−1.16187
$857$	26186.6	1.04378	0.521889	−	0.853013i	$-0.325228\pi$
$857$	26186.6	1.04378	0.521889	+	0.853013i	$0.325228\pi$
$858$	−1542.46	−0.0613737
$859$	−13765.8	−0.546777	−0.273388	−	0.961904i	$-0.588144\pi$
$859$	−13765.8	−0.546777	−0.273388	+	0.961904i	$0.588144\pi$
$860$	21499.0	0.852453
$861$	0	0
$862$	−17845.5	−0.705126
$863$	−21052.9	−0.830414	−0.415207	−	0.909727i	$-0.636291\pi$
$863$	−21052.9	−0.830414	−0.415207	+	0.909727i	$0.636291\pi$
$864$	−18008.2	−0.709087
$865$	−5929.78	−0.233085
$866$	32305.4	1.26765
$867$	13599.9	0.532729
$868$	0	0
$869$	11743.1	0.458409
$870$	26870.3	1.04711
$871$	−13201.1	−0.513549
$872$	−10149.2	−0.394146
$873$	996.777	0.0386435
$874$	4561.93	0.176556
$875$	0	0
$876$	−5987.49	−0.230935
$877$	8478.36	0.326447	0.163224	−	0.986589i	$-0.447811\pi$
$877$	8478.36	0.326447	0.163224	+	0.986589i	$0.447811\pi$
$878$	26309.0	1.01126
$879$	−13514.9	−0.518596
$880$	−2915.79	−0.111694
$881$	−19901.7	−0.761072	−0.380536	−	0.924766i	$-0.624260\pi$
$881$	−19901.7	−0.761072	−0.380536	+	0.924766i	$0.624260\pi$
$882$	0	0
$883$	−35898.3	−1.36815	−0.684073	−	0.729413i	$-0.739793\pi$
$883$	−35898.3	−1.36815	−0.684073	+	0.729413i	$0.739793\pi$
$884$	2286.77	0.0870051
$885$	−46220.5	−1.75558
$886$	−14266.7	−0.540971
$887$	41970.1	1.58875	0.794373	−	0.607430i	$-0.207800\pi$
$887$	41970.1	1.58875	0.794373	+	0.607430i	$0.207800\pi$
$888$	12211.1	0.461460
$889$	0	0
$890$	23936.5	0.901521
$891$	8457.99	0.318017
$892$	−9243.89	−0.346982
$893$	−18009.2	−0.674866
$894$	−18126.4	−0.678117
$895$	−18382.0	−0.686528
$896$	0	0
$897$	−3719.86	−0.138464
$898$	27879.3	1.03602
$899$	−46230.5	−1.71510
$900$	−662.260	−0.0245281
$901$	−16920.2	−0.625631
$902$	8631.76	0.318632
$903$	0	0
$904$	22147.2	0.814828
$905$	−34836.6	−1.27956
$906$	18095.3	0.663550
$907$	−44174.7	−1.61719	−0.808597	−	0.588363i	$-0.799773\pi$
$907$	−44174.7	−1.61719	−0.808597	+	0.588363i	$0.799773\pi$
$908$	13247.3	0.484171
$909$	−1666.64	−0.0608130
$910$	0	0
$911$	1001.93	0.0364383	0.0182192	−	0.999834i	$-0.494200\pi$
$911$	1001.93	0.0364383	0.0182192	+	0.999834i	$0.494200\pi$
$912$	−5563.95	−0.202018
$913$	5090.48	0.184524
$914$	−25034.0	−0.905965
$915$	−36010.7	−1.30107
$916$	−5257.33	−0.189636
$917$	0	0
$918$	13045.2	0.469017
$919$	2062.63	0.0740367	0.0370184	−	0.999315i	$-0.488214\pi$
$919$	2062.63	0.0740367	0.0370184	+	0.999315i	$0.488214\pi$
$920$	−15690.3	−0.562275
$921$	19269.0	0.689398
$922$	3866.06	0.138093
$923$	−10225.8	−0.364667
$924$	0	0
$925$	−3066.55	−0.109003
$926$	4805.50	0.170539
$927$	790.389	0.0280041
$928$	25903.9	0.916313
$929$	−16067.2	−0.567436	−0.283718	−	0.958908i	$-0.591568\pi$
$929$	−16067.2	−0.567436	−0.283718	+	0.958908i	$0.591568\pi$
$930$	−39626.3	−1.39720
$931$	0	0
$932$	−16134.6	−0.567065
$933$	42269.1	1.48320
$934$	−25401.1	−0.889880
$935$	−6354.72	−0.222269
$936$	1677.74	0.0585882
$937$	−11043.2	−0.385021	−0.192510	−	0.981295i	$-0.561663\pi$
$937$	−11043.2	−0.385021	−0.192510	+	0.981295i	$0.561663\pi$
$938$	0	0
$939$	−20874.1	−0.725452
$940$	19026.5	0.660186
$941$	33595.2	1.16384	0.581920	−	0.813246i	$-0.302302\pi$
$941$	33595.2	1.16384	0.581920	+	0.813246i	$0.302302\pi$
$942$	−18061.1	−0.624694
$943$	20816.7	0.718861
$944$	14810.5	0.510635
$945$	0	0
$946$	10127.1	0.348054
$947$	56186.7	1.92801	0.964003	−	0.265892i	$-0.0856663\pi$
$947$	56186.7	1.92801	0.964003	+	0.265892i	$0.0856663\pi$
$948$	−23674.1	−0.811076
$949$	−3809.23	−0.130298
$950$	3117.75	0.106477
$951$	205.598	0.00701050
$952$	0	0
$953$	5829.81	0.198160	0.0990798	−	0.995079i	$-0.468410\pi$
$953$	5829.81	0.198160	0.0990798	+	0.995079i	$0.468410\pi$
$954$	−3813.19	−0.129410
$955$	−7380.19	−0.250071
$956$	−605.267	−0.0204767
$957$	−10081.4	−0.340529
$958$	−14965.8	−0.504722
$959$	0	0
$960$	35461.8	1.19221
$961$	38386.1	1.28851
$962$	2386.32	0.0799771
$963$	−6405.17	−0.214334
$964$	19691.1	0.657893
$965$	−50009.9	−1.66827
$966$	0	0
$967$	−535.705	−0.0178150	−0.00890751	−	0.999960i	$-0.502835\pi$
$967$	−535.705	−0.0178150	−0.00890751	+	0.999960i	$0.502835\pi$
$968$	−29991.1	−0.995816
$969$	−12126.2	−0.402011
$970$	4957.64	0.164103
$971$	33903.8	1.12052	0.560260	−	0.828317i	$-0.310701\pi$
$971$	33903.8	1.12052	0.560260	+	0.828317i	$0.310701\pi$
$972$	−5263.76	−0.173699
$973$	0	0
$974$	−26597.8	−0.874997
$975$	−2542.25	−0.0835049
$976$	11538.9	0.378435
$977$	−12648.8	−0.414199	−0.207099	−	0.978320i	$-0.566402\pi$
$977$	−12648.8	−0.414199	−0.207099	+	0.978320i	$0.566402\pi$
$978$	3605.96	0.117900
$979$	−8980.69	−0.293181
$980$	0	0
$981$	−2234.06	−0.0727094
$982$	28179.9	0.915740
$983$	−35544.3	−1.15329	−0.576647	−	0.816993i	$-0.695639\pi$
$983$	−35544.3	−1.15329	−0.576647	+	0.816993i	$0.695639\pi$
$984$	−56651.1	−1.83534
$985$	20368.6	0.658882
$986$	−18765.0	−0.606084
$987$	0	0
$988$	1932.43	0.0622254
$989$	24422.8	0.785239
$990$	−1432.12	−0.0459755
$991$	41025.1	1.31504	0.657520	−	0.753437i	$-0.271605\pi$
$991$	41025.1	1.31504	0.657520	+	0.753437i	$0.271605\pi$
$992$	−38201.1	−1.22267
$993$	28062.9	0.896828
$994$	0	0
$995$	−31200.0	−0.994078
$996$	−10262.4	−0.326484
$997$	9309.43	0.295720	0.147860	−	0.989008i	$-0.452762\pi$
$997$	9309.43	0.295720	0.147860	+	0.989008i	$0.452762\pi$
$998$	6001.53	0.190356
$999$	−10842.8	−0.343394

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2401.4.a.d.1.13		39
7.6	odd	2		2401.4.a.c.1.13		39
49.8	even	7		49.4.e.a.15.9	✓	78
49.43	even	7		49.4.e.a.36.9	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.15.9	✓	78	49.8	even	7
49.4.e.a.36.9	yes	78	49.43	even	7
2401.4.a.c.1.13		39	7.6	odd	2
2401.4.a.d.1.13		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)

\(f(q)\)	\(=\)	\(q-2.11024 q^{2} -5.68890 q^{3} -3.54689 q^{4} -12.6417 q^{5} +12.0050 q^{6} +24.3667 q^{8} +5.36363 q^{9} +O(q^{10})\)	\(q-2.11024 q^{2} -5.68890 q^{3} -3.54689 q^{4} -12.6417 q^{5} +12.0050 q^{6} +24.3667 q^{8} +5.36363 q^{9} +26.6769 q^{10} -10.0089 q^{11} +20.1779 q^{12} +12.8371 q^{13} +71.9172 q^{15} -23.0445 q^{16} -50.2235 q^{17} -11.3185 q^{18} -42.4412 q^{19} +44.8385 q^{20} +21.1211 q^{22} +50.9366 q^{23} -138.620 q^{24} +34.8114 q^{25} -27.0894 q^{26} +123.087 q^{27} -177.055 q^{29} -151.762 q^{30} +261.107 q^{31} -146.304 q^{32} +56.9395 q^{33} +105.984 q^{34} -19.0242 q^{36} -88.0904 q^{37} +89.5611 q^{38} -73.0292 q^{39} -308.035 q^{40} +408.680 q^{41} +479.476 q^{43} +35.5003 q^{44} -67.8052 q^{45} -107.488 q^{46} +424.333 q^{47} +131.098 q^{48} -73.4605 q^{50} +285.717 q^{51} -45.5319 q^{52} +336.898 q^{53} -259.744 q^{54} +126.529 q^{55} +241.444 q^{57} +373.629 q^{58} -642.691 q^{59} -255.082 q^{60} -500.725 q^{61} -550.999 q^{62} +493.093 q^{64} -162.283 q^{65} -120.156 q^{66} -1028.35 q^{67} +178.137 q^{68} -289.773 q^{69} -796.583 q^{71} +130.694 q^{72} -296.735 q^{73} +185.892 q^{74} -198.039 q^{75} +150.534 q^{76} +154.109 q^{78} -1173.27 q^{79} +291.320 q^{80} -845.050 q^{81} -862.412 q^{82} -508.597 q^{83} +634.909 q^{85} -1011.81 q^{86} +1007.25 q^{87} -243.883 q^{88} +897.274 q^{89} +143.085 q^{90} -180.666 q^{92} -1485.42 q^{93} -895.445 q^{94} +536.527 q^{95} +832.311 q^{96} +185.840 q^{97} -53.6839 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + q^{2} + q^{3} + 145 q^{4} + 27 q^{5} + 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) \) 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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