LMFDB - Embedded newform 525.4.a.s.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(1,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("525.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.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:	$30.9760027530$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.26729725.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 18x^{2} + 19x + 44 $ x^4 - 2x^3 - 18x^2 + 19*x + 44
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.56826$ of defining polynomial
Character	$\chi$	$=$	525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.56826 q^{2} -3.00000 q^{3} +23.0055 q^{4} +16.7048 q^{6} +7.00000 q^{7} -83.5546 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.56826 q^{2} -3.00000 q^{3} +23.0055 q^{4} +16.7048 q^{6} +7.00000 q^{7} -83.5546 q^{8} +9.00000 q^{9} +23.2885 q^{11} -69.0165 q^{12} +46.5366 q^{13} -38.9778 q^{14} +281.210 q^{16} -76.0316 q^{17} -50.1143 q^{18} -114.605 q^{19} -21.0000 q^{21} -129.677 q^{22} -113.880 q^{23} +250.664 q^{24} -259.128 q^{26} -27.0000 q^{27} +161.039 q^{28} +120.470 q^{29} -182.048 q^{31} -897.411 q^{32} -69.8656 q^{33} +423.363 q^{34} +207.050 q^{36} +322.477 q^{37} +638.151 q^{38} -139.610 q^{39} -93.0481 q^{41} +116.933 q^{42} +452.579 q^{43} +535.765 q^{44} +634.113 q^{46} -402.565 q^{47} -843.629 q^{48} +49.0000 q^{49} +228.095 q^{51} +1070.60 q^{52} +495.787 q^{53} +150.343 q^{54} -584.882 q^{56} +343.815 q^{57} -670.808 q^{58} +496.707 q^{59} -265.742 q^{61} +1013.69 q^{62} +63.0000 q^{63} +2747.34 q^{64} +389.030 q^{66} -594.240 q^{67} -1749.14 q^{68} +341.640 q^{69} -510.099 q^{71} -751.991 q^{72} -470.181 q^{73} -1795.63 q^{74} -2636.55 q^{76} +163.020 q^{77} +777.383 q^{78} -487.916 q^{79} +81.0000 q^{81} +518.116 q^{82} +1250.53 q^{83} -483.116 q^{84} -2520.08 q^{86} -361.410 q^{87} -1945.86 q^{88} -1561.98 q^{89} +325.756 q^{91} -2619.87 q^{92} +546.145 q^{93} +2241.59 q^{94} +2692.23 q^{96} -21.5118 q^{97} -272.845 q^{98} +209.597 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{2} - 12 q^{3} + 16 q^{4} + 18 q^{6} + 28 q^{7} - 93 q^{8} + 36 q^{9}+O(q^{10}) $ 4 * q - 6 * q^2 - 12 * q^3 + 16 * q^4 + 18 * q^6 + 28 * q^7 - 93 * q^8 + 36 * q^9	\( 4 q - 6 q^{2} - 12 q^{3} + 16 q^{4} + 18 q^{6} + 28 q^{7} - 93 q^{8} + 36 q^{9} + 57 q^{11} - 48 q^{12} - 43 q^{13} - 42 q^{14} + 216 q^{16} - 99 q^{17} - 54 q^{18} - 12 q^{19} - 84 q^{21} + 41 q^{22} - 156 q^{23} + 279 q^{24} - 81 q^{26} - 108 q^{27} + 112 q^{28} + 378 q^{29} - 93 q^{31} - 690 q^{32} - 171 q^{33} + 783 q^{34} + 144 q^{36} - 81 q^{37} - 216 q^{38} + 129 q^{39} - 465 q^{41} + 126 q^{42} + 64 q^{43} + 681 q^{44} + 310 q^{46} - 744 q^{47} - 648 q^{48} + 196 q^{49} + 297 q^{51} + 727 q^{52} - 729 q^{53} + 162 q^{54} - 651 q^{56} + 36 q^{57} - 1172 q^{58} + 231 q^{59} - 1353 q^{61} + 165 q^{62} + 252 q^{63} + 3107 q^{64} - 123 q^{66} - 1487 q^{67} - 2577 q^{68} + 468 q^{69} - 1725 q^{71} - 837 q^{72} - 512 q^{73} - 1953 q^{74} - 3046 q^{76} + 399 q^{77} + 243 q^{78} + 1629 q^{79} + 324 q^{81} + 693 q^{82} - 321 q^{83} - 336 q^{84} - 4542 q^{86} - 1134 q^{87} - 3482 q^{88} - 978 q^{89} - 301 q^{91} - 852 q^{92} + 279 q^{93} + 2480 q^{94} + 2070 q^{96} - 2616 q^{97} - 294 q^{98} + 513 q^{99}+O(q^{100}) \) 4 * q - 6 * q^2 - 12 * q^3 + 16 * q^4 + 18 * q^6 + 28 * q^7 - 93 * q^8 + 36 * q^9 + 57 * q^11 - 48 * q^12 - 43 * q^13 - 42 * q^14 + 216 * q^16 - 99 * q^17 - 54 * q^18 - 12 * q^19 - 84 * q^21 + 41 * q^22 - 156 * q^23 + 279 * q^24 - 81 * q^26 - 108 * q^27 + 112 * q^28 + 378 * q^29 - 93 * q^31 - 690 * q^32 - 171 * q^33 + 783 * q^34 + 144 * q^36 - 81 * q^37 - 216 * q^38 + 129 * q^39 - 465 * q^41 + 126 * q^42 + 64 * q^43 + 681 * q^44 + 310 * q^46 - 744 * q^47 - 648 * q^48 + 196 * q^49 + 297 * q^51 + 727 * q^52 - 729 * q^53 + 162 * q^54 - 651 * q^56 + 36 * q^57 - 1172 * q^58 + 231 * q^59 - 1353 * q^61 + 165 * q^62 + 252 * q^63 + 3107 * q^64 - 123 * q^66 - 1487 * q^67 - 2577 * q^68 + 468 * q^69 - 1725 * q^71 - 837 * q^72 - 512 * q^73 - 1953 * q^74 - 3046 * q^76 + 399 * q^77 + 243 * q^78 + 1629 * q^79 + 324 * q^81 + 693 * q^82 - 321 * q^83 - 336 * q^84 - 4542 * q^86 - 1134 * q^87 - 3482 * q^88 - 978 * q^89 - 301 * q^91 - 852 * q^92 + 279 * q^93 + 2480 * q^94 + 2070 * q^96 - 2616 * q^97 - 294 * q^98 + 513 * 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 $

$2$	−5.56826	−1.96868	−0.984339	−	0.176289i	$-0.943591\pi$
$2$	−5.56826	−1.96868	−0.984339	+	0.176289i	$0.943591\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	23.0055	2.87569
$5$	0	0
$5$	0	0
$6$	16.7048	1.13662
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−83.5546	−3.69263
$9$	9.00000	0.333333
$10$	0	0
$11$	23.2885	0.638342	0.319171	−	0.947697i	$-0.396596\pi$
$11$	23.2885	0.638342	0.319171	+	0.947697i	$0.396596\pi$
$12$	−69.0165	−1.66028
$13$	46.5366	0.992840	0.496420	−	0.868082i	$-0.334648\pi$
$13$	46.5366	0.992840	0.496420	+	0.868082i	$0.334648\pi$
$14$	−38.9778	−0.744090
$15$	0	0
$16$	281.210	4.39390
$17$	−76.0316	−1.08473	−0.542364	−	0.840144i	$-0.682470\pi$
$17$	−76.0316	−1.08473	−0.542364	+	0.840144i	$0.682470\pi$
$18$	−50.1143	−0.656226
$19$	−114.605	−1.38380	−0.691901	−	0.721993i	$-0.743226\pi$
$19$	−114.605	−1.38380	−0.691901	+	0.721993i	$0.743226\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	−129.677	−1.25669
$23$	−113.880	−1.03242	−0.516209	−	0.856463i	$-0.672657\pi$
$23$	−113.880	−1.03242	−0.516209	+	0.856463i	$0.672657\pi$
$24$	250.664	2.13194
$25$	0	0
$26$	−259.128	−1.95458
$27$	−27.0000	−0.192450
$28$	161.039	1.08691
$29$	120.470	0.771404	0.385702	−	0.922623i	$-0.373959\pi$
$29$	120.470	0.771404	0.385702	+	0.922623i	$0.373959\pi$
$30$	0	0
$31$	−182.048	−1.05474	−0.527369	−	0.849637i	$-0.676821\pi$
$31$	−182.048	−1.05474	−0.527369	+	0.849637i	$0.676821\pi$
$32$	−897.411	−4.95754
$33$	−69.8656	−0.368547
$34$	423.363	2.13548
$35$	0	0
$36$	207.050	0.958563
$37$	322.477	1.43283	0.716417	−	0.697673i	$-0.245781\pi$
$37$	322.477	1.43283	0.716417	+	0.697673i	$0.245781\pi$
$38$	638.151	2.72426
$39$	−139.610	−0.573217
$40$	0	0
$41$	−93.0481	−0.354431	−0.177215	−	0.984172i	$-0.556709\pi$
$41$	−93.0481	−0.354431	−0.177215	+	0.984172i	$0.556709\pi$
$42$	116.933	0.429601
$43$	452.579	1.60506	0.802530	−	0.596612i	$-0.203487\pi$
$43$	452.579	1.60506	0.802530	+	0.596612i	$0.203487\pi$
$44$	535.765	1.83567
$45$	0	0
$46$	634.113	2.03250
$47$	−402.565	−1.24937	−0.624683	−	0.780879i	$-0.714772\pi$
$47$	−402.565	−1.24937	−0.624683	+	0.780879i	$0.714772\pi$
$48$	−843.629	−2.53682
$49$	49.0000	0.142857
$50$	0	0
$51$	228.095	0.626267
$52$	1070.60	2.85510
$53$	495.787	1.28494	0.642468	−	0.766313i	$-0.277911\pi$
$53$	495.787	1.28494	0.642468	+	0.766313i	$0.277911\pi$
$54$	150.343	0.378872
$55$	0	0
$56$	−584.882	−1.39568
$57$	343.815	0.798938
$58$	−670.808	−1.51865
$59$	496.707	1.09603	0.548015	−	0.836468i	$-0.315384\pi$
$59$	496.707	1.09603	0.548015	+	0.836468i	$0.315384\pi$
$60$	0	0
$61$	−265.742	−0.557783	−0.278891	−	0.960323i	$-0.589967\pi$
$61$	−265.742	−0.557783	−0.278891	+	0.960323i	$0.589967\pi$
$62$	1013.69	2.07644
$63$	63.0000	0.125988
$64$	2747.34	5.36590
$65$	0	0
$66$	389.030	0.725550
$67$	−594.240	−1.08355	−0.541776	−	0.840523i	$-0.682248\pi$
$67$	−594.240	−1.08355	−0.541776	+	0.840523i	$0.682248\pi$
$68$	−1749.14	−3.11934
$69$	341.640	0.596066
$70$	0	0
$71$	−510.099	−0.852642	−0.426321	−	0.904572i	$-0.640191\pi$
$71$	−510.099	−0.852642	−0.426321	+	0.904572i	$0.640191\pi$
$72$	−751.991	−1.23088
$73$	−470.181	−0.753843	−0.376921	−	0.926245i	$-0.623017\pi$
$73$	−470.181	−0.753843	−0.376921	+	0.926245i	$0.623017\pi$
$74$	−1795.63	−2.82079
$75$	0	0
$76$	−2636.55	−3.97938
$77$	163.020	0.241271
$78$	777.383	1.12848
$79$	−487.916	−0.694871	−0.347435	−	0.937704i	$-0.612947\pi$
$79$	−487.916	−0.694871	−0.347435	+	0.937704i	$0.612947\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	518.116	0.697760
$83$	1250.53	1.65378	0.826891	−	0.562362i	$-0.190107\pi$
$83$	1250.53	1.65378	0.826891	+	0.562362i	$0.190107\pi$
$84$	−483.116	−0.627527
$85$	0	0
$86$	−2520.08	−3.15985
$87$	−361.410	−0.445370
$88$	−1945.86	−2.35716
$89$	−1561.98	−1.86033	−0.930164	−	0.367145i	$-0.880335\pi$
$89$	−1561.98	−1.86033	−0.930164	+	0.367145i	$0.880335\pi$
$90$	0	0
$91$	325.756	0.375258
$92$	−2619.87	−2.96891
$93$	546.145	0.608953
$94$	2241.59	2.45960
$95$	0	0
$96$	2692.23	2.86224
$97$	−21.5118	−0.0225175	−0.0112587	−	0.999937i	$-0.503584\pi$
$97$	−21.5118	−0.0225175	−0.0112587	+	0.999937i	$0.503584\pi$
$98$	−272.845	−0.281240
$99$	209.597	0.212781
$100$	0	0
$101$	211.353	0.208222	0.104111	−	0.994566i	$-0.466800\pi$
$101$	211.353	0.208222	0.104111	+	0.994566i	$0.466800\pi$
$102$	−1270.09	−1.23292
$103$	1180.82	1.12961	0.564806	−	0.825224i	$-0.308951\pi$
$103$	1180.82	1.12961	0.564806	+	0.825224i	$0.308951\pi$
$104$	−3888.35	−3.66619
$105$	0	0
$106$	−2760.67	−2.52962
$107$	−1114.80	−1.00721	−0.503607	−	0.863933i	$-0.667994\pi$
$107$	−1114.80	−1.00721	−0.503607	+	0.863933i	$0.667994\pi$
$108$	−621.149	−0.553427
$109$	970.519	0.852834	0.426417	−	0.904527i	$-0.359776\pi$
$109$	970.519	0.852834	0.426417	+	0.904527i	$0.359776\pi$
$110$	0	0
$111$	−967.430	−0.827247
$112$	1968.47	1.66074
$113$	−800.030	−0.666022	−0.333011	−	0.942923i	$-0.608065\pi$
$113$	−800.030	−0.666022	−0.333011	+	0.942923i	$0.608065\pi$
$114$	−1914.45	−1.57285
$115$	0	0
$116$	2771.47	2.21832
$117$	418.829	0.330947
$118$	−2765.79	−2.15773
$119$	−532.221	−0.409988
$120$	0	0
$121$	−788.644	−0.592520
$122$	1479.72	1.09809
$123$	279.144	0.204631
$124$	−4188.12	−3.03310
$125$	0	0
$126$	−350.800	−0.248030
$127$	−526.685	−0.367998	−0.183999	−	0.982926i	$-0.558904\pi$
$127$	−526.685	−0.367998	−0.183999	+	0.982926i	$0.558904\pi$
$128$	−8118.62	−5.60618
$129$	−1357.74	−0.926682
$130$	0	0
$131$	827.813	0.552110	0.276055	−	0.961142i	$-0.410973\pi$
$131$	827.813	0.552110	0.276055	+	0.961142i	$0.410973\pi$
$132$	−1607.29	−1.05983
$133$	−802.236	−0.523028
$134$	3308.88	2.13316
$135$	0	0
$136$	6352.79	4.00549
$137$	−1636.01	−1.02025	−0.510124	−	0.860101i	$-0.670401\pi$
$137$	−1636.01	−1.02025	−0.510124	+	0.860101i	$0.670401\pi$
$138$	−1902.34	−1.17346
$139$	−1463.08	−0.892783	−0.446391	−	0.894838i	$-0.647291\pi$
$139$	−1463.08	−0.892783	−0.446391	+	0.894838i	$0.647291\pi$
$140$	0	0
$141$	1207.70	0.721321
$142$	2840.36	1.67858
$143$	1083.77	0.633772
$144$	2530.89	1.46463
$145$	0	0
$146$	2618.09	1.48407
$147$	−147.000	−0.0824786
$148$	7418.74	4.12038
$149$	330.833	0.181898	0.0909492	−	0.995856i	$-0.471010\pi$
$149$	330.833	0.181898	0.0909492	+	0.995856i	$0.471010\pi$
$150$	0	0
$151$	−1139.90	−0.614327	−0.307164	−	0.951657i	$-0.599380\pi$
$151$	−1139.90	−0.614327	−0.307164	+	0.951657i	$0.599380\pi$
$152$	9575.79	5.10986
$153$	−684.284	−0.361576
$154$	−907.737	−0.474984
$155$	0	0
$156$	−3211.79	−1.64839
$157$	−3297.93	−1.67645	−0.838227	−	0.545322i	$-0.816408\pi$
$157$	−3297.93	−1.67645	−0.838227	+	0.545322i	$0.816408\pi$
$158$	2716.84	1.36798
$159$	−1487.36	−0.741858
$160$	0	0
$161$	−797.159	−0.390217
$162$	−451.029	−0.218742
$163$	−2569.02	−1.23449	−0.617243	−	0.786773i	$-0.711750\pi$
$163$	−2569.02	−1.23449	−0.617243	+	0.786773i	$0.711750\pi$
$164$	−2140.62	−1.01923
$165$	0	0
$166$	−6963.30	−3.25576
$167$	−1034.90	−0.479540	−0.239770	−	0.970830i	$-0.577072\pi$
$167$	−1034.90	−0.479540	−0.239770	+	0.970830i	$0.577072\pi$
$168$	1754.65	0.805797
$169$	−31.3467	−0.0142679
$170$	0	0
$171$	−1031.45	−0.461267
$172$	10411.8	4.61565
$173$	−244.188	−0.107314	−0.0536568	−	0.998559i	$-0.517088\pi$
$173$	−244.188	−0.107314	−0.0536568	+	0.998559i	$0.517088\pi$
$174$	2012.42	0.876790
$175$	0	0
$176$	6548.96	2.80481
$177$	−1490.12	−0.632793
$178$	8697.49	3.66238
$179$	1523.83	0.636294	0.318147	−	0.948041i	$-0.396939\pi$
$179$	1523.83	0.636294	0.318147	+	0.948041i	$0.396939\pi$
$180$	0	0
$181$	−3144.63	−1.29137	−0.645687	−	0.763602i	$-0.723429\pi$
$181$	−3144.63	−1.29137	−0.645687	+	0.763602i	$0.723429\pi$
$182$	−1813.89	−0.738763
$183$	797.225	0.322036
$184$	9515.19	3.81233
$185$	0	0
$186$	−3041.08	−1.19883
$187$	−1770.66	−0.692427
$188$	−9261.22	−3.59279
$189$	−189.000	−0.0727393
$190$	0	0
$191$	−734.675	−0.278320	−0.139160	−	0.990270i	$-0.544440\pi$
$191$	−734.675	−0.278320	−0.139160	+	0.990270i	$0.544440\pi$
$192$	−8242.02	−3.09800
$193$	3248.41	1.21153	0.605765	−	0.795643i	$-0.292867\pi$
$193$	3248.41	1.21153	0.605765	+	0.795643i	$0.292867\pi$
$194$	119.783	0.0443297
$195$	0	0
$196$	1127.27	0.410813
$197$	−2915.78	−1.05452	−0.527261	−	0.849703i	$-0.676781\pi$
$197$	−2915.78	−1.05452	−0.527261	+	0.849703i	$0.676781\pi$
$198$	−1167.09	−0.418896
$199$	−1397.88	−0.497955	−0.248977	−	0.968509i	$-0.580095\pi$
$199$	−1397.88	−0.497955	−0.248977	+	0.968509i	$0.580095\pi$
$200$	0	0
$201$	1782.72	0.625589
$202$	−1176.87	−0.409923
$203$	843.290	0.291563
$204$	5247.43	1.80095
$205$	0	0
$206$	−6575.14	−2.22384
$207$	−1024.92	−0.344139
$208$	13086.5	4.36244
$209$	−2668.99	−0.883338
$210$	0	0
$211$	−998.781	−0.325872	−0.162936	−	0.986637i	$-0.552096\pi$
$211$	−998.781	−0.325872	−0.162936	+	0.986637i	$0.552096\pi$
$212$	11405.8	3.69508
$213$	1530.30	0.492273
$214$	6207.50	1.98288
$215$	0	0
$216$	2255.97	0.710646
$217$	−1274.34	−0.398653
$218$	−5404.10	−1.67895
$219$	1410.54	0.435231
$220$	0	0
$221$	−3538.25	−1.07696
$222$	5386.90	1.62858
$223$	−2820.52	−0.846979	−0.423489	−	0.905901i	$-0.639195\pi$
$223$	−2820.52	−0.846979	−0.423489	+	0.905901i	$0.639195\pi$
$224$	−6281.88	−1.87377
$225$	0	0
$226$	4454.78	1.31118
$227$	1420.92	0.415460	0.207730	−	0.978186i	$-0.433392\pi$
$227$	1420.92	0.415460	0.207730	+	0.978186i	$0.433392\pi$
$228$	7909.65	2.29750
$229$	−87.4506	−0.0252354	−0.0126177	−	0.999920i	$-0.504016\pi$
$229$	−87.4506	−0.0252354	−0.0126177	+	0.999920i	$0.504016\pi$
$230$	0	0
$231$	−489.059	−0.139298
$232$	−10065.8	−2.84851
$233$	4719.66	1.32702	0.663509	−	0.748169i	$-0.269067\pi$
$233$	4719.66	1.32702	0.663509	+	0.748169i	$0.269067\pi$
$234$	−2332.15	−0.651527
$235$	0	0
$236$	11427.0	3.15184
$237$	1463.75	0.401184
$238$	2963.54	0.807135
$239$	−850.656	−0.230227	−0.115114	−	0.993352i	$-0.536723\pi$
$239$	−850.656	−0.230227	−0.115114	+	0.993352i	$0.536723\pi$
$240$	0	0
$241$	4036.74	1.07896	0.539480	−	0.841999i	$-0.318621\pi$
$241$	4036.74	1.07896	0.539480	+	0.841999i	$0.318621\pi$
$242$	4391.37	1.16648
$243$	−243.000	−0.0641500
$244$	−6113.52	−1.60401
$245$	0	0
$246$	−1554.35	−0.402852
$247$	−5333.33	−1.37389
$248$	15211.0	3.89475
$249$	−3751.60	−0.954812
$250$	0	0
$251$	4659.33	1.17169	0.585845	−	0.810423i	$-0.300763\pi$
$251$	4659.33	1.17169	0.585845	+	0.810423i	$0.300763\pi$
$252$	1449.35	0.362303
$253$	−2652.10	−0.659035
$254$	2932.72	0.724469
$255$	0	0
$256$	23227.9	5.67086
$257$	1160.22	0.281605	0.140802	−	0.990038i	$-0.455032\pi$
$257$	1160.22	0.281605	0.140802	+	0.990038i	$0.455032\pi$
$258$	7560.23	1.82434
$259$	2257.34	0.541560
$260$	0	0
$261$	1084.23	0.257135
$262$	−4609.48	−1.08693
$263$	−1589.53	−0.372680	−0.186340	−	0.982485i	$-0.559663\pi$
$263$	−1589.53	−0.372680	−0.186340	+	0.982485i	$0.559663\pi$
$264$	5837.59	1.36091
$265$	0	0
$266$	4467.06	1.02967
$267$	4685.93	1.07406
$268$	−13670.8	−3.11596
$269$	4568.96	1.03559	0.517796	−	0.855504i	$-0.326753\pi$
$269$	4568.96	1.03559	0.517796	+	0.855504i	$0.326753\pi$
$270$	0	0
$271$	−6520.72	−1.46164	−0.730822	−	0.682569i	$-0.760863\pi$
$271$	−6520.72	−1.46164	−0.730822	+	0.682569i	$0.760863\pi$
$272$	−21380.8	−4.76618
$273$	−977.268	−0.216656
$274$	9109.75	2.00854
$275$	0	0
$276$	7859.60	1.71410
$277$	4921.65	1.06756	0.533779	−	0.845624i	$-0.320771\pi$
$277$	4921.65	1.06756	0.533779	+	0.845624i	$0.320771\pi$
$278$	8146.81	1.75760
$279$	−1638.44	−0.351579
$280$	0	0
$281$	2378.08	0.504856	0.252428	−	0.967616i	$-0.418771\pi$
$281$	2378.08	0.504856	0.252428	+	0.967616i	$0.418771\pi$
$282$	−6724.76	−1.42005
$283$	−8673.45	−1.82185	−0.910924	−	0.412574i	$-0.864630\pi$
$283$	−8673.45	−1.82185	−0.910924	+	0.412574i	$0.864630\pi$
$284$	−11735.1	−2.45193
$285$	0	0
$286$	−6034.71	−1.24769
$287$	−651.337	−0.133962
$288$	−8076.70	−1.65251
$289$	867.797	0.176633
$290$	0	0
$291$	64.5355	0.0130005
$292$	−10816.8	−2.16782
$293$	−4334.99	−0.864344	−0.432172	−	0.901791i	$-0.642253\pi$
$293$	−4334.99	−0.864344	−0.432172	+	0.901791i	$0.642253\pi$
$294$	818.534	0.162374
$295$	0	0
$296$	−26944.4	−5.29092
$297$	−628.791	−0.122849
$298$	−1842.16	−0.358099
$299$	−5299.58	−1.02503
$300$	0	0
$301$	3168.05	0.606656
$302$	6347.24	1.20941
$303$	−634.060	−0.120217
$304$	−32228.1	−6.08028
$305$	0	0
$306$	3810.27	0.711826
$307$	−5849.36	−1.08743	−0.543715	−	0.839270i	$-0.682983\pi$
$307$	−5849.36	−1.08743	−0.543715	+	0.839270i	$0.682983\pi$
$308$	3750.35	0.693819
$309$	−3542.47	−0.652182
$310$	0	0
$311$	−5005.00	−0.912564	−0.456282	−	0.889835i	$-0.650819\pi$
$311$	−5005.00	−0.912564	−0.456282	+	0.889835i	$0.650819\pi$
$312$	11665.0	2.11667
$313$	−7362.05	−1.32948	−0.664741	−	0.747074i	$-0.731458\pi$
$313$	−7362.05	−1.32948	−0.664741	+	0.747074i	$0.731458\pi$
$314$	18363.7	3.30040
$315$	0	0
$316$	−11224.7	−1.99823
$317$	−7869.89	−1.39438	−0.697188	−	0.716889i	$-0.745566\pi$
$317$	−7869.89	−1.39438	−0.697188	+	0.716889i	$0.745566\pi$
$318$	8282.01	1.46048
$319$	2805.57	0.492419
$320$	0	0
$321$	3344.40	0.581515
$322$	4438.79	0.768211
$323$	8713.61	1.50105
$324$	1863.45	0.319521
$325$	0	0
$326$	14305.0	2.43030
$327$	−2911.56	−0.492384
$328$	7774.60	1.30878
$329$	−2817.96	−0.472216
$330$	0	0
$331$	−2608.54	−0.433167	−0.216584	−	0.976264i	$-0.569491\pi$
$331$	−2608.54	−0.433167	−0.216584	+	0.976264i	$0.569491\pi$
$332$	28769.2	4.75576
$333$	2902.29	0.477611
$334$	5762.61	0.944059
$335$	0	0
$336$	−5905.40	−0.958827
$337$	5355.89	0.865739	0.432870	−	0.901457i	$-0.357501\pi$
$337$	5355.89	0.865739	0.432870	+	0.901457i	$0.357501\pi$
$338$	174.546	0.0280890
$339$	2400.09	0.384528
$340$	0	0
$341$	−4239.64	−0.673283
$342$	5743.36	0.908086
$343$	343.000	0.0539949
$344$	−37815.0	−5.92689
$345$	0	0
$346$	1359.70	0.211266
$347$	−10607.0	−1.64097	−0.820484	−	0.571670i	$-0.806296\pi$
$347$	−10607.0	−1.64097	−0.820484	+	0.571670i	$0.806296\pi$
$348$	−8314.42	−1.28075
$349$	−1896.78	−0.290923	−0.145462	−	0.989364i	$-0.546467\pi$
$349$	−1896.78	−0.290923	−0.145462	+	0.989364i	$0.546467\pi$
$350$	0	0
$351$	−1256.49	−0.191072
$352$	−20899.4	−3.16461
$353$	4040.68	0.609245	0.304622	−	0.952473i	$-0.401470\pi$
$353$	4040.68	0.609245	0.304622	+	0.952473i	$0.401470\pi$
$354$	8297.38	1.24577
$355$	0	0
$356$	−35934.1	−5.34972
$357$	1596.66	0.236707
$358$	−8485.09	−1.25266
$359$	−2054.91	−0.302100	−0.151050	−	0.988526i	$-0.548266\pi$
$359$	−2054.91	−0.302100	−0.151050	+	0.988526i	$0.548266\pi$
$360$	0	0
$361$	6275.34	0.914906
$362$	17510.1	2.54230
$363$	2365.93	0.342091
$364$	7494.19	1.07913
$365$	0	0
$366$	−4439.16	−0.633985
$367$	9866.34	1.40332	0.701661	−	0.712511i	$-0.252442\pi$
$367$	9866.34	1.40332	0.701661	+	0.712511i	$0.252442\pi$
$368$	−32024.1	−4.53634
$369$	−837.433	−0.118144
$370$	0	0
$371$	3470.51	0.485660
$372$	12564.3	1.75116
$373$	−4420.36	−0.613613	−0.306806	−	0.951772i	$-0.599260\pi$
$373$	−4420.36	−0.613613	−0.306806	+	0.951772i	$0.599260\pi$
$374$	9859.52	1.36316
$375$	0	0
$376$	33636.2	4.61344
$377$	5606.26	0.765881
$378$	1052.40	0.143200
$379$	−13.7935	−0.00186945	−0.000934727	−	1.00000i	$-0.500298\pi$
$379$	−13.7935	−0.00186945	−0.000934727		1.00000i	$0.500298\pi$
$380$	0	0
$381$	1580.06	0.212464
$382$	4090.86	0.547923
$383$	1229.76	0.164067	0.0820335	−	0.996630i	$-0.473859\pi$
$383$	1229.76	0.164067	0.0820335	+	0.996630i	$0.473859\pi$
$384$	24355.9	3.23673
$385$	0	0
$386$	−18088.0	−2.38511
$387$	4073.21	0.535020
$388$	−494.891	−0.0647533
$389$	−2827.48	−0.368532	−0.184266	−	0.982876i	$-0.558991\pi$
$389$	−2827.48	−0.368532	−0.184266	+	0.982876i	$0.558991\pi$
$390$	0	0
$391$	8658.47	1.11989
$392$	−4094.18	−0.527518
$393$	−2483.44	−0.318761
$394$	16235.8	2.07601
$395$	0	0
$396$	4821.88	0.611891
$397$	−1322.12	−0.167142	−0.0835711	−	0.996502i	$-0.526633\pi$
$397$	−1322.12	−0.167142	−0.0835711	+	0.996502i	$0.526633\pi$
$398$	7783.76	0.980313
$399$	2406.71	0.301970
$400$	0	0
$401$	7112.69	0.885762	0.442881	−	0.896580i	$-0.353956\pi$
$401$	7112.69	0.885762	0.442881	+	0.896580i	$0.353956\pi$
$402$	−9926.65	−1.23158
$403$	−8471.91	−1.04719
$404$	4862.30	0.598783
$405$	0	0
$406$	−4695.66	−0.573994
$407$	7510.01	0.914637
$408$	−19058.4	−2.31257
$409$	5986.22	0.723715	0.361858	−	0.932233i	$-0.382143\pi$
$409$	5986.22	0.723715	0.361858	+	0.932233i	$0.382143\pi$
$410$	0	0
$411$	4908.04	0.589041
$412$	27165.5	3.24841
$413$	3476.95	0.414260
$414$	5707.02	0.677499
$415$	0	0
$416$	−41762.4	−4.92205
$417$	4389.24	0.515448
$418$	14861.6	1.73901
$419$	−64.5704	−0.00752857	−0.00376428	−	0.999993i	$-0.501198\pi$
$419$	−64.5704	−0.00752857	−0.00376428	+	0.999993i	$0.501198\pi$
$420$	0	0
$421$	−4482.13	−0.518874	−0.259437	−	0.965760i	$-0.583537\pi$
$421$	−4482.13	−0.518874	−0.259437	+	0.965760i	$0.583537\pi$
$422$	5561.47	0.641536
$423$	−3623.09	−0.416455
$424$	−41425.3	−4.74479
$425$	0	0
$426$	−8521.08	−0.969126
$427$	−1860.19	−0.210822
$428$	−25646.6	−2.89643
$429$	−3251.31	−0.365908
$430$	0	0
$431$	10161.5	1.13564	0.567821	−	0.823152i	$-0.307787\pi$
$431$	10161.5	1.13564	0.567821	+	0.823152i	$0.307787\pi$
$432$	−7592.66	−0.845606
$433$	−2027.12	−0.224982	−0.112491	−	0.993653i	$-0.535883\pi$
$433$	−2027.12	−0.224982	−0.112491	+	0.993653i	$0.535883\pi$
$434$	7095.85	0.784819
$435$	0	0
$436$	22327.3	2.45249
$437$	13051.2	1.42866
$438$	−7854.27	−0.856830
$439$	−9366.44	−1.01830	−0.509152	−	0.860676i	$-0.670041\pi$
$439$	−9366.44	−1.01830	−0.509152	+	0.860676i	$0.670041\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	19701.9	2.12019
$443$	−7341.52	−0.787373	−0.393686	−	0.919245i	$-0.628800\pi$
$443$	−7341.52	−0.787373	−0.393686	+	0.919245i	$0.628800\pi$
$444$	−22256.2	−2.37890
$445$	0	0
$446$	15705.4	1.66743
$447$	−992.498	−0.105019
$448$	19231.4	2.02812
$449$	−4667.02	−0.490535	−0.245267	−	0.969455i	$-0.578876\pi$
$449$	−4667.02	−0.490535	−0.245267	+	0.969455i	$0.578876\pi$
$450$	0	0
$451$	−2166.95	−0.226248
$452$	−18405.1	−1.91527
$453$	3419.69	0.354682
$454$	−7912.03	−0.817907
$455$	0	0
$456$	−28727.4	−2.95018
$457$	−9648.38	−0.987598	−0.493799	−	0.869576i	$-0.664392\pi$
$457$	−9648.38	−0.987598	−0.493799	+	0.869576i	$0.664392\pi$
$458$	486.948	0.0496803
$459$	2052.85	0.208756
$460$	0	0
$461$	16097.6	1.62634	0.813168	−	0.582028i	$-0.197741\pi$
$461$	16097.6	1.62634	0.813168	+	0.582028i	$0.197741\pi$
$462$	2723.21	0.274232
$463$	−11024.6	−1.10661	−0.553303	−	0.832980i	$-0.686633\pi$
$463$	−11024.6	−1.10661	−0.553303	+	0.832980i	$0.686633\pi$
$464$	33877.3	3.38947
$465$	0	0
$466$	−26280.3	−2.61247
$467$	−15275.8	−1.51366	−0.756829	−	0.653613i	$-0.773252\pi$
$467$	−15275.8	−1.51366	−0.756829	+	0.653613i	$0.773252\pi$
$468$	9635.38	0.951700
$469$	−4159.68	−0.409544
$470$	0	0
$471$	9893.78	0.967901
$472$	−41502.2	−4.04723
$473$	10539.9	1.02458
$474$	−8150.52	−0.789801
$475$	0	0
$476$	−12244.0	−1.17900
$477$	4462.08	0.428312
$478$	4736.67	0.453243
$479$	−6247.49	−0.595939	−0.297970	−	0.954575i	$-0.596309\pi$
$479$	−6247.49	−0.595939	−0.297970	+	0.954575i	$0.596309\pi$
$480$	0	0
$481$	15007.0	1.42257
$482$	−22477.6	−2.12412
$483$	2391.48	0.225292
$484$	−18143.2	−1.70390
$485$	0	0
$486$	1353.09	0.126291
$487$	−15579.8	−1.44967	−0.724835	−	0.688922i	$-0.758084\pi$
$487$	−15579.8	−1.44967	−0.724835	+	0.688922i	$0.758084\pi$
$488$	22203.9	2.05968
$489$	7707.06	0.712730
$490$	0	0
$491$	5604.60	0.515137	0.257568	−	0.966260i	$-0.417079\pi$
$491$	5604.60	0.515137	0.257568	+	0.966260i	$0.417079\pi$
$492$	6421.86	0.588455
$493$	−9159.52	−0.836763
$494$	29697.4	2.70475
$495$	0	0
$496$	−51193.7	−4.63441
$497$	−3570.69	−0.322268
$498$	20889.9	1.87972
$499$	18016.9	1.61633	0.808163	−	0.588958i	$-0.200462\pi$
$499$	18016.9	1.61633	0.808163	+	0.588958i	$0.200462\pi$
$500$	0	0
$501$	3104.71	0.276862
$502$	−25944.4	−2.30668
$503$	−3405.38	−0.301865	−0.150933	−	0.988544i	$-0.548228\pi$
$503$	−3405.38	−0.301865	−0.150933	+	0.988544i	$0.548228\pi$
$504$	−5263.94	−0.465227
$505$	0	0
$506$	14767.6	1.29743
$507$	94.0400	0.00823760
$508$	−12116.7	−1.05825
$509$	−3669.88	−0.319577	−0.159788	−	0.987151i	$-0.551081\pi$
$509$	−3669.88	−0.319577	−0.159788	+	0.987151i	$0.551081\pi$
$510$	0	0
$511$	−3291.27	−0.284926
$512$	−64389.7	−5.55791
$513$	3094.34	0.266313
$514$	−6460.40	−0.554389
$515$	0	0
$516$	−31235.4	−2.66485
$517$	−9375.16	−0.797522
$518$	−12569.4	−1.06616
$519$	732.563	0.0619576
$520$	0	0
$521$	12171.2	1.02347	0.511736	−	0.859143i	$-0.329003\pi$
$521$	12171.2	1.02347	0.511736	+	0.859143i	$0.329003\pi$
$522$	−6037.27	−0.506215
$523$	−15624.1	−1.30630	−0.653148	−	0.757230i	$-0.726552\pi$
$523$	−15624.1	−1.30630	−0.653148	+	0.757230i	$0.726552\pi$
$524$	19044.3	1.58770
$525$	0	0
$526$	8850.93	0.733686
$527$	13841.4	1.14410
$528$	−19646.9	−1.61936
$529$	801.633	0.0658858
$530$	0	0
$531$	4470.37	0.365343
$532$	−18455.9	−1.50407
$533$	−4330.14	−0.351893
$534$	−26092.5	−2.11448
$535$	0	0
$536$	49651.5	4.00115
$537$	−4571.50	−0.367364
$538$	−25441.2	−2.03875
$539$	1141.14	0.0911917
$540$	0	0
$541$	10905.8	0.866688	0.433344	−	0.901229i	$-0.357334\pi$
$541$	10905.8	0.866688	0.433344	+	0.901229i	$0.357334\pi$
$542$	36309.0	2.87750
$543$	9433.89	0.745575
$544$	68231.5	5.37758
$545$	0	0
$546$	5441.68	0.426525
$547$	9430.33	0.737133	0.368566	−	0.929601i	$-0.379849\pi$
$547$	9430.33	0.737133	0.368566	+	0.929601i	$0.379849\pi$
$548$	−37637.3	−2.93392
$549$	−2391.68	−0.185928
$550$	0	0
$551$	−13806.5	−1.06747
$552$	−28545.6	−2.20105
$553$	−3415.41	−0.262636
$554$	−27405.0	−2.10168
$555$	0	0
$556$	−33658.9	−2.56737
$557$	12304.7	0.936029	0.468015	−	0.883721i	$-0.344969\pi$
$557$	12304.7	0.936029	0.468015	+	0.883721i	$0.344969\pi$
$558$	9123.23	0.692146
$559$	21061.5	1.59357
$560$	0	0
$561$	5311.99	0.399773
$562$	−13241.8	−0.993899
$563$	15768.1	1.18037	0.590184	−	0.807268i	$-0.299055\pi$
$563$	15768.1	1.18037	0.590184	+	0.807268i	$0.299055\pi$
$564$	27783.7	2.07430
$565$	0	0
$566$	48296.0	3.58663
$567$	567.000	0.0419961
$568$	42621.1	3.14849
$569$	243.490	0.0179396	0.00896981	−	0.999960i	$-0.497145\pi$
$569$	243.490	0.0179396	0.00896981	+	0.999960i	$0.497145\pi$
$570$	0	0
$571$	−26619.7	−1.95096	−0.975480	−	0.220090i	$-0.929365\pi$
$571$	−26619.7	−1.95096	−0.975480	+	0.220090i	$0.929365\pi$
$572$	24932.7	1.82253
$573$	2204.02	0.160688
$574$	3626.81	0.263729
$575$	0	0
$576$	24726.1	1.78863
$577$	−4868.88	−0.351290	−0.175645	−	0.984454i	$-0.556201\pi$
$577$	−4868.88	−0.351290	−0.175645	+	0.984454i	$0.556201\pi$
$578$	−4832.12	−0.347733
$579$	−9745.22	−0.699478
$580$	0	0
$581$	8753.74	0.625071
$582$	−359.350	−0.0255937
$583$	11546.2	0.820228
$584$	39285.8	2.78366
$585$	0	0
$586$	24138.4	1.70161
$587$	−12698.7	−0.892898	−0.446449	−	0.894809i	$-0.647312\pi$
$587$	−12698.7	−0.892898	−0.446449	+	0.894809i	$0.647312\pi$
$588$	−3381.81	−0.237183
$589$	20863.7	1.45955
$590$	0	0
$591$	8747.35	0.608829
$592$	90683.5	6.29573
$593$	−22043.0	−1.52647	−0.763237	−	0.646119i	$-0.776391\pi$
$593$	−22043.0	−1.52647	−0.763237	+	0.646119i	$0.776391\pi$
$594$	3501.27	0.241850
$595$	0	0
$596$	7610.97	0.523083
$597$	4193.64	0.287494
$598$	29509.4	2.01794
$599$	−15180.6	−1.03550	−0.517750	−	0.855532i	$-0.673230\pi$
$599$	−15180.6	−1.03550	−0.517750	+	0.855532i	$0.673230\pi$
$600$	0	0
$601$	415.176	0.0281787	0.0140893	−	0.999901i	$-0.495515\pi$
$601$	415.176	0.0281787	0.0140893	+	0.999901i	$0.495515\pi$
$602$	−17640.5	−1.19431
$603$	−5348.16	−0.361184
$604$	−26223.9	−1.76661
$605$	0	0
$606$	3530.61	0.236669
$607$	23973.2	1.60303	0.801516	−	0.597973i	$-0.204027\pi$
$607$	23973.2	1.60303	0.801516	+	0.597973i	$0.204027\pi$
$608$	102848.	6.86025
$609$	−2529.87	−0.168334
$610$	0	0
$611$	−18734.0	−1.24042
$612$	−15742.3	−1.03978
$613$	5616.87	0.370087	0.185043	−	0.982730i	$-0.440757\pi$
$613$	5616.87	0.370087	0.185043	+	0.982730i	$0.440757\pi$
$614$	32570.8	2.14080
$615$	0	0
$616$	−13621.1	−0.890922
$617$	15690.3	1.02377	0.511886	−	0.859053i	$-0.328947\pi$
$617$	15690.3	1.02377	0.511886	+	0.859053i	$0.328947\pi$
$618$	19725.4	1.28394
$619$	7832.79	0.508605	0.254302	−	0.967125i	$-0.418154\pi$
$619$	7832.79	0.508605	0.254302	+	0.967125i	$0.418154\pi$
$620$	0	0
$621$	3074.76	0.198689
$622$	27869.1	1.79654
$623$	−10933.8	−0.703138
$624$	−39259.6	−2.51866
$625$	0	0
$626$	40993.8	2.61732
$627$	8006.96	0.509996
$628$	−75870.5	−4.82096
$629$	−24518.4	−1.55423
$630$	0	0
$631$	−16365.7	−1.03250	−0.516250	−	0.856438i	$-0.672673\pi$
$631$	−16365.7	−1.03250	−0.516250	+	0.856438i	$0.672673\pi$
$632$	40767.6	2.56590
$633$	2996.34	0.188142
$634$	43821.6	2.74507
$635$	0	0
$636$	−34217.5	−2.13335
$637$	2280.29	0.141834
$638$	−15622.1	−0.969415
$639$	−4590.89	−0.284214
$640$	0	0
$641$	−8208.10	−0.505773	−0.252886	−	0.967496i	$-0.581380\pi$
$641$	−8208.10	−0.505773	−0.252886	+	0.967496i	$0.581380\pi$
$642$	−18622.5	−1.14482
$643$	−13351.5	−0.818868	−0.409434	−	0.912340i	$-0.634274\pi$
$643$	−13351.5	−0.818868	−0.409434	+	0.912340i	$0.634274\pi$
$644$	−18339.1	−1.12214
$645$	0	0
$646$	−48519.6	−2.95508
$647$	−23313.9	−1.41663	−0.708317	−	0.705894i	$-0.750545\pi$
$647$	−23313.9	−1.41663	−0.708317	+	0.705894i	$0.750545\pi$
$648$	−6767.92	−0.410292
$649$	11567.6	0.699642
$650$	0	0
$651$	3823.02	0.230162
$652$	−59101.6	−3.55000
$653$	21077.4	1.26313	0.631565	−	0.775323i	$-0.282413\pi$
$653$	21077.4	1.26313	0.631565	+	0.775323i	$0.282413\pi$
$654$	16212.3	0.969345
$655$	0	0
$656$	−26166.0	−1.55733
$657$	−4231.63	−0.251281
$658$	15691.1	0.929640
$659$	31971.5	1.88988	0.944940	−	0.327243i	$-0.106119\pi$
$659$	31971.5	1.88988	0.944940	+	0.327243i	$0.106119\pi$
$660$	0	0
$661$	482.048	0.0283654	0.0141827	−	0.999899i	$-0.495485\pi$
$661$	482.048	0.0283654	0.0141827	+	0.999899i	$0.495485\pi$
$662$	14525.0	0.852766
$663$	10614.7	0.621784
$664$	−104488.	−6.10680
$665$	0	0
$666$	−16160.7	−0.940262
$667$	−13719.1	−0.796411
$668$	−23808.5	−1.37901
$669$	8461.57	0.489003
$670$	0	0
$671$	−6188.74	−0.356056
$672$	18845.6	1.08182
$673$	22561.8	1.29226	0.646132	−	0.763225i	$-0.276385\pi$
$673$	22561.8	1.29226	0.646132	+	0.763225i	$0.276385\pi$
$674$	−29823.0	−1.70436
$675$	0	0
$676$	−721.146	−0.0410302
$677$	−1449.65	−0.0822962	−0.0411481	−	0.999153i	$-0.513102\pi$
$677$	−1449.65	−0.0822962	−0.0411481	+	0.999153i	$0.513102\pi$
$678$	−13364.3	−0.757012
$679$	−150.583	−0.00851081
$680$	0	0
$681$	−4262.75	−0.239866
$682$	23607.4	1.32548
$683$	10176.4	0.570114	0.285057	−	0.958511i	$-0.407987\pi$
$683$	10176.4	0.570114	0.285057	+	0.958511i	$0.407987\pi$
$684$	−23729.0	−1.32646
$685$	0	0
$686$	−1909.91	−0.106299
$687$	262.352	0.0145696
$688$	127269.	7.05247
$689$	23072.2	1.27574
$690$	0	0
$691$	23323.3	1.28402	0.642011	−	0.766695i	$-0.278100\pi$
$691$	23323.3	1.28402	0.642011	+	0.766695i	$0.278100\pi$
$692$	−5617.67	−0.308601
$693$	1467.18	0.0804235
$694$	59062.7	3.23053
$695$	0	0
$696$	30197.5	1.64459
$697$	7074.59	0.384461
$698$	10561.8	0.572734
$699$	−14159.0	−0.766154
$700$	0	0
$701$	−15221.7	−0.820138	−0.410069	−	0.912055i	$-0.634495\pi$
$701$	−15221.7	−0.820138	−0.410069	+	0.912055i	$0.634495\pi$
$702$	6996.45	0.376159
$703$	−36957.5	−1.98276
$704$	63981.6	3.42528
$705$	0	0
$706$	−22499.5	−1.19941
$707$	1479.47	0.0787006
$708$	−34281.0	−1.81972
$709$	−13088.0	−0.693274	−0.346637	−	0.937999i	$-0.612676\pi$
$709$	−13088.0	−0.693274	−0.346637	+	0.937999i	$0.612676\pi$
$710$	0	0
$711$	−4391.24	−0.231624
$712$	130510.	6.86949
$713$	20731.6	1.08893
$714$	−8890.63	−0.465999
$715$	0	0
$716$	35056.5	1.82978
$717$	2551.97	0.132922
$718$	11442.3	0.594738
$719$	−13845.7	−0.718160	−0.359080	−	0.933307i	$-0.616909\pi$
$719$	−13845.7	−0.718160	−0.359080	+	0.933307i	$0.616909\pi$
$720$	0	0
$721$	8265.77	0.426953
$722$	−34942.7	−1.80115
$723$	−12110.2	−0.622937
$724$	−72343.9	−3.71359
$725$	0	0
$726$	−13174.1	−0.673468
$727$	−2691.12	−0.137287	−0.0686437	−	0.997641i	$-0.521867\pi$
$727$	−2691.12	−0.137287	−0.0686437	+	0.997641i	$0.521867\pi$
$728$	−27218.4	−1.38569
$729$	729.000	0.0370370
$730$	0	0
$731$	−34410.3	−1.74105
$732$	18340.6	0.926075
$733$	−765.975	−0.0385975	−0.0192987	−	0.999814i	$-0.506143\pi$
$733$	−765.975	−0.0385975	−0.0192987	+	0.999814i	$0.506143\pi$
$734$	−54938.4	−2.76269
$735$	0	0
$736$	102197.	5.11825
$737$	−13839.0	−0.691676
$738$	4663.04	0.232587
$739$	−20961.2	−1.04340	−0.521698	−	0.853130i	$-0.674701\pi$
$739$	−20961.2	−1.04340	−0.521698	+	0.853130i	$0.674701\pi$
$740$	0	0
$741$	16000.0	0.793218
$742$	−19324.7	−0.956108
$743$	28175.2	1.39118	0.695590	−	0.718439i	$-0.255143\pi$
$743$	28175.2	1.39118	0.695590	+	0.718439i	$0.255143\pi$
$744$	−45632.9	−2.24863
$745$	0	0
$746$	24613.7	1.20801
$747$	11254.8	0.551261
$748$	−40735.0	−1.99120
$749$	−7803.60	−0.380691
$750$	0	0
$751$	10303.4	0.500636	0.250318	−	0.968164i	$-0.419465\pi$
$751$	10303.4	0.500636	0.250318	+	0.968164i	$0.419465\pi$
$752$	−113205.	−5.48959
$753$	−13978.0	−0.676476
$754$	−31217.1	−1.50777
$755$	0	0
$756$	−4348.04	−0.209176
$757$	38444.4	1.84582	0.922909	−	0.385019i	$-0.125805\pi$
$757$	38444.4	1.84582	0.922909	+	0.385019i	$0.125805\pi$
$758$	76.8057	0.00368035
$759$	7956.29	0.380494
$760$	0	0
$761$	−7765.25	−0.369895	−0.184947	−	0.982748i	$-0.559211\pi$
$761$	−7765.25	−0.369895	−0.184947	+	0.982748i	$0.559211\pi$
$762$	−8798.16	−0.418272
$763$	6793.64	0.322341
$764$	−16901.6	−0.800363
$765$	0	0
$766$	−6847.61	−0.322995
$767$	23115.1	1.08818
$768$	−69683.6	−3.27407
$769$	−10320.1	−0.483945	−0.241972	−	0.970283i	$-0.577794\pi$
$769$	−10320.1	−0.483945	−0.241972	+	0.970283i	$0.577794\pi$
$770$	0	0
$771$	−3480.65	−0.162585
$772$	74731.3	3.48399
$773$	167.975	0.00781584	0.00390792	−	0.999992i	$-0.498756\pi$
$773$	167.975	0.00781584	0.00390792	+	0.999992i	$0.498756\pi$
$774$	−22680.7	−1.05328
$775$	0	0
$776$	1797.41	0.0831487
$777$	−6772.01	−0.312670
$778$	15744.1	0.725520
$779$	10663.8	0.490462
$780$	0	0
$781$	−11879.5	−0.544277
$782$	−48212.6	−2.20470
$783$	−3252.69	−0.148457
$784$	13779.3	0.627700
$785$	0	0
$786$	13828.4	0.627537
$787$	12700.6	0.575256	0.287628	−	0.957742i	$-0.407133\pi$
$787$	12700.6	0.575256	0.287628	+	0.957742i	$0.407133\pi$
$788$	−67079.1	−3.03248
$789$	4768.60	0.215167
$790$	0	0
$791$	−5600.21	−0.251733
$792$	−17512.8	−0.785719
$793$	−12366.7	−0.553789
$794$	7361.93	0.329049
$795$	0	0
$796$	−32158.9	−1.43196
$797$	−7995.40	−0.355347	−0.177674	−	0.984089i	$-0.556857\pi$
$797$	−7995.40	−0.355347	−0.177674	+	0.984089i	$0.556857\pi$
$798$	−13401.2	−0.594482
$799$	30607.7	1.35522
$800$	0	0
$801$	−14057.8	−0.620109
$802$	−39605.3	−1.74378
$803$	−10949.8	−0.481209
$804$	41012.4	1.79900
$805$	0	0
$806$	47173.8	2.06157
$807$	−13706.9	−0.597900
$808$	−17659.6	−0.768887
$809$	7248.83	0.315025	0.157513	−	0.987517i	$-0.449652\pi$
$809$	7248.83	0.315025	0.157513	+	0.987517i	$0.449652\pi$
$810$	0	0
$811$	12097.4	0.523793	0.261896	−	0.965096i	$-0.415652\pi$
$811$	12097.4	0.523793	0.261896	+	0.965096i	$0.415652\pi$
$812$	19400.3	0.838445
$813$	19562.1	0.843880
$814$	−41817.7	−1.80063
$815$	0	0
$816$	64142.4	2.75176
$817$	−51867.8	−2.22108
$818$	−33332.8	−1.42476
$819$	2931.80	0.125086
$820$	0	0
$821$	4821.38	0.204954	0.102477	−	0.994735i	$-0.467323\pi$
$821$	4821.38	0.204954	0.102477	+	0.994735i	$0.467323\pi$
$822$	−27329.2	−1.15963
$823$	3733.51	0.158131	0.0790657	−	0.996869i	$-0.474806\pi$
$823$	3733.51	0.158131	0.0790657	+	0.996869i	$0.474806\pi$
$824$	−98663.3	−4.17124
$825$	0	0
$826$	−19360.6	−0.815545
$827$	1160.78	0.0488079	0.0244040	−	0.999702i	$-0.492231\pi$
$827$	1160.78	0.0488079	0.0244040	+	0.999702i	$0.492231\pi$
$828$	−23578.8	−0.989637
$829$	18627.0	0.780389	0.390195	−	0.920732i	$-0.372408\pi$
$829$	18627.0	0.780389	0.390195	+	0.920732i	$0.372408\pi$
$830$	0	0
$831$	−14765.0	−0.616355
$832$	127852.	5.32748
$833$	−3725.55	−0.154961
$834$	−24440.4	−1.01475
$835$	0	0
$836$	−61401.4	−2.54021
$837$	4915.31	0.202984
$838$	359.545	0.0148213
$839$	4213.40	0.173376	0.0866881	−	0.996236i	$-0.472372\pi$
$839$	4213.40	0.173376	0.0866881	+	0.996236i	$0.472372\pi$
$840$	0	0
$841$	−9875.99	−0.404936
$842$	24957.7	1.02150
$843$	−7134.25	−0.291479
$844$	−22977.5	−0.937106
$845$	0	0
$846$	20174.3	0.819866
$847$	−5520.51	−0.223951
$848$	139420.	5.64588
$849$	26020.4	1.05184
$850$	0	0
$851$	−36723.6	−1.47928
$852$	35205.2	1.41562
$853$	3940.85	0.158185	0.0790926	−	0.996867i	$-0.474798\pi$
$853$	3940.85	0.158185	0.0790926	+	0.996867i	$0.474798\pi$
$854$	10358.0	0.415040
$855$	0	0
$856$	93146.7	3.71926
$857$	38267.2	1.52530	0.762650	−	0.646811i	$-0.223898\pi$
$857$	38267.2	1.52530	0.762650	+	0.646811i	$0.223898\pi$
$858$	18104.1	0.720355
$859$	10145.2	0.402969	0.201484	−	0.979492i	$-0.435423\pi$
$859$	10145.2	0.402969	0.201484	+	0.979492i	$0.435423\pi$
$860$	0	0
$861$	1954.01	0.0773432
$862$	−56581.8	−2.23571
$863$	−17608.5	−0.694553	−0.347277	−	0.937763i	$-0.612894\pi$
$863$	−17608.5	−0.694553	−0.347277	+	0.937763i	$0.612894\pi$
$864$	24230.1	0.954079
$865$	0	0
$866$	11287.5	0.442917
$867$	−2603.39	−0.101979
$868$	−29316.8	−1.14640
$869$	−11362.8	−0.443565
$870$	0	0
$871$	−27653.9	−1.07579
$872$	−81091.3	−3.14920
$873$	−193.607	−0.00750583
$874$	−72672.6	−2.81257
$875$	0	0
$876$	32450.3	1.25159
$877$	−23555.5	−0.906972	−0.453486	−	0.891263i	$-0.649820\pi$
$877$	−23555.5	−0.906972	−0.453486	+	0.891263i	$0.649820\pi$
$878$	52154.8	2.00471
$879$	13005.0	0.499029
$880$	0	0
$881$	−43719.7	−1.67191	−0.835955	−	0.548797i	$-0.815086\pi$
$881$	−43719.7	−1.67191	−0.835955	+	0.548797i	$0.815086\pi$
$882$	−2455.60	−0.0937465
$883$	31393.4	1.19646	0.598229	−	0.801325i	$-0.295871\pi$
$883$	31393.4	1.19646	0.598229	+	0.801325i	$0.295871\pi$
$884$	−81399.2	−3.09700
$885$	0	0
$886$	40879.5	1.55008
$887$	−40021.9	−1.51500	−0.757499	−	0.652836i	$-0.773579\pi$
$887$	−40021.9	−1.51500	−0.757499	+	0.652836i	$0.773579\pi$
$888$	80833.2	3.05471
$889$	−3686.80	−0.139090
$890$	0	0
$891$	1886.37	0.0709269
$892$	−64887.6	−2.43565
$893$	46136.0	1.72887
$894$	5526.48	0.206749
$895$	0	0
$896$	−56830.3	−2.11894
$897$	15898.7	0.591799
$898$	25987.2	0.965705
$899$	−21931.4	−0.813628
$900$	0	0
$901$	−37695.5	−1.39380
$902$	12066.2	0.445409
$903$	−9504.15	−0.350253
$904$	66846.2	2.45937
$905$	0	0
$906$	−19041.7	−0.698254
$907$	−2729.28	−0.0999165	−0.0499583	−	0.998751i	$-0.515909\pi$
$907$	−2729.28	−0.0999165	−0.0499583	+	0.998751i	$0.515909\pi$
$908$	32688.9	1.19473
$909$	1902.18	0.0694074
$910$	0	0
$911$	−20874.8	−0.759181	−0.379590	−	0.925155i	$-0.623935\pi$
$911$	−20874.8	−0.759181	−0.379590	+	0.925155i	$0.623935\pi$
$912$	96684.2	3.51045
$913$	29123.1	1.05568
$914$	53724.7	1.94426
$915$	0	0
$916$	−2011.85	−0.0725691
$917$	5794.69	0.208678
$918$	−11430.8	−0.410973
$919$	12339.8	0.442931	0.221466	−	0.975168i	$-0.428916\pi$
$919$	12339.8	0.442931	0.221466	+	0.975168i	$0.428916\pi$
$920$	0	0
$921$	17548.1	0.627827
$922$	−89635.8	−3.20173
$923$	−23738.2	−0.846537
$924$	−11251.1	−0.400577
$925$	0	0
$926$	61388.1	2.17855
$927$	10627.4	0.376538
$928$	−108111.	−3.82427
$929$	−51868.3	−1.83180	−0.915900	−	0.401407i	$-0.868521\pi$
$929$	−51868.3	−1.83180	−0.915900	+	0.401407i	$0.868521\pi$
$930$	0	0
$931$	−5615.65	−0.197686
$932$	108578.	3.81609
$933$	15015.0	0.526869
$934$	85059.5	2.97990
$935$	0	0
$936$	−34995.1	−1.22206
$937$	47757.7	1.66508	0.832538	−	0.553967i	$-0.186887\pi$
$937$	47757.7	1.66508	0.832538	+	0.553967i	$0.186887\pi$
$938$	23162.2	0.806260
$939$	22086.2	0.767577
$940$	0	0
$941$	−41845.5	−1.44966	−0.724828	−	0.688930i	$-0.758081\pi$
$941$	−41845.5	−1.44966	−0.724828	+	0.688930i	$0.758081\pi$
$942$	−55091.1	−1.90548
$943$	10596.3	0.365921
$944$	139679.	4.81585
$945$	0	0
$946$	−58688.9	−2.01706
$947$	−14121.8	−0.484580	−0.242290	−	0.970204i	$-0.577899\pi$
$947$	−14121.8	−0.484580	−0.242290	+	0.970204i	$0.577899\pi$
$948$	33674.2	1.15368
$949$	−21880.6	−0.748445
$950$	0	0
$951$	23609.7	0.805043
$952$	44469.5	1.51393
$953$	31178.0	1.05976	0.529882	−	0.848071i	$-0.322236\pi$
$953$	31178.0	1.05976	0.529882	+	0.848071i	$0.322236\pi$
$954$	−24846.0	−0.843208
$955$	0	0
$956$	−19569.8	−0.662062
$957$	−8416.71	−0.284298
$958$	34787.6	1.17321
$959$	−11452.1	−0.385618
$960$	0	0
$961$	3350.60	0.112470
$962$	−83562.6	−2.80059
$963$	−10033.2	−0.335738
$964$	92867.2	3.10275
$965$	0	0
$966$	−13316.4	−0.443527
$967$	34789.7	1.15694	0.578470	−	0.815704i	$-0.303650\pi$
$967$	34789.7	1.15694	0.578470	+	0.815704i	$0.303650\pi$
$968$	65894.8	2.18795
$969$	−26140.8	−0.866630
$970$	0	0
$971$	20481.9	0.676926	0.338463	−	0.940980i	$-0.390093\pi$
$971$	20481.9	0.676926	0.338463	+	0.940980i	$0.390093\pi$
$972$	−5590.34	−0.184476
$973$	−10241.6	−0.337440
$974$	86752.6	2.85393
$975$	0	0
$976$	−74729.1	−2.45084
$977$	−5605.71	−0.183565	−0.0917823	−	0.995779i	$-0.529256\pi$
$977$	−5605.71	−0.183565	−0.0917823	+	0.995779i	$0.529256\pi$
$978$	−42914.9	−1.40314
$979$	−36376.1	−1.18752
$980$	0	0
$981$	8734.67	0.284278
$982$	−31207.9	−1.01414
$983$	−34728.1	−1.12681	−0.563406	−	0.826180i	$-0.690509\pi$
$983$	−34728.1	−1.12681	−0.563406	+	0.826180i	$0.690509\pi$
$984$	−23323.8	−0.755625
$985$	0	0
$986$	51002.6	1.64732
$987$	8453.87	0.272634
$988$	−122696.	−3.95089
$989$	−51539.6	−1.65709
$990$	0	0
$991$	−2145.57	−0.0687753	−0.0343876	−	0.999409i	$-0.510948\pi$
$991$	−2145.57	−0.0687753	−0.0343876	+	0.999409i	$0.510948\pi$
$992$	163372.	5.22890
$993$	7825.62	0.250089
$994$	19882.5	0.634442
$995$	0	0
$996$	−86307.5	−2.74574
$997$	59620.3	1.89388	0.946938	−	0.321417i	$-0.104159\pi$
$997$	59620.3	1.89388	0.946938	+	0.321417i	$0.104159\pi$
$998$	−100323.	−3.18203
$999$	−8706.87	−0.275749

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.a.s.1.1	✓	4
3.2	odd	2		1575.4.a.bm.1.4		4
5.2	odd	4		525.4.d.o.274.1		8
5.3	odd	4		525.4.d.o.274.8		8
5.4	even	2		525.4.a.v.1.4	yes	4
15.14	odd	2		1575.4.a.bf.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.4.a.s.1.1	✓	4	1.1	even	1	trivial
525.4.a.v.1.4	yes	4	5.4	even	2
525.4.d.o.274.1		8	5.2	odd	4
525.4.d.o.274.8		8	5.3	odd	4
1575.4.a.bf.1.1		4	15.14	odd	2
1575.4.a.bm.1.4		4	3.2	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.a (trivial)

\(f(q)\)	\(=\)	\(q-5.56826 q^{2} -3.00000 q^{3} +23.0055 q^{4} +16.7048 q^{6} +7.00000 q^{7} -83.5546 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.56826 q^{2} -3.00000 q^{3} +23.0055 q^{4} +16.7048 q^{6} +7.00000 q^{7} -83.5546 q^{8} +9.00000 q^{9} +23.2885 q^{11} -69.0165 q^{12} +46.5366 q^{13} -38.9778 q^{14} +281.210 q^{16} -76.0316 q^{17} -50.1143 q^{18} -114.605 q^{19} -21.0000 q^{21} -129.677 q^{22} -113.880 q^{23} +250.664 q^{24} -259.128 q^{26} -27.0000 q^{27} +161.039 q^{28} +120.470 q^{29} -182.048 q^{31} -897.411 q^{32} -69.8656 q^{33} +423.363 q^{34} +207.050 q^{36} +322.477 q^{37} +638.151 q^{38} -139.610 q^{39} -93.0481 q^{41} +116.933 q^{42} +452.579 q^{43} +535.765 q^{44} +634.113 q^{46} -402.565 q^{47} -843.629 q^{48} +49.0000 q^{49} +228.095 q^{51} +1070.60 q^{52} +495.787 q^{53} +150.343 q^{54} -584.882 q^{56} +343.815 q^{57} -670.808 q^{58} +496.707 q^{59} -265.742 q^{61} +1013.69 q^{62} +63.0000 q^{63} +2747.34 q^{64} +389.030 q^{66} -594.240 q^{67} -1749.14 q^{68} +341.640 q^{69} -510.099 q^{71} -751.991 q^{72} -470.181 q^{73} -1795.63 q^{74} -2636.55 q^{76} +163.020 q^{77} +777.383 q^{78} -487.916 q^{79} +81.0000 q^{81} +518.116 q^{82} +1250.53 q^{83} -483.116 q^{84} -2520.08 q^{86} -361.410 q^{87} -1945.86 q^{88} -1561.98 q^{89} +325.756 q^{91} -2619.87 q^{92} +546.145 q^{93} +2241.59 q^{94} +2692.23 q^{96} -21.5118 q^{97} -272.845 q^{98} +209.597 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{2} - 12 q^{3} + 16 q^{4} + 18 q^{6} + 28 q^{7} - 93 q^{8} + 36 q^{9}+O(q^{10}) \) 4 * q - 6 * q^2 - 12 * q^3 + 16 * q^4 + 18 * q^6 + 28 * q^7 - 93 * q^8 + 36 * q^9	\( 4 q - 6 q^{2} - 12 q^{3} + 16 q^{4} + 18 q^{6} + 28 q^{7} - 93 q^{8} + 36 q^{9} + 57 q^{11} - 48 q^{12} - 43 q^{13} - 42 q^{14} + 216 q^{16} - 99 q^{17} - 54 q^{18} - 12 q^{19} - 84 q^{21} + 41 q^{22} - 156 q^{23} + 279 q^{24} - 81 q^{26} - 108 q^{27} + 112 q^{28} + 378 q^{29} - 93 q^{31} - 690 q^{32} - 171 q^{33} + 783 q^{34} + 144 q^{36} - 81 q^{37} - 216 q^{38} + 129 q^{39} - 465 q^{41} + 126 q^{42} + 64 q^{43} + 681 q^{44} + 310 q^{46} - 744 q^{47} - 648 q^{48} + 196 q^{49} + 297 q^{51} + 727 q^{52} - 729 q^{53} + 162 q^{54} - 651 q^{56} + 36 q^{57} - 1172 q^{58} + 231 q^{59} - 1353 q^{61} + 165 q^{62} + 252 q^{63} + 3107 q^{64} - 123 q^{66} - 1487 q^{67} - 2577 q^{68} + 468 q^{69} - 1725 q^{71} - 837 q^{72} - 512 q^{73} - 1953 q^{74} - 3046 q^{76} + 399 q^{77} + 243 q^{78} + 1629 q^{79} + 324 q^{81} + 693 q^{82} - 321 q^{83} - 336 q^{84} - 4542 q^{86} - 1134 q^{87} - 3482 q^{88} - 978 q^{89} - 301 q^{91} - 852 q^{92} + 279 q^{93} + 2480 q^{94} + 2070 q^{96} - 2616 q^{97} - 294 q^{98} + 513 q^{99}+O(q^{100}) \) 4 * q - 6 * q^2 - 12 * q^3 + 16 * q^4 + 18 * q^6 + 28 * q^7 - 93 * q^8 + 36 * q^9 + 57 * q^11 - 48 * q^12 - 43 * q^13 - 42 * q^14 + 216 * q^16 - 99 * q^17 - 54 * q^18 - 12 * q^19 - 84 * q^21 + 41 * q^22 - 156 * q^23 + 279 * q^24 - 81 * q^26 - 108 * q^27 + 112 * q^28 + 378 * q^29 - 93 * q^31 - 690 * q^32 - 171 * q^33 + 783 * q^34 + 144 * q^36 - 81 * q^37 - 216 * q^38 + 129 * q^39 - 465 * q^41 + 126 * q^42 + 64 * q^43 + 681 * q^44 + 310 * q^46 - 744 * q^47 - 648 * q^48 + 196 * q^49 + 297 * q^51 + 727 * q^52 - 729 * q^53 + 162 * q^54 - 651 * q^56 + 36 * q^57 - 1172 * q^58 + 231 * q^59 - 1353 * q^61 + 165 * q^62 + 252 * q^63 + 3107 * q^64 - 123 * q^66 - 1487 * q^67 - 2577 * q^68 + 468 * q^69 - 1725 * q^71 - 837 * q^72 - 512 * q^73 - 1953 * q^74 - 3046 * q^76 + 399 * q^77 + 243 * q^78 + 1629 * q^79 + 324 * q^81 + 693 * q^82 - 321 * q^83 - 336 * q^84 - 4542 * q^86 - 1134 * q^87 - 3482 * q^88 - 978 * q^89 - 301 * q^91 - 852 * q^92 + 279 * q^93 + 2480 * q^94 + 2070 * q^96 - 2616 * q^97 - 294 * q^98 + 513 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more