LMFDB - Embedded newform 825.4.a.bc.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(1,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, 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("825.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.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:	$48.6765757547$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 44x^{5} + 118x^{4} + 515x^{3} - 1279x^{2} - 892x + 1840 $ x^7 - 3x^6 - 44x^5 + 118x^4 + 515x^3 - 1279x^2 - 892x + 1840
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$4.00699$ of defining polynomial
Character	$\chi$	$=$	825.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00699 q^{2} +3.00000 q^{3} +8.05595 q^{4} +12.0210 q^{6} +26.2766 q^{7} +0.224208 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.00699 q^{2} +3.00000 q^{3} +8.05595 q^{4} +12.0210 q^{6} +26.2766 q^{7} +0.224208 q^{8} +9.00000 q^{9} -11.0000 q^{11} +24.1679 q^{12} -11.3069 q^{13} +105.290 q^{14} -63.5492 q^{16} +87.6018 q^{17} +36.0629 q^{18} +148.978 q^{19} +78.8297 q^{21} -44.0769 q^{22} -12.7783 q^{23} +0.672624 q^{24} -45.3065 q^{26} +27.0000 q^{27} +211.683 q^{28} -37.2177 q^{29} -30.4121 q^{31} -256.435 q^{32} -33.0000 q^{33} +351.019 q^{34} +72.5036 q^{36} +122.491 q^{37} +596.955 q^{38} -33.9206 q^{39} +444.960 q^{41} +315.870 q^{42} +36.2510 q^{43} -88.6155 q^{44} -51.2025 q^{46} +78.5138 q^{47} -190.648 q^{48} +347.458 q^{49} +262.805 q^{51} -91.0876 q^{52} -342.345 q^{53} +108.189 q^{54} +5.89142 q^{56} +446.935 q^{57} -149.131 q^{58} +377.123 q^{59} -690.244 q^{61} -121.861 q^{62} +236.489 q^{63} -519.137 q^{64} -132.231 q^{66} -696.564 q^{67} +705.716 q^{68} -38.3349 q^{69} +1014.66 q^{71} +2.01787 q^{72} -889.198 q^{73} +490.818 q^{74} +1200.16 q^{76} -289.042 q^{77} -135.919 q^{78} -858.251 q^{79} +81.0000 q^{81} +1782.95 q^{82} +115.843 q^{83} +635.048 q^{84} +145.257 q^{86} -111.653 q^{87} -2.46629 q^{88} +553.264 q^{89} -297.106 q^{91} -102.941 q^{92} -91.2363 q^{93} +314.604 q^{94} -769.304 q^{96} +336.110 q^{97} +1392.26 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 3 q^{2} + 21 q^{3} + 41 q^{4} + 9 q^{6} + 50 q^{7} + 21 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q + 3 * q^2 + 21 * q^3 + 41 * q^4 + 9 * q^6 + 50 * q^7 + 21 * q^8 + 63 * q^9	\( 7 q + 3 q^{2} + 21 q^{3} + 41 q^{4} + 9 q^{6} + 50 q^{7} + 21 q^{8} + 63 q^{9} - 77 q^{11} + 123 q^{12} + 24 q^{13} + 142 q^{14} + 181 q^{16} + 38 q^{17} + 27 q^{18} + 26 q^{19} + 150 q^{21} - 33 q^{22} + 228 q^{23} + 63 q^{24} + 476 q^{26} + 189 q^{27} + 840 q^{28} + 572 q^{29} - 140 q^{31} + 991 q^{32} - 231 q^{33} - 806 q^{34} + 369 q^{36} - 104 q^{37} + 498 q^{38} + 72 q^{39} + 896 q^{41} + 426 q^{42} + 614 q^{43} - 451 q^{44} - 344 q^{46} + 520 q^{47} + 543 q^{48} + 295 q^{49} + 114 q^{51} - 26 q^{52} + 380 q^{53} + 81 q^{54} + 1522 q^{56} + 78 q^{57} + 1600 q^{58} + 1316 q^{59} - 386 q^{61} + 440 q^{62} + 450 q^{63} + 869 q^{64} - 99 q^{66} + 348 q^{67} + 332 q^{68} + 684 q^{69} + 804 q^{71} + 189 q^{72} + 468 q^{73} - 748 q^{74} - 1698 q^{76} - 550 q^{77} + 1428 q^{78} - 374 q^{79} + 567 q^{81} - 620 q^{82} + 3128 q^{83} + 2520 q^{84} - 2534 q^{86} + 1716 q^{87} - 231 q^{88} + 694 q^{89} - 3376 q^{91} - 1184 q^{92} - 420 q^{93} - 2920 q^{94} + 2973 q^{96} - 8 q^{97} + 4211 q^{98} - 693 q^{99}+O(q^{100}) \) 7 * q + 3 * q^2 + 21 * q^3 + 41 * q^4 + 9 * q^6 + 50 * q^7 + 21 * q^8 + 63 * q^9 - 77 * q^11 + 123 * q^12 + 24 * q^13 + 142 * q^14 + 181 * q^16 + 38 * q^17 + 27 * q^18 + 26 * q^19 + 150 * q^21 - 33 * q^22 + 228 * q^23 + 63 * q^24 + 476 * q^26 + 189 * q^27 + 840 * q^28 + 572 * q^29 - 140 * q^31 + 991 * q^32 - 231 * q^33 - 806 * q^34 + 369 * q^36 - 104 * q^37 + 498 * q^38 + 72 * q^39 + 896 * q^41 + 426 * q^42 + 614 * q^43 - 451 * q^44 - 344 * q^46 + 520 * q^47 + 543 * q^48 + 295 * q^49 + 114 * q^51 - 26 * q^52 + 380 * q^53 + 81 * q^54 + 1522 * q^56 + 78 * q^57 + 1600 * q^58 + 1316 * q^59 - 386 * q^61 + 440 * q^62 + 450 * q^63 + 869 * q^64 - 99 * q^66 + 348 * q^67 + 332 * q^68 + 684 * q^69 + 804 * q^71 + 189 * q^72 + 468 * q^73 - 748 * q^74 - 1698 * q^76 - 550 * q^77 + 1428 * q^78 - 374 * q^79 + 567 * q^81 - 620 * q^82 + 3128 * q^83 + 2520 * q^84 - 2534 * q^86 + 1716 * q^87 - 231 * q^88 + 694 * q^89 - 3376 * q^91 - 1184 * q^92 - 420 * q^93 - 2920 * q^94 + 2973 * q^96 - 8 * q^97 + 4211 * q^98 - 693 * 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 $

$2$	4.00699	1.41668	0.708342	−	0.705869i	$-0.249443\pi$
$2$	4.00699	1.41668	0.708342	+	0.705869i	$0.249443\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	8.05595	1.00699
$5$	0	0
$5$	0	0
$6$	12.0210	0.817923
$7$	26.2766	1.41880	0.709401	−	0.704805i	$-0.248966\pi$
$7$	26.2766	1.41880	0.709401	+	0.704805i	$0.248966\pi$
$8$	0.224208	0.00990869
$9$	9.00000	0.333333
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	24.1679	0.581388
$13$	−11.3069	−0.241228	−0.120614	−	0.992700i	$-0.538486\pi$
$13$	−11.3069	−0.241228	−0.120614	+	0.992700i	$0.538486\pi$
$14$	105.290	2.00999
$15$	0	0
$16$	−63.5492	−0.992957
$17$	87.6018	1.24980	0.624899	−	0.780706i	$-0.285140\pi$
$17$	87.6018	1.24980	0.624899	+	0.780706i	$0.285140\pi$
$18$	36.0629	0.472228
$19$	148.978	1.79884	0.899421	−	0.437083i	$-0.143988\pi$
$19$	148.978	1.79884	0.899421	+	0.437083i	$0.143988\pi$
$20$	0	0
$21$	78.8297	0.819145
$22$	−44.0769	−0.427146
$23$	−12.7783	−0.115846	−0.0579230	−	0.998321i	$-0.518448\pi$
$23$	−12.7783	−0.115846	−0.0579230	+	0.998321i	$0.518448\pi$
$24$	0.672624	0.00572078
$25$	0	0
$26$	−45.3065	−0.341743
$27$	27.0000	0.192450
$28$	211.683	1.42872
$29$	−37.2177	−0.238315	−0.119158	−	0.992875i	$-0.538019\pi$
$29$	−37.2177	−0.238315	−0.119158	+	0.992875i	$0.538019\pi$
$30$	0	0
$31$	−30.4121	−0.176199	−0.0880995	−	0.996112i	$-0.528079\pi$
$31$	−30.4121	−0.176199	−0.0880995	+	0.996112i	$0.528079\pi$
$32$	−256.435	−1.41661
$33$	−33.0000	−0.174078
$34$	351.019	1.77057
$35$	0	0
$36$	72.5036	0.335665
$37$	122.491	0.544252	0.272126	−	0.962262i	$-0.412273\pi$
$37$	122.491	0.544252	0.272126	+	0.962262i	$0.412273\pi$
$38$	596.955	2.54839
$39$	−33.9206	−0.139273
$40$	0	0
$41$	444.960	1.69490	0.847452	−	0.530871i	$-0.178135\pi$
$41$	444.960	1.69490	0.847452	+	0.530871i	$0.178135\pi$
$42$	315.870	1.16047
$43$	36.2510	0.128564	0.0642818	−	0.997932i	$-0.479524\pi$
$43$	36.2510	0.128564	0.0642818	+	0.997932i	$0.479524\pi$
$44$	−88.6155	−0.303620
$45$	0	0
$46$	−51.2025	−0.164117
$47$	78.5138	0.243668	0.121834	−	0.992550i	$-0.461122\pi$
$47$	78.5138	0.243668	0.121834	+	0.992550i	$0.461122\pi$
$48$	−190.648	−0.573284
$49$	347.458	1.01300
$50$	0	0
$51$	262.805	0.721571
$52$	−91.0876	−0.242915
$53$	−342.345	−0.887260	−0.443630	−	0.896210i	$-0.646309\pi$
$53$	−342.345	−0.887260	−0.443630	+	0.896210i	$0.646309\pi$
$54$	108.189	0.272641
$55$	0	0
$56$	5.89142	0.0140585
$57$	446.935	1.03856
$58$	−149.131	−0.337618
$59$	377.123	0.832156	0.416078	−	0.909329i	$-0.363404\pi$
$59$	377.123	0.832156	0.416078	+	0.909329i	$0.363404\pi$
$60$	0	0
$61$	−690.244	−1.44880	−0.724399	−	0.689380i	$-0.757883\pi$
$61$	−690.244	−1.44880	−0.724399	+	0.689380i	$0.757883\pi$
$62$	−121.861	−0.249618
$63$	236.489	0.472934
$64$	−519.137	−1.01394
$65$	0	0
$66$	−132.231	−0.246613
$67$	−696.564	−1.27013	−0.635066	−	0.772458i	$-0.719027\pi$
$67$	−696.564	−1.27013	−0.635066	+	0.772458i	$0.719027\pi$
$68$	705.716	1.25854
$69$	−38.3349	−0.0668837
$70$	0	0
$71$	1014.66	1.69602	0.848011	−	0.529978i	$-0.177800\pi$
$71$	1014.66	1.69602	0.848011	+	0.529978i	$0.177800\pi$
$72$	2.01787	0.00330290
$73$	−889.198	−1.42565	−0.712827	−	0.701339i	$-0.752586\pi$
$73$	−889.198	−1.42565	−0.712827	+	0.701339i	$0.752586\pi$
$74$	490.818	0.771033
$75$	0	0
$76$	1200.16	1.81142
$77$	−289.042	−0.427785
$78$	−135.919	−0.197306
$79$	−858.251	−1.22229	−0.611144	−	0.791519i	$-0.709290\pi$
$79$	−858.251	−1.22229	−0.611144	+	0.791519i	$0.709290\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	1782.95	2.40115
$83$	115.843	0.153198	0.0765989	−	0.997062i	$-0.475594\pi$
$83$	115.843	0.153198	0.0765989	+	0.997062i	$0.475594\pi$
$84$	635.048	0.824875
$85$	0	0
$86$	145.257	0.182134
$87$	−111.653	−0.137591
$88$	−2.46629	−0.00298758
$89$	553.264	0.658943	0.329471	−	0.944166i	$-0.393130\pi$
$89$	553.264	0.658943	0.329471	+	0.944166i	$0.393130\pi$
$90$	0	0
$91$	−297.106	−0.342254
$92$	−102.941	−0.116656
$93$	−91.2363	−0.101729
$94$	314.604	0.345201
$95$	0	0
$96$	−769.304	−0.817883
$97$	336.110	0.351823	0.175911	−	0.984406i	$-0.443713\pi$
$97$	336.110	0.351823	0.175911	+	0.984406i	$0.443713\pi$
$98$	1392.26	1.43510
$99$	−99.0000	−0.100504
$100$	0	0
$101$	1277.11	1.25819	0.629097	−	0.777327i	$-0.283425\pi$
$101$	1277.11	1.25819	0.629097	+	0.777327i	$0.283425\pi$
$102$	1053.06	1.02224
$103$	1075.63	1.02898	0.514490	−	0.857497i	$-0.327981\pi$
$103$	1075.63	1.02898	0.514490	+	0.857497i	$0.327981\pi$
$104$	−2.53509	−0.00239025
$105$	0	0
$106$	−1371.77	−1.25697
$107$	−1903.79	−1.72006	−0.860030	−	0.510244i	$-0.829555\pi$
$107$	−1903.79	−1.72006	−0.860030	+	0.510244i	$0.829555\pi$
$108$	217.511	0.193796
$109$	−894.655	−0.786169	−0.393084	−	0.919502i	$-0.628592\pi$
$109$	−894.655	−0.786169	−0.393084	+	0.919502i	$0.628592\pi$
$110$	0	0
$111$	367.472	0.314224
$112$	−1669.86	−1.40881
$113$	0.252752	0.000210415 0	0.000105208	−	1.00000i	$-0.499967\pi$
$113$	0.252752	0.000210415 0	0.000105208		1.00000i	$0.499967\pi$
$114$	1790.87	1.47131
$115$	0	0
$116$	−299.824	−0.239982
$117$	−101.762	−0.0804092
$118$	1511.13	1.17890
$119$	2301.87	1.77321
$120$	0	0
$121$	121.000	0.0909091
$122$	−2765.80	−2.05249
$123$	1334.88	0.978554
$124$	−244.998	−0.177431
$125$	0	0
$126$	947.609	0.669998
$127$	2393.92	1.67264	0.836321	−	0.548240i	$-0.184702\pi$
$127$	2393.92	1.67264	0.836321	+	0.548240i	$0.184702\pi$
$128$	−28.6979	−0.0198169
$129$	108.753	0.0742262
$130$	0	0
$131$	−2363.05	−1.57604	−0.788019	−	0.615651i	$-0.788893\pi$
$131$	−2363.05	−1.57604	−0.788019	+	0.615651i	$0.788893\pi$
$132$	−265.846	−0.175295
$133$	3914.64	2.55220
$134$	−2791.12	−1.79938
$135$	0	0
$136$	19.6410	0.0123839
$137$	−208.264	−0.129877	−0.0649385	−	0.997889i	$-0.520685\pi$
$137$	−208.264	−0.129877	−0.0649385	+	0.997889i	$0.520685\pi$
$138$	−153.607	−0.0947531
$139$	−612.112	−0.373515	−0.186758	−	0.982406i	$-0.559798\pi$
$139$	−612.112	−0.373515	−0.186758	+	0.982406i	$0.559798\pi$
$140$	0	0
$141$	235.541	0.140682
$142$	4065.72	2.40273
$143$	124.375	0.0727329
$144$	−571.943	−0.330986
$145$	0	0
$146$	−3563.01	−2.01970
$147$	1042.37	0.584854
$148$	986.778	0.548059
$149$	−2116.42	−1.16365	−0.581826	−	0.813313i	$-0.697662\pi$
$149$	−2116.42	−1.16365	−0.581826	+	0.813313i	$0.697662\pi$
$150$	0	0
$151$	−3405.63	−1.83540	−0.917701	−	0.397271i	$-0.869957\pi$
$151$	−3405.63	−1.83540	−0.917701	+	0.397271i	$0.869957\pi$
$152$	33.4022	0.0178242
$153$	788.416	0.416599
$154$	−1158.19	−0.606036
$155$	0	0
$156$	−273.263	−0.140247
$157$	294.346	0.149627	0.0748133	−	0.997198i	$-0.476164\pi$
$157$	294.346	0.149627	0.0748133	+	0.997198i	$0.476164\pi$
$158$	−3439.00	−1.73160
$159$	−1027.04	−0.512260
$160$	0	0
$161$	−335.770	−0.164362
$162$	324.566	0.157409
$163$	−2877.76	−1.38284	−0.691421	−	0.722452i	$-0.743015\pi$
$163$	−2877.76	−1.38284	−0.691421	+	0.722452i	$0.743015\pi$
$164$	3584.58	1.70676
$165$	0	0
$166$	464.181	0.217033
$167$	2506.59	1.16147	0.580735	−	0.814093i	$-0.302765\pi$
$167$	2506.59	1.16147	0.580735	+	0.814093i	$0.302765\pi$
$168$	17.6742	0.00811665
$169$	−2069.15	−0.941809
$170$	0	0
$171$	1340.81	0.599614
$172$	292.037	0.129463
$173$	3092.28	1.35897	0.679485	−	0.733689i	$-0.262203\pi$
$173$	3092.28	1.35897	0.679485	+	0.733689i	$0.262203\pi$
$174$	−447.392	−0.194924
$175$	0	0
$176$	699.042	0.299388
$177$	1131.37	0.480445
$178$	2216.92	0.933514
$179$	−3360.78	−1.40333	−0.701665	−	0.712507i	$-0.747560\pi$
$179$	−3360.78	−1.40333	−0.701665	+	0.712507i	$0.747560\pi$
$180$	0	0
$181$	208.349	0.0855606	0.0427803	−	0.999085i	$-0.486378\pi$
$181$	208.349	0.0855606	0.0427803	+	0.999085i	$0.486378\pi$
$182$	−1190.50	−0.484866
$183$	−2070.73	−0.836464
$184$	−2.86499	−0.00114788
$185$	0	0
$186$	−365.583	−0.144117
$187$	−963.620	−0.376828
$188$	632.503	0.245373
$189$	709.467	0.273048
$190$	0	0
$191$	−324.423	−0.122903	−0.0614514	−	0.998110i	$-0.519573\pi$
$191$	−324.423	−0.122903	−0.0614514	+	0.998110i	$0.519573\pi$
$192$	−1557.41	−0.585398
$193$	−3274.46	−1.22125	−0.610624	−	0.791920i	$-0.709081\pi$
$193$	−3274.46	−1.22125	−0.610624	+	0.791920i	$0.709081\pi$
$194$	1346.79	0.498422
$195$	0	0
$196$	2799.11	1.02008
$197$	−642.826	−0.232484	−0.116242	−	0.993221i	$-0.537085\pi$
$197$	−642.826	−0.232484	−0.116242	+	0.993221i	$0.537085\pi$
$198$	−396.692	−0.142382
$199$	−320.513	−0.114174	−0.0570868	−	0.998369i	$-0.518181\pi$
$199$	−320.513	−0.114174	−0.0570868	+	0.998369i	$0.518181\pi$
$200$	0	0
$201$	−2089.69	−0.733311
$202$	5117.38	1.78246
$203$	−977.953	−0.338122
$204$	2117.15	0.726618
$205$	0	0
$206$	4310.03	1.45774
$207$	−115.005	−0.0386153
$208$	718.542	0.239529
$209$	−1638.76	−0.542371
$210$	0	0
$211$	−5158.61	−1.68310	−0.841548	−	0.540182i	$-0.818356\pi$
$211$	−5158.61	−1.68310	−0.841548	+	0.540182i	$0.818356\pi$
$212$	−2757.92	−0.893465
$213$	3043.97	0.979199
$214$	−7628.47	−2.43678
$215$	0	0
$216$	6.05361	0.00190693
$217$	−799.125	−0.249992
$218$	−3584.87	−1.11375
$219$	−2667.60	−0.823102
$220$	0	0
$221$	−990.501	−0.301486
$222$	1472.45	0.445156
$223$	2948.51	0.885413	0.442706	−	0.896667i	$-0.354018\pi$
$223$	2948.51	0.885413	0.442706	+	0.896667i	$0.354018\pi$
$224$	−6738.22	−2.00990
$225$	0	0
$226$	1.01277	0.000298092 0
$227$	2281.12	0.666974	0.333487	−	0.942755i	$-0.391775\pi$
$227$	2281.12	0.666974	0.333487	+	0.942755i	$0.391775\pi$
$228$	3600.49	1.04583
$229$	3616.61	1.04364	0.521818	−	0.853057i	$-0.325254\pi$
$229$	3616.61	1.04364	0.521818	+	0.853057i	$0.325254\pi$
$230$	0	0
$231$	−867.127	−0.246982
$232$	−8.34450	−0.00236139
$233$	−4571.20	−1.28528	−0.642638	−	0.766170i	$-0.722160\pi$
$233$	−4571.20	−1.28528	−0.642638	+	0.766170i	$0.722160\pi$
$234$	−407.758	−0.113914
$235$	0	0
$236$	3038.08	0.837976
$237$	−2574.75	−0.705688
$238$	9223.59	2.51208
$239$	2515.86	0.680911	0.340455	−	0.940261i	$-0.389419\pi$
$239$	2515.86	0.680911	0.340455	+	0.940261i	$0.389419\pi$
$240$	0	0
$241$	5325.35	1.42339	0.711693	−	0.702490i	$-0.247929\pi$
$241$	5325.35	1.42339	0.711693	+	0.702490i	$0.247929\pi$
$242$	484.846	0.128789
$243$	243.000	0.0641500
$244$	−5560.58	−1.45893
$245$	0	0
$246$	5348.85	1.38630
$247$	−1684.48	−0.433931
$248$	−6.81863	−0.00174590
$249$	347.529	0.0884488
$250$	0	0
$251$	−4417.05	−1.11076	−0.555382	−	0.831595i	$-0.687428\pi$
$251$	−4417.05	−1.11076	−0.555382	+	0.831595i	$0.687428\pi$
$252$	1905.15	0.476242
$253$	140.561	0.0349289
$254$	9592.39	2.36961
$255$	0	0
$256$	4038.10	0.985865
$257$	1049.24	0.254668	0.127334	−	0.991860i	$-0.459358\pi$
$257$	1049.24	0.254668	0.127334	+	0.991860i	$0.459358\pi$
$258$	435.772	0.105155
$259$	3218.63	0.772185
$260$	0	0
$261$	−334.959	−0.0794385
$262$	−9468.73	−2.23275
$263$	−2773.92	−0.650370	−0.325185	−	0.945650i	$-0.605427\pi$
$263$	−2773.92	−0.650370	−0.325185	+	0.945650i	$0.605427\pi$
$264$	−7.39886	−0.00172488
$265$	0	0
$266$	15685.9	3.61566
$267$	1659.79	0.380441
$268$	−5611.49	−1.27902
$269$	−1645.90	−0.373056	−0.186528	−	0.982450i	$-0.559724\pi$
$269$	−1645.90	−0.373056	−0.186528	+	0.982450i	$0.559724\pi$
$270$	0	0
$271$	−8599.58	−1.92763	−0.963814	−	0.266576i	$-0.914108\pi$
$271$	−8599.58	−1.92763	−0.963814	+	0.266576i	$0.914108\pi$
$272$	−5567.03	−1.24099
$273$	−891.317	−0.197600
$274$	−834.510	−0.183995
$275$	0	0
$276$	−308.824	−0.0673515
$277$	3908.67	0.847832	0.423916	−	0.905701i	$-0.360655\pi$
$277$	3908.67	0.847832	0.423916	+	0.905701i	$0.360655\pi$
$278$	−2452.72	−0.529153
$279$	−273.709	−0.0587330
$280$	0	0
$281$	−1987.21	−0.421875	−0.210938	−	0.977500i	$-0.567652\pi$
$281$	−1987.21	−0.421875	−0.210938	+	0.977500i	$0.567652\pi$
$282$	943.811	0.199302
$283$	1229.67	0.258291	0.129145	−	0.991626i	$-0.458777\pi$
$283$	1229.67	0.258291	0.129145	+	0.991626i	$0.458777\pi$
$284$	8174.03	1.70789
$285$	0	0
$286$	498.371	0.103040
$287$	11692.0	2.40473
$288$	−2307.91	−0.472205
$289$	2761.08	0.561994
$290$	0	0
$291$	1008.33	0.203125
$292$	−7163.34	−1.43563
$293$	−5067.22	−1.01034	−0.505171	−	0.863019i	$-0.668571\pi$
$293$	−5067.22	−1.01034	−0.505171	+	0.863019i	$0.668571\pi$
$294$	4176.78	0.828554
$295$	0	0
$296$	27.4634	0.00539282
$297$	−297.000	−0.0580259
$298$	−8480.49	−1.64853
$299$	144.482	0.0279453
$300$	0	0
$301$	952.553	0.182406
$302$	−13646.3	−2.60019
$303$	3831.34	0.726419
$304$	−9467.47	−1.78617
$305$	0	0
$306$	3159.17	0.590190
$307$	321.662	0.0597988	0.0298994	−	0.999553i	$-0.490481\pi$
$307$	321.662	0.0597988	0.0298994	+	0.999553i	$0.490481\pi$
$308$	−2328.51	−0.430777
$309$	3226.89	0.594081
$310$	0	0
$311$	−5135.27	−0.936316	−0.468158	−	0.883645i	$-0.655082\pi$
$311$	−5135.27	−0.936316	−0.468158	+	0.883645i	$0.655082\pi$
$312$	−7.60526	−0.00138001
$313$	−8366.56	−1.51088	−0.755441	−	0.655217i	$-0.772577\pi$
$313$	−8366.56	−1.51088	−0.755441	+	0.655217i	$0.772577\pi$
$314$	1179.44	0.211974
$315$	0	0
$316$	−6914.03	−1.23084
$317$	−7744.61	−1.37218	−0.686089	−	0.727517i	$-0.740674\pi$
$317$	−7744.61	−1.37218	−0.686089	+	0.727517i	$0.740674\pi$
$318$	−4115.32	−0.725710
$319$	409.394	0.0718548
$320$	0	0
$321$	−5711.37	−0.993077
$322$	−1345.43	−0.232850
$323$	13050.8	2.24819
$324$	652.532	0.111888
$325$	0	0
$326$	−11531.1	−1.95905
$327$	−2683.96	−0.453895
$328$	99.7636	0.0167943
$329$	2063.07	0.345717
$330$	0	0
$331$	201.426	0.0334483	0.0167242	−	0.999860i	$-0.494676\pi$
$331$	201.426	0.0334483	0.0167242	+	0.999860i	$0.494676\pi$
$332$	933.225	0.154269
$333$	1102.41	0.181417
$334$	10043.9	1.64544
$335$	0	0
$336$	−5009.57	−0.813376
$337$	1271.19	0.205478	0.102739	−	0.994708i	$-0.467239\pi$
$337$	1271.19	0.205478	0.102739	+	0.994708i	$0.467239\pi$
$338$	−8291.08	−1.33425
$339$	0.758256	0.000121483 0
$340$	0	0
$341$	334.533	0.0531260
$342$	5372.60	0.849464
$343$	117.142	0.0184405
$344$	8.12777	0.00127390
$345$	0	0
$346$	12390.7	1.92523
$347$	7274.99	1.12548	0.562740	−	0.826634i	$-0.309747\pi$
$347$	7274.99	1.12548	0.562740	+	0.826634i	$0.309747\pi$
$348$	−899.472	−0.138554
$349$	293.092	0.0449538	0.0224769	−	0.999747i	$-0.492845\pi$
$349$	293.092	0.0449538	0.0224769	+	0.999747i	$0.492845\pi$
$350$	0	0
$351$	−305.285	−0.0464243
$352$	2820.78	0.427125
$353$	1120.68	0.168974	0.0844868	−	0.996425i	$-0.473075\pi$
$353$	1120.68	0.168974	0.0844868	+	0.996425i	$0.473075\pi$
$354$	4533.38	0.680639
$355$	0	0
$356$	4457.07	0.663551
$357$	6905.62	1.02377
$358$	−13466.6	−1.98808
$359$	−3543.35	−0.520921	−0.260461	−	0.965484i	$-0.583874\pi$
$359$	−3543.35	−0.520921	−0.260461	+	0.965484i	$0.583874\pi$
$360$	0	0
$361$	15335.6	2.23583
$362$	834.853	0.121212
$363$	363.000	0.0524864
$364$	−2393.47	−0.344648
$365$	0	0
$366$	−8297.40	−1.18501
$367$	−5998.09	−0.853128	−0.426564	−	0.904457i	$-0.640276\pi$
$367$	−5998.09	−0.853128	−0.426564	+	0.904457i	$0.640276\pi$
$368$	812.051	0.115030
$369$	4004.64	0.564968
$370$	0	0
$371$	−8995.66	−1.25885
$372$	−734.995	−0.102440
$373$	4701.91	0.652696	0.326348	−	0.945250i	$-0.394182\pi$
$373$	4701.91	0.652696	0.326348	+	0.945250i	$0.394182\pi$
$374$	−3861.21	−0.533846
$375$	0	0
$376$	17.6034	0.00241443
$377$	420.815	0.0574883
$378$	2842.83	0.386823
$379$	−10784.6	−1.46165	−0.730826	−	0.682563i	$-0.760865\pi$
$379$	−10784.6	−1.46165	−0.730826	+	0.682563i	$0.760865\pi$
$380$	0	0
$381$	7181.75	0.965701
$382$	−1299.96	−0.174115
$383$	5317.16	0.709385	0.354692	−	0.934983i	$-0.384586\pi$
$383$	5317.16	0.709385	0.354692	+	0.934983i	$0.384586\pi$
$384$	−86.0937	−0.0114413
$385$	0	0
$386$	−13120.7	−1.73012
$387$	326.259	0.0428545
$388$	2707.69	0.354284
$389$	10677.3	1.39167	0.695833	−	0.718203i	$-0.255035\pi$
$389$	10677.3	1.39167	0.695833	+	0.718203i	$0.255035\pi$
$390$	0	0
$391$	−1119.40	−0.144784
$392$	77.9029	0.0100375
$393$	−7089.16	−0.909926
$394$	−2575.79	−0.329357
$395$	0	0
$396$	−797.539	−0.101207
$397$	8922.89	1.12803	0.564014	−	0.825765i	$-0.309257\pi$
$397$	8922.89	1.12803	0.564014	+	0.825765i	$0.309257\pi$
$398$	−1284.29	−0.161748
$399$	11743.9	1.47351
$400$	0	0
$401$	−3177.53	−0.395707	−0.197853	−	0.980232i	$-0.563397\pi$
$401$	−3177.53	−0.395707	−0.197853	+	0.980232i	$0.563397\pi$
$402$	−8373.37	−1.03887
$403$	343.865	0.0425041
$404$	10288.4	1.26699
$405$	0	0
$406$	−3918.64	−0.479013
$407$	−1347.40	−0.164098
$408$	58.9231	0.00714982
$409$	−2509.89	−0.303438	−0.151719	−	0.988424i	$-0.548481\pi$
$409$	−2509.89	−0.303438	−0.151719	+	0.988424i	$0.548481\pi$
$410$	0	0
$411$	−624.791	−0.0749846
$412$	8665.22	1.03618
$413$	9909.49	1.18066
$414$	−460.822	−0.0547057
$415$	0	0
$416$	2899.47	0.341727
$417$	−1836.34	−0.215649
$418$	−6566.51	−0.768369
$419$	9452.10	1.10207	0.551033	−	0.834484i	$-0.314234\pi$
$419$	9452.10	1.10207	0.551033	+	0.834484i	$0.314234\pi$
$420$	0	0
$421$	−1824.33	−0.211193	−0.105597	−	0.994409i	$-0.533675\pi$
$421$	−1824.33	−0.211193	−0.105597	+	0.994409i	$0.533675\pi$
$422$	−20670.5	−2.38442
$423$	706.624	0.0812228
$424$	−76.7566	−0.00879158
$425$	0	0
$426$	12197.2	1.38722
$427$	−18137.3	−2.05556
$428$	−15336.9	−1.73209
$429$	373.126	0.0419923
$430$	0	0
$431$	15347.3	1.71521	0.857603	−	0.514312i	$-0.171953\pi$
$431$	15347.3	1.71521	0.857603	+	0.514312i	$0.171953\pi$
$432$	−1715.83	−0.191095
$433$	5002.63	0.555222	0.277611	−	0.960694i	$-0.410457\pi$
$433$	5002.63	0.555222	0.277611	+	0.960694i	$0.410457\pi$
$434$	−3202.09	−0.354159
$435$	0	0
$436$	−7207.30	−0.791667
$437$	−1903.69	−0.208389
$438$	−10689.0	−1.16608
$439$	−2498.66	−0.271651	−0.135825	−	0.990733i	$-0.543369\pi$
$439$	−2498.66	−0.271651	−0.135825	+	0.990733i	$0.543369\pi$
$440$	0	0
$441$	3127.12	0.337666
$442$	−3968.93	−0.427110
$443$	−3044.08	−0.326476	−0.163238	−	0.986587i	$-0.552194\pi$
$443$	−3044.08	−0.326476	−0.163238	+	0.986587i	$0.552194\pi$
$444$	2960.33	0.316422
$445$	0	0
$446$	11814.7	1.25435
$447$	−6349.27	−0.671835
$448$	−13641.1	−1.43858
$449$	13184.9	1.38582	0.692911	−	0.721023i	$-0.256328\pi$
$449$	13184.9	1.38582	0.692911	+	0.721023i	$0.256328\pi$
$450$	0	0
$451$	−4894.56	−0.511033
$452$	2.03616	0.000211887 0
$453$	−10216.9	−1.05967
$454$	9140.42	0.944892
$455$	0	0
$456$	100.206	0.0102908
$457$	16938.6	1.73381	0.866907	−	0.498469i	$-0.166104\pi$
$457$	16938.6	1.73381	0.866907	+	0.498469i	$0.166104\pi$
$458$	14491.7	1.47850
$459$	2365.25	0.240524
$460$	0	0
$461$	5188.91	0.524234	0.262117	−	0.965036i	$-0.415579\pi$
$461$	5188.91	0.524234	0.262117	+	0.965036i	$0.415579\pi$
$462$	−3474.57	−0.349895
$463$	−15097.9	−1.51546	−0.757730	−	0.652569i	$-0.773691\pi$
$463$	−15097.9	−1.51546	−0.757730	+	0.652569i	$0.773691\pi$
$464$	2365.15	0.236637
$465$	0	0
$466$	−18316.7	−1.82083
$467$	13597.2	1.34733	0.673665	−	0.739037i	$-0.264719\pi$
$467$	13597.2	1.34733	0.673665	+	0.739037i	$0.264719\pi$
$468$	−819.788	−0.0809716
$469$	−18303.3	−1.80207
$470$	0	0
$471$	883.038	0.0863869
$472$	84.5539	0.00824557
$473$	−398.761	−0.0387634
$474$	−10317.0	−0.999738
$475$	0	0
$476$	18543.8	1.78562
$477$	−3081.11	−0.295753
$478$	10081.0	0.964636
$479$	−6830.32	−0.651535	−0.325767	−	0.945450i	$-0.605623\pi$
$479$	−6830.32	−0.651535	−0.325767	+	0.945450i	$0.605623\pi$
$480$	0	0
$481$	−1384.98	−0.131289
$482$	21338.6	2.01649
$483$	−1007.31	−0.0948947
$484$	974.770	0.0915449
$485$	0	0
$486$	973.698	0.0908803
$487$	−762.315	−0.0709318	−0.0354659	−	0.999371i	$-0.511292\pi$
$487$	−762.315	−0.0709318	−0.0354659	+	0.999371i	$0.511292\pi$
$488$	−154.758	−0.0143557
$489$	−8633.27	−0.798384
$490$	0	0
$491$	1478.23	0.135868	0.0679342	−	0.997690i	$-0.478359\pi$
$491$	1478.23	0.135868	0.0679342	+	0.997690i	$0.478359\pi$
$492$	10753.7	0.985398
$493$	−3260.34	−0.297846
$494$	−6749.69	−0.614743
$495$	0	0
$496$	1932.66	0.174958
$497$	26661.7	2.40632
$498$	1392.54	0.125304
$499$	−11087.2	−0.994648	−0.497324	−	0.867565i	$-0.665684\pi$
$499$	−11087.2	−0.994648	−0.497324	+	0.867565i	$0.665684\pi$
$500$	0	0
$501$	7519.76	0.670575
$502$	−17699.1	−1.57360
$503$	−7336.27	−0.650314	−0.325157	−	0.945660i	$-0.605417\pi$
$503$	−7336.27	−0.650314	−0.325157	+	0.945660i	$0.605417\pi$
$504$	53.0227	0.00468615
$505$	0	0
$506$	563.227	0.0494832
$507$	−6207.46	−0.543754
$508$	19285.3	1.68434
$509$	−15419.2	−1.34272	−0.671360	−	0.741131i	$-0.734290\pi$
$509$	−15419.2	−1.34272	−0.671360	+	0.741131i	$0.734290\pi$
$510$	0	0
$511$	−23365.1	−2.02272
$512$	16410.2	1.41648
$513$	4022.42	0.346187
$514$	4204.29	0.360785
$515$	0	0
$516$	876.110	0.0747454
$517$	−863.651	−0.0734688
$518$	12897.0	1.09394
$519$	9276.85	0.784602
$520$	0	0
$521$	20182.9	1.69717	0.848587	−	0.529056i	$-0.177454\pi$
$521$	20182.9	1.69717	0.848587	+	0.529056i	$0.177454\pi$
$522$	−1342.18	−0.112539
$523$	15479.7	1.29422	0.647112	−	0.762395i	$-0.275977\pi$
$523$	15479.7	1.29422	0.647112	+	0.762395i	$0.275977\pi$
$524$	−19036.7	−1.58706
$525$	0	0
$526$	−11115.1	−0.921369
$527$	−2664.15	−0.220213
$528$	2097.12	0.172852
$529$	−12003.7	−0.986580
$530$	0	0
$531$	3394.10	0.277385
$532$	31536.2	2.57005
$533$	−5031.10	−0.408858
$534$	6650.77	0.538964
$535$	0	0
$536$	−156.175	−0.0125853
$537$	−10082.3	−0.810213
$538$	−6595.09	−0.528503
$539$	−3822.04	−0.305430
$540$	0	0
$541$	−511.002	−0.0406094	−0.0203047	−	0.999794i	$-0.506464\pi$
$541$	−511.002	−0.0406094	−0.0203047	+	0.999794i	$0.506464\pi$
$542$	−34458.4	−2.73084
$543$	625.048	0.0493985
$544$	−22464.1	−1.77048
$545$	0	0
$546$	−3571.49	−0.279937
$547$	18912.8	1.47834	0.739170	−	0.673519i	$-0.235218\pi$
$547$	18912.8	1.47834	0.739170	+	0.673519i	$0.235218\pi$
$548$	−1677.76	−0.130785
$549$	−6212.20	−0.482933
$550$	0	0
$551$	−5544.63	−0.428692
$552$	−8.59498	−0.000662730 0
$553$	−22551.9	−1.73418
$554$	15662.0	1.20111
$555$	0	0
$556$	−4931.14	−0.376128
$557$	−7869.53	−0.598640	−0.299320	−	0.954153i	$-0.596760\pi$
$557$	−7869.53	−0.598640	−0.299320	+	0.954153i	$0.596760\pi$
$558$	−1096.75	−0.0832062
$559$	−409.885	−0.0310131
$560$	0	0
$561$	−2890.86	−0.217562
$562$	−7962.72	−0.597664
$563$	12877.3	0.963964	0.481982	−	0.876181i	$-0.339917\pi$
$563$	12877.3	0.963964	0.481982	+	0.876181i	$0.339917\pi$
$564$	1897.51	0.141666
$565$	0	0
$566$	4927.28	0.365917
$567$	2128.40	0.157645
$568$	227.494	0.0168054
$569$	−7070.93	−0.520965	−0.260482	−	0.965479i	$-0.583882\pi$
$569$	−7070.93	−0.520965	−0.260482	+	0.965479i	$0.583882\pi$
$570$	0	0
$571$	7455.30	0.546400	0.273200	−	0.961957i	$-0.411918\pi$
$571$	7455.30	0.546400	0.273200	+	0.961957i	$0.411918\pi$
$572$	1001.96	0.0732416
$573$	−973.270	−0.0709580
$574$	46849.8	3.40675
$575$	0	0
$576$	−4672.23	−0.337980
$577$	−13840.8	−0.998611	−0.499306	−	0.866426i	$-0.666412\pi$
$577$	−13840.8	−0.998611	−0.499306	+	0.866426i	$0.666412\pi$
$578$	11063.6	0.796168
$579$	−9823.39	−0.705088
$580$	0	0
$581$	3043.95	0.217357
$582$	4040.37	0.287764
$583$	3765.80	0.267519
$584$	−199.365	−0.0141264
$585$	0	0
$586$	−20304.3	−1.43134
$587$	5382.51	0.378466	0.189233	−	0.981932i	$-0.439400\pi$
$587$	5382.51	0.378466	0.189233	+	0.981932i	$0.439400\pi$
$588$	8397.32	0.588945
$589$	−4530.75	−0.316954
$590$	0	0
$591$	−1928.48	−0.134225
$592$	−7784.18	−0.540419
$593$	17176.5	1.18947	0.594735	−	0.803922i	$-0.297257\pi$
$593$	17176.5	1.18947	0.594735	+	0.803922i	$0.297257\pi$
$594$	−1190.08	−0.0822044
$595$	0	0
$596$	−17049.8	−1.17179
$597$	−961.538	−0.0659182
$598$	578.939	0.0395896
$599$	4846.64	0.330598	0.165299	−	0.986243i	$-0.447141\pi$
$599$	4846.64	0.330598	0.165299	+	0.986243i	$0.447141\pi$
$600$	0	0
$601$	−5837.26	−0.396184	−0.198092	−	0.980183i	$-0.563475\pi$
$601$	−5837.26	−0.396184	−0.198092	+	0.980183i	$0.563475\pi$
$602$	3816.87	0.258412
$603$	−6269.08	−0.423377
$604$	−27435.6	−1.84824
$605$	0	0
$606$	15352.2	1.02911
$607$	−22838.2	−1.52714	−0.763572	−	0.645723i	$-0.776556\pi$
$607$	−22838.2	−1.52714	−0.763572	+	0.645723i	$0.776556\pi$
$608$	−38203.3	−2.54827
$609$	−2933.86	−0.195215
$610$	0	0
$611$	−887.744	−0.0587795
$612$	6351.45	0.419513
$613$	22566.4	1.48687	0.743433	−	0.668811i	$-0.233196\pi$
$613$	22566.4	1.48687	0.743433	+	0.668811i	$0.233196\pi$
$614$	1288.90	0.0847160
$615$	0	0
$616$	−64.8056	−0.00423878
$617$	−22553.3	−1.47158	−0.735789	−	0.677211i	$-0.763188\pi$
$617$	−22553.3	−1.47158	−0.735789	+	0.677211i	$0.763188\pi$
$618$	12930.1	0.841626
$619$	−4053.59	−0.263211	−0.131605	−	0.991302i	$-0.542013\pi$
$619$	−4053.59	−0.263211	−0.131605	+	0.991302i	$0.542013\pi$
$620$	0	0
$621$	−345.014	−0.0222946
$622$	−20576.9	−1.32646
$623$	14537.9	0.934909
$624$	2155.63	0.138292
$625$	0	0
$626$	−33524.7	−2.14044
$627$	−4916.29	−0.313138
$628$	2371.24	0.150673
$629$	10730.4	0.680205
$630$	0	0
$631$	18912.2	1.19316	0.596580	−	0.802554i	$-0.296526\pi$
$631$	18912.2	1.19316	0.596580	+	0.802554i	$0.296526\pi$
$632$	−192.427	−0.0121113
$633$	−15475.8	−0.971736
$634$	−31032.6	−1.94394
$635$	0	0
$636$	−8273.76	−0.515842
$637$	−3928.66	−0.244363
$638$	1640.44	0.101796
$639$	9131.91	0.565341
$640$	0	0
$641$	11120.8	0.685248	0.342624	−	0.939473i	$-0.388684\pi$
$641$	11120.8	0.685248	0.342624	+	0.939473i	$0.388684\pi$
$642$	−22885.4	−1.40688
$643$	−6066.39	−0.372061	−0.186030	−	0.982544i	$-0.559562\pi$
$643$	−6066.39	−0.372061	−0.186030	+	0.982544i	$0.559562\pi$
$644$	−2704.94	−0.165512
$645$	0	0
$646$	52294.3	3.18497
$647$	20954.2	1.27325	0.636627	−	0.771172i	$-0.280329\pi$
$647$	20954.2	1.27325	0.636627	+	0.771172i	$0.280329\pi$
$648$	18.1608	0.00110097
$649$	−4148.35	−0.250904
$650$	0	0
$651$	−2397.38	−0.144333
$652$	−23183.1	−1.39251
$653$	9497.10	0.569142	0.284571	−	0.958655i	$-0.408149\pi$
$653$	9497.10	0.569142	0.284571	+	0.958655i	$0.408149\pi$
$654$	−10754.6	−0.643026
$655$	0	0
$656$	−28276.9	−1.68297
$657$	−8002.79	−0.475218
$658$	8266.71	0.489772
$659$	−21562.5	−1.27459	−0.637295	−	0.770620i	$-0.719947\pi$
$659$	−21562.5	−1.27459	−0.637295	+	0.770620i	$0.719947\pi$
$660$	0	0
$661$	−15127.3	−0.890141	−0.445070	−	0.895496i	$-0.646821\pi$
$661$	−15127.3	−0.890141	−0.445070	+	0.895496i	$0.646821\pi$
$662$	807.114	0.0473857
$663$	−2971.50	−0.174063
$664$	25.9729	0.00151799
$665$	0	0
$666$	4417.36	0.257011
$667$	475.578	0.0276079
$668$	20192.9	1.16959
$669$	8845.54	0.511193
$670$	0	0
$671$	7592.69	0.436829
$672$	−20214.7	−1.16041
$673$	2499.23	0.143148	0.0715738	−	0.997435i	$-0.477198\pi$
$673$	2499.23	0.143148	0.0715738	+	0.997435i	$0.477198\pi$
$674$	5093.64	0.291098
$675$	0	0
$676$	−16669.0	−0.948397
$677$	32630.0	1.85240	0.926199	−	0.377036i	$-0.123057\pi$
$677$	32630.0	1.85240	0.926199	+	0.377036i	$0.123057\pi$
$678$	3.03832	0.000172103 0
$679$	8831.82	0.499167
$680$	0	0
$681$	6843.36	0.385078
$682$	1340.47	0.0752628
$683$	−9737.59	−0.545532	−0.272766	−	0.962080i	$-0.587939\pi$
$683$	−9737.59	−0.545532	−0.272766	+	0.962080i	$0.587939\pi$
$684$	10801.5	0.603808
$685$	0	0
$686$	469.388	0.0261244
$687$	10849.8	0.602543
$688$	−2303.73	−0.127658
$689$	3870.85	0.214032
$690$	0	0
$691$	−8508.21	−0.468404	−0.234202	−	0.972188i	$-0.575248\pi$
$691$	−8508.21	−0.468404	−0.234202	+	0.972188i	$0.575248\pi$
$692$	24911.3	1.36848
$693$	−2601.38	−0.142595
$694$	29150.8	1.59445
$695$	0	0
$696$	−25.0335	−0.00136335
$697$	38979.3	2.11829
$698$	1174.42	0.0636853
$699$	−13713.6	−0.742054
$700$	0	0
$701$	−22843.3	−1.23078	−0.615391	−	0.788222i	$-0.711002\pi$
$701$	−22843.3	−1.23078	−0.615391	+	0.788222i	$0.711002\pi$
$702$	−1223.27	−0.0657685
$703$	18248.5	0.979024
$704$	5710.51	0.305714
$705$	0	0
$706$	4490.54	0.239382
$707$	33558.2	1.78513
$708$	9114.25	0.483806
$709$	8510.36	0.450794	0.225397	−	0.974267i	$-0.427632\pi$
$709$	8510.36	0.450794	0.225397	+	0.974267i	$0.427632\pi$
$710$	0	0
$711$	−7724.26	−0.407429
$712$	124.046	0.00652926
$713$	388.615	0.0204120
$714$	27670.8	1.45035
$715$	0	0
$716$	−27074.3	−1.41315
$717$	7547.59	0.393124
$718$	−14198.2	−0.737981
$719$	31326.2	1.62486	0.812428	−	0.583062i	$-0.198146\pi$
$719$	31326.2	1.62486	0.812428	+	0.583062i	$0.198146\pi$
$720$	0	0
$721$	28263.8	1.45992
$722$	61449.5	3.16747
$723$	15976.1	0.821792
$724$	1678.45	0.0861591
$725$	0	0
$726$	1454.54	0.0743566
$727$	13516.6	0.689549	0.344774	−	0.938686i	$-0.387955\pi$
$727$	13516.6	0.689549	0.344774	+	0.938686i	$0.387955\pi$
$728$	−66.6134	−0.00339129
$729$	729.000	0.0370370
$730$	0	0
$731$	3175.66	0.160678
$732$	−16681.7	−0.842315
$733$	9310.89	0.469175	0.234588	−	0.972095i	$-0.424626\pi$
$733$	9310.89	0.469175	0.234588	+	0.972095i	$0.424626\pi$
$734$	−24034.3	−1.20861
$735$	0	0
$736$	3276.80	0.164109
$737$	7662.21	0.382959
$738$	16046.6	0.800382
$739$	14829.0	0.738149	0.369074	−	0.929400i	$-0.379675\pi$
$739$	14829.0	0.738149	0.369074	+	0.929400i	$0.379675\pi$
$740$	0	0
$741$	−5053.44	−0.250530
$742$	−36045.5	−1.78339
$743$	7376.85	0.364240	0.182120	−	0.983276i	$-0.441704\pi$
$743$	7376.85	0.364240	0.182120	+	0.983276i	$0.441704\pi$
$744$	−20.4559	−0.00100800
$745$	0	0
$746$	18840.5	0.924664
$747$	1042.59	0.0510659
$748$	−7762.88	−0.379464
$749$	−50025.1	−2.44042
$750$	0	0
$751$	−2568.19	−0.124786	−0.0623932	−	0.998052i	$-0.519873\pi$
$751$	−2568.19	−0.124786	−0.0623932	+	0.998052i	$0.519873\pi$
$752$	−4989.49	−0.241952
$753$	−13251.2	−0.641300
$754$	1686.20	0.0814427
$755$	0	0
$756$	5715.44	0.274958
$757$	24908.1	1.19590	0.597952	−	0.801532i	$-0.295981\pi$
$757$	24908.1	1.19590	0.597952	+	0.801532i	$0.295981\pi$
$758$	−43213.7	−2.07070
$759$	421.684	0.0201662
$760$	0	0
$761$	33333.8	1.58784	0.793922	−	0.608020i	$-0.208036\pi$
$761$	33333.8	1.58784	0.793922	+	0.608020i	$0.208036\pi$
$762$	28777.2	1.36809
$763$	−23508.5	−1.11542
$764$	−2613.54	−0.123763
$765$	0	0
$766$	21305.8	1.00497
$767$	−4264.07	−0.200739
$768$	12114.3	0.569189
$769$	−27944.9	−1.31043	−0.655215	−	0.755443i	$-0.727422\pi$
$769$	−27944.9	−1.31043	−0.655215	+	0.755443i	$0.727422\pi$
$770$	0	0
$771$	3147.72	0.147033
$772$	−26378.9	−1.22979
$773$	11831.3	0.550510	0.275255	−	0.961371i	$-0.411238\pi$
$773$	11831.3	0.550510	0.275255	+	0.961371i	$0.411238\pi$
$774$	1307.32	0.0607113
$775$	0	0
$776$	75.3586	0.00348610
$777$	9655.89	0.445821
$778$	42783.6	1.97155
$779$	66289.5	3.04887
$780$	0	0
$781$	−11161.2	−0.511370
$782$	−4485.43	−0.205113
$783$	−1004.88	−0.0458638
$784$	−22080.7	−1.00586
$785$	0	0
$786$	−28406.2	−1.28908
$787$	−13469.7	−0.610092	−0.305046	−	0.952338i	$-0.598672\pi$
$787$	−13469.7	−0.610092	−0.305046	+	0.952338i	$0.598672\pi$
$788$	−5178.57	−0.234110
$789$	−8321.77	−0.375491
$790$	0	0
$791$	6.64146	0.000298537 0
$792$	−22.1966	−0.000995860 0
$793$	7804.50	0.349490
$794$	35753.9	1.59806
$795$	0	0
$796$	−2582.04	−0.114972
$797$	−897.262	−0.0398778	−0.0199389	−	0.999801i	$-0.506347\pi$
$797$	−897.262	−0.0398778	−0.0199389	+	0.999801i	$0.506347\pi$
$798$	47057.8	2.08750
$799$	6877.95	0.304536
$800$	0	0
$801$	4979.38	0.219648
$802$	−12732.3	−0.560591
$803$	9781.18	0.429851
$804$	−16834.5	−0.738440
$805$	0	0
$806$	1377.86	0.0602149
$807$	−4937.69	−0.215384
$808$	286.339	0.0124671
$809$	−5655.30	−0.245772	−0.122886	−	0.992421i	$-0.539215\pi$
$809$	−5655.30	−0.245772	−0.122886	+	0.992421i	$0.539215\pi$
$810$	0	0
$811$	9401.84	0.407082	0.203541	−	0.979066i	$-0.434755\pi$
$811$	9401.84	0.407082	0.203541	+	0.979066i	$0.434755\pi$
$812$	−7878.34	−0.340487
$813$	−25798.7	−1.11292
$814$	−5399.00	−0.232475
$815$	0	0
$816$	−16701.1	−0.716489
$817$	5400.63	0.231266
$818$	−10057.1	−0.429875
$819$	−2673.95	−0.114085
$820$	0	0
$821$	3692.36	0.156960	0.0784800	−	0.996916i	$-0.474993\pi$
$821$	3692.36	0.156960	0.0784800	+	0.996916i	$0.474993\pi$
$822$	−2503.53	−0.106229
$823$	26803.8	1.13526	0.567632	−	0.823282i	$-0.307860\pi$
$823$	26803.8	1.13526	0.567632	+	0.823282i	$0.307860\pi$
$824$	241.165	0.0101958
$825$	0	0
$826$	39707.2	1.67263
$827$	−11945.5	−0.502279	−0.251139	−	0.967951i	$-0.580805\pi$
$827$	−11945.5	−0.502279	−0.251139	+	0.967951i	$0.580805\pi$
$828$	−926.472	−0.0388854
$829$	41215.0	1.72673	0.863364	−	0.504582i	$-0.168354\pi$
$829$	41215.0	1.72673	0.863364	+	0.504582i	$0.168354\pi$
$830$	0	0
$831$	11726.0	0.489496
$832$	5869.81	0.244590
$833$	30438.0	1.26604
$834$	−7358.17	−0.305507
$835$	0	0
$836$	−13201.8	−0.546165
$837$	−821.126	−0.0339095
$838$	37874.5	1.56128
$839$	11797.4	0.485447	0.242724	−	0.970095i	$-0.421959\pi$
$839$	11797.4	0.485447	0.242724	+	0.970095i	$0.421959\pi$
$840$	0	0
$841$	−23003.8	−0.943206
$842$	−7310.06	−0.299194
$843$	−5961.62	−0.243570
$844$	−41557.5	−1.69487
$845$	0	0
$846$	2831.43	0.115067
$847$	3179.46	0.128982
$848$	21755.8	0.881010
$849$	3689.01	0.149124
$850$	0	0
$851$	−1565.22	−0.0630494
$852$	24522.1	0.986048
$853$	−36817.4	−1.47785	−0.738923	−	0.673789i	$-0.764666\pi$
$853$	−36817.4	−1.47785	−0.738923	+	0.673789i	$0.764666\pi$
$854$	−72675.8	−2.91208
$855$	0	0
$856$	−426.845	−0.0170435
$857$	−42922.8	−1.71087	−0.855435	−	0.517911i	$-0.826710\pi$
$857$	−42922.8	−1.71087	−0.855435	+	0.517911i	$0.826710\pi$
$858$	1495.11	0.0594899
$859$	11693.5	0.464468	0.232234	−	0.972660i	$-0.425396\pi$
$859$	11693.5	0.464468	0.232234	+	0.972660i	$0.425396\pi$
$860$	0	0
$861$	35076.1	1.38837
$862$	61496.5	2.42991
$863$	28640.1	1.12969	0.564844	−	0.825198i	$-0.308936\pi$
$863$	28640.1	1.12969	0.564844	+	0.825198i	$0.308936\pi$
$864$	−6923.74	−0.272628
$865$	0	0
$866$	20045.5	0.786574
$867$	8283.23	0.324467
$868$	−6437.72	−0.251740
$869$	9440.76	0.368534
$870$	0	0
$871$	7875.95	0.306391
$872$	−200.589	−0.00778990
$873$	3024.99	0.117274
$874$	−7628.07	−0.295221
$875$	0	0
$876$	−21490.0	−0.828859
$877$	−19344.1	−0.744815	−0.372407	−	0.928069i	$-0.621468\pi$
$877$	−19344.1	−0.744815	−0.372407	+	0.928069i	$0.621468\pi$
$878$	−10012.1	−0.384844
$879$	−15201.7	−0.583321
$880$	0	0
$881$	24160.8	0.923949	0.461974	−	0.886893i	$-0.347141\pi$
$881$	24160.8	0.923949	0.461974	+	0.886893i	$0.347141\pi$
$882$	12530.3	0.478366
$883$	−30965.1	−1.18014	−0.590068	−	0.807354i	$-0.700899\pi$
$883$	−30965.1	−1.18014	−0.590068	+	0.807354i	$0.700899\pi$
$884$	−7979.43	−0.303594
$885$	0	0
$886$	−12197.6	−0.462513
$887$	40432.5	1.53054	0.765270	−	0.643709i	$-0.222605\pi$
$887$	40432.5	1.53054	0.765270	+	0.643709i	$0.222605\pi$
$888$	82.3901	0.00311355
$889$	62903.9	2.37315
$890$	0	0
$891$	−891.000	−0.0335013
$892$	23753.1	0.891606
$893$	11696.9	0.438321
$894$	−25441.5	−0.951778
$895$	0	0
$896$	−754.083	−0.0281162
$897$	433.447	0.0161342
$898$	52831.7	1.96327
$899$	1131.87	0.0419910
$900$	0	0
$901$	−29990.1	−1.10889
$902$	−19612.5	−0.723972
$903$	2857.66	0.105312
$904$	0.0566690	2.08494e−6 0
$905$	0	0
$906$	−40938.9	−1.50122
$907$	−13270.3	−0.485814	−0.242907	−	0.970050i	$-0.578101\pi$
$907$	−13270.3	−0.485814	−0.242907	+	0.970050i	$0.578101\pi$
$908$	18376.6	0.671639
$909$	11494.0	0.419398
$910$	0	0
$911$	43574.4	1.58472	0.792362	−	0.610051i	$-0.208851\pi$
$911$	43574.4	1.58472	0.792362	+	0.610051i	$0.208851\pi$
$912$	−28402.4	−1.03125
$913$	−1274.27	−0.0461909
$914$	67872.7	2.45627
$915$	0	0
$916$	29135.3	1.05093
$917$	−62093.0	−2.23609
$918$	9477.52	0.340746
$919$	41317.7	1.48307	0.741537	−	0.670912i	$-0.234097\pi$
$919$	41317.7	1.48307	0.741537	+	0.670912i	$0.234097\pi$
$920$	0	0
$921$	964.986	0.0345248
$922$	20791.9	0.742674
$923$	−11472.6	−0.409128
$924$	−6985.53	−0.248709
$925$	0	0
$926$	−60497.0	−2.14693
$927$	9680.66	0.342993
$928$	9543.90	0.337601
$929$	−27886.3	−0.984844	−0.492422	−	0.870357i	$-0.663888\pi$
$929$	−27886.3	−0.984844	−0.492422	+	0.870357i	$0.663888\pi$
$930$	0	0
$931$	51763.8	1.82222
$932$	−36825.4	−1.29427
$933$	−15405.8	−0.540582
$934$	54483.8	1.90874
$935$	0	0
$936$	−22.8158	−0.000796749 0
$937$	16036.3	0.559105	0.279553	−	0.960130i	$-0.409814\pi$
$937$	16036.3	0.559105	0.279553	+	0.960130i	$0.409814\pi$
$938$	−73341.2	−2.55296
$939$	−25099.7	−0.872308
$940$	0	0
$941$	−1506.93	−0.0522046	−0.0261023	−	0.999659i	$-0.508310\pi$
$941$	−1506.93	−0.0522046	−0.0261023	+	0.999659i	$0.508310\pi$
$942$	3538.32	0.122383
$943$	−5685.83	−0.196348
$944$	−23965.9	−0.826294
$945$	0	0
$946$	−1597.83	−0.0549154
$947$	7327.03	0.251422	0.125711	−	0.992067i	$-0.459879\pi$
$947$	7327.03	0.251422	0.125711	+	0.992067i	$0.459879\pi$
$948$	−20742.1	−0.710624
$949$	10054.0	0.343907
$950$	0	0
$951$	−23233.8	−0.792228
$952$	516.099	0.0175702
$953$	46874.7	1.59331	0.796653	−	0.604437i	$-0.206602\pi$
$953$	46874.7	1.59331	0.796653	+	0.604437i	$0.206602\pi$
$954$	−12346.0	−0.418989
$955$	0	0
$956$	20267.7	0.685673
$957$	1228.18	0.0414854
$958$	−27369.0	−0.923019
$959$	−5472.45	−0.184270
$960$	0	0
$961$	−28866.1	−0.968954
$962$	−5549.61	−0.185994
$963$	−17134.1	−0.573353
$964$	42900.8	1.43334
$965$	0	0
$966$	−4036.28	−0.134436
$967$	−2812.90	−0.0935437	−0.0467719	−	0.998906i	$-0.514893\pi$
$967$	−2812.90	−0.0935437	−0.0467719	+	0.998906i	$0.514893\pi$
$968$	27.1292	0.000900790 0
$969$	39152.4	1.29799
$970$	0	0
$971$	−45216.4	−1.49440	−0.747200	−	0.664599i	$-0.768602\pi$
$971$	−45216.4	−1.49440	−0.747200	+	0.664599i	$0.768602\pi$
$972$	1957.60	0.0645987
$973$	−16084.2	−0.529944
$974$	−3054.59	−0.100488
$975$	0	0
$976$	43864.5	1.43859
$977$	10647.0	0.348647	0.174323	−	0.984688i	$-0.444226\pi$
$977$	10647.0	0.348647	0.174323	+	0.984688i	$0.444226\pi$
$978$	−34593.4	−1.13106
$979$	−6085.91	−0.198679
$980$	0	0
$981$	−8051.89	−0.262056
$982$	5923.23	0.192483
$983$	1993.76	0.0646909	0.0323455	−	0.999477i	$-0.489702\pi$
$983$	1993.76	0.0646909	0.0323455	+	0.999477i	$0.489702\pi$
$984$	299.291	0.00969618
$985$	0	0
$986$	−13064.1	−0.421954
$987$	6189.22	0.199600
$988$	−13570.1	−0.436966
$989$	−463.226	−0.0148936
$990$	0	0
$991$	−23143.6	−0.741858	−0.370929	−	0.928661i	$-0.620961\pi$
$991$	−23143.6	−0.741858	−0.370929	+	0.928661i	$0.620961\pi$
$992$	7798.71	0.249606
$993$	604.279	0.0193114
$994$	106833.	3.40899
$995$	0	0
$996$	2799.68	0.0890674
$997$	3506.68	0.111392	0.0556959	−	0.998448i	$-0.482262\pi$
$997$	3506.68	0.111392	0.0556959	+	0.998448i	$0.482262\pi$
$998$	−44426.1	−1.40910
$999$	3307.24	0.104741

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.a.bc.1.6		7
3.2	odd	2		2475.4.a.bq.1.2		7
5.2	odd	4		165.4.c.a.34.11	yes	14
5.3	odd	4		165.4.c.a.34.4	✓	14
5.4	even	2		825.4.a.bb.1.2		7
15.2	even	4		495.4.c.c.199.4		14
15.8	even	4		495.4.c.c.199.11		14
15.14	odd	2		2475.4.a.br.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.c.a.34.4	✓	14	5.3	odd	4
165.4.c.a.34.11	yes	14	5.2	odd	4
495.4.c.c.199.4		14	15.2	even	4
495.4.c.c.199.11		14	15.8	even	4
825.4.a.bb.1.2		7	5.4	even	2
825.4.a.bc.1.6		7	1.1	even	1	trivial
2475.4.a.bq.1.2		7	3.2	odd	2
2475.4.a.br.1.6		7	15.14	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00699 q^{2} +3.00000 q^{3} +8.05595 q^{4} +12.0210 q^{6} +26.2766 q^{7} +0.224208 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.00699 q^{2} +3.00000 q^{3} +8.05595 q^{4} +12.0210 q^{6} +26.2766 q^{7} +0.224208 q^{8} +9.00000 q^{9} -11.0000 q^{11} +24.1679 q^{12} -11.3069 q^{13} +105.290 q^{14} -63.5492 q^{16} +87.6018 q^{17} +36.0629 q^{18} +148.978 q^{19} +78.8297 q^{21} -44.0769 q^{22} -12.7783 q^{23} +0.672624 q^{24} -45.3065 q^{26} +27.0000 q^{27} +211.683 q^{28} -37.2177 q^{29} -30.4121 q^{31} -256.435 q^{32} -33.0000 q^{33} +351.019 q^{34} +72.5036 q^{36} +122.491 q^{37} +596.955 q^{38} -33.9206 q^{39} +444.960 q^{41} +315.870 q^{42} +36.2510 q^{43} -88.6155 q^{44} -51.2025 q^{46} +78.5138 q^{47} -190.648 q^{48} +347.458 q^{49} +262.805 q^{51} -91.0876 q^{52} -342.345 q^{53} +108.189 q^{54} +5.89142 q^{56} +446.935 q^{57} -149.131 q^{58} +377.123 q^{59} -690.244 q^{61} -121.861 q^{62} +236.489 q^{63} -519.137 q^{64} -132.231 q^{66} -696.564 q^{67} +705.716 q^{68} -38.3349 q^{69} +1014.66 q^{71} +2.01787 q^{72} -889.198 q^{73} +490.818 q^{74} +1200.16 q^{76} -289.042 q^{77} -135.919 q^{78} -858.251 q^{79} +81.0000 q^{81} +1782.95 q^{82} +115.843 q^{83} +635.048 q^{84} +145.257 q^{86} -111.653 q^{87} -2.46629 q^{88} +553.264 q^{89} -297.106 q^{91} -102.941 q^{92} -91.2363 q^{93} +314.604 q^{94} -769.304 q^{96} +336.110 q^{97} +1392.26 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3 q^{2} + 21 q^{3} + 41 q^{4} + 9 q^{6} + 50 q^{7} + 21 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q + 3 * q^2 + 21 * q^3 + 41 * q^4 + 9 * q^6 + 50 * q^7 + 21 * q^8 + 63 * q^9	\( 7 q + 3 q^{2} + 21 q^{3} + 41 q^{4} + 9 q^{6} + 50 q^{7} + 21 q^{8} + 63 q^{9} - 77 q^{11} + 123 q^{12} + 24 q^{13} + 142 q^{14} + 181 q^{16} + 38 q^{17} + 27 q^{18} + 26 q^{19} + 150 q^{21} - 33 q^{22} + 228 q^{23} + 63 q^{24} + 476 q^{26} + 189 q^{27} + 840 q^{28} + 572 q^{29} - 140 q^{31} + 991 q^{32} - 231 q^{33} - 806 q^{34} + 369 q^{36} - 104 q^{37} + 498 q^{38} + 72 q^{39} + 896 q^{41} + 426 q^{42} + 614 q^{43} - 451 q^{44} - 344 q^{46} + 520 q^{47} + 543 q^{48} + 295 q^{49} + 114 q^{51} - 26 q^{52} + 380 q^{53} + 81 q^{54} + 1522 q^{56} + 78 q^{57} + 1600 q^{58} + 1316 q^{59} - 386 q^{61} + 440 q^{62} + 450 q^{63} + 869 q^{64} - 99 q^{66} + 348 q^{67} + 332 q^{68} + 684 q^{69} + 804 q^{71} + 189 q^{72} + 468 q^{73} - 748 q^{74} - 1698 q^{76} - 550 q^{77} + 1428 q^{78} - 374 q^{79} + 567 q^{81} - 620 q^{82} + 3128 q^{83} + 2520 q^{84} - 2534 q^{86} + 1716 q^{87} - 231 q^{88} + 694 q^{89} - 3376 q^{91} - 1184 q^{92} - 420 q^{93} - 2920 q^{94} + 2973 q^{96} - 8 q^{97} + 4211 q^{98} - 693 q^{99}+O(q^{100}) \) 7 * q + 3 * q^2 + 21 * q^3 + 41 * q^4 + 9 * q^6 + 50 * q^7 + 21 * q^8 + 63 * q^9 - 77 * q^11 + 123 * q^12 + 24 * q^13 + 142 * q^14 + 181 * q^16 + 38 * q^17 + 27 * q^18 + 26 * q^19 + 150 * q^21 - 33 * q^22 + 228 * q^23 + 63 * q^24 + 476 * q^26 + 189 * q^27 + 840 * q^28 + 572 * q^29 - 140 * q^31 + 991 * q^32 - 231 * q^33 - 806 * q^34 + 369 * q^36 - 104 * q^37 + 498 * q^38 + 72 * q^39 + 896 * q^41 + 426 * q^42 + 614 * q^43 - 451 * q^44 - 344 * q^46 + 520 * q^47 + 543 * q^48 + 295 * q^49 + 114 * q^51 - 26 * q^52 + 380 * q^53 + 81 * q^54 + 1522 * q^56 + 78 * q^57 + 1600 * q^58 + 1316 * q^59 - 386 * q^61 + 440 * q^62 + 450 * q^63 + 869 * q^64 - 99 * q^66 + 348 * q^67 + 332 * q^68 + 684 * q^69 + 804 * q^71 + 189 * q^72 + 468 * q^73 - 748 * q^74 - 1698 * q^76 - 550 * q^77 + 1428 * q^78 - 374 * q^79 + 567 * q^81 - 620 * q^82 + 3128 * q^83 + 2520 * q^84 - 2534 * q^86 + 1716 * q^87 - 231 * q^88 + 694 * q^89 - 3376 * q^91 - 1184 * q^92 - 420 * q^93 - 2920 * q^94 + 2973 * q^96 - 8 * q^97 + 4211 * q^98 - 693 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more