LMFDB - Embedded newform 538.4.a.c.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,4,Mod(1,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("538.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	538.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:	$31.7430275831$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 8 x^{17} - 299 x^{16} + 2191 x^{15} + 37840 x^{14} - 247598 x^{13} - 2647415 x^{12} + \cdots - 88752454191 $ x^18 - 8x^17 - 299x^16 + 2191x^15 + 37840x^14 - 247598x^13 - 2647415x^12 + 14946954x^11 + 112143744x^10 - 520080033x^9 - 2953528791x^8 + 10430700798x^7 + 47410674521x^6 - 111852486489x^5 - 425662048215x^4 + 497952330084x^3 + 1645078311180x^2 - 37397915784*x - 88752454191
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$7.35951$ of defining polynomial
Character	$\chi$	$=$	538.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} +6.35951 q^{3} +4.00000 q^{4} +6.17843 q^{5} -12.7190 q^{6} -27.3928 q^{7} -8.00000 q^{8} +13.4434 q^{9} -12.3569 q^{10} -40.4875 q^{11} +25.4381 q^{12} +70.4369 q^{13} +54.7855 q^{14} +39.2918 q^{15} +16.0000 q^{16} -109.655 q^{17} -26.8868 q^{18} +124.330 q^{19} +24.7137 q^{20} -174.205 q^{21} +80.9751 q^{22} +47.2294 q^{23} -50.8761 q^{24} -86.8270 q^{25} -140.874 q^{26} -86.2134 q^{27} -109.571 q^{28} -275.186 q^{29} -78.5836 q^{30} +78.4699 q^{31} -32.0000 q^{32} -257.481 q^{33} +219.309 q^{34} -169.244 q^{35} +53.7736 q^{36} -411.965 q^{37} -248.660 q^{38} +447.945 q^{39} -49.4275 q^{40} +367.077 q^{41} +348.409 q^{42} -323.524 q^{43} -161.950 q^{44} +83.0592 q^{45} -94.4588 q^{46} -345.631 q^{47} +101.752 q^{48} +407.364 q^{49} +173.654 q^{50} -697.350 q^{51} +281.748 q^{52} -183.659 q^{53} +172.427 q^{54} -250.150 q^{55} +219.142 q^{56} +790.678 q^{57} +550.373 q^{58} +4.65834 q^{59} +157.167 q^{60} -178.061 q^{61} -156.940 q^{62} -368.252 q^{63} +64.0000 q^{64} +435.190 q^{65} +514.962 q^{66} -184.917 q^{67} -438.619 q^{68} +300.356 q^{69} +338.489 q^{70} -429.952 q^{71} -107.547 q^{72} +608.426 q^{73} +823.930 q^{74} -552.177 q^{75} +497.320 q^{76} +1109.07 q^{77} -895.889 q^{78} +535.072 q^{79} +98.8549 q^{80} -911.247 q^{81} -734.155 q^{82} -601.154 q^{83} -696.819 q^{84} -677.494 q^{85} +647.048 q^{86} -1750.05 q^{87} +323.900 q^{88} -479.696 q^{89} -166.118 q^{90} -1929.46 q^{91} +188.918 q^{92} +499.030 q^{93} +691.261 q^{94} +768.164 q^{95} -203.504 q^{96} +903.154 q^{97} -814.728 q^{98} -544.290 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 36 q^{2} - 10 q^{3} + 72 q^{4} - 26 q^{5} + 20 q^{6} - 9 q^{7} - 144 q^{8} + 178 q^{9} + 52 q^{10} - 130 q^{11} - 40 q^{12} - 27 q^{13} + 18 q^{14} - 143 q^{15} + 288 q^{16} - 110 q^{17} - 356 q^{18}+ \cdots - 9455 q^{99}+O(q^{100}) $ 18 * q - 36 * q^2 - 10 * q^3 + 72 * q^4 - 26 * q^5 + 20 * q^6 - 9 * q^7 - 144 * q^8 + 178 * q^9 + 52 * q^10 - 130 * q^11 - 40 * q^12 - 27 * q^13 + 18 * q^14 - 143 * q^15 + 288 * q^16 - 110 * q^17 - 356 * q^18 - 47 * q^19 - 104 * q^20 + 69 * q^21 + 260 * q^22 - 329 * q^23 + 80 * q^24 + 442 * q^25 + 54 * q^26 - 325 * q^27 - 36 * q^28 - 3 * q^29 + 286 * q^30 + 97 * q^31 - 576 * q^32 - 129 * q^33 + 220 * q^34 - 834 * q^35 + 712 * q^36 - 104 * q^37 + 94 * q^38 - 242 * q^39 + 208 * q^40 + 196 * q^41 - 138 * q^42 - 547 * q^43 - 520 * q^44 - 481 * q^45 + 658 * q^46 - 1074 * q^47 - 160 * q^48 + 1315 * q^49 - 884 * q^50 - 1475 * q^51 - 108 * q^52 - 1681 * q^53 + 650 * q^54 + 163 * q^55 + 72 * q^56 - 1178 * q^57 + 6 * q^58 - 924 * q^59 - 572 * q^60 + 640 * q^61 - 194 * q^62 - 445 * q^63 + 1152 * q^64 - 2052 * q^65 + 258 * q^66 - 1685 * q^67 - 440 * q^68 - 1787 * q^69 + 1668 * q^70 - 3635 * q^71 - 1424 * q^72 - 1136 * q^73 + 208 * q^74 - 3332 * q^75 - 188 * q^76 - 5512 * q^77 + 484 * q^78 - 406 * q^79 - 416 * q^80 - 3194 * q^81 - 392 * q^82 - 6854 * q^83 + 276 * q^84 - 1227 * q^85 + 1094 * q^86 - 8831 * q^87 + 1040 * q^88 - 4690 * q^89 + 962 * q^90 - 5743 * q^91 - 1316 * q^92 - 4097 * q^93 + 2148 * q^94 - 3332 * q^95 + 320 * q^96 - 4132 * q^97 - 2630 * q^98 - 9455 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	6.35951	1.22389	0.611944	−	0.790901i	$-0.290388\pi$
$3$	6.35951	1.22389	0.611944	+	0.790901i	$0.290388\pi$
$4$	4.00000	0.500000
$5$	6.17843	0.552616	0.276308	−	0.961069i	$-0.410889\pi$
$5$	6.17843	0.552616	0.276308	+	0.961069i	$0.410889\pi$
$6$	−12.7190	−0.865420
$7$	−27.3928	−1.47907	−0.739535	−	0.673118i	$-0.764955\pi$
$7$	−27.3928	−1.47907	−0.739535	+	0.673118i	$0.764955\pi$
$8$	−8.00000	−0.353553
$9$	13.4434	0.497904
$10$	−12.3569	−0.390758
$11$	−40.4875	−1.10977	−0.554884	−	0.831928i	$-0.687237\pi$
$11$	−40.4875	−1.10977	−0.554884	+	0.831928i	$0.687237\pi$
$12$	25.4381	0.611944
$13$	70.4369	1.50275	0.751373	−	0.659878i	$-0.229392\pi$
$13$	70.4369	1.50275	0.751373	+	0.659878i	$0.229392\pi$
$14$	54.7855	1.04586
$15$	39.2918	0.676340
$16$	16.0000	0.250000
$17$	−109.655	−1.56442	−0.782211	−	0.623014i	$-0.785908\pi$
$17$	−109.655	−1.56442	−0.782211	+	0.623014i	$0.785908\pi$
$18$	−26.8868	−0.352071
$19$	124.330	1.50122	0.750612	−	0.660743i	$-0.229759\pi$
$19$	124.330	1.50122	0.750612	+	0.660743i	$0.229759\pi$
$20$	24.7137	0.276308
$21$	−174.205	−1.81022
$22$	80.9751	0.784725
$23$	47.2294	0.428175	0.214087	−	0.976815i	$-0.431322\pi$
$23$	47.2294	0.428175	0.214087	+	0.976815i	$0.431322\pi$
$24$	−50.8761	−0.432710
$25$	−86.8270	−0.694616
$26$	−140.874	−1.06260
$27$	−86.2134	−0.614510
$28$	−109.571	−0.739535
$29$	−275.186	−1.76210	−0.881049	−	0.473026i	$-0.843162\pi$
$29$	−275.186	−1.76210	−0.881049	+	0.473026i	$0.843162\pi$
$30$	−78.5836	−0.478245
$31$	78.4699	0.454633	0.227316	−	0.973821i	$-0.427005\pi$
$31$	78.4699	0.454633	0.227316	+	0.973821i	$0.427005\pi$
$32$	−32.0000	−0.176777
$33$	−257.481	−1.35823
$34$	219.309	1.10621
$35$	−169.244	−0.817358
$36$	53.7736	0.248952
$37$	−411.965	−1.83045	−0.915225	−	0.402943i	$-0.867987\pi$
$37$	−411.965	−1.83045	−0.915225	+	0.402943i	$0.867987\pi$
$38$	−248.660	−1.06153
$39$	447.945	1.83919
$40$	−49.4275	−0.195379
$41$	367.077	1.39824	0.699120	−	0.715004i	$-0.253575\pi$
$41$	367.077	1.39824	0.699120	+	0.715004i	$0.253575\pi$
$42$	348.409	1.28002
$43$	−323.524	−1.14737	−0.573686	−	0.819075i	$-0.694487\pi$
$43$	−323.524	−1.14737	−0.573686	+	0.819075i	$0.694487\pi$
$44$	−161.950	−0.554884
$45$	83.0592	0.275150
$46$	−94.4588	−0.302765
$47$	−345.631	−1.07267	−0.536334	−	0.844006i	$-0.680191\pi$
$47$	−345.631	−1.07267	−0.536334	+	0.844006i	$0.680191\pi$
$48$	101.752	0.305972
$49$	407.364	1.18765
$50$	173.654	0.491167
$51$	−697.350	−1.91468
$52$	281.748	0.751373
$53$	−183.659	−0.475991	−0.237995	−	0.971266i	$-0.576490\pi$
$53$	−183.659	−0.475991	−0.237995	+	0.971266i	$0.576490\pi$
$54$	172.427	0.434524
$55$	−250.150	−0.613276
$56$	219.142	0.522930
$57$	790.678	1.83733
$58$	550.373	1.24599
$59$	4.65834	0.0102790	0.00513952	−	0.999987i	$-0.498364\pi$
$59$	4.65834	0.0102790	0.00513952	+	0.999987i	$0.498364\pi$
$60$	157.167	0.338170
$61$	−178.061	−0.373744	−0.186872	−	0.982384i	$-0.559835\pi$
$61$	−178.061	−0.373744	−0.186872	+	0.982384i	$0.559835\pi$
$62$	−156.940	−0.321474
$63$	−368.252	−0.736435
$64$	64.0000	0.125000
$65$	435.190	0.830441
$66$	514.962	0.960416
$67$	−184.917	−0.337183	−0.168591	−	0.985686i	$-0.553922\pi$
$67$	−184.917	−0.337183	−0.168591	+	0.985686i	$0.553922\pi$
$68$	−438.619	−0.782211
$69$	300.356	0.524038
$70$	338.489	0.577959
$71$	−429.952	−0.718675	−0.359337	−	0.933208i	$-0.616997\pi$
$71$	−429.952	−0.718675	−0.359337	+	0.933208i	$0.616997\pi$
$72$	−107.547	−0.176036
$73$	608.426	0.975492	0.487746	−	0.872986i	$-0.337819\pi$
$73$	608.426	0.975492	0.487746	+	0.872986i	$0.337819\pi$
$74$	823.930	1.29432
$75$	−552.177	−0.850132
$76$	497.320	0.750612
$77$	1109.07	1.64143
$78$	−895.889	−1.30051
$79$	535.072	0.762029	0.381015	−	0.924569i	$-0.375575\pi$
$79$	535.072	0.762029	0.381015	+	0.924569i	$0.375575\pi$
$80$	98.8549	0.138154
$81$	−911.247	−1.25000
$82$	−734.155	−0.988705
$83$	−601.154	−0.795003	−0.397502	−	0.917601i	$-0.630123\pi$
$83$	−601.154	−0.795003	−0.397502	+	0.917601i	$0.630123\pi$
$84$	−696.819	−0.905109
$85$	−677.494	−0.864524
$86$	647.048	0.811314
$87$	−1750.05	−2.15661
$88$	323.900	0.392362
$89$	−479.696	−0.571322	−0.285661	−	0.958331i	$-0.592213\pi$
$89$	−479.696	−0.571322	−0.285661	+	0.958331i	$0.592213\pi$
$90$	−166.118	−0.194560
$91$	−1929.46	−2.22267
$92$	188.918	0.214087
$93$	499.030	0.556420
$94$	691.261	0.758491
$95$	768.164	0.829600
$96$	−203.504	−0.216355
$97$	903.154	0.945376	0.472688	−	0.881230i	$-0.343284\pi$
$97$	903.154	0.945376	0.472688	+	0.881230i	$0.343284\pi$
$98$	−814.728	−0.839796
$99$	−544.290	−0.552558
$100$	−347.308	−0.347308
$101$	1647.75	1.62334	0.811669	−	0.584118i	$-0.198559\pi$
$101$	1647.75	1.62334	0.811669	+	0.584118i	$0.198559\pi$
$102$	1394.70	1.35388
$103$	−893.871	−0.855104	−0.427552	−	0.903991i	$-0.640624\pi$
$103$	−893.871	−0.855104	−0.427552	+	0.903991i	$0.640624\pi$
$104$	−563.495	−0.531301
$105$	−1076.31	−1.00036
$106$	367.318	0.336576
$107$	−328.384	−0.296693	−0.148346	−	0.988935i	$-0.547395\pi$
$107$	−328.384	−0.296693	−0.148346	+	0.988935i	$0.547395\pi$
$108$	−344.853	−0.307255
$109$	−1566.74	−1.37675	−0.688376	−	0.725354i	$-0.741676\pi$
$109$	−1566.74	−1.37675	−0.688376	+	0.725354i	$0.741676\pi$
$110$	500.299	0.433651
$111$	−2619.90	−2.24027
$112$	−438.284	−0.369768
$113$	−572.155	−0.476317	−0.238158	−	0.971226i	$-0.576544\pi$
$113$	−572.155	−0.476317	−0.238158	+	0.971226i	$0.576544\pi$
$114$	−1581.36	−1.29919
$115$	291.804	0.236616
$116$	−1100.75	−0.881049
$117$	946.912	0.748222
$118$	−9.31667	−0.00726838
$119$	3003.75	2.31389
$120$	−314.335	−0.239122
$121$	308.241	0.231586
$122$	356.122	0.264277
$123$	2334.43	1.71129
$124$	313.880	0.227316
$125$	−1308.76	−0.936472
$126$	736.504	0.520738
$127$	1310.29	0.915506	0.457753	−	0.889079i	$-0.348654\pi$
$127$	1310.29	0.915506	0.457753	+	0.889079i	$0.348654\pi$
$128$	−128.000	−0.0883883
$129$	−2057.46	−1.40426
$130$	−870.380	−0.587210
$131$	−553.665	−0.369267	−0.184633	−	0.982807i	$-0.559110\pi$
$131$	−553.665	−0.369267	−0.184633	+	0.982807i	$0.559110\pi$
$132$	−1029.92	−0.679117
$133$	−3405.74	−2.22042
$134$	369.835	0.238424
$135$	−532.664	−0.339588
$136$	877.237	0.553107
$137$	2665.66	1.66235	0.831177	−	0.556009i	$-0.187668\pi$
$137$	2665.66	1.66235	0.831177	+	0.556009i	$0.187668\pi$
$138$	−600.712	−0.370551
$139$	131.133	0.0800185	0.0400093	−	0.999199i	$-0.487261\pi$
$139$	131.133	0.0800185	0.0400093	+	0.999199i	$0.487261\pi$
$140$	−676.978	−0.408679
$141$	−2198.04	−1.31283
$142$	859.904	0.508180
$143$	−2851.82	−1.66770
$144$	215.094	0.124476
$145$	−1700.22	−0.973763
$146$	−1216.85	−0.689777
$147$	2590.64	1.45355
$148$	−1647.86	−0.915225
$149$	−439.481	−0.241635	−0.120818	−	0.992675i	$-0.538552\pi$
$149$	−439.481	−0.241635	−0.120818	+	0.992675i	$0.538552\pi$
$150$	1104.35	0.601134
$151$	−1887.85	−1.01742	−0.508711	−	0.860937i	$-0.669878\pi$
$151$	−1887.85	−1.01742	−0.508711	+	0.860937i	$0.669878\pi$
$152$	−994.640	−0.530763
$153$	−1474.13	−0.778931
$154$	−2218.13	−1.16066
$155$	484.821	0.251237
$156$	1791.78	0.919597
$157$	3238.51	1.64625	0.823126	−	0.567859i	$-0.192228\pi$
$157$	3238.51	1.64625	0.823126	+	0.567859i	$0.192228\pi$
$158$	−1070.14	−0.538836
$159$	−1167.98	−0.582560
$160$	−197.710	−0.0976896
$161$	−1293.74	−0.633300
$162$	1822.49	0.883880
$163$	−663.913	−0.319029	−0.159514	−	0.987196i	$-0.550993\pi$
$163$	−663.913	−0.319029	−0.159514	+	0.987196i	$0.550993\pi$
$164$	1468.31	0.699120
$165$	−1590.83	−0.750581
$166$	1202.31	0.562152
$167$	−3567.76	−1.65318	−0.826591	−	0.562803i	$-0.809723\pi$
$167$	−3567.76	−1.65318	−0.826591	+	0.562803i	$0.809723\pi$
$168$	1393.64	0.640009
$169$	2764.36	1.25824
$170$	1354.99	0.611311
$171$	1671.42	0.747465
$172$	−1294.10	−0.573686
$173$	1103.31	0.484874	0.242437	−	0.970167i	$-0.422053\pi$
$173$	1103.31	0.484874	0.242437	+	0.970167i	$0.422053\pi$
$174$	3500.10	1.52495
$175$	2378.43	1.02739
$176$	−647.801	−0.277442
$177$	29.6247	0.0125804
$178$	959.392	0.403986
$179$	3368.29	1.40647	0.703233	−	0.710959i	$-0.251739\pi$
$179$	3368.29	1.40647	0.703233	+	0.710959i	$0.251739\pi$
$180$	332.237	0.137575
$181$	1780.04	0.730992	0.365496	−	0.930813i	$-0.380899\pi$
$181$	1780.04	0.730992	0.365496	+	0.930813i	$0.380899\pi$
$182$	3858.93	1.57166
$183$	−1132.38	−0.457421
$184$	−377.835	−0.151383
$185$	−2545.30	−1.01154
$186$	−998.061	−0.393448
$187$	4439.65	1.73615
$188$	−1382.52	−0.536334
$189$	2361.62	0.908904
$190$	−1536.33	−0.586616
$191$	−330.785	−0.125313	−0.0626564	−	0.998035i	$-0.519957\pi$
$191$	−330.785	−0.125313	−0.0626564	+	0.998035i	$0.519957\pi$
$192$	407.009	0.152986
$193$	−1215.48	−0.453328	−0.226664	−	0.973973i	$-0.572782\pi$
$193$	−1215.48	−0.453328	−0.226664	+	0.973973i	$0.572782\pi$
$194$	−1806.31	−0.668481
$195$	2767.60	1.01637
$196$	1629.46	0.593825
$197$	1866.53	0.675051	0.337526	−	0.941316i	$-0.390410\pi$
$197$	1866.53	0.675051	0.337526	+	0.941316i	$0.390410\pi$
$198$	1088.58	0.390717
$199$	3625.79	1.29158	0.645792	−	0.763513i	$-0.276527\pi$
$199$	3625.79	1.29158	0.645792	+	0.763513i	$0.276527\pi$
$200$	694.616	0.245584
$201$	−1175.98	−0.412674
$202$	−3295.50	−1.14787
$203$	7538.12	2.60627
$204$	−2789.40	−0.957339
$205$	2267.96	0.772690
$206$	1787.74	0.604650
$207$	634.924	0.213190
$208$	1126.99	0.375686
$209$	−5033.81	−1.66601
$210$	2152.62	0.707358
$211$	−3798.32	−1.23928	−0.619638	−	0.784887i	$-0.712721\pi$
$211$	−3798.32	−1.23928	−0.619638	+	0.784887i	$0.712721\pi$
$212$	−734.636	−0.237995
$213$	−2734.28	−0.879578
$214$	656.769	0.209793
$215$	−1998.87	−0.634056
$216$	689.707	0.217262
$217$	−2149.51	−0.672434
$218$	3133.47	0.973511
$219$	3869.30	1.19389
$220$	−1000.60	−0.306638
$221$	−7723.74	−2.35093
$222$	5239.79	1.58411
$223$	−3788.32	−1.13760	−0.568800	−	0.822476i	$-0.692592\pi$
$223$	−3788.32	−1.13760	−0.568800	+	0.822476i	$0.692592\pi$
$224$	876.569	0.261465
$225$	−1167.25	−0.345852
$226$	1144.31	0.336807
$227$	−1698.92	−0.496745	−0.248373	−	0.968665i	$-0.579896\pi$
$227$	−1698.92	−0.496745	−0.248373	+	0.968665i	$0.579896\pi$
$228$	3162.71	0.918665
$229$	4577.02	1.32078	0.660388	−	0.750925i	$-0.270392\pi$
$229$	4577.02	1.32078	0.660388	+	0.750925i	$0.270392\pi$
$230$	−583.608	−0.167313
$231$	7053.12	2.00892
$232$	2201.49	0.622995
$233$	780.610	0.219483	0.109741	−	0.993960i	$-0.464998\pi$
$233$	780.610	0.219483	0.109741	+	0.993960i	$0.464998\pi$
$234$	−1893.82	−0.529073
$235$	−2135.46	−0.592773
$236$	18.6333	0.00513952
$237$	3402.80	0.932639
$238$	−6007.49	−1.63617
$239$	−1222.46	−0.330854	−0.165427	−	0.986222i	$-0.552900\pi$
$239$	−1222.46	−0.330854	−0.165427	+	0.986222i	$0.552900\pi$
$240$	628.669	0.169085
$241$	1200.72	0.320934	0.160467	−	0.987041i	$-0.448700\pi$
$241$	1200.72	0.320934	0.160467	+	0.987041i	$0.448700\pi$
$242$	−616.482	−0.163756
$243$	−3467.32	−0.915346
$244$	−712.245	−0.186872
$245$	2516.87	0.656314
$246$	−4668.87	−1.21007
$247$	8757.42	2.25596
$248$	−627.759	−0.160737
$249$	−3823.05	−0.972996
$250$	2617.52	0.662185
$251$	−5592.27	−1.40630	−0.703150	−	0.711042i	$-0.748224\pi$
$251$	−5592.27	−1.40630	−0.703150	+	0.711042i	$0.748224\pi$
$252$	−1473.01	−0.368217
$253$	−1912.20	−0.475175
$254$	−2620.58	−0.647361
$255$	−4308.53	−1.05808
$256$	256.000	0.0625000
$257$	−1159.99	−0.281550	−0.140775	−	0.990042i	$-0.544959\pi$
$257$	−1159.99	−0.281550	−0.140775	+	0.990042i	$0.544959\pi$
$258$	4114.91	0.992958
$259$	11284.9	2.70737
$260$	1740.76	0.415220
$261$	−3699.44	−0.877355
$262$	1107.33	0.261111
$263$	2853.19	0.668954	0.334477	−	0.942404i	$-0.391440\pi$
$263$	2853.19	0.668954	0.334477	+	0.942404i	$0.391440\pi$
$264$	2059.85	0.480208
$265$	−1134.73	−0.263040
$266$	6811.49	1.57007
$267$	−3050.63	−0.699235
$268$	−739.669	−0.168591
$269$	269.000	0.0609711
$269$	269.000	0.0609711
$270$	1065.33	0.240125
$271$	5693.80	1.27629	0.638143	−	0.769918i	$-0.279703\pi$
$271$	5693.80	1.27629	0.638143	+	0.769918i	$0.279703\pi$
$272$	−1754.47	−0.391105
$273$	−12270.4	−2.72030
$274$	−5331.31	−1.17546
$275$	3515.41	0.770863
$276$	1201.42	0.262019
$277$	7862.07	1.70537	0.852683	−	0.522429i	$-0.174974\pi$
$277$	7862.07	1.70537	0.852683	+	0.522429i	$0.174974\pi$
$278$	−262.267	−0.0565817
$279$	1054.90	0.226363
$280$	1353.96	0.288980
$281$	6976.11	1.48099	0.740497	−	0.672059i	$-0.234590\pi$
$281$	6976.11	1.48099	0.740497	+	0.672059i	$0.234590\pi$
$282$	4396.08	0.928309
$283$	−3720.29	−0.781443	−0.390722	−	0.920509i	$-0.627774\pi$
$283$	−3720.29	−0.781443	−0.390722	+	0.920509i	$0.627774\pi$
$284$	−1719.81	−0.359337
$285$	4885.15	1.01534
$286$	5703.64	1.17924
$287$	−10055.3	−2.06810
$288$	−430.189	−0.0880178
$289$	7111.15	1.44741
$290$	3400.44	0.688554
$291$	5743.62	1.15703
$292$	2433.71	0.487746
$293$	4601.52	0.917487	0.458743	−	0.888569i	$-0.348300\pi$
$293$	4601.52	0.917487	0.458743	+	0.888569i	$0.348300\pi$
$294$	−5181.27	−1.02782
$295$	28.7812	0.00568036
$296$	3295.72	0.647162
$297$	3490.57	0.681964
$298$	878.962	0.170862
$299$	3326.70	0.643437
$300$	−2208.71	−0.425066
$301$	8862.23	1.69704
$302$	3775.69	0.719426
$303$	10478.9	1.98678
$304$	1989.28	0.375306
$305$	−1100.14	−0.206537
$306$	2948.26	0.550788
$307$	2573.22	0.478376	0.239188	−	0.970973i	$-0.423119\pi$
$307$	2573.22	0.478376	0.239188	+	0.970973i	$0.423119\pi$
$308$	4436.26	0.820713
$309$	−5684.58	−1.04655
$310$	−969.642	−0.177652
$311$	−2998.14	−0.546653	−0.273327	−	0.961921i	$-0.588124\pi$
$311$	−2998.14	−0.546653	−0.273327	+	0.961921i	$0.588124\pi$
$312$	−3583.56	−0.650253
$313$	7468.20	1.34865	0.674325	−	0.738435i	$-0.264435\pi$
$313$	7468.20	1.34865	0.674325	+	0.738435i	$0.264435\pi$
$314$	−6477.03	−1.16408
$315$	−2275.22	−0.406966
$316$	2140.29	0.381015
$317$	−8629.09	−1.52889	−0.764445	−	0.644689i	$-0.776987\pi$
$317$	−8629.09	−1.52889	−0.764445	+	0.644689i	$0.776987\pi$
$318$	2335.96	0.411932
$319$	11141.6	1.95552
$320$	395.420	0.0690770
$321$	−2088.37	−0.363119
$322$	2587.49	0.447811
$323$	−13633.4	−2.34855
$324$	−3644.99	−0.624998
$325$	−6115.82	−1.04383
$326$	1327.83	0.225587
$327$	−9963.67	−1.68499
$328$	−2936.62	−0.494353
$329$	9467.78	1.58655
$330$	3181.66	0.530741
$331$	−8905.99	−1.47891	−0.739453	−	0.673209i	$-0.764916\pi$
$331$	−8905.99	−1.47891	−0.739453	+	0.673209i	$0.764916\pi$
$332$	−2404.62	−0.397502
$333$	−5538.21	−0.911388
$334$	7135.52	1.16898
$335$	−1142.50	−0.186332
$336$	−2787.28	−0.452555
$337$	−3263.04	−0.527446	−0.263723	−	0.964598i	$-0.584950\pi$
$337$	−3263.04	−0.527446	−0.263723	+	0.964598i	$0.584950\pi$
$338$	−5528.72	−0.889712
$339$	−3638.62	−0.582959
$340$	−2709.98	−0.432262
$341$	−3177.05	−0.504537
$342$	−3342.84	−0.528537
$343$	−1763.11	−0.277548
$344$	2588.19	0.405657
$345$	1855.73	0.289592
$346$	−2206.62	−0.342858
$347$	−4533.53	−0.701362	−0.350681	−	0.936495i	$-0.614050\pi$
$347$	−4533.53	−0.701362	−0.350681	+	0.936495i	$0.614050\pi$
$348$	−7000.20	−1.07831
$349$	6669.32	1.02292	0.511462	−	0.859306i	$-0.329104\pi$
$349$	6669.32	1.02292	0.511462	+	0.859306i	$0.329104\pi$
$350$	−4756.86	−0.726471
$351$	−6072.60	−0.923452
$352$	1295.60	0.196181
$353$	−7899.51	−1.19107	−0.595536	−	0.803329i	$-0.703060\pi$
$353$	−7899.51	−1.19107	−0.595536	+	0.803329i	$0.703060\pi$
$354$	−59.2495	−0.00889569
$355$	−2656.43	−0.397151
$356$	−1918.78	−0.285661
$357$	19102.4	2.83194
$358$	−6736.57	−0.994522
$359$	−2084.92	−0.306513	−0.153256	−	0.988186i	$-0.548976\pi$
$359$	−2084.92	−0.306513	−0.153256	+	0.988186i	$0.548976\pi$
$360$	−664.473	−0.0972800
$361$	8598.94	1.25367
$362$	−3560.08	−0.516889
$363$	1960.26	0.283435
$364$	−7717.85	−1.11133
$365$	3759.12	0.539073
$366$	2264.77	0.323446
$367$	−8620.84	−1.22617	−0.613085	−	0.790017i	$-0.710072\pi$
$367$	−8620.84	−1.22617	−0.613085	+	0.790017i	$0.710072\pi$
$368$	755.671	0.107044
$369$	4934.77	0.696189
$370$	5090.60	0.715264
$371$	5030.93	0.704024
$372$	1996.12	0.278210
$373$	8148.00	1.13107	0.565533	−	0.824726i	$-0.308671\pi$
$373$	8148.00	1.13107	0.565533	+	0.824726i	$0.308671\pi$
$374$	−8879.30	−1.22764
$375$	−8323.07	−1.14614
$376$	2765.04	0.379245
$377$	−19383.3	−2.64798
$378$	−4723.25	−0.642692
$379$	−6970.22	−0.944686	−0.472343	−	0.881415i	$-0.656592\pi$
$379$	−6970.22	−0.944686	−0.472343	+	0.881415i	$0.656592\pi$
$380$	3072.66	0.414800
$381$	8332.79	1.12048
$382$	661.569	0.0886095
$383$	−1444.60	−0.192730	−0.0963649	−	0.995346i	$-0.530722\pi$
$383$	−1444.60	−0.192730	−0.0963649	+	0.995346i	$0.530722\pi$
$384$	−814.018	−0.108178
$385$	6852.29	0.907078
$386$	2430.96	0.320551
$387$	−4349.27	−0.571281
$388$	3612.62	0.472688
$389$	−12982.9	−1.69219	−0.846094	−	0.533033i	$-0.821052\pi$
$389$	−12982.9	−1.69219	−0.846094	+	0.533033i	$0.821052\pi$
$390$	−5535.19	−0.718680
$391$	−5178.93	−0.669845
$392$	−3258.91	−0.419898
$393$	−3521.04	−0.451942
$394$	−3733.07	−0.477333
$395$	3305.91	0.421109
$396$	−2177.16	−0.276279
$397$	−2000.41	−0.252890	−0.126445	−	0.991974i	$-0.540357\pi$
$397$	−2000.41	−0.252890	−0.126445	+	0.991974i	$0.540357\pi$
$398$	−7251.57	−0.913288
$399$	−21658.9	−2.71754
$400$	−1389.23	−0.173654
$401$	−10956.7	−1.36447	−0.682236	−	0.731132i	$-0.738992\pi$
$401$	−10956.7	−1.36447	−0.682236	+	0.731132i	$0.738992\pi$
$402$	2351.97	0.291805
$403$	5527.18	0.683197
$404$	6590.99	0.811669
$405$	−5630.08	−0.690767
$406$	−15076.2	−1.84291
$407$	16679.5	2.03138
$408$	5578.80	0.676941
$409$	7376.63	0.891812	0.445906	−	0.895080i	$-0.352882\pi$
$409$	7376.63	0.891812	0.445906	+	0.895080i	$0.352882\pi$
$410$	−4535.93	−0.546374
$411$	16952.3	2.03454
$412$	−3575.48	−0.427552
$413$	−127.605	−0.0152034
$414$	−1269.85	−0.150748
$415$	−3714.19	−0.439331
$416$	−2253.98	−0.265650
$417$	833.944	0.0979338
$418$	10067.6	1.17805
$419$	678.679	0.0791304	0.0395652	−	0.999217i	$-0.487403\pi$
$419$	678.679	0.0791304	0.0395652	+	0.999217i	$0.487403\pi$
$420$	−4305.25	−0.500178
$421$	−30.7798	−0.00356322	−0.00178161	−	0.999998i	$-0.500567\pi$
$421$	−30.7798	−0.00356322	−0.00178161	+	0.999998i	$0.500567\pi$
$422$	7596.65	0.876301
$423$	−4646.45	−0.534085
$424$	1469.27	0.168288
$425$	9520.98	1.08667
$426$	5468.57	0.621956
$427$	4877.59	0.552794
$428$	−1313.54	−0.148346
$429$	−18136.2	−2.04108
$430$	3997.75	0.448345
$431$	10181.0	1.13783	0.568914	−	0.822397i	$-0.307364\pi$
$431$	10181.0	1.13783	0.568914	+	0.822397i	$0.307364\pi$
$432$	−1379.41	−0.153628
$433$	−3149.27	−0.349525	−0.174762	−	0.984611i	$-0.555916\pi$
$433$	−3149.27	−0.349525	−0.174762	+	0.984611i	$0.555916\pi$
$434$	4299.02	0.475483
$435$	−10812.6	−1.19178
$436$	−6266.94	−0.688376
$437$	5872.03	0.642786
$438$	−7738.59	−0.844211
$439$	9021.45	0.980798	0.490399	−	0.871498i	$-0.336851\pi$
$439$	9021.45	0.980798	0.490399	+	0.871498i	$0.336851\pi$
$440$	2001.20	0.216826
$441$	5476.36	0.591336
$442$	15447.5	1.66236
$443$	−6946.79	−0.745038	−0.372519	−	0.928025i	$-0.621506\pi$
$443$	−6946.79	−0.745038	−0.372519	+	0.928025i	$0.621506\pi$
$444$	−10479.6	−1.12013
$445$	−2963.77	−0.315722
$446$	7576.64	0.804405
$447$	−2794.88	−0.295735
$448$	−1753.14	−0.184884
$449$	−1814.13	−0.190677	−0.0953384	−	0.995445i	$-0.530393\pi$
$449$	−1814.13	−0.190677	−0.0953384	+	0.995445i	$0.530393\pi$
$450$	2334.50	0.244554
$451$	−14862.1	−1.55172
$452$	−2288.62	−0.238158
$453$	−12005.8	−1.24521
$454$	3397.84	0.351252
$455$	−11921.1	−1.22828
$456$	−6325.42	−0.649595
$457$	−7242.82	−0.741368	−0.370684	−	0.928759i	$-0.620877\pi$
$457$	−7242.82	−0.741368	−0.370684	+	0.928759i	$0.620877\pi$
$458$	−9154.03	−0.933930
$459$	9453.70	0.961353
$460$	1167.22	0.118308
$461$	−10017.5	−1.01207	−0.506033	−	0.862514i	$-0.668888\pi$
$461$	−10017.5	−1.01207	−0.506033	+	0.862514i	$0.668888\pi$
$462$	−14106.2	−1.42052
$463$	9661.74	0.969804	0.484902	−	0.874568i	$-0.338855\pi$
$463$	9661.74	0.969804	0.484902	+	0.874568i	$0.338855\pi$
$464$	−4402.98	−0.440524
$465$	3083.23	0.307486
$466$	−1561.22	−0.155198
$467$	−13821.0	−1.36950	−0.684751	−	0.728777i	$-0.740089\pi$
$467$	−13821.0	−1.36950	−0.684751	+	0.728777i	$0.740089\pi$
$468$	3787.65	0.374111
$469$	5065.40	0.498717
$470$	4270.91	0.419154
$471$	20595.4	2.01483
$472$	−37.2667	−0.00363419
$473$	13098.7	1.27332
$474$	−6805.59	−0.659475
$475$	−10795.2	−1.04277
$476$	12015.0	1.15695
$477$	−2469.00	−0.236998
$478$	2444.91	0.233949
$479$	7605.97	0.725523	0.362762	−	0.931882i	$-0.381834\pi$
$479$	7605.97	0.725523	0.362762	+	0.931882i	$0.381834\pi$
$480$	−1257.34	−0.119561
$481$	−29017.6	−2.75070
$482$	−2401.44	−0.226935
$483$	−8227.59	−0.775089
$484$	1232.96	0.115793
$485$	5580.08	0.522430
$486$	6934.65	0.647247
$487$	14839.7	1.38081	0.690403	−	0.723425i	$-0.257433\pi$
$487$	14839.7	1.38081	0.690403	+	0.723425i	$0.257433\pi$
$488$	1424.49	0.132139
$489$	−4222.16	−0.390456
$490$	−5033.74	−0.464084
$491$	19099.2	1.75547	0.877734	−	0.479148i	$-0.159054\pi$
$491$	19099.2	1.75547	0.877734	+	0.479148i	$0.159054\pi$
$492$	9337.73	0.855645
$493$	30175.5	2.75666
$494$	−17514.8	−1.59520
$495$	−3362.86	−0.305352
$496$	1255.52	0.113658
$497$	11777.6	1.06297
$498$	7646.10	0.688012
$499$	−14020.5	−1.25780	−0.628900	−	0.777486i	$-0.716494\pi$
$499$	−14020.5	−1.25780	−0.628900	+	0.777486i	$0.716494\pi$
$500$	−5235.04	−0.468236
$501$	−22689.2	−2.02331
$502$	11184.5	0.994404
$503$	4852.50	0.430144	0.215072	−	0.976598i	$-0.431001\pi$
$503$	4852.50	0.430144	0.215072	+	0.976598i	$0.431001\pi$
$504$	2946.02	0.260369
$505$	10180.5	0.897082
$506$	3824.41	0.335999
$507$	17580.0	1.53995
$508$	5241.15	0.457753
$509$	19208.0	1.67266	0.836328	−	0.548230i	$-0.184698\pi$
$509$	19208.0	1.67266	0.836328	+	0.548230i	$0.184698\pi$
$510$	8617.06	0.748177
$511$	−16666.5	−1.44282
$512$	−512.000	−0.0441942
$513$	−10718.9	−0.922517
$514$	2319.99	0.199086
$515$	−5522.72	−0.472544
$516$	−8229.82	−0.702128
$517$	13993.7	1.19041
$518$	−22569.7	−1.91440
$519$	7016.52	0.593432
$520$	−3481.52	−0.293605
$521$	−17217.0	−1.44778	−0.723888	−	0.689917i	$-0.757647\pi$
$521$	−17217.0	−1.44778	−0.723888	+	0.689917i	$0.757647\pi$
$522$	7398.88	0.620383
$523$	−2732.00	−0.228417	−0.114209	−	0.993457i	$-0.536433\pi$
$523$	−2732.00	−0.228417	−0.114209	+	0.993457i	$0.536433\pi$
$524$	−2214.66	−0.184633
$525$	15125.7	1.25741
$526$	−5706.37	−0.473022
$527$	−8604.59	−0.711237
$528$	−4119.70	−0.339558
$529$	−9936.38	−0.816667
$530$	2269.45	0.185997
$531$	62.6239	0.00511797
$532$	−13623.0	−1.11021
$533$	25855.8	2.10120
$534$	6101.26	0.494434
$535$	−2028.90	−0.163957
$536$	1479.34	0.119212
$537$	21420.7	1.72136
$538$	−538.000	−0.0431131
$539$	−16493.2	−1.31802
$540$	−2130.65	−0.169794
$541$	14736.7	1.17113	0.585565	−	0.810626i	$-0.300873\pi$
$541$	14736.7	1.17113	0.585565	+	0.810626i	$0.300873\pi$
$542$	−11387.6	−0.902471
$543$	11320.2	0.894653
$544$	3508.95	0.276553
$545$	−9679.97	−0.760815
$546$	24540.9	1.92354
$547$	19894.1	1.55505	0.777525	−	0.628852i	$-0.216475\pi$
$547$	19894.1	1.55505	0.777525	+	0.628852i	$0.216475\pi$
$548$	10662.6	0.831177
$549$	−2393.75	−0.186089
$550$	−7030.82	−0.545082
$551$	−34213.9	−2.64530
$552$	−2402.85	−0.185275
$553$	−14657.1	−1.12710
$554$	−15724.1	−1.20588
$555$	−16186.9	−1.23801
$556$	524.533	0.0400093
$557$	9446.18	0.718577	0.359288	−	0.933227i	$-0.383019\pi$
$557$	9446.18	0.718577	0.359288	+	0.933227i	$0.383019\pi$
$558$	−2109.80	−0.160063
$559$	−22788.1	−1.72421
$560$	−2707.91	−0.204339
$561$	28234.0	2.12485
$562$	−13952.2	−1.04722
$563$	−3008.57	−0.225215	−0.112608	−	0.993640i	$-0.535920\pi$
$563$	−3008.57	−0.225215	−0.112608	+	0.993640i	$0.535920\pi$
$564$	−8792.17	−0.656413
$565$	−3535.02	−0.263220
$566$	7440.58	0.552564
$567$	24961.6	1.84883
$568$	3439.62	0.254090
$569$	−12918.2	−0.951776	−0.475888	−	0.879506i	$-0.657873\pi$
$569$	−12918.2	−0.951776	−0.475888	+	0.879506i	$0.657873\pi$
$570$	−9770.30	−0.717953
$571$	14536.3	1.06537	0.532684	−	0.846314i	$-0.321183\pi$
$571$	14536.3	1.06537	0.532684	+	0.846314i	$0.321183\pi$
$572$	−11407.3	−0.833850
$573$	−2103.63	−0.153369
$574$	20110.5	1.46236
$575$	−4100.79	−0.297417
$576$	860.378	0.0622380
$577$	7050.72	0.508709	0.254355	−	0.967111i	$-0.418137\pi$
$577$	7050.72	0.508709	0.254355	+	0.967111i	$0.418137\pi$
$578$	−14222.3	−1.02348
$579$	−7729.87	−0.554823
$580$	−6800.88	−0.486881
$581$	16467.3	1.17587
$582$	−11487.2	−0.818147
$583$	7435.90	0.528240
$584$	−4867.41	−0.344889
$585$	5850.43	0.413480
$586$	−9203.04	−0.648761
$587$	11549.5	0.812092	0.406046	−	0.913853i	$-0.366907\pi$
$587$	11549.5	0.812092	0.406046	+	0.913853i	$0.366907\pi$
$588$	10362.5	0.726776
$589$	9756.16	0.682505
$590$	−57.5624	−0.00401662
$591$	11870.3	0.826188
$592$	−6591.44	−0.457613
$593$	−27141.0	−1.87950	−0.939752	−	0.341858i	$-0.888944\pi$
$593$	−27141.0	−1.87950	−0.939752	+	0.341858i	$0.888944\pi$
$594$	−6981.13	−0.482221
$595$	18558.4	1.27869
$596$	−1757.92	−0.120818
$597$	23058.2	1.58076
$598$	−6653.39	−0.454979
$599$	24871.7	1.69655	0.848274	−	0.529558i	$-0.177642\pi$
$599$	24871.7	1.69655	0.848274	+	0.529558i	$0.177642\pi$
$600$	4417.42	0.300567
$601$	17802.6	1.20829	0.604145	−	0.796875i	$-0.293515\pi$
$601$	17802.6	1.20829	0.604145	+	0.796875i	$0.293515\pi$
$602$	−17724.5	−1.19999
$603$	−2485.92	−0.167884
$604$	−7551.39	−0.508711
$605$	1904.45	0.127978
$606$	−20957.8	−1.40487
$607$	−13047.0	−0.872427	−0.436214	−	0.899843i	$-0.643681\pi$
$607$	−13047.0	−0.872427	−0.436214	+	0.899843i	$0.643681\pi$
$608$	−3978.56	−0.265381
$609$	47938.7	3.18978
$610$	2200.28	0.146044
$611$	−24345.2	−1.61195
$612$	−5896.53	−0.389466
$613$	15441.5	1.01742	0.508708	−	0.860939i	$-0.330123\pi$
$613$	15441.5	1.01742	0.508708	+	0.860939i	$0.330123\pi$
$614$	−5146.45	−0.338263
$615$	14423.1	0.945686
$616$	−8872.53	−0.580332
$617$	7104.35	0.463550	0.231775	−	0.972769i	$-0.425547\pi$
$617$	7104.35	0.463550	0.231775	+	0.972769i	$0.425547\pi$
$618$	11369.2	0.740024
$619$	−2739.51	−0.177884	−0.0889420	−	0.996037i	$-0.528349\pi$
$619$	−2739.51	−0.177884	−0.0889420	+	0.996037i	$0.528349\pi$
$620$	1939.28	0.125619
$621$	−4071.81	−0.263118
$622$	5996.29	0.386542
$623$	13140.2	0.845026
$624$	7167.11	0.459798
$625$	2767.29	0.177107
$626$	−14936.4	−0.953640
$627$	−32012.6	−2.03901
$628$	12954.1	0.823126
$629$	45173.9	2.86360
$630$	4550.44	0.287768
$631$	−11035.2	−0.696205	−0.348103	−	0.937456i	$-0.613174\pi$
$631$	−11035.2	−0.696205	−0.348103	+	0.937456i	$0.613174\pi$
$632$	−4280.58	−0.269418
$633$	−24155.5	−1.51674
$634$	17258.2	1.08109
$635$	8095.53	0.505923
$636$	−4671.93	−0.291280
$637$	28693.5	1.78474
$638$	−22283.2	−1.38276
$639$	−5780.02	−0.357831
$640$	−790.839	−0.0488448
$641$	9542.16	0.587976	0.293988	−	0.955809i	$-0.405017\pi$
$641$	9542.16	0.587976	0.293988	+	0.955809i	$0.405017\pi$
$642$	4176.73	0.256764
$643$	−11642.5	−0.714053	−0.357026	−	0.934094i	$-0.616209\pi$
$643$	−11642.5	−0.714053	−0.357026	+	0.934094i	$0.616209\pi$
$644$	−5174.98	−0.316650
$645$	−12711.9	−0.776014
$646$	27266.7	1.66067
$647$	25181.2	1.53010	0.765051	−	0.643969i	$-0.222714\pi$
$647$	25181.2	1.53010	0.765051	+	0.643969i	$0.222714\pi$
$648$	7289.97	0.441940
$649$	−188.605	−0.0114074
$650$	12231.6	0.738100
$651$	−13669.8	−0.822984
$652$	−2655.65	−0.159514
$653$	1039.40	0.0622890	0.0311445	−	0.999515i	$-0.490085\pi$
$653$	1039.40	0.0622890	0.0311445	+	0.999515i	$0.490085\pi$
$654$	19927.3	1.19147
$655$	−3420.78	−0.204063
$656$	5873.24	0.349560
$657$	8179.32	0.485701
$658$	−18935.6	−1.12186
$659$	−12230.6	−0.722967	−0.361483	−	0.932379i	$-0.617730\pi$
$659$	−12230.6	−0.722967	−0.361483	+	0.932379i	$0.617730\pi$
$660$	−6363.32	−0.375291
$661$	−10681.1	−0.628514	−0.314257	−	0.949338i	$-0.601755\pi$
$661$	−10681.1	−0.628514	−0.314257	+	0.949338i	$0.601755\pi$
$662$	17812.0	1.04574
$663$	−49119.2	−2.87727
$664$	4809.24	0.281076
$665$	−21042.2	−1.22704
$666$	11076.4	0.644449
$667$	−12996.9	−0.754485
$668$	−14271.0	−0.826591
$669$	−24091.9	−1.39230
$670$	2285.00	0.131757
$671$	7209.26	0.414770
$672$	5574.55	0.320004
$673$	−20703.6	−1.18583	−0.592916	−	0.805264i	$-0.702023\pi$
$673$	−20703.6	−1.18583	−0.592916	+	0.805264i	$0.702023\pi$
$674$	6526.08	0.372960
$675$	7485.64	0.426848
$676$	11057.4	0.629122
$677$	−667.158	−0.0378744	−0.0189372	−	0.999821i	$-0.506028\pi$
$677$	−667.158	−0.0378744	−0.0189372	+	0.999821i	$0.506028\pi$
$678$	7277.25	0.412214
$679$	−24739.9	−1.39828
$680$	5419.95	0.305655
$681$	−10804.3	−0.607961
$682$	6354.11	0.356761
$683$	−9663.02	−0.541354	−0.270677	−	0.962670i	$-0.587248\pi$
$683$	−9663.02	−0.541354	−0.270677	+	0.962670i	$0.587248\pi$
$684$	6685.67	0.373732
$685$	16469.6	0.918643
$686$	3526.22	0.196256
$687$	29107.6	1.61648
$688$	−5176.39	−0.286843
$689$	−12936.4	−0.715293
$690$	−3711.46	−0.204772
$691$	−20862.9	−1.14857	−0.574286	−	0.818655i	$-0.694720\pi$
$691$	−20862.9	−1.14857	−0.574286	+	0.818655i	$0.694720\pi$
$692$	4413.24	0.242437
$693$	14909.6	0.817272
$694$	9067.05	0.495937
$695$	810.198	0.0442195
$696$	14000.4	0.762477
$697$	−40251.7	−2.18744
$698$	−13338.6	−0.723316
$699$	4964.30	0.268622
$700$	9513.73	0.513693
$701$	25666.5	1.38290	0.691448	−	0.722426i	$-0.256973\pi$
$701$	25666.5	1.38290	0.691448	+	0.722426i	$0.256973\pi$
$702$	12145.2	0.652979
$703$	−51219.6	−2.74792
$704$	−2591.20	−0.138721
$705$	−13580.5	−0.725489
$706$	15799.0	0.842215
$707$	−45136.4	−2.40103
$708$	118.499	0.00629020
$709$	−18647.3	−0.987750	−0.493875	−	0.869533i	$-0.664420\pi$
$709$	−18647.3	−0.987750	−0.493875	+	0.869533i	$0.664420\pi$
$710$	5312.86	0.280828
$711$	7193.19	0.379417
$712$	3837.57	0.201993
$713$	3706.09	0.194662
$714$	−38204.7	−2.00249
$715$	−17619.8	−0.921597
$716$	13473.1	0.703233
$717$	−7774.23	−0.404929
$718$	4169.85	0.216737
$719$	10863.7	0.563486	0.281743	−	0.959490i	$-0.409087\pi$
$719$	10863.7	0.563486	0.281743	+	0.959490i	$0.409087\pi$
$720$	1328.95	0.0687874
$721$	24485.6	1.26476
$722$	−17197.9	−0.886481
$723$	7636.00	0.392788
$724$	7120.17	0.365496
$725$	23893.6	1.22398
$726$	−3920.52	−0.200419
$727$	−25838.8	−1.31817	−0.659085	−	0.752068i	$-0.729056\pi$
$727$	−25838.8	−1.31817	−0.659085	+	0.752068i	$0.729056\pi$
$728$	15435.7	0.785831
$729$	2553.17	0.129714
$730$	−7518.24	−0.381182
$731$	35475.9	1.79497
$732$	−4529.53	−0.228711
$733$	−13280.0	−0.669179	−0.334589	−	0.942364i	$-0.608598\pi$
$733$	−13280.0	−0.669179	−0.334589	+	0.942364i	$0.608598\pi$
$734$	17241.7	0.867033
$735$	16006.1	0.803256
$736$	−1511.34	−0.0756913
$737$	7486.84	0.374195
$738$	−9869.53	−0.492280
$739$	−25232.1	−1.25599	−0.627995	−	0.778217i	$-0.716124\pi$
$739$	−25232.1	−1.25599	−0.627995	+	0.778217i	$0.716124\pi$
$740$	−10181.2	−0.505768
$741$	55692.9	2.76104
$742$	−10061.9	−0.497820
$743$	−29048.3	−1.43429	−0.717146	−	0.696923i	$-0.754552\pi$
$743$	−29048.3	−1.43429	−0.717146	+	0.696923i	$0.754552\pi$
$744$	−3992.24	−0.196724
$745$	−2715.30	−0.133532
$746$	−16296.0	−0.799784
$747$	−8081.56	−0.395835
$748$	17758.6	0.868073
$749$	8995.36	0.438830
$750$	16646.1	0.810441
$751$	−33303.9	−1.61821	−0.809106	−	0.587662i	$-0.800048\pi$
$751$	−33303.9	−1.61821	−0.809106	+	0.587662i	$0.800048\pi$
$752$	−5530.09	−0.268167
$753$	−35564.1	−1.72115
$754$	38766.6	1.87241
$755$	−11663.9	−0.562244
$756$	9446.49	0.454452
$757$	22528.3	1.08164	0.540821	−	0.841137i	$-0.318113\pi$
$757$	22528.3	1.08164	0.540821	+	0.841137i	$0.318113\pi$
$758$	13940.4	0.667994
$759$	−12160.7	−0.581561
$760$	−6145.32	−0.293308
$761$	18284.3	0.870967	0.435484	−	0.900197i	$-0.356577\pi$
$761$	18284.3	0.870967	0.435484	+	0.900197i	$0.356577\pi$
$762$	−16665.6	−0.792297
$763$	42917.2	2.03631
$764$	−1323.14	−0.0626564
$765$	−9107.82	−0.430450
$766$	2889.20	0.136281
$767$	328.119	0.0154468
$768$	1628.04	0.0764930
$769$	−3298.29	−0.154667	−0.0773337	−	0.997005i	$-0.524641\pi$
$769$	−3298.29	−0.154667	−0.0773337	+	0.997005i	$0.524641\pi$
$770$	−13704.6	−0.641401
$771$	−7377.00	−0.344586
$772$	−4861.93	−0.226664
$773$	−21641.1	−1.00695	−0.503477	−	0.864009i	$-0.667946\pi$
$773$	−21641.1	−1.00695	−0.503477	+	0.864009i	$0.667946\pi$
$774$	8698.53	0.403956
$775$	−6813.30	−0.315795
$776$	−7225.23	−0.334241
$777$	71766.3	3.31351
$778$	25965.9	1.19656
$779$	45638.7	2.09907
$780$	11070.4	0.508184
$781$	17407.7	0.797563
$782$	10357.9	0.473652
$783$	23724.7	1.08283
$784$	6517.82	0.296913
$785$	20008.9	0.909745
$786$	7042.08	0.319571
$787$	−20051.8	−0.908220	−0.454110	−	0.890946i	$-0.650043\pi$
$787$	−20051.8	−0.908220	−0.454110	+	0.890946i	$0.650043\pi$
$788$	7466.14	0.337526
$789$	18144.9	0.818726
$790$	−6611.81	−0.297769
$791$	15672.9	0.704506
$792$	4354.32	0.195359
$793$	−12542.1	−0.561643
$794$	4000.81	0.178821
$795$	−7216.30	−0.321932
$796$	14503.1	0.645792
$797$	−21663.1	−0.962794	−0.481397	−	0.876503i	$-0.659871\pi$
$797$	−21663.1	−0.962794	−0.481397	+	0.876503i	$0.659871\pi$
$798$	43317.7	1.92159
$799$	37900.0	1.67811
$800$	2778.46	0.122792
$801$	−6448.74	−0.284463
$802$	21913.5	0.964827
$803$	−24633.7	−1.08257
$804$	−4703.93	−0.206337
$805$	−7993.32	−0.349972
$806$	−11054.4	−0.483093
$807$	1710.71	0.0746218
$808$	−13182.0	−0.573937
$809$	−11734.5	−0.509968	−0.254984	−	0.966945i	$-0.582070\pi$
$809$	−11734.5	−0.509968	−0.254984	+	0.966945i	$0.582070\pi$
$810$	11260.2	0.488446
$811$	19350.0	0.837818	0.418909	−	0.908028i	$-0.362413\pi$
$811$	19350.0	0.837818	0.418909	+	0.908028i	$0.362413\pi$
$812$	30152.5	1.30313
$813$	36209.8	1.56203
$814$	−33358.9	−1.43640
$815$	−4101.94	−0.176300
$816$	−11157.6	−0.478669
$817$	−40223.8	−1.72246
$818$	−14753.3	−0.630606
$819$	−25938.5	−1.10667
$820$	9071.85	0.386345
$821$	−27906.0	−1.18627	−0.593134	−	0.805104i	$-0.702110\pi$
$821$	−27906.0	−1.18627	−0.593134	+	0.805104i	$0.702110\pi$
$822$	−33904.5	−1.43863
$823$	−22165.0	−0.938788	−0.469394	−	0.882989i	$-0.655528\pi$
$823$	−22165.0	−0.938788	−0.469394	+	0.882989i	$0.655528\pi$
$824$	7150.97	0.302325
$825$	22356.3	0.943450
$826$	255.209	0.0107505
$827$	−41485.3	−1.74436	−0.872179	−	0.489186i	$-0.837294\pi$
$827$	−41485.3	−1.74436	−0.872179	+	0.489186i	$0.837294\pi$
$828$	2539.70	0.106595
$829$	−37169.9	−1.55725	−0.778626	−	0.627488i	$-0.784083\pi$
$829$	−37169.9	−1.55725	−0.778626	+	0.627488i	$0.784083\pi$
$830$	7428.39	0.310654
$831$	49998.9	2.08718
$832$	4507.96	0.187843
$833$	−44669.4	−1.85799
$834$	−1667.89	−0.0692497
$835$	−22043.2	−0.913575
$836$	−20135.3	−0.833005
$837$	−6765.15	−0.279376
$838$	−1357.36	−0.0559536
$839$	−30671.4	−1.26209	−0.631046	−	0.775746i	$-0.717374\pi$
$839$	−30671.4	−1.26209	−0.631046	+	0.775746i	$0.717374\pi$
$840$	8610.50	0.353679
$841$	51338.5	2.10499
$842$	61.5596	0.00251958
$843$	44364.6	1.81257
$844$	−15193.3	−0.619638
$845$	17079.4	0.695325
$846$	9292.90	0.377655
$847$	−8443.57	−0.342532
$848$	−2938.55	−0.118998
$849$	−23659.2	−0.956400
$850$	−19042.0	−0.768393
$851$	−19456.9	−0.783752
$852$	−10937.1	−0.439789
$853$	30642.8	1.23000	0.614999	−	0.788528i	$-0.289156\pi$
$853$	30642.8	1.23000	0.614999	+	0.788528i	$0.289156\pi$
$854$	−9755.18	−0.390885
$855$	10326.7	0.413061
$856$	2627.08	0.104897
$857$	27495.8	1.09596	0.547980	−	0.836491i	$-0.315397\pi$
$857$	27495.8	1.09596	0.547980	+	0.836491i	$0.315397\pi$
$858$	36272.3	1.44326
$859$	17570.5	0.697902	0.348951	−	0.937141i	$-0.386538\pi$
$859$	17570.5	0.697902	0.348951	+	0.937141i	$0.386538\pi$
$860$	−7995.49	−0.317028
$861$	−63946.6	−2.53112
$862$	−20362.1	−0.804566
$863$	−36296.2	−1.43168	−0.715839	−	0.698265i	$-0.753956\pi$
$863$	−36296.2	−1.43168	−0.715839	+	0.698265i	$0.753956\pi$
$864$	2758.83	0.108631
$865$	6816.73	0.267949
$866$	6298.53	0.247151
$867$	45223.4	1.77147
$868$	−8598.03	−0.336217
$869$	−21663.7	−0.845676
$870$	21625.1	0.842714
$871$	−13025.0	−0.506700
$872$	12533.9	0.486756
$873$	12141.5	0.470706
$874$	−11744.1	−0.454518
$875$	35850.5	1.38511
$876$	15477.2	0.596947
$877$	21916.4	0.843858	0.421929	−	0.906629i	$-0.361353\pi$
$877$	21916.4	0.843858	0.421929	+	0.906629i	$0.361353\pi$
$878$	−18042.9	−0.693529
$879$	29263.4	1.12290
$880$	−4002.39	−0.153319
$881$	−21877.8	−0.836644	−0.418322	−	0.908299i	$-0.637382\pi$
$881$	−21877.8	−0.836644	−0.418322	+	0.908299i	$0.637382\pi$
$882$	−10952.7	−0.418137
$883$	−39950.2	−1.52257	−0.761285	−	0.648417i	$-0.775431\pi$
$883$	−39950.2	−1.52257	−0.761285	+	0.648417i	$0.775431\pi$
$884$	−30895.0	−1.17546
$885$	183.035	0.00695213
$886$	13893.6	0.526822
$887$	−47496.9	−1.79796	−0.898980	−	0.437990i	$-0.855691\pi$
$887$	−47496.9	−1.79796	−0.898980	+	0.437990i	$0.855691\pi$
$888$	20959.2	0.792054
$889$	−35892.4	−1.35410
$890$	5927.54	0.223249
$891$	36894.1	1.38721
$892$	−15153.3	−0.568800
$893$	−42972.2	−1.61031
$894$	5589.77	0.209116
$895$	20810.7	0.777236
$896$	3506.28	0.130733
$897$	21156.2	0.787496
$898$	3628.25	0.134829
$899$	−21593.8	−0.801107
$900$	−4669.00	−0.172926
$901$	20139.1	0.744650
$902$	29724.1	1.09723
$903$	56359.4	2.07699
$904$	4577.24	0.168403
$905$	10997.9	0.403958
$906$	24011.6	0.880498
$907$	15797.8	0.578345	0.289173	−	0.957277i	$-0.406620\pi$
$907$	15797.8	0.578345	0.289173	+	0.957277i	$0.406620\pi$
$908$	−6795.68	−0.248373
$909$	22151.3	0.808266
$910$	23842.1	0.868526
$911$	48925.8	1.77935	0.889673	−	0.456598i	$-0.150932\pi$
$911$	48925.8	1.77935	0.889673	+	0.456598i	$0.150932\pi$
$912$	12650.8	0.459333
$913$	24339.3	0.882270
$914$	14485.6	0.524226
$915$	−6996.35	−0.252778
$916$	18308.1	0.660388
$917$	15166.4	0.546172
$918$	−18907.4	−0.679779
$919$	−55381.3	−1.98788	−0.993940	−	0.109927i	$-0.964938\pi$
$919$	−55381.3	−1.98788	−0.993940	+	0.109927i	$0.964938\pi$
$920$	−2334.43	−0.0836564
$921$	16364.4	0.585480
$922$	20035.0	0.715638
$923$	−30284.5	−1.07999
$924$	28212.5	1.00446
$925$	35769.7	1.27146
$926$	−19323.5	−0.685755
$927$	−12016.7	−0.425760
$928$	8805.96	0.311498
$929$	2585.64	0.0913154	0.0456577	−	0.998957i	$-0.485462\pi$
$929$	2585.64	0.0913154	0.0456577	+	0.998957i	$0.485462\pi$
$930$	−6166.45	−0.217426
$931$	50647.6	1.78293
$932$	3122.44	0.109741
$933$	−19066.7	−0.669043
$934$	27641.9	0.968384
$935$	27430.1	0.959422
$936$	−7575.29	−0.264537
$937$	−23216.3	−0.809439	−0.404720	−	0.914441i	$-0.632631\pi$
$937$	−23216.3	−0.809439	−0.404720	+	0.914441i	$0.632631\pi$
$938$	−10130.8	−0.352646
$939$	47494.1	1.65060
$940$	−8541.82	−0.296387
$941$	−20316.7	−0.703830	−0.351915	−	0.936032i	$-0.614469\pi$
$941$	−20316.7	−0.703830	−0.351915	+	0.936032i	$0.614469\pi$
$942$	−41190.7	−1.42470
$943$	17336.8	0.598691
$944$	74.5334	0.00256976
$945$	14591.1	0.502275
$946$	−26197.4	−0.900371
$947$	−35872.2	−1.23093	−0.615464	−	0.788165i	$-0.711031\pi$
$947$	−35872.2	−1.23093	−0.615464	+	0.788165i	$0.711031\pi$
$948$	13611.2	0.466319
$949$	42855.7	1.46592
$950$	21590.4	0.737352
$951$	−54876.8	−1.87119
$952$	−24030.0	−0.818084
$953$	31515.4	1.07123	0.535616	−	0.844462i	$-0.320079\pi$
$953$	31515.4	1.07123	0.535616	+	0.844462i	$0.320079\pi$
$954$	4938.00	0.167583
$955$	−2043.73	−0.0692498
$956$	−4889.83	−0.165427
$957$	70855.3	2.39334
$958$	−15211.9	−0.513022
$959$	−73019.7	−2.45874
$960$	2514.68	0.0845425
$961$	−23633.5	−0.793309
$962$	58035.1	1.94504
$963$	−4414.60	−0.147724
$964$	4802.88	0.160467
$965$	−7509.78	−0.250516
$966$	16455.2	0.548071
$967$	36425.5	1.21134	0.605670	−	0.795716i	$-0.292905\pi$
$967$	36425.5	1.21134	0.605670	+	0.795716i	$0.292905\pi$
$968$	−2465.93	−0.0818780
$969$	−86701.5	−2.87436
$970$	−11160.2	−0.369413
$971$	4958.17	0.163867	0.0819337	−	0.996638i	$-0.473890\pi$
$971$	4958.17	0.163867	0.0819337	+	0.996638i	$0.473890\pi$
$972$	−13869.3	−0.457673
$973$	−3592.10	−0.118353
$974$	−29679.5	−0.976377
$975$	−38893.7	−1.27753
$976$	−2848.98	−0.0934361
$977$	−28872.8	−0.945469	−0.472734	−	0.881205i	$-0.656733\pi$
$977$	−28872.8	−0.945469	−0.472734	+	0.881205i	$0.656733\pi$
$978$	8444.32	0.276094
$979$	19421.7	0.634035
$980$	10067.5	0.328157
$981$	−21062.3	−0.685490
$982$	−38198.4	−1.24130
$983$	−20864.5	−0.676982	−0.338491	−	0.940970i	$-0.609916\pi$
$983$	−20864.5	−0.676982	−0.338491	+	0.940970i	$0.609916\pi$
$984$	−18675.5	−0.605033
$985$	11532.3	0.373044
$986$	−60350.9	−1.94925
$987$	60210.5	1.94176
$988$	35029.7	1.12798
$989$	−15279.9	−0.491275
$990$	6725.72	0.215917
$991$	−14583.2	−0.467457	−0.233729	−	0.972302i	$-0.575093\pi$
$991$	−14583.2	−0.467457	−0.233729	+	0.972302i	$0.575093\pi$
$992$	−2511.04	−0.0803685
$993$	−56637.8	−1.81002
$994$	−23555.2	−0.751634
$995$	22401.7	0.713750
$996$	−15292.2	−0.486498
$997$	−28556.6	−0.907117	−0.453559	−	0.891226i	$-0.649846\pi$
$997$	−28556.6	−0.907117	−0.453559	+	0.891226i	$0.649846\pi$
$998$	28040.9	0.889399
$999$	35516.9	1.12483

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.4.a.c.1.16	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.4.a.c.1.16	✓	18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	538.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +6.35951 q^{3} +4.00000 q^{4} +6.17843 q^{5} -12.7190 q^{6} -27.3928 q^{7} -8.00000 q^{8} +13.4434 q^{9} -12.3569 q^{10} -40.4875 q^{11} +25.4381 q^{12} +70.4369 q^{13} +54.7855 q^{14} +39.2918 q^{15} +16.0000 q^{16} -109.655 q^{17} -26.8868 q^{18} +124.330 q^{19} +24.7137 q^{20} -174.205 q^{21} +80.9751 q^{22} +47.2294 q^{23} -50.8761 q^{24} -86.8270 q^{25} -140.874 q^{26} -86.2134 q^{27} -109.571 q^{28} -275.186 q^{29} -78.5836 q^{30} +78.4699 q^{31} -32.0000 q^{32} -257.481 q^{33} +219.309 q^{34} -169.244 q^{35} +53.7736 q^{36} -411.965 q^{37} -248.660 q^{38} +447.945 q^{39} -49.4275 q^{40} +367.077 q^{41} +348.409 q^{42} -323.524 q^{43} -161.950 q^{44} +83.0592 q^{45} -94.4588 q^{46} -345.631 q^{47} +101.752 q^{48} +407.364 q^{49} +173.654 q^{50} -697.350 q^{51} +281.748 q^{52} -183.659 q^{53} +172.427 q^{54} -250.150 q^{55} +219.142 q^{56} +790.678 q^{57} +550.373 q^{58} +4.65834 q^{59} +157.167 q^{60} -178.061 q^{61} -156.940 q^{62} -368.252 q^{63} +64.0000 q^{64} +435.190 q^{65} +514.962 q^{66} -184.917 q^{67} -438.619 q^{68} +300.356 q^{69} +338.489 q^{70} -429.952 q^{71} -107.547 q^{72} +608.426 q^{73} +823.930 q^{74} -552.177 q^{75} +497.320 q^{76} +1109.07 q^{77} -895.889 q^{78} +535.072 q^{79} +98.8549 q^{80} -911.247 q^{81} -734.155 q^{82} -601.154 q^{83} -696.819 q^{84} -677.494 q^{85} +647.048 q^{86} -1750.05 q^{87} +323.900 q^{88} -479.696 q^{89} -166.118 q^{90} -1929.46 q^{91} +188.918 q^{92} +499.030 q^{93} +691.261 q^{94} +768.164 q^{95} -203.504 q^{96} +903.154 q^{97} -814.728 q^{98} -544.290 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 36 q^{2} - 10 q^{3} + 72 q^{4} - 26 q^{5} + 20 q^{6} - 9 q^{7} - 144 q^{8} + 178 q^{9} + 52 q^{10} - 130 q^{11} - 40 q^{12} - 27 q^{13} + 18 q^{14} - 143 q^{15} + 288 q^{16} - 110 q^{17} - 356 q^{18}+ \cdots - 9455 q^{99}+O(q^{100}) \) 18 * q - 36 * q^2 - 10 * q^3 + 72 * q^4 - 26 * q^5 + 20 * q^6 - 9 * q^7 - 144 * q^8 + 178 * q^9 + 52 * q^10 - 130 * q^11 - 40 * q^12 - 27 * q^13 + 18 * q^14 - 143 * q^15 + 288 * q^16 - 110 * q^17 - 356 * q^18 - 47 * q^19 - 104 * q^20 + 69 * q^21 + 260 * q^22 - 329 * q^23 + 80 * q^24 + 442 * q^25 + 54 * q^26 - 325 * q^27 - 36 * q^28 - 3 * q^29 + 286 * q^30 + 97 * q^31 - 576 * q^32 - 129 * q^33 + 220 * q^34 - 834 * q^35 + 712 * q^36 - 104 * q^37 + 94 * q^38 - 242 * q^39 + 208 * q^40 + 196 * q^41 - 138 * q^42 - 547 * q^43 - 520 * q^44 - 481 * q^45 + 658 * q^46 - 1074 * q^47 - 160 * q^48 + 1315 * q^49 - 884 * q^50 - 1475 * q^51 - 108 * q^52 - 1681 * q^53 + 650 * q^54 + 163 * q^55 + 72 * q^56 - 1178 * q^57 + 6 * q^58 - 924 * q^59 - 572 * q^60 + 640 * q^61 - 194 * q^62 - 445 * q^63 + 1152 * q^64 - 2052 * q^65 + 258 * q^66 - 1685 * q^67 - 440 * q^68 - 1787 * q^69 + 1668 * q^70 - 3635 * q^71 - 1424 * q^72 - 1136 * q^73 + 208 * q^74 - 3332 * q^75 - 188 * q^76 - 5512 * q^77 + 484 * q^78 - 406 * q^79 - 416 * q^80 - 3194 * q^81 - 392 * q^82 - 6854 * q^83 + 276 * q^84 - 1227 * q^85 + 1094 * q^86 - 8831 * q^87 + 1040 * q^88 - 4690 * q^89 + 962 * q^90 - 5743 * q^91 - 1316 * q^92 - 4097 * q^93 + 2148 * q^94 - 3332 * q^95 + 320 * q^96 - 4132 * q^97 - 2630 * q^98 - 9455 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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