LMFDB - Embedded newform 538.4.a.b.1.3

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:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 4 x^{14} - 262 x^{13} + 870 x^{12} + 26403 x^{11} - 73750 x^{10} - 1270273 x^{9} + \cdots + 4484581281 $ x^15 - 4x^14 - 262x^13 + 870x^12 + 26403x^11 - 73750x^10 - 1270273x^9 + 3200221x^8 + 29622219x^7 - 76420071x^6 - 306845604x^5 + 880769133x^4 + 1044220086x^3 - 3558788460x^2 - 957997854x + 4484581281
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$7.81309$ 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)

$f(q)$	$=$	\(q-2.00000 q^{2} -6.81309 q^{3} +4.00000 q^{4} +10.9766 q^{5} +13.6262 q^{6} -4.36588 q^{7} -8.00000 q^{8} +19.4181 q^{9} -21.9532 q^{10} +42.8218 q^{11} -27.2523 q^{12} +14.5070 q^{13} +8.73175 q^{14} -74.7845 q^{15} +16.0000 q^{16} +81.0612 q^{17} -38.8363 q^{18} +12.3775 q^{19} +43.9064 q^{20} +29.7451 q^{21} -85.6435 q^{22} -80.3207 q^{23} +54.5047 q^{24} -4.51421 q^{25} -29.0139 q^{26} +51.6559 q^{27} -17.4635 q^{28} -280.199 q^{29} +149.569 q^{30} +230.068 q^{31} -32.0000 q^{32} -291.748 q^{33} -162.122 q^{34} -47.9225 q^{35} +77.6725 q^{36} +93.7485 q^{37} -24.7550 q^{38} -98.8372 q^{39} -87.8128 q^{40} -463.927 q^{41} -59.4902 q^{42} +12.0323 q^{43} +171.287 q^{44} +213.145 q^{45} +160.641 q^{46} +435.970 q^{47} -109.009 q^{48} -323.939 q^{49} +9.02842 q^{50} -552.277 q^{51} +58.0279 q^{52} -227.550 q^{53} -103.312 q^{54} +470.038 q^{55} +34.9270 q^{56} -84.3290 q^{57} +560.397 q^{58} +537.036 q^{59} -299.138 q^{60} -513.672 q^{61} -460.136 q^{62} -84.7772 q^{63} +64.0000 q^{64} +159.237 q^{65} +583.497 q^{66} +804.492 q^{67} +324.245 q^{68} +547.231 q^{69} +95.8450 q^{70} -67.2315 q^{71} -155.345 q^{72} +597.947 q^{73} -187.497 q^{74} +30.7557 q^{75} +49.5100 q^{76} -186.955 q^{77} +197.674 q^{78} +710.808 q^{79} +175.626 q^{80} -876.226 q^{81} +927.854 q^{82} -508.468 q^{83} +118.980 q^{84} +889.777 q^{85} -24.0646 q^{86} +1909.02 q^{87} -342.574 q^{88} +1284.51 q^{89} -426.290 q^{90} -63.3356 q^{91} -321.283 q^{92} -1567.47 q^{93} -871.939 q^{94} +135.863 q^{95} +218.019 q^{96} +1553.35 q^{97} +647.878 q^{98} +831.519 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 30 q^{2} + 11 q^{3} + 60 q^{4} + 29 q^{5} - 22 q^{6} + 5 q^{7} - 120 q^{8} + 142 q^{9} - 58 q^{10} + 79 q^{11} + 44 q^{12} - 14 q^{13} - 10 q^{14} + 67 q^{15} + 240 q^{16} + 94 q^{17} - 284 q^{18}+ \cdots + 7068 q^{99}+O(q^{100}) $ 15 * q - 30 * q^2 + 11 * q^3 + 60 * q^4 + 29 * q^5 - 22 * q^6 + 5 * q^7 - 120 * q^8 + 142 * q^9 - 58 * q^10 + 79 * q^11 + 44 * q^12 - 14 * q^13 - 10 * q^14 + 67 * q^15 + 240 * q^16 + 94 * q^17 - 284 * q^18 + 124 * q^19 + 116 * q^20 + 69 * q^21 - 158 * q^22 + 545 * q^23 - 88 * q^24 + 192 * q^25 + 28 * q^26 + 431 * q^27 + 20 * q^28 + 200 * q^29 - 134 * q^30 + 159 * q^31 - 480 * q^32 + 531 * q^33 - 188 * q^34 + 146 * q^35 + 568 * q^36 + 303 * q^37 - 248 * q^38 - 164 * q^39 - 232 * q^40 + 606 * q^41 - 138 * q^42 + 442 * q^43 + 316 * q^44 + 644 * q^45 - 1090 * q^46 + 618 * q^47 + 176 * q^48 + 286 * q^49 - 384 * q^50 - 251 * q^51 - 56 * q^52 + 916 * q^53 - 862 * q^54 + 53 * q^55 - 40 * q^56 + 190 * q^57 - 400 * q^58 + 1377 * q^59 + 268 * q^60 - 1373 * q^61 - 318 * q^62 + 1067 * q^63 + 960 * q^64 + 158 * q^65 - 1062 * q^66 + 1330 * q^67 + 376 * q^68 + 737 * q^69 - 292 * q^70 + 2291 * q^71 - 1136 * q^72 + 924 * q^73 - 606 * q^74 + 4337 * q^75 + 496 * q^76 + 4170 * q^77 + 328 * q^78 + 610 * q^79 + 464 * q^80 + 2255 * q^81 - 1212 * q^82 + 5191 * q^83 + 276 * q^84 + 1517 * q^85 - 884 * q^86 + 7295 * q^87 - 632 * q^88 + 3198 * q^89 - 1288 * q^90 + 4289 * q^91 + 2180 * q^92 + 5255 * q^93 - 1236 * q^94 + 4706 * q^95 - 352 * q^96 + 3806 * q^97 - 572 * q^98 + 7068 * 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
$3$	−6.81309	−1.31118	−0.655589	−	0.755118i	$-0.727580\pi$
$3$	−6.81309	−1.31118	−0.655589	+	0.755118i	$0.727580\pi$
$4$	4.00000	0.500000
$5$	10.9766	0.981777	0.490889	−	0.871222i	$-0.336672\pi$
$5$	10.9766	0.981777	0.490889	+	0.871222i	$0.336672\pi$
$6$	13.6262	0.927143
$7$	−4.36588	−0.235735	−0.117868	−	0.993029i	$-0.537606\pi$
$7$	−4.36588	−0.235735	−0.117868	+	0.993029i	$0.537606\pi$
$8$	−8.00000	−0.353553
$9$	19.4181	0.719190
$10$	−21.9532	−0.694221
$11$	42.8218	1.17375	0.586875	−	0.809678i	$-0.300358\pi$
$11$	42.8218	1.17375	0.586875	+	0.809678i	$0.300358\pi$
$12$	−27.2523	−0.655589
$13$	14.5070	0.309501	0.154750	−	0.987954i	$-0.450543\pi$
$13$	14.5070	0.309501	0.154750	+	0.987954i	$0.450543\pi$
$14$	8.73175	0.166690
$15$	−74.7845	−1.28729
$16$	16.0000	0.250000
$17$	81.0612	1.15648	0.578242	−	0.815865i	$-0.303739\pi$
$17$	81.0612	1.15648	0.578242	+	0.815865i	$0.303739\pi$
$18$	−38.8363	−0.508544
$19$	12.3775	0.149452	0.0747262	−	0.997204i	$-0.476192\pi$
$19$	12.3775	0.149452	0.0747262	+	0.997204i	$0.476192\pi$
$20$	43.9064	0.490889
$21$	29.7451	0.309091
$22$	−85.6435	−0.829967
$23$	−80.3207	−0.728175	−0.364087	−	0.931365i	$-0.618619\pi$
$23$	−80.3207	−0.728175	−0.364087	+	0.931365i	$0.618619\pi$
$24$	54.5047	0.463572
$25$	−4.51421	−0.0361137
$26$	−29.0139	−0.218850
$27$	51.6559	0.368192
$28$	−17.4635	−0.117868
$29$	−280.199	−1.79419	−0.897096	−	0.441835i	$-0.854328\pi$
$29$	−280.199	−1.79419	−0.897096	+	0.441835i	$0.854328\pi$
$30$	149.569	0.910248
$31$	230.068	1.33295	0.666474	−	0.745528i	$-0.267803\pi$
$31$	230.068	1.33295	0.666474	+	0.745528i	$0.267803\pi$
$32$	−32.0000	−0.176777
$33$	−291.748	−1.53900
$34$	−162.122	−0.817758
$35$	−47.9225	−0.231439
$36$	77.6725	0.359595
$37$	93.7485	0.416545	0.208272	−	0.978071i	$-0.433216\pi$
$37$	93.7485	0.416545	0.208272	+	0.978071i	$0.433216\pi$
$38$	−24.7550	−0.105679
$39$	−98.8372	−0.405811
$40$	−87.8128	−0.347111
$41$	−463.927	−1.76715	−0.883576	−	0.468287i	$-0.844871\pi$
$41$	−463.927	−1.76715	−0.883576	+	0.468287i	$0.844871\pi$
$42$	−59.4902	−0.218560
$43$	12.0323	0.0426722	0.0213361	−	0.999772i	$-0.493208\pi$
$43$	12.0323	0.0426722	0.0213361	+	0.999772i	$0.493208\pi$
$44$	171.287	0.586875
$45$	213.145	0.706084
$46$	160.641	0.514897
$47$	435.970	1.35304	0.676518	−	0.736426i	$-0.263488\pi$
$47$	435.970	1.35304	0.676518	+	0.736426i	$0.263488\pi$
$48$	−109.009	−0.327795
$49$	−323.939	−0.944429
$50$	9.02842	0.0255362
$51$	−552.277	−1.51636
$52$	58.0279	0.154750
$53$	−227.550	−0.589742	−0.294871	−	0.955537i	$-0.595277\pi$
$53$	−227.550	−0.589742	−0.294871	+	0.955537i	$0.595277\pi$
$54$	−103.312	−0.260351
$55$	470.038	1.15236
$56$	34.9270	0.0833450
$57$	−84.3290	−0.195959
$58$	560.397	1.26869
$59$	537.036	1.18502	0.592510	−	0.805563i	$-0.298137\pi$
$59$	537.036	1.18502	0.592510	+	0.805563i	$0.298137\pi$
$60$	−299.138	−0.643643
$61$	−513.672	−1.07818	−0.539090	−	0.842248i	$-0.681232\pi$
$61$	−513.672	−1.07818	−0.539090	+	0.842248i	$0.681232\pi$
$62$	−460.136	−0.942537
$63$	−84.7772	−0.169538
$64$	64.0000	0.125000
$65$	159.237	0.303861
$66$	583.497	1.08823
$67$	804.492	1.46693	0.733466	−	0.679727i	$-0.237902\pi$
$67$	804.492	1.46693	0.733466	+	0.679727i	$0.237902\pi$
$68$	324.245	0.578242
$69$	547.231	0.954767
$70$	95.8450	0.163652
$71$	−67.2315	−0.112379	−0.0561895	−	0.998420i	$-0.517895\pi$
$71$	−67.2315	−0.112379	−0.0561895	+	0.998420i	$0.517895\pi$
$72$	−155.345	−0.254272
$73$	597.947	0.958690	0.479345	−	0.877627i	$-0.340874\pi$
$73$	597.947	0.958690	0.479345	+	0.877627i	$0.340874\pi$
$74$	−187.497	−0.294542
$75$	30.7557	0.0473515
$76$	49.5100	0.0747262
$77$	−186.955	−0.276694
$78$	197.674	0.286952
$79$	710.808	1.01231	0.506153	−	0.862444i	$-0.331067\pi$
$79$	710.808	1.01231	0.506153	+	0.862444i	$0.331067\pi$
$80$	175.626	0.245444
$81$	−876.226	−1.20196
$82$	927.854	1.24957
$83$	−508.468	−0.672429	−0.336215	−	0.941785i	$-0.609147\pi$
$83$	−508.468	−0.672429	−0.336215	+	0.941785i	$0.609147\pi$
$84$	118.980	0.154545
$85$	889.777	1.13541
$86$	−24.0646	−0.0301738
$87$	1909.02	2.35251
$88$	−342.574	−0.414983
$89$	1284.51	1.52987	0.764933	−	0.644109i	$-0.222772\pi$
$89$	1284.51	1.52987	0.764933	+	0.644109i	$0.222772\pi$
$90$	−426.290	−0.499277
$91$	−63.3356	−0.0729602
$92$	−321.283	−0.364087
$93$	−1567.47	−1.74773
$94$	−871.939	−0.956741
$95$	135.863	0.146729
$96$	218.019	0.231786
$97$	1553.35	1.62597	0.812984	−	0.582286i	$-0.197841\pi$
$97$	1553.35	1.62597	0.812984	+	0.582286i	$0.197841\pi$
$98$	647.878	0.667812
$99$	831.519	0.844149
$100$	−18.0568	−0.0180568
$101$	1540.97	1.51814	0.759072	−	0.651007i	$-0.225653\pi$
$101$	1540.97	1.51814	0.759072	+	0.651007i	$0.225653\pi$
$102$	1104.55	1.07223
$103$	1397.17	1.33657	0.668286	−	0.743905i	$-0.267028\pi$
$103$	1397.17	1.33657	0.668286	+	0.743905i	$0.267028\pi$
$104$	−116.056	−0.109425
$105$	326.500	0.303458
$106$	455.099	0.417011
$107$	1168.71	1.05592	0.527958	−	0.849270i	$-0.322958\pi$
$107$	1168.71	1.05592	0.527958	+	0.849270i	$0.322958\pi$
$108$	206.624	0.184096
$109$	−246.815	−0.216886	−0.108443	−	0.994103i	$-0.534586\pi$
$109$	−246.815	−0.216886	−0.108443	+	0.994103i	$0.534586\pi$
$110$	−940.075	−0.814842
$111$	−638.716	−0.546165
$112$	−69.8540	−0.0589338
$113$	1440.81	1.19947	0.599733	−	0.800200i	$-0.295274\pi$
$113$	1440.81	1.19947	0.599733	+	0.800200i	$0.295274\pi$
$114$	168.658	0.138564
$115$	−881.648	−0.714905
$116$	−1120.79	−0.897096
$117$	281.698	0.222590
$118$	−1074.07	−0.837935
$119$	−353.903	−0.272624
$120$	598.276	0.455124
$121$	502.704	0.377689
$122$	1027.34	0.762388
$123$	3160.78	2.31705
$124$	920.271	0.666474
$125$	−1421.63	−1.01723
$126$	169.554	0.119882
$127$	−2687.95	−1.87809	−0.939044	−	0.343797i	$-0.888287\pi$
$127$	−2687.95	−1.87809	−0.939044	+	0.343797i	$0.888287\pi$
$128$	−128.000	−0.0883883
$129$	−81.9770	−0.0559510
$130$	−318.475	−0.214862
$131$	1031.74	0.688116	0.344058	−	0.938948i	$-0.388198\pi$
$131$	1031.74	0.688116	0.344058	+	0.938948i	$0.388198\pi$
$132$	−1166.99	−0.769498
$133$	−54.0387	−0.0352312
$134$	−1608.98	−1.03728
$135$	567.006	0.361483
$136$	−648.490	−0.408879
$137$	2653.53	1.65479	0.827397	−	0.561618i	$-0.189821\pi$
$137$	2653.53	1.65479	0.827397	+	0.561618i	$0.189821\pi$
$138$	−1094.46	−0.675122
$139$	−1752.17	−1.06919	−0.534595	−	0.845108i	$-0.679536\pi$
$139$	−1752.17	−1.06919	−0.534595	+	0.845108i	$0.679536\pi$
$140$	−191.690	−0.115720
$141$	−2970.30	−1.77407
$142$	134.463	0.0794639
$143$	621.214	0.363277
$144$	310.690	0.179798
$145$	−3075.63	−1.76150
$146$	−1195.89	−0.677896
$147$	2207.02	1.23832
$148$	374.994	0.208272
$149$	−1196.12	−0.657652	−0.328826	−	0.944390i	$-0.606653\pi$
$149$	−1196.12	−0.657652	−0.328826	+	0.944390i	$0.606653\pi$
$150$	−61.5114	−0.0334826
$151$	−3271.09	−1.76290	−0.881450	−	0.472278i	$-0.843432\pi$
$151$	−3271.09	−1.76290	−0.881450	+	0.472278i	$0.843432\pi$
$152$	−99.0201	−0.0528394
$153$	1574.06	0.831732
$154$	373.909	0.195652
$155$	2525.36	1.30866
$156$	−395.349	−0.202905
$157$	56.4475	0.0286943	0.0143471	−	0.999897i	$-0.495433\pi$
$157$	56.4475	0.0286943	0.0143471	+	0.999897i	$0.495433\pi$
$158$	−1421.62	−0.715809
$159$	1550.31	0.773257
$160$	−351.251	−0.173555
$161$	350.670	0.171656
$162$	1752.45	0.849911
$163$	−1668.75	−0.801883	−0.400942	−	0.916104i	$-0.631317\pi$
$163$	−1668.75	−0.801883	−0.400942	+	0.916104i	$0.631317\pi$
$164$	−1855.71	−0.883576
$165$	−3202.41	−1.51095
$166$	1016.94	0.475479
$167$	−1861.07	−0.862357	−0.431179	−	0.902267i	$-0.641902\pi$
$167$	−1861.07	−0.862357	−0.431179	+	0.902267i	$0.641902\pi$
$168$	−237.961	−0.109280
$169$	−1986.55	−0.904209
$170$	−1779.55	−0.802856
$171$	240.348	0.107485
$172$	48.1292	0.0213361
$173$	2094.04	0.920270	0.460135	−	0.887849i	$-0.347801\pi$
$173$	2094.04	0.920270	0.460135	+	0.887849i	$0.347801\pi$
$174$	−3818.04	−1.66347
$175$	19.7085	0.00851327
$176$	685.148	0.293437
$177$	−3658.87	−1.55377
$178$	−2569.03	−1.08178
$179$	1404.28	0.586372	0.293186	−	0.956055i	$-0.405284\pi$
$179$	1404.28	0.586372	0.293186	+	0.956055i	$0.405284\pi$
$180$	852.580	0.353042
$181$	1015.96	0.417213	0.208606	−	0.978000i	$-0.433107\pi$
$181$	1015.96	0.417213	0.208606	+	0.978000i	$0.433107\pi$
$182$	126.671	0.0515907
$183$	3499.69	1.41369
$184$	642.565	0.257449
$185$	1029.04	0.408954
$186$	3134.94	1.23583
$187$	3471.18	1.35742
$188$	1743.88	0.676518
$189$	−225.523	−0.0867958
$190$	−271.726	−0.103753
$191$	1688.24	0.639563	0.319782	−	0.947491i	$-0.396390\pi$
$191$	1688.24	0.639563	0.319782	+	0.947491i	$0.396390\pi$
$192$	−436.037	−0.163897
$193$	3483.86	1.29934	0.649672	−	0.760214i	$-0.274906\pi$
$193$	3483.86	1.29934	0.649672	+	0.760214i	$0.274906\pi$
$194$	−3106.70	−1.14973
$195$	−1084.90	−0.398416
$196$	−1295.76	−0.472214
$197$	−1948.88	−0.704831	−0.352416	−	0.935844i	$-0.614640\pi$
$197$	−1948.88	−0.704831	−0.352416	+	0.935844i	$0.614640\pi$
$198$	−1663.04	−0.596904
$199$	5303.40	1.88919	0.944594	−	0.328242i	$-0.106456\pi$
$199$	5303.40	1.88919	0.944594	+	0.328242i	$0.106456\pi$
$200$	36.1137	0.0127681
$201$	−5481.08	−1.92341
$202$	−3081.95	−1.07349
$203$	1223.31	0.422954
$204$	−2209.11	−0.758179
$205$	−5092.34	−1.73495
$206$	−2794.33	−0.945099
$207$	−1559.68	−0.523696
$208$	232.112	0.0773752
$209$	530.027	0.175420
$210$	−653.000	−0.214578
$211$	2937.60	0.958449	0.479224	−	0.877692i	$-0.340918\pi$
$211$	2937.60	0.958449	0.479224	+	0.877692i	$0.340918\pi$
$212$	−910.198	−0.294871
$213$	458.054	0.147349
$214$	−2337.41	−0.746646
$215$	132.074	0.0418946
$216$	−413.247	−0.130176
$217$	−1004.45	−0.314223
$218$	493.629	0.153361
$219$	−4073.86	−1.25701
$220$	1880.15	0.576180
$221$	1175.95	0.357933
$222$	1277.43	0.386197
$223$	2235.46	0.671289	0.335645	−	0.941989i	$-0.391046\pi$
$223$	2235.46	0.671289	0.335645	+	0.941989i	$0.391046\pi$
$224$	139.708	0.0416725
$225$	−87.6576	−0.0259726
$226$	−2881.61	−0.848150
$227$	3543.01	1.03594	0.517969	−	0.855399i	$-0.326688\pi$
$227$	3543.01	1.03594	0.517969	+	0.855399i	$0.326688\pi$
$228$	−337.316	−0.0979794
$229$	−508.575	−0.146758	−0.0733790	−	0.997304i	$-0.523378\pi$
$229$	−508.575	−0.146758	−0.0733790	+	0.997304i	$0.523378\pi$
$230$	1763.30	0.505514
$231$	1273.74	0.362795
$232$	2241.59	0.634343
$233$	1701.88	0.478516	0.239258	−	0.970956i	$-0.423096\pi$
$233$	1701.88	0.478516	0.239258	+	0.970956i	$0.423096\pi$
$234$	−563.397	−0.157395
$235$	4785.46	1.32838
$236$	2148.14	0.592510
$237$	−4842.80	−1.32731
$238$	707.806	0.192774
$239$	871.533	0.235878	0.117939	−	0.993021i	$-0.462371\pi$
$239$	871.533	0.235878	0.117939	+	0.993021i	$0.462371\pi$
$240$	−1196.55	−0.321821
$241$	−3234.84	−0.864623	−0.432311	−	0.901724i	$-0.642302\pi$
$241$	−3234.84	−0.864623	−0.432311	+	0.901724i	$0.642302\pi$
$242$	−1005.41	−0.267066
$243$	4575.09	1.20779
$244$	−2054.69	−0.539090
$245$	−3555.75	−0.927219
$246$	−6321.55	−1.63840
$247$	179.560	0.0462556
$248$	−1840.54	−0.471268
$249$	3464.24	0.881675
$250$	2843.25	0.719292
$251$	3737.33	0.939835	0.469917	−	0.882710i	$-0.344284\pi$
$251$	3737.33	0.939835	0.469917	+	0.882710i	$0.344284\pi$
$252$	−339.109	−0.0847692
$253$	−3439.47	−0.854695
$254$	5375.90	1.32801
$255$	−6062.12	−1.48873
$256$	256.000	0.0625000
$257$	2378.81	0.577378	0.288689	−	0.957423i	$-0.406781\pi$
$257$	2378.81	0.577378	0.288689	+	0.957423i	$0.406781\pi$
$258$	163.954	0.0395633
$259$	−409.294	−0.0981942
$260$	636.949	0.151930
$261$	−5440.94	−1.29037
$262$	−2063.47	−0.486571
$263$	−7352.72	−1.72391	−0.861954	−	0.506986i	$-0.830760\pi$
$263$	−7352.72	−1.72391	−0.861954	+	0.506986i	$0.830760\pi$
$264$	2333.99	0.544117
$265$	−2497.72	−0.578995
$266$	108.077	0.0249122
$267$	−8751.50	−2.00593
$268$	3217.97	0.733466
$269$	−269.000	−0.0609711
$269$	−269.000	−0.0609711
$270$	−1134.01	−0.255607
$271$	295.175	0.0661647	0.0330823	−	0.999453i	$-0.489468\pi$
$271$	295.175	0.0661647	0.0330823	+	0.999453i	$0.489468\pi$
$272$	1296.98	0.289121
$273$	431.511	0.0956639
$274$	−5307.07	−1.17012
$275$	−193.307	−0.0423884
$276$	2188.93	0.477384
$277$	5551.91	1.20427	0.602133	−	0.798396i	$-0.294318\pi$
$277$	5551.91	1.20427	0.602133	+	0.798396i	$0.294318\pi$
$278$	3504.35	0.756032
$279$	4467.49	0.958643
$280$	383.380	0.0818262
$281$	6161.18	1.30799	0.653995	−	0.756499i	$-0.273092\pi$
$281$	6161.18	1.30799	0.653995	+	0.756499i	$0.273092\pi$
$282$	5940.60	1.25446
$283$	−4983.98	−1.04688	−0.523440	−	0.852062i	$-0.675352\pi$
$283$	−4983.98	−1.04688	−0.523440	+	0.852062i	$0.675352\pi$
$284$	−268.926	−0.0561895
$285$	−925.646	−0.192388
$286$	−1242.43	−0.256875
$287$	2025.45	0.416580
$288$	−621.380	−0.127136
$289$	1657.92	0.337455
$290$	6151.26	1.24557
$291$	−10583.1	−2.13194
$292$	2391.79	0.479345
$293$	155.885	0.0310815	0.0155408	−	0.999879i	$-0.495053\pi$
$293$	155.885	0.0310815	0.0155408	+	0.999879i	$0.495053\pi$
$294$	−4414.05	−0.875621
$295$	5894.83	1.16342
$296$	−749.988	−0.147271
$297$	2212.00	0.432165
$298$	2392.25	0.465030
$299$	−1165.21	−0.225371
$300$	123.023	0.0236758
$301$	−52.5315	−0.0100593
$302$	6542.19	1.24656
$303$	−10498.8	−1.99056
$304$	198.040	0.0373631
$305$	−5638.37	−1.05853
$306$	−3148.11	−0.588123
$307$	6785.97	1.26155	0.630775	−	0.775966i	$-0.282737\pi$
$307$	6785.97	1.26155	0.630775	+	0.775966i	$0.282737\pi$
$308$	−747.818	−0.138347
$309$	−9519.01	−1.75248
$310$	−5050.73	−0.925361
$311$	1599.69	0.291673	0.145837	−	0.989309i	$-0.453413\pi$
$311$	1599.69	0.291673	0.145837	+	0.989309i	$0.453413\pi$
$312$	790.698	0.143476
$313$	−6297.60	−1.13726	−0.568629	−	0.822594i	$-0.692526\pi$
$313$	−6297.60	−1.13726	−0.568629	+	0.822594i	$0.692526\pi$
$314$	−112.895	−0.0202899
$315$	−930.565	−0.166449
$316$	2843.23	0.506153
$317$	225.200	0.0399006	0.0199503	−	0.999801i	$-0.493649\pi$
$317$	225.200	0.0399006	0.0199503	+	0.999801i	$0.493649\pi$
$318$	−3100.63	−0.546776
$319$	−11998.6	−2.10593
$320$	702.503	0.122722
$321$	−7962.49	−1.38450
$322$	−701.340	−0.121379
$323$	1003.34	0.172839
$324$	−3504.90	−0.600978
$325$	−65.4875	−0.0111772
$326$	3337.51	0.567017
$327$	1681.57	0.284376
$328$	3711.42	0.624783
$329$	−1903.39	−0.318958
$330$	6404.81	1.06840
$331$	−10514.9	−1.74608	−0.873039	−	0.487651i	$-0.837854\pi$
$331$	−10514.9	−1.74608	−0.873039	+	0.487651i	$0.837854\pi$
$332$	−2033.87	−0.336215
$333$	1820.42	0.299575
$334$	3722.13	0.609779
$335$	8830.59	1.44020
$336$	475.921	0.0772727
$337$	6123.68	0.989845	0.494923	−	0.868937i	$-0.335196\pi$
$337$	6123.68	0.989845	0.494923	+	0.868937i	$0.335196\pi$
$338$	3973.10	0.639372
$339$	−9816.33	−1.57271
$340$	3559.11	0.567705
$341$	9851.91	1.56455
$342$	−480.696	−0.0760032
$343$	2911.77	0.458370
$344$	−96.2583	−0.0150869
$345$	6006.74	0.937369
$346$	−4188.07	−0.650729
$347$	3653.06	0.565149	0.282575	−	0.959245i	$-0.408812\pi$
$347$	3653.06	0.565149	0.282575	+	0.959245i	$0.408812\pi$
$348$	7636.07	1.17625
$349$	10099.3	1.54901	0.774504	−	0.632569i	$-0.218000\pi$
$349$	10099.3	1.54901	0.774504	+	0.632569i	$0.218000\pi$
$350$	−39.4170	−0.00601979
$351$	749.371	0.113956
$352$	−1370.30	−0.207492
$353$	−7918.64	−1.19396	−0.596978	−	0.802257i	$-0.703632\pi$
$353$	−7918.64	−1.19396	−0.596978	+	0.802257i	$0.703632\pi$
$354$	7317.75	1.09868
$355$	−737.973	−0.110331
$356$	5138.05	0.764933
$357$	2411.17	0.357459
$358$	−2808.56	−0.414628
$359$	7882.78	1.15888	0.579439	−	0.815016i	$-0.303272\pi$
$359$	7882.78	1.15888	0.579439	+	0.815016i	$0.303272\pi$
$360$	−1705.16	−0.249639
$361$	−6705.80	−0.977664
$362$	−2031.91	−0.295014
$363$	−3424.97	−0.495218
$364$	−253.343	−0.0364801
$365$	6563.42	0.941220
$366$	−6999.38	−0.999627
$367$	−4183.29	−0.595003	−0.297501	−	0.954721i	$-0.596153\pi$
$367$	−4183.29	−0.595003	−0.297501	+	0.954721i	$0.596153\pi$
$368$	−1285.13	−0.182044
$369$	−9008.60	−1.27092
$370$	−2058.08	−0.289174
$371$	993.453	0.139023
$372$	−6269.89	−0.873867
$373$	−10184.2	−1.41372	−0.706858	−	0.707356i	$-0.749888\pi$
$373$	−10184.2	−1.41372	−0.706858	+	0.707356i	$0.749888\pi$
$374$	−6942.37	−0.959843
$375$	9685.66	1.33377
$376$	−3487.76	−0.478371
$377$	−4064.83	−0.555304
$378$	451.047	0.0613739
$379$	3203.75	0.434210	0.217105	−	0.976148i	$-0.430339\pi$
$379$	3203.75	0.434210	0.217105	+	0.976148i	$0.430339\pi$
$380$	543.452	0.0733645
$381$	18313.2	2.46251
$382$	−3376.47	−0.452239
$383$	10771.8	1.43712	0.718558	−	0.695467i	$-0.244803\pi$
$383$	10771.8	1.43712	0.718558	+	0.695467i	$0.244803\pi$
$384$	872.075	0.115893
$385$	−2052.13	−0.271652
$386$	−6967.72	−0.918776
$387$	233.645	0.0306895
$388$	6213.41	0.812984
$389$	2226.02	0.290138	0.145069	−	0.989422i	$-0.453660\pi$
$389$	2226.02	0.290138	0.145069	+	0.989422i	$0.453660\pi$
$390$	2169.79	0.281723
$391$	−6510.89	−0.842122
$392$	2591.51	0.333906
$393$	−7029.30	−0.902243
$394$	3897.75	0.498391
$395$	7802.26	0.993859
$396$	3326.08	0.422075
$397$	−507.500	−0.0641580	−0.0320790	−	0.999485i	$-0.510213\pi$
$397$	−507.500	−0.0641580	−0.0320790	+	0.999485i	$0.510213\pi$
$398$	−10606.8	−1.33586
$399$	368.170	0.0461944
$400$	−72.2274	−0.00902842
$401$	−380.992	−0.0474459	−0.0237230	−	0.999719i	$-0.507552\pi$
$401$	−380.992	−0.0474459	−0.0237230	+	0.999719i	$0.507552\pi$
$402$	10962.2	1.36006
$403$	3337.59	0.412549
$404$	6163.89	0.759072
$405$	−9617.98	−1.18005
$406$	−2446.63	−0.299074
$407$	4014.48	0.488919
$408$	4418.22	0.536113
$409$	−9377.58	−1.13372	−0.566860	−	0.823814i	$-0.691842\pi$
$409$	−9377.58	−1.13372	−0.566860	+	0.823814i	$0.691842\pi$
$410$	10184.7	1.22679
$411$	−18078.8	−2.16973
$412$	5588.67	0.668286
$413$	−2344.63	−0.279351
$414$	3119.35	0.370309
$415$	−5581.25	−0.660176
$416$	−464.223	−0.0547125
$417$	11937.7	1.40190
$418$	−1060.05	−0.124041
$419$	−10205.5	−1.18990	−0.594951	−	0.803762i	$-0.702829\pi$
$419$	−10205.5	−1.18990	−0.594951	+	0.803762i	$0.702829\pi$
$420$	1306.00	0.151729
$421$	3310.61	0.383252	0.191626	−	0.981468i	$-0.438624\pi$
$421$	3310.61	0.383252	0.191626	+	0.981468i	$0.438624\pi$
$422$	−5875.20	−0.677726
$423$	8465.72	0.973090
$424$	1820.40	0.208505
$425$	−365.927	−0.0417649
$426$	−916.107	−0.104191
$427$	2242.63	0.254165
$428$	4674.82	0.527958
$429$	−4232.39	−0.476321
$430$	−264.147	−0.0296240
$431$	−4989.78	−0.557655	−0.278827	−	0.960341i	$-0.589946\pi$
$431$	−4989.78	−0.557655	−0.278827	+	0.960341i	$0.589946\pi$
$432$	826.495	0.0920480
$433$	14694.2	1.63085	0.815425	−	0.578862i	$-0.196503\pi$
$433$	14694.2	1.63085	0.815425	+	0.578862i	$0.196503\pi$
$434$	2008.90	0.222189
$435$	20954.5	2.30964
$436$	−987.258	−0.108443
$437$	−994.170	−0.108827
$438$	8147.73	0.888843
$439$	7286.35	0.792161	0.396081	−	0.918216i	$-0.370370\pi$
$439$	7286.35	0.792161	0.396081	+	0.918216i	$0.370370\pi$
$440$	−3760.30	−0.407421
$441$	−6290.29	−0.679224
$442$	−2351.91	−0.253097
$443$	6330.81	0.678975	0.339487	−	0.940611i	$-0.389746\pi$
$443$	6330.81	0.678975	0.339487	+	0.940611i	$0.389746\pi$
$444$	−2554.87	−0.273082
$445$	14099.6	1.50199
$446$	−4470.92	−0.474673
$447$	8149.29	0.862300
$448$	−279.416	−0.0294669
$449$	536.523	0.0563921	0.0281961	−	0.999602i	$-0.491024\pi$
$449$	536.523	0.0563921	0.0281961	+	0.999602i	$0.491024\pi$
$450$	175.315	0.0183654
$451$	−19866.2	−2.07420
$452$	5763.22	0.599733
$453$	22286.2	2.31148
$454$	−7086.02	−0.732519
$455$	−695.210	−0.0716307
$456$	674.632	0.0692819
$457$	−15325.7	−1.56873	−0.784363	−	0.620302i	$-0.787010\pi$
$457$	−15325.7	−1.56873	−0.784363	+	0.620302i	$0.787010\pi$
$458$	1017.15	0.103774
$459$	4187.29	0.425808
$460$	−3526.59	−0.357453
$461$	−9299.66	−0.939541	−0.469771	−	0.882789i	$-0.655663\pi$
$461$	−9299.66	−0.939541	−0.469771	+	0.882789i	$0.655663\pi$
$462$	−2547.47	−0.256535
$463$	5124.09	0.514334	0.257167	−	0.966367i	$-0.417211\pi$
$463$	5124.09	0.514334	0.257167	+	0.966367i	$0.417211\pi$
$464$	−4483.18	−0.448548
$465$	−17205.5	−1.71589
$466$	−3403.77	−0.338362
$467$	−8778.92	−0.869893	−0.434947	−	0.900456i	$-0.643233\pi$
$467$	−8778.92	−0.869893	−0.434947	+	0.900456i	$0.643233\pi$
$468$	1126.79	0.111295
$469$	−3512.31	−0.345807
$470$	−9570.93	−0.939307
$471$	−384.582	−0.0376233
$472$	−4296.29	−0.418968
$473$	515.244	0.0500866
$474$	9685.60	0.938553
$475$	−55.8747	−0.00539728
$476$	−1415.61	−0.136312
$477$	−4418.59	−0.424137
$478$	−1743.07	−0.166791
$479$	−4476.36	−0.426994	−0.213497	−	0.976944i	$-0.568485\pi$
$479$	−4476.36	−0.426994	−0.213497	+	0.976944i	$0.568485\pi$
$480$	2393.10	0.227562
$481$	1360.01	0.128921
$482$	6469.67	0.611381
$483$	−2389.14	−0.225072
$484$	2010.82	0.188845
$485$	17050.5	1.59634
$486$	−9150.18	−0.854034
$487$	2490.55	0.231741	0.115870	−	0.993264i	$-0.463034\pi$
$487$	2490.55	0.231741	0.115870	+	0.993264i	$0.463034\pi$
$488$	4109.38	0.381194
$489$	11369.4	1.05141
$490$	7111.50	0.655643
$491$	17685.3	1.62551	0.812756	−	0.582604i	$-0.197966\pi$
$491$	17685.3	1.62551	0.812756	+	0.582604i	$0.197966\pi$
$492$	12643.1	1.15853
$493$	−22713.2	−2.07496
$494$	−359.120	−0.0327077
$495$	9127.25	0.828767
$496$	3681.09	0.333237
$497$	293.524	0.0264917
$498$	−6928.48	−0.623439
$499$	8668.95	0.777706	0.388853	−	0.921300i	$-0.372871\pi$
$499$	8668.95	0.777706	0.388853	+	0.921300i	$0.372871\pi$
$500$	−5686.50	−0.508616
$501$	12679.6	1.13070
$502$	−7474.67	−0.664563
$503$	−1594.53	−0.141345	−0.0706726	−	0.997500i	$-0.522515\pi$
$503$	−1594.53	−0.141345	−0.0706726	+	0.997500i	$0.522515\pi$
$504$	678.217	0.0599409
$505$	16914.6	1.49048
$506$	6878.95	0.604361
$507$	13534.5	1.18558
$508$	−10751.8	−0.939044
$509$	−8686.94	−0.756467	−0.378234	−	0.925710i	$-0.623468\pi$
$509$	−8686.94	−0.756467	−0.378234	+	0.925710i	$0.623468\pi$
$510$	12124.2	1.05269
$511$	−2610.56	−0.225997
$512$	−512.000	−0.0441942
$513$	639.372	0.0550272
$514$	−4757.62	−0.408268
$515$	15336.1	1.31222
$516$	−327.908	−0.0279755
$517$	18669.0	1.58813
$518$	818.589	0.0694338
$519$	−14266.9	−1.20664
$520$	−1273.90	−0.107431
$521$	13757.3	1.15685	0.578423	−	0.815737i	$-0.303668\pi$
$521$	13757.3	1.15685	0.578423	+	0.815737i	$0.303668\pi$
$522$	10881.9	0.912426
$523$	−3781.19	−0.316138	−0.158069	−	0.987428i	$-0.550527\pi$
$523$	−3781.19	−0.316138	−0.158069	+	0.987428i	$0.550527\pi$
$524$	4126.94	0.344058
$525$	−134.276	−0.0111624
$526$	14705.4	1.21899
$527$	18649.6	1.54153
$528$	−4667.97	−0.384749
$529$	−5715.59	−0.469762
$530$	4995.44	0.409412
$531$	10428.2	0.852254
$532$	−216.155	−0.0176156
$533$	−6730.18	−0.546935
$534$	17503.0	1.41841
$535$	12828.4	1.03667
$536$	−6435.94	−0.518638
$537$	−9567.46	−0.768839
$538$	538.000	0.0431131
$539$	−13871.6	−1.10852
$540$	2268.03	0.180741
$541$	−846.129	−0.0672420	−0.0336210	−	0.999435i	$-0.510704\pi$
$541$	−846.129	−0.0672420	−0.0336210	+	0.999435i	$0.510704\pi$
$542$	−590.351	−0.0467855
$543$	−6921.80	−0.547041
$544$	−2593.96	−0.204439
$545$	−2709.18	−0.212933
$546$	−863.022	−0.0676446
$547$	−1077.27	−0.0842060	−0.0421030	−	0.999113i	$-0.513406\pi$
$547$	−1077.27	−0.0842060	−0.0421030	+	0.999113i	$0.513406\pi$
$548$	10614.1	0.827397
$549$	−9974.55	−0.775416
$550$	386.613	0.0299732
$551$	−3468.16	−0.268146
$552$	−4377.85	−0.337561
$553$	−3103.30	−0.238636
$554$	−11103.8	−0.851545
$555$	−7010.94	−0.536212
$556$	−7008.70	−0.534595
$557$	17202.9	1.30863	0.654317	−	0.756220i	$-0.272956\pi$
$557$	17202.9	1.30863	0.654317	+	0.756220i	$0.272956\pi$
$558$	−8934.98	−0.677863
$559$	174.552	0.0132071
$560$	−766.760	−0.0578598
$561$	−23649.5	−1.77982
$562$	−12322.4	−0.924888
$563$	−891.139	−0.0667088	−0.0333544	−	0.999444i	$-0.510619\pi$
$563$	−891.139	−0.0667088	−0.0333544	+	0.999444i	$0.510619\pi$
$564$	−11881.2	−0.887036
$565$	15815.1	1.17761
$566$	9967.97	0.740256
$567$	3825.49	0.283343
$568$	537.852	0.0397320
$569$	21115.6	1.55573	0.777866	−	0.628430i	$-0.216302\pi$
$569$	21115.6	1.55573	0.777866	+	0.628430i	$0.216302\pi$
$570$	1851.29	0.136039
$571$	11665.3	0.854952	0.427476	−	0.904027i	$-0.359403\pi$
$571$	11665.3	0.854952	0.427476	+	0.904027i	$0.359403\pi$
$572$	2484.86	0.181638
$573$	−11502.1	−0.838582
$574$	−4050.90	−0.294567
$575$	362.584	0.0262971
$576$	1242.76	0.0898988
$577$	−18980.9	−1.36947	−0.684737	−	0.728791i	$-0.740083\pi$
$577$	−18980.9	−1.36947	−0.684737	+	0.728791i	$0.740083\pi$
$578$	−3315.84	−0.238617
$579$	−23735.8	−1.70367
$580$	−12302.5	−0.880749
$581$	2219.91	0.158515
$582$	21166.2	1.50751
$583$	−9744.08	−0.692210
$584$	−4783.57	−0.338948
$585$	3092.09	0.218534
$586$	−311.769	−0.0219779
$587$	18871.8	1.32696	0.663479	−	0.748195i	$-0.269079\pi$
$587$	18871.8	1.32696	0.663479	+	0.748195i	$0.269079\pi$
$588$	8828.10	0.619158
$589$	2847.67	0.199212
$590$	−11789.7	−0.822666
$591$	13277.9	0.924160
$592$	1499.98	0.104136
$593$	1805.65	0.125041	0.0625203	−	0.998044i	$-0.480086\pi$
$593$	1805.65	0.125041	0.0625203	+	0.998044i	$0.480086\pi$
$594$	−4424.00	−0.305587
$595$	−3884.65	−0.267656
$596$	−4784.49	−0.328826
$597$	−36132.5	−2.47706
$598$	2330.42	0.159361
$599$	−23197.4	−1.58233	−0.791167	−	0.611600i	$-0.790526\pi$
$599$	−23197.4	−1.58233	−0.791167	+	0.611600i	$0.790526\pi$
$600$	−246.046	−0.0167413
$601$	11255.3	0.763916	0.381958	−	0.924180i	$-0.375250\pi$
$601$	11255.3	0.763916	0.381958	+	0.924180i	$0.375250\pi$
$602$	105.063	0.00711303
$603$	15621.7	1.05500
$604$	−13084.4	−0.881450
$605$	5517.98	0.370806
$606$	20997.6	1.40754
$607$	−19788.3	−1.32320	−0.661599	−	0.749858i	$-0.730122\pi$
$607$	−19788.3	−1.32320	−0.661599	+	0.749858i	$0.730122\pi$
$608$	−396.080	−0.0264197
$609$	−8334.53	−0.554569
$610$	11276.7	0.748495
$611$	6324.60	0.418766
$612$	6296.23	0.415866
$613$	4567.25	0.300929	0.150464	−	0.988615i	$-0.451923\pi$
$613$	4567.25	0.300929	0.150464	+	0.988615i	$0.451923\pi$
$614$	−13571.9	−0.892051
$615$	34694.6	2.27483
$616$	1495.64	0.0978261
$617$	3433.52	0.224033	0.112016	−	0.993706i	$-0.464269\pi$
$617$	3433.52	0.224033	0.112016	+	0.993706i	$0.464269\pi$
$618$	19038.0	1.23919
$619$	−4237.77	−0.275170	−0.137585	−	0.990490i	$-0.543934\pi$
$619$	−4237.77	−0.275170	−0.137585	+	0.990490i	$0.543934\pi$
$620$	10101.5	0.654329
$621$	−4149.04	−0.268108
$622$	−3199.39	−0.206244
$623$	−5608.03	−0.360643
$624$	−1581.40	−0.101453
$625$	−15040.3	−0.962582
$626$	12595.2	0.804162
$627$	−3611.12	−0.230007
$628$	225.790	0.0143471
$629$	7599.36	0.481727
$630$	1861.13	0.117697
$631$	−14706.9	−0.927846	−0.463923	−	0.885876i	$-0.653558\pi$
$631$	−14706.9	−0.927846	−0.463923	+	0.885876i	$0.653558\pi$
$632$	−5686.47	−0.357904
$633$	−20014.1	−1.25670
$634$	−450.400	−0.0282140
$635$	−29504.6	−1.84386
$636$	6201.26	0.386629
$637$	−4699.38	−0.292302
$638$	23997.2	1.48912
$639$	−1305.51	−0.0808218
$640$	−1405.01	−0.0867777
$641$	−17175.0	−1.05830	−0.529150	−	0.848529i	$-0.677489\pi$
$641$	−17175.0	−1.05830	−0.529150	+	0.848529i	$0.677489\pi$
$642$	15925.0	0.978986
$643$	−21183.9	−1.29924	−0.649620	−	0.760259i	$-0.725072\pi$
$643$	−21183.9	−1.29924	−0.649620	+	0.760259i	$0.725072\pi$
$644$	1402.68	0.0858282
$645$	−899.829	−0.0549314
$646$	−2006.67	−0.122216
$647$	−22797.5	−1.38526	−0.692630	−	0.721293i	$-0.743548\pi$
$647$	−22797.5	−1.38526	−0.692630	+	0.721293i	$0.743548\pi$
$648$	7009.81	0.424956
$649$	22996.8	1.39092
$650$	130.975	0.00790349
$651$	6843.39	0.412002
$652$	−6675.02	−0.400942
$653$	−14781.3	−0.885813	−0.442907	−	0.896568i	$-0.646053\pi$
$653$	−14781.3	−0.885813	−0.442907	+	0.896568i	$0.646053\pi$
$654$	−3363.14	−0.201084
$655$	11325.0	0.675576
$656$	−7422.84	−0.441788
$657$	11611.0	0.689480
$658$	3806.78	0.225537
$659$	6278.22	0.371115	0.185558	−	0.982633i	$-0.440591\pi$
$659$	6278.22	0.371115	0.185558	+	0.982633i	$0.440591\pi$
$660$	−12809.6	−0.755476
$661$	−22338.9	−1.31449	−0.657247	−	0.753675i	$-0.728279\pi$
$661$	−22338.9	−1.31449	−0.657247	+	0.753675i	$0.728279\pi$
$662$	21029.8	1.23466
$663$	−8011.87	−0.469314
$664$	4067.75	0.237740
$665$	−593.161	−0.0345892
$666$	−3640.84	−0.211831
$667$	22505.7	1.30649
$668$	−7444.27	−0.431179
$669$	−15230.4	−0.880180
$670$	−17661.2	−1.01837
$671$	−21996.3	−1.26551
$672$	−951.843	−0.0546401
$673$	−32188.5	−1.84365	−0.921825	−	0.387607i	$-0.873302\pi$
$673$	−32188.5	−1.84365	−0.921825	+	0.387607i	$0.873302\pi$
$674$	−12247.4	−0.699926
$675$	−233.186	−0.0132968
$676$	−7946.19	−0.452105
$677$	17251.0	0.979333	0.489666	−	0.871910i	$-0.337119\pi$
$677$	17251.0	0.979333	0.489666	+	0.871910i	$0.337119\pi$
$678$	19632.7	1.11208
$679$	−6781.74	−0.383298
$680$	−7118.21	−0.401428
$681$	−24138.8	−1.35830
$682$	−19703.8	−1.10630
$683$	27527.8	1.54220	0.771098	−	0.636716i	$-0.219708\pi$
$683$	27527.8	1.54220	0.771098	+	0.636716i	$0.219708\pi$
$684$	961.393	0.0537423
$685$	29126.8	1.62464
$686$	−5823.55	−0.324117
$687$	3464.96	0.192426
$688$	192.517	0.0106681
$689$	−3301.06	−0.182526
$690$	−12013.5	−0.662820
$691$	1757.83	0.0967743	0.0483871	−	0.998829i	$-0.484592\pi$
$691$	1757.83	0.0967743	0.0483871	+	0.998829i	$0.484592\pi$
$692$	8376.15	0.460135
$693$	−3630.31	−0.198996
$694$	−7306.13	−0.399621
$695$	−19232.9	−1.04971
$696$	−15272.1	−0.831737
$697$	−37606.5	−2.04368
$698$	−20198.6	−1.09531
$699$	−11595.1	−0.627419
$700$	78.8340	0.00425663
$701$	13105.1	0.706098	0.353049	−	0.935605i	$-0.385145\pi$
$701$	13105.1	0.706098	0.353049	+	0.935605i	$0.385145\pi$
$702$	−1498.74	−0.0805789
$703$	1160.37	0.0622536
$704$	2740.59	0.146719
$705$	−32603.8	−1.74174
$706$	15837.3	0.844255
$707$	−6727.70	−0.357880
$708$	−14635.5	−0.776886
$709$	−3131.78	−0.165891	−0.0829453	−	0.996554i	$-0.526433\pi$
$709$	−3131.78	−0.165891	−0.0829453	+	0.996554i	$0.526433\pi$
$710$	1475.95	0.0780159
$711$	13802.6	0.728041
$712$	−10276.1	−0.540890
$713$	−18479.2	−0.970619
$714$	−4822.34	−0.252762
$715$	6818.82	0.356657
$716$	5617.11	0.293186
$717$	−5937.83	−0.309278
$718$	−15765.6	−0.819450
$719$	16893.9	0.876269	0.438135	−	0.898909i	$-0.355639\pi$
$719$	16893.9	0.876269	0.438135	+	0.898909i	$0.355639\pi$
$720$	3410.32	0.176521
$721$	−6099.85	−0.315077
$722$	13411.6	0.691313
$723$	22039.2	1.13367
$724$	4063.83	0.208606
$725$	1264.88	0.0647949
$726$	6849.93	0.350172
$727$	−33263.5	−1.69694	−0.848469	−	0.529245i	$-0.822475\pi$
$727$	−33263.5	−1.69694	−0.848469	+	0.529245i	$0.822475\pi$
$728$	506.685	0.0257953
$729$	−7512.39	−0.381669
$730$	−13126.8	−0.665543
$731$	975.352	0.0493498
$732$	13998.8	0.706843
$733$	28341.9	1.42815	0.714075	−	0.700070i	$-0.246848\pi$
$733$	28341.9	1.42815	0.714075	+	0.700070i	$0.246848\pi$
$734$	8366.58	0.420730
$735$	24225.6	1.21575
$736$	2570.26	0.128724
$737$	34449.8	1.72181
$738$	18017.2	0.898675
$739$	−16211.0	−0.806942	−0.403471	−	0.914993i	$-0.632196\pi$
$739$	−16211.0	−0.806942	−0.403471	+	0.914993i	$0.632196\pi$
$740$	4116.16	0.204477
$741$	−1223.36	−0.0606494
$742$	−1986.91	−0.0983041
$743$	15351.5	0.757997	0.378998	−	0.925397i	$-0.376269\pi$
$743$	15351.5	0.757997	0.378998	+	0.925397i	$0.376269\pi$
$744$	12539.8	0.617917
$745$	−13129.4	−0.645668
$746$	20368.3	0.999648
$747$	−9873.50	−0.483605
$748$	13884.7	0.678712
$749$	−5102.42	−0.248917
$750$	−19371.3	−0.943121
$751$	6189.66	0.300751	0.150375	−	0.988629i	$-0.451952\pi$
$751$	6189.66	0.300751	0.150375	+	0.988629i	$0.451952\pi$
$752$	6975.51	0.338259
$753$	−25462.8	−1.23229
$754$	8129.67	0.392659
$755$	−35905.5	−1.73077
$756$	−902.093	−0.0433979
$757$	8310.68	0.399018	0.199509	−	0.979896i	$-0.436065\pi$
$757$	8310.68	0.399018	0.199509	+	0.979896i	$0.436065\pi$
$758$	−6407.50	−0.307033
$759$	23433.4	1.12066
$760$	−1086.90	−0.0518765
$761$	−20644.0	−0.983371	−0.491685	−	0.870773i	$-0.663619\pi$
$761$	−20644.0	−0.983371	−0.491685	+	0.870773i	$0.663619\pi$
$762$	−36626.5	−1.74126
$763$	1077.56	0.0511276
$764$	6752.95	0.319782
$765$	17277.8	0.816575
$766$	−21543.7	−1.01619
$767$	7790.77	0.366764
$768$	−1744.15	−0.0819487
$769$	−15352.5	−0.719928	−0.359964	−	0.932966i	$-0.617211\pi$
$769$	−15352.5	−0.719928	−0.359964	+	0.932966i	$0.617211\pi$
$770$	4104.25	0.192087
$771$	−16207.1	−0.757046
$772$	13935.4	0.649672
$773$	29217.7	1.35949	0.679746	−	0.733447i	$-0.262090\pi$
$773$	29217.7	1.35949	0.679746	+	0.733447i	$0.262090\pi$
$774$	−467.289	−0.0217007
$775$	−1038.57	−0.0481377
$776$	−12426.8	−0.574867
$777$	2788.56	0.128750
$778$	−4452.04	−0.205159
$779$	−5742.26	−0.264105
$780$	−4339.59	−0.199208
$781$	−2878.97	−0.131905
$782$	13021.8	0.595470
$783$	−14473.9	−0.660607
$784$	−5183.03	−0.236107
$785$	619.602	0.0281714
$786$	14058.6	0.637982
$787$	10971.3	0.496929	0.248464	−	0.968641i	$-0.420074\pi$
$787$	10971.3	0.496929	0.248464	+	0.968641i	$0.420074\pi$
$788$	−7795.51	−0.352416
$789$	50094.7	2.26035
$790$	−15604.5	−0.702765
$791$	−6290.38	−0.282756
$792$	−6652.15	−0.298452
$793$	−7451.83	−0.333697
$794$	1015.00	0.0453665
$795$	17017.2	0.759167
$796$	21213.6	0.944594
$797$	8943.38	0.397479	0.198740	−	0.980052i	$-0.436315\pi$
$797$	8943.38	0.397479	0.198740	+	0.980052i	$0.436315\pi$
$798$	−736.340	−0.0326644
$799$	35340.2	1.56476
$800$	144.455	0.00638406
$801$	24942.8	1.10026
$802$	761.984	0.0335493
$803$	25605.1	1.12526
$804$	−21924.3	−0.961705
$805$	3849.17	0.168528
$806$	−6675.18	−0.291716
$807$	1832.72	0.0799440
$808$	−12327.8	−0.536745
$809$	−9047.14	−0.393177	−0.196589	−	0.980486i	$-0.562986\pi$
$809$	−9047.14	−0.393177	−0.196589	+	0.980486i	$0.562986\pi$
$810$	19236.0	0.834423
$811$	20660.7	0.894570	0.447285	−	0.894391i	$-0.352391\pi$
$811$	20660.7	0.894570	0.447285	+	0.894391i	$0.352391\pi$
$812$	4893.25	0.211477
$813$	−2011.05	−0.0867537
$814$	−8028.95	−0.345718
$815$	−18317.3	−0.787270
$816$	−8836.43	−0.379089
$817$	148.930	0.00637747
$818$	18755.2	0.801661
$819$	−1229.86	−0.0524723
$820$	−20369.4	−0.867475
$821$	−16981.4	−0.721869	−0.360934	−	0.932591i	$-0.617542\pi$
$821$	−16981.4	−0.721869	−0.360934	+	0.932591i	$0.617542\pi$
$822$	36157.5	1.53423
$823$	38928.4	1.64880	0.824399	−	0.566010i	$-0.191513\pi$
$823$	38928.4	1.64880	0.824399	+	0.566010i	$0.191513\pi$
$824$	−11177.3	−0.472549
$825$	1317.01	0.0555788
$826$	4689.27	0.197531
$827$	26389.7	1.10962	0.554812	−	0.831976i	$-0.312790\pi$
$827$	26389.7	1.10962	0.554812	+	0.831976i	$0.312790\pi$
$828$	−6238.71	−0.261848
$829$	26255.4	1.09998	0.549992	−	0.835170i	$-0.314631\pi$
$829$	26255.4	1.09998	0.549992	+	0.835170i	$0.314631\pi$
$830$	11162.5	0.466815
$831$	−37825.6	−1.57901
$832$	928.446	0.0386876
$833$	−26258.9	−1.09222
$834$	−23875.4	−0.991293
$835$	−20428.2	−0.846643
$836$	2120.11	0.0877099
$837$	11884.4	0.490781
$838$	20410.9	0.841388
$839$	−31106.4	−1.27999	−0.639996	−	0.768378i	$-0.721064\pi$
$839$	−31106.4	−1.27999	−0.639996	+	0.768378i	$0.721064\pi$
$840$	−2612.00	−0.107289
$841$	54122.3	2.21913
$842$	−6621.22	−0.271000
$843$	−41976.6	−1.71501
$844$	11750.4	0.479224
$845$	−21805.5	−0.887732
$846$	−16931.4	−0.688079
$847$	−2194.74	−0.0890346
$848$	−3640.79	−0.147436
$849$	33956.3	1.37265
$850$	731.855	0.0295323
$851$	−7529.94	−0.303317
$852$	1832.21	0.0736745
$853$	7352.21	0.295117	0.147558	−	0.989053i	$-0.452859\pi$
$853$	7352.21	0.295117	0.147558	+	0.989053i	$0.452859\pi$
$854$	−4485.26	−0.179722
$855$	2638.21	0.105526
$856$	−9349.65	−0.373323
$857$	−3179.52	−0.126733	−0.0633665	−	0.997990i	$-0.520184\pi$
$857$	−3179.52	−0.126733	−0.0633665	+	0.997990i	$0.520184\pi$
$858$	8464.77	0.336809
$859$	−26140.0	−1.03828	−0.519142	−	0.854688i	$-0.673749\pi$
$859$	−26140.0	−1.03828	−0.519142	+	0.854688i	$0.673749\pi$
$860$	528.295	0.0209473
$861$	−13799.6	−0.546211
$862$	9979.56	0.394321
$863$	−7878.74	−0.310771	−0.155386	−	0.987854i	$-0.549662\pi$
$863$	−7878.74	−0.310771	−0.155386	+	0.987854i	$0.549662\pi$
$864$	−1652.99	−0.0650878
$865$	22985.4	0.903500
$866$	−29388.4	−1.15319
$867$	−11295.5	−0.442464
$868$	−4017.79	−0.157111
$869$	30438.1	1.18819
$870$	−41909.1	−1.63316
$871$	11670.7	0.454016
$872$	1974.52	0.0766807
$873$	30163.2	1.16938
$874$	1988.34	0.0769526
$875$	6206.64	0.239797
$876$	−16295.5	−0.628507
$877$	−34655.2	−1.33435	−0.667175	−	0.744901i	$-0.732497\pi$
$877$	−34655.2	−1.33435	−0.667175	+	0.744901i	$0.732497\pi$
$878$	−14572.7	−0.560142
$879$	−1062.06	−0.0407534
$880$	7520.60	0.288090
$881$	26971.1	1.03142	0.515709	−	0.856764i	$-0.327529\pi$
$881$	26971.1	1.03142	0.515709	+	0.856764i	$0.327529\pi$
$882$	12580.6	0.480284
$883$	−18329.2	−0.698559	−0.349280	−	0.937018i	$-0.613574\pi$
$883$	−18329.2	−0.698559	−0.349280	+	0.937018i	$0.613574\pi$
$884$	4703.81	0.178966
$885$	−40162.0	−1.52546
$886$	−12661.6	−0.480108
$887$	−13799.2	−0.522358	−0.261179	−	0.965290i	$-0.584111\pi$
$887$	−13799.2	−0.522358	−0.261179	+	0.965290i	$0.584111\pi$
$888$	5109.73	0.193098
$889$	11735.3	0.442731
$890$	−28199.2	−1.06207
$891$	−37521.5	−1.41080
$892$	8941.84	0.335645
$893$	5396.22	0.202215
$894$	−16298.6	−0.609738
$895$	15414.2	0.575687
$896$	558.832	0.0208362
$897$	7938.67	0.295501
$898$	−1073.05	−0.0398753
$899$	−64464.7	−2.39157
$900$	−350.630	−0.0129863
$901$	−18445.4	−0.682027
$902$	39732.4	1.46668
$903$	357.901	0.0131896
$904$	−11526.4	−0.424075
$905$	11151.8	0.409610
$906$	−44572.5	−1.63446
$907$	−10859.4	−0.397553	−0.198776	−	0.980045i	$-0.563697\pi$
$907$	−10859.4	−0.397553	−0.198776	+	0.980045i	$0.563697\pi$
$908$	14172.0	0.517969
$909$	29922.8	1.09183
$910$	1390.42	0.0506505
$911$	29073.0	1.05734	0.528668	−	0.848829i	$-0.322692\pi$
$911$	29073.0	1.05734	0.528668	+	0.848829i	$0.322692\pi$
$912$	−1349.26	−0.0489897
$913$	−21773.5	−0.789264
$914$	30651.5	1.10926
$915$	38414.7	1.38793
$916$	−2034.30	−0.0733790
$917$	−4504.43	−0.162213
$918$	−8374.58	−0.301092
$919$	22481.3	0.806953	0.403476	−	0.914990i	$-0.367802\pi$
$919$	22481.3	0.806953	0.403476	+	0.914990i	$0.367802\pi$
$920$	7053.18	0.252757
$921$	−46233.4	−1.65412
$922$	18599.3	0.664356
$923$	−975.325	−0.0347814
$924$	5094.95	0.181398
$925$	−423.201	−0.0150430
$926$	−10248.2	−0.363689
$927$	27130.4	0.961249
$928$	8966.36	0.317171
$929$	−18585.2	−0.656363	−0.328182	−	0.944615i	$-0.606436\pi$
$929$	−18585.2	−0.656363	−0.328182	+	0.944615i	$0.606436\pi$
$930$	34411.0	1.21331
$931$	−4009.56	−0.141147
$932$	6807.54	0.239258
$933$	−10898.9	−0.382436
$934$	17557.8	0.615107
$935$	38101.8	1.33269
$936$	−2253.59	−0.0786974
$937$	1098.03	0.0382831	0.0191415	−	0.999817i	$-0.493907\pi$
$937$	1098.03	0.0382831	0.0191415	+	0.999817i	$0.493907\pi$
$938$	7024.63	0.244523
$939$	42906.1	1.49115
$940$	19141.9	0.664190
$941$	−49152.4	−1.70279	−0.851393	−	0.524528i	$-0.824242\pi$
$941$	−49152.4	−1.70279	−0.851393	+	0.524528i	$0.824242\pi$
$942$	769.163	0.0266037
$943$	37262.9	1.28680
$944$	8592.58	0.296255
$945$	−2475.48	−0.0852141
$946$	−1030.49	−0.0354165
$947$	−23449.3	−0.804648	−0.402324	−	0.915497i	$-0.631797\pi$
$947$	−23449.3	−0.804648	−0.402324	+	0.915497i	$0.631797\pi$
$948$	−19371.2	−0.663657
$949$	8674.40	0.296715
$950$	111.749	0.00381645
$951$	−1534.31	−0.0523168
$952$	2831.23	0.0963871
$953$	−52589.6	−1.78756	−0.893780	−	0.448506i	$-0.851956\pi$
$953$	−52589.6	−1.78756	−0.893780	+	0.448506i	$0.851956\pi$
$954$	8837.17	0.299910
$955$	18531.1	0.627908
$956$	3486.13	0.117939
$957$	81747.5	2.76126
$958$	8952.72	0.301930
$959$	−11585.0	−0.390093
$960$	−4786.21	−0.160911
$961$	23140.2	0.776752
$962$	−2720.01	−0.0911609
$963$	22694.1	0.759405
$964$	−12939.3	−0.432311
$965$	38240.9	1.27567
$966$	4778.29	0.159150
$967$	27847.0	0.926058	0.463029	−	0.886343i	$-0.346763\pi$
$967$	27847.0	0.926058	0.463029	+	0.886343i	$0.346763\pi$
$968$	−4021.63	−0.133533
$969$	−6835.81	−0.226623
$970$	−34101.0	−1.12878
$971$	28912.9	0.955572	0.477786	−	0.878476i	$-0.341440\pi$
$971$	28912.9	0.955572	0.477786	+	0.878476i	$0.341440\pi$
$972$	18300.4	0.603893
$973$	7649.78	0.252046
$974$	−4981.10	−0.163865
$975$	446.172	0.0146553
$976$	−8218.75	−0.269545
$977$	26790.4	0.877279	0.438640	−	0.898663i	$-0.355460\pi$
$977$	26790.4	0.877279	0.438640	+	0.898663i	$0.355460\pi$
$978$	−22738.7	−0.743461
$979$	55005.1	1.79568
$980$	−14223.0	−0.463609
$981$	−4792.68	−0.155982
$982$	−35370.6	−1.14941
$983$	33307.4	1.08071	0.540357	−	0.841436i	$-0.318289\pi$
$983$	33307.4	1.08071	0.540357	+	0.841436i	$0.318289\pi$
$984$	−25286.2	−0.819202
$985$	−21392.0	−0.691987
$986$	45426.5	1.46721
$987$	12968.0	0.418211
$988$	718.241	0.0231278
$989$	−966.441	−0.0310728
$990$	−18254.5	−0.586026
$991$	−9507.98	−0.304774	−0.152387	−	0.988321i	$-0.548696\pi$
$991$	−9507.98	−0.304774	−0.152387	+	0.988321i	$0.548696\pi$
$992$	−7362.17	−0.235634
$993$	71639.0	2.28942
$994$	−587.049	−0.0187324
$995$	58213.3	1.85476
$996$	13857.0	0.440838
$997$	−30680.1	−0.974572	−0.487286	−	0.873242i	$-0.662013\pi$
$997$	−30680.1	−0.974572	−0.487286	+	0.873242i	$0.662013\pi$
$998$	−17337.9	−0.549921
$999$	4842.66	0.153368

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.4.a.b.1.3	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.4.a.b.1.3	✓	15	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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -6.81309 q^{3} +4.00000 q^{4} +10.9766 q^{5} +13.6262 q^{6} -4.36588 q^{7} -8.00000 q^{8} +19.4181 q^{9} -21.9532 q^{10} +42.8218 q^{11} -27.2523 q^{12} +14.5070 q^{13} +8.73175 q^{14} -74.7845 q^{15} +16.0000 q^{16} +81.0612 q^{17} -38.8363 q^{18} +12.3775 q^{19} +43.9064 q^{20} +29.7451 q^{21} -85.6435 q^{22} -80.3207 q^{23} +54.5047 q^{24} -4.51421 q^{25} -29.0139 q^{26} +51.6559 q^{27} -17.4635 q^{28} -280.199 q^{29} +149.569 q^{30} +230.068 q^{31} -32.0000 q^{32} -291.748 q^{33} -162.122 q^{34} -47.9225 q^{35} +77.6725 q^{36} +93.7485 q^{37} -24.7550 q^{38} -98.8372 q^{39} -87.8128 q^{40} -463.927 q^{41} -59.4902 q^{42} +12.0323 q^{43} +171.287 q^{44} +213.145 q^{45} +160.641 q^{46} +435.970 q^{47} -109.009 q^{48} -323.939 q^{49} +9.02842 q^{50} -552.277 q^{51} +58.0279 q^{52} -227.550 q^{53} -103.312 q^{54} +470.038 q^{55} +34.9270 q^{56} -84.3290 q^{57} +560.397 q^{58} +537.036 q^{59} -299.138 q^{60} -513.672 q^{61} -460.136 q^{62} -84.7772 q^{63} +64.0000 q^{64} +159.237 q^{65} +583.497 q^{66} +804.492 q^{67} +324.245 q^{68} +547.231 q^{69} +95.8450 q^{70} -67.2315 q^{71} -155.345 q^{72} +597.947 q^{73} -187.497 q^{74} +30.7557 q^{75} +49.5100 q^{76} -186.955 q^{77} +197.674 q^{78} +710.808 q^{79} +175.626 q^{80} -876.226 q^{81} +927.854 q^{82} -508.468 q^{83} +118.980 q^{84} +889.777 q^{85} -24.0646 q^{86} +1909.02 q^{87} -342.574 q^{88} +1284.51 q^{89} -426.290 q^{90} -63.3356 q^{91} -321.283 q^{92} -1567.47 q^{93} -871.939 q^{94} +135.863 q^{95} +218.019 q^{96} +1553.35 q^{97} +647.878 q^{98} +831.519 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 30 q^{2} + 11 q^{3} + 60 q^{4} + 29 q^{5} - 22 q^{6} + 5 q^{7} - 120 q^{8} + 142 q^{9} - 58 q^{10} + 79 q^{11} + 44 q^{12} - 14 q^{13} - 10 q^{14} + 67 q^{15} + 240 q^{16} + 94 q^{17} - 284 q^{18}+ \cdots + 7068 q^{99}+O(q^{100}) \) 15 * q - 30 * q^2 + 11 * q^3 + 60 * q^4 + 29 * q^5 - 22 * q^6 + 5 * q^7 - 120 * q^8 + 142 * q^9 - 58 * q^10 + 79 * q^11 + 44 * q^12 - 14 * q^13 - 10 * q^14 + 67 * q^15 + 240 * q^16 + 94 * q^17 - 284 * q^18 + 124 * q^19 + 116 * q^20 + 69 * q^21 - 158 * q^22 + 545 * q^23 - 88 * q^24 + 192 * q^25 + 28 * q^26 + 431 * q^27 + 20 * q^28 + 200 * q^29 - 134 * q^30 + 159 * q^31 - 480 * q^32 + 531 * q^33 - 188 * q^34 + 146 * q^35 + 568 * q^36 + 303 * q^37 - 248 * q^38 - 164 * q^39 - 232 * q^40 + 606 * q^41 - 138 * q^42 + 442 * q^43 + 316 * q^44 + 644 * q^45 - 1090 * q^46 + 618 * q^47 + 176 * q^48 + 286 * q^49 - 384 * q^50 - 251 * q^51 - 56 * q^52 + 916 * q^53 - 862 * q^54 + 53 * q^55 - 40 * q^56 + 190 * q^57 - 400 * q^58 + 1377 * q^59 + 268 * q^60 - 1373 * q^61 - 318 * q^62 + 1067 * q^63 + 960 * q^64 + 158 * q^65 - 1062 * q^66 + 1330 * q^67 + 376 * q^68 + 737 * q^69 - 292 * q^70 + 2291 * q^71 - 1136 * q^72 + 924 * q^73 - 606 * q^74 + 4337 * q^75 + 496 * q^76 + 4170 * q^77 + 328 * q^78 + 610 * q^79 + 464 * q^80 + 2255 * q^81 - 1212 * q^82 + 5191 * q^83 + 276 * q^84 + 1517 * q^85 - 884 * q^86 + 7295 * q^87 - 632 * q^88 + 3198 * q^89 - 1288 * q^90 + 4289 * q^91 + 2180 * q^92 + 5255 * q^93 - 1236 * q^94 + 4706 * q^95 - 352 * q^96 + 3806 * q^97 - 572 * q^98 + 7068 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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