LMFDB - Embedded newform 531.8.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,8,Mod(1,531)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("531.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	531.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:	$165.876448532$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + \cdots - 23\!\cdots\!32 $ x^16 - 6x^15 - 1493x^14 + 8791x^13 + 890490x^12 - 5107725x^11 - 269092298x^10 + 1488374176x^9 + 42885295136x^8 - 226132003872x^7 - 3353576629440x^6 + 16796366777600x^5 + 99470801612800x^4 - 494039551757568x^3 - 493048066650624x^2 + 3193975642099712*x - 2385018853548032
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-19.6562$ of defining polynomial
Character	$\chi$	$=$	531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-19.6562 q^{2} +258.365 q^{4} +436.761 q^{5} +956.841 q^{7} -2562.48 q^{8} +O(q^{10})$	\(q-19.6562 q^{2} +258.365 q^{4} +436.761 q^{5} +956.841 q^{7} -2562.48 q^{8} -8585.06 q^{10} -1972.61 q^{11} -5308.65 q^{13} -18807.8 q^{14} +17297.8 q^{16} +19184.9 q^{17} -21442.5 q^{19} +112844. q^{20} +38773.9 q^{22} +34320.3 q^{23} +112635. q^{25} +104348. q^{26} +247214. q^{28} -40010.4 q^{29} -95465.0 q^{31} -12010.9 q^{32} -377103. q^{34} +417911. q^{35} -269178. q^{37} +421478. q^{38} -1.11919e6 q^{40} +360504. q^{41} -929097. q^{43} -509653. q^{44} -674606. q^{46} -54052.8 q^{47} +92001.6 q^{49} -2.21398e6 q^{50} -1.37157e6 q^{52} -680499. q^{53} -861559. q^{55} -2.45188e6 q^{56} +786452. q^{58} -205379. q^{59} -1.27358e6 q^{61} +1.87648e6 q^{62} -1.97803e6 q^{64} -2.31861e6 q^{65} +630075. q^{67} +4.95672e6 q^{68} -8.21453e6 q^{70} -2.05155e6 q^{71} -5.36743e6 q^{73} +5.29101e6 q^{74} -5.54000e6 q^{76} -1.88747e6 q^{77} +4.57098e6 q^{79} +7.55500e6 q^{80} -7.08613e6 q^{82} -9.49376e6 q^{83} +8.37924e6 q^{85} +1.82625e7 q^{86} +5.05477e6 q^{88} +2.45830e6 q^{89} -5.07953e6 q^{91} +8.86717e6 q^{92} +1.06247e6 q^{94} -9.36526e6 q^{95} -1.41914e7 q^{97} -1.80840e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8}+O(q^{10}) $ 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8	\( 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8} - 3479 q^{10} - 898 q^{11} - 8172 q^{13} + 13315 q^{14} + 3138 q^{16} + 44985 q^{17} - 40137 q^{19} - 130657 q^{20} + 109394 q^{22} + 2833 q^{23} + 285746 q^{25} + 129420 q^{26} + 112890 q^{28} - 144375 q^{29} - 141759 q^{31} + 36224 q^{32} - 341332 q^{34} + 78859 q^{35} - 297971 q^{37} - 329075 q^{38} - 203048 q^{40} - 659077 q^{41} - 1431608 q^{43} - 254916 q^{44} + 873113 q^{46} + 1574073 q^{47} + 1893545 q^{49} - 302533 q^{50} - 4972548 q^{52} - 587736 q^{53} - 4624036 q^{55} + 5798506 q^{56} - 6991380 q^{58} - 3286064 q^{59} - 6117131 q^{61} + 11570258 q^{62} - 19063011 q^{64} + 5335514 q^{65} - 16518710 q^{67} + 17284669 q^{68} - 39189486 q^{70} + 10882582 q^{71} - 21097441 q^{73} + 16717030 q^{74} - 40864952 q^{76} + 3404601 q^{77} - 3784458 q^{79} + 27466195 q^{80} - 24990117 q^{82} + 1951425 q^{83} - 23238675 q^{85} + 35910572 q^{86} - 27843055 q^{88} - 10499443 q^{89} + 699217 q^{91} + 20062766 q^{92} - 59358988 q^{94} + 29236333 q^{95} - 25158976 q^{97} - 2120460 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8 - 3479 * q^10 - 898 * q^11 - 8172 * q^13 + 13315 * q^14 + 3138 * q^16 + 44985 * q^17 - 40137 * q^19 - 130657 * q^20 + 109394 * q^22 + 2833 * q^23 + 285746 * q^25 + 129420 * q^26 + 112890 * q^28 - 144375 * q^29 - 141759 * q^31 + 36224 * q^32 - 341332 * q^34 + 78859 * q^35 - 297971 * q^37 - 329075 * q^38 - 203048 * q^40 - 659077 * q^41 - 1431608 * q^43 - 254916 * q^44 + 873113 * q^46 + 1574073 * q^47 + 1893545 * q^49 - 302533 * q^50 - 4972548 * q^52 - 587736 * q^53 - 4624036 * q^55 + 5798506 * q^56 - 6991380 * q^58 - 3286064 * q^59 - 6117131 * q^61 + 11570258 * q^62 - 19063011 * q^64 + 5335514 * q^65 - 16518710 * q^67 + 17284669 * q^68 - 39189486 * q^70 + 10882582 * q^71 - 21097441 * q^73 + 16717030 * q^74 - 40864952 * q^76 + 3404601 * q^77 - 3784458 * q^79 + 27466195 * q^80 - 24990117 * q^82 + 1951425 * q^83 - 23238675 * q^85 + 35910572 * q^86 - 27843055 * q^88 - 10499443 * q^89 + 699217 * q^91 + 20062766 * q^92 - 59358988 * q^94 + 29236333 * q^95 - 25158976 * q^97 - 2120460 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−19.6562	−1.73738	−0.868688	−	0.495359i	$-0.835036\pi$
$2$	−19.6562	−1.73738	−0.868688	+	0.495359i	$0.835036\pi$
$3$	0	0
$3$	0	0
$4$	258.365	2.01848
$5$	436.761	1.56260	0.781302	−	0.624153i	$-0.214556\pi$
$5$	436.761	1.56260	0.781302	+	0.624153i	$0.214556\pi$
$6$	0	0
$7$	956.841	1.05438	0.527189	−	0.849748i	$-0.323246\pi$
$7$	956.841	1.05438	0.527189	+	0.849748i	$0.323246\pi$
$8$	−2562.48	−1.76948
$9$	0	0
$10$	−8585.06	−2.71483
$11$	−1972.61	−0.446855	−0.223427	−	0.974721i	$-0.571725\pi$
$11$	−1972.61	−0.446855	−0.223427	+	0.974721i	$0.571725\pi$
$12$	0	0
$13$	−5308.65	−0.670166	−0.335083	−	0.942189i	$-0.608764\pi$
$13$	−5308.65	−0.670166	−0.335083	+	0.942189i	$0.608764\pi$
$14$	−18807.8	−1.83185
$15$	0	0
$16$	17297.8	1.05577
$17$	19184.9	0.947086	0.473543	−	0.880771i	$-0.342975\pi$
$17$	19184.9	0.947086	0.473543	+	0.880771i	$0.342975\pi$
$18$	0	0
$19$	−21442.5	−0.717196	−0.358598	−	0.933492i	$-0.616745\pi$
$19$	−21442.5	−0.717196	−0.358598	+	0.933492i	$0.616745\pi$
$20$	112844.	3.15408
$21$	0	0
$22$	38773.9	0.776355
$23$	34320.3	0.588171	0.294086	−	0.955779i	$-0.404985\pi$
$23$	34320.3	0.588171	0.294086	+	0.955779i	$0.404985\pi$
$24$	0	0
$25$	112635.	1.44173
$26$	104348.	1.16433
$27$	0	0
$28$	247214.	2.12824
$29$	−40010.4	−0.304635	−0.152318	−	0.988332i	$-0.548674\pi$
$29$	−40010.4	−0.304635	−0.152318	+	0.988332i	$0.548674\pi$
$30$	0	0
$31$	−95465.0	−0.575544	−0.287772	−	0.957699i	$-0.592915\pi$
$31$	−95465.0	−0.575544	−0.287772	+	0.957699i	$0.592915\pi$
$32$	−12010.9	−0.0647961
$33$	0	0
$34$	−377103.	−1.64544
$35$	417911.	1.64758
$36$	0	0
$37$	−269178.	−0.873642	−0.436821	−	0.899549i	$-0.643896\pi$
$37$	−269178.	−0.873642	−0.436821	+	0.899549i	$0.643896\pi$
$38$	421478.	1.24604
$39$	0	0
$40$	−1.11919e6	−2.76499
$41$	360504.	0.816896	0.408448	−	0.912782i	$-0.366070\pi$
$41$	360504.	0.816896	0.408448	+	0.912782i	$0.366070\pi$
$42$	0	0
$43$	−929097.	−1.78206	−0.891028	−	0.453949i	$-0.850015\pi$
$43$	−929097.	−1.78206	−0.891028	+	0.453949i	$0.850015\pi$
$44$	−509653.	−0.901967
$45$	0	0
$46$	−674606.	−1.02187
$47$	−54052.8	−0.0759408	−0.0379704	−	0.999279i	$-0.512089\pi$
$47$	−54052.8	−0.0759408	−0.0379704	+	0.999279i	$0.512089\pi$
$48$	0	0
$49$	92001.6	0.111714
$50$	−2.21398e6	−2.50483
$51$	0	0
$52$	−1.37157e6	−1.35271
$53$	−680499.	−0.627859	−0.313929	−	0.949446i	$-0.601646\pi$
$53$	−680499.	−0.627859	−0.313929	+	0.949446i	$0.601646\pi$
$54$	0	0
$55$	−861559.	−0.698258
$56$	−2.45188e6	−1.86570
$57$	0	0
$58$	786452.	0.529266
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	0	0
$61$	−1.27358e6	−0.718408	−0.359204	−	0.933259i	$-0.616952\pi$
$61$	−1.27358e6	−0.718408	−0.359204	+	0.933259i	$0.616952\pi$
$62$	1.87648e6	0.999936
$63$	0	0
$64$	−1.97803e6	−0.943197
$65$	−2.31861e6	−1.04720
$66$	0	0
$67$	630075.	0.255936	0.127968	−	0.991778i	$-0.459155\pi$
$67$	630075.	0.255936	0.127968	+	0.991778i	$0.459155\pi$
$68$	4.95672e6	1.91167
$69$	0	0
$70$	−8.21453e6	−2.86246
$71$	−2.05155e6	−0.680265	−0.340133	−	0.940377i	$-0.610472\pi$
$71$	−2.05155e6	−0.680265	−0.340133	+	0.940377i	$0.610472\pi$
$72$	0	0
$73$	−5.36743e6	−1.61487	−0.807433	−	0.589959i	$-0.799144\pi$
$73$	−5.36743e6	−1.61487	−0.807433	+	0.589959i	$0.799144\pi$
$74$	5.29101e6	1.51784
$75$	0	0
$76$	−5.54000e6	−1.44764
$77$	−1.88747e6	−0.471154
$78$	0	0
$79$	4.57098e6	1.04307	0.521536	−	0.853229i	$-0.325359\pi$
$79$	4.57098e6	1.04307	0.521536	+	0.853229i	$0.325359\pi$
$80$	7.55500e6	1.64975
$81$	0	0
$82$	−7.08613e6	−1.41926
$83$	−9.49376e6	−1.82249	−0.911245	−	0.411865i	$-0.864878\pi$
$83$	−9.49376e6	−1.82249	−0.911245	+	0.411865i	$0.864878\pi$
$84$	0	0
$85$	8.37924e6	1.47992
$86$	1.82625e7	3.09610
$87$	0	0
$88$	5.05477e6	0.790700
$89$	2.45830e6	0.369633	0.184816	−	0.982773i	$-0.440831\pi$
$89$	2.45830e6	0.369633	0.184816	+	0.982773i	$0.440831\pi$
$90$	0	0
$91$	−5.07953e6	−0.706609
$92$	8.86717e6	1.18721
$93$	0	0
$94$	1.06247e6	0.131938
$95$	−9.36526e6	−1.12069
$96$	0	0
$97$	−1.41914e7	−1.57879	−0.789397	−	0.613883i	$-0.789607\pi$
$97$	−1.41914e7	−1.57879	−0.789397	+	0.613883i	$0.789607\pi$
$98$	−1.80840e6	−0.194090
$99$	0	0
$100$	2.91011e7	2.91011
$101$	−3.81799e6	−0.368731	−0.184366	−	0.982858i	$-0.559023\pi$
$101$	−3.81799e6	−0.368731	−0.184366	+	0.982858i	$0.559023\pi$
$102$	0	0
$103$	1.77672e7	1.60210	0.801049	−	0.598599i	$-0.204276\pi$
$103$	1.77672e7	1.60210	0.801049	+	0.598599i	$0.204276\pi$
$104$	1.36033e7	1.18584
$105$	0	0
$106$	1.33760e7	1.09083
$107$	−2.35965e7	−1.86210	−0.931051	−	0.364888i	$-0.881107\pi$
$107$	−2.35965e7	−1.86210	−0.931051	+	0.364888i	$0.881107\pi$
$108$	0	0
$109$	3.99327e6	0.295349	0.147675	−	0.989036i	$-0.452821\pi$
$109$	3.99327e6	0.295349	0.147675	+	0.989036i	$0.452821\pi$
$110$	1.69350e7	1.21314
$111$	0	0
$112$	1.65512e7	1.11318
$113$	2.69156e6	0.175481	0.0877405	−	0.996143i	$-0.472035\pi$
$113$	2.69156e6	0.175481	0.0877405	+	0.996143i	$0.472035\pi$
$114$	0	0
$115$	1.49898e7	0.919079
$116$	−1.03373e7	−0.614900
$117$	0	0
$118$	4.03696e6	0.226187
$119$	1.83569e7	0.998587
$120$	0	0
$121$	−1.55960e7	−0.800321
$122$	2.50337e7	1.24815
$123$	0	0
$124$	−2.46648e7	−1.16172
$125$	1.50728e7	0.690255
$126$	0	0
$127$	1.72960e6	0.0749261	0.0374631	−	0.999298i	$-0.488072\pi$
$127$	1.72960e6	0.0749261	0.0374631	+	0.999298i	$0.488072\pi$
$128$	4.04178e7	1.70348
$129$	0	0
$130$	4.55750e7	1.81939
$131$	−1.21153e7	−0.470854	−0.235427	−	0.971892i	$-0.575649\pi$
$131$	−1.21153e7	−0.470854	−0.235427	+	0.971892i	$0.575649\pi$
$132$	0	0
$133$	−2.05171e7	−0.756196
$134$	−1.23849e7	−0.444657
$135$	0	0
$136$	−4.91610e7	−1.67585
$137$	3.48264e7	1.15714	0.578571	−	0.815632i	$-0.303611\pi$
$137$	3.48264e7	1.15714	0.578571	+	0.815632i	$0.303611\pi$
$138$	0	0
$139$	3.29388e7	1.04029	0.520147	−	0.854077i	$-0.325877\pi$
$139$	3.29388e7	1.04029	0.520147	+	0.854077i	$0.325877\pi$
$140$	1.07974e8	3.32560
$141$	0	0
$142$	4.03257e7	1.18188
$143$	1.04719e7	0.299467
$144$	0	0
$145$	−1.74750e7	−0.476025
$146$	1.05503e8	2.80563
$147$	0	0
$148$	−6.95461e7	−1.76343
$149$	−3.14675e7	−0.779311	−0.389656	−	0.920961i	$-0.627406\pi$
$149$	−3.14675e7	−0.779311	−0.389656	+	0.920961i	$0.627406\pi$
$150$	0	0
$151$	−2.53600e6	−0.0599419	−0.0299710	−	0.999551i	$-0.509541\pi$
$151$	−2.53600e6	−0.0599419	−0.0299710	+	0.999551i	$0.509541\pi$
$152$	5.49460e7	1.26906
$153$	0	0
$154$	3.71005e7	0.818572
$155$	−4.16954e7	−0.899348
$156$	0	0
$157$	−5.81479e7	−1.19918	−0.599591	−	0.800306i	$-0.704670\pi$
$157$	−5.81479e7	−1.19918	−0.599591	+	0.800306i	$0.704670\pi$
$158$	−8.98479e7	−1.81221
$159$	0	0
$160$	−5.24588e6	−0.101251
$161$	3.28391e7	0.620155
$162$	0	0
$163$	−4.39268e7	−0.794461	−0.397230	−	0.917719i	$-0.630029\pi$
$163$	−4.39268e7	−0.794461	−0.397230	+	0.917719i	$0.630029\pi$
$164$	9.31417e7	1.64889
$165$	0	0
$166$	1.86611e8	3.16635
$167$	9.02250e7	1.49906	0.749530	−	0.661970i	$-0.230280\pi$
$167$	9.02250e7	1.49906	0.749530	+	0.661970i	$0.230280\pi$
$168$	0	0
$169$	−3.45668e7	−0.550878
$170$	−1.64704e8	−2.57118
$171$	0	0
$172$	−2.40046e8	−3.59704
$173$	−2.25125e7	−0.330569	−0.165285	−	0.986246i	$-0.552854\pi$
$173$	−2.25125e7	−0.330569	−0.165285	+	0.986246i	$0.552854\pi$
$174$	0	0
$175$	1.07774e8	1.52013
$176$	−3.41217e7	−0.471777
$177$	0	0
$178$	−4.83208e7	−0.642191
$179$	−1.26881e8	−1.65353	−0.826766	−	0.562546i	$-0.809822\pi$
$179$	−1.26881e8	−1.65353	−0.826766	+	0.562546i	$0.809822\pi$
$180$	0	0
$181$	9.29702e7	1.16538	0.582691	−	0.812694i	$-0.302000\pi$
$181$	9.29702e7	1.16538	0.582691	+	0.812694i	$0.302000\pi$
$182$	9.98442e7	1.22765
$183$	0	0
$184$	−8.79450e7	−1.04076
$185$	−1.17566e8	−1.36516
$186$	0	0
$187$	−3.78444e7	−0.423210
$188$	−1.39653e7	−0.153285
$189$	0	0
$190$	1.84085e8	1.94707
$191$	1.55664e8	1.61649	0.808243	−	0.588850i	$-0.200419\pi$
$191$	1.55664e8	1.61649	0.808243	+	0.588850i	$0.200419\pi$
$192$	0	0
$193$	1.85473e7	0.185708	0.0928539	−	0.995680i	$-0.470401\pi$
$193$	1.85473e7	0.185708	0.0928539	+	0.995680i	$0.470401\pi$
$194$	2.78949e8	2.74296
$195$	0	0
$196$	2.37700e7	0.225493
$197$	−3.60337e7	−0.335798	−0.167899	−	0.985804i	$-0.553698\pi$
$197$	−3.60337e7	−0.335798	−0.167899	+	0.985804i	$0.553698\pi$
$198$	0	0
$199$	3.41912e7	0.307559	0.153780	−	0.988105i	$-0.450855\pi$
$199$	3.41912e7	0.307559	0.153780	+	0.988105i	$0.450855\pi$
$200$	−2.88626e8	−2.55112
$201$	0	0
$202$	7.50471e7	0.640625
$203$	−3.82836e7	−0.321201
$204$	0	0
$205$	1.57454e8	1.27649
$206$	−3.49235e8	−2.78345
$207$	0	0
$208$	−9.18278e7	−0.707543
$209$	4.22977e7	0.320483
$210$	0	0
$211$	1.66203e8	1.21801	0.609005	−	0.793166i	$-0.291569\pi$
$211$	1.66203e8	1.21801	0.609005	+	0.793166i	$0.291569\pi$
$212$	−1.75817e8	−1.26732
$213$	0	0
$214$	4.63816e8	3.23517
$215$	−4.05793e8	−2.78465
$216$	0	0
$217$	−9.13449e7	−0.606841
$218$	−7.84923e7	−0.513133
$219$	0	0
$220$	−2.22597e8	−1.40942
$221$	−1.01846e8	−0.634705
$222$	0	0
$223$	−2.57838e8	−1.55697	−0.778485	−	0.627663i	$-0.784012\pi$
$223$	−2.57838e8	−1.55697	−0.778485	+	0.627663i	$0.784012\pi$
$224$	−1.14925e7	−0.0683197
$225$	0	0
$226$	−5.29058e7	−0.304877
$227$	2.27009e8	1.28811	0.644055	−	0.764979i	$-0.277251\pi$
$227$	2.27009e8	1.28811	0.644055	+	0.764979i	$0.277251\pi$
$228$	0	0
$229$	−7.40017e7	−0.407209	−0.203605	−	0.979053i	$-0.565266\pi$
$229$	−7.40017e7	−0.407209	−0.203605	+	0.979053i	$0.565266\pi$
$230$	−2.94642e8	−1.59679
$231$	0	0
$232$	1.02526e8	0.539046
$233$	−6.77414e7	−0.350839	−0.175420	−	0.984494i	$-0.556128\pi$
$233$	−6.77414e7	−0.350839	−0.175420	+	0.984494i	$0.556128\pi$
$234$	0	0
$235$	−2.36082e7	−0.118665
$236$	−5.30628e7	−0.262783
$237$	0	0
$238$	−3.60827e8	−1.73492
$239$	−1.28770e8	−0.610128	−0.305064	−	0.952332i	$-0.598678\pi$
$239$	−1.28770e8	−0.610128	−0.305064	+	0.952332i	$0.598678\pi$
$240$	0	0
$241$	−2.97076e8	−1.36712	−0.683561	−	0.729893i	$-0.739570\pi$
$241$	−2.97076e8	−1.36712	−0.683561	+	0.729893i	$0.739570\pi$
$242$	3.06557e8	1.39046
$243$	0	0
$244$	−3.29048e8	−1.45009
$245$	4.01827e7	0.174565
$246$	0	0
$247$	1.13831e8	0.480640
$248$	2.44627e8	1.01841
$249$	0	0
$250$	−2.96274e8	−1.19923
$251$	6.81145e7	0.271883	0.135941	−	0.990717i	$-0.456594\pi$
$251$	6.81145e7	0.271883	0.135941	+	0.990717i	$0.456594\pi$
$252$	0	0
$253$	−6.77005e7	−0.262827
$254$	−3.39974e7	−0.130175
$255$	0	0
$256$	−5.41272e8	−2.01640
$257$	1.12934e8	0.415010	0.207505	−	0.978234i	$-0.433466\pi$
$257$	1.12934e8	0.415010	0.207505	+	0.978234i	$0.433466\pi$
$258$	0	0
$259$	−2.57560e8	−0.921149
$260$	−5.99049e8	−2.11376
$261$	0	0
$262$	2.38141e8	0.818050
$263$	−5.13397e8	−1.74024	−0.870119	−	0.492842i	$-0.835958\pi$
$263$	−5.13397e8	−1.74024	−0.870119	+	0.492842i	$0.835958\pi$
$264$	0	0
$265$	−2.97216e8	−0.981095
$266$	4.03287e8	1.31380
$267$	0	0
$268$	1.62789e8	0.516600
$269$	7.41447e7	0.232245	0.116123	−	0.993235i	$-0.462953\pi$
$269$	7.41447e7	0.232245	0.116123	+	0.993235i	$0.462953\pi$
$270$	0	0
$271$	1.72102e8	0.525285	0.262642	−	0.964893i	$-0.415406\pi$
$271$	1.72102e8	0.525285	0.262642	+	0.964893i	$0.415406\pi$
$272$	3.31857e8	0.999907
$273$	0	0
$274$	−6.84554e8	−2.01039
$275$	−2.22186e8	−0.644246
$276$	0	0
$277$	4.25097e8	1.20174	0.600868	−	0.799348i	$-0.294822\pi$
$277$	4.25097e8	1.20174	0.600868	+	0.799348i	$0.294822\pi$
$278$	−6.47451e8	−1.80738
$279$	0	0
$280$	−1.07089e9	−2.91535
$281$	−3.70445e7	−0.0995983	−0.0497991	−	0.998759i	$-0.515858\pi$
$281$	−3.70445e7	−0.0995983	−0.0497991	+	0.998759i	$0.515858\pi$
$282$	0	0
$283$	−2.60297e7	−0.0682679	−0.0341339	−	0.999417i	$-0.510867\pi$
$283$	−2.60297e7	−0.0682679	−0.0341339	+	0.999417i	$0.510867\pi$
$284$	−5.30049e8	−1.37310
$285$	0	0
$286$	−2.05837e8	−0.520287
$287$	3.44945e8	0.861318
$288$	0	0
$289$	−4.22765e7	−0.103028
$290$	3.43492e8	0.827034
$291$	0	0
$292$	−1.38676e9	−3.25957
$293$	−6.51952e8	−1.51418	−0.757092	−	0.653308i	$-0.773381\pi$
$293$	−6.51952e8	−1.51418	−0.757092	+	0.653308i	$0.773381\pi$
$294$	0	0
$295$	−8.97016e7	−0.203434
$296$	6.89762e8	1.54589
$297$	0	0
$298$	6.18532e8	1.35396
$299$	−1.82194e8	−0.394172
$300$	0	0
$301$	−8.88998e8	−1.87896
$302$	4.98481e7	0.104142
$303$	0	0
$304$	−3.70908e8	−0.757196
$305$	−5.56250e8	−1.12259
$306$	0	0
$307$	8.07706e8	1.59320	0.796598	−	0.604510i	$-0.206631\pi$
$307$	8.07706e8	1.59320	0.796598	+	0.604510i	$0.206631\pi$
$308$	−4.87657e8	−0.951014
$309$	0	0
$310$	8.19573e8	1.56251
$311$	1.60231e8	0.302055	0.151027	−	0.988530i	$-0.451742\pi$
$311$	1.60231e8	0.302055	0.151027	+	0.988530i	$0.451742\pi$
$312$	0	0
$313$	2.15368e8	0.396987	0.198494	−	0.980102i	$-0.436395\pi$
$313$	2.15368e8	0.396987	0.198494	+	0.980102i	$0.436395\pi$
$314$	1.14296e9	2.08343
$315$	0	0
$316$	1.18098e9	2.10542
$317$	8.64021e8	1.52341	0.761705	−	0.647924i	$-0.224362\pi$
$317$	8.64021e8	1.52341	0.761705	+	0.647924i	$0.224362\pi$
$318$	0	0
$319$	7.89250e7	0.136128
$320$	−8.63926e8	−1.47384
$321$	0	0
$322$	−6.45490e8	−1.07744
$323$	−4.11373e8	−0.679246
$324$	0	0
$325$	−5.97942e8	−0.966201
$326$	8.63432e8	1.38028
$327$	0	0
$328$	−9.23784e8	−1.44548
$329$	−5.17199e7	−0.0800704
$330$	0	0
$331$	9.12406e8	1.38290	0.691449	−	0.722425i	$-0.256973\pi$
$331$	9.12406e8	1.38290	0.691449	+	0.722425i	$0.256973\pi$
$332$	−2.45286e9	−3.67865
$333$	0	0
$334$	−1.77348e9	−2.60443
$335$	2.75193e8	0.399926
$336$	0	0
$337$	5.45796e8	0.776829	0.388414	−	0.921485i	$-0.373023\pi$
$337$	5.45796e8	0.776829	0.388414	+	0.921485i	$0.373023\pi$
$338$	6.79450e8	0.957082
$339$	0	0
$340$	2.16490e9	2.98719
$341$	1.88315e8	0.257185
$342$	0	0
$343$	−6.99969e8	−0.936589
$344$	2.38079e9	3.15331
$345$	0	0
$346$	4.42510e8	0.574323
$347$	5.84036e8	0.750389	0.375194	−	0.926946i	$-0.377576\pi$
$347$	5.84036e8	0.750389	0.375194	+	0.926946i	$0.377576\pi$
$348$	0	0
$349$	−7.64386e8	−0.962551	−0.481276	−	0.876569i	$-0.659826\pi$
$349$	−7.64386e8	−0.962551	−0.481276	+	0.876569i	$0.659826\pi$
$350$	−2.11843e9	−2.64104
$351$	0	0
$352$	2.36927e7	0.0289545
$353$	1.06373e9	1.28712	0.643559	−	0.765396i	$-0.277457\pi$
$353$	1.06373e9	1.28712	0.643559	+	0.765396i	$0.277457\pi$
$354$	0	0
$355$	−8.96039e8	−1.06299
$356$	6.35140e8	0.746095
$357$	0	0
$358$	2.49400e9	2.87281
$359$	1.09179e9	1.24540	0.622700	−	0.782461i	$-0.286036\pi$
$359$	1.09179e9	1.24540	0.622700	+	0.782461i	$0.286036\pi$
$360$	0	0
$361$	−4.34091e8	−0.485630
$362$	−1.82744e9	−2.02471
$363$	0	0
$364$	−1.31237e9	−1.42627
$365$	−2.34429e9	−2.52340
$366$	0	0
$367$	−1.92123e8	−0.202884	−0.101442	−	0.994841i	$-0.532346\pi$
$367$	−1.92123e8	−0.202884	−0.101442	+	0.994841i	$0.532346\pi$
$368$	5.93665e8	0.620975
$369$	0	0
$370$	2.31091e9	2.37179
$371$	−6.51129e8	−0.662001
$372$	0	0
$373$	−1.24365e9	−1.24085	−0.620423	−	0.784267i	$-0.713039\pi$
$373$	−1.24365e9	−1.24085	−0.620423	+	0.784267i	$0.713039\pi$
$374$	7.43876e8	0.735275
$375$	0	0
$376$	1.38509e8	0.134376
$377$	2.12401e8	0.204156
$378$	0	0
$379$	−2.03376e9	−1.91894	−0.959472	−	0.281805i	$-0.909067\pi$
$379$	−2.03376e9	−1.91894	−0.959472	+	0.281805i	$0.909067\pi$
$380$	−2.41966e9	−2.26210
$381$	0	0
$382$	−3.05976e9	−2.80844
$383$	8.58688e8	0.780979	0.390490	−	0.920607i	$-0.372306\pi$
$383$	8.58688e8	0.780979	0.390490	+	0.920607i	$0.372306\pi$
$384$	0	0
$385$	−8.24375e8	−0.736228
$386$	−3.64569e8	−0.322645
$387$	0	0
$388$	−3.66657e9	−3.18676
$389$	1.79662e9	1.54751	0.773755	−	0.633485i	$-0.218376\pi$
$389$	1.79662e9	1.54751	0.773755	+	0.633485i	$0.218376\pi$
$390$	0	0
$391$	6.58433e8	0.557049
$392$	−2.35752e8	−0.197676
$393$	0	0
$394$	7.08285e8	0.583407
$395$	1.99643e9	1.62991
$396$	0	0
$397$	−1.32366e9	−1.06172	−0.530860	−	0.847460i	$-0.678131\pi$
$397$	−1.32366e9	−1.06172	−0.530860	+	0.847460i	$0.678131\pi$
$398$	−6.72069e8	−0.534347
$399$	0	0
$400$	1.94834e9	1.52214
$401$	1.25074e9	0.968635	0.484317	−	0.874892i	$-0.339068\pi$
$401$	1.25074e9	0.968635	0.484317	+	0.874892i	$0.339068\pi$
$402$	0	0
$403$	5.06790e8	0.385710
$404$	−9.86435e8	−0.744276
$405$	0	0
$406$	7.52510e8	0.558047
$407$	5.30983e8	0.390391
$408$	0	0
$409$	1.84026e9	1.32999	0.664993	−	0.746850i	$-0.268435\pi$
$409$	1.84026e9	1.32999	0.664993	+	0.746850i	$0.268435\pi$
$410$	−3.09495e9	−2.21774
$411$	0	0
$412$	4.59043e9	3.23380
$413$	−1.96515e8	−0.137268
$414$	0	0
$415$	−4.14651e9	−2.84783
$416$	6.37614e7	0.0434242
$417$	0	0
$418$	−8.31411e8	−0.556799
$419$	−1.97514e9	−1.31174	−0.655871	−	0.754873i	$-0.727699\pi$
$419$	−1.97514e9	−1.31174	−0.655871	+	0.754873i	$0.727699\pi$
$420$	0	0
$421$	1.04914e9	0.685247	0.342624	−	0.939473i	$-0.388684\pi$
$421$	1.04914e9	0.685247	0.342624	+	0.939473i	$0.388684\pi$
$422$	−3.26692e9	−2.11614
$423$	0	0
$424$	1.74376e9	1.11098
$425$	2.16091e9	1.36545
$426$	0	0
$427$	−1.21861e9	−0.757474
$428$	−6.09650e9	−3.75861
$429$	0	0
$430$	7.97635e9	4.83798
$431$	−1.15205e9	−0.693109	−0.346554	−	0.938030i	$-0.612648\pi$
$431$	−1.15205e9	−0.693109	−0.346554	+	0.938030i	$0.612648\pi$
$432$	0	0
$433$	2.37623e9	1.40663	0.703317	−	0.710877i	$-0.251702\pi$
$433$	2.37623e9	1.40663	0.703317	+	0.710877i	$0.251702\pi$
$434$	1.79549e9	1.05431
$435$	0	0
$436$	1.03172e9	0.596155
$437$	−7.35913e8	−0.421834
$438$	0	0
$439$	−6.70393e8	−0.378185	−0.189092	−	0.981959i	$-0.560555\pi$
$439$	−6.70393e8	−0.378185	−0.189092	+	0.981959i	$0.560555\pi$
$440$	2.20773e9	1.23555
$441$	0	0
$442$	2.00191e9	1.10272
$443$	2.24468e9	1.22671	0.613354	−	0.789808i	$-0.289820\pi$
$443$	2.24468e9	1.22671	0.613354	+	0.789808i	$0.289820\pi$
$444$	0	0
$445$	1.07369e9	0.577590
$446$	5.06811e9	2.70504
$447$	0	0
$448$	−1.89266e9	−0.994487
$449$	5.76894e8	0.300769	0.150385	−	0.988628i	$-0.451949\pi$
$449$	5.76894e8	0.300769	0.150385	+	0.988628i	$0.451949\pi$
$450$	0	0
$451$	−7.11134e8	−0.365034
$452$	6.95406e8	0.354204
$453$	0	0
$454$	−4.46213e9	−2.23793
$455$	−2.21854e9	−1.10415
$456$	0	0
$457$	9.02311e8	0.442231	0.221116	−	0.975248i	$-0.429030\pi$
$457$	9.02311e8	0.442231	0.221116	+	0.975248i	$0.429030\pi$
$458$	1.45459e9	0.707476
$459$	0	0
$460$	3.87284e9	1.85514
$461$	−1.56907e9	−0.745913	−0.372956	−	0.927849i	$-0.621656\pi$
$461$	−1.56907e9	−0.745913	−0.372956	+	0.927849i	$0.621656\pi$
$462$	0	0
$463$	6.01283e8	0.281543	0.140772	−	0.990042i	$-0.455042\pi$
$463$	6.01283e8	0.281543	0.140772	+	0.990042i	$0.455042\pi$
$464$	−6.92092e8	−0.321626
$465$	0	0
$466$	1.33154e9	0.609540
$467$	2.18611e9	0.993260	0.496630	−	0.867962i	$-0.334571\pi$
$467$	2.18611e9	0.993260	0.496630	+	0.867962i	$0.334571\pi$
$468$	0	0
$469$	6.02882e8	0.269853
$470$	4.64046e8	0.206167
$471$	0	0
$472$	5.26279e8	0.230366
$473$	1.83274e9	0.796320
$474$	0	0
$475$	−2.41519e9	−1.03401
$476$	4.74279e9	2.01563
$477$	0	0
$478$	2.53112e9	1.06002
$479$	−1.17364e9	−0.487936	−0.243968	−	0.969783i	$-0.578449\pi$
$479$	−1.17364e9	−0.487936	−0.243968	+	0.969783i	$0.578449\pi$
$480$	0	0
$481$	1.42897e9	0.585485
$482$	5.83937e9	2.37521
$483$	0	0
$484$	−4.02946e9	−1.61543
$485$	−6.19827e9	−2.46703
$486$	0	0
$487$	1.37532e9	0.539574	0.269787	−	0.962920i	$-0.413047\pi$
$487$	1.37532e9	0.539574	0.269787	+	0.962920i	$0.413047\pi$
$488$	3.26352e9	1.27121
$489$	0	0
$490$	−7.89838e8	−0.303286
$491$	−4.93551e9	−1.88168	−0.940842	−	0.338845i	$-0.889964\pi$
$491$	−4.93551e9	−1.88168	−0.940842	+	0.338845i	$0.889964\pi$
$492$	0	0
$493$	−7.67598e8	−0.288516
$494$	−2.23748e9	−0.835053
$495$	0	0
$496$	−1.65133e9	−0.607643
$497$	−1.96301e9	−0.717257
$498$	0	0
$499$	−4.54580e9	−1.63779	−0.818895	−	0.573943i	$-0.805413\pi$
$499$	−4.54580e9	−1.63779	−0.818895	+	0.573943i	$0.805413\pi$
$500$	3.89429e9	1.39326
$501$	0	0
$502$	−1.33887e9	−0.472362
$503$	−1.13170e9	−0.396500	−0.198250	−	0.980151i	$-0.563526\pi$
$503$	−1.13170e9	−0.396500	−0.198250	+	0.980151i	$0.563526\pi$
$504$	0	0
$505$	−1.66755e9	−0.576181
$506$	1.33073e9	0.456630
$507$	0	0
$508$	4.46869e8	0.151237
$509$	−3.02720e9	−1.01749	−0.508743	−	0.860918i	$-0.669890\pi$
$509$	−3.02720e9	−1.01749	−0.508743	+	0.860918i	$0.669890\pi$
$510$	0	0
$511$	−5.13578e9	−1.70268
$512$	5.46586e9	1.79976
$513$	0	0
$514$	−2.21985e9	−0.721028
$515$	7.76003e9	2.50345
$516$	0	0
$517$	1.06625e8	0.0339345
$518$	5.06265e9	1.60038
$519$	0	0
$520$	5.94139e9	1.85301
$521$	−9.37018e8	−0.290279	−0.145140	−	0.989411i	$-0.546363\pi$
$521$	−9.37018e8	−0.290279	−0.145140	+	0.989411i	$0.546363\pi$
$522$	0	0
$523$	2.52142e9	0.770708	0.385354	−	0.922769i	$-0.374079\pi$
$523$	2.52142e9	0.770708	0.385354	+	0.922769i	$0.374079\pi$
$524$	−3.13018e9	−0.950407
$525$	0	0
$526$	1.00914e10	3.02345
$527$	−1.83149e9	−0.545089
$528$	0	0
$529$	−2.22694e9	−0.654055
$530$	5.84212e9	1.70453
$531$	0	0
$532$	−5.30089e9	−1.52637
$533$	−1.91379e9	−0.547456
$534$	0	0
$535$	−1.03060e10	−2.90973
$536$	−1.61455e9	−0.452872
$537$	0	0
$538$	−1.45740e9	−0.403497
$539$	−1.81483e8	−0.0499201
$540$	0	0
$541$	5.53185e8	0.150204	0.0751018	−	0.997176i	$-0.476072\pi$
$541$	5.53185e8	0.150204	0.0751018	+	0.997176i	$0.476072\pi$
$542$	−3.38288e9	−0.912617
$543$	0	0
$544$	−2.30428e8	−0.0613675
$545$	1.74410e9	0.461514
$546$	0	0
$547$	4.50977e8	0.117814	0.0589072	−	0.998263i	$-0.481238\pi$
$547$	4.50977e8	0.117814	0.0589072	+	0.998263i	$0.481238\pi$
$548$	8.99792e9	2.33566
$549$	0	0
$550$	4.36732e9	1.11930
$551$	8.57924e8	0.218483
$552$	0	0
$553$	4.37370e9	1.09979
$554$	−8.35578e9	−2.08787
$555$	0	0
$556$	8.51024e9	2.09981
$557$	3.86605e9	0.947926	0.473963	−	0.880545i	$-0.342823\pi$
$557$	3.86605e9	0.947926	0.473963	+	0.880545i	$0.342823\pi$
$558$	0	0
$559$	4.93225e9	1.19427
$560$	7.22893e9	1.73947
$561$	0	0
$562$	7.28153e8	0.173040
$563$	−2.10838e9	−0.497930	−0.248965	−	0.968512i	$-0.580090\pi$
$563$	−2.10838e9	−0.497930	−0.248965	+	0.968512i	$0.580090\pi$
$564$	0	0
$565$	1.17557e9	0.274207
$566$	5.11644e8	0.118607
$567$	0	0
$568$	5.25706e9	1.20371
$569$	5.98974e9	1.36306	0.681530	−	0.731790i	$-0.261315\pi$
$569$	5.98974e9	1.36306	0.681530	+	0.731790i	$0.261315\pi$
$570$	0	0
$571$	5.77991e9	1.29925	0.649627	−	0.760253i	$-0.274925\pi$
$571$	5.77991e9	1.29925	0.649627	+	0.760253i	$0.274925\pi$
$572$	2.70557e9	0.604467
$573$	0	0
$574$	−6.78030e9	−1.49643
$575$	3.86568e9	0.847986
$576$	0	0
$577$	8.69442e8	0.188419	0.0942096	−	0.995552i	$-0.469968\pi$
$577$	8.69442e8	0.188419	0.0942096	+	0.995552i	$0.469968\pi$
$578$	8.30994e8	0.178999
$579$	0	0
$580$	−4.51493e9	−0.960845
$581$	−9.08402e9	−1.92159
$582$	0	0
$583$	1.34236e9	0.280562
$584$	1.37539e10	2.85747
$585$	0	0
$586$	1.28149e10	2.63071
$587$	1.19117e9	0.243074	0.121537	−	0.992587i	$-0.461218\pi$
$587$	1.19117e9	0.243074	0.121537	+	0.992587i	$0.461218\pi$
$588$	0	0
$589$	2.04701e9	0.412778
$590$	1.76319e9	0.353441
$591$	0	0
$592$	−4.65618e9	−0.922367
$593$	−5.37577e9	−1.05864	−0.529321	−	0.848421i	$-0.677553\pi$
$593$	−5.37577e9	−1.05864	−0.529321	+	0.848421i	$0.677553\pi$
$594$	0	0
$595$	8.01760e9	1.56040
$596$	−8.13012e9	−1.57302
$597$	0	0
$598$	3.58125e9	0.684826
$599$	7.00918e9	1.33252	0.666260	−	0.745720i	$-0.267894\pi$
$599$	7.00918e9	1.33252	0.666260	+	0.745720i	$0.267894\pi$
$600$	0	0
$601$	5.18595e9	0.974469	0.487235	−	0.873271i	$-0.338006\pi$
$601$	5.18595e9	0.974469	0.487235	+	0.873271i	$0.338006\pi$
$602$	1.74743e10	3.26446
$603$	0	0
$604$	−6.55215e8	−0.120991
$605$	−6.81172e9	−1.25058
$606$	0	0
$607$	5.60023e9	1.01636	0.508178	−	0.861252i	$-0.330319\pi$
$607$	5.60023e9	1.01636	0.508178	+	0.861252i	$0.330319\pi$
$608$	2.57543e8	0.0464715
$609$	0	0
$610$	1.09337e10	1.95036
$611$	2.86947e8	0.0508929
$612$	0	0
$613$	3.23965e9	0.568051	0.284025	−	0.958817i	$-0.408330\pi$
$613$	3.23965e9	0.568051	0.284025	+	0.958817i	$0.408330\pi$
$614$	−1.58764e10	−2.76798
$615$	0	0
$616$	4.83661e9	0.833697
$617$	−1.21036e9	−0.207451	−0.103726	−	0.994606i	$-0.533076\pi$
$617$	−1.21036e9	−0.207451	−0.103726	+	0.994606i	$0.533076\pi$
$618$	0	0
$619$	−9.96098e9	−1.68805	−0.844024	−	0.536305i	$-0.819820\pi$
$619$	−9.96098e9	−1.68805	−0.844024	+	0.536305i	$0.819820\pi$
$620$	−1.07726e10	−1.81531
$621$	0	0
$622$	−3.14953e9	−0.524783
$623$	2.35221e9	0.389733
$624$	0	0
$625$	−2.21642e9	−0.363138
$626$	−4.23332e9	−0.689717
$627$	0	0
$628$	−1.50234e10	−2.42052
$629$	−5.16416e9	−0.827414
$630$	0	0
$631$	8.86210e9	1.40422	0.702108	−	0.712071i	$-0.252243\pi$
$631$	8.86210e9	1.40422	0.702108	+	0.712071i	$0.252243\pi$
$632$	−1.17130e10	−1.84569
$633$	0	0
$634$	−1.69833e10	−2.64674
$635$	7.55424e8	0.117080
$636$	0	0
$637$	−4.88404e8	−0.0748671
$638$	−1.55136e9	−0.236505
$639$	0	0
$640$	1.76529e10	2.66187
$641$	−1.08624e10	−1.62901	−0.814507	−	0.580154i	$-0.802992\pi$
$641$	−1.08624e10	−1.62901	−0.814507	+	0.580154i	$0.802992\pi$
$642$	0	0
$643$	−5.64420e9	−0.837267	−0.418634	−	0.908155i	$-0.637491\pi$
$643$	−5.64420e9	−0.837267	−0.418634	+	0.908155i	$0.637491\pi$
$644$	8.48447e9	1.25177
$645$	0	0
$646$	8.08603e9	1.18011
$647$	−1.50140e7	−0.00217937	−0.00108968	−	0.999999i	$-0.500347\pi$
$647$	−1.50140e7	−0.00217937	−0.00108968	+	0.999999i	$0.500347\pi$
$648$	0	0
$649$	4.05132e8	0.0581756
$650$	1.17533e10	1.67865
$651$	0	0
$652$	−1.13491e10	−1.60360
$653$	3.25704e9	0.457748	0.228874	−	0.973456i	$-0.426496\pi$
$653$	3.25704e9	0.457748	0.228874	+	0.973456i	$0.426496\pi$
$654$	0	0
$655$	−5.29151e9	−0.735758
$656$	6.23592e9	0.862457
$657$	0	0
$658$	1.01661e9	0.139112
$659$	−9.09574e9	−1.23805	−0.619026	−	0.785370i	$-0.712473\pi$
$659$	−9.09574e9	−1.23805	−0.619026	+	0.785370i	$0.712473\pi$
$660$	0	0
$661$	−8.48609e9	−1.14289	−0.571443	−	0.820642i	$-0.693616\pi$
$661$	−8.48609e9	−1.14289	−0.571443	+	0.820642i	$0.693616\pi$
$662$	−1.79344e10	−2.40261
$663$	0	0
$664$	2.43276e10	3.22486
$665$	−8.96106e9	−1.18164
$666$	0	0
$667$	−1.37317e9	−0.179178
$668$	2.33110e10	3.02582
$669$	0	0
$670$	−5.40923e9	−0.694822
$671$	2.51227e9	0.321024
$672$	0	0
$673$	−1.43232e10	−1.81129	−0.905646	−	0.424035i	$-0.860613\pi$
$673$	−1.43232e10	−1.81129	−0.905646	+	0.424035i	$0.860613\pi$
$674$	−1.07283e10	−1.34964
$675$	0	0
$676$	−8.93084e9	−1.11193
$677$	2.38817e9	0.295805	0.147902	−	0.989002i	$-0.452748\pi$
$677$	2.38817e9	0.295805	0.147902	+	0.989002i	$0.452748\pi$
$678$	0	0
$679$	−1.35789e10	−1.66465
$680$	−2.14716e10	−2.61869
$681$	0	0
$682$	−3.70156e9	−0.446827
$683$	−1.52714e10	−1.83403	−0.917013	−	0.398857i	$-0.869407\pi$
$683$	−1.52714e10	−1.83403	−0.917013	+	0.398857i	$0.869407\pi$
$684$	0	0
$685$	1.52108e10	1.80816
$686$	1.37587e10	1.62721
$687$	0	0
$688$	−1.60713e10	−1.88145
$689$	3.61253e9	0.420770
$690$	0	0
$691$	−1.01080e10	−1.16544	−0.582721	−	0.812672i	$-0.698012\pi$
$691$	−1.01080e10	−1.16544	−0.582721	+	0.812672i	$0.698012\pi$
$692$	−5.81645e9	−0.667247
$693$	0	0
$694$	−1.14799e10	−1.30371
$695$	1.43864e10	1.62557
$696$	0	0
$697$	6.91626e9	0.773671
$698$	1.50249e10	1.67231
$699$	0	0
$700$	2.78451e10	3.06835
$701$	−1.18838e10	−1.30299	−0.651494	−	0.758654i	$-0.725857\pi$
$701$	−1.18838e10	−1.30299	−0.651494	+	0.758654i	$0.725857\pi$
$702$	0	0
$703$	5.77185e9	0.626572
$704$	3.90188e9	0.421472
$705$	0	0
$706$	−2.09088e10	−2.23621
$707$	−3.65321e9	−0.388782
$708$	0	0
$709$	−1.60939e10	−1.69589	−0.847946	−	0.530082i	$-0.822161\pi$
$709$	−1.60939e10	−1.69589	−0.847946	+	0.530082i	$0.822161\pi$
$710$	1.76127e10	1.84681
$711$	0	0
$712$	−6.29935e9	−0.654057
$713$	−3.27639e9	−0.338518
$714$	0	0
$715$	4.57372e9	0.467949
$716$	−3.27817e10	−3.33762
$717$	0	0
$718$	−2.14604e10	−2.16373
$719$	−6.07025e9	−0.609053	−0.304527	−	0.952504i	$-0.598498\pi$
$719$	−6.07025e9	−0.609053	−0.304527	+	0.952504i	$0.598498\pi$
$720$	0	0
$721$	1.70004e10	1.68922
$722$	8.53256e9	0.843721
$723$	0	0
$724$	2.40202e10	2.35230
$725$	−4.50659e9	−0.439203
$726$	0	0
$727$	−1.05256e10	−1.01596	−0.507979	−	0.861369i	$-0.669607\pi$
$727$	−1.05256e10	−1.01596	−0.507979	+	0.861369i	$0.669607\pi$
$728$	1.30162e10	1.25033
$729$	0	0
$730$	4.60797e10	4.38409
$731$	−1.78247e10	−1.68776
$732$	0	0
$733$	−8.12696e9	−0.762192	−0.381096	−	0.924536i	$-0.624453\pi$
$733$	−8.12696e9	−0.762192	−0.381096	+	0.924536i	$0.624453\pi$
$734$	3.77639e9	0.352485
$735$	0	0
$736$	−4.12216e8	−0.0381112
$737$	−1.24289e9	−0.114366
$738$	0	0
$739$	−5.50602e9	−0.501860	−0.250930	−	0.968005i	$-0.580736\pi$
$739$	−5.50602e9	−0.501860	−0.250930	+	0.968005i	$0.580736\pi$
$740$	−3.03751e10	−2.75554
$741$	0	0
$742$	1.27987e10	1.15014
$743$	4.28129e9	0.382925	0.191462	−	0.981500i	$-0.438677\pi$
$743$	4.28129e9	0.382925	0.191462	+	0.981500i	$0.438677\pi$
$744$	0	0
$745$	−1.37438e10	−1.21776
$746$	2.44455e10	2.15582
$747$	0	0
$748$	−9.77767e9	−0.854240
$749$	−2.25781e10	−1.96336
$750$	0	0
$751$	7.38153e9	0.635926	0.317963	−	0.948103i	$-0.397001\pi$
$751$	7.38153e9	0.635926	0.317963	+	0.948103i	$0.397001\pi$
$752$	−9.34992e8	−0.0801762
$753$	0	0
$754$	−4.17500e9	−0.354696
$755$	−1.10763e9	−0.0936655
$756$	0	0
$757$	−2.14892e10	−1.80046	−0.900232	−	0.435410i	$-0.856604\pi$
$757$	−2.14892e10	−1.80046	−0.900232	+	0.435410i	$0.856604\pi$
$758$	3.99759e10	3.33393
$759$	0	0
$760$	2.39983e10	1.98304
$761$	−9.48902e9	−0.780504	−0.390252	−	0.920708i	$-0.627612\pi$
$761$	−9.48902e9	−0.780504	−0.390252	+	0.920708i	$0.627612\pi$
$762$	0	0
$763$	3.82092e9	0.311410
$764$	4.02182e10	3.26284
$765$	0	0
$766$	−1.68785e10	−1.35685
$767$	1.09029e9	0.0872482
$768$	0	0
$769$	−2.02433e9	−0.160524	−0.0802620	−	0.996774i	$-0.525576\pi$
$769$	−2.02433e9	−0.160524	−0.0802620	+	0.996774i	$0.525576\pi$
$770$	1.62041e10	1.27911
$771$	0	0
$772$	4.79198e9	0.374847
$773$	5.39051e9	0.419761	0.209880	−	0.977727i	$-0.432693\pi$
$773$	5.39051e9	0.419761	0.209880	+	0.977727i	$0.432693\pi$
$774$	0	0
$775$	−1.07527e10	−0.829781
$776$	3.63652e10	2.79364
$777$	0	0
$778$	−3.53147e10	−2.68861
$779$	−7.73012e9	−0.585875
$780$	0	0
$781$	4.04691e9	0.303980
$782$	−1.29423e10	−0.967803
$783$	0	0
$784$	1.59142e9	0.117945
$785$	−2.53968e10	−1.87385
$786$	0	0
$787$	−3.44573e8	−0.0251982	−0.0125991	−	0.999921i	$-0.504011\pi$
$787$	−3.44573e8	−0.0251982	−0.0125991	+	0.999921i	$0.504011\pi$
$788$	−9.30986e9	−0.677800
$789$	0	0
$790$	−3.92421e10	−2.83177
$791$	2.57540e9	0.185023
$792$	0	0
$793$	6.76098e9	0.481453
$794$	2.60181e10	1.84461
$795$	0	0
$796$	8.83382e9	0.620802
$797$	−7.94031e9	−0.555563	−0.277781	−	0.960644i	$-0.589599\pi$
$797$	−7.94031e9	−0.555563	−0.277781	+	0.960644i	$0.589599\pi$
$798$	0	0
$799$	−1.03700e9	−0.0719225
$800$	−1.35285e9	−0.0934188
$801$	0	0
$802$	−2.45847e10	−1.68288
$803$	1.05878e10	0.721611
$804$	0	0
$805$	1.43428e10	0.969057
$806$	−9.96156e9	−0.670123
$807$	0	0
$808$	9.78352e9	0.652462
$809$	−1.83573e10	−1.21896	−0.609478	−	0.792803i	$-0.708621\pi$
$809$	−1.83573e10	−1.21896	−0.609478	+	0.792803i	$0.708621\pi$
$810$	0	0
$811$	−2.86473e10	−1.88587	−0.942934	−	0.332979i	$-0.891946\pi$
$811$	−2.86473e10	−1.88587	−0.942934	+	0.332979i	$0.891946\pi$
$812$	−9.89115e9	−0.648337
$813$	0	0
$814$	−1.04371e10	−0.678256
$815$	−1.91855e10	−1.24143
$816$	0	0
$817$	1.99222e10	1.27808
$818$	−3.61724e10	−2.31069
$819$	0	0
$820$	4.06807e10	2.57656
$821$	1.87449e10	1.18218	0.591088	−	0.806607i	$-0.298698\pi$
$821$	1.87449e10	1.18218	0.591088	+	0.806607i	$0.298698\pi$
$822$	0	0
$823$	2.20970e10	1.38176	0.690881	−	0.722969i	$-0.257223\pi$
$823$	2.20970e10	1.38176	0.690881	+	0.722969i	$0.257223\pi$
$824$	−4.55281e10	−2.83488
$825$	0	0
$826$	3.86273e9	0.238487
$827$	−7.00279e9	−0.430529	−0.215264	−	0.976556i	$-0.569061\pi$
$827$	−7.00279e9	−0.430529	−0.215264	+	0.976556i	$0.569061\pi$
$828$	0	0
$829$	−1.55766e10	−0.949581	−0.474791	−	0.880099i	$-0.657476\pi$
$829$	−1.55766e10	−0.949581	−0.474791	+	0.880099i	$0.657476\pi$
$830$	8.15045e10	4.94776
$831$	0	0
$832$	1.05007e10	0.632099
$833$	1.76505e9	0.105803
$834$	0	0
$835$	3.94068e10	2.34244
$836$	1.09282e10	0.646887
$837$	0	0
$838$	3.88237e10	2.27899
$839$	2.48824e10	1.45454	0.727268	−	0.686353i	$-0.240790\pi$
$839$	2.48824e10	1.45454	0.727268	+	0.686353i	$0.240790\pi$
$840$	0	0
$841$	−1.56490e10	−0.907197
$842$	−2.06221e10	−1.19053
$843$	0	0
$844$	4.29411e10	2.45853
$845$	−1.50974e10	−0.860804
$846$	0	0
$847$	−1.49229e10	−0.843841
$848$	−1.17711e10	−0.662876
$849$	0	0
$850$	−4.24751e10	−2.37229
$851$	−9.23827e9	−0.513851
$852$	0	0
$853$	−1.67988e10	−0.926736	−0.463368	−	0.886166i	$-0.653359\pi$
$853$	−1.67988e10	−0.926736	−0.463368	+	0.886166i	$0.653359\pi$
$854$	2.39533e10	1.31602
$855$	0	0
$856$	6.04654e10	3.29495
$857$	2.93017e10	1.59023	0.795115	−	0.606458i	$-0.207410\pi$
$857$	2.93017e10	1.59023	0.795115	+	0.606458i	$0.207410\pi$
$858$	0	0
$859$	2.65222e10	1.42769	0.713844	−	0.700305i	$-0.246952\pi$
$859$	2.65222e10	1.42769	0.713844	+	0.700305i	$0.246952\pi$
$860$	−1.04843e11	−5.62075
$861$	0	0
$862$	2.26449e10	1.20419
$863$	−2.67744e10	−1.41802	−0.709009	−	0.705199i	$-0.750858\pi$
$863$	−2.67744e10	−1.41802	−0.709009	+	0.705199i	$0.750858\pi$
$864$	0	0
$865$	−9.83259e9	−0.516549
$866$	−4.67076e10	−2.44385
$867$	0	0
$868$	−2.36003e10	−1.22489
$869$	−9.01675e9	−0.466102
$870$	0	0
$871$	−3.34485e9	−0.171519
$872$	−1.02327e10	−0.522614
$873$	0	0
$874$	1.44652e10	0.732885
$875$	1.44223e10	0.727790
$876$	0	0
$877$	2.17802e10	1.09034	0.545171	−	0.838325i	$-0.316465\pi$
$877$	2.17802e10	1.09034	0.545171	+	0.838325i	$0.316465\pi$
$878$	1.31774e10	0.657049
$879$	0	0
$880$	−1.49031e10	−0.737201
$881$	2.03738e10	1.00382	0.501910	−	0.864920i	$-0.332631\pi$
$881$	2.03738e10	1.00382	0.501910	+	0.864920i	$0.332631\pi$
$882$	0	0
$883$	2.67217e10	1.30618	0.653088	−	0.757282i	$-0.273473\pi$
$883$	2.67217e10	1.30618	0.653088	+	0.757282i	$0.273473\pi$
$884$	−2.63135e10	−1.28114
$885$	0	0
$886$	−4.41218e10	−2.13125
$887$	−6.91217e9	−0.332569	−0.166285	−	0.986078i	$-0.553177\pi$
$887$	−6.91217e9	−0.332569	−0.166285	+	0.986078i	$0.553177\pi$
$888$	0	0
$889$	1.65495e9	0.0790005
$890$	−2.11047e10	−1.00349
$891$	0	0
$892$	−6.66164e10	−3.14271
$893$	1.15903e9	0.0544645
$894$	0	0
$895$	−5.54169e10	−2.58382
$896$	3.86734e10	1.79612
$897$	0	0
$898$	−1.13395e10	−0.522550
$899$	3.81960e9	0.175331
$900$	0	0
$901$	−1.30553e10	−0.594636
$902$	1.39782e10	0.634202
$903$	0	0
$904$	−6.89707e9	−0.310510
$905$	4.06058e10	1.82103
$906$	0	0
$907$	−1.77215e10	−0.788632	−0.394316	−	0.918975i	$-0.629018\pi$
$907$	−1.77215e10	−0.788632	−0.394316	+	0.918975i	$0.629018\pi$
$908$	5.86512e10	2.60002
$909$	0	0
$910$	4.36081e10	1.91832
$911$	2.97591e10	1.30408	0.652042	−	0.758183i	$-0.273913\pi$
$911$	2.97591e10	1.30408	0.652042	+	0.758183i	$0.273913\pi$
$912$	0	0
$913$	1.87275e10	0.814389
$914$	−1.77360e10	−0.768323
$915$	0	0
$916$	−1.91195e10	−0.821942
$917$	−1.15925e10	−0.496458
$918$	0	0
$919$	−7.49318e8	−0.0318465	−0.0159233	−	0.999873i	$-0.505069\pi$
$919$	−7.49318e8	−0.0318465	−0.0159233	+	0.999873i	$0.505069\pi$
$920$	−3.84110e10	−1.62629
$921$	0	0
$922$	3.08418e10	1.29593
$923$	1.08910e10	0.455891
$924$	0	0
$925$	−3.03190e10	−1.25956
$926$	−1.18189e10	−0.489147
$927$	0	0
$928$	4.80560e8	0.0197392
$929$	−3.70776e10	−1.51725	−0.758623	−	0.651529i	$-0.774128\pi$
$929$	−3.70776e10	−1.51725	−0.758623	+	0.651529i	$0.774128\pi$
$930$	0	0
$931$	−1.97274e9	−0.0801211
$932$	−1.75020e10	−0.708161
$933$	0	0
$934$	−4.29706e10	−1.72567
$935$	−1.65290e10	−0.661310
$936$	0	0
$937$	2.52127e10	1.00122	0.500611	−	0.865672i	$-0.333109\pi$
$937$	2.52127e10	1.00122	0.500611	+	0.865672i	$0.333109\pi$
$938$	−1.18504e10	−0.468836
$939$	0	0
$940$	−6.09952e9	−0.239524
$941$	−2.49972e10	−0.977975	−0.488988	−	0.872291i	$-0.662634\pi$
$941$	−2.49972e10	−0.977975	−0.488988	+	0.872291i	$0.662634\pi$
$942$	0	0
$943$	1.23726e10	0.480475
$944$	−3.55260e9	−0.137450
$945$	0	0
$946$	−3.60247e10	−1.38351
$947$	1.83651e10	0.702696	0.351348	−	0.936245i	$-0.385723\pi$
$947$	1.83651e10	0.702696	0.351348	+	0.936245i	$0.385723\pi$
$948$	0	0
$949$	2.84938e10	1.08223
$950$	4.74733e10	1.79646
$951$	0	0
$952$	−4.70393e10	−1.76698
$953$	1.85113e10	0.692805	0.346403	−	0.938086i	$-0.387403\pi$
$953$	1.85113e10	0.692805	0.346403	+	0.938086i	$0.387403\pi$
$954$	0	0
$955$	6.79881e10	2.52593
$956$	−3.32696e10	−1.23153
$957$	0	0
$958$	2.30694e10	0.847728
$959$	3.33233e10	1.22007
$960$	0	0
$961$	−1.83990e10	−0.668749
$962$	−2.80881e10	−1.01721
$963$	0	0
$964$	−7.67540e10	−2.75950
$965$	8.10075e9	0.290188
$966$	0	0
$967$	−4.59158e10	−1.63294	−0.816469	−	0.577389i	$-0.804072\pi$
$967$	−4.59158e10	−1.63294	−0.816469	+	0.577389i	$0.804072\pi$
$968$	3.99644e10	1.41615
$969$	0	0
$970$	1.21834e11	4.28616
$971$	−9.02722e9	−0.316437	−0.158218	−	0.987404i	$-0.550575\pi$
$971$	−9.02722e9	−0.316437	−0.158218	+	0.987404i	$0.550575\pi$
$972$	0	0
$973$	3.15172e10	1.09686
$974$	−2.70335e10	−0.937444
$975$	0	0
$976$	−2.20301e10	−0.758476
$977$	−2.33504e10	−0.801058	−0.400529	−	0.916284i	$-0.631174\pi$
$977$	−2.33504e10	−0.801058	−0.400529	+	0.916284i	$0.631174\pi$
$978$	0	0
$979$	−4.84927e9	−0.165172
$980$	1.03818e10	0.352356
$981$	0	0
$982$	9.70132e10	3.26919
$983$	4.78814e10	1.60779	0.803895	−	0.594771i	$-0.202757\pi$
$983$	4.78814e10	1.60779	0.803895	+	0.594771i	$0.202757\pi$
$984$	0	0
$985$	−1.57381e10	−0.524719
$986$	1.50880e10	0.501261
$987$	0	0
$988$	2.94099e10	0.970162
$989$	−3.18869e10	−1.04815
$990$	0	0
$991$	−1.35826e10	−0.443329	−0.221664	−	0.975123i	$-0.571149\pi$
$991$	−1.35826e10	−0.443329	−0.221664	+	0.975123i	$0.571149\pi$
$992$	1.14662e9	0.0372930
$993$	0	0
$994$	3.85852e10	1.24615
$995$	1.49334e10	0.480594
$996$	0	0
$997$	4.46503e10	1.42689	0.713446	−	0.700710i	$-0.247133\pi$
$997$	4.46503e10	1.42689	0.713446	+	0.700710i	$0.247133\pi$
$998$	8.93530e10	2.84546
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.b.1.1		16
3.2	odd	2		177.8.a.a.1.16	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.a.1.16	✓	16	3.2	odd	2
531.8.a.b.1.1		16	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:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	531.a (trivial)

\(f(q)\)	\(=\)	\(q-19.6562 q^{2} +258.365 q^{4} +436.761 q^{5} +956.841 q^{7} -2562.48 q^{8} +O(q^{10})\)	\(q-19.6562 q^{2} +258.365 q^{4} +436.761 q^{5} +956.841 q^{7} -2562.48 q^{8} -8585.06 q^{10} -1972.61 q^{11} -5308.65 q^{13} -18807.8 q^{14} +17297.8 q^{16} +19184.9 q^{17} -21442.5 q^{19} +112844. q^{20} +38773.9 q^{22} +34320.3 q^{23} +112635. q^{25} +104348. q^{26} +247214. q^{28} -40010.4 q^{29} -95465.0 q^{31} -12010.9 q^{32} -377103. q^{34} +417911. q^{35} -269178. q^{37} +421478. q^{38} -1.11919e6 q^{40} +360504. q^{41} -929097. q^{43} -509653. q^{44} -674606. q^{46} -54052.8 q^{47} +92001.6 q^{49} -2.21398e6 q^{50} -1.37157e6 q^{52} -680499. q^{53} -861559. q^{55} -2.45188e6 q^{56} +786452. q^{58} -205379. q^{59} -1.27358e6 q^{61} +1.87648e6 q^{62} -1.97803e6 q^{64} -2.31861e6 q^{65} +630075. q^{67} +4.95672e6 q^{68} -8.21453e6 q^{70} -2.05155e6 q^{71} -5.36743e6 q^{73} +5.29101e6 q^{74} -5.54000e6 q^{76} -1.88747e6 q^{77} +4.57098e6 q^{79} +7.55500e6 q^{80} -7.08613e6 q^{82} -9.49376e6 q^{83} +8.37924e6 q^{85} +1.82625e7 q^{86} +5.05477e6 q^{88} +2.45830e6 q^{89} -5.07953e6 q^{91} +8.86717e6 q^{92} +1.06247e6 q^{94} -9.36526e6 q^{95} -1.41914e7 q^{97} -1.80840e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8}+O(q^{10}) \) 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8	\( 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8} - 3479 q^{10} - 898 q^{11} - 8172 q^{13} + 13315 q^{14} + 3138 q^{16} + 44985 q^{17} - 40137 q^{19} - 130657 q^{20} + 109394 q^{22} + 2833 q^{23} + 285746 q^{25} + 129420 q^{26} + 112890 q^{28} - 144375 q^{29} - 141759 q^{31} + 36224 q^{32} - 341332 q^{34} + 78859 q^{35} - 297971 q^{37} - 329075 q^{38} - 203048 q^{40} - 659077 q^{41} - 1431608 q^{43} - 254916 q^{44} + 873113 q^{46} + 1574073 q^{47} + 1893545 q^{49} - 302533 q^{50} - 4972548 q^{52} - 587736 q^{53} - 4624036 q^{55} + 5798506 q^{56} - 6991380 q^{58} - 3286064 q^{59} - 6117131 q^{61} + 11570258 q^{62} - 19063011 q^{64} + 5335514 q^{65} - 16518710 q^{67} + 17284669 q^{68} - 39189486 q^{70} + 10882582 q^{71} - 21097441 q^{73} + 16717030 q^{74} - 40864952 q^{76} + 3404601 q^{77} - 3784458 q^{79} + 27466195 q^{80} - 24990117 q^{82} + 1951425 q^{83} - 23238675 q^{85} + 35910572 q^{86} - 27843055 q^{88} - 10499443 q^{89} + 699217 q^{91} + 20062766 q^{92} - 59358988 q^{94} + 29236333 q^{95} - 25158976 q^{97} - 2120460 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8 - 3479 * q^10 - 898 * q^11 - 8172 * q^13 + 13315 * q^14 + 3138 * q^16 + 44985 * q^17 - 40137 * q^19 - 130657 * q^20 + 109394 * q^22 + 2833 * q^23 + 285746 * q^25 + 129420 * q^26 + 112890 * q^28 - 144375 * q^29 - 141759 * q^31 + 36224 * q^32 - 341332 * q^34 + 78859 * q^35 - 297971 * q^37 - 329075 * q^38 - 203048 * q^40 - 659077 * q^41 - 1431608 * q^43 - 254916 * q^44 + 873113 * q^46 + 1574073 * q^47 + 1893545 * q^49 - 302533 * q^50 - 4972548 * q^52 - 587736 * q^53 - 4624036 * q^55 + 5798506 * q^56 - 6991380 * q^58 - 3286064 * q^59 - 6117131 * q^61 + 11570258 * q^62 - 19063011 * q^64 + 5335514 * q^65 - 16518710 * q^67 + 17284669 * q^68 - 39189486 * q^70 + 10882582 * q^71 - 21097441 * q^73 + 16717030 * q^74 - 40864952 * q^76 + 3404601 * q^77 - 3784458 * q^79 + 27466195 * q^80 - 24990117 * q^82 + 1951425 * q^83 - 23238675 * q^85 + 35910572 * q^86 - 27843055 * q^88 - 10499443 * q^89 + 699217 * q^91 + 20062766 * q^92 - 59358988 * q^94 + 29236333 * q^95 - 25158976 * q^97 - 2120460 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more