LMFDB - Embedded newform 531.8.a.b.1.2

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			1.2
Root			$-18.7189$ 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)

$f(q)$	$=$	$q-18.7189 q^{2} +222.398 q^{4} -443.832 q^{5} -1695.79 q^{7} -1767.03 q^{8} +O(q^{10})$	\(q-18.7189 q^{2} +222.398 q^{4} -443.832 q^{5} -1695.79 q^{7} -1767.03 q^{8} +8308.06 q^{10} +2763.59 q^{11} -10956.4 q^{13} +31743.3 q^{14} +4610.01 q^{16} +17168.5 q^{17} -41280.8 q^{19} -98707.5 q^{20} -51731.4 q^{22} -82535.2 q^{23} +118862. q^{25} +205092. q^{26} -377140. q^{28} -103089. q^{29} -162172. q^{31} +139886. q^{32} -321376. q^{34} +752645. q^{35} +446923. q^{37} +772732. q^{38} +784266. q^{40} -371488. q^{41} -790401. q^{43} +614617. q^{44} +1.54497e6 q^{46} +1.11011e6 q^{47} +2.05215e6 q^{49} -2.22497e6 q^{50} -2.43668e6 q^{52} +771292. q^{53} -1.22657e6 q^{55} +2.99652e6 q^{56} +1.92972e6 q^{58} -205379. q^{59} -211813. q^{61} +3.03568e6 q^{62} -3.20860e6 q^{64} +4.86279e6 q^{65} +1.48116e6 q^{67} +3.81824e6 q^{68} -1.40887e7 q^{70} -3.40336e6 q^{71} -3.93442e6 q^{73} -8.36592e6 q^{74} -9.18078e6 q^{76} -4.68646e6 q^{77} +4.55385e6 q^{79} -2.04607e6 q^{80} +6.95386e6 q^{82} +4.51953e6 q^{83} -7.61992e6 q^{85} +1.47955e7 q^{86} -4.88336e6 q^{88} +4.21568e6 q^{89} +1.85797e7 q^{91} -1.83557e7 q^{92} -2.07800e7 q^{94} +1.83217e7 q^{95} -1.59925e6 q^{97} -3.84141e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−18.7189	−1.65454	−0.827268	−	0.561808i	$-0.810106\pi$
$2$	−18.7189	−1.65454	−0.827268	+	0.561808i	$0.810106\pi$
$3$	0	0
$3$	0	0
$4$	222.398	1.73749
$5$	−443.832	−1.58790	−0.793951	−	0.607982i	$-0.791979\pi$
$5$	−443.832	−1.58790	−0.793951	+	0.607982i	$0.791979\pi$
$6$	0	0
$7$	−1695.79	−1.86865	−0.934326	−	0.356419i	$-0.883997\pi$
$7$	−1695.79	−1.86865	−0.934326	+	0.356419i	$0.883997\pi$
$8$	−1767.03	−1.22020
$9$	0	0
$10$	8308.06	2.62724
$11$	2763.59	0.626036	0.313018	−	0.949747i	$-0.398660\pi$
$11$	2763.59	0.626036	0.313018	+	0.949747i	$0.398660\pi$
$12$	0	0
$13$	−10956.4	−1.38314	−0.691568	−	0.722311i	$-0.743080\pi$
$13$	−10956.4	−1.38314	−0.691568	+	0.722311i	$0.743080\pi$
$14$	31743.3	3.09175
$15$	0	0
$16$	4610.01	0.281373
$17$	17168.5	0.847541	0.423771	−	0.905770i	$-0.360706\pi$
$17$	17168.5	0.847541	0.423771	+	0.905770i	$0.360706\pi$
$18$	0	0
$19$	−41280.8	−1.38074	−0.690368	−	0.723459i	$-0.742551\pi$
$19$	−41280.8	−1.38074	−0.690368	+	0.723459i	$0.742551\pi$
$20$	−98707.5	−2.75896
$21$	0	0
$22$	−51731.4	−1.03580
$23$	−82535.2	−1.41446	−0.707232	−	0.706982i	$-0.750056\pi$
$23$	−82535.2	−1.41446	−0.707232	+	0.706982i	$0.750056\pi$
$24$	0	0
$25$	118862.	1.52143
$26$	205092.	2.28845
$27$	0	0
$28$	−377140.	−3.24676
$29$	−103089.	−0.784912	−0.392456	−	0.919771i	$-0.628375\pi$
$29$	−103089.	−0.784912	−0.392456	+	0.919771i	$0.628375\pi$
$30$	0	0
$31$	−162172.	−0.977709	−0.488854	−	0.872365i	$-0.662585\pi$
$31$	−162172.	−0.977709	−0.488854	+	0.872365i	$0.662585\pi$
$32$	139886.	0.754656
$33$	0	0
$34$	−321376.	−1.40229
$35$	752645.	2.96724
$36$	0	0
$37$	446923.	1.45053	0.725265	−	0.688470i	$-0.241717\pi$
$37$	446923.	1.45053	0.725265	+	0.688470i	$0.241717\pi$
$38$	772732.	2.28448
$39$	0	0
$40$	784266.	1.93755
$41$	−371488.	−0.841785	−0.420893	−	0.907111i	$-0.638283\pi$
$41$	−371488.	−0.841785	−0.420893	+	0.907111i	$0.638283\pi$
$42$	0	0
$43$	−790401.	−1.51603	−0.758015	−	0.652237i	$-0.773831\pi$
$43$	−790401.	−1.51603	−0.758015	+	0.652237i	$0.773831\pi$
$44$	614617.	1.08773
$45$	0	0
$46$	1.54497e6	2.34028
$47$	1.11011e6	1.55964	0.779818	−	0.626007i	$-0.215312\pi$
$47$	1.11011e6	1.55964	0.779818	+	0.626007i	$0.215312\pi$
$48$	0	0
$49$	2.05215e6	2.49186
$50$	−2.22497e6	−2.51726
$51$	0	0
$52$	−2.43668e6	−2.40318
$53$	771292.	0.711628	0.355814	−	0.934557i	$-0.384204\pi$
$53$	771292.	0.711628	0.355814	+	0.934557i	$0.384204\pi$
$54$	0	0
$55$	−1.22657e6	−0.994083
$56$	2.99652e6	2.28012
$57$	0	0
$58$	1.92972e6	1.29867
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	0	0
$61$	−211813.	−0.119481	−0.0597403	−	0.998214i	$-0.519027\pi$
$61$	−211813.	−0.119481	−0.0597403	+	0.998214i	$0.519027\pi$
$62$	3.03568e6	1.61765
$63$	0	0
$64$	−3.20860e6	−1.52998
$65$	4.86279e6	2.19628
$66$	0	0
$67$	1.48116e6	0.601644	0.300822	−	0.953680i	$-0.402739\pi$
$67$	1.48116e6	0.601644	0.300822	+	0.953680i	$0.402739\pi$
$68$	3.81824e6	1.47259
$69$	0	0
$70$	−1.40887e7	−4.90940
$71$	−3.40336e6	−1.12851	−0.564253	−	0.825602i	$-0.690836\pi$
$71$	−3.40336e6	−1.12851	−0.564253	+	0.825602i	$0.690836\pi$
$72$	0	0
$73$	−3.93442e6	−1.18372	−0.591862	−	0.806040i	$-0.701607\pi$
$73$	−3.93442e6	−1.18372	−0.591862	+	0.806040i	$0.701607\pi$
$74$	−8.36592e6	−2.39995
$75$	0	0
$76$	−9.18078e6	−2.39901
$77$	−4.68646e6	−1.16984
$78$	0	0
$79$	4.55385e6	1.03916	0.519582	−	0.854421i	$-0.326088\pi$
$79$	4.55385e6	1.03916	0.519582	+	0.854421i	$0.326088\pi$
$80$	−2.04607e6	−0.446793
$81$	0	0
$82$	6.95386e6	1.39276
$83$	4.51953e6	0.867602	0.433801	−	0.901009i	$-0.357172\pi$
$83$	4.51953e6	0.867602	0.433801	+	0.901009i	$0.357172\pi$
$84$	0	0
$85$	−7.61992e6	−1.34581
$86$	1.47955e7	2.50833
$87$	0	0
$88$	−4.88336e6	−0.763887
$89$	4.21568e6	0.633874	0.316937	−	0.948447i	$-0.397346\pi$
$89$	4.21568e6	0.633874	0.316937	+	0.948447i	$0.397346\pi$
$90$	0	0
$91$	1.85797e7	2.58460
$92$	−1.83557e7	−2.45761
$93$	0	0
$94$	−2.07800e7	−2.58047
$95$	1.83217e7	2.19247
$96$	0	0
$97$	−1.59925e6	−0.177916	−0.0889579	−	0.996035i	$-0.528354\pi$
$97$	−1.59925e6	−0.177916	−0.0889579	+	0.996035i	$0.528354\pi$
$98$	−3.84141e7	−4.12287
$99$	0	0
$100$	2.64347e7	2.64347
$101$	1.38691e6	0.133944	0.0669719	−	0.997755i	$-0.478666\pi$
$101$	1.38691e6	0.133944	0.0669719	+	0.997755i	$0.478666\pi$
$102$	0	0
$103$	−1.11202e6	−0.100273	−0.0501363	−	0.998742i	$-0.515966\pi$
$103$	−1.11202e6	−0.100273	−0.0501363	+	0.998742i	$0.515966\pi$
$104$	1.93603e7	1.68770
$105$	0	0
$106$	−1.44378e7	−1.17741
$107$	2.40434e7	1.89737	0.948685	−	0.316223i	$-0.102415\pi$
$107$	2.40434e7	1.89737	0.948685	+	0.316223i	$0.102415\pi$
$108$	0	0
$109$	1.06281e7	0.786070	0.393035	−	0.919524i	$-0.371425\pi$
$109$	1.06281e7	0.786070	0.393035	+	0.919524i	$0.371425\pi$
$110$	2.29601e7	1.64475
$111$	0	0
$112$	−7.81761e6	−0.525788
$113$	−1.82364e7	−1.18895	−0.594477	−	0.804112i	$-0.702641\pi$
$113$	−1.82364e7	−1.18895	−0.594477	+	0.804112i	$0.702641\pi$
$114$	0	0
$115$	3.66318e7	2.24603
$116$	−2.29269e7	−1.36377
$117$	0	0
$118$	3.84447e6	0.215402
$119$	−2.91141e7	−1.58376
$120$	0	0
$121$	−1.18497e7	−0.608079
$122$	3.96491e6	0.197685
$123$	0	0
$124$	−3.60667e7	−1.69876
$125$	−1.80803e7	−0.827982
$126$	0	0
$127$	1.28606e7	0.557119	0.278559	−	0.960419i	$-0.410143\pi$
$127$	1.28606e7	0.557119	0.278559	+	0.960419i	$0.410143\pi$
$128$	4.21561e7	1.77675
$129$	0	0
$130$	−9.10262e7	−3.63383
$131$	1.03027e7	0.400405	0.200203	−	0.979754i	$-0.435840\pi$
$131$	1.03027e7	0.400405	0.200203	+	0.979754i	$0.435840\pi$
$132$	0	0
$133$	7.00035e7	2.58011
$134$	−2.77257e7	−0.995442
$135$	0	0
$136$	−3.03373e7	−1.03417
$137$	4.73008e7	1.57161	0.785807	−	0.618471i	$-0.212248\pi$
$137$	4.73008e7	1.57161	0.785807	+	0.618471i	$0.212248\pi$
$138$	0	0
$139$	5.76637e7	1.82117	0.910585	−	0.413322i	$-0.135631\pi$
$139$	5.76637e7	1.82117	0.910585	+	0.413322i	$0.135631\pi$
$140$	1.67387e8	5.15553
$141$	0	0
$142$	6.37073e7	1.86715
$143$	−3.02789e7	−0.865893
$144$	0	0
$145$	4.57544e7	1.24636
$146$	7.36480e7	1.95851
$147$	0	0
$148$	9.93949e7	2.52028
$149$	−9.45541e6	−0.234168	−0.117084	−	0.993122i	$-0.537355\pi$
$149$	−9.45541e6	−0.234168	−0.117084	+	0.993122i	$0.537355\pi$
$150$	0	0
$151$	−1.54572e7	−0.365353	−0.182677	−	0.983173i	$-0.558476\pi$
$151$	−1.54572e7	−0.365353	−0.182677	+	0.983173i	$0.558476\pi$
$152$	7.29446e7	1.68477
$153$	0	0
$154$	8.77255e7	1.93555
$155$	7.19770e7	1.55251
$156$	0	0
$157$	3.62627e7	0.747845	0.373922	−	0.927460i	$-0.378013\pi$
$157$	3.62627e7	0.747845	0.373922	+	0.927460i	$0.378013\pi$
$158$	−8.52432e7	−1.71933
$159$	0	0
$160$	−6.20858e7	−1.19832
$161$	1.39962e8	2.64314
$162$	0	0
$163$	5.27645e7	0.954301	0.477151	−	0.878822i	$-0.341670\pi$
$163$	5.27645e7	0.954301	0.477151	+	0.878822i	$0.341670\pi$
$164$	−8.26183e7	−1.46259
$165$	0	0
$166$	−8.46008e7	−1.43548
$167$	7.36648e6	0.122392	0.0611959	−	0.998126i	$-0.480509\pi$
$167$	7.36648e6	0.122392	0.0611959	+	0.998126i	$0.480509\pi$
$168$	0	0
$169$	5.72936e7	0.913066
$170$	1.42637e8	2.22669
$171$	0	0
$172$	−1.75784e8	−2.63408
$173$	−7.87542e7	−1.15641	−0.578206	−	0.815891i	$-0.696247\pi$
$173$	−7.87542e7	−1.15641	−0.578206	+	0.815891i	$0.696247\pi$
$174$	0	0
$175$	−2.01564e8	−2.84303
$176$	1.27402e7	0.176149
$177$	0	0
$178$	−7.89130e7	−1.04877
$179$	−2.13413e7	−0.278121	−0.139061	−	0.990284i	$-0.544408\pi$
$179$	−2.13413e7	−0.278121	−0.139061	+	0.990284i	$0.544408\pi$
$180$	0	0
$181$	1.72243e7	0.215907	0.107953	−	0.994156i	$-0.465570\pi$
$181$	1.72243e7	0.215907	0.107953	+	0.994156i	$0.465570\pi$
$182$	−3.47792e8	−4.27631
$183$	0	0
$184$	1.45843e8	1.72592
$185$	−1.98359e8	−2.30330
$186$	0	0
$187$	4.74466e7	0.530591
$188$	2.46886e8	2.70984
$189$	0	0
$190$	−3.42963e8	−3.62752
$191$	−2.66378e7	−0.276619	−0.138309	−	0.990389i	$-0.544167\pi$
$191$	−2.66378e7	−0.276619	−0.138309	+	0.990389i	$0.544167\pi$
$192$	0	0
$193$	−1.69658e8	−1.69873	−0.849365	−	0.527807i	$-0.823015\pi$
$193$	−1.69658e8	−1.69873	−0.849365	+	0.527807i	$0.823015\pi$
$194$	2.99362e7	0.294368
$195$	0	0
$196$	4.56396e8	4.32957
$197$	−6.41433e7	−0.597750	−0.298875	−	0.954292i	$-0.596611\pi$
$197$	−6.41433e7	−0.597750	−0.298875	+	0.954292i	$0.596611\pi$
$198$	0	0
$199$	−1.14787e8	−1.03254	−0.516269	−	0.856427i	$-0.672679\pi$
$199$	−1.14787e8	−1.03254	−0.516269	+	0.856427i	$0.672679\pi$
$200$	−2.10033e8	−1.85645
$201$	0	0
$202$	−2.59614e7	−0.221615
$203$	1.74818e8	1.46673
$204$	0	0
$205$	1.64878e8	1.33667
$206$	2.08158e7	0.165905
$207$	0	0
$208$	−5.05090e7	−0.389177
$209$	−1.14083e8	−0.864389
$210$	0	0
$211$	6.79484e6	0.0497956	0.0248978	−	0.999690i	$-0.492074\pi$
$211$	6.79484e6	0.0497956	0.0248978	+	0.999690i	$0.492074\pi$
$212$	1.71534e8	1.23644
$213$	0	0
$214$	−4.50066e8	−3.13926
$215$	3.50805e8	2.40731
$216$	0	0
$217$	2.75009e8	1.82700
$218$	−1.98946e8	−1.30058
$219$	0	0
$220$	−2.72787e8	−1.72721
$221$	−1.88104e8	−1.17227
$222$	0	0
$223$	2.78892e8	1.68410	0.842052	−	0.539396i	$-0.181347\pi$
$223$	2.78892e8	1.68410	0.842052	+	0.539396i	$0.181347\pi$
$224$	−2.37217e8	−1.41019
$225$	0	0
$226$	3.41367e8	1.96717
$227$	−4.19942e7	−0.238286	−0.119143	−	0.992877i	$-0.538015\pi$
$227$	−4.19942e7	−0.238286	−0.119143	+	0.992877i	$0.538015\pi$
$228$	0	0
$229$	−1.50761e7	−0.0829591	−0.0414795	−	0.999139i	$-0.513207\pi$
$229$	−1.50761e7	−0.0829591	−0.0414795	+	0.999139i	$0.513207\pi$
$230$	−6.85707e8	−3.71613
$231$	0	0
$232$	1.82163e8	0.957748
$233$	−5.24867e7	−0.271834	−0.135917	−	0.990720i	$-0.543398\pi$
$233$	−5.24867e7	−0.271834	−0.135917	+	0.990720i	$0.543398\pi$
$234$	0	0
$235$	−4.92702e8	−2.47655
$236$	−4.56759e7	−0.226201
$237$	0	0
$238$	5.44985e8	2.62039
$239$	−1.82265e8	−0.863597	−0.431799	−	0.901970i	$-0.642121\pi$
$239$	−1.82265e8	−0.863597	−0.431799	+	0.901970i	$0.642121\pi$
$240$	0	0
$241$	−5.51242e7	−0.253678	−0.126839	−	0.991923i	$-0.540483\pi$
$241$	−5.51242e7	−0.253678	−0.126839	+	0.991923i	$0.540483\pi$
$242$	2.21815e8	1.00609
$243$	0	0
$244$	−4.71068e7	−0.207596
$245$	−9.10812e8	−3.95683
$246$	0	0
$247$	4.52288e8	1.90975
$248$	2.86563e8	1.19300
$249$	0	0
$250$	3.38444e8	1.36993
$251$	3.50809e8	1.40027	0.700137	−	0.714009i	$-0.253122\pi$
$251$	3.50809e8	1.40027	0.700137	+	0.714009i	$0.253122\pi$
$252$	0	0
$253$	−2.28093e8	−0.885505
$254$	−2.40736e8	−0.921772
$255$	0	0
$256$	−3.78416e8	−1.40971
$257$	3.34359e8	1.22871	0.614353	−	0.789032i	$-0.289417\pi$
$257$	3.34359e8	1.22871	0.614353	+	0.789032i	$0.289417\pi$
$258$	0	0
$259$	−7.57886e8	−2.71053
$260$	1.08148e9	3.81601
$261$	0	0
$262$	−1.92855e8	−0.662485
$263$	3.99920e8	1.35559	0.677795	−	0.735251i	$-0.262936\pi$
$263$	3.99920e8	1.35559	0.677795	+	0.735251i	$0.262936\pi$
$264$	0	0
$265$	−3.42324e8	−1.13000
$266$	−1.31039e9	−4.26889
$267$	0	0
$268$	3.29407e8	1.04535
$269$	−1.62396e7	−0.0508677	−0.0254338	−	0.999677i	$-0.508097\pi$
$269$	−1.62396e7	−0.0508677	−0.0254338	+	0.999677i	$0.508097\pi$
$270$	0	0
$271$	−4.27140e8	−1.30370	−0.651851	−	0.758347i	$-0.726007\pi$
$271$	−4.27140e8	−1.30370	−0.651851	+	0.758347i	$0.726007\pi$
$272$	7.91470e7	0.238475
$273$	0	0
$274$	−8.85419e8	−2.60029
$275$	3.28485e8	0.952470
$276$	0	0
$277$	−4.70787e8	−1.33090	−0.665449	−	0.746443i	$-0.731760\pi$
$277$	−4.70787e8	−1.33090	−0.665449	+	0.746443i	$0.731760\pi$
$278$	−1.07940e9	−3.01319
$279$	0	0
$280$	−1.32995e9	−3.62061
$281$	3.44673e8	0.926692	0.463346	−	0.886177i	$-0.346649\pi$
$281$	3.44673e8	0.926692	0.463346	+	0.886177i	$0.346649\pi$
$282$	0	0
$283$	3.05838e8	0.802120	0.401060	−	0.916052i	$-0.368642\pi$
$283$	3.05838e8	0.802120	0.401060	+	0.916052i	$0.368642\pi$
$284$	−7.56902e8	−1.96076
$285$	0	0
$286$	5.66789e8	1.43265
$287$	6.29965e8	1.57300
$288$	0	0
$289$	−1.15582e8	−0.281674
$290$	−8.56473e8	−2.06215
$291$	0	0
$292$	−8.75007e8	−2.05670
$293$	8.35017e7	0.193936	0.0969680	−	0.995287i	$-0.469086\pi$
$293$	8.35017e7	0.193936	0.0969680	+	0.995287i	$0.469086\pi$
$294$	0	0
$295$	9.11538e7	0.206727
$296$	−7.89728e8	−1.76993
$297$	0	0
$298$	1.76995e8	0.387440
$299$	9.04286e8	1.95640
$300$	0	0
$301$	1.34035e9	2.83293
$302$	2.89343e8	0.604489
$303$	0	0
$304$	−1.90305e8	−0.388502
$305$	9.40092e7	0.189723
$306$	0	0
$307$	−7.34193e8	−1.44819	−0.724096	−	0.689699i	$-0.757743\pi$
$307$	−7.34193e8	−1.44819	−0.724096	+	0.689699i	$0.757743\pi$
$308$	−1.04226e9	−2.03259
$309$	0	0
$310$	−1.34733e9	−2.56867
$311$	−2.34224e7	−0.0441540	−0.0220770	−	0.999756i	$-0.507028\pi$
$311$	−2.34224e7	−0.0441540	−0.0220770	+	0.999756i	$0.507028\pi$
$312$	0	0
$313$	4.22581e8	0.778941	0.389471	−	0.921039i	$-0.372658\pi$
$313$	4.22581e8	0.778941	0.389471	+	0.921039i	$0.372658\pi$
$314$	−6.78799e8	−1.23734
$315$	0	0
$316$	1.01277e9	1.80553
$317$	1.79803e7	0.0317023	0.0158511	−	0.999874i	$-0.494954\pi$
$317$	1.79803e7	0.0317023	0.0158511	+	0.999874i	$0.494954\pi$
$318$	0	0
$319$	−2.84897e8	−0.491383
$320$	1.42408e9	2.42945
$321$	0	0
$322$	−2.61994e9	−4.37317
$323$	−7.08729e8	−1.17023
$324$	0	0
$325$	−1.30229e9	−2.10435
$326$	−9.87695e8	−1.57892
$327$	0	0
$328$	6.56432e8	1.02714
$329$	−1.88251e9	−2.91442
$330$	0	0
$331$	−2.19639e8	−0.332899	−0.166449	−	0.986050i	$-0.553230\pi$
$331$	−2.19639e8	−0.332899	−0.166449	+	0.986050i	$0.553230\pi$
$332$	1.00514e9	1.50745
$333$	0	0
$334$	−1.37893e8	−0.202502
$335$	−6.57386e8	−0.955352
$336$	0	0
$337$	4.32909e7	0.0616158	0.0308079	−	0.999525i	$-0.490192\pi$
$337$	4.32909e7	0.0616158	0.0308079	+	0.999525i	$0.490192\pi$
$338$	−1.07247e9	−1.51070
$339$	0	0
$340$	−1.69466e9	−2.33833
$341$	−4.48176e8	−0.612080
$342$	0	0
$343$	−2.08346e9	−2.78777
$344$	1.39667e9	1.84986
$345$	0	0
$346$	1.47419e9	1.91332
$347$	−2.07119e8	−0.266114	−0.133057	−	0.991108i	$-0.542479\pi$
$347$	−2.07119e8	−0.266114	−0.133057	+	0.991108i	$0.542479\pi$
$348$	0	0
$349$	−1.35268e9	−1.70336	−0.851680	−	0.524062i	$-0.824416\pi$
$349$	−1.35268e9	−1.70336	−0.851680	+	0.524062i	$0.824416\pi$
$350$	3.77307e9	4.70389
$351$	0	0
$352$	3.86587e8	0.472442
$353$	9.24750e8	1.11896	0.559478	−	0.828845i	$-0.311002\pi$
$353$	9.24750e8	1.11896	0.559478	+	0.828845i	$0.311002\pi$
$354$	0	0
$355$	1.51052e9	1.79196
$356$	9.37560e8	1.10135
$357$	0	0
$358$	3.99486e8	0.460162
$359$	−5.95223e8	−0.678968	−0.339484	−	0.940612i	$-0.610252\pi$
$359$	−5.95223e8	−0.678968	−0.339484	+	0.940612i	$0.610252\pi$
$360$	0	0
$361$	8.10232e8	0.906430
$362$	−3.22421e8	−0.357226
$363$	0	0
$364$	4.13209e9	4.49071
$365$	1.74622e9	1.87964
$366$	0	0
$367$	5.60873e8	0.592289	0.296144	−	0.955143i	$-0.404299\pi$
$367$	5.60873e8	0.592289	0.296144	+	0.955143i	$0.404299\pi$
$368$	−3.80488e8	−0.397992
$369$	0	0
$370$	3.71306e9	3.81089
$371$	−1.30795e9	−1.32979
$372$	0	0
$373$	−6.85459e8	−0.683912	−0.341956	−	0.939716i	$-0.611089\pi$
$373$	−6.85459e8	−0.683912	−0.341956	+	0.939716i	$0.611089\pi$
$374$	−8.88150e8	−0.877881
$375$	0	0
$376$	−1.96160e9	−1.90306
$377$	1.12949e9	1.08564
$378$	0	0
$379$	−1.03369e9	−0.975337	−0.487668	−	0.873029i	$-0.662152\pi$
$379$	−1.03369e9	−0.975337	−0.487668	+	0.873029i	$0.662152\pi$
$380$	4.07472e9	3.80939
$381$	0	0
$382$	4.98632e8	0.457676
$383$	−2.09792e9	−1.90806	−0.954032	−	0.299705i	$-0.903112\pi$
$383$	−2.09792e9	−1.90806	−0.954032	+	0.299705i	$0.903112\pi$
$384$	0	0
$385$	2.08000e9	1.85760
$386$	3.17582e9	2.81061
$387$	0	0
$388$	−3.55670e8	−0.309126
$389$	6.60600e7	0.0569003	0.0284502	−	0.999595i	$-0.490943\pi$
$389$	6.60600e7	0.0569003	0.0284502	+	0.999595i	$0.490943\pi$
$390$	0	0
$391$	−1.41700e9	−1.19882
$392$	−3.62623e9	−3.04056
$393$	0	0
$394$	1.20069e9	0.988998
$395$	−2.02115e9	−1.65009
$396$	0	0
$397$	1.83981e9	1.47573	0.737863	−	0.674951i	$-0.235835\pi$
$397$	1.83981e9	1.47573	0.737863	+	0.674951i	$0.235835\pi$
$398$	2.14868e9	1.70837
$399$	0	0
$400$	5.47955e8	0.428090
$401$	−1.61549e9	−1.25112	−0.625560	−	0.780176i	$-0.715130\pi$
$401$	−1.61549e9	−1.25112	−0.625560	+	0.780176i	$0.715130\pi$
$402$	0	0
$403$	1.77681e9	1.35230
$404$	3.08446e8	0.232726
$405$	0	0
$406$	−3.27240e9	−2.42675
$407$	1.23511e9	0.908083
$408$	0	0
$409$	−1.07871e9	−0.779605	−0.389802	−	0.920899i	$-0.627457\pi$
$409$	−1.07871e9	−0.779605	−0.389802	+	0.920899i	$0.627457\pi$
$410$	−3.08634e9	−2.21157
$411$	0	0
$412$	−2.47311e8	−0.174222
$413$	3.48279e8	0.243278
$414$	0	0
$415$	−2.00591e9	−1.37767
$416$	−1.53264e9	−1.04379
$417$	0	0
$418$	2.13551e9	1.43016
$419$	8.10783e8	0.538463	0.269231	−	0.963076i	$-0.413230\pi$
$419$	8.10783e8	0.538463	0.269231	+	0.963076i	$0.413230\pi$
$420$	0	0
$421$	−1.13878e9	−0.743792	−0.371896	−	0.928274i	$-0.621292\pi$
$421$	−1.13878e9	−0.743792	−0.371896	+	0.928274i	$0.621292\pi$
$422$	−1.27192e8	−0.0823886
$423$	0	0
$424$	−1.36290e9	−0.868327
$425$	2.04068e9	1.28948
$426$	0	0
$427$	3.59189e8	0.223268
$428$	5.34720e9	3.29665
$429$	0	0
$430$	−6.56670e9	−3.98297
$431$	2.09869e9	1.26263	0.631317	−	0.775525i	$-0.282515\pi$
$431$	2.09869e9	1.26263	0.631317	+	0.775525i	$0.282515\pi$
$432$	0	0
$433$	1.85715e9	1.09936	0.549679	−	0.835376i	$-0.314750\pi$
$433$	1.85715e9	1.09936	0.549679	+	0.835376i	$0.314750\pi$
$434$	−5.14787e9	−3.02283
$435$	0	0
$436$	2.36366e9	1.36579
$437$	3.40712e9	1.95300
$438$	0	0
$439$	6.58145e8	0.371275	0.185638	−	0.982618i	$-0.440565\pi$
$439$	6.58145e8	0.371275	0.185638	+	0.982618i	$0.440565\pi$
$440$	2.16739e9	1.21298
$441$	0	0
$442$	3.52111e9	1.93955
$443$	2.56332e8	0.140084	0.0700422	−	0.997544i	$-0.477687\pi$
$443$	2.56332e8	0.140084	0.0700422	+	0.997544i	$0.477687\pi$
$444$	0	0
$445$	−1.87105e9	−1.00653
$446$	−5.22056e9	−2.78641
$447$	0	0
$448$	5.44110e9	2.85900
$449$	−5.70165e8	−0.297261	−0.148631	−	0.988893i	$-0.547487\pi$
$449$	−5.70165e8	−0.297261	−0.148631	+	0.988893i	$0.547487\pi$
$450$	0	0
$451$	−1.02664e9	−0.526987
$452$	−4.05575e9	−2.06579
$453$	0	0
$454$	7.86086e8	0.394253
$455$	−8.24626e9	−4.10409
$456$	0	0
$457$	−1.42553e8	−0.0698669	−0.0349334	−	0.999390i	$-0.511122\pi$
$457$	−1.42553e8	−0.0698669	−0.0349334	+	0.999390i	$0.511122\pi$
$458$	2.82208e8	0.137259
$459$	0	0
$460$	8.14684e9	3.90245
$461$	−2.44186e9	−1.16083	−0.580414	−	0.814321i	$-0.697109\pi$
$461$	−2.44186e9	−1.16083	−0.580414	+	0.814321i	$0.697109\pi$
$462$	0	0
$463$	−2.57981e9	−1.20796	−0.603982	−	0.796998i	$-0.706420\pi$
$463$	−2.57981e9	−1.20796	−0.603982	+	0.796998i	$0.706420\pi$
$464$	−4.75244e8	−0.220853
$465$	0	0
$466$	9.82495e8	0.449759
$467$	1.03284e9	0.469272	0.234636	−	0.972083i	$-0.424610\pi$
$467$	1.03284e9	0.469272	0.234636	+	0.972083i	$0.424610\pi$
$468$	0	0
$469$	−2.51173e9	−1.12426
$470$	9.22285e9	4.09753
$471$	0	0
$472$	3.62912e8	0.158856
$473$	−2.18434e9	−0.949089
$474$	0	0
$475$	−4.90671e9	−2.10069
$476$	−6.47493e9	−2.75176
$477$	0	0
$478$	3.41181e9	1.42885
$479$	2.54815e9	1.05938	0.529688	−	0.848193i	$-0.322309\pi$
$479$	2.54815e9	1.05938	0.529688	+	0.848193i	$0.322309\pi$
$480$	0	0
$481$	−4.89665e9	−2.00628
$482$	1.03187e9	0.419719
$483$	0	0
$484$	−2.63536e9	−1.05653
$485$	7.09797e8	0.282513
$486$	0	0
$487$	−1.38050e9	−0.541608	−0.270804	−	0.962635i	$-0.587289\pi$
$487$	−1.38050e9	−0.541608	−0.270804	+	0.962635i	$0.587289\pi$
$488$	3.74280e8	0.145790
$489$	0	0
$490$	1.70494e10	6.54671
$491$	−3.40284e9	−1.29735	−0.648674	−	0.761067i	$-0.724676\pi$
$491$	−3.40284e9	−1.29735	−0.648674	+	0.761067i	$0.724676\pi$
$492$	0	0
$493$	−1.76989e9	−0.665246
$494$	−8.46634e9	−3.15974
$495$	0	0
$496$	−7.47614e8	−0.275101
$497$	5.77138e9	2.10879
$498$	0	0
$499$	−2.71570e9	−0.978430	−0.489215	−	0.872163i	$-0.662717\pi$
$499$	−2.71570e9	−0.978430	−0.489215	+	0.872163i	$0.662717\pi$
$500$	−4.02103e9	−1.43861
$501$	0	0
$502$	−6.56677e9	−2.31680
$503$	1.12999e9	0.395899	0.197950	−	0.980212i	$-0.436572\pi$
$503$	1.12999e9	0.395899	0.197950	+	0.980212i	$0.436572\pi$
$504$	0	0
$505$	−6.15554e8	−0.212690
$506$	4.26966e9	1.46510
$507$	0	0
$508$	2.86017e9	0.967986
$509$	−2.58498e9	−0.868849	−0.434425	−	0.900708i	$-0.643048\pi$
$509$	−2.58498e9	−0.868849	−0.434425	+	0.900708i	$0.643048\pi$
$510$	0	0
$511$	6.67193e9	2.21197
$512$	1.68757e9	0.555670
$513$	0	0
$514$	−6.25885e9	−2.03294
$515$	4.93550e8	0.159223
$516$	0	0
$517$	3.06788e9	0.976387
$518$	1.41868e10	4.48467
$519$	0	0
$520$	−8.59272e9	−2.67990
$521$	1.68355e9	0.521546	0.260773	−	0.965400i	$-0.416023\pi$
$521$	1.68355e9	0.521546	0.260773	+	0.965400i	$0.416023\pi$
$522$	0	0
$523$	−2.47225e9	−0.755676	−0.377838	−	0.925872i	$-0.623332\pi$
$523$	−2.47225e9	−0.755676	−0.377838	+	0.925872i	$0.623332\pi$
$524$	2.29129e9	0.695699
$525$	0	0
$526$	−7.48608e9	−2.24287
$527$	−2.78424e9	−0.828648
$528$	0	0
$529$	3.40723e9	1.00071
$530$	6.40794e9	1.86962
$531$	0	0
$532$	1.55687e10	4.48291
$533$	4.07016e9	1.16430
$534$	0	0
$535$	−1.06712e10	−3.01284
$536$	−2.61726e9	−0.734125
$537$	0	0
$538$	3.03988e8	0.0841624
$539$	5.67131e9	1.55999
$540$	0	0
$541$	−3.60201e9	−0.978034	−0.489017	−	0.872274i	$-0.662644\pi$
$541$	−3.60201e9	−0.978034	−0.489017	+	0.872274i	$0.662644\pi$
$542$	7.99561e9	2.15702
$543$	0	0
$544$	2.40163e9	0.639602
$545$	−4.71707e9	−1.24820
$546$	0	0
$547$	1.24077e9	0.324141	0.162071	−	0.986779i	$-0.448183\pi$
$547$	1.24077e9	0.324141	0.162071	+	0.986779i	$0.448183\pi$
$548$	1.05196e10	2.73066
$549$	0	0
$550$	−6.14889e9	−1.57590
$551$	4.25561e9	1.08376
$552$	0	0
$553$	−7.72237e9	−1.94184
$554$	8.81262e9	2.20202
$555$	0	0
$556$	1.28243e10	3.16426
$557$	−1.77982e9	−0.436399	−0.218200	−	0.975904i	$-0.570018\pi$
$557$	−1.77982e9	−0.436399	−0.218200	+	0.975904i	$0.570018\pi$
$558$	0	0
$559$	8.65993e9	2.09688
$560$	3.46970e9	0.834900
$561$	0	0
$562$	−6.45192e9	−1.53325
$563$	6.60782e9	1.56056	0.780278	−	0.625433i	$-0.215078\pi$
$563$	6.60782e9	1.56056	0.780278	+	0.625433i	$0.215078\pi$
$564$	0	0
$565$	8.09391e9	1.88794
$566$	−5.72496e9	−1.32714
$567$	0	0
$568$	6.01386e9	1.37700
$569$	−4.59260e9	−1.04512	−0.522560	−	0.852603i	$-0.675023\pi$
$569$	−4.59260e9	−1.04512	−0.522560	+	0.852603i	$0.675023\pi$
$570$	0	0
$571$	3.76881e9	0.847183	0.423592	−	0.905853i	$-0.360769\pi$
$571$	3.76881e9	0.847183	0.423592	+	0.905853i	$0.360769\pi$
$572$	−6.73398e9	−1.50448
$573$	0	0
$574$	−1.17923e10	−2.60259
$575$	−9.81029e9	−2.15201
$576$	0	0
$577$	3.58209e9	0.776284	0.388142	−	0.921600i	$-0.373117\pi$
$577$	3.58209e9	0.776284	0.388142	+	0.921600i	$0.373117\pi$
$578$	2.16357e9	0.466040
$579$	0	0
$580$	1.01757e10	2.16554
$581$	−7.66417e9	−1.62125
$582$	0	0
$583$	2.13153e9	0.445504
$584$	6.95225e9	1.44438
$585$	0	0
$586$	−1.56306e9	−0.320874
$587$	−3.85835e8	−0.0787350	−0.0393675	−	0.999225i	$-0.512534\pi$
$587$	−3.85835e8	−0.0787350	−0.0393675	+	0.999225i	$0.512534\pi$
$588$	0	0
$589$	6.69458e9	1.34996
$590$	−1.70630e9	−0.342037
$591$	0	0
$592$	2.06032e9	0.408140
$593$	1.84467e9	0.363267	0.181634	−	0.983366i	$-0.441861\pi$
$593$	1.84467e9	0.363267	0.181634	+	0.983366i	$0.441861\pi$
$594$	0	0
$595$	1.29218e10	2.51485
$596$	−2.10287e9	−0.406864
$597$	0	0
$598$	−1.69273e10	−3.23693
$599$	−4.66546e9	−0.886953	−0.443476	−	0.896286i	$-0.646255\pi$
$599$	−4.66546e9	−0.886953	−0.443476	+	0.896286i	$0.646255\pi$
$600$	0	0
$601$	2.24604e9	0.422043	0.211021	−	0.977481i	$-0.432321\pi$
$601$	2.24604e9	0.422043	0.211021	+	0.977481i	$0.432321\pi$
$602$	−2.50900e10	−4.68719
$603$	0	0
$604$	−3.43766e9	−0.634796
$605$	5.25930e9	0.965570
$606$	0	0
$607$	9.43363e9	1.71206	0.856029	−	0.516928i	$-0.172925\pi$
$607$	9.43363e9	1.71206	0.856029	+	0.516928i	$0.172925\pi$
$608$	−5.77460e9	−1.04198
$609$	0	0
$610$	−1.75975e9	−0.313904
$611$	−1.21628e10	−2.15719
$612$	0	0
$613$	2.56081e9	0.449020	0.224510	−	0.974472i	$-0.427922\pi$
$613$	2.56081e9	0.449020	0.224510	+	0.974472i	$0.427922\pi$
$614$	1.37433e10	2.39608
$615$	0	0
$616$	8.28114e9	1.42744
$617$	−2.42876e9	−0.416281	−0.208141	−	0.978099i	$-0.566741\pi$
$617$	−2.42876e9	−0.416281	−0.208141	+	0.978099i	$0.566741\pi$
$618$	0	0
$619$	6.53273e9	1.10708	0.553538	−	0.832824i	$-0.313277\pi$
$619$	6.53273e9	1.10708	0.553538	+	0.832824i	$0.313277\pi$
$620$	1.60076e10	2.69746
$621$	0	0
$622$	4.38443e8	0.0730544
$623$	−7.14890e9	−1.18449
$624$	0	0
$625$	−1.26146e9	−0.206678
$626$	−7.91026e9	−1.28879
$627$	0	0
$628$	8.06476e9	1.29937
$629$	7.67299e9	1.22938
$630$	0	0
$631$	−2.21286e9	−0.350631	−0.175315	−	0.984512i	$-0.556095\pi$
$631$	−2.21286e9	−0.350631	−0.175315	+	0.984512i	$0.556095\pi$
$632$	−8.04681e9	−1.26799
$633$	0	0
$634$	−3.36573e8	−0.0524525
$635$	−5.70794e9	−0.884649
$636$	0	0
$637$	−2.24842e10	−3.44658
$638$	5.33296e9	0.813011
$639$	0	0
$640$	−1.87102e10	−2.82130
$641$	−5.20588e9	−0.780713	−0.390356	−	0.920664i	$-0.627648\pi$
$641$	−5.20588e9	−0.780713	−0.390356	+	0.920664i	$0.627648\pi$
$642$	0	0
$643$	−1.18888e10	−1.76359	−0.881796	−	0.471631i	$-0.843665\pi$
$643$	−1.18888e10	−1.76359	−0.881796	+	0.471631i	$0.843665\pi$
$644$	3.11274e10	4.59242
$645$	0	0
$646$	1.32666e10	1.93619
$647$	6.02914e9	0.875166	0.437583	−	0.899178i	$-0.355835\pi$
$647$	6.02914e9	0.875166	0.437583	+	0.899178i	$0.355835\pi$
$648$	0	0
$649$	−5.67583e8	−0.0815029
$650$	2.43776e10	3.48172
$651$	0	0
$652$	1.17347e10	1.65809
$653$	−2.77068e8	−0.0389395	−0.0194697	−	0.999810i	$-0.506198\pi$
$653$	−2.77068e8	−0.0389395	−0.0194697	+	0.999810i	$0.506198\pi$
$654$	0	0
$655$	−4.57265e9	−0.635804
$656$	−1.71256e9	−0.236856
$657$	0	0
$658$	3.52386e10	4.82200
$659$	1.19887e10	1.63182	0.815909	−	0.578181i	$-0.196237\pi$
$659$	1.19887e10	1.63182	0.815909	+	0.578181i	$0.196237\pi$
$660$	0	0
$661$	3.39523e9	0.457261	0.228631	−	0.973513i	$-0.426575\pi$
$661$	3.39523e9	0.457261	0.228631	+	0.973513i	$0.426575\pi$
$662$	4.11142e9	0.550793
$663$	0	0
$664$	−7.98617e9	−1.05865
$665$	−3.10698e10	−4.09697
$666$	0	0
$667$	8.50851e9	1.11023
$668$	1.63829e9	0.212654
$669$	0	0
$670$	1.23056e10	1.58066
$671$	−5.85363e8	−0.0747991
$672$	0	0
$673$	9.44306e9	1.19415	0.597077	−	0.802184i	$-0.296329\pi$
$673$	9.44306e9	1.19415	0.597077	+	0.802184i	$0.296329\pi$
$674$	−8.10359e8	−0.101945
$675$	0	0
$676$	1.27420e10	1.58644
$677$	−2.31127e9	−0.286279	−0.143140	−	0.989703i	$-0.545720\pi$
$677$	−2.31127e9	−0.286279	−0.143140	+	0.989703i	$0.545720\pi$
$678$	0	0
$679$	2.71199e9	0.332463
$680$	1.34647e10	1.64216
$681$	0	0
$682$	8.38938e9	1.01271
$683$	1.31138e10	1.57491	0.787454	−	0.616374i	$-0.211399\pi$
$683$	1.31138e10	1.57491	0.787454	+	0.616374i	$0.211399\pi$
$684$	0	0
$685$	−2.09936e10	−2.49557
$686$	3.90002e10	4.61246
$687$	0	0
$688$	−3.64376e9	−0.426570
$689$	−8.45056e9	−0.984279
$690$	0	0
$691$	8.33408e9	0.960913	0.480457	−	0.877018i	$-0.340471\pi$
$691$	8.33408e9	0.960913	0.480457	+	0.877018i	$0.340471\pi$
$692$	−1.75148e10	−2.00925
$693$	0	0
$694$	3.87705e9	0.440295
$695$	−2.55930e10	−2.89184
$696$	0	0
$697$	−6.37789e9	−0.713448
$698$	2.53207e10	2.81827
$699$	0	0
$700$	−4.48276e10	−4.93972
$701$	2.09612e9	0.229829	0.114914	−	0.993375i	$-0.463341\pi$
$701$	2.09612e9	0.229829	0.114914	+	0.993375i	$0.463341\pi$
$702$	0	0
$703$	−1.84493e10	−2.00280
$704$	−8.86724e9	−0.957821
$705$	0	0
$706$	−1.73103e10	−1.85135
$707$	−2.35190e9	−0.250294
$708$	0	0
$709$	4.17621e8	0.0440069	0.0220035	−	0.999758i	$-0.492996\pi$
$709$	4.17621e8	0.0440069	0.0220035	+	0.999758i	$0.492996\pi$
$710$	−2.82753e10	−2.96486
$711$	0	0
$712$	−7.44925e9	−0.773451
$713$	1.33849e10	1.38293
$714$	0	0
$715$	1.34387e10	1.37495
$716$	−4.74626e9	−0.483232
$717$	0	0
$718$	1.11419e10	1.12338
$719$	6.71535e9	0.673779	0.336890	−	0.941544i	$-0.390625\pi$
$719$	6.71535e9	0.673779	0.336890	+	0.941544i	$0.390625\pi$
$720$	0	0
$721$	1.88575e9	0.187375
$722$	−1.51667e10	−1.49972
$723$	0	0
$724$	3.83066e9	0.375136
$725$	−1.22534e10	−1.19419
$726$	0	0
$727$	−8.79100e9	−0.848531	−0.424266	−	0.905538i	$-0.639468\pi$
$727$	−8.79100e9	−0.848531	−0.424266	+	0.905538i	$0.639468\pi$
$728$	−3.28309e10	−3.15372
$729$	0	0
$730$	−3.26874e10	−3.10992
$731$	−1.35700e10	−1.28490
$732$	0	0
$733$	−1.87568e10	−1.75912	−0.879560	−	0.475787i	$-0.842163\pi$
$733$	−1.87568e10	−1.75912	−0.879560	+	0.475787i	$0.842163\pi$
$734$	−1.04989e10	−0.979963
$735$	0	0
$736$	−1.15455e10	−1.06743
$737$	4.09331e9	0.376651
$738$	0	0
$739$	−3.83197e9	−0.349274	−0.174637	−	0.984633i	$-0.555875\pi$
$739$	−3.83197e9	−0.349274	−0.174637	+	0.984633i	$0.555875\pi$
$740$	−4.41146e10	−4.00195
$741$	0	0
$742$	2.44834e10	2.20018
$743$	1.74075e9	0.155695	0.0778475	−	0.996965i	$-0.475195\pi$
$743$	1.74075e9	0.155695	0.0778475	+	0.996965i	$0.475195\pi$
$744$	0	0
$745$	4.19661e9	0.371836
$746$	1.28311e10	1.13156
$747$	0	0
$748$	1.05521e10	0.921895
$749$	−4.07724e10	−3.54552
$750$	0	0
$751$	1.87554e10	1.61580	0.807900	−	0.589320i	$-0.200604\pi$
$751$	1.87554e10	1.61580	0.807900	+	0.589320i	$0.200604\pi$
$752$	5.11762e9	0.438839
$753$	0	0
$754$	−2.11428e10	−1.79623
$755$	6.86042e9	0.580145
$756$	0	0
$757$	−1.48636e10	−1.24534	−0.622671	−	0.782483i	$-0.713953\pi$
$757$	−1.48636e10	−1.24534	−0.622671	+	0.782483i	$0.713953\pi$
$758$	1.93496e10	1.61373
$759$	0	0
$760$	−3.23751e10	−2.67525
$761$	−2.55852e9	−0.210446	−0.105223	−	0.994449i	$-0.533556\pi$
$761$	−2.55852e9	−0.210446	−0.105223	+	0.994449i	$0.533556\pi$
$762$	0	0
$763$	−1.80229e10	−1.46889
$764$	−5.92421e9	−0.480622
$765$	0	0
$766$	3.92708e10	3.15696
$767$	2.25021e9	0.180069
$768$	0	0
$769$	1.98268e10	1.57221	0.786104	−	0.618094i	$-0.212095\pi$
$769$	1.98268e10	1.57221	0.786104	+	0.618094i	$0.212095\pi$
$770$	−3.89354e10	−3.07346
$771$	0	0
$772$	−3.77317e10	−2.95152
$773$	1.29417e10	1.00777	0.503886	−	0.863770i	$-0.331903\pi$
$773$	1.29417e10	1.00777	0.503886	+	0.863770i	$0.331903\pi$
$774$	0	0
$775$	−1.92760e10	−1.48752
$776$	2.82593e9	0.217092
$777$	0	0
$778$	−1.23657e9	−0.0941436
$779$	1.53353e10	1.16228
$780$	0	0
$781$	−9.40549e9	−0.706485
$782$	2.65248e10	1.98348
$783$	0	0
$784$	9.46046e9	0.701142
$785$	−1.60945e10	−1.18750
$786$	0	0
$787$	9.60328e9	0.702276	0.351138	−	0.936324i	$-0.385795\pi$
$787$	9.60328e9	0.702276	0.351138	+	0.936324i	$0.385795\pi$
$788$	−1.42654e10	−1.03858
$789$	0	0
$790$	3.78337e10	2.73013
$791$	3.09251e10	2.22174
$792$	0	0
$793$	2.32070e9	0.165258
$794$	−3.44392e10	−2.44164
$795$	0	0
$796$	−2.55284e10	−1.79402
$797$	9.10764e9	0.637238	0.318619	−	0.947883i	$-0.396781\pi$
$797$	9.10764e9	0.637238	0.318619	+	0.947883i	$0.396781\pi$
$798$	0	0
$799$	1.90589e10	1.32185
$800$	1.66271e10	1.14816
$801$	0	0
$802$	3.02403e10	2.07002
$803$	−1.08731e10	−0.741053
$804$	0	0
$805$	−6.21197e10	−4.19705
$806$	−3.32601e10	−2.23744
$807$	0	0
$808$	−2.45071e9	−0.163438
$809$	1.78494e10	1.18524	0.592618	−	0.805484i	$-0.298094\pi$
$809$	1.78494e10	1.18524	0.592618	+	0.805484i	$0.298094\pi$
$810$	0	0
$811$	6.82320e9	0.449174	0.224587	−	0.974454i	$-0.427897\pi$
$811$	6.82320e9	0.449174	0.224587	+	0.974454i	$0.427897\pi$
$812$	3.88792e10	2.54842
$813$	0	0
$814$	−2.31200e10	−1.50246
$815$	−2.34186e10	−1.51534
$816$	0	0
$817$	3.26284e10	2.09324
$818$	2.01924e10	1.28988
$819$	0	0
$820$	3.66686e10	2.32245
$821$	−7.07763e9	−0.446362	−0.223181	−	0.974777i	$-0.571644\pi$
$821$	−7.07763e9	−0.446362	−0.223181	+	0.974777i	$0.571644\pi$
$822$	0	0
$823$	−1.02079e10	−0.638317	−0.319159	−	0.947701i	$-0.603400\pi$
$823$	−1.02079e10	−0.638317	−0.319159	+	0.947701i	$0.603400\pi$
$824$	1.96498e9	0.122352
$825$	0	0
$826$	−6.51941e9	−0.402512
$827$	−2.59808e9	−0.159729	−0.0798644	−	0.996806i	$-0.525449\pi$
$827$	−2.59808e9	−0.159729	−0.0798644	+	0.996806i	$0.525449\pi$
$828$	0	0
$829$	2.93686e9	0.179037	0.0895184	−	0.995985i	$-0.471467\pi$
$829$	2.93686e9	0.179037	0.0895184	+	0.995985i	$0.471467\pi$
$830$	3.75486e10	2.27940
$831$	0	0
$832$	3.51546e10	2.11617
$833$	3.52324e10	2.11195
$834$	0	0
$835$	−3.26948e9	−0.194346
$836$	−2.53719e10	−1.50187
$837$	0	0
$838$	−1.51770e10	−0.890905
$839$	−1.16450e10	−0.680728	−0.340364	−	0.940294i	$-0.610550\pi$
$839$	−1.16450e10	−0.680728	−0.340364	+	0.940294i	$0.610550\pi$
$840$	0	0
$841$	−6.62244e9	−0.383912
$842$	2.13167e10	1.23063
$843$	0	0
$844$	1.51116e9	0.0865192
$845$	−2.54287e10	−1.44986
$846$	0	0
$847$	2.00947e10	1.13629
$848$	3.55567e9	0.200233
$849$	0	0
$850$	−3.81993e10	−2.13348
$851$	−3.68869e10	−2.05172
$852$	0	0
$853$	1.63671e10	0.902922	0.451461	−	0.892291i	$-0.350903\pi$
$853$	1.63671e10	0.902922	0.451461	+	0.892291i	$0.350903\pi$
$854$	−6.72364e9	−0.369404
$855$	0	0
$856$	−4.24854e10	−2.31517
$857$	1.66058e10	0.901210	0.450605	−	0.892724i	$-0.351208\pi$
$857$	1.66058e10	0.901210	0.450605	+	0.892724i	$0.351208\pi$
$858$	0	0
$859$	−1.88831e10	−1.01647	−0.508237	−	0.861217i	$-0.669703\pi$
$859$	−1.88831e10	−1.01647	−0.508237	+	0.861217i	$0.669703\pi$
$860$	7.80185e10	4.18266
$861$	0	0
$862$	−3.92852e10	−2.08907
$863$	−2.09759e10	−1.11092	−0.555461	−	0.831543i	$-0.687458\pi$
$863$	−2.09759e10	−1.11092	−0.555461	+	0.831543i	$0.687458\pi$
$864$	0	0
$865$	3.49536e10	1.83627
$866$	−3.47639e10	−1.81893
$867$	0	0
$868$	6.11615e10	3.17438
$869$	1.25850e10	0.650554
$870$	0	0
$871$	−1.62281e10	−0.832156
$872$	−1.87801e10	−0.959161
$873$	0	0
$874$	−6.37776e10	−3.23131
$875$	3.06604e10	1.54721
$876$	0	0
$877$	3.68896e10	1.84674	0.923370	−	0.383911i	$-0.125423\pi$
$877$	3.68896e10	1.84674	0.923370	+	0.383911i	$0.125423\pi$
$878$	−1.23198e10	−0.614288
$879$	0	0
$880$	−5.65450e9	−0.279708
$881$	3.57144e10	1.75966	0.879829	−	0.475291i	$-0.157657\pi$
$881$	3.57144e10	1.75966	0.879829	+	0.475291i	$0.157657\pi$
$882$	0	0
$883$	−3.90952e9	−0.191100	−0.0955501	−	0.995425i	$-0.530461\pi$
$883$	−3.90952e9	−0.191100	−0.0955501	+	0.995425i	$0.530461\pi$
$884$	−4.18341e10	−2.03679
$885$	0	0
$886$	−4.79826e9	−0.231775
$887$	1.25223e10	0.602494	0.301247	−	0.953546i	$-0.402597\pi$
$887$	1.25223e10	0.602494	0.301247	+	0.953546i	$0.402597\pi$
$888$	0	0
$889$	−2.18088e10	−1.04106
$890$	3.50241e10	1.66534
$891$	0	0
$892$	6.20251e10	2.92611
$893$	−4.58262e10	−2.15344
$894$	0	0
$895$	9.47193e9	0.441630
$896$	−7.14878e10	−3.32012
$897$	0	0
$898$	1.06729e10	0.491829
$899$	1.67182e10	0.767416
$900$	0	0
$901$	1.32419e10	0.603134
$902$	1.92176e10	0.871919
$903$	0	0
$904$	3.22244e10	1.45076
$905$	−7.64470e9	−0.342839
$906$	0	0
$907$	2.27291e10	1.01148	0.505739	−	0.862687i	$-0.331220\pi$
$907$	2.27291e10	1.01148	0.505739	+	0.862687i	$0.331220\pi$
$908$	−9.33944e9	−0.414019
$909$	0	0
$910$	1.54361e11	6.79036
$911$	2.77093e10	1.21426	0.607129	−	0.794603i	$-0.292321\pi$
$911$	2.77093e10	1.21426	0.607129	+	0.794603i	$0.292321\pi$
$912$	0	0
$913$	1.24901e10	0.543150
$914$	2.66845e9	0.115597
$915$	0	0
$916$	−3.35289e9	−0.144140
$917$	−1.74711e10	−0.748218
$918$	0	0
$919$	−1.24377e10	−0.528612	−0.264306	−	0.964439i	$-0.585143\pi$
$919$	−1.24377e10	−0.528612	−0.264306	+	0.964439i	$0.585143\pi$
$920$	−6.47296e10	−2.74060
$921$	0	0
$922$	4.57091e10	1.92063
$923$	3.72885e10	1.56088
$924$	0	0
$925$	5.31221e10	2.20688
$926$	4.82913e10	1.99862
$927$	0	0
$928$	−1.44208e10	−0.592339
$929$	3.14739e10	1.28794	0.643970	−	0.765051i	$-0.277286\pi$
$929$	3.14739e10	1.28794	0.643970	+	0.765051i	$0.277286\pi$
$930$	0	0
$931$	−8.47146e10	−3.44060
$932$	−1.16730e10	−0.472308
$933$	0	0
$934$	−1.93337e10	−0.776428
$935$	−2.10583e10	−0.842526
$936$	0	0
$937$	−3.85637e10	−1.53140	−0.765702	−	0.643195i	$-0.777608\pi$
$937$	−3.85637e10	−1.53140	−0.765702	+	0.643195i	$0.777608\pi$
$938$	4.70169e10	1.86013
$939$	0	0
$940$	−1.09576e11	−4.30297
$941$	−2.15748e10	−0.844078	−0.422039	−	0.906578i	$-0.638686\pi$
$941$	−2.15748e10	−0.844078	−0.422039	+	0.906578i	$0.638686\pi$
$942$	0	0
$943$	3.06608e10	1.19067
$944$	−9.46800e8	−0.0366316
$945$	0	0
$946$	4.08886e10	1.57030
$947$	2.58130e10	0.987675	0.493838	−	0.869554i	$-0.335594\pi$
$947$	2.58130e10	0.987675	0.493838	+	0.869554i	$0.335594\pi$
$948$	0	0
$949$	4.31069e10	1.63725
$950$	9.18484e10	3.47567
$951$	0	0
$952$	5.14457e10	1.93250
$953$	−3.92406e10	−1.46862	−0.734311	−	0.678813i	$-0.762495\pi$
$953$	−3.92406e10	−1.46862	−0.734311	+	0.678813i	$0.762495\pi$
$954$	0	0
$955$	1.18227e10	0.439244
$956$	−4.05355e10	−1.50049
$957$	0	0
$958$	−4.76986e10	−1.75278
$959$	−8.02121e10	−2.93680
$960$	0	0
$961$	−1.21292e9	−0.0440859
$962$	9.16601e10	3.31946
$963$	0	0
$964$	−1.22595e10	−0.440762
$965$	7.52997e10	2.69741
$966$	0	0
$967$	−1.78901e9	−0.0636240	−0.0318120	−	0.999494i	$-0.510128\pi$
$967$	−1.78901e9	−0.0636240	−0.0318120	+	0.999494i	$0.510128\pi$
$968$	2.09389e10	0.741977
$969$	0	0
$970$	−1.32866e10	−0.467427
$971$	2.44481e10	0.856993	0.428497	−	0.903543i	$-0.359043\pi$
$971$	2.44481e10	0.856993	0.428497	+	0.903543i	$0.359043\pi$
$972$	0	0
$973$	−9.77854e10	−3.40313
$974$	2.58415e10	0.896109
$975$	0	0
$976$	−9.76459e8	−0.0336186
$977$	−3.42307e10	−1.17432	−0.587158	−	0.809472i	$-0.699753\pi$
$977$	−3.42307e10	−1.17432	−0.587158	+	0.809472i	$0.699753\pi$
$978$	0	0
$979$	1.16504e10	0.396827
$980$	−2.02563e11	−6.87494
$981$	0	0
$982$	6.36975e10	2.14651
$983$	4.53628e10	1.52322	0.761610	−	0.648036i	$-0.224409\pi$
$983$	4.53628e10	1.52322	0.761610	+	0.648036i	$0.224409\pi$
$984$	0	0
$985$	2.84688e10	0.949167
$986$	3.31304e10	1.10067
$987$	0	0
$988$	1.00588e11	3.31816
$989$	6.52359e10	2.14437
$990$	0	0
$991$	2.84050e10	0.927123	0.463561	−	0.886065i	$-0.346571\pi$
$991$	2.84050e10	0.927123	0.463561	+	0.886065i	$0.346571\pi$
$992$	−2.26855e10	−0.737834
$993$	0	0
$994$	−1.08034e11	−3.48906
$995$	5.09460e10	1.63957
$996$	0	0
$997$	−3.63738e10	−1.16240	−0.581201	−	0.813760i	$-0.697417\pi$
$997$	−3.63738e10	−1.16240	−0.581201	+	0.813760i	$0.697417\pi$
$998$	5.08350e10	1.61885
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.b.1.2		16
3.2	odd	2		177.8.a.a.1.15	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.a.1.15	✓	16	3.2	odd	2
531.8.a.b.1.2		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)

\(f(q)\)	\(=\)	\(q-18.7189 q^{2} +222.398 q^{4} -443.832 q^{5} -1695.79 q^{7} -1767.03 q^{8} +O(q^{10})\)	\(q-18.7189 q^{2} +222.398 q^{4} -443.832 q^{5} -1695.79 q^{7} -1767.03 q^{8} +8308.06 q^{10} +2763.59 q^{11} -10956.4 q^{13} +31743.3 q^{14} +4610.01 q^{16} +17168.5 q^{17} -41280.8 q^{19} -98707.5 q^{20} -51731.4 q^{22} -82535.2 q^{23} +118862. q^{25} +205092. q^{26} -377140. q^{28} -103089. q^{29} -162172. q^{31} +139886. q^{32} -321376. q^{34} +752645. q^{35} +446923. q^{37} +772732. q^{38} +784266. q^{40} -371488. q^{41} -790401. q^{43} +614617. q^{44} +1.54497e6 q^{46} +1.11011e6 q^{47} +2.05215e6 q^{49} -2.22497e6 q^{50} -2.43668e6 q^{52} +771292. q^{53} -1.22657e6 q^{55} +2.99652e6 q^{56} +1.92972e6 q^{58} -205379. q^{59} -211813. q^{61} +3.03568e6 q^{62} -3.20860e6 q^{64} +4.86279e6 q^{65} +1.48116e6 q^{67} +3.81824e6 q^{68} -1.40887e7 q^{70} -3.40336e6 q^{71} -3.93442e6 q^{73} -8.36592e6 q^{74} -9.18078e6 q^{76} -4.68646e6 q^{77} +4.55385e6 q^{79} -2.04607e6 q^{80} +6.95386e6 q^{82} +4.51953e6 q^{83} -7.61992e6 q^{85} +1.47955e7 q^{86} -4.88336e6 q^{88} +4.21568e6 q^{89} +1.85797e7 q^{91} -1.83557e7 q^{92} -2.07800e7 q^{94} +1.83217e7 q^{95} -1.59925e6 q^{97} -3.84141e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8}+O(q^{10}) \) 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

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