LMFDB - Embedded newform 198.8.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,8,Mod(1,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, 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("198.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	198.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:	$61.8522350459$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{14881}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3720 $ x^2 - x - 3720
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-60.4939$ of defining polynomial
Character	$\chi$	$=$	198.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} +64.0000 q^{4} -104.506 q^{5} +43.0861 q^{7} -512.000 q^{8} +O(q^{10})$	\(q-8.00000 q^{2} +64.0000 q^{4} -104.506 q^{5} +43.0861 q^{7} -512.000 q^{8} +836.049 q^{10} -1331.00 q^{11} +4494.27 q^{13} -344.689 q^{14} +4096.00 q^{16} +6878.55 q^{17} -21063.0 q^{19} -6688.39 q^{20} +10648.0 q^{22} +60259.0 q^{23} -67203.5 q^{25} -35954.2 q^{26} +2757.51 q^{28} +59039.5 q^{29} -88522.5 q^{31} -32768.0 q^{32} -55028.4 q^{34} -4502.76 q^{35} +382131. q^{37} +168504. q^{38} +53507.1 q^{40} -550122. q^{41} +693613. q^{43} -85184.0 q^{44} -482072. q^{46} +126233. q^{47} -821687. q^{49} +537628. q^{50} +287634. q^{52} +1.19815e6 q^{53} +139098. q^{55} -22060.1 q^{56} -472316. q^{58} -1.31641e6 q^{59} +440165. q^{61} +708180. q^{62} +262144. q^{64} -469679. q^{65} +3.56366e6 q^{67} +440227. q^{68} +36022.1 q^{70} -3.13943e6 q^{71} -4.07747e6 q^{73} -3.05705e6 q^{74} -1.34803e6 q^{76} -57347.6 q^{77} +1.89723e6 q^{79} -428057. q^{80} +4.40097e6 q^{82} -6.49257e6 q^{83} -718851. q^{85} -5.54890e6 q^{86} +681472. q^{88} -9.23033e6 q^{89} +193641. q^{91} +3.85658e6 q^{92} -1.00986e6 q^{94} +2.20122e6 q^{95} -1.38062e7 q^{97} +6.57349e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 16 q^{2} + 128 q^{4} - 331 q^{5} + 1794 q^{7} - 1024 q^{8}+O(q^{10}) $ 2 * q - 16 * q^2 + 128 * q^4 - 331 * q^5 + 1794 * q^7 - 1024 * q^8	\( 2 q - 16 q^{2} + 128 q^{4} - 331 q^{5} + 1794 q^{7} - 1024 q^{8} + 2648 q^{10} - 2662 q^{11} - 5406 q^{13} - 14352 q^{14} + 8192 q^{16} - 15032 q^{17} + 16916 q^{19} - 21184 q^{20} + 21296 q^{22} + 51351 q^{23} - 94029 q^{25} + 43248 q^{26} + 114816 q^{28} + 207130 q^{29} - 19071 q^{31} - 65536 q^{32} + 120256 q^{34} - 401074 q^{35} + 351333 q^{37} - 135328 q^{38} + 169472 q^{40} - 123610 q^{41} - 159822 q^{43} - 170368 q^{44} - 410808 q^{46} - 451160 q^{47} + 1420470 q^{49} + 752232 q^{50} - 345984 q^{52} + 1260832 q^{53} + 440561 q^{55} - 918528 q^{56} - 1657040 q^{58} - 887547 q^{59} - 597918 q^{61} + 152568 q^{62} + 524288 q^{64} + 1772672 q^{65} + 2864711 q^{67} - 962048 q^{68} + 3208592 q^{70} - 1306267 q^{71} - 4577530 q^{73} - 2810664 q^{74} + 1082624 q^{76} - 2387814 q^{77} - 2946342 q^{79} - 1355776 q^{80} + 988880 q^{82} - 9965450 q^{83} + 4243754 q^{85} + 1278576 q^{86} + 1362944 q^{88} - 10185377 q^{89} - 17140888 q^{91} + 3286464 q^{92} + 3609280 q^{94} - 6400800 q^{95} - 27765477 q^{97} - 11363760 q^{98}+O(q^{100}) \) 2 * q - 16 * q^2 + 128 * q^4 - 331 * q^5 + 1794 * q^7 - 1024 * q^8 + 2648 * q^10 - 2662 * q^11 - 5406 * q^13 - 14352 * q^14 + 8192 * q^16 - 15032 * q^17 + 16916 * q^19 - 21184 * q^20 + 21296 * q^22 + 51351 * q^23 - 94029 * q^25 + 43248 * q^26 + 114816 * q^28 + 207130 * q^29 - 19071 * q^31 - 65536 * q^32 + 120256 * q^34 - 401074 * q^35 + 351333 * q^37 - 135328 * q^38 + 169472 * q^40 - 123610 * q^41 - 159822 * q^43 - 170368 * q^44 - 410808 * q^46 - 451160 * q^47 + 1420470 * q^49 + 752232 * q^50 - 345984 * q^52 + 1260832 * q^53 + 440561 * q^55 - 918528 * q^56 - 1657040 * q^58 - 887547 * q^59 - 597918 * q^61 + 152568 * q^62 + 524288 * q^64 + 1772672 * q^65 + 2864711 * q^67 - 962048 * q^68 + 3208592 * q^70 - 1306267 * q^71 - 4577530 * q^73 - 2810664 * q^74 + 1082624 * q^76 - 2387814 * q^77 - 2946342 * q^79 - 1355776 * q^80 + 988880 * q^82 - 9965450 * q^83 + 4243754 * q^85 + 1278576 * q^86 + 1362944 * q^88 - 10185377 * q^89 - 17140888 * q^91 + 3286464 * q^92 + 3609280 * q^94 - 6400800 * q^95 - 27765477 * q^97 - 11363760 * 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 $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	64.0000	0.500000
$5$	−104.506	−0.373893	−0.186946	−	0.982370i	$-0.559859\pi$
$5$	−104.506	−0.373893	−0.186946	+	0.982370i	$0.559859\pi$
$6$	0	0
$7$	43.0861	0.0474781	0.0237391	−	0.999718i	$-0.492443\pi$
$7$	43.0861	0.0474781	0.0237391	+	0.999718i	$0.492443\pi$
$8$	−512.000	−0.353553
$9$	0	0
$10$	836.049	0.264382
$11$	−1331.00	−0.301511
$11$	−1331.00	−0.301511
$12$	0	0
$13$	4494.27	0.567359	0.283679	−	0.958919i	$-0.408445\pi$
$13$	4494.27	0.567359	0.283679	+	0.958919i	$0.408445\pi$
$14$	−344.689	−0.0335721
$15$	0	0
$16$	4096.00	0.250000
$17$	6878.55	0.339567	0.169784	−	0.985481i	$-0.445693\pi$
$17$	6878.55	0.339567	0.169784	+	0.985481i	$0.445693\pi$
$18$	0	0
$19$	−21063.0	−0.704503	−0.352252	−	0.935905i	$-0.614584\pi$
$19$	−21063.0	−0.704503	−0.352252	+	0.935905i	$0.614584\pi$
$20$	−6688.39	−0.186946
$21$	0	0
$22$	10648.0	0.213201
$23$	60259.0	1.03270	0.516350	−	0.856377i	$-0.327290\pi$
$23$	60259.0	1.03270	0.516350	+	0.856377i	$0.327290\pi$
$24$	0	0
$25$	−67203.5	−0.860204
$26$	−35954.2	−0.401183
$27$	0	0
$28$	2757.51	0.0237391
$29$	59039.5	0.449521	0.224760	−	0.974414i	$-0.427840\pi$
$29$	59039.5	0.449521	0.224760	+	0.974414i	$0.427840\pi$
$30$	0	0
$31$	−88522.5	−0.533689	−0.266844	−	0.963740i	$-0.585981\pi$
$31$	−88522.5	−0.533689	−0.266844	+	0.963740i	$0.585981\pi$
$32$	−32768.0	−0.176777
$33$	0	0
$34$	−55028.4	−0.240110
$35$	−4502.76	−0.0177517
$36$	0	0
$37$	382131.	1.24024	0.620120	−	0.784507i	$-0.287084\pi$
$37$	382131.	1.24024	0.620120	+	0.784507i	$0.287084\pi$
$38$	168504.	0.498159
$39$	0	0
$40$	53507.1	0.132191
$41$	−550122.	−1.24657	−0.623283	−	0.781996i	$-0.714202\pi$
$41$	−550122.	−1.24657	−0.623283	+	0.781996i	$0.714202\pi$
$42$	0	0
$43$	693613.	1.33039	0.665193	−	0.746671i	$-0.268349\pi$
$43$	693613.	1.33039	0.665193	+	0.746671i	$0.268349\pi$
$44$	−85184.0	−0.150756
$45$	0	0
$46$	−482072.	−0.730230
$47$	126233.	0.177349	0.0886745	−	0.996061i	$-0.471737\pi$
$47$	126233.	0.177349	0.0886745	+	0.996061i	$0.471737\pi$
$48$	0	0
$49$	−821687.	−0.997746
$50$	537628.	0.608256
$51$	0	0
$52$	287634.	0.283679
$53$	1.19815e6	1.10546	0.552732	−	0.833359i	$-0.313585\pi$
$53$	1.19815e6	1.10546	0.552732	+	0.833359i	$0.313585\pi$
$54$	0	0
$55$	139098.	0.112733
$56$	−22060.1	−0.0167861
$57$	0	0
$58$	−472316.	−0.317859
$59$	−1.31641e6	−0.834469	−0.417234	−	0.908799i	$-0.637001\pi$
$59$	−1.31641e6	−0.834469	−0.417234	+	0.908799i	$0.637001\pi$
$60$	0	0
$61$	440165.	0.248291	0.124145	−	0.992264i	$-0.460381\pi$
$61$	440165.	0.248291	0.124145	+	0.992264i	$0.460381\pi$
$62$	708180.	0.377375
$63$	0	0
$64$	262144.	0.125000
$65$	−469679.	−0.212131
$66$	0	0
$67$	3.56366e6	1.44755	0.723777	−	0.690034i	$-0.242404\pi$
$67$	3.56366e6	1.44755	0.723777	+	0.690034i	$0.242404\pi$
$68$	440227.	0.169784
$69$	0	0
$70$	36022.1	0.0125524
$71$	−3.13943e6	−1.04099	−0.520494	−	0.853865i	$-0.674252\pi$
$71$	−3.13943e6	−1.04099	−0.520494	+	0.853865i	$0.674252\pi$
$72$	0	0
$73$	−4.07747e6	−1.22676	−0.613382	−	0.789787i	$-0.710191\pi$
$73$	−4.07747e6	−1.22676	−0.613382	+	0.789787i	$0.710191\pi$
$74$	−3.05705e6	−0.876982
$75$	0	0
$76$	−1.34803e6	−0.352252
$77$	−57347.6	−0.0143152
$78$	0	0
$79$	1.89723e6	0.432937	0.216468	−	0.976290i	$-0.430546\pi$
$79$	1.89723e6	0.432937	0.216468	+	0.976290i	$0.430546\pi$
$80$	−428057.	−0.0934731
$81$	0	0
$82$	4.40097e6	0.881455
$83$	−6.49257e6	−1.24636	−0.623179	−	0.782079i	$-0.714159\pi$
$83$	−6.49257e6	−1.24636	−0.623179	+	0.782079i	$0.714159\pi$
$84$	0	0
$85$	−718851.	−0.126962
$86$	−5.54890e6	−0.940725
$87$	0	0
$88$	681472.	0.106600
$89$	−9.23033e6	−1.38788	−0.693940	−	0.720032i	$-0.744127\pi$
$89$	−9.23033e6	−1.38788	−0.693940	+	0.720032i	$0.744127\pi$
$90$	0	0
$91$	193641.	0.0269371
$92$	3.85658e6	0.516350
$93$	0	0
$94$	−1.00986e6	−0.125405
$95$	2.20122e6	0.263409
$96$	0	0
$97$	−1.38062e7	−1.53593	−0.767967	−	0.640489i	$-0.778732\pi$
$97$	−1.38062e7	−1.53593	−0.767967	+	0.640489i	$0.778732\pi$
$98$	6.57349e6	0.705513
$99$	0	0
$100$	−4.30102e6	−0.430102
$101$	−6.59478e6	−0.636906	−0.318453	−	0.947939i	$-0.603163\pi$
$101$	−6.59478e6	−0.636906	−0.318453	+	0.947939i	$0.603163\pi$
$102$	0	0
$103$	−1.98787e7	−1.79250	−0.896249	−	0.443551i	$-0.853718\pi$
$103$	−1.98787e7	−1.79250	−0.896249	+	0.443551i	$0.853718\pi$
$104$	−2.30107e6	−0.200592
$105$	0	0
$106$	−9.58517e6	−0.781681
$107$	−2.09533e7	−1.65352	−0.826758	−	0.562558i	$-0.809817\pi$
$107$	−2.09533e7	−1.65352	−0.826758	+	0.562558i	$0.809817\pi$
$108$	0	0
$109$	−598244.	−0.0442472	−0.0221236	−	0.999755i	$-0.507043\pi$
$109$	−598244.	−0.0442472	−0.0221236	+	0.999755i	$0.507043\pi$
$110$	−1.11278e6	−0.0797142
$111$	0	0
$112$	176481.	0.0118695
$113$	1.41807e6	0.0924535	0.0462267	−	0.998931i	$-0.485280\pi$
$113$	1.41807e6	0.0924535	0.0462267	+	0.998931i	$0.485280\pi$
$114$	0	0
$115$	−6.29744e6	−0.386119
$116$	3.77853e6	0.224760
$117$	0	0
$118$	1.05313e7	0.590058
$119$	296370.	0.0161220
$120$	0	0
$121$	1.77156e6	0.0909091
$122$	−3.52132e6	−0.175568
$123$	0	0
$124$	−5.66544e6	−0.266844
$125$	1.51877e7	0.695517
$126$	0	0
$127$	−1.92988e7	−0.836023	−0.418012	−	0.908442i	$-0.637273\pi$
$127$	−1.92988e7	−0.836023	−0.418012	+	0.908442i	$0.637273\pi$
$128$	−2.09715e6	−0.0883883
$129$	0	0
$130$	3.75743e6	0.149999
$131$	−4.22451e7	−1.64182	−0.820912	−	0.571055i	$-0.806534\pi$
$131$	−4.22451e7	−1.64182	−0.820912	+	0.571055i	$0.806534\pi$
$132$	0	0
$133$	−907523.	−0.0334485
$134$	−2.85093e7	−1.02358
$135$	0	0
$136$	−3.52182e6	−0.120055
$137$	7.65888e6	0.254474	0.127237	−	0.991872i	$-0.459389\pi$
$137$	7.65888e6	0.254474	0.127237	+	0.991872i	$0.459389\pi$
$138$	0	0
$139$	−1.46018e7	−0.461164	−0.230582	−	0.973053i	$-0.574063\pi$
$139$	−1.46018e7	−0.461164	−0.230582	+	0.973053i	$0.574063\pi$
$140$	−288177.	−0.00887586
$141$	0	0
$142$	2.51154e7	0.736090
$143$	−5.98188e6	−0.171065
$144$	0	0
$145$	−6.16999e6	−0.168072
$146$	3.26198e7	0.867453
$147$	0	0
$148$	2.44564e7	0.620120
$149$	3.54730e7	0.878507	0.439254	−	0.898363i	$-0.355243\pi$
$149$	3.54730e7	0.878507	0.439254	+	0.898363i	$0.355243\pi$
$150$	0	0
$151$	4.10281e7	0.969754	0.484877	−	0.874582i	$-0.338864\pi$
$151$	4.10281e7	0.969754	0.484877	+	0.874582i	$0.338864\pi$
$152$	1.07843e7	0.249080
$153$	0	0
$154$	458780.	0.0101224
$155$	9.25115e6	0.199542
$156$	0	0
$157$	−6.66977e7	−1.37550	−0.687752	−	0.725946i	$-0.741402\pi$
$157$	−6.66977e7	−1.37550	−0.687752	+	0.725946i	$0.741402\pi$
$158$	−1.51778e7	−0.306133
$159$	0	0
$160$	3.42446e6	0.0660955
$161$	2.59632e6	0.0490307
$162$	0	0
$163$	9.29744e6	0.168154	0.0840769	−	0.996459i	$-0.473206\pi$
$163$	9.29744e6	0.168154	0.0840769	+	0.996459i	$0.473206\pi$
$164$	−3.52078e7	−0.623283
$165$	0	0
$166$	5.19405e7	0.881309
$167$	5.93268e7	0.985696	0.492848	−	0.870115i	$-0.335956\pi$
$167$	5.93268e7	0.985696	0.492848	+	0.870115i	$0.335956\pi$
$168$	0	0
$169$	−4.25500e7	−0.678104
$170$	5.75081e6	0.0897754
$171$	0	0
$172$	4.43912e7	0.665193
$173$	−1.19997e8	−1.76201	−0.881004	−	0.473108i	$-0.843132\pi$
$173$	−1.19997e8	−1.76201	−0.881004	+	0.473108i	$0.843132\pi$
$174$	0	0
$175$	−2.89553e6	−0.0408409
$176$	−5.45178e6	−0.0753778
$177$	0	0
$178$	7.38426e7	0.981380
$179$	−3.18894e7	−0.415586	−0.207793	−	0.978173i	$-0.566628\pi$
$179$	−3.18894e7	−0.415586	−0.207793	+	0.978173i	$0.566628\pi$
$180$	0	0
$181$	2.14661e7	0.269079	0.134539	−	0.990908i	$-0.457045\pi$
$181$	2.14661e7	0.269079	0.134539	+	0.990908i	$0.457045\pi$
$182$	−1.54913e6	−0.0190474
$183$	0	0
$184$	−3.08526e7	−0.365115
$185$	−3.99350e7	−0.463717
$186$	0	0
$187$	−9.15535e6	−0.102383
$188$	8.07888e6	0.0886745
$189$	0	0
$190$	−1.76097e7	−0.186258
$191$	5.37382e7	0.558042	0.279021	−	0.960285i	$-0.409990\pi$
$191$	5.37382e7	0.558042	0.279021	+	0.960285i	$0.409990\pi$
$192$	0	0
$193$	1.72101e8	1.72319	0.861593	−	0.507600i	$-0.169467\pi$
$193$	1.72101e8	1.72319	0.861593	+	0.507600i	$0.169467\pi$
$194$	1.10450e8	1.08607
$195$	0	0
$196$	−5.25879e7	−0.498873
$197$	1.14526e8	1.06726	0.533631	−	0.845718i	$-0.320827\pi$
$197$	1.14526e8	1.06726	0.533631	+	0.845718i	$0.320827\pi$
$198$	0	0
$199$	−3.40644e7	−0.306418	−0.153209	−	0.988194i	$-0.548961\pi$
$199$	−3.40644e7	−0.306418	−0.153209	+	0.988194i	$0.548961\pi$
$200$	3.44082e7	0.304128
$201$	0	0
$202$	5.27583e7	0.450361
$203$	2.54378e6	0.0213424
$204$	0	0
$205$	5.74911e7	0.466082
$206$	1.59030e8	1.26749
$207$	0	0
$208$	1.84085e7	0.141840
$209$	2.80349e7	0.212416
$210$	0	0
$211$	−1.74288e8	−1.27726	−0.638628	−	0.769516i	$-0.720498\pi$
$211$	−1.74288e8	−1.27726	−0.638628	+	0.769516i	$0.720498\pi$
$212$	7.66814e7	0.552732
$213$	0	0
$214$	1.67626e8	1.16921
$215$	−7.24868e7	−0.497421
$216$	0	0
$217$	−3.81409e6	−0.0253385
$218$	4.78596e6	0.0312875
$219$	0	0
$220$	8.90225e6	0.0563664
$221$	3.09141e7	0.192656
$222$	0	0
$223$	1.45730e8	0.879998	0.439999	−	0.897998i	$-0.354979\pi$
$223$	1.45730e8	0.879998	0.439999	+	0.897998i	$0.354979\pi$
$224$	−1.41184e6	−0.00839303
$225$	0	0
$226$	−1.13446e7	−0.0653745
$227$	1.27102e8	0.721211	0.360606	−	0.932718i	$-0.382570\pi$
$227$	1.27102e8	0.721211	0.360606	+	0.932718i	$0.382570\pi$
$228$	0	0
$229$	−1.29750e8	−0.713975	−0.356987	−	0.934109i	$-0.616196\pi$
$229$	−1.29750e8	−0.713975	−0.356987	+	0.934109i	$0.616196\pi$
$230$	5.03795e7	0.273028
$231$	0	0
$232$	−3.02282e7	−0.158930
$233$	1.52210e8	0.788310	0.394155	−	0.919044i	$-0.371037\pi$
$233$	1.52210e8	0.788310	0.394155	+	0.919044i	$0.371037\pi$
$234$	0	0
$235$	−1.31921e7	−0.0663095
$236$	−8.42504e7	−0.417234
$237$	0	0
$238$	−2.37096e6	−0.0114000
$239$	2.43061e8	1.15165	0.575827	−	0.817571i	$-0.304680\pi$
$239$	2.43061e8	1.15165	0.575827	+	0.817571i	$0.304680\pi$
$240$	0	0
$241$	−6.84592e7	−0.315045	−0.157522	−	0.987515i	$-0.550351\pi$
$241$	−6.84592e7	−0.315045	−0.157522	+	0.987515i	$0.550351\pi$
$242$	−1.41725e7	−0.0642824
$243$	0	0
$244$	2.81705e7	0.124145
$245$	8.58713e7	0.373050
$246$	0	0
$247$	−9.46630e7	−0.399706
$248$	4.53235e7	0.188687
$249$	0	0
$250$	−1.21502e8	−0.491804
$251$	−1.67292e8	−0.667755	−0.333878	−	0.942616i	$-0.608357\pi$
$251$	−1.67292e8	−0.667755	−0.333878	+	0.942616i	$0.608357\pi$
$252$	0	0
$253$	−8.02047e7	−0.311371
$254$	1.54391e8	0.591158
$255$	0	0
$256$	1.67772e7	0.0625000
$257$	−3.84789e8	−1.41402	−0.707012	−	0.707202i	$-0.749957\pi$
$257$	−3.84789e8	−1.41402	−0.707012	+	0.707202i	$0.749957\pi$
$258$	0	0
$259$	1.64645e7	0.0588843
$260$	−3.00595e7	−0.106066
$261$	0	0
$262$	3.37960e8	1.16094
$263$	−5.09459e8	−1.72689	−0.863444	−	0.504445i	$-0.831697\pi$
$263$	−5.09459e8	−1.72689	−0.863444	+	0.504445i	$0.831697\pi$
$264$	0	0
$265$	−1.25214e8	−0.413325
$266$	7.26018e6	0.0236517
$267$	0	0
$268$	2.28074e8	0.723777
$269$	5.51297e8	1.72684	0.863421	−	0.504484i	$-0.168317\pi$
$269$	5.51297e8	1.72684	0.863421	+	0.504484i	$0.168317\pi$
$270$	0	0
$271$	3.42271e8	1.04467	0.522333	−	0.852742i	$-0.325062\pi$
$271$	3.42271e8	1.04467	0.522333	+	0.852742i	$0.325062\pi$
$272$	2.81745e7	0.0848918
$273$	0	0
$274$	−6.12710e7	−0.179940
$275$	8.94478e7	0.259361
$276$	0	0
$277$	−5.10974e8	−1.44451	−0.722253	−	0.691629i	$-0.756893\pi$
$277$	−5.10974e8	−1.44451	−0.722253	+	0.691629i	$0.756893\pi$
$278$	1.16815e8	0.326092
$279$	0	0
$280$	2.30541e6	0.00627618
$281$	1.51750e7	0.0407998	0.0203999	−	0.999792i	$-0.493506\pi$
$281$	1.51750e7	0.0407998	0.0203999	+	0.999792i	$0.493506\pi$
$282$	0	0
$283$	−2.25341e8	−0.590999	−0.295500	−	0.955343i	$-0.595486\pi$
$283$	−2.25341e8	−0.590999	−0.295500	+	0.955343i	$0.595486\pi$
$284$	−2.00923e8	−0.520494
$285$	0	0
$286$	4.78550e7	0.120961
$287$	−2.37026e7	−0.0591846
$288$	0	0
$289$	−3.63024e8	−0.884694
$290$	4.93599e7	0.118845
$291$	0	0
$292$	−2.60958e8	−0.613382
$293$	−3.84004e8	−0.891864	−0.445932	−	0.895067i	$-0.647128\pi$
$293$	−3.84004e8	−0.891864	−0.445932	+	0.895067i	$0.647128\pi$
$294$	0	0
$295$	1.37573e8	0.312002
$296$	−1.95651e8	−0.438491
$297$	0	0
$298$	−2.83784e8	−0.621199
$299$	2.70821e8	0.585912
$300$	0	0
$301$	2.98851e7	0.0631643
$302$	−3.28225e8	−0.685720
$303$	0	0
$304$	−8.62741e7	−0.176126
$305$	−4.59999e7	−0.0928341
$306$	0	0
$307$	7.46289e8	1.47205	0.736026	−	0.676954i	$-0.236700\pi$
$307$	7.46289e8	1.47205	0.736026	+	0.676954i	$0.236700\pi$
$308$	−3.67024e6	−0.00715760
$309$	0	0
$310$	−7.40092e7	−0.141098
$311$	−6.40000e8	−1.20648	−0.603238	−	0.797561i	$-0.706123\pi$
$311$	−6.40000e8	−1.20648	−0.603238	+	0.797561i	$0.706123\pi$
$312$	0	0
$313$	1.35452e8	0.249677	0.124839	−	0.992177i	$-0.460159\pi$
$313$	1.35452e8	0.249677	0.124839	+	0.992177i	$0.460159\pi$
$314$	5.33581e8	0.972628
$315$	0	0
$316$	1.21423e8	0.216468
$317$	−9.75198e7	−0.171943	−0.0859717	−	0.996298i	$-0.527399\pi$
$317$	−9.75198e7	−0.171943	−0.0859717	+	0.996298i	$0.527399\pi$
$318$	0	0
$319$	−7.85816e7	−0.135536
$320$	−2.73957e7	−0.0467366
$321$	0	0
$322$	−2.07706e7	−0.0346700
$323$	−1.44883e8	−0.239226
$324$	0	0
$325$	−3.02031e8	−0.488045
$326$	−7.43795e7	−0.118903
$327$	0	0
$328$	2.81662e8	0.440728
$329$	5.43886e6	0.00842020
$330$	0	0
$331$	3.49842e8	0.530242	0.265121	−	0.964215i	$-0.414588\pi$
$331$	3.49842e8	0.530242	0.265121	+	0.964215i	$0.414588\pi$
$332$	−4.15524e8	−0.623179
$333$	0	0
$334$	−4.74614e8	−0.696992
$335$	−3.72425e8	−0.541230
$336$	0	0
$337$	7.20870e8	1.02601	0.513006	−	0.858385i	$-0.328532\pi$
$337$	7.20870e8	1.02601	0.513006	+	0.858385i	$0.328532\pi$
$338$	3.40400e8	0.479492
$339$	0	0
$340$	−4.60064e7	−0.0634808
$341$	1.17823e8	0.160913
$342$	0	0
$343$	−7.08865e7	−0.0948493
$344$	−3.55130e8	−0.470362
$345$	0	0
$346$	9.59974e8	1.24593
$347$	−1.28079e8	−0.164560	−0.0822798	−	0.996609i	$-0.526220\pi$
$347$	−1.28079e8	−0.164560	−0.0822798	+	0.996609i	$0.526220\pi$
$348$	0	0
$349$	−1.00379e8	−0.126402	−0.0632012	−	0.998001i	$-0.520131\pi$
$349$	−1.00379e8	−0.126402	−0.0632012	+	0.998001i	$0.520131\pi$
$350$	2.31643e7	0.0288789
$351$	0	0
$352$	4.36142e7	0.0533002
$353$	−7.51413e8	−0.909216	−0.454608	−	0.890692i	$-0.650221\pi$
$353$	−7.51413e8	−0.909216	−0.454608	+	0.890692i	$0.650221\pi$
$354$	0	0
$355$	3.28089e8	0.389218
$356$	−5.90741e8	−0.693940
$357$	0	0
$358$	2.55115e8	0.293864
$359$	9.17064e8	1.04609	0.523045	−	0.852305i	$-0.324796\pi$
$359$	9.17064e8	1.04609	0.523045	+	0.852305i	$0.324796\pi$
$360$	0	0
$361$	−4.50221e8	−0.503675
$362$	−1.71729e8	−0.190267
$363$	0	0
$364$	1.23930e7	0.0134686
$365$	4.26121e8	0.458678
$366$	0	0
$367$	−9.16435e8	−0.967766	−0.483883	−	0.875133i	$-0.660774\pi$
$367$	−9.16435e8	−0.967766	−0.483883	+	0.875133i	$0.660774\pi$
$368$	2.46821e8	0.258175
$369$	0	0
$370$	3.19480e8	0.327897
$371$	5.16234e7	0.0524854
$372$	0	0
$373$	−1.56099e9	−1.55747	−0.778736	−	0.627352i	$-0.784139\pi$
$373$	−1.56099e9	−1.55747	−0.778736	+	0.627352i	$0.784139\pi$
$374$	7.32428e7	0.0723960
$375$	0	0
$376$	−6.46311e7	−0.0627024
$377$	2.65340e8	0.255040
$378$	0	0
$379$	4.34986e7	0.0410429	0.0205214	−	0.999789i	$-0.493467\pi$
$379$	4.34986e7	0.0410429	0.0205214	+	0.999789i	$0.493467\pi$
$380$	1.40878e8	0.131704
$381$	0	0
$382$	−4.29906e8	−0.394595
$383$	−1.95422e8	−0.177737	−0.0888685	−	0.996043i	$-0.528325\pi$
$383$	−1.95422e8	−0.177737	−0.0888685	+	0.996043i	$0.528325\pi$
$384$	0	0
$385$	5.99317e6	0.00535235
$386$	−1.37681e9	−1.21848
$387$	0	0
$388$	−8.83596e8	−0.767967
$389$	1.60846e9	1.38543	0.692716	−	0.721210i	$-0.256414\pi$
$389$	1.60846e9	1.38543	0.692716	+	0.721210i	$0.256414\pi$
$390$	0	0
$391$	4.14495e8	0.350671
$392$	4.20704e8	0.352756
$393$	0	0
$394$	−9.16205e8	−0.754668
$395$	−1.98272e8	−0.161872
$396$	0	0
$397$	1.20591e9	0.967268	0.483634	−	0.875270i	$-0.339317\pi$
$397$	1.20591e9	0.967268	0.483634	+	0.875270i	$0.339317\pi$
$398$	2.72515e8	0.216670
$399$	0	0
$400$	−2.75265e8	−0.215051
$401$	−7.40689e8	−0.573628	−0.286814	−	0.957986i	$-0.592596\pi$
$401$	−7.40689e8	−0.573628	−0.286814	+	0.957986i	$0.592596\pi$
$402$	0	0
$403$	−3.97845e8	−0.302793
$404$	−4.22066e8	−0.318453
$405$	0	0
$406$	−2.03502e7	−0.0150914
$407$	−5.08616e8	−0.373947
$408$	0	0
$409$	1.37187e7	0.00991476	0.00495738	−	0.999988i	$-0.498422\pi$
$409$	1.37187e7	0.00991476	0.00495738	+	0.999988i	$0.498422\pi$
$410$	−4.59929e8	−0.329570
$411$	0	0
$412$	−1.27224e9	−0.896249
$413$	−5.67190e7	−0.0396190
$414$	0	0
$415$	6.78513e8	0.466004
$416$	−1.47268e8	−0.100296
$417$	0	0
$418$	−2.24279e8	−0.150201
$419$	−1.95596e9	−1.29901	−0.649503	−	0.760359i	$-0.725023\pi$
$419$	−1.95596e9	−1.29901	−0.649503	+	0.760359i	$0.725023\pi$
$420$	0	0
$421$	−2.31110e9	−1.50950	−0.754748	−	0.656015i	$-0.772241\pi$
$421$	−2.31110e9	−1.50950	−0.754748	+	0.656015i	$0.772241\pi$
$422$	1.39430e9	0.903156
$423$	0	0
$424$	−6.13451e8	−0.390840
$425$	−4.62262e8	−0.292097
$426$	0	0
$427$	1.89650e7	0.0117884
$428$	−1.34101e9	−0.826758
$429$	0	0
$430$	5.79895e8	0.351730
$431$	2.03521e9	1.22444	0.612222	−	0.790686i	$-0.290276\pi$
$431$	2.03521e9	1.22444	0.612222	+	0.790686i	$0.290276\pi$
$432$	0	0
$433$	2.81028e9	1.66357	0.831786	−	0.555096i	$-0.187318\pi$
$433$	2.81028e9	1.66357	0.831786	+	0.555096i	$0.187318\pi$
$434$	3.05127e7	0.0179171
$435$	0	0
$436$	−3.82876e7	−0.0221236
$437$	−1.26924e9	−0.727541
$438$	0	0
$439$	1.58225e9	0.892587	0.446293	−	0.894887i	$-0.352744\pi$
$439$	1.58225e9	0.892587	0.446293	+	0.894887i	$0.352744\pi$
$440$	−7.12180e7	−0.0398571
$441$	0	0
$442$	−2.47313e8	−0.136229
$443$	4.88989e8	0.267231	0.133615	−	0.991033i	$-0.457341\pi$
$443$	4.88989e8	0.267231	0.133615	+	0.991033i	$0.457341\pi$
$444$	0	0
$445$	9.64626e8	0.518918
$446$	−1.16584e9	−0.622253
$447$	0	0
$448$	1.12948e7	0.00593477
$449$	−1.81072e9	−0.944036	−0.472018	−	0.881589i	$-0.656474\pi$
$449$	−1.81072e9	−0.944036	−0.472018	+	0.881589i	$0.656474\pi$
$450$	0	0
$451$	7.32212e8	0.375854
$452$	9.07565e7	0.0462267
$453$	0	0
$454$	−1.01682e9	−0.509973
$455$	−2.02366e7	−0.0100716
$456$	0	0
$457$	−8.64311e8	−0.423607	−0.211804	−	0.977312i	$-0.567934\pi$
$457$	−8.64311e8	−0.423607	−0.211804	+	0.977312i	$0.567934\pi$
$458$	1.03800e9	0.504857
$459$	0	0
$460$	−4.03036e8	−0.193060
$461$	−4.85430e8	−0.230767	−0.115383	−	0.993321i	$-0.536810\pi$
$461$	−4.85430e8	−0.230767	−0.115383	+	0.993321i	$0.536810\pi$
$462$	0	0
$463$	1.85376e9	0.867999	0.434000	−	0.900913i	$-0.357102\pi$
$463$	1.85376e9	0.867999	0.434000	+	0.900913i	$0.357102\pi$
$464$	2.41826e8	0.112380
$465$	0	0
$466$	−1.21768e9	−0.557419
$467$	−3.16192e7	−0.0143662	−0.00718310	−	0.999974i	$-0.502286\pi$
$467$	−3.16192e7	−0.0143662	−0.00718310	+	0.999974i	$0.502286\pi$
$468$	0	0
$469$	1.53544e8	0.0687272
$470$	1.05537e8	0.0468879
$471$	0	0
$472$	6.74003e8	0.295029
$473$	−9.23199e8	−0.401126
$474$	0	0
$475$	1.41551e9	0.606017
$476$	1.89677e7	0.00806101
$477$	0	0
$478$	−1.94449e9	−0.814343
$479$	3.11838e9	1.29645	0.648223	−	0.761451i	$-0.275513\pi$
$479$	3.11838e9	1.29645	0.648223	+	0.761451i	$0.275513\pi$
$480$	0	0
$481$	1.71740e9	0.703661
$482$	5.47674e8	0.222770
$483$	0	0
$484$	1.13380e8	0.0454545
$485$	1.44283e9	0.574275
$486$	0	0
$487$	−3.37608e9	−1.32453	−0.662265	−	0.749270i	$-0.730404\pi$
$487$	−3.37608e9	−1.32453	−0.662265	+	0.749270i	$0.730404\pi$
$488$	−2.25364e8	−0.0877840
$489$	0	0
$490$	−6.86970e8	−0.263786
$491$	4.55043e9	1.73487	0.867436	−	0.497548i	$-0.165766\pi$
$491$	4.55043e9	1.73487	0.867436	+	0.497548i	$0.165766\pi$
$492$	0	0
$493$	4.06106e8	0.152642
$494$	7.57304e8	0.282635
$495$	0	0
$496$	−3.62588e8	−0.133422
$497$	−1.35266e8	−0.0494242
$498$	0	0
$499$	−6.25733e8	−0.225443	−0.112722	−	0.993627i	$-0.535957\pi$
$499$	−6.25733e8	−0.225443	−0.112722	+	0.993627i	$0.535957\pi$
$500$	9.72014e8	0.347758
$501$	0	0
$502$	1.33834e9	0.472174
$503$	3.43240e9	1.20257	0.601285	−	0.799035i	$-0.294656\pi$
$503$	3.43240e9	1.20257	0.601285	+	0.799035i	$0.294656\pi$
$504$	0	0
$505$	6.89195e8	0.238135
$506$	6.41638e8	0.220173
$507$	0	0
$508$	−1.23513e9	−0.418012
$509$	−1.36035e9	−0.457234	−0.228617	−	0.973516i	$-0.573420\pi$
$509$	−1.36035e9	−0.457234	−0.228617	+	0.973516i	$0.573420\pi$
$510$	0	0
$511$	−1.75682e8	−0.0582445
$512$	−1.34218e8	−0.0441942
$513$	0	0
$514$	3.07831e9	0.999866
$515$	2.07745e9	0.670202
$516$	0	0
$517$	−1.68016e8	−0.0534727
$518$	−1.31716e8	−0.0416375
$519$	0	0
$520$	2.40476e8	0.0749997
$521$	2.51109e9	0.777912	0.388956	−	0.921256i	$-0.372836\pi$
$521$	2.51109e9	0.777912	0.388956	+	0.921256i	$0.372836\pi$
$522$	0	0
$523$	4.25045e9	1.29921	0.649605	−	0.760272i	$-0.274934\pi$
$523$	4.25045e9	1.29921	0.649605	+	0.760272i	$0.274934\pi$
$524$	−2.70368e9	−0.820912
$525$	0	0
$526$	4.07567e9	1.22109
$527$	−6.08907e8	−0.181223
$528$	0	0
$529$	2.26323e8	0.0664713
$530$	1.00171e9	0.292265
$531$	0	0
$532$	−5.80815e7	−0.0167243
$533$	−2.47240e9	−0.707250
$534$	0	0
$535$	2.18974e9	0.618237
$536$	−1.82460e9	−0.511788
$537$	0	0
$538$	−4.41038e9	−1.22106
$539$	1.09366e9	0.300832
$540$	0	0
$541$	1.06279e9	0.288574	0.144287	−	0.989536i	$-0.453911\pi$
$541$	1.06279e9	0.288574	0.144287	+	0.989536i	$0.453911\pi$
$542$	−2.73817e9	−0.738690
$543$	0	0
$544$	−2.25396e8	−0.0600276
$545$	6.25202e7	0.0165437
$546$	0	0
$547$	−3.28564e9	−0.858350	−0.429175	−	0.903221i	$-0.641196\pi$
$547$	−3.28564e9	−0.858350	−0.429175	+	0.903221i	$0.641196\pi$
$548$	4.90168e8	0.127237
$549$	0	0
$550$	−7.15582e8	−0.183396
$551$	−1.24355e9	−0.316689
$552$	0	0
$553$	8.17441e7	0.0205550
$554$	4.08779e9	1.02142
$555$	0	0
$556$	−9.34516e8	−0.230582
$557$	4.04436e9	0.991645	0.495823	−	0.868424i	$-0.334867\pi$
$557$	4.04436e9	0.991645	0.495823	+	0.868424i	$0.334867\pi$
$558$	0	0
$559$	3.11729e9	0.754806
$560$	−1.84433e7	−0.00443793
$561$	0	0
$562$	−1.21400e8	−0.0288498
$563$	1.60197e9	0.378333	0.189167	−	0.981945i	$-0.439421\pi$
$563$	1.60197e9	0.378333	0.189167	+	0.981945i	$0.439421\pi$
$564$	0	0
$565$	−1.48197e8	−0.0345677
$566$	1.80272e9	0.417899
$567$	0	0
$568$	1.60739e9	0.368045
$569$	5.94461e9	1.35279	0.676396	−	0.736539i	$-0.263541\pi$
$569$	5.94461e9	1.35279	0.676396	+	0.736539i	$0.263541\pi$
$570$	0	0
$571$	−1.01942e9	−0.229154	−0.114577	−	0.993414i	$-0.536551\pi$
$571$	−1.01942e9	−0.229154	−0.114577	+	0.993414i	$0.536551\pi$
$572$	−3.82840e8	−0.0855326
$573$	0	0
$574$	1.89621e8	0.0418499
$575$	−4.04961e9	−0.888334
$576$	0	0
$577$	−5.05194e8	−0.109482	−0.0547410	−	0.998501i	$-0.517433\pi$
$577$	−5.05194e8	−0.109482	−0.0547410	+	0.998501i	$0.517433\pi$
$578$	2.90419e9	0.625573
$579$	0	0
$580$	−3.94879e8	−0.0840362
$581$	−2.79739e8	−0.0591748
$582$	0	0
$583$	−1.59473e9	−0.333310
$584$	2.08767e9	0.433726
$585$	0	0
$586$	3.07203e9	0.630643
$587$	−6.05441e8	−0.123549	−0.0617744	−	0.998090i	$-0.519676\pi$
$587$	−6.05441e8	−0.123549	−0.0617744	+	0.998090i	$0.519676\pi$
$588$	0	0
$589$	1.86455e9	0.375985
$590$	−1.10059e9	−0.220618
$591$	0	0
$592$	1.56521e9	0.310060
$593$	2.44359e8	0.0481212	0.0240606	−	0.999711i	$-0.492341\pi$
$593$	2.44359e8	0.0481212	0.0240606	+	0.999711i	$0.492341\pi$
$594$	0	0
$595$	−3.09725e7	−0.00602790
$596$	2.27027e9	0.439254
$597$	0	0
$598$	−2.16656e9	−0.414302
$599$	−4.76209e9	−0.905324	−0.452662	−	0.891682i	$-0.649526\pi$
$599$	−4.76209e9	−0.905324	−0.452662	+	0.891682i	$0.649526\pi$
$600$	0	0
$601$	−4.27387e9	−0.803083	−0.401542	−	0.915841i	$-0.631525\pi$
$601$	−4.27387e9	−0.803083	−0.401542	+	0.915841i	$0.631525\pi$
$602$	−2.39080e8	−0.0446639
$603$	0	0
$604$	2.62580e9	0.484877
$605$	−1.85139e8	−0.0339902
$606$	0	0
$607$	6.40384e9	1.16220	0.581099	−	0.813833i	$-0.302623\pi$
$607$	6.40384e9	1.16220	0.581099	+	0.813833i	$0.302623\pi$
$608$	6.90193e8	0.124540
$609$	0	0
$610$	3.67999e8	0.0656436
$611$	5.67324e8	0.100621
$612$	0	0
$613$	−8.98899e9	−1.57616	−0.788078	−	0.615575i	$-0.788924\pi$
$613$	−8.98899e9	−1.57616	−0.788078	+	0.615575i	$0.788924\pi$
$614$	−5.97032e9	−1.04090
$615$	0	0
$616$	2.93620e7	0.00506119
$617$	2.11391e9	0.362316	0.181158	−	0.983454i	$-0.442015\pi$
$617$	2.11391e9	0.362316	0.181158	+	0.983454i	$0.442015\pi$
$618$	0	0
$619$	−4.25875e9	−0.721713	−0.360856	−	0.932621i	$-0.617516\pi$
$619$	−4.25875e9	−0.721713	−0.360856	+	0.932621i	$0.617516\pi$
$620$	5.92074e8	0.0997711
$621$	0	0
$622$	5.12000e9	0.853107
$623$	−3.97699e8	−0.0658940
$624$	0	0
$625$	3.66306e9	0.600156
$626$	−1.08361e9	−0.176548
$627$	0	0
$628$	−4.26865e9	−0.687752
$629$	2.62850e9	0.421145
$630$	0	0
$631$	9.55885e9	1.51462	0.757309	−	0.653057i	$-0.226514\pi$
$631$	9.55885e9	1.51462	0.757309	+	0.653057i	$0.226514\pi$
$632$	−9.71380e8	−0.153066
$633$	0	0
$634$	7.80159e8	0.121582
$635$	2.01685e9	0.312583
$636$	0	0
$637$	−3.69289e9	−0.566080
$638$	6.28652e8	0.0958381
$639$	0	0
$640$	2.19165e8	0.0330477
$641$	−7.93190e9	−1.18953	−0.594763	−	0.803901i	$-0.702754\pi$
$641$	−7.93190e9	−1.18953	−0.594763	+	0.803901i	$0.702754\pi$
$642$	0	0
$643$	−3.67790e9	−0.545583	−0.272792	−	0.962073i	$-0.587947\pi$
$643$	−3.67790e9	−0.545583	−0.272792	+	0.962073i	$0.587947\pi$
$644$	1.66165e8	0.0245154
$645$	0	0
$646$	1.15906e9	0.169158
$647$	3.34066e9	0.484917	0.242459	−	0.970162i	$-0.422046\pi$
$647$	3.34066e9	0.484917	0.242459	+	0.970162i	$0.422046\pi$
$648$	0	0
$649$	1.75215e9	0.251602
$650$	2.41625e9	0.345100
$651$	0	0
$652$	5.95036e8	0.0840769
$653$	−1.23649e10	−1.73778	−0.868891	−	0.495004i	$-0.835167\pi$
$653$	−1.23649e10	−1.73778	−0.868891	+	0.495004i	$0.835167\pi$
$654$	0	0
$655$	4.41487e9	0.613865
$656$	−2.25330e9	−0.311642
$657$	0	0
$658$	−4.35109e7	−0.00595398
$659$	−8.58087e9	−1.16797	−0.583986	−	0.811764i	$-0.698508\pi$
$659$	−8.58087e9	−1.16797	−0.583986	+	0.811764i	$0.698508\pi$
$660$	0	0
$661$	−8.09007e9	−1.08955	−0.544775	−	0.838582i	$-0.683385\pi$
$661$	−8.09007e9	−1.08955	−0.544775	+	0.838582i	$0.683385\pi$
$662$	−2.79873e9	−0.374937
$663$	0	0
$664$	3.32419e9	0.440654
$665$	9.48417e7	0.0125062
$666$	0	0
$667$	3.55766e9	0.464220
$668$	3.79691e9	0.492848
$669$	0	0
$670$	2.97940e9	0.382707
$671$	−5.85859e8	−0.0748625
$672$	0	0
$673$	−1.38929e10	−1.75687	−0.878436	−	0.477860i	$-0.841413\pi$
$673$	−1.38929e10	−1.75687	−0.878436	+	0.477860i	$0.841413\pi$
$674$	−5.76696e9	−0.725500
$675$	0	0
$676$	−2.72320e9	−0.339052
$677$	−6.36018e9	−0.787788	−0.393894	−	0.919156i	$-0.628872\pi$
$677$	−6.36018e9	−0.787788	−0.393894	+	0.919156i	$0.628872\pi$
$678$	0	0
$679$	−5.94855e8	−0.0729233
$680$	3.68052e8	0.0448877
$681$	0	0
$682$	−9.42588e8	−0.113783
$683$	7.46187e9	0.896139	0.448069	−	0.893999i	$-0.352112\pi$
$683$	7.46187e9	0.896139	0.448069	+	0.893999i	$0.352112\pi$
$684$	0	0
$685$	−8.00400e8	−0.0951459
$686$	5.67092e8	0.0670686
$687$	0	0
$688$	2.84104e9	0.332596
$689$	5.38480e9	0.627195
$690$	0	0
$691$	−1.01338e10	−1.16842	−0.584212	−	0.811601i	$-0.698596\pi$
$691$	−1.01338e10	−1.16842	−0.584212	+	0.811601i	$0.698596\pi$
$692$	−7.67979e9	−0.881004
$693$	0	0
$694$	1.02463e9	0.116361
$695$	1.52598e9	0.172426
$696$	0	0
$697$	−3.78404e9	−0.423293
$698$	8.03034e8	0.0893800
$699$	0	0
$700$	−1.85314e8	−0.0204205
$701$	−1.31006e10	−1.43641	−0.718206	−	0.695831i	$-0.755036\pi$
$701$	−1.31006e10	−1.43641	−0.718206	+	0.695831i	$0.755036\pi$
$702$	0	0
$703$	−8.04883e9	−0.873754
$704$	−3.48914e8	−0.0376889
$705$	0	0
$706$	6.01130e9	0.642913
$707$	−2.84143e8	−0.0302391
$708$	0	0
$709$	−1.04601e10	−1.10223	−0.551116	−	0.834429i	$-0.685798\pi$
$709$	−1.04601e10	−1.10223	−0.551116	+	0.834429i	$0.685798\pi$
$710$	−2.62471e9	−0.275219
$711$	0	0
$712$	4.72593e9	0.490690
$713$	−5.33428e9	−0.551141
$714$	0	0
$715$	6.25143e8	0.0639600
$716$	−2.04092e9	−0.207793
$717$	0	0
$718$	−7.33651e9	−0.739697
$719$	−6.14452e9	−0.616505	−0.308253	−	0.951305i	$-0.599744\pi$
$719$	−6.14452e9	−0.616505	−0.308253	+	0.951305i	$0.599744\pi$
$720$	0	0
$721$	−8.56497e8	−0.0851045
$722$	3.60177e9	0.356152
$723$	0	0
$724$	1.37383e9	0.134539
$725$	−3.96766e9	−0.386680
$726$	0	0
$727$	−1.47022e9	−0.141910	−0.0709550	−	0.997480i	$-0.522605\pi$
$727$	−1.47022e9	−0.141910	−0.0709550	+	0.997480i	$0.522605\pi$
$728$	−9.91440e7	−0.00952372
$729$	0	0
$730$	−3.40897e9	−0.324334
$731$	4.77105e9	0.451755
$732$	0	0
$733$	6.30989e8	0.0591777	0.0295888	−	0.999562i	$-0.490580\pi$
$733$	6.30989e8	0.0591777	0.0295888	+	0.999562i	$0.490580\pi$
$734$	7.33148e9	0.684314
$735$	0	0
$736$	−1.97457e9	−0.182557
$737$	−4.74324e9	−0.436454
$738$	0	0
$739$	7.22368e9	0.658420	0.329210	−	0.944257i	$-0.393218\pi$
$739$	7.22368e9	0.658420	0.329210	+	0.944257i	$0.393218\pi$
$740$	−2.55584e9	−0.231858
$741$	0	0
$742$	−4.12987e8	−0.0371128
$743$	−7.72789e9	−0.691194	−0.345597	−	0.938383i	$-0.612324\pi$
$743$	−7.72789e9	−0.691194	−0.345597	+	0.938383i	$0.612324\pi$
$744$	0	0
$745$	−3.70714e9	−0.328467
$746$	1.24880e10	1.10130
$747$	0	0
$748$	−5.85942e8	−0.0511917
$749$	−9.02793e8	−0.0785059
$750$	0	0
$751$	−1.54417e10	−1.33032	−0.665158	−	0.746702i	$-0.731636\pi$
$751$	−1.54417e10	−1.33032	−0.665158	+	0.746702i	$0.731636\pi$
$752$	5.17048e8	0.0443373
$753$	0	0
$754$	−2.12272e9	−0.180340
$755$	−4.28769e9	−0.362584
$756$	0	0
$757$	1.94159e10	1.62676	0.813378	−	0.581735i	$-0.197626\pi$
$757$	1.94159e10	1.62676	0.813378	+	0.581735i	$0.197626\pi$
$758$	−3.47989e8	−0.0290217
$759$	0	0
$760$	−1.12702e9	−0.0931290
$761$	−5.03230e8	−0.0413924	−0.0206962	−	0.999786i	$-0.506588\pi$
$761$	−5.03230e8	−0.0413924	−0.0206962	+	0.999786i	$0.506588\pi$
$762$	0	0
$763$	−2.57760e7	−0.00210078
$764$	3.43925e9	0.279021
$765$	0	0
$766$	1.56338e9	0.125679
$767$	−5.91632e9	−0.473443
$768$	0	0
$769$	−1.87701e10	−1.48842	−0.744208	−	0.667948i	$-0.767173\pi$
$769$	−1.87701e10	−1.48842	−0.744208	+	0.667948i	$0.767173\pi$
$770$	−4.79454e7	−0.00378468
$771$	0	0
$772$	1.10144e10	0.861593
$773$	−2.39166e10	−1.86239	−0.931196	−	0.364518i	$-0.881234\pi$
$773$	−2.39166e10	−1.86239	−0.931196	+	0.364518i	$0.881234\pi$
$774$	0	0
$775$	5.94902e9	0.459081
$776$	7.06877e9	0.543035
$777$	0	0
$778$	−1.28676e10	−0.979649
$779$	1.15872e10	0.878210
$780$	0	0
$781$	4.17858e9	0.313870
$782$	−3.31596e9	−0.247962
$783$	0	0
$784$	−3.36563e9	−0.249436
$785$	6.97032e9	0.514291
$786$	0	0
$787$	2.09777e10	1.53408	0.767038	−	0.641602i	$-0.221730\pi$
$787$	2.09777e10	1.53408	0.767038	+	0.641602i	$0.221730\pi$
$788$	7.32964e9	0.533631
$789$	0	0
$790$	1.58618e9	0.114461
$791$	6.10991e7	0.00438952
$792$	0	0
$793$	1.97822e9	0.140870
$794$	−9.64725e9	−0.683962
$795$	0	0
$796$	−2.18012e9	−0.153209
$797$	−1.55513e10	−1.08809	−0.544043	−	0.839057i	$-0.683107\pi$
$797$	−1.55513e10	−1.08809	−0.544043	+	0.839057i	$0.683107\pi$
$798$	0	0
$799$	8.68297e8	0.0602219
$800$	2.20212e9	0.152064
$801$	0	0
$802$	5.92551e9	0.405617
$803$	5.42711e9	0.369883
$804$	0	0
$805$	−2.71332e8	−0.0183322
$806$	3.18276e9	0.214107
$807$	0	0
$808$	3.37653e9	0.225180
$809$	1.19959e10	0.796548	0.398274	−	0.917266i	$-0.369609\pi$
$809$	1.19959e10	0.796548	0.398274	+	0.917266i	$0.369609\pi$
$810$	0	0
$811$	1.18093e10	0.777412	0.388706	−	0.921362i	$-0.372922\pi$
$811$	1.18093e10	0.777412	0.388706	+	0.921362i	$0.372922\pi$
$812$	1.62802e8	0.0106712
$813$	0	0
$814$	4.06893e9	0.264420
$815$	−9.71640e8	−0.0628715
$816$	0	0
$817$	−1.46096e10	−0.937262
$818$	−1.09750e8	−0.00701079
$819$	0	0
$820$	3.67943e9	0.233041
$821$	1.96308e10	1.23805	0.619024	−	0.785372i	$-0.287528\pi$
$821$	1.96308e10	1.23805	0.619024	+	0.785372i	$0.287528\pi$
$822$	0	0
$823$	−2.67601e9	−0.167336	−0.0836679	−	0.996494i	$-0.526663\pi$
$823$	−2.67601e9	−0.167336	−0.0836679	+	0.996494i	$0.526663\pi$
$824$	1.01779e10	0.633744
$825$	0	0
$826$	4.53752e8	0.0280149
$827$	−9.26722e8	−0.0569745	−0.0284872	−	0.999594i	$-0.509069\pi$
$827$	−9.26722e8	−0.0569745	−0.0284872	+	0.999594i	$0.509069\pi$
$828$	0	0
$829$	−2.94467e10	−1.79513	−0.897565	−	0.440882i	$-0.854666\pi$
$829$	−2.94467e10	−1.79513	−0.897565	+	0.440882i	$0.854666\pi$
$830$	−5.42811e9	−0.329515
$831$	0	0
$832$	1.17815e9	0.0709199
$833$	−5.65201e9	−0.338802
$834$	0	0
$835$	−6.20001e9	−0.368544
$836$	1.79423e9	0.106208
$837$	0	0
$838$	1.56477e10	0.918536
$839$	8.93988e9	0.522595	0.261297	−	0.965258i	$-0.415850\pi$
$839$	8.93988e9	0.522595	0.261297	+	0.965258i	$0.415850\pi$
$840$	0	0
$841$	−1.37642e10	−0.797931
$842$	1.84888e10	1.06737
$843$	0	0
$844$	−1.11544e10	−0.638628
$845$	4.44674e9	0.253538
$846$	0	0
$847$	7.63296e7	0.00431619
$848$	4.90761e9	0.276366
$849$	0	0
$850$	3.69810e9	0.206544
$851$	2.30268e10	1.28080
$852$	0	0
$853$	1.71708e10	0.947257	0.473628	−	0.880725i	$-0.342944\pi$
$853$	1.71708e10	0.947257	0.473628	+	0.880725i	$0.342944\pi$
$854$	−1.51720e8	−0.00833565
$855$	0	0
$856$	1.07281e10	0.584606
$857$	7.71458e9	0.418677	0.209339	−	0.977843i	$-0.432869\pi$
$857$	7.71458e9	0.418677	0.209339	+	0.977843i	$0.432869\pi$
$858$	0	0
$859$	1.68606e10	0.907606	0.453803	−	0.891102i	$-0.350067\pi$
$859$	1.68606e10	0.907606	0.453803	+	0.891102i	$0.350067\pi$
$860$	−4.63916e9	−0.248711
$861$	0	0
$862$	−1.62817e10	−0.865813
$863$	2.42922e10	1.28656	0.643278	−	0.765633i	$-0.277574\pi$
$863$	2.42922e10	1.28656	0.643278	+	0.765633i	$0.277574\pi$
$864$	0	0
$865$	1.25404e10	0.658802
$866$	−2.24822e10	−1.17632
$867$	0	0
$868$	−2.44102e8	−0.0126693
$869$	−2.52521e9	−0.130535
$870$	0	0
$871$	1.60161e10	0.821283
$872$	3.06301e8	0.0156438
$873$	0	0
$874$	1.01539e10	0.514449
$875$	6.54379e8	0.0330218
$876$	0	0
$877$	2.67740e10	1.34034	0.670169	−	0.742209i	$-0.266222\pi$
$877$	2.67740e10	1.34034	0.670169	+	0.742209i	$0.266222\pi$
$878$	−1.26580e10	−0.631154
$879$	0	0
$880$	5.69744e8	0.0281832
$881$	−1.10654e10	−0.545197	−0.272598	−	0.962128i	$-0.587883\pi$
$881$	−1.10654e10	−0.545197	−0.272598	+	0.962128i	$0.587883\pi$
$882$	0	0
$883$	2.06264e10	1.00824	0.504118	−	0.863635i	$-0.331818\pi$
$883$	2.06264e10	1.00824	0.504118	+	0.863635i	$0.331818\pi$
$884$	1.97850e9	0.0963282
$885$	0	0
$886$	−3.91191e9	−0.188961
$887$	7.62436e9	0.366835	0.183417	−	0.983035i	$-0.441284\pi$
$887$	7.62436e9	0.366835	0.183417	+	0.983035i	$0.441284\pi$
$888$	0	0
$889$	−8.31512e8	−0.0396928
$890$	−7.71701e9	−0.366931
$891$	0	0
$892$	9.32672e9	0.439999
$893$	−2.65884e9	−0.124943
$894$	0	0
$895$	3.33264e9	0.155385
$896$	−9.03580e7	−0.00419651
$897$	0	0
$898$	1.44857e10	0.667534
$899$	−5.22633e9	−0.239904
$900$	0	0
$901$	8.24151e9	0.375379
$902$	−5.85770e9	−0.265769
$903$	0	0
$904$	−7.26052e8	−0.0326872
$905$	−2.24334e9	−0.100606
$906$	0	0
$907$	−3.36091e10	−1.49566	−0.747828	−	0.663893i	$-0.768903\pi$
$907$	−3.36091e10	−1.49566	−0.747828	+	0.663893i	$0.768903\pi$
$908$	8.13454e9	0.360606
$909$	0	0
$910$	1.61893e8	0.00712170
$911$	3.89170e10	1.70540	0.852698	−	0.522404i	$-0.174965\pi$
$911$	3.89170e10	1.70540	0.852698	+	0.522404i	$0.174965\pi$
$912$	0	0
$913$	8.64161e9	0.375791
$914$	6.91449e9	0.299536
$915$	0	0
$916$	−8.30400e9	−0.356987
$917$	−1.82017e9	−0.0779507
$918$	0	0
$919$	4.35993e10	1.85300	0.926499	−	0.376296i	$-0.122803\pi$
$919$	4.35993e10	1.85300	0.926499	+	0.376296i	$0.122803\pi$
$920$	3.22429e9	0.136514
$921$	0	0
$922$	3.88344e9	0.163177
$923$	−1.41094e10	−0.590614
$924$	0	0
$925$	−2.56805e10	−1.06686
$926$	−1.48301e10	−0.613768
$927$	0	0
$928$	−1.93461e9	−0.0794648
$929$	3.06911e10	1.25591	0.627954	−	0.778250i	$-0.283892\pi$
$929$	3.06911e10	1.25591	0.627954	+	0.778250i	$0.283892\pi$
$930$	0	0
$931$	1.73072e10	0.702915
$932$	9.74143e9	0.394155
$933$	0	0
$934$	2.52954e8	0.0101584
$935$	9.56790e8	0.0382804
$936$	0	0
$937$	3.51153e9	0.139446	0.0697232	−	0.997566i	$-0.477788\pi$
$937$	3.51153e9	0.139446	0.0697232	+	0.997566i	$0.477788\pi$
$938$	−1.22835e9	−0.0485975
$939$	0	0
$940$	−8.44293e8	−0.0331547
$941$	1.84266e10	0.720911	0.360455	−	0.932776i	$-0.382621\pi$
$941$	1.84266e10	0.720911	0.360455	+	0.932776i	$0.382621\pi$
$942$	0	0
$943$	−3.31498e10	−1.28733
$944$	−5.39203e9	−0.208617
$945$	0	0
$946$	7.38559e9	0.283639
$947$	−8.78798e9	−0.336251	−0.168126	−	0.985766i	$-0.553771\pi$
$947$	−8.78798e9	−0.336251	−0.168126	+	0.985766i	$0.553771\pi$
$948$	0	0
$949$	−1.83253e10	−0.696015
$950$	−1.13241e10	−0.428519
$951$	0	0
$952$	−1.51741e8	−0.00569999
$953$	−1.85304e10	−0.693521	−0.346761	−	0.937954i	$-0.612718\pi$
$953$	−1.85304e10	−0.693521	−0.346761	+	0.937954i	$0.612718\pi$
$954$	0	0
$955$	−5.61598e9	−0.208648
$956$	1.55559e10	0.575827
$957$	0	0
$958$	−2.49470e10	−0.916725
$959$	3.29991e8	0.0120819
$960$	0	0
$961$	−1.96764e10	−0.715176
$962$	−1.37392e10	−0.497564
$963$	0	0
$964$	−4.38139e9	−0.157522
$965$	−1.79856e10	−0.644286
$966$	0	0
$967$	4.71498e10	1.67682	0.838412	−	0.545037i	$-0.183484\pi$
$967$	4.71498e10	1.67682	0.838412	+	0.545037i	$0.183484\pi$
$968$	−9.07039e8	−0.0321412
$969$	0	0
$970$	−1.15427e10	−0.406073
$971$	8.76215e9	0.307145	0.153572	−	0.988137i	$-0.450922\pi$
$971$	8.76215e9	0.307145	0.153572	+	0.988137i	$0.450922\pi$
$972$	0	0
$973$	−6.29135e8	−0.0218952
$974$	2.70086e10	0.936583
$975$	0	0
$976$	1.80291e9	0.0620727
$977$	6.33661e9	0.217383	0.108692	−	0.994076i	$-0.465334\pi$
$977$	6.33661e9	0.217383	0.108692	+	0.994076i	$0.465334\pi$
$978$	0	0
$979$	1.22856e10	0.418462
$980$	5.49576e9	0.186525
$981$	0	0
$982$	−3.64035e10	−1.22674
$983$	−4.47312e10	−1.50201	−0.751006	−	0.660295i	$-0.770431\pi$
$983$	−4.47312e10	−1.50201	−0.751006	+	0.660295i	$0.770431\pi$
$984$	0	0
$985$	−1.19686e10	−0.399041
$986$	−3.24885e9	−0.107934
$987$	0	0
$988$	−6.05843e9	−0.199853
$989$	4.17964e10	1.37389
$990$	0	0
$991$	4.62109e10	1.50830	0.754148	−	0.656705i	$-0.228050\pi$
$991$	4.62109e10	1.50830	0.754148	+	0.656705i	$0.228050\pi$
$992$	2.90071e9	0.0943437
$993$	0	0
$994$	1.08212e9	0.0349482
$995$	3.55994e9	0.114567
$996$	0	0
$997$	−1.52392e10	−0.487001	−0.243501	−	0.969901i	$-0.578296\pi$
$997$	−1.52392e10	−0.487001	−0.243501	+	0.969901i	$0.578296\pi$
$998$	5.00587e9	0.159413
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.8.a.f.1.2		2
3.2	odd	2		22.8.a.d.1.2	✓	2
12.11	even	2		176.8.a.e.1.1		2
15.14	odd	2		550.8.a.d.1.1		2
33.32	even	2		242.8.a.h.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.8.a.d.1.2	✓	2	3.2	odd	2
176.8.a.e.1.1		2	12.11	even	2
198.8.a.f.1.2		2	1.1	even	1	trivial
242.8.a.h.1.2		2	33.32	even	2
550.8.a.d.1.1		2	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	198.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} +64.0000 q^{4} -104.506 q^{5} +43.0861 q^{7} -512.000 q^{8} +O(q^{10})\)	\(q-8.00000 q^{2} +64.0000 q^{4} -104.506 q^{5} +43.0861 q^{7} -512.000 q^{8} +836.049 q^{10} -1331.00 q^{11} +4494.27 q^{13} -344.689 q^{14} +4096.00 q^{16} +6878.55 q^{17} -21063.0 q^{19} -6688.39 q^{20} +10648.0 q^{22} +60259.0 q^{23} -67203.5 q^{25} -35954.2 q^{26} +2757.51 q^{28} +59039.5 q^{29} -88522.5 q^{31} -32768.0 q^{32} -55028.4 q^{34} -4502.76 q^{35} +382131. q^{37} +168504. q^{38} +53507.1 q^{40} -550122. q^{41} +693613. q^{43} -85184.0 q^{44} -482072. q^{46} +126233. q^{47} -821687. q^{49} +537628. q^{50} +287634. q^{52} +1.19815e6 q^{53} +139098. q^{55} -22060.1 q^{56} -472316. q^{58} -1.31641e6 q^{59} +440165. q^{61} +708180. q^{62} +262144. q^{64} -469679. q^{65} +3.56366e6 q^{67} +440227. q^{68} +36022.1 q^{70} -3.13943e6 q^{71} -4.07747e6 q^{73} -3.05705e6 q^{74} -1.34803e6 q^{76} -57347.6 q^{77} +1.89723e6 q^{79} -428057. q^{80} +4.40097e6 q^{82} -6.49257e6 q^{83} -718851. q^{85} -5.54890e6 q^{86} +681472. q^{88} -9.23033e6 q^{89} +193641. q^{91} +3.85658e6 q^{92} -1.00986e6 q^{94} +2.20122e6 q^{95} -1.38062e7 q^{97} +6.57349e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 16 q^{2} + 128 q^{4} - 331 q^{5} + 1794 q^{7} - 1024 q^{8}+O(q^{10}) \) 2 * q - 16 * q^2 + 128 * q^4 - 331 * q^5 + 1794 * q^7 - 1024 * q^8	\( 2 q - 16 q^{2} + 128 q^{4} - 331 q^{5} + 1794 q^{7} - 1024 q^{8} + 2648 q^{10} - 2662 q^{11} - 5406 q^{13} - 14352 q^{14} + 8192 q^{16} - 15032 q^{17} + 16916 q^{19} - 21184 q^{20} + 21296 q^{22} + 51351 q^{23} - 94029 q^{25} + 43248 q^{26} + 114816 q^{28} + 207130 q^{29} - 19071 q^{31} - 65536 q^{32} + 120256 q^{34} - 401074 q^{35} + 351333 q^{37} - 135328 q^{38} + 169472 q^{40} - 123610 q^{41} - 159822 q^{43} - 170368 q^{44} - 410808 q^{46} - 451160 q^{47} + 1420470 q^{49} + 752232 q^{50} - 345984 q^{52} + 1260832 q^{53} + 440561 q^{55} - 918528 q^{56} - 1657040 q^{58} - 887547 q^{59} - 597918 q^{61} + 152568 q^{62} + 524288 q^{64} + 1772672 q^{65} + 2864711 q^{67} - 962048 q^{68} + 3208592 q^{70} - 1306267 q^{71} - 4577530 q^{73} - 2810664 q^{74} + 1082624 q^{76} - 2387814 q^{77} - 2946342 q^{79} - 1355776 q^{80} + 988880 q^{82} - 9965450 q^{83} + 4243754 q^{85} + 1278576 q^{86} + 1362944 q^{88} - 10185377 q^{89} - 17140888 q^{91} + 3286464 q^{92} + 3609280 q^{94} - 6400800 q^{95} - 27765477 q^{97} - 11363760 q^{98}+O(q^{100}) \) 2 * q - 16 * q^2 + 128 * q^4 - 331 * q^5 + 1794 * q^7 - 1024 * q^8 + 2648 * q^10 - 2662 * q^11 - 5406 * q^13 - 14352 * q^14 + 8192 * q^16 - 15032 * q^17 + 16916 * q^19 - 21184 * q^20 + 21296 * q^22 + 51351 * q^23 - 94029 * q^25 + 43248 * q^26 + 114816 * q^28 + 207130 * q^29 - 19071 * q^31 - 65536 * q^32 + 120256 * q^34 - 401074 * q^35 + 351333 * q^37 - 135328 * q^38 + 169472 * q^40 - 123610 * q^41 - 159822 * q^43 - 170368 * q^44 - 410808 * q^46 - 451160 * q^47 + 1420470 * q^49 + 752232 * q^50 - 345984 * q^52 + 1260832 * q^53 + 440561 * q^55 - 918528 * q^56 - 1657040 * q^58 - 887547 * q^59 - 597918 * q^61 + 152568 * q^62 + 524288 * q^64 + 1772672 * q^65 + 2864711 * q^67 - 962048 * q^68 + 3208592 * q^70 - 1306267 * q^71 - 4577530 * q^73 - 2810664 * q^74 + 1082624 * q^76 - 2387814 * q^77 - 2946342 * q^79 - 1355776 * q^80 + 988880 * q^82 - 9965450 * q^83 + 4243754 * q^85 + 1278576 * q^86 + 1362944 * q^88 - 10185377 * q^89 - 17140888 * q^91 + 3286464 * q^92 + 3609280 * q^94 - 6400800 * q^95 - 27765477 * q^97 - 11363760 * q^98

Introduction

L-functions

Modular forms

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