LMFDB - Embedded newform 414.8.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,8,Mod(1,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, 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("414.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	414.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:	$129.327400550$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 8367x^{2} - 89140x + 11077220 $ x^4 - 2x^3 - 8367x^2 - 89140*x + 11077220
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5}\cdot 3 $
Twist minimal:	no (minimal twist has level 138)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-65.5856$ of defining polynomial
Character	$\chi$	$=$	414.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} +64.0000 q^{4} -340.987 q^{5} +1267.12 q^{7} -512.000 q^{8} +O(q^{10})$	\(q-8.00000 q^{2} +64.0000 q^{4} -340.987 q^{5} +1267.12 q^{7} -512.000 q^{8} +2727.89 q^{10} -5101.25 q^{11} -5814.29 q^{13} -10137.0 q^{14} +4096.00 q^{16} -6404.73 q^{17} -38566.6 q^{19} -21823.2 q^{20} +40810.0 q^{22} +12167.0 q^{23} +38147.0 q^{25} +46514.3 q^{26} +81095.7 q^{28} +208061. q^{29} +3653.78 q^{31} -32768.0 q^{32} +51237.9 q^{34} -432071. q^{35} +23930.9 q^{37} +308533. q^{38} +174585. q^{40} +1151.50 q^{41} -489302. q^{43} -326480. q^{44} -97336.0 q^{46} -988907. q^{47} +782050. q^{49} -305176. q^{50} -372115. q^{52} +777027. q^{53} +1.73946e6 q^{55} -648766. q^{56} -1.66449e6 q^{58} -1.61187e6 q^{59} -1.04092e6 q^{61} -29230.2 q^{62} +262144. q^{64} +1.98260e6 q^{65} -2.06066e6 q^{67} -409903. q^{68} +3.45657e6 q^{70} -3.58392e6 q^{71} -975850. q^{73} -191447. q^{74} -2.46826e6 q^{76} -6.46390e6 q^{77} +6.00359e6 q^{79} -1.39668e6 q^{80} -9212.01 q^{82} +5.40252e6 q^{83} +2.18393e6 q^{85} +3.91441e6 q^{86} +2.61184e6 q^{88} +4.13911e6 q^{89} -7.36740e6 q^{91} +778688. q^{92} +7.91125e6 q^{94} +1.31507e7 q^{95} +1.18844e7 q^{97} -6.25640e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 32 q^{2} + 256 q^{4} - 270 q^{5} + 2022 q^{7} - 2048 q^{8}+O(q^{10}) $ 4 * q - 32 * q^2 + 256 * q^4 - 270 * q^5 + 2022 * q^7 - 2048 * q^8	\( 4 q - 32 q^{2} + 256 q^{4} - 270 q^{5} + 2022 q^{7} - 2048 q^{8} + 2160 q^{10} - 4120 q^{11} + 8036 q^{13} - 16176 q^{14} + 16384 q^{16} - 37182 q^{17} + 5702 q^{19} - 17280 q^{20} + 32960 q^{22} + 48668 q^{23} + 121480 q^{25} - 64288 q^{26} + 129408 q^{28} - 217716 q^{29} + 222852 q^{31} - 131072 q^{32} + 297456 q^{34} - 68440 q^{35} + 486428 q^{37} - 45616 q^{38} + 138240 q^{40} - 338336 q^{41} + 730974 q^{43} - 263680 q^{44} - 389344 q^{46} - 338248 q^{47} - 310552 q^{49} - 971840 q^{50} + 514304 q^{52} + 375502 q^{53} + 424840 q^{55} - 1035264 q^{56} + 1741728 q^{58} - 71392 q^{59} + 2101164 q^{61} - 1782816 q^{62} + 1048576 q^{64} - 1578780 q^{65} + 4337162 q^{67} - 2379648 q^{68} + 547520 q^{70} - 2288016 q^{71} - 1107328 q^{73} - 3891424 q^{74} + 364928 q^{76} - 5826200 q^{77} + 60610 q^{79} - 1105920 q^{80} + 2706688 q^{82} - 1485464 q^{83} - 8843820 q^{85} - 5847792 q^{86} + 2109440 q^{88} - 1485090 q^{89} - 2898412 q^{91} + 3114752 q^{92} + 2705984 q^{94} - 8545200 q^{95} + 1935444 q^{97} + 2484416 q^{98}+O(q^{100}) \) 4 * q - 32 * q^2 + 256 * q^4 - 270 * q^5 + 2022 * q^7 - 2048 * q^8 + 2160 * q^10 - 4120 * q^11 + 8036 * q^13 - 16176 * q^14 + 16384 * q^16 - 37182 * q^17 + 5702 * q^19 - 17280 * q^20 + 32960 * q^22 + 48668 * q^23 + 121480 * q^25 - 64288 * q^26 + 129408 * q^28 - 217716 * q^29 + 222852 * q^31 - 131072 * q^32 + 297456 * q^34 - 68440 * q^35 + 486428 * q^37 - 45616 * q^38 + 138240 * q^40 - 338336 * q^41 + 730974 * q^43 - 263680 * q^44 - 389344 * q^46 - 338248 * q^47 - 310552 * q^49 - 971840 * q^50 + 514304 * q^52 + 375502 * q^53 + 424840 * q^55 - 1035264 * q^56 + 1741728 * q^58 - 71392 * q^59 + 2101164 * q^61 - 1782816 * q^62 + 1048576 * q^64 - 1578780 * q^65 + 4337162 * q^67 - 2379648 * q^68 + 547520 * q^70 - 2288016 * q^71 - 1107328 * q^73 - 3891424 * q^74 + 364928 * q^76 - 5826200 * q^77 + 60610 * q^79 - 1105920 * q^80 + 2706688 * q^82 - 1485464 * q^83 - 8843820 * q^85 - 5847792 * q^86 + 2109440 * q^88 - 1485090 * q^89 - 2898412 * q^91 + 3114752 * q^92 + 2705984 * q^94 - 8545200 * q^95 + 1935444 * q^97 + 2484416 * 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
$5$	−340.987	−1.21995	−0.609976	−	0.792420i	$-0.708821\pi$
$5$	−340.987	−1.21995	−0.609976	+	0.792420i	$0.708821\pi$
$6$	0	0
$7$	1267.12	1.39629	0.698143	−	0.715958i	$-0.254010\pi$
$7$	1267.12	1.39629	0.698143	+	0.715958i	$0.254010\pi$
$8$	−512.000	−0.353553
$9$	0	0
$10$	2727.89	0.862636
$11$	−5101.25	−1.15559	−0.577793	−	0.816183i	$-0.696086\pi$
$11$	−5101.25	−1.15559	−0.577793	+	0.816183i	$0.696086\pi$
$12$	0	0
$13$	−5814.29	−0.733998	−0.366999	−	0.930221i	$-0.619615\pi$
$13$	−5814.29	−0.733998	−0.366999	+	0.930221i	$0.619615\pi$
$14$	−10137.0	−0.987324
$15$	0	0
$16$	4096.00	0.250000
$17$	−6404.73	−0.316177	−0.158088	−	0.987425i	$-0.550533\pi$
$17$	−6404.73	−0.316177	−0.158088	+	0.987425i	$0.550533\pi$
$18$	0	0
$19$	−38566.6	−1.28995	−0.644977	−	0.764202i	$-0.723133\pi$
$19$	−38566.6	−1.28995	−0.644977	+	0.764202i	$0.723133\pi$
$20$	−21823.2	−0.609976
$21$	0	0
$22$	40810.0	0.817122
$23$	12167.0	0.208514
$23$	12167.0	0.208514
$24$	0	0
$25$	38147.0	0.488281
$26$	46514.3	0.519015
$27$	0	0
$28$	81095.7	0.698143
$29$	208061.	1.58415	0.792077	−	0.610422i	$-0.209000\pi$
$29$	208061.	1.58415	0.792077	+	0.610422i	$0.209000\pi$
$30$	0	0
$31$	3653.78	0.0220281	0.0110140	−	0.999939i	$-0.496494\pi$
$31$	3653.78	0.0220281	0.0110140	+	0.999939i	$0.496494\pi$
$32$	−32768.0	−0.176777
$33$	0	0
$34$	51237.9	0.223571
$35$	−432071.	−1.70340
$36$	0	0
$37$	23930.9	0.0776699	0.0388350	−	0.999246i	$-0.487635\pi$
$37$	23930.9	0.0776699	0.0388350	+	0.999246i	$0.487635\pi$
$38$	308533.	0.912135
$39$	0	0
$40$	174585.	0.431318
$41$	1151.50	0.00260928	0.00130464	−	0.999999i	$-0.499585\pi$
$41$	1151.50	0.00260928	0.00130464	+	0.999999i	$0.499585\pi$
$42$	0	0
$43$	−489302.	−0.938506	−0.469253	−	0.883064i	$-0.655477\pi$
$43$	−489302.	−0.938506	−0.469253	+	0.883064i	$0.655477\pi$
$44$	−326480.	−0.577793
$45$	0	0
$46$	−97336.0	−0.147442
$47$	−988907.	−1.38935	−0.694677	−	0.719322i	$-0.744453\pi$
$47$	−988907.	−1.38935	−0.694677	+	0.719322i	$0.744453\pi$
$48$	0	0
$49$	782050.	0.949617
$50$	−305176.	−0.345267
$51$	0	0
$52$	−372115.	−0.366999
$53$	777027.	0.716920	0.358460	−	0.933545i	$-0.383302\pi$
$53$	777027.	0.716920	0.358460	+	0.933545i	$0.383302\pi$
$54$	0	0
$55$	1.73946e6	1.40976
$56$	−648766.	−0.493662
$57$	0	0
$58$	−1.66449e6	−1.12017
$59$	−1.61187e6	−1.02176	−0.510879	−	0.859652i	$-0.670680\pi$
$59$	−1.61187e6	−1.02176	−0.510879	+	0.859652i	$0.670680\pi$
$60$	0	0
$61$	−1.04092e6	−0.587171	−0.293586	−	0.955933i	$-0.594849\pi$
$61$	−1.04092e6	−0.587171	−0.293586	+	0.955933i	$0.594849\pi$
$62$	−29230.2	−0.0155762
$63$	0	0
$64$	262144.	0.125000
$65$	1.98260e6	0.895442
$66$	0	0
$67$	−2.06066e6	−0.837036	−0.418518	−	0.908209i	$-0.637450\pi$
$67$	−2.06066e6	−0.837036	−0.418518	+	0.908209i	$0.637450\pi$
$68$	−409903.	−0.158088
$69$	0	0
$70$	3.45657e6	1.20449
$71$	−3.58392e6	−1.18838	−0.594189	−	0.804325i	$-0.702527\pi$
$71$	−3.58392e6	−1.18838	−0.594189	+	0.804325i	$0.702527\pi$
$72$	0	0
$73$	−975850.	−0.293598	−0.146799	−	0.989166i	$-0.546897\pi$
$73$	−975850.	−0.293598	−0.146799	+	0.989166i	$0.546897\pi$
$74$	−191447.	−0.0549209
$75$	0	0
$76$	−2.46826e6	−0.644977
$77$	−6.46390e6	−1.61353
$78$	0	0
$79$	6.00359e6	1.36999	0.684993	−	0.728550i	$-0.259805\pi$
$79$	6.00359e6	1.36999	0.684993	+	0.728550i	$0.259805\pi$
$80$	−1.39668e6	−0.304988
$81$	0	0
$82$	−9212.01	−0.00184504
$83$	5.40252e6	1.03711	0.518553	−	0.855046i	$-0.326471\pi$
$83$	5.40252e6	1.03711	0.518553	+	0.855046i	$0.326471\pi$
$84$	0	0
$85$	2.18393e6	0.385720
$86$	3.91441e6	0.663624
$87$	0	0
$88$	2.61184e6	0.408561
$89$	4.13911e6	0.622361	0.311180	−	0.950351i	$-0.399276\pi$
$89$	4.13911e6	0.622361	0.311180	+	0.950351i	$0.399276\pi$
$90$	0	0
$91$	−7.36740e6	−1.02487
$92$	778688.	0.104257
$93$	0	0
$94$	7.91125e6	0.982422
$95$	1.31507e7	1.57368
$96$	0	0
$97$	1.18844e7	1.32214	0.661070	−	0.750324i	$-0.270103\pi$
$97$	1.18844e7	1.32214	0.661070	+	0.750324i	$0.270103\pi$
$98$	−6.25640e6	−0.671481
$99$	0	0
$100$	2.44141e6	0.244141
$101$	−9.54327e6	−0.921663	−0.460832	−	0.887488i	$-0.652449\pi$
$101$	−9.54327e6	−0.921663	−0.460832	+	0.887488i	$0.652449\pi$
$102$	0	0
$103$	−3.12347e6	−0.281648	−0.140824	−	0.990035i	$-0.544975\pi$
$103$	−3.12347e6	−0.281648	−0.140824	+	0.990035i	$0.544975\pi$
$104$	2.97692e6	0.259508
$105$	0	0
$106$	−6.21621e6	−0.506939
$107$	−1.02468e7	−0.808620	−0.404310	−	0.914622i	$-0.632488\pi$
$107$	−1.02468e7	−0.808620	−0.404310	+	0.914622i	$0.632488\pi$
$108$	0	0
$109$	−1.26733e7	−0.937337	−0.468668	−	0.883374i	$-0.655266\pi$
$109$	−1.26733e7	−0.937337	−0.468668	+	0.883374i	$0.655266\pi$
$110$	−1.39157e7	−0.996850
$111$	0	0
$112$	5.19012e6	0.349072
$113$	−543321.	−0.0354227	−0.0177114	−	0.999843i	$-0.505638\pi$
$113$	−543321.	−0.0354227	−0.0177114	+	0.999843i	$0.505638\pi$
$114$	0	0
$115$	−4.14879e6	−0.254377
$116$	1.33159e7	0.792077
$117$	0	0
$118$	1.28950e7	0.722493
$119$	−8.11557e6	−0.441473
$120$	0	0
$121$	6.53557e6	0.335378
$122$	8.32740e6	0.415193
$123$	0	0
$124$	233842.	0.0110140
$125$	1.36320e7	0.624272
$126$	0	0
$127$	−6.08628e6	−0.263657	−0.131828	−	0.991273i	$-0.542085\pi$
$127$	−6.08628e6	−0.263657	−0.131828	+	0.991273i	$0.542085\pi$
$128$	−2.09715e6	−0.0883883
$129$	0	0
$130$	−1.58608e7	−0.633173
$131$	2.60740e7	1.01335	0.506674	−	0.862138i	$-0.330875\pi$
$131$	2.60740e7	1.01335	0.506674	+	0.862138i	$0.330875\pi$
$132$	0	0
$133$	−4.88686e7	−1.80115
$134$	1.64853e7	0.591874
$135$	0	0
$136$	3.27922e6	0.111785
$137$	−4.55380e7	−1.51304	−0.756522	−	0.653968i	$-0.773103\pi$
$137$	−4.55380e7	−1.51304	−0.756522	+	0.653968i	$0.773103\pi$
$138$	0	0
$139$	−4.36079e7	−1.37725	−0.688626	−	0.725116i	$-0.741786\pi$
$139$	−4.36079e7	−1.37725	−0.688626	+	0.725116i	$0.741786\pi$
$140$	−2.76526e7	−0.851701
$141$	0	0
$142$	2.86714e7	0.840310
$143$	2.96601e7	0.848198
$144$	0	0
$145$	−7.09460e7	−1.93259
$146$	7.80680e6	0.207605
$147$	0	0
$148$	1.53158e6	0.0388350
$149$	7.44370e7	1.84347	0.921737	−	0.387816i	$-0.126770\pi$
$149$	7.44370e7	1.84347	0.921737	+	0.387816i	$0.126770\pi$
$150$	0	0
$151$	2.77945e7	0.656962	0.328481	−	0.944511i	$-0.393463\pi$
$151$	2.77945e7	0.656962	0.328481	+	0.944511i	$0.393463\pi$
$152$	1.97461e7	0.456067
$153$	0	0
$154$	5.17112e7	1.14094
$155$	−1.24589e6	−0.0268732
$156$	0	0
$157$	3.33077e7	0.686904	0.343452	−	0.939170i	$-0.388404\pi$
$157$	3.33077e7	0.686904	0.343452	+	0.939170i	$0.388404\pi$
$158$	−4.80287e7	−0.968726
$159$	0	0
$160$	1.11735e7	0.215659
$161$	1.54171e7	0.291146
$162$	0	0
$163$	−1.45963e7	−0.263989	−0.131994	−	0.991250i	$-0.542138\pi$
$163$	−1.45963e7	−0.263989	−0.131994	+	0.991250i	$0.542138\pi$
$164$	73696.1	0.00130464
$165$	0	0
$166$	−4.32201e7	−0.733344
$167$	7.61604e7	1.26538	0.632691	−	0.774404i	$-0.281950\pi$
$167$	7.61604e7	1.26538	0.632691	+	0.774404i	$0.281950\pi$
$168$	0	0
$169$	−2.89426e7	−0.461247
$170$	−1.74714e7	−0.272745
$171$	0	0
$172$	−3.13153e7	−0.469253
$173$	1.17815e8	1.72997	0.864983	−	0.501801i	$-0.167329\pi$
$173$	1.17815e8	1.72997	0.864983	+	0.501801i	$0.167329\pi$
$174$	0	0
$175$	4.83368e7	0.681781
$176$	−2.08947e7	−0.288896
$177$	0	0
$178$	−3.31129e7	−0.440075
$179$	−2.34279e7	−0.305314	−0.152657	−	0.988279i	$-0.548783\pi$
$179$	−2.34279e7	−0.305314	−0.152657	+	0.988279i	$0.548783\pi$
$180$	0	0
$181$	−5.66147e7	−0.709667	−0.354833	−	0.934930i	$-0.615462\pi$
$181$	−5.66147e7	−0.709667	−0.354833	+	0.934930i	$0.615462\pi$
$182$	5.89392e7	0.724694
$183$	0	0
$184$	−6.22950e6	−0.0737210
$185$	−8.16012e6	−0.0947535
$186$	0	0
$187$	3.26721e7	0.365369
$188$	−6.32900e7	−0.694677
$189$	0	0
$190$	−1.05206e8	−1.11276
$191$	1.26851e8	1.31727	0.658636	−	0.752461i	$-0.271134\pi$
$191$	1.26851e8	1.31727	0.658636	+	0.752461i	$0.271134\pi$
$192$	0	0
$193$	1.36553e8	1.36726	0.683630	−	0.729828i	$-0.260400\pi$
$193$	1.36553e8	1.36726	0.683630	+	0.729828i	$0.260400\pi$
$194$	−9.50755e7	−0.934894
$195$	0	0
$196$	5.00512e7	0.474808
$197$	1.16049e8	1.08146	0.540729	−	0.841197i	$-0.318148\pi$
$197$	1.16049e8	1.08146	0.540729	+	0.841197i	$0.318148\pi$
$198$	0	0
$199$	1.41367e7	0.127163	0.0635816	−	0.997977i	$-0.479748\pi$
$199$	1.41367e7	0.127163	0.0635816	+	0.997977i	$0.479748\pi$
$200$	−1.95312e7	−0.172633
$201$	0	0
$202$	7.63462e7	0.651714
$203$	2.63638e8	2.21193
$204$	0	0
$205$	−392647.	−0.00318320
$206$	2.49877e7	0.199155
$207$	0	0
$208$	−2.38153e7	−0.183500
$209$	1.96738e8	1.49065
$210$	0	0
$211$	1.88579e8	1.38199	0.690993	−	0.722861i	$-0.257173\pi$
$211$	1.88579e8	1.38199	0.690993	+	0.722861i	$0.257173\pi$
$212$	4.97297e7	0.358460
$213$	0	0
$214$	8.19743e7	0.571781
$215$	1.66845e8	1.14493
$216$	0	0
$217$	4.62978e6	0.0307575
$218$	1.01386e8	0.662797
$219$	0	0
$220$	1.11325e8	0.704879
$221$	3.72390e7	0.232073
$222$	0	0
$223$	3.17153e8	1.91515	0.957573	−	0.288192i	$-0.0930542\pi$
$223$	3.17153e8	1.91515	0.957573	+	0.288192i	$0.0930542\pi$
$224$	−4.15210e7	−0.246831
$225$	0	0
$226$	4.34657e6	0.0250476
$227$	−9.71697e6	−0.0551366	−0.0275683	−	0.999620i	$-0.508776\pi$
$227$	−9.71697e6	−0.0551366	−0.0275683	+	0.999620i	$0.508776\pi$
$228$	0	0
$229$	2.54644e8	1.40123	0.700614	−	0.713540i	$-0.252909\pi$
$229$	2.54644e8	1.40123	0.700614	+	0.713540i	$0.252909\pi$
$230$	3.31903e7	0.179872
$231$	0	0
$232$	−1.06527e8	−0.560083
$233$	−2.64155e7	−0.136808	−0.0684042	−	0.997658i	$-0.521791\pi$
$233$	−2.64155e7	−0.136808	−0.0684042	+	0.997658i	$0.521791\pi$
$234$	0	0
$235$	3.37204e8	1.69494
$236$	−1.03160e8	−0.510879
$237$	0	0
$238$	6.49245e7	0.312169
$239$	1.27674e7	0.0604936	0.0302468	−	0.999542i	$-0.490371\pi$
$239$	1.27674e7	0.0604936	0.0302468	+	0.999542i	$0.490371\pi$
$240$	0	0
$241$	1.47494e8	0.678757	0.339379	−	0.940650i	$-0.389783\pi$
$241$	1.47494e8	0.678757	0.339379	+	0.940650i	$0.389783\pi$
$242$	−5.22845e7	−0.237148
$243$	0	0
$244$	−6.66192e7	−0.293586
$245$	−2.66669e8	−1.15849
$246$	0	0
$247$	2.24238e8	0.946823
$248$	−1.87074e6	−0.00778810
$249$	0	0
$250$	−1.09056e8	−0.441427
$251$	−2.67374e8	−1.06724	−0.533618	−	0.845726i	$-0.679168\pi$
$251$	−2.67374e8	−1.06724	−0.533618	+	0.845726i	$0.679168\pi$
$252$	0	0
$253$	−6.20669e7	−0.240956
$254$	4.86902e7	0.186433
$255$	0	0
$256$	1.67772e7	0.0625000
$257$	1.37033e8	0.503568	0.251784	−	0.967784i	$-0.418983\pi$
$257$	1.37033e8	0.503568	0.251784	+	0.967784i	$0.418983\pi$
$258$	0	0
$259$	3.03233e7	0.108449
$260$	1.26886e8	0.447721
$261$	0	0
$262$	−2.08592e8	−0.716545
$263$	−1.60586e8	−0.544329	−0.272165	−	0.962251i	$-0.587740\pi$
$263$	−1.60586e8	−0.544329	−0.272165	+	0.962251i	$0.587740\pi$
$264$	0	0
$265$	−2.64956e8	−0.874607
$266$	3.90948e8	1.27360
$267$	0	0
$268$	−1.31882e8	−0.418518
$269$	−4.67109e8	−1.46314	−0.731568	−	0.681768i	$-0.761211\pi$
$269$	−4.67109e8	−1.46314	−0.731568	+	0.681768i	$0.761211\pi$
$270$	0	0
$271$	5.51685e8	1.68383	0.841916	−	0.539609i	$-0.181428\pi$
$271$	5.51685e8	1.68383	0.841916	+	0.539609i	$0.181428\pi$
$272$	−2.62338e7	−0.0790442
$273$	0	0
$274$	3.64304e8	1.06988
$275$	−1.94597e8	−0.564251
$276$	0	0
$277$	4.78153e8	1.35172	0.675862	−	0.737028i	$-0.263772\pi$
$277$	4.78153e8	1.35172	0.675862	+	0.737028i	$0.263772\pi$
$278$	3.48863e8	0.973865
$279$	0	0
$280$	2.21220e8	0.602244
$281$	−7.37447e8	−1.98271	−0.991354	−	0.131218i	$-0.958111\pi$
$281$	−7.37447e8	−1.98271	−0.991354	+	0.131218i	$0.958111\pi$
$282$	0	0
$283$	−6.82950e8	−1.79117	−0.895584	−	0.444893i	$-0.853242\pi$
$283$	−6.82950e8	−1.79117	−0.895584	+	0.444893i	$0.853242\pi$
$284$	−2.29371e8	−0.594189
$285$	0	0
$286$	−2.37281e8	−0.599766
$287$	1.45909e6	0.00364331
$288$	0	0
$289$	−3.69318e8	−0.900032
$290$	5.67568e8	1.36655
$291$	0	0
$292$	−6.24544e7	−0.146799
$293$	4.73242e7	0.109912	0.0549562	−	0.998489i	$-0.482498\pi$
$293$	4.73242e7	0.109912	0.0549562	+	0.998489i	$0.482498\pi$
$294$	0	0
$295$	5.49627e8	1.24650
$296$	−1.22526e7	−0.0274605
$297$	0	0
$298$	−5.95496e8	−1.30353
$299$	−7.07425e7	−0.153049
$300$	0	0
$301$	−6.20004e8	−1.31042
$302$	−2.22356e8	−0.464542
$303$	0	0
$304$	−1.57969e8	−0.322488
$305$	3.54942e8	0.716321
$306$	0	0
$307$	3.47596e8	0.685630	0.342815	−	0.939403i	$-0.388620\pi$
$307$	3.47596e8	0.685630	0.342815	+	0.939403i	$0.388620\pi$
$308$	−4.13689e8	−0.806764
$309$	0	0
$310$	9.96713e6	0.0190022
$311$	8.46459e8	1.59568	0.797838	−	0.602873i	$-0.205977\pi$
$311$	8.46459e8	1.59568	0.797838	+	0.602873i	$0.205977\pi$
$312$	0	0
$313$	5.31447e8	0.979613	0.489806	−	0.871831i	$-0.337067\pi$
$313$	5.31447e8	0.979613	0.489806	+	0.871831i	$0.337067\pi$
$314$	−2.66462e8	−0.485715
$315$	0	0
$316$	3.84230e8	0.684993
$317$	7.52971e8	1.32761	0.663806	−	0.747905i	$-0.268940\pi$
$317$	7.52971e8	1.32761	0.663806	+	0.747905i	$0.268940\pi$
$318$	0	0
$319$	−1.06137e9	−1.83062
$320$	−8.93876e7	−0.152494
$321$	0	0
$322$	−1.23336e8	−0.205871
$323$	2.47009e8	0.407853
$324$	0	0
$325$	−2.21798e8	−0.358398
$326$	1.16770e8	0.186668
$327$	0	0
$328$	−589569.	−0.000922521 0
$329$	−1.25306e9	−1.93994
$330$	0	0
$331$	−1.86489e8	−0.282654	−0.141327	−	0.989963i	$-0.545137\pi$
$331$	−1.86489e8	−0.282654	−0.141327	+	0.989963i	$0.545137\pi$
$332$	3.45761e8	0.518553
$333$	0	0
$334$	−6.09284e8	−0.894760
$335$	7.02657e8	1.02114
$336$	0	0
$337$	−7.20597e8	−1.02562	−0.512811	−	0.858501i	$-0.671396\pi$
$337$	−7.20597e8	−1.02562	−0.512811	+	0.858501i	$0.671396\pi$
$338$	2.31540e8	0.326151
$339$	0	0
$340$	1.39771e8	0.192860
$341$	−1.86388e7	−0.0254553
$342$	0	0
$343$	−5.25761e7	−0.0703491
$344$	2.50522e8	0.331812
$345$	0	0
$346$	−9.42517e8	−1.22327
$347$	8.14326e8	1.04627	0.523137	−	0.852249i	$-0.324762\pi$
$347$	8.14326e8	1.04627	0.523137	+	0.852249i	$0.324762\pi$
$348$	0	0
$349$	−4.25035e8	−0.535224	−0.267612	−	0.963527i	$-0.586234\pi$
$349$	−4.25035e8	−0.535224	−0.267612	+	0.963527i	$0.586234\pi$
$350$	−3.86694e8	−0.482092
$351$	0	0
$352$	1.67158e8	0.204281
$353$	2.10866e8	0.255149	0.127575	−	0.991829i	$-0.459281\pi$
$353$	2.10866e8	0.255149	0.127575	+	0.991829i	$0.459281\pi$
$354$	0	0
$355$	1.22207e9	1.44976
$356$	2.64903e8	0.311180
$357$	0	0
$358$	1.87423e8	0.215890
$359$	9.62505e8	1.09792	0.548962	−	0.835847i	$-0.315023\pi$
$359$	9.62505e8	1.09792	0.548962	+	0.835847i	$0.315023\pi$
$360$	0	0
$361$	5.93513e8	0.663980
$362$	4.52918e8	0.501810
$363$	0	0
$364$	−4.71514e8	−0.512436
$365$	3.32752e8	0.358175
$366$	0	0
$367$	−5.91557e7	−0.0624691	−0.0312345	−	0.999512i	$-0.509944\pi$
$367$	−5.91557e7	−0.0624691	−0.0312345	+	0.999512i	$0.509944\pi$
$368$	4.98360e7	0.0521286
$369$	0	0
$370$	6.52809e7	0.0670009
$371$	9.84586e8	1.00103
$372$	0	0
$373$	−7.57694e8	−0.755984	−0.377992	−	0.925809i	$-0.623385\pi$
$373$	−7.57694e8	−0.755984	−0.377992	+	0.925809i	$0.623385\pi$
$374$	−2.61377e8	−0.258355
$375$	0	0
$376$	5.06320e8	0.491211
$377$	−1.20973e9	−1.16277
$378$	0	0
$379$	−2.47156e8	−0.233203	−0.116601	−	0.993179i	$-0.537200\pi$
$379$	−2.47156e8	−0.233203	−0.116601	+	0.993179i	$0.537200\pi$
$380$	8.41645e8	0.786840
$381$	0	0
$382$	−1.01480e9	−0.931452
$383$	1.95064e9	1.77411	0.887056	−	0.461662i	$-0.152747\pi$
$383$	1.95064e9	1.77411	0.887056	+	0.461662i	$0.152747\pi$
$384$	0	0
$385$	2.20410e9	1.96843
$386$	−1.09243e9	−0.966799
$387$	0	0
$388$	7.60604e8	0.661070
$389$	−1.70660e9	−1.46997	−0.734987	−	0.678082i	$-0.762812\pi$
$389$	−1.70660e9	−1.46997	−0.734987	+	0.678082i	$0.762812\pi$
$390$	0	0
$391$	−7.79264e7	−0.0659274
$392$	−4.00410e8	−0.335740
$393$	0	0
$394$	−9.28392e8	−0.764706
$395$	−2.04714e9	−1.67132
$396$	0	0
$397$	9.51729e8	0.763390	0.381695	−	0.924288i	$-0.375340\pi$
$397$	9.51729e8	0.763390	0.381695	+	0.924288i	$0.375340\pi$
$398$	−1.13093e8	−0.0899179
$399$	0	0
$400$	1.56250e8	0.122070
$401$	−1.03883e9	−0.804522	−0.402261	−	0.915525i	$-0.631775\pi$
$401$	−1.03883e9	−0.804522	−0.402261	+	0.915525i	$0.631775\pi$
$402$	0	0
$403$	−2.12441e7	−0.0161686
$404$	−6.10769e8	−0.460832
$405$	0	0
$406$	−2.10910e9	−1.56407
$407$	−1.22077e8	−0.0897542
$408$	0	0
$409$	2.67559e9	1.93370	0.966849	−	0.255348i	$-0.0821899\pi$
$409$	2.67559e9	1.93370	0.966849	+	0.255348i	$0.0821899\pi$
$410$	3.14117e6	0.00225086
$411$	0	0
$412$	−1.99902e8	−0.140824
$413$	−2.04243e9	−1.42667
$414$	0	0
$415$	−1.84219e9	−1.26522
$416$	1.90523e8	0.129754
$417$	0	0
$418$	−1.57390e9	−1.05405
$419$	−3.41769e8	−0.226978	−0.113489	−	0.993539i	$-0.536203\pi$
$419$	−3.41769e8	−0.226978	−0.113489	+	0.993539i	$0.536203\pi$
$420$	0	0
$421$	1.83184e9	1.19646	0.598232	−	0.801323i	$-0.295870\pi$
$421$	1.83184e9	1.19646	0.598232	+	0.801323i	$0.295870\pi$
$422$	−1.50863e9	−0.977212
$423$	0	0
$424$	−3.97838e8	−0.253469
$425$	−2.44321e8	−0.154383
$426$	0	0
$427$	−1.31898e9	−0.819860
$428$	−6.55794e8	−0.404310
$429$	0	0
$430$	−1.33476e9	−0.809589
$431$	1.20261e9	0.723529	0.361764	−	0.932270i	$-0.382174\pi$
$431$	1.20261e9	0.723529	0.361764	+	0.932270i	$0.382174\pi$
$432$	0	0
$433$	1.83198e9	1.08446	0.542228	−	0.840231i	$-0.317581\pi$
$433$	1.83198e9	1.08446	0.542228	+	0.840231i	$0.317581\pi$
$434$	−3.70382e7	−0.0217488
$435$	0	0
$436$	−8.11089e8	−0.468668
$437$	−4.69240e8	−0.268974
$438$	0	0
$439$	−1.50903e9	−0.851277	−0.425639	−	0.904893i	$-0.639951\pi$
$439$	−1.50903e9	−0.851277	−0.425639	+	0.904893i	$0.639951\pi$
$440$	−8.90603e8	−0.498425
$441$	0	0
$442$	−2.97912e8	−0.164100
$443$	−2.98792e9	−1.63289	−0.816444	−	0.577425i	$-0.804058\pi$
$443$	−2.98792e9	−1.63289	−0.816444	+	0.577425i	$0.804058\pi$
$444$	0	0
$445$	−1.41138e9	−0.759250
$446$	−2.53722e9	−1.35421
$447$	0	0
$448$	3.32168e8	0.174536
$449$	−1.91998e9	−1.00100	−0.500500	−	0.865737i	$-0.666850\pi$
$449$	−1.91998e9	−1.00100	−0.500500	+	0.865737i	$0.666850\pi$
$450$	0	0
$451$	−5.87410e6	−0.00301525
$452$	−3.47725e7	−0.0177114
$453$	0	0
$454$	7.77358e7	0.0389875
$455$	2.51219e9	1.25029
$456$	0	0
$457$	−1.94014e9	−0.950883	−0.475441	−	0.879747i	$-0.657712\pi$
$457$	−1.94014e9	−0.950883	−0.475441	+	0.879747i	$0.657712\pi$
$458$	−2.03715e9	−0.990818
$459$	0	0
$460$	−2.65522e8	−0.127189
$461$	8.14499e8	0.387202	0.193601	−	0.981080i	$-0.437983\pi$
$461$	8.14499e8	0.387202	0.193601	+	0.981080i	$0.437983\pi$
$462$	0	0
$463$	−6.61468e7	−0.0309724	−0.0154862	−	0.999880i	$-0.504930\pi$
$463$	−6.61468e7	−0.0309724	−0.0154862	+	0.999880i	$0.504930\pi$
$464$	8.52217e8	0.396038
$465$	0	0
$466$	2.11324e8	0.0967382
$467$	2.88027e9	1.30865	0.654327	−	0.756212i	$-0.272952\pi$
$467$	2.88027e9	1.30865	0.654327	+	0.756212i	$0.272952\pi$
$468$	0	0
$469$	−2.61110e9	−1.16874
$470$	−2.69763e9	−1.19851
$471$	0	0
$472$	8.25278e8	0.361246
$473$	2.49605e9	1.08452
$474$	0	0
$475$	−1.47120e9	−0.629860
$476$	−5.19396e8	−0.220737
$477$	0	0
$478$	−1.02139e8	−0.0427754
$479$	3.40043e9	1.41371	0.706854	−	0.707360i	$-0.250114\pi$
$479$	3.40043e9	1.41371	0.706854	+	0.707360i	$0.250114\pi$
$480$	0	0
$481$	−1.39141e8	−0.0570096
$482$	−1.17995e9	−0.479954
$483$	0	0
$484$	4.18276e8	0.167689
$485$	−4.05243e9	−1.61295
$486$	0	0
$487$	3.01213e9	1.18174	0.590871	−	0.806766i	$-0.298784\pi$
$487$	3.01213e9	1.18174	0.590871	+	0.806766i	$0.298784\pi$
$488$	5.32954e8	0.207596
$489$	0	0
$490$	2.13335e9	0.819174
$491$	835191.	0.000318420 0	0.000159210	−	1.00000i	$-0.499949\pi$
$491$	835191.	0.000318420 0	0.000159210		1.00000i	$0.499949\pi$
$492$	0	0
$493$	−1.33257e9	−0.500872
$494$	−1.79390e9	−0.669505
$495$	0	0
$496$	1.49659e7	0.00550702
$497$	−4.54126e9	−1.65932
$498$	0	0
$499$	−4.35806e9	−1.57015	−0.785075	−	0.619401i	$-0.787375\pi$
$499$	−4.35806e9	−1.57015	−0.785075	+	0.619401i	$0.787375\pi$
$500$	8.72447e8	0.312136
$501$	0	0
$502$	2.13899e9	0.754650
$503$	2.40286e8	0.0841862	0.0420931	−	0.999114i	$-0.486597\pi$
$503$	2.40286e8	0.0841862	0.0420931	+	0.999114i	$0.486597\pi$
$504$	0	0
$505$	3.25413e9	1.12438
$506$	4.96535e8	0.170382
$507$	0	0
$508$	−3.89522e8	−0.131828
$509$	3.36572e9	1.13127	0.565634	−	0.824656i	$-0.308631\pi$
$509$	3.36572e9	1.13127	0.565634	+	0.824656i	$0.308631\pi$
$510$	0	0
$511$	−1.23652e9	−0.409947
$512$	−1.34218e8	−0.0441942
$513$	0	0
$514$	−1.09626e9	−0.356076
$515$	1.06506e9	0.343597
$516$	0	0
$517$	5.04466e9	1.60552
$518$	−2.42587e8	−0.0766854
$519$	0	0
$520$	−1.01509e9	−0.316587
$521$	−6.69390e8	−0.207371	−0.103685	−	0.994610i	$-0.533063\pi$
$521$	−6.69390e8	−0.207371	−0.103685	+	0.994610i	$0.533063\pi$
$522$	0	0
$523$	6.04759e9	1.84853	0.924265	−	0.381752i	$-0.124679\pi$
$523$	6.04759e9	1.84853	0.924265	+	0.381752i	$0.124679\pi$
$524$	1.66874e9	0.506674
$525$	0	0
$526$	1.28469e9	0.384899
$527$	−2.34015e7	−0.00696476
$528$	0	0
$529$	1.48036e8	0.0434783
$530$	2.11965e9	0.618441
$531$	0	0
$532$	−3.12759e9	−0.900573
$533$	−6.69516e6	−0.00191521
$534$	0	0
$535$	3.49402e9	0.986477
$536$	1.05506e9	0.295937
$537$	0	0
$538$	3.73687e9	1.03459
$539$	−3.98943e9	−1.09736
$540$	0	0
$541$	9.56170e8	0.259624	0.129812	−	0.991539i	$-0.458563\pi$
$541$	9.56170e8	0.259624	0.129812	+	0.991539i	$0.458563\pi$
$542$	−4.41348e9	−1.19065
$543$	0	0
$544$	2.09870e8	0.0558927
$545$	4.32141e9	1.14351
$546$	0	0
$547$	−7.50590e9	−1.96086	−0.980431	−	0.196864i	$-0.936924\pi$
$547$	−7.50590e9	−1.96086	−0.980431	+	0.196864i	$0.936924\pi$
$548$	−2.91443e9	−0.756522
$549$	0	0
$550$	1.55678e9	0.398986
$551$	−8.02420e9	−2.04348
$552$	0	0
$553$	7.60727e9	1.91289
$554$	−3.82523e9	−0.955813
$555$	0	0
$556$	−2.79091e9	−0.688626
$557$	−2.30925e9	−0.566209	−0.283105	−	0.959089i	$-0.591364\pi$
$557$	−2.30925e9	−0.566209	−0.283105	+	0.959089i	$0.591364\pi$
$558$	0	0
$559$	2.84494e9	0.688862
$560$	−1.76976e9	−0.425851
$561$	0	0
$562$	5.89957e9	1.40199
$563$	−2.20676e9	−0.521166	−0.260583	−	0.965451i	$-0.583915\pi$
$563$	−2.20676e9	−0.521166	−0.260583	+	0.965451i	$0.583915\pi$
$564$	0	0
$565$	1.85265e8	0.0432140
$566$	5.46360e9	1.26655
$567$	0	0
$568$	1.83497e9	0.420155
$569$	2.56775e9	0.584332	0.292166	−	0.956368i	$-0.405624\pi$
$569$	2.56775e9	0.584332	0.292166	+	0.956368i	$0.405624\pi$
$570$	0	0
$571$	−3.30249e9	−0.742360	−0.371180	−	0.928561i	$-0.621047\pi$
$571$	−3.30249e9	−0.742360	−0.371180	+	0.928561i	$0.621047\pi$
$572$	1.89825e9	0.424099
$573$	0	0
$574$	−1.16727e7	−0.00257621
$575$	4.64134e8	0.101814
$576$	0	0
$577$	−4.83666e9	−1.04817	−0.524083	−	0.851667i	$-0.675592\pi$
$577$	−4.83666e9	−1.04817	−0.524083	+	0.851667i	$0.675592\pi$
$578$	2.95454e9	0.636419
$579$	0	0
$580$	−4.54054e9	−0.966295
$581$	6.84564e9	1.44810
$582$	0	0
$583$	−3.96381e9	−0.828462
$584$	4.99635e8	0.103803
$585$	0	0
$586$	−3.78593e8	−0.0777198
$587$	−8.36248e9	−1.70648	−0.853241	−	0.521517i	$-0.825366\pi$
$587$	−8.36248e9	−1.70648	−0.853241	+	0.521517i	$0.825366\pi$
$588$	0	0
$589$	−1.40914e8	−0.0284152
$590$	−4.39702e9	−0.881406
$591$	0	0
$592$	9.80209e7	0.0194175
$593$	7.18982e9	1.41588	0.707941	−	0.706272i	$-0.249624\pi$
$593$	7.18982e9	1.41588	0.707941	+	0.706272i	$0.249624\pi$
$594$	0	0
$595$	2.76730e9	0.538576
$596$	4.76397e9	0.921737
$597$	0	0
$598$	5.65940e8	0.108222
$599$	−7.64624e9	−1.45363	−0.726815	−	0.686833i	$-0.759000\pi$
$599$	−7.64624e9	−1.45363	−0.726815	+	0.686833i	$0.759000\pi$
$600$	0	0
$601$	1.72237e9	0.323643	0.161821	−	0.986820i	$-0.448263\pi$
$601$	1.72237e9	0.323643	0.161821	+	0.986820i	$0.448263\pi$
$602$	4.96003e9	0.926609
$603$	0	0
$604$	1.77885e9	0.328481
$605$	−2.22854e9	−0.409145
$606$	0	0
$607$	−4.96333e9	−0.900768	−0.450384	−	0.892835i	$-0.648713\pi$
$607$	−4.96333e9	−0.900768	−0.450384	+	0.892835i	$0.648713\pi$
$608$	1.26375e9	0.228034
$609$	0	0
$610$	−2.83953e9	−0.506515
$611$	5.74979e9	1.01978
$612$	0	0
$613$	5.74407e9	1.00718	0.503591	−	0.863942i	$-0.332012\pi$
$613$	5.74407e9	1.00718	0.503591	+	0.863942i	$0.332012\pi$
$614$	−2.78076e9	−0.484814
$615$	0	0
$616$	3.30951e9	0.570469
$617$	1.05462e10	1.80758	0.903788	−	0.427981i	$-0.140775\pi$
$617$	1.05462e10	1.80758	0.903788	+	0.427981i	$0.140775\pi$
$618$	0	0
$619$	3.60119e9	0.610279	0.305140	−	0.952308i	$-0.401297\pi$
$619$	3.60119e9	0.610279	0.305140	+	0.952308i	$0.401297\pi$
$620$	−7.97370e7	−0.0134366
$621$	0	0
$622$	−6.77167e9	−1.12831
$623$	5.24475e9	0.868994
$624$	0	0
$625$	−7.62856e9	−1.24986
$626$	−4.25157e9	−0.692691
$627$	0	0
$628$	2.13169e9	0.343452
$629$	−1.53271e8	−0.0245574
$630$	0	0
$631$	−2.99729e9	−0.474926	−0.237463	−	0.971397i	$-0.576316\pi$
$631$	−2.99729e9	−0.474926	−0.237463	+	0.971397i	$0.576316\pi$
$632$	−3.07384e9	−0.484363
$633$	0	0
$634$	−6.02377e9	−0.938763
$635$	2.07534e9	0.321648
$636$	0	0
$637$	−4.54707e9	−0.697017
$638$	8.49096e9	1.29445
$639$	0	0
$640$	7.15101e8	0.107829
$641$	−1.30075e9	−0.195069	−0.0975347	−	0.995232i	$-0.531096\pi$
$641$	−1.30075e9	−0.195069	−0.0975347	+	0.995232i	$0.531096\pi$
$642$	0	0
$643$	−9.31677e9	−1.38206	−0.691030	−	0.722826i	$-0.742843\pi$
$643$	−9.31677e9	−1.38206	−0.691030	+	0.722826i	$0.742843\pi$
$644$	9.86691e8	0.145573
$645$	0	0
$646$	−1.97607e9	−0.288396
$647$	9.62984e9	1.39783	0.698914	−	0.715205i	$-0.253667\pi$
$647$	9.62984e9	1.39783	0.698914	+	0.715205i	$0.253667\pi$
$648$	0	0
$649$	8.22256e9	1.18073
$650$	1.77438e9	0.253425
$651$	0	0
$652$	−9.34162e8	−0.131994
$653$	−4.51671e9	−0.634784	−0.317392	−	0.948294i	$-0.602807\pi$
$653$	−4.51671e9	−0.634784	−0.317392	+	0.948294i	$0.602807\pi$
$654$	0	0
$655$	−8.89089e9	−1.23623
$656$	4.71655e6	0.000652321 0
$657$	0	0
$658$	1.00245e10	1.37174
$659$	−6.60804e9	−0.899443	−0.449722	−	0.893169i	$-0.648477\pi$
$659$	−6.60804e9	−0.899443	−0.449722	+	0.893169i	$0.648477\pi$
$660$	0	0
$661$	1.31054e10	1.76500	0.882502	−	0.470308i	$-0.155857\pi$
$661$	1.31054e10	1.76500	0.882502	+	0.470308i	$0.155857\pi$
$662$	1.49191e9	0.199867
$663$	0	0
$664$	−2.76609e9	−0.366672
$665$	1.66635e10	2.19731
$666$	0	0
$667$	2.53148e9	0.330319
$668$	4.87427e9	0.632691
$669$	0	0
$670$	−5.62125e9	−0.722057
$671$	5.31002e9	0.678527
$672$	0	0
$673$	−1.48862e9	−0.188249	−0.0941243	−	0.995560i	$-0.530005\pi$
$673$	−1.48862e9	−0.188249	−0.0941243	+	0.995560i	$0.530005\pi$
$674$	5.76477e9	0.725225
$675$	0	0
$676$	−1.85232e9	−0.230623
$677$	−1.38673e10	−1.71763	−0.858817	−	0.512282i	$-0.828800\pi$
$677$	−1.38673e10	−1.71763	−0.858817	+	0.512282i	$0.828800\pi$
$678$	0	0
$679$	1.50590e10	1.84609
$680$	−1.11817e9	−0.136373
$681$	0	0
$682$	1.49111e8	0.0179996
$683$	6.45650e9	0.775398	0.387699	−	0.921786i	$-0.373270\pi$
$683$	6.45650e9	0.775398	0.387699	+	0.921786i	$0.373270\pi$
$684$	0	0
$685$	1.55279e10	1.84584
$686$	4.20609e8	0.0497443
$687$	0	0
$688$	−2.00418e9	−0.234626
$689$	−4.51786e9	−0.526218
$690$	0	0
$691$	−8.22490e8	−0.0948325	−0.0474163	−	0.998875i	$-0.515099\pi$
$691$	−8.22490e8	−0.0948325	−0.0474163	+	0.998875i	$0.515099\pi$
$692$	7.54013e9	0.864983
$693$	0	0
$694$	−6.51461e9	−0.739827
$695$	1.48697e10	1.68018
$696$	0	0
$697$	−7.37506e6	−0.000824994 0
$698$	3.40028e9	0.378460
$699$	0	0
$700$	3.09355e9	0.340890
$701$	−1.78860e10	−1.96111	−0.980553	−	0.196252i	$-0.937123\pi$
$701$	−1.78860e10	−1.96111	−0.980553	+	0.196252i	$0.937123\pi$
$702$	0	0
$703$	−9.22934e8	−0.100191
$704$	−1.33726e9	−0.144448
$705$	0	0
$706$	−1.68693e9	−0.180418
$707$	−1.20925e10	−1.28691
$708$	0	0
$709$	1.14149e10	1.20285	0.601424	−	0.798930i	$-0.294600\pi$
$709$	1.14149e10	1.20285	0.601424	+	0.798930i	$0.294600\pi$
$710$	−9.77657e9	−1.02514
$711$	0	0
$712$	−2.11923e9	−0.220038
$713$	4.44555e7	0.00459317
$714$	0	0
$715$	−1.01137e10	−1.03476
$716$	−1.49938e9	−0.152657
$717$	0	0
$718$	−7.70004e9	−0.776349
$719$	4.68698e9	0.470264	0.235132	−	0.971963i	$-0.424448\pi$
$719$	4.68698e9	0.470264	0.235132	+	0.971963i	$0.424448\pi$
$720$	0	0
$721$	−3.95781e9	−0.393262
$722$	−4.74811e9	−0.469505
$723$	0	0
$724$	−3.62334e9	−0.354833
$725$	7.93689e9	0.773512
$726$	0	0
$727$	−1.85231e10	−1.78790	−0.893951	−	0.448164i	$-0.852078\pi$
$727$	−1.85231e10	−1.78790	−0.893951	+	0.448164i	$0.852078\pi$
$728$	3.77211e9	0.362347
$729$	0	0
$730$	−2.66201e9	−0.253268
$731$	3.13385e9	0.296734
$732$	0	0
$733$	1.69649e9	0.159107	0.0795534	−	0.996831i	$-0.474651\pi$
$733$	1.69649e9	0.159107	0.0795534	+	0.996831i	$0.474651\pi$
$734$	4.73245e8	0.0441723
$735$	0	0
$736$	−3.98688e8	−0.0368605
$737$	1.05119e10	0.967266
$738$	0	0
$739$	−8.17586e9	−0.745209	−0.372604	−	0.927990i	$-0.621535\pi$
$739$	−8.17586e9	−0.745209	−0.372604	+	0.927990i	$0.621535\pi$
$740$	−5.22247e8	−0.0473768
$741$	0	0
$742$	−7.87669e9	−0.707832
$743$	−1.95551e9	−0.174904	−0.0874519	−	0.996169i	$-0.527872\pi$
$743$	−1.95551e9	−0.174904	−0.0874519	+	0.996169i	$0.527872\pi$
$744$	0	0
$745$	−2.53820e10	−2.24895
$746$	6.06155e9	0.534562
$747$	0	0
$748$	2.09102e9	0.182685
$749$	−1.29839e10	−1.12907
$750$	0	0
$751$	1.41485e10	1.21891	0.609453	−	0.792823i	$-0.291389\pi$
$751$	1.41485e10	1.21891	0.609453	+	0.792823i	$0.291389\pi$
$752$	−4.05056e9	−0.347338
$753$	0	0
$754$	9.67780e9	0.822199
$755$	−9.47757e9	−0.801461
$756$	0	0
$757$	−3.50371e9	−0.293557	−0.146779	−	0.989169i	$-0.546890\pi$
$757$	−3.50371e9	−0.293557	−0.146779	+	0.989169i	$0.546890\pi$
$758$	1.97725e9	0.164899
$759$	0	0
$760$	−6.73316e9	−0.556380
$761$	−1.18352e9	−0.0973485	−0.0486743	−	0.998815i	$-0.515500\pi$
$761$	−1.18352e9	−0.0973485	−0.0486743	+	0.998815i	$0.515500\pi$
$762$	0	0
$763$	−1.60585e10	−1.30879
$764$	8.11844e9	0.658636
$765$	0	0
$766$	−1.56051e10	−1.25449
$767$	9.37189e9	0.749969
$768$	0	0
$769$	1.26642e10	1.00424	0.502118	−	0.864799i	$-0.332554\pi$
$769$	1.26642e10	1.00424	0.502118	+	0.864799i	$0.332554\pi$
$770$	−1.76328e10	−1.39189
$771$	0	0
$772$	8.73941e9	0.683630
$773$	6.91080e9	0.538146	0.269073	−	0.963120i	$-0.413283\pi$
$773$	6.91080e9	0.538146	0.269073	+	0.963120i	$0.413283\pi$
$774$	0	0
$775$	1.39381e8	0.0107559
$776$	−6.08483e9	−0.467447
$777$	0	0
$778$	1.36528e10	1.03943
$779$	−4.44095e7	−0.00336585
$780$	0	0
$781$	1.82825e10	1.37327
$782$	6.23411e8	0.0466177
$783$	0	0
$784$	3.20328e9	0.237404
$785$	−1.13575e10	−0.837990
$786$	0	0
$787$	1.12082e10	0.819644	0.409822	−	0.912166i	$-0.365591\pi$
$787$	1.12082e10	0.819644	0.409822	+	0.912166i	$0.365591\pi$
$788$	7.42714e9	0.540729
$789$	0	0
$790$	1.63771e10	1.18180
$791$	−6.88453e8	−0.0494603
$792$	0	0
$793$	6.05224e9	0.430983
$794$	−7.61383e9	−0.539798
$795$	0	0
$796$	9.04747e8	0.0635816
$797$	−2.00641e9	−0.140383	−0.0701917	−	0.997534i	$-0.522361\pi$
$797$	−2.00641e9	−0.140383	−0.0701917	+	0.997534i	$0.522361\pi$
$798$	0	0
$799$	6.33368e9	0.439281
$800$	−1.25000e9	−0.0863167
$801$	0	0
$802$	8.31061e9	0.568883
$803$	4.97805e9	0.339278
$804$	0	0
$805$	−5.25701e9	−0.355184
$806$	1.69953e8	0.0114329
$807$	0	0
$808$	4.88615e9	0.325857
$809$	2.85624e9	0.189660	0.0948300	−	0.995493i	$-0.469769\pi$
$809$	2.85624e9	0.189660	0.0948300	+	0.995493i	$0.469769\pi$
$810$	0	0
$811$	1.97522e10	1.30030	0.650148	−	0.759808i	$-0.274707\pi$
$811$	1.97522e10	1.30030	0.650148	+	0.759808i	$0.274707\pi$
$812$	1.68728e10	1.10597
$813$	0	0
$814$	9.76619e8	0.0634658
$815$	4.97714e9	0.322054
$816$	0	0
$817$	1.88707e10	1.21063
$818$	−2.14048e10	−1.36733
$819$	0	0
$820$	−2.51294e7	−0.00159160
$821$	−1.99137e10	−1.25589	−0.627943	−	0.778260i	$-0.716103\pi$
$821$	−1.99137e10	−1.25589	−0.627943	+	0.778260i	$0.716103\pi$
$822$	0	0
$823$	2.60455e10	1.62867	0.814336	−	0.580393i	$-0.197101\pi$
$823$	2.60455e10	1.62867	0.814336	+	0.580393i	$0.197101\pi$
$824$	1.59922e9	0.0995776
$825$	0	0
$826$	1.63395e10	1.00881
$827$	−9.95427e9	−0.611984	−0.305992	−	0.952034i	$-0.598988\pi$
$827$	−9.95427e9	−0.611984	−0.305992	+	0.952034i	$0.598988\pi$
$828$	0	0
$829$	−3.29779e9	−0.201040	−0.100520	−	0.994935i	$-0.532051\pi$
$829$	−3.29779e9	−0.201040	−0.100520	+	0.994935i	$0.532051\pi$
$830$	1.47375e10	0.894644
$831$	0	0
$832$	−1.52418e9	−0.0917498
$833$	−5.00882e9	−0.300247
$834$	0	0
$835$	−2.59697e10	−1.54370
$836$	1.25912e10	0.745326
$837$	0	0
$838$	2.73415e9	0.160498
$839$	−1.21672e9	−0.0711252	−0.0355626	−	0.999367i	$-0.511322\pi$
$839$	−1.21672e9	−0.0711252	−0.0355626	+	0.999367i	$0.511322\pi$
$840$	0	0
$841$	2.60394e10	1.50954
$842$	−1.46547e10	−0.846028
$843$	0	0
$844$	1.20690e10	0.690993
$845$	9.86903e9	0.562699
$846$	0	0
$847$	8.28135e9	0.468284
$848$	3.18270e9	0.179230
$849$	0	0
$850$	1.95457e9	0.109165
$851$	2.91167e8	0.0161953
$852$	0	0
$853$	−1.25896e10	−0.694527	−0.347264	−	0.937768i	$-0.612889\pi$
$853$	−1.25896e10	−0.694527	−0.347264	+	0.937768i	$0.612889\pi$
$854$	1.05518e10	0.579728
$855$	0	0
$856$	5.24636e9	0.285890
$857$	3.98461e9	0.216248	0.108124	−	0.994137i	$-0.465516\pi$
$857$	3.98461e9	0.216248	0.108124	+	0.994137i	$0.465516\pi$
$858$	0	0
$859$	−1.29735e10	−0.698361	−0.349181	−	0.937055i	$-0.613540\pi$
$859$	−1.29735e10	−0.698361	−0.349181	+	0.937055i	$0.613540\pi$
$860$	1.06781e10	0.572466
$861$	0	0
$862$	−9.62091e9	−0.511612
$863$	2.90007e10	1.53593	0.767963	−	0.640495i	$-0.221271\pi$
$863$	2.90007e10	1.53593	0.767963	+	0.640495i	$0.221271\pi$
$864$	0	0
$865$	−4.01732e10	−2.11048
$866$	−1.46558e10	−0.766826
$867$	0	0
$868$	2.96306e8	0.0153788
$869$	−3.06258e10	−1.58314
$870$	0	0
$871$	1.19813e10	0.614383
$872$	6.48871e9	0.331399
$873$	0	0
$874$	3.75392e9	0.190193
$875$	1.72734e10	0.871663
$876$	0	0
$877$	−2.05862e10	−1.03057	−0.515286	−	0.857018i	$-0.672314\pi$
$877$	−2.05862e10	−1.03057	−0.515286	+	0.857018i	$0.672314\pi$
$878$	1.20722e10	0.601944
$879$	0	0
$880$	7.12482e9	0.352440
$881$	−4.47154e9	−0.220314	−0.110157	−	0.993914i	$-0.535135\pi$
$881$	−4.47154e9	−0.220314	−0.110157	+	0.993914i	$0.535135\pi$
$882$	0	0
$883$	−6.15100e9	−0.300665	−0.150333	−	0.988635i	$-0.548034\pi$
$883$	−6.15100e9	−0.300665	−0.150333	+	0.988635i	$0.548034\pi$
$884$	2.38329e9	0.116037
$885$	0	0
$886$	2.39034e10	1.15463
$887$	−2.96262e10	−1.42542	−0.712712	−	0.701457i	$-0.752533\pi$
$887$	−2.96262e10	−1.42542	−0.712712	+	0.701457i	$0.752533\pi$
$888$	0	0
$889$	−7.71205e9	−0.368140
$890$	1.12911e10	0.536871
$891$	0	0
$892$	2.02978e10	0.957573
$893$	3.81388e10	1.79220
$894$	0	0
$895$	7.98860e9	0.372469
$896$	−2.65734e9	−0.123415
$897$	0	0
$898$	1.53598e10	0.707813
$899$	7.60208e8	0.0348958
$900$	0	0
$901$	−4.97665e9	−0.226673
$902$	4.69928e7	0.00213210
$903$	0	0
$904$	2.78180e8	0.0125238
$905$	1.93049e10	0.865759
$906$	0	0
$907$	3.02880e10	1.34786	0.673930	−	0.738795i	$-0.264605\pi$
$907$	3.02880e10	1.34786	0.673930	+	0.738795i	$0.264605\pi$
$908$	−6.21886e8	−0.0275683
$909$	0	0
$910$	−2.00975e10	−0.884091
$911$	−9.96481e9	−0.436671	−0.218336	−	0.975874i	$-0.570063\pi$
$911$	−9.96481e9	−0.436671	−0.218336	+	0.975874i	$0.570063\pi$
$912$	0	0
$913$	−2.75596e10	−1.19846
$914$	1.55211e10	0.672376
$915$	0	0
$916$	1.62972e10	0.700614
$917$	3.30389e10	1.41492
$918$	0	0
$919$	−3.72161e10	−1.58171	−0.790855	−	0.612003i	$-0.790364\pi$
$919$	−3.72161e10	−1.58171	−0.790855	+	0.612003i	$0.790364\pi$
$920$	2.12418e9	0.0899360
$921$	0	0
$922$	−6.51599e9	−0.273793
$923$	2.08380e10	0.872267
$924$	0	0
$925$	9.12891e8	0.0379248
$926$	5.29174e8	0.0219008
$927$	0	0
$928$	−6.81773e9	−0.280041
$929$	−2.36879e9	−0.0969328	−0.0484664	−	0.998825i	$-0.515433\pi$
$929$	−2.36879e9	−0.0969328	−0.0484664	+	0.998825i	$0.515433\pi$
$930$	0	0
$931$	−3.01610e10	−1.22496
$932$	−1.69059e9	−0.0684042
$933$	0	0
$934$	−2.30422e10	−0.925357
$935$	−1.11408e10	−0.445733
$936$	0	0
$937$	2.37255e10	0.942166	0.471083	−	0.882089i	$-0.343863\pi$
$937$	2.37255e10	0.942166	0.471083	+	0.882089i	$0.343863\pi$
$938$	2.08888e10	0.826425
$939$	0	0
$940$	2.15811e10	0.847472
$941$	2.53391e10	0.991351	0.495676	−	0.868508i	$-0.334921\pi$
$941$	2.53391e10	0.991351	0.495676	+	0.868508i	$0.334921\pi$
$942$	0	0
$943$	1.40103e7	0.000544073 0
$944$	−6.60223e9	−0.255440
$945$	0	0
$946$	−1.99684e10	−0.766874
$947$	−3.19577e10	−1.22278	−0.611392	−	0.791328i	$-0.709390\pi$
$947$	−3.19577e10	−1.22278	−0.611392	+	0.791328i	$0.709390\pi$
$948$	0	0
$949$	5.67387e9	0.215500
$950$	1.17696e10	0.445378
$951$	0	0
$952$	4.15517e9	0.156084
$953$	−1.06573e10	−0.398861	−0.199431	−	0.979912i	$-0.563909\pi$
$953$	−1.06573e10	−0.398861	−0.199431	+	0.979912i	$0.563909\pi$
$954$	0	0
$955$	−4.32544e10	−1.60701
$956$	8.17113e8	0.0302468
$957$	0	0
$958$	−2.72034e10	−0.999642
$959$	−5.77021e10	−2.11264
$960$	0	0
$961$	−2.74993e10	−0.999515
$962$	1.11313e9	0.0403119
$963$	0	0
$964$	9.43961e9	0.339379
$965$	−4.65628e10	−1.66799
$966$	0	0
$967$	5.33089e10	1.89586	0.947932	−	0.318472i	$-0.103170\pi$
$967$	5.33089e10	1.89586	0.947932	+	0.318472i	$0.103170\pi$
$968$	−3.34621e9	−0.118574
$969$	0	0
$970$	3.24195e10	1.14053
$971$	5.29648e10	1.85661	0.928304	−	0.371823i	$-0.121267\pi$
$971$	5.29648e10	1.85661	0.928304	+	0.371823i	$0.121267\pi$
$972$	0	0
$973$	−5.52565e10	−1.92304
$974$	−2.40970e10	−0.835617
$975$	0	0
$976$	−4.26363e9	−0.146793
$977$	1.79920e10	0.617233	0.308616	−	0.951187i	$-0.400134\pi$
$977$	1.79920e10	0.617233	0.308616	+	0.951187i	$0.400134\pi$
$978$	0	0
$979$	−2.11146e10	−0.719191
$980$	−1.70668e10	−0.579243
$981$	0	0
$982$	−6.68153e6	−0.000225157 0
$983$	−1.56089e10	−0.524124	−0.262062	−	0.965051i	$-0.584403\pi$
$983$	−1.56089e10	−0.524124	−0.262062	+	0.965051i	$0.584403\pi$
$984$	0	0
$985$	−3.95712e10	−1.31933
$986$	1.06606e10	0.354170
$987$	0	0
$988$	1.43512e10	0.473412
$989$	−5.95333e9	−0.195692
$990$	0	0
$991$	4.73053e10	1.54402	0.772009	−	0.635612i	$-0.219252\pi$
$991$	4.73053e10	1.54402	0.772009	+	0.635612i	$0.219252\pi$
$992$	−1.19727e8	−0.00389405
$993$	0	0
$994$	3.63301e10	1.17331
$995$	−4.82042e9	−0.155133
$996$	0	0
$997$	3.63716e10	1.16233	0.581166	−	0.813785i	$-0.302597\pi$
$997$	3.63716e10	1.16233	0.581166	+	0.813785i	$0.302597\pi$
$998$	3.48645e10	1.11026
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.8.a.i.1.2		4
3.2	odd	2		138.8.a.h.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.8.a.h.1.3	✓	4	3.2	odd	2
414.8.a.i.1.2		4	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	414.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} +64.0000 q^{4} -340.987 q^{5} +1267.12 q^{7} -512.000 q^{8} +O(q^{10})\)	\(q-8.00000 q^{2} +64.0000 q^{4} -340.987 q^{5} +1267.12 q^{7} -512.000 q^{8} +2727.89 q^{10} -5101.25 q^{11} -5814.29 q^{13} -10137.0 q^{14} +4096.00 q^{16} -6404.73 q^{17} -38566.6 q^{19} -21823.2 q^{20} +40810.0 q^{22} +12167.0 q^{23} +38147.0 q^{25} +46514.3 q^{26} +81095.7 q^{28} +208061. q^{29} +3653.78 q^{31} -32768.0 q^{32} +51237.9 q^{34} -432071. q^{35} +23930.9 q^{37} +308533. q^{38} +174585. q^{40} +1151.50 q^{41} -489302. q^{43} -326480. q^{44} -97336.0 q^{46} -988907. q^{47} +782050. q^{49} -305176. q^{50} -372115. q^{52} +777027. q^{53} +1.73946e6 q^{55} -648766. q^{56} -1.66449e6 q^{58} -1.61187e6 q^{59} -1.04092e6 q^{61} -29230.2 q^{62} +262144. q^{64} +1.98260e6 q^{65} -2.06066e6 q^{67} -409903. q^{68} +3.45657e6 q^{70} -3.58392e6 q^{71} -975850. q^{73} -191447. q^{74} -2.46826e6 q^{76} -6.46390e6 q^{77} +6.00359e6 q^{79} -1.39668e6 q^{80} -9212.01 q^{82} +5.40252e6 q^{83} +2.18393e6 q^{85} +3.91441e6 q^{86} +2.61184e6 q^{88} +4.13911e6 q^{89} -7.36740e6 q^{91} +778688. q^{92} +7.91125e6 q^{94} +1.31507e7 q^{95} +1.18844e7 q^{97} -6.25640e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 32 q^{2} + 256 q^{4} - 270 q^{5} + 2022 q^{7} - 2048 q^{8}+O(q^{10}) \) 4 * q - 32 * q^2 + 256 * q^4 - 270 * q^5 + 2022 * q^7 - 2048 * q^8	\( 4 q - 32 q^{2} + 256 q^{4} - 270 q^{5} + 2022 q^{7} - 2048 q^{8} + 2160 q^{10} - 4120 q^{11} + 8036 q^{13} - 16176 q^{14} + 16384 q^{16} - 37182 q^{17} + 5702 q^{19} - 17280 q^{20} + 32960 q^{22} + 48668 q^{23} + 121480 q^{25} - 64288 q^{26} + 129408 q^{28} - 217716 q^{29} + 222852 q^{31} - 131072 q^{32} + 297456 q^{34} - 68440 q^{35} + 486428 q^{37} - 45616 q^{38} + 138240 q^{40} - 338336 q^{41} + 730974 q^{43} - 263680 q^{44} - 389344 q^{46} - 338248 q^{47} - 310552 q^{49} - 971840 q^{50} + 514304 q^{52} + 375502 q^{53} + 424840 q^{55} - 1035264 q^{56} + 1741728 q^{58} - 71392 q^{59} + 2101164 q^{61} - 1782816 q^{62} + 1048576 q^{64} - 1578780 q^{65} + 4337162 q^{67} - 2379648 q^{68} + 547520 q^{70} - 2288016 q^{71} - 1107328 q^{73} - 3891424 q^{74} + 364928 q^{76} - 5826200 q^{77} + 60610 q^{79} - 1105920 q^{80} + 2706688 q^{82} - 1485464 q^{83} - 8843820 q^{85} - 5847792 q^{86} + 2109440 q^{88} - 1485090 q^{89} - 2898412 q^{91} + 3114752 q^{92} + 2705984 q^{94} - 8545200 q^{95} + 1935444 q^{97} + 2484416 q^{98}+O(q^{100}) \) 4 * q - 32 * q^2 + 256 * q^4 - 270 * q^5 + 2022 * q^7 - 2048 * q^8 + 2160 * q^10 - 4120 * q^11 + 8036 * q^13 - 16176 * q^14 + 16384 * q^16 - 37182 * q^17 + 5702 * q^19 - 17280 * q^20 + 32960 * q^22 + 48668 * q^23 + 121480 * q^25 - 64288 * q^26 + 129408 * q^28 - 217716 * q^29 + 222852 * q^31 - 131072 * q^32 + 297456 * q^34 - 68440 * q^35 + 486428 * q^37 - 45616 * q^38 + 138240 * q^40 - 338336 * q^41 + 730974 * q^43 - 263680 * q^44 - 389344 * q^46 - 338248 * q^47 - 310552 * q^49 - 971840 * q^50 + 514304 * q^52 + 375502 * q^53 + 424840 * q^55 - 1035264 * q^56 + 1741728 * q^58 - 71392 * q^59 + 2101164 * q^61 - 1782816 * q^62 + 1048576 * q^64 - 1578780 * q^65 + 4337162 * q^67 - 2379648 * q^68 + 547520 * q^70 - 2288016 * q^71 - 1107328 * q^73 - 3891424 * q^74 + 364928 * q^76 - 5826200 * q^77 + 60610 * q^79 - 1105920 * q^80 + 2706688 * q^82 - 1485464 * q^83 - 8843820 * q^85 - 5847792 * q^86 + 2109440 * q^88 - 1485090 * q^89 - 2898412 * q^91 + 3114752 * q^92 + 2705984 * q^94 - 8545200 * q^95 + 1935444 * q^97 + 2484416 * q^98

Introduction

L-functions

Modular forms

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Database

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