LMFDB - Embedded newform 98.6.a.f.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,6,Mod(1,98)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("98.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	98.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,-8,14,32,42,-56,0,-128,652] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$15.7176143417$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{130}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 130 $ x^2 - 130
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 14)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-11.4018$ of defining polynomial
Character	$\chi$	$=$	98.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.00000 q^{2} -15.8035 q^{3} +16.0000 q^{4} +21.0000 q^{5} +63.2140 q^{6} -64.0000 q^{8} +6.75088 q^{9} -84.0000 q^{10} -625.874 q^{11} -252.856 q^{12} +206.821 q^{13} -331.874 q^{15} +256.000 q^{16} -1061.46 q^{17} -27.0035 q^{18} +1883.98 q^{19} +336.000 q^{20} +2503.49 q^{22} +3717.37 q^{23} +1011.42 q^{24} -2684.00 q^{25} -827.284 q^{26} +3733.56 q^{27} -123.747 q^{29} +1327.49 q^{30} +9109.26 q^{31} -1024.00 q^{32} +9891.00 q^{33} +4245.85 q^{34} +108.014 q^{36} -6028.73 q^{37} -7535.92 q^{38} -3268.50 q^{39} -1344.00 q^{40} +17201.9 q^{41} +5401.98 q^{43} -10014.0 q^{44} +141.769 q^{45} -14869.5 q^{46} -1875.24 q^{47} -4045.70 q^{48} +10736.0 q^{50} +16774.8 q^{51} +3309.14 q^{52} +18707.2 q^{53} -14934.3 q^{54} -13143.3 q^{55} -29773.5 q^{57} +494.989 q^{58} +2534.78 q^{59} -5309.98 q^{60} +2094.71 q^{61} -36437.1 q^{62} +4096.00 q^{64} +4343.24 q^{65} -39564.0 q^{66} +58620.8 q^{67} -16983.4 q^{68} -58747.5 q^{69} -31279.5 q^{71} -432.056 q^{72} +7150.47 q^{73} +24114.9 q^{74} +42416.6 q^{75} +30143.7 q^{76} +13074.0 q^{78} +2979.81 q^{79} +5376.00 q^{80} -60643.9 q^{81} -68807.4 q^{82} -45954.6 q^{83} -22290.7 q^{85} -21607.9 q^{86} +1955.64 q^{87} +40055.9 q^{88} -99040.0 q^{89} -567.074 q^{90} +59477.9 q^{92} -143958. q^{93} +7500.97 q^{94} +39563.6 q^{95} +16182.8 q^{96} +115548. q^{97} -4225.20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{2} + 14 q^{3} + 32 q^{4} + 42 q^{5} - 56 q^{6} - 128 q^{8} + 652 q^{9} - 168 q^{10} - 294 q^{11} + 224 q^{12} + 140 q^{13} + 294 q^{15} + 512 q^{16} - 1302 q^{17} - 2608 q^{18} + 1442 q^{19}+ \cdots + 209916 q^{99}+O(q^{100}) $ 2 * q - 8 * q^2 + 14 * q^3 + 32 * q^4 + 42 * q^5 - 56 * q^6 - 128 * q^8 + 652 * q^9 - 168 * q^10 - 294 * q^11 + 224 * q^12 + 140 * q^13 + 294 * q^15 + 512 * q^16 - 1302 * q^17 - 2608 * q^18 + 1442 * q^19 + 672 * q^20 + 1176 * q^22 + 2646 * q^23 - 896 * q^24 - 5368 * q^25 - 560 * q^26 + 15722 * q^27 + 1668 * q^29 - 1176 * q^30 + 14798 * q^31 - 2048 * q^32 + 19782 * q^33 + 5208 * q^34 + 10432 * q^36 + 5182 * q^37 - 5768 * q^38 - 5260 * q^39 - 2688 * q^40 + 5124 * q^41 - 4520 * q^43 - 4704 * q^44 + 13692 * q^45 - 10584 * q^46 + 14994 * q^47 + 3584 * q^48 + 21472 * q^50 + 9606 * q^51 + 2240 * q^52 + 24006 * q^53 - 62888 * q^54 - 6174 * q^55 - 42946 * q^57 - 6672 * q^58 - 38850 * q^59 + 4704 * q^60 + 23618 * q^61 - 59192 * q^62 + 8192 * q^64 + 2940 * q^65 - 79128 * q^66 + 32002 * q^67 - 20832 * q^68 - 90678 * q^69 - 89376 * q^71 - 41728 * q^72 + 47138 * q^73 - 20728 * q^74 - 37576 * q^75 + 23072 * q^76 + 21040 * q^78 - 40970 * q^79 + 10752 * q^80 + 139858 * q^81 - 20496 * q^82 - 68376 * q^83 - 27342 * q^85 + 18080 * q^86 + 55356 * q^87 + 18816 * q^88 - 123102 * q^89 - 54768 * q^90 + 42336 * q^92 + 25586 * q^93 - 59976 * q^94 + 30282 * q^95 - 14336 * q^96 + 43652 * q^97 + 209916 * q^99

Coefficient data

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

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

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

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	−15.8035	−1.01380	−0.506898	−	0.862006i	$-0.669208\pi$
$3$	−15.8035	−1.01380	−0.506898	+	0.862006i	$0.669208\pi$
$4$	16.0000	0.500000
$5$	21.0000	0.375659	0.187830	−	0.982202i	$-0.439855\pi$
$5$	21.0000	0.375659	0.187830	+	0.982202i	$0.439855\pi$
$6$	63.2140	0.716862
$7$	0	0
$7$	0	0
$8$	−64.0000	−0.353553
$9$	6.75088	0.0277814
$10$	−84.0000	−0.265631
$11$	−625.874	−1.55957	−0.779785	−	0.626047i	$-0.784672\pi$
$11$	−625.874	−1.55957	−0.779785	+	0.626047i	$0.784672\pi$
$12$	−252.856	−0.506898
$13$	206.821	0.339419	0.169710	−	0.985494i	$-0.445717\pi$
$13$	206.821	0.339419	0.169710	+	0.985494i	$0.445717\pi$
$14$	0	0
$15$	−331.874	−0.380842
$16$	256.000	0.250000
$17$	−1061.46	−0.890805	−0.445402	−	0.895330i	$-0.646939\pi$
$17$	−1061.46	−0.890805	−0.445402	+	0.895330i	$0.646939\pi$
$18$	−27.0035	−0.0196444
$19$	1883.98	1.19727	0.598635	−	0.801022i	$-0.295710\pi$
$19$	1883.98	1.19727	0.598635	+	0.801022i	$0.295710\pi$
$20$	336.000	0.187830
$21$	0	0
$22$	2503.49	1.10278
$23$	3717.37	1.46526	0.732632	−	0.680625i	$-0.238292\pi$
$23$	3717.37	1.46526	0.732632	+	0.680625i	$0.238292\pi$
$24$	1011.42	0.358431
$25$	−2684.00	−0.858880
$26$	−827.284	−0.240006
$27$	3733.56	0.985631
$28$	0	0
$29$	−123.747	−0.0273238	−0.0136619	−	0.999907i	$-0.504349\pi$
$29$	−123.747	−0.0273238	−0.0136619	+	0.999907i	$0.504349\pi$
$30$	1327.49	0.269296
$31$	9109.26	1.70247	0.851234	−	0.524786i	$-0.175855\pi$
$31$	9109.26	1.70247	0.851234	+	0.524786i	$0.175855\pi$
$32$	−1024.00	−0.176777
$33$	9891.00	1.58109
$34$	4245.85	0.629894
$35$	0	0
$36$	108.014	0.0138907
$37$	−6028.73	−0.723971	−0.361986	−	0.932184i	$-0.617901\pi$
$37$	−6028.73	−0.723971	−0.361986	+	0.932184i	$0.617901\pi$
$38$	−7535.92	−0.846598
$39$	−3268.50	−0.344102
$40$	−1344.00	−0.132816
$41$	17201.9	1.59814	0.799071	−	0.601236i	$-0.205325\pi$
$41$	17201.9	1.59814	0.799071	+	0.601236i	$0.205325\pi$
$42$	0	0
$43$	5401.98	0.445535	0.222767	−	0.974872i	$-0.428491\pi$
$43$	5401.98	0.445535	0.222767	+	0.974872i	$0.428491\pi$
$44$	−10014.0	−0.779785
$45$	141.769	0.0104363
$46$	−14869.5	−1.03610
$47$	−1875.24	−0.123826	−0.0619131	−	0.998082i	$-0.519720\pi$
$47$	−1875.24	−0.123826	−0.0619131	+	0.998082i	$0.519720\pi$
$48$	−4045.70	−0.253449
$49$	0	0
$50$	10736.0	0.607320
$51$	16774.8	0.903094
$52$	3309.14	0.169710
$53$	18707.2	0.914787	0.457393	−	0.889264i	$-0.348783\pi$
$53$	18707.2	0.914787	0.457393	+	0.889264i	$0.348783\pi$
$54$	−14934.3	−0.696946
$55$	−13143.3	−0.585867
$56$	0	0
$57$	−29773.5	−1.21379
$58$	494.989	0.0193208
$59$	2534.78	0.0948004	0.0474002	−	0.998876i	$-0.484906\pi$
$59$	2534.78	0.0948004	0.0474002	+	0.998876i	$0.484906\pi$
$60$	−5309.98	−0.190421
$61$	2094.71	0.0720773	0.0360386	−	0.999350i	$-0.488526\pi$
$61$	2094.71	0.0720773	0.0360386	+	0.999350i	$0.488526\pi$
$62$	−36437.1	−1.20383
$63$	0	0
$64$	4096.00	0.125000
$65$	4343.24	0.127506
$66$	−39564.0	−1.11800
$67$	58620.8	1.59538	0.797691	−	0.603067i	$-0.206055\pi$
$67$	58620.8	1.59538	0.797691	+	0.603067i	$0.206055\pi$
$68$	−16983.4	−0.445402
$69$	−58747.5	−1.48548
$70$	0	0
$71$	−31279.5	−0.736401	−0.368201	−	0.929746i	$-0.620026\pi$
$71$	−31279.5	−0.736401	−0.368201	+	0.929746i	$0.620026\pi$
$72$	−432.056	−0.00982221
$73$	7150.47	0.157046	0.0785231	−	0.996912i	$-0.474980\pi$
$73$	7150.47	0.157046	0.0785231	+	0.996912i	$0.474980\pi$
$74$	24114.9	0.511925
$75$	42416.6	0.870729
$76$	30143.7	0.598635
$77$	0	0
$78$	13074.0	0.243317
$79$	2979.81	0.0537181	0.0268591	−	0.999639i	$-0.491449\pi$
$79$	2979.81	0.0537181	0.0268591	+	0.999639i	$0.491449\pi$
$80$	5376.00	0.0939149
$81$	−60643.9	−1.02701
$82$	−68807.4	−1.13006
$83$	−45954.6	−0.732207	−0.366103	−	0.930574i	$-0.619308\pi$
$83$	−45954.6	−0.732207	−0.366103	+	0.930574i	$0.619308\pi$
$84$	0	0
$85$	−22290.7	−0.334639
$86$	−21607.9	−0.315041
$87$	1955.64	0.0277007
$88$	40055.9	0.551391
$89$	−99040.0	−1.32536	−0.662682	−	0.748900i	$-0.730582\pi$
$89$	−99040.0	−1.32536	−0.662682	+	0.748900i	$0.730582\pi$
$90$	−567.074	−0.00737961
$91$	0	0
$92$	59477.9	0.732632
$93$	−143958.	−1.72595
$94$	7500.97	0.0875584
$95$	39563.6	0.449766
$96$	16182.8	0.179215
$97$	115548.	1.24691	0.623454	−	0.781860i	$-0.285729\pi$
$97$	115548.	1.24691	0.623454	+	0.781860i	$0.285729\pi$
$98$	0	0
$99$	−4225.20	−0.0433271
$100$	−42944.0	−0.429440
$101$	−10951.5	−0.106824	−0.0534120	−	0.998573i	$-0.517010\pi$
$101$	−10951.5	−0.106824	−0.0534120	+	0.998573i	$0.517010\pi$
$102$	−67099.4	−0.638584
$103$	137724.	1.27914	0.639570	−	0.768733i	$-0.279113\pi$
$103$	137724.	1.27914	0.639570	+	0.768733i	$0.279113\pi$
$104$	−13236.5	−0.120003
$105$	0	0
$106$	−74828.9	−0.646852
$107$	75573.0	0.638127	0.319064	−	0.947733i	$-0.396632\pi$
$107$	75573.0	0.638127	0.319064	+	0.947733i	$0.396632\pi$
$108$	59737.0	0.492815
$109$	44526.3	0.358963	0.179482	−	0.983761i	$-0.442558\pi$
$109$	44526.3	0.358963	0.179482	+	0.983761i	$0.442558\pi$
$110$	52573.4	0.414271
$111$	95275.0	0.733959
$112$	0	0
$113$	90456.5	0.666413	0.333207	−	0.942854i	$-0.391869\pi$
$113$	90456.5	0.666413	0.333207	+	0.942854i	$0.391869\pi$
$114$	119094.	0.858277
$115$	78064.7	0.550440
$116$	−1979.96	−0.0136619
$117$	1396.22	0.00942954
$118$	−10139.1	−0.0670340
$119$	0	0
$120$	21239.9	0.134648
$121$	230667.	1.43226
$122$	−8378.82	−0.0509663
$123$	−271850.	−1.62019
$124$	145748.	0.851234
$125$	−121989.	−0.698306
$126$	0	0
$127$	187707.	1.03269	0.516346	−	0.856380i	$-0.327292\pi$
$127$	187707.	1.03269	0.516346	+	0.856380i	$0.327292\pi$
$128$	−16384.0	−0.0883883
$129$	−85370.2	−0.451681
$130$	−17373.0	−0.0901604
$131$	−154412.	−0.786147	−0.393073	−	0.919507i	$-0.628588\pi$
$131$	−154412.	−0.786147	−0.393073	+	0.919507i	$0.628588\pi$
$132$	158256.	0.790543
$133$	0	0
$134$	−234483.	−1.12810
$135$	78404.9	0.370262
$136$	67933.6	0.314947
$137$	109238.	0.497246	0.248623	−	0.968600i	$-0.420022\pi$
$137$	109238.	0.497246	0.248623	+	0.968600i	$0.420022\pi$
$138$	234990.	1.05039
$139$	204695.	0.898609	0.449305	−	0.893379i	$-0.351672\pi$
$139$	204695.	0.898609	0.449305	+	0.893379i	$0.351672\pi$
$140$	0	0
$141$	29635.4	0.125534
$142$	125118.	0.520714
$143$	−129444.	−0.529348
$144$	1728.23	0.00694535
$145$	−2598.69	−0.0102644
$146$	−28601.9	−0.111048
$147$	0	0
$148$	−96459.6	−0.361986
$149$	−406308.	−1.49930	−0.749651	−	0.661833i	$-0.769779\pi$
$149$	−406308.	−1.49930	−0.749651	+	0.661833i	$0.769779\pi$
$150$	−169666.	−0.615698
$151$	−416838.	−1.48773	−0.743866	−	0.668328i	$-0.767010\pi$
$151$	−416838.	−1.48773	−0.743866	+	0.668328i	$0.767010\pi$
$152$	−120575.	−0.423299
$153$	−7165.81	−0.0247478
$154$	0	0
$155$	191295.	0.639548
$156$	−52296.0	−0.172051
$157$	−119291.	−0.386240	−0.193120	−	0.981175i	$-0.561861\pi$
$157$	−119291.	−0.386240	−0.193120	+	0.981175i	$0.561861\pi$
$158$	−11919.2	−0.0379845
$159$	−295640.	−0.927407
$160$	−21504.0	−0.0664078
$161$	0	0
$162$	242576.	0.726205
$163$	47372.4	0.139655	0.0698275	−	0.997559i	$-0.477755\pi$
$163$	47372.4	0.139655	0.0698275	+	0.997559i	$0.477755\pi$
$164$	275230.	0.799071
$165$	207711.	0.593950
$166$	183818.	0.517749
$167$	231669.	0.642802	0.321401	−	0.946943i	$-0.395846\pi$
$167$	231669.	0.642802	0.321401	+	0.946943i	$0.395846\pi$
$168$	0	0
$169$	−328518.	−0.884795
$170$	89162.9	0.236626
$171$	12718.5	0.0332618
$172$	86431.7	0.222767
$173$	−134339.	−0.341262	−0.170631	−	0.985335i	$-0.554581\pi$
$173$	−134339.	−0.341262	−0.170631	+	0.985335i	$0.554581\pi$
$174$	−7822.57	−0.0195874
$175$	0	0
$176$	−160224.	−0.389893
$177$	−40058.4	−0.0961082
$178$	396160.	0.937175
$179$	46584.4	0.108669	0.0543347	−	0.998523i	$-0.482696\pi$
$179$	46584.4	0.108669	0.0543347	+	0.998523i	$0.482696\pi$
$180$	2268.30	0.00521817
$181$	−829210.	−1.88134	−0.940672	−	0.339317i	$-0.889804\pi$
$181$	−829210.	−1.88134	−0.940672	+	0.339317i	$0.889804\pi$
$182$	0	0
$183$	−33103.7	−0.0730716
$184$	−237912.	−0.518049
$185$	−126603.	−0.271967
$186$	575833.	1.22043
$187$	664342.	1.38927
$188$	−30003.9	−0.0619131
$189$	0	0
$190$	−158254.	−0.318032
$191$	−471917.	−0.936013	−0.468006	−	0.883725i	$-0.655028\pi$
$191$	−471917.	−0.936013	−0.468006	+	0.883725i	$0.655028\pi$
$192$	−64731.2	−0.126724
$193$	688354.	1.33021	0.665103	−	0.746752i	$-0.268388\pi$
$193$	688354.	1.33021	0.665103	+	0.746752i	$0.268388\pi$
$194$	−462194.	−0.881698
$195$	−68638.5	−0.129265
$196$	0	0
$197$	311915.	0.572625	0.286313	−	0.958136i	$-0.407570\pi$
$197$	311915.	0.572625	0.286313	+	0.958136i	$0.407570\pi$
$198$	16900.8	0.0306369
$199$	287212.	0.514126	0.257063	−	0.966395i	$-0.417245\pi$
$199$	287212.	0.514126	0.257063	+	0.966395i	$0.417245\pi$
$200$	171776.	0.303660
$201$	−926414.	−1.61739
$202$	43805.9	0.0755360
$203$	0	0
$204$	268397.	0.451547
$205$	361239.	0.600357
$206$	−550898.	−0.904488
$207$	25095.5	0.0407071
$208$	52946.2	0.0848548
$209$	−1.17913e6	−1.86723
$210$	0	0
$211$	−460493.	−0.712061	−0.356031	−	0.934474i	$-0.615870\pi$
$211$	−460493.	−0.712061	−0.356031	+	0.934474i	$0.615870\pi$
$212$	299316.	0.457393
$213$	494326.	0.746560
$214$	−302292.	−0.451224
$215$	113442.	0.167369
$216$	−238948.	−0.348473
$217$	0	0
$218$	−178105.	−0.253825
$219$	−113003.	−0.159213
$220$	−210294.	−0.292934
$221$	−219533.	−0.302356
$222$	−381100.	−0.518987
$223$	1.19776e6	1.61290	0.806449	−	0.591304i	$-0.201387\pi$
$223$	1.19776e6	1.61290	0.806449	+	0.591304i	$0.201387\pi$
$224$	0	0
$225$	−18119.4	−0.0238609
$226$	−361826.	−0.471225
$227$	−894561.	−1.15225	−0.576123	−	0.817363i	$-0.695435\pi$
$227$	−894561.	−1.15225	−0.576123	+	0.817363i	$0.695435\pi$
$228$	−476376.	−0.606893
$229$	259256.	0.326693	0.163347	−	0.986569i	$-0.447771\pi$
$229$	259256.	0.326693	0.163347	+	0.986569i	$0.447771\pi$
$230$	−312259.	−0.389220
$231$	0	0
$232$	7919.83	0.00966042
$233$	211315.	0.255000	0.127500	−	0.991839i	$-0.459305\pi$
$233$	211315.	0.255000	0.127500	+	0.991839i	$0.459305\pi$
$234$	−5584.90	−0.00666769
$235$	−39380.1	−0.0465165
$236$	40556.5	0.0474002
$237$	−47091.5	−0.0544592
$238$	0	0
$239$	463.018	0.000524328 0	0.000262164	−	1.00000i	$-0.499917\pi$
$239$	463.018	0.000524328 0	0.000262164		1.00000i	$0.499917\pi$
$240$	−84959.7	−0.0952105
$241$	−286395.	−0.317631	−0.158815	−	0.987308i	$-0.550767\pi$
$241$	−286395.	−0.317631	−0.158815	+	0.987308i	$0.550767\pi$
$242$	−922667.	−1.01276
$243$	51129.9	0.0555469
$244$	33515.3	0.0360386
$245$	0	0
$246$	1.08740e6	1.14565
$247$	389647.	0.406376
$248$	−582993.	−0.601913
$249$	726244.	0.742308
$250$	487956.	0.493777
$251$	1.37168e6	1.37426	0.687129	−	0.726535i	$-0.258870\pi$
$251$	1.37168e6	1.37426	0.687129	+	0.726535i	$0.258870\pi$
$252$	0	0
$253$	−2.32660e6	−2.28518
$254$	−750828.	−0.730224
$255$	352272.	0.339256
$256$	65536.0	0.0625000
$257$	759223.	0.717029	0.358515	−	0.933524i	$-0.383283\pi$
$257$	759223.	0.717029	0.358515	+	0.933524i	$0.383283\pi$
$258$	341481.	0.319387
$259$	0	0
$260$	69491.9	0.0637530
$261$	−835.404	−0.000759093 0
$262$	617649.	0.555890
$263$	−1.07244e6	−0.956061	−0.478030	−	0.878343i	$-0.658649\pi$
$263$	−1.07244e6	−0.956061	−0.478030	+	0.878343i	$0.658649\pi$
$264$	−633024.	−0.558998
$265$	392852.	0.343648
$266$	0	0
$267$	1.56518e6	1.34365
$268$	937932.	0.797691
$269$	1.76611e6	1.48812	0.744059	−	0.668114i	$-0.232898\pi$
$269$	1.76611e6	1.48812	0.744059	+	0.668114i	$0.232898\pi$
$270$	−313619.	−0.261814
$271$	2.05171e6	1.69704	0.848522	−	0.529160i	$-0.177493\pi$
$271$	2.05171e6	1.69704	0.848522	+	0.529160i	$0.177493\pi$
$272$	−271735.	−0.222701
$273$	0	0
$274$	−436951.	−0.351606
$275$	1.67984e6	1.33948
$276$	−939959.	−0.742739
$277$	870682.	0.681805	0.340903	−	0.940099i	$-0.389267\pi$
$277$	870682.	0.681805	0.340903	+	0.940099i	$0.389267\pi$
$278$	−818781.	−0.635413
$279$	61495.6	0.0472970
$280$	0	0
$281$	2.35412e6	1.77854	0.889270	−	0.457383i	$-0.151213\pi$
$281$	2.35412e6	1.77854	0.889270	+	0.457383i	$0.151213\pi$
$282$	−118542.	−0.0887663
$283$	2.19035e6	1.62573	0.812863	−	0.582454i	$-0.197908\pi$
$283$	2.19035e6	1.62573	0.812863	+	0.582454i	$0.197908\pi$
$284$	−500473.	−0.368201
$285$	−625243.	−0.455970
$286$	517775.	0.374306
$287$	0	0
$288$	−6912.90	−0.00491110
$289$	−293153.	−0.206467
$290$	10394.8	0.00725805
$291$	−1.82607e6	−1.26411
$292$	114408.	0.0785231
$293$	807700.	0.549644	0.274822	−	0.961495i	$-0.411381\pi$
$293$	807700.	0.549644	0.274822	+	0.961495i	$0.411381\pi$
$294$	0	0
$295$	53230.4	0.0356127
$296$	385838.	0.255962
$297$	−2.33674e6	−1.53716
$298$	1.62523e6	1.06017
$299$	768830.	0.497339
$300$	678666.	0.435364
$301$	0	0
$302$	1.66735e6	1.05199
$303$	173072.	0.108298
$304$	482299.	0.299317
$305$	43988.8	0.0270765
$306$	28663.2	0.0174993
$307$	−211516.	−0.128085	−0.0640424	−	0.997947i	$-0.520399\pi$
$307$	−211516.	−0.128085	−0.0640424	+	0.997947i	$0.520399\pi$
$308$	0	0
$309$	−2.17653e6	−1.29679
$310$	−765178.	−0.452229
$311$	291709.	0.171021	0.0855104	−	0.996337i	$-0.472748\pi$
$311$	291709.	0.171021	0.0855104	+	0.996337i	$0.472748\pi$
$312$	209184.	0.121658
$313$	1.99598e6	1.15158	0.575791	−	0.817597i	$-0.304694\pi$
$313$	1.99598e6	1.15158	0.575791	+	0.817597i	$0.304694\pi$
$314$	477162.	0.273113
$315$	0	0
$316$	47677.0	0.0268591
$317$	−2.80957e6	−1.57033	−0.785167	−	0.619285i	$-0.787423\pi$
$317$	−2.80957e6	−1.57033	−0.785167	+	0.619285i	$0.787423\pi$
$318$	1.18256e6	0.655776
$319$	77450.2	0.0426134
$320$	86016.0	0.0469574
$321$	−1.19432e6	−0.646930
$322$	0	0
$323$	−1.99977e6	−1.06653
$324$	−970302.	−0.513505
$325$	−555108.	−0.291520
$326$	−189490.	−0.0987510
$327$	−703671.	−0.363916
$328$	−1.10092e6	−0.565029
$329$	0	0
$330$	−830844.	−0.419986
$331$	1.38050e6	0.692572	0.346286	−	0.938129i	$-0.387443\pi$
$331$	1.38050e6	0.692572	0.346286	+	0.938129i	$0.387443\pi$
$332$	−735274.	−0.366103
$333$	−40699.2	−0.0201129
$334$	−926677.	−0.454530
$335$	1.23104e6	0.599320
$336$	0	0
$337$	566429.	0.271688	0.135844	−	0.990730i	$-0.456625\pi$
$337$	566429.	0.271688	0.135844	+	0.990730i	$0.456625\pi$
$338$	1.31407e6	0.625644
$339$	−1.42953e6	−0.675607
$340$	−356652.	−0.167320
$341$	−5.70125e6	−2.65512
$342$	−50874.1	−0.0235197
$343$	0	0
$344$	−345727.	−0.157520
$345$	−1.23370e6	−0.558034
$346$	537357.	0.241308
$347$	540207.	0.240845	0.120422	−	0.992723i	$-0.461575\pi$
$347$	540207.	0.240845	0.120422	+	0.992723i	$0.461575\pi$
$348$	31290.3	0.0138504
$349$	−1.73807e6	−0.763841	−0.381921	−	0.924195i	$-0.624737\pi$
$349$	−1.73807e6	−0.763841	−0.381921	+	0.924195i	$0.624737\pi$
$350$	0	0
$351$	772180.	0.334542
$352$	640895.	0.275696
$353$	−1.07422e6	−0.458834	−0.229417	−	0.973328i	$-0.573682\pi$
$353$	−1.07422e6	−0.458834	−0.229417	+	0.973328i	$0.573682\pi$
$354$	160234.	0.0679588
$355$	−656870.	−0.276636
$356$	−1.58464e6	−0.662682
$357$	0	0
$358$	−186337.	−0.0768409
$359$	121204.	0.0496341	0.0248170	−	0.999692i	$-0.492100\pi$
$359$	121204.	0.0496341	0.0248170	+	0.999692i	$0.492100\pi$
$360$	−9073.18	−0.00368981
$361$	1.07328e6	0.433455
$362$	3.31684e6	1.33031
$363$	−3.64535e6	−1.45202
$364$	0	0
$365$	150160.	0.0589959
$366$	132415.	0.0516694
$367$	553829.	0.214640	0.107320	−	0.994225i	$-0.465773\pi$
$367$	553829.	0.214640	0.107320	+	0.994225i	$0.465773\pi$
$368$	951646.	0.366316
$369$	116128.	0.0443986
$370$	506413.	0.192309
$371$	0	0
$372$	−2.30333e6	−0.862977
$373$	−501478.	−0.186629	−0.0933146	−	0.995637i	$-0.529746\pi$
$373$	−501478.	−0.186629	−0.0933146	+	0.995637i	$0.529746\pi$
$374$	−2.65737e6	−0.982364
$375$	1.92785e6	0.707939
$376$	120015.	0.0437792
$377$	−25593.6	−0.00927422
$378$	0	0
$379$	999004.	0.357248	0.178624	−	0.983917i	$-0.442835\pi$
$379$	999004.	0.357248	0.178624	+	0.983917i	$0.442835\pi$
$380$	633017.	0.224883
$381$	−2.96643e6	−1.04694
$382$	1.88767e6	0.661861
$383$	−652464.	−0.227279	−0.113640	−	0.993522i	$-0.536251\pi$
$383$	−652464.	−0.227279	−0.113640	+	0.993522i	$0.536251\pi$
$384$	258925.	0.0896077
$385$	0	0
$386$	−2.75342e6	−0.940597
$387$	36468.1	0.0123776
$388$	1.84877e6	0.623454
$389$	−79253.0	−0.0265547	−0.0132774	−	0.999912i	$-0.504226\pi$
$389$	−79253.0	−0.0265547	−0.0132774	+	0.999912i	$0.504226\pi$
$390$	274554.	0.0914042
$391$	−3.94585e6	−1.30526
$392$	0	0
$393$	2.44026e6	0.796992
$394$	−1.24766e6	−0.404907
$395$	62576.0	0.0201797
$396$	−67603.2	−0.0216635
$397$	−4.00886e6	−1.27657	−0.638284	−	0.769801i	$-0.720356\pi$
$397$	−4.00886e6	−1.27657	−0.638284	+	0.769801i	$0.720356\pi$
$398$	−1.14885e6	−0.363542
$399$	0	0
$400$	−687104.	−0.214720
$401$	674418.	0.209444	0.104722	−	0.994502i	$-0.466605\pi$
$401$	674418.	0.209444	0.104722	+	0.994502i	$0.466605\pi$
$402$	3.70565e6	1.14367
$403$	1.88399e6	0.577850
$404$	−175223.	−0.0534120
$405$	−1.27352e6	−0.385806
$406$	0	0
$407$	3.77322e6	1.12908
$408$	−1.07359e6	−0.319292
$409$	2.85413e6	0.843656	0.421828	−	0.906676i	$-0.361389\pi$
$409$	2.85413e6	0.843656	0.421828	+	0.906676i	$0.361389\pi$
$410$	−1.44496e6	−0.424517
$411$	−1.72634e6	−0.504106
$412$	2.20359e6	0.639570
$413$	0	0
$414$	−100382.	−0.0287843
$415$	−965047.	−0.275060
$416$	−211785.	−0.0600014
$417$	−3.23490e6	−0.911006
$418$	4.71653e6	1.32033
$419$	4.66553e6	1.29827	0.649136	−	0.760672i	$-0.275130\pi$
$419$	4.66553e6	1.29827	0.649136	+	0.760672i	$0.275130\pi$
$420$	0	0
$421$	−3.73317e6	−1.02653	−0.513266	−	0.858229i	$-0.671565\pi$
$421$	−3.73317e6	−1.02653	−0.513266	+	0.858229i	$0.671565\pi$
$422$	1.84197e6	0.503503
$423$	−12659.5	−0.00344007
$424$	−1.19726e6	−0.323426
$425$	2.84897e6	0.765095
$426$	−1.97731e6	−0.527898
$427$	0	0
$428$	1.20917e6	0.319064
$429$	2.04567e6	0.536651
$430$	−453766.	−0.118348
$431$	964670.	0.250141	0.125071	−	0.992148i	$-0.460084\pi$
$431$	964670.	0.250141	0.125071	+	0.992148i	$0.460084\pi$
$432$	955793.	0.246408
$433$	6.18096e6	1.58429	0.792147	−	0.610330i	$-0.208963\pi$
$433$	6.18096e6	1.58429	0.792147	+	0.610330i	$0.208963\pi$
$434$	0	0
$435$	41068.5	0.0104060
$436$	712421.	0.179482
$437$	7.00344e6	1.75432
$438$	452010.	0.112580
$439$	215135.	0.0532782	0.0266391	−	0.999645i	$-0.491520\pi$
$439$	215135.	0.0532782	0.0266391	+	0.999645i	$0.491520\pi$
$440$	841174.	0.207135
$441$	0	0
$442$	878132.	0.213798
$443$	−7.19867e6	−1.74278	−0.871391	−	0.490589i	$-0.836782\pi$
$443$	−7.19867e6	−1.74278	−0.871391	+	0.490589i	$0.836782\pi$
$444$	1.52440e6	0.366979
$445$	−2.07984e6	−0.497886
$446$	−4.79103e6	−1.14049
$447$	6.42109e6	1.51999
$448$	0	0
$449$	3.92153e6	0.917994	0.458997	−	0.888438i	$-0.348209\pi$
$449$	3.92153e6	0.917994	0.458997	+	0.888438i	$0.348209\pi$
$450$	72477.5	0.0168722
$451$	−1.07662e7	−2.49242
$452$	1.44730e6	0.333207
$453$	6.58750e6	1.50826
$454$	3.57824e6	0.814761
$455$	0	0
$456$	1.90550e6	0.429138
$457$	1.32168e6	0.296030	0.148015	−	0.988985i	$-0.452712\pi$
$457$	1.32168e6	0.296030	0.148015	+	0.988985i	$0.452712\pi$
$458$	−1.03702e6	−0.231007
$459$	−3.96304e6	−0.878005
$460$	1.24904e6	0.275220
$461$	75459.1	0.0165371	0.00826855	−	0.999966i	$-0.497368\pi$
$461$	75459.1	0.0165371	0.00826855	+	0.999966i	$0.497368\pi$
$462$	0	0
$463$	−3.28757e6	−0.712727	−0.356363	−	0.934347i	$-0.615984\pi$
$463$	−3.28757e6	−0.712727	−0.356363	+	0.934347i	$0.615984\pi$
$464$	−31679.3	−0.00683095
$465$	−3.02312e6	−0.648371
$466$	−845259.	−0.180312
$467$	643382.	0.136514	0.0682569	−	0.997668i	$-0.478256\pi$
$467$	643382.	0.136514	0.0682569	+	0.997668i	$0.478256\pi$
$468$	22339.6	0.00471477
$469$	0	0
$470$	157520.	0.0328921
$471$	1.88521e6	0.391568
$472$	−162226.	−0.0335170
$473$	−3.38096e6	−0.694843
$474$	188366.	0.0385085
$475$	−5.05660e6	−1.02831
$476$	0	0
$477$	126290.	0.0254141
$478$	−1852.07	−0.000370756 0
$479$	7.42648e6	1.47892	0.739459	−	0.673202i	$-0.235081\pi$
$479$	7.42648e6	1.47892	0.739459	+	0.673202i	$0.235081\pi$
$480$	339839.	0.0673240
$481$	−1.24687e6	−0.245730
$482$	1.14558e6	0.224599
$483$	0	0
$484$	3.69067e6	0.716130
$485$	2.42652e6	0.468413
$486$	−204520.	−0.0392776
$487$	−4.17085e6	−0.796896	−0.398448	−	0.917191i	$-0.630451\pi$
$487$	−4.17085e6	−0.796896	−0.398448	+	0.917191i	$0.630451\pi$
$488$	−134061.	−0.0254832
$489$	−748651.	−0.141582
$490$	0	0
$491$	−3.73674e6	−0.699502	−0.349751	−	0.936843i	$-0.613734\pi$
$491$	−3.73674e6	−0.699502	−0.349751	+	0.936843i	$0.613734\pi$
$492$	−4.34959e6	−0.810095
$493$	131353.	0.0243402
$494$	−1.55859e6	−0.287351
$495$	−88729.2	−0.0162762
$496$	2.33197e6	0.425617
$497$	0	0
$498$	−2.90498e6	−0.524891
$499$	8.70862e6	1.56566	0.782831	−	0.622235i	$-0.213775\pi$
$499$	8.70862e6	1.56566	0.782831	+	0.622235i	$0.213775\pi$
$500$	−1.95182e6	−0.349153
$501$	−3.66119e6	−0.651670
$502$	−5.48672e6	−0.971748
$503$	−3.28384e6	−0.578711	−0.289355	−	0.957222i	$-0.593441\pi$
$503$	−3.28384e6	−0.578711	−0.289355	+	0.957222i	$0.593441\pi$
$504$	0	0
$505$	−229981.	−0.0401294
$506$	9.30641e6	1.61587
$507$	5.19174e6	0.897001
$508$	3.00331e6	0.516346
$509$	9.43703e6	1.61451	0.807255	−	0.590203i	$-0.200952\pi$
$509$	9.43703e6	1.61451	0.807255	+	0.590203i	$0.200952\pi$
$510$	−1.40909e6	−0.239890
$511$	0	0
$512$	−262144.	−0.0441942
$513$	7.03396e6	1.18007
$514$	−3.03689e6	−0.507016
$515$	2.89221e6	0.480521
$516$	−1.36592e6	−0.225841
$517$	1.17366e6	0.193116
$518$	0	0
$519$	2.12303e6	0.345970
$520$	−277967.	−0.0450802
$521$	−5.90726e6	−0.953437	−0.476719	−	0.879056i	$-0.658174\pi$
$521$	−5.90726e6	−0.953437	−0.476719	+	0.879056i	$0.658174\pi$
$522$	3341.61	0.000536760 0
$523$	−654337.	−0.104604	−0.0523019	−	0.998631i	$-0.516656\pi$
$523$	−654337.	−0.104604	−0.0523019	+	0.998631i	$0.516656\pi$
$524$	−2.47060e6	−0.393073
$525$	0	0
$526$	4.28978e6	0.676037
$527$	−9.66915e6	−1.51657
$528$	2.53210e6	0.395271
$529$	7.38248e6	1.14700
$530$	−1.57141e6	−0.242996
$531$	17112.0	0.00263369
$532$	0	0
$533$	3.55771e6	0.542440
$534$	−6.26072e6	−0.950103
$535$	1.58703e6	0.239718
$536$	−3.75173e6	−0.564052
$537$	−736196.	−0.110169
$538$	−7.06445e6	−1.05226
$539$	0	0
$540$	1.25448e6	0.185131
$541$	−863115.	−0.126787	−0.0633936	−	0.997989i	$-0.520192\pi$
$541$	−863115.	−0.126787	−0.0633936	+	0.997989i	$0.520192\pi$
$542$	−8.20685e6	−1.19999
$543$	1.31044e7	1.90730
$544$	1.08694e6	0.157474
$545$	935052.	0.134848
$546$	0	0
$547$	−5.45692e6	−0.779794	−0.389897	−	0.920859i	$-0.627489\pi$
$547$	−5.45692e6	−0.779794	−0.389897	+	0.920859i	$0.627489\pi$
$548$	1.74781e6	0.248623
$549$	14141.1	0.00200241
$550$	−6.71938e6	−0.947158
$551$	−233137.	−0.0327139
$552$	3.75984e6	0.525196
$553$	0	0
$554$	−3.48273e6	−0.482109
$555$	2.00078e6	0.275719
$556$	3.27513e6	0.449305
$557$	1.11776e7	1.52655	0.763275	−	0.646074i	$-0.223590\pi$
$557$	1.11776e7	1.52655	0.763275	+	0.646074i	$0.223590\pi$
$558$	−245982.	−0.0334440
$559$	1.11724e6	0.151223
$560$	0	0
$561$	−1.04989e7	−1.40844
$562$	−9.41650e6	−1.25762
$563$	−880265.	−0.117042	−0.0585211	−	0.998286i	$-0.518638\pi$
$563$	−880265.	−0.117042	−0.0585211	+	0.998286i	$0.518638\pi$
$564$	474166.	0.0627672
$565$	1.89959e6	0.250344
$566$	−8.76140e6	−1.14956
$567$	0	0
$568$	2.00189e6	0.260357
$569$	−1.54972e6	−0.200665	−0.100332	−	0.994954i	$-0.531991\pi$
$569$	−1.54972e6	−0.200665	−0.100332	+	0.994954i	$0.531991\pi$
$570$	2.50097e6	0.322420
$571$	−1.09701e7	−1.40806	−0.704032	−	0.710168i	$-0.748619\pi$
$571$	−1.09701e7	−1.40806	−0.704032	+	0.710168i	$0.748619\pi$
$572$	−2.07110e6	−0.264674
$573$	7.45794e6	0.948926
$574$	0	0
$575$	−9.97742e6	−1.25849
$576$	27651.6	0.00347268
$577$	1.25868e7	1.57390	0.786948	−	0.617019i	$-0.211660\pi$
$577$	1.25868e7	1.57390	0.786948	+	0.617019i	$0.211660\pi$
$578$	1.17261e6	0.145994
$579$	−1.08784e7	−1.34856
$580$	−41579.1	−0.00513222
$581$	0	0
$582$	7.30428e6	0.893861
$583$	−1.17084e7	−1.42667
$584$	−457630.	−0.0555242
$585$	29320.7	0.00354230
$586$	−3.23080e6	−0.388657
$587$	−1.19962e7	−1.43697	−0.718484	−	0.695544i	$-0.755164\pi$
$587$	−1.19962e7	−1.43697	−0.718484	+	0.695544i	$0.755164\pi$
$588$	0	0
$589$	1.71617e7	2.03831
$590$	−212921.	−0.0251819
$591$	−4.92935e6	−0.580525
$592$	−1.54335e6	−0.180993
$593$	−5.32309e6	−0.621623	−0.310811	−	0.950472i	$-0.600601\pi$
$593$	−5.32309e6	−0.621623	−0.310811	+	0.950472i	$0.600601\pi$
$594$	9.34696e6	1.08694
$595$	0	0
$596$	−6.50092e6	−0.749651
$597$	−4.53895e6	−0.521218
$598$	−3.07532e6	−0.351672
$599$	7.55513e6	0.860350	0.430175	−	0.902746i	$-0.358452\pi$
$599$	7.55513e6	0.860350	0.430175	+	0.902746i	$0.358452\pi$
$600$	−2.71466e6	−0.307849
$601$	−4.44758e6	−0.502270	−0.251135	−	0.967952i	$-0.580804\pi$
$601$	−4.44758e6	−0.502270	−0.251135	+	0.967952i	$0.580804\pi$
$602$	0	0
$603$	395742.	0.0443219
$604$	−6.66941e6	−0.743866
$605$	4.84400e6	0.538042
$606$	−692286.	−0.0765780
$607$	−5.57320e6	−0.613950	−0.306975	−	0.951718i	$-0.599317\pi$
$607$	−5.57320e6	−0.613950	−0.306975	+	0.951718i	$0.599317\pi$
$608$	−1.92919e6	−0.211649
$609$	0	0
$610$	−175955.	−0.0191460
$611$	−387840.	−0.0420290
$612$	−114653.	−0.0123739
$613$	−1.11265e7	−1.19593	−0.597965	−	0.801522i	$-0.704024\pi$
$613$	−1.11265e7	−1.19593	−0.597965	+	0.801522i	$0.704024\pi$
$614$	846064.	0.0905696
$615$	−5.70884e6	−0.608640
$616$	0	0
$617$	−1.07454e7	−1.13634	−0.568170	−	0.822911i	$-0.692349\pi$
$617$	−1.07454e7	−1.13634	−0.568170	+	0.822911i	$0.692349\pi$
$618$	8.70612e6	0.916966
$619$	−1.35756e7	−1.42408	−0.712038	−	0.702141i	$-0.752228\pi$
$619$	−1.35756e7	−1.42408	−0.712038	+	0.702141i	$0.752228\pi$
$620$	3.06071e6	0.319774
$621$	1.38790e7	1.44421
$622$	−1.16684e6	−0.120930
$623$	0	0
$624$	−836736.	−0.0860254
$625$	5.82573e6	0.596555
$626$	−7.98391e6	−0.814291
$627$	1.86344e7	1.89299
$628$	−1.90865e6	−0.193120
$629$	6.39927e6	0.644917
$630$	0	0
$631$	1.27986e7	1.27964	0.639820	−	0.768525i	$-0.279009\pi$
$631$	1.27986e7	1.27964	0.639820	+	0.768525i	$0.279009\pi$
$632$	−190708.	−0.0189922
$633$	7.27741e6	0.721885
$634$	1.12383e7	1.11039
$635$	3.94184e6	0.387941
$636$	−4.73024e6	−0.463703
$637$	0	0
$638$	−309801.	−0.0301322
$639$	−211164.	−0.0204583
$640$	−344064.	−0.0332039
$641$	−884833.	−0.0850582	−0.0425291	−	0.999095i	$-0.513542\pi$
$641$	−884833.	−0.0850582	−0.0425291	+	0.999095i	$0.513542\pi$
$642$	4.77727e6	0.457449
$643$	−6.66271e6	−0.635511	−0.317756	−	0.948173i	$-0.602929\pi$
$643$	−6.66271e6	−0.635511	−0.317756	+	0.948173i	$0.602929\pi$
$644$	0	0
$645$	−1.79277e6	−0.169678
$646$	7.99910e6	0.754153
$647$	1.69177e7	1.58885	0.794423	−	0.607365i	$-0.207773\pi$
$647$	1.69177e7	1.58885	0.794423	+	0.607365i	$0.207773\pi$
$648$	3.88121e6	0.363103
$649$	−1.58645e6	−0.147848
$650$	2.22043e6	0.206136
$651$	0	0
$652$	757959.	0.0698275
$653$	9.49307e6	0.871212	0.435606	−	0.900137i	$-0.356534\pi$
$653$	9.49307e6	0.871212	0.435606	+	0.900137i	$0.356534\pi$
$654$	2.81469e6	0.257327
$655$	−3.24266e6	−0.295323
$656$	4.40367e6	0.399536
$657$	48272.0	0.00436297
$658$	0	0
$659$	−4.97563e6	−0.446308	−0.223154	−	0.974783i	$-0.571635\pi$
$659$	−4.97563e6	−0.446308	−0.223154	+	0.974783i	$0.571635\pi$
$660$	3.32338e6	0.296975
$661$	−2.11531e7	−1.88309	−0.941543	−	0.336894i	$-0.890624\pi$
$661$	−2.11531e7	−1.88309	−0.941543	+	0.336894i	$0.890624\pi$
$662$	−5.52198e6	−0.489722
$663$	3.46939e6	0.306527
$664$	2.94110e6	0.258874
$665$	0	0
$666$	162797.	0.0142220
$667$	−460015.	−0.0400366
$668$	3.70671e6	0.321401
$669$	−1.89288e7	−1.63515
$670$	−4.92414e6	−0.423783
$671$	−1.31102e6	−0.112410
$672$	0	0
$673$	417573.	0.0355382	0.0177691	−	0.999842i	$-0.494344\pi$
$673$	417573.	0.0355382	0.0177691	+	0.999842i	$0.494344\pi$
$674$	−2.26572e6	−0.192112
$675$	−1.00209e7	−0.846539
$676$	−5.25629e6	−0.442397
$677$	−2.62468e6	−0.220092	−0.110046	−	0.993926i	$-0.535100\pi$
$677$	−2.62468e6	−0.220092	−0.110046	+	0.993926i	$0.535100\pi$
$678$	5.71812e6	0.477726
$679$	0	0
$680$	1.42661e6	0.118313
$681$	1.41372e7	1.16814
$682$	2.28050e7	1.87745
$683$	−8.74455e6	−0.717275	−0.358637	−	0.933477i	$-0.616759\pi$
$683$	−8.74455e6	−0.717275	−0.358637	+	0.933477i	$0.616759\pi$
$684$	203496.	0.0166309
$685$	2.29399e6	0.186795
$686$	0	0
$687$	−4.09716e6	−0.331200
$688$	1.38291e6	0.111384
$689$	3.86905e6	0.310496
$690$	4.93479e6	0.394590
$691$	−4.39667e6	−0.350291	−0.175146	−	0.984543i	$-0.556040\pi$
$691$	−4.39667e6	−0.350291	−0.175146	+	0.984543i	$0.556040\pi$
$692$	−2.14943e6	−0.170631
$693$	0	0
$694$	−2.16083e6	−0.170303
$695$	4.29860e6	0.337571
$696$	−125161.	−0.00979369
$697$	−1.82591e7	−1.42363
$698$	6.95227e6	0.540117
$699$	−3.33951e6	−0.258518
$700$	0	0
$701$	6.51339e6	0.500624	0.250312	−	0.968165i	$-0.419467\pi$
$701$	6.51339e6	0.500624	0.250312	+	0.968165i	$0.419467\pi$
$702$	−3.08872e6	−0.236557
$703$	−1.13580e7	−0.866789
$704$	−2.56358e6	−0.194946
$705$	622343.	0.0471582
$706$	4.29687e6	0.324445
$707$	0	0
$708$	−640934.	−0.0480541
$709$	−1.04651e7	−0.781859	−0.390929	−	0.920421i	$-0.627846\pi$
$709$	−1.04651e7	−0.781859	−0.390929	+	0.920421i	$0.627846\pi$
$710$	2.62748e6	0.195611
$711$	20116.3	0.00149237
$712$	6.33856e6	0.468587
$713$	3.38625e7	2.49457
$714$	0	0
$715$	−2.71832e6	−0.198855
$716$	745350.	0.0543347
$717$	−7317.31	−0.000531562 0
$718$	−484815.	−0.0350966
$719$	1.68149e7	1.21303	0.606516	−	0.795071i	$-0.292567\pi$
$719$	1.68149e7	1.21303	0.606516	+	0.795071i	$0.292567\pi$
$720$	36292.7	0.00260909
$721$	0	0
$722$	−4.29311e6	−0.306499
$723$	4.52605e6	0.322013
$724$	−1.32674e7	−0.940672
$725$	332138.	0.0234679
$726$	1.45814e7	1.02673
$727$	1.71928e7	1.20646	0.603228	−	0.797569i	$-0.293881\pi$
$727$	1.71928e7	1.20646	0.603228	+	0.797569i	$0.293881\pi$
$728$	0	0
$729$	1.39284e7	0.970696
$730$	−600640.	−0.0417164
$731$	−5.73400e6	−0.396885
$732$	−529659.	−0.0365358
$733$	−1.97365e7	−1.35679	−0.678393	−	0.734700i	$-0.737323\pi$
$733$	−1.97365e7	−1.35679	−0.678393	+	0.734700i	$0.737323\pi$
$734$	−2.21531e6	−0.151773
$735$	0	0
$736$	−3.80659e6	−0.259025
$737$	−3.66892e7	−2.48811
$738$	−464511.	−0.0313946
$739$	1.28719e7	0.867022	0.433511	−	0.901148i	$-0.357275\pi$
$739$	1.28719e7	0.867022	0.433511	+	0.901148i	$0.357275\pi$
$740$	−2.02565e6	−0.135983
$741$	−6.15778e6	−0.411983
$742$	0	0
$743$	2.45606e7	1.63218	0.816089	−	0.577927i	$-0.196138\pi$
$743$	2.45606e7	1.63218	0.816089	+	0.577927i	$0.196138\pi$
$744$	9.21333e6	0.610217
$745$	−8.53246e6	−0.563227
$746$	2.00591e6	0.131967
$747$	−310234.	−0.0203417
$748$	1.06295e7	0.694636
$749$	0	0
$750$	−7.71142e6	−0.500589
$751$	−325965.	−0.0210898	−0.0105449	−	0.999944i	$-0.503357\pi$
$751$	−325965.	−0.0210898	−0.0105449	+	0.999944i	$0.503357\pi$
$752$	−480062.	−0.0309566
$753$	−2.16774e7	−1.39322
$754$	102374.	0.00655786
$755$	−8.75360e6	−0.558881
$756$	0	0
$757$	1.84659e7	1.17120	0.585599	−	0.810601i	$-0.300859\pi$
$757$	1.84659e7	1.17120	0.585599	+	0.810601i	$0.300859\pi$
$758$	−3.99602e6	−0.252612
$759$	3.67685e7	2.31671
$760$	−2.53207e6	−0.159016
$761$	−5.12626e6	−0.320877	−0.160439	−	0.987046i	$-0.551291\pi$
$761$	−5.12626e6	−0.320877	−0.160439	+	0.987046i	$0.551291\pi$
$762$	1.18657e7	0.740298
$763$	0	0
$764$	−7.55066e6	−0.468006
$765$	−150482.	−0.00929675
$766$	2.60985e6	0.160711
$767$	524246.	0.0321771
$768$	−1.03570e6	−0.0633622
$769$	−1.63432e6	−0.0996602	−0.0498301	−	0.998758i	$-0.515868\pi$
$769$	−1.63432e6	−0.0996602	−0.0498301	+	0.998758i	$0.515868\pi$
$770$	0	0
$771$	−1.19984e7	−0.726921
$772$	1.10137e7	0.665103
$773$	4.28257e6	0.257784	0.128892	−	0.991659i	$-0.458858\pi$
$773$	4.28257e6	0.257784	0.128892	+	0.991659i	$0.458858\pi$
$774$	−145872.	−0.00875227
$775$	−2.44493e7	−1.46222
$776$	−7.39510e6	−0.440849
$777$	0	0
$778$	317012.	0.0187770
$779$	3.24079e7	1.91341
$780$	−1.09822e6	−0.0646325
$781$	1.95770e7	1.14847
$782$	1.57834e7	0.922962
$783$	−462019.	−0.0269312
$784$	0	0
$785$	−2.50510e6	−0.145095
$786$	−9.76102e6	−0.563559
$787$	7.82963e6	0.450614	0.225307	−	0.974288i	$-0.427662\pi$
$787$	7.82963e6	0.450614	0.225307	+	0.974288i	$0.427662\pi$
$788$	4.99064e6	0.286313
$789$	1.69484e7	0.969250
$790$	−250304.	−0.0142692
$791$	0	0
$792$	270413.	0.0153184
$793$	433229.	0.0244644
$794$	1.60354e7	0.902670
$795$	−6.20844e6	−0.348389
$796$	4.59539e6	0.257063
$797$	3.68238e6	0.205344	0.102672	−	0.994715i	$-0.467261\pi$
$797$	3.68238e6	0.205344	0.102672	+	0.994715i	$0.467261\pi$
$798$	0	0
$799$	1.99050e6	0.110305
$800$	2.74842e6	0.151830
$801$	−668607.	−0.0368205
$802$	−2.69767e6	−0.148099
$803$	−4.47529e6	−0.244925
$804$	−1.48226e7	−0.808695
$805$	0	0
$806$	−7.53595e6	−0.408602
$807$	−2.79108e7	−1.50865
$808$	700894.	0.0377680
$809$	2.08181e7	1.11833	0.559165	−	0.829056i	$-0.311122\pi$
$809$	2.08181e7	1.11833	0.559165	+	0.829056i	$0.311122\pi$
$810$	5.09409e6	0.272806
$811$	−3.03542e7	−1.62057	−0.810283	−	0.586039i	$-0.800687\pi$
$811$	−3.03542e7	−1.62057	−0.810283	+	0.586039i	$0.800687\pi$
$812$	0	0
$813$	−3.24243e7	−1.72046
$814$	−1.50929e7	−0.798383
$815$	994821.	0.0524627
$816$	4.29436e6	0.225774
$817$	1.01772e7	0.533426
$818$	−1.14165e7	−0.596555
$819$	0	0
$820$	5.77982e6	0.300179
$821$	2.74387e7	1.42071	0.710355	−	0.703843i	$-0.248534\pi$
$821$	2.74387e7	1.42071	0.710355	+	0.703843i	$0.248534\pi$
$822$	6.90536e6	0.356457
$823$	1.59126e7	0.818919	0.409459	−	0.912328i	$-0.365717\pi$
$823$	1.59126e7	0.818919	0.409459	+	0.912328i	$0.365717\pi$
$824$	−8.81436e6	−0.452244
$825$	−2.65474e7	−1.35796
$826$	0	0
$827$	1.40824e7	0.716001	0.358001	−	0.933721i	$-0.383459\pi$
$827$	1.40824e7	0.716001	0.358001	+	0.933721i	$0.383459\pi$
$828$	401528.	0.0203536
$829$	−2.18883e7	−1.10618	−0.553089	−	0.833122i	$-0.686551\pi$
$829$	−2.18883e7	−1.10618	−0.553089	+	0.833122i	$0.686551\pi$
$830$	3.86019e6	0.194497
$831$	−1.37598e7	−0.691211
$832$	847139.	0.0424274
$833$	0	0
$834$	1.29396e7	0.644179
$835$	4.86505e6	0.241475
$836$	−1.88661e7	−0.933613
$837$	3.40100e7	1.67801
$838$	−1.86621e7	−0.918017
$839$	1.98669e7	0.974372	0.487186	−	0.873298i	$-0.338023\pi$
$839$	1.98669e7	0.974372	0.487186	+	0.873298i	$0.338023\pi$
$840$	0	0
$841$	−2.04958e7	−0.999253
$842$	1.49327e7	0.725868
$843$	−3.72034e7	−1.80308
$844$	−7.36790e6	−0.356031
$845$	−6.89888e6	−0.332381
$846$	50638.1	0.00243249
$847$	0	0
$848$	4.78905e6	0.228697
$849$	−3.46152e7	−1.64815
$850$	−1.13959e7	−0.541004
$851$	−2.24110e7	−1.06081
$852$	7.90922e6	0.373280
$853$	−8.75258e6	−0.411873	−0.205937	−	0.978565i	$-0.566024\pi$
$853$	−8.75258e6	−0.411873	−0.205937	+	0.978565i	$0.566024\pi$
$854$	0	0
$855$	267089.	0.0124951
$856$	−4.83667e6	−0.225612
$857$	1.95477e6	0.0909166	0.0454583	−	0.998966i	$-0.485525\pi$
$857$	1.95477e6	0.0909166	0.0454583	+	0.998966i	$0.485525\pi$
$858$	−8.18267e6	−0.379469
$859$	−4.98450e6	−0.230483	−0.115241	−	0.993338i	$-0.536764\pi$
$859$	−4.98450e6	−0.230483	−0.115241	+	0.993338i	$0.536764\pi$
$860$	1.81506e6	0.0836847
$861$	0	0
$862$	−3.85868e6	−0.176877
$863$	−1.69931e7	−0.776685	−0.388343	−	0.921515i	$-0.626952\pi$
$863$	−1.69931e7	−0.776685	−0.388343	+	0.921515i	$0.626952\pi$
$864$	−3.82317e6	−0.174237
$865$	−2.82112e6	−0.128198
$866$	−2.47238e7	−1.12027
$867$	4.63285e6	0.209315
$868$	0	0
$869$	−1.86498e6	−0.0837772
$870$	−164274.	−0.00735818
$871$	1.21240e7	0.541503
$872$	−2.84968e6	−0.126913
$873$	780054.	0.0346409
$874$	−2.80138e7	−1.24049
$875$	0	0
$876$	−1.80804e6	−0.0796064
$877$	1.81959e7	0.798869	0.399434	−	0.916762i	$-0.369207\pi$
$877$	1.81959e7	0.798869	0.399434	+	0.916762i	$0.369207\pi$
$878$	−860539.	−0.0376733
$879$	−1.27645e7	−0.557226
$880$	−3.36470e6	−0.146467
$881$	−1.77637e7	−0.771068	−0.385534	−	0.922694i	$-0.625983\pi$
$881$	−1.77637e7	−0.771068	−0.385534	+	0.922694i	$0.625983\pi$
$882$	0	0
$883$	1.71479e6	0.0740131	0.0370065	−	0.999315i	$-0.488218\pi$
$883$	1.71479e6	0.0740131	0.0370065	+	0.999315i	$0.488218\pi$
$884$	−3.51253e6	−0.151178
$885$	−841226.	−0.0361039
$886$	2.87947e7	1.23233
$887$	2.42436e7	1.03464	0.517318	−	0.855793i	$-0.326930\pi$
$887$	2.42436e7	1.03464	0.517318	+	0.855793i	$0.326930\pi$
$888$	−6.09760e6	−0.259494
$889$	0	0
$890$	8.31936e6	0.352058
$891$	3.79554e7	1.60169
$892$	1.91641e7	0.806449
$893$	−3.53292e6	−0.148253
$894$	−2.56843e7	−1.07479
$895$	978272.	0.0408227
$896$	0	0
$897$	−1.21502e7	−0.504200
$898$	−1.56861e7	−0.649120
$899$	−1.12725e6	−0.0465179
$900$	−289910.	−0.0119304
$901$	−1.98570e7	−0.814897
$902$	4.30647e7	1.76240
$903$	0	0
$904$	−5.78921e6	−0.235613
$905$	−1.74134e7	−0.706745
$906$	−2.63500e7	−1.06650
$907$	−1.90432e7	−0.768639	−0.384319	−	0.923200i	$-0.625564\pi$
$907$	−1.90432e7	−0.768639	−0.384319	+	0.923200i	$0.625564\pi$
$908$	−1.43130e7	−0.576123
$909$	−73932.0	−0.00296772
$910$	0	0
$911$	−3.18731e7	−1.27242	−0.636208	−	0.771518i	$-0.719498\pi$
$911$	−3.18731e7	−1.27242	−0.636208	+	0.771518i	$0.719498\pi$
$912$	−7.62201e6	−0.303447
$913$	2.87618e7	1.14193
$914$	−5.28671e6	−0.209325
$915$	−695178.	−0.0274500
$916$	4.14810e6	0.163347
$917$	0	0
$918$	1.58522e7	0.620843
$919$	−2.94858e7	−1.15166	−0.575830	−	0.817569i	$-0.695321\pi$
$919$	−2.94858e7	−1.15166	−0.575830	+	0.817569i	$0.695321\pi$
$920$	−4.99614e6	−0.194610
$921$	3.34270e6	0.129852
$922$	−301836.	−0.0116935
$923$	−6.46927e6	−0.249949
$924$	0	0
$925$	1.61811e7	0.621804
$926$	1.31503e7	0.503974
$927$	929761.	0.0355363
$928$	126717.	0.00483021
$929$	9.73871e6	0.370222	0.185111	−	0.982718i	$-0.440736\pi$
$929$	9.73871e6	0.370222	0.185111	+	0.982718i	$0.440736\pi$
$930$	1.20925e7	0.458468
$931$	0	0
$932$	3.38104e6	0.127500
$933$	−4.61003e6	−0.173380
$934$	−2.57353e6	−0.0965299
$935$	1.39512e7	0.521893
$936$	−89358.4	−0.00333385
$937$	−2.66734e7	−0.992498	−0.496249	−	0.868180i	$-0.665290\pi$
$937$	−2.66734e7	−0.992498	−0.496249	+	0.868180i	$0.665290\pi$
$938$	0	0
$939$	−3.15434e7	−1.16747
$940$	−630081.	−0.0232582
$941$	−3.22865e6	−0.118863	−0.0594315	−	0.998232i	$-0.518929\pi$
$941$	−3.22865e6	−0.118863	−0.0594315	+	0.998232i	$0.518929\pi$
$942$	−7.54084e6	−0.276880
$943$	6.39456e7	2.34170
$944$	648903.	0.0237001
$945$	0	0
$946$	1.35238e7	0.491328
$947$	−4.59244e6	−0.166406	−0.0832029	−	0.996533i	$-0.526515\pi$
$947$	−4.59244e6	−0.166406	−0.0832029	+	0.996533i	$0.526515\pi$
$948$	−753463.	−0.0272296
$949$	1.47887e6	0.0533045
$950$	2.02264e7	0.727126
$951$	4.44011e7	1.59200
$952$	0	0
$953$	2.97125e7	1.05976	0.529880	−	0.848073i	$-0.322237\pi$
$953$	2.97125e7	1.05976	0.529880	+	0.848073i	$0.322237\pi$
$954$	−505161.	−0.0179705
$955$	−9.91025e6	−0.351622
$956$	7408.29	0.000262164 0
$957$	−1.22399e6	−0.0432012
$958$	−2.97059e7	−1.04575
$959$	0	0
$960$	−1.35935e6	−0.0476052
$961$	5.43495e7	1.89840
$962$	4.98747e6	0.173757
$963$	510184.	0.0177281
$964$	−4.58232e6	−0.158815
$965$	1.44554e7	0.499704
$966$	0	0
$967$	7.64435e6	0.262890	0.131445	−	0.991323i	$-0.458038\pi$
$967$	7.64435e6	0.262890	0.131445	+	0.991323i	$0.458038\pi$
$968$	−1.47627e7	−0.506380
$969$	3.16034e7	1.08125
$970$	−9.70607e6	−0.331218
$971$	4.99621e7	1.70056	0.850281	−	0.526329i	$-0.176432\pi$
$971$	4.99621e7	1.70056	0.850281	+	0.526329i	$0.176432\pi$
$972$	818079.	0.0277734
$973$	0	0
$974$	1.66834e7	0.563491
$975$	8.77265e6	0.295542
$976$	536245.	0.0180193
$977$	4.05394e7	1.35876	0.679378	−	0.733789i	$-0.262250\pi$
$977$	4.05394e7	1.35876	0.679378	+	0.733789i	$0.262250\pi$
$978$	2.99460e6	0.100113
$979$	6.19865e7	2.06700
$980$	0	0
$981$	300592.	0.00997251
$982$	1.49470e7	0.494623
$983$	4.13056e7	1.36341	0.681703	−	0.731629i	$-0.261239\pi$
$983$	4.13056e7	1.36341	0.681703	+	0.731629i	$0.261239\pi$
$984$	1.73984e7	0.572824
$985$	6.55021e6	0.215112
$986$	−525413.	−0.0172111
$987$	0	0
$988$	6.23434e6	0.203188
$989$	2.00811e7	0.652826
$990$	354917.	0.0115090
$991$	−1.84084e7	−0.595431	−0.297715	−	0.954655i	$-0.596225\pi$
$991$	−1.84084e7	−0.595431	−0.297715	+	0.954655i	$0.596225\pi$
$992$	−9.32789e6	−0.300957
$993$	−2.18167e7	−0.702126
$994$	0	0
$995$	6.03144e6	0.193136
$996$	1.16199e7	0.371154
$997$	3.39708e7	1.08235	0.541175	−	0.840910i	$-0.317980\pi$
$997$	3.39708e7	1.08235	0.541175	+	0.840910i	$0.317980\pi$
$998$	−3.48345e7	−1.10709
$999$	−2.25086e7	−0.713568

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.6.a.f.1.1		2
3.2	odd	2		882.6.a.bl.1.2		2
4.3	odd	2		784.6.a.r.1.2		2
7.2	even	3		98.6.c.f.67.2		4
7.3	odd	6		14.6.c.b.9.1	✓	4
7.4	even	3		98.6.c.f.79.2		4
7.5	odd	6		14.6.c.b.11.1	yes	4
7.6	odd	2		98.6.a.c.1.2		2
21.5	even	6		126.6.g.e.109.2		4
21.17	even	6		126.6.g.e.37.2		4
21.20	even	2		882.6.a.bt.1.2		2
28.3	even	6		112.6.i.b.65.2		4
28.19	even	6		112.6.i.b.81.2		4
28.27	even	2		784.6.a.bc.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.6.c.b.9.1	✓	4	7.3	odd	6
14.6.c.b.11.1	yes	4	7.5	odd	6
98.6.a.c.1.2		2	7.6	odd	2
98.6.a.f.1.1		2	1.1	even	1	trivial
98.6.c.f.67.2		4	7.2	even	3
98.6.c.f.79.2		4	7.4	even	3
112.6.i.b.65.2		4	28.3	even	6
112.6.i.b.81.2		4	28.19	even	6
126.6.g.e.37.2		4	21.17	even	6
126.6.g.e.109.2		4	21.5	even	6
784.6.a.r.1.2		2	4.3	odd	2
784.6.a.bc.1.1		2	28.27	even	2
882.6.a.bl.1.2		2	3.2	odd	2
882.6.a.bt.1.2		2	21.20	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	98.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -15.8035 q^{3} +16.0000 q^{4} +21.0000 q^{5} +63.2140 q^{6} -64.0000 q^{8} +6.75088 q^{9} -84.0000 q^{10} -625.874 q^{11} -252.856 q^{12} +206.821 q^{13} -331.874 q^{15} +256.000 q^{16} -1061.46 q^{17} -27.0035 q^{18} +1883.98 q^{19} +336.000 q^{20} +2503.49 q^{22} +3717.37 q^{23} +1011.42 q^{24} -2684.00 q^{25} -827.284 q^{26} +3733.56 q^{27} -123.747 q^{29} +1327.49 q^{30} +9109.26 q^{31} -1024.00 q^{32} +9891.00 q^{33} +4245.85 q^{34} +108.014 q^{36} -6028.73 q^{37} -7535.92 q^{38} -3268.50 q^{39} -1344.00 q^{40} +17201.9 q^{41} +5401.98 q^{43} -10014.0 q^{44} +141.769 q^{45} -14869.5 q^{46} -1875.24 q^{47} -4045.70 q^{48} +10736.0 q^{50} +16774.8 q^{51} +3309.14 q^{52} +18707.2 q^{53} -14934.3 q^{54} -13143.3 q^{55} -29773.5 q^{57} +494.989 q^{58} +2534.78 q^{59} -5309.98 q^{60} +2094.71 q^{61} -36437.1 q^{62} +4096.00 q^{64} +4343.24 q^{65} -39564.0 q^{66} +58620.8 q^{67} -16983.4 q^{68} -58747.5 q^{69} -31279.5 q^{71} -432.056 q^{72} +7150.47 q^{73} +24114.9 q^{74} +42416.6 q^{75} +30143.7 q^{76} +13074.0 q^{78} +2979.81 q^{79} +5376.00 q^{80} -60643.9 q^{81} -68807.4 q^{82} -45954.6 q^{83} -22290.7 q^{85} -21607.9 q^{86} +1955.64 q^{87} +40055.9 q^{88} -99040.0 q^{89} -567.074 q^{90} +59477.9 q^{92} -143958. q^{93} +7500.97 q^{94} +39563.6 q^{95} +16182.8 q^{96} +115548. q^{97} -4225.20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{2} + 14 q^{3} + 32 q^{4} + 42 q^{5} - 56 q^{6} - 128 q^{8} + 652 q^{9} - 168 q^{10} - 294 q^{11} + 224 q^{12} + 140 q^{13} + 294 q^{15} + 512 q^{16} - 1302 q^{17} - 2608 q^{18} + 1442 q^{19}+ \cdots + 209916 q^{99}+O(q^{100}) \) 2 * q - 8 * q^2 + 14 * q^3 + 32 * q^4 + 42 * q^5 - 56 * q^6 - 128 * q^8 + 652 * q^9 - 168 * q^10 - 294 * q^11 + 224 * q^12 + 140 * q^13 + 294 * q^15 + 512 * q^16 - 1302 * q^17 - 2608 * q^18 + 1442 * q^19 + 672 * q^20 + 1176 * q^22 + 2646 * q^23 - 896 * q^24 - 5368 * q^25 - 560 * q^26 + 15722 * q^27 + 1668 * q^29 - 1176 * q^30 + 14798 * q^31 - 2048 * q^32 + 19782 * q^33 + 5208 * q^34 + 10432 * q^36 + 5182 * q^37 - 5768 * q^38 - 5260 * q^39 - 2688 * q^40 + 5124 * q^41 - 4520 * q^43 - 4704 * q^44 + 13692 * q^45 - 10584 * q^46 + 14994 * q^47 + 3584 * q^48 + 21472 * q^50 + 9606 * q^51 + 2240 * q^52 + 24006 * q^53 - 62888 * q^54 - 6174 * q^55 - 42946 * q^57 - 6672 * q^58 - 38850 * q^59 + 4704 * q^60 + 23618 * q^61 - 59192 * q^62 + 8192 * q^64 + 2940 * q^65 - 79128 * q^66 + 32002 * q^67 - 20832 * q^68 - 90678 * q^69 - 89376 * q^71 - 41728 * q^72 + 47138 * q^73 - 20728 * q^74 - 37576 * q^75 + 23072 * q^76 + 21040 * q^78 - 40970 * q^79 + 10752 * q^80 + 139858 * q^81 - 20496 * q^82 - 68376 * q^83 - 27342 * q^85 + 18080 * q^86 + 55356 * q^87 + 18816 * q^88 - 123102 * q^89 - 54768 * q^90 + 42336 * q^92 + 25586 * q^93 - 59976 * q^94 + 30282 * q^95 - 14336 * q^96 + 43652 * q^97 + 209916 * q^99

Introduction

L-functions

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