LMFDB - Embedded newform 1911.4.a.bd.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1911,4,Mod(1,1911)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1911, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1911.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1911 = 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1911.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:	$112.752650021$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 63 x^{12} + 408 x^{11} + 1393 x^{10} - 10374 x^{9} - 12229 x^{8} + 122556 x^{7} + \cdots - 43904 $ x^14 - 6x^13 - 63x^12 + 408x^11 + 1393x^10 - 10374x^9 - 12229x^8 + 122556x^7 + 27054x^6 - 691944x^5 + 111012x^4 + 1785120x^3 - 380480x^2 - 1650432*x - 43904
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{3}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-1.11764$ of defining polynomial
Character	$\chi$	$=$	1911.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.11764 q^{2} -3.00000 q^{3} -6.75088 q^{4} +1.89518 q^{5} -3.35291 q^{6} -16.4862 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+1.11764 q^{2} -3.00000 q^{3} -6.75088 q^{4} +1.89518 q^{5} -3.35291 q^{6} -16.4862 q^{8} +9.00000 q^{9} +2.11813 q^{10} +26.8218 q^{11} +20.2527 q^{12} +13.0000 q^{13} -5.68555 q^{15} +35.5815 q^{16} -0.610432 q^{17} +10.0587 q^{18} -90.4176 q^{19} -12.7942 q^{20} +29.9771 q^{22} -108.572 q^{23} +49.4585 q^{24} -121.408 q^{25} +14.5293 q^{26} -27.0000 q^{27} +7.37207 q^{29} -6.35439 q^{30} +223.941 q^{31} +171.656 q^{32} -80.4655 q^{33} -0.682242 q^{34} -60.7580 q^{36} +32.9534 q^{37} -101.054 q^{38} -39.0000 q^{39} -31.2443 q^{40} +186.740 q^{41} +262.697 q^{43} -181.071 q^{44} +17.0567 q^{45} -121.344 q^{46} -187.022 q^{47} -106.745 q^{48} -135.691 q^{50} +1.83130 q^{51} -87.7615 q^{52} +456.212 q^{53} -30.1762 q^{54} +50.8323 q^{55} +271.253 q^{57} +8.23930 q^{58} +78.4456 q^{59} +38.3825 q^{60} +138.355 q^{61} +250.285 q^{62} -92.8023 q^{64} +24.6374 q^{65} -89.9313 q^{66} +322.683 q^{67} +4.12096 q^{68} +325.715 q^{69} +386.900 q^{71} -148.375 q^{72} -637.595 q^{73} +36.8299 q^{74} +364.225 q^{75} +610.399 q^{76} -43.5879 q^{78} -321.857 q^{79} +67.4336 q^{80} +81.0000 q^{81} +208.708 q^{82} +884.900 q^{83} -1.15688 q^{85} +293.600 q^{86} -22.1162 q^{87} -442.189 q^{88} +83.6876 q^{89} +19.0632 q^{90} +732.954 q^{92} -671.823 q^{93} -209.023 q^{94} -171.358 q^{95} -514.969 q^{96} +1581.52 q^{97} +241.396 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 6 q^{2} - 42 q^{3} + 50 q^{4} - 4 q^{5} + 18 q^{6} - 30 q^{8} + 126 q^{9}+O(q^{10}) $ 14 * q - 6 * q^2 - 42 * q^3 + 50 * q^4 - 4 * q^5 + 18 * q^6 - 30 * q^8 + 126 * q^9	\( 14 q - 6 q^{2} - 42 q^{3} + 50 q^{4} - 4 q^{5} + 18 q^{6} - 30 q^{8} + 126 q^{9} + 32 q^{10} - 68 q^{11} - 150 q^{12} + 182 q^{13} + 12 q^{15} - 50 q^{16} - 54 q^{18} + 24 q^{19} + 96 q^{20} - 300 q^{22} - 64 q^{23} + 90 q^{24} - 118 q^{25} - 78 q^{26} - 378 q^{27} - 792 q^{29} - 96 q^{30} + 524 q^{31} - 126 q^{32} + 204 q^{33} - 88 q^{34} + 450 q^{36} - 344 q^{37} + 436 q^{38} - 546 q^{39} + 704 q^{40} + 44 q^{41} + 144 q^{43} - 1248 q^{44} - 36 q^{45} - 972 q^{46} - 236 q^{47} + 150 q^{48} - 714 q^{50} + 650 q^{52} - 1556 q^{53} + 162 q^{54} + 396 q^{55} - 72 q^{57} + 92 q^{58} + 1244 q^{59} - 288 q^{60} + 984 q^{61} + 236 q^{62} - 714 q^{64} - 52 q^{65} + 900 q^{66} - 1396 q^{67} + 960 q^{68} + 192 q^{69} - 1216 q^{71} - 270 q^{72} + 1768 q^{73} - 1212 q^{74} + 354 q^{75} + 496 q^{76} + 234 q^{78} - 1888 q^{79} + 1300 q^{80} + 1134 q^{81} + 1920 q^{82} - 1008 q^{83} + 56 q^{85} - 2128 q^{86} + 2376 q^{87} - 3148 q^{88} - 864 q^{89} + 288 q^{90} + 2856 q^{92} - 1572 q^{93} + 4860 q^{94} - 4984 q^{95} + 378 q^{96} + 1368 q^{97} - 612 q^{99}+O(q^{100}) \) 14 * q - 6 * q^2 - 42 * q^3 + 50 * q^4 - 4 * q^5 + 18 * q^6 - 30 * q^8 + 126 * q^9 + 32 * q^10 - 68 * q^11 - 150 * q^12 + 182 * q^13 + 12 * q^15 - 50 * q^16 - 54 * q^18 + 24 * q^19 + 96 * q^20 - 300 * q^22 - 64 * q^23 + 90 * q^24 - 118 * q^25 - 78 * q^26 - 378 * q^27 - 792 * q^29 - 96 * q^30 + 524 * q^31 - 126 * q^32 + 204 * q^33 - 88 * q^34 + 450 * q^36 - 344 * q^37 + 436 * q^38 - 546 * q^39 + 704 * q^40 + 44 * q^41 + 144 * q^43 - 1248 * q^44 - 36 * q^45 - 972 * q^46 - 236 * q^47 + 150 * q^48 - 714 * q^50 + 650 * q^52 - 1556 * q^53 + 162 * q^54 + 396 * q^55 - 72 * q^57 + 92 * q^58 + 1244 * q^59 - 288 * q^60 + 984 * q^61 + 236 * q^62 - 714 * q^64 - 52 * q^65 + 900 * q^66 - 1396 * q^67 + 960 * q^68 + 192 * q^69 - 1216 * q^71 - 270 * q^72 + 1768 * q^73 - 1212 * q^74 + 354 * q^75 + 496 * q^76 + 234 * q^78 - 1888 * q^79 + 1300 * q^80 + 1134 * q^81 + 1920 * q^82 - 1008 * q^83 + 56 * q^85 - 2128 * q^86 + 2376 * q^87 - 3148 * q^88 - 864 * q^89 + 288 * q^90 + 2856 * q^92 - 1572 * q^93 + 4860 * q^94 - 4984 * q^95 + 378 * q^96 + 1368 * q^97 - 612 * q^99

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 $

$2$	1.11764	0.395145	0.197572	−	0.980288i	$-0.436694\pi$
$2$	1.11764	0.395145	0.197572	+	0.980288i	$0.436694\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−6.75088	−0.843861
$5$	1.89518	0.169510	0.0847552	−	0.996402i	$-0.472989\pi$
$5$	1.89518	0.169510	0.0847552	+	0.996402i	$0.472989\pi$
$6$	−3.35291	−0.228137
$7$	0	0
$7$	0	0
$8$	−16.4862	−0.728592
$9$	9.00000	0.333333
$10$	2.11813	0.0669812
$11$	26.8218	0.735190	0.367595	−	0.929986i	$-0.380181\pi$
$11$	26.8218	0.735190	0.367595	+	0.929986i	$0.380181\pi$
$12$	20.2527	0.487203
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	0	0
$15$	−5.68555	−0.0978669
$16$	35.5815	0.555961
$17$	−0.610432	−0.00870892	−0.00435446	−	0.999991i	$-0.501386\pi$
$17$	−0.610432	−0.00870892	−0.00435446	+	0.999991i	$0.501386\pi$
$18$	10.0587	0.131715
$19$	−90.4176	−1.09175	−0.545874	−	0.837867i	$-0.683802\pi$
$19$	−90.4176	−1.09175	−0.545874	+	0.837867i	$0.683802\pi$
$20$	−12.7942	−0.143043
$21$	0	0
$22$	29.9771	0.290506
$23$	−108.572	−0.984293	−0.492147	−	0.870512i	$-0.663788\pi$
$23$	−108.572	−0.984293	−0.492147	+	0.870512i	$0.663788\pi$
$24$	49.4585	0.420653
$25$	−121.408	−0.971266
$26$	14.5293	0.109593
$27$	−27.0000	−0.192450
$28$	0	0
$29$	7.37207	0.0472055	0.0236027	−	0.999721i	$-0.492486\pi$
$29$	7.37207	0.0472055	0.0236027	+	0.999721i	$0.492486\pi$
$30$	−6.35439	−0.0386716
$31$	223.941	1.29745	0.648726	−	0.761022i	$-0.275302\pi$
$31$	223.941	1.29745	0.648726	+	0.761022i	$0.275302\pi$
$32$	171.656	0.948277
$33$	−80.4655	−0.424462
$34$	−0.682242	−0.00344128
$35$	0	0
$36$	−60.7580	−0.281287
$37$	32.9534	0.146419	0.0732095	−	0.997317i	$-0.476676\pi$
$37$	32.9534	0.146419	0.0732095	+	0.997317i	$0.476676\pi$
$38$	−101.054	−0.431399
$39$	−39.0000	−0.160128
$40$	−31.2443	−0.123504
$41$	186.740	0.711316	0.355658	−	0.934616i	$-0.384257\pi$
$41$	186.740	0.711316	0.355658	+	0.934616i	$0.384257\pi$
$42$	0	0
$43$	262.697	0.931649	0.465824	−	0.884877i	$-0.345758\pi$
$43$	262.697	0.931649	0.465824	+	0.884877i	$0.345758\pi$
$44$	−181.071	−0.620398
$45$	17.0567	0.0565035
$46$	−121.344	−0.388938
$47$	−187.022	−0.580425	−0.290212	−	0.956962i	$-0.593726\pi$
$47$	−187.022	−0.580425	−0.290212	+	0.956962i	$0.593726\pi$
$48$	−106.745	−0.320984
$49$	0	0
$50$	−135.691	−0.383791
$51$	1.83130	0.00502809
$52$	−87.7615	−0.234045
$53$	456.212	1.18237	0.591184	−	0.806536i	$-0.298661\pi$
$53$	456.212	1.18237	0.591184	+	0.806536i	$0.298661\pi$
$54$	−30.1762	−0.0760456
$55$	50.8323	0.124622
$56$	0	0
$57$	271.253	0.630321
$58$	8.23930	0.0186530
$59$	78.4456	0.173097	0.0865487	−	0.996248i	$-0.472416\pi$
$59$	78.4456	0.173097	0.0865487	+	0.996248i	$0.472416\pi$
$60$	38.3825	0.0825860
$61$	138.355	0.290402	0.145201	−	0.989402i	$-0.453617\pi$
$61$	138.355	0.290402	0.145201	+	0.989402i	$0.453617\pi$
$62$	250.285	0.512681
$63$	0	0
$64$	−92.8023	−0.181255
$65$	24.6374	0.0470138
$66$	−89.9313	−0.167724
$67$	322.683	0.588388	0.294194	−	0.955746i	$-0.404949\pi$
$67$	322.683	0.588388	0.294194	+	0.955746i	$0.404949\pi$
$68$	4.12096	0.00734911
$69$	325.715	0.568282
$70$	0	0
$71$	386.900	0.646712	0.323356	−	0.946277i	$-0.395189\pi$
$71$	386.900	0.646712	0.323356	+	0.946277i	$0.395189\pi$
$72$	−148.375	−0.242864
$73$	−637.595	−1.02226	−0.511129	−	0.859504i	$-0.670773\pi$
$73$	−637.595	−1.02226	−0.511129	+	0.859504i	$0.670773\pi$
$74$	36.8299	0.0578567
$75$	364.225	0.560761
$76$	610.399	0.921284
$77$	0	0
$78$	−43.5879	−0.0632738
$79$	−321.857	−0.458376	−0.229188	−	0.973382i	$-0.573607\pi$
$79$	−321.857	−0.458376	−0.229188	+	0.973382i	$0.573607\pi$
$80$	67.4336	0.0942413
$81$	81.0000	0.111111
$82$	208.708	0.281073
$83$	884.900	1.17025	0.585123	−	0.810945i	$-0.301046\pi$
$83$	884.900	1.17025	0.585123	+	0.810945i	$0.301046\pi$
$84$	0	0
$85$	−1.15688	−0.00147625
$86$	293.600	0.368136
$87$	−22.1162	−0.0272541
$88$	−442.189	−0.535653
$89$	83.6876	0.0996727	0.0498364	−	0.998757i	$-0.484130\pi$
$89$	83.6876	0.0996727	0.0498364	+	0.998757i	$0.484130\pi$
$90$	19.0632	0.0223271
$91$	0	0
$92$	732.954	0.830606
$93$	−671.823	−0.749084
$94$	−209.023	−0.229352
$95$	−171.358	−0.185063
$96$	−514.969	−0.547488
$97$	1581.52	1.65545	0.827724	−	0.561135i	$-0.189635\pi$
$97$	1581.52	1.65545	0.827724	+	0.561135i	$0.189635\pi$
$98$	0	0
$99$	241.396	0.245063
$100$	819.613	0.819613
$101$	−92.5063	−0.0911358	−0.0455679	−	0.998961i	$-0.514510\pi$
$101$	−92.5063	−0.0911358	−0.0455679	+	0.998961i	$0.514510\pi$
$102$	2.04673	0.00198683
$103$	99.4434	0.0951306	0.0475653	−	0.998868i	$-0.484854\pi$
$103$	99.4434	0.0951306	0.0475653	+	0.998868i	$0.484854\pi$
$104$	−214.320	−0.202075
$105$	0	0
$106$	509.880	0.467207
$107$	−2100.51	−1.89780	−0.948898	−	0.315584i	$-0.897800\pi$
$107$	−2100.51	−1.89780	−0.948898	+	0.315584i	$0.897800\pi$
$108$	182.274	0.162401
$109$	−1649.62	−1.44958	−0.724792	−	0.688967i	$-0.758064\pi$
$109$	−1649.62	−1.44958	−0.724792	+	0.688967i	$0.758064\pi$
$110$	56.8121	0.0492439
$111$	−98.8601	−0.0845350
$112$	0	0
$113$	−1367.01	−1.13803	−0.569017	−	0.822326i	$-0.692676\pi$
$113$	−1367.01	−1.13803	−0.569017	+	0.822326i	$0.692676\pi$
$114$	303.163	0.249068
$115$	−205.763	−0.166848
$116$	−49.7680	−0.0398348
$117$	117.000	0.0924500
$118$	87.6738	0.0683985
$119$	0	0
$120$	93.7329	0.0713050
$121$	−611.590	−0.459496
$122$	154.630	0.114751
$123$	−560.221	−0.410679
$124$	−1511.80	−1.09487
$125$	−466.989	−0.334150
$126$	0	0
$127$	−1989.33	−1.38995	−0.694977	−	0.719032i	$-0.744586\pi$
$127$	−1989.33	−1.38995	−0.694977	+	0.719032i	$0.744586\pi$
$128$	−1476.97	−1.01990
$129$	−788.090	−0.537888
$130$	27.5357	0.0185772
$131$	166.105	0.110784	0.0553919	−	0.998465i	$-0.482359\pi$
$131$	166.105	0.110784	0.0553919	+	0.998465i	$0.482359\pi$
$132$	543.213	0.358187
$133$	0	0
$134$	360.643	0.232498
$135$	−51.1700	−0.0326223
$136$	10.0637	0.00634525
$137$	−1118.69	−0.697635	−0.348818	−	0.937191i	$-0.613417\pi$
$137$	−1118.69	−0.697635	−0.348818	+	0.937191i	$0.613417\pi$
$138$	364.031	0.224554
$139$	−1253.80	−0.765080	−0.382540	−	0.923939i	$-0.624951\pi$
$139$	−1253.80	−0.765080	−0.382540	+	0.923939i	$0.624951\pi$
$140$	0	0
$141$	561.066	0.335108
$142$	432.414	0.255545
$143$	348.684	0.203905
$144$	320.234	0.185320
$145$	13.9714	0.00800182
$146$	−712.601	−0.403940
$147$	0	0
$148$	−222.464	−0.123557
$149$	−1643.84	−0.903817	−0.451909	−	0.892064i	$-0.649257\pi$
$149$	−1643.84	−0.903817	−0.451909	+	0.892064i	$0.649257\pi$
$150$	407.072	0.221582
$151$	508.200	0.273886	0.136943	−	0.990579i	$-0.456272\pi$
$151$	508.200	0.273886	0.136943	+	0.990579i	$0.456272\pi$
$152$	1490.64	0.795439
$153$	−5.49389	−0.00290297
$154$	0	0
$155$	424.410	0.219932
$156$	263.285	0.135126
$157$	−2325.93	−1.18235	−0.591177	−	0.806542i	$-0.701337\pi$
$157$	−2325.93	−1.18235	−0.591177	+	0.806542i	$0.701337\pi$
$158$	−359.719	−0.181125
$159$	−1368.64	−0.682641
$160$	325.321	0.160743
$161$	0	0
$162$	90.5287	0.0439050
$163$	−2404.17	−1.15527	−0.577635	−	0.816295i	$-0.696024\pi$
$163$	−2404.17	−1.15527	−0.577635	+	0.816295i	$0.696024\pi$
$164$	−1260.66	−0.600252
$165$	−152.497	−0.0719507
$166$	988.998	0.462417
$167$	1734.25	0.803594	0.401797	−	0.915729i	$-0.368386\pi$
$167$	1734.25	0.803594	0.401797	+	0.915729i	$0.368386\pi$
$168$	0	0
$169$	169.000	0.0769231
$170$	−1.29298	−0.000583333 0
$171$	−813.759	−0.363916
$172$	−1773.44	−0.786181
$173$	1200.28	0.527487	0.263744	−	0.964593i	$-0.415043\pi$
$173$	1200.28	0.527487	0.263744	+	0.964593i	$0.415043\pi$
$174$	−24.7179	−0.0107693
$175$	0	0
$176$	954.361	0.408737
$177$	−235.337	−0.0999378
$178$	93.5325	0.0393852
$179$	−985.223	−0.411391	−0.205696	−	0.978616i	$-0.565946\pi$
$179$	−985.223	−0.411391	−0.205696	+	0.978616i	$0.565946\pi$
$180$	−115.148	−0.0476811
$181$	−171.124	−0.0702737	−0.0351368	−	0.999383i	$-0.511187\pi$
$181$	−171.124	−0.0702737	−0.0351368	+	0.999383i	$0.511187\pi$
$182$	0	0
$183$	−415.064	−0.167663
$184$	1789.93	0.717148
$185$	62.4527	0.0248195
$186$	−750.855	−0.295997
$187$	−16.3729	−0.00640270
$188$	1262.56	0.489798
$189$	0	0
$190$	−191.516	−0.0731266
$191$	−1531.69	−0.580257	−0.290129	−	0.956988i	$-0.593698\pi$
$191$	−1531.69	−0.580257	−0.290129	+	0.956988i	$0.593698\pi$
$192$	278.407	0.104647
$193$	−1928.98	−0.719435	−0.359717	−	0.933061i	$-0.617127\pi$
$193$	−1928.98	−0.719435	−0.359717	+	0.933061i	$0.617127\pi$
$194$	1767.56	0.654142
$195$	−73.9122	−0.0271434
$196$	0	0
$197$	−3029.83	−1.09577	−0.547885	−	0.836553i	$-0.684567\pi$
$197$	−3029.83	−1.09577	−0.547885	+	0.836553i	$0.684567\pi$
$198$	269.794	0.0968354
$199$	737.290	0.262639	0.131319	−	0.991340i	$-0.458079\pi$
$199$	737.290	0.262639	0.131319	+	0.991340i	$0.458079\pi$
$200$	2001.56	0.707657
$201$	−968.048	−0.339706
$202$	−103.389	−0.0360119
$203$	0	0
$204$	−12.3629	−0.00424301
$205$	353.908	0.120576
$206$	111.142	0.0375903
$207$	−977.145	−0.328098
$208$	462.560	0.154196
$209$	−2425.17	−0.802642
$210$	0	0
$211$	−3728.13	−1.21638	−0.608188	−	0.793793i	$-0.708103\pi$
$211$	−3728.13	−1.21638	−0.608188	+	0.793793i	$0.708103\pi$
$212$	−3079.83	−0.997754
$213$	−1160.70	−0.373379
$214$	−2347.61	−0.749904
$215$	497.859	0.157924
$216$	445.126	0.140218
$217$	0	0
$218$	−1843.68	−0.572796
$219$	1912.79	0.590201
$220$	−343.163	−0.105164
$221$	−7.93562	−0.00241542
$222$	−110.490	−0.0334036
$223$	1199.28	0.360133	0.180067	−	0.983654i	$-0.442369\pi$
$223$	1199.28	0.360133	0.180067	+	0.983654i	$0.442369\pi$
$224$	0	0
$225$	−1092.67	−0.323755
$226$	−1527.83	−0.449688
$227$	4212.39	1.23166	0.615828	−	0.787880i	$-0.288822\pi$
$227$	4212.39	1.23166	0.615828	+	0.787880i	$0.288822\pi$
$228$	−1831.20	−0.531903
$229$	4186.82	1.20818	0.604090	−	0.796916i	$-0.293537\pi$
$229$	4186.82	1.20818	0.604090	+	0.796916i	$0.293537\pi$
$230$	−229.969	−0.0659291
$231$	0	0
$232$	−121.537	−0.0343935
$233$	1879.89	0.528566	0.264283	−	0.964445i	$-0.414865\pi$
$233$	1879.89	0.528566	0.264283	+	0.964445i	$0.414865\pi$
$234$	130.764	0.0365311
$235$	−354.441	−0.0983881
$236$	−529.577	−0.146070
$237$	965.570	0.264644
$238$	0	0
$239$	−3186.61	−0.862446	−0.431223	−	0.902245i	$-0.641918\pi$
$239$	−3186.61	−0.862446	−0.431223	+	0.902245i	$0.641918\pi$
$240$	−202.301	−0.0544102
$241$	−2173.77	−0.581017	−0.290508	−	0.956872i	$-0.593824\pi$
$241$	−2173.77	−0.581017	−0.290508	+	0.956872i	$0.593824\pi$
$242$	−683.536	−0.181568
$243$	−243.000	−0.0641500
$244$	−934.016	−0.245058
$245$	0	0
$246$	−626.125	−0.162278
$247$	−1175.43	−0.302797
$248$	−3691.93	−0.945312
$249$	−2654.70	−0.675642
$250$	−521.925	−0.132038
$251$	2221.88	0.558740	0.279370	−	0.960184i	$-0.409874\pi$
$251$	2221.88	0.558740	0.279370	+	0.960184i	$0.409874\pi$
$252$	0	0
$253$	−2912.09	−0.723642
$254$	−2223.35	−0.549233
$255$	3.47065	0.000852315 0
$256$	−908.301	−0.221753
$257$	1179.94	0.286393	0.143196	−	0.989694i	$-0.454262\pi$
$257$	1179.94	0.286393	0.143196	+	0.989694i	$0.454262\pi$
$258$	−880.800	−0.212543
$259$	0	0
$260$	−166.324	−0.0396731
$261$	66.3486	0.0157352
$262$	185.646	0.0437757
$263$	7798.96	1.82853	0.914267	−	0.405111i	$-0.132767\pi$
$263$	7798.96	1.82853	0.914267	+	0.405111i	$0.132767\pi$
$264$	1326.57	0.309259
$265$	864.606	0.200424
$266$	0	0
$267$	−251.063	−0.0575461
$268$	−2178.39	−0.496517
$269$	−7021.63	−1.59151	−0.795755	−	0.605618i	$-0.792926\pi$
$269$	−7021.63	−1.59151	−0.795755	+	0.605618i	$0.792926\pi$
$270$	−57.1895	−0.0128905
$271$	−3052.31	−0.684187	−0.342094	−	0.939666i	$-0.611136\pi$
$271$	−3052.31	−0.684187	−0.342094	+	0.939666i	$0.611136\pi$
$272$	−21.7201	−0.00484182
$273$	0	0
$274$	−1250.29	−0.275667
$275$	−3256.39	−0.714065
$276$	−2198.86	−0.479551
$277$	4489.37	0.973790	0.486895	−	0.873460i	$-0.338129\pi$
$277$	4489.37	0.973790	0.486895	+	0.873460i	$0.338129\pi$
$278$	−1401.30	−0.302317
$279$	2015.47	0.432484
$280$	0	0
$281$	8790.96	1.86628	0.933140	−	0.359514i	$-0.117057\pi$
$281$	8790.96	1.86628	0.933140	+	0.359514i	$0.117057\pi$
$282$	627.069	0.132416
$283$	−7076.60	−1.48643	−0.743215	−	0.669052i	$-0.766700\pi$
$283$	−7076.60	−1.48643	−0.743215	+	0.669052i	$0.766700\pi$
$284$	−2611.92	−0.545735
$285$	514.074	0.106846
$286$	389.702	0.0805720
$287$	0	0
$288$	1544.91	0.316092
$289$	−4912.63	−0.999924
$290$	15.6150	0.00316188
$291$	−4744.55	−0.955774
$292$	4304.33	0.862644
$293$	−1345.48	−0.268273	−0.134137	−	0.990963i	$-0.542826\pi$
$293$	−1345.48	−0.268273	−0.134137	+	0.990963i	$0.542826\pi$
$294$	0	0
$295$	148.669	0.0293418
$296$	−543.274	−0.106680
$297$	−724.189	−0.141487
$298$	−1837.22	−0.357139
$299$	−1411.43	−0.272994
$300$	−2458.84	−0.473204
$301$	0	0
$302$	567.984	0.108225
$303$	277.519	0.0526173
$304$	−3217.20	−0.606970
$305$	262.208	0.0492261
$306$	−6.14018	−0.00114709
$307$	175.478	0.0326224	0.0163112	−	0.999867i	$-0.494808\pi$
$307$	175.478	0.0326224	0.0163112	+	0.999867i	$0.494808\pi$
$308$	0	0
$309$	−298.330	−0.0549236
$310$	474.336	0.0869048
$311$	−276.902	−0.0504876	−0.0252438	−	0.999681i	$-0.508036\pi$
$311$	−276.902	−0.0504876	−0.0252438	+	0.999681i	$0.508036\pi$
$312$	642.960	0.116668
$313$	2896.14	0.523001	0.261501	−	0.965203i	$-0.415783\pi$
$313$	2896.14	0.523001	0.261501	+	0.965203i	$0.415783\pi$
$314$	−2599.55	−0.467201
$315$	0	0
$316$	2172.82	0.386806
$317$	−5612.41	−0.994398	−0.497199	−	0.867637i	$-0.665638\pi$
$317$	−5612.41	−0.994398	−0.497199	+	0.867637i	$0.665638\pi$
$318$	−1529.64	−0.269742
$319$	197.732	0.0347050
$320$	−175.878	−0.0307246
$321$	6301.54	1.09569
$322$	0	0
$323$	55.1938	0.00950795
$324$	−546.822	−0.0937623
$325$	−1578.31	−0.269381
$326$	−2686.99	−0.456499
$327$	4948.85	0.836918
$328$	−3078.63	−0.518259
$329$	0	0
$330$	−170.436	−0.0284310
$331$	−3628.90	−0.602605	−0.301302	−	0.953529i	$-0.597421\pi$
$331$	−3628.90	−0.602605	−0.301302	+	0.953529i	$0.597421\pi$
$332$	−5973.86	−0.987525
$333$	296.580	0.0488063
$334$	1938.26	0.317536
$335$	611.544	0.0997379
$336$	0	0
$337$	−238.944	−0.0386234	−0.0193117	−	0.999814i	$-0.506147\pi$
$337$	−238.944	−0.0386234	−0.0193117	+	0.999814i	$0.506147\pi$
$338$	188.881	0.0303958
$339$	4101.04	0.657044
$340$	7.80998	0.00124575
$341$	6006.51	0.953873
$342$	−909.488	−0.143800
$343$	0	0
$344$	−4330.86	−0.678792
$345$	617.290	0.0963298
$346$	1341.47	0.208434
$347$	2269.95	0.351174	0.175587	−	0.984464i	$-0.443818\pi$
$347$	2269.95	0.351174	0.175587	+	0.984464i	$0.443818\pi$
$348$	149.304	0.0229987
$349$	−4420.63	−0.678025	−0.339012	−	0.940782i	$-0.610093\pi$
$349$	−4420.63	−0.678025	−0.339012	+	0.940782i	$0.610093\pi$
$350$	0	0
$351$	−351.000	−0.0533761
$352$	4604.14	0.697163
$353$	−9321.86	−1.40553	−0.702766	−	0.711421i	$-0.748052\pi$
$353$	−9321.86	−1.40553	−0.702766	+	0.711421i	$0.748052\pi$
$354$	−263.021	−0.0394899
$355$	733.246	0.109624
$356$	−564.966	−0.0841099
$357$	0	0
$358$	−1101.12	−0.162559
$359$	−3036.15	−0.446356	−0.223178	−	0.974778i	$-0.571643\pi$
$359$	−3036.15	−0.446356	−0.223178	+	0.974778i	$0.571643\pi$
$360$	−281.199	−0.0411680
$361$	1316.34	0.191915
$362$	−191.255	−0.0277683
$363$	1834.77	0.265290
$364$	0	0
$365$	−1208.36	−0.173284
$366$	−463.891	−0.0662513
$367$	−9660.75	−1.37408	−0.687040	−	0.726620i	$-0.741090\pi$
$367$	−9660.75	−1.37408	−0.687040	+	0.726620i	$0.741090\pi$
$368$	−3863.14	−0.547229
$369$	1680.66	0.237105
$370$	69.7996	0.00980731
$371$	0	0
$372$	4535.40	0.632122
$373$	1465.06	0.203372	0.101686	−	0.994817i	$-0.467576\pi$
$373$	1465.06	0.203372	0.101686	+	0.994817i	$0.467576\pi$
$374$	−18.2990	−0.00252999
$375$	1400.97	0.192922
$376$	3083.27	0.422893
$377$	95.8369	0.0130924
$378$	0	0
$379$	−5702.28	−0.772840	−0.386420	−	0.922323i	$-0.626288\pi$
$379$	−5702.28	−0.772840	−0.386420	+	0.922323i	$0.626288\pi$
$380$	1156.82	0.156167
$381$	5967.98	0.802490
$382$	−1711.87	−0.229286
$383$	7775.87	1.03741	0.518706	−	0.854953i	$-0.326414\pi$
$383$	7775.87	1.03741	0.518706	+	0.854953i	$0.326414\pi$
$384$	4430.91	0.588839
$385$	0	0
$386$	−2155.90	−0.284281
$387$	2364.27	0.310550
$388$	−10676.6	−1.39697
$389$	−10028.0	−1.30704	−0.653520	−	0.756909i	$-0.726709\pi$
$389$	−10028.0	−1.30704	−0.653520	+	0.756909i	$0.726709\pi$
$390$	−82.6071	−0.0107256
$391$	66.2756	0.00857213
$392$	0	0
$393$	−498.316	−0.0639611
$394$	−3386.26	−0.432988
$395$	−609.978	−0.0776996
$396$	−1629.64	−0.206799
$397$	−9294.00	−1.17494	−0.587472	−	0.809245i	$-0.699877\pi$
$397$	−9294.00	−1.17494	−0.587472	+	0.809245i	$0.699877\pi$
$398$	824.024	0.103780
$399$	0	0
$400$	−4319.89	−0.539986
$401$	−10277.0	−1.27982	−0.639912	−	0.768448i	$-0.721029\pi$
$401$	−10277.0	−1.27982	−0.639912	+	0.768448i	$0.721029\pi$
$402$	−1081.93	−0.134233
$403$	2911.23	0.359848
$404$	624.499	0.0769059
$405$	153.510	0.0188345
$406$	0	0
$407$	883.870	0.107646
$408$	−30.1910	−0.00366343
$409$	−5982.19	−0.723227	−0.361614	−	0.932328i	$-0.617774\pi$
$409$	−5982.19	−0.723227	−0.361614	+	0.932328i	$0.617774\pi$
$410$	395.541	0.0476448
$411$	3356.07	0.402780
$412$	−671.331	−0.0802769
$413$	0	0
$414$	−1092.09	−0.129646
$415$	1677.05	0.198369
$416$	2231.53	0.263005
$417$	3761.41	0.441719
$418$	−2710.46	−0.317160
$419$	11302.1	1.31777	0.658884	−	0.752244i	$-0.271029\pi$
$419$	11302.1	1.31777	0.658884	+	0.752244i	$0.271029\pi$
$420$	0	0
$421$	7424.84	0.859536	0.429768	−	0.902939i	$-0.358595\pi$
$421$	7424.84	0.859536	0.429768	+	0.902939i	$0.358595\pi$
$422$	−4166.70	−0.480645
$423$	−1683.20	−0.193475
$424$	−7521.18	−0.861464
$425$	74.1115	0.00845868
$426$	−1297.24	−0.147539
$427$	0	0
$428$	14180.3	1.60147
$429$	−1046.05	−0.117725
$430$	556.426	0.0624029
$431$	4604.27	0.514570	0.257285	−	0.966336i	$-0.417172\pi$
$431$	4604.27	0.514570	0.257285	+	0.966336i	$0.417172\pi$
$432$	−960.701	−0.106995
$433$	12121.7	1.34534	0.672672	−	0.739941i	$-0.265146\pi$
$433$	12121.7	1.34534	0.672672	+	0.739941i	$0.265146\pi$
$434$	0	0
$435$	−41.9143	−0.00461985
$436$	11136.4	1.22325
$437$	9816.79	1.07460
$438$	2137.80	0.233215
$439$	−1311.74	−0.142610	−0.0713050	−	0.997455i	$-0.522716\pi$
$439$	−1311.74	−0.142610	−0.0713050	+	0.997455i	$0.522716\pi$
$440$	−838.029	−0.0907988
$441$	0	0
$442$	−8.86915	−0.000954440 0
$443$	−9737.38	−1.04433	−0.522163	−	0.852845i	$-0.674875\pi$
$443$	−9737.38	−1.04433	−0.522163	+	0.852845i	$0.674875\pi$
$444$	667.393	0.0713358
$445$	158.604	0.0168956
$446$	1340.36	0.142305
$447$	4931.53	0.521819
$448$	0	0
$449$	−2645.79	−0.278090	−0.139045	−	0.990286i	$-0.544403\pi$
$449$	−2645.79	−0.278090	−0.139045	+	0.990286i	$0.544403\pi$
$450$	−1221.21	−0.127930
$451$	5008.72	0.522952
$452$	9228.55	0.960341
$453$	−1524.60	−0.158128
$454$	4707.93	0.486683
$455$	0	0
$456$	−4471.92	−0.459247
$457$	7517.23	0.769455	0.384728	−	0.923030i	$-0.374295\pi$
$457$	7517.23	0.769455	0.384728	+	0.923030i	$0.374295\pi$
$458$	4679.35	0.477406
$459$	16.4817	0.00167603
$460$	1389.08	0.140796
$461$	−14940.2	−1.50940	−0.754699	−	0.656071i	$-0.772217\pi$
$461$	−14940.2	−1.50940	−0.754699	+	0.656071i	$0.772217\pi$
$462$	0	0
$463$	5693.07	0.571446	0.285723	−	0.958312i	$-0.407766\pi$
$463$	5693.07	0.571446	0.285723	+	0.958312i	$0.407766\pi$
$464$	262.309	0.0262444
$465$	−1273.23	−0.126978
$466$	2101.04	0.208860
$467$	−16504.1	−1.63537	−0.817687	−	0.575663i	$-0.804744\pi$
$467$	−16504.1	−1.63537	−0.817687	+	0.575663i	$0.804744\pi$
$468$	−789.854	−0.0780149
$469$	0	0
$470$	−396.137	−0.0388775
$471$	6977.80	0.682633
$472$	−1293.27	−0.126117
$473$	7046.01	0.684938
$474$	1079.16	0.104573
$475$	10977.4	1.06038
$476$	0	0
$477$	4105.91	0.394123
$478$	−3561.48	−0.340791
$479$	−6442.88	−0.614578	−0.307289	−	0.951616i	$-0.599422\pi$
$479$	−6442.88	−0.614578	−0.307289	+	0.951616i	$0.599422\pi$
$480$	−975.962	−0.0928050
$481$	428.394	0.0406093
$482$	−2429.49	−0.229586
$483$	0	0
$484$	4128.77	0.387751
$485$	2997.26	0.280616
$486$	−271.586	−0.0253485
$487$	−786.666	−0.0731976	−0.0365988	−	0.999330i	$-0.511652\pi$
$487$	−786.666	−0.0731976	−0.0365988	+	0.999330i	$0.511652\pi$
$488$	−2280.94	−0.211584
$489$	7212.51	0.666996
$490$	0	0
$491$	8740.82	0.803397	0.401698	−	0.915772i	$-0.368420\pi$
$491$	8740.82	0.803397	0.401698	+	0.915772i	$0.368420\pi$
$492$	3781.99	0.346555
$493$	−4.50015	−0.000411108 0
$494$	−1313.70	−0.119648
$495$	457.491	0.0415408
$496$	7968.16	0.721333
$497$	0	0
$498$	−2967.00	−0.266976
$499$	2899.41	0.260111	0.130056	−	0.991507i	$-0.458484\pi$
$499$	2899.41	0.260111	0.130056	+	0.991507i	$0.458484\pi$
$500$	3152.59	0.281976
$501$	−5202.75	−0.463955
$502$	2483.26	0.220783
$503$	−5248.07	−0.465208	−0.232604	−	0.972571i	$-0.574725\pi$
$503$	−5248.07	−0.465208	−0.232604	+	0.972571i	$0.574725\pi$
$504$	0	0
$505$	−175.317	−0.0154485
$506$	−3254.66	−0.285943
$507$	−507.000	−0.0444116
$508$	13429.7	1.17293
$509$	−4427.48	−0.385550	−0.192775	−	0.981243i	$-0.561749\pi$
$509$	−4427.48	−0.385550	−0.192775	+	0.981243i	$0.561749\pi$
$510$	3.87893	0.000336788 0
$511$	0	0
$512$	10800.6	0.932274
$513$	2441.28	0.210107
$514$	1318.75	0.113167
$515$	188.464	0.0161256
$516$	5320.31	0.453902
$517$	−5016.27	−0.426722
$518$	0	0
$519$	−3600.83	−0.304545
$520$	−406.176	−0.0342538
$521$	−11196.2	−0.941483	−0.470742	−	0.882271i	$-0.656014\pi$
$521$	−11196.2	−0.941483	−0.470742	+	0.882271i	$0.656014\pi$
$522$	74.1537	0.00621766
$523$	16269.8	1.36028	0.680140	−	0.733082i	$-0.261919\pi$
$523$	16269.8	1.36028	0.680140	+	0.733082i	$0.261919\pi$
$524$	−1121.36	−0.0934861
$525$	0	0
$526$	8716.42	0.722536
$527$	−136.701	−0.0112994
$528$	−2863.08	−0.235984
$529$	−379.203	−0.0311665
$530$	966.317	0.0791965
$531$	706.010	0.0576991
$532$	0	0
$533$	2427.63	0.197284
$534$	−280.598	−0.0227390
$535$	−3980.86	−0.321696
$536$	−5319.80	−0.428695
$537$	2955.67	0.237517
$538$	−7847.64	−0.628877
$539$	0	0
$540$	345.443	0.0275287
$541$	−5127.04	−0.407447	−0.203723	−	0.979028i	$-0.565304\pi$
$541$	−5127.04	−0.407447	−0.203723	+	0.979028i	$0.565304\pi$
$542$	−3411.38	−0.270353
$543$	513.372	0.0405725
$544$	−104.785	−0.00825847
$545$	−3126.33	−0.245720
$546$	0	0
$547$	−13250.8	−1.03577	−0.517883	−	0.855451i	$-0.673280\pi$
$547$	−13250.8	−1.03577	−0.517883	+	0.855451i	$0.673280\pi$
$548$	7552.14	0.588707
$549$	1245.19	0.0968005
$550$	−3639.47	−0.282159
$551$	−666.565	−0.0515365
$552$	−5369.78	−0.414046
$553$	0	0
$554$	5017.49	0.384788
$555$	−187.358	−0.0143296
$556$	8464.27	0.645621
$557$	−3786.70	−0.288057	−0.144029	−	0.989574i	$-0.546006\pi$
$557$	−3786.70	−0.288057	−0.144029	+	0.989574i	$0.546006\pi$
$558$	2252.56	0.170894
$559$	3415.06	0.258393
$560$	0	0
$561$	49.1187	0.00369660
$562$	9825.11	0.737451
$563$	6365.14	0.476480	0.238240	−	0.971206i	$-0.423429\pi$
$563$	6365.14	0.476480	0.238240	+	0.971206i	$0.423429\pi$
$564$	−3787.69	−0.282785
$565$	−2590.74	−0.192909
$566$	−7909.07	−0.587355
$567$	0	0
$568$	−6378.49	−0.471189
$569$	−12026.2	−0.886056	−0.443028	−	0.896508i	$-0.646096\pi$
$569$	−12026.2	−0.886056	−0.443028	+	0.896508i	$0.646096\pi$
$570$	574.549	0.0422197
$571$	−17089.3	−1.25248	−0.626239	−	0.779631i	$-0.715407\pi$
$571$	−17089.3	−1.25248	−0.626239	+	0.779631i	$0.715407\pi$
$572$	−2353.92	−0.172067
$573$	4595.07	0.335012
$574$	0	0
$575$	13181.5	0.956011
$576$	−835.221	−0.0604182
$577$	15565.8	1.12307	0.561537	−	0.827451i	$-0.310210\pi$
$577$	15565.8	1.12307	0.561537	+	0.827451i	$0.310210\pi$
$578$	−5490.54	−0.395115
$579$	5786.94	0.415366
$580$	−94.3195	−0.00675242
$581$	0	0
$582$	−5302.68	−0.377669
$583$	12236.4	0.869265
$584$	10511.5	0.744809
$585$	221.737	0.0156713
$586$	−1503.76	−0.106007
$587$	−3797.00	−0.266983	−0.133492	−	0.991050i	$-0.542619\pi$
$587$	−3797.00	−0.266983	−0.133492	+	0.991050i	$0.542619\pi$
$588$	0	0
$589$	−20248.2	−1.41649
$590$	166.158	0.0115943
$591$	9089.50	0.632643
$592$	1172.53	0.0814033
$593$	−17461.4	−1.20920	−0.604599	−	0.796530i	$-0.706667\pi$
$593$	−17461.4	−1.20920	−0.604599	+	0.796530i	$0.706667\pi$
$594$	−809.382	−0.0559080
$595$	0	0
$596$	11097.4	0.762696
$597$	−2211.87	−0.151635
$598$	−1577.47	−0.107872
$599$	1614.11	0.110102	0.0550508	−	0.998484i	$-0.482468\pi$
$599$	1614.11	0.110102	0.0550508	+	0.998484i	$0.482468\pi$
$600$	−6004.67	−0.408566
$601$	8044.16	0.545970	0.272985	−	0.962018i	$-0.411989\pi$
$601$	8044.16	0.545970	0.272985	+	0.962018i	$0.411989\pi$
$602$	0	0
$603$	2904.15	0.196129
$604$	−3430.80	−0.231121
$605$	−1159.08	−0.0778894
$606$	310.166	0.0207915
$607$	4518.55	0.302146	0.151073	−	0.988523i	$-0.451727\pi$
$607$	4518.55	0.302146	0.151073	+	0.988523i	$0.451727\pi$
$608$	−15520.8	−1.03528
$609$	0	0
$610$	293.053	0.0194514
$611$	−2431.29	−0.160981
$612$	37.0886	0.00244970
$613$	8115.82	0.534739	0.267369	−	0.963594i	$-0.413846\pi$
$613$	8115.82	0.534739	0.267369	+	0.963594i	$0.413846\pi$
$614$	196.121	0.0128906
$615$	−1061.72	−0.0696143
$616$	0	0
$617$	21886.5	1.42807	0.714035	−	0.700110i	$-0.246866\pi$
$617$	21886.5	1.42807	0.714035	+	0.700110i	$0.246866\pi$
$618$	−333.425	−0.0217028
$619$	21691.8	1.40851	0.704253	−	0.709949i	$-0.251282\pi$
$619$	21691.8	1.40851	0.704253	+	0.709949i	$0.251282\pi$
$620$	−2865.14	−0.185592
$621$	2931.43	0.189427
$622$	−309.476	−0.0199499
$623$	0	0
$624$	−1387.68	−0.0890251
$625$	14291.0	0.914624
$626$	3236.84	0.206661
$627$	7275.50	0.463406
$628$	15702.1	0.997743
$629$	−20.1158	−0.00127515
$630$	0	0
$631$	4444.07	0.280374	0.140187	−	0.990125i	$-0.455230\pi$
$631$	4444.07	0.280374	0.140187	+	0.990125i	$0.455230\pi$
$632$	5306.18	0.333969
$633$	11184.4	0.702275
$634$	−6272.64	−0.392931
$635$	−3770.14	−0.235612
$636$	9239.50	0.576054
$637$	0	0
$638$	220.993	0.0137135
$639$	3482.10	0.215571
$640$	−2799.13	−0.172884
$641$	22718.7	1.39990	0.699950	−	0.714192i	$-0.253206\pi$
$641$	22718.7	1.39990	0.699950	+	0.714192i	$0.253206\pi$
$642$	7042.84	0.432957
$643$	18235.0	1.11838	0.559190	−	0.829040i	$-0.311112\pi$
$643$	18235.0	1.11838	0.559190	+	0.829040i	$0.311112\pi$
$644$	0	0
$645$	−1493.58	−0.0911776
$646$	61.6867	0.00375702
$647$	−696.760	−0.0423377	−0.0211688	−	0.999776i	$-0.506739\pi$
$647$	−696.760	−0.0423377	−0.0211688	+	0.999776i	$0.506739\pi$
$648$	−1335.38	−0.0809547
$649$	2104.05	0.127259
$650$	−1763.98	−0.106444
$651$	0	0
$652$	16230.3	0.974887
$653$	−27875.3	−1.67052	−0.835258	−	0.549859i	$-0.814682\pi$
$653$	−27875.3	−1.67052	−0.835258	+	0.549859i	$0.814682\pi$
$654$	5531.03	0.330704
$655$	314.800	0.0187790
$656$	6644.51	0.395464
$657$	−5738.36	−0.340753
$658$	0	0
$659$	−21601.6	−1.27690	−0.638451	−	0.769663i	$-0.720424\pi$
$659$	−21601.6	−1.27690	−0.638451	+	0.769663i	$0.720424\pi$
$660$	1029.49	0.0607164
$661$	−410.003	−0.0241260	−0.0120630	−	0.999927i	$-0.503840\pi$
$661$	−410.003	−0.0241260	−0.0120630	+	0.999927i	$0.503840\pi$
$662$	−4055.79	−0.238116
$663$	23.8069	0.00139454
$664$	−14588.6	−0.852632
$665$	0	0
$666$	331.470	0.0192856
$667$	−800.397	−0.0464640
$668$	−11707.7	−0.678122
$669$	−3597.84	−0.207923
$670$	683.484	0.0394109
$671$	3710.92	0.213500
$672$	0	0
$673$	−31584.9	−1.80908	−0.904539	−	0.426392i	$-0.859785\pi$
$673$	−31584.9	−1.80908	−0.904539	+	0.426392i	$0.859785\pi$
$674$	−267.053	−0.0152618
$675$	3278.02	0.186920
$676$	−1140.90	−0.0649124
$677$	−19537.2	−1.10912	−0.554560	−	0.832144i	$-0.687114\pi$
$677$	−19537.2	−1.10912	−0.554560	+	0.832144i	$0.687114\pi$
$678$	4583.48	0.259627
$679$	0	0
$680$	19.0725	0.00107559
$681$	−12637.2	−0.711097
$682$	6713.10	0.376918
$683$	−27684.3	−1.55097	−0.775483	−	0.631368i	$-0.782494\pi$
$683$	−27684.3	−1.55097	−0.775483	+	0.631368i	$0.782494\pi$
$684$	5493.59	0.307095
$685$	−2120.12	−0.118256
$686$	0	0
$687$	−12560.5	−0.697543
$688$	9347.15	0.517961
$689$	5930.76	0.327930
$690$	689.907	0.0380642
$691$	3626.79	0.199666	0.0998332	−	0.995004i	$-0.468169\pi$
$691$	3626.79	0.199666	0.0998332	+	0.995004i	$0.468169\pi$
$692$	−8102.93	−0.445126
$693$	0	0
$694$	2536.99	0.138765
$695$	−2376.19	−0.129689
$696$	364.611	0.0198571
$697$	−113.992	−0.00619479
$698$	−4940.66	−0.267918
$699$	−5639.68	−0.305168
$700$	0	0
$701$	6978.53	0.375999	0.188000	−	0.982169i	$-0.439800\pi$
$701$	6978.53	0.375999	0.188000	+	0.982169i	$0.439800\pi$
$702$	−392.291	−0.0210913
$703$	−2979.57	−0.159853
$704$	−2489.13	−0.133256
$705$	1063.32	0.0568044
$706$	−10418.5	−0.555388
$707$	0	0
$708$	1588.73	0.0843336
$709$	11953.4	0.633170	0.316585	−	0.948564i	$-0.397464\pi$
$709$	11953.4	0.633170	0.316585	+	0.948564i	$0.397464\pi$
$710$	819.504	0.0433175
$711$	−2896.71	−0.152792
$712$	−1379.69	−0.0726207
$713$	−24313.6	−1.27707
$714$	0	0
$715$	660.820	0.0345640
$716$	6651.13	0.347157
$717$	9559.83	0.497934
$718$	−3393.32	−0.176375
$719$	−28862.8	−1.49708	−0.748541	−	0.663089i	$-0.769245\pi$
$719$	−28862.8	−1.49708	−0.748541	+	0.663089i	$0.769245\pi$
$720$	606.902	0.0314138
$721$	0	0
$722$	1471.20	0.0758342
$723$	6521.32	0.335450
$724$	1155.24	0.0593012
$725$	−895.030	−0.0458491
$726$	2050.61	0.104828
$727$	−33971.9	−1.73308	−0.866540	−	0.499107i	$-0.833661\pi$
$727$	−33971.9	−1.73308	−0.866540	+	0.499107i	$0.833661\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−1350.51	−0.0684721
$731$	−160.359	−0.00811365
$732$	2802.05	0.141485
$733$	27605.4	1.39104	0.695519	−	0.718508i	$-0.255175\pi$
$733$	27605.4	1.39104	0.695519	+	0.718508i	$0.255175\pi$
$734$	−10797.2	−0.542960
$735$	0	0
$736$	−18637.0	−0.933383
$737$	8654.94	0.432577
$738$	1878.37	0.0936910
$739$	24153.5	1.20230	0.601151	−	0.799135i	$-0.294709\pi$
$739$	24153.5	1.20230	0.601151	+	0.799135i	$0.294709\pi$
$740$	−421.611	−0.0209442
$741$	3526.29	0.174820
$742$	0	0
$743$	−2834.30	−0.139946	−0.0699732	−	0.997549i	$-0.522291\pi$
$743$	−2834.30	−0.139946	−0.0699732	+	0.997549i	$0.522291\pi$
$744$	11075.8	0.545776
$745$	−3115.38	−0.153207
$746$	1637.41	0.0803615
$747$	7964.10	0.390082
$748$	110.532	0.00540299
$749$	0	0
$750$	1565.78	0.0762320
$751$	−10347.1	−0.502760	−0.251380	−	0.967889i	$-0.580884\pi$
$751$	−10347.1	−0.502760	−0.251380	+	0.967889i	$0.580884\pi$
$752$	−6654.53	−0.322694
$753$	−6665.64	−0.322589
$754$	107.111	0.00517341
$755$	963.133	0.0464265
$756$	0	0
$757$	−8372.22	−0.401973	−0.200987	−	0.979594i	$-0.564415\pi$
$757$	−8372.22	−0.401973	−0.200987	+	0.979594i	$0.564415\pi$
$758$	−6373.08	−0.305384
$759$	8736.27	0.417795
$760$	2825.04	0.134835
$761$	−11718.0	−0.558184	−0.279092	−	0.960264i	$-0.590033\pi$
$761$	−11718.0	−0.558184	−0.279092	+	0.960264i	$0.590033\pi$
$762$	6670.04	0.317100
$763$	0	0
$764$	10340.3	0.489656
$765$	−10.4119	−0.000492084 0
$766$	8690.61	0.409928
$767$	1019.79	0.0480086
$768$	2724.90	0.128029
$769$	35422.5	1.66108	0.830538	−	0.556963i	$-0.188033\pi$
$769$	35422.5	1.66108	0.830538	+	0.556963i	$0.188033\pi$
$770$	0	0
$771$	−3539.83	−0.165349
$772$	13022.3	0.607103
$773$	14957.7	0.695977	0.347989	−	0.937499i	$-0.386865\pi$
$773$	14957.7	0.695977	0.347989	+	0.937499i	$0.386865\pi$
$774$	2642.40	0.122712
$775$	−27188.3	−1.26017
$776$	−26073.1	−1.20615
$777$	0	0
$778$	−11207.7	−0.516470
$779$	−16884.6	−0.776578
$780$	498.973	0.0229052
$781$	10377.4	0.475456
$782$	74.0722	0.00338723
$783$	−199.046	−0.00908470
$784$	0	0
$785$	−4408.07	−0.200422
$786$	−556.937	−0.0252739
$787$	34637.3	1.56885	0.784425	−	0.620223i	$-0.212958\pi$
$787$	34637.3	1.56885	0.784425	+	0.620223i	$0.212958\pi$
$788$	20454.1	0.924678
$789$	−23396.9	−1.05571
$790$	−681.735	−0.0307026
$791$	0	0
$792$	−3979.70	−0.178551
$793$	1798.61	0.0805429
$794$	−10387.3	−0.464273
$795$	−2593.82	−0.115715
$796$	−4977.36	−0.221631
$797$	−8570.03	−0.380886	−0.190443	−	0.981698i	$-0.560992\pi$
$797$	−8570.03	−0.380886	−0.190443	+	0.981698i	$0.560992\pi$
$798$	0	0
$799$	114.164	0.00505487
$800$	−20840.5	−0.921029
$801$	753.189	0.0332242
$802$	−11486.0	−0.505716
$803$	−17101.5	−0.751554
$804$	6535.18	0.286664
$805$	0	0
$806$	3253.70	0.142192
$807$	21064.9	0.918859
$808$	1525.07	0.0664008
$809$	10509.7	0.456738	0.228369	−	0.973575i	$-0.426661\pi$
$809$	10509.7	0.456738	0.228369	+	0.973575i	$0.426661\pi$
$810$	171.569	0.00744235
$811$	25584.5	1.10776	0.553880	−	0.832596i	$-0.313146\pi$
$811$	25584.5	1.10776	0.553880	+	0.832596i	$0.313146\pi$
$812$	0	0
$813$	9156.94	0.395016
$814$	987.847	0.0425356
$815$	−4556.34	−0.195830
$816$	65.1603	0.00279543
$817$	−23752.4	−1.01713
$818$	−6685.92	−0.285780
$819$	0	0
$820$	−2389.19	−0.101749
$821$	23425.1	0.995789	0.497895	−	0.867238i	$-0.334107\pi$
$821$	23425.1	0.995789	0.497895	+	0.867238i	$0.334107\pi$
$822$	3750.87	0.159156
$823$	8693.53	0.368211	0.184105	−	0.982906i	$-0.441061\pi$
$823$	8693.53	0.368211	0.184105	+	0.982906i	$0.441061\pi$
$824$	−1639.44	−0.0693113
$825$	9769.18	0.412265
$826$	0	0
$827$	6642.28	0.279292	0.139646	−	0.990201i	$-0.455404\pi$
$827$	6642.28	0.279292	0.139646	+	0.990201i	$0.455404\pi$
$828$	6596.59	0.276869
$829$	28662.7	1.20084	0.600421	−	0.799684i	$-0.295000\pi$
$829$	28662.7	1.20084	0.600421	+	0.799684i	$0.295000\pi$
$830$	1874.33	0.0783845
$831$	−13468.1	−0.562218
$832$	−1206.43	−0.0502710
$833$	0	0
$834$	4203.89	0.174543
$835$	3286.72	0.136218
$836$	16372.0	0.677318
$837$	−6046.41	−0.249695
$838$	12631.7	0.520709
$839$	−9176.96	−0.377621	−0.188810	−	0.982014i	$-0.560463\pi$
$839$	−9176.96	−0.377621	−0.188810	+	0.982014i	$0.560463\pi$
$840$	0	0
$841$	−24334.7	−0.997772
$842$	8298.29	0.339641
$843$	−26372.9	−1.07750
$844$	25168.2	1.02645
$845$	320.286	0.0130393
$846$	−1881.21	−0.0764506
$847$	0	0
$848$	16232.7	0.657351
$849$	21229.8	0.858191
$850$	82.8299	0.00334240
$851$	−3577.80	−0.144119
$852$	7835.75	0.315080
$853$	24290.7	0.975025	0.487512	−	0.873116i	$-0.337904\pi$
$853$	24290.7	0.975025	0.487512	+	0.873116i	$0.337904\pi$
$854$	0	0
$855$	−1542.22	−0.0616876
$856$	34629.4	1.38272
$857$	21883.8	0.872270	0.436135	−	0.899881i	$-0.356347\pi$
$857$	21883.8	0.872270	0.436135	+	0.899881i	$0.356347\pi$
$858$	−1169.11	−0.0465182
$859$	−8398.81	−0.333602	−0.166801	−	0.985991i	$-0.553344\pi$
$859$	−8398.81	−0.333602	−0.166801	+	0.985991i	$0.553344\pi$
$860$	−3360.99	−0.133266
$861$	0	0
$862$	5145.90	0.203330
$863$	−3118.65	−0.123013	−0.0615065	−	0.998107i	$-0.519590\pi$
$863$	−3118.65	−0.123013	−0.0615065	+	0.998107i	$0.519590\pi$
$864$	−4634.73	−0.182496
$865$	2274.75	0.0894146
$866$	13547.7	0.531606
$867$	14737.9	0.577306
$868$	0	0
$869$	−8632.79	−0.336993
$870$	−46.8450	−0.00182551
$871$	4194.88	0.163189
$872$	27195.9	1.05616
$873$	14233.6	0.551816
$874$	10971.6	0.424623
$875$	0	0
$876$	−12913.0	−0.498048
$877$	−9477.34	−0.364911	−0.182455	−	0.983214i	$-0.558405\pi$
$877$	−9477.34	−0.364911	−0.182455	+	0.983214i	$0.558405\pi$
$878$	−1466.05	−0.0563516
$879$	4036.45	0.154888
$880$	1808.69	0.0692852
$881$	−30054.5	−1.14933	−0.574667	−	0.818387i	$-0.694868\pi$
$881$	−30054.5	−1.14933	−0.574667	+	0.818387i	$0.694868\pi$
$882$	0	0
$883$	18014.9	0.686581	0.343290	−	0.939229i	$-0.388458\pi$
$883$	18014.9	0.686581	0.343290	+	0.939229i	$0.388458\pi$
$884$	53.5725	0.00203828
$885$	−446.007	−0.0169405
$886$	−10882.9	−0.412660
$887$	−46828.0	−1.77264	−0.886318	−	0.463076i	$-0.846746\pi$
$887$	−46828.0	−1.77264	−0.886318	+	0.463076i	$0.846746\pi$
$888$	1629.82	0.0615915
$889$	0	0
$890$	177.261	0.00667620
$891$	2172.57	0.0816877
$892$	−8096.20	−0.303902
$893$	16910.1	0.633678
$894$	5511.66	0.206194
$895$	−1867.18	−0.0697351
$896$	0	0
$897$	4234.29	0.157613
$898$	−2957.03	−0.109886
$899$	1650.91	0.0612468
$900$	7376.52	0.273204
$901$	−278.487	−0.0102971
$902$	5597.94	0.206642
$903$	0	0
$904$	22536.8	0.829162
$905$	−324.311	−0.0119121
$906$	−1703.95	−0.0624835
$907$	−3600.41	−0.131808	−0.0659039	−	0.997826i	$-0.520993\pi$
$907$	−3600.41	−0.131808	−0.0659039	+	0.997826i	$0.520993\pi$
$908$	−28437.3	−1.03935
$909$	−832.557	−0.0303786
$910$	0	0
$911$	−21701.8	−0.789256	−0.394628	−	0.918841i	$-0.629127\pi$
$911$	−21701.8	−0.789256	−0.394628	+	0.918841i	$0.629127\pi$
$912$	9651.59	0.350434
$913$	23734.6	0.860353
$914$	8401.54	0.304046
$915$	−786.623	−0.0284207
$916$	−28264.8	−1.01954
$917$	0	0
$918$	18.4205	0.000662275 0
$919$	24130.9	0.866165	0.433082	−	0.901354i	$-0.357426\pi$
$919$	24130.9	0.866165	0.433082	+	0.901354i	$0.357426\pi$
$920$	3392.25	0.121564
$921$	−526.435	−0.0188346
$922$	−16697.7	−0.596431
$923$	5029.70	0.179366
$924$	0	0
$925$	−4000.81	−0.142212
$926$	6362.80	0.225804
$927$	894.990	0.0317102
$928$	1265.46	0.0447639
$929$	−42011.5	−1.48369	−0.741847	−	0.670569i	$-0.766050\pi$
$929$	−42011.5	−1.48369	−0.741847	+	0.670569i	$0.766050\pi$
$930$	−1423.01	−0.0501745
$931$	0	0
$932$	−12690.9	−0.446036
$933$	830.705	0.0291490
$934$	−18445.6	−0.646210
$935$	−31.0297	−0.00108533
$936$	−1928.88	−0.0673583
$937$	−26525.1	−0.924799	−0.462400	−	0.886672i	$-0.653011\pi$
$937$	−26525.1	−0.924799	−0.462400	+	0.886672i	$0.653011\pi$
$938$	0	0
$939$	−8688.42	−0.301955
$940$	2392.79	0.0830258
$941$	34740.4	1.20351	0.601755	−	0.798681i	$-0.294468\pi$
$941$	34740.4	1.20351	0.601755	+	0.798681i	$0.294468\pi$
$942$	7798.66	0.269739
$943$	−20274.7	−0.700144
$944$	2791.21	0.0962354
$945$	0	0
$946$	7874.89	0.270650
$947$	38032.1	1.30504	0.652522	−	0.757770i	$-0.273711\pi$
$947$	38032.1	1.30504	0.652522	+	0.757770i	$0.273711\pi$
$948$	−6518.45	−0.223322
$949$	−8288.74	−0.283524
$950$	12268.8	0.419003
$951$	16837.2	0.574116
$952$	0	0
$953$	9991.13	0.339606	0.169803	−	0.985478i	$-0.445687\pi$
$953$	9991.13	0.339606	0.169803	+	0.985478i	$0.445687\pi$
$954$	4588.92	0.155736
$955$	−2902.83	−0.0983597
$956$	21512.4	0.727784
$957$	−593.197	−0.0200369
$958$	−7200.81	−0.242847
$959$	0	0
$960$	527.633	0.0177388
$961$	20358.6	0.683380
$962$	478.789	0.0160466
$963$	−18904.6	−0.632599
$964$	14674.9	0.490297
$965$	−3655.77	−0.121952
$966$	0	0
$967$	7235.04	0.240603	0.120302	−	0.992737i	$-0.461614\pi$
$967$	7235.04	0.240603	0.120302	+	0.992737i	$0.461614\pi$
$968$	10082.8	0.334785
$969$	−165.581	−0.00548942
$970$	3349.86	0.110884
$971$	−47615.5	−1.57369	−0.786846	−	0.617149i	$-0.788287\pi$
$971$	−47615.5	−1.57369	−0.786846	+	0.617149i	$0.788287\pi$
$972$	1640.47	0.0541337
$973$	0	0
$974$	−879.208	−0.0289236
$975$	4734.92	0.155527
$976$	4922.87	0.161452
$977$	25874.9	0.847300	0.423650	−	0.905826i	$-0.360749\pi$
$977$	25874.9	0.847300	0.423650	+	0.905826i	$0.360749\pi$
$978$	8060.97	0.263560
$979$	2244.66	0.0732783
$980$	0	0
$981$	−14846.6	−0.483195
$982$	9769.08	0.317458
$983$	−6126.16	−0.198773	−0.0993866	−	0.995049i	$-0.531688\pi$
$983$	−6126.16	−0.198773	−0.0993866	+	0.995049i	$0.531688\pi$
$984$	9235.90	0.299217
$985$	−5742.10	−0.185745
$986$	−5.02954	−0.000162447 0
$987$	0	0
$988$	7935.19	0.255518
$989$	−28521.4	−0.917015
$990$	511.309	0.0164146
$991$	39894.4	1.27880	0.639398	−	0.768876i	$-0.279184\pi$
$991$	39894.4	1.27880	0.639398	+	0.768876i	$0.279184\pi$
$992$	38440.9	1.23034
$993$	10886.7	0.347914
$994$	0	0
$995$	1397.30	0.0445200
$996$	17921.6	0.570148
$997$	−45833.9	−1.45594	−0.727970	−	0.685609i	$-0.759536\pi$
$997$	−45833.9	−1.45594	−0.727970	+	0.685609i	$0.759536\pi$
$998$	3240.50	0.102782
$999$	−889.741	−0.0281783

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1911.4.a.bd.1.9	✓	14
7.6	odd	2		1911.4.a.be.1.9	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1911.4.a.bd.1.9	✓	14	1.1	even	1	trivial
1911.4.a.be.1.9	yes	14	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1911.a (trivial)

\(f(q)\)	\(=\)	\(q+1.11764 q^{2} -3.00000 q^{3} -6.75088 q^{4} +1.89518 q^{5} -3.35291 q^{6} -16.4862 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+1.11764 q^{2} -3.00000 q^{3} -6.75088 q^{4} +1.89518 q^{5} -3.35291 q^{6} -16.4862 q^{8} +9.00000 q^{9} +2.11813 q^{10} +26.8218 q^{11} +20.2527 q^{12} +13.0000 q^{13} -5.68555 q^{15} +35.5815 q^{16} -0.610432 q^{17} +10.0587 q^{18} -90.4176 q^{19} -12.7942 q^{20} +29.9771 q^{22} -108.572 q^{23} +49.4585 q^{24} -121.408 q^{25} +14.5293 q^{26} -27.0000 q^{27} +7.37207 q^{29} -6.35439 q^{30} +223.941 q^{31} +171.656 q^{32} -80.4655 q^{33} -0.682242 q^{34} -60.7580 q^{36} +32.9534 q^{37} -101.054 q^{38} -39.0000 q^{39} -31.2443 q^{40} +186.740 q^{41} +262.697 q^{43} -181.071 q^{44} +17.0567 q^{45} -121.344 q^{46} -187.022 q^{47} -106.745 q^{48} -135.691 q^{50} +1.83130 q^{51} -87.7615 q^{52} +456.212 q^{53} -30.1762 q^{54} +50.8323 q^{55} +271.253 q^{57} +8.23930 q^{58} +78.4456 q^{59} +38.3825 q^{60} +138.355 q^{61} +250.285 q^{62} -92.8023 q^{64} +24.6374 q^{65} -89.9313 q^{66} +322.683 q^{67} +4.12096 q^{68} +325.715 q^{69} +386.900 q^{71} -148.375 q^{72} -637.595 q^{73} +36.8299 q^{74} +364.225 q^{75} +610.399 q^{76} -43.5879 q^{78} -321.857 q^{79} +67.4336 q^{80} +81.0000 q^{81} +208.708 q^{82} +884.900 q^{83} -1.15688 q^{85} +293.600 q^{86} -22.1162 q^{87} -442.189 q^{88} +83.6876 q^{89} +19.0632 q^{90} +732.954 q^{92} -671.823 q^{93} -209.023 q^{94} -171.358 q^{95} -514.969 q^{96} +1581.52 q^{97} +241.396 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 6 q^{2} - 42 q^{3} + 50 q^{4} - 4 q^{5} + 18 q^{6} - 30 q^{8} + 126 q^{9}+O(q^{10}) \) 14 * q - 6 * q^2 - 42 * q^3 + 50 * q^4 - 4 * q^5 + 18 * q^6 - 30 * q^8 + 126 * q^9	\( 14 q - 6 q^{2} - 42 q^{3} + 50 q^{4} - 4 q^{5} + 18 q^{6} - 30 q^{8} + 126 q^{9} + 32 q^{10} - 68 q^{11} - 150 q^{12} + 182 q^{13} + 12 q^{15} - 50 q^{16} - 54 q^{18} + 24 q^{19} + 96 q^{20} - 300 q^{22} - 64 q^{23} + 90 q^{24} - 118 q^{25} - 78 q^{26} - 378 q^{27} - 792 q^{29} - 96 q^{30} + 524 q^{31} - 126 q^{32} + 204 q^{33} - 88 q^{34} + 450 q^{36} - 344 q^{37} + 436 q^{38} - 546 q^{39} + 704 q^{40} + 44 q^{41} + 144 q^{43} - 1248 q^{44} - 36 q^{45} - 972 q^{46} - 236 q^{47} + 150 q^{48} - 714 q^{50} + 650 q^{52} - 1556 q^{53} + 162 q^{54} + 396 q^{55} - 72 q^{57} + 92 q^{58} + 1244 q^{59} - 288 q^{60} + 984 q^{61} + 236 q^{62} - 714 q^{64} - 52 q^{65} + 900 q^{66} - 1396 q^{67} + 960 q^{68} + 192 q^{69} - 1216 q^{71} - 270 q^{72} + 1768 q^{73} - 1212 q^{74} + 354 q^{75} + 496 q^{76} + 234 q^{78} - 1888 q^{79} + 1300 q^{80} + 1134 q^{81} + 1920 q^{82} - 1008 q^{83} + 56 q^{85} - 2128 q^{86} + 2376 q^{87} - 3148 q^{88} - 864 q^{89} + 288 q^{90} + 2856 q^{92} - 1572 q^{93} + 4860 q^{94} - 4984 q^{95} + 378 q^{96} + 1368 q^{97} - 612 q^{99}+O(q^{100}) \) 14 * q - 6 * q^2 - 42 * q^3 + 50 * q^4 - 4 * q^5 + 18 * q^6 - 30 * q^8 + 126 * q^9 + 32 * q^10 - 68 * q^11 - 150 * q^12 + 182 * q^13 + 12 * q^15 - 50 * q^16 - 54 * q^18 + 24 * q^19 + 96 * q^20 - 300 * q^22 - 64 * q^23 + 90 * q^24 - 118 * q^25 - 78 * q^26 - 378 * q^27 - 792 * q^29 - 96 * q^30 + 524 * q^31 - 126 * q^32 + 204 * q^33 - 88 * q^34 + 450 * q^36 - 344 * q^37 + 436 * q^38 - 546 * q^39 + 704 * q^40 + 44 * q^41 + 144 * q^43 - 1248 * q^44 - 36 * q^45 - 972 * q^46 - 236 * q^47 + 150 * q^48 - 714 * q^50 + 650 * q^52 - 1556 * q^53 + 162 * q^54 + 396 * q^55 - 72 * q^57 + 92 * q^58 + 1244 * q^59 - 288 * q^60 + 984 * q^61 + 236 * q^62 - 714 * q^64 - 52 * q^65 + 900 * q^66 - 1396 * q^67 + 960 * q^68 + 192 * q^69 - 1216 * q^71 - 270 * q^72 + 1768 * q^73 - 1212 * q^74 + 354 * q^75 + 496 * q^76 + 234 * q^78 - 1888 * q^79 + 1300 * q^80 + 1134 * q^81 + 1920 * q^82 - 1008 * q^83 + 56 * q^85 - 2128 * q^86 + 2376 * q^87 - 3148 * q^88 - 864 * q^89 + 288 * q^90 + 2856 * q^92 - 1572 * q^93 + 4860 * q^94 - 4984 * q^95 + 378 * q^96 + 1368 * q^97 - 612 * q^99

Introduction

L-functions

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