LMFDB - Embedded newform 1911.4.a.bb.1.5

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:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 3 x^{12} - 75 x^{11} + 220 x^{10} + 2024 x^{9} - 5757 x^{8} - 23683 x^{7} + 64922 x^{6} + \cdots + 1152 $ x^13 - 3x^12 - 75x^11 + 220x^10 + 2024x^9 - 5757x^8 - 23683x^7 + 64922x^6 + 115317x^5 - 311422x^4 - 171120x^3 + 495720x^2 - 51264x + 1152
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.79237$ 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)

$f(q)$	$=$	$q-1.79237 q^{2} -3.00000 q^{3} -4.78741 q^{4} -0.476581 q^{5} +5.37711 q^{6} +22.9198 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.79237 q^{2} -3.00000 q^{3} -4.78741 q^{4} -0.476581 q^{5} +5.37711 q^{6} +22.9198 q^{8} +9.00000 q^{9} +0.854209 q^{10} +15.9222 q^{11} +14.3622 q^{12} -13.0000 q^{13} +1.42974 q^{15} -2.78143 q^{16} +55.9109 q^{17} -16.1313 q^{18} -164.340 q^{19} +2.28159 q^{20} -28.5386 q^{22} +94.9977 q^{23} -68.7593 q^{24} -124.773 q^{25} +23.3008 q^{26} -27.0000 q^{27} +183.799 q^{29} -2.56263 q^{30} -48.7790 q^{31} -178.373 q^{32} -47.7667 q^{33} -100.213 q^{34} -43.0867 q^{36} -92.9783 q^{37} +294.557 q^{38} +39.0000 q^{39} -10.9231 q^{40} +105.115 q^{41} -50.2025 q^{43} -76.2263 q^{44} -4.28923 q^{45} -170.271 q^{46} -340.932 q^{47} +8.34429 q^{48} +223.639 q^{50} -167.733 q^{51} +62.2363 q^{52} +39.4036 q^{53} +48.3940 q^{54} -7.58824 q^{55} +493.019 q^{57} -329.436 q^{58} +565.016 q^{59} -6.84476 q^{60} -231.456 q^{61} +87.4301 q^{62} +341.961 q^{64} +6.19555 q^{65} +85.6157 q^{66} +202.783 q^{67} -267.669 q^{68} -284.993 q^{69} +557.737 q^{71} +206.278 q^{72} -317.973 q^{73} +166.652 q^{74} +374.319 q^{75} +786.761 q^{76} -69.9024 q^{78} -384.861 q^{79} +1.32558 q^{80} +81.0000 q^{81} -188.406 q^{82} +967.477 q^{83} -26.6461 q^{85} +89.9815 q^{86} -551.398 q^{87} +364.934 q^{88} +734.197 q^{89} +7.68788 q^{90} -454.793 q^{92} +146.337 q^{93} +611.076 q^{94} +78.3211 q^{95} +535.118 q^{96} +1671.86 q^{97} +143.300 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 3 q^{2} - 39 q^{3} + 55 q^{4} - 15 q^{5} - 9 q^{6} - 6 q^{8} + 117 q^{9}+O(q^{10}) $ 13 * q + 3 * q^2 - 39 * q^3 + 55 * q^4 - 15 * q^5 - 9 * q^6 - 6 * q^8 + 117 * q^9	\( 13 q + 3 q^{2} - 39 q^{3} + 55 q^{4} - 15 q^{5} - 9 q^{6} - 6 q^{8} + 117 q^{9} - 11 q^{10} + 57 q^{11} - 165 q^{12} - 169 q^{13} + 45 q^{15} + 311 q^{16} - 162 q^{17} + 27 q^{18} - 138 q^{19} - 12 q^{20} - 194 q^{22} - 54 q^{23} + 18 q^{24} + 558 q^{25} - 39 q^{26} - 351 q^{27} + 303 q^{29} + 33 q^{30} - 549 q^{31} - 171 q^{33} - 25 q^{34} + 495 q^{36} + 476 q^{37} - 444 q^{38} + 507 q^{39} - 1442 q^{40} - 534 q^{41} + 430 q^{43} + 414 q^{44} - 135 q^{45} + 273 q^{46} - 414 q^{47} - 933 q^{48} + 633 q^{50} + 486 q^{51} - 715 q^{52} - 1305 q^{53} - 81 q^{54} + 369 q^{55} + 414 q^{57} - 279 q^{58} - 1959 q^{59} + 36 q^{60} - 1262 q^{61} + 669 q^{62} + 342 q^{64} + 195 q^{65} + 582 q^{66} + 2456 q^{67} - 1620 q^{68} + 162 q^{69} + 198 q^{71} - 54 q^{72} - 1284 q^{73} - 2481 q^{74} - 1674 q^{75} - 748 q^{76} + 117 q^{78} + 1015 q^{79} - 372 q^{80} + 1053 q^{81} - 1604 q^{82} + 69 q^{83} + 2824 q^{85} - 1131 q^{86} - 909 q^{87} + 465 q^{88} - 4974 q^{89} - 99 q^{90} + 4122 q^{92} + 1647 q^{93} - 3316 q^{94} + 1848 q^{95} - 1269 q^{97} + 513 q^{99}+O(q^{100}) \) 13 * q + 3 * q^2 - 39 * q^3 + 55 * q^4 - 15 * q^5 - 9 * q^6 - 6 * q^8 + 117 * q^9 - 11 * q^10 + 57 * q^11 - 165 * q^12 - 169 * q^13 + 45 * q^15 + 311 * q^16 - 162 * q^17 + 27 * q^18 - 138 * q^19 - 12 * q^20 - 194 * q^22 - 54 * q^23 + 18 * q^24 + 558 * q^25 - 39 * q^26 - 351 * q^27 + 303 * q^29 + 33 * q^30 - 549 * q^31 - 171 * q^33 - 25 * q^34 + 495 * q^36 + 476 * q^37 - 444 * q^38 + 507 * q^39 - 1442 * q^40 - 534 * q^41 + 430 * q^43 + 414 * q^44 - 135 * q^45 + 273 * q^46 - 414 * q^47 - 933 * q^48 + 633 * q^50 + 486 * q^51 - 715 * q^52 - 1305 * q^53 - 81 * q^54 + 369 * q^55 + 414 * q^57 - 279 * q^58 - 1959 * q^59 + 36 * q^60 - 1262 * q^61 + 669 * q^62 + 342 * q^64 + 195 * q^65 + 582 * q^66 + 2456 * q^67 - 1620 * q^68 + 162 * q^69 + 198 * q^71 - 54 * q^72 - 1284 * q^73 - 2481 * q^74 - 1674 * q^75 - 748 * q^76 + 117 * q^78 + 1015 * q^79 - 372 * q^80 + 1053 * q^81 - 1604 * q^82 + 69 * q^83 + 2824 * q^85 - 1131 * q^86 - 909 * q^87 + 465 * q^88 - 4974 * q^89 - 99 * q^90 + 4122 * q^92 + 1647 * q^93 - 3316 * q^94 + 1848 * q^95 - 1269 * q^97 + 513 * 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 $

$2$	−1.79237	−0.633698	−0.316849	−	0.948476i	$-0.602625\pi$
$2$	−1.79237	−0.633698	−0.316849	+	0.948476i	$0.602625\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−4.78741	−0.598426
$5$	−0.476581	−0.0426267	−0.0213133	−	0.999773i	$-0.506785\pi$
$5$	−0.476581	−0.0426267	−0.0213133	+	0.999773i	$0.506785\pi$
$6$	5.37711	0.365866
$7$	0	0
$7$	0	0
$8$	22.9198	1.01292
$9$	9.00000	0.333333
$10$	0.854209	0.0270125
$11$	15.9222	0.436431	0.218215	−	0.975901i	$-0.429976\pi$
$11$	15.9222	0.436431	0.218215	+	0.975901i	$0.429976\pi$
$12$	14.3622	0.345502
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	0	0
$15$	1.42974	0.0246105
$16$	−2.78143	−0.0434598
$17$	55.9109	0.797670	0.398835	−	0.917023i	$-0.369415\pi$
$17$	55.9109	0.797670	0.398835	+	0.917023i	$0.369415\pi$
$18$	−16.1313	−0.211233
$19$	−164.340	−1.98432	−0.992161	−	0.124969i	$-0.960117\pi$
$19$	−164.340	−1.98432	−0.992161	+	0.124969i	$0.960117\pi$
$20$	2.28159	0.0255089
$21$	0	0
$22$	−28.5386	−0.276565
$23$	94.9977	0.861234	0.430617	−	0.902535i	$-0.358296\pi$
$23$	94.9977	0.861234	0.430617	+	0.902535i	$0.358296\pi$
$24$	−68.7593	−0.584810
$25$	−124.773	−0.998183
$26$	23.3008	0.175756
$27$	−27.0000	−0.192450
$28$	0	0
$29$	183.799	1.17692	0.588460	−	0.808526i	$-0.299734\pi$
$29$	183.799	1.17692	0.588460	+	0.808526i	$0.299734\pi$
$30$	−2.56263	−0.0155957
$31$	−48.7790	−0.282612	−0.141306	−	0.989966i	$-0.545130\pi$
$31$	−48.7790	−0.282612	−0.141306	+	0.989966i	$0.545130\pi$
$32$	−178.373	−0.985380
$33$	−47.7667	−0.251973
$34$	−100.213	−0.505482
$35$	0	0
$36$	−43.0867	−0.199475
$37$	−92.9783	−0.413123	−0.206561	−	0.978434i	$-0.566227\pi$
$37$	−92.9783	−0.413123	−0.206561	+	0.978434i	$0.566227\pi$
$38$	294.557	1.25746
$39$	39.0000	0.160128
$40$	−10.9231	−0.0431774
$41$	105.115	0.400397	0.200198	−	0.979755i	$-0.435841\pi$
$41$	105.115	0.400397	0.200198	+	0.979755i	$0.435841\pi$
$42$	0	0
$43$	−50.2025	−0.178042	−0.0890211	−	0.996030i	$-0.528374\pi$
$43$	−50.2025	−0.178042	−0.0890211	+	0.996030i	$0.528374\pi$
$44$	−76.2263	−0.261172
$45$	−4.28923	−0.0142089
$46$	−170.271	−0.545763
$47$	−340.932	−1.05808	−0.529042	−	0.848595i	$-0.677449\pi$
$47$	−340.932	−1.05808	−0.529042	+	0.848595i	$0.677449\pi$
$48$	8.34429	0.0250915
$49$	0	0
$50$	223.639	0.632547
$51$	−167.733	−0.460535
$52$	62.2363	0.165974
$53$	39.4036	0.102123	0.0510613	−	0.998696i	$-0.483740\pi$
$53$	39.4036	0.102123	0.0510613	+	0.998696i	$0.483740\pi$
$54$	48.3940	0.121955
$55$	−7.58824	−0.0186036
$56$	0	0
$57$	493.019	1.14565
$58$	−329.436	−0.745812
$59$	565.016	1.24676	0.623380	−	0.781919i	$-0.285759\pi$
$59$	565.016	1.24676	0.623380	+	0.781919i	$0.285759\pi$
$60$	−6.84476	−0.0147276
$61$	−231.456	−0.485817	−0.242909	−	0.970049i	$-0.578102\pi$
$61$	−231.456	−0.485817	−0.242909	+	0.970049i	$0.578102\pi$
$62$	87.4301	0.179091
$63$	0	0
$64$	341.961	0.667894
$65$	6.19555	0.0118225
$66$	85.6157	0.159675
$67$	202.783	0.369759	0.184880	−	0.982761i	$-0.440811\pi$
$67$	202.783	0.369759	0.184880	+	0.982761i	$0.440811\pi$
$68$	−267.669	−0.477347
$69$	−284.993	−0.497234
$70$	0	0
$71$	557.737	0.932270	0.466135	−	0.884714i	$-0.345646\pi$
$71$	557.737	0.932270	0.466135	+	0.884714i	$0.345646\pi$
$72$	206.278	0.337640
$73$	−317.973	−0.509806	−0.254903	−	0.966967i	$-0.582044\pi$
$73$	−317.973	−0.509806	−0.254903	+	0.966967i	$0.582044\pi$
$74$	166.652	0.261795
$75$	374.319	0.576301
$76$	786.761	1.18747
$77$	0	0
$78$	−69.9024	−0.101473
$79$	−384.861	−0.548104	−0.274052	−	0.961715i	$-0.588364\pi$
$79$	−384.861	−0.548104	−0.274052	+	0.961715i	$0.588364\pi$
$80$	1.32558	0.00185255
$81$	81.0000	0.111111
$82$	−188.406	−0.253731
$83$	967.477	1.27945	0.639725	−	0.768603i	$-0.279048\pi$
$83$	967.477	1.27945	0.639725	+	0.768603i	$0.279048\pi$
$84$	0	0
$85$	−26.6461	−0.0340020
$86$	89.9815	0.112825
$87$	−551.398	−0.679495
$88$	364.934	0.442070
$89$	734.197	0.874435	0.437218	−	0.899356i	$-0.355964\pi$
$89$	734.197	0.874435	0.437218	+	0.899356i	$0.355964\pi$
$90$	7.68788	0.00900415
$91$	0	0
$92$	−454.793	−0.515385
$93$	146.337	0.163166
$94$	611.076	0.670507
$95$	78.3211	0.0845850
$96$	535.118	0.568909
$97$	1671.86	1.75002	0.875010	−	0.484105i	$-0.160855\pi$
$97$	1671.86	1.75002	0.875010	+	0.484105i	$0.160855\pi$
$98$	0	0
$99$	143.300	0.145477
$100$	597.339	0.597339
$101$	−1169.06	−1.15174	−0.575869	−	0.817542i	$-0.695336\pi$
$101$	−1169.06	−1.15174	−0.575869	+	0.817542i	$0.695336\pi$
$102$	300.639	0.291840
$103$	213.562	0.204300	0.102150	−	0.994769i	$-0.467428\pi$
$103$	213.562	0.204300	0.102150	+	0.994769i	$0.467428\pi$
$104$	−297.957	−0.280934
$105$	0	0
$106$	−70.6258	−0.0647150
$107$	1598.91	1.44461	0.722303	−	0.691577i	$-0.243084\pi$
$107$	1598.91	1.44461	0.722303	+	0.691577i	$0.243084\pi$
$108$	129.260	0.115167
$109$	−82.6173	−0.0725991	−0.0362996	−	0.999341i	$-0.511557\pi$
$109$	−82.6173	−0.0725991	−0.0362996	+	0.999341i	$0.511557\pi$
$110$	13.6009	0.0117891
$111$	278.935	0.238517
$112$	0	0
$113$	−287.057	−0.238974	−0.119487	−	0.992836i	$-0.538125\pi$
$113$	−287.057	−0.238974	−0.119487	+	0.992836i	$0.538125\pi$
$114$	−883.672	−0.725996
$115$	−45.2741	−0.0367115
$116$	−879.923	−0.704300
$117$	−117.000	−0.0924500
$118$	−1012.72	−0.790070
$119$	0	0
$120$	32.7694	0.0249285
$121$	−1077.48	−0.809528
$122$	414.854	0.307862
$123$	−315.346	−0.231169
$124$	233.525	0.169122
$125$	119.037	0.0851759
$126$	0	0
$127$	900.702	0.629326	0.314663	−	0.949203i	$-0.398109\pi$
$127$	900.702	0.629326	0.314663	+	0.949203i	$0.398109\pi$
$128$	814.061	0.562137
$129$	150.608	0.102793
$130$	−11.1047	−0.00749191
$131$	−1154.85	−0.770224	−0.385112	−	0.922870i	$-0.625837\pi$
$131$	−1154.85	−0.770224	−0.385112	+	0.922870i	$0.625837\pi$
$132$	228.679	0.150787
$133$	0	0
$134$	−363.462	−0.234316
$135$	12.8677	0.00820351
$136$	1281.47	0.807976
$137$	−1181.25	−0.736647	−0.368323	−	0.929698i	$-0.620068\pi$
$137$	−1181.25	−0.736647	−0.368323	+	0.929698i	$0.620068\pi$
$138$	510.813	0.315096
$139$	61.6692	0.0376310	0.0188155	−	0.999823i	$-0.494010\pi$
$139$	61.6692	0.0376310	0.0188155	+	0.999823i	$0.494010\pi$
$140$	0	0
$141$	1022.79	0.610886
$142$	−999.671	−0.590778
$143$	−206.989	−0.121044
$144$	−25.0329	−0.0144866
$145$	−87.5952	−0.0501682
$146$	569.924	0.323064
$147$	0	0
$148$	445.125	0.247224
$149$	1160.75	0.638202	0.319101	−	0.947721i	$-0.396619\pi$
$149$	1160.75	0.638202	0.319101	+	0.947721i	$0.396619\pi$
$150$	−670.917	−0.365201
$151$	2907.28	1.56683	0.783413	−	0.621501i	$-0.213477\pi$
$151$	2907.28	1.56683	0.783413	+	0.621501i	$0.213477\pi$
$152$	−3766.63	−2.00996
$153$	503.198	0.265890
$154$	0	0
$155$	23.2471	0.0120468
$156$	−186.709	−0.0958249
$157$	−937.756	−0.476695	−0.238347	−	0.971180i	$-0.576606\pi$
$157$	−937.756	−0.476695	−0.238347	+	0.971180i	$0.576606\pi$
$158$	689.813	0.347333
$159$	−118.211	−0.0589606
$160$	85.0090	0.0420035
$161$	0	0
$162$	−145.182	−0.0704109
$163$	−2249.99	−1.08118	−0.540591	−	0.841286i	$-0.681799\pi$
$163$	−2249.99	−1.08118	−0.540591	+	0.841286i	$0.681799\pi$
$164$	−503.230	−0.239608
$165$	22.7647	0.0107408
$166$	−1734.08	−0.810786
$167$	−2061.69	−0.955320	−0.477660	−	0.878545i	$-0.658515\pi$
$167$	−2061.69	−0.955320	−0.477660	+	0.878545i	$0.658515\pi$
$168$	0	0
$169$	169.000	0.0769231
$170$	47.7596	0.0215470
$171$	−1479.06	−0.661440
$172$	240.340	0.106545
$173$	2137.51	0.939376	0.469688	−	0.882833i	$-0.344366\pi$
$173$	2137.51	0.939376	0.469688	+	0.882833i	$0.344366\pi$
$174$	988.309	0.430595
$175$	0	0
$176$	−44.2866	−0.0189672
$177$	−1695.05	−0.719817
$178$	−1315.95	−0.554128
$179$	−346.050	−0.144497	−0.0722487	−	0.997387i	$-0.523018\pi$
$179$	−346.050	−0.144497	−0.0722487	+	0.997387i	$0.523018\pi$
$180$	20.5343	0.00850297
$181$	−2793.93	−1.14735	−0.573677	−	0.819082i	$-0.694483\pi$
$181$	−2793.93	−1.14735	−0.573677	+	0.819082i	$0.694483\pi$
$182$	0	0
$183$	694.367	0.280487
$184$	2177.33	0.872362
$185$	44.3117	0.0176101
$186$	−262.290	−0.103398
$187$	890.228	0.348128
$188$	1632.18	0.633186
$189$	0	0
$190$	−140.380	−0.0536014
$191$	3148.43	1.19273	0.596367	−	0.802712i	$-0.296610\pi$
$191$	3148.43	1.19273	0.596367	+	0.802712i	$0.296610\pi$
$192$	−1025.88	−0.385609
$193$	−5020.18	−1.87233	−0.936166	−	0.351558i	$-0.885652\pi$
$193$	−5020.18	−1.87233	−0.936166	+	0.351558i	$0.885652\pi$
$194$	−2996.60	−1.10899
$195$	−18.5866	−0.00682573
$196$	0	0
$197$	1066.61	0.385752	0.192876	−	0.981223i	$-0.438219\pi$
$197$	1066.61	0.385752	0.192876	+	0.981223i	$0.438219\pi$
$198$	−256.847	−0.0921885
$199$	−1509.81	−0.537827	−0.268913	−	0.963164i	$-0.586665\pi$
$199$	−1509.81	−0.537827	−0.268913	+	0.963164i	$0.586665\pi$
$200$	−2859.77	−1.01108
$201$	−608.348	−0.213480
$202$	2095.38	0.729855
$203$	0	0
$204$	803.006	0.275596
$205$	−50.0960	−0.0170676
$206$	−382.782	−0.129465
$207$	854.979	0.287078
$208$	36.1586	0.0120536
$209$	−2616.66	−0.866019
$210$	0	0
$211$	3436.41	1.12120	0.560598	−	0.828088i	$-0.310571\pi$
$211$	3436.41	1.12120	0.560598	+	0.828088i	$0.310571\pi$
$212$	−188.641	−0.0611129
$213$	−1673.21	−0.538246
$214$	−2865.85	−0.915445
$215$	23.9256	0.00758935
$216$	−618.834	−0.194937
$217$	0	0
$218$	148.081	0.0460060
$219$	953.918	0.294337
$220$	36.3280	0.0111329
$221$	−726.842	−0.221234
$222$	−499.955	−0.151148
$223$	−864.247	−0.259526	−0.129763	−	0.991545i	$-0.541422\pi$
$223$	−864.247	−0.259526	−0.129763	+	0.991545i	$0.541422\pi$
$224$	0	0
$225$	−1122.96	−0.332728
$226$	514.512	0.151437
$227$	−1794.52	−0.524697	−0.262349	−	0.964973i	$-0.584497\pi$
$227$	−1794.52	−0.524697	−0.262349	+	0.964973i	$0.584497\pi$
$228$	−2360.28	−0.685586
$229$	−1914.89	−0.552574	−0.276287	−	0.961075i	$-0.589104\pi$
$229$	−1914.89	−0.552574	−0.276287	+	0.961075i	$0.589104\pi$
$230$	81.1479	0.0232641
$231$	0	0
$232$	4212.64	1.19213
$233$	−4919.23	−1.38313	−0.691565	−	0.722314i	$-0.743079\pi$
$233$	−4919.23	−1.38313	−0.691565	+	0.722314i	$0.743079\pi$
$234$	209.707	0.0585854
$235$	162.481	0.0451026
$236$	−2704.96	−0.746094
$237$	1154.58	0.316448
$238$	0	0
$239$	6727.67	1.82082	0.910412	−	0.413704i	$-0.135765\pi$
$239$	6727.67	1.82082	0.910412	+	0.413704i	$0.135765\pi$
$240$	−3.97673	−0.00106957
$241$	−3903.86	−1.04344	−0.521721	−	0.853116i	$-0.674710\pi$
$241$	−3903.86	−1.04344	−0.521721	+	0.853116i	$0.674710\pi$
$242$	1931.25	0.512997
$243$	−243.000	−0.0641500
$244$	1108.07	0.290726
$245$	0	0
$246$	565.217	0.146492
$247$	2136.42	0.550352
$248$	−1118.00	−0.286263
$249$	−2902.43	−0.738691
$250$	−213.358	−0.0539758
$251$	−6021.99	−1.51436	−0.757181	−	0.653206i	$-0.773424\pi$
$251$	−6021.99	−1.51436	−0.757181	+	0.653206i	$0.773424\pi$
$252$	0	0
$253$	1512.58	0.375869
$254$	−1614.39	−0.398803
$255$	79.9382	0.0196311
$256$	−4194.79	−1.02412
$257$	3080.11	0.747595	0.373798	−	0.927510i	$-0.378055\pi$
$257$	3080.11	0.747595	0.373798	+	0.927510i	$0.378055\pi$
$258$	−269.945	−0.0651396
$259$	0	0
$260$	−29.6606	−0.00707490
$261$	1654.19	0.392307
$262$	2069.91	0.488090
$263$	−5512.25	−1.29240	−0.646198	−	0.763170i	$-0.723642\pi$
$263$	−5512.25	−1.29240	−0.646198	+	0.763170i	$0.723642\pi$
$264$	−1094.80	−0.255229
$265$	−18.7790	−0.00435315
$266$	0	0
$267$	−2202.59	−0.504855
$268$	−970.804	−0.221274
$269$	6685.35	1.51529	0.757645	−	0.652666i	$-0.226350\pi$
$269$	6685.35	1.51529	0.757645	+	0.652666i	$0.226350\pi$
$270$	−23.0636	−0.00519855
$271$	−8682.44	−1.94620	−0.973101	−	0.230379i	$-0.926003\pi$
$271$	−8682.44	−1.94620	−0.973101	+	0.230379i	$0.926003\pi$
$272$	−155.512	−0.0346666
$273$	0	0
$274$	2117.23	0.466812
$275$	−1986.66	−0.435638
$276$	1364.38	0.297558
$277$	1355.16	0.293947	0.146974	−	0.989140i	$-0.453047\pi$
$277$	1355.16	0.293947	0.146974	+	0.989140i	$0.453047\pi$
$278$	−110.534	−0.0238467
$279$	−439.011	−0.0942040
$280$	0	0
$281$	−1964.39	−0.417031	−0.208515	−	0.978019i	$-0.566863\pi$
$281$	−1964.39	−0.417031	−0.208515	+	0.978019i	$0.566863\pi$
$282$	−1833.23	−0.387117
$283$	−5555.60	−1.16695	−0.583474	−	0.812132i	$-0.698307\pi$
$283$	−5555.60	−1.16695	−0.583474	+	0.812132i	$0.698307\pi$
$284$	−2670.11	−0.557895
$285$	−234.963	−0.0488352
$286$	371.001	0.0767055
$287$	0	0
$288$	−1605.36	−0.328460
$289$	−1786.97	−0.363722
$290$	157.003	0.0317915
$291$	−5015.59	−1.01037
$292$	1522.26	0.305082
$293$	262.189	0.0522773	0.0261387	−	0.999658i	$-0.491679\pi$
$293$	262.189	0.0522773	0.0261387	+	0.999658i	$0.491679\pi$
$294$	0	0
$295$	−269.276	−0.0531452
$296$	−2131.04	−0.418460
$297$	−429.901	−0.0839911
$298$	−2080.49	−0.404427
$299$	−1234.97	−0.238863
$300$	−1792.02	−0.344874
$301$	0	0
$302$	−5210.91	−0.992895
$303$	3507.17	0.664956
$304$	457.099	0.0862383
$305$	110.307	0.0207088
$306$	−901.918	−0.168494
$307$	−3044.11	−0.565917	−0.282959	−	0.959132i	$-0.591316\pi$
$307$	−3044.11	−0.565917	−0.282959	+	0.959132i	$0.591316\pi$
$308$	0	0
$309$	−640.686	−0.117953
$310$	−41.6675	−0.00763404
$311$	5155.90	0.940078	0.470039	−	0.882646i	$-0.344240\pi$
$311$	5155.90	0.940078	0.470039	+	0.882646i	$0.344240\pi$
$312$	893.871	0.162197
$313$	−7698.71	−1.39028	−0.695138	−	0.718876i	$-0.744657\pi$
$313$	−7698.71	−1.39028	−0.695138	+	0.718876i	$0.744657\pi$
$314$	1680.81	0.302081
$315$	0	0
$316$	1842.49	0.328000
$317$	−5327.65	−0.943944	−0.471972	−	0.881613i	$-0.656458\pi$
$317$	−5327.65	−0.943944	−0.471972	+	0.881613i	$0.656458\pi$
$318$	211.878	0.0373632
$319$	2926.50	0.513644
$320$	−162.972	−0.0284701
$321$	−4796.74	−0.834044
$322$	0	0
$323$	−9188.38	−1.58283
$324$	−387.780	−0.0664918
$325$	1622.05	0.276846
$326$	4032.81	0.685143
$327$	247.852	0.0419151
$328$	2409.22	0.405570
$329$	0	0
$330$	−40.8028	−0.00680642
$331$	10170.5	1.68889	0.844444	−	0.535644i	$-0.179931\pi$
$331$	10170.5	1.68889	0.844444	+	0.535644i	$0.179931\pi$
$332$	−4631.71	−0.765657
$333$	−836.805	−0.137708
$334$	3695.31	0.605385
$335$	−96.6423	−0.0157616
$336$	0	0
$337$	6354.67	1.02718	0.513592	−	0.858035i	$-0.328315\pi$
$337$	6354.67	1.02718	0.513592	+	0.858035i	$0.328315\pi$
$338$	−302.911	−0.0487460
$339$	861.171	0.137972
$340$	127.566	0.0203477
$341$	−776.672	−0.123341
$342$	2651.02	0.419154
$343$	0	0
$344$	−1150.63	−0.180343
$345$	135.822	0.0211954
$346$	−3831.21	−0.595281
$347$	6533.16	1.01072	0.505358	−	0.862910i	$-0.331360\pi$
$347$	6533.16	1.01072	0.505358	+	0.862910i	$0.331360\pi$
$348$	2639.77	0.406628
$349$	6137.52	0.941358	0.470679	−	0.882304i	$-0.344009\pi$
$349$	6137.52	0.941358	0.470679	+	0.882304i	$0.344009\pi$
$350$	0	0
$351$	351.000	0.0533761
$352$	−2840.10	−0.430050
$353$	−7620.45	−1.14900	−0.574498	−	0.818506i	$-0.694803\pi$
$353$	−7620.45	−1.14900	−0.574498	+	0.818506i	$0.694803\pi$
$354$	3038.15	0.456147
$355$	−265.807	−0.0397396
$356$	−3514.90	−0.523285
$357$	0	0
$358$	620.251	0.0915678
$359$	−8848.53	−1.30086	−0.650428	−	0.759568i	$-0.725410\pi$
$359$	−8848.53	−1.30086	−0.650428	+	0.759568i	$0.725410\pi$
$360$	−98.3081	−0.0143925
$361$	20148.5	2.93753
$362$	5007.75	0.727076
$363$	3232.45	0.467381
$364$	0	0
$365$	151.540	0.0217314
$366$	−1244.56	−0.177744
$367$	−8351.47	−1.18786	−0.593928	−	0.804518i	$-0.702424\pi$
$367$	−8351.47	−1.18786	−0.593928	+	0.804518i	$0.702424\pi$
$368$	−264.229	−0.0374291
$369$	946.038	0.133466
$370$	−79.4229	−0.0111595
$371$	0	0
$372$	−700.576	−0.0976429
$373$	5882.66	0.816602	0.408301	−	0.912847i	$-0.366121\pi$
$373$	5882.66	0.816602	0.408301	+	0.912847i	$0.366121\pi$
$374$	−1595.62	−0.220608
$375$	−357.111	−0.0491763
$376$	−7814.07	−1.07176
$377$	−2389.39	−0.326419
$378$	0	0
$379$	1399.01	0.189610	0.0948052	−	0.995496i	$-0.469777\pi$
$379$	1399.01	0.189610	0.0948052	+	0.995496i	$0.469777\pi$
$380$	−374.955	−0.0506179
$381$	−2702.11	−0.363341
$382$	−5643.15	−0.755834
$383$	554.983	0.0740426	0.0370213	−	0.999314i	$-0.488213\pi$
$383$	554.983	0.0740426	0.0370213	+	0.999314i	$0.488213\pi$
$384$	−2442.18	−0.324550
$385$	0	0
$386$	8998.01	1.18649
$387$	−451.823	−0.0593474
$388$	−8003.89	−1.04726
$389$	−13379.2	−1.74384	−0.871918	−	0.489652i	$-0.837124\pi$
$389$	−13379.2	−1.74384	−0.871918	+	0.489652i	$0.837124\pi$
$390$	33.3141	0.00432546
$391$	5311.41	0.686981
$392$	0	0
$393$	3464.54	0.444689
$394$	−1911.77	−0.244450
$395$	183.417	0.0233639
$396$	−686.037	−0.0870572
$397$	−4685.80	−0.592376	−0.296188	−	0.955130i	$-0.595716\pi$
$397$	−4685.80	−0.592376	−0.296188	+	0.955130i	$0.595716\pi$
$398$	2706.14	0.340820
$399$	0	0
$400$	347.047	0.0433809
$401$	−8537.60	−1.06321	−0.531605	−	0.846992i	$-0.678411\pi$
$401$	−8537.60	−1.06321	−0.531605	+	0.846992i	$0.678411\pi$
$402$	1090.39	0.135282
$403$	634.127	0.0783825
$404$	5596.76	0.689230
$405$	−38.6030	−0.00473630
$406$	0	0
$407$	−1480.42	−0.180299
$408$	−3844.40	−0.466485
$409$	7761.18	0.938302	0.469151	−	0.883118i	$-0.344560\pi$
$409$	7761.18	0.938302	0.469151	+	0.883118i	$0.344560\pi$
$410$	89.7905	0.0108157
$411$	3543.74	0.425303
$412$	−1022.41	−0.122258
$413$	0	0
$414$	−1532.44	−0.181921
$415$	−461.081	−0.0545387
$416$	2318.85	0.273295
$417$	−185.008	−0.0217263
$418$	4690.02	0.548795
$419$	−14089.6	−1.64277	−0.821384	−	0.570376i	$-0.806798\pi$
$419$	−14089.6	−1.64277	−0.821384	+	0.570376i	$0.806798\pi$
$420$	0	0
$421$	3702.23	0.428589	0.214294	−	0.976769i	$-0.431255\pi$
$421$	3702.23	0.428589	0.214294	+	0.976769i	$0.431255\pi$
$422$	−6159.32	−0.710500
$423$	−3068.38	−0.352695
$424$	903.122	0.103442
$425$	−6976.17	−0.796221
$426$	2999.01	0.341086
$427$	0	0
$428$	−7654.66	−0.864490
$429$	620.968	0.0698848
$430$	−42.8834	−0.00480936
$431$	9726.59	1.08704	0.543519	−	0.839397i	$-0.317092\pi$
$431$	9726.59	1.08704	0.543519	+	0.839397i	$0.317092\pi$
$432$	75.0986	0.00836385
$433$	−8762.04	−0.972463	−0.486232	−	0.873830i	$-0.661629\pi$
$433$	−8762.04	−0.972463	−0.486232	+	0.873830i	$0.661629\pi$
$434$	0	0
$435$	262.786	0.0289646
$436$	395.523	0.0434452
$437$	−15611.9	−1.70897
$438$	−1709.77	−0.186521
$439$	−6347.26	−0.690064	−0.345032	−	0.938591i	$-0.612132\pi$
$439$	−6347.26	−0.690064	−0.345032	+	0.938591i	$0.612132\pi$
$440$	−173.921	−0.0188440
$441$	0	0
$442$	1302.77	0.140196
$443$	5053.36	0.541969	0.270985	−	0.962584i	$-0.412651\pi$
$443$	5053.36	0.541969	0.270985	+	0.962584i	$0.412651\pi$
$444$	−1335.38	−0.142735
$445$	−349.904	−0.0372743
$446$	1549.05	0.164461
$447$	−3482.24	−0.368466
$448$	0	0
$449$	8610.05	0.904974	0.452487	−	0.891771i	$-0.350537\pi$
$449$	8610.05	0.904974	0.452487	+	0.891771i	$0.350537\pi$
$450$	2012.75	0.210849
$451$	1673.67	0.174745
$452$	1374.26	0.143008
$453$	−8721.83	−0.904608
$454$	3216.44	0.332500
$455$	0	0
$456$	11299.9	1.16045
$457$	−11485.1	−1.17560	−0.587802	−	0.809005i	$-0.700007\pi$
$457$	−11485.1	−1.17560	−0.587802	+	0.809005i	$0.700007\pi$
$458$	3432.19	0.350165
$459$	−1509.60	−0.153512
$460$	216.745	0.0219692
$461$	−18160.5	−1.83475	−0.917374	−	0.398026i	$-0.869695\pi$
$461$	−18160.5	−1.83475	−0.917374	+	0.398026i	$0.869695\pi$
$462$	0	0
$463$	−13008.2	−1.30570	−0.652852	−	0.757485i	$-0.726428\pi$
$463$	−13008.2	−1.30570	−0.652852	+	0.757485i	$0.726428\pi$
$464$	−511.225	−0.0511487
$465$	−69.7414	−0.00695523
$466$	8817.08	0.876488
$467$	1946.46	0.192872	0.0964360	−	0.995339i	$-0.469256\pi$
$467$	1946.46	0.192872	0.0964360	+	0.995339i	$0.469256\pi$
$468$	560.127	0.0553245
$469$	0	0
$470$	−291.227	−0.0285815
$471$	2813.27	0.275220
$472$	12950.0	1.26287
$473$	−799.337	−0.0777031
$474$	−2069.44	−0.200533
$475$	20505.1	1.98072
$476$	0	0
$477$	354.632	0.0340409
$478$	−12058.5	−1.15385
$479$	−115.724	−0.0110387	−0.00551936	−	0.999985i	$-0.501757\pi$
$479$	−115.724	−0.0110387	−0.00551936	+	0.999985i	$0.501757\pi$
$480$	−255.027	−0.0242507
$481$	1208.72	0.114580
$482$	6997.16	0.661228
$483$	0	0
$484$	5158.35	0.484443
$485$	−796.778	−0.0745975
$486$	435.546	0.0406518
$487$	13704.8	1.27521	0.637603	−	0.770365i	$-0.279926\pi$
$487$	13704.8	1.27521	0.637603	+	0.770365i	$0.279926\pi$
$488$	−5304.91	−0.492094
$489$	6749.96	0.624220
$490$	0	0
$491$	−11358.3	−1.04397	−0.521987	−	0.852953i	$-0.674809\pi$
$491$	−11358.3	−1.04397	−0.521987	+	0.852953i	$0.674809\pi$
$492$	1509.69	0.138338
$493$	10276.4	0.938794
$494$	−3829.25	−0.348757
$495$	−68.2941	−0.00620120
$496$	135.675	0.0122823
$497$	0	0
$498$	5202.23	0.468108
$499$	2101.11	0.188494	0.0942470	−	0.995549i	$-0.469956\pi$
$499$	2101.11	0.188494	0.0942470	+	0.995549i	$0.469956\pi$
$500$	−569.879	−0.0509715
$501$	6185.08	0.551554
$502$	10793.6	0.959648
$503$	−16067.2	−1.42426	−0.712129	−	0.702048i	$-0.752269\pi$
$503$	−16067.2	−1.42426	−0.712129	+	0.702048i	$0.752269\pi$
$504$	0	0
$505$	557.150	0.0490948
$506$	−2711.10	−0.238188
$507$	−507.000	−0.0444116
$508$	−4312.03	−0.376605
$509$	−20232.3	−1.76185	−0.880923	−	0.473259i	$-0.843078\pi$
$509$	−20232.3	−1.76185	−0.880923	+	0.473259i	$0.843078\pi$
$510$	−143.279	−0.0124402
$511$	0	0
$512$	1006.13	0.0868458
$513$	4437.17	0.381883
$514$	−5520.70	−0.473750
$515$	−101.780	−0.00870863
$516$	−721.020	−0.0615138
$517$	−5428.40	−0.461781
$518$	0	0
$519$	−6412.54	−0.542349
$520$	142.001	0.0119753
$521$	21228.9	1.78514	0.892568	−	0.450913i	$-0.148902\pi$
$521$	21228.9	1.78514	0.892568	+	0.450913i	$0.148902\pi$
$522$	−2964.93	−0.248604
$523$	−21103.9	−1.76445	−0.882225	−	0.470828i	$-0.843955\pi$
$523$	−21103.9	−1.76445	−0.882225	+	0.470828i	$0.843955\pi$
$524$	5528.72	0.460922
$525$	0	0
$526$	9880.00	0.818989
$527$	−2727.28	−0.225431
$528$	132.860	0.0109507
$529$	−3142.44	−0.258276
$530$	33.6589	0.00275858
$531$	5085.14	0.415587
$532$	0	0
$533$	−1366.50	−0.111050
$534$	3947.86	0.319926
$535$	−762.012	−0.0615788
$536$	4647.73	0.374536
$537$	1038.15	0.0834256
$538$	−11982.6	−0.960238
$539$	0	0
$540$	−61.6029	−0.00490919
$541$	21676.9	1.72267	0.861334	−	0.508038i	$-0.169629\pi$
$541$	21676.9	1.72267	0.861334	+	0.508038i	$0.169629\pi$
$542$	15562.1	1.23331
$543$	8381.78	0.662425
$544$	−9972.99	−0.786008
$545$	39.3738	0.00309466
$546$	0	0
$547$	10350.6	0.809071	0.404535	−	0.914522i	$-0.367433\pi$
$547$	10350.6	0.809071	0.404535	+	0.914522i	$0.367433\pi$
$548$	5655.11	0.440829
$549$	−2083.10	−0.161939
$550$	3560.84	0.276063
$551$	−30205.5	−2.33539
$552$	−6531.98	−0.503658
$553$	0	0
$554$	−2428.94	−0.186274
$555$	−132.935	−0.0101672
$556$	−295.236	−0.0225194
$557$	−3513.02	−0.267238	−0.133619	−	0.991033i	$-0.542660\pi$
$557$	−3513.02	−0.267238	−0.133619	+	0.991033i	$0.542660\pi$
$558$	786.871	0.0596969
$559$	652.633	0.0493800
$560$	0	0
$561$	−2670.68	−0.200992
$562$	3520.91	0.264272
$563$	549.870	0.0411621	0.0205811	−	0.999788i	$-0.493448\pi$
$563$	549.870	0.0411621	0.0205811	+	0.999788i	$0.493448\pi$
$564$	−4896.54	−0.365570
$565$	136.806	0.0101867
$566$	9957.70	0.739493
$567$	0	0
$568$	12783.2	0.944315
$569$	−4645.33	−0.342254	−0.171127	−	0.985249i	$-0.554741\pi$
$569$	−4645.33	−0.342254	−0.171127	+	0.985249i	$0.554741\pi$
$570$	421.141	0.0309468
$571$	−19826.7	−1.45310	−0.726550	−	0.687113i	$-0.758878\pi$
$571$	−19826.7	−1.45310	−0.726550	+	0.687113i	$0.758878\pi$
$572$	990.942	0.0724360
$573$	−9445.29	−0.688626
$574$	0	0
$575$	−11853.1	−0.859669
$576$	3077.65	0.222631
$577$	−9651.66	−0.696367	−0.348184	−	0.937426i	$-0.613201\pi$
$577$	−9651.66	−0.696367	−0.348184	+	0.937426i	$0.613201\pi$
$578$	3202.91	0.230490
$579$	15060.5	1.08099
$580$	419.354	0.0300220
$581$	0	0
$582$	8989.79	0.640273
$583$	627.394	0.0445695
$584$	−7287.86	−0.516393
$585$	55.7599	0.00394084
$586$	−469.940	−0.0331281
$587$	15005.0	1.05506	0.527531	−	0.849536i	$-0.323118\pi$
$587$	15005.0	1.05506	0.527531	+	0.849536i	$0.323118\pi$
$588$	0	0
$589$	8016.33	0.560793
$590$	482.642	0.0336780
$591$	−3199.84	−0.222714
$592$	258.613	0.0179542
$593$	18887.7	1.30797	0.653983	−	0.756509i	$-0.273097\pi$
$593$	18887.7	1.30797	0.653983	+	0.756509i	$0.273097\pi$
$594$	770.541	0.0532251
$595$	0	0
$596$	−5556.97	−0.381917
$597$	4529.43	0.310514
$598$	2213.52	0.151367
$599$	−12015.4	−0.819593	−0.409796	−	0.912177i	$-0.634400\pi$
$599$	−12015.4	−0.819593	−0.409796	+	0.912177i	$0.634400\pi$
$600$	8579.30	0.583747
$601$	−23912.8	−1.62300	−0.811501	−	0.584350i	$-0.801349\pi$
$601$	−23912.8	−1.62300	−0.811501	+	0.584350i	$0.801349\pi$
$602$	0	0
$603$	1825.04	0.123253
$604$	−13918.3	−0.937630
$605$	513.507	0.0345075
$606$	−6286.15	−0.421382
$607$	10847.7	0.725361	0.362681	−	0.931914i	$-0.381862\pi$
$607$	10847.7	0.725361	0.362681	+	0.931914i	$0.381862\pi$
$608$	29313.7	1.95531
$609$	0	0
$610$	−197.711	−0.0131231
$611$	4432.11	0.293460
$612$	−2409.02	−0.159116
$613$	1326.01	0.0873690	0.0436845	−	0.999045i	$-0.486090\pi$
$613$	1326.01	0.0873690	0.0436845	+	0.999045i	$0.486090\pi$
$614$	5456.17	0.358621
$615$	150.288	0.00985397
$616$	0	0
$617$	−3292.09	−0.214805	−0.107402	−	0.994216i	$-0.534253\pi$
$617$	−3292.09	−0.214805	−0.107402	+	0.994216i	$0.534253\pi$
$618$	1148.35	0.0747464
$619$	−23494.3	−1.52555	−0.762776	−	0.646662i	$-0.776164\pi$
$619$	−23494.3	−1.52555	−0.762776	+	0.646662i	$0.776164\pi$
$620$	−111.294	−0.00720913
$621$	−2564.94	−0.165745
$622$	−9241.28	−0.595726
$623$	0	0
$624$	−108.476	−0.00695914
$625$	15539.9	0.994552
$626$	13798.9	0.881016
$627$	7849.97	0.499996
$628$	4489.42	0.285267
$629$	−5198.51	−0.329536
$630$	0	0
$631$	−9195.39	−0.580131	−0.290065	−	0.957007i	$-0.593677\pi$
$631$	−9195.39	−0.580131	−0.290065	+	0.957007i	$0.593677\pi$
$632$	−8820.92	−0.555186
$633$	−10309.2	−0.647322
$634$	9549.11	0.598176
$635$	−429.257	−0.0268261
$636$	565.924	0.0352835
$637$	0	0
$638$	−5245.37	−0.325495
$639$	5019.63	0.310757
$640$	−387.966	−0.0239620
$641$	−8930.24	−0.550270	−0.275135	−	0.961406i	$-0.588723\pi$
$641$	−8930.24	−0.550270	−0.275135	+	0.961406i	$0.588723\pi$
$642$	8597.54	0.528532
$643$	−7240.28	−0.444057	−0.222029	−	0.975040i	$-0.571268\pi$
$643$	−7240.28	−0.444057	−0.222029	+	0.975040i	$0.571268\pi$
$644$	0	0
$645$	−71.7767	−0.00438171
$646$	16469.0	1.00304
$647$	17223.3	1.04655	0.523275	−	0.852164i	$-0.324710\pi$
$647$	17223.3	1.04655	0.523275	+	0.852164i	$0.324710\pi$
$648$	1856.50	0.112547
$649$	8996.32	0.544124
$650$	−2907.31	−0.175437
$651$	0	0
$652$	10771.6	0.647007
$653$	−8499.08	−0.509333	−0.254667	−	0.967029i	$-0.581966\pi$
$653$	−8499.08	−0.509333	−0.254667	+	0.967029i	$0.581966\pi$
$654$	−444.242	−0.0265615
$655$	550.377	0.0328321
$656$	−292.371	−0.0174012
$657$	−2861.75	−0.169935
$658$	0	0
$659$	5707.25	0.337364	0.168682	−	0.985671i	$-0.446049\pi$
$659$	5707.25	0.337364	0.168682	+	0.985671i	$0.446049\pi$
$660$	−108.984	−0.00642757
$661$	28413.5	1.67195	0.835973	−	0.548771i	$-0.184904\pi$
$661$	28413.5	1.67195	0.835973	+	0.548771i	$0.184904\pi$
$662$	−18229.3	−1.07025
$663$	2180.53	0.127729
$664$	22174.4	1.29598
$665$	0	0
$666$	1499.86	0.0872651
$667$	17460.5	1.01360
$668$	9870.16	0.571689
$669$	2592.74	0.149837
$670$	173.219	0.00998810
$671$	−3685.29	−0.212026
$672$	0	0
$673$	−10099.0	−0.578437	−0.289218	−	0.957263i	$-0.593395\pi$
$673$	−10099.0	−0.578437	−0.289218	+	0.957263i	$0.593395\pi$
$674$	−11389.9	−0.650924
$675$	3368.87	0.192100
$676$	−809.072	−0.0460328
$677$	7734.77	0.439101	0.219550	−	0.975601i	$-0.429541\pi$
$677$	7734.77	0.439101	0.219550	+	0.975601i	$0.429541\pi$
$678$	−1543.54	−0.0874324
$679$	0	0
$680$	−610.722	−0.0344413
$681$	5383.55	0.302934
$682$	1392.08	0.0781607
$683$	28563.7	1.60023	0.800117	−	0.599844i	$-0.204771\pi$
$683$	28563.7	1.60023	0.800117	+	0.599844i	$0.204771\pi$
$684$	7080.85	0.395823
$685$	562.959	0.0314008
$686$	0	0
$687$	5744.67	0.319029
$688$	139.635	0.00773768
$689$	−512.247	−0.0283237
$690$	−243.444	−0.0134315
$691$	30835.5	1.69759	0.848797	−	0.528719i	$-0.177328\pi$
$691$	30835.5	1.69759	0.848797	+	0.528719i	$0.177328\pi$
$692$	−10233.1	−0.562147
$693$	0	0
$694$	−11709.8	−0.640489
$695$	−29.3903	−0.00160408
$696$	−12637.9	−0.688274
$697$	5877.10	0.319385
$698$	−11000.7	−0.596537
$699$	14757.7	0.798551
$700$	0	0
$701$	−20264.0	−1.09181	−0.545906	−	0.837847i	$-0.683814\pi$
$701$	−20264.0	−1.09181	−0.545906	+	0.837847i	$0.683814\pi$
$702$	−629.122	−0.0338243
$703$	15280.0	0.819768
$704$	5444.80	0.291489
$705$	−487.444	−0.0260400
$706$	13658.7	0.728117
$707$	0	0
$708$	8114.89	0.430757
$709$	−29205.3	−1.54701	−0.773503	−	0.633792i	$-0.781497\pi$
$709$	−29205.3	−1.54701	−0.773503	+	0.633792i	$0.781497\pi$
$710$	476.424	0.0251829
$711$	−3463.75	−0.182701
$712$	16827.6	0.885733
$713$	−4633.89	−0.243395
$714$	0	0
$715$	98.6471	0.00515971
$716$	1656.69	0.0864710
$717$	−20183.0	−1.05125
$718$	15859.8	0.824351
$719$	2357.22	0.122266	0.0611331	−	0.998130i	$-0.480529\pi$
$719$	2357.22	0.122266	0.0611331	+	0.998130i	$0.480529\pi$
$720$	11.9302	0.000617516 0
$721$	0	0
$722$	−36113.6	−1.86151
$723$	11711.6	0.602432
$724$	13375.7	0.686606
$725$	−22933.2	−1.17478
$726$	−5793.74	−0.296179
$727$	11776.0	0.600751	0.300376	−	0.953821i	$-0.402888\pi$
$727$	11776.0	0.600751	0.300376	+	0.953821i	$0.402888\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−271.615	−0.0137711
$731$	−2806.87	−0.142019
$732$	−3324.22	−0.167851
$733$	−16560.6	−0.834486	−0.417243	−	0.908795i	$-0.637004\pi$
$733$	−16560.6	−0.834486	−0.417243	+	0.908795i	$0.637004\pi$
$734$	14968.9	0.752743
$735$	0	0
$736$	−16945.0	−0.848643
$737$	3228.76	0.161374
$738$	−1695.65	−0.0845769
$739$	25371.3	1.26292	0.631460	−	0.775409i	$-0.282456\pi$
$739$	25371.3	1.26292	0.631460	+	0.775409i	$0.282456\pi$
$740$	−212.138	−0.0105383
$741$	−6409.25	−0.317746
$742$	0	0
$743$	−36250.1	−1.78989	−0.894945	−	0.446176i	$-0.852785\pi$
$743$	−36250.1	−1.78989	−0.894945	+	0.446176i	$0.852785\pi$
$744$	3354.01	0.165274
$745$	−553.189	−0.0272044
$746$	−10543.9	−0.517480
$747$	8707.30	0.426484
$748$	−4261.88	−0.208329
$749$	0	0
$750$	640.075	0.0311630
$751$	−10605.7	−0.515323	−0.257661	−	0.966235i	$-0.582952\pi$
$751$	−10605.7	−0.515323	−0.257661	+	0.966235i	$0.582952\pi$
$752$	948.277	0.0459842
$753$	18066.0	0.874317
$754$	4282.67	0.206851
$755$	−1385.55	−0.0667886
$756$	0	0
$757$	−13323.9	−0.639716	−0.319858	−	0.947466i	$-0.603635\pi$
$757$	−13323.9	−0.639716	−0.319858	+	0.947466i	$0.603635\pi$
$758$	−2507.54	−0.120156
$759$	−4537.73	−0.217008
$760$	1795.10	0.0856779
$761$	12992.7	0.618903	0.309451	−	0.950915i	$-0.399855\pi$
$761$	12992.7	0.618903	0.309451	+	0.950915i	$0.399855\pi$
$762$	4843.17	0.230249
$763$	0	0
$764$	−15072.8	−0.713764
$765$	−239.815	−0.0113340
$766$	−994.735	−0.0469207
$767$	−7345.21	−0.345789
$768$	12584.4	0.591275
$769$	−23522.6	−1.10305	−0.551525	−	0.834159i	$-0.685954\pi$
$769$	−23522.6	−1.10305	−0.551525	+	0.834159i	$0.685954\pi$
$770$	0	0
$771$	−9240.33	−0.431624
$772$	24033.6	1.12045
$773$	−286.350	−0.0133238	−0.00666191	−	0.999978i	$-0.502121\pi$
$773$	−286.350	−0.0133238	−0.00666191	+	0.999978i	$0.502121\pi$
$774$	809.834	0.0376084
$775$	6086.30	0.282098
$776$	38318.7	1.77263
$777$	0	0
$778$	23980.5	1.10507
$779$	−17274.6	−0.794516
$780$	88.9819	0.00408470
$781$	8880.42	0.406871
$782$	−9520.01	−0.435339
$783$	−4962.58	−0.226498
$784$	0	0
$785$	446.916	0.0203199
$786$	−6209.73	−0.281799
$787$	−33075.6	−1.49812	−0.749059	−	0.662504i	$-0.769494\pi$
$787$	−33075.6	−1.49812	−0.749059	+	0.662504i	$0.769494\pi$
$788$	−5106.32	−0.230844
$789$	16536.8	0.746165
$790$	−328.752	−0.0148056
$791$	0	0
$792$	3284.41	0.147357
$793$	3008.92	0.134741
$794$	8398.68	0.375388
$795$	56.3370	0.00251329
$796$	7228.08	0.321850
$797$	−6944.23	−0.308629	−0.154315	−	0.988022i	$-0.549317\pi$
$797$	−6944.23	−0.308629	−0.154315	+	0.988022i	$0.549317\pi$
$798$	0	0
$799$	−19061.8	−0.844003
$800$	22256.1	0.983589
$801$	6607.77	0.291478
$802$	15302.5	0.673755
$803$	−5062.84	−0.222495
$804$	2912.41	0.127752
$805$	0	0
$806$	−1136.59	−0.0496708
$807$	−20056.1	−0.874854
$808$	−26794.5	−1.16662
$809$	−19183.7	−0.833698	−0.416849	−	0.908976i	$-0.636866\pi$
$809$	−19183.7	−0.833698	−0.416849	+	0.908976i	$0.636866\pi$
$810$	69.1909	0.00300138
$811$	37892.2	1.64066	0.820329	−	0.571892i	$-0.193790\pi$
$811$	37892.2	1.64066	0.820329	+	0.571892i	$0.193790\pi$
$812$	0	0
$813$	26047.3	1.12364
$814$	2653.47	0.114256
$815$	1072.30	0.0460872
$816$	466.537	0.0200148
$817$	8250.27	0.353293
$818$	−13910.9	−0.594600
$819$	0	0
$820$	239.830	0.0102137
$821$	45862.3	1.94958	0.974789	−	0.223127i	$-0.0716266\pi$
$821$	45862.3	1.94958	0.974789	+	0.223127i	$0.0716266\pi$
$822$	−6351.69	−0.269514
$823$	−12714.7	−0.538526	−0.269263	−	0.963067i	$-0.586780\pi$
$823$	−12714.7	−0.538526	−0.269263	+	0.963067i	$0.586780\pi$
$824$	4894.79	0.206940
$825$	5959.99	0.251516
$826$	0	0
$827$	−4762.04	−0.200233	−0.100116	−	0.994976i	$-0.531921\pi$
$827$	−4762.04	−0.200233	−0.100116	+	0.994976i	$0.531921\pi$
$828$	−4093.14	−0.171795
$829$	−15962.5	−0.668756	−0.334378	−	0.942439i	$-0.608526\pi$
$829$	−15962.5	−0.668756	−0.334378	+	0.942439i	$0.608526\pi$
$830$	826.428	0.0345611
$831$	−4065.47	−0.169711
$832$	−4445.50	−0.185240
$833$	0	0
$834$	331.602	0.0137679
$835$	982.562	0.0407221
$836$	12527.0	0.518248
$837$	1317.03	0.0543887
$838$	25253.7	1.04102
$839$	−16741.7	−0.688902	−0.344451	−	0.938804i	$-0.611935\pi$
$839$	−16741.7	−0.688902	−0.344451	+	0.938804i	$0.611935\pi$
$840$	0	0
$841$	9393.19	0.385140
$842$	−6635.77	−0.271596
$843$	5893.17	0.240773
$844$	−16451.5	−0.670953
$845$	−80.5421	−0.00327897
$846$	5499.68	0.223502
$847$	0	0
$848$	−109.598	−0.00443823
$849$	16666.8	0.673738
$850$	12503.9	0.504564
$851$	−8832.73	−0.355795
$852$	8010.34	0.322101
$853$	11078.3	0.444683	0.222341	−	0.974969i	$-0.428630\pi$
$853$	11078.3	0.444683	0.222341	+	0.974969i	$0.428630\pi$
$854$	0	0
$855$	704.890	0.0281950
$856$	36646.7	1.46327
$857$	44049.5	1.75578	0.877889	−	0.478863i	$-0.158951\pi$
$857$	44049.5	1.75578	0.877889	+	0.478863i	$0.158951\pi$
$858$	−1113.00	−0.0442859
$859$	4157.97	0.165155	0.0825775	−	0.996585i	$-0.473685\pi$
$859$	4157.97	0.165155	0.0825775	+	0.996585i	$0.473685\pi$
$860$	−114.541	−0.00454166
$861$	0	0
$862$	−17433.6	−0.688854
$863$	−5588.02	−0.220415	−0.110208	−	0.993909i	$-0.535152\pi$
$863$	−5588.02	−0.220415	−0.110208	+	0.993909i	$0.535152\pi$
$864$	4816.07	0.189636
$865$	−1018.70	−0.0400425
$866$	15704.8	0.616249
$867$	5360.90	0.209995
$868$	0	0
$869$	−6127.85	−0.239210
$870$	−471.009	−0.0183548
$871$	−2636.18	−0.102553
$872$	−1893.57	−0.0735371
$873$	15046.8	0.583340
$874$	27982.3	1.08297
$875$	0	0
$876$	−4566.79	−0.176139
$877$	−4515.64	−0.173868	−0.0869340	−	0.996214i	$-0.527707\pi$
$877$	−4515.64	−0.173868	−0.0869340	+	0.996214i	$0.527707\pi$
$878$	11376.6	0.437292
$879$	−786.568	−0.0301823
$880$	21.1061	0.000808509 0
$881$	512.431	0.0195962	0.00979808	−	0.999952i	$-0.496881\pi$
$881$	512.431	0.0195962	0.00979808	+	0.999952i	$0.496881\pi$
$882$	0	0
$883$	33455.6	1.27505	0.637526	−	0.770429i	$-0.279958\pi$
$883$	33455.6	1.27505	0.637526	+	0.770429i	$0.279958\pi$
$884$	3479.69	0.132392
$885$	807.827	0.0306834
$886$	−9057.49	−0.343445
$887$	−13956.1	−0.528296	−0.264148	−	0.964482i	$-0.585091\pi$
$887$	−13956.1	−0.528296	−0.264148	+	0.964482i	$0.585091\pi$
$888$	6393.13	0.241598
$889$	0	0
$890$	627.158	0.0236206
$891$	1289.70	0.0484923
$892$	4137.51	0.155307
$893$	56028.6	2.09958
$894$	6241.46	0.233496
$895$	164.921	0.00615944
$896$	0	0
$897$	3704.91	0.137908
$898$	−15432.4	−0.573481
$899$	−8965.55	−0.332612
$900$	5376.05	0.199113
$901$	2203.09	0.0814602
$902$	−2999.84	−0.110736
$903$	0	0
$904$	−6579.28	−0.242062
$905$	1331.53	0.0489078
$906$	15632.7	0.573248
$907$	24752.4	0.906164	0.453082	−	0.891469i	$-0.350324\pi$
$907$	24752.4	0.906164	0.453082	+	0.891469i	$0.350324\pi$
$908$	8591.09	0.313993
$909$	−10521.5	−0.383913
$910$	0	0
$911$	−32581.3	−1.18493	−0.592463	−	0.805598i	$-0.701844\pi$
$911$	−32581.3	−1.18493	−0.592463	+	0.805598i	$0.701844\pi$
$912$	−1371.30	−0.0497897
$913$	15404.4	0.558392
$914$	20585.6	0.744979
$915$	−330.922	−0.0119562
$916$	9167.36	0.330675
$917$	0	0
$918$	2705.75	0.0972801
$919$	2996.63	0.107562	0.0537812	−	0.998553i	$-0.482873\pi$
$919$	2996.63	0.107562	0.0537812	+	0.998553i	$0.482873\pi$
$920$	−1037.67	−0.0371859
$921$	9132.33	0.326732
$922$	32550.3	1.16268
$923$	−7250.58	−0.258565
$924$	0	0
$925$	11601.2	0.412372
$926$	23315.5	0.827423
$927$	1922.06	0.0681000
$928$	−32784.8	−1.15971
$929$	20148.5	0.711572	0.355786	−	0.934567i	$-0.384213\pi$
$929$	20148.5	0.711572	0.355786	+	0.934567i	$0.384213\pi$
$930$	125.002	0.00440752
$931$	0	0
$932$	23550.4	0.827701
$933$	−15467.7	−0.542754
$934$	−3488.77	−0.122223
$935$	−424.265	−0.0148395
$936$	−2681.61	−0.0936445
$937$	13695.6	0.477496	0.238748	−	0.971082i	$-0.423263\pi$
$937$	13695.6	0.477496	0.238748	+	0.971082i	$0.423263\pi$
$938$	0	0
$939$	23096.1	0.802677
$940$	−777.865	−0.0269906
$941$	−6404.32	−0.221865	−0.110932	−	0.993828i	$-0.535384\pi$
$941$	−6404.32	−0.221865	−0.110932	+	0.993828i	$0.535384\pi$
$942$	−5042.42	−0.174406
$943$	9985.72	0.344835
$944$	−1571.55	−0.0541840
$945$	0	0
$946$	1432.71	0.0492403
$947$	−38952.3	−1.33662	−0.668310	−	0.743883i	$-0.732982\pi$
$947$	−38952.3	−1.33662	−0.668310	+	0.743883i	$0.732982\pi$
$948$	−5527.46	−0.189371
$949$	4133.64	0.141395
$950$	−36752.8	−1.25518
$951$	15982.9	0.544987
$952$	0	0
$953$	−25317.6	−0.860563	−0.430282	−	0.902695i	$-0.641586\pi$
$953$	−25317.6	−0.860563	−0.430282	+	0.902695i	$0.641586\pi$
$954$	−635.633	−0.0215717
$955$	−1500.48	−0.0508423
$956$	−32208.1	−1.08963
$957$	−8779.49	−0.296552
$958$	207.420	0.00699522
$959$	0	0
$960$	488.917	0.0164372
$961$	−27411.6	−0.920130
$962$	−2166.47	−0.0726090
$963$	14390.2	0.481535
$964$	18689.4	0.624423
$965$	2392.52	0.0798113
$966$	0	0
$967$	18517.9	0.615817	0.307909	−	0.951416i	$-0.400371\pi$
$967$	18517.9	0.615817	0.307909	+	0.951416i	$0.400371\pi$
$968$	−24695.6	−0.819988
$969$	27565.2	0.913850
$970$	1428.12	0.0472724
$971$	27421.9	0.906295	0.453147	−	0.891436i	$-0.350301\pi$
$971$	27421.9	0.906295	0.453147	+	0.891436i	$0.350301\pi$
$972$	1163.34	0.0383891
$973$	0	0
$974$	−24564.1	−0.808096
$975$	−4866.14	−0.159837
$976$	643.777	0.0211135
$977$	−18325.5	−0.600088	−0.300044	−	0.953925i	$-0.597001\pi$
$977$	−18325.5	−0.600088	−0.300044	+	0.953925i	$0.597001\pi$
$978$	−12098.4	−0.395567
$979$	11690.1	0.381630
$980$	0	0
$981$	−743.556	−0.0241997
$982$	20358.2	0.661565
$983$	24154.6	0.783734	0.391867	−	0.920022i	$-0.371829\pi$
$983$	24154.6	0.783734	0.391867	+	0.920022i	$0.371829\pi$
$984$	−7227.66	−0.234156
$985$	−508.328	−0.0164433
$986$	−18419.1	−0.594912
$987$	0	0
$988$	−10227.9	−0.329345
$989$	−4769.12	−0.153336
$990$	122.408	0.00392969
$991$	−44989.8	−1.44213	−0.721063	−	0.692870i	$-0.756346\pi$
$991$	−44989.8	−1.44213	−0.721063	+	0.692870i	$0.756346\pi$
$992$	8700.85	0.278480
$993$	−30511.5	−0.975080
$994$	0	0
$995$	719.546	0.0229258
$996$	13895.1	0.442052
$997$	−24234.6	−0.769827	−0.384914	−	0.922953i	$-0.625769\pi$
$997$	−24234.6	−0.769827	−0.384914	+	0.922953i	$0.625769\pi$
$998$	−3765.96	−0.119448
$999$	2510.41	0.0795055

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1911.4.a.bb.1.5		13
7.3	odd	6		273.4.i.e.79.9	✓	26
7.5	odd	6		273.4.i.e.235.9	yes	26
7.6	odd	2		1911.4.a.bc.1.5		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.4.i.e.79.9	✓	26	7.3	odd	6
273.4.i.e.235.9	yes	26	7.5	odd	6
1911.4.a.bb.1.5		13	1.1	even	1	trivial
1911.4.a.bc.1.5		13	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)

\(f(q)\)	\(=\)	\(q-1.79237 q^{2} -3.00000 q^{3} -4.78741 q^{4} -0.476581 q^{5} +5.37711 q^{6} +22.9198 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.79237 q^{2} -3.00000 q^{3} -4.78741 q^{4} -0.476581 q^{5} +5.37711 q^{6} +22.9198 q^{8} +9.00000 q^{9} +0.854209 q^{10} +15.9222 q^{11} +14.3622 q^{12} -13.0000 q^{13} +1.42974 q^{15} -2.78143 q^{16} +55.9109 q^{17} -16.1313 q^{18} -164.340 q^{19} +2.28159 q^{20} -28.5386 q^{22} +94.9977 q^{23} -68.7593 q^{24} -124.773 q^{25} +23.3008 q^{26} -27.0000 q^{27} +183.799 q^{29} -2.56263 q^{30} -48.7790 q^{31} -178.373 q^{32} -47.7667 q^{33} -100.213 q^{34} -43.0867 q^{36} -92.9783 q^{37} +294.557 q^{38} +39.0000 q^{39} -10.9231 q^{40} +105.115 q^{41} -50.2025 q^{43} -76.2263 q^{44} -4.28923 q^{45} -170.271 q^{46} -340.932 q^{47} +8.34429 q^{48} +223.639 q^{50} -167.733 q^{51} +62.2363 q^{52} +39.4036 q^{53} +48.3940 q^{54} -7.58824 q^{55} +493.019 q^{57} -329.436 q^{58} +565.016 q^{59} -6.84476 q^{60} -231.456 q^{61} +87.4301 q^{62} +341.961 q^{64} +6.19555 q^{65} +85.6157 q^{66} +202.783 q^{67} -267.669 q^{68} -284.993 q^{69} +557.737 q^{71} +206.278 q^{72} -317.973 q^{73} +166.652 q^{74} +374.319 q^{75} +786.761 q^{76} -69.9024 q^{78} -384.861 q^{79} +1.32558 q^{80} +81.0000 q^{81} -188.406 q^{82} +967.477 q^{83} -26.6461 q^{85} +89.9815 q^{86} -551.398 q^{87} +364.934 q^{88} +734.197 q^{89} +7.68788 q^{90} -454.793 q^{92} +146.337 q^{93} +611.076 q^{94} +78.3211 q^{95} +535.118 q^{96} +1671.86 q^{97} +143.300 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 3 q^{2} - 39 q^{3} + 55 q^{4} - 15 q^{5} - 9 q^{6} - 6 q^{8} + 117 q^{9}+O(q^{10}) \) 13 * q + 3 * q^2 - 39 * q^3 + 55 * q^4 - 15 * q^5 - 9 * q^6 - 6 * q^8 + 117 * q^9	\( 13 q + 3 q^{2} - 39 q^{3} + 55 q^{4} - 15 q^{5} - 9 q^{6} - 6 q^{8} + 117 q^{9} - 11 q^{10} + 57 q^{11} - 165 q^{12} - 169 q^{13} + 45 q^{15} + 311 q^{16} - 162 q^{17} + 27 q^{18} - 138 q^{19} - 12 q^{20} - 194 q^{22} - 54 q^{23} + 18 q^{24} + 558 q^{25} - 39 q^{26} - 351 q^{27} + 303 q^{29} + 33 q^{30} - 549 q^{31} - 171 q^{33} - 25 q^{34} + 495 q^{36} + 476 q^{37} - 444 q^{38} + 507 q^{39} - 1442 q^{40} - 534 q^{41} + 430 q^{43} + 414 q^{44} - 135 q^{45} + 273 q^{46} - 414 q^{47} - 933 q^{48} + 633 q^{50} + 486 q^{51} - 715 q^{52} - 1305 q^{53} - 81 q^{54} + 369 q^{55} + 414 q^{57} - 279 q^{58} - 1959 q^{59} + 36 q^{60} - 1262 q^{61} + 669 q^{62} + 342 q^{64} + 195 q^{65} + 582 q^{66} + 2456 q^{67} - 1620 q^{68} + 162 q^{69} + 198 q^{71} - 54 q^{72} - 1284 q^{73} - 2481 q^{74} - 1674 q^{75} - 748 q^{76} + 117 q^{78} + 1015 q^{79} - 372 q^{80} + 1053 q^{81} - 1604 q^{82} + 69 q^{83} + 2824 q^{85} - 1131 q^{86} - 909 q^{87} + 465 q^{88} - 4974 q^{89} - 99 q^{90} + 4122 q^{92} + 1647 q^{93} - 3316 q^{94} + 1848 q^{95} - 1269 q^{97} + 513 q^{99}+O(q^{100}) \) 13 * q + 3 * q^2 - 39 * q^3 + 55 * q^4 - 15 * q^5 - 9 * q^6 - 6 * q^8 + 117 * q^9 - 11 * q^10 + 57 * q^11 - 165 * q^12 - 169 * q^13 + 45 * q^15 + 311 * q^16 - 162 * q^17 + 27 * q^18 - 138 * q^19 - 12 * q^20 - 194 * q^22 - 54 * q^23 + 18 * q^24 + 558 * q^25 - 39 * q^26 - 351 * q^27 + 303 * q^29 + 33 * q^30 - 549 * q^31 - 171 * q^33 - 25 * q^34 + 495 * q^36 + 476 * q^37 - 444 * q^38 + 507 * q^39 - 1442 * q^40 - 534 * q^41 + 430 * q^43 + 414 * q^44 - 135 * q^45 + 273 * q^46 - 414 * q^47 - 933 * q^48 + 633 * q^50 + 486 * q^51 - 715 * q^52 - 1305 * q^53 - 81 * q^54 + 369 * q^55 + 414 * q^57 - 279 * q^58 - 1959 * q^59 + 36 * q^60 - 1262 * q^61 + 669 * q^62 + 342 * q^64 + 195 * q^65 + 582 * q^66 + 2456 * q^67 - 1620 * q^68 + 162 * q^69 + 198 * q^71 - 54 * q^72 - 1284 * q^73 - 2481 * q^74 - 1674 * q^75 - 748 * q^76 + 117 * q^78 + 1015 * q^79 - 372 * q^80 + 1053 * q^81 - 1604 * q^82 + 69 * q^83 + 2824 * q^85 - 1131 * q^86 - 909 * q^87 + 465 * q^88 - 4974 * q^89 - 99 * q^90 + 4122 * q^92 + 1647 * q^93 - 3316 * q^94 + 1848 * q^95 - 1269 * q^97 + 513 * q^99

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