LMFDB - Embedded newform 1911.4.a.m.1.1

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:	$4$
Coefficient field:	4.4.6295500.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 19x^{2} + 19x + 16 $ x^4 - x^3 - 19x^2 + 19x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-4.27680$ 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)

$f(q)$	$=$	$q-5.27680 q^{2} +3.00000 q^{3} +19.8446 q^{4} +4.51607 q^{5} -15.8304 q^{6} -62.5017 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.27680 q^{2} +3.00000 q^{3} +19.8446 q^{4} +4.51607 q^{5} -15.8304 q^{6} -62.5017 q^{8} +9.00000 q^{9} -23.8304 q^{10} -30.9160 q^{11} +59.5339 q^{12} +13.0000 q^{13} +13.5482 q^{15} +171.052 q^{16} -5.45932 q^{17} -47.4912 q^{18} -126.023 q^{19} +89.6197 q^{20} +163.138 q^{22} +44.0094 q^{23} -187.505 q^{24} -104.605 q^{25} -68.5984 q^{26} +27.0000 q^{27} +268.762 q^{29} -71.4912 q^{30} -72.4285 q^{31} -402.595 q^{32} -92.7480 q^{33} +28.8077 q^{34} +178.602 q^{36} -165.671 q^{37} +664.999 q^{38} +39.0000 q^{39} -282.262 q^{40} +203.539 q^{41} +262.178 q^{43} -613.517 q^{44} +40.6446 q^{45} -232.229 q^{46} +444.827 q^{47} +513.157 q^{48} +551.980 q^{50} -16.3779 q^{51} +257.980 q^{52} -42.5994 q^{53} -142.474 q^{54} -139.619 q^{55} -378.069 q^{57} -1418.21 q^{58} +804.892 q^{59} +268.859 q^{60} +219.059 q^{61} +382.191 q^{62} +755.994 q^{64} +58.7089 q^{65} +489.413 q^{66} -1047.25 q^{67} -108.338 q^{68} +132.028 q^{69} -79.5668 q^{71} -562.516 q^{72} +419.750 q^{73} +874.215 q^{74} -313.815 q^{75} -2500.88 q^{76} -205.795 q^{78} +243.444 q^{79} +772.484 q^{80} +81.0000 q^{81} -1074.04 q^{82} -647.663 q^{83} -24.6547 q^{85} -1383.46 q^{86} +806.287 q^{87} +1932.30 q^{88} -1448.48 q^{89} -214.474 q^{90} +873.350 q^{92} -217.285 q^{93} -2347.27 q^{94} -569.129 q^{95} -1207.78 q^{96} +539.456 q^{97} -278.244 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} + 12 q^{3} + 9 q^{4} + 3 q^{5} - 9 q^{6} - 69 q^{8} + 36 q^{9}+O(q^{10}) $ 4 * q - 3 * q^2 + 12 * q^3 + 9 * q^4 + 3 * q^5 - 9 * q^6 - 69 * q^8 + 36 * q^9	\( 4 q - 3 q^{2} + 12 q^{3} + 9 q^{4} + 3 q^{5} - 9 q^{6} - 69 q^{8} + 36 q^{9} - 41 q^{10} - 9 q^{11} + 27 q^{12} + 52 q^{13} + 9 q^{15} + 161 q^{16} + 75 q^{17} - 27 q^{18} - 87 q^{19} + 123 q^{20} + 33 q^{22} - 105 q^{23} - 207 q^{24} - 309 q^{25} - 39 q^{26} + 108 q^{27} - 219 q^{29} - 123 q^{30} - 62 q^{31} - 585 q^{32} - 27 q^{33} + 305 q^{34} + 81 q^{36} - 551 q^{37} + 759 q^{38} + 156 q^{39} - 23 q^{40} + 198 q^{41} - 71 q^{43} - 789 q^{44} + 27 q^{45} - 425 q^{46} + 912 q^{47} + 483 q^{48} + 228 q^{50} + 225 q^{51} + 117 q^{52} - 18 q^{53} - 81 q^{54} + 477 q^{55} - 261 q^{57} - 1427 q^{58} + 750 q^{59} + 369 q^{60} + 21 q^{61} + 774 q^{62} + 857 q^{64} + 39 q^{65} + 99 q^{66} - 354 q^{67} + 375 q^{68} - 315 q^{69} - 1596 q^{71} - 621 q^{72} - 613 q^{73} + 1797 q^{74} - 927 q^{75} - 3117 q^{76} - 117 q^{78} + 52 q^{79} + 267 q^{80} + 324 q^{81} + 4 q^{82} - 966 q^{83} + 685 q^{85} - 3213 q^{86} - 657 q^{87} + 3429 q^{88} - 870 q^{89} - 369 q^{90} + 435 q^{92} - 186 q^{93} - 3794 q^{94} - 2229 q^{95} - 1755 q^{96} - 506 q^{97} - 81 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 + 12 * q^3 + 9 * q^4 + 3 * q^5 - 9 * q^6 - 69 * q^8 + 36 * q^9 - 41 * q^10 - 9 * q^11 + 27 * q^12 + 52 * q^13 + 9 * q^15 + 161 * q^16 + 75 * q^17 - 27 * q^18 - 87 * q^19 + 123 * q^20 + 33 * q^22 - 105 * q^23 - 207 * q^24 - 309 * q^25 - 39 * q^26 + 108 * q^27 - 219 * q^29 - 123 * q^30 - 62 * q^31 - 585 * q^32 - 27 * q^33 + 305 * q^34 + 81 * q^36 - 551 * q^37 + 759 * q^38 + 156 * q^39 - 23 * q^40 + 198 * q^41 - 71 * q^43 - 789 * q^44 + 27 * q^45 - 425 * q^46 + 912 * q^47 + 483 * q^48 + 228 * q^50 + 225 * q^51 + 117 * q^52 - 18 * q^53 - 81 * q^54 + 477 * q^55 - 261 * q^57 - 1427 * q^58 + 750 * q^59 + 369 * q^60 + 21 * q^61 + 774 * q^62 + 857 * q^64 + 39 * q^65 + 99 * q^66 - 354 * q^67 + 375 * q^68 - 315 * q^69 - 1596 * q^71 - 621 * q^72 - 613 * q^73 + 1797 * q^74 - 927 * q^75 - 3117 * q^76 - 117 * q^78 + 52 * q^79 + 267 * q^80 + 324 * q^81 + 4 * q^82 - 966 * q^83 + 685 * q^85 - 3213 * q^86 - 657 * q^87 + 3429 * q^88 - 870 * q^89 - 369 * q^90 + 435 * q^92 - 186 * q^93 - 3794 * q^94 - 2229 * q^95 - 1755 * q^96 - 506 * q^97 - 81 * 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 $

$2$	−5.27680	−1.86563	−0.932815	−	0.360355i	$-0.882656\pi$
$2$	−5.27680	−1.86563	−0.932815	+	0.360355i	$0.882656\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	19.8446	2.48058
$5$	4.51607	0.403930	0.201965	−	0.979393i	$-0.435267\pi$
$5$	4.51607	0.403930	0.201965	+	0.979393i	$0.435267\pi$
$6$	−15.8304	−1.07712
$7$	0	0
$7$	0	0
$8$	−62.5017	−2.76221
$9$	9.00000	0.333333
$10$	−23.8304	−0.753584
$11$	−30.9160	−0.847411	−0.423706	−	0.905800i	$-0.639271\pi$
$11$	−30.9160	−0.847411	−0.423706	+	0.905800i	$0.639271\pi$
$12$	59.5339	1.43216
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	0	0
$15$	13.5482	0.233209
$16$	171.052	2.67269
$17$	−5.45932	−0.0778870	−0.0389435	−	0.999241i	$-0.512399\pi$
$17$	−5.45932	−0.0778870	−0.0389435	+	0.999241i	$0.512399\pi$
$18$	−47.4912	−0.621877
$19$	−126.023	−1.52167	−0.760834	−	0.648947i	$-0.775210\pi$
$19$	−126.023	−1.52167	−0.760834	+	0.648947i	$0.775210\pi$
$20$	89.6197	1.00198
$21$	0	0
$22$	163.138	1.58096
$23$	44.0094	0.398982	0.199491	−	0.979900i	$-0.436071\pi$
$23$	44.0094	0.398982	0.199491	+	0.979900i	$0.436071\pi$
$24$	−187.505	−1.59476
$25$	−104.605	−0.836841
$26$	−68.5984	−0.517433
$27$	27.0000	0.192450
$28$	0	0
$29$	268.762	1.72096	0.860481	−	0.509482i	$-0.170163\pi$
$29$	268.762	1.72096	0.860481	+	0.509482i	$0.170163\pi$
$30$	−71.4912	−0.435082
$31$	−72.4285	−0.419630	−0.209815	−	0.977741i	$-0.567286\pi$
$31$	−72.4285	−0.419630	−0.209815	+	0.977741i	$0.567286\pi$
$32$	−402.595	−2.22404
$33$	−92.7480	−0.489253
$34$	28.8077	0.145308
$35$	0	0
$36$	178.602	0.826859
$37$	−165.671	−0.736113	−0.368057	−	0.929803i	$-0.619977\pi$
$37$	−165.671	−0.736113	−0.368057	+	0.929803i	$0.619977\pi$
$38$	664.999	2.83887
$39$	39.0000	0.160128
$40$	−282.262	−1.11574
$41$	203.539	0.775304	0.387652	−	0.921806i	$-0.373286\pi$
$41$	203.539	0.775304	0.387652	+	0.921806i	$0.373286\pi$
$42$	0	0
$43$	262.178	0.929810	0.464905	−	0.885361i	$-0.346088\pi$
$43$	262.178	0.929810	0.464905	+	0.885361i	$0.346088\pi$
$44$	−613.517	−2.10207
$45$	40.6446	0.134643
$46$	−232.229	−0.744353
$47$	444.827	1.38053	0.690263	−	0.723558i	$-0.257495\pi$
$47$	444.827	1.38053	0.690263	+	0.723558i	$0.257495\pi$
$48$	513.157	1.54308
$49$	0	0
$50$	551.980	1.56124
$51$	−16.3779	−0.0449681
$52$	257.980	0.687989
$53$	−42.5994	−0.110405	−0.0552027	−	0.998475i	$-0.517580\pi$
$53$	−42.5994	−0.110405	−0.0552027	+	0.998475i	$0.517580\pi$
$54$	−142.474	−0.359041
$55$	−139.619	−0.342295
$56$	0	0
$57$	−378.069	−0.878535
$58$	−1418.21	−3.21068
$59$	804.892	1.77607	0.888034	−	0.459778i	$-0.152071\pi$
$59$	804.892	1.77607	0.888034	+	0.459778i	$0.152071\pi$
$60$	268.859	0.578493
$61$	219.059	0.459797	0.229898	−	0.973215i	$-0.426161\pi$
$61$	219.059	0.459797	0.229898	+	0.973215i	$0.426161\pi$
$62$	382.191	0.782875
$63$	0	0
$64$	755.994	1.47655
$65$	58.7089	0.112030
$66$	489.413	0.912766
$67$	−1047.25	−1.90959	−0.954793	−	0.297272i	$-0.903923\pi$
$67$	−1047.25	−1.90959	−0.954793	+	0.297272i	$0.903923\pi$
$68$	−108.338	−0.193205
$69$	132.028	0.230352
$70$	0	0
$71$	−79.5668	−0.132998	−0.0664989	−	0.997787i	$-0.521183\pi$
$71$	−79.5668	−0.132998	−0.0664989	+	0.997787i	$0.521183\pi$
$72$	−562.516	−0.920738
$73$	419.750	0.672987	0.336494	−	0.941686i	$-0.390759\pi$
$73$	419.750	0.672987	0.336494	+	0.941686i	$0.390759\pi$
$74$	874.215	1.37332
$75$	−313.815	−0.483150
$76$	−2500.88	−3.77462
$77$	0	0
$78$	−205.795	−0.298740
$79$	243.444	0.346703	0.173352	−	0.984860i	$-0.444540\pi$
$79$	243.444	0.346703	0.173352	+	0.984860i	$0.444540\pi$
$80$	772.484	1.07958
$81$	81.0000	0.111111
$82$	−1074.04	−1.44643
$83$	−647.663	−0.856509	−0.428255	−	0.903658i	$-0.640871\pi$
$83$	−647.663	−0.856509	−0.428255	+	0.903658i	$0.640871\pi$
$84$	0	0
$85$	−24.6547	−0.0314609
$86$	−1383.46	−1.73468
$87$	806.287	0.993598
$88$	1932.30	2.34073
$89$	−1448.48	−1.72515	−0.862576	−	0.505927i	$-0.831151\pi$
$89$	−1448.48	−1.72515	−0.862576	+	0.505927i	$0.831151\pi$
$90$	−214.474	−0.251195
$91$	0	0
$92$	873.350	0.989706
$93$	−217.285	−0.242274
$94$	−2347.27	−2.57555
$95$	−569.129	−0.614647
$96$	−1207.78	−1.28405
$97$	539.456	0.564674	0.282337	−	0.959315i	$-0.408890\pi$
$97$	539.456	0.564674	0.282337	+	0.959315i	$0.408890\pi$
$98$	0	0
$99$	−278.244	−0.282470
$100$	−2075.85	−2.07585
$101$	−230.971	−0.227550	−0.113775	−	0.993507i	$-0.536294\pi$
$101$	−230.971	−0.227550	−0.113775	+	0.993507i	$0.536294\pi$
$102$	86.4232	0.0838938
$103$	−173.073	−0.165567	−0.0827833	−	0.996568i	$-0.526381\pi$
$103$	−173.073	−0.165567	−0.0827833	+	0.996568i	$0.526381\pi$
$104$	−812.523	−0.766100
$105$	0	0
$106$	224.789	0.205976
$107$	−2020.31	−1.82533	−0.912666	−	0.408706i	$-0.865980\pi$
$107$	−2020.31	−1.82533	−0.912666	+	0.408706i	$0.865980\pi$
$108$	535.805	0.477388
$109$	−1119.93	−0.984128	−0.492064	−	0.870559i	$-0.663757\pi$
$109$	−1119.93	−0.984128	−0.492064	+	0.870559i	$0.663757\pi$
$110$	736.741	0.638595
$111$	−497.014	−0.424995
$112$	0	0
$113$	−642.814	−0.535140	−0.267570	−	0.963538i	$-0.586221\pi$
$113$	−642.814	−0.535140	−0.267570	+	0.963538i	$0.586221\pi$
$114$	1995.00	1.63902
$115$	198.749	0.161161
$116$	5333.49	4.26898
$117$	117.000	0.0924500
$118$	−4247.25	−3.31349
$119$	0	0
$120$	−846.787	−0.644173
$121$	−375.201	−0.281894
$122$	−1155.93	−0.857811
$123$	610.617	0.447622
$124$	−1437.32	−1.04093
$125$	−1036.91	−0.741954
$126$	0	0
$127$	−1310.73	−0.915816	−0.457908	−	0.889000i	$-0.651401\pi$
$127$	−1310.73	−0.915816	−0.457908	+	0.889000i	$0.651401\pi$
$128$	−768.472	−0.530656
$129$	786.535	0.536826
$130$	−309.795	−0.209006
$131$	1164.14	0.776426	0.388213	−	0.921570i	$-0.373093\pi$
$131$	1164.14	0.776426	0.388213	+	0.921570i	$0.373093\pi$
$132$	−1840.55	−1.21363
$133$	0	0
$134$	5526.14	3.56258
$135$	121.934	0.0777363
$136$	341.217	0.215140
$137$	−138.967	−0.0866622	−0.0433311	−	0.999061i	$-0.513797\pi$
$137$	−138.967	−0.0866622	−0.0433311	+	0.999061i	$0.513797\pi$
$138$	−696.686	−0.429753
$139$	1029.61	0.628273	0.314137	−	0.949378i	$-0.398285\pi$
$139$	1029.61	0.628273	0.314137	+	0.949378i	$0.398285\pi$
$140$	0	0
$141$	1334.48	0.797048
$142$	419.858	0.248125
$143$	−401.908	−0.235030
$144$	1539.47	0.890897
$145$	1213.75	0.695148
$146$	−2214.94	−1.25555
$147$	0	0
$148$	−3287.69	−1.82599
$149$	−2463.30	−1.35437	−0.677186	−	0.735812i	$-0.736801\pi$
$149$	−2463.30	−1.35437	−0.677186	+	0.735812i	$0.736801\pi$
$150$	1655.94	0.901380
$151$	−2436.40	−1.31305	−0.656527	−	0.754303i	$-0.727975\pi$
$151$	−2436.40	−1.31305	−0.656527	+	0.754303i	$0.727975\pi$
$152$	7876.67	4.20317
$153$	−49.1338	−0.0259623
$154$	0	0
$155$	−327.092	−0.169501
$156$	773.940	0.397210
$157$	1693.34	0.860787	0.430393	−	0.902641i	$-0.358375\pi$
$157$	1693.34	0.860787	0.430393	+	0.902641i	$0.358375\pi$
$158$	−1284.60	−0.646820
$159$	−127.798	−0.0637426
$160$	−1818.15	−0.898356
$161$	0	0
$162$	−427.421	−0.207292
$163$	115.624	0.0555607	0.0277804	−	0.999614i	$-0.491156\pi$
$163$	115.624	0.0555607	0.0277804	+	0.999614i	$0.491156\pi$
$164$	4039.16	1.92320
$165$	−418.856	−0.197624
$166$	3417.59	1.59793
$167$	1239.54	0.574364	0.287182	−	0.957876i	$-0.407282\pi$
$167$	1239.54	0.574364	0.287182	+	0.957876i	$0.407282\pi$
$168$	0	0
$169$	169.000	0.0769231
$170$	130.098	0.0586943
$171$	−1134.21	−0.507223
$172$	5202.83	2.30647
$173$	−133.542	−0.0586877	−0.0293439	−	0.999569i	$-0.509342\pi$
$173$	−133.542	−0.0586877	−0.0293439	+	0.999569i	$0.509342\pi$
$174$	−4254.62	−1.85369
$175$	0	0
$176$	−5288.25	−2.26487
$177$	2414.68	1.02541
$178$	7643.34	3.21850
$179$	3489.28	1.45699	0.728494	−	0.685052i	$-0.240221\pi$
$179$	3489.28	1.45699	0.728494	+	0.685052i	$0.240221\pi$
$180$	806.578	0.333993
$181$	−2934.50	−1.20508	−0.602541	−	0.798088i	$-0.705845\pi$
$181$	−2934.50	−1.20508	−0.602541	+	0.798088i	$0.705845\pi$
$182$	0	0
$183$	657.176	0.265464
$184$	−2750.66	−1.10207
$185$	−748.183	−0.297338
$186$	1146.57	0.451993
$187$	168.780	0.0660023
$188$	8827.44	3.42451
$189$	0	0
$190$	3003.18	1.14670
$191$	117.439	0.0444901	0.0222450	−	0.999753i	$-0.492919\pi$
$191$	117.439	0.0444901	0.0222450	+	0.999753i	$0.492919\pi$
$192$	2267.98	0.852487
$193$	−4556.19	−1.69928	−0.849641	−	0.527361i	$-0.823182\pi$
$193$	−4556.19	−1.69928	−0.849641	+	0.527361i	$0.823182\pi$
$194$	−2846.60	−1.05347
$195$	176.127	0.0646805
$196$	0	0
$197$	416.257	0.150544	0.0752718	−	0.997163i	$-0.476018\pi$
$197$	416.257	0.150544	0.0752718	+	0.997163i	$0.476018\pi$
$198$	1468.24	0.526986
$199$	−3481.94	−1.24034	−0.620172	−	0.784466i	$-0.712937\pi$
$199$	−3481.94	−1.24034	−0.620172	+	0.784466i	$0.712937\pi$
$200$	6538.00	2.31153
$201$	−3141.76	−1.10250
$202$	1218.79	0.424524
$203$	0	0
$204$	−325.014	−0.111547
$205$	919.197	0.313168
$206$	913.270	0.308886
$207$	396.084	0.132994
$208$	2223.68	0.741271
$209$	3896.13	1.28948
$210$	0	0
$211$	1259.53	0.410947	0.205473	−	0.978663i	$-0.434127\pi$
$211$	1259.53	0.410947	0.205473	+	0.978663i	$0.434127\pi$
$212$	−845.370	−0.273869
$213$	−238.700	−0.0767863
$214$	10660.8	3.40540
$215$	1184.02	0.375578
$216$	−1687.55	−0.531588
$217$	0	0
$218$	5909.65	1.83602
$219$	1259.25	0.388549
$220$	−2770.68	−0.849088
$221$	−70.9711	−0.0216020
$222$	2622.64	0.792884
$223$	4661.65	1.39985	0.699926	−	0.714216i	$-0.253216\pi$
$223$	4661.65	1.39985	0.699926	+	0.714216i	$0.253216\pi$
$224$	0	0
$225$	−941.446	−0.278947
$226$	3392.00	0.998374
$227$	−1610.47	−0.470884	−0.235442	−	0.971888i	$-0.575654\pi$
$227$	−1610.47	−0.470884	−0.235442	+	0.971888i	$0.575654\pi$
$228$	−7502.65	−2.17928
$229$	−1494.85	−0.431365	−0.215682	−	0.976464i	$-0.569198\pi$
$229$	−1494.85	−0.431365	−0.215682	+	0.976464i	$0.569198\pi$
$230$	−1048.76	−0.300666
$231$	0	0
$232$	−16798.1	−4.75366
$233$	−252.360	−0.0709555	−0.0354778	−	0.999370i	$-0.511295\pi$
$233$	−252.360	−0.0709555	−0.0354778	+	0.999370i	$0.511295\pi$
$234$	−617.386	−0.172478
$235$	2008.87	0.557636
$236$	15972.8	4.40568
$237$	730.331	0.200169
$238$	0	0
$239$	2820.94	0.763478	0.381739	−	0.924270i	$-0.375325\pi$
$239$	2820.94	0.763478	0.381739	+	0.924270i	$0.375325\pi$
$240$	2317.45	0.623295
$241$	2508.81	0.670567	0.335283	−	0.942117i	$-0.391168\pi$
$241$	2508.81	0.670567	0.335283	+	0.942117i	$0.391168\pi$
$242$	1979.86	0.525910
$243$	243.000	0.0641500
$244$	4347.14	1.14056
$245$	0	0
$246$	−3222.11	−0.835098
$247$	−1638.30	−0.422035
$248$	4526.90	1.15911
$249$	−1942.99	−0.494506
$250$	5471.58	1.38421
$251$	−282.809	−0.0711184	−0.0355592	−	0.999368i	$-0.511321\pi$
$251$	−282.809	−0.0711184	−0.0355592	+	0.999368i	$0.511321\pi$
$252$	0	0
$253$	−1360.59	−0.338102
$254$	6916.47	1.70857
$255$	−73.9640	−0.0181639
$256$	−1992.88	−0.486542
$257$	−4758.14	−1.15488	−0.577441	−	0.816433i	$-0.695949\pi$
$257$	−4758.14	−1.15488	−0.577441	+	0.816433i	$0.695949\pi$
$258$	−4150.39	−1.00152
$259$	0	0
$260$	1165.06	0.277899
$261$	2418.86	0.573654
$262$	−6142.96	−1.44852
$263$	−7886.31	−1.84901	−0.924507	−	0.381166i	$-0.875523\pi$
$263$	−7886.31	−1.84901	−0.924507	+	0.381166i	$0.875523\pi$
$264$	5796.91	1.35142
$265$	−192.382	−0.0445960
$266$	0	0
$267$	−4345.44	−0.996018
$268$	−20782.3	−4.73688
$269$	−5009.06	−1.13534	−0.567672	−	0.823255i	$-0.692156\pi$
$269$	−5009.06	−1.13534	−0.567672	+	0.823255i	$0.692156\pi$
$270$	−643.421	−0.145027
$271$	−587.910	−0.131782	−0.0658912	−	0.997827i	$-0.520989\pi$
$271$	−587.910	−0.131782	−0.0658912	+	0.997827i	$0.520989\pi$
$272$	−933.828	−0.208168
$273$	0	0
$274$	733.299	0.161680
$275$	3233.97	0.709148
$276$	2620.05	0.571407
$277$	6183.97	1.34137	0.670684	−	0.741743i	$-0.266001\pi$
$277$	6183.97	1.34137	0.670684	+	0.741743i	$0.266001\pi$
$278$	−5433.02	−1.17213
$279$	−651.856	−0.139877
$280$	0	0
$281$	4330.38	0.919320	0.459660	−	0.888095i	$-0.347971\pi$
$281$	4330.38	0.919320	0.459660	+	0.888095i	$0.347971\pi$
$282$	−7041.80	−1.48700
$283$	5330.60	1.11969	0.559843	−	0.828599i	$-0.310861\pi$
$283$	5330.60	1.11969	0.559843	+	0.828599i	$0.310861\pi$
$284$	−1578.97	−0.329911
$285$	−1707.39	−0.354866
$286$	2120.79	0.438479
$287$	0	0
$288$	−3623.35	−0.741347
$289$	−4883.20	−0.993934
$290$	−6404.71	−1.29689
$291$	1618.37	0.326015
$292$	8329.79	1.66940
$293$	−8759.64	−1.74656	−0.873282	−	0.487214i	$-0.838013\pi$
$293$	−8759.64	−1.74656	−0.873282	+	0.487214i	$0.838013\pi$
$294$	0	0
$295$	3634.95	0.717406
$296$	10354.7	2.03330
$297$	−834.732	−0.163084
$298$	12998.4	2.52676
$299$	572.122	0.110658
$300$	−6227.55	−1.19849
$301$	0	0
$302$	12856.4	2.44967
$303$	−692.914	−0.131376
$304$	−21556.5	−4.06695
$305$	989.285	0.185726
$306$	259.270	0.0484361
$307$	2796.58	0.519899	0.259950	−	0.965622i	$-0.416294\pi$
$307$	2796.58	0.519899	0.259950	+	0.965622i	$0.416294\pi$
$308$	0	0
$309$	−519.218	−0.0955899
$310$	1726.00	0.316226
$311$	6969.77	1.27080	0.635401	−	0.772182i	$-0.280835\pi$
$311$	6969.77	1.27080	0.635401	+	0.772182i	$0.280835\pi$
$312$	−2437.57	−0.442308
$313$	−10337.4	−1.86678	−0.933391	−	0.358861i	$-0.883165\pi$
$313$	−10337.4	−1.86678	−0.933391	+	0.358861i	$0.883165\pi$
$314$	−8935.44	−1.60591
$315$	0	0
$316$	4831.05	0.860025
$317$	143.850	0.0254872	0.0127436	−	0.999919i	$-0.495943\pi$
$317$	143.850	0.0254872	0.0127436	+	0.999919i	$0.495943\pi$
$318$	674.366	0.118920
$319$	−8309.06	−1.45836
$320$	3414.12	0.596422
$321$	−6060.92	−1.05386
$322$	0	0
$323$	688.000	0.118518
$324$	1607.41	0.275620
$325$	−1359.87	−0.232098
$326$	−610.127	−0.103656
$327$	−3359.79	−0.568186
$328$	−12721.6	−2.14156
$329$	0	0
$330$	2210.22	0.368693
$331$	−10524.5	−1.74767	−0.873835	−	0.486223i	$-0.838374\pi$
$331$	−10524.5	−1.74767	−0.873835	+	0.486223i	$0.838374\pi$
$332$	−12852.6	−2.12464
$333$	−1491.04	−0.245371
$334$	−6540.83	−1.07155
$335$	−4729.47	−0.771338
$336$	0	0
$337$	−9670.69	−1.56319	−0.781596	−	0.623784i	$-0.785594\pi$
$337$	−9670.69	−1.56319	−0.781596	+	0.623784i	$0.785594\pi$
$338$	−891.779	−0.143510
$339$	−1928.44	−0.308963
$340$	−489.262	−0.0780411
$341$	2239.20	0.355599
$342$	5984.99	0.946290
$343$	0	0
$344$	−16386.6	−2.56833
$345$	596.248	0.0930462
$346$	704.672	0.109490
$347$	7331.76	1.13426	0.567132	−	0.823627i	$-0.308053\pi$
$347$	7331.76	1.13426	0.567132	+	0.823627i	$0.308053\pi$
$348$	16000.5	2.46470
$349$	−10977.5	−1.68370	−0.841851	−	0.539710i	$-0.818534\pi$
$349$	−10977.5	−1.68370	−0.841851	+	0.539710i	$0.818534\pi$
$350$	0	0
$351$	351.000	0.0533761
$352$	12446.6	1.88468
$353$	3979.94	0.600087	0.300044	−	0.953925i	$-0.402999\pi$
$353$	3979.94	0.600087	0.300044	+	0.953925i	$0.402999\pi$
$354$	−12741.8	−1.91304
$355$	−359.329	−0.0537217
$356$	−28744.6	−4.27938
$357$	0	0
$358$	−18412.2	−2.71820
$359$	−10325.0	−1.51792	−0.758962	−	0.651135i	$-0.774293\pi$
$359$	−10325.0	−1.51792	−0.758962	+	0.651135i	$0.774293\pi$
$360$	−2540.36	−0.371913
$361$	9022.83	1.31547
$362$	15484.8	2.24824
$363$	−1125.60	−0.162752
$364$	0	0
$365$	1895.62	0.271840
$366$	−3467.79	−0.495257
$367$	−463.366	−0.0659060	−0.0329530	−	0.999457i	$-0.510491\pi$
$367$	−463.366	−0.0659060	−0.0329530	+	0.999457i	$0.510491\pi$
$368$	7527.90	1.06636
$369$	1831.85	0.258435
$370$	3948.01	0.554723
$371$	0	0
$372$	−4311.95	−0.600979
$373$	1679.91	0.233197	0.116598	−	0.993179i	$-0.462801\pi$
$373$	1679.91	0.233197	0.116598	+	0.993179i	$0.462801\pi$
$374$	−890.620	−0.123136
$375$	−3110.74	−0.428368
$376$	−27802.5	−3.81331
$377$	3493.91	0.477309
$378$	0	0
$379$	7031.37	0.952975	0.476487	−	0.879181i	$-0.341910\pi$
$379$	7031.37	0.952975	0.476487	+	0.879181i	$0.341910\pi$
$380$	−11294.2	−1.52468
$381$	−3932.19	−0.528747
$382$	−619.703	−0.0830021
$383$	10980.7	1.46497	0.732487	−	0.680781i	$-0.238359\pi$
$383$	10980.7	1.46497	0.732487	+	0.680781i	$0.238359\pi$
$384$	−2305.42	−0.306374
$385$	0	0
$386$	24042.1	3.17023
$387$	2359.61	0.309937
$388$	10705.3	1.40072
$389$	−13821.3	−1.80146	−0.900732	−	0.434376i	$-0.856969\pi$
$389$	−13821.3	−1.80146	−0.900732	+	0.434376i	$0.856969\pi$
$390$	−929.386	−0.120670
$391$	−240.261	−0.0310755
$392$	0	0
$393$	3492.43	0.448269
$394$	−2196.50	−0.280859
$395$	1099.41	0.140044
$396$	−5521.65	−0.700690
$397$	−12515.4	−1.58220	−0.791098	−	0.611689i	$-0.790490\pi$
$397$	−12515.4	−1.58220	−0.791098	+	0.611689i	$0.790490\pi$
$398$	18373.5	2.31402
$399$	0	0
$400$	−17892.9	−2.23662
$401$	13541.1	1.68631	0.843157	−	0.537667i	$-0.180694\pi$
$401$	13541.1	1.68631	0.843157	+	0.537667i	$0.180694\pi$
$402$	16578.4	2.05686
$403$	−941.570	−0.116384
$404$	−4583.54	−0.564455
$405$	365.802	0.0448811
$406$	0	0
$407$	5121.89	0.623791
$408$	1023.65	0.124211
$409$	−11056.4	−1.33668	−0.668341	−	0.743855i	$-0.732995\pi$
$409$	−11056.4	−1.33668	−0.668341	+	0.743855i	$0.732995\pi$
$410$	−4850.42	−0.584256
$411$	−416.900	−0.0500345
$412$	−3434.56	−0.410701
$413$	0	0
$414$	−2090.06	−0.248118
$415$	−2924.89	−0.345969
$416$	−5233.73	−0.616838
$417$	3088.82	0.362734
$418$	−20559.1	−2.40569
$419$	3214.06	0.374743	0.187371	−	0.982289i	$-0.440003\pi$
$419$	3214.06	0.374743	0.187371	+	0.982289i	$0.440003\pi$
$420$	0	0
$421$	−6544.67	−0.757643	−0.378822	−	0.925470i	$-0.623671\pi$
$421$	−6544.67	−0.757643	−0.378822	+	0.925470i	$0.623671\pi$
$422$	−6646.30	−0.766675
$423$	4003.45	0.460176
$424$	2662.54	0.304963
$425$	571.072	0.0651790
$426$	1259.57	0.143255
$427$	0	0
$428$	−40092.3	−4.52788
$429$	−1205.72	−0.135694
$430$	−6247.82	−0.700690
$431$	−10718.6	−1.19791	−0.598954	−	0.800783i	$-0.704417\pi$
$431$	−10718.6	−1.19791	−0.598954	+	0.800783i	$0.704417\pi$
$432$	4618.41	0.514360
$433$	17069.7	1.89450	0.947251	−	0.320492i	$-0.103848\pi$
$433$	17069.7	1.89450	0.947251	+	0.320492i	$0.103848\pi$
$434$	0	0
$435$	3641.25	0.401344
$436$	−22224.6	−2.44121
$437$	−5546.20	−0.607118
$438$	−6644.82	−0.724890
$439$	−4109.35	−0.446763	−0.223381	−	0.974731i	$-0.571710\pi$
$439$	−4109.35	−0.446763	−0.223381	+	0.974731i	$0.571710\pi$
$440$	8726.42	0.945490
$441$	0	0
$442$	374.500	0.0403013
$443$	−1362.68	−0.146146	−0.0730731	−	0.997327i	$-0.523281\pi$
$443$	−1362.68	−0.146146	−0.0730731	+	0.997327i	$0.523281\pi$
$444$	−9863.06	−1.05423
$445$	−6541.44	−0.696840
$446$	−24598.6	−2.61161
$447$	−7389.91	−0.781948
$448$	0	0
$449$	−15065.9	−1.58353	−0.791766	−	0.610825i	$-0.790838\pi$
$449$	−15065.9	−1.58353	−0.791766	+	0.610825i	$0.790838\pi$
$450$	4967.82	0.520412
$451$	−6292.62	−0.657002
$452$	−12756.4	−1.32746
$453$	−7309.19	−0.758092
$454$	8498.14	0.878496
$455$	0	0
$456$	23630.0	2.42670
$457$	9860.45	1.00930	0.504652	−	0.863323i	$-0.331621\pi$
$457$	9860.45	1.00930	0.504652	+	0.863323i	$0.331621\pi$
$458$	7888.03	0.804767
$459$	−147.402	−0.0149894
$460$	3944.11	0.399772
$461$	7482.09	0.755913	0.377956	−	0.925823i	$-0.376627\pi$
$461$	7482.09	0.755913	0.377956	+	0.925823i	$0.376627\pi$
$462$	0	0
$463$	11369.7	1.14124	0.570619	−	0.821215i	$-0.306703\pi$
$463$	11369.7	1.14124	0.570619	+	0.821215i	$0.306703\pi$
$464$	45972.4	4.59960
$465$	−981.276	−0.0978615
$466$	1331.65	0.132377
$467$	−14016.1	−1.38884	−0.694420	−	0.719570i	$-0.744339\pi$
$467$	−14016.1	−1.38884	−0.694420	+	0.719570i	$0.744339\pi$
$468$	2321.82	0.229330
$469$	0	0
$470$	−10600.4	−1.04034
$471$	5080.03	0.496975
$472$	−50307.1	−4.90588
$473$	−8105.51	−0.787932
$474$	−3853.81	−0.373442
$475$	13182.7	1.27339
$476$	0	0
$477$	−383.395	−0.0368018
$478$	−14885.5	−1.42437
$479$	17166.5	1.63749	0.818744	−	0.574158i	$-0.194671\pi$
$479$	17166.5	1.63749	0.818744	+	0.574158i	$0.194671\pi$
$480$	−5454.44	−0.518666
$481$	−2153.73	−0.204161
$482$	−13238.5	−1.25103
$483$	0	0
$484$	−7445.72	−0.699260
$485$	2436.22	0.228089
$486$	−1282.26	−0.119680
$487$	−7984.56	−0.742946	−0.371473	−	0.928444i	$-0.621147\pi$
$487$	−7984.56	−0.742946	−0.371473	+	0.928444i	$0.621147\pi$
$488$	−13691.6	−1.27006
$489$	346.873	0.0320780
$490$	0	0
$491$	−8549.58	−0.785819	−0.392910	−	0.919577i	$-0.628531\pi$
$491$	−8549.58	−0.785819	−0.392910	+	0.919577i	$0.628531\pi$
$492$	12117.5	1.11036
$493$	−1467.26	−0.134041
$494$	8644.99	0.787361
$495$	−1256.57	−0.114098
$496$	−12389.0	−1.12154
$497$	0	0
$498$	10252.8	0.922565
$499$	−3628.98	−0.325562	−0.162781	−	0.986662i	$-0.552046\pi$
$499$	−3628.98	−0.325562	−0.162781	+	0.986662i	$0.552046\pi$
$500$	−20577.1	−1.84048
$501$	3718.63	0.331609
$502$	1492.33	0.132681
$503$	−4874.86	−0.432126	−0.216063	−	0.976379i	$-0.569322\pi$
$503$	−4874.86	−0.432126	−0.216063	+	0.976379i	$0.569322\pi$
$504$	0	0
$505$	−1043.08	−0.0919140
$506$	7179.58	0.630774
$507$	507.000	0.0444116
$508$	−26011.0	−2.27175
$509$	−19339.4	−1.68409	−0.842047	−	0.539404i	$-0.818650\pi$
$509$	−19339.4	−1.68409	−0.842047	+	0.539404i	$0.818650\pi$
$510$	390.293	0.0338872
$511$	0	0
$512$	16663.8	1.43836
$513$	−3402.62	−0.292845
$514$	25107.7	2.15458
$515$	−781.608	−0.0668772
$516$	15608.5	1.33164
$517$	−13752.3	−1.16987
$518$	0	0
$519$	−400.625	−0.0338834
$520$	−3669.41	−0.309450
$521$	12406.1	1.04323	0.521613	−	0.853182i	$-0.325331\pi$
$521$	12406.1	1.04323	0.521613	+	0.853182i	$0.325331\pi$
$522$	−12763.8	−1.07023
$523$	−3551.28	−0.296915	−0.148458	−	0.988919i	$-0.547431\pi$
$523$	−3551.28	−0.296915	−0.148458	+	0.988919i	$0.547431\pi$
$524$	23102.0	1.92598
$525$	0	0
$526$	41614.5	3.44958
$527$	395.410	0.0326837
$528$	−15864.8	−1.30762
$529$	−10230.2	−0.840813
$530$	1015.16	0.0831996
$531$	7244.03	0.592023
$532$	0	0
$533$	2646.01	0.215031
$534$	22930.0	1.85820
$535$	−9123.85	−0.737306
$536$	65455.1	5.27468
$537$	10467.8	0.841192
$538$	26431.8	2.11813
$539$	0	0
$540$	2419.73	0.192831
$541$	−4428.17	−0.351907	−0.175954	−	0.984398i	$-0.556301\pi$
$541$	−4428.17	−0.351907	−0.175954	+	0.984398i	$0.556301\pi$
$542$	3102.29	0.245857
$543$	−8803.51	−0.695755
$544$	2197.89	0.173224
$545$	−5057.69	−0.397518
$546$	0	0
$547$	−8117.69	−0.634529	−0.317265	−	0.948337i	$-0.602764\pi$
$547$	−8117.69	−0.634529	−0.317265	+	0.948337i	$0.602764\pi$
$548$	−2757.74	−0.214972
$549$	1971.53	0.153266
$550$	−17065.0	−1.32301
$551$	−33870.3	−2.61873
$552$	−8251.99	−0.636282
$553$	0	0
$554$	−32631.6	−2.50250
$555$	−2244.55	−0.171668
$556$	20432.1	1.55848
$557$	20990.3	1.59675	0.798373	−	0.602163i	$-0.205694\pi$
$557$	20990.3	1.59675	0.798373	+	0.602163i	$0.205694\pi$
$558$	3439.72	0.260958
$559$	3408.32	0.257883
$560$	0	0
$561$	506.341	0.0381065
$562$	−22850.6	−1.71511
$563$	22820.9	1.70832	0.854160	−	0.520009i	$-0.174072\pi$
$563$	22820.9	1.70832	0.854160	+	0.520009i	$0.174072\pi$
$564$	26482.3	1.97714
$565$	−2902.99	−0.216159
$566$	−28128.5	−2.08892
$567$	0	0
$568$	4973.06	0.367368
$569$	−1403.05	−0.103373	−0.0516863	−	0.998663i	$-0.516460\pi$
$569$	−1403.05	−0.103373	−0.0516863	+	0.998663i	$0.516460\pi$
$570$	9009.55	0.662050
$571$	−18632.3	−1.36557	−0.682783	−	0.730621i	$-0.739231\pi$
$571$	−18632.3	−1.36557	−0.682783	+	0.730621i	$0.739231\pi$
$572$	−7975.72	−0.583009
$573$	352.318	0.0256864
$574$	0	0
$575$	−4603.61	−0.333885
$576$	6803.95	0.492184
$577$	−24152.5	−1.74261	−0.871303	−	0.490745i	$-0.836725\pi$
$577$	−24152.5	−1.74261	−0.871303	+	0.490745i	$0.836725\pi$
$578$	25767.7	1.85431
$579$	−13668.6	−0.981081
$580$	24086.4	1.72437
$581$	0	0
$582$	−8539.80	−0.608223
$583$	1317.00	0.0935587
$584$	−26235.1	−1.85893
$585$	528.380	0.0373433
$586$	46222.9	3.25845
$587$	5810.55	0.408564	0.204282	−	0.978912i	$-0.434514\pi$
$587$	5810.55	0.408564	0.204282	+	0.978912i	$0.434514\pi$
$588$	0	0
$589$	9127.66	0.638538
$590$	−19180.9	−1.33842
$591$	1248.77	0.0869164
$592$	−28338.4	−1.96740
$593$	4639.03	0.321251	0.160626	−	0.987015i	$-0.448649\pi$
$593$	4639.03	0.321251	0.160626	+	0.987015i	$0.448649\pi$
$594$	4404.71	0.304255
$595$	0	0
$596$	−48883.3	−3.35963
$597$	−10445.8	−0.716112
$598$	−3018.97	−0.206446
$599$	−29078.4	−1.98349	−0.991746	−	0.128216i	$-0.959075\pi$
$599$	−29078.4	−1.98349	−0.991746	+	0.128216i	$0.959075\pi$
$600$	19614.0	1.33456
$601$	17055.1	1.15756	0.578778	−	0.815485i	$-0.303530\pi$
$601$	17055.1	1.15756	0.578778	+	0.815485i	$0.303530\pi$
$602$	0	0
$603$	−9425.27	−0.636529
$604$	−48349.4	−3.25713
$605$	−1694.43	−0.113865
$606$	3656.37	0.245099
$607$	16523.3	1.10487	0.552437	−	0.833555i	$-0.313698\pi$
$607$	16523.3	1.10487	0.552437	+	0.833555i	$0.313698\pi$
$608$	50736.2	3.38425
$609$	0	0
$610$	−5220.26	−0.346495
$611$	5782.76	0.382889
$612$	−975.043	−0.0644016
$613$	25900.9	1.70657	0.853287	−	0.521442i	$-0.174606\pi$
$613$	25900.9	1.70657	0.853287	+	0.521442i	$0.174606\pi$
$614$	−14757.0	−0.969940
$615$	2757.59	0.180808
$616$	0	0
$617$	−20790.2	−1.35653	−0.678267	−	0.734815i	$-0.737269\pi$
$617$	−20790.2	−1.35653	−0.678267	+	0.734815i	$0.737269\pi$
$618$	2739.81	0.178335
$619$	−10756.7	−0.698464	−0.349232	−	0.937036i	$-0.613557\pi$
$619$	−10756.7	−0.698464	−0.349232	+	0.937036i	$0.613557\pi$
$620$	−6491.02	−0.420461
$621$	1188.25	0.0767841
$622$	−36778.1	−2.37085
$623$	0	0
$624$	6671.04	0.427973
$625$	8392.87	0.537144
$626$	54548.3	3.48273
$627$	11688.4	0.744481
$628$	33603.8	2.13525
$629$	904.452	0.0573336
$630$	0	0
$631$	13220.5	0.834071	0.417036	−	0.908890i	$-0.363069\pi$
$631$	13220.5	0.834071	0.417036	+	0.908890i	$0.363069\pi$
$632$	−15215.7	−0.957668
$633$	3778.59	0.237260
$634$	−759.070	−0.0475497
$635$	−5919.36	−0.369925
$636$	−2536.11	−0.158118
$637$	0	0
$638$	43845.2	2.72077
$639$	−716.101	−0.0443326
$640$	−3470.47	−0.214348
$641$	−17724.1	−1.09213	−0.546067	−	0.837741i	$-0.683876\pi$
$641$	−17724.1	−1.09213	−0.546067	+	0.837741i	$0.683876\pi$
$642$	31982.3	1.96611
$643$	−21797.5	−1.33687	−0.668437	−	0.743769i	$-0.733036\pi$
$643$	−21797.5	−1.33687	−0.668437	+	0.743769i	$0.733036\pi$
$644$	0	0
$645$	3552.05	0.216840
$646$	−3630.44	−0.221111
$647$	−18551.8	−1.12728	−0.563638	−	0.826022i	$-0.690599\pi$
$647$	−18551.8	−1.12728	−0.563638	+	0.826022i	$0.690599\pi$
$648$	−5062.64	−0.306913
$649$	−24884.0	−1.50506
$650$	7175.74	0.433009
$651$	0	0
$652$	2294.52	0.137823
$653$	−1046.23	−0.0626985	−0.0313493	−	0.999508i	$-0.509980\pi$
$653$	−1046.23	−0.0626985	−0.0313493	+	0.999508i	$0.509980\pi$
$654$	17729.0	1.06003
$655$	5257.36	0.313621
$656$	34815.8	2.07215
$657$	3777.75	0.224329
$658$	0	0
$659$	−3057.41	−0.180728	−0.0903639	−	0.995909i	$-0.528803\pi$
$659$	−3057.41	−0.180728	−0.0903639	+	0.995909i	$0.528803\pi$
$660$	−8312.05	−0.490221
$661$	−1776.79	−0.104552	−0.0522761	−	0.998633i	$-0.516648\pi$
$661$	−1776.79	−0.104552	−0.0522761	+	0.998633i	$0.516648\pi$
$662$	55535.7	3.26051
$663$	−212.913	−0.0124719
$664$	40480.1	2.36586
$665$	0	0
$666$	7867.93	0.457772
$667$	11828.1	0.686633
$668$	24598.3	1.42476
$669$	13984.9	0.808205
$670$	24956.4	1.43903
$671$	−6772.42	−0.389637
$672$	0	0
$673$	30516.7	1.74789	0.873946	−	0.486024i	$-0.161553\pi$
$673$	30516.7	1.74789	0.873946	+	0.486024i	$0.161553\pi$
$674$	51030.3	2.91634
$675$	−2824.34	−0.161050
$676$	3353.74	0.190814
$677$	15339.2	0.870802	0.435401	−	0.900236i	$-0.356607\pi$
$677$	15339.2	0.870802	0.435401	+	0.900236i	$0.356607\pi$
$678$	10176.0	0.576411
$679$	0	0
$680$	1540.96	0.0869016
$681$	−4831.41	−0.271865
$682$	−11815.8	−0.663417
$683$	9804.71	0.549293	0.274646	−	0.961545i	$-0.411439\pi$
$683$	9804.71	0.549293	0.274646	+	0.961545i	$0.411439\pi$
$684$	−22507.9	−1.25821
$685$	−627.583	−0.0350054
$686$	0	0
$687$	−4484.55	−0.249048
$688$	44846.2	2.48510
$689$	−553.793	−0.0306209
$690$	−3146.28	−0.173590
$691$	−4069.26	−0.224026	−0.112013	−	0.993707i	$-0.535730\pi$
$691$	−4069.26	−0.224026	−0.112013	+	0.993707i	$0.535730\pi$
$692$	−2650.08	−0.145580
$693$	0	0
$694$	−38688.2	−2.11612
$695$	4649.77	0.253778
$696$	−50394.3	−2.74453
$697$	−1111.18	−0.0603861
$698$	57926.1	3.14117
$699$	−757.079	−0.0409662
$700$	0	0
$701$	−2751.08	−0.148227	−0.0741133	−	0.997250i	$-0.523613\pi$
$701$	−2751.08	−0.148227	−0.0741133	+	0.997250i	$0.523613\pi$
$702$	−1852.16	−0.0995800
$703$	20878.4	1.12012
$704$	−23372.3	−1.25125
$705$	6026.62	0.321951
$706$	−21001.4	−1.11954
$707$	0	0
$708$	47918.3	2.54362
$709$	−31603.4	−1.67403	−0.837017	−	0.547177i	$-0.815703\pi$
$709$	−31603.4	−1.67403	−0.837017	+	0.547177i	$0.815703\pi$
$710$	1896.11	0.100225
$711$	2190.99	0.115568
$712$	90532.5	4.76524
$713$	−3187.53	−0.167425
$714$	0	0
$715$	−1815.04	−0.0949354
$716$	69243.4	3.61417
$717$	8462.81	0.440794
$718$	54483.1	2.83188
$719$	6936.96	0.359812	0.179906	−	0.983684i	$-0.442421\pi$
$719$	6936.96	0.359812	0.179906	+	0.983684i	$0.442421\pi$
$720$	6952.35	0.359860
$721$	0	0
$722$	−47611.7	−2.45419
$723$	7526.43	0.387152
$724$	−58234.1	−2.98930
$725$	−28113.9	−1.44017
$726$	5939.58	0.303634
$727$	−5739.59	−0.292805	−0.146403	−	0.989225i	$-0.546770\pi$
$727$	−5739.59	−0.292805	−0.146403	+	0.989225i	$0.546770\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−10002.8	−0.507152
$731$	−1431.31	−0.0724201
$732$	13041.4	0.658504
$733$	−2911.62	−0.146716	−0.0733582	−	0.997306i	$-0.523372\pi$
$733$	−2911.62	−0.146716	−0.0733582	+	0.997306i	$0.523372\pi$
$734$	2445.09	0.122956
$735$	0	0
$736$	−17717.9	−0.887353
$737$	32376.9	1.61820
$738$	−9666.32	−0.482144
$739$	3791.79	0.188746	0.0943730	−	0.995537i	$-0.469915\pi$
$739$	3791.79	0.188746	0.0943730	+	0.995537i	$0.469915\pi$
$740$	−14847.4	−0.737570
$741$	−4914.90	−0.243662
$742$	0	0
$743$	−11608.3	−0.573170	−0.286585	−	0.958055i	$-0.592520\pi$
$743$	−11608.3	−0.573170	−0.286585	+	0.958055i	$0.592520\pi$
$744$	13580.7	0.669211
$745$	−11124.4	−0.547071
$746$	−8864.54	−0.435059
$747$	−5828.97	−0.285503
$748$	3349.38	0.163724
$749$	0	0
$750$	16414.7	0.799176
$751$	24525.0	1.19165	0.595824	−	0.803115i	$-0.296825\pi$
$751$	24525.0	1.19165	0.595824	+	0.803115i	$0.296825\pi$
$752$	76088.7	3.68972
$753$	−848.426	−0.0410603
$754$	−18436.7	−0.890482
$755$	−11002.9	−0.530381
$756$	0	0
$757$	4233.15	0.203245	0.101622	−	0.994823i	$-0.467597\pi$
$757$	4233.15	0.203245	0.101622	+	0.994823i	$0.467597\pi$
$758$	−37103.2	−1.77790
$759$	−4081.78	−0.195203
$760$	35571.6	1.69779
$761$	−9669.63	−0.460609	−0.230305	−	0.973119i	$-0.573972\pi$
$761$	−9669.63	−0.460609	−0.230305	+	0.973119i	$0.573972\pi$
$762$	20749.4	0.986446
$763$	0	0
$764$	2330.54	0.110361
$765$	−221.892	−0.0104870
$766$	−57942.7	−2.73310
$767$	10463.6	0.492593
$768$	−5978.63	−0.280905
$769$	−18103.2	−0.848919	−0.424459	−	0.905447i	$-0.639536\pi$
$769$	−18103.2	−0.848919	−0.424459	+	0.905447i	$0.639536\pi$
$770$	0	0
$771$	−14274.4	−0.666771
$772$	−90415.8	−4.21520
$773$	−13982.7	−0.650610	−0.325305	−	0.945609i	$-0.605467\pi$
$773$	−13982.7	−0.650610	−0.325305	+	0.945609i	$0.605467\pi$
$774$	−12451.2	−0.578227
$775$	7576.39	0.351164
$776$	−33716.9	−1.55975
$777$	0	0
$778$	72932.4	3.36087
$779$	−25650.6	−1.17976
$780$	3495.17	0.160445
$781$	2459.89	0.112704
$782$	1267.81	0.0579754
$783$	7256.58	0.331199
$784$	0	0
$785$	7647.26	0.347697
$786$	−18428.9	−0.836305
$787$	31457.7	1.42484	0.712419	−	0.701754i	$-0.247600\pi$
$787$	31457.7	1.42484	0.712419	+	0.701754i	$0.247600\pi$
$788$	8260.46	0.373435
$789$	−23658.9	−1.06753
$790$	−5801.36	−0.261270
$791$	0	0
$792$	17390.7	0.780244
$793$	2847.76	0.127525
$794$	66041.5	2.95179
$795$	−577.146	−0.0257475
$796$	−69097.8	−3.07677
$797$	−10146.3	−0.450943	−0.225471	−	0.974250i	$-0.572392\pi$
$797$	−10146.3	−0.450943	−0.225471	+	0.974250i	$0.572392\pi$
$798$	0	0
$799$	−2428.45	−0.107525
$800$	42113.5	1.86117
$801$	−13036.3	−0.575051
$802$	−71453.9	−3.14604
$803$	−12977.0	−0.570297
$804$	−62347.0	−2.73484
$805$	0	0
$806$	4968.48	0.217130
$807$	−15027.2	−0.655492
$808$	14436.1	0.628541
$809$	10073.5	0.437783	0.218891	−	0.975749i	$-0.429756\pi$
$809$	10073.5	0.437783	0.218891	+	0.975749i	$0.429756\pi$
$810$	−1930.26	−0.0837315
$811$	−11257.4	−0.487422	−0.243711	−	0.969848i	$-0.578365\pi$
$811$	−11257.4	−0.487422	−0.243711	+	0.969848i	$0.578365\pi$
$812$	0	0
$813$	−1763.73	−0.0760846
$814$	−27027.2	−1.16376
$815$	522.168	0.0224426
$816$	−2801.48	−0.120186
$817$	−33040.5	−1.41486
$818$	58342.3	2.49376
$819$	0	0
$820$	18241.1	0.776839
$821$	−5836.98	−0.248127	−0.124063	−	0.992274i	$-0.539593\pi$
$821$	−5836.98	−0.248127	−0.124063	+	0.992274i	$0.539593\pi$
$822$	2199.90	0.0933458
$823$	33930.1	1.43709	0.718546	−	0.695479i	$-0.244808\pi$
$823$	33930.1	1.43709	0.718546	+	0.695479i	$0.244808\pi$
$824$	10817.3	0.457330
$825$	9701.92	0.409427
$826$	0	0
$827$	21632.8	0.909610	0.454805	−	0.890591i	$-0.349709\pi$
$827$	21632.8	0.909610	0.454805	+	0.890591i	$0.349709\pi$
$828$	7860.15	0.329902
$829$	18686.5	0.782880	0.391440	−	0.920204i	$-0.371977\pi$
$829$	18686.5	0.782880	0.391440	+	0.920204i	$0.371977\pi$
$830$	15434.1	0.645451
$831$	18551.9	0.774439
$832$	9827.92	0.409521
$833$	0	0
$834$	−16299.1	−0.676727
$835$	5597.87	0.232003
$836$	77317.3	3.19865
$837$	−1955.57	−0.0807579
$838$	−16960.0	−0.699132
$839$	8863.48	0.364721	0.182361	−	0.983232i	$-0.441626\pi$
$839$	8863.48	0.364721	0.182361	+	0.983232i	$0.441626\pi$
$840$	0	0
$841$	47844.2	1.96171
$842$	34534.9	1.41348
$843$	12991.1	0.530770
$844$	24994.9	1.01939
$845$	763.216	0.0310715
$846$	−21125.4	−0.858518
$847$	0	0
$848$	−7286.73	−0.295079
$849$	15991.8	0.646451
$850$	−3013.44	−0.121600
$851$	−7291.09	−0.293696
$852$	−4736.92	−0.190474
$853$	12977.5	0.520917	0.260458	−	0.965485i	$-0.416126\pi$
$853$	12977.5	0.520917	0.260458	+	0.965485i	$0.416126\pi$
$854$	0	0
$855$	−5122.16	−0.204882
$856$	126273.	5.04196
$857$	8761.85	0.349241	0.174620	−	0.984636i	$-0.444130\pi$
$857$	8761.85	0.349241	0.174620	+	0.984636i	$0.444130\pi$
$858$	6362.37	0.253156
$859$	18268.1	0.725611	0.362806	−	0.931865i	$-0.381819\pi$
$859$	18268.1	0.725611	0.362806	+	0.931865i	$0.381819\pi$
$860$	23496.4	0.931650
$861$	0	0
$862$	56560.1	2.23485
$863$	−34514.3	−1.36139	−0.680696	−	0.732566i	$-0.738323\pi$
$863$	−34514.3	−1.36139	−0.680696	+	0.732566i	$0.738323\pi$
$864$	−10870.1	−0.428017
$865$	−603.083	−0.0237057
$866$	−90073.6	−3.53444
$867$	−14649.6	−0.573848
$868$	0	0
$869$	−7526.31	−0.293800
$870$	−19214.1	−0.748759
$871$	−13614.3	−0.529624
$872$	69997.6	2.71837
$873$	4855.10	0.188225
$874$	29266.2	1.13266
$875$	0	0
$876$	24989.4	0.963827
$877$	−4375.40	−0.168468	−0.0842342	−	0.996446i	$-0.526844\pi$
$877$	−4375.40	−0.168468	−0.0842342	+	0.996446i	$0.526844\pi$
$878$	21684.2	0.833494
$879$	−26278.9	−1.00838
$880$	−23882.1	−0.914848
$881$	−29511.3	−1.12856	−0.564279	−	0.825584i	$-0.690846\pi$
$881$	−29511.3	−1.12856	−0.564279	+	0.825584i	$0.690846\pi$
$882$	0	0
$883$	17823.5	0.679285	0.339642	−	0.940555i	$-0.389694\pi$
$883$	17823.5	0.679285	0.339642	+	0.940555i	$0.389694\pi$
$884$	−1408.40	−0.0535854
$885$	10904.8	0.414195
$886$	7190.58	0.272655
$887$	26189.9	0.991398	0.495699	−	0.868494i	$-0.334912\pi$
$887$	26189.9	0.991398	0.495699	+	0.868494i	$0.334912\pi$
$888$	31064.2	1.17393
$889$	0	0
$890$	34517.9	1.30005
$891$	−2504.20	−0.0941568
$892$	92508.6	3.47244
$893$	−56058.6	−2.10070
$894$	38995.1	1.45883
$895$	15757.8	0.588520
$896$	0	0
$897$	1716.37	0.0638883
$898$	79500.0	2.95429
$899$	−19466.0	−0.722168
$900$	−18682.6	−0.691950
$901$	232.564	0.00859914
$902$	33204.9	1.22572
$903$	0	0
$904$	40177.0	1.47817
$905$	−13252.4	−0.486769
$906$	38569.1	1.41432
$907$	27166.6	0.994546	0.497273	−	0.867594i	$-0.334335\pi$
$907$	27166.6	0.994546	0.497273	+	0.867594i	$0.334335\pi$
$908$	−31959.2	−1.16807
$909$	−2078.74	−0.0758499
$910$	0	0
$911$	−17493.5	−0.636210	−0.318105	−	0.948056i	$-0.603046\pi$
$911$	−17493.5	−0.636210	−0.318105	+	0.948056i	$0.603046\pi$
$912$	−64669.6	−2.34805
$913$	20023.2	0.725816
$914$	−52031.6	−1.88299
$915$	2967.85	0.107229
$916$	−29664.7	−1.07003
$917$	0	0
$918$	777.809	0.0279646
$919$	10934.1	0.392473	0.196237	−	0.980557i	$-0.437128\pi$
$919$	10934.1	0.392473	0.196237	+	0.980557i	$0.437128\pi$
$920$	−12422.2	−0.445160
$921$	8389.73	0.300164
$922$	−39481.5	−1.41025
$923$	−1034.37	−0.0368869
$924$	0	0
$925$	17330.1	0.616010
$926$	−59995.4	−2.12913
$927$	−1557.65	−0.0551888
$928$	−108202.	−3.82749
$929$	−11932.2	−0.421403	−0.210702	−	0.977550i	$-0.567575\pi$
$929$	−11932.2	−0.421403	−0.210702	+	0.977550i	$0.567575\pi$
$930$	5178.00	0.182573
$931$	0	0
$932$	−5007.98	−0.176011
$933$	20909.3	0.733698
$934$	73960.3	2.59106
$935$	762.223	0.0266603
$936$	−7312.70	−0.255367
$937$	32513.4	1.13358	0.566791	−	0.823862i	$-0.308185\pi$
$937$	32513.4	1.13358	0.566791	+	0.823862i	$0.308185\pi$
$938$	0	0
$939$	−31012.1	−1.07779
$940$	39865.3	1.38326
$941$	30576.2	1.05925	0.529625	−	0.848232i	$-0.322333\pi$
$941$	30576.2	1.05925	0.529625	+	0.848232i	$0.322333\pi$
$942$	−26806.3	−0.927173
$943$	8957.63	0.309333
$944$	137679.	4.74688
$945$	0	0
$946$	42771.2	1.46999
$947$	31519.3	1.08156	0.540781	−	0.841163i	$-0.318129\pi$
$947$	31519.3	1.08156	0.540781	+	0.841163i	$0.318129\pi$
$948$	14493.2	0.496535
$949$	5456.76	0.186653
$950$	−69562.3	−2.37568
$951$	431.551	0.0147150
$952$	0	0
$953$	8579.22	0.291614	0.145807	−	0.989313i	$-0.453422\pi$
$953$	8579.22	0.291614	0.145807	+	0.989313i	$0.453422\pi$
$954$	2023.10	0.0686585
$955$	530.364	0.0179709
$956$	55980.4	1.89387
$957$	−24927.2	−0.841986
$958$	−90584.2	−3.05495
$959$	0	0
$960$	10242.4	0.344345
$961$	−24545.1	−0.823911
$962$	11364.8	0.380889
$963$	−18182.8	−0.608444
$964$	49786.4	1.66339
$965$	−20576.1	−0.686390
$966$	0	0
$967$	−37473.2	−1.24618	−0.623091	−	0.782150i	$-0.714123\pi$
$967$	−37473.2	−1.24618	−0.623091	+	0.782150i	$0.714123\pi$
$968$	23450.7	0.778651
$969$	2064.00	0.0684265
$970$	−12855.4	−0.425529
$971$	12147.2	0.401464	0.200732	−	0.979646i	$-0.435668\pi$
$971$	12147.2	0.401464	0.200732	+	0.979646i	$0.435668\pi$
$972$	4822.24	0.159129
$973$	0	0
$974$	42132.9	1.38606
$975$	−4079.60	−0.134002
$976$	37470.5	1.22889
$977$	−12650.5	−0.414252	−0.207126	−	0.978314i	$-0.566411\pi$
$977$	−12650.5	−0.414252	−0.207126	+	0.978314i	$0.566411\pi$
$978$	−1830.38	−0.0598457
$979$	44781.2	1.46191
$980$	0	0
$981$	−10079.4	−0.328043
$982$	45114.4	1.46605
$983$	−50594.9	−1.64163	−0.820817	−	0.571191i	$-0.806482\pi$
$983$	−50594.9	−1.64163	−0.820817	+	0.571191i	$0.806482\pi$
$984$	−38164.7	−1.23643
$985$	1879.85	0.0608090
$986$	7742.43	0.250070
$987$	0	0
$988$	−32511.5	−1.04689
$989$	11538.3	0.370978
$990$	6630.67	0.212865
$991$	−46889.7	−1.50303	−0.751513	−	0.659718i	$-0.770676\pi$
$991$	−46889.7	−1.50303	−0.751513	+	0.659718i	$0.770676\pi$
$992$	29159.3	0.933275
$993$	−31573.5	−1.00902
$994$	0	0
$995$	−15724.7	−0.501011
$996$	−38557.9	−1.22666
$997$	−40855.1	−1.29779	−0.648893	−	0.760879i	$-0.724768\pi$
$997$	−40855.1	−1.29779	−0.648893	+	0.760879i	$0.724768\pi$
$998$	19149.4	0.607378
$999$	−4473.13	−0.141665

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1911.4.a.m.1.1		4
7.6	odd	2		273.4.a.e.1.1	✓	4
21.20	even	2		819.4.a.f.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.4.a.e.1.1	✓	4	7.6	odd	2
819.4.a.f.1.4		4	21.20	even	2
1911.4.a.m.1.1		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-5.27680 q^{2} +3.00000 q^{3} +19.8446 q^{4} +4.51607 q^{5} -15.8304 q^{6} -62.5017 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.27680 q^{2} +3.00000 q^{3} +19.8446 q^{4} +4.51607 q^{5} -15.8304 q^{6} -62.5017 q^{8} +9.00000 q^{9} -23.8304 q^{10} -30.9160 q^{11} +59.5339 q^{12} +13.0000 q^{13} +13.5482 q^{15} +171.052 q^{16} -5.45932 q^{17} -47.4912 q^{18} -126.023 q^{19} +89.6197 q^{20} +163.138 q^{22} +44.0094 q^{23} -187.505 q^{24} -104.605 q^{25} -68.5984 q^{26} +27.0000 q^{27} +268.762 q^{29} -71.4912 q^{30} -72.4285 q^{31} -402.595 q^{32} -92.7480 q^{33} +28.8077 q^{34} +178.602 q^{36} -165.671 q^{37} +664.999 q^{38} +39.0000 q^{39} -282.262 q^{40} +203.539 q^{41} +262.178 q^{43} -613.517 q^{44} +40.6446 q^{45} -232.229 q^{46} +444.827 q^{47} +513.157 q^{48} +551.980 q^{50} -16.3779 q^{51} +257.980 q^{52} -42.5994 q^{53} -142.474 q^{54} -139.619 q^{55} -378.069 q^{57} -1418.21 q^{58} +804.892 q^{59} +268.859 q^{60} +219.059 q^{61} +382.191 q^{62} +755.994 q^{64} +58.7089 q^{65} +489.413 q^{66} -1047.25 q^{67} -108.338 q^{68} +132.028 q^{69} -79.5668 q^{71} -562.516 q^{72} +419.750 q^{73} +874.215 q^{74} -313.815 q^{75} -2500.88 q^{76} -205.795 q^{78} +243.444 q^{79} +772.484 q^{80} +81.0000 q^{81} -1074.04 q^{82} -647.663 q^{83} -24.6547 q^{85} -1383.46 q^{86} +806.287 q^{87} +1932.30 q^{88} -1448.48 q^{89} -214.474 q^{90} +873.350 q^{92} -217.285 q^{93} -2347.27 q^{94} -569.129 q^{95} -1207.78 q^{96} +539.456 q^{97} -278.244 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} + 12 q^{3} + 9 q^{4} + 3 q^{5} - 9 q^{6} - 69 q^{8} + 36 q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 + 12 * q^3 + 9 * q^4 + 3 * q^5 - 9 * q^6 - 69 * q^8 + 36 * q^9	\( 4 q - 3 q^{2} + 12 q^{3} + 9 q^{4} + 3 q^{5} - 9 q^{6} - 69 q^{8} + 36 q^{9} - 41 q^{10} - 9 q^{11} + 27 q^{12} + 52 q^{13} + 9 q^{15} + 161 q^{16} + 75 q^{17} - 27 q^{18} - 87 q^{19} + 123 q^{20} + 33 q^{22} - 105 q^{23} - 207 q^{24} - 309 q^{25} - 39 q^{26} + 108 q^{27} - 219 q^{29} - 123 q^{30} - 62 q^{31} - 585 q^{32} - 27 q^{33} + 305 q^{34} + 81 q^{36} - 551 q^{37} + 759 q^{38} + 156 q^{39} - 23 q^{40} + 198 q^{41} - 71 q^{43} - 789 q^{44} + 27 q^{45} - 425 q^{46} + 912 q^{47} + 483 q^{48} + 228 q^{50} + 225 q^{51} + 117 q^{52} - 18 q^{53} - 81 q^{54} + 477 q^{55} - 261 q^{57} - 1427 q^{58} + 750 q^{59} + 369 q^{60} + 21 q^{61} + 774 q^{62} + 857 q^{64} + 39 q^{65} + 99 q^{66} - 354 q^{67} + 375 q^{68} - 315 q^{69} - 1596 q^{71} - 621 q^{72} - 613 q^{73} + 1797 q^{74} - 927 q^{75} - 3117 q^{76} - 117 q^{78} + 52 q^{79} + 267 q^{80} + 324 q^{81} + 4 q^{82} - 966 q^{83} + 685 q^{85} - 3213 q^{86} - 657 q^{87} + 3429 q^{88} - 870 q^{89} - 369 q^{90} + 435 q^{92} - 186 q^{93} - 3794 q^{94} - 2229 q^{95} - 1755 q^{96} - 506 q^{97} - 81 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 + 12 * q^3 + 9 * q^4 + 3 * q^5 - 9 * q^6 - 69 * q^8 + 36 * q^9 - 41 * q^10 - 9 * q^11 + 27 * q^12 + 52 * q^13 + 9 * q^15 + 161 * q^16 + 75 * q^17 - 27 * q^18 - 87 * q^19 + 123 * q^20 + 33 * q^22 - 105 * q^23 - 207 * q^24 - 309 * q^25 - 39 * q^26 + 108 * q^27 - 219 * q^29 - 123 * q^30 - 62 * q^31 - 585 * q^32 - 27 * q^33 + 305 * q^34 + 81 * q^36 - 551 * q^37 + 759 * q^38 + 156 * q^39 - 23 * q^40 + 198 * q^41 - 71 * q^43 - 789 * q^44 + 27 * q^45 - 425 * q^46 + 912 * q^47 + 483 * q^48 + 228 * q^50 + 225 * q^51 + 117 * q^52 - 18 * q^53 - 81 * q^54 + 477 * q^55 - 261 * q^57 - 1427 * q^58 + 750 * q^59 + 369 * q^60 + 21 * q^61 + 774 * q^62 + 857 * q^64 + 39 * q^65 + 99 * q^66 - 354 * q^67 + 375 * q^68 - 315 * q^69 - 1596 * q^71 - 621 * q^72 - 613 * q^73 + 1797 * q^74 - 927 * q^75 - 3117 * q^76 - 117 * q^78 + 52 * q^79 + 267 * q^80 + 324 * q^81 + 4 * q^82 - 966 * q^83 + 685 * q^85 - 3213 * q^86 - 657 * q^87 + 3429 * q^88 - 870 * q^89 - 369 * q^90 + 435 * q^92 - 186 * q^93 - 3794 * q^94 - 2229 * q^95 - 1755 * q^96 - 506 * q^97 - 81 * q^99

Introduction

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