LMFDB - Embedded newform 1150.4.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,4,Mod(1,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1150.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1150.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:	$67.8521965066$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{73}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 18 $ x^2 - x - 18
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 46)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.77200$ of defining polynomial
Character	$\chi$	$=$	1150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -5.77200 q^{3} +4.00000 q^{4} +11.5440 q^{6} +11.0880 q^{7} -8.00000 q^{8} +6.31601 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -5.77200 q^{3} +4.00000 q^{4} +11.5440 q^{6} +11.0880 q^{7} -8.00000 q^{8} +6.31601 q^{9} -6.00000 q^{11} -23.0880 q^{12} -21.4920 q^{13} -22.1760 q^{14} +16.0000 q^{16} +7.36799 q^{17} -12.6320 q^{18} -93.4400 q^{19} -64.0000 q^{21} +12.0000 q^{22} -23.0000 q^{23} +46.1760 q^{24} +42.9840 q^{26} +119.388 q^{27} +44.3520 q^{28} +112.476 q^{29} +286.268 q^{31} -32.0000 q^{32} +34.6320 q^{33} -14.7360 q^{34} +25.2640 q^{36} +59.3361 q^{37} +186.880 q^{38} +124.052 q^{39} +62.6119 q^{41} +128.000 q^{42} -507.304 q^{43} -24.0000 q^{44} +46.0000 q^{46} -536.300 q^{47} -92.3520 q^{48} -220.056 q^{49} -42.5280 q^{51} -85.9681 q^{52} -187.336 q^{53} -238.776 q^{54} -88.7041 q^{56} +539.336 q^{57} -224.952 q^{58} +49.6799 q^{59} -778.776 q^{61} -572.536 q^{62} +70.0319 q^{63} +64.0000 q^{64} -69.2640 q^{66} +661.232 q^{67} +29.4720 q^{68} +132.756 q^{69} +289.212 q^{71} -50.5280 q^{72} +651.316 q^{73} -118.672 q^{74} -373.760 q^{76} -66.5280 q^{77} -248.104 q^{78} -50.0720 q^{79} -859.640 q^{81} -125.224 q^{82} -807.016 q^{83} -256.000 q^{84} +1014.61 q^{86} -649.212 q^{87} +48.0000 q^{88} +946.104 q^{89} -238.304 q^{91} -92.0000 q^{92} -1652.34 q^{93} +1072.60 q^{94} +184.704 q^{96} -715.529 q^{97} +440.112 q^{98} -37.8960 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} - 3 q^{3} + 8 q^{4} + 6 q^{6} - 12 q^{7} - 16 q^{8} - 13 q^{9}+O(q^{10}) $ 2 * q - 4 * q^2 - 3 * q^3 + 8 * q^4 + 6 * q^6 - 12 * q^7 - 16 * q^8 - 13 * q^9	$ 2 q - 4 q^{2} - 3 q^{3} + 8 q^{4} + 6 q^{6} - 12 q^{7} - 16 q^{8} - 13 q^{9} - 12 q^{11} - 12 q^{12} + 51 q^{13} + 24 q^{14} + 32 q^{16} + 66 q^{17} + 26 q^{18} - 16 q^{19} - 128 q^{21} + 24 q^{22} - 46 q^{23} + 24 q^{24} - 102 q^{26} - 9 q^{27} - 48 q^{28} - 57 q^{29} - 17 q^{31} - 64 q^{32} + 18 q^{33} - 132 q^{34} - 52 q^{36} - 206 q^{37} + 32 q^{38} + 325 q^{39} + 373 q^{41} + 256 q^{42} - 314 q^{43} - 48 q^{44} + 92 q^{46} - 859 q^{47} - 48 q^{48} - 30 q^{49} + 120 q^{51} + 204 q^{52} - 50 q^{53} + 18 q^{54} + 96 q^{56} + 754 q^{57} + 114 q^{58} + 612 q^{59} - 1062 q^{61} + 34 q^{62} + 516 q^{63} + 128 q^{64} - 36 q^{66} + 844 q^{67} + 264 q^{68} + 69 q^{69} + 399 q^{71} + 104 q^{72} + 1277 q^{73} + 412 q^{74} - 64 q^{76} + 72 q^{77} - 650 q^{78} + 122 q^{79} - 694 q^{81} - 746 q^{82} - 1802 q^{83} - 512 q^{84} + 628 q^{86} - 1119 q^{87} + 96 q^{88} + 2046 q^{89} - 1912 q^{91} - 184 q^{92} - 2493 q^{93} + 1718 q^{94} + 96 q^{96} + 910 q^{97} + 60 q^{98} + 78 q^{99}+O(q^{100}) $ 2 * q - 4 * q^2 - 3 * q^3 + 8 * q^4 + 6 * q^6 - 12 * q^7 - 16 * q^8 - 13 * q^9 - 12 * q^11 - 12 * q^12 + 51 * q^13 + 24 * q^14 + 32 * q^16 + 66 * q^17 + 26 * q^18 - 16 * q^19 - 128 * q^21 + 24 * q^22 - 46 * q^23 + 24 * q^24 - 102 * q^26 - 9 * q^27 - 48 * q^28 - 57 * q^29 - 17 * q^31 - 64 * q^32 + 18 * q^33 - 132 * q^34 - 52 * q^36 - 206 * q^37 + 32 * q^38 + 325 * q^39 + 373 * q^41 + 256 * q^42 - 314 * q^43 - 48 * q^44 + 92 * q^46 - 859 * q^47 - 48 * q^48 - 30 * q^49 + 120 * q^51 + 204 * q^52 - 50 * q^53 + 18 * q^54 + 96 * q^56 + 754 * q^57 + 114 * q^58 + 612 * q^59 - 1062 * q^61 + 34 * q^62 + 516 * q^63 + 128 * q^64 - 36 * q^66 + 844 * q^67 + 264 * q^68 + 69 * q^69 + 399 * q^71 + 104 * q^72 + 1277 * q^73 + 412 * q^74 - 64 * q^76 + 72 * q^77 - 650 * q^78 + 122 * q^79 - 694 * q^81 - 746 * q^82 - 1802 * q^83 - 512 * q^84 + 628 * q^86 - 1119 * q^87 + 96 * q^88 + 2046 * q^89 - 1912 * q^91 - 184 * q^92 - 2493 * q^93 + 1718 * q^94 + 96 * q^96 + 910 * q^97 + 60 * q^98 + 78 * 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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−5.77200	−1.11082	−0.555411	−	0.831576i	$-0.687439\pi$
$3$	−5.77200	−1.11082	−0.555411	+	0.831576i	$0.687439\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	11.5440	0.785470
$7$	11.0880	0.598696	0.299348	−	0.954144i	$-0.403231\pi$
$7$	11.0880	0.598696	0.299348	+	0.954144i	$0.403231\pi$
$8$	−8.00000	−0.353553
$9$	6.31601	0.233926
$10$	0	0
$11$	−6.00000	−0.164461	−0.0822304	−	0.996613i	$-0.526204\pi$
$11$	−6.00000	−0.164461	−0.0822304	+	0.996613i	$0.526204\pi$
$12$	−23.0880	−0.555411
$13$	−21.4920	−0.458524	−0.229262	−	0.973365i	$-0.573631\pi$
$13$	−21.4920	−0.458524	−0.229262	+	0.973365i	$0.573631\pi$
$14$	−22.1760	−0.423342
$15$	0	0
$16$	16.0000	0.250000
$17$	7.36799	0.105118	0.0525588	−	0.998618i	$-0.483262\pi$
$17$	7.36799	0.105118	0.0525588	+	0.998618i	$0.483262\pi$
$18$	−12.6320	−0.165411
$19$	−93.4400	−1.12824	−0.564121	−	0.825692i	$-0.690785\pi$
$19$	−93.4400	−1.12824	−0.564121	+	0.825692i	$0.690785\pi$
$20$	0	0
$21$	−64.0000	−0.665045
$22$	12.0000	0.116291
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	46.1760	0.392735
$25$	0	0
$26$	42.9840	0.324226
$27$	119.388	0.850972
$28$	44.3520	0.299348
$29$	112.476	0.720217	0.360108	−	0.932911i	$-0.382740\pi$
$29$	112.476	0.720217	0.360108	+	0.932911i	$0.382740\pi$
$30$	0	0
$31$	286.268	1.65856	0.829279	−	0.558835i	$-0.188752\pi$
$31$	286.268	1.65856	0.829279	+	0.558835i	$0.188752\pi$
$32$	−32.0000	−0.176777
$33$	34.6320	0.182687
$34$	−14.7360	−0.0743294
$35$	0	0
$36$	25.2640	0.116963
$37$	59.3361	0.263643	0.131821	−	0.991273i	$-0.457917\pi$
$37$	59.3361	0.263643	0.131821	+	0.991273i	$0.457917\pi$
$38$	186.880	0.797788
$39$	124.052	0.509339
$40$	0	0
$41$	62.6119	0.238496	0.119248	−	0.992864i	$-0.461952\pi$
$41$	62.6119	0.238496	0.119248	+	0.992864i	$0.461952\pi$
$42$	128.000	0.470258
$43$	−507.304	−1.79914	−0.899572	−	0.436773i	$-0.856121\pi$
$43$	−507.304	−1.79914	−0.899572	+	0.436773i	$0.856121\pi$
$44$	−24.0000	−0.0822304
$45$	0	0
$46$	46.0000	0.147442
$47$	−536.300	−1.66441	−0.832206	−	0.554466i	$-0.812923\pi$
$47$	−536.300	−1.66441	−0.832206	+	0.554466i	$0.812923\pi$
$48$	−92.3520	−0.277706
$49$	−220.056	−0.641563
$50$	0	0
$51$	−42.5280	−0.116767
$52$	−85.9681	−0.229262
$53$	−187.336	−0.485521	−0.242760	−	0.970086i	$-0.578053\pi$
$53$	−187.336	−0.485521	−0.242760	+	0.970086i	$0.578053\pi$
$54$	−238.776	−0.601728
$55$	0	0
$56$	−88.7041	−0.211671
$57$	539.336	1.25328
$58$	−224.952	−0.509270
$59$	49.6799	0.109623	0.0548116	−	0.998497i	$-0.482544\pi$
$59$	49.6799	0.109623	0.0548116	+	0.998497i	$0.482544\pi$
$60$	0	0
$61$	−778.776	−1.63462	−0.817312	−	0.576195i	$-0.804537\pi$
$61$	−778.776	−1.63462	−0.817312	+	0.576195i	$0.804537\pi$
$62$	−572.536	−1.17278
$63$	70.0319	0.140051
$64$	64.0000	0.125000
$65$	0	0
$66$	−69.2640	−0.129179
$67$	661.232	1.20571	0.602853	−	0.797852i	$-0.294030\pi$
$67$	661.232	1.20571	0.602853	+	0.797852i	$0.294030\pi$
$68$	29.4720	0.0525588
$69$	132.756	0.231622
$70$	0	0
$71$	289.212	0.483425	0.241712	−	0.970348i	$-0.422291\pi$
$71$	289.212	0.483425	0.241712	+	0.970348i	$0.422291\pi$
$72$	−50.5280	−0.0827054
$73$	651.316	1.04426	0.522129	−	0.852867i	$-0.325138\pi$
$73$	651.316	1.04426	0.522129	+	0.852867i	$0.325138\pi$
$74$	−118.672	−0.186424
$75$	0	0
$76$	−373.760	−0.564121
$77$	−66.5280	−0.0984620
$78$	−248.104	−0.360157
$79$	−50.0720	−0.0713107	−0.0356554	−	0.999364i	$-0.511352\pi$
$79$	−50.0720	−0.0713107	−0.0356554	+	0.999364i	$0.511352\pi$
$80$	0	0
$81$	−859.640	−1.17920
$82$	−125.224	−0.168642
$83$	−807.016	−1.06725	−0.533624	−	0.845722i	$-0.679170\pi$
$83$	−807.016	−1.06725	−0.533624	+	0.845722i	$0.679170\pi$
$84$	−256.000	−0.332522
$85$	0	0
$86$	1014.61	1.27219
$87$	−649.212	−0.800033
$88$	48.0000	0.0581456
$89$	946.104	1.12682	0.563409	−	0.826178i	$-0.309490\pi$
$89$	946.104	1.12682	0.563409	+	0.826178i	$0.309490\pi$
$90$	0	0
$91$	−238.304	−0.274517
$92$	−92.0000	−0.104257
$93$	−1652.34	−1.84236
$94$	1072.60	1.17692
$95$	0	0
$96$	184.704	0.196367
$97$	−715.529	−0.748978	−0.374489	−	0.927231i	$-0.622182\pi$
$97$	−715.529	−0.748978	−0.374489	+	0.927231i	$0.622182\pi$
$98$	440.112	0.453654
$99$	−37.8960	−0.0384717
$100$	0	0
$101$	−272.544	−0.268507	−0.134253	−	0.990947i	$-0.542864\pi$
$101$	−272.544	−0.268507	−0.134253	+	0.990947i	$0.542864\pi$
$102$	85.0561	0.0825667
$103$	609.904	0.583453	0.291726	−	0.956502i	$-0.405770\pi$
$103$	609.904	0.583453	0.291726	+	0.956502i	$0.405770\pi$
$104$	171.936	0.162113
$105$	0	0
$106$	374.672	0.343315
$107$	212.240	0.191757	0.0958785	−	0.995393i	$-0.469434\pi$
$107$	212.240	0.191757	0.0958785	+	0.995393i	$0.469434\pi$
$108$	477.552	0.425486
$109$	−1287.18	−1.13110	−0.565550	−	0.824714i	$-0.691336\pi$
$109$	−1287.18	−1.13110	−0.565550	+	0.824714i	$0.691336\pi$
$110$	0	0
$111$	−342.488	−0.292860
$112$	177.408	0.149674
$113$	313.336	0.260851	0.130426	−	0.991458i	$-0.458366\pi$
$113$	313.336	0.260851	0.130426	+	0.991458i	$0.458366\pi$
$114$	−1078.67	−0.886201
$115$	0	0
$116$	449.904	0.360108
$117$	−135.744	−0.107261
$118$	−99.3598	−0.0775153
$119$	81.6963	0.0629335
$120$	0	0
$121$	−1295.00	−0.972953
$122$	1557.55	1.15585
$123$	−361.396	−0.264927
$124$	1145.07	0.829279
$125$	0	0
$126$	−140.064	−0.0990308
$127$	1152.43	0.805208	0.402604	−	0.915374i	$-0.368105\pi$
$127$	1152.43	0.805208	0.402604	+	0.915374i	$0.368105\pi$
$128$	−128.000	−0.0883883
$129$	2928.16	1.99853
$130$	0	0
$131$	−2368.37	−1.57959	−0.789793	−	0.613374i	$-0.789812\pi$
$131$	−2368.37	−1.57959	−0.789793	+	0.613374i	$0.789812\pi$
$132$	138.528	0.0913433
$133$	−1036.06	−0.675475
$134$	−1322.46	−0.852563
$135$	0	0
$136$	−58.9439	−0.0371647
$137$	2872.44	1.79131	0.895654	−	0.444752i	$-0.146708\pi$
$137$	2872.44	1.79131	0.895654	+	0.444752i	$0.146708\pi$
$138$	−265.512	−0.163782
$139$	1637.24	0.999054	0.499527	−	0.866298i	$-0.333507\pi$
$139$	1637.24	0.999054	0.499527	+	0.866298i	$0.333507\pi$
$140$	0	0
$141$	3095.52	1.84887
$142$	−578.424	−0.341833
$143$	128.952	0.0754092
$144$	101.056	0.0584815
$145$	0	0
$146$	−1302.63	−0.738401
$147$	1270.16	0.712662
$148$	237.344	0.131821
$149$	3125.40	1.71841	0.859204	−	0.511633i	$-0.170959\pi$
$149$	3125.40	1.71841	0.859204	+	0.511633i	$0.170959\pi$
$150$	0	0
$151$	−370.436	−0.199640	−0.0998200	−	0.995006i	$-0.531827\pi$
$151$	−370.436	−0.199640	−0.0998200	+	0.995006i	$0.531827\pi$
$152$	747.520	0.398894
$153$	46.5363	0.0245898
$154$	133.056	0.0696232
$155$	0	0
$156$	496.208	0.254669
$157$	1993.44	1.01334	0.506669	−	0.862141i	$-0.330877\pi$
$157$	1993.44	1.01334	0.506669	+	0.862141i	$0.330877\pi$
$158$	100.144	0.0504243
$159$	1081.30	0.539327
$160$	0	0
$161$	−255.024	−0.124837
$162$	1719.28	0.833824
$163$	−1722.10	−0.827517	−0.413759	−	0.910387i	$-0.635784\pi$
$163$	−1722.10	−0.827517	−0.413759	+	0.910387i	$0.635784\pi$
$164$	250.448	0.119248
$165$	0	0
$166$	1614.03	0.754658
$167$	1870.88	0.866904	0.433452	−	0.901177i	$-0.357295\pi$
$167$	1870.88	0.866904	0.433452	+	0.901177i	$0.357295\pi$
$168$	512.000	0.235129
$169$	−1735.09	−0.789756
$170$	0	0
$171$	−590.168	−0.263925
$172$	−2029.22	−0.899572
$173$	700.512	0.307855	0.153927	−	0.988082i	$-0.450808\pi$
$173$	700.512	0.307855	0.153927	+	0.988082i	$0.450808\pi$
$174$	1298.42	0.565708
$175$	0	0
$176$	−96.0000	−0.0411152
$177$	−286.752	−0.121772
$178$	−1892.21	−0.796781
$179$	3804.58	1.58865	0.794323	−	0.607495i	$-0.207826\pi$
$179$	3804.58	1.58865	0.794323	+	0.607495i	$0.207826\pi$
$180$	0	0
$181$	3660.10	1.50306	0.751529	−	0.659700i	$-0.229317\pi$
$181$	3660.10	1.50306	0.751529	+	0.659700i	$0.229317\pi$
$182$	476.607	0.194113
$183$	4495.10	1.81578
$184$	184.000	0.0737210
$185$	0	0
$186$	3304.68	1.30275
$187$	−44.2079	−0.0172877
$188$	−2145.20	−0.832206
$189$	1323.78	0.509474
$190$	0	0
$191$	−1999.46	−0.757467	−0.378733	−	0.925506i	$-0.623640\pi$
$191$	−1999.46	−0.757467	−0.378733	+	0.925506i	$0.623640\pi$
$192$	−369.408	−0.138853
$193$	−879.885	−0.328163	−0.164082	−	0.986447i	$-0.552466\pi$
$193$	−879.885	−0.328163	−0.164082	+	0.986447i	$0.552466\pi$
$194$	1431.06	0.529608
$195$	0	0
$196$	−880.224	−0.320781
$197$	2760.80	0.998473	0.499236	−	0.866466i	$-0.333614\pi$
$197$	2760.80	0.998473	0.499236	+	0.866466i	$0.333614\pi$
$198$	75.7921	0.0272036
$199$	3377.19	1.20303	0.601515	−	0.798862i	$-0.294564\pi$
$199$	3377.19	1.20303	0.601515	+	0.798862i	$0.294564\pi$
$200$	0	0
$201$	−3816.63	−1.33933
$202$	545.089	0.189863
$203$	1247.14	0.431191
$204$	−170.112	−0.0583835
$205$	0	0
$206$	−1219.81	−0.412564
$207$	−145.268	−0.0487770
$208$	−343.872	−0.114631
$209$	560.640	0.185552
$210$	0	0
$211$	−1072.19	−0.349823	−0.174912	−	0.984584i	$-0.555964\pi$
$211$	−1072.19	−0.349823	−0.174912	+	0.984584i	$0.555964\pi$
$212$	−749.344	−0.242760
$213$	−1669.33	−0.536999
$214$	−424.480	−0.135593
$215$	0	0
$216$	−955.104	−0.300864
$217$	3174.14	0.992972
$218$	2574.37	0.799809
$219$	−3759.40	−1.15998
$220$	0	0
$221$	−158.353	−0.0481990
$222$	684.976	0.207084
$223$	−1494.88	−0.448899	−0.224450	−	0.974486i	$-0.572058\pi$
$223$	−1494.88	−0.448899	−0.224450	+	0.974486i	$0.572058\pi$
$224$	−354.816	−0.105836
$225$	0	0
$226$	−626.672	−0.184450
$227$	−2714.01	−0.793547	−0.396773	−	0.917917i	$-0.629870\pi$
$227$	−2714.01	−0.793547	−0.396773	+	0.917917i	$0.629870\pi$
$228$	2157.34	0.626639
$229$	2512.00	0.724881	0.362441	−	0.932007i	$-0.381944\pi$
$229$	2512.00	0.724881	0.362441	+	0.932007i	$0.381944\pi$
$230$	0	0
$231$	384.000	0.109374
$232$	−899.808	−0.254635
$233$	1728.36	0.485961	0.242981	−	0.970031i	$-0.421875\pi$
$233$	1728.36	0.485961	0.242981	+	0.970031i	$0.421875\pi$
$234$	271.487	0.0758448
$235$	0	0
$236$	198.720	0.0548116
$237$	289.016	0.0792135
$238$	−163.393	−0.0445007
$239$	−1689.48	−0.457252	−0.228626	−	0.973514i	$-0.573423\pi$
$239$	−1689.48	−0.457252	−0.228626	+	0.973514i	$0.573423\pi$
$240$	0	0
$241$	3155.01	0.843286	0.421643	−	0.906762i	$-0.361454\pi$
$241$	3155.01	0.843286	0.421643	+	0.906762i	$0.361454\pi$
$242$	2590.00	0.687981
$243$	1738.37	0.458915
$244$	−3115.10	−0.817312
$245$	0	0
$246$	722.793	0.187332
$247$	2008.22	0.517327
$248$	−2290.15	−0.586389
$249$	4658.10	1.18552
$250$	0	0
$251$	6341.93	1.59482	0.797408	−	0.603440i	$-0.206204\pi$
$251$	6341.93	1.59482	0.797408	+	0.603440i	$0.206204\pi$
$252$	280.128	0.0700253
$253$	138.000	0.0342924
$254$	−2304.86	−0.569368
$255$	0	0
$256$	256.000	0.0625000
$257$	5956.53	1.44575	0.722875	−	0.690979i	$-0.242820\pi$
$257$	5956.53	1.44575	0.722875	+	0.690979i	$0.242820\pi$
$258$	−5856.32	−1.41317
$259$	657.919	0.157842
$260$	0	0
$261$	710.399	0.168477
$262$	4736.75	1.11694
$263$	7147.68	1.67583	0.837917	−	0.545797i	$-0.183773\pi$
$263$	7147.68	1.67583	0.837917	+	0.545797i	$0.183773\pi$
$264$	−277.056	−0.0645895
$265$	0	0
$266$	2072.13	0.477633
$267$	−5460.91	−1.25169
$268$	2644.93	0.602853
$269$	7432.72	1.68469	0.842343	−	0.538941i	$-0.181176\pi$
$269$	7432.72	1.68469	0.842343	+	0.538941i	$0.181176\pi$
$270$	0	0
$271$	3236.06	0.725376	0.362688	−	0.931911i	$-0.381859\pi$
$271$	3236.06	0.725376	0.362688	+	0.931911i	$0.381859\pi$
$272$	117.888	0.0262794
$273$	1375.49	0.304939
$274$	−5744.88	−1.26665
$275$	0	0
$276$	531.024	0.115811
$277$	−5437.77	−1.17951	−0.589755	−	0.807582i	$-0.700776\pi$
$277$	−5437.77	−1.17951	−0.589755	+	0.807582i	$0.700776\pi$
$278$	−3274.47	−0.706438
$279$	1808.07	0.387980
$280$	0	0
$281$	244.617	0.0519312	0.0259656	−	0.999663i	$-0.491734\pi$
$281$	244.617	0.0519312	0.0259656	+	0.999663i	$0.491734\pi$
$282$	−6191.05	−1.30735
$283$	1050.75	0.220710	0.110355	−	0.993892i	$-0.464801\pi$
$283$	1050.75	0.220710	0.110355	+	0.993892i	$0.464801\pi$
$284$	1156.85	0.241712
$285$	0	0
$286$	−257.904	−0.0533224
$287$	694.242	0.142787
$288$	−202.112	−0.0413527
$289$	−4858.71	−0.988950
$290$	0	0
$291$	4130.03	0.831982
$292$	2605.26	0.522129
$293$	−5643.46	−1.12524	−0.562618	−	0.826717i	$-0.690206\pi$
$293$	−5643.46	−1.12524	−0.562618	+	0.826717i	$0.690206\pi$
$294$	−2540.33	−0.503928
$295$	0	0
$296$	−474.689	−0.0932119
$297$	−716.328	−0.139951
$298$	−6250.80	−1.21510
$299$	494.316	0.0956089
$300$	0	0
$301$	−5624.99	−1.07714
$302$	740.872	0.141167
$303$	1573.13	0.298263
$304$	−1495.04	−0.282061
$305$	0	0
$306$	−93.0725	−0.0173876
$307$	−5876.55	−1.09248	−0.546241	−	0.837628i	$-0.683942\pi$
$307$	−5876.55	−1.09248	−0.546241	+	0.837628i	$0.683942\pi$
$308$	−266.112	−0.0492310
$309$	−3520.37	−0.648113
$310$	0	0
$311$	8748.00	1.59503	0.797514	−	0.603301i	$-0.206148\pi$
$311$	8748.00	1.59503	0.797514	+	0.603301i	$0.206148\pi$
$312$	−992.416	−0.180078
$313$	5029.42	0.908241	0.454120	−	0.890940i	$-0.349954\pi$
$313$	5029.42	0.908241	0.454120	+	0.890940i	$0.349954\pi$
$314$	−3986.88	−0.716537
$315$	0	0
$316$	−200.288	−0.0356554
$317$	7199.63	1.27562	0.637810	−	0.770193i	$-0.279840\pi$
$317$	7199.63	1.27562	0.637810	+	0.770193i	$0.279840\pi$
$318$	−2162.61	−0.381362
$319$	−674.856	−0.118447
$320$	0	0
$321$	−1225.05	−0.213008
$322$	510.048	0.0882729
$323$	−688.465	−0.118598
$324$	−3438.56	−0.589602
$325$	0	0
$326$	3444.20	0.585143
$327$	7429.63	1.25645
$328$	−500.896	−0.0843211
$329$	−5946.50	−0.996478
$330$	0	0
$331$	−772.092	−0.128212	−0.0641058	−	0.997943i	$-0.520420\pi$
$331$	−772.092	−0.128212	−0.0641058	+	0.997943i	$0.520420\pi$
$332$	−3228.06	−0.533624
$333$	374.767	0.0616730
$334$	−3741.76	−0.612994
$335$	0	0
$336$	−1024.00	−0.166261
$337$	11069.6	1.78932	0.894659	−	0.446750i	$-0.147419\pi$
$337$	11069.6	1.78932	0.894659	+	0.446750i	$0.147419\pi$
$338$	3470.19	0.558442
$339$	−1808.58	−0.289759
$340$	0	0
$341$	−1717.61	−0.272768
$342$	1180.34	0.186624
$343$	−6243.17	−0.982797
$344$	4058.43	0.636093
$345$	0	0
$346$	−1401.02	−0.217686
$347$	1202.99	0.186109	0.0930547	−	0.995661i	$-0.470337\pi$
$347$	1202.99	0.186109	0.0930547	+	0.995661i	$0.470337\pi$
$348$	−2596.85	−0.400016
$349$	−4573.69	−0.701501	−0.350750	−	0.936469i	$-0.614073\pi$
$349$	−4573.69	−0.701501	−0.350750	+	0.936469i	$0.614073\pi$
$350$	0	0
$351$	−2565.89	−0.390191
$352$	192.000	0.0290728
$353$	974.740	0.146969	0.0734846	−	0.997296i	$-0.476588\pi$
$353$	974.740	0.146969	0.0734846	+	0.997296i	$0.476588\pi$
$354$	573.505	0.0861058
$355$	0	0
$356$	3784.42	0.563409
$357$	−471.551	−0.0699080
$358$	−7609.16	−1.12334
$359$	−4872.46	−0.716319	−0.358160	−	0.933660i	$-0.616596\pi$
$359$	−4872.46	−0.716319	−0.358160	+	0.933660i	$0.616596\pi$
$360$	0	0
$361$	1872.04	0.272932
$362$	−7320.21	−1.06282
$363$	7474.74	1.08078
$364$	−953.215	−0.137258
$365$	0	0
$366$	−8990.19	−1.28395
$367$	−11508.8	−1.63693	−0.818464	−	0.574557i	$-0.805174\pi$
$367$	−11508.8	−1.63693	−0.818464	+	0.574557i	$0.805174\pi$
$368$	−368.000	−0.0521286
$369$	395.457	0.0557905
$370$	0	0
$371$	−2077.18	−0.290679
$372$	−6609.36	−0.921181
$373$	3989.01	0.553735	0.276868	−	0.960908i	$-0.410704\pi$
$373$	3989.01	0.553735	0.276868	+	0.960908i	$0.410704\pi$
$374$	88.4159	0.0122243
$375$	0	0
$376$	4290.40	0.588459
$377$	−2417.34	−0.330237
$378$	−2647.55	−0.360252
$379$	2191.96	0.297080	0.148540	−	0.988906i	$-0.452543\pi$
$379$	2191.96	0.297080	0.148540	+	0.988906i	$0.452543\pi$
$380$	0	0
$381$	−6651.81	−0.894443
$382$	3998.93	0.535610
$383$	−10659.4	−1.42212	−0.711060	−	0.703131i	$-0.751785\pi$
$383$	−10659.4	−1.42212	−0.711060	+	0.703131i	$0.751785\pi$
$384$	738.816	0.0981837
$385$	0	0
$386$	1759.77	0.232046
$387$	−3204.14	−0.420867
$388$	−2862.11	−0.374489
$389$	8828.21	1.15066	0.575332	−	0.817920i	$-0.304873\pi$
$389$	8828.21	1.15066	0.575332	+	0.817920i	$0.304873\pi$
$390$	0	0
$391$	−169.464	−0.0219185
$392$	1760.45	0.226827
$393$	13670.3	1.75464
$394$	−5521.61	−0.706027
$395$	0	0
$396$	−151.584	−0.0192358
$397$	4309.68	0.544828	0.272414	−	0.962180i	$-0.412178\pi$
$397$	4309.68	0.544828	0.272414	+	0.962180i	$0.412178\pi$
$398$	−6754.39	−0.850670
$399$	5980.16	0.750332
$400$	0	0
$401$	10650.5	1.32634	0.663169	−	0.748470i	$-0.269211\pi$
$401$	10650.5	1.32634	0.663169	+	0.748470i	$0.269211\pi$
$402$	7633.27	0.947047
$403$	−6152.48	−0.760489
$404$	−1090.18	−0.134253
$405$	0	0
$406$	−2494.27	−0.304898
$407$	−356.016	−0.0433589
$408$	340.224	0.0412834
$409$	−299.234	−0.0361764	−0.0180882	−	0.999836i	$-0.505758\pi$
$409$	−299.234	−0.0361764	−0.0180882	+	0.999836i	$0.505758\pi$
$410$	0	0
$411$	−16579.7	−1.98982
$412$	2439.62	0.291726
$413$	550.851	0.0656310
$414$	290.536	0.0344905
$415$	0	0
$416$	687.745	0.0810564
$417$	−9450.13	−1.10977
$418$	−1121.28	−0.131205
$419$	−9596.39	−1.11889	−0.559445	−	0.828868i	$-0.688986\pi$
$419$	−9596.39	−1.11889	−0.559445	+	0.828868i	$0.688986\pi$
$420$	0	0
$421$	14049.2	1.62641	0.813203	−	0.581980i	$-0.197722\pi$
$421$	14049.2	1.62641	0.813203	+	0.581980i	$0.197722\pi$
$422$	2144.38	0.247362
$423$	−3387.27	−0.389350
$424$	1498.69	0.171657
$425$	0	0
$426$	3338.66	0.379716
$427$	−8635.08	−0.978643
$428$	848.959	0.0958785
$429$	−744.312	−0.0837662
$430$	0	0
$431$	−5348.79	−0.597777	−0.298889	−	0.954288i	$-0.596616\pi$
$431$	−5348.79	−0.597777	−0.298889	+	0.954288i	$0.596616\pi$
$432$	1910.21	0.212743
$433$	−10727.2	−1.19057	−0.595284	−	0.803516i	$-0.702960\pi$
$433$	−10727.2	−1.19057	−0.595284	+	0.803516i	$0.702960\pi$
$434$	−6348.29	−0.702137
$435$	0	0
$436$	−5148.74	−0.565550
$437$	2149.12	0.235255
$438$	7518.79	0.820233
$439$	−1425.53	−0.154981	−0.0774907	−	0.996993i	$-0.524691\pi$
$439$	−1425.53	−0.154981	−0.0774907	+	0.996993i	$0.524691\pi$
$440$	0	0
$441$	−1389.88	−0.150078
$442$	316.706	0.0340818
$443$	13585.6	1.45705	0.728524	−	0.685020i	$-0.240207\pi$
$443$	13585.6	1.45705	0.728524	+	0.685020i	$0.240207\pi$
$444$	−1369.95	−0.146430
$445$	0	0
$446$	2989.76	0.317420
$447$	−18039.8	−1.90885
$448$	709.632	0.0748370
$449$	16471.6	1.73128	0.865638	−	0.500670i	$-0.166913\pi$
$449$	16471.6	1.73128	0.865638	+	0.500670i	$0.166913\pi$
$450$	0	0
$451$	−375.672	−0.0392233
$452$	1253.34	0.130426
$453$	2138.16	0.221765
$454$	5428.02	0.561122
$455$	0	0
$456$	−4314.69	−0.443100
$457$	−1032.87	−0.105724	−0.0528619	−	0.998602i	$-0.516834\pi$
$457$	−1032.87	−0.105724	−0.0528619	+	0.998602i	$0.516834\pi$
$458$	−5024.00	−0.512568
$459$	879.650	0.0894522
$460$	0	0
$461$	239.436	0.0241902	0.0120951	−	0.999927i	$-0.496150\pi$
$461$	239.436	0.0241902	0.0120951	+	0.999927i	$0.496150\pi$
$462$	−768.000	−0.0773389
$463$	16596.4	1.66587	0.832935	−	0.553370i	$-0.186659\pi$
$463$	16596.4	1.66587	0.832935	+	0.553370i	$0.186659\pi$
$464$	1799.62	0.180054
$465$	0	0
$466$	−3456.73	−0.343626
$467$	−10251.7	−1.01583	−0.507917	−	0.861406i	$-0.669584\pi$
$467$	−10251.7	−1.01583	−0.507917	+	0.861406i	$0.669584\pi$
$468$	−542.975	−0.0536304
$469$	7331.75	0.721852
$470$	0	0
$471$	−11506.1	−1.12564
$472$	−397.439	−0.0387577
$473$	3043.82	0.295888
$474$	−578.032	−0.0560124
$475$	0	0
$476$	326.785	0.0314668
$477$	−1183.22	−0.113576
$478$	3378.95	0.323326
$479$	−4030.99	−0.384511	−0.192256	−	0.981345i	$-0.561580\pi$
$479$	−4030.99	−0.384511	−0.192256	+	0.981345i	$0.561580\pi$
$480$	0	0
$481$	−1275.25	−0.120887
$482$	−6310.02	−0.596293
$483$	1472.00	0.138671
$484$	−5180.00	−0.486476
$485$	0	0
$486$	−3476.74	−0.324502
$487$	−6054.93	−0.563399	−0.281699	−	0.959503i	$-0.590898\pi$
$487$	−6054.93	−0.563399	−0.281699	+	0.959503i	$0.590898\pi$
$488$	6230.21	0.577927
$489$	9939.97	0.919225
$490$	0	0
$491$	−19864.4	−1.82580	−0.912902	−	0.408178i	$-0.866164\pi$
$491$	−19864.4	−1.82580	−0.912902	+	0.408178i	$0.866164\pi$
$492$	−1445.59	−0.132463
$493$	828.722	0.0757075
$494$	−4016.43	−0.365805
$495$	0	0
$496$	4580.29	0.414639
$497$	3206.79	0.289425
$498$	−9316.20	−0.838291
$499$	−12128.9	−1.08811	−0.544053	−	0.839051i	$-0.683111\pi$
$499$	−12128.9	−1.08811	−0.544053	+	0.839051i	$0.683111\pi$
$500$	0	0
$501$	−10798.7	−0.962977
$502$	−12683.9	−1.12771
$503$	18351.3	1.62673	0.813363	−	0.581756i	$-0.197634\pi$
$503$	18351.3	1.62673	0.813363	+	0.581756i	$0.197634\pi$
$504$	−560.255	−0.0495154
$505$	0	0
$506$	−276.000	−0.0242484
$507$	10015.0	0.877278
$508$	4609.71	0.402604
$509$	−10876.1	−0.947106	−0.473553	−	0.880765i	$-0.657029\pi$
$509$	−10876.1	−0.947106	−0.473553	+	0.880765i	$0.657029\pi$
$510$	0	0
$511$	7221.80	0.625193
$512$	−512.000	−0.0441942
$513$	−11155.6	−0.960103
$514$	−11913.1	−1.02230
$515$	0	0
$516$	11712.6	0.999264
$517$	3217.80	0.273731
$518$	−1315.84	−0.111611
$519$	−4043.35	−0.341972
$520$	0	0
$521$	4317.61	0.363067	0.181533	−	0.983385i	$-0.441894\pi$
$521$	4317.61	0.363067	0.181533	+	0.983385i	$0.441894\pi$
$522$	−1420.80	−0.119132
$523$	11789.9	0.985733	0.492866	−	0.870105i	$-0.335949\pi$
$523$	11789.9	0.985733	0.492866	+	0.870105i	$0.335949\pi$
$524$	−9473.49	−0.789793
$525$	0	0
$526$	−14295.4	−1.18499
$527$	2109.22	0.174344
$528$	554.112	0.0456717
$529$	529.000	0.0434783
$530$	0	0
$531$	313.778	0.0256437
$532$	−4144.26	−0.337737
$533$	−1345.66	−0.109356
$534$	10921.8	0.885082
$535$	0	0
$536$	−5289.86	−0.426282
$537$	−21960.0	−1.76470
$538$	−14865.4	−1.19125
$539$	1320.34	0.105512
$540$	0	0
$541$	8944.99	0.710860	0.355430	−	0.934703i	$-0.384334\pi$
$541$	8944.99	0.710860	0.355430	+	0.934703i	$0.384334\pi$
$542$	−6472.13	−0.512918
$543$	−21126.1	−1.66963
$544$	−235.776	−0.0185823
$545$	0	0
$546$	−2750.98	−0.215625
$547$	−16376.3	−1.28007	−0.640036	−	0.768345i	$-0.721081\pi$
$547$	−16376.3	−1.28007	−0.640036	+	0.768345i	$0.721081\pi$
$548$	11489.8	0.895654
$549$	−4918.75	−0.382381
$550$	0	0
$551$	−10509.8	−0.812579
$552$	−1062.05	−0.0818909
$553$	−555.199	−0.0426934
$554$	10875.5	0.834039
$555$	0	0
$556$	6548.94	0.499527
$557$	−18239.2	−1.38747	−0.693736	−	0.720230i	$-0.744036\pi$
$557$	−18239.2	−1.38747	−0.693736	+	0.720230i	$0.744036\pi$
$558$	−3616.14	−0.274343
$559$	10903.0	0.824951
$560$	0	0
$561$	255.168	0.0192036
$562$	−489.235	−0.0367209
$563$	286.757	0.0214660	0.0107330	−	0.999942i	$-0.496584\pi$
$563$	286.757	0.0214660	0.0107330	+	0.999942i	$0.496584\pi$
$564$	12382.1	0.924433
$565$	0	0
$566$	−2101.51	−0.156065
$567$	−9531.70	−0.705985
$568$	−2313.70	−0.170916
$569$	13951.6	1.02791	0.513955	−	0.857817i	$-0.328180\pi$
$569$	13951.6	1.02791	0.513955	+	0.857817i	$0.328180\pi$
$570$	0	0
$571$	−2020.68	−0.148096	−0.0740481	−	0.997255i	$-0.523592\pi$
$571$	−2020.68	−0.148096	−0.0740481	+	0.997255i	$0.523592\pi$
$572$	515.808	0.0377046
$573$	11540.9	0.841411
$574$	−1388.48	−0.100965
$575$	0	0
$576$	404.224	0.0292408
$577$	21630.4	1.56064	0.780318	−	0.625383i	$-0.215057\pi$
$577$	21630.4	1.56064	0.780318	+	0.625383i	$0.215057\pi$
$578$	9717.43	0.699293
$579$	5078.70	0.364531
$580$	0	0
$581$	−8948.20	−0.638957
$582$	−8260.06	−0.588300
$583$	1124.02	0.0798491
$584$	−5210.53	−0.369201
$585$	0	0
$586$	11286.9	0.795663
$587$	−1510.94	−0.106240	−0.0531202	−	0.998588i	$-0.516917\pi$
$587$	−1510.94	−0.106240	−0.0531202	+	0.998588i	$0.516917\pi$
$588$	5080.66	0.356331
$589$	−26748.9	−1.87126
$590$	0	0
$591$	−15935.4	−1.10913
$592$	949.377	0.0659107
$593$	19464.5	1.34791	0.673957	−	0.738771i	$-0.264593\pi$
$593$	19464.5	1.34791	0.673957	+	0.738771i	$0.264593\pi$
$594$	1432.66	0.0989606
$595$	0	0
$596$	12501.6	0.859204
$597$	−19493.2	−1.33635
$598$	−988.633	−0.0676057
$599$	−11515.5	−0.785497	−0.392748	−	0.919646i	$-0.628476\pi$
$599$	−11515.5	−0.785497	−0.392748	+	0.919646i	$0.628476\pi$
$600$	0	0
$601$	372.589	0.0252882	0.0126441	−	0.999920i	$-0.495975\pi$
$601$	372.589	0.0252882	0.0126441	+	0.999920i	$0.495975\pi$
$602$	11250.0	0.761653
$603$	4176.35	0.282046
$604$	−1481.74	−0.0998200
$605$	0	0
$606$	−3146.25	−0.210904
$607$	19564.0	1.30820	0.654099	−	0.756409i	$-0.273048\pi$
$607$	19564.0	1.30820	0.654099	+	0.756409i	$0.273048\pi$
$608$	2990.08	0.199447
$609$	−7198.47	−0.478976
$610$	0	0
$611$	11526.2	0.763173
$612$	186.145	0.0122949
$613$	14060.7	0.926435	0.463217	−	0.886245i	$-0.346695\pi$
$613$	14060.7	0.926435	0.463217	+	0.886245i	$0.346695\pi$
$614$	11753.1	0.772502
$615$	0	0
$616$	532.224	0.0348116
$617$	282.447	0.0184293	0.00921465	−	0.999958i	$-0.497067\pi$
$617$	282.447	0.0184293	0.00921465	+	0.999958i	$0.497067\pi$
$618$	7040.74	0.458285
$619$	6071.66	0.394250	0.197125	−	0.980378i	$-0.436840\pi$
$619$	6071.66	0.394250	0.197125	+	0.980378i	$0.436840\pi$
$620$	0	0
$621$	−2745.93	−0.177440
$622$	−17496.0	−1.12785
$623$	10490.4	0.674622
$624$	1984.83	0.127335
$625$	0	0
$626$	−10058.8	−0.642223
$627$	−3236.02	−0.206115
$628$	7973.76	0.506669
$629$	437.188	0.0277135
$630$	0	0
$631$	3977.43	0.250933	0.125467	−	0.992098i	$-0.459957\pi$
$631$	3977.43	0.250933	0.125467	+	0.992098i	$0.459957\pi$
$632$	400.576	0.0252121
$633$	6188.69	0.388591
$634$	−14399.3	−0.902000
$635$	0	0
$636$	4325.22	0.269664
$637$	4729.45	0.294172
$638$	1349.71	0.0837549
$639$	1826.66	0.113086
$640$	0	0
$641$	18024.3	1.11064	0.555318	−	0.831638i	$-0.312597\pi$
$641$	18024.3	1.11064	0.555318	+	0.831638i	$0.312597\pi$
$642$	2450.10	0.150619
$643$	−9926.77	−0.608824	−0.304412	−	0.952541i	$-0.598460\pi$
$643$	−9926.77	−0.608824	−0.304412	+	0.952541i	$0.598460\pi$
$644$	−1020.10	−0.0624184
$645$	0	0
$646$	1376.93	0.0838616
$647$	−2274.51	−0.138207	−0.0691036	−	0.997609i	$-0.522014\pi$
$647$	−2274.51	−0.138207	−0.0691036	+	0.997609i	$0.522014\pi$
$648$	6877.12	0.416912
$649$	−298.079	−0.0180287
$650$	0	0
$651$	−18321.2	−1.10302
$652$	−6888.40	−0.413759
$653$	−1794.68	−0.107552	−0.0537758	−	0.998553i	$-0.517126\pi$
$653$	−1794.68	−0.107552	−0.0537758	+	0.998553i	$0.517126\pi$
$654$	−14859.3	−0.888445
$655$	0	0
$656$	1001.79	0.0596240
$657$	4113.72	0.244279
$658$	11893.0	0.704616
$659$	4081.99	0.241292	0.120646	−	0.992696i	$-0.461503\pi$
$659$	4081.99	0.241292	0.120646	+	0.992696i	$0.461503\pi$
$660$	0	0
$661$	−15350.1	−0.903253	−0.451626	−	0.892207i	$-0.649156\pi$
$661$	−15350.1	−0.903253	−0.451626	+	0.892207i	$0.649156\pi$
$662$	1544.18	0.0906593
$663$	914.014	0.0535405
$664$	6456.13	0.377329
$665$	0	0
$666$	−749.534	−0.0436094
$667$	−2586.95	−0.150176
$668$	7483.52	0.433452
$669$	8628.45	0.498647
$670$	0	0
$671$	4672.66	0.268831
$672$	2048.00	0.117564
$673$	−26310.5	−1.50698	−0.753488	−	0.657461i	$-0.771630\pi$
$673$	−26310.5	−1.50698	−0.753488	+	0.657461i	$0.771630\pi$
$674$	−22139.2	−1.26524
$675$	0	0
$676$	−6940.37	−0.394878
$677$	22299.1	1.26591	0.632957	−	0.774187i	$-0.281841\pi$
$677$	22299.1	1.26591	0.632957	+	0.774187i	$0.281841\pi$
$678$	3617.15	0.204891
$679$	−7933.79	−0.448411
$680$	0	0
$681$	15665.3	0.881489
$682$	3435.22	0.192876
$683$	−24001.7	−1.34466	−0.672328	−	0.740253i	$-0.734706\pi$
$683$	−24001.7	−1.34466	−0.672328	+	0.740253i	$0.734706\pi$
$684$	−2360.67	−0.131963
$685$	0	0
$686$	12486.3	0.694943
$687$	−14499.3	−0.805214
$688$	−8116.87	−0.449786
$689$	4026.23	0.222623
$690$	0	0
$691$	9627.58	0.530030	0.265015	−	0.964244i	$-0.414623\pi$
$691$	9627.58	0.530030	0.265015	+	0.964244i	$0.414623\pi$
$692$	2802.05	0.153927
$693$	−420.192	−0.0230328
$694$	−2405.98	−0.131599
$695$	0	0
$696$	5193.70	0.282854
$697$	461.324	0.0250702
$698$	9147.37	0.496036
$699$	−9976.12	−0.539816
$700$	0	0
$701$	11750.7	0.633121	0.316561	−	0.948572i	$-0.397472\pi$
$701$	11750.7	0.633121	0.316561	+	0.948572i	$0.397472\pi$
$702$	5131.78	0.275907
$703$	−5544.36	−0.297453
$704$	−384.000	−0.0205576
$705$	0	0
$706$	−1949.48	−0.103923
$707$	−3021.98	−0.160754
$708$	−1147.01	−0.0608860
$709$	1045.77	0.0553946	0.0276973	−	0.999616i	$-0.491183\pi$
$709$	1045.77	0.0553946	0.0276973	+	0.999616i	$0.491183\pi$
$710$	0	0
$711$	−316.255	−0.0166814
$712$	−7568.83	−0.398390
$713$	−6584.17	−0.345833
$714$	943.103	0.0494324
$715$	0	0
$716$	15218.3	0.794323
$717$	9751.66	0.507925
$718$	9744.92	0.506514
$719$	9367.97	0.485906	0.242953	−	0.970038i	$-0.421884\pi$
$719$	9367.97	0.485906	0.242953	+	0.970038i	$0.421884\pi$
$720$	0	0
$721$	6762.62	0.349311
$722$	−3744.08	−0.192992
$723$	−18210.7	−0.936741
$724$	14640.4	0.751529
$725$	0	0
$726$	−14949.5	−0.764225
$727$	24447.9	1.24721	0.623605	−	0.781740i	$-0.285668\pi$
$727$	24447.9	1.24721	0.623605	+	0.781740i	$0.285668\pi$
$728$	1906.43	0.0970563
$729$	13176.4	0.669432
$730$	0	0
$731$	−3737.81	−0.189122
$732$	17980.4	0.907888
$733$	−24144.2	−1.21662	−0.608312	−	0.793698i	$-0.708153\pi$
$733$	−24144.2	−1.21662	−0.608312	+	0.793698i	$0.708153\pi$
$734$	23017.5	1.15748
$735$	0	0
$736$	736.000	0.0368605
$737$	−3967.39	−0.198291
$738$	−790.915	−0.0394498
$739$	10006.7	0.498108	0.249054	−	0.968490i	$-0.419880\pi$
$739$	10006.7	0.498108	0.249054	+	0.968490i	$0.419880\pi$
$740$	0	0
$741$	−11591.4	−0.574658
$742$	4154.37	0.205541
$743$	7313.96	0.361135	0.180567	−	0.983563i	$-0.442207\pi$
$743$	7313.96	0.361135	0.180567	+	0.983563i	$0.442207\pi$
$744$	13218.7	0.651373
$745$	0	0
$746$	−7978.03	−0.391550
$747$	−5097.12	−0.249657
$748$	−176.832	−0.00864386
$749$	2353.32	0.114804
$750$	0	0
$751$	−3297.61	−0.160228	−0.0801141	−	0.996786i	$-0.525528\pi$
$751$	−3297.61	−0.160228	−0.0801141	+	0.996786i	$0.525528\pi$
$752$	−8580.80	−0.416103
$753$	−36605.6	−1.77156
$754$	4834.68	0.233513
$755$	0	0
$756$	5295.10	0.254737
$757$	23745.7	1.14009	0.570047	−	0.821612i	$-0.306925\pi$
$757$	23745.7	1.14009	0.570047	+	0.821612i	$0.306925\pi$
$758$	−4383.92	−0.210068
$759$	−796.536	−0.0380928
$760$	0	0
$761$	25723.6	1.22533	0.612666	−	0.790342i	$-0.290097\pi$
$761$	25723.6	1.22533	0.612666	+	0.790342i	$0.290097\pi$
$762$	13303.6	0.632467
$763$	−14272.3	−0.677185
$764$	−7997.85	−0.378733
$765$	0	0
$766$	21318.9	1.00559
$767$	−1067.72	−0.0502649
$768$	−1477.63	−0.0694264
$769$	−36423.8	−1.70803	−0.854016	−	0.520246i	$-0.825840\pi$
$769$	−36423.8	−1.70803	−0.854016	+	0.520246i	$0.825840\pi$
$770$	0	0
$771$	−34381.1	−1.60597
$772$	−3519.54	−0.164082
$773$	20401.3	0.949265	0.474633	−	0.880184i	$-0.342581\pi$
$773$	20401.3	0.949265	0.474633	+	0.880184i	$0.342581\pi$
$774$	6408.27	0.297598
$775$	0	0
$776$	5724.23	0.264804
$777$	−3797.51	−0.175334
$778$	−17656.4	−0.813642
$779$	−5850.46	−0.269082
$780$	0	0
$781$	−1735.27	−0.0795044
$782$	338.927	0.0154987
$783$	13428.3	0.612884
$784$	−3520.90	−0.160391
$785$	0	0
$786$	−27340.5	−1.24072
$787$	−23639.8	−1.07073	−0.535367	−	0.844620i	$-0.679827\pi$
$787$	−23639.8	−1.07073	−0.535367	+	0.844620i	$0.679827\pi$
$788$	11043.2	0.499236
$789$	−41256.4	−1.86155
$790$	0	0
$791$	3474.27	0.156171
$792$	303.168	0.0136018
$793$	16737.5	0.749515
$794$	−8619.36	−0.385251
$795$	0	0
$796$	13508.8	0.601515
$797$	41015.8	1.82291	0.911453	−	0.411405i	$-0.134962\pi$
$797$	41015.8	1.82291	0.911453	+	0.411405i	$0.134962\pi$
$798$	−11960.3	−0.530565
$799$	−3951.45	−0.174959
$800$	0	0
$801$	5975.60	0.263592
$802$	−21301.0	−0.937862
$803$	−3907.90	−0.171739
$804$	−15266.5	−0.669663
$805$	0	0
$806$	12305.0	0.537747
$807$	−42901.7	−1.87139
$808$	2180.36	0.0949315
$809$	−30619.8	−1.33070	−0.665349	−	0.746532i	$-0.731717\pi$
$809$	−30619.8	−1.33070	−0.665349	+	0.746532i	$0.731717\pi$
$810$	0	0
$811$	−7000.16	−0.303093	−0.151547	−	0.988450i	$-0.548425\pi$
$811$	−7000.16	−0.303093	−0.151547	+	0.988450i	$0.548425\pi$
$812$	4988.54	0.215595
$813$	−18678.6	−0.805764
$814$	712.033	0.0306594
$815$	0	0
$816$	−680.449	−0.0291918
$817$	47402.5	2.02987
$818$	598.468	0.0255806
$819$	−1505.13	−0.0642166
$820$	0	0
$821$	31972.1	1.35912	0.679558	−	0.733621i	$-0.262171\pi$
$821$	31972.1	1.35912	0.679558	+	0.733621i	$0.262171\pi$
$822$	33159.5	1.40702
$823$	−6616.25	−0.280228	−0.140114	−	0.990135i	$-0.544747\pi$
$823$	−6616.25	−0.280228	−0.140114	+	0.990135i	$0.544747\pi$
$824$	−4879.23	−0.206282
$825$	0	0
$826$	−1101.70	−0.0464081
$827$	18261.5	0.767852	0.383926	−	0.923364i	$-0.374572\pi$
$827$	18261.5	0.767852	0.383926	+	0.923364i	$0.374572\pi$
$828$	−581.073	−0.0243885
$829$	16935.3	0.709513	0.354757	−	0.934959i	$-0.384564\pi$
$829$	16935.3	0.709513	0.354757	+	0.934959i	$0.384564\pi$
$830$	0	0
$831$	31386.8	1.31023
$832$	−1375.49	−0.0573155
$833$	−1621.37	−0.0674396
$834$	18900.3	0.784727
$835$	0	0
$836$	2242.56	0.0927758
$837$	34177.0	1.41139
$838$	19192.8	0.791174
$839$	11971.2	0.492598	0.246299	−	0.969194i	$-0.420785\pi$
$839$	11971.2	0.492598	0.246299	+	0.969194i	$0.420785\pi$
$840$	0	0
$841$	−11738.1	−0.481288
$842$	−28098.4	−1.15004
$843$	−1411.93	−0.0576863
$844$	−4288.77	−0.174912
$845$	0	0
$846$	6774.55	0.275312
$847$	−14359.0	−0.582503
$848$	−2997.38	−0.121380
$849$	−6064.95	−0.245169
$850$	0	0
$851$	−1364.73	−0.0549734
$852$	−6677.33	−0.268499
$853$	−14844.9	−0.595872	−0.297936	−	0.954586i	$-0.596298\pi$
$853$	−14844.9	−0.595872	−0.297936	+	0.954586i	$0.596298\pi$
$854$	17270.2	0.692005
$855$	0	0
$856$	−1697.92	−0.0677963
$857$	−45234.9	−1.80303	−0.901514	−	0.432751i	$-0.857543\pi$
$857$	−45234.9	−1.80303	−0.901514	+	0.432751i	$0.857543\pi$
$858$	1488.62	0.0592317
$859$	−43687.6	−1.73528	−0.867639	−	0.497195i	$-0.834363\pi$
$859$	−43687.6	−1.73528	−0.867639	+	0.497195i	$0.834363\pi$
$860$	0	0
$861$	−4007.16	−0.158611
$862$	10697.6	0.422692
$863$	−22267.6	−0.878331	−0.439165	−	0.898406i	$-0.644726\pi$
$863$	−22267.6	−0.878331	−0.439165	+	0.898406i	$0.644726\pi$
$864$	−3820.42	−0.150432
$865$	0	0
$866$	21454.4	0.841858
$867$	28044.5	1.09855
$868$	12696.6	0.496486
$869$	300.432	0.0117278
$870$	0	0
$871$	−14211.2	−0.552846
$872$	10297.5	0.399904
$873$	−4519.28	−0.175206
$874$	−4298.24	−0.166350
$875$	0	0
$876$	−15037.6	−0.579992
$877$	17550.1	0.675743	0.337871	−	0.941192i	$-0.390293\pi$
$877$	17550.1	0.675743	0.337871	+	0.941192i	$0.390293\pi$
$878$	2851.06	0.109588
$879$	32574.1	1.24994
$880$	0	0
$881$	−28114.7	−1.07515	−0.537577	−	0.843215i	$-0.680660\pi$
$881$	−28114.7	−1.07515	−0.537577	+	0.843215i	$0.680660\pi$
$882$	2779.75	0.106121
$883$	−46811.6	−1.78407	−0.892036	−	0.451964i	$-0.850723\pi$
$883$	−46811.6	−1.78407	−0.892036	+	0.451964i	$0.850723\pi$
$884$	−633.412	−0.0240995
$885$	0	0
$886$	−27171.2	−1.03029
$887$	−1604.14	−0.0607234	−0.0303617	−	0.999539i	$-0.509666\pi$
$887$	−1604.14	−0.0607234	−0.0303617	+	0.999539i	$0.509666\pi$
$888$	2739.90	0.103542
$889$	12778.1	0.482075
$890$	0	0
$891$	5157.84	0.193933
$892$	−5979.52	−0.224450
$893$	50111.9	1.87786
$894$	36079.6	1.34976
$895$	0	0
$896$	−1419.26	−0.0529178
$897$	−2853.20	−0.106204
$898$	−32943.2	−1.22420
$899$	32198.3	1.19452
$900$	0	0
$901$	−1380.29	−0.0510368
$902$	751.343	0.0277350
$903$	32467.5	1.19651
$904$	−2506.69	−0.0922248
$905$	0	0
$906$	−4276.31	−0.156811
$907$	1200.10	0.0439345	0.0219672	−	0.999759i	$-0.493007\pi$
$907$	1200.10	0.0439345	0.0219672	+	0.999759i	$0.493007\pi$
$908$	−10856.0	−0.396773
$909$	−1721.39	−0.0628108
$910$	0	0
$911$	34847.5	1.26734	0.633672	−	0.773602i	$-0.281547\pi$
$911$	34847.5	1.26734	0.633672	+	0.773602i	$0.281547\pi$
$912$	8629.38	0.313319
$913$	4842.10	0.175520
$914$	2065.75	0.0747580
$915$	0	0
$916$	10048.0	0.362441
$917$	−26260.5	−0.945692
$918$	−1759.30	−0.0632522
$919$	−44895.1	−1.61148	−0.805741	−	0.592268i	$-0.798233\pi$
$919$	−44895.1	−1.61148	−0.805741	+	0.592268i	$0.798233\pi$
$920$	0	0
$921$	33919.4	1.21355
$922$	−478.873	−0.0171050
$923$	−6215.75	−0.221662
$924$	1536.00	0.0546869
$925$	0	0
$926$	−33192.7	−1.17795
$927$	3852.16	0.136485
$928$	−3599.23	−0.127318
$929$	17783.9	0.628063	0.314032	−	0.949413i	$-0.398320\pi$
$929$	17783.9	0.628063	0.314032	+	0.949413i	$0.398320\pi$
$930$	0	0
$931$	20562.0	0.723839
$932$	6913.46	0.242981
$933$	−50493.5	−1.77179
$934$	20503.5	0.718303
$935$	0	0
$936$	1085.95	0.0379224
$937$	25058.9	0.873682	0.436841	−	0.899539i	$-0.356097\pi$
$937$	25058.9	0.873682	0.436841	+	0.899539i	$0.356097\pi$
$938$	−14663.5	−0.510426
$939$	−29029.8	−1.00889
$940$	0	0
$941$	29903.4	1.03594	0.517972	−	0.855398i	$-0.326687\pi$
$941$	29903.4	1.03594	0.517972	+	0.855398i	$0.326687\pi$
$942$	23012.3	0.795946
$943$	−1440.07	−0.0497299
$944$	794.878	0.0274058
$945$	0	0
$946$	−6087.65	−0.209225
$947$	−17921.2	−0.614952	−0.307476	−	0.951556i	$-0.599484\pi$
$947$	−17921.2	−0.614952	−0.307476	+	0.951556i	$0.599484\pi$
$948$	1156.06	0.0396068
$949$	−13998.1	−0.478817
$950$	0	0
$951$	−41556.3	−1.41699
$952$	−653.571	−0.0222504
$953$	−31122.3	−1.05787	−0.528935	−	0.848662i	$-0.677408\pi$
$953$	−31122.3	−1.05787	−0.528935	+	0.848662i	$0.677408\pi$
$954$	2366.43	0.0803103
$955$	0	0
$956$	−6757.91	−0.228626
$957$	3895.27	0.131574
$958$	8061.99	0.271890
$959$	31849.6	1.07245
$960$	0	0
$961$	52158.4	1.75081
$962$	2550.50	0.0854798
$963$	1340.51	0.0448570
$964$	12620.0	0.421643
$965$	0	0
$966$	−2944.00	−0.0980555
$967$	−6627.78	−0.220409	−0.110204	−	0.993909i	$-0.535151\pi$
$967$	−6627.78	−0.220409	−0.110204	+	0.993909i	$0.535151\pi$
$968$	10360.0	0.343991
$969$	3973.82	0.131742
$970$	0	0
$971$	38645.1	1.27722	0.638609	−	0.769531i	$-0.279510\pi$
$971$	38645.1	1.27722	0.638609	+	0.769531i	$0.279510\pi$
$972$	6953.47	0.229457
$973$	18153.7	0.598130
$974$	12109.9	0.398383
$975$	0	0
$976$	−12460.4	−0.408656
$977$	14137.0	0.462930	0.231465	−	0.972843i	$-0.425648\pi$
$977$	14137.0	0.462930	0.231465	+	0.972843i	$0.425648\pi$
$978$	−19879.9	−0.649990
$979$	−5676.62	−0.185317
$980$	0	0
$981$	−8129.87	−0.264594
$982$	39728.9	1.29104
$983$	−32966.5	−1.06965	−0.534825	−	0.844963i	$-0.679623\pi$
$983$	−32966.5	−1.06965	−0.534825	+	0.844963i	$0.679623\pi$
$984$	2891.17	0.0936658
$985$	0	0
$986$	−1657.44	−0.0535333
$987$	34323.2	1.10691
$988$	8032.86	0.258663
$989$	11668.0	0.375147
$990$	0	0
$991$	47592.2	1.52555	0.762774	−	0.646666i	$-0.223837\pi$
$991$	47592.2	1.52555	0.762774	+	0.646666i	$0.223837\pi$
$992$	−9160.58	−0.293194
$993$	4456.52	0.142420
$994$	−6413.57	−0.204654
$995$	0	0
$996$	18632.4	0.592761
$997$	−11153.1	−0.354285	−0.177142	−	0.984185i	$-0.556685\pi$
$997$	−11153.1	−0.354285	−0.177142	+	0.984185i	$0.556685\pi$
$998$	24257.8	0.769407
$999$	7084.02	0.224353

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.4.a.j.1.1		2
5.2	odd	4		1150.4.b.j.599.2		4
5.3	odd	4		1150.4.b.j.599.3		4
5.4	even	2		46.4.a.d.1.2	✓	2
15.14	odd	2		414.4.a.f.1.2		2
20.19	odd	2		368.4.a.f.1.1		2
35.34	odd	2		2254.4.a.f.1.1		2
40.19	odd	2		1472.4.a.n.1.2		2
40.29	even	2		1472.4.a.k.1.1		2
115.114	odd	2		1058.4.a.j.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.4.a.d.1.2	✓	2	5.4	even	2
368.4.a.f.1.1		2	20.19	odd	2
414.4.a.f.1.2		2	15.14	odd	2
1058.4.a.j.1.2		2	115.114	odd	2
1150.4.a.j.1.1		2	1.1	even	1	trivial
1150.4.b.j.599.2		4	5.2	odd	4
1150.4.b.j.599.3		4	5.3	odd	4
1472.4.a.k.1.1		2	40.29	even	2
1472.4.a.n.1.2		2	40.19	odd	2
2254.4.a.f.1.1		2	35.34	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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -5.77200 q^{3} +4.00000 q^{4} +11.5440 q^{6} +11.0880 q^{7} -8.00000 q^{8} +6.31601 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -5.77200 q^{3} +4.00000 q^{4} +11.5440 q^{6} +11.0880 q^{7} -8.00000 q^{8} +6.31601 q^{9} -6.00000 q^{11} -23.0880 q^{12} -21.4920 q^{13} -22.1760 q^{14} +16.0000 q^{16} +7.36799 q^{17} -12.6320 q^{18} -93.4400 q^{19} -64.0000 q^{21} +12.0000 q^{22} -23.0000 q^{23} +46.1760 q^{24} +42.9840 q^{26} +119.388 q^{27} +44.3520 q^{28} +112.476 q^{29} +286.268 q^{31} -32.0000 q^{32} +34.6320 q^{33} -14.7360 q^{34} +25.2640 q^{36} +59.3361 q^{37} +186.880 q^{38} +124.052 q^{39} +62.6119 q^{41} +128.000 q^{42} -507.304 q^{43} -24.0000 q^{44} +46.0000 q^{46} -536.300 q^{47} -92.3520 q^{48} -220.056 q^{49} -42.5280 q^{51} -85.9681 q^{52} -187.336 q^{53} -238.776 q^{54} -88.7041 q^{56} +539.336 q^{57} -224.952 q^{58} +49.6799 q^{59} -778.776 q^{61} -572.536 q^{62} +70.0319 q^{63} +64.0000 q^{64} -69.2640 q^{66} +661.232 q^{67} +29.4720 q^{68} +132.756 q^{69} +289.212 q^{71} -50.5280 q^{72} +651.316 q^{73} -118.672 q^{74} -373.760 q^{76} -66.5280 q^{77} -248.104 q^{78} -50.0720 q^{79} -859.640 q^{81} -125.224 q^{82} -807.016 q^{83} -256.000 q^{84} +1014.61 q^{86} -649.212 q^{87} +48.0000 q^{88} +946.104 q^{89} -238.304 q^{91} -92.0000 q^{92} -1652.34 q^{93} +1072.60 q^{94} +184.704 q^{96} -715.529 q^{97} +440.112 q^{98} -37.8960 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} - 3 q^{3} + 8 q^{4} + 6 q^{6} - 12 q^{7} - 16 q^{8} - 13 q^{9}+O(q^{10}) \) 2 * q - 4 * q^2 - 3 * q^3 + 8 * q^4 + 6 * q^6 - 12 * q^7 - 16 * q^8 - 13 * q^9	\( 2 q - 4 q^{2} - 3 q^{3} + 8 q^{4} + 6 q^{6} - 12 q^{7} - 16 q^{8} - 13 q^{9} - 12 q^{11} - 12 q^{12} + 51 q^{13} + 24 q^{14} + 32 q^{16} + 66 q^{17} + 26 q^{18} - 16 q^{19} - 128 q^{21} + 24 q^{22} - 46 q^{23} + 24 q^{24} - 102 q^{26} - 9 q^{27} - 48 q^{28} - 57 q^{29} - 17 q^{31} - 64 q^{32} + 18 q^{33} - 132 q^{34} - 52 q^{36} - 206 q^{37} + 32 q^{38} + 325 q^{39} + 373 q^{41} + 256 q^{42} - 314 q^{43} - 48 q^{44} + 92 q^{46} - 859 q^{47} - 48 q^{48} - 30 q^{49} + 120 q^{51} + 204 q^{52} - 50 q^{53} + 18 q^{54} + 96 q^{56} + 754 q^{57} + 114 q^{58} + 612 q^{59} - 1062 q^{61} + 34 q^{62} + 516 q^{63} + 128 q^{64} - 36 q^{66} + 844 q^{67} + 264 q^{68} + 69 q^{69} + 399 q^{71} + 104 q^{72} + 1277 q^{73} + 412 q^{74} - 64 q^{76} + 72 q^{77} - 650 q^{78} + 122 q^{79} - 694 q^{81} - 746 q^{82} - 1802 q^{83} - 512 q^{84} + 628 q^{86} - 1119 q^{87} + 96 q^{88} + 2046 q^{89} - 1912 q^{91} - 184 q^{92} - 2493 q^{93} + 1718 q^{94} + 96 q^{96} + 910 q^{97} + 60 q^{98} + 78 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 3 * q^3 + 8 * q^4 + 6 * q^6 - 12 * q^7 - 16 * q^8 - 13 * q^9 - 12 * q^11 - 12 * q^12 + 51 * q^13 + 24 * q^14 + 32 * q^16 + 66 * q^17 + 26 * q^18 - 16 * q^19 - 128 * q^21 + 24 * q^22 - 46 * q^23 + 24 * q^24 - 102 * q^26 - 9 * q^27 - 48 * q^28 - 57 * q^29 - 17 * q^31 - 64 * q^32 + 18 * q^33 - 132 * q^34 - 52 * q^36 - 206 * q^37 + 32 * q^38 + 325 * q^39 + 373 * q^41 + 256 * q^42 - 314 * q^43 - 48 * q^44 + 92 * q^46 - 859 * q^47 - 48 * q^48 - 30 * q^49 + 120 * q^51 + 204 * q^52 - 50 * q^53 + 18 * q^54 + 96 * q^56 + 754 * q^57 + 114 * q^58 + 612 * q^59 - 1062 * q^61 + 34 * q^62 + 516 * q^63 + 128 * q^64 - 36 * q^66 + 844 * q^67 + 264 * q^68 + 69 * q^69 + 399 * q^71 + 104 * q^72 + 1277 * q^73 + 412 * q^74 - 64 * q^76 + 72 * q^77 - 650 * q^78 + 122 * q^79 - 694 * q^81 - 746 * q^82 - 1802 * q^83 - 512 * q^84 + 628 * q^86 - 1119 * q^87 + 96 * q^88 + 2046 * q^89 - 1912 * q^91 - 184 * q^92 - 2493 * q^93 + 1718 * q^94 + 96 * q^96 + 910 * q^97 + 60 * q^98 + 78 * q^99

Introduction

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