LMFDB - Embedded newform 1875.4.a.f.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,4,Mod(1,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, 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("1875.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1875.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:	$110.628581261$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 81 x^{12} - 7 x^{11} + 2512 x^{10} + 517 x^{9} - 36970 x^{8} - 12987 x^{7} + 257291 x^{6} + \cdots + 42064 $ x^14 - 81x^12 - 7x^11 + 2512x^10 + 517x^9 - 36970x^8 - 12987x^7 + 257291x^6 + 125779x^5 - 718713x^4 - 371750x^3 + 579848x^2 + 394896x + 42064
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 5^{3} $
Twist minimal:	no (minimal twist has level 75)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$-4.79301$ of defining polynomial
Character	$\chi$	$=$	1875.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.79301 q^{2} -3.00000 q^{3} +14.9730 q^{4} -14.3790 q^{6} -0.140520 q^{7} +33.4216 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.79301 q^{2} -3.00000 q^{3} +14.9730 q^{4} -14.3790 q^{6} -0.140520 q^{7} +33.4216 q^{8} +9.00000 q^{9} +47.3504 q^{11} -44.9190 q^{12} -34.3424 q^{13} -0.673515 q^{14} +40.4065 q^{16} -16.5164 q^{17} +43.1371 q^{18} +91.0020 q^{19} +0.421560 q^{21} +226.951 q^{22} +161.582 q^{23} -100.265 q^{24} -164.604 q^{26} -27.0000 q^{27} -2.10400 q^{28} -12.3327 q^{29} -333.038 q^{31} -73.7042 q^{32} -142.051 q^{33} -79.1633 q^{34} +134.757 q^{36} +281.402 q^{37} +436.174 q^{38} +103.027 q^{39} +125.610 q^{41} +2.02054 q^{42} +529.821 q^{43} +708.977 q^{44} +774.463 q^{46} -75.0713 q^{47} -121.220 q^{48} -342.980 q^{49} +49.5492 q^{51} -514.208 q^{52} +249.426 q^{53} -129.411 q^{54} -4.69641 q^{56} -273.006 q^{57} -59.1108 q^{58} -268.564 q^{59} +369.848 q^{61} -1596.26 q^{62} -1.26468 q^{63} -676.517 q^{64} -680.854 q^{66} +176.506 q^{67} -247.300 q^{68} -484.745 q^{69} +722.104 q^{71} +300.795 q^{72} +2.44271 q^{73} +1348.77 q^{74} +1362.57 q^{76} -6.65368 q^{77} +493.811 q^{78} +607.662 q^{79} +81.0000 q^{81} +602.049 q^{82} +1268.55 q^{83} +6.31201 q^{84} +2539.44 q^{86} +36.9981 q^{87} +1582.53 q^{88} -1337.53 q^{89} +4.82579 q^{91} +2419.36 q^{92} +999.114 q^{93} -359.818 q^{94} +221.113 q^{96} +1431.21 q^{97} -1643.91 q^{98} +426.154 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 42 q^{3} + 50 q^{4} + 27 q^{7} - 21 q^{8} + 126 q^{9}+O(q^{10}) $ 14 * q - 42 * q^3 + 50 * q^4 + 27 * q^7 - 21 * q^8 + 126 * q^9	$ 14 q - 42 q^{3} + 50 q^{4} + 27 q^{7} - 21 q^{8} + 126 q^{9} - 33 q^{11} - 150 q^{12} + 188 q^{13} - 287 q^{14} + 82 q^{16} + 146 q^{17} - 184 q^{19} - 81 q^{21} + 277 q^{22} + 164 q^{23} + 63 q^{24} + 103 q^{26} - 378 q^{27} - 224 q^{28} + 252 q^{29} - 889 q^{31} + 422 q^{32} + 99 q^{33} - 230 q^{34} + 450 q^{36} + 642 q^{37} + 1833 q^{38} - 564 q^{39} - 164 q^{41} + 861 q^{42} + 696 q^{43} - 6 q^{44} - 419 q^{46} - 92 q^{47} - 246 q^{48} + 81 q^{49} - 438 q^{51} + 1956 q^{52} + 949 q^{53} - 2380 q^{56} + 552 q^{57} + 1041 q^{58} - 81 q^{59} - 496 q^{61} + 1454 q^{62} + 243 q^{63} - 3903 q^{64} - 831 q^{66} + 1926 q^{67} + 685 q^{68} - 492 q^{69} + 2498 q^{71} - 189 q^{72} - 1026 q^{73} - 707 q^{74} - 5704 q^{76} + 5434 q^{77} - 309 q^{78} - 695 q^{79} + 1134 q^{81} - 886 q^{82} + 5315 q^{83} + 672 q^{84} + 3997 q^{86} - 756 q^{87} + 2969 q^{88} - 1424 q^{89} - 1194 q^{91} + 1607 q^{92} + 2667 q^{93} - 629 q^{94} - 1266 q^{96} + 291 q^{97} - 1018 q^{98} - 297 q^{99}+O(q^{100}) $ 14 * q - 42 * q^3 + 50 * q^4 + 27 * q^7 - 21 * q^8 + 126 * q^9 - 33 * q^11 - 150 * q^12 + 188 * q^13 - 287 * q^14 + 82 * q^16 + 146 * q^17 - 184 * q^19 - 81 * q^21 + 277 * q^22 + 164 * q^23 + 63 * q^24 + 103 * q^26 - 378 * q^27 - 224 * q^28 + 252 * q^29 - 889 * q^31 + 422 * q^32 + 99 * q^33 - 230 * q^34 + 450 * q^36 + 642 * q^37 + 1833 * q^38 - 564 * q^39 - 164 * q^41 + 861 * q^42 + 696 * q^43 - 6 * q^44 - 419 * q^46 - 92 * q^47 - 246 * q^48 + 81 * q^49 - 438 * q^51 + 1956 * q^52 + 949 * q^53 - 2380 * q^56 + 552 * q^57 + 1041 * q^58 - 81 * q^59 - 496 * q^61 + 1454 * q^62 + 243 * q^63 - 3903 * q^64 - 831 * q^66 + 1926 * q^67 + 685 * q^68 - 492 * q^69 + 2498 * q^71 - 189 * q^72 - 1026 * q^73 - 707 * q^74 - 5704 * q^76 + 5434 * q^77 - 309 * q^78 - 695 * q^79 + 1134 * q^81 - 886 * q^82 + 5315 * q^83 + 672 * q^84 + 3997 * q^86 - 756 * q^87 + 2969 * q^88 - 1424 * q^89 - 1194 * q^91 + 1607 * q^92 + 2667 * q^93 - 629 * q^94 - 1266 * q^96 + 291 * q^97 - 1018 * q^98 - 297 * 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 $

$2$	4.79301	1.69459	0.847293	−	0.531125i	$-0.178231\pi$
$2$	4.79301	1.69459	0.847293	+	0.531125i	$0.178231\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	14.9730	1.87162
$5$	0	0
$5$	0	0
$6$	−14.3790	−0.978370
$7$	−0.140520	−0.00758737	−0.00379368	−	0.999993i	$-0.501208\pi$
$7$	−0.140520	−0.00758737	−0.00379368	+	0.999993i	$0.501208\pi$
$8$	33.4216	1.47704
$9$	9.00000	0.333333
$10$	0	0
$11$	47.3504	1.29788	0.648940	−	0.760839i	$-0.275212\pi$
$11$	47.3504	1.29788	0.648940	+	0.760839i	$0.275212\pi$
$12$	−44.9190	−1.08058
$13$	−34.3424	−0.732682	−0.366341	−	0.930481i	$-0.619390\pi$
$13$	−34.3424	−0.732682	−0.366341	+	0.930481i	$0.619390\pi$
$14$	−0.673515	−0.0128575
$15$	0	0
$16$	40.4065	0.631352
$17$	−16.5164	−0.235636	−0.117818	−	0.993035i	$-0.537590\pi$
$17$	−16.5164	−0.235636	−0.117818	+	0.993035i	$0.537590\pi$
$18$	43.1371	0.564862
$19$	91.0020	1.09881	0.549403	−	0.835558i	$-0.314855\pi$
$19$	91.0020	1.09881	0.549403	+	0.835558i	$0.314855\pi$
$20$	0	0
$21$	0.421560	0.00438057
$22$	226.951	2.19937
$23$	161.582	1.46487	0.732436	−	0.680835i	$-0.238383\pi$
$23$	161.582	1.46487	0.732436	+	0.680835i	$0.238383\pi$
$24$	−100.265	−0.852771
$25$	0	0
$26$	−164.604	−1.24159
$27$	−27.0000	−0.192450
$28$	−2.10400	−0.0142007
$29$	−12.3327	−0.0789698	−0.0394849	−	0.999220i	$-0.512572\pi$
$29$	−12.3327	−0.0789698	−0.0394849	+	0.999220i	$0.512572\pi$
$30$	0	0
$31$	−333.038	−1.92953	−0.964765	−	0.263115i	$-0.915250\pi$
$31$	−333.038	−1.92953	−0.964765	+	0.263115i	$0.915250\pi$
$32$	−73.7042	−0.407162
$33$	−142.051	−0.749332
$34$	−79.1633	−0.399306
$35$	0	0
$36$	134.757	0.623875
$37$	281.402	1.25033	0.625166	−	0.780492i	$-0.285031\pi$
$37$	281.402	1.25033	0.625166	+	0.780492i	$0.285031\pi$
$38$	436.174	1.86202
$39$	103.027	0.423014
$40$	0	0
$41$	125.610	0.478462	0.239231	−	0.970963i	$-0.423105\pi$
$41$	125.610	0.478462	0.239231	+	0.970963i	$0.423105\pi$
$42$	2.02054	0.00742325
$43$	529.821	1.87900	0.939500	−	0.342549i	$-0.111290\pi$
$43$	529.821	1.87900	0.939500	+	0.342549i	$0.111290\pi$
$44$	708.977	2.42914
$45$	0	0
$46$	774.463	2.48235
$47$	−75.0713	−0.232985	−0.116492	−	0.993192i	$-0.537165\pi$
$47$	−75.0713	−0.232985	−0.116492	+	0.993192i	$0.537165\pi$
$48$	−121.220	−0.364511
$49$	−342.980	−0.999942
$50$	0	0
$51$	49.5492	0.136045
$52$	−514.208	−1.37130
$53$	249.426	0.646438	0.323219	−	0.946324i	$-0.395235\pi$
$53$	249.426	0.646438	0.323219	+	0.946324i	$0.395235\pi$
$54$	−129.411	−0.326123
$55$	0	0
$56$	−4.69641	−0.0112069
$57$	−273.006	−0.634395
$58$	−59.1108	−0.133821
$59$	−268.564	−0.592611	−0.296305	−	0.955093i	$-0.595755\pi$
$59$	−268.564	−0.592611	−0.296305	+	0.955093i	$0.595755\pi$
$60$	0	0
$61$	369.848	0.776297	0.388149	−	0.921597i	$-0.373115\pi$
$61$	369.848	0.776297	0.388149	+	0.921597i	$0.373115\pi$
$62$	−1596.26	−3.26975
$63$	−1.26468	−0.00252912
$64$	−676.517	−1.32132
$65$	0	0
$66$	−680.854	−1.26981
$67$	176.506	0.321846	0.160923	−	0.986967i	$-0.448553\pi$
$67$	176.506	0.321846	0.160923	+	0.986967i	$0.448553\pi$
$68$	−247.300	−0.441022
$69$	−484.745	−0.845745
$70$	0	0
$71$	722.104	1.20701	0.603507	−	0.797358i	$-0.293770\pi$
$71$	722.104	1.20701	0.603507	+	0.797358i	$0.293770\pi$
$72$	300.795	0.492347
$73$	2.44271	0.00391641	0.00195820	−	0.999998i	$-0.499377\pi$
$73$	2.44271	0.00391641	0.00195820	+	0.999998i	$0.499377\pi$
$74$	1348.77	2.11879
$75$	0	0
$76$	1362.57	2.05655
$77$	−6.65368	−0.00984750
$78$	493.811	0.716834
$79$	607.662	0.865409	0.432705	−	0.901536i	$-0.357559\pi$
$79$	607.662	0.865409	0.432705	+	0.901536i	$0.357559\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	602.049	0.810795
$83$	1268.55	1.67761	0.838807	−	0.544429i	$-0.183253\pi$
$83$	1268.55	1.67761	0.838807	+	0.544429i	$0.183253\pi$
$84$	6.31201	0.00819878
$85$	0	0
$86$	2539.44	3.18413
$87$	36.9981	0.0455933
$88$	1582.53	1.91702
$89$	−1337.53	−1.59301	−0.796507	−	0.604629i	$-0.793321\pi$
$89$	−1337.53	−1.59301	−0.796507	+	0.604629i	$0.793321\pi$
$90$	0	0
$91$	4.82579	0.00555913
$92$	2419.36	2.74169
$93$	999.114	1.11401
$94$	−359.818	−0.394812
$95$	0	0
$96$	221.113	0.235075
$97$	1431.21	1.49812	0.749059	−	0.662503i	$-0.230506\pi$
$97$	1431.21	1.49812	0.749059	+	0.662503i	$0.230506\pi$
$98$	−1643.91	−1.69449
$99$	426.154	0.432627
$100$	0	0
$101$	−374.102	−0.368559	−0.184280	−	0.982874i	$-0.558995\pi$
$101$	−374.102	−0.368559	−0.184280	+	0.982874i	$0.558995\pi$
$102$	237.490	0.230539
$103$	2017.87	1.93035	0.965177	−	0.261597i	$-0.0842493\pi$
$103$	2017.87	1.93035	0.965177	+	0.261597i	$0.0842493\pi$
$104$	−1147.78	−1.08220
$105$	0	0
$106$	1195.50	1.09545
$107$	−1679.71	−1.51761	−0.758804	−	0.651319i	$-0.774216\pi$
$107$	−1679.71	−1.51761	−0.758804	+	0.651319i	$0.774216\pi$
$108$	−404.271	−0.360194
$109$	20.2283	0.0177754	0.00888772	−	0.999961i	$-0.497171\pi$
$109$	20.2283	0.0177754	0.00888772	+	0.999961i	$0.497171\pi$
$110$	0	0
$111$	−844.207	−0.721879
$112$	−5.67792	−0.00479030
$113$	642.520	0.534896	0.267448	−	0.963572i	$-0.413820\pi$
$113$	642.520	0.534896	0.267448	+	0.963572i	$0.413820\pi$
$114$	−1308.52	−1.07504
$115$	0	0
$116$	−184.657	−0.147802
$117$	−309.081	−0.244227
$118$	−1287.23	−1.00423
$119$	2.32088	0.00178786
$120$	0	0
$121$	911.063	0.684495
$122$	1772.69	1.31550
$123$	−376.829	−0.276240
$124$	−4986.58	−3.61135
$125$	0	0
$126$	−6.06163	−0.00428582
$127$	1185.91	0.828603	0.414302	−	0.910140i	$-0.364026\pi$
$127$	1185.91	0.828603	0.414302	+	0.910140i	$0.364026\pi$
$128$	−2652.92	−1.83193
$129$	−1589.46	−1.08484
$130$	0	0
$131$	−223.094	−0.148793	−0.0743963	−	0.997229i	$-0.523703\pi$
$131$	−223.094	−0.148793	−0.0743963	+	0.997229i	$0.523703\pi$
$132$	−2126.93	−1.40247
$133$	−12.7876	−0.00833704
$134$	845.997	0.545396
$135$	0	0
$136$	−552.005	−0.348045
$137$	1579.55	0.985035	0.492517	−	0.870303i	$-0.336077\pi$
$137$	1579.55	0.985035	0.492517	+	0.870303i	$0.336077\pi$
$138$	−2323.39	−1.43319
$139$	1565.25	0.955128	0.477564	−	0.878597i	$-0.341520\pi$
$139$	1565.25	0.955128	0.477564	+	0.878597i	$0.341520\pi$
$140$	0	0
$141$	225.214	0.134514
$142$	3461.05	2.04539
$143$	−1626.13	−0.950934
$144$	363.659	0.210451
$145$	0	0
$146$	11.7080	0.00663669
$147$	1028.94	0.577317
$148$	4213.43	2.34015
$149$	192.635	0.105915	0.0529574	−	0.998597i	$-0.483135\pi$
$149$	192.635	0.105915	0.0529574	+	0.998597i	$0.483135\pi$
$150$	0	0
$151$	1052.83	0.567406	0.283703	−	0.958912i	$-0.408437\pi$
$151$	1052.83	0.567406	0.283703	+	0.958912i	$0.408437\pi$
$152$	3041.44	1.62298
$153$	−148.648	−0.0785454
$154$	−31.8912	−0.0166874
$155$	0	0
$156$	1542.62	0.791723
$157$	−2045.26	−1.03968	−0.519838	−	0.854265i	$-0.674008\pi$
$157$	−2045.26	−1.03968	−0.519838	+	0.854265i	$0.674008\pi$
$158$	2912.53	1.46651
$159$	−748.277	−0.373221
$160$	0	0
$161$	−22.7054	−0.0111145
$162$	388.234	0.188287
$163$	−848.013	−0.407494	−0.203747	−	0.979024i	$-0.565312\pi$
$163$	−848.013	−0.407494	−0.203747	+	0.979024i	$0.565312\pi$
$164$	1880.75	0.895500
$165$	0	0
$166$	6080.20	2.84286
$167$	−1972.45	−0.913968	−0.456984	−	0.889475i	$-0.651070\pi$
$167$	−1972.45	−0.913968	−0.456984	+	0.889475i	$0.651070\pi$
$168$	14.0892	0.00647028
$169$	−1017.60	−0.463177
$170$	0	0
$171$	819.018	0.366268
$172$	7933.01	3.51678
$173$	−2707.65	−1.18993	−0.594967	−	0.803750i	$-0.702835\pi$
$173$	−2707.65	−1.18993	−0.594967	+	0.803750i	$0.702835\pi$
$174$	177.332	0.0772617
$175$	0	0
$176$	1913.26	0.819419
$177$	805.692	0.342144
$178$	−6410.82	−2.69950
$179$	3132.25	1.30791	0.653953	−	0.756535i	$-0.273109\pi$
$179$	3132.25	1.30791	0.653953	+	0.756535i	$0.273109\pi$
$180$	0	0
$181$	317.051	0.130200	0.0651000	−	0.997879i	$-0.479263\pi$
$181$	317.051	0.130200	0.0651000	+	0.997879i	$0.479263\pi$
$182$	23.1301	0.00942042
$183$	−1109.54	−0.448195
$184$	5400.32	2.16368
$185$	0	0
$186$	4788.77	1.88779
$187$	−782.059	−0.305828
$188$	−1124.04	−0.436059
$189$	3.79404	0.00146019
$190$	0	0
$191$	1679.46	0.636237	0.318119	−	0.948051i	$-0.396949\pi$
$191$	1679.46	0.636237	0.318119	+	0.948051i	$0.396949\pi$
$192$	2029.55	0.762866
$193$	1449.62	0.540653	0.270326	−	0.962769i	$-0.412868\pi$
$193$	1449.62	0.540653	0.270326	+	0.962769i	$0.412868\pi$
$194$	6859.82	2.53869
$195$	0	0
$196$	−5135.44	−1.87152
$197$	1060.62	0.383586	0.191793	−	0.981435i	$-0.438570\pi$
$197$	1060.62	0.383586	0.191793	+	0.981435i	$0.438570\pi$
$198$	2042.56	0.733124
$199$	−183.077	−0.0652159	−0.0326080	−	0.999468i	$-0.510381\pi$
$199$	−183.077	−0.0652159	−0.0326080	+	0.999468i	$0.510381\pi$
$200$	0	0
$201$	−529.519	−0.185818
$202$	−1793.07	−0.624556
$203$	1.73299	0.000599173 0
$204$	741.900	0.254624
$205$	0	0
$206$	9671.67	3.27115
$207$	1454.23	0.488291
$208$	−1387.66	−0.462580
$209$	4308.98	1.42612
$210$	0	0
$211$	−4904.73	−1.60026	−0.800131	−	0.599825i	$-0.795237\pi$
$211$	−4904.73	−1.60026	−0.800131	+	0.599825i	$0.795237\pi$
$212$	3734.65	1.20989
$213$	−2166.31	−0.696870
$214$	−8050.90	−2.57172
$215$	0	0
$216$	−902.384	−0.284257
$217$	46.7985	0.0146400
$218$	96.9547	0.0301220
$219$	−7.32813	−0.00226114
$220$	0	0
$221$	567.212	0.172646
$222$	−4046.30	−1.22329
$223$	4837.42	1.45263	0.726317	−	0.687360i	$-0.241230\pi$
$223$	4837.42	1.45263	0.726317	+	0.687360i	$0.241230\pi$
$224$	10.3569	0.00308929
$225$	0	0
$226$	3079.61	0.906428
$227$	44.8176	0.0131042	0.00655209	−	0.999979i	$-0.497914\pi$
$227$	44.8176	0.0131042	0.00655209	+	0.999979i	$0.497914\pi$
$228$	−4087.72	−1.18735
$229$	−4159.78	−1.20038	−0.600188	−	0.799859i	$-0.704908\pi$
$229$	−4159.78	−1.20038	−0.600188	+	0.799859i	$0.704908\pi$
$230$	0	0
$231$	19.9610	0.00568546
$232$	−412.179	−0.116642
$233$	−2945.40	−0.828152	−0.414076	−	0.910242i	$-0.635895\pi$
$233$	−2945.40	−0.828152	−0.414076	+	0.910242i	$0.635895\pi$
$234$	−1481.43	−0.413864
$235$	0	0
$236$	−4021.21	−1.10914
$237$	−1822.99	−0.499644
$238$	11.1240	0.00302968
$239$	2174.54	0.588533	0.294266	−	0.955723i	$-0.404925\pi$
$239$	2174.54	0.588533	0.294266	+	0.955723i	$0.404925\pi$
$240$	0	0
$241$	2300.69	0.614939	0.307470	−	0.951558i	$-0.400518\pi$
$241$	2300.69	0.614939	0.307470	+	0.951558i	$0.400518\pi$
$242$	4366.74	1.15994
$243$	−243.000	−0.0641500
$244$	5537.72	1.45294
$245$	0	0
$246$	−1806.15	−0.468112
$247$	−3125.23	−0.805074
$248$	−11130.7	−2.85000
$249$	−3805.66	−0.968571
$250$	0	0
$251$	3368.55	0.847096	0.423548	−	0.905874i	$-0.360785\pi$
$251$	3368.55	0.847096	0.423548	+	0.905874i	$0.360785\pi$
$252$	−18.9360	−0.00473357
$253$	7650.95	1.90123
$254$	5684.09	1.40414
$255$	0	0
$256$	−7303.36	−1.78305
$257$	−404.905	−0.0982772	−0.0491386	−	0.998792i	$-0.515648\pi$
$257$	−404.905	−0.0982772	−0.0491386	+	0.998792i	$0.515648\pi$
$258$	−7618.33	−1.83836
$259$	−39.5427	−0.00948672
$260$	0	0
$261$	−110.994	−0.0263233
$262$	−1069.29	−0.252142
$263$	1514.70	0.355135	0.177567	−	0.984109i	$-0.443177\pi$
$263$	1514.70	0.355135	0.177567	+	0.984109i	$0.443177\pi$
$264$	−4747.59	−1.10679
$265$	0	0
$266$	−61.2912	−0.0141278
$267$	4012.60	0.919727
$268$	2642.83	0.602374
$269$	−1891.88	−0.428811	−0.214405	−	0.976745i	$-0.568781\pi$
$269$	−1891.88	−0.428811	−0.214405	+	0.976745i	$0.568781\pi$
$270$	0	0
$271$	−2094.31	−0.469448	−0.234724	−	0.972062i	$-0.575419\pi$
$271$	−2094.31	−0.469448	−0.234724	+	0.972062i	$0.575419\pi$
$272$	−667.370	−0.148769
$273$	−14.4774	−0.00320956
$274$	7570.79	1.66923
$275$	0	0
$276$	−7258.08	−1.58292
$277$	1492.73	0.323789	0.161894	−	0.986808i	$-0.448240\pi$
$277$	1492.73	0.323789	0.161894	+	0.986808i	$0.448240\pi$
$278$	7502.27	1.61855
$279$	−2997.34	−0.643176
$280$	0	0
$281$	2069.49	0.439344	0.219672	−	0.975574i	$-0.429501\pi$
$281$	2069.49	0.439344	0.219672	+	0.975574i	$0.429501\pi$
$282$	1079.45	0.227945
$283$	−3398.90	−0.713935	−0.356967	−	0.934117i	$-0.616189\pi$
$283$	−3398.90	−0.713935	−0.356967	+	0.934117i	$0.616189\pi$
$284$	10812.1	2.25908
$285$	0	0
$286$	−7794.05	−1.61144
$287$	−17.6507	−0.00363026
$288$	−663.338	−0.135721
$289$	−4640.21	−0.944476
$290$	0	0
$291$	−4293.64	−0.864939
$292$	36.5747	0.00733004
$293$	−7677.60	−1.53082	−0.765410	−	0.643543i	$-0.777464\pi$
$293$	−7677.60	−1.53082	−0.765410	+	0.643543i	$0.777464\pi$
$294$	4931.73	0.978314
$295$	0	0
$296$	9404.93	1.84679
$297$	−1278.46	−0.249777
$298$	923.304	0.179482
$299$	−5549.09	−1.07329
$300$	0	0
$301$	−74.4505	−0.0142567
$302$	5046.24	0.961518
$303$	1122.31	0.212788
$304$	3677.07	0.693732
$305$	0	0
$306$	−712.470	−0.133102
$307$	4507.90	0.838043	0.419022	−	0.907976i	$-0.362373\pi$
$307$	4507.90	0.838043	0.419022	+	0.907976i	$0.362373\pi$
$308$	−99.6255	−0.0184308
$309$	−6053.61	−1.11449
$310$	0	0
$311$	7065.19	1.28820	0.644100	−	0.764941i	$-0.277232\pi$
$311$	7065.19	1.28820	0.644100	+	0.764941i	$0.277232\pi$
$312$	3443.34	0.624809
$313$	−2063.81	−0.372694	−0.186347	−	0.982484i	$-0.559665\pi$
$313$	−2063.81	−0.372694	−0.186347	+	0.982484i	$0.559665\pi$
$314$	−9802.94	−1.76182
$315$	0	0
$316$	9098.52	1.61972
$317$	−8596.49	−1.52311	−0.761557	−	0.648098i	$-0.775565\pi$
$317$	−8596.49	−1.52311	−0.761557	+	0.648098i	$0.775565\pi$
$318$	−3586.50	−0.632456
$319$	−583.959	−0.102493
$320$	0	0
$321$	5039.14	0.876192
$322$	−108.827	−0.0188345
$323$	−1503.03	−0.258918
$324$	1212.81	0.207958
$325$	0	0
$326$	−4064.54	−0.690533
$327$	−60.6850	−0.0102627
$328$	4198.08	0.706708
$329$	10.5490	0.00176774
$330$	0	0
$331$	259.628	0.0431131	0.0215566	−	0.999768i	$-0.493138\pi$
$331$	259.628	0.0431131	0.0215566	+	0.999768i	$0.493138\pi$
$332$	18994.1	3.13986
$333$	2532.62	0.416777
$334$	−9453.97	−1.54880
$335$	0	0
$336$	17.0338	0.00276568
$337$	−6721.19	−1.08643	−0.543215	−	0.839594i	$-0.682793\pi$
$337$	−6721.19	−1.08643	−0.543215	+	0.839594i	$0.682793\pi$
$338$	−4877.38	−0.784894
$339$	−1927.56	−0.308822
$340$	0	0
$341$	−15769.5	−2.50430
$342$	3925.57	0.620673
$343$	96.3940	0.0151743
$344$	17707.5	2.77536
$345$	0	0
$346$	−12977.8	−2.01645
$347$	7139.56	1.10453	0.552264	−	0.833669i	$-0.313764\pi$
$347$	7139.56	1.10453	0.552264	+	0.833669i	$0.313764\pi$
$348$	553.972	0.0853334
$349$	−11473.4	−1.75976	−0.879879	−	0.475198i	$-0.842376\pi$
$349$	−11473.4	−1.75976	−0.879879	+	0.475198i	$0.842376\pi$
$350$	0	0
$351$	927.244	0.141005
$352$	−3489.92	−0.528448
$353$	−59.6020	−0.00898667	−0.00449333	−	0.999990i	$-0.501430\pi$
$353$	−59.6020	−0.00898667	−0.00449333	+	0.999990i	$0.501430\pi$
$354$	3861.69	0.579793
$355$	0	0
$356$	−20026.9	−2.98152
$357$	−6.96265	−0.00103222
$358$	15012.9	2.21636
$359$	−7801.88	−1.14698	−0.573492	−	0.819211i	$-0.694412\pi$
$359$	−7801.88	−1.14698	−0.573492	+	0.819211i	$0.694412\pi$
$360$	0	0
$361$	1422.37	0.207373
$362$	1519.63	0.220635
$363$	−2733.19	−0.395193
$364$	72.2565	0.0104046
$365$	0	0
$366$	−5318.06	−0.759506
$367$	1583.29	0.225197	0.112599	−	0.993641i	$-0.464083\pi$
$367$	1583.29	0.225197	0.112599	+	0.993641i	$0.464083\pi$
$368$	6528.94	0.924850
$369$	1130.49	0.159487
$370$	0	0
$371$	−35.0493	−0.00490477
$372$	14959.7	2.08502
$373$	11181.2	1.55212	0.776059	−	0.630661i	$-0.217216\pi$
$373$	11181.2	1.55212	0.776059	+	0.630661i	$0.217216\pi$
$374$	−3748.42	−0.518252
$375$	0	0
$376$	−2509.01	−0.344128
$377$	423.534	0.0578598
$378$	18.1849	0.00247442
$379$	−11723.0	−1.58885	−0.794423	−	0.607365i	$-0.792227\pi$
$379$	−11723.0	−1.58885	−0.794423	+	0.607365i	$0.792227\pi$
$380$	0	0
$381$	−3557.73	−0.478394
$382$	8049.67	1.07816
$383$	9272.02	1.23702	0.618509	−	0.785778i	$-0.287737\pi$
$383$	9272.02	1.23702	0.618509	+	0.785778i	$0.287737\pi$
$384$	7958.77	1.05767
$385$	0	0
$386$	6948.05	0.916183
$387$	4768.39	0.626333
$388$	21429.5	2.80391
$389$	−1341.15	−0.174805	−0.0874023	−	0.996173i	$-0.527857\pi$
$389$	−1341.15	−0.174805	−0.0874023	+	0.996173i	$0.527857\pi$
$390$	0	0
$391$	−2668.74	−0.345177
$392$	−11463.0	−1.47696
$393$	669.283	0.0859054
$394$	5083.59	0.650019
$395$	0	0
$396$	6380.80	0.809715
$397$	−11366.3	−1.43692	−0.718459	−	0.695569i	$-0.755152\pi$
$397$	−11366.3	−1.43692	−0.718459	+	0.695569i	$0.755152\pi$
$398$	−877.490	−0.110514
$399$	38.3628	0.00481339
$400$	0	0
$401$	−12421.7	−1.54690	−0.773451	−	0.633856i	$-0.781471\pi$
$401$	−12421.7	−1.54690	−0.773451	+	0.633856i	$0.781471\pi$
$402$	−2537.99	−0.314884
$403$	11437.3	1.41373
$404$	−5601.42	−0.689805
$405$	0	0
$406$	8.30625	0.00101535
$407$	13324.5	1.62278
$408$	1656.02	0.200944
$409$	12917.8	1.56172	0.780860	−	0.624706i	$-0.214781\pi$
$409$	12917.8	1.56172	0.780860	+	0.624706i	$0.214781\pi$
$410$	0	0
$411$	−4738.64	−0.568710
$412$	30213.5	3.61290
$413$	37.7386	0.00449636
$414$	6970.16	0.827451
$415$	0	0
$416$	2531.18	0.298320
$417$	−4695.75	−0.551443
$418$	20653.0	2.41668
$419$	−4162.80	−0.485361	−0.242680	−	0.970106i	$-0.578027\pi$
$419$	−4162.80	−0.485361	−0.242680	+	0.970106i	$0.578027\pi$
$420$	0	0
$421$	−14947.3	−1.73037	−0.865186	−	0.501451i	$-0.832800\pi$
$421$	−14947.3	−1.73037	−0.865186	+	0.501451i	$0.832800\pi$
$422$	−23508.4	−2.71178
$423$	−675.642	−0.0776615
$424$	8336.21	0.954817
$425$	0	0
$426$	−10383.2	−1.18091
$427$	−51.9710	−0.00589005
$428$	−25150.4	−2.84039
$429$	4878.38	0.549022
$430$	0	0
$431$	−12762.9	−1.42638	−0.713188	−	0.700973i	$-0.752749\pi$
$431$	−12762.9	−1.42638	−0.713188	+	0.700973i	$0.752749\pi$
$432$	−1090.98	−0.121504
$433$	−777.497	−0.0862913	−0.0431456	−	0.999069i	$-0.513738\pi$
$433$	−777.497	−0.0862913	−0.0431456	+	0.999069i	$0.513738\pi$
$434$	224.306	0.0248088
$435$	0	0
$436$	302.879	0.0332689
$437$	14704.2	1.60961
$438$	−35.1239	−0.00383170
$439$	9936.45	1.08028	0.540138	−	0.841577i	$-0.318372\pi$
$439$	9936.45	1.08028	0.540138	+	0.841577i	$0.318372\pi$
$440$	0	0
$441$	−3086.82	−0.333314
$442$	2718.66	0.292564
$443$	−7139.86	−0.765745	−0.382873	−	0.923801i	$-0.625065\pi$
$443$	−7139.86	−0.765745	−0.382873	+	0.923801i	$0.625065\pi$
$444$	−12640.3	−1.35109
$445$	0	0
$446$	23185.8	2.46162
$447$	−577.906	−0.0611499
$448$	95.0642	0.0100254
$449$	10438.2	1.09712	0.548560	−	0.836111i	$-0.315176\pi$
$449$	10438.2	1.09712	0.548560	+	0.836111i	$0.315176\pi$
$450$	0	0
$451$	5947.67	0.620986
$452$	9620.45	1.00112
$453$	−3158.50	−0.327592
$454$	214.811	0.0222062
$455$	0	0
$456$	−9124.31	−0.937029
$457$	−5039.76	−0.515864	−0.257932	−	0.966163i	$-0.583041\pi$
$457$	−5039.76	−0.515864	−0.257932	+	0.966163i	$0.583041\pi$
$458$	−19937.9	−2.03414
$459$	445.943	0.0453482
$460$	0	0
$461$	1832.68	0.185155	0.0925775	−	0.995705i	$-0.470489\pi$
$461$	1832.68	0.185155	0.0925775	+	0.995705i	$0.470489\pi$
$462$	95.6736	0.00963450
$463$	−1887.49	−0.189458	−0.0947290	−	0.995503i	$-0.530198\pi$
$463$	−1887.49	−0.189458	−0.0947290	+	0.995503i	$0.530198\pi$
$464$	−498.321	−0.0498577
$465$	0	0
$466$	−14117.3	−1.40337
$467$	3944.31	0.390837	0.195419	−	0.980720i	$-0.437393\pi$
$467$	3944.31	0.390837	0.195419	+	0.980720i	$0.437393\pi$
$468$	−4627.87	−0.457101
$469$	−24.8027	−0.00244196
$470$	0	0
$471$	6135.77	0.600257
$472$	−8975.85	−0.875311
$473$	25087.3	2.43872
$474$	−8737.60	−0.846690
$475$	0	0
$476$	34.7506	0.00334620
$477$	2244.83	0.215479
$478$	10422.6	0.997320
$479$	−10759.1	−1.02630	−0.513150	−	0.858299i	$-0.671522\pi$
$479$	−10759.1	−1.02630	−0.513150	+	0.858299i	$0.671522\pi$
$480$	0	0
$481$	−9664.02	−0.916095
$482$	11027.2	1.04207
$483$	68.1163	0.00641698
$484$	13641.3	1.28112
$485$	0	0
$486$	−1164.70	−0.108708
$487$	−3191.34	−0.296948	−0.148474	−	0.988916i	$-0.547436\pi$
$487$	−3191.34	−0.296948	−0.148474	+	0.988916i	$0.547436\pi$
$488$	12360.9	1.14662
$489$	2544.04	0.235267
$490$	0	0
$491$	933.900	0.0858377	0.0429189	−	0.999079i	$-0.486334\pi$
$491$	933.900	0.0858377	0.0429189	+	0.999079i	$0.486334\pi$
$492$	−5642.25	−0.517017
$493$	203.692	0.0186082
$494$	−14979.3	−1.36427
$495$	0	0
$496$	−13456.9	−1.21821
$497$	−101.470	−0.00915806
$498$	−18240.6	−1.64133
$499$	5499.10	0.493333	0.246667	−	0.969100i	$-0.420665\pi$
$499$	5499.10	0.493333	0.246667	+	0.969100i	$0.420665\pi$
$500$	0	0
$501$	5917.34	0.527679
$502$	16145.5	1.43548
$503$	11172.5	0.990374	0.495187	−	0.868787i	$-0.335100\pi$
$503$	11172.5	0.990374	0.495187	+	0.868787i	$0.335100\pi$
$504$	−42.2677	−0.00373562
$505$	0	0
$506$	36671.1	3.22180
$507$	3052.80	0.267416
$508$	17756.6	1.55083
$509$	−8576.81	−0.746877	−0.373439	−	0.927655i	$-0.621821\pi$
$509$	−8576.81	−0.746877	−0.373439	+	0.927655i	$0.621821\pi$
$510$	0	0
$511$	−0.343250	−2.97152e−5 0
$512$	−13781.7	−1.18960
$513$	−2457.05	−0.211465
$514$	−1940.71	−0.166539
$515$	0	0
$516$	−23799.0	−2.03041
$517$	−3554.66	−0.302386
$518$	−189.529	−0.0160761
$519$	8122.94	0.687008
$520$	0	0
$521$	−19732.4	−1.65929	−0.829647	−	0.558289i	$-0.811458\pi$
$521$	−19732.4	−1.65929	−0.829647	+	0.558289i	$0.811458\pi$
$522$	−531.997	−0.0446071
$523$	−16353.7	−1.36730	−0.683651	−	0.729809i	$-0.739609\pi$
$523$	−16353.7	−1.36730	−0.683651	+	0.729809i	$0.739609\pi$
$524$	−3340.39	−0.278484
$525$	0	0
$526$	7259.98	0.601807
$527$	5500.59	0.454667
$528$	−5739.79	−0.473092
$529$	13941.6	1.14585
$530$	0	0
$531$	−2417.08	−0.197537
$532$	−191.469	−0.0156038
$533$	−4313.73	−0.350560
$534$	19232.5	1.55856
$535$	0	0
$536$	5899.13	0.475380
$537$	−9396.75	−0.755120
$538$	−9067.82	−0.726657
$539$	−16240.3	−1.29781
$540$	0	0
$541$	14238.7	1.13155	0.565776	−	0.824559i	$-0.308577\pi$
$541$	14238.7	1.13155	0.565776	+	0.824559i	$0.308577\pi$
$542$	−10038.1	−0.795521
$543$	−951.153	−0.0751710
$544$	1217.33	0.0959421
$545$	0	0
$546$	−69.3903	−0.00543888
$547$	−7018.76	−0.548630	−0.274315	−	0.961640i	$-0.588451\pi$
$547$	−7018.76	−0.548630	−0.274315	+	0.961640i	$0.588451\pi$
$548$	23650.5	1.84361
$549$	3328.63	0.258766
$550$	0	0
$551$	−1122.30	−0.0867725
$552$	−16201.0	−1.24920
$553$	−85.3887	−0.00656618
$554$	7154.68	0.548688
$555$	0	0
$556$	23436.5	1.78764
$557$	−6144.57	−0.467421	−0.233711	−	0.972306i	$-0.575087\pi$
$557$	−6144.57	−0.467421	−0.233711	+	0.972306i	$0.575087\pi$
$558$	−14366.3	−1.08992
$559$	−18195.3	−1.37671
$560$	0	0
$561$	2346.18	0.176570
$562$	9919.12	0.744507
$563$	−17169.5	−1.28527	−0.642635	−	0.766172i	$-0.722159\pi$
$563$	−17169.5	−1.28527	−0.642635	+	0.766172i	$0.722159\pi$
$564$	3372.12	0.251759
$565$	0	0
$566$	−16291.0	−1.20982
$567$	−11.3821	−0.000843041 0
$568$	24133.9	1.78281
$569$	−15575.2	−1.14754	−0.573768	−	0.819018i	$-0.694519\pi$
$569$	−15575.2	−1.14754	−0.573768	+	0.819018i	$0.694519\pi$
$570$	0	0
$571$	−21207.6	−1.55431	−0.777156	−	0.629308i	$-0.783339\pi$
$571$	−21207.6	−1.55431	−0.777156	+	0.629308i	$0.783339\pi$
$572$	−24348.0	−1.77979
$573$	−5038.37	−0.367332
$574$	−84.5999	−0.00615180
$575$	0	0
$576$	−6088.65	−0.440441
$577$	2071.25	0.149441	0.0747205	−	0.997205i	$-0.476194\pi$
$577$	2071.25	0.149441	0.0747205	+	0.997205i	$0.476194\pi$
$578$	−22240.6	−1.60050
$579$	−4348.86	−0.312146
$580$	0	0
$581$	−178.257	−0.0127287
$582$	−20579.5	−1.46571
$583$	11810.4	0.839000
$584$	81.6394	0.00578470
$585$	0	0
$586$	−36798.9	−2.59411
$587$	−20730.6	−1.45766	−0.728828	−	0.684697i	$-0.759935\pi$
$587$	−20730.6	−1.45766	−0.728828	+	0.684697i	$0.759935\pi$
$588$	15406.3	1.08052
$589$	−30307.1	−2.12018
$590$	0	0
$591$	−3181.87	−0.221463
$592$	11370.5	0.789399
$593$	1924.00	0.133236	0.0666182	−	0.997779i	$-0.478779\pi$
$593$	1924.00	0.133236	0.0666182	+	0.997779i	$0.478779\pi$
$594$	−6127.68	−0.423269
$595$	0	0
$596$	2884.33	0.198233
$597$	549.230	0.0376524
$598$	−26596.9	−1.81878
$599$	−8088.34	−0.551720	−0.275860	−	0.961198i	$-0.588963\pi$
$599$	−8088.34	−0.551720	−0.275860	+	0.961198i	$0.588963\pi$
$600$	0	0
$601$	19953.8	1.35430	0.677149	−	0.735846i	$-0.263215\pi$
$601$	19953.8	1.35430	0.677149	+	0.735846i	$0.263215\pi$
$602$	−356.842	−0.0241592
$603$	1588.56	0.107282
$604$	15764.0	1.06197
$605$	0	0
$606$	5379.22	0.360588
$607$	3633.68	0.242976	0.121488	−	0.992593i	$-0.461233\pi$
$607$	3633.68	0.242976	0.121488	+	0.992593i	$0.461233\pi$
$608$	−6707.23	−0.447392
$609$	−5.19897	−0.000345933 0
$610$	0	0
$611$	2578.13	0.170704
$612$	−2225.70	−0.147007
$613$	1581.91	0.104230	0.0521148	−	0.998641i	$-0.483404\pi$
$613$	1581.91	0.104230	0.0521148	+	0.998641i	$0.483404\pi$
$614$	21606.4	1.42014
$615$	0	0
$616$	−222.377	−0.0145452
$617$	−4454.03	−0.290620	−0.145310	−	0.989386i	$-0.546418\pi$
$617$	−4454.03	−0.290620	−0.145310	+	0.989386i	$0.546418\pi$
$618$	−29015.0	−1.88860
$619$	−2630.26	−0.170790	−0.0853951	−	0.996347i	$-0.527215\pi$
$619$	−2630.26	−0.170790	−0.0853951	+	0.996347i	$0.527215\pi$
$620$	0	0
$621$	−4362.70	−0.281915
$622$	33863.6	2.18297
$623$	187.950	0.0120868
$624$	4162.97	0.267071
$625$	0	0
$626$	−9891.85	−0.631562
$627$	−12927.0	−0.823370
$628$	−30623.6	−1.94588
$629$	−4647.75	−0.294623
$630$	0	0
$631$	−16896.4	−1.06599	−0.532993	−	0.846120i	$-0.678933\pi$
$631$	−16896.4	−1.06599	−0.532993	+	0.846120i	$0.678933\pi$
$632$	20309.1	1.27825
$633$	14714.2	0.923912
$634$	−41203.1	−2.58105
$635$	0	0
$636$	−11203.9	−0.698530
$637$	11778.8	0.732640
$638$	−2798.92	−0.173684
$639$	6498.93	0.402338
$640$	0	0
$641$	28804.5	1.77490	0.887448	−	0.460908i	$-0.152476\pi$
$641$	28804.5	1.77490	0.887448	+	0.460908i	$0.152476\pi$
$642$	24152.7	1.48478
$643$	−10219.9	−0.626801	−0.313400	−	0.949621i	$-0.601468\pi$
$643$	−10219.9	−0.626801	−0.313400	+	0.949621i	$0.601468\pi$
$644$	−339.968	−0.0208022
$645$	0	0
$646$	−7204.03	−0.438759
$647$	1792.38	0.108912	0.0544558	−	0.998516i	$-0.482658\pi$
$647$	1792.38	0.108912	0.0544558	+	0.998516i	$0.482658\pi$
$648$	2707.15	0.164116
$649$	−12716.6	−0.769138
$650$	0	0
$651$	−140.396	−0.00845243
$652$	−12697.3	−0.762675
$653$	13405.4	0.803359	0.401679	−	0.915780i	$-0.368427\pi$
$653$	13405.4	0.803359	0.401679	+	0.915780i	$0.368427\pi$
$654$	−290.864	−0.0173910
$655$	0	0
$656$	5075.44	0.302077
$657$	21.9844	0.00130547
$658$	50.5616	0.00299559
$659$	−15441.6	−0.912778	−0.456389	−	0.889780i	$-0.650858\pi$
$659$	−15441.6	−0.912778	−0.456389	+	0.889780i	$0.650858\pi$
$660$	0	0
$661$	4356.59	0.256356	0.128178	−	0.991751i	$-0.459087\pi$
$661$	4356.59	0.256356	0.128178	+	0.991751i	$0.459087\pi$
$662$	1244.40	0.0730589
$663$	−1701.64	−0.0996774
$664$	42397.2	2.47791
$665$	0	0
$666$	12138.9	0.706265
$667$	−1992.74	−0.115681
$668$	−29533.4	−1.71060
$669$	−14512.3	−0.838679
$670$	0	0
$671$	17512.4	1.00754
$672$	−31.0707	−0.00178360
$673$	17617.2	1.00905	0.504527	−	0.863396i	$-0.331667\pi$
$673$	17617.2	1.00905	0.504527	+	0.863396i	$0.331667\pi$
$674$	−32214.8	−1.84105
$675$	0	0
$676$	−15236.5	−0.866894
$677$	−3294.63	−0.187036	−0.0935178	−	0.995618i	$-0.529811\pi$
$677$	−3294.63	−0.187036	−0.0935178	+	0.995618i	$0.529811\pi$
$678$	−9238.83	−0.523326
$679$	−201.114	−0.0113668
$680$	0	0
$681$	−134.453	−0.00756570
$682$	−75583.4	−4.24375
$683$	−4829.50	−0.270565	−0.135282	−	0.990807i	$-0.543194\pi$
$683$	−4829.50	−0.270565	−0.135282	+	0.990807i	$0.543194\pi$
$684$	12263.2	0.685517
$685$	0	0
$686$	462.018	0.0257142
$687$	12479.3	0.693037
$688$	21408.2	1.18631
$689$	−8565.87	−0.473634
$690$	0	0
$691$	23330.5	1.28442	0.642211	−	0.766528i	$-0.278017\pi$
$691$	23330.5	1.28442	0.642211	+	0.766528i	$0.278017\pi$
$692$	−40541.5	−2.22711
$693$	−59.8831	−0.00328250
$694$	34220.0	1.87172
$695$	0	0
$696$	1236.54	0.0673432
$697$	−2074.62	−0.112743
$698$	−54992.0	−2.98206
$699$	8836.19	0.478134
$700$	0	0
$701$	27619.7	1.48813	0.744066	−	0.668106i	$-0.232895\pi$
$701$	27619.7	1.48813	0.744066	+	0.668106i	$0.232895\pi$
$702$	4444.30	0.238945
$703$	25608.2	1.37387
$704$	−32033.4	−1.71492
$705$	0	0
$706$	−285.673	−0.0152287
$707$	52.5688	0.00279640
$708$	12063.6	0.640365
$709$	25819.3	1.36765	0.683826	−	0.729645i	$-0.260315\pi$
$709$	25819.3	1.36765	0.683826	+	0.729645i	$0.260315\pi$
$710$	0	0
$711$	5468.96	0.288470
$712$	−44702.6	−2.35295
$713$	−53812.8	−2.82651
$714$	−33.3721	−0.00174919
$715$	0	0
$716$	46899.1	2.44791
$717$	−6523.62	−0.339790
$718$	−37394.5	−1.94366
$719$	−16339.0	−0.847484	−0.423742	−	0.905783i	$-0.639284\pi$
$719$	−16339.0	−0.847484	−0.423742	+	0.905783i	$0.639284\pi$
$720$	0	0
$721$	−283.551	−0.0146463
$722$	6817.44	0.351411
$723$	−6902.06	−0.355035
$724$	4747.20	0.243685
$725$	0	0
$726$	−13100.2	−0.669689
$727$	7287.52	0.371773	0.185887	−	0.982571i	$-0.440484\pi$
$727$	7287.52	0.371773	0.185887	+	0.982571i	$0.440484\pi$
$728$	161.286	0.00821106
$729$	729.000	0.0370370
$730$	0	0
$731$	−8750.74	−0.442760
$732$	−16613.2	−0.838853
$733$	12030.1	0.606197	0.303098	−	0.952959i	$-0.401979\pi$
$733$	12030.1	0.606197	0.303098	+	0.952959i	$0.401979\pi$
$734$	7588.76	0.381616
$735$	0	0
$736$	−11909.2	−0.596440
$737$	8357.64	0.417718
$738$	5418.44	0.270265
$739$	−15163.0	−0.754778	−0.377389	−	0.926055i	$-0.623178\pi$
$739$	−15163.0	−0.754778	−0.377389	+	0.926055i	$0.623178\pi$
$740$	0	0
$741$	9375.68	0.464810
$742$	−167.992	−0.00831155
$743$	22772.8	1.12443	0.562216	−	0.826991i	$-0.309949\pi$
$743$	22772.8	1.12443	0.562216	+	0.826991i	$0.309949\pi$
$744$	33392.0	1.64545
$745$	0	0
$746$	53591.6	2.63020
$747$	11417.0	0.559205
$748$	−11709.8	−0.572394
$749$	236.034	0.0115147
$750$	0	0
$751$	−27855.5	−1.35348	−0.676739	−	0.736223i	$-0.736608\pi$
$751$	−27855.5	−1.35348	−0.676739	+	0.736223i	$0.736608\pi$
$752$	−3033.37	−0.147095
$753$	−10105.6	−0.489071
$754$	2030.01	0.0980484
$755$	0	0
$756$	56.8081	0.00273293
$757$	−302.235	−0.0145111	−0.00725557	−	0.999974i	$-0.502310\pi$
$757$	−302.235	−0.0145111	−0.00725557	+	0.999974i	$0.502310\pi$
$758$	−56188.7	−2.69244
$759$	−22952.9	−1.09768
$760$	0	0
$761$	−4497.19	−0.214222	−0.107111	−	0.994247i	$-0.534160\pi$
$761$	−4497.19	−0.214222	−0.107111	+	0.994247i	$0.534160\pi$
$762$	−17052.3	−0.810680
$763$	−2.84249	−0.000134869 0
$764$	25146.5	1.19080
$765$	0	0
$766$	44440.9	2.09623
$767$	9223.13	0.434195
$768$	21910.1	1.02944
$769$	2438.76	0.114362	0.0571808	−	0.998364i	$-0.481789\pi$
$769$	2438.76	0.114362	0.0571808	+	0.998364i	$0.481789\pi$
$770$	0	0
$771$	1214.71	0.0567404
$772$	21705.1	1.01190
$773$	37464.5	1.74321	0.871607	−	0.490205i	$-0.163078\pi$
$773$	37464.5	1.74321	0.871607	+	0.490205i	$0.163078\pi$
$774$	22855.0	1.06138
$775$	0	0
$776$	47833.4	2.21278
$777$	118.628	0.00547716
$778$	−6428.15	−0.296222
$779$	11430.7	0.525736
$780$	0	0
$781$	34191.9	1.56656
$782$	−12791.3	−0.584932
$783$	332.983	0.0151978
$784$	−13858.6	−0.631315
$785$	0	0
$786$	3207.88	0.145574
$787$	−30317.8	−1.37321	−0.686603	−	0.727033i	$-0.740899\pi$
$787$	−30317.8	−1.37321	−0.686603	+	0.727033i	$0.740899\pi$
$788$	15880.7	0.717928
$789$	−4544.10	−0.205037
$790$	0	0
$791$	−90.2870	−0.00405845
$792$	14242.8	0.639008
$793$	−12701.4	−0.568779
$794$	−54478.7	−2.43498
$795$	0	0
$796$	−2741.21	−0.122060
$797$	23627.1	1.05008	0.525041	−	0.851077i	$-0.324050\pi$
$797$	23627.1	1.05008	0.525041	+	0.851077i	$0.324050\pi$
$798$	183.874	0.00815671
$799$	1239.91	0.0548996
$800$	0	0
$801$	−12037.8	−0.531005
$802$	−59537.2	−2.62136
$803$	115.663	0.00508303
$804$	−7928.48	−0.347781
$805$	0	0
$806$	54819.2	2.39569
$807$	5675.65	0.247574
$808$	−12503.1	−0.544378
$809$	−30566.8	−1.32839	−0.664197	−	0.747558i	$-0.731226\pi$
$809$	−30566.8	−1.32839	−0.664197	+	0.747558i	$0.731226\pi$
$810$	0	0
$811$	36976.4	1.60101	0.800504	−	0.599328i	$-0.204565\pi$
$811$	36976.4	1.60101	0.800504	+	0.599328i	$0.204565\pi$
$812$	25.9481	0.00112143
$813$	6282.94	0.271036
$814$	63864.6	2.74994
$815$	0	0
$816$	2002.11	0.0858920
$817$	48214.8	2.06466
$818$	61915.1	2.64647
$819$	43.4321	0.00185304
$820$	0	0
$821$	−9499.03	−0.403798	−0.201899	−	0.979406i	$-0.564711\pi$
$821$	−9499.03	−0.403798	−0.201899	+	0.979406i	$0.564711\pi$
$822$	−22712.4	−0.963728
$823$	4753.25	0.201322	0.100661	−	0.994921i	$-0.467904\pi$
$823$	4753.25	0.201322	0.100661	+	0.994921i	$0.467904\pi$
$824$	67440.5	2.85121
$825$	0	0
$826$	180.882	0.00761947
$827$	−13224.0	−0.556039	−0.278020	−	0.960575i	$-0.589678\pi$
$827$	−13224.0	−0.556039	−0.278020	+	0.960575i	$0.589678\pi$
$828$	21774.2	0.913897
$829$	−10210.7	−0.427782	−0.213891	−	0.976858i	$-0.568614\pi$
$829$	−10210.7	−0.427782	−0.213891	+	0.976858i	$0.568614\pi$
$830$	0	0
$831$	−4478.19	−0.186939
$832$	23233.2	0.968109
$833$	5664.80	0.235623
$834$	−22506.8	−0.934469
$835$	0	0
$836$	64518.4	2.66916
$837$	8992.03	0.371338
$838$	−19952.4	−0.822485
$839$	−6722.41	−0.276619	−0.138310	−	0.990389i	$-0.544167\pi$
$839$	−6722.41	−0.276619	−0.138310	+	0.990389i	$0.544167\pi$
$840$	0	0
$841$	−24236.9	−0.993764
$842$	−71642.6	−2.93227
$843$	−6208.48	−0.253655
$844$	−73438.4	−2.99509
$845$	0	0
$846$	−3238.36	−0.131604
$847$	−128.023	−0.00519351
$848$	10078.4	0.408130
$849$	10196.7	0.412191
$850$	0	0
$851$	45469.4	1.83158
$852$	−32436.2	−1.30428
$853$	3785.52	0.151950	0.0759752	−	0.997110i	$-0.475793\pi$
$853$	3785.52	0.151950	0.0759752	+	0.997110i	$0.475793\pi$
$854$	−249.098	−0.00998121
$855$	0	0
$856$	−56138.8	−2.24157
$857$	−13421.7	−0.534979	−0.267489	−	0.963561i	$-0.586194\pi$
$857$	−13421.7	−0.534979	−0.267489	+	0.963561i	$0.586194\pi$
$858$	23382.1	0.930365
$859$	491.965	0.0195409	0.00977045	−	0.999952i	$-0.496890\pi$
$859$	491.965	0.0195409	0.00977045	+	0.999952i	$0.496890\pi$
$860$	0	0
$861$	52.9520	0.00209593
$862$	−61172.8	−2.41712
$863$	8088.10	0.319029	0.159515	−	0.987196i	$-0.449007\pi$
$863$	8088.10	0.319029	0.159515	+	0.987196i	$0.449007\pi$
$864$	1990.01	0.0783583
$865$	0	0
$866$	−3726.55	−0.146228
$867$	13920.6	0.545293
$868$	700.714	0.0274007
$869$	28773.1	1.12320
$870$	0	0
$871$	−6061.64	−0.235811
$872$	676.064	0.0262551
$873$	12880.9	0.499373
$874$	70477.7	2.72762
$875$	0	0
$876$	−109.724	−0.00423200
$877$	−12000.4	−0.462058	−0.231029	−	0.972947i	$-0.574209\pi$
$877$	−12000.4	−0.462058	−0.231029	+	0.972947i	$0.574209\pi$
$878$	47625.6	1.83062
$879$	23032.8	0.883820
$880$	0	0
$881$	−2285.38	−0.0873964	−0.0436982	−	0.999045i	$-0.513914\pi$
$881$	−2285.38	−0.0873964	−0.0436982	+	0.999045i	$0.513914\pi$
$882$	−14795.2	−0.564830
$883$	−19226.6	−0.732759	−0.366379	−	0.930466i	$-0.619403\pi$
$883$	−19226.6	−0.732759	−0.366379	+	0.930466i	$0.619403\pi$
$884$	8492.87	0.323129
$885$	0	0
$886$	−34221.5	−1.29762
$887$	−14952.8	−0.566028	−0.283014	−	0.959116i	$-0.591334\pi$
$887$	−14952.8	−0.566028	−0.283014	+	0.959116i	$0.591334\pi$
$888$	−28214.8	−1.06625
$889$	−166.644	−0.00628692
$890$	0	0
$891$	3835.38	0.144209
$892$	72430.6	2.71879
$893$	−6831.64	−0.256005
$894$	−2769.91	−0.103624
$895$	0	0
$896$	372.789	0.0138996
$897$	16647.3	0.619662
$898$	50030.2	1.85916
$899$	4107.26	0.152375
$900$	0	0
$901$	−4119.61	−0.152324
$902$	28507.3	1.05231
$903$	223.352	0.00823109
$904$	21474.1	0.790064
$905$	0	0
$906$	−15138.7	−0.555133
$907$	−48744.8	−1.78450	−0.892251	−	0.451540i	$-0.850875\pi$
$907$	−48744.8	−1.78450	−0.892251	+	0.451540i	$0.850875\pi$
$908$	671.053	0.0245261
$909$	−3366.92	−0.122853
$910$	0	0
$911$	−35064.7	−1.27524	−0.637621	−	0.770350i	$-0.720081\pi$
$911$	−35064.7	−1.27524	−0.637621	+	0.770350i	$0.720081\pi$
$912$	−11031.2	−0.400527
$913$	60066.6	2.17734
$914$	−24155.6	−0.874177
$915$	0	0
$916$	−62284.4	−2.24665
$917$	31.3492	0.00112894
$918$	2137.41	0.0768465
$919$	−20159.6	−0.723617	−0.361808	−	0.932253i	$-0.617841\pi$
$919$	−20159.6	−0.723617	−0.361808	+	0.932253i	$0.617841\pi$
$920$	0	0
$921$	−13523.7	−0.483845
$922$	8784.07	0.313761
$923$	−24798.8	−0.884357
$924$	298.877	0.0106410
$925$	0	0
$926$	−9046.76	−0.321053
$927$	18160.8	0.643451
$928$	908.972	0.0321535
$929$	22221.8	0.784793	0.392397	−	0.919796i	$-0.371646\pi$
$929$	22221.8	0.784793	0.392397	+	0.919796i	$0.371646\pi$
$930$	0	0
$931$	−31211.9	−1.09874
$932$	−44101.4	−1.54999
$933$	−21195.6	−0.743743
$934$	18905.2	0.662308
$935$	0	0
$936$	−10330.0	−0.360734
$937$	−8123.54	−0.283228	−0.141614	−	0.989922i	$-0.545229\pi$
$937$	−8123.54	−0.283228	−0.141614	+	0.989922i	$0.545229\pi$
$938$	−118.880	−0.00413812
$939$	6191.42	0.215175
$940$	0	0
$941$	−41826.3	−1.44899	−0.724494	−	0.689281i	$-0.757927\pi$
$941$	−41826.3	−1.44899	−0.724494	+	0.689281i	$0.757927\pi$
$942$	29408.8	1.01719
$943$	20296.2	0.700885
$944$	−10851.7	−0.374146
$945$	0	0
$946$	120244.	4.13262
$947$	−32843.5	−1.12700	−0.563501	−	0.826115i	$-0.690546\pi$
$947$	−32843.5	−1.12700	−0.563501	+	0.826115i	$0.690546\pi$
$948$	−27295.6	−0.935146
$949$	−83.8885	−0.00286948
$950$	0	0
$951$	25789.5	0.879370
$952$	77.5678	0.00264074
$953$	12579.4	0.427583	0.213791	−	0.976879i	$-0.431419\pi$
$953$	12579.4	0.427583	0.213791	+	0.976879i	$0.431419\pi$
$954$	10759.5	0.365149
$955$	0	0
$956$	32559.4	1.10151
$957$	1751.88	0.0591746
$958$	−51568.8	−1.73916
$959$	−221.958	−0.00747382
$960$	0	0
$961$	81123.3	2.72308
$962$	−46319.8	−1.55240
$963$	−15117.4	−0.505870
$964$	34448.2	1.15093
$965$	0	0
$966$	326.482	0.0108741
$967$	−41883.1	−1.39283	−0.696417	−	0.717637i	$-0.745223\pi$
$967$	−41883.1	−1.39283	−0.696417	+	0.717637i	$0.745223\pi$
$968$	30449.2	1.01103
$969$	4509.08	0.149487
$970$	0	0
$971$	55390.3	1.83065	0.915323	−	0.402720i	$-0.131935\pi$
$971$	55390.3	1.83065	0.915323	+	0.402720i	$0.131935\pi$
$972$	−3638.44	−0.120065
$973$	−219.949	−0.00724691
$974$	−15296.2	−0.503204
$975$	0	0
$976$	14944.2	0.490117
$977$	35463.4	1.16128	0.580642	−	0.814159i	$-0.302802\pi$
$977$	35463.4	1.16128	0.580642	+	0.814159i	$0.302802\pi$
$978$	12193.6	0.398680
$979$	−63332.8	−2.06754
$980$	0	0
$981$	182.055	0.00592515
$982$	4476.20	0.145459
$983$	34670.9	1.12495	0.562477	−	0.826813i	$-0.309849\pi$
$983$	34670.9	1.12495	0.562477	+	0.826813i	$0.309849\pi$
$984$	−12594.2	−0.408018
$985$	0	0
$986$	976.298	0.0315331
$987$	−31.6471	−0.00102060
$988$	−46794.0	−1.50680
$989$	85609.3	2.75250
$990$	0	0
$991$	−37280.3	−1.19500	−0.597501	−	0.801868i	$-0.703840\pi$
$991$	−37280.3	−1.19500	−0.597501	+	0.801868i	$0.703840\pi$
$992$	24546.3	0.785631
$993$	−778.884	−0.0248914
$994$	−486.347	−0.0155191
$995$	0	0
$996$	−56982.2	−1.81280
$997$	34383.2	1.09220	0.546101	−	0.837719i	$-0.316111\pi$
$997$	34383.2	1.09220	0.546101	+	0.837719i	$0.316111\pi$
$998$	26357.3	0.835996
$999$	−7597.86	−0.240626

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.4.a.f.1.13		14
5.4	even	2		1875.4.a.g.1.2		14
25.4	even	10		75.4.g.b.16.7	✓	28
25.19	even	10		75.4.g.b.61.7	yes	28
75.29	odd	10		225.4.h.a.91.1		28
75.44	odd	10		225.4.h.a.136.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.16.7	✓	28	25.4	even	10
75.4.g.b.61.7	yes	28	25.19	even	10
225.4.h.a.91.1		28	75.29	odd	10
225.4.h.a.136.1		28	75.44	odd	10
1875.4.a.f.1.13		14	1.1	even	1	trivial
1875.4.a.g.1.2		14	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1875.a (trivial)

\(f(q)\)	\(=\)	\(q+4.79301 q^{2} -3.00000 q^{3} +14.9730 q^{4} -14.3790 q^{6} -0.140520 q^{7} +33.4216 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.79301 q^{2} -3.00000 q^{3} +14.9730 q^{4} -14.3790 q^{6} -0.140520 q^{7} +33.4216 q^{8} +9.00000 q^{9} +47.3504 q^{11} -44.9190 q^{12} -34.3424 q^{13} -0.673515 q^{14} +40.4065 q^{16} -16.5164 q^{17} +43.1371 q^{18} +91.0020 q^{19} +0.421560 q^{21} +226.951 q^{22} +161.582 q^{23} -100.265 q^{24} -164.604 q^{26} -27.0000 q^{27} -2.10400 q^{28} -12.3327 q^{29} -333.038 q^{31} -73.7042 q^{32} -142.051 q^{33} -79.1633 q^{34} +134.757 q^{36} +281.402 q^{37} +436.174 q^{38} +103.027 q^{39} +125.610 q^{41} +2.02054 q^{42} +529.821 q^{43} +708.977 q^{44} +774.463 q^{46} -75.0713 q^{47} -121.220 q^{48} -342.980 q^{49} +49.5492 q^{51} -514.208 q^{52} +249.426 q^{53} -129.411 q^{54} -4.69641 q^{56} -273.006 q^{57} -59.1108 q^{58} -268.564 q^{59} +369.848 q^{61} -1596.26 q^{62} -1.26468 q^{63} -676.517 q^{64} -680.854 q^{66} +176.506 q^{67} -247.300 q^{68} -484.745 q^{69} +722.104 q^{71} +300.795 q^{72} +2.44271 q^{73} +1348.77 q^{74} +1362.57 q^{76} -6.65368 q^{77} +493.811 q^{78} +607.662 q^{79} +81.0000 q^{81} +602.049 q^{82} +1268.55 q^{83} +6.31201 q^{84} +2539.44 q^{86} +36.9981 q^{87} +1582.53 q^{88} -1337.53 q^{89} +4.82579 q^{91} +2419.36 q^{92} +999.114 q^{93} -359.818 q^{94} +221.113 q^{96} +1431.21 q^{97} -1643.91 q^{98} +426.154 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 42 q^{3} + 50 q^{4} + 27 q^{7} - 21 q^{8} + 126 q^{9}+O(q^{10}) \) 14 * q - 42 * q^3 + 50 * q^4 + 27 * q^7 - 21 * q^8 + 126 * q^9	\( 14 q - 42 q^{3} + 50 q^{4} + 27 q^{7} - 21 q^{8} + 126 q^{9} - 33 q^{11} - 150 q^{12} + 188 q^{13} - 287 q^{14} + 82 q^{16} + 146 q^{17} - 184 q^{19} - 81 q^{21} + 277 q^{22} + 164 q^{23} + 63 q^{24} + 103 q^{26} - 378 q^{27} - 224 q^{28} + 252 q^{29} - 889 q^{31} + 422 q^{32} + 99 q^{33} - 230 q^{34} + 450 q^{36} + 642 q^{37} + 1833 q^{38} - 564 q^{39} - 164 q^{41} + 861 q^{42} + 696 q^{43} - 6 q^{44} - 419 q^{46} - 92 q^{47} - 246 q^{48} + 81 q^{49} - 438 q^{51} + 1956 q^{52} + 949 q^{53} - 2380 q^{56} + 552 q^{57} + 1041 q^{58} - 81 q^{59} - 496 q^{61} + 1454 q^{62} + 243 q^{63} - 3903 q^{64} - 831 q^{66} + 1926 q^{67} + 685 q^{68} - 492 q^{69} + 2498 q^{71} - 189 q^{72} - 1026 q^{73} - 707 q^{74} - 5704 q^{76} + 5434 q^{77} - 309 q^{78} - 695 q^{79} + 1134 q^{81} - 886 q^{82} + 5315 q^{83} + 672 q^{84} + 3997 q^{86} - 756 q^{87} + 2969 q^{88} - 1424 q^{89} - 1194 q^{91} + 1607 q^{92} + 2667 q^{93} - 629 q^{94} - 1266 q^{96} + 291 q^{97} - 1018 q^{98} - 297 q^{99}+O(q^{100}) \) 14 * q - 42 * q^3 + 50 * q^4 + 27 * q^7 - 21 * q^8 + 126 * q^9 - 33 * q^11 - 150 * q^12 + 188 * q^13 - 287 * q^14 + 82 * q^16 + 146 * q^17 - 184 * q^19 - 81 * q^21 + 277 * q^22 + 164 * q^23 + 63 * q^24 + 103 * q^26 - 378 * q^27 - 224 * q^28 + 252 * q^29 - 889 * q^31 + 422 * q^32 + 99 * q^33 - 230 * q^34 + 450 * q^36 + 642 * q^37 + 1833 * q^38 - 564 * q^39 - 164 * q^41 + 861 * q^42 + 696 * q^43 - 6 * q^44 - 419 * q^46 - 92 * q^47 - 246 * q^48 + 81 * q^49 - 438 * q^51 + 1956 * q^52 + 949 * q^53 - 2380 * q^56 + 552 * q^57 + 1041 * q^58 - 81 * q^59 - 496 * q^61 + 1454 * q^62 + 243 * q^63 - 3903 * q^64 - 831 * q^66 + 1926 * q^67 + 685 * q^68 - 492 * q^69 + 2498 * q^71 - 189 * q^72 - 1026 * q^73 - 707 * q^74 - 5704 * q^76 + 5434 * q^77 - 309 * q^78 - 695 * q^79 + 1134 * q^81 - 886 * q^82 + 5315 * q^83 + 672 * q^84 + 3997 * q^86 - 756 * q^87 + 2969 * q^88 - 1424 * q^89 - 1194 * q^91 + 1607 * q^92 + 2667 * q^93 - 629 * q^94 - 1266 * q^96 + 291 * q^97 - 1018 * q^98 - 297 * q^99

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