LMFDB - Embedded newform 1875.4.a.f.1.1

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			1.1
Root			$4.81720$ 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)

$f(q)$	$=$	$q-4.81720 q^{2} -3.00000 q^{3} +15.2054 q^{4} +14.4516 q^{6} -1.13492 q^{7} -34.7100 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.81720 q^{2} -3.00000 q^{3} +15.2054 q^{4} +14.4516 q^{6} -1.13492 q^{7} -34.7100 q^{8} +9.00000 q^{9} -57.5251 q^{11} -45.6163 q^{12} +41.9803 q^{13} +5.46712 q^{14} +45.5614 q^{16} +107.739 q^{17} -43.3548 q^{18} -53.2840 q^{19} +3.40475 q^{21} +277.110 q^{22} +17.2342 q^{23} +104.130 q^{24} -202.228 q^{26} -27.0000 q^{27} -17.2569 q^{28} +140.284 q^{29} -242.942 q^{31} +58.2010 q^{32} +172.575 q^{33} -519.002 q^{34} +136.849 q^{36} -349.267 q^{37} +256.680 q^{38} -125.941 q^{39} -8.55390 q^{41} -16.4014 q^{42} -111.804 q^{43} -874.693 q^{44} -83.0205 q^{46} +322.875 q^{47} -136.684 q^{48} -341.712 q^{49} -323.218 q^{51} +638.329 q^{52} +410.636 q^{53} +130.064 q^{54} +39.3929 q^{56} +159.852 q^{57} -675.775 q^{58} +666.424 q^{59} +296.261 q^{61} +1170.30 q^{62} -10.2143 q^{63} -644.858 q^{64} -831.330 q^{66} +840.470 q^{67} +1638.22 q^{68} -51.7025 q^{69} -56.3365 q^{71} -312.390 q^{72} -216.805 q^{73} +1682.49 q^{74} -810.206 q^{76} +65.2862 q^{77} +606.683 q^{78} +419.925 q^{79} +81.0000 q^{81} +41.2059 q^{82} -1457.55 q^{83} +51.7707 q^{84} +538.582 q^{86} -420.852 q^{87} +1996.69 q^{88} -1225.87 q^{89} -47.6442 q^{91} +262.053 q^{92} +728.827 q^{93} -1555.36 q^{94} -174.603 q^{96} -519.015 q^{97} +1646.10 q^{98} -517.726 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.81720	−1.70314	−0.851569	−	0.524243i	$-0.824348\pi$
$2$	−4.81720	−1.70314	−0.851569	+	0.524243i	$0.824348\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	15.2054	1.90068
$5$	0	0
$5$	0	0
$6$	14.4516	0.983307
$7$	−1.13492	−0.0612798	−0.0306399	−	0.999530i	$-0.509755\pi$
$7$	−1.13492	−0.0612798	−0.0306399	+	0.999530i	$0.509755\pi$
$8$	−34.7100	−1.53398
$9$	9.00000	0.333333
$10$	0	0
$11$	−57.5251	−1.57677	−0.788385	−	0.615182i	$-0.789082\pi$
$11$	−57.5251	−1.57677	−0.788385	+	0.615182i	$0.789082\pi$
$12$	−45.6163	−1.09736
$13$	41.9803	0.895635	0.447817	−	0.894125i	$-0.352201\pi$
$13$	41.9803	0.895635	0.447817	+	0.894125i	$0.352201\pi$
$14$	5.46712	0.104368
$15$	0	0
$16$	45.5614	0.711898
$17$	107.739	1.53710	0.768548	−	0.639792i	$-0.220980\pi$
$17$	107.739	1.53710	0.768548	+	0.639792i	$0.220980\pi$
$18$	−43.3548	−0.567713
$19$	−53.2840	−0.643378	−0.321689	−	0.946845i	$-0.604251\pi$
$19$	−53.2840	−0.643378	−0.321689	+	0.946845i	$0.604251\pi$
$20$	0	0
$21$	3.40475	0.0353799
$22$	277.110	2.68546
$23$	17.2342	0.156242	0.0781212	−	0.996944i	$-0.475108\pi$
$23$	17.2342	0.156242	0.0781212	+	0.996944i	$0.475108\pi$
$24$	104.130	0.885642
$25$	0	0
$26$	−202.228	−1.52539
$27$	−27.0000	−0.192450
$28$	−17.2569	−0.116473
$29$	140.284	0.898278	0.449139	−	0.893462i	$-0.351731\pi$
$29$	140.284	0.898278	0.449139	+	0.893462i	$0.351731\pi$
$30$	0	0
$31$	−242.942	−1.40754	−0.703769	−	0.710428i	$-0.748501\pi$
$31$	−242.942	−1.40754	−0.703769	+	0.710428i	$0.748501\pi$
$32$	58.2010	0.321518
$33$	172.575	0.910349
$34$	−519.002	−2.61789
$35$	0	0
$36$	136.849	0.633559
$37$	−349.267	−1.55187	−0.775935	−	0.630813i	$-0.782722\pi$
$37$	−349.267	−1.55187	−0.775935	+	0.630813i	$0.782722\pi$
$38$	256.680	1.09576
$39$	−125.941	−0.517095
$40$	0	0
$41$	−8.55390	−0.0325828	−0.0162914	−	0.999867i	$-0.505186\pi$
$41$	−8.55390	−0.0325828	−0.0162914	+	0.999867i	$0.505186\pi$
$42$	−16.4014	−0.0602568
$43$	−111.804	−0.396510	−0.198255	−	0.980150i	$-0.563527\pi$
$43$	−111.804	−0.396510	−0.198255	+	0.980150i	$0.563527\pi$
$44$	−874.693	−2.99693
$45$	0	0
$46$	−83.0205	−0.266102
$47$	322.875	1.00205	0.501023	−	0.865434i	$-0.332957\pi$
$47$	322.875	1.00205	0.501023	+	0.865434i	$0.332957\pi$
$48$	−136.684	−0.411014
$49$	−341.712	−0.996245
$50$	0	0
$51$	−323.218	−0.887443
$52$	638.329	1.70231
$53$	410.636	1.06425	0.532124	−	0.846666i	$-0.321394\pi$
$53$	410.636	1.06425	0.532124	+	0.846666i	$0.321394\pi$
$54$	130.064	0.327769
$55$	0	0
$56$	39.3929	0.0940018
$57$	159.852	0.371455
$58$	−675.775	−1.52989
$59$	666.424	1.47053	0.735263	−	0.677782i	$-0.237059\pi$
$59$	666.424	1.47053	0.735263	+	0.677782i	$0.237059\pi$
$60$	0	0
$61$	296.261	0.621842	0.310921	−	0.950436i	$-0.399363\pi$
$61$	296.261	0.621842	0.310921	+	0.950436i	$0.399363\pi$
$62$	1170.30	2.39723
$63$	−10.2143	−0.0204266
$64$	−644.858	−1.25949
$65$	0	0
$66$	−831.330	−1.55045
$67$	840.470	1.53253	0.766267	−	0.642522i	$-0.222112\pi$
$67$	840.470	1.53253	0.766267	+	0.642522i	$0.222112\pi$
$68$	1638.22	2.92152
$69$	−51.7025	−0.0902066
$70$	0	0
$71$	−56.3365	−0.0941678	−0.0470839	−	0.998891i	$-0.514993\pi$
$71$	−56.3365	−0.0941678	−0.0470839	+	0.998891i	$0.514993\pi$
$72$	−312.390	−0.511326
$73$	−216.805	−0.347605	−0.173802	−	0.984781i	$-0.555605\pi$
$73$	−216.805	−0.347605	−0.173802	+	0.984781i	$0.555605\pi$
$74$	1682.49	2.64305
$75$	0	0
$76$	−810.206	−1.22285
$77$	65.2862	0.0966241
$78$	606.683	0.880684
$79$	419.925	0.598041	0.299020	−	0.954247i	$-0.403340\pi$
$79$	419.925	0.598041	0.299020	+	0.954247i	$0.403340\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	41.2059	0.0554930
$83$	−1457.55	−1.92756	−0.963779	−	0.266700i	$-0.914067\pi$
$83$	−1457.55	−1.92756	−0.963779	+	0.266700i	$0.914067\pi$
$84$	51.7707	0.0672458
$85$	0	0
$86$	538.582	0.675311
$87$	−420.852	−0.518621
$88$	1996.69	2.41873
$89$	−1225.87	−1.46002	−0.730012	−	0.683434i	$-0.760486\pi$
$89$	−1225.87	−1.46002	−0.730012	+	0.683434i	$0.760486\pi$
$90$	0	0
$91$	−47.6442	−0.0548843
$92$	262.053	0.296966
$93$	728.827	0.812643
$94$	−1555.36	−1.70662
$95$	0	0
$96$	−174.603	−0.185629
$97$	−519.015	−0.543278	−0.271639	−	0.962399i	$-0.587566\pi$
$97$	−519.015	−0.543278	−0.271639	+	0.962399i	$0.587566\pi$
$98$	1646.10	1.69674
$99$	−517.726	−0.525590
$100$	0	0
$101$	1607.10	1.58329	0.791645	−	0.610981i	$-0.209225\pi$
$101$	1607.10	1.58329	0.791645	+	0.610981i	$0.209225\pi$
$102$	1557.01	1.51144
$103$	348.501	0.333387	0.166693	−	0.986009i	$-0.446691\pi$
$103$	348.501	0.333387	0.166693	+	0.986009i	$0.446691\pi$
$104$	−1457.14	−1.37388
$105$	0	0
$106$	−1978.11	−1.81256
$107$	−1553.10	−1.40321	−0.701605	−	0.712566i	$-0.747533\pi$
$107$	−1553.10	−1.40321	−0.701605	+	0.712566i	$0.747533\pi$
$108$	−410.546	−0.365786
$109$	365.995	0.321614	0.160807	−	0.986986i	$-0.448590\pi$
$109$	365.995	0.321614	0.160807	+	0.986986i	$0.448590\pi$
$110$	0	0
$111$	1047.80	0.895973
$112$	−51.7085	−0.0436249
$113$	214.014	0.178166	0.0890828	−	0.996024i	$-0.471606\pi$
$113$	214.014	0.178166	0.0890828	+	0.996024i	$0.471606\pi$
$114$	−770.039	−0.632638
$115$	0	0
$116$	2133.07	1.70734
$117$	377.823	0.298545
$118$	−3210.30	−2.50451
$119$	−122.275	−0.0941929
$120$	0	0
$121$	1978.14	1.48620
$122$	−1427.15	−1.05908
$123$	25.6617	0.0188117
$124$	−3694.04	−2.67528
$125$	0	0
$126$	49.2041	0.0347893
$127$	−779.537	−0.544667	−0.272334	−	0.962203i	$-0.587795\pi$
$127$	−779.537	−0.544667	−0.272334	+	0.962203i	$0.587795\pi$
$128$	2640.80	1.82356
$129$	335.412	0.228925
$130$	0	0
$131$	847.951	0.565541	0.282770	−	0.959188i	$-0.408747\pi$
$131$	847.951	0.565541	0.282770	+	0.959188i	$0.408747\pi$
$132$	2624.08	1.73028
$133$	60.4729	0.0394261
$134$	−4048.71	−2.61012
$135$	0	0
$136$	−3739.63	−2.35787
$137$	1270.83	0.792512	0.396256	−	0.918140i	$-0.370309\pi$
$137$	1270.83	0.792512	0.396256	+	0.918140i	$0.370309\pi$
$138$	249.062	0.153634
$139$	−685.272	−0.418158	−0.209079	−	0.977899i	$-0.567047\pi$
$139$	−685.272	−0.418158	−0.209079	+	0.977899i	$0.567047\pi$
$140$	0	0
$141$	−968.626	−0.578532
$142$	271.384	0.160381
$143$	−2414.92	−1.41221
$144$	410.053	0.237299
$145$	0	0
$146$	1044.39	0.592019
$147$	1025.14	0.575182
$148$	−5310.76	−2.94960
$149$	−2370.55	−1.30338	−0.651688	−	0.758488i	$-0.725939\pi$
$149$	−2370.55	−1.30338	−0.651688	+	0.758488i	$0.725939\pi$
$150$	0	0
$151$	−1177.98	−0.634850	−0.317425	−	0.948283i	$-0.602818\pi$
$151$	−1177.98	−0.634850	−0.317425	+	0.948283i	$0.602818\pi$
$152$	1849.49	0.986928
$153$	969.654	0.512365
$154$	−314.497	−0.164564
$155$	0	0
$156$	−1914.99	−0.982831
$157$	−1663.45	−0.845593	−0.422797	−	0.906225i	$-0.638952\pi$
$157$	−1663.45	−0.845593	−0.422797	+	0.906225i	$0.638952\pi$
$158$	−2022.86	−1.01855
$159$	−1231.91	−0.614444
$160$	0	0
$161$	−19.5594	−0.00957450
$162$	−390.193	−0.189238
$163$	1240.55	0.596118	0.298059	−	0.954547i	$-0.403661\pi$
$163$	1240.55	0.596118	0.298059	+	0.954547i	$0.403661\pi$
$164$	−130.066	−0.0619294
$165$	0	0
$166$	7021.33	3.28290
$167$	−3637.25	−1.68538	−0.842691	−	0.538398i	$-0.819030\pi$
$167$	−3637.25	−1.68538	−0.842691	+	0.538398i	$0.819030\pi$
$168$	−118.179	−0.0542720
$169$	−434.651	−0.197838
$170$	0	0
$171$	−479.556	−0.214459
$172$	−1700.03	−0.753638
$173$	−2289.22	−1.00605	−0.503024	−	0.864273i	$-0.667779\pi$
$173$	−2289.22	−1.00605	−0.503024	+	0.864273i	$0.667779\pi$
$174$	2027.33	0.883283
$175$	0	0
$176$	−2620.93	−1.12250
$177$	−1999.27	−0.849008
$178$	5905.27	2.48662
$179$	−2259.85	−0.943626	−0.471813	−	0.881699i	$-0.656400\pi$
$179$	−2259.85	−0.943626	−0.471813	+	0.881699i	$0.656400\pi$
$180$	0	0
$181$	−51.6267	−0.0212010	−0.0106005	−	0.999944i	$-0.503374\pi$
$181$	−51.6267	−0.0212010	−0.0106005	+	0.999944i	$0.503374\pi$
$182$	229.512	0.0934755
$183$	−888.783	−0.359020
$184$	−598.198	−0.239672
$185$	0	0
$186$	−3510.90	−1.38404
$187$	−6197.72	−2.42365
$188$	4909.45	1.90457
$189$	30.6428	0.0117933
$190$	0	0
$191$	1755.19	0.664926	0.332463	−	0.943116i	$-0.392120\pi$
$191$	1755.19	0.664926	0.332463	+	0.943116i	$0.392120\pi$
$192$	1934.57	0.727165
$193$	4463.71	1.66479	0.832397	−	0.554180i	$-0.186968\pi$
$193$	4463.71	1.66479	0.832397	+	0.554180i	$0.186968\pi$
$194$	2500.20	0.925277
$195$	0	0
$196$	−5195.87	−1.89354
$197$	3534.93	1.27844	0.639222	−	0.769022i	$-0.279256\pi$
$197$	3534.93	1.27844	0.639222	+	0.769022i	$0.279256\pi$
$198$	2493.99	0.895152
$199$	−3943.80	−1.40487	−0.702434	−	0.711749i	$-0.747903\pi$
$199$	−3943.80	−1.40487	−0.702434	+	0.711749i	$0.747903\pi$
$200$	0	0
$201$	−2521.41	−0.884809
$202$	−7741.72	−2.69656
$203$	−159.211	−0.0550463
$204$	−4914.67	−1.68674
$205$	0	0
$206$	−1678.80	−0.567803
$207$	155.108	0.0520808
$208$	1912.69	0.637600
$209$	3065.17	1.01446
$210$	0	0
$211$	−3136.79	−1.02344	−0.511719	−	0.859153i	$-0.670991\pi$
$211$	−3136.79	−1.02344	−0.511719	+	0.859153i	$0.670991\pi$
$212$	6243.89	2.02279
$213$	169.009	0.0543678
$214$	7481.58	2.38986
$215$	0	0
$216$	937.169	0.295214
$217$	275.719	0.0862537
$218$	−1763.07	−0.547753
$219$	650.416	0.200690
$220$	0	0
$221$	4522.93	1.37668
$222$	−5047.47	−1.52596
$223$	2339.00	0.702381	0.351191	−	0.936304i	$-0.385777\pi$
$223$	2339.00	0.702381	0.351191	+	0.936304i	$0.385777\pi$
$224$	−66.0533	−0.0197026
$225$	0	0
$226$	−1030.95	−0.303441
$227$	−1011.42	−0.295728	−0.147864	−	0.989008i	$-0.547240\pi$
$227$	−1011.42	−0.295728	−0.147864	+	0.989008i	$0.547240\pi$
$228$	2430.62	0.706015
$229$	−3053.36	−0.881101	−0.440550	−	0.897728i	$-0.645217\pi$
$229$	−3053.36	−0.881101	−0.440550	+	0.897728i	$0.645217\pi$
$230$	0	0
$231$	−195.859	−0.0557860
$232$	−4869.25	−1.37794
$233$	6403.12	1.80035	0.900176	−	0.435526i	$-0.143438\pi$
$233$	6403.12	1.80035	0.900176	+	0.435526i	$0.143438\pi$
$234$	−1820.05	−0.508463
$235$	0	0
$236$	10133.3	2.79499
$237$	−1259.77	−0.345279
$238$	589.024	0.160423
$239$	−3833.08	−1.03741	−0.518705	−	0.854953i	$-0.673586\pi$
$239$	−3833.08	−1.03741	−0.518705	+	0.854953i	$0.673586\pi$
$240$	0	0
$241$	−3560.08	−0.951556	−0.475778	−	0.879565i	$-0.657834\pi$
$241$	−3560.08	−0.951556	−0.475778	+	0.879565i	$0.657834\pi$
$242$	−9529.08	−2.53121
$243$	−243.000	−0.0641500
$244$	4504.77	1.18192
$245$	0	0
$246$	−123.618	−0.0320389
$247$	−2236.88	−0.576232
$248$	8432.51	2.15913
$249$	4372.66	1.11288
$250$	0	0
$251$	177.342	0.0445964	0.0222982	−	0.999751i	$-0.492902\pi$
$251$	177.342	0.0445964	0.0222982	+	0.999751i	$0.492902\pi$
$252$	−155.312	−0.0388244
$253$	−991.398	−0.246358
$254$	3755.19	0.927643
$255$	0	0
$256$	−7562.40	−1.84629
$257$	6061.58	1.47125	0.735624	−	0.677390i	$-0.236889\pi$
$257$	6061.58	1.47125	0.735624	+	0.677390i	$0.236889\pi$
$258$	−1615.75	−0.389891
$259$	396.389	0.0950982
$260$	0	0
$261$	1262.55	0.299426
$262$	−4084.75	−0.963194
$263$	−372.991	−0.0874511	−0.0437255	−	0.999044i	$-0.513923\pi$
$263$	−372.991	−0.0874511	−0.0437255	+	0.999044i	$0.513923\pi$
$264$	−5990.08	−1.39645
$265$	0	0
$266$	−291.310	−0.0671480
$267$	3677.62	0.842946
$268$	12779.7	2.91285
$269$	2711.00	0.614471	0.307235	−	0.951634i	$-0.400596\pi$
$269$	2711.00	0.614471	0.307235	+	0.951634i	$0.400596\pi$
$270$	0	0
$271$	−5495.61	−1.23186	−0.615931	−	0.787800i	$-0.711220\pi$
$271$	−5495.61	−1.23186	−0.615931	+	0.787800i	$0.711220\pi$
$272$	4908.76	1.09425
$273$	142.933	0.0316875
$274$	−6121.83	−1.34976
$275$	0	0
$276$	−786.159	−0.171454
$277$	798.612	0.173227	0.0866137	−	0.996242i	$-0.472395\pi$
$277$	798.612	0.173227	0.0866137	+	0.996242i	$0.472395\pi$
$278$	3301.09	0.712181
$279$	−2186.48	−0.469180
$280$	0	0
$281$	1987.98	0.422039	0.211020	−	0.977482i	$-0.432322\pi$
$281$	1987.98	0.422039	0.211020	+	0.977482i	$0.432322\pi$
$282$	4666.07	0.985320
$283$	−877.987	−0.184420	−0.0922101	−	0.995740i	$-0.529393\pi$
$283$	−877.987	−0.184420	−0.0922101	+	0.995740i	$0.529393\pi$
$284$	−856.620	−0.178983
$285$	0	0
$286$	11633.2	2.40519
$287$	9.70797	0.00199667
$288$	523.809	0.107173
$289$	6694.77	1.36266
$290$	0	0
$291$	1557.04	0.313662
$292$	−3296.62	−0.660684
$293$	−115.531	−0.0230355	−0.0115178	−	0.999934i	$-0.503666\pi$
$293$	−115.531	−0.0230355	−0.0115178	+	0.999934i	$0.503666\pi$
$294$	−4938.29	−0.979614
$295$	0	0
$296$	12123.1	2.38053
$297$	1553.18	0.303450
$298$	11419.4	2.21983
$299$	723.497	0.139936
$300$	0	0
$301$	126.888	0.0242981
$302$	5674.55	1.08124
$303$	−4821.30	−0.914113
$304$	−2427.70	−0.458019
$305$	0	0
$306$	−4671.02	−0.872629
$307$	4930.95	0.916691	0.458345	−	0.888774i	$-0.348442\pi$
$307$	4930.95	0.916691	0.458345	+	0.888774i	$0.348442\pi$
$308$	992.704	0.183651
$309$	−1045.50	−0.192481
$310$	0	0
$311$	6968.39	1.27055	0.635275	−	0.772286i	$-0.280887\pi$
$311$	6968.39	1.27055	0.635275	+	0.772286i	$0.280887\pi$
$312$	4371.41	0.793212
$313$	4501.12	0.812837	0.406419	−	0.913687i	$-0.366777\pi$
$313$	4501.12	0.812837	0.406419	+	0.913687i	$0.366777\pi$
$314$	8013.20	1.44016
$315$	0	0
$316$	6385.13	1.13668
$317$	2229.04	0.394938	0.197469	−	0.980309i	$-0.436728\pi$
$317$	2229.04	0.394938	0.197469	+	0.980309i	$0.436728\pi$
$318$	5934.34	1.04648
$319$	−8069.84	−1.41638
$320$	0	0
$321$	4659.29	0.810144
$322$	94.2214	0.0163067
$323$	−5740.78	−0.988934
$324$	1231.64	0.211186
$325$	0	0
$326$	−5975.97	−1.01527
$327$	−1097.98	−0.185684
$328$	296.905	0.0499813
$329$	−366.437	−0.0614052
$330$	0	0
$331$	10187.5	1.69171	0.845855	−	0.533413i	$-0.179091\pi$
$331$	10187.5	1.69171	0.845855	+	0.533413i	$0.179091\pi$
$332$	−22162.7	−3.66367
$333$	−3143.41	−0.517290
$334$	17521.3	2.87044
$335$	0	0
$336$	155.125	0.0251869
$337$	−1585.76	−0.256326	−0.128163	−	0.991753i	$-0.540908\pi$
$337$	−1585.76	−0.256326	−0.128163	+	0.991753i	$0.540908\pi$
$338$	2093.80	0.336946
$339$	−642.041	−0.102864
$340$	0	0
$341$	13975.3	2.21937
$342$	2310.12	0.365254
$343$	777.091	0.122329
$344$	3880.71	0.608238
$345$	0	0
$346$	11027.6	1.71344
$347$	−1112.45	−0.172102	−0.0860512	−	0.996291i	$-0.527425\pi$
$347$	−1112.45	−0.172102	−0.0860512	+	0.996291i	$0.527425\pi$
$348$	−6399.22	−0.985731
$349$	5181.97	0.794798	0.397399	−	0.917646i	$-0.369913\pi$
$349$	5181.97	0.794798	0.397399	+	0.917646i	$0.369913\pi$
$350$	0	0
$351$	−1133.47	−0.172365
$352$	−3348.02	−0.506960
$353$	−7180.29	−1.08263	−0.541315	−	0.840820i	$-0.682073\pi$
$353$	−7180.29	−1.08263	−0.541315	+	0.840820i	$0.682073\pi$
$354$	9630.89	1.44598
$355$	0	0
$356$	−18639.9	−2.77504
$357$	366.826	0.0543823
$358$	10886.1	1.60712
$359$	−5942.90	−0.873688	−0.436844	−	0.899537i	$-0.643904\pi$
$359$	−5942.90	−0.873688	−0.436844	+	0.899537i	$0.643904\pi$
$360$	0	0
$361$	−4019.82	−0.586064
$362$	248.696	0.0361082
$363$	−5934.41	−0.858060
$364$	−724.450	−0.104317
$365$	0	0
$366$	4281.45	0.611461
$367$	6868.02	0.976860	0.488430	−	0.872603i	$-0.337570\pi$
$367$	6868.02	0.976860	0.488430	+	0.872603i	$0.337570\pi$
$368$	785.214	0.111229
$369$	−76.9851	−0.0108609
$370$	0	0
$371$	−466.038	−0.0652169
$372$	11082.1	1.54457
$373$	−4160.27	−0.577508	−0.288754	−	0.957403i	$-0.593241\pi$
$373$	−4160.27	−0.577508	−0.288754	+	0.957403i	$0.593241\pi$
$374$	29855.6	4.12780
$375$	0	0
$376$	−11207.0	−1.53712
$377$	5889.16	0.804529
$378$	−147.612	−0.0200856
$379$	3883.57	0.526347	0.263173	−	0.964749i	$-0.415231\pi$
$379$	3883.57	0.526347	0.263173	+	0.964749i	$0.415231\pi$
$380$	0	0
$381$	2338.61	0.314464
$382$	−8455.09	−1.13246
$383$	6600.16	0.880555	0.440277	−	0.897862i	$-0.354880\pi$
$383$	6600.16	0.880555	0.440277	+	0.897862i	$0.354880\pi$
$384$	−7922.40	−1.05283
$385$	0	0
$386$	−21502.6	−2.83537
$387$	−1006.24	−0.132170
$388$	−7891.83	−1.03260
$389$	−9481.99	−1.23588	−0.617938	−	0.786227i	$-0.712032\pi$
$389$	−9481.99	−1.23588	−0.617938	+	0.786227i	$0.712032\pi$
$390$	0	0
$391$	1856.80	0.240160
$392$	11860.8	1.52822
$393$	−2543.85	−0.326515
$394$	−17028.5	−2.17737
$395$	0	0
$396$	−7872.24	−0.998977
$397$	−743.303	−0.0939680	−0.0469840	−	0.998896i	$-0.514961\pi$
$397$	−743.303	−0.0939680	−0.0469840	+	0.998896i	$0.514961\pi$
$398$	18998.1	2.39268
$399$	−181.419	−0.0227627
$400$	0	0
$401$	8535.31	1.06292	0.531462	−	0.847082i	$-0.321643\pi$
$401$	8535.31	1.06292	0.531462	+	0.847082i	$0.321643\pi$
$402$	12146.1	1.50695
$403$	−10198.8	−1.26064
$404$	24436.6	3.00932
$405$	0	0
$406$	766.949	0.0937513
$407$	20091.6	2.44694
$408$	11218.9	1.36132
$409$	2509.21	0.303355	0.151678	−	0.988430i	$-0.451532\pi$
$409$	2509.21	0.303355	0.151678	+	0.988430i	$0.451532\pi$
$410$	0	0
$411$	−3812.48	−0.457557
$412$	5299.10	0.633661
$413$	−756.336	−0.0901134
$414$	−747.185	−0.0887008
$415$	0	0
$416$	2443.30	0.287963
$417$	2055.82	0.241424
$418$	−14765.5	−1.72776
$419$	4729.99	0.551492	0.275746	−	0.961231i	$-0.411075\pi$
$419$	4729.99	0.551492	0.275746	+	0.961231i	$0.411075\pi$
$420$	0	0
$421$	8162.56	0.944938	0.472469	−	0.881347i	$-0.343363\pi$
$421$	8162.56	0.944938	0.472469	+	0.881347i	$0.343363\pi$
$422$	15110.5	1.74305
$423$	2905.88	0.334016
$424$	−14253.1	−1.63253
$425$	0	0
$426$	−814.153	−0.0925958
$427$	−336.232	−0.0381063
$428$	−23615.5	−2.66705
$429$	7244.77	0.815340
$430$	0	0
$431$	7671.00	0.857307	0.428653	−	0.903469i	$-0.358988\pi$
$431$	7671.00	0.857307	0.428653	+	0.903469i	$0.358988\pi$
$432$	−1230.16	−0.137005
$433$	13737.1	1.52463	0.762313	−	0.647209i	$-0.224064\pi$
$433$	13737.1	1.52463	0.762313	+	0.647209i	$0.224064\pi$
$434$	−1328.19	−0.146902
$435$	0	0
$436$	5565.10	0.611285
$437$	−918.306	−0.100523
$438$	−3133.18	−0.341802
$439$	12181.4	1.32434	0.662172	−	0.749352i	$-0.269635\pi$
$439$	12181.4	1.32434	0.662172	+	0.749352i	$0.269635\pi$
$440$	0	0
$441$	−3075.41	−0.332082
$442$	−21787.9	−2.34467
$443$	3654.36	0.391927	0.195964	−	0.980611i	$-0.437217\pi$
$443$	3654.36	0.391927	0.195964	+	0.980611i	$0.437217\pi$
$444$	15932.3	1.70296
$445$	0	0
$446$	−11267.4	−1.19625
$447$	7111.65	0.752504
$448$	731.860	0.0771811
$449$	2365.17	0.248595	0.124297	−	0.992245i	$-0.460332\pi$
$449$	2365.17	0.248595	0.124297	+	0.992245i	$0.460332\pi$
$450$	0	0
$451$	492.064	0.0513756
$452$	3254.17	0.338635
$453$	3533.93	0.366531
$454$	4872.21	0.503665
$455$	0	0
$456$	−5548.46	−0.569803
$457$	2585.28	0.264626	0.132313	−	0.991208i	$-0.457760\pi$
$457$	2585.28	0.264626	0.132313	+	0.991208i	$0.457760\pi$
$458$	14708.7	1.50064
$459$	−2908.96	−0.295814
$460$	0	0
$461$	3966.86	0.400771	0.200385	−	0.979717i	$-0.435781\pi$
$461$	3966.86	0.400771	0.200385	+	0.979717i	$0.435781\pi$
$462$	943.490	0.0950111
$463$	−5456.09	−0.547658	−0.273829	−	0.961778i	$-0.588290\pi$
$463$	−5456.09	−0.547658	−0.273829	+	0.961778i	$0.588290\pi$
$464$	6391.53	0.639482
$465$	0	0
$466$	−30845.1	−3.06625
$467$	14709.4	1.45753	0.728767	−	0.684762i	$-0.240094\pi$
$467$	14709.4	1.45753	0.728767	+	0.684762i	$0.240094\pi$
$468$	5744.96	0.567438
$469$	−953.864	−0.0939133
$470$	0	0
$471$	4990.36	0.488203
$472$	−23131.5	−2.25575
$473$	6431.53	0.625205
$474$	6068.58	0.588058
$475$	0	0
$476$	−1859.25	−0.179030
$477$	3695.72	0.354749
$478$	18464.7	1.76685
$479$	10246.1	0.977359	0.488679	−	0.872463i	$-0.337479\pi$
$479$	10246.1	0.977359	0.488679	+	0.872463i	$0.337479\pi$
$480$	0	0
$481$	−14662.4	−1.38991
$482$	17149.6	1.62063
$483$	58.6781	0.00552784
$484$	30078.4	2.82479
$485$	0	0
$486$	1170.58	0.109256
$487$	−4409.12	−0.410259	−0.205130	−	0.978735i	$-0.565762\pi$
$487$	−4409.12	−0.410259	−0.205130	+	0.978735i	$0.565762\pi$
$488$	−10283.2	−0.953891
$489$	−3721.64	−0.344169
$490$	0	0
$491$	−3227.96	−0.296692	−0.148346	−	0.988936i	$-0.547395\pi$
$491$	−3227.96	−0.296692	−0.148346	+	0.988936i	$0.547395\pi$
$492$	390.197	0.0357550
$493$	15114.1	1.38074
$494$	10775.5	0.981402
$495$	0	0
$496$	−11068.8	−1.00202
$497$	63.9373	0.00577058
$498$	−21064.0	−1.89538
$499$	−10683.6	−0.958442	−0.479221	−	0.877694i	$-0.659081\pi$
$499$	−10683.6	−0.958442	−0.479221	+	0.877694i	$0.659081\pi$
$500$	0	0
$501$	10911.7	0.973055
$502$	−854.290	−0.0759538
$503$	6207.86	0.550288	0.275144	−	0.961403i	$-0.411275\pi$
$503$	6207.86	0.550288	0.275144	+	0.961403i	$0.411275\pi$
$504$	354.536	0.0313339
$505$	0	0
$506$	4775.76	0.419582
$507$	1303.95	0.114222
$508$	−11853.2	−1.03524
$509$	20063.6	1.74716	0.873578	−	0.486685i	$-0.161794\pi$
$509$	20063.6	1.74716	0.873578	+	0.486685i	$0.161794\pi$
$510$	0	0
$511$	246.056	0.0213011
$512$	15303.2	1.32092
$513$	1438.67	0.123818
$514$	−29199.8	−2.50574
$515$	0	0
$516$	5100.08	0.435113
$517$	−18573.4	−1.58000
$518$	−1909.49	−0.161965
$519$	6867.66	0.580842
$520$	0	0
$521$	−10202.7	−0.857942	−0.428971	−	0.903318i	$-0.641124\pi$
$521$	−10202.7	−0.857942	−0.428971	+	0.903318i	$0.641124\pi$
$522$	−6081.98	−0.509964
$523$	3949.39	0.330200	0.165100	−	0.986277i	$-0.447205\pi$
$523$	3949.39	0.330200	0.165100	+	0.986277i	$0.447205\pi$
$524$	12893.5	1.07491
$525$	0	0
$526$	1796.77	0.148941
$527$	−26174.4	−2.16352
$528$	7862.78	0.648075
$529$	−11870.0	−0.975588
$530$	0	0
$531$	5997.81	0.490175
$532$	919.516	0.0749363
$533$	−359.096	−0.0291823
$534$	−17715.8	−1.43565
$535$	0	0
$536$	−29172.7	−2.35087
$537$	6779.55	0.544803
$538$	−13059.4	−1.04653
$539$	19657.0	1.57085
$540$	0	0
$541$	23606.3	1.87600	0.937998	−	0.346640i	$-0.112677\pi$
$541$	23606.3	1.87600	0.937998	+	0.346640i	$0.112677\pi$
$542$	26473.5	2.09803
$543$	154.880	0.0122404
$544$	6270.54	0.494204
$545$	0	0
$546$	−688.535	−0.0539681
$547$	7592.65	0.593489	0.296744	−	0.954957i	$-0.404099\pi$
$547$	7592.65	0.593489	0.296744	+	0.954957i	$0.404099\pi$
$548$	19323.5	1.50631
$549$	2666.35	0.207281
$550$	0	0
$551$	−7474.88	−0.577932
$552$	1794.59	0.138375
$553$	−476.580	−0.0366478
$554$	−3847.08	−0.295030
$555$	0	0
$556$	−10419.9	−0.794784
$557$	7392.19	0.562329	0.281164	−	0.959660i	$-0.409279\pi$
$557$	7392.19	0.562329	0.281164	+	0.959660i	$0.409279\pi$
$558$	10532.7	0.799077
$559$	−4693.57	−0.355128
$560$	0	0
$561$	18593.2	1.39929
$562$	−9576.51	−0.718791
$563$	−5960.45	−0.446186	−0.223093	−	0.974797i	$-0.571615\pi$
$563$	−5960.45	−0.446186	−0.223093	+	0.974797i	$0.571615\pi$
$564$	−14728.4	−1.09960
$565$	0	0
$566$	4229.44	0.314093
$567$	−91.9283	−0.00680886
$568$	1955.44	0.144451
$569$	2054.92	0.151400	0.0757002	−	0.997131i	$-0.475881\pi$
$569$	2054.92	0.151400	0.0757002	+	0.997131i	$0.475881\pi$
$570$	0	0
$571$	15032.4	1.10172	0.550862	−	0.834596i	$-0.314299\pi$
$571$	15032.4	1.10172	0.550862	+	0.834596i	$0.314299\pi$
$572$	−36719.9	−2.68416
$573$	−5265.56	−0.383895
$574$	−46.7652	−0.00340060
$575$	0	0
$576$	−5803.72	−0.419829
$577$	−9550.84	−0.689093	−0.344547	−	0.938769i	$-0.611967\pi$
$577$	−9550.84	−0.689093	−0.344547	+	0.938769i	$0.611967\pi$
$578$	−32250.0	−2.32080
$579$	−13391.1	−0.961169
$580$	0	0
$581$	1654.20	0.118120
$582$	−7500.59	−0.534209
$583$	−23621.9	−1.67807
$584$	7525.30	0.533218
$585$	0	0
$586$	556.537	0.0392327
$587$	1568.37	0.110279	0.0551393	−	0.998479i	$-0.482440\pi$
$587$	1568.37	0.110279	0.0551393	+	0.998479i	$0.482440\pi$
$588$	15587.6	1.09324
$589$	12944.9	0.905580
$590$	0	0
$591$	−10604.8	−0.738110
$592$	−15913.1	−1.10477
$593$	−11899.9	−0.824061	−0.412031	−	0.911170i	$-0.635180\pi$
$593$	−11899.9	−0.824061	−0.412031	+	0.911170i	$0.635180\pi$
$594$	−7481.97	−0.516816
$595$	0	0
$596$	−36045.2	−2.47730
$597$	11831.4	0.811100
$598$	−3485.23	−0.238331
$599$	−8134.32	−0.554857	−0.277428	−	0.960746i	$-0.589482\pi$
$599$	−8134.32	−0.554857	−0.277428	+	0.960746i	$0.589482\pi$
$600$	0	0
$601$	20859.5	1.41577	0.707884	−	0.706329i	$-0.249650\pi$
$601$	20859.5	1.41577	0.707884	+	0.706329i	$0.249650\pi$
$602$	−611.246	−0.0413829
$603$	7564.23	0.510845
$604$	−17911.6	−1.20665
$605$	0	0
$606$	23225.1	1.55686
$607$	8452.89	0.565226	0.282613	−	0.959234i	$-0.408799\pi$
$607$	8452.89	0.565226	0.282613	+	0.959234i	$0.408799\pi$
$608$	−3101.18	−0.206858
$609$	477.632	0.0317810
$610$	0	0
$611$	13554.4	0.897468
$612$	14744.0	0.973841
$613$	−9372.02	−0.617508	−0.308754	−	0.951142i	$-0.599912\pi$
$613$	−9372.02	−0.617508	−0.308754	+	0.951142i	$0.599912\pi$
$614$	−23753.4	−1.56125
$615$	0	0
$616$	−2266.08	−0.148219
$617$	14435.0	0.941867	0.470933	−	0.882169i	$-0.343917\pi$
$617$	14435.0	0.941867	0.470933	+	0.882169i	$0.343917\pi$
$618$	5036.40	0.327821
$619$	6690.40	0.434426	0.217213	−	0.976124i	$-0.430303\pi$
$619$	6690.40	0.434426	0.217213	+	0.976124i	$0.430303\pi$
$620$	0	0
$621$	−465.323	−0.0300689
$622$	−33568.1	−2.16392
$623$	1391.26	0.0894700
$624$	−5738.06	−0.368119
$625$	0	0
$626$	−21682.8	−1.38437
$627$	−9195.50	−0.585699
$628$	−25293.5	−1.60720
$629$	−37629.8	−2.38537
$630$	0	0
$631$	−4738.33	−0.298938	−0.149469	−	0.988766i	$-0.547756\pi$
$631$	−4738.33	−0.298938	−0.149469	+	0.988766i	$0.547756\pi$
$632$	−14575.6	−0.917381
$633$	9410.36	0.590882
$634$	−10737.7	−0.672634
$635$	0	0
$636$	−18731.7	−1.16786
$637$	−14345.2	−0.892272
$638$	38874.0	2.41229
$639$	−507.028	−0.0313893
$640$	0	0
$641$	−25399.8	−1.56510	−0.782551	−	0.622586i	$-0.786082\pi$
$641$	−25399.8	−1.56510	−0.782551	+	0.622586i	$0.786082\pi$
$642$	−22444.7	−1.37979
$643$	−16102.4	−0.987585	−0.493792	−	0.869580i	$-0.664390\pi$
$643$	−16102.4	−0.987585	−0.493792	+	0.869580i	$0.664390\pi$
$644$	−297.408	−0.0181980
$645$	0	0
$646$	27654.5	1.68429
$647$	−5513.27	−0.335006	−0.167503	−	0.985872i	$-0.553570\pi$
$647$	−5513.27	−0.335006	−0.167503	+	0.985872i	$0.553570\pi$
$648$	−2811.51	−0.170442
$649$	−38336.1	−2.31868
$650$	0	0
$651$	−827.158	−0.0497986
$652$	18863.1	1.13303
$653$	22658.8	1.35790	0.678949	−	0.734186i	$-0.262436\pi$
$653$	22658.8	1.35790	0.678949	+	0.734186i	$0.262436\pi$
$654$	5289.21	0.316245
$655$	0	0
$656$	−389.728	−0.0231956
$657$	−1951.25	−0.115868
$658$	1765.20	0.104581
$659$	−11925.2	−0.704913	−0.352457	−	0.935828i	$-0.614654\pi$
$659$	−11925.2	−0.704913	−0.352457	+	0.935828i	$0.614654\pi$
$660$	0	0
$661$	11764.3	0.692253	0.346126	−	0.938188i	$-0.387497\pi$
$661$	11764.3	0.692253	0.346126	+	0.938188i	$0.387497\pi$
$662$	−49075.2	−2.88121
$663$	−13568.8	−0.794825
$664$	50591.7	2.95683
$665$	0	0
$666$	15142.4	0.881016
$667$	2417.68	0.140349
$668$	−55305.9	−3.20337
$669$	−7017.00	−0.405520
$670$	0	0
$671$	−17042.4	−0.980501
$672$	198.160	0.0113753
$673$	8534.10	0.488804	0.244402	−	0.969674i	$-0.421408\pi$
$673$	8534.10	0.488804	0.244402	+	0.969674i	$0.421408\pi$
$674$	7638.94	0.436559
$675$	0	0
$676$	−6609.05	−0.376027
$677$	21182.5	1.20252	0.601262	−	0.799052i	$-0.294665\pi$
$677$	21182.5	1.20252	0.601262	+	0.799052i	$0.294665\pi$
$678$	3092.84	0.175191
$679$	589.039	0.0332919
$680$	0	0
$681$	3034.26	0.170739
$682$	−67321.7	−3.77988
$683$	579.322	0.0324555	0.0162278	−	0.999868i	$-0.494834\pi$
$683$	579.322	0.0324555	0.0162278	+	0.999868i	$0.494834\pi$
$684$	−7291.85	−0.407618
$685$	0	0
$686$	−3743.40	−0.208344
$687$	9160.09	0.508704
$688$	−5093.95	−0.282275
$689$	17238.6	0.953178
$690$	0	0
$691$	23575.5	1.29791	0.648954	−	0.760827i	$-0.275207\pi$
$691$	23575.5	1.29791	0.648954	+	0.760827i	$0.275207\pi$
$692$	−34808.6	−1.91217
$693$	587.576	0.0322080
$694$	5358.90	0.293114
$695$	0	0
$696$	14607.7	0.795553
$697$	−921.592	−0.0500829
$698$	−24962.6	−1.35365
$699$	−19209.3	−1.03943
$700$	0	0
$701$	12531.0	0.675162	0.337581	−	0.941297i	$-0.390391\pi$
$701$	12531.0	0.675162	0.337581	+	0.941297i	$0.390391\pi$
$702$	5460.15	0.293561
$703$	18610.4	0.998440
$704$	37095.5	1.98592
$705$	0	0
$706$	34588.9	1.84387
$707$	−1823.92	−0.0970236
$708$	−30399.8	−1.61369
$709$	−939.532	−0.0497671	−0.0248835	−	0.999690i	$-0.507921\pi$
$709$	−939.532	−0.0497671	−0.0248835	+	0.999690i	$0.507921\pi$
$710$	0	0
$711$	3779.32	0.199347
$712$	42550.0	2.23965
$713$	−4186.91	−0.219917
$714$	−1767.07	−0.0926205
$715$	0	0
$716$	−34361.9	−1.79353
$717$	11499.2	0.598949
$718$	28628.1	1.48801
$719$	30555.3	1.58487	0.792434	−	0.609958i	$-0.208814\pi$
$719$	30555.3	1.58487	0.792434	+	0.609958i	$0.208814\pi$
$720$	0	0
$721$	−395.520	−0.0204299
$722$	19364.3	0.998148
$723$	10680.2	0.549381
$724$	−785.006	−0.0402963
$725$	0	0
$726$	28587.3	1.46139
$727$	7612.80	0.388367	0.194184	−	0.980965i	$-0.437794\pi$
$727$	7612.80	0.388367	0.194184	+	0.980965i	$0.437794\pi$
$728$	1653.73	0.0841913
$729$	729.000	0.0370370
$730$	0	0
$731$	−12045.7	−0.609474
$732$	−13514.3	−0.682382
$733$	−4959.06	−0.249887	−0.124943	−	0.992164i	$-0.539875\pi$
$733$	−4959.06	−0.249887	−0.124943	+	0.992164i	$0.539875\pi$
$734$	−33084.6	−1.66373
$735$	0	0
$736$	1003.05	0.0502348
$737$	−48348.1	−2.41645
$738$	370.853	0.0184977
$739$	24559.8	1.22253	0.611264	−	0.791427i	$-0.290661\pi$
$739$	24559.8	1.22253	0.611264	+	0.791427i	$0.290661\pi$
$740$	0	0
$741$	6710.64	0.332688
$742$	2245.00	0.111073
$743$	1368.49	0.0675709	0.0337855	−	0.999429i	$-0.489244\pi$
$743$	1368.49	0.0675709	0.0337855	+	0.999429i	$0.489244\pi$
$744$	−25297.5	−1.24658
$745$	0	0
$746$	20040.8	0.983576
$747$	−13118.0	−0.642520
$748$	−94238.9	−4.60657
$749$	1762.64	0.0859884
$750$	0	0
$751$	3672.88	0.178462	0.0892312	−	0.996011i	$-0.471559\pi$
$751$	3672.88	0.178462	0.0892312	+	0.996011i	$0.471559\pi$
$752$	14710.7	0.713355
$753$	−532.025	−0.0257478
$754$	−28369.3	−1.37022
$755$	0	0
$756$	465.936	0.0224153
$757$	31304.6	1.50302	0.751509	−	0.659722i	$-0.229326\pi$
$757$	31304.6	1.50302	0.751509	+	0.659722i	$0.229326\pi$
$758$	−18707.9	−0.896441
$759$	2974.19	0.142235
$760$	0	0
$761$	−6294.67	−0.299844	−0.149922	−	0.988698i	$-0.547902\pi$
$761$	−6294.67	−0.299844	−0.149922	+	0.988698i	$0.547902\pi$
$762$	−11265.6	−0.535575
$763$	−415.374	−0.0197084
$764$	26688.4	1.26381
$765$	0	0
$766$	−31794.3	−1.49971
$767$	27976.7	1.31705
$768$	22687.2	1.06596
$769$	−23691.5	−1.11097	−0.555485	−	0.831526i	$-0.687468\pi$
$769$	−23691.5	−1.11097	−0.555485	+	0.831526i	$0.687468\pi$
$770$	0	0
$771$	−18184.7	−0.849426
$772$	67872.6	3.16423
$773$	15818.0	0.736007	0.368004	−	0.929824i	$-0.380041\pi$
$773$	15818.0	0.736007	0.368004	+	0.929824i	$0.380041\pi$
$774$	4847.24	0.225104
$775$	0	0
$776$	18015.0	0.833376
$777$	−1189.17	−0.0549050
$778$	45676.6	2.10487
$779$	455.786	0.0209631
$780$	0	0
$781$	3240.76	0.148481
$782$	−8944.58	−0.409025
$783$	−3787.66	−0.172874
$784$	−15568.9	−0.709224
$785$	0	0
$786$	12254.3	0.556100
$787$	20834.7	0.943682	0.471841	−	0.881684i	$-0.343590\pi$
$787$	20834.7	0.943682	0.471841	+	0.881684i	$0.343590\pi$
$788$	53750.1	2.42991
$789$	1118.97	0.0504899
$790$	0	0
$791$	−242.888	−0.0109179
$792$	17970.2	0.806243
$793$	12437.1	0.556943
$794$	3580.64	0.160040
$795$	0	0
$796$	−59967.1	−2.67020
$797$	5340.31	0.237344	0.118672	−	0.992933i	$-0.462136\pi$
$797$	5340.31	0.237344	0.118672	+	0.992933i	$0.462136\pi$
$798$	873.931	0.0387679
$799$	34786.4	1.54024
$800$	0	0
$801$	−11032.9	−0.486675
$802$	−41116.3	−1.81031
$803$	12471.7	0.548093
$804$	−38339.1	−1.68174
$805$	0	0
$806$	49129.6	2.14704
$807$	−8133.00	−0.354765
$808$	−55782.3	−2.42873
$809$	−22843.9	−0.992766	−0.496383	−	0.868104i	$-0.665339\pi$
$809$	−22843.9	−0.992766	−0.496383	+	0.868104i	$0.665339\pi$
$810$	0	0
$811$	−27738.5	−1.20102	−0.600512	−	0.799615i	$-0.705037\pi$
$811$	−27738.5	−1.20102	−0.600512	+	0.799615i	$0.705037\pi$
$812$	−2420.86	−0.104625
$813$	16486.8	0.711216
$814$	−96785.5	−4.16748
$815$	0	0
$816$	−14726.3	−0.631768
$817$	5957.36	0.255106
$818$	−12087.4	−0.516656
$819$	−428.798	−0.0182948
$820$	0	0
$821$	34362.2	1.46072	0.730358	−	0.683064i	$-0.239353\pi$
$821$	34362.2	1.46072	0.730358	+	0.683064i	$0.239353\pi$
$822$	18365.5	0.779283
$823$	−1827.02	−0.0773826	−0.0386913	−	0.999251i	$-0.512319\pi$
$823$	−1827.02	−0.0773826	−0.0386913	+	0.999251i	$0.512319\pi$
$824$	−12096.5	−0.511408
$825$	0	0
$826$	3643.42	0.153476
$827$	−36184.3	−1.52146	−0.760732	−	0.649066i	$-0.775160\pi$
$827$	−36184.3	−1.52146	−0.760732	+	0.649066i	$0.775160\pi$
$828$	2358.48	0.0989888
$829$	−29912.0	−1.25318	−0.626591	−	0.779348i	$-0.715550\pi$
$829$	−29912.0	−1.25318	−0.626591	+	0.779348i	$0.715550\pi$
$830$	0	0
$831$	−2395.84	−0.100013
$832$	−27071.3	−1.12804
$833$	−36815.8	−1.53132
$834$	−9903.28	−0.411178
$835$	0	0
$836$	46607.2	1.92816
$837$	6559.44	0.270881
$838$	−22785.3	−0.939267
$839$	−23063.1	−0.949018	−0.474509	−	0.880251i	$-0.657374\pi$
$839$	−23063.1	−0.949018	−0.474509	+	0.880251i	$0.657374\pi$
$840$	0	0
$841$	−4709.44	−0.193097
$842$	−39320.7	−1.60936
$843$	−5963.95	−0.243665
$844$	−47696.2	−1.94522
$845$	0	0
$846$	−13998.2	−0.568875
$847$	−2245.02	−0.0910742
$848$	18709.2	0.757636
$849$	2633.96	0.106475
$850$	0	0
$851$	−6019.34	−0.242468
$852$	2569.86	0.103336
$853$	−28689.4	−1.15159	−0.575795	−	0.817594i	$-0.695307\pi$
$853$	−28689.4	−1.15159	−0.575795	+	0.817594i	$0.695307\pi$
$854$	1619.70	0.0649003
$855$	0	0
$856$	53907.9	2.15249
$857$	21086.4	0.840489	0.420244	−	0.907411i	$-0.361944\pi$
$857$	21086.4	0.840489	0.420244	+	0.907411i	$0.361944\pi$
$858$	−34899.5	−1.38864
$859$	6131.88	0.243559	0.121779	−	0.992557i	$-0.461140\pi$
$859$	6131.88	0.243559	0.121779	+	0.992557i	$0.461140\pi$
$860$	0	0
$861$	−29.1239	−0.00115278
$862$	−36952.8	−1.46011
$863$	−33975.6	−1.34014	−0.670071	−	0.742297i	$-0.733736\pi$
$863$	−33975.6	−1.34014	−0.670071	+	0.742297i	$0.733736\pi$
$864$	−1571.43	−0.0618762
$865$	0	0
$866$	−66174.4	−2.59665
$867$	−20084.3	−0.786734
$868$	4192.43	0.163940
$869$	−24156.2	−0.942973
$870$	0	0
$871$	35283.2	1.37259
$872$	−12703.7	−0.493349
$873$	−4671.13	−0.181093
$874$	4423.66	0.171204
$875$	0	0
$876$	9889.85	0.381446
$877$	−13991.4	−0.538719	−0.269359	−	0.963040i	$-0.586812\pi$
$877$	−13991.4	−0.538719	−0.269359	+	0.963040i	$0.586812\pi$
$878$	−58680.3	−2.25554
$879$	346.594	0.0132996
$880$	0	0
$881$	−18927.2	−0.723806	−0.361903	−	0.932216i	$-0.617873\pi$
$881$	−18927.2	−0.723806	−0.361903	+	0.932216i	$0.617873\pi$
$882$	14814.9	0.565581
$883$	18667.8	0.711464	0.355732	−	0.934588i	$-0.384232\pi$
$883$	18667.8	0.711464	0.355732	+	0.934588i	$0.384232\pi$
$884$	68773.1	2.61662
$885$	0	0
$886$	−17603.8	−0.667506
$887$	3261.04	0.123444	0.0617221	−	0.998093i	$-0.480341\pi$
$887$	3261.04	0.123444	0.0617221	+	0.998093i	$0.480341\pi$
$888$	−36369.2	−1.37440
$889$	884.710	0.0333771
$890$	0	0
$891$	−4659.53	−0.175197
$892$	35565.5	1.33500
$893$	−17204.1	−0.644695
$894$	−34258.2	−1.28162
$895$	0	0
$896$	−2997.09	−0.111747
$897$	−2170.49	−0.0807922
$898$	−11393.5	−0.423391
$899$	−34080.9	−1.26436
$900$	0	0
$901$	44241.6	1.63585
$902$	−2370.37	−0.0874997
$903$	−380.665	−0.0140285
$904$	−7428.41	−0.273302
$905$	0	0
$906$	−17023.6	−0.624253
$907$	48067.7	1.75972	0.879858	−	0.475236i	$-0.157637\pi$
$907$	48067.7	1.75972	0.879858	+	0.475236i	$0.157637\pi$
$908$	−15379.0	−0.562083
$909$	14463.9	0.527763
$910$	0	0
$911$	5147.13	0.187192	0.0935961	−	0.995610i	$-0.470164\pi$
$911$	5147.13	0.187192	0.0935961	+	0.995610i	$0.470164\pi$
$912$	7283.09	0.264438
$913$	83846.0	3.03932
$914$	−12453.8	−0.450694
$915$	0	0
$916$	−46427.7	−1.67469
$917$	−962.354	−0.0346562
$918$	14013.1	0.503812
$919$	−8122.08	−0.291537	−0.145769	−	0.989319i	$-0.546565\pi$
$919$	−8122.08	−0.291537	−0.145769	+	0.989319i	$0.546565\pi$
$920$	0	0
$921$	−14792.8	−0.529252
$922$	−19109.2	−0.682567
$923$	−2365.03	−0.0843399
$924$	−2978.11	−0.106031
$925$	0	0
$926$	26283.1	0.932738
$927$	3136.51	0.111129
$928$	8164.66	0.288813
$929$	33652.8	1.18850	0.594248	−	0.804282i	$-0.297450\pi$
$929$	33652.8	1.18850	0.594248	+	0.804282i	$0.297450\pi$
$930$	0	0
$931$	18207.8	0.640962
$932$	97362.1	3.42189
$933$	−20905.2	−0.733552
$934$	−70857.9	−2.48238
$935$	0	0
$936$	−13114.2	−0.457961
$937$	24955.5	0.870074	0.435037	−	0.900412i	$-0.356735\pi$
$937$	24955.5	0.870074	0.435037	+	0.900412i	$0.356735\pi$
$938$	4594.95	0.159947
$939$	−13503.3	−0.469292
$940$	0	0
$941$	−8018.46	−0.277783	−0.138892	−	0.990308i	$-0.544354\pi$
$941$	−8018.46	−0.277783	−0.138892	+	0.990308i	$0.544354\pi$
$942$	−24039.6	−0.831478
$943$	−147.419	−0.00509082
$944$	30363.2	1.04686
$945$	0	0
$946$	−30982.0	−1.06481
$947$	33776.5	1.15902	0.579508	−	0.814967i	$-0.303245\pi$
$947$	33776.5	1.15902	0.579508	+	0.814967i	$0.303245\pi$
$948$	−19155.4	−0.656264
$949$	−9101.56	−0.311327
$950$	0	0
$951$	−6687.13	−0.228018
$952$	4244.17	0.144490
$953$	−46529.2	−1.58156	−0.790781	−	0.612099i	$-0.790325\pi$
$953$	−46529.2	−1.58156	−0.790781	+	0.612099i	$0.790325\pi$
$954$	−17803.0	−0.604187
$955$	0	0
$956$	−58283.6	−1.97178
$957$	24209.5	0.817746
$958$	−49357.4	−1.66458
$959$	−1442.28	−0.0485650
$960$	0	0
$961$	29229.9	0.981166
$962$	70631.5	2.36721
$963$	−13977.9	−0.467737
$964$	−54132.6	−1.80860
$965$	0	0
$966$	−282.664	−0.00941467
$967$	1863.17	0.0619603	0.0309802	−	0.999520i	$-0.490137\pi$
$967$	1863.17	0.0619603	0.0309802	+	0.999520i	$0.490137\pi$
$968$	−68661.1	−2.27980
$969$	17222.3	0.570961
$970$	0	0
$971$	47640.0	1.57450	0.787250	−	0.616634i	$-0.211504\pi$
$971$	47640.0	1.57450	0.787250	+	0.616634i	$0.211504\pi$
$972$	−3694.92	−0.121929
$973$	777.727	0.0256247
$974$	21239.6	0.698728
$975$	0	0
$976$	13498.1	0.442688
$977$	60295.1	1.97442	0.987212	−	0.159413i	$-0.0509603\pi$
$977$	60295.1	1.97442	0.987212	+	0.159413i	$0.0509603\pi$
$978$	17927.9	0.586167
$979$	70518.4	2.30212
$980$	0	0
$981$	3293.95	0.107205
$982$	15549.7	0.505308
$983$	−21489.8	−0.697271	−0.348635	−	0.937258i	$-0.613355\pi$
$983$	−21489.8	−0.697271	−0.348635	+	0.937258i	$0.613355\pi$
$984$	−890.716	−0.0288567
$985$	0	0
$986$	−72807.6	−2.35159
$987$	1099.31	0.0354523
$988$	−34012.7	−1.09523
$989$	−1926.85	−0.0619517
$990$	0	0
$991$	27153.4	0.870389	0.435195	−	0.900336i	$-0.356680\pi$
$991$	27153.4	0.870389	0.435195	+	0.900336i	$0.356680\pi$
$992$	−14139.5	−0.452549
$993$	−30562.5	−0.976709
$994$	−307.999	−0.00982809
$995$	0	0
$996$	66488.2	2.11522
$997$	24390.8	0.774788	0.387394	−	0.921914i	$-0.373375\pi$
$997$	24390.8	0.774788	0.387394	+	0.921914i	$0.373375\pi$
$998$	51464.9	1.63236
$999$	9430.22	0.298658

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.4.a.f.1.1		14
5.4	even	2		1875.4.a.g.1.14		14
25.9	even	10		75.4.g.b.31.7	✓	28
25.14	even	10		75.4.g.b.46.7	yes	28
75.14	odd	10		225.4.h.a.46.1		28
75.59	odd	10		225.4.h.a.181.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.31.7	✓	28	25.9	even	10
75.4.g.b.46.7	yes	28	25.14	even	10
225.4.h.a.46.1		28	75.14	odd	10
225.4.h.a.181.1		28	75.59	odd	10
1875.4.a.f.1.1		14	1.1	even	1	trivial
1875.4.a.g.1.14		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)

\(f(q)\)	\(=\)	\(q-4.81720 q^{2} -3.00000 q^{3} +15.2054 q^{4} +14.4516 q^{6} -1.13492 q^{7} -34.7100 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.81720 q^{2} -3.00000 q^{3} +15.2054 q^{4} +14.4516 q^{6} -1.13492 q^{7} -34.7100 q^{8} +9.00000 q^{9} -57.5251 q^{11} -45.6163 q^{12} +41.9803 q^{13} +5.46712 q^{14} +45.5614 q^{16} +107.739 q^{17} -43.3548 q^{18} -53.2840 q^{19} +3.40475 q^{21} +277.110 q^{22} +17.2342 q^{23} +104.130 q^{24} -202.228 q^{26} -27.0000 q^{27} -17.2569 q^{28} +140.284 q^{29} -242.942 q^{31} +58.2010 q^{32} +172.575 q^{33} -519.002 q^{34} +136.849 q^{36} -349.267 q^{37} +256.680 q^{38} -125.941 q^{39} -8.55390 q^{41} -16.4014 q^{42} -111.804 q^{43} -874.693 q^{44} -83.0205 q^{46} +322.875 q^{47} -136.684 q^{48} -341.712 q^{49} -323.218 q^{51} +638.329 q^{52} +410.636 q^{53} +130.064 q^{54} +39.3929 q^{56} +159.852 q^{57} -675.775 q^{58} +666.424 q^{59} +296.261 q^{61} +1170.30 q^{62} -10.2143 q^{63} -644.858 q^{64} -831.330 q^{66} +840.470 q^{67} +1638.22 q^{68} -51.7025 q^{69} -56.3365 q^{71} -312.390 q^{72} -216.805 q^{73} +1682.49 q^{74} -810.206 q^{76} +65.2862 q^{77} +606.683 q^{78} +419.925 q^{79} +81.0000 q^{81} +41.2059 q^{82} -1457.55 q^{83} +51.7707 q^{84} +538.582 q^{86} -420.852 q^{87} +1996.69 q^{88} -1225.87 q^{89} -47.6442 q^{91} +262.053 q^{92} +728.827 q^{93} -1555.36 q^{94} -174.603 q^{96} -519.015 q^{97} +1646.10 q^{98} -517.726 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 42 q^{3} + 50 q^{4} + 27 q^{7} - 21 q^{8} + 126 q^{9}+O(q^{10}) \) 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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