LMFDB - Embedded newform 1875.4.a.g.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:	$1$
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			$-4.95189$ 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)

$f(q)$	$=$	$q-4.95189 q^{2} +3.00000 q^{3} +16.5212 q^{4} -14.8557 q^{6} +28.2766 q^{7} -42.1962 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.95189 q^{2} +3.00000 q^{3} +16.5212 q^{4} -14.8557 q^{6} +28.2766 q^{7} -42.1962 q^{8} +9.00000 q^{9} -9.92047 q^{11} +49.5637 q^{12} -92.2599 q^{13} -140.023 q^{14} +76.7811 q^{16} -19.6128 q^{17} -44.5670 q^{18} -76.9153 q^{19} +84.8297 q^{21} +49.1251 q^{22} +101.305 q^{23} -126.589 q^{24} +456.861 q^{26} +27.0000 q^{27} +467.164 q^{28} +216.896 q^{29} +105.058 q^{31} -42.6422 q^{32} -29.7614 q^{33} +97.1204 q^{34} +148.691 q^{36} -331.223 q^{37} +380.876 q^{38} -276.780 q^{39} +95.1262 q^{41} -420.068 q^{42} -67.8112 q^{43} -163.898 q^{44} -501.652 q^{46} +117.427 q^{47} +230.343 q^{48} +456.565 q^{49} -58.8384 q^{51} -1524.25 q^{52} -222.826 q^{53} -133.701 q^{54} -1193.16 q^{56} -230.746 q^{57} -1074.05 q^{58} +174.679 q^{59} -472.301 q^{61} -520.234 q^{62} +254.489 q^{63} -403.089 q^{64} +147.375 q^{66} -125.684 q^{67} -324.027 q^{68} +303.915 q^{69} +927.678 q^{71} -379.766 q^{72} +101.255 q^{73} +1640.18 q^{74} -1270.73 q^{76} -280.517 q^{77} +1370.58 q^{78} +295.407 q^{79} +81.0000 q^{81} -471.055 q^{82} -1112.32 q^{83} +1401.49 q^{84} +335.794 q^{86} +650.688 q^{87} +418.606 q^{88} +127.735 q^{89} -2608.80 q^{91} +1673.68 q^{92} +315.173 q^{93} -581.488 q^{94} -127.927 q^{96} -1520.97 q^{97} -2260.86 q^{98} -89.2842 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.95189	−1.75076	−0.875379	−	0.483437i	$-0.839388\pi$
$2$	−4.95189	−1.75076	−0.875379	+	0.483437i	$0.839388\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	16.5212	2.06515
$5$	0	0
$5$	0	0
$6$	−14.8557	−1.01080
$7$	28.2766	1.52679	0.763396	−	0.645931i	$-0.223531\pi$
$7$	28.2766	1.52679	0.763396	+	0.645931i	$0.223531\pi$
$8$	−42.1962	−1.86483
$9$	9.00000	0.333333
$10$	0	0
$11$	−9.92047	−0.271921	−0.135961	−	0.990714i	$-0.543412\pi$
$11$	−9.92047	−0.271921	−0.135961	+	0.990714i	$0.543412\pi$
$12$	49.5637	1.19232
$13$	−92.2599	−1.96833	−0.984165	−	0.177253i	$-0.943279\pi$
$13$	−92.2599	−1.96833	−0.984165	+	0.177253i	$0.943279\pi$
$14$	−140.023	−2.67304
$15$	0	0
$16$	76.7811	1.19970
$17$	−19.6128	−0.279812	−0.139906	−	0.990165i	$-0.544680\pi$
$17$	−19.6128	−0.279812	−0.139906	+	0.990165i	$0.544680\pi$
$18$	−44.5670	−0.583586
$19$	−76.9153	−0.928715	−0.464357	−	0.885648i	$-0.653715\pi$
$19$	−76.9153	−0.928715	−0.464357	+	0.885648i	$0.653715\pi$
$20$	0	0
$21$	84.8297	0.881494
$22$	49.1251	0.476068
$23$	101.305	0.918416	0.459208	−	0.888329i	$-0.348133\pi$
$23$	101.305	0.918416	0.459208	+	0.888329i	$0.348133\pi$
$24$	−126.589	−1.07666
$25$	0	0
$26$	456.861	3.44607
$27$	27.0000	0.192450
$28$	467.164	3.15306
$29$	216.896	1.38885	0.694424	−	0.719566i	$-0.255659\pi$
$29$	216.896	1.38885	0.694424	+	0.719566i	$0.255659\pi$
$30$	0	0
$31$	105.058	0.608675	0.304337	−	0.952564i	$-0.401565\pi$
$31$	105.058	0.608675	0.304337	+	0.952564i	$0.401565\pi$
$32$	−42.6422	−0.235567
$33$	−29.7614	−0.156994
$34$	97.1204	0.489883
$35$	0	0
$36$	148.691	0.688384
$37$	−331.223	−1.47169	−0.735847	−	0.677148i	$-0.763216\pi$
$37$	−331.223	−1.47169	−0.735847	+	0.677148i	$0.763216\pi$
$38$	380.876	1.62595
$39$	−276.780	−1.13642
$40$	0	0
$41$	95.1262	0.362347	0.181173	−	0.983451i	$-0.442010\pi$
$41$	95.1262	0.362347	0.181173	+	0.983451i	$0.442010\pi$
$42$	−420.068	−1.54328
$43$	−67.8112	−0.240491	−0.120245	−	0.992744i	$-0.538368\pi$
$43$	−67.8112	−0.240491	−0.120245	+	0.992744i	$0.538368\pi$
$44$	−163.898	−0.561559
$45$	0	0
$46$	−501.652	−1.60792
$47$	117.427	0.364437	0.182219	−	0.983258i	$-0.441672\pi$
$47$	117.427	0.364437	0.182219	+	0.983258i	$0.441672\pi$
$48$	230.343	0.692650
$49$	456.565	1.33109
$50$	0	0
$51$	−58.8384	−0.161549
$52$	−1524.25	−4.06490
$53$	−222.826	−0.577499	−0.288750	−	0.957405i	$-0.593240\pi$
$53$	−222.826	−0.577499	−0.288750	+	0.957405i	$0.593240\pi$
$54$	−133.701	−0.336934
$55$	0	0
$56$	−1193.16	−2.84720
$57$	−230.746	−0.536194
$58$	−1074.05	−2.43154
$59$	174.679	0.385446	0.192723	−	0.981253i	$-0.438268\pi$
$59$	174.679	0.385446	0.192723	+	0.981253i	$0.438268\pi$
$60$	0	0
$61$	−472.301	−0.991344	−0.495672	−	0.868510i	$-0.665078\pi$
$61$	−472.301	−0.991344	−0.495672	+	0.868510i	$0.665078\pi$
$62$	−520.234	−1.06564
$63$	254.489	0.508931
$64$	−403.089	−0.787284
$65$	0	0
$66$	147.375	0.274858
$67$	−125.684	−0.229175	−0.114587	−	0.993413i	$-0.536555\pi$
$67$	−125.684	−0.229175	−0.114587	+	0.993413i	$0.536555\pi$
$68$	−324.027	−0.577854
$69$	303.915	0.530248
$70$	0	0
$71$	927.678	1.55063	0.775317	−	0.631572i	$-0.217590\pi$
$71$	927.678	1.55063	0.775317	+	0.631572i	$0.217590\pi$
$72$	−379.766	−0.621609
$73$	101.255	0.162342	0.0811709	−	0.996700i	$-0.474134\pi$
$73$	101.255	0.162342	0.0811709	+	0.996700i	$0.474134\pi$
$74$	1640.18	2.57658
$75$	0	0
$76$	−1270.73	−1.91794
$77$	−280.517	−0.415167
$78$	1370.58	1.98959
$79$	295.407	0.420707	0.210353	−	0.977625i	$-0.432539\pi$
$79$	295.407	0.420707	0.210353	+	0.977625i	$0.432539\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−471.055	−0.634381
$83$	−1112.32	−1.47100	−0.735500	−	0.677525i	$-0.763053\pi$
$83$	−1112.32	−1.47100	−0.735500	+	0.677525i	$0.763053\pi$
$84$	1401.49	1.82042
$85$	0	0
$86$	335.794	0.421041
$87$	650.688	0.801851
$88$	418.606	0.507086
$89$	127.735	0.152133	0.0760666	−	0.997103i	$-0.475764\pi$
$89$	127.735	0.152133	0.0760666	+	0.997103i	$0.475764\pi$
$90$	0	0
$91$	−2608.80	−3.00523
$92$	1673.68	1.89667
$93$	315.173	0.351419
$94$	−581.488	−0.638042
$95$	0	0
$96$	−127.927	−0.136005
$97$	−1520.97	−1.59207	−0.796035	−	0.605250i	$-0.793073\pi$
$97$	−1520.97	−1.59207	−0.796035	+	0.605250i	$0.793073\pi$
$98$	−2260.86	−2.33042
$99$	−89.2842	−0.0906404
$100$	0	0
$101$	441.976	0.435428	0.217714	−	0.976013i	$-0.430140\pi$
$101$	441.976	0.435428	0.217714	+	0.976013i	$0.430140\pi$
$102$	291.361	0.282834
$103$	−1555.99	−1.48851	−0.744255	−	0.667896i	$-0.767195\pi$
$103$	−1555.99	−1.48851	−0.744255	+	0.667896i	$0.767195\pi$
$104$	3893.02	3.67059
$105$	0	0
$106$	1103.41	1.01106
$107$	−1108.54	−1.00156	−0.500779	−	0.865575i	$-0.666953\pi$
$107$	−1108.54	−1.00156	−0.500779	+	0.865575i	$0.666953\pi$
$108$	446.073	0.397439
$109$	1105.86	0.971767	0.485884	−	0.874024i	$-0.338498\pi$
$109$	1105.86	0.971767	0.485884	+	0.874024i	$0.338498\pi$
$110$	0	0
$111$	−993.668	−0.849683
$112$	2171.11	1.83170
$113$	219.414	0.182662	0.0913308	−	0.995821i	$-0.470888\pi$
$113$	219.414	0.182662	0.0913308	+	0.995821i	$0.470888\pi$
$114$	1142.63	0.938745
$115$	0	0
$116$	3583.39	2.86818
$117$	−830.339	−0.656110
$118$	−864.992	−0.674822
$119$	−554.583	−0.427214
$120$	0	0
$121$	−1232.58	−0.926059
$122$	2338.78	1.73560
$123$	285.379	0.209201
$124$	1735.68	1.25701
$125$	0	0
$126$	−1260.20	−0.891014
$127$	1254.78	0.876720	0.438360	−	0.898800i	$-0.355560\pi$
$127$	1254.78	0.876720	0.438360	+	0.898800i	$0.355560\pi$
$128$	2337.19	1.61391
$129$	−203.434	−0.138847
$130$	0	0
$131$	−1360.84	−0.907609	−0.453805	−	0.891101i	$-0.649934\pi$
$131$	−1360.84	−0.907609	−0.453805	+	0.891101i	$0.649934\pi$
$132$	−491.695	−0.324216
$133$	−2174.90	−1.41795
$134$	622.372	0.401230
$135$	0	0
$136$	827.585	0.521800
$137$	−2290.71	−1.42853	−0.714264	−	0.699876i	$-0.753239\pi$
$137$	−2290.71	−1.42853	−0.714264	+	0.699876i	$0.753239\pi$
$138$	−1504.95	−0.928335
$139$	1947.64	1.18847	0.594233	−	0.804293i	$-0.297456\pi$
$139$	1947.64	1.18847	0.594233	+	0.804293i	$0.297456\pi$
$140$	0	0
$141$	352.282	0.210408
$142$	−4593.76	−2.71479
$143$	915.262	0.535231
$144$	691.030	0.399902
$145$	0	0
$146$	−501.402	−0.284221
$147$	1369.69	0.768507
$148$	−5472.21	−3.03927
$149$	−998.135	−0.548795	−0.274397	−	0.961616i	$-0.588478\pi$
$149$	−998.135	−0.548795	−0.274397	+	0.961616i	$0.588478\pi$
$150$	0	0
$151$	−2961.42	−1.59601	−0.798003	−	0.602654i	$-0.794110\pi$
$151$	−2961.42	−1.59601	−0.798003	+	0.602654i	$0.794110\pi$
$152$	3245.53	1.73189
$153$	−176.515	−0.0932706
$154$	1389.09	0.726857
$155$	0	0
$156$	−4572.74	−2.34687
$157$	−924.225	−0.469816	−0.234908	−	0.972018i	$-0.575479\pi$
$157$	−924.225	−0.469816	−0.234908	+	0.972018i	$0.575479\pi$
$158$	−1462.82	−0.736556
$159$	−668.477	−0.333419
$160$	0	0
$161$	2864.56	1.40223
$162$	−401.103	−0.194529
$163$	796.093	0.382545	0.191273	−	0.981537i	$-0.438739\pi$
$163$	796.093	0.382545	0.191273	+	0.981537i	$0.438739\pi$
$164$	1571.60	0.748302
$165$	0	0
$166$	5508.09	2.57537
$167$	1631.50	0.755983	0.377992	−	0.925809i	$-0.376615\pi$
$167$	1631.50	0.755983	0.377992	+	0.925809i	$0.376615\pi$
$168$	−3579.49	−1.64383
$169$	6314.89	2.87433
$170$	0	0
$171$	−692.238	−0.309572
$172$	−1120.32	−0.496651
$173$	277.716	0.122048	0.0610241	−	0.998136i	$-0.480563\pi$
$173$	277.716	0.122048	0.0610241	+	0.998136i	$0.480563\pi$
$174$	−3222.14	−1.40385
$175$	0	0
$176$	−761.705	−0.326225
$177$	524.038	0.222537
$178$	−632.529	−0.266348
$179$	−3218.41	−1.34389	−0.671943	−	0.740603i	$-0.734540\pi$
$179$	−3218.41	−1.34389	−0.671943	+	0.740603i	$0.734540\pi$
$180$	0	0
$181$	−145.382	−0.0597027	−0.0298514	−	0.999554i	$-0.509503\pi$
$181$	−145.382	−0.0597027	−0.0298514	+	0.999554i	$0.509503\pi$
$182$	12918.5	5.26143
$183$	−1416.90	−0.572352
$184$	−4274.69	−1.71269
$185$	0	0
$186$	−1560.70	−0.615249
$187$	194.568	0.0760868
$188$	1940.05	0.752619
$189$	763.468	0.293831
$190$	0	0
$191$	−1216.19	−0.460734	−0.230367	−	0.973104i	$-0.573993\pi$
$191$	−1216.19	−0.460734	−0.230367	+	0.973104i	$0.573993\pi$
$192$	−1209.27	−0.454538
$193$	−94.8613	−0.0353796	−0.0176898	−	0.999844i	$-0.505631\pi$
$193$	−94.8613	−0.0353796	−0.0176898	+	0.999844i	$0.505631\pi$
$194$	7531.67	2.78733
$195$	0	0
$196$	7543.01	2.74891
$197$	−3329.68	−1.20421	−0.602107	−	0.798415i	$-0.705672\pi$
$197$	−3329.68	−1.20421	−0.602107	+	0.798415i	$0.705672\pi$
$198$	442.126	0.158689
$199$	1975.34	0.703658	0.351829	−	0.936064i	$-0.385560\pi$
$199$	1975.34	0.703658	0.351829	+	0.936064i	$0.385560\pi$
$200$	0	0
$201$	−377.051	−0.132314
$202$	−2188.62	−0.762329
$203$	6133.08	2.12048
$204$	−972.082	−0.333624
$205$	0	0
$206$	7705.10	2.60602
$207$	911.745	0.306139
$208$	−7083.82	−2.36142
$209$	763.036	0.252537
$210$	0	0
$211$	−1915.23	−0.624880	−0.312440	−	0.949937i	$-0.601146\pi$
$211$	−1915.23	−0.624880	−0.312440	+	0.949937i	$0.601146\pi$
$212$	−3681.35	−1.19262
$213$	2783.03	0.895260
$214$	5489.37	1.75349
$215$	0	0
$216$	−1139.30	−0.358886
$217$	2970.67	0.929320
$218$	−5476.12	−1.70133
$219$	303.764	0.0937281
$220$	0	0
$221$	1809.47	0.550762
$222$	4920.54	1.48759
$223$	2286.67	0.686668	0.343334	−	0.939213i	$-0.388444\pi$
$223$	2286.67	0.686668	0.343334	+	0.939213i	$0.388444\pi$
$224$	−1205.78	−0.359662
$225$	0	0
$226$	−1086.52	−0.319796
$227$	−4443.67	−1.29928	−0.649640	−	0.760242i	$-0.725081\pi$
$227$	−4443.67	−1.29928	−0.649640	+	0.760242i	$0.725081\pi$
$228$	−3812.20	−1.10732
$229$	−445.935	−0.128682	−0.0643411	−	0.997928i	$-0.520495\pi$
$229$	−445.935	−0.128682	−0.0643411	+	0.997928i	$0.520495\pi$
$230$	0	0
$231$	−841.551	−0.239697
$232$	−9152.18	−2.58996
$233$	−1989.69	−0.559438	−0.279719	−	0.960082i	$-0.590241\pi$
$233$	−1989.69	−0.559438	−0.279719	+	0.960082i	$0.590241\pi$
$234$	4111.75	1.14869
$235$	0	0
$236$	2885.91	0.796004
$237$	886.220	0.242895
$238$	2746.23	0.747949
$239$	270.159	0.0731178	0.0365589	−	0.999331i	$-0.488360\pi$
$239$	270.159	0.0731178	0.0365589	+	0.999331i	$0.488360\pi$
$240$	0	0
$241$	1719.33	0.459551	0.229775	−	0.973244i	$-0.426201\pi$
$241$	1719.33	0.459551	0.229775	+	0.973244i	$0.426201\pi$
$242$	6103.62	1.62130
$243$	243.000	0.0641500
$244$	−7802.99	−2.04728
$245$	0	0
$246$	−1413.16	−0.366260
$247$	7096.20	1.82802
$248$	−4433.03	−1.13507
$249$	−3336.96	−0.849282
$250$	0	0
$251$	−1294.19	−0.325453	−0.162727	−	0.986671i	$-0.552029\pi$
$251$	−1294.19	−0.325453	−0.162727	+	0.986671i	$0.552029\pi$
$252$	4204.47	1.05102
$253$	−1004.99	−0.249737
$254$	−6213.52	−1.53492
$255$	0	0
$256$	−8348.81	−2.03828
$257$	5290.69	1.28414	0.642070	−	0.766646i	$-0.278076\pi$
$257$	5290.69	1.28414	0.642070	+	0.766646i	$0.278076\pi$
$258$	1007.38	0.243088
$259$	−9365.85	−2.24697
$260$	0	0
$261$	1952.06	0.462949
$262$	6738.71	1.58900
$263$	−2364.44	−0.554363	−0.277182	−	0.960818i	$-0.589400\pi$
$263$	−2364.44	−0.554363	−0.277182	+	0.960818i	$0.589400\pi$
$264$	1255.82	0.292766
$265$	0	0
$266$	10769.9	2.48249
$267$	383.204	0.0878341
$268$	−2076.45	−0.473281
$269$	−3891.67	−0.882080	−0.441040	−	0.897487i	$-0.645390\pi$
$269$	−3891.67	−0.882080	−0.441040	+	0.897487i	$0.645390\pi$
$270$	0	0
$271$	−2343.65	−0.525337	−0.262669	−	0.964886i	$-0.584603\pi$
$271$	−2343.65	−0.525337	−0.262669	+	0.964886i	$0.584603\pi$
$272$	−1505.89	−0.335692
$273$	−7826.39	−1.73507
$274$	11343.3	2.50101
$275$	0	0
$276$	5021.05	1.09504
$277$	−4216.10	−0.914516	−0.457258	−	0.889334i	$-0.651168\pi$
$277$	−4216.10	−0.914516	−0.457258	+	0.889334i	$0.651168\pi$
$278$	−9644.51	−2.08072
$279$	945.519	0.202892
$280$	0	0
$281$	−7235.84	−1.53613	−0.768067	−	0.640369i	$-0.778781\pi$
$281$	−7235.84	−1.53613	−0.768067	+	0.640369i	$0.778781\pi$
$282$	−1744.46	−0.368374
$283$	5145.49	1.08080	0.540402	−	0.841407i	$-0.318272\pi$
$283$	5145.49	1.08080	0.540402	+	0.841407i	$0.318272\pi$
$284$	15326.4	3.20230
$285$	0	0
$286$	−4532.28	−0.937060
$287$	2689.84	0.553228
$288$	−383.780	−0.0785224
$289$	−4528.34	−0.921705
$290$	0	0
$291$	−4562.90	−0.919183
$292$	1672.85	0.335261
$293$	1230.73	0.245392	0.122696	−	0.992444i	$-0.460846\pi$
$293$	1230.73	0.245392	0.122696	+	0.992444i	$0.460846\pi$
$294$	−6782.58	−1.34547
$295$	0	0
$296$	13976.3	2.74445
$297$	−267.853	−0.0523313
$298$	4942.66	0.960807
$299$	−9346.40	−1.80775
$300$	0	0
$301$	−1917.47	−0.367179
$302$	14664.6	2.79422
$303$	1325.93	0.251395
$304$	−5905.64	−1.11418
$305$	0	0
$306$	874.084	0.163294
$307$	−4082.53	−0.758964	−0.379482	−	0.925199i	$-0.623898\pi$
$307$	−4082.53	−0.758964	−0.379482	+	0.925199i	$0.623898\pi$
$308$	−4634.48	−0.857384
$309$	−4667.98	−0.859391
$310$	0	0
$311$	1112.65	0.202870	0.101435	−	0.994842i	$-0.467657\pi$
$311$	1112.65	0.202870	0.101435	+	0.994842i	$0.467657\pi$
$312$	11679.1	2.11922
$313$	5842.44	1.05506	0.527531	−	0.849536i	$-0.323118\pi$
$313$	5842.44	1.05506	0.527531	+	0.849536i	$0.323118\pi$
$314$	4576.66	0.822535
$315$	0	0
$316$	4880.48	0.868824
$317$	9629.18	1.70608	0.853042	−	0.521842i	$-0.174755\pi$
$317$	9629.18	1.70608	0.853042	+	0.521842i	$0.174755\pi$
$318$	3310.23	0.583737
$319$	−2151.71	−0.377657
$320$	0	0
$321$	−3325.62	−0.578250
$322$	−14185.0	−2.45496
$323$	1508.52	0.259865
$324$	1338.22	0.229461
$325$	0	0
$326$	−3942.17	−0.669744
$327$	3317.59	0.561050
$328$	−4013.96	−0.675714
$329$	3320.45	0.556420
$330$	0	0
$331$	−5464.07	−0.907349	−0.453674	−	0.891168i	$-0.649887\pi$
$331$	−5464.07	−0.907349	−0.453674	+	0.891168i	$0.649887\pi$
$332$	−18376.9	−3.03784
$333$	−2981.00	−0.490565
$334$	−8079.01	−1.32354
$335$	0	0
$336$	6513.32	1.05753
$337$	−10638.7	−1.71966	−0.859831	−	0.510579i	$-0.829431\pi$
$337$	−10638.7	−1.71966	−0.859831	+	0.510579i	$0.829431\pi$
$338$	−31270.7	−5.03225
$339$	658.243	0.105460
$340$	0	0
$341$	−1042.22	−0.165512
$342$	3427.89	0.541985
$343$	3211.23	0.505510
$344$	2861.37	0.448474
$345$	0	0
$346$	−1375.22	−0.213677
$347$	−12036.4	−1.86210	−0.931051	−	0.364888i	$-0.881107\pi$
$347$	−12036.4	−1.86210	−0.931051	+	0.364888i	$0.881107\pi$
$348$	10750.2	1.65595
$349$	−1475.05	−0.226239	−0.113120	−	0.993581i	$-0.536084\pi$
$349$	−1475.05	−0.226239	−0.113120	+	0.993581i	$0.536084\pi$
$350$	0	0
$351$	−2491.02	−0.378805
$352$	423.031	0.0640557
$353$	5537.88	0.834990	0.417495	−	0.908679i	$-0.362908\pi$
$353$	5537.88	0.834990	0.417495	+	0.908679i	$0.362908\pi$
$354$	−2594.98	−0.389609
$355$	0	0
$356$	2110.33	0.314178
$357$	−1663.75	−0.246652
$358$	15937.2	2.35282
$359$	4764.83	0.700496	0.350248	−	0.936657i	$-0.386097\pi$
$359$	4764.83	0.700496	0.350248	+	0.936657i	$0.386097\pi$
$360$	0	0
$361$	−943.038	−0.137489
$362$	719.918	0.104525
$363$	−3697.75	−0.534660
$364$	−43100.5	−6.20626
$365$	0	0
$366$	7016.35	1.00205
$367$	−13284.0	−1.88942	−0.944712	−	0.327900i	$-0.893659\pi$
$367$	−13284.0	−1.88942	−0.944712	+	0.327900i	$0.893659\pi$
$368$	7778.31	1.10183
$369$	856.136	0.120782
$370$	0	0
$371$	−6300.75	−0.881721
$372$	5207.05	0.725733
$373$	9594.38	1.33184	0.665922	−	0.746021i	$-0.268038\pi$
$373$	9594.38	1.33184	0.665922	+	0.746021i	$0.268038\pi$
$374$	−963.480	−0.133210
$375$	0	0
$376$	−4954.99	−0.679612
$377$	−20010.8	−2.73371
$378$	−3780.61	−0.514427
$379$	3308.43	0.448397	0.224199	−	0.974543i	$-0.428024\pi$
$379$	3308.43	0.448397	0.224199	+	0.974543i	$0.428024\pi$
$380$	0	0
$381$	3764.33	0.506174
$382$	6022.42	0.806633
$383$	10418.6	1.38998	0.694991	−	0.719019i	$-0.255408\pi$
$383$	10418.6	1.38998	0.694991	+	0.719019i	$0.255408\pi$
$384$	7011.58	0.931792
$385$	0	0
$386$	469.743	0.0619411
$387$	−610.301	−0.0801636
$388$	−25128.3	−3.28787
$389$	5369.28	0.699828	0.349914	−	0.936782i	$-0.386211\pi$
$389$	5369.28	0.699828	0.349914	+	0.936782i	$0.386211\pi$
$390$	0	0
$391$	−1986.87	−0.256984
$392$	−19265.3	−2.48226
$393$	−4082.51	−0.524009
$394$	16488.2	2.10829
$395$	0	0
$396$	−1475.08	−0.187186
$397$	−3634.27	−0.459442	−0.229721	−	0.973256i	$-0.573781\pi$
$397$	−3634.27	−0.459442	−0.229721	+	0.973256i	$0.573781\pi$
$398$	−9781.66	−1.23194
$399$	−6524.70	−0.818656
$400$	0	0
$401$	13921.2	1.73364	0.866820	−	0.498621i	$-0.166160\pi$
$401$	13921.2	1.73364	0.866820	+	0.498621i	$0.166160\pi$
$402$	1867.12	0.231650
$403$	−9692.61	−1.19807
$404$	7301.98	0.899226
$405$	0	0
$406$	−30370.3	−3.71245
$407$	3285.88	0.400185
$408$	2482.76	0.301261
$409$	−77.4049	−0.00935801	−0.00467901	−	0.999989i	$-0.501489\pi$
$409$	−77.4049	−0.00935801	−0.00467901	+	0.999989i	$0.501489\pi$
$410$	0	0
$411$	−6872.13	−0.824761
$412$	−25706.9	−3.07400
$413$	4939.33	0.588495
$414$	−4514.86	−0.535975
$415$	0	0
$416$	3934.17	0.463674
$417$	5842.93	0.686161
$418$	−3778.47	−0.442132
$419$	−9731.89	−1.13469	−0.567344	−	0.823481i	$-0.692029\pi$
$419$	−9731.89	−1.13469	−0.567344	+	0.823481i	$0.692029\pi$
$420$	0	0
$421$	−2067.95	−0.239396	−0.119698	−	0.992810i	$-0.538193\pi$
$421$	−2067.95	−0.239396	−0.119698	+	0.992810i	$0.538193\pi$
$422$	9484.00	1.09401
$423$	1056.85	0.121479
$424$	9402.40	1.07694
$425$	0	0
$426$	−13781.3	−1.56738
$427$	−13355.1	−1.51358
$428$	−18314.5	−2.06837
$429$	2745.78	0.309016
$430$	0	0
$431$	−7910.22	−0.884041	−0.442021	−	0.897005i	$-0.645738\pi$
$431$	−7910.22	−0.884041	−0.442021	+	0.897005i	$0.645738\pi$
$432$	2073.09	0.230883
$433$	−8190.70	−0.909053	−0.454526	−	0.890733i	$-0.650192\pi$
$433$	−8190.70	−0.909053	−0.454526	+	0.890733i	$0.650192\pi$
$434$	−14710.4	−1.62701
$435$	0	0
$436$	18270.2	2.00685
$437$	−7791.91	−0.852946
$438$	−1504.21	−0.164095
$439$	1420.57	0.154442	0.0772210	−	0.997014i	$-0.475395\pi$
$439$	1420.57	0.154442	0.0772210	+	0.997014i	$0.475395\pi$
$440$	0	0
$441$	4109.08	0.443698
$442$	−8960.32	−0.964251
$443$	−12966.5	−1.39064	−0.695322	−	0.718698i	$-0.744738\pi$
$443$	−12966.5	−1.39064	−0.695322	+	0.718698i	$0.744738\pi$
$444$	−16416.6	−1.75473
$445$	0	0
$446$	−11323.4	−1.20219
$447$	−2994.40	−0.316847
$448$	−11398.0	−1.20202
$449$	3893.44	0.409227	0.204613	−	0.978843i	$-0.434406\pi$
$449$	3893.44	0.409227	0.204613	+	0.978843i	$0.434406\pi$
$450$	0	0
$451$	−943.696	−0.0985298
$452$	3624.99	0.377224
$453$	−8884.25	−0.921454
$454$	22004.6	2.27473
$455$	0	0
$456$	9736.60	0.999908
$457$	13592.6	1.39133	0.695663	−	0.718369i	$-0.255111\pi$
$457$	13592.6	1.39133	0.695663	+	0.718369i	$0.255111\pi$
$458$	2208.22	0.225291
$459$	−529.545	−0.0538498
$460$	0	0
$461$	−10079.2	−1.01829	−0.509147	−	0.860680i	$-0.670039\pi$
$461$	−10079.2	−1.01829	−0.509147	+	0.860680i	$0.670039\pi$
$462$	4167.27	0.419651
$463$	−11345.9	−1.13885	−0.569424	−	0.822044i	$-0.692834\pi$
$463$	−11345.9	−1.13885	−0.569424	+	0.822044i	$0.692834\pi$
$464$	16653.5	1.66621
$465$	0	0
$466$	9852.73	0.979440
$467$	−780.833	−0.0773718	−0.0386859	−	0.999251i	$-0.512317\pi$
$467$	−780.833	−0.0773718	−0.0386859	+	0.999251i	$0.512317\pi$
$468$	−13718.2	−1.35497
$469$	−3553.91	−0.349902
$470$	0	0
$471$	−2772.67	−0.271249
$472$	−7370.79	−0.718789
$473$	672.719	0.0653946
$474$	−4388.46	−0.425251
$475$	0	0
$476$	−9162.39	−0.882263
$477$	−2005.43	−0.192500
$478$	−1337.80	−0.128012
$479$	−15318.7	−1.46123	−0.730617	−	0.682788i	$-0.760767\pi$
$479$	−15318.7	−1.46123	−0.730617	+	0.682788i	$0.760767\pi$
$480$	0	0
$481$	30558.6	2.89678
$482$	−8513.93	−0.804562
$483$	8593.68	0.809578
$484$	−20363.8	−1.91245
$485$	0	0
$486$	−1203.31	−0.112311
$487$	−9262.14	−0.861823	−0.430911	−	0.902394i	$-0.641808\pi$
$487$	−9262.14	−0.861823	−0.430911	+	0.902394i	$0.641808\pi$
$488$	19929.3	1.84868
$489$	2388.28	0.220862
$490$	0	0
$491$	3196.74	0.293823	0.146911	−	0.989150i	$-0.453067\pi$
$491$	3196.74	0.293823	0.146911	+	0.989150i	$0.453067\pi$
$492$	4714.80	0.432032
$493$	−4253.94	−0.388616
$494$	−35139.6	−3.20042
$495$	0	0
$496$	8066.45	0.730230
$497$	26231.6	2.36750
$498$	16524.3	1.48689
$499$	7859.90	0.705125	0.352563	−	0.935788i	$-0.385310\pi$
$499$	7859.90	0.705125	0.352563	+	0.935788i	$0.385310\pi$
$500$	0	0
$501$	4894.50	0.436467
$502$	6408.70	0.569789
$503$	−14779.3	−1.31009	−0.655045	−	0.755590i	$-0.727350\pi$
$503$	−14779.3	−1.31009	−0.655045	+	0.755590i	$0.727350\pi$
$504$	−10738.5	−0.949067
$505$	0	0
$506$	4976.62	0.437229
$507$	18944.7	1.65949
$508$	20730.4	1.81056
$509$	8543.83	0.744006	0.372003	−	0.928232i	$-0.378671\pi$
$509$	8543.83	0.744006	0.372003	+	0.928232i	$0.378671\pi$
$510$	0	0
$511$	2863.13	0.247862
$512$	22644.8	1.95463
$513$	−2076.71	−0.178731
$514$	−26198.9	−2.24822
$515$	0	0
$516$	−3360.97	−0.286741
$517$	−1164.94	−0.0990983
$518$	46378.7	3.93390
$519$	833.147	0.0704645
$520$	0	0
$521$	7402.74	0.622495	0.311248	−	0.950329i	$-0.399253\pi$
$521$	7402.74	0.622495	0.311248	+	0.950329i	$0.399253\pi$
$522$	−9666.41	−0.810512
$523$	−732.790	−0.0612670	−0.0306335	−	0.999531i	$-0.509752\pi$
$523$	−732.790	−0.0612670	−0.0306335	+	0.999531i	$0.509752\pi$
$524$	−22482.7	−1.87435
$525$	0	0
$526$	11708.4	0.970556
$527$	−2060.47	−0.170314
$528$	−2285.11	−0.188346
$529$	−1904.29	−0.156513
$530$	0	0
$531$	1572.11	0.128482
$532$	−35932.0	−2.92829
$533$	−8776.34	−0.713218
$534$	−1897.59	−0.153776
$535$	0	0
$536$	5303.38	0.427371
$537$	−9655.24	−0.775893
$538$	19271.1	1.54431
$539$	−4529.34	−0.361953
$540$	0	0
$541$	−11205.0	−0.890467	−0.445234	−	0.895414i	$-0.646879\pi$
$541$	−11205.0	−0.890467	−0.445234	+	0.895414i	$0.646879\pi$
$542$	11605.5	0.919738
$543$	−436.147	−0.0344694
$544$	836.333	0.0659145
$545$	0	0
$546$	38755.4	3.03769
$547$	7504.96	0.586634	0.293317	−	0.956015i	$-0.405241\pi$
$547$	7504.96	0.586634	0.293317	+	0.956015i	$0.405241\pi$
$548$	−37845.3	−2.95013
$549$	−4250.71	−0.330448
$550$	0	0
$551$	−16682.6	−1.28984
$552$	−12824.1	−0.988819
$553$	8353.09	0.642332
$554$	20877.7	1.60110
$555$	0	0
$556$	32177.4	2.45437
$557$	12871.1	0.979112	0.489556	−	0.871972i	$-0.337159\pi$
$557$	12871.1	0.979112	0.489556	+	0.871972i	$0.337159\pi$
$558$	−4682.11	−0.355214
$559$	6256.25	0.473366
$560$	0	0
$561$	583.704	0.0439287
$562$	35831.1	2.68940
$563$	525.300	0.0393228	0.0196614	−	0.999807i	$-0.493741\pi$
$563$	525.300	0.0393228	0.0196614	+	0.999807i	$0.493741\pi$
$564$	5820.14	0.434525
$565$	0	0
$566$	−25479.9	−1.89223
$567$	2290.40	0.169644
$568$	−39144.5	−2.89166
$569$	12768.5	0.940747	0.470374	−	0.882467i	$-0.344119\pi$
$569$	12768.5	0.940747	0.470374	+	0.882467i	$0.344119\pi$
$570$	0	0
$571$	−24.0985	−0.00176619	−0.000883093	−	1.00000i	$-0.500281\pi$
$571$	−24.0985	−0.00176619	−0.000883093		1.00000i	$0.500281\pi$
$572$	15121.2	1.10533
$573$	−3648.56	−0.266005
$574$	−13319.8	−0.968568
$575$	0	0
$576$	−3627.80	−0.262428
$577$	−1831.98	−0.132177	−0.0660885	−	0.997814i	$-0.521052\pi$
$577$	−1831.98	−0.132177	−0.0660885	+	0.997814i	$0.521052\pi$
$578$	22423.8	1.61368
$579$	−284.584	−0.0204264
$580$	0	0
$581$	−31452.6	−2.24591
$582$	22595.0	1.60927
$583$	2210.54	0.157034
$584$	−4272.56	−0.302739
$585$	0	0
$586$	−6094.42	−0.429621
$587$	11952.2	0.840410	0.420205	−	0.907429i	$-0.361958\pi$
$587$	11952.2	0.840410	0.420205	+	0.907429i	$0.361958\pi$
$588$	22629.0	1.58708
$589$	−8080.54	−0.565285
$590$	0	0
$591$	−9989.05	−0.695253
$592$	−25431.6	−1.76560
$593$	6599.09	0.456985	0.228493	−	0.973546i	$-0.426620\pi$
$593$	6599.09	0.456985	0.228493	+	0.973546i	$0.426620\pi$
$594$	1326.38	0.0916194
$595$	0	0
$596$	−16490.4	−1.13335
$597$	5926.01	0.406257
$598$	46282.3	3.16493
$599$	5436.04	0.370802	0.185401	−	0.982663i	$-0.440642\pi$
$599$	5436.04	0.370802	0.185401	+	0.982663i	$0.440642\pi$
$600$	0	0
$601$	−20520.7	−1.39277	−0.696385	−	0.717668i	$-0.745209\pi$
$601$	−20520.7	−1.39277	−0.696385	+	0.717668i	$0.745209\pi$
$602$	9495.09	0.642842
$603$	−1131.15	−0.0763916
$604$	−48926.3	−3.29600
$605$	0	0
$606$	−6565.85	−0.440131
$607$	7627.67	0.510045	0.255023	−	0.966935i	$-0.417917\pi$
$607$	7627.67	0.510045	0.255023	+	0.966935i	$0.417917\pi$
$608$	3279.84	0.218775
$609$	18399.2	1.22426
$610$	0	0
$611$	−10833.8	−0.717333
$612$	−2916.25	−0.192618
$613$	−7610.43	−0.501439	−0.250720	−	0.968060i	$-0.580667\pi$
$613$	−7610.43	−0.501439	−0.250720	+	0.968060i	$0.580667\pi$
$614$	20216.2	1.32876
$615$	0	0
$616$	11836.7	0.774214
$617$	−14502.4	−0.946267	−0.473133	−	0.880991i	$-0.656877\pi$
$617$	−14502.4	−0.946267	−0.473133	+	0.880991i	$0.656877\pi$
$618$	23115.3	1.50459
$619$	−22021.3	−1.42991	−0.714954	−	0.699172i	$-0.753552\pi$
$619$	−22021.3	−1.42991	−0.714954	+	0.699172i	$0.753552\pi$
$620$	0	0
$621$	2735.24	0.176749
$622$	−5509.73	−0.355177
$623$	3611.90	0.232276
$624$	−21251.5	−1.36336
$625$	0	0
$626$	−28931.1	−1.84716
$627$	2289.11	0.145802
$628$	−15269.3	−0.970243
$629$	6496.20	0.411797
$630$	0	0
$631$	13701.4	0.864413	0.432206	−	0.901775i	$-0.357735\pi$
$631$	13701.4	0.864413	0.432206	+	0.901775i	$0.357735\pi$
$632$	−12465.0	−0.784545
$633$	−5745.68	−0.360775
$634$	−47682.6	−2.98694
$635$	0	0
$636$	−11044.1	−0.688562
$637$	−42122.6	−2.62003
$638$	10655.0	0.661186
$639$	8349.10	0.516878
$640$	0	0
$641$	−2309.45	−0.142306	−0.0711528	−	0.997465i	$-0.522668\pi$
$641$	−2309.45	−0.142306	−0.0711528	+	0.997465i	$0.522668\pi$
$642$	16468.1	1.01238
$643$	2768.05	0.169768	0.0848842	−	0.996391i	$-0.472948\pi$
$643$	2768.05	0.169768	0.0848842	+	0.996391i	$0.472948\pi$
$644$	47326.0	2.89582
$645$	0	0
$646$	−7470.05	−0.454961
$647$	−10901.1	−0.662393	−0.331197	−	0.943562i	$-0.607452\pi$
$647$	−10901.1	−0.662393	−0.331197	+	0.943562i	$0.607452\pi$
$648$	−3417.89	−0.207203
$649$	−1732.90	−0.104811
$650$	0	0
$651$	8912.02	0.536543
$652$	13152.4	0.790014
$653$	9894.06	0.592932	0.296466	−	0.955043i	$-0.404192\pi$
$653$	9894.06	0.592932	0.296466	+	0.955043i	$0.404192\pi$
$654$	−16428.4	−0.982263
$655$	0	0
$656$	7303.90	0.434709
$657$	911.292	0.0541140
$658$	−16442.5	−0.974157
$659$	−13651.5	−0.806958	−0.403479	−	0.914989i	$-0.632199\pi$
$659$	−13651.5	−0.806958	−0.403479	+	0.914989i	$0.632199\pi$
$660$	0	0
$661$	−5867.49	−0.345263	−0.172632	−	0.984986i	$-0.555227\pi$
$661$	−5867.49	−0.345263	−0.172632	+	0.984986i	$0.555227\pi$
$662$	27057.5	1.58855
$663$	5428.42	0.317983
$664$	46935.7	2.74316
$665$	0	0
$666$	14761.6	0.858860
$667$	21972.7	1.27554
$668$	26954.4	1.56122
$669$	6860.02	0.396448
$670$	0	0
$671$	4685.45	0.269567
$672$	−3617.33	−0.207651
$673$	−27053.1	−1.54951	−0.774754	−	0.632262i	$-0.782126\pi$
$673$	−27053.1	−1.54951	−0.774754	+	0.632262i	$0.782126\pi$
$674$	52681.6	3.01071
$675$	0	0
$676$	104330.	5.93592
$677$	33037.9	1.87555	0.937777	−	0.347239i	$-0.112881\pi$
$677$	33037.9	1.87555	0.937777	+	0.347239i	$0.112881\pi$
$678$	−3259.55	−0.184634
$679$	−43007.8	−2.43076
$680$	0	0
$681$	−13331.0	−0.750140
$682$	5160.97	0.289771
$683$	21098.2	1.18199	0.590996	−	0.806674i	$-0.298735\pi$
$683$	21098.2	1.18199	0.590996	+	0.806674i	$0.298735\pi$
$684$	−11436.6	−0.639313
$685$	0	0
$686$	−15901.7	−0.885027
$687$	−1337.80	−0.0742947
$688$	−5206.62	−0.288518
$689$	20557.9	1.13671
$690$	0	0
$691$	−15304.3	−0.842553	−0.421276	−	0.906932i	$-0.638418\pi$
$691$	−15304.3	−0.842553	−0.421276	+	0.906932i	$0.638418\pi$
$692$	4588.20	0.252048
$693$	−2524.65	−0.138389
$694$	59603.1	3.26009
$695$	0	0
$696$	−27456.5	−1.49531
$697$	−1865.69	−0.101389
$698$	7304.27	0.396090
$699$	−5969.07	−0.322992
$700$	0	0
$701$	−1568.71	−0.0845213	−0.0422607	−	0.999107i	$-0.513456\pi$
$701$	−1568.71	−0.0845213	−0.0422607	+	0.999107i	$0.513456\pi$
$702$	12335.2	0.663197
$703$	25476.1	1.36678
$704$	3998.83	0.214079
$705$	0	0
$706$	−27423.0	−1.46186
$707$	12497.6	0.664808
$708$	8657.74	0.459573
$709$	24085.5	1.27581	0.637906	−	0.770114i	$-0.279801\pi$
$709$	24085.5	1.27581	0.637906	+	0.770114i	$0.279801\pi$
$710$	0	0
$711$	2658.66	0.140236
$712$	−5389.92	−0.283702
$713$	10642.9	0.559017
$714$	8238.70	0.431829
$715$	0	0
$716$	−53172.2	−2.77533
$717$	810.478	0.0422146
$718$	−23594.9	−1.22640
$719$	17170.7	0.890627	0.445313	−	0.895375i	$-0.353092\pi$
$719$	17170.7	0.890627	0.445313	+	0.895375i	$0.353092\pi$
$720$	0	0
$721$	−43998.1	−2.27264
$722$	4669.82	0.240710
$723$	5157.99	0.265322
$724$	−2401.90	−0.123295
$725$	0	0
$726$	18310.9	0.936061
$727$	19404.9	0.989943	0.494971	−	0.868909i	$-0.335179\pi$
$727$	19404.9	0.989943	0.494971	+	0.868909i	$0.335179\pi$
$728$	110081.	5.60423
$729$	729.000	0.0370370
$730$	0	0
$731$	1329.97	0.0672922
$732$	−23409.0	−1.18200
$733$	−22558.7	−1.13673	−0.568367	−	0.822775i	$-0.692424\pi$
$733$	−22558.7	−1.13673	−0.568367	+	0.822775i	$0.692424\pi$
$734$	65780.9	3.30793
$735$	0	0
$736$	−4319.87	−0.216349
$737$	1246.84	0.0623175
$738$	−4239.49	−0.211460
$739$	5378.11	0.267709	0.133855	−	0.991001i	$-0.457264\pi$
$739$	5378.11	0.267709	0.133855	+	0.991001i	$0.457264\pi$
$740$	0	0
$741$	21288.6	1.05541
$742$	31200.6	1.54368
$743$	−6218.08	−0.307025	−0.153512	−	0.988147i	$-0.549058\pi$
$743$	−6218.08	−0.307025	−0.153512	+	0.988147i	$0.549058\pi$
$744$	−13299.1	−0.655334
$745$	0	0
$746$	−47510.3	−2.33174
$747$	−10010.9	−0.490333
$748$	3214.50	0.157131
$749$	−31345.7	−1.52917
$750$	0	0
$751$	−28975.1	−1.40788	−0.703939	−	0.710261i	$-0.748577\pi$
$751$	−28975.1	−1.40788	−0.703939	+	0.710261i	$0.748577\pi$
$752$	9016.21	0.437217
$753$	−3882.58	−0.187900
$754$	99091.3	4.78606
$755$	0	0
$756$	12613.4	0.606807
$757$	433.605	0.0208185	0.0104093	−	0.999946i	$-0.496687\pi$
$757$	433.605	0.0208185	0.0104093	+	0.999946i	$0.496687\pi$
$758$	−16383.0	−0.785035
$759$	−3014.98	−0.144186
$760$	0	0
$761$	−32201.6	−1.53391	−0.766956	−	0.641699i	$-0.778230\pi$
$761$	−32201.6	−1.53391	−0.766956	+	0.641699i	$0.778230\pi$
$762$	−18640.6	−0.886189
$763$	31270.1	1.48369
$764$	−20092.9	−0.951486
$765$	0	0
$766$	−51591.5	−2.43352
$767$	−16115.9	−0.758684
$768$	−25046.4	−1.17680
$769$	17728.8	0.831361	0.415681	−	0.909511i	$-0.363543\pi$
$769$	17728.8	0.831361	0.415681	+	0.909511i	$0.363543\pi$
$770$	0	0
$771$	15872.1	0.741399
$772$	−1567.22	−0.0730643
$773$	37345.9	1.73769	0.868847	−	0.495080i	$-0.164861\pi$
$773$	37345.9	1.73769	0.868847	+	0.495080i	$0.164861\pi$
$774$	3022.14	0.140347
$775$	0	0
$776$	64179.0	2.96893
$777$	−28097.5	−1.29729
$778$	−26588.1	−1.22523
$779$	−7316.66	−0.336517
$780$	0	0
$781$	−9203.00	−0.421651
$782$	9838.79	0.449916
$783$	5856.19	0.267284
$784$	35055.6	1.59692
$785$	0	0
$786$	20216.1	0.917412
$787$	−29752.6	−1.34761	−0.673803	−	0.738911i	$-0.735340\pi$
$787$	−29752.6	−1.34761	−0.673803	+	0.738911i	$0.735340\pi$
$788$	−55010.5	−2.48689
$789$	−7093.32	−0.320062
$790$	0	0
$791$	6204.28	0.278886
$792$	3767.45	0.169029
$793$	43574.5	1.95129
$794$	17996.5	0.804372
$795$	0	0
$796$	32635.0	1.45316
$797$	38068.9	1.69193	0.845965	−	0.533238i	$-0.179025\pi$
$797$	38068.9	1.69193	0.845965	+	0.533238i	$0.179025\pi$
$798$	32309.6	1.43327
$799$	−2303.08	−0.101974
$800$	0	0
$801$	1149.61	0.0507111
$802$	−68936.1	−3.03519
$803$	−1004.49	−0.0441442
$804$	−6229.35	−0.273249
$805$	0	0
$806$	47996.8	2.09754
$807$	−11675.0	−0.509269
$808$	−18649.7	−0.811997
$809$	38246.4	1.66214	0.831070	−	0.556168i	$-0.187729\pi$
$809$	38246.4	1.66214	0.831070	+	0.556168i	$0.187729\pi$
$810$	0	0
$811$	14312.9	0.619721	0.309861	−	0.950782i	$-0.399718\pi$
$811$	14312.9	0.619721	0.309861	+	0.950782i	$0.399718\pi$
$812$	101326.	4.37912
$813$	−7030.94	−0.303304
$814$	−16271.3	−0.700627
$815$	0	0
$816$	−4517.68	−0.193812
$817$	5215.72	0.223347
$818$	383.301	0.0163836
$819$	−23479.2	−1.00174
$820$	0	0
$821$	3187.21	0.135486	0.0677431	−	0.997703i	$-0.478420\pi$
$821$	3187.21	0.135486	0.0677431	+	0.997703i	$0.478420\pi$
$822$	34030.0	1.44396
$823$	1125.25	0.0476595	0.0238298	−	0.999716i	$-0.492414\pi$
$823$	1125.25	0.0476595	0.0238298	+	0.999716i	$0.492414\pi$
$824$	65656.9	2.77581
$825$	0	0
$826$	−24459.0	−1.03031
$827$	−18498.6	−0.777824	−0.388912	−	0.921275i	$-0.627149\pi$
$827$	−18498.6	−0.777824	−0.388912	+	0.921275i	$0.627149\pi$
$828$	15063.2	0.632223
$829$	−21867.6	−0.916156	−0.458078	−	0.888912i	$-0.651462\pi$
$829$	−21867.6	−0.916156	−0.458078	+	0.888912i	$0.651462\pi$
$830$	0	0
$831$	−12648.3	−0.527996
$832$	37189.0	1.54963
$833$	−8954.51	−0.372456
$834$	−28933.5	−1.20130
$835$	0	0
$836$	12606.3	0.521528
$837$	2836.56	0.117140
$838$	48191.3	1.98656
$839$	15634.6	0.643345	0.321672	−	0.946851i	$-0.395755\pi$
$839$	15634.6	0.643345	0.321672	+	0.946851i	$0.395755\pi$
$840$	0	0
$841$	22654.9	0.928896
$842$	10240.3	0.419124
$843$	−21707.5	−0.886888
$844$	−31641.9	−1.29047
$845$	0	0
$846$	−5233.39	−0.212681
$847$	−34853.3	−1.41390
$848$	−17108.8	−0.692829
$849$	15436.5	0.624002
$850$	0	0
$851$	−33554.5	−1.35163
$852$	45979.1	1.84885
$853$	43860.1	1.76054	0.880270	−	0.474474i	$-0.157362\pi$
$853$	43860.1	1.76054	0.880270	+	0.474474i	$0.157362\pi$
$854$	66132.8	2.64990
$855$	0	0
$856$	46776.2	1.86773
$857$	−32206.5	−1.28373	−0.641863	−	0.766819i	$-0.721838\pi$
$857$	−32206.5	−1.28373	−0.641863	+	0.766819i	$0.721838\pi$
$858$	−13596.8	−0.541012
$859$	11852.2	0.470772	0.235386	−	0.971902i	$-0.424365\pi$
$859$	11852.2	0.470772	0.235386	+	0.971902i	$0.424365\pi$
$860$	0	0
$861$	8069.53	0.319406
$862$	39170.5	1.54774
$863$	−11179.3	−0.440961	−0.220481	−	0.975391i	$-0.570763\pi$
$863$	−11179.3	−0.440961	−0.220481	+	0.975391i	$0.570763\pi$
$864$	−1151.34	−0.0453349
$865$	0	0
$866$	40559.5	1.59153
$867$	−13585.0	−0.532147
$868$	49079.2	1.91919
$869$	−2930.57	−0.114399
$870$	0	0
$871$	11595.6	0.451092
$872$	−46663.3	−1.81218
$873$	−13688.7	−0.530690
$874$	38584.7	1.49330
$875$	0	0
$876$	5018.55	0.193563
$877$	−9836.83	−0.378753	−0.189376	−	0.981905i	$-0.560647\pi$
$877$	−9836.83	−0.378753	−0.189376	+	0.981905i	$0.560647\pi$
$878$	−7034.50	−0.270391
$879$	3692.18	0.141677
$880$	0	0
$881$	26039.3	0.995783	0.497892	−	0.867239i	$-0.334108\pi$
$881$	26039.3	0.995783	0.497892	+	0.867239i	$0.334108\pi$
$882$	−20347.7	−0.776807
$883$	1238.88	0.0472159	0.0236079	−	0.999721i	$-0.492485\pi$
$883$	1238.88	0.0472159	0.0236079	+	0.999721i	$0.492485\pi$
$884$	29894.7	1.13741
$885$	0	0
$886$	64208.5	2.43468
$887$	−27114.3	−1.02639	−0.513195	−	0.858272i	$-0.671538\pi$
$887$	−27114.3	−1.02639	−0.513195	+	0.858272i	$0.671538\pi$
$888$	41929.0	1.58451
$889$	35480.8	1.33857
$890$	0	0
$891$	−803.558	−0.0302135
$892$	37778.7	1.41808
$893$	−9031.97	−0.338458
$894$	14828.0	0.554722
$895$	0	0
$896$	66087.8	2.46411
$897$	−28039.2	−1.04370
$898$	−19279.9	−0.716457
$899$	22786.6	0.845356
$900$	0	0
$901$	4370.23	0.161591
$902$	4673.08	0.172502
$903$	−5752.40	−0.211991
$904$	−9258.44	−0.340632
$905$	0	0
$906$	43993.9	1.61324
$907$	10290.2	0.376716	0.188358	−	0.982100i	$-0.439684\pi$
$907$	10290.2	0.376716	0.188358	+	0.982100i	$0.439684\pi$
$908$	−73414.9	−2.68321
$909$	3977.78	0.145143
$910$	0	0
$911$	31269.5	1.13722	0.568609	−	0.822608i	$-0.307482\pi$
$911$	31269.5	1.13722	0.568609	+	0.822608i	$0.307482\pi$
$912$	−17716.9	−0.643274
$913$	11034.7	0.399996
$914$	−67309.1	−2.43587
$915$	0	0
$916$	−7367.39	−0.265748
$917$	−38479.8	−1.38573
$918$	2622.25	0.0942780
$919$	−17466.0	−0.626932	−0.313466	−	0.949599i	$-0.601490\pi$
$919$	−17466.0	−0.626932	−0.313466	+	0.949599i	$0.601490\pi$
$920$	0	0
$921$	−12247.6	−0.438188
$922$	49910.9	1.78279
$923$	−85587.5	−3.05216
$924$	−13903.4	−0.495011
$925$	0	0
$926$	56183.4	1.99385
$927$	−14003.9	−0.496170
$928$	−9248.92	−0.327167
$929$	−16800.8	−0.593345	−0.296672	−	0.954979i	$-0.595877\pi$
$929$	−16800.8	−0.593345	−0.296672	+	0.954979i	$0.595877\pi$
$930$	0	0
$931$	−35116.8	−1.23621
$932$	−32872.1	−1.15532
$933$	3337.96	0.117127
$934$	3866.60	0.135459
$935$	0	0
$936$	35037.2	1.22353
$937$	1905.93	0.0664505	0.0332252	−	0.999448i	$-0.489422\pi$
$937$	1905.93	0.0664505	0.0332252	+	0.999448i	$0.489422\pi$
$938$	17598.6	0.612594
$939$	17527.3	0.609140
$940$	0	0
$941$	8426.95	0.291935	0.145968	−	0.989289i	$-0.453371\pi$
$941$	8426.95	0.291935	0.145968	+	0.989289i	$0.453371\pi$
$942$	13730.0	0.474891
$943$	9636.76	0.332785
$944$	13412.1	0.462421
$945$	0	0
$946$	−3331.23	−0.114490
$947$	−42729.0	−1.46622	−0.733108	−	0.680113i	$-0.761931\pi$
$947$	−42729.0	−1.46622	−0.733108	+	0.680113i	$0.761931\pi$
$948$	14641.4	0.501616
$949$	−9341.74	−0.319542
$950$	0	0
$951$	28887.5	0.985008
$952$	23401.3	0.796680
$953$	−2854.92	−0.0970408	−0.0485204	−	0.998822i	$-0.515451\pi$
$953$	−2854.92	−0.0970408	−0.0485204	+	0.998822i	$0.515451\pi$
$954$	9930.68	0.337021
$955$	0	0
$956$	4463.37	0.151000
$957$	−6455.13	−0.218040
$958$	75856.7	2.55827
$959$	−64773.4	−2.18107
$960$	0	0
$961$	−18753.9	−0.629515
$962$	−151323.	−5.07156
$963$	−9976.87	−0.333853
$964$	28405.4	0.949043
$965$	0	0
$966$	−42555.0	−1.41737
$967$	−11899.1	−0.395709	−0.197854	−	0.980231i	$-0.563397\pi$
$967$	−11899.1	−0.395709	−0.197854	+	0.980231i	$0.563397\pi$
$968$	52010.4	1.72694
$969$	4525.57	0.150033
$970$	0	0
$971$	−1616.24	−0.0534166	−0.0267083	−	0.999643i	$-0.508503\pi$
$971$	−1616.24	−0.0534166	−0.0267083	+	0.999643i	$0.508503\pi$
$972$	4014.66	0.132480
$973$	55072.6	1.81454
$974$	45865.1	1.50884
$975$	0	0
$976$	−36263.8	−1.18932
$977$	−42150.9	−1.38027	−0.690136	−	0.723680i	$-0.742449\pi$
$977$	−42150.9	−1.38027	−0.690136	+	0.723680i	$0.742449\pi$
$978$	−11826.5	−0.386677
$979$	−1267.19	−0.0413683
$980$	0	0
$981$	9952.78	0.323922
$982$	−15829.9	−0.514412
$983$	−109.496	−0.00355276	−0.00177638	−	0.999998i	$-0.500565\pi$
$983$	−109.496	−0.00355276	−0.00177638	+	0.999998i	$0.500565\pi$
$984$	−12041.9	−0.390123
$985$	0	0
$986$	21065.0	0.680372
$987$	9961.34	0.321249
$988$	117238.	3.77514
$989$	−6869.61	−0.220871
$990$	0	0
$991$	−24448.0	−0.783671	−0.391835	−	0.920035i	$-0.628160\pi$
$991$	−24448.0	−0.783671	−0.391835	+	0.920035i	$0.628160\pi$
$992$	−4479.89	−0.143384
$993$	−16392.2	−0.523858
$994$	−129896.	−4.14491
$995$	0	0
$996$	−55130.7	−1.75390
$997$	5350.04	0.169947	0.0849737	−	0.996383i	$-0.472919\pi$
$997$	5350.04	0.169947	0.0849737	+	0.996383i	$0.472919\pi$
$998$	−38921.4	−1.23450
$999$	−8943.01	−0.283228

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.4.a.g.1.1		14
5.4	even	2		1875.4.a.f.1.14		14
25.11	even	5		75.4.g.b.46.1	yes	28
25.16	even	5		75.4.g.b.31.1	✓	28
75.11	odd	10		225.4.h.a.46.7		28
75.41	odd	10		225.4.h.a.181.7		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.31.1	✓	28	25.16	even	5
75.4.g.b.46.1	yes	28	25.11	even	5
225.4.h.a.46.7		28	75.11	odd	10
225.4.h.a.181.7		28	75.41	odd	10
1875.4.a.f.1.14		14	5.4	even	2
1875.4.a.g.1.1		14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-4.95189 q^{2} +3.00000 q^{3} +16.5212 q^{4} -14.8557 q^{6} +28.2766 q^{7} -42.1962 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.95189 q^{2} +3.00000 q^{3} +16.5212 q^{4} -14.8557 q^{6} +28.2766 q^{7} -42.1962 q^{8} +9.00000 q^{9} -9.92047 q^{11} +49.5637 q^{12} -92.2599 q^{13} -140.023 q^{14} +76.7811 q^{16} -19.6128 q^{17} -44.5670 q^{18} -76.9153 q^{19} +84.8297 q^{21} +49.1251 q^{22} +101.305 q^{23} -126.589 q^{24} +456.861 q^{26} +27.0000 q^{27} +467.164 q^{28} +216.896 q^{29} +105.058 q^{31} -42.6422 q^{32} -29.7614 q^{33} +97.1204 q^{34} +148.691 q^{36} -331.223 q^{37} +380.876 q^{38} -276.780 q^{39} +95.1262 q^{41} -420.068 q^{42} -67.8112 q^{43} -163.898 q^{44} -501.652 q^{46} +117.427 q^{47} +230.343 q^{48} +456.565 q^{49} -58.8384 q^{51} -1524.25 q^{52} -222.826 q^{53} -133.701 q^{54} -1193.16 q^{56} -230.746 q^{57} -1074.05 q^{58} +174.679 q^{59} -472.301 q^{61} -520.234 q^{62} +254.489 q^{63} -403.089 q^{64} +147.375 q^{66} -125.684 q^{67} -324.027 q^{68} +303.915 q^{69} +927.678 q^{71} -379.766 q^{72} +101.255 q^{73} +1640.18 q^{74} -1270.73 q^{76} -280.517 q^{77} +1370.58 q^{78} +295.407 q^{79} +81.0000 q^{81} -471.055 q^{82} -1112.32 q^{83} +1401.49 q^{84} +335.794 q^{86} +650.688 q^{87} +418.606 q^{88} +127.735 q^{89} -2608.80 q^{91} +1673.68 q^{92} +315.173 q^{93} -581.488 q^{94} -127.927 q^{96} -1520.97 q^{97} -2260.86 q^{98} -89.2842 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 42 q^{3} + 50 q^{4} - 27 q^{7} + 21 q^{8} + 126 q^{9}+O(q^{10}) \) 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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