LMFDB - Embedded newform 1875.4.a.f.1.8

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			1.8
Root			$-0.574607$ 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)

$f(q)$	$=$	$q+0.574607 q^{2} -3.00000 q^{3} -7.66983 q^{4} -1.72382 q^{6} +2.67744 q^{7} -9.00399 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+0.574607 q^{2} -3.00000 q^{3} -7.66983 q^{4} -1.72382 q^{6} +2.67744 q^{7} -9.00399 q^{8} +9.00000 q^{9} -63.0399 q^{11} +23.0095 q^{12} -14.1745 q^{13} +1.53847 q^{14} +56.1849 q^{16} -30.3957 q^{17} +5.17146 q^{18} +27.5206 q^{19} -8.03231 q^{21} -36.2232 q^{22} -116.254 q^{23} +27.0120 q^{24} -8.14478 q^{26} -27.0000 q^{27} -20.5355 q^{28} -40.2108 q^{29} -222.867 q^{31} +104.316 q^{32} +189.120 q^{33} -17.4655 q^{34} -69.0284 q^{36} -82.8950 q^{37} +15.8135 q^{38} +42.5236 q^{39} +144.092 q^{41} -4.61542 q^{42} -433.956 q^{43} +483.505 q^{44} -66.8006 q^{46} -459.261 q^{47} -168.555 q^{48} -335.831 q^{49} +91.1870 q^{51} +108.716 q^{52} +247.479 q^{53} -15.5144 q^{54} -24.1076 q^{56} -82.5619 q^{57} -23.1054 q^{58} +310.464 q^{59} +2.08511 q^{61} -128.061 q^{62} +24.0969 q^{63} -389.538 q^{64} +108.669 q^{66} -654.469 q^{67} +233.129 q^{68} +348.763 q^{69} -908.004 q^{71} -81.0359 q^{72} +878.547 q^{73} -47.6320 q^{74} -211.079 q^{76} -168.785 q^{77} +24.4343 q^{78} -1139.01 q^{79} +81.0000 q^{81} +82.7962 q^{82} +986.642 q^{83} +61.6064 q^{84} -249.354 q^{86} +120.632 q^{87} +567.611 q^{88} +988.777 q^{89} -37.9514 q^{91} +891.652 q^{92} +668.602 q^{93} -263.894 q^{94} -312.948 q^{96} -1537.91 q^{97} -192.971 q^{98} -567.359 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.574607	0.203154	0.101577	−	0.994828i	$-0.467611\pi$
$2$	0.574607	0.203154	0.101577	+	0.994828i	$0.467611\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.66983	−0.958728
$5$	0	0
$5$	0	0
$6$	−1.72382	−0.117291
$7$	2.67744	0.144568	0.0722840	−	0.997384i	$-0.476971\pi$
$7$	2.67744	0.144568	0.0722840	+	0.997384i	$0.476971\pi$
$8$	−9.00399	−0.397924
$9$	9.00000	0.333333
$10$	0	0
$11$	−63.0399	−1.72793	−0.863966	−	0.503550i	$-0.832027\pi$
$11$	−63.0399	−1.72793	−0.863966	+	0.503550i	$0.832027\pi$
$12$	23.0095	0.553522
$13$	−14.1745	−0.302408	−0.151204	−	0.988503i	$-0.548315\pi$
$13$	−14.1745	−0.302408	−0.151204	+	0.988503i	$0.548315\pi$
$14$	1.53847	0.0293696
$15$	0	0
$16$	56.1849	0.877889
$17$	−30.3957	−0.433649	−0.216824	−	0.976211i	$-0.569570\pi$
$17$	−30.3957	−0.433649	−0.216824	+	0.976211i	$0.569570\pi$
$18$	5.17146	0.0677180
$19$	27.5206	0.332298	0.166149	−	0.986101i	$-0.446867\pi$
$19$	27.5206	0.332298	0.166149	+	0.986101i	$0.446867\pi$
$20$	0	0
$21$	−8.03231	−0.0834663
$22$	−36.2232	−0.351037
$23$	−116.254	−1.05395	−0.526973	−	0.849882i	$-0.676673\pi$
$23$	−116.254	−1.05395	−0.526973	+	0.849882i	$0.676673\pi$
$24$	27.0120	0.229741
$25$	0	0
$26$	−8.14478	−0.0614355
$27$	−27.0000	−0.192450
$28$	−20.5355	−0.138601
$29$	−40.2108	−0.257481	−0.128741	−	0.991678i	$-0.541093\pi$
$29$	−40.2108	−0.257481	−0.128741	+	0.991678i	$0.541093\pi$
$30$	0	0
$31$	−222.867	−1.29123	−0.645616	−	0.763663i	$-0.723399\pi$
$31$	−222.867	−1.29123	−0.645616	+	0.763663i	$0.723399\pi$
$32$	104.316	0.576270
$33$	189.120	0.997622
$34$	−17.4655	−0.0880975
$35$	0	0
$36$	−69.0284	−0.319576
$37$	−82.8950	−0.368320	−0.184160	−	0.982896i	$-0.558956\pi$
$37$	−82.8950	−0.368320	−0.184160	+	0.982896i	$0.558956\pi$
$38$	15.8135	0.0675078
$39$	42.5236	0.174596
$40$	0	0
$41$	144.092	0.548863	0.274432	−	0.961607i	$-0.411510\pi$
$41$	144.092	0.548863	0.274432	+	0.961607i	$0.411510\pi$
$42$	−4.61542	−0.0169565
$43$	−433.956	−1.53901	−0.769507	−	0.638638i	$-0.779498\pi$
$43$	−433.956	−1.53901	−0.769507	+	0.638638i	$0.779498\pi$
$44$	483.505	1.65662
$45$	0	0
$46$	−66.8006	−0.214113
$47$	−459.261	−1.42532	−0.712661	−	0.701509i	$-0.752510\pi$
$47$	−459.261	−1.42532	−0.712661	+	0.701509i	$0.752510\pi$
$48$	−168.555	−0.506849
$49$	−335.831	−0.979100
$50$	0	0
$51$	91.1870	0.250367
$52$	108.716	0.289927
$53$	247.479	0.641392	0.320696	−	0.947182i	$-0.396083\pi$
$53$	247.479	0.641392	0.320696	+	0.947182i	$0.396083\pi$
$54$	−15.5144	−0.0390970
$55$	0	0
$56$	−24.1076	−0.0575270
$57$	−82.5619	−0.191853
$58$	−23.1054	−0.0523084
$59$	310.464	0.685068	0.342534	−	0.939505i	$-0.388715\pi$
$59$	310.464	0.685068	0.342534	+	0.939505i	$0.388715\pi$
$60$	0	0
$61$	2.08511	0.00437657	0.00218828	−	0.999998i	$-0.499303\pi$
$61$	2.08511	0.00437657	0.00218828	+	0.999998i	$0.499303\pi$
$62$	−128.061	−0.262319
$63$	24.0969	0.0481893
$64$	−389.538	−0.760817
$65$	0	0
$66$	108.669	0.202671
$67$	−654.469	−1.19337	−0.596687	−	0.802474i	$-0.703517\pi$
$67$	−654.469	−1.19337	−0.596687	+	0.802474i	$0.703517\pi$
$68$	233.129	0.415751
$69$	348.763	0.608495
$70$	0	0
$71$	−908.004	−1.51775	−0.758875	−	0.651236i	$-0.774251\pi$
$71$	−908.004	−1.51775	−0.758875	+	0.651236i	$0.774251\pi$
$72$	−81.0359	−0.132641
$73$	878.547	1.40858	0.704288	−	0.709914i	$-0.251266\pi$
$73$	878.547	1.40858	0.704288	+	0.709914i	$0.251266\pi$
$74$	−47.6320	−0.0748258
$75$	0	0
$76$	−211.079	−0.318584
$77$	−168.785	−0.249804
$78$	24.4343	0.0354698
$79$	−1139.01	−1.62213	−0.811066	−	0.584954i	$-0.801113\pi$
$79$	−1139.01	−1.62213	−0.811066	+	0.584954i	$0.801113\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	82.7962	0.111504
$83$	986.642	1.30480	0.652398	−	0.757877i	$-0.273763\pi$
$83$	986.642	1.30480	0.652398	+	0.757877i	$0.273763\pi$
$84$	61.6064	0.0800215
$85$	0	0
$86$	−249.354	−0.312657
$87$	120.632	0.148657
$88$	567.611	0.687585
$89$	988.777	1.17764	0.588821	−	0.808263i	$-0.299592\pi$
$89$	988.777	1.17764	0.588821	+	0.808263i	$0.299592\pi$
$90$	0	0
$91$	−37.9514	−0.0437185
$92$	891.652	1.01045
$93$	668.602	0.745493
$94$	−263.894	−0.289560
$95$	0	0
$96$	−312.948	−0.332710
$97$	−1537.91	−1.60981	−0.804905	−	0.593404i	$-0.797784\pi$
$97$	−1537.91	−1.60981	−0.804905	+	0.593404i	$0.797784\pi$
$98$	−192.971	−0.198908
$99$	−567.359	−0.575977
$100$	0	0
$101$	−266.284	−0.262339	−0.131170	−	0.991360i	$-0.541873\pi$
$101$	−266.284	−0.262339	−0.131170	+	0.991360i	$0.541873\pi$
$102$	52.3966	0.0508631
$103$	779.801	0.745982	0.372991	−	0.927835i	$-0.378332\pi$
$103$	779.801	0.745982	0.372991	+	0.927835i	$0.378332\pi$
$104$	127.627	0.120335
$105$	0	0
$106$	142.203	0.130301
$107$	−526.990	−0.476132	−0.238066	−	0.971249i	$-0.576513\pi$
$107$	−526.990	−0.476132	−0.238066	+	0.971249i	$0.576513\pi$
$108$	207.085	0.184507
$109$	−58.3681	−0.0512904	−0.0256452	−	0.999671i	$-0.508164\pi$
$109$	−58.3681	−0.0512904	−0.0256452	+	0.999671i	$0.508164\pi$
$110$	0	0
$111$	248.685	0.212650
$112$	150.431	0.126915
$113$	47.2456	0.0393318	0.0196659	−	0.999807i	$-0.493740\pi$
$113$	47.2456	0.0393318	0.0196659	+	0.999807i	$0.493740\pi$
$114$	−47.4406	−0.0389756
$115$	0	0
$116$	308.410	0.246855
$117$	−127.571	−0.100803
$118$	178.395	0.139174
$119$	−81.3824	−0.0626917
$120$	0	0
$121$	2643.03	1.98575
$122$	1.19812	0.000889117 0
$123$	−432.276	−0.316886
$124$	1709.35	1.23794
$125$	0	0
$126$	13.8462	0.00978985
$127$	1570.80	1.09753	0.548765	−	0.835977i	$-0.315098\pi$
$127$	1570.80	1.09753	0.548765	+	0.835977i	$0.315098\pi$
$128$	−1058.36	−0.730833
$129$	1301.87	0.888551
$130$	0	0
$131$	−2897.96	−1.93280	−0.966398	−	0.257051i	$-0.917249\pi$
$131$	−2897.96	−1.93280	−0.966398	+	0.257051i	$0.917249\pi$
$132$	−1450.52	−0.956449
$133$	73.6847	0.0480397
$134$	−376.062	−0.242439
$135$	0	0
$136$	273.682	0.172559
$137$	−1304.00	−0.813199	−0.406599	−	0.913607i	$-0.633286\pi$
$137$	−1304.00	−0.813199	−0.406599	+	0.913607i	$0.633286\pi$
$138$	200.402	0.123618
$139$	1235.90	0.754154	0.377077	−	0.926182i	$-0.376929\pi$
$139$	1235.90	0.754154	0.377077	+	0.926182i	$0.376929\pi$
$140$	0	0
$141$	1377.78	0.822910
$142$	−521.745	−0.308337
$143$	893.562	0.522541
$144$	505.664	0.292630
$145$	0	0
$146$	504.819	0.286158
$147$	1007.49	0.565284
$148$	635.790	0.353119
$149$	−810.211	−0.445470	−0.222735	−	0.974879i	$-0.571499\pi$
$149$	−810.211	−0.445470	−0.222735	+	0.974879i	$0.571499\pi$
$150$	0	0
$151$	−3447.19	−1.85781	−0.928903	−	0.370324i	$-0.879247\pi$
$151$	−3447.19	−1.85781	−0.928903	+	0.370324i	$0.879247\pi$
$152$	−247.795	−0.132229
$153$	−273.561	−0.144550
$154$	−96.9852	−0.0507486
$155$	0	0
$156$	−326.149	−0.167390
$157$	804.338	0.408873	0.204437	−	0.978880i	$-0.434464\pi$
$157$	804.338	0.408873	0.204437	+	0.978880i	$0.434464\pi$
$158$	−654.482	−0.329543
$159$	−742.436	−0.370308
$160$	0	0
$161$	−311.264	−0.152367
$162$	46.5431	0.0225727
$163$	−3158.75	−1.51787	−0.758934	−	0.651168i	$-0.774280\pi$
$163$	−3158.75	−1.51787	−0.758934	+	0.651168i	$0.774280\pi$
$164$	−1105.16	−0.526211
$165$	0	0
$166$	566.931	0.265075
$167$	2816.19	1.30493	0.652465	−	0.757819i	$-0.273735\pi$
$167$	2816.19	1.30493	0.652465	+	0.757819i	$0.273735\pi$
$168$	72.3228	0.0332132
$169$	−1996.08	−0.908549
$170$	0	0
$171$	247.686	0.110766
$172$	3328.37	1.47550
$173$	3667.09	1.61158	0.805790	−	0.592201i	$-0.201741\pi$
$173$	3667.09	1.61158	0.805790	+	0.592201i	$0.201741\pi$
$174$	69.3162	0.0302003
$175$	0	0
$176$	−3541.89	−1.51693
$177$	−931.393	−0.395524
$178$	568.158	0.239243
$179$	2430.07	1.01470	0.507351	−	0.861739i	$-0.330625\pi$
$179$	2430.07	1.01470	0.507351	+	0.861739i	$0.330625\pi$
$180$	0	0
$181$	−3282.53	−1.34800	−0.674001	−	0.738730i	$-0.735426\pi$
$181$	−3282.53	−1.34800	−0.674001	+	0.738730i	$0.735426\pi$
$182$	−21.8071	−0.00888160
$183$	−6.25532	−0.00252681
$184$	1046.75	0.419390
$185$	0	0
$186$	384.183	0.151450
$187$	1916.14	0.749316
$188$	3522.45	1.36650
$189$	−72.2907	−0.0278221
$190$	0	0
$191$	2132.58	0.807896	0.403948	−	0.914782i	$-0.367638\pi$
$191$	2132.58	0.807896	0.403948	+	0.914782i	$0.367638\pi$
$192$	1168.61	0.439258
$193$	3868.32	1.44274	0.721368	−	0.692552i	$-0.243514\pi$
$193$	3868.32	1.44274	0.721368	+	0.692552i	$0.243514\pi$
$194$	−883.696	−0.327040
$195$	0	0
$196$	2575.77	0.938691
$197$	1765.50	0.638513	0.319256	−	0.947668i	$-0.396567\pi$
$197$	1765.50	0.638513	0.319256	+	0.947668i	$0.396567\pi$
$198$	−326.008	−0.117012
$199$	3952.78	1.40807	0.704033	−	0.710167i	$-0.251381\pi$
$199$	3952.78	1.40807	0.704033	+	0.710167i	$0.251381\pi$
$200$	0	0
$201$	1963.41	0.688995
$202$	−153.009	−0.0532953
$203$	−107.662	−0.0372235
$204$	−699.388	−0.240034
$205$	0	0
$206$	448.079	0.151549
$207$	−1046.29	−0.351315
$208$	−796.394	−0.265481
$209$	−1734.90	−0.574189
$210$	0	0
$211$	4765.80	1.55493	0.777467	−	0.628923i	$-0.216504\pi$
$211$	4765.80	1.55493	0.777467	+	0.628923i	$0.216504\pi$
$212$	−1898.12	−0.614921
$213$	2724.01	0.876273
$214$	−302.812	−0.0967281
$215$	0	0
$216$	243.108	0.0765805
$217$	−596.713	−0.186671
$218$	−33.5387	−0.0104199
$219$	−2635.64	−0.813242
$220$	0	0
$221$	430.844	0.131139
$222$	142.896	0.0432007
$223$	2200.13	0.660681	0.330340	−	0.943862i	$-0.392836\pi$
$223$	2200.13	0.660681	0.330340	+	0.943862i	$0.392836\pi$
$224$	279.300	0.0833102
$225$	0	0
$226$	27.1477	0.00799042
$227$	−975.112	−0.285112	−0.142556	−	0.989787i	$-0.545532\pi$
$227$	−975.112	−0.285112	−0.142556	+	0.989787i	$0.545532\pi$
$228$	633.236	0.183934
$229$	1594.46	0.460107	0.230054	−	0.973178i	$-0.426110\pi$
$229$	1594.46	0.460107	0.230054	+	0.973178i	$0.426110\pi$
$230$	0	0
$231$	506.356	0.144224
$232$	362.057	0.102458
$233$	4682.15	1.31647	0.658235	−	0.752812i	$-0.271303\pi$
$233$	4682.15	1.31647	0.658235	+	0.752812i	$0.271303\pi$
$234$	−73.3030	−0.0204785
$235$	0	0
$236$	−2381.21	−0.656794
$237$	3417.03	0.936539
$238$	−46.7629	−0.0127361
$239$	72.3131	0.0195713	0.00978566	−	0.999952i	$-0.496885\pi$
$239$	72.3131	0.0195713	0.00978566	+	0.999952i	$0.496885\pi$
$240$	0	0
$241$	1833.18	0.489981	0.244991	−	0.969525i	$-0.421215\pi$
$241$	1833.18	0.489981	0.244991	+	0.969525i	$0.421215\pi$
$242$	1518.70	0.403413
$243$	−243.000	−0.0641500
$244$	−15.9924	−0.00419594
$245$	0	0
$246$	−248.389	−0.0643768
$247$	−390.092	−0.100490
$248$	2006.69	0.513812
$249$	−2959.93	−0.753324
$250$	0	0
$251$	−211.935	−0.0532956	−0.0266478	−	0.999645i	$-0.508483\pi$
$251$	−211.935	−0.0532956	−0.0266478	+	0.999645i	$0.508483\pi$
$252$	−184.819	−0.0462005
$253$	7328.68	1.82115
$254$	902.594	0.222968
$255$	0	0
$256$	2508.17	0.612345
$257$	7074.89	1.71720	0.858599	−	0.512648i	$-0.171335\pi$
$257$	7074.89	1.71720	0.858599	+	0.512648i	$0.171335\pi$
$258$	748.062	0.180513
$259$	−221.946	−0.0532473
$260$	0	0
$261$	−361.897	−0.0858271
$262$	−1665.19	−0.392655
$263$	5055.58	1.18533	0.592663	−	0.805451i	$-0.298077\pi$
$263$	5055.58	1.18533	0.592663	+	0.805451i	$0.298077\pi$
$264$	−1702.83	−0.396978
$265$	0	0
$266$	42.3397	0.00975945
$267$	−2966.33	−0.679912
$268$	5019.66	1.14412
$269$	2308.52	0.523245	0.261622	−	0.965170i	$-0.415742\pi$
$269$	2308.52	0.523245	0.261622	+	0.965170i	$0.415742\pi$
$270$	0	0
$271$	−587.972	−0.131796	−0.0658981	−	0.997826i	$-0.520991\pi$
$271$	−587.972	−0.131796	−0.0658981	+	0.997826i	$0.520991\pi$
$272$	−1707.78	−0.380695
$273$	113.854	0.0252409
$274$	−749.287	−0.165205
$275$	0	0
$276$	−2674.96	−0.583382
$277$	3029.17	0.657059	0.328530	−	0.944494i	$-0.393447\pi$
$277$	3029.17	0.657059	0.328530	+	0.944494i	$0.393447\pi$
$278$	710.155	0.153210
$279$	−2005.81	−0.430410
$280$	0	0
$281$	−6152.70	−1.30619	−0.653095	−	0.757276i	$-0.726530\pi$
$281$	−6152.70	−1.30619	−0.653095	+	0.757276i	$0.726530\pi$
$282$	791.683	0.167178
$283$	5565.56	1.16904	0.584520	−	0.811380i	$-0.301283\pi$
$283$	5565.56	1.16904	0.584520	+	0.811380i	$0.301283\pi$
$284$	6964.23	1.45511
$285$	0	0
$286$	513.446	0.106156
$287$	385.797	0.0793480
$288$	938.845	0.192090
$289$	−3989.10	−0.811949
$290$	0	0
$291$	4613.74	0.929424
$292$	−6738.30	−1.35044
$293$	−2865.97	−0.571440	−0.285720	−	0.958313i	$-0.592233\pi$
$293$	−2865.97	−0.571440	−0.285720	+	0.958313i	$0.592233\pi$
$294$	578.913	0.114840
$295$	0	0
$296$	746.385	0.146563
$297$	1702.08	0.332541
$298$	−465.553	−0.0904991
$299$	1647.85	0.318722
$300$	0	0
$301$	−1161.89	−0.222492
$302$	−1980.78	−0.377421
$303$	798.853	0.151462
$304$	1546.24	0.291721
$305$	0	0
$306$	−157.190	−0.0293658
$307$	1957.38	0.363888	0.181944	−	0.983309i	$-0.441761\pi$
$307$	1957.38	0.363888	0.181944	+	0.983309i	$0.441761\pi$
$308$	1294.55	0.239494
$309$	−2339.40	−0.430693
$310$	0	0
$311$	3499.26	0.638021	0.319011	−	0.947751i	$-0.396649\pi$
$311$	3499.26	0.638021	0.319011	+	0.947751i	$0.396649\pi$
$312$	−382.882	−0.0694757
$313$	−429.181	−0.0775040	−0.0387520	−	0.999249i	$-0.512338\pi$
$313$	−429.181	−0.0775040	−0.0387520	+	0.999249i	$0.512338\pi$
$314$	462.178	0.0830643
$315$	0	0
$316$	8736.00	1.55518
$317$	−3968.68	−0.703165	−0.351583	−	0.936157i	$-0.614356\pi$
$317$	−3968.68	−0.703165	−0.351583	+	0.936157i	$0.614356\pi$
$318$	−426.608	−0.0752296
$319$	2534.89	0.444910
$320$	0	0
$321$	1580.97	0.274895
$322$	−178.854	−0.0309539
$323$	−836.508	−0.144101
$324$	−621.256	−0.106525
$325$	0	0
$326$	−1815.04	−0.308361
$327$	175.104	0.0296125
$328$	−1297.40	−0.218406
$329$	−1229.64	−0.206056
$330$	0	0
$331$	−6176.77	−1.02570	−0.512849	−	0.858479i	$-0.671410\pi$
$331$	−6176.77	−1.02570	−0.512849	+	0.858479i	$0.671410\pi$
$332$	−7567.38	−1.25094
$333$	−746.055	−0.122773
$334$	1618.20	0.265102
$335$	0	0
$336$	−451.294	−0.0732741
$337$	8275.17	1.33762	0.668809	−	0.743435i	$-0.266805\pi$
$337$	8275.17	1.33762	0.668809	+	0.743435i	$0.266805\pi$
$338$	−1146.96	−0.184575
$339$	−141.737	−0.0227082
$340$	0	0
$341$	14049.5	2.23116
$342$	142.322	0.0225026
$343$	−1817.53	−0.286114
$344$	3907.33	0.612410
$345$	0	0
$346$	2107.13	0.327399
$347$	−3785.11	−0.585578	−0.292789	−	0.956177i	$-0.594583\pi$
$347$	−3785.11	−0.585578	−0.292789	+	0.956177i	$0.594583\pi$
$348$	−925.230	−0.142522
$349$	−7094.08	−1.08807	−0.544037	−	0.839061i	$-0.683105\pi$
$349$	−7094.08	−1.08807	−0.544037	+	0.839061i	$0.683105\pi$
$350$	0	0
$351$	382.712	0.0581985
$352$	−6576.08	−0.995756
$353$	1751.44	0.264079	0.132039	−	0.991244i	$-0.457847\pi$
$353$	1751.44	0.264079	0.132039	+	0.991244i	$0.457847\pi$
$354$	−535.185	−0.0803524
$355$	0	0
$356$	−7583.75	−1.12904
$357$	244.147	0.0361951
$358$	1396.33	0.206141
$359$	−327.803	−0.0481916	−0.0240958	−	0.999710i	$-0.507671\pi$
$359$	−327.803	−0.0481916	−0.0240958	+	0.999710i	$0.507671\pi$
$360$	0	0
$361$	−6101.61	−0.889578
$362$	−1886.16	−0.273852
$363$	−7929.10	−1.14647
$364$	291.081	0.0419142
$365$	0	0
$366$	−3.59435	−0.000513332 0
$367$	5830.12	0.829237	0.414618	−	0.909995i	$-0.363915\pi$
$367$	5830.12	0.829237	0.414618	+	0.909995i	$0.363915\pi$
$368$	−6531.74	−0.925246
$369$	1296.83	0.182954
$370$	0	0
$371$	662.608	0.0927247
$372$	−5128.06	−0.714725
$373$	−2871.23	−0.398570	−0.199285	−	0.979942i	$-0.563862\pi$
$373$	−2871.23	−0.398570	−0.199285	+	0.979942i	$0.563862\pi$
$374$	1101.03	0.152227
$375$	0	0
$376$	4135.18	0.567169
$377$	569.969	0.0778645
$378$	−41.5387	−0.00565217
$379$	−11091.6	−1.50326	−0.751630	−	0.659585i	$-0.770732\pi$
$379$	−11091.6	−1.50326	−0.751630	+	0.659585i	$0.770732\pi$
$380$	0	0
$381$	−4712.41	−0.633659
$382$	1225.39	0.164127
$383$	−716.613	−0.0956063	−0.0478032	−	0.998857i	$-0.515222\pi$
$383$	−716.613	−0.0956063	−0.0478032	+	0.998857i	$0.515222\pi$
$384$	3175.08	0.421947
$385$	0	0
$386$	2222.76	0.293098
$387$	−3905.60	−0.513005
$388$	11795.5	1.54337
$389$	7568.62	0.986490	0.493245	−	0.869891i	$-0.335811\pi$
$389$	7568.62	0.986490	0.493245	+	0.869891i	$0.335811\pi$
$390$	0	0
$391$	3533.63	0.457042
$392$	3023.82	0.389607
$393$	8693.89	1.11590
$394$	1014.47	0.129716
$395$	0	0
$396$	4351.55	0.552206
$397$	−712.778	−0.0901090	−0.0450545	−	0.998985i	$-0.514346\pi$
$397$	−712.778	−0.0901090	−0.0450545	+	0.998985i	$0.514346\pi$
$398$	2271.29	0.286054
$399$	−221.054	−0.0277357
$400$	0	0
$401$	−5539.33	−0.689828	−0.344914	−	0.938634i	$-0.612092\pi$
$401$	−5539.33	−0.689828	−0.344914	+	0.938634i	$0.612092\pi$
$402$	1128.19	0.139972
$403$	3159.04	0.390479
$404$	2042.36	0.251512
$405$	0	0
$406$	−61.8632	−0.00756211
$407$	5225.69	0.636432
$408$	−821.046	−0.0996271
$409$	−8742.40	−1.05693	−0.528465	−	0.848955i	$-0.677232\pi$
$409$	−8742.40	−1.05693	−0.528465	+	0.848955i	$0.677232\pi$
$410$	0	0
$411$	3912.00	0.469501
$412$	−5980.94	−0.715194
$413$	831.248	0.0990389
$414$	−601.205	−0.0713711
$415$	0	0
$416$	−1478.63	−0.174269
$417$	−3707.69	−0.435411
$418$	−996.884	−0.116649
$419$	3242.47	0.378055	0.189027	−	0.981972i	$-0.439467\pi$
$419$	3242.47	0.378055	0.189027	+	0.981972i	$0.439467\pi$
$420$	0	0
$421$	−1743.07	−0.201786	−0.100893	−	0.994897i	$-0.532170\pi$
$421$	−1743.07	−0.201786	−0.100893	+	0.994897i	$0.532170\pi$
$422$	2738.46	0.315891
$423$	−4133.35	−0.475107
$424$	−2228.29	−0.255225
$425$	0	0
$426$	1565.24	0.178019
$427$	5.58274	0.000632711 0
$428$	4041.92	0.456481
$429$	−2680.68	−0.301689
$430$	0	0
$431$	6721.37	0.751177	0.375588	−	0.926787i	$-0.377441\pi$
$431$	6721.37	0.751177	0.375588	+	0.926787i	$0.377441\pi$
$432$	−1516.99	−0.168950
$433$	5771.39	0.640543	0.320271	−	0.947326i	$-0.396226\pi$
$433$	5771.39	0.640543	0.320271	+	0.947326i	$0.396226\pi$
$434$	−342.875	−0.0379229
$435$	0	0
$436$	447.673	0.0491735
$437$	−3199.40	−0.350224
$438$	−1514.46	−0.165213
$439$	−6213.04	−0.675472	−0.337736	−	0.941241i	$-0.609661\pi$
$439$	−6213.04	−0.675472	−0.337736	+	0.941241i	$0.609661\pi$
$440$	0	0
$441$	−3022.48	−0.326367
$442$	247.566	0.0266414
$443$	6346.31	0.680638	0.340319	−	0.940310i	$-0.389465\pi$
$443$	6346.31	0.680638	0.340319	+	0.940310i	$0.389465\pi$
$444$	−1907.37	−0.203873
$445$	0	0
$446$	1264.21	0.134220
$447$	2430.63	0.257192
$448$	−1042.96	−0.109990
$449$	−2732.09	−0.287161	−0.143581	−	0.989639i	$-0.545862\pi$
$449$	−2732.09	−0.287161	−0.143581	+	0.989639i	$0.545862\pi$
$450$	0	0
$451$	−9083.55	−0.948399
$452$	−362.366	−0.0377085
$453$	10341.6	1.07260
$454$	−560.306	−0.0579217
$455$	0	0
$456$	743.386	0.0763427
$457$	−11572.5	−1.18455	−0.592276	−	0.805735i	$-0.701770\pi$
$457$	−11572.5	−1.18455	−0.592276	+	0.805735i	$0.701770\pi$
$458$	916.185	0.0934727
$459$	820.683	0.0834557
$460$	0	0
$461$	−3619.92	−0.365719	−0.182859	−	0.983139i	$-0.558535\pi$
$461$	−3619.92	−0.365719	−0.182859	+	0.983139i	$0.558535\pi$
$462$	290.955	0.0292997
$463$	12563.6	1.26108	0.630538	−	0.776159i	$-0.282834\pi$
$463$	12563.6	1.26108	0.630538	+	0.776159i	$0.282834\pi$
$464$	−2259.24	−0.226040
$465$	0	0
$466$	2690.39	0.267446
$467$	−17437.4	−1.72785	−0.863925	−	0.503620i	$-0.832001\pi$
$467$	−17437.4	−1.72785	−0.863925	+	0.503620i	$0.832001\pi$
$468$	978.446	0.0966425
$469$	−1752.30	−0.172524
$470$	0	0
$471$	−2413.01	−0.236063
$472$	−2795.42	−0.272605
$473$	27356.5	2.65931
$474$	1963.45	0.190262
$475$	0	0
$476$	624.189	0.0601043
$477$	2227.31	0.213797
$478$	41.5516	0.00397599
$479$	−686.135	−0.0654495	−0.0327247	−	0.999464i	$-0.510418\pi$
$479$	−686.135	−0.0654495	−0.0327247	+	0.999464i	$0.510418\pi$
$480$	0	0
$481$	1175.00	0.111383
$482$	1053.36	0.0995417
$483$	933.791	0.0879689
$484$	−20271.6	−1.90380
$485$	0	0
$486$	−139.629	−0.0130323
$487$	−3936.76	−0.366307	−0.183154	−	0.983084i	$-0.558631\pi$
$487$	−3936.76	−0.366307	−0.183154	+	0.983084i	$0.558631\pi$
$488$	−18.7743	−0.00174154
$489$	9476.25	0.876342
$490$	0	0
$491$	−19506.8	−1.79294	−0.896468	−	0.443108i	$-0.853876\pi$
$491$	−19506.8	−1.79294	−0.896468	+	0.443108i	$0.853876\pi$
$492$	3315.48	0.303808
$493$	1222.23	0.111656
$494$	−224.150	−0.0204149
$495$	0	0
$496$	−12521.8	−1.13356
$497$	−2431.12	−0.219418
$498$	−1700.79	−0.153041
$499$	−8132.04	−0.729539	−0.364770	−	0.931098i	$-0.618852\pi$
$499$	−8132.04	−0.729539	−0.364770	+	0.931098i	$0.618852\pi$
$500$	0	0
$501$	−8448.56	−0.753401
$502$	−121.779	−0.0108272
$503$	−21609.4	−1.91554	−0.957771	−	0.287533i	$-0.907165\pi$
$503$	−21609.4	−1.91554	−0.957771	+	0.287533i	$0.907165\pi$
$504$	−216.968	−0.0191757
$505$	0	0
$506$	4211.10	0.369973
$507$	5988.25	0.524551
$508$	−12047.8	−1.05223
$509$	15048.4	1.31043	0.655213	−	0.755444i	$-0.272579\pi$
$509$	15048.4	1.31043	0.655213	+	0.755444i	$0.272579\pi$
$510$	0	0
$511$	2352.25	0.203635
$512$	9908.09	0.855234
$513$	−743.057	−0.0639508
$514$	4065.28	0.348856
$515$	0	0
$516$	−9985.10	−0.851879
$517$	28951.8	2.46286
$518$	−127.532	−0.0108174
$519$	−11001.3	−0.930447
$520$	0	0
$521$	8187.21	0.688461	0.344230	−	0.938885i	$-0.388140\pi$
$521$	8187.21	0.688461	0.344230	+	0.938885i	$0.388140\pi$
$522$	−207.949	−0.0174361
$523$	−13493.6	−1.12818	−0.564088	−	0.825715i	$-0.690772\pi$
$523$	−13493.6	−1.12818	−0.564088	+	0.825715i	$0.690772\pi$
$524$	22226.9	1.85303
$525$	0	0
$526$	2904.97	0.240804
$527$	6774.20	0.559941
$528$	10625.7	0.875801
$529$	1348.11	0.110800
$530$	0	0
$531$	2794.18	0.228356
$532$	−565.149	−0.0460570
$533$	−2042.44	−0.165981
$534$	−1704.47	−0.138127
$535$	0	0
$536$	5892.83	0.474872
$537$	−7290.20	−0.585839
$538$	1326.49	0.106299
$539$	21170.8	1.69182
$540$	0	0
$541$	−7930.74	−0.630257	−0.315129	−	0.949049i	$-0.602048\pi$
$541$	−7930.74	−0.630257	−0.315129	+	0.949049i	$0.602048\pi$
$542$	−337.853	−0.0267749
$543$	9847.58	0.778269
$544$	−3170.76	−0.249899
$545$	0	0
$546$	65.4213	0.00512779
$547$	14716.4	1.15032	0.575161	−	0.818040i	$-0.304940\pi$
$547$	14716.4	1.15032	0.575161	+	0.818040i	$0.304940\pi$
$548$	10001.5	0.779637
$549$	18.7660	0.00145886
$550$	0	0
$551$	−1106.63	−0.0855606
$552$	−3140.26	−0.242135
$553$	−3049.62	−0.234508
$554$	1740.58	0.133484
$555$	0	0
$556$	−9479.12	−0.723029
$557$	−22711.9	−1.72771	−0.863856	−	0.503739i	$-0.831957\pi$
$557$	−22711.9	−1.72771	−0.863856	+	0.503739i	$0.831957\pi$
$558$	−1152.55	−0.0874396
$559$	6151.12	0.465411
$560$	0	0
$561$	−5748.42	−0.432618
$562$	−3535.38	−0.265358
$563$	−2315.50	−0.173333	−0.0866667	−	0.996237i	$-0.527622\pi$
$563$	−2315.50	−0.173333	−0.0866667	+	0.996237i	$0.527622\pi$
$564$	−10567.4	−0.788947
$565$	0	0
$566$	3198.01	0.237495
$567$	216.872	0.0160631
$568$	8175.66	0.603949
$569$	−6485.63	−0.477841	−0.238921	−	0.971039i	$-0.576794\pi$
$569$	−6485.63	−0.477841	−0.238921	+	0.971039i	$0.576794\pi$
$570$	0	0
$571$	−1530.21	−0.112149	−0.0560746	−	0.998427i	$-0.517858\pi$
$571$	−1530.21	−0.112149	−0.0560746	+	0.998427i	$0.517858\pi$
$572$	−6853.46	−0.500975
$573$	−6397.74	−0.466439
$574$	221.682	0.0161199
$575$	0	0
$576$	−3505.84	−0.253606
$577$	−7945.59	−0.573274	−0.286637	−	0.958039i	$-0.592537\pi$
$577$	−7945.59	−0.573274	−0.286637	+	0.958039i	$0.592537\pi$
$578$	−2292.17	−0.164951
$579$	−11605.0	−0.832964
$580$	0	0
$581$	2641.67	0.188632
$582$	2651.09	0.188816
$583$	−15601.0	−1.10828
$584$	−7910.42	−0.560506
$585$	0	0
$586$	−1646.81	−0.116090
$587$	2795.82	0.196586	0.0982930	−	0.995158i	$-0.468662\pi$
$587$	2795.82	0.196586	0.0982930	+	0.995158i	$0.468662\pi$
$588$	−7727.31	−0.541954
$589$	−6133.45	−0.429074
$590$	0	0
$591$	−5296.51	−0.368645
$592$	−4657.44	−0.323344
$593$	−18900.9	−1.30889	−0.654443	−	0.756112i	$-0.727097\pi$
$593$	−18900.9	−1.30889	−0.654443	+	0.756112i	$0.727097\pi$
$594$	978.025	0.0675570
$595$	0	0
$596$	6214.18	0.427085
$597$	−11858.3	−0.812947
$598$	946.867	0.0647496
$599$	5146.04	0.351021	0.175511	−	0.984478i	$-0.443842\pi$
$599$	5146.04	0.351021	0.175511	+	0.984478i	$0.443842\pi$
$600$	0	0
$601$	−1011.92	−0.0686805	−0.0343403	−	0.999410i	$-0.510933\pi$
$601$	−1011.92	−0.0686805	−0.0343403	+	0.999410i	$0.510933\pi$
$602$	−667.629	−0.0452002
$603$	−5890.22	−0.397791
$604$	26439.4	1.78113
$605$	0	0
$606$	459.026	0.0307701
$607$	−10173.3	−0.680263	−0.340131	−	0.940378i	$-0.610472\pi$
$607$	−10173.3	−0.680263	−0.340131	+	0.940378i	$0.610472\pi$
$608$	2870.84	0.191494
$609$	322.985	0.0214910
$610$	0	0
$611$	6509.81	0.431029
$612$	2098.16	0.138584
$613$	−22073.6	−1.45440	−0.727198	−	0.686428i	$-0.759178\pi$
$613$	−22073.6	−1.45440	−0.727198	+	0.686428i	$0.759178\pi$
$614$	1124.72	0.0739253
$615$	0	0
$616$	1519.74	0.0994028
$617$	23102.6	1.50742	0.753709	−	0.657208i	$-0.228263\pi$
$617$	23102.6	1.50742	0.753709	+	0.657208i	$0.228263\pi$
$618$	−1344.24	−0.0874970
$619$	1334.98	0.0866842	0.0433421	−	0.999060i	$-0.486199\pi$
$619$	1334.98	0.0866842	0.0433421	+	0.999060i	$0.486199\pi$
$620$	0	0
$621$	3138.87	0.202832
$622$	2010.70	0.129617
$623$	2647.39	0.170249
$624$	2389.18	0.153275
$625$	0	0
$626$	−246.610	−0.0157453
$627$	5204.70	0.331508
$628$	−6169.13	−0.391999
$629$	2519.65	0.159722
$630$	0	0
$631$	−6270.57	−0.395606	−0.197803	−	0.980242i	$-0.563381\pi$
$631$	−6270.57	−0.395606	−0.197803	+	0.980242i	$0.563381\pi$
$632$	10255.6	0.645485
$633$	−14297.4	−0.897742
$634$	−2280.43	−0.142851
$635$	0	0
$636$	5694.35	0.355025
$637$	4760.25	0.296088
$638$	1456.56	0.0903853
$639$	−8172.04	−0.505917
$640$	0	0
$641$	9140.07	0.563200	0.281600	−	0.959532i	$-0.409135\pi$
$641$	9140.07	0.563200	0.281600	+	0.959532i	$0.409135\pi$
$642$	908.436	0.0558460
$643$	12262.8	0.752095	0.376047	−	0.926600i	$-0.377283\pi$
$643$	12262.8	0.752095	0.376047	+	0.926600i	$0.377283\pi$
$644$	2387.34	0.146078
$645$	0	0
$646$	−480.663	−0.0292747
$647$	16281.8	0.989341	0.494671	−	0.869081i	$-0.335289\pi$
$647$	16281.8	0.989341	0.494671	+	0.869081i	$0.335289\pi$
$648$	−729.323	−0.0442137
$649$	−19571.7	−1.18375
$650$	0	0
$651$	1790.14	0.107774
$652$	24227.1	1.45522
$653$	−4710.81	−0.282310	−0.141155	−	0.989988i	$-0.545082\pi$
$653$	−4710.81	−0.282310	−0.141155	+	0.989988i	$0.545082\pi$
$654$	100.616	0.00601590
$655$	0	0
$656$	8095.79	0.481841
$657$	7906.92	0.469526
$658$	−706.560	−0.0418611
$659$	16675.5	0.985715	0.492858	−	0.870110i	$-0.335952\pi$
$659$	16675.5	0.985715	0.492858	+	0.870110i	$0.335952\pi$
$660$	0	0
$661$	−18772.5	−1.10464	−0.552319	−	0.833633i	$-0.686257\pi$
$661$	−18772.5	−1.10464	−0.552319	+	0.833633i	$0.686257\pi$
$662$	−3549.21	−0.208375
$663$	−1292.53	−0.0757131
$664$	−8883.71	−0.519209
$665$	0	0
$666$	−428.688	−0.0249419
$667$	4674.69	0.271371
$668$	−21599.7	−1.25107
$669$	−6600.40	−0.381444
$670$	0	0
$671$	−131.445	−0.00756241
$672$	−837.899	−0.0480992
$673$	−29963.4	−1.71620	−0.858101	−	0.513480i	$-0.828356\pi$
$673$	−29963.4	−1.71620	−0.858101	+	0.513480i	$0.828356\pi$
$674$	4754.96	0.271742
$675$	0	0
$676$	15309.6	0.871052
$677$	21583.4	1.22528	0.612641	−	0.790361i	$-0.290107\pi$
$677$	21583.4	1.22528	0.612641	+	0.790361i	$0.290107\pi$
$678$	−81.4430	−0.00461327
$679$	−4117.67	−0.232727
$680$	0	0
$681$	2925.34	0.164610
$682$	8072.96	0.453269
$683$	−5945.53	−0.333088	−0.166544	−	0.986034i	$-0.553261\pi$
$683$	−5945.53	−0.333088	−0.166544	+	0.986034i	$0.553261\pi$
$684$	−1899.71	−0.106195
$685$	0	0
$686$	−1044.36	−0.0581253
$687$	−4783.37	−0.265643
$688$	−24381.7	−1.35108
$689$	−3507.89	−0.193962
$690$	0	0
$691$	−15083.0	−0.830366	−0.415183	−	0.909738i	$-0.636282\pi$
$691$	−15083.0	−0.830366	−0.415183	+	0.909738i	$0.636282\pi$
$692$	−28125.9	−1.54507
$693$	−1519.07	−0.0832679
$694$	−2174.95	−0.118963
$695$	0	0
$696$	−1086.17	−0.0591541
$697$	−4379.77	−0.238014
$698$	−4076.31	−0.221047
$699$	−14046.4	−0.760065
$700$	0	0
$701$	29869.3	1.60934	0.804671	−	0.593722i	$-0.202342\pi$
$701$	29869.3	1.60934	0.804671	+	0.593722i	$0.202342\pi$
$702$	219.909	0.0118233
$703$	−2281.32	−0.122392
$704$	24556.5	1.31464
$705$	0	0
$706$	1006.39	0.0536487
$707$	−712.959	−0.0379259
$708$	7143.63	0.379200
$709$	11476.1	0.607888	0.303944	−	0.952690i	$-0.401696\pi$
$709$	11476.1	0.607888	0.303944	+	0.952690i	$0.401696\pi$
$710$	0	0
$711$	−10251.1	−0.540711
$712$	−8902.93	−0.468612
$713$	25909.3	1.36089
$714$	140.289	0.00735318
$715$	0	0
$716$	−18638.2	−0.972824
$717$	−216.939	−0.0112995
$718$	−188.358	−0.00979031
$719$	8693.34	0.450913	0.225457	−	0.974253i	$-0.427613\pi$
$719$	8693.34	0.450913	0.225457	+	0.974253i	$0.427613\pi$
$720$	0	0
$721$	2087.87	0.107845
$722$	−3506.03	−0.180721
$723$	−5499.54	−0.282891
$724$	25176.4	1.29237
$725$	0	0
$726$	−4556.11	−0.232911
$727$	−15117.2	−0.771204	−0.385602	−	0.922665i	$-0.626006\pi$
$727$	−15117.2	−0.771204	−0.385602	+	0.922665i	$0.626006\pi$
$728$	341.714	0.0173966
$729$	729.000	0.0370370
$730$	0	0
$731$	13190.4	0.667392
$732$	47.9772	0.00242253
$733$	33626.3	1.69443	0.847213	−	0.531253i	$-0.178278\pi$
$733$	33626.3	1.69443	0.847213	+	0.531253i	$0.178278\pi$
$734$	3350.03	0.168463
$735$	0	0
$736$	−12127.2	−0.607357
$737$	41257.7	2.06207
$738$	745.166	0.0371679
$739$	−9535.66	−0.474661	−0.237331	−	0.971429i	$-0.576273\pi$
$739$	−9535.66	−0.474661	−0.237331	+	0.971429i	$0.576273\pi$
$740$	0	0
$741$	1170.28	0.0580178
$742$	380.739	0.0188374
$743$	−39282.1	−1.93960	−0.969798	−	0.243909i	$-0.921570\pi$
$743$	−39282.1	−1.93960	−0.969798	+	0.243909i	$0.921570\pi$
$744$	−6020.08	−0.296649
$745$	0	0
$746$	−1649.83	−0.0809711
$747$	8879.78	0.434932
$748$	−14696.5	−0.718390
$749$	−1410.98	−0.0688333
$750$	0	0
$751$	15625.4	0.759226	0.379613	−	0.925145i	$-0.376057\pi$
$751$	15625.4	0.759226	0.379613	+	0.925145i	$0.376057\pi$
$752$	−25803.5	−1.25127
$753$	635.804	0.0307702
$754$	327.508	0.0158185
$755$	0	0
$756$	554.458	0.0266738
$757$	28389.3	1.36305	0.681524	−	0.731796i	$-0.261318\pi$
$757$	28389.3	1.36305	0.681524	+	0.731796i	$0.261318\pi$
$758$	−6373.29	−0.305393
$759$	−21986.0	−1.05144
$760$	0	0
$761$	−9084.82	−0.432752	−0.216376	−	0.976310i	$-0.569424\pi$
$761$	−9084.82	−0.432752	−0.216376	+	0.976310i	$0.569424\pi$
$762$	−2707.78	−0.128730
$763$	−156.277	−0.00741494
$764$	−16356.5	−0.774553
$765$	0	0
$766$	−411.771	−0.0194228
$767$	−4400.69	−0.207170
$768$	−7524.50	−0.353538
$769$	12609.4	0.591298	0.295649	−	0.955297i	$-0.404464\pi$
$769$	12609.4	0.591298	0.295649	+	0.955297i	$0.404464\pi$
$770$	0	0
$771$	−21224.7	−0.991425
$772$	−29669.4	−1.38319
$773$	12686.6	0.590306	0.295153	−	0.955450i	$-0.404629\pi$
$773$	12686.6	0.590306	0.295153	+	0.955450i	$0.404629\pi$
$774$	−2244.18	−0.104219
$775$	0	0
$776$	13847.4	0.640582
$777$	665.838	0.0307423
$778$	4348.98	0.200409
$779$	3965.51	0.182386
$780$	0	0
$781$	57240.5	2.62257
$782$	2030.45	0.0928499
$783$	1085.69	0.0495523
$784$	−18868.6	−0.859541
$785$	0	0
$786$	4995.57	0.226700
$787$	5836.27	0.264346	0.132173	−	0.991227i	$-0.457805\pi$
$787$	5836.27	0.264346	0.132173	+	0.991227i	$0.457805\pi$
$788$	−13541.1	−0.612160
$789$	−15166.7	−0.684348
$790$	0	0
$791$	126.497	0.00568612
$792$	5108.50	0.229195
$793$	−29.5554	−0.00132351
$794$	−409.567	−0.0183060
$795$	0	0
$796$	−30317.1	−1.34995
$797$	10338.0	0.459461	0.229731	−	0.973254i	$-0.426216\pi$
$797$	10338.0	0.459461	0.229731	+	0.973254i	$0.426216\pi$
$798$	−127.019	−0.00563462
$799$	13959.5	0.618089
$800$	0	0
$801$	8898.99	0.392547
$802$	−3182.93	−0.140141
$803$	−55383.5	−2.43393
$804$	−15059.0	−0.660559
$805$	0	0
$806$	1815.21	0.0793274
$807$	−6925.56	−0.302096
$808$	2397.62	0.104391
$809$	22851.2	0.993085	0.496542	−	0.868013i	$-0.334603\pi$
$809$	22851.2	0.993085	0.496542	+	0.868013i	$0.334603\pi$
$810$	0	0
$811$	16826.5	0.728553	0.364277	−	0.931291i	$-0.381316\pi$
$811$	16826.5	0.728553	0.364277	+	0.931291i	$0.381316\pi$
$812$	825.747	0.0356873
$813$	1763.92	0.0760926
$814$	3002.72	0.129294
$815$	0	0
$816$	5123.33	0.219795
$817$	−11942.7	−0.511412
$818$	−5023.44	−0.214719
$819$	−341.563	−0.0145728
$820$	0	0
$821$	−39058.2	−1.66034	−0.830171	−	0.557509i	$-0.811757\pi$
$821$	−39058.2	−1.66034	−0.830171	+	0.557509i	$0.811757\pi$
$822$	2247.86	0.0953810
$823$	−14479.7	−0.613283	−0.306642	−	0.951825i	$-0.599205\pi$
$823$	−14479.7	−0.613283	−0.306642	+	0.951825i	$0.599205\pi$
$824$	−7021.32	−0.296844
$825$	0	0
$826$	477.641	0.0201202
$827$	22582.7	0.949550	0.474775	−	0.880107i	$-0.342530\pi$
$827$	22582.7	0.949550	0.474775	+	0.880107i	$0.342530\pi$
$828$	8024.87	0.336816
$829$	−30685.6	−1.28559	−0.642795	−	0.766038i	$-0.722225\pi$
$829$	−30685.6	−1.28559	−0.642795	+	0.766038i	$0.722225\pi$
$830$	0	0
$831$	−9087.52	−0.379353
$832$	5521.52	0.230077
$833$	10207.8	0.424586
$834$	−2130.46	−0.0884556
$835$	0	0
$836$	13306.4	0.550491
$837$	6017.42	0.248498
$838$	1863.14	0.0768033
$839$	28634.7	1.17828	0.589141	−	0.808030i	$-0.299466\pi$
$839$	28634.7	1.17828	0.589141	+	0.808030i	$0.299466\pi$
$840$	0	0
$841$	−22772.1	−0.933703
$842$	−1001.58	−0.0409937
$843$	18458.1	0.754129
$844$	−36552.9	−1.49076
$845$	0	0
$846$	−2375.05	−0.0965200
$847$	7076.55	0.287076
$848$	13904.5	0.563071
$849$	−16696.7	−0.674945
$850$	0	0
$851$	9636.91	0.388189
$852$	−20892.7	−0.840108
$853$	31283.2	1.25570	0.627852	−	0.778333i	$-0.283934\pi$
$853$	31283.2	1.25570	0.627852	+	0.778333i	$0.283934\pi$
$854$	3.20788	0.000128538 0
$855$	0	0
$856$	4745.01	0.189464
$857$	18790.1	0.748958	0.374479	−	0.927235i	$-0.377822\pi$
$857$	18790.1	0.748958	0.374479	+	0.927235i	$0.377822\pi$
$858$	−1540.34	−0.0612894
$859$	43722.6	1.73667	0.868333	−	0.495982i	$-0.165192\pi$
$859$	43722.6	1.73667	0.868333	+	0.495982i	$0.165192\pi$
$860$	0	0
$861$	−1157.39	−0.0458116
$862$	3862.14	0.152605
$863$	6207.23	0.244839	0.122420	−	0.992478i	$-0.460935\pi$
$863$	6207.23	0.244839	0.122420	+	0.992478i	$0.460935\pi$
$864$	−2816.53	−0.110903
$865$	0	0
$866$	3316.28	0.130129
$867$	11967.3	0.468779
$868$	4576.69	0.178966
$869$	71803.0	2.80294
$870$	0	0
$871$	9276.79	0.360886
$872$	525.546	0.0204097
$873$	−13841.2	−0.536603
$874$	−1838.39	−0.0711495
$875$	0	0
$876$	20214.9	0.779678
$877$	−6575.05	−0.253163	−0.126581	−	0.991956i	$-0.540400\pi$
$877$	−6575.05	−0.253163	−0.126581	+	0.991956i	$0.540400\pi$
$878$	−3570.05	−0.137225
$879$	8597.92	0.329921
$880$	0	0
$881$	51486.2	1.96892	0.984458	−	0.175620i	$-0.0561929\pi$
$881$	51486.2	1.96892	0.984458	+	0.175620i	$0.0561929\pi$
$882$	−1736.74	−0.0663027
$883$	−37420.9	−1.42618	−0.713088	−	0.701075i	$-0.752704\pi$
$883$	−37420.9	−1.42618	−0.713088	+	0.701075i	$0.752704\pi$
$884$	−3304.50	−0.125727
$885$	0	0
$886$	3646.63	0.138274
$887$	−41538.1	−1.57239	−0.786197	−	0.617975i	$-0.787953\pi$
$887$	−41538.1	−1.57239	−0.786197	+	0.617975i	$0.787953\pi$
$888$	−2239.16	−0.0846184
$889$	4205.72	0.158667
$890$	0	0
$891$	−5106.23	−0.191992
$892$	−16874.6	−0.633414
$893$	−12639.2	−0.473632
$894$	1396.66	0.0522497
$895$	0	0
$896$	−2833.69	−0.105655
$897$	−4943.56	−0.184014
$898$	−1569.88	−0.0583380
$899$	8961.68	0.332468
$900$	0	0
$901$	−7522.27	−0.278139
$902$	−5219.47	−0.192671
$903$	3485.67	0.128456
$904$	−425.399	−0.0156511
$905$	0	0
$906$	5942.34	0.217904
$907$	14471.6	0.529792	0.264896	−	0.964277i	$-0.414662\pi$
$907$	14471.6	0.529792	0.264896	+	0.964277i	$0.414662\pi$
$908$	7478.94	0.273345
$909$	−2396.56	−0.0874465
$910$	0	0
$911$	−19755.1	−0.718457	−0.359229	−	0.933250i	$-0.616960\pi$
$911$	−19755.1	−0.718457	−0.359229	+	0.933250i	$0.616960\pi$
$912$	−4638.73	−0.168425
$913$	−62197.9	−2.25460
$914$	−6649.65	−0.240646
$915$	0	0
$916$	−12229.2	−0.441118
$917$	−7759.11	−0.279420
$918$	471.570	0.0169544
$919$	8793.86	0.315650	0.157825	−	0.987467i	$-0.449552\pi$
$919$	8793.86	0.315650	0.157825	+	0.987467i	$0.449552\pi$
$920$	0	0
$921$	−5872.14	−0.210091
$922$	−2080.03	−0.0742973
$923$	12870.5	0.458980
$924$	−3883.66	−0.138272
$925$	0	0
$926$	7219.10	0.256193
$927$	7018.21	0.248661
$928$	−4194.63	−0.148379
$929$	30970.5	1.09377	0.546883	−	0.837209i	$-0.315814\pi$
$929$	30970.5	1.09377	0.546883	+	0.837209i	$0.315814\pi$
$930$	0	0
$931$	−9242.29	−0.325353
$932$	−35911.3	−1.26214
$933$	−10497.8	−0.368362
$934$	−10019.6	−0.351020
$935$	0	0
$936$	1148.65	0.0401118
$937$	27616.9	0.962867	0.481433	−	0.876483i	$-0.340116\pi$
$937$	27616.9	0.962867	0.481433	+	0.876483i	$0.340116\pi$
$938$	−1006.88	−0.0350489
$939$	1287.54	0.0447470
$940$	0	0
$941$	−25741.6	−0.891767	−0.445883	−	0.895091i	$-0.647110\pi$
$941$	−25741.6	−0.891767	−0.445883	+	0.895091i	$0.647110\pi$
$942$	−1386.53	−0.0479572
$943$	−16751.3	−0.578472
$944$	17443.4	0.601414
$945$	0	0
$946$	15719.2	0.540250
$947$	9854.74	0.338158	0.169079	−	0.985602i	$-0.445921\pi$
$947$	9854.74	0.338158	0.169079	+	0.985602i	$0.445921\pi$
$948$	−26208.0	−0.897886
$949$	−12453.0	−0.425965
$950$	0	0
$951$	11906.0	0.405973
$952$	732.766	0.0249465
$953$	−16998.2	−0.577780	−0.288890	−	0.957362i	$-0.593286\pi$
$953$	−16998.2	−0.577780	−0.288890	+	0.957362i	$0.593286\pi$
$954$	1279.83	0.0434338
$955$	0	0
$956$	−554.629	−0.0187636
$957$	−7604.66	−0.256869
$958$	−394.257	−0.0132963
$959$	−3491.38	−0.117562
$960$	0	0
$961$	19878.9	0.667278
$962$	675.161	0.0226279
$963$	−4742.91	−0.158711
$964$	−14060.2	−0.469759
$965$	0	0
$966$	536.563	0.0178712
$967$	−43798.0	−1.45651	−0.728257	−	0.685304i	$-0.759669\pi$
$967$	−43798.0	−1.45651	−0.728257	+	0.685304i	$0.759669\pi$
$968$	−23797.8	−0.790177
$969$	2509.52	0.0831966
$970$	0	0
$971$	12878.7	0.425640	0.212820	−	0.977091i	$-0.431735\pi$
$971$	12878.7	0.425640	0.212820	+	0.977091i	$0.431735\pi$
$972$	1863.77	0.0615025
$973$	3309.04	0.109027
$974$	−2262.09	−0.0744168
$975$	0	0
$976$	117.151	0.00384214
$977$	−44394.8	−1.45375	−0.726877	−	0.686768i	$-0.759029\pi$
$977$	−44394.8	−1.45375	−0.726877	+	0.686768i	$0.759029\pi$
$978$	5445.12	0.178032
$979$	−62332.4	−2.03489
$980$	0	0
$981$	−525.313	−0.0170968
$982$	−11208.8	−0.364242
$983$	6366.79	0.206581	0.103290	−	0.994651i	$-0.467063\pi$
$983$	6366.79	0.206581	0.103290	+	0.994651i	$0.467063\pi$
$984$	3892.21	0.126097
$985$	0	0
$986$	702.303	0.0226835
$987$	3688.93	0.118966
$988$	2991.94	0.0963424
$989$	50449.3	1.62204
$990$	0	0
$991$	−39651.1	−1.27100	−0.635500	−	0.772101i	$-0.719206\pi$
$991$	−39651.1	−1.27100	−0.635500	+	0.772101i	$0.719206\pi$
$992$	−23248.7	−0.744098
$993$	18530.3	0.592187
$994$	−1396.94	−0.0445757
$995$	0	0
$996$	22702.1	0.722233
$997$	34445.0	1.09417	0.547083	−	0.837078i	$-0.315738\pi$
$997$	34445.0	1.09417	0.547083	+	0.837078i	$0.315738\pi$
$998$	−4672.72	−0.148209
$999$	2238.16	0.0708833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.4.a.f.1.8		14
5.4	even	2		1875.4.a.g.1.7		14
25.9	even	10		75.4.g.b.31.4	✓	28
25.14	even	10		75.4.g.b.46.4	yes	28
75.14	odd	10		225.4.h.a.46.4		28
75.59	odd	10		225.4.h.a.181.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.31.4	✓	28	25.9	even	10
75.4.g.b.46.4	yes	28	25.14	even	10
225.4.h.a.46.4		28	75.14	odd	10
225.4.h.a.181.4		28	75.59	odd	10
1875.4.a.f.1.8		14	1.1	even	1	trivial
1875.4.a.g.1.7		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)

\(f(q)\)	\(=\)	\(q+0.574607 q^{2} -3.00000 q^{3} -7.66983 q^{4} -1.72382 q^{6} +2.67744 q^{7} -9.00399 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+0.574607 q^{2} -3.00000 q^{3} -7.66983 q^{4} -1.72382 q^{6} +2.67744 q^{7} -9.00399 q^{8} +9.00000 q^{9} -63.0399 q^{11} +23.0095 q^{12} -14.1745 q^{13} +1.53847 q^{14} +56.1849 q^{16} -30.3957 q^{17} +5.17146 q^{18} +27.5206 q^{19} -8.03231 q^{21} -36.2232 q^{22} -116.254 q^{23} +27.0120 q^{24} -8.14478 q^{26} -27.0000 q^{27} -20.5355 q^{28} -40.2108 q^{29} -222.867 q^{31} +104.316 q^{32} +189.120 q^{33} -17.4655 q^{34} -69.0284 q^{36} -82.8950 q^{37} +15.8135 q^{38} +42.5236 q^{39} +144.092 q^{41} -4.61542 q^{42} -433.956 q^{43} +483.505 q^{44} -66.8006 q^{46} -459.261 q^{47} -168.555 q^{48} -335.831 q^{49} +91.1870 q^{51} +108.716 q^{52} +247.479 q^{53} -15.5144 q^{54} -24.1076 q^{56} -82.5619 q^{57} -23.1054 q^{58} +310.464 q^{59} +2.08511 q^{61} -128.061 q^{62} +24.0969 q^{63} -389.538 q^{64} +108.669 q^{66} -654.469 q^{67} +233.129 q^{68} +348.763 q^{69} -908.004 q^{71} -81.0359 q^{72} +878.547 q^{73} -47.6320 q^{74} -211.079 q^{76} -168.785 q^{77} +24.4343 q^{78} -1139.01 q^{79} +81.0000 q^{81} +82.7962 q^{82} +986.642 q^{83} +61.6064 q^{84} -249.354 q^{86} +120.632 q^{87} +567.611 q^{88} +988.777 q^{89} -37.9514 q^{91} +891.652 q^{92} +668.602 q^{93} -263.894 q^{94} -312.948 q^{96} -1537.91 q^{97} -192.971 q^{98} -567.359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 42 q^{3} + 50 q^{4} + 27 q^{7} - 21 q^{8} + 126 q^{9}+O(q^{10}) \) 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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