LMFDB - Embedded newform 1875.4.a.f.1.6

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			1.6
Root			$1.33976$ 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)

$f(q)$	$=$	$q-1.33976 q^{2} -3.00000 q^{3} -6.20504 q^{4} +4.01928 q^{6} +12.2101 q^{7} +19.0313 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.33976 q^{2} -3.00000 q^{3} -6.20504 q^{4} +4.01928 q^{6} +12.2101 q^{7} +19.0313 q^{8} +9.00000 q^{9} -2.48229 q^{11} +18.6151 q^{12} -85.6202 q^{13} -16.3586 q^{14} +24.1429 q^{16} +5.54850 q^{17} -12.0578 q^{18} -24.1374 q^{19} -36.6303 q^{21} +3.32567 q^{22} +103.353 q^{23} -57.0940 q^{24} +114.710 q^{26} -27.0000 q^{27} -75.7642 q^{28} -114.245 q^{29} +153.871 q^{31} -184.596 q^{32} +7.44687 q^{33} -7.43365 q^{34} -55.8454 q^{36} +342.674 q^{37} +32.3383 q^{38} +256.861 q^{39} +34.6755 q^{41} +49.0758 q^{42} +154.740 q^{43} +15.4027 q^{44} -138.468 q^{46} -338.534 q^{47} -72.4288 q^{48} -193.913 q^{49} -16.6455 q^{51} +531.277 q^{52} -645.636 q^{53} +36.1735 q^{54} +232.375 q^{56} +72.4123 q^{57} +153.060 q^{58} +662.854 q^{59} -357.681 q^{61} -206.150 q^{62} +109.891 q^{63} +54.1714 q^{64} -9.97701 q^{66} +531.377 q^{67} -34.4287 q^{68} -310.059 q^{69} -634.801 q^{71} +171.282 q^{72} -962.898 q^{73} -459.101 q^{74} +149.774 q^{76} -30.3090 q^{77} -344.131 q^{78} +568.744 q^{79} +81.0000 q^{81} -46.4568 q^{82} +319.838 q^{83} +227.293 q^{84} -207.315 q^{86} +342.734 q^{87} -47.2413 q^{88} -1334.71 q^{89} -1045.43 q^{91} -641.309 q^{92} -461.613 q^{93} +453.554 q^{94} +553.789 q^{96} -399.297 q^{97} +259.797 q^{98} -22.3406 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.33976	−0.473676	−0.236838	−	0.971549i	$-0.576111\pi$
$2$	−1.33976	−0.473676	−0.236838	+	0.971549i	$0.576111\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−6.20504	−0.775631
$5$	0	0
$5$	0	0
$6$	4.01928	0.273477
$7$	12.2101	0.659284	0.329642	−	0.944106i	$-0.393072\pi$
$7$	12.2101	0.659284	0.329642	+	0.944106i	$0.393072\pi$
$8$	19.0313	0.841074
$9$	9.00000	0.333333
$10$	0	0
$11$	−2.48229	−0.0680398	−0.0340199	−	0.999421i	$-0.510831\pi$
$11$	−2.48229	−0.0680398	−0.0340199	+	0.999421i	$0.510831\pi$
$12$	18.6151	0.447811
$13$	−85.6202	−1.82667	−0.913337	−	0.407204i	$-0.866504\pi$
$13$	−85.6202	−1.82667	−0.913337	+	0.407204i	$0.866504\pi$
$14$	−16.3586	−0.312287
$15$	0	0
$16$	24.1429	0.377233
$17$	5.54850	0.0791593	0.0395797	−	0.999216i	$-0.487398\pi$
$17$	5.54850	0.0791593	0.0395797	+	0.999216i	$0.487398\pi$
$18$	−12.0578	−0.157892
$19$	−24.1374	−0.291448	−0.145724	−	0.989325i	$-0.546551\pi$
$19$	−24.1374	−0.291448	−0.145724	+	0.989325i	$0.546551\pi$
$20$	0	0
$21$	−36.6303	−0.380638
$22$	3.32567	0.0322289
$23$	103.353	0.936981	0.468491	−	0.883468i	$-0.344798\pi$
$23$	103.353	0.936981	0.468491	+	0.883468i	$0.344798\pi$
$24$	−57.0940	−0.485595
$25$	0	0
$26$	114.710	0.865253
$27$	−27.0000	−0.192450
$28$	−75.7642	−0.511361
$29$	−114.245	−0.731541	−0.365770	−	0.930705i	$-0.619194\pi$
$29$	−114.245	−0.731541	−0.365770	+	0.930705i	$0.619194\pi$
$30$	0	0
$31$	153.871	0.891485	0.445742	−	0.895161i	$-0.352940\pi$
$31$	153.871	0.891485	0.445742	+	0.895161i	$0.352940\pi$
$32$	−184.596	−1.01976
$33$	7.44687	0.0392828
$34$	−7.43365	−0.0374959
$35$	0	0
$36$	−55.8454	−0.258544
$37$	342.674	1.52258	0.761288	−	0.648414i	$-0.224567\pi$
$37$	342.674	1.52258	0.761288	+	0.648414i	$0.224567\pi$
$38$	32.3383	0.138052
$39$	256.861	1.05463
$40$	0	0
$41$	34.6755	0.132083	0.0660414	−	0.997817i	$-0.478963\pi$
$41$	34.6755	0.132083	0.0660414	+	0.997817i	$0.478963\pi$
$42$	49.0758	0.180299
$43$	154.740	0.548783	0.274391	−	0.961618i	$-0.411524\pi$
$43$	154.740	0.548783	0.274391	+	0.961618i	$0.411524\pi$
$44$	15.4027	0.0527738
$45$	0	0
$46$	−138.468	−0.443826
$47$	−338.534	−1.05064	−0.525321	−	0.850904i	$-0.676055\pi$
$47$	−338.534	−1.05064	−0.525321	+	0.850904i	$0.676055\pi$
$48$	−72.4288	−0.217796
$49$	−193.913	−0.565345
$50$	0	0
$51$	−16.6455	−0.0457027
$52$	531.277	1.41682
$53$	−645.636	−1.67330	−0.836650	−	0.547738i	$-0.815489\pi$
$53$	−645.636	−1.67330	−0.836650	+	0.547738i	$0.815489\pi$
$54$	36.1735	0.0911591
$55$	0	0
$56$	232.375	0.554507
$57$	72.4123	0.168267
$58$	153.060	0.346514
$59$	662.854	1.46265	0.731325	−	0.682030i	$-0.238903\pi$
$59$	662.854	1.46265	0.731325	+	0.682030i	$0.238903\pi$
$60$	0	0
$61$	−357.681	−0.750759	−0.375379	−	0.926871i	$-0.622488\pi$
$61$	−357.681	−0.750759	−0.375379	+	0.926871i	$0.622488\pi$
$62$	−206.150	−0.422275
$63$	109.891	0.219761
$64$	54.1714	0.105803
$65$	0	0
$66$	−9.97701	−0.0186073
$67$	531.377	0.968926	0.484463	−	0.874812i	$-0.339015\pi$
$67$	531.377	0.968926	0.484463	+	0.874812i	$0.339015\pi$
$68$	−34.4287	−0.0613984
$69$	−310.059	−0.540966
$70$	0	0
$71$	−634.801	−1.06109	−0.530543	−	0.847658i	$-0.678012\pi$
$71$	−634.801	−1.06109	−0.530543	+	0.847658i	$0.678012\pi$
$72$	171.282	0.280358
$73$	−962.898	−1.54382	−0.771909	−	0.635734i	$-0.780698\pi$
$73$	−962.898	−1.54382	−0.771909	+	0.635734i	$0.780698\pi$
$74$	−459.101	−0.721208
$75$	0	0
$76$	149.774	0.226056
$77$	−30.3090	−0.0448576
$78$	−344.131	−0.499554
$79$	568.744	0.809984	0.404992	−	0.914320i	$-0.367274\pi$
$79$	568.744	0.809984	0.404992	+	0.914320i	$0.367274\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−46.4568	−0.0625645
$83$	319.838	0.422973	0.211486	−	0.977381i	$-0.432170\pi$
$83$	319.838	0.422973	0.211486	+	0.977381i	$0.432170\pi$
$84$	227.293	0.295234
$85$	0	0
$86$	−207.315	−0.259945
$87$	342.734	0.422355
$88$	−47.2413	−0.0572266
$89$	−1334.71	−1.58966	−0.794828	−	0.606835i	$-0.792439\pi$
$89$	−1334.71	−1.58966	−0.794828	+	0.606835i	$0.792439\pi$
$90$	0	0
$91$	−1045.43	−1.20430
$92$	−641.309	−0.726751
$93$	−461.613	−0.514699
$94$	453.554	0.497665
$95$	0	0
$96$	553.789	0.588759
$97$	−399.297	−0.417964	−0.208982	−	0.977920i	$-0.567015\pi$
$97$	−399.297	−0.417964	−0.208982	+	0.977920i	$0.567015\pi$
$98$	259.797	0.267791
$99$	−22.3406	−0.0226799
$100$	0	0
$101$	−131.408	−0.129461	−0.0647307	−	0.997903i	$-0.520619\pi$
$101$	−131.408	−0.129461	−0.0647307	+	0.997903i	$0.520619\pi$
$102$	22.3010	0.0216483
$103$	−18.8410	−0.0180238	−0.00901192	−	0.999959i	$-0.502869\pi$
$103$	−18.8410	−0.0180238	−0.00901192	+	0.999959i	$0.502869\pi$
$104$	−1629.47	−1.53637
$105$	0	0
$106$	864.997	0.792603
$107$	1832.09	1.65528	0.827640	−	0.561259i	$-0.189683\pi$
$107$	1832.09	1.65528	0.827640	+	0.561259i	$0.189683\pi$
$108$	167.536	0.149270
$109$	−1337.65	−1.17544	−0.587722	−	0.809063i	$-0.699975\pi$
$109$	−1337.65	−1.17544	−0.587722	+	0.809063i	$0.699975\pi$
$110$	0	0
$111$	−1028.02	−0.879059
$112$	294.788	0.248704
$113$	−36.2244	−0.0301566	−0.0150783	−	0.999886i	$-0.504800\pi$
$113$	−36.2244	−0.0301566	−0.0150783	+	0.999886i	$0.504800\pi$
$114$	−97.0150	−0.0797043
$115$	0	0
$116$	708.893	0.567405
$117$	−770.582	−0.608891
$118$	−888.065	−0.692822
$119$	67.7477	0.0521884
$120$	0	0
$121$	−1324.84	−0.995371
$122$	479.206	0.355617
$123$	−104.026	−0.0762581
$124$	−954.776	−0.691463
$125$	0	0
$126$	−147.227	−0.104096
$127$	1397.61	0.976520	0.488260	−	0.872698i	$-0.337632\pi$
$127$	1397.61	0.976520	0.488260	+	0.872698i	$0.337632\pi$
$128$	1404.20	0.969644
$129$	−464.220	−0.316840
$130$	0	0
$131$	−2838.05	−1.89284	−0.946418	−	0.322945i	$-0.895327\pi$
$131$	−2838.05	−1.89284	−0.946418	+	0.322945i	$0.895327\pi$
$132$	−46.2081	−0.0304690
$133$	−294.720	−0.192147
$134$	−711.918	−0.458958
$135$	0	0
$136$	105.595	0.0665789
$137$	810.294	0.505314	0.252657	−	0.967556i	$-0.418696\pi$
$137$	810.294	0.505314	0.252657	+	0.967556i	$0.418696\pi$
$138$	415.404	0.256243
$139$	−3140.44	−1.91632	−0.958161	−	0.286230i	$-0.907598\pi$
$139$	−3140.44	−1.91632	−0.958161	+	0.286230i	$0.907598\pi$
$140$	0	0
$141$	1015.60	0.606589
$142$	850.481	0.502611
$143$	212.534	0.124287
$144$	217.286	0.125744
$145$	0	0
$146$	1290.05	0.731270
$147$	581.740	0.326402
$148$	−2126.31	−1.18096
$149$	−1008.26	−0.554362	−0.277181	−	0.960818i	$-0.589400\pi$
$149$	−1008.26	−0.554362	−0.277181	+	0.960818i	$0.589400\pi$
$150$	0	0
$151$	−2162.97	−1.16570	−0.582848	−	0.812581i	$-0.698062\pi$
$151$	−2162.97	−1.16570	−0.582848	+	0.812581i	$0.698062\pi$
$152$	−459.368	−0.245129
$153$	49.9365	0.0263864
$154$	40.6068	0.0212480
$155$	0	0
$156$	−1593.83	−0.818004
$157$	2618.64	1.33115	0.665575	−	0.746331i	$-0.268186\pi$
$157$	2618.64	1.33115	0.665575	+	0.746331i	$0.268186\pi$
$158$	−761.980	−0.383670
$159$	1936.91	0.966080
$160$	0	0
$161$	1261.95	0.617737
$162$	−108.521	−0.0526307
$163$	323.254	0.155333	0.0776663	−	0.996979i	$-0.475253\pi$
$163$	323.254	0.155333	0.0776663	+	0.996979i	$0.475253\pi$
$164$	−215.163	−0.102447
$165$	0	0
$166$	−428.505	−0.200352
$167$	−158.987	−0.0736692	−0.0368346	−	0.999321i	$-0.511727\pi$
$167$	−158.987	−0.0736692	−0.0368346	+	0.999321i	$0.511727\pi$
$168$	−697.124	−0.320145
$169$	5133.82	2.33674
$170$	0	0
$171$	−217.237	−0.0971492
$172$	−960.170	−0.425653
$173$	3292.67	1.44703	0.723516	−	0.690307i	$-0.242525\pi$
$173$	3292.67	1.44703	0.723516	+	0.690307i	$0.242525\pi$
$174$	−459.181	−0.200060
$175$	0	0
$176$	−59.9297	−0.0256669
$177$	−1988.56	−0.844461
$178$	1788.20	0.752983
$179$	2818.95	1.17708	0.588542	−	0.808467i	$-0.299702\pi$
$179$	2818.95	1.17708	0.588542	+	0.808467i	$0.299702\pi$
$180$	0	0
$181$	417.600	0.171492	0.0857458	−	0.996317i	$-0.472673\pi$
$181$	417.600	0.171492	0.0857458	+	0.996317i	$0.472673\pi$
$182$	1400.63	0.570447
$183$	1073.04	0.433451
$184$	1966.94	0.788071
$185$	0	0
$186$	618.450	0.243801
$187$	−13.7730	−0.00538599
$188$	2100.62	0.814911
$189$	−329.673	−0.126879
$190$	0	0
$191$	521.598	0.197599	0.0987997	−	0.995107i	$-0.468500\pi$
$191$	521.598	0.197599	0.0987997	+	0.995107i	$0.468500\pi$
$192$	−162.514	−0.0610857
$193$	4528.65	1.68901	0.844506	−	0.535547i	$-0.179894\pi$
$193$	4528.65	1.68901	0.844506	+	0.535547i	$0.179894\pi$
$194$	534.962	0.197980
$195$	0	0
$196$	1203.24	0.438499
$197$	2780.69	1.00566	0.502832	−	0.864384i	$-0.332291\pi$
$197$	2780.69	1.00566	0.502832	+	0.864384i	$0.332291\pi$
$198$	29.9310	0.0107430
$199$	4988.03	1.77685	0.888423	−	0.459026i	$-0.151801\pi$
$199$	4988.03	1.77685	0.888423	+	0.459026i	$0.151801\pi$
$200$	0	0
$201$	−1594.13	−0.559410
$202$	176.055	0.0613228
$203$	−1394.94	−0.482293
$204$	103.286	0.0354484
$205$	0	0
$206$	25.2424	0.00853747
$207$	930.176	0.312327
$208$	−2067.12	−0.689083
$209$	59.9161	0.0198300
$210$	0	0
$211$	3752.11	1.22420	0.612100	−	0.790781i	$-0.290325\pi$
$211$	3752.11	1.22420	0.612100	+	0.790781i	$0.290325\pi$
$212$	4006.20	1.29786
$213$	1904.40	0.612618
$214$	−2454.56	−0.784068
$215$	0	0
$216$	−513.846	−0.161865
$217$	1878.78	0.587741
$218$	1792.13	0.556780
$219$	2888.69	0.891323
$220$	0	0
$221$	−475.063	−0.144598
$222$	1377.30	0.416390
$223$	−1637.57	−0.491748	−0.245874	−	0.969302i	$-0.579075\pi$
$223$	−1637.57	−0.491748	−0.245874	+	0.969302i	$0.579075\pi$
$224$	−2253.94	−0.672312
$225$	0	0
$226$	48.5319	0.0142845
$227$	3793.11	1.10906	0.554532	−	0.832162i	$-0.312897\pi$
$227$	3793.11	1.10906	0.554532	+	0.832162i	$0.312897\pi$
$228$	−449.321	−0.130513
$229$	90.2198	0.0260345	0.0130172	−	0.999915i	$-0.495856\pi$
$229$	90.2198	0.0260345	0.0130172	+	0.999915i	$0.495856\pi$
$230$	0	0
$231$	90.9270	0.0258985
$232$	−2174.23	−0.615280
$233$	−3618.41	−1.01738	−0.508691	−	0.860949i	$-0.669870\pi$
$233$	−3618.41	−1.01738	−0.508691	+	0.860949i	$0.669870\pi$
$234$	1032.39	0.288418
$235$	0	0
$236$	−4113.04	−1.13448
$237$	−1706.23	−0.467644
$238$	−90.7657	−0.0247204
$239$	−1470.76	−0.398056	−0.199028	−	0.979994i	$-0.563778\pi$
$239$	−1470.76	−0.398056	−0.199028	+	0.979994i	$0.563778\pi$
$240$	0	0
$241$	−3946.47	−1.05483	−0.527416	−	0.849607i	$-0.676839\pi$
$241$	−3946.47	−1.05483	−0.527416	+	0.849607i	$0.676839\pi$
$242$	1774.96	0.471484
$243$	−243.000	−0.0641500
$244$	2219.42	0.582312
$245$	0	0
$246$	139.370	0.0361217
$247$	2066.65	0.532380
$248$	2928.37	0.749805
$249$	−959.513	−0.244203
$250$	0	0
$251$	3410.52	0.857649	0.428825	−	0.903388i	$-0.358928\pi$
$251$	3410.52	0.857649	0.428825	+	0.903388i	$0.358928\pi$
$252$	−681.878	−0.170454
$253$	−256.552	−0.0637521
$254$	−1872.46	−0.462554
$255$	0	0
$256$	−2314.65	−0.565101
$257$	6919.87	1.67957	0.839785	−	0.542918i	$-0.182681\pi$
$257$	6919.87	1.67957	0.839785	+	0.542918i	$0.182681\pi$
$258$	621.944	0.150080
$259$	4184.09	1.00381
$260$	0	0
$261$	−1028.20	−0.243847
$262$	3802.30	0.896592
$263$	−3808.56	−0.892951	−0.446475	−	0.894796i	$-0.647321\pi$
$263$	−3808.56	−0.892951	−0.446475	+	0.894796i	$0.647321\pi$
$264$	141.724	0.0330398
$265$	0	0
$266$	394.855	0.0910154
$267$	4004.14	0.917788
$268$	−3297.22	−0.751529
$269$	2586.34	0.586214	0.293107	−	0.956080i	$-0.405311\pi$
$269$	2586.34	0.586214	0.293107	+	0.956080i	$0.405311\pi$
$270$	0	0
$271$	1065.41	0.238816	0.119408	−	0.992845i	$-0.461900\pi$
$271$	1065.41	0.238816	0.119408	+	0.992845i	$0.461900\pi$
$272$	133.957	0.0298615
$273$	3136.29	0.695301
$274$	−1085.60	−0.239356
$275$	0	0
$276$	1923.93	0.419590
$277$	2468.28	0.535396	0.267698	−	0.963503i	$-0.413737\pi$
$277$	2468.28	0.535396	0.267698	+	0.963503i	$0.413737\pi$
$278$	4207.44	0.907717
$279$	1384.84	0.297162
$280$	0	0
$281$	3108.83	0.659991	0.329996	−	0.943982i	$-0.392953\pi$
$281$	3108.83	0.659991	0.329996	+	0.943982i	$0.392953\pi$
$282$	−1360.66	−0.287327
$283$	6454.03	1.35566	0.677831	−	0.735217i	$-0.262920\pi$
$283$	6454.03	1.35566	0.677831	+	0.735217i	$0.262920\pi$
$284$	3938.97	0.823010
$285$	0	0
$286$	−284.744	−0.0588717
$287$	423.391	0.0870801
$288$	−1661.37	−0.339920
$289$	−4882.21	−0.993734
$290$	0	0
$291$	1197.89	0.241312
$292$	5974.82	1.19743
$293$	−835.063	−0.166501	−0.0832507	−	0.996529i	$-0.526530\pi$
$293$	−835.063	−0.166501	−0.0832507	+	0.996529i	$0.526530\pi$
$294$	−779.392	−0.154609
$295$	0	0
$296$	6521.55	1.28060
$297$	67.0218	0.0130943
$298$	1350.83	0.262588
$299$	−8849.10	−1.71156
$300$	0	0
$301$	1889.39	0.361803
$302$	2897.86	0.552163
$303$	394.224	0.0747445
$304$	−582.748	−0.109944
$305$	0	0
$306$	−66.9029	−0.0124986
$307$	−2681.88	−0.498577	−0.249289	−	0.968429i	$-0.580197\pi$
$307$	−2681.88	−0.498577	−0.249289	+	0.968429i	$0.580197\pi$
$308$	188.069	0.0347929
$309$	56.5229	0.0104061
$310$	0	0
$311$	8133.63	1.48301	0.741504	−	0.670948i	$-0.234113\pi$
$311$	8133.63	1.48301	0.741504	+	0.670948i	$0.234113\pi$
$312$	4888.40	0.887023
$313$	−7723.68	−1.39479	−0.697394	−	0.716688i	$-0.745657\pi$
$313$	−7723.68	−1.39479	−0.697394	+	0.716688i	$0.745657\pi$
$314$	−3508.35	−0.630534
$315$	0	0
$316$	−3529.08	−0.628248
$317$	−3220.49	−0.570602	−0.285301	−	0.958438i	$-0.592093\pi$
$317$	−3220.49	−0.570602	−0.285301	+	0.958438i	$0.592093\pi$
$318$	−2594.99	−0.457610
$319$	283.588	0.0497739
$320$	0	0
$321$	−5496.28	−0.955677
$322$	−1690.71	−0.292607
$323$	−133.926	−0.0230708
$324$	−502.609	−0.0861812
$325$	0	0
$326$	−433.083	−0.0735774
$327$	4012.94	0.678643
$328$	659.920	0.111092
$329$	−4133.53	−0.692672
$330$	0	0
$331$	4197.98	0.697105	0.348553	−	0.937289i	$-0.386673\pi$
$331$	4197.98	0.697105	0.348553	+	0.937289i	$0.386673\pi$
$332$	−1984.61	−0.328071
$333$	3084.07	0.507525
$334$	213.004	0.0348954
$335$	0	0
$336$	−884.363	−0.143589
$337$	−1285.13	−0.207731	−0.103865	−	0.994591i	$-0.533121\pi$
$337$	−1285.13	−0.207731	−0.103865	+	0.994591i	$0.533121\pi$
$338$	−6878.08	−1.10686
$339$	108.673	0.0174109
$340$	0	0
$341$	−381.952	−0.0606565
$342$	291.045	0.0460173
$343$	−6555.77	−1.03201
$344$	2944.91	0.461567
$345$	0	0
$346$	−4411.38	−0.685425
$347$	311.212	0.0481461	0.0240731	−	0.999710i	$-0.492337\pi$
$347$	311.212	0.0481461	0.0240731	+	0.999710i	$0.492337\pi$
$348$	−2126.68	−0.327592
$349$	−3853.76	−0.591081	−0.295540	−	0.955330i	$-0.595500\pi$
$349$	−3853.76	−0.591081	−0.295540	+	0.955330i	$0.595500\pi$
$350$	0	0
$351$	2311.75	0.351544
$352$	458.222	0.0693844
$353$	−1202.75	−0.181349	−0.0906743	−	0.995881i	$-0.528902\pi$
$353$	−1202.75	−0.181349	−0.0906743	+	0.995881i	$0.528902\pi$
$354$	2664.20	0.400001
$355$	0	0
$356$	8281.96	1.23299
$357$	−203.243	−0.0301310
$358$	−3776.71	−0.557557
$359$	10915.2	1.60469	0.802345	−	0.596860i	$-0.203585\pi$
$359$	10915.2	1.60469	0.802345	+	0.596860i	$0.203585\pi$
$360$	0	0
$361$	−6276.38	−0.915058
$362$	−559.484	−0.0812315
$363$	3974.51	0.574677
$364$	6486.95	0.934089
$365$	0	0
$366$	−1437.62	−0.205316
$367$	145.288	0.0206647	0.0103324	−	0.999947i	$-0.496711\pi$
$367$	145.288	0.0206647	0.0103324	+	0.999947i	$0.496711\pi$
$368$	2495.24	0.353461
$369$	312.079	0.0440276
$370$	0	0
$371$	−7883.28	−1.10318
$372$	2864.33	0.399216
$373$	3519.41	0.488547	0.244274	−	0.969706i	$-0.421451\pi$
$373$	3519.41	0.488547	0.244274	+	0.969706i	$0.421451\pi$
$374$	18.4525	0.00255122
$375$	0	0
$376$	−6442.75	−0.883669
$377$	9781.64	1.33629
$378$	441.682	0.0600997
$379$	−404.362	−0.0548040	−0.0274020	−	0.999624i	$-0.508723\pi$
$379$	−404.362	−0.0548040	−0.0274020	+	0.999624i	$0.508723\pi$
$380$	0	0
$381$	−4192.84	−0.563794
$382$	−698.816	−0.0935982
$383$	4183.62	0.558154	0.279077	−	0.960269i	$-0.409971\pi$
$383$	4183.62	0.558154	0.279077	+	0.960269i	$0.409971\pi$
$384$	−4212.59	−0.559824
$385$	0	0
$386$	−6067.30	−0.800045
$387$	1392.66	0.182928
$388$	2477.66	0.324185
$389$	−10258.6	−1.33710	−0.668551	−	0.743666i	$-0.733085\pi$
$389$	−10258.6	−1.33710	−0.668551	+	0.743666i	$0.733085\pi$
$390$	0	0
$391$	573.453	0.0741708
$392$	−3690.43	−0.475497
$393$	8514.15	1.09283
$394$	−3725.45	−0.476360
$395$	0	0
$396$	138.624	0.0175913
$397$	10191.6	1.28841	0.644207	−	0.764852i	$-0.277188\pi$
$397$	10191.6	1.28841	0.644207	+	0.764852i	$0.277188\pi$
$398$	−6682.77	−0.841650
$399$	884.161	0.110936
$400$	0	0
$401$	5912.32	0.736277	0.368139	−	0.929771i	$-0.379995\pi$
$401$	5912.32	0.736277	0.368139	+	0.929771i	$0.379995\pi$
$402$	2135.75	0.264979
$403$	−13174.5	−1.62845
$404$	815.393	0.100414
$405$	0	0
$406$	1868.88	0.228451
$407$	−850.616	−0.103596
$408$	−316.786	−0.0384393
$409$	5656.62	0.683867	0.341934	−	0.939724i	$-0.388918\pi$
$409$	5656.62	0.683867	0.341934	+	0.939724i	$0.388918\pi$
$410$	0	0
$411$	−2430.88	−0.291743
$412$	116.909	0.0139798
$413$	8093.52	0.964301
$414$	−1246.21	−0.147942
$415$	0	0
$416$	15805.2	1.86277
$417$	9421.32	1.10639
$418$	−80.2731	−0.00939303
$419$	13703.9	1.59781	0.798903	−	0.601460i	$-0.205414\pi$
$419$	13703.9	1.59781	0.798903	+	0.601460i	$0.205414\pi$
$420$	0	0
$421$	9214.65	1.06673	0.533367	−	0.845884i	$-0.320927\pi$
$421$	9214.65	1.06673	0.533367	+	0.845884i	$0.320927\pi$
$422$	−5026.93	−0.579874
$423$	−3046.80	−0.350214
$424$	−12287.3	−1.40737
$425$	0	0
$426$	−2551.44	−0.290183
$427$	−4367.32	−0.494963
$428$	−11368.2	−1.28389
$429$	−637.602	−0.0717569
$430$	0	0
$431$	7565.73	0.845542	0.422771	−	0.906237i	$-0.361058\pi$
$431$	7565.73	0.845542	0.422771	+	0.906237i	$0.361058\pi$
$432$	−651.859	−0.0725986
$433$	−4046.69	−0.449126	−0.224563	−	0.974460i	$-0.572095\pi$
$433$	−4046.69	−0.449126	−0.224563	+	0.974460i	$0.572095\pi$
$434$	−2517.11	−0.278399
$435$	0	0
$436$	8300.17	0.911711
$437$	−2494.67	−0.273081
$438$	−3870.15	−0.422199
$439$	3903.40	0.424372	0.212186	−	0.977229i	$-0.431942\pi$
$439$	3903.40	0.424372	0.212186	+	0.977229i	$0.431942\pi$
$440$	0	0
$441$	−1745.22	−0.188448
$442$	636.471	0.0684928
$443$	−2288.91	−0.245484	−0.122742	−	0.992439i	$-0.539169\pi$
$443$	−2288.91	−0.245484	−0.122742	+	0.992439i	$0.539169\pi$
$444$	6378.93	0.681825
$445$	0	0
$446$	2193.95	0.232930
$447$	3024.78	0.320061
$448$	661.438	0.0697545
$449$	10025.3	1.05373	0.526863	−	0.849950i	$-0.323368\pi$
$449$	10025.3	1.05373	0.526863	+	0.849950i	$0.323368\pi$
$450$	0	0
$451$	−86.0745	−0.00898690
$452$	224.774	0.0233904
$453$	6488.92	0.673015
$454$	−5081.86	−0.525338
$455$	0	0
$456$	1378.10	0.141525
$457$	3293.06	0.337075	0.168537	−	0.985695i	$-0.446096\pi$
$457$	3293.06	0.337075	0.168537	+	0.985695i	$0.446096\pi$
$458$	−120.873	−0.0123319
$459$	−149.809	−0.0152342
$460$	0	0
$461$	−831.332	−0.0839891	−0.0419945	−	0.999118i	$-0.513371\pi$
$461$	−831.332	−0.0839891	−0.0419945	+	0.999118i	$0.513371\pi$
$462$	−121.820	−0.0122675
$463$	9026.62	0.906053	0.453027	−	0.891497i	$-0.350344\pi$
$463$	9026.62	0.906053	0.453027	+	0.891497i	$0.350344\pi$
$464$	−2758.20	−0.275962
$465$	0	0
$466$	4847.80	0.481910
$467$	−1315.72	−0.130373	−0.0651867	−	0.997873i	$-0.520764\pi$
$467$	−1315.72	−0.130373	−0.0651867	+	0.997873i	$0.520764\pi$
$468$	4781.49	0.472275
$469$	6488.17	0.638797
$470$	0	0
$471$	−7855.93	−0.768540
$472$	12615.0	1.23020
$473$	−384.110	−0.0373391
$474$	2285.94	0.221512
$475$	0	0
$476$	−420.378	−0.0404790
$477$	−5810.72	−0.557767
$478$	1970.46	0.188550
$479$	9331.15	0.890086	0.445043	−	0.895509i	$-0.353188\pi$
$479$	9331.15	0.890086	0.445043	+	0.895509i	$0.353188\pi$
$480$	0	0
$481$	−29339.8	−2.78125
$482$	5287.32	0.499649
$483$	−3785.85	−0.356650
$484$	8220.68	0.772040
$485$	0	0
$486$	325.562	0.0303864
$487$	2055.48	0.191258	0.0956288	−	0.995417i	$-0.469514\pi$
$487$	2055.48	0.191258	0.0956288	+	0.995417i	$0.469514\pi$
$488$	−6807.14	−0.631444
$489$	−969.763	−0.0896814
$490$	0	0
$491$	3570.13	0.328142	0.164071	−	0.986449i	$-0.447537\pi$
$491$	3570.13	0.328142	0.164071	+	0.986449i	$0.447537\pi$
$492$	645.488	0.0591481
$493$	−633.886	−0.0579083
$494$	−2768.81	−0.252176
$495$	0	0
$496$	3714.89	0.336298
$497$	−7750.99	−0.699556
$498$	1285.52	0.115673
$499$	−316.957	−0.0284347	−0.0142174	−	0.999899i	$-0.504526\pi$
$499$	−316.957	−0.0284347	−0.0142174	+	0.999899i	$0.504526\pi$
$500$	0	0
$501$	476.960	0.0425329
$502$	−4569.27	−0.406248
$503$	10584.0	0.938204	0.469102	−	0.883144i	$-0.344578\pi$
$503$	10584.0	0.938204	0.469102	+	0.883144i	$0.344578\pi$
$504$	2091.37	0.184836
$505$	0	0
$506$	343.718	0.0301979
$507$	−15401.4	−1.34912
$508$	−8672.24	−0.757418
$509$	−14819.6	−1.29051	−0.645253	−	0.763969i	$-0.723248\pi$
$509$	−14819.6	−1.29051	−0.645253	+	0.763969i	$0.723248\pi$
$510$	0	0
$511$	−11757.1	−1.01781
$512$	−8132.48	−0.701969
$513$	651.710	0.0560891
$514$	−9270.96	−0.795573
$515$	0	0
$516$	2880.51	0.245751
$517$	840.338	0.0714856
$518$	−5605.67	−0.475481
$519$	−9878.00	−0.835445
$520$	0	0
$521$	4097.71	0.344576	0.172288	−	0.985047i	$-0.444884\pi$
$521$	4097.71	0.344576	0.172288	+	0.985047i	$0.444884\pi$
$522$	1377.54	0.115505
$523$	−6037.27	−0.504764	−0.252382	−	0.967628i	$-0.581214\pi$
$523$	−6037.27	−0.504764	−0.252382	+	0.967628i	$0.581214\pi$
$524$	17610.2	1.46814
$525$	0	0
$526$	5102.56	0.422970
$527$	853.752	0.0705693
$528$	179.789	0.0148188
$529$	−1485.18	−0.122066
$530$	0	0
$531$	5965.69	0.487550
$532$	1828.75	0.149035
$533$	−2968.92	−0.241272
$534$	−5364.59	−0.434735
$535$	0	0
$536$	10112.8	0.814939
$537$	−8456.84	−0.679589
$538$	−3465.07	−0.277676
$539$	481.349	0.0384660
$540$	0	0
$541$	4908.65	0.390091	0.195046	−	0.980794i	$-0.437515\pi$
$541$	4908.65	0.390091	0.195046	+	0.980794i	$0.437515\pi$
$542$	−1427.39	−0.113121
$543$	−1252.80	−0.0990107
$544$	−1024.23	−0.0807236
$545$	0	0
$546$	−4201.88	−0.329348
$547$	17573.7	1.37367	0.686836	−	0.726812i	$-0.258999\pi$
$547$	17573.7	1.37367	0.686836	+	0.726812i	$0.258999\pi$
$548$	−5027.91	−0.391937
$549$	−3219.12	−0.250253
$550$	0	0
$551$	2757.57	0.213206
$552$	−5900.83	−0.454993
$553$	6944.43	0.534009
$554$	−3306.90	−0.253604
$555$	0	0
$556$	19486.6	1.48636
$557$	23625.5	1.79721	0.898603	−	0.438764i	$-0.144583\pi$
$557$	23625.5	1.79721	0.898603	+	0.438764i	$0.144583\pi$
$558$	−1855.35	−0.140758
$559$	−13248.9	−1.00245
$560$	0	0
$561$	41.3189	0.00310960
$562$	−4165.09	−0.312622
$563$	23159.1	1.73364	0.866819	−	0.498623i	$-0.166161\pi$
$563$	23159.1	1.73364	0.866819	+	0.498623i	$0.166161\pi$
$564$	−6301.85	−0.470489
$565$	0	0
$566$	−8646.85	−0.642146
$567$	989.018	0.0732537
$568$	−12081.1	−0.892452
$569$	−8494.69	−0.625862	−0.312931	−	0.949776i	$-0.601311\pi$
$569$	−8494.69	−0.625862	−0.312931	+	0.949776i	$0.601311\pi$
$570$	0	0
$571$	15461.7	1.13319	0.566594	−	0.823997i	$-0.308261\pi$
$571$	15461.7	1.13319	0.566594	+	0.823997i	$0.308261\pi$
$572$	−1318.78	−0.0964005
$573$	−1564.79	−0.114084
$574$	−567.242	−0.0412478
$575$	0	0
$576$	487.542	0.0352678
$577$	−26438.3	−1.90752	−0.953760	−	0.300570i	$-0.902823\pi$
$577$	−26438.3	−1.90752	−0.953760	+	0.300570i	$0.902823\pi$
$578$	6540.99	0.470708
$579$	−13585.9	−0.975151
$580$	0	0
$581$	3905.25	0.278859
$582$	−1604.89	−0.114304
$583$	1602.65	0.113851
$584$	−18325.2	−1.29847
$585$	0	0
$586$	1118.78	0.0788678
$587$	5948.84	0.418288	0.209144	−	0.977885i	$-0.432932\pi$
$587$	5948.84	0.418288	0.209144	+	0.977885i	$0.432932\pi$
$588$	−3609.72	−0.253167
$589$	−3714.05	−0.259821
$590$	0	0
$591$	−8342.07	−0.580621
$592$	8273.16	0.574366
$593$	11755.3	0.814054	0.407027	−	0.913416i	$-0.366566\pi$
$593$	11755.3	0.814054	0.407027	+	0.913416i	$0.366566\pi$
$594$	−89.7931	−0.00620245
$595$	0	0
$596$	6256.31	0.429980
$597$	−14964.1	−1.02586
$598$	11855.7	0.810726
$599$	−10184.4	−0.694698	−0.347349	−	0.937736i	$-0.612918\pi$
$599$	−10184.4	−0.694698	−0.347349	+	0.937736i	$0.612918\pi$
$600$	0	0
$601$	−16384.2	−1.11202	−0.556012	−	0.831174i	$-0.687669\pi$
$601$	−16384.2	−1.11202	−0.556012	+	0.831174i	$0.687669\pi$
$602$	−2531.33	−0.171378
$603$	4782.39	0.322975
$604$	13421.3	0.904150
$605$	0	0
$606$	−528.166	−0.0354047
$607$	−20161.1	−1.34813	−0.674066	−	0.738672i	$-0.735453\pi$
$607$	−20161.1	−1.34813	−0.674066	+	0.738672i	$0.735453\pi$
$608$	4455.68	0.297207
$609$	4184.81	0.278452
$610$	0	0
$611$	28985.3	1.91918
$612$	−309.858	−0.0204661
$613$	3158.17	0.208087	0.104043	−	0.994573i	$-0.466822\pi$
$613$	3158.17	0.208087	0.104043	+	0.994573i	$0.466822\pi$
$614$	3593.08	0.236164
$615$	0	0
$616$	−576.821	−0.0377285
$617$	−6576.62	−0.429116	−0.214558	−	0.976711i	$-0.568831\pi$
$617$	−6576.62	−0.429116	−0.214558	+	0.976711i	$0.568831\pi$
$618$	−75.7271	−0.00492911
$619$	−21106.1	−1.37048	−0.685240	−	0.728318i	$-0.740303\pi$
$619$	−21106.1	−1.37048	−0.685240	+	0.728318i	$0.740303\pi$
$620$	0	0
$621$	−2790.53	−0.180322
$622$	−10897.1	−0.702466
$623$	−16297.0	−1.04803
$624$	6201.37	0.397842
$625$	0	0
$626$	10347.9	0.660678
$627$	−179.748	−0.0114489
$628$	−16248.8	−1.03248
$629$	1901.33	0.120526
$630$	0	0
$631$	−26852.1	−1.69408	−0.847039	−	0.531530i	$-0.821617\pi$
$631$	−26852.1	−1.69408	−0.847039	+	0.531530i	$0.821617\pi$
$632$	10824.0	0.681257
$633$	−11256.3	−0.706792
$634$	4314.68	0.270281
$635$	0	0
$636$	−12018.6	−0.749322
$637$	16602.9	1.03270
$638$	−379.940	−0.0235767
$639$	−5713.21	−0.353695
$640$	0	0
$641$	25421.5	1.56644	0.783221	−	0.621743i	$-0.213575\pi$
$641$	25421.5	1.56644	0.783221	+	0.621743i	$0.213575\pi$
$642$	7363.69	0.452682
$643$	10481.7	0.642856	0.321428	−	0.946934i	$-0.395837\pi$
$643$	10481.7	0.642856	0.321428	+	0.946934i	$0.395837\pi$
$644$	−7830.46	−0.479135
$645$	0	0
$646$	179.429	0.0109281
$647$	−18921.8	−1.14975	−0.574877	−	0.818240i	$-0.694950\pi$
$647$	−18921.8	−1.14975	−0.574877	+	0.818240i	$0.694950\pi$
$648$	1541.54	0.0934527
$649$	−1645.40	−0.0995184
$650$	0	0
$651$	−5636.34	−0.339333
$652$	−2005.81	−0.120481
$653$	12657.4	0.758536	0.379268	−	0.925287i	$-0.376176\pi$
$653$	12657.4	0.758536	0.379268	+	0.925287i	$0.376176\pi$
$654$	−5376.38	−0.321457
$655$	0	0
$656$	837.167	0.0498261
$657$	−8666.08	−0.514606
$658$	5537.94	0.328102
$659$	12138.5	0.717526	0.358763	−	0.933429i	$-0.383199\pi$
$659$	12138.5	0.717526	0.358763	+	0.933429i	$0.383199\pi$
$660$	0	0
$661$	4177.69	0.245830	0.122915	−	0.992417i	$-0.460776\pi$
$661$	4177.69	0.245830	0.122915	+	0.992417i	$0.460776\pi$
$662$	−5624.28	−0.330202
$663$	1425.19	0.0834839
$664$	6086.94	0.355752
$665$	0	0
$666$	−4131.91	−0.240403
$667$	−11807.5	−0.685440
$668$	986.519	0.0571401
$669$	4912.71	0.283911
$670$	0	0
$671$	887.866	0.0510815
$672$	6761.83	0.388159
$673$	−7570.21	−0.433596	−0.216798	−	0.976216i	$-0.569561\pi$
$673$	−7570.21	−0.433596	−0.216798	+	0.976216i	$0.569561\pi$
$674$	1721.76	0.0983972
$675$	0	0
$676$	−31855.6	−1.81245
$677$	33332.1	1.89226	0.946128	−	0.323791i	$-0.104958\pi$
$677$	33332.1	1.89226	0.946128	+	0.323791i	$0.104958\pi$
$678$	−145.596	−0.00824716
$679$	−4875.46	−0.275557
$680$	0	0
$681$	−11379.3	−0.640319
$682$	511.724	0.0287315
$683$	34915.5	1.95608	0.978042	−	0.208408i	$-0.0668283\pi$
$683$	34915.5	1.95608	0.978042	+	0.208408i	$0.0668283\pi$
$684$	1347.96	0.0753519
$685$	0	0
$686$	8783.15	0.488837
$687$	−270.659	−0.0150310
$688$	3735.88	0.207019
$689$	55279.5	3.05658
$690$	0	0
$691$	−33698.0	−1.85519	−0.927593	−	0.373593i	$-0.878126\pi$
$691$	−33698.0	−1.85519	−0.927593	+	0.373593i	$0.878126\pi$
$692$	−20431.1	−1.12236
$693$	−272.781	−0.0149525
$694$	−416.949	−0.0228057
$695$	0	0
$696$	6522.68	0.355232
$697$	192.397	0.0104556
$698$	5163.12	0.279981
$699$	10855.2	0.587385
$700$	0	0
$701$	23077.6	1.24341	0.621704	−	0.783252i	$-0.286441\pi$
$701$	23077.6	1.24341	0.621704	+	0.783252i	$0.286441\pi$
$702$	−3097.18	−0.166518
$703$	−8271.27	−0.443751
$704$	−134.469	−0.00719885
$705$	0	0
$706$	1611.40	0.0859006
$707$	−1604.51	−0.0853518
$708$	12339.1	0.654990
$709$	−18761.4	−0.993795	−0.496898	−	0.867809i	$-0.665528\pi$
$709$	−18761.4	−0.993795	−0.496898	+	0.867809i	$0.665528\pi$
$710$	0	0
$711$	5118.70	0.269995
$712$	−25401.4	−1.33702
$713$	15903.0	0.835305
$714$	272.297	0.0142724
$715$	0	0
$716$	−17491.7	−0.912982
$717$	4412.27	0.229818
$718$	−14623.8	−0.760104
$719$	−13386.3	−0.694334	−0.347167	−	0.937803i	$-0.612856\pi$
$719$	−13386.3	−0.694334	−0.347167	+	0.937803i	$0.612856\pi$
$720$	0	0
$721$	−230.050	−0.0118828
$722$	8408.85	0.433442
$723$	11839.4	0.609007
$724$	−2591.23	−0.133014
$725$	0	0
$726$	−5324.89	−0.272211
$727$	10059.3	0.513177	0.256589	−	0.966521i	$-0.417401\pi$
$727$	10059.3	0.513177	0.256589	+	0.966521i	$0.417401\pi$
$728$	−19896.0	−1.01290
$729$	729.000	0.0370370
$730$	0	0
$731$	858.576	0.0434413
$732$	−6658.27	−0.336198
$733$	2861.45	0.144189	0.0720943	−	0.997398i	$-0.477032\pi$
$733$	2861.45	0.144189	0.0720943	+	0.997398i	$0.477032\pi$
$734$	−194.650	−0.00978839
$735$	0	0
$736$	−19078.6	−0.955497
$737$	−1319.03	−0.0659256
$738$	−418.111	−0.0208548
$739$	30134.2	1.50000	0.750002	−	0.661436i	$-0.230053\pi$
$739$	30134.2	1.50000	0.750002	+	0.661436i	$0.230053\pi$
$740$	0	0
$741$	−6199.95	−0.307370
$742$	10561.7	0.522550
$743$	−1183.79	−0.0584508	−0.0292254	−	0.999573i	$-0.509304\pi$
$743$	−1183.79	−0.0584508	−0.0292254	+	0.999573i	$0.509304\pi$
$744$	−8785.11	−0.432900
$745$	0	0
$746$	−4715.16	−0.231413
$747$	2878.54	0.140991
$748$	85.4619	0.00417754
$749$	22370.0	1.09130
$750$	0	0
$751$	33092.2	1.60793	0.803964	−	0.594679i	$-0.202721\pi$
$751$	33092.2	1.60793	0.803964	+	0.594679i	$0.202721\pi$
$752$	−8173.20	−0.396338
$753$	−10231.6	−0.495164
$754$	−13105.0	−0.632968
$755$	0	0
$756$	2045.63	0.0984114
$757$	−14001.4	−0.672246	−0.336123	−	0.941818i	$-0.609116\pi$
$757$	−14001.4	−0.672246	−0.336123	+	0.941818i	$0.609116\pi$
$758$	541.748	0.0259593
$759$	769.655	0.0368073
$760$	0	0
$761$	−16873.5	−0.803765	−0.401883	−	0.915691i	$-0.631644\pi$
$761$	−16873.5	−0.803765	−0.401883	+	0.915691i	$0.631644\pi$
$762$	5617.39	0.267056
$763$	−16332.8	−0.774951
$764$	−3236.54	−0.153264
$765$	0	0
$766$	−5605.05	−0.264385
$767$	−56753.7	−2.67178
$768$	6943.96	0.326261
$769$	6946.78	0.325757	0.162879	−	0.986646i	$-0.447922\pi$
$769$	6946.78	0.325757	0.162879	+	0.986646i	$0.447922\pi$
$770$	0	0
$771$	−20759.6	−0.969701
$772$	−28100.5	−1.31005
$773$	8416.36	0.391611	0.195806	−	0.980643i	$-0.437268\pi$
$773$	8416.36	0.391611	0.195806	+	0.980643i	$0.437268\pi$
$774$	−1865.83	−0.0866485
$775$	0	0
$776$	−7599.16	−0.351539
$777$	−12552.3	−0.579550
$778$	13744.1	0.633354
$779$	−836.976	−0.0384952
$780$	0	0
$781$	1575.76	0.0721961
$782$	−768.290	−0.0351330
$783$	3084.60	0.140785
$784$	−4681.64	−0.213267
$785$	0	0
$786$	−11406.9	−0.517647
$787$	12401.9	0.561729	0.280864	−	0.959747i	$-0.409379\pi$
$787$	12401.9	0.561729	0.280864	+	0.959747i	$0.409379\pi$
$788$	−17254.3	−0.780024
$789$	11425.7	0.515545
$790$	0	0
$791$	−442.303	−0.0198818
$792$	−425.172	−0.0190755
$793$	30624.7	1.37139
$794$	−13654.2	−0.610291
$795$	0	0
$796$	−30951.0	−1.37818
$797$	−33365.5	−1.48290	−0.741448	−	0.671010i	$-0.765861\pi$
$797$	−33365.5	−1.48290	−0.741448	+	0.671010i	$0.765861\pi$
$798$	−1184.56	−0.0525477
$799$	−1878.35	−0.0831682
$800$	0	0
$801$	−12012.4	−0.529885
$802$	−7921.09	−0.348757
$803$	2390.19	0.105041
$804$	9891.66	0.433895
$805$	0	0
$806$	17650.6	0.771360
$807$	−7759.01	−0.338451
$808$	−2500.87	−0.108887
$809$	14601.5	0.634561	0.317281	−	0.948332i	$-0.397230\pi$
$809$	14601.5	0.634561	0.317281	+	0.948332i	$0.397230\pi$
$810$	0	0
$811$	5860.35	0.253742	0.126871	−	0.991919i	$-0.459507\pi$
$811$	5860.35	0.253742	0.126871	+	0.991919i	$0.459507\pi$
$812$	8655.65	0.374081
$813$	−3196.23	−0.137880
$814$	1139.62	0.0490709
$815$	0	0
$816$	−401.871	−0.0172406
$817$	−3735.03	−0.159941
$818$	−7578.50	−0.323932
$819$	−9408.88	−0.401432
$820$	0	0
$821$	15407.4	0.654961	0.327480	−	0.944858i	$-0.393800\pi$
$821$	15407.4	0.654961	0.327480	+	0.944858i	$0.393800\pi$
$822$	3256.80	0.138192
$823$	41672.3	1.76501	0.882505	−	0.470303i	$-0.155855\pi$
$823$	41672.3	1.76501	0.882505	+	0.470303i	$0.155855\pi$
$824$	−358.569	−0.0151594
$825$	0	0
$826$	−10843.4	−0.456767
$827$	15362.1	0.645939	0.322969	−	0.946409i	$-0.395319\pi$
$827$	15362.1	0.645939	0.322969	+	0.946409i	$0.395319\pi$
$828$	−5771.78	−0.242250
$829$	14841.3	0.621783	0.310892	−	0.950445i	$-0.399372\pi$
$829$	14841.3	0.621783	0.310892	+	0.950445i	$0.399372\pi$
$830$	0	0
$831$	−7404.84	−0.309111
$832$	−4638.16	−0.193268
$833$	−1075.93	−0.0447523
$834$	−12622.3	−0.524070
$835$	0	0
$836$	−371.782	−0.0153808
$837$	−4154.51	−0.171566
$838$	−18360.0	−0.756843
$839$	4413.86	0.181625	0.0908126	−	0.995868i	$-0.471054\pi$
$839$	4413.86	0.181625	0.0908126	+	0.995868i	$0.471054\pi$
$840$	0	0
$841$	−11337.2	−0.464848
$842$	−12345.4	−0.505287
$843$	−9326.50	−0.381046
$844$	−23282.0	−0.949526
$845$	0	0
$846$	4081.98	0.165888
$847$	−16176.4	−0.656232
$848$	−15587.5	−0.631225
$849$	−19362.1	−0.782692
$850$	0	0
$851$	35416.4	1.42663
$852$	−11816.9	−0.475165
$853$	5775.19	0.231816	0.115908	−	0.993260i	$-0.463022\pi$
$853$	5775.19	0.231816	0.115908	+	0.993260i	$0.463022\pi$
$854$	5851.15	0.234452
$855$	0	0
$856$	34867.2	1.39221
$857$	4100.45	0.163441	0.0817203	−	0.996655i	$-0.473959\pi$
$857$	4100.45	0.163441	0.0817203	+	0.996655i	$0.473959\pi$
$858$	854.233	0.0339896
$859$	−9834.24	−0.390617	−0.195308	−	0.980742i	$-0.562571\pi$
$859$	−9834.24	−0.390617	−0.195308	+	0.980742i	$0.562571\pi$
$860$	0	0
$861$	−1270.17	−0.0502757
$862$	−10136.3	−0.400513
$863$	−17159.3	−0.676835	−0.338418	−	0.940996i	$-0.609892\pi$
$863$	−17159.3	−0.676835	−0.338418	+	0.940996i	$0.609892\pi$
$864$	4984.10	0.196253
$865$	0	0
$866$	5421.59	0.212740
$867$	14646.6	0.573732
$868$	−11657.9	−0.455870
$869$	−1411.79	−0.0551112
$870$	0	0
$871$	−45496.6	−1.76991
$872$	−25457.2	−0.988636
$873$	−3593.67	−0.139321
$874$	3342.26	0.129352
$875$	0	0
$876$	−17924.5	−0.691338
$877$	8821.46	0.339657	0.169829	−	0.985474i	$-0.445679\pi$
$877$	8821.46	0.339657	0.169829	+	0.985474i	$0.445679\pi$
$878$	−5229.62	−0.201015
$879$	2505.19	0.0961296
$880$	0	0
$881$	−29862.0	−1.14197	−0.570986	−	0.820960i	$-0.693439\pi$
$881$	−29862.0	−1.14197	−0.570986	+	0.820960i	$0.693439\pi$
$882$	2338.18	0.0892635
$883$	−6987.51	−0.266306	−0.133153	−	0.991095i	$-0.542510\pi$
$883$	−6987.51	−0.266306	−0.133153	+	0.991095i	$0.542510\pi$
$884$	2947.79	0.112155
$885$	0	0
$886$	3066.58	0.116280
$887$	−43884.1	−1.66120	−0.830599	−	0.556871i	$-0.812002\pi$
$887$	−43884.1	−1.66120	−0.830599	+	0.556871i	$0.812002\pi$
$888$	−19564.7	−0.739354
$889$	17065.0	0.643803
$890$	0	0
$891$	−201.065	−0.00755998
$892$	10161.2	0.381415
$893$	8171.33	0.306207
$894$	−4052.48	−0.151605
$895$	0	0
$896$	17145.4	0.639271
$897$	26547.3	0.988170
$898$	−13431.5	−0.499125
$899$	−17578.9	−0.652157
$900$	0	0
$901$	−3582.31	−0.132457
$902$	115.319	0.00425688
$903$	−5668.18	−0.208887
$904$	−689.398	−0.0253640
$905$	0	0
$906$	−8693.59	−0.318791
$907$	−20572.4	−0.753138	−0.376569	−	0.926389i	$-0.622896\pi$
$907$	−20572.4	−0.753138	−0.376569	+	0.926389i	$0.622896\pi$
$908$	−23536.4	−0.860225
$909$	−1182.67	−0.0431538
$910$	0	0
$911$	−7334.49	−0.266743	−0.133371	−	0.991066i	$-0.542580\pi$
$911$	−7334.49	−0.266743	−0.133371	+	0.991066i	$0.542580\pi$
$912$	1748.24	0.0634761
$913$	−793.929	−0.0287790
$914$	−4411.91	−0.159664
$915$	0	0
$916$	−559.818	−0.0201931
$917$	−34652.9	−1.24792
$918$	200.709	0.00721609
$919$	−39912.4	−1.43263	−0.716316	−	0.697776i	$-0.754173\pi$
$919$	−39912.4	−1.43263	−0.716316	+	0.697776i	$0.754173\pi$
$920$	0	0
$921$	8045.65	0.287854
$922$	1113.78	0.0397837
$923$	54351.8	1.93826
$924$	−564.206	−0.0200877
$925$	0	0
$926$	−12093.5	−0.429176
$927$	−169.569	−0.00600794
$928$	21089.1	0.745997
$929$	20640.3	0.728939	0.364470	−	0.931215i	$-0.381250\pi$
$929$	20640.3	0.728939	0.364470	+	0.931215i	$0.381250\pi$
$930$	0	0
$931$	4680.57	0.164768
$932$	22452.4	0.789112
$933$	−24400.9	−0.856216
$934$	1762.75	0.0617548
$935$	0	0
$936$	−14665.2	−0.512123
$937$	−26571.7	−0.926426	−0.463213	−	0.886247i	$-0.653303\pi$
$937$	−26571.7	−0.926426	−0.463213	+	0.886247i	$0.653303\pi$
$938$	−8692.59	−0.302583
$939$	23171.1	0.805281
$940$	0	0
$941$	12981.8	0.449729	0.224864	−	0.974390i	$-0.427806\pi$
$941$	12981.8	0.449729	0.224864	+	0.974390i	$0.427806\pi$
$942$	10525.1	0.364039
$943$	3583.81	0.123759
$944$	16003.3	0.551760
$945$	0	0
$946$	514.615	0.0176866
$947$	−46541.8	−1.59705	−0.798525	−	0.601962i	$-0.794386\pi$
$947$	−46541.8	−1.59705	−0.798525	+	0.601962i	$0.794386\pi$
$948$	10587.2	0.362719
$949$	82443.5	2.82005
$950$	0	0
$951$	9661.47	0.329437
$952$	1289.33	0.0438944
$953$	37254.2	1.26630	0.633149	−	0.774030i	$-0.281762\pi$
$953$	37254.2	1.26630	0.633149	+	0.774030i	$0.281762\pi$
$954$	7784.97	0.264201
$955$	0	0
$956$	9126.11	0.308744
$957$	−850.764	−0.0287370
$958$	−12501.5	−0.421613
$959$	9893.77	0.333146
$960$	0	0
$961$	−6114.75	−0.205255
$962$	39308.3	1.31741
$963$	16488.8	0.551760
$964$	24488.0	0.818160
$965$	0	0
$966$	5072.13	0.168937
$967$	31683.5	1.05364	0.526822	−	0.849976i	$-0.323384\pi$
$967$	31683.5	1.05364	0.526822	+	0.849976i	$0.323384\pi$
$968$	−25213.5	−0.837181
$969$	401.779	0.0133199
$970$	0	0
$971$	27098.4	0.895600	0.447800	−	0.894134i	$-0.352208\pi$
$971$	27098.4	0.895600	0.447800	+	0.894134i	$0.352208\pi$
$972$	1507.83	0.0497567
$973$	−38345.1	−1.26340
$974$	−2753.84	−0.0905943
$975$	0	0
$976$	−8635.46	−0.283211
$977$	−49633.9	−1.62531	−0.812655	−	0.582745i	$-0.801979\pi$
$977$	−49633.9	−1.62531	−0.812655	+	0.582745i	$0.801979\pi$
$978$	1299.25	0.0424799
$979$	3313.15	0.108160
$980$	0	0
$981$	−12038.8	−0.391815
$982$	−4783.11	−0.155433
$983$	−34761.1	−1.12788	−0.563940	−	0.825816i	$-0.690715\pi$
$983$	−34761.1	−1.12788	−0.563940	+	0.825816i	$0.690715\pi$
$984$	−1979.76	−0.0641387
$985$	0	0
$986$	849.254	0.0274298
$987$	12400.6	0.399914
$988$	−12823.7	−0.412930
$989$	15992.8	0.514199
$990$	0	0
$991$	19537.0	0.626249	0.313125	−	0.949712i	$-0.398624\pi$
$991$	19537.0	0.626249	0.313125	+	0.949712i	$0.398624\pi$
$992$	−28404.0	−0.909101
$993$	−12593.9	−0.402474
$994$	10384.5	0.331363
$995$	0	0
$996$	5953.82	0.189412
$997$	−33389.3	−1.06063	−0.530315	−	0.847801i	$-0.677926\pi$
$997$	−33389.3	−1.06063	−0.530315	+	0.847801i	$0.677926\pi$
$998$	424.646	0.0134689
$999$	−9252.20	−0.293020

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.4.a.f.1.6		14
5.4	even	2		1875.4.a.g.1.9		14
25.4	even	10		75.4.g.b.16.3	✓	28
25.19	even	10		75.4.g.b.61.3	yes	28
75.29	odd	10		225.4.h.a.91.5		28
75.44	odd	10		225.4.h.a.136.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.16.3	✓	28	25.4	even	10
75.4.g.b.61.3	yes	28	25.19	even	10
225.4.h.a.91.5		28	75.29	odd	10
225.4.h.a.136.5		28	75.44	odd	10
1875.4.a.f.1.6		14	1.1	even	1	trivial
1875.4.a.g.1.9		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)

\(f(q)\)	\(=\)	\(q-1.33976 q^{2} -3.00000 q^{3} -6.20504 q^{4} +4.01928 q^{6} +12.2101 q^{7} +19.0313 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.33976 q^{2} -3.00000 q^{3} -6.20504 q^{4} +4.01928 q^{6} +12.2101 q^{7} +19.0313 q^{8} +9.00000 q^{9} -2.48229 q^{11} +18.6151 q^{12} -85.6202 q^{13} -16.3586 q^{14} +24.1429 q^{16} +5.54850 q^{17} -12.0578 q^{18} -24.1374 q^{19} -36.6303 q^{21} +3.32567 q^{22} +103.353 q^{23} -57.0940 q^{24} +114.710 q^{26} -27.0000 q^{27} -75.7642 q^{28} -114.245 q^{29} +153.871 q^{31} -184.596 q^{32} +7.44687 q^{33} -7.43365 q^{34} -55.8454 q^{36} +342.674 q^{37} +32.3383 q^{38} +256.861 q^{39} +34.6755 q^{41} +49.0758 q^{42} +154.740 q^{43} +15.4027 q^{44} -138.468 q^{46} -338.534 q^{47} -72.4288 q^{48} -193.913 q^{49} -16.6455 q^{51} +531.277 q^{52} -645.636 q^{53} +36.1735 q^{54} +232.375 q^{56} +72.4123 q^{57} +153.060 q^{58} +662.854 q^{59} -357.681 q^{61} -206.150 q^{62} +109.891 q^{63} +54.1714 q^{64} -9.97701 q^{66} +531.377 q^{67} -34.4287 q^{68} -310.059 q^{69} -634.801 q^{71} +171.282 q^{72} -962.898 q^{73} -459.101 q^{74} +149.774 q^{76} -30.3090 q^{77} -344.131 q^{78} +568.744 q^{79} +81.0000 q^{81} -46.4568 q^{82} +319.838 q^{83} +227.293 q^{84} -207.315 q^{86} +342.734 q^{87} -47.2413 q^{88} -1334.71 q^{89} -1045.43 q^{91} -641.309 q^{92} -461.613 q^{93} +453.554 q^{94} +553.789 q^{96} -399.297 q^{97} +259.797 q^{98} -22.3406 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 42 q^{3} + 50 q^{4} + 27 q^{7} - 21 q^{8} + 126 q^{9}+O(q^{10}) \) 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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