LMFDB - Embedded newform 1875.4.a.g.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1875.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			1.9
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	$-0.423889\pi$
$2$	1.33976	0.473676	0.236838	+	0.971549i	$0.423889\pi$
$3$	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	$-0.606928\pi$
$7$	−12.2101	−0.659284	−0.329642	+	0.944106i	$0.606928\pi$
$8$	−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	$-0.133496\pi$
$13$	85.6202	1.82667	0.913337	+	0.407204i	$0.133496\pi$
$14$	−16.3586	−0.312287
$15$	0	0
$16$	24.1429	0.377233
$17$	−5.54850	−0.0791593	−0.0395797	−	0.999216i	$-0.512602\pi$
$17$	−5.54850	−0.0791593	−0.0395797	+	0.999216i	$0.512602\pi$
$18$	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	$-0.655202\pi$
$23$	−103.353	−0.936981	−0.468491	+	0.883468i	$0.655202\pi$
$24$	−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	$-0.775433\pi$
$37$	−342.674	−1.52258	−0.761288	+	0.648414i	$0.775433\pi$
$38$	−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	$-0.588476\pi$
$43$	−154.740	−0.548783	−0.274391	+	0.961618i	$0.588476\pi$
$44$	15.4027	0.0527738
$45$	0	0
$46$	−138.468	−0.443826
$47$	338.534	1.05064	0.525321	−	0.850904i	$-0.323945\pi$
$47$	338.534	1.05064	0.525321	+	0.850904i	$0.323945\pi$
$48$	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	$-0.184511\pi$
$53$	645.636	1.67330	0.836650	+	0.547738i	$0.184511\pi$
$54$	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	$-0.660985\pi$
$67$	−531.377	−0.968926	−0.484463	+	0.874812i	$0.660985\pi$
$68$	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	$-0.219302\pi$
$73$	962.898	1.54382	0.771909	+	0.635734i	$0.219302\pi$
$74$	−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	$-0.567830\pi$
$83$	−319.838	−0.422973	−0.211486	+	0.977381i	$0.567830\pi$
$84$	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	$-0.432985\pi$
$97$	399.297	0.417964	0.208982	+	0.977920i	$0.432985\pi$
$98$	−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	$-0.497131\pi$
$103$	18.8410	0.0180238	0.00901192	+	0.999959i	$0.497131\pi$
$104$	−1629.47	−1.53637
$105$	0	0
$106$	864.997	0.792603
$107$	−1832.09	−1.65528	−0.827640	−	0.561259i	$-0.810317\pi$
$107$	−1832.09	−1.65528	−0.827640	+	0.561259i	$0.810317\pi$
$108$	−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	$-0.495200\pi$
$113$	36.2244	0.0301566	0.0150783	+	0.999886i	$0.495200\pi$
$114$	−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	$-0.662368\pi$
$127$	−1397.61	−0.976520	−0.488260	+	0.872698i	$0.662368\pi$
$128$	−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	$-0.581304\pi$
$137$	−810.294	−0.505314	−0.252657	+	0.967556i	$0.581304\pi$
$138$	−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	$-0.731814\pi$
$157$	−2618.64	−1.33115	−0.665575	+	0.746331i	$0.731814\pi$
$158$	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	$-0.524747\pi$
$163$	−323.254	−0.155333	−0.0776663	+	0.996979i	$0.524747\pi$
$164$	−215.163	−0.102447
$165$	0	0
$166$	−428.505	−0.200352
$167$	158.987	0.0736692	0.0368346	−	0.999321i	$-0.488273\pi$
$167$	158.987	0.0736692	0.0368346	+	0.999321i	$0.488273\pi$
$168$	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	$-0.757475\pi$
$173$	−3292.67	−1.44703	−0.723516	+	0.690307i	$0.757475\pi$
$174$	−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	$-0.820106\pi$
$193$	−4528.65	−1.68901	−0.844506	+	0.535547i	$0.820106\pi$
$194$	534.962	0.197980
$195$	0	0
$196$	1203.24	0.438499
$197$	−2780.69	−1.00566	−0.502832	−	0.864384i	$-0.667709\pi$
$197$	−2780.69	−1.00566	−0.502832	+	0.864384i	$0.667709\pi$
$198$	−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	$-0.420925\pi$
$223$	1637.57	0.491748	0.245874	+	0.969302i	$0.420925\pi$
$224$	−2253.94	−0.672312
$225$	0	0
$226$	48.5319	0.0142845
$227$	−3793.11	−1.10906	−0.554532	−	0.832162i	$-0.687103\pi$
$227$	−3793.11	−1.10906	−0.554532	+	0.832162i	$0.687103\pi$
$228$	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	$-0.330130\pi$
$233$	3618.41	1.01738	0.508691	+	0.860949i	$0.330130\pi$
$234$	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	$-0.817319\pi$
$257$	−6919.87	−1.67957	−0.839785	+	0.542918i	$0.817319\pi$
$258$	−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	$-0.352679\pi$
$263$	3808.56	0.892951	0.446475	+	0.894796i	$0.352679\pi$
$264$	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	$-0.586263\pi$
$277$	−2468.28	−0.535396	−0.267698	+	0.963503i	$0.586263\pi$
$278$	−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	$-0.737080\pi$
$283$	−6454.03	−1.35566	−0.677831	+	0.735217i	$0.737080\pi$
$284$	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	$-0.473470\pi$
$293$	835.063	0.166501	0.0832507	+	0.996529i	$0.473470\pi$
$294$	−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	$-0.419803\pi$
$307$	2681.88	0.498577	0.249289	+	0.968429i	$0.419803\pi$
$308$	−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	$-0.254343\pi$
$313$	7723.68	1.39479	0.697394	+	0.716688i	$0.254343\pi$
$314$	−3508.35	−0.630534
$315$	0	0
$316$	−3529.08	−0.628248
$317$	3220.49	0.570602	0.285301	−	0.958438i	$-0.407907\pi$
$317$	3220.49	0.570602	0.285301	+	0.958438i	$0.407907\pi$
$318$	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	$-0.466879\pi$
$337$	1285.13	0.207731	0.103865	+	0.994591i	$0.466879\pi$
$338$	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	$-0.507663\pi$
$347$	−311.212	−0.0481461	−0.0240731	+	0.999710i	$0.507663\pi$
$348$	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	$-0.471098\pi$
$353$	1202.75	0.181349	0.0906743	+	0.995881i	$0.471098\pi$
$354$	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	$-0.503289\pi$
$367$	−145.288	−0.0206647	−0.0103324	+	0.999947i	$0.503289\pi$
$368$	−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	$-0.578549\pi$
$373$	−3519.41	−0.488547	−0.244274	+	0.969706i	$0.578549\pi$
$374$	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	$-0.590029\pi$
$383$	−4183.62	−0.558154	−0.279077	+	0.960269i	$0.590029\pi$
$384$	−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	$-0.722812\pi$
$397$	−10191.6	−1.28841	−0.644207	+	0.764852i	$0.722812\pi$
$398$	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	$-0.427905\pi$
$433$	4046.69	0.449126	0.224563	+	0.974460i	$0.427905\pi$
$434$	−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	$-0.460831\pi$
$443$	2288.91	0.245484	0.122742	+	0.992439i	$0.460831\pi$
$444$	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	$-0.553904\pi$
$457$	−3293.06	−0.337075	−0.168537	+	0.985695i	$0.553904\pi$
$458$	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	$-0.649656\pi$
$463$	−9026.62	−0.906053	−0.453027	+	0.891497i	$0.649656\pi$
$464$	−2758.20	−0.275962
$465$	0	0
$466$	4847.80	0.481910
$467$	1315.72	0.130373	0.0651867	−	0.997873i	$-0.479236\pi$
$467$	1315.72	0.130373	0.0651867	+	0.997873i	$0.479236\pi$
$468$	−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	$-0.530486\pi$
$487$	−2055.48	−0.191258	−0.0956288	+	0.995417i	$0.530486\pi$
$488$	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	$-0.655422\pi$
$503$	−10584.0	−0.938204	−0.469102	+	0.883144i	$0.655422\pi$
$504$	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	$-0.418786\pi$
$523$	6037.27	0.504764	0.252382	+	0.967628i	$0.418786\pi$
$524$	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	$-0.741001\pi$
$547$	−17573.7	−1.37367	−0.686836	+	0.726812i	$0.741001\pi$
$548$	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	$-0.855417\pi$
$557$	−23625.5	−1.79721	−0.898603	+	0.438764i	$0.855417\pi$
$558$	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	$-0.833839\pi$
$563$	−23159.1	−1.73364	−0.866819	+	0.498623i	$0.833839\pi$
$564$	−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	$-0.0971768\pi$
$577$	26438.3	1.90752	0.953760	+	0.300570i	$0.0971768\pi$
$578$	−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	$-0.567068\pi$
$587$	−5948.84	−0.418288	−0.209144	+	0.977885i	$0.567068\pi$
$588$	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	$-0.633434\pi$
$593$	−11755.3	−0.814054	−0.407027	+	0.913416i	$0.633434\pi$
$594$	−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	$-0.264547\pi$
$607$	20161.1	1.34813	0.674066	+	0.738672i	$0.264547\pi$
$608$	−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	$-0.533178\pi$
$613$	−3158.17	−0.208087	−0.104043	+	0.994573i	$0.533178\pi$
$614$	3593.08	0.236164
$615$	0	0
$616$	−576.821	−0.0377285
$617$	6576.62	0.429116	0.214558	−	0.976711i	$-0.431169\pi$
$617$	6576.62	0.429116	0.214558	+	0.976711i	$0.431169\pi$
$618$	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	$-0.604163\pi$
$643$	−10481.7	−0.642856	−0.321428	+	0.946934i	$0.604163\pi$
$644$	−7830.46	−0.479135
$645$	0	0
$646$	179.429	0.0109281
$647$	18921.8	1.14975	0.574877	−	0.818240i	$-0.305050\pi$
$647$	18921.8	1.14975	0.574877	+	0.818240i	$0.305050\pi$
$648$	−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	$-0.623824\pi$
$653$	−12657.4	−0.758536	−0.379268	+	0.925287i	$0.623824\pi$
$654$	−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	$-0.430439\pi$
$673$	7570.21	0.433596	0.216798	+	0.976216i	$0.430439\pi$
$674$	1721.76	0.0983972
$675$	0	0
$676$	−31855.6	−1.81245
$677$	−33332.1	−1.89226	−0.946128	−	0.323791i	$-0.895042\pi$
$677$	−33332.1	−1.89226	−0.946128	+	0.323791i	$0.895042\pi$
$678$	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	$-0.933172\pi$
$683$	−34915.5	−1.95608	−0.978042	+	0.208408i	$0.933172\pi$
$684$	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	$-0.582599\pi$
$727$	−10059.3	−0.513177	−0.256589	+	0.966521i	$0.582599\pi$
$728$	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	$-0.522968\pi$
$733$	−2861.45	−0.144189	−0.0720943	+	0.997398i	$0.522968\pi$
$734$	−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	$-0.490696\pi$
$743$	1183.79	0.0584508	0.0292254	+	0.999573i	$0.490696\pi$
$744$	−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	$-0.390884\pi$
$757$	14001.4	0.672246	0.336123	+	0.941818i	$0.390884\pi$
$758$	−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	$-0.562732\pi$
$773$	−8416.36	−0.391611	−0.195806	+	0.980643i	$0.562732\pi$
$774$	−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	$-0.590621\pi$
$787$	−12401.9	−0.561729	−0.280864	+	0.959747i	$0.590621\pi$
$788$	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	$-0.234139\pi$
$797$	33365.5	1.48290	0.741448	+	0.671010i	$0.234139\pi$
$798$	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	$-0.844145\pi$
$823$	−41672.3	−1.76501	−0.882505	+	0.470303i	$0.844145\pi$
$824$	−358.569	−0.0151594
$825$	0	0
$826$	−10843.4	−0.456767
$827$	−15362.1	−0.645939	−0.322969	−	0.946409i	$-0.604681\pi$
$827$	−15362.1	−0.645939	−0.322969	+	0.946409i	$0.604681\pi$
$828$	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	$-0.536978\pi$
$853$	−5775.19	−0.231816	−0.115908	+	0.993260i	$0.536978\pi$
$854$	5851.15	0.234452
$855$	0	0
$856$	34867.2	1.39221
$857$	−4100.45	−0.163441	−0.0817203	−	0.996655i	$-0.526041\pi$
$857$	−4100.45	−0.163441	−0.0817203	+	0.996655i	$0.526041\pi$
$858$	−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	$-0.390108\pi$
$863$	17159.3	0.676835	0.338418	+	0.940996i	$0.390108\pi$
$864$	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	$-0.554321\pi$
$877$	−8821.46	−0.339657	−0.169829	+	0.985474i	$0.554321\pi$
$878$	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	$-0.457490\pi$
$883$	6987.51	0.266306	0.133153	+	0.991095i	$0.457490\pi$
$884$	2947.79	0.112155
$885$	0	0
$886$	3066.58	0.116280
$887$	43884.1	1.66120	0.830599	−	0.556871i	$-0.187998\pi$
$887$	43884.1	1.66120	0.830599	+	0.556871i	$0.187998\pi$
$888$	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	$-0.377104\pi$
$907$	20572.4	0.753138	0.376569	+	0.926389i	$0.377104\pi$
$908$	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	$-0.346697\pi$
$937$	26571.7	0.926426	0.463213	+	0.886247i	$0.346697\pi$
$938$	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	$-0.205614\pi$
$947$	46541.8	1.59705	0.798525	+	0.601962i	$0.205614\pi$
$948$	−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	$-0.718238\pi$
$953$	−37254.2	−1.26630	−0.633149	+	0.774030i	$0.718238\pi$
$954$	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	$-0.676616\pi$
$967$	−31683.5	−1.05364	−0.526822	+	0.849976i	$0.676616\pi$
$968$	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	$-0.198021\pi$
$977$	49633.9	1.62531	0.812655	+	0.582745i	$0.198021\pi$
$978$	−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	$-0.309285\pi$
$983$	34761.1	1.12788	0.563940	+	0.825816i	$0.309285\pi$
$984$	−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	$-0.322074\pi$
$997$	33389.3	1.06063	0.530315	+	0.847801i	$0.322074\pi$
$998$	−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.g.1.9		14
5.4	even	2		1875.4.a.f.1.6		14
25.6	even	5		75.4.g.b.61.3	yes	28
25.21	even	5		75.4.g.b.16.3	✓	28
75.56	odd	10		225.4.h.a.136.5		28
75.71	odd	10		225.4.h.a.91.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.16.3	✓	28	25.21	even	5
75.4.g.b.61.3	yes	28	25.6	even	5
225.4.h.a.91.5		28	75.71	odd	10
225.4.h.a.136.5		28	75.56	odd	10
1875.4.a.f.1.6		14	5.4	even	2
1875.4.a.g.1.9		14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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