LMFDB - Embedded newform 1875.4.a.f.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:	$0$
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			1.9
Root			$-0.955230$ of defining polynomial
Character	$\chi$	$=$	1875.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.955230 q^{2} -3.00000 q^{3} -7.08754 q^{4} -2.86569 q^{6} -12.4836 q^{7} -14.4121 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+0.955230 q^{2} -3.00000 q^{3} -7.08754 q^{4} -2.86569 q^{6} -12.4836 q^{7} -14.4121 q^{8} +9.00000 q^{9} -44.7266 q^{11} +21.2626 q^{12} +7.13628 q^{13} -11.9247 q^{14} +42.9334 q^{16} -26.5116 q^{17} +8.59707 q^{18} -46.3901 q^{19} +37.4507 q^{21} -42.7241 q^{22} -145.454 q^{23} +43.2362 q^{24} +6.81679 q^{26} -27.0000 q^{27} +88.4777 q^{28} -213.354 q^{29} -148.082 q^{31} +156.308 q^{32} +134.180 q^{33} -25.3247 q^{34} -63.7878 q^{36} -402.312 q^{37} -44.3132 q^{38} -21.4089 q^{39} +233.656 q^{41} +35.7740 q^{42} -87.5080 q^{43} +317.001 q^{44} -138.942 q^{46} +75.9842 q^{47} -128.800 q^{48} -187.161 q^{49} +79.5348 q^{51} -50.5787 q^{52} -167.029 q^{53} -25.7912 q^{54} +179.914 q^{56} +139.170 q^{57} -203.802 q^{58} -595.082 q^{59} -865.794 q^{61} -141.452 q^{62} -112.352 q^{63} -194.158 q^{64} +128.172 q^{66} +406.302 q^{67} +187.902 q^{68} +436.361 q^{69} +526.158 q^{71} -129.709 q^{72} -1001.69 q^{73} -384.301 q^{74} +328.792 q^{76} +558.347 q^{77} -20.4504 q^{78} -133.956 q^{79} +81.0000 q^{81} +223.195 q^{82} -516.642 q^{83} -265.433 q^{84} -83.5903 q^{86} +640.061 q^{87} +644.602 q^{88} -610.698 q^{89} -89.0862 q^{91} +1030.91 q^{92} +444.246 q^{93} +72.5824 q^{94} -468.924 q^{96} +1639.57 q^{97} -178.782 q^{98} -402.539 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 42 q^{3} + 50 q^{4} + 27 q^{7} - 21 q^{8} + 126 q^{9}+O(q^{10}) $ 14 * q - 42 * q^3 + 50 * q^4 + 27 * q^7 - 21 * q^8 + 126 * q^9	$ 14 q - 42 q^{3} + 50 q^{4} + 27 q^{7} - 21 q^{8} + 126 q^{9} - 33 q^{11} - 150 q^{12} + 188 q^{13} - 287 q^{14} + 82 q^{16} + 146 q^{17} - 184 q^{19} - 81 q^{21} + 277 q^{22} + 164 q^{23} + 63 q^{24} + 103 q^{26} - 378 q^{27} - 224 q^{28} + 252 q^{29} - 889 q^{31} + 422 q^{32} + 99 q^{33} - 230 q^{34} + 450 q^{36} + 642 q^{37} + 1833 q^{38} - 564 q^{39} - 164 q^{41} + 861 q^{42} + 696 q^{43} - 6 q^{44} - 419 q^{46} - 92 q^{47} - 246 q^{48} + 81 q^{49} - 438 q^{51} + 1956 q^{52} + 949 q^{53} - 2380 q^{56} + 552 q^{57} + 1041 q^{58} - 81 q^{59} - 496 q^{61} + 1454 q^{62} + 243 q^{63} - 3903 q^{64} - 831 q^{66} + 1926 q^{67} + 685 q^{68} - 492 q^{69} + 2498 q^{71} - 189 q^{72} - 1026 q^{73} - 707 q^{74} - 5704 q^{76} + 5434 q^{77} - 309 q^{78} - 695 q^{79} + 1134 q^{81} - 886 q^{82} + 5315 q^{83} + 672 q^{84} + 3997 q^{86} - 756 q^{87} + 2969 q^{88} - 1424 q^{89} - 1194 q^{91} + 1607 q^{92} + 2667 q^{93} - 629 q^{94} - 1266 q^{96} + 291 q^{97} - 1018 q^{98} - 297 q^{99}+O(q^{100}) $ 14 * q - 42 * q^3 + 50 * q^4 + 27 * q^7 - 21 * q^8 + 126 * q^9 - 33 * q^11 - 150 * q^12 + 188 * q^13 - 287 * q^14 + 82 * q^16 + 146 * q^17 - 184 * q^19 - 81 * q^21 + 277 * q^22 + 164 * q^23 + 63 * q^24 + 103 * q^26 - 378 * q^27 - 224 * q^28 + 252 * q^29 - 889 * q^31 + 422 * q^32 + 99 * q^33 - 230 * q^34 + 450 * q^36 + 642 * q^37 + 1833 * q^38 - 564 * q^39 - 164 * q^41 + 861 * q^42 + 696 * q^43 - 6 * q^44 - 419 * q^46 - 92 * q^47 - 246 * q^48 + 81 * q^49 - 438 * q^51 + 1956 * q^52 + 949 * q^53 - 2380 * q^56 + 552 * q^57 + 1041 * q^58 - 81 * q^59 - 496 * q^61 + 1454 * q^62 + 243 * q^63 - 3903 * q^64 - 831 * q^66 + 1926 * q^67 + 685 * q^68 - 492 * q^69 + 2498 * q^71 - 189 * q^72 - 1026 * q^73 - 707 * q^74 - 5704 * q^76 + 5434 * q^77 - 309 * q^78 - 695 * q^79 + 1134 * q^81 - 886 * q^82 + 5315 * q^83 + 672 * q^84 + 3997 * q^86 - 756 * q^87 + 2969 * q^88 - 1424 * q^89 - 1194 * q^91 + 1607 * q^92 + 2667 * q^93 - 629 * q^94 - 1266 * q^96 + 291 * q^97 - 1018 * q^98 - 297 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.955230	0.337725	0.168862	−	0.985640i	$-0.445991\pi$
$2$	0.955230	0.337725	0.168862	+	0.985640i	$0.445991\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.08754	−0.885942
$5$	0	0
$5$	0	0
$6$	−2.86569	−0.194986
$7$	−12.4836	−0.674049	−0.337024	−	0.941496i	$-0.609420\pi$
$7$	−12.4836	−0.674049	−0.337024	+	0.941496i	$0.609420\pi$
$8$	−14.4121	−0.636929
$9$	9.00000	0.333333
$10$	0	0
$11$	−44.7266	−1.22596	−0.612980	−	0.790098i	$-0.710029\pi$
$11$	−44.7266	−1.22596	−0.612980	+	0.790098i	$0.710029\pi$
$12$	21.2626	0.511499
$13$	7.13628	0.152250	0.0761250	−	0.997098i	$-0.475745\pi$
$13$	7.13628	0.152250	0.0761250	+	0.997098i	$0.475745\pi$
$14$	−11.9247	−0.227643
$15$	0	0
$16$	42.9334	0.670835
$17$	−26.5116	−0.378236	−0.189118	−	0.981954i	$-0.560563\pi$
$17$	−26.5116	−0.378236	−0.189118	+	0.981954i	$0.560563\pi$
$18$	8.59707	0.112575
$19$	−46.3901	−0.560138	−0.280069	−	0.959980i	$-0.590357\pi$
$19$	−46.3901	−0.560138	−0.280069	+	0.959980i	$0.590357\pi$
$20$	0	0
$21$	37.4507	0.389162
$22$	−42.7241	−0.414037
$23$	−145.454	−1.31866	−0.659330	−	0.751854i	$-0.729160\pi$
$23$	−145.454	−1.31866	−0.659330	+	0.751854i	$0.729160\pi$
$24$	43.2362	0.367731
$25$	0	0
$26$	6.81679	0.0514186
$27$	−27.0000	−0.192450
$28$	88.4777	0.597168
$29$	−213.354	−1.36616	−0.683082	−	0.730341i	$-0.739361\pi$
$29$	−213.354	−1.36616	−0.683082	+	0.730341i	$0.739361\pi$
$30$	0	0
$31$	−148.082	−0.857945	−0.428972	−	0.903318i	$-0.641124\pi$
$31$	−148.082	−0.857945	−0.428972	+	0.903318i	$0.641124\pi$
$32$	156.308	0.863487
$33$	134.180	0.707809
$34$	−25.3247	−0.127740
$35$	0	0
$36$	−63.7878	−0.295314
$37$	−402.312	−1.78756	−0.893781	−	0.448505i	$-0.851957\pi$
$37$	−402.312	−1.78756	−0.893781	+	0.448505i	$0.851957\pi$
$38$	−44.3132	−0.189173
$39$	−21.4089	−0.0879015
$40$	0	0
$41$	233.656	0.890022	0.445011	−	0.895525i	$-0.353200\pi$
$41$	233.656	0.890022	0.445011	+	0.895525i	$0.353200\pi$
$42$	35.7740	0.131430
$43$	−87.5080	−0.310345	−0.155173	−	0.987887i	$-0.549593\pi$
$43$	−87.5080	−0.310345	−0.155173	+	0.987887i	$0.549593\pi$
$44$	317.001	1.08613
$45$	0	0
$46$	−138.942	−0.445344
$47$	75.9842	0.235818	0.117909	−	0.993024i	$-0.462381\pi$
$47$	75.9842	0.235818	0.117909	+	0.993024i	$0.462381\pi$
$48$	−128.800	−0.387307
$49$	−187.161	−0.545658
$50$	0	0
$51$	79.5348	0.218375
$52$	−50.5787	−0.134885
$53$	−167.029	−0.432891	−0.216446	−	0.976295i	$-0.569446\pi$
$53$	−167.029	−0.432891	−0.216446	+	0.976295i	$0.569446\pi$
$54$	−25.7912	−0.0649952
$55$	0	0
$56$	179.914	0.429321
$57$	139.170	0.323396
$58$	−203.802	−0.461388
$59$	−595.082	−1.31310	−0.656551	−	0.754282i	$-0.727985\pi$
$59$	−595.082	−1.31310	−0.656551	+	0.754282i	$0.727985\pi$
$60$	0	0
$61$	−865.794	−1.81727	−0.908636	−	0.417589i	$-0.862875\pi$
$61$	−865.794	−1.81727	−0.908636	+	0.417589i	$0.862875\pi$
$62$	−141.452	−0.289749
$63$	−112.352	−0.224683
$64$	−194.158	−0.379214
$65$	0	0
$66$	128.172	0.239044
$67$	406.302	0.740862	0.370431	−	0.928860i	$-0.379210\pi$
$67$	406.302	0.740862	0.370431	+	0.928860i	$0.379210\pi$
$68$	187.902	0.335095
$69$	436.361	0.761329
$70$	0	0
$71$	526.158	0.879486	0.439743	−	0.898124i	$-0.355070\pi$
$71$	526.158	0.879486	0.439743	+	0.898124i	$0.355070\pi$
$72$	−129.709	−0.212310
$73$	−1001.69	−1.60602	−0.803009	−	0.595967i	$-0.796769\pi$
$73$	−1001.69	−1.60602	−0.803009	+	0.595967i	$0.796769\pi$
$74$	−384.301	−0.603704
$75$	0	0
$76$	328.792	0.496250
$77$	558.347	0.826357
$78$	−20.4504	−0.0296865
$79$	−133.956	−0.190774	−0.0953872	−	0.995440i	$-0.530409\pi$
$79$	−133.956	−0.190774	−0.0953872	+	0.995440i	$0.530409\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	223.195	0.300582
$83$	−516.642	−0.683238	−0.341619	−	0.939838i	$-0.610975\pi$
$83$	−516.642	−0.683238	−0.341619	+	0.939838i	$0.610975\pi$
$84$	−265.433	−0.344775
$85$	0	0
$86$	−83.5903	−0.104811
$87$	640.061	0.788756
$88$	644.602	0.780850
$89$	−610.698	−0.727347	−0.363673	−	0.931527i	$-0.618478\pi$
$89$	−610.698	−0.727347	−0.363673	+	0.931527i	$0.618478\pi$
$90$	0	0
$91$	−89.0862	−0.102624
$92$	1030.91	1.16826
$93$	444.246	0.495335
$94$	72.5824	0.0796415
$95$	0	0
$96$	−468.924	−0.498534
$97$	1639.57	1.71621	0.858107	−	0.513471i	$-0.171641\pi$
$97$	1639.57	1.71621	0.858107	+	0.513471i	$0.171641\pi$
$98$	−178.782	−0.184282
$99$	−402.539	−0.408653
$100$	0	0
$101$	−433.248	−0.426830	−0.213415	−	0.976962i	$-0.568459\pi$
$101$	−433.248	−0.426830	−0.213415	+	0.976962i	$0.568459\pi$
$102$	75.9741	0.0737505
$103$	−81.3244	−0.0777974	−0.0388987	−	0.999243i	$-0.512385\pi$
$103$	−81.3244	−0.0777974	−0.0388987	+	0.999243i	$0.512385\pi$
$104$	−102.849	−0.0969725
$105$	0	0
$106$	−159.551	−0.146198
$107$	−391.773	−0.353964	−0.176982	−	0.984214i	$-0.556633\pi$
$107$	−391.773	−0.353964	−0.176982	+	0.984214i	$0.556633\pi$
$108$	191.363	0.170500
$109$	1815.92	1.59572	0.797862	−	0.602840i	$-0.205964\pi$
$109$	1815.92	1.59572	0.797862	+	0.602840i	$0.205964\pi$
$110$	0	0
$111$	1206.94	1.03205
$112$	−535.962	−0.452176
$113$	−1087.20	−0.905094	−0.452547	−	0.891741i	$-0.649485\pi$
$113$	−1087.20	−0.905094	−0.452547	+	0.891741i	$0.649485\pi$
$114$	132.940	0.109219
$115$	0	0
$116$	1512.15	1.21034
$117$	64.2266	0.0507500
$118$	−568.440	−0.443467
$119$	330.959	0.254949
$120$	0	0
$121$	669.465	0.502979
$122$	−827.033	−0.613738
$123$	−700.967	−0.513854
$124$	1049.54	0.760089
$125$	0	0
$126$	−107.322	−0.0758810
$127$	−871.466	−0.608898	−0.304449	−	0.952529i	$-0.598472\pi$
$127$	−871.466	−0.608898	−0.304449	+	0.952529i	$0.598472\pi$
$128$	−1435.93	−0.991557
$129$	262.524	0.179178
$130$	0	0
$131$	1708.16	1.13925	0.569627	−	0.821904i	$-0.307088\pi$
$131$	1708.16	1.13925	0.569627	+	0.821904i	$0.307088\pi$
$132$	−951.003	−0.627077
$133$	579.114	0.377560
$134$	388.112	0.250207
$135$	0	0
$136$	382.087	0.240910
$137$	2401.86	1.49784	0.748921	−	0.662659i	$-0.230572\pi$
$137$	2401.86	1.49784	0.748921	+	0.662659i	$0.230572\pi$
$138$	416.825	0.257120
$139$	−2161.94	−1.31923	−0.659617	−	0.751602i	$-0.729282\pi$
$139$	−2161.94	−1.31923	−0.659617	+	0.751602i	$0.729282\pi$
$140$	0	0
$141$	−227.953	−0.136150
$142$	502.602	0.297024
$143$	−319.181	−0.186652
$144$	386.401	0.223612
$145$	0	0
$146$	−956.847	−0.542392
$147$	561.482	0.315036
$148$	2851.40	1.58368
$149$	−1527.70	−0.839959	−0.419980	−	0.907534i	$-0.637963\pi$
$149$	−1527.70	−0.839959	−0.419980	+	0.907534i	$0.637963\pi$
$150$	0	0
$151$	2584.71	1.39299	0.696493	−	0.717564i	$-0.254743\pi$
$151$	2584.71	1.39299	0.696493	+	0.717564i	$0.254743\pi$
$152$	668.578	0.356768
$153$	−238.605	−0.126079
$154$	533.349	0.279081
$155$	0	0
$156$	151.736	0.0778757
$157$	692.965	0.352259	0.176129	−	0.984367i	$-0.443642\pi$
$157$	692.965	0.352259	0.176129	+	0.984367i	$0.443642\pi$
$158$	−127.958	−0.0644293
$159$	501.088	0.249930
$160$	0	0
$161$	1815.78	0.888841
$162$	77.3736	0.0375250
$163$	3620.52	1.73976	0.869881	−	0.493262i	$-0.164195\pi$
$163$	3620.52	1.73976	0.869881	+	0.493262i	$0.164195\pi$
$164$	−1656.04	−0.788508
$165$	0	0
$166$	−493.511	−0.230746
$167$	−1555.61	−0.720817	−0.360409	−	0.932794i	$-0.617363\pi$
$167$	−1555.61	−0.720817	−0.360409	+	0.932794i	$0.617363\pi$
$168$	−539.742	−0.247869
$169$	−2146.07	−0.976820
$170$	0	0
$171$	−417.511	−0.186713
$172$	620.216	0.274948
$173$	2175.91	0.956250	0.478125	−	0.878292i	$-0.341317\pi$
$173$	2175.91	0.956250	0.478125	+	0.878292i	$0.341317\pi$
$174$	611.405	0.266382
$175$	0	0
$176$	−1920.27	−0.822417
$177$	1785.24	0.758120
$178$	−583.357	−0.245643
$179$	−1865.44	−0.778937	−0.389468	−	0.921040i	$-0.627341\pi$
$179$	−1865.44	−0.778937	−0.389468	+	0.921040i	$0.627341\pi$
$180$	0	0
$181$	−257.830	−0.105881	−0.0529403	−	0.998598i	$-0.516859\pi$
$181$	−257.830	−0.105881	−0.0529403	+	0.998598i	$0.516859\pi$
$182$	−85.0978	−0.0346586
$183$	2597.38	1.04920
$184$	2096.29	0.839893
$185$	0	0
$186$	424.357	0.167287
$187$	1185.77	0.463702
$188$	−538.541	−0.208921
$189$	337.056	0.129721
$190$	0	0
$191$	−3960.87	−1.50052	−0.750258	−	0.661145i	$-0.770071\pi$
$191$	−3960.87	−1.50052	−0.750258	+	0.661145i	$0.770071\pi$
$192$	582.473	0.218939
$193$	−1253.72	−0.467590	−0.233795	−	0.972286i	$-0.575114\pi$
$193$	−1253.72	−0.467590	−0.233795	+	0.972286i	$0.575114\pi$
$194$	1566.16	0.579608
$195$	0	0
$196$	1326.51	0.483422
$197$	5059.84	1.82994	0.914971	−	0.403519i	$-0.132213\pi$
$197$	5059.84	1.82994	0.914971	+	0.403519i	$0.132213\pi$
$198$	−384.517	−0.138012
$199$	−5323.91	−1.89649	−0.948246	−	0.317536i	$-0.897145\pi$
$199$	−5323.91	−1.89649	−0.948246	+	0.317536i	$0.897145\pi$
$200$	0	0
$201$	−1218.91	−0.427737
$202$	−413.852	−0.144151
$203$	2663.41	0.920862
$204$	−563.706	−0.193467
$205$	0	0
$206$	−77.6835	−0.0262741
$207$	−1309.08	−0.439553
$208$	306.385	0.102135
$209$	2074.87	0.686707
$210$	0	0
$211$	−1029.61	−0.335931	−0.167965	−	0.985793i	$-0.553720\pi$
$211$	−1029.61	−0.335931	−0.167965	+	0.985793i	$0.553720\pi$
$212$	1183.83	0.383517
$213$	−1578.47	−0.507771
$214$	−374.233	−0.119542
$215$	0	0
$216$	389.126	0.122577
$217$	1848.59	0.578297
$218$	1734.62	0.538915
$219$	3005.08	0.927235
$220$	0	0
$221$	−189.194	−0.0575864
$222$	1152.90	0.348548
$223$	−1245.08	−0.373886	−0.186943	−	0.982371i	$-0.559858\pi$
$223$	−1245.08	−0.373886	−0.186943	+	0.982371i	$0.559858\pi$
$224$	−1951.28	−0.582032
$225$	0	0
$226$	−1038.53	−0.305673
$227$	4598.29	1.34449	0.672245	−	0.740329i	$-0.265330\pi$
$227$	4598.29	1.34449	0.672245	+	0.740329i	$0.265330\pi$
$228$	−986.375	−0.286510
$229$	6354.76	1.83378	0.916888	−	0.399145i	$-0.130693\pi$
$229$	6354.76	1.83378	0.916888	+	0.399145i	$0.130693\pi$
$230$	0	0
$231$	−1675.04	−0.477097
$232$	3074.87	0.870150
$233$	−635.967	−0.178814	−0.0894068	−	0.995995i	$-0.528497\pi$
$233$	−635.967	−0.178814	−0.0894068	+	0.995995i	$0.528497\pi$
$234$	61.3511	0.0171395
$235$	0	0
$236$	4217.66	1.16333
$237$	401.867	0.110144
$238$	316.142	0.0861028
$239$	−6458.06	−1.74786	−0.873928	−	0.486056i	$-0.838435\pi$
$239$	−6458.06	−1.74786	−0.873928	+	0.486056i	$0.838435\pi$
$240$	0	0
$241$	509.747	0.136248	0.0681239	−	0.997677i	$-0.478299\pi$
$241$	509.747	0.136248	0.0681239	+	0.997677i	$0.478299\pi$
$242$	639.493	0.169868
$243$	−243.000	−0.0641500
$244$	6136.35	1.61000
$245$	0	0
$246$	−669.585	−0.173541
$247$	−331.053	−0.0852810
$248$	2134.17	0.546450
$249$	1549.92	0.394468
$250$	0	0
$251$	2645.82	0.665349	0.332674	−	0.943042i	$-0.392049\pi$
$251$	2645.82	0.665349	0.332674	+	0.943042i	$0.392049\pi$
$252$	796.299	0.199056
$253$	6505.64	1.61662
$254$	−832.450	−0.205640
$255$	0	0
$256$	181.620	0.0443408
$257$	3975.12	0.964829	0.482415	−	0.875943i	$-0.339760\pi$
$257$	3975.12	0.964829	0.482415	+	0.875943i	$0.339760\pi$
$258$	250.771	0.0605128
$259$	5022.29	1.20490
$260$	0	0
$261$	−1920.18	−0.455388
$262$	1631.68	0.384754
$263$	−4820.25	−1.13015	−0.565075	−	0.825040i	$-0.691153\pi$
$263$	−4820.25	−1.13015	−0.565075	+	0.825040i	$0.691153\pi$
$264$	−1933.81	−0.450824
$265$	0	0
$266$	553.187	0.127512
$267$	1832.09	0.419934
$268$	−2879.68	−0.656360
$269$	4196.29	0.951123	0.475562	−	0.879682i	$-0.342245\pi$
$269$	4196.29	0.951123	0.475562	+	0.879682i	$0.342245\pi$
$270$	0	0
$271$	−2039.98	−0.457269	−0.228634	−	0.973512i	$-0.573426\pi$
$271$	−2039.98	−0.457269	−0.228634	+	0.973512i	$0.573426\pi$
$272$	−1138.24	−0.253734
$273$	267.259	0.0592499
$274$	2294.32	0.505858
$275$	0	0
$276$	−3092.72	−0.674493
$277$	4613.40	1.00069	0.500347	−	0.865825i	$-0.333206\pi$
$277$	4613.40	1.00069	0.500347	+	0.865825i	$0.333206\pi$
$278$	−2065.15	−0.445538
$279$	−1332.74	−0.285982
$280$	0	0
$281$	−2512.14	−0.533317	−0.266658	−	0.963791i	$-0.585919\pi$
$281$	−2512.14	−0.533317	−0.266658	+	0.963791i	$0.585919\pi$
$282$	−217.747	−0.0459811
$283$	−1061.91	−0.223054	−0.111527	−	0.993761i	$-0.535574\pi$
$283$	−1061.91	−0.223054	−0.111527	+	0.993761i	$0.535574\pi$
$284$	−3729.17	−0.779174
$285$	0	0
$286$	−304.892	−0.0630371
$287$	−2916.85	−0.599918
$288$	1406.77	0.287829
$289$	−4210.13	−0.856938
$290$	0	0
$291$	−4918.70	−0.990856
$292$	7099.54	1.42284
$293$	7941.52	1.58344	0.791721	−	0.610883i	$-0.209186\pi$
$293$	7941.52	1.58344	0.791721	+	0.610883i	$0.209186\pi$
$294$	536.345	0.106395
$295$	0	0
$296$	5798.15	1.13855
$297$	1207.62	0.235936
$298$	−1459.30	−0.283675
$299$	−1038.00	−0.200766
$300$	0	0
$301$	1092.41	0.209188
$302$	2468.99	0.470446
$303$	1299.75	0.246430
$304$	−1991.69	−0.375760
$305$	0	0
$306$	−227.922	−0.0425799
$307$	5405.88	1.00498	0.502492	−	0.864582i	$-0.332417\pi$
$307$	5405.88	1.00498	0.502492	+	0.864582i	$0.332417\pi$
$308$	−3957.30	−0.732104
$309$	243.973	0.0449164
$310$	0	0
$311$	−4625.83	−0.843431	−0.421715	−	0.906728i	$-0.638572\pi$
$311$	−4625.83	−0.843431	−0.421715	+	0.906728i	$0.638572\pi$
$312$	308.546	0.0559871
$313$	1053.32	0.190214	0.0951069	−	0.995467i	$-0.469681\pi$
$313$	1053.32	0.190214	0.0951069	+	0.995467i	$0.469681\pi$
$314$	661.941	0.118967
$315$	0	0
$316$	949.415	0.169015
$317$	−2710.00	−0.480154	−0.240077	−	0.970754i	$-0.577173\pi$
$317$	−2710.00	−0.480154	−0.240077	+	0.970754i	$0.577173\pi$
$318$	478.654	0.0844075
$319$	9542.57	1.67486
$320$	0	0
$321$	1175.32	0.204361
$322$	1734.49	0.300184
$323$	1229.88	0.211864
$324$	−574.090	−0.0984380
$325$	0	0
$326$	3458.43	0.587561
$327$	−5447.77	−0.921292
$328$	−3367.46	−0.566881
$329$	−948.554	−0.158953
$330$	0	0
$331$	−4387.70	−0.728609	−0.364304	−	0.931280i	$-0.618693\pi$
$331$	−4387.70	−0.728609	−0.364304	+	0.931280i	$0.618693\pi$
$332$	3661.72	0.605309
$333$	−3620.81	−0.595854
$334$	−1485.96	−0.243438
$335$	0	0
$336$	1607.89	0.261064
$337$	3872.64	0.625983	0.312992	−	0.949756i	$-0.398669\pi$
$337$	3872.64	0.625983	0.312992	+	0.949756i	$0.398669\pi$
$338$	−2049.99	−0.329896
$339$	3261.61	0.522556
$340$	0	0
$341$	6623.19	1.05181
$342$	−398.819	−0.0630575
$343$	6618.29	1.04185
$344$	1261.17	0.197668
$345$	0	0
$346$	2078.49	0.322949
$347$	−5782.93	−0.894651	−0.447326	−	0.894371i	$-0.647623\pi$
$347$	−5782.93	−0.894651	−0.447326	+	0.894371i	$0.647623\pi$
$348$	−4536.45	−0.698792
$349$	−2916.63	−0.447345	−0.223673	−	0.974664i	$-0.571805\pi$
$349$	−2916.63	−0.447345	−0.223673	+	0.974664i	$0.571805\pi$
$350$	0	0
$351$	−192.680	−0.0293005
$352$	−6991.11	−1.05860
$353$	3487.56	0.525847	0.262924	−	0.964817i	$-0.415313\pi$
$353$	3487.56	0.525847	0.262924	+	0.964817i	$0.415313\pi$
$354$	1705.32	0.256036
$355$	0	0
$356$	4328.34	0.644387
$357$	−992.878	−0.147195
$358$	−1781.93	−0.263066
$359$	10606.5	1.55931	0.779653	−	0.626212i	$-0.215396\pi$
$359$	10606.5	1.55931	0.779653	+	0.626212i	$0.215396\pi$
$360$	0	0
$361$	−4706.96	−0.686245
$362$	−246.287	−0.0357585
$363$	−2008.39	−0.290395
$364$	631.402	0.0909188
$365$	0	0
$366$	2481.10	0.354342
$367$	2685.12	0.381913	0.190957	−	0.981598i	$-0.438841\pi$
$367$	2685.12	0.381913	0.190957	+	0.981598i	$0.438841\pi$
$368$	−6244.83	−0.884604
$369$	2102.90	0.296674
$370$	0	0
$371$	2085.12	0.291790
$372$	−3148.61	−0.438838
$373$	688.479	0.0955712	0.0477856	−	0.998858i	$-0.484784\pi$
$373$	688.479	0.0955712	0.0477856	+	0.998858i	$0.484784\pi$
$374$	1132.69	0.156604
$375$	0	0
$376$	−1095.09	−0.150199
$377$	−1522.55	−0.207999
$378$	321.966	0.0438099
$379$	−12235.4	−1.65829	−0.829146	−	0.559033i	$-0.811173\pi$
$379$	−12235.4	−1.65829	−0.829146	+	0.559033i	$0.811173\pi$
$380$	0	0
$381$	2614.40	0.351548
$382$	−3783.54	−0.506762
$383$	−1902.17	−0.253777	−0.126888	−	0.991917i	$-0.540499\pi$
$383$	−1902.17	−0.253777	−0.126888	+	0.991917i	$0.540499\pi$
$384$	4307.78	0.572476
$385$	0	0
$386$	−1197.59	−0.157917
$387$	−787.572	−0.103448
$388$	−11620.5	−1.52047
$389$	187.985	0.0245019	0.0122509	−	0.999925i	$-0.496100\pi$
$389$	187.985	0.0245019	0.0122509	+	0.999925i	$0.496100\pi$
$390$	0	0
$391$	3856.21	0.498765
$392$	2697.37	0.347546
$393$	−5124.47	−0.657748
$394$	4833.31	0.618017
$395$	0	0
$396$	2853.01	0.362043
$397$	7547.41	0.954140	0.477070	−	0.878865i	$-0.341699\pi$
$397$	7547.41	0.954140	0.477070	+	0.878865i	$0.341699\pi$
$398$	−5085.56	−0.640493
$399$	−1737.34	−0.217985
$400$	0	0
$401$	5396.95	0.672097	0.336049	−	0.941845i	$-0.390909\pi$
$401$	5396.95	0.672097	0.336049	+	0.941845i	$0.390909\pi$
$402$	−1164.34	−0.144457
$403$	−1056.75	−0.130622
$404$	3070.66	0.378147
$405$	0	0
$406$	2544.17	0.310998
$407$	17994.1	2.19148
$408$	−1146.26	−0.139089
$409$	−4090.41	−0.494518	−0.247259	−	0.968949i	$-0.579530\pi$
$409$	−4090.41	−0.494518	−0.247259	+	0.968949i	$0.579530\pi$
$410$	0	0
$411$	−7205.57	−0.864780
$412$	576.390	0.0689240
$413$	7428.73	0.885095
$414$	−1250.48	−0.148448
$415$	0	0
$416$	1115.46	0.131466
$417$	6485.83	0.761661
$418$	1981.98	0.231918
$419$	2841.80	0.331339	0.165670	−	0.986181i	$-0.447021\pi$
$419$	2841.80	0.331339	0.165670	+	0.986181i	$0.447021\pi$
$420$	0	0
$421$	−16539.8	−1.91473	−0.957363	−	0.288889i	$-0.906714\pi$
$421$	−16539.8	−1.91473	−0.957363	+	0.288889i	$0.906714\pi$
$422$	−983.516	−0.113452
$423$	683.858	0.0786060
$424$	2407.24	0.275721
$425$	0	0
$426$	−1507.81	−0.171487
$427$	10808.2	1.22493
$428$	2776.71	0.313592
$429$	957.544	0.107764
$430$	0	0
$431$	−2301.49	−0.257214	−0.128607	−	0.991696i	$-0.541050\pi$
$431$	−2301.49	−0.257214	−0.128607	+	0.991696i	$0.541050\pi$
$432$	−1159.20	−0.129102
$433$	7556.52	0.838668	0.419334	−	0.907832i	$-0.362264\pi$
$433$	7556.52	0.838668	0.419334	+	0.907832i	$0.362264\pi$
$434$	1765.83	0.195305
$435$	0	0
$436$	−12870.4	−1.41372
$437$	6747.61	0.738632
$438$	2870.54	0.313150
$439$	−8328.02	−0.905409	−0.452705	−	0.891660i	$-0.649541\pi$
$439$	−8328.02	−0.905409	−0.452705	+	0.891660i	$0.649541\pi$
$440$	0	0
$441$	−1684.45	−0.181886
$442$	−180.724	−0.0194484
$443$	−11675.9	−1.25223	−0.626114	−	0.779731i	$-0.715356\pi$
$443$	−11675.9	−1.25223	−0.626114	+	0.779731i	$0.715356\pi$
$444$	−8554.21	−0.914335
$445$	0	0
$446$	−1189.34	−0.126271
$447$	4583.10	0.484951
$448$	2423.78	0.255609
$449$	−1034.94	−0.108779	−0.0543893	−	0.998520i	$-0.517321\pi$
$449$	−1034.94	−0.108779	−0.0543893	+	0.998520i	$0.517321\pi$
$450$	0	0
$451$	−10450.6	−1.09113
$452$	7705.60	0.801861
$453$	−7754.13	−0.804241
$454$	4392.43	0.454068
$455$	0	0
$456$	−2005.73	−0.205980
$457$	−15279.9	−1.56403	−0.782016	−	0.623259i	$-0.785808\pi$
$457$	−15279.9	−1.56403	−0.782016	+	0.623259i	$0.785808\pi$
$458$	6070.26	0.619311
$459$	715.814	0.0727915
$460$	0	0
$461$	15795.3	1.59580	0.797898	−	0.602793i	$-0.205946\pi$
$461$	15795.3	1.59580	0.797898	+	0.602793i	$0.205946\pi$
$462$	−1600.05	−0.161128
$463$	−1773.18	−0.177985	−0.0889923	−	0.996032i	$-0.528365\pi$
$463$	−1773.18	−0.177985	−0.0889923	+	0.996032i	$0.528365\pi$
$464$	−9160.01	−0.916471
$465$	0	0
$466$	−607.494	−0.0603898
$467$	−13051.2	−1.29323	−0.646615	−	0.762817i	$-0.723816\pi$
$467$	−13051.2	−1.29323	−0.646615	+	0.762817i	$0.723816\pi$
$468$	−455.208	−0.0449615
$469$	−5072.10	−0.499377
$470$	0	0
$471$	−2078.90	−0.203377
$472$	8576.35	0.836353
$473$	3913.93	0.380471
$474$	383.875	0.0371982
$475$	0	0
$476$	−2345.69	−0.225870
$477$	−1503.26	−0.144297
$478$	−6168.94	−0.590294
$479$	−633.119	−0.0603924	−0.0301962	−	0.999544i	$-0.509613\pi$
$479$	−633.119	−0.0603924	−0.0301962	+	0.999544i	$0.509613\pi$
$480$	0	0
$481$	−2871.02	−0.272156
$482$	486.926	0.0460142
$483$	−5447.34	−0.513173
$484$	−4744.85	−0.445610
$485$	0	0
$486$	−232.121	−0.0216651
$487$	6437.29	0.598976	0.299488	−	0.954100i	$-0.403184\pi$
$487$	6437.29	0.598976	0.299488	+	0.954100i	$0.403184\pi$
$488$	12477.9	1.15747
$489$	−10861.6	−1.00445
$490$	0	0
$491$	3114.41	0.286256	0.143128	−	0.989704i	$-0.454284\pi$
$491$	3114.41	0.286256	0.143128	+	0.989704i	$0.454284\pi$
$492$	4968.13	0.455245
$493$	5656.35	0.516733
$494$	−316.232	−0.0288015
$495$	0	0
$496$	−6357.67	−0.575540
$497$	−6568.33	−0.592816
$498$	1480.53	0.133222
$499$	−7664.80	−0.687623	−0.343811	−	0.939039i	$-0.611718\pi$
$499$	−7664.80	−0.687623	−0.343811	+	0.939039i	$0.611718\pi$
$500$	0	0
$501$	4666.82	0.416164
$502$	2527.37	0.224705
$503$	−8278.58	−0.733844	−0.366922	−	0.930252i	$-0.619588\pi$
$503$	−8278.58	−0.733844	−0.366922	+	0.930252i	$0.619588\pi$
$504$	1619.22	0.143107
$505$	0	0
$506$	6214.38	0.545974
$507$	6438.22	0.563967
$508$	6176.55	0.539449
$509$	−7111.22	−0.619252	−0.309626	−	0.950858i	$-0.600204\pi$
$509$	−7111.22	−0.619252	−0.309626	+	0.950858i	$0.600204\pi$
$510$	0	0
$511$	12504.7	1.08253
$512$	11660.9	1.00653
$513$	1252.53	0.107799
$514$	3797.15	0.325847
$515$	0	0
$516$	−1860.65	−0.158741
$517$	−3398.51	−0.289103
$518$	4797.44	0.406926
$519$	−6527.72	−0.552091
$520$	0	0
$521$	−812.539	−0.0683262	−0.0341631	−	0.999416i	$-0.510877\pi$
$521$	−812.539	−0.0683262	−0.0341631	+	0.999416i	$0.510877\pi$
$522$	−1834.22	−0.153796
$523$	−6446.12	−0.538946	−0.269473	−	0.963008i	$-0.586850\pi$
$523$	−6446.12	−0.538946	−0.269473	+	0.963008i	$0.586850\pi$
$524$	−12106.6	−1.00931
$525$	0	0
$526$	−4604.45	−0.381680
$527$	3925.89	0.324506
$528$	5760.80	0.474823
$529$	8989.76	0.738865
$530$	0	0
$531$	−5355.73	−0.437701
$532$	−4104.49	−0.334497
$533$	1667.43	0.135506
$534$	1750.07	0.141822
$535$	0	0
$536$	−5855.66	−0.471877
$537$	5596.33	0.449719
$538$	4008.42	0.321218
$539$	8371.06	0.668955
$540$	0	0
$541$	−4552.44	−0.361783	−0.180892	−	0.983503i	$-0.557898\pi$
$541$	−4552.44	−0.361783	−0.180892	+	0.983503i	$0.557898\pi$
$542$	−1948.65	−0.154431
$543$	773.491	0.0611302
$544$	−4143.97	−0.326602
$545$	0	0
$546$	255.293	0.0200102
$547$	−14318.6	−1.11923	−0.559615	−	0.828753i	$-0.689051\pi$
$547$	−14318.6	−1.11923	−0.559615	+	0.828753i	$0.689051\pi$
$548$	−17023.2	−1.32700
$549$	−7792.15	−0.605757
$550$	0	0
$551$	9897.50	0.765241
$552$	−6288.86	−0.484913
$553$	1672.24	0.128591
$554$	4406.86	0.337959
$555$	0	0
$556$	15322.8	1.16877
$557$	14882.2	1.13210	0.566050	−	0.824371i	$-0.308471\pi$
$557$	14882.2	1.13210	0.566050	+	0.824371i	$0.308471\pi$
$558$	−1273.07	−0.0965831
$559$	−624.482	−0.0472500
$560$	0	0
$561$	−3557.32	−0.267719
$562$	−2399.68	−0.180114
$563$	−5655.46	−0.423356	−0.211678	−	0.977339i	$-0.567893\pi$
$563$	−5655.46	−0.423356	−0.211678	+	0.977339i	$0.567893\pi$
$564$	1615.62	0.120621
$565$	0	0
$566$	−1014.37	−0.0753308
$567$	−1011.17	−0.0748943
$568$	−7583.03	−0.560170
$569$	−10016.7	−0.738001	−0.369001	−	0.929429i	$-0.620300\pi$
$569$	−10016.7	−0.738001	−0.369001	+	0.929429i	$0.620300\pi$
$570$	0	0
$571$	−17386.3	−1.27424	−0.637121	−	0.770764i	$-0.719875\pi$
$571$	−17386.3	−1.27424	−0.637121	+	0.770764i	$0.719875\pi$
$572$	2262.21	0.165363
$573$	11882.6	0.866324
$574$	−2786.27	−0.202607
$575$	0	0
$576$	−1747.42	−0.126405
$577$	8886.10	0.641132	0.320566	−	0.947226i	$-0.396127\pi$
$577$	8886.10	0.641132	0.320566	+	0.947226i	$0.396127\pi$
$578$	−4021.65	−0.289409
$579$	3761.16	0.269963
$580$	0	0
$581$	6449.52	0.460536
$582$	−4698.49	−0.334637
$583$	7470.65	0.530708
$584$	14436.5	1.02292
$585$	0	0
$586$	7585.97	0.534767
$587$	−20817.3	−1.46375	−0.731876	−	0.681438i	$-0.761355\pi$
$587$	−20817.3	−1.46375	−0.731876	+	0.681438i	$0.761355\pi$
$588$	−3979.53	−0.279104
$589$	6869.54	0.480568
$590$	0	0
$591$	−15179.5	−1.05652
$592$	−17272.7	−1.19916
$593$	−24320.9	−1.68422	−0.842108	−	0.539309i	$-0.818686\pi$
$593$	−24320.9	−1.68422	−0.842108	+	0.539309i	$0.818686\pi$
$594$	1153.55	0.0796815
$595$	0	0
$596$	10827.6	0.744155
$597$	15971.7	1.09494
$598$	−991.527	−0.0678036
$599$	18650.6	1.27219	0.636096	−	0.771610i	$-0.280548\pi$
$599$	18650.6	1.27219	0.636096	+	0.771610i	$0.280548\pi$
$600$	0	0
$601$	−15558.8	−1.05600	−0.528000	−	0.849245i	$-0.677058\pi$
$601$	−15558.8	−1.05600	−0.528000	+	0.849245i	$0.677058\pi$
$602$	1043.50	0.0706479
$603$	3656.72	0.246954
$604$	−18319.2	−1.23410
$605$	0	0
$606$	1241.56	0.0832257
$607$	−27620.1	−1.84690	−0.923448	−	0.383722i	$-0.874642\pi$
$607$	−27620.1	−1.84690	−0.923448	+	0.383722i	$0.874642\pi$
$608$	−7251.14	−0.483672
$609$	−7990.24	−0.531660
$610$	0	0
$611$	542.245	0.0359033
$612$	1691.12	0.111698
$613$	10581.1	0.697173	0.348587	−	0.937277i	$-0.386662\pi$
$613$	10581.1	0.697173	0.348587	+	0.937277i	$0.386662\pi$
$614$	5163.86	0.339408
$615$	0	0
$616$	−8046.93	−0.526331
$617$	−26415.2	−1.72356	−0.861780	−	0.507283i	$-0.830650\pi$
$617$	−26415.2	−1.72356	−0.861780	+	0.507283i	$0.830650\pi$
$618$	233.051	0.0151694
$619$	−4747.92	−0.308296	−0.154148	−	0.988048i	$-0.549263\pi$
$619$	−4747.92	−0.308296	−0.154148	+	0.988048i	$0.549263\pi$
$620$	0	0
$621$	3927.25	0.253776
$622$	−4418.73	−0.284847
$623$	7623.68	0.490267
$624$	−919.156	−0.0589674
$625$	0	0
$626$	1006.16	0.0642399
$627$	−6224.61	−0.396471
$628$	−4911.42	−0.312081
$629$	10666.0	0.676120
$630$	0	0
$631$	−24505.3	−1.54602	−0.773012	−	0.634391i	$-0.781251\pi$
$631$	−24505.3	−1.54602	−0.773012	+	0.634391i	$0.781251\pi$
$632$	1930.58	0.121510
$633$	3088.84	0.193950
$634$	−2588.68	−0.162160
$635$	0	0
$636$	−3551.48	−0.221423
$637$	−1335.63	−0.0830764
$638$	9115.35	0.565643
$639$	4735.42	0.293162
$640$	0	0
$641$	−6380.17	−0.393138	−0.196569	−	0.980490i	$-0.562980\pi$
$641$	−6380.17	−0.393138	−0.196569	+	0.980490i	$0.562980\pi$
$642$	1122.70	0.0690178
$643$	21527.0	1.32029	0.660143	−	0.751140i	$-0.270496\pi$
$643$	21527.0	1.32029	0.660143	+	0.751140i	$0.270496\pi$
$644$	−12869.4	−0.787462
$645$	0	0
$646$	1174.82	0.0715519
$647$	−23849.2	−1.44916	−0.724581	−	0.689189i	$-0.757967\pi$
$647$	−23849.2	−1.44916	−0.724581	+	0.689189i	$0.757967\pi$
$648$	−1167.38	−0.0707699
$649$	26615.9	1.60981
$650$	0	0
$651$	−5545.77	−0.333880
$652$	−25660.6	−1.54133
$653$	−11845.8	−0.709898	−0.354949	−	0.934886i	$-0.615502\pi$
$653$	−11845.8	−0.709898	−0.354949	+	0.934886i	$0.615502\pi$
$654$	−5203.87	−0.311143
$655$	0	0
$656$	10031.6	0.597058
$657$	−9015.24	−0.535339
$658$	−906.087	−0.0536823
$659$	−13126.8	−0.775944	−0.387972	−	0.921671i	$-0.626824\pi$
$659$	−13126.8	−0.775944	−0.387972	+	0.921671i	$0.626824\pi$
$660$	0	0
$661$	24494.4	1.44133	0.720667	−	0.693281i	$-0.243836\pi$
$661$	24494.4	1.44133	0.720667	+	0.693281i	$0.243836\pi$
$662$	−4191.26	−0.246069
$663$	567.583	0.0332475
$664$	7445.87	0.435174
$665$	0	0
$666$	−3458.71	−0.201235
$667$	31033.1	1.80151
$668$	11025.4	0.638602
$669$	3735.24	0.215863
$670$	0	0
$671$	38724.0	2.22790
$672$	5853.83	0.336037
$673$	28081.1	1.60839	0.804196	−	0.594364i	$-0.202596\pi$
$673$	28081.1	1.60839	0.804196	+	0.594364i	$0.202596\pi$
$674$	3699.27	0.211410
$675$	0	0
$676$	15210.4	0.865406
$677$	6825.24	0.387467	0.193733	−	0.981054i	$-0.437940\pi$
$677$	6825.24	0.387467	0.193733	+	0.981054i	$0.437940\pi$
$678$	3115.59	0.176480
$679$	−20467.6	−1.15681
$680$	0	0
$681$	−13794.9	−0.776242
$682$	6326.67	0.355221
$683$	31450.7	1.76197	0.880987	−	0.473140i	$-0.156879\pi$
$683$	31450.7	1.76197	0.880987	+	0.473140i	$0.156879\pi$
$684$	2959.12	0.165417
$685$	0	0
$686$	6321.99	0.351858
$687$	−19064.3	−1.05873
$688$	−3757.02	−0.208190
$689$	−1191.97	−0.0659077
$690$	0	0
$691$	6136.45	0.337832	0.168916	−	0.985630i	$-0.445973\pi$
$691$	6136.45	0.337832	0.168916	+	0.985630i	$0.445973\pi$
$692$	−15421.8	−0.847182
$693$	5025.12	0.275452
$694$	−5524.03	−0.302146
$695$	0	0
$696$	−9224.60	−0.502382
$697$	−6194.59	−0.336638
$698$	−2786.05	−0.151080
$699$	1907.90	0.103238
$700$	0	0
$701$	5291.43	0.285099	0.142550	−	0.989788i	$-0.454470\pi$
$701$	5291.43	0.285099	0.142550	+	0.989788i	$0.454470\pi$
$702$	−184.053	−0.00989551
$703$	18663.3	1.00128
$704$	8684.00	0.464902
$705$	0	0
$706$	3331.42	0.177592
$707$	5408.48	0.287704
$708$	−12653.0	−0.671650
$709$	−4385.62	−0.232307	−0.116153	−	0.993231i	$-0.537056\pi$
$709$	−4385.62	−0.232307	−0.116153	+	0.993231i	$0.537056\pi$
$710$	0	0
$711$	−1205.60	−0.0635915
$712$	8801.42	0.463268
$713$	21539.1	1.13134
$714$	−948.427	−0.0497115
$715$	0	0
$716$	13221.4	0.690093
$717$	19374.2	1.00912
$718$	10131.7	0.526616
$719$	6410.26	0.332493	0.166246	−	0.986084i	$-0.446835\pi$
$719$	6410.26	0.332493	0.166246	+	0.986084i	$0.446835\pi$
$720$	0	0
$721$	1015.22	0.0524393
$722$	−4496.23	−0.231762
$723$	−1529.24	−0.0786627
$724$	1827.38	0.0938040
$725$	0	0
$726$	−1918.48	−0.0980736
$727$	−31663.6	−1.61532	−0.807661	−	0.589647i	$-0.799267\pi$
$727$	−31663.6	−1.61532	−0.807661	+	0.589647i	$0.799267\pi$
$728$	1283.92	0.0653642
$729$	729.000	0.0370370
$730$	0	0
$731$	2319.98	0.117384
$732$	−18409.0	−0.929532
$733$	−25767.7	−1.29843	−0.649215	−	0.760605i	$-0.724903\pi$
$733$	−25767.7	−1.29843	−0.649215	+	0.760605i	$0.724903\pi$
$734$	2564.91	0.128982
$735$	0	0
$736$	−22735.5	−1.13865
$737$	−18172.5	−0.908267
$738$	2008.75	0.100194
$739$	3389.01	0.168697	0.0843484	−	0.996436i	$-0.473119\pi$
$739$	3389.01	0.168697	0.0843484	+	0.996436i	$0.473119\pi$
$740$	0	0
$741$	993.159	0.0492370
$742$	1991.77	0.0985447
$743$	17203.7	0.849453	0.424727	−	0.905322i	$-0.360370\pi$
$743$	17203.7	0.849453	0.424727	+	0.905322i	$0.360370\pi$
$744$	−6402.50	−0.315493
$745$	0	0
$746$	657.655	0.0322768
$747$	−4649.77	−0.227746
$748$	−8404.21	−0.410813
$749$	4890.72	0.238589
$750$	0	0
$751$	17081.3	0.829970	0.414985	−	0.909828i	$-0.363787\pi$
$751$	17081.3	0.829970	0.414985	+	0.909828i	$0.363787\pi$
$752$	3262.27	0.158195
$753$	−7937.46	−0.384139
$754$	−1454.39	−0.0702463
$755$	0	0
$756$	−2388.90	−0.114925
$757$	−4684.65	−0.224923	−0.112461	−	0.993656i	$-0.535873\pi$
$757$	−4684.65	−0.224923	−0.112461	+	0.993656i	$0.535873\pi$
$758$	−11687.7	−0.560046
$759$	−19516.9	−0.933359
$760$	0	0
$761$	25366.8	1.20834	0.604169	−	0.796856i	$-0.293505\pi$
$761$	25366.8	1.20834	0.604169	+	0.796856i	$0.293505\pi$
$762$	2497.35	0.118726
$763$	−22669.2	−1.07560
$764$	28072.8	1.32937
$765$	0	0
$766$	−1817.01	−0.0857068
$767$	−4246.67	−0.199920
$768$	−544.859	−0.0256001
$769$	−21287.7	−0.998250	−0.499125	−	0.866530i	$-0.666345\pi$
$769$	−21287.7	−0.998250	−0.499125	+	0.866530i	$0.666345\pi$
$770$	0	0
$771$	−11925.4	−0.557044
$772$	8885.79	0.414257
$773$	−23748.4	−1.10501	−0.552504	−	0.833511i	$-0.686327\pi$
$773$	−23748.4	−1.10501	−0.552504	+	0.833511i	$0.686327\pi$
$774$	−752.312	−0.0349371
$775$	0	0
$776$	−23629.5	−1.09311
$777$	−15066.9	−0.695651
$778$	179.569	0.00827490
$779$	−10839.3	−0.498535
$780$	0	0
$781$	−23533.2	−1.07821
$782$	3683.57	0.168445
$783$	5760.55	0.262919
$784$	−8035.46	−0.366047
$785$	0	0
$786$	−4895.04	−0.222138
$787$	−19191.0	−0.869231	−0.434615	−	0.900616i	$-0.643116\pi$
$787$	−19191.0	−0.869231	−0.434615	+	0.900616i	$0.643116\pi$
$788$	−35861.8	−1.62122
$789$	14460.8	0.652492
$790$	0	0
$791$	13572.2	0.610077
$792$	5801.42	0.260283
$793$	−6178.55	−0.276680
$794$	7209.51	0.322237
$795$	0	0
$796$	37733.4	1.68018
$797$	20205.5	0.898012	0.449006	−	0.893529i	$-0.351778\pi$
$797$	20205.5	0.898012	0.449006	+	0.893529i	$0.351778\pi$
$798$	−1659.56	−0.0736188
$799$	−2014.46	−0.0891948
$800$	0	0
$801$	−5496.28	−0.242449
$802$	5155.33	0.226984
$803$	44802.3	1.96891
$804$	8639.05	0.378950
$805$	0	0
$806$	−1009.44	−0.0441143
$807$	−12588.9	−0.549131
$808$	6244.00	0.271861
$809$	−18217.3	−0.791700	−0.395850	−	0.918315i	$-0.629550\pi$
$809$	−18217.3	−0.791700	−0.395850	+	0.918315i	$0.629550\pi$
$810$	0	0
$811$	−25637.1	−1.11004	−0.555019	−	0.831837i	$-0.687289\pi$
$811$	−25637.1	−1.11004	−0.555019	+	0.831837i	$0.687289\pi$
$812$	−18877.0	−0.815830
$813$	6119.93	0.264004
$814$	17188.5	0.740117
$815$	0	0
$816$	3414.71	0.146493
$817$	4059.51	0.173836
$818$	−3907.29	−0.167011
$819$	−801.776	−0.0342080
$820$	0	0
$821$	−3325.18	−0.141352	−0.0706758	−	0.997499i	$-0.522516\pi$
$821$	−3325.18	−0.141352	−0.0706758	+	0.997499i	$0.522516\pi$
$822$	−6882.97	−0.292057
$823$	−4282.17	−0.181370	−0.0906848	−	0.995880i	$-0.528906\pi$
$823$	−4282.17	−0.181370	−0.0906848	+	0.995880i	$0.528906\pi$
$824$	1172.05	0.0495515
$825$	0	0
$826$	7096.15	0.298918
$827$	15503.1	0.651869	0.325935	−	0.945392i	$-0.394321\pi$
$827$	15503.1	0.651869	0.325935	+	0.945392i	$0.394321\pi$
$828$	9278.17	0.389419
$829$	26065.5	1.09203	0.546015	−	0.837775i	$-0.316144\pi$
$829$	26065.5	1.09203	0.546015	+	0.837775i	$0.316144\pi$
$830$	0	0
$831$	−13840.2	−0.577751
$832$	−1385.56	−0.0577353
$833$	4961.93	0.206388
$834$	6195.46	0.257232
$835$	0	0
$836$	−14705.7	−0.608383
$837$	3998.21	0.165112
$838$	2714.57	0.111901
$839$	44675.9	1.83836	0.919180	−	0.393838i	$-0.128853\pi$
$839$	44675.9	1.83836	0.919180	+	0.393838i	$0.128853\pi$
$840$	0	0
$841$	21130.8	0.866406
$842$	−15799.3	−0.646650
$843$	7536.43	0.307910
$844$	7297.41	0.297615
$845$	0	0
$846$	653.242	0.0265472
$847$	−8357.30	−0.339032
$848$	−7171.14	−0.290399
$849$	3185.74	0.128780
$850$	0	0
$851$	58517.8	2.35719
$852$	11187.5	0.449856
$853$	16623.4	0.667261	0.333631	−	0.942704i	$-0.391726\pi$
$853$	16623.4	0.667261	0.333631	+	0.942704i	$0.391726\pi$
$854$	10324.3	0.413689
$855$	0	0
$856$	5646.26	0.225450
$857$	5804.93	0.231380	0.115690	−	0.993285i	$-0.463092\pi$
$857$	5804.93	0.231380	0.115690	+	0.993285i	$0.463092\pi$
$858$	914.675	0.0363945
$859$	−30984.8	−1.23072	−0.615360	−	0.788246i	$-0.710989\pi$
$859$	−30984.8	−1.23072	−0.615360	+	0.788246i	$0.710989\pi$
$860$	0	0
$861$	8750.56	0.346363
$862$	−2198.46	−0.0868674
$863$	−3511.89	−0.138524	−0.0692620	−	0.997599i	$-0.522064\pi$
$863$	−3511.89	−0.138524	−0.0692620	+	0.997599i	$0.522064\pi$
$864$	−4220.31	−0.166178
$865$	0	0
$866$	7218.22	0.283239
$867$	12630.4	0.494753
$868$	−13101.9	−0.512337
$869$	5991.37	0.233882
$870$	0	0
$871$	2899.49	0.112796
$872$	−26171.2	−1.01636
$873$	14756.1	0.572071
$874$	6445.52	0.249454
$875$	0	0
$876$	−21298.6	−0.821476
$877$	−36724.0	−1.41401	−0.707003	−	0.707211i	$-0.749953\pi$
$877$	−36724.0	−1.41401	−0.707003	+	0.707211i	$0.749953\pi$
$878$	−7955.18	−0.305779
$879$	−23824.5	−0.914200
$880$	0	0
$881$	41245.8	1.57731	0.788654	−	0.614838i	$-0.210779\pi$
$881$	41245.8	1.57731	0.788654	+	0.614838i	$0.210779\pi$
$882$	−1609.03	−0.0614274
$883$	−2065.87	−0.0787340	−0.0393670	−	0.999225i	$-0.512534\pi$
$883$	−2065.87	−0.0787340	−0.0393670	+	0.999225i	$0.512534\pi$
$884$	1340.92	0.0510182
$885$	0	0
$886$	−11153.1	−0.422909
$887$	10866.5	0.411342	0.205671	−	0.978621i	$-0.434062\pi$
$887$	10866.5	0.411342	0.205671	+	0.978621i	$0.434062\pi$
$888$	−17394.5	−0.657342
$889$	10879.0	0.410427
$890$	0	0
$891$	−3622.85	−0.136218
$892$	8824.54	0.331242
$893$	−3524.92	−0.132091
$894$	4377.91	0.163780
$895$	0	0
$896$	17925.5	0.668358
$897$	3114.00	0.115912
$898$	−988.601	−0.0367372
$899$	31593.8	1.17209
$900$	0	0
$901$	4428.22	0.163735
$902$	−9982.74	−0.368502
$903$	−3277.23	−0.120775
$904$	15668.9	0.576481
$905$	0	0
$906$	−7406.98	−0.271612
$907$	−12436.5	−0.455290	−0.227645	−	0.973744i	$-0.573103\pi$
$907$	−12436.5	−0.455290	−0.227645	+	0.973744i	$0.573103\pi$
$908$	−32590.6	−1.19114
$909$	−3899.24	−0.142277
$910$	0	0
$911$	19230.5	0.699380	0.349690	−	0.936866i	$-0.386287\pi$
$911$	19230.5	0.699380	0.349690	+	0.936866i	$0.386287\pi$
$912$	5975.06	0.216945
$913$	23107.6	0.837623
$914$	−14595.8	−0.528212
$915$	0	0
$916$	−45039.6	−1.62462
$917$	−21323.9	−0.767912
$918$	683.767	0.0245835
$919$	−24215.5	−0.869201	−0.434600	−	0.900623i	$-0.643110\pi$
$919$	−24215.5	−0.869201	−0.434600	+	0.900623i	$0.643110\pi$
$920$	0	0
$921$	−16217.7	−0.580228
$922$	15088.2	0.538940
$923$	3754.82	0.133902
$924$	11871.9	0.422681
$925$	0	0
$926$	−1693.80	−0.0601098
$927$	−731.920	−0.0259325
$928$	−33348.8	−1.17967
$929$	−19194.4	−0.677878	−0.338939	−	0.940808i	$-0.610068\pi$
$929$	−19194.4	−0.677878	−0.338939	+	0.940808i	$0.610068\pi$
$930$	0	0
$931$	8682.41	0.305644
$932$	4507.44	0.158418
$933$	13877.5	0.486955
$934$	−12466.9	−0.436756
$935$	0	0
$936$	−925.637	−0.0323242
$937$	−37196.1	−1.29685	−0.648423	−	0.761281i	$-0.724571\pi$
$937$	−37196.1	−1.29685	−0.648423	+	0.761281i	$0.724571\pi$
$938$	−4845.02	−0.168652
$939$	−3159.95	−0.109820
$940$	0	0
$941$	33682.5	1.16686	0.583431	−	0.812163i	$-0.301710\pi$
$941$	33682.5	1.16686	0.583431	+	0.812163i	$0.301710\pi$
$942$	−1985.82	−0.0686854
$943$	−33986.1	−1.17364
$944$	−25548.9	−0.880875
$945$	0	0
$946$	3738.70	0.128494
$947$	−44386.5	−1.52309	−0.761546	−	0.648110i	$-0.775560\pi$
$947$	−44386.5	−1.52309	−0.761546	+	0.648110i	$0.775560\pi$
$948$	−2848.24	−0.0975809
$949$	−7148.37	−0.244516
$950$	0	0
$951$	8130.01	0.277217
$952$	−4769.81	−0.162385
$953$	−7655.67	−0.260222	−0.130111	−	0.991499i	$-0.541533\pi$
$953$	−7655.67	−0.260222	−0.130111	+	0.991499i	$0.541533\pi$
$954$	−1435.96	−0.0487327
$955$	0	0
$956$	45771.8	1.54850
$957$	−28627.7	−0.966983
$958$	−604.774	−0.0203960
$959$	−29983.7	−1.00962
$960$	0	0
$961$	−7862.76	−0.263931
$962$	−2742.48	−0.0919139
$963$	−3525.96	−0.117988
$964$	−3612.85	−0.120708
$965$	0	0
$966$	−5203.46	−0.173311
$967$	14646.4	0.487070	0.243535	−	0.969892i	$-0.421693\pi$
$967$	14646.4	0.487070	0.243535	+	0.969892i	$0.421693\pi$
$968$	−9648.37	−0.320362
$969$	−3689.63	−0.122320
$970$	0	0
$971$	−44429.7	−1.46840	−0.734200	−	0.678933i	$-0.762443\pi$
$971$	−44429.7	−1.46840	−0.734200	+	0.678933i	$0.762443\pi$
$972$	1722.27	0.0568332
$973$	26988.7	0.889229
$974$	6149.09	0.202289
$975$	0	0
$976$	−37171.5	−1.21909
$977$	−4615.83	−0.151150	−0.0755749	−	0.997140i	$-0.524079\pi$
$977$	−4615.83	−0.151150	−0.0755749	+	0.997140i	$0.524079\pi$
$978$	−10375.3	−0.339228
$979$	27314.4	0.891698
$980$	0	0
$981$	16343.3	0.531908
$982$	2974.98	0.0966756
$983$	20086.5	0.651738	0.325869	−	0.945415i	$-0.394343\pi$
$983$	20086.5	0.651738	0.325869	+	0.945415i	$0.394343\pi$
$984$	10102.4	0.327289
$985$	0	0
$986$	5403.12	0.174513
$987$	2845.66	0.0917714
$988$	2346.35	0.0755540
$989$	12728.4	0.409240
$990$	0	0
$991$	983.787	0.0315348	0.0157674	−	0.999876i	$-0.494981\pi$
$991$	983.787	0.0315348	0.0157674	+	0.999876i	$0.494981\pi$
$992$	−23146.4	−0.740824
$993$	13163.1	0.420663
$994$	−6274.26	−0.200209
$995$	0	0
$996$	−10985.1	−0.349476
$997$	−884.133	−0.0280850	−0.0140425	−	0.999901i	$-0.504470\pi$
$997$	−884.133	−0.0280850	−0.0140425	+	0.999901i	$0.504470\pi$
$998$	−7321.65	−0.232227
$999$	10862.4	0.344016

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.4.a.f.1.9		14
5.4	even	2		1875.4.a.g.1.6		14
25.4	even	10		75.4.g.b.16.5	✓	28
25.19	even	10		75.4.g.b.61.5	yes	28
75.29	odd	10		225.4.h.a.91.3		28
75.44	odd	10		225.4.h.a.136.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.16.5	✓	28	25.4	even	10
75.4.g.b.61.5	yes	28	25.19	even	10
225.4.h.a.91.3		28	75.29	odd	10
225.4.h.a.136.3		28	75.44	odd	10
1875.4.a.f.1.9		14	1.1	even	1	trivial
1875.4.a.g.1.6		14	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.955230 q^{2} -3.00000 q^{3} -7.08754 q^{4} -2.86569 q^{6} -12.4836 q^{7} -14.4121 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+0.955230 q^{2} -3.00000 q^{3} -7.08754 q^{4} -2.86569 q^{6} -12.4836 q^{7} -14.4121 q^{8} +9.00000 q^{9} -44.7266 q^{11} +21.2626 q^{12} +7.13628 q^{13} -11.9247 q^{14} +42.9334 q^{16} -26.5116 q^{17} +8.59707 q^{18} -46.3901 q^{19} +37.4507 q^{21} -42.7241 q^{22} -145.454 q^{23} +43.2362 q^{24} +6.81679 q^{26} -27.0000 q^{27} +88.4777 q^{28} -213.354 q^{29} -148.082 q^{31} +156.308 q^{32} +134.180 q^{33} -25.3247 q^{34} -63.7878 q^{36} -402.312 q^{37} -44.3132 q^{38} -21.4089 q^{39} +233.656 q^{41} +35.7740 q^{42} -87.5080 q^{43} +317.001 q^{44} -138.942 q^{46} +75.9842 q^{47} -128.800 q^{48} -187.161 q^{49} +79.5348 q^{51} -50.5787 q^{52} -167.029 q^{53} -25.7912 q^{54} +179.914 q^{56} +139.170 q^{57} -203.802 q^{58} -595.082 q^{59} -865.794 q^{61} -141.452 q^{62} -112.352 q^{63} -194.158 q^{64} +128.172 q^{66} +406.302 q^{67} +187.902 q^{68} +436.361 q^{69} +526.158 q^{71} -129.709 q^{72} -1001.69 q^{73} -384.301 q^{74} +328.792 q^{76} +558.347 q^{77} -20.4504 q^{78} -133.956 q^{79} +81.0000 q^{81} +223.195 q^{82} -516.642 q^{83} -265.433 q^{84} -83.5903 q^{86} +640.061 q^{87} +644.602 q^{88} -610.698 q^{89} -89.0862 q^{91} +1030.91 q^{92} +444.246 q^{93} +72.5824 q^{94} -468.924 q^{96} +1639.57 q^{97} -178.782 q^{98} -402.539 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 42 q^{3} + 50 q^{4} + 27 q^{7} - 21 q^{8} + 126 q^{9}+O(q^{10}) \) 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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