LMFDB - Embedded newform 1875.4.a.g.1.4

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			1.4
Root			$-2.93781$ 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)

$f(q)$	$=$	$q-2.93781 q^{2} +3.00000 q^{3} +0.630743 q^{4} -8.81344 q^{6} +18.9115 q^{7} +21.6495 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.93781 q^{2} +3.00000 q^{3} +0.630743 q^{4} -8.81344 q^{6} +18.9115 q^{7} +21.6495 q^{8} +9.00000 q^{9} -6.06780 q^{11} +1.89223 q^{12} +78.2499 q^{13} -55.5585 q^{14} -68.6481 q^{16} +38.4010 q^{17} -26.4403 q^{18} -92.9560 q^{19} +56.7346 q^{21} +17.8261 q^{22} -81.0304 q^{23} +64.9485 q^{24} -229.884 q^{26} +27.0000 q^{27} +11.9283 q^{28} -11.1518 q^{29} -223.883 q^{31} +28.4793 q^{32} -18.2034 q^{33} -112.815 q^{34} +5.67669 q^{36} -107.757 q^{37} +273.087 q^{38} +234.750 q^{39} -350.722 q^{41} -166.676 q^{42} -356.550 q^{43} -3.82722 q^{44} +238.052 q^{46} -291.736 q^{47} -205.944 q^{48} +14.6457 q^{49} +115.203 q^{51} +49.3556 q^{52} +684.808 q^{53} -79.3209 q^{54} +409.425 q^{56} -278.868 q^{57} +32.7619 q^{58} -223.962 q^{59} -697.692 q^{61} +657.726 q^{62} +170.204 q^{63} +465.518 q^{64} +53.4782 q^{66} -909.057 q^{67} +24.2211 q^{68} -243.091 q^{69} +201.818 q^{71} +194.845 q^{72} -291.944 q^{73} +316.570 q^{74} -58.6314 q^{76} -114.751 q^{77} -689.651 q^{78} +709.283 q^{79} +81.0000 q^{81} +1030.36 q^{82} -1108.78 q^{83} +35.7849 q^{84} +1047.48 q^{86} -33.4554 q^{87} -131.365 q^{88} +3.77998 q^{89} +1479.82 q^{91} -51.1094 q^{92} -671.649 q^{93} +857.065 q^{94} +85.4379 q^{96} +18.4630 q^{97} -43.0264 q^{98} -54.6102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.93781	−1.03867	−0.519337	−	0.854570i	$-0.673821\pi$
$2$	−2.93781	−1.03867	−0.519337	+	0.854570i	$0.673821\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	0.630743	0.0788429
$5$	0	0
$5$	0	0
$6$	−8.81344	−0.599678
$7$	18.9115	1.02113	0.510563	−	0.859840i	$-0.329437\pi$
$7$	18.9115	1.02113	0.510563	+	0.859840i	$0.329437\pi$
$8$	21.6495	0.956782
$9$	9.00000	0.333333
$10$	0	0
$11$	−6.06780	−0.166319	−0.0831596	−	0.996536i	$-0.526501\pi$
$11$	−6.06780	−0.166319	−0.0831596	+	0.996536i	$0.526501\pi$
$12$	1.89223	0.0455200
$13$	78.2499	1.66943	0.834716	−	0.550681i	$-0.185632\pi$
$13$	78.2499	1.66943	0.834716	+	0.550681i	$0.185632\pi$
$14$	−55.5585	−1.06062
$15$	0	0
$16$	−68.6481	−1.07263
$17$	38.4010	0.547859	0.273930	−	0.961750i	$-0.411676\pi$
$17$	38.4010	0.547859	0.273930	+	0.961750i	$0.411676\pi$
$18$	−26.4403	−0.346225
$19$	−92.9560	−1.12240	−0.561199	−	0.827681i	$-0.689660\pi$
$19$	−92.9560	−1.12240	−0.561199	+	0.827681i	$0.689660\pi$
$20$	0	0
$21$	56.7346	0.589548
$22$	17.8261	0.172751
$23$	−81.0304	−0.734609	−0.367305	−	0.930101i	$-0.619719\pi$
$23$	−81.0304	−0.734609	−0.367305	+	0.930101i	$0.619719\pi$
$24$	64.9485	0.552398
$25$	0	0
$26$	−229.884	−1.73399
$27$	27.0000	0.192450
$28$	11.9283	0.0805085
$29$	−11.1518	−0.0714083	−0.0357041	−	0.999362i	$-0.511367\pi$
$29$	−11.1518	−0.0714083	−0.0357041	+	0.999362i	$0.511367\pi$
$30$	0	0
$31$	−223.883	−1.29712	−0.648558	−	0.761166i	$-0.724627\pi$
$31$	−223.883	−1.29712	−0.648558	+	0.761166i	$0.724627\pi$
$32$	28.4793	0.157327
$33$	−18.2034	−0.0960245
$34$	−112.815	−0.569047
$35$	0	0
$36$	5.67669	0.0262810
$37$	−107.757	−0.478788	−0.239394	−	0.970923i	$-0.576949\pi$
$37$	−107.757	−0.478788	−0.239394	+	0.970923i	$0.576949\pi$
$38$	273.087	1.16581
$39$	234.750	0.963847
$40$	0	0
$41$	−350.722	−1.33594	−0.667971	−	0.744188i	$-0.732837\pi$
$41$	−350.722	−1.33594	−0.667971	+	0.744188i	$0.732837\pi$
$42$	−166.676	−0.612347
$43$	−356.550	−1.26450	−0.632249	−	0.774765i	$-0.717868\pi$
$43$	−356.550	−1.26450	−0.632249	+	0.774765i	$0.717868\pi$
$44$	−3.82722	−0.0131131
$45$	0	0
$46$	238.052	0.763019
$47$	−291.736	−0.905405	−0.452703	−	0.891662i	$-0.649540\pi$
$47$	−291.736	−0.905405	−0.452703	+	0.891662i	$0.649540\pi$
$48$	−205.944	−0.619281
$49$	14.6457	0.0426989
$50$	0	0
$51$	115.203	0.316307
$52$	49.3556	0.131623
$53$	684.808	1.77482	0.887412	−	0.460978i	$-0.152501\pi$
$53$	684.808	1.77482	0.887412	+	0.460978i	$0.152501\pi$
$54$	−79.3209	−0.199893
$55$	0	0
$56$	409.425	0.976995
$57$	−278.868	−0.648017
$58$	32.7619	0.0741699
$59$	−223.962	−0.494193	−0.247097	−	0.968991i	$-0.579477\pi$
$59$	−223.962	−0.494193	−0.247097	+	0.968991i	$0.579477\pi$
$60$	0	0
$61$	−697.692	−1.46443	−0.732216	−	0.681073i	$-0.761514\pi$
$61$	−697.692	−1.46443	−0.732216	+	0.681073i	$0.761514\pi$
$62$	657.726	1.34728
$63$	170.204	0.340375
$64$	465.518	0.909215
$65$	0	0
$66$	53.4782	0.0997381
$67$	−909.057	−1.65760	−0.828798	−	0.559547i	$-0.810975\pi$
$67$	−909.057	−1.65760	−0.828798	+	0.559547i	$0.810975\pi$
$68$	24.2211	0.0431948
$69$	−243.091	−0.424127
$70$	0	0
$71$	201.818	0.337343	0.168671	−	0.985672i	$-0.446052\pi$
$71$	201.818	0.337343	0.168671	+	0.985672i	$0.446052\pi$
$72$	194.845	0.318927
$73$	−291.944	−0.468075	−0.234037	−	0.972228i	$-0.575194\pi$
$73$	−291.944	−0.468075	−0.234037	+	0.972228i	$0.575194\pi$
$74$	316.570	0.497304
$75$	0	0
$76$	−58.6314	−0.0884932
$77$	−114.751	−0.169833
$78$	−689.651	−1.00112
$79$	709.283	1.01013	0.505067	−	0.863080i	$-0.331468\pi$
$79$	709.283	1.01013	0.505067	+	0.863080i	$0.331468\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	1030.36	1.38761
$83$	−1108.78	−1.46632	−0.733159	−	0.680058i	$-0.761955\pi$
$83$	−1108.78	−1.46632	−0.733159	+	0.680058i	$0.761955\pi$
$84$	35.7849	0.0464816
$85$	0	0
$86$	1047.48	1.31340
$87$	−33.4554	−0.0412276
$88$	−131.365	−0.159131
$89$	3.77998	0.00450199	0.00225099	−	0.999997i	$-0.499283\pi$
$89$	3.77998	0.00450199	0.00225099	+	0.999997i	$0.499283\pi$
$90$	0	0
$91$	1479.82	1.70470
$92$	−51.1094	−0.0579187
$93$	−671.649	−0.748890
$94$	857.065	0.940421
$95$	0	0
$96$	85.4379	0.0908330
$97$	18.4630	0.0193261	0.00966305	−	0.999953i	$-0.496924\pi$
$97$	18.4630	0.0193261	0.00966305	+	0.999953i	$0.496924\pi$
$98$	−43.0264	−0.0443502
$99$	−54.6102	−0.0554398
$100$	0	0
$101$	−1332.50	−1.31276	−0.656381	−	0.754430i	$-0.727913\pi$
$101$	−1332.50	−1.31276	−0.656381	+	0.754430i	$0.727913\pi$
$102$	−338.445	−0.328539
$103$	1678.64	1.60584	0.802921	−	0.596086i	$-0.203278\pi$
$103$	1678.64	1.60584	0.802921	+	0.596086i	$0.203278\pi$
$104$	1694.07	1.59728
$105$	0	0
$106$	−2011.84	−1.84346
$107$	1550.64	1.40099	0.700496	−	0.713657i	$-0.252962\pi$
$107$	1550.64	1.40099	0.700496	+	0.713657i	$0.252962\pi$
$108$	17.0301	0.0151733
$109$	446.988	0.392786	0.196393	−	0.980525i	$-0.437077\pi$
$109$	446.988	0.392786	0.196393	+	0.980525i	$0.437077\pi$
$110$	0	0
$111$	−323.271	−0.276428
$112$	−1298.24	−1.09529
$113$	−621.799	−0.517645	−0.258823	−	0.965925i	$-0.583335\pi$
$113$	−621.799	−0.517645	−0.258823	+	0.965925i	$0.583335\pi$
$114$	819.262	0.673079
$115$	0	0
$116$	−7.03393	−0.00563003
$117$	704.249	0.556477
$118$	657.959	0.513306
$119$	726.221	0.559433
$120$	0	0
$121$	−1294.18	−0.972338
$122$	2049.69	1.52107
$123$	−1052.17	−0.771306
$124$	−141.213	−0.102268
$125$	0	0
$126$	−500.027	−0.353539
$127$	−700.130	−0.489185	−0.244593	−	0.969626i	$-0.578654\pi$
$127$	−700.130	−0.489185	−0.244593	+	0.969626i	$0.578654\pi$
$128$	−1595.44	−1.10170
$129$	−1069.65	−0.730058
$130$	0	0
$131$	−581.895	−0.388094	−0.194047	−	0.980992i	$-0.562161\pi$
$131$	−581.895	−0.388094	−0.194047	+	0.980992i	$0.562161\pi$
$132$	−11.4817	−0.00757084
$133$	−1757.94	−1.14611
$134$	2670.64	1.72170
$135$	0	0
$136$	831.362	0.524181
$137$	602.012	0.375426	0.187713	−	0.982224i	$-0.439892\pi$
$137$	602.012	0.375426	0.187713	+	0.982224i	$0.439892\pi$
$138$	714.157	0.440529
$139$	−185.689	−0.113309	−0.0566546	−	0.998394i	$-0.518043\pi$
$139$	−185.689	−0.113309	−0.0566546	+	0.998394i	$0.518043\pi$
$140$	0	0
$141$	−875.208	−0.522736
$142$	−592.902	−0.350389
$143$	−474.805	−0.277659
$144$	−617.833	−0.357542
$145$	0	0
$146$	857.676	0.486177
$147$	43.9371	0.0246522
$148$	−67.9670	−0.0377490
$149$	2586.71	1.42223	0.711113	−	0.703078i	$-0.248192\pi$
$149$	2586.71	1.42223	0.711113	+	0.703078i	$0.248192\pi$
$150$	0	0
$151$	−276.537	−0.149035	−0.0745175	−	0.997220i	$-0.523742\pi$
$151$	−276.537	−0.149035	−0.0745175	+	0.997220i	$0.523742\pi$
$152$	−2012.45	−1.07389
$153$	345.609	0.182620
$154$	337.118	0.176401
$155$	0	0
$156$	148.067	0.0759925
$157$	−3052.85	−1.55187	−0.775937	−	0.630810i	$-0.782723\pi$
$157$	−3052.85	−1.55187	−0.775937	+	0.630810i	$0.782723\pi$
$158$	−2083.74	−1.04920
$159$	2054.42	1.02469
$160$	0	0
$161$	−1532.41	−0.750129
$162$	−237.963	−0.115408
$163$	−802.885	−0.385808	−0.192904	−	0.981218i	$-0.561791\pi$
$163$	−802.885	−0.385808	−0.192904	+	0.981218i	$0.561791\pi$
$164$	−221.215	−0.105329
$165$	0	0
$166$	3257.39	1.52302
$167$	2831.04	1.31181	0.655906	−	0.754842i	$-0.272287\pi$
$167$	2831.04	1.31181	0.655906	+	0.754842i	$0.272287\pi$
$168$	1228.27	0.564068
$169$	3926.05	1.78700
$170$	0	0
$171$	−836.604	−0.374133
$172$	−224.892	−0.0996966
$173$	−4121.25	−1.81117	−0.905586	−	0.424162i	$-0.860569\pi$
$173$	−4121.25	−1.81117	−0.905586	+	0.424162i	$0.860569\pi$
$174$	98.2858	0.0428220
$175$	0	0
$176$	416.543	0.178398
$177$	−671.887	−0.285323
$178$	−11.1049	−0.00467610
$179$	−1764.28	−0.736696	−0.368348	−	0.929688i	$-0.620076\pi$
$179$	−1764.28	−0.736696	−0.368348	+	0.929688i	$0.620076\pi$
$180$	0	0
$181$	−1492.92	−0.613082	−0.306541	−	0.951857i	$-0.599172\pi$
$181$	−1492.92	−0.613082	−0.306541	+	0.951857i	$0.599172\pi$
$182$	−4347.45	−1.77063
$183$	−2093.08	−0.845490
$184$	−1754.27	−0.702860
$185$	0	0
$186$	1973.18	0.777852
$187$	−233.010	−0.0911195
$188$	−184.010	−0.0713848
$189$	510.611	0.196516
$190$	0	0
$191$	3658.72	1.38605	0.693025	−	0.720913i	$-0.256277\pi$
$191$	3658.72	1.38605	0.693025	+	0.720913i	$0.256277\pi$
$192$	1396.55	0.524935
$193$	−4695.92	−1.75140	−0.875699	−	0.482858i	$-0.839599\pi$
$193$	−4695.92	−1.75140	−0.875699	+	0.482858i	$0.839599\pi$
$194$	−54.2408	−0.0200735
$195$	0	0
$196$	9.23768	0.00336650
$197$	481.723	0.174220	0.0871101	−	0.996199i	$-0.472237\pi$
$197$	481.723	0.174220	0.0871101	+	0.996199i	$0.472237\pi$
$198$	160.435	0.0575838
$199$	494.959	0.176315	0.0881575	−	0.996107i	$-0.471902\pi$
$199$	494.959	0.176315	0.0881575	+	0.996107i	$0.471902\pi$
$200$	0	0
$201$	−2727.17	−0.957014
$202$	3914.64	1.36353
$203$	−210.898	−0.0729169
$204$	72.6634	0.0249385
$205$	0	0
$206$	−4931.54	−1.66795
$207$	−729.274	−0.244870
$208$	−5371.71	−1.79068
$209$	564.039	0.186677
$210$	0	0
$211$	473.778	0.154579	0.0772897	−	0.997009i	$-0.475373\pi$
$211$	473.778	0.154579	0.0772897	+	0.997009i	$0.475373\pi$
$212$	431.938	0.139932
$213$	605.453	0.194765
$214$	−4555.49	−1.45517
$215$	0	0
$216$	584.536	0.184133
$217$	−4233.97	−1.32452
$218$	−1313.17	−0.407976
$219$	−875.832	−0.270243
$220$	0	0
$221$	3004.87	0.914613
$222$	949.710	0.287119
$223$	5065.81	1.52122	0.760609	−	0.649210i	$-0.224900\pi$
$223$	5065.81	1.52122	0.760609	+	0.649210i	$0.224900\pi$
$224$	538.587	0.160651
$225$	0	0
$226$	1826.73	0.537665
$227$	5292.51	1.54747	0.773737	−	0.633507i	$-0.218385\pi$
$227$	5292.51	1.54747	0.773737	+	0.633507i	$0.218385\pi$
$228$	−175.894	−0.0510915
$229$	489.750	0.141326	0.0706628	−	0.997500i	$-0.477489\pi$
$229$	489.750	0.141326	0.0706628	+	0.997500i	$0.477489\pi$
$230$	0	0
$231$	−344.254	−0.0980531
$232$	−241.431	−0.0683221
$233$	−2179.85	−0.612905	−0.306452	−	0.951886i	$-0.599142\pi$
$233$	−2179.85	−0.612905	−0.306452	+	0.951886i	$0.599142\pi$
$234$	−2068.95	−0.577998
$235$	0	0
$236$	−141.263	−0.0389636
$237$	2127.85	0.583201
$238$	−2133.50	−0.581069
$239$	4435.50	1.20045	0.600227	−	0.799829i	$-0.295077\pi$
$239$	4435.50	1.20045	0.600227	+	0.799829i	$0.295077\pi$
$240$	0	0
$241$	2402.85	0.642246	0.321123	−	0.947038i	$-0.395940\pi$
$241$	2402.85	0.642246	0.321123	+	0.947038i	$0.395940\pi$
$242$	3802.06	1.00994
$243$	243.000	0.0641500
$244$	−440.064	−0.115460
$245$	0	0
$246$	3091.07	0.801135
$247$	−7273.80	−1.87377
$248$	−4846.95	−1.24106
$249$	−3326.34	−0.846579
$250$	0	0
$251$	−3459.69	−0.870014	−0.435007	−	0.900427i	$-0.643254\pi$
$251$	−3459.69	−0.870014	−0.435007	+	0.900427i	$0.643254\pi$
$252$	107.355	0.0268362
$253$	491.677	0.122180
$254$	2056.85	0.508104
$255$	0	0
$256$	962.957	0.235097
$257$	4772.57	1.15838	0.579192	−	0.815191i	$-0.303368\pi$
$257$	4772.57	1.15838	0.579192	+	0.815191i	$0.303368\pi$
$258$	3142.43	0.758292
$259$	−2037.85	−0.488903
$260$	0	0
$261$	−100.366	−0.0238028
$262$	1709.50	0.403103
$263$	4200.63	0.984875	0.492437	−	0.870348i	$-0.336106\pi$
$263$	4200.63	0.984875	0.492437	+	0.870348i	$0.336106\pi$
$264$	−394.095	−0.0918744
$265$	0	0
$266$	5164.50	1.19044
$267$	11.3399	0.00259923
$268$	−573.381	−0.130690
$269$	−2269.20	−0.514334	−0.257167	−	0.966367i	$-0.582789\pi$
$269$	−2269.20	−0.514334	−0.257167	+	0.966367i	$0.582789\pi$
$270$	0	0
$271$	−779.306	−0.174684	−0.0873422	−	0.996178i	$-0.527837\pi$
$271$	−779.306	−0.174684	−0.0873422	+	0.996178i	$0.527837\pi$
$272$	−2636.15	−0.587648
$273$	4439.47	0.984209
$274$	−1768.60	−0.389945
$275$	0	0
$276$	−153.328	−0.0334394
$277$	−5055.27	−1.09654	−0.548270	−	0.836302i	$-0.684713\pi$
$277$	−5055.27	−1.09654	−0.548270	+	0.836302i	$0.684713\pi$
$278$	545.521	0.117691
$279$	−2014.95	−0.432372
$280$	0	0
$281$	−2469.22	−0.524203	−0.262101	−	0.965040i	$-0.584416\pi$
$281$	−2469.22	−0.524203	−0.262101	+	0.965040i	$0.584416\pi$
$282$	2571.20	0.542952
$283$	1897.20	0.398506	0.199253	−	0.979948i	$-0.436149\pi$
$283$	1897.20	0.398506	0.199253	+	0.979948i	$0.436149\pi$
$284$	127.295	0.0265971
$285$	0	0
$286$	1394.89	0.288397
$287$	−6632.69	−1.36416
$288$	256.314	0.0524425
$289$	−3438.37	−0.699850
$290$	0	0
$291$	55.3890	0.0111579
$292$	−184.142	−0.0369043
$293$	1090.95	0.217522	0.108761	−	0.994068i	$-0.465312\pi$
$293$	1090.95	0.217522	0.108761	+	0.994068i	$0.465312\pi$
$294$	−129.079	−0.0256056
$295$	0	0
$296$	−2332.88	−0.458095
$297$	−163.831	−0.0320082
$298$	−7599.27	−1.47723
$299$	−6340.62	−1.22638
$300$	0	0
$301$	−6742.91	−1.29121
$302$	812.415	0.154799
$303$	−3997.51	−0.757923
$304$	6381.26	1.20392
$305$	0	0
$306$	−1015.33	−0.189682
$307$	8283.37	1.53992	0.769962	−	0.638090i	$-0.220275\pi$
$307$	8283.37	1.53992	0.769962	+	0.638090i	$0.220275\pi$
$308$	−72.3787	−0.0133901
$309$	5035.93	0.927133
$310$	0	0
$311$	−764.692	−0.139427	−0.0697133	−	0.997567i	$-0.522208\pi$
$311$	−764.692	−0.139427	−0.0697133	+	0.997567i	$0.522208\pi$
$312$	5082.21	0.922191
$313$	−5614.42	−1.01388	−0.506942	−	0.861980i	$-0.669224\pi$
$313$	−5614.42	−1.01388	−0.506942	+	0.861980i	$0.669224\pi$
$314$	8968.71	1.61189
$315$	0	0
$316$	447.376	0.0796419
$317$	−8497.23	−1.50553	−0.752764	−	0.658291i	$-0.771280\pi$
$317$	−8497.23	−1.50553	−0.752764	+	0.658291i	$0.771280\pi$
$318$	−6035.51	−1.06432
$319$	67.6670	0.0118766
$320$	0	0
$321$	4651.92	0.808863
$322$	4501.93	0.779139
$323$	−3569.60	−0.614916
$324$	51.0902	0.00876032
$325$	0	0
$326$	2358.72	0.400729
$327$	1340.96	0.226775
$328$	−7592.96	−1.27820
$329$	−5517.17	−0.924533
$330$	0	0
$331$	−3246.92	−0.539175	−0.269587	−	0.962976i	$-0.586887\pi$
$331$	−3246.92	−0.539175	−0.269587	+	0.962976i	$0.586887\pi$
$332$	−699.355	−0.115609
$333$	−969.813	−0.159596
$334$	−8317.08	−1.36255
$335$	0	0
$336$	−3894.72	−0.632364
$337$	−7415.88	−1.19872	−0.599360	−	0.800480i	$-0.704578\pi$
$337$	−7415.88	−1.19872	−0.599360	+	0.800480i	$0.704578\pi$
$338$	−11534.0	−1.85611
$339$	−1865.40	−0.298863
$340$	0	0
$341$	1358.48	0.215735
$342$	2457.79	0.388602
$343$	−6209.68	−0.977525
$344$	−7719.13	−1.20985
$345$	0	0
$346$	12107.5	1.88122
$347$	623.312	0.0964298	0.0482149	−	0.998837i	$-0.484647\pi$
$347$	623.312	0.0964298	0.0482149	+	0.998837i	$0.484647\pi$
$348$	−21.1018	−0.00325050
$349$	12079.4	1.85271	0.926356	−	0.376649i	$-0.122924\pi$
$349$	12079.4	1.85271	0.926356	+	0.376649i	$0.122924\pi$
$350$	0	0
$351$	2112.75	0.321282
$352$	−172.807	−0.0261666
$353$	1262.99	0.190431	0.0952157	−	0.995457i	$-0.469646\pi$
$353$	1262.99	0.190431	0.0952157	+	0.995457i	$0.469646\pi$
$354$	1973.88	0.296357
$355$	0	0
$356$	2.38420	0.000354950 0
$357$	2178.66	0.322989
$358$	5183.13	0.765186
$359$	−157.161	−0.0231048	−0.0115524	−	0.999933i	$-0.503677\pi$
$359$	−157.161	−0.0231048	−0.0115524	+	0.999933i	$0.503677\pi$
$360$	0	0
$361$	1781.83	0.259779
$362$	4385.92	0.636792
$363$	−3882.55	−0.561380
$364$	933.389	0.134404
$365$	0	0
$366$	6149.06	0.878188
$367$	6891.00	0.980129	0.490065	−	0.871686i	$-0.336973\pi$
$367$	6891.00	0.980129	0.490065	+	0.871686i	$0.336973\pi$
$368$	5562.58	0.787961
$369$	−3156.50	−0.445314
$370$	0	0
$371$	12950.8	1.81232
$372$	−423.638	−0.0590446
$373$	−3858.64	−0.535637	−0.267819	−	0.963469i	$-0.586303\pi$
$373$	−3858.64	−0.535637	−0.267819	+	0.963469i	$0.586303\pi$
$374$	684.538	0.0946434
$375$	0	0
$376$	−6315.93	−0.866275
$377$	−872.628	−0.119211
$378$	−1500.08	−0.204116
$379$	−5013.61	−0.679503	−0.339752	−	0.940515i	$-0.610343\pi$
$379$	−5013.61	−0.679503	−0.339752	+	0.940515i	$0.610343\pi$
$380$	0	0
$381$	−2100.39	−0.282431
$382$	−10748.6	−1.43965
$383$	14018.1	1.87021	0.935103	−	0.354375i	$-0.115306\pi$
$383$	14018.1	1.87021	0.935103	+	0.354375i	$0.115306\pi$
$384$	−4786.32	−0.636070
$385$	0	0
$386$	13795.7	1.81913
$387$	−3208.95	−0.421499
$388$	11.6454	0.00152373
$389$	−97.0621	−0.0126510	−0.00632551	−	0.999980i	$-0.502013\pi$
$389$	−97.0621	−0.0126510	−0.00632551	+	0.999980i	$0.502013\pi$
$390$	0	0
$391$	−3111.65	−0.402462
$392$	317.072	0.0408535
$393$	−1745.68	−0.224066
$394$	−1415.21	−0.180958
$395$	0	0
$396$	−34.4450	−0.00437103
$397$	−5233.93	−0.661671	−0.330836	−	0.943688i	$-0.607331\pi$
$397$	−5233.93	−0.661671	−0.330836	+	0.943688i	$0.607331\pi$
$398$	−1454.10	−0.183134
$399$	−5273.82	−0.661708
$400$	0	0
$401$	−10349.0	−1.28879	−0.644396	−	0.764692i	$-0.722891\pi$
$401$	−10349.0	−1.28879	−0.644396	+	0.764692i	$0.722891\pi$
$402$	8011.92	0.994025
$403$	−17518.8	−2.16545
$404$	−840.466	−0.103502
$405$	0	0
$406$	619.578	0.0757368
$407$	653.848	0.0796316
$408$	2494.09	0.302636
$409$	−10190.2	−1.23196	−0.615982	−	0.787760i	$-0.711241\pi$
$409$	−10190.2	−1.23196	−0.615982	+	0.787760i	$0.711241\pi$
$410$	0	0
$411$	1806.04	0.216752
$412$	1058.79	0.126609
$413$	−4235.47	−0.504634
$414$	2142.47	0.254340
$415$	0	0
$416$	2228.50	0.262647
$417$	−557.068	−0.0654191
$418$	−1657.04	−0.193896
$419$	10381.0	1.21037	0.605186	−	0.796084i	$-0.293099\pi$
$419$	10381.0	1.21037	0.605186	+	0.796084i	$0.293099\pi$
$420$	0	0
$421$	−9792.21	−1.13359	−0.566797	−	0.823857i	$-0.691818\pi$
$421$	−9792.21	−1.13359	−0.566797	+	0.823857i	$0.691818\pi$
$422$	−1391.87	−0.160557
$423$	−2625.62	−0.301802
$424$	14825.8	1.69812
$425$	0	0
$426$	−1778.71	−0.202297
$427$	−13194.4	−1.49537
$428$	978.056	0.110458
$429$	−1424.41	−0.160306
$430$	0	0
$431$	3964.56	0.443077	0.221538	−	0.975152i	$-0.428892\pi$
$431$	3964.56	0.443077	0.221538	+	0.975152i	$0.428892\pi$
$432$	−1853.50	−0.206427
$433$	4463.23	0.495356	0.247678	−	0.968842i	$-0.420332\pi$
$433$	4463.23	0.495356	0.247678	+	0.968842i	$0.420332\pi$
$434$	12438.6	1.37574
$435$	0	0
$436$	281.934	0.0309684
$437$	7532.27	0.824524
$438$	2573.03	0.280694
$439$	−16584.3	−1.80302	−0.901510	−	0.432759i	$-0.857540\pi$
$439$	−16584.3	−1.80302	−0.901510	+	0.432759i	$0.857540\pi$
$440$	0	0
$441$	131.811	0.0142330
$442$	−8827.75	−0.949985
$443$	5664.63	0.607528	0.303764	−	0.952747i	$-0.401757\pi$
$443$	5664.63	0.607528	0.303764	+	0.952747i	$0.401757\pi$
$444$	−203.901	−0.0217944
$445$	0	0
$446$	−14882.4	−1.58005
$447$	7760.13	0.821122
$448$	8803.65	0.928423
$449$	−14047.7	−1.47651	−0.738253	−	0.674524i	$-0.764349\pi$
$449$	−14047.7	−1.47651	−0.738253	+	0.674524i	$0.764349\pi$
$450$	0	0
$451$	2128.11	0.222193
$452$	−392.195	−0.0408127
$453$	−829.612	−0.0860454
$454$	−15548.4	−1.60732
$455$	0	0
$456$	−6037.35	−0.620011
$457$	−11501.1	−1.17724	−0.588622	−	0.808409i	$-0.700329\pi$
$457$	−11501.1	−1.17724	−0.588622	+	0.808409i	$0.700329\pi$
$458$	−1438.79	−0.146791
$459$	1036.83	0.105436
$460$	0	0
$461$	1610.43	0.162701	0.0813506	−	0.996686i	$-0.474077\pi$
$461$	1610.43	0.162701	0.0813506	+	0.996686i	$0.474077\pi$
$462$	1011.35	0.101845
$463$	1962.72	0.197010	0.0985048	−	0.995137i	$-0.468594\pi$
$463$	1962.72	0.197010	0.0985048	+	0.995137i	$0.468594\pi$
$464$	765.551	0.0765944
$465$	0	0
$466$	6403.99	0.636608
$467$	1575.00	0.156065	0.0780327	−	0.996951i	$-0.475136\pi$
$467$	1575.00	0.156065	0.0780327	+	0.996951i	$0.475136\pi$
$468$	444.200	0.0438743
$469$	−17191.7	−1.69262
$470$	0	0
$471$	−9158.56	−0.895975
$472$	−4848.67	−0.472835
$473$	2163.48	0.210310
$474$	−6251.23	−0.605756
$475$	0	0
$476$	458.059	0.0441073
$477$	6163.27	0.591608
$478$	−13030.7	−1.24688
$479$	9805.74	0.935356	0.467678	−	0.883899i	$-0.345091\pi$
$479$	9805.74	0.935356	0.467678	+	0.883899i	$0.345091\pi$
$480$	0	0
$481$	−8431.97	−0.799303
$482$	−7059.13	−0.667084
$483$	−4597.23	−0.433087
$484$	−816.296	−0.0766619
$485$	0	0
$486$	−713.888	−0.0666309
$487$	−7812.04	−0.726894	−0.363447	−	0.931615i	$-0.618400\pi$
$487$	−7812.04	−0.726894	−0.363447	+	0.931615i	$0.618400\pi$
$488$	−15104.7	−1.40114
$489$	−2408.65	−0.222747
$490$	0	0
$491$	5018.71	0.461285	0.230643	−	0.973039i	$-0.425917\pi$
$491$	5018.71	0.461285	0.230643	+	0.973039i	$0.425917\pi$
$492$	−663.646	−0.0608120
$493$	−428.241	−0.0391217
$494$	21369.1	1.94623
$495$	0	0
$496$	15369.1	1.39132
$497$	3816.68	0.344470
$498$	9772.16	0.879319
$499$	−16251.9	−1.45798	−0.728991	−	0.684523i	$-0.760011\pi$
$499$	−16251.9	−1.45798	−0.728991	+	0.684523i	$0.760011\pi$
$500$	0	0
$501$	8493.13	0.757376
$502$	10163.9	0.903660
$503$	110.493	0.00979454	0.00489727	−	0.999988i	$-0.498441\pi$
$503$	110.493	0.00979454	0.00489727	+	0.999988i	$0.498441\pi$
$504$	3684.82	0.325665
$505$	0	0
$506$	−1444.45	−0.126905
$507$	11778.1	1.03173
$508$	−441.602	−0.0385688
$509$	14861.5	1.29415	0.647076	−	0.762425i	$-0.275992\pi$
$509$	14861.5	1.29415	0.647076	+	0.762425i	$0.275992\pi$
$510$	0	0
$511$	−5521.10	−0.477963
$512$	9934.53	0.857516
$513$	−2509.81	−0.216006
$514$	−14020.9	−1.20318
$515$	0	0
$516$	−674.675	−0.0575599
$517$	1770.20	0.150586
$518$	5986.82	0.507810
$519$	−12363.8	−1.04568
$520$	0	0
$521$	−7723.54	−0.649471	−0.324736	−	0.945805i	$-0.605275\pi$
$521$	−7723.54	−0.649471	−0.324736	+	0.945805i	$0.605275\pi$
$522$	294.857	0.0247233
$523$	−4636.06	−0.387611	−0.193806	−	0.981040i	$-0.562083\pi$
$523$	−4636.06	−0.387611	−0.193806	+	0.981040i	$0.562083\pi$
$524$	−367.026	−0.0305985
$525$	0	0
$526$	−12340.7	−1.02296
$527$	−8597.32	−0.710636
$528$	1249.63	0.102998
$529$	−5601.07	−0.460349
$530$	0	0
$531$	−2015.66	−0.164731
$532$	−1108.81	−0.0903627
$533$	−27444.0	−2.23026
$534$	−33.3146	−0.00269975
$535$	0	0
$536$	−19680.6	−1.58596
$537$	−5292.84	−0.425331
$538$	6666.50	0.534225
$539$	−88.8673	−0.00710165
$540$	0	0
$541$	−8330.42	−0.662020	−0.331010	−	0.943627i	$-0.607389\pi$
$541$	−8330.42	−0.662020	−0.331010	+	0.943627i	$0.607389\pi$
$542$	2289.45	0.181440
$543$	−4478.76	−0.353963
$544$	1093.63	0.0861932
$545$	0	0
$546$	−13042.3	−1.02227
$547$	14465.8	1.13073	0.565367	−	0.824839i	$-0.308735\pi$
$547$	14465.8	1.13073	0.565367	+	0.824839i	$0.308735\pi$
$548$	379.715	0.0295997
$549$	−6279.23	−0.488144
$550$	0	0
$551$	1036.63	0.0801486
$552$	−5262.80	−0.405797
$553$	13413.6	1.03147
$554$	14851.4	1.13895
$555$	0	0
$556$	−117.122	−0.00893362
$557$	21991.8	1.67293	0.836467	−	0.548017i	$-0.184617\pi$
$557$	21991.8	1.67293	0.836467	+	0.548017i	$0.184617\pi$
$558$	5919.54	0.449093
$559$	−27900.0	−2.11099
$560$	0	0
$561$	−699.029	−0.0526079
$562$	7254.09	0.544476
$563$	−12734.2	−0.953257	−0.476629	−	0.879105i	$-0.658141\pi$
$563$	−12734.2	−0.953257	−0.476629	+	0.879105i	$0.658141\pi$
$564$	−552.031	−0.0412140
$565$	0	0
$566$	−5573.63	−0.413917
$567$	1531.83	0.113458
$568$	4369.25	0.322763
$569$	−3811.13	−0.280792	−0.140396	−	0.990095i	$-0.544838\pi$
$569$	−3811.13	−0.280792	−0.140396	+	0.990095i	$0.544838\pi$
$570$	0	0
$571$	−20736.9	−1.51981	−0.759907	−	0.650032i	$-0.774755\pi$
$571$	−20736.9	−1.51981	−0.759907	+	0.650032i	$0.774755\pi$
$572$	−299.480	−0.0218914
$573$	10976.2	0.800237
$574$	19485.6	1.41692
$575$	0	0
$576$	4189.66	0.303072
$577$	−26536.7	−1.91463	−0.957313	−	0.289055i	$-0.906659\pi$
$577$	−26536.7	−1.91463	−0.957313	+	0.289055i	$0.906659\pi$
$578$	10101.3	0.726916
$579$	−14087.8	−1.01117
$580$	0	0
$581$	−20968.7	−1.49729
$582$	−162.722	−0.0115894
$583$	−4155.28	−0.295187
$584$	−6320.44	−0.447845
$585$	0	0
$586$	−3205.01	−0.225935
$587$	−20068.1	−1.41107	−0.705535	−	0.708675i	$-0.749293\pi$
$587$	−20068.1	−1.41107	−0.705535	+	0.708675i	$0.749293\pi$
$588$	27.7130	0.00194365
$589$	20811.3	1.45588
$590$	0	0
$591$	1445.17	0.100586
$592$	7397.31	0.513560
$593$	5902.00	0.408712	0.204356	−	0.978897i	$-0.434490\pi$
$593$	5902.00	0.408712	0.204356	+	0.978897i	$0.434490\pi$
$594$	481.304	0.0332460
$595$	0	0
$596$	1631.55	0.112132
$597$	1484.88	0.101796
$598$	18627.6	1.27381
$599$	−1759.46	−0.120016	−0.0600079	−	0.998198i	$-0.519113\pi$
$599$	−1759.46	−0.120016	−0.0600079	+	0.998198i	$0.519113\pi$
$600$	0	0
$601$	22974.1	1.55929	0.779646	−	0.626220i	$-0.215399\pi$
$601$	22974.1	1.55929	0.779646	+	0.626220i	$0.215399\pi$
$602$	19809.4	1.34115
$603$	−8181.51	−0.552532
$604$	−174.424	−0.0117503
$605$	0	0
$606$	11743.9	0.787235
$607$	−18961.8	−1.26794	−0.633968	−	0.773359i	$-0.718575\pi$
$607$	−18961.8	−1.26794	−0.633968	+	0.773359i	$0.718575\pi$
$608$	−2647.32	−0.176584
$609$	−632.693	−0.0420986
$610$	0	0
$611$	−22828.3	−1.51151
$612$	217.990	0.0143983
$613$	22034.1	1.45180	0.725898	−	0.687802i	$-0.241424\pi$
$613$	22034.1	1.45180	0.725898	+	0.687802i	$0.241424\pi$
$614$	−24335.0	−1.59948
$615$	0	0
$616$	−2484.31	−0.162493
$617$	6369.17	0.415581	0.207790	−	0.978173i	$-0.433373\pi$
$617$	6369.17	0.415581	0.207790	+	0.978173i	$0.433373\pi$
$618$	−14794.6	−0.962989
$619$	8293.26	0.538504	0.269252	−	0.963070i	$-0.413223\pi$
$619$	8293.26	0.538504	0.269252	+	0.963070i	$0.413223\pi$
$620$	0	0
$621$	−2187.82	−0.141376
$622$	2246.52	0.144819
$623$	71.4852	0.00459710
$624$	−16115.1	−1.03385
$625$	0	0
$626$	16494.1	1.05309
$627$	1692.12	0.107778
$628$	−1925.57	−0.122354
$629$	−4137.97	−0.262308
$630$	0	0
$631$	23021.2	1.45239	0.726197	−	0.687486i	$-0.241286\pi$
$631$	23021.2	1.45239	0.726197	+	0.687486i	$0.241286\pi$
$632$	15355.6	0.966478
$633$	1421.33	0.0892464
$634$	24963.3	1.56375
$635$	0	0
$636$	1295.81	0.0807899
$637$	1146.03	0.0712829
$638$	−198.793	−0.0123359
$639$	1816.36	0.112448
$640$	0	0
$641$	−23230.0	−1.43141	−0.715703	−	0.698405i	$-0.753894\pi$
$641$	−23230.0	−1.43141	−0.715703	+	0.698405i	$0.753894\pi$
$642$	−13666.5	−0.840144
$643$	17439.0	1.06956	0.534780	−	0.844991i	$-0.320395\pi$
$643$	17439.0	1.06956	0.534780	+	0.844991i	$0.320395\pi$
$644$	−966.556	−0.0591423
$645$	0	0
$646$	10486.8	0.638697
$647$	16358.0	0.993970	0.496985	−	0.867759i	$-0.334440\pi$
$647$	16358.0	0.993970	0.496985	+	0.867759i	$0.334440\pi$
$648$	1753.61	0.106309
$649$	1358.96	0.0821939
$650$	0	0
$651$	−12701.9	−0.764711
$652$	−506.414	−0.0304182
$653$	16212.4	0.971578	0.485789	−	0.874076i	$-0.338532\pi$
$653$	16212.4	0.971578	0.485789	+	0.874076i	$0.338532\pi$
$654$	−3939.50	−0.235545
$655$	0	0
$656$	24076.4	1.43297
$657$	−2627.50	−0.156025
$658$	16208.4	0.960288
$659$	10801.8	0.638509	0.319255	−	0.947669i	$-0.396567\pi$
$659$	10801.8	0.638509	0.319255	+	0.947669i	$0.396567\pi$
$660$	0	0
$661$	15197.2	0.894257	0.447129	−	0.894470i	$-0.352447\pi$
$661$	15197.2	0.894257	0.447129	+	0.894470i	$0.352447\pi$
$662$	9538.84	0.560027
$663$	9014.62	0.528052
$664$	−24004.5	−1.40295
$665$	0	0
$666$	2849.13	0.165768
$667$	903.636	0.0524572
$668$	1785.66	0.103427
$669$	15197.4	0.878276
$670$	0	0
$671$	4233.46	0.243563
$672$	1615.76	0.0927520
$673$	9418.08	0.539436	0.269718	−	0.962939i	$-0.413070\pi$
$673$	9418.08	0.539436	0.269718	+	0.962939i	$0.413070\pi$
$674$	21786.5	1.24508
$675$	0	0
$676$	2476.33	0.140892
$677$	−15337.3	−0.870694	−0.435347	−	0.900263i	$-0.643374\pi$
$677$	−15337.3	−0.870694	−0.435347	+	0.900263i	$0.643374\pi$
$678$	5480.19	0.310421
$679$	349.163	0.0197344
$680$	0	0
$681$	15877.5	0.893434
$682$	−3990.95	−0.224079
$683$	7284.14	0.408082	0.204041	−	0.978962i	$-0.434592\pi$
$683$	7284.14	0.408082	0.204041	+	0.978962i	$0.434592\pi$
$684$	−527.682	−0.0294977
$685$	0	0
$686$	18242.9	1.01533
$687$	1469.25	0.0815944
$688$	24476.5	1.35633
$689$	53586.2	2.96295
$690$	0	0
$691$	13477.0	0.741952	0.370976	−	0.928642i	$-0.379023\pi$
$691$	13477.0	0.741952	0.370976	+	0.928642i	$0.379023\pi$
$692$	−2599.45	−0.142798
$693$	−1032.76	−0.0566110
$694$	−1831.17	−0.100159
$695$	0	0
$696$	−724.294	−0.0394458
$697$	−13468.1	−0.731907
$698$	−35487.1	−1.92436
$699$	−6539.55	−0.353861
$700$	0	0
$701$	16099.1	0.867413	0.433706	−	0.901054i	$-0.357206\pi$
$701$	16099.1	0.867413	0.433706	+	0.901054i	$0.357206\pi$
$702$	−6206.85	−0.333707
$703$	10016.7	0.537391
$704$	−2824.67	−0.151220
$705$	0	0
$706$	−3710.44	−0.197796
$707$	−25199.6	−1.34050
$708$	−423.788	−0.0224957
$709$	5904.28	0.312750	0.156375	−	0.987698i	$-0.450019\pi$
$709$	5904.28	0.312750	0.156375	+	0.987698i	$0.450019\pi$
$710$	0	0
$711$	6383.55	0.336711
$712$	81.8347	0.00430742
$713$	18141.3	0.952873
$714$	−6400.50	−0.335480
$715$	0	0
$716$	−1112.81	−0.0580832
$717$	13306.5	0.693083
$718$	461.710	0.0239984
$719$	−4498.52	−0.233333	−0.116666	−	0.993171i	$-0.537221\pi$
$719$	−4498.52	−0.233333	−0.116666	+	0.993171i	$0.537221\pi$
$720$	0	0
$721$	31745.7	1.63977
$722$	−5234.67	−0.269826
$723$	7208.55	0.370801
$724$	−941.649	−0.0483372
$725$	0	0
$726$	11406.2	0.583090
$727$	−6071.72	−0.309749	−0.154874	−	0.987934i	$-0.549497\pi$
$727$	−6071.72	−0.309749	−0.154874	+	0.987934i	$0.549497\pi$
$728$	32037.5	1.63103
$729$	729.000	0.0370370
$730$	0	0
$731$	−13691.9	−0.692767
$732$	−1320.19	−0.0666608
$733$	26010.2	1.31065	0.655326	−	0.755346i	$-0.272531\pi$
$733$	26010.2	1.31065	0.655326	+	0.755346i	$0.272531\pi$
$734$	−20244.5	−1.01803
$735$	0	0
$736$	−2307.69	−0.115574
$737$	5515.98	0.275690
$738$	9273.20	0.462536
$739$	30788.2	1.53256	0.766281	−	0.642505i	$-0.222105\pi$
$739$	30788.2	1.53256	0.766281	+	0.642505i	$0.222105\pi$
$740$	0	0
$741$	−21821.4	−1.08182
$742$	−38046.9	−1.88241
$743$	29872.6	1.47499	0.737496	−	0.675352i	$-0.236008\pi$
$743$	29872.6	1.47499	0.737496	+	0.675352i	$0.236008\pi$
$744$	−14540.9	−0.716524
$745$	0	0
$746$	11336.0	0.556352
$747$	−9979.01	−0.488772
$748$	−146.969	−0.00718412
$749$	29325.0	1.43059
$750$	0	0
$751$	−22462.4	−1.09143	−0.545716	−	0.837970i	$-0.683742\pi$
$751$	−22462.4	−1.09143	−0.545716	+	0.837970i	$0.683742\pi$
$752$	20027.1	0.971162
$753$	−10379.1	−0.502303
$754$	2563.62	0.123822
$755$	0	0
$756$	322.064	0.0154939
$757$	22613.9	1.08575	0.542876	−	0.839813i	$-0.317335\pi$
$757$	22613.9	1.08575	0.542876	+	0.839813i	$0.317335\pi$
$758$	14729.0	0.705782
$759$	1475.03	0.0705404
$760$	0	0
$761$	16492.8	0.785630	0.392815	−	0.919617i	$-0.371501\pi$
$761$	16492.8	0.785630	0.392815	+	0.919617i	$0.371501\pi$
$762$	6170.56	0.293354
$763$	8453.22	0.401084
$764$	2307.71	0.109280
$765$	0	0
$766$	−41182.4	−1.94253
$767$	−17525.0	−0.825022
$768$	2888.87	0.135733
$769$	2387.75	0.111970	0.0559848	−	0.998432i	$-0.482170\pi$
$769$	2387.75	0.111970	0.0559848	+	0.998432i	$0.482170\pi$
$770$	0	0
$771$	14317.7	0.668793
$772$	−2961.92	−0.138085
$773$	−38692.0	−1.80033	−0.900164	−	0.435552i	$-0.856553\pi$
$773$	−38692.0	−1.80033	−0.900164	+	0.435552i	$0.856553\pi$
$774$	9427.30	0.437800
$775$	0	0
$776$	399.714	0.0184909
$777$	−6113.55	−0.282268
$778$	285.150	0.0131403
$779$	32601.7	1.49946
$780$	0	0
$781$	−1224.59	−0.0561066
$782$	9141.43	0.418027
$783$	−301.099	−0.0137425
$784$	−1005.40	−0.0458000
$785$	0	0
$786$	5128.49	0.232732
$787$	−4595.35	−0.208140	−0.104070	−	0.994570i	$-0.533187\pi$
$787$	−4595.35	−0.208140	−0.104070	+	0.994570i	$0.533187\pi$
$788$	303.844	0.0137360
$789$	12601.9	0.568618
$790$	0	0
$791$	−11759.2	−0.528581
$792$	−1182.28	−0.0530437
$793$	−54594.3	−2.44477
$794$	15376.3	0.687261
$795$	0	0
$796$	312.192	0.0139012
$797$	3304.77	0.146877	0.0734386	−	0.997300i	$-0.476603\pi$
$797$	3304.77	0.146877	0.0734386	+	0.997300i	$0.476603\pi$
$798$	15493.5	0.687298
$799$	−11202.9	−0.496034
$800$	0	0
$801$	34.0198	0.00150066
$802$	30403.5	1.33863
$803$	1771.46	0.0778498
$804$	−1720.14	−0.0754537
$805$	0	0
$806$	51467.0	2.24919
$807$	−6807.61	−0.296951
$808$	−28848.0	−1.25603
$809$	35354.6	1.53647	0.768233	−	0.640171i	$-0.221136\pi$
$809$	35354.6	1.53647	0.768233	+	0.640171i	$0.221136\pi$
$810$	0	0
$811$	−18463.0	−0.799413	−0.399706	−	0.916643i	$-0.630888\pi$
$811$	−18463.0	−0.799413	−0.399706	+	0.916643i	$0.630888\pi$
$812$	−133.022	−0.00574898
$813$	−2337.92	−0.100854
$814$	−1920.88	−0.0827112
$815$	0	0
$816$	−7908.46	−0.339279
$817$	33143.5	1.41927
$818$	29936.9	1.27961
$819$	13318.4	0.568234
$820$	0	0
$821$	−26364.4	−1.12074	−0.560368	−	0.828244i	$-0.689340\pi$
$821$	−26364.4	−1.12074	−0.560368	+	0.828244i	$0.689340\pi$
$822$	−5305.80	−0.225135
$823$	19987.6	0.846565	0.423283	−	0.905998i	$-0.360878\pi$
$823$	19987.6	0.846565	0.423283	+	0.905998i	$0.360878\pi$
$824$	36341.8	1.53644
$825$	0	0
$826$	12443.0	0.524150
$827$	24278.1	1.02084	0.510419	−	0.859926i	$-0.329490\pi$
$827$	24278.1	1.02084	0.510419	+	0.859926i	$0.329490\pi$
$828$	−459.984	−0.0193062
$829$	21565.7	0.903507	0.451754	−	0.892143i	$-0.350799\pi$
$829$	21565.7	0.903507	0.451754	+	0.892143i	$0.350799\pi$
$830$	0	0
$831$	−15165.8	−0.633087
$832$	36426.7	1.51787
$833$	562.410	0.0233930
$834$	1636.56	0.0679491
$835$	0	0
$836$	355.764	0.0147181
$837$	−6044.84	−0.249630
$838$	−30497.5	−1.25718
$839$	−2389.16	−0.0983111	−0.0491556	−	0.998791i	$-0.515653\pi$
$839$	−2389.16	−0.0983111	−0.0491556	+	0.998791i	$0.515653\pi$
$840$	0	0
$841$	−24264.6	−0.994901
$842$	28767.7	1.17743
$843$	−7407.65	−0.302649
$844$	298.832	0.0121875
$845$	0	0
$846$	7713.59	0.313474
$847$	−24474.9	−0.992880
$848$	−47010.8	−1.90372
$849$	5691.61	0.230077
$850$	0	0
$851$	8731.59	0.351722
$852$	381.885	0.0153558
$853$	30059.9	1.20660	0.603301	−	0.797514i	$-0.293852\pi$
$853$	30059.9	1.20660	0.603301	+	0.797514i	$0.293852\pi$
$854$	38762.7	1.55320
$855$	0	0
$856$	33570.6	1.34044
$857$	−6412.98	−0.255617	−0.127808	−	0.991799i	$-0.540794\pi$
$857$	−6412.98	−0.255617	−0.127808	+	0.991799i	$0.540794\pi$
$858$	4184.66	0.166506
$859$	−18231.4	−0.724153	−0.362077	−	0.932148i	$-0.617932\pi$
$859$	−18231.4	−0.724153	−0.362077	+	0.932148i	$0.617932\pi$
$860$	0	0
$861$	−19898.1	−0.787601
$862$	−11647.1	−0.460212
$863$	35338.5	1.39390	0.696951	−	0.717119i	$-0.254540\pi$
$863$	35338.5	1.39390	0.696951	+	0.717119i	$0.254540\pi$
$864$	768.941	0.0302777
$865$	0	0
$866$	−13112.1	−0.514513
$867$	−10315.1	−0.404059
$868$	−2670.55	−0.104429
$869$	−4303.79	−0.168005
$870$	0	0
$871$	−71133.6	−2.76725
$872$	9677.06	0.375810
$873$	166.167	0.00644204
$874$	−22128.4	−0.856412
$875$	0	0
$876$	−552.425	−0.0213067
$877$	−6562.08	−0.252663	−0.126332	−	0.991988i	$-0.540320\pi$
$877$	−6562.08	−0.252663	−0.126332	+	0.991988i	$0.540320\pi$
$878$	48721.6	1.87275
$879$	3272.85	0.125587
$880$	0	0
$881$	25684.7	0.982225	0.491112	−	0.871096i	$-0.336590\pi$
$881$	25684.7	0.982225	0.491112	+	0.871096i	$0.336590\pi$
$882$	−387.237	−0.0147834
$883$	−3752.59	−0.143018	−0.0715090	−	0.997440i	$-0.522781\pi$
$883$	−3752.59	−0.143018	−0.0715090	+	0.997440i	$0.522781\pi$
$884$	1895.30	0.0721107
$885$	0	0
$886$	−16641.6	−0.631023
$887$	−11797.0	−0.446567	−0.223283	−	0.974754i	$-0.571678\pi$
$887$	−11797.0	−0.446567	−0.223283	+	0.974754i	$0.571678\pi$
$888$	−6998.65	−0.264481
$889$	−13240.5	−0.499520
$890$	0	0
$891$	−491.492	−0.0184799
$892$	3195.22	0.119937
$893$	27118.6	1.01623
$894$	−22797.8	−0.852878
$895$	0	0
$896$	−30172.2	−1.12498
$897$	−19021.9	−0.708051
$898$	41269.5	1.53361
$899$	2496.70	0.0926248
$900$	0	0
$901$	26297.3	0.972353
$902$	−6252.00	−0.230786
$903$	−20228.7	−0.745482
$904$	−13461.6	−0.495274
$905$	0	0
$906$	2437.24	0.0893731
$907$	7027.72	0.257278	0.128639	−	0.991691i	$-0.458939\pi$
$907$	7027.72	0.257278	0.128639	+	0.991691i	$0.458939\pi$
$908$	3338.22	0.122007
$909$	−11992.5	−0.437587
$910$	0	0
$911$	−16469.5	−0.598965	−0.299483	−	0.954102i	$-0.596814\pi$
$911$	−16469.5	−0.598965	−0.299483	+	0.954102i	$0.596814\pi$
$912$	19143.8	0.695081
$913$	6727.85	0.243877
$914$	33788.2	1.22277
$915$	0	0
$916$	308.906	0.0111425
$917$	−11004.5	−0.396293
$918$	−3046.00	−0.109513
$919$	16066.4	0.576693	0.288346	−	0.957526i	$-0.406895\pi$
$919$	16066.4	0.576693	0.288346	+	0.957526i	$0.406895\pi$
$920$	0	0
$921$	24850.1	0.889075
$922$	−4731.15	−0.168993
$923$	15792.2	0.563171
$924$	−217.136	−0.00773079
$925$	0	0
$926$	−5766.11	−0.204629
$927$	15107.8	0.535281
$928$	−317.596	−0.0112345
$929$	−5289.23	−0.186797	−0.0933983	−	0.995629i	$-0.529773\pi$
$929$	−5289.23	−0.186797	−0.0933983	+	0.995629i	$0.529773\pi$
$930$	0	0
$931$	−1361.41	−0.0479252
$932$	−1374.93	−0.0483232
$933$	−2294.08	−0.0804980
$934$	−4627.07	−0.162101
$935$	0	0
$936$	15246.6	0.532427
$937$	−2422.61	−0.0844644	−0.0422322	−	0.999108i	$-0.513447\pi$
$937$	−2422.61	−0.0844644	−0.0422322	+	0.999108i	$0.513447\pi$
$938$	50505.9	1.75808
$939$	−16843.3	−0.585366
$940$	0	0
$941$	29639.1	1.02679	0.513394	−	0.858153i	$-0.328388\pi$
$941$	29639.1	1.02679	0.513394	+	0.858153i	$0.328388\pi$
$942$	26906.1	0.930626
$943$	28419.2	0.981394
$944$	15374.6	0.530085
$945$	0	0
$946$	−6355.89	−0.218444
$947$	−39542.9	−1.35689	−0.678444	−	0.734652i	$-0.737345\pi$
$947$	−39542.9	−1.35689	−0.678444	+	0.734652i	$0.737345\pi$
$948$	1342.13	0.0459813
$949$	−22844.6	−0.781419
$950$	0	0
$951$	−25491.7	−0.869217
$952$	15722.3	0.535255
$953$	24751.1	0.841309	0.420654	−	0.907221i	$-0.361800\pi$
$953$	24751.1	0.841309	0.420654	+	0.907221i	$0.361800\pi$
$954$	−18106.5	−0.614487
$955$	0	0
$956$	2797.66	0.0946473
$957$	203.001	0.00685694
$958$	−28807.4	−0.971530
$959$	11385.0	0.383358
$960$	0	0
$961$	20332.6	0.682508
$962$	24771.6	0.830215
$963$	13955.8	0.466997
$964$	1515.58	0.0506365
$965$	0	0
$966$	13505.8	0.449836
$967$	−28010.8	−0.931506	−0.465753	−	0.884915i	$-0.654216\pi$
$967$	−28010.8	−0.931506	−0.465753	+	0.884915i	$0.654216\pi$
$968$	−28018.4	−0.930315
$969$	−10708.8	−0.355022
$970$	0	0
$971$	14899.5	0.492427	0.246214	−	0.969216i	$-0.420813\pi$
$971$	14899.5	0.492427	0.246214	+	0.969216i	$0.420813\pi$
$972$	153.271	0.00505777
$973$	−3511.67	−0.115703
$974$	22950.3	0.755005
$975$	0	0
$976$	47895.2	1.57079
$977$	−42226.4	−1.38275	−0.691373	−	0.722498i	$-0.742994\pi$
$977$	−42226.4	−1.38275	−0.691373	+	0.722498i	$0.742994\pi$
$978$	7076.17	0.231361
$979$	−22.9362	−0.000748768 0
$980$	0	0
$981$	4022.89	0.130929
$982$	−14744.0	−0.479125
$983$	−17746.0	−0.575797	−0.287898	−	0.957661i	$-0.592957\pi$
$983$	−17746.0	−0.575797	−0.287898	+	0.957661i	$0.592957\pi$
$984$	−22778.9	−0.737971
$985$	0	0
$986$	1258.09	0.0406346
$987$	−16551.5	−0.533779
$988$	−4587.90	−0.147733
$989$	28891.4	0.928912
$990$	0	0
$991$	−17686.2	−0.566923	−0.283461	−	0.958984i	$-0.591483\pi$
$991$	−17686.2	−0.566923	−0.283461	+	0.958984i	$0.591483\pi$
$992$	−6376.03	−0.204072
$993$	−9740.76	−0.311293
$994$	−11212.7	−0.357791
$995$	0	0
$996$	−2098.06	−0.0667467
$997$	−9253.67	−0.293949	−0.146974	−	0.989140i	$-0.546953\pi$
$997$	−9253.67	−0.293949	−0.146974	+	0.989140i	$0.546953\pi$
$998$	47744.9	1.51437
$999$	−2909.44	−0.0921427

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.4.a.g.1.4		14
5.4	even	2		1875.4.a.f.1.11		14
25.11	even	5		75.4.g.b.46.2	yes	28
25.16	even	5		75.4.g.b.31.2	✓	28
75.11	odd	10		225.4.h.a.46.6		28
75.41	odd	10		225.4.h.a.181.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.31.2	✓	28	25.16	even	5
75.4.g.b.46.2	yes	28	25.11	even	5
225.4.h.a.46.6		28	75.11	odd	10
225.4.h.a.181.6		28	75.41	odd	10
1875.4.a.f.1.11		14	5.4	even	2
1875.4.a.g.1.4		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)

\(f(q)\)	\(=\)	\(q-2.93781 q^{2} +3.00000 q^{3} +0.630743 q^{4} -8.81344 q^{6} +18.9115 q^{7} +21.6495 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.93781 q^{2} +3.00000 q^{3} +0.630743 q^{4} -8.81344 q^{6} +18.9115 q^{7} +21.6495 q^{8} +9.00000 q^{9} -6.06780 q^{11} +1.89223 q^{12} +78.2499 q^{13} -55.5585 q^{14} -68.6481 q^{16} +38.4010 q^{17} -26.4403 q^{18} -92.9560 q^{19} +56.7346 q^{21} +17.8261 q^{22} -81.0304 q^{23} +64.9485 q^{24} -229.884 q^{26} +27.0000 q^{27} +11.9283 q^{28} -11.1518 q^{29} -223.883 q^{31} +28.4793 q^{32} -18.2034 q^{33} -112.815 q^{34} +5.67669 q^{36} -107.757 q^{37} +273.087 q^{38} +234.750 q^{39} -350.722 q^{41} -166.676 q^{42} -356.550 q^{43} -3.82722 q^{44} +238.052 q^{46} -291.736 q^{47} -205.944 q^{48} +14.6457 q^{49} +115.203 q^{51} +49.3556 q^{52} +684.808 q^{53} -79.3209 q^{54} +409.425 q^{56} -278.868 q^{57} +32.7619 q^{58} -223.962 q^{59} -697.692 q^{61} +657.726 q^{62} +170.204 q^{63} +465.518 q^{64} +53.4782 q^{66} -909.057 q^{67} +24.2211 q^{68} -243.091 q^{69} +201.818 q^{71} +194.845 q^{72} -291.944 q^{73} +316.570 q^{74} -58.6314 q^{76} -114.751 q^{77} -689.651 q^{78} +709.283 q^{79} +81.0000 q^{81} +1030.36 q^{82} -1108.78 q^{83} +35.7849 q^{84} +1047.48 q^{86} -33.4554 q^{87} -131.365 q^{88} +3.77998 q^{89} +1479.82 q^{91} -51.1094 q^{92} -671.649 q^{93} +857.065 q^{94} +85.4379 q^{96} +18.4630 q^{97} -43.0264 q^{98} -54.6102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 42 q^{3} + 50 q^{4} - 27 q^{7} + 21 q^{8} + 126 q^{9}+O(q^{10}) \) 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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