LMFDB - Embedded newform 1875.2.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,2,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, 2, names="a")

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

chi := DirichletCharacter("1875.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
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:	$14.9719503790$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.44400625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 11x^{4} - x^{3} + 29x^{2} + 3x - 1 $ x^6 - 11x^4 - x^3 + 29x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.01887$ 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)

$f(q)$	$=$	$q-2.01887 q^{2} -1.00000 q^{3} +2.07584 q^{4} +2.01887 q^{6} +1.01887 q^{7} -0.153106 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.01887 q^{2} -1.00000 q^{3} +2.07584 q^{4} +2.01887 q^{6} +1.01887 q^{7} -0.153106 q^{8} +1.00000 q^{9} +4.75961 q^{11} -2.07584 q^{12} -0.103837 q^{13} -2.05697 q^{14} -3.84257 q^{16} -5.83776 q^{17} -2.01887 q^{18} -0.724404 q^{19} -1.01887 q^{21} -9.60904 q^{22} -9.07152 q^{23} +0.153106 q^{24} +0.209634 q^{26} -1.00000 q^{27} +2.11501 q^{28} -3.98847 q^{29} +1.06662 q^{31} +8.06387 q^{32} -4.75961 q^{33} +11.7857 q^{34} +2.07584 q^{36} +4.02621 q^{37} +1.46248 q^{38} +0.103837 q^{39} +7.20977 q^{41} +2.05697 q^{42} +8.62791 q^{43} +9.88018 q^{44} +18.3142 q^{46} -8.19797 q^{47} +3.84257 q^{48} -5.96190 q^{49} +5.83776 q^{51} -0.215549 q^{52} -4.36719 q^{53} +2.01887 q^{54} -0.155995 q^{56} +0.724404 q^{57} +8.05221 q^{58} -4.91285 q^{59} +6.96435 q^{61} -2.15338 q^{62} +1.01887 q^{63} -8.59476 q^{64} +9.60904 q^{66} -9.91998 q^{67} -12.1183 q^{68} +9.07152 q^{69} -10.7866 q^{71} -0.153106 q^{72} +8.63115 q^{73} -8.12840 q^{74} -1.50375 q^{76} +4.84943 q^{77} -0.209634 q^{78} +2.48291 q^{79} +1.00000 q^{81} -14.5556 q^{82} +4.24385 q^{83} -2.11501 q^{84} -17.4186 q^{86} +3.98847 q^{87} -0.728724 q^{88} -18.3752 q^{89} -0.105797 q^{91} -18.8310 q^{92} -1.06662 q^{93} +16.5506 q^{94} -8.06387 q^{96} +6.69876 q^{97} +12.0363 q^{98} +4.75961 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 3 * q^8 + 6 * q^9	$ 6 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 3 q^{8} + 6 q^{9} + 3 q^{11} - 10 q^{12} - 6 q^{13} - 22 q^{14} + 18 q^{16} - 13 q^{17} + 11 q^{19} + 6 q^{21} - 16 q^{22} - 13 q^{23} + 3 q^{24} - 28 q^{26} - 6 q^{27} - 7 q^{28} - 3 q^{29} - 11 q^{31} - 16 q^{32} - 3 q^{33} + 15 q^{34} + 10 q^{36} - 21 q^{37} + 9 q^{38} + 6 q^{39} - q^{41} + 22 q^{42} - 2 q^{43} + 9 q^{44} + 19 q^{46} - 14 q^{47} - 18 q^{48} - 14 q^{49} + 13 q^{51} - 13 q^{52} - 23 q^{53} - 35 q^{56} - 11 q^{57} - 22 q^{58} + 9 q^{59} + 11 q^{61} + 23 q^{62} - 6 q^{63} - 23 q^{64} + 16 q^{66} - 8 q^{67} - 50 q^{68} + 13 q^{69} - 8 q^{71} - 3 q^{72} - 13 q^{73} - 22 q^{74} - 26 q^{76} + 13 q^{77} + 28 q^{78} - 5 q^{79} + 6 q^{81} + 13 q^{82} + 20 q^{83} + 7 q^{84} - 37 q^{86} + 3 q^{87} - 28 q^{88} - 4 q^{89} + 34 q^{91} - 61 q^{92} + 11 q^{93} + 41 q^{94} + 16 q^{96} + 7 q^{97} + 41 q^{98} + 3 q^{99}+O(q^{100}) $ 6 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 3 * q^8 + 6 * q^9 + 3 * q^11 - 10 * q^12 - 6 * q^13 - 22 * q^14 + 18 * q^16 - 13 * q^17 + 11 * q^19 + 6 * q^21 - 16 * q^22 - 13 * q^23 + 3 * q^24 - 28 * q^26 - 6 * q^27 - 7 * q^28 - 3 * q^29 - 11 * q^31 - 16 * q^32 - 3 * q^33 + 15 * q^34 + 10 * q^36 - 21 * q^37 + 9 * q^38 + 6 * q^39 - q^41 + 22 * q^42 - 2 * q^43 + 9 * q^44 + 19 * q^46 - 14 * q^47 - 18 * q^48 - 14 * q^49 + 13 * q^51 - 13 * q^52 - 23 * q^53 - 35 * q^56 - 11 * q^57 - 22 * q^58 + 9 * q^59 + 11 * q^61 + 23 * q^62 - 6 * q^63 - 23 * q^64 + 16 * q^66 - 8 * q^67 - 50 * q^68 + 13 * q^69 - 8 * q^71 - 3 * q^72 - 13 * q^73 - 22 * q^74 - 26 * q^76 + 13 * q^77 + 28 * q^78 - 5 * q^79 + 6 * q^81 + 13 * q^82 + 20 * q^83 + 7 * q^84 - 37 * q^86 + 3 * q^87 - 28 * q^88 - 4 * q^89 + 34 * q^91 - 61 * q^92 + 11 * q^93 + 41 * q^94 + 16 * q^96 + 7 * q^97 + 41 * q^98 + 3 * 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 $

$2$	−2.01887	−1.42756	−0.713778	−	0.700372i	$-0.753018\pi$
$2$	−2.01887	−1.42756	−0.713778	+	0.700372i	$0.753018\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.07584	1.03792
$5$	0	0
$5$	0	0
$6$	2.01887	0.824200
$7$	1.01887	0.385097	0.192548	−	0.981287i	$-0.438325\pi$
$7$	1.01887	0.385097	0.192548	+	0.981287i	$0.438325\pi$
$8$	−0.153106	−0.0541311
$9$	1.00000	0.333333
$10$	0	0
$11$	4.75961	1.43508	0.717538	−	0.696519i	$-0.245269\pi$
$11$	4.75961	1.43508	0.717538	+	0.696519i	$0.245269\pi$
$12$	−2.07584	−0.599243
$13$	−0.103837	−0.0287992	−0.0143996	−	0.999896i	$-0.504584\pi$
$13$	−0.103837	−0.0287992	−0.0143996	+	0.999896i	$0.504584\pi$
$14$	−2.05697	−0.549748
$15$	0	0
$16$	−3.84257	−0.960643
$17$	−5.83776	−1.41587	−0.707933	−	0.706280i	$-0.750372\pi$
$17$	−5.83776	−1.41587	−0.707933	+	0.706280i	$0.750372\pi$
$18$	−2.01887	−0.475852
$19$	−0.724404	−0.166190	−0.0830949	−	0.996542i	$-0.526480\pi$
$19$	−0.724404	−0.166190	−0.0830949	+	0.996542i	$0.526480\pi$
$20$	0	0
$21$	−1.01887	−0.222336
$22$	−9.60904	−2.04865
$23$	−9.07152	−1.89154	−0.945771	−	0.324834i	$-0.894692\pi$
$23$	−9.07152	−1.89154	−0.945771	+	0.324834i	$0.894692\pi$
$24$	0.153106	0.0312526
$25$	0	0
$26$	0.209634	0.0411126
$27$	−1.00000	−0.192450
$28$	2.11501	0.399699
$29$	−3.98847	−0.740641	−0.370320	−	0.928904i	$-0.620752\pi$
$29$	−3.98847	−0.740641	−0.370320	+	0.928904i	$0.620752\pi$
$30$	0	0
$31$	1.06662	0.191571	0.0957857	−	0.995402i	$-0.469464\pi$
$31$	1.06662	0.191571	0.0957857	+	0.995402i	$0.469464\pi$
$32$	8.06387	1.42550
$33$	−4.75961	−0.828542
$34$	11.7857	2.02123
$35$	0	0
$36$	2.07584	0.345973
$37$	4.02621	0.661905	0.330953	−	0.943647i	$-0.392630\pi$
$37$	4.02621	0.661905	0.330953	+	0.943647i	$0.392630\pi$
$38$	1.46248	0.237245
$39$	0.103837	0.0166273
$40$	0	0
$41$	7.20977	1.12598	0.562988	−	0.826465i	$-0.309652\pi$
$41$	7.20977	1.12598	0.562988	+	0.826465i	$0.309652\pi$
$42$	2.05697	0.317397
$43$	8.62791	1.31574	0.657872	−	0.753130i	$-0.271457\pi$
$43$	8.62791	1.31574	0.657872	+	0.753130i	$0.271457\pi$
$44$	9.88018	1.48949
$45$	0	0
$46$	18.3142	2.70028
$47$	−8.19797	−1.19580	−0.597899	−	0.801572i	$-0.703997\pi$
$47$	−8.19797	−1.19580	−0.597899	+	0.801572i	$0.703997\pi$
$48$	3.84257	0.554628
$49$	−5.96190	−0.851700
$50$	0	0
$51$	5.83776	0.817451
$52$	−0.215549	−0.0298913
$53$	−4.36719	−0.599880	−0.299940	−	0.953958i	$-0.596967\pi$
$53$	−4.36719	−0.599880	−0.299940	+	0.953958i	$0.596967\pi$
$54$	2.01887	0.274733
$55$	0	0
$56$	−0.155995	−0.0208457
$57$	0.724404	0.0959497
$58$	8.05221	1.05731
$59$	−4.91285	−0.639599	−0.319799	−	0.947485i	$-0.603616\pi$
$59$	−4.91285	−0.639599	−0.319799	+	0.947485i	$0.603616\pi$
$60$	0	0
$61$	6.96435	0.891694	0.445847	−	0.895109i	$-0.352903\pi$
$61$	6.96435	0.891694	0.445847	+	0.895109i	$0.352903\pi$
$62$	−2.15338	−0.273479
$63$	1.01887	0.128366
$64$	−8.59476	−1.07435
$65$	0	0
$66$	9.60904	1.18279
$67$	−9.91998	−1.21192	−0.605959	−	0.795496i	$-0.707210\pi$
$67$	−9.91998	−1.21192	−0.605959	+	0.795496i	$0.707210\pi$
$68$	−12.1183	−1.46955
$69$	9.07152	1.09208
$70$	0	0
$71$	−10.7866	−1.28013	−0.640065	−	0.768320i	$-0.721093\pi$
$71$	−10.7866	−1.28013	−0.640065	+	0.768320i	$0.721093\pi$
$72$	−0.153106	−0.0180437
$73$	8.63115	1.01020	0.505100	−	0.863061i	$-0.331456\pi$
$73$	8.63115	1.01020	0.505100	+	0.863061i	$0.331456\pi$
$74$	−8.12840	−0.944907
$75$	0	0
$76$	−1.50375	−0.172491
$77$	4.84943	0.552644
$78$	−0.209634	−0.0237363
$79$	2.48291	0.279350	0.139675	−	0.990197i	$-0.455394\pi$
$79$	2.48291	0.279350	0.139675	+	0.990197i	$0.455394\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−14.5556	−1.60740
$83$	4.24385	0.465823	0.232911	−	0.972498i	$-0.425175\pi$
$83$	4.24385	0.465823	0.232911	+	0.972498i	$0.425175\pi$
$84$	−2.11501	−0.230766
$85$	0	0
$86$	−17.4186	−1.87830
$87$	3.98847	0.427609
$88$	−0.728724	−0.0776823
$89$	−18.3752	−1.94777	−0.973884	−	0.227047i	$-0.927093\pi$
$89$	−18.3752	−1.94777	−0.973884	+	0.227047i	$0.927093\pi$
$90$	0	0
$91$	−0.105797	−0.0110905
$92$	−18.8310	−1.96327
$93$	−1.06662	−0.110604
$94$	16.5506	1.70707
$95$	0	0
$96$	−8.06387	−0.823015
$97$	6.69876	0.680156	0.340078	−	0.940397i	$-0.389546\pi$
$97$	6.69876	0.680156	0.340078	+	0.940397i	$0.389546\pi$
$98$	12.0363	1.21585
$99$	4.75961	0.478359
$100$	0	0
$101$	5.66147	0.563337	0.281669	−	0.959512i	$-0.409112\pi$
$101$	5.66147	0.563337	0.281669	+	0.959512i	$0.409112\pi$
$102$	−11.7857	−1.16696
$103$	0.594489	0.0585767	0.0292884	−	0.999571i	$-0.490676\pi$
$103$	0.594489	0.0585767	0.0292884	+	0.999571i	$0.490676\pi$
$104$	0.0158981	0.00155893
$105$	0	0
$106$	8.81680	0.856363
$107$	1.38651	0.134039	0.0670193	−	0.997752i	$-0.478651\pi$
$107$	1.38651	0.134039	0.0670193	+	0.997752i	$0.478651\pi$
$108$	−2.07584	−0.199748
$109$	−8.85677	−0.848325	−0.424162	−	0.905586i	$-0.639431\pi$
$109$	−8.85677	−0.848325	−0.424162	+	0.905586i	$0.639431\pi$
$110$	0	0
$111$	−4.02621	−0.382151
$112$	−3.91508	−0.369941
$113$	6.59039	0.619971	0.309986	−	0.950741i	$-0.399676\pi$
$113$	6.59039	0.619971	0.309986	+	0.950741i	$0.399676\pi$
$114$	−1.46248	−0.136974
$115$	0	0
$116$	−8.27942	−0.768725
$117$	−0.103837	−0.00959975
$118$	9.91841	0.913064
$119$	−5.94793	−0.545245
$120$	0	0
$121$	11.6539	1.05945
$122$	−14.0601	−1.27294
$123$	−7.20977	−0.650083
$124$	2.21414	0.198836
$125$	0	0
$126$	−2.05697	−0.183249
$127$	−7.29144	−0.647011	−0.323505	−	0.946226i	$-0.604861\pi$
$127$	−7.29144	−0.647011	−0.323505	+	0.946226i	$0.604861\pi$
$128$	1.22397	0.108184
$129$	−8.62791	−0.759645
$130$	0	0
$131$	−9.55386	−0.834725	−0.417362	−	0.908740i	$-0.637045\pi$
$131$	−9.55386	−0.834725	−0.417362	+	0.908740i	$0.637045\pi$
$132$	−9.88018	−0.859959
$133$	−0.738074	−0.0639991
$134$	20.0271	1.73008
$135$	0	0
$136$	0.893796	0.0766424
$137$	−6.19984	−0.529688	−0.264844	−	0.964291i	$-0.585320\pi$
$137$	−6.19984	−0.529688	−0.264844	+	0.964291i	$0.585320\pi$
$138$	−18.3142	−1.55901
$139$	−0.906531	−0.0768910	−0.0384455	−	0.999261i	$-0.512241\pi$
$139$	−0.906531	−0.0768910	−0.0384455	+	0.999261i	$0.512241\pi$
$140$	0	0
$141$	8.19797	0.690394
$142$	21.7767	1.82746
$143$	−0.494225	−0.0413291
$144$	−3.84257	−0.320214
$145$	0	0
$146$	−17.4252	−1.44212
$147$	5.96190	0.491729
$148$	8.35776	0.687004
$149$	−4.89808	−0.401267	−0.200633	−	0.979666i	$-0.564300\pi$
$149$	−4.89808	−0.401267	−0.200633	+	0.979666i	$0.564300\pi$
$150$	0	0
$151$	−10.2626	−0.835161	−0.417581	−	0.908640i	$-0.637122\pi$
$151$	−10.2626	−0.835161	−0.417581	+	0.908640i	$0.637122\pi$
$152$	0.110911	0.00899603
$153$	−5.83776	−0.471955
$154$	−9.79036	−0.788930
$155$	0	0
$156$	0.215549	0.0172577
$157$	−8.89537	−0.709928	−0.354964	−	0.934880i	$-0.615507\pi$
$157$	−8.89537	−0.709928	−0.354964	+	0.934880i	$0.615507\pi$
$158$	−5.01268	−0.398788
$159$	4.36719	0.346341
$160$	0	0
$161$	−9.24270	−0.728427
$162$	−2.01887	−0.158617
$163$	11.7791	0.922607	0.461304	−	0.887242i	$-0.347382\pi$
$163$	11.7791	0.922607	0.461304	+	0.887242i	$0.347382\pi$
$164$	14.9663	1.16867
$165$	0	0
$166$	−8.56778	−0.664989
$167$	17.3762	1.34461	0.672306	−	0.740274i	$-0.265304\pi$
$167$	17.3762	1.34461	0.672306	+	0.740274i	$0.265304\pi$
$168$	0.155995	0.0120353
$169$	−12.9892	−0.999171
$170$	0	0
$171$	−0.724404	−0.0553966
$172$	17.9101	1.36564
$173$	−12.9596	−0.985298	−0.492649	−	0.870228i	$-0.663971\pi$
$173$	−12.9596	−0.985298	−0.492649	+	0.870228i	$0.663971\pi$
$174$	−8.05221	−0.610436
$175$	0	0
$176$	−18.2892	−1.37860
$177$	4.91285	0.369273
$178$	37.0971	2.78055
$179$	1.09897	0.0821409	0.0410704	−	0.999156i	$-0.486923\pi$
$179$	1.09897	0.0821409	0.0410704	+	0.999156i	$0.486923\pi$
$180$	0	0
$181$	−14.9797	−1.11343	−0.556716	−	0.830703i	$-0.687939\pi$
$181$	−14.9797	−1.11343	−0.556716	+	0.830703i	$0.687939\pi$
$182$	0.213590	0.0158323
$183$	−6.96435	−0.514820
$184$	1.38890	0.102391
$185$	0	0
$186$	2.15338	0.157893
$187$	−27.7855	−2.03188
$188$	−17.0177	−1.24114
$189$	−1.01887	−0.0741119
$190$	0	0
$191$	−12.7404	−0.921862	−0.460931	−	0.887436i	$-0.652484\pi$
$191$	−12.7404	−0.921862	−0.460931	+	0.887436i	$0.652484\pi$
$192$	8.59476	0.620273
$193$	−4.38386	−0.315557	−0.157779	−	0.987475i	$-0.550433\pi$
$193$	−4.38386	−0.315557	−0.157779	+	0.987475i	$0.550433\pi$
$194$	−13.5239	−0.970962
$195$	0	0
$196$	−12.3759	−0.883996
$197$	3.22165	0.229533	0.114767	−	0.993392i	$-0.463388\pi$
$197$	3.22165	0.229533	0.114767	+	0.993392i	$0.463388\pi$
$198$	−9.60904	−0.682885
$199$	−2.70518	−0.191765	−0.0958825	−	0.995393i	$-0.530567\pi$
$199$	−2.70518	−0.191765	−0.0958825	+	0.995393i	$0.530567\pi$
$200$	0	0
$201$	9.91998	0.699701
$202$	−11.4298	−0.804196
$203$	−4.06374	−0.285218
$204$	12.1183	0.848447
$205$	0	0
$206$	−1.20020	−0.0836216
$207$	−9.07152	−0.630514
$208$	0.399002	0.0276658
$209$	−3.44788	−0.238495
$210$	0	0
$211$	26.4435	1.82044	0.910222	−	0.414122i	$-0.135911\pi$
$211$	26.4435	1.82044	0.910222	+	0.414122i	$0.135911\pi$
$212$	−9.06559	−0.622627
$213$	10.7866	0.739084
$214$	−2.79918	−0.191348
$215$	0	0
$216$	0.153106	0.0104175
$217$	1.08675	0.0737736
$218$	17.8807	1.21103
$219$	−8.63115	−0.583239
$220$	0	0
$221$	0.606177	0.0407759
$222$	8.12840	0.545543
$223$	−8.03245	−0.537893	−0.268946	−	0.963155i	$-0.586675\pi$
$223$	−8.03245	−0.537893	−0.268946	+	0.963155i	$0.586675\pi$
$224$	8.21604	0.548957
$225$	0	0
$226$	−13.3051	−0.885044
$227$	16.4576	1.09233	0.546166	−	0.837677i	$-0.316087\pi$
$227$	16.4576	1.09233	0.546166	+	0.837677i	$0.316087\pi$
$228$	1.50375	0.0995880
$229$	0.409285	0.0270463	0.0135231	−	0.999909i	$-0.495695\pi$
$229$	0.409285	0.0270463	0.0135231	+	0.999909i	$0.495695\pi$
$230$	0	0
$231$	−4.84943	−0.319069
$232$	0.610658	0.0400917
$233$	−18.4641	−1.20962	−0.604811	−	0.796369i	$-0.706751\pi$
$233$	−18.4641	−1.20962	−0.604811	+	0.796369i	$0.706751\pi$
$234$	0.209634	0.0137042
$235$	0	0
$236$	−10.1983	−0.663852
$237$	−2.48291	−0.161283
$238$	12.0081	0.778369
$239$	−4.61682	−0.298637	−0.149319	−	0.988789i	$-0.547708\pi$
$239$	−4.61682	−0.298637	−0.149319	+	0.988789i	$0.547708\pi$
$240$	0	0
$241$	−29.2022	−1.88108	−0.940540	−	0.339682i	$-0.889681\pi$
$241$	−29.2022	−1.88108	−0.940540	+	0.339682i	$0.889681\pi$
$242$	−23.5277	−1.51242
$243$	−1.00000	−0.0641500
$244$	14.4569	0.925506
$245$	0	0
$246$	14.5556	0.928030
$247$	0.0752201	0.00478614
$248$	−0.163307	−0.0103700
$249$	−4.24385	−0.268943
$250$	0	0
$251$	0.389664	0.0245954	0.0122977	−	0.999924i	$-0.496085\pi$
$251$	0.389664	0.0245954	0.0122977	+	0.999924i	$0.496085\pi$
$252$	2.11501	0.133233
$253$	−43.1769	−2.71451
$254$	14.7205	0.923645
$255$	0	0
$256$	14.7185	0.919906
$257$	8.03324	0.501100	0.250550	−	0.968104i	$-0.419389\pi$
$257$	8.03324	0.501100	0.250550	+	0.968104i	$0.419389\pi$
$258$	17.4186	1.08444
$259$	4.10219	0.254898
$260$	0	0
$261$	−3.98847	−0.246880
$262$	19.2880	1.19162
$263$	−24.2131	−1.49304	−0.746522	−	0.665360i	$-0.768278\pi$
$263$	−24.2131	−1.49304	−0.746522	+	0.665360i	$0.768278\pi$
$264$	0.728724	0.0448499
$265$	0	0
$266$	1.49008	0.0913624
$267$	18.3752	1.12454
$268$	−20.5923	−1.25787
$269$	26.4063	1.61002	0.805009	−	0.593263i	$-0.202161\pi$
$269$	26.4063	1.61002	0.805009	+	0.593263i	$0.202161\pi$
$270$	0	0
$271$	−10.4088	−0.632287	−0.316144	−	0.948711i	$-0.602388\pi$
$271$	−10.4088	−0.632287	−0.316144	+	0.948711i	$0.602388\pi$
$272$	22.4320	1.36014
$273$	0.105797	0.00640310
$274$	12.5167	0.756160
$275$	0	0
$276$	18.8310	1.13349
$277$	−24.5207	−1.47330	−0.736652	−	0.676272i	$-0.763595\pi$
$277$	−24.5207	−1.47330	−0.736652	+	0.676272i	$0.763595\pi$
$278$	1.83017	0.109766
$279$	1.06662	0.0638572
$280$	0	0
$281$	−14.4228	−0.860393	−0.430197	−	0.902735i	$-0.641556\pi$
$281$	−14.4228	−0.860393	−0.430197	+	0.902735i	$0.641556\pi$
$282$	−16.5506	−0.985576
$283$	2.14925	0.127760	0.0638798	−	0.997958i	$-0.479653\pi$
$283$	2.14925	0.127760	0.0638798	+	0.997958i	$0.479653\pi$
$284$	−22.3912	−1.32867
$285$	0	0
$286$	0.997775	0.0589997
$287$	7.34582	0.433610
$288$	8.06387	0.475168
$289$	17.0795	1.00468
$290$	0	0
$291$	−6.69876	−0.392688
$292$	17.9169	1.04851
$293$	−9.02970	−0.527521	−0.263760	−	0.964588i	$-0.584963\pi$
$293$	−9.02970	−0.527521	−0.263760	+	0.964588i	$0.584963\pi$
$294$	−12.0363	−0.701972
$295$	0	0
$296$	−0.616437	−0.0358297
$297$	−4.75961	−0.276181
$298$	9.88860	0.572831
$299$	0.941960	0.0544750
$300$	0	0
$301$	8.79072	0.506689
$302$	20.7189	1.19224
$303$	−5.66147	−0.325243
$304$	2.78358	0.159649
$305$	0	0
$306$	11.7857	0.673743
$307$	5.03454	0.287336	0.143668	−	0.989626i	$-0.454110\pi$
$307$	5.03454	0.287336	0.143668	+	0.989626i	$0.454110\pi$
$308$	10.0666	0.573599
$309$	−0.594489	−0.0338193
$310$	0	0
$311$	−4.89158	−0.277376	−0.138688	−	0.990336i	$-0.544289\pi$
$311$	−4.89158	−0.277376	−0.138688	+	0.990336i	$0.544289\pi$
$312$	−0.0158981	−0.000900051 0
$313$	−3.17282	−0.179338	−0.0896691	−	0.995972i	$-0.528581\pi$
$313$	−3.17282	−0.179338	−0.0896691	+	0.995972i	$0.528581\pi$
$314$	17.9586	1.01346
$315$	0	0
$316$	5.15413	0.289942
$317$	−19.9953	−1.12305	−0.561524	−	0.827461i	$-0.689785\pi$
$317$	−19.9953	−1.12305	−0.561524	+	0.827461i	$0.689785\pi$
$318$	−8.81680	−0.494422
$319$	−18.9836	−1.06288
$320$	0	0
$321$	−1.38651	−0.0773872
$322$	18.6598	1.03987
$323$	4.22890	0.235302
$324$	2.07584	0.115324
$325$	0	0
$326$	−23.7804	−1.31707
$327$	8.85677	0.489780
$328$	−1.10386	−0.0609503
$329$	−8.35267	−0.460498
$330$	0	0
$331$	6.01724	0.330738	0.165369	−	0.986232i	$-0.447119\pi$
$331$	6.01724	0.330738	0.165369	+	0.986232i	$0.447119\pi$
$332$	8.80954	0.483486
$333$	4.02621	0.220635
$334$	−35.0803	−1.91951
$335$	0	0
$336$	3.91508	0.213585
$337$	22.8136	1.24274	0.621369	−	0.783518i	$-0.286577\pi$
$337$	22.8136	1.24274	0.621369	+	0.783518i	$0.286577\pi$
$338$	26.2235	1.42637
$339$	−6.59039	−0.357941
$340$	0	0
$341$	5.07672	0.274920
$342$	1.46248	0.0790818
$343$	−13.2065	−0.713084
$344$	−1.32098	−0.0712227
$345$	0	0
$346$	26.1637	1.40657
$347$	9.79068	0.525591	0.262796	−	0.964852i	$-0.415356\pi$
$347$	9.79068	0.525591	0.262796	+	0.964852i	$0.415356\pi$
$348$	8.27942	0.443823
$349$	−1.28648	−0.0688639	−0.0344320	−	0.999407i	$-0.510962\pi$
$349$	−1.28648	−0.0688639	−0.0344320	+	0.999407i	$0.510962\pi$
$350$	0	0
$351$	0.103837	0.00554242
$352$	38.3809	2.04571
$353$	1.16422	0.0619654	0.0309827	−	0.999520i	$-0.490136\pi$
$353$	1.16422	0.0619654	0.0309827	+	0.999520i	$0.490136\pi$
$354$	−9.91841	−0.527158
$355$	0	0
$356$	−38.1439	−2.02162
$357$	5.94793	0.314798
$358$	−2.21868	−0.117261
$359$	19.0504	1.00544	0.502720	−	0.864449i	$-0.332333\pi$
$359$	19.0504	1.00544	0.502720	+	0.864449i	$0.332333\pi$
$360$	0	0
$361$	−18.4752	−0.972381
$362$	30.2421	1.58949
$363$	−11.6539	−0.611671
$364$	−0.219617	−0.0115110
$365$	0	0
$366$	14.0601	0.734935
$367$	16.7694	0.875357	0.437679	−	0.899131i	$-0.355801\pi$
$367$	16.7694	0.875357	0.437679	+	0.899131i	$0.355801\pi$
$368$	34.8580	1.81710
$369$	7.20977	0.375326
$370$	0	0
$371$	−4.44960	−0.231012
$372$	−2.21414	−0.114798
$373$	−17.0520	−0.882920	−0.441460	−	0.897281i	$-0.645539\pi$
$373$	−17.0520	−0.882920	−0.441460	+	0.897281i	$0.645539\pi$
$374$	56.0953	2.90062
$375$	0	0
$376$	1.25516	0.0647298
$377$	0.414152	0.0213299
$378$	2.05697	0.105799
$379$	1.66611	0.0855825	0.0427913	−	0.999084i	$-0.486375\pi$
$379$	1.66611	0.0855825	0.0427913	+	0.999084i	$0.486375\pi$
$380$	0	0
$381$	7.29144	0.373552
$382$	25.7212	1.31601
$383$	3.05361	0.156032	0.0780162	−	0.996952i	$-0.475141\pi$
$383$	3.05361	0.156032	0.0780162	+	0.996952i	$0.475141\pi$
$384$	−1.22397	−0.0624603
$385$	0	0
$386$	8.85045	0.450476
$387$	8.62791	0.438581
$388$	13.9055	0.705947
$389$	28.2725	1.43347	0.716737	−	0.697343i	$-0.245635\pi$
$389$	28.2725	1.43347	0.716737	+	0.697343i	$0.245635\pi$
$390$	0	0
$391$	52.9574	2.67817
$392$	0.912802	0.0461035
$393$	9.55386	0.481928
$394$	−6.50410	−0.327672
$395$	0	0
$396$	9.88018	0.496498
$397$	−20.4783	−1.02778	−0.513888	−	0.857858i	$-0.671795\pi$
$397$	−20.4783	−1.02778	−0.513888	+	0.857858i	$0.671795\pi$
$398$	5.46140	0.273755
$399$	0.738074	0.0369499
$400$	0	0
$401$	25.5952	1.27816	0.639081	−	0.769139i	$-0.279315\pi$
$401$	25.5952	1.27816	0.639081	+	0.769139i	$0.279315\pi$
$402$	−20.0271	−0.998863
$403$	−0.110755	−0.00551711
$404$	11.7523	0.584698
$405$	0	0
$406$	8.20416	0.407165
$407$	19.1632	0.949885
$408$	−0.893796	−0.0442495
$409$	−12.0402	−0.595349	−0.297675	−	0.954667i	$-0.596211\pi$
$409$	−12.0402	−0.595349	−0.297675	+	0.954667i	$0.596211\pi$
$410$	0	0
$411$	6.19984	0.305816
$412$	1.23406	0.0607979
$413$	−5.00556	−0.246307
$414$	18.3142	0.900095
$415$	0	0
$416$	−0.837329	−0.0410534
$417$	0.906531	0.0443930
$418$	6.96083	0.340465
$419$	−34.6045	−1.69054	−0.845270	−	0.534340i	$-0.820560\pi$
$419$	−34.6045	−1.69054	−0.845270	+	0.534340i	$0.820560\pi$
$420$	0	0
$421$	−14.9525	−0.728738	−0.364369	−	0.931255i	$-0.618715\pi$
$421$	−14.9525	−0.728738	−0.364369	+	0.931255i	$0.618715\pi$
$422$	−53.3859	−2.59879
$423$	−8.19797	−0.398599
$424$	0.668643	0.0324722
$425$	0	0
$426$	−21.7767	−1.05508
$427$	7.09577	0.343389
$428$	2.87816	0.139121
$429$	0.494225	0.0238614
$430$	0	0
$431$	4.81107	0.231741	0.115871	−	0.993264i	$-0.463034\pi$
$431$	4.81107	0.231741	0.115871	+	0.993264i	$0.463034\pi$
$432$	3.84257	0.184876
$433$	10.3435	0.497077	0.248538	−	0.968622i	$-0.420050\pi$
$433$	10.3435	0.497077	0.248538	+	0.968622i	$0.420050\pi$
$434$	−2.19401	−0.105316
$435$	0	0
$436$	−18.3852	−0.880492
$437$	6.57145	0.314355
$438$	17.4252	0.832607
$439$	30.7640	1.46829	0.734143	−	0.678995i	$-0.237584\pi$
$439$	30.7640	1.46829	0.734143	+	0.678995i	$0.237584\pi$
$440$	0	0
$441$	−5.96190	−0.283900
$442$	−1.22379	−0.0582099
$443$	−17.7545	−0.843543	−0.421772	−	0.906702i	$-0.638592\pi$
$443$	−17.7545	−0.843543	−0.421772	+	0.906702i	$0.638592\pi$
$444$	−8.35776	−0.396642
$445$	0	0
$446$	16.2165	0.767873
$447$	4.89808	0.231671
$448$	−8.75695	−0.413727
$449$	−37.2184	−1.75645	−0.878223	−	0.478251i	$-0.841271\pi$
$449$	−37.2184	−1.75645	−0.878223	+	0.478251i	$0.841271\pi$
$450$	0	0
$451$	34.3157	1.61586
$452$	13.6806	0.643480
$453$	10.2626	0.482181
$454$	−33.2258	−1.55937
$455$	0	0
$456$	−0.110911	−0.00519386
$457$	−27.6987	−1.29569	−0.647846	−	0.761772i	$-0.724330\pi$
$457$	−27.6987	−1.29569	−0.647846	+	0.761772i	$0.724330\pi$
$458$	−0.826293	−0.0386101
$459$	5.83776	0.272484
$460$	0	0
$461$	9.81742	0.457243	0.228621	−	0.973515i	$-0.426578\pi$
$461$	9.81742	0.457243	0.228621	+	0.973515i	$0.426578\pi$
$462$	9.79036	0.455489
$463$	−3.72732	−0.173223	−0.0866115	−	0.996242i	$-0.527604\pi$
$463$	−3.72732	−0.173223	−0.0866115	+	0.996242i	$0.527604\pi$
$464$	15.3260	0.711492
$465$	0	0
$466$	37.2766	1.72680
$467$	−7.09925	−0.328514	−0.164257	−	0.986418i	$-0.552523\pi$
$467$	−7.09925	−0.328514	−0.164257	+	0.986418i	$0.552523\pi$
$468$	−0.215549	−0.00996376
$469$	−10.1072	−0.466706
$470$	0	0
$471$	8.89537	0.409877
$472$	0.752186	0.0346222
$473$	41.0655	1.88819
$474$	5.01268	0.230240
$475$	0	0
$476$	−12.3469	−0.565920
$477$	−4.36719	−0.199960
$478$	9.32076	0.426322
$479$	−28.4451	−1.29969	−0.649845	−	0.760066i	$-0.725166\pi$
$479$	−28.4451	−1.29969	−0.649845	+	0.760066i	$0.725166\pi$
$480$	0	0
$481$	−0.418070	−0.0190624
$482$	58.9555	2.68535
$483$	9.24270	0.420557
$484$	24.1916	1.09962
$485$	0	0
$486$	2.01887	0.0915778
$487$	−14.7384	−0.667860	−0.333930	−	0.942598i	$-0.608375\pi$
$487$	−14.7384	−0.667860	−0.333930	+	0.942598i	$0.608375\pi$
$488$	−1.06628	−0.0482684
$489$	−11.7791	−0.532668
$490$	0	0
$491$	−28.4014	−1.28174	−0.640869	−	0.767650i	$-0.721426\pi$
$491$	−28.4014	−1.28174	−0.640869	+	0.767650i	$0.721426\pi$
$492$	−14.9663	−0.674733
$493$	23.2838	1.04865
$494$	−0.151860	−0.00683248
$495$	0	0
$496$	−4.09858	−0.184032
$497$	−10.9901	−0.492974
$498$	8.56778	0.383931
$499$	26.3842	1.18112	0.590559	−	0.806995i	$-0.298907\pi$
$499$	26.3842	1.18112	0.590559	+	0.806995i	$0.298907\pi$
$500$	0	0
$501$	−17.3762	−0.776312
$502$	−0.786682	−0.0351113
$503$	16.6592	0.742795	0.371398	−	0.928474i	$-0.378879\pi$
$503$	16.6592	0.742795	0.371398	+	0.928474i	$0.378879\pi$
$504$	−0.155995	−0.00694857
$505$	0	0
$506$	87.1686	3.87512
$507$	12.9892	0.576871
$508$	−15.1358	−0.671544
$509$	−31.7760	−1.40845	−0.704223	−	0.709979i	$-0.748704\pi$
$509$	−31.7760	−1.40845	−0.704223	+	0.709979i	$0.748704\pi$
$510$	0	0
$511$	8.79403	0.389025
$512$	−32.1627	−1.42140
$513$	0.724404	0.0319832
$514$	−16.2181	−0.715349
$515$	0	0
$516$	−17.9101	−0.788450
$517$	−39.0192	−1.71606
$518$	−8.28179	−0.363881
$519$	12.9596	0.568862
$520$	0	0
$521$	−0.592363	−0.0259519	−0.0129759	−	0.999916i	$-0.504130\pi$
$521$	−0.592363	−0.0259519	−0.0129759	+	0.999916i	$0.504130\pi$
$522$	8.05221	0.352436
$523$	−17.2298	−0.753405	−0.376703	−	0.926334i	$-0.622942\pi$
$523$	−17.2298	−0.753405	−0.376703	+	0.926334i	$0.622942\pi$
$524$	−19.8323	−0.866376
$525$	0	0
$526$	48.8832	2.13141
$527$	−6.22670	−0.271240
$528$	18.2892	0.795934
$529$	59.2924	2.57793
$530$	0	0
$531$	−4.91285	−0.213200
$532$	−1.53212	−0.0664259
$533$	−0.748642	−0.0324273
$534$	−37.0971	−1.60535
$535$	0	0
$536$	1.51881	0.0656025
$537$	−1.09897	−0.0474241
$538$	−53.3108	−2.29839
$539$	−28.3763	−1.22226
$540$	0	0
$541$	14.7990	0.636258	0.318129	−	0.948047i	$-0.396945\pi$
$541$	14.7990	0.636258	0.318129	+	0.948047i	$0.396945\pi$
$542$	21.0139	0.902626
$543$	14.9797	0.642840
$544$	−47.0750	−2.01832
$545$	0	0
$546$	−0.213590	−0.00914079
$547$	6.50806	0.278264	0.139132	−	0.990274i	$-0.455569\pi$
$547$	6.50806	0.278264	0.139132	+	0.990274i	$0.455569\pi$
$548$	−12.8699	−0.549773
$549$	6.96435	0.297231
$550$	0	0
$551$	2.88927	0.123087
$552$	−1.38890	−0.0591156
$553$	2.52977	0.107577
$554$	49.5041	2.10323
$555$	0	0
$556$	−1.88181	−0.0798066
$557$	−6.67224	−0.282712	−0.141356	−	0.989959i	$-0.545146\pi$
$557$	−6.67224	−0.282712	−0.141356	+	0.989959i	$0.545146\pi$
$558$	−2.15338	−0.0911597
$559$	−0.895898	−0.0378924
$560$	0	0
$561$	27.7855	1.17310
$562$	29.1178	1.22826
$563$	20.0663	0.845694	0.422847	−	0.906201i	$-0.361031\pi$
$563$	20.0663	0.845694	0.422847	+	0.906201i	$0.361031\pi$
$564$	17.0177	0.716573
$565$	0	0
$566$	−4.33906	−0.182384
$567$	1.01887	0.0427885
$568$	1.65149	0.0692949
$569$	−21.5938	−0.905261	−0.452631	−	0.891698i	$-0.649514\pi$
$569$	−21.5938	−0.905261	−0.452631	+	0.891698i	$0.649514\pi$
$570$	0	0
$571$	−26.3338	−1.10203	−0.551017	−	0.834494i	$-0.685760\pi$
$571$	−26.3338	−1.10203	−0.551017	+	0.834494i	$0.685760\pi$
$572$	−1.02593	−0.0428963
$573$	12.7404	0.532237
$574$	−14.8303	−0.619003
$575$	0	0
$576$	−8.59476	−0.358115
$577$	−9.18240	−0.382268	−0.191134	−	0.981564i	$-0.561217\pi$
$577$	−9.18240	−0.382268	−0.191134	+	0.981564i	$0.561217\pi$
$578$	−34.4813	−1.43423
$579$	4.38386	0.182187
$580$	0	0
$581$	4.32393	0.179387
$582$	13.5239	0.560585
$583$	−20.7861	−0.860874
$584$	−1.32148	−0.0546832
$585$	0	0
$586$	18.2298	0.753066
$587$	39.9771	1.65003	0.825017	−	0.565108i	$-0.191166\pi$
$587$	39.9771	1.65003	0.825017	+	0.565108i	$0.191166\pi$
$588$	12.3759	0.510375
$589$	−0.772668	−0.0318372
$590$	0	0
$591$	−3.22165	−0.132521
$592$	−15.4710	−0.635855
$593$	−41.6331	−1.70967	−0.854834	−	0.518902i	$-0.826341\pi$
$593$	−41.6331	−1.70967	−0.854834	+	0.518902i	$0.826341\pi$
$594$	9.60904	0.394264
$595$	0	0
$596$	−10.1676	−0.416482
$597$	2.70518	0.110716
$598$	−1.90170	−0.0777661
$599$	39.0726	1.59646	0.798232	−	0.602350i	$-0.205769\pi$
$599$	39.0726	1.59646	0.798232	+	0.602350i	$0.205769\pi$
$600$	0	0
$601$	5.46965	0.223112	0.111556	−	0.993758i	$-0.464417\pi$
$601$	5.46965	0.223112	0.111556	+	0.993758i	$0.464417\pi$
$602$	−17.7473	−0.723327
$603$	−9.91998	−0.403973
$604$	−21.3036	−0.866829
$605$	0	0
$606$	11.4298	0.464303
$607$	42.3108	1.71734	0.858671	−	0.512527i	$-0.171291\pi$
$607$	42.3108	1.71734	0.858671	+	0.512527i	$0.171291\pi$
$608$	−5.84150	−0.236904
$609$	4.06374	0.164671
$610$	0	0
$611$	0.851254	0.0344380
$612$	−12.1183	−0.489851
$613$	−34.0064	−1.37351	−0.686753	−	0.726891i	$-0.740965\pi$
$613$	−34.0064	−1.37351	−0.686753	+	0.726891i	$0.740965\pi$
$614$	−10.1641	−0.410189
$615$	0	0
$616$	−0.742476	−0.0299152
$617$	23.3173	0.938717	0.469359	−	0.883008i	$-0.344485\pi$
$617$	23.3173	0.938717	0.469359	+	0.883008i	$0.344485\pi$
$618$	1.20020	0.0482790
$619$	35.2998	1.41882	0.709409	−	0.704797i	$-0.248962\pi$
$619$	35.2998	1.41882	0.709409	+	0.704797i	$0.248962\pi$
$620$	0	0
$621$	9.07152	0.364027
$622$	9.87547	0.395970
$623$	−18.7219	−0.750079
$624$	−0.399002	−0.0159729
$625$	0	0
$626$	6.40551	0.256016
$627$	3.44788	0.137695
$628$	−18.4653	−0.736847
$629$	−23.5041	−0.937169
$630$	0	0
$631$	−3.50433	−0.139505	−0.0697526	−	0.997564i	$-0.522221\pi$
$631$	−3.50433	−0.139505	−0.0697526	+	0.997564i	$0.522221\pi$
$632$	−0.380149	−0.0151215
$633$	−26.4435	−1.05103
$634$	40.3679	1.60321
$635$	0	0
$636$	9.06559	0.359474
$637$	0.619067	0.0245283
$638$	38.3254	1.51732
$639$	−10.7866	−0.426710
$640$	0	0
$641$	−9.28841	−0.366870	−0.183435	−	0.983032i	$-0.558722\pi$
$641$	−9.28841	−0.366870	−0.183435	+	0.983032i	$0.558722\pi$
$642$	2.79918	0.110475
$643$	−0.0291680	−0.00115028	−0.000575138	−	1.00000i	$-0.500183\pi$
$643$	−0.0291680	−0.00115028	−0.000575138		1.00000i	$0.500183\pi$
$644$	−19.1863	−0.756048
$645$	0	0
$646$	−8.53760	−0.335908
$647$	−0.844100	−0.0331850	−0.0165925	−	0.999862i	$-0.505282\pi$
$647$	−0.844100	−0.0331850	−0.0165925	+	0.999862i	$0.505282\pi$
$648$	−0.153106	−0.00601457
$649$	−23.3833	−0.917874
$650$	0	0
$651$	−1.08675	−0.0425932
$652$	24.4514	0.957591
$653$	38.0711	1.48984	0.744918	−	0.667156i	$-0.232489\pi$
$653$	38.0711	1.48984	0.744918	+	0.667156i	$0.232489\pi$
$654$	−17.8807	−0.699189
$655$	0	0
$656$	−27.7041	−1.08166
$657$	8.63115	0.336733
$658$	16.8630	0.657387
$659$	37.8343	1.47382	0.736908	−	0.675993i	$-0.236285\pi$
$659$	37.8343	1.47382	0.736908	+	0.675993i	$0.236285\pi$
$660$	0	0
$661$	−18.5614	−0.721956	−0.360978	−	0.932574i	$-0.617557\pi$
$661$	−18.5614	−0.721956	−0.360978	+	0.932574i	$0.617557\pi$
$662$	−12.1480	−0.472147
$663$	−0.606177	−0.0235420
$664$	−0.649758	−0.0252155
$665$	0	0
$666$	−8.12840	−0.314969
$667$	36.1815	1.40095
$668$	36.0702	1.39560
$669$	8.03245	0.310553
$670$	0	0
$671$	33.1476	1.27965
$672$	−8.21604	−0.316941
$673$	18.1607	0.700044	0.350022	−	0.936742i	$-0.386174\pi$
$673$	18.1607	0.700044	0.350022	+	0.936742i	$0.386174\pi$
$674$	−46.0578	−1.77408
$675$	0	0
$676$	−26.9635	−1.03706
$677$	−5.64312	−0.216883	−0.108441	−	0.994103i	$-0.534586\pi$
$677$	−5.64312	−0.216883	−0.108441	+	0.994103i	$0.534586\pi$
$678$	13.3051	0.510981
$679$	6.82517	0.261926
$680$	0	0
$681$	−16.4576	−0.630658
$682$	−10.2492	−0.392464
$683$	30.4468	1.16502	0.582508	−	0.812825i	$-0.302071\pi$
$683$	30.4468	1.16502	0.582508	+	0.812825i	$0.302071\pi$
$684$	−1.50375	−0.0574971
$685$	0	0
$686$	26.6622	1.01797
$687$	−0.409285	−0.0156152
$688$	−33.1534	−1.26396
$689$	0.453477	0.0172761
$690$	0	0
$691$	−9.22470	−0.350924	−0.175462	−	0.984486i	$-0.556142\pi$
$691$	−9.22470	−0.350924	−0.175462	+	0.984486i	$0.556142\pi$
$692$	−26.9020	−1.02266
$693$	4.84943	0.184215
$694$	−19.7661	−0.750311
$695$	0	0
$696$	−0.610658	−0.0231469
$697$	−42.0889	−1.59423
$698$	2.59724	0.0983071
$699$	18.4641	0.698375
$700$	0	0
$701$	−19.9822	−0.754717	−0.377358	−	0.926067i	$-0.623168\pi$
$701$	−19.9822	−0.754717	−0.377358	+	0.926067i	$0.623168\pi$
$702$	−0.209634	−0.00791212
$703$	−2.91661	−0.110002
$704$	−40.9077	−1.54177
$705$	0	0
$706$	−2.35042	−0.0884591
$707$	5.76830	0.216939
$708$	10.1983	0.383275
$709$	−26.8259	−1.00747	−0.503734	−	0.863859i	$-0.668041\pi$
$709$	−26.8259	−1.00747	−0.503734	+	0.863859i	$0.668041\pi$
$710$	0	0
$711$	2.48291	0.0931166
$712$	2.81335	0.105435
$713$	−9.67591	−0.362366
$714$	−12.0081	−0.449391
$715$	0	0
$716$	2.28128	0.0852556
$717$	4.61682	0.172418
$718$	−38.4602	−1.43532
$719$	38.8224	1.44783	0.723915	−	0.689889i	$-0.242341\pi$
$719$	38.8224	1.44783	0.723915	+	0.689889i	$0.242341\pi$
$720$	0	0
$721$	0.605707	0.0225577
$722$	37.2991	1.38813
$723$	29.2022	1.08604
$724$	−31.0954	−1.15565
$725$	0	0
$726$	23.5277	0.873196
$727$	29.5764	1.09693	0.548465	−	0.836174i	$-0.315213\pi$
$727$	29.5764	1.09693	0.548465	+	0.836174i	$0.315213\pi$
$728$	0.0161981	0.000600341 0
$729$	1.00000	0.0370370
$730$	0	0
$731$	−50.3677	−1.86292
$732$	−14.4569	−0.534341
$733$	−48.8782	−1.80536	−0.902679	−	0.430315i	$-0.858402\pi$
$733$	−48.8782	−1.80536	−0.902679	+	0.430315i	$0.858402\pi$
$734$	−33.8553	−1.24962
$735$	0	0
$736$	−73.1515	−2.69640
$737$	−47.2152	−1.73920
$738$	−14.5556	−0.535799
$739$	21.7603	0.800466	0.400233	−	0.916413i	$-0.368929\pi$
$739$	21.7603	0.800466	0.400233	+	0.916413i	$0.368929\pi$
$740$	0	0
$741$	−0.0752201	−0.00276328
$742$	8.98317	0.329783
$743$	−9.75724	−0.357959	−0.178979	−	0.983853i	$-0.557280\pi$
$743$	−9.75724	−0.357959	−0.178979	+	0.983853i	$0.557280\pi$
$744$	0.163307	0.00598711
$745$	0	0
$746$	34.4258	1.26042
$747$	4.24385	0.155274
$748$	−57.6782	−2.10892
$749$	1.41267	0.0516178
$750$	0	0
$751$	−17.6413	−0.643741	−0.321871	−	0.946784i	$-0.604312\pi$
$751$	−17.6413	−0.643741	−0.321871	+	0.946784i	$0.604312\pi$
$752$	31.5013	1.14873
$753$	−0.389664	−0.0142002
$754$	−0.836118	−0.0304496
$755$	0	0
$756$	−2.11501	−0.0769221
$757$	−44.2551	−1.60848	−0.804240	−	0.594305i	$-0.797427\pi$
$757$	−44.2551	−1.60848	−0.804240	+	0.594305i	$0.797427\pi$
$758$	−3.36367	−0.122174
$759$	43.1769	1.56722
$760$	0	0
$761$	39.8755	1.44549	0.722743	−	0.691117i	$-0.242881\pi$
$761$	39.8755	1.44549	0.722743	+	0.691117i	$0.242881\pi$
$762$	−14.7205	−0.533266
$763$	−9.02390	−0.326687
$764$	−26.4470	−0.956818
$765$	0	0
$766$	−6.16485	−0.222745
$767$	0.510137	0.0184200
$768$	−14.7185	−0.531108
$769$	35.2667	1.27175	0.635876	−	0.771792i	$-0.280639\pi$
$769$	35.2667	1.27175	0.635876	+	0.771792i	$0.280639\pi$
$770$	0	0
$771$	−8.03324	−0.289310
$772$	−9.10018	−0.327523
$773$	−23.2417	−0.835946	−0.417973	−	0.908459i	$-0.637259\pi$
$773$	−23.2417	−0.835946	−0.417973	+	0.908459i	$0.637259\pi$
$774$	−17.4186	−0.626100
$775$	0	0
$776$	−1.02562	−0.0368176
$777$	−4.10219	−0.147165
$778$	−57.0786	−2.04637
$779$	−5.22279	−0.187126
$780$	0	0
$781$	−51.3399	−1.83709
$782$	−106.914	−3.82324
$783$	3.98847	0.142536
$784$	22.9091	0.818180
$785$	0	0
$786$	−19.2880	−0.687980
$787$	6.83095	0.243497	0.121749	−	0.992561i	$-0.461150\pi$
$787$	6.83095	0.243497	0.121749	+	0.992561i	$0.461150\pi$
$788$	6.68762	0.238237
$789$	24.2131	0.862010
$790$	0	0
$791$	6.71475	0.238749
$792$	−0.728724	−0.0258941
$793$	−0.723159	−0.0256801
$794$	41.3430	1.46721
$795$	0	0
$796$	−5.61551	−0.199036
$797$	53.9287	1.91025	0.955126	−	0.296198i	$-0.0957190\pi$
$797$	53.9287	1.91025	0.955126	+	0.296198i	$0.0957190\pi$
$798$	−1.49008	−0.0527481
$799$	47.8578	1.69309
$800$	0	0
$801$	−18.3752	−0.649256
$802$	−51.6734	−1.82465
$803$	41.0809	1.44971
$804$	20.5923	0.726233
$805$	0	0
$806$	0.223601	0.00787599
$807$	−26.4063	−0.929544
$808$	−0.866804	−0.0304941
$809$	−18.4104	−0.647275	−0.323637	−	0.946181i	$-0.604906\pi$
$809$	−18.4104	−0.647275	−0.323637	+	0.946181i	$0.604906\pi$
$810$	0	0
$811$	−11.7910	−0.414040	−0.207020	−	0.978337i	$-0.566376\pi$
$811$	−11.7910	−0.414040	−0.207020	+	0.978337i	$0.566376\pi$
$812$	−8.43565	−0.296033
$813$	10.4088	0.365051
$814$	−38.6880	−1.35601
$815$	0	0
$816$	−22.4320	−0.785279
$817$	−6.25009	−0.218663
$818$	24.3076	0.849895
$819$	−0.105797	−0.00369683
$820$	0	0
$821$	−12.3261	−0.430185	−0.215093	−	0.976594i	$-0.569005\pi$
$821$	−12.3261	−0.430185	−0.215093	+	0.976594i	$0.569005\pi$
$822$	−12.5167	−0.436569
$823$	2.81852	0.0982475	0.0491237	−	0.998793i	$-0.484357\pi$
$823$	2.81852	0.0982475	0.0491237	+	0.998793i	$0.484357\pi$
$824$	−0.0910197	−0.00317082
$825$	0	0
$826$	10.1056	0.351618
$827$	−37.4251	−1.30140	−0.650700	−	0.759335i	$-0.725524\pi$
$827$	−37.4251	−1.30140	−0.650700	+	0.759335i	$0.725524\pi$
$828$	−18.8310	−0.654422
$829$	30.9434	1.07471	0.537355	−	0.843356i	$-0.319424\pi$
$829$	30.9434	1.07471	0.537355	+	0.843356i	$0.319424\pi$
$830$	0	0
$831$	24.5207	0.850613
$832$	0.892455	0.0309403
$833$	34.8042	1.20589
$834$	−1.83017	−0.0633736
$835$	0	0
$836$	−7.15724	−0.247538
$837$	−1.06662	−0.0368679
$838$	69.8620	2.41334
$839$	−26.6975	−0.921701	−0.460851	−	0.887478i	$-0.652456\pi$
$839$	−26.6975	−0.921701	−0.460851	+	0.887478i	$0.652456\pi$
$840$	0	0
$841$	−13.0921	−0.451451
$842$	30.1871	1.04032
$843$	14.4228	0.496748
$844$	54.8923	1.88947
$845$	0	0
$846$	16.5506	0.569023
$847$	11.8738	0.407989
$848$	16.7813	0.576271
$849$	−2.14925	−0.0737620
$850$	0	0
$851$	−36.5239	−1.25202
$852$	22.3912	0.767109
$853$	29.2600	1.00184	0.500921	−	0.865493i	$-0.332995\pi$
$853$	29.2600	1.00184	0.500921	+	0.865493i	$0.332995\pi$
$854$	−14.3254	−0.490207
$855$	0	0
$856$	−0.212282	−0.00725566
$857$	−33.5284	−1.14531	−0.572654	−	0.819797i	$-0.694086\pi$
$857$	−33.5284	−1.14531	−0.572654	+	0.819797i	$0.694086\pi$
$858$	−0.997775	−0.0340635
$859$	−25.8243	−0.881115	−0.440557	−	0.897725i	$-0.645219\pi$
$859$	−25.8243	−0.881115	−0.440557	+	0.897725i	$0.645219\pi$
$860$	0	0
$861$	−7.34582	−0.250345
$862$	−9.71293	−0.330824
$863$	−28.8886	−0.983378	−0.491689	−	0.870771i	$-0.663620\pi$
$863$	−28.8886	−0.983378	−0.491689	+	0.870771i	$0.663620\pi$
$864$	−8.06387	−0.274338
$865$	0	0
$866$	−20.8822	−0.709605
$867$	−17.0795	−0.580050
$868$	2.25592	0.0765710
$869$	11.8177	0.400888
$870$	0	0
$871$	1.03006	0.0349023
$872$	1.35602	0.0459207
$873$	6.69876	0.226719
$874$	−13.2669	−0.448759
$875$	0	0
$876$	−17.9169	−0.605355
$877$	−15.1004	−0.509905	−0.254953	−	0.966954i	$-0.582060\pi$
$877$	−15.1004	−0.509905	−0.254953	+	0.966954i	$0.582060\pi$
$878$	−62.1086	−2.09606
$879$	9.02970	0.304564
$880$	0	0
$881$	36.6216	1.23381	0.616906	−	0.787037i	$-0.288386\pi$
$881$	36.6216	1.23381	0.616906	+	0.787037i	$0.288386\pi$
$882$	12.0363	0.405284
$883$	−34.5459	−1.16256	−0.581281	−	0.813703i	$-0.697448\pi$
$883$	−34.5459	−1.16256	−0.581281	+	0.813703i	$0.697448\pi$
$884$	1.25832	0.0423220
$885$	0	0
$886$	35.8441	1.20421
$887$	33.0360	1.10924	0.554620	−	0.832104i	$-0.312864\pi$
$887$	33.0360	1.10924	0.554620	+	0.832104i	$0.312864\pi$
$888$	0.616437	0.0206863
$889$	−7.42903	−0.249162
$890$	0	0
$891$	4.75961	0.159453
$892$	−16.6741	−0.558289
$893$	5.93864	0.198729
$894$	−9.88860	−0.330724
$895$	0	0
$896$	1.24706	0.0416614
$897$	−0.941960	−0.0314511
$898$	75.1392	2.50743
$899$	−4.25420	−0.141886
$900$	0	0
$901$	25.4947	0.849350
$902$	−69.2789	−2.30674
$903$	−8.79072	−0.292537
$904$	−1.00903	−0.0335597
$905$	0	0
$906$	−20.7189	−0.688340
$907$	−44.2708	−1.46999	−0.734994	−	0.678074i	$-0.762815\pi$
$907$	−44.2708	−1.46999	−0.734994	+	0.678074i	$0.762815\pi$
$908$	34.1634	1.13375
$909$	5.66147	0.187779
$910$	0	0
$911$	−38.8844	−1.28830	−0.644148	−	0.764901i	$-0.722788\pi$
$911$	−38.8844	−1.28830	−0.644148	+	0.764901i	$0.722788\pi$
$912$	−2.78358	−0.0921734
$913$	20.1991	0.668492
$914$	55.9201	1.84967
$915$	0	0
$916$	0.849608	0.0280719
$917$	−9.73414	−0.321450
$918$	−11.7857	−0.388986
$919$	−28.5303	−0.941127	−0.470563	−	0.882366i	$-0.655949\pi$
$919$	−28.5303	−0.941127	−0.470563	+	0.882366i	$0.655949\pi$
$920$	0	0
$921$	−5.03454	−0.165894
$922$	−19.8201	−0.652740
$923$	1.12005	0.0368668
$924$	−10.0666	−0.331168
$925$	0	0
$926$	7.52497	0.247286
$927$	0.594489	0.0195256
$928$	−32.1625	−1.05579
$929$	36.3886	1.19387	0.596936	−	0.802289i	$-0.296385\pi$
$929$	36.3886	1.19387	0.596936	+	0.802289i	$0.296385\pi$
$930$	0	0
$931$	4.31883	0.141544
$932$	−38.3284	−1.25549
$933$	4.89158	0.160143
$934$	14.3325	0.468973
$935$	0	0
$936$	0.0158981	0.000519645 0
$937$	−47.3354	−1.54638	−0.773189	−	0.634175i	$-0.781340\pi$
$937$	−47.3354	−1.54638	−0.773189	+	0.634175i	$0.781340\pi$
$938$	20.4051	0.666249
$939$	3.17282	0.103541
$940$	0	0
$941$	52.9254	1.72532	0.862659	−	0.505787i	$-0.168798\pi$
$941$	52.9254	1.72532	0.862659	+	0.505787i	$0.168798\pi$
$942$	−17.9586	−0.585123
$943$	−65.4035	−2.12983
$944$	18.8780	0.614426
$945$	0	0
$946$	−82.9059	−2.69550
$947$	18.9330	0.615239	0.307619	−	0.951509i	$-0.400468\pi$
$947$	18.9330	0.615239	0.307619	+	0.951509i	$0.400468\pi$
$948$	−5.15413	−0.167398
$949$	−0.896234	−0.0290930
$950$	0	0
$951$	19.9953	0.648392
$952$	0.910662	0.0295147
$953$	−11.4499	−0.370899	−0.185450	−	0.982654i	$-0.559374\pi$
$953$	−11.4499	−0.370899	−0.185450	+	0.982654i	$0.559374\pi$
$954$	8.81680	0.285454
$955$	0	0
$956$	−9.58377	−0.309961
$957$	18.9836	0.613652
$958$	57.4270	1.85538
$959$	−6.31683	−0.203981
$960$	0	0
$961$	−29.8623	−0.963300
$962$	0.844030	0.0272126
$963$	1.38651	0.0446795
$964$	−60.6191	−1.95241
$965$	0	0
$966$	−18.6598	−0.600370
$967$	−36.9926	−1.18960	−0.594801	−	0.803873i	$-0.702769\pi$
$967$	−36.9926	−1.18960	−0.594801	+	0.803873i	$0.702769\pi$
$968$	−1.78428	−0.0573490
$969$	−4.22890	−0.135852
$970$	0	0
$971$	−30.2897	−0.972043	−0.486022	−	0.873947i	$-0.661552\pi$
$971$	−30.2897	−0.972043	−0.486022	+	0.873947i	$0.661552\pi$
$972$	−2.07584	−0.0665825
$973$	−0.923638	−0.0296105
$974$	29.7549	0.953408
$975$	0	0
$976$	−26.7610	−0.856600
$977$	16.6410	0.532394	0.266197	−	0.963919i	$-0.414233\pi$
$977$	16.6410	0.532394	0.266197	+	0.963919i	$0.414233\pi$
$978$	23.7804	0.760413
$979$	−87.4588	−2.79520
$980$	0	0
$981$	−8.85677	−0.282775
$982$	57.3388	1.82975
$983$	26.1897	0.835320	0.417660	−	0.908603i	$-0.362850\pi$
$983$	26.1897	0.835320	0.417660	+	0.908603i	$0.362850\pi$
$984$	1.10386	0.0351897
$985$	0	0
$986$	−47.0069	−1.49700
$987$	8.35267	0.265868
$988$	0.156145	0.00496762
$989$	−78.2682	−2.48878
$990$	0	0
$991$	−24.8373	−0.788982	−0.394491	−	0.918900i	$-0.629079\pi$
$991$	−24.8373	−0.788982	−0.394491	+	0.918900i	$0.629079\pi$
$992$	8.60112	0.273086
$993$	−6.01724	−0.190951
$994$	22.1876	0.703749
$995$	0	0
$996$	−8.80954	−0.279141
$997$	25.0863	0.794490	0.397245	−	0.917713i	$-0.369966\pi$
$997$	25.0863	0.794490	0.397245	+	0.917713i	$0.369966\pi$
$998$	−53.2662	−1.68611
$999$	−4.02621	−0.127384

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.a.j.1.2		6
3.2	odd	2		5625.2.a.p.1.5		6
5.2	odd	4		1875.2.b.f.1249.4		12
5.3	odd	4		1875.2.b.f.1249.9		12
5.4	even	2		1875.2.a.k.1.5		6
15.14	odd	2		5625.2.a.q.1.2		6
25.3	odd	20		375.2.i.d.49.5		24
25.4	even	10		375.2.g.c.76.1		12
25.6	even	5		75.2.g.c.61.3	yes	12
25.8	odd	20		375.2.i.d.199.2		24
25.17	odd	20		375.2.i.d.199.5		24
25.19	even	10		375.2.g.c.301.1		12
25.21	even	5		75.2.g.c.16.3	✓	12
25.22	odd	20		375.2.i.d.49.2		24
75.56	odd	10		225.2.h.d.136.1		12
75.71	odd	10		225.2.h.d.91.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.16.3	✓	12	25.21	even	5
75.2.g.c.61.3	yes	12	25.6	even	5
225.2.h.d.91.1		12	75.71	odd	10
225.2.h.d.136.1		12	75.56	odd	10
375.2.g.c.76.1		12	25.4	even	10
375.2.g.c.301.1		12	25.19	even	10
375.2.i.d.49.2		24	25.22	odd	20
375.2.i.d.49.5		24	25.3	odd	20
375.2.i.d.199.2		24	25.8	odd	20
375.2.i.d.199.5		24	25.17	odd	20
1875.2.a.j.1.2		6	1.1	even	1	trivial
1875.2.a.k.1.5		6	5.4	even	2
1875.2.b.f.1249.4		12	5.2	odd	4
1875.2.b.f.1249.9		12	5.3	odd	4
5625.2.a.p.1.5		6	3.2	odd	2
5625.2.a.q.1.2		6	15.14	odd	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.a (trivial)

\(f(q)\)	\(=\)	\(q-2.01887 q^{2} -1.00000 q^{3} +2.07584 q^{4} +2.01887 q^{6} +1.01887 q^{7} -0.153106 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.01887 q^{2} -1.00000 q^{3} +2.07584 q^{4} +2.01887 q^{6} +1.01887 q^{7} -0.153106 q^{8} +1.00000 q^{9} +4.75961 q^{11} -2.07584 q^{12} -0.103837 q^{13} -2.05697 q^{14} -3.84257 q^{16} -5.83776 q^{17} -2.01887 q^{18} -0.724404 q^{19} -1.01887 q^{21} -9.60904 q^{22} -9.07152 q^{23} +0.153106 q^{24} +0.209634 q^{26} -1.00000 q^{27} +2.11501 q^{28} -3.98847 q^{29} +1.06662 q^{31} +8.06387 q^{32} -4.75961 q^{33} +11.7857 q^{34} +2.07584 q^{36} +4.02621 q^{37} +1.46248 q^{38} +0.103837 q^{39} +7.20977 q^{41} +2.05697 q^{42} +8.62791 q^{43} +9.88018 q^{44} +18.3142 q^{46} -8.19797 q^{47} +3.84257 q^{48} -5.96190 q^{49} +5.83776 q^{51} -0.215549 q^{52} -4.36719 q^{53} +2.01887 q^{54} -0.155995 q^{56} +0.724404 q^{57} +8.05221 q^{58} -4.91285 q^{59} +6.96435 q^{61} -2.15338 q^{62} +1.01887 q^{63} -8.59476 q^{64} +9.60904 q^{66} -9.91998 q^{67} -12.1183 q^{68} +9.07152 q^{69} -10.7866 q^{71} -0.153106 q^{72} +8.63115 q^{73} -8.12840 q^{74} -1.50375 q^{76} +4.84943 q^{77} -0.209634 q^{78} +2.48291 q^{79} +1.00000 q^{81} -14.5556 q^{82} +4.24385 q^{83} -2.11501 q^{84} -17.4186 q^{86} +3.98847 q^{87} -0.728724 q^{88} -18.3752 q^{89} -0.105797 q^{91} -18.8310 q^{92} -1.06662 q^{93} +16.5506 q^{94} -8.06387 q^{96} +6.69876 q^{97} +12.0363 q^{98} +4.75961 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 3 * q^8 + 6 * q^9	\( 6 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 3 q^{8} + 6 q^{9} + 3 q^{11} - 10 q^{12} - 6 q^{13} - 22 q^{14} + 18 q^{16} - 13 q^{17} + 11 q^{19} + 6 q^{21} - 16 q^{22} - 13 q^{23} + 3 q^{24} - 28 q^{26} - 6 q^{27} - 7 q^{28} - 3 q^{29} - 11 q^{31} - 16 q^{32} - 3 q^{33} + 15 q^{34} + 10 q^{36} - 21 q^{37} + 9 q^{38} + 6 q^{39} - q^{41} + 22 q^{42} - 2 q^{43} + 9 q^{44} + 19 q^{46} - 14 q^{47} - 18 q^{48} - 14 q^{49} + 13 q^{51} - 13 q^{52} - 23 q^{53} - 35 q^{56} - 11 q^{57} - 22 q^{58} + 9 q^{59} + 11 q^{61} + 23 q^{62} - 6 q^{63} - 23 q^{64} + 16 q^{66} - 8 q^{67} - 50 q^{68} + 13 q^{69} - 8 q^{71} - 3 q^{72} - 13 q^{73} - 22 q^{74} - 26 q^{76} + 13 q^{77} + 28 q^{78} - 5 q^{79} + 6 q^{81} + 13 q^{82} + 20 q^{83} + 7 q^{84} - 37 q^{86} + 3 q^{87} - 28 q^{88} - 4 q^{89} + 34 q^{91} - 61 q^{92} + 11 q^{93} + 41 q^{94} + 16 q^{96} + 7 q^{97} + 41 q^{98} + 3 q^{99}+O(q^{100}) \) 6 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 3 * q^8 + 6 * q^9 + 3 * q^11 - 10 * q^12 - 6 * q^13 - 22 * q^14 + 18 * q^16 - 13 * q^17 + 11 * q^19 + 6 * q^21 - 16 * q^22 - 13 * q^23 + 3 * q^24 - 28 * q^26 - 6 * q^27 - 7 * q^28 - 3 * q^29 - 11 * q^31 - 16 * q^32 - 3 * q^33 + 15 * q^34 + 10 * q^36 - 21 * q^37 + 9 * q^38 + 6 * q^39 - q^41 + 22 * q^42 - 2 * q^43 + 9 * q^44 + 19 * q^46 - 14 * q^47 - 18 * q^48 - 14 * q^49 + 13 * q^51 - 13 * q^52 - 23 * q^53 - 35 * q^56 - 11 * q^57 - 22 * q^58 + 9 * q^59 + 11 * q^61 + 23 * q^62 - 6 * q^63 - 23 * q^64 + 16 * q^66 - 8 * q^67 - 50 * q^68 + 13 * q^69 - 8 * q^71 - 3 * q^72 - 13 * q^73 - 22 * q^74 - 26 * q^76 + 13 * q^77 + 28 * q^78 - 5 * q^79 + 6 * q^81 + 13 * q^82 + 20 * q^83 + 7 * q^84 - 37 * q^86 + 3 * q^87 - 28 * q^88 - 4 * q^89 + 34 * q^91 - 61 * q^92 + 11 * q^93 + 41 * q^94 + 16 * q^96 + 7 * q^97 + 41 * q^98 + 3 * q^99

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