LMFDB - Embedded newform 9555.2.a.cp.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9555,2,Mod(1,9555)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9555, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("9555.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9555 = 3 \cdot 5 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9555.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:	$76.2970591313$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 10x^{7} + 31x^{6} + 30x^{5} - 97x^{4} - 27x^{3} + 89x^{2} + 16x - 16 $ x^9 - 3x^8 - 10x^7 + 31x^6 + 30x^5 - 97x^4 - 27x^3 + 89x^2 + 16x - 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1365)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$1.74101$ of defining polynomial
Character	$\chi$	$=$	9555.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.74101 q^{2} -1.00000 q^{3} +1.03110 q^{4} +1.00000 q^{5} -1.74101 q^{6} -1.68686 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.74101 q^{2} -1.00000 q^{3} +1.03110 q^{4} +1.00000 q^{5} -1.74101 q^{6} -1.68686 q^{8} +1.00000 q^{9} +1.74101 q^{10} +5.62077 q^{11} -1.03110 q^{12} -1.00000 q^{13} -1.00000 q^{15} -4.99903 q^{16} +0.541104 q^{17} +1.74101 q^{18} -1.64615 q^{19} +1.03110 q^{20} +9.78579 q^{22} +0.431853 q^{23} +1.68686 q^{24} +1.00000 q^{25} -1.74101 q^{26} -1.00000 q^{27} +6.71152 q^{29} -1.74101 q^{30} +0.457975 q^{31} -5.32963 q^{32} -5.62077 q^{33} +0.942065 q^{34} +1.03110 q^{36} -6.01409 q^{37} -2.86595 q^{38} +1.00000 q^{39} -1.68686 q^{40} -0.741370 q^{41} +9.01883 q^{43} +5.79559 q^{44} +1.00000 q^{45} +0.751858 q^{46} +3.51587 q^{47} +4.99903 q^{48} +1.74101 q^{50} -0.541104 q^{51} -1.03110 q^{52} +8.31960 q^{53} -1.74101 q^{54} +5.62077 q^{55} +1.64615 q^{57} +11.6848 q^{58} +7.40551 q^{59} -1.03110 q^{60} -7.17958 q^{61} +0.797337 q^{62} +0.719138 q^{64} -1.00000 q^{65} -9.78579 q^{66} -7.56720 q^{67} +0.557934 q^{68} -0.431853 q^{69} -9.23194 q^{71} -1.68686 q^{72} +0.558480 q^{73} -10.4706 q^{74} -1.00000 q^{75} -1.69735 q^{76} +1.74101 q^{78} -5.68609 q^{79} -4.99903 q^{80} +1.00000 q^{81} -1.29073 q^{82} +8.69856 q^{83} +0.541104 q^{85} +15.7018 q^{86} -6.71152 q^{87} -9.48143 q^{88} -9.75511 q^{89} +1.74101 q^{90} +0.445284 q^{92} -0.457975 q^{93} +6.12116 q^{94} -1.64615 q^{95} +5.32963 q^{96} -9.41625 q^{97} +5.62077 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 3 q^{2} - 9 q^{3} + 11 q^{4} + 9 q^{5} - 3 q^{6} + 12 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 3 * q^2 - 9 * q^3 + 11 * q^4 + 9 * q^5 - 3 * q^6 + 12 * q^8 + 9 * q^9	$ 9 q + 3 q^{2} - 9 q^{3} + 11 q^{4} + 9 q^{5} - 3 q^{6} + 12 q^{8} + 9 q^{9} + 3 q^{10} + 3 q^{11} - 11 q^{12} - 9 q^{13} - 9 q^{15} + 11 q^{16} + 3 q^{18} + 4 q^{19} + 11 q^{20} + 11 q^{22} + 15 q^{23} - 12 q^{24} + 9 q^{25} - 3 q^{26} - 9 q^{27} + 30 q^{29} - 3 q^{30} + 2 q^{31} + 27 q^{32} - 3 q^{33} - 12 q^{34} + 11 q^{36} + 21 q^{37} + 14 q^{38} + 9 q^{39} + 12 q^{40} - 4 q^{41} + 15 q^{43} + 21 q^{44} + 9 q^{45} - 23 q^{46} - 7 q^{47} - 11 q^{48} + 3 q^{50} - 11 q^{52} + 15 q^{53} - 3 q^{54} + 3 q^{55} - 4 q^{57} - 6 q^{58} - 7 q^{59} - 11 q^{60} + 2 q^{61} - 33 q^{62} + 12 q^{64} - 9 q^{65} - 11 q^{66} + 21 q^{67} + 23 q^{68} - 15 q^{69} + 21 q^{71} + 12 q^{72} + 33 q^{73} - 18 q^{74} - 9 q^{75} - 13 q^{76} + 3 q^{78} - 13 q^{79} + 11 q^{80} + 9 q^{81} + 34 q^{82} + q^{83} + 20 q^{86} - 30 q^{87} + 8 q^{88} + 14 q^{89} + 3 q^{90} + 46 q^{92} - 2 q^{93} + 7 q^{94} + 4 q^{95} - 27 q^{96} + 12 q^{97} + 3 q^{99}+O(q^{100}) $ 9 * q + 3 * q^2 - 9 * q^3 + 11 * q^4 + 9 * q^5 - 3 * q^6 + 12 * q^8 + 9 * q^9 + 3 * q^10 + 3 * q^11 - 11 * q^12 - 9 * q^13 - 9 * q^15 + 11 * q^16 + 3 * q^18 + 4 * q^19 + 11 * q^20 + 11 * q^22 + 15 * q^23 - 12 * q^24 + 9 * q^25 - 3 * q^26 - 9 * q^27 + 30 * q^29 - 3 * q^30 + 2 * q^31 + 27 * q^32 - 3 * q^33 - 12 * q^34 + 11 * q^36 + 21 * q^37 + 14 * q^38 + 9 * q^39 + 12 * q^40 - 4 * q^41 + 15 * q^43 + 21 * q^44 + 9 * q^45 - 23 * q^46 - 7 * q^47 - 11 * q^48 + 3 * q^50 - 11 * q^52 + 15 * q^53 - 3 * q^54 + 3 * q^55 - 4 * q^57 - 6 * q^58 - 7 * q^59 - 11 * q^60 + 2 * q^61 - 33 * q^62 + 12 * q^64 - 9 * q^65 - 11 * q^66 + 21 * q^67 + 23 * q^68 - 15 * q^69 + 21 * q^71 + 12 * q^72 + 33 * q^73 - 18 * q^74 - 9 * q^75 - 13 * q^76 + 3 * q^78 - 13 * q^79 + 11 * q^80 + 9 * q^81 + 34 * q^82 + q^83 + 20 * q^86 - 30 * q^87 + 8 * q^88 + 14 * q^89 + 3 * q^90 + 46 * q^92 - 2 * q^93 + 7 * q^94 + 4 * q^95 - 27 * q^96 + 12 * q^97 + 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 $

$2$	1.74101	1.23108	0.615539	−	0.788107i	$-0.288938\pi$
$2$	1.74101	1.23108	0.615539	+	0.788107i	$0.288938\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.03110	0.515551
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.74101	−0.710763
$7$	0	0
$7$	0	0
$8$	−1.68686	−0.596394
$9$	1.00000	0.333333
$10$	1.74101	0.550555
$11$	5.62077	1.69473	0.847363	−	0.531015i	$-0.178189\pi$
$11$	5.62077	1.69473	0.847363	+	0.531015i	$0.178189\pi$
$12$	−1.03110	−0.297654
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	−1.00000	−0.258199
$16$	−4.99903	−1.24976
$17$	0.541104	0.131237	0.0656185	−	0.997845i	$-0.479098\pi$
$17$	0.541104	0.131237	0.0656185	+	0.997845i	$0.479098\pi$
$18$	1.74101	0.410359
$19$	−1.64615	−0.377652	−0.188826	−	0.982011i	$-0.560468\pi$
$19$	−1.64615	−0.377652	−0.188826	+	0.982011i	$0.560468\pi$
$20$	1.03110	0.230562
$21$	0	0
$22$	9.78579	2.08634
$23$	0.431853	0.0900475	0.0450238	−	0.998986i	$-0.485664\pi$
$23$	0.431853	0.0900475	0.0450238	+	0.998986i	$0.485664\pi$
$24$	1.68686	0.344328
$25$	1.00000	0.200000
$26$	−1.74101	−0.341439
$27$	−1.00000	−0.192450
$28$	0	0
$29$	6.71152	1.24630	0.623149	−	0.782103i	$-0.285853\pi$
$29$	6.71152	1.24630	0.623149	+	0.782103i	$0.285853\pi$
$30$	−1.74101	−0.317863
$31$	0.457975	0.0822547	0.0411273	−	0.999154i	$-0.486905\pi$
$31$	0.457975	0.0822547	0.0411273	+	0.999154i	$0.486905\pi$
$32$	−5.32963	−0.942155
$33$	−5.62077	−0.978450
$34$	0.942065	0.161563
$35$	0	0
$36$	1.03110	0.171850
$37$	−6.01409	−0.988711	−0.494355	−	0.869260i	$-0.664596\pi$
$37$	−6.01409	−0.988711	−0.494355	+	0.869260i	$0.664596\pi$
$38$	−2.86595	−0.464919
$39$	1.00000	0.160128
$40$	−1.68686	−0.266715
$41$	−0.741370	−0.115783	−0.0578913	−	0.998323i	$-0.518438\pi$
$41$	−0.741370	−0.115783	−0.0578913	+	0.998323i	$0.518438\pi$
$42$	0	0
$43$	9.01883	1.37536	0.687679	−	0.726015i	$-0.258630\pi$
$43$	9.01883	1.37536	0.687679	+	0.726015i	$0.258630\pi$
$44$	5.79559	0.873718
$45$	1.00000	0.149071
$46$	0.751858	0.110855
$47$	3.51587	0.512843	0.256421	−	0.966565i	$-0.417457\pi$
$47$	3.51587	0.512843	0.256421	+	0.966565i	$0.417457\pi$
$48$	4.99903	0.721548
$49$	0	0
$50$	1.74101	0.246215
$51$	−0.541104	−0.0757697
$52$	−1.03110	−0.142988
$53$	8.31960	1.14279	0.571393	−	0.820677i	$-0.306403\pi$
$53$	8.31960	1.14279	0.571393	+	0.820677i	$0.306403\pi$
$54$	−1.74101	−0.236921
$55$	5.62077	0.757904
$56$	0	0
$57$	1.64615	0.218037
$58$	11.6848	1.53429
$59$	7.40551	0.964115	0.482057	−	0.876140i	$-0.339890\pi$
$59$	7.40551	0.964115	0.482057	+	0.876140i	$0.339890\pi$
$60$	−1.03110	−0.133115
$61$	−7.17958	−0.919251	−0.459625	−	0.888113i	$-0.652016\pi$
$61$	−7.17958	−0.919251	−0.459625	+	0.888113i	$0.652016\pi$
$62$	0.797337	0.101262
$63$	0	0
$64$	0.719138	0.0898922
$65$	−1.00000	−0.124035
$66$	−9.78579	−1.20455
$67$	−7.56720	−0.924480	−0.462240	−	0.886755i	$-0.652954\pi$
$67$	−7.56720	−0.924480	−0.462240	+	0.886755i	$0.652954\pi$
$68$	0.557934	0.0676594
$69$	−0.431853	−0.0519890
$70$	0	0
$71$	−9.23194	−1.09563	−0.547815	−	0.836600i	$-0.684540\pi$
$71$	−9.23194	−1.09563	−0.547815	+	0.836600i	$0.684540\pi$
$72$	−1.68686	−0.198798
$73$	0.558480	0.0653652	0.0326826	−	0.999466i	$-0.489595\pi$
$73$	0.558480	0.0653652	0.0326826	+	0.999466i	$0.489595\pi$
$74$	−10.4706	−1.21718
$75$	−1.00000	−0.115470
$76$	−1.69735	−0.194699
$77$	0	0
$78$	1.74101	0.197130
$79$	−5.68609	−0.639736	−0.319868	−	0.947462i	$-0.603638\pi$
$79$	−5.68609	−0.639736	−0.319868	+	0.947462i	$0.603638\pi$
$80$	−4.99903	−0.558909
$81$	1.00000	0.111111
$82$	−1.29073	−0.142537
$83$	8.69856	0.954791	0.477395	−	0.878689i	$-0.341581\pi$
$83$	8.69856	0.954791	0.477395	+	0.878689i	$0.341581\pi$
$84$	0	0
$85$	0.541104	0.0586909
$86$	15.7018	1.69317
$87$	−6.71152	−0.719551
$88$	−9.48143	−1.01072
$89$	−9.75511	−1.03404	−0.517020	−	0.855973i	$-0.672959\pi$
$89$	−9.75511	−1.03404	−0.517020	+	0.855973i	$0.672959\pi$
$90$	1.74101	0.183518
$91$	0	0
$92$	0.445284	0.0464241
$93$	−0.457975	−0.0474898
$94$	6.12116	0.631349
$95$	−1.64615	−0.168891
$96$	5.32963	0.543954
$97$	−9.41625	−0.956075	−0.478037	−	0.878339i	$-0.658652\pi$
$97$	−9.41625	−0.956075	−0.478037	+	0.878339i	$0.658652\pi$
$98$	0	0
$99$	5.62077	0.564908
$100$	1.03110	0.103110
$101$	1.19348	0.118756	0.0593781	−	0.998236i	$-0.481088\pi$
$101$	1.19348	0.118756	0.0593781	+	0.998236i	$0.481088\pi$
$102$	−0.942065	−0.0932783
$103$	2.06916	0.203880	0.101940	−	0.994791i	$-0.467495\pi$
$103$	2.06916	0.203880	0.101940	+	0.994791i	$0.467495\pi$
$104$	1.68686	0.165410
$105$	0	0
$106$	14.4845	1.40686
$107$	9.27441	0.896591	0.448295	−	0.893885i	$-0.352031\pi$
$107$	9.27441	0.896591	0.448295	+	0.893885i	$0.352031\pi$
$108$	−1.03110	−0.0992179
$109$	13.1740	1.26184	0.630922	−	0.775847i	$-0.282677\pi$
$109$	13.1740	1.26184	0.630922	+	0.775847i	$0.282677\pi$
$110$	9.78579	0.933039
$111$	6.01409	0.570832
$112$	0	0
$113$	14.8369	1.39574	0.697871	−	0.716223i	$-0.254131\pi$
$113$	14.8369	1.39574	0.697871	+	0.716223i	$0.254131\pi$
$114$	2.86595	0.268421
$115$	0.431853	0.0402705
$116$	6.92027	0.642531
$117$	−1.00000	−0.0924500
$118$	12.8930	1.18690
$119$	0	0
$120$	1.68686	0.153988
$121$	20.5930	1.87209
$122$	−12.4997	−1.13167
$123$	0.741370	0.0668471
$124$	0.472219	0.0424065
$125$	1.00000	0.0894427
$126$	0	0
$127$	16.1970	1.43725	0.718627	−	0.695395i	$-0.244771\pi$
$127$	16.1970	1.43725	0.718627	+	0.695395i	$0.244771\pi$
$128$	11.9113	1.05282
$129$	−9.01883	−0.794063
$130$	−1.74101	−0.152696
$131$	10.0895	0.881528	0.440764	−	0.897623i	$-0.354708\pi$
$131$	10.0895	0.881528	0.440764	+	0.897623i	$0.354708\pi$
$132$	−5.79559	−0.504441
$133$	0	0
$134$	−13.1745	−1.13811
$135$	−1.00000	−0.0860663
$136$	−0.912764	−0.0782689
$137$	20.2107	1.72672	0.863359	−	0.504591i	$-0.168357\pi$
$137$	20.2107	1.72672	0.863359	+	0.504591i	$0.168357\pi$
$138$	−0.751858	−0.0640024
$139$	−14.1964	−1.20413	−0.602063	−	0.798448i	$-0.705655\pi$
$139$	−14.1964	−1.20413	−0.602063	+	0.798448i	$0.705655\pi$
$140$	0	0
$141$	−3.51587	−0.296090
$142$	−16.0729	−1.34880
$143$	−5.62077	−0.470032
$144$	−4.99903	−0.416586
$145$	6.71152	0.557362
$146$	0.972317	0.0804696
$147$	0	0
$148$	−6.20115	−0.509731
$149$	5.40254	0.442593	0.221297	−	0.975207i	$-0.428971\pi$
$149$	5.40254	0.442593	0.221297	+	0.975207i	$0.428971\pi$
$150$	−1.74101	−0.142153
$151$	10.7280	0.873029	0.436515	−	0.899697i	$-0.356213\pi$
$151$	10.7280	0.873029	0.436515	+	0.899697i	$0.356213\pi$
$152$	2.77681	0.225229
$153$	0.541104	0.0437456
$154$	0	0
$155$	0.457975	0.0367854
$156$	1.03110	0.0825543
$157$	−7.16037	−0.571459	−0.285730	−	0.958310i	$-0.592236\pi$
$157$	−7.16037	−0.571459	−0.285730	+	0.958310i	$0.592236\pi$
$158$	−9.89953	−0.787564
$159$	−8.31960	−0.659787
$160$	−5.32963	−0.421345
$161$	0	0
$162$	1.74101	0.136786
$163$	−1.64944	−0.129194	−0.0645972	−	0.997911i	$-0.520576\pi$
$163$	−1.64944	−0.129194	−0.0645972	+	0.997911i	$0.520576\pi$
$164$	−0.764429	−0.0596919
$165$	−5.62077	−0.437576
$166$	15.1442	1.17542
$167$	9.74025	0.753723	0.376862	−	0.926270i	$-0.377003\pi$
$167$	9.74025	0.753723	0.376862	+	0.926270i	$0.377003\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0.942065	0.0722531
$171$	−1.64615	−0.125884
$172$	9.29934	0.709068
$173$	6.98008	0.530686	0.265343	−	0.964154i	$-0.414515\pi$
$173$	6.98008	0.530686	0.265343	+	0.964154i	$0.414515\pi$
$174$	−11.6848	−0.885823
$175$	0	0
$176$	−28.0984	−2.11800
$177$	−7.40551	−0.556632
$178$	−16.9837	−1.27298
$179$	0.773332	0.0578016	0.0289008	−	0.999582i	$-0.490799\pi$
$179$	0.773332	0.0578016	0.0289008	+	0.999582i	$0.490799\pi$
$180$	1.03110	0.0768539
$181$	−11.9659	−0.889421	−0.444710	−	0.895674i	$-0.646693\pi$
$181$	−11.9659	−0.889421	−0.444710	+	0.895674i	$0.646693\pi$
$182$	0	0
$183$	7.17958	0.530730
$184$	−0.728473	−0.0537038
$185$	−6.01409	−0.442165
$186$	−0.797337	−0.0584636
$187$	3.04142	0.222411
$188$	3.62523	0.264397
$189$	0	0
$190$	−2.86595	−0.207918
$191$	2.41590	0.174809	0.0874043	−	0.996173i	$-0.472143\pi$
$191$	2.41590	0.174809	0.0874043	+	0.996173i	$0.472143\pi$
$192$	−0.719138	−0.0518993
$193$	−1.83973	−0.132426	−0.0662132	−	0.997805i	$-0.521092\pi$
$193$	−1.83973	−0.132426	−0.0662132	+	0.997805i	$0.521092\pi$
$194$	−16.3937	−1.17700
$195$	1.00000	0.0716115
$196$	0	0
$197$	13.0474	0.929588	0.464794	−	0.885419i	$-0.346128\pi$
$197$	13.0474	0.929588	0.464794	+	0.885419i	$0.346128\pi$
$198$	9.78579	0.695446
$199$	−20.7001	−1.46739	−0.733695	−	0.679479i	$-0.762206\pi$
$199$	−20.7001	−1.46739	−0.733695	+	0.679479i	$0.762206\pi$
$200$	−1.68686	−0.119279
$201$	7.56720	0.533749
$202$	2.07786	0.146198
$203$	0	0
$204$	−0.557934	−0.0390632
$205$	−0.741370	−0.0517795
$206$	3.60242	0.250992
$207$	0.431853	0.0300158
$208$	4.99903	0.346621
$209$	−9.25260	−0.640016
$210$	0	0
$211$	−21.7490	−1.49726	−0.748632	−	0.662986i	$-0.769289\pi$
$211$	−21.7490	−1.49726	−0.748632	+	0.662986i	$0.769289\pi$
$212$	8.57836	0.589165
$213$	9.23194	0.632562
$214$	16.1468	1.10377
$215$	9.01883	0.615079
$216$	1.68686	0.114776
$217$	0	0
$218$	22.9361	1.55343
$219$	−0.558480	−0.0377386
$220$	5.79559	0.390739
$221$	−0.541104	−0.0363986
$222$	10.4706	0.702739
$223$	3.99472	0.267506	0.133753	−	0.991015i	$-0.457297\pi$
$223$	3.99472	0.267506	0.133753	+	0.991015i	$0.457297\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	25.8312	1.71827
$227$	−12.5473	−0.832793	−0.416397	−	0.909183i	$-0.636707\pi$
$227$	−12.5473	−0.832793	−0.416397	+	0.909183i	$0.636707\pi$
$228$	1.69735	0.112409
$229$	−19.0685	−1.26008	−0.630041	−	0.776562i	$-0.716962\pi$
$229$	−19.0685	−1.26008	−0.630041	+	0.776562i	$0.716962\pi$
$230$	0.751858	0.0495761
$231$	0	0
$232$	−11.3214	−0.743285
$233$	−10.4049	−0.681645	−0.340823	−	0.940128i	$-0.610706\pi$
$233$	−10.4049	−0.681645	−0.340823	+	0.940128i	$0.610706\pi$
$234$	−1.74101	−0.113813
$235$	3.51587	0.229350
$236$	7.63584	0.497051
$237$	5.68609	0.369352
$238$	0	0
$239$	11.4452	0.740325	0.370163	−	0.928967i	$-0.379302\pi$
$239$	11.4452	0.740325	0.370163	+	0.928967i	$0.379302\pi$
$240$	4.99903	0.322686
$241$	29.2257	1.88259	0.941295	−	0.337585i	$-0.109610\pi$
$241$	29.2257	1.88259	0.941295	+	0.337585i	$0.109610\pi$
$242$	35.8526	2.30469
$243$	−1.00000	−0.0641500
$244$	−7.40288	−0.473921
$245$	0	0
$246$	1.29073	0.0822939
$247$	1.64615	0.104742
$248$	−0.772537	−0.0490562
$249$	−8.69856	−0.551249
$250$	1.74101	0.110111
$251$	0.373783	0.0235930	0.0117965	−	0.999930i	$-0.496245\pi$
$251$	0.373783	0.0235930	0.0117965	+	0.999930i	$0.496245\pi$
$252$	0	0
$253$	2.42734	0.152606
$254$	28.1991	1.76937
$255$	−0.541104	−0.0338852
$256$	19.2994	1.20621
$257$	18.5222	1.15538	0.577692	−	0.816254i	$-0.303953\pi$
$257$	18.5222	1.15538	0.577692	+	0.816254i	$0.303953\pi$
$258$	−15.7018	−0.977554
$259$	0	0
$260$	−1.03110	−0.0639463
$261$	6.71152	0.415433
$262$	17.5660	1.08523
$263$	31.5872	1.94775	0.973875	−	0.227085i	$-0.0729195\pi$
$263$	31.5872	1.94775	0.973875	+	0.227085i	$0.0729195\pi$
$264$	9.48143	0.583541
$265$	8.31960	0.511069
$266$	0	0
$267$	9.75511	0.597003
$268$	−7.80256	−0.476617
$269$	−22.4041	−1.36600	−0.683000	−	0.730419i	$-0.739325\pi$
$269$	−22.4041	−1.36600	−0.683000	+	0.730419i	$0.739325\pi$
$270$	−1.74101	−0.105954
$271$	−0.588091	−0.0357240	−0.0178620	−	0.999840i	$-0.505686\pi$
$271$	−0.588091	−0.0357240	−0.0178620	+	0.999840i	$0.505686\pi$
$272$	−2.70500	−0.164014
$273$	0	0
$274$	35.1870	2.12572
$275$	5.62077	0.338945
$276$	−0.445284	−0.0268030
$277$	1.02933	0.0618461	0.0309231	−	0.999522i	$-0.490155\pi$
$277$	1.02933	0.0618461	0.0309231	+	0.999522i	$0.490155\pi$
$278$	−24.7161	−1.48237
$279$	0.457975	0.0274182
$280$	0	0
$281$	−13.5223	−0.806673	−0.403336	−	0.915052i	$-0.632150\pi$
$281$	−13.5223	−0.806673	−0.403336	+	0.915052i	$0.632150\pi$
$282$	−6.12116	−0.364509
$283$	13.6664	0.812386	0.406193	−	0.913787i	$-0.366856\pi$
$283$	13.6664	0.812386	0.406193	+	0.913787i	$0.366856\pi$
$284$	−9.51908	−0.564853
$285$	1.64615	0.0975093
$286$	−9.78579	−0.578646
$287$	0	0
$288$	−5.32963	−0.314052
$289$	−16.7072	−0.982777
$290$	11.6848	0.686155
$291$	9.41625	0.551990
$292$	0.575850	0.0336991
$293$	29.8642	1.74469	0.872343	−	0.488895i	$-0.162600\pi$
$293$	29.8642	1.74469	0.872343	+	0.488895i	$0.162600\pi$
$294$	0	0
$295$	7.40551	0.431165
$296$	10.1449	0.589661
$297$	−5.62077	−0.326150
$298$	9.40586	0.544867
$299$	−0.431853	−0.0249747
$300$	−1.03110	−0.0595307
$301$	0	0
$302$	18.6775	1.07477
$303$	−1.19348	−0.0685639
$304$	8.22914	0.471973
$305$	−7.17958	−0.411101
$306$	0.942065	0.0538543
$307$	19.1723	1.09422	0.547109	−	0.837061i	$-0.315728\pi$
$307$	19.1723	1.09422	0.547109	+	0.837061i	$0.315728\pi$
$308$	0	0
$309$	−2.06916	−0.117710
$310$	0.797337	0.0452857
$311$	29.4996	1.67277	0.836385	−	0.548143i	$-0.184665\pi$
$311$	29.4996	1.67277	0.836385	+	0.548143i	$0.184665\pi$
$312$	−1.68686	−0.0954994
$313$	−4.68219	−0.264653	−0.132326	−	0.991206i	$-0.542245\pi$
$313$	−4.68219	−0.264653	−0.132326	+	0.991206i	$0.542245\pi$
$314$	−12.4662	−0.703511
$315$	0	0
$316$	−5.86295	−0.329817
$317$	−24.4394	−1.37265	−0.686327	−	0.727293i	$-0.740778\pi$
$317$	−24.4394	−1.37265	−0.686327	+	0.727293i	$0.740778\pi$
$318$	−14.4845	−0.812249
$319$	37.7239	2.11213
$320$	0.719138	0.0402010
$321$	−9.27441	−0.517647
$322$	0	0
$323$	−0.890736	−0.0495619
$324$	1.03110	0.0572835
$325$	−1.00000	−0.0554700
$326$	−2.87169	−0.159048
$327$	−13.1740	−0.728525
$328$	1.25058	0.0690520
$329$	0	0
$330$	−9.78579	−0.538690
$331$	16.4775	0.905683	0.452842	−	0.891591i	$-0.350410\pi$
$331$	16.4775	0.905683	0.452842	+	0.891591i	$0.350410\pi$
$332$	8.96911	0.492244
$333$	−6.01409	−0.329570
$334$	16.9578	0.927892
$335$	−7.56720	−0.413440
$336$	0	0
$337$	−12.4912	−0.680439	−0.340219	−	0.940346i	$-0.610501\pi$
$337$	−12.4912	−0.680439	−0.340219	+	0.940346i	$0.610501\pi$
$338$	1.74101	0.0946983
$339$	−14.8369	−0.805832
$340$	0.557934	0.0302582
$341$	2.57417	0.139399
$342$	−2.86595	−0.154973
$343$	0	0
$344$	−15.2135	−0.820255
$345$	−0.431853	−0.0232502
$346$	12.1524	0.653315
$347$	8.02349	0.430723	0.215362	−	0.976534i	$-0.430907\pi$
$347$	8.02349	0.430723	0.215362	+	0.976534i	$0.430907\pi$
$348$	−6.92027	−0.370965
$349$	−5.42829	−0.290570	−0.145285	−	0.989390i	$-0.546410\pi$
$349$	−5.42829	−0.290570	−0.145285	+	0.989390i	$0.546410\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	−29.9566	−1.59669
$353$	28.1299	1.49720	0.748601	−	0.663020i	$-0.230726\pi$
$353$	28.1299	1.49720	0.748601	+	0.663020i	$0.230726\pi$
$354$	−12.8930	−0.685257
$355$	−9.23194	−0.489980
$356$	−10.0585	−0.533100
$357$	0	0
$358$	1.34638	0.0711582
$359$	5.13188	0.270850	0.135425	−	0.990788i	$-0.456760\pi$
$359$	5.13188	0.270850	0.135425	+	0.990788i	$0.456760\pi$
$360$	−1.68686	−0.0889051
$361$	−16.2902	−0.857379
$362$	−20.8328	−1.09495
$363$	−20.5930	−1.08085
$364$	0	0
$365$	0.558480	0.0292322
$366$	12.4997	0.653369
$367$	−24.5761	−1.28286	−0.641431	−	0.767181i	$-0.721659\pi$
$367$	−24.5761	−1.28286	−0.641431	+	0.767181i	$0.721659\pi$
$368$	−2.15885	−0.112538
$369$	−0.741370	−0.0385942
$370$	−10.4706	−0.544339
$371$	0	0
$372$	−0.472219	−0.0244834
$373$	23.1885	1.20065	0.600327	−	0.799755i	$-0.295037\pi$
$373$	23.1885	1.20065	0.600327	+	0.799755i	$0.295037\pi$
$374$	5.29513	0.273805
$375$	−1.00000	−0.0516398
$376$	−5.93077	−0.305856
$377$	−6.71152	−0.345661
$378$	0	0
$379$	−20.9081	−1.07398	−0.536989	−	0.843589i	$-0.680438\pi$
$379$	−20.9081	−1.07398	−0.536989	+	0.843589i	$0.680438\pi$
$380$	−1.69735	−0.0870720
$381$	−16.1970	−0.829799
$382$	4.20610	0.215203
$383$	26.7818	1.36849	0.684243	−	0.729254i	$-0.260133\pi$
$383$	26.7818	1.36849	0.684243	+	0.729254i	$0.260133\pi$
$384$	−11.9113	−0.607846
$385$	0	0
$386$	−3.20297	−0.163027
$387$	9.01883	0.458453
$388$	−9.70912	−0.492906
$389$	28.7682	1.45860	0.729302	−	0.684191i	$-0.239845\pi$
$389$	28.7682	1.45860	0.729302	+	0.684191i	$0.239845\pi$
$390$	1.74101	0.0881593
$391$	0.233677	0.0118176
$392$	0	0
$393$	−10.0895	−0.508950
$394$	22.7156	1.14439
$395$	−5.68609	−0.286098
$396$	5.79559	0.291239
$397$	30.2101	1.51620	0.758102	−	0.652136i	$-0.226127\pi$
$397$	30.2101	1.51620	0.758102	+	0.652136i	$0.226127\pi$
$398$	−36.0390	−1.80647
$399$	0	0
$400$	−4.99903	−0.249952
$401$	−21.3215	−1.06474	−0.532371	−	0.846511i	$-0.678699\pi$
$401$	−21.3215	−1.06474	−0.532371	+	0.846511i	$0.678699\pi$
$402$	13.1745	0.657086
$403$	−0.457975	−0.0228133
$404$	1.23061	0.0612249
$405$	1.00000	0.0496904
$406$	0	0
$407$	−33.8038	−1.67559
$408$	0.912764	0.0451886
$409$	31.2361	1.54453	0.772263	−	0.635303i	$-0.219125\pi$
$409$	31.2361	1.54453	0.772263	+	0.635303i	$0.219125\pi$
$410$	−1.29073	−0.0637446
$411$	−20.2107	−0.996921
$412$	2.13351	0.105111
$413$	0	0
$414$	0.751858	0.0369518
$415$	8.69856	0.426995
$416$	5.32963	0.261307
$417$	14.1964	0.695203
$418$	−16.1088	−0.787909
$419$	30.2822	1.47938	0.739691	−	0.672947i	$-0.234972\pi$
$419$	30.2822	1.47938	0.739691	+	0.672947i	$0.234972\pi$
$420$	0	0
$421$	17.0240	0.829700	0.414850	−	0.909890i	$-0.363834\pi$
$421$	17.0240	0.829700	0.414850	+	0.909890i	$0.363834\pi$
$422$	−37.8652	−1.84325
$423$	3.51587	0.170948
$424$	−14.0340	−0.681550
$425$	0.541104	0.0262474
$426$	16.0729	0.778733
$427$	0	0
$428$	9.56287	0.462239
$429$	5.62077	0.271373
$430$	15.7018	0.757210
$431$	24.5289	1.18152	0.590759	−	0.806848i	$-0.298828\pi$
$431$	24.5289	1.18152	0.590759	+	0.806848i	$0.298828\pi$
$432$	4.99903	0.240516
$433$	30.7393	1.47724	0.738618	−	0.674124i	$-0.235479\pi$
$433$	30.7393	1.47724	0.738618	+	0.674124i	$0.235479\pi$
$434$	0	0
$435$	−6.71152	−0.321793
$436$	13.5838	0.650545
$437$	−0.710893	−0.0340066
$438$	−0.972317	−0.0464591
$439$	−1.75048	−0.0835457	−0.0417729	−	0.999127i	$-0.513301\pi$
$439$	−1.75048	−0.0835457	−0.0417729	+	0.999127i	$0.513301\pi$
$440$	−9.48143	−0.452009
$441$	0	0
$442$	−0.942065	−0.0448095
$443$	−10.5655	−0.501982	−0.250991	−	0.967989i	$-0.580756\pi$
$443$	−10.5655	−0.501982	−0.250991	+	0.967989i	$0.580756\pi$
$444$	6.20115	0.294293
$445$	−9.75511	−0.462437
$446$	6.95483	0.329321
$447$	−5.40254	−0.255531
$448$	0	0
$449$	28.4862	1.34435	0.672173	−	0.740395i	$-0.265361\pi$
$449$	28.4862	1.34435	0.672173	+	0.740395i	$0.265361\pi$
$450$	1.74101	0.0820718
$451$	−4.16707	−0.196220
$452$	15.2984	0.719577
$453$	−10.7280	−0.504044
$454$	−21.8449	−1.02523
$455$	0	0
$456$	−2.77681	−0.130036
$457$	−0.864695	−0.0404487	−0.0202244	−	0.999795i	$-0.506438\pi$
$457$	−0.864695	−0.0404487	−0.0202244	+	0.999795i	$0.506438\pi$
$458$	−33.1984	−1.55126
$459$	−0.541104	−0.0252566
$460$	0.445284	0.0207615
$461$	11.3601	0.529091	0.264545	−	0.964373i	$-0.414778\pi$
$461$	11.3601	0.529091	0.264545	+	0.964373i	$0.414778\pi$
$462$	0	0
$463$	−21.6617	−1.00670	−0.503352	−	0.864081i	$-0.667900\pi$
$463$	−21.6617	−1.00670	−0.503352	+	0.864081i	$0.667900\pi$
$464$	−33.5511	−1.55757
$465$	−0.457975	−0.0212381
$466$	−18.1149	−0.839158
$467$	−23.0046	−1.06453	−0.532263	−	0.846579i	$-0.678658\pi$
$467$	−23.0046	−1.06453	−0.532263	+	0.846579i	$0.678658\pi$
$468$	−1.03110	−0.0476627
$469$	0	0
$470$	6.12116	0.282348
$471$	7.16037	0.329932
$472$	−12.4920	−0.574992
$473$	50.6927	2.33085
$474$	9.89953	0.454700
$475$	−1.64615	−0.0755304
$476$	0	0
$477$	8.31960	0.380928
$478$	19.9261	0.911398
$479$	−34.8676	−1.59314	−0.796570	−	0.604547i	$-0.793354\pi$
$479$	−34.8676	−1.59314	−0.796570	+	0.604547i	$0.793354\pi$
$480$	5.32963	0.243263
$481$	6.01409	0.274219
$482$	50.8820	2.31761
$483$	0	0
$484$	21.2335	0.965160
$485$	−9.41625	−0.427570
$486$	−1.74101	−0.0789736
$487$	1.87174	0.0848166	0.0424083	−	0.999100i	$-0.486497\pi$
$487$	1.87174	0.0848166	0.0424083	+	0.999100i	$0.486497\pi$
$488$	12.1109	0.548235
$489$	1.64944	0.0745904
$490$	0	0
$491$	−12.3070	−0.555407	−0.277703	−	0.960667i	$-0.589573\pi$
$491$	−12.3070	−0.555407	−0.277703	+	0.960667i	$0.589573\pi$
$492$	0.764429	0.0344631
$493$	3.63163	0.163560
$494$	2.86595	0.128945
$495$	5.62077	0.252635
$496$	−2.28943	−0.102798
$497$	0	0
$498$	−15.1442	−0.678630
$499$	−16.0073	−0.716584	−0.358292	−	0.933610i	$-0.616641\pi$
$499$	−16.0073	−0.716584	−0.358292	+	0.933610i	$0.616641\pi$
$500$	1.03110	0.0461123
$501$	−9.74025	−0.435162
$502$	0.650759	0.0290448
$503$	−0.648466	−0.0289137	−0.0144568	−	0.999895i	$-0.504602\pi$
$503$	−0.648466	−0.0289137	−0.0144568	+	0.999895i	$0.504602\pi$
$504$	0	0
$505$	1.19348	0.0531094
$506$	4.22602	0.187870
$507$	−1.00000	−0.0444116
$508$	16.7008	0.740979
$509$	−30.1078	−1.33450	−0.667251	−	0.744833i	$-0.732529\pi$
$509$	−30.1078	−1.33450	−0.667251	+	0.744833i	$0.732529\pi$
$510$	−0.942065	−0.0417153
$511$	0	0
$512$	9.77772	0.432118
$513$	1.64615	0.0726791
$514$	32.2473	1.42237
$515$	2.06916	0.0911780
$516$	−9.29934	−0.409381
$517$	19.7619	0.869127
$518$	0	0
$519$	−6.98008	−0.306392
$520$	1.68686	0.0739735
$521$	−40.1282	−1.75805	−0.879024	−	0.476778i	$-0.841805\pi$
$521$	−40.1282	−1.75805	−0.879024	+	0.476778i	$0.841805\pi$
$522$	11.6848	0.511430
$523$	32.3022	1.41248	0.706238	−	0.707975i	$-0.250391\pi$
$523$	32.3022	1.41248	0.706238	+	0.707975i	$0.250391\pi$
$524$	10.4034	0.454473
$525$	0	0
$526$	54.9935	2.39783
$527$	0.247812	0.0107948
$528$	28.0984	1.22283
$529$	−22.8135	−0.991891
$530$	14.4845	0.629166
$531$	7.40551	0.321372
$532$	0	0
$533$	0.741370	0.0321123
$534$	16.9837	0.734957
$535$	9.27441	0.400968
$536$	12.7648	0.551354
$537$	−0.773332	−0.0333718
$538$	−39.0056	−1.68165
$539$	0	0
$540$	−1.03110	−0.0443716
$541$	46.0767	1.98099	0.990497	−	0.137535i	$-0.0439180\pi$
$541$	46.0767	1.98099	0.990497	+	0.137535i	$0.0439180\pi$
$542$	−1.02387	−0.0439790
$543$	11.9659	0.513507
$544$	−2.88389	−0.123646
$545$	13.1740	0.564313
$546$	0	0
$547$	−19.2189	−0.821742	−0.410871	−	0.911693i	$-0.634775\pi$
$547$	−19.2189	−0.821742	−0.410871	+	0.911693i	$0.634775\pi$
$548$	20.8393	0.890211
$549$	−7.17958	−0.306417
$550$	9.78579	0.417268
$551$	−11.0481	−0.470667
$552$	0.728473	0.0310059
$553$	0	0
$554$	1.79206	0.0761374
$555$	6.01409	0.255284
$556$	−14.6380	−0.620789
$557$	12.4968	0.529506	0.264753	−	0.964316i	$-0.414710\pi$
$557$	12.4968	0.529506	0.264753	+	0.964316i	$0.414710\pi$
$558$	0.797337	0.0337540
$559$	−9.01883	−0.381456
$560$	0	0
$561$	−3.04142	−0.128409
$562$	−23.5424	−0.993076
$563$	−31.7532	−1.33824	−0.669119	−	0.743155i	$-0.733328\pi$
$563$	−31.7532	−1.33824	−0.669119	+	0.743155i	$0.733328\pi$
$564$	−3.62523	−0.152650
$565$	14.8369	0.624195
$566$	23.7934	1.00011
$567$	0	0
$568$	15.5730	0.653426
$569$	−1.83806	−0.0770555	−0.0385278	−	0.999258i	$-0.512267\pi$
$569$	−1.83806	−0.0770555	−0.0385278	+	0.999258i	$0.512267\pi$
$570$	2.86595	0.120041
$571$	−31.3866	−1.31349	−0.656744	−	0.754114i	$-0.728067\pi$
$571$	−31.3866	−1.31349	−0.656744	+	0.754114i	$0.728067\pi$
$572$	−5.79559	−0.242326
$573$	−2.41590	−0.100926
$574$	0	0
$575$	0.431853	0.0180095
$576$	0.719138	0.0299641
$577$	−23.4778	−0.977394	−0.488697	−	0.872453i	$-0.662528\pi$
$577$	−23.4778	−0.977394	−0.488697	+	0.872453i	$0.662528\pi$
$578$	−29.0874	−1.20987
$579$	1.83973	0.0764564
$580$	6.92027	0.287349
$581$	0	0
$582$	16.3937	0.679543
$583$	46.7625	1.93671
$584$	−0.942076	−0.0389834
$585$	−1.00000	−0.0413449
$586$	51.9938	2.14784
$587$	8.06147	0.332733	0.166366	−	0.986064i	$-0.446797\pi$
$587$	8.06147	0.332733	0.166366	+	0.986064i	$0.446797\pi$
$588$	0	0
$589$	−0.753893	−0.0310636
$590$	12.8930	0.530798
$591$	−13.0474	−0.536698
$592$	30.0646	1.23565
$593$	33.6133	1.38033	0.690166	−	0.723651i	$-0.257537\pi$
$593$	33.6133	1.38033	0.690166	+	0.723651i	$0.257537\pi$
$594$	−9.78579	−0.401516
$595$	0	0
$596$	5.57058	0.228180
$597$	20.7001	0.847198
$598$	−0.751858	−0.0307458
$599$	26.4092	1.07905	0.539524	−	0.841970i	$-0.318604\pi$
$599$	26.4092	1.07905	0.539524	+	0.841970i	$0.318604\pi$
$600$	1.68686	0.0688656
$601$	−2.88237	−0.117574	−0.0587871	−	0.998271i	$-0.518723\pi$
$601$	−2.88237	−0.117574	−0.0587871	+	0.998271i	$0.518723\pi$
$602$	0	0
$603$	−7.56720	−0.308160
$604$	11.0616	0.450091
$605$	20.5930	0.837226
$606$	−2.07786	−0.0844075
$607$	29.4539	1.19550	0.597749	−	0.801683i	$-0.296062\pi$
$607$	29.4539	1.19550	0.597749	+	0.801683i	$0.296062\pi$
$608$	8.77336	0.355807
$609$	0	0
$610$	−12.4997	−0.506098
$611$	−3.51587	−0.142237
$612$	0.557934	0.0225531
$613$	−23.3417	−0.942764	−0.471382	−	0.881929i	$-0.656245\pi$
$613$	−23.3417	−0.942764	−0.471382	+	0.881929i	$0.656245\pi$
$614$	33.3790	1.34707
$615$	0.741370	0.0298949
$616$	0	0
$617$	−5.25234	−0.211451	−0.105726	−	0.994395i	$-0.533717\pi$
$617$	−5.25234	−0.211451	−0.105726	+	0.994395i	$0.533717\pi$
$618$	−3.60242	−0.144910
$619$	−42.2637	−1.69872	−0.849361	−	0.527812i	$-0.823013\pi$
$619$	−42.2637	−1.69872	−0.849361	+	0.527812i	$0.823013\pi$
$620$	0.472219	0.0189648
$621$	−0.431853	−0.0173297
$622$	51.3590	2.05931
$623$	0	0
$624$	−4.99903	−0.200121
$625$	1.00000	0.0400000
$626$	−8.15171	−0.325808
$627$	9.25260	0.369513
$628$	−7.38307	−0.294617
$629$	−3.25425	−0.129755
$630$	0	0
$631$	0.228232	0.00908579	0.00454289	−	0.999990i	$-0.498554\pi$
$631$	0.228232	0.00908579	0.00454289	+	0.999990i	$0.498554\pi$
$632$	9.59162	0.381534
$633$	21.7490	0.864445
$634$	−42.5492	−1.68984
$635$	16.1970	0.642760
$636$	−8.57836	−0.340154
$637$	0	0
$638$	65.6776	2.60020
$639$	−9.23194	−0.365210
$640$	11.9113	0.470835
$641$	−29.2411	−1.15496	−0.577478	−	0.816406i	$-0.695963\pi$
$641$	−29.2411	−1.15496	−0.577478	+	0.816406i	$0.695963\pi$
$642$	−16.1468	−0.637263
$643$	12.3892	0.488582	0.244291	−	0.969702i	$-0.421445\pi$
$643$	12.3892	0.488582	0.244291	+	0.969702i	$0.421445\pi$
$644$	0	0
$645$	−9.01883	−0.355116
$646$	−1.55078	−0.0610145
$647$	−12.0608	−0.474158	−0.237079	−	0.971490i	$-0.576190\pi$
$647$	−12.0608	−0.474158	−0.237079	+	0.971490i	$0.576190\pi$
$648$	−1.68686	−0.0662660
$649$	41.6246	1.63391
$650$	−1.74101	−0.0682879
$651$	0	0
$652$	−1.70075	−0.0666063
$653$	−30.0083	−1.17431	−0.587157	−	0.809473i	$-0.699753\pi$
$653$	−30.0083	−1.17431	−0.587157	+	0.809473i	$0.699753\pi$
$654$	−22.9361	−0.896871
$655$	10.0895	0.394231
$656$	3.70613	0.144700
$657$	0.558480	0.0217884
$658$	0	0
$659$	45.5910	1.77597	0.887987	−	0.459868i	$-0.152103\pi$
$659$	45.5910	1.77597	0.887987	+	0.459868i	$0.152103\pi$
$660$	−5.79559	−0.225593
$661$	−32.2496	−1.25436	−0.627182	−	0.778873i	$-0.715792\pi$
$661$	−32.2496	−1.25436	−0.627182	+	0.778873i	$0.715792\pi$
$662$	28.6874	1.11497
$663$	0.541104	0.0210147
$664$	−14.6732	−0.569431
$665$	0	0
$666$	−10.4706	−0.405727
$667$	2.89839	0.112226
$668$	10.0432	0.388583
$669$	−3.99472	−0.154445
$670$	−13.1745	−0.508977
$671$	−40.3547	−1.55788
$672$	0	0
$673$	35.2770	1.35983	0.679913	−	0.733293i	$-0.262017\pi$
$673$	35.2770	1.35983	0.679913	+	0.733293i	$0.262017\pi$
$674$	−21.7472	−0.837673
$675$	−1.00000	−0.0384900
$676$	1.03110	0.0396578
$677$	4.18570	0.160870	0.0804348	−	0.996760i	$-0.474369\pi$
$677$	4.18570	0.160870	0.0804348	+	0.996760i	$0.474369\pi$
$678$	−25.8312	−0.992042
$679$	0	0
$680$	−0.912764	−0.0350029
$681$	12.5473	0.480813
$682$	4.48164	0.171611
$683$	−24.6779	−0.944273	−0.472137	−	0.881525i	$-0.656517\pi$
$683$	−24.6779	−0.944273	−0.472137	+	0.881525i	$0.656517\pi$
$684$	−1.69735	−0.0648996
$685$	20.2107	0.772211
$686$	0	0
$687$	19.0685	0.727509
$688$	−45.0854	−1.71887
$689$	−8.31960	−0.316952
$690$	−0.751858	−0.0286228
$691$	−11.9305	−0.453858	−0.226929	−	0.973911i	$-0.572869\pi$
$691$	−11.9305	−0.453858	−0.226929	+	0.973911i	$0.572869\pi$
$692$	7.19718	0.273596
$693$	0	0
$694$	13.9689	0.530254
$695$	−14.1964	−0.538502
$696$	11.3214	0.429136
$697$	−0.401158	−0.0151949
$698$	−9.45069	−0.357714
$699$	10.4049	0.393548
$700$	0	0
$701$	−15.6866	−0.592475	−0.296238	−	0.955114i	$-0.595732\pi$
$701$	−15.6866	−0.592475	−0.296238	+	0.955114i	$0.595732\pi$
$702$	1.74101	0.0657100
$703$	9.90008	0.373388
$704$	4.04211	0.152343
$705$	−3.51587	−0.132415
$706$	48.9743	1.84317
$707$	0	0
$708$	−7.63584	−0.286972
$709$	−50.6358	−1.90167	−0.950834	−	0.309700i	$-0.899771\pi$
$709$	−50.6358	−1.90167	−0.950834	+	0.309700i	$0.899771\pi$
$710$	−16.0729	−0.603204
$711$	−5.68609	−0.213245
$712$	16.4555	0.616695
$713$	0.197778	0.00740683
$714$	0	0
$715$	−5.62077	−0.210205
$716$	0.797385	0.0297997
$717$	−11.4452	−0.427427
$718$	8.93463	0.333437
$719$	−15.5263	−0.579034	−0.289517	−	0.957173i	$-0.593495\pi$
$719$	−15.5263	−0.579034	−0.289517	+	0.957173i	$0.593495\pi$
$720$	−4.99903	−0.186303
$721$	0	0
$722$	−28.3613	−1.05550
$723$	−29.2257	−1.08691
$724$	−12.3381	−0.458542
$725$	6.71152	0.249260
$726$	−35.8526	−1.33061
$727$	−1.82342	−0.0676267	−0.0338134	−	0.999428i	$-0.510765\pi$
$727$	−1.82342	−0.0676267	−0.0338134	+	0.999428i	$0.510765\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0.972317	0.0359871
$731$	4.88012	0.180498
$732$	7.40288	0.273618
$733$	47.1837	1.74277	0.871385	−	0.490600i	$-0.163222\pi$
$733$	47.1837	1.74277	0.871385	+	0.490600i	$0.163222\pi$
$734$	−42.7871	−1.57930
$735$	0	0
$736$	−2.30162	−0.0848387
$737$	−42.5335	−1.56674
$738$	−1.29073	−0.0475124
$739$	−39.9941	−1.47121	−0.735603	−	0.677413i	$-0.763101\pi$
$739$	−39.9941	−1.47121	−0.735603	+	0.677413i	$0.763101\pi$
$740$	−6.20115	−0.227959
$741$	−1.64615	−0.0604727
$742$	0	0
$743$	−39.6958	−1.45630	−0.728149	−	0.685419i	$-0.759619\pi$
$743$	−39.6958	−1.45630	−0.728149	+	0.685419i	$0.759619\pi$
$744$	0.772537	0.0283226
$745$	5.40254	0.197934
$746$	40.3713	1.47810
$747$	8.69856	0.318264
$748$	3.13601	0.114664
$749$	0	0
$750$	−1.74101	−0.0635726
$751$	−12.3135	−0.449327	−0.224663	−	0.974436i	$-0.572128\pi$
$751$	−12.3135	−0.449327	−0.224663	+	0.974436i	$0.572128\pi$
$752$	−17.5760	−0.640929
$753$	−0.373783	−0.0136214
$754$	−11.6848	−0.425536
$755$	10.7280	0.390431
$756$	0	0
$757$	−23.0202	−0.836685	−0.418342	−	0.908289i	$-0.637389\pi$
$757$	−23.0202	−0.836685	−0.418342	+	0.908289i	$0.637389\pi$
$758$	−36.4012	−1.32215
$759$	−2.42734	−0.0881070
$760$	2.77681	0.100726
$761$	−3.82368	−0.138608	−0.0693042	−	0.997596i	$-0.522078\pi$
$761$	−3.82368	−0.138608	−0.0693042	+	0.997596i	$0.522078\pi$
$762$	−28.1991	−1.02155
$763$	0	0
$764$	2.49104	0.0901228
$765$	0.541104	0.0195636
$766$	46.6273	1.68471
$767$	−7.40551	−0.267397
$768$	−19.2994	−0.696406
$769$	−11.9949	−0.432549	−0.216274	−	0.976333i	$-0.569391\pi$
$769$	−11.9949	−0.432549	−0.216274	+	0.976333i	$0.569391\pi$
$770$	0	0
$771$	−18.5222	−0.667062
$772$	−1.89695	−0.0682726
$773$	−18.4266	−0.662760	−0.331380	−	0.943497i	$-0.607514\pi$
$773$	−18.4266	−0.662760	−0.331380	+	0.943497i	$0.607514\pi$
$774$	15.7018	0.564391
$775$	0.457975	0.0164509
$776$	15.8839	0.570197
$777$	0	0
$778$	50.0856	1.79566
$779$	1.22040	0.0437255
$780$	1.03110	0.0369194
$781$	−51.8906	−1.85679
$782$	0.406833	0.0145483
$783$	−6.71152	−0.239850
$784$	0	0
$785$	−7.16037	−0.255564
$786$	−17.5660	−0.626557
$787$	−22.8854	−0.815775	−0.407888	−	0.913032i	$-0.633735\pi$
$787$	−22.8854	−0.815775	−0.407888	+	0.913032i	$0.633735\pi$
$788$	13.4532	0.479250
$789$	−31.5872	−1.12453
$790$	−9.89953	−0.352209
$791$	0	0
$792$	−9.48143	−0.336908
$793$	7.17958	0.254954
$794$	52.5961	1.86656
$795$	−8.31960	−0.295066
$796$	−21.3439	−0.756515
$797$	−0.716627	−0.0253842	−0.0126921	−	0.999919i	$-0.504040\pi$
$797$	−0.716627	−0.0253842	−0.0126921	+	0.999919i	$0.504040\pi$
$798$	0	0
$799$	1.90245	0.0673039
$800$	−5.32963	−0.188431
$801$	−9.75511	−0.344680
$802$	−37.1208	−1.31078
$803$	3.13909	0.110776
$804$	7.80256	0.275175
$805$	0	0
$806$	−0.797337	−0.0280850
$807$	22.4041	0.788660
$808$	−2.01324	−0.0708254
$809$	−3.63647	−0.127851	−0.0639257	−	0.997955i	$-0.520362\pi$
$809$	−3.63647	−0.127851	−0.0639257	+	0.997955i	$0.520362\pi$
$810$	1.74101	0.0611727
$811$	21.4384	0.752803	0.376402	−	0.926457i	$-0.377161\pi$
$811$	21.4384	0.752803	0.376402	+	0.926457i	$0.377161\pi$
$812$	0	0
$813$	0.588091	0.0206253
$814$	−58.8527	−2.06278
$815$	−1.64944	−0.0577775
$816$	2.70500	0.0946938
$817$	−14.8463	−0.519406
$818$	54.3823	1.90143
$819$	0	0
$820$	−0.764429	−0.0266950
$821$	36.2907	1.26655	0.633277	−	0.773926i	$-0.281710\pi$
$821$	36.2907	1.26655	0.633277	+	0.773926i	$0.281710\pi$
$822$	−35.1870	−1.22729
$823$	35.6616	1.24308	0.621542	−	0.783381i	$-0.286507\pi$
$823$	35.6616	1.24308	0.621542	+	0.783381i	$0.286507\pi$
$824$	−3.49037	−0.121593
$825$	−5.62077	−0.195690
$826$	0	0
$827$	−3.01320	−0.104779	−0.0523896	−	0.998627i	$-0.516684\pi$
$827$	−3.01320	−0.104779	−0.0523896	+	0.998627i	$0.516684\pi$
$828$	0.445284	0.0154747
$829$	−11.3628	−0.394645	−0.197323	−	0.980339i	$-0.563225\pi$
$829$	−11.3628	−0.394645	−0.197323	+	0.980339i	$0.563225\pi$
$830$	15.1442	0.525664
$831$	−1.02933	−0.0357069
$832$	−0.719138	−0.0249316
$833$	0	0
$834$	24.7161	0.855849
$835$	9.74025	0.337075
$836$	−9.54039	−0.329961
$837$	−0.457975	−0.0158299
$838$	52.7215	1.82123
$839$	−35.1601	−1.21386	−0.606931	−	0.794754i	$-0.707600\pi$
$839$	−35.1601	−1.21386	−0.606931	+	0.794754i	$0.707600\pi$
$840$	0	0
$841$	16.0446	0.553261
$842$	29.6389	1.02142
$843$	13.5223	0.465733
$844$	−22.4255	−0.771916
$845$	1.00000	0.0344010
$846$	6.12116	0.210450
$847$	0	0
$848$	−41.5900	−1.42821
$849$	−13.6664	−0.469031
$850$	0.942065	0.0323126
$851$	−2.59720	−0.0890309
$852$	9.51908	0.326118
$853$	−20.5937	−0.705116	−0.352558	−	0.935790i	$-0.614688\pi$
$853$	−20.5937	−0.705116	−0.352558	+	0.935790i	$0.614688\pi$
$854$	0	0
$855$	−1.64615	−0.0562970
$856$	−15.6446	−0.534721
$857$	24.8121	0.847565	0.423782	−	0.905764i	$-0.360702\pi$
$857$	24.8121	0.847565	0.423782	+	0.905764i	$0.360702\pi$
$858$	9.78579	0.334081
$859$	−10.9164	−0.372464	−0.186232	−	0.982506i	$-0.559628\pi$
$859$	−10.9164	−0.372464	−0.186232	+	0.982506i	$0.559628\pi$
$860$	9.29934	0.317105
$861$	0	0
$862$	42.7050	1.45454
$863$	27.0588	0.921093	0.460547	−	0.887635i	$-0.347653\pi$
$863$	27.0588	0.921093	0.460547	+	0.887635i	$0.347653\pi$
$864$	5.32963	0.181318
$865$	6.98008	0.237330
$866$	53.5173	1.81859
$867$	16.7072	0.567406
$868$	0	0
$869$	−31.9602	−1.08418
$870$	−11.6848	−0.396152
$871$	7.56720	0.256405
$872$	−22.2227	−0.752555
$873$	−9.41625	−0.318692
$874$	−1.23767	−0.0418648
$875$	0	0
$876$	−0.575850	−0.0194562
$877$	−42.0863	−1.42115	−0.710577	−	0.703619i	$-0.751566\pi$
$877$	−42.0863	−1.42115	−0.710577	+	0.703619i	$0.751566\pi$
$878$	−3.04759	−0.102851
$879$	−29.8642	−1.00729
$880$	−28.0984	−0.947197
$881$	−14.7102	−0.495599	−0.247800	−	0.968811i	$-0.579707\pi$
$881$	−14.7102	−0.495599	−0.247800	+	0.968811i	$0.579707\pi$
$882$	0	0
$883$	−45.9076	−1.54491	−0.772457	−	0.635067i	$-0.780972\pi$
$883$	−45.9076	−1.54491	−0.772457	+	0.635067i	$0.780972\pi$
$884$	−0.557934	−0.0187653
$885$	−7.40551	−0.248933
$886$	−18.3946	−0.617978
$887$	33.2481	1.11636	0.558182	−	0.829719i	$-0.311499\pi$
$887$	33.2481	1.11636	0.558182	+	0.829719i	$0.311499\pi$
$888$	−10.1449	−0.340441
$889$	0	0
$890$	−16.9837	−0.569295
$891$	5.62077	0.188303
$892$	4.11897	0.137913
$893$	−5.78764	−0.193676
$894$	−9.40586	−0.314579
$895$	0.773332	0.0258497
$896$	0	0
$897$	0.431853	0.0144191
$898$	49.5946	1.65499
$899$	3.07371	0.102514
$900$	1.03110	0.0343701
$901$	4.50177	0.149976
$902$	−7.25489	−0.241562
$903$	0	0
$904$	−25.0278	−0.832412
$905$	−11.9659	−0.397761
$906$	−18.6775	−0.620517
$907$	−35.8279	−1.18965	−0.594824	−	0.803856i	$-0.702778\pi$
$907$	−35.8279	−1.18965	−0.594824	+	0.803856i	$0.702778\pi$
$908$	−12.9375	−0.429348
$909$	1.19348	0.0395854
$910$	0	0
$911$	−22.4028	−0.742236	−0.371118	−	0.928586i	$-0.621026\pi$
$911$	−22.4028	−0.742236	−0.371118	+	0.928586i	$0.621026\pi$
$912$	−8.22914	−0.272494
$913$	48.8926	1.61811
$914$	−1.50544	−0.0497955
$915$	7.17958	0.237350
$916$	−19.6616	−0.649637
$917$	0	0
$918$	−0.942065	−0.0310928
$919$	−23.2398	−0.766610	−0.383305	−	0.923622i	$-0.625214\pi$
$919$	−23.2398	−0.766610	−0.383305	+	0.923622i	$0.625214\pi$
$920$	−0.728473	−0.0240171
$921$	−19.1723	−0.631748
$922$	19.7779	0.651352
$923$	9.23194	0.303873
$924$	0	0
$925$	−6.01409	−0.197742
$926$	−37.7131	−1.23933
$927$	2.06916	0.0679601
$928$	−35.7700	−1.17421
$929$	7.94298	0.260601	0.130300	−	0.991475i	$-0.458406\pi$
$929$	7.94298	0.260601	0.130300	+	0.991475i	$0.458406\pi$
$930$	−0.797337	−0.0261457
$931$	0	0
$932$	−10.7285	−0.351423
$933$	−29.4996	−0.965774
$934$	−40.0512	−1.31051
$935$	3.04142	0.0994650
$936$	1.68686	0.0551366
$937$	−38.8549	−1.26933	−0.634666	−	0.772786i	$-0.718863\pi$
$937$	−38.8549	−1.26933	−0.634666	+	0.772786i	$0.718863\pi$
$938$	0	0
$939$	4.68219	0.152797
$940$	3.62523	0.118242
$941$	57.0841	1.86089	0.930444	−	0.366435i	$-0.119422\pi$
$941$	57.0841	1.86089	0.930444	+	0.366435i	$0.119422\pi$
$942$	12.4662	0.406172
$943$	−0.320163	−0.0104259
$944$	−37.0204	−1.20491
$945$	0	0
$946$	88.2564	2.86946
$947$	−32.4516	−1.05454	−0.527268	−	0.849699i	$-0.676784\pi$
$947$	−32.4516	−1.05454	−0.527268	+	0.849699i	$0.676784\pi$
$948$	5.86295	0.190420
$949$	−0.558480	−0.0181290
$950$	−2.86595	−0.0929837
$951$	24.4394	0.792502
$952$	0	0
$953$	42.5926	1.37971	0.689854	−	0.723948i	$-0.257675\pi$
$953$	42.5926	1.37971	0.689854	+	0.723948i	$0.257675\pi$
$954$	14.4845	0.468952
$955$	2.41590	0.0781768
$956$	11.8011	0.381676
$957$	−37.7239	−1.21944
$958$	−60.7046	−1.96128
$959$	0	0
$960$	−0.719138	−0.0232101
$961$	−30.7903	−0.993234
$962$	10.4706	0.337585
$963$	9.27441	0.298864
$964$	30.1347	0.970572
$965$	−1.83973	−0.0592229
$966$	0	0
$967$	−46.4588	−1.49401	−0.747007	−	0.664816i	$-0.768510\pi$
$967$	−46.4588	−1.49401	−0.747007	+	0.664816i	$0.768510\pi$
$968$	−34.7375	−1.11650
$969$	0.890736	0.0286146
$970$	−16.3937	−0.526371
$971$	31.6006	1.01411	0.507055	−	0.861914i	$-0.330734\pi$
$971$	31.6006	1.01411	0.507055	+	0.861914i	$0.330734\pi$
$972$	−1.03110	−0.0330726
$973$	0	0
$974$	3.25871	0.104416
$975$	1.00000	0.0320256
$976$	35.8909	1.14884
$977$	−11.9786	−0.383229	−0.191614	−	0.981470i	$-0.561372\pi$
$977$	−11.9786	−0.383229	−0.191614	+	0.981470i	$0.561372\pi$
$978$	2.87169	0.0918266
$979$	−54.8312	−1.75241
$980$	0	0
$981$	13.1740	0.420614
$982$	−21.4265	−0.683749
$983$	−39.0438	−1.24531	−0.622653	−	0.782498i	$-0.713945\pi$
$983$	−39.0438	−1.24531	−0.622653	+	0.782498i	$0.713945\pi$
$984$	−1.25058	−0.0398672
$985$	13.0474	0.415724
$986$	6.32269	0.201356
$987$	0	0
$988$	1.69735	0.0539998
$989$	3.89480	0.123848
$990$	9.78579	0.311013
$991$	−14.9688	−0.475499	−0.237750	−	0.971326i	$-0.576410\pi$
$991$	−14.9688	−0.475499	−0.237750	+	0.971326i	$0.576410\pi$
$992$	−2.44084	−0.0774967
$993$	−16.4775	−0.522897
$994$	0	0
$995$	−20.7001	−0.656237
$996$	−8.96911	−0.284197
$997$	−0.719728	−0.0227940	−0.0113970	−	0.999935i	$-0.503628\pi$
$997$	−0.719728	−0.0227940	−0.0113970	+	0.999935i	$0.503628\pi$
$998$	−27.8688	−0.882171
$999$	6.01409	0.190277

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9555.2.a.cp.1.7		9
7.2	even	3		1365.2.r.m.781.3	✓	18
7.4	even	3		1365.2.r.m.1171.3	yes	18
7.6	odd	2		9555.2.a.cq.1.7		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1365.2.r.m.781.3	✓	18	7.2	even	3
1365.2.r.m.1171.3	yes	18	7.4	even	3
9555.2.a.cp.1.7		9	1.1	even	1	trivial
9555.2.a.cq.1.7		9	7.6	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:	\( N \)	\(=\)	\( 9555 = 3 \cdot 5 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9555.a (trivial)

\(f(q)\)	\(=\)	\(q+1.74101 q^{2} -1.00000 q^{3} +1.03110 q^{4} +1.00000 q^{5} -1.74101 q^{6} -1.68686 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.74101 q^{2} -1.00000 q^{3} +1.03110 q^{4} +1.00000 q^{5} -1.74101 q^{6} -1.68686 q^{8} +1.00000 q^{9} +1.74101 q^{10} +5.62077 q^{11} -1.03110 q^{12} -1.00000 q^{13} -1.00000 q^{15} -4.99903 q^{16} +0.541104 q^{17} +1.74101 q^{18} -1.64615 q^{19} +1.03110 q^{20} +9.78579 q^{22} +0.431853 q^{23} +1.68686 q^{24} +1.00000 q^{25} -1.74101 q^{26} -1.00000 q^{27} +6.71152 q^{29} -1.74101 q^{30} +0.457975 q^{31} -5.32963 q^{32} -5.62077 q^{33} +0.942065 q^{34} +1.03110 q^{36} -6.01409 q^{37} -2.86595 q^{38} +1.00000 q^{39} -1.68686 q^{40} -0.741370 q^{41} +9.01883 q^{43} +5.79559 q^{44} +1.00000 q^{45} +0.751858 q^{46} +3.51587 q^{47} +4.99903 q^{48} +1.74101 q^{50} -0.541104 q^{51} -1.03110 q^{52} +8.31960 q^{53} -1.74101 q^{54} +5.62077 q^{55} +1.64615 q^{57} +11.6848 q^{58} +7.40551 q^{59} -1.03110 q^{60} -7.17958 q^{61} +0.797337 q^{62} +0.719138 q^{64} -1.00000 q^{65} -9.78579 q^{66} -7.56720 q^{67} +0.557934 q^{68} -0.431853 q^{69} -9.23194 q^{71} -1.68686 q^{72} +0.558480 q^{73} -10.4706 q^{74} -1.00000 q^{75} -1.69735 q^{76} +1.74101 q^{78} -5.68609 q^{79} -4.99903 q^{80} +1.00000 q^{81} -1.29073 q^{82} +8.69856 q^{83} +0.541104 q^{85} +15.7018 q^{86} -6.71152 q^{87} -9.48143 q^{88} -9.75511 q^{89} +1.74101 q^{90} +0.445284 q^{92} -0.457975 q^{93} +6.12116 q^{94} -1.64615 q^{95} +5.32963 q^{96} -9.41625 q^{97} +5.62077 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 3 q^{2} - 9 q^{3} + 11 q^{4} + 9 q^{5} - 3 q^{6} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 3 * q^2 - 9 * q^3 + 11 * q^4 + 9 * q^5 - 3 * q^6 + 12 * q^8 + 9 * q^9	\( 9 q + 3 q^{2} - 9 q^{3} + 11 q^{4} + 9 q^{5} - 3 q^{6} + 12 q^{8} + 9 q^{9} + 3 q^{10} + 3 q^{11} - 11 q^{12} - 9 q^{13} - 9 q^{15} + 11 q^{16} + 3 q^{18} + 4 q^{19} + 11 q^{20} + 11 q^{22} + 15 q^{23} - 12 q^{24} + 9 q^{25} - 3 q^{26} - 9 q^{27} + 30 q^{29} - 3 q^{30} + 2 q^{31} + 27 q^{32} - 3 q^{33} - 12 q^{34} + 11 q^{36} + 21 q^{37} + 14 q^{38} + 9 q^{39} + 12 q^{40} - 4 q^{41} + 15 q^{43} + 21 q^{44} + 9 q^{45} - 23 q^{46} - 7 q^{47} - 11 q^{48} + 3 q^{50} - 11 q^{52} + 15 q^{53} - 3 q^{54} + 3 q^{55} - 4 q^{57} - 6 q^{58} - 7 q^{59} - 11 q^{60} + 2 q^{61} - 33 q^{62} + 12 q^{64} - 9 q^{65} - 11 q^{66} + 21 q^{67} + 23 q^{68} - 15 q^{69} + 21 q^{71} + 12 q^{72} + 33 q^{73} - 18 q^{74} - 9 q^{75} - 13 q^{76} + 3 q^{78} - 13 q^{79} + 11 q^{80} + 9 q^{81} + 34 q^{82} + q^{83} + 20 q^{86} - 30 q^{87} + 8 q^{88} + 14 q^{89} + 3 q^{90} + 46 q^{92} - 2 q^{93} + 7 q^{94} + 4 q^{95} - 27 q^{96} + 12 q^{97} + 3 q^{99}+O(q^{100}) \) 9 * q + 3 * q^2 - 9 * q^3 + 11 * q^4 + 9 * q^5 - 3 * q^6 + 12 * q^8 + 9 * q^9 + 3 * q^10 + 3 * q^11 - 11 * q^12 - 9 * q^13 - 9 * q^15 + 11 * q^16 + 3 * q^18 + 4 * q^19 + 11 * q^20 + 11 * q^22 + 15 * q^23 - 12 * q^24 + 9 * q^25 - 3 * q^26 - 9 * q^27 + 30 * q^29 - 3 * q^30 + 2 * q^31 + 27 * q^32 - 3 * q^33 - 12 * q^34 + 11 * q^36 + 21 * q^37 + 14 * q^38 + 9 * q^39 + 12 * q^40 - 4 * q^41 + 15 * q^43 + 21 * q^44 + 9 * q^45 - 23 * q^46 - 7 * q^47 - 11 * q^48 + 3 * q^50 - 11 * q^52 + 15 * q^53 - 3 * q^54 + 3 * q^55 - 4 * q^57 - 6 * q^58 - 7 * q^59 - 11 * q^60 + 2 * q^61 - 33 * q^62 + 12 * q^64 - 9 * q^65 - 11 * q^66 + 21 * q^67 + 23 * q^68 - 15 * q^69 + 21 * q^71 + 12 * q^72 + 33 * q^73 - 18 * q^74 - 9 * q^75 - 13 * q^76 + 3 * q^78 - 13 * q^79 + 11 * q^80 + 9 * q^81 + 34 * q^82 + q^83 + 20 * q^86 - 30 * q^87 + 8 * q^88 + 14 * q^89 + 3 * q^90 + 46 * q^92 - 2 * q^93 + 7 * q^94 + 4 * q^95 - 27 * q^96 + 12 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more