LMFDB - Embedded newform 1150.2.b.g.599.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(599,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1150.599");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$9.18279623245$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{21})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 11x^{2} + 25 $ x^4 + 11*x^2 + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			599.4
Root			$1.79129i$ of defining polynomial
Character	$\chi$	$=$	1150.599
Dual form			1150.2.b.g.599.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.79129i q^{3} -1.00000 q^{4} -1.79129 q^{6} -2.79129i q^{7} -1.00000i q^{8} -0.208712 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.79129i q^{3} -1.00000 q^{4} -1.79129 q^{6} -2.79129i q^{7} -1.00000i q^{8} -0.208712 q^{9} +3.79129 q^{11} -1.79129i q^{12} +1.20871i q^{13} +2.79129 q^{14} +1.00000 q^{16} +3.79129i q^{17} -0.208712i q^{18} -1.20871 q^{19} +5.00000 q^{21} +3.79129i q^{22} +1.00000i q^{23} +1.79129 q^{24} -1.20871 q^{26} +5.00000i q^{27} +2.79129i q^{28} +1.58258 q^{29} +10.3739 q^{31} +1.00000i q^{32} +6.79129i q^{33} -3.79129 q^{34} +0.208712 q^{36} +4.00000i q^{37} -1.20871i q^{38} -2.16515 q^{39} -2.20871 q^{41} +5.00000i q^{42} -7.16515i q^{43} -3.79129 q^{44} -1.00000 q^{46} +13.5826i q^{47} +1.79129i q^{48} -0.791288 q^{49} -6.79129 q^{51} -1.20871i q^{52} +6.00000i q^{53} -5.00000 q^{54} -2.79129 q^{56} -2.16515i q^{57} +1.58258i q^{58} +4.41742 q^{59} -3.37386 q^{61} +10.3739i q^{62} +0.582576i q^{63} -1.00000 q^{64} -6.79129 q^{66} +7.16515i q^{67} -3.79129i q^{68} -1.79129 q^{69} -5.37386 q^{71} +0.208712i q^{72} -14.7477i q^{73} -4.00000 q^{74} +1.20871 q^{76} -10.5826i q^{77} -2.16515i q^{78} -8.00000 q^{79} -9.58258 q^{81} -2.20871i q^{82} -6.00000i q^{83} -5.00000 q^{84} +7.16515 q^{86} +2.83485i q^{87} -3.79129i q^{88} +3.16515 q^{89} +3.37386 q^{91} -1.00000i q^{92} +18.5826i q^{93} -13.5826 q^{94} -1.79129 q^{96} -14.9564i q^{97} -0.791288i q^{98} -0.791288 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 2 q^{6} - 10 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 2 * q^6 - 10 * q^9	$ 4 q - 4 q^{4} + 2 q^{6} - 10 q^{9} + 6 q^{11} + 2 q^{14} + 4 q^{16} - 14 q^{19} + 20 q^{21} - 2 q^{24} - 14 q^{26} - 12 q^{29} + 14 q^{31} - 6 q^{34} + 10 q^{36} + 28 q^{39} - 18 q^{41} - 6 q^{44} - 4 q^{46} + 6 q^{49} - 18 q^{51} - 20 q^{54} - 2 q^{56} + 36 q^{59} + 14 q^{61} - 4 q^{64} - 18 q^{66} + 2 q^{69} + 6 q^{71} - 16 q^{74} + 14 q^{76} - 32 q^{79} - 20 q^{81} - 20 q^{84} - 8 q^{86} - 24 q^{89} - 14 q^{91} - 36 q^{94} + 2 q^{96} + 6 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 2 * q^6 - 10 * q^9 + 6 * q^11 + 2 * q^14 + 4 * q^16 - 14 * q^19 + 20 * q^21 - 2 * q^24 - 14 * q^26 - 12 * q^29 + 14 * q^31 - 6 * q^34 + 10 * q^36 + 28 * q^39 - 18 * q^41 - 6 * q^44 - 4 * q^46 + 6 * q^49 - 18 * q^51 - 20 * q^54 - 2 * q^56 + 36 * q^59 + 14 * q^61 - 4 * q^64 - 18 * q^66 + 2 * q^69 + 6 * q^71 - 16 * q^74 + 14 * q^76 - 32 * q^79 - 20 * q^81 - 20 * q^84 - 8 * q^86 - 24 * q^89 - 14 * q^91 - 36 * q^94 + 2 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	1.79129i	1.03420i	0.855925	+	0.517100i	$0.172989\pi$
$3$	1.79129i	1.03420i	−0.855925	+	0.517100i	$0.827011\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.79129	−0.731290
$7$	− 2.79129i	− 1.05501i	−0.849553	−	0.527504i	$-0.823128\pi$
$7$	− 2.79129i	− 1.05501i	0.849553	−	0.527504i	$-0.176872\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−0.208712	−0.0695707
$10$	0	0
$11$	3.79129	1.14312	0.571558	−	0.820562i	$-0.306339\pi$
$11$	3.79129	1.14312	0.571558	+	0.820562i	$0.306339\pi$
$12$	− 1.79129i	− 0.517100i
$13$	1.20871i	0.335236i	0.985852	+	0.167618i	$0.0536076\pi$
$13$	1.20871i	0.335236i	−0.985852	+	0.167618i	$0.946392\pi$
$14$	2.79129	0.746003
$15$	0	0
$16$	1.00000	0.250000
$17$	3.79129i	0.919522i	0.888043	+	0.459761i	$0.152065\pi$
$17$	3.79129i	0.919522i	−0.888043	+	0.459761i	$0.847935\pi$
$18$	− 0.208712i	− 0.0491939i
$19$	−1.20871	−0.277298	−0.138649	−	0.990342i	$-0.544276\pi$
$19$	−1.20871	−0.277298	−0.138649	+	0.990342i	$0.544276\pi$
$20$	0	0
$21$	5.00000	1.09109
$22$	3.79129i	0.808305i
$23$	1.00000i	0.208514i
$23$	1.00000i	0.208514i
$24$	1.79129	0.365645
$25$	0	0
$26$	−1.20871	−0.237048
$27$	5.00000i	0.962250i
$28$	2.79129i	0.527504i
$29$	1.58258	0.293877	0.146938	−	0.989146i	$-0.453058\pi$
$29$	1.58258	0.293877	0.146938	+	0.989146i	$0.453058\pi$
$30$	0	0
$31$	10.3739	1.86320	0.931600	−	0.363484i	$-0.118413\pi$
$31$	10.3739	1.86320	0.931600	+	0.363484i	$0.118413\pi$
$32$	1.00000i	0.176777i
$33$	6.79129i	1.18221i
$34$	−3.79129	−0.650201
$35$	0	0
$36$	0.208712	0.0347854
$37$	4.00000i	0.657596i	0.944400	+	0.328798i	$0.106644\pi$
$37$	4.00000i	0.657596i	−0.944400	+	0.328798i	$0.893356\pi$
$38$	− 1.20871i	− 0.196079i
$39$	−2.16515	−0.346702
$40$	0	0
$41$	−2.20871	−0.344943	−0.172471	−	0.985015i	$-0.555175\pi$
$41$	−2.20871	−0.344943	−0.172471	+	0.985015i	$0.555175\pi$
$42$	5.00000i	0.771517i
$43$	− 7.16515i	− 1.09268i	−0.837565	−	0.546338i	$-0.816022\pi$
$43$	− 7.16515i	− 1.09268i	0.837565	−	0.546338i	$-0.183978\pi$
$44$	−3.79129	−0.571558
$45$	0	0
$46$	−1.00000	−0.147442
$47$	13.5826i	1.98122i	0.136710	+	0.990611i	$0.456347\pi$
$47$	13.5826i	1.98122i	−0.136710	+	0.990611i	$0.543653\pi$
$48$	1.79129i	0.258550i
$49$	−0.791288	−0.113041
$50$	0	0
$51$	−6.79129	−0.950971
$52$	− 1.20871i	− 0.167618i
$53$	6.00000i	0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$	6.00000i	0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$	−5.00000	−0.680414
$55$	0	0
$56$	−2.79129	−0.373002
$57$	− 2.16515i	− 0.286781i
$58$	1.58258i	0.207802i
$59$	4.41742	0.575100	0.287550	−	0.957766i	$-0.407159\pi$
$59$	4.41742	0.575100	0.287550	+	0.957766i	$0.407159\pi$
$60$	0	0
$61$	−3.37386	−0.431979	−0.215989	−	0.976396i	$-0.569298\pi$
$61$	−3.37386	−0.431979	−0.215989	+	0.976396i	$0.569298\pi$
$62$	10.3739i	1.31748i
$63$	0.582576i	0.0733976i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−6.79129	−0.835950
$67$	7.16515i	0.875363i	0.899130	+	0.437681i	$0.144200\pi$
$67$	7.16515i	0.875363i	−0.899130	+	0.437681i	$0.855800\pi$
$68$	− 3.79129i	− 0.459761i
$69$	−1.79129	−0.215646
$70$	0	0
$71$	−5.37386	−0.637760	−0.318880	−	0.947795i	$-0.603307\pi$
$71$	−5.37386	−0.637760	−0.318880	+	0.947795i	$0.603307\pi$
$72$	0.208712i	0.0245970i
$73$	− 14.7477i	− 1.72609i	−0.505126	−	0.863045i	$-0.668554\pi$
$73$	− 14.7477i	− 1.72609i	0.505126	−	0.863045i	$-0.331446\pi$
$74$	−4.00000	−0.464991
$75$	0	0
$76$	1.20871	0.138649
$77$	− 10.5826i	− 1.20600i
$78$	− 2.16515i	− 0.245155i
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	0	0
$81$	−9.58258	−1.06473
$82$	− 2.20871i	− 0.243911i
$83$	− 6.00000i	− 0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$	− 6.00000i	− 0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$	−5.00000	−0.545545
$85$	0	0
$86$	7.16515	0.772638
$87$	2.83485i	0.303928i
$88$	− 3.79129i	− 0.404153i
$89$	3.16515	0.335505	0.167753	−	0.985829i	$-0.446349\pi$
$89$	3.16515	0.335505	0.167753	+	0.985829i	$0.446349\pi$
$90$	0	0
$91$	3.37386	0.353677
$92$	− 1.00000i	− 0.104257i
$93$	18.5826i	1.92692i
$94$	−13.5826	−1.40094
$95$	0	0
$96$	−1.79129	−0.182823
$97$	− 14.9564i	− 1.51860i	−0.650743	−	0.759298i	$-0.725542\pi$
$97$	− 14.9564i	− 1.51860i	0.650743	−	0.759298i	$-0.274458\pi$
$98$	− 0.791288i	− 0.0799321i
$99$	−0.791288	−0.0795274
$100$	0	0
$101$	13.5826	1.35152	0.675758	−	0.737123i	$-0.263816\pi$
$101$	13.5826	1.35152	0.675758	+	0.737123i	$0.263816\pi$
$102$	− 6.79129i	− 0.672438i
$103$	7.37386i	0.726568i	0.931678	+	0.363284i	$0.118345\pi$
$103$	7.37386i	0.726568i	−0.931678	+	0.363284i	$0.881655\pi$
$104$	1.20871	0.118524
$105$	0	0
$106$	−6.00000	−0.582772
$107$	− 13.5826i	− 1.31308i	−0.754292	−	0.656539i	$-0.772020\pi$
$107$	− 13.5826i	− 1.31308i	0.754292	−	0.656539i	$-0.227980\pi$
$108$	− 5.00000i	− 0.481125i
$109$	−10.3739	−0.993636	−0.496818	−	0.867855i	$-0.665498\pi$
$109$	−10.3739	−0.993636	−0.496818	+	0.867855i	$0.665498\pi$
$110$	0	0
$111$	−7.16515	−0.680086
$112$	− 2.79129i	− 0.263752i
$113$	6.00000i	0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$	6.00000i	0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$	2.16515	0.202785
$115$	0	0
$116$	−1.58258	−0.146938
$117$	− 0.252273i	− 0.0233226i
$118$	4.41742i	0.406657i
$119$	10.5826	0.970103
$120$	0	0
$121$	3.37386	0.306715
$122$	− 3.37386i	− 0.305455i
$123$	− 3.95644i	− 0.356740i
$124$	−10.3739	−0.931600
$125$	0	0
$126$	−0.582576	−0.0519000
$127$	14.7477i	1.30865i	0.756214	+	0.654325i	$0.227047\pi$
$127$	14.7477i	1.30865i	−0.756214	+	0.654325i	$0.772953\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	12.8348	1.13005
$130$	0	0
$131$	9.16515	0.800763	0.400381	−	0.916349i	$-0.368878\pi$
$131$	9.16515	0.800763	0.400381	+	0.916349i	$0.368878\pi$
$132$	− 6.79129i	− 0.591106i
$133$	3.37386i	0.292551i
$134$	−7.16515	−0.618975
$135$	0	0
$136$	3.79129	0.325100
$137$	0.791288i	0.0676043i	0.999429	+	0.0338021i	$0.0107616\pi$
$137$	0.791288i	0.0676043i	−0.999429	+	0.0338021i	$0.989238\pi$
$138$	− 1.79129i	− 0.152485i
$139$	14.7477	1.25089	0.625443	−	0.780270i	$-0.284918\pi$
$139$	14.7477	1.25089	0.625443	+	0.780270i	$0.284918\pi$
$140$	0	0
$141$	−24.3303	−2.04898
$142$	− 5.37386i	− 0.450965i
$143$	4.58258i	0.383214i
$144$	−0.208712	−0.0173927
$145$	0	0
$146$	14.7477	1.22053
$147$	− 1.41742i	− 0.116907i
$148$	− 4.00000i	− 0.328798i
$149$	−12.7913	−1.04790	−0.523952	−	0.851748i	$-0.675543\pi$
$149$	−12.7913	−1.04790	−0.523952	+	0.851748i	$0.675543\pi$
$150$	0	0
$151$	−6.20871	−0.505258	−0.252629	−	0.967563i	$-0.581295\pi$
$151$	−6.20871	−0.505258	−0.252629	+	0.967563i	$0.581295\pi$
$152$	1.20871i	0.0980395i
$153$	− 0.791288i	− 0.0639718i
$154$	10.5826	0.852768
$155$	0	0
$156$	2.16515	0.173351
$157$	− 12.7477i	− 1.01738i	−0.860950	−	0.508690i	$-0.830130\pi$
$157$	− 12.7477i	− 1.01738i	0.860950	−	0.508690i	$-0.169870\pi$
$158$	− 8.00000i	− 0.636446i
$159$	−10.7477	−0.852350
$160$	0	0
$161$	2.79129	0.219984
$162$	− 9.58258i	− 0.752878i
$163$	22.3739i	1.75246i	0.481897	+	0.876228i	$0.339948\pi$
$163$	22.3739i	1.75246i	−0.481897	+	0.876228i	$0.660052\pi$
$164$	2.20871	0.172471
$165$	0	0
$166$	6.00000	0.465690
$167$	18.3303i	1.41844i	0.704987	+	0.709221i	$0.250953\pi$
$167$	18.3303i	1.41844i	−0.704987	+	0.709221i	$0.749047\pi$
$168$	− 5.00000i	− 0.385758i
$169$	11.5390	0.887617
$170$	0	0
$171$	0.252273	0.0192918
$172$	7.16515i	0.546338i
$173$	− 14.2087i	− 1.08027i	−0.841579	−	0.540134i	$-0.818373\pi$
$173$	− 14.2087i	− 1.08027i	0.841579	−	0.540134i	$-0.181627\pi$
$174$	−2.83485	−0.214909
$175$	0	0
$176$	3.79129	0.285779
$177$	7.91288i	0.594768i
$178$	3.16515i	0.237238i
$179$	16.7477	1.25178	0.625892	−	0.779910i	$-0.284735\pi$
$179$	16.7477	1.25178	0.625892	+	0.779910i	$0.284735\pi$
$180$	0	0
$181$	13.5390	1.00635	0.503174	−	0.864185i	$-0.332166\pi$
$181$	13.5390	1.00635	0.503174	+	0.864185i	$0.332166\pi$
$182$	3.37386i	0.250087i
$183$	− 6.04356i	− 0.446753i
$184$	1.00000	0.0737210
$185$	0	0
$186$	−18.5826	−1.36254
$187$	14.3739i	1.05112i
$188$	− 13.5826i	− 0.990611i
$189$	13.9564	1.01518
$190$	0	0
$191$	16.4174	1.18792	0.593962	−	0.804493i	$-0.297563\pi$
$191$	16.4174	1.18792	0.593962	+	0.804493i	$0.297563\pi$
$192$	− 1.79129i	− 0.129275i
$193$	6.74773i	0.485712i	0.970062	+	0.242856i	$0.0780843\pi$
$193$	6.74773i	0.485712i	−0.970062	+	0.242856i	$0.921916\pi$
$194$	14.9564	1.07381
$195$	0	0
$196$	0.791288	0.0565206
$197$	− 20.5390i	− 1.46334i	−0.681657	−	0.731672i	$-0.738740\pi$
$197$	− 20.5390i	− 1.46334i	0.681657	−	0.731672i	$-0.261260\pi$
$198$	− 0.791288i	− 0.0562344i
$199$	−20.3303	−1.44118	−0.720588	−	0.693363i	$-0.756128\pi$
$199$	−20.3303	−1.44118	−0.720588	+	0.693363i	$0.756128\pi$
$200$	0	0
$201$	−12.8348	−0.905300
$202$	13.5826i	0.955667i
$203$	− 4.41742i	− 0.310042i
$204$	6.79129	0.475485
$205$	0	0
$206$	−7.37386	−0.513761
$207$	− 0.208712i	− 0.0145065i
$208$	1.20871i	0.0838091i
$209$	−4.58258	−0.316983
$210$	0	0
$211$	−10.0000	−0.688428	−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000	−0.688428	−0.344214	+	0.938891i	$0.611855\pi$
$212$	− 6.00000i	− 0.412082i
$213$	− 9.62614i	− 0.659572i
$214$	13.5826	0.928486
$215$	0	0
$216$	5.00000	0.340207
$217$	− 28.9564i	− 1.96569i
$218$	− 10.3739i	− 0.702607i
$219$	26.4174	1.78512
$220$	0	0
$221$	−4.58258	−0.308257
$222$	− 7.16515i	− 0.480893i
$223$	11.1652i	0.747674i	0.927494	+	0.373837i	$0.121958\pi$
$223$	11.1652i	0.747674i	−0.927494	+	0.373837i	$0.878042\pi$
$224$	2.79129	0.186501
$225$	0	0
$226$	−6.00000	−0.399114
$227$	− 4.74773i	− 0.315118i	−0.987510	−	0.157559i	$-0.949638\pi$
$227$	− 4.74773i	− 0.315118i	0.987510	−	0.157559i	$-0.0503624\pi$
$228$	2.16515i	0.143391i
$229$	16.3303	1.07914	0.539568	−	0.841942i	$-0.318587\pi$
$229$	16.3303	1.07914	0.539568	+	0.841942i	$0.318587\pi$
$230$	0	0
$231$	18.9564	1.24724
$232$	− 1.58258i	− 0.103901i
$233$	7.58258i	0.496751i	0.968664	+	0.248376i	$0.0798967\pi$
$233$	7.58258i	0.496751i	−0.968664	+	0.248376i	$0.920103\pi$
$234$	0.252273	0.0164916
$235$	0	0
$236$	−4.41742	−0.287550
$237$	− 14.3303i	− 0.930853i
$238$	10.5826i	0.685966i
$239$	−3.16515	−0.204737	−0.102368	−	0.994747i	$-0.532642\pi$
$239$	−3.16515	−0.204737	−0.102368	+	0.994747i	$0.532642\pi$
$240$	0	0
$241$	−28.0000	−1.80364	−0.901819	−	0.432113i	$-0.857768\pi$
$241$	−28.0000	−1.80364	−0.901819	+	0.432113i	$0.857768\pi$
$242$	3.37386i	0.216880i
$243$	− 2.16515i	− 0.138895i
$244$	3.37386	0.215989
$245$	0	0
$246$	3.95644	0.252253
$247$	− 1.46099i	− 0.0929603i
$248$	− 10.3739i	− 0.658741i
$249$	10.7477	0.681110
$250$	0	0
$251$	30.7913	1.94353	0.971764	−	0.235953i	$-0.0758212\pi$
$251$	30.7913	1.94353	0.971764	+	0.235953i	$0.0758212\pi$
$252$	− 0.582576i	− 0.0366988i
$253$	3.79129i	0.238356i
$254$	−14.7477	−0.925355
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 22.7477i	− 1.41896i	−0.704723	−	0.709482i	$-0.748929\pi$
$257$	− 22.7477i	− 1.41896i	0.704723	−	0.709482i	$-0.251071\pi$
$258$	12.8348i	0.799063i
$259$	11.1652	0.693769
$260$	0	0
$261$	−0.330303	−0.0204452
$262$	9.16515i	0.566225i
$263$	15.7913i	0.973733i	0.873477	+	0.486866i	$0.161860\pi$
$263$	15.7913i	0.973733i	−0.873477	+	0.486866i	$0.838140\pi$
$264$	6.79129	0.417975
$265$	0	0
$266$	−3.37386	−0.206865
$267$	5.66970i	0.346980i
$268$	− 7.16515i	− 0.437681i
$269$	−16.7477	−1.02113	−0.510563	−	0.859840i	$-0.670563\pi$
$269$	−16.7477	−1.02113	−0.510563	+	0.859840i	$0.670563\pi$
$270$	0	0
$271$	−23.1216	−1.40454	−0.702268	−	0.711912i	$-0.747829\pi$
$271$	−23.1216	−1.40454	−0.702268	+	0.711912i	$0.747829\pi$
$272$	3.79129i	0.229881i
$273$	6.04356i	0.365773i
$274$	−0.791288	−0.0478034
$275$	0	0
$276$	1.79129	0.107823
$277$	1.16515i	0.0700072i	0.999387	+	0.0350036i	$0.0111443\pi$
$277$	1.16515i	0.0700072i	−0.999387	+	0.0350036i	$0.988856\pi$
$278$	14.7477i	0.884510i
$279$	−2.16515	−0.129624
$280$	0	0
$281$	−16.7477	−0.999086	−0.499543	−	0.866289i	$-0.666499\pi$
$281$	−16.7477	−0.999086	−0.499543	+	0.866289i	$0.666499\pi$
$282$	− 24.3303i	− 1.44885i
$283$	− 28.3303i	− 1.68406i	−0.539429	−	0.842031i	$-0.681360\pi$
$283$	− 28.3303i	− 1.68406i	0.539429	−	0.842031i	$-0.318640\pi$
$284$	5.37386	0.318880
$285$	0	0
$286$	−4.58258	−0.270973
$287$	6.16515i	0.363917i
$288$	− 0.208712i	− 0.0122985i
$289$	2.62614	0.154479
$290$	0	0
$291$	26.7913	1.57053
$292$	14.7477i	0.863045i
$293$	− 27.4955i	− 1.60630i	−0.595776	−	0.803151i	$-0.703155\pi$
$293$	− 27.4955i	− 1.60630i	0.595776	−	0.803151i	$-0.296845\pi$
$294$	1.41742	0.0826659
$295$	0	0
$296$	4.00000	0.232495
$297$	18.9564i	1.09996i
$298$	− 12.7913i	− 0.740979i
$299$	−1.20871	−0.0699016
$300$	0	0
$301$	−20.0000	−1.15278
$302$	− 6.20871i	− 0.357271i
$303$	24.3303i	1.39774i
$304$	−1.20871	−0.0693244
$305$	0	0
$306$	0.791288	0.0452349
$307$	− 16.5390i	− 0.943931i	−0.881617	−	0.471966i	$-0.843545\pi$
$307$	− 16.5390i	− 0.943931i	0.881617	−	0.471966i	$-0.156455\pi$
$308$	10.5826i	0.602998i
$309$	−13.2087	−0.751417
$310$	0	0
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	2.16515i	0.122578i
$313$	− 18.3739i	− 1.03855i	−0.854607	−	0.519276i	$-0.826202\pi$
$313$	− 18.3739i	− 1.03855i	0.854607	−	0.519276i	$-0.173798\pi$
$314$	12.7477	0.719396
$315$	0	0
$316$	8.00000	0.450035
$317$	− 5.20871i	− 0.292550i	−0.989244	−	0.146275i	$-0.953271\pi$
$317$	− 5.20871i	− 0.292550i	0.989244	−	0.146275i	$-0.0467285\pi$
$318$	− 10.7477i	− 0.602703i
$319$	6.00000	0.335936
$320$	0	0
$321$	24.3303	1.35799
$322$	2.79129i	0.155552i
$323$	− 4.58258i	− 0.254981i
$324$	9.58258	0.532365
$325$	0	0
$326$	−22.3739	−1.23917
$327$	− 18.5826i	− 1.02762i
$328$	2.20871i	0.121956i
$329$	37.9129	2.09020
$330$	0	0
$331$	6.74773	0.370889	0.185444	−	0.982655i	$-0.440628\pi$
$331$	6.74773	0.370889	0.185444	+	0.982655i	$0.440628\pi$
$332$	6.00000i	0.329293i
$333$	− 0.834849i	− 0.0457494i
$334$	−18.3303	−1.00299
$335$	0	0
$336$	5.00000	0.272772
$337$	16.7913i	0.914680i	0.889292	+	0.457340i	$0.151198\pi$
$337$	16.7913i	0.914680i	−0.889292	+	0.457340i	$0.848802\pi$
$338$	11.5390i	0.627640i
$339$	−10.7477	−0.583736
$340$	0	0
$341$	39.3303	2.12986
$342$	0.252273i	0.0136414i
$343$	− 17.3303i	− 0.935748i
$344$	−7.16515	−0.386319
$345$	0	0
$346$	14.2087	0.763865
$347$	− 9.79129i	− 0.525624i	−0.964847	−	0.262812i	$-0.915350\pi$
$347$	− 9.79129i	− 0.525624i	0.964847	−	0.262812i	$-0.0846499\pi$
$348$	− 2.83485i	− 0.151964i
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	0	0
$351$	−6.04356	−0.322581
$352$	3.79129i	0.202076i
$353$	− 15.1652i	− 0.807160i	−0.914944	−	0.403580i	$-0.867766\pi$
$353$	− 15.1652i	− 0.807160i	0.914944	−	0.403580i	$-0.132234\pi$
$354$	−7.91288	−0.420565
$355$	0	0
$356$	−3.16515	−0.167753
$357$	18.9564i	1.00328i
$358$	16.7477i	0.885145i
$359$	9.16515	0.483718	0.241859	−	0.970311i	$-0.422243\pi$
$359$	9.16515	0.483718	0.241859	+	0.970311i	$0.422243\pi$
$360$	0	0
$361$	−17.5390	−0.923106
$362$	13.5390i	0.711595i
$363$	6.04356i	0.317205i
$364$	−3.37386	−0.176838
$365$	0	0
$366$	6.04356	0.315902
$367$	0.834849i	0.0435787i	0.999763	+	0.0217894i	$0.00693632\pi$
$367$	0.834849i	0.0435787i	−0.999763	+	0.0217894i	$0.993064\pi$
$368$	1.00000i	0.0521286i
$369$	0.460985	0.0239979
$370$	0	0
$371$	16.7477	0.869499
$372$	− 18.5826i	− 0.963462i
$373$	− 14.7477i	− 0.763608i	−0.924243	−	0.381804i	$-0.875303\pi$
$373$	− 14.7477i	− 0.763608i	0.924243	−	0.381804i	$-0.124697\pi$
$374$	−14.3739	−0.743255
$375$	0	0
$376$	13.5826	0.700468
$377$	1.91288i	0.0985183i
$378$	13.9564i	0.717842i
$379$	−7.37386	−0.378770	−0.189385	−	0.981903i	$-0.560649\pi$
$379$	−7.37386	−0.378770	−0.189385	+	0.981903i	$0.560649\pi$
$380$	0	0
$381$	−26.4174	−1.35341
$382$	16.4174i	0.839989i
$383$	− 24.0000i	− 1.22634i	−0.789950	−	0.613171i	$-0.789894\pi$
$383$	− 24.0000i	− 1.22634i	0.789950	−	0.613171i	$-0.210106\pi$
$384$	1.79129	0.0914113
$385$	0	0
$386$	−6.74773	−0.343450
$387$	1.49545i	0.0760182i
$388$	14.9564i	0.759298i
$389$	−29.7042	−1.50606	−0.753031	−	0.657986i	$-0.771409\pi$
$389$	−29.7042	−1.50606	−0.753031	+	0.657986i	$0.771409\pi$
$390$	0	0
$391$	−3.79129	−0.191734
$392$	0.791288i	0.0399661i
$393$	16.4174i	0.828150i
$394$	20.5390	1.03474
$395$	0	0
$396$	0.791288	0.0397637
$397$	− 16.5390i	− 0.830069i	−0.909806	−	0.415035i	$-0.863769\pi$
$397$	− 16.5390i	− 0.830069i	0.909806	−	0.415035i	$-0.136231\pi$
$398$	− 20.3303i	− 1.01907i
$399$	−6.04356	−0.302556
$400$	0	0
$401$	22.7477	1.13597	0.567984	−	0.823040i	$-0.307724\pi$
$401$	22.7477	1.13597	0.567984	+	0.823040i	$0.307724\pi$
$402$	− 12.8348i	− 0.640144i
$403$	12.5390i	0.624613i
$404$	−13.5826	−0.675758
$405$	0	0
$406$	4.41742	0.219233
$407$	15.1652i	0.751709i
$408$	6.79129i	0.336219i
$409$	22.7913	1.12696	0.563478	−	0.826131i	$-0.309463\pi$
$409$	22.7913	1.12696	0.563478	+	0.826131i	$0.309463\pi$
$410$	0	0
$411$	−1.41742	−0.0699164
$412$	− 7.37386i	− 0.363284i
$413$	− 12.3303i	− 0.606735i
$414$	0.208712	0.0102576
$415$	0	0
$416$	−1.20871	−0.0592620
$417$	26.4174i	1.29367i
$418$	− 4.58258i	− 0.224141i
$419$	−39.1652	−1.91334	−0.956671	−	0.291170i	$-0.905956\pi$
$419$	−39.1652	−1.91334	−0.956671	+	0.291170i	$0.905956\pi$
$420$	0	0
$421$	−23.1216	−1.12688	−0.563439	−	0.826158i	$-0.690522\pi$
$421$	−23.1216	−1.12688	−0.563439	+	0.826158i	$0.690522\pi$
$422$	− 10.0000i	− 0.486792i
$423$	− 2.83485i	− 0.137835i
$424$	6.00000	0.291386
$425$	0	0
$426$	9.62614	0.466388
$427$	9.41742i	0.455741i
$428$	13.5826i	0.656539i
$429$	−8.20871	−0.396320
$430$	0	0
$431$	−19.9129	−0.959170	−0.479585	−	0.877496i	$-0.659213\pi$
$431$	−19.9129	−0.959170	−0.479585	+	0.877496i	$0.659213\pi$
$432$	5.00000i	0.240563i
$433$	1.53901i	0.0739603i	0.999316	+	0.0369802i	$0.0117738\pi$
$433$	1.53901i	0.0739603i	−0.999316	+	0.0369802i	$0.988226\pi$
$434$	28.9564	1.38995
$435$	0	0
$436$	10.3739	0.496818
$437$	− 1.20871i	− 0.0578205i
$438$	26.4174i	1.26227i
$439$	−25.5390	−1.21891	−0.609455	−	0.792820i	$-0.708612\pi$
$439$	−25.5390	−1.21891	−0.609455	+	0.792820i	$0.708612\pi$
$440$	0	0
$441$	0.165151	0.00786435
$442$	− 4.58258i	− 0.217971i
$443$	− 35.2087i	− 1.67282i	−0.548107	−	0.836408i	$-0.684651\pi$
$443$	− 35.2087i	− 1.67282i	0.548107	−	0.836408i	$-0.315349\pi$
$444$	7.16515	0.340043
$445$	0	0
$446$	−11.1652	−0.528685
$447$	− 22.9129i	− 1.08374i
$448$	2.79129i	0.131876i
$449$	−25.1216	−1.18556	−0.592781	−	0.805364i	$-0.701970\pi$
$449$	−25.1216	−1.18556	−0.592781	+	0.805364i	$0.701970\pi$
$450$	0	0
$451$	−8.37386	−0.394310
$452$	− 6.00000i	− 0.282216i
$453$	− 11.1216i	− 0.522538i
$454$	4.74773	0.222822
$455$	0	0
$456$	−2.16515	−0.101393
$457$	10.0000i	0.467780i	0.972263	+	0.233890i	$0.0751456\pi$
$457$	10.0000i	0.467780i	−0.972263	+	0.233890i	$0.924854\pi$
$458$	16.3303i	0.763065i
$459$	−18.9564	−0.884811
$460$	0	0
$461$	−1.25227	−0.0583242	−0.0291621	−	0.999575i	$-0.509284\pi$
$461$	−1.25227	−0.0583242	−0.0291621	+	0.999575i	$0.509284\pi$
$462$	18.9564i	0.881933i
$463$	− 10.0000i	− 0.464739i	−0.972628	−	0.232370i	$-0.925352\pi$
$463$	− 10.0000i	− 0.464739i	0.972628	−	0.232370i	$-0.0746479\pi$
$464$	1.58258	0.0734692
$465$	0	0
$466$	−7.58258	−0.351256
$467$	− 25.9129i	− 1.19911i	−0.800335	−	0.599553i	$-0.795345\pi$
$467$	− 25.9129i	− 1.19911i	0.800335	−	0.599553i	$-0.204655\pi$
$468$	0.252273i	0.0116613i
$469$	20.0000	0.923514
$470$	0	0
$471$	22.8348	1.05217
$472$	− 4.41742i	− 0.203328i
$473$	− 27.1652i	− 1.24905i
$474$	14.3303	0.658213
$475$	0	0
$476$	−10.5826	−0.485052
$477$	− 1.25227i	− 0.0573376i
$478$	− 3.16515i	− 0.144771i
$479$	39.4955	1.80459	0.902297	−	0.431116i	$-0.141880\pi$
$479$	39.4955	1.80459	0.902297	+	0.431116i	$0.141880\pi$
$480$	0	0
$481$	−4.83485	−0.220450
$482$	− 28.0000i	− 1.27537i
$483$	5.00000i	0.227508i
$484$	−3.37386	−0.153357
$485$	0	0
$486$	2.16515	0.0982133
$487$	− 15.5826i	− 0.706114i	−0.935602	−	0.353057i	$-0.885142\pi$
$487$	− 15.5826i	− 0.706114i	0.935602	−	0.353057i	$-0.114858\pi$
$488$	3.37386i	0.152728i
$489$	−40.0780	−1.81239
$490$	0	0
$491$	−16.7477	−0.755814	−0.377907	−	0.925843i	$-0.623356\pi$
$491$	−16.7477	−0.755814	−0.377907	+	0.925843i	$0.623356\pi$
$492$	3.95644i	0.178370i
$493$	6.00000i	0.270226i
$494$	1.46099	0.0657328
$495$	0	0
$496$	10.3739	0.465800
$497$	15.0000i	0.672842i
$498$	10.7477i	0.481617i
$499$	−23.1652	−1.03701	−0.518507	−	0.855073i	$-0.673512\pi$
$499$	−23.1652	−1.03701	−0.518507	+	0.855073i	$0.673512\pi$
$500$	0	0
$501$	−32.8348	−1.46695
$502$	30.7913i	1.37428i
$503$	18.7913i	0.837862i	0.908018	+	0.418931i	$0.137595\pi$
$503$	18.7913i	0.837862i	−0.908018	+	0.418931i	$0.862405\pi$
$504$	0.582576	0.0259500
$505$	0	0
$506$	−3.79129	−0.168543
$507$	20.6697i	0.917973i
$508$	− 14.7477i	− 0.654325i
$509$	−7.25227	−0.321451	−0.160726	−	0.986999i	$-0.551383\pi$
$509$	−7.25227	−0.321451	−0.160726	+	0.986999i	$0.551383\pi$
$510$	0	0
$511$	−41.1652	−1.82104
$512$	1.00000i	0.0441942i
$513$	− 6.04356i	− 0.266830i
$514$	22.7477	1.00336
$515$	0	0
$516$	−12.8348	−0.565023
$517$	51.4955i	2.26477i
$518$	11.1652i	0.490569i
$519$	25.4519	1.11721
$520$	0	0
$521$	18.0000	0.788594	0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000	0.788594	0.394297	+	0.918983i	$0.370988\pi$
$522$	− 0.330303i	− 0.0144570i
$523$	− 1.16515i	− 0.0509485i	−0.999675	−	0.0254743i	$-0.991890\pi$
$523$	− 1.16515i	− 0.0509485i	0.999675	−	0.0254743i	$-0.00810958\pi$
$524$	−9.16515	−0.400381
$525$	0	0
$526$	−15.7913	−0.688533
$527$	39.3303i	1.71325i
$528$	6.79129i	0.295553i
$529$	−1.00000	−0.0434783
$530$	0	0
$531$	−0.921970	−0.0400101
$532$	− 3.37386i	− 0.146276i
$533$	− 2.66970i	− 0.115637i
$534$	−5.66970	−0.245352
$535$	0	0
$536$	7.16515	0.309487
$537$	30.0000i	1.29460i
$538$	− 16.7477i	− 0.722046i
$539$	−3.00000	−0.129219
$540$	0	0
$541$	38.3303	1.64795	0.823974	−	0.566627i	$-0.191752\pi$
$541$	38.3303	1.64795	0.823974	+	0.566627i	$0.191752\pi$
$542$	− 23.1216i	− 0.993157i
$543$	24.2523i	1.04076i
$544$	−3.79129	−0.162550
$545$	0	0
$546$	−6.04356	−0.258641
$547$	− 15.1216i	− 0.646553i	−0.946305	−	0.323276i	$-0.895216\pi$
$547$	− 15.1216i	− 0.646553i	0.946305	−	0.323276i	$-0.104784\pi$
$548$	− 0.791288i	− 0.0338021i
$549$	0.704166	0.0300531
$550$	0	0
$551$	−1.91288	−0.0814914
$552$	1.79129i	0.0762423i
$553$	22.3303i	0.949581i
$554$	−1.16515	−0.0495025
$555$	0	0
$556$	−14.7477	−0.625443
$557$	− 30.3303i	− 1.28514i	−0.766229	−	0.642568i	$-0.777869\pi$
$557$	− 30.3303i	− 1.28514i	0.766229	−	0.642568i	$-0.222131\pi$
$558$	− 2.16515i	− 0.0916582i
$559$	8.66061	0.366305
$560$	0	0
$561$	−25.7477	−1.08707
$562$	− 16.7477i	− 0.706460i
$563$	3.16515i	0.133395i	0.997773	+	0.0666976i	$0.0212463\pi$
$563$	3.16515i	0.133395i	−0.997773	+	0.0666976i	$0.978754\pi$
$564$	24.3303	1.02449
$565$	0	0
$566$	28.3303	1.19081
$567$	26.7477i	1.12330i
$568$	5.37386i	0.225482i
$569$	−15.4955	−0.649603	−0.324802	−	0.945782i	$-0.605298\pi$
$569$	−15.4955	−0.649603	−0.324802	+	0.945782i	$0.605298\pi$
$570$	0	0
$571$	30.1216	1.26055	0.630275	−	0.776372i	$-0.282942\pi$
$571$	30.1216	1.26055	0.630275	+	0.776372i	$0.282942\pi$
$572$	− 4.58258i	− 0.191607i
$573$	29.4083i	1.22855i
$574$	−6.16515	−0.257328
$575$	0	0
$576$	0.208712	0.00869634
$577$	− 22.8348i	− 0.950627i	−0.879816	−	0.475314i	$-0.842335\pi$
$577$	− 22.8348i	− 0.950627i	0.879816	−	0.475314i	$-0.157665\pi$
$578$	2.62614i	0.109233i
$579$	−12.0871	−0.502324
$580$	0	0
$581$	−16.7477	−0.694813
$582$	26.7913i	1.11053i
$583$	22.7477i	0.942115i
$584$	−14.7477	−0.610265
$585$	0	0
$586$	27.4955	1.13583
$587$	26.2087i	1.08175i	0.841103	+	0.540875i	$0.181907\pi$
$587$	26.2087i	1.08175i	−0.841103	+	0.540875i	$0.818093\pi$
$588$	1.41742i	0.0584536i
$589$	−12.5390	−0.516661
$590$	0	0
$591$	36.7913	1.51339
$592$	4.00000i	0.164399i
$593$	13.9129i	0.571333i	0.958329	+	0.285667i	$0.0922150\pi$
$593$	13.9129i	0.571333i	−0.958329	+	0.285667i	$0.907785\pi$
$594$	−18.9564	−0.777792
$595$	0	0
$596$	12.7913	0.523952
$597$	− 36.4174i	− 1.49047i
$598$	− 1.20871i	− 0.0494279i
$599$	40.1216	1.63932	0.819662	−	0.572848i	$-0.194161\pi$
$599$	40.1216	1.63932	0.819662	+	0.572848i	$0.194161\pi$
$600$	0	0
$601$	−22.7913	−0.929676	−0.464838	−	0.885396i	$-0.653887\pi$
$601$	−22.7913	−0.929676	−0.464838	+	0.885396i	$0.653887\pi$
$602$	− 20.0000i	− 0.815139i
$603$	− 1.49545i	− 0.0608996i
$604$	6.20871	0.252629
$605$	0	0
$606$	−24.3303	−0.988351
$607$	28.0000i	1.13648i	0.822861	+	0.568242i	$0.192376\pi$
$607$	28.0000i	1.13648i	−0.822861	+	0.568242i	$0.807624\pi$
$608$	− 1.20871i	− 0.0490198i
$609$	7.91288	0.320646
$610$	0	0
$611$	−16.4174	−0.664178
$612$	0.791288i	0.0319859i
$613$	14.0000i	0.565455i	0.959200	+	0.282727i	$0.0912392\pi$
$613$	14.0000i	0.565455i	−0.959200	+	0.282727i	$0.908761\pi$
$614$	16.5390	0.667460
$615$	0	0
$616$	−10.5826	−0.426384
$617$	− 44.8693i	− 1.80637i	−0.429251	−	0.903185i	$-0.641222\pi$
$617$	− 44.8693i	− 1.80637i	0.429251	−	0.903185i	$-0.358778\pi$
$618$	− 13.2087i	− 0.531332i
$619$	−2.79129	−0.112191	−0.0560957	−	0.998425i	$-0.517865\pi$
$619$	−2.79129	−0.112191	−0.0560957	+	0.998425i	$0.517865\pi$
$620$	0	0
$621$	−5.00000	−0.200643
$622$	12.0000i	0.481156i
$623$	− 8.83485i	− 0.353961i
$624$	−2.16515	−0.0866754
$625$	0	0
$626$	18.3739	0.734367
$627$	− 8.20871i	− 0.327824i
$628$	12.7477i	0.508690i
$629$	−15.1652	−0.604674
$630$	0	0
$631$	−17.9129	−0.713100	−0.356550	−	0.934276i	$-0.616047\pi$
$631$	−17.9129	−0.713100	−0.356550	+	0.934276i	$0.616047\pi$
$632$	8.00000i	0.318223i
$633$	− 17.9129i	− 0.711973i
$634$	5.20871	0.206864
$635$	0	0
$636$	10.7477	0.426175
$637$	− 0.956439i	− 0.0378955i
$638$	6.00000i	0.237542i
$639$	1.12159	0.0443694
$640$	0	0
$641$	−3.16515	−0.125016	−0.0625080	−	0.998044i	$-0.519910\pi$
$641$	−3.16515	−0.125016	−0.0625080	+	0.998044i	$0.519910\pi$
$642$	24.3303i	0.960240i
$643$	− 20.7477i	− 0.818210i	−0.912487	−	0.409105i	$-0.865841\pi$
$643$	− 20.7477i	− 0.818210i	0.912487	−	0.409105i	$-0.134159\pi$
$644$	−2.79129	−0.109992
$645$	0	0
$646$	4.58258	0.180299
$647$	− 2.83485i	− 0.111449i	−0.998446	−	0.0557247i	$-0.982253\pi$
$647$	− 2.83485i	− 0.111449i	0.998446	−	0.0557247i	$-0.0177469\pi$
$648$	9.58258i	0.376439i
$649$	16.7477	0.657406
$650$	0	0
$651$	51.8693	2.03292
$652$	− 22.3739i	− 0.876228i
$653$	35.5390i	1.39075i	0.718647	+	0.695375i	$0.244762\pi$
$653$	35.5390i	1.39075i	−0.718647	+	0.695375i	$0.755238\pi$
$654$	18.5826	0.726636
$655$	0	0
$656$	−2.20871	−0.0862357
$657$	3.07803i	0.120085i
$658$	37.9129i	1.47800i
$659$	27.1652	1.05820	0.529102	−	0.848558i	$-0.322529\pi$
$659$	27.1652	1.05820	0.529102	+	0.848558i	$0.322529\pi$
$660$	0	0
$661$	−39.3739	−1.53147	−0.765733	−	0.643159i	$-0.777624\pi$
$661$	−39.3739	−1.53147	−0.765733	+	0.643159i	$0.777624\pi$
$662$	6.74773i	0.262258i
$663$	− 8.20871i	− 0.318800i
$664$	−6.00000	−0.232845
$665$	0	0
$666$	0.834849	0.0323497
$667$	1.58258i	0.0612776i
$668$	− 18.3303i	− 0.709221i
$669$	−20.0000	−0.773245
$670$	0	0
$671$	−12.7913	−0.493802
$672$	5.00000i	0.192879i
$673$	38.0000i	1.46479i	0.680879	+	0.732396i	$0.261598\pi$
$673$	38.0000i	1.46479i	−0.680879	+	0.732396i	$0.738402\pi$
$674$	−16.7913	−0.646776
$675$	0	0
$676$	−11.5390	−0.443808
$677$	30.6606i	1.17838i	0.807993	+	0.589191i	$0.200554\pi$
$677$	30.6606i	1.17838i	−0.807993	+	0.589191i	$0.799446\pi$
$678$	− 10.7477i	− 0.412764i
$679$	−41.7477	−1.60213
$680$	0	0
$681$	8.50455	0.325895
$682$	39.3303i	1.50604i
$683$	2.37386i	0.0908334i	0.998968	+	0.0454167i	$0.0144616\pi$
$683$	2.37386i	0.0908334i	−0.998968	+	0.0454167i	$0.985538\pi$
$684$	−0.252273	−0.00964590
$685$	0	0
$686$	17.3303	0.661674
$687$	29.2523i	1.11604i
$688$	− 7.16515i	− 0.273169i
$689$	−7.25227	−0.276290
$690$	0	0
$691$	15.2523	0.580224	0.290112	−	0.956993i	$-0.406307\pi$
$691$	15.2523	0.580224	0.290112	+	0.956993i	$0.406307\pi$
$692$	14.2087i	0.540134i
$693$	2.20871i	0.0839020i
$694$	9.79129	0.371672
$695$	0	0
$696$	2.83485	0.107455
$697$	− 8.37386i	− 0.317183i
$698$	− 26.0000i	− 0.984115i
$699$	−13.5826	−0.513740
$700$	0	0
$701$	9.62614	0.363574	0.181787	−	0.983338i	$-0.441812\pi$
$701$	9.62614	0.363574	0.181787	+	0.983338i	$0.441812\pi$
$702$	− 6.04356i	− 0.228100i
$703$	− 4.83485i	− 0.182350i
$704$	−3.79129	−0.142890
$705$	0	0
$706$	15.1652	0.570748
$707$	− 37.9129i	− 1.42586i
$708$	− 7.91288i	− 0.297384i
$709$	−34.5390	−1.29714	−0.648570	−	0.761155i	$-0.724633\pi$
$709$	−34.5390	−1.29714	−0.648570	+	0.761155i	$0.724633\pi$
$710$	0	0
$711$	1.66970	0.0626185
$712$	− 3.16515i	− 0.118619i
$713$	10.3739i	0.388504i
$714$	−18.9564	−0.709427
$715$	0	0
$716$	−16.7477	−0.625892
$717$	− 5.66970i	− 0.211739i
$718$	9.16515i	0.342040i
$719$	29.5390	1.10162	0.550810	−	0.834631i	$-0.314319\pi$
$719$	29.5390	1.10162	0.550810	+	0.834631i	$0.314319\pi$
$720$	0	0
$721$	20.5826	0.766535
$722$	− 17.5390i	− 0.652735i
$723$	− 50.1561i	− 1.86532i
$724$	−13.5390	−0.503174
$725$	0	0
$726$	−6.04356	−0.224298
$727$	2.12159i	0.0786854i	0.999226	+	0.0393427i	$0.0125264\pi$
$727$	2.12159i	0.0786854i	−0.999226	+	0.0393427i	$0.987474\pi$
$728$	− 3.37386i	− 0.125044i
$729$	−24.8693	−0.921086
$730$	0	0
$731$	27.1652	1.00474
$732$	6.04356i	0.223376i
$733$	26.0000i	0.960332i	0.877178	+	0.480166i	$0.159424\pi$
$733$	26.0000i	0.960332i	−0.877178	+	0.480166i	$0.840576\pi$
$734$	−0.834849	−0.0308148
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	27.1652i	1.00064i
$738$	0.460985i	0.0169691i
$739$	−8.00000	−0.294285	−0.147142	−	0.989115i	$-0.547008\pi$
$739$	−8.00000	−0.294285	−0.147142	+	0.989115i	$0.547008\pi$
$740$	0	0
$741$	2.61704	0.0961395
$742$	16.7477i	0.614828i
$743$	9.95644i	0.365266i	0.983181	+	0.182633i	$0.0584621\pi$
$743$	9.95644i	0.365266i	−0.983181	+	0.182633i	$0.941538\pi$
$744$	18.5826	0.681270
$745$	0	0
$746$	14.7477	0.539953
$747$	1.25227i	0.0458183i
$748$	− 14.3739i	− 0.525561i
$749$	−37.9129	−1.38531
$750$	0	0
$751$	18.7477	0.684114	0.342057	−	0.939679i	$-0.388876\pi$
$751$	18.7477	0.684114	0.342057	+	0.939679i	$0.388876\pi$
$752$	13.5826i	0.495306i
$753$	55.1561i	2.01000i
$754$	−1.91288	−0.0696629
$755$	0	0
$756$	−13.9564	−0.507591
$757$	− 26.3303i	− 0.956991i	−0.878090	−	0.478496i	$-0.841182\pi$
$757$	− 26.3303i	− 0.956991i	0.878090	−	0.478496i	$-0.158818\pi$
$758$	− 7.37386i	− 0.267831i
$759$	−6.79129	−0.246508
$760$	0	0
$761$	−33.9564	−1.23092	−0.615460	−	0.788168i	$-0.711030\pi$
$761$	−33.9564	−1.23092	−0.615460	+	0.788168i	$0.711030\pi$
$762$	− 26.4174i	− 0.957002i
$763$	28.9564i	1.04829i
$764$	−16.4174	−0.593962
$765$	0	0
$766$	24.0000	0.867155
$767$	5.33939i	0.192794i
$768$	1.79129i	0.0646375i
$769$	3.66970	0.132333	0.0661663	−	0.997809i	$-0.478923\pi$
$769$	3.66970	0.132333	0.0661663	+	0.997809i	$0.478923\pi$
$770$	0	0
$771$	40.7477	1.46749
$772$	− 6.74773i	− 0.242856i
$773$	− 21.4955i	− 0.773138i	−0.922261	−	0.386569i	$-0.873660\pi$
$773$	− 21.4955i	− 0.773138i	0.922261	−	0.386569i	$-0.126340\pi$
$774$	−1.49545	−0.0537530
$775$	0	0
$776$	−14.9564	−0.536905
$777$	20.0000i	0.717496i
$778$	− 29.7042i	− 1.06495i
$779$	2.66970	0.0956518
$780$	0	0
$781$	−20.3739	−0.729034
$782$	− 3.79129i	− 0.135576i
$783$	7.91288i	0.282783i
$784$	−0.791288	−0.0282603
$785$	0	0
$786$	−16.4174	−0.585590
$787$	8.41742i	0.300049i	0.988682	+	0.150024i	$0.0479352\pi$
$787$	8.41742i	0.300049i	−0.988682	+	0.150024i	$0.952065\pi$
$788$	20.5390i	0.731672i
$789$	−28.2867	−1.00703
$790$	0	0
$791$	16.7477	0.595481
$792$	0.791288i	0.0281172i
$793$	− 4.07803i	− 0.144815i
$794$	16.5390	0.586948
$795$	0	0
$796$	20.3303	0.720588
$797$	49.9129i	1.76800i	0.467482	+	0.884002i	$0.345161\pi$
$797$	49.9129i	1.76800i	−0.467482	+	0.884002i	$0.654839\pi$
$798$	− 6.04356i	− 0.213940i
$799$	−51.4955	−1.82178
$800$	0	0
$801$	−0.660606	−0.0233413
$802$	22.7477i	0.803250i
$803$	− 55.9129i	− 1.97312i
$804$	12.8348	0.452650
$805$	0	0
$806$	−12.5390	−0.441668
$807$	− 30.0000i	− 1.05605i
$808$	− 13.5826i	− 0.477833i
$809$	−11.0436	−0.388271	−0.194135	−	0.980975i	$-0.562190\pi$
$809$	−11.0436	−0.388271	−0.194135	+	0.980975i	$0.562190\pi$
$810$	0	0
$811$	−47.9129	−1.68245	−0.841224	−	0.540686i	$-0.818165\pi$
$811$	−47.9129	−1.68245	−0.841224	+	0.540686i	$0.818165\pi$
$812$	4.41742i	0.155021i
$813$	− 41.4174i	− 1.45257i
$814$	−15.1652	−0.531538
$815$	0	0
$816$	−6.79129	−0.237743
$817$	8.66061i	0.302996i
$818$	22.7913i	0.796879i
$819$	−0.704166	−0.0246056
$820$	0	0
$821$	2.83485	0.0989369	0.0494684	−	0.998776i	$-0.484247\pi$
$821$	2.83485	0.0989369	0.0494684	+	0.998776i	$0.484247\pi$
$822$	− 1.41742i	− 0.0494383i
$823$	41.1652i	1.43493i	0.696596	+	0.717463i	$0.254697\pi$
$823$	41.1652i	1.43493i	−0.696596	+	0.717463i	$0.745303\pi$
$824$	7.37386	0.256881
$825$	0	0
$826$	12.3303	0.429026
$827$	− 41.0780i	− 1.42842i	−0.699930	−	0.714212i	$-0.746785\pi$
$827$	− 41.0780i	− 1.42842i	0.699930	−	0.714212i	$-0.253215\pi$
$828$	0.208712i	0.00725325i
$829$	31.4955	1.09388	0.546941	−	0.837171i	$-0.315792\pi$
$829$	31.4955	1.09388	0.546941	+	0.837171i	$0.315792\pi$
$830$	0	0
$831$	−2.08712	−0.0724014
$832$	− 1.20871i	− 0.0419046i
$833$	− 3.00000i	− 0.103944i
$834$	−26.4174	−0.914761
$835$	0	0
$836$	4.58258	0.158492
$837$	51.8693i	1.79287i
$838$	− 39.1652i	− 1.35294i
$839$	22.4174	0.773935	0.386968	−	0.922093i	$-0.373522\pi$
$839$	22.4174	0.773935	0.386968	+	0.922093i	$0.373522\pi$
$840$	0	0
$841$	−26.4955	−0.913636
$842$	− 23.1216i	− 0.796823i
$843$	− 30.0000i	− 1.03325i
$844$	10.0000	0.344214
$845$	0	0
$846$	2.83485	0.0974641
$847$	− 9.41742i	− 0.323587i
$848$	6.00000i	0.206041i
$849$	50.7477	1.74166
$850$	0	0
$851$	−4.00000	−0.137118
$852$	9.62614i	0.329786i
$853$	8.46099i	0.289699i	0.989454	+	0.144849i	$0.0462697\pi$
$853$	8.46099i	0.289699i	−0.989454	+	0.144849i	$0.953730\pi$
$854$	−9.41742	−0.322258
$855$	0	0
$856$	−13.5826	−0.464243
$857$	− 9.16515i	− 0.313076i	−0.987672	−	0.156538i	$-0.949967\pi$
$857$	− 9.16515i	− 0.313076i	0.987672	−	0.156538i	$-0.0500333\pi$
$858$	− 8.20871i	− 0.280241i
$859$	−0.747727	−0.0255121	−0.0127561	−	0.999919i	$-0.504060\pi$
$859$	−0.747727	−0.0255121	−0.0127561	+	0.999919i	$0.504060\pi$
$860$	0	0
$861$	−11.0436	−0.376364
$862$	− 19.9129i	− 0.678235i
$863$	− 31.5826i	− 1.07508i	−0.843237	−	0.537542i	$-0.819353\pi$
$863$	− 31.5826i	− 1.07508i	0.843237	−	0.537542i	$-0.180647\pi$
$864$	−5.00000	−0.170103
$865$	0	0
$866$	−1.53901	−0.0522979
$867$	4.70417i	0.159762i
$868$	28.9564i	0.982846i
$869$	−30.3303	−1.02889
$870$	0	0
$871$	−8.66061	−0.293453
$872$	10.3739i	0.351303i
$873$	3.12159i	0.105650i
$874$	1.20871	0.0408853
$875$	0	0
$876$	−26.4174	−0.892562
$877$	− 7.70417i	− 0.260151i	−0.991504	−	0.130076i	$-0.958478\pi$
$877$	− 7.70417i	− 0.260151i	0.991504	−	0.130076i	$-0.0415220\pi$
$878$	− 25.5390i	− 0.861900i
$879$	49.2523	1.66124
$880$	0	0
$881$	−6.33030	−0.213273	−0.106637	−	0.994298i	$-0.534008\pi$
$881$	−6.33030	−0.213273	−0.106637	+	0.994298i	$0.534008\pi$
$882$	0.165151i	0.00556094i
$883$	− 12.0436i	− 0.405298i	−0.979251	−	0.202649i	$-0.935045\pi$
$883$	− 12.0436i	− 0.405298i	0.979251	−	0.202649i	$-0.0649551\pi$
$884$	4.58258	0.154129
$885$	0	0
$886$	35.2087	1.18286
$887$	3.16515i	0.106275i	0.998587	+	0.0531377i	$0.0169222\pi$
$887$	3.16515i	0.106275i	−0.998587	+	0.0531377i	$0.983078\pi$
$888$	7.16515i	0.240447i
$889$	41.1652	1.38063
$890$	0	0
$891$	−36.3303	−1.21711
$892$	− 11.1652i	− 0.373837i
$893$	− 16.4174i	− 0.549388i
$894$	22.9129	0.766321
$895$	0	0
$896$	−2.79129	−0.0932504
$897$	− 2.16515i	− 0.0722923i
$898$	− 25.1216i	− 0.838318i
$899$	16.4174	0.547552
$900$	0	0
$901$	−22.7477	−0.757837
$902$	− 8.37386i	− 0.278819i
$903$	− 35.8258i	− 1.19221i
$904$	6.00000	0.199557
$905$	0	0
$906$	11.1216	0.369490
$907$	20.7477i	0.688917i	0.938802	+	0.344458i	$0.111937\pi$
$907$	20.7477i	0.688917i	−0.938802	+	0.344458i	$0.888063\pi$
$908$	4.74773i	0.157559i
$909$	−2.83485	−0.0940260
$910$	0	0
$911$	13.5826	0.450011	0.225005	−	0.974358i	$-0.427760\pi$
$911$	13.5826	0.450011	0.225005	+	0.974358i	$0.427760\pi$
$912$	− 2.16515i	− 0.0716953i
$913$	− 22.7477i	− 0.752840i
$914$	−10.0000	−0.330771
$915$	0	0
$916$	−16.3303	−0.539568
$917$	− 25.5826i	− 0.844811i
$918$	− 18.9564i	− 0.625656i
$919$	36.8348	1.21507	0.607535	−	0.794293i	$-0.292159\pi$
$919$	36.8348	1.21507	0.607535	+	0.794293i	$0.292159\pi$
$920$	0	0
$921$	29.6261	0.976214
$922$	− 1.25227i	− 0.0412414i
$923$	− 6.49545i	− 0.213800i
$924$	−18.9564	−0.623621
$925$	0	0
$926$	10.0000	0.328620
$927$	− 1.53901i	− 0.0505479i
$928$	1.58258i	0.0519506i
$929$	39.4955	1.29580	0.647902	−	0.761724i	$-0.275647\pi$
$929$	39.4955	1.29580	0.647902	+	0.761724i	$0.275647\pi$
$930$	0	0
$931$	0.956439	0.0313460
$932$	− 7.58258i	− 0.248376i
$933$	21.4955i	0.703730i
$934$	25.9129	0.847895
$935$	0	0
$936$	−0.252273	−0.00824580
$937$	− 58.3739i	− 1.90699i	−0.301407	−	0.953495i	$-0.597456\pi$
$937$	− 58.3739i	− 1.90699i	0.301407	−	0.953495i	$-0.402544\pi$
$938$	20.0000i	0.653023i
$939$	32.9129	1.07407
$940$	0	0
$941$	54.9564	1.79153	0.895764	−	0.444529i	$-0.146629\pi$
$941$	54.9564	1.79153	0.895764	+	0.444529i	$0.146629\pi$
$942$	22.8348i	0.744000i
$943$	− 2.20871i	− 0.0719256i
$944$	4.41742	0.143775
$945$	0	0
$946$	27.1652	0.883215
$947$	29.5390i	0.959889i	0.877299	+	0.479945i	$0.159343\pi$
$947$	29.5390i	0.959889i	−0.877299	+	0.479945i	$0.840657\pi$
$948$	14.3303i	0.465427i
$949$	17.8258	0.578649
$950$	0	0
$951$	9.33030	0.302556
$952$	− 10.5826i	− 0.342983i
$953$	− 26.5390i	− 0.859683i	−0.902904	−	0.429842i	$-0.858569\pi$
$953$	− 26.5390i	− 0.859683i	0.902904	−	0.429842i	$-0.141431\pi$
$954$	1.25227	0.0405438
$955$	0	0
$956$	3.16515	0.102368
$957$	10.7477i	0.347425i
$958$	39.4955i	1.27604i
$959$	2.20871	0.0713230
$960$	0	0
$961$	76.6170	2.47152
$962$	− 4.83485i	− 0.155882i
$963$	2.83485i	0.0913517i
$964$	28.0000	0.901819
$965$	0	0
$966$	−5.00000	−0.160872
$967$	5.25227i	0.168902i	0.996428	+	0.0844509i	$0.0269136\pi$
$967$	5.25227i	0.168902i	−0.996428	+	0.0844509i	$0.973086\pi$
$968$	− 3.37386i	− 0.108440i
$969$	8.20871	0.263702
$970$	0	0
$971$	−6.95644	−0.223243	−0.111621	−	0.993751i	$-0.535604\pi$
$971$	−6.95644	−0.223243	−0.111621	+	0.993751i	$0.535604\pi$
$972$	2.16515i	0.0694473i
$973$	− 41.1652i	− 1.31969i
$974$	15.5826	0.499298
$975$	0	0
$976$	−3.37386	−0.107995
$977$	− 7.12159i	− 0.227840i	−0.993490	−	0.113920i	$-0.963659\pi$
$977$	− 7.12159i	− 0.227840i	0.993490	−	0.113920i	$-0.0363407\pi$
$978$	− 40.0780i	− 1.28155i
$979$	12.0000	0.383522
$980$	0	0
$981$	2.16515	0.0691280
$982$	− 16.7477i	− 0.534441i
$983$	− 0.626136i	− 0.0199707i	−0.999950	−	0.00998533i	$-0.996822\pi$
$983$	− 0.626136i	− 0.0199707i	0.999950	−	0.00998533i	$-0.00317848\pi$
$984$	−3.95644	−0.126127
$985$	0	0
$986$	−6.00000	−0.191079
$987$	67.9129i	2.16169i
$988$	1.46099i	0.0464801i
$989$	7.16515	0.227839
$990$	0	0
$991$	−37.7913	−1.20048	−0.600240	−	0.799820i	$-0.704928\pi$
$991$	−37.7913	−1.20048	−0.600240	+	0.799820i	$0.704928\pi$
$992$	10.3739i	0.329370i
$993$	12.0871i	0.383573i
$994$	−15.0000	−0.475771
$995$	0	0
$996$	−10.7477	−0.340555
$997$	− 11.4955i	− 0.364065i	−0.983293	−	0.182032i	$-0.941732\pi$
$997$	− 11.4955i	− 0.364065i	0.983293	−	0.182032i	$-0.0582676\pi$
$998$	− 23.1652i	− 0.733280i
$999$	−20.0000	−0.632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.b.g.599.4		4
5.2	odd	4		230.2.a.a.1.2	✓	2
5.3	odd	4		1150.2.a.o.1.1		2
5.4	even	2	inner	1150.2.b.g.599.1		4
15.2	even	4		2070.2.a.x.1.2		2
20.3	even	4		9200.2.a.bs.1.2		2
20.7	even	4		1840.2.a.n.1.1		2
40.27	even	4		7360.2.a.bk.1.2		2
40.37	odd	4		7360.2.a.bq.1.1		2
115.22	even	4		5290.2.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.a.a.1.2	✓	2	5.2	odd	4
1150.2.a.o.1.1		2	5.3	odd	4
1150.2.b.g.599.1		4	5.4	even	2	inner
1150.2.b.g.599.4		4	1.1	even	1	trivial
1840.2.a.n.1.1		2	20.7	even	4
2070.2.a.x.1.2		2	15.2	even	4
5290.2.a.e.1.2		2	115.22	even	4
7360.2.a.bk.1.2		2	40.27	even	4
7360.2.a.bq.1.1		2	40.37	odd	4
9200.2.a.bs.1.2		2	20.3	even	4

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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.79129i q^{3} -1.00000 q^{4} -1.79129 q^{6} -2.79129i q^{7} -1.00000i q^{8} -0.208712 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.79129i q^{3} -1.00000 q^{4} -1.79129 q^{6} -2.79129i q^{7} -1.00000i q^{8} -0.208712 q^{9} +3.79129 q^{11} -1.79129i q^{12} +1.20871i q^{13} +2.79129 q^{14} +1.00000 q^{16} +3.79129i q^{17} -0.208712i q^{18} -1.20871 q^{19} +5.00000 q^{21} +3.79129i q^{22} +1.00000i q^{23} +1.79129 q^{24} -1.20871 q^{26} +5.00000i q^{27} +2.79129i q^{28} +1.58258 q^{29} +10.3739 q^{31} +1.00000i q^{32} +6.79129i q^{33} -3.79129 q^{34} +0.208712 q^{36} +4.00000i q^{37} -1.20871i q^{38} -2.16515 q^{39} -2.20871 q^{41} +5.00000i q^{42} -7.16515i q^{43} -3.79129 q^{44} -1.00000 q^{46} +13.5826i q^{47} +1.79129i q^{48} -0.791288 q^{49} -6.79129 q^{51} -1.20871i q^{52} +6.00000i q^{53} -5.00000 q^{54} -2.79129 q^{56} -2.16515i q^{57} +1.58258i q^{58} +4.41742 q^{59} -3.37386 q^{61} +10.3739i q^{62} +0.582576i q^{63} -1.00000 q^{64} -6.79129 q^{66} +7.16515i q^{67} -3.79129i q^{68} -1.79129 q^{69} -5.37386 q^{71} +0.208712i q^{72} -14.7477i q^{73} -4.00000 q^{74} +1.20871 q^{76} -10.5826i q^{77} -2.16515i q^{78} -8.00000 q^{79} -9.58258 q^{81} -2.20871i q^{82} -6.00000i q^{83} -5.00000 q^{84} +7.16515 q^{86} +2.83485i q^{87} -3.79129i q^{88} +3.16515 q^{89} +3.37386 q^{91} -1.00000i q^{92} +18.5826i q^{93} -13.5826 q^{94} -1.79129 q^{96} -14.9564i q^{97} -0.791288i q^{98} -0.791288 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 2 q^{6} - 10 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 2 * q^6 - 10 * q^9	\( 4 q - 4 q^{4} + 2 q^{6} - 10 q^{9} + 6 q^{11} + 2 q^{14} + 4 q^{16} - 14 q^{19} + 20 q^{21} - 2 q^{24} - 14 q^{26} - 12 q^{29} + 14 q^{31} - 6 q^{34} + 10 q^{36} + 28 q^{39} - 18 q^{41} - 6 q^{44} - 4 q^{46} + 6 q^{49} - 18 q^{51} - 20 q^{54} - 2 q^{56} + 36 q^{59} + 14 q^{61} - 4 q^{64} - 18 q^{66} + 2 q^{69} + 6 q^{71} - 16 q^{74} + 14 q^{76} - 32 q^{79} - 20 q^{81} - 20 q^{84} - 8 q^{86} - 24 q^{89} - 14 q^{91} - 36 q^{94} + 2 q^{96} + 6 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 2 * q^6 - 10 * q^9 + 6 * q^11 + 2 * q^14 + 4 * q^16 - 14 * q^19 + 20 * q^21 - 2 * q^24 - 14 * q^26 - 12 * q^29 + 14 * q^31 - 6 * q^34 + 10 * q^36 + 28 * q^39 - 18 * q^41 - 6 * q^44 - 4 * q^46 + 6 * q^49 - 18 * q^51 - 20 * q^54 - 2 * q^56 + 36 * q^59 + 14 * q^61 - 4 * q^64 - 18 * q^66 + 2 * q^69 + 6 * q^71 - 16 * q^74 + 14 * q^76 - 32 * q^79 - 20 * q^81 - 20 * q^84 - 8 * q^86 - 24 * q^89 - 14 * q^91 - 36 * q^94 + 2 * q^96 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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