LMFDB - Embedded newform 2070.2.d.h.829.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(829,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2070.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.d (of order $2$, degree $1$, 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:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} + 10x^{12} + 55x^{10} + 58x^{8} + 495x^{6} + 810x^{4} + 729x^{2} + 6561 $ x^16 + x^14 + 10x^12 + 55x^10 + 58x^8 + 495x^6 + 810x^4 + 729x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			829.6
Root			$-1.13883 + 1.30502i$ of defining polynomial
Character	$\chi$	$=$	2070.829
Dual form			2070.2.d.h.829.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(1.43942 + 1.71116i) q^{5} +1.24894i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.43942 + 1.71116i) q^{5} +1.24894i q^{7} +1.00000i q^{8} +(1.71116 - 1.43942i) q^{10} +2.41817 q^{11} -5.80425i q^{13} +1.24894 q^{14} +1.00000 q^{16} -5.22007i q^{17} +1.42233 q^{19} +(-1.43942 - 1.71116i) q^{20} -2.41817i q^{22} +1.00000i q^{23} +(-0.856164 + 4.92615i) q^{25} -5.80425 q^{26} -1.24894i q^{28} -0.788275 q^{29} +0.287672 q^{31} -1.00000i q^{32} -5.22007 q^{34} +(-2.13714 + 1.79775i) q^{35} +4.12777i q^{37} -1.42233i q^{38} +(-1.71116 + 1.43942i) q^{40} +5.01597 q^{41} +2.09056i q^{43} -2.41817 q^{44} +1.00000 q^{46} -10.5570i q^{47} +5.44015 q^{49} +(4.92615 + 0.856164i) q^{50} +5.80425i q^{52} -3.42233i q^{53} +(3.48075 + 4.13788i) q^{55} -1.24894 q^{56} +0.788275i q^{58} +5.01597 q^{59} +14.0671 q^{61} -0.287672i q^{62} -1.00000 q^{64} +(9.93202 - 8.35473i) q^{65} +9.42477i q^{67} +5.22007i q^{68} +(1.79775 + 2.13714i) q^{70} +11.5619 q^{71} +0.741689i q^{73} +4.12777 q^{74} -1.42233 q^{76} +3.02015i q^{77} -0.375418 q^{79} +(1.43942 + 1.71116i) q^{80} -5.01597i q^{82} -5.04691i q^{83} +(8.93240 - 7.51386i) q^{85} +2.09056 q^{86} +2.41817i q^{88} -3.81362 q^{89} +7.24916 q^{91} -1.00000i q^{92} -10.5570 q^{94} +(2.04732 + 2.43384i) q^{95} +0.788275i q^{97} -5.44015i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4}+O(q^{10}) $ 16 * q - 16 * q^4	$ 16 q - 16 q^{4} + 16 q^{16} - 32 q^{19} + 32 q^{31} + 8 q^{34} + 16 q^{46} - 96 q^{49} + 24 q^{55} + 24 q^{61} - 16 q^{64} - 8 q^{70} + 32 q^{76} - 24 q^{79} + 24 q^{85} + 80 q^{91} - 32 q^{94}+O(q^{100}) $ 16 * q - 16 * q^4 + 16 * q^16 - 32 * q^19 + 32 * q^31 + 8 * q^34 + 16 * q^46 - 96 * q^49 + 24 * q^55 + 24 * q^61 - 16 * q^64 - 8 * q^70 + 32 * q^76 - 24 * q^79 + 24 * q^85 + 80 * q^91 - 32 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$1$	$-1$	$1$

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
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	1.43942	+	1.71116i	0.643726	+	0.765256i
$5$	1.43942	+	1.71116i	0.643726	+	0.765256i
$6$		0			0
$7$			1.24894i			0.472055i	0.971746	+	0.236028i	$0.0758456\pi$
$7$			1.24894i			0.472055i	−0.971746	+	0.236028i	$0.924154\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	1.71116	−	1.43942i	0.541118	−	0.455183i
$11$	2.41817			0.729104			0.364552	−	0.931183i	$-0.381222\pi$
$11$	2.41817			0.729104			0.364552	+	0.931183i	$0.381222\pi$
$12$		0			0
$13$		−	5.80425i		−	1.60981i	−0.593404	−	0.804905i	$-0.702216\pi$
$13$		−	5.80425i		−	1.60981i	0.593404	−	0.804905i	$-0.297784\pi$
$14$	1.24894			0.333794
$15$		0			0
$16$	1.00000			0.250000
$17$		−	5.22007i		−	1.26605i	−0.774130	−	0.633027i	$-0.781812\pi$
$17$		−	5.22007i		−	1.26605i	0.774130	−	0.633027i	$-0.218188\pi$
$18$		0			0
$19$	1.42233			0.326304			0.163152	−	0.986601i	$-0.447834\pi$
$19$	1.42233			0.326304			0.163152	+	0.986601i	$0.447834\pi$
$20$	−1.43942	−	1.71116i	−0.321863	−	0.382628i
$21$		0			0
$22$		−	2.41817i		−	0.515555i
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$		0			0
$25$	−0.856164	+	4.92615i	−0.171233	+	0.985231i
$26$	−5.80425			−1.13831
$27$		0			0
$28$		−	1.24894i		−	0.236028i
$29$	−0.788275			−0.146379			−0.0731895	−	0.997318i	$-0.523318\pi$
$29$	−0.788275			−0.146379			−0.0731895	+	0.997318i	$0.523318\pi$
$30$		0			0
$31$	0.287672			0.0516675			0.0258337	−	0.999666i	$-0.491776\pi$
$31$	0.287672			0.0516675			0.0258337	+	0.999666i	$0.491776\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−5.22007			−0.895235
$35$	−2.13714	+	1.79775i	−0.361243	+	0.303874i
$36$		0			0
$37$			4.12777i			0.678602i	0.940678	+	0.339301i	$0.110190\pi$
$37$			4.12777i			0.678602i	−0.940678	+	0.339301i	$0.889810\pi$
$38$		−	1.42233i		−	0.230732i
$39$		0			0
$40$	−1.71116	+	1.43942i	−0.270559	+	0.227592i
$41$	5.01597			0.783364			0.391682	−	0.920101i	$-0.371893\pi$
$41$	5.01597			0.783364			0.391682	+	0.920101i	$0.371893\pi$
$42$		0			0
$43$			2.09056i			0.318807i	0.987214	+	0.159403i	$0.0509571\pi$
$43$			2.09056i			0.318807i	−0.987214	+	0.159403i	$0.949043\pi$
$44$	−2.41817			−0.364552
$45$		0			0
$46$	1.00000			0.147442
$47$		−	10.5570i		−	1.53989i	−0.638108	−	0.769947i	$-0.720283\pi$
$47$		−	10.5570i		−	1.53989i	0.638108	−	0.769947i	$-0.279717\pi$
$48$		0			0
$49$	5.44015			0.777164
$50$	4.92615	+	0.856164i	0.696663	+	0.121080i
$51$		0			0
$52$			5.80425i			0.804905i
$53$		−	3.42233i		−	0.470093i	−0.971984	−	0.235046i	$-0.924476\pi$
$53$		−	3.42233i		−	0.470093i	0.971984	−	0.235046i	$-0.0755242\pi$
$54$		0			0
$55$	3.48075	+	4.13788i	0.469344	+	0.557951i
$56$	−1.24894			−0.166897
$57$		0			0
$58$			0.788275i			0.103506i
$59$	5.01597			0.653024			0.326512	−	0.945193i	$-0.394127\pi$
$59$	5.01597			0.653024			0.326512	+	0.945193i	$0.394127\pi$
$60$		0			0
$61$	14.0671			1.80110			0.900551	−	0.434750i	$-0.143163\pi$
$61$	14.0671			1.80110			0.900551	+	0.434750i	$0.143163\pi$
$62$		−	0.287672i		−	0.0365344i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	9.93202	−	8.35473i	1.23192	−	1.03628i
$66$		0			0
$67$			9.42477i			1.15142i	0.817654	+	0.575709i	$0.195274\pi$
$67$			9.42477i			1.15142i	−0.817654	+	0.575709i	$0.804726\pi$
$68$			5.22007i			0.633027i
$69$		0			0
$70$	1.79775	+	2.13714i	0.214872	+	0.255437i
$71$	11.5619			1.37215			0.686073	−	0.727532i	$-0.259333\pi$
$71$	11.5619			1.37215			0.686073	+	0.727532i	$0.259333\pi$
$72$		0			0
$73$			0.741689i			0.0868081i	0.999058	+	0.0434041i	$0.0138203\pi$
$73$			0.741689i			0.0868081i	−0.999058	+	0.0434041i	$0.986180\pi$
$74$	4.12777			0.479844
$75$		0			0
$76$	−1.42233			−0.163152
$77$			3.02015i			0.344178i
$78$		0			0
$79$	−0.375418			−0.0422378			−0.0211189	−	0.999777i	$-0.506723\pi$
$79$	−0.375418			−0.0422378			−0.0211189	+	0.999777i	$0.506723\pi$
$80$	1.43942	+	1.71116i	0.160932	+	0.191314i
$81$		0			0
$82$		−	5.01597i		−	0.553922i
$83$		−	5.04691i		−	0.553970i	−0.960874	−	0.276985i	$-0.910665\pi$
$83$		−	5.04691i		−	0.553970i	0.960874	−	0.276985i	$-0.0893353\pi$
$84$		0			0
$85$	8.93240	−	7.51386i	0.968855	−	0.814992i
$86$	2.09056			0.225431
$87$		0			0
$88$			2.41817i			0.257777i
$89$	−3.81362			−0.404243			−0.202121	−	0.979360i	$-0.564784\pi$
$89$	−3.81362			−0.404243			−0.202121	+	0.979360i	$0.564784\pi$
$90$		0			0
$91$	7.24916			0.759919
$92$		−	1.00000i		−	0.104257i
$93$		0			0
$94$	−10.5570			−1.08887
$95$	2.04732	+	2.43384i	0.210051	+	0.249706i
$96$		0			0
$97$			0.788275i			0.0800372i	0.999199	+	0.0400186i	$0.0127417\pi$
$97$			0.788275i			0.0800372i	−0.999199	+	0.0400186i	$0.987258\pi$
$98$		−	5.44015i		−	0.549538i
$99$		0			0
$100$	0.856164	−	4.92615i	0.0856164	−	0.492615i
$101$	12.3036			1.22425			0.612127	−	0.790759i	$-0.290314\pi$
$101$	12.3036			1.22425			0.612127	+	0.790759i	$0.290314\pi$
$102$		0			0
$103$			5.52323i			0.544220i	0.962266	+	0.272110i	$0.0877214\pi$
$103$			5.52323i			0.544220i	−0.962266	+	0.272110i	$0.912279\pi$
$104$	5.80425			0.569153
$105$		0			0
$106$	−3.42233			−0.332406
$107$		−	12.4716i		−	1.20567i	−0.797865	−	0.602836i	$-0.794037\pi$
$107$		−	12.4716i		−	1.20567i	0.797865	−	0.602836i	$-0.205963\pi$
$108$		0			0
$109$	−7.79775			−0.746889			−0.373444	−	0.927653i	$-0.621823\pi$
$109$	−7.79775			−0.746889			−0.373444	+	0.927653i	$0.621823\pi$
$110$	4.13788	−	3.48075i	0.394531	−	0.331876i
$111$		0			0
$112$			1.24894i			0.118014i
$113$		−	1.62458i		−	0.152828i	−0.997076	−	0.0764139i	$-0.975653\pi$
$113$		−	1.62458i		−	0.152828i	0.997076	−	0.0764139i	$-0.0243470\pi$
$114$		0			0
$115$	−1.71116	+	1.43942i	−0.159567	+	0.134226i
$116$	0.788275			0.0731895
$117$		0			0
$118$		−	5.01597i		−	0.461758i
$119$	6.51956			0.597647
$120$		0			0
$121$	−5.15247			−0.468407
$122$		−	14.0671i		−	1.27357i
$123$		0			0
$124$	−0.287672			−0.0258337
$125$	−9.66183	+	5.62575i	−0.864180	+	0.503182i
$126$		0			0
$127$			20.6725i			1.83439i	0.398438	+	0.917195i	$0.369552\pi$
$127$			20.6725i			1.83439i	−0.398438	+	0.917195i	$0.630448\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−8.35473	−	9.93202i	−0.732758	−	0.871096i
$131$	−7.35442			−0.642559			−0.321280	−	0.946984i	$-0.604113\pi$
$131$	−7.35442			−0.642559			−0.321280	+	0.946984i	$0.604113\pi$
$132$		0			0
$133$			1.77640i			0.154034i
$134$	9.42477			0.814176
$135$		0			0
$136$	5.22007			0.447618
$137$		−	9.22007i		−	0.787724i	−0.919170	−	0.393862i	$-0.871139\pi$
$137$		−	9.22007i		−	0.787724i	0.919170	−	0.393862i	$-0.128861\pi$
$138$		0			0
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$	2.13714	−	1.79775i	0.180622	−	0.151937i
$141$		0			0
$142$		−	11.5619i		−	0.970254i
$143$		−	14.0356i		−	1.17372i
$144$		0			0
$145$	−1.13466	−	1.34887i	−0.0942280	−	0.112017i
$146$	0.741689			0.0613826
$147$		0			0
$148$		−	4.12777i		−	0.339301i
$149$	−15.4087			−1.26233			−0.631163	−	0.775650i	$-0.717422\pi$
$149$	−15.4087			−1.26233			−0.631163	+	0.775650i	$0.717422\pi$
$150$		0			0
$151$	14.1525			1.15171			0.575856	−	0.817551i	$-0.304669\pi$
$151$	14.1525			1.15171			0.575856	+	0.817551i	$0.304669\pi$
$152$			1.42233i			0.115366i
$153$		0			0
$154$	3.02015			0.243370
$155$	0.414080	+	0.492254i	0.0332597	+	0.0395388i
$156$		0			0
$157$		−	18.0747i		−	1.44252i	−0.692665	−	0.721260i	$-0.743563\pi$
$157$		−	18.0747i		−	1.44252i	0.692665	−	0.721260i	$-0.256437\pi$
$158$			0.375418i			0.0298666i
$159$		0			0
$160$	1.71116	−	1.43942i	0.135279	−	0.113796i
$161$	−1.24894			−0.0984303
$162$		0			0
$163$			19.8640i			1.55587i	0.628344	+	0.777936i	$0.283733\pi$
$163$			19.8640i			1.55587i	−0.628344	+	0.777936i	$0.716267\pi$
$164$	−5.01597			−0.391682
$165$		0			0
$166$	−5.04691			−0.391716
$167$			2.55698i			0.197865i	0.995094	+	0.0989327i	$0.0315428\pi$
$167$			2.55698i			0.197865i	−0.995094	+	0.0989327i	$0.968457\pi$
$168$		0			0
$169$	−20.6893			−1.59149
$170$	−7.51386	−	8.93240i	−0.576286	−	0.685084i
$171$		0			0
$172$		−	2.09056i		−	0.159403i
$173$		−	11.2848i		−	0.857968i	−0.903312	−	0.428984i	$-0.858872\pi$
$173$		−	11.2848i		−	0.857968i	0.903312	−	0.428984i	$-0.141128\pi$
$174$		0			0
$175$	−6.15247	−	1.06930i	−0.465083	−	0.0808313i
$176$	2.41817			0.182276
$177$		0			0
$178$			3.81362i			0.285843i
$179$	11.4289			0.854233			0.427116	−	0.904197i	$-0.359529\pi$
$179$	11.4289			0.854233			0.427116	+	0.904197i	$0.359529\pi$
$180$		0			0
$181$	7.21775			0.536491			0.268245	−	0.963351i	$-0.413556\pi$
$181$	7.21775			0.536491			0.268245	+	0.963351i	$0.413556\pi$
$182$		−	7.24916i		−	0.537344i
$183$		0			0
$184$	−1.00000			−0.0737210
$185$	−7.06330	+	5.94158i	−0.519304	+	0.436834i
$186$		0			0
$187$		−	12.6230i		−	0.923085i
$188$			10.5570i			0.769947i
$189$		0			0
$190$	2.43384	−	2.04732i	0.176569	−	0.148528i
$191$	8.25555			0.597350			0.298675	−	0.954355i	$-0.403455\pi$
$191$	8.25555			0.597350			0.298675	+	0.954355i	$0.403455\pi$
$192$		0			0
$193$			2.49788i			0.179801i	0.995951	+	0.0899007i	$0.0286550\pi$
$193$			2.49788i			0.179801i	−0.995951	+	0.0899007i	$0.971345\pi$
$194$	0.788275			0.0565948
$195$		0			0
$196$	−5.44015			−0.388582
$197$			15.1140i			1.07683i	0.842681	+	0.538413i	$0.180976\pi$
$197$			15.1140i			1.07683i	−0.842681	+	0.538413i	$0.819024\pi$
$198$		0			0
$199$	−4.37542			−0.310165			−0.155083	−	0.987902i	$-0.549564\pi$
$199$	−4.37542			−0.310165			−0.155083	+	0.987902i	$0.549564\pi$
$200$	−4.92615	−	0.856164i	−0.348332	−	0.0605399i
$201$		0			0
$202$		−	12.3036i		−	0.865678i
$203$		−	0.984509i		−	0.0690990i
$204$		0			0
$205$	7.22007	+	8.58315i	0.504272	+	0.599474i
$206$	5.52323			0.384821
$207$		0			0
$208$		−	5.80425i		−	0.402452i
$209$	3.43942			0.237910
$210$		0			0
$211$	18.0356			1.24162			0.620812	−	0.783959i	$-0.286803\pi$
$211$	18.0356			1.24162			0.620812	+	0.783959i	$0.286803\pi$
$212$			3.42233i			0.235046i
$213$		0			0
$214$	−12.4716			−0.852539
$215$	−3.57729	+	3.00918i	−0.243969	+	0.205224i
$216$		0			0
$217$			0.359286i			0.0243899i
$218$			7.79775i			0.528130i
$219$		0			0
$220$	−3.48075	−	4.13788i	−0.234672	−	0.278976i
$221$	−30.2986			−2.03810
$222$		0			0
$223$		−	11.7416i		−	0.786273i	−0.919480	−	0.393136i	$-0.871390\pi$
$223$		−	11.7416i		−	0.786273i	0.919480	−	0.393136i	$-0.128610\pi$
$224$	1.24894			0.0834484
$225$		0			0
$226$	−1.62458			−0.108066
$227$		−	9.21775i		−	0.611803i	−0.952063	−	0.305902i	$-0.901042\pi$
$227$		−	9.21775i		−	0.611803i	0.952063	−	0.305902i	$-0.0989579\pi$
$228$		0			0
$229$	−8.95309			−0.591637			−0.295818	−	0.955244i	$-0.595592\pi$
$229$	−8.95309			−0.591637			−0.295818	+	0.955244i	$0.595592\pi$
$230$	1.43942	+	1.71116i	0.0949123	+	0.112831i
$231$		0			0
$232$		−	0.788275i		−	0.0517528i
$233$			10.9971i			0.720446i	0.932866	+	0.360223i	$0.117299\pi$
$233$			10.9971i			0.720446i	−0.932866	+	0.360223i	$0.882701\pi$
$234$		0			0
$235$	18.0647	−	15.1959i	1.17841	−	0.991271i
$236$	−5.01597			−0.326512
$237$		0			0
$238$		−	6.51956i		−	0.422601i
$239$	27.2651			1.76363			0.881815	−	0.471596i	$-0.156322\pi$
$239$	27.2651			1.76363			0.881815	+	0.471596i	$0.156322\pi$
$240$		0			0
$241$	−28.3988			−1.82933			−0.914663	−	0.404218i	$-0.867544\pi$
$241$	−28.3988			−1.82933			−0.914663	+	0.404218i	$0.867544\pi$
$242$			5.15247i			0.331214i
$243$		0			0
$244$	−14.0671			−0.900551
$245$	7.83063	+	9.30898i	0.500281	+	0.594729i
$246$		0			0
$247$		−	8.25555i		−	0.525288i
$248$			0.287672i			0.0182672i
$249$		0			0
$250$	5.62575	+	9.66183i	0.355803	+	0.611068i
$251$	0.734934			0.0463886			0.0231943	−	0.999731i	$-0.492616\pi$
$251$	0.734934			0.0463886			0.0231943	+	0.999731i	$0.492616\pi$
$252$		0			0
$253$			2.41817i			0.152029i
$254$	20.6725			1.29711
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	11.8648i		−	0.740106i	−0.929011	−	0.370053i	$-0.879340\pi$
$257$		−	11.8648i		−	0.740106i	0.929011	−	0.370053i	$-0.120660\pi$
$258$		0			0
$259$	−5.15534			−0.320338
$260$	−9.93202	+	8.35473i	−0.615958	+	0.518138i
$261$		0			0
$262$			7.35442i			0.454358i
$263$			23.5541i			1.45241i	0.687479	+	0.726204i	$0.258717\pi$
$263$			23.5541i			1.45241i	−0.687479	+	0.726204i	$0.741283\pi$
$264$		0			0
$265$	5.85616	−	4.92615i	0.359741	−	0.302611i
$266$	1.77640			0.108918
$267$		0			0
$268$		−	9.42477i		−	0.575709i
$269$	−29.6698			−1.80900			−0.904499	−	0.426476i	$-0.859755\pi$
$269$	−29.6698			−1.80900			−0.904499	+	0.426476i	$0.859755\pi$
$270$		0			0
$271$	14.6738			0.891371			0.445686	−	0.895190i	$-0.352960\pi$
$271$	14.6738			0.891371			0.445686	+	0.895190i	$0.352960\pi$
$272$		−	5.22007i		−	0.316513i
$273$		0			0
$274$	−9.22007			−0.557005
$275$	−2.07035	+	11.9123i	−0.124847	+	0.718336i
$276$		0			0
$277$		−	19.2554i		−	1.15695i	−0.815702	−	0.578473i	$-0.803649\pi$
$277$		−	19.2554i		−	1.15695i	0.815702	−	0.578473i	$-0.196351\pi$
$278$			8.00000i			0.479808i
$279$		0			0
$280$	−1.79775	−	2.13714i	−0.107436	−	0.127719i
$281$	2.79912			0.166981			0.0834906	−	0.996509i	$-0.473393\pi$
$281$	2.79912			0.166981			0.0834906	+	0.996509i	$0.473393\pi$
$282$		0			0
$283$		−	20.3118i		−	1.20741i	−0.797208	−	0.603705i	$-0.793690\pi$
$283$		−	20.3118i		−	1.20741i	0.797208	−	0.603705i	$-0.206310\pi$
$284$	−11.5619			−0.686073
$285$		0			0
$286$	−14.0356			−0.829945
$287$			6.26466i			0.369791i
$288$		0			0
$289$	−10.2492			−0.602892
$290$	−1.34887	+	1.13466i	−0.0792082	+	0.0666293i
$291$		0			0
$292$		−	0.741689i		−	0.0434041i
$293$			2.84698i			0.166323i	0.996536	+	0.0831613i	$0.0265017\pi$
$293$			2.84698i			0.166323i	−0.996536	+	0.0831613i	$0.973498\pi$
$294$		0			0
$295$	7.22007	+	8.58315i	0.420369	+	0.499731i
$296$	−4.12777			−0.239922
$297$		0			0
$298$			15.4087i			0.892600i
$299$	5.80425			0.335668
$300$		0			0
$301$	−2.61098			−0.150494
$302$		−	14.1525i		−	0.814383i
$303$		0			0
$304$	1.42233			0.0815761
$305$	20.2483	+	24.0710i	1.15942	+	1.37830i
$306$		0			0
$307$		−	8.25555i		−	0.471169i	−0.971854	−	0.235584i	$-0.924300\pi$
$307$		−	8.25555i		−	0.471169i	0.971854	−	0.235584i	$-0.0757004\pi$
$308$		−	3.02015i		−	0.172089i
$309$		0			0
$310$	0.492254	−	0.414080i	0.0279582	−	0.0235182i
$311$	−22.2289			−1.26048			−0.630242	−	0.776399i	$-0.717044\pi$
$311$	−22.2289			−1.26048			−0.630242	+	0.776399i	$0.717044\pi$
$312$		0			0
$313$			13.9733i			0.789819i	0.918720	+	0.394909i	$0.129224\pi$
$313$			13.9733i			0.789819i	−0.918720	+	0.394909i	$0.870776\pi$
$314$	−18.0747			−1.02002
$315$		0			0
$316$	0.375418			0.0211189
$317$		−	5.82916i		−	0.327398i	−0.986510	−	0.163699i	$-0.947657\pi$
$317$		−	5.82916i		−	0.327398i	0.986510	−	0.163699i	$-0.0523427\pi$
$318$		0			0
$319$	−1.90618			−0.106726
$320$	−1.43942	−	1.71116i	−0.0804658	−	0.0956570i
$321$		0			0
$322$			1.24894i			0.0696008i
$323$		−	7.42466i		−	0.413119i
$324$		0			0
$325$	28.5926	+	4.96939i	1.58603	+	0.275652i
$326$	19.8640			1.10017
$327$		0			0
$328$			5.01597i			0.276961i
$329$	13.1850			0.726915
$330$		0			0
$331$	31.7249			1.74376			0.871880	−	0.489719i	$-0.162901\pi$
$331$	31.7249			1.74376			0.871880	+	0.489719i	$0.162901\pi$
$332$			5.04691i			0.276985i
$333$		0			0
$334$	2.55698			0.139912
$335$	−16.1273	+	13.5662i	−0.881130	+	0.741199i
$336$		0			0
$337$			11.6753i			0.635994i	0.948092	+	0.317997i	$0.103010\pi$
$337$			11.6753i			0.635994i	−0.948092	+	0.317997i	$0.896990\pi$
$338$			20.6893i			1.12535i
$339$		0			0
$340$	−8.93240	+	7.51386i	−0.484427	+	0.407496i
$341$	0.695639			0.0376710
$342$		0			0
$343$			15.5370i			0.838920i
$344$	−2.09056			−0.112715
$345$		0			0
$346$	−11.2848			−0.606675
$347$		−	7.59549i		−	0.407747i	−0.978997	−	0.203874i	$-0.934647\pi$
$347$		−	7.59549i		−	0.407747i	0.978997	−	0.203874i	$-0.0653532\pi$
$348$		0			0
$349$	−9.24916			−0.495096			−0.247548	−	0.968876i	$-0.579625\pi$
$349$	−9.24916			−0.495096			−0.247548	+	0.968876i	$0.579625\pi$
$350$	−1.06930	+	6.15247i	−0.0571564	+	0.328864i
$351$		0			0
$352$		−	2.41817i		−	0.128889i
$353$		−	26.2463i		−	1.39695i	−0.715635	−	0.698475i	$-0.753862\pi$
$353$		−	26.2463i		−	1.39695i	0.715635	−	0.698475i	$-0.246138\pi$
$354$		0			0
$355$	16.6424	+	19.7843i	0.883287	+	1.05004i
$356$	3.81362			0.202121
$357$		0			0
$358$		−	11.4289i		−	0.604034i
$359$	−17.2730			−0.911634			−0.455817	−	0.890074i	$-0.650653\pi$
$359$	−17.2730			−0.911634			−0.455817	+	0.890074i	$0.650653\pi$
$360$		0			0
$361$	−16.9770			−0.893525
$362$		−	7.21775i		−	0.379356i
$363$		0			0
$364$	−7.24916			−0.379959
$365$	−1.26915	+	1.06760i	−0.0664304	+	0.0558807i
$366$		0			0
$367$			17.8005i			0.929176i	0.885527	+	0.464588i	$0.153798\pi$
$367$			17.8005i			0.929176i	−0.885527	+	0.464588i	$0.846202\pi$
$368$			1.00000i			0.0521286i
$369$		0			0
$370$	5.94158	+	7.06330i	0.308888	+	0.367203i
$371$	4.27429			0.221910
$372$		0			0
$373$		−	9.81918i		−	0.508418i	−0.967149	−	0.254209i	$-0.918185\pi$
$373$		−	9.81918i		−	0.508418i	0.967149	−	0.254209i	$-0.0818151\pi$
$374$	−12.6230			−0.652720
$375$		0			0
$376$	10.5570			0.544435
$377$			4.57534i			0.235642i
$378$		0			0
$379$	−16.6715			−0.856357			−0.428179	−	0.903694i	$-0.640845\pi$
$379$	−16.6715			−0.856357			−0.428179	+	0.903694i	$0.640845\pi$
$380$	−2.04732	−	2.43384i	−0.105025	−	0.124853i
$381$		0			0
$382$		−	8.25555i		−	0.422390i
$383$			9.11397i			0.465702i	0.972512	+	0.232851i	$0.0748054\pi$
$383$			9.11397i			0.465702i	−0.972512	+	0.232851i	$0.925195\pi$
$384$		0			0
$385$	−5.16797	+	4.34725i	−0.263384	+	0.221556i
$386$	2.49788			0.127139
$387$		0			0
$388$		−	0.788275i		−	0.0400186i
$389$	−32.7086			−1.65839			−0.829195	−	0.558959i	$-0.811201\pi$
$389$	−32.7086			−1.65839			−0.829195	+	0.558959i	$0.811201\pi$
$390$		0			0
$391$	5.22007			0.263990
$392$			5.44015i			0.274769i
$393$		0			0
$394$	15.1140			0.761431
$395$	−0.540382	−	0.642401i	−0.0271896	−	0.0323227i
$396$		0			0
$397$			33.7644i			1.69459i	0.531125	+	0.847294i	$0.321769\pi$
$397$			33.7644i			1.69459i	−0.531125	+	0.847294i	$0.678231\pi$
$398$			4.37542i			0.219320i
$399$		0			0
$400$	−0.856164	+	4.92615i	−0.0428082	+	0.246308i
$401$	−33.6164			−1.67872			−0.839362	−	0.543572i	$-0.817071\pi$
$401$	−33.6164			−1.67872			−0.839362	+	0.543572i	$0.817071\pi$
$402$		0			0
$403$		−	1.66972i		−	0.0831748i
$404$	−12.3036			−0.612127
$405$		0			0
$406$	−0.984509			−0.0488604
$407$			9.98164i			0.494771i
$408$		0			0
$409$	−24.4401			−1.20849			−0.604244	−	0.796800i	$-0.706525\pi$
$409$	−24.4401			−1.20849			−0.604244	+	0.796800i	$0.706525\pi$
$410$	8.58315	−	7.22007i	0.423892	−	0.356574i
$411$		0			0
$412$		−	5.52323i		−	0.272110i
$413$			6.26466i			0.308264i
$414$		0			0
$415$	8.63609	−	7.26460i	0.423929	−	0.356605i
$416$	−5.80425			−0.284577
$417$		0			0
$418$		−	3.43942i		−	0.168228i
$419$	−34.6526			−1.69289			−0.846445	−	0.532476i	$-0.821262\pi$
$419$	−34.6526			−1.69289			−0.846445	+	0.532476i	$0.821262\pi$
$420$		0			0
$421$	−9.72073			−0.473759			−0.236880	−	0.971539i	$-0.576125\pi$
$421$	−9.72073			−0.473759			−0.236880	+	0.971539i	$0.576125\pi$
$422$		−	18.0356i		−	0.877961i
$423$		0			0
$424$	3.42233			0.166203
$425$	25.7149	+	4.46924i	1.24735	+	0.216790i
$426$		0			0
$427$			17.5689i			0.850220i
$428$			12.4716i			0.602836i
$429$		0			0
$430$	3.00918	+	3.57729i	0.145116	+	0.172512i
$431$	−13.9469			−0.671801			−0.335900	−	0.941897i	$-0.609041\pi$
$431$	−13.9469			−0.671801			−0.335900	+	0.941897i	$0.609041\pi$
$432$		0			0
$433$		−	15.1608i		−	0.728580i	−0.931286	−	0.364290i	$-0.881312\pi$
$433$		−	15.1608i		−	0.728580i	0.931286	−	0.364290i	$-0.118688\pi$
$434$	0.359286			0.0172463
$435$		0			0
$436$	7.79775			0.373444
$437$			1.42233i			0.0680392i
$438$		0			0
$439$	13.1140			0.625895			0.312948	−	0.949770i	$-0.398684\pi$
$439$	13.1140			0.625895			0.312948	+	0.949770i	$0.398684\pi$
$440$	−4.13788	+	3.48075i	−0.197266	+	0.165938i
$441$		0			0
$442$			30.2986i			1.44116i
$443$			4.00000i			0.190046i	0.995475	+	0.0950229i	$0.0302924\pi$
$443$			4.00000i			0.190046i	−0.995475	+	0.0950229i	$0.969708\pi$
$444$		0			0
$445$	−5.48938	−	6.52573i	−0.260222	−	0.309349i
$446$	−11.7416			−0.555979
$447$		0			0
$448$		−	1.24894i		−	0.0590069i
$449$	34.7121			1.63817			0.819083	−	0.573675i	$-0.194483\pi$
$449$	34.7121			1.63817			0.819083	+	0.573675i	$0.194483\pi$
$450$		0			0
$451$	12.1295			0.571154
$452$			1.62458i			0.0764139i
$453$		0			0
$454$	−9.21775			−0.432610
$455$	10.4346	+	12.4045i	0.489180	+	0.581532i
$456$		0			0
$457$		−	19.5716i		−	0.915519i	−0.889076	−	0.457759i	$-0.848652\pi$
$457$		−	19.5716i		−	0.915519i	0.889076	−	0.457759i	$-0.151348\pi$
$458$			8.95309i			0.418350i
$459$		0			0
$460$	1.71116	−	1.43942i	0.0797834	−	0.0671131i
$461$	16.2186			0.755376			0.377688	−	0.925933i	$-0.376719\pi$
$461$	16.2186			0.755376			0.377688	+	0.925933i	$0.376719\pi$
$462$		0			0
$463$			29.6496i			1.37793i	0.724794	+	0.688966i	$0.241935\pi$
$463$			29.6496i			1.37793i	−0.724794	+	0.688966i	$0.758065\pi$
$464$	−0.788275			−0.0365947
$465$		0			0
$466$	10.9971			0.509432
$467$			33.3519i			1.54334i	0.636023	+	0.771670i	$0.280578\pi$
$467$			33.3519i			1.54334i	−0.636023	+	0.771670i	$0.719422\pi$
$468$		0			0
$469$	−11.7710			−0.543533
$470$	−15.1959	−	18.0647i	−0.700934	−	0.833264i
$471$		0			0
$472$			5.01597i			0.230879i
$473$			5.05531i			0.232444i
$474$		0			0
$475$	−1.21775	+	7.00660i	−0.0558740	+	0.321485i
$476$	−6.51956			−0.298824
$477$		0			0
$478$		−	27.2651i		−	1.24707i
$479$	−2.49788			−0.114131			−0.0570656	−	0.998370i	$-0.518174\pi$
$479$	−2.49788			−0.114131			−0.0570656	+	0.998370i	$0.518174\pi$
$480$		0			0
$481$	23.9586			1.09242
$482$			28.3988i			1.29353i
$483$		0			0
$484$	5.15247			0.234203
$485$	−1.34887	+	1.13466i	−0.0612489	+	0.0515221i
$486$		0			0
$487$			3.37263i			0.152828i	0.997076	+	0.0764142i	$0.0243471\pi$
$487$			3.37263i			0.152828i	−0.997076	+	0.0764142i	$0.975653\pi$
$488$			14.0671i			0.636786i
$489$		0			0
$490$	9.30898	−	7.83063i	0.420537	−	0.353752i
$491$	26.3634			1.18976			0.594882	−	0.803813i	$-0.297199\pi$
$491$	26.3634			1.18976			0.594882	+	0.803813i	$0.297199\pi$
$492$		0			0
$493$			4.11485i			0.185324i
$494$	−8.25555			−0.371435
$495$		0			0
$496$	0.287672			0.0129169
$497$			14.4401i			0.647729i
$498$		0			0
$499$	−39.3833			−1.76304			−0.881519	−	0.472149i	$-0.843478\pi$
$499$	−39.3833			−1.76304			−0.881519	+	0.472149i	$0.843478\pi$
$500$	9.66183	−	5.62575i	0.432090	−	0.251591i
$501$		0			0
$502$		−	0.734934i		−	0.0328017i
$503$		−	5.15534i		−	0.229865i	−0.993373	−	0.114933i	$-0.963335\pi$
$503$		−	5.15534i		−	0.229865i	0.993373	−	0.114933i	$-0.0366652\pi$
$504$		0			0
$505$	17.7100	+	21.0535i	0.788085	+	0.936868i
$506$	2.41817			0.107501
$507$		0			0
$508$		−	20.6725i		−	0.917195i
$509$	−5.46517			−0.242240			−0.121120	−	0.992638i	$-0.538649\pi$
$509$	−5.46517			−0.242240			−0.121120	+	0.992638i	$0.538649\pi$
$510$		0			0
$511$	−0.926326			−0.0409782
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−11.8648			−0.523334
$515$	−9.45115	+	7.95022i	−0.416467	+	0.350329i
$516$		0			0
$517$		−	25.5285i		−	1.12274i
$518$			5.15534i			0.226513i
$519$		0			0
$520$	8.35473	+	9.93202i	0.366379	+	0.435548i
$521$	2.07764			0.0910229			0.0455115	−	0.998964i	$-0.485508\pi$
$521$	2.07764			0.0910229			0.0455115	+	0.998964i	$0.485508\pi$
$522$		0			0
$523$		−	19.2569i		−	0.842044i	−0.907050	−	0.421022i	$-0.861672\pi$
$523$		−	19.2569i		−	0.842044i	0.907050	−	0.421022i	$-0.138328\pi$
$524$	7.35442			0.321280
$525$		0			0
$526$	23.5541			1.02701
$527$		−	1.50167i		−	0.0654138i
$528$		0			0
$529$	−1.00000			−0.0434783
$530$	−4.92615	−	5.85616i	−0.213978	−	0.254376i
$531$		0			0
$532$		−	1.77640i		−	0.0770169i
$533$		−	29.1140i		−	1.26107i
$534$		0			0
$535$	21.3409	−	17.9518i	0.922647	−	0.776123i
$536$	−9.42477			−0.407088
$537$		0			0
$538$			29.6698i			1.27915i
$539$	13.1552			0.566634
$540$		0			0
$541$	−6.75084			−0.290241			−0.145121	−	0.989414i	$-0.546357\pi$
$541$	−6.75084			−0.290241			−0.145121	+	0.989414i	$0.546357\pi$
$542$		−	14.6738i		−	0.630295i
$543$		0			0
$544$	−5.22007			−0.223809
$545$	−11.2242	−	13.3432i	−0.480792	−	0.571561i
$546$		0			0
$547$			33.9704i			1.45247i	0.687446	+	0.726235i	$0.258732\pi$
$547$			33.9704i			1.45247i	−0.687446	+	0.726235i	$0.741268\pi$
$548$			9.22007i			0.393862i
$549$		0			0
$550$	11.9123	+	2.07035i	0.507940	+	0.0882799i
$551$	−1.12119			−0.0477641
$552$		0			0
$553$		−	0.468874i		−	0.0199386i
$554$	−19.2554			−0.818084
$555$		0			0
$556$	8.00000			0.339276
$557$			37.8625i			1.60428i	0.597133	+	0.802142i	$0.296306\pi$
$557$			37.8625i			1.60428i	−0.597133	+	0.802142i	$0.703694\pi$
$558$		0			0
$559$	12.1341			0.513218
$560$	−2.13714	+	1.79775i	−0.0903108	+	0.0759686i
$561$		0			0
$562$		−	2.79912i		−	0.118074i
$563$		−	8.81789i		−	0.371630i	−0.982585	−	0.185815i	$-0.940508\pi$
$563$		−	8.81789i		−	0.371630i	0.982585	−	0.185815i	$-0.0594925\pi$
$564$		0			0
$565$	2.77993	−	2.33845i	0.116952	−	0.0983793i
$566$	−20.3118			−0.853768
$567$		0			0
$568$			11.5619i			0.485127i
$569$	11.0547			0.463436			0.231718	−	0.972783i	$-0.425565\pi$
$569$	11.0547			0.463436			0.231718	+	0.972783i	$0.425565\pi$
$570$		0			0
$571$	10.9822			0.459590			0.229795	−	0.973239i	$-0.426194\pi$
$571$	10.9822			0.459590			0.229795	+	0.973239i	$0.426194\pi$
$572$			14.0356i			0.586859i
$573$		0			0
$574$	6.26466			0.261482
$575$	−4.92615	−	0.856164i	−0.205435	−	0.0357045i
$576$		0			0
$577$		−	32.9761i		−	1.37281i	−0.727217	−	0.686407i	$-0.759187\pi$
$577$		−	32.9761i		−	1.37281i	0.727217	−	0.686407i	$-0.240813\pi$
$578$			10.2492i			0.426309i
$579$		0			0
$580$	1.13466	+	1.34887i	0.0471140	+	0.0560087i
$581$	6.30329			0.261505
$582$		0			0
$583$		−	8.27576i		−	0.342747i
$584$	−0.741689			−0.0306913
$585$		0			0
$586$	2.84698			0.117608
$587$		−	42.3988i		−	1.74998i	−0.484137	−	0.874992i	$-0.660866\pi$
$587$		−	42.3988i		−	1.74998i	0.484137	−	0.874992i	$-0.339134\pi$
$588$		0			0
$589$	0.409164			0.0168593
$590$	8.58315	−	7.22007i	0.353363	−	0.297246i
$591$		0			0
$592$			4.12777i			0.169650i
$593$		−	10.1755i		−	0.417857i	−0.977931	−	0.208929i	$-0.933002\pi$
$593$		−	10.1755i		−	0.417857i	0.977931	−	0.208929i	$-0.0669976\pi$
$594$		0			0
$595$	9.38436	+	11.1560i	0.384721	+	0.457353i
$596$	15.4087			0.631163
$597$		0			0
$598$		−	5.80425i		−	0.237353i
$599$	33.8778			1.38421			0.692104	−	0.721797i	$-0.256684\pi$
$599$	33.8778			1.38421			0.692104	+	0.721797i	$0.256684\pi$
$600$		0			0
$601$	−18.5926			−0.758409			−0.379204	−	0.925313i	$-0.623802\pi$
$601$	−18.5926			−0.758409			−0.379204	+	0.925313i	$0.623802\pi$
$602$			2.61098i			0.106416i
$603$		0			0
$604$	−14.1525			−0.575856
$605$	−7.41655	−	8.81673i	−0.301526	−	0.358451i
$606$		0			0
$607$			24.7403i			1.00418i	0.864816	+	0.502088i	$0.167435\pi$
$607$			24.7403i			1.00418i	−0.864816	+	0.502088i	$0.832565\pi$
$608$		−	1.42233i		−	0.0576830i
$609$		0			0
$610$	24.0710	−	20.2483i	0.974608	−	0.819832i
$611$	−61.2754			−2.47894
$612$		0			0
$613$			13.9599i			0.563834i	0.959439	+	0.281917i	$0.0909702\pi$
$613$			13.9599i			0.563834i	−0.959439	+	0.281917i	$0.909030\pi$
$614$	−8.25555			−0.333167
$615$		0			0
$616$	−3.02015			−0.121685
$617$			14.9508i			0.601895i	0.953641	+	0.300948i	$0.0973029\pi$
$617$			14.9508i			0.601895i	−0.953641	+	0.300948i	$0.902697\pi$
$618$		0			0
$619$	39.5874			1.59115			0.795576	−	0.605853i	$-0.207168\pi$
$619$	39.5874			1.59115			0.795576	+	0.605853i	$0.207168\pi$
$620$	−0.414080	−	0.492254i	−0.0166299	−	0.0197694i
$621$		0			0
$622$			22.2289i			0.891296i
$623$		−	4.76299i		−	0.190825i
$624$		0			0
$625$	−23.5340	−	8.43519i	−0.941359	−	0.337408i
$626$	13.9733			0.558486
$627$		0			0
$628$			18.0747i			0.721260i
$629$	21.5473			0.859146
$630$		0			0
$631$	−39.5250			−1.57347			−0.786733	−	0.617293i	$-0.788229\pi$
$631$	−39.5250			−1.57347			−0.786733	+	0.617293i	$0.788229\pi$
$632$		−	0.375418i		−	0.0149333i
$633$		0			0
$634$	−5.82916			−0.231506
$635$	−35.3741	+	29.7564i	−1.40378	+	1.18085i
$636$		0			0
$637$		−	31.5760i		−	1.25109i
$638$			1.90618i			0.0754664i
$639$		0			0
$640$	−1.71116	+	1.43942i	−0.0676397	+	0.0568979i
$641$	−8.60953			−0.340056			−0.170028	−	0.985439i	$-0.554386\pi$
$641$	−8.60953			−0.340056			−0.170028	+	0.985439i	$0.554386\pi$
$642$		0			0
$643$			25.9359i			1.02281i	0.859340	+	0.511405i	$0.170875\pi$
$643$			25.9359i			1.02281i	−0.859340	+	0.511405i	$0.829125\pi$
$644$	1.24894			0.0492152
$645$		0			0
$646$	−7.42466			−0.292119
$647$			14.6156i			0.574600i	0.957841	+	0.287300i	$0.0927577\pi$
$647$			14.6156i			0.574600i	−0.957841	+	0.287300i	$0.907242\pi$
$648$		0			0
$649$	12.1295			0.476123
$650$	4.96939	−	28.5926i	0.194915	−	1.12149i
$651$		0			0
$652$		−	19.8640i		−	0.777936i
$653$			4.03564i			0.157927i	0.996878	+	0.0789633i	$0.0251610\pi$
$653$			4.03564i			0.157927i	−0.996878	+	0.0789633i	$0.974839\pi$
$654$		0			0
$655$	−10.5861	−	12.5846i	−0.413632	−	0.491722i
$656$	5.01597			0.195841
$657$		0			0
$658$		−	13.1850i		−	0.514007i
$659$	−31.6859			−1.23431			−0.617153	−	0.786843i	$-0.711714\pi$
$659$	−31.6859			−1.23431			−0.617153	+	0.786843i	$0.711714\pi$
$660$		0			0
$661$	6.98873			0.271830			0.135915	−	0.990721i	$-0.456603\pi$
$661$	6.98873			0.271830			0.135915	+	0.990721i	$0.456603\pi$
$662$		−	31.7249i		−	1.23303i
$663$		0			0
$664$	5.04691			0.195858
$665$	−3.03972	+	2.55698i	−0.117875	+	0.0991556i
$666$		0			0
$667$		−	0.788275i		−	0.0305221i
$668$		−	2.55698i		−	0.0989327i
$669$		0			0
$670$	13.5662	+	16.1273i	0.524107	+	0.623053i
$671$	34.0165			1.31319
$672$		0			0
$673$		−	42.9677i		−	1.65628i	−0.560520	−	0.828141i	$-0.689399\pi$
$673$		−	42.9677i		−	1.65628i	0.560520	−	0.828141i	$-0.310601\pi$
$674$	11.6753			0.449716
$675$		0			0
$676$	20.6893			0.795743
$677$			4.40218i			0.169190i	0.996415	+	0.0845948i	$0.0269596\pi$
$677$			4.40218i			0.169190i	−0.996415	+	0.0845948i	$0.973040\pi$
$678$		0			0
$679$	−0.984509			−0.0377820
$680$	7.51386	+	8.93240i	0.288143	+	0.342542i
$681$		0			0
$682$		−	0.695639i		−	0.0266374i
$683$			40.0881i			1.53393i	0.641690	+	0.766964i	$0.278233\pi$
$683$			40.0881i			1.53393i	−0.641690	+	0.766964i	$0.721767\pi$
$684$		0			0
$685$	15.7771	−	13.2715i	0.602810	−	0.507079i
$686$	15.5370			0.593206
$687$		0			0
$688$			2.09056i			0.0797017i
$689$	−19.8640			−0.756760
$690$		0			0
$691$	−12.5340			−0.476815			−0.238407	−	0.971165i	$-0.576625\pi$
$691$	−12.5340			−0.476815			−0.238407	+	0.971165i	$0.576625\pi$
$692$			11.2848i			0.428984i
$693$		0			0
$694$	−7.59549			−0.288321
$695$	−11.5153	−	13.6893i	−0.436801	−	0.519265i
$696$		0			0
$697$		−	26.1838i		−	0.991780i
$698$			9.24916i			0.350086i
$699$		0			0
$700$	6.15247	+	1.06930i	0.232542	+	0.0404157i
$701$	24.4530			0.923578			0.461789	−	0.886990i	$-0.347208\pi$
$701$	24.4530			0.923578			0.461789	+	0.886990i	$0.347208\pi$
$702$		0			0
$703$			5.87105i			0.221431i
$704$	−2.41817			−0.0911381
$705$		0			0
$706$	−26.2463			−0.987792
$707$			15.3665i			0.577916i
$708$		0			0
$709$	−39.1764			−1.47130			−0.735650	−	0.677362i	$-0.763123\pi$
$709$	−39.1764			−1.47130			−0.735650	+	0.677362i	$0.763123\pi$
$710$	19.7843	−	16.6424i	0.742493	−	0.624578i
$711$		0			0
$712$		−	3.81362i		−	0.142921i
$713$			0.287672i			0.0107734i
$714$		0			0
$715$	24.0173	−	20.2031i	0.898195	−	0.755554i
$716$	−11.4289			−0.427116
$717$		0			0
$718$			17.2730i			0.644622i
$719$	−43.7761			−1.63257			−0.816287	−	0.577646i	$-0.803971\pi$
$719$	−43.7761			−1.63257			−0.816287	+	0.577646i	$0.803971\pi$
$720$		0			0
$721$	−6.89818			−0.256902
$722$			16.9770i			0.631818i
$723$		0			0
$724$	−7.21775			−0.268245
$725$	0.674893	−	3.88316i	0.0250649	−	0.144217i
$726$		0			0
$727$		−	25.3873i		−	0.941562i	−0.882250	−	0.470781i	$-0.843972\pi$
$727$		−	25.3873i		−	0.941562i	0.882250	−	0.470781i	$-0.156028\pi$
$728$			7.24916i			0.268672i
$729$		0			0
$730$	1.06760	+	1.26915i	0.0395136	+	0.0469734i
$731$	10.9129			0.403627
$732$		0			0
$733$			47.8775i			1.76840i	0.467111	+	0.884199i	$0.345295\pi$
$733$			47.8775i			1.76840i	−0.467111	+	0.884199i	$0.654705\pi$
$734$	17.8005			0.657027
$735$		0			0
$736$	1.00000			0.0368605
$737$			22.7907i			0.839505i
$738$		0			0
$739$	10.8400			0.398756			0.199378	−	0.979923i	$-0.436108\pi$
$739$	10.8400			0.398756			0.199378	+	0.979923i	$0.436108\pi$
$740$	7.06330	−	5.94158i	0.259652	−	0.218417i
$741$		0			0
$742$		−	4.27429i		−	0.156914i
$743$		−	33.6893i		−	1.23594i	−0.786201	−	0.617970i	$-0.787955\pi$
$743$		−	33.6893i		−	1.23594i	0.786201	−	0.617970i	$-0.212045\pi$
$744$		0			0
$745$	−22.1795	−	26.3667i	−0.812593	−	0.966003i
$746$	−9.81918			−0.359506
$747$		0			0
$748$			12.6230i			0.461543i
$749$	15.5762			0.569144
$750$		0			0
$751$	−19.7587			−0.721005			−0.360503	−	0.932758i	$-0.617395\pi$
$751$	−19.7587			−0.721005			−0.360503	+	0.932758i	$0.617395\pi$
$752$		−	10.5570i		−	0.384974i
$753$		0			0
$754$	4.57534			0.166624
$755$	20.3713	+	24.2172i	0.741387	+	0.881354i
$756$		0			0
$757$			9.03036i			0.328214i	0.986443	+	0.164107i	$0.0524743\pi$
$757$			9.03036i			0.328214i	−0.986443	+	0.164107i	$0.947526\pi$
$758$			16.6715i			0.605536i
$759$		0			0
$760$	−2.43384	+	2.04732i	−0.0882845	+	0.0742641i
$761$	8.65816			0.313858			0.156929	−	0.987610i	$-0.449841\pi$
$761$	8.65816			0.313858			0.156929	+	0.987610i	$0.449841\pi$
$762$		0			0
$763$		−	9.73892i		−	0.352573i
$764$	−8.25555			−0.298675
$765$		0			0
$766$	9.11397			0.329301
$767$		−	29.1140i		−	1.05124i
$768$		0			0
$769$	−1.65367			−0.0596330			−0.0298165	−	0.999555i	$-0.509492\pi$
$769$	−1.65367			−0.0596330			−0.0298165	+	0.999555i	$0.509492\pi$
$770$	4.34725	+	5.16797i	0.156664	+	0.186241i
$771$		0			0
$772$		−	2.49788i		−	0.0899007i
$773$			13.5208i			0.486309i	0.969988	+	0.243155i	$0.0781823\pi$
$773$			13.5208i			0.486309i	−0.969988	+	0.243155i	$0.921818\pi$
$774$		0			0
$775$	−0.246295	+	1.41712i	−0.00884716	+	0.0509044i
$776$	−0.788275			−0.0282974
$777$		0			0
$778$			32.7086i			1.17266i
$779$	7.13436			0.255615
$780$		0			0
$781$	27.9586			1.00044
$782$		−	5.22007i		−	0.186669i
$783$		0			0
$784$	5.44015			0.194291
$785$	30.9288	−	26.0170i	1.10390	−	0.928588i
$786$		0			0
$787$			28.9295i			1.03123i	0.856821	+	0.515613i	$0.172436\pi$
$787$			28.9295i			1.03123i	−0.856821	+	0.515613i	$0.827564\pi$
$788$		−	15.1140i		−	0.538413i
$789$		0			0
$790$	−0.642401	+	0.540382i	−0.0228556	+	0.0192259i
$791$	2.02901			0.0721432
$792$		0			0
$793$		−	81.6487i		−	2.89943i
$794$	33.7644			1.19825
$795$		0			0
$796$	4.37542			0.155083
$797$			14.6761i			0.519856i	0.965628	+	0.259928i	$0.0836988\pi$
$797$			14.6761i			0.519856i	−0.965628	+	0.259928i	$0.916301\pi$
$798$		0			0
$799$	−55.1082			−1.94959
$800$	4.92615	+	0.856164i	0.174166	+	0.0302700i
$801$		0			0
$802$			33.6164i			1.18704i
$803$			1.79353i			0.0632922i
$804$		0			0
$805$	−1.79775	−	2.13714i	−0.0633622	−	0.0753244i
$806$	−1.66972			−0.0588134
$807$		0			0
$808$			12.3036i			0.432839i
$809$	−4.34055			−0.152605			−0.0763027	−	0.997085i	$-0.524312\pi$
$809$	−4.34055			−0.152605			−0.0763027	+	0.997085i	$0.524312\pi$
$810$		0			0
$811$	0.580000			0.0203665			0.0101833	−	0.999948i	$-0.496759\pi$
$811$	0.580000			0.0203665			0.0101833	+	0.999948i	$0.496759\pi$
$812$			0.984509i			0.0345495i
$813$		0			0
$814$	9.98164			0.349856
$815$	−33.9906	+	28.5926i	−1.19064	+	1.00156i
$816$		0			0
$817$			2.97346i			0.104028i
$818$			24.4401i			0.854530i
$819$		0			0
$820$	−7.22007	−	8.58315i	−0.252136	−	0.299737i
$821$	−5.46517			−0.190736			−0.0953679	−	0.995442i	$-0.530403\pi$
$821$	−5.46517			−0.190736			−0.0953679	+	0.995442i	$0.530403\pi$
$822$		0			0
$823$			38.6209i			1.34624i	0.739533	+	0.673121i	$0.235047\pi$
$823$			38.6209i			1.34624i	−0.739533	+	0.673121i	$0.764953\pi$
$824$	−5.52323			−0.192411
$825$		0			0
$826$	6.26466			0.217975
$827$		−	5.79775i		−	0.201607i	−0.994906	−	0.100804i	$-0.967859\pi$
$827$		−	5.79775i		−	0.201607i	0.994906	−	0.100804i	$-0.0321414\pi$
$828$		0			0
$829$	−51.2434			−1.77976			−0.889879	−	0.456197i	$-0.849211\pi$
$829$	−51.2434			−1.77976			−0.889879	+	0.456197i	$0.849211\pi$
$830$	−7.26460	−	8.63609i	−0.252158	−	0.299763i
$831$		0			0
$832$			5.80425i			0.201226i
$833$		−	28.3980i		−	0.983931i
$834$		0			0
$835$	−4.37542	+	3.68056i	−0.151418	+	0.127371i
$836$	−3.43942			−0.118955
$837$		0			0
$838$			34.6526i			1.19705i
$839$	−43.0148			−1.48504			−0.742518	−	0.669827i	$-0.766368\pi$
$839$	−43.0148			−1.48504			−0.742518	+	0.669827i	$0.766368\pi$
$840$		0			0
$841$	−28.3786			−0.978573
$842$			9.72073i			0.334998i
$843$		0			0
$844$	−18.0356			−0.620812
$845$	−29.7805	−	35.4028i	−1.02448	−	1.21789i
$846$		0			0
$847$		−	6.43514i		−	0.221114i
$848$		−	3.42233i		−	0.117523i
$849$		0			0
$850$	4.46924	−	25.7149i	0.153294	−	0.882013i
$851$	−4.12777			−0.141498
$852$		0			0
$853$			12.3103i			0.421497i	0.977540	+	0.210748i	$0.0675901\pi$
$853$			12.3103i			0.421497i	−0.977540	+	0.210748i	$0.932410\pi$
$854$	17.5689			0.601196
$855$		0			0
$856$	12.4716			0.426269
$857$			21.3078i			0.727861i	0.931426	+	0.363931i	$0.118565\pi$
$857$			21.3078i			0.727861i	−0.931426	+	0.363931i	$0.881435\pi$
$858$		0			0
$859$	−13.1507			−0.448696			−0.224348	−	0.974509i	$-0.572025\pi$
$859$	−13.1507			−0.448696			−0.224348	+	0.974509i	$0.572025\pi$
$860$	3.57729	−	3.00918i	0.121984	−	0.102612i
$861$		0			0
$862$			13.9469i			0.475035i
$863$		−	6.49833i		−	0.221206i	−0.993865	−	0.110603i	$-0.964722\pi$
$863$		−	6.49833i		−	0.221206i	0.993865	−	0.110603i	$-0.0352782\pi$
$864$		0			0
$865$	19.3101	−	16.2435i	0.656565	−	0.552296i
$866$	−15.1608			−0.515184
$867$		0			0
$868$		−	0.359286i		−	0.0121950i
$869$	−0.907822			−0.0307958
$870$		0			0
$871$	54.7037			1.85356
$872$		−	7.79775i		−	0.264065i
$873$		0			0
$874$	1.42233			0.0481110
$875$	−7.02622	−	12.0671i	−0.237530	−	0.407941i
$876$		0			0
$877$			42.0604i			1.42028i	0.704062	+	0.710139i	$0.251368\pi$
$877$			42.0604i			1.42028i	−0.704062	+	0.710139i	$0.748632\pi$
$878$		−	13.1140i		−	0.442575i
$879$		0			0
$880$	3.48075	+	4.13788i	0.117336	+	0.139488i
$881$	−40.1225			−1.35176			−0.675881	−	0.737011i	$-0.736237\pi$
$881$	−40.1225			−1.35176			−0.675881	+	0.737011i	$0.736237\pi$
$882$		0			0
$883$		−	5.53197i		−	0.186166i	−0.995658	−	0.0930828i	$-0.970328\pi$
$883$		−	5.53197i		−	0.186166i	0.995658	−	0.0930828i	$-0.0296721\pi$
$884$	30.2986			1.01905
$885$		0			0
$886$	4.00000			0.134383
$887$		−	11.4833i		−	0.385572i	−0.981241	−	0.192786i	$-0.938248\pi$
$887$		−	11.4833i		−	0.385572i	0.981241	−	0.192786i	$-0.0617523\pi$
$888$		0			0
$889$	−25.8188			−0.865934
$890$	−6.52573	+	5.48938i	−0.218743	+	0.184005i
$891$		0			0
$892$			11.7416i			0.393136i
$893$		−	15.0155i		−	0.502474i
$894$		0			0
$895$	16.4509	+	19.5566i	0.549892	+	0.653707i
$896$	−1.24894			−0.0417242
$897$		0			0
$898$		−	34.7121i		−	1.15836i
$899$	−0.226765			−0.00756303
$900$		0			0
$901$	−17.8648			−0.595163
$902$		−	12.1295i		−	0.403867i
$903$		0			0
$904$	1.62458			0.0540328
$905$	10.3893	+	12.3507i	0.345353	+	0.410553i
$906$		0			0
$907$		−	41.4998i		−	1.37798i	−0.724772	−	0.688989i	$-0.758055\pi$
$907$		−	41.4998i		−	1.37798i	0.724772	−	0.688989i	$-0.241945\pi$
$908$			9.21775i			0.305902i
$909$		0			0
$910$	12.4045	−	10.4346i	0.411205	−	0.345902i
$911$	25.9147			0.858593			0.429297	−	0.903164i	$-0.358761\pi$
$911$	25.9147			0.858593			0.429297	+	0.903164i	$0.358761\pi$
$912$		0			0
$913$		−	12.2043i		−	0.403902i
$914$	−19.5716			−0.647370
$915$		0			0
$916$	8.95309			0.295818
$917$		−	9.18524i		−	0.303323i
$918$		0			0
$919$	36.2927			1.19718			0.598592	−	0.801054i	$-0.295727\pi$
$919$	36.2927			1.19718			0.598592	+	0.801054i	$0.295727\pi$
$920$	−1.43942	−	1.71116i	−0.0474561	−	0.0564154i
$921$		0			0
$922$		−	16.2186i		−	0.534131i
$923$		−	67.1082i		−	2.20889i
$924$		0			0
$925$	−20.3340	−	3.53405i	−0.668579	−	0.116199i
$926$	29.6496			0.974345
$927$		0			0
$928$			0.788275i			0.0258764i
$929$	57.6102			1.89013			0.945065	−	0.326881i	$-0.105998\pi$
$929$	57.6102			1.89013			0.945065	+	0.326881i	$0.105998\pi$
$930$		0			0
$931$	7.73767			0.253592
$932$		−	10.9971i		−	0.360223i
$933$		0			0
$934$	33.3519			1.09131
$935$	21.6000	−	18.1698i	0.706396	−	0.594214i
$936$		0			0
$937$		−	47.2358i		−	1.54313i	−0.636153	−	0.771563i	$-0.719475\pi$
$937$		−	47.2358i		−	1.54313i	0.636153	−	0.771563i	$-0.280525\pi$
$938$			11.7710i			0.384336i
$939$		0			0
$940$	−18.0647	+	15.1959i	−0.589206	+	0.495635i
$941$	32.6412			1.06407			0.532037	−	0.846721i	$-0.321427\pi$
$941$	32.6412			1.06407			0.532037	+	0.846721i	$0.321427\pi$
$942$		0			0
$943$			5.01597i			0.163343i
$944$	5.01597			0.163256
$945$		0			0
$946$	5.05531			0.164362
$947$		−	23.5495i		−	0.765255i	−0.923903	−	0.382627i	$-0.875019\pi$
$947$		−	23.5495i		−	0.765255i	0.923903	−	0.382627i	$-0.124981\pi$
$948$		0			0
$949$	4.30495			0.139745
$950$	7.00660	+	1.21775i	0.227324	+	0.0395089i
$951$		0			0
$952$			6.51956i			0.211300i
$953$		−	29.3956i		−	0.952216i	−0.879387	−	0.476108i	$-0.842047\pi$
$953$		−	29.3956i		−	0.952216i	0.879387	−	0.476108i	$-0.157953\pi$
$954$		0			0
$955$	11.8832	+	14.1266i	0.384530	+	0.457126i
$956$	−27.2651			−0.881815
$957$		0			0
$958$			2.49788i			0.0807029i
$959$	11.5153			0.371849
$960$		0			0
$961$	−30.9172			−0.997330
$962$		−	23.9586i		−	0.772457i
$963$		0			0
$964$	28.3988			0.914663
$965$	−4.27429	+	3.59549i	−0.137594	+	0.115743i
$966$		0			0
$967$			15.5903i			0.501350i	0.968071	+	0.250675i	$0.0806526\pi$
$967$			15.5903i			0.501350i	−0.968071	+	0.250675i	$0.919347\pi$
$968$		−	5.15247i		−	0.165607i
$969$		0			0
$970$	1.13466	+	1.34887i	0.0364316	+	0.0433095i
$971$	−3.43267			−0.110160			−0.0550798	−	0.998482i	$-0.517541\pi$
$971$	−3.43267			−0.110160			−0.0550798	+	0.998482i	$0.517541\pi$
$972$		0			0
$973$		−	9.99153i		−	0.320314i
$974$	3.37263			0.108066
$975$		0			0
$976$	14.0671			0.450276
$977$			54.1004i			1.73082i	0.501061	+	0.865412i	$0.332943\pi$
$977$			54.1004i			1.73082i	−0.501061	+	0.865412i	$0.667057\pi$
$978$		0			0
$979$	−9.22196			−0.294735
$980$	−7.83063	−	9.30898i	−0.250140	−	0.297365i
$981$		0			0
$982$		−	26.3634i		−	0.841290i
$983$		−	53.9529i		−	1.72083i	−0.509594	−	0.860415i	$-0.670204\pi$
$983$		−	53.9529i		−	1.72083i	0.509594	−	0.860415i	$-0.329796\pi$
$984$		0			0
$985$	−25.8625	+	21.7553i	−0.824047	+	0.693181i
$986$	4.11485			0.131044
$987$		0			0
$988$			8.25555i			0.262644i
$989$	−2.09056			−0.0664758
$990$		0			0
$991$	−42.5156			−1.35055			−0.675276	−	0.737565i	$-0.735976\pi$
$991$	−42.5156			−1.35055			−0.675276	+	0.737565i	$0.735976\pi$
$992$		−	0.287672i		−	0.00913360i
$993$		0			0
$994$	14.4401			0.458014
$995$	−6.29805	−	7.48706i	−0.199661	−	0.237356i
$996$		0			0
$997$			50.1026i			1.58676i	0.608724	+	0.793382i	$0.291682\pi$
$997$			50.1026i			1.58676i	−0.608724	+	0.793382i	$0.708318\pi$
$998$			39.3833i			1.24666i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.d.h.829.6	yes	16
3.2	odd	2	inner	2070.2.d.h.829.11	yes	16
5.4	even	2	inner	2070.2.d.h.829.14	yes	16
15.14	odd	2	inner	2070.2.d.h.829.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.d.h.829.3	✓	16	15.14	odd	2	inner
2070.2.d.h.829.6	yes	16	1.1	even	1	trivial
2070.2.d.h.829.11	yes	16	3.2	odd	2	inner
2070.2.d.h.829.14	yes	16	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.43942 + 1.71116i) q^{5} +1.24894i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.43942 + 1.71116i) q^{5} +1.24894i q^{7} +1.00000i q^{8} +(1.71116 - 1.43942i) q^{10} +2.41817 q^{11} -5.80425i q^{13} +1.24894 q^{14} +1.00000 q^{16} -5.22007i q^{17} +1.42233 q^{19} +(-1.43942 - 1.71116i) q^{20} -2.41817i q^{22} +1.00000i q^{23} +(-0.856164 + 4.92615i) q^{25} -5.80425 q^{26} -1.24894i q^{28} -0.788275 q^{29} +0.287672 q^{31} -1.00000i q^{32} -5.22007 q^{34} +(-2.13714 + 1.79775i) q^{35} +4.12777i q^{37} -1.42233i q^{38} +(-1.71116 + 1.43942i) q^{40} +5.01597 q^{41} +2.09056i q^{43} -2.41817 q^{44} +1.00000 q^{46} -10.5570i q^{47} +5.44015 q^{49} +(4.92615 + 0.856164i) q^{50} +5.80425i q^{52} -3.42233i q^{53} +(3.48075 + 4.13788i) q^{55} -1.24894 q^{56} +0.788275i q^{58} +5.01597 q^{59} +14.0671 q^{61} -0.287672i q^{62} -1.00000 q^{64} +(9.93202 - 8.35473i) q^{65} +9.42477i q^{67} +5.22007i q^{68} +(1.79775 + 2.13714i) q^{70} +11.5619 q^{71} +0.741689i q^{73} +4.12777 q^{74} -1.42233 q^{76} +3.02015i q^{77} -0.375418 q^{79} +(1.43942 + 1.71116i) q^{80} -5.01597i q^{82} -5.04691i q^{83} +(8.93240 - 7.51386i) q^{85} +2.09056 q^{86} +2.41817i q^{88} -3.81362 q^{89} +7.24916 q^{91} -1.00000i q^{92} -10.5570 q^{94} +(2.04732 + 2.43384i) q^{95} +0.788275i q^{97} -5.44015i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4}+O(q^{10}) \) 16 * q - 16 * q^4	\( 16 q - 16 q^{4} + 16 q^{16} - 32 q^{19} + 32 q^{31} + 8 q^{34} + 16 q^{46} - 96 q^{49} + 24 q^{55} + 24 q^{61} - 16 q^{64} - 8 q^{70} + 32 q^{76} - 24 q^{79} + 24 q^{85} + 80 q^{91} - 32 q^{94}+O(q^{100}) \) 16 * q - 16 * q^4 + 16 * q^16 - 32 * q^19 + 32 * q^31 + 8 * q^34 + 16 * q^46 - 96 * q^49 + 24 * q^55 + 24 * q^61 - 16 * q^64 - 8 * q^70 + 32 * q^76 - 24 * q^79 + 24 * q^85 + 80 * q^91 - 32 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more