LMFDB - Embedded newform 3236.1.l.a.723.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3236,1,Mod(7,3236)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3236, base_ring=CyclotomicField(202))

chi = DirichletCharacter(H, H._module([101, 148]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("3236.7");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3236 = 2^{2} \cdot 809 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3236.l (of order $202$, degree $100$, 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:	$1.61497438088$
Analytic rank:	$0$
Dimension:	$100$
Coefficient field:	$\Q(\zeta_{202})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{100} - x^{99} + x^{98} - x^{97} + x^{96} - x^{95} + x^{94} - x^{93} + x^{92} - x^{91} + x^{90} + \cdots + 1 $ x^100 - x^99 + x^98 - x^97 + x^96 - x^95 + x^94 - x^93 + x^92 - x^91 + x^90 - x^89 + x^88 - x^87 + x^86 - x^85 + x^84 - x^83 + x^82 - x^81 + x^80 - x^79 + x^78 - x^77 + x^76 - x^75 + x^74 - x^73 + x^72 - x^71 + x^70 - x^69 + x^68 - x^67 + x^66 - x^65 + x^64 - x^63 + x^62 - x^61 + x^60 - x^59 + x^58 - x^57 + x^56 - x^55 + x^54 - x^53 + x^52 - x^51 + x^50 - x^49 + x^48 - x^47 + x^46 - x^45 + x^44 - x^43 + x^42 - x^41 + x^40 - x^39 + x^38 - x^37 + x^36 - x^35 + x^34 - x^33 + x^32 - x^31 + x^30 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 - x^21 + x^20 - x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{101}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{101} - \cdots)$

Embedding invariants

Embedding label			723.1
Root			$0.407684 + 0.913123i$ of defining polynomial
Character	$\chi$	$=$	3236.723
Dual form			3236.1.l.a.555.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0466404 + 0.998912i) q^{2} +(-0.995649 - 0.0931793i) q^{4} +(0.227305 + 0.253503i) q^{5} +(0.139515 - 0.990220i) q^{8} +(-0.942034 - 0.335517i) q^{9} +O(q^{10})$	\(q+(-0.0466404 + 0.998912i) q^{2} +(-0.995649 - 0.0931793i) q^{4} +(0.227305 + 0.253503i) q^{5} +(0.139515 - 0.990220i) q^{8} +(-0.942034 - 0.335517i) q^{9} +(-0.263829 + 0.215234i) q^{10} +(0.152247 + 0.742733i) q^{13} +(0.982635 + 0.185548i) q^{16} +(-0.740276 + 1.80702i) q^{17} +(0.379088 - 0.925360i) q^{18} +(-0.202695 - 0.273580i) q^{20} +(0.0960559 - 0.878835i) q^{25} +(-0.749026 + 0.117440i) q^{26} +(0.434163 + 0.549414i) q^{29} +(-0.231176 + 0.972912i) q^{32} +(-1.77053 - 0.823751i) q^{34} +(0.906673 + 0.421835i) q^{36} +(-0.960838 + 0.783861i) q^{37} +(0.282736 - 0.189715i) q^{40} +(-0.0804571 + 0.132913i) q^{41} +(-0.129075 - 0.315073i) q^{45} +(0.0776838 + 0.996978i) q^{49} +(0.873398 + 0.136941i) q^{50} +(-0.0823775 - 0.753688i) q^{52} +(-1.81832 + 0.402287i) q^{53} +(-0.569066 + 0.408066i) q^{58} +(-0.351539 + 0.858112i) q^{61} +(-0.961071 - 0.276302i) q^{64} +(-0.153679 + 0.207422i) q^{65} +(0.905432 - 1.73018i) q^{68} +(-0.463664 + 0.886011i) q^{72} +(-0.776240 - 0.249549i) q^{73} +(-0.738194 - 0.996352i) q^{74} +(0.176321 + 0.291277i) q^{80} +(0.774857 + 0.632136i) q^{81} +(-0.129015 - 0.0865686i) q^{82} +(-0.626355 + 0.223084i) q^{85} +(0.352896 + 1.72159i) q^{89} +(0.320751 - 0.114239i) q^{90} +(-1.78277 + 0.111049i) q^{97} +(-0.999516 + 0.0310999i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - q^{2} - q^{4} - 2 q^{5} - q^{8} - q^{9}+O(q^{10}) $ 100 * q - q^2 - q^4 - 2 * q^5 - q^8 - q^9	$ 100 q - q^{2} - q^{4} - 2 q^{5} - q^{8} - q^{9} - 2 q^{10} - 2 q^{13} - q^{16} - 2 q^{17} - q^{18} - 2 q^{20} - 3 q^{25} - 2 q^{26} - 2 q^{29} - q^{32} - 2 q^{34} - q^{36} - 2 q^{37} - 2 q^{40} - 2 q^{41} - 2 q^{45} - q^{49} - 3 q^{50} - 2 q^{52} - 2 q^{53} - 2 q^{58} - 2 q^{61} - q^{64} - 4 q^{65} - 2 q^{68} - q^{72} - 2 q^{73} - 2 q^{74} - 2 q^{80} - q^{81} - 2 q^{82} - 4 q^{85} - 2 q^{89} - 2 q^{90} - 2 q^{97} - q^{98}+O(q^{100}) $ 100 * q - q^2 - q^4 - 2 * q^5 - q^8 - q^9 - 2 * q^10 - 2 * q^13 - q^16 - 2 * q^17 - q^18 - 2 * q^20 - 3 * q^25 - 2 * q^26 - 2 * q^29 - q^32 - 2 * q^34 - q^36 - 2 * q^37 - 2 * q^40 - 2 * q^41 - 2 * q^45 - q^49 - 3 * q^50 - 2 * q^52 - 2 * q^53 - 2 * q^58 - 2 * q^61 - q^64 - 4 * q^65 - 2 * q^68 - q^72 - 2 * q^73 - 2 * q^74 - 2 * q^80 - q^81 - 2 * q^82 - 4 * q^85 - 2 * q^89 - 2 * q^90 - 2 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3236\mathbb{Z}\right)^\times$.

$n$	$1619$	$1621$
$\chi(n)$	$-1$	$e\left(\frac{56}{101}\right)$

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 $

$2$	−0.0466404	+	0.998912i	−0.0466404	+	0.998912i
$2$	−0.0466404	+	0.998912i	−0.0466404	+	0.998912i
$3$		0			0		0.170244	−	0.985402i	$-0.445545\pi$
$3$		0			0		−0.170244	+	0.985402i	$0.554455\pi$
$4$	−0.995649	−	0.0931793i	−0.995649	−	0.0931793i
$5$	0.227305	+	0.253503i	0.227305	+	0.253503i	0.847315	−	0.531091i	$-0.178218\pi$
$5$	0.227305	+	0.253503i	0.227305	+	0.253503i	−0.620010	+	0.784594i	$0.712871\pi$
$6$		0			0
$7$		0			0		−0.734059	−	0.679086i	$-0.762376\pi$
$7$		0			0		0.734059	+	0.679086i	$0.237624\pi$
$8$	0.139515	−	0.990220i	0.139515	−	0.990220i
$9$	−0.942034	−	0.335517i	−0.942034	−	0.335517i
$10$	−0.263829	+	0.215234i	−0.263829	+	0.215234i
$11$		0			0		0.995649	−	0.0931793i	$-0.0297030\pi$
$11$		0			0		−0.995649	+	0.0931793i	$0.970297\pi$
$12$		0			0
$13$	0.152247	+	0.742733i	0.152247	+	0.742733i	0.982635	+	0.185548i	$0.0594059\pi$
$13$	0.152247	+	0.742733i	0.152247	+	0.742733i	−0.830388	+	0.557186i	$0.811881\pi$
$14$		0			0
$15$		0			0
$16$	0.982635	+	0.185548i	0.982635	+	0.185548i
$17$	−0.740276	+	1.80702i	−0.740276	+	1.80702i	−0.170244	+	0.985402i	$0.554455\pi$
$17$	−0.740276	+	1.80702i	−0.740276	+	1.80702i	−0.570032	+	0.821622i	$0.693069\pi$
$18$	0.379088	−	0.925360i	0.379088	−	0.925360i
$19$		0			0		0.490994	−	0.871163i	$-0.336634\pi$
$19$		0			0		−0.490994	+	0.871163i	$0.663366\pi$
$20$	−0.202695	−	0.273580i	−0.202695	−	0.273580i
$21$		0			0
$22$		0			0
$23$		0			0		0.0776838	−	0.996978i	$-0.475248\pi$
$23$		0			0		−0.0776838	+	0.996978i	$0.524752\pi$
$24$		0			0
$25$	0.0960559	−	0.878835i	0.0960559	−	0.878835i
$26$	−0.749026	+	0.117440i	−0.749026	+	0.117440i
$27$		0			0
$28$		0			0
$29$	0.434163	+	0.549414i	0.434163	+	0.549414i	0.952013	−	0.306057i	$-0.0990099\pi$
$29$	0.434163	+	0.549414i	0.434163	+	0.549414i	−0.517850	+	0.855472i	$0.673267\pi$
$30$		0			0
$31$		0			0		0.320826	−	0.947138i	$-0.396040\pi$
$31$		0			0		−0.320826	+	0.947138i	$0.603960\pi$
$32$	−0.231176	+	0.972912i	−0.231176	+	0.972912i
$33$		0			0
$34$	−1.77053	−	0.823751i	−1.77053	−	0.823751i
$35$		0			0
$36$	0.906673	+	0.421835i	0.906673	+	0.421835i
$37$	−0.960838	+	0.783861i	−0.960838	+	0.783861i	−0.976389	−	0.216018i	$-0.930693\pi$
$37$	−0.960838	+	0.783861i	−0.960838	+	0.783861i	0.0155518	+	0.999879i	$0.495050\pi$
$38$		0			0
$39$		0			0
$40$	0.282736	−	0.189715i	0.282736	−	0.189715i
$41$	−0.0804571	+	0.132913i	−0.0804571	+	0.132913i	−0.893115	−	0.449828i	$-0.851485\pi$
$41$	−0.0804571	+	0.132913i	−0.0804571	+	0.132913i	0.812658	+	0.582741i	$0.198020\pi$
$42$		0			0
$43$		0			0		0.931144	−	0.364652i	$-0.118812\pi$
$43$		0			0		−0.931144	+	0.364652i	$0.881188\pi$
$44$		0			0
$45$	−0.129075	−	0.315073i	−0.129075	−	0.315073i
$46$		0			0
$47$		0			0		−0.878693	−	0.477387i	$-0.841584\pi$
$47$		0			0		0.878693	+	0.477387i	$0.158416\pi$
$48$		0			0
$49$	0.0776838	+	0.996978i	0.0776838	+	0.996978i
$50$	0.873398	+	0.136941i	0.873398	+	0.136941i
$51$		0			0
$52$	−0.0823775	−	0.753688i	−0.0823775	−	0.753688i
$53$	−1.81832	+	0.402287i	−1.81832	+	0.402287i	−0.987930	−	0.154898i	$-0.950495\pi$
$53$	−1.81832	+	0.402287i	−1.81832	+	0.402287i	−0.830388	+	0.557186i	$0.811881\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−0.569066	+	0.408066i	−0.569066	+	0.408066i
$59$		0			0		0.919353	−	0.393434i	$-0.128713\pi$
$59$		0			0		−0.919353	+	0.393434i	$0.871287\pi$
$60$		0			0
$61$	−0.351539	+	0.858112i	−0.351539	+	0.858112i	0.644110	+	0.764933i	$0.277228\pi$
$61$	−0.351539	+	0.858112i	−0.351539	+	0.858112i	−0.995649	+	0.0931793i	$0.970297\pi$
$62$		0			0
$63$		0			0
$64$	−0.961071	−	0.276302i	−0.961071	−	0.276302i
$65$	−0.153679	+	0.207422i	−0.153679	+	0.207422i
$66$		0			0
$67$		0			0		0.544204	−	0.838953i	$-0.316832\pi$
$67$		0			0		−0.544204	+	0.838953i	$0.683168\pi$
$68$	0.905432	−	1.73018i	0.905432	−	1.73018i
$69$		0			0
$70$		0			0
$71$		0			0		−0.595309	−	0.803497i	$-0.702970\pi$
$71$		0			0		0.595309	+	0.803497i	$0.297030\pi$
$72$	−0.463664	+	0.886011i	−0.463664	+	0.886011i
$73$	−0.776240	−	0.249549i	−0.776240	−	0.249549i	−0.108652	−	0.994080i	$-0.534653\pi$
$73$	−0.776240	−	0.249549i	−0.776240	−	0.249549i	−0.667588	+	0.744531i	$0.732673\pi$
$74$	−0.738194	−	0.996352i	−0.738194	−	0.996352i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.931144	−	0.364652i	$-0.118812\pi$
$79$		0			0		−0.931144	+	0.364652i	$0.881188\pi$
$80$	0.176321	+	0.291277i	0.176321	+	0.291277i
$81$	0.774857	+	0.632136i	0.774857	+	0.632136i
$82$	−0.129015	−	0.0865686i	−0.129015	−	0.0865686i
$83$		0			0		−0.999516	−	0.0310999i	$-0.990099\pi$
$83$		0			0		0.999516	+	0.0310999i	$0.00990099\pi$
$84$		0			0
$85$	−0.626355	+	0.223084i	−0.626355	+	0.223084i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.352896	+	1.72159i	0.352896	+	1.72159i	0.644110	+	0.764933i	$0.277228\pi$
$89$	0.352896	+	1.72159i	0.352896	+	1.72159i	−0.291215	+	0.956658i	$0.594059\pi$
$90$	0.320751	−	0.114239i	0.320751	−	0.114239i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.78277	+	0.111049i	−1.78277	+	0.111049i	−0.919353	−	0.393434i	$-0.871287\pi$
$97$	−1.78277	+	0.111049i	−1.78277	+	0.111049i	−0.863422	+	0.504483i	$0.831683\pi$
$98$	−0.999516	+	0.0310999i	−0.999516	+	0.0310999i
$99$		0			0
$100$	−0.177527	+	0.866061i	−0.177527	+	0.866061i
$101$	0.278491	+	1.97661i	0.278491	+	1.97661i	0.200807	+	0.979631i	$0.435644\pi$
$101$	0.278491	+	1.97661i	0.278491	+	1.97661i	0.0776838	+	0.996978i	$0.475248\pi$
$102$		0			0
$103$		0			0		−0.644110	−	0.764933i	$-0.722772\pi$
$103$		0			0		0.644110	+	0.764933i	$0.277228\pi$
$104$	0.756710	−	0.0471356i	0.756710	−	0.0471356i
$105$		0			0
$106$	−0.317043	−	1.83510i	−0.317043	−	1.83510i
$107$		0			0		0.350126	−	0.936702i	$-0.386139\pi$
$107$		0			0		−0.350126	+	0.936702i	$0.613861\pi$
$108$		0			0
$109$	1.59709	−	1.14524i	1.59709	−	1.14524i	0.690420	−	0.723409i	$-0.257426\pi$
$109$	1.59709	−	1.14524i	1.59709	−	1.14524i	0.906673	−	0.421835i	$-0.138614\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.652036	−	1.74441i	−0.652036	−	1.74441i	−0.667588	−	0.744531i	$-0.732673\pi$
$113$	−0.652036	−	1.74441i	−0.652036	−	1.74441i	0.0155518	−	0.999879i	$-0.495050\pi$
$114$		0			0
$115$		0			0
$116$	−0.381081	−	0.587479i	−0.381081	−	0.587479i
$117$	0.105777	−	0.750762i	0.105777	−	0.750762i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.982635	−	0.185548i	0.982635	−	0.185548i
$122$	−0.840782	−	0.391179i	−0.840782	−	0.391179i
$123$		0			0
$124$		0			0
$125$	0.521321	−	0.373829i	0.521321	−	0.373829i
$126$		0			0
$127$		0			0		−0.961071	−	0.276302i	$-0.910891\pi$
$127$		0			0		0.961071	+	0.276302i	$0.0891089\pi$
$128$	0.320826	−	0.947138i	0.320826	−	0.947138i
$129$		0			0
$130$	−0.200029	−	0.163186i	−0.200029	−	0.163186i
$131$		0			0		−0.139515	−	0.990220i	$-0.544554\pi$
$131$		0			0		0.139515	+	0.990220i	$0.455446\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	1.68607	+	0.985143i	1.68607	+	0.985143i
$137$	0.0885914	+	0.198426i	0.0885914	+	0.198426i	0.952013	−	0.306057i	$-0.0990099\pi$
$137$	0.0885914	+	0.198426i	0.0885914	+	0.198426i	−0.863422	+	0.504483i	$0.831683\pi$
$138$		0			0
$139$		0			0		−0.108652	−	0.994080i	$-0.534653\pi$
$139$		0			0		0.108652	+	0.994080i	$0.465347\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.863422	−	0.504483i	−0.863422	−	0.504483i
$145$	−0.0405907	+	0.234947i	−0.0405907	+	0.234947i
$146$	0.285482	−	0.763756i	0.285482	−	0.763756i
$147$		0			0
$148$	1.02970	−	0.690921i	1.02970	−	0.690921i
$149$	−1.55796	+	0.976520i	−1.55796	+	0.976520i	−0.570032	+	0.821622i	$0.693069\pi$
$149$	−1.55796	+	0.976520i	−1.55796	+	0.976520i	−0.987930	+	0.154898i	$0.950495\pi$
$150$		0			0
$151$		0			0		0.961071	−	0.276302i	$-0.0891089\pi$
$151$		0			0		−0.961071	+	0.276302i	$0.910891\pi$
$152$		0			0
$153$	1.30365	−	1.45390i	1.30365	−	1.45390i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.502882	−	0.293826i	0.502882	−	0.293826i	−0.231176	−	0.972912i	$-0.574257\pi$
$157$	0.502882	−	0.293826i	0.502882	−	0.293826i	0.734059	+	0.679086i	$0.237624\pi$
$158$		0			0
$159$		0			0
$160$	−0.299184	+	0.162544i	−0.299184	+	0.162544i
$161$		0			0
$162$	−0.667588	+	0.744531i	−0.667588	+	0.744531i
$163$		0			0		0.812658	−	0.582741i	$-0.198020\pi$
$163$		0			0		−0.812658	+	0.582741i	$0.801980\pi$
$164$	0.0924918	−	0.124837i	0.0924918	−	0.124837i
$165$		0			0
$166$		0			0
$167$		0			0		0.544204	−	0.838953i	$-0.316832\pi$
$167$		0			0		−0.544204	+	0.838953i	$0.683168\pi$
$168$		0			0
$169$	0.390879	−	0.167275i	0.390879	−	0.167275i
$170$	−0.193628	−	0.636078i	−0.193628	−	0.636078i
$171$		0			0
$172$		0			0
$173$	0.0805407	−	1.72496i	0.0805407	−	1.72496i	−0.463664	−	0.886011i	$-0.653465\pi$
$173$	0.0805407	−	1.72496i	0.0805407	−	1.72496i	0.544204	−	0.838953i	$-0.316832\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−1.73618	+	0.272216i	−1.73618	+	0.272216i
$179$		0			0		−0.919353	−	0.393434i	$-0.871287\pi$
$179$		0			0		0.919353	+	0.393434i	$0.128713\pi$
$180$	0.0991549	+	0.325730i	0.0991549	+	0.325730i
$181$	0.252989	−	0.117705i	0.252989	−	0.117705i	−0.291215	−	0.956658i	$-0.594059\pi$
$181$	0.252989	−	0.117705i	0.252989	−	0.117705i	0.544204	+	0.838953i	$0.316832\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.417115	−	0.0653996i	−0.417115	−	0.0653996i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.463664	−	0.886011i	$-0.653465\pi$
$191$		0			0		0.463664	+	0.886011i	$0.346535\pi$
$192$		0			0
$193$	1.40797	−	1.38624i	1.40797	−	1.38624i	0.595309	−	0.803497i	$-0.297030\pi$
$193$	1.40797	−	1.38624i	1.40797	−	1.38624i	0.812658	−	0.582741i	$-0.198020\pi$
$194$	−0.0277791	−	1.78601i	−0.0277791	−	1.78601i
$195$		0			0
$196$	0.0155518	−	0.999879i	0.0155518	−	0.999879i
$197$	0.798955	−	0.739123i	0.798955	−	0.739123i	−0.170244	−	0.985402i	$-0.554455\pi$
$197$	0.798955	−	0.739123i	0.798955	−	0.739123i	0.969199	+	0.246279i	$0.0792079\pi$
$198$		0			0
$199$		0			0		−0.291215	−	0.956658i	$-0.594059\pi$
$199$		0			0		0.291215	+	0.956658i	$0.405941\pi$
$200$	−0.856838	−	0.217727i	−0.856838	−	0.217727i
$201$		0			0
$202$	−1.98745	+	0.185998i	−1.98745	+	0.185998i
$203$		0			0
$204$		0			0
$205$	−0.0519821	+	0.00981561i	−0.0519821	+	0.00981561i
$206$		0			0
$207$		0			0
$208$	0.0117910	+	0.758085i	0.0117910	+	0.758085i
$209$		0			0
$210$		0			0
$211$		0			0		−0.0776838	−	0.996978i	$-0.524752\pi$
$211$		0			0		0.0776838	+	0.996978i	$0.475248\pi$
$212$	1.84789	−	0.231108i	1.84789	−	0.231108i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	1.06951	+	1.64877i	1.06951	+	1.64877i
$219$		0			0
$220$		0			0
$221$	−1.45484	−	0.274713i	−1.45484	−	0.274713i
$222$		0			0
$223$		0			0		0.998066	−	0.0621696i	$-0.0198020\pi$
$223$		0			0		−0.998066	+	0.0621696i	$0.980198\pi$
$224$		0			0
$225$	−0.385352	+	0.795664i	−0.385352	+	0.795664i
$226$	1.77292	−	0.569967i	1.77292	−	0.569967i
$227$		0			0		−0.987930	−	0.154898i	$-0.950495\pi$
$227$		0			0		0.987930	+	0.154898i	$0.0495050\pi$
$228$		0			0
$229$	−0.415053	+	1.53309i	−0.415053	+	1.53309i	0.379088	+	0.925360i	$0.376238\pi$
$229$	−0.415053	+	1.53309i	−0.415053	+	1.53309i	−0.794142	+	0.607733i	$0.792079\pi$
$230$		0			0
$231$		0			0
$232$	0.604614	−	0.353266i	0.604614	−	0.353266i
$233$	1.19308	+	0.855532i	1.19308	+	0.855532i	0.992270	−	0.124099i	$-0.0396040\pi$
$233$	1.19308	+	0.855532i	1.19308	+	0.855532i	0.200807	+	0.979631i	$0.435644\pi$
$234$	0.745011	+	0.140678i	0.745011	+	0.140678i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$	−1.45931	+	0.792832i	−1.45931	+	0.792832i	−0.995649	−	0.0931793i	$-0.970297\pi$
$241$	−1.45931	+	0.792832i	−1.45931	+	0.792832i	−0.463664	+	0.886011i	$0.653465\pi$
$242$	0.139515	+	0.990220i	0.139515	+	0.990220i
$243$		0			0
$244$	0.429968	−	0.821622i	0.429968	−	0.821622i
$245$	−0.235079	+	0.246311i	−0.235079	+	0.246311i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	0.349108	+	0.538189i	0.349108	+	0.538189i
$251$		0			0		−0.754823	−	0.655929i	$-0.772277\pi$
$251$		0			0		0.754823	+	0.655929i	$0.227723\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.931144	+	0.364652i	0.931144	+	0.364652i
$257$	−0.572289	+	1.39697i	−0.572289	+	1.39697i	0.320826	+	0.947138i	$0.396040\pi$
$257$	−0.572289	+	1.39697i	−0.572289	+	1.39697i	−0.893115	+	0.449828i	$0.851485\pi$
$258$		0			0
$259$		0			0
$260$	0.172337	−	0.192200i	0.172337	−	0.192200i
$261$	−0.224659	−	0.663236i	−0.224659	−	0.663236i
$262$		0			0
$263$		0			0		0.690420	−	0.723409i	$-0.257426\pi$
$263$		0			0		−0.690420	+	0.723409i	$0.742574\pi$
$264$		0			0
$265$	−0.515294	−	0.369507i	−0.515294	−	0.369507i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.61275	−	0.201700i	1.61275	−	0.201700i	0.734059	−	0.679086i	$-0.237624\pi$
$269$	1.61275	−	0.201700i	1.61275	−	0.201700i	0.878693	+	0.477387i	$0.158416\pi$
$270$		0			0
$271$		0			0		−0.0776838	−	0.996978i	$-0.524752\pi$
$271$		0			0		0.0776838	+	0.996978i	$0.475248\pi$
$272$	−1.06271	+	1.63829i	−1.06271	+	1.63829i
$273$		0			0
$274$	−0.202342	+	0.0792403i	−0.202342	+	0.0792403i
$275$		0			0
$276$		0			0
$277$	1.87676	−	0.415217i	1.87676	−	0.415217i	0.878693	−	0.477387i	$-0.158416\pi$
$277$	1.87676	−	0.415217i	1.87676	−	0.415217i	0.998066	+	0.0621696i	$0.0198020\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.136578	−	0.504483i	0.136578	−	0.504483i	−0.863422	−	0.504483i	$-0.831683\pi$
$281$	0.136578	−	0.504483i	0.136578	−	0.504483i	1.00000			$0$
$282$		0			0
$283$		0			0		−0.690420	−	0.723409i	$-0.742574\pi$
$283$		0			0		0.690420	+	0.723409i	$0.257426\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.544204	−	0.838953i	0.544204	−	0.838953i
$289$	−2.00474	−	1.97381i	−2.00474	−	1.97381i
$290$	−0.232798	−	0.0515045i	−0.232798	−	0.0515045i
$291$		0			0
$292$	0.749610	+	0.320793i	0.749610	+	0.320793i
$293$	0.0502356	+	0.459615i	0.0502356	+	0.459615i	0.992270	+	0.124099i	$0.0396040\pi$
$293$	0.0502356	+	0.459615i	0.0502356	+	0.459615i	−0.942034	+	0.335517i	$0.891089\pi$
$294$		0			0
$295$		0			0
$296$	0.642143	+	1.06080i	0.642143	+	1.06080i
$297$		0			0
$298$	−0.902794	−	1.60181i	−0.902794	−	1.60181i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.297441	+	0.105937i	−0.297441	+	0.105937i
$306$	1.39152	+	1.37004i	1.39152	+	1.37004i
$307$		0			0		0.690420	−	0.723409i	$-0.257426\pi$
$307$		0			0		−0.690420	+	0.723409i	$0.742574\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.969199	−	0.246279i	$-0.920792\pi$
$311$		0			0		0.969199	+	0.246279i	$0.0792079\pi$
$312$		0			0
$313$	−0.699749	+	1.24155i	−0.699749	+	1.24155i	0.261322	+	0.965252i	$0.415842\pi$
$313$	−0.699749	+	1.24155i	−0.699749	+	1.24155i	−0.961071	+	0.276302i	$0.910891\pi$
$314$	0.270051	+	0.516039i	0.270051	+	0.516039i
$315$		0			0
$316$		0			0
$317$	1.37017	+	1.43563i	1.37017	+	1.43563i	0.774857	+	0.632136i	$0.217822\pi$
$317$	1.37017	+	1.43563i	1.37017	+	1.43563i	0.595309	+	0.803497i	$0.297030\pi$
$318$		0			0
$319$		0			0
$320$	−0.148413	−	0.306439i	−0.148413	−	0.306439i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.712584	−	0.701587i	−0.712584	−	0.701587i
$325$	0.667364	−	0.0624562i	0.667364	−	0.0624562i
$326$		0			0
$327$		0			0
$328$	0.120388	+	0.0982136i	0.120388	+	0.0982136i
$329$		0			0
$330$		0			0
$331$		0			0		0.0466404	−	0.998912i	$-0.485149\pi$
$331$		0			0		−0.0466404	+	0.998912i	$0.514851\pi$
$332$		0			0
$333$	1.16814	−	0.416047i	1.16814	−	0.416047i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.480494	−	1.77481i	−0.480494	−	1.77481i	−0.620010	−	0.784594i	$-0.712871\pi$
$337$	−0.480494	−	1.77481i	−0.480494	−	1.77481i	0.139515	−	0.990220i	$-0.455446\pi$
$338$	0.148863	+	0.398256i	0.148863	+	0.398256i
$339$		0			0
$340$	0.644417	−	0.163750i	0.644417	−	0.163750i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	1.71933	+	0.160906i	1.71933	+	0.160906i
$347$		0			0		−0.644110	−	0.764933i	$-0.722772\pi$
$347$		0			0		0.644110	+	0.764933i	$0.277228\pi$
$348$		0			0
$349$	1.17001	−	0.733352i	1.17001	−	0.733352i	0.200807	−	0.979631i	$-0.435644\pi$
$349$	1.17001	−	0.733352i	1.17001	−	0.733352i	0.969199	+	0.246279i	$0.0792079\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.598527	+	0.553705i	−0.598527	+	0.553705i	−0.919353	−	0.393434i	$-0.871287\pi$
$353$	−0.598527	+	0.553705i	−0.598527	+	0.553705i	0.320826	+	0.947138i	$0.396040\pi$
$354$		0			0
$355$		0			0
$356$	−0.190944	−	1.74698i	−0.190944	−	1.74698i
$357$		0			0
$358$		0			0
$359$		0			0		−0.878693	−	0.477387i	$-0.841584\pi$
$359$		0			0		0.878693	+	0.477387i	$0.158416\pi$
$360$	−0.330000	+	0.0838548i	−0.330000	+	0.0838548i
$361$	−0.517850	−	0.855472i	−0.517850	−	0.855472i
$362$	0.105777	+	0.258204i	0.105777	+	0.258204i
$363$		0			0
$364$		0			0
$365$	−0.113182	−	0.253503i	−0.113182	−	0.253503i
$366$		0			0
$367$		0			0		0.231176	−	0.972912i	$-0.425743\pi$
$367$		0			0		−0.231176	+	0.972912i	$0.574257\pi$
$368$		0			0
$369$	0.120388	−	0.0982136i	0.120388	−	0.0982136i
$370$	0.0847829	−	0.413610i	0.0847829	−	0.413610i
$371$		0			0
$372$		0			0
$373$	−0.134148	+	0.0783803i	−0.134148	+	0.0783803i	−0.570032	−	0.821622i	$-0.693069\pi$
$373$	−0.134148	+	0.0783803i	−0.134148	+	0.0783803i	0.435884	+	0.900003i	$0.356436\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.341968	+	0.406115i	−0.341968	+	0.406115i
$378$		0			0
$379$		0			0		0.490994	−	0.871163i	$-0.336634\pi$
$379$		0			0		−0.490994	+	0.871163i	$0.663366\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.407684	−	0.913123i	$-0.633663\pi$
$383$		0			0		0.407684	+	0.913123i	$0.366337\pi$
$384$		0			0
$385$		0			0
$386$	1.31906	+	1.47109i	1.31906	+	1.47109i
$387$		0			0
$388$	1.78537	+	0.0555515i	1.78537	+	0.0555515i
$389$	1.81072	+	0.520571i	1.81072	+	0.520571i	0.998066	−	0.0621696i	$-0.0198020\pi$
$389$	1.81072	+	0.520571i	1.81072	+	0.520571i	0.812658	+	0.582741i	$0.198020\pi$
$390$		0			0
$391$		0			0
$392$	0.998066	+	0.0621696i	0.998066	+	0.0621696i
$393$		0			0
$394$	0.701055	+	0.832559i	0.701055	+	0.832559i
$395$		0			0
$396$		0			0
$397$	−0.496936	−	0.716265i	−0.496936	−	0.716265i	0.490994	−	0.871163i	$-0.336634\pi$
$397$	−0.496936	−	0.716265i	−0.496936	−	0.716265i	−0.987930	+	0.154898i	$0.950495\pi$
$398$		0			0
$399$		0			0
$400$	0.257454	−	0.845751i	0.257454	−	0.845751i
$401$	−1.27267	+	1.51140i	−1.27267	+	1.51140i	−0.517850	+	0.855472i	$0.673267\pi$
$401$	−1.27267	+	1.51140i	−1.27267	+	1.51140i	−0.754823	+	0.655929i	$0.772277\pi$
$402$		0			0
$403$		0			0
$404$	−0.0931003	−	1.99396i	−0.0931003	−	1.99396i
$405$	0.0158805	+	0.340117i	0.0158805	+	0.340117i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	0.582148	−	1.91239i	0.582148	−	1.91239i	0.261322	−	0.965252i	$-0.415842\pi$
$409$	0.582148	−	1.91239i	0.582148	−	1.91239i	0.320826	−	0.947138i	$-0.396040\pi$
$410$	−0.00738046	−	0.0523833i	−0.00738046	−	0.0523833i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−0.757810	−	0.0235792i	−0.757810	−	0.0235792i
$417$		0			0
$418$		0			0
$419$		0			0		0.754823	−	0.655929i	$-0.227723\pi$
$419$		0			0		−0.754823	+	0.655929i	$0.772277\pi$
$420$		0			0
$421$	1.99034	+	0.0619291i	1.99034	+	0.0619291i	0.998066	−	0.0621696i	$-0.0198020\pi$
$421$	1.99034	+	0.0619291i	1.99034	+	0.0619291i	0.992270	+	0.124099i	$0.0396040\pi$
$422$		0			0
$423$		0			0
$424$	0.144670	+	1.85666i	0.144670	+	1.85666i
$425$	1.51697	+	0.824155i	1.51697	+	0.824155i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.261322	−	0.965252i	$-0.584158\pi$
$431$		0			0		0.261322	+	0.965252i	$0.415842\pi$
$432$		0			0
$433$	0.922559	−	1.24519i	0.922559	−	1.24519i	−0.0466404	−	0.998912i	$-0.514851\pi$
$433$	0.922559	−	1.24519i	0.922559	−	1.24519i	0.969199	−	0.246279i	$-0.0792079\pi$
$434$		0			0
$435$		0			0
$436$	−1.69686	+	0.991445i	−1.69686	+	0.991445i
$437$		0			0
$438$		0			0
$439$		0			0		0.200807	−	0.979631i	$-0.435644\pi$
$439$		0			0		−0.200807	+	0.979631i	$0.564356\pi$
$440$		0			0
$441$	0.261322	−	0.965252i	0.261322	−	0.965252i
$442$	0.342268	−	1.44045i	0.342268	−	1.44045i
$443$		0			0		0.570032	−	0.821622i	$-0.306931\pi$
$443$		0			0		−0.570032	+	0.821622i	$0.693069\pi$
$444$		0			0
$445$	−0.356214	+	0.480787i	−0.356214	+	0.480787i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.57525	−	0.400281i	1.57525	−	0.400281i	0.644110	−	0.764933i	$-0.277228\pi$
$449$	1.57525	−	0.400281i	1.57525	−	0.400281i	0.931144	+	0.364652i	$0.118812\pi$
$450$	−0.776825	−	0.422042i	−0.776825	−	0.422042i
$451$		0			0
$452$	0.486657	+	1.79758i	0.486657	+	1.79758i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.0895202	−	0.635376i	0.0895202	−	0.635376i	−0.893115	−	0.449828i	$-0.851485\pi$
$457$	0.0895202	−	0.635376i	0.0895202	−	0.635376i	0.982635	−	0.185548i	$-0.0594059\pi$
$458$	−1.51207	−	0.486106i	−1.51207	−	0.486106i
$459$		0			0
$460$		0			0
$461$	1.04812	−	0.448540i	1.04812	−	0.448540i	0.200807	−	0.979631i	$-0.435644\pi$
$461$	1.04812	−	0.448540i	1.04812	−	0.448540i	0.847315	+	0.531091i	$0.178218\pi$
$462$		0			0
$463$		0			0		−0.995649	−	0.0931793i	$-0.970297\pi$
$463$		0			0		0.995649	+	0.0931793i	$0.0297030\pi$
$464$	0.324682	+	0.620432i	0.324682	+	0.620432i
$465$		0			0
$466$	−0.910247	+	1.15188i	−0.910247	+	1.15188i
$467$		0			0		−0.620010	−	0.784594i	$-0.712871\pi$
$467$		0			0		0.620010	+	0.784594i	$0.287129\pi$
$468$	−0.175273	+	0.737639i	−0.175273	+	0.737639i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.84789	+	0.231108i	1.84789	+	0.231108i
$478$		0			0
$479$		0			0		−0.570032	−	0.821622i	$-0.693069\pi$
$479$		0			0		0.570032	+	0.821622i	$0.306931\pi$
$480$		0			0
$481$	−0.728485	−	0.594305i	−0.728485	−	0.594305i
$482$	−0.723906	−	1.49470i	−0.723906	−	1.49470i
$483$		0			0
$484$	−0.995649	+	0.0931793i	−0.995649	+	0.0931793i
$485$	−0.433385	−	0.426697i	−0.433385	−	0.426697i
$486$		0			0
$487$		0			0		−0.644110	−	0.764933i	$-0.722772\pi$
$487$		0			0		0.644110	+	0.764933i	$0.277228\pi$
$488$	0.800674	+	0.467821i	0.800674	+	0.467821i
$489$		0			0
$490$	−0.235079	−	0.246311i	−0.235079	−	0.246311i
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$	−1.31421	+	0.377826i	−1.31421	+	0.377826i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		−0.350126	−	0.936702i	$-0.613861\pi$
$499$		0			0		0.350126	+	0.936702i	$0.386139\pi$
$500$	−0.553886	+	0.323626i	−0.553886	+	0.323626i
$501$		0			0
$502$		0			0
$503$		0			0		−0.712584	−	0.701587i	$-0.752475\pi$
$503$		0			0		0.712584	+	0.701587i	$0.247525\pi$
$504$		0			0
$505$	−0.437774	+	0.519892i	−0.437774	+	0.519892i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.85869	+	0.727892i	1.85869	+	0.727892i	0.952013	+	0.306057i	$0.0990099\pi$
$509$	1.85869	+	0.727892i	1.85869	+	0.727892i	0.906673	+	0.421835i	$0.138614\pi$
$510$		0			0
$511$		0			0
$512$	−0.407684	+	0.913123i	−0.407684	+	0.913123i
$513$		0			0
$514$	−1.36875	−	0.636822i	−1.36875	−	0.636822i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	0.183953	+	0.181114i	0.183953	+	0.181114i
$521$	−0.821556	+	1.26652i	−0.821556	+	1.26652i	0.139515	+	0.990220i	$0.455446\pi$
$521$	−0.821556	+	1.26652i	−0.821556	+	1.26652i	−0.961071	+	0.276302i	$0.910891\pi$
$522$	0.672993	−	0.193481i	0.672993	−	0.193481i
$523$		0			0		0.969199	−	0.246279i	$-0.0792079\pi$
$523$		0			0		−0.969199	+	0.246279i	$0.920792\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.987930	−	0.154898i	−0.987930	−	0.154898i
$530$	0.393139	−	0.497500i	0.393139	−	0.497500i
$531$		0			0
$532$		0			0
$533$	−0.110968	−	0.0395226i	−0.110968	−	0.0395226i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	0.126261	+	1.62040i	0.126261	+	1.62040i
$539$		0			0
$540$		0			0
$541$	−0.738194	+	0.934152i	−0.738194	+	0.934152i	−0.999516	−	0.0310999i	$-0.990099\pi$
$541$	−0.738194	+	0.934152i	−0.738194	+	0.934152i	0.261322	+	0.965252i	$0.415842\pi$
$542$		0			0
$543$		0			0
$544$	−1.58694	−	1.13796i	−1.58694	−	1.13796i
$545$	0.653350	+	0.144548i	0.653350	+	0.144548i
$546$		0			0
$547$		0			0		0.995649	−	0.0931793i	$-0.0297030\pi$
$547$		0			0		−0.995649	+	0.0931793i	$0.970297\pi$
$548$	−0.0697168	−	0.205817i	−0.0697168	−	0.205817i
$549$	0.619073	−	0.690424i	0.619073	−	0.690424i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.327232	+	1.89408i	0.327232	+	1.89408i
$555$		0			0
$556$		0			0
$557$	0.330477	+	0.806700i	0.330477	+	0.806700i	0.998066	+	0.0621696i	$0.0198020\pi$
$557$	0.330477	+	0.806700i	0.330477	+	0.806700i	−0.667588	+	0.744531i	$0.732673\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.497564	+	0.159959i	0.497564	+	0.159959i
$563$		0			0		0.690420	−	0.723409i	$-0.257426\pi$
$563$		0			0		−0.690420	+	0.723409i	$0.742574\pi$
$564$		0			0
$565$	0.294002	−	0.561807i	0.294002	−	0.561807i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.19952	−	0.469752i	1.19952	−	0.469752i	0.320826	−	0.947138i	$-0.396040\pi$
$569$	1.19952	−	0.469752i	1.19952	−	0.469752i	0.878693	+	0.477387i	$0.158416\pi$
$570$		0			0
$571$		0			0		−0.379088	−	0.925360i	$-0.623762\pi$
$571$		0			0		0.379088	+	0.925360i	$0.376238\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.812658	+	0.582741i	0.812658	+	0.582741i
$577$	−1.19225	+	0.696610i	−1.19225	+	0.696610i	−0.961071	−	0.276302i	$-0.910891\pi$
$577$	−1.19225	+	0.696610i	−1.19225	+	0.696610i	−0.231176	+	0.972912i	$0.574257\pi$
$578$	2.06516	−	1.91050i	2.06516	−	1.91050i
$579$		0			0
$580$	0.0623062	−	0.230142i	0.0623062	−	0.230142i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.355406	+	0.733833i	−0.355406	+	0.733833i
$585$	0.214364	−	0.143837i	0.214364	−	0.143837i
$586$	−0.461458	+	0.0287443i	−0.461458	+	0.0287443i
$587$		0			0		0.893115	−	0.449828i	$-0.148515\pi$
$587$		0			0		−0.893115	+	0.449828i	$0.851485\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−1.08960	+	0.591968i	−1.08960	+	0.591968i
$593$	−1.44005	−	1.10203i	−1.44005	−	1.10203i	−0.976389	−	0.216018i	$-0.930693\pi$
$593$	−1.44005	−	1.10203i	−1.44005	−	1.10203i	−0.463664	−	0.886011i	$-0.653465\pi$
$594$		0			0
$595$		0			0
$596$	1.64218	−	0.827102i	1.64218	−	0.827102i
$597$		0			0
$598$		0			0
$599$		0			0		0.231176	−	0.972912i	$-0.425743\pi$
$599$		0			0		−0.231176	+	0.972912i	$0.574257\pi$
$600$		0			0
$601$	0.00624583	+	0.401566i	0.00624583	+	0.401566i	0.982635	+	0.185548i	$0.0594059\pi$
$601$	0.00624583	+	0.401566i	0.00624583	+	0.401566i	−0.976389	+	0.216018i	$0.930693\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.270395	+	0.206925i	0.270395	+	0.206925i
$606$		0			0
$607$		0			0		0.995649	−	0.0931793i	$-0.0297030\pi$
$607$		0			0		−0.995649	+	0.0931793i	$0.970297\pi$
$608$		0			0
$609$		0			0
$610$	−0.0919490	−	0.302058i	−0.0919490	−	0.302058i
$611$		0			0
$612$	−1.43345	+	1.32611i	−1.43345	+	1.32611i
$613$	0.000483718	−	0.0310999i	0.000483718	−	0.0310999i	−0.999516	−	0.0310999i	$-0.990099\pi$
$613$	0.000483718	−	0.0310999i	0.000483718	−	0.0310999i	1.00000			$0$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.404207	+	0.834597i	−0.404207	+	0.834597i	0.595309	+	0.803497i	$0.297030\pi$
$617$	−0.404207	+	0.834597i	−0.404207	+	0.834597i	−0.999516	+	0.0310999i	$0.990099\pi$
$618$		0			0
$619$		0			0		−0.170244	−	0.985402i	$-0.554455\pi$
$619$		0			0		0.170244	+	0.985402i	$0.445545\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.649929	−	0.143791i	−0.649929	−	0.143791i
$626$	−1.20757	−	0.756894i	−1.20757	−	0.756894i
$627$		0			0
$628$	−0.528073	+	0.245689i	−0.528073	+	0.245689i
$629$	−0.705171	−	2.31653i	−0.705171	−	2.31653i
$630$		0			0
$631$		0			0		0.987930	−	0.154898i	$-0.0495050\pi$
$631$		0			0		−0.987930	+	0.154898i	$0.950495\pi$
$632$		0			0
$633$		0			0
$634$	−1.49798	+	1.30172i	−1.49798	+	1.30172i
$635$		0			0
$636$		0			0
$637$	−0.728662	+	0.209486i	−0.728662	+	0.209486i
$638$		0			0
$639$		0			0
$640$	0.313028	−	0.133959i	0.313028	−	0.133959i
$641$	0.981988	+	1.74233i	0.981988	+	1.74233i	0.490994	+	0.871163i	$0.336634\pi$
$641$	0.981988	+	1.74233i	0.981988	+	1.74233i	0.490994	+	0.871163i	$0.336634\pi$
$642$		0			0
$643$		0			0		0.0776838	−	0.996978i	$-0.475248\pi$
$643$		0			0		−0.0776838	+	0.996978i	$0.524752\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.667588	−	0.744531i	$-0.267327\pi$
$647$		0			0		−0.667588	+	0.744531i	$0.732673\pi$
$648$	0.734059	−	0.679086i	0.734059	−	0.679086i
$649$		0			0
$650$	0.0312621	+	0.669551i	0.0312621	+	0.669551i
$651$		0			0
$652$		0			0
$653$	−0.925533	−	0.0576516i	−0.925533	−	0.0576516i	−0.407684	−	0.913123i	$-0.633663\pi$
$653$	−0.925533	−	0.0576516i	−0.925533	−	0.0576516i	−0.517850	+	0.855472i	$0.673267\pi$
$654$		0			0
$655$		0			0
$656$	−0.103722	+	0.115676i	−0.103722	+	0.115676i
$657$	0.647517	+	0.495525i	0.647517	+	0.495525i
$658$		0			0
$659$		0			0		0.320826	−	0.947138i	$-0.396040\pi$
$659$		0			0		−0.320826	+	0.947138i	$0.603960\pi$
$660$		0			0
$661$	−0.433997	+	0.291210i	−0.433997	+	0.291210i	−0.754823	−	0.655929i	$-0.772277\pi$
$661$	−0.433997	+	0.291210i	−0.433997	+	0.291210i	0.320826	+	0.947138i	$0.396040\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.361112	+	1.18627i	0.361112	+	1.18627i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.451262	−	0.263665i	−0.451262	−	0.263665i	0.261322	−	0.965252i	$-0.415842\pi$
$673$	−0.451262	−	0.263665i	−0.451262	−	0.263665i	−0.712584	+	0.701587i	$0.752475\pi$
$674$	1.79529	−	0.397193i	1.79529	−	0.397193i
$675$		0			0
$676$	−0.404765	+	0.130126i	−0.404765	+	0.130126i
$677$	−0.202695	+	1.17324i	−0.202695	+	1.17324i	0.690420	+	0.723409i	$0.257426\pi$
$677$	−0.202695	+	1.17324i	−0.202695	+	1.17324i	−0.893115	+	0.449828i	$0.851485\pi$
$678$		0			0
$679$		0			0
$680$	0.133516	+	0.651353i	0.133516	+	0.651353i
$681$		0			0
$682$		0			0
$683$		0			0		0.906673	−	0.421835i	$-0.138614\pi$
$683$		0			0		−0.906673	+	0.421835i	$0.861386\pi$
$684$		0			0
$685$	−0.0301642	+	0.0675614i	−0.0301642	+	0.0675614i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.575626	−	1.28928i	−0.575626	−	1.28928i
$690$		0			0
$691$		0			0		−0.350126	−	0.936702i	$-0.613861\pi$
$691$		0			0		0.350126	+	0.936702i	$0.386139\pi$
$692$	−0.240921	+	1.70995i	−0.240921	+	1.70995i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−0.180616	−	0.243780i	−0.180616	−	0.243780i
$698$	0.677984	+	1.20294i	0.677984	+	1.20294i
$699$		0			0
$700$		0			0
$701$	−0.559765	+	0.806823i	−0.559765	+	0.806823i	−0.995649	−	0.0931793i	$-0.970297\pi$
$701$	−0.559765	+	0.806823i	−0.559765	+	0.806823i	0.435884	+	0.900003i	$0.356436\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.525187	−	0.623701i	−0.525187	−	0.623701i
$707$		0			0
$708$		0			0
$709$	−0.207976	+	1.01460i	−0.207976	+	1.01460i	0.734059	+	0.679086i	$0.237624\pi$
$709$	−0.207976	+	1.01460i	−0.207976	+	1.01460i	−0.942034	+	0.335517i	$0.891089\pi$
$710$		0			0
$711$		0			0
$712$	1.75399	−	0.109256i	1.75399	−	0.109256i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.942034	−	0.335517i	$-0.108911\pi$
$719$		0			0		−0.942034	+	0.335517i	$0.891089\pi$
$720$	−0.0683722	−	0.333552i	−0.0683722	−	0.333552i
$721$		0			0
$722$	0.878693	−	0.477387i	0.878693	−	0.477387i
$723$		0			0
$724$	−0.262856	+	0.0936194i	−0.262856	+	0.0936194i
$725$	0.524548	−	0.328783i	0.524548	−	0.328783i
$726$		0			0
$727$		0			0		−0.830388	−	0.557186i	$-0.811881\pi$
$727$		0			0		0.830388	+	0.557186i	$0.188119\pi$
$728$		0			0
$729$	−0.517850	−	0.855472i	−0.517850	−	0.855472i
$730$	0.258506	−	0.101235i	0.258506	−	0.101235i
$731$		0			0
$732$		0			0
$733$	0.123870	−	0.178542i	0.123870	−	0.178542i	−0.754823	−	0.655929i	$-0.772277\pi$
$733$	0.123870	−	0.178542i	0.123870	−	0.178542i	0.878693	+	0.477387i	$0.158416\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	0.0924918	+	0.124837i	0.0924918	+	0.124837i
$739$		0			0		−0.998066	−	0.0621696i	$-0.980198\pi$
$739$		0			0		0.998066	+	0.0621696i	$0.0198020\pi$
$740$	0.409206	+	0.103982i	0.409206	+	0.103982i
$741$		0			0
$742$		0			0
$743$		0			0		−0.992270	−	0.124099i	$-0.960396\pi$
$743$		0			0		0.992270	+	0.124099i	$0.0396040\pi$
$744$		0			0
$745$	−0.601684	−	0.172980i	−0.601684	−	0.172980i
$746$	−0.0720383	−	0.137658i	−0.0720383	−	0.137658i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.812658	−	0.582741i	$-0.198020\pi$
$751$		0			0		−0.812658	+	0.582741i	$0.801980\pi$
$752$		0			0
$753$		0			0
$754$	−0.389723	−	0.360537i	−0.389723	−	0.360537i
$755$		0			0
$756$		0			0
$757$	−0.139968	−	1.28059i	−0.139968	−	1.28059i	−0.830388	−	0.557186i	$-0.811881\pi$
$757$	−0.139968	−	1.28059i	−0.139968	−	1.28059i	0.690420	−	0.723409i	$-0.257426\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.416867	+	1.11525i	−0.416867	+	1.11525i	0.544204	+	0.838953i	$0.316832\pi$
$761$	−0.416867	+	1.11525i	−0.416867	+	1.11525i	−0.961071	+	0.276302i	$0.910891\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.664896			0.664896
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−0.532820	+	0.357519i	−0.532820	+	0.357519i	−0.794142	−	0.607733i	$-0.792079\pi$
$769$	−0.532820	+	0.357519i	−0.532820	+	0.357519i	0.261322	+	0.965252i	$0.415842\pi$
$770$		0			0
$771$		0			0
$772$	−1.53101	+	1.24901i	−1.53101	+	1.24901i
$773$	−1.12429	−	0.523083i	−1.12429	−	0.523083i	−0.231176	−	0.972912i	$-0.574257\pi$
$773$	−1.12429	−	0.523083i	−1.12429	−	0.523083i	−0.893115	+	0.449828i	$0.851485\pi$
$774$		0			0
$775$		0			0
$776$	−0.138761	+	1.78083i	−0.138761	+	1.78083i
$777$		0			0
$778$	−0.604458	+	1.78447i	−0.604458	+	1.78447i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.108652	+	0.994080i	−0.108652	+	0.994080i
$785$	0.188793	+	0.0606941i	0.188793	+	0.0606941i
$786$		0			0
$787$		0			0		−0.0466404	−	0.998912i	$-0.514851\pi$
$787$		0			0		0.0466404	+	0.998912i	$0.485149\pi$
$788$	−0.864350	+	0.661461i	−0.864350	+	0.661461i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−0.690869	−	0.130455i	−0.690869	−	0.130455i
$794$	0.738663	−	0.462989i	0.738663	−	0.462989i
$795$		0			0
$796$		0			0
$797$	0.404974	−	1.49586i	0.404974	−	1.49586i	−0.407684	−	0.913123i	$-0.633663\pi$
$797$	0.404974	−	1.49586i	0.404974	−	1.49586i	0.812658	−	0.582741i	$-0.198020\pi$
$798$		0			0
$799$		0			0
$800$	0.832823	+	0.296620i	0.832823	+	0.296620i
$801$	0.245182	−	1.74020i	0.245182	−	1.74020i
$802$	−1.45040	−	1.34178i	−1.45040	−	1.34178i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	1.99613			1.99613
$809$	0.200807	−	0.979631i	0.200807	−	0.979631i
$809$	0.200807	−	0.979631i	0.200807	−	0.979631i
$810$	−0.340487			−0.340487
$811$		0			0		0.0466404	−	0.998912i	$-0.485149\pi$
$811$		0			0		−0.0466404	+	0.998912i	$0.514851\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	1.88316	+	0.670709i	1.88316	+	0.670709i
$819$		0			0
$820$	0.0526705	−	0.00492925i	0.0526705	−	0.00492925i
$821$	0.473867	−	1.75033i	0.473867	−	1.75033i	−0.170244	−	0.985402i	$-0.554455\pi$
$821$	0.473867	−	1.75033i	0.473867	−	1.75033i	0.644110	−	0.764933i	$-0.277228\pi$
$822$		0			0
$823$		0			0		0.712584	−	0.701587i	$-0.247525\pi$
$823$		0			0		−0.712584	+	0.701587i	$0.752475\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.379088	−	0.925360i	$-0.376238\pi$
$827$		0			0		−0.379088	+	0.925360i	$0.623762\pi$
$828$		0			0
$829$	0.766889	+	1.03508i	0.766889	+	1.03508i	0.998066	+	0.0621696i	$0.0198020\pi$
$829$	0.766889	+	1.03508i	0.766889	+	1.03508i	−0.231176	+	0.972912i	$0.574257\pi$
$830$		0			0
$831$		0			0
$832$	0.0588981	−	0.755886i	0.0588981	−	0.755886i
$833$	−1.85907	−	0.597662i	−1.85907	−	0.597662i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.490994	−	0.871163i	$-0.663366\pi$
$839$		0			0		0.490994	+	0.871163i	$0.336634\pi$
$840$		0			0
$841$	0.117818	−	0.495841i	0.117818	−	0.495841i
$842$	−0.154692	+	1.98528i	−0.154692	+	1.98528i
$843$		0			0
$844$		0			0
$845$	0.131254	+	0.0610666i	0.131254	+	0.0610666i
$846$		0			0
$847$		0			0
$848$	−1.86139	+	0.0579169i	−1.86139	+	0.0579169i
$849$		0			0
$850$	−0.894011	+	1.47688i	−0.894011	+	1.47688i
$851$		0			0
$852$		0			0
$853$	0.871769			0.871769			0.435884	−	0.900003i	$-0.356436\pi$
$853$	0.871769			0.871769			0.435884	+	0.900003i	$0.356436\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.666650	+	1.78351i	−0.666650	+	1.78351i	−0.0466404	+	0.998912i	$0.514851\pi$
$857$	−0.666650	+	1.78351i	−0.666650	+	1.78351i	−0.620010	+	0.784594i	$0.712871\pi$
$858$		0			0
$859$		0			0		−0.987930	−	0.154898i	$-0.950495\pi$
$859$		0			0		0.987930	+	0.154898i	$0.0495050\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.847315	−	0.531091i	$-0.821782\pi$
$863$		0			0		0.847315	+	0.531091i	$0.178218\pi$
$864$		0			0
$865$	0.455591	−	0.371676i	0.455591	−	0.371676i
$866$	1.20081	+	0.979631i	1.20081	+	0.979631i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.911224	−	1.74125i	−0.911224	−	1.74125i
$873$	1.71669	+	0.493538i	1.71669	+	0.493538i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.840782	+	1.60664i	−0.840782	+	1.60664i	−0.0466404	+	0.998912i	$0.514851\pi$
$877$	−0.840782	+	1.60664i	−0.840782	+	1.60664i	−0.794142	+	0.607733i	$0.792079\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.324682	−	0.620432i	0.324682	−	0.620432i	−0.667588	−	0.744531i	$-0.732673\pi$
$881$	0.324682	−	0.620432i	0.324682	−	0.620432i	0.992270	+	0.124099i	$0.0396040\pi$
$882$	0.952013	+	0.306057i	0.952013	+	0.306057i
$883$		0			0		−0.595309	−	0.803497i	$-0.702970\pi$
$883$		0			0		0.595309	+	0.803497i	$0.297030\pi$
$884$	1.42292	+	0.409079i	1.42292	+	0.409079i
$885$		0			0
$886$		0			0
$887$		0			0		0.0155518	−	0.999879i	$-0.495050\pi$
$887$		0			0		−0.0155518	+	0.999879i	$0.504950\pi$
$888$		0			0
$889$		0			0
$890$	−0.463649	−	0.378250i	−0.463649	−	0.378250i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.326375	+	1.59221i	0.326375	+	1.59221i
$899$		0			0
$900$	0.457815	−	0.756296i	0.457815	−	0.756296i
$901$	0.619114	−	3.58355i	0.619114	−	3.58355i
$902$		0			0
$903$		0			0
$904$	−1.81832	+	0.402287i	−1.81832	+	0.402287i
$905$	0.0873444	+	0.0373787i	0.0873444	+	0.0373787i
$906$		0			0
$907$		0			0		0.999516	−	0.0310999i	$-0.00990099\pi$
$907$		0			0		−0.999516	+	0.0310999i	$0.990099\pi$
$908$		0			0
$909$	0.400837	−	1.95547i	0.400837	−	1.95547i
$910$		0			0
$911$		0			0		0.570032	−	0.821622i	$-0.306931\pi$
$911$		0			0		−0.570032	+	0.821622i	$0.693069\pi$
$912$		0			0
$913$		0			0
$914$	0.630509	+	0.119057i	0.630509	+	0.119057i
$915$		0			0
$916$	0.556100	−	1.48775i	0.556100	−	1.48775i
$917$		0			0
$918$		0			0
$919$		0			0		0.712584	−	0.701587i	$-0.247525\pi$
$919$		0			0		−0.712584	+	0.701587i	$0.752475\pi$
$920$		0			0
$921$		0			0
$922$	0.399167	+	1.06790i	0.399167	+	1.06790i
$923$		0			0
$924$		0			0
$925$	0.596590	+	0.919712i	0.596590	+	0.919712i
$926$		0			0
$927$		0			0
$928$	−0.634900	+	0.295391i	−0.634900	+	0.295391i
$929$	−0.0126804	−	0.0284014i	−0.0126804	−	0.0284014i	0.906673	−	0.421835i	$-0.138614\pi$
$929$	−0.0126804	−	0.0284014i	−0.0126804	−	0.0284014i	−0.919353	+	0.393434i	$0.871287\pi$
$930$		0			0
$931$		0			0
$932$	−1.10817	−	0.962980i	−1.10817	−	0.962980i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−0.728662	−	0.209486i	−0.728662	−	0.209486i
$937$	0.0498460	−	0.147155i	0.0498460	−	0.147155i	−0.919353	−	0.393434i	$-0.871287\pi$
$937$	0.0498460	−	0.147155i	0.0498460	−	0.147155i	0.969199	+	0.246279i	$0.0792079\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.257007	−	1.48761i	0.257007	−	1.48761i	−0.517850	−	0.855472i	$-0.673267\pi$
$941$	0.257007	−	1.48761i	0.257007	−	1.48761i	0.774857	−	0.632136i	$-0.217822\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.291215	−	0.956658i	$-0.405941\pi$
$947$		0			0		−0.291215	+	0.956658i	$0.594059\pi$
$948$		0			0
$949$	0.0671679	−	0.614533i	0.0671679	−	0.614533i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.67365	−	0.977889i	−1.67365	−	0.977889i	−0.961071	−	0.276302i	$-0.910891\pi$
$953$	−1.67365	−	0.977889i	−1.67365	−	0.977889i	−0.712584	−	0.701587i	$-0.752475\pi$
$954$	−0.317043	+	1.83510i	−0.317043	+	1.83510i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.794142	−	0.607733i	−0.794142	−	0.607733i
$962$	0.627635	−	0.699973i	0.627635	−	0.699973i
$963$		0			0
$964$	1.52684	−	0.653405i	1.52684	−	0.653405i
$965$	0.671454	+	0.0418249i	0.671454	+	0.0418249i
$966$		0			0
$967$		0			0		−0.320826	−	0.947138i	$-0.603960\pi$
$967$		0			0		0.320826	+	0.947138i	$0.396040\pi$
$968$	−0.0466404	−	0.998912i	−0.0466404	−	0.998912i
$969$		0			0
$970$	0.446446	−	0.413012i	0.446446	−	0.413012i
$971$		0			0		0.667588	−	0.744531i	$-0.267327\pi$
$971$		0			0		−0.667588	+	0.744531i	$0.732673\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−0.504655	+	0.777984i	−0.504655	+	0.777984i
$977$	−0.925066	−	1.64133i	−0.925066	−	1.64133i	−0.754823	−	0.655929i	$-0.772277\pi$
$977$	−0.925066	−	1.64133i	−0.925066	−	1.64133i	−0.170244	−	0.985402i	$-0.554455\pi$
$978$		0			0
$979$		0			0
$980$	0.257007	−	0.223335i	0.257007	−	0.223335i
$981$	−1.88876	+	0.543008i	−1.88876	+	0.543008i
$982$		0			0
$983$		0			0		−0.435884	−	0.900003i	$-0.643564\pi$
$983$		0			0		0.435884	+	0.900003i	$0.356436\pi$
$984$		0			0
$985$	0.368977	+	0.0345312i	0.368977	+	0.0345312i
$986$	−0.316120	−	1.33040i	−0.316120	−	1.33040i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.830388	−	0.557186i	$-0.811881\pi$
$991$		0			0		0.830388	+	0.557186i	$0.188119\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	1.48326	+	0.995262i	1.48326	+	0.995262i	0.992270	+	0.124099i	$0.0396040\pi$
$997$	1.48326	+	0.995262i	1.48326	+	0.995262i	0.490994	+	0.871163i	$0.336634\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3236.1.l.a.723.1	yes	100
4.3	odd	2	CM	3236.1.l.a.723.1	yes	100
809.555	even	101	inner	3236.1.l.a.555.1	✓	100
3236.555	odd	202	inner	3236.1.l.a.555.1	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3236.1.l.a.555.1	✓	100	809.555	even	101	inner
3236.1.l.a.555.1	✓	100	3236.555	odd	202	inner
3236.1.l.a.723.1	yes	100	1.1	even	1	trivial
3236.1.l.a.723.1	yes	100	4.3	odd	2	CM

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:	\( N \)	\(=\)	\( 3236 = 2^{2} \cdot 809 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3236.l (of order \(202\), degree \(100\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0466404 + 0.998912i) q^{2} +(-0.995649 - 0.0931793i) q^{4} +(0.227305 + 0.253503i) q^{5} +(0.139515 - 0.990220i) q^{8} +(-0.942034 - 0.335517i) q^{9} +O(q^{10})\)	\(q+(-0.0466404 + 0.998912i) q^{2} +(-0.995649 - 0.0931793i) q^{4} +(0.227305 + 0.253503i) q^{5} +(0.139515 - 0.990220i) q^{8} +(-0.942034 - 0.335517i) q^{9} +(-0.263829 + 0.215234i) q^{10} +(0.152247 + 0.742733i) q^{13} +(0.982635 + 0.185548i) q^{16} +(-0.740276 + 1.80702i) q^{17} +(0.379088 - 0.925360i) q^{18} +(-0.202695 - 0.273580i) q^{20} +(0.0960559 - 0.878835i) q^{25} +(-0.749026 + 0.117440i) q^{26} +(0.434163 + 0.549414i) q^{29} +(-0.231176 + 0.972912i) q^{32} +(-1.77053 - 0.823751i) q^{34} +(0.906673 + 0.421835i) q^{36} +(-0.960838 + 0.783861i) q^{37} +(0.282736 - 0.189715i) q^{40} +(-0.0804571 + 0.132913i) q^{41} +(-0.129075 - 0.315073i) q^{45} +(0.0776838 + 0.996978i) q^{49} +(0.873398 + 0.136941i) q^{50} +(-0.0823775 - 0.753688i) q^{52} +(-1.81832 + 0.402287i) q^{53} +(-0.569066 + 0.408066i) q^{58} +(-0.351539 + 0.858112i) q^{61} +(-0.961071 - 0.276302i) q^{64} +(-0.153679 + 0.207422i) q^{65} +(0.905432 - 1.73018i) q^{68} +(-0.463664 + 0.886011i) q^{72} +(-0.776240 - 0.249549i) q^{73} +(-0.738194 - 0.996352i) q^{74} +(0.176321 + 0.291277i) q^{80} +(0.774857 + 0.632136i) q^{81} +(-0.129015 - 0.0865686i) q^{82} +(-0.626355 + 0.223084i) q^{85} +(0.352896 + 1.72159i) q^{89} +(0.320751 - 0.114239i) q^{90} +(-1.78277 + 0.111049i) q^{97} +(-0.999516 + 0.0310999i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - q^{2} - q^{4} - 2 q^{5} - q^{8} - q^{9}+O(q^{10}) \) 100 * q - q^2 - q^4 - 2 * q^5 - q^8 - q^9	\( 100 q - q^{2} - q^{4} - 2 q^{5} - q^{8} - q^{9} - 2 q^{10} - 2 q^{13} - q^{16} - 2 q^{17} - q^{18} - 2 q^{20} - 3 q^{25} - 2 q^{26} - 2 q^{29} - q^{32} - 2 q^{34} - q^{36} - 2 q^{37} - 2 q^{40} - 2 q^{41} - 2 q^{45} - q^{49} - 3 q^{50} - 2 q^{52} - 2 q^{53} - 2 q^{58} - 2 q^{61} - q^{64} - 4 q^{65} - 2 q^{68} - q^{72} - 2 q^{73} - 2 q^{74} - 2 q^{80} - q^{81} - 2 q^{82} - 4 q^{85} - 2 q^{89} - 2 q^{90} - 2 q^{97} - q^{98}+O(q^{100}) \) 100 * q - q^2 - q^4 - 2 * q^5 - q^8 - q^9 - 2 * q^10 - 2 * q^13 - q^16 - 2 * q^17 - q^18 - 2 * q^20 - 3 * q^25 - 2 * q^26 - 2 * q^29 - q^32 - 2 * q^34 - q^36 - 2 * q^37 - 2 * q^40 - 2 * q^41 - 2 * q^45 - q^49 - 3 * q^50 - 2 * q^52 - 2 * q^53 - 2 * q^58 - 2 * q^61 - q^64 - 4 * q^65 - 2 * q^68 - q^72 - 2 * q^73 - 2 * q^74 - 2 * q^80 - q^81 - 2 * q^82 - 4 * q^85 - 2 * q^89 - 2 * q^90 - 2 * q^97 - q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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