LMFDB - Embedded newform 414.2.i.h.325.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.i (of order $11$, degree $10$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 8 x^{18} + 53 x^{16} + 358 x^{14} + 1753 x^{12} + 7149 x^{10} + 23268 x^{8} + 37292 x^{6} + \cdots + 58081 $ x^20 + 8x^18 + 53x^16 + 358x^14 + 1753x^12 + 7149x^10 + 23268x^8 + 37292x^6 + 19057x^4 - 81217*x^2 + 58081
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			325.2
Root			$1.36939 - 1.58036i$ of defining polynomial
Character	$\chi$	$=$	414.325
Dual form			414.2.i.h.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(-0.959493 + 0.281733i) q^{4} +(1.16535 - 1.34489i) q^{5} +(0.701495 - 0.450824i) q^{7} +(-0.415415 - 0.909632i) q^{8} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{2} +(-0.959493 + 0.281733i) q^{4} +(1.16535 - 1.34489i) q^{5} +(0.701495 - 0.450824i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(1.49704 + 0.962092i) q^{10} +(0.558660 - 3.88556i) q^{11} +(3.85660 + 2.47849i) q^{13} +(0.546068 + 0.630196i) q^{14} +(0.841254 - 0.540641i) q^{16} +(1.11920 + 0.328626i) q^{17} +(3.59583 - 1.05583i) q^{19} +(-0.739247 + 1.61873i) q^{20} +3.92552 q^{22} +(-3.39982 - 3.38249i) q^{23} +(0.260897 + 1.81458i) q^{25} +(-1.90441 + 4.17008i) q^{26} +(-0.546068 + 0.630196i) q^{28} +(1.04435 + 0.306648i) q^{29} +(2.92901 + 6.41364i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-0.166002 + 1.15457i) q^{34} +(0.211181 - 1.46880i) q^{35} +(-3.56741 - 4.11701i) q^{37} +(1.55682 + 3.40897i) q^{38} +(-1.70746 - 0.501354i) q^{40} +(-0.951383 + 1.09795i) q^{41} +(1.62767 - 3.56409i) q^{43} +(0.558660 + 3.88556i) q^{44} +(2.86422 - 3.84659i) q^{46} +5.02025 q^{47} +(-2.61905 + 5.73492i) q^{49} +(-1.75898 + 0.516483i) q^{50} +(-4.39866 - 1.29156i) q^{52} +(-9.43102 + 6.06095i) q^{53} +(-4.57461 - 5.27938i) q^{55} +(-0.701495 - 0.450824i) q^{56} +(-0.154901 + 1.07736i) q^{58} +(3.29551 + 2.11789i) q^{59} +(-1.74100 - 3.81226i) q^{61} +(-5.93152 + 3.81196i) q^{62} +(-0.654861 + 0.755750i) q^{64} +(7.82758 - 2.29839i) q^{65} +(-0.292710 - 2.03585i) q^{67} -1.16645 q^{68} +1.48390 q^{70} +(-1.11498 - 7.75489i) q^{71} +(-13.2507 + 3.89077i) q^{73} +(3.56741 - 4.11701i) q^{74} +(-3.15271 + 2.02613i) q^{76} +(-1.35981 - 2.97756i) q^{77} +(-8.04988 - 5.17334i) q^{79} +(0.253255 - 1.76143i) q^{80} +(-1.22217 - 0.785444i) q^{82} +(-8.44359 - 9.74442i) q^{83} +(1.74622 - 1.12223i) q^{85} +(3.75945 + 1.10388i) q^{86} +(-3.76651 + 1.10595i) q^{88} +(-0.860921 + 1.88515i) q^{89} +3.82275 q^{91} +(4.21506 + 2.28763i) q^{92} +(0.714456 + 4.96915i) q^{94} +(2.77043 - 6.06640i) q^{95} +(8.21945 - 9.48575i) q^{97} +(-6.04928 - 1.77623i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8}+O(q^{10}) $ 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8	$ 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8} - 2 q^{10} - 2 q^{11} - 18 q^{14} - 2 q^{16} + 18 q^{17} + 16 q^{19} + 2 q^{20} + 24 q^{22} - 2 q^{23} + 38 q^{25} + 18 q^{28} - 30 q^{29} + 14 q^{31} + 2 q^{32} + 4 q^{34} + 48 q^{35} - 20 q^{37} - 16 q^{38} - 2 q^{40} - 12 q^{41} - 28 q^{43} - 2 q^{44} + 2 q^{46} + 32 q^{47} + 6 q^{49} + 6 q^{50} - 46 q^{53} - 28 q^{55} + 4 q^{56} - 14 q^{58} - 50 q^{61} + 8 q^{62} - 2 q^{64} + 16 q^{65} - 8 q^{67} - 48 q^{68} - 48 q^{70} + 12 q^{71} - 18 q^{73} + 20 q^{74} - 6 q^{76} - 4 q^{77} - 18 q^{79} + 2 q^{80} - 10 q^{82} - 44 q^{83} + 32 q^{85} + 28 q^{86} + 2 q^{88} + 44 q^{91} - 2 q^{92} + 12 q^{94} + 64 q^{95} + 14 q^{97} - 28 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8 - 2 * q^10 - 2 * q^11 - 18 * q^14 - 2 * q^16 + 18 * q^17 + 16 * q^19 + 2 * q^20 + 24 * q^22 - 2 * q^23 + 38 * q^25 + 18 * q^28 - 30 * q^29 + 14 * q^31 + 2 * q^32 + 4 * q^34 + 48 * q^35 - 20 * q^37 - 16 * q^38 - 2 * q^40 - 12 * q^41 - 28 * q^43 - 2 * q^44 + 2 * q^46 + 32 * q^47 + 6 * q^49 + 6 * q^50 - 46 * q^53 - 28 * q^55 + 4 * q^56 - 14 * q^58 - 50 * q^61 + 8 * q^62 - 2 * q^64 + 16 * q^65 - 8 * q^67 - 48 * q^68 - 48 * q^70 + 12 * q^71 - 18 * q^73 + 20 * q^74 - 6 * q^76 - 4 * q^77 - 18 * q^79 + 2 * q^80 - 10 * q^82 - 44 * q^83 + 32 * q^85 + 28 * q^86 + 2 * q^88 + 44 * q^91 - 2 * q^92 + 12 * q^94 + 64 * q^95 + 14 * q^97 - 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$3$		0			0
$3$		0			0
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	1.16535	−	1.34489i	0.521161	−	0.601451i	−0.432760	−	0.901509i	$-0.642460\pi$
$5$	1.16535	−	1.34489i	0.521161	−	0.601451i	0.953921	+	0.300057i	$0.0970059\pi$
$6$		0			0
$7$	0.701495	−	0.450824i	0.265140	−	0.170395i	−0.401315	−	0.915940i	$-0.631447\pi$
$7$	0.701495	−	0.450824i	0.265140	−	0.170395i	0.666456	+	0.745545i	$0.267811\pi$
$8$	−0.415415	−	0.909632i	−0.146871	−	0.321603i
$9$		0			0
$10$	1.49704	+	0.962092i	0.473407	+	0.304240i
$11$	0.558660	−	3.88556i	0.168442	−	1.17154i	−0.713663	−	0.700489i	$-0.752965\pi$
$11$	0.558660	−	3.88556i	0.168442	−	1.17154i	0.882105	−	0.471052i	$-0.156126\pi$
$12$		0			0
$13$	3.85660	+	2.47849i	1.06963	+	0.687409i	0.952139	−	0.305665i	$-0.0988787\pi$
$13$	3.85660	+	2.47849i	1.06963	+	0.687409i	0.117490	+	0.993074i	$0.462515\pi$
$14$	0.546068	+	0.630196i	0.145943	+	0.168427i
$15$		0			0
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	1.11920	+	0.328626i	0.271445	+	0.0797034i	0.414622	−	0.909994i	$-0.363914\pi$
$17$	1.11920	+	0.328626i	0.271445	+	0.0797034i	−0.143177	+	0.989697i	$0.545732\pi$
$18$		0			0
$19$	3.59583	−	1.05583i	0.824940	−	0.242224i	0.158098	−	0.987423i	$-0.449464\pi$
$19$	3.59583	−	1.05583i	0.824940	−	0.242224i	0.666842	+	0.745199i	$0.267646\pi$
$20$	−0.739247	+	1.61873i	−0.165301	+	0.361958i
$21$		0			0
$22$	3.92552			0.836923
$23$	−3.39982	−	3.38249i	−0.708911	−	0.705298i
$23$	−3.39982	−	3.38249i	−0.708911	−	0.705298i
$24$		0			0
$25$	0.260897	+	1.81458i	0.0521794	+	0.362916i
$26$	−1.90441	+	4.17008i	−0.373485	+	0.817819i
$27$		0			0
$28$	−0.546068	+	0.630196i	−0.103197	+	0.119096i
$29$	1.04435	+	0.306648i	0.193931	+	0.0569432i	0.377256	−	0.926109i	$-0.376868\pi$
$29$	1.04435	+	0.306648i	0.193931	+	0.0569432i	−0.183325	+	0.983052i	$0.558686\pi$
$30$		0			0
$31$	2.92901	+	6.41364i	0.526066	+	1.15192i	0.967091	+	0.254430i	$0.0818878\pi$
$31$	2.92901	+	6.41364i	0.526066	+	1.15192i	−0.441025	+	0.897495i	$0.645385\pi$
$32$	0.654861	+	0.755750i	0.115764	+	0.133599i
$33$		0			0
$34$	−0.166002	+	1.15457i	−0.0284692	+	0.198008i
$35$	0.211181	−	1.46880i	0.0356962	−	0.248272i
$36$		0			0
$37$	−3.56741	−	4.11701i	−0.586478	−	0.676832i	0.382507	−	0.923953i	$-0.375061\pi$
$37$	−3.56741	−	4.11701i	−0.586478	−	0.676832i	−0.968985	+	0.247121i	$0.920515\pi$
$38$	1.55682	+	3.40897i	0.252550	+	0.553008i
$39$		0			0
$40$	−1.70746	−	0.501354i	−0.269972	−	0.0792711i
$41$	−0.951383	+	1.09795i	−0.148581	+	0.171472i	−0.825161	−	0.564897i	$-0.808916\pi$
$41$	−0.951383	+	1.09795i	−0.148581	+	0.171472i	0.676580	+	0.736369i	$0.263461\pi$
$42$		0			0
$43$	1.62767	−	3.56409i	0.248217	−	0.543519i	−0.743980	−	0.668202i	$-0.767064\pi$
$43$	1.62767	−	3.56409i	0.248217	−	0.543519i	0.992197	+	0.124683i	$0.0397915\pi$
$44$	0.558660	+	3.88556i	0.0842211	+	0.585771i
$45$		0			0
$46$	2.86422	−	3.84659i	0.422306	−	0.567149i
$47$	5.02025			0.732279			0.366139	−	0.930560i	$-0.380679\pi$
$47$	5.02025			0.732279			0.366139	+	0.930560i	$0.380679\pi$
$48$		0			0
$49$	−2.61905	+	5.73492i	−0.374150	+	0.819275i
$50$	−1.75898	+	0.516483i	−0.248757	+	0.0730417i
$51$		0			0
$52$	−4.39866	−	1.29156i	−0.609984	−	0.179107i
$53$	−9.43102	+	6.06095i	−1.29545	+	0.832535i	−0.992709	−	0.120538i	$-0.961538\pi$
$53$	−9.43102	+	6.06095i	−1.29545	+	0.832535i	−0.302741	+	0.953073i	$0.597902\pi$
$54$		0			0
$55$	−4.57461	−	5.27938i	−0.616840	−	0.711871i
$56$	−0.701495	−	0.450824i	−0.0937413	−	0.0602439i
$57$		0			0
$58$	−0.154901	+	1.07736i	−0.0203395	+	0.141464i
$59$	3.29551	+	2.11789i	0.429038	+	0.275726i	0.737287	−	0.675580i	$-0.236107\pi$
$59$	3.29551	+	2.11789i	0.429038	+	0.275726i	−0.308249	+	0.951306i	$0.599743\pi$
$60$		0			0
$61$	−1.74100	−	3.81226i	−0.222912	−	0.488109i	0.764825	−	0.644239i	$-0.222826\pi$
$61$	−1.74100	−	3.81226i	−0.222912	−	0.488109i	−0.987737	+	0.156129i	$0.950098\pi$
$62$	−5.93152	+	3.81196i	−0.753304	+	0.484119i
$63$		0			0
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	7.82758	−	2.29839i	0.970892	−	0.285080i
$66$		0			0
$67$	−0.292710	−	2.03585i	−0.0357603	−	0.248718i	0.964098	−	0.265546i	$-0.0855523\pi$
$67$	−0.292710	−	2.03585i	−0.0357603	−	0.248718i	−0.999858	+	0.0168281i	$0.994643\pi$
$68$	−1.16645			−0.141452
$69$		0			0
$70$	1.48390			0.177360
$71$	−1.11498	−	7.75489i	−0.132324	−	0.920336i	−0.942514	−	0.334167i	$-0.891545\pi$
$71$	−1.11498	−	7.75489i	−0.132324	−	0.920336i	0.810189	−	0.586168i	$-0.199364\pi$
$72$		0			0
$73$	−13.2507	+	3.89077i	−1.55088	+	0.455380i	−0.941364	−	0.337392i	$-0.890455\pi$
$73$	−13.2507	+	3.89077i	−1.55088	+	0.455380i	−0.609518	+	0.792772i	$0.708637\pi$
$74$	3.56741	−	4.11701i	0.414703	−	0.478592i
$75$		0			0
$76$	−3.15271	+	2.02613i	−0.361641	+	0.232412i
$77$	−1.35981	−	2.97756i	−0.154964	−	0.339325i
$78$		0			0
$79$	−8.04988	−	5.17334i	−0.905682	−	0.582047i	0.00278807	−	0.999996i	$-0.499113\pi$
$79$	−8.04988	−	5.17334i	−0.905682	−	0.582047i	−0.908470	+	0.417950i	$0.862749\pi$
$80$	0.253255	−	1.76143i	0.0283148	−	0.196933i
$81$		0			0
$82$	−1.22217	−	0.785444i	−0.134967	−	0.0867378i
$83$	−8.44359	−	9.74442i	−0.926804	−	1.06959i	−0.997399	−	0.0720836i	$-0.977035\pi$
$83$	−8.44359	−	9.74442i	−0.926804	−	1.06959i	0.0705947	−	0.997505i	$-0.477510\pi$
$84$		0			0
$85$	1.74622	−	1.12223i	0.189404	−	0.121723i
$86$	3.75945	+	1.10388i	0.405392	+	0.119034i
$87$		0			0
$88$	−3.76651	+	1.10595i	−0.401511	+	0.117894i
$89$	−0.860921	+	1.88515i	−0.0912575	+	0.199826i	−0.949757	−	0.312989i	$-0.898670\pi$
$89$	−0.860921	+	1.88515i	−0.0912575	+	0.199826i	0.858499	+	0.512814i	$0.171397\pi$
$90$		0			0
$91$	3.82275			0.400733
$92$	4.21506	+	2.28763i	0.439450	+	0.238502i
$93$		0			0
$94$	0.714456	+	4.96915i	0.0736905	+	0.512529i
$95$	2.77043	−	6.06640i	0.284240	−	0.622399i
$96$		0			0
$97$	8.21945	−	9.48575i	0.834559	−	0.963132i	−0.165173	−	0.986265i	$-0.552818\pi$
$97$	8.21945	−	9.48575i	0.834559	−	0.963132i	0.999732	+	0.0231321i	$0.00736382\pi$
$98$	−6.04928	−	1.77623i	−0.611069	−	0.179426i
$99$		0			0
$100$	−0.761555	−	1.66757i	−0.0761555	−	0.166757i
$101$	7.88974	+	9.10524i	0.785058	+	0.906006i	0.997464	−	0.0711760i	$-0.0226752\pi$
$101$	7.88974	+	9.10524i	0.785058	+	0.906006i	−0.212405	+	0.977182i	$0.568130\pi$
$102$		0			0
$103$	−1.85337	+	12.8905i	−0.182618	+	1.27014i	0.667925	+	0.744229i	$0.267183\pi$
$103$	−1.85337	+	12.8905i	−0.182618	+	1.27014i	−0.850543	+	0.525906i	$0.823726\pi$
$104$	0.652422	−	4.53769i	0.0639752	−	0.444957i
$105$		0			0
$106$	−7.34143	−	8.47246i	−0.713063	−	0.822918i
$107$	−2.01044	−	4.40225i	−0.194357	−	0.425582i	0.787214	−	0.616680i	$-0.211523\pi$
$107$	−2.01044	−	4.40225i	−0.194357	−	0.425582i	−0.981571	+	0.191098i	$0.938795\pi$
$108$		0			0
$109$	−0.967072	−	0.283958i	−0.0926287	−	0.0271982i	0.235090	−	0.971974i	$-0.424462\pi$
$109$	−0.967072	−	0.283958i	−0.0926287	−	0.0271982i	−0.327719	+	0.944775i	$0.606280\pi$
$110$	4.57461	−	5.27938i	0.436172	−	0.503369i
$111$		0			0
$112$	0.346402	−	0.758514i	0.0327319	−	0.0716728i
$113$	1.49478	+	10.3964i	0.140617	+	0.978015i	0.930900	+	0.365273i	$0.119024\pi$
$113$	1.49478	+	10.3964i	0.140617	+	0.978015i	−0.790283	+	0.612742i	$0.790067\pi$
$114$		0			0
$115$	−8.51104	+	0.630584i	−0.793659	+	0.0588023i
$116$	−1.08844			−0.101059
$117$		0			0
$118$	−1.62734	+	3.56337i	−0.149808	+	0.328035i
$119$	0.933263	−	0.274031i	0.0855521	−	0.0251204i
$120$		0			0
$121$	−4.23108	−	1.24236i	−0.384643	−	0.112941i
$122$	3.52568	−	2.26582i	0.319200	−	0.205138i
$123$		0			0
$124$	−4.61730	−	5.32865i	−0.414646	−	0.478527i
$125$	10.2297	+	6.57420i	0.914969	+	0.588015i
$126$		0			0
$127$	0.760504	−	5.28942i	0.0674838	−	0.469360i	−0.927857	−	0.372937i	$-0.878351\pi$
$127$	0.760504	−	5.28942i	0.0674838	−	0.469360i	0.995340	−	0.0964230i	$-0.0307401\pi$
$128$	−0.841254	−	0.540641i	−0.0743570	−	0.0477863i
$129$		0			0
$130$	3.38897	+	7.42081i	0.297233	+	0.650848i
$131$	−8.93068	+	5.73940i	−0.780277	+	0.501454i	−0.869126	−	0.494592i	$-0.835318\pi$
$131$	−8.93068	+	5.73940i	−0.780277	+	0.501454i	0.0888485	+	0.996045i	$0.471681\pi$
$132$		0			0
$133$	2.04646	−	2.36175i	0.177451	−	0.204789i
$134$	1.97347	−	0.579462i	0.170482	−	0.0500579i
$135$		0			0
$136$	−0.166002	−	1.15457i	−0.0142346	−	0.0990038i
$137$	−11.2545			−0.961534			−0.480767	−	0.876848i	$-0.659642\pi$
$137$	−11.2545			−0.961534			−0.480767	+	0.876848i	$0.659642\pi$
$138$		0			0
$139$	−5.20054			−0.441104			−0.220552	−	0.975375i	$-0.570786\pi$
$139$	−5.20054			−0.441104			−0.220552	+	0.975375i	$0.570786\pi$
$140$	0.211181	+	1.46880i	0.0178481	+	0.124136i
$141$		0			0
$142$	7.51727	−	2.20727i	0.630836	−	0.185230i
$143$	11.7849	−	13.6004i	0.985499	−	1.13733i
$144$		0			0
$145$	1.62944	−	1.04718i	0.135318	−	0.0869633i
$146$	−5.73694	−	12.5622i	−0.474793	−	1.03965i
$147$		0			0
$148$	4.58280	+	2.94518i	0.376704	+	0.242093i
$149$	−2.72290	+	18.9382i	−0.223068	+	1.55148i	0.503265	+	0.864132i	$0.332132\pi$
$149$	−2.72290	+	18.9382i	−0.223068	+	1.55148i	−0.726333	+	0.687343i	$0.758777\pi$
$150$		0			0
$151$	−9.77300	−	6.28073i	−0.795315	−	0.511118i	0.0787686	−	0.996893i	$-0.474901\pi$
$151$	−9.77300	−	6.28073i	−0.795315	−	0.511118i	−0.874084	+	0.485775i	$0.838538\pi$
$152$	−2.45418	−	2.83227i	−0.199060	−	0.229728i
$153$		0			0
$154$	2.75373	−	1.76972i	0.221902	−	0.142608i
$155$	12.0390	+	3.53496i	0.966992	+	0.283934i
$156$		0			0
$157$	2.69355	−	0.790896i	0.214968	−	0.0631204i	−0.172475	−	0.985014i	$-0.555176\pi$
$157$	2.69355	−	0.790896i	0.214968	−	0.0631204i	0.387443	+	0.921893i	$0.373358\pi$
$158$	3.97507	−	8.70419i	0.316239	−	0.692468i
$159$		0			0
$160$	1.77954			0.140685
$161$	−3.90986	−	0.840081i	−0.308140	−	0.0662077i
$162$		0			0
$163$	3.16344	+	22.0022i	0.247780	+	1.72334i	0.610990	+	0.791638i	$0.290771\pi$
$163$	3.16344	+	22.0022i	0.247780	+	1.72334i	−0.363211	+	0.931707i	$0.618320\pi$
$164$	0.603516	−	1.32151i	0.0471266	−	0.103193i
$165$		0			0
$166$	8.44359	−	9.74442i	0.655349	−	0.756313i
$167$	−18.4559	−	5.41915i	−1.42816	−	0.419347i	−0.525906	−	0.850543i	$-0.676274\pi$
$167$	−18.4559	−	5.41915i	−1.42816	−	0.419347i	−0.902258	+	0.431196i	$0.858092\pi$
$168$		0			0
$169$	3.33009	+	7.29189i	0.256161	+	0.560914i
$170$	1.35932	+	1.56874i	0.104255	+	0.120317i
$171$		0			0
$172$	−0.557613	+	3.87829i	−0.0425176	+	0.295717i
$173$	−3.15404	+	21.9368i	−0.239797	+	1.66783i	0.413333	+	0.910580i	$0.364364\pi$
$173$	−3.15404	+	21.9368i	−0.239797	+	1.66783i	−0.653130	+	0.757245i	$0.726545\pi$
$174$		0			0
$175$	1.00107	+	1.15530i	0.0756740	+	0.0873325i
$176$	−1.63072	−	3.57078i	−0.122920	−	0.269158i
$177$		0			0
$178$	−1.98849	−	0.583873i	−0.149043	−	0.0437631i
$179$	5.70447	−	6.58330i	0.426372	−	0.492059i	−0.501396	−	0.865218i	$-0.667180\pi$
$179$	5.70447	−	6.58330i	0.426372	−	0.492059i	0.927767	+	0.373159i	$0.121725\pi$
$180$		0			0
$181$	8.41947	−	18.4361i	0.625814	−	1.37034i	−0.285399	−	0.958409i	$-0.592126\pi$
$181$	8.41947	−	18.4361i	0.625814	−	1.37034i	0.911214	−	0.411934i	$-0.135146\pi$
$182$	0.544034	+	3.78384i	0.0403265	+	0.280477i
$183$		0			0
$184$	−1.66448	+	4.49772i	−0.122707	+	0.331576i
$185$	−9.69419			−0.712731
$186$		0			0
$187$	1.90215	−	4.16512i	0.139099	−	0.304584i
$188$	−4.81690	+	1.41437i	−0.351308	+	0.103153i
$189$		0			0
$190$	6.39892	+	1.87889i	0.464227	+	0.136309i
$191$	−18.6810	+	12.0056i	−1.35171	+	0.868692i	−0.997781	−	0.0665801i	$-0.978791\pi$
$191$	−18.6810	+	12.0056i	−1.35171	+	0.868692i	−0.353930	+	0.935272i	$0.615155\pi$
$192$		0			0
$193$	12.5085	+	14.4356i	0.900381	+	1.03910i	0.999033	+	0.0439732i	$0.0140016\pi$
$193$	12.5085	+	14.4356i	0.900381	+	1.03910i	−0.0986516	+	0.995122i	$0.531453\pi$
$194$	10.5590	+	6.78583i	0.758089	+	0.487194i
$195$		0			0
$196$	0.897247	−	6.24049i	0.0640891	−	0.445749i
$197$	19.4517	+	12.5009i	1.38588	+	0.890650i	0.999498	−	0.0316889i	$-0.0100886\pi$
$197$	19.4517	+	12.5009i	1.38588	+	0.890650i	0.386381	+	0.922339i	$0.373725\pi$
$198$		0			0
$199$	6.34744	+	13.8989i	0.449958	+	0.985270i	0.989663	+	0.143416i	$0.0458086\pi$
$199$	6.34744	+	13.8989i	0.449958	+	0.985270i	−0.539705	+	0.841854i	$0.681464\pi$
$200$	1.54222	−	0.991124i	0.109051	−	0.0700830i
$201$		0			0
$202$	−7.88974	+	9.10524i	−0.555120	+	0.640643i
$203$	0.870850	−	0.255705i	0.0611217	−	0.0179469i
$204$		0			0
$205$	0.367929	+	2.55900i	0.0256973	+	0.178729i
$206$	−13.0230			−0.907357
$207$		0			0
$208$	4.58435			0.317868
$209$	−2.09365	−	14.5617i	−0.144821	−	1.00725i
$210$		0			0
$211$	5.95651	−	1.74899i	0.410063	−	0.120405i	−0.0701934	−	0.997533i	$-0.522362\pi$
$211$	5.95651	−	1.74899i	0.410063	−	0.120405i	0.480257	+	0.877128i	$0.340543\pi$
$212$	7.34143	−	8.47246i	0.504211	−	0.581891i
$213$		0			0
$214$	4.07133	−	2.61648i	0.278310	−	0.178859i
$215$	−2.89650	−	6.34244i	−0.197539	−	0.432551i
$216$		0			0
$217$	4.94611	+	3.17867i	0.335764	+	0.215782i
$218$	0.143439	−	0.997640i	0.00971492	−	0.0675687i
$219$		0			0
$220$	5.87667	+	3.77671i	0.396205	+	0.254626i
$221$	3.50180	+	4.04129i	0.235557	+	0.271847i
$222$		0			0
$223$	13.0207	−	8.36791i	0.871932	−	0.560357i	−0.0264113	−	0.999651i	$-0.508408\pi$
$223$	13.0207	−	8.36791i	0.871932	−	0.560357i	0.898343	+	0.439295i	$0.144772\pi$
$224$	0.800092	+	0.234928i	0.0534584	+	0.0156968i
$225$		0			0
$226$	−10.0779	+	2.95914i	−0.670371	+	0.196839i
$227$	−5.43120	+	11.8927i	−0.360481	+	0.789344i	0.639311	+	0.768949i	$0.279220\pi$
$227$	−5.43120	+	11.8927i	−0.360481	+	0.789344i	−0.999792	+	0.0203955i	$0.993507\pi$
$228$		0			0
$229$	24.8420			1.64160			0.820801	−	0.571214i	$-0.193527\pi$
$229$	24.8420			1.64160			0.820801	+	0.571214i	$0.193527\pi$
$230$	−1.83541	−	8.33467i	−0.121024	−	0.549572i
$231$		0			0
$232$	−0.154901	−	1.07736i	−0.0101697	−	0.0707321i
$233$	2.12474	−	4.65254i	0.139196	−	0.304798i	−0.827177	−	0.561942i	$-0.810054\pi$
$233$	2.12474	−	4.65254i	0.139196	−	0.304798i	0.966373	+	0.257144i	$0.0827816\pi$
$234$		0			0
$235$	5.85035	−	6.75167i	0.381635	−	0.440430i
$236$	−3.75869	−	1.10365i	−0.244670	−	0.0718416i
$237$		0			0
$238$	0.404059	+	0.884765i	0.0261912	+	0.0573508i
$239$	15.9779	+	18.4395i	1.03353	+	1.19275i	0.980975	+	0.194133i	$0.0621894\pi$
$239$	15.9779	+	18.4395i	1.03353	+	1.19275i	0.0525498	+	0.998618i	$0.483265\pi$
$240$		0			0
$241$	1.29344	−	8.99605i	0.0833176	−	0.579486i	−0.904806	−	0.425824i	$-0.859984\pi$
$241$	1.29344	−	8.99605i	0.0833176	−	0.579486i	0.988123	−	0.153662i	$-0.0491067\pi$
$242$	0.627566	−	4.36482i	0.0403415	−	0.280581i
$243$		0			0
$244$	2.74451	+	3.16734i	0.175699	+	0.202768i
$245$	4.66071	+	10.2055i	0.297762	+	0.652007i
$246$		0			0
$247$	16.4846	+	4.84030i	1.04889	+	0.307981i
$248$	4.61730	−	5.32865i	0.293199	−	0.338370i
$249$		0			0
$250$	−5.05145	+	11.0611i	−0.319482	+	0.699568i
$251$	0.361100	+	2.51151i	0.0227925	+	0.158525i	0.998039	−	0.0625953i	$-0.0199377\pi$
$251$	0.361100	+	2.51151i	0.0227925	+	0.158525i	−0.975247	+	0.221120i	$0.929029\pi$
$252$		0			0
$253$	−15.0422	+	11.3206i	−0.945696	+	0.711717i
$254$	5.34381			0.335300
$255$		0			0
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−27.9783	+	8.21516i	−1.74524	+	0.512447i	−0.989762	−	0.142731i	$-0.954412\pi$
$257$	−27.9783	+	8.21516i	−1.74524	+	0.512447i	−0.755474	+	0.655178i	$0.772593\pi$
$258$		0			0
$259$	−4.35856	−	1.27979i	−0.270828	−	0.0795223i
$260$	−6.86298	+	4.41057i	−0.425624	+	0.273532i
$261$		0			0
$262$	−6.95195	−	8.02298i	−0.429493	−	0.495661i
$263$	3.26594	+	2.09889i	0.201387	+	0.129423i	0.637447	−	0.770494i	$-0.279990\pi$
$263$	3.26594	+	2.09889i	0.201387	+	0.129423i	−0.436061	+	0.899917i	$0.643627\pi$
$264$		0			0
$265$	−2.83916	+	19.7468i	−0.174408	+	1.21303i
$266$	2.62895	+	1.68952i	0.161191	+	0.103591i
$267$		0			0
$268$	0.854418	+	1.87091i	0.0521919	+	0.114284i
$269$	−2.98920	+	1.92104i	−0.182255	+	0.117128i	−0.628587	−	0.777739i	$-0.716366\pi$
$269$	−2.98920	+	1.92104i	−0.182255	+	0.117128i	0.446332	+	0.894867i	$0.352730\pi$
$270$		0			0
$271$	14.5110	−	16.7466i	0.881483	−	1.01729i	−0.118222	−	0.992987i	$-0.537719\pi$
$271$	14.5110	−	16.7466i	0.881483	−	1.01729i	0.999705	−	0.0242981i	$-0.00773507\pi$
$272$	1.11920	−	0.328626i	0.0678612	−	0.0199259i
$273$		0			0
$274$	−1.60168	−	11.1399i	−0.0967609	−	0.672987i
$275$	7.19641			0.433960
$276$		0			0
$277$	−13.4979			−0.811008			−0.405504	−	0.914093i	$-0.632904\pi$
$277$	−13.4979			−0.811008			−0.405504	+	0.914093i	$0.632904\pi$
$278$	−0.740114	−	5.14761i	−0.0443891	−	0.308733i
$279$		0			0
$280$	−1.42379	+	0.418064i	−0.0850880	+	0.0249841i
$281$	20.1354	−	23.2375i	1.20118	−	1.38624i	0.299350	−	0.954143i	$-0.403230\pi$
$281$	20.1354	−	23.2375i	1.20118	−	1.38624i	0.901830	−	0.432092i	$-0.142224\pi$
$282$		0			0
$283$	−17.2757	+	11.1024i	−1.02693	+	0.659969i	−0.941721	−	0.336394i	$-0.890793\pi$
$283$	−17.2757	+	11.1024i	−1.02693	+	0.659969i	−0.0852108	+	0.996363i	$0.527156\pi$
$284$	3.25462	+	7.12663i	0.193126	+	0.422888i
$285$		0			0
$286$	15.1392	+	9.72936i	0.895198	+	0.575309i
$287$	−0.172407	+	1.19912i	−0.0101769	+	0.0707816i
$288$		0			0
$289$	−13.1567	−	8.45530i	−0.773924	−	0.497371i
$290$	1.26841	+	1.46382i	0.0744837	+	0.0859588i
$291$		0			0
$292$	11.6178	−	7.46633i	0.679883	−	0.436934i
$293$	−7.35485	−	2.15958i	−0.429675	−	0.126164i	0.0597420	−	0.998214i	$-0.480972\pi$
$293$	−7.35485	−	2.15958i	−0.429675	−	0.126164i	−0.489417	+	0.872050i	$0.662790\pi$
$294$		0			0
$295$	6.68874	−	1.96399i	0.389434	−	0.114348i
$296$	−2.26301	+	4.95529i	−0.131535	+	0.288021i
$297$		0			0
$298$	−19.1329			−1.10834
$299$	−4.72829	−	21.4713i	−0.273444	−	1.24172i
$300$		0			0
$301$	−0.464977	−	3.23398i	−0.0268008	−	0.186404i
$302$	4.82595	−	10.5674i	0.277702	−	0.608084i
$303$		0			0
$304$	2.45418	−	2.83227i	0.140757	−	0.162442i
$305$	−7.15593	−	2.10117i	−0.409747	−	0.120313i
$306$		0			0
$307$	0.333786	+	0.730889i	0.0190502	+	0.0417141i	0.918918	−	0.394449i	$-0.129064\pi$
$307$	0.333786	+	0.730889i	0.0190502	+	0.0417141i	−0.899868	+	0.436163i	$0.856337\pi$
$308$	2.14360	+	2.47385i	0.122143	+	0.140961i
$309$		0			0
$310$	−1.78565	+	12.4195i	−0.101418	+	0.705380i
$311$	3.74102	−	26.0194i	0.212134	−	1.47542i	−0.553879	−	0.832597i	$-0.686853\pi$
$311$	3.74102	−	26.0194i	0.212134	−	1.47542i	0.766013	−	0.642826i	$-0.222238\pi$
$312$		0			0
$313$	−10.7210	−	12.3727i	−0.605989	−	0.699348i	0.366995	−	0.930223i	$-0.380387\pi$
$313$	−10.7210	−	12.3727i	−0.605989	−	0.699348i	−0.972984	+	0.230875i	$0.925841\pi$
$314$	1.16618	+	2.55357i	0.0658112	+	0.144106i
$315$		0			0
$316$	9.18130	+	2.69587i	0.516489	+	0.151655i
$317$	8.39948	−	9.69352i	0.471762	−	0.544442i	−0.469139	−	0.883124i	$-0.655436\pi$
$317$	8.39948	−	9.69352i	0.471762	−	0.544442i	0.940901	+	0.338682i	$0.109981\pi$
$318$		0			0
$319$	1.77494	−	3.88657i	0.0993774	−	0.217606i
$320$	0.253255	+	1.76143i	0.0141574	+	0.0984667i
$321$		0			0
$322$	0.275099	−	3.98962i	0.0153307	−	0.222333i
$323$	4.37141			0.243232
$324$		0			0
$325$	−3.49124	+	7.64474i	−0.193659	+	0.424054i
$326$	−21.3280	+	6.26248i	−1.18125	+	0.346847i
$327$		0			0
$328$	1.39395	+	0.409301i	0.0769682	+	0.0225999i
$329$	3.52168	−	2.26325i	0.194157	−	0.124777i
$330$		0			0
$331$	−8.94893	−	10.3276i	−0.491878	−	0.567657i	0.454489	−	0.890753i	$-0.349822\pi$
$331$	−8.94893	−	10.3276i	−0.491878	−	0.567657i	−0.946366	+	0.323095i	$0.895277\pi$
$332$	10.8469	+	6.97087i	0.595300	+	0.382576i
$333$		0			0
$334$	2.73744	−	19.0393i	0.149786	−	1.04179i
$335$	−3.07909	−	1.97881i	−0.168229	−	0.108114i
$336$		0			0
$337$	−4.28057	−	9.37315i	−0.233178	−	0.510588i	0.756484	−	0.654013i	$-0.226916\pi$
$337$	−4.28057	−	9.37315i	−0.233178	−	0.510588i	−0.989661	+	0.143425i	$0.954188\pi$
$338$	−6.74374	+	4.33394i	−0.366811	+	0.235735i
$339$		0			0
$340$	−1.35932	+	1.56874i	−0.0737194	+	0.0850767i
$341$	26.5569	−	7.79782i	1.43814	−	0.422276i
$342$		0			0
$343$	1.57889	+	10.9814i	0.0852521	+	0.592941i
$344$	−3.91817			−0.211253
$345$		0			0
$346$	−22.1624			−1.19146
$347$	−4.11275	−	28.6048i	−0.220784	−	1.53559i	−0.735084	−	0.677976i	$-0.762857\pi$
$347$	−4.11275	−	28.6048i	−0.220784	−	1.53559i	0.514300	−	0.857610i	$-0.328052\pi$
$348$		0			0
$349$	−11.9686	+	3.51429i	−0.640663	+	0.188116i	−0.585899	−	0.810384i	$-0.699259\pi$
$349$	−11.9686	+	3.51429i	−0.640663	+	0.188116i	−0.0547635	+	0.998499i	$0.517440\pi$
$350$	−1.00107	+	1.15530i	−0.0535096	+	0.0617534i
$351$		0			0
$352$	3.30236	−	2.12230i	0.176016	−	0.113119i
$353$	−15.3173	−	33.5402i	−0.815256	−	1.78516i	−0.582926	−	0.812526i	$-0.698092\pi$
$353$	−15.3173	−	33.5402i	−0.815256	−	1.78516i	−0.232331	−	0.972637i	$-0.574635\pi$
$354$		0			0
$355$	−11.7288	−	7.53763i	−0.622499	−	0.400056i
$356$	0.294938	−	2.05134i	0.0156317	−	0.108721i
$357$		0			0
$358$	7.32813	+	4.70950i	0.387303	+	0.248905i
$359$	4.05875	+	4.68405i	0.214213	+	0.247215i	0.852679	−	0.522435i	$-0.174976\pi$
$359$	4.05875	+	4.68405i	0.214213	+	0.247215i	−0.638466	+	0.769650i	$0.720431\pi$
$360$		0			0
$361$	−4.16860	+	2.67900i	−0.219400	+	0.141000i
$362$	19.4466	+	5.71005i	1.02209	+	0.300113i
$363$		0			0
$364$	−3.66790	+	1.07699i	−0.192250	+	0.0564498i
$365$	−10.2091	+	22.3549i	−0.534370	+	1.17011i
$366$		0			0
$367$	−9.47250			−0.494460			−0.247230	−	0.968957i	$-0.579520\pi$
$367$	−9.47250			−0.494460			−0.247230	+	0.968957i	$0.579520\pi$
$368$	−4.68882	−	1.00745i	−0.244422	−	0.0525170i
$369$		0			0
$370$	−1.37963	−	9.59551i	−0.0717234	−	0.498847i
$371$	−3.88340	+	8.50345i	−0.201616	+	0.441477i
$372$		0			0
$373$	−20.1607	+	23.2667i	−1.04388	+	1.20470i	−0.0655089	+	0.997852i	$0.520867\pi$
$373$	−20.1607	+	23.2667i	−1.04388	+	1.20470i	−0.978372	+	0.206851i	$0.933678\pi$
$374$	4.39343	+	1.29003i	0.227179	+	0.0667057i
$375$		0			0
$376$	−2.08549	−	4.56658i	−0.107551	−	0.235503i
$377$	3.26761	+	3.77103i	0.168291	+	0.194218i
$378$		0			0
$379$	3.97384	−	27.6387i	0.204123	−	1.41970i	−0.587762	−	0.809034i	$-0.699991\pi$
$379$	3.97384	−	27.6387i	0.204123	−	1.41970i	0.791885	−	0.610670i	$-0.209100\pi$
$380$	−0.949107	+	6.60119i	−0.0486882	+	0.338634i
$381$		0			0
$382$	−14.5419	−	16.7823i	−0.744031	−	0.858657i
$383$	1.62858	+	3.56610i	0.0832167	+	0.182219i	0.946666	−	0.322216i	$-0.104428\pi$
$383$	1.62858	+	3.56610i	0.0832167	+	0.182219i	−0.863449	+	0.504436i	$0.831701\pi$
$384$		0			0
$385$	−5.58913	−	1.64112i	−0.284849	−	0.0836391i
$386$	−12.5085	+	14.4356i	−0.636666	+	0.734751i
$387$		0			0
$388$	−5.21406	+	11.4172i	−0.264704	+	0.579621i
$389$	4.96240	+	34.5143i	0.251604	+	1.74994i	0.588588	+	0.808433i	$0.299684\pi$
$389$	4.96240	+	34.5143i	0.251604	+	1.74994i	−0.336984	+	0.941510i	$0.609407\pi$
$390$		0			0
$391$	−2.69349	−	4.90294i	−0.136216	−	0.247952i
$392$	6.30466			0.318434
$393$		0			0
$394$	−9.60536	+	21.0328i	−0.483911	+	1.05962i
$395$	−16.3385	+	4.79741i	−0.822079	+	0.241384i
$396$		0			0
$397$	1.93527	+	0.568247i	0.0971285	+	0.0285195i	0.329936	−	0.944003i	$-0.392973\pi$
$397$	1.93527	+	0.568247i	0.0971285	+	0.0285195i	−0.232807	+	0.972523i	$0.574791\pi$
$398$	−12.8541	+	8.26086i	−0.644320	+	0.414079i
$399$		0			0
$400$	1.20052	+	1.38547i	0.0600258	+	0.0692735i
$401$	18.0520	+	11.6013i	0.901472	+	0.579341i	0.907226	−	0.420643i	$-0.138195\pi$
$401$	18.0520	+	11.6013i	0.901472	+	0.579341i	−0.00575439	+	0.999983i	$0.501832\pi$
$402$		0			0
$403$	−4.60010	+	31.9944i	−0.229147	+	1.59376i
$404$	−10.1354	−	6.51362i	−0.504255	−	0.324065i
$405$		0			0
$406$	0.377037	+	0.825595i	0.0187120	+	0.0409736i
$407$	−17.9899	+	11.5614i	−0.891724	+	0.573076i
$408$		0			0
$409$	10.4050	−	12.0080i	0.514495	−	0.593759i	−0.437749	−	0.899097i	$-0.644224\pi$
$409$	10.4050	−	12.0080i	0.514495	−	0.593759i	0.952244	+	0.305338i	$0.0987695\pi$
$410$	−2.48059	+	0.728368i	−0.122508	+	0.0359715i
$411$		0			0
$412$	−1.85337	−	12.8905i	−0.0913089	−	0.635068i
$413$	3.26658			0.160738
$414$		0			0
$415$	−22.9449			−1.12632
$416$	0.652422	+	4.53769i	0.0319876	+	0.222479i
$417$		0			0
$418$	14.1155	−	4.14469i	0.690412	−	0.202723i
$419$	18.2237	−	21.0312i	0.890284	−	1.02744i	−0.109158	−	0.994024i	$-0.534815\pi$
$419$	18.2237	−	21.0312i	0.890284	−	1.02744i	0.999441	−	0.0334179i	$-0.0106392\pi$
$420$		0			0
$421$	10.6927	−	6.87180i	0.521132	−	0.334911i	−0.253488	−	0.967339i	$-0.581578\pi$
$421$	10.6927	−	6.87180i	0.521132	−	0.334911i	0.774620	+	0.632428i	$0.217941\pi$
$422$	2.57889	+	5.64698i	0.125538	+	0.274891i
$423$		0			0
$424$	9.43102	+	6.06095i	0.458011	+	0.294346i
$425$	−0.304322	+	2.11661i	−0.0147618	+	0.102671i
$426$		0			0
$427$	−2.93996	−	1.88940i	−0.142275	−	0.0914343i
$428$	3.16926	+	3.65753i	0.153192	+	0.176793i
$429$		0			0
$430$	5.86567	−	3.76964i	0.282868	−	0.181788i
$431$	35.1767	+	10.3288i	1.69440	+	0.497521i	0.979456	−	0.201659i	$-0.0646332\pi$
$431$	35.1767	+	10.3288i	1.69440	+	0.497521i	0.714946	+	0.699180i	$0.246451\pi$
$432$		0			0
$433$	6.66431	−	1.95682i	0.320266	−	0.0940387i	−0.117648	−	0.993055i	$-0.537535\pi$
$433$	6.66431	−	1.95682i	0.320266	−	0.0940387i	0.437914	+	0.899017i	$0.355717\pi$
$434$	−2.44241	+	5.34814i	−0.117240	+	0.256719i
$435$		0			0
$436$	1.00790			0.0482696
$437$	−15.7965	−	8.57322i	−0.755650	−	0.410113i
$438$		0			0
$439$	−3.18594	−	22.1587i	−0.152057	−	1.05758i	−0.912765	−	0.408484i	$-0.866057\pi$
$439$	−3.18594	−	22.1587i	−0.152057	−	1.05758i	0.760709	−	0.649094i	$-0.224852\pi$
$440$	−2.90193	+	6.35434i	−0.138344	+	0.302931i
$441$		0			0
$442$	−3.50180	+	4.04129i	−0.166564	+	0.192225i
$443$	−27.8322	−	8.17227i	−1.32235	−	0.388276i	−0.457008	−	0.889462i	$-0.651079\pi$
$443$	−27.8322	−	8.17227i	−1.32235	−	0.388276i	−0.865339	+	0.501186i	$0.832897\pi$
$444$		0			0
$445$	1.53204	+	3.35471i	0.0726258	+	0.159028i
$446$	10.1358	+	11.6973i	0.479943	+	0.553884i
$447$		0			0
$448$	−0.118672	+	0.825382i	−0.00560672	+	0.0389956i
$449$	5.26744	−	36.6359i	0.248586	−	1.72895i	−0.357813	−	0.933793i	$-0.616477\pi$
$449$	5.26744	−	36.6359i	0.248586	−	1.72895i	0.606399	−	0.795161i	$-0.292614\pi$
$450$		0			0
$451$	3.73467	+	4.31004i	0.175859	+	0.202952i
$452$	−4.36325	−	9.55418i	−0.205230	−	0.449391i
$453$		0			0
$454$	−12.5446	−	3.68341i	−0.588745	−	0.172871i
$455$	4.45485	−	5.14117i	0.208846	−	0.241022i
$456$		0			0
$457$	−2.65280	+	5.80881i	−0.124093	+	0.271725i	−0.961475	−	0.274893i	$-0.911358\pi$
$457$	−2.65280	+	5.80881i	−0.124093	+	0.271725i	0.837382	+	0.546618i	$0.184085\pi$
$458$	3.53538	+	24.5891i	0.165197	+	1.14897i
$459$		0			0
$460$	7.98863	−	3.00288i	0.372472	−	0.140010i
$461$	−6.03086			−0.280885			−0.140443	−	0.990089i	$-0.544853\pi$
$461$	−6.03086			−0.280885			−0.140443	+	0.990089i	$0.544853\pi$
$462$		0			0
$463$	0.444225	−	0.972717i	0.0206449	−	0.0452060i	−0.899029	−	0.437890i	$-0.855726\pi$
$463$	0.444225	−	0.972717i	0.0206449	−	0.0452060i	0.919674	+	0.392684i	$0.128453\pi$
$464$	1.04435	−	0.306648i	0.0484827	−	0.0142358i
$465$		0			0
$466$	4.90756	+	1.44099i	0.227338	+	0.0667526i
$467$	0.797300	−	0.512394i	0.0368947	−	0.0237108i	−0.522063	−	0.852907i	$-0.674838\pi$
$467$	0.797300	−	0.512394i	0.0368947	−	0.0237108i	0.558958	+	0.829196i	$0.311201\pi$
$468$		0			0
$469$	−1.12314	−	1.29618i	−0.0518619	−	0.0598518i
$470$	7.51554	+	4.82994i	0.346666	+	0.222789i
$471$		0			0
$472$	0.557501	−	3.87750i	0.0256610	−	0.178476i
$473$	−12.9392	−	8.31551i	−0.594944	−	0.382348i
$474$		0			0
$475$	2.85403	+	6.24946i	0.130952	+	0.286745i
$476$	−0.818256	+	0.525861i	−0.0375047	+	0.0241028i
$477$		0			0
$478$	−15.9779	+	18.4395i	−0.730813	+	0.843403i
$479$	−16.8359	+	4.94346i	−0.769250	+	0.225872i	−0.642731	−	0.766092i	$-0.722199\pi$
$479$	−16.8359	+	4.94346i	−0.769250	+	0.225872i	−0.126519	+	0.991964i	$0.540381\pi$
$480$		0			0
$481$	−3.55412	−	24.7194i	−0.162054	−	1.12711i
$482$	9.08856			0.413972
$483$		0			0
$484$	4.40970			0.200441
$485$	−3.17872	−	22.1085i	−0.144338	−	1.00389i
$486$		0			0
$487$	−31.2604	+	9.17889i	−1.41654	+	0.415935i	−0.898332	−	0.439317i	$-0.855221\pi$
$487$	−31.2604	+	9.17889i	−1.41654	+	0.415935i	−0.518213	+	0.855252i	$0.673402\pi$
$488$	−2.74451	+	3.16734i	−0.124238	+	0.143379i
$489$		0			0
$490$	−9.43836	+	6.06566i	−0.426382	+	0.274019i
$491$	8.43219	+	18.4639i	0.380540	+	0.833265i	0.998878	+	0.0473535i	$0.0150787\pi$
$491$	8.43219	+	18.4639i	0.380540	+	0.833265i	−0.618339	+	0.785912i	$0.712194\pi$
$492$		0			0
$493$	1.06806	+	0.686399i	0.0481029	+	0.0309139i
$494$	−2.44504	+	17.0056i	−0.110008	+	0.765119i
$495$		0			0
$496$	5.93152	+	3.81196i	0.266333	+	0.171162i
$497$	−4.27824	−	4.93735i	−0.191905	−	0.221471i
$498$		0			0
$499$	−6.59030	+	4.23533i	−0.295022	+	0.189599i	−0.679776	−	0.733420i	$-0.737923\pi$
$499$	−6.59030	+	4.23533i	−0.295022	+	0.189599i	0.384753	+	0.923019i	$0.374287\pi$
$500$	−11.6675	−	3.42587i	−0.521784	−	0.153210i
$501$		0			0
$502$	−2.43455	+	0.714850i	−0.108659	+	0.0319053i
$503$	−5.32610	+	11.6625i	−0.237479	+	0.520007i	−0.990421	−	0.138080i	$-0.955907\pi$
$503$	−5.32610	+	11.6625i	−0.237479	+	0.520007i	0.752942	+	0.658087i	$0.228634\pi$
$504$		0			0
$505$	21.4398			0.954060
$506$	−13.3461	−	13.2780i	−0.593304	−	0.590280i
$507$		0			0
$508$	0.760504	+	5.28942i	0.0337419	+	0.234680i
$509$	2.93766	−	6.43258i	0.130209	−	0.285119i	−0.833287	−	0.552841i	$-0.813544\pi$
$509$	2.93766	−	6.43258i	0.130209	−	0.285119i	0.963496	+	0.267722i	$0.0862709\pi$
$510$		0			0
$511$	−7.54128	+	8.70311i	−0.333607	+	0.385003i
$512$	0.959493	+	0.281733i	0.0424040	+	0.0124509i
$513$		0			0
$514$	−12.1133	−	26.5243i	−0.534293	−	1.16994i
$515$	15.1764	+	17.5145i	0.668751	+	0.771780i
$516$		0			0
$517$	2.80461	−	19.5065i	0.123347	−	0.857895i
$518$	0.646475	−	4.49633i	0.0284045	−	0.197558i
$519$		0			0
$520$	−5.34238	−	6.16544i	−0.234279	−	0.270372i
$521$	−10.9841	−	24.0519i	−0.481223	−	1.05373i	−0.982125	−	0.188227i	$-0.939726\pi$
$521$	−10.9841	−	24.0519i	−0.481223	−	1.05373i	0.500903	−	0.865504i	$-0.333001\pi$
$522$		0			0
$523$	28.5300	+	8.37715i	1.24753	+	0.366307i	0.837839	−	0.545918i	$-0.183819\pi$
$523$	28.5300	+	8.37715i	1.24753	+	0.366307i	0.409689	+	0.912225i	$0.365637\pi$
$524$	6.95195	−	8.02298i	0.303697	−	0.350485i
$525$		0			0
$526$	−1.61274	+	3.53140i	−0.0703187	+	0.153976i
$527$	1.17045	+	8.14068i	0.0509857	+	0.354613i
$528$		0			0
$529$	0.117537	+	22.9997i	0.00511032	+	0.999987i
$530$	−19.9498			−0.866565
$531$		0			0
$532$	−1.29819	+	2.84263i	−0.0562836	+	0.123244i
$533$	−6.39037	+	1.87638i	−0.276798	+	0.0812752i
$534$		0			0
$535$	−8.26340	−	2.42635i	−0.357258	−	0.104900i
$536$	−1.73027	+	1.11198i	−0.0747365	+	0.0480302i
$537$		0			0
$538$	−2.32690	−	2.68538i	−0.100320	−	0.115775i
$539$	20.8202	+	13.3804i	0.896791	+	0.576333i
$540$		0			0
$541$	0.957249	−	6.65781i	0.0411553	−	0.286242i	−0.958842	−	0.283940i	$-0.908358\pi$
$541$	0.957249	−	6.65781i	0.0411553	−	0.286242i	0.999997	−	0.00230152i	$-0.000732599\pi$
$542$	18.6413	+	11.9800i	0.800713	+	0.514587i
$543$		0			0
$544$	0.484559	+	1.06104i	0.0207753	+	0.0454915i
$545$	−1.50887	+	0.969692i	−0.0646329	+	0.0415370i
$546$		0			0
$547$	28.2543	−	32.6073i	1.20807	−	1.39419i	0.312111	−	0.950045i	$-0.398964\pi$
$547$	28.2543	−	32.6073i	1.20807	−	1.39419i	0.895957	−	0.444140i	$-0.146491\pi$
$548$	10.7986	−	3.17075i	0.461292	−	0.135448i
$549$		0			0
$550$	1.02416	+	7.12316i	0.0436702	+	0.303733i
$551$	4.07907			0.173774
$552$		0			0
$553$	−7.97922			−0.339311
$554$	−1.92095	−	13.3605i	−0.0816132	−	0.567632i
$555$		0			0
$556$	4.98988	−	1.46516i	0.211618	−	0.0621367i
$557$	13.2344	−	15.2733i	0.560759	−	0.647150i	−0.402597	−	0.915377i	$-0.631892\pi$
$557$	13.2344	−	15.2733i	0.560759	−	0.647150i	0.963356	+	0.268227i	$0.0864378\pi$
$558$		0			0
$559$	15.1108	−	9.71113i	0.639120	−	0.410737i
$560$	−0.616436	−	1.34981i	−0.0260492	−	0.0570397i
$561$		0			0
$562$	25.8666	+	16.6234i	1.09112	+	0.701218i
$563$	−0.474192	+	3.29807i	−0.0199848	+	0.138997i	−0.997371	−	0.0724650i	$-0.976913\pi$
$563$	−0.474192	+	3.29807i	−0.0199848	+	0.138997i	0.977386	+	0.211462i	$0.0678225\pi$
$564$		0			0
$565$	15.7240	+	10.1052i	0.661513	+	0.425128i
$566$	−13.4480	−	15.5198i	−0.565261	−	0.652346i
$567$		0			0
$568$	−6.59091	+	4.23572i	−0.276548	+	0.177727i
$569$	−10.5390	−	3.09452i	−0.441817	−	0.129729i	0.0532556	−	0.998581i	$-0.483040\pi$
$569$	−10.5390	−	3.09452i	−0.441817	−	0.129729i	−0.495072	+	0.868852i	$0.664858\pi$
$570$		0			0
$571$	17.0769	−	5.01424i	0.714648	−	0.209839i	0.0958566	−	0.995395i	$-0.469441\pi$
$571$	17.0769	−	5.01424i	0.714648	−	0.209839i	0.618791	+	0.785556i	$0.287623\pi$
$572$	−7.47580	+	16.3697i	−0.312579	+	0.684452i
$573$		0			0
$574$	−1.21145			−0.0505648
$575$	5.25079	−	7.05172i	0.218973	−	0.294077i
$576$		0			0
$577$	0.910122	+	6.33004i	0.0378889	+	0.263523i	0.999957	−	0.00928687i	$-0.00295615\pi$
$577$	0.910122	+	6.33004i	0.0378889	+	0.263523i	−0.962068	+	0.272810i	$0.912047\pi$
$578$	6.49684	−	14.2261i	0.270233	−	0.591728i
$579$		0			0
$580$	−1.26841	+	1.46382i	−0.0526679	+	0.0607820i
$581$	−10.3161	−	3.02909i	−0.427986	−	0.125668i
$582$		0			0
$583$	18.2815	+	40.0308i	0.757141	+	1.65791i
$584$	9.04373	+	10.4370i	0.374232	+	0.431887i
$585$		0			0
$586$	1.09089	−	7.58733i	0.0450644	−	0.313430i
$587$	−1.29685	+	9.01976i	−0.0535265	+	0.372285i	0.945398	+	0.325918i	$0.105673\pi$
$587$	−1.29685	+	9.01976i	−0.0535265	+	0.372285i	−0.998924	+	0.0463669i	$0.985236\pi$
$588$		0			0
$589$	17.3040	+	19.9698i	0.712997	+	0.822843i
$590$	2.89591	+	6.34116i	0.119223	+	0.261061i
$591$		0			0
$592$	−5.22692	−	1.53476i	−0.214825	−	0.0630783i
$593$	24.3462	−	28.0970i	0.999779	−	1.15381i	0.0116881	−	0.999932i	$-0.496279\pi$
$593$	24.3462	−	28.0970i	0.999779	−	1.15381i	0.988090	−	0.153874i	$-0.0491751\pi$
$594$		0			0
$595$	0.719039	−	1.57447i	0.0294777	−	0.0645472i
$596$	−2.72290	−	18.9382i	−0.111534	−	0.775738i
$597$		0			0
$598$	20.5799	−	7.73586i	0.841574	−	0.316343i
$599$	−7.27761			−0.297355			−0.148677	−	0.988886i	$-0.547502\pi$
$599$	−7.27761			−0.297355			−0.148677	+	0.988886i	$0.547502\pi$
$600$		0			0
$601$	14.4914	−	31.7316i	0.591115	−	1.29436i	−0.343652	−	0.939097i	$-0.611664\pi$
$601$	14.4914	−	31.7316i	0.591115	−	1.29436i	0.934766	−	0.355263i	$-0.115609\pi$
$602$	3.13489	−	0.920487i	0.127769	−	0.0375163i
$603$		0			0
$604$	11.1466	+	3.27294i	0.453549	+	0.133174i
$605$	−6.60152	+	4.24254i	−0.268390	+	0.172484i
$606$		0			0
$607$	20.2006	+	23.3127i	0.819916	+	0.946234i	0.999295	−	0.0375461i	$-0.0119541\pi$
$607$	20.2006	+	23.3127i	0.819916	+	0.946234i	−0.179378	+	0.983780i	$0.557409\pi$
$608$	3.15271	+	2.02613i	0.127859	+	0.0821702i
$609$		0			0
$610$	1.06139	−	7.38212i	0.0429744	−	0.298893i
$611$	19.3611	+	12.4426i	0.783267	+	0.503375i
$612$		0			0
$613$	5.05572	+	11.0705i	0.204199	+	0.447132i	0.983830	−	0.179107i	$-0.0573207\pi$
$613$	5.05572	+	11.0705i	0.204199	+	0.447132i	−0.779631	+	0.626239i	$0.784593\pi$
$614$	−0.675947	+	0.434405i	−0.0272790	+	0.0175312i
$615$		0			0
$616$	−2.14360	+	2.47385i	−0.0863681	+	0.0996742i
$617$	3.94735	−	1.15905i	0.158914	−	0.0466615i	−0.201308	−	0.979528i	$-0.564519\pi$
$617$	3.94735	−	1.15905i	0.158914	−	0.0466615i	0.360222	+	0.932867i	$0.382701\pi$
$618$		0			0
$619$	4.02711	+	28.0091i	0.161863	+	1.12578i	0.895118	+	0.445829i	$0.147091\pi$
$619$	4.02711	+	28.0091i	0.161863	+	1.12578i	−0.733255	+	0.679954i	$0.762000\pi$
$620$	−12.5472			−0.503908
$621$		0			0
$622$	26.2869			1.05401
$623$	0.245940	+	1.71055i	0.00985338	+	0.0685318i
$624$		0			0
$625$	11.9678	−	3.51406i	0.478712	−	0.140562i
$626$	10.7210	−	12.3727i	0.428499	−	0.494514i
$627$		0			0
$628$	−2.36162	+	1.51772i	−0.0942388	+	0.0605636i
$629$	−2.63967	−	5.78008i	−0.105251	−	0.230467i
$630$		0			0
$631$	−15.0210	−	9.65341i	−0.597976	−	0.384296i	0.206355	−	0.978477i	$-0.433840\pi$
$631$	−15.0210	−	9.65341i	−0.597976	−	0.384296i	−0.804331	+	0.594181i	$0.797476\pi$
$632$	−1.36180	+	9.47151i	−0.0541694	+	0.376757i
$633$		0			0
$634$	10.7902	+	6.93445i	0.428534	+	0.275402i
$635$	−6.22741	−	7.18682i	−0.247127	−	0.285200i
$636$		0			0
$637$	−24.3146	+	15.6260i	−0.963379	+	0.619126i
$638$	4.09961	+	1.20375i	0.162305	+	0.0476571i
$639$		0			0
$640$	−1.70746	+	0.501354i	−0.0674931	+	0.0198178i
$641$	17.0223	−	37.2737i	0.672342	−	1.47222i	−0.198216	−	0.980158i	$-0.563515\pi$
$641$	17.0223	−	37.2737i	0.672342	−	1.47222i	0.870558	−	0.492065i	$-0.163758\pi$
$642$		0			0
$643$	−22.3907			−0.883003			−0.441501	−	0.897261i	$-0.645554\pi$
$643$	−22.3907			−0.883003			−0.441501	+	0.897261i	$0.645554\pi$
$644$	3.98816	−	0.295484i	0.157156	−	0.0116437i
$645$		0			0
$646$	0.622117	+	4.32692i	0.0244769	+	0.170240i
$647$	−2.74606	+	6.01304i	−0.107959	+	0.236397i	−0.955899	−	0.293695i	$-0.905115\pi$
$647$	−2.74606	+	6.01304i	−0.107959	+	0.236397i	0.847940	+	0.530091i	$0.177842\pi$
$648$		0			0
$649$	10.0703	−	11.6217i	0.395293	−	0.456192i
$650$	−8.06379	−	2.36774i	−0.316288	−	0.0928704i
$651$		0			0
$652$	−9.23403	−	20.2197i	−0.361633	−	0.791865i
$653$	26.6892	+	30.8010i	1.04443	+	1.20534i	0.978229	+	0.207530i	$0.0665425\pi$
$653$	26.6892	+	30.8010i	1.04443	+	1.20534i	0.0662013	+	0.997806i	$0.478912\pi$
$654$		0			0
$655$	−2.68853	+	18.6992i	−0.105050	+	0.730637i
$656$	−0.206755	+	1.43801i	−0.00807243	+	0.0561450i
$657$		0			0
$658$	2.74140	+	3.16374i	0.106871	+	0.123336i
$659$	11.3551	+	24.8643i	0.442333	+	0.968574i	0.991164	+	0.132641i	$0.0423457\pi$
$659$	11.3551	+	24.8643i	0.442333	+	0.968574i	−0.548831	+	0.835933i	$0.684927\pi$
$660$		0			0
$661$	−9.64856	−	2.83307i	−0.375285	−	0.110194i	0.0886498	−	0.996063i	$-0.471745\pi$
$661$	−9.64856	−	2.83307i	−0.375285	−	0.110194i	−0.463935	+	0.885869i	$0.653563\pi$
$662$	8.94893	−	10.3276i	0.347810	−	0.401394i
$663$		0			0
$664$	−5.35624	+	11.7285i	−0.207862	+	0.455155i
$665$	−0.791431	−	5.50453i	−0.0306904	−	0.213456i
$666$		0			0
$667$	−2.51336	−	4.57505i	−0.0973177	−	0.177146i
$668$	19.2351			0.744228
$669$		0			0
$670$	1.52047	−	3.32937i	0.0587409	−	0.128625i
$671$	−15.7854	+	4.63501i	−0.609388	+	0.178933i
$672$		0			0
$673$	16.8156	+	4.93750i	0.648193	+	0.190327i	0.589270	−	0.807936i	$-0.299415\pi$
$673$	16.8156	+	4.93750i	0.648193	+	0.190327i	0.0589225	+	0.998263i	$0.481234\pi$
$674$	8.66855	−	5.57094i	0.333900	−	0.214585i
$675$		0			0
$676$	−5.24956	−	6.05832i	−0.201906	−	0.233012i
$677$	7.76677	+	4.99140i	0.298501	+	0.191835i	0.681315	−	0.731991i	$-0.261408\pi$
$677$	7.76677	+	4.99140i	0.298501	+	0.191835i	−0.382814	+	0.923826i	$0.625045\pi$
$678$		0			0
$679$	1.48951	−	10.3597i	0.0571620	−	0.397570i
$680$	−1.74622	−	1.12223i	−0.0669645	−	0.0430355i
$681$		0			0
$682$	11.4979	+	25.1769i	0.440277	+	0.964073i
$683$	−25.8749	+	16.6288i	−0.990076	+	0.636283i	−0.932163	−	0.362038i	$-0.882081\pi$
$683$	−25.8749	+	16.6288i	−0.990076	+	0.636283i	−0.0579130	+	0.998322i	$0.518445\pi$
$684$		0			0
$685$	−13.1154	+	15.1360i	−0.501114	+	0.578316i
$686$	−10.6449	+	3.12564i	−0.406426	+	0.119337i
$687$		0			0
$688$	−0.557613	−	3.87829i	−0.0212588	−	0.147858i
$689$	−51.3937			−1.95794
$690$		0			0
$691$	39.1989			1.49119			0.745597	−	0.666397i	$-0.232164\pi$
$691$	39.1989			1.49119			0.745597	+	0.666397i	$0.232164\pi$
$692$	−3.15404	−	21.9368i	−0.119899	−	0.833913i
$693$		0			0
$694$	27.7283	−	8.14178i	1.05255	−	0.309058i
$695$	−6.06045	+	6.99414i	−0.229886	+	0.265303i
$696$		0			0
$697$	−1.42560	+	0.916177i	−0.0539984	+	0.0347027i
$698$	−5.18182	−	11.3466i	−0.196135	−	0.429476i
$699$		0			0
$700$	−1.28601	−	0.826467i	−0.0486065	−	0.0312375i
$701$	−4.74277	+	32.9867i	−0.179132	+	1.24589i	0.679645	+	0.733541i	$0.262134\pi$
$701$	−4.74277	+	32.9867i	−0.179132	+	1.24589i	−0.858777	+	0.512349i	$0.828775\pi$
$702$		0			0
$703$	−17.1747	−	11.0375i	−0.647754	−	0.416286i
$704$	2.57067	+	2.96671i	0.0968857	+	0.111812i
$705$		0			0
$706$	31.0189	−	19.9346i	1.16741	−	0.750250i
$707$	9.63948	+	2.83041i	0.362530	+	0.106448i
$708$		0			0
$709$	2.06587	−	0.606594i	0.0775854	−	0.0227811i	−0.242709	−	0.970099i	$-0.578036\pi$
$709$	2.06587	−	0.606594i	0.0775854	−	0.0227811i	0.320295	+	0.947318i	$0.396218\pi$
$710$	5.79173	−	12.6821i	0.217360	−	0.475952i
$711$		0			0
$712$	2.07244			0.0776678
$713$	11.7360	−	31.7126i	0.439515	−	1.18765i
$714$		0			0
$715$	−4.55757	−	31.6986i	−0.170443	−	1.18546i
$716$	−3.61866	+	7.92377i	−0.135236	+	0.296125i
$717$		0			0
$718$	−4.05875	+	4.68405i	−0.151471	+	0.174807i
$719$	−4.10901	−	1.20651i	−0.153240	−	0.0449954i	0.204213	−	0.978927i	$-0.434537\pi$
$719$	−4.10901	−	1.20651i	−0.153240	−	0.0449954i	−0.357453	+	0.933931i	$0.616355\pi$
$720$		0			0
$721$	4.51120	+	9.87814i	0.168006	+	0.367881i
$722$	−3.24498	−	3.74491i	−0.120766	−	0.139371i
$723$		0			0
$724$	−2.88438	+	20.0613i	−0.107197	+	0.745573i
$725$	−0.283970	+	1.97506i	−0.0105464	+	0.0733517i
$726$		0			0
$727$	24.7411	+	28.5527i	0.917595	+	1.05896i	0.998063	+	0.0622044i	$0.0198131\pi$
$727$	24.7411	+	28.5527i	0.917595	+	1.05896i	−0.0804680	+	0.996757i	$0.525641\pi$
$728$	−1.58803	−	3.47730i	−0.0588562	−	0.128877i
$729$		0			0
$730$	−23.5802	−	6.92378i	−0.872743	−	0.256261i
$731$	2.99293	−	3.45402i	0.110697	−	0.127752i
$732$		0			0
$733$	18.5407	−	40.5984i	0.684815	−	1.49954i	−0.172645	−	0.984984i	$-0.555231\pi$
$733$	18.5407	−	40.5984i	0.684815	−	1.49954i	0.857460	−	0.514551i	$-0.172041\pi$
$734$	−1.34808	−	9.37608i	−0.0497584	−	0.346078i
$735$		0			0
$736$	0.329907	−	4.78447i	0.0121605	−	0.176358i
$737$	−8.07393			−0.297407
$738$		0			0
$739$	−9.45615	+	20.7061i	−0.347850	+	0.761686i	0.652143	+	0.758096i	$0.273870\pi$
$739$	−9.45615	+	20.7061i	−0.347850	+	0.761686i	−0.999994	+	0.00358991i	$0.998857\pi$
$740$	9.30150	−	2.73117i	0.341930	−	0.100400i
$741$		0			0
$742$	−8.96956	−	2.63370i	−0.329283	−	0.0966862i
$743$	−2.78006	+	1.78664i	−0.101990	+	0.0655453i	−0.590642	−	0.806934i	$-0.701125\pi$
$743$	−2.78006	+	1.78664i	−0.101990	+	0.0655453i	0.488651	+	0.872479i	$0.337489\pi$
$744$		0			0
$745$	22.2966	+	25.7316i	0.816883	+	0.942733i
$746$	−25.8990	−	16.6443i	−0.948231	−	0.609391i
$747$		0			0
$748$	−0.651646	+	4.53230i	−0.0238265	+	0.165717i
$749$	−3.39496	−	2.18181i	−0.124049	−	0.0797215i
$750$		0			0
$751$	−21.9354	−	48.0317i	−0.800433	−	1.75270i	−0.644016	−	0.765012i	$-0.722733\pi$
$751$	−21.9354	−	48.0317i	−0.800433	−	1.75270i	−0.156417	−	0.987691i	$-0.549994\pi$
$752$	4.22330	−	2.71415i	0.154008	−	0.0989750i
$753$		0			0
$754$	−3.26761	+	3.77103i	−0.118999	+	0.137333i
$755$	−19.8358	+	5.82433i	−0.721900	+	0.211969i
$756$		0			0
$757$	2.08575	+	14.5067i	0.0758078	+	0.527255i	0.991973	+	0.126453i	$0.0403593\pi$
$757$	2.08575	+	14.5067i	0.0758078	+	0.527255i	−0.916165	+	0.400802i	$0.868732\pi$
$758$	27.9229			1.01421
$759$		0			0
$760$	−6.66907			−0.241913
$761$	3.68838	+	25.6532i	0.133704	+	0.929929i	0.940668	+	0.339329i	$0.110200\pi$
$761$	3.68838	+	25.6532i	0.133704	+	0.929929i	−0.806964	+	0.590600i	$0.798891\pi$
$762$		0			0
$763$	−0.806412	+	0.236784i	−0.0291941	+	0.00857215i
$764$	14.5419	−	16.7823i	0.526109	−	0.607162i
$765$		0			0
$766$	−3.29803	+	2.11952i	−0.119163	+	0.0765812i
$767$	7.46029	+	16.3357i	0.269375	+	0.589850i
$768$		0			0
$769$	−44.2385	−	28.4304i	−1.59528	−	1.02523i	−0.969457	−	0.245261i	$-0.921126\pi$
$769$	−44.2385	−	28.4304i	−1.59528	−	1.02523i	−0.625824	−	0.779964i	$-0.715237\pi$
$770$	0.828997	−	5.76580i	0.0298750	−	0.207785i
$771$		0			0
$772$	−16.0688	−	10.3268i	−0.578328	−	0.371669i
$773$	2.66647	+	3.07727i	0.0959064	+	0.110682i	0.801674	−	0.597762i	$-0.203943\pi$
$773$	2.66647	+	3.07727i	0.0959064	+	0.110682i	−0.705767	+	0.708444i	$0.749398\pi$
$774$		0			0
$775$	−10.8739	+	6.98823i	−0.390602	+	0.251025i
$776$	−12.0430	−	3.53615i	−0.432320	−	0.126940i
$777$		0			0
$778$	−33.4568	+	9.82379i	−1.19948	+	0.352200i
$779$	−2.26176	+	4.95256i	−0.0810358	+	0.177444i
$780$		0			0
$781$	−30.7550			−1.10050
$782$	4.46971	−	3.36384i	0.159836	−	0.120291i
$783$		0			0
$784$	0.897247	+	6.24049i	0.0320445	+	0.222875i
$785$	2.07526	−	4.54418i	0.0740692	−	0.162189i
$786$		0			0
$787$	0.0451653	−	0.0521236i	0.00160997	−	0.00185800i	−0.754944	−	0.655789i	$-0.772336\pi$
$787$	0.0451653	−	0.0521236i	0.00160997	−	0.00185800i	0.756554	+	0.653931i	$0.226881\pi$
$788$	−22.1857	−	6.51431i	−0.790333	−	0.232063i
$789$		0			0
$790$	−7.07379	−	15.4894i	−0.251674	−	0.551090i
$791$	5.73555	+	6.61917i	0.203933	+	0.235351i
$792$		0			0
$793$	2.73429	−	19.0174i	0.0970975	−	0.675328i
$794$	−0.287045	+	1.99644i	−0.0101869	+	0.0708512i
$795$		0			0
$796$	−10.0061	−	11.5477i	−0.354657	−	0.409296i
$797$	−0.890693	−	1.95035i	−0.0315500	−	0.0690848i	0.893201	−	0.449658i	$-0.148454\pi$
$797$	−0.890693	−	1.95035i	−0.0315500	−	0.0690848i	−0.924751	+	0.380573i	$0.875727\pi$
$798$		0			0
$799$	5.61865	+	1.64978i	0.198773	+	0.0583651i
$800$	−1.20052	+	1.38547i	−0.0424446	+	0.0489837i
$801$		0			0
$802$	−8.91415	+	19.5193i	−0.314769	+	0.689249i
$803$	7.71517	+	53.6602i	0.272263	+	1.89363i
$804$		0			0
$805$	−5.68618	+	4.27933i	−0.200411	+	0.150827i
$806$	−32.3234			−1.13854
$807$		0			0
$808$	5.00491	−	10.9592i	0.176072	−	0.385544i
$809$	−24.7343	+	7.26265i	−0.869612	+	0.255341i	−0.685950	−	0.727648i	$-0.740613\pi$
$809$	−24.7343	+	7.26265i	−0.869612	+	0.255341i	−0.183662	+	0.982990i	$0.558795\pi$
$810$		0			0
$811$	20.2710	+	5.95210i	0.711810	+	0.209006i	0.617539	−	0.786540i	$-0.288130\pi$
$811$	20.2710	+	5.95210i	0.711810	+	0.209006i	0.0942712	+	0.995547i	$0.469948\pi$
$812$	−0.763534	+	0.490694i	−0.0267948	+	0.0172200i
$813$		0			0
$814$	−14.0039	−	16.1614i	−0.490837	−	0.566456i
$815$	33.2770	+	21.3858i	1.16564	+	0.749112i
$816$		0			0
$817$	2.08973	−	14.5344i	0.0731105	−	0.508494i
$818$	13.3666	+	8.59019i	0.467352	+	0.300349i
$819$		0			0
$820$	−1.07398	−	2.35169i	−0.0375050	−	0.0821245i
$821$	25.2898	−	16.2528i	0.882621	−	0.567226i	−0.0189675	−	0.999820i	$-0.506038\pi$
$821$	25.2898	−	16.2528i	0.882621	−	0.567226i	0.901589	+	0.432594i	$0.142402\pi$
$822$		0			0
$823$	−12.3091	+	14.2054i	−0.429067	+	0.495170i	−0.928578	−	0.371138i	$-0.878968\pi$
$823$	−12.3091	+	14.2054i	−0.429067	+	0.495170i	0.499511	+	0.866308i	$0.333513\pi$
$824$	12.4955	−	3.66901i	0.435301	−	0.127816i
$825$		0			0
$826$	0.464883	+	3.23333i	0.0161753	+	0.112502i
$827$	−49.2602			−1.71295			−0.856473	−	0.516192i	$-0.827349\pi$
$827$	−49.2602			−1.71295			−0.856473	+	0.516192i	$0.827349\pi$
$828$		0			0
$829$	10.0455			0.348896			0.174448	−	0.984666i	$-0.444186\pi$
$829$	10.0455			0.348896			0.174448	+	0.984666i	$0.444186\pi$
$830$	−3.26540	−	22.7113i	−0.113344	−	0.788322i
$831$		0			0
$832$	−4.39866	+	1.29156i	−0.152496	+	0.0447768i
$833$	−4.81587	+	5.55782i	−0.166860	+	0.192567i
$834$		0			0
$835$	−28.7958	+	18.5059i	−0.996520	+	0.640424i
$836$	6.11134	+	13.3820i	0.211365	+	0.462825i
$837$		0			0
$838$	23.4106	+	15.0451i	0.808707	+	0.519725i
$839$	0.193912	−	1.34869i	0.00669458	−	0.0465618i	−0.986200	−	0.165556i	$-0.947058\pi$
$839$	0.193912	−	1.34869i	0.00669458	−	0.0465618i	0.992895	+	0.118995i	$0.0379671\pi$
$840$		0			0
$841$	−23.3997	−	15.0381i	−0.806887	−	0.518555i
$842$	8.32359	+	9.60594i	0.286850	+	0.331042i
$843$		0			0
$844$	−5.22249	+	3.35629i	−0.179765	+	0.115528i
$845$	13.6875	+	4.01901i	0.470864	+	0.138258i
$846$		0			0
$847$	−3.52816	+	1.03596i	−0.121229	+	0.0355961i
$848$	−4.65708	+	10.1976i	−0.159925	+	0.350187i
$849$		0			0
$850$	−2.13837			−0.0733456
$851$	−1.79719	+	26.0638i	−0.0616070	+	0.893455i
$852$		0			0
$853$	4.34451	+	30.2167i	0.148753	+	1.03460i	0.918264	+	0.395968i	$0.129591\pi$
$853$	4.34451	+	30.2167i	0.148753	+	1.03460i	−0.769511	+	0.638634i	$0.779500\pi$
$854$	1.45177	−	3.17892i	0.0496784	−	0.108781i
$855$		0			0
$856$	−3.16926	+	3.65753i	−0.108323	+	0.125012i
$857$	−5.39610	−	1.58444i	−0.184327	−	0.0541234i	0.188266	−	0.982118i	$-0.439713\pi$
$857$	−5.39610	−	1.58444i	−0.184327	−	0.0541234i	−0.372593	+	0.927995i	$0.621531\pi$
$858$		0			0
$859$	−12.6640	−	27.7303i	−0.432090	−	0.946145i	−0.992983	−	0.118257i	$-0.962269\pi$
$859$	−12.6640	−	27.7303i	−0.432090	−	0.946145i	0.560893	−	0.827888i	$-0.310458\pi$
$860$	4.56604	+	5.26949i	0.155701	+	0.179688i
$861$		0			0
$862$	−5.21751	+	36.2886i	−0.177709	+	1.23599i
$863$	−4.36919	+	30.3884i	−0.148729	+	1.03443i	0.769575	+	0.638556i	$0.220468\pi$
$863$	−4.36919	+	30.3884i	−0.148729	+	1.03443i	−0.918304	+	0.395876i	$0.870441\pi$
$864$		0			0
$865$	25.8270	+	29.8059i	0.878143	+	1.01343i
$866$	2.88533	+	6.31799i	0.0980475	+	0.214694i
$867$		0			0
$868$	−5.64130	−	1.65643i	−0.191478	−	0.0562230i
$869$	−24.5985	+	28.3882i	−0.834447	+	0.963003i
$870$		0			0
$871$	3.91695	−	8.57693i	0.132721	−	0.290618i
$872$	0.143439	+	0.997640i	0.00485746	+	0.0337844i
$873$		0			0
$874$	6.23788	−	16.8558i	0.211000	−	0.570157i
$875$	10.1399			0.342790
$876$		0			0
$877$	21.8082	−	47.7533i	0.736411	−	1.61251i	−0.0529590	−	0.998597i	$-0.516865\pi$
$877$	21.8082	−	47.7533i	0.736411	−	1.61251i	0.789370	−	0.613918i	$-0.210407\pi$
$878$	21.4798	−	6.30703i	0.724907	−	0.212852i
$879$		0			0
$880$	−6.70265	−	1.96808i	−0.225946	−	0.0663438i
$881$	4.68148	−	3.00861i	0.157723	−	0.101363i	−0.459399	−	0.888230i	$-0.651935\pi$
$881$	4.68148	−	3.00861i	0.157723	−	0.101363i	0.617122	+	0.786868i	$0.288299\pi$
$882$		0			0
$883$	−18.2403	−	21.0504i	−0.613834	−	0.708402i	0.360690	−	0.932686i	$-0.382541\pi$
$883$	−18.2403	−	21.0504i	−0.613834	−	0.708402i	−0.974524	+	0.224284i	$0.927996\pi$
$884$	−4.49852	−	2.89102i	−0.151302	−	0.0972356i
$885$		0			0
$886$	4.12815	−	28.7119i	0.138688	−	0.964597i
$887$	−6.75333	−	4.34010i	−0.226754	−	0.145726i	0.422331	−	0.906442i	$-0.361212\pi$
$887$	−6.75333	−	4.34010i	−0.226754	−	0.145726i	−0.649086	+	0.760715i	$0.724848\pi$
$888$		0			0
$889$	−1.85111	−	4.05336i	−0.0620841	−	0.135945i
$890$	−3.10253	+	1.99387i	−0.103997	+	0.0668348i
$891$		0			0
$892$	−10.1358	+	11.6973i	−0.339371	+	0.391655i
$893$	18.0520	−	5.30054i	0.604086	−	0.177376i
$894$		0			0
$895$	−2.20609	−	15.3437i	−0.0737416	−	0.512884i
$896$	−0.833869			−0.0278576
$897$		0			0
$898$	37.0126			1.23513
$899$	1.09218	+	7.59626i	0.0364261	+	0.253349i
$900$		0			0
$901$	−12.5469	+	3.68411i	−0.417999	+	0.122736i
$902$	−3.73467	+	4.31004i	−0.124351	+	0.143509i
$903$		0			0
$904$	8.83598	−	5.67854i	0.293880	−	0.188865i
$905$	−14.9828	−	32.8077i	−0.498045	−	1.09057i
$906$		0			0
$907$	−44.4453	−	28.5633i	−1.47578	−	0.948428i	−0.997533	−	0.0702039i	$-0.977635\pi$
$907$	−44.4453	−	28.5633i	−1.47578	−	0.948428i	−0.478250	−	0.878224i	$-0.658729\pi$
$908$	1.86065	−	12.9411i	0.0617477	−	0.429465i
$909$		0			0
$910$	5.72283	+	3.67784i	0.189710	+	0.121919i
$911$	6.10699	+	7.04785i	0.202334	+	0.233506i	0.847844	−	0.530246i	$-0.177901\pi$
$911$	6.10699	+	7.04785i	0.202334	+	0.233506i	−0.645510	+	0.763752i	$0.723355\pi$
$912$		0			0
$913$	−42.5796	+	27.3643i	−1.40918	+	0.905625i
$914$	−6.12722	−	1.79911i	−0.202670	−	0.0595094i
$915$		0			0
$916$	−23.8357	+	6.99879i	−0.787553	+	0.231246i
$917$	−3.67737	+	8.05232i	−0.121438	+	0.265911i
$918$		0			0
$919$	13.1566			0.433997			0.216998	−	0.976172i	$-0.430373\pi$
$919$	13.1566			0.433997			0.216998	+	0.976172i	$0.430373\pi$
$920$	4.10922	+	7.47996i	0.135477	+	0.246607i
$921$		0			0
$922$	−0.858281	−	5.96948i	−0.0282660	−	0.196594i
$923$	14.9203	−	32.6710i	0.491109	−	1.07538i
$924$		0			0
$925$	6.53991	−	7.54746i	0.215031	−	0.248159i
$926$	1.02604	+	0.301271i	0.0337176	+	0.00990039i
$927$		0			0
$928$	0.452153	+	0.990078i	0.0148427	+	0.0325009i
$929$	−19.6379	−	22.6634i	−0.644299	−	0.743561i	0.335829	−	0.941923i	$-0.390983\pi$
$929$	−19.6379	−	22.6634i	−0.644299	−	0.743561i	−0.980129	+	0.198362i	$0.936438\pi$
$930$		0			0
$931$	−3.36256	+	23.3871i	−0.110203	+	0.766481i
$932$	−0.727904	+	5.06268i	−0.0238433	+	0.165834i
$933$		0			0
$934$	0.620646	+	0.716264i	0.0203082	+	0.0234369i
$935$	−3.38494	−	7.41199i	−0.110699	−	0.242398i
$936$		0			0
$937$	−20.5084	−	6.02181i	−0.669980	−	0.196724i	−0.0709859	−	0.997477i	$-0.522615\pi$
$937$	−20.5084	−	6.02181i	−0.669980	−	0.196724i	−0.598994	+	0.800753i	$0.704433\pi$
$938$	1.12314	−	1.29618i	0.0366719	−	0.0423216i
$939$		0			0
$940$	−3.71121	+	8.12641i	−0.121046	+	0.265054i
$941$	−0.750500	−	5.21984i	−0.0244656	−	0.170162i	0.973925	−	0.226869i	$-0.0728490\pi$
$941$	−0.750500	−	5.21984i	−0.0244656	−	0.170162i	−0.998391	+	0.0567071i	$0.981940\pi$
$942$		0			0
$943$	6.94835	−	0.514804i	0.226269	−	0.0167643i
$944$	3.91737			0.127500
$945$		0			0
$946$	6.38943	−	13.9909i	0.207738	−	0.454883i
$947$	6.48498	−	1.90416i	0.210734	−	0.0618770i	−0.174662	−	0.984628i	$-0.555883\pi$
$947$	6.48498	−	1.90416i	0.210734	−	0.0618770i	0.385395	+	0.922752i	$0.374065\pi$
$948$		0			0
$949$	−60.7461	−	17.8367i	−1.97190	−	0.579003i
$950$	−5.77967	+	3.71437i	−0.187517	+	0.120510i
$951$		0			0
$952$	−0.636959	−	0.735090i	−0.0206440	−	0.0238244i
$953$	−7.28209	−	4.67991i	−0.235890	−	0.151597i	0.417356	−	0.908743i	$-0.362957\pi$
$953$	−7.28209	−	4.67991i	−0.235890	−	0.151597i	−0.653246	+	0.757146i	$0.726593\pi$
$954$		0			0
$955$	−5.62382	+	39.1145i	−0.181983	+	1.26572i
$956$	−20.5257	−	13.1911i	−0.663848	−	0.426629i
$957$		0			0
$958$	−7.28913	−	15.9610i	−0.235501	−	0.515676i
$959$	−7.89496	+	5.07378i	−0.254941	+	0.163841i
$960$		0			0
$961$	−12.2550	+	14.1431i	−0.395324	+	0.456228i
$962$	23.9620	−	7.03589i	0.772567	−	0.226846i
$963$		0			0
$964$	1.29344	+	8.99605i	0.0416588	+	0.289743i
$965$	33.9910			1.09421
$966$		0			0
$967$	9.42139			0.302971			0.151486	−	0.988459i	$-0.451594\pi$
$967$	9.42139			0.302971			0.151486	+	0.988459i	$0.451594\pi$
$968$	0.627566	+	4.36482i	0.0201707	+	0.140290i
$969$		0			0
$970$	21.4311	−	6.29272i	0.688110	−	0.202047i
$971$	23.6126	−	27.2504i	0.757764	−	0.874507i	−0.237532	−	0.971380i	$-0.576339\pi$
$971$	23.6126	−	27.2504i	0.757764	−	0.874507i	0.995297	+	0.0968730i	$0.0308841\pi$
$972$		0			0
$973$	−3.64816	+	2.34453i	−0.116955	+	0.0751621i
$974$	−13.5343	−	29.6359i	−0.433666	−	0.949597i
$975$		0			0
$976$	−3.52568	−	2.26582i	−0.112854	−	0.0725271i
$977$	6.13639	−	42.6795i	0.196320	−	1.36544i	−0.618527	−	0.785763i	$-0.712270\pi$
$977$	6.13639	−	42.6795i	0.196320	−	1.36544i	0.814848	−	0.579675i	$-0.196821\pi$
$978$		0			0
$979$	6.84392	+	4.39832i	0.218733	+	0.140571i
$980$	−7.34714	−	8.47905i	−0.234696	−	0.270853i
$981$		0			0
$982$	−17.0760	+	10.9741i	−0.544916	+	0.350196i
$983$	−6.86116	−	2.01462i	−0.218837	−	0.0642563i	0.170476	−	0.985362i	$-0.445469\pi$
$983$	−6.86116	−	2.01462i	−0.218837	−	0.0642563i	−0.389313	+	0.921105i	$0.627288\pi$
$984$		0			0
$985$	39.4803	−	11.5925i	1.25795	−	0.369367i
$986$	−0.527412	+	1.15487i	−0.0167962	+	0.0367786i
$987$		0			0
$988$	−17.1805			−0.546584
$989$	−17.5893	+	6.61170i	−0.559306	+	0.210240i
$990$		0			0
$991$	−3.97373	−	27.6379i	−0.126230	−	0.877946i	−0.950273	−	0.311419i	$-0.899196\pi$
$991$	−3.97373	−	27.6379i	−0.126230	−	0.877946i	0.824043	−	0.566527i	$-0.191713\pi$
$992$	−2.92901	+	6.41364i	−0.0929963	+	0.203633i
$993$		0			0
$994$	4.27824	−	4.93735i	0.135698	−	0.156603i
$995$	26.0895	+	7.66057i	0.827093	+	0.242856i
$996$		0			0
$997$	2.92906	+	6.41376i	0.0927644	+	0.203126i	0.950327	−	0.311255i	$-0.100749\pi$
$997$	2.92906	+	6.41376i	0.0927644	+	0.203126i	−0.857562	+	0.514380i	$0.828022\pi$
$998$	−5.13012	−	5.92047i	−0.162391	−	0.187409i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.h.325.2	yes	20
3.2	odd	2		414.2.i.g.325.1	yes	20
23.8	even	11	inner	414.2.i.h.307.2	yes	20
23.10	odd	22		9522.2.a.ch.1.6		10
23.13	even	11		9522.2.a.cg.1.5		10
69.8	odd	22		414.2.i.g.307.1	✓	20
69.56	even	22		9522.2.a.ci.1.5		10
69.59	odd	22		9522.2.a.cj.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.i.g.307.1	✓	20	69.8	odd	22
414.2.i.g.325.1	yes	20	3.2	odd	2
414.2.i.h.307.2	yes	20	23.8	even	11	inner
414.2.i.h.325.2	yes	20	1.1	even	1	trivial
9522.2.a.cg.1.5		10	23.13	even	11
9522.2.a.ch.1.6		10	23.10	odd	22
9522.2.a.ci.1.5		10	69.56	even	22
9522.2.a.cj.1.6		10	69.59	odd	22

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(-0.959493 + 0.281733i) q^{4} +(1.16535 - 1.34489i) q^{5} +(0.701495 - 0.450824i) q^{7} +(-0.415415 - 0.909632i) q^{8} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{2} +(-0.959493 + 0.281733i) q^{4} +(1.16535 - 1.34489i) q^{5} +(0.701495 - 0.450824i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(1.49704 + 0.962092i) q^{10} +(0.558660 - 3.88556i) q^{11} +(3.85660 + 2.47849i) q^{13} +(0.546068 + 0.630196i) q^{14} +(0.841254 - 0.540641i) q^{16} +(1.11920 + 0.328626i) q^{17} +(3.59583 - 1.05583i) q^{19} +(-0.739247 + 1.61873i) q^{20} +3.92552 q^{22} +(-3.39982 - 3.38249i) q^{23} +(0.260897 + 1.81458i) q^{25} +(-1.90441 + 4.17008i) q^{26} +(-0.546068 + 0.630196i) q^{28} +(1.04435 + 0.306648i) q^{29} +(2.92901 + 6.41364i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-0.166002 + 1.15457i) q^{34} +(0.211181 - 1.46880i) q^{35} +(-3.56741 - 4.11701i) q^{37} +(1.55682 + 3.40897i) q^{38} +(-1.70746 - 0.501354i) q^{40} +(-0.951383 + 1.09795i) q^{41} +(1.62767 - 3.56409i) q^{43} +(0.558660 + 3.88556i) q^{44} +(2.86422 - 3.84659i) q^{46} +5.02025 q^{47} +(-2.61905 + 5.73492i) q^{49} +(-1.75898 + 0.516483i) q^{50} +(-4.39866 - 1.29156i) q^{52} +(-9.43102 + 6.06095i) q^{53} +(-4.57461 - 5.27938i) q^{55} +(-0.701495 - 0.450824i) q^{56} +(-0.154901 + 1.07736i) q^{58} +(3.29551 + 2.11789i) q^{59} +(-1.74100 - 3.81226i) q^{61} +(-5.93152 + 3.81196i) q^{62} +(-0.654861 + 0.755750i) q^{64} +(7.82758 - 2.29839i) q^{65} +(-0.292710 - 2.03585i) q^{67} -1.16645 q^{68} +1.48390 q^{70} +(-1.11498 - 7.75489i) q^{71} +(-13.2507 + 3.89077i) q^{73} +(3.56741 - 4.11701i) q^{74} +(-3.15271 + 2.02613i) q^{76} +(-1.35981 - 2.97756i) q^{77} +(-8.04988 - 5.17334i) q^{79} +(0.253255 - 1.76143i) q^{80} +(-1.22217 - 0.785444i) q^{82} +(-8.44359 - 9.74442i) q^{83} +(1.74622 - 1.12223i) q^{85} +(3.75945 + 1.10388i) q^{86} +(-3.76651 + 1.10595i) q^{88} +(-0.860921 + 1.88515i) q^{89} +3.82275 q^{91} +(4.21506 + 2.28763i) q^{92} +(0.714456 + 4.96915i) q^{94} +(2.77043 - 6.06640i) q^{95} +(8.21945 - 9.48575i) q^{97} +(-6.04928 - 1.77623i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8}+O(q^{10}) \) 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8} - 2 q^{10} - 2 q^{11} - 18 q^{14} - 2 q^{16} + 18 q^{17} + 16 q^{19} + 2 q^{20} + 24 q^{22} - 2 q^{23} + 38 q^{25} + 18 q^{28} - 30 q^{29} + 14 q^{31} + 2 q^{32} + 4 q^{34} + 48 q^{35} - 20 q^{37} - 16 q^{38} - 2 q^{40} - 12 q^{41} - 28 q^{43} - 2 q^{44} + 2 q^{46} + 32 q^{47} + 6 q^{49} + 6 q^{50} - 46 q^{53} - 28 q^{55} + 4 q^{56} - 14 q^{58} - 50 q^{61} + 8 q^{62} - 2 q^{64} + 16 q^{65} - 8 q^{67} - 48 q^{68} - 48 q^{70} + 12 q^{71} - 18 q^{73} + 20 q^{74} - 6 q^{76} - 4 q^{77} - 18 q^{79} + 2 q^{80} - 10 q^{82} - 44 q^{83} + 32 q^{85} + 28 q^{86} + 2 q^{88} + 44 q^{91} - 2 q^{92} + 12 q^{94} + 64 q^{95} + 14 q^{97} - 28 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8 - 2 * q^10 - 2 * q^11 - 18 * q^14 - 2 * q^16 + 18 * q^17 + 16 * q^19 + 2 * q^20 + 24 * q^22 - 2 * q^23 + 38 * q^25 + 18 * q^28 - 30 * q^29 + 14 * q^31 + 2 * q^32 + 4 * q^34 + 48 * q^35 - 20 * q^37 - 16 * q^38 - 2 * q^40 - 12 * q^41 - 28 * q^43 - 2 * q^44 + 2 * q^46 + 32 * q^47 + 6 * q^49 + 6 * q^50 - 46 * q^53 - 28 * q^55 + 4 * q^56 - 14 * q^58 - 50 * q^61 + 8 * q^62 - 2 * q^64 + 16 * q^65 - 8 * q^67 - 48 * q^68 - 48 * q^70 + 12 * q^71 - 18 * q^73 + 20 * q^74 - 6 * q^76 - 4 * q^77 - 18 * q^79 + 2 * q^80 - 10 * q^82 - 44 * q^83 + 32 * q^85 + 28 * q^86 + 2 * q^88 + 44 * q^91 - 2 * q^92 + 12 * q^94 + 64 * q^95 + 14 * q^97 - 28 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more