LMFDB - Embedded newform 729.2.e.k.406.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			406.1
Root			$1.13697i$ of defining polynomial
Character	$\chi$	$=$	729.406
Dual form			729.2.e.k.325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.595778 - 0.499917i) q^{2} +(-0.242262 - 1.37394i) q^{4} +(2.23304 + 0.812759i) q^{5} +(-0.434359 + 2.46337i) q^{7} +(-1.32025 + 2.28674i) q^{8} +O(q^{10})$	\(q+(-0.595778 - 0.499917i) q^{2} +(-0.242262 - 1.37394i) q^{4} +(2.23304 + 0.812759i) q^{5} +(-0.434359 + 2.46337i) q^{7} +(-1.32025 + 2.28674i) q^{8} +(-0.924081 - 1.60056i) q^{10} +(2.95192 - 1.07441i) q^{11} +(1.02392 - 0.859169i) q^{13} +(1.49026 - 1.25048i) q^{14} +(-0.692233 + 0.251952i) q^{16} +(3.13726 + 5.43389i) q^{17} +(-4.03234 + 6.98422i) q^{19} +(0.575699 - 3.26495i) q^{20} +(-2.29581 - 0.835605i) q^{22} +(-0.704074 - 3.99300i) q^{23} +(0.495652 + 0.415902i) q^{25} -1.03954 q^{26} +3.48975 q^{28} +(7.11443 + 5.96971i) q^{29} +(0.491741 + 2.78880i) q^{31} +(5.50090 + 2.00216i) q^{32} +(0.847385 - 4.80576i) q^{34} +(-2.97207 + 5.14778i) q^{35} +(-2.76596 - 4.79078i) q^{37} +(5.89391 - 2.14521i) q^{38} +(-4.80674 + 4.03334i) q^{40} +(5.44333 - 4.56750i) q^{41} +(-2.19597 + 0.799267i) q^{43} +(-2.19131 - 3.79547i) q^{44} +(-1.57670 + 2.73092i) q^{46} +(0.801248 - 4.54411i) q^{47} +(0.698301 + 0.254161i) q^{49} +(-0.0873823 - 0.495570i) q^{50} +(-1.42850 - 1.19865i) q^{52} -0.135496 q^{53} +7.46499 q^{55} +(-5.05964 - 4.24554i) q^{56} +(-1.25426 - 7.11324i) q^{58} +(-3.75759 - 1.36765i) q^{59} +(0.0593526 - 0.336605i) q^{61} +(1.10120 - 1.90733i) q^{62} +(-1.53974 - 2.66690i) q^{64} +(2.98474 - 1.08636i) q^{65} +(7.75461 - 6.50689i) q^{67} +(6.70579 - 5.62682i) q^{68} +(4.34415 - 1.58114i) q^{70} +(4.09540 + 7.09344i) q^{71} +(6.15722 - 10.6646i) q^{73} +(-0.747095 + 4.23698i) q^{74} +(10.5728 + 3.84817i) q^{76} +(1.36448 + 7.73837i) q^{77} +(3.12600 + 2.62302i) q^{79} -1.75056 q^{80} -5.52638 q^{82} +(-0.699573 - 0.587012i) q^{83} +(2.58917 + 14.6839i) q^{85} +(1.70788 + 0.621616i) q^{86} +(-1.44038 + 8.16879i) q^{88} +(-1.86437 + 3.22919i) q^{89} +(1.67171 + 2.89548i) q^{91} +(-5.31556 + 1.93471i) q^{92} +(-2.74904 + 2.30672i) q^{94} +(-14.6809 + 12.3187i) q^{95} +(5.63467 - 2.05085i) q^{97} +(-0.288973 - 0.500515i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 6 * q^7 - 6 * q^8	$ 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 6 q^{10} + 15 q^{11} - 3 q^{13} + 21 q^{14} + 9 q^{16} + 9 q^{17} - 12 q^{19} + 3 q^{20} + 33 q^{22} - 15 q^{23} - 12 q^{25} + 48 q^{26} + 6 q^{28} + 6 q^{29} - 12 q^{31} + 27 q^{32} + 27 q^{34} - 30 q^{35} - 3 q^{37} + 39 q^{38} + 24 q^{40} + 39 q^{41} + 24 q^{43} + 33 q^{44} + 3 q^{46} + 42 q^{47} - 30 q^{49} + 15 q^{50} - 45 q^{52} - 18 q^{53} + 30 q^{55} - 12 q^{56} - 30 q^{58} - 15 q^{59} - 3 q^{61} + 30 q^{62} - 6 q^{64} + 6 q^{65} - 3 q^{67} - 36 q^{68} - 75 q^{70} - 12 q^{73} - 60 q^{74} + 30 q^{76} - 33 q^{77} + 33 q^{79} - 42 q^{80} - 42 q^{82} + 33 q^{83} - 18 q^{85} + 30 q^{86} - 42 q^{88} + 9 q^{89} - 18 q^{91} - 33 q^{92} - 66 q^{94} - 12 q^{95} + 15 q^{97} - 18 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 6 * q^10 + 15 * q^11 - 3 * q^13 + 21 * q^14 + 9 * q^16 + 9 * q^17 - 12 * q^19 + 3 * q^20 + 33 * q^22 - 15 * q^23 - 12 * q^25 + 48 * q^26 + 6 * q^28 + 6 * q^29 - 12 * q^31 + 27 * q^32 + 27 * q^34 - 30 * q^35 - 3 * q^37 + 39 * q^38 + 24 * q^40 + 39 * q^41 + 24 * q^43 + 33 * q^44 + 3 * q^46 + 42 * q^47 - 30 * q^49 + 15 * q^50 - 45 * q^52 - 18 * q^53 + 30 * q^55 - 12 * q^56 - 30 * q^58 - 15 * q^59 - 3 * q^61 + 30 * q^62 - 6 * q^64 + 6 * q^65 - 3 * q^67 - 36 * q^68 - 75 * q^70 - 12 * q^73 - 60 * q^74 + 30 * q^76 - 33 * q^77 + 33 * q^79 - 42 * q^80 - 42 * q^82 + 33 * q^83 - 18 * q^85 + 30 * q^86 - 42 * q^88 + 9 * q^89 - 18 * q^91 - 33 * q^92 - 66 * q^94 - 12 * q^95 + 15 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−0.595778	−	0.499917i	−0.421278	−	0.353495i	0.407371	−	0.913263i	$-0.366446\pi$
$2$	−0.595778	−	0.499917i	−0.421278	−	0.353495i	−0.828649	+	0.559768i	$0.810890\pi$
$3$		0			0
$3$		0			0
$4$	−0.242262	−	1.37394i	−0.121131	−	0.686969i
$5$	2.23304	+	0.812759i	0.998644	+	0.363477i	0.789062	−	0.614314i	$-0.210567\pi$
$5$	2.23304	+	0.812759i	0.998644	+	0.363477i	0.209583	+	0.977791i	$0.432789\pi$
$6$		0			0
$7$	−0.434359	+	2.46337i	−0.164172	+	0.931068i	0.785741	+	0.618555i	$0.212282\pi$
$7$	−0.434359	+	2.46337i	−0.164172	+	0.931068i	−0.949914	+	0.312513i	$0.898829\pi$
$8$	−1.32025	+	2.28674i	−0.466780	+	0.808486i
$9$		0			0
$10$	−0.924081	−	1.60056i	−0.292220	−	0.506140i
$11$	2.95192	−	1.07441i	0.890038	−	0.323947i	0.143784	−	0.989609i	$-0.454073\pi$
$11$	2.95192	−	1.07441i	0.890038	−	0.323947i	0.746254	+	0.665662i	$0.231851\pi$
$12$		0			0
$13$	1.02392	−	0.859169i	0.283984	−	0.238291i	−0.489657	−	0.871915i	$-0.662878\pi$
$13$	1.02392	−	0.859169i	0.283984	−	0.238291i	0.773641	+	0.633624i	$0.218434\pi$
$14$	1.49026	−	1.25048i	0.398290	−	0.334205i
$15$		0			0
$16$	−0.692233	+	0.251952i	−0.173058	+	0.0629881i
$17$	3.13726	+	5.43389i	0.760897	+	1.31791i	0.942389	+	0.334520i	$0.108574\pi$
$17$	3.13726	+	5.43389i	0.760897	+	1.31791i	−0.181492	+	0.983392i	$0.558093\pi$
$18$		0			0
$19$	−4.03234	+	6.98422i	−0.925083	+	1.60229i	−0.133656	+	0.991028i	$0.542672\pi$
$19$	−4.03234	+	6.98422i	−0.925083	+	1.60229i	−0.791427	+	0.611263i	$0.790662\pi$
$20$	0.575699	−	3.26495i	0.128730	−	0.730066i
$21$		0			0
$22$	−2.29581	−	0.835605i	−0.489467	−	0.178152i
$23$	−0.704074	−	3.99300i	−0.146810	−	0.832598i	−0.965896	−	0.258929i	$-0.916631\pi$
$23$	−0.704074	−	3.99300i	−0.146810	−	0.832598i	0.819087	−	0.573669i	$-0.194481\pi$
$24$		0			0
$25$	0.495652	+	0.415902i	0.0991305	+	0.0831803i
$26$	−1.03954			−0.203871
$27$		0			0
$28$	3.48975			0.659501
$29$	7.11443	+	5.96971i	1.32112	+	1.10855i	0.986067	+	0.166347i	$0.0531973\pi$
$29$	7.11443	+	5.96971i	1.32112	+	1.10855i	0.335049	+	0.942201i	$0.391247\pi$
$30$		0			0
$31$	0.491741	+	2.78880i	0.0883192	+	0.500883i	0.996591	+	0.0825022i	$0.0262912\pi$
$31$	0.491741	+	2.78880i	0.0883192	+	0.500883i	−0.908272	+	0.418381i	$0.862598\pi$
$32$	5.50090	+	2.00216i	0.972430	+	0.353936i
$33$		0			0
$34$	0.847385	−	4.80576i	0.145325	−	0.824181i
$35$	−2.97207	+	5.14778i	−0.502372	+	0.870133i
$36$		0			0
$37$	−2.76596	−	4.79078i	−0.454720	−	0.787599i	0.543952	−	0.839117i	$-0.316927\pi$
$37$	−2.76596	−	4.79078i	−0.454720	−	0.787599i	−0.998672	+	0.0515178i	$0.983594\pi$
$38$	5.89391	−	2.14521i	0.956119	−	0.347999i
$39$		0			0
$40$	−4.80674	+	4.03334i	−0.760013	+	0.637726i
$41$	5.44333	−	4.56750i	0.850105	−	0.713323i	−0.109708	−	0.993964i	$-0.534991\pi$
$41$	5.44333	−	4.56750i	0.850105	−	0.713323i	0.959813	+	0.280641i	$0.0905470\pi$
$42$		0			0
$43$	−2.19597	+	0.799267i	−0.334882	+	0.121887i	−0.503988	−	0.863711i	$-0.668134\pi$
$43$	−2.19597	+	0.799267i	−0.334882	+	0.121887i	0.169106	+	0.985598i	$0.445912\pi$
$44$	−2.19131	−	3.79547i	−0.330353	−	0.572188i
$45$		0			0
$46$	−1.57670	+	2.73092i	−0.232471	+	0.402652i
$47$	0.801248	−	4.54411i	0.116874	−	0.662826i	−0.868931	−	0.494933i	$-0.835193\pi$
$47$	0.801248	−	4.54411i	0.116874	−	0.662826i	0.985805	−	0.167893i	$-0.0536963\pi$
$48$		0			0
$49$	0.698301	+	0.254161i	0.0997573	+	0.0363087i
$50$	−0.0873823	−	0.495570i	−0.0123577	−	0.0700842i
$51$		0			0
$52$	−1.42850	−	1.19865i	−0.198097	−	0.166224i
$53$	−0.135496			−0.0186118			−0.00930588	−	0.999957i	$-0.502962\pi$
$53$	−0.135496			−0.0186118			−0.00930588	+	0.999957i	$0.502962\pi$
$54$		0			0
$55$	7.46499			1.00658
$56$	−5.05964	−	4.24554i	−0.676123	−	0.567335i
$57$		0			0
$58$	−1.25426	−	7.11324i	−0.164692	−	0.934015i
$59$	−3.75759	−	1.36765i	−0.489196	−	0.178053i	0.0856324	−	0.996327i	$-0.472709\pi$
$59$	−3.75759	−	1.36765i	−0.489196	−	0.178053i	−0.574828	+	0.818274i	$0.694931\pi$
$60$		0			0
$61$	0.0593526	−	0.336605i	0.00759932	−	0.0430979i	−0.980772	−	0.195156i	$-0.937479\pi$
$61$	0.0593526	−	0.336605i	0.00759932	−	0.0430979i	0.988372	+	0.152058i	$0.0485899\pi$
$62$	1.10120	−	1.90733i	0.139852	−	0.242232i
$63$		0			0
$64$	−1.53974	−	2.66690i	−0.192467	−	0.333363i
$65$	2.98474	−	1.08636i	0.370212	−	0.134746i
$66$		0			0
$67$	7.75461	−	6.50689i	0.947376	−	0.794943i	−0.0314778	−	0.999504i	$-0.510021\pi$
$67$	7.75461	−	6.50689i	0.947376	−	0.794943i	0.978854	+	0.204562i	$0.0655769\pi$
$68$	6.70579	−	5.62682i	0.813196	−	0.682353i
$69$		0			0
$70$	4.34415	−	1.58114i	0.519225	−	0.188983i
$71$	4.09540	+	7.09344i	0.486035	+	0.841837i	0.999871	−	0.0160515i	$-0.00510955\pi$
$71$	4.09540	+	7.09344i	0.486035	+	0.841837i	−0.513837	+	0.857888i	$0.671776\pi$
$72$		0			0
$73$	6.15722	−	10.6646i	0.720648	−	1.24820i	−0.240092	−	0.970750i	$-0.577178\pi$
$73$	6.15722	−	10.6646i	0.720648	−	1.24820i	0.960740	−	0.277449i	$-0.0894890\pi$
$74$	−0.747095	+	4.23698i	−0.0868480	+	0.492539i
$75$		0			0
$76$	10.5728	+	3.84817i	1.21278	+	0.441416i
$77$	1.36448	+	7.73837i	0.155497	+	0.881869i
$78$		0			0
$79$	3.12600	+	2.62302i	0.351702	+	0.295113i	0.801473	−	0.598031i	$-0.204050\pi$
$79$	3.12600	+	2.62302i	0.351702	+	0.295113i	−0.449771	+	0.893144i	$0.648494\pi$
$80$	−1.75056			−0.195718
$81$		0			0
$82$	−5.52638			−0.610287
$83$	−0.699573	−	0.587012i	−0.0767881	−	0.0644329i	0.603586	−	0.797298i	$-0.293738\pi$
$83$	−0.699573	−	0.587012i	−0.0767881	−	0.0644329i	−0.680374	+	0.732865i	$0.738183\pi$
$84$		0			0
$85$	2.58917	+	14.6839i	0.280835	+	1.59269i
$86$	1.70788	+	0.621616i	0.184165	+	0.0670306i
$87$		0			0
$88$	−1.44038	+	8.16879i	−0.153545	+	0.870795i
$89$	−1.86437	+	3.22919i	−0.197623	+	0.342293i	−0.947757	−	0.318992i	$-0.896656\pi$
$89$	−1.86437	+	3.22919i	−0.197623	+	0.342293i	0.750134	+	0.661286i	$0.229989\pi$
$90$		0			0
$91$	1.67171	+	2.89548i	0.175243	+	0.303529i
$92$	−5.31556	+	1.93471i	−0.554186	+	0.201707i
$93$		0			0
$94$	−2.74904	+	2.30672i	−0.283542	+	0.237920i
$95$	−14.6809	+	12.3187i	−1.50622	+	1.26387i
$96$		0			0
$97$	5.63467	−	2.05085i	0.572115	−	0.208233i	−0.0397303	−	0.999210i	$-0.512650\pi$
$97$	5.63467	−	2.05085i	0.572115	−	0.208233i	0.611845	+	0.790978i	$0.290428\pi$
$98$	−0.288973	−	0.500515i	−0.0291907	−	0.0505597i
$99$		0			0
$100$	0.451345	−	0.781752i	0.0451345	−	0.0781752i
$101$	−1.77498	+	10.0664i	−0.176617	+	1.00165i	0.759643	+	0.650340i	$0.225374\pi$
$101$	−1.77498	+	10.0664i	−0.176617	+	1.00165i	−0.936261	+	0.351306i	$0.885738\pi$
$102$		0			0
$103$	−8.01939	−	2.91882i	−0.790174	−	0.287600i	−0.0847658	−	0.996401i	$-0.527014\pi$
$103$	−8.01939	−	2.91882i	−0.790174	−	0.287600i	−0.705409	+	0.708801i	$0.749236\pi$
$104$	0.612870	+	3.47576i	0.0600968	+	0.340826i
$105$		0			0
$106$	0.0807253	+	0.0677366i	0.00784073	+	0.00657916i
$107$	7.74500			0.748738			0.374369	−	0.927280i	$-0.377859\pi$
$107$	7.74500			0.748738			0.374369	+	0.927280i	$0.377859\pi$
$108$		0			0
$109$	1.25438			0.120148			0.0600738	−	0.998194i	$-0.480866\pi$
$109$	1.25438			0.120148			0.0600738	+	0.998194i	$0.480866\pi$
$110$	−4.44747	−	3.73187i	−0.424050	−	0.355820i
$111$		0			0
$112$	−0.319975	−	1.81467i	−0.0302348	−	0.171470i
$113$	−16.6897	−	6.07454i	−1.57003	−	0.571445i	−0.597025	−	0.802223i	$-0.703651\pi$
$113$	−16.6897	−	6.07454i	−1.57003	−	0.571445i	−0.973006	+	0.230778i	$0.925873\pi$
$114$		0			0
$115$	1.67312	−	9.48876i	0.156020	−	0.884831i
$116$	6.47846	−	11.2210i	0.601509	−	1.04185i
$117$		0			0
$118$	1.55497	+	2.69329i	0.143147	+	0.247938i
$119$	−14.7484	+	5.36798i	−1.35198	+	0.492082i
$120$		0			0
$121$	−0.867002	+	0.727501i	−0.0788184	+	0.0661365i
$122$	−0.203636	+	0.170871i	−0.0184363	+	0.0154699i
$123$		0			0
$124$	3.71250	−	1.35124i	0.333393	−	0.121345i
$125$	−5.17209	−	8.95832i	−0.462606	−	0.801256i
$126$		0			0
$127$	1.98279	−	3.43429i	0.175944	−	0.304744i	−0.764543	−	0.644572i	$-0.777036\pi$
$127$	1.98279	−	3.43429i	0.175944	−	0.304744i	0.940488	+	0.339828i	$0.110369\pi$
$128$	1.61716	−	9.17137i	0.142938	−	0.810643i
$129$		0			0
$130$	−2.32133	−	0.844896i	−0.203594	−	0.0741022i
$131$	0.0177987	+	0.100941i	0.00155508	+	0.00881927i	0.985575	−	0.169237i	$-0.0541303\pi$
$131$	0.0177987	+	0.100941i	0.00155508	+	0.00881927i	−0.984020	+	0.178056i	$0.943019\pi$
$132$		0			0
$133$	−15.4533	−	12.9668i	−1.33997	−	1.12437i
$134$	−7.87292			−0.680117
$135$		0			0
$136$	−16.5679			−1.42068
$137$	5.83691	+	4.89775i	0.498681	+	0.418443i	0.857125	−	0.515108i	$-0.172248\pi$
$137$	5.83691	+	4.89775i	0.498681	+	0.418443i	−0.358444	+	0.933551i	$0.616693\pi$
$138$		0			0
$139$	−1.81301	−	10.2821i	−0.153778	−	0.872117i	−0.959895	−	0.280361i	$-0.909546\pi$
$139$	−1.81301	−	10.2821i	−0.153778	−	0.872117i	0.806117	−	0.591756i	$-0.201565\pi$
$140$	7.79274	+	2.83633i	0.658607	+	0.239713i
$141$		0			0
$142$	1.10618	−	6.27347i	0.0928288	−	0.526458i
$143$	2.09943	−	3.63631i	0.175563	−	0.304084i
$144$		0			0
$145$	11.0348	+	19.1129i	0.916394	+	1.58724i
$146$	−8.99975	+	3.27564i	−0.744825	+	0.271094i
$147$		0			0
$148$	−5.91214	+	4.96087i	−0.485975	+	0.407781i
$149$	−6.91936	+	5.80603i	−0.566856	+	0.475648i	−0.880601	−	0.473859i	$-0.842861\pi$
$149$	−6.91936	+	5.80603i	−0.566856	+	0.475648i	0.313745	+	0.949507i	$0.398416\pi$
$150$		0			0
$151$	−22.4496	+	8.17099i	−1.82692	+	0.664946i	−0.833216	+	0.552948i	$0.813503\pi$
$151$	−22.4496	+	8.17099i	−1.82692	+	0.664946i	−0.993708	+	0.111998i	$0.964275\pi$
$152$	−10.6474	−	18.4419i	−0.863620	−	1.49583i
$153$		0			0
$154$	3.05561	−	5.29248i	0.246228	−	0.426480i
$155$	−1.16855	+	6.62716i	−0.0938599	+	0.532306i
$156$		0			0
$157$	−2.54843	−	0.927554i	−0.203387	−	0.0740269i	0.238318	−	0.971187i	$-0.423404\pi$
$157$	−2.54843	−	0.927554i	−0.203387	−	0.0740269i	−0.441705	+	0.897160i	$0.645626\pi$
$158$	−0.551105	−	3.12547i	−0.0438436	−	0.248649i
$159$		0			0
$160$	10.6564	+	8.94180i	0.842465	+	0.706912i
$161$	10.1421			0.799308
$162$		0			0
$163$	−22.0489			−1.72701			−0.863504	−	0.504343i	$-0.831735\pi$
$163$	−22.0489			−1.72701			−0.863504	+	0.504343i	$0.831735\pi$
$164$	−7.59416	−	6.37226i	−0.593005	−	0.497590i
$165$		0			0
$166$	0.123333	+	0.699457i	0.00957251	+	0.0542884i
$167$	−8.41101	−	3.06136i	−0.650863	−	0.236895i	−0.00457649	−	0.999990i	$-0.501457\pi$
$167$	−8.41101	−	3.06136i	−0.650863	−	0.236895i	−0.646287	+	0.763095i	$0.723679\pi$
$168$		0			0
$169$	−1.94719	+	11.0431i	−0.149784	+	0.849466i
$170$	5.79816	−	10.0427i	0.444699	−	0.770241i
$171$		0			0
$172$	1.63014	+	2.82349i	0.124297	+	0.215289i
$173$	−2.47538	+	0.900966i	−0.188200	+	0.0684992i	−0.434401	−	0.900720i	$-0.643040\pi$
$173$	−2.47538	+	0.900966i	−0.188200	+	0.0684992i	0.246201	+	0.969219i	$0.420818\pi$
$174$		0			0
$175$	−1.23981	+	1.04033i	−0.0937211	+	0.0786413i
$176$	−1.77272	+	1.48749i	−0.133624	+	0.112124i
$177$		0			0
$178$	2.72508	−	0.991847i	0.204253	−	0.0743421i
$179$	−1.84227	−	3.19090i	−0.137697	−	0.238499i	0.788927	−	0.614487i	$-0.210637\pi$
$179$	−1.84227	−	3.19090i	−0.137697	−	0.238499i	−0.926625	+	0.375988i	$0.877303\pi$
$180$		0			0
$181$	0.134255	−	0.232536i	0.00997906	−	0.0172842i	−0.860993	−	0.508617i	$-0.830157\pi$
$181$	0.134255	−	0.232536i	0.00997906	−	0.0172842i	0.870972	+	0.491333i	$0.163490\pi$
$182$	0.451534	−	2.56078i	0.0334699	−	0.189817i
$183$		0			0
$184$	10.0605	+	3.66173i	0.741672	+	0.269946i
$185$	−2.28273	−	12.9460i	−0.167830	−	0.951811i
$186$		0			0
$187$	15.0992	+	12.6697i	1.10416	+	0.926502i
$188$	−6.43743			−0.469498
$189$		0			0
$190$	14.9049			1.08131
$191$	−1.83696	−	1.54140i	−0.132918	−	0.111531i	0.573905	−	0.818922i	$-0.305428\pi$
$191$	−1.83696	−	1.54140i	−0.132918	−	0.111531i	−0.706823	+	0.707390i	$0.749872\pi$
$192$		0			0
$193$	0.0861647	+	0.488664i	0.00620227	+	0.0351748i	0.987752	−	0.156033i	$-0.0498706\pi$
$193$	0.0861647	+	0.488664i	0.00620227	+	0.0351748i	−0.981550	+	0.191208i	$0.938760\pi$
$194$	−4.38227	−	1.59502i	−0.314629	−	0.114515i
$195$		0			0
$196$	0.180029	−	1.02099i	0.0128592	−	0.0729282i
$197$	11.0734	−	19.1797i	0.788946	−	1.36649i	−0.137667	−	0.990479i	$-0.543960\pi$
$197$	11.0734	−	19.1797i	0.788946	−	1.36649i	0.926613	−	0.376016i	$-0.122706\pi$
$198$		0			0
$199$	−1.06624	−	1.84677i	−0.0755834	−	0.130914i	0.825756	−	0.564027i	$-0.190749\pi$
$199$	−1.06624	−	1.84677i	−0.0755834	−	0.130914i	−0.901340	+	0.433113i	$0.857415\pi$
$200$	−1.60545	+	0.584335i	−0.113522	+	0.0413187i
$201$		0			0
$202$	6.08987	−	5.11001i	0.428482	−	0.359539i
$203$	−17.7959	+	14.9325i	−1.24902	+	1.04806i
$204$		0			0
$205$	15.8674	−	5.77527i	1.10823	−	0.403362i
$206$	3.31861	+	5.74800i	0.231218	+	0.400482i
$207$		0			0
$208$	−0.492320	+	0.852724i	−0.0341363	+	0.0591257i
$209$	−4.39923	+	24.9493i	−0.304301	+	1.72578i
$210$		0			0
$211$	−18.8019	−	6.84334i	−1.29438	−	0.471115i	−0.399216	−	0.916857i	$-0.630718\pi$
$211$	−18.8019	−	6.84334i	−1.29438	−	0.471115i	−0.895162	+	0.445742i	$0.852940\pi$
$212$	0.0328255	+	0.186163i	0.00225446	+	0.0127857i
$213$		0			0
$214$	−4.61430	−	3.87186i	−0.315427	−	0.264675i
$215$	−5.55329			−0.378731
$216$		0			0
$217$	−7.08345			−0.480856
$218$	−0.747330	−	0.627084i	−0.0506156	−	0.0424715i
$219$		0			0
$220$	−1.80848	−	10.2564i	−0.121928	−	0.691488i
$221$	7.88093	+	2.86842i	0.530129	+	0.192951i
$222$		0			0
$223$	−2.30578	+	13.0767i	−0.154407	+	0.875683i	0.804920	+	0.593384i	$0.202208\pi$
$223$	−2.30578	+	13.0767i	−0.154407	+	0.875683i	−0.959326	+	0.282299i	$0.908903\pi$
$224$	−7.32144	+	12.6811i	−0.489185	+	0.847292i
$225$		0			0
$226$	6.90656	+	11.9625i	0.459418	+	0.795735i
$227$	11.7188	−	4.26531i	0.777807	−	0.283099i	0.0775490	−	0.996989i	$-0.475291\pi$
$227$	11.7188	−	4.26531i	0.777807	−	0.283099i	0.700258	+	0.713890i	$0.253068\pi$
$228$		0			0
$229$	19.6579	−	16.4949i	1.29903	−	1.09002i	0.308719	−	0.951153i	$-0.400100\pi$
$229$	19.6579	−	16.4949i	1.29903	−	1.09002i	0.990312	−	0.138862i	$-0.0443445\pi$
$230$	−5.74040	+	4.81677i	−0.378511	+	0.317608i
$231$		0			0
$232$	−23.0440	+	8.38735i	−1.51292	+	0.550656i
$233$	2.69821	+	4.67344i	0.176766	+	0.306167i	0.940771	−	0.339043i	$-0.110103\pi$
$233$	2.69821	+	4.67344i	0.176766	+	0.306167i	−0.764005	+	0.645210i	$0.776770\pi$
$234$		0			0
$235$	5.48248	−	9.49593i	0.357637	−	0.619446i
$236$	−0.968743	+	5.49402i	−0.0630598	+	0.357630i
$237$		0			0
$238$	11.4703	+	4.17485i	0.743510	+	0.270616i
$239$	1.45362	+	8.24387i	0.0940266	+	0.533252i	0.995041	+	0.0994629i	$0.0317124\pi$
$239$	1.45362	+	8.24387i	0.0940266	+	0.533252i	−0.901015	+	0.433789i	$0.857176\pi$
$240$		0			0
$241$	−0.338737	−	0.284234i	−0.0218200	−	0.0183091i	0.631812	−	0.775121i	$-0.282311\pi$
$241$	−0.338737	−	0.284234i	−0.0218200	−	0.0183091i	−0.653632	+	0.756812i	$0.726756\pi$
$242$	0.880231			0.0565834
$243$		0			0
$244$	−0.476854			−0.0305274
$245$	1.35276	+	1.13510i	0.0864246	+	0.0725189i
$246$		0			0
$247$	1.87184	+	10.6157i	0.119102	+	0.675463i
$248$	−7.02649	−	2.55743i	−0.446183	−	0.162397i
$249$		0			0
$250$	−1.39700	+	7.92278i	−0.0883540	+	0.501080i
$251$	−8.51427	+	14.7471i	−0.537416	+	0.930832i	0.461626	+	0.887074i	$0.347266\pi$
$251$	−8.51427	+	14.7471i	−0.537416	+	0.930832i	−0.999042	+	0.0437571i	$0.986067\pi$
$252$		0			0
$253$	−6.36850	−	11.0306i	−0.400384	−	0.693486i
$254$	−2.89816	+	1.05484i	−0.181847	+	0.0661869i
$255$		0			0
$256$	−10.2664	+	8.61455i	−0.641651	+	0.538409i
$257$	15.9925	−	13.4193i	0.997584	−	0.837073i	0.0109365	−	0.999940i	$-0.496519\pi$
$257$	15.9925	−	13.4193i	0.997584	−	0.837073i	0.986648	+	0.162867i	$0.0520743\pi$
$258$		0			0
$259$	13.0029	−	4.73267i	0.807961	−	0.294074i
$260$	−2.21568	−	3.83767i	−0.137411	−	0.238002i
$261$		0			0
$262$	0.0398582	−	0.0690364i	0.00246245	−	0.00426508i
$263$	3.36731	−	19.0970i	0.207637	−	1.17757i	−0.685599	−	0.727980i	$-0.740459\pi$
$263$	3.36731	−	19.0970i	0.207637	−	1.17757i	0.893236	−	0.449589i	$-0.148429\pi$
$264$		0			0
$265$	−0.302567	−	0.110125i	−0.0185865	−	0.00676495i
$266$	2.72438	+	15.4507i	0.167042	+	0.947343i
$267$		0			0
$268$	−10.8187	−	9.07797i	−0.660857	−	0.554525i
$269$	18.6791			1.13889			0.569443	−	0.822031i	$-0.307159\pi$
$269$	18.6791			1.13889			0.569443	+	0.822031i	$0.307159\pi$
$270$		0			0
$271$	12.9378			0.785917			0.392958	−	0.919556i	$-0.371452\pi$
$271$	12.9378			0.785917			0.392958	+	0.919556i	$0.371452\pi$
$272$	−3.54080	−	2.97108i	−0.214692	−	0.180148i
$273$		0			0
$274$	−1.02903	−	5.83594i	−0.0621662	−	0.352562i
$275$	1.90998	+	0.695175i	0.115176	+	0.0419206i
$276$		0			0
$277$	1.81312	−	10.2827i	0.108940	−	0.617828i	−0.880634	−	0.473798i	$-0.842883\pi$
$277$	1.81312	−	10.2827i	0.108940	−	0.617828i	0.989573	−	0.144030i	$-0.0460061\pi$
$278$	−4.06005	+	7.03221i	−0.243505	+	0.421764i
$279$		0			0
$280$	−7.84776	−	13.5927i	−0.468994	−	0.812321i
$281$	−13.4806	+	4.90655i	−0.804187	+	0.292700i	−0.711221	−	0.702969i	$-0.751857\pi$
$281$	−13.4806	+	4.90655i	−0.804187	+	0.292700i	−0.0929668	+	0.995669i	$0.529635\pi$
$282$		0			0
$283$	−14.3194	+	12.0154i	−0.851198	+	0.714240i	−0.960053	−	0.279818i	$-0.909726\pi$
$283$	−14.3194	+	12.0154i	−0.851198	+	0.714240i	0.108855	+	0.994058i	$0.465282\pi$
$284$	8.75378	−	7.34530i	0.519441	−	0.435863i
$285$		0			0
$286$	−3.06864	+	1.11689i	−0.181453	+	0.0660434i
$287$	8.88709	+	15.3929i	0.524588	+	0.908614i
$288$		0			0
$289$	−11.1848	+	19.3726i	−0.657929	+	1.13957i
$290$	2.98055	−	16.9035i	0.175024	−	0.992610i
$291$		0			0
$292$	−16.1442	−	5.87600i	−0.944766	−	0.343867i
$293$	−1.87335	−	10.6243i	−0.109442	−	0.620677i	−0.989353	−	0.145538i	$-0.953509\pi$
$293$	−1.87335	−	10.6243i	−0.109442	−	0.620677i	0.879911	−	0.475139i	$-0.157602\pi$
$294$		0			0
$295$	−7.27926	−	6.10802i	−0.423815	−	0.355623i
$296$	14.6070			0.849017
$297$		0			0
$298$	7.02493			0.406943
$299$	−4.15158	−	3.48359i	−0.240092	−	0.201461i
$300$		0			0
$301$	−1.01506	−	5.75666i	−0.0585068	−	0.331809i
$302$	17.4598	+	6.35485i	1.00470	+	0.365680i
$303$		0			0
$304$	1.03163	−	5.85067i	0.0591681	−	0.335559i
$305$	0.406116	−	0.703413i	0.0232541	−	0.0402773i
$306$		0			0
$307$	−0.0248747	−	0.0430843i	−0.00141967	−	0.00245895i	0.865315	−	0.501229i	$-0.167119\pi$
$307$	−0.0248747	−	0.0430843i	−0.00141967	−	0.00245895i	−0.866734	+	0.498770i	$0.833785\pi$
$308$	10.3015	−	3.74943i	0.586981	−	0.213644i
$309$		0			0
$310$	4.00922	−	3.36413i	0.227708	−	0.191070i
$311$	10.1389	−	8.50759i	0.574927	−	0.482421i	−0.308350	−	0.951273i	$-0.599777\pi$
$311$	10.1389	−	8.50759i	0.574927	−	0.482421i	0.883277	+	0.468852i	$0.155332\pi$
$312$		0			0
$313$	14.1733	−	5.15866i	0.801123	−	0.291585i	0.0911710	−	0.995835i	$-0.470939\pi$
$313$	14.1733	−	5.15866i	0.801123	−	0.291585i	0.709952	+	0.704250i	$0.248717\pi$
$314$	1.05460	+	1.82662i	0.0595145	+	0.103082i
$315$		0			0
$316$	2.84656	−	4.93038i	0.160131	−	0.277356i
$317$	1.49873	−	8.49970i	0.0841769	−	0.477391i	−0.913354	−	0.407166i	$-0.866517\pi$
$317$	1.49873	−	8.49970i	0.0841769	−	0.477391i	0.997531	−	0.0702251i	$-0.0223718\pi$
$318$		0			0
$319$	27.4152	+	9.97831i	1.53496	+	0.558678i
$320$	−1.27074	−	7.20673i	−0.0710365	−	0.402868i
$321$		0			0
$322$	−6.04242	−	5.07019i	−0.336731	−	0.282551i
$323$	−50.6020			−2.81557
$324$		0			0
$325$	0.864837			0.0479725
$326$	13.1363	+	11.0226i	0.727551	+	0.610488i
$327$		0			0
$328$	3.25812	+	18.4777i	0.179900	+	1.02026i
$329$	10.8458	+	3.94755i	0.597949	+	0.217636i
$330$		0			0
$331$	5.38752	−	30.5541i	0.296125	−	1.67941i	−0.366471	−	0.930430i	$-0.619434\pi$
$331$	5.38752	−	30.5541i	0.296125	−	1.67941i	0.662596	−	0.748977i	$-0.269455\pi$
$332$	−0.637037	+	1.10338i	−0.0349619	+	0.0605559i
$333$		0			0
$334$	3.48067	+	6.02869i	0.190454	+	0.329875i
$335$	22.6048	−	8.22749i	1.23503	−	0.449516i
$336$		0			0
$337$	−18.2834	+	15.3416i	−0.995962	+	0.835711i	−0.986420	−	0.164243i	$-0.947482\pi$
$337$	−18.2834	+	15.3416i	−0.995962	+	0.835711i	−0.00954207	+	0.999954i	$0.503037\pi$
$338$	6.68070	−	5.60578i	0.363382	−	0.304914i
$339$		0			0
$340$	19.5475	−	7.11471i	1.06011	−	0.385850i
$341$	4.44790	+	7.70399i	0.240867	+	0.417194i
$342$		0			0
$343$	−9.68422	+	16.7736i	−0.522899	+	0.905688i
$344$	1.07151	−	6.07685i	0.0577721	−	0.327642i
$345$		0			0
$346$	1.92519	+	0.700711i	0.103499	+	0.0376704i
$347$	3.80485	+	21.5784i	0.204255	+	1.15839i	0.898608	+	0.438752i	$0.144580\pi$
$347$	3.80485	+	21.5784i	0.204255	+	1.15839i	−0.694353	+	0.719634i	$0.744309\pi$
$348$		0			0
$349$	12.1394	+	10.1862i	0.649807	+	0.545253i	0.907012	−	0.421104i	$-0.138357\pi$
$349$	12.1394	+	10.1862i	0.649807	+	0.545253i	−0.257205	+	0.966357i	$0.582802\pi$
$350$	1.25873			0.0672819
$351$		0			0
$352$	18.3894			0.980157
$353$	9.88725	+	8.29639i	0.526245	+	0.441572i	0.866802	−	0.498652i	$-0.166171\pi$
$353$	9.88725	+	8.29639i	0.526245	+	0.441572i	−0.340557	+	0.940224i	$0.610616\pi$
$354$		0			0
$355$	3.37992	+	19.1685i	0.179388	+	1.01736i
$356$	4.88837	+	1.77922i	0.259083	+	0.0942985i
$357$		0			0
$358$	−0.497603	+	2.82204i	−0.0262991	+	0.149150i
$359$	−12.9142	+	22.3681i	−0.681588	+	1.18054i	0.292909	+	0.956140i	$0.405377\pi$
$359$	−12.9142	+	22.3681i	−0.681588	+	1.18054i	−0.974496	+	0.224404i	$0.927956\pi$
$360$		0			0
$361$	−23.0196	−	39.8711i	−1.21156	−	2.09848i
$362$	−0.196234	+	0.0714235i	−0.0103138	+	0.00375393i
$363$		0			0
$364$	3.57322	−	2.99829i	0.187288	−	0.157153i
$365$	22.4171	−	18.8101i	1.17336	−	0.984568i
$366$		0			0
$367$	−15.0112	+	5.46363i	−0.783578	+	0.285199i	−0.702664	−	0.711522i	$-0.748006\pi$
$367$	−15.0112	+	5.46363i	−0.783578	+	0.285199i	−0.0809141	+	0.996721i	$0.525784\pi$
$368$	1.49343	+	2.58669i	0.0778503	+	0.134841i
$369$		0			0
$370$	−5.11194	+	8.85413i	−0.265757	+	0.460304i
$371$	0.0588538	−	0.333777i	0.00305554	−	0.0173288i
$372$		0			0
$373$	−1.71641	−	0.624722i	−0.0888724	−	0.0323469i	0.297201	−	0.954815i	$-0.403947\pi$
$373$	−1.71641	−	0.624722i	−0.0888724	−	0.0323469i	−0.386074	+	0.922468i	$0.626169\pi$
$374$	−2.66195	−	15.0967i	−0.137646	−	0.780630i
$375$		0			0
$376$	9.33336	+	7.83162i	0.481331	+	0.403885i
$377$	12.4136			0.639332
$378$		0			0
$379$	1.14694			0.0589141			0.0294571	−	0.999566i	$-0.490622\pi$
$379$	1.14694			0.0589141			0.0294571	+	0.999566i	$0.490622\pi$
$380$	20.4817	+	17.1862i	1.05069	+	0.881635i
$381$		0			0
$382$	0.323852	+	1.83666i	0.0165697	+	0.0939716i
$383$	−20.5112	−	7.46546i	−1.04807	−	0.381467i	−0.240138	−	0.970739i	$-0.577193\pi$
$383$	−20.5112	−	7.46546i	−1.04807	−	0.381467i	−0.807935	+	0.589272i	$0.799415\pi$
$384$		0			0
$385$	−3.24249	+	18.3891i	−0.165253	+	0.937194i
$386$	0.192957	−	0.334210i	0.00982123	−	0.0170109i
$387$		0			0
$388$	−4.18281	−	7.24484i	−0.212350	−	0.367801i
$389$	24.6164	−	8.95962i	1.24810	−	0.454271i	0.368340	−	0.929691i	$-0.379926\pi$
$389$	24.6164	−	8.95962i	1.24810	−	0.454271i	0.879759	+	0.475420i	$0.157704\pi$
$390$		0			0
$391$	19.4887	−	16.3529i	0.985584	−	0.827003i
$392$	−1.50313	+	1.26128i	−0.0759197	+	0.0637042i
$393$		0			0
$394$	−16.1855	+	5.89104i	−0.815414	+	0.296787i
$395$	4.84858	+	8.39798i	0.243958	+	0.422548i
$396$		0			0
$397$	−2.09915	+	3.63584i	−0.105353	+	0.182478i	−0.913883	−	0.405979i	$-0.866931\pi$
$397$	−2.09915	+	3.63584i	−0.105353	+	0.182478i	0.808529	+	0.588456i	$0.200264\pi$
$398$	−0.287994	+	1.63330i	−0.0144358	+	0.0818697i
$399$		0			0
$400$	−0.447894	−	0.163020i	−0.0223947	−	0.00815101i
$401$	−1.35963	−	7.71086i	−0.0678968	−	0.385062i	−0.999753	−	0.0222335i	$-0.992922\pi$
$401$	−1.35963	−	7.71086i	−0.0678968	−	0.385062i	0.931856	−	0.362828i	$-0.118189\pi$
$402$		0			0
$403$	2.89955	+	2.43301i	0.144437	+	0.121197i
$404$	14.2606			0.709493
$405$		0			0
$406$	18.0674			0.896669
$407$	−13.3122	−	11.1702i	−0.659859	−	0.553687i
$408$		0			0
$409$	−3.02651	−	17.1642i	−0.149651	−	0.848716i	−0.963514	−	0.267658i	$-0.913750\pi$
$409$	−3.02651	−	17.1642i	−0.149651	−	0.848716i	0.813863	−	0.581057i	$-0.197361\pi$
$410$	−12.3406	−	4.49161i	−0.609459	−	0.221825i
$411$		0			0
$412$	−2.06748	+	11.7253i	−0.101857	+	0.577662i
$413$	5.00118	−	8.66229i	0.246092	−	0.426243i
$414$		0			0
$415$	−1.08507	−	1.87940i	−0.0532642	−	0.0922563i
$416$	7.35266	−	2.67615i	0.360494	−	0.131209i
$417$		0			0
$418$	15.0935	−	12.6650i	0.738249	−	0.619464i
$419$	8.79662	−	7.38124i	0.429743	−	0.360597i	−0.402112	−	0.915591i	$-0.631724\pi$
$419$	8.79662	−	7.38124i	0.429743	−	0.360597i	0.831855	+	0.554993i	$0.187279\pi$
$420$		0			0
$421$	−6.85151	+	2.49375i	−0.333922	+	0.121538i	−0.503539	−	0.863972i	$-0.667969\pi$
$421$	−6.85151	+	2.49375i	−0.333922	+	0.121538i	0.169617	+	0.985510i	$0.445747\pi$
$422$	7.78066	+	13.4765i	0.378757	+	0.656026i
$423$		0			0
$424$	0.178889	−	0.309844i	0.00868759	−	0.0150474i
$425$	−0.704975	+	3.99811i	−0.0341963	+	0.193937i
$426$		0			0
$427$	0.803405	+	0.292416i	0.0388795	+	0.0141510i
$428$	−1.87632	−	10.6411i	−0.0906954	−	0.514359i
$429$		0			0
$430$	3.30853	+	2.77618i	0.159551	+	0.133879i
$431$	0.389084			0.0187415			0.00937075	−	0.999956i	$-0.497017\pi$
$431$	0.389084			0.0187415			0.00937075	+	0.999956i	$0.497017\pi$
$432$		0			0
$433$	24.1011			1.15822			0.579112	−	0.815248i	$-0.303400\pi$
$433$	24.1011			1.15822			0.579112	+	0.815248i	$0.303400\pi$
$434$	4.22016	+	3.54113i	0.202574	+	0.169980i
$435$		0			0
$436$	−0.303888	−	1.72344i	−0.0145536	−	0.0825376i
$437$	30.7271	+	11.1837i	1.46988	+	0.534991i
$438$		0			0
$439$	6.36691	−	36.1086i	0.303876	−	1.72337i	−0.324871	−	0.945758i	$-0.605321\pi$
$439$	6.36691	−	36.1086i	0.303876	−	1.72337i	0.628748	−	0.777609i	$-0.283568\pi$
$440$	−9.85567	+	17.0705i	−0.469851	+	0.813805i
$441$		0			0
$442$	−3.26131	−	5.64875i	−0.155125	−	0.268684i
$443$	35.5078	−	12.9238i	1.68703	−	0.614028i	0.692782	−	0.721147i	$-0.256385\pi$
$443$	35.5078	−	12.9238i	1.68703	−	0.614028i	0.994246	+	0.107118i	$0.0341624\pi$
$444$		0			0
$445$	−6.78776	+	5.69561i	−0.321771	+	0.269998i
$446$	7.91101	−	6.63813i	0.374597	−	0.314324i
$447$		0			0
$448$	7.23838	−	2.63456i	0.341981	−	0.124471i
$449$	−5.89289	−	10.2068i	−0.278103	−	0.481688i	0.692811	−	0.721120i	$-0.256372\pi$
$449$	−5.89289	−	10.2068i	−0.278103	−	0.481688i	−0.970913	+	0.239432i	$0.923039\pi$
$450$		0			0
$451$	11.1609	−	19.3313i	0.525547	−	0.910274i
$452$	−4.30276	+	24.4022i	−0.202385	+	1.14778i
$453$		0			0
$454$	−9.11412	−	3.31727i	−0.427747	−	0.155687i
$455$	1.37965	+	7.82441i	0.0646792	+	0.366814i
$456$		0			0
$457$	−15.2105	−	12.7631i	−0.711517	−	0.597034i	0.213507	−	0.976942i	$-0.431511\pi$
$457$	−15.2105	−	12.7631i	−0.711517	−	0.597034i	−0.925024	+	0.379908i	$0.875956\pi$
$458$	−19.9578			−0.932568
$459$		0			0
$460$	−13.4423			−0.626750
$461$	−5.85398	−	4.91207i	−0.272647	−	0.228778i	0.496204	−	0.868206i	$-0.334727\pi$
$461$	−5.85398	−	4.91207i	−0.272647	−	0.228778i	−0.768851	+	0.639428i	$0.779171\pi$
$462$		0			0
$463$	−2.77046	−	15.7120i	−0.128754	−	0.730200i	−0.979007	−	0.203826i	$-0.934662\pi$
$463$	−2.77046	−	15.7120i	−0.128754	−	0.730200i	0.850253	−	0.526374i	$-0.176449\pi$
$464$	−6.42893	−	2.33994i	−0.298455	−	0.108629i
$465$		0			0
$466$	0.728797	−	4.13321i	0.0337609	−	0.191467i
$467$	−13.0703	+	22.6385i	−0.604822	+	1.04758i	0.387257	+	0.921972i	$0.373423\pi$
$467$	−13.0703	+	22.6385i	−0.604822	+	1.04758i	−0.992080	+	0.125611i	$0.959911\pi$
$468$		0			0
$469$	12.6606	+	21.9288i	0.584613	+	1.01258i
$470$	−8.01351	+	2.91668i	−0.369636	+	0.134536i
$471$		0			0
$472$	8.08842	−	6.78699i	0.372300	−	0.312397i
$473$	−5.62359	+	4.71875i	−0.258573	+	0.216968i
$474$		0			0
$475$	−4.90339	+	1.78469i	−0.224983	+	0.0818871i
$476$	10.9483	+	18.9629i	0.501812	+	0.869164i
$477$		0			0
$478$	3.25522	−	5.63820i	0.148890	−	0.257885i
$479$	6.83310	−	38.7525i	0.312213	−	1.77065i	−0.275229	−	0.961379i	$-0.588754\pi$
$479$	6.83310	−	38.7525i	0.312213	−	1.77065i	0.587442	−	0.809267i	$-0.300135\pi$
$480$		0			0
$481$	−6.94820	−	2.52894i	−0.316811	−	0.115310i
$482$	0.0597185	+	0.338680i	0.00272010	+	0.0154265i
$483$		0			0
$484$	1.20958	+	1.01496i	0.0549811	+	0.0461346i
$485$	14.2493			0.647027
$486$		0			0
$487$	11.7133			0.530779			0.265389	−	0.964141i	$-0.414500\pi$
$487$	11.7133			0.530779			0.265389	+	0.964141i	$0.414500\pi$
$488$	0.691370	+	0.580128i	0.0312968	+	0.0262612i
$489$		0			0
$490$	−0.238488	−	1.35253i	−0.0107738	−	0.0611013i
$491$	36.2250	+	13.1848i	1.63481	+	0.595023i	0.986121	−	0.166030i	$-0.0530947\pi$
$491$	36.2250	+	13.1848i	1.63481	+	0.595023i	0.648691	+	0.761052i	$0.275317\pi$
$492$		0			0
$493$	−10.1190	+	57.3876i	−0.455736	+	2.58461i
$494$	4.19178	−	7.26038i	0.188597	−	0.326660i
$495$		0			0
$496$	−1.04304	−	1.80660i	−0.0468340	−	0.0811189i
$497$	−19.2527	+	7.00740i	−0.863601	+	0.314325i
$498$		0			0
$499$	−22.6455	+	19.0018i	−1.01375	+	0.850638i	−0.988830	−	0.149051i	$-0.952378\pi$
$499$	−22.6455	+	19.0018i	−1.01375	+	0.850638i	−0.0249220	+	0.999689i	$0.507934\pi$
$500$	−11.0552	+	9.27638i	−0.494402	+	0.414853i
$501$		0			0
$502$	12.4450	−	4.52959i	0.555445	−	0.202166i
$503$	−17.7888	−	30.8110i	−0.793161	−	1.37380i	−0.924000	−	0.382392i	$-0.875100\pi$
$503$	−17.7888	−	30.8110i	−0.793161	−	1.37380i	0.130839	−	0.991404i	$-0.458233\pi$
$504$		0			0
$505$	−12.1452	+	21.0361i	−0.540453	+	0.936092i
$506$	−1.72015	+	9.75548i	−0.0764702	+	0.433684i
$507$		0			0
$508$	−5.19886	−	1.89223i	−0.230662	−	0.0839541i
$509$	−4.92854	−	27.9512i	−0.218454	−	1.23891i	−0.874812	−	0.484463i	$-0.839015\pi$
$509$	−4.92854	−	27.9512i	−0.218454	−	1.23891i	0.656358	−	0.754450i	$-0.272096\pi$
$510$		0			0
$511$	23.5965	+	19.7998i	1.04385	+	0.875892i
$512$	−8.20265			−0.362510
$513$		0			0
$514$	−16.2365			−0.716161
$515$	−15.5353	−	13.0357i	−0.684567	−	0.574420i
$516$		0			0
$517$	−2.51702	−	14.2747i	−0.110698	−	0.627801i
$518$	−10.1128	−	3.68075i	−0.444330	−	0.161723i
$519$		0			0
$520$	−1.45639	+	8.25961i	−0.0638670	+	0.362208i
$521$	12.7176	−	22.0275i	0.557167	−	0.965041i	−0.440565	−	0.897721i	$-0.645222\pi$
$521$	12.7176	−	22.0275i	0.557167	−	0.965041i	0.997731	−	0.0673204i	$-0.0214450\pi$
$522$		0			0
$523$	−4.20395	−	7.28145i	−0.183826	−	0.318396i	0.759354	−	0.650677i	$-0.225515\pi$
$523$	−4.20395	−	7.28145i	−0.183826	−	0.318396i	−0.943180	+	0.332282i	$0.892182\pi$
$524$	0.134375	−	0.0489085i	0.00587020	−	0.00213658i
$525$		0			0
$526$	−11.5531	+	9.69416i	−0.503737	+	0.422686i
$527$	−13.6113	+	11.4212i	−0.592918	+	0.497517i
$528$		0			0
$529$	6.16460	−	2.24373i	0.268026	−	0.0975535i
$530$	0.125209	+	0.216868i	0.00543873	+	0.00942016i
$531$		0			0
$532$	−14.0719	+	24.3732i	−0.610093	+	1.05671i
$533$	1.64927	−	9.35348i	0.0714379	−	0.405144i
$534$		0			0
$535$	17.2949	+	6.29482i	0.747723	+	0.272149i
$536$	4.64155	+	26.3235i	0.200484	+	1.13700i
$537$		0			0
$538$	−11.1286	−	9.33801i	−0.479788	−	0.402590i
$539$	2.33440			0.100550
$540$		0			0
$541$	−12.8635			−0.553043			−0.276522	−	0.961008i	$-0.589182\pi$
$541$	−12.8635			−0.553043			−0.276522	+	0.961008i	$0.589182\pi$
$542$	−7.70806	−	6.46783i	−0.331090	−	0.277817i
$543$		0			0
$544$	6.37820	+	36.1726i	0.273463	+	1.55089i
$545$	2.80107	+	1.01951i	0.119985	+	0.0436708i
$546$		0			0
$547$	2.27340	−	12.8931i	0.0972034	−	0.551268i	−0.896847	−	0.442342i	$-0.854148\pi$
$547$	2.27340	−	12.8931i	0.0972034	−	0.551268i	0.994050	−	0.108926i	$-0.0347411\pi$
$548$	5.31514	−	9.20609i	0.227051	−	0.393265i
$549$		0			0
$550$	−0.790392	−	1.36900i	−0.0337024	−	0.0583743i
$551$	−70.3817	+	25.6168i	−2.99836	+	1.09131i
$552$		0			0
$553$	−7.81929	+	6.56116i	−0.332510	+	0.279009i
$554$	−6.22071	+	5.21980i	−0.264293	+	0.221768i
$555$		0			0
$556$	−13.6878	+	4.98193i	−0.580490	+	0.211281i
$557$	−2.29110	−	3.96830i	−0.0970769	−	0.168142i	0.813397	−	0.581710i	$-0.197616\pi$
$557$	−2.29110	−	3.96830i	−0.0970769	−	0.168142i	−0.910474	+	0.413567i	$0.864283\pi$
$558$		0			0
$559$	−1.56179	+	2.70509i	−0.0660565	+	0.114413i
$560$	0.760371	−	4.31228i	0.0321316	−	0.182227i
$561$		0			0
$562$	10.4843	+	3.81598i	0.442255	+	0.160968i
$563$	2.13308	+	12.0973i	0.0898986	+	0.509840i	0.996192	+	0.0871905i	$0.0277889\pi$
$563$	2.13308	+	12.0973i	0.0898986	+	0.509840i	−0.906293	+	0.422650i	$0.861100\pi$
$564$		0			0
$565$	−32.3315	−	27.1293i	−1.36020	−	1.14134i
$566$	14.5378			0.611071
$567$		0			0
$568$	−21.6278			−0.907484
$569$	11.1028	+	9.31634i	0.465453	+	0.390561i	0.845133	−	0.534557i	$-0.179521\pi$
$569$	11.1028	+	9.31634i	0.465453	+	0.390561i	−0.379680	+	0.925118i	$0.623966\pi$
$570$		0			0
$571$	−3.82814	−	21.7104i	−0.160203	−	0.908554i	−0.953874	−	0.300207i	$-0.902944\pi$
$571$	−3.82814	−	21.7104i	−0.160203	−	0.908554i	0.793672	−	0.608346i	$-0.208167\pi$
$572$	−5.50467	−	2.00354i	−0.230162	−	0.0837721i
$573$		0			0
$574$	2.40044	−	13.6135i	0.100192	−	0.568218i
$575$	1.31172	−	2.27197i	0.0547025	−	0.0947475i
$576$		0			0
$577$	15.7418	+	27.2655i	0.655338	+	1.13508i	0.981809	+	0.189872i	$0.0608072\pi$
$577$	15.7418	+	27.2655i	0.655338	+	1.13508i	−0.326471	+	0.945207i	$0.605859\pi$
$578$	16.3483	−	5.95031i	0.680001	−	0.247500i
$579$		0			0
$580$	23.5866	−	19.7915i	0.979380	−	0.821798i
$581$	1.74990	−	1.46834i	0.0725979	−	0.0609169i
$582$		0			0
$583$	−0.399973	+	0.145578i	−0.0165652	+	0.00602923i
$584$	16.2582	+	28.1600i	0.672768	+	1.16527i
$585$		0			0
$586$	−4.19516	+	7.26623i	−0.173300	+	0.300165i
$587$	−2.49523	+	14.1511i	−0.102989	+	0.584080i	0.889015	+	0.457877i	$0.151390\pi$
$587$	−2.49523	+	14.1511i	−0.102989	+	0.584080i	−0.992004	+	0.126203i	$0.959721\pi$
$588$		0			0
$589$	−21.4605	−	7.81097i	−0.884263	−	0.321845i
$590$	1.28332	+	7.27804i	0.0528333	+	0.299632i
$591$		0			0
$592$	3.12173	+	2.61944i	0.128302	+	0.107659i
$593$	−41.0988			−1.68772			−0.843862	−	0.536560i	$-0.819724\pi$
$593$	−41.0988			−1.68772			−0.843862	+	0.536560i	$0.819724\pi$
$594$		0			0
$595$	−37.2966			−1.52901
$596$	9.65342	+	8.10018i	0.395419	+	0.331796i
$597$		0			0
$598$	0.731913	+	4.15089i	0.0299301	+	0.169742i
$599$	−8.04580	−	2.92843i	−0.328742	−	0.119652i	0.172376	−	0.985031i	$-0.444856\pi$
$599$	−8.04580	−	2.92843i	−0.328742	−	0.119652i	−0.501118	+	0.865379i	$0.667078\pi$
$600$		0			0
$601$	−0.283951	+	1.61037i	−0.0115826	+	0.0656883i	−0.990051	−	0.140707i	$-0.955062\pi$
$601$	−0.283951	+	1.61037i	−0.0115826	+	0.0656883i	0.978469	+	0.206396i	$0.0661734\pi$
$602$	−2.27311	+	3.93713i	−0.0926449	+	0.160466i
$603$		0			0
$604$	16.6651	+	28.8648i	0.678094	+	1.17449i
$605$	−2.52733	+	0.919873i	−0.102751	+	0.0373982i
$606$		0			0
$607$	5.03248	−	4.22275i	0.204262	−	0.171396i	−0.534918	−	0.844904i	$-0.679658\pi$
$607$	5.03248	−	4.22275i	0.204262	−	0.171396i	0.739180	+	0.673508i	$0.235213\pi$
$608$	−36.1651	+	30.3461i	−1.46669	+	1.23070i
$609$		0			0
$610$	−0.593602	+	0.216054i	−0.0240343	+	0.00874775i
$611$	−3.08374	−	5.34120i	−0.124755	−	0.216082i
$612$		0			0
$613$	13.1363	−	22.7527i	0.530569	−	0.918973i	−0.468795	−	0.883307i	$-0.655312\pi$
$613$	13.1363	−	22.7527i	0.530569	−	0.918973i	0.999364	−	0.0356656i	$-0.0113551\pi$
$614$	−0.00671875	+	0.0381039i	−0.000271147	+	0.00153775i
$615$		0			0
$616$	−19.4971	−	7.09638i	−0.785562	−	0.285921i
$617$	−1.08930	−	6.17772i	−0.0438535	−	0.248706i	0.954998	−	0.296611i	$-0.0958565\pi$
$617$	−1.08930	−	6.17772i	−0.0438535	−	0.248706i	−0.998852	+	0.0479054i	$0.984745\pi$
$618$		0			0
$619$	3.78493	+	3.17593i	0.152129	+	0.127651i	0.715676	−	0.698433i	$-0.246119\pi$
$619$	3.78493	+	3.17593i	0.152129	+	0.127651i	−0.563546	+	0.826084i	$0.690563\pi$
$620$	9.38839			0.377047
$621$		0			0
$622$	−10.2936			−0.412738
$623$	−7.14489	−	5.99528i	−0.286254	−	0.240196i
$624$		0			0
$625$	−4.83028	−	27.3939i	−0.193211	−	1.09576i
$626$	−11.0230	−	4.01206i	−0.440569	−	0.160354i
$627$		0			0
$628$	−0.657012	+	3.72610i	−0.0262176	+	0.148688i
$629$	17.3550	−	30.0598i	0.691991	−	1.19856i
$630$		0			0
$631$	3.46210	+	5.99653i	0.137824	+	0.238718i	0.926673	−	0.375869i	$-0.122656\pi$
$631$	3.46210	+	5.99653i	0.137824	+	0.238718i	−0.788849	+	0.614587i	$0.789322\pi$
$632$	−10.1253	+	3.68530i	−0.402762	+	0.146593i
$633$		0			0
$634$	−5.14205	+	4.31469i	−0.204217	+	0.171358i
$635$	7.21889	−	6.05737i	0.286473	−	0.240379i
$636$		0			0
$637$	0.933370	−	0.339719i	0.0369815	−	0.0134601i
$638$	−11.3450	−	19.6502i	−0.449154	−	0.777957i
$639$		0			0
$640$	11.0653	−	19.1657i	0.437394	−	0.757589i
$641$	−5.88995	+	33.4036i	−0.232639	+	1.31936i	0.614890	+	0.788613i	$0.289200\pi$
$641$	−5.88995	+	33.4036i	−0.232639	+	1.31936i	−0.847529	+	0.530749i	$0.821911\pi$
$642$		0			0
$643$	−7.25745	−	2.64150i	−0.286206	−	0.104170i	0.194928	−	0.980818i	$-0.437553\pi$
$643$	−7.25745	−	2.64150i	−0.286206	−	0.104170i	−0.481134	+	0.876647i	$0.659775\pi$
$644$	−2.45704	−	13.9346i	−0.0968210	−	0.549099i
$645$		0			0
$646$	30.1476	+	25.2968i	1.18614	+	0.995289i
$647$	35.1862			1.38331			0.691655	−	0.722228i	$-0.256882\pi$
$647$	35.1862			1.38331			0.691655	+	0.722228i	$0.256882\pi$
$648$		0			0
$649$	−12.5615			−0.493083
$650$	−0.515251	−	0.432347i	−0.0202098	−	0.0169580i
$651$		0			0
$652$	5.34163	+	30.2939i	0.209194	+	1.18640i
$653$	−18.3353	−	6.67349i	−0.717514	−	0.261154i	−0.0426440	−	0.999090i	$-0.513578\pi$
$653$	−18.3353	−	6.67349i	−0.717514	−	0.261154i	−0.674870	+	0.737937i	$0.735800\pi$
$654$		0			0
$655$	−0.0422958	+	0.239871i	−0.00165263	+	0.00937255i
$656$	−2.61726	+	4.53323i	−0.102187	+	0.176993i
$657$		0			0
$658$	−4.48824	−	7.77386i	−0.174970	−	0.303057i
$659$	−21.6942	+	7.89603i	−0.845085	+	0.307586i	−0.728035	−	0.685540i	$-0.759566\pi$
$659$	−21.6942	+	7.89603i	−0.845085	+	0.307586i	−0.117050	+	0.993126i	$0.537344\pi$
$660$		0			0
$661$	−5.26760	+	4.42004i	−0.204886	+	0.171920i	−0.739457	−	0.673204i	$-0.764918\pi$
$661$	−5.26760	+	4.42004i	−0.204886	+	0.171920i	0.534571	+	0.845123i	$0.320473\pi$
$662$	−18.4843	+	15.5102i	−0.718412	+	0.602819i
$663$		0			0
$664$	2.26596	−	0.824741i	0.0879362	−	0.0320062i
$665$	−23.9688	−	41.5152i	−0.929471	−	1.60989i
$666$		0			0
$667$	18.8280	−	32.6110i	0.729023	−	1.26270i
$668$	−2.16844	+	12.2978i	−0.0838995	+	0.475818i
$669$		0			0
$670$	−17.5805	−	6.39879i	−0.679195	−	0.247207i
$671$	−0.186449	−	1.05740i	−0.00719777	−	0.0408206i
$672$		0			0
$673$	−23.4964	−	19.7158i	−0.905718	−	0.759988i	0.0655815	−	0.997847i	$-0.479110\pi$
$673$	−23.4964	−	19.7158i	−0.905718	−	0.759988i	−0.971300	+	0.237859i	$0.923554\pi$
$674$	18.5624			0.714997
$675$		0			0
$676$	15.6442			0.601700
$677$	−10.4059	−	8.73161i	−0.399932	−	0.335583i	0.420535	−	0.907276i	$-0.361842\pi$
$677$	−10.4059	−	8.73161i	−0.399932	−	0.335583i	−0.820467	+	0.571693i	$0.806287\pi$
$678$		0			0
$679$	2.60455	+	14.7711i	0.0999534	+	0.566864i
$680$	−36.9967	−	13.4657i	−1.41876	−	0.516386i
$681$		0			0
$682$	1.20139	−	6.81344i	0.0460037	−	0.260900i
$683$	3.03350	−	5.25418i	0.116074	−	0.201045i	−0.802135	−	0.597143i	$-0.796302\pi$
$683$	3.03350	−	5.25418i	0.116074	−	0.201045i	0.918208	+	0.396098i	$0.129636\pi$
$684$		0			0
$685$	9.05335	+	15.6809i	0.345911	+	0.599135i
$686$	14.1550	−	5.15201i	0.540442	−	0.196705i
$687$		0			0
$688$	1.31875	−	1.10656i	0.0502767	−	0.0421871i
$689$	−0.138736	+	0.116414i	−0.00528544	+	0.00443501i
$690$		0			0
$691$	−19.4188	+	7.06787i	−0.738727	+	0.268875i	−0.683854	−	0.729619i	$-0.739698\pi$
$691$	−19.4188	+	7.06787i	−0.738727	+	0.268875i	−0.0548728	+	0.998493i	$0.517475\pi$
$692$	1.83756	+	3.18275i	0.0698537	+	0.120990i
$693$		0			0
$694$	8.52054	−	14.7580i	0.323435	−	0.560206i
$695$	4.30835	−	24.4339i	0.163425	−	0.926830i
$696$		0			0
$697$	41.8964	+	15.2490i	1.58694	+	0.577599i
$698$	−2.14015	−	12.1374i	−0.0810058	−	0.459407i
$699$		0			0
$700$	1.72970	+	1.45139i	0.0653766	+	0.0548575i
$701$	11.0222			0.416303			0.208151	−	0.978097i	$-0.433255\pi$
$701$	11.0222			0.416303			0.208151	+	0.978097i	$0.433255\pi$
$702$		0			0
$703$	44.6131			1.68262
$704$	−7.41054	−	6.21818i	−0.279295	−	0.234356i
$705$		0			0
$706$	−1.74310	−	9.88560i	−0.0656024	−	0.372050i
$707$	−24.0264	−	8.74489i	−0.903605	−	0.328885i
$708$		0			0
$709$	−1.90795	+	10.8205i	−0.0716546	+	0.406373i	0.927792	+	0.373099i	$0.121705\pi$
$709$	−1.90795	+	10.8205i	−0.0716546	+	0.406373i	−0.999446	+	0.0332746i	$0.989406\pi$
$710$	7.56897	−	13.1098i	0.284058	−	0.492003i
$711$		0			0
$712$	−4.92288	−	8.52669i	−0.184493	−	0.319551i
$713$	10.7895	−	3.92704i	0.404068	−	0.147069i
$714$		0			0
$715$	7.64354	−	6.41369i	0.285852	−	0.239858i
$716$	−3.93778	+	3.30419i	−0.147162	+	0.123483i
$717$		0			0
$718$	18.8762	−	6.87038i	0.704454	−	0.256400i
$719$	−16.3529	−	28.3240i	−0.609859	−	1.05631i	−0.991263	−	0.131898i	$-0.957893\pi$
$719$	−16.3529	−	28.3240i	−0.609859	−	1.05631i	0.381404	−	0.924408i	$-0.375441\pi$
$720$		0			0
$721$	10.6734	−	18.4870i	0.397500	−	0.688490i
$722$	−6.21768	+	35.2622i	−0.231398	+	1.31232i
$723$		0			0
$724$	−0.352014	−	0.128123i	−0.0130825	−	0.00476164i
$725$	1.04347	+	5.91781i	0.0387535	+	0.219782i
$726$		0			0
$727$	29.4625	+	24.7220i	1.09271	+	0.916888i	0.996913	−	0.0785129i	$-0.0250172\pi$
$727$	29.4625	+	24.7220i	1.09271	+	0.916888i	0.0957920	+	0.995401i	$0.469462\pi$
$728$	−8.82830			−0.327199
$729$		0			0
$730$	−22.7591			−0.842352
$731$	−11.2325	−	9.42515i	−0.415447	−	0.348602i
$732$		0			0
$733$	2.44978	+	13.8934i	0.0904849	+	0.513165i	0.996038	+	0.0889317i	$0.0283453\pi$
$733$	2.44978	+	13.8934i	0.0904849	+	0.513165i	−0.905553	+	0.424233i	$0.860544\pi$
$734$	11.6747	+	4.24924i	0.430921	+	0.156842i
$735$		0			0
$736$	4.12160	−	23.3748i	0.151924	−	0.861605i
$737$	15.8999	−	27.5395i	0.585681	−	1.01443i
$738$		0			0
$739$	5.92286	+	10.2587i	0.217876	+	0.377372i	0.954158	−	0.299302i	$-0.0967539\pi$
$739$	5.92286	+	10.2587i	0.217876	+	0.377372i	−0.736283	+	0.676674i	$0.763421\pi$
$740$	−17.2340	+	6.27267i	−0.633535	+	0.230588i
$741$		0			0
$742$	−0.201924	+	0.169435i	−0.00741288	+	0.00622014i
$743$	−16.6749	+	13.9919i	−0.611743	+	0.513314i	−0.895196	−	0.445673i	$-0.852965\pi$
$743$	−16.6749	+	13.9919i	−0.611743	+	0.513314i	0.283453	+	0.958986i	$0.408520\pi$
$744$		0			0
$745$	−20.1701	+	7.34131i	−0.738974	+	0.268965i
$746$	0.710290	+	1.23026i	0.0260056	+	0.0450429i
$747$		0			0
$748$	13.7494	−	23.8147i	0.502729	−	0.870753i
$749$	−3.36412	+	19.0788i	−0.122922	+	0.697126i
$750$		0			0
$751$	39.9830	+	14.5526i	1.45900	+	0.531033i	0.945090	−	0.326811i	$-0.105974\pi$
$751$	39.9830	+	14.5526i	1.45900	+	0.531033i	0.513911	+	0.857844i	$0.328196\pi$
$752$	0.590247	+	3.34746i	0.0215241	+	0.122069i
$753$		0			0
$754$	−7.39574	−	6.20576i	−0.269337	−	0.226000i
$755$	−56.7719			−2.06614
$756$		0			0
$757$	−20.6382			−0.750110			−0.375055	−	0.927003i	$-0.622376\pi$
$757$	−20.6382			−0.750110			−0.375055	+	0.927003i	$0.622376\pi$
$758$	−0.683318	−	0.573372i	−0.0248192	−	0.0208258i
$759$		0			0
$760$	−8.78728	−	49.8352i	−0.318748	−	1.80771i
$761$	46.4631	+	16.9112i	1.68429	+	0.613030i	0.993887	−	0.110398i	$-0.0352125\pi$
$761$	46.4631	+	16.9112i	1.68429	+	0.613030i	0.690400	+	0.723428i	$0.257435\pi$
$762$		0			0
$763$	−0.544851	+	3.09000i	−0.0197249	+	0.111866i
$764$	−1.67275	+	2.89729i	−0.0605181	+	0.104820i
$765$		0			0
$766$	8.48799	+	14.7016i	0.306684	+	0.531192i
$767$	−5.02250	+	1.82804i	−0.181352	+	0.0660067i
$768$		0			0
$769$	16.9553	−	14.2272i	0.611424	−	0.513046i	−0.283670	−	0.958922i	$-0.591552\pi$
$769$	16.9553	−	14.2272i	0.611424	−	0.513046i	0.895095	+	0.445876i	$0.147108\pi$
$770$	11.1248	−	9.33482i	0.400910	−	0.336403i
$771$		0			0
$772$	0.650520	−	0.236770i	0.0234127	−	0.00852153i
$773$	−10.9836	−	19.0241i	−0.395051	−	0.684248i	0.598057	−	0.801454i	$-0.295940\pi$
$773$	−10.9836	−	19.0241i	−0.395051	−	0.684248i	−0.993108	+	0.117206i	$0.962606\pi$
$774$		0			0
$775$	−0.916134	+	1.58679i	−0.0329085	+	0.0569992i
$776$	−2.74941	+	15.5927i	−0.0986982	+	0.559745i
$777$		0			0
$778$	−19.1449	−	6.96819i	−0.686379	−	0.249822i
$779$	9.95104	+	56.4351i	0.356533	+	2.02200i

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.595778 - 0.499917i) q^{2} +(-0.242262 - 1.37394i) q^{4} +(2.23304 + 0.812759i) q^{5} +(-0.434359 + 2.46337i) q^{7} +(-1.32025 + 2.28674i) q^{8} +O(q^{10})\)	\(q+(-0.595778 - 0.499917i) q^{2} +(-0.242262 - 1.37394i) q^{4} +(2.23304 + 0.812759i) q^{5} +(-0.434359 + 2.46337i) q^{7} +(-1.32025 + 2.28674i) q^{8} +(-0.924081 - 1.60056i) q^{10} +(2.95192 - 1.07441i) q^{11} +(1.02392 - 0.859169i) q^{13} +(1.49026 - 1.25048i) q^{14} +(-0.692233 + 0.251952i) q^{16} +(3.13726 + 5.43389i) q^{17} +(-4.03234 + 6.98422i) q^{19} +(0.575699 - 3.26495i) q^{20} +(-2.29581 - 0.835605i) q^{22} +(-0.704074 - 3.99300i) q^{23} +(0.495652 + 0.415902i) q^{25} -1.03954 q^{26} +3.48975 q^{28} +(7.11443 + 5.96971i) q^{29} +(0.491741 + 2.78880i) q^{31} +(5.50090 + 2.00216i) q^{32} +(0.847385 - 4.80576i) q^{34} +(-2.97207 + 5.14778i) q^{35} +(-2.76596 - 4.79078i) q^{37} +(5.89391 - 2.14521i) q^{38} +(-4.80674 + 4.03334i) q^{40} +(5.44333 - 4.56750i) q^{41} +(-2.19597 + 0.799267i) q^{43} +(-2.19131 - 3.79547i) q^{44} +(-1.57670 + 2.73092i) q^{46} +(0.801248 - 4.54411i) q^{47} +(0.698301 + 0.254161i) q^{49} +(-0.0873823 - 0.495570i) q^{50} +(-1.42850 - 1.19865i) q^{52} -0.135496 q^{53} +7.46499 q^{55} +(-5.05964 - 4.24554i) q^{56} +(-1.25426 - 7.11324i) q^{58} +(-3.75759 - 1.36765i) q^{59} +(0.0593526 - 0.336605i) q^{61} +(1.10120 - 1.90733i) q^{62} +(-1.53974 - 2.66690i) q^{64} +(2.98474 - 1.08636i) q^{65} +(7.75461 - 6.50689i) q^{67} +(6.70579 - 5.62682i) q^{68} +(4.34415 - 1.58114i) q^{70} +(4.09540 + 7.09344i) q^{71} +(6.15722 - 10.6646i) q^{73} +(-0.747095 + 4.23698i) q^{74} +(10.5728 + 3.84817i) q^{76} +(1.36448 + 7.73837i) q^{77} +(3.12600 + 2.62302i) q^{79} -1.75056 q^{80} -5.52638 q^{82} +(-0.699573 - 0.587012i) q^{83} +(2.58917 + 14.6839i) q^{85} +(1.70788 + 0.621616i) q^{86} +(-1.44038 + 8.16879i) q^{88} +(-1.86437 + 3.22919i) q^{89} +(1.67171 + 2.89548i) q^{91} +(-5.31556 + 1.93471i) q^{92} +(-2.74904 + 2.30672i) q^{94} +(-14.6809 + 12.3187i) q^{95} +(5.63467 - 2.05085i) q^{97} +(-0.288973 - 0.500515i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 6 * q^7 - 6 * q^8	\( 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 6 q^{10} + 15 q^{11} - 3 q^{13} + 21 q^{14} + 9 q^{16} + 9 q^{17} - 12 q^{19} + 3 q^{20} + 33 q^{22} - 15 q^{23} - 12 q^{25} + 48 q^{26} + 6 q^{28} + 6 q^{29} - 12 q^{31} + 27 q^{32} + 27 q^{34} - 30 q^{35} - 3 q^{37} + 39 q^{38} + 24 q^{40} + 39 q^{41} + 24 q^{43} + 33 q^{44} + 3 q^{46} + 42 q^{47} - 30 q^{49} + 15 q^{50} - 45 q^{52} - 18 q^{53} + 30 q^{55} - 12 q^{56} - 30 q^{58} - 15 q^{59} - 3 q^{61} + 30 q^{62} - 6 q^{64} + 6 q^{65} - 3 q^{67} - 36 q^{68} - 75 q^{70} - 12 q^{73} - 60 q^{74} + 30 q^{76} - 33 q^{77} + 33 q^{79} - 42 q^{80} - 42 q^{82} + 33 q^{83} - 18 q^{85} + 30 q^{86} - 42 q^{88} + 9 q^{89} - 18 q^{91} - 33 q^{92} - 66 q^{94} - 12 q^{95} + 15 q^{97} - 18 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 6 * q^10 + 15 * q^11 - 3 * q^13 + 21 * q^14 + 9 * q^16 + 9 * q^17 - 12 * q^19 + 3 * q^20 + 33 * q^22 - 15 * q^23 - 12 * q^25 + 48 * q^26 + 6 * q^28 + 6 * q^29 - 12 * q^31 + 27 * q^32 + 27 * q^34 - 30 * q^35 - 3 * q^37 + 39 * q^38 + 24 * q^40 + 39 * q^41 + 24 * q^43 + 33 * q^44 + 3 * q^46 + 42 * q^47 - 30 * q^49 + 15 * q^50 - 45 * q^52 - 18 * q^53 + 30 * q^55 - 12 * q^56 - 30 * q^58 - 15 * q^59 - 3 * q^61 + 30 * q^62 - 6 * q^64 + 6 * q^65 - 3 * q^67 - 36 * q^68 - 75 * q^70 - 12 * q^73 - 60 * q^74 + 30 * q^76 - 33 * q^77 + 33 * q^79 - 42 * q^80 - 42 * q^82 + 33 * q^83 - 18 * q^85 + 30 * q^86 - 42 * q^88 + 9 * q^89 - 18 * q^91 - 33 * q^92 - 66 * q^94 - 12 * q^95 + 15 * q^97 - 18 * q^98

Introduction

L-functions

Modular forms

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Database

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