LMFDB - Embedded newform 836.2.j.b.685.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [836,2,Mod(229,836)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(836, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 0]))

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

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

chi := DirichletCharacter("836.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 836 = 2^{2} \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	836.j (of order $5$, degree $4$, 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:	$6.67549360898$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
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} + 3 x^{18} - x^{17} + 54 x^{16} - 67 x^{15} + 423 x^{14} - 418 x^{13} + 1762 x^{12} - 726 x^{11} + \cdots + 81 $ x^20 + 3x^18 - x^17 + 54x^16 - 67x^15 + 423x^14 - 418x^13 + 1762x^12 - 726x^11 + 3458x^10 + 2637x^9 + 9293x^8 + 10286x^7 + 19508x^6 + 18758x^5 + 20611x^4 + 10338x^3 + 3429x^2 + 675*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			685.2
Root			$0.444729 - 1.36874i$ of defining polynomial
Character	$\chi$	$=$	836.685
Dual form			836.2.j.b.609.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.444729 - 1.36874i) q^{3} +(1.18149 + 0.858404i) q^{5} +(0.910570 - 2.80245i) q^{7} +(0.751396 - 0.545921i) q^{9} +(-1.13357 - 3.11689i) q^{11} +(-2.39150 + 1.73752i) q^{13} +(0.649484 - 1.99891i) q^{15} +(-0.901971 - 0.655320i) q^{17} +(0.309017 + 0.951057i) q^{19} -4.24077 q^{21} +6.23162 q^{23} +(-0.886020 - 2.72689i) q^{25} +(-4.57434 - 3.32345i) q^{27} +(-1.68336 + 5.18085i) q^{29} +(4.00663 - 2.91099i) q^{31} +(-3.76207 + 2.93773i) q^{33} +(3.48146 - 2.52943i) q^{35} +(-0.880550 + 2.71005i) q^{37} +(3.44178 + 2.50060i) q^{39} +(-3.78902 - 11.6614i) q^{41} -1.95512 q^{43} +1.35639 q^{45} +(-1.24603 - 3.83489i) q^{47} +(-1.36145 - 0.989153i) q^{49} +(-0.495828 + 1.52600i) q^{51} +(-0.0606444 + 0.0440608i) q^{53} +(1.33625 - 4.65564i) q^{55} +(1.16432 - 0.845925i) q^{57} +(0.907196 - 2.79206i) q^{59} +(0.0599368 + 0.0435466i) q^{61} +(-0.845717 - 2.60285i) q^{63} -4.31703 q^{65} +3.18622 q^{67} +(-2.77138 - 8.52944i) q^{69} +(-9.36673 - 6.80533i) q^{71} +(-0.149260 + 0.459374i) q^{73} +(-3.33835 + 2.42546i) q^{75} +(-9.76712 + 0.338611i) q^{77} +(-4.27115 + 3.10317i) q^{79} +(-1.65356 + 5.08914i) q^{81} +(6.79125 + 4.93413i) q^{83} +(-0.503142 - 1.54851i) q^{85} +7.83986 q^{87} +7.78559 q^{89} +(2.69169 + 8.28418i) q^{91} +(-5.76624 - 4.18942i) q^{93} +(-0.451290 + 1.38893i) q^{95} +(-3.84654 + 2.79467i) q^{97} +(-2.55334 - 1.72318i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5} + 15 q^{7} + 9 q^{9} + 2 q^{11} + 4 q^{13} + 15 q^{15} + 7 q^{17} - 5 q^{19} - 12 q^{21} - 16 q^{23} - 5 q^{25} - 3 q^{27} + 16 q^{29} + q^{31} - 27 q^{33} - 13 q^{35} + 14 q^{37} - 29 q^{39}+ \cdots - 35 q^{99}+O(q^{100}) $ 20 * q - 4 * q^5 + 15 * q^7 + 9 * q^9 + 2 * q^11 + 4 * q^13 + 15 * q^15 + 7 * q^17 - 5 * q^19 - 12 * q^21 - 16 * q^23 - 5 * q^25 - 3 * q^27 + 16 * q^29 + q^31 - 27 * q^33 - 13 * q^35 + 14 * q^37 - 29 * q^39 - 5 * q^41 + 28 * q^43 - 4 * q^47 - 4 * q^49 + 4 * q^51 - 17 * q^55 + 42 * q^59 + 27 * q^61 + 22 * q^63 - 14 * q^65 - 34 * q^67 - 11 * q^69 + 32 * q^71 - 7 * q^73 + 13 * q^75 - 60 * q^77 + 2 * q^79 - 9 * q^81 + 33 * q^83 + 27 * q^85 - 2 * q^87 - 70 * q^89 - 10 * q^91 + 7 * q^93 - 4 * q^95 - 6 * q^97 - 35 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/836\mathbb{Z}\right)^\times$.

$n$	$419$	$705$	$761$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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			0
$2$		0			0
$3$	−0.444729	−	1.36874i	−0.256765	−	0.790240i	−0.993477	−	0.114034i	$-0.963623\pi$
$3$	−0.444729	−	1.36874i	−0.256765	−	0.790240i	0.736712	−	0.676206i	$-0.236377\pi$
$4$		0			0
$5$	1.18149	+	0.858404i	0.528379	+	0.383890i	0.819751	−	0.572720i	$-0.194112\pi$
$5$	1.18149	+	0.858404i	0.528379	+	0.383890i	−0.291372	+	0.956610i	$0.594112\pi$
$6$		0			0
$7$	0.910570	−	2.80245i	0.344163	−	1.05923i	−0.617867	−	0.786283i	$-0.712003\pi$
$7$	0.910570	−	2.80245i	0.344163	−	1.05923i	0.962030	−	0.272943i	$-0.0879970\pi$
$8$		0			0
$9$	0.751396	−	0.545921i	0.250465	−	0.181974i
$10$		0			0
$11$	−1.13357	−	3.11689i	−0.341783	−	0.939779i
$11$	−1.13357	−	3.11689i	−0.341783	−	0.939779i
$12$		0			0
$13$	−2.39150	+	1.73752i	−0.663282	+	0.481902i	−0.867770	−	0.496967i	$-0.834447\pi$
$13$	−2.39150	+	1.73752i	−0.663282	+	0.481902i	0.204488	+	0.978869i	$0.434447\pi$
$14$		0			0
$15$	0.649484	−	1.99891i	0.167696	−	0.516116i
$16$		0			0
$17$	−0.901971	−	0.655320i	−0.218760	−	0.158939i	0.473008	−	0.881058i	$-0.343168\pi$
$17$	−0.901971	−	0.655320i	−0.218760	−	0.158939i	−0.691768	+	0.722119i	$0.743168\pi$
$18$		0			0
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$20$		0			0
$21$	−4.24077			−0.925411
$22$		0			0
$23$	6.23162			1.29938			0.649691	−	0.760198i	$-0.274898\pi$
$23$	6.23162			1.29938			0.649691	+	0.760198i	$0.274898\pi$
$24$		0			0
$25$	−0.886020	−	2.72689i	−0.177204	−	0.545378i
$26$		0			0
$27$	−4.57434	−	3.32345i	−0.880332	−	0.639599i
$28$		0			0
$29$	−1.68336	+	5.18085i	−0.312592	+	0.962060i	0.664142	+	0.747606i	$0.268797\pi$
$29$	−1.68336	+	5.18085i	−0.312592	+	0.962060i	−0.976734	+	0.214453i	$0.931203\pi$
$30$		0			0
$31$	4.00663	−	2.91099i	0.719612	−	0.522829i	−0.166648	−	0.986016i	$-0.553294\pi$
$31$	4.00663	−	2.91099i	0.719612	−	0.522829i	0.886260	+	0.463188i	$0.153294\pi$
$32$		0			0
$33$	−3.76207	+	2.93773i	−0.654893	+	0.511393i
$34$		0			0
$35$	3.48146	−	2.52943i	0.588474	−	0.427552i
$36$		0			0
$37$	−0.880550	+	2.71005i	−0.144761	+	0.445530i	−0.996980	−	0.0776556i	$-0.975257\pi$
$37$	−0.880550	+	2.71005i	−0.144761	+	0.445530i	0.852219	+	0.523186i	$0.175257\pi$
$38$		0			0
$39$	3.44178	+	2.50060i	0.551126	+	0.400416i
$40$		0			0
$41$	−3.78902	−	11.6614i	−0.591746	−	1.82121i	−0.570301	−	0.821436i	$-0.693174\pi$
$41$	−3.78902	−	11.6614i	−0.591746	−	1.82121i	−0.0214444	−	0.999770i	$-0.506826\pi$
$42$		0			0
$43$	−1.95512			−0.298154			−0.149077	−	0.988826i	$-0.547630\pi$
$43$	−1.95512			−0.298154			−0.149077	+	0.988826i	$0.547630\pi$
$44$		0			0
$45$	1.35639			0.202199
$46$		0			0
$47$	−1.24603	−	3.83489i	−0.181753	−	0.559377i	0.818125	−	0.575041i	$-0.195014\pi$
$47$	−1.24603	−	3.83489i	−0.181753	−	0.559377i	−0.999877	+	0.0156639i	$0.995014\pi$
$48$		0			0
$49$	−1.36145	−	0.989153i	−0.194493	−	0.141308i
$50$		0			0
$51$	−0.495828	+	1.52600i	−0.0694298	+	0.213683i
$52$		0			0
$53$	−0.0606444	+	0.0440608i	−0.00833015	+	0.00605221i	−0.591943	−	0.805980i	$-0.701639\pi$
$53$	−0.0606444	+	0.0440608i	−0.00833015	+	0.00605221i	0.583612	+	0.812032i	$0.301639\pi$
$54$		0			0
$55$	1.33625	−	4.65564i	0.180180	−	0.627767i
$56$		0			0
$57$	1.16432	−	0.845925i	0.154217	−	0.112046i
$58$		0			0
$59$	0.907196	−	2.79206i	0.118107	−	0.363496i	−0.874475	−	0.485070i	$-0.838794\pi$
$59$	0.907196	−	2.79206i	0.118107	−	0.363496i	0.992582	+	0.121574i	$0.0387942\pi$
$60$		0			0
$61$	0.0599368	+	0.0435466i	0.00767412	+	0.00557557i	0.591616	−	0.806220i	$-0.298490\pi$
$61$	0.0599368	+	0.0435466i	0.00767412	+	0.00557557i	−0.583942	+	0.811796i	$0.698490\pi$
$62$		0			0
$63$	−0.845717	−	2.60285i	−0.106550	−	0.327928i
$64$		0			0
$65$	−4.31703			−0.535462
$66$		0			0
$67$	3.18622			0.389259			0.194630	−	0.980877i	$-0.437650\pi$
$67$	3.18622			0.389259			0.194630	+	0.980877i	$0.437650\pi$
$68$		0			0
$69$	−2.77138	−	8.52944i	−0.333635	−	1.02682i
$70$		0			0
$71$	−9.36673	−	6.80533i	−1.11163	−	0.807644i	−0.128707	−	0.991683i	$-0.541083\pi$
$71$	−9.36673	−	6.80533i	−1.11163	−	0.807644i	−0.982919	+	0.184039i	$0.941083\pi$
$72$		0			0
$73$	−0.149260	+	0.459374i	−0.0174695	+	0.0537657i	−0.959411	−	0.282011i	$-0.908999\pi$
$73$	−0.149260	+	0.459374i	−0.0174695	+	0.0537657i	0.941942	+	0.335776i	$0.108999\pi$
$74$		0			0
$75$	−3.33835	+	2.42546i	−0.385480	+	0.280067i
$76$		0			0
$77$	−9.76712	+	0.338611i	−1.11307	+	0.0385883i
$78$		0			0
$79$	−4.27115	+	3.10317i	−0.480542	+	0.349134i	−0.801536	−	0.597947i	$-0.795983\pi$
$79$	−4.27115	+	3.10317i	−0.480542	+	0.349134i	0.320993	+	0.947081i	$0.395983\pi$
$80$		0			0
$81$	−1.65356	+	5.08914i	−0.183729	+	0.565460i
$82$		0			0
$83$	6.79125	+	4.93413i	0.745436	+	0.541591i	0.894409	−	0.447250i	$-0.147597\pi$
$83$	6.79125	+	4.93413i	0.745436	+	0.541591i	−0.148973	+	0.988841i	$0.547597\pi$
$84$		0			0
$85$	−0.503142	−	1.54851i	−0.0545734	−	0.167960i
$86$		0			0
$87$	7.83986			0.840521
$88$		0			0
$89$	7.78559			0.825271			0.412635	−	0.910896i	$-0.364608\pi$
$89$	7.78559			0.825271			0.412635	+	0.910896i	$0.364608\pi$
$90$		0			0
$91$	2.69169	+	8.28418i	0.282166	+	0.868418i
$92$		0			0
$93$	−5.76624	−	4.18942i	−0.597931	−	0.434422i
$94$		0			0
$95$	−0.451290	+	1.38893i	−0.0463013	+	0.142501i
$96$		0			0
$97$	−3.84654	+	2.79467i	−0.390557	+	0.283756i	−0.765684	−	0.643218i	$-0.777599\pi$
$97$	−3.84654	+	2.79467i	−0.390557	+	0.283756i	0.375127	+	0.926973i	$0.377599\pi$
$98$		0			0
$99$	−2.55334	−	1.72318i	−0.256620	−	0.173187i
$100$		0			0
$101$	1.51615	−	1.10154i	0.150862	−	0.109608i	−0.509794	−	0.860297i	$-0.670278\pi$
$101$	1.51615	−	1.10154i	0.150862	−	0.109608i	0.660656	+	0.750689i	$0.270278\pi$
$102$		0			0
$103$	−0.830742	+	2.55676i	−0.0818554	+	0.251925i	−0.983606	−	0.180332i	$-0.942283\pi$
$103$	−0.830742	+	2.55676i	−0.0818554	+	0.251925i	0.901750	+	0.432257i	$0.142283\pi$
$104$		0			0
$105$	−5.01043	−	3.64029i	−0.488968	−	0.355256i
$106$		0			0
$107$	0.820248	+	2.52446i	0.0792964	+	0.244049i	0.982844	−	0.184438i	$-0.0590466\pi$
$107$	0.820248	+	2.52446i	0.0792964	+	0.244049i	−0.903548	+	0.428488i	$0.859047\pi$
$108$		0			0
$109$	8.05431			0.771463			0.385731	−	0.922611i	$-0.373949\pi$
$109$	8.05431			0.771463			0.385731	+	0.922611i	$0.373949\pi$
$110$		0			0
$111$	4.10095			0.389245
$112$		0			0
$113$	0.0797114	+	0.245326i	0.00749862	+	0.0230784i	0.954736	−	0.297455i	$-0.0961378\pi$
$113$	0.0797114	+	0.245326i	0.00749862	+	0.0230784i	−0.947237	+	0.320533i	$0.896138\pi$
$114$		0			0
$115$	7.36260	+	5.34924i	0.686566	+	0.498820i
$116$		0			0
$117$	−0.848410	+	2.61114i	−0.0784356	+	0.241400i
$118$		0			0
$119$	−2.65781	+	1.93101i	−0.243641	+	0.177016i
$120$		0			0
$121$	−8.43005	+	7.06642i	−0.766368	+	0.642401i
$122$		0			0
$123$	−14.2763	+	10.3723i	−1.28725	+	0.935242i
$124$		0			0
$125$	3.55039	−	10.9270i	0.317557	−	0.977340i
$126$		0			0
$127$	15.9850	+	11.6138i	1.41844	+	1.03056i	0.992027	+	0.126025i	$0.0402221\pi$
$127$	15.9850	+	11.6138i	1.41844	+	1.03056i	0.426410	+	0.904530i	$0.359778\pi$
$128$		0			0
$129$	0.869501	+	2.67605i	0.0765553	+	0.235613i
$130$		0			0
$131$	4.64754			0.406057			0.203029	−	0.979173i	$-0.434922\pi$
$131$	4.64754			0.406057			0.203029	+	0.979173i	$0.434922\pi$
$132$		0			0
$133$	2.94667			0.255508
$134$		0			0
$135$	−2.55168	−	7.85326i	−0.219614	−	0.675901i
$136$		0			0
$137$	9.46074	+	6.87363i	0.808286	+	0.587254i	0.913333	−	0.407213i	$-0.133499\pi$
$137$	9.46074	+	6.87363i	0.808286	+	0.587254i	−0.105047	+	0.994467i	$0.533499\pi$
$138$		0			0
$139$	5.20941	−	16.0329i	0.441856	−	1.35989i	−0.444039	−	0.896007i	$-0.646455\pi$
$139$	5.20941	−	16.0329i	0.441856	−	1.35989i	0.885895	−	0.463886i	$-0.153545\pi$
$140$		0			0
$141$	−4.69481	+	3.41098i	−0.395374	+	0.287256i
$142$		0			0
$143$	8.12660	+	5.48444i	0.679580	+	0.458632i
$144$		0			0
$145$	−6.43614	+	4.67613i	−0.534492	+	0.388331i
$146$		0			0
$147$	−0.748411	+	2.30337i	−0.0617279	+	0.189979i
$148$		0			0
$149$	11.4868	+	8.34565i	0.941036	+	0.683703i	0.948670	−	0.316268i	$-0.102430\pi$
$149$	11.4868	+	8.34565i	0.941036	+	0.683703i	−0.00763386	+	0.999971i	$0.502430\pi$
$150$		0			0
$151$	4.71828	+	14.5214i	0.383968	+	1.18173i	0.937226	+	0.348722i	$0.113384\pi$
$151$	4.71828	+	14.5214i	0.383968	+	1.18173i	−0.553258	+	0.833010i	$0.686616\pi$
$152$		0			0
$153$	−1.03549			−0.0837145
$154$		0			0
$155$	7.23260			0.580936
$156$		0			0
$157$	6.00898	+	18.4937i	0.479569	+	1.47596i	0.839695	+	0.543058i	$0.182734\pi$
$157$	6.00898	+	18.4937i	0.479569	+	1.47596i	−0.360126	+	0.932904i	$0.617266\pi$
$158$		0			0
$159$	0.0872779	+	0.0634111i	0.00692159	+	0.00502883i
$160$		0			0
$161$	5.67433	−	17.4638i	0.447200	−	1.37634i
$162$		0			0
$163$	15.7633	−	11.4527i	1.23468	−	0.897047i	0.237447	−	0.971400i	$-0.423689\pi$
$163$	15.7633	−	11.4527i	1.23468	−	0.897047i	0.997232	+	0.0743537i	$0.0236894\pi$
$164$		0			0
$165$	−6.96662	+	0.241522i	−0.542350	+	0.0188024i
$166$		0			0
$167$	6.18705	−	4.49516i	0.478769	−	0.347846i	−0.322080	−	0.946712i	$-0.604382\pi$
$167$	6.18705	−	4.49516i	0.478769	−	0.347846i	0.800849	+	0.598867i	$0.204382\pi$
$168$		0			0
$169$	−1.31695	+	4.05317i	−0.101304	+	0.311782i
$170$		0			0
$171$	0.751396	+	0.545921i	0.0574607	+	0.0417477i
$172$		0			0
$173$	−0.529979	−	1.63111i	−0.0402935	−	0.124011i	0.928886	−	0.370365i	$-0.120767\pi$
$173$	−0.529979	−	1.63111i	−0.0402935	−	0.124011i	−0.969180	+	0.246354i	$0.920767\pi$
$174$		0			0
$175$	−8.44875			−0.638665
$176$		0			0
$177$	−4.22505			−0.317574
$178$		0			0
$179$	−2.59553	−	7.98823i	−0.193999	−	0.597068i	−0.999987	−	0.00513580i	$-0.998365\pi$
$179$	−2.59553	−	7.98823i	−0.193999	−	0.597068i	0.805988	−	0.591932i	$-0.201635\pi$
$180$		0			0
$181$	16.2215	+	11.7856i	1.20573	+	0.876015i	0.994836	−	0.101493i	$-0.0323620\pi$
$181$	16.2215	+	11.7856i	1.20573	+	0.876015i	0.210896	+	0.977509i	$0.432362\pi$
$182$		0			0
$183$	0.0329482	−	0.101404i	0.00243560	−	0.00749601i
$184$		0			0
$185$	−3.36668	+	2.44604i	−0.247523	+	0.179836i
$186$		0			0
$187$	−1.02012	+	3.55420i	−0.0745985	+	0.259909i
$188$		0			0
$189$	−13.4791	+	9.79311i	−0.980457	+	0.712344i
$190$		0			0
$191$	−4.15467	+	12.7868i	−0.300622	+	0.925219i	0.680653	+	0.732606i	$0.261696\pi$
$191$	−4.15467	+	12.7868i	−0.300622	+	0.925219i	−0.981275	+	0.192613i	$0.938304\pi$
$192$		0			0
$193$	9.68381	+	7.03570i	0.697056	+	0.506441i	0.878972	−	0.476873i	$-0.158230\pi$
$193$	9.68381	+	7.03570i	0.697056	+	0.506441i	−0.181916	+	0.983314i	$0.558230\pi$
$194$		0			0
$195$	1.91991	+	5.90887i	0.137488	+	0.423143i
$196$		0			0
$197$	−18.0316			−1.28469			−0.642347	−	0.766414i	$-0.722039\pi$
$197$	−18.0316			−1.28469			−0.642347	+	0.766414i	$0.722039\pi$
$198$		0			0
$199$	21.3508			1.51352			0.756760	−	0.653693i	$-0.226781\pi$
$199$	21.3508			1.51352			0.756760	+	0.653693i	$0.226781\pi$
$200$		0			0
$201$	−1.41701	−	4.36110i	−0.0999480	−	0.307608i
$202$		0			0
$203$	12.9862	+	9.43506i	0.911455	+	0.662211i
$204$		0			0
$205$	5.53350	−	17.0304i	0.386476	−	1.18945i
$206$		0			0
$207$	4.68242	−	3.40197i	0.325450	−	0.236454i
$208$		0			0
$209$	2.61405	−	2.04126i	0.180818	−	0.141197i
$210$		0			0
$211$	−22.5653	+	16.3947i	−1.55346	+	1.12866i	−0.612337	+	0.790597i	$0.709770\pi$
$211$	−22.5653	+	16.3947i	−1.55346	+	1.12866i	−0.941125	+	0.338059i	$0.890230\pi$
$212$		0			0
$213$	−5.14904	+	15.8471i	−0.352806	+	1.08583i
$214$		0			0
$215$	−2.30996	−	1.67829i	−0.157538	−	0.114458i
$216$		0			0
$217$	−4.50957	−	13.8790i	−0.306129	−	0.942169i
$218$		0			0
$219$	0.695143			0.0469734
$220$		0			0
$221$	3.29570			0.221692
$222$		0			0
$223$	2.30587	+	7.09673i	0.154412	+	0.475232i	0.998101	−	0.0616008i	$-0.0196206\pi$
$223$	2.30587	+	7.09673i	0.154412	+	0.475232i	−0.843689	+	0.536833i	$0.819621\pi$
$224$		0			0
$225$	−2.15442	−	1.56528i	−0.143628	−	0.104352i
$226$		0			0
$227$	−8.55548	+	26.3311i	−0.567847	+	1.74765i	0.0914899	+	0.995806i	$0.470837\pi$
$227$	−8.55548	+	26.3311i	−0.567847	+	1.74765i	−0.659337	+	0.751848i	$0.729163\pi$
$228$		0			0
$229$	17.0410	−	12.3810i	1.12610	−	0.818162i	0.140980	−	0.990012i	$-0.454975\pi$
$229$	17.0410	−	12.3810i	1.12610	−	0.818162i	0.985123	+	0.171851i	$0.0549747\pi$
$230$		0			0
$231$	4.80719	+	13.2180i	0.316290	+	0.869682i
$232$		0			0
$233$	−20.1169	+	14.6158i	−1.31790	+	0.957513i	−0.317948	+	0.948108i	$0.602994\pi$
$233$	−20.1169	+	14.6158i	−1.31790	+	0.957513i	−0.999956	+	0.00940470i	$0.997006\pi$
$234$		0			0
$235$	1.81971	−	5.60049i	0.118705	−	0.365336i
$236$		0			0
$237$	6.14693	+	4.46601i	0.399286	+	0.290098i
$238$		0			0
$239$	−4.85432	−	14.9401i	−0.314000	−	0.966393i	−0.976164	−	0.217034i	$-0.930362\pi$
$239$	−4.85432	−	14.9401i	−0.314000	−	0.966393i	0.662164	−	0.749359i	$-0.269638\pi$
$240$		0			0
$241$	−14.3016			−0.921249			−0.460624	−	0.887595i	$-0.652374\pi$
$241$	−14.3016			−0.921249			−0.460624	+	0.887595i	$0.652374\pi$
$242$		0			0
$243$	−9.26150			−0.594126
$244$		0			0
$245$	−0.759451	−	2.33735i	−0.0485196	−	0.149328i
$246$		0			0
$247$	−2.39150	−	1.73752i	−0.152167	−	0.110556i
$248$		0			0
$249$	3.73326	−	11.4898i	0.236585	−	0.728135i
$250$		0			0
$251$	−0.284593	+	0.206769i	−0.0179633	+	0.0130511i	−0.596731	−	0.802442i	$-0.703534\pi$
$251$	−0.284593	+	0.206769i	−0.0179633	+	0.0130511i	0.578767	+	0.815493i	$0.303534\pi$
$252$		0			0
$253$	−7.06396	−	19.4233i	−0.444107	−	1.22113i
$254$		0			0
$255$	−1.89574	+	1.37734i	−0.118716	+	0.0862522i
$256$		0			0
$257$	0.362330	−	1.11514i	0.0226015	−	0.0695604i	−0.939120	−	0.343590i	$-0.888357\pi$
$257$	0.362330	−	1.11514i	0.0226015	−	0.0695604i	0.961721	+	0.274030i	$0.0883568\pi$
$258$		0			0
$259$	6.79298	+	4.93539i	0.422095	+	0.306670i
$260$		0			0
$261$	1.56347	+	4.81185i	0.0967761	+	0.297846i
$262$		0			0
$263$	−11.5816			−0.714154			−0.357077	−	0.934075i	$-0.616227\pi$
$263$	−11.5816			−0.714154			−0.357077	+	0.934075i	$0.616227\pi$
$264$		0			0
$265$	−0.109473			−0.00672486
$266$		0			0
$267$	−3.46248	−	10.6564i	−0.211900	−	0.652162i
$268$		0			0
$269$	−0.665649	−	0.483622i	−0.0405853	−	0.0294870i	0.567308	−	0.823506i	$-0.307985\pi$
$269$	−0.665649	−	0.483622i	−0.0405853	−	0.0294870i	−0.607893	+	0.794019i	$0.707985\pi$
$270$		0			0
$271$	3.61488	−	11.1254i	0.219588	−	0.675822i	−0.779208	−	0.626765i	$-0.784378\pi$
$271$	3.61488	−	11.1254i	0.219588	−	0.675822i	0.998796	−	0.0490570i	$-0.0156216\pi$
$272$		0			0
$273$	10.1418	−	7.36844i	0.613809	−	0.445958i
$274$		0			0
$275$	−7.49506	+	5.85274i	−0.451969	+	0.352934i
$276$		0			0
$277$	−1.23962	+	0.900637i	−0.0744816	+	0.0541140i	−0.624403	−	0.781102i	$-0.714658\pi$
$277$	−1.23962	+	0.900637i	−0.0744816	+	0.0541140i	0.549921	+	0.835216i	$0.314658\pi$
$278$		0			0
$279$	1.42140	−	4.37461i	0.0850968	−	0.261901i
$280$		0			0
$281$	−12.3427	−	8.96749i	−0.736303	−	0.534955i	0.155248	−	0.987876i	$-0.450382\pi$
$281$	−12.3427	−	8.96749i	−0.736303	−	0.534955i	−0.891551	+	0.452920i	$0.850382\pi$
$282$		0			0
$283$	2.77098	+	8.52820i	0.164718	+	0.506949i	0.999015	−	0.0443653i	$-0.0141265\pi$
$283$	2.77098	+	8.52820i	0.164718	+	0.506949i	−0.834298	+	0.551314i	$0.814127\pi$
$284$		0			0
$285$	2.10178			0.124498
$286$		0			0
$287$	−36.1306			−2.13272
$288$		0			0
$289$	−4.86918	−	14.9858i	−0.286422	−	0.881518i
$290$		0			0
$291$	5.53584	+	4.02202i	0.324516	+	0.235775i
$292$		0			0
$293$	−4.55441	+	14.0170i	−0.266072	+	0.818885i	0.725373	+	0.688356i	$0.241667\pi$
$293$	−4.55441	+	14.0170i	−0.266072	+	0.818885i	−0.991445	+	0.130528i	$0.958333\pi$
$294$		0			0
$295$	3.46856	−	2.52006i	0.201947	−	0.146723i
$296$		0			0
$297$	−5.17353	+	18.0251i	−0.300199	+	1.04592i
$298$		0			0
$299$	−14.9029	+	10.8276i	−0.861857	+	0.626175i
$300$		0			0
$301$	−1.78028	+	5.47913i	−0.102614	+	0.315812i
$302$		0			0
$303$	−2.18200	−	1.58532i	−0.125353	−	0.0910740i
$304$		0			0
$305$	0.0334342	+	0.102900i	0.00191444	+	0.00589203i
$306$		0			0
$307$	5.58452			0.318726			0.159363	−	0.987220i	$-0.449056\pi$
$307$	5.58452			0.318726			0.159363	+	0.987220i	$0.449056\pi$
$308$		0			0
$309$	3.86899			0.220099
$310$		0			0
$311$	−8.80809	−	27.1085i	−0.499461	−	1.53718i	−0.809888	−	0.586585i	$-0.800472\pi$
$311$	−8.80809	−	27.1085i	−0.499461	−	1.53718i	0.310427	−	0.950597i	$-0.399528\pi$
$312$		0			0
$313$	13.4224	+	9.75197i	0.758681	+	0.551214i	0.898505	−	0.438962i	$-0.144654\pi$
$313$	13.4224	+	9.75197i	0.758681	+	0.551214i	−0.139825	+	0.990176i	$0.544654\pi$
$314$		0			0
$315$	1.23509	−	3.80121i	0.0695893	−	0.214174i
$316$		0			0
$317$	−17.9155	+	13.0164i	−1.00624	+	0.731073i	−0.963416	−	0.268010i	$-0.913634\pi$
$317$	−17.9155	+	13.0164i	−1.00624	+	0.731073i	−0.0428195	+	0.999083i	$0.513634\pi$
$318$		0			0
$319$	18.0564	−	0.625986i	1.01096	−	0.0350485i
$320$		0			0
$321$	3.09054	−	2.24541i	0.172497	−	0.125326i
$322$		0			0
$323$	0.344522	−	1.06033i	0.0191697	−	0.0589984i
$324$		0			0
$325$	6.85695	+	4.98187i	0.380355	+	0.276344i
$326$		0			0
$327$	−3.58199	−	11.0242i	−0.198084	−	0.609641i
$328$		0			0
$329$	−11.8817			−0.655059
$330$		0			0
$331$	23.4297			1.28781			0.643907	−	0.765104i	$-0.277312\pi$
$331$	23.4297			1.28781			0.643907	+	0.765104i	$0.277312\pi$
$332$		0			0
$333$	0.817834	+	2.51704i	0.0448170	+	0.137933i
$334$		0			0
$335$	3.76450	+	2.73507i	0.205676	+	0.149433i
$336$		0			0
$337$	−4.97422	+	15.3091i	−0.270963	+	0.833938i	0.719296	+	0.694703i	$0.244464\pi$
$337$	−4.97422	+	15.3091i	−0.270963	+	0.833938i	−0.990259	+	0.139235i	$0.955536\pi$
$338$		0			0
$339$	0.300337	−	0.218208i	0.0163121	−	0.0118514i
$340$		0			0
$341$	−13.6150	−	9.18844i	−0.737295	−	0.497582i
$342$		0			0
$343$	12.6756	−	9.20935i	0.684417	−	0.497258i
$344$		0			0
$345$	4.04734	−	12.4564i	0.217901	−	0.670632i
$346$		0			0
$347$	3.10113	+	2.25311i	0.166478	+	0.120953i	0.667905	−	0.744247i	$-0.267191\pi$
$347$	3.10113	+	2.25311i	0.166478	+	0.120953i	−0.501427	+	0.865200i	$0.667191\pi$
$348$		0			0
$349$	−1.40223	−	4.31562i	−0.0750596	−	0.231010i	0.906487	−	0.422234i	$-0.138754\pi$
$349$	−1.40223	−	4.31562i	−0.0750596	−	0.231010i	−0.981546	+	0.191225i	$0.938754\pi$
$350$		0			0
$351$	16.7141			0.892132
$352$		0			0
$353$	27.3402			1.45517			0.727586	−	0.686017i	$-0.240642\pi$
$353$	27.3402			1.45517			0.727586	+	0.686017i	$0.240642\pi$
$354$		0			0
$355$	−5.22499	−	16.0809i	−0.277314	−	0.853484i
$356$		0			0
$357$	3.82505	+	2.77906i	0.202443	+	0.147084i
$358$		0			0
$359$	7.70706	−	23.7199i	0.406763	−	1.25189i	−0.512651	−	0.858597i	$-0.671336\pi$
$359$	7.70706	−	23.7199i	0.406763	−	1.25189i	0.919414	−	0.393291i	$-0.128664\pi$
$360$		0			0
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$		0			0
$363$	13.4211	+	8.39587i	0.704428	+	0.440669i
$364$		0			0
$365$	−0.570678	+	0.414622i	−0.0298706	+	0.0217023i
$366$		0			0
$367$	−5.48434	+	16.8791i	−0.286280	+	0.881079i	0.699732	+	0.714405i	$0.253303\pi$
$367$	−5.48434	+	16.8791i	−0.286280	+	0.881079i	−0.986012	+	0.166674i	$0.946697\pi$
$368$		0			0
$369$	−9.21327	−	6.69383i	−0.479624	−	0.348467i
$370$		0			0
$371$	0.0682569	+	0.210073i	0.00354372	+	0.0109065i
$372$		0			0
$373$	21.7030			1.12374			0.561870	−	0.827225i	$-0.310082\pi$
$373$	21.7030			1.12374			0.561870	+	0.827225i	$0.310082\pi$
$374$		0			0
$375$	−16.5351			−0.853871
$376$		0			0
$377$	−4.97610	−	15.3149i	−0.256282	−	0.788756i
$378$		0			0
$379$	1.28126	+	0.930890i	0.0658139	+	0.0478166i	0.620206	−	0.784439i	$-0.287049\pi$
$379$	1.28126	+	0.930890i	0.0658139	+	0.0478166i	−0.554392	+	0.832256i	$0.687049\pi$
$380$		0			0
$381$	8.78719	−	27.0442i	0.450182	−	1.38552i
$382$		0			0
$383$	26.9390	−	19.5724i	1.37652	−	1.00010i	0.379325	−	0.925264i	$-0.376156\pi$
$383$	26.9390	−	19.5724i	1.37652	−	1.00010i	0.997196	−	0.0748369i	$-0.0238436\pi$
$384$		0			0
$385$	−11.8304	−	7.98407i	−0.602935	−	0.406906i
$386$		0			0
$387$	−1.46907	+	1.06734i	−0.0746772	+	0.0542562i
$388$		0			0
$389$	9.26830	−	28.5249i	0.469921	−	1.44627i	−0.382765	−	0.923846i	$-0.625028\pi$
$389$	9.26830	−	28.5249i	0.469921	−	1.44627i	0.852686	−	0.522423i	$-0.174972\pi$
$390$		0			0
$391$	−5.62074	−	4.08371i	−0.284253	−	0.206522i
$392$		0			0
$393$	−2.06690	−	6.36125i	−0.104261	−	0.320883i
$394$		0			0
$395$	−7.71011			−0.387938
$396$		0			0
$397$	3.94977			0.198234			0.0991168	−	0.995076i	$-0.468398\pi$
$397$	3.94977			0.198234			0.0991168	+	0.995076i	$0.468398\pi$
$398$		0			0
$399$	−1.31047	−	4.03321i	−0.0656055	−	0.201913i
$400$		0			0
$401$	28.2071	+	20.4937i	1.40860	+	1.02341i	0.993524	+	0.113618i	$0.0362440\pi$
$401$	28.2071	+	20.4937i	1.40860	+	1.02341i	0.415073	+	0.909788i	$0.363756\pi$
$402$		0			0
$403$	−4.52393	+	13.9232i	−0.225353	+	0.693565i
$404$		0			0
$405$	−6.32221	+	4.59335i	−0.314153	+	0.228246i
$406$		0			0
$407$	9.44511	−	0.327447i	0.468177	−	0.0162310i
$408$		0			0
$409$	−3.18228	+	2.31206i	−0.157354	+	0.114324i	−0.663676	−	0.748020i	$-0.731005\pi$
$409$	−3.18228	+	2.31206i	−0.157354	+	0.114324i	0.506322	+	0.862344i	$0.331005\pi$
$410$		0			0
$411$	5.20072	−	16.0062i	0.256532	−	0.789526i
$412$		0			0
$413$	−6.99854	−	5.08474i	−0.344376	−	0.250204i
$414$		0			0
$415$	3.78833	+	11.6593i	0.185962	+	0.572331i
$416$		0			0
$417$	−24.2616			−1.18810
$418$		0			0
$419$	−22.8214			−1.11490			−0.557449	−	0.830211i	$-0.688220\pi$
$419$	−22.8214			−1.11490			−0.557449	+	0.830211i	$0.688220\pi$
$420$		0			0
$421$	8.45973	+	26.0364i	0.412302	+	1.26894i	0.914642	+	0.404265i	$0.132473\pi$
$421$	8.45973	+	26.0364i	0.412302	+	1.26894i	−0.502340	+	0.864670i	$0.667527\pi$
$422$		0			0
$423$	−3.02982	−	2.20129i	−0.147315	−	0.107030i
$424$		0			0
$425$	−0.987822	+	3.04020i	−0.0479164	+	0.147471i
$426$		0			0
$427$	0.176614	−	0.128317i	0.00854694	−	0.00620971i
$428$		0			0
$429$	3.89262	−	13.5623i	0.187937	−	0.654792i
$430$		0			0
$431$	12.6649	−	9.20162i	0.610049	−	0.443227i	−0.239383	−	0.970925i	$-0.576945\pi$
$431$	12.6649	−	9.20162i	0.610049	−	0.443227i	0.849432	+	0.527699i	$0.176945\pi$
$432$		0			0
$433$	6.49529	−	19.9905i	0.312144	−	0.960680i	−0.664770	−	0.747048i	$-0.731471\pi$
$433$	6.49529	−	19.9905i	0.312144	−	0.960680i	0.976914	−	0.213632i	$-0.0685295\pi$
$434$		0			0
$435$	9.26272	+	6.72976i	0.444114	+	0.322667i
$436$		0			0
$437$	1.92568	+	5.92662i	0.0921176	+	0.283509i
$438$		0			0
$439$	−12.7001			−0.606144			−0.303072	−	0.952968i	$-0.598012\pi$
$439$	−12.7001			−0.606144			−0.303072	+	0.952968i	$0.598012\pi$
$440$		0			0
$441$	−1.56299			−0.0744281
$442$		0			0
$443$	−4.97295	−	15.3052i	−0.236272	−	0.727171i	−0.996950	−	0.0780415i	$-0.975133\pi$
$443$	−4.97295	−	15.3052i	−0.236272	−	0.727171i	0.760678	−	0.649129i	$-0.224867\pi$
$444$		0			0
$445$	9.19861	+	6.68318i	0.436056	+	0.316813i
$446$		0			0
$447$	6.31448	−	19.4340i	0.298665	−	0.919195i
$448$		0			0
$449$	0.734658	−	0.533760i	0.0346706	−	0.0251897i	−0.570315	−	0.821426i	$-0.693179\pi$
$449$	0.734658	−	0.533760i	0.0346706	−	0.0251897i	0.604986	+	0.796236i	$0.293179\pi$
$450$		0			0
$451$	−32.0523	+	25.0290i	−1.50928	+	1.17857i
$452$		0			0
$453$	17.7776	−	12.9162i	0.835263	−	0.606854i
$454$		0			0
$455$	−3.93096	+	12.0982i	−0.184286	+	0.567175i
$456$		0			0
$457$	17.1170	+	12.4362i	0.800698	+	0.581741i	0.911119	−	0.412144i	$-0.135220\pi$
$457$	17.1170	+	12.4362i	0.800698	+	0.581741i	−0.110421	+	0.993885i	$0.535220\pi$
$458$		0			0
$459$	1.94800	+	5.99532i	0.0909247	+	0.279837i
$460$		0			0
$461$	−27.9700			−1.30269			−0.651347	−	0.758780i	$-0.725796\pi$
$461$	−27.9700			−1.30269			−0.651347	+	0.758780i	$0.725796\pi$
$462$		0			0
$463$	−29.9663			−1.39265			−0.696325	−	0.717726i	$-0.745183\pi$
$463$	−29.9663			−1.39265			−0.696325	+	0.717726i	$0.745183\pi$
$464$		0			0
$465$	−3.21655	−	9.89952i	−0.149164	−	0.459079i
$466$		0			0
$467$	2.25594	+	1.63904i	0.104393	+	0.0758456i	0.638757	−	0.769409i	$-0.279449\pi$
$467$	2.25594	+	1.63904i	0.104393	+	0.0758456i	−0.534364	+	0.845254i	$0.679449\pi$
$468$		0			0
$469$	2.90128	−	8.92922i	0.133969	−	0.412313i
$470$		0			0
$471$	22.6407	−	16.4494i	1.04323	−	0.757949i
$472$		0			0
$473$	2.21627	+	6.09392i	0.101904	+	0.280199i
$474$		0			0
$475$	2.31963	−	1.68531i	0.106432	−	0.0773273i
$476$		0			0
$477$	−0.0215143	+	0.0662142i	−0.000985072	+	0.00303174i
$478$		0			0
$479$	−12.7337	−	9.25158i	−0.581818	−	0.422716i	0.257561	−	0.966262i	$-0.417081\pi$
$479$	−12.7337	−	9.25158i	−0.581818	−	0.422716i	−0.839379	+	0.543546i	$0.817081\pi$
$480$		0			0
$481$	−2.60295	−	8.01106i	−0.118684	−	0.365273i
$482$		0			0
$483$	−26.4268			−1.20246
$484$		0			0
$485$	−6.94360			−0.315293
$486$		0			0
$487$	−8.95663	−	27.5657i	−0.405864	−	1.24912i	−0.920172	−	0.391515i	$-0.871951\pi$
$487$	−8.95663	−	27.5657i	−0.405864	−	1.24912i	0.514308	−	0.857606i	$-0.328049\pi$
$488$		0			0
$489$	−22.6862	−	16.4825i	−1.02590	−	0.745363i
$490$		0			0
$491$	1.63727	−	5.03898i	0.0738887	−	0.227406i	−0.907291	−	0.420504i	$-0.861853\pi$
$491$	1.63727	−	5.03898i	0.0738887	−	0.227406i	0.981180	+	0.193098i	$0.0618534\pi$
$492$		0			0
$493$	4.91346	−	3.56984i	0.221291	−	0.160777i
$494$		0			0
$495$	−1.53756	−	4.22772i	−0.0691081	−	0.190022i
$496$		0			0
$497$	−27.6006	+	20.0530i	−1.23806	+	0.899501i
$498$		0			0
$499$	−8.48604	+	26.1173i	−0.379887	+	1.16917i	0.560235	+	0.828334i	$0.310711\pi$
$499$	−8.48604	+	26.1173i	−0.379887	+	1.16917i	−0.940122	+	0.340839i	$0.889289\pi$
$500$		0			0
$501$	−8.90425	−	6.46932i	−0.397813	−	0.289028i
$502$		0			0
$503$	−7.65020	−	23.5449i	−0.341106	−	1.04982i	−0.963636	−	0.267219i	$-0.913895\pi$
$503$	−7.65020	−	23.5449i	−0.341106	−	1.04982i	0.622530	−	0.782596i	$-0.286105\pi$
$504$		0			0
$505$	2.73688			0.121790
$506$		0			0
$507$	6.13341			0.272394
$508$		0			0
$509$	−9.59152	−	29.5197i	−0.425137	−	1.30844i	−0.902863	−	0.429928i	$-0.858539\pi$
$509$	−9.59152	−	29.5197i	−0.425137	−	1.30844i	0.477727	−	0.878509i	$-0.341461\pi$
$510$		0			0
$511$	1.15146	+	0.836585i	0.0509376	+	0.0370084i
$512$		0			0
$513$	1.74724	−	5.37746i	0.0771426	−	0.237421i
$514$		0			0
$515$	−3.17625	+	2.30768i	−0.139962	+	0.101688i
$516$		0			0
$517$	−10.5405	+	8.23086i	−0.463571	+	0.361993i
$518$		0			0
$519$	−1.99686	+	1.45080i	−0.0876523	+	0.0636831i
$520$		0			0
$521$	−1.84110	+	5.66632i	−0.0806601	+	0.248246i	−0.983252	−	0.182251i	$-0.941662\pi$
$521$	−1.84110	+	5.66632i	−0.0806601	+	0.248246i	0.902592	+	0.430497i	$0.141662\pi$
$522$		0			0
$523$	−6.17055	−	4.48317i	−0.269819	−	0.196035i	0.444645	−	0.895707i	$-0.353330\pi$
$523$	−6.17055	−	4.48317i	−0.269819	−	0.196035i	−0.714465	+	0.699671i	$0.753330\pi$
$524$		0			0
$525$	3.75741	+	11.5641i	0.163987	+	0.504699i
$526$		0			0
$527$	−5.52149			−0.240520
$528$		0			0
$529$	15.8331			0.688394
$530$		0			0
$531$	−0.842583	−	2.59320i	−0.0365650	−	0.112535i
$532$		0			0
$533$	29.3234	+	21.3047i	1.27014	+	0.922809i
$534$		0			0
$535$	−1.19789	+	3.68674i	−0.0517895	+	0.159392i
$536$		0			0
$537$	−9.77947	+	7.10520i	−0.422015	+	0.306612i
$538$		0			0
$539$	−1.53979	+	5.36477i	−0.0663233	+	0.231077i
$540$		0			0
$541$	14.4458	−	10.4955i	0.621072	−	0.451235i	−0.232224	−	0.972662i	$-0.574600\pi$
$541$	14.4458	−	10.4955i	0.621072	−	0.451235i	0.853296	+	0.521427i	$0.174600\pi$
$542$		0			0
$543$	8.91719	−	27.4443i	0.382673	−	1.17775i
$544$		0			0
$545$	9.51610	+	6.91385i	0.407625	+	0.296157i
$546$		0			0
$547$	6.12941	+	18.8644i	0.262075	+	0.806583i	0.992353	+	0.123433i	$0.0393905\pi$
$547$	6.12941	+	18.8644i	0.262075	+	0.806583i	−0.730278	+	0.683150i	$0.760610\pi$
$548$		0			0
$549$	0.0688093			0.00293671
$550$		0			0
$551$	−5.44747			−0.232070
$552$		0			0
$553$	4.80730	+	14.7953i	0.204427	+	0.629162i
$554$		0			0
$555$	4.84524	+	3.52027i	0.205669	+	0.149427i
$556$		0			0
$557$	−0.939857	+	2.89258i	−0.0398230	+	0.122563i	−0.968992	−	0.247094i	$-0.920525\pi$
$557$	−0.939857	+	2.89258i	−0.0398230	+	0.122563i	0.929169	+	0.369656i	$0.120525\pi$
$558$		0			0
$559$	4.67567	−	3.39708i	0.197760	−	0.143681i
$560$		0			0
$561$	5.31844	−	0.184382i	0.224545	−	0.00778461i
$562$		0			0
$563$	11.7859	−	8.56296i	0.496716	−	0.360886i	−0.311045	−	0.950395i	$-0.600679\pi$
$563$	11.7859	−	8.56296i	0.496716	−	0.360886i	0.807761	+	0.589510i	$0.200679\pi$
$564$		0			0
$565$	−0.116411	+	0.358276i	−0.00489744	+	0.0150728i
$566$		0			0
$567$	12.7564	+	9.26804i	0.535717	+	0.389221i
$568$		0			0
$569$	−4.64990	−	14.3109i	−0.194934	−	0.599944i	−0.999977	−	0.00672879i	$-0.997858\pi$
$569$	−4.64990	−	14.3109i	−0.194934	−	0.599944i	0.805044	−	0.593216i	$-0.202142\pi$
$570$		0			0
$571$	9.64735			0.403729			0.201864	−	0.979413i	$-0.435300\pi$
$571$	9.64735			0.403729			0.201864	+	0.979413i	$0.435300\pi$
$572$		0			0
$573$	19.3494			0.808334
$574$		0			0
$575$	−5.52134	−	16.9929i	−0.230256	−	0.708654i
$576$		0			0
$577$	−2.08946	−	1.51808i	−0.0869855	−	0.0631987i	0.543442	−	0.839446i	$-0.317121\pi$
$577$	−2.08946	−	1.51808i	−0.0869855	−	0.0631987i	−0.630428	+	0.776248i	$0.717121\pi$
$578$		0			0
$579$	5.32334	−	16.3836i	0.221230	−	0.680877i
$580$		0			0
$581$	20.0115	−	14.5392i	0.830219	−	0.603189i
$582$		0			0
$583$	0.206077	+	0.139076i	0.00853485	+	0.00575996i
$584$		0			0
$585$	−3.24380	+	2.35676i	−0.134115	+	0.0974400i
$586$		0			0
$587$	−6.89037	+	21.2064i	−0.284396	+	0.875281i	0.702183	+	0.711997i	$0.252209\pi$
$587$	−6.89037	+	21.2064i	−0.284396	+	0.875281i	−0.986579	+	0.163285i	$0.947791\pi$
$588$		0			0
$589$	4.00663	+	2.91099i	0.165090	+	0.119945i
$590$		0			0
$591$	8.01916	+	24.6804i	0.329864	+	1.01522i
$592$		0			0
$593$	−15.2005			−0.624208			−0.312104	−	0.950048i	$-0.601034\pi$
$593$	−15.2005			−0.624208			−0.312104	+	0.950048i	$0.601034\pi$
$594$		0			0
$595$	−4.79777			−0.196689
$596$		0			0
$597$	−9.49534	−	29.2236i	−0.388618	−	1.19604i
$598$		0			0
$599$	17.8600	+	12.9760i	0.729738	+	0.530186i	0.889481	−	0.456973i	$-0.151066\pi$
$599$	17.8600	+	12.9760i	0.729738	+	0.530186i	−0.159743	+	0.987159i	$0.551066\pi$
$600$		0			0
$601$	−5.10665	+	15.7167i	−0.208305	+	0.641096i	0.791257	+	0.611484i	$0.209427\pi$
$601$	−5.10665	+	15.7167i	−0.208305	+	0.641096i	−0.999561	+	0.0296118i	$0.990573\pi$
$602$		0			0
$603$	2.39412	−	1.73943i	0.0974960	−	0.0708350i
$604$		0			0
$605$	−16.0259	+	1.11252i	−0.651544	+	0.0452304i
$606$		0			0
$607$	−6.40771	+	4.65548i	−0.260081	+	0.188960i	−0.710183	−	0.704017i	$-0.751388\pi$
$607$	−6.40771	+	4.65548i	−0.260081	+	0.188960i	0.450102	+	0.892977i	$0.351388\pi$
$608$		0			0
$609$	7.13874	−	21.9708i	0.289276	−	0.890301i
$610$		0			0
$611$	9.64310	+	7.00613i	0.390118	+	0.283437i
$612$		0			0
$613$	5.81789	+	17.9056i	0.234982	+	0.723201i	0.997124	+	0.0757907i	$0.0241481\pi$
$613$	5.81789	+	17.9056i	0.234982	+	0.723201i	−0.762141	+	0.647411i	$0.775852\pi$
$614$		0			0
$615$	−25.7710			−1.03919
$616$		0			0
$617$	−13.2885			−0.534975			−0.267487	−	0.963561i	$-0.586193\pi$
$617$	−13.2885			−0.534975			−0.267487	+	0.963561i	$0.586193\pi$
$618$		0			0
$619$	−12.0924	−	37.2166i	−0.486035	−	1.49586i	−0.830477	−	0.557053i	$-0.811932\pi$
$619$	−12.0924	−	37.2166i	−0.486035	−	1.49586i	0.344442	−	0.938807i	$-0.388068\pi$
$620$		0			0
$621$	−28.5055	−	20.7105i	−1.14389	−	0.831083i
$622$		0			0
$623$	7.08933	−	21.8187i	0.284028	−	0.874148i
$624$		0			0
$625$	1.97638	−	1.43592i	0.0790551	−	0.0574369i
$626$		0			0
$627$	−3.95649	−	2.67014i	−0.158007	−	0.106635i
$628$		0			0
$629$	2.57018	−	1.86735i	0.102480	−	0.0744560i
$630$		0			0
$631$	−6.84149	+	21.0559i	−0.272355	+	0.838224i	0.717552	+	0.696505i	$0.245263\pi$
$631$	−6.84149	+	21.0559i	−0.272355	+	0.838224i	−0.989907	+	0.141718i	$0.954737\pi$
$632$		0			0
$633$	32.4754	+	23.5948i	1.29078	+	0.937809i
$634$		0			0
$635$	8.91681	+	27.4431i	0.353853	+	1.08905i
$636$		0			0
$637$	4.97458			0.197100
$638$		0			0
$639$	−10.7533			−0.425394
$640$		0			0
$641$	−2.38545	−	7.34167i	−0.0942197	−	0.289978i	0.892830	−	0.450394i	$-0.148717\pi$
$641$	−2.38545	−	7.34167i	−0.0942197	−	0.289978i	−0.987050	+	0.160416i	$0.948717\pi$
$642$		0			0
$643$	−34.4678	−	25.0424i	−1.35928	−	0.987574i	−0.998490	−	0.0549265i	$-0.982508\pi$
$643$	−34.4678	−	25.0424i	−1.35928	−	0.987574i	−0.360789	−	0.932648i	$-0.617492\pi$
$644$		0			0
$645$	−1.26982	+	3.90811i	−0.0499992	+	0.153882i
$646$		0			0
$647$	8.58585	−	6.23799i	0.337545	−	0.245241i	−0.406080	−	0.913837i	$-0.633105\pi$
$647$	8.58585	−	6.23799i	0.337545	−	0.245241i	0.743625	+	0.668597i	$0.233105\pi$
$648$		0			0
$649$	−9.73093	+	0.337356i	−0.381972	+	0.0132424i
$650$		0			0
$651$	−16.9912	+	12.3448i	−0.665937	+	0.483832i
$652$		0			0
$653$	−14.9279	+	45.9434i	−0.584175	+	1.79791i	0.0183831	+	0.999831i	$0.494148\pi$
$653$	−14.9279	+	45.9434i	−0.584175	+	1.79791i	−0.602558	+	0.798075i	$0.705852\pi$
$654$		0			0
$655$	5.49103	+	3.98946i	0.214552	+	0.155881i
$656$		0			0
$657$	0.138629	+	0.426656i	0.00540843	+	0.0166455i
$658$		0			0
$659$	1.71267			0.0667161			0.0333581	−	0.999443i	$-0.489380\pi$
$659$	1.71267			0.0667161			0.0333581	+	0.999443i	$0.489380\pi$
$660$		0			0
$661$	48.7587			1.89649			0.948246	−	0.317536i	$-0.102855\pi$
$661$	48.7587			1.89649			0.948246	+	0.317536i	$0.102855\pi$
$662$		0			0
$663$	−1.46569	−	4.51094i	−0.0569228	−	0.175190i
$664$		0			0
$665$	3.48146	+	2.52943i	0.135005	+	0.0980871i
$666$		0			0
$667$	−10.4901	+	32.2851i	−0.406177	+	1.25008i
$668$		0			0
$669$	8.68806	−	6.31225i	0.335900	−	0.244046i
$670$		0			0
$671$	0.0677878	−	0.236180i	0.00261692	−	0.00911761i
$672$		0			0
$673$	−13.1869	+	9.58082i	−0.508316	+	0.369313i	−0.812184	−	0.583401i	$-0.801722\pi$
$673$	−13.1869	+	9.58082i	−0.508316	+	0.369313i	0.303868	+	0.952714i	$0.401722\pi$
$674$		0			0
$675$	−5.00973	+	15.4184i	−0.192825	+	0.593453i
$676$		0			0
$677$	0.432090	+	0.313932i	0.0166066	+	0.0120654i	0.596058	−	0.802942i	$-0.296733\pi$
$677$	0.432090	+	0.313932i	0.0166066	+	0.0120654i	−0.579451	+	0.815007i	$0.696733\pi$
$678$		0			0
$679$	4.32938	+	13.3245i	0.166146	+	0.511346i
$680$		0			0
$681$	39.8451			1.52687
$682$		0			0
$683$	−22.9689			−0.878882			−0.439441	−	0.898271i	$-0.644823\pi$
$683$	−22.9689			−0.878882			−0.439441	+	0.898271i	$0.644823\pi$
$684$		0			0
$685$	5.27743	+	16.2423i	0.201640	+	0.620585i
$686$		0			0
$687$	−24.5250	−	17.8185i	−0.935688	−	0.679817i
$688$		0			0
$689$	0.0684743	−	0.210742i	0.00260866	−	0.00802864i
$690$		0			0
$691$	−39.3754	+	28.6079i	−1.49791	+	1.08830i	−0.526708	+	0.850046i	$0.676574\pi$
$691$	−39.3754	+	28.6079i	−1.49791	+	1.08830i	−0.971204	+	0.238251i	$0.923426\pi$
$692$		0			0
$693$	−7.15413	+	5.58651i	−0.271763	+	0.212214i
$694$		0			0
$695$	19.9176	−	14.4710i	0.755517	−	0.548915i
$696$		0			0
$697$	−4.22437	+	13.0013i	−0.160009	+	0.492458i
$698$		0			0
$699$	28.9518	+	21.0347i	1.09506	+	0.795605i
$700$		0			0
$701$	7.40026	+	22.7756i	0.279504	+	0.860224i	0.987992	+	0.154502i	$0.0493773\pi$
$701$	7.40026	+	22.7756i	0.279504	+	0.860224i	−0.708489	+	0.705722i	$0.750623\pi$
$702$		0			0
$703$	−2.84952			−0.107472
$704$		0			0
$705$	−8.47488			−0.319182
$706$		0			0
$707$	−1.70646	−	5.25195i	−0.0641781	−	0.197520i
$708$		0			0
$709$	20.6628	+	15.0124i	0.776008	+	0.563803i	0.903778	−	0.428001i	$-0.140782\pi$
$709$	20.6628	+	15.0124i	0.776008	+	0.563803i	−0.127770	+	0.991804i	$0.540782\pi$
$710$		0			0
$711$	−1.51524	+	4.66343i	−0.0568259	+	0.174892i
$712$		0			0
$713$	24.9678	−	18.1402i	0.935051	−	0.679354i
$714$		0			0
$715$	4.89364	+	13.4557i	0.183012	+	0.503215i
$716$		0			0
$717$	−18.2902	+	13.2886i	−0.683059	+	0.496271i
$718$		0			0
$719$	9.37470	−	28.8524i	0.349617	−	1.07601i	−0.609448	−	0.792826i	$-0.708609\pi$
$719$	9.37470	−	28.8524i	0.349617	−	1.07601i	0.959065	−	0.283185i	$-0.0913912\pi$
$720$		0			0
$721$	6.40874	+	4.65622i	0.238674	+	0.173407i
$722$		0			0
$723$	6.36035	+	19.5752i	0.236544	+	0.728008i
$724$		0			0
$725$	15.6191			0.580079
$726$		0			0
$727$	−21.9102			−0.812605			−0.406302	−	0.913739i	$-0.633182\pi$
$727$	−21.9102			−0.812605			−0.406302	+	0.913739i	$0.633182\pi$
$728$		0			0
$729$	9.07955	+	27.9440i	0.336280	+	1.03496i
$730$		0			0
$731$	1.76347	+	1.28123i	0.0652242	+	0.0473881i
$732$		0			0
$733$	−10.3997	+	32.0070i	−0.384122	+	1.18221i	0.552994	+	0.833185i	$0.313485\pi$
$733$	−10.3997	+	32.0070i	−0.384122	+	1.18221i	−0.937115	+	0.349020i	$0.886515\pi$
$734$		0			0
$735$	−2.86147	+	2.07898i	−0.105547	+	0.0766842i
$736$		0			0
$737$	−3.61180	−	9.93112i	−0.133042	−	0.365818i
$738$		0			0
$739$	−18.6794	+	13.5714i	−0.687132	+	0.499230i	−0.875716	−	0.482827i	$-0.839610\pi$
$739$	−18.6794	+	13.5714i	−0.687132	+	0.499230i	0.188584	+	0.982057i	$0.439610\pi$
$740$		0			0
$741$	−1.31464	+	4.04606i	−0.0482946	+	0.148636i
$742$		0			0
$743$	−34.0341	−	24.7272i	−1.24859	−	0.907154i	−0.250451	−	0.968129i	$-0.580579\pi$
$743$	−34.0341	−	24.7272i	−1.24859	−	0.907154i	−0.998139	+	0.0609749i	$0.980579\pi$
$744$		0			0
$745$	6.40762	+	19.7206i	0.234757	+	0.722508i
$746$		0			0
$747$	7.79657			0.285261
$748$		0			0
$749$	7.82157			0.285794
$750$		0			0
$751$	−9.97077	−	30.6869i	−0.363838	−	1.11978i	−0.950705	−	0.310096i	$-0.899639\pi$
$751$	−9.97077	−	30.6869i	−0.363838	−	1.11978i	0.586867	−	0.809684i	$-0.300361\pi$
$752$		0			0
$753$	0.409578	+	0.297576i	0.0149259	+	0.0108443i
$754$		0			0
$755$	−6.89059	+	21.2071i	−0.250774	+	0.771804i
$756$		0			0
$757$	31.5798	−	22.9441i	1.14779	−	0.833917i	0.159603	−	0.987181i	$-0.448979\pi$
$757$	31.5798	−	22.9441i	1.14779	−	0.833917i	0.988185	+	0.153264i	$0.0489786\pi$
$758$		0			0
$759$	−23.4438	+	18.3068i	−0.850957	+	0.664495i
$760$		0			0
$761$	43.4969	−	31.6023i	1.57676	−	1.14558i	0.656468	−	0.754354i	$-0.272050\pi$
$761$	43.4969	−	31.6023i	1.57676	−	1.14558i	0.920293	−	0.391229i	$-0.127950\pi$
$762$		0			0
$763$	7.33401	−	22.5718i	0.265509	−	0.817153i
$764$		0			0
$765$	−1.22342	−	0.888870i	−0.0442330	−	0.0321372i
$766$		0			0
$767$	2.68172	+	8.25348i	0.0968313	+	0.298016i
$768$		0			0
$769$	37.2325			1.34264			0.671319	−	0.741168i	$-0.265728\pi$
$769$	37.2325			1.34264			0.671319	+	0.741168i	$0.265728\pi$
$770$		0			0
$771$	−1.68747			−0.0607727
$772$		0			0
$773$	2.83313	+	8.71946i	0.101900	+	0.313617i	0.988990	−	0.147979i	$-0.0472768\pi$
$773$	2.83313	+	8.71946i	0.101900	+	0.313617i	−0.887090	+	0.461596i	$0.847277\pi$
$774$		0			0
$775$	−11.4879	−	8.34644i	−0.412657	−	0.299813i
$776$		0			0
$777$	3.73421	−	11.4927i	0.133964	−	0.412299i
$778$		0			0
$779$	9.91978	−	7.20715i	0.355413	−	0.258223i
$780$		0			0
$781$	−10.5937	+	36.9094i	−0.379071	+	1.32072i
$782$		0			0
$783$	24.9186	−	18.1044i	0.890517	−	0.646999i
$784$		0			0
$785$	−8.77554	+	27.0083i	−0.313212	+	0.963969i
$786$		0			0
$787$	−1.82857	−	1.32853i	−0.0651815	−	0.0473572i	0.554717	−	0.832039i	$-0.312826\pi$
$787$	−1.82857	−	1.32853i	−0.0651815	−	0.0473572i	−0.619899	+	0.784682i	$0.712826\pi$
$788$		0			0
$789$	5.15069	+	15.8522i	0.183370	+	0.564353i
$790$		0			0
$791$	0.760097			0.0270259
$792$		0			0
$793$	−0.219002			−0.00777699
$794$		0			0
$795$	0.0486858	+	0.149839i	0.00172671	+	0.00531426i
$796$		0			0
$797$	−23.8779	−	17.3483i	−0.845798	−	0.614508i	0.0781865	−	0.996939i	$-0.475087\pi$
$797$	−23.8779	−	17.3483i	−0.845798	−	0.614508i	−0.923984	+	0.382431i	$0.875087\pi$
$798$		0			0
$799$	−1.38920	+	4.27552i	−0.0491463	+	0.151257i
$800$		0			0
$801$	5.85006	−	4.25032i	0.206702	−	0.150178i
$802$		0			0
$803$	1.60102	−	0.0555047i	0.0564987	−	0.00195872i
$804$		0			0
$805$	21.6951	−	15.7624i	0.764653	−	0.555553i
$806$		0			0
$807$	−0.365918	+	1.12618i	−0.0128809	+	0.0396434i
$808$		0			0
$809$	36.9244	+	26.8272i	1.29819	+	0.943193i	0.999936	−	0.0112921i	$-0.00359448\pi$
$809$	36.9244	+	26.8272i	1.29819	+	0.943193i	0.298258	+	0.954485i	$0.403594\pi$
$810$		0			0
$811$	−8.31247	−	25.5832i	−0.291890	−	0.898346i	−0.984248	−	0.176792i	$-0.943428\pi$
$811$	−8.31247	−	25.5832i	−0.291890	−	0.898346i	0.692358	−	0.721554i	$-0.256572\pi$
$812$		0			0
$813$	−16.8354			−0.590445
$814$		0			0
$815$	28.4553			0.996746
$816$		0			0
$817$	−0.604167	−	1.85943i	−0.0211371	−	0.0650534i
$818$		0			0
$819$	6.54504	+	4.75525i	0.228702	+	0.166162i
$820$		0			0
$821$	−8.56963	+	26.3746i	−0.299082	+	0.920480i	0.682738	+	0.730664i	$0.260789\pi$
$821$	−8.56963	+	26.3746i	−0.299082	+	0.920480i	−0.981820	+	0.189816i	$0.939211\pi$
$822$		0			0
$823$	0.410277	−	0.298084i	0.0143014	−	0.0103906i	−0.580612	−	0.814181i	$-0.697187\pi$
$823$	0.410277	−	0.298084i	0.0143014	−	0.0103906i	0.594913	+	0.803790i	$0.297187\pi$
$824$		0			0
$825$	11.3441	+	7.65588i	0.394952	+	0.266543i
$826$		0			0
$827$	−1.51155	+	1.09821i	−0.0525618	+	0.0381884i	−0.613756	−	0.789496i	$-0.710342\pi$
$827$	−1.51155	+	1.09821i	−0.0525618	+	0.0381884i	0.561194	+	0.827684i	$0.310342\pi$
$828$		0			0
$829$	13.3355	−	41.0425i	0.463161	−	1.42546i	−0.398119	−	0.917334i	$-0.630337\pi$
$829$	13.3355	−	41.0425i	0.463161	−	1.42546i	0.861281	−	0.508130i	$-0.169663\pi$
$830$		0			0
$831$	1.78403	+	1.29617i	0.0618873	+	0.0449638i
$832$		0			0
$833$	0.579778	+	1.78437i	0.0200881	+	0.0618249i
$834$		0			0
$835$	11.1686			0.386506
$836$		0			0
$837$	−28.0022			−0.967898
$838$		0			0
$839$	−5.24736	−	16.1497i	−0.181159	−	0.557550i	0.818702	−	0.574218i	$-0.194694\pi$
$839$	−5.24736	−	16.1497i	−0.181159	−	0.557550i	−0.999861	+	0.0166686i	$0.994694\pi$
$840$		0			0
$841$	−0.546012	−	0.396701i	−0.0188280	−	0.0136793i
$842$		0			0
$843$	−6.78497	+	20.8820i	−0.233687	+	0.719214i
$844$		0			0
$845$	−5.03523	+	3.65831i	−0.173217	+	0.125850i
$846$		0			0
$847$	12.1271	+	30.0592i	0.416692	+	1.03285i
$848$		0			0
$849$	10.4405	−	7.58548i	0.358318	−	0.260333i
$850$		0			0
$851$	−5.48725	+	16.8880i	−0.188100	+	0.578914i
$852$		0			0
$853$	−16.5048	−	11.9914i	−0.565114	−	0.410579i	0.268213	−	0.963360i	$-0.413567\pi$
$853$	−16.5048	−	11.9914i	−0.565114	−	0.410579i	−0.833327	+	0.552780i	$0.813567\pi$
$854$		0			0
$855$	0.419147	+	1.29000i	0.0143345	+	0.0441172i
$856$		0			0
$857$	−24.6779			−0.842981			−0.421490	−	0.906833i	$-0.638493\pi$
$857$	−24.6779			−0.842981			−0.421490	+	0.906833i	$0.638493\pi$
$858$		0			0
$859$	−3.52545			−0.120287			−0.0601433	−	0.998190i	$-0.519156\pi$
$859$	−3.52545			−0.120287			−0.0601433	+	0.998190i	$0.519156\pi$
$860$		0			0
$861$	16.0684	+	49.4533i	0.547608	+	1.68536i
$862$		0			0
$863$	31.8266	+	23.1234i	1.08339	+	0.787130i	0.978271	−	0.207329i	$-0.0664772\pi$
$863$	31.8266	+	23.1234i	1.08339	+	0.787130i	0.105121	+	0.994459i	$0.466477\pi$
$864$		0			0
$865$	0.773983	−	2.38207i	0.0263162	−	0.0809929i
$866$		0			0
$867$	−18.3461	+	13.3293i	−0.623068	+	0.452685i
$868$		0			0
$869$	14.5139	+	9.79507i	0.492350	+	0.332275i
$870$		0			0
$871$	−7.61984	+	5.53614i	−0.258189	+	0.187585i
$872$		0			0
$873$	−1.36460	+	4.19981i	−0.0461848	+	0.142142i
$874$		0			0
$875$	−27.3894	−	19.8996i	−0.925932	−	0.672729i
$876$		0			0
$877$	−15.7541	−	48.4860i	−0.531977	−	1.63726i	−0.750093	−	0.661333i	$-0.769991\pi$
$877$	−15.7541	−	48.4860i	−0.531977	−	1.63726i	0.218116	−	0.975923i	$-0.430009\pi$
$878$		0			0
$879$	21.2111			0.715433
$880$		0			0
$881$	−11.9057			−0.401112			−0.200556	−	0.979682i	$-0.564275\pi$
$881$	−11.9057			−0.401112			−0.200556	+	0.979682i	$0.564275\pi$
$882$		0			0
$883$	15.9426	+	49.0663i	0.536512	+	1.65121i	0.740360	+	0.672210i	$0.234655\pi$
$883$	15.9426	+	49.0663i	0.536512	+	1.65121i	−0.203849	+	0.979002i	$0.565345\pi$
$884$		0			0
$885$	−4.99186	−	3.62680i	−0.167800	−	0.121914i
$886$		0			0
$887$	−3.71113	+	11.4217i	−0.124607	+	0.383502i	−0.993829	−	0.110920i	$-0.964620\pi$
$887$	−3.71113	+	11.4217i	−0.124607	+	0.383502i	0.869222	+	0.494422i	$0.164620\pi$
$888$		0			0
$889$	47.1024	−	34.2219i	1.57976	−	1.14777i
$890$		0			0
$891$	17.7367	−	0.614905i	0.594203	−	0.0206001i
$892$		0			0
$893$	3.26216	−	2.37010i	0.109164	−	0.0793122i
$894$		0			0
$895$	3.79053	−	11.6660i	0.126703	−	0.389953i
$896$		0			0
$897$	21.4479	+	15.5828i	0.716123	+	0.520294i
$898$		0			0
$899$	8.33678	+	25.6580i	0.278047	+	0.855742i
$900$		0			0
$901$	0.0835735			0.00278424
$902$		0			0
$903$	8.29123			0.275915
$904$		0			0
$905$	9.04873	+	27.8491i	0.300790	+	0.925736i
$906$		0			0
$907$	−26.2567	−	19.0766i	−0.871839	−	0.633428i	0.0592407	−	0.998244i	$-0.481132\pi$
$907$	−26.2567	−	19.0766i	−0.871839	−	0.633428i	−0.931080	+	0.364816i	$0.881132\pi$
$908$		0			0
$909$	0.537870	−	1.65539i	0.0178400	−	0.0549059i
$910$		0			0
$911$	−2.28751	+	1.66197i	−0.0757886	+	0.0550636i	−0.625034	−	0.780597i	$-0.714915\pi$
$911$	−2.28751	+	1.66197i	−0.0757886	+	0.0550636i	0.549246	+	0.835661i	$0.314915\pi$
$912$		0			0
$913$	7.68083	−	26.7608i	0.254198	−	0.885652i
$914$		0			0
$915$	0.125974	−	0.0915252i	0.00416456	−	0.00302573i
$916$		0			0
$917$	4.23191	−	13.0245i	0.139750	−	0.430106i
$918$		0			0
$919$	27.7668	+	20.1737i	0.915941	+	0.665470i	0.942510	−	0.334177i	$-0.108458\pi$
$919$	27.7668	+	20.1737i	0.915941	+	0.665470i	−0.0265692	+	0.999647i	$0.508458\pi$
$920$		0			0
$921$	−2.48360	−	7.64374i	−0.0818375	−	0.251870i
$922$		0			0
$923$	34.2249			1.12653
$924$		0			0
$925$	8.17020			0.268635
$926$		0			0
$927$	0.771574	+	2.37466i	0.0253418	+	0.0779941i
$928$		0			0
$929$	34.8929	+	25.3512i	1.14480	+	0.831745i	0.987781	−	0.155851i	$-0.0498120\pi$
$929$	34.8929	+	25.3512i	1.14480	+	0.831745i	0.157018	+	0.987596i	$0.449812\pi$
$930$		0			0
$931$	0.520028	−	1.60048i	0.0170432	−	0.0524537i
$932$		0			0
$933$	−33.1872	+	24.1119i	−1.08650	+	0.789388i
$934$		0			0
$935$	−4.25620	+	3.32358i	−0.139193	+	0.108693i
$936$		0			0
$937$	−44.7267	+	32.4958i	−1.46116	+	1.06159i	−0.478097	+	0.878307i	$0.658673\pi$
$937$	−44.7267	+	32.4958i	−1.46116	+	1.06159i	−0.983060	+	0.183286i	$0.941327\pi$
$938$		0			0
$939$	7.37852	−	22.7088i	0.240789	−	0.741072i
$940$		0			0
$941$	−10.4023	−	7.55768i	−0.339104	−	0.246373i	0.405180	−	0.914237i	$-0.367209\pi$
$941$	−10.4023	−	7.55768i	−0.339104	−	0.246373i	−0.744284	+	0.667864i	$0.767209\pi$
$942$		0			0
$943$	−23.6117	−	72.6694i	−0.768904	−	2.36644i
$944$		0			0
$945$	−24.3318			−0.791515
$946$		0			0
$947$	−5.74390			−0.186652			−0.0933258	−	0.995636i	$-0.529750\pi$
$947$	−5.74390			−0.186652			−0.0933258	+	0.995636i	$0.529750\pi$
$948$		0			0
$949$	−0.441220	−	1.35793i	−0.0143226	−	0.0440804i
$950$		0			0
$951$	25.7836	+	18.7328i	0.836089	+	0.607454i
$952$		0			0
$953$	−1.09429	+	3.36786i	−0.0354474	+	0.109096i	−0.967215	−	0.253960i	$-0.918267\pi$
$953$	−1.09429	+	3.36786i	−0.0354474	+	0.109096i	0.931767	+	0.363056i	$0.118267\pi$
$954$		0			0
$955$	−15.8849	+	11.5411i	−0.514024	+	0.373460i
$956$		0			0
$957$	−8.88700	−	24.4360i	−0.287276	−	0.789904i
$958$		0			0
$959$	27.8777	−	20.2543i	0.900216	−	0.654045i
$960$		0			0
$961$	−2.00029	+	6.15627i	−0.0645256	+	0.198589i
$962$		0			0
$963$	1.99449	+	1.44908i	0.0642716	+	0.0466960i
$964$		0			0
$965$	5.40187	+	16.6252i	0.173892	+	0.535185i
$966$		0			0
$967$	−48.5614			−1.56163			−0.780815	−	0.624762i	$-0.785196\pi$
$967$	−48.5614			−1.56163			−0.780815	+	0.624762i	$0.785196\pi$
$968$		0			0
$969$	−1.60453			−0.0515450
$970$		0			0
$971$	−5.49626	−	16.9157i	−0.176383	−	0.542852i	0.823311	−	0.567591i	$-0.192125\pi$
$971$	−5.49626	−	16.9157i	−0.176383	−	0.542852i	−0.999694	+	0.0247390i	$0.992125\pi$
$972$		0			0
$973$	−40.1878	−	29.1982i	−1.28836	−	0.936050i
$974$		0			0
$975$	3.76937	−	11.6009i	0.120717	−	0.371527i
$976$		0			0
$977$	−17.2000	+	12.4966i	−0.550278	+	0.399800i	−0.827888	−	0.560894i	$-0.810458\pi$
$977$	−17.2000	+	12.4966i	−0.550278	+	0.399800i	0.277610	+	0.960694i	$0.410458\pi$
$978$		0			0
$979$	−8.82549	−	24.2669i	−0.282064	−	0.775572i
$980$		0			0
$981$	6.05198	−	4.39702i	0.193225	−	0.140386i
$982$		0			0
$983$	−16.7843	+	51.6568i	−0.535336	+	1.64760i	0.207585	+	0.978217i	$0.433440\pi$
$983$	−16.7843	+	51.6568i	−0.535336	+	1.64760i	−0.742921	+	0.669379i	$0.766560\pi$
$984$		0			0
$985$	−21.3041	−	15.4783i	−0.678806	−	0.493181i
$986$		0			0
$987$	5.28414	+	16.2629i	0.168196	+	0.517654i
$988$		0			0
$989$	−12.1836			−0.387416
$990$		0			0
$991$	−15.7311			−0.499714			−0.249857	−	0.968283i	$-0.580384\pi$
$991$	−15.7311			−0.499714			−0.249857	+	0.968283i	$0.580384\pi$
$992$		0			0
$993$	−10.4199	−	32.0691i	−0.330665	−	1.01768i
$994$		0			0
$995$	25.2258	+	18.3276i	0.799712	+	0.581025i
$996$		0			0
$997$	8.60209	−	26.4745i	0.272431	−	0.838456i	−0.717457	−	0.696603i	$-0.754694\pi$
$997$	8.60209	−	26.4745i	0.272431	−	0.838456i	0.989888	−	0.141853i	$-0.0453061\pi$
$998$		0			0
$999$	13.0347	−	9.47024i	0.412399	−	0.299625i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	836.2.j.b.685.2	yes	20
11.2	odd	10		9196.2.a.t.1.3		10
11.4	even	5	inner	836.2.j.b.609.2	✓	20
11.9	even	5		9196.2.a.s.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
836.2.j.b.609.2	✓	20	11.4	even	5	inner
836.2.j.b.685.2	yes	20	1.1	even	1	trivial
9196.2.a.s.1.3		10	11.9	even	5
9196.2.a.t.1.3		10	11.2	odd	10

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:	\( N \)	\(=\)	\( 836 = 2^{2} \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	836.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.444729 - 1.36874i) q^{3} +(1.18149 + 0.858404i) q^{5} +(0.910570 - 2.80245i) q^{7} +(0.751396 - 0.545921i) q^{9} +(-1.13357 - 3.11689i) q^{11} +(-2.39150 + 1.73752i) q^{13} +(0.649484 - 1.99891i) q^{15} +(-0.901971 - 0.655320i) q^{17} +(0.309017 + 0.951057i) q^{19} -4.24077 q^{21} +6.23162 q^{23} +(-0.886020 - 2.72689i) q^{25} +(-4.57434 - 3.32345i) q^{27} +(-1.68336 + 5.18085i) q^{29} +(4.00663 - 2.91099i) q^{31} +(-3.76207 + 2.93773i) q^{33} +(3.48146 - 2.52943i) q^{35} +(-0.880550 + 2.71005i) q^{37} +(3.44178 + 2.50060i) q^{39} +(-3.78902 - 11.6614i) q^{41} -1.95512 q^{43} +1.35639 q^{45} +(-1.24603 - 3.83489i) q^{47} +(-1.36145 - 0.989153i) q^{49} +(-0.495828 + 1.52600i) q^{51} +(-0.0606444 + 0.0440608i) q^{53} +(1.33625 - 4.65564i) q^{55} +(1.16432 - 0.845925i) q^{57} +(0.907196 - 2.79206i) q^{59} +(0.0599368 + 0.0435466i) q^{61} +(-0.845717 - 2.60285i) q^{63} -4.31703 q^{65} +3.18622 q^{67} +(-2.77138 - 8.52944i) q^{69} +(-9.36673 - 6.80533i) q^{71} +(-0.149260 + 0.459374i) q^{73} +(-3.33835 + 2.42546i) q^{75} +(-9.76712 + 0.338611i) q^{77} +(-4.27115 + 3.10317i) q^{79} +(-1.65356 + 5.08914i) q^{81} +(6.79125 + 4.93413i) q^{83} +(-0.503142 - 1.54851i) q^{85} +7.83986 q^{87} +7.78559 q^{89} +(2.69169 + 8.28418i) q^{91} +(-5.76624 - 4.18942i) q^{93} +(-0.451290 + 1.38893i) q^{95} +(-3.84654 + 2.79467i) q^{97} +(-2.55334 - 1.72318i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5} + 15 q^{7} + 9 q^{9} + 2 q^{11} + 4 q^{13} + 15 q^{15} + 7 q^{17} - 5 q^{19} - 12 q^{21} - 16 q^{23} - 5 q^{25} - 3 q^{27} + 16 q^{29} + q^{31} - 27 q^{33} - 13 q^{35} + 14 q^{37} - 29 q^{39}+ \cdots - 35 q^{99}+O(q^{100}) \) 20 * q - 4 * q^5 + 15 * q^7 + 9 * q^9 + 2 * q^11 + 4 * q^13 + 15 * q^15 + 7 * q^17 - 5 * q^19 - 12 * q^21 - 16 * q^23 - 5 * q^25 - 3 * q^27 + 16 * q^29 + q^31 - 27 * q^33 - 13 * q^35 + 14 * q^37 - 29 * q^39 - 5 * q^41 + 28 * q^43 - 4 * q^47 - 4 * q^49 + 4 * q^51 - 17 * q^55 + 42 * q^59 + 27 * q^61 + 22 * q^63 - 14 * q^65 - 34 * q^67 - 11 * q^69 + 32 * q^71 - 7 * q^73 + 13 * q^75 - 60 * q^77 + 2 * q^79 - 9 * q^81 + 33 * q^83 + 27 * q^85 - 2 * q^87 - 70 * q^89 - 10 * q^91 + 7 * q^93 - 4 * q^95 - 6 * q^97 - 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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