LMFDB - Embedded newform 460.2.m.a.41.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(41,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("460.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.m (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			41.3
Character	$\chi$	$=$	460.41
Dual form			460.2.m.a.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939578 - 1.08433i) q^{3} +(-0.142315 + 0.989821i) q^{5} +(2.04060 + 4.46829i) q^{7} +(0.133978 + 0.931838i) q^{9} +O(q^{10})$	\(q+(0.939578 - 1.08433i) q^{3} +(-0.142315 + 0.989821i) q^{5} +(2.04060 + 4.46829i) q^{7} +(0.133978 + 0.931838i) q^{9} +(-1.32995 + 0.390508i) q^{11} +(-1.48189 + 3.24489i) q^{13} +(0.939578 + 1.08433i) q^{15} +(-0.499590 + 0.321067i) q^{17} +(-3.22610 - 2.07329i) q^{19} +(6.76240 + 1.98562i) q^{21} +(0.607574 - 4.75719i) q^{23} +(-0.959493 - 0.281733i) q^{25} +(4.75733 + 3.05735i) q^{27} +(3.59036 - 2.30739i) q^{29} +(4.36493 + 5.03739i) q^{31} +(-0.826150 + 1.80902i) q^{33} +(-4.71321 + 1.38392i) q^{35} +(-0.914003 - 6.35703i) q^{37} +(2.12618 + 4.65569i) q^{39} +(1.61198 - 11.2116i) q^{41} +(6.29004 - 7.25910i) q^{43} -0.941420 q^{45} +10.3743 q^{47} +(-11.2175 + 12.9457i) q^{49} +(-0.121261 + 0.843388i) q^{51} +(-3.64954 - 7.99137i) q^{53} +(-0.197262 - 1.37199i) q^{55} +(-5.27930 + 1.55014i) q^{57} +(-3.29047 + 7.20513i) q^{59} +(-1.06322 - 1.22702i) q^{61} +(-3.89032 + 2.50016i) q^{63} +(-3.00097 - 1.92861i) q^{65} +(-10.7510 - 3.15677i) q^{67} +(-4.58750 - 5.12856i) q^{69} +(7.56643 + 2.22170i) q^{71} +(5.94562 + 3.82102i) q^{73} +(-1.20701 + 0.775698i) q^{75} +(-4.45879 - 5.14572i) q^{77} +(-5.03366 + 11.0222i) q^{79} +(5.07521 - 1.49022i) q^{81} +(0.930302 + 6.47039i) q^{83} +(-0.246700 - 0.540197i) q^{85} +(0.871456 - 6.06111i) q^{87} +(-2.15781 + 2.49024i) q^{89} -17.5231 q^{91} +9.56339 q^{93} +(2.51131 - 2.89820i) q^{95} +(2.53238 - 17.6131i) q^{97} +(-0.542074 - 1.18698i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.939578	−	1.08433i	0.542466	−	0.626039i	−0.416645	−	0.909069i	$-0.636794\pi$
$3$	0.939578	−	1.08433i	0.542466	−	0.626039i	0.959111	+	0.283030i	$0.0913397\pi$
$4$		0			0
$5$	−0.142315	+	0.989821i	−0.0636451	+	0.442662i
$5$	−0.142315	+	0.989821i	−0.0636451	+	0.442662i
$6$		0			0
$7$	2.04060	+	4.46829i	0.771274	+	1.68885i	0.723829	+	0.689980i	$0.242381\pi$
$7$	2.04060	+	4.46829i	0.771274	+	1.68885i	0.0474449	+	0.998874i	$0.484892\pi$
$8$		0			0
$9$	0.133978	+	0.931838i	0.0446593	+	0.310613i
$10$		0			0
$11$	−1.32995	+	0.390508i	−0.400994	+	0.117743i	−0.476010	−	0.879440i	$-0.657917\pi$
$11$	−1.32995	+	0.390508i	−0.400994	+	0.117743i	0.0750159	+	0.997182i	$0.476099\pi$
$12$		0			0
$13$	−1.48189	+	3.24489i	−0.411003	+	0.899971i	0.585032	+	0.811010i	$0.301082\pi$
$13$	−1.48189	+	3.24489i	−0.411003	+	0.899971i	−0.996035	+	0.0889609i	$0.971645\pi$
$14$		0			0
$15$	0.939578	+	1.08433i	0.242598	+	0.279973i
$16$		0			0
$17$	−0.499590	+	0.321067i	−0.121168	+	0.0778701i	−0.599821	−	0.800134i	$-0.704762\pi$
$17$	−0.499590	+	0.321067i	−0.121168	+	0.0778701i	0.478653	+	0.878004i	$0.341125\pi$
$18$		0			0
$19$	−3.22610	−	2.07329i	−0.740118	−	0.475645i	0.115464	−	0.993312i	$-0.463164\pi$
$19$	−3.22610	−	2.07329i	−0.740118	−	0.475645i	−0.855582	+	0.517667i	$0.826801\pi$
$20$		0			0
$21$	6.76240	+	1.98562i	1.47568	+	0.433298i
$22$		0			0
$23$	0.607574	−	4.75719i	0.126688	−	0.991943i
$23$	0.607574	−	4.75719i	0.126688	−	0.991943i
$24$		0			0
$25$	−0.959493	−	0.281733i	−0.191899	−	0.0563465i
$26$		0			0
$27$	4.75733	+	3.05735i	0.915549	+	0.588388i
$28$		0			0
$29$	3.59036	−	2.30739i	0.666713	−	0.428471i	−0.163026	−	0.986622i	$-0.552125\pi$
$29$	3.59036	−	2.30739i	0.666713	−	0.428471i	0.829739	+	0.558151i	$0.188489\pi$
$30$		0			0
$31$	4.36493	+	5.03739i	0.783964	+	0.904743i	0.997389	−	0.0722167i	$-0.0230073\pi$
$31$	4.36493	+	5.03739i	0.783964	+	0.904743i	−0.213425	+	0.976959i	$0.568462\pi$
$32$		0			0
$33$	−0.826150	+	1.80902i	−0.143814	+	0.314909i
$34$		0			0
$35$	−4.71321	+	1.38392i	−0.796678	+	0.233926i
$36$		0			0
$37$	−0.914003	−	6.35703i	−0.150261	−	1.04509i	−0.915781	−	0.401677i	$-0.868427\pi$
$37$	−0.914003	−	6.35703i	−0.150261	−	1.04509i	0.765520	−	0.643412i	$-0.222482\pi$
$38$		0			0
$39$	2.12618	+	4.65569i	0.340462	+	0.745507i
$40$		0			0
$41$	1.61198	−	11.2116i	0.251749	−	1.75095i	−0.335958	−	0.941877i	$-0.609060\pi$
$41$	1.61198	−	11.2116i	0.251749	−	1.75095i	0.587707	−	0.809074i	$-0.300031\pi$
$42$		0			0
$43$	6.29004	−	7.25910i	0.959222	−	1.10700i	−0.0349704	−	0.999388i	$-0.511134\pi$
$43$	6.29004	−	7.25910i	0.959222	−	1.10700i	0.994193	−	0.107613i	$-0.0343209\pi$
$44$		0			0
$45$	−0.941420			−0.140339
$46$		0			0
$47$	10.3743			1.51325			0.756627	−	0.653847i	$-0.226846\pi$
$47$	10.3743			1.51325			0.756627	+	0.653847i	$0.226846\pi$
$48$		0			0
$49$	−11.2175	+	12.9457i	−1.60250	+	1.84939i
$50$		0			0
$51$	−0.121261	+	0.843388i	−0.0169799	+	0.118098i
$52$		0			0
$53$	−3.64954	−	7.99137i	−0.501302	−	1.09770i	−0.976044	−	0.217574i	$-0.930186\pi$
$53$	−3.64954	−	7.99137i	−0.501302	−	1.09770i	0.474742	−	0.880125i	$-0.342541\pi$
$54$		0			0
$55$	−0.197262	−	1.37199i	−0.0265988	−	0.184998i
$56$		0			0
$57$	−5.27930	+	1.55014i	−0.699261	+	0.205321i
$58$		0			0
$59$	−3.29047	+	7.20513i	−0.428383	+	0.938028i	0.565203	+	0.824952i	$0.308798\pi$
$59$	−3.29047	+	7.20513i	−0.428383	+	0.938028i	−0.993586	+	0.113076i	$0.963930\pi$
$60$		0			0
$61$	−1.06322	−	1.22702i	−0.136131	−	0.157104i	0.683590	−	0.729866i	$-0.260417\pi$
$61$	−1.06322	−	1.22702i	−0.136131	−	0.157104i	−0.819722	+	0.572762i	$0.805872\pi$
$62$		0			0
$63$	−3.89032	+	2.50016i	−0.490135	+	0.314990i
$64$		0			0
$65$	−3.00097	−	1.92861i	−0.372224	−	0.239214i
$66$		0			0
$67$	−10.7510	−	3.15677i	−1.31344	−	0.385661i	−0.451320	−	0.892362i	$-0.649047\pi$
$67$	−10.7510	−	3.15677i	−1.31344	−	0.385661i	−0.862122	+	0.506701i	$0.830865\pi$
$68$		0			0
$69$	−4.58750	−	5.12856i	−0.552271	−	0.617406i
$70$		0			0
$71$	7.56643	+	2.22170i	0.897970	+	0.263668i	0.697969	−	0.716128i	$-0.254087\pi$
$71$	7.56643	+	2.22170i	0.897970	+	0.263668i	0.200001	+	0.979796i	$0.435905\pi$
$72$		0			0
$73$	5.94562	+	3.82102i	0.695883	+	0.447217i	0.840173	−	0.542319i	$-0.182454\pi$
$73$	5.94562	+	3.82102i	0.695883	+	0.447217i	−0.144290	+	0.989535i	$0.546090\pi$
$74$		0			0
$75$	−1.20701	+	0.775698i	−0.139373	+	0.0895699i
$76$		0			0
$77$	−4.45879	−	5.14572i	−0.508126	−	0.586409i
$78$		0			0
$79$	−5.03366	+	11.0222i	−0.566332	+	1.24009i	0.382396	+	0.923998i	$0.375099\pi$
$79$	−5.03366	+	11.0222i	−0.566332	+	1.24009i	−0.948728	+	0.316095i	$0.897628\pi$
$80$		0			0
$81$	5.07521	−	1.49022i	0.563912	−	0.165580i
$82$		0			0
$83$	0.930302	+	6.47039i	0.102114	+	0.710218i	0.974986	+	0.222268i	$0.0713460\pi$
$83$	0.930302	+	6.47039i	0.102114	+	0.710218i	−0.872872	+	0.487950i	$0.837745\pi$
$84$		0			0
$85$	−0.246700	−	0.540197i	−0.0267583	−	0.0585926i
$86$		0			0
$87$	0.871456	−	6.06111i	0.0934299	−	0.649819i
$88$		0			0
$89$	−2.15781	+	2.49024i	−0.228727	+	0.263965i	−0.858499	−	0.512815i	$-0.828603\pi$
$89$	−2.15781	+	2.49024i	−0.228727	+	0.263965i	0.629772	+	0.776780i	$0.283148\pi$
$90$		0			0
$91$	−17.5231			−1.83692
$92$		0			0
$93$	9.56339			0.991677
$94$		0			0
$95$	2.51131	−	2.89820i	0.257655	−	0.297349i
$96$		0			0
$97$	2.53238	−	17.6131i	0.257124	−	1.78833i	−0.295951	−	0.955203i	$-0.595637\pi$
$97$	2.53238	−	17.6131i	0.257124	−	1.78833i	0.553075	−	0.833132i	$-0.313454\pi$
$98$		0			0
$99$	−0.542074	−	1.18698i	−0.0544804	−	0.119296i
$100$		0			0
$101$	−1.24990	−	8.69322i	−0.124369	−	0.865007i	−0.952514	−	0.304494i	$-0.901513\pi$
$101$	−1.24990	−	8.69322i	−0.124369	−	0.865007i	0.828145	−	0.560514i	$-0.189396\pi$
$102$		0			0
$103$	10.9132	−	3.20440i	1.07531	−	0.315739i	0.304308	−	0.952574i	$-0.401575\pi$
$103$	10.9132	−	3.20440i	1.07531	−	0.315739i	0.771000	+	0.636835i	$0.219757\pi$
$104$		0			0
$105$	−2.92780	+	6.41099i	−0.285724	+	0.625648i
$106$		0			0
$107$	5.61560	+	6.48074i	0.542880	+	0.626517i	0.959209	−	0.282697i	$-0.0912290\pi$
$107$	5.61560	+	6.48074i	0.542880	+	0.626517i	−0.416329	+	0.909214i	$0.636684\pi$
$108$		0			0
$109$	0.367043	−	0.235884i	0.0351563	−	0.0225936i	−0.522945	−	0.852367i	$-0.675167\pi$
$109$	0.367043	−	0.235884i	0.0351563	−	0.0225936i	0.558101	+	0.829773i	$0.311530\pi$
$110$		0			0
$111$	−7.75190	−	4.98185i	−0.735778	−	0.472856i
$112$		0			0
$113$	1.86035	+	0.546247i	0.175007	+	0.0513866i	0.368062	−	0.929801i	$-0.380021\pi$
$113$	1.86035	+	0.546247i	0.175007	+	0.0513866i	−0.193055	+	0.981188i	$0.561840\pi$
$114$		0			0
$115$	4.62230	+	1.27841i	0.431032	+	0.119212i
$116$		0			0
$117$	−3.22225	−	0.946139i	−0.297897	−	0.0874706i
$118$		0			0
$119$	−2.45408	−	1.57714i	−0.224965	−	0.144576i
$120$		0			0
$121$	−7.63753	+	4.90834i	−0.694320	+	0.446213i
$122$		0			0
$123$	−10.6425	−	12.2820i	−0.959598	−	1.10743i
$124$		0			0
$125$	0.415415	−	0.909632i	0.0371558	−	0.0813600i
$126$		0			0
$127$	−9.72416	+	2.85527i	−0.862880	+	0.253364i	−0.683084	−	0.730340i	$-0.739362\pi$
$127$	−9.72416	+	2.85527i	−0.862880	+	0.253364i	−0.179796	+	0.983704i	$0.557544\pi$
$128$		0			0
$129$	−1.96128	−	13.6410i	−0.172681	−	1.20102i
$130$		0			0
$131$	1.68689	+	3.69378i	0.147385	+	0.322727i	0.968897	−	0.247463i	$-0.0795968\pi$
$131$	1.68689	+	3.69378i	0.147385	+	0.322727i	−0.821513	+	0.570190i	$0.806870\pi$
$132$		0			0
$133$	2.68087	−	18.6459i	0.232461	−	1.61680i
$134$		0			0
$135$	−3.70327	+	4.27380i	−0.318727	+	0.367830i
$136$		0			0
$137$	−8.09574			−0.691665			−0.345833	−	0.938296i	$-0.612404\pi$
$137$	−8.09574			−0.691665			−0.345833	+	0.938296i	$0.612404\pi$
$138$		0			0
$139$	−10.0808			−0.855039			−0.427519	−	0.904006i	$-0.640612\pi$
$139$	−10.0808			−0.855039			−0.427519	+	0.904006i	$0.640612\pi$
$140$		0			0
$141$	9.74750	−	11.2492i	0.820888	−	0.947355i
$142$		0			0
$143$	0.703683	−	4.89423i	0.0588450	−	0.409276i
$144$		0			0
$145$	1.77294	+	3.88219i	0.147234	+	0.322399i
$146$		0			0
$147$	3.49770	+	24.3270i	0.288485	+	2.00646i
$148$		0			0
$149$	−5.90081	+	1.73263i	−0.483413	+	0.141943i	−0.514353	−	0.857578i	$-0.671968\pi$
$149$	−5.90081	+	1.73263i	−0.483413	+	0.141943i	0.0309403	+	0.999521i	$0.490150\pi$
$150$		0			0
$151$	−3.01023	+	6.59149i	−0.244969	+	0.536408i	−0.991678	−	0.128743i	$-0.958906\pi$
$151$	−3.01023	+	6.59149i	−0.244969	+	0.536408i	0.746709	+	0.665151i	$0.231633\pi$
$152$		0			0
$153$	−0.366116	−	0.422520i	−0.0295987	−	0.0341588i
$154$		0			0
$155$	−5.60731	+	3.60360i	−0.450390	+	0.289448i
$156$		0			0
$157$	0.983305	+	0.631932i	0.0784763	+	0.0504336i	0.579291	−	0.815121i	$-0.303330\pi$
$157$	0.983305	+	0.631932i	0.0784763	+	0.0504336i	−0.500814	+	0.865555i	$0.666966\pi$
$158$		0			0
$159$	−12.0943	−	3.55121i	−0.959141	−	0.281629i
$160$		0			0
$161$	22.4963	−	6.99270i	1.77296	−	0.551102i
$162$		0			0
$163$	13.0288	+	3.82560i	1.02049	+	0.299644i	0.748840	−	0.662751i	$-0.230611\pi$
$163$	13.0288	+	3.82560i	1.02049	+	0.299644i	0.271654	+	0.962395i	$0.412430\pi$
$164$		0			0
$165$	−1.67303	−	1.07519i	−0.130245	−	0.0837035i
$166$		0			0
$167$	14.3770	−	9.23955i	1.11253	−	0.714978i	0.150685	−	0.988582i	$-0.451852\pi$
$167$	14.3770	−	9.23955i	1.11253	−	0.714978i	0.961843	+	0.273604i	$0.0882157\pi$
$168$		0			0
$169$	0.179872	+	0.207584i	0.0138363	+	0.0159680i
$170$		0			0
$171$	1.49974	−	3.28398i	0.114688	−	0.251132i
$172$		0			0
$173$	8.48305	−	2.49085i	0.644954	−	0.189376i	0.0571330	−	0.998367i	$-0.481804\pi$
$173$	8.48305	−	2.49085i	0.644954	−	0.189376i	0.587821	+	0.808991i	$0.299986\pi$
$174$		0			0
$175$	−0.699078	−	4.86219i	−0.0528453	−	0.367547i
$176$		0			0
$177$	4.72109	+	10.3377i	0.354859	+	0.777032i
$178$		0			0
$179$	1.45237	−	10.1014i	0.108555	−	0.755016i	−0.860728	−	0.509066i	$-0.829991\pi$
$179$	1.45237	−	10.1014i	0.108555	−	0.755016i	0.969283	−	0.245950i	$-0.0790999\pi$
$180$		0			0
$181$	−7.51262	+	8.67002i	−0.558408	+	0.644438i	−0.962821	−	0.270139i	$-0.912930\pi$
$181$	−7.51262	+	8.67002i	−0.558408	+	0.644438i	0.404413	+	0.914576i	$0.367476\pi$
$182$		0			0
$183$	−2.32948			−0.172200
$184$		0			0
$185$	6.42240			0.472184
$186$		0			0
$187$	0.539049	−	0.622095i	0.0394191	−	0.0454921i
$188$		0			0
$189$	−3.95332	+	27.4960i	−0.287562	+	2.00004i
$190$		0			0
$191$	−7.99636	−	17.5096i	−0.578596	−	1.26695i	−0.942093	−	0.335353i	$-0.891144\pi$
$191$	−7.99636	−	17.5096i	−0.578596	−	1.26695i	0.363497	−	0.931596i	$-0.381583\pi$
$192$		0			0
$193$	−0.292207	−	2.03234i	−0.0210335	−	0.146291i	0.976598	−	0.215071i	$-0.0689984\pi$
$193$	−0.292207	−	2.03234i	−0.0210335	−	0.146291i	−0.997632	+	0.0687801i	$0.978089\pi$
$194$		0			0
$195$	−4.91089	+	1.44197i	−0.351676	+	0.103261i
$196$		0			0
$197$	2.37336	−	5.19692i	0.169095	−	0.370265i	−0.806046	−	0.591853i	$-0.798397\pi$
$197$	2.37336	−	5.19692i	0.169095	−	0.370265i	0.975140	+	0.221588i	$0.0711239\pi$
$198$		0			0
$199$	−0.582305	−	0.672016i	−0.0412785	−	0.0476379i	0.734735	−	0.678354i	$-0.237307\pi$
$199$	−0.582305	−	0.672016i	−0.0412785	−	0.0476379i	−0.776013	+	0.630716i	$0.782761\pi$
$200$		0			0
$201$	−13.5244	+	8.69159i	−0.953936	+	0.613057i
$202$		0			0
$203$	17.6365	+	11.3343i	1.23784	+	0.795513i
$204$		0			0
$205$	10.8680	+	3.19114i	0.759056	+	0.222879i
$206$		0			0
$207$	4.51433	−	0.0711984i	0.313768	−	0.00494863i
$208$		0			0
$209$	5.10018	+	1.49755i	0.352787	+	0.103587i
$210$		0			0
$211$	18.5839	+	11.9431i	1.27937	+	0.822200i	0.990810	−	0.135263i	$-0.0431878\pi$
$211$	18.5839	+	11.9431i	1.27937	+	0.822200i	0.288558	+	0.957462i	$0.406824\pi$
$212$		0			0
$213$	9.51831	−	6.11705i	0.652184	−	0.419133i
$214$		0			0
$215$	6.29004	+	7.25910i	0.428977	+	0.495066i
$216$		0			0
$217$	−13.6015	+	29.7830i	−0.923327	+	2.02180i
$218$		0			0
$219$	9.72963	−	2.85688i	0.657467	−	0.193050i
$220$		0			0
$221$	−0.301489	−	2.09690i	−0.0202803	−	0.141053i
$222$		0			0
$223$	4.03163	+	8.82803i	0.269978	+	0.591169i	0.995256	−	0.0972866i	$-0.0310163\pi$
$223$	4.03163	+	8.82803i	0.269978	+	0.591169i	−0.725279	+	0.688455i	$0.758289\pi$
$224$		0			0
$225$	0.133978	−	0.931838i	0.00893187	−	0.0621225i
$226$		0			0
$227$	2.47411	−	2.85528i	0.164212	−	0.189511i	−0.667680	−	0.744449i	$-0.732712\pi$
$227$	2.47411	−	2.85528i	0.164212	−	0.189511i	0.831892	+	0.554937i	$0.187258\pi$
$228$		0			0
$229$	−3.48252			−0.230131			−0.115066	−	0.993358i	$-0.536708\pi$
$229$	−3.48252			−0.230131			−0.115066	+	0.993358i	$0.536708\pi$
$230$		0			0
$231$	−9.76904			−0.642756
$232$		0			0
$233$	−4.65210	+	5.36881i	−0.304769	+	0.351723i	−0.887388	−	0.461023i	$-0.847483\pi$
$233$	−4.65210	+	5.36881i	−0.304769	+	0.351723i	0.582619	+	0.812746i	$0.302028\pi$
$234$		0			0
$235$	−1.47642	+	10.2687i	−0.0963112	+	0.669859i
$236$		0			0
$237$	7.22218	+	15.8144i	0.469131	+	1.02725i
$238$		0			0
$239$	2.61575	+	18.1929i	0.169199	+	1.17680i	0.880545	+	0.473962i	$0.157177\pi$
$239$	2.61575	+	18.1929i	0.169199	+	1.17680i	−0.711346	+	0.702842i	$0.751914\pi$
$240$		0			0
$241$	5.77594	−	1.69597i	0.372061	−	0.109247i	−0.0903560	−	0.995910i	$-0.528800\pi$
$241$	5.77594	−	1.69597i	0.372061	−	0.109247i	0.462417	+	0.886663i	$0.346982\pi$
$242$		0			0
$243$	−3.89491	+	8.52867i	−0.249859	+	0.547114i
$244$		0			0
$245$	−11.2175	−	12.9457i	−0.716661	−	0.827071i
$246$		0			0
$247$	11.5083	−	7.39595i	0.732257	−	0.470593i
$248$		0			0
$249$	7.89014	+	5.07068i	0.500017	+	0.321342i
$250$		0			0
$251$	−13.6071	−	3.99541i	−0.858873	−	0.252188i	−0.177497	−	0.984121i	$-0.556800\pi$
$251$	−13.6071	−	3.99541i	−0.858873	−	0.252188i	−0.681376	+	0.731934i	$0.738618\pi$
$252$		0			0
$253$	1.04968	+	6.56407i	0.0659927	+	0.412680i
$254$		0			0
$255$	−0.817546	−	0.240053i	−0.0511967	−	0.0150327i
$256$		0			0
$257$	−23.8817	−	15.3479i	−1.48970	−	0.957373i	−0.996151	−	0.0876569i	$-0.972062\pi$
$257$	−23.8817	−	15.3479i	−1.48970	−	0.957373i	−0.493551	−	0.869717i	$-0.664302\pi$
$258$		0			0
$259$	26.5399	−	17.0562i	1.64911	−	1.05982i
$260$		0			0
$261$	2.63114	+	3.03650i	0.162863	+	0.187954i
$262$		0			0
$263$	1.34888	−	2.95363i	0.0831752	−	0.182128i	−0.863475	−	0.504392i	$-0.831717\pi$
$263$	1.34888	−	2.95363i	0.0831752	−	0.182128i	0.946650	+	0.322264i	$0.104444\pi$
$264$		0			0
$265$	8.42941	−	2.47510i	0.517815	−	0.152044i
$266$		0			0
$267$	0.672818	+	4.67955i	0.0411758	+	0.286384i
$268$		0			0
$269$	−10.2695	−	22.4870i	−0.626141	−	1.37106i	−0.910968	−	0.412478i	$-0.864663\pi$
$269$	−10.2695	−	22.4870i	−0.626141	−	1.37106i	0.284827	−	0.958579i	$-0.408064\pi$
$270$		0			0
$271$	−1.94730	+	13.5437i	−0.118290	+	0.822723i	0.841148	+	0.540804i	$0.181880\pi$
$271$	−1.94730	+	13.5437i	−0.118290	+	0.822723i	−0.959438	+	0.281919i	$0.909029\pi$
$272$		0			0
$273$	−16.4643	+	19.0008i	−0.996463	+	1.14998i
$274$		0			0
$275$	1.38609			0.0835846
$276$		0			0
$277$	−18.5368			−1.11377			−0.556885	−	0.830590i	$-0.688004\pi$
$277$	−18.5368			−1.11377			−0.556885	+	0.830590i	$0.688004\pi$
$278$		0			0
$279$	−4.10923	+	4.74230i	−0.246013	+	0.283914i
$280$		0			0
$281$	−4.06775	+	28.2918i	−0.242662	+	1.68775i	0.395992	+	0.918254i	$0.370401\pi$
$281$	−4.06775	+	28.2918i	−0.242662	+	1.68775i	−0.638653	+	0.769495i	$0.720508\pi$
$282$		0			0
$283$	6.40447	+	14.0238i	0.380706	+	0.833630i	0.998867	+	0.0475791i	$0.0151506\pi$
$283$	6.40447	+	14.0238i	0.380706	+	0.833630i	−0.618161	+	0.786051i	$0.712122\pi$
$284$		0			0
$285$	−0.783042	−	5.44617i	−0.0463834	−	0.322604i
$286$		0			0
$287$	53.3858	−	15.6755i	3.15127	−	0.925295i
$288$		0			0
$289$	−6.91555	+	15.1429i	−0.406797	+	0.890761i
$290$		0			0
$291$	−16.7190	−	19.2948i	−0.980086	−	1.13108i
$292$		0			0
$293$	10.2141	−	6.56418i	0.596712	−	0.383484i	−0.207141	−	0.978311i	$-0.566416\pi$
$293$	10.2141	−	6.56418i	0.596712	−	0.383484i	0.803853	+	0.594827i	$0.202780\pi$
$294$		0			0
$295$	−6.66351	−	4.28238i	−0.387965	−	0.249330i
$296$		0			0
$297$	−7.52092	−	2.20834i	−0.436408	−	0.128141i
$298$		0			0
$299$	14.5362	+	9.02116i	0.840650	+	0.521707i
$300$		0			0
$301$	45.2712	+	13.2928i	2.60939	+	0.766185i
$302$		0			0
$303$	−10.6007	−	6.81265i	−0.608994	−	0.391377i
$304$		0			0
$305$	1.36584	−	0.877775i	0.0782080	−	0.0502612i
$306$		0			0
$307$	−20.9173	−	24.1398i	−1.19381	−	1.37773i	−0.907745	−	0.419522i	$-0.862198\pi$
$307$	−20.9173	−	24.1398i	−1.19381	−	1.37773i	−0.286067	−	0.958210i	$-0.592348\pi$
$308$		0			0
$309$	6.77916	−	14.8443i	0.385653	−	0.844462i
$310$		0			0
$311$	3.61402	−	1.06117i	0.204932	−	0.0601735i	−0.177655	−	0.984093i	$-0.556851\pi$
$311$	3.61402	−	1.06117i	0.204932	−	0.0601735i	0.382587	+	0.923919i	$0.375033\pi$
$312$		0			0
$313$	−0.150542	−	1.04704i	−0.00850915	−	0.0591824i	0.985124	−	0.171842i	$-0.0549720\pi$
$313$	−0.150542	−	1.04704i	−0.00850915	−	0.0591824i	−0.993634	+	0.112660i	$0.964063\pi$
$314$		0			0
$315$	−1.92106	−	4.20653i	−0.108239	−	0.237011i
$316$		0			0
$317$	3.53299	−	24.5725i	0.198432	−	1.38013i	−0.610402	−	0.792092i	$-0.708992\pi$
$317$	3.53299	−	24.5725i	0.198432	−	1.38013i	0.808834	−	0.588036i	$-0.200099\pi$
$318$		0			0
$319$	−3.87394	+	4.47077i	−0.216899	+	0.250315i
$320$		0			0
$321$	12.3036			0.686718
$322$		0			0
$323$	2.27739			0.126717
$324$		0			0
$325$	2.33606	−	2.69595i	0.129581	−	0.149545i
$326$		0			0
$327$	0.0890890	−	0.619627i	0.00492663	−	0.0342655i
$328$		0			0
$329$	21.1699	+	46.3555i	1.16713	+	2.55566i
$330$		0			0
$331$	−3.25595	−	22.6456i	−0.178963	−	1.24472i	−0.859168	−	0.511694i	$-0.829018\pi$
$331$	−3.25595	−	22.6456i	−0.178963	−	1.24472i	0.680205	−	0.733022i	$-0.261891\pi$
$332$		0			0
$333$	5.80126	−	1.70341i	0.317907	−	0.0933460i
$334$		0			0
$335$	4.65467	−	10.1923i	0.254312	−	0.556865i
$336$		0			0
$337$	5.93365	+	6.84780i	0.323227	+	0.373024i	0.893987	−	0.448093i	$-0.147897\pi$
$337$	5.93365	+	6.84780i	0.323227	+	0.373024i	−0.570760	+	0.821117i	$0.693351\pi$
$338$		0			0
$339$	2.34025	−	1.50399i	0.127105	−	0.0816855i
$340$		0			0
$341$	−7.77226	−	4.99493i	−0.420892	−	0.270491i
$342$		0			0
$343$	−47.7431	−	14.0186i	−2.57788	−	0.756935i
$344$		0			0
$345$	5.72923	−	3.81094i	0.308451	−	0.205174i
$346$		0			0
$347$	−17.3678	−	5.09966i	−0.932354	−	0.273764i	−0.219932	−	0.975515i	$-0.570584\pi$
$347$	−17.3678	−	5.09966i	−0.932354	−	0.273764i	−0.712422	+	0.701751i	$0.752402\pi$
$348$		0			0
$349$	−0.607633	−	0.390502i	−0.0325258	−	0.0209031i	0.524277	−	0.851548i	$-0.324336\pi$
$349$	−0.607633	−	0.390502i	−0.0325258	−	0.0209031i	−0.556803	+	0.830645i	$0.687972\pi$
$350$		0			0
$351$	−16.9706	+	10.9064i	−0.905825	+	0.582139i
$352$		0			0
$353$	−12.1372	−	14.0071i	−0.646000	−	0.745523i	0.334424	−	0.942423i	$-0.391458\pi$
$353$	−12.1372	−	14.0071i	−0.646000	−	0.745523i	−0.980424	+	0.196899i	$0.936913\pi$
$354$		0			0
$355$	−3.27591	+	7.17323i	−0.173867	+	0.380716i
$356$		0			0
$357$	−4.01594	+	1.17919i	−0.212546	+	0.0624092i
$358$		0			0
$359$	−4.23150	−	29.4308i	−0.223330	−	1.55330i	−0.725314	−	0.688418i	$-0.758305\pi$
$359$	−4.23150	−	29.4308i	−0.223330	−	1.55330i	0.501984	−	0.864877i	$-0.332604\pi$
$360$		0			0
$361$	−1.78369	−	3.90574i	−0.0938785	−	0.205565i
$362$		0			0
$363$	−1.85379	+	12.8934i	−0.0972986	+	0.676727i
$364$		0			0
$365$	−4.62828	+	5.34132i	−0.242255	+	0.279577i
$366$		0			0
$367$	−10.2518			−0.535138			−0.267569	−	0.963539i	$-0.586220\pi$
$367$	−10.2518			−0.535138			−0.267569	+	0.963539i	$0.586220\pi$
$368$		0			0
$369$	10.6633			0.555110
$370$		0			0
$371$	28.2605	−	32.6143i	1.46721	−	1.69325i
$372$		0			0
$373$	−2.39725	+	16.6732i	−0.124125	+	0.863306i	0.828680	+	0.559723i	$0.189092\pi$
$373$	−2.39725	+	16.6732i	−0.124125	+	0.863306i	−0.952805	+	0.303584i	$0.901817\pi$
$374$		0			0
$375$	−0.596027	−	1.30512i	−0.0307787	−	0.0673960i
$376$		0			0
$377$	2.16669	+	15.0696i	0.111590	+	0.776126i
$378$		0			0
$379$	17.4561	−	5.12557i	0.896659	−	0.263283i	0.199243	−	0.979950i	$-0.436152\pi$
$379$	17.4561	−	5.12557i	0.896659	−	0.263283i	0.697415	+	0.716667i	$0.254333\pi$
$380$		0			0
$381$	−6.04055	+	13.2270i	−0.309467	+	0.677638i
$382$		0			0
$383$	−9.29071	−	10.7220i	−0.474733	−	0.547871i	0.466989	−	0.884263i	$-0.345339\pi$
$383$	−9.29071	−	10.7220i	−0.474733	−	0.547871i	−0.941722	+	0.336392i	$0.890793\pi$
$384$		0			0
$385$	5.72789	−	3.68109i	0.291920	−	0.187606i
$386$		0			0
$387$	7.60703	+	4.88874i	0.386687	+	0.248509i
$388$		0			0
$389$	−11.7928	−	3.46267i	−0.597917	−	0.175564i	−0.0312505	−	0.999512i	$-0.509949\pi$
$389$	−11.7928	−	3.46267i	−0.597917	−	0.175564i	−0.566666	+	0.823947i	$0.691767\pi$
$390$		0			0
$391$	1.22384	+	2.57171i	0.0618921	+	0.130057i
$392$		0			0
$393$	5.59025	+	1.64145i	0.281991	+	0.0828000i
$394$		0			0
$395$	−10.1936	−	6.55105i	−0.512897	−	0.329619i
$396$		0			0
$397$	13.1192	−	8.43118i	0.658432	−	0.423149i	−0.168307	−	0.985735i	$-0.553830\pi$
$397$	13.1192	−	8.43118i	0.658432	−	0.423149i	0.826739	+	0.562586i	$0.190193\pi$
$398$		0			0
$399$	−17.6994	−	20.4262i	−0.886079	−	1.02259i
$400$		0			0
$401$	−10.3192	+	22.5959i	−0.515316	+	1.12838i	0.455867	+	0.890048i	$0.349329\pi$
$401$	−10.3192	+	22.5959i	−0.515316	+	1.12838i	−0.971183	+	0.238336i	$0.923398\pi$
$402$		0			0
$403$	−22.8142	+	6.69884i	−1.13645	+	0.333693i
$404$		0			0
$405$	0.752770	+	5.23563i	0.0374054	+	0.260161i
$406$		0			0
$407$	3.69805	+	8.09759i	0.183305	+	0.401383i
$408$		0			0
$409$	1.34291	−	9.34011i	0.0664024	−	0.461839i	−0.929307	−	0.369307i	$-0.879595\pi$
$409$	1.34291	−	9.34011i	0.0664024	−	0.461839i	0.995710	−	0.0925316i	$-0.0294959\pi$
$410$		0			0
$411$	−7.60658	+	8.77846i	−0.375205	+	0.433009i
$412$		0			0
$413$	−38.9091			−1.91459
$414$		0			0
$415$	−6.53693			−0.320885
$416$		0			0
$417$	−9.47166	+	10.9309i	−0.463829	+	0.535287i
$418$		0			0
$419$	5.62592	−	39.1291i	0.274844	−	1.91158i	−0.119890	−	0.992787i	$-0.538254\pi$
$419$	5.62592	−	39.1291i	0.274844	−	1.91158i	0.394735	−	0.918795i	$-0.370837\pi$
$420$		0			0
$421$	1.18970	+	2.60508i	0.0579825	+	0.126964i	0.936405	−	0.350920i	$-0.114131\pi$
$421$	1.18970	+	2.60508i	0.0579825	+	0.126964i	−0.878423	+	0.477884i	$0.841404\pi$
$422$		0			0
$423$	1.38993	+	9.66720i	0.0675809	+	0.470035i
$424$		0			0
$425$	0.569808	−	0.167311i	0.0276397	−	0.00811576i
$426$		0			0
$427$	3.31308	−	7.25463i	0.160331	−	0.351076i
$428$		0			0
$429$	−4.64579	−	5.36153i	−0.224301	−	0.258857i
$430$		0			0
$431$	−16.2842	+	10.4653i	−0.784385	+	0.504093i	−0.870486	−	0.492193i	$-0.836195\pi$
$431$	−16.2842	+	10.4653i	−0.784385	+	0.504093i	0.0861015	+	0.996286i	$0.472559\pi$
$432$		0			0
$433$	−14.9421	−	9.60272i	−0.718073	−	0.461477i	0.129893	−	0.991528i	$-0.458536\pi$
$433$	−14.9421	−	9.60272i	−0.718073	−	0.461477i	−0.847966	+	0.530051i	$0.822173\pi$
$434$		0			0
$435$	5.87539	+	1.72517i	0.281704	+	0.0827156i
$436$		0			0
$437$	−11.8231	+	14.0875i	−0.565577	+	0.673896i
$438$		0			0
$439$	0.274828	+	0.0806967i	0.0131168	+	0.00385144i	0.288284	−	0.957545i	$-0.406915\pi$
$439$	0.274828	+	0.0806967i	0.0131168	+	0.00385144i	−0.275168	+	0.961396i	$0.588733\pi$
$440$		0			0
$441$	−13.5662	−	8.71847i	−0.646009	−	0.415165i
$442$		0			0
$443$	−31.9527	+	20.5348i	−1.51812	+	0.975636i	−0.525980	+	0.850497i	$0.676301\pi$
$443$	−31.9527	+	20.5348i	−1.51812	+	0.975636i	−0.992139	+	0.125139i	$0.960062\pi$
$444$		0			0
$445$	−2.15781	−	2.49024i	−0.102290	−	0.118049i
$446$		0			0
$447$	−3.66552	+	8.02637i	−0.173373	+	0.379634i
$448$		0			0
$449$	20.5136	−	6.02334i	0.968097	−	0.284259i	0.240795	−	0.970576i	$-0.422592\pi$
$449$	20.5136	−	6.02334i	0.968097	−	0.284259i	0.727302	+	0.686317i	$0.240774\pi$
$450$		0			0
$451$	2.23435	+	15.5403i	0.105212	+	0.731763i
$452$		0			0
$453$	4.31901	+	9.45731i	0.202925	+	0.444343i
$454$		0			0
$455$	2.49379	−	17.3447i	0.116911	−	0.813132i
$456$		0			0
$457$	10.1245	−	11.6843i	0.473605	−	0.546569i	−0.467806	−	0.883831i	$-0.654955\pi$
$457$	10.1245	−	11.6843i	0.473605	−	0.546569i	0.941411	+	0.337262i	$0.109501\pi$
$458$		0			0
$459$	−3.35833			−0.156753
$460$		0			0
$461$	16.0685			0.748384			0.374192	−	0.927351i	$-0.377920\pi$
$461$	16.0685			0.748384			0.374192	+	0.927351i	$0.377920\pi$
$462$		0			0
$463$	14.6760	−	16.9370i	0.682050	−	0.787127i	−0.304161	−	0.952621i	$-0.598376\pi$
$463$	14.6760	−	16.9370i	0.682050	−	0.787127i	0.986211	+	0.165493i	$0.0529216\pi$
$464$		0			0
$465$	−1.36101	+	9.46605i	−0.0631154	+	0.438978i
$466$		0			0
$467$	4.99664	+	10.9411i	0.231217	+	0.506295i	0.989306	−	0.145857i	$-0.0465939\pi$
$467$	4.99664	+	10.9411i	0.231217	+	0.506295i	−0.758089	+	0.652151i	$0.773867\pi$
$468$		0			0
$469$	−7.83307	−	54.4802i	−0.361698	−	2.51566i
$470$		0			0
$471$	1.60911	−	0.472479i	0.0741441	−	0.0217707i
$472$		0			0
$473$	−5.53069	+	12.1105i	−0.254301	+	0.556843i
$474$		0			0
$475$	2.51131	+	2.89820i	0.115227	+	0.132979i
$476$		0			0
$477$	6.95770	−	4.47144i	0.318571	−	0.204733i
$478$		0			0
$479$	22.0927	+	14.1981i	1.00944	+	0.648728i	0.937248	−	0.348663i	$-0.113364\pi$
$479$	22.0927	+	14.1981i	1.00944	+	0.648728i	0.0721923	+	0.997391i	$0.477000\pi$
$480$		0			0
$481$	21.9823	+	6.45460i	1.00231	+	0.294304i
$482$		0			0
$483$	13.5546	−	30.9636i	0.616757	−	1.40889i
$484$		0			0
$485$	17.0734	+	5.01320i	0.775262	+	0.227638i
$486$		0			0
$487$	−13.6617	−	8.77986i	−0.619072	−	0.397853i	0.193177	−	0.981164i	$-0.438121\pi$
$487$	−13.6617	−	8.77986i	−0.619072	−	0.397853i	−0.812249	+	0.583310i	$0.801757\pi$
$488$		0			0
$489$	16.3898	−	10.5331i	0.741171	−	0.476322i
$490$		0			0
$491$	−19.5449	−	22.5560i	−0.882047	−	1.01794i	−0.999690	−	0.0248805i	$-0.992079\pi$
$491$	−19.5449	−	22.5560i	−0.882047	−	1.01794i	0.117644	−	0.993056i	$-0.462466\pi$
$492$		0			0
$493$	−1.05288	+	2.30549i	−0.0474194	+	0.103834i
$494$		0			0
$495$	1.25204	−	0.367632i	0.0562750	−	0.0165238i
$496$		0			0
$497$	5.51283	+	38.3426i	0.247284	+	1.71990i
$498$		0			0
$499$	6.06707	+	13.2850i	0.271599	+	0.594719i	0.995455	−	0.0952319i	$-0.0303593\pi$
$499$	6.06707	+	13.2850i	0.271599	+	0.594719i	−0.723856	+	0.689951i	$0.757632\pi$
$500$		0			0
$501$	3.48960	−	24.2707i	0.155904	−	1.08434i
$502$		0			0
$503$	8.60184	−	9.92705i	0.383537	−	0.442625i	−0.530850	−	0.847466i	$-0.678127\pi$
$503$	8.60184	−	9.92705i	0.383537	−	0.442625i	0.914387	+	0.404840i	$0.132673\pi$
$504$		0			0
$505$	8.78261			0.390821
$506$		0			0
$507$	0.394094			0.0175023
$508$		0			0
$509$	−5.83927	+	6.73888i	−0.258821	+	0.298695i	−0.870256	−	0.492599i	$-0.836047\pi$
$509$	−5.83927	+	6.73888i	−0.258821	+	0.298695i	0.611435	+	0.791294i	$0.290592\pi$
$510$		0			0
$511$	−4.94078	+	34.3639i	−0.218567	+	1.52017i
$512$		0			0
$513$	−9.00886	−	19.7266i	−0.397751	−	0.870952i
$514$		0			0
$515$	1.61868	+	11.2581i	0.0713274	+	0.496093i
$516$		0			0
$517$	−13.7973	+	4.05126i	−0.606806	+	0.178174i
$518$		0			0
$519$	5.26958	−	11.5388i	0.231309	−	0.506496i
$520$		0			0
$521$	−11.6573	−	13.4533i	−0.510717	−	0.589399i	0.440565	−	0.897721i	$-0.354778\pi$
$521$	−11.6573	−	13.4533i	−0.510717	−	0.589399i	−0.951282	+	0.308322i	$0.900233\pi$
$522$		0			0
$523$	−16.8496	+	10.8286i	−0.736783	+	0.473502i	−0.854438	−	0.519553i	$-0.826099\pi$
$523$	−16.8496	+	10.8286i	−0.736783	+	0.473502i	0.117655	+	0.993055i	$0.462462\pi$
$524$		0			0
$525$	−5.92906	−	3.81038i	−0.258766	−	0.166299i
$526$		0			0
$527$	−3.79801	−	1.11520i	−0.165444	−	0.0485787i
$528$		0			0
$529$	−22.2617	−	5.78069i	−0.967900	−	0.251334i
$530$		0			0
$531$	−7.15486	−	2.10086i	−0.310495	−	0.0911694i
$532$		0			0
$533$	33.9915	+	21.8450i	1.47234	+	0.946213i
$534$		0			0
$535$	−7.21396	+	4.63613i	−0.311887	+	0.200437i
$536$		0			0
$537$	−9.58867	−	11.0659i	−0.413782	−	0.477530i
$538$		0			0
$539$	9.86331	−	21.5976i	0.424843	−	0.930276i
$540$		0			0
$541$	24.5052	−	7.19538i	1.05356	−	0.309353i	0.291306	−	0.956630i	$-0.405910\pi$
$541$	24.5052	−	7.19538i	1.05356	−	0.309353i	0.762255	+	0.647276i	$0.224092\pi$
$542$		0			0
$543$	2.34248	+	16.2923i	0.100526	+	0.699171i
$544$		0			0
$545$	0.181247	+	0.396877i	0.00776379	+	0.0170003i
$546$		0			0
$547$	3.69999	−	25.7340i	0.158200	−	1.10031i	−0.743747	−	0.668461i	$-0.766953\pi$
$547$	3.69999	−	25.7340i	0.158200	−	1.10031i	0.901948	−	0.431846i	$-0.142137\pi$
$548$		0			0
$549$	1.00094	−	1.15514i	0.0427189	−	0.0493003i
$550$		0			0
$551$	−16.3667			−0.697247
$552$		0			0
$553$	−59.5220			−2.53113
$554$		0			0
$555$	6.03435	−	6.96401i	0.256144	−	0.295606i
$556$		0			0
$557$	−5.08816	+	35.3890i	−0.215592	+	1.49948i	0.538453	+	0.842656i	$0.319009\pi$
$557$	−5.08816	+	35.3890i	−0.215592	+	1.49948i	−0.754045	+	0.656823i	$0.771900\pi$
$558$		0			0
$559$	14.2338	+	31.1677i	0.602026	+	1.31825i
$560$		0			0
$561$	−0.168079	−	1.16901i	−0.00709630	−	0.0493558i
$562$		0			0
$563$	34.1468	−	10.0264i	1.43912	−	0.422562i	0.533188	−	0.845997i	$-0.320994\pi$
$563$	34.1468	−	10.0264i	1.43912	−	0.422562i	0.905927	+	0.423434i	$0.139176\pi$
$564$		0			0
$565$	−0.805442	+	1.76367i	−0.0338852	+	0.0741982i
$566$		0			0
$567$	17.0152	+	19.6366i	0.714570	+	0.824658i
$568$		0			0
$569$	−25.6244	+	16.4678i	−1.07423	+	0.690367i	−0.953218	−	0.302284i	$-0.902251\pi$
$569$	−25.6244	+	16.4678i	−1.07423	+	0.690367i	−0.121014	+	0.992651i	$0.538615\pi$
$570$		0			0
$571$	−35.0677	−	22.5366i	−1.46754	−	0.943128i	−0.998192	−	0.0601129i	$-0.980854\pi$
$571$	−35.0677	−	22.5366i	−1.46754	−	0.943128i	−0.469344	−	0.883015i	$-0.655510\pi$
$572$		0			0
$573$	−26.4994	−	7.78092i	−1.10703	−	0.325053i
$574$		0			0
$575$	−1.92322	+	4.39332i	−0.0802037	+	0.183214i
$576$		0			0
$577$	37.3530	+	10.9678i	1.55503	+	0.456597i	0.942598	−	0.333929i	$-0.108375\pi$
$577$	37.3530	+	10.9678i	1.55503	+	0.456597i	0.612429	+	0.790526i	$0.290193\pi$
$578$		0			0
$579$	−2.47828	−	1.59270i	−0.102994	−	0.0661902i
$580$		0			0
$581$	−27.0132	+	17.3603i	−1.12070	+	0.720228i
$582$		0			0
$583$	7.97438	+	9.20293i	0.330265	+	0.381146i
$584$		0			0
$585$	1.39508	−	3.05481i	0.0576796	−	0.126301i
$586$		0			0
$587$	6.07814	−	1.78470i	0.250872	−	0.0736626i	−0.153879	−	0.988090i	$-0.549177\pi$
$587$	6.07814	−	1.78470i	0.250872	−	0.0736626i	0.404751	+	0.914427i	$0.367358\pi$
$588$		0			0
$589$	−3.63772	−	25.3009i	−0.149890	−	1.04250i
$590$		0			0
$591$	−3.40523	−	7.45642i	−0.140073	−	0.306716i
$592$		0			0
$593$	−3.19668	+	22.2334i	−0.131272	+	0.913017i	0.812627	+	0.582784i	$0.198037\pi$
$593$	−3.19668	+	22.2334i	−0.131272	+	0.913017i	−0.943899	+	0.330233i	$0.892873\pi$
$594$		0			0
$595$	1.91034	−	2.20465i	0.0783163	−	0.0903818i
$596$		0			0
$597$	−1.27581			−0.0522154
$598$		0			0
$599$	32.9724			1.34721			0.673607	−	0.739089i	$-0.264744\pi$
$599$	32.9724			1.34721			0.673607	+	0.739089i	$0.264744\pi$
$600$		0			0
$601$	11.2818	−	13.0199i	0.460194	−	0.531092i	−0.477464	−	0.878651i	$-0.658444\pi$
$601$	11.2818	−	13.0199i	0.460194	−	0.531092i	0.937658	+	0.347559i	$0.112989\pi$
$602$		0			0
$603$	1.50121	−	10.4411i	0.0611338	−	0.425195i
$604$		0			0
$605$	−3.77145	−	8.25832i	−0.153331	−	0.335748i
$606$		0			0
$607$	2.27505	+	15.8233i	0.0923414	+	0.642249i	0.982454	+	0.186507i	$0.0597168\pi$
$607$	2.27505	+	15.8233i	0.0923414	+	0.642249i	−0.890112	+	0.455742i	$0.849374\pi$
$608$		0			0
$609$	28.8611	−	8.47437i	1.16951	−	0.343399i
$610$		0			0
$611$	−15.3737	+	33.6636i	−0.621952	+	1.36188i
$612$		0			0
$613$	25.4910	+	29.4182i	1.02957	+	1.18819i	0.981914	+	0.189326i	$0.0606302\pi$
$613$	25.4910	+	29.4182i	1.02957	+	1.18819i	0.0476575	+	0.998864i	$0.484824\pi$
$614$		0			0
$615$	13.6716	−	8.78621i	0.551293	−	0.354294i
$616$		0			0
$617$	−33.1260	−	21.2888i	−1.33360	−	0.857054i	−0.337169	−	0.941444i	$-0.609470\pi$
$617$	−33.1260	−	21.2888i	−1.33360	−	0.857054i	−0.996433	+	0.0843898i	$0.973106\pi$
$618$		0			0
$619$	−21.1724	−	6.21677i	−0.850989	−	0.249873i	−0.172979	−	0.984925i	$-0.555339\pi$
$619$	−21.1724	−	6.21677i	−0.850989	−	0.249873i	−0.678010	+	0.735052i	$0.737158\pi$
$620$		0			0
$621$	17.4348	−	20.7740i	0.699636	−	0.833630i
$622$		0			0
$623$	−15.5303	−	4.56011i	−0.622209	−	0.182697i
$624$		0			0
$625$	0.841254	+	0.540641i	0.0336501	+	0.0216256i
$626$		0			0
$627$	6.41585	−	4.12322i	0.256224	−	0.164665i
$628$		0			0
$629$	2.49766	+	2.88245i	0.0995881	+	0.114931i
$630$		0			0
$631$	−3.60808	+	7.90060i	−0.143636	+	0.314518i	−0.967753	−	0.251901i	$-0.918944\pi$
$631$	−3.60808	+	7.90060i	−0.143636	+	0.314518i	0.824118	+	0.566419i	$0.191672\pi$
$632$		0			0
$633$	30.4113	−	8.92957i	1.20874	−	0.354919i
$634$		0			0
$635$	−1.44232	−	10.0315i	−0.0572366	−	0.398089i
$636$		0			0
$637$	−25.3843	−	55.5838i	−1.00576	−	2.20231i
$638$		0			0
$639$	−1.05653	+	7.34834i	−0.0417958	+	0.290696i
$640$		0			0
$641$	−3.63046	+	4.18977i	−0.143394	+	0.165486i	−0.822904	−	0.568181i	$-0.807647\pi$
$641$	−3.63046	+	4.18977i	−0.143394	+	0.165486i	0.679509	+	0.733667i	$0.262193\pi$
$642$		0			0
$643$	22.4843			0.886695			0.443348	−	0.896350i	$-0.353791\pi$
$643$	22.4843			0.886695			0.443348	+	0.896350i	$0.353791\pi$
$644$		0			0
$645$	13.7812			0.542636
$646$		0			0
$647$	−18.9567	+	21.8773i	−0.745267	+	0.860083i	−0.994101	−	0.108463i	$-0.965407\pi$
$647$	−18.9567	+	21.8773i	−0.745267	+	0.860083i	0.248834	+	0.968546i	$0.419953\pi$
$648$		0			0
$649$	1.56250	−	10.8674i	0.0613333	−	0.426583i
$650$		0			0
$651$	19.5150	+	42.7320i	0.764855	+	1.67480i
$652$		0			0
$653$	6.56313	+	45.6476i	0.256835	+	1.78633i	0.555038	+	0.831825i	$0.312704\pi$
$653$	6.56313	+	45.6476i	0.256835	+	1.78633i	−0.298203	+	0.954502i	$0.596387\pi$
$654$		0			0
$655$	−3.89626	+	1.14404i	−0.152239	+	0.0447015i
$656$		0			0
$657$	−2.76399	+	6.05229i	−0.107833	+	0.236122i
$658$		0			0
$659$	18.3622	+	21.1911i	0.715288	+	0.825487i	0.990732	−	0.135831i	$-0.0433703\pi$
$659$	18.3622	+	21.1911i	0.715288	+	0.825487i	−0.275444	+	0.961317i	$0.588825\pi$
$660$		0			0
$661$	18.9456	−	12.1756i	0.736897	−	0.473575i	−0.117580	−	0.993063i	$-0.537514\pi$
$661$	18.9456	−	12.1756i	0.736897	−	0.473575i	0.854478	+	0.519488i	$0.173877\pi$
$662$		0			0
$663$	−2.55701	−	1.64329i	−0.0993059	−	0.0638200i
$664$		0			0
$665$	18.0746	+	5.30717i	0.700902	+	0.205803i
$666$		0			0
$667$	−8.79526	−	18.4819i	−0.340554	−	0.715624i
$668$		0			0
$669$	13.3605	+	3.92301i	0.516548	+	0.151672i
$670$		0			0
$671$	1.89319	+	1.21668i	0.0730857	+	0.0469693i
$672$		0			0
$673$	−31.6573	+	20.3449i	−1.22030	+	0.784239i	−0.982353	−	0.187039i	$-0.940111\pi$
$673$	−31.6573	+	20.3449i	−1.22030	+	0.784239i	−0.237948	+	0.971278i	$0.576475\pi$
$674$		0			0
$675$	−3.70327	−	4.27380i	−0.142539	−	0.164499i
$676$		0			0
$677$	1.74027	−	3.81067i	0.0668842	−	0.146456i	−0.873238	−	0.487295i	$-0.837984\pi$
$677$	1.74027	−	3.81067i	0.0668842	−	0.146456i	0.940122	+	0.340839i	$0.110711\pi$
$678$		0			0
$679$	83.8677	−	24.6258i	3.21855	−	0.945051i
$680$		0			0
$681$	−0.771444	−	5.36551i	−0.0295618	−	0.205607i
$682$		0			0
$683$	2.34134	+	5.12683i	0.0895890	+	0.196173i	0.949123	−	0.314907i	$-0.101973\pi$
$683$	2.34134	+	5.12683i	0.0895890	+	0.196173i	−0.859534	+	0.511079i	$0.829246\pi$
$684$		0			0
$685$	1.15214	−	8.01333i	0.0440211	−	0.306174i
$686$		0			0
$687$	−3.27210	+	3.77620i	−0.124838	+	0.144071i
$688$		0			0
$689$	31.3393			1.19393
$690$		0			0
$691$	10.5414			0.401013			0.200507	−	0.979692i	$-0.435741\pi$
$691$	10.5414			0.401013			0.200507	+	0.979692i	$0.435741\pi$
$692$		0			0
$693$	4.19759	−	4.84428i	0.159453	−	0.184019i
$694$		0			0
$695$	1.43464	−	9.97815i	0.0544191	−	0.378493i
$696$		0			0
$697$	2.79433	+	6.11873i	0.105843	+	0.231763i
$698$		0			0
$699$	1.45056	+	10.0888i	0.0548651	+	0.381595i
$700$		0			0
$701$	−13.7535	+	4.03839i	−0.519463	+	0.152528i	−0.530945	−	0.847406i	$-0.678163\pi$
$701$	−13.7535	+	4.03839i	−0.519463	+	0.152528i	0.0114827	+	0.999934i	$0.496345\pi$
$702$		0			0
$703$	−10.2313	+	22.4034i	−0.385881	+	0.844961i
$704$		0			0
$705$	9.74750	+	11.2492i	0.367112	+	0.423670i
$706$		0			0
$707$	36.2933	−	23.3243i	1.36495	−	0.877199i
$708$		0			0
$709$	−28.5018	−	18.3170i	−1.07041	−	0.687909i	−0.118085	−	0.993003i	$-0.537676\pi$
$709$	−28.5018	−	18.3170i	−1.07041	−	0.687909i	−0.952322	+	0.305095i	$0.901312\pi$
$710$		0			0
$711$	−10.9453	−	3.21383i	−0.410480	−	0.120528i
$712$		0			0
$713$	26.6159	−	17.7042i	0.996772	−	0.663027i
$714$		0			0
$715$	4.74426	+	1.39304i	0.177425	+	0.0520968i
$716$		0			0
$717$	22.1849	+	14.2573i	0.828509	+	0.532450i
$718$		0			0
$719$	−18.3407	+	11.7869i	−0.683994	+	0.439576i	−0.835946	−	0.548812i	$-0.815080\pi$
$719$	−18.3407	+	11.7869i	−0.683994	+	0.439576i	0.151952	+	0.988388i	$0.451444\pi$
$720$		0			0
$721$	36.5876	+	42.2243i	1.36259	+	1.57252i
$722$		0			0
$723$	3.58796	−	7.85653i	0.133437	−	0.292187i
$724$		0			0
$725$	−4.09499	+	1.20240i	−0.152084	+	0.0446560i
$726$		0			0
$727$	−0.209062	−	1.45406i	−0.00775367	−	0.0539279i	0.985577	−	0.169226i	$-0.0541268\pi$
$727$	−0.209062	−	1.45406i	−0.00775367	−	0.0539279i	−0.993331	+	0.115298i	$0.963218\pi$
$728$		0			0
$729$	12.1803	+	26.6711i	0.451122	+	0.987820i
$730$		0			0
$731$	−0.811785	+	5.64609i	−0.0300250	+	0.208828i
$732$		0			0
$733$	8.09618	−	9.34349i	0.299039	−	0.345110i	−0.586267	−	0.810118i	$-0.699403\pi$
$733$	8.09618	−	9.34349i	0.299039	−	0.345110i	0.885306	+	0.465008i	$0.153949\pi$
$734$		0			0
$735$	−24.5772			−0.906542
$736$		0			0
$737$	15.5310			0.572091
$738$		0			0
$739$	−31.7705	+	36.6652i	−1.16870	+	1.34875i	−0.243210	+	0.969974i	$0.578200\pi$
$739$	−31.7705	+	36.6652i	−1.16870	+	1.34875i	−0.925488	+	0.378776i	$0.876345\pi$
$740$		0			0
$741$	2.79331	−	19.4279i	0.102615	−	0.713702i
$742$		0			0
$743$	11.9052	+	26.0688i	0.436761	+	0.956373i	0.992181	+	0.124803i	$0.0398300\pi$
$743$	11.9052	+	26.0688i	0.436761	+	0.956373i	−0.555421	+	0.831570i	$0.687443\pi$
$744$		0			0
$745$	−0.875225	−	6.08733i	−0.0320658	−	0.223022i
$746$		0			0
$747$	−5.90472	+	1.73378i	−0.216042	+	0.0634357i
$748$		0			0
$749$	−17.4986	+	38.3167i	−0.639387	+	1.40006i
$750$		0			0
$751$	24.3360	+	28.0852i	0.888034	+	1.02485i	0.999517	+	0.0310790i	$0.00989435\pi$
$751$	24.3360	+	28.0852i	0.888034	+	1.02485i	−0.111483	+	0.993766i	$0.535560\pi$
$752$		0			0
$753$	−17.1173	+	11.0006i	−0.623788	+	0.400884i
$754$		0			0
$755$	−6.09600	−	3.91766i	−0.221856	−	0.142578i
$756$		0			0
$757$	7.53081	+	2.21125i	0.273712	+	0.0803691i	0.415708	−	0.909498i	$-0.363534\pi$
$757$	7.53081	+	2.21125i	0.273712	+	0.0803691i	−0.141996	+	0.989867i	$0.545352\pi$
$758$		0			0
$759$	8.10388	+	5.02926i	0.294152	+	0.182551i
$760$		0			0
$761$	−36.2218	−	10.6357i	−1.31304	−	0.385543i	−0.451063	−	0.892492i	$-0.648955\pi$
$761$	−36.2218	−	10.6357i	−1.31304	−	0.385543i	−0.861976	+	0.506949i	$0.830773\pi$
$762$		0			0
$763$	1.80298	+	1.15871i	0.0652724	+	0.0419480i
$764$		0			0
$765$	0.470324	−	0.302259i	0.0170046	−	0.0109282i
$766$		0			0
$767$	−18.5037	−	21.3545i	−0.668131	−	0.771065i
$768$		0			0
$769$	−7.19779	+	15.7610i	−0.259559	+	0.568355i	−0.993882	−	0.110445i	$-0.964772\pi$
$769$	−7.19779	+	15.7610i	−0.259559	+	0.568355i	0.734323	+	0.678800i	$0.237500\pi$
$770$		0			0
$771$	−39.0809	+	11.4752i	−1.40747	+	0.413269i
$772$		0			0
$773$	−3.54849	−	24.6803i	−0.127630	−	0.887688i	−0.948546	−	0.316639i	$-0.897446\pi$
$773$	−3.54849	−	24.6803i	−0.127630	−	0.887688i	0.820916	−	0.571049i	$-0.193463\pi$
$774$		0			0
$775$	−2.76892	−	6.06309i	−0.0994625	−	0.217792i
$776$		0			0
$777$	6.44179	−	44.8037i	0.231098	−	1.60732i
$778$		0			0
$779$	−28.4452	+	32.8275i	−1.01915	+	1.17617i
$780$		0			0
$781$	−10.9305			−0.391126
$782$		0			0
$783$	24.1350			0.862516
$784$		0			0
$785$	−0.765438	+	0.883363i	−0.0273197	+	0.0315286i
$786$		0			0
$787$	0.673295	−	4.68287i	0.0240004	−	0.166926i	−0.974296	−	0.225271i	$-0.927673\pi$
$787$	0.673295	−	4.68287i	0.0240004	−	0.166926i	0.998296	+	0.0583448i	$0.0185823\pi$
$788$		0			0
$789$	−1.93533	−	4.23779i	−0.0688997	−	0.150869i
$790$		0			0
$791$	1.35543	+	9.42723i	0.0481936	+	0.335194i
$792$		0			0
$793$	5.55713	−	1.63172i	0.197339	−	0.0579441i
$794$		0			0
$795$	5.23626	−	11.4658i	0.185711	−	0.406651i
$796$		0			0
$797$	17.6822	+	20.4063i	0.626335	+	0.722830i	0.976897	−	0.213710i	$-0.0685548\pi$
$797$	17.6822	+	20.4063i	0.626335	+	0.722830i	−0.350562	+	0.936540i	$0.614009\pi$
$798$		0			0
$799$	−5.18291	+	3.33086i	−0.183358	+	0.117837i
$800$		0			0
$801$	−2.60960	−	1.67709i	−0.0922056	−	0.0592569i
$802$		0			0
$803$	−9.39950	−	2.75994i	−0.331701	−	0.0973963i
$804$		0			0
$805$	3.71996	+	23.2625i	0.131111	+	0.819895i
$806$		0			0
$807$	−34.0323	−	9.99279i	−1.19799	−	0.351763i
$808$		0			0
$809$	−41.3553	−	26.5774i	−1.45397	−	0.934412i	−0.999036	−	0.0438886i	$-0.986025\pi$
$809$	−41.3553	−	26.5774i	−1.45397	−	0.934412i	−0.454937	−	0.890524i	$-0.650338\pi$
$810$		0			0
$811$	19.0420	−	12.2376i	0.668656	−	0.429719i	−0.161785	−	0.986826i	$-0.551725\pi$
$811$	19.0420	−	12.2376i	0.668656	−	0.429719i	0.830441	+	0.557107i	$0.188089\pi$
$812$		0			0
$813$	12.8563	+	14.8369i	0.450889	+	0.520353i
$814$		0			0
$815$	−5.64085	+	12.3517i	−0.197590	+	0.432662i
$816$		0			0
$817$	−35.3425	+	10.3775i	−1.23648	+	0.363063i
$818$		0			0
$819$	−2.34770	−	16.3286i	−0.0820354	−	0.570569i
$820$		0			0
$821$	11.2470	+	24.6276i	0.392524	+	0.859509i	0.997974	+	0.0636249i	$0.0202661\pi$
$821$	11.2470	+	24.6276i	0.392524	+	0.859509i	−0.605449	+	0.795884i	$0.707007\pi$
$822$		0			0
$823$	3.31473	−	23.0545i	0.115544	−	0.803629i	−0.846823	−	0.531875i	$-0.821487\pi$
$823$	3.31473	−	23.0545i	0.115544	−	0.803629i	0.962367	−	0.271753i	$-0.0876035\pi$
$824$		0			0
$825$	1.30234	−	1.50298i	0.0453418	−	0.0523272i
$826$		0			0
$827$	6.28635			0.218598			0.109299	−	0.994009i	$-0.465139\pi$
$827$	6.28635			0.218598			0.109299	+	0.994009i	$0.465139\pi$
$828$		0			0
$829$	35.0549			1.21751			0.608754	−	0.793359i	$-0.291670\pi$
$829$	35.0549			1.21751			0.608754	+	0.793359i	$0.291670\pi$
$830$		0			0
$831$	−17.4168	+	20.1000i	−0.604182	+	0.697263i
$832$		0			0
$833$	1.44772	−	10.0691i	0.0501605	−	0.348874i
$834$		0			0
$835$	7.09944	+	15.5456i	0.245686	+	0.537978i
$836$		0			0
$837$	5.36432	+	37.3097i	0.185418	+	1.28961i
$838$		0			0
$839$	−46.3147	+	13.5992i	−1.59896	+	0.469498i	−0.955257	−	0.295776i	$-0.904422\pi$
$839$	−46.3147	+	13.5992i	−1.59896	+	0.469498i	−0.643705	+	0.765274i	$0.722604\pi$
$840$		0			0
$841$	−4.48036	+	9.81063i	−0.154495	+	0.338298i
$842$		0			0
$843$	26.8557	+	30.9932i	0.924960	+	1.06746i
$844$		0			0
$845$	−0.231069	+	0.148499i	−0.00794903	+	0.00510853i
$846$		0			0
$847$	−37.5170	−	24.1107i	−1.28910	−	0.828454i
$848$		0			0
$849$	21.2240	+	6.23192i	0.728405	+	0.213879i
$850$		0			0
$851$	−30.7969	+	0.485718i	−1.05571	+	0.0166502i
$852$		0			0
$853$	29.1915	+	8.57139i	0.999497	+	0.293479i	0.740250	−	0.672332i	$-0.234707\pi$
$853$	29.1915	+	8.57139i	0.999497	+	0.293479i	0.259247	+	0.965811i	$0.416526\pi$
$854$		0			0
$855$	3.03711	+	1.95183i	0.103867	+	0.0667513i
$856$		0			0
$857$	−39.5837	+	25.4389i	−1.35215	+	0.868976i	−0.997810	−	0.0661401i	$-0.978932\pi$
$857$	−39.5837	+	25.4389i	−1.35215	+	0.868976i	−0.354342	+	0.935116i	$0.615295\pi$
$858$		0			0
$859$	16.0882	+	18.5668i	0.548922	+	0.633490i	0.960632	−	0.277825i	$-0.0896136\pi$
$859$	16.0882	+	18.5668i	0.548922	+	0.633490i	−0.411709	+	0.911315i	$0.635068\pi$
$860$		0			0
$861$	33.1627	−	72.6163i	1.13018	−	2.47476i
$862$		0			0
$863$	12.7686	−	3.74919i	0.434647	−	0.127624i	−0.0570874	−	0.998369i	$-0.518181\pi$
$863$	12.7686	−	3.74919i	0.434647	−	0.127624i	0.491734	+	0.870745i	$0.336363\pi$
$864$		0			0
$865$	1.25823	+	8.75118i	0.0427811	+	0.297549i
$866$		0			0
$867$	9.92226	+	21.7267i	0.336978	+	0.737878i
$868$		0			0
$869$	2.39026	−	16.6246i	0.0810840	−	0.563951i
$870$		0			0
$871$	26.1752	−	30.2078i	0.886913	−	1.02355i
$872$		0			0
$873$	16.7518			0.566962
$874$		0			0
$875$	4.91219			0.166062
$876$		0			0
$877$	33.6598	−	38.8454i	1.13661	−	1.31172i	0.192796	−	0.981239i	$-0.438245\pi$
$877$	33.6598	−	38.8454i	1.13661	−	1.31172i	0.943814	−	0.330478i	$-0.107210\pi$
$878$		0			0
$879$	2.47917	−	17.2430i	0.0836202	−	0.581592i
$880$		0			0
$881$	−19.3707	−	42.4158i	−0.652614	−	1.42903i	−0.889247	−	0.457427i	$-0.848771\pi$
$881$	−19.3707	−	42.4158i	−0.652614	−	1.42903i	0.236633	−	0.971599i	$-0.423956\pi$
$882$		0			0
$883$	−1.63738	−	11.3882i	−0.0551022	−	0.383245i	−0.998647	−	0.0519997i	$-0.983441\pi$
$883$	−1.63738	−	11.3882i	−0.0551022	−	0.383245i	0.943545	−	0.331245i	$-0.107469\pi$
$884$		0			0
$885$	−10.9044	+	3.20182i	−0.366547	+	0.107628i
$886$		0			0
$887$	3.13132	−	6.85664i	0.105139	−	0.230223i	−0.849749	−	0.527187i	$-0.823247\pi$
$887$	3.13132	−	6.85664i	0.105139	−	0.230223i	0.954889	+	0.296964i	$0.0959740\pi$
$888$		0			0
$889$	−32.6013	−	37.6239i	−1.09341	−	1.26186i
$890$		0			0
$891$	−6.16782	+	3.96382i	−0.206630	+	0.132793i
$892$		0			0
$893$	−33.4687	−	21.5090i	−1.11999	−	0.719771i
$894$		0			0
$895$	9.79191	+	2.87516i	0.327308	+	0.0961062i
$896$		0			0
$897$	23.4398	−	7.28598i	0.782633	−	0.243272i
$898$		0			0
$899$	27.2949	+	8.01450i	0.910335	+	0.267299i
$900$		0			0
$901$	4.38903	+	2.82066i	0.146220	+	0.0939698i
$902$		0			0
$903$	56.9496	−	36.5993i	1.89516	−	1.21795i
$904$		0			0
$905$	−7.51262	−	8.67002i	−0.249728	−	0.288201i
$906$		0			0
$907$	−22.2140	+	48.6418i	−0.737602	+	1.61512i	0.0498562	+	0.998756i	$0.484124\pi$
$907$	−22.2140	+	48.6418i	−0.737602	+	1.61512i	−0.787459	+	0.616368i	$0.788604\pi$
$908$		0			0
$909$	7.93321	−	2.32940i	0.263128	−	0.0772613i
$910$		0			0
$911$	−3.60454	−	25.0701i	−0.119424	−	0.830609i	−0.958193	−	0.286122i	$-0.907634\pi$
$911$	−3.60454	−	25.0701i	−0.119424	−	0.830609i	0.838769	−	0.544487i	$-0.183276\pi$
$912$		0			0
$913$	−3.76399	−	8.24199i	−0.124570	−	0.272770i
$914$		0			0
$915$	0.331519	−	2.30577i	0.0109597	−	0.0762262i
$916$		0			0
$917$	−13.0626	+	15.0751i	−0.431365	+	0.497822i
$918$		0			0
$919$	−28.7689			−0.948997			−0.474499	−	0.880256i	$-0.657371\pi$
$919$	−28.7689			−0.948997			−0.474499	+	0.880256i	$0.657371\pi$
$920$		0			0
$921$	−45.8290			−1.51012
$922$		0			0
$923$	−18.4218	+	21.2599i	−0.606362	+	0.699779i
$924$		0			0
$925$	−0.914003	+	6.35703i	−0.0300522	+	0.209018i
$926$		0			0
$927$	4.44811	+	9.73999i	0.146095	+	0.319903i
$928$		0			0
$929$	−6.69929	−	46.5946i	−0.219797	−	1.52872i	−0.738787	−	0.673939i	$-0.764601\pi$
$929$	−6.69929	−	46.5946i	−0.219797	−	1.52872i	0.518991	−	0.854780i	$-0.326308\pi$
$930$		0			0
$931$	63.0290	−	18.5070i	2.06569	−	0.606542i
$932$		0			0
$933$	2.24499	−	4.91584i	0.0734977	−	0.160937i
$934$		0			0
$935$	0.539049	+	0.622095i	0.0176288	+	0.0203447i
$936$		0			0
$937$	42.7900	−	27.4995i	1.39789	−	0.898368i	0.398068	−	0.917356i	$-0.369681\pi$
$937$	42.7900	−	27.4995i	1.39789	−	0.898368i	0.999820	+	0.0189876i	$0.00604432\pi$
$938$		0			0
$939$	−1.27679	−	0.820542i	−0.0416664	−	0.0267774i
$940$		0			0
$941$	−31.5782	−	9.27219i	−1.02942	−	0.302265i	−0.276945	−	0.960886i	$-0.589322\pi$
$941$	−31.5782	−	9.27219i	−1.02942	−	0.302265i	−0.752475	+	0.658621i	$0.771140\pi$
$942$		0			0
$943$	−52.3561	−	14.4803i	−1.70495	−	0.471545i
$944$		0			0
$945$	−26.6535	−	7.82616i	−0.867037	−	0.254585i
$946$		0			0
$947$	−0.904966	−	0.581586i	−0.0294074	−	0.0188990i	0.525855	−	0.850575i	$-0.323746\pi$
$947$	−0.904966	−	0.581586i	−0.0294074	−	0.0188990i	−0.555262	+	0.831676i	$0.687382\pi$
$948$		0			0
$949$	−21.2096	+	13.6306i	−0.688492	+	0.442467i
$950$		0			0
$951$	−23.3252	−	26.9187i	−0.756371	−	0.872898i
$952$		0			0
$953$	7.43141	−	16.2725i	0.240727	−	0.527119i	−0.750249	−	0.661155i	$-0.770067\pi$
$953$	7.43141	−	16.2725i	0.240727	−	0.527119i	0.990976	+	0.134036i	$0.0427939\pi$
$954$		0			0
$955$	18.4694	−	5.42309i	0.597654	−	0.175487i
$956$		0			0
$957$	1.20792	+	8.40127i	0.0390465	+	0.271574i
$958$		0			0
$959$	−16.5201	−	36.1741i	−0.533463	−	1.16812i
$960$		0			0
$961$	−1.91099	+	13.2913i	−0.0616450	+	0.428750i
$962$		0			0
$963$	−5.28663	+	6.10110i	−0.170359	+	0.196605i
$964$		0			0
$965$	2.05324			0.0660962
$966$		0			0
$967$	7.22005			0.232181			0.116091	−	0.993239i	$-0.462964\pi$
$967$	7.22005			0.232181			0.116091	+	0.993239i	$0.462964\pi$
$968$		0			0
$969$	2.13978	−	2.46944i	0.0687398	−	0.0793300i
$970$		0			0
$971$	1.28040	−	8.90534i	0.0410898	−	0.285786i	−0.958908	−	0.283717i	$-0.908432\pi$
$971$	1.28040	−	8.90534i	0.0410898	−	0.285786i	0.999998	−	0.00206898i	$-0.000658578\pi$
$972$		0			0
$973$	−20.5708	−	45.0437i	−0.659469	−	1.44404i
$974$		0			0
$975$	−0.728398	−	5.06612i	−0.0233274	−	0.162246i
$976$		0			0
$977$	−13.1997	+	3.87579i	−0.422296	+	0.123997i	−0.485974	−	0.873973i	$-0.661535\pi$
$977$	−13.1997	+	3.87579i	−0.422296	+	0.123997i	0.0636779	+	0.997971i	$0.479717\pi$
$978$		0			0
$979$	1.89731	−	4.15453i	0.0606383	−	0.132779i
$980$		0			0
$981$	0.268981	+	0.310421i	0.00858791	+	0.00991098i
$982$		0			0
$983$	11.8002	−	7.58356i	0.376369	−	0.241878i	−0.338756	−	0.940874i	$-0.610006\pi$
$983$	11.8002	−	7.58356i	0.376369	−	0.241878i	0.715125	+	0.698996i	$0.246370\pi$
$984$		0			0
$985$	4.80626	+	3.08880i	0.153140	+	0.0984173i
$986$		0			0
$987$	70.1555	+	20.5995i	2.23307	+	0.655689i
$988$		0			0
$989$	−30.7112	−	34.3334i	−0.976560	−	1.09174i
$990$		0			0
$991$	34.1630	+	10.0312i	1.08522	+	0.318650i	0.774966	−	0.632002i	$-0.217767\pi$
$991$	34.1630	+	10.0312i	1.08522	+	0.318650i	0.310257	+	0.950653i	$0.399585\pi$
$992$		0			0
$993$	−27.6146	−	17.7468i	−0.876322	−	0.563178i
$994$		0			0
$995$	0.748046	−	0.480740i	0.0237147	−	0.0152405i
$996$		0			0
$997$	−10.1775	−	11.7455i	−0.322325	−	0.371983i	0.571343	−	0.820711i	$-0.306423\pi$
$997$	−10.1775	−	11.7455i	−0.322325	−	0.371983i	−0.893668	+	0.448728i	$0.851877\pi$
$998$		0			0
$999$	15.0875	−	33.0369i	0.477346	−	1.04524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.m.a.41.3	✓	30
23.9	even	11	inner	460.2.m.a.101.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.a.41.3	✓	30	1.1	even	1	trivial
460.2.m.a.101.3	yes	30	23.9	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939578 - 1.08433i) q^{3} +(-0.142315 + 0.989821i) q^{5} +(2.04060 + 4.46829i) q^{7} +(0.133978 + 0.931838i) q^{9} +O(q^{10})\)	\(q+(0.939578 - 1.08433i) q^{3} +(-0.142315 + 0.989821i) q^{5} +(2.04060 + 4.46829i) q^{7} +(0.133978 + 0.931838i) q^{9} +(-1.32995 + 0.390508i) q^{11} +(-1.48189 + 3.24489i) q^{13} +(0.939578 + 1.08433i) q^{15} +(-0.499590 + 0.321067i) q^{17} +(-3.22610 - 2.07329i) q^{19} +(6.76240 + 1.98562i) q^{21} +(0.607574 - 4.75719i) q^{23} +(-0.959493 - 0.281733i) q^{25} +(4.75733 + 3.05735i) q^{27} +(3.59036 - 2.30739i) q^{29} +(4.36493 + 5.03739i) q^{31} +(-0.826150 + 1.80902i) q^{33} +(-4.71321 + 1.38392i) q^{35} +(-0.914003 - 6.35703i) q^{37} +(2.12618 + 4.65569i) q^{39} +(1.61198 - 11.2116i) q^{41} +(6.29004 - 7.25910i) q^{43} -0.941420 q^{45} +10.3743 q^{47} +(-11.2175 + 12.9457i) q^{49} +(-0.121261 + 0.843388i) q^{51} +(-3.64954 - 7.99137i) q^{53} +(-0.197262 - 1.37199i) q^{55} +(-5.27930 + 1.55014i) q^{57} +(-3.29047 + 7.20513i) q^{59} +(-1.06322 - 1.22702i) q^{61} +(-3.89032 + 2.50016i) q^{63} +(-3.00097 - 1.92861i) q^{65} +(-10.7510 - 3.15677i) q^{67} +(-4.58750 - 5.12856i) q^{69} +(7.56643 + 2.22170i) q^{71} +(5.94562 + 3.82102i) q^{73} +(-1.20701 + 0.775698i) q^{75} +(-4.45879 - 5.14572i) q^{77} +(-5.03366 + 11.0222i) q^{79} +(5.07521 - 1.49022i) q^{81} +(0.930302 + 6.47039i) q^{83} +(-0.246700 - 0.540197i) q^{85} +(0.871456 - 6.06111i) q^{87} +(-2.15781 + 2.49024i) q^{89} -17.5231 q^{91} +9.56339 q^{93} +(2.51131 - 2.89820i) q^{95} +(2.53238 - 17.6131i) q^{97} +(-0.542074 - 1.18698i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more