LMFDB - Embedded newform 460.2.m.a.261.1

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			261.1
Character	$\chi$	$=$	460.261
Dual form			460.2.m.a.141.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08673 - 2.37960i) q^{3} +(-0.654861 - 0.755750i) q^{5} +(0.0544585 + 0.0349983i) q^{7} +(-2.51694 + 2.90471i) q^{9} +O(q^{10})$	\(q+(-1.08673 - 2.37960i) q^{3} +(-0.654861 - 0.755750i) q^{5} +(0.0544585 + 0.0349983i) q^{7} +(-2.51694 + 2.90471i) q^{9} +(-0.824724 - 5.73608i) q^{11} +(-3.15165 + 2.02545i) q^{13} +(-1.08673 + 2.37960i) q^{15} +(-1.70862 + 0.501697i) q^{17} +(3.27048 + 0.960300i) q^{19} +(0.0241006 - 0.167623i) q^{21} +(-4.09742 + 2.49222i) q^{23} +(-0.142315 + 0.989821i) q^{25} +(2.11716 + 0.621655i) q^{27} +(-1.26492 + 0.371413i) q^{29} +(-1.01893 + 2.23114i) q^{31} +(-12.7533 + 8.19607i) q^{33} +(-0.00921274 - 0.0640760i) q^{35} +(-1.23564 + 1.42600i) q^{37} +(8.24474 + 5.29857i) q^{39} +(-0.0704270 - 0.0812771i) q^{41} +(-0.298488 - 0.653598i) q^{43} +3.84348 q^{45} +0.878185 q^{47} +(-2.90616 - 6.36361i) q^{49} +(3.05065 + 3.52064i) q^{51} +(-7.32895 - 4.71003i) q^{53} +(-3.79496 + 4.37962i) q^{55} +(-1.26899 - 8.82603i) q^{57} +(12.8806 - 8.27784i) q^{59} +(0.555050 - 1.21539i) q^{61} +(-0.238729 + 0.0700971i) q^{63} +(3.59462 + 1.05548i) q^{65} +(1.53543 - 10.6792i) q^{67} +(10.3833 + 7.04185i) q^{69} +(1.57890 - 10.9815i) q^{71} +(-4.82197 - 1.41586i) q^{73} +(2.51004 - 0.737014i) q^{75} +(0.155840 - 0.341242i) q^{77} +(-6.43071 + 4.13277i) q^{79} +(0.819465 + 5.69950i) q^{81} +(8.70437 - 10.0454i) q^{83} +(1.49807 + 0.962750i) q^{85} +(2.25843 + 2.60637i) q^{87} +(0.981628 + 2.14946i) q^{89} -0.242522 q^{91} +6.41651 q^{93} +(-1.41596 - 3.10053i) q^{95} +(4.21722 + 4.86694i) q^{97} +(18.7374 + 12.0418i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{11}\right)$

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
$3$	−1.08673	−	2.37960i	−0.627422	−	1.37386i	−0.909996	−	0.414618i	$-0.863915\pi$
$3$	−1.08673	−	2.37960i	−0.627422	−	1.37386i	0.282573	−	0.959246i	$-0.408812\pi$
$4$		0			0
$5$	−0.654861	−	0.755750i	−0.292863	−	0.337981i
$5$	−0.654861	−	0.755750i	−0.292863	−	0.337981i
$6$		0			0
$7$	0.0544585	+	0.0349983i	0.0205834	+	0.0132281i	0.550892	−	0.834577i	$-0.314288\pi$
$7$	0.0544585	+	0.0349983i	0.0205834	+	0.0132281i	−0.530309	+	0.847805i	$0.677924\pi$
$8$		0			0
$9$	−2.51694	+	2.90471i	−0.838981	+	0.968236i
$10$		0			0
$11$	−0.824724	−	5.73608i	−0.248664	−	1.72949i	−0.605953	−	0.795500i	$-0.707208\pi$
$11$	−0.824724	−	5.73608i	−0.248664	−	1.72949i	0.357289	−	0.933994i	$-0.383701\pi$
$12$		0			0
$13$	−3.15165	+	2.02545i	−0.874112	+	0.561758i	−0.899008	−	0.437933i	$-0.855711\pi$
$13$	−3.15165	+	2.02545i	−0.874112	+	0.561758i	0.0248961	+	0.999690i	$0.492075\pi$
$14$		0			0
$15$	−1.08673	+	2.37960i	−0.280592	+	0.614410i
$16$		0			0
$17$	−1.70862	+	0.501697i	−0.414402	+	0.121679i	−0.482286	−	0.876014i	$-0.660193\pi$
$17$	−1.70862	+	0.501697i	−0.414402	+	0.121679i	0.0678839	+	0.997693i	$0.478375\pi$
$18$		0			0
$19$	3.27048	+	0.960300i	0.750300	+	0.220308i	0.634456	−	0.772959i	$-0.281224\pi$
$19$	3.27048	+	0.960300i	0.750300	+	0.220308i	0.115845	+	0.993267i	$0.463043\pi$
$20$		0			0
$21$	0.0241006	−	0.167623i	0.00525918	−	0.0365784i
$22$		0			0
$23$	−4.09742	+	2.49222i	−0.854371	+	0.519664i
$23$	−4.09742	+	2.49222i	−0.854371	+	0.519664i
$24$		0			0
$25$	−0.142315	+	0.989821i	−0.0284630	+	0.197964i
$26$		0			0
$27$	2.11716	+	0.621655i	0.407448	+	0.119637i
$28$		0			0
$29$	−1.26492	+	0.371413i	−0.234889	+	0.0689696i	−0.397059	−	0.917793i	$-0.629969\pi$
$29$	−1.26492	+	0.371413i	−0.234889	+	0.0689696i	0.162170	+	0.986763i	$0.448151\pi$
$30$		0			0
$31$	−1.01893	+	2.23114i	−0.183004	+	0.400724i	−0.978793	−	0.204850i	$-0.934329\pi$
$31$	−1.01893	+	2.23114i	−0.183004	+	0.400724i	0.795789	+	0.605574i	$0.207057\pi$
$32$		0			0
$33$	−12.7533	+	8.19607i	−2.22007	+	1.42675i
$34$		0			0
$35$	−0.00921274	−	0.0640760i	−0.00155724	−	0.0108308i
$36$		0			0
$37$	−1.23564	+	1.42600i	−0.203138	+	0.234433i	−0.848173	−	0.529719i	$-0.822297\pi$
$37$	−1.23564	+	1.42600i	−0.203138	+	0.234433i	0.645035	+	0.764153i	$0.276843\pi$
$38$		0			0
$39$	8.24474	+	5.29857i	1.32022	+	0.848451i
$40$		0			0
$41$	−0.0704270	−	0.0812771i	−0.0109988	−	0.0126933i	0.750223	−	0.661184i	$-0.229946\pi$
$41$	−0.0704270	−	0.0812771i	−0.0109988	−	0.0126933i	−0.761222	+	0.648491i	$0.775400\pi$
$42$		0			0
$43$	−0.298488	−	0.653598i	−0.0455190	−	0.0996728i	0.885506	−	0.464627i	$-0.153812\pi$
$43$	−0.298488	−	0.653598i	−0.0455190	−	0.0996728i	−0.931025	+	0.364955i	$0.881084\pi$
$44$		0			0
$45$	3.84348			0.572952
$46$		0			0
$47$	0.878185			0.128096			0.0640482	−	0.997947i	$-0.479599\pi$
$47$	0.878185			0.128096			0.0640482	+	0.997947i	$0.479599\pi$
$48$		0			0
$49$	−2.90616	−	6.36361i	−0.415166	−	0.909087i
$50$		0			0
$51$	3.05065	+	3.52064i	0.427176	+	0.492988i
$52$		0			0
$53$	−7.32895	−	4.71003i	−1.00671	−	0.646972i	−0.0701691	−	0.997535i	$-0.522354\pi$
$53$	−7.32895	−	4.71003i	−1.00671	−	0.646972i	−0.936539	+	0.350563i	$0.885990\pi$
$54$		0			0
$55$	−3.79496	+	4.37962i	−0.511713	+	0.590548i
$56$		0			0
$57$	−1.26899	−	8.82603i	−0.168082	−	1.16904i
$58$		0			0
$59$	12.8806	−	8.27784i	1.67691	−	1.07768i	0.794386	−	0.607414i	$-0.207793\pi$
$59$	12.8806	−	8.27784i	1.67691	−	1.07768i	0.882523	−	0.470270i	$-0.155843\pi$
$60$		0			0
$61$	0.555050	−	1.21539i	0.0710668	−	0.155615i	−0.870765	−	0.491700i	$-0.836376\pi$
$61$	0.555050	−	1.21539i	0.0710668	−	0.155615i	0.941832	+	0.336085i	$0.109103\pi$
$62$		0			0
$63$	−0.238729	+	0.0700971i	−0.0300770	+	0.00883141i
$64$		0			0
$65$	3.59462	+	1.05548i	0.445858	+	0.130916i
$66$		0			0
$67$	1.53543	−	10.6792i	0.187583	−	1.30467i	−0.650660	−	0.759369i	$-0.725508\pi$
$67$	1.53543	−	10.6792i	0.187583	−	1.30467i	0.838243	−	0.545297i	$-0.183583\pi$
$68$		0			0
$69$	10.3833	+	7.04185i	1.25000	+	0.847739i
$70$		0			0
$71$	1.57890	−	10.9815i	0.187381	−	1.30326i	−0.651374	−	0.758757i	$-0.725807\pi$
$71$	1.57890	−	10.9815i	0.187381	−	1.30326i	0.838756	−	0.544508i	$-0.183284\pi$
$72$		0			0
$73$	−4.82197	−	1.41586i	−0.564369	−	0.165714i	−0.0129114	−	0.999917i	$-0.504110\pi$
$73$	−4.82197	−	1.41586i	−0.564369	−	0.165714i	−0.551458	+	0.834203i	$0.685928\pi$
$74$		0			0
$75$	2.51004	−	0.737014i	0.289834	−	0.0851030i
$76$		0			0
$77$	0.155840	−	0.341242i	0.0177596	−	0.0388882i
$78$		0			0
$79$	−6.43071	+	4.13277i	−0.723512	+	0.464973i	−0.849857	−	0.527014i	$-0.823312\pi$
$79$	−6.43071	+	4.13277i	−0.723512	+	0.464973i	0.126345	+	0.991986i	$0.459675\pi$
$80$		0			0
$81$	0.819465	+	5.69950i	0.0910516	+	0.633278i
$82$		0			0
$83$	8.70437	−	10.0454i	0.955428	−	1.10262i	−0.0392122	−	0.999231i	$-0.512485\pi$
$83$	8.70437	−	10.0454i	0.955428	−	1.10262i	0.994641	−	0.103392i	$-0.0329697\pi$
$84$		0			0
$85$	1.49807	+	0.962750i	0.162488	+	0.104425i
$86$		0			0
$87$	2.25843	+	2.60637i	0.242129	+	0.279432i
$88$		0			0
$89$	0.981628	+	2.14946i	0.104052	+	0.227843i	0.954496	−	0.298223i	$-0.0963939\pi$
$89$	0.981628	+	2.14946i	0.104052	+	0.227843i	−0.850444	+	0.526066i	$0.823667\pi$
$90$		0			0
$91$	−0.242522			−0.0254232
$92$		0			0
$93$	6.41651			0.665361
$94$		0			0
$95$	−1.41596	−	3.10053i	−0.145275	−	0.318108i
$96$		0			0
$97$	4.21722	+	4.86694i	0.428194	+	0.494163i	0.928316	−	0.371793i	$-0.121257\pi$
$97$	4.21722	+	4.86694i	0.428194	+	0.494163i	−0.500122	+	0.865955i	$0.666711\pi$
$98$		0			0
$99$	18.7374	+	12.0418i	1.88318	+	1.21025i
$100$		0			0
$101$	7.44091	−	8.58727i	0.740399	−	0.854466i	−0.253202	−	0.967413i	$-0.581484\pi$
$101$	7.44091	−	8.58727i	0.740399	−	0.854466i	0.993601	+	0.112948i	$0.0360293\pi$
$102$		0			0
$103$	−2.49247	−	17.3355i	−0.245591	−	1.70812i	−0.623123	−	0.782123i	$-0.714137\pi$
$103$	−2.49247	−	17.3355i	−0.245591	−	1.70812i	0.377533	−	0.925996i	$-0.376773\pi$
$104$		0			0
$105$	−0.142464	+	0.0915558i	−0.0139030	+	0.00893493i
$106$		0			0
$107$	−5.10088	+	11.1694i	−0.493121	+	1.07978i	0.485523	+	0.874224i	$0.338629\pi$
$107$	−5.10088	+	11.1694i	−0.493121	+	1.07978i	−0.978644	+	0.205561i	$0.934098\pi$
$108$		0			0
$109$	−10.4148	+	3.05807i	−0.997558	+	0.292910i	−0.739454	−	0.673207i	$-0.764916\pi$
$109$	−10.4148	+	3.05807i	−0.997558	+	0.292910i	−0.258105	+	0.966117i	$0.583098\pi$
$110$		0			0
$111$	4.73612	+	1.39065i	0.449533	+	0.131995i
$112$		0			0
$113$	2.22817	−	15.4973i	0.209609	−	1.45786i	−0.564828	−	0.825209i	$-0.691057\pi$
$113$	2.22817	−	15.4973i	0.209609	−	1.45786i	0.774437	−	0.632652i	$-0.218033\pi$
$114$		0			0
$115$	4.56673	+	1.46456i	0.425850	+	0.136571i
$116$		0			0
$117$	2.04921	−	14.2526i	0.189449	−	1.31765i
$118$		0			0
$119$	−0.110608	−	0.0324773i	−0.0101394	−	0.00297719i
$120$		0			0
$121$	−21.6681	+	6.36232i	−1.96982	+	0.578392i
$122$		0			0
$123$	−0.116872	+	0.255914i	−0.0105380	+	0.0230750i
$124$		0			0
$125$	0.841254	−	0.540641i	0.0752440	−	0.0483564i
$126$		0			0
$127$	1.96308	+	13.6535i	0.174195	+	1.21155i	0.869901	+	0.493226i	$0.164183\pi$
$127$	1.96308	+	13.6535i	0.174195	+	1.21155i	−0.695706	+	0.718327i	$0.744908\pi$
$128$		0			0
$129$	−1.23093	+	1.42057i	−0.108377	+	0.125074i
$130$		0			0
$131$	−15.9747	−	10.2663i	−1.39571	−	0.896971i	−0.395941	−	0.918276i	$-0.629582\pi$
$131$	−15.9747	−	10.2663i	−1.39571	−	0.896971i	−0.999773	+	0.0213045i	$0.993218\pi$
$132$		0			0
$133$	0.144497	+	0.166758i	0.0125294	+	0.0144598i
$134$		0			0
$135$	−0.916631	−	2.00714i	−0.0788910	−	0.172747i
$136$		0			0
$137$	16.1235			1.37752			0.688760	−	0.724990i	$-0.258156\pi$
$137$	16.1235			1.37752			0.688760	+	0.724990i	$0.258156\pi$
$138$		0			0
$139$	19.0178			1.61307			0.806536	−	0.591184i	$-0.201339\pi$
$139$	19.0178			1.61307			0.806536	+	0.591184i	$0.201339\pi$
$140$		0			0
$141$	−0.954348	−	2.08973i	−0.0803706	−	0.175987i
$142$		0			0
$143$	14.2174	+	16.4077i	1.18892	+	1.37208i
$144$		0			0
$145$	1.10904	+	0.712736i	0.0921007	+	0.0591895i
$146$		0			0
$147$	−11.9846	+	13.8310i	−0.988477	+	1.14076i
$148$		0			0
$149$	1.05958	+	7.36956i	0.0868045	+	0.603738i	0.986069	+	0.166334i	$0.0531930\pi$
$149$	1.05958	+	7.36956i	0.0868045	+	0.603738i	−0.899265	+	0.437404i	$0.855898\pi$
$150$		0			0
$151$	1.44428	−	0.928183i	0.117534	−	0.0755345i	−0.480553	−	0.876966i	$-0.659564\pi$
$151$	1.44428	−	0.928183i	0.117534	−	0.0755345i	0.598087	+	0.801431i	$0.295928\pi$
$152$		0			0
$153$	2.84323	−	6.22580i	0.229861	−	0.503326i
$154$		0			0
$155$	2.35343	−	0.691031i	0.189032	−	0.0555049i
$156$		0			0
$157$	11.8120	+	3.46830i	0.942697	+	0.276801i	0.716743	−	0.697337i	$-0.245632\pi$
$157$	11.8120	+	3.46830i	0.942697	+	0.276801i	0.225954	+	0.974138i	$0.427450\pi$
$158$		0			0
$159$	−3.24342	+	22.5585i	−0.257220	+	1.78900i
$160$		0			0
$161$	−0.310363	−	0.00768017i	−0.0244600	−	0.000605283i
$162$		0			0
$163$	−1.67265	+	11.6336i	−0.131012	+	0.911211i	0.813226	+	0.581948i	$0.197709\pi$
$163$	−1.67265	+	11.6336i	−0.131012	+	0.911211i	−0.944238	+	0.329263i	$0.893200\pi$
$164$		0			0
$165$	14.5458	+	4.27104i	1.13239	+	0.332500i
$166$		0			0
$167$	−21.1058	+	6.19723i	−1.63322	+	0.479556i	−0.964527	−	0.263984i	$-0.914963\pi$
$167$	−21.1058	+	6.19723i	−1.63322	+	0.479556i	−0.668691	+	0.743541i	$0.733145\pi$
$168$		0			0
$169$	0.430103	−	0.941795i	0.0330849	−	0.0724458i
$170$		0			0
$171$	−11.0210	+	7.08277i	−0.842798	+	0.541633i
$172$		0			0
$173$	−1.06525	−	7.40900i	−0.0809897	−	0.563296i	−0.989400	−	0.145216i	$-0.953612\pi$
$173$	−1.06525	−	7.40900i	−0.0809897	−	0.563296i	0.908410	−	0.418080i	$-0.137297\pi$
$174$		0			0
$175$	−0.0423924	+	0.0489234i	−0.00320456	+	0.00369826i
$176$		0			0
$177$	−33.6956	−	21.6549i	−2.53272	−	1.62768i
$178$		0			0
$179$	−9.56587	−	11.0396i	−0.714987	−	0.825139i	0.275708	−	0.961242i	$-0.411088\pi$
$179$	−9.56587	−	11.0396i	−0.714987	−	0.825139i	−0.990695	+	0.136102i	$0.956542\pi$
$180$		0			0
$181$	4.39220	+	9.61758i	0.326470	+	0.714869i	0.999698	−	0.0245653i	$-0.00782017\pi$
$181$	4.39220	+	9.61758i	0.326470	+	0.714869i	−0.673228	+	0.739435i	$0.735093\pi$
$182$		0			0
$183$	−3.49533			−0.258382
$184$		0			0
$185$	1.88687			0.138726
$186$		0			0
$187$	4.28692	+	9.38705i	0.313491	+	0.686449i
$188$		0			0
$189$	0.0935405	+	0.107952i	0.00680407	+	0.00785232i
$190$		0			0
$191$	14.7857	+	9.50217i	1.06985	+	0.687553i	0.952192	−	0.305501i	$-0.0988239\pi$
$191$	14.7857	+	9.50217i	1.06985	+	0.687553i	0.117661	+	0.993054i	$0.462460\pi$
$192$		0			0
$193$	8.41940	−	9.71650i	0.606042	−	0.699409i	−0.366952	−	0.930240i	$-0.619599\pi$
$193$	8.41940	−	9.71650i	0.606042	−	0.699409i	0.972994	+	0.230831i	$0.0741443\pi$
$194$		0			0
$195$	−1.39476	−	9.70079i	−0.0998810	−	0.694688i
$196$		0			0
$197$	−2.75418	+	1.77001i	−0.196228	+	0.126108i	−0.635065	−	0.772459i	$-0.719027\pi$
$197$	−2.75418	+	1.77001i	−0.196228	+	0.126108i	0.438838	+	0.898566i	$0.355390\pi$
$198$		0			0
$199$	9.71532	−	21.2736i	0.688701	−	1.50804i	−0.164453	−	0.986385i	$-0.552586\pi$
$199$	9.71532	−	21.2736i	0.688701	−	1.50804i	0.853154	−	0.521660i	$-0.174687\pi$
$200$		0			0
$201$	−27.0807	+	7.95162i	−1.91013	+	0.560864i
$202$		0			0
$203$	−0.0818843	−	0.0240434i	−0.00574715	−	0.00168752i
$204$		0			0
$205$	−0.0153053	+	0.106450i	−0.00106897	+	0.00743482i
$206$		0			0
$207$	3.07379	−	18.1746i	0.213643	−	1.26322i
$208$		0			0
$209$	2.81112	−	19.5517i	0.194449	−	1.35242i
$210$		0			0
$211$	−25.9891	−	7.63108i	−1.78916	−	0.525345i	−0.792716	−	0.609591i	$-0.791334\pi$
$211$	−25.9891	−	7.63108i	−1.78916	−	0.525345i	−0.996445	+	0.0842454i	$0.973152\pi$
$212$		0			0
$213$	−27.8474	+	8.17674i	−1.90807	+	0.560261i
$214$		0			0
$215$	−0.298488	+	0.653598i	−0.0203567	+	0.0445750i
$216$		0			0
$217$	−0.133575	+	0.0858436i	−0.00906768	+	0.00582744i
$218$		0			0
$219$	1.87099	+	13.0130i	0.126430	+	0.879338i
$220$		0			0
$221$	4.36883	−	5.04190i	0.293880	−	0.339155i
$222$		0			0
$223$	−4.10368	−	2.63728i	−0.274803	−	0.176605i	0.395979	−	0.918259i	$-0.370405\pi$
$223$	−4.10368	−	2.63728i	−0.274803	−	0.176605i	−0.670782	+	0.741654i	$0.734042\pi$
$224$		0			0
$225$	−2.51694	−	2.90471i	−0.167796	−	0.193647i
$226$		0			0
$227$	−6.10354	−	13.3649i	−0.405106	−	0.887058i	−0.996727	−	0.0808422i	$-0.974239\pi$
$227$	−6.10354	−	13.3649i	−0.405106	−	0.887058i	0.591621	−	0.806216i	$-0.298488\pi$
$228$		0			0
$229$	11.1857			0.739171			0.369585	−	0.929197i	$-0.379500\pi$
$229$	11.1857			0.739171			0.369585	+	0.929197i	$0.379500\pi$
$230$		0			0
$231$	−0.981377			−0.0645698
$232$		0			0
$233$	−8.86878	−	19.4199i	−0.581013	−	1.27224i	−0.940722	−	0.339177i	$-0.889851\pi$
$233$	−8.86878	−	19.4199i	−0.581013	−	1.27224i	0.359709	−	0.933065i	$-0.382876\pi$
$234$		0			0
$235$	−0.575089	−	0.663688i	−0.0375147	−	0.0432942i
$236$		0			0
$237$	16.8228	+	10.8113i	1.09276	+	0.702272i
$238$		0			0
$239$	−6.83331	+	7.88606i	−0.442010	+	0.510107i	−0.932416	−	0.361387i	$-0.882303\pi$
$239$	−6.83331	+	7.88606i	−0.442010	+	0.510107i	0.490406	+	0.871494i	$0.336849\pi$
$240$		0			0
$241$	3.82894	+	26.6308i	0.246644	+	1.71544i	0.617346	+	0.786692i	$0.288208\pi$
$241$	3.82894	+	26.6308i	0.246644	+	1.71544i	−0.370702	+	0.928752i	$0.620883\pi$
$242$		0			0
$243$	18.2408	−	11.7226i	1.17015	−	0.752008i
$244$		0			0
$245$	−2.90616	+	6.36361i	−0.185668	+	0.406556i
$246$		0			0
$247$	−12.2525	+	3.59765i	−0.779606	+	0.228913i
$248$		0			0
$249$	−33.3633	−	9.79634i	−2.11431	−	0.620818i
$250$		0			0
$251$	0.352955	−	2.45486i	0.0222783	−	0.154949i	−0.975646	−	0.219353i	$-0.929605\pi$
$251$	0.352955	−	2.45486i	0.0222783	−	0.154949i	0.997924	+	0.0644037i	$0.0205145\pi$
$252$		0			0
$253$	17.6748	+	21.4477i	1.11121	+	1.34841i
$254$		0			0
$255$	0.662969	−	4.61105i	0.0415167	−	0.288755i
$256$		0			0
$257$	14.8676	+	4.36554i	0.927418	+	0.272315i	0.710356	−	0.703843i	$-0.248534\pi$
$257$	14.8676	+	4.36554i	0.927418	+	0.272315i	0.217063	+	0.976158i	$0.430352\pi$
$258$		0			0
$259$	−0.117199	+	0.0344127i	−0.00728238	+	0.00213830i
$260$		0			0
$261$	2.10488	−	4.60904i	0.130289	−	0.285292i
$262$		0			0
$263$	−9.43624	+	6.06431i	−0.581864	+	0.373941i	−0.798213	−	0.602375i	$-0.794221\pi$
$263$	−9.43624	+	6.06431i	−0.581864	+	0.373941i	0.216350	+	0.976316i	$0.430585\pi$
$264$		0			0
$265$	1.23984	+	8.62326i	0.0761626	+	0.529723i
$266$		0			0
$267$	4.04811	−	4.67177i	0.247740	−	0.285907i
$268$		0			0
$269$	10.2596	+	6.59344i	0.625539	+	0.402009i	0.814655	−	0.579945i	$-0.196926\pi$
$269$	10.2596	+	6.59344i	0.625539	+	0.402009i	−0.189117	+	0.981955i	$0.560562\pi$
$270$		0			0
$271$	−8.93878	−	10.3159i	−0.542992	−	0.626646i	0.416244	−	0.909253i	$-0.363346\pi$
$271$	−8.93878	−	10.3159i	−0.542992	−	0.626646i	−0.959236	+	0.282607i	$0.908801\pi$
$272$		0			0
$273$	0.263555	+	0.577105i	0.0159511	+	0.0349280i
$274$		0			0
$275$	5.79507			0.349456
$276$		0			0
$277$	−17.5457			−1.05422			−0.527109	−	0.849797i	$-0.676724\pi$
$277$	−17.5457			−1.05422			−0.527109	+	0.849797i	$0.676724\pi$
$278$		0			0
$279$	−3.91622	−	8.57532i	−0.234458	−	0.513391i
$280$		0			0
$281$	15.3782	+	17.7474i	0.917388	+	1.05872i	0.998077	+	0.0619825i	$0.0197423\pi$
$281$	15.3782	+	17.7474i	0.917388	+	1.05872i	−0.0806896	+	0.996739i	$0.525712\pi$
$282$		0			0
$283$	−3.55779	−	2.28646i	−0.211489	−	0.135916i	0.430608	−	0.902539i	$-0.358299\pi$
$283$	−3.55779	−	2.28646i	−0.211489	−	0.135916i	−0.642097	+	0.766623i	$0.721935\pi$
$284$		0			0
$285$	−5.83925	+	6.73886i	−0.345888	+	0.399176i
$286$		0			0
$287$	−0.000990784	−	0.00689106i	−5.84842e−5	−	0.000406766i
$288$		0			0
$289$	−11.6336	+	7.47647i	−0.684330	+	0.439792i
$290$		0			0
$291$	6.99839	−	15.3243i	0.410253	−	0.898329i
$292$		0			0
$293$	24.8945	−	7.30969i	1.45435	−	0.427036i	0.543374	−	0.839491i	$-0.317147\pi$
$293$	24.8945	−	7.30969i	1.45435	−	0.427036i	0.910978	+	0.412454i	$0.135328\pi$
$294$		0			0
$295$	−14.6910	−	4.31366i	−0.855341	−	0.251151i
$296$		0			0
$297$	1.81979	−	12.6569i	0.105595	−	0.734428i
$298$		0			0
$299$	7.86578	−	16.1537i	0.454890	−	0.934194i
$300$		0			0
$301$	0.00661963	−	0.0460406i	0.000381549	−	0.00265373i
$302$		0			0
$303$	−28.5205	−	8.37438i	−1.63846	−	0.481096i
$304$		0			0
$305$	−1.28201	+	0.376432i	−0.0734077	+	0.0215544i
$306$		0			0
$307$	−0.602560	+	1.31942i	−0.0343899	+	0.0753034i	−0.926047	−	0.377407i	$-0.876816\pi$
$307$	−0.602560	+	1.31942i	−0.0343899	+	0.0753034i	0.891657	+	0.452711i	$0.149543\pi$
$308$		0			0
$309$	−38.5430	+	24.7701i	−2.19263	+	1.40912i
$310$		0			0
$311$	0.354101	+	2.46282i	0.0200792	+	0.139654i	0.997395	−	0.0721333i	$-0.0229807\pi$
$311$	0.354101	+	2.46282i	0.0200792	+	0.139654i	−0.977316	+	0.211787i	$0.932072\pi$
$312$		0			0
$313$	−12.6641	+	14.6151i	−0.715816	+	0.826095i	−0.990797	−	0.135354i	$-0.956783\pi$
$313$	−12.6641	+	14.6151i	−0.715816	+	0.826095i	0.274982	+	0.961450i	$0.411328\pi$
$314$		0			0
$315$	0.209310	+	0.134515i	0.0117933	+	0.00757908i
$316$		0			0
$317$	−5.88940	−	6.79673i	−0.330782	−	0.381743i	0.565858	−	0.824502i	$-0.308545\pi$
$317$	−5.88940	−	6.79673i	−0.330782	−	0.381743i	−0.896640	+	0.442760i	$0.853999\pi$
$318$		0			0
$319$	3.17366	+	6.94935i	0.177691	+	0.389089i
$320$		0			0
$321$	32.1219			1.79287
$322$		0			0
$323$	−6.06981			−0.337733
$324$		0			0
$325$	−1.55630	−	3.40783i	−0.0863281	−	0.189032i
$326$		0			0
$327$	18.5950	+	21.4598i	1.02831	+	1.18673i
$328$		0			0
$329$	0.0478246	+	0.0307350i	0.00263666	+	0.00169448i
$330$		0			0
$331$	3.01753	−	3.48241i	0.165858	−	0.191411i	−0.666736	−	0.745294i	$-0.732309\pi$
$331$	3.01753	−	3.48241i	0.165858	−	0.191411i	0.832594	+	0.553883i	$0.186855\pi$
$332$		0			0
$333$	−1.03209	−	7.17834i	−0.0565581	−	0.393370i
$334$		0			0
$335$	−9.07626	+	5.83296i	−0.495889	+	0.318689i
$336$		0			0
$337$	−6.92004	+	15.1528i	−0.376958	+	0.825424i	0.622137	+	0.782908i	$0.286265\pi$
$337$	−6.92004	+	15.1528i	−0.376958	+	0.825424i	−0.999096	+	0.0425157i	$0.986463\pi$
$338$		0			0
$339$	−39.2987	+	11.5391i	−2.13441	+	0.626720i
$340$		0			0
$341$	13.6383	+	4.00457i	0.738556	+	0.216860i
$342$		0			0
$343$	0.128940	−	0.896796i	0.00696209	−	0.0484224i
$344$		0			0
$345$	−1.47772	−	12.4586i	−0.0795577	−	0.670748i
$346$		0			0
$347$	−1.53348	+	10.6656i	−0.0823216	+	0.572559i	0.906357	+	0.422512i	$0.138852\pi$
$347$	−1.53348	+	10.6656i	−0.0823216	+	0.572559i	−0.988679	+	0.150047i	$0.952057\pi$
$348$		0			0
$349$	31.9663	+	9.38615i	1.71112	+	0.502429i	0.983090	−	0.183121i	$-0.0586202\pi$
$349$	31.9663	+	9.38615i	1.71112	+	0.502429i	0.728025	+	0.685550i	$0.240438\pi$
$350$		0			0
$351$	−7.93169	+	2.32895i	−0.423362	+	0.124310i
$352$		0			0
$353$	−2.22376	+	4.86936i	−0.118359	+	0.259170i	−0.959534	−	0.281593i	$-0.909137\pi$
$353$	−2.22376	+	4.86936i	−0.118359	+	0.259170i	0.841175	+	0.540763i	$0.181864\pi$
$354$		0			0
$355$	−9.33323	+	5.99810i	−0.495356	+	0.318346i
$356$		0			0
$357$	0.0429173	+	0.298496i	0.00227142	+	0.0157981i
$358$		0			0
$359$	17.4800	−	20.1730i	0.922561	−	1.06469i	−0.0751571	−	0.997172i	$-0.523946\pi$
$359$	17.4800	−	20.1730i	0.922561	−	1.06469i	0.997718	−	0.0675202i	$-0.0215087\pi$
$360$		0			0
$361$	−6.20994	−	3.99088i	−0.326839	−	0.210047i
$362$		0			0
$363$	38.6871	+	44.6472i	2.03054	+	2.34337i
$364$		0			0
$365$	2.08768	+	4.57139i	0.109274	+	0.239278i
$366$		0			0
$367$	36.8508			1.92360			0.961799	−	0.273758i	$-0.0882666\pi$
$367$	36.8508			1.92360			0.961799	+	0.273758i	$0.0882666\pi$
$368$		0			0
$369$	0.413347			0.0215180
$370$		0			0
$371$	−0.234280	−	0.513002i	−0.0121632	−	0.0266337i
$372$		0			0
$373$	7.19723	+	8.30605i	0.372659	+	0.430071i	0.910841	−	0.412757i	$-0.135434\pi$
$373$	7.19723	+	8.30605i	0.372659	+	0.430071i	−0.538182	+	0.842828i	$0.680889\pi$
$374$		0			0
$375$	−2.20072	−	1.41432i	−0.113645	−	0.0730351i
$376$		0			0
$377$	3.23430	−	3.73258i	0.166575	−	0.192238i
$378$		0			0
$379$	−1.98479	−	13.8045i	−0.101952	−	0.709092i	−0.975121	−	0.221674i	$-0.928848\pi$
$379$	−1.98479	−	13.8045i	−0.101952	−	0.709092i	0.873169	−	0.487418i	$-0.162061\pi$
$380$		0			0
$381$	30.3566	−	19.5090i	1.55521	−	0.999476i
$382$		0			0
$383$	−4.53694	+	9.93451i	−0.231827	+	0.507630i	−0.989417	−	0.145101i	$-0.953649\pi$
$383$	−4.53694	+	9.93451i	−0.231827	+	0.507630i	0.757590	+	0.652731i	$0.226377\pi$
$384$		0			0
$385$	−0.359947	+	0.105690i	−0.0183446	+	0.00538647i
$386$		0			0
$387$	2.64979	+	0.778048i	0.134696	+	0.0395504i
$388$		0			0
$389$	−1.87506	+	13.0414i	−0.0950695	+	0.661223i	0.885440	+	0.464753i	$0.153857\pi$
$389$	−1.87506	+	13.0414i	−0.0950695	+	0.661223i	−0.980510	+	0.196470i	$0.937052\pi$
$390$		0			0
$391$	5.75061	−	6.31393i	0.290821	−	0.319309i
$392$		0			0
$393$	−7.06959	+	49.1700i	−0.356613	+	2.48030i
$394$		0			0
$395$	7.33456	+	2.15362i	0.369042	+	0.108360i
$396$		0			0
$397$	8.24921	−	2.42219i	0.414016	−	0.121566i	−0.0680895	−	0.997679i	$-0.521690\pi$
$397$	8.24921	−	2.42219i	0.414016	−	0.121566i	0.482106	+	0.876113i	$0.339872\pi$
$398$		0			0
$399$	0.239789	−	0.525065i	0.0120045	−	0.0262861i
$400$		0			0
$401$	17.5090	−	11.2523i	0.874357	−	0.561915i	−0.0247259	−	0.999694i	$-0.507871\pi$
$401$	17.5090	−	11.2523i	0.874357	−	0.561915i	0.899082	+	0.437779i	$0.144235\pi$
$402$		0			0
$403$	−1.30774	−	9.09555i	−0.0651433	−	0.453082i
$404$		0			0
$405$	3.77076	−	4.35169i	0.187371	−	0.216237i
$406$		0			0
$407$	9.19873	+	5.91167i	0.455964	+	0.293031i
$408$		0			0
$409$	−8.81821	−	10.1768i	−0.436033	−	0.503208i	0.494622	−	0.869108i	$-0.335307\pi$
$409$	−8.81821	−	10.1768i	−0.436033	−	0.503208i	−0.930654	+	0.365900i	$0.880761\pi$
$410$		0			0
$411$	−17.5218	−	38.3674i	−0.864286	−	1.89252i
$412$		0			0
$413$	0.991168			0.0487722
$414$		0			0
$415$	−13.2919			−0.652476
$416$		0			0
$417$	−20.6672	−	45.2549i	−1.01208	−	2.21614i
$418$		0			0
$419$	−14.8040	−	17.0848i	−0.723224	−	0.834645i	0.268467	−	0.963289i	$-0.413483\pi$
$419$	−14.8040	−	17.0848i	−0.723224	−	0.834645i	−0.991691	+	0.128644i	$0.958938\pi$
$420$		0			0
$421$	−3.89603	−	2.50383i	−0.189881	−	0.122029i	0.442246	−	0.896894i	$-0.354182\pi$
$421$	−3.89603	−	2.50383i	−0.189881	−	0.122029i	−0.632127	+	0.774864i	$0.717818\pi$
$422$		0			0
$423$	−2.21034	+	2.55087i	−0.107470	+	0.124028i
$424$		0			0
$425$	−0.253428	−	1.76263i	−0.0122931	−	0.0855002i
$426$		0			0
$427$	0.0727638	−	0.0467624i	0.00352129	−	0.00226299i
$428$		0			0
$429$	23.5934	−	51.6624i	1.13910	−	2.49428i
$430$		0			0
$431$	27.8595	−	8.18029i	1.34195	−	0.394031i	0.469582	−	0.882889i	$-0.344405\pi$
$431$	27.8595	−	8.18029i	1.34195	−	0.394031i	0.872363	+	0.488858i	$0.162586\pi$
$432$		0			0
$433$	27.4854	+	8.07045i	1.32087	+	0.387841i	0.864805	−	0.502107i	$-0.167442\pi$
$433$	27.4854	+	8.07045i	1.32087	+	0.387841i	0.456061	+	0.889949i	$0.349260\pi$
$434$		0			0
$435$	0.490805	−	3.41362i	0.0235323	−	0.163671i
$436$		0			0
$437$	−15.7938	+	4.21602i	−0.755521	+	0.201679i
$438$		0			0
$439$	0.178976	−	1.24480i	0.00854204	−	0.0594112i	−0.985105	−	0.171956i	$-0.944991\pi$
$439$	0.178976	−	1.24480i	0.00854204	−	0.0594112i	0.993647	+	0.112545i	$0.0359003\pi$
$440$		0			0
$441$	25.7991	+	7.57529i	1.22853	+	0.360728i
$442$		0			0
$443$	−12.8094	+	3.76119i	−0.608594	+	0.178699i	−0.571486	−	0.820612i	$-0.693633\pi$
$443$	−12.8094	+	3.76119i	−0.608594	+	0.178699i	−0.0371082	+	0.999311i	$0.511815\pi$
$444$		0			0
$445$	0.981628	−	2.14946i	0.0465336	−	0.101894i
$446$		0			0
$447$	16.3851	−	10.5301i	0.774991	−	0.498056i
$448$		0			0
$449$	−2.36172	−	16.4261i	−0.111456	−	0.775196i	−0.966505	−	0.256648i	$-0.917382\pi$
$449$	−2.36172	−	16.4261i	−0.111456	−	0.775196i	0.855049	−	0.518548i	$-0.173527\pi$
$450$		0			0
$451$	−0.408129	+	0.471006i	−0.0192181	+	0.0221788i
$452$		0			0
$453$	−3.77825	−	2.42813i	−0.177517	−	0.114084i
$454$		0			0
$455$	0.158818	+	0.183286i	0.00744550	+	0.00859256i
$456$		0			0
$457$	−0.977533	−	2.14050i	−0.0457271	−	0.100128i	0.885390	−	0.464849i	$-0.153892\pi$
$457$	−0.977533	−	2.14050i	−0.0457271	−	0.100128i	−0.931117	+	0.364721i	$0.881164\pi$
$458$		0			0
$459$	−3.92932			−0.183405
$460$		0			0
$461$	1.30382			0.0607249			0.0303625	−	0.999539i	$-0.490334\pi$
$461$	1.30382			0.0607249			0.0303625	+	0.999539i	$0.490334\pi$
$462$		0			0
$463$	−11.1553	−	24.4268i	−0.518433	−	1.13521i	−0.970030	−	0.242987i	$-0.921873\pi$
$463$	−11.1553	−	24.4268i	−0.518433	−	1.13521i	0.451597	−	0.892222i	$-0.350855\pi$
$464$		0			0
$465$	−4.20192	−	4.84927i	−0.194859	−	0.224880i
$466$		0			0
$467$	11.9402	+	7.67353i	0.552528	+	0.355088i	0.786921	−	0.617054i	$-0.211674\pi$
$467$	11.9402	+	7.67353i	0.552528	+	0.355088i	−0.234393	+	0.972142i	$0.575310\pi$
$468$		0			0
$469$	0.457370	−	0.527833i	0.0211194	−	0.0243731i
$470$		0			0
$471$	−4.58320	−	31.8768i	−0.211183	−	1.46881i
$472$		0			0
$473$	−3.50292	+	2.25119i	−0.161065	+	0.103510i
$474$		0			0
$475$	−1.41596	+	3.10053i	−0.0649689	+	0.142262i
$476$		0			0
$477$	32.1278	−	9.43357i	1.47103	−	0.431934i
$478$		0			0
$479$	−9.00073	−	2.64285i	−0.411254	−	0.120755i	0.0695599	−	0.997578i	$-0.477840\pi$
$479$	−9.00073	−	2.64285i	−0.411254	−	0.120755i	−0.480814	+	0.876823i	$0.659659\pi$
$480$		0			0
$481$	1.00602	−	6.99699i	0.0458703	−	0.319035i
$482$		0			0
$483$	0.319004	+	0.746886i	0.0145152	+	0.0339845i
$484$		0			0
$485$	0.916490	−	6.37433i	0.0416157	−	0.289443i
$486$		0			0
$487$	20.7429	+	6.09067i	0.939952	+	0.275995i	0.715597	−	0.698513i	$-0.246155\pi$
$487$	20.7429	+	6.09067i	0.939952	+	0.275995i	0.224354	+	0.974508i	$0.427973\pi$
$488$		0			0
$489$	29.5010	−	8.66227i	1.33408	−	0.391721i
$490$		0			0
$491$	−17.4103	+	38.1231i	−0.785714	+	1.72047i	−0.0971830	+	0.995267i	$0.530983\pi$
$491$	−17.4103	+	38.1231i	−0.785714	+	1.72047i	−0.688531	+	0.725207i	$0.741744\pi$
$492$		0			0
$493$	1.97493	−	1.26921i	0.0889464	−	0.0571624i
$494$		0			0
$495$	−3.16981	−	22.0465i	−0.142472	−	0.990917i
$496$		0			0
$497$	0.470319	−	0.542777i	0.0210967	−	0.0243469i
$498$		0			0
$499$	9.75265	+	6.26765i	0.436588	+	0.280578i	0.740416	−	0.672149i	$-0.234628\pi$
$499$	9.75265	+	6.26765i	0.436588	+	0.280578i	−0.303828	+	0.952727i	$0.598265\pi$
$500$		0			0
$501$	37.6832	+	43.4887i	1.68356	+	1.94293i
$502$		0			0
$503$	2.03334	+	4.45239i	0.0906621	+	0.198522i	0.949531	−	0.313673i	$-0.101560\pi$
$503$	2.03334	+	4.45239i	0.0906621	+	0.198522i	−0.858869	+	0.512195i	$0.828832\pi$
$504$		0			0
$505$	−11.3626			−0.505629
$506$		0			0
$507$	−2.70850			−0.120289
$508$		0			0
$509$	−13.3829	−	29.3044i	−0.593185	−	1.29889i	−0.933498	−	0.358581i	$-0.883261\pi$
$509$	−13.3829	−	29.3044i	−0.593185	−	1.29889i	0.340314	−	0.940312i	$-0.389467\pi$
$510$		0			0
$511$	−0.213045	−	0.245866i	−0.00942453	−	0.0108765i
$512$		0			0
$513$	6.32716	+	4.06622i	0.279351	+	0.179528i
$514$		0			0
$515$	−11.4691	+	13.2360i	−0.505389	+	0.583249i
$516$		0			0
$517$	−0.724261	−	5.03734i	−0.0318529	−	0.221542i
$518$		0			0
$519$	−16.4728	+	10.5864i	−0.723076	+	0.464693i
$520$		0			0
$521$	−2.12966	+	4.66330i	−0.0933020	+	0.204303i	−0.950529	−	0.310636i	$-0.899458\pi$
$521$	−2.12966	+	4.66330i	−0.0933020	+	0.204303i	0.857227	+	0.514939i	$0.172185\pi$
$522$		0			0
$523$	16.6666	−	4.89376i	0.728781	−	0.213989i	0.103765	−	0.994602i	$-0.466911\pi$
$523$	16.6666	−	4.89376i	0.728781	−	0.213989i	0.625015	+	0.780612i	$0.285093\pi$
$524$		0			0
$525$	0.162487	+	0.0477105i	0.00709152	+	0.00208226i
$526$		0			0
$527$	0.621606	−	4.32337i	0.0270776	−	0.188329i
$528$		0			0
$529$	10.5777	−	20.4233i	0.459898	−	0.887972i
$530$		0			0
$531$	−8.37496	+	58.2492i	−0.363443	+	2.52780i
$532$		0			0
$533$	0.386584	+	0.113511i	0.0167448	+	0.00491672i
$534$		0			0
$535$	11.7816	−	3.45940i	0.509364	−	0.149563i
$536$		0			0
$537$	−15.8744	+	34.7600i	−0.685029	+	1.50001i
$538$		0			0
$539$	−34.1054	+	21.9182i	−1.46902	+	0.944085i
$540$		0			0
$541$	4.71171	+	32.7706i	0.202572	+	1.40892i	0.796615	+	0.604487i	$0.206622\pi$
$541$	4.71171	+	32.7706i	0.202572	+	1.40892i	−0.594043	+	0.804433i	$0.702469\pi$
$542$		0			0
$543$	18.1129	−	20.9034i	0.777298	−	0.897050i
$544$		0			0
$545$	9.13138	+	5.86838i	0.391146	+	0.251374i
$546$		0			0
$547$	5.81210	+	6.70752i	0.248508	+	0.286793i	0.866275	−	0.499568i	$-0.166508\pi$
$547$	5.81210	+	6.70752i	0.248508	+	0.286793i	−0.617767	+	0.786361i	$0.711963\pi$
$548$		0			0
$549$	2.13332	+	4.67132i	0.0910479	+	0.199367i
$550$		0			0
$551$	−4.49355			−0.191432
$552$		0			0
$553$	−0.494847			−0.0210430
$554$		0			0
$555$	−2.05052	−	4.49000i	−0.0870396	−	0.190590i
$556$		0			0
$557$	−3.76373	−	4.34358i	−0.159474	−	0.184043i	0.670389	−	0.742010i	$-0.266127\pi$
$557$	−3.76373	−	4.34358i	−0.159474	−	0.184043i	−0.829864	+	0.557966i	$0.811582\pi$
$558$		0			0
$559$	2.26456	+	1.45534i	0.0957806	+	0.0615545i
$560$		0			0
$561$	17.6787	−	20.4023i	0.746396	−	0.861387i
$562$		0			0
$563$	0.819990	+	5.70316i	0.0345585	+	0.240359i	0.999778	−	0.0210823i	$-0.00671119\pi$
$563$	0.819990	+	5.70316i	0.0345585	+	0.240359i	−0.965219	+	0.261442i	$0.915802\pi$
$564$		0			0
$565$	−13.1712	+	8.46461i	−0.554116	+	0.356109i
$566$		0			0
$567$	−0.154846	+	0.339066i	−0.00650294	+	0.0142394i
$568$		0			0
$569$	−22.0700	+	6.48033i	−0.925222	+	0.271670i	−0.709435	−	0.704771i	$-0.751050\pi$
$569$	−22.0700	+	6.48033i	−0.925222	+	0.271670i	−0.215787	+	0.976440i	$0.569232\pi$
$570$		0			0
$571$	−8.06585	−	2.36835i	−0.337545	−	0.0991122i	0.108567	−	0.994089i	$-0.465374\pi$
$571$	−8.06585	−	2.36835i	−0.337545	−	0.0991122i	−0.446113	+	0.894977i	$0.647192\pi$
$572$		0			0
$573$	6.54339	−	45.5102i	0.273354	−	1.90122i
$574$		0			0
$575$	−1.88373	−	4.41039i	−0.0785570	−	0.183926i
$576$		0			0
$577$	−2.26843	+	15.7773i	−0.0944360	+	0.656817i	0.886535	+	0.462662i	$0.153106\pi$
$577$	−2.26843	+	15.7773i	−0.0944360	+	0.656817i	−0.980971	+	0.194155i	$0.937803\pi$
$578$		0			0
$579$	−32.2710	−	9.47562i	−1.34114	−	0.393793i
$580$		0			0
$581$	0.825598	−	0.242418i	0.0342516	−	0.0100572i
$582$		0			0
$583$	−20.9728	+	45.9239i	−0.868603	+	1.90197i
$584$		0			0
$585$	−12.1133	+	7.78476i	−0.500824	+	0.321860i
$586$		0			0
$587$	−4.47077	−	31.0949i	−0.184528	−	1.28342i	−0.845891	−	0.533356i	$-0.820930\pi$
$587$	−4.47077	−	31.0949i	−0.184528	−	1.28342i	0.661362	−	0.750067i	$-0.269979\pi$
$588$		0			0
$589$	−5.47494	+	6.31842i	−0.225591	+	0.260346i
$590$		0			0
$591$	7.20496	+	4.63035i	0.296372	+	0.190467i
$592$		0			0
$593$	12.5227	+	14.4520i	0.514245	+	0.593471i	0.952181	−	0.305536i	$-0.0988356\pi$
$593$	12.5227	+	14.4520i	0.514245	+	0.593471i	−0.437935	+	0.899006i	$0.644290\pi$
$594$		0			0
$595$	0.0478879	+	0.104860i	0.00196321	+	0.00429883i
$596$		0			0
$597$	−61.1806			−2.50395
$598$		0			0
$599$	−39.8003			−1.62620			−0.813098	−	0.582126i	$-0.802221\pi$
$599$	−39.8003			−1.62620			−0.813098	+	0.582126i	$0.802221\pi$
$600$		0			0
$601$	−11.4277	−	25.0232i	−0.466145	−	1.02072i	−0.986044	−	0.166488i	$-0.946757\pi$
$601$	−11.4277	−	25.0232i	−0.466145	−	1.02072i	0.519898	−	0.854228i	$-0.325970\pi$
$602$		0			0
$603$	27.1552	+	31.3388i	1.10585	+	1.27621i
$604$		0			0
$605$	18.9979	+	12.2092i	0.772374	+	0.496374i
$606$		0			0
$607$	20.2039	−	23.3165i	0.820051	−	0.946389i	−0.179249	−	0.983804i	$-0.557367\pi$
$607$	20.2039	−	23.3165i	0.820051	−	0.946389i	0.999300	+	0.0374144i	$0.0119121\pi$
$608$		0			0
$609$	0.0317722	+	0.220980i	0.00128747	+	0.00895458i
$610$		0			0
$611$	−2.76774	+	1.77872i	−0.111971	+	0.0719592i
$612$		0			0
$613$	18.1595	−	39.7637i	0.733455	−	1.60604i	−0.0605756	−	0.998164i	$-0.519294\pi$
$613$	18.1595	−	39.7637i	0.733455	−	1.60604i	0.794030	−	0.607878i	$-0.207979\pi$
$614$		0			0
$615$	0.269942	−	0.0792621i	0.0108851	−	0.00319616i
$616$		0			0
$617$	−13.3389	−	3.91666i	−0.537005	−	0.157679i	0.00197396	−	0.999998i	$-0.499372\pi$
$617$	−13.3389	−	3.91666i	−0.537005	−	0.157679i	−0.538979	+	0.842319i	$0.681190\pi$
$618$		0			0
$619$	−4.82263	+	33.5421i	−0.193838	+	1.34817i	0.627895	+	0.778298i	$0.283917\pi$
$619$	−4.82263	+	33.5421i	−0.193838	+	1.34817i	−0.821733	+	0.569873i	$0.806992\pi$
$620$		0			0
$621$	−10.2242	+	2.72926i	−0.410283	+	0.109521i
$622$		0			0
$623$	−0.0217698	+	0.151412i	−0.000872187	+	0.00606619i
$624$		0			0
$625$	−0.959493	−	0.281733i	−0.0383797	−	0.0112693i
$626$		0			0
$627$	−49.5803	+	14.5581i	−1.98005	+	0.581394i
$628$		0			0
$629$	1.39582	−	3.05642i	0.0556550	−	0.121867i
$630$		0			0
$631$	−7.17855	+	4.61338i	−0.285774	+	0.183656i	−0.675672	−	0.737202i	$-0.736146\pi$
$631$	−7.17855	+	4.61338i	−0.285774	+	0.183656i	0.389898	+	0.920858i	$0.372510\pi$
$632$		0			0
$633$	10.0841	+	70.1365i	0.400807	+	2.78768i
$634$		0			0
$635$	9.03309	−	10.4247i	0.358467	−	0.413693i
$636$		0			0
$637$	22.0484	+	14.1696i	0.873588	+	0.561421i
$638$		0			0
$639$	27.9240	+	32.2261i	1.10466	+	1.27484i
$640$		0			0
$641$	−3.62416	−	7.93581i	−0.143146	−	0.313445i	0.824456	−	0.565926i	$-0.191481\pi$
$641$	−3.62416	−	7.93581i	−0.143146	−	0.313445i	−0.967602	+	0.252480i	$0.918754\pi$
$642$		0			0
$643$	−0.118338			−0.00466680			−0.00233340	−	0.999997i	$-0.500743\pi$
$643$	−0.118338			−0.00466680			−0.00233340	+	0.999997i	$0.500743\pi$
$644$		0			0
$645$	1.87968			0.0740122
$646$		0			0
$647$	14.6796	+	32.1439i	0.577115	+	1.26371i	0.942922	+	0.333015i	$0.108066\pi$
$647$	14.6796	+	32.1439i	0.577115	+	1.26371i	−0.365807	+	0.930691i	$0.619207\pi$
$648$		0			0
$649$	−58.1053	−	67.0571i	−2.28083	−	2.63222i
$650$		0			0
$651$	0.349433	+	0.224567i	0.0136954	+	0.00880148i
$652$		0			0
$653$	28.0706	−	32.3952i	1.09849	−	1.26772i	0.137690	−	0.990475i	$-0.456032\pi$
$653$	28.0706	−	32.3952i	1.09849	−	1.26772i	0.960798	−	0.277248i	$-0.0894224\pi$
$654$		0			0
$655$	2.70244	+	18.7959i	0.105593	+	0.734415i
$656$		0			0
$657$	16.2493	−	10.4428i	0.633945	−	0.407411i
$658$		0			0
$659$	−13.4612	+	29.4758i	−0.524373	+	1.14822i	0.443385	+	0.896331i	$0.353778\pi$
$659$	−13.4612	+	29.4758i	−0.524373	+	1.14822i	−0.967757	+	0.251885i	$0.918950\pi$
$660$		0			0
$661$	−31.0309	+	9.11149i	−1.20696	+	0.354396i	−0.822511	−	0.568749i	$-0.807427\pi$
$661$	−31.0309	+	9.11149i	−1.20696	+	0.354396i	−0.384451	+	0.923145i	$0.625609\pi$
$662$		0			0
$663$	−16.7454	−	4.91691i	−0.650339	−	0.190957i
$664$		0			0
$665$	0.0314021	−	0.218407i	0.00121772	−	0.00846944i
$666$		0			0
$667$	4.25725	−	4.67429i	0.164841	−	0.180989i
$668$		0			0
$669$	−1.81608	+	12.6311i	−0.0702138	+	0.488348i
$670$		0			0
$671$	−7.42934	−	2.18145i	−0.286806	−	0.0842140i
$672$		0			0
$673$	36.1768	−	10.6225i	1.39451	−	0.409466i	0.503717	−	0.863869i	$-0.331965\pi$
$673$	36.1768	−	10.6225i	1.39451	−	0.409466i	0.890796	+	0.454403i	$0.150147\pi$
$674$		0			0
$675$	−0.916631	+	2.00714i	−0.0352811	+	0.0772549i
$676$		0			0
$677$	−28.2760	+	18.1719i	−1.08674	+	0.698403i	−0.956104	−	0.293028i	$-0.905337\pi$
$677$	−28.2760	+	18.1719i	−1.08674	+	0.698403i	−0.130632	+	0.991431i	$0.541701\pi$
$678$		0			0
$679$	0.0593290	+	0.412642i	0.00227684	+	0.0158357i
$680$		0			0
$681$	−25.1702	+	29.0480i	−0.964525	+	1.11312i
$682$		0			0
$683$	0.546455	+	0.351185i	0.0209095	+	0.0134377i	0.551054	−	0.834470i	$-0.314226\pi$
$683$	0.546455	+	0.351185i	0.0209095	+	0.0134377i	−0.530144	+	0.847907i	$0.677862\pi$
$684$		0			0
$685$	−10.5586	−	12.1853i	−0.403424	−	0.465576i
$686$		0			0
$687$	−12.1558	−	26.6175i	−0.463772	−	1.01552i
$688$		0			0
$689$	32.6382			1.24342
$690$		0			0
$691$	−44.9140			−1.70861			−0.854305	−	0.519773i	$-0.826017\pi$
$691$	−44.9140			−1.70861			−0.854305	+	0.519773i	$0.826017\pi$
$692$		0			0
$693$	0.598968	+	1.31156i	0.0227529	+	0.0498220i
$694$		0			0
$695$	−12.4540	−	14.3727i	−0.472409	−	0.545189i
$696$		0			0
$697$	0.161110	+	0.103539i	0.00610247	+	0.00392182i
$698$		0			0
$699$	−36.5737	+	42.2083i	−1.38335	+	1.59647i
$700$		0			0
$701$	1.94415	+	13.5218i	0.0734294	+	0.510713i	0.993030	+	0.117859i	$0.0376031\pi$
$701$	1.94415	+	13.5218i	0.0734294	+	0.510713i	−0.919601	+	0.392854i	$0.871488\pi$
$702$		0			0
$703$	−5.41053	+	3.47713i	−0.204062	+	0.131143i
$704$		0			0
$705$	−0.954348	+	2.08973i	−0.0359428	+	0.0787038i
$706$		0			0
$707$	0.705761	−	0.207230i	0.0265429	−	0.00779370i
$708$		0			0
$709$	18.8162	+	5.52494i	0.706658	+	0.207493i	0.615264	−	0.788321i	$-0.289050\pi$
$709$	18.8162	+	5.52494i	0.706658	+	0.207493i	0.0913940	+	0.995815i	$0.470868\pi$
$710$		0			0
$711$	4.18126	−	29.0813i	0.156809	−	1.09063i
$712$		0			0
$713$	−1.38552	−	11.6813i	−0.0518882	−	0.437468i
$714$		0			0
$715$	3.08973	−	21.4895i	0.115549	−	0.803663i
$716$		0			0
$717$	26.1916	+	7.69055i	0.978144	+	0.287209i
$718$		0			0
$719$	31.5351	−	9.25955i	1.17606	−	0.345323i	0.365408	−	0.930848i	$-0.380930\pi$
$719$	31.5351	−	9.25955i	1.17606	−	0.345323i	0.810655	+	0.585524i	$0.199111\pi$
$720$		0			0
$721$	0.470978	−	1.03130i	0.0175402	−	0.0384076i
$722$		0			0
$723$	59.2098	−	38.0518i	2.20204	−	1.41516i
$724$		0			0
$725$	−0.187616	−	1.30490i	−0.00696789	−	0.0484627i
$726$		0			0
$727$	22.7009	−	26.1983i	0.841931	−	0.971641i	−0.157944	−	0.987448i	$-0.550486\pi$
$727$	22.7009	−	26.1983i	0.841931	−	0.971641i	0.999875	+	0.0158076i	$0.00503193\pi$
$728$		0			0
$729$	−33.1859	−	21.3273i	−1.22911	−	0.789899i
$730$		0			0
$731$	0.837913	+	0.967003i	0.0309913	+	0.0357659i
$732$		0			0
$733$	−15.4169	−	33.7583i	−0.569437	−	1.24689i	−0.947097	−	0.320949i	$-0.895998\pi$
$733$	−15.4169	−	33.7583i	−0.569437	−	1.24689i	0.377660	−	0.925944i	$-0.376729\pi$
$734$		0			0
$735$	18.3011			0.675045
$736$		0			0
$737$	−62.5228			−2.30306
$738$		0			0
$739$	−9.83154	−	21.5281i	−0.361659	−	0.791923i	−0.999759	−	0.0219691i	$-0.993006\pi$
$739$	−9.83154	−	21.5281i	−0.361659	−	0.791923i	0.638100	−	0.769954i	$-0.279721\pi$
$740$		0			0
$741$	21.8761	+	25.2463i	0.803637	+	0.927447i
$742$		0			0
$743$	−35.4486	−	22.7814i	−1.30048	−	0.835769i	−0.307218	−	0.951639i	$-0.599398\pi$
$743$	−35.4486	−	22.7814i	−1.30048	−	0.835769i	−0.993264	+	0.115870i	$0.963034\pi$
$744$		0			0
$745$	4.87567	−	5.62682i	0.178631	−	0.206151i
$746$		0			0
$747$	7.27048	+	50.5673i	0.266013	+	1.85016i
$748$		0			0
$749$	−0.668696	+	0.429745i	−0.0244336	+	0.0157025i
$750$		0			0
$751$	11.9646	−	26.1989i	0.436595	−	0.956010i	−0.555616	−	0.831439i	$-0.687517\pi$
$751$	11.9646	−	26.1989i	0.436595	−	0.956010i	0.992211	−	0.124571i	$-0.0397554\pi$
$752$		0			0
$753$	−6.22514	+	1.82787i	−0.226857	+	0.0666112i
$754$		0			0
$755$	−1.64728	−	0.483684i	−0.0599506	−	0.0176031i
$756$		0			0
$757$	0.514907	−	3.58125i	0.0187146	−	0.130163i	−0.978322	−	0.207088i	$-0.933601\pi$
$757$	0.514907	−	3.58125i	0.0187146	−	0.130163i	0.997037	+	0.0769254i	$0.0245103\pi$
$758$		0			0
$759$	31.8293	−	65.3669i	1.15533	−	2.37267i
$760$		0			0
$761$	1.04364	−	7.25865i	0.0378318	−	0.263126i	−0.962123	−	0.272615i	$-0.912111\pi$
$761$	1.04364	−	7.25865i	0.0378318	−	0.263126i	0.999955	+	0.00948916i	$0.00302054\pi$
$762$		0			0
$763$	−0.674202	−	0.197964i	−0.0244078	−	0.00716677i
$764$		0			0
$765$	−6.56706	+	1.92826i	−0.237433	+	0.0697165i
$766$		0			0
$767$	−23.8288	+	52.1778i	−0.860408	+	1.88403i
$768$		0			0
$769$	−3.51169	+	2.25683i	−0.126635	+	0.0813833i	−0.602425	−	0.798176i	$-0.705799\pi$
$769$	−3.51169	+	2.25683i	−0.126635	+	0.0813833i	0.475790	+	0.879559i	$0.342162\pi$
$770$		0			0
$771$	−5.76885	−	40.1232i	−0.207760	−	1.44500i
$772$		0			0
$773$	−8.17733	+	9.43714i	−0.294118	+	0.339430i	−0.883506	−	0.468420i	$-0.844823\pi$
$773$	−8.17733	+	9.43714i	−0.294118	+	0.339430i	0.589388	+	0.807850i	$0.299369\pi$
$774$		0			0
$775$	−2.06342	−	1.32608i	−0.0741202	−	0.0476341i
$776$		0			0
$777$	0.209252	+	0.241489i	0.00750686	+	0.00866338i
$778$		0			0
$779$	−0.152280	−	0.333446i	−0.00545599	−	0.0119470i
$780$		0			0
$781$	−64.2930			−2.30058
$782$		0			0
$783$	−2.90892			−0.103956
$784$		0			0
$785$	−5.11402	−	11.1981i	−0.182527	−	0.399679i
$786$		0			0
$787$	−0.202945	−	0.234211i	−0.00723422	−	0.00834873i	0.752121	−	0.659025i	$-0.229031\pi$
$787$	−0.202945	−	0.234211i	−0.00723422	−	0.00834873i	−0.759355	+	0.650676i	$0.774485\pi$
$788$		0			0
$789$	24.6853	+	15.8642i	0.878818	+	0.564782i
$790$		0			0
$791$	0.663722	−	0.765976i	0.0235992	−	0.0272350i
$792$		0			0
$793$	0.712380	+	4.95471i	0.0252974	+	0.175947i
$794$		0			0
$795$	19.1726	−	12.3215i	0.679980	−	0.436997i
$796$		0			0
$797$	0.965264	−	2.11363i	0.0341914	−	0.0748687i	−0.891766	−	0.452497i	$-0.850533\pi$
$797$	0.965264	−	2.11363i	0.0341914	−	0.0748687i	0.925957	+	0.377629i	$0.123260\pi$
$798$		0			0
$799$	−1.50049	+	0.440583i	−0.0530835	+	0.0155867i
$800$		0			0
$801$	−8.71427	−	2.55874i	−0.307903	−	0.0904086i
$802$		0			0
$803$	−4.14468	+	28.8269i	−0.146263	+	1.01728i
$804$		0			0
$805$	0.197440	+	0.239586i	0.00695885	+	0.00844430i
$806$		0			0
$807$	4.54038	−	31.5790i	0.159829	−	1.11163i
$808$		0			0
$809$	21.7237	+	6.37864i	0.763763	+	0.224261i	0.640339	−	0.768093i	$-0.278794\pi$
$809$	21.7237	+	6.37864i	0.763763	+	0.224261i	0.123425	+	0.992354i	$0.460612\pi$
$810$		0			0
$811$	−13.2895	+	3.90216i	−0.466659	+	0.137023i	−0.506605	−	0.862178i	$-0.669100\pi$
$811$	−13.2895	+	3.90216i	−0.466659	+	0.137023i	0.0399459	+	0.999202i	$0.487281\pi$
$812$		0			0
$813$	−14.8337	+	32.4813i	−0.520241	+	1.13917i
$814$		0			0
$815$	9.88742	−	6.35426i	0.346341	−	0.222580i
$816$		0			0
$817$	−0.348550	−	2.42422i	−0.0121942	−	0.0848127i
$818$		0			0
$819$	0.610413	−	0.704454i	0.0213296	−	0.0246156i
$820$		0			0
$821$	−20.5322	−	13.1952i	−0.716579	−	0.460517i	0.130866	−	0.991400i	$-0.458224\pi$
$821$	−20.5322	−	13.1952i	−0.716579	−	0.460517i	−0.847445	+	0.530883i	$0.821860\pi$
$822$		0			0
$823$	−5.65674	−	6.52822i	−0.197181	−	0.227560i	0.648545	−	0.761176i	$-0.275378\pi$
$823$	−5.65674	−	6.52822i	−0.197181	−	0.227560i	−0.845726	+	0.533617i	$0.820832\pi$
$824$		0			0
$825$	−6.29766	−	13.7900i	−0.219256	−	0.480105i
$826$		0			0
$827$	29.6917			1.03248			0.516241	−	0.856444i	$-0.327331\pi$
$827$	29.6917			1.03248			0.516241	+	0.856444i	$0.327331\pi$
$828$		0			0
$829$	−15.5676			−0.540684			−0.270342	−	0.962764i	$-0.587137\pi$
$829$	−15.5676			−0.540684			−0.270342	+	0.962764i	$0.587137\pi$
$830$		0			0
$831$	19.0674	+	41.7518i	0.661440	+	1.44835i
$832$		0			0
$833$	8.15815	+	9.41501i	0.282663	+	0.326211i
$834$		0			0
$835$	18.5049	+	11.8924i	0.640390	+	0.411553i
$836$		0			0
$837$	−3.54423	+	4.09026i	−0.122506	+	0.141380i
$838$		0			0
$839$	5.68380	+	39.5317i	0.196227	+	1.36479i	0.815112	+	0.579304i	$0.196676\pi$
$839$	5.68380	+	39.5317i	0.196227	+	1.36479i	−0.618885	+	0.785482i	$0.712415\pi$
$840$		0			0
$841$	−22.9343	+	14.7390i	−0.790837	+	0.508240i
$842$		0			0
$843$	25.5198	−	55.8806i	0.878950	−	1.92463i
$844$		0			0
$845$	−0.993419	+	0.291694i	−0.0341747	+	0.0100346i
$846$		0			0
$847$	−1.40268	−	0.411864i	−0.0481967	−	0.0141518i
$848$		0			0
$849$	−1.57450	+	10.9509i	−0.0540367	+	0.375833i
$850$		0			0
$851$	1.50901	−	8.92242i	0.0517282	−	0.305857i
$852$		0			0
$853$	−1.92987	+	13.4226i	−0.0660775	+	0.459579i	0.929740	+	0.368216i	$0.120031\pi$
$853$	−1.92987	+	13.4226i	−0.0660775	+	0.459579i	−0.995818	+	0.0913630i	$0.970878\pi$
$854$		0			0
$855$	12.5700	+	3.69089i	0.429886	+	0.126226i
$856$		0			0
$857$	−9.99575	+	2.93502i	−0.341448	+	0.100258i	−0.447961	−	0.894053i	$-0.647850\pi$
$857$	−9.99575	+	2.93502i	−0.341448	+	0.100258i	0.106513	+	0.994311i	$0.466031\pi$
$858$		0			0
$859$	19.8050	−	43.3668i	0.675737	−	1.47966i	−0.191361	−	0.981520i	$-0.561290\pi$
$859$	19.8050	−	43.3668i	0.675737	−	1.47966i	0.867098	−	0.498138i	$-0.165983\pi$
$860$		0			0
$861$	−0.0153213	+	0.00984637i	−0.000522147	+	0.000335563i
$862$		0			0
$863$	6.18427	+	43.0125i	0.210515	+	1.46416i	0.771443	+	0.636299i	$0.219536\pi$
$863$	6.18427	+	43.0125i	0.210515	+	1.46416i	−0.560928	+	0.827865i	$0.689555\pi$
$864$		0			0
$865$	−4.90175	+	5.65692i	−0.166665	+	0.192341i
$866$		0			0
$867$	30.4336	+	19.5585i	1.03358	+	0.664241i
$868$		0			0
$869$	29.0095	+	33.4787i	0.984079	+	1.13569i
$870$		0			0
$871$	16.7909	+	36.7669i	0.568938	+	1.24580i
$872$		0			0
$873$	−24.7515			−0.837713
$874$		0			0
$875$	0.0647349			0.00218844
$876$		0			0
$877$	−18.9995	−	41.6032i	−0.641569	−	1.40484i	−0.898743	−	0.438475i	$-0.855519\pi$
$877$	−18.9995	−	41.6032i	−0.641569	−	1.40484i	0.257175	−	0.966365i	$-0.417208\pi$
$878$		0			0
$879$	−44.4477	−	51.2953i	−1.49918	−	1.73015i
$880$		0			0
$881$	1.82325	+	1.17173i	0.0614267	+	0.0394765i	0.570994	−	0.820954i	$-0.306558\pi$
$881$	1.82325	+	1.17173i	0.0614267	+	0.0394765i	−0.509567	+	0.860431i	$0.670194\pi$
$882$		0			0
$883$	20.5814	−	23.7522i	0.692619	−	0.799325i	−0.295116	−	0.955461i	$-0.595358\pi$
$883$	20.5814	−	23.7522i	0.692619	−	0.799325i	0.987736	+	0.156136i	$0.0499039\pi$
$884$		0			0
$885$	5.70029	+	39.6464i	0.191613	+	1.33270i
$886$		0			0
$887$	−38.3656	+	24.6560i	−1.28819	+	0.827869i	−0.991874	−	0.127221i	$-0.959394\pi$
$887$	−38.3656	+	24.6560i	−1.28819	+	0.827869i	−0.296315	+	0.955090i	$0.595758\pi$
$888$		0			0
$889$	−0.370944	+	0.812254i	−0.0124411	+	0.0272421i
$890$		0			0
$891$	32.0170	−	9.40104i	1.07261	−	0.314947i
$892$		0			0
$893$	2.87209	+	0.843322i	0.0961108	+	0.0282207i
$894$		0			0
$895$	−2.07886	+	14.4588i	−0.0694887	+	0.483305i
$896$		0			0
$897$	−46.9874	−	1.16274i	−1.56886	−	0.0388228i
$898$		0			0
$899$	0.460183	−	3.20064i	0.0153480	−	0.106747i
$900$		0			0
$901$	14.8854	+	4.37076i	0.495905	+	0.145611i
$902$		0			0
$903$	−0.116752	+	0.0342814i	−0.00388526	+	0.00114082i
$904$		0			0
$905$	4.39220	−	9.61758i	0.146002	−	0.319699i
$906$		0			0
$907$	34.7055	−	22.3039i	1.15238	−	0.740588i	0.182267	−	0.983249i	$-0.441657\pi$
$907$	34.7055	−	22.3039i	1.15238	−	0.740588i	0.970111	+	0.242661i	$0.0780202\pi$
$908$		0			0
$909$	6.21515	+	43.2273i	0.206144	+	1.43376i
$910$		0			0
$911$	31.5909	−	36.4578i	1.04665	−	1.20790i	0.0690133	−	0.997616i	$-0.478015\pi$
$911$	31.5909	−	36.4578i	1.04665	−	1.20790i	0.977640	−	0.210286i	$-0.0674397\pi$
$912$		0			0
$913$	−64.7998	−	41.6443i	−2.14456	−	1.37823i
$914$		0			0
$915$	2.28895	+	2.64159i	0.0756705	+	0.0873284i
$916$		0			0
$917$	−0.510653	−	1.11817i	−0.0168633	−	0.0369254i
$918$		0			0
$919$	35.7960			1.18080			0.590400	−	0.807111i	$-0.298970\pi$
$919$	35.7960			1.18080			0.590400	+	0.807111i	$0.298970\pi$
$920$		0			0
$921$	3.79452			0.125034
$922$		0			0
$923$	17.2663	+	37.8079i	0.568327	+	1.24446i
$924$		0			0
$925$	−1.23564	−	1.42600i	−0.0406276	−	0.0468867i
$926$		0			0
$927$	56.6280	+	36.3926i	1.85991	+	1.19529i
$928$		0			0
$929$	−15.2927	+	17.6487i	−0.501737	+	0.579035i	−0.948964	−	0.315386i	$-0.897866\pi$
$929$	−15.2927	+	17.6487i	−0.501737	+	0.579035i	0.447227	+	0.894420i	$0.352412\pi$
$930$		0			0
$931$	−3.39358	−	23.6029i	−0.111220	−	0.773553i
$932$		0			0
$933$	5.47573	−	3.51904i	0.179267	−	0.115208i
$934$		0			0
$935$	4.28692	−	9.38705i	0.140197	−	0.306989i
$936$		0			0
$937$	30.1775	−	8.86091i	0.985856	−	0.289473i	0.251216	−	0.967931i	$-0.419170\pi$
$937$	30.1775	−	8.86091i	0.985856	−	0.289473i	0.734639	+	0.678458i	$0.237351\pi$
$938$		0			0
$939$	48.5406	+	14.2528i	1.58406	+	0.465122i
$940$		0			0
$941$	−8.30548	+	57.7659i	−0.270751	+	1.88311i	0.169937	+	0.985455i	$0.445643\pi$
$941$	−8.30548	+	57.7659i	−0.270751	+	1.88311i	−0.440688	+	0.897660i	$0.645266\pi$
$942$		0			0
$943$	0.491129	+	0.157506i	0.0159934	+	0.00512912i
$944$		0			0
$945$	0.0203283	−	0.141386i	0.000661280	−	0.00459930i
$946$		0			0
$947$	−26.7574	−	7.85668i	−0.869498	−	0.255308i	−0.183596	−	0.983002i	$-0.558774\pi$
$947$	−26.7574	−	7.85668i	−0.869498	−	0.255308i	−0.685902	+	0.727694i	$0.740592\pi$
$948$		0			0
$949$	18.0649	−	5.30434i	0.586412	−	0.172186i
$950$		0			0
$951$	−9.77334	+	21.4006i	−0.316922	+	0.693963i
$952$		0			0
$953$	49.0251	−	31.5065i	1.58808	−	1.02060i	0.615464	−	0.788165i	$-0.288969\pi$
$953$	49.0251	−	31.5065i	1.58808	−	1.02060i	0.972613	−	0.232430i	$-0.0746678\pi$
$954$		0			0
$955$	−2.50129	−	17.3969i	−0.0809399	−	0.562949i
$956$		0			0
$957$	13.0878	−	15.1041i	0.423068	−	0.488246i
$958$		0			0
$959$	0.878059	+	0.564294i	0.0283540	+	0.0182220i
$960$		0			0
$961$	16.3609	+	18.8815i	0.527772	+	0.609081i
$962$		0			0
$963$	−19.6051	−	42.9293i	−0.631767	−	1.38338i
$964$		0			0
$965$	−12.8568			−0.413874
$966$		0			0
$967$	8.17064			0.262750			0.131375	−	0.991333i	$-0.458061\pi$
$967$	8.17064			0.262750			0.131375	+	0.991333i	$0.458061\pi$
$968$		0			0
$969$	6.59622	+	14.4437i	0.211901	+	0.463999i
$970$		0			0
$971$	−14.7465	−	17.0184i	−0.473239	−	0.546147i	0.468071	−	0.883691i	$-0.344949\pi$
$971$	−14.7465	−	17.0184i	−0.473239	−	0.546147i	−0.941310	+	0.337544i	$0.890404\pi$
$972$		0			0
$973$	1.03568	+	0.665593i	0.0332025	+	0.0213379i
$974$		0			0
$975$	−6.41799	+	7.40676i	−0.205540	+	0.237206i
$976$		0			0
$977$	3.20452	+	22.2879i	0.102522	+	0.713053i	0.974643	+	0.223764i	$0.0718346\pi$
$977$	3.20452	+	22.2879i	0.102522	+	0.713053i	−0.872122	+	0.489289i	$0.837256\pi$
$978$		0			0
$979$	11.5199	−	7.40341i	0.368179	−	0.236614i
$980$		0			0
$981$	17.3307	−	37.9490i	0.553327	−	1.21162i
$982$		0			0
$983$	−50.9802	+	14.9691i	−1.62602	+	0.477441i	−0.962626	−	0.270834i	$-0.912701\pi$
$983$	−50.9802	+	14.9691i	−1.62602	+	0.477441i	−0.663389	+	0.748275i	$0.730882\pi$
$984$		0			0
$985$	3.14129	+	0.922366i	0.100090	+	0.0293890i
$986$		0			0
$987$	0.0211648	−	0.147204i	0.000673682	−	0.00468556i
$988$		0			0
$989$	2.85194	+	1.93416i	0.0906865	+	0.0615029i
$990$		0			0
$991$	−5.42836	+	37.7551i	−0.172437	+	1.19933i	0.701277	+	0.712889i	$0.252614\pi$
$991$	−5.42836	+	37.7551i	−0.172437	+	1.19933i	−0.873714	+	0.486440i	$0.838295\pi$
$992$		0			0
$993$	−11.5660	−	3.39608i	−0.367035	−	0.107771i
$994$		0			0
$995$	−22.4397	+	6.58889i	−0.711386	+	0.208882i
$996$		0			0
$997$	14.4319	−	31.6014i	0.457062	−	1.00083i	−0.531085	−	0.847319i	$-0.678215\pi$
$997$	14.4319	−	31.6014i	0.457062	−	1.00083i	0.988147	−	0.153508i	$-0.0490572\pi$
$998$		0			0
$999$	−3.50253	+	2.25094i	−0.110815	+	0.0712165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.m.a.261.1	yes	30
23.3	even	11	inner	460.2.m.a.141.1	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.a.141.1	✓	30	23.3	even	11	inner
460.2.m.a.261.1	yes	30	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-1.08673 - 2.37960i) q^{3} +(-0.654861 - 0.755750i) q^{5} +(0.0544585 + 0.0349983i) q^{7} +(-2.51694 + 2.90471i) q^{9} +O(q^{10})\)	\(q+(-1.08673 - 2.37960i) q^{3} +(-0.654861 - 0.755750i) q^{5} +(0.0544585 + 0.0349983i) q^{7} +(-2.51694 + 2.90471i) q^{9} +(-0.824724 - 5.73608i) q^{11} +(-3.15165 + 2.02545i) q^{13} +(-1.08673 + 2.37960i) q^{15} +(-1.70862 + 0.501697i) q^{17} +(3.27048 + 0.960300i) q^{19} +(0.0241006 - 0.167623i) q^{21} +(-4.09742 + 2.49222i) q^{23} +(-0.142315 + 0.989821i) q^{25} +(2.11716 + 0.621655i) q^{27} +(-1.26492 + 0.371413i) q^{29} +(-1.01893 + 2.23114i) q^{31} +(-12.7533 + 8.19607i) q^{33} +(-0.00921274 - 0.0640760i) q^{35} +(-1.23564 + 1.42600i) q^{37} +(8.24474 + 5.29857i) q^{39} +(-0.0704270 - 0.0812771i) q^{41} +(-0.298488 - 0.653598i) q^{43} +3.84348 q^{45} +0.878185 q^{47} +(-2.90616 - 6.36361i) q^{49} +(3.05065 + 3.52064i) q^{51} +(-7.32895 - 4.71003i) q^{53} +(-3.79496 + 4.37962i) q^{55} +(-1.26899 - 8.82603i) q^{57} +(12.8806 - 8.27784i) q^{59} +(0.555050 - 1.21539i) q^{61} +(-0.238729 + 0.0700971i) q^{63} +(3.59462 + 1.05548i) q^{65} +(1.53543 - 10.6792i) q^{67} +(10.3833 + 7.04185i) q^{69} +(1.57890 - 10.9815i) q^{71} +(-4.82197 - 1.41586i) q^{73} +(2.51004 - 0.737014i) q^{75} +(0.155840 - 0.341242i) q^{77} +(-6.43071 + 4.13277i) q^{79} +(0.819465 + 5.69950i) q^{81} +(8.70437 - 10.0454i) q^{83} +(1.49807 + 0.962750i) q^{85} +(2.25843 + 2.60637i) q^{87} +(0.981628 + 2.14946i) q^{89} -0.242522 q^{91} +6.41651 q^{93} +(-1.41596 - 3.10053i) q^{95} +(4.21722 + 4.86694i) q^{97} +(18.7374 + 12.0418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) \) 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

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