LMFDB - Embedded newform 840.2.e.d.491.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(491,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.491"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [44,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			491.3
Character	$\chi$	$=$	840.491
Dual form			840.2.e.d.491.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39982 - 0.201241i) q^{2} +(-1.38582 + 1.03899i) q^{3} +(1.91900 + 0.563404i) q^{4} -1.00000 q^{5} +(2.14899 - 1.17551i) q^{6} +1.00000i q^{7} +(-2.57288 - 1.17485i) q^{8} +(0.841016 - 2.87970i) q^{9} +(1.39982 + 0.201241i) q^{10} -2.85691i q^{11} +(-3.24477 + 1.21304i) q^{12} +3.04377i q^{13} +(0.201241 - 1.39982i) q^{14} +(1.38582 - 1.03899i) q^{15} +(3.36515 + 2.16235i) q^{16} +1.28528i q^{17} +(-1.75679 + 3.86183i) q^{18} +3.94860 q^{19} +(-1.91900 - 0.563404i) q^{20} +(-1.03899 - 1.38582i) q^{21} +(-0.574929 + 3.99917i) q^{22} +6.49052 q^{23} +(4.78621 - 1.04506i) q^{24} +1.00000 q^{25} +(0.612531 - 4.26073i) q^{26} +(1.82647 + 4.86457i) q^{27} +(-0.563404 + 1.91900i) q^{28} -8.08470 q^{29} +(-2.14899 + 1.17551i) q^{30} -4.16256i q^{31} +(-4.27546 - 3.70411i) q^{32} +(2.96829 + 3.95918i) q^{33} +(0.258651 - 1.79916i) q^{34} -1.00000i q^{35} +(3.23635 - 5.05233i) q^{36} +4.91028i q^{37} +(-5.52733 - 0.794620i) q^{38} +(-3.16243 - 4.21812i) q^{39} +(2.57288 + 1.17485i) q^{40} +5.60633i q^{41} +(1.17551 + 2.14899i) q^{42} +0.729398 q^{43} +(1.60960 - 5.48243i) q^{44} +(-0.841016 + 2.87970i) q^{45} +(-9.08557 - 1.30616i) q^{46} +2.24535 q^{47} +(-6.91016 + 0.499713i) q^{48} -1.00000 q^{49} +(-1.39982 - 0.201241i) q^{50} +(-1.33539 - 1.78117i) q^{51} +(-1.71487 + 5.84100i) q^{52} -9.29752 q^{53} +(-1.57779 - 7.17709i) q^{54} +2.85691i q^{55} +(1.17485 - 2.57288i) q^{56} +(-5.47206 + 4.10254i) q^{57} +(11.3171 + 1.62698i) q^{58} +13.8177i q^{59} +(3.24477 - 1.21304i) q^{60} +6.42611i q^{61} +(-0.837678 + 5.82684i) q^{62} +(2.87970 + 0.841016i) q^{63} +(5.23947 + 6.04549i) q^{64} -3.04377i q^{65} +(-3.35833 - 6.13949i) q^{66} -10.4615 q^{67} +(-0.724130 + 2.46645i) q^{68} +(-8.99471 + 6.74356i) q^{69} +(-0.201241 + 1.39982i) q^{70} +7.47462 q^{71} +(-5.54705 + 6.42108i) q^{72} +6.39674 q^{73} +(0.988150 - 6.87351i) q^{74} +(-1.38582 + 1.03899i) q^{75} +(7.57737 + 2.22465i) q^{76} +2.85691 q^{77} +(3.57798 + 6.54103i) q^{78} +7.77084i q^{79} +(-3.36515 - 2.16235i) q^{80} +(-7.58538 - 4.84375i) q^{81} +(1.12822 - 7.84786i) q^{82} +4.35530i q^{83} +(-1.21304 - 3.24477i) q^{84} -1.28528i q^{85} +(-1.02103 - 0.146785i) q^{86} +(11.2040 - 8.39990i) q^{87} +(-3.35644 + 7.35051i) q^{88} +9.27251i q^{89} +(1.75679 - 3.86183i) q^{90} -3.04377 q^{91} +(12.4553 + 3.65678i) q^{92} +(4.32484 + 5.76857i) q^{93} +(-3.14310 - 0.451858i) q^{94} -3.94860 q^{95} +(9.77356 + 0.691099i) q^{96} -18.4478 q^{97} +(1.39982 + 0.201241i) q^{98} +(-8.22707 - 2.40271i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} + 4 q^{3} - 2 q^{4} - 44 q^{5} - 6 q^{6} - 22 q^{8} + 4 q^{9} - 2 q^{10} + 6 q^{12} + 4 q^{14} - 4 q^{15} + 22 q^{16} + 2 q^{18} + 16 q^{19} + 2 q^{20} + 16 q^{23} + 10 q^{24} + 44 q^{25}+ \cdots - 64 q^{99}+O(q^{100}) $ 44 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 - 44 * q^5 - 6 * q^6 - 22 * q^8 + 4 * q^9 - 2 * q^10 + 6 * q^12 + 4 * q^14 - 4 * q^15 + 22 * q^16 + 2 * q^18 + 16 * q^19 + 2 * q^20 + 16 * q^23 + 10 * q^24 + 44 * q^25 - 16 * q^26 + 4 * q^27 + 16 * q^29 + 6 * q^30 - 18 * q^32 + 24 * q^33 + 20 * q^34 - 46 * q^36 + 8 * q^38 - 16 * q^39 + 22 * q^40 - 4 * q^42 + 24 * q^43 + 32 * q^44 - 4 * q^45 - 24 * q^47 + 18 * q^48 - 44 * q^49 + 2 * q^50 - 20 * q^52 - 32 * q^53 + 2 * q^54 + 8 * q^56 - 4 * q^58 - 6 * q^60 + 32 * q^62 - 50 * q^64 - 8 * q^66 + 24 * q^67 - 28 * q^68 - 8 * q^69 - 4 * q^70 + 8 * q^71 + 2 * q^72 + 8 * q^73 - 48 * q^74 + 4 * q^75 + 12 * q^76 + 8 * q^77 - 84 * q^78 - 22 * q^80 + 20 * q^81 - 8 * q^82 + 4 * q^84 - 4 * q^86 - 16 * q^87 - 28 * q^88 - 2 * q^90 - 16 * q^91 + 76 * q^92 + 16 * q^93 - 16 * q^95 + 38 * q^96 + 24 * q^97 - 2 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$1$	$-1$	$1$	$-1$	$-1$

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 $

$2$	−1.39982	−	0.201241i	−0.989824	−	0.142299i
$2$	−1.39982	−	0.201241i	−0.989824	−	0.142299i
$3$	−1.38582	+	1.03899i	−0.800106	+	0.599859i
$3$	−1.38582	+	1.03899i	−0.800106	+	0.599859i
$4$	1.91900	+	0.563404i	0.959502	+	0.281702i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	2.14899	−	1.17551i	0.877323	−	0.479900i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−2.57288	−	1.17485i	−0.909652	−	0.415371i
$9$	0.841016	−	2.87970i	0.280339	−	0.959901i
$10$	1.39982	+	0.201241i	0.442663	+	0.0636380i
$11$		−	2.85691i		−	0.861392i	−0.902497	−	0.430696i	$-0.858268\pi$
$11$		−	2.85691i		−	0.861392i	0.902497	−	0.430696i	$-0.141732\pi$
$12$	−3.24477	+	1.21304i	−0.936684	+	0.350175i
$13$			3.04377i			0.844189i	0.906552	+	0.422094i	$0.138705\pi$
$13$			3.04377i			0.844189i	−0.906552	+	0.422094i	$0.861295\pi$
$14$	0.201241	−	1.39982i	0.0537840	−	0.374118i
$15$	1.38582	−	1.03899i	0.357818	−	0.268265i
$16$	3.36515	+	2.16235i	0.841288	+	0.540587i
$17$			1.28528i			0.311726i	0.987779	+	0.155863i	$0.0498158\pi$
$17$			1.28528i			0.311726i	−0.987779	+	0.155863i	$0.950184\pi$
$18$	−1.75679	+	3.86183i	−0.414079	+	0.910241i
$19$	3.94860			0.905870			0.452935	−	0.891543i	$-0.350377\pi$
$19$	3.94860			0.905870			0.452935	+	0.891543i	$0.350377\pi$
$20$	−1.91900	−	0.563404i	−0.429102	−	0.125981i
$21$	−1.03899	−	1.38582i	−0.226725	−	0.302412i
$22$	−0.574929	+	3.99917i	−0.122575	+	0.852626i
$23$	6.49052			1.35337			0.676683	−	0.736274i	$-0.263417\pi$
$23$	6.49052			1.35337			0.676683	+	0.736274i	$0.263417\pi$
$24$	4.78621	−	1.04506i	0.976982	−	0.213322i
$25$	1.00000			0.200000
$26$	0.612531	−	4.26073i	0.120127	−	0.835598i
$27$	1.82647	+	4.86457i	0.351505	+	0.936186i
$28$	−0.563404	+	1.91900i	−0.106473	+	0.362658i
$29$	−8.08470			−1.50129			−0.750646	−	0.660705i	$-0.770258\pi$
$29$	−8.08470			−1.50129			−0.750646	+	0.660705i	$0.770258\pi$
$30$	−2.14899	+	1.17551i	−0.392351	+	0.214618i
$31$		−	4.16256i		−	0.747617i	−0.927506	−	0.373809i	$-0.878052\pi$
$31$		−	4.16256i		−	0.747617i	0.927506	−	0.373809i	$-0.121948\pi$
$32$	−4.27546	−	3.70411i	−0.755802	−	0.654800i
$33$	2.96829	+	3.95918i	0.516714	+	0.689205i
$34$	0.258651	−	1.79916i	0.0443583	−	0.308554i
$35$		−	1.00000i		−	0.169031i
$36$	3.23635	−	5.05233i	0.539391	−	0.842055i
$37$			4.91028i			0.807245i	0.914926	+	0.403622i	$0.132249\pi$
$37$			4.91028i			0.807245i	−0.914926	+	0.403622i	$0.867751\pi$
$38$	−5.52733	−	0.794620i	−0.896652	−	0.128904i
$39$	−3.16243	−	4.21812i	−0.506394	−	0.675440i
$40$	2.57288	+	1.17485i	0.406809	+	0.185760i
$41$			5.60633i			0.875561i	0.899082	+	0.437781i	$0.144235\pi$
$41$			5.60633i			0.875561i	−0.899082	+	0.437781i	$0.855765\pi$
$42$	1.17551	+	2.14899i	0.181385	+	0.331597i
$43$	0.729398			0.111232			0.0556161	−	0.998452i	$-0.482288\pi$
$43$	0.729398			0.111232			0.0556161	+	0.998452i	$0.482288\pi$
$44$	1.60960	−	5.48243i	0.242656	−	0.826508i
$45$	−0.841016	+	2.87970i	−0.125371	+	0.429281i
$46$	−9.08557	−	1.30616i	−1.33959	−	0.192583i
$47$	2.24535			0.327519			0.163759	−	0.986500i	$-0.447638\pi$
$47$	2.24535			0.327519			0.163759	+	0.986500i	$0.447638\pi$
$48$	−6.91016	+	0.499713i	−0.997395	+	0.0721274i
$49$	−1.00000			−0.142857
$50$	−1.39982	−	0.201241i	−0.197965	−	0.0284598i
$51$	−1.33539	−	1.78117i	−0.186991	−	0.249414i
$52$	−1.71487	+	5.84100i	−0.237810	+	0.810001i
$53$	−9.29752			−1.27711			−0.638556	−	0.769575i	$-0.720468\pi$
$53$	−9.29752			−1.27711			−0.638556	+	0.769575i	$0.720468\pi$
$54$	−1.57779	−	7.17709i	−0.214709	−	0.976678i
$55$			2.85691i			0.385226i
$56$	1.17485	−	2.57288i	0.156996	−	0.343816i
$57$	−5.47206	+	4.10254i	−0.724792	+	0.543394i
$58$	11.3171	+	1.62698i	1.48601	+	0.213632i
$59$			13.8177i			1.79892i	0.437006	+	0.899459i	$0.356039\pi$
$59$			13.8177i			1.79892i	−0.437006	+	0.899459i	$0.643961\pi$
$60$	3.24477	−	1.21304i	0.418898	−	0.156603i
$61$			6.42611i			0.822779i	0.911460	+	0.411389i	$0.134956\pi$
$61$			6.42611i			0.822779i	−0.911460	+	0.411389i	$0.865044\pi$
$62$	−0.837678	+	5.82684i	−0.106385	+	0.740009i
$63$	2.87970	+	0.841016i	0.362809	+	0.105958i
$64$	5.23947	+	6.04549i	0.654933	+	0.755687i
$65$		−	3.04377i		−	0.377533i
$66$	−3.35833	−	6.13949i	−0.413382	−	0.755719i
$67$	−10.4615			−1.27807			−0.639035	−	0.769178i	$-0.720666\pi$
$67$	−10.4615			−1.27807			−0.639035	+	0.769178i	$0.720666\pi$
$68$	−0.724130	+	2.46645i	−0.0878137	+	0.299101i
$69$	−8.99471	+	6.74356i	−1.08284	+	0.811829i
$70$	−0.201241	+	1.39982i	−0.0240529	+	0.167311i
$71$	7.47462			0.887074			0.443537	−	0.896256i	$-0.353723\pi$
$71$	7.47462			0.887074			0.443537	+	0.896256i	$0.353723\pi$
$72$	−5.54705	+	6.42108i	−0.653726	+	0.756731i
$73$	6.39674			0.748681			0.374341	−	0.927291i	$-0.377869\pi$
$73$	6.39674			0.748681			0.374341	+	0.927291i	$0.377869\pi$
$74$	0.988150	−	6.87351i	0.114870	−	0.799030i
$75$	−1.38582	+	1.03899i	−0.160021	+	0.119972i
$76$	7.57737	+	2.22465i	0.869185	+	0.255185i
$77$	2.85691			0.325576
$78$	3.57798	+	6.54103i	0.405126	+	0.740626i
$79$			7.77084i			0.874288i	0.899392	+	0.437144i	$0.144010\pi$
$79$			7.77084i			0.874288i	−0.899392	+	0.437144i	$0.855990\pi$
$80$	−3.36515	−	2.16235i	−0.376235	−	0.241758i
$81$	−7.58538	−	4.84375i	−0.842821	−	0.538195i
$82$	1.12822	−	7.84786i	0.124591	−	0.866651i
$83$			4.35530i			0.478056i	0.971013	+	0.239028i	$0.0768288\pi$
$83$			4.35530i			0.478056i	−0.971013	+	0.239028i	$0.923171\pi$
$84$	−1.21304	−	3.24477i	−0.132354	−	0.354033i
$85$		−	1.28528i		−	0.139408i
$86$	−1.02103	−	0.146785i	−0.110100	−	0.0158282i
$87$	11.2040	−	8.39990i	1.20119	−	0.900563i
$88$	−3.35644	+	7.35051i	−0.357798	+	0.783567i
$89$			9.27251i			0.982884i	0.870910	+	0.491442i	$0.163530\pi$
$89$			9.27251i			0.982884i	−0.870910	+	0.491442i	$0.836470\pi$
$90$	1.75679	−	3.86183i	0.185182	−	0.407072i
$91$	−3.04377			−0.319073
$92$	12.4553	+	3.65678i	1.29856	+	0.381246i
$93$	4.32484	+	5.76857i	0.448465	+	0.598173i
$94$	−3.14310	−	0.451858i	−0.324186	−	0.0466056i
$95$	−3.94860			−0.405118
$96$	9.77356	+	0.691099i	0.997509	+	0.0705350i
$97$	−18.4478			−1.87310			−0.936548	−	0.350540i	$-0.885998\pi$
$97$	−18.4478			−1.87310			−0.936548	+	0.350540i	$0.885998\pi$
$98$	1.39982	+	0.201241i	0.141403	+	0.0203284i
$99$	−8.22707	−	2.40271i	−0.826851	−	0.241481i
$100$	1.91900	+	0.563404i	0.191900	+	0.0563404i
$101$	3.65249			0.363436			0.181718	−	0.983351i	$-0.441834\pi$
$101$	3.65249			0.363436			0.181718	+	0.983351i	$0.441834\pi$
$102$	1.51086	+	2.76205i	0.149597	+	0.273484i
$103$			11.1466i			1.09831i	0.835720	+	0.549156i	$0.185051\pi$
$103$			11.1466i			1.09831i	−0.835720	+	0.549156i	$0.814949\pi$
$104$	3.57596	−	7.83126i	0.350652	−	0.767918i
$105$	1.03899	+	1.38582i	0.101395	+	0.135243i
$106$	13.0149	+	1.87104i	1.26412	+	0.181732i
$107$			7.64658i			0.739223i	0.929186	+	0.369611i	$0.120509\pi$
$107$			7.64658i			0.739223i	−0.929186	+	0.369611i	$0.879491\pi$
$108$	0.764293	+	10.3642i	0.0735441	+	0.997292i
$109$			9.65989i			0.925249i	0.886554	+	0.462625i	$0.153092\pi$
$109$			9.65989i			0.925249i	−0.886554	+	0.462625i	$0.846908\pi$
$110$	0.574929	−	3.99917i	0.0548173	−	0.381306i
$111$	−5.10171	−	6.80478i	−0.484233	−	0.645881i
$112$	−2.16235	+	3.36515i	−0.204323	+	0.317977i
$113$			13.9427i			1.31162i	0.754926	+	0.655809i	$0.227673\pi$
$113$			13.9427i			1.31162i	−0.754926	+	0.655809i	$0.772327\pi$
$114$	8.48551	−	4.64162i	0.794741	−	0.434728i
$115$	−6.49052			−0.605244
$116$	−15.5146	−	4.55495i	−1.44049	−	0.422917i
$117$	8.76514	+	2.55986i	0.810338	+	0.236659i
$118$	2.78070	−	19.3424i	0.255984	−	1.78061i
$119$	−1.28528			−0.117821
$120$	−4.78621	+	1.04506i	−0.436920	+	0.0954004i
$121$	2.83804			0.258003
$122$	1.29320	−	8.99541i	0.117081	−	0.814406i
$123$	−5.82490	−	7.76938i	−0.525213	−	0.700542i
$124$	2.34520	−	7.98796i	0.210605	−	0.717340i
$125$	−1.00000			−0.0894427
$126$	−3.86183	−	1.75679i	−0.344039	−	0.156507i
$127$		−	18.5692i		−	1.64775i	−0.566770	−	0.823876i	$-0.691807\pi$
$127$		−	18.5692i		−	1.64775i	0.566770	−	0.823876i	$-0.308193\pi$
$128$	−6.11772	−	9.51701i	−0.540735	−	0.841193i
$129$	−1.01082	+	0.757834i	−0.0889975	+	0.0667236i
$130$	−0.612531	+	4.26073i	−0.0537225	+	0.373691i
$131$		−	12.8703i		−	1.12448i	−0.826974	−	0.562241i	$-0.809939\pi$
$131$		−	12.8703i		−	1.12448i	0.826974	−	0.562241i	$-0.190061\pi$
$132$	3.46555	+	9.27003i	0.301638	+	0.806853i
$133$			3.94860i			0.342387i
$134$	14.6442	+	2.10527i	1.26506	+	0.181868i
$135$	−1.82647	−	4.86457i	−0.157198	−	0.418675i
$136$	1.51001	−	3.30687i	0.129482	−	0.283562i
$137$			11.4022i			0.974159i	0.873358	+	0.487080i	$0.161938\pi$
$137$			11.4022i			0.974159i	−0.873358	+	0.487080i	$0.838062\pi$
$138$	13.9481	−	7.62967i	1.18734	−	0.649481i
$139$	6.49495			0.550894			0.275447	−	0.961316i	$-0.411174\pi$
$139$	6.49495			0.550894			0.275447	+	0.961316i	$0.411174\pi$
$140$	0.563404	−	1.91900i	0.0476163	−	0.162185i
$141$	−3.11167	+	2.33289i	−0.262050	+	0.196465i
$142$	−10.4631	−	1.50420i	−0.878047	−	0.126230i
$143$	8.69578			0.727178
$144$	9.05707	−	7.87207i	0.754756	−	0.656006i
$145$	8.08470			0.671398
$146$	−8.95429	−	1.28729i	−0.741063	−	0.106537i
$147$	1.38582	−	1.03899i	0.114301	−	0.0856941i
$148$	−2.76647	+	9.42284i	−0.227402	+	0.774553i
$149$	−0.0620351			−0.00508211			−0.00254106	−	0.999997i	$-0.500809\pi$
$149$	−0.0620351			−0.00508211			−0.00254106	+	0.999997i	$0.500809\pi$
$150$	2.14899	−	1.17551i	0.175465	−	0.0959801i
$151$		−	10.0164i		−	0.815125i	−0.913177	−	0.407563i	$-0.866379\pi$
$151$		−	10.0164i		−	0.815125i	0.913177	−	0.407563i	$-0.133621\pi$
$152$	−10.1593	−	4.63900i	−0.824027	−	0.376273i
$153$	3.70122	+	1.08094i	0.299226	+	0.0873887i
$154$	−3.99917	−	0.574929i	−0.322263	−	0.0463291i
$155$			4.16256i			0.334344i
$156$	−3.69221	−	9.87632i	−0.295613	−	0.790739i
$157$		−	3.29079i		−	0.262634i	−0.991340	−	0.131317i	$-0.958079\pi$
$157$		−	3.29079i		−	0.262634i	0.991340	−	0.131317i	$-0.0419205\pi$
$158$	1.56381	−	10.8778i	0.124410	−	0.865391i
$159$	12.8847	−	9.66000i	1.02183	−	0.766088i
$160$	4.27546	+	3.70411i	0.338005	+	0.292836i
$161$			6.49052i			0.511524i
$162$	9.64343	+	8.30688i	0.757659	+	0.652650i
$163$	−15.2336			−1.19318			−0.596592	−	0.802544i	$-0.703479\pi$
$163$	−15.2336			−1.19318			−0.596592	+	0.802544i	$0.703479\pi$
$164$	−3.15863	+	10.7586i	−0.246647	+	0.840103i
$165$	−2.96829	−	3.95918i	−0.231081	−	0.308222i
$166$	0.876465	−	6.09664i	0.0680269	−	0.473191i
$167$	12.3172			0.953130			0.476565	−	0.879139i	$-0.341882\pi$
$167$	12.3172			0.953130			0.476565	+	0.879139i	$0.341882\pi$
$168$	1.04506	+	4.78621i	0.0806281	+	0.369264i
$169$	3.73549			0.287345
$170$	−0.258651	+	1.79916i	−0.0198376	+	0.137989i
$171$	3.32083	−	11.3708i	0.253950	−	0.869546i
$172$	1.39972	+	0.410946i	0.106727	+	0.0313343i
$173$	11.6711			0.887339			0.443670	−	0.896190i	$-0.353676\pi$
$173$	11.6711			0.887339			0.443670	+	0.896190i	$0.353676\pi$
$174$	−17.3740	+	9.50366i	−1.31712	+	0.720470i
$175$			1.00000i			0.0755929i
$176$	6.17764	−	9.61395i	0.465657	−	0.724679i
$177$	−14.3564	−	19.1490i	−1.07910	−	1.43932i
$178$	1.86601	−	12.9799i	0.139863	−	0.972882i
$179$			9.73630i			0.727725i	0.931453	+	0.363863i	$0.118542\pi$
$179$			9.73630i			0.727725i	−0.931453	+	0.363863i	$0.881458\pi$
$180$	−3.23635	+	5.05233i	−0.241223	+	0.376579i
$181$		−	18.2683i		−	1.35787i	−0.734198	−	0.678935i	$-0.762442\pi$
$181$		−	18.2683i		−	1.35787i	0.734198	−	0.678935i	$-0.237558\pi$
$182$	4.26073	+	0.612531i	0.315826	+	0.0454038i
$183$	−6.67664	−	8.90546i	−0.493551	−	0.658310i
$184$	−16.6993	−	7.62537i	−1.23109	−	0.562149i
$185$		−	4.91028i		−	0.361011i
$186$	−4.89313	−	8.94531i	−0.358782	−	0.655902i
$187$	3.67193			0.268518
$188$	4.30884	+	1.26504i	0.314255	+	0.0922626i
$189$	−4.86457	+	1.82647i	−0.353845	+	0.132856i
$190$	5.52733	+	0.794620i	0.400995	+	0.0576478i
$191$	10.5098			0.760460			0.380230	−	0.924892i	$-0.375845\pi$
$191$	10.5098			0.760460			0.380230	+	0.924892i	$0.375845\pi$
$192$	−13.5422	−	2.93426i	−0.977321	−	0.211762i
$193$	−10.4765			−0.754118			−0.377059	−	0.926189i	$-0.623065\pi$
$193$	−10.4765			−0.754118			−0.377059	+	0.926189i	$0.623065\pi$
$194$	25.8237	+	3.71247i	1.85403	+	0.266540i
$195$	3.16243	+	4.21812i	0.226466	+	0.302066i
$196$	−1.91900	−	0.563404i	−0.137072	−	0.0402431i
$197$	11.0037			0.783985			0.391992	−	0.919968i	$-0.371786\pi$
$197$	11.0037			0.783985			0.391992	+	0.919968i	$0.371786\pi$
$198$	11.0329	+	5.01899i	0.784075	+	0.356684i
$199$			20.7285i			1.46940i	0.678392	+	0.734701i	$0.262677\pi$
$199$			20.7285i			1.46940i	−0.678392	+	0.734701i	$0.737323\pi$
$200$	−2.57288	−	1.17485i	−0.181930	−	0.0830743i
$201$	14.4977	−	10.8693i	1.02259	−	0.766662i
$202$	−5.11283	−	0.735031i	−0.359738	−	0.0517166i
$203$		−	8.08470i		−	0.567435i
$204$	−1.55909	−	4.17043i	−0.109158	−	0.291989i
$205$		−	5.60633i		−	0.391563i
$206$	2.24316	−	15.6033i	0.156289	−	1.08714i
$207$	5.45863	−	18.6908i	0.379401	−	1.29910i
$208$	−6.58168	+	10.2427i	−0.456357	+	0.710206i
$209$		−	11.2808i		−	0.780310i
$210$	−1.17551	−	2.14899i	−0.0811180	−	0.148295i
$211$	23.1084			1.59085			0.795423	−	0.606055i	$-0.207249\pi$
$211$	23.1084			1.59085			0.795423	+	0.606055i	$0.207249\pi$
$212$	−17.8420	−	5.23826i	−1.22539	−	0.359765i
$213$	−10.3585	+	7.76603i	−0.709753	+	0.532119i
$214$	1.53881	−	10.7039i	0.105191	−	0.731700i
$215$	−0.729398			−0.0497445
$216$	1.01582	−	14.6618i	0.0691179	−	0.997608i
$217$	4.16256			0.282573
$218$	1.94397	−	13.5221i	0.131662	−	0.915834i
$219$	−8.86475	+	6.64612i	−0.599024	+	0.449103i
$220$	−1.60960	+	5.48243i	−0.108519	+	0.369625i
$221$	−3.91209			−0.263155
$222$	5.77208	+	10.5522i	0.387397	+	0.708214i
$223$		−	14.3613i		−	0.961702i	−0.876802	−	0.480851i	$-0.840328\pi$
$223$		−	14.3613i		−	0.961702i	0.876802	−	0.480851i	$-0.159672\pi$
$224$	3.70411	−	4.27546i	0.247491	−	0.285666i
$225$	0.841016	−	2.87970i	0.0560677	−	0.191980i
$226$	2.80585	−	19.5173i	0.186642	−	1.29827i
$227$		−	21.6874i		−	1.43944i	−0.694262	−	0.719722i	$-0.744269\pi$
$227$		−	21.6874i		−	1.43944i	0.694262	−	0.719722i	$-0.255731\pi$
$228$	−12.8123	+	4.78981i	−0.848515	+	0.317213i
$229$			13.2057i			0.872658i	0.899787	+	0.436329i	$0.143722\pi$
$229$			13.2057i			0.872658i	−0.899787	+	0.436329i	$0.856278\pi$
$230$	9.08557	+	1.30616i	0.599085	+	0.0861256i
$231$	−3.95918	+	2.96829i	−0.260495	+	0.195299i
$232$	20.8010	+	9.49830i	1.36565	+	0.623594i
$233$		−	20.2597i		−	1.32725i	−0.748063	−	0.663627i	$-0.769016\pi$
$233$		−	20.2597i		−	1.32725i	0.748063	−	0.663627i	$-0.230984\pi$
$234$	−11.7545	−	5.34725i	−0.768415	−	0.349561i
$235$	−2.24535			−0.146471
$236$	−7.78497	+	26.5163i	−0.506758	+	1.72606i
$237$	−8.07379	−	10.7690i	−0.524449	−	0.699523i
$238$	1.79916	+	0.258651i	0.116622	+	0.0167658i
$239$	−12.8981			−0.834311			−0.417155	−	0.908835i	$-0.636973\pi$
$239$	−12.8981			−0.834311			−0.417155	+	0.908835i	$0.636973\pi$
$240$	6.91016	−	0.499713i	0.446049	−	0.0322563i
$241$	−20.5868			−1.32611			−0.663055	−	0.748571i	$-0.730740\pi$
$241$	−20.5868			−1.32611			−0.663055	+	0.748571i	$0.730740\pi$
$242$	−3.97275	−	0.571130i	−0.255378	−	0.0367136i
$243$	15.5446	−	1.16852i	0.997186	−	0.0749607i
$244$	−3.62049	+	12.3317i	−0.231778	+	0.789458i
$245$	1.00000			0.0638877
$246$	6.59030	+	12.0480i	0.420182	+	0.768150i
$247$			12.0186i			0.764726i
$248$	−4.89037	+	10.7098i	−0.310539	+	0.680071i
$249$	−4.52509	−	6.03567i	−0.286766	−	0.382495i
$250$	1.39982	+	0.201241i	0.0885325	+	0.0127276i
$251$			13.9970i			0.883480i	0.897143	+	0.441740i	$0.145639\pi$
$251$			13.9970i			0.883480i	−0.897143	+	0.441740i	$0.854361\pi$
$252$	5.05233	+	3.23635i	0.318267	+	0.203871i
$253$		−	18.5428i		−	1.16578i
$254$	−3.73689	+	25.9936i	−0.234473	+	1.63098i
$255$	1.33539	+	1.78117i	0.0836251	+	0.111541i
$256$	6.64850	+	14.5533i	0.415531	+	0.909579i
$257$			29.6479i			1.84938i	0.380717	+	0.924692i	$0.375677\pi$
$257$			29.6479i			1.84938i	−0.380717	+	0.924692i	$0.624323\pi$
$258$	1.56747	−	0.857415i	0.0975865	−	0.0533803i
$259$	−4.91028			−0.305110
$260$	1.71487	−	5.84100i	0.106352	−	0.362243i
$261$	−6.79936	+	23.2816i	−0.420870	+	1.44109i
$262$	−2.59003	+	18.0161i	−0.160013	+	1.11304i
$263$	−29.4334			−1.81494			−0.907471	−	0.420114i	$-0.861990\pi$
$263$	−29.4334			−1.81494			−0.907471	+	0.420114i	$0.861990\pi$
$264$	−2.98564	−	13.6738i	−0.183754	−	0.841565i
$265$	9.29752			0.571142
$266$	0.794620	−	5.52733i	0.0487213	−	0.338903i
$267$	−9.63401	−	12.8501i	−0.589592	−	0.786411i
$268$	−20.0756	−	5.89402i	−1.22631	−	0.360035i
$269$	2.30022			0.140247			0.0701234	−	0.997538i	$-0.477661\pi$
$269$	2.30022			0.140247			0.0701234	+	0.997538i	$0.477661\pi$
$270$	1.57779	+	7.17709i	0.0960209	+	0.436784i
$271$		−	5.90367i		−	0.358623i	−0.983792	−	0.179311i	$-0.942613\pi$
$271$		−	5.90367i		−	0.358623i	0.983792	−	0.179311i	$-0.0573869\pi$
$272$	−2.77922	+	4.32516i	−0.168515	+	0.262251i
$273$	4.21812	−	3.16243i	0.255292	−	0.191399i
$274$	2.29460	−	15.9611i	0.138622	−	0.964246i
$275$		−	2.85691i		−	0.172278i
$276$	−21.0602	+	7.87326i	−1.26768	+	0.473914i
$277$		−	7.11393i		−	0.427435i	−0.976896	−	0.213717i	$-0.931443\pi$
$277$		−	7.11393i		−	0.427435i	0.976896	−	0.213717i	$-0.0685572\pi$
$278$	−9.09177	−	1.30705i	−0.545288	−	0.0783917i
$279$	−11.9869	−	3.50077i	−0.717638	−	0.209586i
$280$	−1.17485	+	2.57288i	−0.0702106	+	0.153759i
$281$		−	6.26029i		−	0.373458i	−0.982412	−	0.186729i	$-0.940211\pi$
$281$		−	6.26029i		−	0.373458i	0.982412	−	0.186729i	$-0.0597886\pi$
$282$	4.82525	−	2.63944i	0.287340	−	0.157176i
$283$	5.22868			0.310813			0.155406	−	0.987851i	$-0.450331\pi$
$283$	5.22868			0.310813			0.155406	+	0.987851i	$0.450331\pi$
$284$	14.3438	+	4.21123i	0.851150	+	0.249890i
$285$	5.47206	−	4.10254i	0.324137	−	0.243013i
$286$	−12.1725	−	1.74995i	−0.719778	−	0.103477i
$287$	−5.60633			−0.330931
$288$	−14.2625	+	9.19685i	−0.840424	+	0.541929i
$289$	15.3481			0.902827
$290$	−11.3171	−	1.62698i	−0.664566	−	0.0955393i
$291$	25.5655	−	19.1671i	1.49867	−	1.12359i
$292$	12.2754	+	3.60395i	0.718361	+	0.210905i
$293$	−6.39839			−0.373798			−0.186899	−	0.982379i	$-0.559844\pi$
$293$	−6.39839			−0.373798			−0.186899	+	0.982379i	$0.559844\pi$
$294$	−2.14899	+	1.17551i	−0.125332	+	0.0685572i
$295$		−	13.8177i		−	0.804500i
$296$	5.76883	−	12.6336i	0.335306	−	0.734312i
$297$	13.8976	−	5.21808i	0.806423	−	0.302783i
$298$	0.0868381	+	0.0124840i	0.00503039	+	0.000723179i
$299$			19.7556i			1.14250i
$300$	−3.24477	+	1.21304i	−0.187337	+	0.0700349i
$301$			0.729398i			0.0420418i
$302$	−2.01572	+	14.0212i	−0.115992	+	0.806830i
$303$	−5.06170	+	3.79488i	−0.290787	+	0.218010i
$304$	13.2876	+	8.53824i	0.762098	+	0.489702i
$305$		−	6.42611i		−	0.367958i
$306$	−4.96352	−	2.25796i	−0.283746	−	0.129079i
$307$	21.1230			1.20555			0.602776	−	0.797910i	$-0.294061\pi$
$307$	21.1230			1.20555			0.602776	+	0.797910i	$0.294061\pi$
$308$	5.48243	+	1.60960i	0.312390	+	0.0917153i
$309$	−11.5812	−	15.4473i	−0.658832	−	0.878766i
$310$	0.837678	−	5.82684i	0.0475769	−	0.330942i
$311$	3.94554			0.223731			0.111866	−	0.993723i	$-0.464317\pi$
$311$	3.94554			0.223731			0.111866	+	0.993723i	$0.464317\pi$
$312$	3.18092	+	14.5681i	0.180084	+	0.824757i
$313$	16.8063			0.949948			0.474974	−	0.880000i	$-0.342457\pi$
$313$	16.8063			0.949948			0.474974	+	0.880000i	$0.342457\pi$
$314$	−0.662242	+	4.60652i	−0.0373725	+	0.259961i
$315$	−2.87970	−	0.841016i	−0.162253	−	0.0473859i
$316$	−4.37812	+	14.9123i	−0.246288	+	0.838881i
$317$	9.68195			0.543792			0.271896	−	0.962327i	$-0.412349\pi$
$317$	9.68195			0.543792			0.271896	+	0.962327i	$0.412349\pi$
$318$	−19.9803	+	10.9293i	−1.12044	+	0.612887i
$319$			23.0973i			1.29320i
$320$	−5.23947	−	6.04549i	−0.292895	−	0.337953i
$321$	−7.94469	−	10.5968i	−0.443429	−	0.591456i
$322$	1.30616	−	9.08557i	0.0727894	−	0.506319i
$323$			5.07505i			0.282383i
$324$	−11.8274	−	13.5688i	−0.657078	−	0.753823i
$325$			3.04377i			0.168838i
$326$	21.3243	+	3.06562i	1.18104	+	0.169789i
$327$	−10.0365	−	13.3869i	−0.555019	−	0.740297i
$328$	6.58658	−	14.4244i	0.363683	−	0.796456i
$329$			2.24535i			0.123790i
$330$	3.35833	+	6.13949i	0.184870	+	0.337968i
$331$	26.0727			1.43309			0.716543	−	0.697543i	$-0.245724\pi$
$331$	26.0727			1.43309			0.716543	+	0.697543i	$0.245724\pi$
$332$	−2.45379	+	8.35783i	−0.134669	+	0.458696i
$333$	14.1401	+	4.12962i	0.774875	+	0.226302i
$334$	−17.2418	−	2.47872i	−0.943430	−	0.135629i
$335$	10.4615			0.571570
$336$	−0.499713	−	6.91016i	−0.0272616	−	0.376980i
$337$	26.0027			1.41646			0.708228	−	0.705984i	$-0.249495\pi$
$337$	26.0027			1.41646			0.708228	+	0.705984i	$0.249495\pi$
$338$	−5.22902	−	0.751734i	−0.284421	−	0.0408889i
$339$	−14.4863	−	19.3221i	−0.786786	−	1.04943i
$340$	0.724130	−	2.46645i	0.0392715	−	0.133762i
$341$	−11.8921			−0.643991
$342$	−6.93685	+	15.2488i	−0.375102	+	0.824560i
$343$		−	1.00000i		−	0.0539949i
$344$	−1.87666	−	0.856932i	−0.101183	−	0.0462027i
$345$	8.99471	−	6.74356i	0.484259	−	0.363061i
$346$	−16.3375	−	2.34871i	−0.878309	−	0.126267i
$347$			24.3234i			1.30575i	0.757466	+	0.652874i	$0.226437\pi$
$347$			24.3234i			1.30575i	−0.757466	+	0.652874i	$0.773563\pi$
$348$	26.2330	−	9.80707i	1.40624	−	0.525714i
$349$			23.4782i			1.25676i	0.777906	+	0.628381i	$0.216282\pi$
$349$			23.4782i			1.25676i	−0.777906	+	0.628381i	$0.783718\pi$
$350$	0.201241	−	1.39982i	0.0107568	−	0.0748236i
$351$	−14.8066	+	5.55935i	−0.790318	+	0.296736i
$352$	−10.5823	+	12.2146i	−0.564040	+	0.651042i
$353$			1.69751i			0.0903495i	0.998979	+	0.0451747i	$0.0143845\pi$
$353$			1.69751i			0.0903495i	−0.998979	+	0.0451747i	$0.985616\pi$
$354$	16.2429	+	29.6942i	0.863301	+	1.57823i
$355$	−7.47462			−0.396712
$356$	−5.22417	+	17.7940i	−0.276880	+	0.943079i
$357$	1.78117	−	1.33539i	0.0942695	−	0.0706761i
$358$	1.95934	−	13.6291i	0.103555	−	0.720320i
$359$	4.28103			0.225944			0.112972	−	0.993598i	$-0.463963\pi$
$359$	4.28103			0.225944			0.112972	+	0.993598i	$0.463963\pi$
$360$	5.54705	−	6.42108i	0.292355	−	0.338421i
$361$	−3.40858			−0.179399
$362$	−3.67633	+	25.5723i	−0.193224	+	1.34405i
$363$	−3.93302	+	2.94868i	−0.206430	+	0.154766i
$364$	−5.84100	−	1.71487i	−0.306152	−	0.0898836i
$365$	−6.39674			−0.334821
$366$	7.55396	+	13.8097i	0.394852	+	0.721843i
$367$			32.0443i			1.67270i	0.548195	+	0.836351i	$0.315315\pi$
$367$			32.0443i			1.67270i	−0.548195	+	0.836351i	$0.684685\pi$
$368$	21.8416	+	14.0348i	1.13857	+	0.731612i
$369$	16.1446	+	4.71501i	0.840452	+	0.245454i
$370$	−0.988150	+	6.87351i	−0.0513715	+	0.357337i
$371$		−	9.29752i		−	0.482703i
$372$	5.04935	+	13.5065i	0.261796	+	0.700281i
$373$			21.9064i			1.13427i	0.823624	+	0.567136i	$0.191949\pi$
$373$			21.9064i			1.13427i	−0.823624	+	0.567136i	$0.808051\pi$
$374$	−5.14005	−	0.738944i	−0.265786	−	0.0382099i
$375$	1.38582	−	1.03899i	0.0715636	−	0.0536530i
$376$	−5.77704	−	2.63795i	−0.297928	−	0.136042i
$377$		−	24.6079i		−	1.26737i
$378$	7.17709	−	1.57779i	0.369150	−	0.0811525i
$379$	−21.0759			−1.08260			−0.541299	−	0.840830i	$-0.682067\pi$
$379$	−21.0759			−1.08260			−0.541299	+	0.840830i	$0.682067\pi$
$380$	−7.57737	−	2.22465i	−0.388711	−	0.114122i
$381$	19.2932	+	25.7337i	0.988419	+	1.31838i
$382$	−14.7118	−	2.11500i	−0.752721	−	0.108213i
$383$	17.9894			0.919213			0.459607	−	0.888123i	$-0.347990\pi$
$383$	17.9894			0.919213			0.459607	+	0.888123i	$0.347990\pi$
$384$	18.3661	+	6.83268i	0.937242	+	0.348679i
$385$	−2.85691			−0.145602
$386$	14.6653	+	2.10831i	0.746444	+	0.107310i
$387$	0.613435	−	2.10045i	0.0311827	−	0.106772i
$388$	−35.4015	−	10.3936i	−1.79724	−	0.527654i
$389$	6.91343			0.350525			0.175262	−	0.984522i	$-0.443923\pi$
$389$	6.91343			0.350525			0.175262	+	0.984522i	$0.443923\pi$
$390$	−3.57798	−	6.54103i	−0.181178	−	0.331218i
$391$			8.34212i			0.421879i
$392$	2.57288	+	1.17485i	0.129950	+	0.0593388i
$393$	13.3720	+	17.8359i	0.674530	+	0.899704i
$394$	−15.4033	−	2.21441i	−0.776007	−	0.111560i
$395$		−	7.77084i		−	0.390993i
$396$	−14.4341	−	9.24597i	−0.725340	−	0.464628i
$397$		−	31.2585i		−	1.56882i	−0.620244	−	0.784409i	$-0.712966\pi$
$397$		−	31.2585i		−	1.56882i	0.620244	−	0.784409i	$-0.287034\pi$
$398$	4.17142	−	29.0161i	0.209094	−	1.45445i
$399$	−4.10254	−	5.47206i	−0.205384	−	0.273946i
$400$	3.36515	+	2.16235i	0.168258	+	0.108117i
$401$			21.4911i			1.07321i	0.843832	+	0.536607i	$0.180294\pi$
$401$			21.4911i			1.07321i	−0.843832	+	0.536607i	$0.819706\pi$
$402$	−22.4816	+	12.2976i	−1.12128	+	0.613346i
$403$	12.6698			0.631130
$404$	7.00914	+	2.05783i	0.348718	+	0.102381i
$405$	7.58538	+	4.84375i	0.376921	+	0.240688i
$406$	−1.62698	+	11.3171i	−0.0807454	+	0.561661i
$407$	14.0282			0.695354
$408$	1.34319	+	6.15162i	0.0664979	+	0.304550i
$409$	6.16866			0.305021			0.152510	−	0.988302i	$-0.451264\pi$
$409$	6.16866			0.305021			0.152510	+	0.988302i	$0.451264\pi$
$410$	−1.12822	+	7.84786i	−0.0557190	+	0.387578i
$411$	−11.8468	−	15.8015i	−0.584358	−	0.779430i
$412$	−6.28006	+	21.3905i	−0.309396	+	1.05383i
$413$	−13.8177			−0.679927
$414$	−11.4025	+	25.0652i	−0.560400	+	1.23189i
$415$		−	4.35530i		−	0.213793i
$416$	11.2744	−	13.0135i	0.552775	−	0.638040i
$417$	−9.00085	+	6.74816i	−0.440774	+	0.330459i
$418$	−2.27016	+	15.7911i	−0.111037	+	0.772369i
$419$			28.6257i			1.39846i	0.714899	+	0.699228i	$0.246473\pi$
$419$			28.6257i			1.39846i	−0.714899	+	0.699228i	$0.753527\pi$
$420$	1.21304	+	3.24477i	0.0591903	+	0.158329i
$421$		−	37.0133i		−	1.80392i	−0.431823	−	0.901958i	$-0.642129\pi$
$421$		−	37.0133i		−	1.80392i	0.431823	−	0.901958i	$-0.357871\pi$
$422$	−32.3476	−	4.65035i	−1.57466	−	0.226376i
$423$	1.88838	−	6.46595i	0.0918161	−	0.314385i
$424$	23.9214	+	10.9232i	1.16173	+	0.530476i
$425$			1.28528i			0.0623451i
$426$	16.0629	−	8.78650i	0.778251	−	0.425707i
$427$	−6.42611			−0.310981
$428$	−4.30811	+	14.6738i	−0.208240	+	0.709286i
$429$	−12.0508	+	9.03480i	−0.581819	+	0.436204i
$430$	1.02103	+	0.146785i	0.0492383	+	0.00707860i
$431$	−17.5103			−0.843442			−0.421721	−	0.906726i	$-0.638574\pi$
$431$	−17.5103			−0.843442			−0.421721	+	0.906726i	$0.638574\pi$
$432$	−4.37253	+	20.3195i	−0.210373	+	0.977621i
$433$	−37.2684			−1.79101			−0.895503	−	0.445055i	$-0.853184\pi$
$433$	−37.2684			−1.79101			−0.895503	+	0.445055i	$0.853184\pi$
$434$	−5.82684	−	0.837678i	−0.279697	−	0.0402098i
$435$	−11.2040	+	8.39990i	−0.537190	+	0.402744i
$436$	−5.44242	+	18.5374i	−0.260644	+	0.887779i
$437$	25.6284			1.22597
$438$	13.7465	−	7.51943i	0.656835	−	0.359292i
$439$			11.5022i			0.548972i	0.961591	+	0.274486i	$0.0885077\pi$
$439$			11.5022i			0.548972i	−0.961591	+	0.274486i	$0.911492\pi$
$440$	3.35644	−	7.35051i	0.160012	−	0.350422i
$441$	−0.841016	+	2.87970i	−0.0400484	+	0.137129i
$442$	5.47622	+	0.787273i	0.260477	+	0.0374467i
$443$		−	18.7110i		−	0.888989i	−0.895782	−	0.444494i	$-0.853383\pi$
$443$		−	18.7110i		−	0.888989i	0.895782	−	0.444494i	$-0.146617\pi$
$444$	−5.95636	−	15.9327i	−0.282676	−	0.756133i
$445$		−	9.27251i		−	0.439559i
$446$	−2.89008	+	20.1032i	−0.136849	+	0.951916i
$447$	0.0859697	−	0.0644536i	0.00406623	−	0.00304855i
$448$	−6.04549	+	5.23947i	−0.285623	+	0.247542i
$449$		−	28.1448i		−	1.32824i	−0.747628	−	0.664118i	$-0.768807\pi$
$449$		−	28.1448i		−	1.32824i	0.747628	−	0.664118i	$-0.231193\pi$
$450$	−1.75679	+	3.86183i	−0.0828158	+	0.182048i
$451$	16.0168			0.754202
$452$	−7.85537	+	26.7561i	−0.369485	+	1.25850i
$453$	10.4069	+	13.8810i	0.488960	+	0.652186i
$454$	−4.36440	+	30.3585i	−0.204832	+	1.42480i
$455$	3.04377			0.142694
$456$	18.8988	−	4.12652i	0.885019	−	0.193242i
$457$	−8.45271			−0.395401			−0.197700	−	0.980262i	$-0.563347\pi$
$457$	−8.45271			−0.395401			−0.197700	+	0.980262i	$0.563347\pi$
$458$	2.65753	−	18.4856i	0.124178	−	0.863777i
$459$	−6.25232	+	2.34752i	−0.291833	+	0.109573i
$460$	−12.4553	−	3.65678i	−0.580733	−	0.170498i
$461$	−7.28165			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$461$	−7.28165			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$462$	6.13949	−	3.35833i	0.285635	−	0.156244i
$463$			5.39911i			0.250918i	0.992099	+	0.125459i	$0.0400404\pi$
$463$			5.39911i			0.250918i	−0.992099	+	0.125459i	$0.959960\pi$
$464$	−27.2063	−	17.4819i	−1.26302	−	0.811579i
$465$	−4.32484	−	5.76857i	−0.200560	−	0.267511i
$466$	−4.07708	+	28.3599i	−0.188867	+	1.31375i
$467$		−	19.8769i		−	0.919795i	−0.887972	−	0.459897i	$-0.847886\pi$
$467$		−	19.8769i		−	0.919795i	0.887972	−	0.459897i	$-0.152114\pi$
$468$	15.3781	+	9.85069i	0.710854	+	0.455348i
$469$		−	10.4615i		−	0.483065i
$470$	3.14310	+	0.451858i	0.144980	+	0.0208426i
$471$	3.41908	+	4.56045i	0.157543	+	0.210135i
$472$	16.2337	−	35.5515i	0.747219	−	1.63639i
$473$		−	2.08383i		−	0.0958145i
$474$	9.13470	+	16.6995i	0.419571	+	0.767033i
$475$	3.94860			0.181174
$476$	−2.46645	−	0.724130i	−0.113050	−	0.0331905i
$477$	−7.81936	+	26.7741i	−0.358024	+	1.22590i
$478$	18.0551	+	2.59564i	0.825821	+	0.118722i
$479$	−4.94246			−0.225827			−0.112913	−	0.993605i	$-0.536018\pi$
$479$	−4.94246			−0.225827			−0.112913	+	0.993605i	$0.536018\pi$
$480$	−9.77356	−	0.691099i	−0.446100	−	0.0315442i
$481$	−14.9457			−0.681467
$482$	28.8178	+	4.14290i	1.31261	+	0.188704i
$483$	−6.74356	−	8.99471i	−0.306842	−	0.409274i
$484$	5.44621	+	1.59896i	0.247555	+	0.0726800i
$485$	18.4478			0.837674
$486$	−21.9948	−	1.49249i	−0.997706	−	0.0677008i
$487$		−	34.2345i		−	1.55132i	−0.631154	−	0.775658i	$-0.717418\pi$
$487$		−	34.2345i		−	1.55132i	0.631154	−	0.775658i	$-0.282582\pi$
$488$	7.54970	−	16.5336i	0.341759	−	0.748442i
$489$	21.1110	−	15.8275i	0.954674	−	0.715743i
$490$	−1.39982	−	0.201241i	−0.0632375	−	0.00909115i
$491$			21.4705i			0.968951i	0.874805	+	0.484476i	$0.160990\pi$
$491$			21.4705i			0.968951i	−0.874805	+	0.484476i	$0.839010\pi$
$492$	−6.80070	−	18.1912i	−0.306599	−	0.820125i
$493$		−	10.3911i		−	0.467991i
$494$	2.41864	−	16.8239i	0.108820	−	0.756944i
$495$	8.22707	+	2.40271i	0.369779	+	0.107994i
$496$	9.00089	−	14.0076i	0.404152	−	0.628961i
$497$			7.47462i			0.335283i
$498$	5.11970	+	9.35951i	0.229419	+	0.419409i
$499$	−7.35182			−0.329113			−0.164556	−	0.986368i	$-0.552619\pi$
$499$	−7.35182			−0.329113			−0.164556	+	0.986368i	$0.552619\pi$
$500$	−1.91900	−	0.563404i	−0.0858205	−	0.0251962i
$501$	−17.0694	+	12.7973i	−0.762605	+	0.571743i
$502$	2.81676	−	19.5933i	0.125718	−	0.874490i
$503$	−14.3257			−0.638752			−0.319376	−	0.947628i	$-0.603473\pi$
$503$	−14.3257			−0.638752			−0.319376	+	0.947628i	$0.603473\pi$
$504$	−6.42108	−	5.54705i	−0.286018	−	0.247085i
$505$	−3.65249			−0.162534
$506$	−3.73159	+	25.9567i	−0.165889	+	1.15392i
$507$	−5.17673	+	3.88112i	−0.229907	+	0.172367i
$508$	10.4620	−	35.6344i	0.464175	−	1.58102i
$509$	−15.3543			−0.680570			−0.340285	−	0.940322i	$-0.610523\pi$
$509$	−15.3543			−0.680570			−0.340285	+	0.940322i	$0.610523\pi$
$510$	−1.51086	−	2.76205i	−0.0669019	−	0.122306i
$511$			6.39674i			0.282975i
$512$	−6.37801	−	21.7099i	−0.281871	−	0.959452i
$513$	7.21200	+	19.2082i	0.318418	+	0.848063i
$514$	5.96637	−	41.5017i	0.263165	−	1.83056i
$515$		−	11.1466i		−	0.491180i
$516$	−2.36673	+	0.884789i	−0.104189	+	0.0389507i
$517$		−	6.41479i		−	0.282122i
$518$	6.87351	+	0.988150i	0.302005	+	0.0434168i
$519$	−16.1741	+	12.1261i	−0.709965	+	0.532278i
$520$	−3.57596	+	7.83126i	−0.156816	+	0.343423i
$521$			11.8887i			0.520855i	0.965493	+	0.260428i	$0.0838636\pi$
$521$			11.8887i			0.520855i	−0.965493	+	0.260428i	$0.916136\pi$
$522$	14.2031	−	31.2217i	0.621653	−	1.36654i
$523$	−11.4811			−0.502035			−0.251017	−	0.967983i	$-0.580765\pi$
$523$	−11.4811			−0.502035			−0.251017	+	0.967983i	$0.580765\pi$
$524$	7.25116	−	24.6981i	0.316769	−	1.07894i
$525$	−1.03899	−	1.38582i	−0.0453451	−	0.0604823i
$526$	41.2016	+	5.92322i	1.79647	+	0.258265i
$527$	5.35004			0.233051
$528$	1.42764	+	19.7417i	0.0621300	+	0.859149i
$529$	19.1268			0.831600
$530$	−13.0149	−	1.87104i	−0.565330	−	0.0812730i
$531$	39.7910	+	11.6209i	1.72678	+	0.504306i
$532$	−2.22465	+	7.57737i	−0.0964510	+	0.328521i
$533$	−17.0643			−0.739139
$534$	10.8999	+	19.9266i	0.471686	+	0.862307i
$535$		−	7.64658i		−	0.330590i
$536$	26.9161	+	12.2906i	1.16260	+	0.530874i
$537$	−10.1159	−	13.4928i	−0.436532	−	0.582257i
$538$	−3.21989	−	0.462898i	−0.138820	−	0.0199570i
$539$			2.85691i			0.123056i
$540$	−0.764293	−	10.3642i	−0.0328899	−	0.446003i
$541$		−	27.7212i		−	1.19183i	−0.803049	−	0.595913i	$-0.796790\pi$
$541$		−	27.7212i		−	1.19183i	0.803049	−	0.595913i	$-0.203210\pi$
$542$	−1.18806	+	8.26409i	−0.0510316	+	0.354973i
$543$	18.9805	+	25.3166i	0.814530	+	1.08644i
$544$	4.76081	−	5.49516i	0.204118	−	0.235603i
$545$		−	9.65989i		−	0.413784i
$546$	−6.54103	+	3.57798i	−0.279930	+	0.153123i
$547$	4.66664			0.199531			0.0997655	−	0.995011i	$-0.468191\pi$
$547$	4.66664			0.199531			0.0997655	+	0.995011i	$0.468191\pi$
$548$	−6.42406	+	21.8809i	−0.274422	+	0.934708i
$549$	18.5053	+	5.40446i	0.789786	+	0.230657i
$550$	−0.574929	+	3.99917i	−0.0245151	+	0.170525i
$551$	−31.9232			−1.35998
$552$	31.0650	−	6.78297i	1.32221	−	0.288702i
$553$	−7.77084			−0.330450
$554$	−1.43162	+	9.95824i	−0.0608235	+	0.423085i
$555$	5.10171	+	6.80478i	0.216556	+	0.288847i
$556$	12.4638	+	3.65928i	0.528584	+	0.155188i
$557$	−36.4827			−1.54582			−0.772911	−	0.634514i	$-0.781200\pi$
$557$	−36.4827			−1.54582			−0.772911	+	0.634514i	$0.781200\pi$
$558$	16.0751	+	7.31272i	0.680512	+	0.309572i
$559$			2.22012i			0.0939009i
$560$	2.16235	−	3.36515i	0.0913759	−	0.142204i
$561$	−5.08865	+	3.81508i	−0.214843	+	0.161073i
$562$	−1.25983	+	8.76329i	−0.0531426	+	0.369657i
$563$		−	40.6742i		−	1.71421i	−0.515139	−	0.857107i	$-0.672260\pi$
$563$		−	40.6742i		−	1.71421i	0.515139	−	0.857107i	$-0.327740\pi$
$564$	−7.28566	+	2.72370i	−0.306782	+	0.114689i
$565$		−	13.9427i		−	0.586574i
$566$	−7.31923	−	1.05223i	−0.307650	−	0.0442284i
$567$	4.84375	−	7.58538i	0.203418	−	0.318556i
$568$	−19.2313	−	8.78154i	−0.806929	−	0.368465i
$569$		−	30.0628i		−	1.26030i	−0.776474	−	0.630149i	$-0.782994\pi$
$569$		−	30.0628i		−	1.26030i	0.776474	−	0.630149i	$-0.217006\pi$
$570$	−8.48551	+	4.64162i	−0.355419	+	0.194416i
$571$	−17.9374			−0.750655			−0.375327	−	0.926892i	$-0.622470\pi$
$571$	−17.9374			−0.750655			−0.375327	+	0.926892i	$0.622470\pi$
$572$	16.6872	+	4.89924i	0.697728	+	0.204847i
$573$	−14.5647	+	10.9195i	−0.608449	+	0.456169i
$574$	7.84786	+	1.12822i	0.327563	+	0.0470912i
$575$	6.49052			0.270673
$576$	21.8157	−	10.0038i	0.908988	−	0.416823i
$577$	−10.0101			−0.416724			−0.208362	−	0.978052i	$-0.566813\pi$
$577$	−10.0101			−0.416724			−0.208362	+	0.978052i	$0.566813\pi$
$578$	−21.4846	−	3.08866i	−0.893640	−	0.128471i
$579$	14.5186	−	10.8850i	0.603374	−	0.452365i
$580$	15.5146	+	4.55495i	0.644208	+	0.189134i
$581$	−4.35530			−0.180688
$582$	−39.6443	+	21.6856i	−1.64331	+	0.898899i
$583$			26.5622i			1.10010i
$584$	−16.4581	−	7.51519i	−0.681040	−	0.310981i
$585$	−8.76514	−	2.55986i	−0.362394	−	0.105837i
$586$	8.95660	+	1.28762i	0.369994	+	0.0531911i
$587$		−	16.4546i		−	0.679154i	−0.940578	−	0.339577i	$-0.889716\pi$
$587$		−	16.4546i		−	0.679154i	0.940578	−	0.339577i	$-0.110284\pi$
$588$	3.24477	−	1.21304i	0.133812	−	0.0500249i
$589$		−	16.4363i		−	0.677244i
$590$	−2.78070	+	19.3424i	−0.114480	+	0.796313i
$591$	−15.2493	+	11.4327i	−0.627271	+	0.470280i
$592$	−10.6177	+	16.5238i	−0.436386	+	0.679125i
$593$			34.3939i			1.41239i	0.708019	+	0.706194i	$0.249589\pi$
$593$			34.3939i			1.41239i	−0.708019	+	0.706194i	$0.750411\pi$
$594$	−20.5043	+	4.50760i	−0.841303	+	0.184949i
$595$	1.28528			0.0526913
$596$	−0.119046	−	0.0349508i	−0.00487630	−	0.00143164i
$597$	−21.5366	−	28.7260i	−0.881433	−	1.17568i
$598$	3.97564	−	27.6543i	0.162576	−	1.13087i
$599$	12.3780			0.505751			0.252876	−	0.967499i	$-0.418624\pi$
$599$	12.3780			0.505751			0.252876	+	0.967499i	$0.418624\pi$
$600$	4.78621	−	1.04506i	0.195396	−	0.0426644i
$601$	−39.1651			−1.59758			−0.798789	−	0.601611i	$-0.794526\pi$
$601$	−39.1651			−1.59758			−0.798789	+	0.601611i	$0.794526\pi$
$602$	0.146785	−	1.02103i	0.00598251	−	0.0416140i
$603$	−8.79825	+	30.1259i	−0.358292	+	1.22682i
$604$	5.64329	−	19.2216i	0.229622	−	0.782114i
$605$	−2.83804			−0.115383
$606$	7.84917	−	4.29354i	0.318851	−	0.174413i
$607$			14.2863i			0.579862i	0.957048	+	0.289931i	$0.0936323\pi$
$607$			14.2863i			0.579862i	−0.957048	+	0.289931i	$0.906368\pi$
$608$	−16.8821	−	14.6260i	−0.684659	−	0.593164i
$609$	8.39990	+	11.2040i	0.340381	+	0.454008i
$610$	−1.29320	+	8.99541i	−0.0523600	+	0.364213i
$611$			6.83433i			0.276488i
$612$	6.49365	+	4.15961i	0.262490	+	0.168142i
$613$		−	43.0830i		−	1.74011i	−0.492958	−	0.870053i	$-0.664085\pi$
$613$		−	43.0830i		−	1.74011i	0.492958	−	0.870053i	$-0.335915\pi$
$614$	−29.5684	−	4.25081i	−1.19328	−	0.171549i
$615$	5.82490	+	7.76938i	0.234882	+	0.313292i
$616$	−7.35051	−	3.35644i	−0.296161	−	0.135235i
$617$			9.35216i			0.376504i	0.982121	+	0.188252i	$0.0602822\pi$
$617$			9.35216i			0.376504i	−0.982121	+	0.188252i	$0.939718\pi$
$618$	13.1030	+	23.9541i	0.527080	+	0.963574i
$619$	19.0055			0.763894			0.381947	−	0.924184i	$-0.375254\pi$
$619$	19.0055			0.763894			0.381947	+	0.924184i	$0.375254\pi$
$620$	−2.34520	+	7.98796i	−0.0941855	+	0.320804i
$621$	11.8547	+	31.5735i	0.475715	+	1.26700i
$622$	−5.52305	−	0.794005i	−0.221454	−	0.0318367i
$623$	−9.27251			−0.371495
$624$	−1.52101	−	21.0329i	−0.0608891	−	0.841990i
$625$	1.00000			0.0400000
$626$	−23.5258	−	3.38212i	−0.940281	−	0.135177i
$627$	11.7206	+	15.6332i	0.468076	+	0.624330i
$628$	1.85404	−	6.31504i	0.0739844	−	0.251997i
$629$	−6.31107			−0.251639
$630$	3.86183	+	1.75679i	0.153859	+	0.0699921i
$631$			30.7556i			1.22436i	0.790718	+	0.612181i	$0.209708\pi$
$631$			30.7556i			1.22436i	−0.790718	+	0.612181i	$0.790292\pi$
$632$	9.12955	−	19.9935i	0.363154	−	0.795297i
$633$	−32.0241	+	24.0093i	−1.27284	+	0.954283i
$634$	−13.5530	−	1.94841i	−0.538259	−	0.0773811i
$635$			18.5692i			0.736897i
$636$	30.1683	−	11.2783i	1.19625	−	0.447212i
$637$		−	3.04377i		−	0.120598i
$638$	4.64813	−	32.3321i	0.184021	−	1.28004i
$639$	6.28627	−	21.5247i	0.248681	−	0.851504i
$640$	6.11772	+	9.51701i	0.241824	+	0.376193i
$641$			21.8643i			0.863587i	0.901972	+	0.431794i	$0.142119\pi$
$641$			21.8643i			0.863587i	−0.901972	+	0.431794i	$0.857881\pi$
$642$	8.98864	+	16.4325i	0.354753	+	0.648537i
$643$	32.0015			1.26202			0.631008	−	0.775777i	$-0.282642\pi$
$643$	32.0015			1.26202			0.631008	+	0.775777i	$0.282642\pi$
$644$	−3.65678	+	12.4553i	−0.144097	+	0.490809i
$645$	1.01082	−	0.757834i	0.0398009	−	0.0298397i
$646$	1.02131	−	7.10416i	0.0401828	−	0.279510i
$647$	31.5018			1.23846			0.619232	−	0.785208i	$-0.287444\pi$
$647$	31.5018			1.23846			0.619232	+	0.785208i	$0.287444\pi$
$648$	13.8256	+	21.3741i	0.543123	+	0.839653i
$649$	39.4761			1.54957
$650$	0.612531	−	4.26073i	0.0240254	−	0.167120i
$651$	−5.76857	+	4.32484i	−0.226088	+	0.169504i
$652$	−29.2333	−	8.58265i	−1.14486	−	0.336122i
$653$	29.7838			1.16553			0.582766	−	0.812640i	$-0.301971\pi$
$653$	29.7838			1.16553			0.582766	+	0.812640i	$0.301971\pi$
$654$	11.3553	+	20.7590i	0.444027	+	0.811743i
$655$			12.8703i			0.502883i
$656$	−12.1228	+	18.8661i	−0.473317	+	0.736599i
$657$	5.37976	−	18.4207i	0.209884	−	0.718660i
$658$	0.451858	−	3.14310i	0.0176152	−	0.122531i
$659$		−	8.89311i		−	0.346426i	−0.984884	−	0.173213i	$-0.944585\pi$
$659$		−	8.89311i		−	0.346426i	0.984884	−	0.173213i	$-0.0554149\pi$
$660$	−3.46555	−	9.27003i	−0.134896	−	0.360836i
$661$			41.8860i			1.62918i	0.580040	+	0.814588i	$0.303037\pi$
$661$			41.8860i			1.62918i	−0.580040	+	0.814588i	$0.696963\pi$
$662$	−36.4971	−	5.24690i	−1.41850	−	0.203927i
$663$	5.42146	−	4.06460i	0.210552	−	0.157856i
$664$	5.11681	−	11.2057i	0.198571	−	0.434865i
$665$		−	3.94860i		−	0.153120i
$666$	−18.9626	−	8.62631i	−0.734787	−	0.334263i
$667$	−52.4739			−2.03180
$668$	23.6367	+	6.93953i	0.914530	+	0.268498i
$669$	14.9212	+	19.9022i	0.576886	+	0.769464i
$670$	−14.6442	−	2.10527i	−0.565754	−	0.0813339i
$671$	18.3588			0.708735
$672$	−0.691099	+	9.77356i	−0.0266597	+	0.377023i
$673$	14.7424			0.568277			0.284139	−	0.958783i	$-0.408292\pi$
$673$	14.7424			0.568277			0.284139	+	0.958783i	$0.408292\pi$
$674$	−36.3991	−	5.23281i	−1.40204	−	0.201560i
$675$	1.82647	+	4.86457i	0.0703009	+	0.187237i
$676$	7.16842	+	2.10459i	0.275708	+	0.0809457i
$677$	7.62818			0.293175			0.146587	−	0.989198i	$-0.453171\pi$
$677$	7.62818			0.293175			0.146587	+	0.989198i	$0.453171\pi$
$678$	16.3898	+	29.9628i	0.629446	+	1.15071i
$679$		−	18.4478i		−	0.707963i
$680$	−1.51001	+	3.30687i	−0.0579061	+	0.126813i
$681$	22.5329	+	30.0549i	0.863464	+	1.15171i
$682$	16.6468	+	2.39317i	0.637438	+	0.0916393i
$683$		−	18.2715i		−	0.699141i	−0.936910	−	0.349570i	$-0.886328\pi$
$683$		−	18.2715i		−	0.699141i	0.936910	−	0.349570i	$-0.113672\pi$
$684$	12.7790	−	19.9496i	0.488619	−	0.762793i
$685$		−	11.4022i		−	0.435657i
$686$	−0.201241	+	1.39982i	−0.00768342	+	0.0534455i
$687$	−13.7205	−	18.3008i	−0.523472	−	0.698219i
$688$	2.45454	+	1.57721i	0.0935783	+	0.0601307i
$689$		−	28.2995i		−	1.07812i
$690$	−13.9481	+	7.62967i	−0.530994	+	0.290457i
$691$	−39.1887			−1.49081			−0.745404	−	0.666614i	$-0.767743\pi$
$691$	−39.1887			−1.49081			−0.745404	+	0.666614i	$0.767743\pi$
$692$	22.3969	+	6.57555i	0.851404	+	0.249965i
$693$	2.40271	−	8.22707i	0.0912714	−	0.312520i
$694$	4.89487	−	34.0484i	0.185807	−	1.29246i
$695$	−6.49495			−0.246367
$696$	−38.6951	+	8.44899i	−1.46674	+	0.320258i
$697$	−7.20569			−0.272935
$698$	4.72479	−	32.8654i	0.178836	−	1.24397i
$699$	21.0495	+	28.0763i	0.796166	+	1.06194i
$700$	−0.563404	+	1.91900i	−0.0212947	+	0.0725315i
$701$	−10.8563			−0.410036			−0.205018	−	0.978758i	$-0.565725\pi$
$701$	−10.8563			−0.410036			−0.205018	+	0.978758i	$0.565725\pi$
$702$	21.8454	−	4.80241i	0.824501	−	0.181255i
$703$			19.3887i			0.731259i
$704$	17.2715	−	14.9687i	0.650943	−	0.564154i
$705$	3.11167	−	2.33289i	0.117192	−	0.0878618i
$706$	0.341609	−	2.37622i	0.0128566	−	0.0894300i
$707$			3.65249i			0.137366i
$708$	−16.7615	−	44.8354i	−0.629935	−	1.68502i
$709$		−	18.5207i		−	0.695559i	−0.937576	−	0.347780i	$-0.886936\pi$
$709$		−	18.5207i		−	0.695559i	0.937576	−	0.347780i	$-0.113064\pi$
$710$	10.4631	+	1.50420i	0.392675	+	0.0564517i
$711$	22.3777	+	6.53540i	0.839230	+	0.245097i
$712$	10.8938	−	23.8571i	0.408262	−	0.894082i
$713$		−	27.0171i		−	1.01180i
$714$	−2.76205	+	1.51086i	−0.103367	+	0.0565425i
$715$	−8.69578			−0.325204
$716$	−5.48547	+	18.6840i	−0.205002	+	0.698254i
$717$	17.8745	−	13.4010i	0.667537	−	0.500469i
$718$	−5.99268	−	0.861519i	−0.223645	−	0.0321516i
$719$	6.32683			0.235951			0.117976	−	0.993017i	$-0.462360\pi$
$719$	6.32683			0.235951			0.117976	+	0.993017i	$0.462360\pi$
$720$	−9.05707	+	7.87207i	−0.337537	+	0.293375i
$721$	−11.1466			−0.415123
$722$	4.77140	+	0.685946i	0.177573	+	0.0255283i
$723$	28.5296	−	21.3893i	1.06103	−	0.795478i
$724$	10.2924	−	35.0569i	0.382514	−	1.30288i
$725$	−8.08470			−0.300258
$726$	6.09893	−	3.33614i	0.226352	−	0.123816i
$727$			25.4813i			0.945048i	0.881318	+	0.472524i	$0.156657\pi$
$727$			25.4813i			0.945048i	−0.881318	+	0.472524i	$0.843343\pi$
$728$	7.83126	+	3.57596i	0.290246	+	0.132534i
$729$	−20.3280	+	17.7700i	−0.752889	+	0.658148i
$730$	8.95429	+	1.28729i	0.331413	+	0.0476446i
$731$			0.937479i			0.0346739i
$732$	−7.79513	−	20.8512i	−0.288116	−	0.770684i
$733$		−	12.4086i		−	0.458321i	−0.973389	−	0.229161i	$-0.926402\pi$
$733$		−	12.4086i		−	0.458321i	0.973389	−	0.229161i	$-0.0735981\pi$
$734$	6.44864	−	44.8564i	0.238024	−	1.65568i
$735$	−1.38582	+	1.03899i	−0.0511169	+	0.0383236i
$736$	−27.7499	−	24.0416i	−1.02288	−	0.886184i
$737$			29.8875i			1.10092i
$738$	−21.6507	−	9.84912i	−0.796972	−	0.362551i
$739$	−5.75195			−0.211589			−0.105794	−	0.994388i	$-0.533739\pi$
$739$	−5.75195			−0.211589			−0.105794	+	0.994388i	$0.533739\pi$
$740$	2.76647	−	9.42284i	0.101697	−	0.346391i
$741$	−12.4872	−	16.6557i	−0.458728	−	0.611861i
$742$	−1.87104	+	13.0149i	−0.0686882	+	0.477791i
$743$	−34.2168			−1.25529			−0.627646	−	0.778498i	$-0.715982\pi$
$743$	−34.2168			−1.25529			−0.627646	+	0.778498i	$0.715982\pi$
$744$	−4.35012	−	19.9229i	−0.159483	−	0.730408i
$745$	0.0620351			0.00227279
$746$	4.40848	−	30.6651i	0.161406	−	1.12273i
$747$	12.5420	+	3.66287i	0.458886	+	0.134018i
$748$	7.04645	+	2.06878i	0.257644	+	0.0756420i
$749$	−7.64658			−0.279400
$750$	−2.14899	+	1.17551i	−0.0784702	+	0.0429236i
$751$		−	35.6068i		−	1.29931i	−0.760230	−	0.649655i	$-0.774914\pi$
$751$		−	35.6068i		−	1.29931i	0.760230	−	0.649655i	$-0.225086\pi$
$752$	7.55596	+	4.85524i	0.275537	+	0.177052i
$753$	−14.5426	−	19.3973i	−0.529963	−	0.706878i
$754$	−4.95213	+	34.4468i	−0.180346	+	1.25448i
$755$			10.0164i			0.364535i
$756$	−10.3642	+	0.764293i	−0.376941	+	0.0277971i
$757$			22.8319i			0.829839i	0.909858	+	0.414920i	$0.136190\pi$
$757$			22.8319i			0.829839i	−0.909858	+	0.414920i	$0.863810\pi$
$758$	29.5025	+	4.24134i	1.07158	+	0.154052i
$759$	19.2658	+	25.6971i	0.699303	+	0.932747i
$760$	10.1593	+	4.63900i	0.368516	+	0.168274i
$761$		−	9.30353i		−	0.337253i	−0.985680	−	0.168626i	$-0.946067\pi$
$761$		−	9.30353i		−	0.337253i	0.985680	−	0.168626i	$-0.0539331\pi$
$762$	−21.8283	−	39.9051i	−0.790757	−	1.44561i
$763$	−9.65989			−0.349711
$764$	20.1683	+	5.92124i	0.729663	+	0.214223i
$765$	−3.70122	−	1.08094i	−0.133818	−	0.0390814i
$766$	−25.1819	−	3.62020i	−0.909859	−	0.130803i
$767$	−42.0580			−1.51863
$768$	−24.3343	−	13.2606i	−0.878088	−	0.478499i
$769$	−29.8781			−1.07743			−0.538717	−	0.842487i	$-0.681091\pi$
$769$	−29.8781			−1.07743			−0.538717	+	0.842487i	$0.681091\pi$
$770$	3.99917	+	0.574929i	0.144120	+	0.0207190i
$771$	−30.8037	−	41.0867i	−1.10937	−	1.47970i
$772$	−20.1045	−	5.90253i	−0.723578	−	0.212437i
$773$	−2.88681			−0.103831			−0.0519156	−	0.998651i	$-0.516533\pi$
$773$	−2.88681			−0.103831			−0.0519156	+	0.998651i	$0.516533\pi$
$774$	−1.28140	+	2.81681i	−0.0460589	+	0.101248i
$775$		−	4.16256i		−	0.149523i
$776$	47.4642	+	21.6734i	1.70386	+	0.778030i
$777$	6.80478	−	5.10171i	0.244120	−	0.183023i
$778$	−9.67757	−	1.39127i	−0.346958	−	0.0498793i
$779$			22.1371i			0.793145i
$780$	3.69221	+	9.87632i	0.132202	+	0.353629i
$781$		−	21.3544i		−	0.764119i
$782$	1.67878	−	11.6775i	0.0600330	−	0.417586i
$783$	−14.7665	−	39.3286i	−0.527711	−	1.40549i
$784$	−3.36515	−	2.16235i	−0.120184	−	0.0772267i
$785$			3.29079i			0.117453i
$786$	−15.1292	−	27.6581i	−0.539639	−	0.986534i
$787$	53.5286			1.90809			0.954044	−	0.299667i	$-0.0968756\pi$
$787$	53.5286			1.90809			0.954044	+	0.299667i	$0.0968756\pi$
$788$	21.1162	+	6.19955i	0.752235	+	0.220850i
$789$	40.7895	−	30.5809i	1.45215	−	1.08871i
$790$	−1.56381	+	10.8778i	−0.0556380	+	0.387014i
$791$	−13.9427			−0.495745
$792$	18.3445	+	15.8474i	0.651842	+	0.563114i
$793$	−19.5596			−0.694581
$794$	−6.29049	+	43.7563i	−0.223241	+	1.55285i
$795$	−12.8847	+	9.66000i	−0.456974	+	0.342605i
$796$	−11.6785	+	39.7780i	−0.413933	+	1.40989i
$797$	52.7611			1.86889			0.934447	−	0.356101i	$-0.115894\pi$
$797$	52.7611			1.86889			0.934447	+	0.356101i	$0.115894\pi$
$798$	4.64162	+	8.48551i	0.164312	+	0.300384i
$799$			2.88590i			0.102096i
$800$	−4.27546	−	3.70411i	−0.151160	−	0.130960i
$801$	26.7021	+	7.79833i	0.943471	+	0.275540i
$802$	4.32489	−	30.0837i	0.152717	−	1.06229i
$803$		−	18.2749i		−	0.644908i
$804$	33.9450	−	12.6902i	1.19715	−	0.447547i
$805$		−	6.49052i		−	0.228761i
$806$	−17.7355	−	2.54969i	−0.624707	−	0.0898092i
$807$	−3.18770	+	2.38989i	−0.112212	+	0.0841282i
$808$	−9.39743	−	4.29112i	−0.330600	−	0.150961i
$809$		−	49.0054i		−	1.72294i	−0.507810	−	0.861469i	$-0.669545\pi$
$809$		−	49.0054i		−	1.72294i	0.507810	−	0.861469i	$-0.330455\pi$
$810$	−9.64343	−	8.30688i	−0.338835	−	0.291874i
$811$	−18.9030			−0.663773			−0.331886	−	0.943319i	$-0.607685\pi$
$811$	−18.9030			−0.663773			−0.331886	+	0.943319i	$0.607685\pi$
$812$	4.55495	−	15.5146i	0.159847	−	0.544455i
$813$	6.13384	+	8.18145i	0.215123	+	0.286936i
$814$	−19.6370	−	2.82306i	−0.688278	−	0.0989482i
$815$	15.2336			0.533609
$816$	−0.642270	−	8.88147i	−0.0224840	−	0.310914i
$817$	2.88010			0.100762
$818$	−8.63503	−	1.24139i	−0.301917	−	0.0434042i
$819$	−2.55986	+	8.76514i	−0.0894486	+	0.306279i
$820$	3.15863	−	10.7586i	0.110304	−	0.375705i
$821$	51.1462			1.78502			0.892508	−	0.451032i	$-0.148944\pi$
$821$	51.1462			1.78502			0.892508	+	0.451032i	$0.148944\pi$
$822$	13.4035	+	24.5033i	0.467499	+	0.854652i
$823$		−	2.55019i		−	0.0888939i	−0.999012	−	0.0444470i	$-0.985847\pi$
$823$		−	2.55019i		−	0.0888939i	0.999012	−	0.0444470i	$-0.0141526\pi$
$824$	13.0956	−	28.6790i	0.456207	−	0.999081i
$825$	2.96829	+	3.95918i	0.103343	+	0.137841i
$826$	19.3424	+	2.78070i	0.673008	+	0.0967529i
$827$		−	26.7188i		−	0.929103i	−0.885546	−	0.464551i	$-0.846216\pi$
$827$		−	26.7188i		−	0.929103i	0.885546	−	0.464551i	$-0.153784\pi$
$828$	21.0056	−	32.7922i	0.729994	−	1.13961i
$829$		−	34.0332i		−	1.18202i	−0.806663	−	0.591011i	$-0.798729\pi$
$829$		−	34.0332i		−	1.18202i	0.806663	−	0.591011i	$-0.201271\pi$
$830$	−0.876465	+	6.09664i	−0.0304225	+	0.211618i
$831$	7.39128	+	9.85866i	0.256401	+	0.341993i
$832$	−18.4011	+	15.9477i	−0.637942	+	0.552887i
$833$		−	1.28528i		−	0.0445322i
$834$	13.9576	−	7.63488i	0.483312	−	0.264374i
$835$	−12.3172			−0.426253
$836$	6.35565	−	21.6479i	0.219815	−	0.748709i
$837$	20.2490	−	7.60279i	0.699909	−	0.262791i
$838$	5.76067	−	40.0709i	0.198999	−	1.38422i
$839$	15.2429			0.526243			0.263122	−	0.964763i	$-0.415248\pi$
$839$	15.2429			0.526243			0.263122	+	0.964763i	$0.415248\pi$
$840$	−1.04506	−	4.78621i	−0.0360580	−	0.165140i
$841$	36.3624			1.25388
$842$	−7.44860	+	51.8120i	−0.256696	+	1.78556i
$843$	6.50435	+	8.67566i	0.224022	+	0.298806i
$844$	44.3450	+	13.0193i	1.52642	+	0.448144i
$845$	−3.73549			−0.128505
$846$	−3.94461	+	8.67117i	−0.135618	+	0.298121i
$847$			2.83804i			0.0975161i
$848$	−31.2876	−	20.1045i	−1.07442	−	0.690391i
$849$	−7.24603	+	5.43253i	−0.248683	+	0.186444i
$850$	0.258651	−	1.79916i	0.00887165	−	0.0617107i
$851$			31.8702i			1.09250i
$852$	−24.2534	+	9.06701i	−0.830909	+	0.310631i
$853$			4.04187i			0.138391i	0.997603	+	0.0691955i	$0.0220432\pi$
$853$			4.04187i			0.138391i	−0.997603	+	0.0691955i	$0.977957\pi$
$854$	8.99541	+	1.29320i	0.307817	+	0.0442523i
$855$	−3.32083	+	11.3708i	−0.113570	+	0.388873i
$856$	8.98357	−	19.6738i	0.307052	−	0.672435i
$857$			6.05379i			0.206794i	0.994640	+	0.103397i	$0.0329712\pi$
$857$			6.05379i			0.206794i	−0.994640	+	0.103397i	$0.967029\pi$
$858$	18.6872	−	10.2220i	0.637970	−	0.348973i
$859$	−43.9905			−1.50094			−0.750468	−	0.660906i	$-0.770172\pi$
$859$	−43.9905			−1.50094			−0.750468	+	0.660906i	$0.770172\pi$
$860$	−1.39972	−	0.410946i	−0.0477300	−	0.0140131i
$861$	7.76938	−	5.82490i	0.264780	−	0.198512i
$862$	24.5113	+	3.52380i	0.834859	+	0.120021i
$863$	−39.5265			−1.34550			−0.672750	−	0.739870i	$-0.734887\pi$
$863$	−39.5265			−1.34550			−0.672750	+	0.739870i	$0.734887\pi$
$864$	10.2099	−	27.5637i	0.347347	−	0.937737i
$865$	−11.6711			−0.396830
$866$	52.1692	+	7.49994i	1.77278	+	0.254858i
$867$	−21.2697	+	15.9464i	−0.722357	+	0.541569i
$868$	7.98796	+	2.34520i	0.271129	+	0.0796012i
$869$	22.2006			0.753104
$870$	17.3740	−	9.50366i	0.589033	−	0.322204i
$871$		−	31.8422i		−	1.07893i
$872$	11.3489	−	24.8538i	0.384322	−	0.841655i
$873$	−15.5149	+	53.1243i	−0.525101	+	1.79799i
$874$	−35.8753	−	5.15750i	−1.21350	−	0.174455i
$875$		−	1.00000i		−	0.0338062i
$876$	−20.7559	+	7.75950i	−0.701278	+	0.262169i
$877$		−	29.6435i		−	1.00099i	−0.865740	−	0.500495i	$-0.833152\pi$
$877$		−	29.6435i		−	1.00099i	0.865740	−	0.500495i	$-0.166848\pi$
$878$	2.31473	−	16.1011i	0.0781182	−	0.543386i
$879$	8.86704	−	6.64784i	0.299078	−	0.224226i
$880$	−6.17764	+	9.61395i	−0.208248	+	0.324086i
$881$		−	14.7690i		−	0.497581i	−0.968557	−	0.248790i	$-0.919967\pi$
$881$		−	14.7690i		−	0.497581i	0.968557	−	0.248790i	$-0.0800330\pi$
$882$	1.75679	−	3.86183i	0.0591541	−	0.130034i
$883$	54.1838			1.82343			0.911715	−	0.410823i	$-0.134759\pi$
$883$	54.1838			1.82343			0.911715	+	0.410823i	$0.134759\pi$
$884$	−7.50731	−	2.20408i	−0.252498	−	0.0741314i
$885$	14.3564	+	19.1490i	0.482587	+	0.643685i
$886$	−3.76543	+	26.1921i	−0.126502	+	0.879942i
$887$	−10.5944			−0.355725			−0.177862	−	0.984055i	$-0.556918\pi$
$887$	−10.5944			−0.355725			−0.177862	+	0.984055i	$0.556918\pi$
$888$	5.13153	+	23.5016i	0.172203	+	0.788663i
$889$	18.5692			0.622792
$890$	−1.86601	+	12.9799i	−0.0625488	+	0.435086i
$891$	−13.8382	+	21.6708i	−0.463597	+	0.725999i
$892$	8.09120	−	27.5593i	0.270913	−	0.922755i
$893$	8.86600			0.296689
$894$	−0.133313	+	0.0729229i	−0.00445865	+	0.00243891i
$895$		−	9.73630i		−	0.325449i
$896$	9.51701	−	6.11772i	0.317941	−	0.204379i
$897$	−20.5258	−	27.3778i	−0.685337	−	0.914118i
$898$	−5.66390	+	39.3977i	−0.189007	+	1.31472i
$899$			33.6530i			1.12239i
$900$	3.23635	−	5.05233i	0.107878	−	0.168411i
$901$		−	11.9499i		−	0.398109i
$902$	−22.4207	−	3.22324i	−0.746527	−	0.107322i
$903$	−0.757834	−	1.01082i	−0.0252191	−	0.0336379i
$904$	16.3805	−	35.8730i	0.544809	−	1.19312i
$905$			18.2683i			0.607258i
$906$	−11.7744	−	21.5252i	−0.391179	−	0.715128i
$907$	22.1956			0.736994			0.368497	−	0.929629i	$-0.379873\pi$
$907$	22.1956			0.736994			0.368497	+	0.929629i	$0.379873\pi$
$908$	12.2188	−	41.6182i	0.405494	−	1.38115i
$909$	3.07180	−	10.5181i	0.101885	−	0.348863i
$910$	−4.26073	−	0.612531i	−0.141242	−	0.0203052i
$911$	−0.0887953			−0.00294192			−0.00147096	−	0.999999i	$-0.500468\pi$
$911$	−0.0887953			−0.00294192			−0.00147096	+	0.999999i	$0.500468\pi$
$912$	−27.2854	+	1.97317i	−0.903511	+	0.0653381i
$913$	12.4427			0.411794
$914$	11.8323	+	1.70103i	0.391377	+	0.0562652i
$915$	6.67664	+	8.90546i	0.220723	+	0.294405i
$916$	−7.44015	+	25.3418i	−0.245829	+	0.837317i
$917$	12.8703			0.425014
$918$	9.22455	−	2.02789i	0.304456	−	0.0669304i
$919$			43.6803i			1.44088i	0.693518	+	0.720440i	$0.256060\pi$
$919$			43.6803i			1.44088i	−0.693518	+	0.720440i	$0.743940\pi$
$920$	16.6993	+	7.62537i	0.550561	+	0.251401i
$921$	−29.2727	+	21.9465i	−0.964569	+	0.723161i
$922$	10.1930	+	1.46537i	0.335689	+	0.0482593i
$923$			22.7510i			0.748858i
$924$	−9.27003	+	3.46555i	−0.304962	+	0.114008i
$925$			4.91028i			0.161449i
$926$	1.08652	−	7.55780i	0.0357054	−	0.248365i
$927$	32.0990	+	9.37451i	1.05427	+	0.307899i
$928$	34.5658	+	29.9466i	1.13468	+	0.983046i
$929$		−	27.2270i		−	0.893288i	−0.894712	−	0.446644i	$-0.852619\pi$
$929$		−	27.2270i		−	0.893288i	0.894712	−	0.446644i	$-0.147381\pi$
$930$	4.89313	+	8.94531i	0.160452	+	0.293328i
$931$	−3.94860			−0.129410
$932$	11.4144	−	38.8784i	0.373890	−	1.27350i
$933$	−5.46782	+	4.09936i	−0.179008	+	0.134207i
$934$	−4.00006	+	27.8242i	−0.130886	+	0.910434i
$935$	−3.67193			−0.120085
$936$	−19.5443	−	16.8839i	−0.638824	−	0.551868i
$937$	−39.9883			−1.30636			−0.653181	−	0.757202i	$-0.726566\pi$
$937$	−39.9883			−1.30636			−0.653181	+	0.757202i	$0.726566\pi$
$938$	−2.10527	+	14.6442i	−0.0687397	+	0.478149i
$939$	−23.2906	+	17.4615i	−0.760059	+	0.569835i
$940$	−4.30884	−	1.26504i	−0.140539	−	0.0412611i
$941$	57.5225			1.87518			0.937590	−	0.347742i	$-0.113051\pi$
$941$	57.5225			1.87518			0.937590	+	0.347742i	$0.113051\pi$
$942$	−3.86836	−	7.07188i	−0.126038	−	0.230414i
$943$			36.3880i			1.18495i
$944$	−29.8788	+	46.4988i	−0.972471	+	1.51341i
$945$	4.86457	−	1.82647i	0.158244	−	0.0594151i
$946$	−0.419352	+	2.91699i	−0.0136343	+	0.0948395i
$947$		−	49.5149i		−	1.60902i	−0.593940	−	0.804509i	$-0.702428\pi$
$947$		−	49.5149i		−	1.60902i	0.593940	−	0.804509i	$-0.297572\pi$
$948$	−9.42634	−	25.2146i	−0.306153	−	0.818932i
$949$			19.4702i			0.632029i
$950$	−5.52733	−	0.794620i	−0.179330	−	0.0257809i
$951$	−13.4175	+	10.0594i	−0.435091	+	0.326199i
$952$	3.30687	+	1.51001i	0.107176	+	0.0489396i
$953$			53.7496i			1.74112i	0.492062	+	0.870560i	$0.336243\pi$
$953$			53.7496i			1.74112i	−0.492062	+	0.870560i	$0.663757\pi$
$954$	16.3338	−	35.9054i	0.528825	−	1.16248i
$955$	−10.5098			−0.340088
$956$	−24.7516	−	7.26686i	−0.800523	−	0.235027i
$957$	−23.9978	−	32.0088i	−0.775738	−	1.03470i
$958$	6.91856	+	0.994626i	0.223528	+	0.0321349i
$959$	−11.4022			−0.368198
$960$	13.5422	+	2.93426i	0.437071	+	0.0947027i
$961$	13.6731			0.441069
$962$	20.9214	+	3.00770i	0.674532	+	0.0969721i
$963$	22.0199	+	6.43089i	0.709581	+	0.207233i
$964$	−39.5061	−	11.5987i	−1.27240	−	0.373567i
$965$	10.4765			0.337252
$966$	7.62967	+	13.9481i	0.245481	+	0.448772i
$967$		−	2.58376i		−	0.0830882i	−0.999137	−	0.0415441i	$-0.986772\pi$
$967$		−	2.58376i		−	0.0830882i	0.999137	−	0.0415441i	$-0.0132277\pi$
$968$	−7.30194	−	3.33426i	−0.234693	−	0.107167i
$969$	−5.27290	−	7.03312i	−0.169390	−	0.225936i
$970$	−25.8237	−	3.71247i	−0.829149	−	0.119200i
$971$		−	20.2510i		−	0.649886i	−0.945734	−	0.324943i	$-0.894655\pi$
$971$		−	20.2510i		−	0.649886i	0.945734	−	0.324943i	$-0.105345\pi$
$972$	30.4885	+	6.51549i	0.977919	+	0.208984i
$973$			6.49495i			0.208218i
$974$	−6.88940	+	47.9223i	−0.220751	+	1.53553i
$975$	−3.16243	−	4.21812i	−0.101279	−	0.135088i
$976$	−13.8955	+	21.6248i	−0.444784	+	0.692194i
$977$			11.0186i			0.352517i	0.984344	+	0.176259i	$0.0563995\pi$
$977$			11.0186i			0.352517i	−0.984344	+	0.176259i	$0.943601\pi$
$978$	−32.7368	+	17.9072i	−1.04681	+	0.572610i
$979$	26.4908			0.846649
$980$	1.91900	+	0.563404i	0.0613003	+	0.0179973i
$981$	27.8176	+	8.12412i	0.888148	+	0.259383i
$982$	4.32075	−	30.0549i	0.137881	−	0.959091i
$983$	−5.70220			−0.181872			−0.0909360	−	0.995857i	$-0.528986\pi$
$983$	−5.70220			−0.181872			−0.0909360	+	0.995857i	$0.528986\pi$
$984$	5.85894	+	26.8331i	0.186776	+	0.855407i
$985$	−11.0037			−0.350609
$986$	−2.09112	+	14.5457i	−0.0665947	+	0.463229i
$987$	−2.33289	−	3.11167i	−0.0742568	−	0.0990454i
$988$	−6.77133	+	23.0638i	−0.215425	+	0.733756i
$989$	4.73417			0.150538
$990$	−11.0329	−	5.01899i	−0.350649	−	0.159514i
$991$			27.7163i			0.880437i	0.897891	+	0.440218i	$0.145099\pi$
$991$			27.7163i			0.880437i	−0.897891	+	0.440218i	$0.854901\pi$
$992$	−15.4186	+	17.7968i	−0.489540	+	0.565050i
$993$	−36.1322	+	27.0892i	−1.14662	+	0.859649i
$994$	1.50420	−	10.4631i	0.0477104	−	0.331871i
$995$		−	20.7285i		−	0.657136i
$996$	−5.28315	−	14.1319i	−0.167403	−	0.447788i
$997$			25.2870i			0.800846i	0.916330	+	0.400423i	$0.131137\pi$
$997$			25.2870i			0.800846i	−0.916330	+	0.400423i	$0.868863\pi$
$998$	10.2912	+	1.47949i	0.325763	+	0.0468324i
$999$	−23.8864	+	8.96848i	−0.755731	+	0.283750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.e.d.491.3	yes	44
3.2	odd	2		840.2.e.c.491.42	yes	44
4.3	odd	2		3360.2.e.c.911.37		44
8.3	odd	2		840.2.e.c.491.41	✓	44
8.5	even	2		3360.2.e.d.911.37		44
12.11	even	2		3360.2.e.d.911.38		44
24.5	odd	2		3360.2.e.c.911.38		44
24.11	even	2	inner	840.2.e.d.491.4	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.e.c.491.41	✓	44	8.3	odd	2
840.2.e.c.491.42	yes	44	3.2	odd	2
840.2.e.d.491.3	yes	44	1.1	even	1	trivial
840.2.e.d.491.4	yes	44	24.11	even	2	inner
3360.2.e.c.911.37		44	4.3	odd	2
3360.2.e.c.911.38		44	24.5	odd	2
3360.2.e.d.911.37		44	8.5	even	2
3360.2.e.d.911.38		44	12.11	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39982 - 0.201241i) q^{2} +(-1.38582 + 1.03899i) q^{3} +(1.91900 + 0.563404i) q^{4} -1.00000 q^{5} +(2.14899 - 1.17551i) q^{6} +1.00000i q^{7} +(-2.57288 - 1.17485i) q^{8} +(0.841016 - 2.87970i) q^{9} +(1.39982 + 0.201241i) q^{10} -2.85691i q^{11} +(-3.24477 + 1.21304i) q^{12} +3.04377i q^{13} +(0.201241 - 1.39982i) q^{14} +(1.38582 - 1.03899i) q^{15} +(3.36515 + 2.16235i) q^{16} +1.28528i q^{17} +(-1.75679 + 3.86183i) q^{18} +3.94860 q^{19} +(-1.91900 - 0.563404i) q^{20} +(-1.03899 - 1.38582i) q^{21} +(-0.574929 + 3.99917i) q^{22} +6.49052 q^{23} +(4.78621 - 1.04506i) q^{24} +1.00000 q^{25} +(0.612531 - 4.26073i) q^{26} +(1.82647 + 4.86457i) q^{27} +(-0.563404 + 1.91900i) q^{28} -8.08470 q^{29} +(-2.14899 + 1.17551i) q^{30} -4.16256i q^{31} +(-4.27546 - 3.70411i) q^{32} +(2.96829 + 3.95918i) q^{33} +(0.258651 - 1.79916i) q^{34} -1.00000i q^{35} +(3.23635 - 5.05233i) q^{36} +4.91028i q^{37} +(-5.52733 - 0.794620i) q^{38} +(-3.16243 - 4.21812i) q^{39} +(2.57288 + 1.17485i) q^{40} +5.60633i q^{41} +(1.17551 + 2.14899i) q^{42} +0.729398 q^{43} +(1.60960 - 5.48243i) q^{44} +(-0.841016 + 2.87970i) q^{45} +(-9.08557 - 1.30616i) q^{46} +2.24535 q^{47} +(-6.91016 + 0.499713i) q^{48} -1.00000 q^{49} +(-1.39982 - 0.201241i) q^{50} +(-1.33539 - 1.78117i) q^{51} +(-1.71487 + 5.84100i) q^{52} -9.29752 q^{53} +(-1.57779 - 7.17709i) q^{54} +2.85691i q^{55} +(1.17485 - 2.57288i) q^{56} +(-5.47206 + 4.10254i) q^{57} +(11.3171 + 1.62698i) q^{58} +13.8177i q^{59} +(3.24477 - 1.21304i) q^{60} +6.42611i q^{61} +(-0.837678 + 5.82684i) q^{62} +(2.87970 + 0.841016i) q^{63} +(5.23947 + 6.04549i) q^{64} -3.04377i q^{65} +(-3.35833 - 6.13949i) q^{66} -10.4615 q^{67} +(-0.724130 + 2.46645i) q^{68} +(-8.99471 + 6.74356i) q^{69} +(-0.201241 + 1.39982i) q^{70} +7.47462 q^{71} +(-5.54705 + 6.42108i) q^{72} +6.39674 q^{73} +(0.988150 - 6.87351i) q^{74} +(-1.38582 + 1.03899i) q^{75} +(7.57737 + 2.22465i) q^{76} +2.85691 q^{77} +(3.57798 + 6.54103i) q^{78} +7.77084i q^{79} +(-3.36515 - 2.16235i) q^{80} +(-7.58538 - 4.84375i) q^{81} +(1.12822 - 7.84786i) q^{82} +4.35530i q^{83} +(-1.21304 - 3.24477i) q^{84} -1.28528i q^{85} +(-1.02103 - 0.146785i) q^{86} +(11.2040 - 8.39990i) q^{87} +(-3.35644 + 7.35051i) q^{88} +9.27251i q^{89} +(1.75679 - 3.86183i) q^{90} -3.04377 q^{91} +(12.4553 + 3.65678i) q^{92} +(4.32484 + 5.76857i) q^{93} +(-3.14310 - 0.451858i) q^{94} -3.94860 q^{95} +(9.77356 + 0.691099i) q^{96} -18.4478 q^{97} +(1.39982 + 0.201241i) q^{98} +(-8.22707 - 2.40271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} + 4 q^{3} - 2 q^{4} - 44 q^{5} - 6 q^{6} - 22 q^{8} + 4 q^{9} - 2 q^{10} + 6 q^{12} + 4 q^{14} - 4 q^{15} + 22 q^{16} + 2 q^{18} + 16 q^{19} + 2 q^{20} + 16 q^{23} + 10 q^{24} + 44 q^{25}+ \cdots - 64 q^{99}+O(q^{100}) \) 44 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 - 44 * q^5 - 6 * q^6 - 22 * q^8 + 4 * q^9 - 2 * q^10 + 6 * q^12 + 4 * q^14 - 4 * q^15 + 22 * q^16 + 2 * q^18 + 16 * q^19 + 2 * q^20 + 16 * q^23 + 10 * q^24 + 44 * q^25 - 16 * q^26 + 4 * q^27 + 16 * q^29 + 6 * q^30 - 18 * q^32 + 24 * q^33 + 20 * q^34 - 46 * q^36 + 8 * q^38 - 16 * q^39 + 22 * q^40 - 4 * q^42 + 24 * q^43 + 32 * q^44 - 4 * q^45 - 24 * q^47 + 18 * q^48 - 44 * q^49 + 2 * q^50 - 20 * q^52 - 32 * q^53 + 2 * q^54 + 8 * q^56 - 4 * q^58 - 6 * q^60 + 32 * q^62 - 50 * q^64 - 8 * q^66 + 24 * q^67 - 28 * q^68 - 8 * q^69 - 4 * q^70 + 8 * q^71 + 2 * q^72 + 8 * q^73 - 48 * q^74 + 4 * q^75 + 12 * q^76 + 8 * q^77 - 84 * q^78 - 22 * q^80 + 20 * q^81 - 8 * q^82 + 4 * q^84 - 4 * q^86 - 16 * q^87 - 28 * q^88 - 2 * q^90 - 16 * q^91 + 76 * q^92 + 16 * q^93 - 16 * q^95 + 38 * q^96 + 24 * q^97 - 2 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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