LMFDB - Embedded newform 644.2.bc.a.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(5,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 3]))

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

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

chi := DirichletCharacter("644.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.bc (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			33.1
Character	$\chi$	$=$	644.33
Dual form			644.2.bc.a.605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.04644 - 0.145120i) q^{3} +(-1.07542 - 1.51021i) q^{5} +(0.0585572 + 2.64510i) q^{7} +(6.27334 + 0.599031i) q^{9} +(-0.768950 + 3.98969i) q^{11} +(-0.754092 - 2.56820i) q^{13} +(3.05703 + 4.75684i) q^{15} +(-2.43273 + 1.91312i) q^{17} +(-0.706577 - 0.555658i) q^{19} +(0.205466 - 8.06665i) q^{21} +(3.02028 - 3.72530i) q^{23} +(0.511122 - 1.47679i) q^{25} +(-9.96788 - 1.43316i) q^{27} +(0.0489273 + 0.340297i) q^{29} +(2.94183 - 5.70636i) q^{31} +(2.92155 - 12.0428i) q^{33} +(3.93169 - 2.93302i) q^{35} +(1.03813 - 10.8718i) q^{37} +(1.92460 + 7.93332i) q^{39} +(-0.0451801 - 0.0206330i) q^{41} +(0.464852 - 0.723324i) q^{43} +(-5.84179 - 10.1183i) q^{45} +(0.203874 + 0.117706i) q^{47} +(-6.99314 + 0.309780i) q^{49} +(7.68881 - 5.47518i) q^{51} +(4.58060 - 1.11124i) q^{53} +(6.85222 - 3.12930i) q^{55} +(2.07191 + 1.79532i) q^{57} +(3.94835 - 4.14091i) q^{59} +(-0.335125 - 7.03513i) q^{61} +(-1.21715 + 16.6287i) q^{63} +(-3.06757 + 3.90073i) q^{65} +(-15.0219 - 5.19913i) q^{67} +(-9.74173 + 10.9106i) q^{69} +(8.53411 + 9.84889i) q^{71} +(3.52355 + 8.80140i) q^{73} +(-1.77142 + 4.42478i) q^{75} +(-10.5982 - 1.80033i) q^{77} +(7.98905 + 1.93812i) q^{79} +(11.5946 + 2.23468i) q^{81} +(-2.99479 - 6.55767i) q^{83} +(5.50542 + 1.61654i) q^{85} +(-0.0996703 - 1.04379i) q^{87} +(9.24084 - 4.76398i) q^{89} +(6.74900 - 2.14504i) q^{91} +(-9.79023 + 16.9572i) q^{93} +(-0.0792968 + 1.66465i) q^{95} +(6.46235 - 14.1506i) q^{97} +(-7.21383 + 24.5681i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71}+ \cdots + 242 q^{99}+O(q^{100}) $ 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{22}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−3.04644	−	0.145120i	−1.75886	−	0.0837851i	−0.856870	−	0.515532i	$-0.827594\pi$
$3$	−3.04644	−	0.145120i	−1.75886	−	0.0837851i	−0.901995	+	0.431747i	$0.857897\pi$
$4$		0			0
$5$	−1.07542	−	1.51021i	−0.480941	−	0.675387i	0.500810	−	0.865557i	$-0.333035\pi$
$5$	−1.07542	−	1.51021i	−0.480941	−	0.675387i	−0.981751	+	0.190170i	$0.939096\pi$
$6$		0			0
$7$	0.0585572	+	2.64510i	0.0221326	+	0.999755i
$7$	0.0585572	+	2.64510i	0.0221326	+	0.999755i
$8$		0			0
$9$	6.27334	+	0.599031i	2.09111	+	0.199677i
$10$		0			0
$11$	−0.768950	+	3.98969i	−0.231847	+	1.20294i	0.660233	+	0.751061i	$0.270457\pi$
$11$	−0.768950	+	3.98969i	−0.231847	+	1.20294i	−0.892080	+	0.451877i	$0.850755\pi$
$12$		0			0
$13$	−0.754092	−	2.56820i	−0.209148	−	0.712291i	−0.995521	−	0.0945399i	$-0.969862\pi$
$13$	−0.754092	−	2.56820i	−0.209148	−	0.712291i	0.786374	−	0.617751i	$-0.211956\pi$
$14$		0			0
$15$	3.05703	+	4.75684i	0.789323	+	1.22821i
$16$		0			0
$17$	−2.43273	+	1.91312i	−0.590024	+	0.464000i	−0.867984	−	0.496592i	$-0.834584\pi$
$17$	−2.43273	+	1.91312i	−0.590024	+	0.464000i	0.277959	+	0.960593i	$0.410342\pi$
$18$		0			0
$19$	−0.706577	−	0.555658i	−0.162100	−	0.127477i	0.533814	−	0.845602i	$-0.320758\pi$
$19$	−0.706577	−	0.555658i	−0.162100	−	0.127477i	−0.695914	+	0.718125i	$0.745001\pi$
$20$		0			0
$21$	0.205466	−	8.06665i	0.0448364	−	1.76029i
$22$		0			0
$23$	3.02028	−	3.72530i	0.629772	−	0.776780i
$23$	3.02028	−	3.72530i	0.629772	−	0.776780i
$24$		0			0
$25$	0.511122	−	1.47679i	0.102224	−	0.295358i
$26$		0			0
$27$	−9.96788	−	1.43316i	−1.91832	−	0.275813i
$28$		0			0
$29$	0.0489273	+	0.340297i	0.00908556	+	0.0631915i	0.993860	−	0.110647i	$-0.0352922\pi$
$29$	0.0489273	+	0.340297i	0.00908556	+	0.0631915i	−0.984774	+	0.173838i	$0.944383\pi$
$30$		0			0
$31$	2.94183	−	5.70636i	0.528368	−	1.02489i	−0.462058	−	0.886850i	$-0.652889\pi$
$31$	2.94183	−	5.70636i	0.528368	−	1.02489i	0.990426	−	0.138042i	$-0.0440809\pi$
$32$		0			0
$33$	2.92155	−	12.0428i	0.508576	−	2.09638i
$34$		0			0
$35$	3.93169	−	2.93302i	0.664577	−	0.495771i
$36$		0			0
$37$	1.03813	−	10.8718i	0.170668	−	1.78732i	−0.353233	−	0.935536i	$-0.614918\pi$
$37$	1.03813	−	10.8718i	0.170668	−	1.78732i	0.523900	−	0.851780i	$-0.324476\pi$
$38$		0			0
$39$	1.92460	+	7.93332i	0.308183	+	1.27035i
$40$		0			0
$41$	−0.0451801	−	0.0206330i	−0.00705594	−	0.00322234i	0.411884	−	0.911236i	$-0.364871\pi$
$41$	−0.0451801	−	0.0206330i	−0.00705594	−	0.00322234i	−0.418940	+	0.908014i	$0.637598\pi$
$42$		0			0
$43$	0.464852	−	0.723324i	0.0708893	−	0.110306i	−0.803999	−	0.594631i	$-0.797298\pi$
$43$	0.464852	−	0.723324i	0.0708893	−	0.110306i	0.874888	+	0.484325i	$0.160935\pi$
$44$		0			0
$45$	−5.84179	−	10.1183i	−0.870843	−	1.50834i
$46$		0			0
$47$	0.203874	+	0.117706i	0.0297380	+	0.0171693i	0.514795	−	0.857313i	$-0.327868\pi$
$47$	0.203874	+	0.117706i	0.0297380	+	0.0171693i	−0.485057	+	0.874482i	$0.661201\pi$
$48$		0			0
$49$	−6.99314	+	0.309780i	−0.999020	+	0.0442543i
$50$		0			0
$51$	7.68881	−	5.47518i	1.07665	−	0.766679i
$52$		0			0
$53$	4.58060	−	1.11124i	0.629193	−	0.152641i	0.0915327	−	0.995802i	$-0.470823\pi$
$53$	4.58060	−	1.11124i	0.629193	−	0.152641i	0.537660	+	0.843161i	$0.319308\pi$
$54$		0			0
$55$	6.85222	−	3.12930i	0.923953	−	0.421955i
$56$		0			0
$57$	2.07191	+	1.79532i	0.274431	+	0.237796i
$58$		0			0
$59$	3.94835	−	4.14091i	0.514031	−	0.539100i	−0.414649	−	0.909981i	$-0.636096\pi$
$59$	3.94835	−	4.14091i	0.514031	−	0.539100i	0.928680	+	0.370881i	$0.120944\pi$
$60$		0			0
$61$	−0.335125	−	7.03513i	−0.0429083	−	0.900757i	−0.913023	−	0.407908i	$-0.866259\pi$
$61$	−0.335125	−	7.03513i	−0.0429083	−	0.900757i	0.870115	−	0.492849i	$-0.164044\pi$
$62$		0			0
$63$	−1.21715	+	16.6287i	−0.153347	+	2.09502i
$64$		0			0
$65$	−3.06757	+	3.90073i	−0.380485	+	0.483826i
$66$		0			0
$67$	−15.0219	−	5.19913i	−1.83522	−	0.635175i	−0.995786	−	0.0917096i	$-0.970767\pi$
$67$	−15.0219	−	5.19913i	−1.83522	−	0.635175i	−0.839432	−	0.543465i	$-0.817112\pi$
$68$		0			0
$69$	−9.74173	+	10.9106i	−1.17277	+	1.31348i
$70$		0			0
$71$	8.53411	+	9.84889i	1.01281	+	1.16885i	0.985578	+	0.169219i	$0.0541245\pi$
$71$	8.53411	+	9.84889i	1.01281	+	1.16885i	0.0272342	+	0.999629i	$0.491330\pi$
$72$		0			0
$73$	3.52355	+	8.80140i	0.412400	+	1.03013i	0.978584	+	0.205847i	$0.0659949\pi$
$73$	3.52355	+	8.80140i	0.412400	+	1.03013i	−0.566184	+	0.824279i	$0.691581\pi$
$74$		0			0
$75$	−1.77142	+	4.42478i	−0.204546	+	0.510930i
$76$		0			0
$77$	−10.5982	−	1.80033i	−1.20777	−	0.205166i
$78$		0			0
$79$	7.98905	+	1.93812i	0.898839	+	0.218056i	0.658453	−	0.752622i	$-0.271211\pi$
$79$	7.98905	+	1.93812i	0.898839	+	0.218056i	0.240386	+	0.970677i	$0.422726\pi$
$80$		0			0
$81$	11.5946	+	2.23468i	1.28829	+	0.248298i
$82$		0			0
$83$	−2.99479	−	6.55767i	−0.328721	−	0.719798i	0.671046	−	0.741416i	$-0.265845\pi$
$83$	−2.99479	−	6.55767i	−0.328721	−	0.719798i	−0.999766	+	0.0216181i	$0.993118\pi$
$84$		0			0
$85$	5.50542	+	1.61654i	0.597147	+	0.175338i
$86$		0			0
$87$	−0.0996703	−	1.04379i	−0.0106858	−	0.111906i
$88$		0			0
$89$	9.24084	−	4.76398i	0.979527	−	0.504981i	0.107376	−	0.994218i	$-0.465755\pi$
$89$	9.24084	−	4.76398i	0.979527	−	0.504981i	0.872151	+	0.489237i	$0.162725\pi$
$90$		0			0
$91$	6.74900	−	2.14504i	0.707488	−	0.224861i
$92$		0			0
$93$	−9.79023	+	16.9572i	−1.01520	+	1.75838i
$94$		0			0
$95$	−0.0792968	+	1.66465i	−0.00813568	+	0.170789i
$96$		0			0
$97$	6.46235	−	14.1506i	0.656152	−	1.43677i	−0.229912	−	0.973211i	$-0.573844\pi$
$97$	6.46235	−	14.1506i	0.656152	−	1.43677i	0.886065	−	0.463562i	$-0.153429\pi$
$98$		0			0
$99$	−7.21383	+	24.5681i	−0.725018	+	2.46918i
$100$		0			0
$101$	15.2513	+	10.8604i	1.51756	+	1.08065i	0.969767	+	0.244032i	$0.0784703\pi$
$101$	15.2513	+	10.8604i	1.51756	+	1.08065i	0.547791	+	0.836616i	$0.315469\pi$
$102$		0			0
$103$	−5.92974	−	17.1329i	−0.584275	−	1.68815i	−0.717065	−	0.697006i	$-0.754515\pi$
$103$	−5.92974	−	17.1329i	−0.584275	−	1.68815i	0.132790	−	0.991144i	$-0.457606\pi$
$104$		0			0
$105$	−12.4033	+	8.36472i	−1.21044	+	0.816313i
$106$		0			0
$107$	−5.28203	+	0.251614i	−0.510633	+	0.0243244i	−0.301318	−	0.953524i	$-0.597426\pi$
$107$	−5.28203	+	0.251614i	−0.510633	+	0.0243244i	−0.209315	+	0.977848i	$0.567123\pi$
$108$		0			0
$109$	−7.21693	−	9.17707i	−0.691256	−	0.879004i	0.306076	−	0.952007i	$-0.400984\pi$
$109$	−7.21693	−	9.17707i	−0.691256	−	0.879004i	−0.997332	+	0.0730035i	$0.976742\pi$
$110$		0			0
$111$	−4.74033	+	32.9697i	−0.449932	+	3.12935i
$112$		0			0
$113$	−2.84922	+	2.46886i	−0.268032	+	0.232251i	−0.778498	−	0.627647i	$-0.784018\pi$
$113$	−2.84922	+	2.46886i	−0.268032	+	0.232251i	0.510466	+	0.859898i	$0.329473\pi$
$114$		0			0
$115$	−8.87406	−	0.555010i	−0.827510	−	0.0517550i
$116$		0			0
$117$	−3.19224	−	16.5629i	−0.295123	−	1.53124i
$118$		0			0
$119$	−5.20286	−	6.32280i	−0.476945	−	0.579610i
$120$		0			0
$121$	−5.11430	−	2.04746i	−0.464937	−	0.186133i
$122$		0			0
$123$	0.134644	+	0.0694139i	0.0121405	+	0.00625884i
$124$		0			0
$125$	−11.6744	+	3.42790i	−1.04419	+	0.306601i
$126$		0			0
$127$	−4.65401	+	5.37101i	−0.412977	+	0.476600i	−0.923685	−	0.383154i	$-0.874838\pi$
$127$	−4.65401	+	5.37101i	−0.412977	+	0.476600i	0.510708	+	0.859754i	$0.329383\pi$
$128$		0			0
$129$	−1.52111	+	2.13611i	−0.133927	+	0.188074i
$130$		0			0
$131$	0.934761	+	0.980349i	0.0816705	+	0.0856535i	0.763301	−	0.646043i	$-0.223577\pi$
$131$	0.934761	+	0.980349i	0.0816705	+	0.0856535i	−0.681631	+	0.731696i	$0.738729\pi$
$132$		0			0
$133$	1.42840	−	1.90151i	0.123858	−	0.164882i
$134$		0			0
$135$	8.55524	+	16.5949i	0.736318	+	1.42826i
$136$		0			0
$137$	1.50791	−	0.870592i	0.128829	−	0.0743797i	−0.434200	−	0.900816i	$-0.642969\pi$
$137$	1.50791	−	0.870592i	0.128829	−	0.0743797i	0.563030	+	0.826437i	$0.309636\pi$
$138$		0			0
$139$			11.4078i			0.967594i	0.875180	+	0.483797i	$0.160743\pi$
$139$			11.4078i			0.967594i	−0.875180	+	0.483797i	$0.839257\pi$
$140$		0			0
$141$	−0.604008	−	0.388172i	−0.0508666	−	0.0326900i
$142$		0			0
$143$	10.8262	−	1.03378i	0.905332	−	0.0864487i
$144$		0			0
$145$	0.461303	−	0.439851i	0.0383091	−	0.0365276i
$146$		0			0
$147$	21.3492	+	0.0711180i	1.76085	+	0.00586571i
$148$		0			0
$149$	7.04958	−	2.43989i	0.577524	−	0.199883i	−0.0226621	−	0.999743i	$-0.507214\pi$
$149$	7.04958	−	2.43989i	0.577524	−	0.199883i	0.600187	+	0.799860i	$0.295093\pi$
$150$		0			0
$151$	10.2417	+	9.76547i	0.833460	+	0.794703i	0.980930	−	0.194364i	$-0.0622642\pi$
$151$	10.2417	+	9.76547i	0.833460	+	0.794703i	−0.147469	+	0.989067i	$0.547113\pi$
$152$		0			0
$153$	−16.4074	+	10.5444i	−1.32646	+	0.852463i
$154$		0			0
$155$	−11.7815	+	1.69392i	−0.946313	+	0.136059i
$156$		0			0
$157$	1.83406	−	0.734248i	0.146374	−	0.0585994i	−0.297319	−	0.954778i	$-0.596092\pi$
$157$	1.83406	−	0.734248i	0.146374	−	0.0585994i	0.443693	+	0.896179i	$0.353668\pi$
$158$		0			0
$159$	−14.1158	+	2.72059i	−1.11945	+	0.215757i
$160$		0			0
$161$	10.0307	+	7.77082i	0.790528	+	0.612426i
$162$		0			0
$163$	16.0238	−	3.08833i	1.25508	−	0.241897i	0.481980	−	0.876182i	$-0.339918\pi$
$163$	16.0238	−	3.08833i	1.25508	−	0.241897i	0.773099	+	0.634285i	$0.218706\pi$
$164$		0			0
$165$	−21.3290	+	8.53885i	−1.66046	+	0.664749i
$166$		0			0
$167$	−23.9241	+	3.43976i	−1.85130	+	0.266177i	−0.976058	−	0.217511i	$-0.930206\pi$
$167$	−23.9241	+	3.43976i	−1.85130	+	0.266177i	−0.875241	+	0.483687i	$0.839297\pi$
$168$		0			0
$169$	4.90929	−	3.15501i	0.377638	−	0.242693i
$170$		0			0
$171$	−4.09974	−	3.90910i	−0.313515	−	0.298936i
$172$		0			0
$173$	13.1373	−	4.54685i	0.998808	−	0.345691i	0.221739	−	0.975106i	$-0.428827\pi$
$173$	13.1373	−	4.54685i	0.998808	−	0.345691i	0.777069	+	0.629415i	$0.216706\pi$
$174$		0			0
$175$	3.93619	+	1.26549i	0.297548	+	0.0956623i
$176$		0			0
$177$	−12.6293	+	12.0421i	−0.949280	+	0.905136i
$178$		0			0
$179$	2.28256	−	0.217958i	0.170606	−	0.0162909i	−0.00940328	−	0.999956i	$-0.502993\pi$
$179$	2.28256	−	0.217958i	0.170606	−	0.0162909i	0.180010	+	0.983665i	$0.442387\pi$
$180$		0			0
$181$	7.06707	+	4.54173i	0.525291	+	0.337584i	0.776262	−	0.630411i	$-0.217113\pi$
$181$	7.06707	+	4.54173i	0.525291	+	0.337584i	−0.250971	+	0.967995i	$0.580750\pi$
$182$		0			0
$183$			21.4808i			1.58790i
$184$		0			0
$185$	−17.5352	+	10.1239i	−1.28921	+	0.744326i
$186$		0			0
$187$	−5.76212	−	11.1769i	−0.421368	−	0.817339i
$188$		0			0
$189$	3.20718	−	26.4500i	0.233288	−	1.92395i
$190$		0			0
$191$	−15.0017	−	15.7333i	−1.08548	−	1.13842i	−0.989720	−	0.143017i	$-0.954320\pi$
$191$	−15.0017	−	15.7333i	−1.08548	−	1.13842i	−0.0957621	−	0.995404i	$-0.530529\pi$
$192$		0			0
$193$	7.08486	−	9.94929i	0.509979	−	0.716165i	−0.476660	−	0.879088i	$-0.658153\pi$
$193$	7.08486	−	9.94929i	0.509979	−	0.716165i	0.986639	+	0.162922i	$0.0520920\pi$
$194$		0			0
$195$	9.91124	−	11.4382i	0.709758	−	0.819105i
$196$		0			0
$197$	15.6291	−	4.58913i	1.11353	−	0.326962i	0.327316	−	0.944915i	$-0.393856\pi$
$197$	15.6291	−	4.58913i	1.11353	−	0.326962i	0.786215	+	0.617953i	$0.212038\pi$
$198$		0			0
$199$	−7.29527	−	3.76097i	−0.517148	−	0.266608i	0.179834	−	0.983697i	$-0.442444\pi$
$199$	−7.29527	−	3.76097i	−0.517148	−	0.266608i	−0.696982	+	0.717089i	$0.745474\pi$
$200$		0			0
$201$	45.0089	+	18.0188i	3.17468	+	1.27095i
$202$		0			0
$203$	−0.897254	+	0.149344i	−0.0629749	+	0.0104819i
$204$		0			0
$205$	0.0174271	+	0.0904206i	0.00121716	+	0.00631525i
$206$		0			0
$207$	21.1788	−	21.5609i	1.47203	−	1.49858i
$208$		0			0
$209$	2.76023	−	2.39175i	0.190929	−	0.165441i
$210$		0			0
$211$	2.95873	−	20.5784i	0.203688	−	1.41668i	−0.589533	−	0.807744i	$-0.700688\pi$
$211$	2.95873	−	20.5784i	0.203688	−	1.41668i	0.793221	−	0.608934i	$-0.208403\pi$
$212$		0			0
$213$	−24.5694	−	31.2426i	−1.68347	−	2.14070i
$214$		0			0
$215$	−1.59228	+	0.0758498i	−0.108593	+	0.00517291i
$216$		0			0
$217$	15.2662	+	7.44730i	1.03633	+	0.505556i
$218$		0			0
$219$	−9.45703	−	27.3243i	−0.639047	−	1.84640i
$220$		0			0
$221$	6.74779	+	4.80508i	0.453906	+	0.323225i
$222$		0			0
$223$	2.49454	−	8.49562i	0.167047	−	0.568909i	−0.832835	−	0.553521i	$-0.813284\pi$
$223$	2.49454	−	8.49562i	0.167047	−	0.568909i	0.999882	−	0.0153872i	$-0.00489811\pi$
$224$		0			0
$225$	4.09109	−	8.95823i	0.272739	−	0.597215i
$226$		0			0
$227$	−0.914116	+	19.1897i	−0.0606720	+	1.27366i	0.739197	+	0.673489i	$0.235205\pi$
$227$	−0.914116	+	19.1897i	−0.0606720	+	1.27366i	−0.799870	+	0.600174i	$0.795098\pi$
$228$		0			0
$229$	−3.06866	+	5.31508i	−0.202783	+	0.351230i	−0.949424	−	0.313997i	$-0.898332\pi$
$229$	−3.06866	+	5.31508i	−0.202783	+	0.351230i	0.746641	+	0.665227i	$0.231665\pi$
$230$		0			0
$231$	32.0255	+	7.02260i	2.10712	+	0.462053i
$232$		0			0
$233$	−15.5033	+	7.99253i	−1.01566	+	0.523608i	−0.883901	−	0.467674i	$-0.845092\pi$
$233$	−15.5033	+	7.99253i	−1.01566	+	0.523608i	−0.131757	+	0.991282i	$0.542062\pi$
$234$		0			0
$235$	−0.0414874	−	0.434476i	−0.00270634	−	0.0283421i
$236$		0			0
$237$	−24.0569	−	7.06376i	−1.56267	−	0.458840i
$238$		0			0
$239$	−12.5066	−	27.3857i	−0.808988	−	1.77144i	−0.611700	−	0.791090i	$-0.709514\pi$
$239$	−12.5066	−	27.3857i	−0.808988	−	1.77144i	−0.197288	−	0.980346i	$-0.563213\pi$
$240$		0			0
$241$	30.3060	+	5.84100i	1.95218	+	0.376252i	0.996698	+	0.0812011i	$0.0258756\pi$
$241$	30.3060	+	5.84100i	1.95218	+	0.376252i	0.955482	+	0.295051i	$0.0953365\pi$
$242$		0			0
$243$	−5.63851	−	1.36789i	−0.361711	−	0.0877500i
$244$		0			0
$245$	7.98838	+	10.2280i	0.510359	+	0.653442i
$246$		0			0
$247$	−0.894219	+	2.23365i	−0.0568978	+	0.142124i
$248$		0			0
$249$	8.17180	+	20.4122i	0.517867	+	1.29357i
$250$		0			0
$251$	−10.3345	−	11.9267i	−0.652311	−	0.752807i	0.329190	−	0.944264i	$-0.393224\pi$
$251$	−10.3345	−	11.9267i	−0.652311	−	0.752807i	−0.981501	+	0.191457i	$0.938679\pi$
$252$		0			0
$253$	12.5404	+	14.9146i	0.788406	+	0.937671i
$254$		0			0
$255$	−16.5374	−	5.72364i	−1.03561	−	0.358428i
$256$		0			0
$257$	−12.7044	+	16.1549i	−0.792478	+	1.00772i	0.207090	+	0.978322i	$0.433601\pi$
$257$	−12.7044	+	16.1549i	−0.792478	+	1.00772i	−0.999568	+	0.0293960i	$0.990642\pi$
$258$		0			0
$259$	28.8179	+	2.10934i	1.79065	+	0.131068i
$260$		0			0
$261$	0.103089	+	2.16410i	0.00638105	+	0.133955i
$262$		0			0
$263$	6.14946	−	6.44937i	0.379192	−	0.397685i	−0.506287	−	0.862365i	$-0.668982\pi$
$263$	6.14946	−	6.44937i	0.379192	−	0.397685i	0.885479	+	0.464680i	$0.153831\pi$
$264$		0			0
$265$	−6.60426	−	5.72262i	−0.405696	−	0.351538i
$266$		0			0
$267$	−28.8430	+	13.1722i	−1.76517	+	0.806124i
$268$		0			0
$269$	−16.8735	+	4.09348i	−1.02880	+	0.249584i	−0.714422	−	0.699715i	$-0.753310\pi$
$269$	−16.8735	+	4.09348i	−1.02880	+	0.249584i	−0.314376	+	0.949299i	$0.601795\pi$
$270$		0			0
$271$	−4.39370	+	3.12874i	−0.266898	+	0.190057i	−0.705669	−	0.708542i	$-0.749353\pi$
$271$	−4.39370	+	3.12874i	−0.266898	+	0.190057i	0.438771	+	0.898599i	$0.355414\pi$
$272$		0			0
$273$	−20.8717	+	5.55532i	−1.26322	+	0.336223i
$274$		0			0
$275$	5.49891	+	3.17480i	0.331597	+	0.191447i
$276$		0			0
$277$	0.645784	+	1.11853i	0.0388014	+	0.0672060i	0.884774	−	0.466020i	$-0.154313\pi$
$277$	0.645784	+	1.11853i	0.0388014	+	0.0672060i	−0.845973	+	0.533226i	$0.820979\pi$
$278$		0			0
$279$	21.8734	−	34.0357i	1.30953	−	2.03766i
$280$		0			0
$281$	−14.0197	−	6.40257i	−0.836344	−	0.381945i	−0.0492558	−	0.998786i	$-0.515685\pi$
$281$	−14.0197	−	6.40257i	−0.836344	−	0.381945i	−0.787088	+	0.616841i	$0.788412\pi$
$282$		0			0
$283$	0.921147	+	3.79702i	0.0547565	+	0.225709i	0.992615	−	0.121309i	$-0.0387093\pi$
$283$	0.921147	+	3.79702i	0.0547565	+	0.225709i	−0.937858	+	0.347019i	$0.887194\pi$
$284$		0			0
$285$	0.483147	−	5.05974i	0.0286191	−	0.299713i
$286$		0			0
$287$	0.0519309	−	0.120714i	0.00306538	−	0.00712553i
$288$		0			0
$289$	−1.74975	+	7.21256i	−0.102926	+	0.424269i
$290$		0			0
$291$	−21.7407	+	42.1711i	−1.27446	+	2.47211i
$292$		0			0
$293$	−3.86152	−	26.8574i	−0.225592	−	1.56903i	−0.716356	−	0.697735i	$-0.754191\pi$
$293$	−3.86152	−	26.8574i	−0.225592	−	1.56903i	0.490763	−	0.871293i	$-0.336718\pi$
$294$		0			0
$295$	−10.4998	−	1.50964i	−0.611320	−	0.0878946i
$296$		0			0
$297$	13.3827	−	38.6667i	0.776542	−	2.24367i
$298$		0			0
$299$	−11.8449	−	4.94747i	−0.685009	−	0.286120i
$300$		0			0
$301$	1.94049	+	1.18723i	0.111848	+	0.0684306i
$302$		0			0
$303$	−44.8861	−	35.2988i	−2.57864	−	2.02786i
$304$		0			0
$305$	−10.2641	+	8.07181i	−0.587723	+	0.462191i
$306$		0			0
$307$	3.75513	+	5.84310i	0.214317	+	0.333484i	0.931722	−	0.363173i	$-0.118307\pi$
$307$	3.75513	+	5.84310i	0.214317	+	0.333484i	−0.717405	+	0.696656i	$0.754670\pi$
$308$		0			0
$309$	15.5783	+	53.0548i	0.886218	+	3.01818i
$310$		0			0
$311$	−1.80553	+	9.36800i	−0.102382	+	0.531210i	0.894133	+	0.447801i	$0.147793\pi$
$311$	−1.80553	+	9.36800i	−0.102382	+	0.531210i	−0.996515	+	0.0834088i	$0.973419\pi$
$312$		0			0
$313$	−3.58781	−	0.342594i	−0.202795	−	0.0193646i	−0.00683591	−	0.999977i	$-0.502176\pi$
$313$	−3.58781	−	0.342594i	−0.202795	−	0.0193646i	−0.195959	+	0.980612i	$0.562782\pi$
$314$		0			0
$315$	26.4218	−	16.0446i	1.48870	−	0.904013i
$316$		0			0
$317$	13.3838	+	18.7949i	0.751707	+	1.05562i	0.996295	+	0.0859977i	$0.0274078\pi$
$317$	13.3838	+	18.7949i	0.751707	+	1.05562i	−0.244588	+	0.969627i	$0.578653\pi$
$318$		0			0
$319$	−1.39530	−	0.0664664i	−0.0781218	−	0.00372140i
$320$		0			0
$321$	16.1279			0.900172
$322$		0			0
$323$	2.78196			0.154792
$324$		0			0
$325$	−4.17813	−	0.199029i	−0.231761	−	0.0110401i
$326$		0			0
$327$	20.6542	+	29.0047i	1.14218	+	1.60397i
$328$		0			0
$329$	−0.299407	+	0.546159i	−0.0165069	+	0.0301107i
$330$		0			0
$331$	−26.8350	−	2.56243i	−1.47498	−	0.140844i	−0.673646	−	0.739055i	$-0.735273\pi$
$331$	−26.8350	−	2.56243i	−1.47498	−	0.140844i	−0.801339	+	0.598211i	$0.795879\pi$
$332$		0			0
$333$	13.0251	−	67.5807i	0.713772	−	3.70340i
$334$		0			0
$335$	8.30302	+	28.2775i	0.453642	+	1.54496i
$336$		0			0
$337$	−17.9490	−	27.9291i	−0.977742	−	1.52140i	−0.848100	−	0.529836i	$-0.822254\pi$
$337$	−17.9490	−	27.9291i	−0.977742	−	1.52140i	−0.129642	−	0.991561i	$-0.541383\pi$
$338$		0			0
$339$	9.03827	−	7.10777i	0.490891	−	0.386041i
$340$		0			0
$341$	20.5045	+	16.1249i	1.11038	+	0.873212i
$342$		0			0
$343$	−1.22890	−	18.4794i	−0.0663543	−	0.997796i
$344$		0			0
$345$	26.9538	+	2.97861i	1.45114	+	0.160363i
$346$		0			0
$347$	3.53974	−	10.2274i	0.190023	−	0.549036i	−0.809238	−	0.587482i	$-0.800119\pi$
$347$	3.53974	−	10.2274i	0.190023	−	0.549036i	0.999261	+	0.0384458i	$0.0122407\pi$
$348$		0			0
$349$	−15.1377	−	2.17647i	−0.810303	−	0.116504i	−0.275305	−	0.961357i	$-0.588779\pi$
$349$	−15.1377	−	2.17647i	−0.810303	−	0.116504i	−0.534998	+	0.844853i	$0.679688\pi$
$350$		0			0
$351$	3.83604	+	26.6803i	0.204753	+	1.42409i
$352$		0			0
$353$	−10.4787	+	20.3257i	−0.557722	+	1.08183i	0.426433	+	0.904519i	$0.359770\pi$
$353$	−10.4787	+	20.3257i	−0.557722	+	1.08183i	−0.984155	+	0.177311i	$0.943260\pi$
$354$		0			0
$355$	5.69618	−	23.4800i	0.302322	−	1.24619i
$356$		0			0
$357$	14.9327	+	20.0171i	0.790320	+	1.05942i
$358$		0			0
$359$	1.23578	−	12.9416i	0.0652218	−	0.683033i	−0.902446	−	0.430804i	$-0.858230\pi$
$359$	1.23578	−	12.9416i	0.0652218	−	0.683033i	0.967667	−	0.252230i	$-0.0811638\pi$
$360$		0			0
$361$	−4.28892	−	17.6792i	−0.225733	−	0.930484i
$362$		0			0
$363$	15.2833	+	6.97965i	0.802166	+	0.366337i
$364$		0			0
$365$	9.50269	−	14.7865i	0.497394	−	0.773960i
$366$		0			0
$367$	4.45159	+	7.71038i	0.232371	+	0.402479i	0.958505	−	0.285074i	$-0.0920183\pi$
$367$	4.45159	+	7.71038i	0.232371	+	0.402479i	−0.726134	+	0.687553i	$0.758685\pi$
$368$		0			0
$369$	−0.271070	−	0.156502i	−0.0141113	−	0.00814719i
$370$		0			0
$371$	3.20757	+	12.0511i	0.166529	+	0.625661i
$372$		0			0
$373$	−8.89872	+	6.33675i	−0.460758	+	0.328105i	−0.786754	−	0.617267i	$-0.788240\pi$
$373$	−8.89872	+	6.33675i	−0.460758	+	0.328105i	0.325996	+	0.945371i	$0.394301\pi$
$374$		0			0
$375$	36.0627	−	8.74873i	1.86227	−	0.451782i
$376$		0			0
$377$	0.837055	−	0.382270i	0.0431105	−	0.0196879i
$378$		0			0
$379$	−3.49220	−	3.02601i	−0.179382	−	0.155436i	0.560541	−	0.828126i	$-0.310593\pi$
$379$	−3.49220	−	3.02601i	−0.179382	−	0.155436i	−0.739924	+	0.672691i	$0.765139\pi$
$380$		0			0
$381$	14.9576	−	15.6871i	0.766302	−	0.803674i
$382$		0			0
$383$	−0.112987	−	2.37189i	−0.00577336	−	0.121198i	−0.999914	−	0.0131046i	$-0.995829\pi$
$383$	−0.112987	−	2.37189i	−0.00577336	−	0.121198i	0.994141	−	0.108093i	$-0.0344745\pi$
$384$		0			0
$385$	8.67858	+	17.9416i	0.442301	+	0.914388i
$386$		0			0
$387$	3.34947	−	4.25920i	0.170263	−	0.216507i
$388$		0			0
$389$	−23.1655	−	8.01765i	−1.17454	−	0.406511i	−0.331025	−	0.943622i	$-0.607394\pi$
$389$	−23.1655	−	8.01765i	−1.17454	−	0.406511i	−0.843512	+	0.537111i	$0.819516\pi$
$390$		0			0
$391$	−0.220577	+	14.8408i	−0.0111551	+	0.750534i
$392$		0			0
$393$	−2.70543	−	3.12223i	−0.136471	−	0.157496i
$394$		0			0
$395$	−5.66459	−	14.1495i	−0.285016	−	0.711936i
$396$		0			0
$397$	−4.11268	+	10.2730i	−0.206409	+	0.515586i	−0.995062	−	0.0992529i	$-0.968355\pi$
$397$	−4.11268	+	10.2730i	−0.206409	+	0.515586i	0.788653	+	0.614839i	$0.210779\pi$
$398$		0			0
$399$	−4.62748	+	5.58554i	−0.231664	+	0.279627i
$400$		0			0
$401$	6.01208	+	1.45851i	0.300229	+	0.0728347i	0.383044	−	0.923730i	$-0.374876\pi$
$401$	6.01208	+	1.45851i	0.300229	+	0.0728347i	−0.0828149	+	0.996565i	$0.526391\pi$
$402$		0			0
$403$	−16.8735	−	3.25210i	−0.840528	−	0.161999i
$404$		0			0
$405$	−9.09421	−	19.9135i	−0.451895	−	0.989512i
$406$		0			0
$407$	42.5769	+	12.5017i	2.11046	+	0.619687i
$408$		0			0
$409$	−2.65694	−	27.8247i	−0.131377	−	1.37584i	−0.785222	−	0.619214i	$-0.787451\pi$
$409$	−2.65694	−	27.8247i	−0.131377	−	1.37584i	0.653845	−	0.756629i	$-0.273155\pi$
$410$		0			0
$411$	−4.72010	+	2.43338i	−0.232826	+	0.120030i
$412$		0			0
$413$	11.1843	+	10.2013i	0.550345	+	0.501974i
$414$		0			0
$415$	−6.68283	+	11.5750i	−0.328047	+	0.568194i
$416$		0			0
$417$	1.65549	−	34.7531i	0.0810699	−	1.70187i
$418$		0			0
$419$	−8.79756	+	19.2640i	−0.429789	+	0.941106i	0.563572	+	0.826067i	$0.309427\pi$
$419$	−8.79756	+	19.2640i	−0.429789	+	0.941106i	−0.993361	+	0.115039i	$0.963301\pi$
$420$		0			0
$421$	−5.62080	+	19.1427i	−0.273941	+	0.932958i	0.701495	+	0.712675i	$0.252516\pi$
$421$	−5.62080	+	19.1427i	−0.273941	+	0.932958i	−0.975436	+	0.220283i	$0.929302\pi$
$422$		0			0
$423$	1.20846	+	0.860539i	0.0587573	+	0.0418409i
$424$		0			0
$425$	1.58186	+	4.57048i	0.0767313	+	0.221701i
$426$		0			0
$427$	18.5890	−	1.29840i	0.899586	−	0.0628339i
$428$		0			0
$429$	−33.1314	+	1.57824i	−1.59960	+	0.0761983i
$430$		0			0
$431$	−2.67618	−	3.40304i	−0.128907	−	0.163919i	0.717315	−	0.696749i	$-0.245371\pi$
$431$	−2.67618	−	3.40304i	−0.128907	−	0.163919i	−0.846222	+	0.532830i	$0.821128\pi$
$432$		0			0
$433$	2.50284	−	17.4076i	0.120279	−	0.836558i	−0.836961	−	0.547262i	$-0.815670\pi$
$433$	2.50284	−	17.4076i	0.120279	−	0.836558i	0.957240	−	0.289295i	$-0.0934210\pi$
$434$		0			0
$435$	−1.46916	+	1.27304i	−0.0704410	+	0.0610375i
$436$		0			0
$437$	−4.20406	+	0.953970i	−0.201107	+	0.0456346i
$438$		0			0
$439$	6.71126	+	34.8213i	0.320311	+	1.66193i	0.683300	+	0.730137i	$0.260544\pi$
$439$	6.71126	+	34.8213i	0.320311	+	1.66193i	−0.362990	+	0.931793i	$0.618244\pi$
$440$		0			0
$441$	−44.0559	−	2.24576i	−2.09790	−	0.106941i
$442$		0			0
$443$	−17.1900	−	6.88184i	−0.816722	−	0.326966i	−0.0745851	−	0.997215i	$-0.523763\pi$
$443$	−17.1900	−	6.88184i	−0.816722	−	0.326966i	−0.742137	+	0.670249i	$0.766187\pi$
$444$		0			0
$445$	−17.1324	−	8.83236i	−0.812153	−	0.418694i
$446$		0			0
$447$	−21.8302	+	6.40994i	−1.03253	+	0.303180i
$448$		0			0
$449$	9.36865	−	10.8120i	0.442134	−	0.510250i	−0.490318	−	0.871543i	$-0.663119\pi$
$449$	9.36865	−	10.8120i	0.442134	−	0.510250i	0.932452	+	0.361294i	$0.117665\pi$
$450$		0			0
$451$	0.117061	−	0.164389i	0.00551217	−	0.00774076i
$452$		0			0
$453$	−29.7837	−	31.2362i	−1.39936	−	1.46761i
$454$		0			0
$455$	−10.4975	−	7.88561i	−0.492128	−	0.369683i
$456$		0			0
$457$	−2.72413	−	5.28408i	−0.127430	−	0.247179i	0.816486	−	0.577365i	$-0.195919\pi$
$457$	−2.72413	−	5.28408i	−0.127430	−	0.247179i	−0.943916	+	0.330186i	$0.892889\pi$
$458$		0			0
$459$	26.9910	−	15.5833i	1.25983	−	0.727365i
$460$		0			0
$461$			13.0169i			0.606259i	0.952949	+	0.303129i	$0.0980314\pi$
$461$			13.0169i			0.606259i	−0.952949	+	0.303129i	$0.901969\pi$
$462$		0			0
$463$	2.83339	+	1.82091i	0.131679	+	0.0846248i	0.604822	−	0.796361i	$-0.293244\pi$
$463$	2.83339	+	1.82091i	0.131679	+	0.0846248i	−0.473143	+	0.880986i	$0.656881\pi$
$464$		0			0
$465$	36.1375	−	3.45071i	1.67584	−	0.160023i
$466$		0			0
$467$	24.2334	−	23.1065i	1.12139	−	1.06924i	0.124359	−	0.992237i	$-0.460313\pi$
$467$	24.2334	−	23.1065i	1.12139	−	1.06924i	0.997031	−	0.0770052i	$-0.0245358\pi$
$468$		0			0
$469$	12.8726	−	40.0389i	0.594401	−	1.84883i
$470$		0			0
$471$	−5.69392	+	1.97069i	−0.262362	+	0.0908044i
$472$		0			0
$473$	2.52839	+	2.41082i	0.116256	+	0.110849i
$474$		0			0
$475$	−1.18174	+	0.759457i	−0.0542219	+	0.0348463i
$476$		0			0
$477$	29.4013	−	4.22727i	1.34619	−	0.193553i
$478$		0			0
$479$	−20.9331	+	8.38033i	−0.956456	+	0.382907i	−0.796785	−	0.604263i	$-0.793468\pi$
$479$	−20.9331	+	8.38033i	−0.956456	+	0.382907i	−0.159671	+	0.987170i	$0.551043\pi$
$480$		0			0
$481$	−28.7039	+	5.53222i	−1.30878	+	0.252247i
$482$		0			0
$483$	−29.4302	−	25.1290i	−1.33912	−	1.14341i
$484$		0			0
$485$	−28.3201	+	5.45825i	−1.28595	+	0.247846i
$486$		0			0
$487$	4.10235	−	1.64233i	0.185895	−	0.0744213i	−0.276847	−	0.960914i	$-0.589290\pi$
$487$	4.10235	−	1.64233i	0.185895	−	0.0744213i	0.462743	+	0.886493i	$0.346865\pi$
$488$		0			0
$489$	−49.2637	+	7.08305i	−2.22778	+	0.320307i
$490$		0			0
$491$	35.3730	−	22.7329i	1.59636	−	1.02592i	0.627405	−	0.778693i	$-0.284117\pi$
$491$	35.3730	−	22.7329i	1.59636	−	1.02592i	0.968958	−	0.247227i	$-0.0795192\pi$
$492$		0			0
$493$	−0.770056	−	0.734247i	−0.0346816	−	0.0330688i
$494$		0			0
$495$	44.8609	−	15.5265i	2.01635	−	0.697864i
$496$		0			0
$497$	−25.5516	+	23.1503i	−1.14615	+	1.03843i
$498$		0			0
$499$	15.5349	−	14.8125i	0.695438	−	0.663099i	−0.257495	−	0.966280i	$-0.582897\pi$
$499$	15.5349	−	14.8125i	0.695438	−	0.663099i	0.952933	+	0.303181i	$0.0980487\pi$
$500$		0			0
$501$	73.3824	−	7.00717i	3.27849	−	0.313057i
$502$		0			0
$503$	19.8386	+	12.7495i	0.884558	+	0.568471i	0.902173	−	0.431374i	$-0.141971\pi$
$503$	19.8386	+	12.7495i	0.884558	+	0.568471i	−0.0176155	+	0.999845i	$0.505607\pi$
$504$		0			0
$505$		−	34.7121i		−	1.54467i
$506$		0			0
$507$	−15.4137	+	8.89912i	−0.684547	+	0.395224i
$508$		0			0
$509$	14.5795	+	28.2802i	0.646223	+	1.25350i	0.953361	+	0.301833i	$0.0975986\pi$
$509$	14.5795	+	28.2802i	0.646223	+	1.25350i	−0.307137	+	0.951665i	$0.599371\pi$
$510$		0			0
$511$	−23.0743	+	9.83554i	−1.02075	+	0.435098i
$512$		0			0
$513$	6.24672	+	6.55138i	0.275800	+	0.289250i
$514$		0			0
$515$	−19.4973	+	27.3801i	−0.859154	+	1.20651i
$516$		0			0
$517$	−0.626381	+	0.722882i	−0.0275482	+	0.0317923i
$518$		0			0
$519$	−40.6818	+	11.9452i	−1.78573	+	0.524338i
$520$		0			0
$521$	35.5306	+	18.3173i	1.55662	+	0.802495i	0.999608	−	0.0280068i	$-0.00891600\pi$
$521$	35.5306	+	18.3173i	1.55662	+	0.802495i	0.557016	+	0.830502i	$0.311946\pi$
$522$		0			0
$523$	−7.20362	−	2.88390i	−0.314992	−	0.126104i	0.208779	−	0.977963i	$-0.433051\pi$
$523$	−7.20362	−	2.88390i	−0.314992	−	0.126104i	−0.523771	+	0.851859i	$0.675475\pi$
$524$		0			0
$525$	−11.8077	−	4.42648i	−0.515332	−	0.193187i
$526$		0			0
$527$	3.76027	+	19.5101i	0.163800	+	0.849874i
$528$		0			0
$529$	−4.75579	−	22.5029i	−0.206773	−	0.978389i
$530$		0			0
$531$	27.2499	−	23.6121i	1.18254	−	1.02468i
$532$		0			0
$533$	−0.0189199	+	0.131591i	−0.000819512	+	0.00569983i
$534$		0			0
$535$	6.06037	+	7.70639i	0.262013	+	0.333176i
$536$		0			0
$537$	−6.98531	+	0.332751i	−0.301438	+	0.0143593i
$538$		0			0
$539$	4.14145	−	28.1387i	0.178385	−	1.21202i
$540$		0			0
$541$	11.0550	+	31.9412i	0.475290	+	1.37326i	0.886925	+	0.461913i	$0.152837\pi$
$541$	11.0550	+	31.9412i	0.475290	+	1.37326i	−0.411635	+	0.911349i	$0.635042\pi$
$542$		0			0
$543$	−20.8703	−	14.8617i	−0.895631	−	0.637776i
$544$		0			0
$545$	−6.09811	+	20.7683i	−0.261214	+	0.889614i
$546$		0			0
$547$	0.105008	−	0.229936i	0.00448984	−	0.00983137i	−0.907374	−	0.420325i	$-0.861916\pi$
$547$	0.105008	−	0.229936i	0.00448984	−	0.00983137i	0.911864	+	0.410493i	$0.134643\pi$
$548$		0			0
$549$	2.11191	−	44.3345i	0.0901343	−	1.89215i
$550$		0			0
$551$	0.154518	−	0.267633i	0.00658268	−	0.0114015i
$552$		0			0
$553$	−4.65872	+	21.2454i	−0.198109	+	0.903445i
$554$		0			0
$555$	54.8891	−	28.2973i	2.32991	−	1.20115i
$556$		0			0
$557$	3.37924	+	35.3890i	0.143183	+	1.49948i	0.726462	+	0.687206i	$0.241163\pi$
$557$	3.37924	+	35.3890i	0.143183	+	1.49948i	−0.583279	+	0.812272i	$0.698231\pi$
$558$		0			0
$559$	−2.20818	−	0.648382i	−0.0933963	−	0.0274236i
$560$		0			0
$561$	15.9320	+	34.8861i	0.672648	+	1.47289i
$562$		0			0
$563$	1.12001	+	0.215864i	0.0472027	+	0.00909758i	0.212798	−	0.977096i	$-0.431742\pi$
$563$	1.12001	+	0.215864i	0.0472027	+	0.00909758i	−0.165595	+	0.986194i	$0.552955\pi$
$564$		0			0
$565$	6.79261	+	1.64787i	0.285767	+	0.0693264i
$566$		0			0
$567$	−5.23201	+	30.7998i	−0.219724	+	1.29347i
$568$		0			0
$569$	0.578397	−	1.44477i	0.0242477	−	0.0605677i	−0.915750	−	0.401749i	$-0.868403\pi$
$569$	0.578397	−	1.44477i	0.0242477	−	0.0605677i	0.939998	+	0.341181i	$0.110827\pi$
$570$		0			0
$571$	4.19827	+	10.4868i	0.175692	+	0.438857i	0.989909	−	0.141703i	$-0.0452578\pi$
$571$	4.19827	+	10.4868i	0.175692	+	0.438857i	−0.814217	+	0.580560i	$0.802834\pi$
$572$		0			0
$573$	43.4185	+	50.1076i	1.81383	+	2.09328i
$574$		0			0
$575$	−3.95776	−	6.36441i	−0.165050	−	0.265414i
$576$		0			0
$577$	−10.8837	−	3.76687i	−0.453092	−	0.156817i	0.0909842	−	0.995852i	$-0.470999\pi$
$577$	−10.8837	−	3.76687i	−0.453092	−	0.156817i	−0.544077	+	0.839036i	$0.683120\pi$
$578$		0			0
$579$	−23.0275	+	29.2818i	−0.956988	+	1.21691i
$580$		0			0
$581$	17.1704	−	8.30552i	0.712346	−	0.344571i
$582$		0			0
$583$	0.911257	+	19.1296i	0.0377404	+	0.792269i
$584$		0			0
$585$	−21.5805	+	22.6330i	−0.892245	+	0.935760i
$586$		0			0
$587$	−28.5271	−	24.7189i	−1.17744	−	1.02026i	−0.999343	−	0.0362460i	$-0.988460\pi$
$587$	−28.5271	−	24.7189i	−1.17744	−	1.02026i	−0.178098	−	0.984013i	$-0.556995\pi$
$588$		0			0
$589$	−5.24941	+	2.39733i	−0.216298	+	0.0987801i
$590$		0			0
$591$	−48.2793	+	11.7124i	−1.98594	+	0.481785i
$592$		0			0
$593$	−6.70539	+	4.77488i	−0.275357	+	0.196081i	−0.709390	−	0.704816i	$-0.751030\pi$
$593$	−6.70539	+	4.77488i	−0.275357	+	0.196081i	0.434033	+	0.900897i	$0.357090\pi$
$594$		0			0
$595$	−3.95353	+	14.6571i	−0.162079	+	0.600881i
$596$		0			0
$597$	21.6788	+	12.5163i	0.887256	+	0.512257i
$598$		0			0
$599$	−12.7957	−	22.1629i	−0.522820	−	0.905551i	−0.999647	−	0.0265539i	$-0.991547\pi$
$599$	−12.7957	−	22.1629i	−0.522820	−	0.905551i	0.476827	−	0.878997i	$-0.341787\pi$
$600$		0			0
$601$	23.9256	−	37.2289i	0.975944	−	1.51860i	0.125795	−	0.992056i	$-0.459852\pi$
$601$	23.9256	−	37.2289i	0.975944	−	1.51860i	0.850149	−	0.526542i	$-0.176512\pi$
$602$		0			0
$603$	−91.1231	−	41.6145i	−3.71082	−	1.69467i
$604$		0			0
$605$	2.40791	+	9.92555i	0.0978956	+	0.403531i
$606$		0			0
$607$	2.08185	−	21.8021i	0.0844995	−	0.884919i	−0.849487	−	0.527610i	$-0.823088\pi$
$607$	2.08185	−	21.8021i	0.0844995	−	0.884919i	0.933986	−	0.357309i	$-0.116306\pi$
$608$		0			0
$609$	2.75511	−	0.324760i	0.111643	−	0.0131599i
$610$		0			0
$611$	0.148555	−	0.612350i	0.00600987	−	0.0247730i
$612$		0			0
$613$	−18.3210	+	35.5377i	−0.739976	+	1.43535i	0.154386	+	0.988011i	$0.450660\pi$
$613$	−18.3210	+	35.5377i	−0.739976	+	1.43535i	−0.894362	+	0.447343i	$0.852370\pi$
$614$		0			0
$615$	−0.0399689	−	0.277990i	−0.00161170	−	0.0112096i
$616$		0			0
$617$	−42.5996	−	6.12490i	−1.71500	−	0.246579i	−0.786412	−	0.617702i	$-0.788064\pi$
$617$	−42.5996	−	6.12490i	−1.71500	−	0.246579i	−0.928584	+	0.371123i	$0.878973\pi$
$618$		0			0
$619$	0.994657	−	2.87387i	0.0399787	−	0.115511i	−0.923245	−	0.384212i	$-0.874473\pi$
$619$	0.994657	−	2.87387i	0.0399787	−	0.115511i	0.963224	+	0.268701i	$0.0865944\pi$
$620$		0			0
$621$	−35.4448	+	32.8048i	−1.42235	+	1.31641i
$622$		0			0
$623$	13.1424	+	24.1640i	0.526537	+	0.968111i
$624$		0			0
$625$	11.5897	+	9.11423i	0.463587	+	0.364569i
$626$		0			0
$627$	−8.75597	+	6.88577i	−0.349680	+	0.274991i
$628$		0			0
$629$	18.2736	+	28.4343i	0.728617	+	1.13375i
$630$		0			0
$631$	9.31767	+	31.7331i	0.370930	+	1.26327i	0.907727	+	0.419561i	$0.137816\pi$
$631$	9.31767	+	31.7331i	0.370930	+	1.26327i	−0.536796	+	0.843712i	$0.680366\pi$
$632$		0			0
$633$	−12.0000	+	62.2617i	−0.476956	+	2.47468i
$634$		0			0
$635$	13.1164	+	1.25246i	0.520507	+	0.0497024i
$636$		0			0
$637$	6.06905	+	17.7262i	0.240465	+	0.702338i
$638$		0			0
$639$	47.6376	+	66.8976i	1.88451	+	2.64643i
$640$		0			0
$641$	−23.9403	−	1.14042i	−0.945587	−	0.0450439i	−0.430879	−	0.902410i	$-0.641797\pi$
$641$	−23.9403	−	1.14042i	−0.945587	−	0.0450439i	−0.514708	+	0.857366i	$0.672100\pi$
$642$		0			0
$643$	3.03496			0.119687			0.0598435	−	0.998208i	$-0.480940\pi$
$643$	3.03496			0.119687			0.0598435	+	0.998208i	$0.480940\pi$
$644$		0			0
$645$	4.86181			0.191433
$646$		0			0
$647$	−0.592413	−	0.0282201i	−0.0232902	−	0.00110945i	0.0359336	−	0.999354i	$-0.488560\pi$
$647$	−0.592413	−	0.0282201i	−0.0232902	−	0.00110945i	−0.0592238	+	0.998245i	$0.518863\pi$
$648$		0			0
$649$	13.4849	+	18.9368i	0.529327	+	0.743336i
$650$		0			0
$651$	−45.4268	−	24.9032i	−1.78041	−	0.976033i
$652$		0			0
$653$	23.2680	+	2.22183i	0.910548	+	0.0869468i	0.539806	−	0.841789i	$-0.318497\pi$
$653$	23.2680	+	2.22183i	0.910548	+	0.0869468i	0.370742	+	0.928736i	$0.379104\pi$
$654$		0			0
$655$	0.475277	−	2.46597i	0.0185706	−	0.0963535i
$656$		0			0
$657$	16.8321	+	57.3249i	0.656683	+	2.23646i
$658$		0			0
$659$	12.1075	+	18.8396i	0.471641	+	0.733887i	0.992828	−	0.119555i	$-0.0381469\pi$
$659$	12.1075	+	18.8396i	0.471641	+	0.733887i	−0.521187	+	0.853443i	$0.674511\pi$
$660$		0			0
$661$	−16.9975	+	13.3670i	−0.661125	+	0.519915i	−0.891404	−	0.453210i	$-0.850279\pi$
$661$	−16.9975	+	13.3670i	−0.661125	+	0.519915i	0.230279	+	0.973125i	$0.426036\pi$
$662$		0			0
$663$	−19.8594	−	15.6176i	−0.771277	−	0.606539i
$664$		0			0
$665$	−4.40780	−	0.112271i	−0.170927	−	0.00435369i
$666$		0			0
$667$	1.41548	+	0.845523i	0.0548077	+	0.0327388i
$668$		0			0
$669$	−8.83235	+	25.5194i	−0.341478	+	0.986637i
$670$		0			0
$671$	28.3257	+	4.07262i	1.09350	+	0.157222i
$672$		0			0
$673$	4.41024	+	30.6739i	0.170002	+	1.18239i	0.878874	+	0.477054i	$0.158295\pi$
$673$	4.41024	+	30.6739i	0.170002	+	1.18239i	−0.708872	+	0.705337i	$0.750796\pi$
$674$		0			0
$675$	−7.21129	+	13.9879i	−0.277563	+	0.538396i
$676$		0			0
$677$	2.68950	−	11.0863i	0.103366	−	0.426080i	−0.896490	−	0.443064i	$-0.853891\pi$
$677$	2.68950	−	11.0863i	0.103366	−	0.426080i	0.999856	+	0.0169845i	$0.00540658\pi$
$678$		0			0
$679$	37.8081	+	16.2650i	1.45094	+	0.624192i
$680$		0			0
$681$	5.56961	−	58.3276i	0.213428	−	2.23512i
$682$		0			0
$683$	10.9613	+	45.1832i	0.419424	+	1.72889i	0.653733	+	0.756725i	$0.273202\pi$
$683$	10.9613	+	45.1832i	0.419424	+	1.72889i	−0.234309	+	0.972162i	$0.575283\pi$
$684$		0			0
$685$	−2.93641	−	1.34101i	−0.112194	−	0.0512375i
$686$		0			0
$687$	10.1198	−	15.7468i	0.386095	−	0.600776i
$688$		0			0
$689$	−6.30808	−	10.9259i	−0.240319	−	0.416244i
$690$		0			0
$691$	−20.9079	−	12.0712i	−0.795374	−	0.459209i	0.0464770	−	0.998919i	$-0.485201\pi$
$691$	−20.9079	−	12.0712i	−0.795374	−	0.459209i	−0.841851	+	0.539710i	$0.818534\pi$
$692$		0			0
$693$	−65.4075	−	17.6427i	−2.48462	−	0.670191i
$694$		0			0
$695$	17.2281	−	12.2681i	0.653500	−	0.465355i
$696$		0			0
$697$	0.149385	−	0.0362403i	0.00565834	−	0.00137270i
$698$		0			0
$699$	48.3899	−	22.0989i	1.83028	−	0.835859i
$700$		0			0
$701$	−6.54003	−	5.66697i	−0.247014	−	0.214038i	0.522550	−	0.852609i	$-0.324981\pi$
$701$	−6.54003	−	5.66697i	−0.247014	−	0.214038i	−0.769564	+	0.638570i	$0.779526\pi$
$702$		0			0
$703$	−6.77453	+	7.10493i	−0.255506	+	0.267967i
$704$		0			0
$705$	0.0633379	+	1.32963i	0.00238544	+	0.0500766i
$706$		0			0
$707$	−27.8337	+	40.9771i	−1.04680	+	1.54110i
$708$		0			0
$709$	5.13394	−	6.52834i	0.192809	−	0.245177i	−0.680030	−	0.733184i	$-0.738033\pi$
$709$	5.13394	−	6.52834i	0.192809	−	0.245177i	0.872840	+	0.488007i	$0.162276\pi$
$710$		0			0
$711$	48.9571	+	16.9442i	1.83603	+	0.635457i
$712$		0			0
$713$	−12.3728	−	28.1940i	−0.463363	−	1.05587i
$714$		0			0
$715$	−13.2039	−	15.2381i	−0.493798	−	0.569873i
$716$		0			0
$717$	34.1266	+	85.2440i	1.27448	+	3.18350i
$718$		0			0
$719$	13.3172	−	33.2646i	0.496646	−	1.24056i	−0.442415	−	0.896811i	$-0.645878\pi$
$719$	13.3172	−	33.2646i	0.496646	−	1.24056i	0.939061	−	0.343751i	$-0.111698\pi$
$720$		0			0
$721$	44.9709	−	16.6880i	1.67481	−	0.621495i
$722$		0			0
$723$	−91.4778	−	22.1923i	−3.40210	−	0.825339i
$724$		0			0
$725$	0.527554	+	0.101678i	0.0195929	+	0.00377622i
$726$		0			0
$727$	−11.6687	−	25.5510i	−0.432769	−	0.947633i	−0.992869	−	0.119208i	$-0.961965\pi$
$727$	−11.6687	−	25.5510i	−0.432769	−	0.947633i	0.560100	−	0.828425i	$-0.310763\pi$
$728$		0			0
$729$	−17.0102	−	4.99465i	−0.630007	−	0.184987i
$730$		0			0
$731$	0.252946	+	2.64897i	0.00935556	+	0.0979759i
$732$		0			0
$733$	7.68535	−	3.96207i	0.283865	−	0.146343i	−0.310414	−	0.950601i	$-0.600468\pi$
$733$	7.68535	−	3.96207i	0.283865	−	0.146343i	0.594279	+	0.804259i	$0.297437\pi$
$734$		0			0
$735$	−22.8518	−	32.3182i	−0.842903	−	1.19208i
$736$		0			0
$737$	32.2940	−	55.9349i	1.18957	−	2.06039i
$738$		0			0
$739$	−0.665719	+	13.9752i	−0.0244889	+	0.514085i	0.952984	+	0.303022i	$0.0979955\pi$
$739$	−0.665719	+	13.9752i	−0.0244889	+	0.514085i	−0.977472	+	0.211063i	$0.932308\pi$
$740$		0			0
$741$	3.04833	−	6.67492i	0.111983	−	0.245209i
$742$		0			0
$743$	−3.67874	+	12.5286i	−0.134960	+	0.459631i	−0.999044	−	0.0437166i	$-0.986080\pi$
$743$	−3.67874	+	12.5286i	−0.134960	+	0.459631i	0.864084	+	0.503347i	$0.167898\pi$
$744$		0			0
$745$	−11.2660	−	8.02247i	−0.412754	−	0.293921i
$746$		0			0
$747$	−14.8591	−	42.9325i	−0.543665	−	1.57082i
$748$		0			0
$749$	−0.974846	−	13.9568i	−0.0356201	−	0.509969i
$750$		0			0
$751$	3.56528	−	0.169835i	0.130099	−	0.00619738i	0.0175686	−	0.999846i	$-0.494407\pi$
$751$	3.56528	−	0.169835i	0.130099	−	0.00619738i	0.112530	+	0.993648i	$0.464104\pi$
$752$		0			0
$753$	29.7528	+	37.8338i	1.08425	+	1.37874i
$754$		0			0
$755$	3.73380	−	25.9691i	0.135887	−	0.945114i
$756$		0			0
$757$	26.2936	−	22.7836i	0.955658	−	0.828082i	−0.0295295	−	0.999564i	$-0.509401\pi$
$757$	26.2936	−	22.7836i	0.955658	−	0.828082i	0.985187	+	0.171482i	$0.0548554\pi$
$758$		0			0
$759$	−36.0391	−	47.2562i	−1.30814	−	1.71529i
$760$		0			0
$761$	−1.70101	−	8.82566i	−0.0616614	−	0.319930i	0.937981	−	0.346688i	$-0.112694\pi$
$761$	−1.70101	−	8.82566i	−0.0616614	−	0.319930i	−0.999642	+	0.0267582i	$0.991482\pi$
$762$		0			0
$763$	23.8517	−	19.6269i	0.863489	−	0.710541i
$764$		0			0
$765$	33.5690	+	13.4390i	1.21369	+	0.485888i
$766$		0			0
$767$	−13.6121	−	7.01753i	−0.491505	−	0.253388i
$768$		0			0
$769$	−3.42687	+	1.00622i	−0.123576	+	0.0362853i	−0.342936	−	0.939359i	$-0.611421\pi$
$769$	−3.42687	+	1.00622i	−0.123576	+	0.0362853i	0.219360	+	0.975644i	$0.429603\pi$
$770$		0			0
$771$	41.0476	−	47.3715i	1.47829	−	1.70604i
$772$		0			0
$773$	5.39428	−	7.57521i	0.194019	−	0.272461i	−0.706094	−	0.708118i	$-0.749544\pi$
$773$	5.39428	−	7.57521i	0.194019	−	0.272461i	0.900113	+	0.435657i	$0.143484\pi$
$774$		0			0
$775$	−6.92346	−	7.26111i	−0.248698	−	0.260827i
$776$		0			0
$777$	−87.4859	−	10.6080i	−3.13854	−	0.380561i
$778$		0			0
$779$	0.0204583	+	0.0396835i	0.000732994	+	0.00142181i
$780$		0			0
$781$	−45.8563	+	26.4752i	−1.64087	+	0.947356i
$782$		0			0
$783$		−	3.46216i		−	0.123727i
$784$		0			0
$785$	−3.08125	−	1.98020i	−0.109975	−	0.0706764i
$786$		0			0
$787$	36.4048	−	3.47624i	1.29769	−	0.123915i	0.576756	−	0.816917i	$-0.304318\pi$
$787$	36.4048	−	3.47624i	1.29769	−	0.123915i	0.720936	+	0.693002i	$0.243712\pi$
$788$		0			0
$789$	−19.6699	+	18.7552i	−0.700267	+	0.667703i
$790$		0			0
$791$	−6.69724	−	7.39191i	−0.238127	−	0.262826i
$792$		0			0
$793$	−17.8149	+	6.16581i	−0.632627	+	0.218954i
$794$		0			0
$795$	19.2890	+	18.3920i	0.684111	+	0.652299i
$796$		0			0
$797$	−21.2193	+	13.6368i	−0.751627	+	0.483041i	−0.859508	−	0.511123i	$-0.829230\pi$
$797$	−21.2193	+	13.6368i	−0.751627	+	0.483041i	0.107881	+	0.994164i	$0.465593\pi$
$798$		0			0
$799$	−0.721157	+	0.103687i	−0.0255127	+	0.00366817i
$800$		0			0
$801$	60.8247	−	24.3505i	2.14914	−	0.860384i
$802$		0			0
$803$	−37.8243	+	7.29004i	−1.33479	+	0.257260i
$804$		0			0
$805$	0.948419	−	23.5053i	0.0334274	−	0.828453i
$806$		0			0
$807$	51.9983	−	10.0219i	1.83043	−	0.352786i
$808$		0			0
$809$	7.94177	−	3.17941i	0.279218	−	0.111782i	−0.227827	−	0.973702i	$-0.573162\pi$
$809$	7.94177	−	3.17941i	0.279218	−	0.111782i	0.507045	+	0.861920i	$0.330738\pi$
$810$		0			0
$811$	−34.6922	+	4.98799i	−1.21821	+	0.175152i	−0.721282	−	0.692641i	$-0.756447\pi$
$811$	−34.6922	+	4.98799i	−1.21821	+	0.175152i	−0.496926	+	0.867793i	$0.665538\pi$
$812$		0			0
$813$	13.8392	−	8.89391i	0.485362	−	0.311923i
$814$		0			0
$815$	−21.8963	−	20.8781i	−0.766993	−	0.731327i
$816$		0			0
$817$	−0.730375	+	0.252785i	−0.0255526	+	0.00884384i
$818$		0			0
$819$	43.6237	−	9.41369i	1.52434	−	0.328941i
$820$		0			0
$821$	−7.08501	+	6.75555i	−0.247269	+	0.235770i	−0.803570	−	0.595211i	$-0.797069\pi$
$821$	−7.08501	+	6.75555i	−0.247269	+	0.235770i	0.556301	+	0.830981i	$0.312220\pi$
$822$		0			0
$823$	1.03130	−	0.0984768i	0.0359487	−	0.00343269i	−0.0770662	−	0.997026i	$-0.524555\pi$
$823$	1.03130	−	0.0984768i	0.0359487	−	0.00343269i	0.113015	+	0.993593i	$0.463949\pi$
$824$		0			0
$825$	−16.2914	−	10.4698i	−0.567193	−	0.364513i
$826$		0			0
$827$		−	42.5045i		−	1.47802i	−0.673692	−	0.739012i	$-0.735292\pi$
$827$		−	42.5045i		−	1.47802i	0.673692	−	0.739012i	$-0.264708\pi$
$828$		0			0
$829$	13.3676	−	7.71777i	0.464275	−	0.268049i	−0.249565	−	0.968358i	$-0.580288\pi$
$829$	13.3676	−	7.71777i	0.464275	−	0.268049i	0.713840	+	0.700309i	$0.246954\pi$
$830$		0			0
$831$	−1.80502	−	3.50126i	−0.0626156	−	0.121457i
$832$		0			0
$833$	16.4198	−	14.1323i	0.568912	−	0.489657i
$834$		0			0
$835$	30.9231	+	32.4312i	1.07014	+	1.12233i
$836$		0			0
$837$	−37.5020	+	52.6641i	−1.29626	+	1.82034i
$838$		0			0
$839$	23.3595	−	26.9583i	0.806459	−	0.930704i	−0.192258	−	0.981344i	$-0.561581\pi$
$839$	23.3595	−	26.9583i	0.806459	−	0.930704i	0.998717	+	0.0506409i	$0.0161264\pi$
$840$		0			0
$841$	27.7119	−	8.13694i	0.955582	−	0.280584i
$842$		0			0
$843$	41.7810	+	21.5396i	1.43901	+	0.741863i
$844$		0			0
$845$	−10.0443	−	4.02112i	−0.345533	−	0.138331i
$846$		0			0
$847$	5.11626	−	13.6478i	0.175797	−	0.468942i
$848$		0			0
$849$	−2.25520	−	11.7011i	−0.0773982	−	0.401580i
$850$		0			0
$851$	−37.3654	−	36.7033i	−1.28087	−	1.25817i
$852$		0			0
$853$	−5.85326	+	5.07188i	−0.200412	+	0.173658i	−0.749285	−	0.662248i	$-0.769603\pi$
$853$	−5.85326	+	5.07188i	−0.200412	+	0.173658i	0.548873	+	0.835906i	$0.315057\pi$
$854$		0			0
$855$	−1.49463	+	10.3954i	−0.0511153	+	0.355515i
$856$		0			0
$857$	1.22952	+	1.56346i	0.0419995	+	0.0534067i	0.806599	−	0.591099i	$-0.201306\pi$
$857$	1.22952	+	1.56346i	0.0419995	+	0.0534067i	−0.764600	+	0.644506i	$0.777063\pi$
$858$		0			0
$859$	−18.1649	+	0.865302i	−0.619779	+	0.0295237i	−0.355124	−	0.934819i	$-0.615561\pi$
$859$	−18.1649	+	0.865302i	−0.619779	+	0.0295237i	−0.264655	+	0.964343i	$0.585258\pi$
$860$		0			0
$861$	−0.175723	+	0.360213i	−0.00598861	+	0.0122760i
$862$		0			0
$863$	−6.23133	−	18.0043i	−0.212117	−	0.612872i	0.787879	−	0.615831i	$-0.211179\pi$
$863$	−6.23133	−	18.0043i	−0.212117	−	0.612872i	−0.999996	+	0.00295874i	$0.999058\pi$
$864$		0			0
$865$	−20.9947	−	14.9503i	−0.713843	−	0.508325i
$866$		0			0
$867$	6.37720	−	21.7187i	0.216581	−	0.737607i
$868$		0			0
$869$	−13.8757	+	30.3835i	−0.470701	+	1.03069i
$870$		0			0
$871$	−2.02452	+	42.4999i	−0.0685982	+	1.44005i
$872$		0			0
$873$	49.0172	−	84.9002i	1.65898	−	2.87344i
$874$		0			0
$875$	−9.75077	−	30.6792i	−0.329636	−	1.03715i
$876$		0			0
$877$	−10.8203	+	5.57828i	−0.365377	+	0.188365i	−0.631132	−	0.775676i	$-0.717409\pi$
$877$	−10.8203	+	5.57828i	−0.365377	+	0.188365i	0.265755	+	0.964041i	$0.414379\pi$
$878$		0			0
$879$	7.86634	+	82.3800i	0.265325	+	2.77861i
$880$		0			0
$881$	−4.15953	−	1.22135i	−0.140138	−	0.0411483i	0.210911	−	0.977505i	$-0.432357\pi$
$881$	−4.15953	−	1.22135i	−0.140138	−	0.0411483i	−0.351049	+	0.936357i	$0.614175\pi$
$882$		0			0
$883$	−6.83203	−	14.9600i	−0.229916	−	0.503446i	0.759151	−	0.650915i	$-0.225615\pi$
$883$	−6.83203	−	14.9600i	−0.229916	−	0.503446i	−0.989067	+	0.147469i	$0.952887\pi$
$884$		0			0
$885$	31.7679	+	6.12275i	1.06787	+	0.205814i
$886$		0			0
$887$	32.4668	+	7.87636i	1.09013	+	0.264462i	0.740249	−	0.672332i	$-0.234707\pi$
$887$	32.4668	+	7.87636i	1.09013	+	0.264462i	0.349879	+	0.936795i	$0.386223\pi$
$888$		0			0
$889$	−14.4794	−	11.9958i	−0.485624	−	0.402327i
$890$		0			0
$891$	−17.8314	+	44.5406i	−0.597373	+	1.49217i
$892$		0			0
$893$	−0.0786478	−	0.196453i	−0.00263185	−	0.00657404i
$894$		0			0
$895$	−2.78386	−	3.21275i	−0.0930542	−	0.107390i
$896$		0			0
$897$	35.3669	+	16.7911i	1.18087	+	0.560639i
$898$		0			0
$899$	2.08579	+	0.721899i	0.0695649	+	0.0240767i
$900$		0			0
$901$	−9.01743	+	11.4666i	−0.300414	+	0.382008i
$902$		0			0
$903$	−5.73930	−	3.89842i	−0.190992	−	0.129731i
$904$		0			0
$905$	−0.741072	−	15.5570i	−0.0246341	−	0.517133i
$906$		0			0
$907$	−21.3775	+	22.4200i	−0.709827	+	0.744445i	−0.975592	−	0.219593i	$-0.929527\pi$
$907$	−21.3775	+	22.4200i	−0.709827	+	0.744445i	0.265764	+	0.964038i	$0.414376\pi$
$908$		0			0
$909$	89.1707	+	77.2668i	2.95760	+	2.56278i
$910$		0			0
$911$	27.0362	−	12.3470i	0.895749	−	0.409075i	0.0863027	−	0.996269i	$-0.472495\pi$
$911$	27.0362	−	12.3470i	0.895749	−	0.409075i	0.809446	+	0.587194i	$0.199768\pi$
$912$		0			0
$913$	28.4659	−	6.90576i	0.942085	−	0.228547i
$914$		0			0
$915$	32.4405	−	23.1008i	1.07245	−	0.763688i
$916$		0			0
$917$	−2.53839	+	2.52995i	−0.0838250	+	0.0835462i
$918$		0			0
$919$	−23.6640	−	13.6624i	−0.780604	−	0.450682i	0.0560404	−	0.998428i	$-0.482152\pi$
$919$	−23.6640	−	13.6624i	−0.780604	−	0.450682i	−0.836644	+	0.547747i	$0.815486\pi$
$920$		0			0
$921$	−10.5919	−	18.3456i	−0.349013	−	0.604509i
$922$		0			0
$923$	18.8584	−	29.3443i	0.620733	−	0.965879i
$924$		0			0
$925$	−15.5248	−	7.08993i	−0.510451	−	0.233115i
$926$		0			0
$927$	−26.9362	−	111.032i	−0.884699	−	3.64678i
$928$		0			0
$929$	1.89076	−	19.8009i	0.0620338	−	0.649648i	−0.909969	−	0.414677i	$-0.863895\pi$
$929$	1.89076	−	19.8009i	0.0620338	−	0.649648i	0.972002	−	0.234971i	$-0.0754994\pi$
$930$		0			0
$931$	5.11333	+	3.66691i	0.167582	+	0.120178i
$932$		0			0
$933$	6.85994	−	28.2770i	0.224584	−	0.925749i
$934$		0			0
$935$	−10.6829	+	20.7219i	−0.349368	+	0.677678i
$936$		0			0
$937$	1.96445	+	13.6631i	0.0641759	+	0.446353i	0.996421	+	0.0845266i	$0.0269378\pi$
$937$	1.96445	+	13.6631i	0.0641759	+	0.446353i	−0.932245	+	0.361827i	$0.882153\pi$
$938$		0			0
$939$	10.8803	+	1.56436i	0.355067	+	0.0510509i
$940$		0			0
$941$	−2.35022	+	6.79050i	−0.0766149	+	0.221364i	−0.976804	−	0.214135i	$-0.931307\pi$
$941$	−2.35022	+	6.79050i	−0.0766149	+	0.221364i	0.900189	+	0.435499i	$0.143428\pi$
$942$		0			0
$943$	−0.213321	+	0.105992i	−0.00694668	+	0.00345157i
$944$		0			0
$945$	−43.3941	+	23.6012i	−1.41161	+	0.767749i
$946$		0			0
$947$	12.9640	+	10.1950i	0.421273	+	0.331292i	0.806188	−	0.591659i	$-0.201527\pi$
$947$	12.9640	+	10.1950i	0.421273	+	0.331292i	−0.384915	+	0.922952i	$0.625769\pi$
$948$		0			0
$949$	19.9467	−	15.6863i	0.647497	−	0.509197i
$950$		0			0
$951$	−38.0454	−	59.1997i	−1.23371	−	1.91968i
$952$		0			0
$953$	−9.61171	−	32.7345i	−0.311354	−	1.06037i	−0.955382	−	0.295372i	$-0.904556\pi$
$953$	−9.61171	−	32.7345i	−0.311354	−	1.06037i	0.644028	−	0.765002i	$-0.277262\pi$
$954$		0			0
$955$	−7.62756	+	39.5755i	−0.246822	+	1.28063i
$956$		0			0
$957$	4.24106	+	0.404972i	0.137094	+	0.0130909i
$958$		0			0
$959$	2.39111	+	3.93760i	0.0772128	+	0.127152i
$960$		0			0
$961$	−5.92636	−	8.32241i	−0.191173	−	0.268465i
$962$		0			0
$963$	−33.2867	−	1.58564i	−1.07265	−	0.0510965i
$964$		0			0
$965$	−22.6447			−0.728959
$966$		0			0
$967$	49.3752			1.58780			0.793900	−	0.608048i	$-0.208047\pi$
$967$	49.3752			1.58780			0.793900	+	0.608048i	$0.208047\pi$
$968$		0			0
$969$	−8.47507	−	0.403717i	−0.272258	−	0.0129693i
$970$		0			0
$971$	−21.6936	−	30.4644i	−0.696181	−	0.977649i	−0.999692	−	0.0248212i	$-0.992098\pi$
$971$	−21.6936	−	30.4644i	−0.696181	−	0.977649i	0.303511	−	0.952828i	$-0.401841\pi$
$972$		0			0
$973$	−30.1747	+	0.668007i	−0.967356	+	0.0214153i
$974$		0			0
$975$	12.6995	+	1.21266i	0.406711	+	0.0388362i
$976$		0			0
$977$	2.45578	−	12.7418i	0.0785674	−	0.407646i	−0.921258	−	0.388952i	$-0.872837\pi$
$977$	2.45578	−	12.7418i	0.0785674	−	0.407646i	0.999825	−	0.0186940i	$-0.00595082\pi$
$978$		0			0
$979$	11.9011	+	40.5314i	0.380360	+	1.29539i
$980$		0			0
$981$	−39.7769	−	61.8940i	−1.26998	−	1.97612i
$982$		0			0
$983$	−15.4382	+	12.1408i	−0.492403	+	0.387230i	−0.833257	−	0.552886i	$-0.813526\pi$
$983$	−15.4382	+	12.1408i	−0.492403	+	0.387230i	0.340853	+	0.940116i	$0.389284\pi$
$984$		0			0
$985$	−23.7384	−	18.6681i	−0.756369	−	0.594815i
$986$		0			0
$987$	0.991386	−	1.62039i	0.0315562	−	0.0515777i
$988$		0			0
$989$	−1.29062	−	3.91636i	−0.0410393	−	0.124533i
$990$		0			0
$991$	14.2979	−	41.3112i	0.454189	−	1.31229i	−0.452978	−	0.891522i	$-0.649638\pi$
$991$	14.2979	−	41.3112i	0.454189	−	1.31229i	0.907167	−	0.420771i	$-0.138240\pi$
$992$		0			0
$993$	81.3794	+	11.7006i	2.58250	+	0.371307i
$994$		0			0
$995$	2.16559	+	15.0620i	0.0686539	+	0.477498i
$996$		0			0
$997$	24.3115	−	47.1578i	0.769954	−	1.49350i	−0.0970929	−	0.995275i	$-0.530954\pi$
$997$	24.3115	−	47.1578i	0.769954	−	1.49350i	0.867047	−	0.498227i	$-0.166015\pi$
$998$		0			0
$999$	−25.9291	+	106.881i	−0.820360	+	3.38157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.bc.a.33.1	✓	320
7.3	odd	6	inner	644.2.bc.a.493.1	yes	320
23.7	odd	22	inner	644.2.bc.a.145.1	yes	320
161.122	even	66	inner	644.2.bc.a.605.1	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.bc.a.33.1	✓	320	1.1	even	1	trivial
644.2.bc.a.145.1	yes	320	23.7	odd	22	inner
644.2.bc.a.493.1	yes	320	7.3	odd	6	inner
644.2.bc.a.605.1	yes	320	161.122	even	66	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.bc (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.04644 - 0.145120i) q^{3} +(-1.07542 - 1.51021i) q^{5} +(0.0585572 + 2.64510i) q^{7} +(6.27334 + 0.599031i) q^{9} +(-0.768950 + 3.98969i) q^{11} +(-0.754092 - 2.56820i) q^{13} +(3.05703 + 4.75684i) q^{15} +(-2.43273 + 1.91312i) q^{17} +(-0.706577 - 0.555658i) q^{19} +(0.205466 - 8.06665i) q^{21} +(3.02028 - 3.72530i) q^{23} +(0.511122 - 1.47679i) q^{25} +(-9.96788 - 1.43316i) q^{27} +(0.0489273 + 0.340297i) q^{29} +(2.94183 - 5.70636i) q^{31} +(2.92155 - 12.0428i) q^{33} +(3.93169 - 2.93302i) q^{35} +(1.03813 - 10.8718i) q^{37} +(1.92460 + 7.93332i) q^{39} +(-0.0451801 - 0.0206330i) q^{41} +(0.464852 - 0.723324i) q^{43} +(-5.84179 - 10.1183i) q^{45} +(0.203874 + 0.117706i) q^{47} +(-6.99314 + 0.309780i) q^{49} +(7.68881 - 5.47518i) q^{51} +(4.58060 - 1.11124i) q^{53} +(6.85222 - 3.12930i) q^{55} +(2.07191 + 1.79532i) q^{57} +(3.94835 - 4.14091i) q^{59} +(-0.335125 - 7.03513i) q^{61} +(-1.21715 + 16.6287i) q^{63} +(-3.06757 + 3.90073i) q^{65} +(-15.0219 - 5.19913i) q^{67} +(-9.74173 + 10.9106i) q^{69} +(8.53411 + 9.84889i) q^{71} +(3.52355 + 8.80140i) q^{73} +(-1.77142 + 4.42478i) q^{75} +(-10.5982 - 1.80033i) q^{77} +(7.98905 + 1.93812i) q^{79} +(11.5946 + 2.23468i) q^{81} +(-2.99479 - 6.55767i) q^{83} +(5.50542 + 1.61654i) q^{85} +(-0.0996703 - 1.04379i) q^{87} +(9.24084 - 4.76398i) q^{89} +(6.74900 - 2.14504i) q^{91} +(-9.79023 + 16.9572i) q^{93} +(-0.0792968 + 1.66465i) q^{95} +(6.46235 - 14.1506i) q^{97} +(-7.21383 + 24.5681i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71}+ \cdots + 242 q^{99}+O(q^{100}) \) 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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