LMFDB - Embedded newform 504.2.cx.a.425.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(185,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))

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

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

chi := DirichletCharacter("504.185");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cx (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			425.17
Character	$\chi$	$=$	504.425
Dual form			504.2.cx.a.185.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.958980 - 1.44234i) q^{3} +4.11484 q^{5} +(-2.54819 - 0.711830i) q^{7} +(-1.16071 - 2.76636i) q^{9} +O(q^{10})$	\(q+(0.958980 - 1.44234i) q^{3} +4.11484 q^{5} +(-2.54819 - 0.711830i) q^{7} +(-1.16071 - 2.76636i) q^{9} -5.82138i q^{11} +(-2.52259 + 1.45642i) q^{13} +(3.94605 - 5.93502i) q^{15} +(1.58162 + 2.73945i) q^{17} +(0.722488 + 0.417129i) q^{19} +(-3.47037 + 2.99274i) q^{21} +7.09758i q^{23} +11.9319 q^{25} +(-5.10314 - 0.978735i) q^{27} +(-1.91234 - 1.10409i) q^{29} +(3.66696 + 2.11712i) q^{31} +(-8.39644 - 5.58259i) q^{33} +(-10.4854 - 2.92907i) q^{35} +(1.82507 - 3.16112i) q^{37} +(-0.318458 + 5.03512i) q^{39} +(2.04811 + 3.54743i) q^{41} +(0.155460 - 0.269265i) q^{43} +(-4.77615 - 11.3831i) q^{45} +(0.502335 + 0.870070i) q^{47} +(5.98660 + 3.62776i) q^{49} +(5.46798 + 0.345835i) q^{51} +(-1.94801 + 1.12469i) q^{53} -23.9541i q^{55} +(1.29450 - 0.642058i) q^{57} +(2.51748 - 4.36040i) q^{59} +(-3.98673 + 2.30174i) q^{61} +(0.988547 + 7.87545i) q^{63} +(-10.3801 + 5.99293i) q^{65} +(4.99726 - 8.65551i) q^{67} +(10.2371 + 6.80644i) q^{69} +11.4186i q^{71} +(-3.04990 + 1.76086i) q^{73} +(11.4425 - 17.2099i) q^{75} +(-4.14384 + 14.8340i) q^{77} +(0.579351 + 1.00346i) q^{79} +(-6.30549 + 6.42190i) q^{81} +(-7.57669 + 13.1232i) q^{83} +(6.50813 + 11.2724i) q^{85} +(-3.42638 + 1.69945i) q^{87} +(4.82266 - 8.35309i) q^{89} +(7.46478 - 1.91558i) q^{91} +(6.57016 - 3.25874i) q^{93} +(2.97292 + 1.71642i) q^{95} +(5.06969 + 2.92699i) q^{97} +(-16.1040 + 6.75696i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{9}+O(q^{10}) $ 48 * q + 2 * q^9	$ 48 q + 2 q^{9} + 8 q^{15} - 10 q^{21} + 48 q^{25} + 18 q^{27} + 18 q^{29} + 18 q^{31} + 12 q^{33} - 4 q^{39} - 6 q^{41} - 6 q^{43} - 18 q^{45} + 18 q^{47} - 12 q^{49} + 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61} - 32 q^{63} - 36 q^{65} - 12 q^{77} + 6 q^{79} + 6 q^{81} - 54 q^{87} - 18 q^{89} + 6 q^{91} + 4 q^{93} - 54 q^{95} - 64 q^{99}+O(q^{100}) $ 48 * q + 2 * q^9 + 8 * q^15 - 10 * q^21 + 48 * q^25 + 18 * q^27 + 18 * q^29 + 18 * q^31 + 12 * q^33 - 4 * q^39 - 6 * q^41 - 6 * q^43 - 18 * q^45 + 18 * q^47 - 12 * q^49 + 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 - 32 * q^63 - 36 * q^65 - 12 * q^77 + 6 * q^79 + 6 * q^81 - 54 * q^87 - 18 * q^89 + 6 * q^91 + 4 * q^93 - 54 * q^95 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.958980	−	1.44234i	0.553668	−	0.832738i
$3$	0.958980	−	1.44234i	0.553668	−	0.832738i
$4$		0			0
$5$	4.11484			1.84021			0.920106	−	0.391669i	$-0.128102\pi$
$5$	4.11484			1.84021			0.920106	+	0.391669i	$0.128102\pi$
$6$		0			0
$7$	−2.54819	−	0.711830i	−0.963127	−	0.269047i
$7$	−2.54819	−	0.711830i	−0.963127	−	0.269047i
$8$		0			0
$9$	−1.16071	−	2.76636i	−0.386905	−	0.922120i
$10$		0			0
$11$		−	5.82138i		−	1.75521i	−0.479381	−	0.877607i	$-0.659139\pi$
$11$		−	5.82138i		−	1.75521i	0.479381	−	0.877607i	$-0.340861\pi$
$12$		0			0
$13$	−2.52259	+	1.45642i	−0.699641	+	0.403938i	−0.807214	−	0.590259i	$-0.799025\pi$
$13$	−2.52259	+	1.45642i	−0.699641	+	0.403938i	0.107573	+	0.994197i	$0.465692\pi$
$14$		0			0
$15$	3.94605	−	5.93502i	1.01887	−	1.53241i
$16$		0			0
$17$	1.58162	+	2.73945i	0.383600	+	0.664415i	0.991574	−	0.129542i	$-0.0413508\pi$
$17$	1.58162	+	2.73945i	0.383600	+	0.664415i	−0.607974	+	0.793957i	$0.708017\pi$
$18$		0			0
$19$	0.722488	+	0.417129i	0.165750	+	0.0956959i	0.580580	−	0.814203i	$-0.302826\pi$
$19$	0.722488	+	0.417129i	0.165750	+	0.0956959i	−0.414830	+	0.909899i	$0.636159\pi$
$20$		0			0
$21$	−3.47037	+	2.99274i	−0.757297	+	0.653070i
$22$		0			0
$23$			7.09758i			1.47995i	0.672636	+	0.739973i	$0.265162\pi$
$23$			7.09758i			1.47995i	−0.672636	+	0.739973i	$0.734838\pi$
$24$		0			0
$25$	11.9319			2.38638
$26$		0			0
$27$	−5.10314	−	0.978735i	−0.982100	−	0.188358i
$28$		0			0
$29$	−1.91234	−	1.10409i	−0.355113	−	0.205025i	0.311822	−	0.950141i	$-0.399061\pi$
$29$	−1.91234	−	1.10409i	−0.355113	−	0.205025i	−0.666935	+	0.745116i	$0.732394\pi$
$30$		0			0
$31$	3.66696	+	2.11712i	0.658606	+	0.380246i	0.791746	−	0.610851i	$-0.209173\pi$
$31$	3.66696	+	2.11712i	0.658606	+	0.380246i	−0.133140	+	0.991097i	$0.542506\pi$
$32$		0			0
$33$	−8.39644	−	5.58259i	−1.46163	−	0.971805i
$34$		0			0
$35$	−10.4854	−	2.92907i	−1.77236	−	0.495103i
$36$		0			0
$37$	1.82507	−	3.16112i	0.300040	−	0.519684i	−0.676105	−	0.736806i	$-0.736333\pi$
$37$	1.82507	−	3.16112i	0.300040	−	0.519684i	0.976145	+	0.217121i	$0.0696667\pi$
$38$		0			0
$39$	−0.318458	+	5.03512i	−0.0509941	+	0.806265i
$40$		0			0
$41$	2.04811	+	3.54743i	0.319861	+	0.554016i	0.980459	−	0.196724i	$-0.0630303\pi$
$41$	2.04811	+	3.54743i	0.319861	+	0.554016i	−0.660598	+	0.750740i	$0.729697\pi$
$42$		0			0
$43$	0.155460	−	0.269265i	0.0237074	−	0.0410625i	−0.853928	−	0.520391i	$-0.825786\pi$
$43$	0.155460	−	0.269265i	0.0237074	−	0.0410625i	0.877636	+	0.479328i	$0.159120\pi$
$44$		0			0
$45$	−4.77615	−	11.3831i	−0.711987	−	1.69690i
$46$		0			0
$47$	0.502335	+	0.870070i	0.0732731	+	0.126913i	0.900334	−	0.435200i	$-0.143322\pi$
$47$	0.502335	+	0.870070i	0.0732731	+	0.126913i	−0.827061	+	0.562112i	$0.809989\pi$
$48$		0			0
$49$	5.98660	+	3.62776i	0.855228	+	0.518252i
$50$		0			0
$51$	5.46798	+	0.345835i	0.765670	+	0.0484266i
$52$		0			0
$53$	−1.94801	+	1.12469i	−0.267580	+	0.154487i	−0.627787	−	0.778385i	$-0.716039\pi$
$53$	−1.94801	+	1.12469i	−0.267580	+	0.154487i	0.360207	+	0.932872i	$0.382706\pi$
$54$		0			0
$55$		−	23.9541i		−	3.22997i
$56$		0			0
$57$	1.29450	−	0.642058i	0.171460	−	0.0850427i
$58$		0			0
$59$	2.51748	−	4.36040i	0.327748	−	0.567676i	−0.654317	−	0.756221i	$-0.727044\pi$
$59$	2.51748	−	4.36040i	0.327748	−	0.567676i	0.982065	+	0.188545i	$0.0603770\pi$
$60$		0			0
$61$	−3.98673	+	2.30174i	−0.510449	+	0.294708i	−0.733018	−	0.680209i	$-0.761889\pi$
$61$	−3.98673	+	2.30174i	−0.510449	+	0.294708i	0.222569	+	0.974917i	$0.428556\pi$
$62$		0			0
$63$	0.988547	+	7.87545i	0.124545	+	0.992214i
$64$		0			0
$65$	−10.3801	+	5.99293i	−1.28749	+	0.743331i
$66$		0			0
$67$	4.99726	−	8.65551i	0.610513	−	1.05744i	−0.380641	−	0.924723i	$-0.624297\pi$
$67$	4.99726	−	8.65551i	0.610513	−	1.05744i	0.991154	−	0.132717i	$-0.0423700\pi$
$68$		0			0
$69$	10.2371	+	6.80644i	1.23241	+	0.819398i
$70$		0			0
$71$			11.4186i			1.35514i	0.735458	+	0.677571i	$0.236967\pi$
$71$			11.4186i			1.35514i	−0.735458	+	0.677571i	$0.763033\pi$
$72$		0			0
$73$	−3.04990	+	1.76086i	−0.356964	+	0.206093i	−0.667748	−	0.744387i	$-0.732742\pi$
$73$	−3.04990	+	1.76086i	−0.356964	+	0.206093i	0.310784	+	0.950480i	$0.399408\pi$
$74$		0			0
$75$	11.4425	−	17.2099i	1.32126	−	1.98723i
$76$		0			0
$77$	−4.14384	+	14.8340i	−0.472234	+	1.69049i
$78$		0			0
$79$	0.579351	+	1.00346i	0.0651820	+	0.112899i	0.896775	−	0.442487i	$-0.145904\pi$
$79$	0.579351	+	1.00346i	0.0651820	+	0.112899i	−0.831593	+	0.555386i	$0.812571\pi$
$80$		0			0
$81$	−6.30549	+	6.42190i	−0.700610	+	0.713545i
$82$		0			0
$83$	−7.57669	+	13.1232i	−0.831650	+	1.44046i	0.0650797	+	0.997880i	$0.479270\pi$
$83$	−7.57669	+	13.1232i	−0.831650	+	1.44046i	−0.896729	+	0.442579i	$0.854063\pi$
$84$		0			0
$85$	6.50813	+	11.2724i	0.705905	+	1.22266i
$86$		0			0
$87$	−3.42638	+	1.69945i	−0.367346	+	0.182201i
$88$		0			0
$89$	4.82266	−	8.35309i	0.511201	−	0.885426i	−0.488715	−	0.872444i	$-0.662534\pi$
$89$	4.82266	−	8.35309i	0.511201	−	0.885426i	0.999916	−	0.0129824i	$-0.00413254\pi$
$90$		0			0
$91$	7.46478	−	1.91558i	0.782521	−	0.200808i
$92$		0			0
$93$	6.57016	−	3.25874i	0.681294	−	0.337916i
$94$		0			0
$95$	2.97292	+	1.71642i	0.305015	+	0.176101i
$96$		0			0
$97$	5.06969	+	2.92699i	0.514749	+	0.297190i	0.734784	−	0.678302i	$-0.237284\pi$
$97$	5.06969	+	2.92699i	0.514749	+	0.297190i	−0.220035	+	0.975492i	$0.570617\pi$
$98$		0			0
$99$	−16.1040	+	6.75696i	−1.61852	+	0.679100i
$100$		0			0
$101$	5.85264			0.582359			0.291180	−	0.956668i	$-0.405952\pi$
$101$	5.85264			0.582359			0.291180	+	0.956668i	$0.405952\pi$
$102$		0			0
$103$		−	0.780268i		−	0.0768821i	−0.999261	−	0.0384410i	$-0.987761\pi$
$103$		−	0.780268i		−	0.0768821i	0.999261	−	0.0384410i	$-0.0122392\pi$
$104$		0			0
$105$	−14.2800	+	12.3147i	−1.39359	+	1.20179i
$106$		0			0
$107$	−7.15538	−	4.13116i	−0.691737	−	0.399374i	0.112526	−	0.993649i	$-0.464106\pi$
$107$	−7.15538	−	4.13116i	−0.691737	−	0.399374i	−0.804262	+	0.594274i	$0.797439\pi$
$108$		0			0
$109$	3.63584	+	6.29745i	0.348250	+	0.603187i	0.985939	−	0.167107i	$-0.0534427\pi$
$109$	3.63584	+	6.29745i	0.348250	+	0.603187i	−0.637689	+	0.770294i	$0.720109\pi$
$110$		0			0
$111$	−2.80921	−	5.66383i	−0.266639	−	0.537587i
$112$		0			0
$113$	−16.0816	+	9.28474i	−1.51283	+	0.873435i	−0.512947	+	0.858421i	$0.671446\pi$
$113$	−16.0816	+	9.28474i	−1.51283	+	0.873435i	−0.999887	+	0.0150145i	$0.995221\pi$
$114$		0			0
$115$			29.2054i			2.72342i
$116$		0			0
$117$	6.95698	+	5.28791i	0.643173	+	0.488867i
$118$		0			0
$119$	−2.08026	−	8.10650i	−0.190697	−	0.743122i
$120$		0			0
$121$	−22.8885			−2.08077
$122$		0			0
$123$	7.08072	+	0.447837i	0.638447	+	0.0403801i
$124$		0			0
$125$	28.5237			2.55124
$126$		0			0
$127$	4.38363			0.388984			0.194492	−	0.980904i	$-0.437694\pi$
$127$	4.38363			0.388984			0.194492	+	0.980904i	$0.437694\pi$
$128$		0			0
$129$	−0.239289	−	0.482446i	−0.0210682	−	0.0424770i
$130$		0			0
$131$	−15.7084			−1.37245			−0.686224	−	0.727391i	$-0.740733\pi$
$131$	−15.7084			−1.37245			−0.686224	+	0.727391i	$0.740733\pi$
$132$		0			0
$133$	−1.54412	−	1.57721i	−0.133892	−	0.136762i
$134$		0			0
$135$	−20.9986	−	4.02734i	−1.80727	−	0.346618i
$136$		0			0
$137$		−	18.4638i		−	1.57747i	−0.614734	−	0.788734i	$-0.710737\pi$
$137$		−	18.4638i		−	1.57747i	0.614734	−	0.788734i	$-0.289263\pi$
$138$		0			0
$139$	3.80522	−	2.19695i	0.322755	−	0.186343i	−0.329865	−	0.944028i	$-0.607003\pi$
$139$	3.80522	−	2.19695i	0.322755	−	0.186343i	0.652620	+	0.757685i	$0.273670\pi$
$140$		0			0
$141$	1.73667	+	0.109840i	0.146254	+	0.00925018i
$142$		0			0
$143$	8.47837	+	14.6850i	0.708997	+	1.22802i
$144$		0			0
$145$	−7.86898	−	4.54316i	−0.653483	−	0.377289i
$146$		0			0
$147$	10.9735	−	5.15578i	0.905080	−	0.425241i
$148$		0			0
$149$		−	20.5051i		−	1.67984i	−0.542706	−	0.839922i	$-0.682600\pi$
$149$		−	20.5051i		−	1.67984i	0.542706	−	0.839922i	$-0.317400\pi$
$150$		0			0
$151$	5.41552			0.440709			0.220354	−	0.975420i	$-0.429279\pi$
$151$	5.41552			0.440709			0.220354	+	0.975420i	$0.429279\pi$
$152$		0			0
$153$	5.74250	−	7.55506i	0.464253	−	0.610790i
$154$		0			0
$155$	15.0890	+	8.71162i	1.21197	+	0.699734i
$156$		0			0
$157$	9.74596	+	5.62683i	0.777812	+	0.449070i	0.835654	−	0.549256i	$-0.185089\pi$
$157$	9.74596	+	5.62683i	0.777812	+	0.449070i	−0.0578423	+	0.998326i	$0.518422\pi$
$158$		0			0
$159$	−0.245922	+	3.88826i	−0.0195029	+	0.308359i
$160$		0			0
$161$	5.05227	−	18.0860i	0.398175	−	1.42538i
$162$		0			0
$163$	−1.25819	+	2.17924i	−0.0985487	+	0.170691i	−0.911084	−	0.412220i	$-0.864753\pi$
$163$	−1.25819	+	2.17924i	−0.0985487	+	0.170691i	0.812535	+	0.582912i	$0.198087\pi$
$164$		0			0
$165$	−34.5500	−	22.9715i	−2.68971	−	1.78833i
$166$		0			0
$167$	9.38259	+	16.2511i	0.726047	+	1.25755i	0.958542	+	0.284952i	$0.0919777\pi$
$167$	9.38259	+	16.2511i	0.726047	+	1.25755i	−0.232495	+	0.972598i	$0.574689\pi$
$168$		0			0
$169$	−2.25769	+	3.91043i	−0.173668	+	0.300803i
$170$		0			0
$171$	0.315326	−	2.48283i	0.0241136	−	0.189867i
$172$		0			0
$173$	4.85857	+	8.41530i	0.369391	+	0.639803i	0.989470	−	0.144735i	$-0.0462331\pi$
$173$	4.85857	+	8.41530i	0.369391	+	0.639803i	−0.620080	+	0.784539i	$0.712900\pi$
$174$		0			0
$175$	−30.4048	−	8.49349i	−2.29839	−	0.642048i
$176$		0			0
$177$	−3.87499	−	7.81261i	−0.291262	−	0.587232i
$178$		0			0
$179$	−9.24569	+	5.33800i	−0.691055	+	0.398981i	−0.804007	−	0.594619i	$-0.797303\pi$
$179$	−9.24569	+	5.33800i	−0.691055	+	0.398981i	0.112952	+	0.993600i	$0.463969\pi$
$180$		0			0
$181$		−	4.34901i		−	0.323259i	−0.986851	−	0.161630i	$-0.948325\pi$
$181$		−	4.34901i		−	0.323259i	0.986851	−	0.161630i	$-0.0516750\pi$
$182$		0			0
$183$	−0.503295	+	7.95757i	−0.0372046	+	0.588240i
$184$		0			0
$185$	7.50988	−	13.0075i	0.552137	−	0.956330i
$186$		0			0
$187$	15.9474	−	9.20724i	1.16619	−	0.673300i
$188$		0			0
$189$	12.3071	+	6.12658i	0.895211	+	0.445643i
$190$		0			0
$191$	−21.4704	+	12.3959i	−1.55354	+	0.896937i	−0.555691	+	0.831389i	$0.687546\pi$
$191$	−21.4704	+	12.3959i	−1.55354	+	0.896937i	−0.997849	+	0.0655476i	$0.979121\pi$
$192$		0			0
$193$	−13.3256	+	23.0806i	−0.959198	+	1.66138i	−0.234743	+	0.972058i	$0.575425\pi$
$193$	−13.3256	+	23.0806i	−0.959198	+	1.66138i	−0.724455	+	0.689322i	$0.757909\pi$
$194$		0			0
$195$	−1.31040	+	20.7187i	−0.0938400	+	1.48370i
$196$		0			0
$197$			6.11068i			0.435368i	0.976019	+	0.217684i	$0.0698502\pi$
$197$			6.11068i			0.435368i	−0.976019	+	0.217684i	$0.930150\pi$
$198$		0			0
$199$	−0.385220	+	0.222407i	−0.0273075	+	0.0157660i	−0.513592	−	0.858035i	$-0.671685\pi$
$199$	−0.385220	+	0.222407i	−0.0273075	+	0.0157660i	0.486284	+	0.873801i	$0.338352\pi$
$200$		0			0
$201$	−7.69195	−	15.5082i	−0.542549	−	1.09387i
$202$		0			0
$203$	4.08710	+	4.17470i	0.286858	+	0.293007i
$204$		0			0
$205$	8.42765	+	14.5971i	0.588613	+	1.01951i
$206$		0			0
$207$	19.6344	−	8.23825i	1.36469	−	0.572598i
$208$		0			0
$209$	2.42827	−	4.20588i	0.167967	−	0.290927i
$210$		0			0
$211$	−4.23912	−	7.34236i	−0.291833	−	0.505469i	0.682410	−	0.730969i	$-0.260932\pi$
$211$	−4.23912	−	7.34236i	−0.291833	−	0.505469i	−0.974243	+	0.225500i	$0.927598\pi$
$212$		0			0
$213$	16.4696	+	10.9502i	1.12848	+	0.750298i
$214$		0			0
$215$	0.639693	−	1.10798i	0.0436267	−	0.0755636i
$216$		0			0
$217$	−7.83710	−	8.00509i	−0.532017	−	0.543421i
$218$		0			0
$219$	−0.385027	+	6.08763i	−0.0260177	+	0.411364i
$220$		0			0
$221$	−7.97958	−	4.60701i	−0.536764	−	0.309901i
$222$		0			0
$223$	−7.25738	−	4.19005i	−0.485990	−	0.280587i	0.236919	−	0.971529i	$-0.423862\pi$
$223$	−7.25738	−	4.19005i	−0.485990	−	0.280587i	−0.722909	+	0.690943i	$0.757196\pi$
$224$		0			0
$225$	−13.8495	−	33.0079i	−0.923302	−	2.20053i
$226$		0			0
$227$	−2.22151			−0.147447			−0.0737233	−	0.997279i	$-0.523488\pi$
$227$	−2.22151			−0.147447			−0.0737233	+	0.997279i	$0.523488\pi$
$228$		0			0
$229$		−	23.6040i		−	1.55980i	−0.625907	−	0.779898i	$-0.715271\pi$
$229$		−	23.6040i		−	1.55980i	0.625907	−	0.779898i	$-0.284729\pi$
$230$		0			0
$231$	17.4219	+	20.2024i	1.14628	+	1.32922i
$232$		0			0
$233$	−6.69275	−	3.86406i	−0.438457	−	0.253143i	0.264486	−	0.964390i	$-0.414798\pi$
$233$	−6.69275	−	3.86406i	−0.438457	−	0.253143i	−0.702943	+	0.711246i	$0.748131\pi$
$234$		0			0
$235$	2.06703	+	3.58020i	0.134838	+	0.233546i
$236$		0			0
$237$	2.00293	+	0.126680i	0.130104	+	0.00822874i
$238$		0			0
$239$	16.2873	−	9.40346i	1.05354	−	0.608259i	0.129899	−	0.991527i	$-0.458535\pi$
$239$	16.2873	−	9.40346i	1.05354	−	0.608259i	0.923637	+	0.383268i	$0.125201\pi$
$240$		0			0
$241$		−	24.9125i		−	1.60476i	−0.596815	−	0.802379i	$-0.703567\pi$
$241$		−	24.9125i		−	1.60476i	0.596815	−	0.802379i	$-0.296433\pi$
$242$		0			0
$243$	3.21576	+	15.2532i	0.206291	+	0.978491i
$244$		0			0
$245$	24.6339	+	14.9277i	1.57380	+	0.953694i
$246$		0			0
$247$	−2.43006			−0.154621
$248$		0			0
$249$	11.6623	+	23.5131i	0.739068	+	1.49008i
$250$		0			0
$251$	−3.39294			−0.214161			−0.107080	−	0.994250i	$-0.534150\pi$
$251$	−3.39294			−0.214161			−0.107080	+	0.994250i	$0.534150\pi$
$252$		0			0
$253$	41.3177			2.59762
$254$		0			0
$255$	22.4999	+	1.42306i	1.40900	+	0.0891152i
$256$		0			0
$257$	4.95421			0.309035			0.154518	−	0.987990i	$-0.450618\pi$
$257$	4.95421			0.309035			0.154518	+	0.987990i	$0.450618\pi$
$258$		0			0
$259$	−6.90082	+	6.75600i	−0.428796	+	0.419797i
$260$		0			0
$261$	−0.834632	+	6.57176i	−0.0516624	+	0.406782i
$262$		0			0
$263$			2.91442i			0.179711i	0.995955	+	0.0898553i	$0.0286405\pi$
$263$			2.91442i			0.179711i	−0.995955	+	0.0898553i	$0.971360\pi$
$264$		0			0
$265$	−8.01576	+	4.62790i	−0.492404	+	0.284290i
$266$		0			0
$267$	−7.42320	−	14.9664i	−0.454292	−	0.915928i
$268$		0			0
$269$	−9.41429	−	16.3060i	−0.573999	−	0.994196i	−0.996150	−	0.0876702i	$-0.972058\pi$
$269$	−9.41429	−	16.3060i	−0.573999	−	0.994196i	0.422150	−	0.906526i	$-0.361276\pi$
$270$		0			0
$271$	−13.6959	−	7.90734i	−0.831967	−	0.480336i	0.0225585	−	0.999746i	$-0.492819\pi$
$271$	−13.6959	−	7.90734i	−0.831967	−	0.480336i	−0.854526	+	0.519409i	$0.826152\pi$
$272$		0			0
$273$	4.39564	−	12.6038i	0.266037	−	0.762816i
$274$		0			0
$275$		−	69.4602i		−	4.18861i
$276$		0			0
$277$	−4.90462			−0.294690			−0.147345	−	0.989085i	$-0.547073\pi$
$277$	−4.90462			−0.294690			−0.147345	+	0.989085i	$0.547073\pi$
$278$		0			0
$279$	1.60043	−	12.6015i	0.0958150	−	0.754433i
$280$		0			0
$281$	2.77186	+	1.60034i	0.165355	+	0.0954680i	0.580394	−	0.814336i	$-0.302899\pi$
$281$	2.77186	+	1.60034i	0.165355	+	0.0954680i	−0.415039	+	0.909804i	$0.636232\pi$
$282$		0			0
$283$	4.38850	+	2.53370i	0.260869	+	0.150613i	0.624731	−	0.780840i	$-0.285209\pi$
$283$	4.38850	+	2.53370i	0.260869	+	0.150613i	−0.363862	+	0.931453i	$0.618542\pi$
$284$		0			0
$285$	5.32664	−	2.64197i	0.315523	−	0.156497i
$286$		0			0
$287$	−2.69382	−	10.4975i	−0.159011	−	0.619646i
$288$		0			0
$289$	3.49694	−	6.05687i	0.205702	−	0.356287i
$290$		0			0
$291$	9.08345	−	4.50531i	0.532481	−	0.264106i
$292$		0			0
$293$	−12.3751	−	21.4343i	−0.722961	−	1.25221i	−0.959808	−	0.280658i	$-0.909447\pi$
$293$	−12.3751	−	21.4343i	−0.722961	−	1.25221i	0.236847	−	0.971547i	$-0.423886\pi$
$294$		0			0
$295$	10.3590	−	17.9424i	0.603126	−	1.04464i
$296$		0			0
$297$	−5.69760	+	29.7074i	−0.330608	+	1.72380i
$298$		0			0
$299$	−10.3370	−	17.9043i	−0.597807	−	1.03543i
$300$		0			0
$301$	−0.587813	+	0.575477i	−0.0338810	+	0.0331700i
$302$		0			0
$303$	5.61256	−	8.44152i	0.322433	−	0.484953i
$304$		0			0
$305$	−16.4048	+	9.47130i	−0.939335	+	0.542325i
$306$		0			0
$307$		−	19.8011i		−	1.13011i	−0.825054	−	0.565055i	$-0.808855\pi$
$307$		−	19.8011i		−	1.13011i	0.825054	−	0.565055i	$-0.191145\pi$
$308$		0			0
$309$	−1.12541	−	0.748261i	−0.0640226	−	0.0425671i
$310$		0			0
$311$	−6.02449	+	10.4347i	−0.341617	+	0.591699i	−0.984733	−	0.174070i	$-0.944308\pi$
$311$	−6.02449	+	10.4347i	−0.341617	+	0.591699i	0.643116	+	0.765769i	$0.277641\pi$
$312$		0			0
$313$	26.0564	−	15.0437i	1.47279	−	0.850318i	0.473262	−	0.880922i	$-0.343076\pi$
$313$	26.0564	−	15.0437i	1.47279	−	0.850318i	0.999532	+	0.0306036i	$0.00974294\pi$
$314$		0			0
$315$	4.06771	+	32.4062i	0.229190	+	1.82588i
$316$		0			0
$317$	−10.9888	+	6.34436i	−0.617190	+	0.356335i	−0.775774	−	0.631011i	$-0.782640\pi$
$317$	−10.9888	+	6.34436i	−0.617190	+	0.356335i	0.158584	+	0.987345i	$0.449307\pi$
$318$		0			0
$319$	−6.42734	+	11.1325i	−0.359862	+	0.623299i
$320$		0			0
$321$	−12.8204	+	6.35882i	−0.715566	+	0.354915i
$322$		0			0
$323$			2.63896i			0.146836i
$324$		0			0
$325$	−30.0993	+	17.3778i	−1.66961	+	0.963950i
$326$		0			0
$327$	12.5698	+	0.795006i	0.695111	+	0.0439639i
$328$		0			0
$329$	−0.660706	−	2.57469i	−0.0364259	−	0.141947i
$330$		0			0
$331$	2.95408	+	5.11662i	0.162371	+	0.281235i	0.935719	−	0.352748i	$-0.114753\pi$
$331$	2.95408	+	5.11662i	0.162371	+	0.281235i	−0.773348	+	0.633982i	$0.781419\pi$
$332$		0			0
$333$	−10.8632	−	1.37965i	−0.595298	−	0.0756045i
$334$		0			0
$335$	20.5629	−	35.6161i	1.12347	−	1.94591i
$336$		0			0
$337$	−10.5675	−	18.3034i	−0.575647	−	0.997051i	−0.995971	−	0.0896763i	$-0.971417\pi$
$337$	−10.5675	−	18.3034i	−0.575647	−	0.997051i	0.420323	−	0.907374i	$-0.361917\pi$
$338$		0			0
$339$	−2.03019	+	32.0992i	−0.110265	+	1.74339i
$340$		0			0
$341$	12.3246	−	21.3468i	0.667414	−	1.15599i
$342$		0			0
$343$	−12.6727	−	13.5057i	−0.684259	−	0.729239i
$344$		0			0
$345$	42.1242	+	28.0074i	2.26789	+	1.50787i
$346$		0			0
$347$	25.6322	+	14.7988i	1.37601	+	0.794439i	0.991676	−	0.128756i	$-0.0410982\pi$
$347$	25.6322	+	14.7988i	1.37601	+	0.794439i	0.384333	+	0.923195i	$0.374432\pi$
$348$		0			0
$349$	−6.60232	−	3.81185i	−0.353414	−	0.204044i	0.312774	−	0.949828i	$-0.398742\pi$
$349$	−6.60232	−	3.81185i	−0.353414	−	0.204044i	−0.666188	+	0.745784i	$0.732075\pi$
$350$		0			0
$351$	14.2986	−	4.96336i	0.763202	−	0.264925i
$352$		0			0
$353$	10.4945			0.558568			0.279284	−	0.960208i	$-0.409903\pi$
$353$	10.4945			0.558568			0.279284	+	0.960208i	$0.409903\pi$
$354$		0			0
$355$			46.9858i			2.49375i
$356$		0			0
$357$	−13.6873	−	4.77353i	−0.724409	−	0.252642i
$358$		0			0
$359$	4.65028	+	2.68484i	0.245432	+	0.141700i	0.617671	−	0.786437i	$-0.288076\pi$
$359$	4.65028	+	2.68484i	0.245432	+	0.141700i	−0.372239	+	0.928137i	$0.621410\pi$
$360$		0			0
$361$	−9.15201	−	15.8517i	−0.481685	−	0.834302i
$362$		0			0
$363$	−21.9496	+	33.0131i	−1.15206	+	1.73274i
$364$		0			0
$365$	−12.5498	+	7.24566i	−0.656889	+	0.379255i
$366$		0			0
$367$		−	11.1054i		−	0.579698i	−0.957072	−	0.289849i	$-0.906395\pi$
$367$		−	11.1054i		−	0.579698i	0.957072	−	0.289849i	$-0.0936051\pi$
$368$		0			0
$369$	7.43620	−	9.78337i	0.387113	−	0.509302i
$370$		0			0
$371$	5.76450	−	1.47926i	0.299278	−	0.0767995i
$372$		0			0
$373$	−35.4042			−1.83316			−0.916580	−	0.399850i	$-0.869062\pi$
$373$	−35.4042			−1.83316			−0.916580	+	0.399850i	$0.869062\pi$
$374$		0			0
$375$	27.3536	−	41.1410i	1.41254	−	2.12451i
$376$		0			0
$377$	6.43208			0.331269
$378$		0			0
$379$	−26.5906			−1.36587			−0.682933	−	0.730481i	$-0.739296\pi$
$379$	−26.5906			−1.36587			−0.682933	+	0.730481i	$0.739296\pi$
$380$		0			0
$381$	4.20382	−	6.32271i	0.215368	−	0.323922i
$382$		0			0
$383$	−24.5913			−1.25655			−0.628277	−	0.777989i	$-0.716240\pi$
$383$	−24.5913			−1.25655			−0.628277	+	0.777989i	$0.716240\pi$
$384$		0			0
$385$	−17.0512	+	61.0396i	−0.869011	+	3.11087i
$386$		0			0
$387$	−0.925327	−	0.117519i	−0.0470370	−	0.00597383i
$388$		0			0
$389$			19.0987i			0.968344i	0.874973	+	0.484172i	$0.160879\pi$
$389$			19.0987i			0.968344i	−0.874973	+	0.484172i	$0.839121\pi$
$390$		0			0
$391$	−19.4435	+	11.2257i	−0.983298	+	0.567708i
$392$		0			0
$393$	−15.0640	+	22.6569i	−0.759880	+	1.14289i
$394$		0			0
$395$	2.38394	+	4.12910i	0.119949	+	0.207757i
$396$		0			0
$397$	17.8857	+	10.3263i	0.897655	+	0.518261i	0.876439	−	0.481513i	$-0.159913\pi$
$397$	17.8857	+	10.3263i	0.897655	+	0.518261i	0.0212165	+	0.999775i	$0.493246\pi$
$398$		0			0
$399$	−3.75566	+	0.714629i	−0.188018	+	0.0357762i
$400$		0			0
$401$			15.4357i			0.770823i	0.922745	+	0.385412i	$0.125941\pi$
$401$			15.4357i			0.770823i	−0.922745	+	0.385412i	$0.874059\pi$
$402$		0			0
$403$	−12.3337			−0.614384
$404$		0			0
$405$	−25.9461	+	26.4251i	−1.28927	+	1.31307i
$406$		0			0
$407$	−18.4021	−	10.6244i	−0.912157	−	0.526634i
$408$		0			0
$409$	−16.1611	−	9.33064i	−0.799117	−	0.461370i	0.0440453	−	0.999030i	$-0.485975\pi$
$409$	−16.1611	−	9.33064i	−0.799117	−	0.461370i	−0.843162	+	0.537659i	$0.819309\pi$
$410$		0			0
$411$	−26.6311	−	17.7064i	−1.31362	−	0.873393i
$412$		0			0
$413$	−9.51889	+	9.31914i	−0.468394	+	0.458565i
$414$		0			0
$415$	−31.1769	+	53.9999i	−1.53041	+	2.65075i
$416$		0			0
$417$	0.480381	−	7.59527i	0.0235244	−	0.371942i
$418$		0			0
$419$	14.3576	+	24.8681i	0.701414	+	1.21488i	0.967970	+	0.251065i	$0.0807807\pi$
$419$	14.3576	+	24.8681i	0.701414	+	1.21488i	−0.266557	+	0.963819i	$0.585886\pi$
$420$		0			0
$421$	12.8338	−	22.2287i	0.625479	−	1.08336i	−0.362969	−	0.931801i	$-0.618237\pi$
$421$	12.8338	−	22.2287i	0.625479	−	1.08336i	0.988448	−	0.151560i	$-0.0484296\pi$
$422$		0			0
$423$	1.82386	−	2.39954i	0.0886791	−	0.116670i
$424$		0			0
$425$	18.8718	+	32.6869i	0.915416	+	1.58555i
$426$		0			0
$427$	11.7974	−	3.02741i	0.570918	−	0.146507i
$428$		0			0
$429$	29.3114	+	1.85387i	1.41517	+	0.0895055i
$430$		0			0
$431$	−17.0243	+	9.82896i	−0.820030	+	0.473444i	−0.850427	−	0.526094i	$-0.823656\pi$
$431$	−17.0243	+	9.82896i	−0.820030	+	0.473444i	0.0303970	+	0.999538i	$0.490323\pi$
$432$		0			0
$433$		−	7.07732i		−	0.340114i	−0.985434	−	0.170057i	$-0.945605\pi$
$433$		−	7.07732i		−	0.340114i	0.985434	−	0.170057i	$-0.0543952\pi$
$434$		0			0
$435$	−14.0990	+	6.99298i	−0.675995	+	0.335288i
$436$		0			0
$437$	−2.96060	+	5.12791i	−0.141625	+	0.245301i
$438$		0			0
$439$	16.8368	−	9.72072i	0.803575	−	0.463945i	−0.0411444	−	0.999153i	$-0.513100\pi$
$439$	16.8368	−	9.72072i	0.803575	−	0.463945i	0.844720	+	0.535209i	$0.179767\pi$
$440$		0			0
$441$	3.08698	−	20.7719i	0.146999	−	0.989137i
$442$		0			0
$443$	29.8951	−	17.2600i	1.42036	−	0.820045i	0.424030	−	0.905648i	$-0.360615\pi$
$443$	29.8951	−	17.2600i	1.42036	−	0.820045i	0.996329	+	0.0856030i	$0.0272817\pi$
$444$		0			0
$445$	19.8445	−	34.3716i	0.940718	−	1.62937i
$446$		0			0
$447$	−29.5754	−	19.6640i	−1.39887	−	0.930076i
$448$		0			0
$449$			10.9491i			0.516720i	0.966049	+	0.258360i	$0.0831821\pi$
$449$			10.9491i			0.516720i	−0.966049	+	0.258360i	$0.916818\pi$
$450$		0			0
$451$	20.6510	−	11.9228i	0.972417	−	0.561425i
$452$		0			0
$453$	5.19338	−	7.81104i	0.244006	−	0.366995i
$454$		0			0
$455$	30.7164	−	7.88231i	1.44001	−	0.369529i
$456$		0			0
$457$	9.59613	+	16.6210i	0.448888	+	0.777497i	0.998314	−	0.0580457i	$-0.0184869\pi$
$457$	9.59613	+	16.6210i	0.448888	+	0.777497i	−0.549426	+	0.835542i	$0.685154\pi$
$458$		0			0
$459$	−5.39005	−	15.5278i	−0.251586	−	0.724776i
$460$		0			0
$461$	16.2492	−	28.1444i	0.756799	−	1.31081i	−0.187676	−	0.982231i	$-0.560095\pi$
$461$	16.2492	−	28.1444i	0.756799	−	1.31081i	0.944475	−	0.328584i	$-0.106571\pi$
$462$		0			0
$463$	13.9136	+	24.0991i	0.646621	+	1.11998i	0.983924	+	0.178585i	$0.0571519\pi$
$463$	13.9136	+	24.0991i	0.646621	+	1.11998i	−0.337303	+	0.941396i	$0.609515\pi$
$464$		0			0
$465$	27.0352	−	13.4092i	1.25373	−	0.621837i
$466$		0			0
$467$	−0.0869153	+	0.150542i	−0.00402196	+	0.00696624i	−0.868029	−	0.496513i	$-0.834614\pi$
$467$	−0.0869153	+	0.150542i	−0.00402196	+	0.00696624i	0.864007	+	0.503479i	$0.167947\pi$
$468$		0			0
$469$	−18.8953	+	18.4987i	−0.872502	+	0.854192i
$470$		0			0
$471$	17.4620	−	8.66100i	0.804607	−	0.399078i
$472$		0			0
$473$	−1.56749	−	0.904992i	−0.0720734	−	0.0416116i
$474$		0			0
$475$	8.62066	+	4.97714i	0.395543	+	0.228367i
$476$		0			0
$477$	5.37237	+	4.08346i	0.245984	+	0.186969i
$478$		0			0
$479$	−2.93195			−0.133964			−0.0669822	−	0.997754i	$-0.521337\pi$
$479$	−2.93195			−0.133964			−0.0669822	+	0.997754i	$0.521337\pi$
$480$		0			0
$481$			10.6323i			0.484790i
$482$		0			0
$483$	−21.2412	−	24.6312i	−0.966509	−	1.12076i
$484$		0			0
$485$	20.8610	+	12.0441i	0.947247	+	0.546893i
$486$		0			0
$487$	18.7014	+	32.3917i	0.847440	+	1.46781i	0.883486	+	0.468458i	$0.155190\pi$
$487$	18.7014	+	32.3917i	0.847440	+	1.46781i	−0.0360460	+	0.999350i	$0.511476\pi$
$488$		0			0
$489$	1.93664	+	3.90459i	0.0875780	+	0.176572i
$490$		0			0
$491$	−7.27844	+	4.20221i	−0.328472	+	0.189643i	−0.655162	−	0.755488i	$-0.727400\pi$
$491$	−7.27844	+	4.20221i	−0.328472	+	0.189643i	0.326691	+	0.945131i	$0.394066\pi$
$492$		0			0
$493$		−	6.98503i		−	0.314590i
$494$		0			0
$495$	−66.2656	+	27.8038i	−2.97842	+	1.24969i
$496$		0			0
$497$	8.12812	−	29.0969i	0.364596	−	1.30517i
$498$		0			0
$499$	−0.0352479			−0.00157791			−0.000788956	−	1.00000i	$-0.500251\pi$
$499$	−0.0352479			−0.00157791			−0.000788956		1.00000i	$0.500251\pi$
$500$		0			0
$501$	32.4374	+	2.05158i	1.44920	+	0.0916579i
$502$		0			0
$503$	−14.9085			−0.664736			−0.332368	−	0.943150i	$-0.607848\pi$
$503$	−14.9085			−0.664736			−0.332368	+	0.943150i	$0.607848\pi$
$504$		0			0
$505$	24.0827			1.07166
$506$		0			0
$507$	3.47511	+	7.00639i	0.154335	+	0.311165i
$508$		0			0
$509$	−14.4128			−0.638836			−0.319418	−	0.947614i	$-0.603487\pi$
$509$	−14.4128			−0.638836			−0.319418	+	0.947614i	$0.603487\pi$
$510$		0			0
$511$	9.02517	−	2.31600i	0.399250	−	0.102454i
$512$		0			0
$513$	−3.27870	−	2.83579i	−0.144758	−	0.125203i
$514$		0			0
$515$		−	3.21068i		−	0.141479i
$516$		0			0
$517$	5.06501	−	2.92429i	0.222759	−	0.128610i
$518$		0			0
$519$	16.7970	+	1.06237i	0.737308	+	0.0466328i
$520$		0			0
$521$	−10.4159	−	18.0409i	−0.456330	−	0.790386i	0.542434	−	0.840098i	$-0.317503\pi$
$521$	−10.4159	−	18.0409i	−0.456330	−	0.790386i	−0.998764	+	0.0497124i	$0.984170\pi$
$522$		0			0
$523$	12.6684	+	7.31408i	0.553949	+	0.319822i	0.750713	−	0.660628i	$-0.229710\pi$
$523$	12.6684	+	7.31408i	0.553949	+	0.319822i	−0.196764	+	0.980451i	$0.563043\pi$
$524$		0			0
$525$	−41.4082	+	35.7091i	−1.80720	+	1.55847i
$526$		0			0
$527$			13.3940i			0.583450i
$528$		0			0
$529$	−27.3756			−1.19024
$530$		0			0
$531$	−14.9845	−	1.90307i	−0.650272	−	0.0825864i
$532$		0			0
$533$	−10.3331	−	5.96582i	−0.447576	−	0.258408i
$534$		0			0
$535$	−29.4432	−	16.9991i	−1.27294	−	0.734934i
$536$		0			0
$537$	−1.16720	+	18.4545i	−0.0503683	+	0.796371i
$538$		0			0
$539$	21.1186	−	34.8503i	0.909643	−	1.50111i
$540$		0			0
$541$	3.60713	−	6.24773i	0.155083	−	0.268611i	−0.778006	−	0.628256i	$-0.783769\pi$
$541$	3.60713	−	6.24773i	0.155083	−	0.268611i	0.933089	+	0.359645i	$0.117102\pi$
$542$		0			0
$543$	−6.27277	−	4.17061i	−0.269190	−	0.178978i
$544$		0			0
$545$	14.9609	+	25.9130i	0.640854	+	1.10999i
$546$		0			0
$547$	3.81987	−	6.61620i	0.163326	−	0.282888i	−0.772734	−	0.634730i	$-0.781111\pi$
$547$	3.81987	−	6.61620i	0.163326	−	0.282888i	0.936059	+	0.351842i	$0.114445\pi$
$548$		0			0
$549$	10.9949	+	8.35708i	0.469251	+	0.356671i
$550$		0			0
$551$	−0.921096	−	1.59539i	−0.0392400	−	0.0679657i
$552$		0			0
$553$	−0.762002	−	2.96942i	−0.0324036	−	0.126273i
$554$		0			0
$555$	−11.5595	−	23.3058i	−0.490671	−	0.989274i
$556$		0			0
$557$	−8.13965	+	4.69943i	−0.344888	+	0.199121i	−0.662432	−	0.749122i	$-0.730475\pi$
$557$	−8.13965	+	4.69943i	−0.344888	+	0.199121i	0.317543	+	0.948244i	$0.397142\pi$
$558$		0			0
$559$			0.905659i			0.0383053i
$560$		0			0
$561$	2.01324	−	31.8312i	0.0849990	−	1.34391i
$562$		0			0
$563$	2.06352	−	3.57413i	0.0869671	−	0.150631i	−0.819261	−	0.573421i	$-0.805616\pi$
$563$	2.06352	−	3.57413i	0.0869671	−	0.150631i	0.906228	+	0.422790i	$0.138949\pi$
$564$		0			0
$565$	−66.1734	+	38.2052i	−2.78394	+	1.60731i
$566$		0			0
$567$	20.6389	−	11.8758i	0.866753	−	0.498738i
$568$		0			0
$569$	−15.7740	+	9.10715i	−0.661282	+	0.381792i	−0.792765	−	0.609527i	$-0.791359\pi$
$569$	−15.7740	+	9.10715i	−0.661282	+	0.381792i	0.131483	+	0.991318i	$0.458026\pi$
$570$		0			0
$571$	22.5913	−	39.1293i	0.945417	−	1.63751i	0.190502	−	0.981687i	$-0.438988\pi$
$571$	22.5913	−	39.1293i	0.945417	−	1.63751i	0.754915	−	0.655823i	$-0.227678\pi$
$572$		0			0
$573$	−2.71047	+	42.8551i	−0.113231	+	1.79030i
$574$		0			0
$575$			84.6876i			3.53172i
$576$		0			0
$577$	7.04322	−	4.06641i	0.293213	−	0.169287i	−0.346177	−	0.938169i	$-0.612520\pi$
$577$	7.04322	−	4.06641i	0.293213	−	0.169287i	0.639390	+	0.768883i	$0.279187\pi$
$578$		0			0
$579$	20.5112	+	41.3540i	0.852417	+	1.71861i
$580$		0			0
$581$	28.6484	−	28.0472i	1.18853	−	1.16359i
$582$		0			0
$583$	6.54723	+	11.3401i	0.271158	+	0.469660i
$584$		0			0
$585$	28.6269	+	21.7589i	1.18358	+	0.899620i
$586$		0			0
$587$	12.4379	−	21.5430i	0.513366	−	0.889175i	−0.486514	−	0.873673i	$-0.661732\pi$
$587$	12.4379	−	21.5430i	0.513366	−	0.889175i	0.999880	−	0.0155026i	$-0.00493481\pi$
$588$		0			0
$589$	1.76622	+	3.05919i	0.0727760	+	0.126052i
$590$		0			0
$591$	8.81370	+	5.86002i	0.362547	+	0.241049i
$592$		0			0
$593$	−15.6229	+	27.0596i	−0.641554	+	1.11120i	0.343532	+	0.939141i	$0.388377\pi$
$593$	−15.6229	+	27.0596i	−0.641554	+	1.11120i	−0.985086	+	0.172063i	$0.944957\pi$
$594$		0			0
$595$	−8.55993	−	33.3570i	−0.350923	−	1.36750i
$596$		0			0
$597$	−0.0486312	+	0.768904i	−0.00199034	+	0.0314692i
$598$		0			0
$599$	−5.54125	−	3.19925i	−0.226410	−	0.130718i	0.382505	−	0.923953i	$-0.375061\pi$
$599$	−5.54125	−	3.19925i	−0.226410	−	0.130718i	−0.608915	+	0.793236i	$0.708395\pi$
$600$		0			0
$601$	36.0541	+	20.8158i	1.47068	+	0.849095i	0.999458	−	0.0329215i	$-0.0104811\pi$
$601$	36.0541	+	20.8158i	1.47068	+	0.849095i	0.471218	+	0.882017i	$0.343814\pi$
$602$		0			0
$603$	−29.7447	−	3.77765i	−1.21130	−	0.153838i
$604$		0			0
$605$	−94.1826			−3.82907
$606$		0			0
$607$		−	25.0762i		−	1.01781i	−0.860822	−	0.508907i	$-0.830050\pi$
$607$		−	25.0762i		−	1.01781i	0.860822	−	0.508907i	$-0.169950\pi$
$608$		0			0
$609$	9.94080	−	1.89154i	0.402822	−	0.0766491i
$610$		0			0
$611$	−2.53437	−	1.46322i	−0.102530	−	0.0591956i
$612$		0			0
$613$	15.3779	+	26.6352i	0.621106	+	1.07579i	0.989280	+	0.146030i	$0.0466497\pi$
$613$	15.3779	+	26.6352i	0.621106	+	1.07579i	−0.368174	+	0.929757i	$0.620017\pi$
$614$		0			0
$615$	29.1360	+	1.84278i	1.17488	+	0.0743079i
$616$		0			0
$617$	−10.1910	+	5.88375i	−0.410272	+	0.236871i	−0.690907	−	0.722944i	$-0.742788\pi$
$617$	−10.1910	+	5.88375i	−0.410272	+	0.236871i	0.280634	+	0.959815i	$0.409455\pi$
$618$		0			0
$619$		−	7.09698i		−	0.285252i	−0.989777	−	0.142626i	$-0.954445\pi$
$619$		−	7.09698i		−	0.285252i	0.989777	−	0.142626i	$-0.0455546\pi$
$620$		0			0
$621$	6.94665	−	36.2199i	0.278759	−	1.45346i
$622$		0			0
$623$	−18.2351	+	17.8524i	−0.730572	+	0.715241i
$624$		0			0
$625$	57.7108			2.30843
$626$		0			0
$627$	−3.73767	−	7.53575i	−0.149268	−	0.300949i
$628$		0			0
$629$	11.5463			0.460381
$630$		0			0
$631$	13.0686			0.520252			0.260126	−	0.965575i	$-0.416236\pi$
$631$	13.0686			0.520252			0.260126	+	0.965575i	$0.416236\pi$
$632$		0			0
$633$	−14.6554	−	0.926918i	−0.582502	−	0.0368417i
$634$		0			0
$635$	18.0379			0.715814
$636$		0			0
$637$	−20.3853	−	0.432378i	−0.807694	−	0.0171314i
$638$		0			0
$639$	31.5880	−	13.2538i	1.24960	−	0.524310i
$640$		0			0
$641$			12.6115i			0.498123i	0.968488	+	0.249062i	$0.0801221\pi$
$641$			12.6115i			0.498123i	−0.968488	+	0.249062i	$0.919878\pi$
$642$		0			0
$643$	12.3449	−	7.12736i	0.486837	−	0.281076i	−0.236424	−	0.971650i	$-0.575975\pi$
$643$	12.3449	−	7.12736i	0.486837	−	0.281076i	0.723261	+	0.690574i	$0.242642\pi$
$644$		0			0
$645$	−0.984636	−	1.98519i	−0.0387700	−	0.0781667i
$646$		0			0
$647$	−20.0060	−	34.6515i	−0.786519	−	1.36229i	−0.928088	−	0.372362i	$-0.878548\pi$
$647$	−20.0060	−	34.6515i	−0.786519	−	1.36229i	0.141569	−	0.989928i	$-0.454785\pi$
$648$		0			0
$649$	−25.3836	−	14.6552i	−0.996392	−	0.575267i
$650$		0			0
$651$	−19.0617	+	3.62707i	−0.747088	+	0.142156i
$652$		0			0
$653$			14.6331i			0.572638i	0.958134	+	0.286319i	$0.0924317\pi$
$653$			14.6331i			0.572638i	−0.958134	+	0.286319i	$0.907568\pi$
$654$		0			0
$655$	−64.6375			−2.52559
$656$		0			0
$657$	8.41123	+	6.39326i	0.328153	+	0.249425i
$658$		0			0
$659$	−23.7553	−	13.7151i	−0.925374	−	0.534265i	−0.0400285	−	0.999199i	$-0.512745\pi$
$659$	−23.7553	−	13.7151i	−0.925374	−	0.534265i	−0.885346	+	0.464934i	$0.846078\pi$
$660$		0			0
$661$	30.8389	+	17.8048i	1.19949	+	0.692528i	0.960442	−	0.278479i	$-0.0898304\pi$
$661$	30.8389	+	17.8048i	1.19949	+	0.692528i	0.239051	+	0.971007i	$0.423164\pi$
$662$		0			0
$663$	−14.2972	+	7.09126i	−0.555255	+	0.275402i
$664$		0			0
$665$	−6.35379	−	6.48998i	−0.246389	−	0.251671i
$666$		0			0
$667$	7.83637	−	13.5730i	0.303426	−	0.525548i
$668$		0			0
$669$	−13.0032	+	6.44946i	−0.502732	+	0.249351i
$670$		0			0
$671$	13.3993	+	23.2083i	0.517275	+	0.895947i
$672$		0			0
$673$	6.35937	−	11.0147i	0.245136	−	0.424587i	−0.717034	−	0.697038i	$-0.754501\pi$
$673$	6.35937	−	11.0147i	0.245136	−	0.424587i	0.962170	+	0.272451i	$0.0878342\pi$
$674$		0			0
$675$	−60.8902	−	11.6782i	−2.34367	−	0.449493i
$676$		0			0
$677$	14.0278	+	24.2968i	0.539131	+	0.933803i	0.998951	+	0.0457904i	$0.0145807\pi$
$677$	14.0278	+	24.2968i	0.539131	+	0.933803i	−0.459820	+	0.888012i	$0.652086\pi$
$678$		0			0
$679$	−10.8350	−	11.0673i	−0.415810	−	0.424723i
$680$		0			0
$681$	−2.13038	+	3.20418i	−0.0816364	+	0.122784i
$682$		0			0
$683$	−14.4564	+	8.34638i	−0.553157	+	0.319365i	−0.750394	−	0.660990i	$-0.770136\pi$
$683$	−14.4564	+	8.34638i	−0.553157	+	0.319365i	0.197237	+	0.980356i	$0.436803\pi$
$684$		0			0
$685$		−	75.9756i		−	2.90288i
$686$		0			0
$687$	−34.0451	−	22.6358i	−1.29890	−	0.863608i
$688$		0			0
$689$	3.27603	−	5.67424i	0.124807	−	0.216171i
$690$		0			0
$691$	26.3650	−	15.2218i	1.00297	−	0.579066i	0.0938458	−	0.995587i	$-0.470084\pi$
$691$	26.3650	−	15.2218i	1.00297	−	0.579066i	0.909126	+	0.416521i	$0.136751\pi$
$692$		0			0
$693$	45.8460	−	5.75471i	1.74155	−	0.218603i
$694$		0			0
$695$	15.6579	−	9.04009i	0.593938	−	0.342910i
$696$		0			0
$697$	−6.47868	+	11.2214i	−0.245398	+	0.425041i
$698$		0			0
$699$	−11.9915	+	5.94769i	−0.453561	+	0.224962i
$700$		0			0
$701$		−	6.16940i		−	0.233015i	−0.993190	−	0.116507i	$-0.962830\pi$
$701$		−	6.16940i		−	0.233015i	0.993190	−	0.116507i	$-0.0371699\pi$
$702$		0			0
$703$	2.63719	−	1.52258i	0.0994633	−	0.0574252i
$704$		0			0
$705$	7.14612	+	0.451973i	0.269138	+	0.0170223i
$706$		0			0
$707$	−14.9137	−	4.16608i	−0.560886	−	0.156682i
$708$		0			0
$709$	−12.7487	−	22.0813i	−0.478786	−	0.829282i	0.520918	−	0.853607i	$-0.325590\pi$
$709$	−12.7487	−	22.0813i	−0.478786	−	0.829282i	−0.999704	+	0.0243250i	$0.992256\pi$
$710$		0			0
$711$	2.10348	−	2.76743i	0.0788868	−	0.103787i
$712$		0			0
$713$	−15.0264	+	26.0265i	−0.562744	+	0.974702i
$714$		0			0
$715$	34.8871	+	60.4263i	1.30471	+	2.25982i
$716$		0			0
$717$	2.05615	−	32.5096i	0.0767881	−	1.21409i
$718$		0			0
$719$	12.1263	−	21.0034i	0.452236	−	0.783296i	−0.546289	−	0.837597i	$-0.683960\pi$
$719$	12.1263	−	21.0034i	0.452236	−	0.783296i	0.998525	+	0.0543012i	$0.0172931\pi$
$720$		0			0
$721$	−0.555418	+	1.98827i	−0.0206849	+	0.0740472i
$722$		0			0
$723$	−35.9324	−	23.8906i	−1.33634	−	0.888502i
$724$		0			0
$725$	−22.8179	−	13.1739i	−0.847435	−	0.489267i
$726$		0			0
$727$	−13.5251	−	7.80870i	−0.501617	−	0.289609i	0.227764	−	0.973716i	$-0.426859\pi$
$727$	−13.5251	−	7.80870i	−0.501617	−	0.289609i	−0.729381	+	0.684108i	$0.760192\pi$
$728$		0			0
$729$	25.0842	+	9.98925i	0.929043	+	0.369972i
$730$		0			0
$731$	0.983516			0.0363767
$732$		0			0
$733$			35.7036i			1.31874i	0.751818	+	0.659371i	$0.229177\pi$
$733$			35.7036i			1.31874i	−0.751818	+	0.659371i	$0.770823\pi$
$734$		0			0
$735$	45.1542	−	21.2152i	1.66554	−	0.782534i
$736$		0			0
$737$	−50.3871	−	29.0910i	−1.85603	−	1.07158i
$738$		0			0
$739$	7.27883	+	12.6073i	0.267756	+	0.463767i	0.968282	−	0.249860i	$-0.0803846\pi$
$739$	7.27883	+	12.6073i	0.267756	+	0.463767i	−0.700526	+	0.713627i	$0.747051\pi$
$740$		0			0
$741$	−2.33038	+	3.50498i	−0.0856085	+	0.128759i
$742$		0			0
$743$	0.0287226	−	0.0165830i	0.00105373	−	0.000608372i	−0.499473	−	0.866329i	$-0.666473\pi$
$743$	0.0287226	−	0.0165830i	0.00105373	−	0.000608372i	0.500527	+	0.865721i	$0.333140\pi$
$744$		0			0
$745$		−	84.3753i		−	3.09127i
$746$		0			0
$747$	45.0979	+	5.72755i	1.65005	+	0.209560i
$748$		0			0
$749$	15.2926	+	15.6204i	0.558780	+	0.570758i
$750$		0			0
$751$	23.7899			0.868106			0.434053	−	0.900887i	$-0.357083\pi$
$751$	23.7899			0.868106			0.434053	+	0.900887i	$0.357083\pi$
$752$		0			0
$753$	−3.25377	+	4.89379i	−0.118574	+	0.178340i
$754$		0			0
$755$	22.2840			0.810998
$756$		0			0
$757$	−33.2060			−1.20689			−0.603446	−	0.797404i	$-0.706206\pi$
$757$	−33.2060			−1.20689			−0.603446	+	0.797404i	$0.706206\pi$
$758$		0			0
$759$	39.6229	−	59.5944i	1.43822	−	2.16314i
$760$		0			0
$761$	−42.5675			−1.54307			−0.771535	−	0.636187i	$-0.780511\pi$
$761$	−42.5675			−1.54307			−0.771535	+	0.636187i	$0.780511\pi$
$762$		0			0
$763$	−4.78210	−	18.6352i	−0.173124	−	0.674641i
$764$		0			0
$765$	23.6295	−	31.0878i	0.854325	−	1.12398i
$766$		0			0
$767$			14.6660i			0.529559i
$768$		0			0
$769$	27.1091	−	15.6514i	0.977578	−	0.564405i	0.0760402	−	0.997105i	$-0.475772\pi$
$769$	27.1091	−	15.6514i	0.977578	−	0.564405i	0.901538	+	0.432700i	$0.142439\pi$
$770$		0			0
$771$	4.75099	−	7.14568i	0.171103	−	0.257345i
$772$		0			0
$773$	0.165130	+	0.286014i	0.00593932	+	0.0102872i	0.868980	−	0.494848i	$-0.164776\pi$
$773$	0.165130	+	0.286014i	0.00593932	+	0.0102872i	−0.863040	+	0.505135i	$0.831443\pi$
$774$		0			0
$775$	43.7539	+	25.2613i	1.57168	+	0.907413i
$776$		0			0
$777$	3.12673	+	16.4322i	0.112171	+	0.589503i
$778$		0			0
$779$			3.41730i			0.122438i
$780$		0			0
$781$	66.4722			2.37856
$782$		0			0
$783$	8.67835	+	7.50601i	0.310139	+	0.268243i
$784$		0			0
$785$	40.1031	+	23.1535i	1.43134	+	0.826384i
$786$		0			0
$787$	−6.50328	−	3.75467i	−0.231817	−	0.133840i	0.379593	−	0.925154i	$-0.376064\pi$
$787$	−6.50328	−	3.75467i	−0.231817	−	0.133840i	−0.611410	+	0.791314i	$0.709397\pi$
$788$		0			0
$789$	4.20359	+	2.79487i	0.149652	+	0.0995000i
$790$		0			0
$791$	47.5883	−	12.2119i	1.69205	−	0.434206i
$792$		0			0
$793$	6.70460	−	11.6127i	0.238087	−	0.412379i
$794$		0			0
$795$	−1.01193	+	15.9995i	−0.0358894	+	0.567445i
$796$		0			0
$797$	3.58136	+	6.20310i	0.126858	+	0.219725i	0.922458	−	0.386098i	$-0.126177\pi$
$797$	3.58136	+	6.20310i	0.126858	+	0.219725i	−0.795600	+	0.605823i	$0.792844\pi$
$798$		0			0
$799$	−1.58901	+	2.75225i	−0.0562151	+	0.0973675i
$800$		0			0
$801$	−28.7054	−	3.64566i	−1.01425	−	0.128813i
$802$		0			0
$803$	10.2506	+	17.7546i	0.361737	+	0.626547i
$804$		0			0
$805$	20.7893	−	74.4210i	0.732726	−	2.62300i
$806$		0			0
$807$	−32.5470	−	2.05851i	−1.14571	−	0.0724631i
$808$		0			0
$809$	39.9767	−	23.0806i	1.40551	−	0.811469i	0.410556	−	0.911836i	$-0.365335\pi$
$809$	39.9767	−	23.0806i	1.40551	−	0.811469i	0.994951	+	0.100366i	$0.0320014\pi$
$810$		0			0
$811$			22.8560i			0.802581i	0.915951	+	0.401290i	$0.131438\pi$
$811$			22.8560i			0.802581i	−0.915951	+	0.401290i	$0.868562\pi$
$812$		0			0
$813$	−24.5392	+	12.1712i	−0.860628	+	0.426864i
$814$		0			0
$815$	−5.17723	+	8.96723i	−0.181351	+	0.314108i
$816$		0			0
$817$	0.224636	−	0.129694i	0.00785902	−	0.00453741i
$818$		0			0
$819$	−13.9637	−	18.4268i	−0.487930	−	0.643885i
$820$		0			0
$821$	−1.65766	+	0.957051i	−0.0578527	+	0.0334013i	−0.528647	−	0.848842i	$-0.677301\pi$
$821$	−1.65766	+	0.957051i	−0.0578527	+	0.0334013i	0.470795	+	0.882243i	$0.343967\pi$
$822$		0			0
$823$	7.54735	−	13.0724i	0.263084	−	0.455675i	−0.703976	−	0.710224i	$-0.748594\pi$
$823$	7.54735	−	13.0724i	0.263084	−	0.455675i	0.967060	+	0.254549i	$0.0819270\pi$
$824$		0			0
$825$	−100.186	−	66.6110i	−3.48801	−	2.31910i
$826$		0			0
$827$		−	14.4077i		−	0.501004i	−0.968116	−	0.250502i	$-0.919404\pi$
$827$		−	14.4077i		−	0.501004i	0.968116	−	0.250502i	$-0.0805956\pi$
$828$		0			0
$829$	−37.1450	+	21.4457i	−1.29010	+	0.744840i	−0.978672	−	0.205430i	$-0.934141\pi$
$829$	−37.1450	+	21.4457i	−1.29010	+	0.744840i	−0.311429	+	0.950270i	$0.600807\pi$
$830$		0			0
$831$	−4.70344	+	7.07415i	−0.163160	+	0.245400i
$832$		0			0
$833$	−0.469548	+	22.1377i	−0.0162689	+	0.767027i
$834$		0			0
$835$	38.6079	+	66.8708i	1.33608	+	2.31416i
$836$		0			0
$837$	−16.6409	−	14.3930i	−0.575195	−	0.497494i
$838$		0			0
$839$	−12.5327	+	21.7073i	−0.432678	+	0.749421i	−0.997103	−	0.0760639i	$-0.975765\pi$
$839$	−12.5327	+	21.7073i	−0.432678	+	0.749421i	0.564425	+	0.825485i	$0.309098\pi$
$840$		0			0
$841$	−12.0620	−	20.8919i	−0.415930	−	0.720412i
$842$		0			0
$843$	4.96640	−	2.46329i	0.171052	−	0.0848402i
$844$		0			0
$845$	−9.29003	+	16.0908i	−0.319587	+	0.553541i
$846$		0			0
$847$	58.3244	+	16.2927i	2.00405	+	0.559825i
$848$		0			0
$849$	7.86296	−	3.89996i	0.269856	−	0.133846i
$850$		0			0
$851$	22.4363	+	12.9536i	0.769105	+	0.444043i
$852$		0			0
$853$	−14.9013	−	8.60328i	−0.510211	−	0.294571i	0.222709	−	0.974885i	$-0.428510\pi$
$853$	−14.9013	−	8.60328i	−0.510211	−	0.294571i	−0.732920	+	0.680314i	$0.761843\pi$
$854$		0			0
$855$	1.29752	−	10.2164i	0.0443741	−	0.349395i
$856$		0			0
$857$	48.6968			1.66345			0.831726	−	0.555187i	$-0.187353\pi$
$857$	48.6968			1.66345			0.831726	+	0.555187i	$0.187353\pi$
$858$		0			0
$859$		−	3.09785i		−	0.105697i	−0.998603	−	0.0528487i	$-0.983170\pi$
$859$		−	3.09785i		−	0.105697i	0.998603	−	0.0528487i	$-0.0168301\pi$
$860$		0			0
$861$	−17.7243	−	6.18145i	−0.604042	−	0.210663i
$862$		0			0
$863$	22.2443	+	12.8427i	0.757203	+	0.437172i	0.828291	−	0.560299i	$-0.189314\pi$
$863$	22.2443	+	12.8427i	0.757203	+	0.437172i	−0.0710874	+	0.997470i	$0.522647\pi$
$864$		0			0
$865$	19.9923	+	34.6276i	0.679757	+	1.17737i
$866$		0			0
$867$	−5.38260	−	10.8522i	−0.182803	−	0.368560i
$868$		0			0
$869$	5.84156	−	3.37262i	0.198161	−	0.114408i
$870$		0			0
$871$			29.1124i			0.986437i
$872$		0			0
$873$	2.21264	−	17.4220i	0.0748864	−	0.589644i
$874$		0			0
$875$	−72.6839	−	20.3040i	−2.45716	−	0.686401i
$876$		0			0
$877$	1.25325			0.0423193			0.0211597	−	0.999776i	$-0.493264\pi$
$877$	1.25325			0.0423193			0.0211597	+	0.999776i	$0.493264\pi$
$878$		0			0
$879$	−42.7831	−	2.70592i	−1.44304	−	0.0912684i
$880$		0			0
$881$	18.7429			0.631464			0.315732	−	0.948848i	$-0.397750\pi$
$881$	18.7429			0.631464			0.315732	+	0.948848i	$0.397750\pi$
$882$		0			0
$883$	39.3701			1.32491			0.662454	−	0.749103i	$-0.269515\pi$
$883$	39.3701			1.32491			0.662454	+	0.749103i	$0.269515\pi$
$884$		0			0
$885$	−15.9450	−	32.1476i	−0.535984	−	1.08063i
$886$		0			0
$887$	−37.1909			−1.24875			−0.624374	−	0.781126i	$-0.714646\pi$
$887$	−37.1909			−1.24875			−0.624374	+	0.781126i	$0.714646\pi$
$888$		0			0
$889$	−11.1703	−	3.12040i	−0.374641	−	0.104655i
$890$		0			0
$891$	37.3844	+	36.7067i	1.25242	+	1.22972i
$892$		0			0
$893$			0.838154i			0.0280478i
$894$		0			0
$895$	−38.0445	+	21.9650i	−1.27169	+	0.734210i
$896$		0			0
$897$	−35.7372	−	2.26028i	−1.19323	−	0.0754686i
$898$		0			0
$899$	−4.67499	−	8.09732i	−0.155920	−	0.270061i
$900$		0			0
$901$	−6.16204	−	3.55766i	−0.205287	−	0.118523i
$902$		0			0
$903$	0.266336	+	1.39970i	0.00886309	+	0.0465791i
$904$		0			0
$905$		−	17.8955i		−	0.594866i
$906$		0			0
$907$	−30.8590			−1.02466			−0.512328	−	0.858790i	$-0.671217\pi$
$907$	−30.8590			−1.02466			−0.512328	+	0.858790i	$0.671217\pi$
$908$		0			0
$909$	−6.79324	−	16.1905i	−0.225317	−	0.537005i
$910$		0			0
$911$	−14.7486	−	8.51511i	−0.488643	−	0.282118i	0.235368	−	0.971906i	$-0.424370\pi$
$911$	−14.7486	−	8.51511i	−0.488643	−	0.282118i	−0.724011	+	0.689788i	$0.757704\pi$
$912$		0			0
$913$	76.3953	+	44.1068i	2.52831	+	1.45972i
$914$		0			0
$915$	−2.07098	+	32.7441i	−0.0684645	+	1.08249i
$916$		0			0
$917$	40.0280	+	11.1817i	1.32184	+	0.369252i
$918$		0			0
$919$	−8.44635	+	14.6295i	−0.278619	+	0.482583i	−0.971042	−	0.238909i	$-0.923210\pi$
$919$	−8.44635	+	14.6295i	−0.278619	+	0.482583i	0.692422	+	0.721492i	$0.256543\pi$
$920$		0			0
$921$	−28.5600	−	18.9889i	−0.941085	−	0.625705i
$922$		0			0
$923$	−16.6303	−	28.8045i	−0.547393	−	0.948112i
$924$		0			0
$925$	21.7766	−	37.7182i	0.716010	−	1.24017i
$926$		0			0
$927$	−2.15850	+	0.905668i	−0.0708945	+	0.0297460i
$928$		0			0
$929$	−3.39678	−	5.88339i	−0.111445	−	0.193028i	0.804908	−	0.593399i	$-0.202214\pi$
$929$	−3.39678	−	5.88339i	−0.111445	−	0.193028i	−0.916353	+	0.400371i	$0.868881\pi$
$930$		0			0
$931$	2.81200	+	5.11820i	0.0921596	+	0.167742i
$932$		0			0
$933$	9.27309	+	18.6961i	0.303587	+	0.612082i
$934$		0			0
$935$	65.6210	−	37.8863i	2.14604	−	1.23901i
$936$		0			0
$937$			5.14535i			0.168091i	0.996462	+	0.0840456i	$0.0267841\pi$
$937$			5.14535i			0.168091i	−0.996462	+	0.0840456i	$0.973216\pi$
$938$		0			0
$939$	3.28942	−	52.0088i	0.107346	−	1.69724i
$940$		0			0
$941$	0.460454	−	0.797529i	0.0150104	−	0.0259987i	−0.858423	−	0.512943i	$-0.828555\pi$
$941$	0.460454	−	0.797529i	0.0150104	−	0.0259987i	0.873433	+	0.486944i	$0.161889\pi$
$942$		0			0
$943$	−25.1782	+	14.5366i	−0.819914	+	0.473378i
$944$		0			0
$945$	50.6418	+	25.2099i	1.64738	+	0.820078i
$946$		0			0
$947$	21.2033	−	12.2417i	0.689015	−	0.397803i	−0.114228	−	0.993455i	$-0.536439\pi$
$947$	21.2033	−	12.2417i	0.689015	−	0.397803i	0.803243	+	0.595652i	$0.203106\pi$
$948$		0			0
$949$	5.12910	−	8.88386i	0.166498	−	0.288382i
$950$		0			0
$951$	−1.38725	+	21.9337i	−0.0449846	+	0.711248i
$952$		0			0
$953$			9.80916i			0.317750i	0.987299	+	0.158875i	$0.0507866\pi$
$953$			9.80916i			0.317750i	−0.987299	+	0.158875i	$0.949213\pi$
$954$		0			0
$955$	−88.3471	+	51.0072i	−2.85884	+	1.65055i
$956$		0			0
$957$	9.89318	+	19.9463i	0.319801	+	0.644771i
$958$		0			0
$959$	−13.1431	+	47.0494i	−0.424412	+	1.51930i
$960$		0			0
$961$	−6.53559	−	11.3200i	−0.210825	−	0.365160i
$962$		0			0
$963$	−3.12293	+	24.5894i	−0.100635	+	0.792384i
$964$		0			0
$965$	−54.8327	+	94.9731i	−1.76513	+	3.05729i
$966$		0			0
$967$	−18.1376	−	31.4152i	−0.583264	−	1.01024i	−0.995089	−	0.0989807i	$-0.968442\pi$
$967$	−18.1376	−	31.4152i	−0.583264	−	1.01024i	0.411825	−	0.911263i	$-0.364892\pi$
$968$		0			0
$969$	3.80629	+	2.53071i	0.122276	+	0.0812982i
$970$		0			0
$971$	−1.09772	+	1.90130i	−0.0352274	+	0.0610157i	−0.883102	−	0.469182i	$-0.844549\pi$
$971$	−1.09772	+	1.90130i	−0.0352274	+	0.0610157i	0.847874	+	0.530198i	$0.177882\pi$
$972$		0			0
$973$	−11.2603	+	2.88958i	−0.360989	+	0.0926356i
$974$		0			0
$975$	−3.79981	+	60.0786i	−0.121691	+	1.92405i
$976$		0			0
$977$	−36.9950	−	21.3591i	−1.18357	−	0.683337i	−0.226736	−	0.973956i	$-0.572805\pi$
$977$	−36.9950	−	21.3591i	−1.18357	−	0.683337i	−0.956839	+	0.290619i	$0.906139\pi$
$978$		0			0
$979$	−48.6266	−	28.0746i	−1.55411	−	0.897267i
$980$		0			0
$981$	13.2009	−	17.3676i	0.421471	−	0.554504i
$982$		0			0
$983$	45.7562			1.45940			0.729698	−	0.683770i	$-0.239661\pi$
$983$	45.7562			1.45940			0.729698	+	0.683770i	$0.239661\pi$
$984$		0			0
$985$			25.1444i			0.801169i
$986$		0			0
$987$	−4.34719	−	1.51611i	−0.138373	−	0.0482582i
$988$		0			0
$989$	1.91113	+	1.10339i	0.0607703	+	0.0350857i
$990$		0			0
$991$	−8.30690	−	14.3880i	−0.263877	−	0.457049i	0.703392	−	0.710803i	$-0.251668\pi$
$991$	−8.30690	−	14.3880i	−0.263877	−	0.457049i	−0.967269	+	0.253754i	$0.918335\pi$
$992$		0			0
$993$	10.2128	+	0.645934i	0.324094	+	0.0204981i
$994$		0			0
$995$	−1.58512	+	0.915169i	−0.0502517	+	0.0290128i
$996$		0			0
$997$			21.4826i			0.680361i	0.940360	+	0.340181i	$0.110488\pi$
$997$			21.4826i			0.680361i	−0.940360	+	0.340181i	$0.889512\pi$
$998$		0			0
$999$	−12.4075	+	14.3454i	−0.392556	+	0.453868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cx.a.425.17	yes	48
3.2	odd	2		1512.2.cx.a.89.1		48
4.3	odd	2		1008.2.df.e.929.8		48
7.3	odd	6		504.2.bs.a.353.23	yes	48
9.4	even	3		1512.2.bs.a.1097.1		48
9.5	odd	6		504.2.bs.a.257.23	✓	48
12.11	even	2		3024.2.df.e.1601.1		48
21.17	even	6		1512.2.bs.a.521.1		48
28.3	even	6		1008.2.ca.e.353.2		48
36.23	even	6		1008.2.ca.e.257.2		48
36.31	odd	6		3024.2.ca.e.2609.1		48
63.31	odd	6		1512.2.cx.a.17.1		48
63.59	even	6	inner	504.2.cx.a.185.17	yes	48
84.59	odd	6		3024.2.ca.e.2033.1		48
252.31	even	6		3024.2.df.e.17.1		48
252.59	odd	6		1008.2.df.e.689.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.23	✓	48	9.5	odd	6
504.2.bs.a.353.23	yes	48	7.3	odd	6
504.2.cx.a.185.17	yes	48	63.59	even	6	inner
504.2.cx.a.425.17	yes	48	1.1	even	1	trivial
1008.2.ca.e.257.2		48	36.23	even	6
1008.2.ca.e.353.2		48	28.3	even	6
1008.2.df.e.689.8		48	252.59	odd	6
1008.2.df.e.929.8		48	4.3	odd	2
1512.2.bs.a.521.1		48	21.17	even	6
1512.2.bs.a.1097.1		48	9.4	even	3
1512.2.cx.a.17.1		48	63.31	odd	6
1512.2.cx.a.89.1		48	3.2	odd	2
3024.2.ca.e.2033.1		48	84.59	odd	6
3024.2.ca.e.2609.1		48	36.31	odd	6
3024.2.df.e.17.1		48	252.31	even	6
3024.2.df.e.1601.1		48	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cx (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.958980 - 1.44234i) q^{3} +4.11484 q^{5} +(-2.54819 - 0.711830i) q^{7} +(-1.16071 - 2.76636i) q^{9} +O(q^{10})\)	\(q+(0.958980 - 1.44234i) q^{3} +4.11484 q^{5} +(-2.54819 - 0.711830i) q^{7} +(-1.16071 - 2.76636i) q^{9} -5.82138i q^{11} +(-2.52259 + 1.45642i) q^{13} +(3.94605 - 5.93502i) q^{15} +(1.58162 + 2.73945i) q^{17} +(0.722488 + 0.417129i) q^{19} +(-3.47037 + 2.99274i) q^{21} +7.09758i q^{23} +11.9319 q^{25} +(-5.10314 - 0.978735i) q^{27} +(-1.91234 - 1.10409i) q^{29} +(3.66696 + 2.11712i) q^{31} +(-8.39644 - 5.58259i) q^{33} +(-10.4854 - 2.92907i) q^{35} +(1.82507 - 3.16112i) q^{37} +(-0.318458 + 5.03512i) q^{39} +(2.04811 + 3.54743i) q^{41} +(0.155460 - 0.269265i) q^{43} +(-4.77615 - 11.3831i) q^{45} +(0.502335 + 0.870070i) q^{47} +(5.98660 + 3.62776i) q^{49} +(5.46798 + 0.345835i) q^{51} +(-1.94801 + 1.12469i) q^{53} -23.9541i q^{55} +(1.29450 - 0.642058i) q^{57} +(2.51748 - 4.36040i) q^{59} +(-3.98673 + 2.30174i) q^{61} +(0.988547 + 7.87545i) q^{63} +(-10.3801 + 5.99293i) q^{65} +(4.99726 - 8.65551i) q^{67} +(10.2371 + 6.80644i) q^{69} +11.4186i q^{71} +(-3.04990 + 1.76086i) q^{73} +(11.4425 - 17.2099i) q^{75} +(-4.14384 + 14.8340i) q^{77} +(0.579351 + 1.00346i) q^{79} +(-6.30549 + 6.42190i) q^{81} +(-7.57669 + 13.1232i) q^{83} +(6.50813 + 11.2724i) q^{85} +(-3.42638 + 1.69945i) q^{87} +(4.82266 - 8.35309i) q^{89} +(7.46478 - 1.91558i) q^{91} +(6.57016 - 3.25874i) q^{93} +(2.97292 + 1.71642i) q^{95} +(5.06969 + 2.92699i) q^{97} +(-16.1040 + 6.75696i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{9}+O(q^{10}) \) 48 * q + 2 * q^9	\( 48 q + 2 q^{9} + 8 q^{15} - 10 q^{21} + 48 q^{25} + 18 q^{27} + 18 q^{29} + 18 q^{31} + 12 q^{33} - 4 q^{39} - 6 q^{41} - 6 q^{43} - 18 q^{45} + 18 q^{47} - 12 q^{49} + 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61} - 32 q^{63} - 36 q^{65} - 12 q^{77} + 6 q^{79} + 6 q^{81} - 54 q^{87} - 18 q^{89} + 6 q^{91} + 4 q^{93} - 54 q^{95} - 64 q^{99}+O(q^{100}) \) 48 * q + 2 * q^9 + 8 * q^15 - 10 * q^21 + 48 * q^25 + 18 * q^27 + 18 * q^29 + 18 * q^31 + 12 * q^33 - 4 * q^39 - 6 * q^41 - 6 * q^43 - 18 * q^45 + 18 * q^47 - 12 * q^49 + 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 - 32 * q^63 - 36 * q^65 - 12 * q^77 + 6 * q^79 + 6 * q^81 - 54 * q^87 - 18 * q^89 + 6 * q^91 + 4 * q^93 - 54 * q^95 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more