LMFDB - Embedded newform 1344.2.q.z.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(193,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("1344.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.q (of order $3$, degree $2$, not 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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1156923.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 27x^{2} - 18x + 4 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 27x^2 - 18*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 672)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.2
Root			$0.500000 - 1.51496i$ of defining polynomial
Character	$\chi$	$=$	1344.193
Dual form			1344.2.q.z.961.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(0.227452 + 0.393958i) q^{5} +(2.16908 - 1.51496i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(0.227452 + 0.393958i) q^{5} +(2.16908 - 1.51496i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-2.89653 + 5.01694i) q^{11} +5.88325 q^{13} +0.454904 q^{15} +(-1.45490 + 2.51997i) q^{17} +(2.94163 + 5.09505i) q^{19} +(-0.227452 - 2.63596i) q^{21} +(1.45490 + 2.51997i) q^{23} +(2.39653 - 4.15091i) q^{25} -1.00000 q^{27} -3.54510 q^{29} +(2.16908 - 3.75696i) q^{31} +(2.89653 + 5.01694i) q^{33} +(1.09019 + 0.509947i) q^{35} +(3.85144 + 6.67088i) q^{37} +(2.94163 - 5.09505i) q^{39} +9.58612 q^{41} -10.7931 q^{43} +(0.227452 - 0.393958i) q^{45} +(-2.45490 - 4.25202i) q^{47} +(2.40981 - 6.57212i) q^{49} +(1.45490 + 2.51997i) q^{51} +(6.56561 - 11.3720i) q^{53} -2.63529 q^{55} +5.88325 q^{57} +(-0.896531 + 1.55284i) q^{59} +(2.33816 + 4.04981i) q^{61} +(-2.39653 - 1.12100i) q^{63} +(1.33816 + 2.31776i) q^{65} +(3.94163 - 6.82710i) q^{67} +2.90981 q^{69} -0.909808 q^{71} +(-2.60347 + 4.50934i) q^{73} +(-2.39653 - 4.15091i) q^{75} +(1.31764 + 15.2703i) q^{77} +(1.37602 + 2.38333i) q^{79} +(-0.500000 + 0.866025i) q^{81} -9.97345 q^{83} -1.32368 q^{85} +(-1.77255 + 3.07014i) q^{87} +(2.45490 + 4.25202i) q^{89} +(12.7612 - 8.91288i) q^{91} +(-2.16908 - 3.75696i) q^{93} +(-1.33816 + 2.31776i) q^{95} -5.79306 q^{97} +5.79306 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 3 q^{7} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 3 * q^7 - 3 * q^9	$ 6 q + 3 q^{3} - 3 q^{7} - 3 q^{9} + 6 q^{13} - 6 q^{17} + 3 q^{19} + 6 q^{23} - 3 q^{25} - 6 q^{27} - 24 q^{29} - 3 q^{31} + 12 q^{35} + 3 q^{37} + 3 q^{39} - 12 q^{41} - 30 q^{43} - 12 q^{47} + 9 q^{49} + 6 q^{51} + 6 q^{53} - 24 q^{55} + 6 q^{57} + 12 q^{59} - 18 q^{61} + 3 q^{63} - 24 q^{65} + 9 q^{67} + 12 q^{69} - 33 q^{73} + 3 q^{75} + 12 q^{77} + 27 q^{79} - 3 q^{81} - 36 q^{83} - 72 q^{85} - 12 q^{87} + 12 q^{89} + 51 q^{91} + 3 q^{93} + 24 q^{95}+O(q^{100}) $ 6 * q + 3 * q^3 - 3 * q^7 - 3 * q^9 + 6 * q^13 - 6 * q^17 + 3 * q^19 + 6 * q^23 - 3 * q^25 - 6 * q^27 - 24 * q^29 - 3 * q^31 + 12 * q^35 + 3 * q^37 + 3 * q^39 - 12 * q^41 - 30 * q^43 - 12 * q^47 + 9 * q^49 + 6 * q^51 + 6 * q^53 - 24 * q^55 + 6 * q^57 + 12 * q^59 - 18 * q^61 + 3 * q^63 - 24 * q^65 + 9 * q^67 + 12 * q^69 - 33 * q^73 + 3 * q^75 + 12 * q^77 + 27 * q^79 - 3 * q^81 - 36 * q^83 - 72 * q^85 - 12 * q^87 + 12 * q^89 + 51 * q^91 + 3 * q^93 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	0.227452	+	0.393958i	0.101720	+	0.176184i	0.912393	−	0.409315i	$-0.134232\pi$
$5$	0.227452	+	0.393958i	0.101720	+	0.176184i	−0.810674	+	0.585498i	$0.800899\pi$
$6$		0			0
$7$	2.16908	−	1.51496i	0.819835	−	0.572600i
$7$	2.16908	−	1.51496i	0.819835	−	0.572600i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−2.89653	+	5.01694i	−0.873337	+	1.51266i	−0.0148132	+	0.999890i	$0.504715\pi$
$11$	−2.89653	+	5.01694i	−0.873337	+	1.51266i	−0.858524	+	0.512774i	$0.828618\pi$
$12$		0			0
$13$	5.88325			1.63172			0.815861	−	0.578249i	$-0.196264\pi$
$13$	5.88325			1.63172			0.815861	+	0.578249i	$0.196264\pi$
$14$		0			0
$15$	0.454904			0.117456
$16$		0			0
$17$	−1.45490	+	2.51997i	−0.352866	+	0.611182i	−0.986750	−	0.162246i	$-0.948126\pi$
$17$	−1.45490	+	2.51997i	−0.352866	+	0.611182i	0.633884	+	0.773428i	$0.281460\pi$
$18$		0			0
$19$	2.94163	+	5.09505i	0.674856	+	1.16888i	0.976511	+	0.215467i	$0.0691274\pi$
$19$	2.94163	+	5.09505i	0.674856	+	1.16888i	−0.301656	+	0.953417i	$0.597539\pi$
$20$		0			0
$21$	−0.227452	−	2.63596i	−0.0496341	−	0.575213i
$22$		0			0
$23$	1.45490	+	2.51997i	0.303368	+	0.525450i	0.976897	−	0.213712i	$-0.0685554\pi$
$23$	1.45490	+	2.51997i	0.303368	+	0.525450i	−0.673528	+	0.739161i	$0.735222\pi$
$24$		0			0
$25$	2.39653	−	4.15091i	0.479306	−	0.830183i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−3.54510			−0.658308			−0.329154	−	0.944276i	$-0.606763\pi$
$29$	−3.54510			−0.658308			−0.329154	+	0.944276i	$0.606763\pi$
$30$		0			0
$31$	2.16908	−	3.75696i	0.389578	−	0.674769i	−0.602815	−	0.797881i	$-0.705954\pi$
$31$	2.16908	−	3.75696i	0.389578	−	0.674769i	0.992393	+	0.123112i	$0.0392875\pi$
$32$		0			0
$33$	2.89653	+	5.01694i	0.504221	+	0.873337i
$34$		0			0
$35$	1.09019	+	0.509947i	0.184276	+	0.0861968i
$36$		0			0
$37$	3.85144	+	6.67088i	0.633172	+	1.09669i	0.986899	+	0.161338i	$0.0515808\pi$
$37$	3.85144	+	6.67088i	0.633172	+	1.09669i	−0.353727	+	0.935349i	$0.615086\pi$
$38$		0			0
$39$	2.94163	−	5.09505i	0.471037	−	0.815861i
$40$		0			0
$41$	9.58612			1.49710			0.748551	−	0.663078i	$-0.230750\pi$
$41$	9.58612			1.49710			0.748551	+	0.663078i	$0.230750\pi$
$42$		0			0
$43$	−10.7931			−1.64593			−0.822963	−	0.568095i	$-0.807681\pi$
$43$	−10.7931			−1.64593			−0.822963	+	0.568095i	$0.807681\pi$
$44$		0			0
$45$	0.227452	−	0.393958i	0.0339065	−	0.0587279i
$46$		0			0
$47$	−2.45490	−	4.25202i	−0.358085	−	0.620221i	0.629556	−	0.776955i	$-0.283237\pi$
$47$	−2.45490	−	4.25202i	−0.358085	−	0.620221i	−0.987641	+	0.156734i	$0.949903\pi$
$48$		0			0
$49$	2.40981	−	6.57212i	0.344258	−	0.938875i
$50$		0			0
$51$	1.45490	+	2.51997i	0.203727	+	0.352866i
$52$		0			0
$53$	6.56561	−	11.3720i	0.901856	−	1.56206i	0.0767730	−	0.997049i	$-0.475538\pi$
$53$	6.56561	−	11.3720i	0.901856	−	1.56206i	0.825083	−	0.565012i	$-0.191128\pi$
$54$		0			0
$55$	−2.63529			−0.355342
$56$		0			0
$57$	5.88325			0.779256
$58$		0			0
$59$	−0.896531	+	1.55284i	−0.116718	+	0.202162i	−0.918465	−	0.395501i	$-0.870571\pi$
$59$	−0.896531	+	1.55284i	−0.116718	+	0.202162i	0.801747	+	0.597664i	$0.203904\pi$
$60$		0			0
$61$	2.33816	+	4.04981i	0.299370	+	0.518525i	0.975992	−	0.217806i	$-0.0698900\pi$
$61$	2.33816	+	4.04981i	0.299370	+	0.518525i	−0.676622	+	0.736331i	$0.736557\pi$
$62$		0			0
$63$	−2.39653	−	1.12100i	−0.301935	−	0.141233i
$64$		0			0
$65$	1.33816	+	2.31776i	0.165978	+	0.287482i
$66$		0			0
$67$	3.94163	−	6.82710i	0.481546	−	0.834063i	−0.518229	−	0.855242i	$-0.673409\pi$
$67$	3.94163	−	6.82710i	0.481546	−	0.834063i	0.999776	+	0.0211789i	$0.00674196\pi$
$68$		0			0
$69$	2.90981			0.350300
$70$		0			0
$71$	−0.909808			−0.107974			−0.0539872	−	0.998542i	$-0.517193\pi$
$71$	−0.909808			−0.107974			−0.0539872	+	0.998542i	$0.517193\pi$
$72$		0			0
$73$	−2.60347	+	4.50934i	−0.304713	+	0.527778i	−0.977197	−	0.212333i	$-0.931894\pi$
$73$	−2.60347	+	4.50934i	−0.304713	+	0.527778i	0.672484	+	0.740111i	$0.265227\pi$
$74$		0			0
$75$	−2.39653	−	4.15091i	−0.276728	−	0.479306i
$76$		0			0
$77$	1.31764	+	15.2703i	0.150159	+	1.74021i
$78$		0			0
$79$	1.37602	+	2.38333i	0.154814	+	0.268146i	0.932991	−	0.359899i	$-0.117189\pi$
$79$	1.37602	+	2.38333i	0.154814	+	0.268146i	−0.778177	+	0.628045i	$0.783856\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−9.97345			−1.09473			−0.547364	−	0.836895i	$-0.684369\pi$
$83$	−9.97345			−1.09473			−0.547364	+	0.836895i	$0.684369\pi$
$84$		0			0
$85$	−1.32368			−0.143574
$86$		0			0
$87$	−1.77255	+	3.07014i	−0.190037	+	0.329154i
$88$		0			0
$89$	2.45490	+	4.25202i	0.260219	+	0.450713i	0.966300	−	0.257418i	$-0.0828718\pi$
$89$	2.45490	+	4.25202i	0.260219	+	0.450713i	−0.706081	+	0.708131i	$0.749538\pi$
$90$		0			0
$91$	12.7612	−	8.91288i	1.33774	−	0.934324i
$92$		0			0
$93$	−2.16908	−	3.75696i	−0.224923	−	0.389578i
$94$		0			0
$95$	−1.33816	+	2.31776i	−0.137292	+	0.237797i
$96$		0			0
$97$	−5.79306			−0.588196			−0.294098	−	0.955775i	$-0.595019\pi$
$97$	−5.79306			−0.588196			−0.294098	+	0.955775i	$0.595019\pi$
$98$		0			0
$99$	5.79306			0.582225
$100$		0			0
$101$	8.33816	−	14.4421i	0.829678	−	1.43704i	−0.0686134	−	0.997643i	$-0.521858\pi$
$101$	8.33816	−	14.4421i	0.829678	−	1.43704i	0.898291	−	0.439401i	$-0.144809\pi$
$102$		0			0
$103$	0.396531	+	0.686812i	0.0390714	+	0.0676736i	0.884900	−	0.465781i	$-0.154227\pi$
$103$	0.396531	+	0.686812i	0.0390714	+	0.0676736i	−0.845828	+	0.533455i	$0.820893\pi$
$104$		0			0
$105$	0.986723	−	0.689160i	0.0962943	−	0.0672552i
$106$		0			0
$107$	5.98672	+	10.3693i	0.578758	+	1.00244i	0.995622	+	0.0934699i	$0.0297959\pi$
$107$	5.98672	+	10.3693i	0.578758	+	1.00244i	−0.416864	+	0.908969i	$0.636871\pi$
$108$		0			0
$109$	−2.30634	+	3.99470i	−0.220907	+	0.382623i	−0.955084	−	0.296336i	$-0.904235\pi$
$109$	−2.30634	+	3.99470i	−0.220907	+	0.382623i	0.734176	+	0.678959i	$0.237568\pi$
$110$		0			0
$111$	7.70287			0.731124
$112$		0			0
$113$	8.00000			0.752577			0.376288	−	0.926503i	$-0.377200\pi$
$113$	8.00000			0.752577			0.376288	+	0.926503i	$0.377200\pi$
$114$		0			0
$115$	−0.661842	+	1.14634i	−0.0617171	+	0.106897i
$116$		0			0
$117$	−2.94163	−	5.09505i	−0.271954	−	0.471037i
$118$		0			0
$119$	0.661842	+	7.67013i	0.0606709	+	0.703119i
$120$		0			0
$121$	−11.2798	−	19.5372i	−1.02544	−	1.77611i
$122$		0			0
$123$	4.79306	−	8.30183i	0.432176	−	0.748551i
$124$		0			0
$125$	4.45490			0.398459
$126$		0			0
$127$	−1.24797			−0.110739			−0.0553696	−	0.998466i	$-0.517634\pi$
$127$	−1.24797			−0.110739			−0.0553696	+	0.998466i	$0.517634\pi$
$128$		0			0
$129$	−5.39653	+	9.34707i	−0.475138	+	0.822963i
$130$		0			0
$131$	−2.89653	−	5.01694i	−0.253071	−	0.438332i	0.711299	−	0.702890i	$-0.248107\pi$
$131$	−2.89653	−	5.01694i	−0.253071	−	0.438332i	−0.964370	+	0.264558i	$0.914774\pi$
$132$		0			0
$133$	14.0994	+	6.59512i	1.22257	+	0.571870i
$134$		0			0
$135$	−0.227452	−	0.393958i	−0.0195760	−	0.0339065i
$136$		0			0
$137$	1.54510	−	2.67618i	0.132006	−	0.228642i	−0.792443	−	0.609945i	$-0.791191\pi$
$137$	1.54510	−	2.67618i	0.132006	−	0.228642i	0.924450	+	0.381303i	$0.124525\pi$
$138$		0			0
$139$	5.70287			0.483711			0.241856	−	0.970312i	$-0.422244\pi$
$139$	5.70287			0.483711			0.241856	+	0.970312i	$0.422244\pi$
$140$		0			0
$141$	−4.90981			−0.413480
$142$		0			0
$143$	−17.0410	+	29.5159i	−1.42504	+	2.46825i
$144$		0			0
$145$	−0.806339	−	1.39662i	−0.0669628	−	0.115983i
$146$		0			0
$147$	−4.48672	−	5.37302i	−0.370059	−	0.443159i
$148$		0			0
$149$	1.54510	+	2.67618i	0.126579	+	0.219242i	0.922349	−	0.386357i	$-0.126267\pi$
$149$	1.54510	+	2.67618i	0.126579	+	0.219242i	−0.795770	+	0.605599i	$0.792934\pi$
$150$		0			0
$151$	0.862740	−	1.49431i	0.0702088	−	0.121605i	−0.828784	−	0.559569i	$-0.810967\pi$
$151$	0.862740	−	1.49431i	0.0702088	−	0.121605i	0.898993	+	0.437964i	$0.144300\pi$
$152$		0			0
$153$	2.90981			0.235244
$154$		0			0
$155$	1.97345			0.158511
$156$		0			0
$157$	−2.79306	+	4.83773i	−0.222911	+	0.386093i	−0.955691	−	0.294373i	$-0.904889\pi$
$157$	−2.79306	+	4.83773i	−0.222911	+	0.386093i	0.732780	+	0.680466i	$0.238222\pi$
$158$		0			0
$159$	−6.56561	−	11.3720i	−0.520687	−	0.901856i
$160$		0			0
$161$	6.97345	+	3.26189i	0.549585	+	0.257073i
$162$		0			0
$163$	−4.42835	−	7.67013i	−0.346855	−	0.600771i	0.638834	−	0.769345i	$-0.279417\pi$
$163$	−4.42835	−	7.67013i	−0.346855	−	0.600771i	−0.985689	+	0.168574i	$0.946084\pi$
$164$		0			0
$165$	−1.31764	+	2.28223i	−0.102578	+	0.177671i
$166$		0			0
$167$	−17.4057			−1.34690			−0.673448	−	0.739234i	$-0.735188\pi$
$167$	−17.4057			−1.34690			−0.673448	+	0.739234i	$0.735188\pi$
$168$		0			0
$169$	21.6127			1.66251
$170$		0			0
$171$	2.94163	−	5.09505i	0.224952	−	0.389628i
$172$		0			0
$173$	−8.33816	−	14.4421i	−0.633938	−	1.09801i	−0.986739	−	0.162315i	$-0.948104\pi$
$173$	−8.33816	−	14.4421i	−0.633938	−	1.09801i	0.352801	−	0.935699i	$-0.385229\pi$
$174$		0			0
$175$	−1.09019	−	12.6343i	−0.0824108	−	0.955064i
$176$		0			0
$177$	0.896531	+	1.55284i	0.0673874	+	0.116718i
$178$		0			0
$179$	3.09019	−	5.35237i	0.230972	−	0.400055i	−0.727123	−	0.686508i	$-0.759143\pi$
$179$	3.09019	−	5.35237i	0.230972	−	0.400055i	0.958094	+	0.286453i	$0.0924762\pi$
$180$		0			0
$181$	3.20694			0.238370			0.119185	−	0.992872i	$-0.461972\pi$
$181$	3.20694			0.238370			0.119185	+	0.992872i	$0.461972\pi$
$182$		0			0
$183$	4.67632			0.345683
$184$		0			0
$185$	−1.75203	+	3.03461i	−0.128812	+	0.223109i
$186$		0			0
$187$	−8.42835	−	14.5983i	−0.616342	−	1.06754i
$188$		0			0
$189$	−2.16908	+	1.51496i	−0.157777	+	0.110197i
$190$		0			0
$191$	10.6763	+	18.4919i	0.772511	+	1.33803i	0.936183	+	0.351514i	$0.114333\pi$
$191$	10.6763	+	18.4919i	0.772511	+	1.33803i	−0.163672	+	0.986515i	$0.552334\pi$
$192$		0			0
$193$	−8.20287	+	14.2078i	−0.590456	+	1.02270i	0.403716	+	0.914885i	$0.367719\pi$
$193$	−8.20287	+	14.2078i	−0.590456	+	1.02270i	−0.994171	+	0.107814i	$0.965615\pi$
$194$		0			0
$195$	2.67632			0.191655
$196$		0			0
$197$	−24.6763			−1.75811			−0.879057	−	0.476716i	$-0.841827\pi$
$197$	−24.6763			−1.75811			−0.879057	+	0.476716i	$0.841827\pi$
$198$		0			0
$199$	6.90981	−	11.9681i	0.489823	−	0.848399i	−0.510108	−	0.860110i	$-0.670395\pi$
$199$	6.90981	−	11.9681i	0.489823	−	0.848399i	0.999931	+	0.0117114i	$0.00372795\pi$
$200$		0			0
$201$	−3.94163	−	6.82710i	−0.278021	−	0.481546i
$202$		0			0
$203$	−7.68959	+	5.37067i	−0.539704	+	0.376947i
$204$		0			0
$205$	2.18038	+	3.77654i	0.152285	+	0.263765i
$206$		0			0
$207$	1.45490	−	2.51997i	0.101123	−	0.175150i
$208$		0			0
$209$	−34.0821			−2.35751
$210$		0			0
$211$	11.5861			0.797622			0.398811	−	0.917033i	$-0.369423\pi$
$211$	11.5861			0.797622			0.398811	+	0.917033i	$0.369423\pi$
$212$		0			0
$213$	−0.454904	+	0.787917i	−0.0311695	+	0.0539872i
$214$		0			0
$215$	−2.45490	−	4.25202i	−0.167423	−	0.289985i
$216$		0			0
$217$	−0.986723	−	11.4352i	−0.0669831	−	0.776272i
$218$		0			0
$219$	2.60347	+	4.50934i	0.175926	+	0.304713i
$220$		0			0
$221$	−8.55957	+	14.8256i	−0.575779	+	0.997279i
$222$		0			0
$223$	−20.4549			−1.36976			−0.684881	−	0.728655i	$-0.740146\pi$
$223$	−20.4549			−1.36976			−0.684881	+	0.728655i	$0.740146\pi$
$224$		0			0
$225$	−4.79306			−0.319537
$226$		0			0
$227$	−8.86998	+	15.3633i	−0.588721	+	1.01969i	0.405679	+	0.914016i	$0.367035\pi$
$227$	−8.86998	+	15.3633i	−0.588721	+	1.01969i	−0.994400	+	0.105679i	$0.966298\pi$
$228$		0			0
$229$	−12.0994	−	20.9568i	−0.799551	−	1.38486i	−0.919909	−	0.392132i	$-0.871738\pi$
$229$	−12.0994	−	20.9568i	−0.799551	−	1.38486i	0.120358	−	0.992731i	$-0.461596\pi$
$230$		0			0
$231$	13.8833	+	6.49402i	0.913451	+	0.427275i
$232$		0			0
$233$	−11.3382	−	19.6383i	−0.742787	−	1.28655i	−0.951221	−	0.308509i	$-0.900170\pi$
$233$	−11.3382	−	19.6383i	−0.742787	−	1.28655i	0.208434	−	0.978036i	$-0.433163\pi$
$234$		0			0
$235$	1.11675	−	1.93426i	0.0728485	−	0.126177i
$236$		0			0
$237$	2.75203			0.178764
$238$		0			0
$239$	−2.90981			−0.188220			−0.0941099	−	0.995562i	$-0.530001\pi$
$239$	−2.90981			−0.188220			−0.0941099	+	0.995562i	$0.530001\pi$
$240$		0			0
$241$	−10.8700	+	18.8274i	−0.700197	+	1.21278i	0.268200	+	0.963363i	$0.413571\pi$
$241$	−10.8700	+	18.8274i	−0.700197	+	1.21278i	−0.968397	+	0.249413i	$0.919762\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	3.13726	−	0.545479i	0.200432	−	0.0348494i
$246$		0			0
$247$	17.3063	+	29.9755i	1.10118	+	1.90729i
$248$		0			0
$249$	−4.98672	+	8.63726i	−0.316021	+	0.547364i
$250$		0			0
$251$	−8.02655			−0.506632			−0.253316	−	0.967384i	$-0.581521\pi$
$251$	−8.02655			−0.506632			−0.253316	+	0.967384i	$0.581521\pi$
$252$		0			0
$253$	−16.8567			−1.05977
$254$		0			0
$255$	−0.661842	+	1.14634i	−0.0414461	+	0.0717868i
$256$		0			0
$257$	6.45490	+	11.1802i	0.402646	+	0.697403i	0.994044	−	0.108976i	$-0.0347573\pi$
$257$	6.45490	+	11.1802i	0.402646	+	0.697403i	−0.591398	+	0.806379i	$0.701424\pi$
$258$		0			0
$259$	18.4602	+	8.63491i	1.14706	+	0.536547i
$260$		0			0
$261$	1.77255	+	3.07014i	0.109718	+	0.190037i
$262$		0			0
$263$	4.45490	−	7.71612i	0.274701	−	0.475796i	−0.695359	−	0.718663i	$-0.744754\pi$
$263$	4.45490	−	7.71612i	0.274701	−	0.475796i	0.970060	+	0.242867i	$0.0780877\pi$
$264$		0			0
$265$	5.97345			0.366946
$266$		0			0
$267$	4.90981			0.300475
$268$		0			0
$269$	−3.02051	+	5.23168i	−0.184164	+	0.318981i	−0.943295	−	0.331957i	$-0.892291\pi$
$269$	−3.02051	+	5.23168i	−0.184164	+	0.318981i	0.759130	+	0.650938i	$0.225624\pi$
$270$		0			0
$271$	6.68236	+	11.5742i	0.405924	+	0.703081i	0.994429	−	0.105413i	$-0.0336164\pi$
$271$	6.68236	+	11.5742i	0.405924	+	0.703081i	−0.588504	+	0.808494i	$0.700283\pi$
$272$		0			0
$273$	−1.33816	−	15.5080i	−0.0809890	−	0.938587i
$274$		0			0
$275$	13.8833	+	24.0465i	0.837192	+	1.45006i
$276$		0			0
$277$	2.39653	−	4.15091i	0.143994	−	0.249404i	−0.785003	−	0.619491i	$-0.787339\pi$
$277$	2.39653	−	4.15091i	0.143994	−	0.249404i	0.928997	+	0.370087i	$0.120672\pi$
$278$		0			0
$279$	−4.33816			−0.259719
$280$		0			0
$281$	7.32368			0.436894			0.218447	−	0.975849i	$-0.429901\pi$
$281$	7.32368			0.436894			0.218447	+	0.975849i	$0.429901\pi$
$282$		0			0
$283$	−6.60347	+	11.4375i	−0.392535	+	0.679891i	−0.992783	−	0.119923i	$-0.961735\pi$
$283$	−6.60347	+	11.4375i	−0.392535	+	0.679891i	0.600248	+	0.799814i	$0.295069\pi$
$284$		0			0
$285$	1.33816	+	2.31776i	0.0792656	+	0.137292i
$286$		0			0
$287$	20.7931	−	14.5226i	1.22738	−	0.857240i
$288$		0			0
$289$	4.26651	+	7.38981i	0.250971	+	0.434695i
$290$		0			0
$291$	−2.89653	+	5.01694i	−0.169798	+	0.294098i
$292$		0			0
$293$	−7.54510			−0.440789			−0.220395	−	0.975411i	$-0.570735\pi$
$293$	−7.54510			−0.440789			−0.220395	+	0.975411i	$0.570735\pi$
$294$		0			0
$295$	−0.815671			−0.0474902
$296$		0			0
$297$	2.89653	−	5.01694i	0.168074	−	0.291112i
$298$		0			0
$299$	8.55957	+	14.8256i	0.495013	+	0.857387i
$300$		0			0
$301$	−23.4110	+	16.3510i	−1.34939	+	0.942458i
$302$		0			0
$303$	−8.33816	−	14.4421i	−0.479015	−	0.829678i
$304$		0			0
$305$	−1.06364	+	1.84227i	−0.0609037	+	0.105488i
$306$		0			0
$307$	−23.1086			−1.31888			−0.659439	−	0.751758i	$-0.729206\pi$
$307$	−23.1086			−1.31888			−0.659439	+	0.751758i	$0.729206\pi$
$308$		0			0
$309$	0.793062			0.0451157
$310$		0			0
$311$	3.70287	−	6.41356i	0.209971	−	0.363680i	−0.741734	−	0.670694i	$-0.765997\pi$
$311$	3.70287	−	6.41356i	0.209971	−	0.363680i	0.951705	+	0.307014i	$0.0993299\pi$
$312$		0			0
$313$	−7.29306	−	12.6320i	−0.412228	−	0.714000i	0.582905	−	0.812540i	$-0.301916\pi$
$313$	−7.29306	−	12.6320i	−0.412228	−	0.714000i	−0.995133	+	0.0985402i	$0.968583\pi$
$314$		0			0
$315$	−0.103469	−	1.19911i	−0.00582981	−	0.0675620i
$316$		0			0
$317$	0.682356	+	1.18188i	0.0383249	+	0.0663807i	0.884552	−	0.466442i	$-0.154464\pi$
$317$	0.682356	+	1.18188i	0.0383249	+	0.0663807i	−0.846227	+	0.532823i	$0.821131\pi$
$318$		0			0
$319$	10.2685	−	17.7855i	0.574925	−	0.995799i
$320$		0			0
$321$	11.9734			0.668293
$322$		0			0
$323$	−17.1191			−0.952534
$324$		0			0
$325$	14.0994	−	24.4209i	0.782094	−	1.35463i
$326$		0			0
$327$	2.30634	+	3.99470i	0.127541	+	0.220907i
$328$		0			0
$329$	−11.7665	−	5.50389i	−0.648709	−	0.303439i
$330$		0			0
$331$	5.48672	+	9.50328i	0.301578	+	0.522348i	0.976493	−	0.215547i	$-0.0691534\pi$
$331$	5.48672	+	9.50328i	0.301578	+	0.522348i	−0.674916	+	0.737895i	$0.735820\pi$
$332$		0			0
$333$	3.85144	−	6.67088i	0.211057	−	0.365562i
$334$		0			0
$335$	3.58612			0.195931
$336$		0			0
$337$	−22.1722			−1.20780			−0.603900	−	0.797060i	$-0.706387\pi$
$337$	−22.1722			−1.20780			−0.603900	+	0.797060i	$0.706387\pi$
$338$		0			0
$339$	4.00000	−	6.92820i	0.217250	−	0.376288i
$340$		0			0
$341$	12.5656	+	21.7643i	0.680466	+	1.17860i
$342$		0			0
$343$	−4.72942	−	17.9062i	−0.255365	−	0.966845i
$344$		0			0
$345$	0.661842	+	1.14634i	0.0356324	+	0.0617171i
$346$		0			0
$347$	0.116746	−	0.202210i	0.00626725	−	0.0108552i	−0.862875	−	0.505418i	$-0.831338\pi$
$347$	0.116746	−	0.202210i	0.00626725	−	0.0108552i	0.869142	+	0.494563i	$0.164672\pi$
$348$		0			0
$349$	−7.35263			−0.393577			−0.196789	−	0.980446i	$-0.563051\pi$
$349$	−7.35263			−0.393577			−0.196789	+	0.980446i	$0.563051\pi$
$350$		0			0
$351$	−5.88325			−0.314025
$352$		0			0
$353$	−9.58612	+	16.6037i	−0.510218	+	0.883723i	0.489712	+	0.871884i	$0.337102\pi$
$353$	−9.58612	+	16.6037i	−0.510218	+	0.883723i	−0.999930	+	0.0118391i	$0.996231\pi$
$354$		0			0
$355$	−0.206938	−	0.358427i	−0.0109831	−	0.0190233i
$356$		0			0
$357$	6.97345	+	3.26189i	0.369074	+	0.172638i
$358$		0			0
$359$	−10.4694	−	18.1335i	−0.552553	−	0.957049i	−0.998089	−	0.0617857i	$-0.980320\pi$
$359$	−10.4694	−	18.1335i	−0.552553	−	0.957049i	0.445537	−	0.895264i	$-0.353013\pi$
$360$		0			0
$361$	−7.80634	+	13.5210i	−0.410860	+	0.711630i
$362$		0			0
$363$	−22.5596			−1.18407
$364$		0			0
$365$	−2.36866			−0.123981
$366$		0			0
$367$	12.5072	−	21.6632i	0.652872	−	1.13081i	−0.329550	−	0.944138i	$-0.606897\pi$
$367$	12.5072	−	21.6632i	0.652872	−	1.13081i	0.982423	−	0.186670i	$-0.0597696\pi$
$368$		0			0
$369$	−4.79306	−	8.30183i	−0.249517	−	0.432176i
$370$		0			0
$371$	−2.98672	−	34.6133i	−0.155063	−	1.79703i
$372$		0			0
$373$	−10.1630	−	17.6029i	−0.526222	−	0.911444i	−0.999533	−	0.0305483i	$-0.990275\pi$
$373$	−10.1630	−	17.6029i	−0.526222	−	0.911444i	0.473311	−	0.880895i	$-0.343059\pi$
$374$		0			0
$375$	2.22745	−	3.85806i	0.115025	−	0.199229i
$376$		0			0
$377$	−20.8567			−1.07417
$378$		0			0
$379$	−20.7931			−1.06807			−0.534034	−	0.845463i	$-0.679325\pi$
$379$	−20.7931			−1.06807			−0.534034	+	0.845463i	$0.679325\pi$
$380$		0			0
$381$	−0.623983	+	1.08077i	−0.0319676	+	0.0553696i
$382$		0			0
$383$	12.5861	+	21.7998i	0.643121	+	1.11392i	0.984732	+	0.174077i	$0.0556941\pi$
$383$	12.5861	+	21.7998i	0.643121	+	1.11392i	−0.341611	+	0.939841i	$0.610973\pi$
$384$		0			0
$385$	−5.71615	+	3.99235i	−0.291322	+	0.203469i
$386$		0			0
$387$	5.39653	+	9.34707i	0.274321	+	0.475138i
$388$		0			0
$389$	12.2214	−	21.1681i	0.619650	−	1.07327i	−0.369899	−	0.929072i	$-0.620608\pi$
$389$	12.2214	−	21.1681i	0.619650	−	1.07327i	0.989549	−	0.144194i	$-0.0460589\pi$
$390$		0			0
$391$	−8.46698			−0.428194
$392$		0			0
$393$	−5.79306			−0.292221
$394$		0			0
$395$	−0.625956	+	1.08419i	−0.0314952	+	0.0545514i
$396$		0			0
$397$	−4.39653	−	7.61502i	−0.220656	−	0.382187i	0.734352	−	0.678769i	$-0.237486\pi$
$397$	−4.39653	−	7.61502i	−0.220656	−	0.382187i	−0.955007	+	0.296583i	$0.904153\pi$
$398$		0			0
$399$	12.7612	−	8.91288i	0.638861	−	0.446202i
$400$		0			0
$401$	−16.5596	−	28.6820i	−0.826945	−	1.43231i	−0.900423	−	0.435015i	$-0.856743\pi$
$401$	−16.5596	−	28.6820i	−0.826945	−	1.43231i	0.0734778	−	0.997297i	$-0.476590\pi$
$402$		0			0
$403$	12.7612	−	22.1031i	0.635683	−	1.10103i
$404$		0			0
$405$	−0.454904			−0.0226044
$406$		0			0
$407$	−44.6232			−2.21189
$408$		0			0
$409$	3.47345	−	6.01618i	0.171751	−	0.297481i	−0.767281	−	0.641311i	$-0.778391\pi$
$409$	3.47345	−	6.01618i	0.171751	−	0.297481i	0.939032	+	0.343830i	$0.111724\pi$
$410$		0			0
$411$	−1.54510	−	2.67618i	−0.0762140	−	0.132006i
$412$		0			0
$413$	0.407836	+	4.72643i	0.0200683	+	0.232573i
$414$		0			0
$415$	−2.26848	−	3.92912i	−0.111355	−	0.192873i
$416$		0			0
$417$	2.85144	−	4.93883i	0.139635	−	0.241856i
$418$		0			0
$419$	−29.2254			−1.42775			−0.713876	−	0.700272i	$-0.753062\pi$
$419$	−29.2254			−1.42775			−0.713876	+	0.700272i	$0.753062\pi$
$420$		0			0
$421$	−33.2359			−1.61982			−0.809909	−	0.586556i	$-0.800484\pi$
$421$	−33.2359			−1.61982			−0.809909	+	0.586556i	$0.800484\pi$
$422$		0			0
$423$	−2.45490	+	4.25202i	−0.119362	+	0.206740i
$424$		0			0
$425$	6.97345	+	12.0784i	0.338262	+	0.585887i
$426$		0			0
$427$	11.2069	+	5.24215i	0.542342	+	0.253685i
$428$		0			0
$429$	17.0410	+	29.5159i	0.822749	+	1.42504i
$430$		0			0
$431$	3.09019	−	5.35237i	0.148849	−	0.257815i	−0.781953	−	0.623337i	$-0.785776\pi$
$431$	3.09019	−	5.35237i	0.148849	−	0.257815i	0.930802	+	0.365523i	$0.119110\pi$
$432$		0			0
$433$	16.6127			0.798354			0.399177	−	0.916874i	$-0.369296\pi$
$433$	16.6127			0.798354			0.399177	+	0.916874i	$0.369296\pi$
$434$		0			0
$435$	−1.61268			−0.0773220
$436$		0			0
$437$	−8.55957	+	14.8256i	−0.409460	+	0.709205i
$438$		0			0
$439$	−13.8136	−	23.9258i	−0.659286	−	1.14192i	−0.980801	−	0.195012i	$-0.937525\pi$
$439$	−13.8136	−	23.9258i	−0.659286	−	1.14192i	0.321515	−	0.946905i	$-0.395808\pi$
$440$		0			0
$441$	−6.89653	+	1.19911i	−0.328406	+	0.0571003i
$442$		0			0
$443$	10.0133	+	17.3435i	0.475745	+	0.824015i	0.999614	−	0.0277842i	$-0.00884512\pi$
$443$	10.0133	+	17.3435i	0.475745	+	0.824015i	−0.523869	+	0.851799i	$0.675512\pi$
$444$		0			0
$445$	−1.11675	+	1.93426i	−0.0529388	+	0.0916927i
$446$		0			0
$447$	3.09019			0.146161
$448$		0			0
$449$	15.0371			0.709644			0.354822	−	0.934934i	$-0.384541\pi$
$449$	15.0371			0.709644			0.354822	+	0.934934i	$0.384541\pi$
$450$		0			0
$451$	−27.7665	+	48.0930i	−1.30747	+	2.26461i
$452$		0			0
$453$	−0.862740	−	1.49431i	−0.0405351	−	0.0702088i
$454$		0			0
$455$	6.41388	+	3.00015i	0.300687	+	0.140649i
$456$		0			0
$457$	21.0596	+	36.4762i	0.985125	+	1.70629i	0.641379	+	0.767224i	$0.278363\pi$
$457$	21.0596	+	36.4762i	0.985125	+	1.70629i	0.343746	+	0.939063i	$0.388304\pi$
$458$		0			0
$459$	1.45490	−	2.51997i	0.0679091	−	0.117622i
$460$		0			0
$461$	−20.9098			−0.973867			−0.486933	−	0.873439i	$-0.661885\pi$
$461$	−20.9098			−0.973867			−0.486933	+	0.873439i	$0.661885\pi$
$462$		0			0
$463$	38.1457			1.77278			0.886390	−	0.462939i	$-0.153205\pi$
$463$	38.1457			1.77278			0.886390	+	0.462939i	$0.153205\pi$
$464$		0			0
$465$	0.986723	−	1.70905i	0.0457582	−	0.0792555i
$466$		0			0
$467$	−5.76651	−	9.98789i	−0.266842	−	0.462184i	0.701202	−	0.712962i	$-0.252647\pi$
$467$	−5.76651	−	9.98789i	−0.266842	−	0.462184i	−0.968045	+	0.250778i	$0.919314\pi$
$468$		0			0
$469$	−1.79306	−	20.7799i	−0.0827959	−	0.959527i
$470$		0			0
$471$	2.79306	+	4.83773i	0.128698	+	0.222911i
$472$		0			0
$473$	31.2624	−	54.1481i	1.43745	−	2.48973i
$474$		0			0
$475$	28.1988			1.29385
$476$		0			0
$477$	−13.1312			−0.601237
$478$		0			0
$479$	−3.66184	+	6.34250i	−0.167314	+	0.289796i	−0.937475	−	0.348054i	$-0.886843\pi$
$479$	−3.66184	+	6.34250i	−0.167314	+	0.289796i	0.770161	+	0.637850i	$0.220176\pi$
$480$		0			0
$481$	22.6590	+	39.2465i	1.03316	+	1.78949i
$482$		0			0
$483$	6.31160	−	4.40824i	0.287188	−	0.200582i
$484$		0			0
$485$	−1.31764	−	2.28223i	−0.0598311	−	0.103631i
$486$		0			0
$487$	−13.0258	+	22.5613i	−0.590254	+	1.02235i	0.403943	+	0.914784i	$0.367639\pi$
$487$	−13.0258	+	22.5613i	−0.590254	+	1.02235i	−0.994198	+	0.107567i	$0.965694\pi$
$488$		0			0
$489$	−8.85670			−0.400514
$490$		0			0
$491$	7.37919			0.333018			0.166509	−	0.986040i	$-0.446751\pi$
$491$	7.37919			0.333018			0.166509	+	0.986040i	$0.446751\pi$
$492$		0			0
$493$	5.15777	−	8.93353i	0.232294	−	0.402346i
$494$		0			0
$495$	1.31764	+	2.28223i	0.0592237	+	0.102578i
$496$		0			0
$497$	−1.97345	+	1.37832i	−0.0885211	+	0.0618261i
$498$		0			0
$499$	−0.175119	−	0.303315i	−0.00783940	−	0.0135782i	0.862079	−	0.506774i	$-0.169162\pi$
$499$	−0.175119	−	0.303315i	−0.00783940	−	0.0135782i	−0.869918	+	0.493196i	$0.835829\pi$
$500$		0			0
$501$	−8.70287	+	15.0738i	−0.388816	+	0.673448i
$502$		0			0
$503$	14.9098			0.664795			0.332398	−	0.943139i	$-0.392142\pi$
$503$	14.9098			0.664795			0.332398	+	0.943139i	$0.392142\pi$
$504$		0			0
$505$	7.58612			0.337578
$506$		0			0
$507$	10.8063	−	18.7171i	0.479926	−	0.831257i
$508$		0			0
$509$	8.44886	+	14.6339i	0.374489	+	0.648635i	0.990250	−	0.139298i	$-0.0444847\pi$
$509$	8.44886	+	14.6339i	0.374489	+	0.648635i	−0.615761	+	0.787933i	$0.711151\pi$
$510$		0			0
$511$	1.18433	+	13.7253i	0.0523916	+	0.607170i
$512$		0			0
$513$	−2.94163	−	5.09505i	−0.129876	−	0.224952i
$514$		0			0
$515$	−0.180384	+	0.312434i	−0.00794865	+	0.0137675i
$516$		0			0
$517$	28.4428			1.25091
$518$		0			0
$519$	−16.6763			−0.732009
$520$		0			0
$521$	−3.79306	+	6.56978i	−0.166177	+	0.287827i	−0.937073	−	0.349134i	$-0.886476\pi$
$521$	−3.79306	+	6.56978i	−0.166177	+	0.287827i	0.770896	+	0.636962i	$0.219809\pi$
$522$		0			0
$523$	−21.2572	−	36.8185i	−0.929511	−	1.60996i	−0.784140	−	0.620584i	$-0.786896\pi$
$523$	−21.2572	−	36.8185i	−0.929511	−	1.60996i	−0.145371	−	0.989377i	$-0.546438\pi$
$524$		0			0
$525$	−11.4867	−	5.37302i	−0.501322	−	0.234498i
$526$		0			0
$527$	6.31160	+	10.9320i	0.274938	+	0.476206i
$528$		0			0
$529$	7.26651	−	12.5860i	0.315935	−	0.547216i
$530$		0			0
$531$	1.79306			0.0778123
$532$		0			0
$533$	56.3976			2.44285
$534$		0			0
$535$	−2.72338	+	4.71704i	−0.117742	+	0.203935i
$536$		0			0
$537$	−3.09019	−	5.35237i	−0.133352	−	0.230972i
$538$		0			0
$539$	25.9919	+	31.1262i	1.11955	+	1.34070i
$540$		0			0
$541$	7.03182	+	12.1795i	0.302322	+	0.523636i	0.976661	−	0.214785i	$-0.0689050\pi$
$541$	7.03182	+	12.1795i	0.302322	+	0.523636i	−0.674340	+	0.738421i	$0.735572\pi$
$542$		0			0
$543$	1.60347	−	2.77729i	0.0688114	−	0.119185i
$544$		0			0
$545$	−2.09833			−0.0898824
$546$		0			0
$547$	4.49593			0.192232			0.0961161	−	0.995370i	$-0.469358\pi$
$547$	4.49593			0.192232			0.0961161	+	0.995370i	$0.469358\pi$
$548$		0			0
$549$	2.33816	−	4.04981i	0.0997902	−	0.172842i
$550$		0			0
$551$	−10.4283	−	18.0624i	−0.444263	−	0.769485i
$552$		0			0
$553$	6.59533	+	3.08503i	0.280462	+	0.131189i
$554$		0			0
$555$	1.75203	+	3.03461i	0.0743697	+	0.128812i
$556$		0			0
$557$	15.9303	−	27.5921i	0.674989	−	1.16912i	−0.301483	−	0.953472i	$-0.597482\pi$
$557$	15.9303	−	27.5921i	0.674989	−	1.16912i	0.976472	−	0.215644i	$-0.0691852\pi$
$558$		0			0
$559$	−63.4983			−2.68569
$560$		0			0
$561$	−16.8567			−0.711690
$562$		0			0
$563$	23.0688	−	39.9563i	0.972233	−	1.68396i	0.283454	−	0.958986i	$-0.408520\pi$
$563$	23.0688	−	39.9563i	0.972233	−	1.68396i	0.688779	−	0.724972i	$-0.258147\pi$
$564$		0			0
$565$	1.81962	+	3.15167i	0.0765518	+	0.132592i
$566$		0			0
$567$	0.227452	+	2.63596i	0.00955209	+	0.110700i
$568$		0			0
$569$	8.31160	+	14.3961i	0.348441	+	0.603517i	0.985973	−	0.166907i	$-0.0533780\pi$
$569$	8.31160	+	14.3961i	0.348441	+	0.603517i	−0.637532	+	0.770424i	$0.720045\pi$
$570$		0			0
$571$	18.2532	−	31.6155i	0.763874	−	1.32307i	−0.176966	−	0.984217i	$-0.556628\pi$
$571$	18.2532	−	31.6155i	0.763874	−	1.32307i	0.940840	−	0.338852i	$-0.110038\pi$
$572$		0			0
$573$	21.3526			0.892019
$574$		0			0
$575$	13.9469			0.581626
$576$		0			0
$577$	7.59019	−	13.1466i	0.315984	−	0.547300i	−0.663662	−	0.748032i	$-0.730999\pi$
$577$	7.59019	−	13.1466i	0.315984	−	0.547300i	0.979646	+	0.200732i	$0.0643321\pi$
$578$		0			0
$579$	8.20287	+	14.2078i	0.340900	+	0.590456i
$580$		0			0
$581$	−21.6332	+	15.1093i	−0.897496	+	0.626841i
$582$		0			0
$583$	38.0350	+	65.8785i	1.57525	+	2.72841i
$584$		0			0
$585$	1.33816	−	2.31776i	0.0553260	−	0.0958275i
$586$		0			0
$587$	−8.20694			−0.338737			−0.169368	−	0.985553i	$-0.554173\pi$
$587$	−8.20694			−0.338737			−0.169368	+	0.985553i	$0.554173\pi$
$588$		0			0
$589$	25.5225			1.05164
$590$		0			0
$591$	−12.3382	+	21.3703i	−0.507524	+	0.879057i
$592$		0			0
$593$	2.77859	+	4.81266i	0.114103	+	0.197632i	0.917421	−	0.397918i	$-0.130267\pi$
$593$	2.77859	+	4.81266i	0.114103	+	0.197632i	−0.803318	+	0.595550i	$0.796934\pi$
$594$		0			0
$595$	−2.87117	+	2.00532i	−0.117707	+	0.0822103i
$596$		0			0
$597$	−6.90981	−	11.9681i	−0.282800	−	0.489823i
$598$		0			0
$599$	17.7931	−	30.8185i	0.727005	−	1.25921i	−0.231139	−	0.972921i	$-0.574245\pi$
$599$	17.7931	−	30.8185i	0.727005	−	1.25921i	0.958143	−	0.286288i	$-0.0924216\pi$
$600$		0			0
$601$	1.18038			0.0481489			0.0240744	−	0.999710i	$-0.492336\pi$
$601$	1.18038			0.0481489			0.0240744	+	0.999710i	$0.492336\pi$
$602$		0			0
$603$	−7.88325			−0.321031
$604$		0			0
$605$	5.13122	−	8.88753i	0.208614	−	0.361330i
$606$		0			0
$607$	−6.16908	−	10.6852i	−0.250395	−	0.433697i	0.713239	−	0.700920i	$-0.247227\pi$
$607$	−6.16908	−	10.6852i	−0.250395	−	0.433697i	−0.963635	+	0.267223i	$0.913894\pi$
$608$		0			0
$609$	0.806339	+	9.34472i	0.0326745	+	0.378667i
$610$		0			0
$611$	−14.4428	−	25.0157i	−0.584294	−	1.01203i
$612$		0			0
$613$	−10.5451	+	18.2646i	−0.425912	+	0.737702i	−0.996505	−	0.0835312i	$-0.973380\pi$
$613$	−10.5451	+	18.2646i	−0.425912	+	0.737702i	0.570593	+	0.821233i	$0.306713\pi$
$614$		0			0
$615$	4.36077			0.175843
$616$		0			0
$617$	15.3526			0.618074			0.309037	−	0.951050i	$-0.399993\pi$
$617$	15.3526			0.618074			0.309037	+	0.951050i	$0.399993\pi$
$618$		0			0
$619$	−9.21615	+	15.9628i	−0.370428	+	0.641601i	−0.989631	−	0.143630i	$-0.954122\pi$
$619$	−9.21615	+	15.9628i	−0.370428	+	0.641601i	0.619203	+	0.785231i	$0.287456\pi$
$620$		0			0
$621$	−1.45490	−	2.51997i	−0.0583833	−	0.101123i
$622$		0			0
$623$	11.7665	+	5.50389i	0.471415	+	0.220509i
$624$		0			0
$625$	−10.9694	−	18.9995i	−0.438775	−	0.759981i
$626$		0			0
$627$	−17.0410	+	29.5159i	−0.680553	+	1.17875i
$628$		0			0
$629$	−22.4139			−0.893700
$630$		0			0
$631$	−5.91375			−0.235423			−0.117711	−	0.993048i	$-0.537556\pi$
$631$	−5.91375			−0.235423			−0.117711	+	0.993048i	$0.537556\pi$
$632$		0			0
$633$	5.79306	−	10.0339i	0.230254	−	0.398811i
$634$		0			0
$635$	−0.283853	−	0.491647i	−0.0112643	−	0.0195104i
$636$		0			0
$637$	14.1775	−	38.6655i	0.561734	−	1.53198i
$638$		0			0
$639$	0.454904	+	0.787917i	0.0179957	+	0.0311695i
$640$		0			0
$641$	−23.0821	+	39.9793i	−0.911686	+	1.57909i	−0.100005	+	0.994987i	$0.531886\pi$
$641$	−23.0821	+	39.9793i	−0.911686	+	1.57909i	−0.811681	+	0.584100i	$0.801447\pi$
$642$		0			0
$643$	31.0555			1.22471			0.612355	−	0.790583i	$-0.290222\pi$
$643$	31.0555			1.22471			0.612355	+	0.790583i	$0.290222\pi$
$644$		0			0
$645$	−4.90981			−0.193324
$646$		0			0
$647$	−8.51854	+	14.7545i	−0.334898	+	0.580061i	−0.983465	−	0.181097i	$-0.942035\pi$
$647$	−8.51854	+	14.7545i	−0.334898	+	0.580061i	0.648567	+	0.761158i	$0.275369\pi$
$648$		0			0
$649$	−5.19366	−	8.99568i	−0.203869	−	0.353111i
$650$		0			0
$651$	−10.3965	−	4.86307i	−0.407472	−	0.190599i
$652$		0			0
$653$	−4.06968	−	7.04889i	−0.159259	−	0.275844i	0.775343	−	0.631541i	$-0.217577\pi$
$653$	−4.06968	−	7.04889i	−0.159259	−	0.275844i	−0.934602	+	0.355696i	$0.884244\pi$
$654$		0			0
$655$	1.31764	−	2.28223i	0.0514846	−	0.0891740i
$656$		0			0
$657$	5.20694			0.203142
$658$		0			0
$659$	41.1191			1.60177			0.800887	−	0.598815i	$-0.204362\pi$
$659$	41.1191			1.60177			0.800887	+	0.598815i	$0.204362\pi$
$660$		0			0
$661$	−6.67105	+	11.5546i	−0.259474	+	0.449422i	−0.966101	−	0.258164i	$-0.916882\pi$
$661$	−6.67105	+	11.5546i	−0.259474	+	0.449422i	0.706627	+	0.707586i	$0.250216\pi$
$662$		0			0
$663$	8.55957	+	14.8256i	0.332426	+	0.575779i
$664$		0			0
$665$	0.608734	+	7.05465i	0.0236057	+	0.273568i
$666$		0			0
$667$	−5.15777	−	8.93353i	−0.199710	−	0.345908i
$668$		0			0
$669$	−10.2275	+	17.7145i	−0.395416	+	0.684881i
$670$		0			0
$671$	−27.0902			−1.04581
$672$		0			0
$673$	9.75837			0.376158			0.188079	−	0.982154i	$-0.439774\pi$
$673$	9.75837			0.376158			0.188079	+	0.982154i	$0.439774\pi$
$674$		0			0
$675$	−2.39653	+	4.15091i	−0.0922425	+	0.159769i
$676$		0			0
$677$	16.2275	+	28.1068i	0.623672	+	1.08023i	0.988796	+	0.149272i	$0.0476931\pi$
$677$	16.2275	+	28.1068i	0.623672	+	1.08023i	−0.365124	+	0.930959i	$0.618974\pi$
$678$		0			0
$679$	−12.5656	+	8.77624i	−0.482224	+	0.336801i
$680$		0			0
$681$	8.86998	+	15.3633i	0.339898	+	0.588721i
$682$		0			0
$683$	18.4827	−	32.0129i	0.707219	−	1.22494i	−0.258666	−	0.965967i	$-0.583283\pi$
$683$	18.4827	−	32.0129i	0.707219	−	1.22494i	0.965885	−	0.258973i	$-0.0833839\pi$
$684$		0			0
$685$	1.40574			0.0537106
$686$		0			0
$687$	−24.1988			−0.923242
$688$		0			0
$689$	38.6272	−	66.9042i	1.47158	−	2.54885i
$690$		0			0
$691$	7.12596	+	12.3425i	0.271084	+	0.469531i	0.969140	−	0.246512i	$-0.0792845\pi$
$691$	7.12596	+	12.3425i	0.271084	+	0.469531i	−0.698056	+	0.716044i	$0.745951\pi$
$692$		0			0
$693$	12.5656	−	8.77624i	0.477328	−	0.333382i
$694$		0			0
$695$	1.29713	+	2.24669i	0.0492029	+	0.0852220i
$696$		0			0
$697$	−13.9469	+	24.1567i	−0.528276	+	0.915001i
$698$		0			0
$699$	−22.6763			−0.857697
$700$		0			0
$701$	51.3937			1.94111			0.970556	−	0.240876i	$-0.0774347\pi$
$701$	51.3937			1.94111			0.970556	+	0.240876i	$0.0774347\pi$
$702$		0			0
$703$	−22.6590	+	39.2465i	−0.854599	+	1.48021i
$704$		0			0
$705$	−1.11675	−	1.93426i	−0.0420591	−	0.0728485i
$706$		0			0
$707$	−3.79306	−	43.9580i	−0.142653	−	1.65321i
$708$		0			0
$709$	12.5861	+	21.7998i	0.472682	+	0.818709i	0.999511	−	0.0312621i	$-0.00995266\pi$
$709$	12.5861	+	21.7998i	0.472682	+	0.818709i	−0.526829	+	0.849971i	$0.676619\pi$
$710$		0			0
$711$	1.37602	−	2.38333i	0.0516047	−	0.0893819i
$712$		0			0
$713$	12.6232			0.472743
$714$		0			0
$715$	−15.5041			−0.579819
$716$		0			0
$717$	−1.45490	+	2.51997i	−0.0543344	+	0.0941099i
$718$		0			0
$719$	−4.09019	−	7.08442i	−0.152538	−	0.264204i	0.779622	−	0.626251i	$-0.215411\pi$
$719$	−4.09019	−	7.08442i	−0.152538	−	0.264204i	−0.932160	+	0.362047i	$0.882078\pi$
$720$		0			0
$721$	1.90060	+	0.889022i	0.0707820	+	0.0331089i
$722$		0			0
$723$	10.8700	+	18.8274i	0.404259	+	0.700197i
$724$		0			0
$725$	−8.49593	+	14.7154i	−0.315531	+	0.546516i
$726$		0			0
$727$	26.9614			0.999942			0.499971	−	0.866042i	$-0.333344\pi$
$727$	26.9614			0.999942			0.499971	+	0.866042i	$0.333344\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	15.7029	−	27.1982i	0.580792	−	1.00596i
$732$		0			0
$733$	−10.7347	−	18.5930i	−0.396495	−	0.686749i	0.596796	−	0.802393i	$-0.296440\pi$
$733$	−10.7347	−	18.5930i	−0.396495	−	0.686749i	−0.993291	+	0.115644i	$0.963107\pi$
$734$		0			0
$735$	1.09623	−	2.98969i	0.0404351	−	0.110276i
$736$		0			0
$737$	22.8341	+	39.5498i	0.841105	+	1.45684i
$738$		0			0
$739$	−0.671052	+	1.16230i	−0.0246850	+	0.0427557i	−0.878104	−	0.478470i	$-0.841192\pi$
$739$	−0.671052	+	1.16230i	−0.0246850	+	0.0427557i	0.853419	+	0.521226i	$0.174525\pi$
$740$		0			0
$741$	34.6127			1.27153
$742$		0			0
$743$	26.9919			0.990236			0.495118	−	0.868826i	$-0.335125\pi$
$743$	26.9919			0.990236			0.495118	+	0.868826i	$0.335125\pi$
$744$		0			0
$745$	−0.702870	+	1.21741i	−0.0257512	+	0.0446024i
$746$		0			0
$747$	4.98672	+	8.63726i	0.182455	+	0.316021i
$748$		0			0
$749$	28.6947	+	13.4222i	1.04848	+	0.490437i
$750$		0			0
$751$	6.44360	+	11.1606i	0.235130	+	0.407258i	0.959311	−	0.282353i	$-0.0911150\pi$
$751$	6.44360	+	11.1606i	0.235130	+	0.407258i	−0.724180	+	0.689611i	$0.757782\pi$
$752$		0			0
$753$	−4.01328	+	6.95120i	−0.146252	+	0.253316i
$754$		0			0
$755$	0.784928			0.0285664
$756$		0			0
$757$	26.3897			0.959151			0.479575	−	0.877501i	$-0.340791\pi$
$757$	26.3897			0.959151			0.479575	+	0.877501i	$0.340791\pi$
$758$		0			0
$759$	−8.42835	+	14.5983i	−0.305930	+	0.529886i
$760$		0			0
$761$	−15.2214	−	26.3643i	−0.551776	−	0.955704i	−0.998147	−	0.0608556i	$-0.980617\pi$
$761$	−15.2214	−	26.3643i	−0.551776	−	0.955704i	0.446371	−	0.894848i	$-0.352716\pi$
$762$		0			0
$763$	1.04916	+	12.1588i	0.0379823	+	0.440179i
$764$		0			0
$765$	0.661842	+	1.14634i	0.0239289	+	0.0414461i
$766$		0			0
$767$	−5.27452	+	9.13574i	−0.190452	+	0.329872i
$768$		0			0
$769$	42.1191			1.51886			0.759428	−	0.650592i	$-0.225479\pi$
$769$	42.1191			1.51886			0.759428	+	0.650592i	$0.225479\pi$
$770$		0			0
$771$	12.9098			0.464935
$772$		0			0
$773$	19.0145	−	32.9340i	0.683903	−	1.18455i	−0.289877	−	0.957064i	$-0.593614\pi$
$773$	19.0145	−	32.9340i	0.683903	−	1.18455i	0.973780	−	0.227491i	$-0.0730522\pi$
$774$		0			0
$775$	−10.3965	−	18.0073i	−0.373454	−	0.646842i
$776$		0			0
$777$	16.7081	−	11.6695i	0.599401	−	0.418642i
$778$		0			0
$779$	28.1988	+	48.8418i	1.01033	+	1.74994i
$780$		0			0
$781$	2.63529	−	4.56445i	0.0942980	−	0.163329i
$782$		0			0
$783$	3.54510			0.126691
$784$		0			0
$785$	−2.54115			−0.0906976
$786$		0			0
$787$	−15.7931	+	27.3544i	−0.562962	+	0.975079i	0.434274	+	0.900781i	$0.357005\pi$
$787$	−15.7931	+	27.3544i	−0.562962	+	0.975079i	−0.997236	+	0.0742978i	$0.976328\pi$
$788$		0			0
$789$	−4.45490	−	7.71612i	−0.158599	−	0.274701i
$790$		0			0
$791$	17.3526	−	12.1197i	0.616989	−	0.430925i
$792$		0			0
$793$	13.7560	+	23.8261i	0.488489	+	0.846088i
$794$		0			0
$795$	2.98672	−	5.17316i	0.105928	−	0.183473i
$796$		0			0
$797$	−45.2133			−1.60154			−0.800768	−	0.598974i	$-0.795575\pi$
$797$	−45.2133			−1.60154			−0.800768	+	0.598974i	$0.795575\pi$
$798$		0			0
$799$	14.2866			0.505424
$800$		0			0
$801$	2.45490	−	4.25202i	0.0867398	−	0.150238i
$802$		0			0
$803$	−15.0821	−	26.1229i	−0.532234	−	0.921857i
$804$		0			0
$805$	0.301075	+	3.48917i	0.0106115	+	0.122977i
$806$		0			0
$807$	3.02051	+	5.23168i	0.106327	+	0.184164i
$808$		0			0
$809$	−0.495933	+	0.858981i	−0.0174361	+	0.0302002i	−0.874612	−	0.484824i	$-0.838884\pi$
$809$	−0.495933	+	0.858981i	−0.0174361	+	0.0302002i	0.857176	+	0.515024i	$0.172217\pi$
$810$		0			0
$811$	−23.6151			−0.829237			−0.414619	−	0.909995i	$-0.636085\pi$
$811$	−23.6151			−0.829237			−0.414619	+	0.909995i	$0.636085\pi$
$812$		0			0
$813$	13.3647			0.468721
$814$		0			0
$815$	2.01447	−	3.48917i	0.0705640	−	0.122220i
$816$		0			0
$817$	−31.7492	−	54.9912i	−1.11076	−	1.92390i
$818$		0			0
$819$	−14.0994	−	6.59512i	−0.492673	−	0.230452i
$820$		0			0
$821$	−17.6332	−	30.5416i	−0.615403	−	1.06591i	−0.990314	−	0.138848i	$-0.955660\pi$
$821$	−17.6332	−	30.5416i	−0.615403	−	1.06591i	0.374911	−	0.927061i	$-0.377673\pi$
$822$		0			0
$823$	5.27058	−	9.12890i	0.183721	−	0.318214i	−0.759424	−	0.650596i	$-0.774519\pi$
$823$	5.27058	−	9.12890i	0.183721	−	0.318214i	0.943145	+	0.332382i	$0.107852\pi$
$824$		0			0
$825$	27.7665			0.966706
$826$		0			0
$827$	−31.4323			−1.09301			−0.546504	−	0.837456i	$-0.684042\pi$
$827$	−31.4323			−1.09301			−0.546504	+	0.837456i	$0.684042\pi$
$828$		0			0
$829$	−12.7612	+	22.1031i	−0.443216	+	0.767673i	−0.997926	−	0.0643708i	$-0.979496\pi$
$829$	−12.7612	+	22.1031i	−0.443216	+	0.767673i	0.554710	+	0.832044i	$0.312829\pi$
$830$		0			0
$831$	−2.39653	−	4.15091i	−0.0831347	−	0.143994i
$832$		0			0
$833$	13.0555	+	15.6345i	0.452346	+	0.541702i
$834$		0			0
$835$	−3.95897	−	6.85714i	−0.137006	−	0.237301i
$836$		0			0
$837$	−2.16908	+	3.75696i	−0.0749743	+	0.129859i
$838$		0			0
$839$	2.78253			0.0960637			0.0480318	−	0.998846i	$-0.484705\pi$
$839$	2.78253			0.0960637			0.0480318	+	0.998846i	$0.484705\pi$
$840$		0			0
$841$	−16.4323			−0.566631
$842$		0			0
$843$	3.66184	−	6.34250i	0.126121	−	0.218447i
$844$		0			0
$845$	4.91585	+	8.51450i	0.169110	+	0.292908i
$846$		0			0
$847$	−54.0647	−	25.2893i	−1.85769	−	0.868949i
$848$		0			0
$849$	6.60347	+	11.4375i	0.226630	+	0.392535i
$850$		0			0
$851$	−11.2069	+	19.4110i	−0.384169	+	0.665400i
$852$		0			0
$853$	−18.7931			−0.643462			−0.321731	−	0.946831i	$-0.604265\pi$
$853$	−18.7931			−0.643462			−0.321731	+	0.946831i	$0.604265\pi$
$854$		0			0
$855$	2.67632			0.0915281
$856$		0			0
$857$	−10.4694	+	18.1335i	−0.357627	+	0.619428i	−0.987564	−	0.157218i	$-0.949747\pi$
$857$	−10.4694	+	18.1335i	−0.357627	+	0.619428i	0.629937	+	0.776646i	$0.283081\pi$
$858$		0			0
$859$	5.79306	+	10.0339i	0.197657	+	0.342352i	0.947768	−	0.318960i	$-0.103334\pi$
$859$	5.79306	+	10.0339i	0.197657	+	0.342352i	−0.750111	+	0.661311i	$0.770000\pi$
$860$		0			0
$861$	−2.18038	−	25.2686i	−0.0743073	−	0.861152i
$862$		0			0
$863$	−14.7665	−	25.5763i	−0.502658	−	0.870629i	−0.999995	−	0.00307167i	$-0.999022\pi$
$863$	−14.7665	−	25.5763i	−0.502658	−	0.870629i	0.497337	−	0.867557i	$-0.334311\pi$
$864$		0			0
$865$	3.79306	−	6.56978i	0.128968	−	0.223379i
$866$		0			0
$867$	8.53302			0.289796
$868$		0			0
$869$	−15.9427			−0.540819
$870$		0			0
$871$	23.1896	−	40.1656i	0.785749	−	1.36096i
$872$		0			0
$873$	2.89653	+	5.01694i	0.0980327	+	0.169798i
$874$		0			0
$875$	9.66304	−	6.74899i	0.326670	−	0.228158i
$876$		0			0
$877$	2.61268	+	4.52529i	0.0882239	+	0.152808i	0.906760	−	0.421646i	$-0.138548\pi$
$877$	2.61268	+	4.52529i	0.0882239	+	0.152808i	−0.818537	+	0.574454i	$0.805214\pi$
$878$		0			0
$879$	−3.77255	+	6.53424i	−0.127245	+	0.220395i
$880$		0			0
$881$	−13.1433			−0.442809			−0.221405	−	0.975182i	$-0.571064\pi$
$881$	−13.1433			−0.442809			−0.221405	+	0.975182i	$0.571064\pi$
$882$		0			0
$883$	−7.96531			−0.268054			−0.134027	−	0.990978i	$-0.542791\pi$
$883$	−7.96531			−0.268054			−0.134027	+	0.990978i	$0.542791\pi$
$884$		0			0
$885$	−0.407836	+	0.706392i	−0.0137092	+	0.0237451i
$886$		0			0
$887$	−19.8977	−	34.4639i	−0.668100	−	1.15718i	−0.978435	−	0.206556i	$-0.933774\pi$
$887$	−19.8977	−	34.4639i	−0.668100	−	1.15718i	0.310334	−	0.950627i	$-0.399559\pi$
$888$		0			0
$889$	−2.70694	+	1.89062i	−0.0907878	+	0.0634092i
$890$		0			0
$891$	−2.89653	−	5.01694i	−0.0970374	−	0.168074i
$892$		0			0
$893$	14.4428	−	25.0157i	0.483311	−	0.837119i
$894$		0			0
$895$	2.81148			0.0939775
$896$		0			0
$897$	17.1191			0.571591
$898$		0			0
$899$	−7.68959	+	13.3188i	−0.256462	+	0.444206i
$900$		0			0
$901$	19.1047	+	33.0903i	0.636469	+	1.10240i
$902$		0			0
$903$	2.45490	+	28.4500i	0.0816941	+	0.946758i
$904$		0			0
$905$	0.729425	+	1.26340i	0.0242469	+	0.0419968i
$906$		0			0
$907$	−5.79833	+	10.0430i	−0.192530	+	0.333472i	−0.946088	−	0.323909i	$-0.895003\pi$
$907$	−5.79833	+	10.0430i	−0.192530	+	0.333472i	0.753558	+	0.657382i	$0.228336\pi$
$908$		0			0
$909$	−16.6763			−0.553118
$910$		0			0
$911$	34.4959			1.14290			0.571451	−	0.820636i	$-0.306381\pi$
$911$	34.4959			1.14290			0.571451	+	0.820636i	$0.306381\pi$
$912$		0			0
$913$	28.8884	−	50.0362i	0.956066	−	1.65596i
$914$		0			0
$915$	1.06364	+	1.84227i	0.0351628	+	0.0609037i
$916$		0			0
$917$	−13.8833	−	6.49402i	−0.458465	−	0.214451i
$918$		0			0
$919$	0.927153	+	1.60588i	0.0305839	+	0.0529729i	0.880912	−	0.473280i	$-0.156930\pi$
$919$	0.927153	+	1.60588i	0.0305839	+	0.0529729i	−0.850328	+	0.526253i	$0.823597\pi$
$920$		0			0
$921$	−11.5543	+	20.0126i	−0.380727	+	0.659439i
$922$		0			0
$923$	−5.35263			−0.176184
$924$		0			0
$925$	36.9203			1.21393
$926$		0			0
$927$	0.396531	−	0.686812i	0.0130238	−	0.0225579i
$928$		0			0
$929$	11.5596	+	20.0218i	0.379257	+	0.656893i	0.990954	−	0.134199i	$-0.0428462\pi$
$929$	11.5596	+	20.0218i	0.379257	+	0.656893i	−0.611697	+	0.791092i	$0.709513\pi$
$930$		0			0
$931$	40.5740	−	7.05465i	1.32976	−	0.231207i
$932$		0			0
$933$	−3.70287	−	6.41356i	−0.121227	−	0.209971i
$934$		0			0
$935$	3.83409	−	6.64084i	0.125388	−	0.217179i
$936$		0			0
$937$	−43.3445			−1.41600			−0.708002	−	0.706211i	$-0.750403\pi$
$937$	−43.3445			−1.41600			−0.708002	+	0.706211i	$0.750403\pi$
$938$		0			0
$939$	−14.5861			−0.476000
$940$		0			0
$941$	−14.5656	+	25.2284i	−0.474825	+	0.822422i	−0.999584	−	0.0288292i	$-0.990822\pi$
$941$	−14.5656	+	25.2284i	−0.474825	+	0.822422i	0.524759	+	0.851251i	$0.324155\pi$
$942$		0			0
$943$	13.9469	+	24.1567i	0.454173	+	0.786651i
$944$		0			0
$945$	−1.09019	−	0.509947i	−0.0354639	−	0.0165886i
$946$		0			0
$947$	−6.97345	−	12.0784i	−0.226607	−	0.392494i	0.730194	−	0.683240i	$-0.239430\pi$
$947$	−6.97345	−	12.0784i	−0.226607	−	0.392494i	−0.956800	+	0.290746i	$0.906096\pi$
$948$		0			0
$949$	−15.3169	+	26.5296i	−0.497207	+	0.861187i
$950$		0			0
$951$	1.36471			0.0442538
$952$		0			0
$953$	−39.7134			−1.28644			−0.643222	−	0.765680i	$-0.722403\pi$
$953$	−39.7134			−1.28644			−0.643222	+	0.765680i	$0.722403\pi$
$954$		0			0
$955$	−4.85670	+	8.41205i	−0.157159	+	0.272208i
$956$		0			0
$957$	−10.2685	−	17.7855i	−0.331933	−	0.574925i
$958$		0			0
$959$	−0.702870	−	8.14561i	−0.0226969	−	0.263035i
$960$		0			0
$961$	6.09019	+	10.5485i	0.196458	+	0.340275i
$962$		0			0
$963$	5.98672	−	10.3693i	0.192919	−	0.334146i
$964$		0			0
$965$	−7.46304			−0.240244
$966$		0			0
$967$	−12.5717			−0.404277			−0.202139	−	0.979357i	$-0.564789\pi$
$967$	−12.5717			−0.404277			−0.202139	+	0.979357i	$0.564789\pi$
$968$		0			0
$969$	−8.55957	+	14.8256i	−0.274973	+	0.476267i
$970$		0			0
$971$	7.07691	+	12.2576i	0.227109	+	0.393364i	0.956950	−	0.290253i	$-0.0937393\pi$
$971$	7.07691	+	12.2576i	0.227109	+	0.393364i	−0.729841	+	0.683617i	$0.760406\pi$
$972$		0			0
$973$	12.3700	−	8.63961i	0.396563	−	0.276973i
$974$		0			0
$975$	−14.0994	−	24.4209i	−0.451542	−	0.782094i
$976$		0			0
$977$	23.2624	−	40.2917i	0.744231	−	1.28905i	−0.206322	−	0.978484i	$-0.566149\pi$
$977$	23.2624	−	40.2917i	0.744231	−	1.28905i	0.950553	−	0.310562i	$-0.100517\pi$
$978$		0			0
$979$	−28.4428			−0.909037
$980$		0			0
$981$	4.61268			0.147271
$982$		0			0
$983$	25.2359	−	43.7098i	0.804900	−	1.39413i	−0.111459	−	0.993769i	$-0.535552\pi$
$983$	25.2359	−	43.7098i	0.804900	−	1.39413i	0.916359	−	0.400358i	$-0.131114\pi$
$984$		0			0
$985$	−5.61268	−	9.72144i	−0.178835	−	0.309751i
$986$		0			0
$987$	−10.6498	+	7.43815i	−0.338986	+	0.236759i
$988$		0			0
$989$	−15.7029	−	27.1982i	−0.499322	−	0.864851i
$990$		0			0
$991$	1.98870	−	3.44452i	0.0631730	−	0.109419i	−0.832709	−	0.553711i	$-0.813211\pi$
$991$	1.98870	−	3.44452i	0.0631730	−	0.109419i	0.895882	+	0.444292i	$0.146545\pi$
$992$		0			0
$993$	10.9734			0.348232
$994$		0			0
$995$	6.28660			0.199299
$996$		0			0
$997$	−22.0092	+	38.1211i	−0.697039	+	1.20731i	0.272450	+	0.962170i	$0.412166\pi$
$997$	−22.0092	+	38.1211i	−0.697039	+	1.20731i	−0.969489	+	0.245136i	$0.921167\pi$
$998$		0			0
$999$	−3.85144	−	6.67088i	−0.121854	−	0.211057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.q.z.193.2		6
4.3	odd	2		1344.2.q.y.193.2		6
7.2	even	3	inner	1344.2.q.z.961.2		6
7.3	odd	6		9408.2.a.ei.1.2		3
7.4	even	3		9408.2.a.eh.1.2		3
8.3	odd	2		672.2.q.l.193.2	yes	6
8.5	even	2		672.2.q.k.193.2	✓	6
24.5	odd	2		2016.2.s.u.865.2		6
24.11	even	2		2016.2.s.v.865.2		6
28.3	even	6		9408.2.a.eg.1.2		3
28.11	odd	6		9408.2.a.ej.1.2		3
28.23	odd	6		1344.2.q.y.961.2		6
56.3	even	6		4704.2.a.bv.1.2		3
56.11	odd	6		4704.2.a.bs.1.2		3
56.37	even	6		672.2.q.k.289.2	yes	6
56.45	odd	6		4704.2.a.bt.1.2		3
56.51	odd	6		672.2.q.l.289.2	yes	6
56.53	even	6		4704.2.a.bu.1.2		3
168.107	even	6		2016.2.s.v.289.2		6
168.149	odd	6		2016.2.s.u.289.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.q.k.193.2	✓	6	8.5	even	2
672.2.q.k.289.2	yes	6	56.37	even	6
672.2.q.l.193.2	yes	6	8.3	odd	2
672.2.q.l.289.2	yes	6	56.51	odd	6
1344.2.q.y.193.2		6	4.3	odd	2
1344.2.q.y.961.2		6	28.23	odd	6
1344.2.q.z.193.2		6	1.1	even	1	trivial
1344.2.q.z.961.2		6	7.2	even	3	inner
2016.2.s.u.289.2		6	168.149	odd	6
2016.2.s.u.865.2		6	24.5	odd	2
2016.2.s.v.289.2		6	168.107	even	6
2016.2.s.v.865.2		6	24.11	even	2
4704.2.a.bs.1.2		3	56.11	odd	6
4704.2.a.bt.1.2		3	56.45	odd	6
4704.2.a.bu.1.2		3	56.53	even	6
4704.2.a.bv.1.2		3	56.3	even	6
9408.2.a.eg.1.2		3	28.3	even	6
9408.2.a.eh.1.2		3	7.4	even	3
9408.2.a.ei.1.2		3	7.3	odd	6
9408.2.a.ej.1.2		3	28.11	odd	6

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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(0.227452 + 0.393958i) q^{5} +(2.16908 - 1.51496i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(0.227452 + 0.393958i) q^{5} +(2.16908 - 1.51496i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-2.89653 + 5.01694i) q^{11} +5.88325 q^{13} +0.454904 q^{15} +(-1.45490 + 2.51997i) q^{17} +(2.94163 + 5.09505i) q^{19} +(-0.227452 - 2.63596i) q^{21} +(1.45490 + 2.51997i) q^{23} +(2.39653 - 4.15091i) q^{25} -1.00000 q^{27} -3.54510 q^{29} +(2.16908 - 3.75696i) q^{31} +(2.89653 + 5.01694i) q^{33} +(1.09019 + 0.509947i) q^{35} +(3.85144 + 6.67088i) q^{37} +(2.94163 - 5.09505i) q^{39} +9.58612 q^{41} -10.7931 q^{43} +(0.227452 - 0.393958i) q^{45} +(-2.45490 - 4.25202i) q^{47} +(2.40981 - 6.57212i) q^{49} +(1.45490 + 2.51997i) q^{51} +(6.56561 - 11.3720i) q^{53} -2.63529 q^{55} +5.88325 q^{57} +(-0.896531 + 1.55284i) q^{59} +(2.33816 + 4.04981i) q^{61} +(-2.39653 - 1.12100i) q^{63} +(1.33816 + 2.31776i) q^{65} +(3.94163 - 6.82710i) q^{67} +2.90981 q^{69} -0.909808 q^{71} +(-2.60347 + 4.50934i) q^{73} +(-2.39653 - 4.15091i) q^{75} +(1.31764 + 15.2703i) q^{77} +(1.37602 + 2.38333i) q^{79} +(-0.500000 + 0.866025i) q^{81} -9.97345 q^{83} -1.32368 q^{85} +(-1.77255 + 3.07014i) q^{87} +(2.45490 + 4.25202i) q^{89} +(12.7612 - 8.91288i) q^{91} +(-2.16908 - 3.75696i) q^{93} +(-1.33816 + 2.31776i) q^{95} -5.79306 q^{97} +5.79306 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 3 q^{7} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 3 * q^7 - 3 * q^9	\( 6 q + 3 q^{3} - 3 q^{7} - 3 q^{9} + 6 q^{13} - 6 q^{17} + 3 q^{19} + 6 q^{23} - 3 q^{25} - 6 q^{27} - 24 q^{29} - 3 q^{31} + 12 q^{35} + 3 q^{37} + 3 q^{39} - 12 q^{41} - 30 q^{43} - 12 q^{47} + 9 q^{49} + 6 q^{51} + 6 q^{53} - 24 q^{55} + 6 q^{57} + 12 q^{59} - 18 q^{61} + 3 q^{63} - 24 q^{65} + 9 q^{67} + 12 q^{69} - 33 q^{73} + 3 q^{75} + 12 q^{77} + 27 q^{79} - 3 q^{81} - 36 q^{83} - 72 q^{85} - 12 q^{87} + 12 q^{89} + 51 q^{91} + 3 q^{93} + 24 q^{95}+O(q^{100}) \) 6 * q + 3 * q^3 - 3 * q^7 - 3 * q^9 + 6 * q^13 - 6 * q^17 + 3 * q^19 + 6 * q^23 - 3 * q^25 - 6 * q^27 - 24 * q^29 - 3 * q^31 + 12 * q^35 + 3 * q^37 + 3 * q^39 - 12 * q^41 - 30 * q^43 - 12 * q^47 + 9 * q^49 + 6 * q^51 + 6 * q^53 - 24 * q^55 + 6 * q^57 + 12 * q^59 - 18 * q^61 + 3 * q^63 - 24 * q^65 + 9 * q^67 + 12 * q^69 - 33 * q^73 + 3 * q^75 + 12 * q^77 + 27 * q^79 - 3 * q^81 - 36 * q^83 - 72 * q^85 - 12 * q^87 + 12 * q^89 + 51 * q^91 + 3 * q^93 + 24 * q^95

Introduction

L-functions

Modular forms

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Database

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