LMFDB - Embedded newform 2970.2.t.a.791.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2970,2,Mod(791,2970)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2970, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2970.791"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2970 = 2 \cdot 3^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2970.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$23.7155694003$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 990)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			791.20
Character	$\chi$	$=$	2970.791
Dual form			2970.2.t.a.2771.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.915692 + 0.528675i) q^{7} +1.00000 q^{8} +1.00000i q^{10} +(1.83929 + 2.75989i) q^{11} +(4.33706 - 2.50400i) q^{13} +(-0.915692 + 0.528675i) q^{14} +(-0.500000 + 0.866025i) q^{16} -4.08152 q^{17} -1.38667i q^{19} +(-0.866025 - 0.500000i) q^{20} +(-3.30978 + 0.212926i) q^{22} +(4.52401 - 2.61194i) q^{23} +(0.500000 - 0.866025i) q^{25} +5.00801i q^{26} -1.05735i q^{28} +(-3.32715 + 5.76280i) q^{29} +(3.35865 + 5.81736i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.04076 - 3.53470i) q^{34} +1.05735 q^{35} +5.98254 q^{37} +(1.20089 + 0.693335i) q^{38} +(0.866025 - 0.500000i) q^{40} +(1.10662 + 1.91672i) q^{41} +(2.85341 + 1.64742i) q^{43} +(1.47049 - 2.97282i) q^{44} +5.22388i q^{46} +(-1.01676 - 0.587024i) q^{47} +(-2.94100 - 5.09397i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-4.33706 - 2.50400i) q^{52} -0.0346036i q^{53} +(2.97282 + 1.47049i) q^{55} +(0.915692 + 0.528675i) q^{56} +(-3.32715 - 5.76280i) q^{58} +(9.41442 - 5.43542i) q^{59} +(-3.91068 - 2.25783i) q^{61} -6.71730 q^{62} +1.00000 q^{64} +(2.50400 - 4.33706i) q^{65} +(-4.21923 - 7.30793i) q^{67} +(2.04076 + 3.53470i) q^{68} +(-0.528675 + 0.915692i) q^{70} -5.03435i q^{71} +12.8897i q^{73} +(-2.99127 + 5.18103i) q^{74} +(-1.20089 + 0.693335i) q^{76} +(0.225138 + 3.49960i) q^{77} +(-8.56074 - 4.94255i) q^{79} +1.00000i q^{80} -2.21324 q^{82} +(-1.65561 + 2.86759i) q^{83} +(-3.53470 + 2.04076i) q^{85} +(-2.85341 + 1.64742i) q^{86} +(1.83929 + 2.75989i) q^{88} +3.71184i q^{89} +5.29522 q^{91} +(-4.52401 - 2.61194i) q^{92} +(1.01676 - 0.587024i) q^{94} +(-0.693335 - 1.20089i) q^{95} +(-2.76338 + 4.78632i) q^{97} +5.88201 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8} + 12 q^{11} - 24 q^{13} - 24 q^{16} - 12 q^{17} - 6 q^{22} - 36 q^{23} + 24 q^{25} - 24 q^{32} + 6 q^{34} + 6 q^{38} - 6 q^{41} - 30 q^{43} - 6 q^{44} + 24 q^{49} + 24 q^{50}+ \cdots - 48 q^{98}+O(q^{100}) $ 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8 + 12 * q^11 - 24 * q^13 - 24 * q^16 - 12 * q^17 - 6 * q^22 - 36 * q^23 + 24 * q^25 - 24 * q^32 + 6 * q^34 + 6 * q^38 - 6 * q^41 - 30 * q^43 - 6 * q^44 + 24 * q^49 + 24 * q^50 + 24 * q^52 + 54 * q^59 + 48 * q^64 - 6 * q^67 + 6 * q^68 - 6 * q^76 + 18 * q^77 + 12 * q^82 + 36 * q^83 + 30 * q^86 + 12 * q^88 + 24 * q^91 + 36 * q^92 + 6 * q^97 - 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2970\mathbb{Z}\right)^\times$.

$n$	$541$	$1541$	$2377$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$		0			0
$7$	0.915692	+	0.528675i	0.346099	+	0.199820i	0.662966	−	0.748650i	$-0.269297\pi$
$7$	0.915692	+	0.528675i	0.346099	+	0.199820i	−0.316867	+	0.948470i	$0.602631\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$			1.00000i			0.316228i
$11$	1.83929	+	2.75989i	0.554567	+	0.832139i
$11$	1.83929	+	2.75989i	0.554567	+	0.832139i
$12$		0			0
$13$	4.33706	−	2.50400i	1.20288	−	0.694486i	0.241689	−	0.970354i	$-0.422299\pi$
$13$	4.33706	−	2.50400i	1.20288	−	0.694486i	0.961196	+	0.275868i	$0.0889652\pi$
$14$	−0.915692	+	0.528675i	−0.244729	+	0.141294i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.08152			−0.989914			−0.494957	−	0.868917i	$-0.664816\pi$
$17$	−4.08152			−0.989914			−0.494957	+	0.868917i	$0.664816\pi$
$18$		0			0
$19$		−	1.38667i		−	0.318124i	−0.987269	−	0.159062i	$-0.949153\pi$
$19$		−	1.38667i		−	0.318124i	0.987269	−	0.159062i	$-0.0508469\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$		0			0
$22$	−3.30978	+	0.212926i	−0.705648	+	0.0453961i
$23$	4.52401	−	2.61194i	0.943322	−	0.544627i	0.0523215	−	0.998630i	$-0.483338\pi$
$23$	4.52401	−	2.61194i	0.943322	−	0.544627i	0.891000	+	0.454003i	$0.150005\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$			5.00801i			0.982151i
$27$		0			0
$28$		−	1.05735i		−	0.199820i
$29$	−3.32715	+	5.76280i	−0.617837	+	1.07013i	0.372043	+	0.928216i	$0.378658\pi$
$29$	−3.32715	+	5.76280i	−0.617837	+	1.07013i	−0.989880	+	0.141909i	$0.954676\pi$
$30$		0			0
$31$	3.35865	+	5.81736i	0.603232	+	1.04483i	0.992328	+	0.123631i	$0.0394539\pi$
$31$	3.35865	+	5.81736i	0.603232	+	1.04483i	−0.389097	+	0.921197i	$0.627213\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	2.04076	−	3.53470i	0.349987	−	0.606196i
$35$	1.05735			0.178725
$36$		0			0
$37$	5.98254			0.983524			0.491762	−	0.870730i	$-0.336353\pi$
$37$	5.98254			0.983524			0.491762	+	0.870730i	$0.336353\pi$
$38$	1.20089	+	0.693335i	0.194810	+	0.112474i
$39$		0			0
$40$	0.866025	−	0.500000i	0.136931	−	0.0790569i
$41$	1.10662	+	1.91672i	0.172825	+	0.299342i	0.939406	−	0.342805i	$-0.111377\pi$
$41$	1.10662	+	1.91672i	0.172825	+	0.299342i	−0.766581	+	0.642147i	$0.778044\pi$
$42$		0			0
$43$	2.85341	+	1.64742i	0.435141	+	0.251228i	0.701534	−	0.712636i	$-0.252499\pi$
$43$	2.85341	+	1.64742i	0.435141	+	0.251228i	−0.266394	+	0.963864i	$0.585832\pi$
$44$	1.47049	−	2.97282i	0.221685	−	0.448169i
$45$		0			0
$46$			5.22388i			0.770219i
$47$	−1.01676	−	0.587024i	−0.148309	−	0.0856263i	0.424009	−	0.905658i	$-0.360622\pi$
$47$	−1.01676	−	0.587024i	−0.148309	−	0.0856263i	−0.572318	+	0.820032i	$0.693956\pi$
$48$		0			0
$49$	−2.94100	−	5.09397i	−0.420144	−	0.727710i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$		0			0
$52$	−4.33706	−	2.50400i	−0.601442	−	0.347243i
$53$		−	0.0346036i		−	0.00475317i	−0.999997	−	0.00237658i	$-0.999244\pi$
$53$		−	0.0346036i		−	0.00475317i	0.999997	−	0.00237658i	$-0.000756491\pi$
$54$		0			0
$55$	2.97282	+	1.47049i	0.400855	+	0.198281i
$56$	0.915692	+	0.528675i	0.122365	+	0.0706472i
$57$		0			0
$58$	−3.32715	−	5.76280i	−0.436877	−	0.756693i
$59$	9.41442	−	5.43542i	1.22565	−	0.707631i	0.259535	−	0.965734i	$-0.416431\pi$
$59$	9.41442	−	5.43542i	1.22565	−	0.707631i	0.966117	+	0.258103i	$0.0830973\pi$
$60$		0			0
$61$	−3.91068	−	2.25783i	−0.500712	−	0.289086i	0.228296	−	0.973592i	$-0.426685\pi$
$61$	−3.91068	−	2.25783i	−0.500712	−	0.289086i	−0.729007	+	0.684506i	$0.760018\pi$
$62$	−6.71730			−0.853098
$63$		0			0
$64$	1.00000			0.125000
$65$	2.50400	−	4.33706i	0.310584	−	0.537946i
$66$		0			0
$67$	−4.21923	−	7.30793i	−0.515461	−	0.892805i	−0.999839	−	0.0179463i	$-0.994287\pi$
$67$	−4.21923	−	7.30793i	−0.515461	−	0.892805i	0.484377	−	0.874859i	$-0.339046\pi$
$68$	2.04076	+	3.53470i	0.247479	+	0.428645i
$69$		0			0
$70$	−0.528675	+	0.915692i	−0.0631888	+	0.109446i
$71$		−	5.03435i		−	0.597467i	−0.954337	−	0.298734i	$-0.903436\pi$
$71$		−	5.03435i		−	0.597467i	0.954337	−	0.298734i	$-0.0965642\pi$
$72$		0			0
$73$			12.8897i			1.50862i	0.656519	+	0.754310i	$0.272028\pi$
$73$			12.8897i			1.50862i	−0.656519	+	0.754310i	$0.727972\pi$
$74$	−2.99127	+	5.18103i	−0.347728	+	0.602283i
$75$		0			0
$76$	−1.20089	+	0.693335i	−0.137752	+	0.0795309i
$77$	0.225138	+	3.49960i	0.0256568	+	0.398817i
$78$		0			0
$79$	−8.56074	−	4.94255i	−0.963159	−	0.556080i	−0.0660149	−	0.997819i	$-0.521029\pi$
$79$	−8.56074	−	4.94255i	−0.963159	−	0.556080i	−0.897144	+	0.441739i	$0.854362\pi$
$80$			1.00000i			0.111803i
$81$		0			0
$82$	−2.21324			−0.244412
$83$	−1.65561	+	2.86759i	−0.181726	+	0.314759i	−0.942468	−	0.334295i	$-0.891502\pi$
$83$	−1.65561	+	2.86759i	−0.181726	+	0.314759i	0.760742	+	0.649054i	$0.224835\pi$
$84$		0			0
$85$	−3.53470	+	2.04076i	−0.383392	+	0.221352i
$86$	−2.85341	+	1.64742i	−0.307691	+	0.177645i
$87$		0			0
$88$	1.83929	+	2.75989i	0.196069	+	0.294206i
$89$			3.71184i			0.393454i	0.980458	+	0.196727i	$0.0630313\pi$
$89$			3.71184i			0.393454i	−0.980458	+	0.196727i	$0.936969\pi$
$90$		0			0
$91$	5.29522			0.555090
$92$	−4.52401	−	2.61194i	−0.471661	−	0.272313i
$93$		0			0
$94$	1.01676	−	0.587024i	0.104870	−	0.0605469i
$95$	−0.693335	−	1.20089i	−0.0711346	−	0.123209i
$96$		0			0
$97$	−2.76338	+	4.78632i	−0.280579	+	0.485977i	−0.971527	−	0.236927i	$-0.923860\pi$
$97$	−2.76338	+	4.78632i	−0.280579	+	0.485977i	0.690949	+	0.722904i	$0.257193\pi$
$98$	5.88201			0.594173
$99$		0			0
$100$	−1.00000			−0.100000
$101$	8.10726	−	14.0422i	0.806703	−	1.39725i	−0.108433	−	0.994104i	$-0.534583\pi$
$101$	8.10726	−	14.0422i	0.806703	−	1.39725i	0.915135	−	0.403146i	$-0.132083\pi$
$102$		0			0
$103$	0.0495545	+	0.0858309i	0.00488275	+	0.00845717i	0.868456	−	0.495765i	$-0.165112\pi$
$103$	0.0495545	+	0.0858309i	0.00488275	+	0.00845717i	−0.863574	+	0.504223i	$0.831779\pi$
$104$	4.33706	−	2.50400i	0.425284	−	0.245538i
$105$		0			0
$106$	0.0299676	+	0.0173018i	0.00291071	+	0.00168050i
$107$	14.5678			1.40833			0.704163	−	0.710039i	$-0.251323\pi$
$107$	14.5678			1.40833			0.704163	+	0.710039i	$0.251323\pi$
$108$		0			0
$109$		−	0.522284i		−	0.0500257i	−0.999687	−	0.0250129i	$-0.992037\pi$
$109$		−	0.522284i		−	0.0500257i	0.999687	−	0.0250129i	$-0.00796267\pi$
$110$	−2.75989	+	1.83929i	−0.263145	+	0.175370i
$111$		0			0
$112$	−0.915692	+	0.528675i	−0.0865248	+	0.0499551i
$113$	11.8462	−	6.83942i	1.11440	−	0.643399i	0.174434	−	0.984669i	$-0.444190\pi$
$113$	11.8462	−	6.83942i	1.11440	−	0.643399i	0.939965	+	0.341270i	$0.110857\pi$
$114$		0			0
$115$	2.61194	−	4.52401i	0.243565	−	0.421866i
$116$	6.65431			0.617837
$117$		0			0
$118$			10.8708i			1.00074i
$119$	−3.73742	−	2.15780i	−0.342608	−	0.197805i
$120$		0			0
$121$	−4.23402	+	10.1525i	−0.384911	+	0.922954i
$122$	3.91068	−	2.25783i	0.354057	−	0.204415i
$123$		0			0
$124$	3.35865	−	5.81736i	0.301616	−	0.522414i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$			16.8759i			1.49749i	0.662856	+	0.748747i	$0.269344\pi$
$127$			16.8759i			1.49749i	−0.662856	+	0.748747i	$0.730656\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	2.50400	+	4.33706i	0.219616	+	0.380386i
$131$	−5.09537	−	8.82545i	−0.445185	−	0.771083i	0.552880	−	0.833261i	$-0.313529\pi$
$131$	−5.09537	−	8.82545i	−0.445185	−	0.771083i	−0.998065	+	0.0621779i	$0.980195\pi$
$132$		0			0
$133$	0.733098	−	1.26976i	0.0635676	−	0.110102i
$134$	8.43847			0.728973
$135$		0			0
$136$	−4.08152			−0.349987
$137$	14.0381	+	8.10490i	1.19936	+	0.692448i	0.960412	−	0.278585i	$-0.0898654\pi$
$137$	14.0381	+	8.10490i	1.19936	+	0.692448i	0.238944	+	0.971033i	$0.423199\pi$
$138$		0			0
$139$	10.3611	−	5.98197i	0.878815	−	0.507384i	0.00854719	−	0.999963i	$-0.497279\pi$
$139$	10.3611	−	5.98197i	0.878815	−	0.507384i	0.870267	+	0.492580i	$0.163946\pi$
$140$	−0.528675	−	0.915692i	−0.0446812	−	0.0773901i
$141$		0			0
$142$	4.35988	+	2.51718i	0.365873	+	0.211237i
$143$	14.8879	+	7.36424i	1.24499	+	0.615828i
$144$		0			0
$145$			6.65431i			0.552610i
$146$	−11.1628	−	6.44483i	−0.923837	−	0.533378i
$147$		0			0
$148$	−2.99127	−	5.18103i	−0.245881	−	0.425878i
$149$	9.11819	+	15.7932i	0.746991	+	1.29383i	0.949259	+	0.314497i	$0.101836\pi$
$149$	9.11819	+	15.7932i	0.746991	+	1.29383i	−0.202267	+	0.979330i	$0.564831\pi$
$150$		0			0
$151$	4.70634	+	2.71721i	0.382997	+	0.221123i	0.679121	−	0.734026i	$-0.262361\pi$
$151$	4.70634	+	2.71721i	0.382997	+	0.221123i	−0.296125	+	0.955149i	$0.595694\pi$
$152$		−	1.38667i		−	0.112474i
$153$		0			0
$154$	−3.14331	−	1.55483i	−0.253295	−	0.125291i
$155$	5.81736	+	3.35865i	0.467261	+	0.269773i
$156$		0			0
$157$	3.89848	+	6.75237i	0.311133	+	0.538898i	0.978608	−	0.205734i	$-0.0659583\pi$
$157$	3.89848	+	6.75237i	0.311133	+	0.538898i	−0.667475	+	0.744632i	$0.732625\pi$
$158$	8.56074	−	4.94255i	0.681056	−	0.393208i
$159$		0			0
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	5.52347			0.435310
$162$		0			0
$163$	−7.29928			−0.571723			−0.285862	−	0.958271i	$-0.592280\pi$
$163$	−7.29928			−0.571723			−0.285862	+	0.958271i	$0.592280\pi$
$164$	1.10662	−	1.91672i	0.0864126	−	0.149671i
$165$		0			0
$166$	−1.65561	−	2.86759i	−0.128500	−	0.222568i
$167$	−0.940284	−	1.62862i	−0.0727614	−	0.126026i	0.827349	−	0.561688i	$-0.189848\pi$
$167$	−0.940284	−	1.62862i	−0.0727614	−	0.126026i	−0.900111	+	0.435661i	$0.856514\pi$
$168$		0			0
$169$	6.04008	−	10.4617i	0.464621	−	0.804748i
$170$		−	4.08152i		−	0.313038i
$171$		0			0
$172$		−	3.29483i		−	0.251228i
$173$	−9.37390	+	16.2361i	−0.712684	+	1.23441i	0.251162	+	0.967945i	$0.419187\pi$
$173$	−9.37390	+	16.2361i	−0.712684	+	1.23441i	−0.963846	+	0.266460i	$0.914146\pi$
$174$		0			0
$175$	0.915692	−	0.528675i	0.0692198	−	0.0399641i
$176$	−3.30978	+	0.212926i	−0.249484	+	0.0160499i
$177$		0			0
$178$	−3.21455	−	1.85592i	−0.240940	−	0.139107i
$179$		−	8.56019i		−	0.639819i	−0.947448	−	0.319909i	$-0.896347\pi$
$179$		−	8.56019i		−	0.639819i	0.947448	−	0.319909i	$-0.103653\pi$
$180$		0			0
$181$	13.5719			1.00879			0.504395	−	0.863473i	$-0.331716\pi$
$181$	13.5719			1.00879			0.504395	+	0.863473i	$0.331716\pi$
$182$	−2.64761	+	4.58580i	−0.196254	+	0.339922i
$183$		0			0
$184$	4.52401	−	2.61194i	0.333515	−	0.192555i
$185$	5.18103	−	2.99127i	0.380917	−	0.219923i
$186$		0			0
$187$	−7.50710	−	11.2646i	−0.548974	−	0.823746i
$188$			1.17405i			0.0856263i
$189$		0			0
$190$	1.38667			0.100600
$191$	0.648106	+	0.374184i	0.0468953	+	0.0270750i	0.523264	−	0.852170i	$-0.324714\pi$
$191$	0.648106	+	0.374184i	0.0468953	+	0.0270750i	−0.476369	+	0.879245i	$0.658047\pi$
$192$		0			0
$193$	10.8573	−	6.26848i	0.781527	−	0.451215i	−0.0554439	−	0.998462i	$-0.517657\pi$
$193$	10.8573	−	6.26848i	0.781527	−	0.451215i	0.836971	+	0.547247i	$0.184324\pi$
$194$	−2.76338	−	4.78632i	−0.198399	−	0.343638i
$195$		0			0
$196$	−2.94100	+	5.09397i	−0.210072	+	0.363855i
$197$	−2.06029			−0.146790			−0.0733948	−	0.997303i	$-0.523383\pi$
$197$	−2.06029			−0.146790			−0.0733948	+	0.997303i	$0.523383\pi$
$198$		0			0
$199$	19.7096			1.39717			0.698587	−	0.715525i	$-0.253812\pi$
$199$	19.7096			1.39717			0.698587	+	0.715525i	$0.253812\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$		0			0
$202$	8.10726	+	14.0422i	0.570425	+	0.988005i
$203$	−6.09330	+	3.51797i	−0.427666	+	0.246913i
$204$		0			0
$205$	1.91672	+	1.10662i	0.133870	+	0.0772898i
$206$	−0.0991090			−0.00690525
$207$		0			0
$208$			5.00801i			0.347243i
$209$	3.82706	−	2.55049i	0.264723	−	0.176421i
$210$		0			0
$211$	−15.7652	+	9.10203i	−1.08532	+	0.626609i	−0.932326	−	0.361618i	$-0.882224\pi$
$211$	−15.7652	+	9.10203i	−1.08532	+	0.626609i	−0.152993	+	0.988227i	$0.548891\pi$
$212$	−0.0299676	+	0.0173018i	−0.00205818	+	0.00118829i
$213$		0			0
$214$	−7.28392	+	12.6161i	−0.497918	+	0.862420i
$215$	3.29483			0.224706
$216$		0			0
$217$			7.10254i			0.482152i
$218$	0.452311	+	0.261142i	0.0306344	+	0.0176868i
$219$		0			0
$220$	−0.212926	−	3.30978i	−0.0143555	−	0.223146i
$221$	−17.7018	+	10.2201i	−1.19075	+	0.687481i
$222$		0			0
$223$	−2.85879	+	4.95157i	−0.191439	+	0.331582i	−0.945727	−	0.324961i	$-0.894649\pi$
$223$	−2.85879	+	4.95157i	−0.191439	+	0.331582i	0.754288	+	0.656543i	$0.227982\pi$
$224$		−	1.05735i		−	0.0706472i
$225$		0			0
$226$			13.6788i			0.909903i
$227$	−6.12933	+	10.6163i	−0.406818	+	0.704630i	−0.994531	−	0.104440i	$-0.966695\pi$
$227$	−6.12933	+	10.6163i	−0.406818	+	0.704630i	0.587713	+	0.809069i	$0.300028\pi$
$228$		0			0
$229$	9.63480	+	16.6880i	0.636685	+	1.10277i	0.986155	+	0.165824i	$0.0530283\pi$
$229$	9.63480	+	16.6880i	0.636685	+	1.10277i	−0.349470	+	0.936948i	$0.613638\pi$
$230$	2.61194	+	4.52401i	0.172226	+	0.298304i
$231$		0			0
$232$	−3.32715	+	5.76280i	−0.218438	+	0.378346i
$233$	23.5355			1.54186			0.770930	−	0.636919i	$-0.219792\pi$
$233$	23.5355			1.54186			0.770930	+	0.636919i	$0.219792\pi$
$234$		0			0
$235$	−1.17405			−0.0765865
$236$	−9.41442	−	5.43542i	−0.612826	−	0.353815i
$237$		0			0
$238$	3.73742	−	2.15780i	0.242261	−	0.139869i
$239$	−0.402515	−	0.697176i	−0.0260365	−	0.0450966i	0.852714	−	0.522379i	$-0.174955\pi$
$239$	−0.402515	−	0.697176i	−0.0260365	−	0.0450966i	−0.878750	+	0.477282i	$0.841622\pi$
$240$		0			0
$241$	−22.0083	−	12.7065i	−1.41768	−	0.818499i	−0.421586	−	0.906788i	$-0.638527\pi$
$241$	−22.0083	−	12.7065i	−1.41768	−	0.818499i	−0.996095	+	0.0882896i	$0.971860\pi$
$242$	−6.67531	−	8.74301i	−0.429105	−	0.562022i
$243$		0			0
$244$			4.51567i			0.289086i
$245$	−5.09397	−	2.94100i	−0.325442	−	0.187894i
$246$		0			0
$247$	−3.47223	−	6.01407i	−0.220932	−	0.382666i
$248$	3.35865	+	5.81736i	0.213275	+	0.369402i
$249$		0			0
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$		−	30.2373i		−	1.90856i	−0.298910	−	0.954281i	$-0.596623\pi$
$251$		−	30.2373i		−	1.90856i	0.298910	−	0.954281i	$-0.403377\pi$
$252$		0			0
$253$	15.5296	+	7.68167i	0.976340	+	0.482942i
$254$	−14.6149	−	8.43794i	−0.917023	−	0.529444i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−18.6493	+	10.7672i	−1.16331	+	0.671637i	−0.952095	−	0.305803i	$-0.901075\pi$
$257$	−18.6493	+	10.7672i	−1.16331	+	0.671637i	−0.211214	+	0.977440i	$0.567742\pi$
$258$		0			0
$259$	5.47817	+	3.16282i	0.340397	+	0.196528i
$260$	−5.00801			−0.310584
$261$		0			0
$262$	10.1907			0.629586
$263$	−4.55377	+	7.88736i	−0.280798	+	0.486356i	−0.971581	−	0.236706i	$-0.923932\pi$
$263$	−4.55377	+	7.88736i	−0.280798	+	0.486356i	0.690784	+	0.723061i	$0.257266\pi$
$264$		0			0
$265$	−0.0173018	−	0.0299676i	−0.00106284	−	0.00184089i
$266$	0.733098	+	1.26976i	0.0449491	+	0.0778541i
$267$		0			0
$268$	−4.21923	+	7.30793i	−0.257731	+	0.446403i
$269$			6.51179i			0.397031i	0.980098	+	0.198515i	$0.0636120\pi$
$269$			6.51179i			0.397031i	−0.980098	+	0.198515i	$0.936388\pi$
$270$		0			0
$271$			21.1590i			1.28532i	0.766153	+	0.642658i	$0.222168\pi$
$271$			21.1590i			1.28532i	−0.766153	+	0.642658i	$0.777832\pi$
$272$	2.04076	−	3.53470i	0.123739	−	0.214323i
$273$		0			0
$274$	−14.0381	+	8.10490i	−0.848073	+	0.489635i
$275$	3.30978	−	0.212926i	0.199587	−	0.0128399i
$276$		0			0
$277$	−9.87865	−	5.70344i	−0.593550	−	0.342686i	0.172950	−	0.984931i	$-0.444670\pi$
$277$	−9.87865	−	5.70344i	−0.593550	−	0.342686i	−0.766500	+	0.642244i	$0.778004\pi$
$278$			11.9639i			0.717549i
$279$		0			0
$280$	1.05735			0.0631888
$281$	12.1595	−	21.0609i	0.725376	−	1.25639i	−0.233443	−	0.972370i	$-0.574999\pi$
$281$	12.1595	−	21.0609i	0.725376	−	1.25639i	0.958819	−	0.284018i	$-0.0916674\pi$
$282$		0			0
$283$	15.0537	−	8.69126i	0.894850	−	0.516642i	0.0193242	−	0.999813i	$-0.493849\pi$
$283$	15.0537	−	8.69126i	0.894850	−	0.516642i	0.875526	+	0.483171i	$0.160515\pi$
$284$	−4.35988	+	2.51718i	−0.258711	+	0.149367i
$285$		0			0
$286$	−13.8216	+	9.21119i	−0.817286	+	0.544669i
$287$			2.34017i			0.138136i
$288$		0			0
$289$	−0.341192			−0.0200701
$290$	−5.76280	−	3.32715i	−0.338403	−	0.195377i
$291$		0			0
$292$	11.1628	−	6.44483i	0.653251	−	0.377155i
$293$	4.16935	+	7.22153i	0.243576	+	0.421886i	0.961730	−	0.273998i	$-0.0883461\pi$
$293$	4.16935	+	7.22153i	0.243576	+	0.421886i	−0.718154	+	0.695884i	$0.755013\pi$
$294$		0			0
$295$	5.43542	−	9.41442i	0.316462	−	0.548129i
$296$	5.98254			0.347728
$297$		0			0
$298$	−18.2364			−1.05641
$299$	13.0806	−	22.6563i	0.756471	−	1.31025i
$300$		0			0
$301$	1.74190	+	3.01705i	0.100401	+	0.173900i
$302$	−4.70634	+	2.71721i	−0.270820	+	0.156358i
$303$		0			0
$304$	1.20089	+	0.693335i	0.0688758	+	0.0397655i
$305$	−4.51567			−0.258566
$306$		0			0
$307$		−	13.4611i		−	0.768267i	−0.923277	−	0.384134i	$-0.874500\pi$
$307$		−	13.4611i		−	0.768267i	0.923277	−	0.384134i	$-0.125500\pi$
$308$	2.91817	−	1.94478i	0.166278	−	0.110814i
$309$		0			0
$310$	−5.81736	+	3.35865i	−0.330404	+	0.190759i
$311$	23.1813	−	13.3837i	1.31449	−	0.758922i	0.331655	−	0.943401i	$-0.392393\pi$
$311$	23.1813	−	13.3837i	1.31449	−	0.758922i	0.982836	+	0.184479i	$0.0590598\pi$
$312$		0			0
$313$	−10.3246	+	17.8827i	−0.583579	+	1.01079i	0.411472	+	0.911422i	$0.365015\pi$
$313$	−10.3246	+	17.8827i	−0.583579	+	1.01079i	−0.995051	+	0.0993655i	$0.968319\pi$
$314$	−7.79696			−0.440008
$315$		0			0
$316$			9.88509i			0.556080i
$317$	5.43650	+	3.13877i	0.305344	+	0.176291i	0.644841	−	0.764317i	$-0.276923\pi$
$317$	5.43650	+	3.13877i	0.305344	+	0.176291i	−0.339497	+	0.940607i	$0.610257\pi$
$318$		0			0
$319$	−22.0243	+	1.41688i	−1.23312	+	0.0793299i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$		0			0
$322$	−2.76174	+	4.78347i	−0.153905	+	0.266572i
$323$			5.65972i			0.314915i
$324$		0			0
$325$		−	5.00801i		−	0.277794i
$326$	3.64964	−	6.32136i	0.202135	−	0.350108i
$327$		0			0
$328$	1.10662	+	1.91672i	0.0611029	+	0.105833i
$329$	−0.620690	−	1.07507i	−0.0342198	−	0.0592704i
$330$		0			0
$331$	−14.6814	+	25.4289i	−0.806962	+	1.39770i	0.107996	+	0.994151i	$0.465557\pi$
$331$	−14.6814	+	25.4289i	−0.806962	+	1.39770i	−0.914958	+	0.403548i	$0.867777\pi$
$332$	3.31121			0.181726
$333$		0			0
$334$	1.88057			0.102900
$335$	−7.30793	−	4.21923i	−0.399275	−	0.230521i
$336$		0			0
$337$	17.1659	−	9.91076i	0.935089	−	0.539874i	0.0466712	−	0.998910i	$-0.485139\pi$
$337$	17.1659	−	9.91076i	0.935089	−	0.539874i	0.888417	+	0.459037i	$0.151805\pi$
$338$	6.04008	+	10.4617i	0.328537	+	0.569042i
$339$		0			0
$340$	3.53470	+	2.04076i	0.191696	+	0.110676i
$341$	−9.87774	+	19.9693i	−0.534910	+	1.08140i
$342$		0			0
$343$		−	13.6208i		−	0.735454i
$344$	2.85341	+	1.64742i	0.153845	+	0.0888227i
$345$		0			0
$346$	−9.37390	−	16.2361i	−0.503944	−	0.872857i
$347$	3.66105	+	6.34113i	0.196536	+	0.340410i	0.947403	−	0.320043i	$-0.103698\pi$
$347$	3.66105	+	6.34113i	0.196536	+	0.340410i	−0.750867	+	0.660453i	$0.770364\pi$
$348$		0			0
$349$	6.53255	+	3.77157i	0.349679	+	0.201888i	0.664544	−	0.747249i	$-0.268626\pi$
$349$	6.53255	+	3.77157i	0.349679	+	0.201888i	−0.314865	+	0.949137i	$0.601959\pi$
$350$			1.05735i			0.0565178i
$351$		0			0
$352$	1.47049	−	2.97282i	0.0783775	−	0.158452i
$353$	9.12857	+	5.27038i	0.485865	+	0.280514i	0.722857	−	0.690997i	$-0.242828\pi$
$353$	9.12857	+	5.27038i	0.485865	+	0.280514i	−0.236992	+	0.971511i	$0.576162\pi$
$354$		0			0
$355$	−2.51718	−	4.35988i	−0.133598	−	0.231398i
$356$	3.21455	−	1.85592i	0.170371	−	0.0983635i
$357$		0			0
$358$	7.41335	+	4.28010i	0.391808	+	0.226210i
$359$	−31.7635			−1.67641			−0.838206	−	0.545354i	$-0.816395\pi$
$359$	−31.7635			−1.67641			−0.838206	+	0.545354i	$0.816395\pi$
$360$		0			0
$361$	17.0771			0.898797
$362$	−6.78594	+	11.7536i	−0.356661	+	0.617755i
$363$		0			0
$364$	−2.64761	−	4.58580i	−0.138772	−	0.240361i
$365$	6.44483	+	11.1628i	0.337338	+	0.584286i
$366$		0			0
$367$	−0.0479495	+	0.0830510i	−0.00250294	+	0.00433523i	−0.867274	−	0.497831i	$-0.834130\pi$
$367$	−0.0479495	+	0.0830510i	−0.00250294	+	0.00433523i	0.864771	+	0.502166i	$0.167463\pi$
$368$			5.22388i			0.272313i
$369$		0			0
$370$			5.98254i			0.311018i
$371$	0.0182941	−	0.0316862i	0.000949780	−	0.00164507i
$372$		0			0
$373$	12.8307	−	7.40784i	0.664351	−	0.383563i	−0.129582	−	0.991569i	$-0.541364\pi$
$373$	12.8307	−	7.40784i	0.664351	−	0.383563i	0.793933	+	0.608006i	$0.208030\pi$
$374$	13.5089	−	0.869063i	0.698531	−	0.0449382i
$375$		0			0
$376$	−1.01676	−	0.587024i	−0.0524352	−	0.0302735i
$377$			33.3248i			1.71632i
$378$		0			0
$379$	−5.85541			−0.300772			−0.150386	−	0.988627i	$-0.548052\pi$
$379$	−5.85541			−0.300772			−0.150386	+	0.988627i	$0.548052\pi$
$380$	−0.693335	+	1.20089i	−0.0355673	+	0.0616044i
$381$		0			0
$382$	−0.648106	+	0.374184i	−0.0331600	+	0.0191449i
$383$	4.27679	−	2.46921i	0.218534	−	0.126171i	−0.386737	−	0.922190i	$-0.626398\pi$
$383$	4.27679	−	2.46921i	0.218534	−	0.126171i	0.605271	+	0.796019i	$0.293065\pi$
$384$		0			0
$385$	1.94478	+	2.91817i	0.0991149	+	0.148724i
$386$			12.5370i			0.638114i
$387$		0			0
$388$	5.52676			0.280579
$389$	−30.4964	−	17.6071i	−1.54623	−	0.892715i	−0.998425	−	0.0561072i	$-0.982131\pi$
$389$	−30.4964	−	17.6071i	−1.54623	−	0.892715i	−0.547803	−	0.836608i	$-0.684536\pi$
$390$		0			0
$391$	−18.4648	+	10.6607i	−0.933807	+	0.539134i
$392$	−2.94100	−	5.09397i	−0.148543	−	0.257284i
$393$		0			0
$394$	1.03014	−	1.78426i	0.0518979	−	0.0898899i
$395$	−9.88509			−0.497373
$396$		0			0
$397$	−12.4144			−0.623060			−0.311530	−	0.950236i	$-0.600841\pi$
$397$	−12.4144			−0.623060			−0.311530	+	0.950236i	$0.600841\pi$
$398$	−9.85479	+	17.0690i	−0.493976	+	0.855591i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−20.4887	+	11.8291i	−1.02316	+	0.590719i	−0.915016	−	0.403417i	$-0.867822\pi$
$401$	−20.4887	+	11.8291i	−1.02316	+	0.590719i	−0.108139	+	0.994136i	$0.534489\pi$
$402$		0			0
$403$	29.1334	+	16.8202i	1.45124	+	0.837872i
$404$	−16.2145			−0.806703
$405$		0			0
$406$		−	7.03594i		−	0.349188i
$407$	11.0036	+	16.5112i	0.545430	+	0.818429i
$408$		0			0
$409$	16.4693	−	9.50856i	0.814355	−	0.470168i	−0.0341109	−	0.999418i	$-0.510860\pi$
$409$	16.4693	−	9.50856i	0.814355	−	0.470168i	0.848466	+	0.529250i	$0.177527\pi$
$410$	−1.91672	+	1.10662i	−0.0946602	+	0.0546521i
$411$		0			0
$412$	0.0495545	−	0.0858309i	0.00244138	−	0.00422859i
$413$	11.4943			0.565597
$414$		0			0
$415$			3.31121i			0.162541i
$416$	−4.33706	−	2.50400i	−0.212642	−	0.122769i
$417$		0			0
$418$	0.295258	+	4.58957i	0.0144416	+	0.224483i
$419$	−3.86278	+	2.23018i	−0.188709	+	0.108951i	−0.591378	−	0.806394i	$-0.701416\pi$
$419$	−3.86278	+	2.23018i	−0.188709	+	0.108951i	0.402669	+	0.915346i	$0.368083\pi$
$420$		0			0
$421$	12.3649	−	21.4167i	0.602629	−	1.04378i	−0.389792	−	0.920903i	$-0.627453\pi$
$421$	12.3649	−	21.4167i	0.602629	−	1.04378i	0.992421	−	0.122881i	$-0.0392135\pi$
$422$		−	18.2041i		−	0.886159i
$423$		0			0
$424$		−	0.0346036i		−	0.00168050i
$425$	−2.04076	+	3.53470i	−0.0989914	+	0.171458i
$426$		0			0
$427$	−2.38732	−	4.13496i	−0.115531	−	0.200105i
$428$	−7.28392	−	12.6161i	−0.352081	−	0.609823i
$429$		0			0
$430$	−1.64742	+	2.85341i	−0.0794454	+	0.137604i
$431$	−6.85682			−0.330282			−0.165141	−	0.986270i	$-0.552808\pi$
$431$	−6.85682			−0.330282			−0.165141	+	0.986270i	$0.552808\pi$
$432$		0			0
$433$	23.1663			1.11330			0.556651	−	0.830747i	$-0.312086\pi$
$433$	23.1663			1.11330			0.556651	+	0.830747i	$0.312086\pi$
$434$	−6.15098	−	3.55127i	−0.295257	−	0.170467i
$435$		0			0
$436$	−0.452311	+	0.261142i	−0.0216618	+	0.0125064i
$437$	−3.62190	−	6.27331i	−0.173259	−	0.300093i
$438$		0			0
$439$	−28.5870	−	16.5047i	−1.36438	−	0.787728i	−0.374181	−	0.927356i	$-0.622076\pi$
$439$	−28.5870	−	16.5047i	−1.36438	−	0.787728i	−0.990204	+	0.139628i	$0.955409\pi$
$440$	2.97282	+	1.47049i	0.141724	+	0.0701029i
$441$		0			0
$442$		−	20.4403i		−	0.972245i
$443$	20.7202	+	11.9628i	0.984447	+	0.568371i	0.903610	−	0.428357i	$-0.140907\pi$
$443$	20.7202	+	11.9628i	0.984447	+	0.568371i	0.0808370	+	0.996727i	$0.474241\pi$
$444$		0			0
$445$	1.85592	+	3.21455i	0.0879790	+	0.152384i
$446$	−2.85879	−	4.95157i	−0.135368	−	0.234464i
$447$		0			0
$448$	0.915692	+	0.528675i	0.0432624	+	0.0249776i
$449$		−	4.03838i		−	0.190583i	−0.995449	−	0.0952915i	$-0.969622\pi$
$449$		−	4.03838i		−	0.190583i	0.995449	−	0.0952915i	$-0.0303783\pi$
$450$		0			0
$451$	−3.25455	+	6.57957i	−0.153251	+	0.309820i
$452$	−11.8462	−	6.83942i	−0.557200	−	0.321699i
$453$		0			0
$454$	−6.12933	−	10.6163i	−0.287664	−	0.498249i
$455$	4.58580	−	2.64761i	0.214985	−	0.124122i
$456$		0			0
$457$	−34.4097	−	19.8664i	−1.60962	−	0.929313i	−0.989455	−	0.144839i	$-0.953734\pi$
$457$	−34.4097	−	19.8664i	−1.60962	−	0.929313i	−0.620162	−	0.784474i	$-0.712933\pi$
$458$	−19.2696			−0.900409
$459$		0			0
$460$	−5.22388			−0.243565
$461$	12.3436	−	21.3798i	0.574900	−	0.995756i	−0.421153	−	0.906990i	$-0.638374\pi$
$461$	12.3436	−	21.3798i	0.574900	−	0.995756i	0.996052	−	0.0887662i	$-0.0282924\pi$
$462$		0			0
$463$	−7.42646	−	12.8630i	−0.345137	−	0.597794i	0.640242	−	0.768173i	$-0.278834\pi$
$463$	−7.42646	−	12.8630i	−0.345137	−	0.597794i	−0.985379	+	0.170379i	$0.945501\pi$
$464$	−3.32715	−	5.76280i	−0.154459	−	0.267531i
$465$		0			0
$466$	−11.7677	+	20.3823i	−0.545130	+	0.944193i
$467$			17.9420i			0.830256i	0.909763	+	0.415128i	$0.136263\pi$
$467$			17.9420i			0.830256i	−0.909763	+	0.415128i	$0.863737\pi$
$468$		0			0
$469$		−	8.92242i		−	0.411999i
$470$	0.587024	−	1.01676i	0.0270774	−	0.0468995i
$471$		0			0
$472$	9.41442	−	5.43542i	0.433334	−	0.250185i
$473$	0.701556	+	10.9052i	0.0322576	+	0.501420i
$474$		0			0
$475$	−1.20089	−	0.693335i	−0.0551006	−	0.0318124i
$476$			4.31560i			0.197805i
$477$		0			0
$478$	0.805030			0.0368212
$479$	−16.3488	+	28.3170i	−0.746997	+	1.29384i	0.202258	+	0.979332i	$0.435172\pi$
$479$	−16.3488	+	28.3170i	−0.746997	+	1.29384i	−0.949256	+	0.314505i	$0.898161\pi$
$480$		0			0
$481$	25.9467	−	14.9803i	1.18307	−	0.683044i
$482$	22.0083	−	12.7065i	1.00245	−	0.578766i
$483$		0			0
$484$	10.9093	−	1.40948i	0.495878	−	0.0640673i
$485$			5.52676i			0.250957i
$486$		0			0
$487$	−41.1610			−1.86518			−0.932591	−	0.360936i	$-0.882457\pi$
$487$	−41.1610			−1.86518			−0.932591	+	0.360936i	$0.882457\pi$
$488$	−3.91068	−	2.25783i	−0.177028	−	0.102207i
$489$		0			0
$490$	5.09397	−	2.94100i	0.230122	−	0.132861i
$491$	−19.6521	−	34.0384i	−0.886885	−	1.53613i	−0.843538	−	0.537069i	$-0.819531\pi$
$491$	−19.6521	−	34.0384i	−0.886885	−	1.53613i	−0.0433467	−	0.999060i	$-0.513802\pi$
$492$		0			0
$493$	13.5798	−	23.5210i	0.611606	−	1.05933i
$494$	6.94445			0.312446
$495$		0			0
$496$	−6.71730			−0.301616
$497$	2.66154	−	4.60992i	0.119386	−	0.206783i
$498$		0			0
$499$	−19.9968	−	34.6354i	−0.895178	−	1.55049i	−0.833584	−	0.552393i	$-0.813715\pi$
$499$	−19.9968	−	34.6354i	−0.895178	−	1.55049i	−0.0615941	−	0.998101i	$-0.519618\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$		0			0
$502$	26.1863	+	15.1187i	1.16875	+	0.674779i
$503$	−26.7500			−1.19272			−0.596362	−	0.802715i	$-0.703388\pi$
$503$	−26.7500			−1.19272			−0.596362	+	0.802715i	$0.703388\pi$
$504$		0			0
$505$		−	16.2145i		−	0.721537i
$506$	−14.4173	+	9.60823i	−0.640929	+	0.427138i
$507$		0			0
$508$	14.6149	−	8.43794i	0.648434	−	0.374373i
$509$	5.00397	−	2.88905i	0.221797	−	0.128055i	−0.384985	−	0.922923i	$-0.625793\pi$
$509$	5.00397	−	2.88905i	0.221797	−	0.128055i	0.606782	+	0.794868i	$0.292460\pi$
$510$		0			0
$511$	−6.81444	+	11.8030i	−0.301453	+	0.522132i
$512$	1.00000			0.0441942
$513$		0			0
$514$		−	21.5343i		−	0.949838i
$515$	0.0858309	+	0.0495545i	0.00378216	+	0.00218363i
$516$		0			0
$517$	−0.249986	−	3.88585i	−0.0109944	−	0.170899i
$518$	−5.47817	+	3.16282i	−0.240697	+	0.138966i
$519$		0			0
$520$	2.50400	−	4.33706i	0.109808	−	0.190193i
$521$			29.7698i			1.30424i	0.758117	+	0.652119i	$0.226120\pi$
$521$			29.7698i			1.30424i	−0.758117	+	0.652119i	$0.773880\pi$
$522$		0			0
$523$			0.902037i			0.0394433i	0.999806	+	0.0197217i	$0.00627801\pi$
$523$			0.902037i			0.0394433i	−0.999806	+	0.0197217i	$0.993722\pi$
$524$	−5.09537	+	8.82545i	−0.222592	+	0.385541i
$525$		0			0
$526$	−4.55377	−	7.88736i	−0.198554	−	0.343905i
$527$	−13.7084	−	23.7437i	−0.597147	−	1.03429i
$528$		0			0
$529$	2.14445	−	3.71430i	0.0932370	−	0.161491i
$530$	0.0346036			0.00150308
$531$		0			0
$532$	−1.46620			−0.0635676
$533$	9.59897	+	5.54197i	0.415777	+	0.240049i
$534$		0			0
$535$	12.6161	−	7.28392i	0.545442	−	0.314911i
$536$	−4.21923	−	7.30793i	−0.182243	−	0.315654i
$537$		0			0
$538$	−5.63937	−	3.25589i	−0.243131	−	0.140372i
$539$	8.64945	−	17.4862i	0.372558	−	0.753182i
$540$		0			0
$541$		−	40.9054i		−	1.75866i	−0.476212	−	0.879330i	$-0.657991\pi$
$541$		−	40.9054i		−	1.75866i	0.476212	−	0.879330i	$-0.342009\pi$
$542$	−18.3242	−	10.5795i	−0.787092	−	0.454428i
$543$		0			0
$544$	2.04076	+	3.53470i	0.0874969	+	0.151549i
$545$	−0.261142	−	0.452311i	−0.0111861	−	0.0193749i
$546$		0			0
$547$	0.575875	+	0.332482i	0.0246227	+	0.0142159i	0.512261	−	0.858830i	$-0.328808\pi$
$547$	0.575875	+	0.332482i	0.0246227	+	0.0142159i	−0.487638	+	0.873046i	$0.662141\pi$
$548$		−	16.2098i		−	0.692448i
$549$		0			0
$550$	−1.47049	+	2.97282i	−0.0627020	+	0.126761i
$551$	7.99110	+	4.61366i	0.340432	+	0.196549i
$552$		0			0
$553$	−5.22600	−	9.05170i	−0.222232	−	0.384918i
$554$	9.87865	−	5.70344i	0.419703	−	0.242316i
$555$		0			0
$556$	−10.3611	−	5.98197i	−0.439407	−	0.253692i
$557$	−23.0650			−0.977294			−0.488647	−	0.872482i	$-0.662509\pi$
$557$	−23.0650			−0.977294			−0.488647	+	0.872482i	$0.662509\pi$
$558$		0			0
$559$	16.5005			0.697899
$560$	−0.528675	+	0.915692i	−0.0223406	+	0.0386951i
$561$		0			0
$562$	12.1595	+	21.0609i	0.512918	+	0.888401i
$563$	6.36854	+	11.0306i	0.268402	+	0.464886i	0.968449	−	0.249210i	$-0.0801711\pi$
$563$	6.36854	+	11.0306i	0.268402	+	0.464886i	−0.700047	+	0.714097i	$0.746838\pi$
$564$		0			0
$565$	6.83942	−	11.8462i	0.287737	−	0.498375i
$566$			17.3825i			0.730642i
$567$		0			0
$568$		−	5.03435i		−	0.211237i
$569$	1.05386	−	1.82534i	0.0441801	−	0.0765222i	−0.843090	−	0.537773i	$-0.819266\pi$
$569$	1.05386	−	1.82534i	0.0441801	−	0.0765222i	0.887270	+	0.461251i	$0.152599\pi$
$570$		0			0
$571$	15.0594	−	8.69454i	0.630216	−	0.363855i	−0.150620	−	0.988592i	$-0.548127\pi$
$571$	15.0594	−	8.69454i	0.630216	−	0.363855i	0.780836	+	0.624737i	$0.214794\pi$
$572$	−1.06634	−	16.5754i	−0.0445858	−	0.693053i
$573$		0			0
$574$	−2.02665	−	1.17009i	−0.0845907	−	0.0488385i
$575$		−	5.22388i		−	0.217851i
$576$		0			0
$577$	−32.1255			−1.33740			−0.668701	−	0.743532i	$-0.733149\pi$
$577$	−32.1255			−1.33740			−0.668701	+	0.743532i	$0.733149\pi$
$578$	0.170596	−	0.295481i	0.00709585	−	0.0122904i
$579$		0			0
$580$	5.76280	−	3.32715i	0.239287	−	0.138153i
$581$	−3.03205	+	1.75056i	−0.125791	+	0.0726253i
$582$		0			0
$583$	0.0955022	−	0.0636460i	0.00395530	−	0.00263595i
$584$			12.8897i			0.533378i
$585$		0			0
$586$	−8.33870			−0.344469
$587$	15.7386	+	9.08669i	0.649602	+	0.375048i	0.788304	−	0.615286i	$-0.210960\pi$
$587$	15.7386	+	9.08669i	0.649602	+	0.375048i	−0.138702	+	0.990334i	$0.544293\pi$
$588$		0			0
$589$	8.06675	−	4.65734i	0.332385	−	0.191902i
$590$	5.43542	+	9.41442i	0.223773	+	0.387585i
$591$		0			0
$592$	−2.99127	+	5.18103i	−0.122941	+	0.212939i
$593$	35.1732			1.44439			0.722195	−	0.691689i	$-0.243133\pi$
$593$	35.1732			1.44439			0.722195	+	0.691689i	$0.243133\pi$
$594$		0			0
$595$	−4.31560			−0.176922
$596$	9.11819	−	15.7932i	0.373496	−	0.646914i
$597$		0			0
$598$	13.0806	+	22.6563i	0.534906	+	0.926484i
$599$	−26.0983	+	15.0679i	−1.06635	+	0.615656i	−0.927181	−	0.374613i	$-0.877776\pi$
$599$	−26.0983	+	15.0679i	−1.06635	+	0.615656i	−0.139167	+	0.990269i	$0.544442\pi$
$600$		0			0
$601$	−27.2900	−	15.7559i	−1.11318	−	0.642697i	−0.173532	−	0.984828i	$-0.555518\pi$
$601$	−27.2900	−	15.7559i	−1.11318	−	0.642697i	−0.939652	+	0.342131i	$0.888851\pi$
$602$	−3.48379			−0.141989
$603$		0			0
$604$		−	5.43442i		−	0.221123i
$605$	1.40948	+	10.9093i	0.0573035	+	0.443527i
$606$		0			0
$607$	21.1523	−	12.2123i	0.858547	−	0.495682i	−0.00497869	−	0.999988i	$-0.501585\pi$
$607$	21.1523	−	12.2123i	0.858547	−	0.495682i	0.863525	+	0.504305i	$0.168251\pi$
$608$	−1.20089	+	0.693335i	−0.0487026	+	0.0281184i
$609$		0			0
$610$	2.25783	−	3.91068i	0.0914170	−	0.158339i
$611$	−5.87965			−0.237865
$612$		0			0
$613$		−	3.19506i		−	0.129047i	−0.997916	−	0.0645236i	$-0.979447\pi$
$613$		−	3.19506i		−	0.129047i	0.997916	−	0.0645236i	$-0.0205528\pi$
$614$	11.6577	+	6.73057i	0.470466	+	0.271624i
$615$		0			0
$616$	0.225138	+	3.49960i	0.00907106	+	0.141003i
$617$	−20.6567	+	11.9261i	−0.831607	+	0.480128i	−0.854403	−	0.519612i	$-0.826077\pi$
$617$	−20.6567	+	11.9261i	−0.831607	+	0.480128i	0.0227957	+	0.999740i	$0.492743\pi$
$618$		0			0
$619$	−17.3766	+	30.0971i	−0.698424	+	1.20971i	0.270589	+	0.962695i	$0.412782\pi$
$619$	−17.3766	+	30.0971i	−0.698424	+	1.20971i	−0.969013	+	0.247011i	$0.920552\pi$
$620$		−	6.71730i		−	0.269773i
$621$		0			0
$622$			26.7675i			1.07328i
$623$	−1.96236	+	3.39890i	−0.0786202	+	0.136174i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−10.3246	−	17.8827i	−0.412652	−	0.714735i
$627$		0			0
$628$	3.89848	−	6.75237i	0.155566	−	0.269449i
$629$	−24.4179			−0.973604
$630$		0			0
$631$	−26.2444			−1.04477			−0.522387	−	0.852708i	$-0.674958\pi$
$631$	−26.2444			−1.04477			−0.522387	+	0.852708i	$0.674958\pi$
$632$	−8.56074	−	4.94255i	−0.340528	−	0.196604i
$633$		0			0
$634$	−5.43650	+	3.13877i	−0.215911	+	0.124656i
$635$	8.43794	+	14.6149i	0.334850	+	0.579977i
$636$		0			0
$637$	−25.5106	−	14.7286i	−1.01077	−	0.583568i
$638$	9.78511	−	19.7821i	0.387396	−	0.783179i
$639$		0			0
$640$			1.00000i			0.0395285i
$641$	7.89607	+	4.55880i	0.311876	+	0.180062i	0.647766	−	0.761840i	$-0.275704\pi$
$641$	7.89607	+	4.55880i	0.311876	+	0.180062i	−0.335890	+	0.941901i	$0.609037\pi$
$642$		0			0
$643$	−11.9790	−	20.7482i	−0.472405	−	0.818230i	0.527096	−	0.849806i	$-0.323281\pi$
$643$	−11.9790	−	20.7482i	−0.472405	−	0.818230i	−0.999501	+	0.0315756i	$0.989947\pi$
$644$	−2.76174	−	4.78347i	−0.108828	−	0.188495i
$645$		0			0
$646$	−4.90146	−	2.82986i	−0.192845	−	0.111339i
$647$		−	12.2356i		−	0.481033i	−0.970645	−	0.240516i	$-0.922683\pi$
$647$		−	12.2356i		−	0.481033i	0.970645	−	0.240516i	$-0.0773168\pi$
$648$		0			0
$649$	32.3170	+	15.9855i	1.26855	+	0.627485i
$650$	4.33706	+	2.50400i	0.170114	+	0.0982151i
$651$		0			0
$652$	3.64964	+	6.32136i	0.142931	+	0.247563i
$653$	−29.2278	+	16.8747i	−1.14377	+	0.660357i	−0.947362	−	0.320165i	$-0.896262\pi$
$653$	−29.2278	+	16.8747i	−1.14377	+	0.660357i	−0.196410	+	0.980522i	$0.562928\pi$
$654$		0			0
$655$	−8.82545	−	5.09537i	−0.344839	−	0.199093i
$656$	−2.21324			−0.0864126
$657$		0			0
$658$	1.24138			0.0483941
$659$	21.2069	−	36.7314i	0.826102	−	1.43085i	−0.0749725	−	0.997186i	$-0.523887\pi$
$659$	21.2069	−	36.7314i	0.826102	−	1.43085i	0.901074	−	0.433665i	$-0.142780\pi$
$660$		0			0
$661$	16.3119	+	28.2531i	0.634460	+	1.09892i	0.986629	+	0.162980i	$0.0521107\pi$
$661$	16.3119	+	28.2531i	0.634460	+	1.09892i	−0.352170	+	0.935936i	$0.614556\pi$
$662$	−14.6814	−	25.4289i	−0.570608	−	0.988323i
$663$		0			0
$664$	−1.65561	+	2.86759i	−0.0642499	+	0.111284i
$665$		−	1.46620i		−	0.0568566i
$666$		0			0
$667$			34.7613i			1.34596i
$668$	−0.940284	+	1.62862i	−0.0363807	+	0.0630132i
$669$		0			0
$670$	7.30793	−	4.21923i	0.282330	−	0.163003i
$671$	−0.961504	−	14.9459i	−0.0371185	−	0.576979i
$672$		0			0
$673$	30.8226	+	17.7954i	1.18812	+	0.685963i	0.957880	−	0.287170i	$-0.0927144\pi$
$673$	30.8226	+	17.7954i	1.18812	+	0.685963i	0.230243	+	0.973133i	$0.426048\pi$
$674$			19.8215i			0.763497i
$675$		0			0
$676$	−12.0802			−0.464621
$677$	16.1560	−	27.9830i	0.620926	−	1.07548i	−0.368388	−	0.929672i	$-0.620090\pi$
$677$	16.1560	−	27.9830i	0.620926	−	1.07548i	0.989314	−	0.145803i	$-0.0465766\pi$
$678$		0			0
$679$	−5.06081	+	2.92186i	−0.194216	+	0.112131i
$680$	−3.53470	+	2.04076i	−0.135550	+	0.0782596i
$681$		0			0
$682$	−12.3551	−	18.5390i	−0.473100	−	0.709896i
$683$		−	2.61049i		−	0.0998875i	−0.998752	−	0.0499438i	$-0.984096\pi$
$683$		−	2.61049i		−	0.0998875i	0.998752	−	0.0499438i	$-0.0159042\pi$
$684$		0			0
$685$	16.2098			0.619345
$686$	11.7960	+	6.81040i	0.450372	+	0.260022i
$687$		0			0
$688$	−2.85341	+	1.64742i	−0.108785	+	0.0628071i
$689$	−0.0866475	−	0.150078i	−0.00330101	−	0.00571751i
$690$		0			0
$691$	−2.16019	+	3.74157i	−0.0821777	+	0.142336i	−0.904185	−	0.427141i	$-0.859521\pi$
$691$	−2.16019	+	3.74157i	−0.0821777	+	0.142336i	0.822007	+	0.569477i	$0.192854\pi$
$692$	18.7478			0.712684
$693$		0			0
$694$	−7.32211			−0.277943
$695$	5.98197	−	10.3611i	0.226909	−	0.393018i
$696$		0			0
$697$	−4.51670	−	7.82315i	−0.171082	−	0.296323i
$698$	−6.53255	+	3.77157i	−0.247261	+	0.142756i
$699$		0			0
$700$	−0.915692	−	0.528675i	−0.0346099	−	0.0199820i
$701$	−44.1237			−1.66653			−0.833265	−	0.552874i	$-0.813531\pi$
$701$	−44.1237			−1.66653			−0.833265	+	0.552874i	$0.813531\pi$
$702$		0			0
$703$		−	8.29581i		−	0.312882i
$704$	1.83929	+	2.75989i	0.0693209	+	0.104017i
$705$		0			0
$706$	−9.12857	+	5.27038i	−0.343558	+	0.198354i
$707$	14.8475	−	8.57222i	0.558398	−	0.322391i
$708$		0			0
$709$	−15.5092	+	26.8627i	−0.582459	+	1.00885i	0.412728	+	0.910854i	$0.364576\pi$
$709$	−15.5092	+	26.8627i	−0.582459	+	1.00885i	−0.995187	+	0.0979942i	$0.968757\pi$
$710$	5.03435			0.188936
$711$		0			0
$712$			3.71184i			0.139107i
$713$	30.3892	+	17.5452i	1.13808	+	0.657072i
$714$		0			0
$715$	16.5754	−	1.06634i	0.619886	−	0.0398787i
$716$	−7.41335	+	4.28010i	−0.277050	+	0.159955i
$717$		0			0
$718$	15.8817	−	27.5080i	0.592701	−	1.02659i
$719$		−	13.8269i		−	0.515656i	−0.966191	−	0.257828i	$-0.916993\pi$
$719$		−	13.8269i		−	0.515656i	0.966191	−	0.257828i	$-0.0830068\pi$
$720$		0			0
$721$			0.104793i			0.00390269i
$722$	−8.53857	+	14.7892i	−0.317773	+	0.550399i
$723$		0			0
$724$	−6.78594	−	11.7536i	−0.252197	−	0.436819i
$725$	3.32715	+	5.76280i	0.123567	+	0.214025i
$726$		0			0
$727$	25.9981	−	45.0300i	0.964216	−	1.67007i	0.252509	−	0.967595i	$-0.418744\pi$
$727$	25.9981	−	45.0300i	0.964216	−	1.67007i	0.711707	−	0.702476i	$-0.247922\pi$
$728$	5.29522			0.196254
$729$		0			0
$730$	−12.8897			−0.477067
$731$	−11.6462	−	6.72396i	−0.430752	−	0.248695i
$732$		0			0
$733$	12.1638	−	7.02279i	0.449281	−	0.259393i	−0.258245	−	0.966079i	$-0.583144\pi$
$733$	12.1638	−	7.02279i	0.449281	−	0.259393i	0.707527	+	0.706687i	$0.249811\pi$
$734$	−0.0479495	−	0.0830510i	−0.00176985	−	0.00306547i
$735$		0			0
$736$	−4.52401	−	2.61194i	−0.166757	−	0.0962773i
$737$	12.4087	−	25.0860i	0.457080	−	0.924056i
$738$		0			0
$739$		−	1.73685i		−	0.0638911i	−0.999490	−	0.0319455i	$-0.989830\pi$
$739$		−	1.73685i		−	0.0638911i	0.999490	−	0.0319455i	$-0.0101703\pi$
$740$	−5.18103	−	2.99127i	−0.190459	−	0.109961i
$741$		0			0
$742$	0.0182941	+	0.0316862i	0.000671596	+	0.00116324i
$743$	−1.07106	−	1.85513i	−0.0392933	−	0.0680580i	0.845710	−	0.533643i	$-0.179177\pi$
$743$	−1.07106	−	1.85513i	−0.0392933	−	0.0680580i	−0.885003	+	0.465585i	$0.845844\pi$
$744$		0			0
$745$	15.7932	+	9.11819i	0.578617	+	0.334065i
$746$			14.8157i			0.542440i
$747$		0			0
$748$	−6.00184	+	12.1336i	−0.219449	+	0.443649i
$749$	13.3397	+	7.70165i	0.487420	+	0.281412i
$750$		0			0
$751$	18.8637	+	32.6729i	0.688348	+	1.19225i	0.972372	+	0.233436i	$0.0749969\pi$
$751$	18.8637	+	32.6729i	0.688348	+	1.19225i	−0.284025	+	0.958817i	$0.591670\pi$
$752$	1.01676	−	0.587024i	0.0370773	−	0.0214066i
$753$		0			0
$754$	−28.8602	−	16.6624i	−1.05102	−	0.606809i
$755$	5.43442			0.197779
$756$		0			0
$757$	23.4098			0.850845			0.425422	−	0.904995i	$-0.360126\pi$
$757$	23.4098			0.850845			0.425422	+	0.904995i	$0.360126\pi$
$758$	2.92771	−	5.07094i	0.106339	−	0.184185i
$759$		0			0
$760$	−0.693335	−	1.20089i	−0.0251499	−	0.0435609i
$761$	−13.4756	−	23.3404i	−0.488490	−	0.846089i	0.511423	−	0.859329i	$-0.329119\pi$
$761$	−13.4756	−	23.3404i	−0.488490	−	0.846089i	−0.999912	+	0.0132405i	$0.995785\pi$
$762$		0			0
$763$	0.276119	−	0.478252i	0.00999617	−	0.0173139i
$764$		−	0.748369i		−	0.0270750i
$765$		0			0
$766$			4.93842i			0.178432i
$767$	27.2206	−	47.1475i	0.982879	−	1.70240i
$768$		0			0
$769$	11.9803	−	6.91685i	0.432022	−	0.249428i	−0.268186	−	0.963367i	$-0.586424\pi$
$769$	11.9803	−	6.91685i	0.432022	−	0.249428i	0.700208	+	0.713939i	$0.253091\pi$
$770$	−3.49960	+	0.225138i	−0.126117	+	0.00811340i
$771$		0			0
$772$	−10.8573	−	6.26848i	−0.390764	−	0.225608i
$773$		−	40.2226i		−	1.44671i	−0.690478	−	0.723353i	$-0.742600\pi$
$773$		−	40.2226i		−	1.44671i	0.690478	−	0.723353i	$-0.257400\pi$
$774$		0			0
$775$	6.71730			0.241293
$776$	−2.76338	+	4.78632i	−0.0991996	+	0.171819i
$777$		0			0
$778$	30.4964	−	17.6071i	1.09335	−	0.631245i
$779$	2.65786	−	1.53452i	0.0952278	−	0.0549798i
$780$		0			0
$781$	13.8943	−	9.25963i	0.497176	−	0.331336i
$782$		−	21.3214i		−	0.762450i
$783$		0			0
$784$	5.88201			0.210072
$785$	6.75237	+	3.89848i	0.241002	+	0.139143i
$786$		0			0
$787$	−40.0385	+	23.1162i	−1.42722	+	0.824004i	−0.996900	−	0.0786737i	$-0.974931\pi$
$787$	−40.0385	+	23.1162i	−1.42722	+	0.824004i	−0.430317	+	0.902678i	$0.641598\pi$
$788$	1.03014	+	1.78426i	0.0366974	+	0.0635617i
$789$		0			0
$790$	4.94255	−	8.56074i	0.175848	−	0.304578i
$791$	14.4633			0.514257
$792$		0			0
$793$	−22.6145			−0.803064
$794$	6.20719	−	10.7512i	0.220285	−	0.381544i
$795$		0			0
$796$	−9.85479	−	17.0690i	−0.349294	−	0.604994i
$797$	−14.4588	+	8.34779i	−0.512157	+	0.295694i	−0.733720	−	0.679452i	$-0.762217\pi$
$797$	−14.4588	+	8.34779i	−0.512157	+	0.295694i	0.221563	+	0.975146i	$0.428884\pi$
$798$		0			0
$799$	4.14991	+	2.39595i	0.146813	+	0.0847627i
$800$	−1.00000			−0.0353553
$801$		0			0
$802$		−	23.6583i		−	0.835403i
$803$	−35.5741	+	23.7078i	−1.25538	+	0.836631i
$804$		0			0
$805$	4.78347	−	2.76174i	0.168595	−	0.0973384i
$806$	−29.1334	+	16.8202i	−1.02618	+	0.592465i
$807$		0			0
$808$	8.10726	−	14.0422i	0.285213	−	0.494003i
$809$	−7.89639			−0.277622			−0.138811	−	0.990319i	$-0.544328\pi$
$809$	−7.89639			−0.277622			−0.138811	+	0.990319i	$0.544328\pi$
$810$		0			0
$811$		−	43.3459i		−	1.52208i	−0.648706	−	0.761040i	$-0.724689\pi$
$811$		−	43.3459i		−	1.52208i	0.648706	−	0.761040i	$-0.275311\pi$
$812$	6.09330	+	3.51797i	0.213833	+	0.123456i
$813$		0			0
$814$	−19.8009	+	1.27384i	−0.694022	+	0.0446481i
$815$	−6.32136	+	3.64964i	−0.221428	+	0.127841i
$816$		0			0
$817$	2.28442	−	3.95673i	0.0799217	−	0.138429i
$818$			19.0171i			0.664918i
$819$		0			0
$820$		−	2.21324i		−	0.0772898i
$821$	−18.1604	+	31.4547i	−0.633802	+	1.09778i	0.352965	+	0.935636i	$0.385173\pi$
$821$	−18.1604	+	31.4547i	−0.633802	+	1.09778i	−0.986768	+	0.162141i	$0.948160\pi$
$822$		0			0
$823$	−14.8019	−	25.6377i	−0.515963	−	0.893674i	−0.999828	−	0.0185314i	$-0.994101\pi$
$823$	−14.8019	−	25.6377i	−0.515963	−	0.893674i	0.483865	−	0.875142i	$-0.339232\pi$
$824$	0.0495545	+	0.0858309i	0.00172631	+	0.00299006i
$825$		0			0
$826$	−5.74714	+	9.95434i	−0.199969	+	0.346356i
$827$	−12.8344			−0.446295			−0.223148	−	0.974785i	$-0.571633\pi$
$827$	−12.8344			−0.446295			−0.223148	+	0.974785i	$0.571633\pi$
$828$		0			0
$829$	−4.28623			−0.148867			−0.0744334	−	0.997226i	$-0.523715\pi$
$829$	−4.28623			−0.148867			−0.0744334	+	0.997226i	$0.523715\pi$
$830$	−2.86759	−	1.65561i	−0.0995356	−	0.0574669i
$831$		0			0
$832$	4.33706	−	2.50400i	0.150361	−	0.0868107i
$833$	12.0038	+	20.7911i	0.415906	+	0.720370i
$834$		0			0
$835$	−1.62862	−	0.940284i	−0.0563607	−	0.0325399i
$836$	−4.12232	−	2.03909i	−0.142573	−	0.0705233i
$837$		0			0
$838$		−	4.46035i		−	0.154080i
$839$	−21.6342	−	12.4905i	−0.746896	−	0.431220i	0.0776755	−	0.996979i	$-0.475250\pi$
$839$	−21.6342	−	12.4905i	−0.746896	−	0.431220i	−0.824571	+	0.565758i	$0.808584\pi$
$840$		0			0
$841$	−7.63991	−	13.2327i	−0.263445	−	0.456300i
$842$	12.3649	+	21.4167i	0.426123	+	0.738067i
$843$		0			0
$844$	15.7652	+	9.10203i	0.542660	+	0.313305i
$845$		−	12.0802i		−	0.415570i
$846$		0			0
$847$	−9.24443	+	7.05814i	−0.317642	+	0.242521i
$848$	0.0299676	+	0.0173018i	0.00102909	+	0.000594146i
$849$		0			0
$850$	−2.04076	−	3.53470i	−0.0699975	−	0.121239i
$851$	27.0651	−	15.6260i	0.927779	−	0.535654i
$852$		0			0
$853$	32.8015	+	18.9379i	1.12310	+	0.648423i	0.942191	−	0.335076i	$-0.108762\pi$
$853$	32.8015	+	18.9379i	1.12310	+	0.648423i	0.180911	+	0.983500i	$0.442095\pi$
$854$	4.77464			0.163385
$855$		0			0
$856$	14.5678			0.497918
$857$	9.26853	−	16.0536i	0.316607	−	0.548379i	−0.663171	−	0.748468i	$-0.730790\pi$
$857$	9.26853	−	16.0536i	0.316607	−	0.548379i	0.979778	+	0.200089i	$0.0641231\pi$
$858$		0			0
$859$	−14.1421	−	24.4949i	−0.482524	−	0.835755i	0.517275	−	0.855819i	$-0.326946\pi$
$859$	−14.1421	−	24.4949i	−0.482524	−	0.835755i	−0.999799	+	0.0200639i	$0.993613\pi$
$860$	−1.64742	−	2.85341i	−0.0561764	−	0.0973004i
$861$		0			0
$862$	3.42841	−	5.93818i	0.116772	−	0.202255i
$863$		−	38.0301i		−	1.29456i	−0.762252	−	0.647280i	$-0.775906\pi$
$863$		−	38.0301i		−	1.29456i	0.762252	−	0.647280i	$-0.224094\pi$
$864$		0			0
$865$			18.7478i			0.637444i
$866$	−11.5832	+	20.0626i	−0.393612	+	0.681755i
$867$		0			0
$868$	6.15098	−	3.55127i	0.208778	−	0.120538i
$869$	−2.10480	−	32.7175i	−0.0714003	−	1.10987i
$870$		0			0
$871$	−36.5982	−	21.1300i	−1.24008	−	0.715961i
$872$		−	0.522284i		−	0.0176868i
$873$		0			0
$874$	7.24379			0.245025
$875$	0.528675	−	0.915692i	0.0178725	−	0.0309561i
$876$		0			0
$877$	−34.2501	+	19.7743i	−1.15654	+	0.667731i	−0.950474	−	0.310805i	$-0.899401\pi$
$877$	−34.2501	+	19.7743i	−1.15654	+	0.667731i	−0.206071	+	0.978537i	$0.566068\pi$
$878$	28.5870	−	16.5047i	0.964766	−	0.557008i
$879$		0			0
$880$	−2.75989	+	1.83929i	−0.0930360	+	0.0620025i
$881$			1.43415i			0.0483176i	0.999708	+	0.0241588i	$0.00769073\pi$
$881$			1.43415i			0.0483176i	−0.999708	+	0.0241588i	$0.992309\pi$
$882$		0			0
$883$	29.5724			0.995192			0.497596	−	0.867409i	$-0.334216\pi$
$883$	29.5724			0.995192			0.497596	+	0.867409i	$0.334216\pi$
$884$	17.7018	+	10.2201i	0.595376	+	0.343741i
$885$		0			0
$886$	−20.7202	+	11.9628i	−0.696109	+	0.401899i
$887$	−0.459977	−	0.796704i	−0.0154445	−	0.0267507i	0.858200	−	0.513316i	$-0.171583\pi$
$887$	−0.459977	−	0.796704i	−0.0154445	−	0.0267507i	−0.873644	+	0.486565i	$0.838250\pi$
$888$		0			0
$889$	−8.92187	+	15.4531i	−0.299230	+	0.518281i
$890$	−3.71184			−0.124421
$891$		0			0
$892$	5.71758			0.191439
$893$	−0.814009	+	1.40990i	−0.0272398	+	0.0471806i
$894$		0			0
$895$	−4.28010	−	7.41335i	−0.143068	−	0.247801i
$896$	−0.915692	+	0.528675i	−0.0305911	+	0.0176618i
$897$		0			0
$898$	3.49734	+	2.01919i	0.116708	+	0.0673813i
$899$	−44.6990			−1.49080
$900$		0			0
$901$			0.141235i			0.00470523i
$902$	−4.07080	−	6.10831i	−0.135543	−	0.203384i
$903$		0			0
$904$	11.8462	−	6.83942i	0.394000	−	0.227476i
$905$	11.7536	−	6.78594i	0.390703	−	0.225572i
$906$		0			0
$907$	−18.0827	+	31.3201i	−0.600425	+	1.03997i	0.392331	+	0.919824i	$0.371669\pi$
$907$	−18.0827	+	31.3201i	−0.600425	+	1.03997i	−0.992757	+	0.120143i	$0.961665\pi$
$908$	12.2587			0.406818
$909$		0			0
$910$			5.29522i			0.175535i
$911$	−7.17296	−	4.14131i	−0.237651	−	0.137208i	0.376446	−	0.926439i	$-0.377146\pi$
$911$	−7.17296	−	4.14131i	−0.237651	−	0.137208i	−0.614097	+	0.789231i	$0.710479\pi$
$912$		0			0
$913$	−10.9594	+	0.705044i	−0.362703	+	0.0233335i
$914$	34.4097	−	19.8664i	1.13817	−	0.657123i
$915$		0			0
$916$	9.63480	−	16.6880i	0.318343	−	0.551386i
$917$		−	10.7752i		−	0.355828i
$918$		0			0
$919$			7.65289i			0.252446i	0.992002	+	0.126223i	$0.0402854\pi$
$919$			7.65289i			0.252446i	−0.992002	+	0.126223i	$0.959715\pi$
$920$	2.61194	−	4.52401i	0.0861131	−	0.149152i
$921$		0			0
$922$	12.3436	+	21.3798i	0.406516	+	0.704106i
$923$	−12.6060	−	21.8343i	−0.414933	−	0.718684i
$924$		0			0
$925$	2.99127	−	5.18103i	0.0983524	−	0.170351i
$926$	14.8529			0.488097
$927$		0			0
$928$	6.65431			0.218438
$929$	22.3193	+	12.8861i	0.732274	+	0.422778i	0.819253	−	0.573432i	$-0.194388\pi$
$929$	22.3193	+	12.8861i	0.732274	+	0.422778i	−0.0869797	+	0.996210i	$0.527722\pi$
$930$		0			0
$931$	−7.06365	+	4.07820i	−0.231502	+	0.133658i
$932$	−11.7677	−	20.3823i	−0.385465	−	0.667645i
$933$		0			0
$934$	−15.5382	−	8.97099i	−0.508426	−	0.293540i
$935$	−12.1336	−	6.00184i	−0.396812	−	0.196281i
$936$		0			0
$937$		−	25.7244i		−	0.840380i	−0.907436	−	0.420190i	$-0.861963\pi$
$937$		−	25.7244i		−	0.840380i	0.907436	−	0.420190i	$-0.138037\pi$
$938$	7.72704	+	4.46121i	0.252297	+	0.145664i
$939$		0			0
$940$	0.587024	+	1.01676i	0.0191466	+	0.0331629i
$941$	20.6037	+	35.6867i	0.671663	+	1.16335i	0.977432	+	0.211249i	$0.0677530\pi$
$941$	20.6037	+	35.6867i	0.671663	+	1.16335i	−0.305769	+	0.952106i	$0.598914\pi$
$942$		0			0
$943$	10.0127	+	5.78085i	0.326059	+	0.188250i
$944$			10.8708i			0.353815i
$945$		0			0
$946$	−9.79494	−	4.84502i	−0.318461	−	0.157525i
$947$	−39.6156	−	22.8721i	−1.28733	−	0.743242i	−0.309156	−	0.951011i	$-0.600046\pi$
$947$	−39.6156	−	22.8721i	−1.28733	−	0.743242i	−0.978178	+	0.207769i	$0.933380\pi$
$948$		0			0
$949$	32.2757	+	55.9032i	1.04772	+	1.81470i
$950$	1.20089	−	0.693335i	0.0389620	−	0.0224947i
$951$		0			0
$952$	−3.73742	−	2.15780i	−0.121130	−	0.0699347i
$953$	−48.5152			−1.57156			−0.785781	−	0.618505i	$-0.787739\pi$
$953$	−48.5152			−1.57156			−0.785781	+	0.618505i	$0.787739\pi$
$954$		0			0
$955$	0.748369			0.0242166
$956$	−0.402515	+	0.697176i	−0.0130183	+	0.0225483i
$957$		0			0
$958$	−16.3488	−	28.3170i	−0.528207	−	0.914881i
$959$	8.56972	+	14.8432i	0.276731	+	0.479312i
$960$		0			0
$961$	−7.06108	+	12.2302i	−0.227777	+	0.394521i
$962$			29.9606i			0.965969i
$963$		0			0
$964$			25.4130i			0.818499i
$965$	6.26848	−	10.8573i	0.201790	−	0.349510i
$966$		0			0
$967$	−6.60473	+	3.81324i	−0.212394	+	0.122626i	−0.602423	−	0.798177i	$-0.705798\pi$
$967$	−6.60473	+	3.81324i	−0.212394	+	0.122626i	0.390030	+	0.920802i	$0.372465\pi$
$968$	−4.23402	+	10.1525i	−0.136086	+	0.326313i
$969$		0			0
$970$	−4.78632	−	2.76338i	−0.153679	−	0.0887268i
$971$		−	49.9776i		−	1.60386i	−0.597419	−	0.801929i	$-0.703807\pi$
$971$		−	49.9776i		−	1.60386i	0.597419	−	0.801929i	$-0.296193\pi$
$972$		0			0
$973$	12.6501			0.405543
$974$	20.5805	−	35.6464i	0.659441	−	1.14219i
$975$		0			0
$976$	3.91068	−	2.25783i	0.125178	−	0.0722715i
$977$	−52.6085	+	30.3735i	−1.68310	+	0.971736i	−0.723512	+	0.690312i	$0.757473\pi$
$977$	−52.6085	+	30.3735i	−1.68310	+	0.971736i	−0.959584	+	0.281424i	$0.909193\pi$
$978$		0			0
$979$	−10.2443	+	6.82715i	−0.327408	+	0.218197i
$980$			5.88201i			0.187894i
$981$		0			0
$982$	39.3041			1.25424
$983$	7.03999	+	4.06454i	0.224541	+	0.129639i	0.608051	−	0.793898i	$-0.291952\pi$
$983$	7.03999	+	4.06454i	0.224541	+	0.129639i	−0.383510	+	0.923537i	$0.625285\pi$
$984$		0			0
$985$	−1.78426	+	1.03014i	−0.0568513	+	0.0328231i
$986$	13.5798	+	23.5210i	0.432470	+	0.749061i
$987$		0			0
$988$	−3.47223	+	6.01407i	−0.110466	+	0.191333i
$989$	17.2118			0.547303
$990$		0			0
$991$	−24.1067			−0.765775			−0.382887	−	0.923795i	$-0.625070\pi$
$991$	−24.1067			−0.765775			−0.382887	+	0.923795i	$0.625070\pi$
$992$	3.35865	−	5.81736i	0.106637	−	0.184701i
$993$		0			0
$994$	2.66154	+	4.60992i	0.0844188	+	0.146218i
$995$	17.0690	−	9.85479i	0.541123	−	0.312418i
$996$		0			0
$997$	32.0996	+	18.5327i	1.01661	+	0.586937i	0.913119	−	0.407693i	$-0.133667\pi$
$997$	32.0996	+	18.5327i	1.01661	+	0.586937i	0.103487	+	0.994631i	$0.467000\pi$
$998$	39.9935			1.26597
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2970.2.t.a.791.20		48
3.2	odd	2		990.2.t.b.461.24	yes	48
9.4	even	3		990.2.t.a.131.24	✓	48
9.5	odd	6		2970.2.t.b.2771.20		48
11.10	odd	2		2970.2.t.b.791.20		48
33.32	even	2		990.2.t.a.461.24	yes	48
99.32	even	6	inner	2970.2.t.a.2771.20		48
99.76	odd	6		990.2.t.b.131.24	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.24	✓	48	9.4	even	3
990.2.t.a.461.24	yes	48	33.32	even	2
990.2.t.b.131.24	yes	48	99.76	odd	6
990.2.t.b.461.24	yes	48	3.2	odd	2
2970.2.t.a.791.20		48	1.1	even	1	trivial
2970.2.t.a.2771.20		48	99.32	even	6	inner
2970.2.t.b.791.20		48	11.10	odd	2
2970.2.t.b.2771.20		48	9.5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2970 = 2 \cdot 3^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2970.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.915692 + 0.528675i) q^{7} +1.00000 q^{8} +1.00000i q^{10} +(1.83929 + 2.75989i) q^{11} +(4.33706 - 2.50400i) q^{13} +(-0.915692 + 0.528675i) q^{14} +(-0.500000 + 0.866025i) q^{16} -4.08152 q^{17} -1.38667i q^{19} +(-0.866025 - 0.500000i) q^{20} +(-3.30978 + 0.212926i) q^{22} +(4.52401 - 2.61194i) q^{23} +(0.500000 - 0.866025i) q^{25} +5.00801i q^{26} -1.05735i q^{28} +(-3.32715 + 5.76280i) q^{29} +(3.35865 + 5.81736i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.04076 - 3.53470i) q^{34} +1.05735 q^{35} +5.98254 q^{37} +(1.20089 + 0.693335i) q^{38} +(0.866025 - 0.500000i) q^{40} +(1.10662 + 1.91672i) q^{41} +(2.85341 + 1.64742i) q^{43} +(1.47049 - 2.97282i) q^{44} +5.22388i q^{46} +(-1.01676 - 0.587024i) q^{47} +(-2.94100 - 5.09397i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-4.33706 - 2.50400i) q^{52} -0.0346036i q^{53} +(2.97282 + 1.47049i) q^{55} +(0.915692 + 0.528675i) q^{56} +(-3.32715 - 5.76280i) q^{58} +(9.41442 - 5.43542i) q^{59} +(-3.91068 - 2.25783i) q^{61} -6.71730 q^{62} +1.00000 q^{64} +(2.50400 - 4.33706i) q^{65} +(-4.21923 - 7.30793i) q^{67} +(2.04076 + 3.53470i) q^{68} +(-0.528675 + 0.915692i) q^{70} -5.03435i q^{71} +12.8897i q^{73} +(-2.99127 + 5.18103i) q^{74} +(-1.20089 + 0.693335i) q^{76} +(0.225138 + 3.49960i) q^{77} +(-8.56074 - 4.94255i) q^{79} +1.00000i q^{80} -2.21324 q^{82} +(-1.65561 + 2.86759i) q^{83} +(-3.53470 + 2.04076i) q^{85} +(-2.85341 + 1.64742i) q^{86} +(1.83929 + 2.75989i) q^{88} +3.71184i q^{89} +5.29522 q^{91} +(-4.52401 - 2.61194i) q^{92} +(1.01676 - 0.587024i) q^{94} +(-0.693335 - 1.20089i) q^{95} +(-2.76338 + 4.78632i) q^{97} +5.88201 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8} + 12 q^{11} - 24 q^{13} - 24 q^{16} - 12 q^{17} - 6 q^{22} - 36 q^{23} + 24 q^{25} - 24 q^{32} + 6 q^{34} + 6 q^{38} - 6 q^{41} - 30 q^{43} - 6 q^{44} + 24 q^{49} + 24 q^{50}+ \cdots - 48 q^{98}+O(q^{100}) \) 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8 + 12 * q^11 - 24 * q^13 - 24 * q^16 - 12 * q^17 - 6 * q^22 - 36 * q^23 + 24 * q^25 - 24 * q^32 + 6 * q^34 + 6 * q^38 - 6 * q^41 - 30 * q^43 - 6 * q^44 + 24 * q^49 + 24 * q^50 + 24 * q^52 + 54 * q^59 + 48 * q^64 - 6 * q^67 + 6 * q^68 - 6 * q^76 + 18 * q^77 + 12 * q^82 + 36 * q^83 + 30 * q^86 + 12 * q^88 + 24 * q^91 + 36 * q^92 + 6 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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