LMFDB - Embedded newform 360.2.q.d.241.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(121,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("360.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			241.3
Root			$-1.62241 - 0.606458i$ of defining polynomial
Character	$\chi$	$=$	360.241
Dual form			360.2.q.d.121.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.62241 + 0.606458i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(2.62241 - 4.54214i) q^{7} +(2.26442 + 1.96784i) q^{9} +(-1.33641 + 2.31473i) q^{11} +(-1.90841 - 3.30545i) q^{13} +(-0.285997 - 1.70828i) q^{15} +3.52884 q^{17} -4.67282 q^{19} +(7.00924 - 5.77883i) q^{21} +(2.47842 + 4.29275i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(2.48040 + 4.56592i) q^{27} +(0.928007 - 1.60735i) q^{29} +(4.33641 + 7.51089i) q^{31} +(-3.57199 + 2.94497i) q^{33} -5.24482 q^{35} -2.67282 q^{37} +(-1.09159 - 6.52016i) q^{39} +(1.83641 + 3.18076i) q^{41} +(-1.76442 + 3.05606i) q^{43} +(0.571993 - 2.94497i) q^{45} +(-4.63164 + 8.02224i) q^{47} +(-10.2541 - 17.7605i) q^{49} +(5.72522 + 2.14009i) q^{51} -2.85601 q^{53} +2.67282 q^{55} +(-7.58123 - 2.83387i) q^{57} +(-2.10083 - 3.63875i) q^{59} +(3.98040 - 6.89425i) q^{61} +(14.8765 - 5.12483i) q^{63} +(-1.90841 + 3.30545i) q^{65} +(0.429983 + 0.744753i) q^{67} +(1.41764 + 8.46766i) q^{69} -15.1625 q^{71} +6.28797 q^{73} +(-1.33641 + 1.10182i) q^{75} +(7.00924 + 12.1404i) q^{77} +(-2.81681 + 4.87886i) q^{79} +(1.25518 + 8.91204i) q^{81} +(1.94958 - 3.37678i) q^{83} +(-1.76442 - 3.05606i) q^{85} +(2.48040 - 2.04499i) q^{87} -11.0000 q^{89} -20.0185 q^{91} +(2.48040 + 14.8156i) q^{93} +(2.33641 + 4.04678i) q^{95} +(1.91764 - 3.32145i) q^{97} +(-7.58123 + 2.61168i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} - 3 q^{5} + 5 q^{7} + 5 q^{9} + 2 q^{11} - q^{15} + 4 q^{17} - 8 q^{19} + 12 q^{21} + 7 q^{23} - 3 q^{25} + 2 q^{27} + 7 q^{29} + 16 q^{31} - 20 q^{33} - 10 q^{35} + 4 q^{37} - 18 q^{39} + q^{41}+ \cdots - 14 q^{99}+O(q^{100}) $ 6 * q - q^3 - 3 * q^5 + 5 * q^7 + 5 * q^9 + 2 * q^11 - q^15 + 4 * q^17 - 8 * q^19 + 12 * q^21 + 7 * q^23 - 3 * q^25 + 2 * q^27 + 7 * q^29 + 16 * q^31 - 20 * q^33 - 10 * q^35 + 4 * q^37 - 18 * q^39 + q^41 - 2 * q^43 + 2 * q^45 + 13 * q^47 - 10 * q^49 - 20 * q^53 - 4 * q^55 - 14 * q^57 + 6 * q^59 + 11 * q^61 + 27 * q^63 - q^67 - 33 * q^69 - 28 * q^71 + 32 * q^73 + 2 * q^75 + 12 * q^77 + 6 * q^79 + 29 * q^81 + 21 * q^83 - 2 * q^85 + 2 * q^87 - 66 * q^89 - 60 * q^91 + 2 * q^93 + 4 * q^95 - 30 * q^97 - 14 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.62241	+	0.606458i	0.936698	+	0.350138i
$3$	1.62241	+	0.606458i	0.936698	+	0.350138i
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	2.62241	−	4.54214i	0.991177	−	1.71677i	0.380803	−	0.924656i	$-0.375648\pi$
$7$	2.62241	−	4.54214i	0.991177	−	1.71677i	0.610374	−	0.792113i	$-0.291019\pi$
$8$		0			0
$9$	2.26442	+	1.96784i	0.754806	+	0.655948i
$10$		0			0
$11$	−1.33641	+	2.31473i	−0.402943	+	0.697918i	−0.994080	−	0.108653i	$-0.965346\pi$
$11$	−1.33641	+	2.31473i	−0.402943	+	0.697918i	0.591136	+	0.806572i	$0.298679\pi$
$12$		0			0
$13$	−1.90841	−	3.30545i	−0.529296	−	0.916768i	−0.999416	−	0.0341656i	$-0.989123\pi$
$13$	−1.90841	−	3.30545i	−0.529296	−	0.916768i	0.470120	−	0.882603i	$-0.344211\pi$
$14$		0			0
$15$	−0.285997	−	1.70828i	−0.0738440	−	0.441075i
$16$		0			0
$17$	3.52884			0.855869			0.427934	−	0.903810i	$-0.359241\pi$
$17$	3.52884			0.855869			0.427934	+	0.903810i	$0.359241\pi$
$18$		0			0
$19$	−4.67282			−1.07202			−0.536010	−	0.844212i	$-0.680069\pi$
$19$	−4.67282			−1.07202			−0.536010	+	0.844212i	$0.680069\pi$
$20$		0			0
$21$	7.00924	−	5.77883i	1.52954	−	1.26105i
$22$		0			0
$23$	2.47842	+	4.29275i	0.516787	+	0.895101i	0.999810	+	0.0194933i	$0.00620531\pi$
$23$	2.47842	+	4.29275i	0.516787	+	0.895101i	−0.483023	+	0.875608i	$0.660461\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	2.48040	+	4.56592i	0.477353	+	0.878712i
$28$		0			0
$29$	0.928007	−	1.60735i	0.172327	−	0.298478i	−0.766906	−	0.641759i	$-0.778205\pi$
$29$	0.928007	−	1.60735i	0.172327	−	0.298478i	0.939233	+	0.343281i	$0.111538\pi$
$30$		0			0
$31$	4.33641	+	7.51089i	0.778843	+	1.34899i	0.932609	+	0.360888i	$0.117526\pi$
$31$	4.33641	+	7.51089i	0.778843	+	1.34899i	−0.153767	+	0.988107i	$0.549140\pi$
$32$		0			0
$33$	−3.57199	+	2.94497i	−0.621804	+	0.512653i
$34$		0			0
$35$	−5.24482			−0.886536
$36$		0			0
$37$	−2.67282			−0.439410			−0.219705	−	0.975566i	$-0.570509\pi$
$37$	−2.67282			−0.439410			−0.219705	+	0.975566i	$0.570509\pi$
$38$		0			0
$39$	−1.09159	−	6.52016i	−0.174795	−	1.04406i
$40$		0			0
$41$	1.83641	+	3.18076i	0.286799	+	0.496751i	0.973044	−	0.230620i	$-0.0740754\pi$
$41$	1.83641	+	3.18076i	0.286799	+	0.496751i	−0.686245	+	0.727371i	$0.740742\pi$
$42$		0			0
$43$	−1.76442	+	3.05606i	−0.269071	+	0.466045i	−0.968622	−	0.248538i	$-0.920050\pi$
$43$	−1.76442	+	3.05606i	−0.269071	+	0.466045i	0.699551	+	0.714583i	$0.253383\pi$
$44$		0			0
$45$	0.571993	−	2.94497i	0.0852677	−	0.439010i
$46$		0			0
$47$	−4.63164	+	8.02224i	−0.675595	+	1.17016i	0.300700	+	0.953719i	$0.402780\pi$
$47$	−4.63164	+	8.02224i	−0.675595	+	1.17016i	−0.976295	+	0.216446i	$0.930554\pi$
$48$		0			0
$49$	−10.2541	−	17.7605i	−1.46486	−	2.53722i
$50$		0			0
$51$	5.72522	+	2.14009i	0.801691	+	0.299673i
$52$		0			0
$53$	−2.85601			−0.392304			−0.196152	−	0.980574i	$-0.562845\pi$
$53$	−2.85601			−0.392304			−0.196152	+	0.980574i	$0.562845\pi$
$54$		0			0
$55$	2.67282			0.360403
$56$		0			0
$57$	−7.58123	−	2.83387i	−1.00416	−	0.375355i
$58$		0			0
$59$	−2.10083	−	3.63875i	−0.273505	−	0.473724i	0.696252	−	0.717797i	$-0.254850\pi$
$59$	−2.10083	−	3.63875i	−0.273505	−	0.473724i	−0.969757	+	0.244073i	$0.921516\pi$
$60$		0			0
$61$	3.98040	−	6.89425i	0.509638	−	0.882719i	−0.490300	−	0.871554i	$-0.663113\pi$
$61$	3.98040	−	6.89425i	0.509638	−	0.882719i	0.999938	−	0.0111647i	$-0.00355392\pi$
$62$		0			0
$63$	14.8765	−	5.12483i	1.87426	−	0.645668i
$64$		0			0
$65$	−1.90841	+	3.30545i	−0.236709	+	0.409991i
$66$		0			0
$67$	0.429983	+	0.744753i	0.0525308	+	0.0909860i	0.891095	−	0.453817i	$-0.149938\pi$
$67$	0.429983	+	0.744753i	0.0525308	+	0.0909860i	−0.838564	+	0.544803i	$0.816605\pi$
$68$		0			0
$69$	1.41764	+	8.46766i	0.170664	+	1.01939i
$70$		0			0
$71$	−15.1625			−1.79945			−0.899726	−	0.436454i	$-0.856234\pi$
$71$	−15.1625			−1.79945			−0.899726	+	0.436454i	$0.856234\pi$
$72$		0			0
$73$	6.28797			0.735952			0.367976	−	0.929835i	$-0.380051\pi$
$73$	6.28797			0.735952			0.367976	+	0.929835i	$0.380051\pi$
$74$		0			0
$75$	−1.33641	+	1.10182i	−0.154316	+	0.127227i
$76$		0			0
$77$	7.00924	+	12.1404i	0.798777	+	1.38352i
$78$		0			0
$79$	−2.81681	+	4.87886i	−0.316916	+	0.548914i	−0.979843	−	0.199770i	$-0.935981\pi$
$79$	−2.81681	+	4.87886i	−0.316916	+	0.548914i	0.662927	+	0.748684i	$0.269314\pi$
$80$		0			0
$81$	1.25518	+	8.91204i	0.139465	+	0.990227i
$82$		0			0
$83$	1.94958	−	3.37678i	0.213995	−	0.370650i	−0.738966	−	0.673742i	$-0.764686\pi$
$83$	1.94958	−	3.37678i	0.213995	−	0.370650i	0.952961	+	0.303093i	$0.0980191\pi$
$84$		0			0
$85$	−1.76442	−	3.05606i	−0.191378	−	0.331477i
$86$		0			0
$87$	2.48040	−	2.04499i	0.265927	−	0.219246i
$88$		0			0
$89$	−11.0000			−1.16600			−0.582999	−	0.812473i	$-0.698121\pi$
$89$	−11.0000			−1.16600			−0.582999	+	0.812473i	$0.698121\pi$
$90$		0			0
$91$	−20.0185			−2.09851
$92$		0			0
$93$	2.48040	+	14.8156i	0.257205	+	1.53630i
$94$		0			0
$95$	2.33641	+	4.04678i	0.239711	+	0.415191i
$96$		0			0
$97$	1.91764	−	3.32145i	0.194707	−	0.337242i	−0.752097	−	0.659052i	$-0.770958\pi$
$97$	1.91764	−	3.32145i	0.194707	−	0.337242i	0.946804	+	0.321810i	$0.104291\pi$
$98$		0			0
$99$	−7.58123	+	2.61168i	−0.761942	+	0.262483i
$100$		0			0
$101$	5.24482	−	9.08429i	0.521879	−	0.903921i	−0.477797	−	0.878470i	$-0.658565\pi$
$101$	5.24482	−	9.08429i	0.521879	−	0.903921i	0.999676	−	0.0254505i	$-0.00810201\pi$
$102$		0			0
$103$	−2.05239	−	3.55485i	−0.202228	−	0.350269i	0.747018	−	0.664804i	$-0.231485\pi$
$103$	−2.05239	−	3.55485i	−0.202228	−	0.350269i	−0.949246	+	0.314534i	$0.898152\pi$
$104$		0			0
$105$	−8.50924	−	3.18076i	−0.830416	−	0.310410i
$106$		0			0
$107$	−19.7345			−1.90780			−0.953901	−	0.300122i	$-0.902972\pi$
$107$	−19.7345			−1.90780			−0.953901	+	0.300122i	$0.902972\pi$
$108$		0			0
$109$	−9.50811			−0.910711			−0.455356	−	0.890310i	$-0.650488\pi$
$109$	−9.50811			−0.910711			−0.455356	+	0.890310i	$0.650488\pi$
$110$		0			0
$111$	−4.33641	−	1.62095i	−0.411594	−	0.153854i
$112$		0			0
$113$	4.71598	+	8.16832i	0.443642	+	0.768411i	0.997957	−	0.0638967i	$-0.0203528\pi$
$113$	4.71598	+	8.16832i	0.443642	+	0.768411i	−0.554314	+	0.832307i	$0.687019\pi$
$114$		0			0
$115$	2.47842	−	4.29275i	0.231114	−	0.400301i
$116$		0			0
$117$	2.18319	−	11.2404i	0.201836	−	1.03917i
$118$		0			0
$119$	9.25405	−	16.0285i	0.848318	−	1.46933i
$120$		0			0
$121$	1.92801	+	3.33941i	0.175273	+	0.303582i
$122$		0			0
$123$	1.05042	+	6.27420i	0.0947128	+	0.565725i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	18.6089			1.65128			0.825638	−	0.564200i	$-0.190815\pi$
$127$	18.6089			1.65128			0.825638	+	0.564200i	$0.190815\pi$
$128$		0			0
$129$	−4.71598	+	3.88814i	−0.415219	+	0.342331i
$130$		0			0
$131$	7.67282	+	13.2897i	0.670378	+	1.16113i	0.977797	+	0.209554i	$0.0672012\pi$
$131$	7.67282	+	13.2897i	0.670378	+	1.16113i	−0.307419	+	0.951574i	$0.599465\pi$
$132$		0			0
$133$	−12.2541	+	21.2246i	−1.06256	+	1.84041i
$134$		0			0
$135$	2.71400	−	4.43105i	0.233584	−	0.381364i
$136$		0			0
$137$	−0.244817	+	0.424035i	−0.0209161	+	0.0362278i	−0.876294	−	0.481777i	$-0.839992\pi$
$137$	−0.244817	+	0.424035i	−0.0209161	+	0.0362278i	0.855378	+	0.518005i	$0.173325\pi$
$138$		0			0
$139$	5.34565	+	9.25893i	0.453412	+	0.785332i	0.998595	−	0.0529843i	$-0.0168733\pi$
$139$	5.34565	+	9.25893i	0.453412	+	0.785332i	−0.545183	+	0.838317i	$0.683540\pi$
$140$		0			0
$141$	−12.3796	+	10.2065i	−1.04255	+	0.859539i
$142$		0			0
$143$	10.2017			0.853106
$144$		0			0
$145$	−1.85601			−0.154134
$146$		0			0
$147$	−5.86525	−	35.0335i	−0.483758	−	2.88951i
$148$		0			0
$149$	−1.93724	−	3.35540i	−0.158705	−	0.274885i	0.775697	−	0.631106i	$-0.217399\pi$
$149$	−1.93724	−	3.35540i	−0.158705	−	0.274885i	−0.934402	+	0.356220i	$0.884065\pi$
$150$		0			0
$151$	7.33641	−	12.7070i	0.597029	−	1.03408i	−0.396228	−	0.918152i	$-0.629681\pi$
$151$	7.33641	−	12.7070i	0.597029	−	1.03408i	0.993257	−	0.115932i	$-0.0369855\pi$
$152$		0			0
$153$	7.99076	+	6.94420i	0.646015	+	0.561405i
$154$		0			0
$155$	4.33641	−	7.51089i	0.348309	−	0.603289i
$156$		0			0
$157$	6.59046	+	11.4150i	0.525976	+	0.911018i	0.999542	+	0.0302592i	$0.00963329\pi$
$157$	6.59046	+	11.4150i	0.525976	+	0.911018i	−0.473566	+	0.880758i	$0.657033\pi$
$158$		0			0
$159$	−4.63362	−	1.73205i	−0.367470	−	0.137361i
$160$		0			0
$161$	25.9977			2.04891
$162$		0			0
$163$	20.8745			1.63502			0.817508	−	0.575917i	$-0.195355\pi$
$163$	20.8745			1.63502			0.817508	+	0.575917i	$0.195355\pi$
$164$		0			0
$165$	4.33641	+	1.62095i	0.337589	+	0.126191i
$166$		0			0
$167$	−0.00197644	−	0.00342329i	−0.000152941	−	0.000264902i	0.865949	−	0.500132i	$-0.166715\pi$
$167$	−0.00197644	−	0.00342329i	−0.000152941	−	0.000264902i	−0.866102	+	0.499868i	$0.833382\pi$
$168$		0			0
$169$	−0.784020	+	1.35796i	−0.0603092	+	0.104459i
$170$		0			0
$171$	−10.5812	−	9.19539i	−0.809167	−	0.703189i
$172$		0			0
$173$	10.3064	−	17.8513i	0.783584	−	1.35721i	−0.146257	−	0.989247i	$-0.546723\pi$
$173$	10.3064	−	17.8513i	0.783584	−	1.35721i	0.929841	−	0.367961i	$-0.119944\pi$
$174$		0			0
$175$	2.62241	+	4.54214i	0.198235	+	0.343354i
$176$		0			0
$177$	−1.20166	−	7.17760i	−0.0903224	−	0.539501i
$178$		0			0
$179$	4.10478			0.306806			0.153403	−	0.988164i	$-0.450977\pi$
$179$	4.10478			0.306806			0.153403	+	0.988164i	$0.450977\pi$
$180$		0			0
$181$	−4.43196			−0.329425			−0.164712	−	0.986342i	$-0.552670\pi$
$181$	−4.43196			−0.329425			−0.164712	+	0.986342i	$0.552670\pi$
$182$		0			0
$183$	10.6389	−	8.77135i	0.786450	−	0.648397i
$184$		0			0
$185$	1.33641	+	2.31473i	0.0982550	+	0.170183i
$186$		0			0
$187$	−4.71598	+	8.16832i	−0.344867	+	0.597326i
$188$		0			0
$189$	27.2437	+	0.707378i	1.98169	+	0.0514542i
$190$		0			0
$191$	8.58123	−	14.8631i	0.620916	−	1.07546i	−0.368400	−	0.929668i	$-0.620094\pi$
$191$	8.58123	−	14.8631i	0.620916	−	1.07546i	0.989316	−	0.145790i	$-0.0465725\pi$
$192$		0			0
$193$	−2.94761	−	5.10541i	−0.212173	−	0.367495i	0.740221	−	0.672364i	$-0.234721\pi$
$193$	−2.94761	−	5.10541i	−0.212173	−	0.367495i	−0.952394	+	0.304868i	$0.901388\pi$
$194$		0			0
$195$	−5.10083	+	4.20543i	−0.365278	+	0.301157i
$196$		0			0
$197$	−21.8353			−1.55570			−0.777850	−	0.628450i	$-0.783690\pi$
$197$	−21.8353			−1.55570			−0.777850	+	0.628450i	$0.783690\pi$
$198$		0			0
$199$	−13.2488			−0.939180			−0.469590	−	0.882885i	$-0.655598\pi$
$199$	−13.2488			−0.939180			−0.469590	+	0.882885i	$0.655598\pi$
$200$		0			0
$201$	0.245947	+	1.46906i	0.0173478	+	0.103619i
$202$		0			0
$203$	−4.86723	−	8.43028i	−0.341612	−	0.591690i
$204$		0			0
$205$	1.83641	−	3.18076i	0.128261	−	0.222154i
$206$		0			0
$207$	−2.83528	+	14.5977i	−0.197066	+	1.01461i
$208$		0			0
$209$	6.24482	−	10.8163i	0.431963	−	0.748182i
$210$		0			0
$211$	−0.192425	−	0.333290i	−0.0132471	−	0.0229447i	0.859326	−	0.511428i	$-0.170883\pi$
$211$	−0.192425	−	0.333290i	−0.0132471	−	0.0229447i	−0.872573	+	0.488484i	$0.837550\pi$
$212$		0			0
$213$	−24.5997	−	9.19539i	−1.68554	−	0.630057i
$214$		0			0
$215$	3.52884			0.240665
$216$		0			0
$217$	45.4874			3.08788
$218$		0			0
$219$	10.2017	+	3.81339i	0.689364	+	0.257685i
$220$		0			0
$221$	−6.73445	−	11.6644i	−0.453008	−	0.784633i
$222$		0			0
$223$	5.71400	−	9.89694i	0.382638	−	0.662748i	−0.608800	−	0.793323i	$-0.708349\pi$
$223$	5.71400	−	9.89694i	0.382638	−	0.662748i	0.991438	+	0.130575i	$0.0416823\pi$
$224$		0			0
$225$	−2.83641	+	0.977122i	−0.189094	+	0.0651415i
$226$		0			0
$227$	−8.97003	+	15.5366i	−0.595362	+	1.03120i	0.398134	+	0.917327i	$0.369658\pi$
$227$	−8.97003	+	15.5366i	−0.595362	+	1.03120i	−0.993496	+	0.113870i	$0.963675\pi$
$228$		0			0
$229$	2.45684	+	4.25538i	0.162353	+	0.281203i	0.935712	−	0.352765i	$-0.114758\pi$
$229$	2.45684	+	4.25538i	0.162353	+	0.281203i	−0.773359	+	0.633968i	$0.781425\pi$
$230$		0			0
$231$	4.00924	+	23.9474i	0.263788	+	1.57562i
$232$		0			0
$233$	4.59442			0.300990			0.150495	−	0.988611i	$-0.451913\pi$
$233$	4.59442			0.300990			0.150495	+	0.988611i	$0.451913\pi$
$234$		0			0
$235$	9.26329			0.604270
$236$		0			0
$237$	−7.52884	+	6.20723i	−0.489051	+	0.403203i
$238$		0			0
$239$	−13.1193	−	22.7233i	−0.848617	−	1.46985i	−0.882443	−	0.470420i	$-0.844102\pi$
$239$	−13.1193	−	22.7233i	−0.848617	−	1.46985i	0.0338255	−	0.999428i	$-0.489231\pi$
$240$		0			0
$241$	0.447608	−	0.775280i	0.0288330	−	0.0499402i	−0.851249	−	0.524762i	$-0.824154\pi$
$241$	0.447608	−	0.775280i	0.0288330	−	0.0499402i	0.880082	+	0.474822i	$0.157488\pi$
$242$		0			0
$243$	−3.36836	+	15.2202i	−0.216080	+	0.976376i
$244$		0			0
$245$	−10.2541	+	17.7605i	−0.655107	+	1.13468i
$246$		0			0
$247$	8.91764	+	15.4458i	0.567416	+	0.982793i
$248$		0			0
$249$	5.21090	−	4.29618i	0.330227	−	0.272259i
$250$		0			0
$251$	2.10478			0.132853			0.0664264	−	0.997791i	$-0.478840\pi$
$251$	2.10478			0.132853			0.0664264	+	0.997791i	$0.478840\pi$
$252$		0			0
$253$	−13.2488			−0.832943
$254$		0			0
$255$	−1.00924	−	6.02823i	−0.0632008	−	0.377502i
$256$		0			0
$257$	2.34565	+	4.06278i	0.146317	+	0.253429i	0.929864	−	0.367904i	$-0.119925\pi$
$257$	2.34565	+	4.06278i	0.146317	+	0.253429i	−0.783546	+	0.621333i	$0.786591\pi$
$258$		0			0
$259$	−7.00924	+	12.1404i	−0.435533	+	0.754365i
$260$		0			0
$261$	5.26442	−	1.81355i	0.325859	−	0.112256i
$262$		0			0
$263$	−4.90841	+	8.50161i	−0.302665	+	0.524232i	−0.976739	−	0.214433i	$-0.931210\pi$
$263$	−4.90841	+	8.50161i	−0.302665	+	0.524232i	0.674074	+	0.738664i	$0.264543\pi$
$264$		0			0
$265$	1.42801	+	2.47338i	0.0877218	+	0.151939i
$266$		0			0
$267$	−17.8465	−	6.67103i	−1.09219	−	0.408261i
$268$		0			0
$269$	20.4504			1.24688			0.623442	−	0.781869i	$-0.285734\pi$
$269$	20.4504			1.24688			0.623442	+	0.781869i	$0.285734\pi$
$270$		0			0
$271$	−5.03920			−0.306110			−0.153055	−	0.988218i	$-0.548911\pi$
$271$	−5.03920			−0.306110			−0.153055	+	0.988218i	$0.548911\pi$
$272$		0			0
$273$	−32.4781	−	12.1404i	−1.96567	−	0.734768i
$274$		0			0
$275$	−1.33641	−	2.31473i	−0.0805887	−	0.139584i
$276$		0			0
$277$	−0.523554	+	0.906823i	−0.0314573	+	0.0544857i	−0.881325	−	0.472510i	$-0.843348\pi$
$277$	−0.523554	+	0.906823i	−0.0314573	+	0.0544857i	0.849868	+	0.526995i	$0.176682\pi$
$278$		0			0
$279$	−4.96080	+	25.5412i	−0.296995	+	1.52911i
$280$		0			0
$281$	−0.879568	+	1.52346i	−0.0524706	+	0.0908818i	−0.891068	−	0.453870i	$-0.850043\pi$
$281$	−0.879568	+	1.52346i	−0.0524706	+	0.0908818i	0.838597	+	0.544752i	$0.183376\pi$
$282$		0			0
$283$	−1.43922	−	2.49280i	−0.0855527	−	0.148182i	0.820074	−	0.572258i	$-0.193932\pi$
$283$	−1.43922	−	2.49280i	−0.0855527	−	0.148182i	−0.905627	+	0.424076i	$0.860599\pi$
$284$		0			0
$285$	1.33641	+	7.98247i	0.0791622	+	0.472841i
$286$		0			0
$287$	19.2633			1.13708
$288$		0			0
$289$	−4.54731			−0.267489
$290$		0			0
$291$	5.12552	−	4.22578i	0.300463	−	0.247720i
$292$		0			0
$293$	−12.4557	−	21.5739i	−0.727671	−	1.26036i	−0.957865	−	0.287218i	$-0.907270\pi$
$293$	−12.4557	−	21.5739i	−0.727671	−	1.26036i	0.230195	−	0.973145i	$-0.426064\pi$
$294$		0			0
$295$	−2.10083	+	3.63875i	−0.122315	+	0.211856i
$296$		0			0
$297$	−13.8837	−	0.360489i	−0.805615	−	0.0209177i
$298$		0			0
$299$	9.45967	−	16.3846i	0.547067	−	0.947547i
$300$		0			0
$301$	9.25405	+	16.0285i	0.533395	+	0.923867i
$302$		0			0
$303$	14.0185	−	11.5577i	0.805340	−	0.663971i
$304$		0			0
$305$	−7.96080			−0.455834
$306$		0			0
$307$	−1.32322			−0.0755203			−0.0377602	−	0.999287i	$-0.512022\pi$
$307$	−1.32322			−0.0755203			−0.0377602	+	0.999287i	$0.512022\pi$
$308$		0			0
$309$	−1.17395	−	7.01210i	−0.0667839	−	0.398905i
$310$		0			0
$311$	−2.47645	−	4.28933i	−0.140426	−	0.243226i	0.787231	−	0.616658i	$-0.211514\pi$
$311$	−2.47645	−	4.28933i	−0.140426	−	0.243226i	−0.927657	+	0.373433i	$0.878181\pi$
$312$		0			0
$313$	−4.80757	+	8.32696i	−0.271740	+	0.470668i	−0.969308	−	0.245851i	$-0.920932\pi$
$313$	−4.80757	+	8.32696i	−0.271740	+	0.470668i	0.697567	+	0.716519i	$0.254266\pi$
$314$		0			0
$315$	−11.8765	−	10.3210i	−0.669163	−	0.581521i
$316$		0			0
$317$	6.15322	−	10.6577i	0.345599	−	0.598596i	−0.639863	−	0.768489i	$-0.721009\pi$
$317$	6.15322	−	10.6577i	0.345599	−	0.598596i	0.985462	+	0.169893i	$0.0543423\pi$
$318$		0			0
$319$	2.48040	+	4.29618i	0.138876	+	0.240540i
$320$		0			0
$321$	−32.0173	−	11.9681i	−1.78703	−	0.667995i
$322$		0			0
$323$	−16.4896			−0.917508
$324$		0			0
$325$	3.81681			0.211719
$326$		0			0
$327$	−15.4260	−	5.76626i	−0.853061	−	0.318875i
$328$		0			0
$329$	24.2921	+	42.0752i	1.33927	+	2.31968i
$330$		0			0
$331$	−0.773654	+	1.34001i	−0.0425239	+	0.0736535i	−0.886504	−	0.462721i	$-0.846873\pi$
$331$	−0.773654	+	1.34001i	−0.0425239	+	0.0736535i	0.843980	+	0.536374i	$0.180207\pi$
$332$		0			0
$333$	−6.05239	−	5.25970i	−0.331669	−	0.288230i
$334$		0			0
$335$	0.429983	−	0.744753i	0.0234925	−	0.0406902i
$336$		0			0
$337$	−16.1585	−	27.9874i	−0.880210	−	1.52457i	−0.851107	−	0.524992i	$-0.824068\pi$
$337$	−16.1585	−	27.9874i	−0.880210	−	1.52457i	−0.0291025	−	0.999576i	$-0.509265\pi$
$338$		0			0
$339$	2.69751	+	16.1124i	0.146509	+	0.875105i
$340$		0			0
$341$	−23.1809			−1.25532
$342$		0			0
$343$	−70.8475			−3.82541
$344$		0			0
$345$	6.62438	−	5.46154i	0.356645	−	0.294039i
$346$		0			0
$347$	12.5420	+	21.7234i	0.673291	+	1.16617i	0.976965	+	0.213399i	$0.0684533\pi$
$347$	12.5420	+	21.7234i	0.673291	+	1.16617i	−0.303674	+	0.952776i	$0.598213\pi$
$348$		0			0
$349$	−10.3745	+	17.9691i	−0.555333	+	0.961866i	0.442544	+	0.896747i	$0.354076\pi$
$349$	−10.3745	+	17.9691i	−0.555333	+	0.961866i	−0.997878	+	0.0651190i	$0.979257\pi$
$350$		0			0
$351$	10.3588	−	16.9125i	0.552914	−	0.902721i
$352$		0			0
$353$	9.05767	−	15.6884i	0.482091	−	0.835007i	−0.517697	−	0.855564i	$-0.673211\pi$
$353$	9.05767	−	15.6884i	0.482091	−	0.835007i	0.999789	+	0.0205571i	$0.00654399\pi$
$354$		0			0
$355$	7.58123	+	13.1311i	0.402370	+	0.696925i
$356$		0			0
$357$	24.7345	−	20.3926i	1.30909	−	1.07929i
$358$		0			0
$359$	25.3720			1.33908			0.669542	−	0.742774i	$-0.266490\pi$
$359$	25.3720			1.33908			0.669542	+	0.742774i	$0.266490\pi$
$360$		0			0
$361$	2.83528			0.149225
$362$		0			0
$363$	1.10281	+	6.58713i	0.0578823	+	0.345735i
$364$		0			0
$365$	−3.14399	−	5.44554i	−0.164564	−	0.285033i
$366$		0			0
$367$	−3.09159	+	5.35480i	−0.161380	+	0.279518i	−0.935364	−	0.353687i	$-0.884928\pi$
$367$	−3.09159	+	5.35480i	−0.161380	+	0.279518i	0.773984	+	0.633205i	$0.218261\pi$
$368$		0			0
$369$	−2.10083	+	10.8163i	−0.109365	+	0.563076i
$370$		0			0
$371$	−7.48963	+	12.9724i	−0.388842	+	0.673495i
$372$		0			0
$373$	8.40727	+	14.5618i	0.435312	+	0.753983i	0.997321	−	0.0731484i	$-0.0233047\pi$
$373$	8.40727	+	14.5618i	0.435312	+	0.753983i	−0.562009	+	0.827131i	$0.689971\pi$
$374$		0			0
$375$	1.62241	+	0.606458i	0.0837808	+	0.0313173i
$376$		0			0
$377$	−7.08405			−0.364847
$378$		0			0
$379$	22.0000			1.13006			0.565032	−	0.825069i	$-0.308864\pi$
$379$	22.0000			1.13006			0.565032	+	0.825069i	$0.308864\pi$
$380$		0			0
$381$	30.1913	+	11.2855i	1.54675	+	0.578175i
$382$		0			0
$383$	3.39804	+	5.88558i	0.173632	+	0.300739i	0.939687	−	0.342036i	$-0.111116\pi$
$383$	3.39804	+	5.88558i	0.173632	+	0.300739i	−0.766055	+	0.642775i	$0.777783\pi$
$384$		0			0
$385$	7.00924	−	12.1404i	0.357224	−	0.618730i
$386$		0			0
$387$	−10.0092	+	3.44811i	−0.508798	+	0.175277i
$388$		0			0
$389$	4.30757	−	7.46094i	0.218403	−	0.378285i	−0.735917	−	0.677072i	$-0.763249\pi$
$389$	4.30757	−	7.46094i	0.218403	−	0.378285i	0.954320	+	0.298787i	$0.0965820\pi$
$390$		0			0
$391$	8.74595	+	15.1484i	0.442302	+	0.766089i
$392$		0			0
$393$	4.38880	+	26.2146i	0.221386	+	1.32235i
$394$		0			0
$395$	5.63362			0.283458
$396$		0			0
$397$	22.4033			1.12439			0.562195	−	0.827005i	$-0.309957\pi$
$397$	22.4033			1.12439			0.562195	+	0.827005i	$0.309957\pi$
$398$		0			0
$399$	−32.7529	+	27.0035i	−1.63970	+	1.35186i
$400$		0			0
$401$	−6.95684	−	12.0496i	−0.347408	−	0.601729i	0.638380	−	0.769721i	$-0.279605\pi$
$401$	−6.95684	−	12.0496i	−0.347408	−	0.601729i	−0.985788	+	0.167993i	$0.946272\pi$
$402$		0			0
$403$	16.5513	−	28.6676i	0.824477	−	1.42804i
$404$		0			0
$405$	7.09046	−	5.54304i	0.352328	−	0.275436i
$406$		0			0
$407$	3.57199	−	6.18687i	0.177057	−	0.306672i
$408$		0			0
$409$	−15.3064	−	26.5115i	−0.756855	−	1.31091i	−0.944447	−	0.328664i	$-0.893402\pi$
$409$	−15.3064	−	26.5115i	−0.756855	−	1.31091i	0.187592	−	0.982247i	$-0.439932\pi$
$410$		0			0
$411$	−0.654353	+	0.539488i	−0.0322768	+	0.0266110i
$412$		0			0
$413$	−22.0369			−1.08437
$414$		0			0
$415$	−3.89917			−0.191403
$416$		0			0
$417$	3.05767	+	18.2637i	0.149735	+	0.894376i
$418$		0			0
$419$	6.86525	+	11.8910i	0.335389	+	0.580911i	0.983560	−	0.180584i	$-0.0577988\pi$
$419$	6.86525	+	11.8910i	0.335389	+	0.580911i	−0.648170	+	0.761496i	$0.724465\pi$
$420$		0			0
$421$	−7.96080	+	13.7885i	−0.387985	+	0.672011i	−0.992178	−	0.124827i	$-0.960162\pi$
$421$	−7.96080	+	13.7885i	−0.387985	+	0.672011i	0.604193	+	0.796838i	$0.293496\pi$
$422$		0			0
$423$	−26.2745	+	9.05136i	−1.27751	+	0.440092i
$424$		0			0
$425$	−1.76442	+	3.05606i	−0.0855869	+	0.148241i
$426$		0			0
$427$	−20.8765	−	36.1591i	−1.01028	−	1.74986i
$428$		0			0
$429$	16.5513	+	6.18687i	0.799102	+	0.298705i
$430$		0			0
$431$	−25.2672			−1.21708			−0.608540	−	0.793523i	$-0.708245\pi$
$431$	−25.2672			−1.21708			−0.608540	+	0.793523i	$0.708245\pi$
$432$		0			0
$433$	9.24086			0.444088			0.222044	−	0.975037i	$-0.428727\pi$
$433$	9.24086			0.444088			0.222044	+	0.975037i	$0.428727\pi$
$434$		0			0
$435$	−3.01121	−	1.12559i	−0.144377	−	0.0539681i
$436$		0			0
$437$	−11.5812	−	20.0593i	−0.554005	−	0.959565i
$438$		0			0
$439$	8.71598	−	15.0965i	0.415991	−	0.720518i	−0.579541	−	0.814943i	$-0.696768\pi$
$439$	8.71598	−	15.0965i	0.415991	−	0.720518i	0.995532	+	0.0944256i	$0.0301014\pi$
$440$		0			0
$441$	11.7305	−	60.3957i	0.558595	−	2.87598i
$442$		0			0
$443$	1.81483	−	3.14338i	0.0862254	−	0.149347i	−0.819687	−	0.572811i	$-0.805853\pi$
$443$	1.81483	−	3.14338i	0.0862254	−	0.149347i	0.905913	+	0.423464i	$0.139186\pi$
$444$		0			0
$445$	5.50000	+	9.52628i	0.260725	+	0.451589i
$446$		0			0
$447$	−1.10809	−	6.61869i	−0.0524108	−	0.313053i
$448$		0			0
$449$	−39.6785			−1.87254			−0.936271	−	0.351278i	$-0.885747\pi$
$449$	−39.6785			−1.87254			−0.936271	+	0.351278i	$0.885747\pi$
$450$		0			0
$451$	−9.81681			−0.462256
$452$		0			0
$453$	19.6089	−	16.1668i	0.921308	−	0.759582i
$454$		0			0
$455$	10.0092	+	17.3365i	0.469240	+	0.812748i
$456$		0			0
$457$	−2.84678	+	4.93076i	−0.133167	+	0.230651i	−0.924896	−	0.380221i	$-0.875848\pi$
$457$	−2.84678	+	4.93076i	−0.133167	+	0.230651i	0.791729	+	0.610873i	$0.209181\pi$
$458$		0			0
$459$	8.75292	+	16.1124i	0.408551	+	0.752062i
$460$		0			0
$461$	−8.65850	+	14.9970i	−0.403267	+	0.698479i	−0.994118	−	0.108302i	$-0.965459\pi$
$461$	−8.65850	+	14.9970i	−0.403267	+	0.698479i	0.590851	+	0.806780i	$0.298792\pi$
$462$		0			0
$463$	−12.8837	−	22.3153i	−0.598757	−	1.03708i	−0.993005	−	0.118074i	$-0.962328\pi$
$463$	−12.8837	−	22.3153i	−0.598757	−	1.03708i	0.394248	−	0.919004i	$-0.371005\pi$
$464$		0			0
$465$	11.5905	−	9.55588i	0.537495	−	0.443143i
$466$		0			0
$467$	−1.04711			−0.0484544			−0.0242272	−	0.999706i	$-0.507713\pi$
$467$	−1.04711			−0.0484544			−0.0242272	+	0.999706i	$0.507713\pi$
$468$		0			0
$469$	4.51037			0.208269
$470$		0			0
$471$	3.76970	+	22.5167i	0.173699	+	1.03751i
$472$		0			0
$473$	−4.71598	−	8.16832i	−0.216841	−	0.375580i
$474$		0			0
$475$	2.33641	−	4.04678i	0.107202	−	0.185679i
$476$		0			0
$477$	−6.46721	−	5.62019i	−0.296113	−	0.257331i
$478$		0			0
$479$	−11.2880	+	19.5513i	−0.515761	+	0.893324i	0.484072	+	0.875028i	$0.339157\pi$
$479$	−11.2880	+	19.5513i	−0.515761	+	0.893324i	−0.999833	+	0.0182955i	$0.994176\pi$
$480$		0			0
$481$	5.10083	+	8.83490i	0.232578	+	0.402837i
$482$		0			0
$483$	42.1790	+	15.7665i	1.91921	+	0.717402i
$484$		0			0
$485$	−3.83528			−0.174151
$486$		0			0
$487$	0.923855			0.0418638			0.0209319	−	0.999781i	$-0.493337\pi$
$487$	0.923855			0.0418638			0.0209319	+	0.999781i	$0.493337\pi$
$488$		0			0
$489$	33.8669	+	12.6595i	1.53152	+	0.572482i
$490$		0			0
$491$	−4.04316	−	7.00295i	−0.182465	−	0.316039i	0.760254	−	0.649626i	$-0.225074\pi$
$491$	−4.04316	−	7.00295i	−0.182465	−	0.316039i	−0.942719	+	0.333587i	$0.891741\pi$
$492$		0			0
$493$	3.27478	−	5.67209i	0.147489	−	0.255458i
$494$		0			0
$495$	6.05239	+	5.25970i	0.272035	+	0.236406i
$496$		0			0
$497$	−39.7622	+	68.8701i	−1.78358	+	3.08925i
$498$		0			0
$499$	6.34169	+	10.9841i	0.283893	+	0.491718i	0.972340	−	0.233569i	$-0.0750405\pi$
$499$	6.34169	+	10.9841i	0.283893	+	0.491718i	−0.688447	+	0.725287i	$0.741707\pi$
$500$		0			0
$501$	−0.00113051	−	0.00675261i	−5.05075e−5	−	0.000301684i
$502$		0			0
$503$	4.93837			0.220191			0.110096	−	0.993921i	$-0.464884\pi$
$503$	4.93837			0.220191			0.110096	+	0.993921i	$0.464884\pi$
$504$		0			0
$505$	−10.4896			−0.466783
$506$		0			0
$507$	−2.09555	+	1.72770i	−0.0930665	+	0.0767296i
$508$		0			0
$509$	−7.60478	−	13.1719i	−0.337076	−	0.583833i	0.646805	−	0.762655i	$-0.276105\pi$
$509$	−7.60478	−	13.1719i	−0.337076	−	0.583833i	−0.983881	+	0.178822i	$0.942771\pi$
$510$		0			0
$511$	16.4896	−	28.5609i	0.729458	−	1.26346i
$512$		0			0
$513$	−11.5905	−	21.3357i	−0.511732	−	0.941996i
$514$		0			0
$515$	−2.05239	+	3.55485i	−0.0904392	+	0.156645i
$516$		0			0
$517$	−12.3796	−	21.4420i	−0.544453	−	0.943020i
$518$		0			0
$519$	27.5473	−	22.7117i	1.20919	−	0.996931i
$520$		0			0
$521$	22.1809			0.971764			0.485882	−	0.874024i	$-0.338498\pi$
$521$	22.1809			0.971764			0.485882	+	0.874024i	$0.338498\pi$
$522$		0			0
$523$	−9.46495			−0.413873			−0.206937	−	0.978354i	$-0.566349\pi$
$523$	−9.46495			−0.413873			−0.206937	+	0.978354i	$0.566349\pi$
$524$		0			0
$525$	1.50000	+	8.95959i	0.0654654	+	0.391029i
$526$		0			0
$527$	15.3025	+	26.5047i	0.666587	+	1.15456i
$528$		0			0
$529$	−0.785151	+	1.35992i	−0.0341370	+	0.0591270i
$530$		0			0
$531$	2.40332	−	12.3737i	0.104295	−	0.536975i
$532$		0			0
$533$	7.00924	−	12.1404i	0.303604	−	0.525857i
$534$		0			0
$535$	9.86723	+	17.0905i	0.426597	+	0.738888i
$536$		0			0
$537$	6.65964	+	2.48938i	0.287384	+	0.107425i
$538$		0			0
$539$	54.8145			2.36103
$540$		0			0
$541$	−2.42405			−0.104218			−0.0521091	−	0.998641i	$-0.516594\pi$
$541$	−2.42405			−0.104218			−0.0521091	+	0.998641i	$0.516594\pi$
$542$		0			0
$543$	−7.19045	−	2.68780i	−0.308572	−	0.115344i
$544$		0			0
$545$	4.75405	+	8.23426i	0.203641	+	0.352717i
$546$		0			0
$547$	7.64088	−	13.2344i	0.326700	−	0.565862i	−0.655155	−	0.755495i	$-0.727397\pi$
$547$	7.64088	−	13.2344i	0.326700	−	0.565862i	0.981855	+	0.189633i	$0.0607299\pi$
$548$		0			0
$549$	22.5801	−	7.77867i	0.963695	−	0.331986i
$550$		0			0
$551$	−4.33641	+	7.51089i	−0.184737	+	0.319974i
$552$		0			0
$553$	14.7737	+	25.5887i	0.628240	+	1.08814i
$554$		0			0
$555$	0.764419	+	4.56592i	0.0324478	+	0.193813i
$556$		0			0
$557$	38.9793			1.65160			0.825802	−	0.563960i	$-0.190723\pi$
$557$	38.9793			1.65160			0.825802	+	0.563960i	$0.190723\pi$
$558$		0			0
$559$	13.4689			0.569674
$560$		0			0
$561$	−12.6050	+	10.3923i	−0.532183	+	0.438763i
$562$		0			0
$563$	2.30447	+	3.99146i	0.0971217	+	0.168220i	0.910492	−	0.413526i	$-0.135703\pi$
$563$	2.30447	+	3.99146i	0.0971217	+	0.168220i	−0.813370	+	0.581746i	$0.802370\pi$
$564$		0			0
$565$	4.71598	−	8.16832i	0.198403	−	0.343644i
$566$		0			0
$567$	43.7714	+	17.6698i	1.83823	+	0.742062i
$568$		0			0
$569$	−5.69129	+	9.85761i	−0.238591	+	0.413253i	−0.960310	−	0.278934i	$-0.910019\pi$
$569$	−5.69129	+	9.85761i	−0.238591	+	0.413253i	0.721719	+	0.692186i	$0.243352\pi$
$570$		0			0
$571$	−22.6129	−	39.1667i	−0.946320	−	1.63907i	−0.753087	−	0.657921i	$-0.771436\pi$
$571$	−22.6129	−	39.1667i	−0.946320	−	1.63907i	−0.193233	−	0.981153i	$-0.561897\pi$
$572$		0			0
$573$	22.9361	−	18.9099i	0.958170	−	0.789973i
$574$		0			0
$575$	−4.95684			−0.206715
$576$		0			0
$577$	5.14399			0.214147			0.107073	−	0.994251i	$-0.465852\pi$
$577$	5.14399			0.214147			0.107073	+	0.994251i	$0.465852\pi$
$578$		0			0
$579$	−1.68601	−	10.0707i	−0.0700683	−	0.418522i
$580$		0			0
$581$	−10.2252	−	17.7106i	−0.424213	−	0.734759i
$582$		0			0
$583$	3.81681	−	6.61091i	0.158076	−	0.273796i
$584$		0			0
$585$	−10.8260	+	3.72949i	−0.447602	+	0.154195i
$586$		0			0
$587$	21.6409	−	37.4831i	0.893215	−	1.54709i	0.0572160	−	0.998362i	$-0.481778\pi$
$587$	21.6409	−	37.4831i	0.893215	−	1.54709i	0.835999	−	0.548731i	$-0.184889\pi$
$588$		0			0
$589$	−20.2633	−	35.0970i	−0.834934	−	1.44615i
$590$		0			0
$591$	−35.4257	−	13.2422i	−1.45722	−	0.544710i
$592$		0			0
$593$	33.3641			1.37010			0.685050	−	0.728496i	$-0.259780\pi$
$593$	33.3641			1.37010			0.685050	+	0.728496i	$0.259780\pi$
$594$		0			0
$595$	−18.5081			−0.758758
$596$		0			0
$597$	−21.4949	−	8.03482i	−0.879728	−	0.328843i
$598$		0			0
$599$	−20.0577	−	34.7409i	−0.819534	−	1.41948i	−0.906026	−	0.423223i	$-0.860899\pi$
$599$	−20.0577	−	34.7409i	−0.819534	−	1.41948i	0.0864914	−	0.996253i	$-0.472434\pi$
$600$		0			0
$601$	2.98153	−	5.16416i	0.121619	−	0.210650i	−0.798787	−	0.601614i	$-0.794525\pi$
$601$	2.98153	−	5.16416i	0.121619	−	0.210650i	0.920406	+	0.390963i	$0.127858\pi$
$602$		0			0
$603$	−0.491895	+	2.53257i	−0.0200315	+	0.103134i
$604$		0			0
$605$	1.92801	−	3.33941i	0.0783846	−	0.135766i
$606$		0			0
$607$	7.57002	+	13.1117i	0.307258	+	0.532186i	0.977761	−	0.209720i	$-0.0672554\pi$
$607$	7.57002	+	13.1117i	0.307258	+	0.532186i	−0.670504	+	0.741906i	$0.733922\pi$
$608$		0			0
$609$	−2.78402	−	16.6291i	−0.112814	−	0.673846i
$610$		0			0
$611$	35.3562			1.43036
$612$		0			0
$613$	28.5081			1.15143			0.575716	−	0.817650i	$-0.304723\pi$
$613$	28.5081			1.15143			0.575716	+	0.817650i	$0.304723\pi$
$614$		0			0
$615$	4.90841	−	4.04678i	0.197926	−	0.163182i
$616$		0			0
$617$	−8.71598	−	15.0965i	−0.350892	−	0.607763i	0.635514	−	0.772089i	$-0.280788\pi$
$617$	−8.71598	−	15.0965i	−0.350892	−	0.607763i	−0.986406	+	0.164326i	$0.947455\pi$
$618$		0			0
$619$	−14.8260	+	25.6795i	−0.595909	+	1.03214i	0.397509	+	0.917598i	$0.369875\pi$
$619$	−14.8260	+	25.6795i	−0.595909	+	1.03214i	−0.993418	+	0.114546i	$0.963459\pi$
$620$		0			0
$621$	−13.4529	+	21.9640i	−0.539846	+	0.881385i
$622$		0			0
$623$	−28.8465	+	49.9636i	−1.15571	+	2.00175i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	16.6913	−	13.7613i	0.666586	−	0.549574i
$628$		0			0
$629$	−9.43196			−0.376077
$630$		0			0
$631$	−40.1233			−1.59728			−0.798641	−	0.601808i	$-0.794447\pi$
$631$	−40.1233			−1.59728			−0.798641	+	0.601808i	$0.794447\pi$
$632$		0			0
$633$	−0.110066	−	0.657431i	−0.00437473	−	0.0261305i
$634$		0			0
$635$	−9.30447	−	16.1158i	−0.369237	−	0.639536i
$636$		0			0
$637$	−39.1378	+	67.7886i	−1.55070	+	2.68588i
$638$		0			0
$639$	−34.3342	−	29.8373i	−1.35824	−	1.18035i
$640$		0			0
$641$	−2.20674	+	3.82219i	−0.0871612	+	0.150968i	−0.906310	−	0.422613i	$-0.861113\pi$
$641$	−2.20674	+	3.82219i	−0.0871612	+	0.150968i	0.819149	+	0.573581i	$0.194446\pi$
$642$		0			0
$643$	−9.91566	−	17.1744i	−0.391036	−	0.677294i	0.601551	−	0.798835i	$-0.294550\pi$
$643$	−9.91566	−	17.1744i	−0.391036	−	0.677294i	−0.992586	+	0.121541i	$0.961216\pi$
$644$		0			0
$645$	5.72522	+	2.14009i	0.225430	+	0.0842660i
$646$		0			0
$647$	−42.6873			−1.67821			−0.839106	−	0.543967i	$-0.816921\pi$
$647$	−42.6873			−1.67821			−0.839106	+	0.543967i	$0.816921\pi$
$648$		0			0
$649$	11.2303			0.440828
$650$		0			0
$651$	73.7991	+	27.5862i	2.89241	+	1.08119i
$652$		0			0
$653$	18.6821	+	32.3583i	0.731085	+	1.26628i	0.956420	+	0.291996i	$0.0943193\pi$
$653$	18.6821	+	32.3583i	0.731085	+	1.26628i	−0.225334	+	0.974282i	$0.572347\pi$
$654$		0			0
$655$	7.67282	−	13.2897i	0.299802	−	0.519272i
$656$		0			0
$657$	14.2386	+	12.3737i	0.555501	+	0.482746i
$658$		0			0
$659$	2.71598	−	4.70422i	0.105800	−	0.183250i	−0.808265	−	0.588819i	$-0.799593\pi$
$659$	2.71598	−	4.70422i	0.105800	−	0.183250i	0.914065	+	0.405569i	$0.132926\pi$
$660$		0			0
$661$	−8.54731	−	14.8044i	−0.332452	−	0.575823i	0.650540	−	0.759472i	$-0.274543\pi$
$661$	−8.54731	−	14.8044i	−0.332452	−	0.575823i	−0.982992	+	0.183648i	$0.941209\pi$
$662$		0			0
$663$	−3.85206	−	23.0086i	−0.149602	−	0.893580i
$664$		0			0
$665$	24.5081			0.950384
$666$		0			0
$667$	9.19997			0.356224
$668$		0			0
$669$	15.2725	−	12.5916i	0.590470	−	0.486819i
$670$		0			0
$671$	10.6389	+	18.4271i	0.410710	+	0.711371i
$672$		0			0
$673$	19.7005	−	34.1223i	0.759400	−	1.31532i	−0.183757	−	0.982972i	$-0.558826\pi$
$673$	19.7005	−	34.1223i	0.759400	−	1.31532i	0.943157	−	0.332347i	$-0.107841\pi$
$674$		0			0
$675$	−5.19440	−	0.134872i	−0.199933	−	0.00519122i
$676$		0			0
$677$	−6.13475	+	10.6257i	−0.235778	+	0.408379i	−0.959498	−	0.281714i	$-0.909097\pi$
$677$	−6.13475	+	10.6257i	−0.235778	+	0.408379i	0.723721	+	0.690093i	$0.242430\pi$
$678$		0			0
$679$	−10.0577	−	17.4204i	−0.385978	−	0.668534i
$680$		0			0
$681$	−23.9753	+	19.7667i	−0.918736	+	0.757461i
$682$		0			0
$683$	11.8952			0.455158			0.227579	−	0.973760i	$-0.426919\pi$
$683$	11.8952			0.455158			0.227579	+	0.973760i	$0.426919\pi$
$684$		0			0
$685$	0.489634			0.0187080
$686$		0			0
$687$	1.40530	+	8.39393i	0.0536155	+	0.320249i
$688$		0			0
$689$	5.45043	+	9.44042i	0.207645	+	0.359651i
$690$		0			0
$691$	2.63362	−	4.56156i	0.100188	−	0.173530i	−0.811574	−	0.584249i	$-0.801389\pi$
$691$	2.63362	−	4.56156i	0.100188	−	0.173530i	0.911762	+	0.410719i	$0.134722\pi$
$692$		0			0
$693$	−8.01847	+	41.2839i	−0.304597	+	1.56825i
$694$		0			0
$695$	5.34565	−	9.25893i	0.202772	−	0.351211i
$696$		0			0
$697$	6.48040	+	11.2244i	0.245463	+	0.425154i
$698$		0			0
$699$	7.45402	+	2.78632i	0.281937	+	0.105388i
$700$		0			0
$701$	−22.1131			−0.835200			−0.417600	−	0.908631i	$-0.637129\pi$
$701$	−22.1131			−0.835200			−0.417600	+	0.908631i	$0.637129\pi$
$702$		0			0
$703$	12.4896			0.471055
$704$		0			0
$705$	15.0288	+	5.61779i	0.566019	+	0.211578i
$706$		0			0
$707$	−27.5081	−	47.6454i	−1.03455	−	1.79189i
$708$		0			0
$709$	−8.70561	+	15.0786i	−0.326946	+	0.566287i	−0.981904	−	0.189378i	$-0.939353\pi$
$709$	−8.70561	+	15.0786i	−0.326946	+	0.566287i	0.654958	+	0.755665i	$0.272686\pi$
$710$		0			0
$711$	−15.9793	+	5.50474i	−0.599269	+	0.206444i
$712$		0			0
$713$	−21.4949	+	37.2303i	−0.804991	+	1.39429i
$714$		0			0
$715$	−5.10083	−	8.83490i	−0.190760	−	0.330406i
$716$		0			0
$717$	−7.50415	−	44.8228i	−0.280248	−	1.67394i
$718$		0			0
$719$	−19.4689			−0.726068			−0.363034	−	0.931776i	$-0.618259\pi$
$719$	−19.4689			−0.726068			−0.363034	+	0.931776i	$0.618259\pi$
$720$		0			0
$721$	−21.5288			−0.801776
$722$		0			0
$723$	1.19638	−	0.986366i	0.0444938	−	0.0366833i
$724$		0			0
$725$	0.928007	+	1.60735i	0.0344653	+	0.0596957i
$726$		0			0
$727$	11.9628	−	20.7201i	0.443675	−	0.768467i	−0.554284	−	0.832328i	$-0.687008\pi$
$727$	11.9628	−	20.7201i	0.443675	−	0.768467i	0.997959	+	0.0638604i	$0.0203412\pi$
$728$		0			0
$729$	−14.6952	+	22.6506i	−0.544268	+	0.838911i
$730$		0			0
$731$	−6.22635	+	10.7843i	−0.230290	+	0.398873i
$732$		0			0
$733$	2.05767	+	3.56400i	0.0760019	+	0.131639i	0.901522	−	0.432734i	$-0.142451\pi$
$733$	2.05767	+	3.56400i	0.0760019	+	0.131639i	−0.825520	+	0.564373i	$0.809118\pi$
$734$		0			0
$735$	−27.4073	+	22.5962i	−1.01093	+	0.833474i
$736$		0			0
$737$	−2.29854			−0.0846678
$738$		0			0
$739$	16.8145			0.618533			0.309267	−	0.950975i	$-0.399916\pi$
$739$	16.8145			0.618533			0.309267	+	0.950975i	$0.399916\pi$
$740$		0			0
$741$	5.10083	+	30.4676i	0.187384	+	1.11925i
$742$		0			0
$743$	−13.6801	−	23.6946i	−0.501874	−	0.869271i	−0.999998	−	0.00216476i	$-0.999311\pi$
$743$	−13.6801	−	23.6946i	−0.501874	−	0.869271i	0.498124	−	0.867106i	$-0.334022\pi$
$744$		0			0
$745$	−1.93724	+	3.35540i	−0.0709751	+	0.122932i
$746$		0			0
$747$	11.0597	−	3.80997i	0.404651	−	0.139399i
$748$		0			0
$749$	−51.7518	+	89.6367i	−1.89097	+	3.27525i
$750$		0			0
$751$	−2.23558	−	3.87214i	−0.0815775	−	0.141296i	0.822350	−	0.568982i	$-0.192662\pi$
$751$	−2.23558	−	3.87214i	−0.0815775	−	0.141296i	−0.903928	+	0.427685i	$0.859329\pi$
$752$		0			0
$753$	3.41482	+	1.27646i	0.124443	+	0.0465168i
$754$		0			0
$755$	−14.6728			−0.533999
$756$		0			0
$757$	−17.7753			−0.646056			−0.323028	−	0.946389i	$-0.604701\pi$
$757$	−17.7753			−0.646056			−0.323028	+	0.946389i	$0.604701\pi$
$758$		0			0
$759$	−21.4949	−	8.03482i	−0.780216	−	0.291645i
$760$		0			0
$761$	20.1952	+	34.9792i	0.732077	+	1.26799i	0.955994	+	0.293387i	$0.0947823\pi$
$761$	20.1952	+	34.9792i	0.732077	+	1.26799i	−0.223917	+	0.974608i	$0.571884\pi$
$762$		0			0
$763$	−24.9341	+	43.1872i	−0.902676	+	1.56348i
$764$		0			0
$765$	2.01847	−	10.3923i	0.0729780	−	0.375735i
$766$		0			0
$767$	−8.01847	+	13.8884i	−0.289530	+	0.501481i
$768$		0			0
$769$	19.8496	+	34.3805i	0.715795	+	1.23979i	0.962652	+	0.270741i	$0.0872688\pi$
$769$	19.8496	+	34.3805i	0.715795	+	1.23979i	−0.246857	+	0.969052i	$0.579398\pi$
$770$		0			0
$771$	1.34169	+	8.01402i	0.0483199	+	0.288618i
$772$		0			0
$773$	8.97927			0.322962			0.161481	−	0.986876i	$-0.448373\pi$
$773$	8.97927			0.322962			0.161481	+	0.986876i	$0.448373\pi$
$774$		0			0
$775$	−8.67282			−0.311537
$776$		0			0
$777$	−18.7345	+	15.4458i	−0.672095	+	0.554115i
$778$		0			0
$779$	−8.58123	−	14.8631i	−0.307454	−	0.532527i
$780$		0			0
$781$	20.2633	−	35.0970i	0.725077	−	1.25587i
$782$		0			0
$783$	9.64088	+	0.250324i	0.344537	+	0.00894585i
$784$		0			0
$785$	6.59046	−	11.4150i	0.235224	−	0.407420i
$786$		0			0
$787$	−17.9476	−	31.0862i	−0.639763	−	1.10810i	−0.985485	−	0.169765i	$-0.945699\pi$
$787$	−17.9476	−	31.0862i	−0.639763	−	1.10810i	0.345721	−	0.938337i	$-0.387634\pi$
$788$		0			0
$789$	−13.1193	+	10.8163i	−0.467060	+	0.385072i
$790$		0			0
$791$	49.4689			1.75891
$792$		0			0
$793$	−30.3849			−1.07900
$794$		0			0
$795$	0.816810	+	4.87886i	0.0289693	+	0.173035i
$796$		0			0
$797$	−18.9229	−	32.7755i	−0.670284	−	1.16097i	−0.977823	−	0.209431i	$-0.932839\pi$
$797$	−18.9229	−	32.7755i	−0.670284	−	1.16097i	0.307539	−	0.951535i	$-0.400495\pi$
$798$		0			0
$799$	−16.3443	+	28.3092i	−0.578220	+	1.00151i
$800$		0			0
$801$	−24.9086	−	21.6463i	−0.880102	−	0.764834i
$802$		0			0
$803$	−8.40332	+	14.5550i	−0.296547	+	0.513634i
$804$		0			0
$805$	−12.9989	−	22.5147i	−0.458150	−	0.793539i
$806$		0			0
$807$	33.1790	+	12.4023i	1.16795	+	0.436582i
$808$		0			0
$809$	−27.8722			−0.979935			−0.489968	−	0.871741i	$-0.662991\pi$
$809$	−27.8722			−0.979935			−0.489968	+	0.871741i	$0.662991\pi$
$810$		0			0
$811$	48.3249			1.69692			0.848459	−	0.529262i	$-0.177531\pi$
$811$	48.3249			1.69692			0.848459	+	0.529262i	$0.177531\pi$
$812$		0			0
$813$	−8.17565	−	3.05606i	−0.286732	−	0.107181i
$814$		0			0
$815$	−10.4372	−	18.0778i	−0.365601	−	0.633239i
$816$		0			0
$817$	8.24482	−	14.2804i	0.288450	−	0.499609i
$818$		0			0
$819$	−45.3302	−	39.3932i	−1.58397	−	1.37651i
$820$		0			0
$821$	14.8549	−	25.7294i	0.518439	−	0.897963i	−0.481331	−	0.876539i	$-0.659847\pi$
$821$	14.8549	−	25.7294i	0.518439	−	0.897963i	0.999770	−	0.0214240i	$-0.00682000\pi$
$822$		0			0
$823$	15.1028	+	26.1588i	0.526451	+	0.911839i	0.999525	+	0.0308169i	$0.00981088\pi$
$823$	15.1028	+	26.1588i	0.526451	+	0.911839i	−0.473074	+	0.881023i	$0.656856\pi$
$824$		0			0
$825$	−0.764419	−	4.56592i	−0.0266136	−	0.158965i
$826$		0			0
$827$	−1.14003			−0.0396429			−0.0198214	−	0.999804i	$-0.506310\pi$
$827$	−1.14003			−0.0396429			−0.0198214	+	0.999804i	$0.506310\pi$
$828$		0			0
$829$	−17.9608			−0.623804			−0.311902	−	0.950114i	$-0.600966\pi$
$829$	−17.9608			−0.623804			−0.311902	+	0.950114i	$0.600966\pi$
$830$		0			0
$831$	−1.39937	+	1.15372i	−0.0485436	+	0.0400222i
$832$		0			0
$833$	−36.1849	−	62.6741i	−1.25373	−	2.17153i
$834$		0			0
$835$	−0.00197644	+	0.00342329i	−6.83975e−5	+	0.000118468i
$836$		0			0
$837$	−23.5381	+	38.4297i	−0.813595	+	1.32832i
$838$		0			0
$839$	−0.605914	+	1.04947i	−0.0209185	+	0.0362318i	−0.876295	−	0.481775i	$-0.839992\pi$
$839$	−0.605914	+	1.04947i	−0.0209185	+	0.0362318i	0.855377	+	0.518007i	$0.173326\pi$
$840$		0			0
$841$	12.7776	+	22.1315i	0.440607	+	0.763154i
$842$		0			0
$843$	−2.35093	+	1.93825i	−0.0809703	+	0.0667568i
$844$		0			0
$845$	1.56804			0.0539422
$846$		0			0
$847$	20.2241			0.694908
$848$		0			0
$849$	−0.823223	−	4.91716i	−0.0282530	−	0.168757i
$850$		0			0
$851$	−6.62438	−	11.4738i	−0.227081	−	0.393316i
$852$		0			0
$853$	−17.6821	+	30.6262i	−0.605422	+	1.04862i	0.386562	+	0.922263i	$0.373662\pi$
$853$	−17.6821	+	30.6262i	−0.605422	+	1.04862i	−0.991985	+	0.126359i	$0.959671\pi$
$854$		0			0
$855$	−2.67282	+	13.7613i	−0.0914086	+	0.470627i
$856$		0			0
$857$	20.9061	−	36.2105i	0.714140	−	1.23693i	−0.249150	−	0.968465i	$-0.580151\pi$
$857$	20.9061	−	36.2105i	0.714140	−	1.23693i	0.963290	−	0.268462i	$-0.0865155\pi$
$858$		0			0
$859$	5.88767	+	10.1977i	0.200885	+	0.347943i	0.948814	−	0.315836i	$-0.102285\pi$
$859$	5.88767	+	10.1977i	0.200885	+	0.347943i	−0.747929	+	0.663779i	$0.768952\pi$
$860$		0			0
$861$	31.2529	+	11.6824i	1.06510	+	0.398134i
$862$		0			0
$863$	−26.1193			−0.889111			−0.444556	−	0.895751i	$-0.646638\pi$
$863$	−26.1193			−0.889111			−0.444556	+	0.895751i	$0.646638\pi$
$864$		0			0
$865$	−20.6129			−0.700859
$866$		0			0
$867$	−7.37759	−	2.75775i	−0.250556	−	0.0936581i
$868$		0			0
$869$	−7.52884	−	13.0403i	−0.255398	−	0.442363i
$870$		0			0
$871$	1.64116	−	2.84258i	0.0556087	−	0.0963171i
$872$		0			0
$873$	10.8784	−	3.74754i	0.368179	−	0.126835i
$874$		0			0
$875$	2.62241	−	4.54214i	0.0886536	−	0.153553i
$876$		0			0
$877$	26.3117	+	45.5732i	0.888484	+	1.53890i	0.841668	+	0.539996i	$0.181574\pi$
$877$	26.3117	+	45.5732i	0.888484	+	1.53890i	0.0468161	+	0.998904i	$0.485093\pi$
$878$		0			0
$879$	−7.12458	−	42.5556i	−0.240306	−	1.43536i
$880$		0			0
$881$	−12.8089			−0.431543			−0.215771	−	0.976444i	$-0.569227\pi$
$881$	−12.8089			−0.431543			−0.215771	+	0.976444i	$0.569227\pi$
$882$		0			0
$883$	21.7529			0.732044			0.366022	−	0.930606i	$-0.380719\pi$
$883$	21.7529			0.732044			0.366022	+	0.930606i	$0.380719\pi$
$884$		0			0
$885$	−5.61515	+	4.62947i	−0.188751	+	0.155618i
$886$		0			0
$887$	16.5236	+	28.6196i	0.554807	+	0.960953i	0.997919	+	0.0644870i	$0.0205411\pi$
$887$	16.5236	+	28.6196i	0.554807	+	0.960953i	−0.443112	+	0.896466i	$0.646126\pi$
$888$		0			0
$889$	48.8002	−	84.5245i	1.63671	−	2.83486i
$890$		0			0
$891$	−22.3064	−	9.00475i	−0.747294	−	0.301670i
$892$		0			0
$893$	21.6429	−	37.4865i	0.724251	−	1.25444i
$894$		0			0
$895$	−2.05239	−	3.55485i	−0.0686039	−	0.118825i
$896$		0			0
$897$	25.2840	−	20.8457i	0.844209	−	0.696016i
$898$		0			0
$899$	16.0969			0.536861
$900$		0			0
$901$	−10.0784			−0.335760
$902$		0			0
$903$	5.29326	+	31.6169i	0.176149	+	1.05215i
$904$		0			0
$905$	2.21598	+	3.83819i	0.0736617	+	0.127586i
$906$		0			0
$907$	−24.5924	+	42.5954i	−0.816579	+	1.41436i	0.0916102	+	0.995795i	$0.470799\pi$
$907$	−24.5924	+	42.5954i	−0.816579	+	1.41436i	−0.908189	+	0.418561i	$0.862535\pi$
$908$		0			0
$909$	29.7529	−	10.2497i	0.986842	−	0.339960i
$910$		0			0
$911$	3.22635	−	5.58819i	0.106894	−	0.185145i	−0.807617	−	0.589708i	$-0.799243\pi$
$911$	3.22635	−	5.58819i	0.106894	−	0.185145i	0.914510	+	0.404563i	$0.132576\pi$
$912$		0			0
$913$	5.21090	+	9.02554i	0.172456	+	0.298702i
$914$		0			0
$915$	−12.9157	−	4.82788i	−0.426979	−	0.159605i
$916$		0			0
$917$	80.4851			2.65785
$918$		0			0
$919$	−19.5552			−0.645067			−0.322533	−	0.946558i	$-0.604534\pi$
$919$	−19.5552			−0.645067			−0.322533	+	0.946558i	$0.604534\pi$
$920$		0			0
$921$	−2.14681	−	0.802479i	−0.0707398	−	0.0264426i
$922$		0			0
$923$	28.9361	+	50.1188i	0.952444	+	1.64968i
$924$		0			0
$925$	1.33641	−	2.31473i	0.0439410	−	0.0761080i
$926$		0			0
$927$	2.34791	−	12.0884i	0.0771154	−	0.397037i
$928$		0			0
$929$	25.5865	−	44.3171i	0.839466	−	1.45400i	−0.0508754	−	0.998705i	$-0.516201\pi$
$929$	25.5865	−	44.3171i	0.839466	−	1.45400i	0.890342	−	0.455293i	$-0.150466\pi$
$930$		0			0
$931$	47.9154	+	82.9919i	1.57036	+	2.71995i
$932$		0			0
$933$	−1.41651	−	8.46090i	−0.0463745	−	0.276998i
$934$		0			0
$935$	9.43196			0.308458
$936$		0			0
$937$	−37.6627			−1.23039			−0.615193	−	0.788377i	$-0.710922\pi$
$937$	−37.6627			−1.23039			−0.615193	+	0.788377i	$0.710922\pi$
$938$		0			0
$939$	−12.8498	+	10.5941i	−0.419337	+	0.345727i
$940$		0			0
$941$	12.9073	+	22.3561i	0.420765	+	0.728787i	0.996014	−	0.0891915i	$-0.0284283\pi$
$941$	12.9073	+	22.3561i	0.420765	+	0.728787i	−0.575249	+	0.817978i	$0.695095\pi$
$942$		0			0
$943$	−9.10281	+	15.7665i	−0.296428	+	0.513429i
$944$		0			0
$945$	−13.0092	−	23.9474i	−0.423190	−	0.779009i
$946$		0			0
$947$	0.919617	−	1.59282i	0.0298835	−	0.0517598i	−0.850697	−	0.525657i	$-0.823820\pi$
$947$	0.919617	−	1.59282i	0.0298835	−	0.0517598i	0.880580	+	0.473897i	$0.157153\pi$
$948$		0			0
$949$	−12.0000	−	20.7846i	−0.389536	−	0.674697i
$950$		0			0
$951$	16.4465	−	13.5595i	0.533314	−	0.439696i
$952$		0			0
$953$	39.7674			1.28819			0.644097	−	0.764944i	$-0.277233\pi$
$953$	39.7674			1.28819			0.644097	+	0.764944i	$0.277233\pi$
$954$		0			0
$955$	−17.1625			−0.555364
$956$		0			0
$957$	1.41877	+	8.47441i	0.0458624	+	0.273939i
$958$		0			0
$959$	1.28402	+	2.22399i	0.0414632	+	0.0718163i
$960$		0			0
$961$	−22.1089	+	38.2938i	−0.713191	+	1.23528i
$962$		0			0
$963$	−44.6871	−	38.8343i	−1.44002	−	1.25142i
$964$		0			0
$965$	−2.94761	+	5.10541i	−0.0948869	+	0.164349i
$966$		0			0
$967$	−4.85271	−	8.40514i	−0.156053	−	0.270291i	0.777389	−	0.629020i	$-0.216544\pi$
$967$	−4.85271	−	8.40514i	−0.156053	−	0.270291i	−0.933442	+	0.358729i	$0.883210\pi$
$968$		0			0
$969$	−26.7529	−	10.0003i	−0.859428	−	0.321255i
$970$		0			0
$971$	13.8247			0.443656			0.221828	−	0.975086i	$-0.428798\pi$
$971$	13.8247			0.443656			0.221828	+	0.975086i	$0.428798\pi$
$972$		0			0
$973$	56.0739			1.79765
$974$		0			0
$975$	6.19243	+	2.31473i	0.198316	+	0.0741308i
$976$		0			0
$977$	−17.9885	−	31.1570i	−0.575503	−	0.996801i	−0.995987	−	0.0895006i	$-0.971473\pi$
$977$	−17.9885	−	31.1570i	−0.575503	−	0.996801i	0.420484	−	0.907300i	$-0.361860\pi$
$978$		0			0
$979$	14.7005	−	25.4621i	0.469831	−	0.813771i
$980$		0			0
$981$	−21.5303	−	18.7105i	−0.687411	−	0.597379i
$982$		0			0
$983$	11.2745	−	19.5280i	0.359601	−	0.622847i	−0.628293	−	0.777976i	$-0.716246\pi$
$983$	11.2745	−	19.5280i	0.359601	−	0.622847i	0.987894	+	0.155130i	$0.0495796\pi$
$984$		0			0
$985$	10.9176	+	18.9099i	0.347865	+	0.602520i
$986$		0			0
$987$	13.8949	+	82.9953i	0.442281	+	2.64177i
$988$		0			0
$989$	−17.4919			−0.556210
$990$		0			0
$991$	−13.8767			−0.440809			−0.220405	−	0.975409i	$-0.570738\pi$
$991$	−13.8767			−0.440809			−0.220405	+	0.975409i	$0.570738\pi$
$992$		0			0
$993$	−2.06784	+	1.70485i	−0.0656210	+	0.0541019i
$994$		0			0
$995$	6.62438	+	11.4738i	0.210007	+	0.363743i
$996$		0			0
$997$	−17.7529	+	30.7490i	−0.562241	+	0.973829i	0.435060	+	0.900402i	$0.356727\pi$
$997$	−17.7529	+	30.7490i	−0.562241	+	0.973829i	−0.997301	+	0.0734279i	$0.976606\pi$
$998$		0			0
$999$	−6.62967	−	12.2039i	−0.209753	−	0.386114i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.q.d.241.3	yes	6
3.2	odd	2		1080.2.q.d.721.3		6
4.3	odd	2		720.2.q.j.241.1		6
9.2	odd	6		3240.2.a.q.1.1		3
9.4	even	3	inner	360.2.q.d.121.3	✓	6
9.5	odd	6		1080.2.q.d.361.3		6
9.7	even	3		3240.2.a.r.1.1		3
12.11	even	2		2160.2.q.j.721.1		6
36.7	odd	6		6480.2.a.bx.1.3		3
36.11	even	6		6480.2.a.bu.1.3		3
36.23	even	6		2160.2.q.j.1441.1		6
36.31	odd	6		720.2.q.j.481.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.q.d.121.3	✓	6	9.4	even	3	inner
360.2.q.d.241.3	yes	6	1.1	even	1	trivial
720.2.q.j.241.1		6	4.3	odd	2
720.2.q.j.481.1		6	36.31	odd	6
1080.2.q.d.361.3		6	9.5	odd	6
1080.2.q.d.721.3		6	3.2	odd	2
2160.2.q.j.721.1		6	12.11	even	2
2160.2.q.j.1441.1		6	36.23	even	6
3240.2.a.q.1.1		3	9.2	odd	6
3240.2.a.r.1.1		3	9.7	even	3
6480.2.a.bu.1.3		3	36.11	even	6
6480.2.a.bx.1.3		3	36.7	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.62241 + 0.606458i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(2.62241 - 4.54214i) q^{7} +(2.26442 + 1.96784i) q^{9} +(-1.33641 + 2.31473i) q^{11} +(-1.90841 - 3.30545i) q^{13} +(-0.285997 - 1.70828i) q^{15} +3.52884 q^{17} -4.67282 q^{19} +(7.00924 - 5.77883i) q^{21} +(2.47842 + 4.29275i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(2.48040 + 4.56592i) q^{27} +(0.928007 - 1.60735i) q^{29} +(4.33641 + 7.51089i) q^{31} +(-3.57199 + 2.94497i) q^{33} -5.24482 q^{35} -2.67282 q^{37} +(-1.09159 - 6.52016i) q^{39} +(1.83641 + 3.18076i) q^{41} +(-1.76442 + 3.05606i) q^{43} +(0.571993 - 2.94497i) q^{45} +(-4.63164 + 8.02224i) q^{47} +(-10.2541 - 17.7605i) q^{49} +(5.72522 + 2.14009i) q^{51} -2.85601 q^{53} +2.67282 q^{55} +(-7.58123 - 2.83387i) q^{57} +(-2.10083 - 3.63875i) q^{59} +(3.98040 - 6.89425i) q^{61} +(14.8765 - 5.12483i) q^{63} +(-1.90841 + 3.30545i) q^{65} +(0.429983 + 0.744753i) q^{67} +(1.41764 + 8.46766i) q^{69} -15.1625 q^{71} +6.28797 q^{73} +(-1.33641 + 1.10182i) q^{75} +(7.00924 + 12.1404i) q^{77} +(-2.81681 + 4.87886i) q^{79} +(1.25518 + 8.91204i) q^{81} +(1.94958 - 3.37678i) q^{83} +(-1.76442 - 3.05606i) q^{85} +(2.48040 - 2.04499i) q^{87} -11.0000 q^{89} -20.0185 q^{91} +(2.48040 + 14.8156i) q^{93} +(2.33641 + 4.04678i) q^{95} +(1.91764 - 3.32145i) q^{97} +(-7.58123 + 2.61168i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} - 3 q^{5} + 5 q^{7} + 5 q^{9} + 2 q^{11} - q^{15} + 4 q^{17} - 8 q^{19} + 12 q^{21} + 7 q^{23} - 3 q^{25} + 2 q^{27} + 7 q^{29} + 16 q^{31} - 20 q^{33} - 10 q^{35} + 4 q^{37} - 18 q^{39} + q^{41}+ \cdots - 14 q^{99}+O(q^{100}) \) 6 * q - q^3 - 3 * q^5 + 5 * q^7 + 5 * q^9 + 2 * q^11 - q^15 + 4 * q^17 - 8 * q^19 + 12 * q^21 + 7 * q^23 - 3 * q^25 + 2 * q^27 + 7 * q^29 + 16 * q^31 - 20 * q^33 - 10 * q^35 + 4 * q^37 - 18 * q^39 + q^41 - 2 * q^43 + 2 * q^45 + 13 * q^47 - 10 * q^49 - 20 * q^53 - 4 * q^55 - 14 * q^57 + 6 * q^59 + 11 * q^61 + 27 * q^63 - q^67 - 33 * q^69 - 28 * q^71 + 32 * q^73 + 2 * q^75 + 12 * q^77 + 6 * q^79 + 29 * q^81 + 21 * q^83 - 2 * q^85 + 2 * q^87 - 66 * q^89 - 60 * q^91 + 2 * q^93 + 4 * q^95 - 30 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more