LMFDB - Embedded newform 603.2.g.h.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(37,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("603.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.g (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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 11x^{10} + 89x^{8} + 326x^{6} + 881x^{4} + 416x^{2} + 169 $ x^12 + 11x^10 + 89x^8 + 326x^6 + 881x^4 + 416*x^2 + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.3
Root			$0.347450 + 0.601802i$ of defining polynomial
Character	$\chi$	$=$	603.37
Dual form			603.2.g.h.163.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.347450 - 0.601802i) q^{2} +(0.758557 - 1.31386i) q^{4} +3.13894 q^{5} +(0.667930 - 1.15689i) q^{7} -2.44404 q^{8} +O(q^{10})$	\(q+(-0.347450 - 0.601802i) q^{2} +(0.758557 - 1.31386i) q^{4} +3.13894 q^{5} +(0.667930 - 1.15689i) q^{7} -2.44404 q^{8} +(-1.09063 - 1.88902i) q^{10} +(0.694901 - 1.20360i) q^{11} +(-2.75856 - 4.77796i) q^{13} -0.928289 q^{14} +(-0.667930 - 1.15689i) q^{16} +(1.22202 + 2.11660i) q^{17} +(0.926486 + 1.60472i) q^{19} +(2.38107 - 4.12413i) q^{20} -0.965774 q^{22} +(3.25564 + 5.63893i) q^{23} +4.85297 q^{25} +(-1.91692 + 3.32021i) q^{26} +(-1.01332 - 1.75513i) q^{28} +(-1.68617 + 2.92053i) q^{29} +(-0.335859 + 0.581725i) q^{31} +(-2.90819 + 5.03713i) q^{32} +(0.849184 - 1.47083i) q^{34} +(2.09659 - 3.63141i) q^{35} +(-5.09442 - 8.82379i) q^{37} +(0.643816 - 1.11512i) q^{38} -7.67172 q^{40} +(-2.03362 + 3.52233i) q^{41} +4.51711 q^{43} +(-1.05424 - 1.82600i) q^{44} +(2.26235 - 3.91850i) q^{46} +(5.17256 - 8.95914i) q^{47} +(2.60774 + 4.51674i) q^{49} +(-1.68617 - 2.92053i) q^{50} -8.37009 q^{52} -5.22365 q^{53} +(2.18125 - 3.77804i) q^{55} +(-1.63245 + 2.82748i) q^{56} +2.34344 q^{58} -0.461512 q^{59} +(1.33207 + 2.30721i) q^{61} +0.466777 q^{62} +1.37009 q^{64} +(-8.65896 - 14.9978i) q^{65} +(4.92270 - 6.53965i) q^{67} +3.70789 q^{68} -2.91385 q^{70} +(3.25564 - 5.63893i) q^{71} +(6.43981 + 11.1541i) q^{73} +(-3.54011 + 6.13165i) q^{74} +2.81117 q^{76} +(-0.928289 - 1.60784i) q^{77} +(-1.27567 + 2.20952i) q^{79} +(-2.09659 - 3.63141i) q^{80} +2.82632 q^{82} +(-1.91692 - 3.32021i) q^{83} +(3.83586 + 6.64390i) q^{85} +(-1.56947 - 2.71841i) q^{86} +(-1.69837 + 2.94166i) q^{88} +8.26042 q^{89} -7.37009 q^{91} +9.87835 q^{92} -7.18883 q^{94} +(2.90819 + 5.03713i) q^{95} +(2.15082 + 3.72532i) q^{97} +(1.81212 - 3.13868i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{4} + 6 q^{7}+O(q^{10}) $ 12 * q - 10 * q^4 + 6 * q^7	$ 12 q - 10 q^{4} + 6 q^{7} + 4 q^{10} - 14 q^{13} - 6 q^{16} - 10 q^{19} - 88 q^{22} + 16 q^{25} + 20 q^{28} - 26 q^{34} - 38 q^{37} - 84 q^{40} + 16 q^{43} + 2 q^{46} - 24 q^{49} - 20 q^{52} - 8 q^{55} + 12 q^{58} + 18 q^{61} - 64 q^{64} + 44 q^{67} + 148 q^{70} + 24 q^{73} + 80 q^{76} + 42 q^{79} + 56 q^{82} + 42 q^{85} + 52 q^{88} - 8 q^{91} - 40 q^{94} + 62 q^{97}+O(q^{100}) $ 12 * q - 10 * q^4 + 6 * q^7 + 4 * q^10 - 14 * q^13 - 6 * q^16 - 10 * q^19 - 88 * q^22 + 16 * q^25 + 20 * q^28 - 26 * q^34 - 38 * q^37 - 84 * q^40 + 16 * q^43 + 2 * q^46 - 24 * q^49 - 20 * q^52 - 8 * q^55 + 12 * q^58 + 18 * q^61 - 64 * q^64 + 44 * q^67 + 148 * q^70 + 24 * q^73 + 80 * q^76 + 42 * q^79 + 56 * q^82 + 42 * q^85 + 52 * q^88 - 8 * q^91 - 40 * q^94 + 62 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.347450	−	0.601802i	−0.245684	−	0.425538i	0.716639	−	0.697444i	$-0.245679\pi$
$2$	−0.347450	−	0.601802i	−0.245684	−	0.425538i	−0.962324	+	0.271906i	$0.912346\pi$
$3$		0			0
$3$		0			0
$4$	0.758557	−	1.31386i	0.379278	−	0.656929i
$5$	3.13894			1.40378			0.701889	−	0.712286i	$-0.252340\pi$
$5$	3.13894			1.40378			0.701889	+	0.712286i	$0.252340\pi$
$6$		0			0
$7$	0.667930	−	1.15689i	0.252454	−	0.437263i	−0.711747	−	0.702436i	$-0.752096\pi$
$7$	0.667930	−	1.15689i	0.252454	−	0.437263i	0.964201	+	0.265173i	$0.0854292\pi$
$8$	−2.44404			−0.864100
$9$		0			0
$10$	−1.09063	−	1.88902i	−0.344887	−	0.597361i
$11$	0.694901	−	1.20360i	0.209520	−	0.362900i	−0.742043	−	0.670352i	$-0.766143\pi$
$11$	0.694901	−	1.20360i	0.209520	−	0.362900i	0.951564	+	0.307452i	$0.0994764\pi$
$12$		0			0
$13$	−2.75856	−	4.77796i	−0.765086	−	1.32517i	−0.940201	−	0.340620i	$-0.889363\pi$
$13$	−2.75856	−	4.77796i	−0.765086	−	1.32517i	0.175115	−	0.984548i	$-0.443970\pi$
$14$	−0.928289			−0.248096
$15$		0			0
$16$	−0.667930	−	1.15689i	−0.166982	−	0.289222i
$17$	1.22202	+	2.11660i	0.296384	+	0.513352i	0.975306	−	0.220859i	$-0.0708859\pi$
$17$	1.22202	+	2.11660i	0.296384	+	0.513352i	−0.678922	+	0.734210i	$0.737553\pi$
$18$		0			0
$19$	0.926486	+	1.60472i	0.212550	+	0.368148i	0.952512	−	0.304501i	$-0.0984897\pi$
$19$	0.926486	+	1.60472i	0.212550	+	0.368148i	−0.739962	+	0.672649i	$0.765156\pi$
$20$	2.38107	−	4.12413i	0.532423	−	0.922183i
$21$		0			0
$22$	−0.965774			−0.205904
$23$	3.25564	+	5.63893i	0.678848	+	1.17580i	0.975328	+	0.220760i	$0.0708536\pi$
$23$	3.25564	+	5.63893i	0.678848	+	1.17580i	−0.296481	+	0.955039i	$0.595813\pi$
$24$		0			0
$25$	4.85297			0.970594
$26$	−1.91692	+	3.32021i	−0.375939	+	0.651146i
$27$		0			0
$28$	−1.01332	−	1.75513i	−0.191500	−	0.331688i
$29$	−1.68617	+	2.92053i	−0.313113	+	0.542328i	−0.979035	−	0.203694i	$-0.934705\pi$
$29$	−1.68617	+	2.92053i	−0.313113	+	0.542328i	0.665921	+	0.746022i	$0.268039\pi$
$30$		0			0
$31$	−0.335859	+	0.581725i	−0.0603221	+	0.104481i	−0.894609	−	0.446849i	$-0.852546\pi$
$31$	−0.335859	+	0.581725i	−0.0603221	+	0.104481i	0.834287	+	0.551330i	$0.185879\pi$
$32$	−2.90819	+	5.03713i	−0.514100	+	0.890447i
$33$		0			0
$34$	0.849184	−	1.47083i	0.145634	−	0.252245i
$35$	2.09659	−	3.63141i	0.354389	−	0.613820i
$36$		0			0
$37$	−5.09442	−	8.82379i	−0.837517	−	1.45062i	−0.891965	−	0.452105i	$-0.850673\pi$
$37$	−5.09442	−	8.82379i	−0.837517	−	1.45062i	0.0544480	−	0.998517i	$-0.482660\pi$
$38$	0.643816	−	1.11512i	0.104441	−	0.180897i
$39$		0			0
$40$	−7.67172			−1.21301
$41$	−2.03362	+	3.52233i	−0.317598	+	0.550095i	−0.979986	−	0.199065i	$-0.936209\pi$
$41$	−2.03362	+	3.52233i	−0.317598	+	0.550095i	0.662389	+	0.749160i	$0.269543\pi$
$42$		0			0
$43$	4.51711			0.688853			0.344427	−	0.938813i	$-0.388073\pi$
$43$	4.51711			0.688853			0.344427	+	0.938813i	$0.388073\pi$
$44$	−1.05424	−	1.82600i	−0.158933	−	0.275280i
$45$		0			0
$46$	2.26235	−	3.91850i	0.333565	−	0.577751i
$47$	5.17256	−	8.95914i	0.754496	−	1.30682i	−0.191129	−	0.981565i	$-0.561215\pi$
$47$	5.17256	−	8.95914i	0.754496	−	1.30682i	0.945625	−	0.325260i	$-0.105452\pi$
$48$		0			0
$49$	2.60774	+	4.51674i	0.372534	+	0.645248i
$50$	−1.68617	−	2.92053i	−0.238460	−	0.413025i
$51$		0			0
$52$	−8.37009			−1.16072
$53$	−5.22365			−0.717523			−0.358761	−	0.933429i	$-0.616801\pi$
$53$	−5.22365			−0.717523			−0.358761	+	0.933429i	$0.616801\pi$
$54$		0			0
$55$	2.18125	−	3.77804i	0.294120	−	0.509431i
$56$	−1.63245	+	2.82748i	−0.218145	+	0.377839i
$57$		0			0
$58$	2.34344			0.307708
$59$	−0.461512			−0.0600837			−0.0300419	−	0.999549i	$-0.509564\pi$
$59$	−0.461512			−0.0600837			−0.0300419	+	0.999549i	$0.509564\pi$
$60$		0			0
$61$	1.33207	+	2.30721i	0.170554	+	0.295408i	0.938614	−	0.344970i	$-0.112111\pi$
$61$	1.33207	+	2.30721i	0.170554	+	0.295408i	−0.768060	+	0.640378i	$0.778778\pi$
$62$	0.466777			0.0592808
$63$		0			0
$64$	1.37009			0.171261
$65$	−8.65896	−	14.9978i	−1.07401	−	1.86024i
$66$		0			0
$67$	4.92270	−	6.53965i	0.601403	−	0.798946i
$67$	4.92270	−	6.53965i	0.601403	−	0.798946i
$68$	3.70789			0.449648
$69$		0			0
$70$	−2.91385			−0.348271
$71$	3.25564	−	5.63893i	0.386373	−	0.669218i	−0.605585	−	0.795780i	$-0.707061\pi$
$71$	3.25564	−	5.63893i	0.386373	−	0.669218i	0.991959	+	0.126562i	$0.0403943\pi$
$72$		0			0
$73$	6.43981	+	11.1541i	0.753723	+	1.30549i	0.946007	+	0.324147i	$0.105077\pi$
$73$	6.43981	+	11.1541i	0.753723	+	1.30549i	−0.192284	+	0.981339i	$0.561589\pi$
$74$	−3.54011	+	6.13165i	−0.411530	+	0.712790i
$75$		0			0
$76$	2.81117			0.322463
$77$	−0.928289	−	1.60784i	−0.105788	−	0.183231i
$78$		0			0
$79$	−1.27567	+	2.20952i	−0.143524	+	0.248591i	−0.928821	−	0.370528i	$-0.879177\pi$
$79$	−1.27567	+	2.20952i	−0.143524	+	0.248591i	0.785297	+	0.619119i	$0.212510\pi$
$80$	−2.09659	−	3.63141i	−0.234406	−	0.406004i
$81$		0			0
$82$	2.82632			0.312115
$83$	−1.91692	−	3.32021i	−0.210410	−	0.364440i	0.741433	−	0.671027i	$-0.234146\pi$
$83$	−1.91692	−	3.32021i	−0.210410	−	0.364440i	−0.951843	+	0.306587i	$0.900813\pi$
$84$		0			0
$85$	3.83586	+	6.64390i	0.416057	+	0.720632i
$86$	−1.56947	−	2.71841i	−0.169241	−	0.293133i
$87$		0			0
$88$	−1.69837	+	2.94166i	−0.181047	+	0.313582i
$89$	8.26042			0.875603			0.437801	−	0.899072i	$-0.355757\pi$
$89$	8.26042			0.875603			0.437801	+	0.899072i	$0.355757\pi$
$90$		0			0
$91$	−7.37009			−0.772595
$92$	9.87835			1.02989
$93$		0			0
$94$	−7.18883			−0.741471
$95$	2.90819	+	5.03713i	0.298374	+	0.516799i
$96$		0			0
$97$	2.15082	+	3.72532i	0.218382	+	0.378249i	0.954314	−	0.298807i	$-0.0965887\pi$
$97$	2.15082	+	3.72532i	0.218382	+	0.378249i	−0.735931	+	0.677056i	$0.763255\pi$
$98$	1.81212	−	3.13868i	0.183052	−	0.317055i
$99$		0			0
$100$	3.68125	−	6.37612i	0.368125	−	0.637612i
$101$	−9.12310	+	15.8017i	−0.907782	+	1.57233i	−0.0906443	+	0.995883i	$0.528893\pi$
$101$	−9.12310	+	15.8017i	−0.907782	+	1.57233i	−0.817138	+	0.576442i	$0.804441\pi$
$102$		0			0
$103$	−1.44360	+	2.50039i	−0.142242	+	0.246370i	−0.928341	−	0.371731i	$-0.878764\pi$
$103$	−1.44360	+	2.50039i	−0.142242	+	0.246370i	0.786099	+	0.618101i	$0.212098\pi$
$104$	6.74203	+	11.6775i	0.661111	+	1.14508i
$105$		0			0
$106$	1.81496	+	3.14360i	0.176284	+	0.305333i
$107$	−14.7717			−1.42803			−0.714017	−	0.700128i	$-0.753126\pi$
$107$	−14.7717			−1.42803			−0.714017	+	0.700128i	$0.753126\pi$
$108$		0			0
$109$	−11.1813			−1.07097			−0.535485	−	0.844545i	$-0.679871\pi$
$109$	−11.1813			−1.07097			−0.535485	+	0.844545i	$0.679871\pi$
$110$	−3.03151			−0.289043
$111$		0			0
$112$	−1.78452			−0.168621
$113$	−7.15246	+	12.3884i	−0.672847	+	1.16541i	0.304246	+	0.952593i	$0.401595\pi$
$113$	−7.15246	+	12.3884i	−0.672847	+	1.16541i	−0.977093	+	0.212812i	$0.931738\pi$
$114$		0			0
$115$	10.2193	+	17.7003i	0.952952	+	1.65056i
$116$	2.55811	+	4.43077i	0.237514	+	0.411387i
$117$		0			0
$118$	0.160352	+	0.277739i	0.0147616	+	0.0255679i
$119$	3.26490			0.299293
$120$		0			0
$121$	4.53423	+	7.85351i	0.412202	+	0.713956i
$122$	0.925657	−	1.60328i	0.0838050	−	0.145155i
$123$		0			0
$124$	0.509536	+	0.882543i	0.0457577	+	0.0792547i
$125$	−0.461512			−0.0412789
$126$		0			0
$127$	1.59063	−	2.75505i	0.141145	−	0.244471i	−0.786783	−	0.617230i	$-0.788255\pi$
$127$	1.59063	−	2.75505i	0.141145	−	0.244471i	0.927928	+	0.372759i	$0.121588\pi$
$128$	5.34034	+	9.24974i	0.472024	+	0.817569i
$129$		0			0
$130$	−6.01711	+	10.4219i	−0.527736	+	0.914065i
$131$	13.5862			1.18704			0.593518	−	0.804821i	$-0.297739\pi$
$131$	13.5862			1.18704			0.593518	+	0.804821i	$0.297739\pi$
$132$		0			0
$133$	2.47531			0.214637
$134$	−5.64597	−	0.690283i	−0.487737	−	0.0596314i
$135$		0			0
$136$	−2.98668	−	5.17307i	−0.256105	−	0.443587i
$137$	8.95532			0.765105			0.382552	−	0.923934i	$-0.375045\pi$
$137$	8.95532			0.765105			0.382552	+	0.923934i	$0.375045\pi$
$138$		0			0
$139$	6.73259			0.571051			0.285526	−	0.958371i	$-0.407832\pi$
$139$	6.73259			0.571051			0.285526	+	0.958371i	$0.407832\pi$
$140$	−3.18077	−	5.50926i	−0.268824	−	0.465617i
$141$		0			0
$142$	−4.52469			−0.379704
$143$	−7.66769			−0.641204
$144$		0			0
$145$	−5.29278	+	9.16737i	−0.439542	+	0.761309i
$146$	4.47503	−	7.75098i	0.370356	−	0.641475i
$147$		0			0
$148$	−15.4576			−1.27061
$149$	2.90556			0.238032			0.119016	−	0.992892i	$-0.462026\pi$
$149$	2.90556			0.238032			0.119016	+	0.992892i	$0.462026\pi$
$150$		0			0
$151$	10.7966	+	18.7002i	0.878613	+	1.52180i	0.852864	+	0.522133i	$0.174864\pi$
$151$	10.7966	+	18.7002i	0.878613	+	1.52180i	0.0257485	+	0.999668i	$0.491803\pi$
$152$	−2.26437	−	3.92201i	−0.183665	−	0.318117i
$153$		0			0
$154$	−0.645069	+	1.11729i	−0.0519811	+	0.0900339i
$155$	−1.05424	+	1.82600i	−0.0846788	+	0.146668i
$156$		0			0
$157$	2.85297	+	4.94149i	0.227692	+	0.394374i	0.957124	−	0.289680i	$-0.0935487\pi$
$157$	2.85297	+	4.94149i	0.227692	+	0.394374i	−0.729432	+	0.684054i	$0.760215\pi$
$158$	1.77293			0.141047
$159$		0			0
$160$	−9.12864	+	15.8113i	−0.721683	+	1.24999i
$161$	8.69815			0.685510
$162$		0			0
$163$	12.0551	−	20.8801i	0.944231	−	1.63546i	0.186946	−	0.982370i	$-0.440141\pi$
$163$	12.0551	−	20.8801i	0.944231	−	1.63546i	0.757285	−	0.653085i	$-0.226526\pi$
$164$	3.08523	+	5.34377i	0.240916	+	0.417278i
$165$		0			0
$166$	−1.33207	+	2.30721i	−0.103389	+	0.179075i
$167$	12.7236	−	22.0378i	0.984578	−	1.70534i	0.340783	−	0.940142i	$-0.389308\pi$
$167$	12.7236	−	22.0378i	0.984578	−	1.70534i	0.643795	−	0.765198i	$-0.277359\pi$
$168$		0			0
$169$	−8.71927	+	15.1022i	−0.670713	+	1.16171i
$170$	2.66554	−	4.61685i	0.204438	−	0.354096i
$171$		0			0
$172$	3.42649	−	5.93485i	0.261267	−	0.452528i
$173$	−3.55200	−	6.15225i	−0.270054	−	0.467747i	0.698821	−	0.715296i	$-0.253708\pi$
$173$	−3.55200	−	6.15225i	−0.270054	−	0.467747i	−0.968875	+	0.247549i	$0.920375\pi$
$174$		0			0
$175$	3.24144	−	5.61434i	0.245030	−	0.424405i
$176$	−1.85658			−0.139945
$177$		0			0
$178$	−2.87009	−	4.97113i	−0.215122	−	0.372602i
$179$	−2.90556			−0.217171			−0.108586	−	0.994087i	$-0.534632\pi$
$179$	−2.90556			−0.217171			−0.108586	+	0.994087i	$0.534632\pi$
$180$		0			0
$181$	−5.66414	+	9.81058i	−0.421012	+	0.729215i	−0.996039	−	0.0889201i	$-0.971658\pi$
$181$	−5.66414	+	9.81058i	−0.421012	+	0.729215i	0.575026	+	0.818135i	$0.304992\pi$
$182$	2.56074	+	4.43533i	0.189815	+	0.328768i
$183$		0			0
$184$	−7.95692	−	13.7818i	−0.586592	−	1.01601i
$185$	−15.9911	−	27.6974i	−1.17569	−	2.03635i
$186$		0			0
$187$	3.39673			0.248394
$188$	−7.84736	−	13.5920i	−0.572328	−	0.991301i
$189$		0			0
$190$	2.02090	−	3.50030i	0.146612	−	0.253939i
$191$	10.3570	+	17.9389i	0.749407	+	1.29801i	0.948107	+	0.317951i	$0.102995\pi$
$191$	10.3570	+	17.9389i	0.749407	+	1.29801i	−0.198700	+	0.980060i	$0.563672\pi$
$192$		0			0
$193$	0.629915			0.0453422			0.0226711	−	0.999743i	$-0.492783\pi$
$193$	0.629915			0.0453422			0.0226711	+	0.999743i	$0.492783\pi$
$194$	1.49460	−	2.58873i	0.107306	−	0.185860i
$195$		0			0
$196$	7.91247			0.565177
$197$	−10.6926	+	18.5201i	−0.761814	+	1.31950i	0.180100	+	0.983648i	$0.442358\pi$
$197$	−10.6926	+	18.5201i	−0.761814	+	1.31950i	−0.941915	+	0.335853i	$0.890976\pi$
$198$		0			0
$199$	−6.83207	−	11.8335i	−0.484313	−	0.838854i	0.515525	−	0.856875i	$-0.327597\pi$
$199$	−6.83207	−	11.8335i	−0.484313	−	0.838854i	−0.999838	+	0.0180205i	$0.994264\pi$
$200$	−11.8609			−0.838691
$201$		0			0
$202$	12.6793			0.892112
$203$	2.25248	+	3.90141i	0.158093	+	0.273825i
$204$		0			0
$205$	−6.38341	+	11.0564i	−0.445837	+	0.772212i
$206$	2.00632			0.139787
$207$		0			0
$208$	−3.68504	+	6.38268i	−0.255512	+	0.442559i
$209$	2.57526			0.178135
$210$		0			0
$211$	4.84540	+	8.39247i	0.333571	+	0.577762i	0.983209	−	0.182482i	$-0.0584131\pi$
$211$	4.84540	+	8.39247i	0.333571	+	0.577762i	−0.649638	+	0.760243i	$0.725080\pi$
$212$	−3.96243	+	6.86313i	−0.272141	+	0.471362i
$213$		0			0
$214$	5.13243	+	8.88963i	0.350846	+	0.607683i
$215$	14.1790			0.966998
$216$		0			0
$217$	0.448660	+	0.777102i	0.0304570	+	0.0527532i
$218$	3.88493	+	6.72890i	0.263121	+	0.455738i
$219$		0			0
$220$	−3.30921	−	5.73172i	−0.223107	−	0.386432i
$221$	6.74203	−	11.6775i	0.453518	−	0.785517i
$222$		0			0
$223$	8.71352			0.583501			0.291750	−	0.956495i	$-0.405762\pi$
$223$	8.71352			0.583501			0.291750	+	0.956495i	$0.405762\pi$
$224$	3.88493	+	6.72890i	0.259573	+	0.449593i
$225$		0			0
$226$	9.94050			0.661232
$227$	−11.6812	+	20.2324i	−0.775309	+	1.34287i	0.159312	+	0.987228i	$0.449072\pi$
$227$	−11.6812	+	20.2324i	−0.775309	+	1.34287i	−0.934621	+	0.355646i	$0.884261\pi$
$228$		0			0
$229$	−11.1629	−	19.3347i	−0.737663	−	1.27767i	−0.953545	−	0.301251i	$-0.902596\pi$
$229$	−11.1629	−	19.3347i	−0.737663	−	1.27767i	0.215882	−	0.976419i	$-0.430737\pi$
$230$	7.10138	−	12.2999i	0.468251	−	0.811034i
$231$		0			0
$232$	4.12107	−	7.13789i	0.270561	−	0.468626i
$233$	7.03840	−	12.1909i	0.461101	−	0.798650i	−0.537915	−	0.842999i	$-0.680788\pi$
$233$	7.03840	−	12.1909i	0.461101	−	0.798650i	0.999016	+	0.0443488i	$0.0141213\pi$
$234$		0			0
$235$	16.2364	−	28.1222i	1.05914	−	1.83449i
$236$	−0.350083	+	0.606361i	−0.0227885	+	0.0394708i
$237$		0			0
$238$	−1.13439	−	1.96482i	−0.0735316	−	0.127360i
$239$	−11.1541	+	19.3194i	−0.721498	+	1.24967i	0.238902	+	0.971044i	$0.423213\pi$
$239$	−11.1541	+	19.3194i	−0.721498	+	1.24967i	−0.960399	+	0.278627i	$0.910121\pi$
$240$		0			0
$241$	−4.19641			−0.270314			−0.135157	−	0.990824i	$-0.543154\pi$
$241$	−4.19641			−0.270314			−0.135157	+	0.990824i	$0.543154\pi$
$242$	3.15084	−	5.45741i	0.202543	−	0.350816i
$243$		0			0
$244$	4.04180			0.258750
$245$	8.18555	+	14.1778i	0.522956	+	0.905786i
$246$		0			0
$247$	5.11153	−	8.85343i	0.325239	−	0.563330i
$248$	0.820854	−	1.42176i	0.0521243	−	0.0902819i
$249$		0			0
$250$	0.160352	+	0.277739i	0.0101416	+	0.0175657i
$251$	2.79149	+	4.83501i	0.176198	+	0.305183i	0.940575	−	0.339586i	$-0.110287\pi$
$251$	2.79149	+	4.83501i	0.176198	+	0.305183i	−0.764378	+	0.644769i	$0.776954\pi$
$252$		0			0
$253$	9.04938			0.568930
$254$	−2.21066			−0.138709
$255$		0			0
$256$	5.08109	−	8.80071i	0.317568	−	0.550044i
$257$	−7.67958	+	13.3014i	−0.479039	+	0.829720i	−0.999711	−	0.0240367i	$-0.992348\pi$
$257$	−7.67958	+	13.3014i	−0.479039	+	0.829720i	0.520672	+	0.853757i	$0.325681\pi$
$258$		0			0
$259$	−13.6108			−0.845737
$260$	−26.2732			−1.62940
$261$		0			0
$262$	−4.72054	−	8.17622i	−0.291636	−	0.505128i
$263$	−24.7575			−1.52661			−0.763306	−	0.646037i	$-0.776425\pi$
$263$	−24.7575			−1.52661			−0.763306	+	0.646037i	$0.776425\pi$
$264$		0			0
$265$	−16.3967			−1.00724
$266$	−0.860047	−	1.48965i	−0.0527329	−	0.0913360i
$267$		0			0
$268$	−4.85803	−	11.4284i	−0.296752	−	0.698102i
$269$	5.32582			0.324721			0.162360	−	0.986732i	$-0.448089\pi$
$269$	5.32582			0.324721			0.162360	+	0.986732i	$0.448089\pi$
$270$		0			0
$271$	−4.39673			−0.267083			−0.133541	−	0.991043i	$-0.542635\pi$
$271$	−4.39673			−0.267083			−0.133541	+	0.991043i	$0.542635\pi$
$272$	1.63245	−	2.82748i	0.0989818	−	0.171441i
$273$		0			0
$274$	−3.11153	−	5.38933i	−0.187974	−	0.325581i
$275$	3.37233	−	5.84105i	0.203359	−	0.352229i
$276$		0			0
$277$	−3.15460			−0.189542			−0.0947709	−	0.995499i	$-0.530212\pi$
$277$	−3.15460			−0.189542			−0.0947709	+	0.995499i	$0.530212\pi$
$278$	−2.33924	−	4.05169i	−0.140298	−	0.243004i
$279$		0			0
$280$	−5.12417	+	8.87532i	−0.306228	+	0.530402i
$281$	−7.32287	−	12.6836i	−0.436846	−	0.756639i	0.560598	−	0.828088i	$-0.310571\pi$
$281$	−7.32287	−	12.6836i	−0.436846	−	0.756639i	−0.997444	+	0.0714485i	$0.977238\pi$
$282$		0			0
$283$	12.5438			0.745649			0.372825	−	0.927902i	$-0.378389\pi$
$283$	12.5438			0.745649			0.372825	+	0.927902i	$0.378389\pi$
$284$	−4.93917	−	8.55490i	−0.293086	−	0.507640i
$285$		0			0
$286$	2.66414	+	4.61443i	0.157534	+	0.272857i
$287$	2.71663	+	4.70533i	0.160357	+	0.277747i
$288$		0			0
$289$	5.51332	−	9.54936i	0.324313	−	0.561727i
$290$	7.35592			0.431954
$291$		0			0
$292$	19.5398			1.14348
$293$	−0.461512			−0.0269618			−0.0134809	−	0.999909i	$-0.504291\pi$
$293$	−0.461512			−0.0269618			−0.0134809	+	0.999909i	$0.504291\pi$
$294$		0			0
$295$	−1.44866			−0.0843443
$296$	12.4510	+	21.5657i	0.723698	+	1.25348i
$297$		0			0
$298$	−1.00954	−	1.74857i	−0.0584809	−	0.101292i
$299$	17.9617	−	31.1106i	1.03875	−	1.79917i
$300$		0			0
$301$	3.01711	−	5.22579i	0.173904	−	0.301210i
$302$	7.50254	−	12.9948i	0.431723	−	0.747766i
$303$		0			0
$304$	1.23765	−	2.14368i	0.0709844	−	0.122949i
$305$	4.18130	+	7.24222i	0.239420	+	0.414688i
$306$		0			0
$307$	−8.25477	−	14.2977i	−0.471124	−	0.816012i	0.528330	−	0.849039i	$-0.322818\pi$
$307$	−8.25477	−	14.2977i	−0.471124	−	0.816012i	−0.999454	+	0.0330276i	$0.989485\pi$
$308$	−2.81664			−0.160493
$309$		0			0
$310$	1.46519			0.0832171
$311$	−27.3275			−1.54960			−0.774800	−	0.632207i	$-0.782149\pi$
$311$	−27.3275			−1.54960			−0.774800	+	0.632207i	$0.782149\pi$
$312$		0			0
$313$	−30.1711			−1.70537			−0.852687	−	0.522423i	$-0.825028\pi$
$313$	−30.1711			−1.70537			−0.852687	+	0.522423i	$0.825028\pi$
$314$	1.98253	−	3.43385i	0.111881	−	0.193783i
$315$		0			0
$316$	1.93534	+	3.35210i	0.108871	+	0.188570i
$317$	13.7148	+	23.7548i	0.770301	+	1.33420i	0.937398	+	0.348260i	$0.113227\pi$
$317$	13.7148	+	23.7548i	0.770301	+	1.33420i	−0.167097	+	0.985941i	$0.553439\pi$
$318$		0			0
$319$	2.34344	+	4.05895i	0.131207	+	0.227258i
$320$	4.30062			0.240412
$321$		0			0
$322$	−3.02217	−	5.23456i	−0.168419	−	0.291711i
$323$	−2.26437	+	3.92201i	−0.125993	+	0.218226i
$324$		0			0
$325$	−13.3872	−	23.1873i	−0.742588	−	1.28620i
$326$	−16.7542			−0.927931
$327$		0			0
$328$	4.97025	−	8.60872i	0.274436	−	0.475337i
$329$	−6.90981	−	11.9681i	−0.380950	−	0.659825i
$330$		0			0
$331$	−12.3479	+	21.3872i	−0.678703	+	1.17555i	0.296669	+	0.954980i	$0.404124\pi$
$331$	−12.3479	+	21.3872i	−0.678703	+	1.17555i	−0.975372	+	0.220567i	$0.929209\pi$
$332$	−5.81638			−0.319215
$333$		0			0
$334$	−17.6832			−0.967582
$335$	15.4521	−	20.5276i	0.844237	−	1.12154i
$336$		0			0
$337$	−3.27946	−	5.68019i	−0.178643	−	0.309420i	0.762773	−	0.646667i	$-0.223838\pi$
$337$	−3.27946	−	5.68019i	−0.178643	−	0.309420i	−0.941416	+	0.337247i	$0.890504\pi$
$338$	12.1180			0.659135
$339$		0			0
$340$	11.6389			0.631206
$341$	0.466777	+	0.808482i	0.0252774	+	0.0437817i
$342$		0			0
$343$	16.3182			0.881098
$344$	−11.0400			−0.595238
$345$		0			0
$346$	−2.46829	+	4.27520i	−0.132696	+	0.229836i
$347$	−4.17866	+	7.23766i	−0.224322	+	0.388538i	−0.956116	−	0.292989i	$-0.905350\pi$
$347$	−4.17866	+	7.23766i	−0.224322	+	0.388538i	0.731794	+	0.681526i	$0.238684\pi$
$348$		0			0
$349$	−8.65656			−0.463375			−0.231688	−	0.972790i	$-0.574425\pi$
$349$	−8.65656			−0.463375			−0.231688	+	0.972790i	$0.574425\pi$
$350$	−4.50496			−0.240800
$351$		0			0
$352$	4.04180	+	7.00061i	0.215429	+	0.373134i
$353$	−17.7821	−	30.7994i	−0.946443	−	1.63929i	−0.752835	−	0.658209i	$-0.771314\pi$
$353$	−17.7821	−	30.7994i	−0.946443	−	1.63929i	−0.193608	−	0.981079i	$-0.562019\pi$
$354$		0			0
$355$	10.2193	−	17.7003i	0.542382	−	0.939434i
$356$	6.26600	−	10.8530i	0.332097	−	0.575209i
$357$		0			0
$358$	1.00954	+	1.74857i	0.0533556	+	0.0924147i
$359$	−34.1743			−1.80365			−0.901826	−	0.432100i	$-0.857773\pi$
$359$	−34.1743			−1.80365			−0.901826	+	0.432100i	$0.857773\pi$
$360$		0			0
$361$	7.78325	−	13.4810i	0.409645	−	0.709525i
$362$	7.87203			0.413745
$363$		0			0
$364$	−5.59063	+	9.68325i	−0.293028	+	0.507540i
$365$	20.2142	+	35.0120i	1.05806	+	1.83261i
$366$		0			0
$367$	11.6115	−	20.1118i	0.606117	−	1.04983i	−0.385757	−	0.922600i	$-0.626060\pi$
$367$	11.6115	−	20.1118i	0.606117	−	1.04983i	0.991874	−	0.127225i	$-0.0406070\pi$
$368$	4.34907	−	7.53282i	0.226711	−	0.392675i
$369$		0			0
$370$	−11.1122	+	19.2469i	−0.577697	+	1.00060i
$371$	−3.48903	+	6.04317i	−0.181141	+	0.313746i
$372$		0			0
$373$	4.84540	−	8.39247i	0.250885	−	0.434546i	−0.712885	−	0.701281i	$-0.752612\pi$
$373$	4.84540	−	8.39247i	0.250885	−	0.434546i	0.963770	+	0.266736i	$0.0859450\pi$
$374$	−1.18020	−	2.04416i	−0.0610265	−	0.105701i
$375$		0			0
$376$	−12.6420	+	21.8965i	−0.651960	+	1.12923i
$377$	18.6055			0.958234
$378$		0			0
$379$	−1.46450	−	2.53659i	−0.0752264	−	0.130296i	0.825958	−	0.563731i	$-0.190635\pi$
$379$	−1.46450	−	2.53659i	−0.0752264	−	0.130296i	−0.901185	+	0.433435i	$0.857301\pi$
$380$	8.82410			0.452667
$381$		0			0
$382$	7.19710	−	12.4657i	0.368235	−	0.637802i
$383$	−4.24427	−	7.35129i	−0.216872	−	0.375634i	0.736978	−	0.675917i	$-0.236252\pi$
$383$	−4.24427	−	7.35129i	−0.216872	−	0.375634i	−0.953850	+	0.300283i	$0.902919\pi$
$384$		0			0
$385$	−2.91385	−	5.04693i	−0.148503	−	0.257216i
$386$	−0.218864	−	0.379084i	−0.0111399	−	0.0192948i
$387$		0			0
$388$	6.52606			0.331311
$389$	−15.3354	−	26.5617i	−0.777535	−	1.34673i	−0.933359	−	0.358945i	$-0.883137\pi$
$389$	−15.3354	−	26.5617i	−0.777535	−	1.34673i	0.155824	−	0.987785i	$-0.450197\pi$
$390$		0			0
$391$	−7.95692	+	13.7818i	−0.402399	+	0.696975i
$392$	−6.37343	−	11.0391i	−0.321907	−	0.557559i
$393$		0			0
$394$	14.8605			0.748664
$395$	−4.00426	+	6.93558i	−0.201476	+	0.348967i
$396$		0			0
$397$	−33.6349			−1.68809			−0.844045	−	0.536273i	$-0.819832\pi$
$397$	−33.6349			−1.68809			−0.844045	+	0.536273i	$0.819832\pi$
$398$	−4.74761	+	8.22310i	−0.237976	+	0.412187i
$399$		0			0
$400$	−3.24144	−	5.61434i	−0.162072	−	0.280717i
$401$	25.6567			1.28124			0.640618	−	0.767860i	$-0.278678\pi$
$401$	25.6567			1.28124			0.640618	+	0.767860i	$0.278678\pi$
$402$		0			0
$403$	3.70594			0.184606
$404$	13.8408	+	23.9729i	0.688604	+	1.19270i
$405$		0			0
$406$	1.56525	−	2.71109i	0.0776821	−	0.134549i
$407$	−14.1604			−0.701907
$408$		0			0
$409$	18.3910	−	31.8541i	0.909376	−	1.57509i	0.0944425	−	0.995530i	$-0.469893\pi$
$409$	18.3910	−	31.8541i	0.909376	−	1.57509i	0.814933	−	0.579555i	$-0.196774\pi$
$410$	8.87167			0.438141
$411$		0			0
$412$	2.19010	+	3.79337i	0.107899	+	0.186886i
$413$	−0.308257	+	0.533918i	−0.0151684	+	0.0262724i
$414$		0			0
$415$	−6.01711	−	10.4219i	−0.295368	−	0.511593i
$416$	32.0896			1.57332
$417$		0			0
$418$	−0.894776	−	1.54980i	−0.0437649	−	0.0758031i
$419$	10.4081	+	18.0274i	0.508469	+	0.880694i	0.999952	+	0.00980684i	$0.00312166\pi$
$419$	10.4081	+	18.0274i	0.508469	+	0.880694i	−0.491483	+	0.870887i	$0.663545\pi$
$420$		0			0
$421$	2.15082	+	3.72532i	0.104824	+	0.181561i	0.913666	−	0.406465i	$-0.133239\pi$
$421$	2.15082	+	3.72532i	0.104824	+	0.181561i	−0.808842	+	0.588026i	$0.799905\pi$
$422$	3.36707	−	5.83193i	0.163906	−	0.283894i
$423$		0			0
$424$	12.7668			0.620012
$425$	5.93044	+	10.2718i	0.287669	+	0.498257i
$426$		0			0
$427$	3.55892			0.172228
$428$	−11.2052	+	19.4079i	−0.541622	+	0.938117i
$429$		0			0
$430$	−4.92649	−	8.53292i	−0.237576	−	0.411494i
$431$	12.1335	−	21.0158i	0.584448	−	1.01229i	−0.410496	−	0.911862i	$-0.634644\pi$
$431$	12.1335	−	21.0158i	0.584448	−	1.01229i	0.994944	−	0.100431i	$-0.0320223\pi$
$432$		0			0
$433$	1.87009	−	3.23908i	0.0898706	−	0.155660i	−0.817586	−	0.575807i	$-0.804688\pi$
$433$	1.87009	−	3.23908i	0.0898706	−	0.155660i	0.907456	+	0.420147i	$0.138021\pi$
$434$	0.311774	−	0.540009i	0.0149656	−	0.0259213i
$435$		0			0
$436$	−8.48161	+	14.6906i	−0.406196	+	0.703552i
$437$	−6.03261	+	10.4488i	−0.288579	+	0.499833i
$438$		0			0
$439$	3.72054	+	6.44417i	0.177572	+	0.307563i	0.941048	−	0.338272i	$-0.109842\pi$
$439$	3.72054	+	6.44417i	0.177572	+	0.307563i	−0.763477	+	0.645836i	$0.776509\pi$
$440$	−5.33108	+	9.23370i	−0.254149	+	0.440200i
$441$		0			0
$442$	−9.37009			−0.445690
$443$	2.03625	−	3.52689i	0.0967451	−	0.167567i	−0.813590	−	0.581438i	$-0.802490\pi$
$443$	2.03625	−	3.52689i	0.0967451	−	0.167567i	0.910336	+	0.413871i	$0.135823\pi$
$444$		0			0
$445$	25.9290			1.22915
$446$	−3.02752	−	5.24381i	−0.143357	−	0.248302i
$447$		0			0
$448$	0.915121	−	1.58504i	0.0432354	−	0.0748859i
$449$	11.1422	−	19.2988i	0.525833	−	0.910769i	−0.473715	−	0.880678i	$-0.657087\pi$
$449$	11.1422	−	19.2988i	0.525833	−	0.910769i	0.999547	−	0.0300903i	$-0.00957950\pi$
$450$		0			0
$451$	2.82632	+	4.89533i	0.133086	+	0.230512i
$452$	10.8511	+	18.7946i	0.510392	+	0.884026i
$453$		0			0
$454$	16.2346			0.761925
$455$	−23.1343			−1.08455
$456$		0			0
$457$	−5.69837	+	9.86986i	−0.266558	+	0.461693i	−0.967971	−	0.251063i	$-0.919220\pi$
$457$	−5.69837	+	9.86986i	−0.266558	+	0.461693i	0.701412	+	0.712756i	$0.252553\pi$
$458$	−7.75708	+	13.4357i	−0.362465	+	0.627807i
$459$		0			0
$460$	31.0076			1.44574
$461$	−2.06092			−0.0959865			−0.0479933	−	0.998848i	$-0.515283\pi$
$461$	−2.06092			−0.0959865			−0.0479933	+	0.998848i	$0.515283\pi$
$462$		0			0
$463$	9.14197	+	15.8344i	0.424863	+	0.735885i	0.996408	−	0.0846864i	$-0.0269889\pi$
$463$	9.14197	+	15.8344i	0.424863	+	0.735885i	−0.571544	+	0.820571i	$0.693656\pi$
$464$	4.50496			0.209138
$465$		0			0
$466$	−9.78197			−0.453141
$467$	1.17094	+	2.02812i	0.0541845	+	0.0938503i	0.891845	−	0.452340i	$-0.149411\pi$
$467$	1.17094	+	2.02812i	0.0541845	+	0.0938503i	−0.837661	+	0.546191i	$0.816077\pi$
$468$		0			0
$469$	−4.27763	−	10.0630i	−0.197523	−	0.464668i
$470$	−22.5653			−1.04086
$471$		0			0
$472$	1.12796			0.0519184
$473$	3.13894	−	5.43681i	0.144329	−	0.249985i
$474$		0			0
$475$	4.49621	+	7.78767i	0.206300	+	0.357323i
$476$	2.47661	−	4.28961i	0.113515	−	0.196614i
$477$		0			0
$478$	15.5020			0.709043
$479$	15.4547	+	26.7683i	0.706144	+	1.22308i	0.966277	+	0.257504i	$0.0829000\pi$
$479$	15.4547	+	26.7683i	0.706144	+	1.22308i	−0.260134	+	0.965573i	$0.583767\pi$
$480$		0			0
$481$	−28.1065	+	48.6818i	−1.28154	+	2.21970i
$482$	1.45804	+	2.52540i	0.0664120	+	0.115029i
$483$		0			0
$484$	13.7579			0.625358
$485$	6.75129	+	11.6936i	0.306560	+	0.530978i
$486$		0			0
$487$	−8.69837	−	15.0660i	−0.394161	−	0.682706i	0.598833	−	0.800874i	$-0.295631\pi$
$487$	−8.69837	−	15.0660i	−0.394161	−	0.682706i	−0.992994	+	0.118168i	$0.962298\pi$
$488$	−3.25564	−	5.63893i	−0.147376	−	0.255262i
$489$		0			0
$490$	5.68814	−	9.85216i	0.256964	−	0.445075i
$491$	−11.2787			−0.509000			−0.254500	−	0.967073i	$-0.581911\pi$
$491$	−11.2787			−0.509000			−0.254500	+	0.967073i	$0.581911\pi$
$492$		0			0
$493$	−8.24213			−0.371207
$494$	−7.10401			−0.319624
$495$		0			0
$496$	0.897321			0.0402909
$497$	−4.34907	−	7.53282i	−0.195083	−	0.337893i
$498$		0			0
$499$	16.0609	+	27.8183i	0.718984	+	1.24532i	0.961403	+	0.275144i	$0.0887257\pi$
$499$	16.0609	+	27.8183i	0.718984	+	1.24532i	−0.242419	+	0.970172i	$0.577941\pi$
$500$	−0.350083	+	0.606361i	−0.0156562	+	0.0271173i
$501$		0			0
$502$	1.93981	−	3.35985i	0.0865780	−	0.149957i
$503$	−6.31708	+	10.9415i	−0.281665	+	0.487858i	−0.971795	−	0.235828i	$-0.924220\pi$
$503$	−6.31708	+	10.9415i	−0.281665	+	0.487858i	0.690130	+	0.723685i	$0.257553\pi$
$504$		0			0
$505$	−28.6369	+	49.6006i	−1.27433	+	2.20720i
$506$	−3.14421	−	5.44593i	−0.139777	−	0.242101i
$507$		0			0
$508$	−2.41316	−	4.17972i	−0.107067	−	0.185445i
$509$	−19.0723			−0.845366			−0.422683	−	0.906278i	$-0.638912\pi$
$509$	−19.0723			−0.845366			−0.422683	+	0.906278i	$0.638912\pi$
$510$		0			0
$511$	17.2054			0.761120
$512$	14.2997			0.631961
$513$		0			0
$514$	10.6731			0.470770
$515$	−4.53138	+	7.84858i	−0.199676	+	0.345850i
$516$		0			0
$517$	−7.18883	−	12.4514i	−0.316164	−	0.547613i
$518$	4.72909	+	8.19103i	0.207784	+	0.359893i
$519$		0			0
$520$	21.1629	+	36.6552i	0.928053	+	1.60744i
$521$	28.9744			1.26939			0.634697	−	0.772761i	$-0.281125\pi$
$521$	28.9744			1.26939			0.634697	+	0.772761i	$0.281125\pi$
$522$		0			0
$523$	−10.9829	−	19.0229i	−0.480248	−	0.831814i	0.519495	−	0.854473i	$-0.326120\pi$
$523$	−10.9829	−	19.0229i	−0.480248	−	0.831814i	−0.999743	+	0.0226593i	$0.992787\pi$
$524$	10.3059	−	17.8504i	0.450217	−	0.779798i
$525$		0			0
$526$	8.60199	+	14.8991i	0.375065	+	0.649631i
$527$	−1.64171			−0.0715139
$528$		0			0
$529$	−9.69837	+	16.7981i	−0.421668	+	0.730351i
$530$	5.69705	+	9.86758i	0.247464	+	0.428620i
$531$		0			0
$532$	1.87766	−	3.25221i	0.0814070	−	0.141001i
$533$	22.4394			0.971958
$534$		0			0
$535$	−46.3675			−2.00464
$536$	−12.0313	+	15.9832i	−0.519673	+	0.690369i
$537$		0			0
$538$	−1.85046	−	3.20508i	−0.0797788	−	0.138181i
$539$	7.24848			0.312214
$540$		0			0
$541$	−31.6198			−1.35944			−0.679721	−	0.733471i	$-0.737899\pi$
$541$	−31.6198			−1.35944			−0.679721	+	0.733471i	$0.737899\pi$
$542$	1.52765	+	2.64596i	0.0656180	+	0.113654i
$543$		0			0
$544$	−14.2155			−0.609484
$545$	−35.0973			−1.50340
$546$		0			0
$547$	20.3232	−	35.2009i	0.868958	−	1.50508i	0.00589566	−	0.999983i	$-0.498123\pi$
$547$	20.3232	−	35.2009i	0.868958	−	1.50508i	0.863063	−	0.505097i	$-0.168543\pi$
$548$	6.79312	−	11.7660i	0.290188	−	0.502620i
$549$		0			0
$550$	−4.68687			−0.199849
$551$	−6.24884			−0.266210
$552$		0			0
$553$	1.70412	+	2.95161i	0.0724663	+	0.125515i
$554$	1.09607	+	1.89845i	0.0465675	+	0.0806572i
$555$		0			0
$556$	5.10705	−	8.84568i	0.216587	−	0.375140i
$557$	17.1382	−	29.6843i	0.726171	−	1.25776i	−0.232320	−	0.972639i	$-0.574632\pi$
$557$	17.1382	−	29.6843i	0.726171	−	1.25776i	0.958490	−	0.285125i	$-0.0920351\pi$
$558$		0			0
$559$	−12.4607	−	21.5826i	−0.527032	−	0.912846i
$560$	−5.60151			−0.236707
$561$		0			0
$562$	−5.08867	+	8.81383i	−0.214653	+	0.371789i
$563$	26.8660			1.13227			0.566133	−	0.824314i	$-0.308439\pi$
$563$	26.8660			1.13227			0.566133	+	0.824314i	$0.308439\pi$
$564$		0			0
$565$	−22.4512	+	38.8866i	−0.944528	+	1.63597i
$566$	−4.35833	−	7.54886i	−0.183194	−	0.317302i
$567$		0			0
$568$	−7.95692	+	13.7818i	−0.333865	+	0.578271i
$569$	9.69867	−	16.7986i	0.406590	−	0.704234i	−0.587915	−	0.808922i	$-0.700051\pi$
$569$	9.69867	−	16.7986i	0.406590	−	0.704234i	0.994505	+	0.104689i	$0.0333846\pi$
$570$		0			0
$571$	−8.12289	+	14.0693i	−0.339933	+	0.588780i	−0.984420	−	0.175835i	$-0.943738\pi$
$571$	−8.12289	+	14.0693i	−0.339933	+	0.588780i	0.644487	+	0.764615i	$0.277071\pi$
$572$	−5.81638	+	10.0743i	−0.243195	+	0.421226i
$573$		0			0
$574$	1.88778	−	3.26974i	0.0787946	−	0.136476i
$575$	15.7995	+	27.3656i	0.658886	+	1.14122i
$576$		0			0
$577$	−7.96829	+	13.8015i	−0.331724	+	0.574563i	−0.982850	−	0.184407i	$-0.940964\pi$
$577$	−7.96829	+	13.8015i	−0.331724	+	0.574563i	0.651126	+	0.758970i	$0.274297\pi$
$578$	−7.66242			−0.318715
$579$		0			0
$580$	8.02975	+	13.9079i	0.333417	+	0.577496i
$581$	−5.12148			−0.212475
$582$		0			0
$583$	−3.62991	+	6.28720i	−0.150336	+	0.260389i
$584$	−15.7392	−	27.2611i	−0.651292	−	1.12807i
$585$		0			0
$586$	0.160352	+	0.277739i	0.00662410	+	0.0114733i
$587$	−23.4135	−	40.5534i	−0.966378	−	1.67382i	−0.705865	−	0.708346i	$-0.749442\pi$
$587$	−23.4135	−	40.5534i	−0.966378	−	1.67382i	−0.260513	−	0.965470i	$-0.583892\pi$
$588$		0			0
$589$	−1.24467			−0.0512859
$590$	0.503337	+	0.871806i	0.0207221	+	0.0358917i
$591$		0			0
$592$	−6.80542	+	11.7873i	−0.279701	+	0.484456i
$593$	−8.23664	−	14.2663i	−0.338238	−	0.585846i	0.645863	−	0.763453i	$-0.276498\pi$
$593$	−8.23664	−	14.2663i	−0.338238	−	0.585846i	−0.984101	+	0.177607i	$0.943164\pi$
$594$		0			0
$595$	10.2483			0.420141
$596$	2.20403	−	3.81749i	0.0902805	−	0.156370i
$597$		0			0
$598$	−24.9632			−1.02082
$599$	5.98679	−	10.3694i	0.244614	−	0.423683i	−0.717409	−	0.696652i	$-0.754672\pi$
$599$	5.98679	−	10.3694i	0.244614	−	0.423683i	0.962023	+	0.272969i	$0.0880056\pi$
$600$		0			0
$601$	17.0476	+	29.5272i	0.695384	+	1.20444i	0.970051	+	0.242901i	$0.0780991\pi$
$601$	17.0476	+	29.5272i	0.695384	+	1.20444i	−0.274667	+	0.961539i	$0.588568\pi$
$602$	−4.19319			−0.170902
$603$		0			0
$604$	32.7592			1.33295
$605$	14.2327	+	24.6517i	0.578641	+	1.00224i
$606$		0			0
$607$	1.32449	−	2.29409i	0.0537595	−	0.0931142i	−0.837893	−	0.545834i	$-0.816213\pi$
$607$	1.32449	−	2.29409i	0.0537595	−	0.0931142i	0.891653	+	0.452720i	$0.149546\pi$
$608$	−10.7776			−0.437089
$609$		0			0
$610$	2.90558	−	5.03262i	0.117644	−	0.203765i
$611$	−57.0752			−2.30902
$612$		0			0
$613$	17.5209	+	30.3471i	0.707663	+	1.22571i	0.965722	+	0.259578i	$0.0835836\pi$
$613$	17.5209	+	30.3471i	0.707663	+	1.22571i	−0.258059	+	0.966129i	$0.583083\pi$
$614$	−5.73624	+	9.93546i	−0.231496	+	0.400963i
$615$		0			0
$616$	2.26878	+	3.92964i	0.0914117	+	0.158330i
$617$	−20.9422			−0.843099			−0.421550	−	0.906805i	$-0.638514\pi$
$617$	−20.9422			−0.843099			−0.421550	+	0.906805i	$0.638514\pi$
$618$		0			0
$619$	−4.53044	−	7.84695i	−0.182094	−	0.315395i	0.760500	−	0.649338i	$-0.224954\pi$
$619$	−4.53044	−	7.84695i	−0.182094	−	0.315395i	−0.942593	+	0.333943i	$0.891621\pi$
$620$	1.59941	+	2.77025i	0.0642337	+	0.111256i
$621$		0			0
$622$	9.49494	+	16.4457i	0.380712	+	0.659413i
$623$	5.51738	−	9.55638i	0.221049	−	0.382868i
$624$		0			0
$625$	−25.7135			−1.02854
$626$	10.4830	+	18.1570i	0.418984	+	0.725701i
$627$		0			0
$628$	8.65656			0.345435
$629$	12.4510	−	21.5657i	0.496453	−	0.859882i
$630$		0			0
$631$	10.9829	+	19.0229i	0.437222	+	0.757290i	0.997474	−	0.0710316i	$-0.0226291\pi$
$631$	10.9829	+	19.0229i	0.437222	+	0.757290i	−0.560252	+	0.828322i	$0.689296\pi$
$632$	3.11779	−	5.40018i	0.124019	−	0.214807i
$633$		0			0
$634$	9.53044	−	16.5072i	0.378502	−	0.655585i
$635$	4.99289	−	8.64794i	0.198137	−	0.343183i
$636$		0			0
$637$	14.3872	−	24.9194i	0.570042	−	0.987341i
$638$	1.62846	−	2.82057i	0.0644712	−	0.111667i
$639$		0			0
$640$	16.7630	+	29.0344i	0.662617	+	1.14769i
$641$	−0.629291	+	1.08996i	−0.0248555	+	0.0430510i	−0.878186	−	0.478320i	$-0.841246\pi$
$641$	−0.629291	+	1.08996i	−0.0248555	+	0.0430510i	0.853330	+	0.521371i	$0.174579\pi$
$642$		0			0
$643$	−11.3359			−0.447043			−0.223521	−	0.974699i	$-0.571755\pi$
$643$	−11.3359			−0.447043			−0.223521	+	0.974699i	$0.571755\pi$
$644$	6.59804	−	11.4281i	0.259999	−	0.450332i
$645$		0			0
$646$	3.14703			0.123818
$647$	−0.709425	−	1.22876i	−0.0278904	−	0.0483076i	0.851743	−	0.523959i	$-0.175546\pi$
$647$	−0.709425	−	1.22876i	−0.0278904	−	0.0483076i	−0.879634	+	0.475652i	$0.842212\pi$
$648$		0			0
$649$	−0.320705	+	0.555477i	−0.0125888	+	0.0218044i
$650$	−9.30277	+	16.1129i	−0.364885	+	0.631999i
$651$		0			0
$652$	−18.2890	−	31.6775i	−0.716252	−	1.24059i
$653$	−11.5280	−	19.9670i	−0.451124	−	0.781369i	0.547333	−	0.836915i	$-0.315643\pi$
$653$	−11.5280	−	19.9670i	−0.451124	−	0.781369i	−0.998456	+	0.0555462i	$0.982310\pi$
$654$		0			0
$655$	42.6464			1.66633
$656$	5.43325			0.212133
$657$		0			0
$658$	−4.80163	+	8.31667i	−0.187187	+	0.324218i
$659$	3.13631	−	5.43225i	0.122173	−	0.211610i	−0.798451	−	0.602060i	$-0.794347\pi$
$659$	3.13631	−	5.43225i	0.122173	−	0.211610i	0.920624	+	0.390449i	$0.127680\pi$
$660$		0			0
$661$	21.9899			0.855307			0.427654	−	0.903943i	$-0.359340\pi$
$661$	21.9899			0.855307			0.427654	+	0.903943i	$0.359340\pi$
$662$	17.1611			0.666987
$663$		0			0
$664$	4.68504	+	8.11473i	0.181815	+	0.314913i
$665$	7.76986			0.301302
$666$		0			0
$667$	−21.9582			−0.850225
$668$	−19.3031	−	33.4339i	−0.746858	−	1.29360i
$669$		0			0
$670$	−17.7224	−	2.16676i	−0.684675	−	0.0837092i
$671$	3.70263			0.142938
$672$		0			0
$673$	−18.5070			−0.713392			−0.356696	−	0.934220i	$-0.616097\pi$
$673$	−18.5070			−0.713392			−0.356696	+	0.934220i	$0.616097\pi$
$674$	−2.27890	+	3.94717i	−0.0877798	+	0.152039i
$675$		0			0
$676$	13.2281	+	22.9118i	0.508774	+	0.881222i
$677$	−4.19582	+	7.26737i	−0.161258	+	0.279308i	−0.935320	−	0.353802i	$-0.884889\pi$
$677$	−4.19582	+	7.26737i	−0.161258	+	0.279308i	0.774062	+	0.633110i	$0.218222\pi$
$678$		0			0
$679$	5.74637			0.220526
$680$	−9.37501	−	16.2380i	−0.359515	−	0.622698i
$681$		0			0
$682$	0.324364	−	0.561815i	0.0124205	−	0.0215130i
$683$	2.34187	+	4.05625i	0.0896093	+	0.155208i	0.907346	−	0.420385i	$-0.138105\pi$
$683$	2.34187	+	4.05625i	0.0896093	+	0.155208i	−0.817737	+	0.575592i	$0.804771\pi$
$684$		0			0
$685$	28.1103			1.07404
$686$	−5.66975	−	9.82029i	−0.216472	−	0.374941i
$687$		0			0
$688$	−3.01711	−	5.22579i	−0.115026	−	0.199232i
$689$	14.4097	+	24.9584i	0.548967	+	0.950838i
$690$		0			0
$691$	9.84918	−	17.0593i	0.374681	−	0.648966i	−0.615599	−	0.788060i	$-0.711086\pi$
$691$	9.84918	−	17.0593i	0.374681	−	0.648966i	0.990279	+	0.139094i	$0.0444190\pi$
$692$	−10.7776			−0.409702
$693$		0			0
$694$	5.80751			0.220450
$695$	21.1332			0.801629
$696$		0			0
$697$	−9.94050			−0.376523
$698$	3.00773	+	5.20953i	0.113844	+	0.197184i
$699$		0			0
$700$	−4.91764	−	8.51760i	−0.185869	−	0.321935i
$701$	−5.36412	+	9.29094i	−0.202600	+	0.350914i	−0.949365	−	0.314174i	$-0.898273\pi$
$701$	−5.36412	+	9.29094i	−0.202600	+	0.350914i	0.746765	+	0.665088i	$0.231606\pi$
$702$		0			0
$703$	9.43981	−	16.3502i	0.356029	−	0.616661i
$704$	0.952073	−	1.64904i	0.0358826	−	0.0621505i
$705$		0			0
$706$	−12.3568	+	21.4025i	−0.465053	+	0.805495i
$707$	12.1872	+	21.1088i	0.458346	+	0.793878i
$708$		0			0
$709$	−17.1103	−	29.6358i	−0.642589	−	1.11300i	−0.984853	−	0.173393i	$-0.944527\pi$
$709$	−17.1103	−	29.6358i	−0.642589	−	1.11300i	0.342264	−	0.939604i	$-0.388806\pi$
$710$	−14.2028			−0.533020
$711$		0			0
$712$	−20.1888			−0.756608
$713$	−4.37374			−0.163798
$714$		0			0
$715$	−24.0685			−0.900109
$716$	−2.20403	+	3.81749i	−0.0823684	+	0.142666i
$717$		0			0
$718$	11.8739	+	20.5662i	0.443129	+	0.767522i
$719$	7.03840	+	12.1909i	0.262488	+	0.454643i	0.966902	−	0.255146i	$-0.0821237\pi$
$719$	7.03840	+	12.1909i	0.262488	+	0.454643i	−0.704414	+	0.709789i	$0.748790\pi$
$720$		0			0
$721$	1.92845	+	3.34017i	0.0718191	+	0.124394i
$722$	−10.8172			−0.402573
$723$		0			0
$724$	8.59314	+	14.8838i	0.319362	+	0.553151i
$725$	−8.18292	+	14.1732i	−0.303906	+	0.526381i
$726$		0			0
$727$	−24.9949	−	43.2925i	−0.927011	−	1.60563i	−0.788295	−	0.615298i	$-0.789036\pi$
$727$	−24.9949	−	43.2925i	−0.927011	−	1.60563i	−0.138716	−	0.990332i	$-0.544298\pi$
$728$	18.0128			0.667599
$729$		0			0
$730$	14.0469	−	24.3299i	0.519898	−	0.900489i
$731$	5.52001	+	9.56094i	0.204165	+	0.353624i
$732$		0			0
$733$	−1.02090	+	1.76825i	−0.0377079	+	0.0653119i	−0.884263	−	0.466988i	$-0.845339\pi$
$733$	−1.02090	+	1.76825i	−0.0377079	+	0.0653119i	0.846556	+	0.532300i	$0.178672\pi$
$734$	−16.1377			−0.595654
$735$		0			0
$736$	−37.8720			−1.39598
$737$	−4.45036	−	10.4694i	−0.163931	−	0.385645i
$738$		0			0
$739$	−7.04376	−	12.2002i	−0.259109	−	0.448790i	0.706894	−	0.707319i	$-0.250096\pi$
$739$	−7.04376	−	12.2002i	−0.259109	−	0.448790i	−0.966003	+	0.258529i	$0.916762\pi$
$740$	−48.5206			−1.78365
$741$		0			0
$742$	4.84905			0.178014
$743$	4.37549	+	7.57857i	0.160521	+	0.278031i	0.935056	−	0.354501i	$-0.115349\pi$
$743$	4.37549	+	7.57857i	0.160521	+	0.278031i	−0.774535	+	0.632532i	$0.782016\pi$
$744$		0			0
$745$	9.12038			0.334145
$746$	−6.73414			−0.246554
$747$		0			0
$748$	2.57662	−	4.46283i	0.0942104	−	0.163177i
$749$	−9.86645	+	17.0892i	−0.360512	+	0.624426i
$750$		0			0
$751$	33.9214			1.23781			0.618905	−	0.785466i	$-0.287577\pi$
$751$	33.9214			1.23781			0.618905	+	0.785466i	$0.287577\pi$
$752$	−13.8196			−0.503950
$753$		0			0
$754$	−6.46450	−	11.1968i	−0.235423	−	0.407765i
$755$	33.8898	+	58.6989i	1.23338	+	2.13627i
$756$		0			0
$757$	12.1667	−	21.0733i	0.442205	−	0.765921i	−0.555648	−	0.831418i	$-0.687530\pi$
$757$	12.1667	−	21.0733i	0.442205	−	0.765921i	0.997853	+	0.0654966i	$0.0208632\pi$
$758$	−1.01768	+	1.76268i	−0.0369639	+	0.0640233i
$759$		0			0
$760$	−7.10774	−	12.3110i	−0.257825	−	0.446566i
$761$	−8.20759			−0.297525			−0.148762	−	0.988873i	$-0.547529\pi$
$761$	−8.20759			−0.297525			−0.148762	+	0.988873i	$0.547529\pi$
$762$		0			0
$763$	−7.46829	+	12.9355i	−0.270370	+	0.468295i
$764$	31.4255			1.13694
$765$		0			0
$766$	−2.94935	+	5.10842i	−0.106564	+	0.184575i
$767$	1.27311	+	2.20509i	0.0459692	+	0.0796210i
$768$		0			0
$769$	3.34540	−	5.79439i	0.120638	−	0.208951i	−0.799381	−	0.600824i	$-0.794839\pi$
$769$	3.34540	−	5.79439i	0.120638	−	0.208951i	0.920019	+	0.391873i	$0.128173\pi$
$770$	−2.02483	+	3.50712i	−0.0729700	+	0.126388i
$771$		0			0
$772$	0.477826	−	0.827619i	0.0171973	−	0.0297866i
$773$	16.3385	−	28.2992i	0.587656	−	1.01785i	−0.406882	−	0.913481i	$-0.633384\pi$
$773$	16.3385	−	28.2992i	0.587656	−	1.01785i	0.994539	−	0.104370i	$-0.0332826\pi$
$774$		0			0
$775$	−1.62991	+	2.82309i	−0.0585483	+	0.101409i
$776$	−5.25669	−	9.10485i	−0.188704	−	0.326845i
$777$		0			0
$778$	−10.6566	+	18.4577i	−0.382056	+	0.661741i
$779$	−7.53647			−0.270022
$780$		0			0
$781$	−4.52469	−	7.83699i	−0.161906	−	0.280430i
$782$	11.0585			0.395453
$783$		0			0
$784$	3.48357	−	6.03373i	0.124413	−	0.215490i
$785$	8.95532	+	15.5111i	0.319629	+	0.553614i
$786$		0			0
$787$	−9.95692	−	17.2459i	−0.354926	−	0.614750i	0.632179	−	0.774822i	$-0.282161\pi$
$787$	−9.95692	−	17.2459i	−0.354926	−	0.614750i	−0.987105	+	0.160072i	$0.948827\pi$
$788$	16.2218	+	28.0971i	0.577879	+	1.00092i
$789$		0			0
$790$	5.56512			0.197998
$791$	9.55468	+	16.5492i	0.339725	+	0.588421i
$792$		0			0
$793$	7.34918	−	12.7292i	0.260977	−	0.452026i
$794$	11.6865	+	20.2416i	0.414737	+	0.718346i
$795$		0			0
$796$	−20.7300			−0.734757
$797$	8.42557	−	14.5935i	0.298449	−	0.516929i	−0.677332	−	0.735677i	$-0.736864\pi$
$797$	8.42557	−	14.5935i	0.298449	−	0.516929i	0.975781	+	0.218748i	$0.0701974\pi$
$798$		0			0
$799$	25.2839			0.894481
$800$	−14.1134	+	24.4451i	−0.498983	+	0.864263i
$801$		0			0
$802$	−8.91443	−	15.4403i	−0.314780	−	0.545214i
$803$	17.9001			0.631681
$804$		0			0
$805$	27.3030			0.962305
$806$	−1.28763	−	2.23024i	−0.0453549	−	0.0785570i
$807$		0			0
$808$	22.2973	−	38.6200i	0.784415	−	1.35865i
$809$	−19.2952			−0.678382			−0.339191	−	0.940717i	$-0.610153\pi$
$809$	−19.2952			−0.678382			−0.339191	+	0.940717i	$0.610153\pi$
$810$		0			0
$811$	−11.9436	+	20.6869i	−0.419396	+	0.726416i	−0.995879	−	0.0906936i	$-0.971092\pi$
$811$	−11.9436	+	20.6869i	−0.419396	+	0.726416i	0.576482	+	0.817110i	$0.304425\pi$
$812$	6.83454			0.239845
$813$		0			0
$814$	4.92005	+	8.52178i	0.172448	+	0.298688i
$815$	37.8404	−	65.5415i	1.32549	−	2.29582i
$816$		0			0
$817$	4.18504	+	7.24871i	0.146416	+	0.253600i
$818$	−25.5598			−0.893678
$819$		0			0
$820$	9.68436	+	16.7738i	0.338192	+	0.585766i
$821$	8.76113	+	15.1747i	0.305765	+	0.529601i	0.977431	−	0.211253i	$-0.0677543\pi$
$821$	8.76113	+	15.1747i	0.305765	+	0.529601i	−0.671666	+	0.740854i	$0.734421\pi$
$822$		0			0
$823$	14.4252	+	24.9852i	0.502831	+	0.870929i	0.999995	+	0.00327244i	$0.00104165\pi$
$823$	14.4252	+	24.9852i	0.502831	+	0.870929i	−0.497163	+	0.867657i	$0.665625\pi$
$824$	3.52822	−	6.11106i	0.122911	−	0.212889i
$825$		0			0
$826$	0.428417			0.0149065
$827$	−25.4643	−	44.1054i	−0.885479	−	1.53370i	−0.845163	−	0.534508i	$-0.820497\pi$
$827$	−25.4643	−	44.1054i	−0.885479	−	1.53370i	−0.0403163	−	0.999187i	$-0.512837\pi$
$828$		0			0
$829$	−25.2497			−0.876959			−0.438479	−	0.898741i	$-0.644483\pi$
$829$	−25.2497			−0.876959			−0.438479	+	0.898741i	$0.644483\pi$
$830$	−4.18130	+	7.24222i	−0.145135	+	0.251381i
$831$		0			0
$832$	−3.77946	−	6.54621i	−0.131029	−	0.226949i
$833$	−6.37343	+	11.0391i	−0.220826	+	0.382482i
$834$		0			0
$835$	39.9385	−	69.1756i	1.38213	−	2.39392i
$836$	1.95348	−	3.38353i	0.0675626	−	0.117022i
$837$		0			0
$838$	7.23259	−	12.5272i	0.249846	−	0.432746i
$839$	−0.413060	+	0.715440i	−0.0142604	+	0.0246997i	−0.873068	−	0.487599i	$-0.837873\pi$
$839$	−0.413060	+	0.715440i	−0.0142604	+	0.0246997i	0.858807	+	0.512299i	$0.171206\pi$
$840$		0			0
$841$	8.81368	+	15.2657i	0.303920	+	0.526405i
$842$	1.49460	−	2.58873i	0.0515074	−	0.0892135i
$843$		0			0
$844$	14.7020			0.506065
$845$	−27.3693	+	47.4050i	−0.941533	+	1.63078i
$846$		0			0
$847$	12.1142			0.416248
$848$	3.48903	+	6.04317i	0.119814	+	0.207523i
$849$		0			0
$850$	4.12107	−	7.13789i	0.141351	−	0.244828i
$851$	33.1712	−	57.4541i	1.13709	−	1.96950i
$852$		0			0
$853$	−18.0438	−	31.2527i	−0.617807	−	1.07007i	−0.989885	−	0.141871i	$-0.954688\pi$
$853$	−18.0438	−	31.2527i	−0.617807	−	1.07007i	0.372078	−	0.928201i	$-0.378645\pi$
$854$	−1.23655	−	2.14176i	−0.0423138	−	0.0732896i
$855$		0			0
$856$	36.1027			1.23396
$857$	3.09138			0.105599			0.0527997	−	0.998605i	$-0.483186\pi$
$857$	3.09138			0.105599			0.0527997	+	0.998605i	$0.483186\pi$
$858$		0			0
$859$	−10.4005	+	18.0142i	−0.354861	+	0.614638i	−0.987094	−	0.160141i	$-0.948805\pi$
$859$	−10.4005	+	18.0142i	−0.354861	+	0.614638i	0.632233	+	0.774778i	$0.282139\pi$
$860$	10.7555	−	18.6292i	0.366761	−	0.635249i
$861$		0			0
$862$	−16.8631			−0.574359
$863$	−32.0896			−1.09234			−0.546172	−	0.837673i	$-0.683915\pi$
$863$	−32.0896			−1.09234			−0.546172	+	0.837673i	$0.683915\pi$
$864$		0			0
$865$	−11.1495	−	19.3116i	−0.379096	−	0.656613i
$866$	−2.59905			−0.0883192
$867$		0			0
$868$	1.36134			0.0462068
$869$	1.77293	+	3.07080i	0.0601424	+	0.104170i
$870$		0			0
$871$	−44.8257	−	5.48045i	−1.51886	−	0.185698i
$872$	27.3275			0.925425
$873$		0			0
$874$	8.38413			0.283597
$875$	−0.308257	+	0.533918i	−0.0104210	+	0.0180497i
$876$		0			0
$877$	17.4347	+	30.1979i	0.588730	+	1.01971i	0.994399	+	0.105690i	$0.0337051\pi$
$877$	17.4347	+	30.1979i	0.588730	+	1.01971i	−0.405669	+	0.914020i	$0.632962\pi$
$878$	2.58541	−	4.47806i	0.0872532	−	0.151127i
$879$		0			0
$880$	−5.82770			−0.196452
$881$	−15.6974	−	27.1886i	−0.528857	−	0.916008i	−0.999434	−	0.0336485i	$-0.989287\pi$
$881$	−15.6974	−	27.1886i	−0.528857	−	0.916008i	0.470576	−	0.882359i	$-0.344046\pi$
$882$		0			0
$883$	−23.5083	+	40.7175i	−0.791116	+	1.37025i	0.134160	+	0.990960i	$0.457166\pi$
$883$	−23.5083	+	40.7175i	−0.791116	+	1.37025i	−0.925276	+	0.379294i	$0.876167\pi$
$884$	−10.2284	−	17.7162i	−0.344019	−	0.595859i
$885$		0			0
$886$	−2.82998			−0.0950751
$887$	−2.27890	−	3.94717i	−0.0765179	−	0.132533i	0.825227	−	0.564801i	$-0.191047\pi$
$887$	−2.27890	−	3.94717i	−0.0765179	−	0.132533i	−0.901745	+	0.432268i	$0.857714\pi$
$888$		0			0
$889$	−2.12485	−	3.68035i	−0.0712653	−	0.123435i
$890$	−9.00904	−	15.6041i	−0.301984	−	0.523051i
$891$		0			0
$892$	6.60970	−	11.4483i	0.221309	−	0.383319i
$893$	19.1692			0.641474
$894$		0			0
$895$	−9.12038			−0.304861
$896$	14.2679			0.476657
$897$		0			0
$898$	−15.4854			−0.516756
$899$	−1.13263	−	1.96177i	−0.0377753	−	0.0654287i
$900$		0			0
$901$	−6.38341	−	11.0564i	−0.212662	−	0.368342i
$902$	1.96401	−	3.40177i	0.0653945	−	0.113267i
$903$		0			0
$904$	17.4809	−	30.2779i	0.581407	−	1.00703i
$905$	−17.7794	+	30.7949i	−0.591008	+	1.02366i
$906$		0			0
$907$	19.6438	−	34.0241i	0.652262	−	1.12975i	−0.330311	−	0.943872i	$-0.607154\pi$
$907$	19.6438	−	34.0241i	0.652262	−	1.12975i	0.982573	−	0.185878i	$-0.0595129\pi$
$908$	17.7217	+	30.6949i	0.588116	+	1.01865i
$909$		0			0
$910$	8.03801	+	13.9223i	0.266458	+	0.461518i
$911$	46.6227			1.54468			0.772339	−	0.635211i	$-0.219087\pi$
$911$	46.6227			1.54468			0.772339	+	0.635211i	$0.219087\pi$
$912$		0			0
$913$	−5.32828			−0.176340
$914$	7.91960			0.261957
$915$		0			0
$916$	−33.8707			−1.11912
$917$	9.07465	−	15.7178i	0.299671	−	0.519046i
$918$		0			0
$919$	−22.8612	−	39.5968i	−0.754123	−	1.30618i	−0.945809	−	0.324722i	$-0.894729\pi$
$919$	−22.8612	−	39.5968i	−0.754123	−	1.30618i	0.191687	−	0.981456i	$-0.438604\pi$
$920$	−24.9763	−	43.2603i	−0.823446	−	1.42625i
$921$		0			0
$922$	0.716066	+	1.24026i	0.0235824	+	0.0408459i
$923$	−35.9235			−1.18243
$924$		0			0
$925$	−24.7231	−	42.8216i	−0.812889	−	1.40797i
$926$	6.35276	−	11.0033i	0.208765	−	0.361591i
$927$		0			0
$928$	−9.80738	−	16.9869i	−0.321943	−	0.557622i
$929$	−13.1300			−0.430781			−0.215390	−	0.976528i	$-0.569102\pi$
$929$	−13.1300			−0.430781			−0.215390	+	0.976528i	$0.569102\pi$
$930$		0			0
$931$	−4.83207	+	8.36939i	−0.158365	+	0.274296i
$932$	−10.6780	−	18.4949i	−0.349771	−	0.605821i
$933$		0			0
$934$	0.813685	−	1.40934i	0.0266246	−	0.0461151i
$935$	10.6622			0.348690
$936$		0			0
$937$	−43.0126			−1.40516			−0.702580	−	0.711604i	$-0.747969\pi$
$937$	−43.0126			−1.40516			−0.702580	+	0.711604i	$0.747969\pi$
$938$	−4.56969	+	6.07069i	−0.149206	+	0.198215i
$939$		0			0
$940$	−24.6324	−	42.6646i	−0.803421	−	1.39157i
$941$	−34.3734			−1.12054			−0.560270	−	0.828310i	$-0.689303\pi$
$941$	−34.3734			−1.12054			−0.560270	+	0.828310i	$0.689303\pi$
$942$		0			0
$943$	−26.4829			−0.862401
$944$	0.308257	+	0.533918i	0.0100329	+	0.0173775i
$945$		0			0
$946$	−4.36251			−0.141837
$947$	50.4142			1.63824			0.819121	−	0.573621i	$-0.194462\pi$
$947$	50.4142			1.63824			0.819121	+	0.573621i	$0.194462\pi$
$948$		0			0
$949$	35.5292	−	61.5383i	1.15333	−	1.99762i
$950$	3.12442	−	5.41165i	0.101370	−	0.175577i
$951$		0			0
$952$	−7.97955			−0.258619
$953$	−0.928289			−0.0300702			−0.0150351	−	0.999887i	$-0.504786\pi$
$953$	−0.928289			−0.0300702			−0.0150351	+	0.999887i	$0.504786\pi$
$954$		0			0
$955$	32.5101	+	56.3091i	1.05200	+	1.82212i
$956$	16.9220	+	29.3098i	0.547297	+	0.947946i
$957$		0			0
$958$	10.7395	−	18.6013i	0.346977	−	0.600982i
$959$	5.98152	−	10.3603i	0.193153	−	0.334552i
$960$		0			0
$961$	15.2744	+	26.4560i	0.492722	+	0.853420i
$962$	39.0624			1.25942
$963$		0			0
$964$	−3.18321	+	5.51349i	−0.102524	+	0.177577i
$965$	1.97727			0.0636505
$966$		0			0
$967$	5.74144	−	9.94447i	0.184632	−	0.319793i	−0.758820	−	0.651300i	$-0.774224\pi$
$967$	5.74144	−	9.94447i	0.184632	−	0.319793i	0.943453	+	0.331508i	$0.107557\pi$
$968$	−11.0818	−	19.1943i	−0.356184	−	0.616929i
$969$		0			0
$970$	4.69148	−	8.12588i	0.150634	−	0.260906i
$971$	−6.34087	+	10.9827i	−0.203488	+	0.352452i	−0.949650	−	0.313313i	$-0.898561\pi$
$971$	−6.34087	+	10.9827i	−0.203488	+	0.352452i	0.746162	+	0.665765i	$0.231894\pi$
$972$		0			0
$973$	4.49690	−	7.78886i	0.144164	−	0.249699i
$974$	−6.04450	+	10.4694i	−0.193678	+	0.335461i
$975$		0			0
$976$	1.77946	−	3.08211i	0.0569591	−	0.0986560i
$977$	18.0247	+	31.2197i	0.576661	+	0.998807i	0.995859	+	0.0909118i	$0.0289781\pi$
$977$	18.0247	+	31.2197i	0.576661	+	0.998807i	−0.419198	+	0.907895i	$0.637689\pi$
$978$		0			0
$979$	5.74017	−	9.94227i	0.183457	−	0.317756i
$980$	24.8368			0.793383
$981$		0			0
$982$	3.91878	+	6.78753i	0.125053	+	0.216599i
$983$	−34.3972			−1.09710			−0.548550	−	0.836118i	$-0.684820\pi$
$983$	−34.3972			−1.09710			−0.548550	+	0.836118i	$0.684820\pi$
$984$		0			0
$985$	−33.5634	+	58.1335i	−1.06942	+	1.85229i
$986$	2.86373	+	4.96013i	0.0911998	+	0.157963i
$987$		0			0
$988$	−7.75477	−	13.4317i	−0.246712	−	0.427318i
$989$	14.7061	+	25.4717i	0.467626	+	0.809953i
$990$		0			0
$991$	−21.0912			−0.669984			−0.334992	−	0.942221i	$-0.608734\pi$
$991$	−21.0912			−0.669984			−0.334992	+	0.942221i	$0.608734\pi$
$992$	−1.95348	−	3.38353i	−0.0620231	−	0.107427i
$993$		0			0
$994$	−3.02217	+	5.23456i	−0.0958575	+	0.166030i
$995$	−21.4455	−	37.1447i	−0.679868	−	1.17757i
$996$		0			0
$997$	43.5564			1.37944			0.689722	−	0.724074i	$-0.257733\pi$
$997$	43.5564			1.37944			0.689722	+	0.724074i	$0.257733\pi$
$998$	11.1607	−	19.3309i	0.353286	−	0.611910i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.g.h.37.3	✓	12
3.2	odd	2	inner	603.2.g.h.37.4	yes	12
67.29	even	3	inner	603.2.g.h.163.3	yes	12
201.29	odd	6	inner	603.2.g.h.163.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.g.h.37.3	✓	12	1.1	even	1	trivial
603.2.g.h.37.4	yes	12	3.2	odd	2	inner
603.2.g.h.163.3	yes	12	67.29	even	3	inner
603.2.g.h.163.4	yes	12	201.29	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.347450 - 0.601802i) q^{2} +(0.758557 - 1.31386i) q^{4} +3.13894 q^{5} +(0.667930 - 1.15689i) q^{7} -2.44404 q^{8} +O(q^{10})\)	\(q+(-0.347450 - 0.601802i) q^{2} +(0.758557 - 1.31386i) q^{4} +3.13894 q^{5} +(0.667930 - 1.15689i) q^{7} -2.44404 q^{8} +(-1.09063 - 1.88902i) q^{10} +(0.694901 - 1.20360i) q^{11} +(-2.75856 - 4.77796i) q^{13} -0.928289 q^{14} +(-0.667930 - 1.15689i) q^{16} +(1.22202 + 2.11660i) q^{17} +(0.926486 + 1.60472i) q^{19} +(2.38107 - 4.12413i) q^{20} -0.965774 q^{22} +(3.25564 + 5.63893i) q^{23} +4.85297 q^{25} +(-1.91692 + 3.32021i) q^{26} +(-1.01332 - 1.75513i) q^{28} +(-1.68617 + 2.92053i) q^{29} +(-0.335859 + 0.581725i) q^{31} +(-2.90819 + 5.03713i) q^{32} +(0.849184 - 1.47083i) q^{34} +(2.09659 - 3.63141i) q^{35} +(-5.09442 - 8.82379i) q^{37} +(0.643816 - 1.11512i) q^{38} -7.67172 q^{40} +(-2.03362 + 3.52233i) q^{41} +4.51711 q^{43} +(-1.05424 - 1.82600i) q^{44} +(2.26235 - 3.91850i) q^{46} +(5.17256 - 8.95914i) q^{47} +(2.60774 + 4.51674i) q^{49} +(-1.68617 - 2.92053i) q^{50} -8.37009 q^{52} -5.22365 q^{53} +(2.18125 - 3.77804i) q^{55} +(-1.63245 + 2.82748i) q^{56} +2.34344 q^{58} -0.461512 q^{59} +(1.33207 + 2.30721i) q^{61} +0.466777 q^{62} +1.37009 q^{64} +(-8.65896 - 14.9978i) q^{65} +(4.92270 - 6.53965i) q^{67} +3.70789 q^{68} -2.91385 q^{70} +(3.25564 - 5.63893i) q^{71} +(6.43981 + 11.1541i) q^{73} +(-3.54011 + 6.13165i) q^{74} +2.81117 q^{76} +(-0.928289 - 1.60784i) q^{77} +(-1.27567 + 2.20952i) q^{79} +(-2.09659 - 3.63141i) q^{80} +2.82632 q^{82} +(-1.91692 - 3.32021i) q^{83} +(3.83586 + 6.64390i) q^{85} +(-1.56947 - 2.71841i) q^{86} +(-1.69837 + 2.94166i) q^{88} +8.26042 q^{89} -7.37009 q^{91} +9.87835 q^{92} -7.18883 q^{94} +(2.90819 + 5.03713i) q^{95} +(2.15082 + 3.72532i) q^{97} +(1.81212 - 3.13868i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{4} + 6 q^{7}+O(q^{10}) \) 12 * q - 10 * q^4 + 6 * q^7	\( 12 q - 10 q^{4} + 6 q^{7} + 4 q^{10} - 14 q^{13} - 6 q^{16} - 10 q^{19} - 88 q^{22} + 16 q^{25} + 20 q^{28} - 26 q^{34} - 38 q^{37} - 84 q^{40} + 16 q^{43} + 2 q^{46} - 24 q^{49} - 20 q^{52} - 8 q^{55} + 12 q^{58} + 18 q^{61} - 64 q^{64} + 44 q^{67} + 148 q^{70} + 24 q^{73} + 80 q^{76} + 42 q^{79} + 56 q^{82} + 42 q^{85} + 52 q^{88} - 8 q^{91} - 40 q^{94} + 62 q^{97}+O(q^{100}) \) 12 * q - 10 * q^4 + 6 * q^7 + 4 * q^10 - 14 * q^13 - 6 * q^16 - 10 * q^19 - 88 * q^22 + 16 * q^25 + 20 * q^28 - 26 * q^34 - 38 * q^37 - 84 * q^40 + 16 * q^43 + 2 * q^46 - 24 * q^49 - 20 * q^52 - 8 * q^55 + 12 * q^58 + 18 * q^61 - 64 * q^64 + 44 * q^67 + 148 * q^70 + 24 * q^73 + 80 * q^76 + 42 * q^79 + 56 * q^82 + 42 * q^85 + 52 * q^88 - 8 * q^91 - 40 * q^94 + 62 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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