LMFDB - Embedded newform 432.2.k.d.109.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(109,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("432.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.k (of order $4$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.5
Character	$\chi$	$=$	432.109
Dual form			432.2.k.d.325.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.636726 + 1.26277i) q^{2} +(-1.18916 - 1.60807i) q^{4} +(-1.27540 + 1.27540i) q^{5} +0.0285435i q^{7} +(2.78779 - 0.477727i) q^{8} +O(q^{10})$	\(q+(-0.636726 + 1.26277i) q^{2} +(-1.18916 - 1.60807i) q^{4} +(-1.27540 + 1.27540i) q^{5} +0.0285435i q^{7} +(2.78779 - 0.477727i) q^{8} +(-0.798453 - 2.42262i) q^{10} +(-2.94156 + 2.94156i) q^{11} +(-1.34564 - 1.34564i) q^{13} +(-0.0360437 - 0.0181744i) q^{14} +(-1.17180 + 3.82451i) q^{16} -1.40161 q^{17} +(-5.46493 - 5.46493i) q^{19} +(3.56760 + 0.534285i) q^{20} +(-1.84153 - 5.58747i) q^{22} -0.0963791i q^{23} +1.74670i q^{25} +(2.55604 - 0.842426i) q^{26} +(0.0459000 - 0.0339427i) q^{28} +(-6.62741 - 6.62741i) q^{29} -3.75086 q^{31} +(-4.08335 - 3.91488i) q^{32} +(0.892444 - 1.76991i) q^{34} +(-0.0364044 - 0.0364044i) q^{35} +(4.36597 - 4.36597i) q^{37} +(10.3806 - 3.42126i) q^{38} +(-2.94626 + 4.16485i) q^{40} +5.24322i q^{41} +(-5.87378 + 5.87378i) q^{43} +(8.22822 + 1.23226i) q^{44} +(0.121704 + 0.0613671i) q^{46} -3.04768 q^{47} +6.99919 q^{49} +(-2.20567 - 1.11217i) q^{50} +(-0.563710 + 3.76407i) q^{52} +(-0.358246 + 0.358246i) q^{53} -7.50333i q^{55} +(0.0136360 + 0.0795732i) q^{56} +(12.5887 - 4.14903i) q^{58} +(-4.94884 + 4.94884i) q^{59} +(6.84320 + 6.84320i) q^{61} +(2.38827 - 4.73646i) q^{62} +(7.54355 - 2.66361i) q^{64} +3.43247 q^{65} +(1.56428 + 1.56428i) q^{67} +(1.66674 + 2.25390i) q^{68} +(0.0691499 - 0.0227906i) q^{70} -13.1820i q^{71} +7.44056i q^{73} +(2.73327 + 8.29312i) q^{74} +(-2.28934 + 15.2867i) q^{76} +(-0.0839622 - 0.0839622i) q^{77} -2.58559 q^{79} +(-3.38327 - 6.37231i) q^{80} +(-6.62096 - 3.33849i) q^{82} +(-7.92875 - 7.92875i) q^{83} +(1.78762 - 1.78762i) q^{85} +(-3.67722 - 11.1572i) q^{86} +(-6.79518 + 9.60570i) q^{88} +9.64812i q^{89} +(0.0384093 - 0.0384093i) q^{91} +(-0.154985 + 0.114610i) q^{92} +(1.94054 - 3.84851i) q^{94} +13.9400 q^{95} +2.24923 q^{97} +(-4.45657 + 8.83834i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} + 24 q^{16} + 16 q^{19} + 32 q^{22} + 24 q^{28} - 8 q^{34} + 56 q^{40} - 16 q^{43} - 32 q^{49} - 16 q^{52} - 32 q^{61} + 24 q^{64} + 32 q^{67} - 96 q^{70} - 48 q^{76} - 32 q^{79} + 32 q^{85} - 88 q^{88} - 48 q^{91} - 96 q^{94}+O(q^{100}) $ 32 * q - 8 * q^10 + 24 * q^16 + 16 * q^19 + 32 * q^22 + 24 * q^28 - 8 * q^34 + 56 * q^40 - 16 * q^43 - 32 * q^49 - 16 * q^52 - 32 * q^61 + 24 * q^64 + 32 * q^67 - 96 * q^70 - 48 * q^76 - 32 * q^79 + 32 * q^85 - 88 * q^88 - 48 * q^91 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−0.636726	+	1.26277i	−0.450234	+	0.892911i
$2$	−0.636726	+	1.26277i	−0.450234	+	0.892911i
$3$		0			0
$3$		0			0
$4$	−1.18916	−	1.60807i	−0.594579	−	0.804037i
$5$	−1.27540	+	1.27540i	−0.570377	+	0.570377i	−0.932234	−	0.361857i	$-0.882143\pi$
$5$	−1.27540	+	1.27540i	−0.570377	+	0.570377i	0.361857	+	0.932234i	$0.382143\pi$
$6$		0			0
$7$			0.0285435i			0.0107884i	0.999985	+	0.00539421i	$0.00171704\pi$
$7$			0.0285435i			0.0107884i	−0.999985	+	0.00539421i	$0.998283\pi$
$8$	2.78779	−	0.477727i	0.985633	−	0.168902i
$9$		0			0
$10$	−0.798453	−	2.42262i	−0.252493	−	0.766099i
$11$	−2.94156	+	2.94156i	−0.886913	+	0.886913i	−0.994225	−	0.107313i	$-0.965775\pi$
$11$	−2.94156	+	2.94156i	−0.886913	+	0.886913i	0.107313	+	0.994225i	$0.465775\pi$
$12$		0			0
$13$	−1.34564	−	1.34564i	−0.373214	−	0.373214i	0.495432	−	0.868646i	$-0.335010\pi$
$13$	−1.34564	−	1.34564i	−0.373214	−	0.373214i	−0.868646	+	0.495432i	$0.835010\pi$
$14$	−0.0360437	−	0.0181744i	−0.00963310	−	0.00485731i
$15$		0			0
$16$	−1.17180	+	3.82451i	−0.292951	+	0.956128i
$17$	−1.40161			−0.339941			−0.169970	−	0.985449i	$-0.554367\pi$
$17$	−1.40161			−0.339941			−0.169970	+	0.985449i	$0.554367\pi$
$18$		0			0
$19$	−5.46493	−	5.46493i	−1.25374	−	1.25374i	−0.954031	−	0.299709i	$-0.903110\pi$
$19$	−5.46493	−	5.46493i	−1.25374	−	1.25374i	−0.299709	−	0.954031i	$-0.596890\pi$
$20$	3.56760	+	0.534285i	0.797739	+	0.119470i
$21$		0			0
$22$	−1.84153	−	5.58747i	−0.392616	−	1.19125i
$23$		−	0.0963791i		−	0.0200964i	−0.999950	−	0.0100482i	$-0.996801\pi$
$23$		−	0.0963791i		−	0.0200964i	0.999950	−	0.0100482i	$-0.00319850\pi$
$24$		0			0
$25$			1.74670i			0.349340i
$26$	2.55604	−	0.842426i	0.501280	−	0.165213i
$27$		0			0
$28$	0.0459000	−	0.0339427i	0.00867429	−	0.00641457i
$29$	−6.62741	−	6.62741i	−1.23068	−	1.23068i	−0.963703	−	0.266977i	$-0.913975\pi$
$29$	−6.62741	−	6.62741i	−1.23068	−	1.23068i	−0.266977	−	0.963703i	$-0.586025\pi$
$30$		0			0
$31$	−3.75086			−0.673674			−0.336837	−	0.941563i	$-0.609357\pi$
$31$	−3.75086			−0.673674			−0.336837	+	0.941563i	$0.609357\pi$
$32$	−4.08335	−	3.91488i	−0.721840	−	0.692059i
$33$		0			0
$34$	0.892444	−	1.76991i	0.153053	−	0.303537i
$35$	−0.0364044	−	0.0364044i	−0.00615347	−	0.00615347i
$36$		0			0
$37$	4.36597	−	4.36597i	0.717760	−	0.717760i	−0.250386	−	0.968146i	$-0.580557\pi$
$37$	4.36597	−	4.36597i	0.717760	−	0.717760i	0.968146	+	0.250386i	$0.0805575\pi$
$38$	10.3806	−	3.42126i	1.68395	−	0.555002i
$39$		0			0
$40$	−2.94626	+	4.16485i	−0.465845	+	0.658520i
$41$			5.24322i			0.818853i	0.912343	+	0.409426i	$0.134271\pi$
$41$			5.24322i			0.818853i	−0.912343	+	0.409426i	$0.865729\pi$
$42$		0			0
$43$	−5.87378	+	5.87378i	−0.895743	+	0.895743i	−0.995056	−	0.0993134i	$-0.968335\pi$
$43$	−5.87378	+	5.87378i	−0.895743	+	0.895743i	0.0993134	+	0.995056i	$0.468335\pi$
$44$	8.22822	+	1.23226i	1.24045	+	0.185770i
$45$		0			0
$46$	0.121704	+	0.0613671i	0.0179443	+	0.00904809i
$47$	−3.04768			−0.444549			−0.222275	−	0.974984i	$-0.571348\pi$
$47$	−3.04768			−0.444549			−0.222275	+	0.974984i	$0.571348\pi$
$48$		0			0
$49$	6.99919			0.999884
$50$	−2.20567	−	1.11217i	−0.311929	−	0.157284i
$51$		0			0
$52$	−0.563710	+	3.76407i	−0.0781724	+	0.521983i
$53$	−0.358246	+	0.358246i	−0.0492089	+	0.0492089i	−0.731283	−	0.682074i	$-0.761078\pi$
$53$	−0.358246	+	0.358246i	−0.0492089	+	0.0492089i	0.682074	+	0.731283i	$0.261078\pi$
$54$		0			0
$55$		−	7.50333i		−	1.01175i
$56$	0.0136360	+	0.0795732i	0.00182219	+	0.0106334i
$57$		0			0
$58$	12.5887	−	4.14903i	1.65298	−	0.544794i
$59$	−4.94884	+	4.94884i	−0.644285	+	0.644285i	−0.951606	−	0.307321i	$-0.900567\pi$
$59$	−4.94884	+	4.94884i	−0.644285	+	0.644285i	0.307321	+	0.951606i	$0.400567\pi$
$60$		0			0
$61$	6.84320	+	6.84320i	0.876182	+	0.876182i	0.993137	−	0.116956i	$-0.0373135\pi$
$61$	6.84320	+	6.84320i	0.876182	+	0.876182i	−0.116956	+	0.993137i	$0.537313\pi$
$62$	2.38827	−	4.73646i	0.303311	−	0.601531i
$63$		0			0
$64$	7.54355	−	2.66361i	0.942944	−	0.332951i
$65$	3.43247			0.425746
$66$		0			0
$67$	1.56428	+	1.56428i	0.191107	+	0.191107i	0.796174	−	0.605067i	$-0.206854\pi$
$67$	1.56428	+	1.56428i	0.191107	+	0.191107i	−0.605067	+	0.796174i	$0.706854\pi$
$68$	1.66674	+	2.25390i	0.202122	+	0.273325i
$69$		0			0
$70$	0.0691499	−	0.0227906i	0.00826500	−	0.00272400i
$71$		−	13.1820i		−	1.56442i	−0.623016	−	0.782209i	$-0.714093\pi$
$71$		−	13.1820i		−	1.56442i	0.623016	−	0.782209i	$-0.285907\pi$
$72$		0			0
$73$			7.44056i			0.870852i	0.900225	+	0.435426i	$0.143402\pi$
$73$			7.44056i			0.870852i	−0.900225	+	0.435426i	$0.856598\pi$
$74$	2.73327	+	8.29312i	0.317736	+	0.964056i
$75$		0			0
$76$	−2.28934	+	15.2867i	−0.262605	+	1.75350i
$77$	−0.0839622	−	0.0839622i	−0.00956839	−	0.00956839i
$78$		0			0
$79$	−2.58559			−0.290901			−0.145451	−	0.989366i	$-0.546463\pi$
$79$	−2.58559			−0.290901			−0.145451	+	0.989366i	$0.546463\pi$
$80$	−3.38327	−	6.37231i	−0.378261	−	0.712446i
$81$		0			0
$82$	−6.62096	−	3.33849i	−0.731163	−	0.368675i
$83$	−7.92875	−	7.92875i	−0.870293	−	0.870293i	0.122211	−	0.992504i	$-0.461002\pi$
$83$	−7.92875	−	7.92875i	−0.870293	−	0.870293i	−0.992504	+	0.122211i	$0.961002\pi$
$84$		0			0
$85$	1.78762	−	1.78762i	0.193895	−	0.193895i
$86$	−3.67722	−	11.1572i	−0.396525	−	1.20311i
$87$		0			0
$88$	−6.79518	+	9.60570i	−0.724369	+	1.02397i
$89$			9.64812i			1.02270i	0.859373	+	0.511349i	$0.170854\pi$
$89$			9.64812i			1.02270i	−0.859373	+	0.511349i	$0.829146\pi$
$90$		0			0
$91$	0.0384093	−	0.0384093i	0.00402639	−	0.00402639i
$92$	−0.154985	+	0.114610i	−0.0161583	+	0.0119489i
$93$		0			0
$94$	1.94054	−	3.84851i	0.200151	−	0.396943i
$95$	13.9400			1.43021
$96$		0			0
$97$	2.24923			0.228374			0.114187	−	0.993459i	$-0.463574\pi$
$97$	2.24923			0.228374			0.114187	+	0.993459i	$0.463574\pi$
$98$	−4.45657	+	8.83834i	−0.450181	+	0.892807i
$99$		0			0
$100$	2.80882	−	2.07710i	0.280882	−	0.207710i
$101$	−6.83626	+	6.83626i	−0.680233	+	0.680233i	−0.960053	−	0.279820i	$-0.909725\pi$
$101$	−6.83626	+	6.83626i	−0.680233	+	0.680233i	0.279820	+	0.960053i	$0.409725\pi$
$102$		0			0
$103$			9.97809i			0.983171i	0.870829	+	0.491585i	$0.163582\pi$
$103$			9.97809i			0.983171i	−0.870829	+	0.491585i	$0.836418\pi$
$104$	−4.39422	−	3.10852i	−0.430889	−	0.304815i
$105$		0			0
$106$	−0.224276	−	0.680486i	−0.0217837	−	0.0660946i
$107$	−13.2184	+	13.2184i	−1.27787	+	1.27787i	−0.336018	+	0.941856i	$0.609080\pi$
$107$	−13.2184	+	13.2184i	−1.27787	+	1.27787i	−0.941856	+	0.336018i	$0.890920\pi$
$108$		0			0
$109$	14.1522	+	14.1522i	1.35553	+	1.35553i	0.879343	+	0.476189i	$0.157982\pi$
$109$	14.1522	+	14.1522i	1.35553	+	1.35553i	0.476189	+	0.879343i	$0.342018\pi$
$110$	9.47496	+	4.77757i	0.903402	+	0.455524i
$111$		0			0
$112$	−0.109165	−	0.0334473i	−0.0103151	−	0.00316047i
$113$	18.3762			1.72869			0.864345	−	0.502899i	$-0.167733\pi$
$113$	18.3762			1.72869			0.864345	+	0.502899i	$0.167733\pi$
$114$		0			0
$115$	0.122922	+	0.122922i	0.0114625	+	0.0114625i
$116$	−2.77632	+	18.5384i	−0.257775	+	1.72125i
$117$		0			0
$118$	−3.09817	−	9.40029i	−0.285210	−	0.865367i
$119$		−	0.0400069i		−	0.00366743i
$120$		0			0
$121$		−	6.30551i		−	0.573228i
$122$	−12.9986	+	4.28412i	−1.17684	+	0.387866i
$123$		0			0
$124$	4.46036	+	6.03165i	0.400553	+	0.541658i
$125$	−8.60475	−	8.60475i	−0.769633	−	0.769633i
$126$		0			0
$127$	−14.6055			−1.29603			−0.648015	−	0.761628i	$-0.724400\pi$
$127$	−14.6055			−1.29603			−0.648015	+	0.761628i	$0.724400\pi$
$128$	−1.43967	+	11.2217i	−0.127250	+	0.991871i
$129$		0			0
$130$	−2.18554	+	4.33441i	−0.191685	+	0.380153i
$131$	13.3712	+	13.3712i	1.16825	+	1.16825i	0.982621	+	0.185626i	$0.0594312\pi$
$131$	13.3712	+	13.3712i	1.16825	+	1.16825i	0.185626	+	0.982621i	$0.440569\pi$
$132$		0			0
$133$	0.155988	−	0.155988i	0.0135259	−	0.0135259i
$134$	−2.97133	+	0.979299i	−0.256684	+	0.0845986i
$135$		0			0
$136$	−3.90740	+	0.669588i	−0.335057	+	0.0574167i
$137$		−	0.807029i		−	0.0689491i	−0.999406	−	0.0344746i	$-0.989024\pi$
$137$		−	0.807029i		−	0.0689491i	0.999406	−	0.0344746i	$-0.0109758\pi$
$138$		0			0
$139$	3.37103	−	3.37103i	0.285927	−	0.285927i	−0.549540	−	0.835467i	$-0.685197\pi$
$139$	3.37103	−	3.37103i	0.285927	−	0.285927i	0.835467	+	0.549540i	$0.185197\pi$
$140$	−0.0152503	+	0.101832i	−0.00128889	+	0.00860634i
$141$		0			0
$142$	16.6458	+	8.39334i	1.39689	+	0.704354i
$143$	7.91656			0.662016
$144$		0			0
$145$	16.9052			1.40390
$146$	−9.39569	−	4.73760i	−0.777593	−	0.392087i
$147$		0			0
$148$	−12.2126	−	1.82897i	−1.00387	−	0.150340i
$149$	10.0486	−	10.0486i	0.823215	−	0.823215i	−0.163353	−	0.986568i	$-0.552231\pi$
$149$	10.0486	−	10.0486i	0.823215	−	0.823215i	0.986568	+	0.163353i	$0.0522310\pi$
$150$		0			0
$151$			1.41441i			0.115103i	0.998343	+	0.0575516i	$0.0183294\pi$
$151$			1.41441i			0.115103i	−0.998343	+	0.0575516i	$0.981671\pi$
$152$	−17.8458	−	12.6243i	−1.44749	−	1.02397i
$153$		0			0
$154$	0.159486	−	0.0525637i	0.0128517	−	0.00423571i
$155$	4.78385	−	4.78385i	0.384248	−	0.384248i
$156$		0			0
$157$	−11.4626	−	11.4626i	−0.914812	−	0.914812i	0.0818344	−	0.996646i	$-0.473922\pi$
$157$	−11.4626	−	11.4626i	−0.914812	−	0.914812i	−0.996646	+	0.0818344i	$0.973922\pi$
$158$	1.64631	−	3.26499i	0.130974	−	0.259749i
$159$		0			0
$160$	10.2010	−	0.214863i	0.806456	−	0.0169864i
$161$	0.00275100			0.000216809
$162$		0			0
$163$	−7.72401	−	7.72401i	−0.604991	−	0.604991i	0.336642	−	0.941633i	$-0.390709\pi$
$163$	−7.72401	−	7.72401i	−0.604991	−	0.604991i	−0.941633	+	0.336642i	$0.890709\pi$
$164$	8.43148	−	6.23502i	0.658388	−	0.486873i
$165$		0			0
$166$	15.0606	−	4.96372i	1.16893	−	0.385259i
$167$		−	11.0083i		−	0.851847i	−0.904759	−	0.425924i	$-0.859949\pi$
$167$		−	11.0083i		−	0.851847i	0.904759	−	0.425924i	$-0.140051\pi$
$168$		0			0
$169$		−	9.37849i		−	0.721423i
$170$	1.11912	+	3.39557i	0.0858327	+	0.260428i
$171$		0			0
$172$	16.4303	+	2.46061i	1.25280	+	0.187620i
$173$	−15.7036	−	15.7036i	−1.19392	−	1.19392i	−0.975956	−	0.217966i	$-0.930058\pi$
$173$	−15.7036	−	15.7036i	−1.19392	−	1.19392i	−0.217966	−	0.975956i	$-0.569942\pi$
$174$		0			0
$175$	−0.0498569			−0.00376882
$176$	−7.80309	−	14.6969i	−0.588180	−	1.10782i
$177$		0			0
$178$	−12.1833	−	6.14321i	−0.913179	−	0.460453i
$179$	10.2452	+	10.2452i	0.765759	+	0.765759i	0.977357	−	0.211598i	$-0.0678667\pi$
$179$	10.2452	+	10.2452i	0.765759	+	0.765759i	−0.211598	+	0.977357i	$0.567867\pi$
$180$		0			0
$181$	−14.8996	+	14.8996i	−1.10748	+	1.10748i	−0.113994	+	0.993481i	$0.536365\pi$
$181$	−14.8996	+	14.8996i	−1.10748	+	1.10748i	−0.993481	+	0.113994i	$0.963635\pi$
$182$	0.0240458	+	0.0729582i	0.00178239	+	0.00540802i
$183$		0			0
$184$	−0.0460429	−	0.268685i	−0.00339433	−	0.0198077i
$185$			11.1367i			0.818788i
$186$		0			0
$187$	4.12292	−	4.12292i	0.301498	−	0.301498i
$188$	3.62417	+	4.90089i	0.264320	+	0.357434i
$189$		0			0
$190$	−8.87594	+	17.6029i	−0.643928	+	1.27705i
$191$	15.8341			1.14571			0.572857	−	0.819655i	$-0.305835\pi$
$191$	15.8341			1.14571			0.572857	+	0.819655i	$0.305835\pi$
$192$		0			0
$193$	−15.0444			−1.08292			−0.541459	−	0.840727i	$-0.682128\pi$
$193$	−15.0444			−1.08292			−0.541459	+	0.840727i	$0.682128\pi$
$194$	−1.43214	+	2.84025i	−0.102822	+	0.203918i
$195$		0			0
$196$	−8.32314	−	11.2552i	−0.594510	−	0.803943i
$197$	12.2231	−	12.2231i	0.870860	−	0.870860i	−0.121707	−	0.992566i	$-0.538837\pi$
$197$	12.2231	−	12.2231i	0.870860	−	0.870860i	0.992566	+	0.121707i	$0.0388367\pi$
$198$		0			0
$199$		−	14.5968i		−	1.03474i	−0.855761	−	0.517371i	$-0.826911\pi$
$199$		−	14.5968i		−	1.03474i	0.855761	−	0.517371i	$-0.173089\pi$
$200$	0.834445	+	4.86943i	0.0590042	+	0.344321i
$201$		0			0
$202$	−4.27977	−	12.9854i	−0.301124	−	0.913651i
$203$	0.189169	−	0.189169i	0.0132771	−	0.0132771i
$204$		0			0
$205$	−6.68721	−	6.68721i	−0.467055	−	0.467055i
$206$	−12.6000	−	6.35332i	−0.877884	−	0.442657i
$207$		0			0
$208$	6.72325	−	3.56960i	0.466173	−	0.247507i
$209$	32.1508			2.22392
$210$		0			0
$211$	5.80796	+	5.80796i	0.399837	+	0.399837i	0.878175	−	0.478339i	$-0.158761\pi$
$211$	5.80796	+	5.80796i	0.399837	+	0.399837i	−0.478339	+	0.878175i	$0.658761\pi$
$212$	1.00210	+	0.150075i	0.0688244	+	0.0103072i
$213$		0			0
$214$	−8.27526	−	25.1083i	−0.565685	−	1.71637i
$215$		−	14.9829i		−	1.02182i
$216$		0			0
$217$		−	0.107062i		−	0.00726787i
$218$	−26.8819	+	8.85982i	−1.82067	+	0.600063i
$219$		0			0
$220$	−12.0659	+	8.92266i	−0.813484	+	0.601565i
$221$	1.88607	+	1.88607i	0.126871	+	0.126871i
$222$		0			0
$223$	6.61413			0.442915			0.221458	−	0.975170i	$-0.428919\pi$
$223$	6.61413			0.442915			0.221458	+	0.975170i	$0.428919\pi$
$224$	0.111744	−	0.116553i	0.00746623	−	0.00778752i
$225$		0			0
$226$	−11.7006	+	23.2049i	−0.778314	+	1.54357i
$227$	−12.4158	−	12.4158i	−0.824065	−	0.824065i	0.162623	−	0.986688i	$-0.448005\pi$
$227$	−12.4158	−	12.4158i	−0.824065	−	0.824065i	−0.986688	+	0.162623i	$0.948005\pi$
$228$		0			0
$229$	7.94219	−	7.94219i	0.524835	−	0.524835i	−0.394193	−	0.919028i	$-0.628976\pi$
$229$	7.94219	−	7.94219i	0.524835	−	0.524835i	0.919028	+	0.394193i	$0.128976\pi$
$230$	−0.233490	+	0.0769542i	−0.0153959	+	0.00507421i
$231$		0			0
$232$	−21.6419	−	15.3097i	−1.42086	−	1.00513i
$233$		−	11.7989i		−	0.772969i	−0.922296	−	0.386484i	$-0.873689\pi$
$233$		−	11.7989i		−	0.772969i	0.922296	−	0.386484i	$-0.126311\pi$
$234$		0			0
$235$	3.88701	−	3.88701i	0.253561	−	0.253561i
$236$	13.8431	+	2.07314i	0.901107	+	0.134950i
$237$		0			0
$238$	0.0505194	+	0.0254734i	0.00327468	+	0.00165120i
$239$	11.0575			0.715252			0.357626	−	0.933865i	$-0.383586\pi$
$239$	11.0575			0.715252			0.357626	+	0.933865i	$0.383586\pi$
$240$		0			0
$241$	−11.6277			−0.749007			−0.374504	−	0.927225i	$-0.622187\pi$
$241$	−11.6277			−0.749007			−0.374504	+	0.927225i	$0.622187\pi$
$242$	7.96238	+	4.01488i	0.511841	+	0.258086i
$243$		0			0
$244$	2.86672	−	19.1420i	0.183523	−	1.22544i
$245$	−8.92678	+	8.92678i	−0.570311	+	0.570311i
$246$		0			0
$247$			14.7077i			0.935827i
$248$	−10.4566	+	1.79189i	−0.663995	+	0.113785i
$249$		0			0
$250$	16.3447	−	5.38692i	1.03373	−	0.340699i
$251$	−7.76540	+	7.76540i	−0.490148	+	0.490148i	−0.908353	−	0.418205i	$-0.862659\pi$
$251$	−7.76540	+	7.76540i	−0.490148	+	0.490148i	0.418205	+	0.908353i	$0.362659\pi$
$252$		0			0
$253$	0.283505	+	0.283505i	0.0178238	+	0.0178238i
$254$	9.29971	−	18.4433i	0.583516	−	1.15724i
$255$		0			0
$256$	−13.2538	−	8.96314i	−0.828360	−	0.560196i
$257$	−5.80652			−0.362201			−0.181100	−	0.983465i	$-0.557966\pi$
$257$	−5.80652			−0.362201			−0.181100	+	0.983465i	$0.557966\pi$
$258$		0			0
$259$	0.124620	+	0.124620i	0.00774350	+	0.00774350i
$260$	−4.08175	−	5.51966i	−0.253140	−	0.342315i
$261$		0			0
$262$	−25.3985	+	8.37090i	−1.56912	+	0.517156i
$263$			8.53133i			0.526064i	0.964787	+	0.263032i	$0.0847225\pi$
$263$			8.53133i			0.526064i	−0.964787	+	0.263032i	$0.915277\pi$
$264$		0			0
$265$		−	0.913816i		−	0.0561353i
$266$	0.0976547	+	0.296298i	0.00598760	+	0.0181672i
$267$		0			0
$268$	0.655298	−	4.37564i	0.0400287	−	0.267285i
$269$	16.5412	+	16.5412i	1.00853	+	1.00853i	0.999963	+	0.00857022i	$0.00272802\pi$
$269$	16.5412	+	16.5412i	1.00853	+	1.00853i	0.00857022	+	0.999963i	$0.497272\pi$
$270$		0			0
$271$	−2.20592			−0.134000			−0.0670002	−	0.997753i	$-0.521343\pi$
$271$	−2.20592			−0.134000			−0.0670002	+	0.997753i	$0.521343\pi$
$272$	1.64241	−	5.36048i	0.0995859	−	0.325027i
$273$		0			0
$274$	1.01909	+	0.513856i	0.0615654	+	0.0310432i
$275$	−5.13801	−	5.13801i	−0.309834	−	0.309834i
$276$		0			0
$277$	6.47067	−	6.47067i	0.388785	−	0.388785i	−0.485469	−	0.874254i	$-0.661351\pi$
$277$	6.47067	−	6.47067i	0.388785	−	0.388785i	0.874254	+	0.485469i	$0.161351\pi$
$278$	2.11040	+	6.40325i	0.126573	+	0.384041i
$279$		0			0
$280$	−0.118879	−	0.0840965i	−0.00710439	−	0.00502573i
$281$			13.4291i			0.801111i	0.916272	+	0.400556i	$0.131183\pi$
$281$			13.4291i			0.801111i	−0.916272	+	0.400556i	$0.868817\pi$
$282$		0			0
$283$	−10.7630	+	10.7630i	−0.639793	+	0.639793i	−0.950504	−	0.310711i	$-0.899433\pi$
$283$	−10.7630	+	10.7630i	−0.639793	+	0.639793i	0.310711	+	0.950504i	$0.399433\pi$
$284$	−21.1977	+	15.6755i	−1.25785	+	0.930171i
$285$		0			0
$286$	−5.04069	+	9.99677i	−0.298062	+	0.591122i
$287$	−0.149660			−0.00883413
$288$		0			0
$289$	−15.0355			−0.884440
$290$	−10.7640	+	21.3474i	−0.632085	+	1.25356i
$291$		0			0
$292$	11.9650	−	8.84801i	0.700197	−	0.517790i
$293$	−8.87904	+	8.87904i	−0.518719	+	0.518719i	−0.917184	−	0.398465i	$-0.869543\pi$
$293$	−8.87904	+	8.87904i	−0.518719	+	0.518719i	0.398465	+	0.917184i	$0.369543\pi$
$294$		0			0
$295$		−	12.6235i		−	0.734970i
$296$	10.0857	−	14.2571i	0.586217	−	0.828679i
$297$		0			0
$298$	6.29084	+	19.0873i	0.364418	+	1.10570i
$299$	−0.129692	+	0.129692i	−0.00750027	+	0.00750027i
$300$		0			0
$301$	−0.167658	−	0.167658i	−0.00966365	−	0.00966365i
$302$	−1.78607	−	0.900594i	−0.102777	−	0.0518233i
$303$		0			0
$304$	27.3045	−	14.4969i	1.56602	−	0.831451i
$305$	−17.4557			−0.999508
$306$		0			0
$307$	7.93904	+	7.93904i	0.453105	+	0.453105i	0.896384	−	0.443279i	$-0.146185\pi$
$307$	7.93904	+	7.93904i	0.453105	+	0.453105i	−0.443279	+	0.896384i	$0.646185\pi$
$308$	−0.0351730	+	0.234862i	−0.00200417	+	0.0133825i
$309$		0			0
$310$	2.99488	+	9.08689i	0.170098	+	0.516101i
$311$		−	2.88242i		−	0.163447i	−0.996655	−	0.0817236i	$-0.973958\pi$
$311$		−	2.88242i		−	0.163447i	0.996655	−	0.0817236i	$-0.0260425\pi$
$312$		0			0
$313$		−	7.41960i		−	0.419380i	−0.977768	−	0.209690i	$-0.932754\pi$
$313$		−	7.41960i		−	0.419380i	0.977768	−	0.209690i	$-0.0672455\pi$
$314$	21.7730	−	7.17602i	1.22872	−	0.404966i
$315$		0			0
$316$	3.07467	+	4.15782i	0.172964	+	0.233895i
$317$	−11.4863	−	11.4863i	−0.645137	−	0.645137i	0.306677	−	0.951814i	$-0.400783\pi$
$317$	−11.4863	−	11.4863i	−0.645137	−	0.645137i	−0.951814	+	0.306677i	$0.900783\pi$
$318$		0			0
$319$	38.9898			2.18301
$320$	−6.22390	+	13.0182i	−0.347926	+	0.727741i
$321$		0			0
$322$	−0.00175163	+	0.00347386i	−9.76146e−5	+	0.000193591i
$323$	7.65971	+	7.65971i	0.426198	+	0.426198i
$324$		0			0
$325$	2.35043	−	2.35043i	0.130378	−	0.130378i
$326$	14.6717	−	4.83554i	0.812590	−	0.267816i
$327$		0			0
$328$	2.50483	+	14.6170i	0.138306	+	0.807088i
$329$		−	0.0869913i		−	0.00479599i
$330$		0			0
$331$	7.54396	−	7.54396i	0.414654	−	0.414654i	−0.468702	−	0.883356i	$-0.655278\pi$
$331$	7.54396	−	7.54396i	0.414654	−	0.414654i	0.883356	+	0.468702i	$0.155278\pi$
$332$	−3.32147	+	22.1786i	−0.182289	+	1.21721i
$333$		0			0
$334$	13.9009	+	7.00927i	0.760624	+	0.383530i
$335$	−3.99016			−0.218006
$336$		0			0
$337$	−13.7980			−0.751625			−0.375812	−	0.926696i	$-0.622636\pi$
$337$	−13.7980			−0.751625			−0.375812	+	0.926696i	$0.622636\pi$
$338$	11.8428	+	5.97154i	0.644166	+	0.324809i
$339$		0			0
$340$	−5.00039	−	0.748860i	−0.271184	−	0.0406127i
$341$	11.0334	−	11.0334i	0.597490	−	0.597490i
$342$		0			0
$343$			0.399585i			0.0215756i
$344$	−13.5688	+	19.1809i	−0.731581	+	1.03417i
$345$		0			0
$346$	29.8289	−	9.83108i	1.60361	−	0.528522i
$347$	−13.5604	+	13.5604i	−0.727958	+	0.727958i	−0.970213	−	0.242255i	$-0.922113\pi$
$347$	−13.5604	+	13.5604i	−0.727958	+	0.727958i	0.242255	+	0.970213i	$0.422113\pi$
$348$		0			0
$349$	−22.1111	−	22.1111i	−1.18358	−	1.18358i	−0.978810	−	0.204772i	$-0.934355\pi$
$349$	−22.1111	−	22.1111i	−1.18358	−	1.18358i	−0.204772	−	0.978810i	$-0.565645\pi$
$350$	0.0317452	−	0.0629576i	0.00169685	−	0.00336522i
$351$		0			0
$352$	23.5272	−	0.495554i	1.25401	−	0.0264131i
$353$	15.1027			0.803833			0.401917	−	0.915676i	$-0.368344\pi$
$353$	15.1027			0.803833			0.401917	+	0.915676i	$0.368344\pi$
$354$		0			0
$355$	16.8124	+	16.8124i	0.892308	+	0.892308i
$356$	15.5149	−	11.4731i	0.822287	−	0.608076i
$357$		0			0
$358$	−19.4606	+	6.41388i	−1.02852	+	0.338984i
$359$		−	9.48202i		−	0.500442i	−0.968189	−	0.250221i	$-0.919497\pi$
$359$		−	9.48202i		−	0.500442i	0.968189	−	0.250221i	$-0.0805033\pi$
$360$		0			0
$361$			40.7308i			2.14373i
$362$	−9.32772	−	28.3016i	−0.490254	−	1.48750i
$363$		0			0
$364$	−0.107440	−	0.0160902i	−0.00563137	−	0.000843357i
$365$	−9.48970	−	9.48970i	−0.496714	−	0.496714i
$366$		0			0
$367$	10.1944			0.532141			0.266071	−	0.963954i	$-0.414275\pi$
$367$	10.1944			0.532141			0.266071	+	0.963954i	$0.414275\pi$
$368$	0.368603	+	0.112937i	0.0192148	+	0.00588726i
$369$		0			0
$370$	−14.0631	−	7.09105i	−0.731105	−	0.368646i
$371$	−0.0102256	−	0.0102256i	−0.000530886	−	0.000530886i
$372$		0			0
$373$	−17.2413	+	17.2413i	−0.892719	+	0.892719i	−0.994778	−	0.102059i	$-0.967457\pi$
$373$	−17.2413	+	17.2413i	−0.892719	+	0.892719i	0.102059	+	0.994778i	$0.467457\pi$
$374$	2.58111	+	7.83146i	0.133466	+	0.404955i
$375$		0			0
$376$	−8.49629	+	1.45596i	−0.438163	+	0.0750853i
$377$			17.8363i			0.918614i
$378$		0			0
$379$	−1.84029	+	1.84029i	−0.0945294	+	0.0945294i	−0.752790	−	0.658261i	$-0.771292\pi$
$379$	−1.84029	+	1.84029i	−0.0945294	+	0.0945294i	0.658261	+	0.752790i	$0.271292\pi$
$380$	−16.5768	−	22.4165i	−0.850373	−	1.14994i
$381$		0			0
$382$	−10.0820	+	19.9947i	−0.515839	+	1.02302i
$383$	−35.8130			−1.82996			−0.914980	−	0.403500i	$-0.867794\pi$
$383$	−35.8130			−1.82996			−0.914980	+	0.403500i	$0.867794\pi$
$384$		0			0
$385$	0.214171			0.0109152
$386$	9.57914	−	18.9975i	0.487566	−	0.966948i
$387$		0			0
$388$	−2.67469	−	3.61692i	−0.135787	−	0.183621i
$389$	−17.8816	+	17.8816i	−0.906633	+	0.906633i	−0.995999	−	0.0893658i	$-0.971516\pi$
$389$	−17.8816	+	17.8816i	−0.906633	+	0.906633i	0.0893658	+	0.995999i	$0.471516\pi$
$390$		0			0
$391$			0.135086i			0.00683160i
$392$	19.5123	−	3.34370i	0.985518	−	0.168882i
$393$		0			0
$394$	7.65215	+	23.2177i	0.385510	+	1.16969i
$395$	3.29766	−	3.29766i	0.165924	−	0.165924i
$396$		0			0
$397$	3.08353	+	3.08353i	0.154758	+	0.154758i	0.780239	−	0.625481i	$-0.215097\pi$
$397$	3.08353	+	3.08353i	0.154758	+	0.154758i	−0.625481	+	0.780239i	$0.715097\pi$
$398$	18.4324	+	9.29419i	0.923933	+	0.465876i
$399$		0			0
$400$	−6.68027	−	2.04679i	−0.334013	−	0.102339i
$401$	−18.2632			−0.912018			−0.456009	−	0.889975i	$-0.650722\pi$
$401$	−18.2632			−0.912018			−0.456009	+	0.889975i	$0.650722\pi$
$402$		0			0
$403$	5.04731	+	5.04731i	0.251424	+	0.251424i
$404$	19.1226	+	2.86381i	0.951385	+	0.142480i
$405$		0			0
$406$	0.118428	+	0.359326i	0.00587747	+	0.0178331i
$407$			25.6855i			1.27318i
$408$		0			0
$409$		−	27.1008i		−	1.34005i	−0.742339	−	0.670024i	$-0.766284\pi$
$409$		−	27.1008i		−	1.34005i	0.742339	−	0.670024i	$-0.233716\pi$
$410$	12.7023	−	4.18646i	0.627322	−	0.206755i
$411$		0			0
$412$	16.0455	−	11.8655i	0.790506	−	0.584573i
$413$	−0.141257	−	0.141257i	−0.00695081	−	0.00695081i
$414$		0			0
$415$	20.2247			0.992791
$416$	0.226696	+	10.7628i	0.0111147	+	0.527687i
$417$		0			0
$418$	−20.4712	+	40.5989i	−1.00128	+	1.98576i
$419$	−11.6631	−	11.6631i	−0.569781	−	0.569781i	0.362286	−	0.932067i	$-0.381996\pi$
$419$	−11.6631	−	11.6631i	−0.569781	−	0.569781i	−0.932067	+	0.362286i	$0.881996\pi$
$420$		0			0
$421$	−2.87987	+	2.87987i	−0.140356	+	0.140356i	−0.773794	−	0.633438i	$-0.781643\pi$
$421$	−2.87987	+	2.87987i	−0.140356	+	0.140356i	0.633438	+	0.773794i	$0.281643\pi$
$422$	−11.0322	+	3.63602i	−0.537038	+	0.176999i
$423$		0			0
$424$	−0.827571	+	1.16986i	−0.0401904	+	0.0568134i
$425$		−	2.44819i		−	0.118755i
$426$		0			0
$427$	−0.195329	+	0.195329i	−0.00945262	+	0.00945262i
$428$	36.9750	+	5.53739i	1.78725	+	0.267660i
$429$		0			0
$430$	18.9199	+	9.53998i	0.912396	+	0.460059i
$431$	−10.3732			−0.499662			−0.249831	−	0.968289i	$-0.580375\pi$
$431$	−10.3732			−0.499662			−0.249831	+	0.968289i	$0.580375\pi$
$432$		0			0
$433$	9.86432			0.474049			0.237024	−	0.971504i	$-0.423828\pi$
$433$	9.86432			0.474049			0.237024	+	0.971504i	$0.423828\pi$
$434$	0.135195	+	0.0681695i	0.00648956	+	0.00327224i
$435$		0			0
$436$	5.92855	−	39.5869i	0.283926	−	1.89587i
$437$	−0.526705	+	0.526705i	−0.0251957	+	0.0251957i
$438$		0			0
$439$			31.1121i			1.48490i	0.669902	+	0.742450i	$0.266336\pi$
$439$			31.1121i			1.48490i	−0.669902	+	0.742450i	$0.733664\pi$
$440$	−3.58455	−	20.9177i	−0.170887	−	0.997213i
$441$		0			0
$442$	−3.58257	+	1.18075i	−0.170406	+	0.0561628i
$443$	17.9988	−	17.9988i	0.855149	−	0.855149i	−0.135613	−	0.990762i	$-0.543300\pi$
$443$	17.9988	−	17.9988i	0.855149	−	0.855149i	0.990762	+	0.135613i	$0.0433004\pi$
$444$		0			0
$445$	−12.3052	−	12.3052i	−0.583324	−	0.583324i
$446$	−4.21139	+	8.35210i	−0.199415	+	0.395484i
$447$		0			0
$448$	0.0760286	+	0.215319i	0.00359201	+	0.0101729i
$449$	−18.6610			−0.880669			−0.440335	−	0.897834i	$-0.645140\pi$
$449$	−18.6610			−0.880669			−0.440335	+	0.897834i	$0.645140\pi$
$450$		0			0
$451$	−15.4232	−	15.4232i	−0.726251	−	0.726251i
$452$	−21.8523	−	29.5503i	−1.02784	−	1.38993i
$453$		0			0
$454$	23.5837	−	7.77278i	1.10684	−	0.364795i
$455$			0.0979746i			0.00459312i
$456$		0			0
$457$			22.5444i			1.05458i	0.849685	+	0.527291i	$0.176792\pi$
$457$			22.5444i			1.05458i	−0.849685	+	0.527291i	$0.823208\pi$
$458$	4.97213	+	15.0861i	0.232332	+	0.704929i
$459$		0			0
$460$	0.0514939	−	0.343842i	0.00240092	−	0.0160317i
$461$	12.5887	+	12.5887i	0.586312	+	0.586312i	0.936631	−	0.350319i	$-0.113927\pi$
$461$	12.5887	+	12.5887i	0.586312	+	0.586312i	−0.350319	+	0.936631i	$0.613927\pi$
$462$		0			0
$463$	−0.705882			−0.0328051			−0.0164026	−	0.999865i	$-0.505221\pi$
$463$	−0.705882			−0.0328051			−0.0164026	+	0.999865i	$0.505221\pi$
$464$	33.1126	−	17.5806i	1.53722	−	0.816159i
$465$		0			0
$466$	14.8992	+	7.51264i	0.690192	+	0.348016i
$467$	7.66787	+	7.66787i	0.354827	+	0.354827i	0.861902	−	0.507075i	$-0.169273\pi$
$467$	7.66787	+	7.66787i	0.354827	+	0.354827i	−0.507075	+	0.861902i	$0.669273\pi$
$468$		0			0
$469$	−0.0446499	+	0.0446499i	−0.00206174	+	0.00206174i
$470$	2.43343	+	7.38336i	0.112246	+	0.340569i
$471$		0			0
$472$	−11.4321	+	16.1605i	−0.526207	+	0.743849i
$473$		−	34.5561i		−	1.58889i
$474$		0			0
$475$	9.54558	−	9.54558i	0.437981	−	0.437981i
$476$	−0.0643340	+	0.0475746i	−0.00294875	+	0.00218058i
$477$		0			0
$478$	−7.04062	+	13.9631i	−0.322031	+	0.638656i
$479$	−6.35824			−0.290516			−0.145258	−	0.989394i	$-0.546401\pi$
$479$	−6.35824			−0.290516			−0.145258	+	0.989394i	$0.546401\pi$
$480$		0			0
$481$	−11.7501			−0.535756
$482$	7.40368	−	14.6831i	0.337228	−	0.668797i
$483$		0			0
$484$	−10.1397	+	7.49825i	−0.460896	+	0.340830i
$485$	−2.86867	+	2.86867i	−0.130259	+	0.130259i
$486$		0			0
$487$			30.8131i			1.39628i	0.715964	+	0.698138i	$0.245988\pi$
$487$			30.8131i			1.39628i	−0.715964	+	0.698138i	$0.754012\pi$
$488$	22.3466	+	15.8082i	1.01158	+	0.715605i
$489$		0			0
$490$	−5.58852	−	16.9563i	−0.252464	−	0.766010i
$491$	1.70806	−	1.70806i	0.0770838	−	0.0770838i	−0.667514	−	0.744597i	$-0.732641\pi$
$491$	1.70806	−	1.70806i	0.0770838	−	0.0770838i	0.744597	+	0.667514i	$0.232641\pi$
$492$		0			0
$493$	9.28907	+	9.28907i	0.418359	+	0.418359i
$494$	−18.5724	−	9.36476i	−0.835610	−	0.421341i
$495$		0			0
$496$	4.39526	−	14.3452i	0.197353	−	0.644118i
$497$	0.376261			0.0168776
$498$		0			0
$499$	5.92647	+	5.92647i	0.265305	+	0.265305i	0.827205	−	0.561900i	$-0.189929\pi$
$499$	5.92647	+	5.92647i	0.265305	+	0.265305i	−0.561900	+	0.827205i	$0.689929\pi$
$500$	−3.60466	+	24.0695i	−0.161205	+	1.07642i
$501$		0			0
$502$	−4.86145	−	14.7503i	−0.216977	−	0.658339i
$503$		−	29.4209i		−	1.31182i	−0.754841	−	0.655908i	$-0.772286\pi$
$503$		−	29.4209i		−	1.31182i	0.754841	−	0.655908i	$-0.227714\pi$
$504$		0			0
$505$		−	17.4380i		−	0.775979i
$506$	−0.538515	+	0.177485i	−0.0239399	+	0.00789018i
$507$		0			0
$508$	17.3683	+	23.4867i	0.770592	+	1.04206i
$509$	−2.36102	−	2.36102i	−0.104650	−	0.104650i	0.652843	−	0.757493i	$-0.273576\pi$
$509$	−2.36102	−	2.36102i	−0.104650	−	0.104650i	−0.757493	+	0.652843i	$0.773576\pi$
$510$		0			0
$511$	−0.212379			−0.00939511
$512$	19.7574	−	11.0293i	0.873161	−	0.487432i
$513$		0			0
$514$	3.69716	−	7.33228i	0.163075	−	0.323413i
$515$	−12.7261	−	12.7261i	−0.560778	−	0.560778i
$516$		0			0
$517$	8.96492	−	8.96492i	0.394277	−	0.394277i
$518$	−0.236715	+	0.0780170i	−0.0104006	+	0.00342787i
$519$		0			0
$520$	9.56901	−	1.63978i	0.419629	−	0.0719093i
$521$		−	5.16972i		−	0.226489i	−0.993567	−	0.113245i	$-0.963876\pi$
$521$		−	5.16972i		−	0.226489i	0.993567	−	0.113245i	$-0.0361244\pi$
$522$		0			0
$523$	10.0252	−	10.0252i	0.438370	−	0.438370i	−0.453093	−	0.891463i	$-0.649679\pi$
$523$	10.0252	−	10.0252i	0.438370	−	0.438370i	0.891463	+	0.453093i	$0.149679\pi$
$524$	5.60139	−	37.4023i	0.244698	−	1.63393i
$525$		0			0
$526$	−10.7731	−	5.43212i	−0.469728	−	0.236852i
$527$	5.25725			0.229009
$528$		0			0
$529$	22.9907			0.999596
$530$	1.15394	+	0.581851i	0.0501238	+	0.0252740i
$531$		0			0
$532$	−0.436335	−	0.0653457i	−0.0189175	−	0.00283309i
$533$	7.05549	−	7.05549i	0.305607	−	0.305607i
$534$		0			0
$535$		−	33.7176i		−	1.45774i
$536$	5.10817	+	3.61358i	0.220639	+	0.156083i
$537$		0			0
$538$	−31.4199	+	10.3554i	−1.35461	+	0.446455i
$539$	−20.5885	+	20.5885i	−0.886809	+	0.886809i
$540$		0			0
$541$	−11.2354	−	11.2354i	−0.483049	−	0.483049i	0.423055	−	0.906104i	$-0.360958\pi$
$541$	−11.2354	−	11.2354i	−0.483049	−	0.483049i	−0.906104	+	0.423055i	$0.860958\pi$
$542$	1.40457	−	2.78557i	0.0603315	−	0.119650i
$543$		0			0
$544$	5.72327	+	5.48714i	0.245383	+	0.235259i
$545$	−36.0994			−1.54633
$546$		0			0
$547$	15.4429	+	15.4429i	0.660292	+	0.660292i	0.955449	−	0.295156i	$-0.0953718\pi$
$547$	15.4429	+	15.4429i	0.660292	+	0.660292i	−0.295156	+	0.955449i	$0.595372\pi$
$548$	−1.29776	+	0.959685i	−0.0554376	+	0.0409957i
$549$		0			0
$550$	9.75962	−	3.21660i	0.416152	−	0.137156i
$551$			72.4366i			3.08590i
$552$		0			0
$553$		−	0.0738017i		−	0.00313837i
$554$	4.05090	+	12.2910i	0.172106	+	0.522194i
$555$		0			0
$556$	−9.42956	−	1.41217i	−0.399902	−	0.0598896i
$557$	15.6808	+	15.6808i	0.664415	+	0.664415i	0.956418	−	0.292003i	$-0.0943216\pi$
$557$	15.6808	+	15.6808i	0.664415	+	0.664415i	−0.292003	+	0.956418i	$0.594322\pi$
$558$		0			0
$559$	15.8080			0.668608
$560$	0.181888	−	0.0965703i	0.00768616	−	0.00408084i
$561$		0			0
$562$	−16.9578	−	8.55064i	−0.715321	−	0.360687i
$563$	−4.87050	−	4.87050i	−0.205267	−	0.205267i	0.596985	−	0.802252i	$-0.296365\pi$
$563$	−4.87050	−	4.87050i	−0.205267	−	0.205267i	−0.802252	+	0.596985i	$0.796365\pi$
$564$		0			0
$565$	−23.4371	+	23.4371i	−0.986005	+	0.986005i
$566$	−6.73806	−	20.4442i	−0.283222	−	0.859334i
$567$		0			0
$568$	−6.29741	−	36.7487i	−0.264233	−	1.54194i
$569$		−	28.7055i		−	1.20340i	−0.798724	−	0.601698i	$-0.794491\pi$
$569$		−	28.7055i		−	1.20340i	0.798724	−	0.601698i	$-0.205509\pi$
$570$		0			0
$571$	3.49180	−	3.49180i	0.146127	−	0.146127i	−0.630258	−	0.776385i	$-0.717051\pi$
$571$	3.49180	−	3.49180i	0.146127	−	0.146127i	0.776385	+	0.630258i	$0.217051\pi$
$572$	−9.41405	−	12.7304i	−0.393621	−	0.532286i
$573$		0			0
$574$	0.0952922	−	0.188985i	0.00397742	−	0.00788809i
$575$	0.168345			0.00702048
$576$		0			0
$577$	−20.7416			−0.863483			−0.431741	−	0.901997i	$-0.642101\pi$
$577$	−20.7416			−0.863483			−0.431741	+	0.901997i	$0.642101\pi$
$578$	9.57349	−	18.9863i	0.398205	−	0.789726i
$579$		0			0
$580$	−20.1030	−	27.1849i	−0.834732	−	1.12879i
$581$	0.226314	−	0.226314i	0.00938909	−	0.00938909i
$582$		0			0
$583$		−	2.10760i		−	0.0872880i
$584$	3.55456	+	20.7427i	0.147089	+	0.858340i
$585$		0			0
$586$	−5.55863	−	16.8657i	−0.229625	−	0.696714i
$587$	24.3151	−	24.3151i	1.00359	−	1.00359i	0.00359999	−	0.999994i	$-0.498854\pi$
$587$	24.3151	−	24.3151i	1.00359	−	1.00359i	0.999994	−	0.00359999i	$-0.00114591\pi$
$588$		0			0
$589$	20.4981	+	20.4981i	0.844611	+	0.844611i
$590$	15.9406	+	8.03774i	0.656263	+	0.330908i
$591$		0			0
$592$	11.5816	+	21.8137i	0.476002	+	0.896539i
$593$	−39.1962			−1.60960			−0.804798	−	0.593548i	$-0.797727\pi$
$593$	−39.1962			−1.60960			−0.804798	+	0.593548i	$0.797727\pi$
$594$		0			0
$595$	0.0510249	+	0.0510249i	0.00209182	+	0.00209182i
$596$	−28.1083	−	4.20951i	−1.15136	−	0.172428i
$597$		0			0
$598$	−0.0811923	−	0.246349i	−0.00332020	−	0.0100739i
$599$			7.93358i			0.324157i	0.986778	+	0.162079i	$0.0518198\pi$
$599$			7.93358i			0.324157i	−0.986778	+	0.162079i	$0.948180\pi$
$600$		0			0
$601$		−	15.8403i		−	0.646140i	−0.946375	−	0.323070i	$-0.895285\pi$
$601$		−	15.8403i		−	0.646140i	0.946375	−	0.323070i	$-0.104715\pi$
$602$	0.318465	−	0.104961i	0.0129797	−	0.00427788i
$603$		0			0
$604$	2.27448	−	1.68196i	0.0925472	−	0.0684380i
$605$	8.04206	+	8.04206i	0.326956	+	0.326956i
$606$		0			0
$607$	−42.8817			−1.74051			−0.870257	−	0.492598i	$-0.836047\pi$
$607$	−42.8817			−1.74051			−0.870257	+	0.492598i	$0.836047\pi$
$608$	0.920657	+	43.7097i	0.0373376	+	1.77266i
$609$		0			0
$610$	11.1145	−	22.0424i	0.450012	−	0.892472i
$611$	4.10108	+	4.10108i	0.165912	+	0.165912i
$612$		0			0
$613$	7.04384	−	7.04384i	0.284498	−	0.284498i	−0.550402	−	0.834900i	$-0.685526\pi$
$613$	7.04384	−	7.04384i	0.284498	−	0.284498i	0.834900	+	0.550402i	$0.185526\pi$
$614$	−15.0801	+	4.97016i	−0.608585	+	0.200579i
$615$		0			0
$616$	−0.274180	−	0.193958i	−0.0110470	−	0.00781480i
$617$			7.62227i			0.306861i	0.988159	+	0.153430i	$0.0490321\pi$
$617$			7.62227i			0.306861i	−0.988159	+	0.153430i	$0.950968\pi$
$618$		0			0
$619$	−9.48463	+	9.48463i	−0.381219	+	0.381219i	−0.871541	−	0.490322i	$-0.836879\pi$
$619$	−9.48463	+	9.48463i	−0.381219	+	0.381219i	0.490322	+	0.871541i	$0.336879\pi$
$620$	−13.3815	−	2.00403i	−0.537416	−	0.0804836i
$621$		0			0
$622$	3.63983	+	1.83532i	0.145944	+	0.0735895i
$623$	−0.275391			−0.0110333
$624$		0			0
$625$	13.2155			0.528622
$626$	9.36922	+	4.72425i	0.374469	+	0.188819i
$627$		0			0
$628$	−4.80183	+	32.0634i	−0.191614	+	1.27947i
$629$	−6.11939	+	6.11939i	−0.243996	+	0.243996i
$630$		0			0
$631$		−	36.0068i		−	1.43341i	−0.697376	−	0.716705i	$-0.745649\pi$
$631$		−	36.0068i		−	1.43341i	0.697376	−	0.716705i	$-0.254351\pi$
$632$	−7.20808	+	1.23521i	−0.286722	+	0.0491338i
$633$		0			0
$634$	21.8182	−	7.19090i	0.866512	−	0.285587i
$635$	18.6279	−	18.6279i	0.739226	−	0.739226i
$636$		0			0
$637$	−9.41840	−	9.41840i	−0.373171	−	0.373171i
$638$	−24.8259	+	49.2350i	−0.982865	+	1.94923i
$639$		0			0
$640$	−12.4761	−	16.1484i	−0.493160	−	0.638321i
$641$	28.6960			1.13342			0.566712	−	0.823916i	$-0.308215\pi$
$641$	28.6960			1.13342			0.566712	+	0.823916i	$0.308215\pi$
$642$		0			0
$643$	−10.5720	−	10.5720i	−0.416919	−	0.416919i	0.467222	−	0.884140i	$-0.345255\pi$
$643$	−10.5720	−	10.5720i	−0.416919	−	0.416919i	−0.884140	+	0.467222i	$0.845255\pi$
$644$	−0.00327137	−	0.00442380i	−0.000128910	−	0.000174322i
$645$		0			0
$646$	−14.5496	+	4.79528i	−0.572445	+	0.188668i
$647$			21.9228i			0.861873i	0.902382	+	0.430937i	$0.141817\pi$
$647$			21.9228i			0.861873i	−0.902382	+	0.430937i	$0.858183\pi$
$648$		0			0
$649$		−	29.1146i		−	1.14285i
$650$	1.47146	+	4.46463i	0.0577156	+	0.175117i
$651$		0			0
$652$	−3.23570	+	21.6058i	−0.126720	+	0.846150i
$653$	10.0797	+	10.0797i	0.394448	+	0.394448i	0.876269	−	0.481821i	$-0.160025\pi$
$653$	10.0797	+	10.0797i	0.394448	+	0.394448i	−0.481821	+	0.876269i	$0.660025\pi$
$654$		0			0
$655$	−34.1073			−1.33268
$656$	−20.0527	−	6.14401i	−0.782928	−	0.239883i
$657$		0			0
$658$	0.109850	+	0.0553897i	0.00428239	+	0.00215931i
$659$	19.8253	+	19.8253i	0.772285	+	0.772285i	0.978505	−	0.206221i	$-0.0661165\pi$
$659$	19.8253	+	19.8253i	0.772285	+	0.772285i	−0.206221	+	0.978505i	$0.566117\pi$
$660$		0			0
$661$	−3.61520	+	3.61520i	−0.140615	+	0.140615i	−0.773910	−	0.633295i	$-0.781702\pi$
$661$	−3.61520	+	3.61520i	−0.140615	+	0.140615i	0.633295	+	0.773910i	$0.281702\pi$
$662$	4.72282	+	14.3297i	0.183558	+	0.556940i
$663$		0			0
$664$	−25.8915	−	18.3159i	−1.00478	−	0.710795i
$665$			0.397895i			0.0154297i
$666$		0			0
$667$	−0.638744	+	0.638744i	−0.0247323	+	0.0247323i
$668$	−17.7021	+	13.0906i	−0.684917	+	0.506491i
$669$		0			0
$670$	2.54064	−	5.03864i	0.0981535	−	0.194660i
$671$	−40.2593			−1.55419
$672$		0			0
$673$	−44.0684			−1.69871			−0.849356	−	0.527821i	$-0.823009\pi$
$673$	−44.0684			−1.69871			−0.849356	+	0.527821i	$0.823009\pi$
$674$	8.78555	−	17.4236i	0.338407	−	0.671134i
$675$		0			0
$676$	−15.0813	+	11.1525i	−0.580050	+	0.428943i
$677$	−1.29007	+	1.29007i	−0.0495812	+	0.0495812i	−0.731463	−	0.681881i	$-0.761162\pi$
$677$	−1.29007	+	1.29007i	−0.0495812	+	0.0495812i	0.681881	+	0.731463i	$0.261162\pi$
$678$		0			0
$679$			0.0642007i			0.00246380i
$680$	4.12952	−	5.83750i	0.158360	−	0.223858i
$681$		0			0
$682$	6.90732	+	20.9578i	0.264495	+	0.802515i
$683$	19.4992	−	19.4992i	0.746115	−	0.746115i	−0.227632	−	0.973747i	$-0.573098\pi$
$683$	19.4992	−	19.4992i	0.746115	−	0.746115i	0.973747	+	0.227632i	$0.0730984\pi$
$684$		0			0
$685$	1.02929	+	1.02929i	0.0393270	+	0.0393270i
$686$	−0.504583	−	0.254427i	−0.0192651	−	0.00971405i
$687$		0			0
$688$	−15.5814	−	29.3472i	−0.594036	−	1.11885i
$689$	0.964142			0.0367309
$690$		0			0
$691$	−24.1345	−	24.1345i	−0.918121	−	0.918121i	0.0787719	−	0.996893i	$-0.474900\pi$
$691$	−24.1345	−	24.1345i	−0.918121	−	0.918121i	−0.996893	+	0.0787719i	$0.974900\pi$
$692$	−6.57847	+	43.9266i	−0.250076	+	1.66984i
$693$		0			0
$694$	−8.48933	−	25.7578i	−0.322251	−	0.977753i
$695$			8.59884i			0.326173i
$696$		0			0
$697$		−	7.34896i		−	0.278362i
$698$	41.9999	−	13.8425i	1.58972	−	0.523945i
$699$		0			0
$700$	0.0592877	+	0.0801735i	0.00224087	+	0.00303027i
$701$	32.4089	+	32.4089i	1.22407	+	1.22407i	0.966173	+	0.257895i	$0.0830288\pi$
$701$	32.4089	+	32.4089i	1.22407	+	1.22407i	0.257895	+	0.966173i	$0.416971\pi$
$702$		0			0
$703$	−47.7194			−1.79977
$704$	−14.3546	+	30.0249i	−0.541011	+	1.13161i
$705$		0			0
$706$	−9.61626	+	19.0711i	−0.361913	+	0.717751i
$707$	−0.195131	−	0.195131i	−0.00733864	−	0.00733864i
$708$		0			0
$709$	22.6980	−	22.6980i	0.852441	−	0.852441i	−0.137992	−	0.990433i	$-0.544065\pi$
$709$	22.6980	−	22.6980i	0.852441	−	0.852441i	0.990433	+	0.137992i	$0.0440649\pi$
$710$	−31.9350	+	10.5252i	−1.19850	+	0.395005i
$711$		0			0
$712$	4.60917	+	26.8969i	0.172736	+	1.00801i
$713$			0.361504i			0.0135384i
$714$		0			0
$715$	−10.0968	+	10.0968i	−0.377599	+	0.377599i
$716$	4.29185	−	28.6581i	0.160394	−	1.07100i
$717$		0			0
$718$	11.9736	+	6.03745i	0.446850	+	0.225316i
$719$	−22.9238			−0.854915			−0.427457	−	0.904035i	$-0.640591\pi$
$719$	−22.9238			−0.854915			−0.427457	+	0.904035i	$0.640591\pi$
$720$		0			0
$721$	−0.284809			−0.0106069
$722$	−51.4335	−	25.9344i	−1.91416	−	0.965178i
$723$		0			0
$724$	41.6775	+	6.24165i	1.54893	+	0.231969i
$725$	11.5761	−	11.5761i	0.429925	−	0.429925i
$726$		0			0
$727$		−	2.48990i		−	0.0923451i	−0.998933	−	0.0461726i	$-0.985298\pi$
$727$		−	2.48990i		−	0.0923451i	0.998933	−	0.0461726i	$-0.0147024\pi$
$728$	0.0887279	−	0.125426i	0.00328848	−	0.00464861i
$729$		0			0
$730$	18.0256	−	5.94094i	0.667158	−	0.219884i
$731$	8.23276	−	8.23276i	0.304500	−	0.304500i
$732$		0			0
$733$	15.0437	+	15.0437i	0.555652	+	0.555652i	0.928067	−	0.372415i	$-0.121470\pi$
$733$	15.0437	+	15.0437i	0.555652	+	0.555652i	−0.372415	+	0.928067i	$0.621470\pi$
$734$	−6.49102	+	12.8731i	−0.239588	+	0.475155i
$735$		0			0
$736$	−0.377313	+	0.393549i	−0.0139079	+	0.0145064i
$737$	−9.20281			−0.338990
$738$		0			0
$739$	11.5660	+	11.5660i	0.425463	+	0.425463i	0.887079	−	0.461617i	$-0.152730\pi$
$739$	11.5660	+	11.5660i	0.425463	+	0.425463i	−0.461617	+	0.887079i	$0.652730\pi$
$740$	17.9087	−	13.2433i	0.658336	−	0.486835i
$741$		0			0
$742$	0.0194234	−	0.00640163i	0.000713057	−	0.000235011i
$743$		−	41.4164i		−	1.51942i	−0.650262	−	0.759710i	$-0.725341\pi$
$743$		−	41.4164i		−	1.51942i	0.650262	−	0.759710i	$-0.274659\pi$
$744$		0			0
$745$			25.6320i			0.939086i
$746$	−10.7937	−	32.7497i	−0.395186	−	1.19905i
$747$		0			0
$748$	−11.5328	−	1.72715i	−0.421680	−	0.0631510i
$749$	−0.377300	−	0.377300i	−0.0137862	−	0.0137862i
$750$		0			0
$751$	30.5841			1.11603			0.558015	−	0.829831i	$-0.311563\pi$
$751$	30.5841			1.11603			0.558015	+	0.829831i	$0.311563\pi$
$752$	3.57128	−	11.6559i	0.130231	−	0.425046i
$753$		0			0
$754$	−22.5230	−	11.3568i	−0.820240	−	0.413591i
$755$	−1.80394	−	1.80394i	−0.0656522	−	0.0656522i
$756$		0			0
$757$	15.8712	−	15.8712i	0.576848	−	0.576848i	−0.357185	−	0.934034i	$-0.616264\pi$
$757$	15.8712	−	15.8712i	0.576848	−	0.576848i	0.934034	+	0.357185i	$0.116264\pi$
$758$	−1.15210	−	3.49562i	−0.0418460	−	0.126967i
$759$		0			0
$760$	38.8617	−	6.65949i	1.40966	−	0.241565i
$761$		−	1.00976i		−	0.0366037i	−0.999833	−	0.0183018i	$-0.994174\pi$
$761$		−	1.00976i		−	0.0366037i	0.999833	−	0.0183018i	$-0.00582598\pi$
$762$		0			0
$763$	−0.403952	+	0.403952i	−0.0146240	+	0.0146240i
$764$	−18.8292	−	25.4624i	−0.681218	−	0.921196i
$765$		0			0
$766$	22.8031	−	45.2235i	0.823909	−	1.63399i
$767$	13.3187			0.480912
$768$		0			0
$769$	9.63556			0.347467			0.173734	−	0.984793i	$-0.444417\pi$
$769$	9.63556			0.347467			0.173734	+	0.984793i	$0.444417\pi$
$770$	−0.136368	+	0.270448i	−0.00491438	+	0.00974628i
$771$		0			0
$772$	17.8901	+	24.1924i	0.643880	+	0.870705i
$773$	36.4254	−	36.4254i	1.31013	−	1.31013i	0.388817	−	0.921315i	$-0.372884\pi$
$773$	36.4254	−	36.4254i	1.31013	−	1.31013i	0.921315	−	0.388817i	$-0.127116\pi$
$774$		0			0
$775$		−	6.55162i		−	0.235341i
$776$	6.27037	−	1.07452i	0.225093	−	0.0385729i
$777$		0			0
$778$	−11.1946	−	33.9660i	−0.401346	−	1.21774i
$779$	28.6538	−	28.6538i	1.02663	−	1.02663i
$780$		0			0
$781$	38.7757	+	38.7757i	1.38750	+	1.38750i
$782$	−0.170582	−	0.0860129i	−0.00610001	−	0.00307582i
$783$		0			0
$784$	−8.20166	+	26.7685i	−0.292916	+	0.956016i
$785$	29.2387			1.04358
$786$		0			0
$787$	−20.6472	−	20.6472i	−0.735994	−	0.735994i	0.235806	−	0.971800i	$-0.424227\pi$
$787$	−20.6472	−	20.6472i	−0.735994	−	0.735994i	−0.971800	+	0.235806i	$0.924227\pi$
$788$	−34.1908	−	5.12044i	−1.21800	−	0.182408i
$789$		0			0
$790$	2.06447	+	6.26389i	0.0734506	+	0.222859i
$791$			0.524521i			0.0186498i
$792$		0			0
$793$		−	18.4170i		−	0.654007i
$794$	−5.85714	+	1.93041i	−0.207862	+	0.0685078i
$795$		0			0
$796$	−23.4728	+	17.3580i	−0.831971	+	0.615237i
$797$	24.5110	+	24.5110i	0.868225	+	0.868225i	0.992276	−	0.124051i	$-0.0395885\pi$
$797$	24.5110	+	24.5110i	0.868225	+	0.868225i	−0.124051	+	0.992276i	$0.539589\pi$
$798$		0			0
$799$	4.27166			0.151121
$800$	6.83812	−	7.13238i	0.241764	−	0.252168i
$801$		0			0
$802$	11.6286	−	23.0621i	0.410621	−	0.814351i
$803$	−21.8868	−	21.8868i	−0.772369	−	0.772369i
$804$		0			0
$805$	−0.00350863	+	0.00350863i	−0.000123663	+	0.000123663i
$806$	−9.58733	+	3.15982i	−0.337699	+	0.111300i
$807$		0			0
$808$	−15.7922	+	22.3239i	−0.555567	+	0.785353i
$809$		−	21.7195i		−	0.763615i	−0.924242	−	0.381808i	$-0.875302\pi$
$809$		−	21.7195i		−	0.763615i	0.924242	−	0.381808i	$-0.124698\pi$
$810$		0			0
$811$	−1.56931	+	1.56931i	−0.0551060	+	0.0551060i	−0.734123	−	0.679017i	$-0.762406\pi$
$811$	−1.56931	+	1.56931i	−0.0551060	+	0.0551060i	0.679017	+	0.734123i	$0.262406\pi$
$812$	−0.529151	−	0.0792459i	−0.0185696	−	0.00278099i
$813$		0			0
$814$	−32.4348	−	16.3546i	−1.13684	−	0.573229i
$815$	19.7024			0.690146
$816$		0			0
$817$	64.1995			2.24606
$818$	34.2220	+	17.2558i	1.19654	+	0.603335i
$819$		0			0
$820$	−2.80137	+	18.7057i	−0.0978281	+	0.653231i
$821$	−21.6698	+	21.6698i	−0.756281	+	0.756281i	−0.975643	−	0.219362i	$-0.929602\pi$
$821$	−21.6698	+	21.6698i	−0.756281	+	0.756281i	0.219362	+	0.975643i	$0.429602\pi$
$822$		0			0
$823$			16.0490i			0.559432i	0.960083	+	0.279716i	$0.0902404\pi$
$823$			16.0490i			0.559432i	−0.960083	+	0.279716i	$0.909760\pi$
$824$	4.76680	+	27.8168i	0.166060	+	0.969045i
$825$		0			0
$826$	0.268317	−	0.0884327i	0.00933594	−	0.00307697i
$827$	34.3436	−	34.3436i	1.19424	−	1.19424i	0.218381	−	0.975863i	$-0.429922\pi$
$827$	34.3436	−	34.3436i	1.19424	−	1.19424i	0.975863	−	0.218381i	$-0.0700777\pi$
$828$		0			0
$829$	−14.0607	−	14.0607i	−0.488348	−	0.488348i	0.419437	−	0.907785i	$-0.362228\pi$
$829$	−14.0607	−	14.0607i	−0.488348	−	0.488348i	−0.907785	+	0.419437i	$0.862228\pi$
$830$	−12.8776	+	25.5391i	−0.446988	+	0.886474i
$831$		0			0
$832$	−13.7352	−	6.56666i	−0.476182	−	0.227658i
$833$	−9.81015			−0.339901
$834$		0			0
$835$	14.0400	+	14.0400i	0.485874	+	0.485874i
$836$	−38.2324	−	51.7008i	−1.32229	−	1.78811i
$837$		0			0
$838$	22.1540	−	7.30159i	0.765298	−	0.252229i
$839$		−	7.82530i		−	0.270159i	−0.990835	−	0.135080i	$-0.956871\pi$
$839$		−	7.82530i		−	0.270159i	0.990835	−	0.135080i	$-0.0431291\pi$
$840$		0			0
$841$			58.8452i			2.02915i
$842$	−1.80291	−	5.47029i	−0.0621325	−	0.188519i
$843$		0			0
$844$	2.43304	−	16.2462i	0.0837488	−	0.559218i
$845$	11.9614	+	11.9614i	0.411483	+	0.411483i
$846$		0			0
$847$	0.179981			0.00618422
$848$	−0.950322	−	1.78991i	−0.0326342	−	0.0614657i
$849$		0			0
$850$	3.09150	+	1.55883i	0.106038	+	0.0534674i
$851$	−0.420788	−	0.420788i	−0.0144244	−	0.0144244i
$852$		0			0
$853$	−21.7707	+	21.7707i	−0.745415	+	0.745415i	−0.973614	−	0.228199i	$-0.926716\pi$
$853$	−21.7707	+	21.7707i	−0.745415	+	0.745415i	0.228199	+	0.973614i	$0.426716\pi$
$854$	−0.122284	−	0.371025i	−0.00418446	−	0.0126962i
$855$		0			0
$856$	−30.5354	+	43.1650i	−1.04368	+	1.47535i
$857$			2.21631i			0.0757076i	0.999283	+	0.0378538i	$0.0120521\pi$
$857$			2.21631i			0.0757076i	−0.999283	+	0.0378538i	$0.987948\pi$
$858$		0			0
$859$	16.6172	−	16.6172i	0.566970	−	0.566970i	−0.364308	−	0.931278i	$-0.618695\pi$
$859$	16.6172	−	16.6172i	0.566970	−	0.566970i	0.931278	+	0.364308i	$0.118695\pi$
$860$	−24.0935	+	17.8170i	−0.821583	+	0.607555i
$861$		0			0
$862$	6.60492	−	13.0990i	0.224965	−	0.446153i
$863$	7.04849			0.239934			0.119967	−	0.992778i	$-0.461721\pi$
$863$	7.04849			0.239934			0.119967	+	0.992778i	$0.461721\pi$
$864$		0			0
$865$	40.0568			1.36197
$866$	−6.28087	+	12.4563i	−0.213433	+	0.423283i
$867$		0			0
$868$	−0.172164	+	0.127314i	−0.00584364	+	0.00432133i
$869$	7.60565	−	7.60565i	0.258004	−	0.258004i
$870$		0			0
$871$		−	4.20991i		−	0.142647i
$872$	46.2142	+	32.6924i	1.56501	+	1.10710i
$873$		0			0
$874$	−0.329738	−	1.00047i	−0.0111536	−	0.0338415i
$875$	0.245610	−	0.245610i	0.00830312	−	0.00830312i
$876$		0			0
$877$	6.33196	+	6.33196i	0.213815	+	0.213815i	0.805886	−	0.592071i	$-0.201689\pi$
$877$	6.33196	+	6.33196i	0.213815	+	0.213815i	−0.592071	+	0.805886i	$0.701689\pi$
$878$	−39.2873	−	19.8099i	−1.32588	−	0.668552i
$879$		0			0
$880$	28.6966	+	8.79242i	0.967362	+	0.296393i
$881$	11.9032			0.401028			0.200514	−	0.979691i	$-0.435739\pi$
$881$	11.9032			0.401028			0.200514	+	0.979691i	$0.435739\pi$
$882$		0			0
$883$	14.9623	+	14.9623i	0.503523	+	0.503523i	0.912531	−	0.409008i	$-0.134125\pi$
$883$	14.9623	+	14.9623i	0.503523	+	0.503523i	−0.409008	+	0.912531i	$0.634125\pi$
$884$	0.790102	−	5.27577i	0.0265740	−	0.177443i
$885$		0			0
$886$	11.2680	+	34.1886i	0.378555	+	1.14859i
$887$			46.0437i			1.54600i	0.634408	+	0.772999i	$0.281244\pi$
$887$			46.0437i			1.54600i	−0.634408	+	0.772999i	$0.718756\pi$
$888$		0			0
$889$		−	0.416892i		−	0.0139821i
$890$	23.3737	−	7.70357i	0.783488	−	0.258224i
$891$		0			0
$892$	−7.86525	−	10.6360i	−0.263348	−	0.356120i
$893$	16.6553	+	16.6553i	0.557349	+	0.557349i
$894$		0			0
$895$	−26.1334			−0.873543
$896$	−0.320307	−	0.0410931i	−0.0107007	−	0.00137282i
$897$		0			0
$898$	11.8820	−	23.5645i	0.396507	−	0.786359i
$899$	24.8585	+	24.8585i	0.829077	+	0.829077i
$900$		0			0
$901$	0.502122	−	0.502122i	0.0167281	−	0.0167281i
$902$	29.2963	−	9.65555i	0.975460	−	0.321495i
$903$		0			0
$904$	51.2291	−	8.77882i	1.70385	−	0.291979i
$905$		−	38.0059i		−	1.26336i
$906$		0			0
$907$	−38.7104	+	38.7104i	−1.28536	+	1.28536i	−0.347781	+	0.937576i	$0.613065\pi$
$907$	−38.7104	+	38.7104i	−1.28536	+	1.28536i	−0.937576	+	0.347781i	$0.886935\pi$
$908$	−5.20116	+	34.7299i	−0.172607	+	1.15255i
$909$		0			0
$910$	−0.123719	−	0.0623830i	−0.00410125	−	0.00206798i
$911$	11.8652			0.393112			0.196556	−	0.980493i	$-0.437024\pi$
$911$	11.8652			0.393112			0.196556	+	0.980493i	$0.437024\pi$
$912$		0			0
$913$	46.6457			1.54375
$914$	−28.4683	−	14.3546i	−0.941647	−	0.474808i
$915$		0			0
$916$	−22.2162	−	3.32710i	−0.734042	−	0.109931i
$917$	−0.381660	+	0.381660i	−0.0126035	+	0.0126035i
$918$		0			0
$919$			24.1156i			0.795500i	0.917494	+	0.397750i	$0.130209\pi$
$919$			24.1156i			0.795500i	−0.917494	+	0.397750i	$0.869791\pi$
$920$	0.401404	+	0.283958i	0.0132339	+	0.00936182i
$921$		0			0
$922$	−23.9121	+	7.88100i	−0.787502	+	0.259547i
$923$	−17.7383	+	17.7383i	−0.583863	+	0.583863i
$924$		0			0
$925$	7.62603	+	7.62603i	0.250742	+	0.250742i
$926$	0.449454	−	0.891364i	0.0147700	−	0.0292920i
$927$		0			0
$928$	1.11650	+	53.0076i	0.0366508	+	1.74006i
$929$	−15.9280			−0.522582			−0.261291	−	0.965260i	$-0.584148\pi$
$929$	−15.9280			−0.522582			−0.261291	+	0.965260i	$0.584148\pi$
$930$		0			0
$931$	−38.2500	−	38.2500i	−1.25359	−	1.25359i
$932$	−18.9734	+	14.0307i	−0.621495	+	0.459591i
$933$		0			0
$934$	−14.5651	+	4.80040i	−0.476584	+	0.157074i
$935$			10.5168i			0.343935i
$936$		0			0
$937$		−	17.8923i		−	0.584516i	−0.956340	−	0.292258i	$-0.905593\pi$
$937$		−	17.8923i		−	0.584516i	0.956340	−	0.292258i	$-0.0944065\pi$
$938$	−0.0279526	−	0.0848121i	−0.000912685	−	0.00276921i
$939$		0			0
$940$	−10.8729	−	1.62833i	−0.354634	−	0.0531102i
$941$	−2.24760	−	2.24760i	−0.0732698	−	0.0732698i	0.669522	−	0.742792i	$-0.266499\pi$
$941$	−2.24760	−	2.24760i	−0.0732698	−	0.0732698i	−0.742792	+	0.669522i	$0.766499\pi$
$942$		0			0
$943$	0.505337			0.0164560
$944$	−13.1278	−	24.7260i	−0.427275	−	0.804762i
$945$		0			0
$946$	43.6363	+	22.0028i	1.41874	+	0.715372i
$947$	−13.2537	−	13.2537i	−0.430688	−	0.430688i	0.458174	−	0.888862i	$-0.348504\pi$
$947$	−13.2537	−	13.2537i	−0.430688	−	0.430688i	−0.888862	+	0.458174i	$0.848504\pi$
$948$		0			0
$949$	10.0123	−	10.0123i	0.325014	−	0.325014i
$950$	5.97592	+	18.1318i	0.193884	+	0.588272i
$951$		0			0
$952$	−0.0191124	−	0.111531i	−0.000619436	−	0.00361474i
$953$		−	54.0901i		−	1.75215i	−0.482174	−	0.876075i	$-0.660153\pi$
$953$		−	54.0901i		−	1.75215i	0.482174	−	0.876075i	$-0.339847\pi$
$954$		0			0
$955$	−20.1948	+	20.1948i	−0.653489	+	0.653489i
$956$	−13.1492	−	17.7813i	−0.425274	−	0.575089i
$957$		0			0
$958$	4.04846	−	8.02898i	0.130800	−	0.259405i
$959$	0.0230354			0.000743852
$960$		0			0
$961$	−16.9311			−0.546164
$962$	7.48157	−	14.8376i	0.241216	−	0.478383i
$963$		0			0
$964$	13.8272	+	18.6982i	0.445344	+	0.602229i
$965$	19.1876	−	19.1876i	0.617671	−	0.617671i
$966$		0			0
$967$			1.91914i			0.0617153i	0.999524	+	0.0308577i	$0.00982385\pi$
$967$			1.91914i			0.0617153i	−0.999524	+	0.0308577i	$0.990176\pi$
$968$	−3.01231	−	17.5784i	−0.0968193	−	0.564992i
$969$		0			0
$970$	−1.79590	−	5.44901i	−0.0576629	−	0.174957i
$971$	−13.4577	+	13.4577i	−0.431878	+	0.431878i	−0.889267	−	0.457389i	$-0.848785\pi$
$971$	−13.4577	+	13.4577i	−0.431878	+	0.431878i	0.457389	+	0.889267i	$0.348785\pi$
$972$		0			0
$973$	0.0962209	+	0.0962209i	0.00308470	+	0.00308470i
$974$	−38.9098	−	19.6195i	−1.24675	−	0.628650i
$975$		0			0
$976$	−34.1908	+	18.1530i	−1.09442	+	0.581064i
$977$	−25.1141			−0.803471			−0.401735	−	0.915756i	$-0.631593\pi$
$977$	−25.1141			−0.803471			−0.401735	+	0.915756i	$0.631593\pi$
$978$		0			0
$979$	−28.3805	−	28.3805i	−0.907044	−	0.907044i
$980$	24.9703	+	3.73956i	0.797646	+	0.119456i
$981$		0			0
$982$	1.06932	+	3.24445i	0.0341232	+	0.103535i
$983$		−	11.1195i		−	0.354655i	−0.984152	−	0.177328i	$-0.943255\pi$
$983$		−	11.1195i		−	0.354655i	0.984152	−	0.177328i	$-0.0567453\pi$
$984$		0			0
$985$			31.1787i			0.993437i
$986$	−17.6445	+	5.81533i	−0.561916	+	0.185198i
$987$		0			0
$988$	23.6510	−	17.4898i	0.752439	−	0.556423i
$989$	0.566110	+	0.566110i	0.0180012	+	0.0180012i
$990$		0			0
$991$	28.5845			0.908017			0.454008	−	0.890997i	$-0.349994\pi$
$991$	28.5845			0.908017			0.454008	+	0.890997i	$0.349994\pi$
$992$	15.3160	+	14.6842i	0.486285	+	0.466222i
$993$		0			0
$994$	−0.239575	+	0.475129i	−0.00759886	+	0.0150702i
$995$	18.6168	+	18.6168i	0.590194	+	0.590194i
$996$		0			0
$997$	38.4206	−	38.4206i	1.21679	−	1.21679i	0.248043	−	0.968749i	$-0.420212\pi$
$997$	38.4206	−	38.4206i	1.21679	−	1.21679i	0.968749	−	0.248043i	$-0.0797875\pi$
$998$	−11.2573	+	3.71021i	−0.356343	+	0.117445i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.k.d.109.5	✓	32
3.2	odd	2	inner	432.2.k.d.109.12	yes	32
4.3	odd	2		1728.2.k.d.1297.5		32
12.11	even	2		1728.2.k.d.1297.12		32
16.5	even	4	inner	432.2.k.d.325.5	yes	32
16.11	odd	4		1728.2.k.d.433.5		32
48.5	odd	4	inner	432.2.k.d.325.12	yes	32
48.11	even	4		1728.2.k.d.433.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.k.d.109.5	✓	32	1.1	even	1	trivial
432.2.k.d.109.12	yes	32	3.2	odd	2	inner
432.2.k.d.325.5	yes	32	16.5	even	4	inner
432.2.k.d.325.12	yes	32	48.5	odd	4	inner
1728.2.k.d.433.5		32	16.11	odd	4
1728.2.k.d.433.12		32	48.11	even	4
1728.2.k.d.1297.5		32	4.3	odd	2
1728.2.k.d.1297.12		32	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.636726 + 1.26277i) q^{2} +(-1.18916 - 1.60807i) q^{4} +(-1.27540 + 1.27540i) q^{5} +0.0285435i q^{7} +(2.78779 - 0.477727i) q^{8} +O(q^{10})\)	\(q+(-0.636726 + 1.26277i) q^{2} +(-1.18916 - 1.60807i) q^{4} +(-1.27540 + 1.27540i) q^{5} +0.0285435i q^{7} +(2.78779 - 0.477727i) q^{8} +(-0.798453 - 2.42262i) q^{10} +(-2.94156 + 2.94156i) q^{11} +(-1.34564 - 1.34564i) q^{13} +(-0.0360437 - 0.0181744i) q^{14} +(-1.17180 + 3.82451i) q^{16} -1.40161 q^{17} +(-5.46493 - 5.46493i) q^{19} +(3.56760 + 0.534285i) q^{20} +(-1.84153 - 5.58747i) q^{22} -0.0963791i q^{23} +1.74670i q^{25} +(2.55604 - 0.842426i) q^{26} +(0.0459000 - 0.0339427i) q^{28} +(-6.62741 - 6.62741i) q^{29} -3.75086 q^{31} +(-4.08335 - 3.91488i) q^{32} +(0.892444 - 1.76991i) q^{34} +(-0.0364044 - 0.0364044i) q^{35} +(4.36597 - 4.36597i) q^{37} +(10.3806 - 3.42126i) q^{38} +(-2.94626 + 4.16485i) q^{40} +5.24322i q^{41} +(-5.87378 + 5.87378i) q^{43} +(8.22822 + 1.23226i) q^{44} +(0.121704 + 0.0613671i) q^{46} -3.04768 q^{47} +6.99919 q^{49} +(-2.20567 - 1.11217i) q^{50} +(-0.563710 + 3.76407i) q^{52} +(-0.358246 + 0.358246i) q^{53} -7.50333i q^{55} +(0.0136360 + 0.0795732i) q^{56} +(12.5887 - 4.14903i) q^{58} +(-4.94884 + 4.94884i) q^{59} +(6.84320 + 6.84320i) q^{61} +(2.38827 - 4.73646i) q^{62} +(7.54355 - 2.66361i) q^{64} +3.43247 q^{65} +(1.56428 + 1.56428i) q^{67} +(1.66674 + 2.25390i) q^{68} +(0.0691499 - 0.0227906i) q^{70} -13.1820i q^{71} +7.44056i q^{73} +(2.73327 + 8.29312i) q^{74} +(-2.28934 + 15.2867i) q^{76} +(-0.0839622 - 0.0839622i) q^{77} -2.58559 q^{79} +(-3.38327 - 6.37231i) q^{80} +(-6.62096 - 3.33849i) q^{82} +(-7.92875 - 7.92875i) q^{83} +(1.78762 - 1.78762i) q^{85} +(-3.67722 - 11.1572i) q^{86} +(-6.79518 + 9.60570i) q^{88} +9.64812i q^{89} +(0.0384093 - 0.0384093i) q^{91} +(-0.154985 + 0.114610i) q^{92} +(1.94054 - 3.84851i) q^{94} +13.9400 q^{95} +2.24923 q^{97} +(-4.45657 + 8.83834i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} + 24 q^{16} + 16 q^{19} + 32 q^{22} + 24 q^{28} - 8 q^{34} + 56 q^{40} - 16 q^{43} - 32 q^{49} - 16 q^{52} - 32 q^{61} + 24 q^{64} + 32 q^{67} - 96 q^{70} - 48 q^{76} - 32 q^{79} + 32 q^{85} - 88 q^{88} - 48 q^{91} - 96 q^{94}+O(q^{100}) \) 32 * q - 8 * q^10 + 24 * q^16 + 16 * q^19 + 32 * q^22 + 24 * q^28 - 8 * q^34 + 56 * q^40 - 16 * q^43 - 32 * q^49 - 16 * q^52 - 32 * q^61 + 24 * q^64 + 32 * q^67 - 96 * q^70 - 48 * q^76 - 32 * q^79 + 32 * q^85 - 88 * q^88 - 48 * q^91 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more