LMFDB - Embedded newform 432.2.l.b.107.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(107,432)]

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([2, 1, 2]))

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

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

chi := DirichletCharacter("432.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.l (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			107.14
Character	$\chi$	$=$	432.107
Dual form			432.2.l.b.323.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19933 - 0.749398i) q^{2} +(0.876807 - 1.79756i) q^{4} +(-2.15382 + 2.15382i) q^{5} +4.43758 q^{7} +(-0.295500 - 2.81295i) q^{8} +O(q^{10})$	\(q+(1.19933 - 0.749398i) q^{2} +(0.876807 - 1.79756i) q^{4} +(-2.15382 + 2.15382i) q^{5} +4.43758 q^{7} +(-0.295500 - 2.81295i) q^{8} +(-0.969085 + 4.19723i) q^{10} +(3.87657 + 3.87657i) q^{11} +(0.958389 - 0.958389i) q^{13} +(5.32214 - 3.32551i) q^{14} +(-2.46242 - 3.15222i) q^{16} -2.92448i q^{17} +(-4.16292 - 4.16292i) q^{19} +(1.98313 + 5.76011i) q^{20} +(7.55439 + 1.74421i) q^{22} -1.03692i q^{23} -4.27792i q^{25} +(0.431215 - 1.86764i) q^{26} +(3.89090 - 7.97680i) q^{28} +(0.941127 + 0.941127i) q^{29} +0.537179i q^{31} +(-5.31553 - 1.93523i) q^{32} +(-2.19160 - 3.50743i) q^{34} +(-9.55776 + 9.55776i) q^{35} +(5.89772 + 5.89772i) q^{37} +(-8.11241 - 1.87305i) q^{38} +(6.69505 + 5.42214i) q^{40} -3.55608 q^{41} +(-8.23479 + 8.23479i) q^{43} +(10.3674 - 3.56935i) q^{44} +(-0.777069 - 1.24362i) q^{46} -0.595112 q^{47} +12.6921 q^{49} +(-3.20586 - 5.13065i) q^{50} +(-0.882437 - 2.56308i) q^{52} +(-6.92245 + 6.92245i) q^{53} -16.6989 q^{55} +(-1.31130 - 12.4827i) q^{56} +(1.83400 + 0.423448i) q^{58} +(-7.50660 - 7.50660i) q^{59} +(0.900652 - 0.900652i) q^{61} +(0.402561 + 0.644258i) q^{62} +(-7.82536 + 1.66245i) q^{64} +4.12840i q^{65} +(-2.68757 - 2.68757i) q^{67} +(-5.25691 - 2.56420i) q^{68} +(-4.30039 + 18.6255i) q^{70} -0.430434i q^{71} -5.99346i q^{73} +(11.4931 + 2.65360i) q^{74} +(-11.1331 + 3.83300i) q^{76} +(17.2026 + 17.2026i) q^{77} -0.295266i q^{79} +(12.0929 + 1.48571i) q^{80} +(-4.26493 + 2.66492i) q^{82} +(-1.58742 + 1.58742i) q^{83} +(6.29881 + 6.29881i) q^{85} +(-3.70514 + 16.0474i) q^{86} +(9.75906 - 12.0501i) q^{88} -11.5832 q^{89} +(4.25293 - 4.25293i) q^{91} +(-1.86393 - 0.909182i) q^{92} +(-0.713739 + 0.445976i) q^{94} +17.9324 q^{95} -3.49925 q^{97} +(15.2221 - 9.51143i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 8 q^{10} - 8 q^{16} - 16 q^{19} + 16 q^{22} + 24 q^{28} + 24 q^{34} - 24 q^{40} - 16 q^{43} + 32 q^{46} + 32 q^{49} + 48 q^{52} - 32 q^{55} + 32 q^{61} - 24 q^{64} - 32 q^{67} - 48 q^{76} - 80 q^{82} + 32 q^{85} - 24 q^{88} - 48 q^{91}+O(q^{100}) $ 32 * q + 8 * q^10 - 8 * q^16 - 16 * q^19 + 16 * q^22 + 24 * q^28 + 24 * q^34 - 24 * q^40 - 16 * q^43 + 32 * q^46 + 32 * q^49 + 48 * q^52 - 32 * q^55 + 32 * q^61 - 24 * q^64 - 32 * q^67 - 48 * q^76 - 80 * q^82 + 32 * q^85 - 24 * q^88 - 48 * q^91

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.19933	−	0.749398i	0.848058	−	0.529904i
$2$	1.19933	−	0.749398i	0.848058	−	0.529904i
$3$		0			0
$3$		0			0
$4$	0.876807	−	1.79756i	0.438403	−	0.898778i
$5$	−2.15382	+	2.15382i	−0.963219	+	0.963219i	−0.999347	−	0.0361278i	$-0.988498\pi$
$5$	−2.15382	+	2.15382i	−0.963219	+	0.963219i	0.0361278	+	0.999347i	$0.488498\pi$
$6$		0			0
$7$	4.43758			1.67725			0.838623	−	0.544712i	$-0.183361\pi$
$7$	4.43758			1.67725			0.838623	+	0.544712i	$0.183361\pi$
$8$	−0.295500	−	2.81295i	−0.104475	−	0.994528i
$9$		0			0
$10$	−0.969085	+	4.19723i	−0.306452	+	1.32728i
$11$	3.87657	+	3.87657i	1.16883	+	1.16883i	0.982484	+	0.186345i	$0.0596642\pi$
$11$	3.87657	+	3.87657i	1.16883	+	1.16883i	0.186345	+	0.982484i	$0.440336\pi$
$12$		0			0
$13$	0.958389	−	0.958389i	0.265809	−	0.265809i	−0.561600	−	0.827409i	$-0.689814\pi$
$13$	0.958389	−	0.958389i	0.265809	−	0.265809i	0.827409	+	0.561600i	$0.189814\pi$
$14$	5.32214	−	3.32551i	1.42240	−	0.888780i
$15$		0			0
$16$	−2.46242	−	3.15222i	−0.615605	−	0.788055i
$17$		−	2.92448i		−	0.709290i	−0.935001	−	0.354645i	$-0.884602\pi$
$17$		−	2.92448i		−	0.709290i	0.935001	−	0.354645i	$-0.115398\pi$
$18$		0			0
$19$	−4.16292	−	4.16292i	−0.955038	−	0.955038i	0.0439935	−	0.999032i	$-0.485992\pi$
$19$	−4.16292	−	4.16292i	−0.955038	−	0.955038i	−0.999032	+	0.0439935i	$0.985992\pi$
$20$	1.98313	+	5.76011i	0.443442	+	1.28800i
$21$		0			0
$22$	7.55439	+	1.74421i	1.61060	+	0.371867i
$23$		−	1.03692i		−	0.216214i	−0.994139	−	0.108107i	$-0.965521\pi$
$23$		−	1.03692i		−	0.216214i	0.994139	−	0.108107i	$-0.0344789\pi$
$24$		0			0
$25$		−	4.27792i		−	0.855583i
$26$	0.431215	−	1.86764i	0.0845682	−	0.366275i
$27$		0			0
$28$	3.89090	−	7.97680i	0.735311	−	1.50747i
$29$	0.941127	+	0.941127i	0.174763	+	0.174763i	0.789068	−	0.614305i	$-0.210564\pi$
$29$	0.941127	+	0.941127i	0.174763	+	0.174763i	−0.614305	+	0.789068i	$0.710564\pi$
$30$		0			0
$31$			0.537179i			0.0964803i	0.998836	+	0.0482401i	$0.0153613\pi$
$31$			0.537179i			0.0964803i	−0.998836	+	0.0482401i	$0.984639\pi$
$32$	−5.31553	−	1.93523i	−0.939662	−	0.342104i
$33$		0			0
$34$	−2.19160	−	3.50743i	−0.375856	−	0.601519i
$35$	−9.55776	+	9.55776i	−1.61556	+	1.61556i
$36$		0			0
$37$	5.89772	+	5.89772i	0.969579	+	0.969579i	0.999551	−	0.0299713i	$-0.00954159\pi$
$37$	5.89772	+	5.89772i	0.969579	+	0.969579i	−0.0299713	+	0.999551i	$0.509542\pi$
$38$	−8.11241	−	1.87305i	−1.31601	−	0.303849i
$39$		0			0
$40$	6.69505	+	5.42214i	1.05858	+	0.857316i
$41$	−3.55608			−0.555367			−0.277683	−	0.960673i	$-0.589567\pi$
$41$	−3.55608			−0.555367			−0.277683	+	0.960673i	$0.589567\pi$
$42$		0			0
$43$	−8.23479	+	8.23479i	−1.25579	+	1.25579i	−0.302712	+	0.953082i	$0.597892\pi$
$43$	−8.23479	+	8.23479i	−1.25579	+	1.25579i	−0.953082	+	0.302712i	$0.902108\pi$
$44$	10.3674	−	3.56935i	1.56294	−	0.538100i
$45$		0			0
$46$	−0.777069	−	1.24362i	−0.114573	−	0.183362i
$47$	−0.595112			−0.0868061			−0.0434030	−	0.999058i	$-0.513820\pi$
$47$	−0.595112			−0.0868061			−0.0434030	+	0.999058i	$0.513820\pi$
$48$		0			0
$49$	12.6921			1.81316
$50$	−3.20586	−	5.13065i	−0.453377	−	0.725584i
$51$		0			0
$52$	−0.882437	−	2.56308i	−0.122372	−	0.355435i
$53$	−6.92245	+	6.92245i	−0.950872	+	0.950872i	−0.998848	−	0.0479768i	$-0.984723\pi$
$53$	−6.92245	+	6.92245i	−0.950872	+	0.950872i	0.0479768	+	0.998848i	$0.484723\pi$
$54$		0			0
$55$	−16.6989			−2.25168
$56$	−1.31130	−	12.4827i	−0.175230	−	1.66807i
$57$		0			0
$58$	1.83400	+	0.423448i	0.240817	+	0.0556014i
$59$	−7.50660	−	7.50660i	−0.977276	−	0.977276i	0.0224716	−	0.999747i	$-0.492846\pi$
$59$	−7.50660	−	7.50660i	−0.977276	−	0.977276i	−0.999747	+	0.0224716i	$0.992846\pi$
$60$		0			0
$61$	0.900652	−	0.900652i	0.115317	−	0.115317i	−0.647094	−	0.762410i	$-0.724016\pi$
$61$	0.900652	−	0.900652i	0.115317	−	0.115317i	0.762410	+	0.647094i	$0.224016\pi$
$62$	0.402561	+	0.644258i	0.0511253	+	0.0818208i
$63$		0			0
$64$	−7.82536	+	1.66245i	−0.978170	+	0.207806i
$65$			4.12840i			0.512066i
$66$		0			0
$67$	−2.68757	−	2.68757i	−0.328338	−	0.328338i	0.523616	−	0.851954i	$-0.324583\pi$
$67$	−2.68757	−	2.68757i	−0.328338	−	0.328338i	−0.851954	+	0.523616i	$0.824583\pi$
$68$	−5.25691	−	2.56420i	−0.637494	−	0.310955i
$69$		0			0
$70$	−4.30039	+	18.6255i	−0.513995	+	2.22618i
$71$		−	0.430434i		−	0.0510831i	−0.999674	−	0.0255415i	$-0.991869\pi$
$71$		−	0.430434i		−	0.0510831i	0.999674	−	0.0255415i	$-0.00813101\pi$
$72$		0			0
$73$		−	5.99346i		−	0.701482i	−0.936473	−	0.350741i	$-0.885930\pi$
$73$		−	5.99346i		−	0.701482i	0.936473	−	0.350741i	$-0.114070\pi$
$74$	11.4931	+	2.65360i	1.33604	+	0.308475i
$75$		0			0
$76$	−11.1331	+	3.83300i	−1.27706	+	0.439676i
$77$	17.2026	+	17.2026i	1.96042	+	1.96042i
$78$		0			0
$79$		−	0.295266i		−	0.0332200i	−0.999862	−	0.0166100i	$-0.994713\pi$
$79$		−	0.295266i		−	0.0332200i	0.999862	−	0.0166100i	$-0.00528737\pi$
$80$	12.0929	+	1.48571i	1.35203	+	0.166107i
$81$		0			0
$82$	−4.26493	+	2.66492i	−0.470983	+	0.294291i
$83$	−1.58742	+	1.58742i	−0.174242	+	0.174242i	−0.788840	−	0.614598i	$-0.789318\pi$
$83$	−1.58742	+	1.58742i	−0.174242	+	0.174242i	0.614598	+	0.788840i	$0.289318\pi$
$84$		0			0
$85$	6.29881	+	6.29881i	0.683202	+	0.683202i
$86$	−3.70514	+	16.0474i	−0.399535	+	1.73044i
$87$		0			0
$88$	9.75906	−	12.0501i	1.04032	−	1.28455i
$89$	−11.5832			−1.22781			−0.613907	−	0.789379i	$-0.710403\pi$
$89$	−11.5832			−1.22781			−0.613907	+	0.789379i	$0.710403\pi$
$90$		0			0
$91$	4.25293	−	4.25293i	0.445828	−	0.445828i
$92$	−1.86393	−	0.909182i	−0.194328	−	0.0947888i
$93$		0			0
$94$	−0.713739	+	0.445976i	−0.0736165	+	0.0459989i
$95$	17.9324			1.83982
$96$		0			0
$97$	−3.49925			−0.355295			−0.177648	−	0.984094i	$-0.556849\pi$
$97$	−3.49925			−0.355295			−0.177648	+	0.984094i	$0.556849\pi$
$98$	15.2221	−	9.51143i	1.53766	−	0.960799i
$99$		0			0
$100$	−7.68980	−	3.75091i	−0.768980	−	0.375091i
$101$	11.1414	−	11.1414i	1.10861	−	1.10861i	0.115272	−	0.993334i	$-0.463226\pi$
$101$	11.1414	−	11.1414i	1.10861	−	1.10861i	0.993334	−	0.115272i	$-0.0367740\pi$
$102$		0			0
$103$	−5.81039			−0.572514			−0.286257	−	0.958153i	$-0.592411\pi$
$103$	−5.81039			−0.572514			−0.286257	+	0.958153i	$0.592411\pi$
$104$	−2.97910	−	2.41270i	−0.292125	−	0.236584i
$105$		0			0
$106$	−3.11467	+	13.4900i	−0.302523	+	1.31026i
$107$	−3.73819	−	3.73819i	−0.361385	−	0.361385i	0.502938	−	0.864323i	$-0.332252\pi$
$107$	−3.73819	−	3.73819i	−0.361385	−	0.361385i	−0.864323	+	0.502938i	$0.832252\pi$
$108$		0			0
$109$	0.937009	−	0.937009i	0.0897492	−	0.0897492i	−0.660807	−	0.750556i	$-0.729786\pi$
$109$	0.937009	−	0.937009i	0.0897492	−	0.0897492i	0.750556	+	0.660807i	$0.229786\pi$
$110$	−20.0276	+	12.5141i	−1.90955	+	1.19317i
$111$		0			0
$112$	−10.9272	−	13.9882i	−1.03252	−	1.32176i
$113$		−	16.7260i		−	1.57345i	−0.617306	−	0.786723i	$-0.711776\pi$
$113$		−	16.7260i		−	1.57345i	0.617306	−	0.786723i	$-0.288224\pi$
$114$		0			0
$115$	2.23335	+	2.23335i	0.208261	+	0.208261i
$116$	2.51692	−	0.866543i	0.233690	−	0.0804565i
$117$		0			0
$118$	−14.6283	−	3.37750i	−1.34665	−	0.310924i
$119$		−	12.9776i		−	1.18965i
$120$		0			0
$121$			19.0556i			1.73232i
$122$	0.405237	−	1.75513i	0.0366884	−	0.158902i
$123$		0			0
$124$	0.965611	+	0.471003i	0.0867144	+	0.0422973i
$125$	−1.55524	−	1.55524i	−0.139105	−	0.139105i
$126$		0			0
$127$			8.33709i			0.739797i	0.929072	+	0.369899i	$0.120608\pi$
$127$			8.33709i			0.739797i	−0.929072	+	0.369899i	$0.879392\pi$
$128$	−8.13939	+	7.85814i	−0.719427	+	0.694568i
$129$		0			0
$130$	3.09382	+	4.95134i	0.271346	+	0.434261i
$131$	−1.90494	+	1.90494i	−0.166435	+	0.166435i	−0.785410	−	0.618975i	$-0.787548\pi$
$131$	−1.90494	+	1.90494i	−0.166435	+	0.166435i	0.618975	+	0.785410i	$0.287548\pi$
$132$		0			0
$133$	−18.4733	−	18.4733i	−1.60183	−	1.60183i
$134$	−5.23734	−	1.20924i	−0.452438	−	0.104462i
$135$		0			0
$136$	−8.22640	+	0.864183i	−0.705408	+	0.0741030i
$137$	2.46703			0.210773			0.105386	−	0.994431i	$-0.466392\pi$
$137$	2.46703			0.210773			0.105386	+	0.994431i	$0.466392\pi$
$138$		0			0
$139$	−7.77654	+	7.77654i	−0.659597	+	0.659597i	−0.955285	−	0.295688i	$-0.904451\pi$
$139$	−7.77654	+	7.77654i	−0.659597	+	0.659597i	0.295688	+	0.955285i	$0.404451\pi$
$140$	8.80031	+	25.5609i	0.743762	+	2.16029i
$141$		0			0
$142$	−0.322566	−	0.516234i	−0.0270691	−	0.0433214i
$143$	7.43052			0.621372
$144$		0			0
$145$	−4.05404			−0.336670
$146$	−4.49148	−	7.18816i	−0.371718	−	0.594897i
$147$		0			0
$148$	15.7727	−	5.43033i	1.29650	−	0.446370i
$149$	10.1845	−	10.1845i	0.834346	−	0.834346i	−0.153762	−	0.988108i	$-0.549139\pi$
$149$	10.1845	−	10.1845i	0.834346	−	0.834346i	0.988108	+	0.153762i	$0.0491389\pi$
$150$		0			0
$151$	−3.83664			−0.312222			−0.156111	−	0.987740i	$-0.549896\pi$
$151$	−3.83664			−0.312222			−0.156111	+	0.987740i	$0.549896\pi$
$152$	−10.4799	+	12.9402i	−0.850034	+	1.04959i
$153$		0			0
$154$	33.5232	+	7.74008i	2.70138	+	0.623713i
$155$	−1.15699	−	1.15699i	−0.0929317	−	0.0929317i
$156$		0			0
$157$	11.4332	−	11.4332i	0.912471	−	0.912471i	−0.0839952	−	0.996466i	$-0.526768\pi$
$157$	11.4332	−	11.4332i	0.912471	−	0.912471i	0.996466	+	0.0839952i	$0.0267680\pi$
$158$	−0.221272	−	0.354123i	−0.0176034	−	0.0281725i
$159$		0			0
$160$	15.6169	−	7.28056i	1.23462	−	0.575579i
$161$		−	4.60143i		−	0.362644i
$162$		0			0
$163$	6.79011	+	6.79011i	0.531842	+	0.531842i	0.921120	−	0.389278i	$-0.127275\pi$
$163$	6.79011	+	6.79011i	0.531842	+	0.531842i	−0.389278	+	0.921120i	$0.627275\pi$
$164$	−3.11800	+	6.39226i	−0.243475	+	0.499152i
$165$		0			0
$166$	−0.714241	+	3.09346i	−0.0554358	+	0.240099i
$167$			12.5245i			0.969171i	0.874744	+	0.484586i	$0.161030\pi$
$167$			12.5245i			0.969171i	−0.874744	+	0.484586i	$0.838970\pi$
$168$		0			0
$169$			11.1630i			0.858691i
$170$	12.2747	+	2.83407i	0.941426	+	0.217363i
$171$		0			0
$172$	7.58218	+	22.0228i	0.578136	+	1.67922i
$173$	2.42516	+	2.42516i	0.184382	+	0.184382i	0.793262	−	0.608880i	$-0.208381\pi$
$173$	2.42516	+	2.42516i	0.184382	+	0.184382i	−0.608880	+	0.793262i	$0.708381\pi$
$174$		0			0
$175$		−	18.9836i		−	1.43502i
$176$	2.67406	−	21.7655i	0.201565	−	1.64064i
$177$		0			0
$178$	−13.8921	+	8.68040i	−1.04126	+	0.650623i
$179$	−9.20486	+	9.20486i	−0.688004	+	0.688004i	−0.961790	−	0.273787i	$-0.911724\pi$
$179$	−9.20486	+	9.20486i	−0.688004	+	0.688004i	0.273787	+	0.961790i	$0.411724\pi$
$180$		0			0
$181$	5.85737	+	5.85737i	0.435375	+	0.435375i	0.890452	−	0.455077i	$-0.150388\pi$
$181$	5.85737	+	5.85737i	0.435375	+	0.435375i	−0.455077	+	0.890452i	$0.650388\pi$
$182$	1.91355	−	8.28782i	0.141842	−	0.614334i
$183$		0			0
$184$	−2.91681	+	0.306411i	−0.215030	+	0.0225889i
$185$	−25.4053			−1.86784
$186$		0			0
$187$	11.3369	−	11.3369i	0.829039	−	0.829039i
$188$	−0.521799	+	1.06975i	−0.0380561	+	0.0780194i
$189$		0			0
$190$	21.5069	−	13.4385i	1.56028	−	0.974930i
$191$	25.2535			1.82728			0.913638	−	0.406529i	$-0.133261\pi$
$191$	25.2535			1.82728			0.913638	+	0.406529i	$0.133261\pi$
$192$		0			0
$193$	−0.379606			−0.0273247			−0.0136623	−	0.999907i	$-0.504349\pi$
$193$	−0.379606			−0.0273247			−0.0136623	+	0.999907i	$0.504349\pi$
$194$	−4.19677	+	2.62233i	−0.301311	+	0.188272i
$195$		0			0
$196$	11.1285	−	22.8148i	0.794894	−	1.62963i
$197$	−6.63718	+	6.63718i	−0.472879	+	0.472879i	−0.902845	−	0.429966i	$-0.858526\pi$
$197$	−6.63718	+	6.63718i	−0.472879	+	0.472879i	0.429966	+	0.902845i	$0.358526\pi$
$198$		0			0
$199$	7.89951			0.559982			0.279991	−	0.960003i	$-0.409669\pi$
$199$	7.89951			0.559982			0.279991	+	0.960003i	$0.409669\pi$
$200$	−12.0336	+	1.26412i	−0.850901	+	0.0893870i
$201$		0			0
$202$	5.01291	−	21.7115i	0.352707	−	1.52762i
$203$	4.17632	+	4.17632i	0.293120	+	0.293120i
$204$		0			0
$205$	7.65918	−	7.65918i	0.534940	−	0.534940i
$206$	−6.96860	+	4.35429i	−0.485525	+	0.303378i
$207$		0			0
$208$	−5.38101	−	0.661097i	−0.373106	−	0.0458388i
$209$		−	32.2756i		−	2.23255i
$210$		0			0
$211$	−14.2447	−	14.2447i	−0.980644	−	0.980644i	0.0191721	−	0.999816i	$-0.493897\pi$
$211$	−14.2447	−	14.2447i	−0.980644	−	0.980644i	−0.999816	+	0.0191721i	$0.993897\pi$
$212$	6.37385	+	18.5131i	0.437757	+	1.27149i
$213$		0			0
$214$	−7.28473	−	1.68195i	−0.497974	−	0.114976i
$215$		−	35.4726i		−	2.41921i
$216$		0			0
$217$			2.38378i			0.161821i
$218$	0.421595	−	1.82598i	0.0285540	−	0.123671i
$219$		0			0
$220$	−14.6417	+	30.0172i	−0.987143	+	2.02376i
$221$	−2.80279	−	2.80279i	−0.188536	−	0.188536i
$222$		0			0
$223$			16.9978i			1.13826i	0.822248	+	0.569129i	$0.192720\pi$
$223$			16.9978i			1.13826i	−0.822248	+	0.569129i	$0.807280\pi$
$224$	−23.5881	−	8.58775i	−1.57605	−	0.573793i
$225$		0			0
$226$	−12.5344	−	20.0600i	−0.833776	−	1.33437i
$227$	−4.52420	+	4.52420i	−0.300282	+	0.300282i	−0.841124	−	0.540842i	$-0.818106\pi$
$227$	−4.52420	+	4.52420i	−0.300282	+	0.300282i	0.540842	+	0.841124i	$0.318106\pi$
$228$		0			0
$229$	3.84057	+	3.84057i	0.253792	+	0.253792i	0.822523	−	0.568731i	$-0.192566\pi$
$229$	3.84057	+	3.84057i	0.253792	+	0.253792i	−0.568731	+	0.822523i	$0.692566\pi$
$230$	4.35221	+	1.00487i	0.286976	+	0.0662590i
$231$		0			0
$232$	2.36924	−	2.92544i	0.155548	−	0.192065i
$233$	22.5716			1.47872			0.739358	−	0.673313i	$-0.235129\pi$
$233$	22.5716			1.47872			0.739358	+	0.673313i	$0.235129\pi$
$234$		0			0
$235$	1.28177	−	1.28177i	0.0836133	−	0.0836133i
$236$	−20.0754	+	6.91170i	−1.30680	+	0.449913i
$237$		0			0
$238$	−9.72538	−	15.5645i	−0.630403	−	1.00890i
$239$	−11.3171			−0.732043			−0.366022	−	0.930606i	$-0.619280\pi$
$239$	−11.3171			−0.732043			−0.366022	+	0.930606i	$0.619280\pi$
$240$		0			0
$241$	10.4313			0.671938			0.335969	−	0.941873i	$-0.390936\pi$
$241$	10.4313			0.671938			0.335969	+	0.941873i	$0.390936\pi$
$242$	14.2802	+	22.8540i	0.917965	+	1.46911i
$243$		0			0
$244$	−0.829275	−	2.40867i	−0.0530889	−	0.154199i
$245$	−27.3365	+	27.3365i	−1.74647	+	1.74647i
$246$		0			0
$247$	−7.97939			−0.507716
$248$	1.51106	−	0.158736i	0.0959523	−	0.0100798i
$249$		0			0
$250$	−3.03075	−	0.699761i	−0.191681	−	0.0442567i
$251$	8.28993	+	8.28993i	0.523256	+	0.523256i	0.918553	−	0.395297i	$-0.129358\pi$
$251$	8.28993	+	8.28993i	0.523256	+	0.523256i	−0.395297	+	0.918553i	$0.629358\pi$
$252$		0			0
$253$	4.01971	−	4.01971i	0.252717	−	0.252717i
$254$	6.24780	+	9.99896i	0.392022	+	0.627391i
$255$		0			0
$256$	−3.87298	+	15.5242i	−0.242061	+	0.970261i
$257$		−	10.4541i		−	0.652111i	−0.945351	−	0.326056i	$-0.894280\pi$
$257$		−	10.4541i		−	0.652111i	0.945351	−	0.326056i	$-0.105720\pi$
$258$		0			0
$259$	26.1716	+	26.1716i	1.62622	+	1.62622i
$260$	7.42104	+	3.61981i	0.460233	+	0.224491i
$261$		0			0
$262$	−0.857102	+	3.71221i	−0.0529520	+	0.229341i
$263$		−	26.2790i		−	1.62043i	−0.586131	−	0.810216i	$-0.699350\pi$
$263$		−	26.2790i		−	1.62043i	0.586131	−	0.810216i	$-0.300650\pi$
$264$		0			0
$265$		−	29.8195i		−	1.83180i
$266$	−35.9994	−	8.31180i	−2.20727	−	0.509629i
$267$		0			0
$268$	−7.18753	+	2.47458i	−0.439048	+	0.151159i
$269$	7.65131	+	7.65131i	0.466509	+	0.466509i	0.900781	−	0.434273i	$-0.142995\pi$
$269$	7.65131	+	7.65131i	0.466509	+	0.466509i	−0.434273	+	0.900781i	$0.642995\pi$
$270$		0			0
$271$		−	20.7407i		−	1.25991i	−0.776632	−	0.629954i	$-0.783074\pi$
$271$		−	20.7407i		−	1.25991i	0.776632	−	0.629954i	$-0.216926\pi$
$272$	−9.21859	+	7.20129i	−0.558959	+	0.436642i
$273$		0			0
$274$	2.95880	−	1.84879i	0.178748	−	0.111689i
$275$	16.5836	−	16.5836i	1.00003	−	1.00003i
$276$		0			0
$277$	1.73459	+	1.73459i	0.104221	+	0.104221i	0.757295	−	0.653073i	$-0.226521\pi$
$277$	1.73459	+	1.73459i	0.104221	+	0.104221i	−0.653073	+	0.757295i	$0.726521\pi$
$278$	−3.49895	+	15.1544i	−0.209853	+	0.908900i
$279$		0			0
$280$	29.7098	+	24.0612i	1.77550	+	1.43793i
$281$	15.3010			0.912780			0.456390	−	0.889780i	$-0.349142\pi$
$281$	15.3010			0.912780			0.456390	+	0.889780i	$0.349142\pi$
$282$		0			0
$283$	5.98683	−	5.98683i	0.355880	−	0.355880i	−0.506412	−	0.862292i	$-0.669028\pi$
$283$	5.98683	−	5.98683i	0.355880	−	0.355880i	0.862292	+	0.506412i	$0.169028\pi$
$284$	−0.773729	−	0.377407i	−0.0459124	−	0.0223950i
$285$		0			0
$286$	8.91168	−	5.56842i	0.526959	−	0.329267i
$287$	−15.7804			−0.931487
$288$		0			0
$289$	8.44743			0.496908
$290$	−4.86215	+	3.03809i	−0.285516	+	0.178403i
$291$		0			0
$292$	−10.7736	−	5.25511i	−0.630476	−	0.307532i
$293$	18.9198	−	18.9198i	1.10531	−	1.10531i	0.111548	−	0.993759i	$-0.464419\pi$
$293$	18.9198	−	18.9198i	1.10531	−	1.10531i	0.993759	−	0.111548i	$-0.0355810\pi$
$294$		0			0
$295$	32.3358			1.88266
$296$	14.8472	−	18.3328i	0.862977	−	1.06557i
$297$		0			0
$298$	4.58238	−	19.8468i	0.265450	−	1.14970i
$299$	−0.993777	−	0.993777i	−0.0574716	−	0.0574716i
$300$		0			0
$301$	−36.5425	+	36.5425i	−2.10628	+	2.10628i
$302$	−4.60142	+	2.87517i	−0.264782	+	0.165448i
$303$		0			0
$304$	−2.87158	+	23.3733i	−0.164696	+	1.34055i
$305$			3.87969i			0.222151i
$306$		0			0
$307$	−8.95056	−	8.95056i	−0.510835	−	0.510835i	0.403947	−	0.914782i	$-0.367638\pi$
$307$	−8.95056	−	8.95056i	−0.510835	−	0.510835i	−0.914782	+	0.403947i	$0.867638\pi$
$308$	46.0059	−	15.8393i	2.62143	−	0.902526i
$309$		0			0
$310$	−2.25466	−	0.520573i	−0.128056	−	0.0295665i
$311$			21.2347i			1.20411i	0.798456	+	0.602054i	$0.205651\pi$
$311$			21.2347i			1.20411i	−0.798456	+	0.602054i	$0.794349\pi$
$312$		0			0
$313$		−	27.9336i		−	1.57890i	−0.613816	−	0.789449i	$-0.710366\pi$
$313$		−	27.9336i		−	1.57890i	0.613816	−	0.789449i	$-0.289634\pi$
$314$	5.14423	−	22.2803i	0.290306	−	1.25735i
$315$		0			0
$316$	−0.530757	−	0.258891i	−0.0298574	−	0.0145638i
$317$	16.4337	+	16.4337i	0.923008	+	0.923008i	0.997241	−	0.0742326i	$-0.0236507\pi$
$317$	16.4337	+	16.4337i	0.923008	+	0.923008i	−0.0742326	+	0.997241i	$0.523651\pi$
$318$		0			0
$319$			7.29669i			0.408536i
$320$	13.2738	−	20.4351i	0.742029	−	1.14236i
$321$		0			0
$322$	−3.44830	−	5.51866i	−0.192166	−	0.307543i
$323$	−12.1744	+	12.1744i	−0.677399	+	0.677399i
$324$		0			0
$325$	−4.09991	−	4.09991i	−0.227422	−	0.227422i
$326$	13.2321	+	3.05512i	0.732858	+	0.169208i
$327$		0			0
$328$	1.05082	+	10.0031i	0.0580219	+	0.552328i
$329$	−2.64086			−0.145595
$330$		0			0
$331$	11.6888	−	11.6888i	0.642477	−	0.642477i	−0.308687	−	0.951164i	$-0.599889\pi$
$331$	11.6888	−	11.6888i	0.642477	−	0.642477i	0.951164	+	0.308687i	$0.0998895\pi$
$332$	1.46162	+	4.24535i	0.0802168	+	0.232994i
$333$		0			0
$334$	9.38579	+	15.0210i	0.513568	+	0.821913i
$335$	11.5771			0.632524
$336$		0			0
$337$	−25.9722			−1.41480			−0.707399	−	0.706815i	$-0.750131\pi$
$337$	−25.9722			−1.41480			−0.707399	+	0.706815i	$0.750131\pi$
$338$	8.36551	+	13.3881i	0.455024	+	0.728219i
$339$		0			0
$340$	16.8453	−	5.79963i	0.913565	−	0.314529i
$341$	−2.08241	+	2.08241i	−0.112769	+	0.112769i
$342$		0			0
$343$	25.2591			1.36387
$344$	25.5974	+	20.7307i	1.38012	+	1.11772i
$345$		0			0
$346$	4.72599	+	1.09117i	0.254071	+	0.0586617i
$347$	−4.89209	−	4.89209i	−0.262621	−	0.262621i	0.563497	−	0.826118i	$-0.309456\pi$
$347$	−4.89209	−	4.89209i	−0.262621	−	0.262621i	−0.826118	+	0.563497i	$0.809456\pi$
$348$		0			0
$349$	−24.2030	+	24.2030i	−1.29556	+	1.29556i	−0.364260	+	0.931297i	$0.618678\pi$
$349$	−24.2030	+	24.2030i	−1.29556	+	1.29556i	−0.931297	+	0.364260i	$0.881322\pi$
$350$	−14.2263	−	22.7677i	−0.760425	−	1.21698i
$351$		0			0
$352$	−13.1039	−	28.1081i	−0.698443	−	1.49817i
$353$			19.0186i			1.01226i	0.862457	+	0.506130i	$0.168924\pi$
$353$			19.0186i			1.01226i	−0.862457	+	0.506130i	$0.831076\pi$
$354$		0			0
$355$	0.927079	+	0.927079i	0.0492042	+	0.0492042i
$356$	−10.1562	+	20.8214i	−0.538277	+	1.10353i
$357$		0			0
$358$	−4.14161	+	17.9378i	−0.218891	+	0.948043i
$359$		−	7.24591i		−	0.382424i	−0.981549	−	0.191212i	$-0.938758\pi$
$359$		−	7.24591i		−	0.382424i	0.981549	−	0.191212i	$-0.0612419\pi$
$360$		0			0
$361$			15.6597i			0.824196i
$362$	11.4144	+	2.63545i	0.599930	+	0.138516i
$363$		0			0
$364$	−3.91588	−	11.3739i	−0.205248	−	0.596153i
$365$	12.9089	+	12.9089i	0.675681	+	0.675681i
$366$		0			0
$367$			21.9249i			1.14447i	0.820090	+	0.572234i	$0.193923\pi$
$367$			21.9249i			1.14447i	−0.820090	+	0.572234i	$0.806077\pi$
$368$	−3.26861	+	2.55334i	−0.170388	+	0.133102i
$369$		0			0
$370$	−30.4695	+	19.0387i	−1.58403	+	0.989774i
$371$	−30.7189	+	30.7189i	−1.59485	+	1.59485i
$372$		0			0
$373$	−2.59366	−	2.59366i	−0.134295	−	0.134295i	0.636764	−	0.771059i	$-0.280273\pi$
$373$	−2.59366	−	2.59366i	−0.134295	−	0.134295i	−0.771059	+	0.636764i	$0.780273\pi$
$374$	5.10091	−	22.0926i	0.263762	−	1.14238i
$375$		0			0
$376$	0.175856	+	1.67402i	0.00906906	+	0.0863310i
$377$	1.80393			0.0929072
$378$		0			0
$379$	−14.2797	+	14.2797i	−0.733498	+	0.733498i	−0.971311	−	0.237813i	$-0.923570\pi$
$379$	−14.2797	+	14.2797i	−0.733498	+	0.733498i	0.237813	+	0.971311i	$0.423570\pi$
$380$	15.7232	−	32.2345i	0.806585	−	1.65359i
$381$		0			0
$382$	30.2873	−	18.9249i	1.54964	−	0.968281i
$383$	−29.8133			−1.52339			−0.761694	−	0.647937i	$-0.775632\pi$
$383$	−29.8133			−1.52339			−0.761694	+	0.647937i	$0.775632\pi$
$384$		0			0
$385$	−74.1026			−3.77662
$386$	−0.455275	+	0.284476i	−0.0231729	+	0.0144795i
$387$		0			0
$388$	−3.06817	+	6.29010i	−0.155763	+	0.319331i
$389$	0.152904	−	0.152904i	0.00775255	−	0.00775255i	−0.703220	−	0.710972i	$-0.748255\pi$
$389$	0.152904	−	0.152904i	0.00775255	−	0.00775255i	0.710972	+	0.703220i	$0.248255\pi$
$390$		0			0
$391$	−3.03246			−0.153358
$392$	−3.75051	−	35.7022i	−0.189430	−	1.80323i
$393$		0			0
$394$	−2.98631	+	12.9341i	−0.150448	+	0.651609i
$395$	0.635951	+	0.635951i	0.0319982	+	0.0319982i
$396$		0			0
$397$	−19.2908	+	19.2908i	−0.968178	+	0.968178i	−0.999509	−	0.0313315i	$-0.990025\pi$
$397$	−19.2908	+	19.2908i	−0.968178	+	0.968178i	0.0313315	+	0.999509i	$0.490025\pi$
$398$	9.47416	−	5.91988i	0.474897	−	0.296737i
$399$		0			0
$400$	−13.4849	+	10.5340i	−0.674247	+	0.526701i
$401$			33.0883i			1.65235i	0.563414	+	0.826175i	$0.309488\pi$
$401$			33.0883i			1.65235i	−0.563414	+	0.826175i	$0.690512\pi$
$402$		0			0
$403$	0.514827	+	0.514827i	0.0256454	+	0.0256454i
$404$	−10.2584	−	29.7960i	−0.510374	−	1.48241i
$405$		0			0
$406$	8.13854	+	1.87908i	0.403909	+	0.0932573i
$407$			45.7258i			2.26655i
$408$		0			0
$409$			25.6866i			1.27012i	0.772463	+	0.635060i	$0.219025\pi$
$409$			25.6866i			1.27012i	−0.772463	+	0.635060i	$0.780975\pi$
$410$	3.44615	−	14.9257i	0.170193	−	0.737127i
$411$		0			0
$412$	−5.09459	+	10.4445i	−0.250992	+	0.514563i
$413$	−33.3111	−	33.3111i	−1.63913	−	1.63913i
$414$		0			0
$415$		−	6.83806i		−	0.335667i
$416$	−6.94906	+	3.23964i	−0.340706	+	0.158836i
$417$		0			0
$418$	−24.1873	−	38.7093i	−1.18304	−	1.89333i
$419$	18.7724	−	18.7724i	0.917092	−	0.917092i	−0.0797250	−	0.996817i	$-0.525404\pi$
$419$	18.7724	−	18.7724i	0.917092	−	0.917092i	0.996817	+	0.0797250i	$0.0254042\pi$
$420$		0			0
$421$	−12.1013	−	12.1013i	−0.589779	−	0.589779i	0.347792	−	0.937572i	$-0.386931\pi$
$421$	−12.1013	−	12.1013i	−0.589779	−	0.589779i	−0.937572	+	0.347792i	$0.886931\pi$
$422$	−27.7591	−	6.40921i	−1.35129	−	0.311995i
$423$		0			0
$424$	21.5181	+	17.4269i	1.04501	+	0.846326i
$425$	−12.5107			−0.606857
$426$		0			0
$427$	3.99671	−	3.99671i	0.193415	−	0.193415i
$428$	−9.99728	+	3.44194i	−0.483237	+	0.166372i
$429$		0			0
$430$	−26.5831	−	42.5435i	−1.28195	−	2.05163i
$431$	35.0028			1.68603			0.843013	−	0.537894i	$-0.180780\pi$
$431$	35.0028			1.68603			0.843013	+	0.537894i	$0.180780\pi$
$432$		0			0
$433$	22.4261			1.07773			0.538865	−	0.842392i	$-0.318853\pi$
$433$	22.4261			1.07773			0.538865	+	0.842392i	$0.318853\pi$
$434$	1.78640	+	2.85894i	0.0857497	+	0.137234i
$435$		0			0
$436$	−0.862751	−	2.50590i	−0.0413183	−	0.120011i
$437$	−4.31663	+	4.31663i	−0.206492	+	0.206492i
$438$		0			0
$439$	21.6049			1.03115			0.515573	−	0.856846i	$-0.327579\pi$
$439$	21.6049			1.03115			0.515573	+	0.856846i	$0.327579\pi$
$440$	4.93452	+	46.9731i	0.235244	+	2.23936i
$441$		0			0
$442$	−5.46188	−	1.26108i	−0.259795	−	0.0599834i
$443$	−15.2420	−	15.2420i	−0.724168	−	0.724168i	0.245283	−	0.969451i	$-0.421119\pi$
$443$	−15.2420	−	15.2420i	−0.724168	−	0.724168i	−0.969451	+	0.245283i	$0.921119\pi$
$444$		0			0
$445$	24.9481	−	24.9481i	1.18265	−	1.18265i
$446$	12.7381	+	20.3861i	0.603168	+	0.965309i
$447$		0			0
$448$	−34.7256	+	7.37726i	−1.64063	+	0.348543i
$449$			23.7386i			1.12029i	0.828394	+	0.560146i	$0.189255\pi$
$449$			23.7386i			1.12029i	−0.828394	+	0.560146i	$0.810745\pi$
$450$		0			0
$451$	−13.7854	−	13.7854i	−0.649129	−	0.649129i
$452$	−30.0659	−	14.6654i	−1.41418	−	0.689804i
$453$		0			0
$454$	−2.03561	+	8.81646i	−0.0955358	+	0.413777i
$455$			18.3201i			0.858860i
$456$		0			0
$457$		−	35.6764i		−	1.66887i	−0.551106	−	0.834435i	$-0.685794\pi$
$457$		−	35.6764i		−	1.66887i	0.551106	−	0.834435i	$-0.314206\pi$
$458$	7.48425	+	1.72802i	0.349716	+	0.0807449i
$459$		0			0
$460$	5.97280	−	2.05636i	0.278483	−	0.0958782i
$461$	−20.4940	−	20.4940i	−0.954501	−	0.954501i	0.0445084	−	0.999009i	$-0.485828\pi$
$461$	−20.4940	−	20.4940i	−0.954501	−	0.954501i	−0.999009	+	0.0445084i	$0.985828\pi$
$462$		0			0
$463$			0.751263i			0.0349141i	0.999848	+	0.0174571i	$0.00555704\pi$
$463$			0.751263i			0.0349141i	−0.999848	+	0.0174571i	$0.994443\pi$
$464$	0.649189	−	5.28409i	0.0301378	−	0.245308i
$465$		0			0
$466$	27.0709	−	16.9151i	1.25404	−	0.783577i
$467$	17.8154	−	17.8154i	0.824398	−	0.824398i	−0.162337	−	0.986735i	$-0.551903\pi$
$467$	17.8154	−	17.8154i	0.824398	−	0.824398i	0.986735	+	0.162337i	$0.0519032\pi$
$468$		0			0
$469$	−11.9263	−	11.9263i	−0.550705	−	0.550705i
$470$	0.576715	−	2.49782i	0.0266019	−	0.115216i
$471$		0			0
$472$	−18.8975	+	23.3339i	−0.869827	+	1.07403i
$473$	−63.8455			−2.93562
$474$		0			0
$475$	−17.8086	+	17.8086i	−0.817115	+	0.817115i
$476$	−23.3280	−	11.3788i	−1.06924	−	0.521548i
$477$		0			0
$478$	−13.5730	+	8.48102i	−0.620815	+	0.387913i
$479$	−24.0217			−1.09758			−0.548789	−	0.835961i	$-0.684911\pi$
$479$	−24.0217			−1.09758			−0.548789	+	0.835961i	$0.684911\pi$
$480$		0			0
$481$	11.3046			0.515447
$482$	12.5106	−	7.81718i	0.569842	−	0.356063i
$483$		0			0
$484$	34.2534	+	16.7080i	1.55697	+	0.759457i
$485$	7.53677	−	7.53677i	0.342227	−	0.342227i
$486$		0			0
$487$	8.50863			0.385563			0.192781	−	0.981242i	$-0.438249\pi$
$487$	8.50863			0.385563			0.192781	+	0.981242i	$0.438249\pi$
$488$	−2.79963	−	2.26735i	−0.126733	−	0.102638i
$489$		0			0
$490$	−12.2997	+	53.2716i	−0.555645	+	2.40657i
$491$	−23.0382	−	23.0382i	−1.03970	−	1.03970i	−0.999179	−	0.0405223i	$-0.987098\pi$
$491$	−23.0382	−	23.0382i	−1.03970	−	1.03970i	−0.0405223	−	0.999179i	$-0.512902\pi$
$492$		0			0
$493$	2.75230	−	2.75230i	0.123958	−	0.123958i
$494$	−9.56996	+	5.97973i	−0.430573	+	0.269041i
$495$		0			0
$496$	1.69331	−	1.32276i	0.0760318	−	0.0593937i
$497$		−	1.91008i		−	0.0856790i
$498$		0			0
$499$	15.3223	+	15.3223i	0.685921	+	0.685921i	0.961328	−	0.275406i	$-0.0888124\pi$
$499$	15.3223	+	15.3223i	0.685921	+	0.685921i	−0.275406	+	0.961328i	$0.588812\pi$
$500$	−4.15928	+	1.43199i	−0.186009	+	0.0640405i
$501$		0			0
$502$	16.1549	+	3.72995i	0.721027	+	0.166476i
$503$			18.8263i			0.839423i	0.907658	+	0.419711i	$0.137869\pi$
$503$			18.8263i			0.839423i	−0.907658	+	0.419711i	$0.862131\pi$
$504$		0			0
$505$			47.9930i			2.13566i
$506$	1.80862	−	7.83333i	0.0804028	−	0.348234i
$507$		0			0
$508$	14.9864	+	7.31002i	0.664914	+	0.324330i
$509$	20.7015	+	20.7015i	0.917576	+	0.917576i	0.996853	−	0.0792764i	$-0.0252610\pi$
$509$	20.7015	+	20.7015i	0.917576	+	0.917576i	−0.0792764	+	0.996853i	$0.525261\pi$
$510$		0			0
$511$		−	26.5965i		−	1.17656i
$512$	6.98878	+	21.5211i	0.308864	+	0.951106i
$513$		0			0
$514$	−7.83430	−	12.5380i	−0.345556	−	0.553028i
$515$	12.5145	−	12.5145i	0.551457	−	0.551457i
$516$		0			0
$517$	−2.30699	−	2.30699i	−0.101461	−	0.101461i
$518$	51.0014	+	11.7756i	2.24087	+	0.517389i
$519$		0			0
$520$	11.6130	−	1.21994i	0.509263	−	0.0534980i
$521$	29.1698			1.27795			0.638976	−	0.769226i	$-0.279358\pi$
$521$	29.1698			1.27795			0.638976	+	0.769226i	$0.279358\pi$
$522$		0			0
$523$	−0.0752256	+	0.0752256i	−0.00328939	+	0.00328939i	−0.708750	−	0.705460i	$-0.750740\pi$
$523$	−0.0752256	+	0.0752256i	−0.00328939	+	0.00328939i	0.705460	+	0.708750i	$0.250740\pi$
$524$	1.75397	+	5.09450i	0.0766226	+	0.222554i
$525$		0			0
$526$	−19.6934	−	31.5173i	−0.858674	−	1.37422i
$527$	1.57097			0.0684325
$528$		0			0
$529$	21.9248			0.953252
$530$	−22.3466	−	35.7635i	−0.970676	−	1.55347i
$531$		0			0
$532$	−49.4042	+	17.0093i	−2.14194	+	0.737445i
$533$	−3.40811	+	3.40811i	−0.147622	+	0.147622i
$534$		0			0
$535$	16.1028			0.696185
$536$	−6.76581	+	8.35416i	−0.292238	+	0.360845i
$537$		0			0
$538$	14.9104	+	3.44261i	0.642831	+	0.148421i
$539$	49.2018	+	49.2018i	2.11927	+	2.11927i
$540$		0			0
$541$	19.5905	−	19.5905i	0.842261	−	0.842261i	−0.146892	−	0.989153i	$-0.546927\pi$
$541$	19.5905	−	19.5905i	0.842261	−	0.842261i	0.989153	+	0.146892i	$0.0469269\pi$
$542$	−15.5430	−	24.8751i	−0.667631	−	1.06848i
$543$		0			0
$544$	−5.65955	+	15.5451i	−0.242651	+	0.666493i
$545$			4.03630i			0.172896i
$546$		0			0
$547$	−13.0527	−	13.0527i	−0.558092	−	0.558092i	0.370672	−	0.928764i	$-0.379128\pi$
$547$	−13.0527	−	13.0527i	−0.558092	−	0.558092i	−0.928764	+	0.370672i	$0.879128\pi$
$548$	2.16311	−	4.43463i	0.0924035	−	0.189438i
$549$		0			0
$550$	7.46159	−	32.3171i	0.318163	−	1.37800i
$551$		−	7.83566i		−	0.333810i
$552$		0			0
$553$		−	1.31027i		−	0.0557181i
$554$	3.38025	+	0.780456i	0.143613	+	0.0331584i
$555$		0			0
$556$	7.16024	+	20.7973i	0.303662	+	0.882001i
$557$	−5.12009	−	5.12009i	−0.216945	−	0.216945i	0.590265	−	0.807210i	$-0.299023\pi$
$557$	−5.12009	−	5.12009i	−0.216945	−	0.216945i	−0.807210	+	0.590265i	$0.799023\pi$
$558$		0			0
$559$			15.7843i			0.667604i
$560$	53.6634	+	6.59294i	2.26769	+	0.278603i
$561$		0			0
$562$	18.3510	−	11.4665i	0.774090	−	0.483686i
$563$	−10.4367	+	10.4367i	−0.439855	+	0.439855i	−0.891963	−	0.452108i	$-0.850672\pi$
$563$	−10.4367	+	10.4367i	−0.439855	+	0.439855i	0.452108	+	0.891963i	$0.350672\pi$
$564$		0			0
$565$	36.0248	+	36.0248i	1.51557	+	1.51557i
$566$	2.69370	−	11.6667i	0.113224	−	0.490389i
$567$		0			0
$568$	−1.21079	+	0.127193i	−0.0508035	+	0.00533691i
$569$	9.19641			0.385534			0.192767	−	0.981245i	$-0.438254\pi$
$569$	9.19641			0.385534			0.192767	+	0.981245i	$0.438254\pi$
$570$		0			0
$571$	28.9688	−	28.9688i	1.21231	−	1.21231i	0.242040	−	0.970266i	$-0.422183\pi$
$571$	28.9688	−	28.9688i	1.21231	−	1.21231i	0.970266	−	0.242040i	$-0.0778165\pi$
$572$	6.51513	−	13.3568i	0.272411	−	0.558475i
$573$		0			0
$574$	−18.9260	+	11.8258i	−0.789955	+	0.493599i
$575$	−4.43588			−0.184989
$576$		0			0
$577$	−15.0829			−0.627911			−0.313956	−	0.949438i	$-0.601654\pi$
$577$	−15.0829			−0.627911			−0.313956	+	0.949438i	$0.601654\pi$
$578$	10.1313	−	6.33049i	0.421407	−	0.263314i
$579$		0			0
$580$	−3.55461	+	7.28737i	−0.147597	+	0.302592i
$581$	−7.04432	+	7.04432i	−0.292248	+	0.292248i
$582$		0			0
$583$	−53.6707			−2.22281
$584$	−16.8593	+	1.77107i	−0.697643	+	0.0732873i
$585$		0			0
$586$	8.51273	−	36.8697i	0.351657	−	1.52307i
$587$	22.4225	+	22.4225i	0.925476	+	0.925476i	0.997409	−	0.0719337i	$-0.0229170\pi$
$587$	22.4225	+	22.4225i	0.925476	+	0.925476i	−0.0719337	+	0.997409i	$0.522917\pi$
$588$		0			0
$589$	2.23623	−	2.23623i	0.0921424	−	0.0921424i
$590$	38.7814	−	24.2324i	1.59661	−	0.997630i
$591$		0			0
$592$	4.06825	−	33.1136i	0.167204	−	1.36096i
$593$		−	11.0547i		−	0.453963i	−0.973899	−	0.226982i	$-0.927114\pi$
$593$		−	11.0547i		−	0.453963i	0.973899	−	0.226982i	$-0.0728857\pi$
$594$		0			0
$595$	27.9515	+	27.9515i	1.14590	+	1.14590i
$596$	−9.37737	−	27.2370i	−0.384112	−	1.11567i
$597$		0			0
$598$	−1.93661	−	0.447137i	−0.0791937	−	0.0182848i
$599$			36.3277i			1.48431i	0.670229	+	0.742154i	$0.266196\pi$
$599$			36.3277i			1.48431i	−0.670229	+	0.742154i	$0.733804\pi$
$600$		0			0
$601$			17.8018i			0.726152i	0.931759	+	0.363076i	$0.118274\pi$
$601$			17.8018i			0.726152i	−0.931759	+	0.363076i	$0.881726\pi$
$602$	−16.4418	+	71.2116i	−0.670119	+	2.90237i
$603$		0			0
$604$	−3.36400	+	6.89659i	−0.136879	+	0.280618i
$605$	−41.0423	−	41.0423i	−1.66861	−	1.66861i
$606$		0			0
$607$			23.8122i			0.966507i	0.875480	+	0.483254i	$0.160545\pi$
$607$			23.8122i			0.966507i	−0.875480	+	0.483254i	$0.839455\pi$
$608$	14.0719	+	30.1843i	0.570690	+	1.22414i
$609$		0			0
$610$	2.90743	+	4.65305i	0.117718	+	0.188396i
$611$	−0.570349	+	0.570349i	−0.0230739	+	0.0230739i
$612$		0			0
$613$	−26.0701	−	26.0701i	−1.05296	−	1.05296i	−0.998517	−	0.0544454i	$-0.982661\pi$
$613$	−26.0701	−	26.0701i	−1.05296	−	1.05296i	−0.0544454	−	0.998517i	$-0.517339\pi$
$614$	−17.4422	−	4.02719i	−0.703911	−	0.162524i
$615$		0			0
$616$	43.3066	−	53.4733i	1.74487	−	2.15450i
$617$	8.00278			0.322180			0.161090	−	0.986940i	$-0.448499\pi$
$617$	8.00278			0.322180			0.161090	+	0.986940i	$0.448499\pi$
$618$		0			0
$619$	17.7469	−	17.7469i	0.713309	−	0.713309i	−0.253917	−	0.967226i	$-0.581719\pi$
$619$	17.7469	−	17.7469i	0.713309	−	0.713309i	0.967226	+	0.253917i	$0.0817189\pi$
$620$	−3.09421	+	1.06530i	−0.124267	+	0.0427834i
$621$		0			0
$622$	15.9132	+	25.4675i	0.638061	+	1.02115i
$623$	−51.4012			−2.05935
$624$		0			0
$625$	28.0890			1.12356
$626$	−20.9333	−	33.5017i	−0.836664	−	1.33900i
$627$		0			0
$628$	−10.5271	−	30.5766i	−0.420079	−	1.22014i
$629$	17.2478	−	17.2478i	0.687713	−	0.687713i
$630$		0			0
$631$	−25.9587			−1.03340			−0.516700	−	0.856167i	$-0.672840\pi$
$631$	−25.9587			−1.03340			−0.516700	+	0.856167i	$0.672840\pi$
$632$	−0.830568	+	0.0872510i	−0.0330382	+	0.00347066i
$633$		0			0
$634$	32.0249	+	7.39413i	1.27187	+	0.293658i
$635$	−17.9566	−	17.9566i	−0.712587	−	0.712587i
$636$		0			0
$637$	12.1640	−	12.1640i	0.481954	−	0.481954i
$638$	5.46812	+	8.75117i	0.216485	+	0.346462i
$639$		0			0
$640$	0.605755	−	34.4559i	0.0239446	−	1.36199i
$641$			24.4769i			0.966781i	0.875405	+	0.483390i	$0.160595\pi$
$641$			24.4769i			0.966781i	−0.875405	+	0.483390i	$0.839405\pi$
$642$		0			0
$643$	−6.46298	−	6.46298i	−0.254875	−	0.254875i	0.568091	−	0.822966i	$-0.307682\pi$
$643$	−6.46298	−	6.46298i	−0.254875	−	0.254875i	−0.822966	+	0.568091i	$0.807682\pi$
$644$	−8.27134	−	4.03457i	−0.325936	−	0.158984i
$645$		0			0
$646$	−5.47769	+	23.7245i	−0.215517	+	0.933430i
$647$			5.68783i			0.223612i	0.993730	+	0.111806i	$0.0356635\pi$
$647$			5.68783i			0.223612i	−0.993730	+	0.111806i	$0.964337\pi$
$648$		0			0
$649$		−	58.1997i		−	2.28454i
$650$	−7.98963	−	1.84470i	−0.313379	−	0.0723551i
$651$		0			0
$652$	18.1592	−	6.25199i	0.711170	−	0.244847i
$653$	−3.29850	−	3.29850i	−0.129080	−	0.129080i	0.639615	−	0.768695i	$-0.279094\pi$
$653$	−3.29850	−	3.29850i	−0.129080	−	0.129080i	−0.768695	+	0.639615i	$0.779094\pi$
$654$		0			0
$655$		−	8.20580i		−	0.320627i
$656$	8.75657	+	11.2096i	0.341887	+	0.437660i
$657$		0			0
$658$	−3.16727	+	1.97905i	−0.123473	+	0.0771515i
$659$	12.0553	−	12.0553i	0.469607	−	0.469607i	−0.432180	−	0.901787i	$-0.642256\pi$
$659$	12.0553	−	12.0553i	0.469607	−	0.469607i	0.901787	+	0.432180i	$0.142256\pi$
$660$		0			0
$661$	6.47601	+	6.47601i	0.251888	+	0.251888i	0.821744	−	0.569857i	$-0.193001\pi$
$661$	6.47601	+	6.47601i	0.251888	+	0.251888i	−0.569857	+	0.821744i	$0.693001\pi$
$662$	5.25924	−	22.7784i	0.204406	−	0.885309i
$663$		0			0
$664$	4.93443	+	3.99626i	0.191493	+	0.155085i
$665$	79.5763			3.08584
$666$		0			0
$667$	0.975877	−	0.975877i	0.0377861	−	0.0377861i
$668$	22.5134	+	10.9815i	0.871070	+	0.424888i
$669$		0			0
$670$	13.8848	−	8.67584i	0.536417	−	0.335177i
$671$	6.98288			0.269571
$672$		0			0
$673$	8.50383			0.327798			0.163899	−	0.986477i	$-0.447593\pi$
$673$	8.50383			0.327798			0.163899	+	0.986477i	$0.447593\pi$
$674$	−31.1494	+	19.4635i	−1.19983	+	0.749707i
$675$		0			0
$676$	20.0661	+	9.78778i	0.771773	+	0.376453i
$677$	−4.08999	+	4.08999i	−0.157191	+	0.157191i	−0.781321	−	0.624130i	$-0.785454\pi$
$677$	−4.08999	+	4.08999i	−0.157191	+	0.157191i	0.624130	+	0.781321i	$0.285454\pi$
$678$		0			0
$679$	−15.5282			−0.595918
$680$	15.8569	−	19.5795i	0.608085	−	0.750840i
$681$		0			0
$682$	−0.936955	+	4.05806i	−0.0358778	+	0.155391i
$683$	−31.1600	−	31.1600i	−1.19230	−	1.19230i	−0.976419	−	0.215884i	$-0.930737\pi$
$683$	−31.1600	−	31.1600i	−1.19230	−	1.19230i	−0.215884	−	0.976419i	$-0.569263\pi$
$684$		0			0
$685$	−5.31355	+	5.31355i	−0.203020	+	0.203020i
$686$	30.2942	−	18.9291i	1.15664	−	0.722718i
$687$		0			0
$688$	46.2354	+	5.68036i	1.76271	+	0.216562i
$689$			13.2688i			0.505501i
$690$		0			0
$691$	5.83396	+	5.83396i	0.221934	+	0.221934i	0.809313	−	0.587378i	$-0.199840\pi$
$691$	5.83396	+	5.83396i	0.221934	+	0.221934i	−0.587378	+	0.809313i	$0.699840\pi$
$692$	6.48576	−	2.23297i	0.246552	−	0.0848847i
$693$		0			0
$694$	−9.53337	−	2.20113i	−0.361882	−	0.0835539i
$695$		−	33.4986i		−	1.27067i
$696$		0			0
$697$			10.3997i			0.393916i
$698$	−10.8898	+	47.1652i	−0.412186	+	1.78523i
$699$		0			0
$700$	−34.1241	−	16.6449i	−1.28977	−	0.629120i
$701$	9.38249	+	9.38249i	0.354372	+	0.354372i	0.861733	−	0.507362i	$-0.169379\pi$
$701$	9.38249	+	9.38249i	0.354372	+	0.354372i	−0.507362	+	0.861733i	$0.669379\pi$
$702$		0			0
$703$		−	49.1034i		−	1.85197i
$704$	−36.7801	−	23.8909i	−1.38620	−	0.900423i
$705$		0			0
$706$	14.2525	+	22.8097i	0.536401	+	0.858455i
$707$	49.4406	−	49.4406i	1.85941	−	1.85941i
$708$		0			0
$709$	−9.11028	−	9.11028i	−0.342144	−	0.342144i	0.515029	−	0.857173i	$-0.327781\pi$
$709$	−9.11028	−	9.11028i	−0.342144	−	0.342144i	−0.857173	+	0.515029i	$0.827781\pi$
$710$	1.80663	+	0.417127i	0.0678015	+	0.0156545i
$711$		0			0
$712$	3.42282	+	32.5828i	0.128276	+	1.22109i
$713$	0.557014			0.0208604
$714$		0			0
$715$	−16.0040	+	16.0040i	−0.598517	+	0.598517i
$716$	8.47538	+	24.6171i	0.316740	+	0.919986i
$717$		0			0
$718$	−5.43007	−	8.69027i	−0.202648	−	0.324318i
$719$	−2.74474			−0.102362			−0.0511808	−	0.998689i	$-0.516298\pi$
$719$	−2.74474			−0.102362			−0.0511808	+	0.998689i	$0.516298\pi$
$720$		0			0
$721$	−25.7840			−0.960248
$722$	11.7354	+	18.7813i	0.436745	+	0.698966i
$723$		0			0
$724$	15.6647	−	5.39317i	0.582175	−	0.200436i
$725$	4.02606	−	4.02606i	0.149524	−	0.149524i
$726$		0			0
$727$	−24.0902			−0.893455			−0.446728	−	0.894670i	$-0.647411\pi$
$727$	−24.0902			−0.893455			−0.446728	+	0.894670i	$0.647411\pi$
$728$	−13.2200	−	10.7065i	−0.489966	−	0.396810i
$729$		0			0
$730$	25.1559	+	5.80817i	0.931062	+	0.214970i
$731$	24.0825	+	24.0825i	0.890722	+	0.890722i
$732$		0			0
$733$	−1.51161	+	1.51161i	−0.0558326	+	0.0558326i	−0.734472	−	0.678639i	$-0.762570\pi$
$733$	−1.51161	+	1.51161i	−0.0558326	+	0.0558326i	0.678639	+	0.734472i	$0.262570\pi$
$734$	16.4304	+	26.2953i	0.606459	+	0.970575i
$735$		0			0
$736$	−2.00669	+	5.51180i	−0.0739676	+	0.203168i
$737$		−	20.8371i		−	0.767543i
$738$		0			0
$739$	9.09968	+	9.09968i	0.334737	+	0.334737i	0.854382	−	0.519645i	$-0.173936\pi$
$739$	9.09968	+	9.09968i	0.334737	+	0.334737i	−0.519645	+	0.854382i	$0.673936\pi$
$740$	−22.2755	+	45.6675i	−0.818865	+	1.67877i
$741$		0			0
$742$	−13.8216	+	59.8629i	−0.507406	+	2.19764i
$743$		−	15.6710i		−	0.574913i	−0.957794	−	0.287457i	$-0.907190\pi$
$743$		−	15.6710i		−	0.574913i	0.957794	−	0.287457i	$-0.0928097\pi$
$744$		0			0
$745$			43.8712i			1.60732i
$746$	−5.05435	−	1.16698i	−0.185053	−	0.0427263i
$747$		0			0
$748$	−10.4385	−	30.3191i	−0.381669	−	1.10858i
$749$	−16.5885	−	16.5885i	−0.606131	−	0.606131i
$750$		0			0
$751$		−	8.47523i		−	0.309265i	−0.987972	−	0.154633i	$-0.950581\pi$
$751$		−	8.47523i		−	0.309265i	0.987972	−	0.154633i	$-0.0494194\pi$
$752$	1.46542	+	1.87592i	0.0534382	+	0.0684079i
$753$		0			0
$754$	2.16352	−	1.35186i	0.0787907	−	0.0492319i
$755$	8.26346	−	8.26346i	0.300738	−	0.300738i
$756$		0			0
$757$	−0.974342	−	0.974342i	−0.0354130	−	0.0354130i	0.689179	−	0.724592i	$-0.257972\pi$
$757$	−0.974342	−	0.974342i	−0.0354130	−	0.0354130i	−0.724592	+	0.689179i	$0.757972\pi$
$758$	−6.42496	+	27.8273i	−0.233365	+	1.01073i
$759$		0			0
$760$	−5.29901	−	50.4428i	−0.192215	−	1.82975i
$761$	51.2861			1.85912			0.929560	−	0.368671i	$-0.120187\pi$
$761$	51.2861			1.85912			0.929560	+	0.368671i	$0.120187\pi$
$762$		0			0
$763$	4.15805	−	4.15805i	0.150532	−	0.150532i
$764$	22.1424	−	45.3945i	0.801084	−	1.64232i
$765$		0			0
$766$	−35.7561	+	22.3420i	−1.29192	+	0.807249i
$767$	−14.3885			−0.519538
$768$		0			0
$769$	−7.31412			−0.263754			−0.131877	−	0.991266i	$-0.542100\pi$
$769$	−7.31412			−0.263754			−0.131877	+	0.991266i	$0.542100\pi$
$770$	−88.8739	+	55.5323i	−3.20279	+	2.00125i
$771$		0			0
$772$	−0.332842	+	0.682364i	−0.0119792	+	0.0245588i
$773$	−20.8665	+	20.8665i	−0.750514	+	0.750514i	−0.974575	−	0.224061i	$-0.928069\pi$
$773$	−20.8665	+	20.8665i	−0.750514	+	0.750514i	0.224061	+	0.974575i	$0.428069\pi$
$774$		0			0
$775$	2.29801			0.0825469
$776$	1.03403	+	9.84321i	0.0371194	+	0.353351i
$777$		0			0
$778$	0.0687972	−	0.297969i	0.00246650	−	0.0106827i
$779$	14.8037	+	14.8037i	0.530397	+	0.530397i
$780$		0			0
$781$	1.66861	−	1.66861i	0.0597074	−	0.0597074i
$782$	−3.63694	+	2.27252i	−0.130057	+	0.0812651i
$783$		0			0
$784$	−31.2533	−	40.0083i	−1.11619	−	1.42887i
$785$			49.2503i			1.75782i
$786$		0			0
$787$	35.3022	+	35.3022i	1.25839	+	1.25839i	0.951863	+	0.306523i	$0.0991656\pi$
$787$	35.3022	+	35.3022i	1.25839	+	1.25839i	0.306523	+	0.951863i	$0.400834\pi$
$788$	6.11118	+	17.7502i	0.217702	+	0.632325i
$789$		0			0
$790$	1.23930	+	0.286138i	0.0440922	+	0.0101803i
$791$		−	74.2228i		−	2.63906i
$792$		0			0
$793$		−	1.72635i		−	0.0613045i
$794$	−8.67965	+	37.5926i	−0.308029	+	1.33411i
$795$		0			0
$796$	6.92635	−	14.1998i	0.245498	−	0.503299i
$797$	−11.6144	−	11.6144i	−0.411403	−	0.411403i	0.470824	−	0.882227i	$-0.343957\pi$
$797$	−11.6144	−	11.6144i	−0.411403	−	0.411403i	−0.882227	+	0.470824i	$0.843957\pi$
$798$		0			0
$799$			1.74039i			0.0615707i
$800$	−8.27877	+	22.7394i	−0.292699	+	0.803959i
$801$		0			0
$802$	24.7963	+	39.6839i	0.875587	+	1.40129i
$803$	23.2341	−	23.2341i	0.819912	−	0.819912i
$804$		0			0
$805$	9.91068	+	9.91068i	0.349305	+	0.349305i
$806$	1.00326	+	0.231640i	0.0353383	+	0.00815916i
$807$		0			0
$808$	−34.6323	−	28.0478i	−1.21836	−	0.986718i
$809$	−14.7130			−0.517280			−0.258640	−	0.965974i	$-0.583274\pi$
$809$	−14.7130			−0.517280			−0.258640	+	0.965974i	$0.583274\pi$
$810$		0			0
$811$	12.8141	−	12.8141i	0.449963	−	0.449963i	−0.445379	−	0.895342i	$-0.646931\pi$
$811$	12.8141	−	12.8141i	0.449963	−	0.449963i	0.895342	+	0.445379i	$0.146931\pi$
$812$	11.1690	−	3.84535i	0.391955	−	0.134945i
$813$		0			0
$814$	34.2668	+	54.8406i	1.20105	+	1.92216i
$815$	−29.2494			−1.02456
$816$		0			0
$817$	68.5615			2.39866
$818$	19.2495	+	30.8068i	0.673042	+	1.07714i
$819$		0			0
$820$	−7.05219	−	20.4834i	−0.246273	−	0.715312i
$821$	28.4466	−	28.4466i	0.992793	−	0.992793i	−0.00718078	−	0.999974i	$-0.502286\pi$
$821$	28.4466	−	28.4466i	0.992793	−	0.992793i	0.999974	+	0.00718078i	$0.00228573\pi$
$822$		0			0
$823$	16.4859			0.574661			0.287331	−	0.957831i	$-0.407232\pi$
$823$	16.4859			0.574661			0.287331	+	0.957831i	$0.407232\pi$
$824$	1.71697	+	16.3443i	0.0598134	+	0.569381i
$825$		0			0
$826$	−64.9144	−	14.9879i	−2.25866	−	0.521496i
$827$	−2.63590	−	2.63590i	−0.0916592	−	0.0916592i	0.659790	−	0.751450i	$-0.270645\pi$
$827$	−2.63590	−	2.63590i	−0.0916592	−	0.0916592i	−0.751450	+	0.659790i	$0.770645\pi$
$828$		0			0
$829$	15.7682	−	15.7682i	0.547652	−	0.547652i	−0.378109	−	0.925761i	$-0.623426\pi$
$829$	15.7682	−	15.7682i	0.547652	−	0.547652i	0.925761	+	0.378109i	$0.123426\pi$
$830$	−5.12443	−	8.20113i	−0.177871	−	0.284665i
$831$		0			0
$832$	−5.90647	+	9.09302i	−0.204770	+	0.315244i
$833$		−	37.1178i		−	1.28605i
$834$		0			0
$835$	−26.9755	−	26.9755i	−0.933525	−	0.933525i
$836$	−58.0173	−	28.2995i	−2.00657	−	0.978759i
$837$		0			0
$838$	8.44640	−	36.5824i	0.291776	−	1.26372i
$839$		−	2.54273i		−	0.0877849i	−0.999036	−	0.0438925i	$-0.986024\pi$
$839$		−	2.54273i		−	0.0877849i	0.999036	−	0.0438925i	$-0.0139759\pi$
$840$		0			0
$841$		−	27.2286i		−	0.938916i
$842$	−23.5821	−	5.44480i	−0.812693	−	0.187640i
$843$		0			0
$844$	−38.0954	+	13.1158i	−1.31130	+	0.451464i
$845$	−24.0431	−	24.0431i	−0.827108	−	0.827108i
$846$		0			0
$847$			84.5605i			2.90553i
$848$	38.8671	+	4.77510i	1.33470	+	0.163978i
$849$		0			0
$850$	−15.0045	+	9.37546i	−0.514649	+	0.321576i
$851$	6.11549	−	6.11549i	0.209636	−	0.209636i
$852$		0			0
$853$	25.3815	+	25.3815i	0.869045	+	0.869045i	0.992367	−	0.123321i	$-0.0393546\pi$
$853$	25.3815	+	25.3815i	0.869045	+	0.869045i	−0.123321	+	0.992367i	$0.539355\pi$
$854$	1.79827	−	7.78853i	0.0615355	−	0.266518i
$855$		0			0
$856$	−9.41071	+	11.6200i	−0.321651	+	0.397163i
$857$	18.4742			0.631068			0.315534	−	0.948914i	$-0.397816\pi$
$857$	18.4742			0.631068			0.315534	+	0.948914i	$0.397816\pi$
$858$		0			0
$859$	−27.2053	+	27.2053i	−0.928232	+	0.928232i	−0.997592	−	0.0693601i	$-0.977904\pi$
$859$	−27.2053	+	27.2053i	−0.928232	+	0.928232i	0.0693601	+	0.997592i	$0.477904\pi$
$860$	−63.7640	−	31.1026i	−2.17433	−	1.06059i
$861$		0			0
$862$	41.9801	−	26.2310i	1.42985	−	0.893432i
$863$	−37.7697			−1.28570			−0.642848	−	0.765994i	$-0.722247\pi$
$863$	−37.7697			−1.28570			−0.642848	+	0.765994i	$0.722247\pi$
$864$		0			0
$865$	−10.4467			−0.355200
$866$	26.8964	−	16.8061i	0.913976	−	0.571093i
$867$		0			0
$868$	4.28497	+	2.09011i	0.145441	+	0.0709430i
$869$	1.14462	−	1.14462i	0.0388285	−	0.0388285i
$870$		0			0
$871$	−5.15147			−0.174551
$872$	−2.91264	−	2.35887i	−0.0986346	−	0.0798815i
$873$		0			0
$874$	−1.94221	+	8.41195i	−0.0656963	+	0.284539i
$875$	−6.90150	−	6.90150i	−0.233313	−	0.233313i
$876$		0			0
$877$	24.7218	−	24.7218i	0.834797	−	0.834797i	−0.153371	−	0.988169i	$-0.549013\pi$
$877$	24.7218	−	24.7218i	0.834797	−	0.834797i	0.988169	+	0.153371i	$0.0490131\pi$
$878$	25.9115	−	16.1907i	0.874471	−	0.546408i
$879$		0			0
$880$	41.1197	+	52.6386i	1.38614	+	1.77445i
$881$			21.1729i			0.713332i	0.934232	+	0.356666i	$0.116087\pi$
$881$			21.1729i			0.713332i	−0.934232	+	0.356666i	$0.883913\pi$
$882$		0			0
$883$	−38.0335	−	38.0335i	−1.27993	−	1.27993i	−0.940706	−	0.339223i	$-0.889836\pi$
$883$	−38.0335	−	38.0335i	−1.27993	−	1.27993i	−0.339223	−	0.940706i	$-0.610164\pi$
$884$	−7.49567	+	2.58067i	−0.252107	+	0.0867972i
$885$		0			0
$886$	−29.7025	−	6.85793i	−0.997876	−	0.230397i
$887$			42.6689i			1.43268i	0.697750	+	0.716341i	$0.254185\pi$
$887$			42.6689i			1.43268i	−0.697750	+	0.716341i	$0.745815\pi$
$888$		0			0
$889$			36.9965i			1.24082i
$890$	11.2251	−	48.6172i	0.376265	−	1.62965i
$891$		0			0
$892$	30.5545	+	14.9038i	1.02304	+	0.499016i
$893$	2.47740	+	2.47740i	0.0829031	+	0.0829031i
$894$		0			0
$895$		−	39.6513i		−	1.32540i
$896$	−36.1192	+	34.8711i	−1.20666	+	1.16496i
$897$		0			0
$898$	17.7896	+	28.4705i	0.593647	+	0.950072i
$899$	−0.505554	+	0.505554i	−0.0168612	+	0.0168612i
$900$		0			0
$901$	20.2445	+	20.2445i	0.674444	+	0.674444i
$902$	−26.8640	−	6.20256i	−0.894475	−	0.206523i
$903$		0			0
$904$	−47.0493	+	4.94252i	−1.56484	+	0.164386i
$905$	−25.2315			−0.838723
$906$		0			0
$907$	−21.3751	+	21.3751i	−0.709747	+	0.709747i	−0.966482	−	0.256735i	$-0.917353\pi$
$907$	−21.3751	+	21.3751i	−0.709747	+	0.709747i	0.256735	+	0.966482i	$0.417353\pi$
$908$	4.16566	+	12.0994i	0.138242	+	0.401532i
$909$		0			0
$910$	13.7291	+	21.9720i	0.455114	+	0.728363i
$911$	−24.3455			−0.806602			−0.403301	−	0.915067i	$-0.632137\pi$
$911$	−24.3455			−0.806602			−0.403301	+	0.915067i	$0.632137\pi$
$912$		0			0
$913$	−12.3075			−0.407319
$914$	−26.7358	−	42.7879i	−0.884341	−	1.41530i
$915$		0			0
$916$	10.2711	−	3.53621i	0.339366	−	0.116840i
$917$	−8.45331	+	8.45331i	−0.279153	+	0.279153i
$918$		0			0
$919$	−15.5190			−0.511925			−0.255963	−	0.966687i	$-0.582392\pi$
$919$	−15.5190			−0.511925			−0.255963	+	0.966687i	$0.582392\pi$
$920$	5.62235	−	6.94226i	0.185363	−	0.228880i
$921$		0			0
$922$	−39.9373	−	9.22101i	−1.31527	−	0.303678i
$923$	−0.412523	−	0.412523i	−0.0135784	−	0.0135784i
$924$		0			0
$925$	25.2300	−	25.2300i	0.829556	−	0.829556i
$926$	0.562994	+	0.901015i	0.0185011	+	0.0296092i
$927$		0			0
$928$	−3.18129	−	6.82389i	−0.104431	−	0.224005i
$929$			2.71572i			0.0890997i	0.999007	+	0.0445499i	$0.0141854\pi$
$929$			2.71572i			0.0890997i	−0.999007	+	0.0445499i	$0.985815\pi$
$930$		0			0
$931$	−52.8361	−	52.8361i	−1.73163	−	1.73163i
$932$	19.7909	−	40.5737i	0.648274	−	1.32904i
$933$		0			0
$934$	8.01581	−	34.7174i	0.262285	−	1.13599i
$935$			48.8355i			1.59709i
$936$		0			0
$937$		−	22.7682i		−	0.743805i	−0.928272	−	0.371902i	$-0.878706\pi$
$937$		−	22.7682i		−	0.743805i	0.928272	−	0.371902i	$-0.121294\pi$
$938$	−23.2411	−	5.36608i	−0.758850	−	0.175209i
$939$		0			0
$940$	−1.18019	−	3.42791i	−0.0384935	−	0.111806i
$941$	−20.7427	−	20.7427i	−0.676193	−	0.676193i	0.282944	−	0.959137i	$-0.408689\pi$
$941$	−20.7427	−	20.7427i	−0.676193	−	0.676193i	−0.959137	+	0.282944i	$0.908689\pi$
$942$		0			0
$943$			3.68739i			0.120078i
$944$	−5.17805	+	42.1468i	−0.168531	+	1.37176i
$945$		0			0
$946$	−76.5721	+	47.8456i	−2.48957	+	1.55560i
$947$	3.93162	−	3.93162i	0.127760	−	0.127760i	−0.640335	−	0.768096i	$-0.721205\pi$
$947$	3.93162	−	3.93162i	0.127760	−	0.127760i	0.768096	+	0.640335i	$0.221205\pi$
$948$		0			0
$949$	−5.74407	−	5.74407i	−0.186460	−	0.186460i
$950$	−8.01275	+	34.7042i	−0.259968	+	1.12595i
$951$		0			0
$952$	−36.5053	+	3.83488i	−1.18314	+	0.124289i
$953$	−23.8211			−0.771640			−0.385820	−	0.922574i	$-0.626081\pi$
$953$	−23.8211			−0.771640			−0.385820	+	0.922574i	$0.626081\pi$
$954$		0			0
$955$	−54.3915	+	54.3915i	−1.76007	+	1.76007i
$956$	−9.92292	+	20.3432i	−0.320930	+	0.657945i
$957$		0			0
$958$	−28.8100	+	18.0018i	−0.930810	+	0.581611i
$959$	10.9477			0.353518
$960$		0			0
$961$	30.7114			0.990692
$962$	13.5580	−	8.47166i	0.437128	−	0.273137i
$963$		0			0
$964$	9.14622	−	18.7508i	0.294580	−	0.603923i
$965$	0.817606	−	0.817606i	0.0263197	−	0.0263197i
$966$		0			0
$967$	−15.6138			−0.502107			−0.251053	−	0.967973i	$-0.580777\pi$
$967$	−15.6138			−0.502107			−0.251053	+	0.967973i	$0.580777\pi$
$968$	53.6023	−	5.63092i	1.72284	−	0.180984i
$969$		0			0
$970$	3.39107	−	14.6871i	0.108881	−	0.471576i
$971$	17.4485	+	17.4485i	0.559948	+	0.559948i	0.929293	−	0.369344i	$-0.120418\pi$
$971$	17.4485	+	17.4485i	0.559948	+	0.559948i	−0.369344	+	0.929293i	$0.620418\pi$
$972$		0			0
$973$	−34.5090	+	34.5090i	−1.10631	+	1.10631i
$974$	10.2047	−	6.37635i	0.326980	−	0.204311i
$975$		0			0
$976$	−5.05684	−	0.621270i	−0.161865	−	0.0198864i
$977$		−	47.4237i		−	1.51722i	−0.651546	−	0.758609i	$-0.725879\pi$
$977$		−	47.4237i		−	1.51722i	0.651546	−	0.758609i	$-0.274121\pi$
$978$		0			0
$979$	−44.9029	−	44.9029i	−1.43510	−	1.43510i
$980$	25.1701	+	73.1079i	0.804030	+	2.33535i
$981$		0			0
$982$	−44.8953	−	10.3658i	−1.43267	−	0.330785i
$983$			41.7345i			1.33113i	0.746342	+	0.665563i	$0.231808\pi$
$983$			41.7345i			1.33113i	−0.746342	+	0.665563i	$0.768192\pi$
$984$		0			0
$985$		−	28.5906i		−	0.910973i
$986$	1.23836	−	5.36350i	0.0394375	−	0.170809i
$987$		0			0
$988$	−6.99638	+	14.3434i	−0.222585	+	0.456324i
$989$	8.53885	+	8.53885i	0.271520	+	0.271520i
$990$		0			0
$991$		−	0.724503i		−	0.0230146i	−0.999934	−	0.0115073i	$-0.996337\pi$
$991$		−	0.724503i		−	0.0230146i	0.999934	−	0.0115073i	$-0.00366297\pi$
$992$	1.03957	−	2.85539i	0.0330063	−	0.0906589i
$993$		0			0
$994$	−1.43141	−	2.29083i	−0.0454016	−	0.0726607i
$995$	−17.0142	+	17.0142i	−0.539385	+	0.539385i
$996$		0			0
$997$	−40.6118	−	40.6118i	−1.28619	−	1.28619i	−0.937083	−	0.349106i	$-0.886485\pi$
$997$	−40.6118	−	40.6118i	−1.28619	−	1.28619i	−0.349106	−	0.937083i	$-0.613515\pi$
$998$	29.8591	+	6.89408i	0.945173	+	0.218228i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.l.b.107.14	yes	32
3.2	odd	2	inner	432.2.l.b.107.3	✓	32
4.3	odd	2		1728.2.l.b.1295.2		32
12.11	even	2		1728.2.l.b.1295.15		32
16.3	odd	4	inner	432.2.l.b.323.3	yes	32
16.13	even	4		1728.2.l.b.431.15		32
48.29	odd	4		1728.2.l.b.431.2		32
48.35	even	4	inner	432.2.l.b.323.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.l.b.107.3	✓	32	3.2	odd	2	inner
432.2.l.b.107.14	yes	32	1.1	even	1	trivial
432.2.l.b.323.3	yes	32	16.3	odd	4	inner
432.2.l.b.323.14	yes	32	48.35	even	4	inner
1728.2.l.b.431.2		32	48.29	odd	4
1728.2.l.b.431.15		32	16.13	even	4
1728.2.l.b.1295.2		32	4.3	odd	2
1728.2.l.b.1295.15		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.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19933 - 0.749398i) q^{2} +(0.876807 - 1.79756i) q^{4} +(-2.15382 + 2.15382i) q^{5} +4.43758 q^{7} +(-0.295500 - 2.81295i) q^{8} +O(q^{10})\)	\(q+(1.19933 - 0.749398i) q^{2} +(0.876807 - 1.79756i) q^{4} +(-2.15382 + 2.15382i) q^{5} +4.43758 q^{7} +(-0.295500 - 2.81295i) q^{8} +(-0.969085 + 4.19723i) q^{10} +(3.87657 + 3.87657i) q^{11} +(0.958389 - 0.958389i) q^{13} +(5.32214 - 3.32551i) q^{14} +(-2.46242 - 3.15222i) q^{16} -2.92448i q^{17} +(-4.16292 - 4.16292i) q^{19} +(1.98313 + 5.76011i) q^{20} +(7.55439 + 1.74421i) q^{22} -1.03692i q^{23} -4.27792i q^{25} +(0.431215 - 1.86764i) q^{26} +(3.89090 - 7.97680i) q^{28} +(0.941127 + 0.941127i) q^{29} +0.537179i q^{31} +(-5.31553 - 1.93523i) q^{32} +(-2.19160 - 3.50743i) q^{34} +(-9.55776 + 9.55776i) q^{35} +(5.89772 + 5.89772i) q^{37} +(-8.11241 - 1.87305i) q^{38} +(6.69505 + 5.42214i) q^{40} -3.55608 q^{41} +(-8.23479 + 8.23479i) q^{43} +(10.3674 - 3.56935i) q^{44} +(-0.777069 - 1.24362i) q^{46} -0.595112 q^{47} +12.6921 q^{49} +(-3.20586 - 5.13065i) q^{50} +(-0.882437 - 2.56308i) q^{52} +(-6.92245 + 6.92245i) q^{53} -16.6989 q^{55} +(-1.31130 - 12.4827i) q^{56} +(1.83400 + 0.423448i) q^{58} +(-7.50660 - 7.50660i) q^{59} +(0.900652 - 0.900652i) q^{61} +(0.402561 + 0.644258i) q^{62} +(-7.82536 + 1.66245i) q^{64} +4.12840i q^{65} +(-2.68757 - 2.68757i) q^{67} +(-5.25691 - 2.56420i) q^{68} +(-4.30039 + 18.6255i) q^{70} -0.430434i q^{71} -5.99346i q^{73} +(11.4931 + 2.65360i) q^{74} +(-11.1331 + 3.83300i) q^{76} +(17.2026 + 17.2026i) q^{77} -0.295266i q^{79} +(12.0929 + 1.48571i) q^{80} +(-4.26493 + 2.66492i) q^{82} +(-1.58742 + 1.58742i) q^{83} +(6.29881 + 6.29881i) q^{85} +(-3.70514 + 16.0474i) q^{86} +(9.75906 - 12.0501i) q^{88} -11.5832 q^{89} +(4.25293 - 4.25293i) q^{91} +(-1.86393 - 0.909182i) q^{92} +(-0.713739 + 0.445976i) q^{94} +17.9324 q^{95} -3.49925 q^{97} +(15.2221 - 9.51143i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 8 q^{10} - 8 q^{16} - 16 q^{19} + 16 q^{22} + 24 q^{28} + 24 q^{34} - 24 q^{40} - 16 q^{43} + 32 q^{46} + 32 q^{49} + 48 q^{52} - 32 q^{55} + 32 q^{61} - 24 q^{64} - 32 q^{67} - 48 q^{76} - 80 q^{82} + 32 q^{85} - 24 q^{88} - 48 q^{91}+O(q^{100}) \) 32 * q + 8 * q^10 - 8 * q^16 - 16 * q^19 + 16 * q^22 + 24 * q^28 + 24 * q^34 - 24 * q^40 - 16 * q^43 + 32 * q^46 + 32 * q^49 + 48 * q^52 - 32 * q^55 + 32 * q^61 - 24 * q^64 - 32 * q^67 - 48 * q^76 - 80 * q^82 + 32 * q^85 - 24 * q^88 - 48 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more