LMFDB - Embedded newform 432.2.u.f.193.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, not 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:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.4
Character	$\chi$	$=$	432.193
Dual form			432.2.u.f.385.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.631172 + 1.61295i) q^{3} +(0.156760 - 0.889029i) q^{5} +(-1.02544 + 0.860449i) q^{7} +(-2.20324 + 2.03610i) q^{9} +O(q^{10})$	\(q+(0.631172 + 1.61295i) q^{3} +(0.156760 - 0.889029i) q^{5} +(-1.02544 + 0.860449i) q^{7} +(-2.20324 + 2.03610i) q^{9} +(1.03113 + 5.84785i) q^{11} +(-0.904496 + 0.329210i) q^{13} +(1.53291 - 0.308284i) q^{15} +(0.115754 - 0.200493i) q^{17} +(0.756818 + 1.31085i) q^{19} +(-2.03510 - 1.11090i) q^{21} +(3.42896 + 2.87724i) q^{23} +(3.93266 + 1.43137i) q^{25} +(-4.67477 - 2.26860i) q^{27} +(5.21260 + 1.89723i) q^{29} +(-7.24273 - 6.07737i) q^{31} +(-8.78150 + 5.35417i) q^{33} +(0.604216 + 1.04653i) q^{35} +(1.74855 - 3.02858i) q^{37} +(-1.10189 - 1.25112i) q^{39} +(-5.06233 + 1.84254i) q^{41} +(-1.47774 - 8.38066i) q^{43} +(1.46478 + 2.27793i) q^{45} +(-5.18989 + 4.35484i) q^{47} +(-0.904376 + 5.12897i) q^{49} +(0.396446 + 0.0601614i) q^{51} +5.69117 q^{53} +5.36055 q^{55} +(-1.63666 + 2.04808i) q^{57} +(-0.506665 + 2.87344i) q^{59} +(10.2708 - 8.61822i) q^{61} +(0.507339 - 3.98369i) q^{63} +(0.150888 + 0.855730i) q^{65} +(11.6329 - 4.23402i) q^{67} +(-2.47659 + 7.34679i) q^{69} +(7.56504 - 13.1030i) q^{71} +(-2.83442 - 4.90937i) q^{73} +(0.173448 + 7.24665i) q^{75} +(-6.08915 - 5.10940i) q^{77} +(-6.84689 - 2.49206i) q^{79} +(0.708568 - 8.97206i) q^{81} +(5.91102 + 2.15143i) q^{83} +(-0.160098 - 0.134338i) q^{85} +(0.229899 + 9.60516i) q^{87} +(7.28626 + 12.6202i) q^{89} +(0.644241 - 1.11586i) q^{91} +(5.23112 - 15.5181i) q^{93} +(1.28402 - 0.467345i) q^{95} +(-2.69669 - 15.2937i) q^{97} +(-14.1787 - 10.7848i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{7} - 6 q^{9}+O(q^{10}) $ 30 * q - 3 * q^7 - 6 * q^9	$ 30 q - 3 q^{7} - 6 q^{9} + 3 q^{11} - 12 q^{13} - 15 q^{15} + 6 q^{17} + 9 q^{19} + 30 q^{21} + 12 q^{23} + 24 q^{25} + 15 q^{27} - 9 q^{29} - 27 q^{31} - 30 q^{33} + 18 q^{35} - 15 q^{37} + 21 q^{39} - 15 q^{41} + 30 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{49} + 6 q^{51} - 18 q^{53} - 54 q^{55} - 72 q^{57} + 12 q^{59} + 6 q^{61} + 54 q^{63} - 54 q^{65} + 45 q^{67} + 9 q^{69} - 36 q^{73} - 69 q^{75} + 12 q^{77} - 45 q^{79} - 30 q^{81} + 3 q^{83} + 57 q^{85} + 60 q^{87} + 36 q^{89} + 39 q^{91} + 30 q^{93} - 51 q^{95} - 84 q^{97} - 162 q^{99}+O(q^{100}) $ 30 * q - 3 * q^7 - 6 * q^9 + 3 * q^11 - 12 * q^13 - 15 * q^15 + 6 * q^17 + 9 * q^19 + 30 * q^21 + 12 * q^23 + 24 * q^25 + 15 * q^27 - 9 * q^29 - 27 * q^31 - 30 * q^33 + 18 * q^35 - 15 * q^37 + 21 * q^39 - 15 * q^41 + 30 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^49 + 6 * q^51 - 18 * q^53 - 54 * q^55 - 72 * q^57 + 12 * q^59 + 6 * q^61 + 54 * q^63 - 54 * q^65 + 45 * q^67 + 9 * q^69 - 36 * q^73 - 69 * q^75 + 12 * q^77 - 45 * q^79 - 30 * q^81 + 3 * q^83 + 57 * q^85 + 60 * q^87 + 36 * q^89 + 39 * q^91 + 30 * q^93 - 51 * q^95 - 84 * q^97 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.631172	+	1.61295i	0.364407	+	0.931240i
$3$	0.631172	+	1.61295i	0.364407	+	0.931240i
$4$		0			0
$5$	0.156760	−	0.889029i	0.0701051	−	0.397586i	−0.929482	−	0.368867i	$-0.879746\pi$
$5$	0.156760	−	0.889029i	0.0701051	−	0.397586i	0.999588	−	0.0287195i	$-0.00914295\pi$
$6$		0			0
$7$	−1.02544	+	0.860449i	−0.387581	+	0.325219i	−0.815670	−	0.578518i	$-0.803631\pi$
$7$	−1.02544	+	0.860449i	−0.387581	+	0.325219i	0.428089	+	0.903737i	$0.359187\pi$
$8$		0			0
$9$	−2.20324	+	2.03610i	−0.734415	+	0.678701i
$10$		0			0
$11$	1.03113	+	5.84785i	0.310899	+	1.76319i	0.594349	+	0.804207i	$0.297410\pi$
$11$	1.03113	+	5.84785i	0.310899	+	1.76319i	−0.283450	+	0.958987i	$0.591479\pi$
$12$		0			0
$13$	−0.904496	+	0.329210i	−0.250862	+	0.0913063i	−0.464391	−	0.885631i	$-0.653727\pi$
$13$	−0.904496	+	0.329210i	−0.250862	+	0.0913063i	0.213529	+	0.976937i	$0.431504\pi$
$14$		0			0
$15$	1.53291	−	0.308284i	0.395795	−	0.0795986i
$16$		0			0
$17$	0.115754	−	0.200493i	0.0280746	−	0.0486266i	−0.851647	−	0.524116i	$-0.824396\pi$
$17$	0.115754	−	0.200493i	0.0280746	−	0.0486266i	0.879721	+	0.475490i	$0.157729\pi$
$18$		0			0
$19$	0.756818	+	1.31085i	0.173626	+	0.300729i	0.939685	−	0.342041i	$-0.111118\pi$
$19$	0.756818	+	1.31085i	0.173626	+	0.300729i	−0.766059	+	0.642770i	$0.777785\pi$
$20$		0			0
$21$	−2.03510	−	1.11090i	−0.444094	−	0.242419i
$22$		0			0
$23$	3.42896	+	2.87724i	0.714988	+	0.599946i	0.925994	−	0.377539i	$-0.123229\pi$
$23$	3.42896	+	2.87724i	0.714988	+	0.599946i	−0.211006	+	0.977485i	$0.567674\pi$
$24$		0			0
$25$	3.93266	+	1.43137i	0.786533	+	0.286274i
$26$		0			0
$27$	−4.67477	−	2.26860i	−0.899659	−	0.436592i
$28$		0			0
$29$	5.21260	+	1.89723i	0.967955	+	0.352307i	0.777146	−	0.629320i	$-0.216667\pi$
$29$	5.21260	+	1.89723i	0.967955	+	0.352307i	0.190809	+	0.981627i	$0.438889\pi$
$30$		0			0
$31$	−7.24273	−	6.07737i	−1.30083	−	1.09153i	−0.990001	−	0.141063i	$-0.954948\pi$
$31$	−7.24273	−	6.07737i	−1.30083	−	1.09153i	−0.310832	−	0.950465i	$-0.600608\pi$
$32$		0			0
$33$	−8.78150	+	5.35417i	−1.52866	+	0.932042i
$34$		0			0
$35$	0.604216	+	1.04653i	0.102131	+	0.176896i
$36$		0			0
$37$	1.74855	−	3.02858i	0.287460	−	0.497895i	−0.685743	−	0.727844i	$-0.740522\pi$
$37$	1.74855	−	3.02858i	0.287460	−	0.497895i	0.973203	+	0.229949i	$0.0738558\pi$
$38$		0			0
$39$	−1.10189	−	1.25112i	−0.176444	−	0.200340i
$40$		0			0
$41$	−5.06233	+	1.84254i	−0.790604	+	0.287756i	−0.705587	−	0.708623i	$-0.749317\pi$
$41$	−5.06233	+	1.84254i	−0.790604	+	0.287756i	−0.0850167	+	0.996380i	$0.527094\pi$
$42$		0			0
$43$	−1.47774	−	8.38066i	−0.225353	−	1.27804i	−0.862010	−	0.506891i	$-0.830794\pi$
$43$	−1.47774	−	8.38066i	−0.225353	−	1.27804i	0.636657	−	0.771147i	$-0.280317\pi$
$44$		0			0
$45$	1.46478	+	2.27793i	0.218356	+	0.339573i
$46$		0			0
$47$	−5.18989	+	4.35484i	−0.757023	+	0.635218i	−0.937350	−	0.348389i	$-0.886729\pi$
$47$	−5.18989	+	4.35484i	−0.757023	+	0.635218i	0.180327	+	0.983607i	$0.442284\pi$
$48$		0			0
$49$	−0.904376	+	5.12897i	−0.129197	+	0.732710i
$50$		0			0
$51$	0.396446	+	0.0601614i	0.0555136	+	0.00842428i
$52$		0			0
$53$	5.69117			0.781742			0.390871	−	0.920445i	$-0.372174\pi$
$53$	5.69117			0.781742			0.390871	+	0.920445i	$0.372174\pi$
$54$		0			0
$55$	5.36055			0.722817
$56$		0			0
$57$	−1.63666	+	2.04808i	−0.216780	+	0.271275i
$58$		0			0
$59$	−0.506665	+	2.87344i	−0.0659622	+	0.374090i	0.933901	+	0.357533i	$0.116382\pi$
$59$	−0.506665	+	2.87344i	−0.0659622	+	0.374090i	−0.999863	+	0.0165578i	$0.994729\pi$
$60$		0			0
$61$	10.2708	−	8.61822i	1.31504	−	1.10345i	0.327709	−	0.944779i	$-0.393723\pi$
$61$	10.2708	−	8.61822i	1.31504	−	1.10345i	0.987331	−	0.158671i	$-0.0507211\pi$
$62$		0			0
$63$	0.507339	−	3.98369i	0.0639186	−	0.501897i
$64$		0			0
$65$	0.150888	+	0.855730i	0.0187154	+	0.106140i
$66$		0			0
$67$	11.6329	−	4.23402i	1.42118	−	0.517268i	0.486791	−	0.873518i	$-0.338167\pi$
$67$	11.6329	−	4.23402i	1.42118	−	0.517268i	0.934390	+	0.356251i	$0.115945\pi$
$68$		0			0
$69$	−2.47659	+	7.34679i	−0.298147	+	0.884450i
$70$		0			0
$71$	7.56504	−	13.1030i	0.897805	−	1.55504i	0.0675098	−	0.997719i	$-0.478495\pi$
$71$	7.56504	−	13.1030i	0.897805	−	1.55504i	0.830295	−	0.557325i	$-0.188172\pi$
$72$		0			0
$73$	−2.83442	−	4.90937i	−0.331744	−	0.574598i	0.651110	−	0.758984i	$-0.274304\pi$
$73$	−2.83442	−	4.90937i	−0.331744	−	0.574598i	−0.982854	+	0.184386i	$0.940970\pi$
$74$		0			0
$75$	0.173448	+	7.24665i	0.0200281	+	0.836771i
$76$		0			0
$77$	−6.08915	−	5.10940i	−0.693923	−	0.582270i
$78$		0			0
$79$	−6.84689	−	2.49206i	−0.770335	−	0.280379i	−0.0731983	−	0.997317i	$-0.523321\pi$
$79$	−6.84689	−	2.49206i	−0.770335	−	0.280379i	−0.697136	+	0.716938i	$0.745543\pi$
$80$		0			0
$81$	0.708568	−	8.97206i	0.0787298	−	0.996896i
$82$		0			0
$83$	5.91102	+	2.15143i	0.648818	+	0.236151i	0.645401	−	0.763844i	$-0.276690\pi$
$83$	5.91102	+	2.15143i	0.648818	+	0.236151i	0.00341695	+	0.999994i	$0.498912\pi$
$84$		0			0
$85$	−0.160098	−	0.134338i	−0.0173651	−	0.0145710i
$86$		0			0
$87$	0.229899	+	9.60516i	0.0246478	+	1.02978i
$88$		0			0
$89$	7.28626	+	12.6202i	0.772342	+	1.33774i	0.936276	+	0.351265i	$0.114248\pi$
$89$	7.28626	+	12.6202i	0.772342	+	1.33774i	−0.163934	+	0.986471i	$0.552418\pi$
$90$		0			0
$91$	0.644241	−	1.11586i	0.0675348	−	0.116974i
$92$		0			0
$93$	5.23112	−	15.5181i	0.542442	−	1.60915i
$94$		0			0
$95$	1.28402	−	0.467345i	0.131738	−	0.0479486i
$96$		0			0
$97$	−2.69669	−	15.2937i	−0.273807	−	1.55284i	−0.742725	−	0.669597i	$-0.766467\pi$
$97$	−2.69669	−	15.2937i	−0.273807	−	1.55284i	0.468918	−	0.883242i	$-0.344644\pi$
$98$		0			0
$99$	−14.1787	−	10.7848i	−1.42501	−	1.08391i
$100$		0			0
$101$	6.39732	−	5.36799i	0.636557	−	0.534135i	−0.266402	−	0.963862i	$-0.585835\pi$
$101$	6.39732	−	5.36799i	0.636557	−	0.534135i	0.902959	+	0.429727i	$0.141390\pi$
$102$		0			0
$103$	−1.33422	+	7.56673i	−0.131464	+	0.745572i	0.845792	+	0.533512i	$0.179128\pi$
$103$	−1.33422	+	7.56673i	−0.131464	+	0.745572i	−0.977257	+	0.212060i	$0.931983\pi$
$104$		0			0
$105$	−1.30665	+	1.63511i	−0.127516	+	0.159571i
$106$		0			0
$107$	−1.19122			−0.115159			−0.0575796	−	0.998341i	$-0.518338\pi$
$107$	−1.19122			−0.115159			−0.0575796	+	0.998341i	$0.518338\pi$
$108$		0			0
$109$	−1.38953			−0.133093			−0.0665464	−	0.997783i	$-0.521198\pi$
$109$	−1.38953			−0.133093			−0.0665464	+	0.997783i	$0.521198\pi$
$110$		0			0
$111$	5.98860	+	0.908779i	0.568412	+	0.0862575i
$112$		0			0
$113$	−0.110653	+	0.627546i	−0.0104094	+	0.0590346i	−0.989570	−	0.144053i	$-0.953986\pi$
$113$	−0.110653	+	0.627546i	−0.0104094	+	0.0590346i	0.979161	+	0.203087i	$0.0650976\pi$
$114$		0			0
$115$	3.09548	−	2.59741i	0.288655	−	0.242210i
$116$		0			0
$117$	1.32252	−	2.56698i	0.122267	−	0.237317i
$118$		0			0
$119$	0.0538140	+	0.305195i	0.00493312	+	0.0279771i
$120$		0			0
$121$	−22.7975	+	8.29762i	−2.07250	+	0.754329i
$122$		0			0
$123$	−6.16713	−	7.00235i	−0.556072	−	0.631381i
$124$		0			0
$125$	4.14588	−	7.18087i	0.370818	−	0.642276i
$126$		0			0
$127$	8.69082	+	15.0529i	0.771185	+	1.33573i	0.936914	+	0.349561i	$0.113669\pi$
$127$	8.69082	+	15.0529i	0.771185	+	1.33573i	−0.165728	+	0.986171i	$0.552998\pi$
$128$		0			0
$129$	12.5849	−	7.67316i	1.10804	−	0.675584i
$130$		0			0
$131$	−1.88714	−	1.58350i	−0.164880	−	0.138351i	0.556614	−	0.830771i	$-0.312100\pi$
$131$	−1.88714	−	1.58350i	−0.164880	−	0.138351i	−0.721495	+	0.692420i	$0.756545\pi$
$132$		0			0
$133$	−1.90399	−	0.692996i	−0.165097	−	0.0600904i
$134$		0			0
$135$	−2.74967	+	3.80038i	−0.236654	+	0.327085i
$136$		0			0
$137$	1.30358	+	0.474463i	0.111372	+	0.0405361i	0.397105	−	0.917773i	$-0.370015\pi$
$137$	1.30358	+	0.474463i	0.111372	+	0.0405361i	−0.285733	+	0.958309i	$0.592237\pi$
$138$		0			0
$139$	−6.07139	−	5.09450i	−0.514968	−	0.432110i	0.347905	−	0.937530i	$-0.386893\pi$
$139$	−6.07139	−	5.09450i	−0.514968	−	0.432110i	−0.862873	+	0.505420i	$0.831338\pi$
$140$		0			0
$141$	−10.2999	−	5.62241i	−0.867405	−	0.473492i
$142$		0			0
$143$	−2.85783	−	4.94990i	−0.238983	−	0.413931i
$144$		0			0
$145$	2.50382	−	4.33674i	0.207931	−	0.360147i
$146$		0			0
$147$	−8.84362	+	1.77855i	−0.729409	+	0.146692i
$148$		0			0
$149$	−13.9297	+	5.07001i	−1.14117	+	0.415351i	−0.842335	−	0.538954i	$-0.818820\pi$
$149$	−13.9297	+	5.07001i	−1.14117	+	0.415351i	−0.298833	+	0.954305i	$0.596597\pi$
$150$		0			0
$151$	−0.641032	−	3.63547i	−0.0521664	−	0.295850i	0.947551	−	0.319603i	$-0.103550\pi$
$151$	−0.641032	−	3.63547i	−0.0521664	−	0.295850i	−0.999718	+	0.0237528i	$0.992439\pi$
$152$		0			0
$153$	0.153188	+	0.677422i	0.0123845	+	0.0547663i
$154$		0			0
$155$	−6.53833	+	5.48631i	−0.525171	+	0.440671i
$156$		0			0
$157$	2.37866	−	13.4900i	0.189837	−	1.07662i	−0.729744	−	0.683721i	$-0.760361\pi$
$157$	2.37866	−	13.4900i	0.189837	−	1.07662i	0.919581	−	0.392901i	$-0.128528\pi$
$158$		0			0
$159$	3.59211	+	9.17960i	0.284873	+	0.727990i
$160$		0			0
$161$	−5.99192			−0.472230
$162$		0			0
$163$	19.7624			1.54791			0.773954	−	0.633241i	$-0.218276\pi$
$163$	19.7624			1.54791			0.773954	+	0.633241i	$0.218276\pi$
$164$		0			0
$165$	3.38343	+	8.64633i	0.263400	+	0.673116i
$166$		0			0
$167$	2.86005	−	16.2201i	0.221317	−	1.25515i	−0.648285	−	0.761398i	$-0.724514\pi$
$167$	2.86005	−	16.2201i	0.221317	−	1.25515i	0.869602	−	0.493753i	$-0.164375\pi$
$168$		0			0
$169$	−9.24884	+	7.76070i	−0.711450	+	0.596977i
$170$		0			0
$171$	−4.33648	−	1.34716i	−0.331619	−	0.103020i
$172$		0			0
$173$	3.83955	+	21.7752i	0.291915	+	1.65553i	0.679481	+	0.733693i	$0.262205\pi$
$173$	3.83955	+	21.7752i	0.291915	+	1.65553i	−0.387566	+	0.921842i	$0.626684\pi$
$174$		0			0
$175$	−5.26434	+	1.91606i	−0.397947	+	0.144841i
$176$		0			0
$177$	−4.95453	+	0.996408i	−0.372405	+	0.0748946i
$178$		0			0
$179$	6.79967	−	11.7774i	0.508231	−	0.880282i	−0.491723	−	0.870752i	$-0.663633\pi$
$179$	6.79967	−	11.7774i	0.508231	−	0.880282i	0.999955	−	0.00953089i	$-0.00303382\pi$
$180$		0			0
$181$	5.40909	+	9.36882i	0.402055	+	0.696379i	0.993974	−	0.109618i	$-0.0349628\pi$
$181$	5.40909	+	9.36882i	0.402055	+	0.696379i	−0.591919	+	0.805997i	$0.701629\pi$
$182$		0			0
$183$	20.3834	+	11.1267i	1.50679	+	0.822513i
$184$		0			0
$185$	−2.41839	−	2.02927i	−0.177804	−	0.149195i
$186$		0			0
$187$	1.29181	+	0.470180i	0.0944665	+	0.0343830i
$188$		0			0
$189$	6.74572	−	1.69608i	0.490679	−	0.123371i
$190$		0			0
$191$	−5.39658	−	1.96420i	−0.390483	−	0.142124i	0.139315	−	0.990248i	$-0.455510\pi$
$191$	−5.39658	−	1.96420i	−0.390483	−	0.142124i	−0.529798	+	0.848124i	$0.677732\pi$
$192$		0			0
$193$	17.3170	+	14.5307i	1.24651	+	1.04594i	0.996987	+	0.0775732i	$0.0247171\pi$
$193$	17.3170	+	14.5307i	1.24651	+	1.04594i	0.249520	+	0.968370i	$0.419727\pi$
$194$		0			0
$195$	−1.28502	+	0.783489i	−0.0920220	+	0.0561068i
$196$		0			0
$197$	2.42213	+	4.19525i	0.172570	+	0.298899i	0.939317	−	0.343049i	$-0.111460\pi$
$197$	2.42213	+	4.19525i	0.172570	+	0.298899i	−0.766748	+	0.641948i	$0.778126\pi$
$198$		0			0
$199$	−5.02931	+	8.71102i	−0.356518	+	0.617508i	−0.987377	−	0.158390i	$-0.949370\pi$
$199$	−5.02931	+	8.71102i	−0.356518	+	0.617508i	0.630858	+	0.775898i	$0.282703\pi$
$200$		0			0
$201$	14.1716	+	16.0909i	0.999589	+	1.13496i
$202$		0			0
$203$	−6.97769	+	2.53967i	−0.489738	+	0.178250i
$204$		0			0
$205$	0.844500	+	4.78940i	0.0589825	+	0.334506i
$206$		0			0
$207$	−13.4132	+	0.642457i	−0.932282	+	0.0446538i
$208$		0			0
$209$	−6.88527	+	5.77742i	−0.476264	+	0.399633i
$210$		0			0
$211$	−1.15769	+	6.56556i	−0.0796984	+	0.451992i	0.918677	+	0.395010i	$0.129259\pi$
$211$	−1.15769	+	6.56556i	−0.0796984	+	0.451992i	−0.998375	+	0.0569820i	$0.981852\pi$
$212$		0			0
$213$	25.9094	+	3.93180i	1.77528	+	0.269402i
$214$		0			0
$215$	−7.68230			−0.523929
$216$		0			0
$217$	12.6563			0.859164
$218$		0			0
$219$	6.12958	−	7.67045i	0.414198	−	0.518321i
$220$		0			0
$221$	−0.0386953	+	0.219452i	−0.00260293	+	0.0147620i
$222$		0			0
$223$	−3.88846	+	3.26281i	−0.260391	+	0.218494i	−0.763631	−	0.645653i	$-0.776585\pi$
$223$	−3.88846	+	3.26281i	−0.260391	+	0.218494i	0.503241	+	0.864146i	$0.332141\pi$
$224$		0			0
$225$	−11.5790	+	4.85365i	−0.771936	+	0.323576i
$226$		0			0
$227$	3.33236	+	18.8988i	0.221177	+	1.25436i	0.869861	+	0.493298i	$0.164209\pi$
$227$	3.33236	+	18.8988i	0.221177	+	1.25436i	−0.648684	+	0.761058i	$0.724680\pi$
$228$		0			0
$229$	−27.4236	+	9.98138i	−1.81220	+	0.659588i	−0.815474	+	0.578794i	$0.803523\pi$
$229$	−27.4236	+	9.98138i	−1.81220	+	0.659588i	−0.996731	+	0.0807942i	$0.974254\pi$
$230$		0			0
$231$	4.39793	−	13.0464i	0.289363	−	0.858392i
$232$		0			0
$233$	6.01606	−	10.4201i	0.394125	−	0.682645i	−0.598864	−	0.800851i	$-0.704381\pi$
$233$	6.01606	−	10.4201i	0.394125	−	0.682645i	0.992989	+	0.118206i	$0.0377143\pi$
$234$		0			0
$235$	3.05801	+	5.29663i	0.199483	+	0.345514i
$236$		0			0
$237$	−0.301979	−	12.6166i	−0.0196156	−	0.819538i
$238$		0			0
$239$	−16.6873	−	14.0023i	−1.07941	−	0.905731i	−0.0835369	−	0.996505i	$-0.526622\pi$
$239$	−16.6873	−	14.0023i	−1.07941	−	0.905731i	−0.995872	+	0.0907734i	$0.971066\pi$
$240$		0			0
$241$	1.26498	+	0.460417i	0.0814848	+	0.0296580i	0.382441	−	0.923980i	$-0.375084\pi$
$241$	1.26498	+	0.460417i	0.0814848	+	0.0296580i	−0.300956	+	0.953638i	$0.597306\pi$
$242$		0			0
$243$	14.9188	−	4.52003i	0.957039	−	0.289960i
$244$		0			0
$245$	4.41804	+	1.60803i	0.282258	+	0.102734i
$246$		0			0
$247$	−1.11608	−	0.936505i	−0.0710146	−	0.0595884i
$248$		0			0
$249$	0.260703	+	10.8921i	0.0165214	+	0.690260i
$250$		0			0
$251$	6.52612	+	11.3036i	0.411925	+	0.713475i	0.995100	−	0.0988716i	$-0.0315233\pi$
$251$	6.52612	+	11.3036i	0.411925	+	0.713475i	−0.583175	+	0.812346i	$0.698190\pi$
$252$		0			0
$253$	−13.2900	+	23.0189i	−0.835533	+	1.44719i
$254$		0			0
$255$	0.115632	−	0.343022i	0.00724117	−	0.0214809i
$256$		0			0
$257$	7.19027	−	2.61704i	0.448517	−	0.163247i	−0.107879	−	0.994164i	$-0.534406\pi$
$257$	7.19027	−	2.61704i	0.448517	−	0.163247i	0.556396	+	0.830917i	$0.312184\pi$
$258$		0			0
$259$	0.812898	+	4.61017i	0.0505110	+	0.286462i
$260$		0			0
$261$	−15.3476	+	6.43332i	−0.949991	+	0.398213i
$262$		0			0
$263$	14.9427	−	12.5384i	0.921408	−	0.773153i	−0.0528468	−	0.998603i	$-0.516830\pi$
$263$	14.9427	−	12.5384i	0.921408	−	0.773153i	0.974255	+	0.225449i	$0.0723851\pi$
$264$		0			0
$265$	0.892147	−	5.05962i	0.0548042	−	0.310810i
$266$		0			0
$267$	−15.7569	+	19.7179i	−0.964306	+	1.20672i
$268$		0			0
$269$	−18.2206			−1.11093			−0.555465	−	0.831540i	$-0.687460\pi$
$269$	−18.2206			−1.11093			−0.555465	+	0.831540i	$0.687460\pi$
$270$		0			0
$271$	−25.8725			−1.57164			−0.785820	−	0.618455i	$-0.787759\pi$
$271$	−25.8725			−1.57164			−0.785820	+	0.618455i	$0.787759\pi$
$272$		0			0
$273$	2.20645	+	0.334833i	0.133541	+	0.0202650i
$274$		0			0
$275$	−4.31535	+	24.4736i	−0.260226	+	1.47581i
$276$		0			0
$277$	5.35363	−	4.49223i	0.321669	−	0.269912i	−0.467626	−	0.883926i	$-0.654891\pi$
$277$	5.35363	−	4.49223i	0.321669	−	0.269912i	0.789295	+	0.614014i	$0.210446\pi$
$278$		0			0
$279$	28.3317	−	1.35701i	1.69617	−	0.0812421i
$280$		0			0
$281$	−5.01403	−	28.4360i	−0.299112	−	1.69635i	−0.650002	−	0.759933i	$-0.725232\pi$
$281$	−5.01403	−	28.4360i	−0.299112	−	1.69635i	0.350890	−	0.936417i	$-0.385879\pi$
$282$		0			0
$283$	−10.1684	+	3.70101i	−0.604451	+	0.220002i	−0.626073	−	0.779764i	$-0.715339\pi$
$283$	−10.1684	+	3.70101i	−0.604451	+	0.220002i	0.0216226	+	0.999766i	$0.493117\pi$
$284$		0			0
$285$	1.56425	+	1.77609i	0.0926579	+	0.105207i
$286$		0			0
$287$	3.60572	−	6.24530i	0.212839	−	0.368648i
$288$		0			0
$289$	8.47320	+	14.6760i	0.498424	+	0.863295i
$290$		0			0
$291$	22.9659	−	14.0026i	1.34629	−	0.820846i
$292$		0			0
$293$	−15.4850	−	12.9935i	−0.904645	−	0.759087i	0.0664476	−	0.997790i	$-0.478833\pi$
$293$	−15.4850	−	12.9935i	−0.904645	−	0.759087i	−0.971093	+	0.238702i	$0.923278\pi$
$294$		0			0
$295$	2.47515	+	0.900881i	0.144109	+	0.0524513i
$296$		0			0
$297$	8.44613	−	29.6766i	0.490094	−	1.72201i
$298$		0			0
$299$	−4.04870	−	1.47361i	−0.234142	−	0.0852208i
$300$		0			0
$301$	8.72646	+	7.32237i	0.502985	+	0.422054i
$302$		0			0
$303$	12.6961	+	6.93046i	0.729373	+	0.398145i
$304$		0			0
$305$	−6.05180	−	10.4820i	−0.346525	−	0.600199i
$306$		0			0
$307$	0.314413	−	0.544579i	0.0179445	−	0.0310807i	−0.856914	−	0.515460i	$-0.827621\pi$
$307$	0.314413	−	0.544579i	0.0179445	−	0.0310807i	0.874858	+	0.484379i	$0.160954\pi$
$308$		0			0
$309$	−13.0469	+	2.62387i	−0.742213	+	0.149267i
$310$		0			0
$311$	−23.8552	+	8.68260i	−1.35271	+	0.492345i	−0.913792	−	0.406183i	$-0.866859\pi$
$311$	−23.8552	+	8.68260i	−1.35271	+	0.492345i	−0.438915	+	0.898528i	$0.644637\pi$
$312$		0			0
$313$	−1.43959	−	8.16431i	−0.0813703	−	0.461474i	−0.998081	−	0.0619222i	$-0.980277\pi$
$313$	−1.43959	−	8.16431i	−0.0813703	−	0.461474i	0.916711	−	0.399552i	$-0.130834\pi$
$314$		0			0
$315$	−3.46208	−	1.07552i	−0.195066	−	0.0605987i
$316$		0			0
$317$	−14.2737	+	11.9771i	−0.801691	+	0.672699i	−0.948609	−	0.316450i	$-0.897509\pi$
$317$	−14.2737	+	11.9771i	−0.801691	+	0.672699i	0.146918	+	0.989149i	$0.453065\pi$
$318$		0			0
$319$	−5.71984	+	32.4388i	−0.320249	+	1.81622i
$320$		0			0
$321$	−0.751862	−	1.92138i	−0.0419648	−	0.107241i
$322$		0			0
$323$	0.350421			0.0194979
$324$		0			0
$325$	−4.02830			−0.223450
$326$		0			0
$327$	−0.877032	−	2.24125i	−0.0485000	−	0.123941i
$328$		0			0
$329$	1.57482	−	8.93127i	0.0868229	−	0.492397i
$330$		0			0
$331$	11.9269	−	10.0079i	0.655562	−	0.550082i	−0.253191	−	0.967416i	$-0.581480\pi$
$331$	11.9269	−	10.0079i	0.655562	−	0.550082i	0.908753	+	0.417334i	$0.137036\pi$
$332$		0			0
$333$	2.31401	+	10.2329i	0.126807	+	0.560761i
$334$		0			0
$335$	−1.94060	−	11.0057i	−0.106026	−	0.601305i
$336$		0			0
$337$	7.16759	−	2.60879i	0.390443	−	0.142110i	−0.139336	−	0.990245i	$-0.544497\pi$
$337$	7.16759	−	2.60879i	0.390443	−	0.142110i	0.529780	+	0.848135i	$0.322275\pi$
$338$		0			0
$339$	−1.08204	+	0.217611i	−0.0587686	+	0.0118190i
$340$		0			0
$341$	28.0714	−	48.6210i	1.52015	−	2.63298i
$342$		0			0
$343$	−8.17100	−	14.1526i	−0.441193	−	0.764168i
$344$		0			0
$345$	6.14329	+	3.35345i	0.330743	+	0.180544i
$346$		0			0
$347$	−4.26883	−	3.58198i	−0.229163	−	0.192291i	0.520975	−	0.853572i	$-0.325568\pi$
$347$	−4.26883	−	3.58198i	−0.229163	−	0.192291i	−0.750138	+	0.661281i	$0.770013\pi$
$348$		0			0
$349$	0.735164	+	0.267578i	0.0393525	+	0.0143231i	0.361621	−	0.932325i	$-0.382223\pi$
$349$	0.735164	+	0.267578i	0.0393525	+	0.0143231i	−0.322269	+	0.946648i	$0.604446\pi$
$350$		0			0
$351$	4.97515	+	0.512962i	0.265554	+	0.0273799i
$352$		0			0
$353$	−8.42054	−	3.06482i	−0.448180	−	0.163124i	0.108063	−	0.994144i	$-0.465535\pi$
$353$	−8.42054	−	3.06482i	−0.448180	−	0.163124i	−0.556243	+	0.831020i	$0.687757\pi$
$354$		0			0
$355$	−10.4631	−	8.77957i	−0.555323	−	0.465971i
$356$		0			0
$357$	−0.458299	+	0.279430i	−0.0242558	+	0.0147890i
$358$		0			0
$359$	9.08904	+	15.7427i	0.479701	+	0.830867i	0.999729	−	0.0232826i	$-0.00741176\pi$
$359$	9.08904	+	15.7427i	0.479701	+	0.830867i	−0.520028	+	0.854149i	$0.674078\pi$
$360$		0			0
$361$	8.35445	−	14.4703i	0.439708	−	0.761597i
$362$		0			0
$363$	−27.7729	−	31.5342i	−1.45770	−	1.65511i
$364$		0			0
$365$	−4.80890	+	1.75030i	−0.251709	+	0.0916146i
$366$		0			0
$367$	−1.72293	−	9.77125i	−0.0899365	−	0.510055i	−0.996182	−	0.0873029i	$-0.972175\pi$
$367$	−1.72293	−	9.77125i	−0.0899365	−	0.510055i	0.906245	−	0.422752i	$-0.138936\pi$
$368$		0			0
$369$	7.40196	−	14.3670i	0.385331	−	0.747916i
$370$		0			0
$371$	−5.83597	+	4.89696i	−0.302988	+	0.254238i
$372$		0			0
$373$	3.92986	−	22.2873i	0.203480	−	1.15399i	−0.696333	−	0.717719i	$-0.745186\pi$
$373$	3.92986	−	22.2873i	0.203480	−	1.15399i	0.899813	−	0.436275i	$-0.143703\pi$
$374$		0			0
$375$	14.1992	+	2.15475i	0.733242	+	0.111271i
$376$		0			0
$377$	−5.33936			−0.274991
$378$		0			0
$379$	0.717464			0.0368537			0.0184268	−	0.999830i	$-0.494134\pi$
$379$	0.717464			0.0368537			0.0184268	+	0.999830i	$0.494134\pi$
$380$		0			0
$381$	−18.7943	+	23.5189i	−0.962861	+	1.20491i
$382$		0			0
$383$	2.26212	−	12.8291i	0.115589	−	0.655538i	−0.870868	−	0.491517i	$-0.836442\pi$
$383$	2.26212	−	12.8291i	0.115589	−	0.655538i	0.986457	−	0.164021i	$-0.0524464\pi$
$384$		0			0
$385$	−5.49694	+	4.61248i	−0.280150	+	0.235074i
$386$		0			0
$387$	20.3197	+	15.4558i	1.03291	+	0.785663i
$388$		0			0
$389$	1.90171	+	10.7851i	0.0964206	+	0.546829i	0.994303	+	0.106593i	$0.0339941\pi$
$389$	1.90171	+	10.7851i	0.0964206	+	0.546829i	−0.897882	+	0.440236i	$0.854895\pi$
$390$		0			0
$391$	0.973783	−	0.354428i	0.0492463	−	0.0179242i
$392$		0			0
$393$	1.36300	−	4.04333i	0.0687543	−	0.203959i
$394$		0			0
$395$	−3.28883	+	5.69643i	−0.165479	+	0.286618i
$396$		0			0
$397$	7.15881	+	12.3994i	0.359290	+	0.622309i	0.987842	−	0.155458i	$-0.0496854\pi$
$397$	7.15881	+	12.3994i	0.359290	+	0.622309i	−0.628552	+	0.777768i	$0.716352\pi$
$398$		0			0
$399$	−0.0839746	−	3.50845i	−0.00420399	−	0.175642i
$400$		0			0
$401$	14.1425	+	11.8670i	0.706242	+	0.592607i	0.923542	−	0.383497i	$-0.125281\pi$
$401$	14.1425	+	11.8670i	0.706242	+	0.592607i	−0.217300	+	0.976105i	$0.569725\pi$
$402$		0			0
$403$	8.55175	+	3.11258i	0.425993	+	0.155049i
$404$		0			0
$405$	−7.86535	−	2.03640i	−0.390833	−	0.101189i
$406$		0			0
$407$	19.5137	+	7.10240i	0.967257	+	0.352053i
$408$		0			0
$409$	5.63619	+	4.72932i	0.278692	+	0.233850i	0.771409	−	0.636339i	$-0.219552\pi$
$409$	5.63619	+	4.72932i	0.278692	+	0.233850i	−0.492718	+	0.870189i	$0.663997\pi$
$410$		0			0
$411$	0.0574936	+	2.40208i	0.00283595	+	0.118486i
$412$		0			0
$413$	−1.95289	−	3.38251i	−0.0960956	−	0.166442i
$414$		0			0
$415$	2.83930	−	4.91781i	0.139376	−	0.241406i
$416$		0			0
$417$	4.38511	−	13.0084i	0.214740	−	0.637023i
$418$		0			0
$419$	20.3161	−	7.39447i	0.992508	−	0.361243i	0.205817	−	0.978590i	$-0.434015\pi$
$419$	20.3161	−	7.39447i	0.992508	−	0.361243i	0.786691	+	0.617347i	$0.211793\pi$
$420$		0			0
$421$	4.54204	+	25.7592i	0.221366	+	1.25543i	0.869512	+	0.493911i	$0.164433\pi$
$421$	4.54204	+	25.7592i	0.221366	+	1.25543i	−0.648147	+	0.761515i	$0.724456\pi$
$422$		0			0
$423$	2.56770	−	20.1619i	0.124846	−	0.980306i
$424$		0			0
$425$	0.742203	−	0.622782i	0.0360021	−	0.0302094i
$426$		0			0
$427$	−3.11658	+	17.6750i	−0.150822	+	0.855352i
$428$		0			0
$429$	6.18018	−	7.73378i	0.298382	−	0.373390i
$430$		0			0
$431$	−14.7608			−0.711004			−0.355502	−	0.934675i	$-0.615690\pi$
$431$	−14.7608			−0.711004			−0.355502	+	0.934675i	$0.615690\pi$
$432$		0			0
$433$	17.8478			0.857710			0.428855	−	0.903373i	$-0.358917\pi$
$433$	17.8478			0.857710			0.428855	+	0.903373i	$0.358917\pi$
$434$		0			0
$435$	8.57531	+	1.30132i	0.411155	+	0.0623934i
$436$		0			0
$437$	−1.17652	+	6.67240i	−0.0562808	+	0.319184i
$438$		0			0
$439$	2.97913	−	2.49978i	0.142186	−	0.119308i	−0.568921	−	0.822393i	$-0.692639\pi$
$439$	2.97913	−	2.49978i	0.142186	−	0.119308i	0.711107	+	0.703084i	$0.248194\pi$
$440$		0			0
$441$	−8.45056	−	13.1418i	−0.402407	−	0.625799i
$442$		0			0
$443$	−5.02831	−	28.5170i	−0.238902	−	1.35488i	−0.834237	−	0.551405i	$-0.814092\pi$
$443$	−5.02831	−	28.5170i	−0.238902	−	1.35488i	0.595335	−	0.803478i	$-0.297019\pi$
$444$		0			0
$445$	12.3619	−	4.49936i	0.586010	−	0.213290i
$446$		0			0
$447$	−16.9697	−	19.2680i	−0.802642	−	0.911344i
$448$		0			0
$449$	−7.12436	+	12.3398i	−0.336219	+	0.582349i	−0.983718	−	0.179717i	$-0.942482\pi$
$449$	−7.12436	+	12.3398i	−0.336219	+	0.582349i	0.647499	+	0.762066i	$0.275815\pi$
$450$		0			0
$451$	−15.9948	−	27.7039i	−0.753168	−	1.30452i
$452$		0			0
$453$	5.45925	−	3.32856i	0.256498	−	0.156389i
$454$		0			0
$455$	−0.891039	−	0.747671i	−0.0417726	−	0.0350513i
$456$		0			0
$457$	−32.6750	−	11.8927i	−1.52847	−	0.556318i	−0.565225	−	0.824937i	$-0.691211\pi$
$457$	−32.6750	−	11.8927i	−1.52847	−	0.556318i	−0.963247	+	0.268619i	$0.913433\pi$
$458$		0			0
$459$	−0.995963	+	0.674656i	−0.0464876	+	0.0314902i
$460$		0			0
$461$	−12.1617	−	4.42649i	−0.566425	−	0.206162i	0.0429040	−	0.999079i	$-0.486339\pi$
$461$	−12.1617	−	4.42649i	−0.566425	−	0.206162i	−0.609329	+	0.792917i	$0.708561\pi$
$462$		0			0
$463$	−11.2013	−	9.39901i	−0.520569	−	0.436809i	0.344261	−	0.938874i	$-0.388129\pi$
$463$	−11.2013	−	9.39901i	−0.520569	−	0.436809i	−0.864830	+	0.502065i	$0.832574\pi$
$464$		0			0
$465$	−12.9760	−	7.08323i	−0.601747	−	0.328477i
$466$		0			0
$467$	9.54657	+	16.5351i	0.441763	+	0.765155i	0.997820	−	0.0659885i	$-0.0210201\pi$
$467$	9.54657	+	16.5351i	0.441763	+	0.765155i	−0.556058	+	0.831144i	$0.687687\pi$
$468$		0			0
$469$	−8.28569	+	14.3512i	−0.382598	+	0.662678i
$470$		0			0
$471$	23.2601	−	4.67786i	1.07177	−	0.215545i
$472$		0			0
$473$	47.4851	−	17.2832i	2.18337	−	0.794681i
$474$		0			0
$475$	1.10000	+	6.23841i	0.0504715	+	0.286238i
$476$		0			0
$477$	−12.5390	+	11.5878i	−0.574123	+	0.530569i
$478$		0			0
$479$	4.40831	−	3.69901i	0.201421	−	0.169012i	−0.536498	−	0.843901i	$-0.680253\pi$
$479$	4.40831	−	3.69901i	0.201421	−	0.169012i	0.737919	+	0.674890i	$0.235809\pi$
$480$		0			0
$481$	−0.584520	+	3.31498i	−0.0266518	+	0.151150i
$482$		0			0
$483$	−3.78193	−	9.66470i	−0.172084	−	0.439759i
$484$		0			0
$485$	−14.0193			−0.636582
$486$		0			0
$487$	−0.662146			−0.0300047			−0.0150023	−	0.999887i	$-0.504776\pi$
$487$	−0.662146			−0.0300047			−0.0150023	+	0.999887i	$0.504776\pi$
$488$		0			0
$489$	12.4735	+	31.8758i	0.564069	+	1.44147i
$490$		0			0
$491$	0.439135	−	2.49046i	0.0198179	−	0.112393i	−0.973294	−	0.229562i	$-0.926271\pi$
$491$	0.439135	−	2.49046i	0.0198179	−	0.112393i	0.993112	+	0.117169i	$0.0373818\pi$
$492$		0			0
$493$	0.983762	−	0.825475i	0.0443064	−	0.0371775i
$494$		0			0
$495$	−11.8106	+	10.9146i	−0.530847	+	0.490577i
$496$		0			0
$497$	3.51697	+	19.9457i	0.157758	+	0.894688i
$498$		0			0
$499$	26.1568	−	9.52029i	1.17094	−	0.426187i	0.317946	−	0.948109i	$-0.397007\pi$
$499$	26.1568	−	9.52029i	1.17094	−	0.426187i	0.852993	+	0.521922i	$0.174785\pi$
$500$		0			0
$501$	27.9675	−	5.62456i	1.24950	−	0.251287i
$502$		0			0
$503$	6.98704	−	12.1019i	0.311537	−	0.539597i	−0.667159	−	0.744916i	$-0.732490\pi$
$503$	6.98704	−	12.1019i	0.311537	−	0.539597i	0.978695	+	0.205318i	$0.0658230\pi$
$504$		0			0
$505$	−3.76946	−	6.52889i	−0.167739	−	0.290532i
$506$		0			0
$507$	−18.3553	−	10.0196i	−0.815186	−	0.444987i
$508$		0			0
$509$	12.3392	+	10.3538i	0.546924	+	0.458924i	0.873898	−	0.486110i	$-0.161584\pi$
$509$	12.3392	+	10.3538i	0.546924	+	0.458924i	−0.326974	+	0.945033i	$0.606029\pi$
$510$		0			0
$511$	7.13080	+	2.59540i	0.315448	+	0.114814i
$512$		0			0
$513$	−0.564159	−	7.84483i	−0.0249082	−	0.346358i
$514$		0			0
$515$	6.51789	+	2.37232i	0.287213	+	0.104537i
$516$		0			0
$517$	−30.8179	−	25.8593i	−1.35537	−	1.13729i
$518$		0			0
$519$	−32.6989	+	19.9369i	−1.43532	+	0.875132i
$520$		0			0
$521$	12.2082	+	21.1451i	0.534849	+	0.926386i	0.999171	+	0.0407191i	$0.0129649\pi$
$521$	12.2082	+	21.1451i	0.534849	+	0.926386i	−0.464322	+	0.885667i	$0.653702\pi$
$522$		0			0
$523$	9.15655	−	15.8596i	0.400388	−	0.693493i	−0.593385	−	0.804919i	$-0.702209\pi$
$523$	9.15655	−	15.8596i	0.400388	−	0.693493i	0.993773	+	0.111427i	$0.0355420\pi$
$524$		0			0
$525$	−6.41323	−	7.28178i	−0.279896	−	0.317803i
$526$		0			0
$527$	−2.05685	+	0.748631i	−0.0895977	+	0.0326109i
$528$		0			0
$529$	−0.514641	−	2.91868i	−0.0223757	−	0.126899i
$530$		0			0
$531$	−4.73432	−	7.36252i	−0.205452	−	0.319506i
$532$		0			0
$533$	3.97228	−	3.33314i	0.172058	−	0.144374i
$534$		0			0
$535$	−0.186735	+	1.05903i	−0.00807325	+	0.0457857i
$536$		0			0
$537$	23.2881	+	3.53401i	1.00496	+	0.152504i
$538$		0			0
$539$	−30.9260			−1.33208
$540$		0			0
$541$	−2.63588			−0.113325			−0.0566626	−	0.998393i	$-0.518046\pi$
$541$	−2.63588			−0.113325			−0.0566626	+	0.998393i	$0.518046\pi$
$542$		0			0
$543$	−11.6974	+	14.6380i	−0.501984	+	0.628175i
$544$		0			0
$545$	−0.217822	+	1.23533i	−0.00933049	+	0.0529158i
$546$		0			0
$547$	4.17151	−	3.50032i	0.178361	−	0.149663i	−0.549236	−	0.835667i	$-0.685081\pi$
$547$	4.17151	−	3.50032i	0.178361	−	0.149663i	0.727597	+	0.686004i	$0.240637\pi$
$548$		0			0
$549$	−5.08148	+	39.9004i	−0.216872	+	1.70291i
$550$		0			0
$551$	1.45801	+	8.26878i	0.0621133	+	0.352262i
$552$		0			0
$553$	9.16538	−	3.33593i	0.389752	−	0.141858i
$554$		0			0
$555$	1.74670	−	5.18158i	0.0741434	−	0.219946i
$556$		0			0
$557$	−6.26979	+	10.8596i	−0.265660	+	0.460136i	−0.967736	−	0.251965i	$-0.918923\pi$
$557$	−6.26979	+	10.8596i	−0.265660	+	0.460136i	0.702077	+	0.712101i	$0.252256\pi$
$558$		0			0
$559$	4.09560	+	7.09378i	0.173225	+	0.300035i
$560$		0			0
$561$	0.0569747	+	2.38040i	0.00240547	+	0.100500i
$562$		0			0
$563$	−19.7542	−	16.5757i	−0.832541	−	0.698585i	0.123332	−	0.992365i	$-0.460642\pi$
$563$	−19.7542	−	16.5757i	−0.832541	−	0.698585i	−0.955873	+	0.293781i	$0.905086\pi$
$564$		0			0
$565$	0.540561	+	0.196748i	0.0227416	+	0.00827726i
$566$		0			0
$567$	6.99340	+	9.81003i	0.293695	+	0.411982i
$568$		0			0
$569$	−15.8746	−	5.77788i	−0.665497	−	0.242221i	−0.0128893	−	0.999917i	$-0.504103\pi$
$569$	−15.8746	−	5.77788i	−0.665497	−	0.242221i	−0.652608	+	0.757696i	$0.726325\pi$
$570$		0			0
$571$	0.500657	+	0.420101i	0.0209518	+	0.0175807i	0.653203	−	0.757182i	$-0.273425\pi$
$571$	0.500657	+	0.420101i	0.0209518	+	0.0175807i	−0.632252	+	0.774763i	$0.717869\pi$
$572$		0			0
$573$	−0.238014	−	9.94419i	−0.00994316	−	0.415424i
$574$		0			0
$575$	9.36655	+	16.2233i	0.390612	+	0.676560i
$576$		0			0
$577$	12.3273	−	21.3515i	0.513192	−	0.888875i	−0.486691	−	0.873574i	$-0.661796\pi$
$577$	12.3273	−	21.3515i	0.513192	−	0.888875i	0.999883	−	0.0153004i	$-0.00487045\pi$
$578$		0			0
$579$	−12.5073	+	37.1029i	−0.519788	+	1.54195i
$580$		0			0
$581$	−7.91261	+	2.87995i	−0.328270	+	0.119481i
$582$		0			0
$583$	5.86836	+	33.2811i	0.243043	+	1.37836i
$584$		0			0
$585$	−2.07480	−	1.57816i	−0.0857824	−	0.0652488i
$586$		0			0
$587$	12.3466	−	10.3600i	0.509599	−	0.427605i	−0.351389	−	0.936230i	$-0.614290\pi$
$587$	12.3466	−	10.3600i	0.509599	−	0.427605i	0.860988	+	0.508625i	$0.169846\pi$
$588$		0			0
$589$	2.48508	−	14.0936i	0.102396	−	0.580716i
$590$		0			0
$591$	−5.23797	+	6.55471i	−0.215461	+	0.269625i
$592$		0			0
$593$	−40.0436			−1.64439			−0.822197	−	0.569203i	$-0.807252\pi$
$593$	−40.0436			−1.64439			−0.822197	+	0.569203i	$0.807252\pi$
$594$		0			0
$595$	0.279763			0.0114692
$596$		0			0
$597$	−17.2248	−	2.61390i	−0.704966	−	0.106980i
$598$		0			0
$599$	−0.517573	+	2.93530i	−0.0211474	+	0.119933i	−0.993554	−	0.113359i	$-0.963839\pi$
$599$	−0.517573	+	2.93530i	−0.0211474	+	0.119933i	0.972407	+	0.233293i	$0.0749500\pi$
$600$		0			0
$601$	−8.50542	+	7.13689i	−0.346943	+	0.291120i	−0.799561	−	0.600585i	$-0.794935\pi$
$601$	−8.50542	+	7.13689i	−0.346943	+	0.291120i	0.452618	+	0.891705i	$0.350490\pi$
$602$		0			0
$603$	−17.0092	+	33.0143i	−0.692666	+	1.34445i
$604$		0			0
$605$	3.80309	+	21.5684i	0.154618	+	0.876881i
$606$		0			0
$607$	17.0013	−	6.18796i	0.690060	−	0.251161i	0.0268993	−	0.999638i	$-0.491437\pi$
$607$	17.0013	−	6.18796i	0.690060	−	0.251161i	0.663161	+	0.748477i	$0.269214\pi$
$608$		0			0
$609$	−8.50050	−	9.65173i	−0.344457	−	0.391108i
$610$		0			0
$611$	3.26058	−	5.64749i	0.131909	−	0.228473i
$612$		0			0
$613$	−15.2618	−	26.4342i	−0.616418	−	1.06767i	−0.990134	−	0.140124i	$-0.955250\pi$
$613$	−15.2618	−	26.4342i	−0.616418	−	1.06767i	0.373716	−	0.927543i	$-0.378083\pi$
$614$		0			0
$615$	−7.19206	+	4.38508i	−0.290012	+	0.176823i
$616$		0			0
$617$	18.2602	+	15.3221i	0.735127	+	0.616845i	0.931524	−	0.363680i	$-0.118480\pi$
$617$	18.2602	+	15.3221i	0.735127	+	0.616845i	−0.196397	+	0.980524i	$0.562924\pi$
$618$		0			0
$619$	1.11597	+	0.406179i	0.0448545	+	0.0163257i	0.364350	−	0.931262i	$-0.381291\pi$
$619$	1.11597	+	0.406179i	0.0448545	+	0.0163257i	−0.319495	+	0.947588i	$0.603513\pi$
$620$		0			0
$621$	−9.50229	−	21.2294i	−0.381314	−	0.851906i
$622$		0			0
$623$	−18.3307	−	6.67181i	−0.734402	−	0.267301i
$624$		0			0
$625$	10.2956	+	8.63902i	0.411823	+	0.345561i
$626$		0			0
$627$	−13.6645	−	7.45907i	−0.545708	−	0.297887i
$628$		0			0
$629$	−0.404805	−	0.701143i	−0.0161406	−	0.0279564i
$630$		0			0
$631$	6.20702	−	10.7509i	0.247098	−	0.427986i	−0.715622	−	0.698488i	$-0.753856\pi$
$631$	6.20702	−	10.7509i	0.247098	−	0.427986i	0.962719	+	0.270502i	$0.0871898\pi$
$632$		0			0
$633$	−11.3207	+	2.27670i	−0.449955	+	0.0904909i
$634$		0			0
$635$	14.7449	−	5.36670i	0.585133	−	0.212971i
$636$		0			0
$637$	−0.870502	−	4.93686i	−0.0344905	−	0.195606i
$638$		0			0
$639$	10.0115	+	44.2724i	0.396049	+	1.75139i
$640$		0			0
$641$	−0.832650	+	0.698676i	−0.0328877	+	0.0275960i	−0.659083	−	0.752070i	$-0.729056\pi$
$641$	−0.832650	+	0.698676i	−0.0328877	+	0.0275960i	0.626196	+	0.779666i	$0.284611\pi$
$642$		0			0
$643$	1.11501	−	6.32352i	0.0439716	−	0.249375i	−0.954897	−	0.296938i	$-0.904034\pi$
$643$	1.11501	−	6.32352i	0.0439716	−	0.249375i	0.998868	+	0.0475631i	$0.0151455\pi$
$644$		0			0
$645$	−4.84885	−	12.3912i	−0.190923	−	0.487903i
$646$		0			0
$647$	−3.86655			−0.152010			−0.0760049	−	0.997107i	$-0.524216\pi$
$647$	−3.86655			−0.152010			−0.0760049	+	0.997107i	$0.524216\pi$
$648$		0			0
$649$	−17.3259			−0.680102
$650$		0			0
$651$	7.98828	+	20.4140i	0.313086	+	0.800087i
$652$		0			0
$653$	−5.72846	+	32.4877i	−0.224172	+	1.27134i	0.640090	+	0.768300i	$0.278897\pi$
$653$	−5.72846	+	32.4877i	−0.224172	+	1.27134i	−0.864262	+	0.503042i	$0.832214\pi$
$654$		0			0
$655$	−1.70360	+	1.42949i	−0.0665653	+	0.0558549i
$656$		0			0
$657$	16.2409	+	5.04535i	0.633618	+	0.196838i
$658$		0			0
$659$	−1.54779	−	8.77796i	−0.0602934	−	0.341941i	0.939707	−	0.341982i	$-0.111098\pi$
$659$	−1.54779	−	8.77796i	−0.0602934	−	0.341941i	−1.00000		4.08662e-5i	$0.999987\pi$
$660$		0			0
$661$	26.8170	−	9.76058i	1.04306	−	0.379643i	0.237020	−	0.971505i	$-0.423829\pi$
$661$	26.8170	−	9.76058i	1.04306	−	0.379643i	0.806039	+	0.591862i	$0.201607\pi$
$662$		0			0
$663$	−0.378390	+	0.0760982i	−0.0146954	+	0.00295541i
$664$		0			0
$665$	−0.914564	+	1.58407i	−0.0354653	+	0.0614276i
$666$		0			0
$667$	12.4150	+	21.5034i	0.480711	+	0.832616i
$668$		0			0
$669$	−7.71705	−	4.21252i	−0.298358	−	0.162865i
$670$		0			0
$671$	60.9887	+	51.1756i	2.35444	+	1.97561i
$672$		0			0
$673$	−25.1477	−	9.15300i	−0.969371	−	0.352822i	−0.191672	−	0.981459i	$-0.561391\pi$
$673$	−25.1477	−	9.15300i	−0.969371	−	0.352822i	−0.777699	+	0.628637i	$0.783613\pi$
$674$		0			0
$675$	−15.1371	−	15.6130i	−0.582626	−	0.600944i
$676$		0			0
$677$	44.5946	+	16.2311i	1.71391	+	0.623812i	0.997284	−	0.0736482i	$-0.0234642\pi$
$677$	44.5946	+	16.2311i	1.71391	+	0.623812i	0.716624	+	0.697460i	$0.245686\pi$
$678$		0			0
$679$	15.9247	+	13.3624i	0.611135	+	0.512803i
$680$		0			0
$681$	−28.3796	+	17.3033i	−1.08751	+	0.663065i
$682$		0			0
$683$	21.0930	+	36.5342i	0.807103	+	1.39794i	0.914862	+	0.403766i	$0.132299\pi$
$683$	21.0930	+	36.5342i	0.807103	+	1.39794i	−0.107759	+	0.994177i	$0.534368\pi$
$684$		0			0
$685$	0.626160	−	1.08454i	0.0239243	−	0.0414382i
$686$		0			0
$687$	−33.4085	−	37.9331i	−1.27462	−	1.44724i
$688$		0			0
$689$	−5.14764	+	1.87359i	−0.196109	+	0.0713780i
$690$		0			0
$691$	−1.80897	−	10.2592i	−0.0688164	−	0.390277i	−0.999689	−	0.0249335i	$-0.992063\pi$
$691$	−1.80897	−	10.2592i	−0.0688164	−	0.390277i	0.930873	−	0.365344i	$-0.119049\pi$
$692$		0			0
$693$	23.8191	−	1.14087i	0.904814	−	0.0433382i
$694$		0			0
$695$	−5.48091	+	4.59903i	−0.207903	+	0.174451i
$696$		0			0
$697$	−0.216572	+	1.22824i	−0.00820326	+	0.0465230i
$698$		0			0
$699$	20.6043	+	3.12674i	0.779328	+	0.118264i
$700$		0			0
$701$	33.0394			1.24788			0.623941	−	0.781471i	$-0.285530\pi$
$701$	33.0394			1.24788			0.623941	+	0.781471i	$0.285530\pi$
$702$		0			0
$703$	5.29334			0.199642
$704$		0			0
$705$	−6.61309	+	8.27552i	−0.249063	+	0.311674i
$706$		0			0
$707$	−1.94121	+	11.0091i	−0.0730066	+	0.414041i
$708$		0			0
$709$	−8.62850	+	7.24017i	−0.324050	+	0.271910i	−0.790270	−	0.612758i	$-0.790060\pi$
$709$	−8.62850	+	7.24017i	−0.324050	+	0.271910i	0.466220	+	0.884669i	$0.345615\pi$
$710$		0			0
$711$	20.1595	−	8.45034i	0.756039	−	0.316913i
$712$		0			0
$713$	−7.34898	−	41.6782i	−0.275222	−	1.56086i
$714$		0			0
$715$	−4.84860	+	1.76475i	−0.181327	+	0.0659977i
$716$		0			0
$717$	12.0525	−	35.7536i	0.450109	−	1.33524i
$718$		0			0
$719$	−2.58952	+	4.48517i	−0.0965726	+	0.167269i	−0.910264	−	0.414029i	$-0.864121\pi$
$719$	−2.58952	+	4.48517i	−0.0965726	+	0.167269i	0.813691	+	0.581297i	$0.197455\pi$
$720$		0			0
$721$	−5.14262	−	8.90728i	−0.191521	−	0.331724i
$722$		0			0
$723$	0.0557915	+	2.33096i	0.00207491	+	0.0866895i
$724$		0			0
$725$	17.7837	+	14.9223i	0.660472	+	0.554202i
$726$		0			0
$727$	1.54638	+	0.562835i	0.0573519	+	0.0208744i	0.370537	−	0.928818i	$-0.379174\pi$
$727$	1.54638	+	0.562835i	0.0573519	+	0.0208744i	−0.313185	+	0.949692i	$0.601396\pi$
$728$		0			0
$729$	16.7069	+	21.2104i	0.618774	+	0.785569i
$730$		0			0
$731$	−1.85131	−	0.673823i	−0.0684734	−	0.0249223i
$732$		0			0
$733$	−1.95210	−	1.63800i	−0.0721023	−	0.0605010i	0.606024	−	0.795446i	$-0.292763\pi$
$733$	−1.95210	−	1.63800i	−0.0721023	−	0.0605010i	−0.678127	+	0.734945i	$0.737208\pi$
$734$		0			0
$735$	0.194855	+	8.14104i	0.00718735	+	0.300287i
$736$		0			0
$737$	36.7550	+	63.6615i	1.35389	+	2.34500i
$738$		0			0
$739$	−21.4906	+	37.2228i	−0.790544	+	1.36926i	0.135087	+	0.990834i	$0.456869\pi$
$739$	−21.4906	+	37.2228i	−0.790544	+	1.36926i	−0.925631	+	0.378428i	$0.876465\pi$
$740$		0			0
$741$	0.806099	−	2.39129i	0.0296128	−	0.0878461i
$742$		0			0
$743$	−8.57581	+	3.12134i	−0.314616	+	0.114511i	−0.494502	−	0.869177i	$-0.664649\pi$
$743$	−8.57581	+	3.12134i	−0.314616	+	0.114511i	0.179886	+	0.983688i	$0.442427\pi$
$744$		0			0
$745$	2.32376	+	13.1787i	0.0851361	+	0.482831i
$746$		0			0
$747$	−17.4040	+	7.29530i	−0.636777	+	0.266921i
$748$		0			0
$749$	1.22152	−	1.02498i	0.0446335	−	0.0374519i
$750$		0			0
$751$	8.14998	−	46.2208i	0.297397	−	1.68662i	−0.359901	−	0.932991i	$-0.617189\pi$
$751$	8.14998	−	46.2208i	0.297397	−	1.68662i	0.657297	−	0.753631i	$-0.271700\pi$
$752$		0			0
$753$	−14.1130	+	17.6608i	−0.514308	+	0.643596i
$754$		0			0
$755$	−3.33253			−0.121283
$756$		0			0
$757$	−45.5817			−1.65669			−0.828347	−	0.560215i	$-0.810718\pi$
$757$	−45.5817			−1.65669			−0.828347	+	0.560215i	$0.810718\pi$
$758$		0			0
$759$	−45.5167	−	6.90723i	−1.65215	−	0.250716i
$760$		0			0
$761$	1.52918	−	8.67243i	0.0554328	−	0.314375i	−0.944466	−	0.328610i	$-0.893420\pi$
$761$	1.52918	−	8.67243i	0.0554328	−	0.314375i	0.999899	+	0.0142343i	$0.00453108\pi$
$762$		0			0
$763$	1.42488	−	1.19562i	0.0515842	−	0.0432843i
$764$		0			0
$765$	0.626262	−	0.0299963i	0.0226426	−	0.00108452i
$766$		0			0
$767$	−0.487688	−	2.76582i	−0.0176094	−	0.0998678i
$768$		0			0
$769$	13.5046	−	4.91526i	0.486987	−	0.177249i	−0.0868451	−	0.996222i	$-0.527679\pi$
$769$	13.5046	−	4.91526i	0.486987	−	0.177249i	0.573832	+	0.818973i	$0.305456\pi$
$770$		0			0
$771$	8.75947	+	9.94577i	0.315465	+	0.358188i
$772$		0			0
$773$	0.866174	−	1.50026i	0.0311541	−	0.0539605i	−0.850028	−	0.526738i	$-0.823415\pi$
$773$	0.866174	−	1.50026i	0.0311541	−	0.0539605i	0.881182	+	0.472777i	$0.156748\pi$
$774$		0			0
$775$	−19.7842	−	34.2673i	−0.710671	−	1.23092i
$776$		0			0
$777$	−6.92292	+	4.22098i	−0.248358	+	0.151427i
$778$		0			0
$779$	−6.24656	−	5.24148i	−0.223806	−	0.187796i
$780$		0			0
$781$	84.4251	+	30.7282i	3.02097	+	1.09954i
$782$		0			0
$783$	−20.0636	−	20.6944i	−0.717015	−	0.739558i
$784$		0			0
$785$	−11.6202	−	4.22939i	−0.414741	−	0.150953i
$786$		0			0
$787$	25.6205	+	21.4982i	0.913273	+	0.766327i	0.972739	−	0.231903i	$-0.0744952\pi$
$787$	25.6205	+	21.4982i	0.913273	+	0.766327i	−0.0594656	+	0.998230i	$0.518940\pi$
$788$		0			0
$789$	29.6554	+	16.1880i	1.05576	+	0.576309i
$790$		0			0
$791$	−0.426503	−	0.738724i	−0.0151647	−	0.0262660i
$792$		0			0
$793$	−6.45269	+	11.1764i	−0.229142	+	0.396885i
$794$		0			0
$795$	8.72403	−	1.75450i	0.309410	−	0.0622256i
$796$		0			0
$797$	−27.0563	+	9.84767i	−0.958382	+	0.348822i	−0.773399	−	0.633919i	$-0.781445\pi$
$797$	−27.0563	+	9.84767i	−0.958382	+	0.348822i	−0.184983	+	0.982742i	$0.559223\pi$
$798$		0			0
$799$	0.272359	+	1.54463i	0.00963538	+	0.0546450i
$800$		0			0
$801$	−41.7494	−	12.9697i	−1.47514	−	0.458263i
$802$		0			0
$803$	25.7866	−	21.6375i	0.909989	−	0.763571i
$804$		0			0
$805$	−0.939293	+	5.32700i	−0.0331057	+	0.187752i
$806$		0			0
$807$	−11.5003	−	29.3890i	−0.404831	−	1.03454i
$808$		0			0
$809$	−20.4970			−0.720637			−0.360318	−	0.932829i	$-0.617332\pi$
$809$	−20.4970			−0.720637			−0.360318	+	0.932829i	$0.617332\pi$
$810$		0			0
$811$	−44.9718			−1.57917			−0.789586	−	0.613640i	$-0.789705\pi$
$811$	−44.9718			−1.57917			−0.789586	+	0.613640i	$0.789705\pi$
$812$		0			0
$813$	−16.3300	−	41.7311i	−0.572717	−	1.46357i
$814$		0			0
$815$	3.09795	−	17.5693i	0.108516	−	0.615427i
$816$		0			0
$817$	9.86739	−	8.27972i	0.345216	−	0.289671i
$818$		0			0
$819$	0.852582	+	3.77025i	0.0297916	+	0.131743i
$820$		0			0
$821$	−6.34040	−	35.9582i	−0.221282	−	1.25495i	−0.869667	−	0.493638i	$-0.835667\pi$
$821$	−6.34040	−	35.9582i	−0.221282	−	1.25495i	0.648386	−	0.761312i	$-0.275444\pi$
$822$		0			0
$823$	26.6284	−	9.69196i	0.928209	−	0.337840i	0.166710	−	0.986006i	$-0.446686\pi$
$823$	26.6284	−	9.69196i	0.928209	−	0.337840i	0.761499	+	0.648166i	$0.224464\pi$
$824$		0			0
$825$	−42.1985	+	8.48657i	−1.46916	+	0.295464i
$826$		0			0
$827$	0.449708	−	0.778917i	0.0156379	−	0.0270856i	−0.858101	−	0.513482i	$-0.828355\pi$
$827$	0.449708	−	0.778917i	0.0156379	−	0.0270856i	0.873738	+	0.486396i	$0.161689\pi$
$828$		0			0
$829$	−4.89803	−	8.48364i	−0.170116	−	0.294649i	0.768344	−	0.640037i	$-0.221081\pi$
$829$	−4.89803	−	8.48364i	−0.170116	−	0.294649i	−0.938460	+	0.345387i	$0.887747\pi$
$830$		0			0
$831$	10.6248	+	5.79980i	0.368571	+	0.201193i
$832$		0			0
$833$	0.923636	+	0.775022i	0.0320021	+	0.0268529i
$834$		0			0
$835$	−13.9718	−	5.08533i	−0.483515	−	0.175985i
$836$		0			0
$837$	20.0709	+	44.8412i	0.693753	+	1.54994i
$838$		0			0
$839$	−18.0765	−	6.57930i	−0.624069	−	0.227143i	0.0105788	−	0.999944i	$-0.496633\pi$
$839$	−18.0765	−	6.57930i	−0.624069	−	0.227143i	−0.634648	+	0.772802i	$0.718855\pi$
$840$		0			0
$841$	1.35640	+	1.13815i	0.0467724	+	0.0392467i
$842$		0			0
$843$	42.7013	−	26.0354i	1.47071	−	0.896707i
$844$		0			0
$845$	5.44964	+	9.43906i	0.187473	+	0.324714i
$846$		0			0
$847$	16.2379	−	28.1248i	0.557940	−	0.966381i
$848$		0			0
$849$	−12.3876	−	14.0653i	−0.425141	−	0.482718i
$850$		0			0
$851$	14.7097	−	5.35388i	0.504241	−	0.183529i
$852$		0			0
$853$	−7.27991	−	41.2864i	−0.249259	−	1.41362i	−0.810389	−	0.585893i	$-0.800744\pi$
$853$	−7.27991	−	41.2864i	−0.249259	−	1.41362i	0.561129	−	0.827728i	$-0.310367\pi$
$854$		0			0
$855$	−1.87745	+	3.64408i	−0.0642074	+	0.124625i
$856$		0			0
$857$	14.4504	−	12.1253i	0.493615	−	0.414192i	−0.361705	−	0.932293i	$-0.617805\pi$
$857$	14.4504	−	12.1253i	0.493615	−	0.414192i	0.855320	+	0.518100i	$0.173361\pi$
$858$		0			0
$859$	4.40138	−	24.9615i	0.150173	−	0.851675i	−0.812894	−	0.582412i	$-0.802109\pi$
$859$	4.40138	−	24.9615i	0.150173	−	0.851675i	0.963067	−	0.269262i	$-0.0867799\pi$
$860$		0			0
$861$	12.3492	+	1.87401i	0.420860	+	0.0638662i
$862$		0			0
$863$	−9.80628			−0.333810			−0.166905	−	0.985973i	$-0.553377\pi$
$863$	−9.80628			−0.333810			−0.166905	+	0.985973i	$0.553377\pi$
$864$		0			0
$865$	19.9606			0.678682
$866$		0			0
$867$	−18.3237	+	22.9300i	−0.622305	+	0.778743i
$868$		0			0
$869$	7.51316	−	42.6092i	0.254866	−	1.44542i
$870$		0			0
$871$	−9.12800	+	7.65930i	−0.309291	+	0.259526i
$872$		0			0
$873$	37.0810	+	28.2050i	1.25500	+	0.954594i
$874$		0			0
$875$	1.92741	+	10.9309i	0.0651583	+	0.369531i
$876$		0			0
$877$	7.26345	−	2.64368i	0.245269	−	0.0892707i	−0.216460	−	0.976291i	$-0.569451\pi$
$877$	7.26345	−	2.64368i	0.245269	−	0.0892707i	0.461730	+	0.887021i	$0.347229\pi$
$878$		0			0
$879$	11.1842	−	33.1778i	0.377233	−	1.11906i
$880$		0			0
$881$	−17.1331	+	29.6754i	−0.577229	+	0.999790i	0.418567	+	0.908186i	$0.362533\pi$
$881$	−17.1331	+	29.6754i	−0.577229	+	0.999790i	−0.995796	+	0.0916038i	$0.970801\pi$
$882$		0			0
$883$	−15.6815	−	27.1612i	−0.527726	−	0.914048i	−0.999478	−	0.0323165i	$-0.989712\pi$
$883$	−15.6815	−	27.1612i	−0.527726	−	0.914048i	0.471752	−	0.881731i	$-0.343622\pi$
$884$		0			0
$885$	0.109165	+	4.56092i	0.00366955	+	0.153314i
$886$		0			0
$887$	21.7456	+	18.2467i	0.730146	+	0.612666i	0.930172	−	0.367125i	$-0.119658\pi$
$887$	21.7456	+	18.2467i	0.730146	+	0.612666i	−0.200025	+	0.979791i	$0.564102\pi$
$888$		0			0
$889$	−21.8642	−	7.95792i	−0.733302	−	0.266900i
$890$		0			0
$891$	53.1979	−	5.10780i	1.78220	−	0.171118i
$892$		0			0
$893$	−9.63633	−	3.50734i	−0.322468	−	0.117369i
$894$		0			0
$895$	−9.40452	−	7.89133i	−0.314358	−	0.263778i
$896$		0			0
$897$	−0.178566	−	7.46046i	−0.00596214	−	0.249098i
$898$		0			0
$899$	−26.2233	−	45.4200i	−0.874595	−	1.51484i
$900$		0			0
$901$	0.658779	−	1.14104i	0.0219471	−	0.0380135i
$902$		0			0
$903$	−6.30275	+	18.6971i	−0.209742	+	0.622199i
$904$		0			0
$905$	9.17709	−	3.34019i	0.305057	−	0.111032i
$906$		0			0
$907$	−1.70418	−	9.66486i	−0.0565862	−	0.320917i	0.943355	−	0.331786i	$-0.107651\pi$
$907$	−1.70418	−	9.66486i	−0.0565862	−	0.320917i	−0.999941	+	0.0108695i	$0.996540\pi$
$908$		0			0
$909$	−3.16508	+	24.8526i	−0.104979	+	0.824308i
$910$		0			0
$911$	−20.8958	+	17.5337i	−0.692309	+	0.580916i	−0.919574	−	0.392917i	$-0.871466\pi$
$911$	−20.8958	+	17.5337i	−0.692309	+	0.580916i	0.227265	+	0.973833i	$0.427022\pi$
$912$		0			0
$913$	−6.48622	+	36.7852i	−0.214663	+	1.21741i
$914$		0			0
$915$	13.0873	−	16.3772i	0.432653	−	0.541415i
$916$		0			0
$917$	3.29767			0.108899
$918$		0			0
$919$	15.0995			0.498088			0.249044	−	0.968492i	$-0.419884\pi$
$919$	15.0995			0.498088			0.249044	+	0.968492i	$0.419884\pi$
$920$		0			0
$921$	1.07683	+	0.163410i	0.0354827	+	0.00538456i
$922$		0			0
$923$	−2.52890	+	14.3421i	−0.0832398	+	0.472076i
$924$		0			0
$925$	11.2115	−	9.40755i	0.368631	−	0.309318i
$926$		0			0
$927$	−12.4670	−	19.3880i	−0.409471	−	0.636784i
$928$		0			0
$929$	−5.54702	−	31.4587i	−0.181992	−	1.03213i	−0.929760	−	0.368167i	$-0.879986\pi$
$929$	−5.54702	−	31.4587i	−0.181992	−	1.03213i	0.747768	−	0.663960i	$-0.231126\pi$
$930$		0			0
$931$	−7.40775	+	2.69620i	−0.242779	+	0.0883644i
$932$		0			0
$933$	−29.0614	−	32.9972i	−0.951427	−	1.08028i
$934$		0			0
$935$	0.620508	−	1.07475i	0.0202928	−	0.0351481i
$936$		0			0
$937$	−14.1774	−	24.5560i	−0.463155	−	0.802209i	0.535961	−	0.844243i	$-0.319949\pi$
$937$	−14.1774	−	24.5560i	−0.463155	−	0.802209i	−0.999116	+	0.0420343i	$0.986616\pi$
$938$		0			0
$939$	12.2600	−	7.47507i	0.400091	−	0.243940i
$940$		0			0
$941$	−39.0506	−	32.7674i	−1.27301	−	1.06819i	−0.994167	−	0.107850i	$-0.965603\pi$
$941$	−39.0506	−	32.7674i	−1.27301	−	1.06819i	−0.278847	−	0.960336i	$-0.589952\pi$
$942$		0			0
$943$	−22.6600	−	8.24756i	−0.737910	−	0.268577i
$944$		0			0
$945$	−0.450404	−	6.26302i	−0.0146516	−	0.203736i
$946$		0			0
$947$	−1.89505	−	0.689743i	−0.0615810	−	0.0224136i	0.311046	−	0.950395i	$-0.399321\pi$
$947$	−1.89505	−	0.689743i	−0.0615810	−	0.0224136i	−0.372627	+	0.927981i	$0.621543\pi$
$948$		0			0
$949$	4.17994	+	3.50738i	0.135686	+	0.113854i
$950$		0			0
$951$	−28.3276	−	15.4633i	−0.918586	−	0.501430i
$952$		0			0
$953$	−15.4955	−	26.8390i	−0.501949	−	0.869401i	−0.999997	−	0.00225177i	$-0.999283\pi$
$953$	−15.4955	−	26.8390i	−0.501949	−	0.869401i	0.498049	−	0.867149i	$-0.334050\pi$
$954$		0			0
$955$	−2.59220	+	4.48981i	−0.0838815	+	0.145287i
$956$		0			0
$957$	−55.9325	+	11.2486i	−1.80804	+	0.363616i
$958$		0			0
$959$	−1.74499	+	0.635126i	−0.0563488	+	0.0205093i
$960$		0			0
$961$	10.1396	+	57.5045i	0.327084	+	1.85498i
$962$		0			0
$963$	2.62454	−	2.42544i	0.0845746	−	0.0781586i
$964$		0			0
$965$	15.6328	−	13.1175i	0.503239	−	0.422268i
$966$		0			0
$967$	10.4311	−	59.1578i	0.335442	−	1.90239i	−0.0873838	−	0.996175i	$-0.527851\pi$
$967$	10.4311	−	59.1578i	0.335442	−	1.90239i	0.422826	−	0.906211i	$-0.361038\pi$
$968$		0			0
$969$	0.221176	+	0.565212i	0.00710518	+	0.0181572i
$970$		0			0
$971$	−29.2112			−0.937432			−0.468716	−	0.883349i	$-0.655283\pi$
$971$	−29.2112			−0.937432			−0.468716	+	0.883349i	$0.655283\pi$
$972$		0			0
$973$	10.6094			0.340122
$974$		0			0
$975$	−2.54255	−	6.49746i	−0.0814267	−	0.208085i
$976$		0			0
$977$	−2.69531	+	15.2859i	−0.0862306	+	0.489038i	0.910854	+	0.412730i	$0.135425\pi$
$977$	−2.69531	+	15.2859i	−0.0862306	+	0.489038i	−0.997084	+	0.0763087i	$0.975687\pi$
$978$		0			0
$979$	−66.2878	+	55.6221i	−2.11857	+	1.77769i
$980$		0			0
$981$	3.06147	−	2.82922i	0.0977453	−	0.0903302i
$982$		0			0
$983$	0.487009	+	2.76196i	0.0155332	+	0.0880929i	0.991589	−	0.129428i	$-0.0413141\pi$
$983$	0.487009	+	2.76196i	0.0155332	+	0.0880929i	−0.976056	+	0.217521i	$0.930203\pi$
$984$		0			0
$985$	4.10939	−	1.49570i	0.130936	−	0.0476569i
$986$		0			0
$987$	15.3997	−	3.09705i	0.490178	−	0.0985801i
$988$		0			0
$989$	19.0461	−	32.9888i	0.605630	−	1.04898i
$990$		0			0
$991$	24.3849	+	42.2360i	0.774613	+	1.34167i	0.935011	+	0.354617i	$0.115389\pi$
$991$	24.3849	+	42.2360i	0.774613	+	1.34167i	−0.160398	+	0.987052i	$0.551278\pi$
$992$		0			0
$993$	23.6702	+	12.9209i	0.751150	+	0.410032i
$994$		0			0
$995$	6.95596	+	5.83674i	0.220519	+	0.185037i
$996$		0			0
$997$	34.9059	+	12.7047i	1.10548	+	0.402362i	0.829334	−	0.558753i	$-0.188720\pi$
$997$	34.9059	+	12.7047i	1.10548	+	0.402362i	0.276147	+	0.961115i	$0.410942\pi$
$998$		0			0
$999$	−15.0447	+	10.1911i	−0.475993	+	0.322433i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.f.193.4		30
4.3	odd	2		216.2.q.b.193.2	yes	30
12.11	even	2		648.2.q.b.145.2		30
27.7	even	9	inner	432.2.u.f.385.4		30
108.7	odd	18		216.2.q.b.169.2	✓	30
108.47	even	18		648.2.q.b.505.2		30
108.67	odd	18		5832.2.a.k.1.10		15
108.95	even	18		5832.2.a.l.1.6		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.b.169.2	✓	30	108.7	odd	18
216.2.q.b.193.2	yes	30	4.3	odd	2
432.2.u.f.193.4		30	1.1	even	1	trivial
432.2.u.f.385.4		30	27.7	even	9	inner
648.2.q.b.145.2		30	12.11	even	2
648.2.q.b.505.2		30	108.47	even	18
5832.2.a.k.1.10		15	108.67	odd	18
5832.2.a.l.1.6		15	108.95	even	18

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.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.631172 + 1.61295i) q^{3} +(0.156760 - 0.889029i) q^{5} +(-1.02544 + 0.860449i) q^{7} +(-2.20324 + 2.03610i) q^{9} +O(q^{10})\)	\(q+(0.631172 + 1.61295i) q^{3} +(0.156760 - 0.889029i) q^{5} +(-1.02544 + 0.860449i) q^{7} +(-2.20324 + 2.03610i) q^{9} +(1.03113 + 5.84785i) q^{11} +(-0.904496 + 0.329210i) q^{13} +(1.53291 - 0.308284i) q^{15} +(0.115754 - 0.200493i) q^{17} +(0.756818 + 1.31085i) q^{19} +(-2.03510 - 1.11090i) q^{21} +(3.42896 + 2.87724i) q^{23} +(3.93266 + 1.43137i) q^{25} +(-4.67477 - 2.26860i) q^{27} +(5.21260 + 1.89723i) q^{29} +(-7.24273 - 6.07737i) q^{31} +(-8.78150 + 5.35417i) q^{33} +(0.604216 + 1.04653i) q^{35} +(1.74855 - 3.02858i) q^{37} +(-1.10189 - 1.25112i) q^{39} +(-5.06233 + 1.84254i) q^{41} +(-1.47774 - 8.38066i) q^{43} +(1.46478 + 2.27793i) q^{45} +(-5.18989 + 4.35484i) q^{47} +(-0.904376 + 5.12897i) q^{49} +(0.396446 + 0.0601614i) q^{51} +5.69117 q^{53} +5.36055 q^{55} +(-1.63666 + 2.04808i) q^{57} +(-0.506665 + 2.87344i) q^{59} +(10.2708 - 8.61822i) q^{61} +(0.507339 - 3.98369i) q^{63} +(0.150888 + 0.855730i) q^{65} +(11.6329 - 4.23402i) q^{67} +(-2.47659 + 7.34679i) q^{69} +(7.56504 - 13.1030i) q^{71} +(-2.83442 - 4.90937i) q^{73} +(0.173448 + 7.24665i) q^{75} +(-6.08915 - 5.10940i) q^{77} +(-6.84689 - 2.49206i) q^{79} +(0.708568 - 8.97206i) q^{81} +(5.91102 + 2.15143i) q^{83} +(-0.160098 - 0.134338i) q^{85} +(0.229899 + 9.60516i) q^{87} +(7.28626 + 12.6202i) q^{89} +(0.644241 - 1.11586i) q^{91} +(5.23112 - 15.5181i) q^{93} +(1.28402 - 0.467345i) q^{95} +(-2.69669 - 15.2937i) q^{97} +(-14.1787 - 10.7848i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{7} - 6 q^{9}+O(q^{10}) \) 30 * q - 3 * q^7 - 6 * q^9	\( 30 q - 3 q^{7} - 6 q^{9} + 3 q^{11} - 12 q^{13} - 15 q^{15} + 6 q^{17} + 9 q^{19} + 30 q^{21} + 12 q^{23} + 24 q^{25} + 15 q^{27} - 9 q^{29} - 27 q^{31} - 30 q^{33} + 18 q^{35} - 15 q^{37} + 21 q^{39} - 15 q^{41} + 30 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{49} + 6 q^{51} - 18 q^{53} - 54 q^{55} - 72 q^{57} + 12 q^{59} + 6 q^{61} + 54 q^{63} - 54 q^{65} + 45 q^{67} + 9 q^{69} - 36 q^{73} - 69 q^{75} + 12 q^{77} - 45 q^{79} - 30 q^{81} + 3 q^{83} + 57 q^{85} + 60 q^{87} + 36 q^{89} + 39 q^{91} + 30 q^{93} - 51 q^{95} - 84 q^{97} - 162 q^{99}+O(q^{100}) \) 30 * q - 3 * q^7 - 6 * q^9 + 3 * q^11 - 12 * q^13 - 15 * q^15 + 6 * q^17 + 9 * q^19 + 30 * q^21 + 12 * q^23 + 24 * q^25 + 15 * q^27 - 9 * q^29 - 27 * q^31 - 30 * q^33 + 18 * q^35 - 15 * q^37 + 21 * q^39 - 15 * q^41 + 30 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^49 + 6 * q^51 - 18 * q^53 - 54 * q^55 - 72 * q^57 + 12 * q^59 + 6 * q^61 + 54 * q^63 - 54 * q^65 + 45 * q^67 + 9 * q^69 - 36 * q^73 - 69 * q^75 + 12 * q^77 - 45 * q^79 - 30 * q^81 + 3 * q^83 + 57 * q^85 + 60 * q^87 + 36 * q^89 + 39 * q^91 + 30 * q^93 - 51 * q^95 - 84 * q^97 - 162 * q^99

Introduction

L-functions

Modular forms

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Database

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