LMFDB - Embedded newform 432.2.be.a.191.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(47,432)]

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([9, 0, 7]))

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

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

chi := DirichletCharacter("432.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.be (of order $18$, degree $6$, 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:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			191.3
Character	$\chi$	$=$	432.191
Dual form			432.2.be.a.95.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573329 + 1.63441i) q^{3} +(2.37464 + 2.82999i) q^{5} +(1.65095 + 4.53595i) q^{7} +(-2.34259 - 1.87411i) q^{9} +O(q^{10})$	\(q+(-0.573329 + 1.63441i) q^{3} +(2.37464 + 2.82999i) q^{5} +(1.65095 + 4.53595i) q^{7} +(-2.34259 - 1.87411i) q^{9} +(-1.42517 - 1.19586i) q^{11} +(-0.547976 - 3.10773i) q^{13} +(-5.98681 + 2.25862i) q^{15} +(4.94276 - 2.85370i) q^{17} +(-4.12046 - 2.37895i) q^{19} +(-8.36014 + 0.0977383i) q^{21} +(2.05907 + 0.749439i) q^{23} +(-1.50167 + 8.51639i) q^{25} +(4.40613 - 2.75427i) q^{27} +(-1.39301 - 0.245625i) q^{29} +(0.634435 - 1.74310i) q^{31} +(2.77162 - 1.64369i) q^{33} +(-8.91627 + 15.4434i) q^{35} +(2.01876 + 3.49659i) q^{37} +(5.39347 + 0.886132i) q^{39} +(2.96851 - 0.523429i) q^{41} +(-4.32602 + 5.15555i) q^{43} +(-0.259104 - 11.0798i) q^{45} +(6.36875 - 2.31804i) q^{47} +(-12.4869 + 10.4777i) q^{49} +(1.83029 + 9.71459i) q^{51} -3.09898i q^{53} -6.87297i q^{55} +(6.25055 - 5.37060i) q^{57} +(6.96871 - 5.84744i) q^{59} +(-2.99167 + 1.08888i) q^{61} +(4.63336 - 13.7199i) q^{63} +(7.49359 - 8.93051i) q^{65} +(-3.41454 + 0.602076i) q^{67} +(-2.40541 + 2.93568i) q^{69} +(-6.15069 - 10.6533i) q^{71} +(-3.95392 + 6.84839i) q^{73} +(-13.0583 - 7.33704i) q^{75} +(3.07148 - 8.43882i) q^{77} +(12.7241 + 2.24360i) q^{79} +(1.97544 + 8.78053i) q^{81} +(0.606931 - 3.44208i) q^{83} +(19.8132 + 7.21142i) q^{85} +(1.20010 - 2.13592i) q^{87} +(8.76278 + 5.05919i) q^{89} +(13.1918 - 7.61630i) q^{91} +(2.48519 + 2.03629i) q^{93} +(-3.05222 - 17.3100i) q^{95} +(0.536739 + 0.450377i) q^{97} +(1.09742 + 5.47234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{5} - 12 q^{9}+O(q^{10}) $ 36 * q - 6 * q^5 - 12 * q^9	$ 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97}+O(q^{100}) $ 36 * q - 6 * q^5 - 12 * q^9 - 36 * q^21 + 18 * q^25 - 24 * q^29 - 36 * q^33 - 18 * q^41 - 18 * q^45 + 42 * q^65 + 54 * q^69 - 18 * q^73 + 90 * q^77 + 36 * q^81 + 72 * q^85 + 72 * q^89 + 54 * q^93 + 54 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{18}\right)$

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
$3$	−0.573329	+	1.63441i	−0.331012	+	0.943627i
$3$	−0.573329	+	1.63441i	−0.331012	+	0.943627i
$4$		0			0
$5$	2.37464	+	2.82999i	1.06197	+	1.26561i	0.962706	+	0.270549i	$0.0872052\pi$
$5$	2.37464	+	2.82999i	1.06197	+	1.26561i	0.0992664	+	0.995061i	$0.468350\pi$
$6$		0			0
$7$	1.65095	+	4.53595i	0.624001	+	1.71443i	0.696976	+	0.717094i	$0.254528\pi$
$7$	1.65095	+	4.53595i	0.624001	+	1.71443i	−0.0729754	+	0.997334i	$0.523249\pi$
$8$		0			0
$9$	−2.34259	−	1.87411i	−0.780863	−	0.624703i
$10$		0			0
$11$	−1.42517	−	1.19586i	−0.429706	−	0.360566i	0.402135	−	0.915580i	$-0.368268\pi$
$11$	−1.42517	−	1.19586i	−0.429706	−	0.360566i	−0.831841	+	0.555015i	$0.812713\pi$
$12$		0			0
$13$	−0.547976	−	3.10773i	−0.151981	−	0.861928i	−0.961494	−	0.274826i	$-0.911380\pi$
$13$	−0.547976	−	3.10773i	−0.151981	−	0.861928i	0.809513	−	0.587102i	$-0.199731\pi$
$14$		0			0
$15$	−5.98681	+	2.25862i	−1.54579	+	0.583174i
$16$		0			0
$17$	4.94276	−	2.85370i	1.19879	−	0.692124i	0.238508	−	0.971141i	$-0.423342\pi$
$17$	4.94276	−	2.85370i	1.19879	−	0.692124i	0.960286	+	0.279016i	$0.0900084\pi$
$18$		0			0
$19$	−4.12046	−	2.37895i	−0.945298	−	0.545768i	−0.0536810	−	0.998558i	$-0.517095\pi$
$19$	−4.12046	−	2.37895i	−0.945298	−	0.545768i	−0.891617	+	0.452790i	$0.850429\pi$
$20$		0			0
$21$	−8.36014	+	0.0977383i	−1.82433	+	0.0213283i
$22$		0			0
$23$	2.05907	+	0.749439i	0.429345	+	0.156269i	0.547648	−	0.836709i	$-0.315523\pi$
$23$	2.05907	+	0.749439i	0.429345	+	0.156269i	−0.118303	+	0.992978i	$0.537745\pi$
$24$		0			0
$25$	−1.50167	+	8.51639i	−0.300334	+	1.70328i
$26$		0			0
$27$	4.40613	−	2.75427i	0.847961	−	0.530059i
$28$		0			0
$29$	−1.39301	−	0.245625i	−0.258675	−	0.0456114i	0.0428066	−	0.999083i	$-0.486370\pi$
$29$	−1.39301	−	0.245625i	−0.258675	−	0.0456114i	−0.301482	+	0.953472i	$0.597481\pi$
$30$		0			0
$31$	0.634435	−	1.74310i	0.113948	−	0.313069i	−0.869589	−	0.493776i	$-0.835616\pi$
$31$	0.634435	−	1.74310i	0.113948	−	0.313069i	0.983537	+	0.180707i	$0.0578385\pi$
$32$		0			0
$33$	2.77162	−	1.64369i	0.482477	−	0.286130i
$34$		0			0
$35$	−8.91627	+	15.4434i	−1.50713	+	2.61042i
$36$		0			0
$37$	2.01876	+	3.49659i	0.331882	+	0.574836i	0.982881	−	0.184242i	$-0.0589831\pi$
$37$	2.01876	+	3.49659i	0.331882	+	0.574836i	−0.650999	+	0.759079i	$0.725650\pi$
$38$		0			0
$39$	5.39347	+	0.886132i	0.863646	+	0.141895i
$40$		0			0
$41$	2.96851	−	0.523429i	0.463604	−	0.0817459i	0.0630326	−	0.998011i	$-0.479923\pi$
$41$	2.96851	−	0.523429i	0.463604	−	0.0817459i	0.400571	+	0.916266i	$0.368812\pi$
$42$		0			0
$43$	−4.32602	+	5.15555i	−0.659711	+	0.786213i	−0.987344	−	0.158592i	$-0.949305\pi$
$43$	−4.32602	+	5.15555i	−0.659711	+	0.786213i	0.327633	+	0.944805i	$0.393749\pi$
$44$		0			0
$45$	−0.259104	−	11.0798i	−0.0386250	−	1.65168i
$46$		0			0
$47$	6.36875	−	2.31804i	0.928978	−	0.338120i	0.167174	−	0.985927i	$-0.446536\pi$
$47$	6.36875	−	2.31804i	0.928978	−	0.338120i	0.761804	+	0.647807i	$0.224314\pi$
$48$		0			0
$49$	−12.4869	+	10.4777i	−1.78384	+	1.49682i
$50$		0			0
$51$	1.83029	+	9.71459i	0.256292	+	1.36032i
$52$		0			0
$53$		−	3.09898i		−	0.425677i	−0.977087	−	0.212839i	$-0.931729\pi$
$53$		−	3.09898i		−	0.425677i	0.977087	−	0.212839i	$-0.0682709\pi$
$54$		0			0
$55$		−	6.87297i		−	0.926750i
$56$		0			0
$57$	6.25055	−	5.37060i	0.827906	−	0.711353i
$58$		0			0
$59$	6.96871	−	5.84744i	0.907248	−	0.761272i	−0.0643451	−	0.997928i	$-0.520496\pi$
$59$	6.96871	−	5.84744i	0.907248	−	0.761272i	0.971594	+	0.236656i	$0.0760514\pi$
$60$		0			0
$61$	−2.99167	+	1.08888i	−0.383044	+	0.139417i	−0.526363	−	0.850260i	$-0.676445\pi$
$61$	−2.99167	+	1.08888i	−0.383044	+	0.139417i	0.143319	+	0.989677i	$0.454223\pi$
$62$		0			0
$63$	4.63336	−	13.7199i	0.583749	−	1.72855i
$64$		0			0
$65$	7.49359	−	8.93051i	0.929465	−	1.10769i
$66$		0			0
$67$	−3.41454	+	0.602076i	−0.417153	+	0.0735553i	−0.378285	−	0.925689i	$-0.623486\pi$
$67$	−3.41454	+	0.602076i	−0.417153	+	0.0735553i	−0.0388676	+	0.999244i	$0.512375\pi$
$68$		0			0
$69$	−2.40541	+	2.93568i	−0.289578	+	0.353415i
$70$		0			0
$71$	−6.15069	−	10.6533i	−0.729953	−	1.26431i	−0.956903	−	0.290409i	$-0.906209\pi$
$71$	−6.15069	−	10.6533i	−0.729953	−	1.26431i	0.226950	−	0.973906i	$-0.427125\pi$
$72$		0			0
$73$	−3.95392	+	6.84839i	−0.462771	+	0.801543i	−0.999098	−	0.0424675i	$-0.986478\pi$
$73$	−3.95392	+	6.84839i	−0.462771	+	0.801543i	0.536327	+	0.844010i	$0.319811\pi$
$74$		0			0
$75$	−13.0583	−	7.33704i	−1.50784	−	0.847208i
$76$		0			0
$77$	3.07148	−	8.43882i	0.350027	−	0.961693i
$78$		0			0
$79$	12.7241	+	2.24360i	1.43157	+	0.252425i	0.835051	−	0.550173i	$-0.185438\pi$
$79$	12.7241	+	2.24360i	1.43157	+	0.252425i	0.596521	+	0.802598i	$0.296549\pi$
$80$		0			0
$81$	1.97544	+	8.78053i	0.219493	+	0.975614i
$82$		0			0
$83$	0.606931	−	3.44208i	0.0666193	−	0.377817i	−0.933210	−	0.359332i	$-0.883005\pi$
$83$	0.606931	−	3.44208i	0.0666193	−	0.377817i	0.999829	−	0.0184850i	$-0.00588431\pi$
$84$		0			0
$85$	19.8132	+	7.21142i	2.14905	+	0.782189i
$86$		0			0
$87$	1.20010	−	2.13592i	0.128665	−	0.228995i
$88$		0			0
$89$	8.76278	+	5.05919i	0.928853	+	0.536273i	0.886448	−	0.462827i	$-0.153165\pi$
$89$	8.76278	+	5.05919i	0.928853	+	0.536273i	0.0424041	+	0.999101i	$0.486498\pi$
$90$		0			0
$91$	13.1918	−	7.61630i	1.38288	−	0.798405i
$92$		0			0
$93$	2.48519	+	2.03629i	0.257702	+	0.211154i
$94$		0			0
$95$	−3.05222	−	17.3100i	−0.313151	−	1.77597i
$96$		0			0
$97$	0.536739	+	0.450377i	0.0544976	+	0.0457289i	0.669630	−	0.742695i	$-0.266453\pi$
$97$	0.536739	+	0.450377i	0.0544976	+	0.0457289i	−0.615132	+	0.788424i	$0.710897\pi$
$98$		0			0
$99$	1.09742	+	5.47234i	0.110295	+	0.549991i
$100$		0			0
$101$	5.49484	+	15.0969i	0.546757	+	1.50220i	0.838064	+	0.545572i	$0.183688\pi$
$101$	5.49484	+	15.0969i	0.546757	+	1.50220i	−0.291307	+	0.956630i	$0.594090\pi$
$102$		0			0
$103$	−8.19836	−	9.77043i	−0.807808	−	0.962709i	0.192017	−	0.981392i	$-0.438497\pi$
$103$	−8.19836	−	9.77043i	−0.807808	−	0.962709i	−0.999825	+	0.0186829i	$0.994053\pi$
$104$		0			0
$105$	−20.1289	−	23.4270i	−1.96438	−	2.28624i
$106$		0			0
$107$	8.37346			0.809493			0.404747	−	0.914429i	$-0.367360\pi$
$107$	8.37346			0.809493			0.404747	+	0.914429i	$0.367360\pi$
$108$		0			0
$109$	−9.09331			−0.870981			−0.435491	−	0.900193i	$-0.643425\pi$
$109$	−9.09331			−0.870981			−0.435491	+	0.900193i	$0.643425\pi$
$110$		0			0
$111$	−6.87228	+	1.29478i	−0.652288	+	0.122895i
$112$		0			0
$113$	−2.29677	−	2.73719i	−0.216062	−	0.257493i	0.647117	−	0.762391i	$-0.275975\pi$
$113$	−2.29677	−	2.73719i	−0.216062	−	0.257493i	−0.863179	+	0.504898i	$0.831530\pi$
$114$		0			0
$115$	2.76864	+	7.60679i	0.258177	+	0.709336i
$116$		0			0
$117$	−4.54053	+	8.30709i	−0.419773	+	0.767991i
$118$		0			0
$119$	21.1045	+	17.7088i	1.93465	+	1.62336i
$120$		0			0
$121$	−1.30910	−	7.42427i	−0.119009	−	0.674934i
$122$		0			0
$123$	−0.846437	+	5.15186i	−0.0763207	+	0.464528i
$124$		0			0
$125$	−11.6705	+	6.73796i	−1.04384	+	0.602661i
$126$		0			0
$127$	4.83978	+	2.79425i	0.429461	+	0.247949i	0.699117	−	0.715007i	$-0.253577\pi$
$127$	4.83978	+	2.79425i	0.429461	+	0.247949i	−0.269656	+	0.962957i	$0.586910\pi$
$128$		0			0
$129$	−5.94604	−	10.0263i	−0.523520	−	0.882767i
$130$		0			0
$131$	−20.9936	−	7.64103i	−1.83422	−	0.667600i	−0.991642	−	0.129020i	$-0.958817\pi$
$131$	−20.9936	−	7.64103i	−1.83422	−	0.667600i	−0.842574	−	0.538580i	$-0.818961\pi$
$132$		0			0
$133$	3.98812	−	22.6177i	0.345813	−	1.96121i
$134$		0			0
$135$	18.2575	+	5.92891i	1.57136	+	0.510279i
$136$		0			0
$137$	2.03860	+	0.359460i	0.174169	+	0.0307108i	0.260053	−	0.965594i	$-0.416260\pi$
$137$	2.03860	+	0.359460i	0.174169	+	0.0307108i	−0.0858832	+	0.996305i	$0.527371\pi$
$138$		0			0
$139$	−5.43218	+	14.9248i	−0.460751	+	1.26590i	0.464170	+	0.885746i	$0.346353\pi$
$139$	−5.43218	+	14.9248i	−0.460751	+	1.26590i	−0.924922	+	0.380158i	$0.875870\pi$
$140$		0			0
$141$	0.137231	+	11.7381i	0.0115569	+	0.988530i
$142$		0			0
$143$	−2.93545	+	5.08435i	−0.245475	+	0.425175i
$144$		0			0
$145$	−2.61278	−	4.52547i	−0.216980	−	0.375820i
$146$		0			0
$147$	−9.96583	−	26.4159i	−0.821968	−	2.17875i
$148$		0			0
$149$	0.0121528	−	0.00214287i	0.000995597	−	0.000175551i	−0.173150	−	0.984895i	$-0.555395\pi$
$149$	0.0121528	−	0.00214287i	0.000995597	−	0.000175551i	0.174146	+	0.984720i	$0.444284\pi$
$150$		0			0
$151$	9.33895	−	11.1297i	0.759993	−	0.905724i	−0.237855	−	0.971301i	$-0.576444\pi$
$151$	9.33895	−	11.1297i	0.759993	−	0.905724i	0.997848	+	0.0655768i	$0.0208887\pi$
$152$		0			0
$153$	−16.9270	−	2.57821i	−1.36847	−	0.208436i
$154$		0			0
$155$	6.43950	−	2.34379i	0.517233	−	0.188257i
$156$		0			0
$157$	−3.89430	+	3.26770i	−0.310799	+	0.260791i	−0.784822	−	0.619721i	$-0.787246\pi$
$157$	−3.89430	+	3.26770i	−0.310799	+	0.260791i	0.474023	+	0.880512i	$0.342801\pi$
$158$		0			0
$159$	5.06500	+	1.77673i	0.401681	+	0.140904i
$160$		0			0
$161$			10.5771i			0.833593i
$162$		0			0
$163$		−	13.0371i		−	1.02115i	−0.859835	−	0.510573i	$-0.829433\pi$
$163$		−	13.0371i		−	1.02115i	0.859835	−	0.510573i	$-0.170567\pi$
$164$		0			0
$165$	11.2332	+	3.94047i	0.874506	+	0.306765i
$166$		0			0
$167$	−8.81147	+	7.39370i	−0.681852	+	0.572142i	−0.916547	−	0.399927i	$-0.869035\pi$
$167$	−8.81147	+	7.39370i	−0.681852	+	0.572142i	0.234695	+	0.972069i	$0.424591\pi$
$168$		0			0
$169$	2.85831	−	1.04034i	0.219870	−	0.0800263i
$170$		0			0
$171$	5.19413	+	13.2951i	0.397205	+	1.01670i
$172$		0			0
$173$	9.56938	−	11.4043i	0.727546	−	0.867056i	−0.267794	−	0.963476i	$-0.586295\pi$
$173$	9.56938	−	11.4043i	0.727546	−	0.867056i	0.995341	+	0.0964201i	$0.0307392\pi$
$174$		0			0
$175$	−41.1091	+	7.24864i	−3.10756	+	0.547946i
$176$		0			0
$177$	5.56175	+	14.7422i	0.418047	+	1.10809i
$178$		0			0
$179$	4.27899	+	7.41142i	0.319827	+	0.553956i	0.980452	−	0.196760i	$-0.0630420\pi$
$179$	4.27899	+	7.41142i	0.319827	+	0.553956i	−0.660625	+	0.750716i	$0.729709\pi$
$180$		0			0
$181$	3.37390	−	5.84376i	0.250780	−	0.434363i	−0.712961	−	0.701204i	$-0.752646\pi$
$181$	3.37390	−	5.84376i	0.250780	−	0.434363i	0.963741	+	0.266840i	$0.0859796\pi$
$182$		0			0
$183$	−0.0644630	−	5.51390i	−0.00476524	−	0.407599i
$184$		0			0
$185$	−5.10149	+	14.0162i	−0.375069	+	1.03049i
$186$		0			0
$187$	−10.4569	−	1.84383i	−0.764685	−	0.134835i
$188$		0			0
$189$	19.7675	+	15.4388i	1.43788	+	1.12301i
$190$		0			0
$191$	−3.35224	+	19.0115i	−0.242560	+	1.37562i	0.583532	+	0.812090i	$0.301670\pi$
$191$	−3.35224	+	19.0115i	−0.242560	+	1.37562i	−0.826092	+	0.563535i	$0.809441\pi$
$192$		0			0
$193$	3.09626	+	1.12695i	0.222873	+	0.0811193i	0.451043	−	0.892502i	$-0.351052\pi$
$193$	3.09626	+	1.12695i	0.222873	+	0.0811193i	−0.228170	+	0.973621i	$0.573274\pi$
$194$		0			0
$195$	10.2998	+	17.3677i	0.737585	+	1.24373i
$196$		0			0
$197$	−17.1401	−	9.89582i	−1.22118	−	0.705048i	−0.256009	−	0.966674i	$-0.582408\pi$
$197$	−17.1401	−	9.89582i	−1.22118	−	0.705048i	−0.965169	+	0.261626i	$0.915741\pi$
$198$		0			0
$199$	9.91625	−	5.72515i	0.702944	−	0.405845i	−0.105499	−	0.994419i	$-0.533644\pi$
$199$	9.91625	−	5.72515i	0.702944	−	0.405845i	0.808443	+	0.588574i	$0.200311\pi$
$200$		0			0
$201$	0.973618	−	5.92595i	0.0686737	−	0.417984i
$202$		0			0
$203$	−1.18564	−	6.72413i	−0.0832160	−	0.471941i
$204$		0			0
$205$	8.53046	+	7.15790i	0.595793	+	0.499930i
$206$		0			0
$207$	−3.41901	−	5.61454i	−0.237638	−	0.390237i
$208$		0			0
$209$	3.02747	+	8.31791i	0.209415	+	0.575362i
$210$		0			0
$211$	−2.02336	−	2.41135i	−0.139294	−	0.166004i	0.691887	−	0.722005i	$-0.256779\pi$
$211$	−2.02336	−	2.41135i	−0.139294	−	0.166004i	−0.831181	+	0.556001i	$0.812335\pi$
$212$		0			0
$213$	20.9382	−	3.94490i	1.43466	−	0.270300i
$214$		0			0
$215$	−24.8629			−1.69563
$216$		0			0
$217$	8.95401			0.607838
$218$		0			0
$219$	−8.92617	−	10.3887i	−0.603175	−	0.702003i
$220$		0			0
$221$	−11.5770	−	13.7970i	−0.778756	−	0.928085i
$222$		0			0
$223$	4.77636	+	13.1229i	0.319849	+	0.878777i	0.990563	+	0.137061i	$0.0437656\pi$
$223$	4.77636	+	13.1229i	0.319849	+	0.878777i	−0.670714	+	0.741716i	$0.734012\pi$
$224$		0			0
$225$	19.4784	−	17.1361i	1.29856	−	1.14241i
$226$		0			0
$227$	8.05793	+	6.76141i	0.534824	+	0.448770i	0.869763	−	0.493469i	$-0.164271\pi$
$227$	8.05793	+	6.76141i	0.534824	+	0.448770i	−0.334940	+	0.942240i	$0.608716\pi$
$228$		0			0
$229$	−3.38255	−	19.1834i	−0.223525	−	1.26768i	−0.865484	−	0.500936i	$-0.832989\pi$
$229$	−3.38255	−	19.1834i	−0.223525	−	1.26768i	0.641959	−	0.766739i	$-0.278122\pi$
$230$		0			0
$231$	12.0315	+	9.85827i	0.791616	+	0.648627i
$232$		0			0
$233$	11.4956	−	6.63697i	0.753099	−	0.434802i	−0.0737134	−	0.997279i	$-0.523485\pi$
$233$	11.4956	−	6.63697i	0.753099	−	0.434802i	0.826813	+	0.562477i	$0.190152\pi$
$234$		0			0
$235$	21.6835	+	12.5190i	1.41448	+	0.816649i
$236$		0			0
$237$	−10.9620	+	19.5100i	−0.712061	+	1.26731i
$238$		0			0
$239$	0.990737	+	0.360599i	0.0640854	+	0.0233252i	0.373864	−	0.927484i	$-0.378033\pi$
$239$	0.990737	+	0.360599i	0.0640854	+	0.0233252i	−0.309779	+	0.950809i	$0.600255\pi$
$240$		0			0
$241$	−3.42363	+	19.4164i	−0.220535	+	1.25072i	0.650503	+	0.759503i	$0.274558\pi$
$241$	−3.42363	+	19.4164i	−0.220535	+	1.25072i	−0.871039	+	0.491214i	$0.836553\pi$
$242$		0			0
$243$	−15.4836	−	1.80546i	−0.993270	−	0.115820i
$244$		0			0
$245$	−59.3038	−	10.4569i	−3.78878	−	0.668065i
$246$		0			0
$247$	−5.13521	+	14.1089i	−0.326746	+	0.897726i
$248$		0			0
$249$	5.27779	+	2.96542i	0.334466	+	0.187926i
$250$		0			0
$251$	−0.0488134	+	0.0845473i	−0.00308107	+	0.00533658i	−0.867562	−	0.497329i	$-0.834314\pi$
$251$	−0.0488134	+	0.0845473i	−0.00308107	+	0.00533658i	0.864481	+	0.502666i	$0.167647\pi$
$252$		0			0
$253$	−2.03830	−	3.53044i	−0.128147	−	0.221957i
$254$		0			0
$255$	−23.1459	+	28.2484i	−1.44945	+	1.76898i
$256$		0			0
$257$	0.343995	−	0.0606556i	0.0214578	−	0.00378359i	−0.162909	−	0.986641i	$-0.552088\pi$
$257$	0.343995	−	0.0606556i	0.0214578	−	0.00378359i	0.184367	+	0.982858i	$0.440977\pi$
$258$		0			0
$259$	−12.5275	+	14.9297i	−0.778421	+	0.927686i
$260$		0			0
$261$	2.80291	+	3.18604i	0.173496	+	0.197211i
$262$		0			0
$263$	10.5968	−	3.85692i	0.653427	−	0.237828i	0.00603076	−	0.999982i	$-0.498080\pi$
$263$	10.5968	−	3.85692i	0.653427	−	0.237828i	0.647396	+	0.762154i	$0.275858\pi$
$264$		0			0
$265$	8.77008	−	7.35897i	0.538742	−	0.452058i
$266$		0			0
$267$	−13.2927	+	11.4214i	−0.813503	+	0.698977i
$268$		0			0
$269$		−	12.4872i		−	0.761358i	−0.924707	−	0.380679i	$-0.875690\pi$
$269$		−	12.4872i		−	0.761358i	0.924707	−	0.380679i	$-0.124310\pi$
$270$		0			0
$271$		−	5.62766i		−	0.341856i	−0.985284	−	0.170928i	$-0.945323\pi$
$271$		−	5.62766i		−	0.341856i	0.985284	−	0.170928i	$-0.0546765\pi$
$272$		0			0
$273$	4.88490	+	25.9275i	0.295648	+	1.56920i
$274$		0			0
$275$	12.3246	−	10.3415i	0.743199	−	0.623618i
$276$		0			0
$277$	−5.69447	+	2.07262i	−0.342148	+	0.124532i	−0.507378	−	0.861723i	$-0.669385\pi$
$277$	−5.69447	+	2.07262i	−0.342148	+	0.124532i	0.165231	+	0.986255i	$0.447163\pi$
$278$		0			0
$279$	−4.75297	+	2.89435i	−0.284553	+	0.173280i
$280$		0			0
$281$	−0.792494	+	0.944457i	−0.0472762	+	0.0563416i	−0.789164	−	0.614182i	$-0.789486\pi$
$281$	−0.792494	+	0.944457i	−0.0472762	+	0.0563416i	0.741888	+	0.670524i	$0.233931\pi$
$282$		0			0
$283$	16.7598	−	2.95521i	0.996270	−	0.175669i	0.348339	−	0.937369i	$-0.386746\pi$
$283$	16.7598	−	2.95521i	0.996270	−	0.175669i	0.647931	+	0.761699i	$0.275635\pi$
$284$		0			0
$285$	30.0416	+	4.93575i	1.77951	+	0.292369i
$286$		0			0
$287$	7.27512	+	12.6009i	0.429437	+	0.743806i
$288$		0			0
$289$	7.78722	−	13.4879i	0.458072	−	0.793403i
$290$		0			0
$291$	−1.04383	+	0.619037i	−0.0611903	+	0.0362886i
$292$		0			0
$293$	−7.16622	+	19.6890i	−0.418655	+	1.15025i	0.533812	+	0.845603i	$0.320759\pi$
$293$	−7.16622	+	19.6890i	−0.418655	+	1.15025i	−0.952467	+	0.304642i	$0.901463\pi$
$294$		0			0
$295$	33.0964	+	5.83579i	1.92695	+	0.339773i
$296$		0			0
$297$	−9.57322	−	1.34382i	−0.555495	−	0.0779763i
$298$		0			0
$299$	1.20073	−	6.80969i	0.0694401	−	0.393815i
$300$		0			0
$301$	−30.5273	−	11.1110i	−1.75957	−	0.640430i
$302$		0			0
$303$	−27.8249	+	0.325301i	−1.59850	+	0.0186881i
$304$		0			0
$305$	−10.1857	−	5.88070i	−0.583230	−	0.336728i
$306$		0			0
$307$	−13.2034	+	7.62299i	−0.753558	+	0.435067i	−0.826978	−	0.562234i	$-0.809942\pi$
$307$	−13.2034	+	7.62299i	−0.753558	+	0.435067i	0.0734201	+	0.997301i	$0.476609\pi$
$308$		0			0
$309$	20.6692	−	7.79781i	1.17583	−	0.443602i
$310$		0			0
$311$	−3.33655	−	18.9225i	−0.189199	−	1.07300i	−0.920441	−	0.390881i	$-0.872170\pi$
$311$	−3.33655	−	18.9225i	−0.189199	−	1.07300i	0.731243	−	0.682117i	$-0.238941\pi$
$312$		0			0
$313$	−24.8029	−	20.8121i	−1.40194	−	1.17637i	−0.960229	−	0.279214i	$-0.909926\pi$
$313$	−24.8029	−	20.8121i	−1.40194	−	1.17637i	−0.441714	−	0.897156i	$-0.645629\pi$
$314$		0			0
$315$	49.8298	−	19.4676i	2.80759	−	1.09687i
$316$		0			0
$317$	4.65940	+	12.8016i	0.261698	+	0.719009i	0.999053	+	0.0435038i	$0.0138520\pi$
$317$	4.65940	+	12.8016i	0.261698	+	0.719009i	−0.737356	+	0.675505i	$0.763926\pi$
$318$		0			0
$319$	1.69154	+	2.01590i	0.0947082	+	0.112869i
$320$		0			0
$321$	−4.80075	+	13.6857i	−0.267952	+	0.763859i
$322$		0			0
$323$	−27.1552			−1.51096
$324$		0			0
$325$	27.2895			1.51375
$326$		0			0
$327$	5.21346	−	14.8622i	0.288305	−	0.821881i
$328$		0			0
$329$	21.0290	+	25.0614i	1.15937	+	1.38168i
$330$		0			0
$331$	−3.41105	−	9.37178i	−0.187488	−	0.515119i	0.809962	−	0.586482i	$-0.199487\pi$
$331$	−3.41105	−	9.37178i	−0.187488	−	0.515119i	−0.997450	+	0.0713625i	$0.977265\pi$
$332$		0			0
$333$	1.82387	−	11.9745i	0.0999477	−	0.656196i
$334$		0			0
$335$	−9.81219	−	8.23341i	−0.536097	−	0.449839i
$336$		0			0
$337$	1.08115	+	6.13149i	0.0588938	+	0.334004i	0.999991	−	0.00413138i	$-0.00131506\pi$
$337$	1.08115	+	6.13149i	0.0588938	+	0.334004i	−0.941098	+	0.338135i	$0.890204\pi$
$338$		0			0
$339$	5.79050	−	2.18456i	0.314497	−	0.118649i
$340$		0			0
$341$	−2.98868	+	1.72551i	−0.161846	+	0.0934418i
$342$		0			0
$343$	−38.8793	−	22.4470i	−2.09929	−	1.21202i
$344$		0			0
$345$	−14.0199	+	0.163907i	−0.754809	+	0.00882446i
$346$		0			0
$347$	−5.36415	−	1.95239i	−0.287962	−	0.104810i	0.194000	−	0.981001i	$-0.437854\pi$
$347$	−5.36415	−	1.95239i	−0.287962	−	0.104810i	−0.481963	+	0.876192i	$0.660076\pi$
$348$		0			0
$349$	1.78457	−	10.1208i	0.0955260	−	0.541755i	−0.899059	−	0.437828i	$-0.855748\pi$
$349$	1.78457	−	10.1208i	0.0955260	−	0.541755i	0.994585	−	0.103927i	$-0.0331409\pi$
$350$		0			0
$351$	−10.9740	−	12.1838i	−0.585747	−	0.650322i
$352$		0			0
$353$	−27.2427	−	4.80362i	−1.44998	−	0.255671i	−0.607466	−	0.794345i	$-0.707814\pi$
$353$	−27.2427	−	4.80362i	−1.44998	−	0.255671i	−0.842514	+	0.538675i	$0.818925\pi$
$354$		0			0
$355$	15.5431	−	42.7042i	0.824940	−	2.26650i
$356$		0			0
$357$	−41.0432	+	24.3404i	−2.17224	+	1.28823i
$358$		0			0
$359$	6.23714	−	10.8031i	0.329184	−	0.570163i	−0.653166	−	0.757215i	$-0.726560\pi$
$359$	6.23714	−	10.8031i	0.329184	−	0.570163i	0.982350	+	0.187051i	$0.0598931\pi$
$360$		0			0
$361$	1.81879	+	3.15024i	0.0957258	+	0.165802i
$362$		0			0
$363$	12.8848	+	2.11694i	0.676279	+	0.111111i
$364$		0			0
$365$	−28.7700	+	5.07293i	−1.50589	+	0.265529i
$366$		0			0
$367$	−13.2693	+	15.8137i	−0.692651	+	0.825470i	−0.991674	−	0.128777i	$-0.958895\pi$
$367$	−13.2693	+	15.8137i	−0.692651	+	0.825470i	0.299022	+	0.954246i	$0.403339\pi$
$368$		0			0
$369$	−7.93497	−	4.33714i	−0.413078	−	0.225782i
$370$		0			0
$371$	14.0568	−	5.11626i	0.729793	−	0.265623i
$372$		0			0
$373$	28.7631	−	24.1351i	1.48930	−	1.24967i	0.593788	−	0.804621i	$-0.297632\pi$
$373$	28.7631	−	24.1351i	1.48930	−	1.24967i	0.895508	−	0.445046i	$-0.146813\pi$
$374$		0			0
$375$	−4.32156	−	22.9374i	−0.223164	−	1.18448i
$376$		0			0
$377$			4.46368i			0.229891i
$378$		0			0
$379$		−	8.06037i		−	0.414033i	−0.978337	−	0.207017i	$-0.933625\pi$
$379$		−	8.06037i		−	0.414033i	0.978337	−	0.207017i	$-0.0663754\pi$
$380$		0			0
$381$	−7.34173	+	6.30816i	−0.376128	+	0.323177i
$382$		0			0
$383$	11.2804	−	9.46540i	0.576403	−	0.483659i	−0.307361	−	0.951593i	$-0.599446\pi$
$383$	11.2804	−	9.46540i	0.576403	−	0.483659i	0.883764	+	0.467934i	$0.155001\pi$
$384$		0			0
$385$	31.1754	−	11.3469i	1.58885	−	0.578293i
$386$		0			0
$387$	19.7961	−	3.96990i	1.00629	−	0.201801i
$388$		0			0
$389$	10.0983	−	12.0347i	0.512006	−	0.610185i	−0.446665	−	0.894701i	$-0.647389\pi$
$389$	10.0983	−	12.0347i	0.512006	−	0.610185i	0.958671	+	0.284516i	$0.0918330\pi$
$390$		0			0
$391$	12.3161	−	2.17167i	0.622854	−	0.109826i
$392$		0			0
$393$	24.5248	−	29.9313i	1.23711	−	1.50983i
$394$		0			0
$395$	23.8658	+	41.3368i	1.20082	+	2.07988i
$396$		0			0
$397$	13.2048	−	22.8714i	0.662729	−	1.14788i	−0.317166	−	0.948370i	$-0.602731\pi$
$397$	13.2048	−	22.8714i	0.662729	−	1.14788i	0.979896	−	0.199511i	$-0.0639353\pi$
$398$		0			0
$399$	34.6801	+	19.4856i	1.73618	+	0.975501i
$400$		0			0
$401$	12.5892	−	34.5886i	0.628676	−	1.72727i	−0.0560039	−	0.998431i	$-0.517836\pi$
$401$	12.5892	−	34.5886i	0.628676	−	1.72727i	0.684680	−	0.728844i	$-0.259942\pi$
$402$		0			0
$403$	−5.76472	−	1.01648i	−0.287161	−	0.0506343i
$404$		0			0
$405$	−20.1578	+	26.4411i	−1.00165	+	1.31387i
$406$		0			0
$407$	1.30436	−	7.39740i	0.0646548	−	0.366676i
$408$		0			0
$409$	−7.85859	−	2.86029i	−0.388582	−	0.141432i	0.140338	−	0.990104i	$-0.455181\pi$
$409$	−7.85859	−	2.86029i	−0.388582	−	0.141432i	−0.528921	+	0.848671i	$0.677403\pi$
$410$		0			0
$411$	−1.75629	+	3.12582i	−0.0866316	+	0.154185i
$412$		0			0
$413$	38.0287	+	21.9559i	1.87127	+	1.08038i
$414$		0			0
$415$	11.1823	−	6.45610i	0.548917	−	0.316917i
$416$		0			0
$417$	−21.2788	−	17.4352i	−1.04203	−	0.853806i
$418$		0			0
$419$	6.20113	+	35.1684i	0.302945	+	1.71809i	0.633023	+	0.774133i	$0.281814\pi$
$419$	6.20113	+	35.1684i	0.302945	+	1.71809i	−0.330078	+	0.943954i	$0.607075\pi$
$420$		0			0
$421$	12.9806	+	10.8920i	0.632637	+	0.530846i	0.901747	−	0.432264i	$-0.142285\pi$
$421$	12.9806	+	10.8920i	0.632637	+	0.530846i	−0.269110	+	0.963109i	$0.586730\pi$
$422$		0			0
$423$	−19.2636	−	6.50553i	−0.936629	−	0.316310i
$424$		0			0
$425$	16.8808	+	46.3797i	0.818841	+	2.24975i
$426$		0			0
$427$	−9.87821	−	11.7724i	−0.478040	−	0.569706i
$428$		0			0
$429$	−6.62693	−	7.71273i	−0.319951	−	0.372374i
$430$		0			0
$431$	−27.5395			−1.32653			−0.663265	−	0.748385i	$-0.730830\pi$
$431$	−27.5395			−1.32653			−0.663265	+	0.748385i	$0.730830\pi$
$432$		0			0
$433$	−35.4470			−1.70347			−0.851737	−	0.523970i	$-0.824450\pi$
$433$	−35.4470			−1.70347			−0.851737	+	0.523970i	$0.824450\pi$
$434$		0			0
$435$	8.89445	−	1.67577i	0.426456	−	0.0803470i
$436$		0			0
$437$	−6.70142	−	7.98645i	−0.320573	−	0.382043i
$438$		0			0
$439$	12.1961	+	33.5086i	0.582089	+	1.59928i	0.784604	+	0.619997i	$0.212866\pi$
$439$	12.1961	+	33.5086i	0.582089	+	1.59928i	−0.202515	+	0.979279i	$0.564911\pi$
$440$		0			0
$441$	48.8881	−	1.14326i	2.32800	−	0.0544408i
$442$		0			0
$443$	−26.4763	−	22.2162i	−1.25793	−	1.05553i	−0.995900	−	0.0904644i	$-0.971165\pi$
$443$	−26.4763	−	22.2162i	−1.25793	−	1.05553i	−0.262026	−	0.965061i	$-0.584391\pi$
$444$		0			0
$445$	6.49101	+	36.8123i	0.307703	+	1.74507i
$446$		0			0
$447$	−0.00346523	+	0.0210912i	−0.000163900	+	0.000997582i
$448$		0			0
$449$	−24.1659	+	13.9522i	−1.14046	+	0.658444i	−0.946544	−	0.322574i	$-0.895452\pi$
$449$	−24.1659	+	13.9522i	−1.14046	+	0.658444i	−0.193915	+	0.981018i	$0.562118\pi$
$450$		0			0
$451$	−4.85659	−	2.80395i	−0.228688	−	0.132033i
$452$		0			0
$453$	12.8362	+	21.6447i	0.603099	+	1.01695i
$454$		0			0
$455$	52.8799	+	19.2467i	2.47905	+	0.902299i
$456$		0			0
$457$	−0.691971	+	3.92436i	−0.0323690	+	0.183574i	−0.996706	−	0.0811054i	$-0.974155\pi$
$457$	−0.691971	+	3.92436i	−0.0323690	+	0.183574i	0.964337	+	0.264679i	$0.0852661\pi$
$458$		0			0
$459$	13.9186	−	26.1875i	0.649664	−	1.22233i
$460$		0			0
$461$	21.9503	+	3.87044i	1.02233	+	0.180264i	0.659589	−	0.751626i	$-0.270730\pi$
$461$	21.9503	+	3.87044i	1.02233	+	0.180264i	0.362740	+	0.931890i	$0.381841\pi$
$462$		0			0
$463$	−5.76889	+	15.8499i	−0.268103	+	0.736607i	0.730457	+	0.682959i	$0.239307\pi$
$463$	−5.76889	+	15.8499i	−0.268103	+	0.736607i	−0.998560	+	0.0536484i	$0.982915\pi$
$464$		0			0
$465$	0.138755	+	11.8685i	0.00643461	+	0.550390i
$466$		0			0
$467$	12.4601	−	21.5816i	0.576586	−	0.998677i	−0.419281	−	0.907857i	$-0.637718\pi$
$467$	12.4601	−	21.5816i	0.576586	−	0.998677i	0.995867	−	0.0908205i	$-0.0289490\pi$
$468$		0			0
$469$	−8.36823	−	14.4942i	−0.386409	−	0.669280i
$470$		0			0
$471$	−3.10805	−	8.23834i	−0.143211	−	0.379603i
$472$		0			0
$473$	12.3306	−	2.17422i	0.566963	−	0.0999709i
$474$		0			0
$475$	26.4476	−	31.5190i	1.21350	−	1.44619i
$476$		0			0
$477$	−5.80782	+	7.25963i	−0.265922	+	0.332396i
$478$		0			0
$479$	−28.6520	+	10.4285i	−1.30914	+	0.476489i	−0.899964	−	0.435965i	$-0.856407\pi$
$479$	−28.6520	+	10.4285i	−1.30914	+	0.476489i	−0.409179	+	0.912454i	$0.634185\pi$
$480$		0			0
$481$	9.76023	−	8.18980i	0.445028	−	0.373423i
$482$		0			0
$483$	−17.2873	−	6.06416i	−0.786601	−	0.275929i
$484$		0			0
$485$			2.58845i			0.117536i
$486$		0			0
$487$		−	22.0685i		−	1.00002i	−0.866020	−	0.500009i	$-0.833330\pi$
$487$		−	22.0685i		−	1.00002i	0.866020	−	0.500009i	$-0.166670\pi$
$488$		0			0
$489$	21.3080	+	7.47455i	0.963580	+	0.338011i
$490$		0			0
$491$	−6.01397	+	5.04632i	−0.271407	+	0.227737i	−0.768325	−	0.640060i	$-0.778909\pi$
$491$	−6.01397	+	5.04632i	−0.271407	+	0.227737i	0.496918	+	0.867797i	$0.334465\pi$
$492$		0			0
$493$	−7.58623	+	2.76116i	−0.341667	+	0.124357i
$494$		0			0
$495$	−12.8807	+	16.1005i	−0.578944	+	0.723665i
$496$		0			0
$497$	38.1684	−	45.4873i	1.71209	−	2.04038i
$498$		0			0
$499$	13.4404	−	2.36991i	0.601676	−	0.106092i	0.135490	−	0.990779i	$-0.456739\pi$
$499$	13.4404	−	2.36991i	0.601676	−	0.106092i	0.466185	+	0.884687i	$0.345628\pi$
$500$		0			0
$501$	−7.03247	−	18.6406i	−0.314187	−	0.832799i
$502$		0			0
$503$	−11.0130	−	19.0751i	−0.491047	−	0.850518i	0.508900	−	0.860826i	$-0.330052\pi$
$503$	−11.0130	−	19.0751i	−0.491047	−	0.850518i	−0.999947	+	0.0103076i	$0.996719\pi$
$504$		0			0
$505$	−29.6759	+	51.4002i	−1.32056	+	2.28728i
$506$		0			0
$507$	0.0615895	+	5.26811i	0.00273529	+	0.233965i
$508$		0			0
$509$	−3.43266	+	9.43115i	−0.152150	+	0.418028i	−0.992227	−	0.124438i	$-0.960287\pi$
$509$	−3.43266	+	9.43115i	−0.152150	+	0.418028i	0.840077	+	0.542466i	$0.182509\pi$
$510$		0			0
$511$	−37.5917	−	6.62842i	−1.66296	−	0.293224i
$512$		0			0
$513$	−24.7076	+	0.866884i	−1.09087	+	0.0382739i
$514$		0			0
$515$	8.18202	−	46.4025i	0.360543	−	2.04474i
$516$		0			0
$517$	−11.8486	−	4.31255i	−0.521102	−	0.189666i
$518$		0			0
$519$	13.1530	+	22.1787i	0.577351	+	0.973538i
$520$		0			0
$521$	−35.1651	−	20.3026i	−1.54061	−	0.889471i	−0.998800	−	0.0489699i	$-0.984406\pi$
$521$	−35.1651	−	20.3026i	−1.54061	−	0.889471i	−0.541809	−	0.840501i	$-0.682261\pi$
$522$		0			0
$523$	−3.46003	+	1.99765i	−0.151296	+	0.0873510i	−0.573737	−	0.819040i	$-0.694507\pi$
$523$	−3.46003	+	1.99765i	−0.151296	+	0.0873510i	0.422441	+	0.906391i	$0.361174\pi$
$524$		0			0
$525$	11.7218	−	71.3450i	0.511581	−	3.11375i
$526$		0			0
$527$	−1.83842	−	10.4262i	−0.0800827	−	0.454172i
$528$		0			0
$529$	−13.9409	−	11.6978i	−0.606127	−	0.508601i
$530$		0			0
$531$	−27.2835	+	0.638031i	−1.18400	+	0.0276882i
$532$		0			0
$533$	−3.25335	−	8.93850i	−0.140918	−	0.387169i
$534$		0			0
$535$	19.8840	+	23.6968i	0.859660	+	1.02450i
$536$		0			0
$537$	−14.5666	+	2.74443i	−0.628594	+	0.118431i
$538$		0			0
$539$	30.3259			1.30623
$540$		0			0
$541$	−6.69974			−0.288044			−0.144022	−	0.989574i	$-0.546004\pi$
$541$	−6.69974			−0.288044			−0.144022	+	0.989574i	$0.546004\pi$
$542$		0			0
$543$	7.61675	+	8.86473i	0.326866	+	0.380422i
$544$		0			0
$545$	−21.5934	−	25.7340i	−0.924958	−	1.10232i
$546$		0			0
$547$	−2.26190	−	6.21452i	−0.0967118	−	0.265714i	0.881897	−	0.471441i	$-0.156266\pi$
$547$	−2.26190	−	6.21452i	−0.0967118	−	0.265714i	−0.978609	+	0.205728i	$0.934044\pi$
$548$		0			0
$549$	9.04893	+	3.05592i	0.386199	+	0.130423i
$550$		0			0
$551$	5.15550	+	4.32598i	0.219632	+	0.184293i
$552$		0			0
$553$	10.8300	+	61.4199i	0.460538	+	2.61184i
$554$		0			0
$555$	−19.9834	−	16.3738i	−0.848249	−	0.695031i
$556$		0			0
$557$	−13.2924	+	7.67438i	−0.563217	+	0.325174i	−0.754436	−	0.656374i	$-0.772089\pi$
$557$	−13.2924	+	7.67438i	−0.563217	+	0.325174i	0.191218	+	0.981548i	$0.438756\pi$
$558$		0			0
$559$	18.3926	+	10.6190i	0.777923	+	0.449134i
$560$		0			0
$561$	9.00883	−	16.0337i	0.380353	−	0.676945i
$562$		0			0
$563$	−36.0325	−	13.1147i	−1.51859	−	0.552721i	−0.557793	−	0.829980i	$-0.688352\pi$
$563$	−36.0325	−	13.1147i	−1.51859	−	0.552721i	−0.960795	+	0.277260i	$0.910574\pi$
$564$		0			0
$565$	2.29220	−	12.9997i	0.0964335	−	0.546901i
$566$		0			0
$567$	−36.5667	+	23.4567i	−1.53566	+	0.985089i
$568$		0			0
$569$	−19.7034	−	3.47425i	−0.826010	−	0.145648i	−0.255365	−	0.966845i	$-0.582196\pi$
$569$	−19.7034	−	3.47425i	−0.826010	−	0.145648i	−0.570645	+	0.821197i	$0.693307\pi$
$570$		0			0
$571$	−1.06544	+	2.92726i	−0.0445871	+	0.122502i	−0.959988	−	0.280042i	$-0.909652\pi$
$571$	−1.06544	+	2.92726i	−0.0445871	+	0.122502i	0.915401	+	0.402544i	$0.131874\pi$
$572$		0			0
$573$	−29.1507	−	16.3788i	−1.21779	−	0.684234i
$574$		0			0
$575$	−9.47455	+	16.4104i	−0.395116	+	0.684361i
$576$		0			0
$577$	12.1671	+	21.0741i	0.506524	+	0.877326i	0.999971	+	0.00754987i	$0.00240322\pi$
$577$	12.1671	+	21.0741i	0.506524	+	0.877326i	−0.493447	+	0.869776i	$0.664263\pi$
$578$		0			0
$579$	−3.61706	+	4.41444i	−0.150320	+	0.183458i
$580$		0			0
$581$	16.6151	−	2.92969i	0.689311	−	0.121544i
$582$		0			0
$583$	−3.70595	+	4.41658i	−0.153485	+	0.182916i
$584$		0			0
$585$	−34.2911	+	6.87671i	−1.41776	+	0.284317i
$586$		0			0
$587$	−3.52035	+	1.28130i	−0.145301	+	0.0528851i	−0.413647	−	0.910437i	$-0.635745\pi$
$587$	−3.52035	+	1.28130i	−0.145301	+	0.0528851i	0.268346	+	0.963323i	$0.413523\pi$
$588$		0			0
$589$	−6.76090	+	5.67307i	−0.278578	+	0.233755i
$590$		0			0
$591$	26.0007	−	22.3403i	1.06953	−	0.918958i
$592$		0			0
$593$		−	4.69426i		−	0.192770i	−0.995344	−	0.0963851i	$-0.969272\pi$
$593$		−	4.69426i		−	0.192770i	0.995344	−	0.0963851i	$-0.0307280\pi$
$594$		0			0
$595$			101.777i			4.17247i
$596$		0			0
$597$	3.67197	+	19.4896i	0.150284	+	0.797657i
$598$		0			0
$599$	−4.44701	+	3.73149i	−0.181700	+	0.152464i	−0.729101	−	0.684406i	$-0.760062\pi$
$599$	−4.44701	+	3.73149i	−0.181700	+	0.152464i	0.547401	+	0.836870i	$0.315617\pi$
$600$		0			0
$601$	−28.7503	+	10.4643i	−1.17275	+	0.426847i	−0.853636	−	0.520870i	$-0.825608\pi$
$601$	−28.7503	+	10.4643i	−1.17275	+	0.426847i	−0.319115	+	0.947716i	$0.603386\pi$
$602$		0			0
$603$	9.12723	+	4.98881i	0.371689	+	0.203160i
$604$		0			0
$605$	17.9020	−	21.3347i	0.727818	−	0.867380i
$606$		0			0
$607$	21.6831	−	3.82332i	0.880091	−	0.155184i	0.284697	−	0.958618i	$-0.408107\pi$
$607$	21.6831	−	3.82332i	0.880091	−	0.155184i	0.595394	+	0.803434i	$0.296996\pi$
$608$		0			0
$609$	11.6697	+	1.91731i	0.472882	+	0.0776932i
$610$		0			0
$611$	−10.6938	−	18.5221i	−0.432623	−	0.749325i
$612$		0			0
$613$	−18.0463	+	31.2571i	−0.728884	+	1.26246i	0.228472	+	0.973551i	$0.426627\pi$
$613$	−18.0463	+	31.2571i	−0.728884	+	1.26246i	−0.957355	+	0.288913i	$0.906706\pi$
$614$		0			0
$615$	−16.5897	+	9.83843i	−0.668961	+	0.396724i
$616$		0			0
$617$	10.9870	−	30.1864i	0.442319	−	1.21526i	−0.495645	−	0.868525i	$-0.665068\pi$
$617$	10.9870	−	30.1864i	0.442319	−	1.21526i	0.937963	−	0.346735i	$-0.112710\pi$
$618$		0			0
$619$	2.25438	+	0.397508i	0.0906113	+	0.0159772i	0.218770	−	0.975776i	$-0.429796\pi$
$619$	2.25438	+	0.397508i	0.0906113	+	0.0159772i	−0.128159	+	0.991754i	$0.540907\pi$
$620$		0			0
$621$	11.1367	−	2.36909i	0.446899	−	0.0950684i
$622$		0			0
$623$	−8.48133	+	48.1000i	−0.339797	+	1.92709i
$624$		0			0
$625$	−6.15036	−	2.23855i	−0.246014	−	0.0895419i
$626$		0			0
$627$	−15.3306	+	0.179230i	−0.612245	+	0.00715776i
$628$		0			0
$629$	19.9565	+	11.5219i	0.795716	+	0.459407i
$630$		0			0
$631$	−31.9016	+	18.4184i	−1.26998	+	0.733224i	−0.974984	−	0.222274i	$-0.928652\pi$
$631$	−31.9016	+	18.4184i	−1.26998	+	0.733224i	−0.294997	+	0.955498i	$0.595319\pi$
$632$		0			0
$633$	5.10118	−	1.92451i	0.202754	−	0.0764922i
$634$		0			0
$635$	3.58506	+	20.3319i	0.142269	+	0.806846i
$636$		0			0
$637$	39.4045	+	33.0643i	1.56126	+	1.31006i
$638$		0			0
$639$	−5.55692	+	36.4834i	−0.219828	+	1.44326i
$640$		0			0
$641$	14.1337	+	38.8319i	0.558246	+	1.53377i	0.822180	+	0.569228i	$0.192758\pi$
$641$	14.1337	+	38.8319i	0.558246	+	1.53377i	−0.263934	+	0.964541i	$0.585020\pi$
$642$		0			0
$643$	5.07677	+	6.05026i	0.200208	+	0.238599i	0.856802	−	0.515646i	$-0.172448\pi$
$643$	5.07677	+	6.05026i	0.200208	+	0.238599i	−0.656594	+	0.754244i	$0.728003\pi$
$644$		0			0
$645$	14.2546	−	40.6361i	0.561275	−	1.60005i
$646$		0			0
$647$	36.4092			1.43139			0.715696	−	0.698412i	$-0.246109\pi$
$647$	36.4092			1.43139			0.715696	+	0.698412i	$0.246109\pi$
$648$		0			0
$649$	−16.9243			−0.664338
$650$		0			0
$651$	−5.13359	+	14.6345i	−0.201201	+	0.573572i
$652$		0			0
$653$	27.7883	+	33.1168i	1.08744	+	1.29596i	0.952310	+	0.305134i	$0.0987012\pi$
$653$	27.7883	+	33.1168i	1.08744	+	1.29596i	0.135131	+	0.990828i	$0.456854\pi$
$654$		0			0
$655$	−28.2282	−	77.5563i	−1.10297	−	3.03038i
$656$		0			0
$657$	22.0970	−	8.63288i	0.862087	−	0.336801i
$658$		0			0
$659$	29.9790	+	25.1554i	1.16782	+	0.979915i	0.999983	−	0.00590020i	$-0.00187810\pi$
$659$	29.9790	+	25.1554i	1.16782	+	0.979915i	0.167835	+	0.985815i	$0.446323\pi$
$660$		0			0
$661$	0.241985	+	1.37236i	0.00941211	+	0.0533787i	0.989152	−	0.146895i	$-0.0469280\pi$
$661$	0.241985	+	1.37236i	0.00941211	+	0.0533787i	−0.979740	+	0.200274i	$0.935817\pi$
$662$		0			0
$663$	29.1874	−	11.0114i	1.13354	−	0.427648i
$664$		0			0
$665$	73.4783	−	42.4227i	2.84937	−	1.64508i
$666$		0			0
$667$	−2.68421	−	1.54973i	−0.103933	−	0.0600058i
$668$		0			0
$669$	−24.1867	+	0.282766i	−0.935111	+	0.0109324i
$670$		0			0
$671$	5.56579	+	2.02578i	0.214865	+	0.0782045i
$672$		0			0
$673$	−0.968471	+	5.49247i	−0.0373318	+	0.211719i	−0.997768	−	0.0667824i	$-0.978727\pi$
$673$	−0.968471	+	5.49247i	−0.0373318	+	0.211719i	0.960436	+	0.278502i	$0.0898378\pi$
$674$		0			0
$675$	16.8399	+	41.6604i	0.648167	+	1.60351i
$676$		0			0
$677$	−9.29541	−	1.63903i	−0.357252	−	0.0629931i	−0.00785791	−	0.999969i	$-0.502501\pi$
$677$	−9.29541	−	1.63903i	−0.357252	−	0.0629931i	−0.349394	+	0.936976i	$0.613612\pi$
$678$		0			0
$679$	−1.15676	+	3.17817i	−0.0443924	+	0.121967i
$680$		0			0
$681$	−15.6708	+	9.29345i	−0.600504	+	0.356126i
$682$		0			0
$683$	16.8492	−	29.1836i	0.644716	−	1.11668i	−0.339651	−	0.940551i	$-0.610309\pi$
$683$	16.8492	−	29.1836i	0.644716	−	1.11668i	0.984367	−	0.176129i	$-0.0563576\pi$
$684$		0			0
$685$	3.82368	+	6.62281i	0.146095	+	0.253045i
$686$		0			0
$687$	33.2929	+	5.46993i	1.27020	+	0.208691i
$688$		0			0
$689$	−9.63078	+	1.69817i	−0.366903	+	0.0646950i
$690$		0			0
$691$	−14.9399	+	17.8047i	−0.568341	+	0.677322i	−0.971290	−	0.237900i	$-0.923541\pi$
$691$	−14.9399	+	17.8047i	−0.568341	+	0.677322i	0.402949	+	0.915222i	$0.367985\pi$
$692$		0			0
$693$	−23.0105	+	14.0124i	−0.874095	+	0.532287i
$694$		0			0
$695$	−55.1365	+	20.0680i	−2.09145	+	0.761224i
$696$		0			0
$697$	13.1789	−	11.0584i	0.499187	−	0.418868i
$698$		0			0
$699$	4.25678	+	22.5936i	0.161006	+	0.854569i
$700$		0			0
$701$			10.4531i			0.394807i	0.980322	+	0.197404i	$0.0632509\pi$
$701$			10.4531i			0.394807i	−0.980322	+	0.197404i	$0.936749\pi$
$702$		0			0
$703$		−	19.2101i		−	0.724523i
$704$		0			0
$705$	−32.8930	+	28.2623i	−1.23882	+	1.06442i
$706$		0			0
$707$	−59.4073	+	49.8486i	−2.23424	+	1.87475i
$708$		0			0
$709$	−28.9016	+	10.5193i	−1.08542	+	0.395062i	−0.821924	−	0.569598i	$-0.807099\pi$
$709$	−28.9016	+	10.5193i	−1.08542	+	0.395062i	−0.263500	+	0.964660i	$0.584877\pi$
$710$		0			0
$711$	−25.6025	−	29.1021i	−0.960170	−	1.09142i
$712$		0			0
$713$	2.61269	−	3.11368i	0.0978459	−	0.116608i
$714$		0			0
$715$	−21.3593	+	3.76622i	−0.798793	+	0.140849i
$716$		0			0
$717$	−1.15738	+	1.41253i	−0.0432233	+	0.0527518i
$718$		0			0
$719$	−12.4453	−	21.5560i	−0.464133	−	0.803902i	0.535029	−	0.844834i	$-0.320301\pi$
$719$	−12.4453	−	21.5560i	−0.464133	−	0.803902i	−0.999162	+	0.0409318i	$0.986967\pi$
$720$		0			0
$721$	30.7831	−	53.3179i	1.14642	−	1.98566i
$722$		0			0
$723$	−29.7714	−	16.7276i	−1.10721	−	0.622105i
$724$		0			0
$725$	4.18367	−	11.4945i	0.155378	−	0.426897i
$726$		0			0
$727$	5.41385	+	0.954608i	0.200789	+	0.0354044i	0.273138	−	0.961975i	$-0.411939\pi$
$727$	5.41385	+	0.954608i	0.200789	+	0.0354044i	−0.0723492	+	0.997379i	$0.523050\pi$
$728$		0			0
$729$	11.8280	−	24.2713i	0.438075	−	0.898938i
$730$		0			0
$731$	−6.67005	+	37.8278i	−0.246701	+	1.39911i
$732$		0			0
$733$	−6.66244	−	2.42493i	−0.246083	−	0.0895668i	0.216034	−	0.976386i	$-0.430688\pi$
$733$	−6.66244	−	2.42493i	−0.246083	−	0.0895668i	−0.462117	+	0.886819i	$0.652910\pi$
$734$		0			0
$735$	51.0914	−	90.9315i	1.88453	−	3.35406i
$736$		0			0
$737$	5.58631	+	3.22526i	0.205774	+	0.118804i
$738$		0			0
$739$	−5.95487	+	3.43805i	−0.219054	+	0.126471i	−0.605512	−	0.795836i	$-0.707032\pi$
$739$	−5.95487	+	3.43805i	−0.219054	+	0.126471i	0.386458	+	0.922307i	$0.373698\pi$
$740$		0			0
$741$	−20.1155	−	16.4821i	−0.738962	−	0.605483i
$742$		0			0
$743$	6.16444	+	34.9603i	0.226151	+	1.28257i	0.860472	+	0.509498i	$0.170169\pi$
$743$	6.16444	+	34.9603i	0.226151	+	1.28257i	−0.634321	+	0.773070i	$0.718720\pi$
$744$		0			0
$745$	0.0349229	+	0.0293038i	0.00127948	+	0.00107361i
$746$		0			0
$747$	−7.87261	+	6.92591i	−0.288044	+	0.253406i
$748$		0			0
$749$	13.8242	+	37.9816i	0.505124	+	1.38782i
$750$		0			0
$751$	−5.00356	−	5.96301i	−0.182583	−	0.217593i	0.666988	−	0.745069i	$-0.267583\pi$
$751$	−5.00356	−	5.96301i	−0.182583	−	0.217593i	−0.849570	+	0.527475i	$0.823139\pi$
$752$		0			0
$753$	−0.110199	−	0.128254i	−0.00401587	−	0.00467385i
$754$		0			0
$755$	53.6737			1.95338
$756$		0			0
$757$	32.7105			1.18888			0.594442	−	0.804139i	$-0.297373\pi$
$757$	32.7105			1.18888			0.594442	+	0.804139i	$0.297373\pi$
$758$		0			0
$759$	6.93880	−	1.30731i	0.251862	−	0.0474525i
$760$		0			0
$761$	14.5967	+	17.3956i	0.529129	+	0.630591i	0.962714	−	0.270521i	$-0.0871960\pi$
$761$	14.5967	+	17.3956i	0.529129	+	0.630591i	−0.433585	+	0.901113i	$0.642752\pi$
$762$		0			0
$763$	−15.0126	−	41.2468i	−0.543493	−	1.49323i
$764$		0			0
$765$	−32.8992	−	54.0255i	−1.18947	−	1.95330i
$766$		0			0
$767$	−21.9909	−	18.4526i	−0.794046	−	0.666284i
$768$		0			0
$769$	−4.71101	−	26.7175i	−0.169883	−	0.963457i	−0.943885	−	0.330273i	$-0.892859\pi$
$769$	−4.71101	−	26.7175i	−0.169883	−	0.963457i	0.774002	−	0.633183i	$-0.218252\pi$
$770$		0			0
$771$	−0.0980861	+	0.597004i	−0.00353249	+	0.0215006i
$772$		0			0
$773$	5.42573	−	3.13255i	0.195150	−	0.112670i	−0.399241	−	0.916846i	$-0.630726\pi$
$773$	5.42573	−	3.13255i	0.195150	−	0.112670i	0.594391	+	0.804176i	$0.297393\pi$
$774$		0			0
$775$	13.8922	+	8.02065i	0.499021	+	0.288110i
$776$		0			0
$777$	−17.2189	−	29.0347i	−0.617723	−	1.04161i
$778$		0			0
$779$	−13.4768	−	4.90517i	−0.482858	−	0.175746i
$780$		0			0
$781$	−3.97409	+	22.5382i	−0.142204	+	0.806479i
$782$		0			0
$783$	−6.81429	+	2.75446i	−0.243523	+	0.0984363i
$784$		0			0
$785$	−18.4951	−	3.26119i	−0.660120	−	0.116397i
$786$		0			0
$787$	6.22777	−	17.1107i	0.221996	−	0.609929i	−0.777832	−	0.628472i	$-0.783681\pi$
$787$	6.22777	−	17.1107i	0.221996	−	0.609929i	0.999828	+	0.0185432i	$0.00590281\pi$
$788$		0			0
$789$	0.228334	+	19.5308i	0.00812892	+	0.695314i
$790$		0			0
$791$	8.62389	−	14.9370i	0.306630	−	0.531099i
$792$		0			0
$793$	5.02330	+	8.70062i	0.178383	+	0.308968i
$794$		0			0
$795$	6.99943	+	18.5530i	0.248244	+	0.658007i
$796$		0			0
$797$	49.0093	−	8.64165i	1.73600	−	0.306103i	0.785968	−	0.618267i	$-0.212165\pi$
$797$	49.0093	−	8.64165i	1.73600	−	0.306103i	0.950028	+	0.312163i	$0.101054\pi$
$798$		0			0
$799$	24.8642	−	29.6320i	0.879632	−	1.04831i
$800$		0			0
$801$	−11.0461	−	28.2740i	−0.390295	−	0.999013i
$802$		0			0
$803$	13.8247	−	5.03179i	0.487864	−	0.177568i
$804$		0			0
$805$	−29.9331	+	25.1169i	−1.05500	+	0.885253i
$806$		0			0
$807$	20.4092	+	7.15927i	0.718438	+	0.252018i
$808$		0			0
$809$			34.6586i			1.21853i	0.792966	+	0.609265i	$0.208536\pi$
$809$			34.6586i			1.21853i	−0.792966	+	0.609265i	$0.791464\pi$
$810$		0			0
$811$			44.0065i			1.54528i	0.634846	+	0.772639i	$0.281064\pi$
$811$			44.0065i			1.54528i	−0.634846	+	0.772639i	$0.718936\pi$
$812$		0			0
$813$	9.19790	+	3.22650i	0.322584	+	0.113158i
$814$		0			0
$815$	36.8949	−	30.9585i	1.29237	−	1.08443i
$816$		0			0
$817$	30.0899	−	10.9518i	1.05271	−	0.383157i
$818$		0			0
$819$	−45.1767	−	6.88104i	−1.57860	−	0.240443i
$820$		0			0
$821$	20.2895	−	24.1800i	0.708107	−	0.843889i	−0.285311	−	0.958435i	$-0.592097\pi$
$821$	20.2895	−	24.1800i	0.708107	−	0.843889i	0.993418	+	0.114546i	$0.0365413\pi$
$822$		0			0
$823$	−15.4724	+	2.72820i	−0.539335	+	0.0950992i	−0.436678	−	0.899618i	$-0.643845\pi$
$823$	−15.4724	+	2.72820i	−0.539335	+	0.0950992i	−0.102656	+	0.994717i	$0.532734\pi$
$824$		0			0
$825$	9.83627	+	26.0725i	0.342455	+	0.907727i
$826$		0			0
$827$	−19.9795	−	34.6054i	−0.694754	−	1.20335i	−0.970264	−	0.242050i	$-0.922180\pi$
$827$	−19.9795	−	34.6054i	−0.694754	−	1.20335i	0.275510	−	0.961298i	$-0.411153\pi$
$828$		0			0
$829$	−4.33415	+	7.50697i	−0.150531	+	0.260728i	−0.931423	−	0.363939i	$-0.881432\pi$
$829$	−4.33415	+	7.50697i	−0.150531	+	0.260728i	0.780892	+	0.624667i	$0.214765\pi$
$830$		0			0
$831$	−0.122702	−	10.4954i	−0.00425647	−	0.364081i
$832$		0			0
$833$	−31.8193	+	87.4228i	−1.10247	+	3.02902i
$834$		0			0
$835$	−41.8482	−	7.37897i	−1.44822	−	0.255360i
$836$		0			0
$837$	−2.00555	−	9.42771i	−0.0693218	−	0.325869i
$838$		0			0
$839$	4.14764	−	23.5225i	0.143193	−	0.812085i	−0.825608	−	0.564244i	$-0.809168\pi$
$839$	4.14764	−	23.5225i	0.143193	−	0.812085i	0.968801	−	0.247841i	$-0.0797211\pi$
$840$		0			0
$841$	−25.3709	−	9.23427i	−0.874860	−	0.318423i
$842$		0			0
$843$	−1.08927	−	1.83674i	−0.0375165	−	0.0632608i
$844$		0			0
$845$	9.73163	+	5.61856i	0.334778	+	0.193284i
$846$		0			0
$847$	31.5149	−	18.1951i	1.08286	−	0.625191i
$848$		0			0
$849$	−4.77888	+	29.0868i	−0.164011	+	0.998255i
$850$		0			0
$851$	1.53628	+	8.71266i	0.0526629	+	0.298666i
$852$		0			0
$853$	−21.1155	−	17.7180i	−0.722982	−	0.606654i	0.205226	−	0.978715i	$-0.434207\pi$
$853$	−21.1155	−	17.7180i	−0.722982	−	0.606654i	−0.928208	+	0.372061i	$0.878651\pi$
$854$		0			0
$855$	−25.2907	+	46.2704i	−0.864925	+	1.58241i
$856$		0			0
$857$	−13.9699	−	38.3821i	−0.477204	−	1.31111i	−0.911857	−	0.410508i	$-0.865351\pi$
$857$	−13.9699	−	38.3821i	−0.477204	−	1.31111i	0.434653	−	0.900598i	$-0.356871\pi$
$858$		0			0
$859$	25.6741	+	30.5972i	0.875988	+	1.04396i	0.998672	+	0.0515161i	$0.0164054\pi$
$859$	25.6741	+	30.5972i	0.875988	+	1.04396i	−0.122684	+	0.992446i	$0.539150\pi$
$860$		0			0
$861$	−24.7660	+	4.66608i	−0.844024	+	0.159019i
$862$		0			0
$863$	48.9308			1.66562			0.832812	−	0.553556i	$-0.186729\pi$
$863$	48.9308			1.66562			0.832812	+	0.553556i	$0.186729\pi$
$864$		0			0
$865$	54.9980			1.86999
$866$		0			0
$867$	17.5800	+	20.4605i	0.597050	+	0.694874i
$868$		0			0
$869$	−15.4510	−	18.4138i	−0.524138	−	0.624644i
$870$		0			0
$871$	3.74218	+	10.2815i	0.126799	+	0.348377i
$872$		0			0
$873$	−0.413302	−	2.06096i	−0.0139882	−	0.0697528i
$874$		0			0
$875$	−49.8304	−	41.8127i	−1.68458	−	1.41353i
$876$		0			0
$877$	0.332846	+	1.88766i	0.0112394	+	0.0637419i	0.989912	−	0.141686i	$-0.0452524\pi$
$877$	0.332846	+	1.88766i	0.0112394	+	0.0637419i	−0.978672	+	0.205428i	$0.934141\pi$
$878$		0			0
$879$	−28.0713	−	23.0008i	−0.946823	−	0.775799i
$880$		0			0
$881$	−6.82991	+	3.94325i	−0.230105	+	0.132851i	−0.610621	−	0.791923i	$-0.709080\pi$
$881$	−6.82991	+	3.94325i	−0.230105	+	0.132851i	0.380515	+	0.924775i	$0.375747\pi$
$882$		0			0
$883$	35.9411	+	20.7506i	1.20951	+	0.698313i	0.962653	−	0.270738i	$-0.0872676\pi$
$883$	35.9411	+	20.7506i	1.20951	+	0.698313i	0.246861	+	0.969051i	$0.420601\pi$
$884$		0			0
$885$	−28.5132	+	50.7472i	−0.958460	+	1.70585i
$886$		0			0
$887$	18.9386	+	6.89309i	0.635896	+	0.231447i	0.639796	−	0.768545i	$-0.279019\pi$
$887$	18.9386	+	6.89309i	0.635896	+	0.231447i	−0.00389928	+	0.999992i	$0.501241\pi$
$888$		0			0
$889$	−4.68433	+	26.5662i	−0.157107	+	0.891001i
$890$		0			0
$891$	7.68495	−	14.8761i	0.257456	−	0.498368i
$892$		0			0
$893$	−31.7567	−	5.59956i	−1.06270	−	0.187382i
$894$		0			0
$895$	−10.8132	+	29.7090i	−0.361445	+	0.993062i
$896$		0			0
$897$	10.4414	+	5.86668i	0.348628	+	0.195883i
$898$		0			0
$899$	−1.31192	+	2.27231i	−0.0437550	+	0.0757858i
$900$		0			0
$901$	−8.84356	−	15.3175i	−0.294622	−	0.510300i
$902$		0			0
$903$	35.6622	−	43.5239i	1.18676	−	1.44838i
$904$		0			0
$905$	24.5496	−	4.32876i	0.816056	−	0.143893i
$906$		0			0
$907$	20.0300	−	23.8708i	0.665086	−	0.792618i	−0.323020	−	0.946392i	$-0.604698\pi$
$907$	20.0300	−	23.8708i	0.665086	−	0.792618i	0.988106	+	0.153774i	$0.0491427\pi$
$908$		0			0
$909$	15.4212	−	45.6638i	0.511488	−	1.51457i
$910$		0			0
$911$	28.6080	−	10.4125i	0.947824	−	0.344980i	0.178573	−	0.983927i	$-0.442852\pi$
$911$	28.6080	−	10.4125i	0.947824	−	0.344980i	0.769251	+	0.638947i	$0.220630\pi$
$912$		0			0
$913$	−4.98123	+	4.17975i	−0.164855	+	0.138329i
$914$		0			0
$915$	15.4512	−	13.2760i	0.510801	−	0.438890i
$916$		0			0
$917$		−	107.841i		−	3.56122i
$918$		0			0
$919$		−	16.2067i		−	0.534608i	−0.963612	−	0.267304i	$-0.913867\pi$
$919$		−	16.2067i		−	0.534608i	0.963612	−	0.267304i	$-0.0861329\pi$
$920$		0			0
$921$	−4.88919	−	25.9502i	−0.161104	−	0.855090i
$922$		0			0
$923$	−29.7371	+	24.9524i	−0.978810	+	0.821319i
$924$		0			0
$925$	−32.8099	+	11.9418i	−1.07878	+	0.392644i
$926$		0			0
$927$	0.894547	+	38.2527i	0.0293808	+	1.25638i
$928$		0			0
$929$	−21.4916	+	25.6127i	−0.705118	+	0.840327i	−0.993095	−	0.117310i	$-0.962573\pi$
$929$	−21.4916	+	25.6127i	−0.705118	+	0.840327i	0.287977	+	0.957637i	$0.407017\pi$
$930$		0			0
$931$	76.3778	−	13.4675i	2.50318	−	0.441378i
$932$		0			0
$933$	32.8401	+	5.39554i	1.07514	+	0.176642i
$934$		0			0
$935$	−19.6134	−	33.9714i	−0.641426	−	1.11098i
$936$		0			0
$937$	2.22315	−	3.85062i	0.0726273	−	0.125794i	−0.827425	−	0.561577i	$-0.810195\pi$
$937$	2.22315	−	3.85062i	0.0726273	−	0.125794i	0.900052	+	0.435783i	$0.143528\pi$
$938$		0			0
$939$	48.2357	−	28.6059i	1.57411	−	0.933519i
$940$		0			0
$941$	8.70336	−	23.9123i	0.283721	−	0.779518i	−0.713189	−	0.700972i	$-0.752750\pi$
$941$	8.70336	−	23.9123i	0.283721	−	0.779518i	0.996910	−	0.0785463i	$-0.0250278\pi$
$942$		0			0
$943$	6.50464	+	1.14694i	0.211820	+	0.0373496i
$944$		0			0
$945$	3.24907	+	92.6036i	0.105692	+	3.01240i
$946$		0			0
$947$	5.32222	−	30.1838i	0.172949	−	0.980843i	−0.767536	−	0.641006i	$-0.778517\pi$
$947$	5.32222	−	30.1838i	0.172949	−	0.980843i	0.940485	−	0.339836i	$-0.110372\pi$
$948$		0			0
$949$	23.4496	+	8.53494i	0.761205	+	0.277056i
$950$		0			0
$951$	−23.5944	+	0.275842i	−0.765101	+	0.00894479i
$952$		0			0
$953$	−3.55758	−	2.05397i	−0.115241	−	0.0665345i	0.441271	−	0.897374i	$-0.354528\pi$
$953$	−3.55758	−	2.05397i	−0.115241	−	0.0665345i	−0.556513	+	0.830839i	$0.687861\pi$
$954$		0			0
$955$	−61.7628	+	35.6587i	−1.99860	+	1.15389i
$956$		0			0
$957$	−4.26462	+	1.60890i	−0.137856	+	0.0520083i
$958$		0			0
$959$	1.73514	+	9.84045i	0.0560305	+	0.317765i
$960$		0			0
$961$	21.1115	+	17.7147i	0.681016	+	0.571440i
$962$		0			0
$963$	−19.6156	−	15.6928i	−0.632103	−	0.505693i
$964$		0			0
$965$	4.16326	+	11.4385i	0.134020	+	0.368217i
$966$		0			0
$967$	15.4682	+	18.4343i	0.497425	+	0.592808i	0.955090	−	0.296317i	$-0.0957585\pi$
$967$	15.4682	+	18.4343i	0.497425	+	0.592808i	−0.457665	+	0.889125i	$0.651314\pi$
$968$		0			0
$969$	15.5689	−	44.3828i	0.500144	−	1.42578i
$970$		0			0
$971$	34.7188			1.11418			0.557090	−	0.830452i	$-0.311918\pi$
$971$	34.7188			1.11418			0.557090	+	0.830452i	$0.311918\pi$
$972$		0			0
$973$	−76.6664			−2.45781
$974$		0			0
$975$	−15.6459	+	44.6022i	−0.501068	+	1.42841i
$976$		0			0
$977$	−23.3599	−	27.8393i	−0.747350	−	0.890657i	0.249628	−	0.968342i	$-0.419692\pi$
$977$	−23.3599	−	27.8393i	−0.747350	−	0.890657i	−0.996978	+	0.0776850i	$0.975247\pi$
$978$		0			0
$979$	−6.43837	−	17.6893i	−0.205771	−	0.565352i
$980$		0			0
$981$	21.3019	+	17.0419i	0.680117	+	0.544104i
$982$		0			0
$983$	−28.0213	−	23.5127i	−0.893742	−	0.749939i	0.0752152	−	0.997167i	$-0.476036\pi$
$983$	−28.0213	−	23.5127i	−0.893742	−	0.749939i	−0.968957	+	0.247229i	$0.920480\pi$
$984$		0			0
$985$	−12.6965	−	72.0052i	−0.404543	−	2.29428i
$986$		0			0
$987$	−53.0171	+	20.0016i	−1.68755	+	0.636657i
$988$		0			0
$989$	−12.7713	+	7.37353i	−0.406104	+	0.234464i
$990$		0			0
$991$	−17.9982	−	10.3913i	−0.571732	−	0.330090i	0.186109	−	0.982529i	$-0.440412\pi$
$991$	−17.9982	−	10.3913i	−0.571732	−	0.330090i	−0.757841	+	0.652439i	$0.773746\pi$
$992$		0			0
$993$	17.2730	−	0.201938i	0.548141	−	0.00640832i
$994$		0			0
$995$	39.7497	+	14.4677i	1.26015	+	0.458657i
$996$		0			0
$997$	−5.65156	+	32.0516i	−0.178987	+	1.01508i	0.754454	+	0.656353i	$0.227902\pi$
$997$	−5.65156	+	32.0516i	−0.178987	+	1.01508i	−0.933441	+	0.358731i	$0.883209\pi$
$998$		0			0
$999$	18.5255	+	9.84626i	0.586120	+	0.311522i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.a.191.3	yes	36
4.3	odd	2	inner	432.2.be.a.191.4	yes	36
27.14	odd	18	inner	432.2.be.a.95.4	yes	36
108.95	even	18	inner	432.2.be.a.95.3	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.a.95.3	✓	36	108.95	even	18	inner
432.2.be.a.95.4	yes	36	27.14	odd	18	inner
432.2.be.a.191.3	yes	36	1.1	even	1	trivial
432.2.be.a.191.4	yes	36	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.573329 + 1.63441i) q^{3} +(2.37464 + 2.82999i) q^{5} +(1.65095 + 4.53595i) q^{7} +(-2.34259 - 1.87411i) q^{9} +O(q^{10})\)	\(q+(-0.573329 + 1.63441i) q^{3} +(2.37464 + 2.82999i) q^{5} +(1.65095 + 4.53595i) q^{7} +(-2.34259 - 1.87411i) q^{9} +(-1.42517 - 1.19586i) q^{11} +(-0.547976 - 3.10773i) q^{13} +(-5.98681 + 2.25862i) q^{15} +(4.94276 - 2.85370i) q^{17} +(-4.12046 - 2.37895i) q^{19} +(-8.36014 + 0.0977383i) q^{21} +(2.05907 + 0.749439i) q^{23} +(-1.50167 + 8.51639i) q^{25} +(4.40613 - 2.75427i) q^{27} +(-1.39301 - 0.245625i) q^{29} +(0.634435 - 1.74310i) q^{31} +(2.77162 - 1.64369i) q^{33} +(-8.91627 + 15.4434i) q^{35} +(2.01876 + 3.49659i) q^{37} +(5.39347 + 0.886132i) q^{39} +(2.96851 - 0.523429i) q^{41} +(-4.32602 + 5.15555i) q^{43} +(-0.259104 - 11.0798i) q^{45} +(6.36875 - 2.31804i) q^{47} +(-12.4869 + 10.4777i) q^{49} +(1.83029 + 9.71459i) q^{51} -3.09898i q^{53} -6.87297i q^{55} +(6.25055 - 5.37060i) q^{57} +(6.96871 - 5.84744i) q^{59} +(-2.99167 + 1.08888i) q^{61} +(4.63336 - 13.7199i) q^{63} +(7.49359 - 8.93051i) q^{65} +(-3.41454 + 0.602076i) q^{67} +(-2.40541 + 2.93568i) q^{69} +(-6.15069 - 10.6533i) q^{71} +(-3.95392 + 6.84839i) q^{73} +(-13.0583 - 7.33704i) q^{75} +(3.07148 - 8.43882i) q^{77} +(12.7241 + 2.24360i) q^{79} +(1.97544 + 8.78053i) q^{81} +(0.606931 - 3.44208i) q^{83} +(19.8132 + 7.21142i) q^{85} +(1.20010 - 2.13592i) q^{87} +(8.76278 + 5.05919i) q^{89} +(13.1918 - 7.61630i) q^{91} +(2.48519 + 2.03629i) q^{93} +(-3.05222 - 17.3100i) q^{95} +(0.536739 + 0.450377i) q^{97} +(1.09742 + 5.47234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{5} - 12 q^{9}+O(q^{10}) \) 36 * q - 6 * q^5 - 12 * q^9	\( 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97}+O(q^{100}) \) 36 * q - 6 * q^5 - 12 * q^9 - 36 * q^21 + 18 * q^25 - 24 * q^29 - 36 * q^33 - 18 * q^41 - 18 * q^45 + 42 * q^65 + 54 * q^69 - 18 * q^73 + 90 * q^77 + 36 * q^81 + 72 * q^85 + 72 * q^89 + 54 * q^93 + 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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