LMFDB - Embedded newform 432.2.be.a.191.4

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			191.4
Character	$\chi$	$=$	432.191
Dual form			432.2.be.a.95.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.573329 - 1.63441i) q^{3} +(2.37464 + 2.82999i) q^{5} +(-1.65095 - 4.53595i) q^{7} +(-2.34259 - 1.87411i) q^{9} +O(q^{10})$	\(q+(0.573329 - 1.63441i) q^{3} +(2.37464 + 2.82999i) q^{5} +(-1.65095 - 4.53595i) q^{7} +(-2.34259 - 1.87411i) q^{9} +(1.42517 + 1.19586i) q^{11} +(-0.547976 - 3.10773i) q^{13} +(5.98681 - 2.25862i) q^{15} +(4.94276 - 2.85370i) q^{17} +(4.12046 + 2.37895i) q^{19} +(-8.36014 + 0.0977383i) q^{21} +(-2.05907 - 0.749439i) q^{23} +(-1.50167 + 8.51639i) q^{25} +(-4.40613 + 2.75427i) q^{27} +(-1.39301 - 0.245625i) q^{29} +(-0.634435 + 1.74310i) q^{31} +(2.77162 - 1.64369i) q^{33} +(8.91627 - 15.4434i) q^{35} +(2.01876 + 3.49659i) q^{37} +(-5.39347 - 0.886132i) q^{39} +(2.96851 - 0.523429i) q^{41} +(4.32602 - 5.15555i) q^{43} +(-0.259104 - 11.0798i) q^{45} +(-6.36875 + 2.31804i) q^{47} +(-12.4869 + 10.4777i) q^{49} +(-1.83029 - 9.71459i) q^{51} -3.09898i q^{53} +6.87297i q^{55} +(6.25055 - 5.37060i) q^{57} +(-6.96871 + 5.84744i) q^{59} +(-2.99167 + 1.08888i) q^{61} +(-4.63336 + 13.7199i) q^{63} +(7.49359 - 8.93051i) q^{65} +(3.41454 - 0.602076i) q^{67} +(-2.40541 + 2.93568i) q^{69} +(6.15069 + 10.6533i) q^{71} +(-3.95392 + 6.84839i) q^{73} +(13.0583 + 7.33704i) q^{75} +(3.07148 - 8.43882i) q^{77} +(-12.7241 - 2.24360i) q^{79} +(1.97544 + 8.78053i) q^{81} +(-0.606931 + 3.44208i) q^{83} +(19.8132 + 7.21142i) q^{85} +(-1.20010 + 2.13592i) q^{87} +(8.76278 + 5.05919i) q^{89} +(-13.1918 + 7.61630i) q^{91} +(2.48519 + 2.03629i) q^{93} +(3.05222 + 17.3100i) q^{95} +(0.536739 + 0.450377i) q^{97} +(-1.09742 - 5.47234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.745472\pi$
$7$	−1.65095	−	4.53595i	−0.624001	−	1.71443i	0.0729754	−	0.997334i	$-0.476751\pi$
$8$		0			0
$9$	−2.34259	−	1.87411i	−0.780863	−	0.624703i
$10$		0			0
$11$	1.42517	+	1.19586i	0.429706	+	0.360566i	0.831841	−	0.555015i	$-0.187287\pi$
$11$	1.42517	+	1.19586i	0.429706	+	0.360566i	−0.402135	+	0.915580i	$0.631732\pi$
$12$		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	0.891617	−	0.452790i	$-0.149571\pi$
$19$	4.12046	+	2.37895i	0.945298	+	0.545768i	0.0536810	+	0.998558i	$0.482905\pi$
$20$		0			0
$21$	−8.36014	+	0.0977383i	−1.82433	+	0.0213283i
$22$		0			0
$23$	−2.05907	−	0.749439i	−0.429345	−	0.156269i	0.118303	−	0.992978i	$-0.462255\pi$
$23$	−2.05907	−	0.749439i	−0.429345	−	0.156269i	−0.547648	+	0.836709i	$0.684477\pi$
$24$		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	−0.983537	−	0.180707i	$-0.942161\pi$
$31$	−0.634435	+	1.74310i	−0.113948	+	0.313069i	0.869589	+	0.493776i	$0.164384\pi$
$32$		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	−0.327633	−	0.944805i	$-0.606251\pi$
$43$	4.32602	−	5.15555i	0.659711	−	0.786213i	0.987344	+	0.158592i	$0.0506954\pi$
$44$		0			0
$45$	−0.259104	−	11.0798i	−0.0386250	−	1.65168i
$46$		0			0
$47$	−6.36875	+	2.31804i	−0.928978	+	0.338120i	−0.761804	−	0.647807i	$-0.775686\pi$
$47$	−6.36875	+	2.31804i	−0.928978	+	0.338120i	−0.167174	+	0.985927i	$0.553464\pi$
$48$		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	−0.971594	−	0.236656i	$-0.923949\pi$
$59$	−6.96871	+	5.84744i	−0.907248	+	0.761272i	0.0643451	+	0.997928i	$0.479504\pi$
$60$		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	0.0388676	−	0.999244i	$-0.487625\pi$
$67$	3.41454	−	0.602076i	0.417153	−	0.0735553i	0.378285	+	0.925689i	$0.376514\pi$
$68$		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	$0.0937912\pi$
$71$	6.15069	+	10.6533i	0.729953	+	1.26431i	−0.226950	+	0.973906i	$0.572875\pi$
$72$		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	−0.596521	−	0.802598i	$-0.703451\pi$
$79$	−12.7241	−	2.24360i	−1.43157	−	0.252425i	−0.835051	+	0.550173i	$0.814562\pi$
$80$		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	$0.116995\pi$
$83$	−0.606931	+	3.44208i	−0.0666193	+	0.377817i	−0.999829	+	0.0184850i	$0.994116\pi$
$84$		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	0.999825	−	0.0186829i	$-0.00594731\pi$
$103$	8.19836	+	9.77043i	0.807808	+	0.962709i	−0.192017	+	0.981392i	$0.561503\pi$
$104$		0			0
$105$	−20.1289	−	23.4270i	−1.96438	−	2.28624i
$106$		0			0
$107$	−8.37346			−0.809493			−0.404747	−	0.914429i	$-0.632640\pi$
$107$	−8.37346			−0.809493			−0.404747	+	0.914429i	$0.632640\pi$
$108$		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	0.269656	−	0.962957i	$-0.413090\pi$
$127$	−4.83978	−	2.79425i	−0.429461	−	0.247949i	−0.699117	+	0.715007i	$0.746423\pi$
$128$		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	$0.0411832\pi$
$131$	20.9936	+	7.64103i	1.83422	+	0.667600i	0.842574	+	0.538580i	$0.181039\pi$
$132$		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	$-0.653647\pi$
$139$	5.43218	−	14.9248i	0.460751	−	1.26590i	0.924922	−	0.380158i	$-0.124130\pi$
$140$		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	−0.997848	−	0.0655768i	$-0.979111\pi$
$151$	−9.33895	+	11.1297i	−0.759993	+	0.905724i	0.237855	+	0.971301i	$0.423556\pi$
$152$		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	$0.170567\pi$
$163$			13.0371i			1.02115i	−0.859835	+	0.510573i	$0.829433\pi$
$164$		0			0
$165$	11.2332	+	3.94047i	0.874506	+	0.306765i
$166$		0			0
$167$	8.81147	−	7.39370i	0.681852	−	0.572142i	−0.234695	−	0.972069i	$-0.575409\pi$
$167$	8.81147	−	7.39370i	0.681852	−	0.572142i	0.916547	+	0.399927i	$0.130965\pi$
$168$		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	0.660625	−	0.750716i	$-0.270291\pi$
$179$	−4.27899	−	7.41142i	−0.319827	−	0.553956i	−0.980452	+	0.196760i	$0.936958\pi$
$180$		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	$-0.698330\pi$
$191$	3.35224	−	19.0115i	0.242560	−	1.37562i	0.826092	−	0.563535i	$-0.190559\pi$
$192$		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	−0.808443	−	0.588574i	$-0.799689\pi$
$199$	−9.91625	+	5.72515i	−0.702944	+	0.405845i	0.105499	+	0.994419i	$0.466356\pi$
$200$		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	0.831181	−	0.556001i	$-0.187665\pi$
$211$	2.02336	+	2.41135i	0.139294	+	0.166004i	−0.691887	+	0.722005i	$0.743221\pi$
$212$		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	$-0.956234\pi$
$223$	−4.77636	−	13.1229i	−0.319849	−	0.878777i	0.670714	−	0.741716i	$-0.265988\pi$
$224$		0			0
$225$	19.4784	−	17.1361i	1.29856	−	1.14241i
$226$		0			0
$227$	−8.05793	−	6.76141i	−0.534824	−	0.448770i	0.334940	−	0.942240i	$-0.391284\pi$
$227$	−8.05793	−	6.76141i	−0.534824	−	0.448770i	−0.869763	+	0.493469i	$0.835729\pi$
$228$		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	0.309779	−	0.950809i	$-0.399745\pi$
$239$	−0.990737	−	0.360599i	−0.0640854	−	0.0233252i	−0.373864	+	0.927484i	$0.621967\pi$
$240$		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	−0.864481	−	0.502666i	$-0.832353\pi$
$251$	0.0488134	−	0.0845473i	0.00308107	−	0.00533658i	0.867562	+	0.497329i	$0.165686\pi$
$252$		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	−0.647396	−	0.762154i	$-0.724142\pi$
$263$	−10.5968	+	3.85692i	−0.653427	+	0.237828i	−0.00603076	+	0.999982i	$0.501920\pi$
$264$		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	$0.0546765\pi$
$271$			5.62766i			0.341856i	−0.985284	+	0.170928i	$0.945323\pi$
$272$		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	−0.647931	−	0.761699i	$-0.724365\pi$
$283$	−16.7598	+	2.95521i	−0.996270	+	0.175669i	−0.348339	+	0.937369i	$0.613254\pi$
$284$		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	−0.0734201	−	0.997301i	$-0.523391\pi$
$307$	13.2034	−	7.62299i	0.753558	−	0.435067i	0.826978	+	0.562234i	$0.190058\pi$
$308$		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	$0.127830\pi$
$311$	3.33655	+	18.9225i	0.189199	+	1.07300i	−0.731243	+	0.682117i	$0.761059\pi$
$312$		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	0.997450	−	0.0713625i	$-0.0227347\pi$
$331$	3.41105	+	9.37178i	0.187488	+	0.515119i	−0.809962	+	0.586482i	$0.800513\pi$
$332$		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	0.481963	−	0.876192i	$-0.339924\pi$
$347$	5.36415	+	1.95239i	0.287962	+	0.104810i	−0.194000	+	0.981001i	$0.562146\pi$
$348$		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	−0.982350	−	0.187051i	$-0.940107\pi$
$359$	−6.23714	+	10.8031i	−0.329184	+	0.570163i	0.653166	+	0.757215i	$0.273440\pi$
$360$		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	−0.299022	−	0.954246i	$-0.596661\pi$
$367$	13.2693	−	15.8137i	0.692651	−	0.825470i	0.991674	+	0.128777i	$0.0411050\pi$
$368$		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	$0.0663754\pi$
$379$			8.06037i			0.414033i	−0.978337	+	0.207017i	$0.933625\pi$
$380$		0			0
$381$	−7.34173	+	6.30816i	−0.376128	+	0.323177i
$382$		0			0
$383$	−11.2804	+	9.46540i	−0.576403	+	0.483659i	−0.883764	−	0.467934i	$-0.844999\pi$
$383$	−11.2804	+	9.46540i	−0.576403	+	0.483659i	0.307361	+	0.951593i	$0.400554\pi$
$384$		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	$-0.718186\pi$
$419$	−6.20113	−	35.1684i	−0.302945	−	1.71809i	0.330078	−	0.943954i	$-0.392925\pi$
$420$		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	$-0.269170\pi$
$431$	27.5395			1.32653			0.663265	+	0.748385i	$0.269170\pi$
$432$		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	$-0.787134\pi$
$439$	−12.1961	−	33.5086i	−0.582089	−	1.59928i	0.202515	−	0.979279i	$-0.435089\pi$
$440$		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	$0.0288351\pi$
$443$	26.4763	+	22.2162i	1.25793	+	1.05553i	0.262026	+	0.965061i	$0.415609\pi$
$444$		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	$-0.760693\pi$
$463$	5.76889	−	15.8499i	0.268103	−	0.736607i	0.998560	−	0.0536484i	$-0.0170850\pi$
$464$		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	$0.362282\pi$
$467$	−12.4601	+	21.5816i	−0.576586	+	0.998677i	−0.995867	+	0.0908205i	$0.971051\pi$
$468$		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	0.409179	−	0.912454i	$-0.365815\pi$
$479$	28.6520	−	10.4285i	1.30914	−	0.476489i	0.899964	+	0.435965i	$0.143593\pi$
$480$		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	$0.166670\pi$
$487$			22.0685i			1.00002i	−0.866020	+	0.500009i	$0.833330\pi$
$488$		0			0
$489$	21.3080	+	7.47455i	0.963580	+	0.338011i
$490$		0			0
$491$	6.01397	−	5.04632i	0.271407	−	0.227737i	−0.496918	−	0.867797i	$-0.665535\pi$
$491$	6.01397	−	5.04632i	0.271407	−	0.227737i	0.768325	+	0.640060i	$0.221091\pi$
$492$		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	−0.466185	−	0.884687i	$-0.654372\pi$
$499$	−13.4404	+	2.36991i	−0.601676	+	0.106092i	−0.135490	+	0.990779i	$0.543261\pi$
$500$		0			0
$501$	−7.03247	−	18.6406i	−0.314187	−	0.832799i
$502$		0			0
$503$	11.0130	+	19.0751i	0.491047	+	0.850518i	0.999947	−	0.0103076i	$-0.00328106\pi$
$503$	11.0130	+	19.0751i	0.491047	+	0.850518i	−0.508900	+	0.860826i	$0.669948\pi$
$504$		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	−0.422441	−	0.906391i	$-0.638826\pi$
$523$	3.46003	−	1.99765i	0.151296	−	0.0873510i	0.573737	+	0.819040i	$0.305493\pi$
$524$		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	0.978609	−	0.205728i	$-0.0659561\pi$
$547$	2.26190	+	6.21452i	0.0967118	+	0.265714i	−0.881897	+	0.471441i	$0.843734\pi$
$548$		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	0.960795	−	0.277260i	$-0.0894262\pi$
$563$	36.0325	+	13.1147i	1.51859	+	0.552721i	0.557793	+	0.829980i	$0.311648\pi$
$564$		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	−0.915401	−	0.402544i	$-0.868126\pi$
$571$	1.06544	−	2.92726i	0.0445871	−	0.122502i	0.959988	+	0.280042i	$0.0903483\pi$
$572$		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	−0.268346	−	0.963323i	$-0.586477\pi$
$587$	3.52035	−	1.28130i	0.145301	−	0.0528851i	0.413647	+	0.910437i	$0.364255\pi$
$588$		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	−0.547401	−	0.836870i	$-0.684383\pi$
$599$	4.44701	−	3.73149i	0.181700	−	0.152464i	0.729101	+	0.684406i	$0.239938\pi$
$600$		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	−0.595394	−	0.803434i	$-0.703004\pi$
$607$	−21.6831	+	3.82332i	−0.880091	+	0.155184i	−0.284697	+	0.958618i	$0.591893\pi$
$608$		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	0.128159	−	0.991754i	$-0.459093\pi$
$619$	−2.25438	−	0.397508i	−0.0906113	−	0.0159772i	−0.218770	+	0.975776i	$0.570204\pi$
$620$		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	0.294997	−	0.955498i	$-0.404681\pi$
$631$	31.9016	−	18.4184i	1.26998	−	0.733224i	0.974984	+	0.222274i	$0.0713479\pi$
$632$		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	0.656594	−	0.754244i	$-0.271997\pi$
$643$	−5.07677	−	6.05026i	−0.200208	−	0.238599i	−0.856802	+	0.515646i	$0.827552\pi$
$644$		0			0
$645$	14.2546	−	40.6361i	0.561275	−	1.60005i
$646$		0			0
$647$	−36.4092			−1.43139			−0.715696	−	0.698412i	$-0.753891\pi$
$647$	−36.4092			−1.43139			−0.715696	+	0.698412i	$0.753891\pi$
$648$		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	−0.167835	−	0.985815i	$-0.553677\pi$
$659$	−29.9790	−	25.1554i	−1.16782	−	0.979915i	−0.999983	+	0.00590020i	$0.998122\pi$
$660$		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	$0.389691\pi$
$683$	−16.8492	+	29.1836i	−0.644716	+	1.11668i	−0.984367	+	0.176129i	$0.943642\pi$
$684$		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	−0.402949	−	0.915222i	$-0.632015\pi$
$691$	14.9399	−	17.8047i	0.568341	−	0.677322i	0.971290	+	0.237900i	$0.0764592\pi$
$692$		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	0.999162	−	0.0409318i	$-0.0130326\pi$
$719$	12.4453	+	21.5560i	0.464133	+	0.803902i	−0.535029	+	0.844834i	$0.679699\pi$
$720$		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	0.0723492	−	0.997379i	$-0.476950\pi$
$727$	−5.41385	−	0.954608i	−0.200789	−	0.0354044i	−0.273138	+	0.961975i	$0.588061\pi$
$728$		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	−0.386458	−	0.922307i	$-0.626302\pi$
$739$	5.95487	−	3.43805i	0.219054	−	0.126471i	0.605512	+	0.795836i	$0.292968\pi$
$740$		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	$-0.829831\pi$
$743$	−6.16444	−	34.9603i	−0.226151	−	1.28257i	0.634321	−	0.773070i	$-0.281280\pi$
$744$		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	0.849570	−	0.527475i	$-0.176861\pi$
$751$	5.00356	+	5.96301i	0.182583	+	0.217593i	−0.666988	+	0.745069i	$0.732417\pi$
$752$		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	−0.999828	−	0.0185432i	$-0.994097\pi$
$787$	−6.22777	+	17.1107i	−0.221996	+	0.609929i	0.777832	+	0.628472i	$0.216319\pi$
$788$		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	$-0.718936\pi$
$811$		−	44.0065i		−	1.54528i	0.634846	−	0.772639i	$-0.281064\pi$
$812$		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	0.102656	−	0.994717i	$-0.467266\pi$
$823$	15.4724	−	2.72820i	0.539335	−	0.0950992i	0.436678	+	0.899618i	$0.356155\pi$
$824$		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	$0.0778199\pi$
$827$	19.9795	+	34.6054i	0.694754	+	1.20335i	−0.275510	+	0.961298i	$0.588847\pi$
$828$		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	$0.190832\pi$
$839$	−4.14764	+	23.5225i	−0.143193	+	0.812085i	−0.968801	+	0.247841i	$0.920279\pi$
$840$		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	$-0.983595\pi$
$859$	−25.6741	−	30.5972i	−0.875988	−	1.04396i	0.122684	−	0.992446i	$-0.460850\pi$
$860$		0			0
$861$	−24.7660	+	4.66608i	−0.844024	+	0.159019i
$862$		0			0
$863$	−48.9308			−1.66562			−0.832812	−	0.553556i	$-0.813271\pi$
$863$	−48.9308			−1.66562			−0.832812	+	0.553556i	$0.813271\pi$
$864$		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	−0.246861	−	0.969051i	$-0.579399\pi$
$883$	−35.9411	−	20.7506i	−1.20951	−	0.698313i	−0.962653	+	0.270738i	$0.912732\pi$
$884$		0			0
$885$	−28.5132	+	50.7472i	−0.958460	+	1.70585i
$886$		0			0
$887$	−18.9386	−	6.89309i	−0.635896	−	0.231447i	0.00389928	−	0.999992i	$-0.498759\pi$
$887$	−18.9386	−	6.89309i	−0.635896	−	0.231447i	−0.639796	+	0.768545i	$0.720981\pi$
$888$		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	−0.988106	−	0.153774i	$-0.950857\pi$
$907$	−20.0300	+	23.8708i	−0.665086	+	0.792618i	0.323020	+	0.946392i	$0.395302\pi$
$908$		0			0
$909$	15.4212	−	45.6638i	0.511488	−	1.51457i
$910$		0			0
$911$	−28.6080	+	10.4125i	−0.947824	+	0.344980i	−0.769251	−	0.638947i	$-0.779370\pi$
$911$	−28.6080	+	10.4125i	−0.947824	+	0.344980i	−0.178573	+	0.983927i	$0.557148\pi$
$912$		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	$0.0861329\pi$
$919$			16.2067i			0.534608i	−0.963612	+	0.267304i	$0.913867\pi$
$920$		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	$0.221483\pi$
$947$	−5.32222	+	30.1838i	−0.172949	+	0.980843i	−0.940485	+	0.339836i	$0.889628\pi$
$948$		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	0.457665	−	0.889125i	$-0.348686\pi$
$967$	−15.4682	−	18.4343i	−0.497425	−	0.592808i	−0.955090	+	0.296317i	$0.904241\pi$
$968$		0			0
$969$	15.5689	−	44.3828i	0.500144	−	1.42578i
$970$		0			0
$971$	−34.7188			−1.11418			−0.557090	−	0.830452i	$-0.688082\pi$
$971$	−34.7188			−1.11418			−0.557090	+	0.830452i	$0.688082\pi$
$972$		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	0.968957	−	0.247229i	$-0.0795199\pi$
$983$	28.0213	+	23.5127i	0.893742	+	0.749939i	−0.0752152	+	0.997167i	$0.523964\pi$
$984$		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	0.757841	−	0.652439i	$-0.226254\pi$
$991$	17.9982	+	10.3913i	0.571732	+	0.330090i	−0.186109	+	0.982529i	$0.559588\pi$
$992$		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.191.4	yes	36
4.3	odd	2	inner	432.2.be.a.191.3	yes	36
27.14	odd	18	inner	432.2.be.a.95.3	✓	36
108.95	even	18	inner	432.2.be.a.95.4	yes	36

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

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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