LMFDB - Embedded newform 864.2.bi.a.95.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(95,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 17]))

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

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

chi := DirichletCharacter("864.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bi (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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			95.8
Character	$\chi$	$=$	864.95
Dual form			864.2.bi.a.191.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37511 + 1.05313i) q^{3} +(-2.70735 + 3.22649i) q^{5} +(-1.09514 + 3.00888i) q^{7} +(0.781832 - 2.89633i) q^{9} +O(q^{10})$	\(q+(-1.37511 + 1.05313i) q^{3} +(-2.70735 + 3.22649i) q^{5} +(-1.09514 + 3.00888i) q^{7} +(0.781832 - 2.89633i) q^{9} +(-3.08685 + 2.59017i) q^{11} +(-0.566736 + 3.21412i) q^{13} +(0.324973 - 7.28795i) q^{15} +(5.46002 + 3.15234i) q^{17} +(1.40054 - 0.808603i) q^{19} +(-1.66281 - 5.29086i) q^{21} +(-5.79404 + 2.10886i) q^{23} +(-2.21227 - 12.5464i) q^{25} +(1.97511 + 4.80613i) q^{27} +(0.703445 - 0.124036i) q^{29} +(0.713613 + 1.96063i) q^{31} +(1.51695 - 6.81262i) q^{33} +(-6.74319 - 11.6795i) q^{35} +(5.34490 - 9.25763i) q^{37} +(-2.60556 - 5.01660i) q^{39} +(2.61448 + 0.461004i) q^{41} +(0.700363 + 0.834660i) q^{43} +(7.22829 + 10.3639i) q^{45} +(3.53067 + 1.28506i) q^{47} +(-2.49172 - 2.09080i) q^{49} +(-10.8279 + 1.41531i) q^{51} +7.95497i q^{53} -16.9722i q^{55} +(-1.07433 + 2.58687i) q^{57} +(-11.7468 - 9.85673i) q^{59} +(4.39315 + 1.59898i) q^{61} +(7.85850 + 5.52434i) q^{63} +(-8.83596 - 10.5303i) q^{65} +(2.59524 + 0.457612i) q^{67} +(5.74652 - 9.00178i) q^{69} +(-2.55096 + 4.41839i) q^{71} +(-0.592851 - 1.02685i) q^{73} +(16.2551 + 14.9228i) q^{75} +(-4.41299 - 12.1246i) q^{77} +(3.23818 - 0.570978i) q^{79} +(-7.77748 - 4.52889i) q^{81} +(0.925883 + 5.25094i) q^{83} +(-24.9531 + 9.08220i) q^{85} +(-0.836685 + 0.911382i) q^{87} +(-2.18184 + 1.25968i) q^{89} +(-9.05024 - 5.22516i) q^{91} +(-3.04610 - 1.94455i) q^{93} +(-1.18280 + 6.70800i) q^{95} +(-5.89280 + 4.94464i) q^{97} +(5.08861 + 10.9656i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) $ 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.37511	+	1.05313i	−0.793918	+	0.608025i
$3$	−1.37511	+	1.05313i	−0.793918	+	0.608025i
$4$		0			0
$5$	−2.70735	+	3.22649i	−1.21076	+	1.44293i	−0.347868	+	0.937543i	$0.613094\pi$
$5$	−2.70735	+	3.22649i	−1.21076	+	1.44293i	−0.862893	+	0.505386i	$0.831350\pi$
$6$		0			0
$7$	−1.09514	+	3.00888i	−0.413925	+	1.13725i	0.541160	+	0.840920i	$0.317985\pi$
$7$	−1.09514	+	3.00888i	−0.413925	+	1.13725i	−0.955085	+	0.296331i	$0.904237\pi$
$8$		0			0
$9$	0.781832	−	2.89633i	0.260611	−	0.965444i
$10$		0			0
$11$	−3.08685	+	2.59017i	−0.930720	+	0.780967i	−0.975947	−	0.218010i	$-0.930044\pi$
$11$	−3.08685	+	2.59017i	−0.930720	+	0.780967i	0.0452265	+	0.998977i	$0.485599\pi$
$12$		0			0
$13$	−0.566736	+	3.21412i	−0.157184	+	0.891436i	0.799577	+	0.600563i	$0.205057\pi$
$13$	−0.566736	+	3.21412i	−0.157184	+	0.891436i	−0.956762	+	0.290873i	$0.906054\pi$
$14$		0			0
$15$	0.324973	−	7.28795i	0.0839077	−	1.88174i
$16$		0			0
$17$	5.46002	+	3.15234i	1.32425	+	0.764555i	0.984403	−	0.175926i	$-0.0562920\pi$
$17$	5.46002	+	3.15234i	1.32425	+	0.764555i	0.339845	+	0.940481i	$0.389625\pi$
$18$		0			0
$19$	1.40054	−	0.808603i	0.321306	−	0.185506i	−0.330668	−	0.943747i	$-0.607274\pi$
$19$	1.40054	−	0.808603i	0.321306	−	0.185506i	0.651975	+	0.758241i	$0.273941\pi$
$20$		0			0
$21$	−1.66281	−	5.29086i	−0.362854	−	1.15456i
$22$		0			0
$23$	−5.79404	+	2.10886i	−1.20814	+	0.439727i	−0.866059	−	0.499943i	$-0.833354\pi$
$23$	−5.79404	+	2.10886i	−1.20814	+	0.439727i	−0.342082	+	0.939670i	$0.611132\pi$
$24$		0			0
$25$	−2.21227	−	12.5464i	−0.442454	−	2.50928i
$26$		0			0
$27$	1.97511	+	4.80613i	0.380111	+	0.924941i
$28$		0			0
$29$	0.703445	−	0.124036i	0.130626	−	0.0230330i	−0.107953	−	0.994156i	$-0.534429\pi$
$29$	0.703445	−	0.124036i	0.130626	−	0.0230330i	0.238579	+	0.971123i	$0.423318\pi$
$30$		0			0
$31$	0.713613	+	1.96063i	0.128169	+	0.352140i	0.987134	−	0.159893i	$-0.0511148\pi$
$31$	0.713613	+	1.96063i	0.128169	+	0.352140i	−0.858966	+	0.512033i	$0.828893\pi$
$32$		0			0
$33$	1.51695	−	6.81262i	0.264068	−	1.18592i
$34$		0			0
$35$	−6.74319	−	11.6795i	−1.13981	−	1.97420i
$36$		0			0
$37$	5.34490	−	9.25763i	0.878696	−	1.52195i	0.0259223	−	0.999664i	$-0.491748\pi$
$37$	5.34490	−	9.25763i	0.878696	−	1.52195i	0.852773	−	0.522281i	$-0.174919\pi$
$38$		0			0
$39$	−2.60556	−	5.01660i	−0.417224	−	0.803299i
$40$		0			0
$41$	2.61448	+	0.461004i	0.408313	+	0.0719967i	0.374033	−	0.927416i	$-0.377975\pi$
$41$	2.61448	+	0.461004i	0.408313	+	0.0719967i	0.0342808	+	0.999412i	$0.489086\pi$
$42$		0			0
$43$	0.700363	+	0.834660i	0.106804	+	0.127284i	0.816798	−	0.576923i	$-0.195747\pi$
$43$	0.700363	+	0.834660i	0.106804	+	0.127284i	−0.709994	+	0.704208i	$0.751302\pi$
$44$		0			0
$45$	7.22829	+	10.3639i	1.07753	+	1.54497i
$46$		0			0
$47$	3.53067	+	1.28506i	0.515001	+	0.187445i	0.586429	−	0.810001i	$-0.300533\pi$
$47$	3.53067	+	1.28506i	0.515001	+	0.187445i	−0.0714281	+	0.997446i	$0.522756\pi$
$48$		0			0
$49$	−2.49172	−	2.09080i	−0.355960	−	0.298686i
$50$		0			0
$51$	−10.8279	+	1.41531i	−1.51621	+	0.198182i
$52$		0			0
$53$			7.95497i			1.09270i	0.837557	+	0.546350i	$0.183983\pi$
$53$			7.95497i			1.09270i	−0.837557	+	0.546350i	$0.816017\pi$
$54$		0			0
$55$		−	16.9722i		−	2.28853i
$56$		0			0
$57$	−1.07433	+	2.58687i	−0.142298	+	0.342639i
$58$		0			0
$59$	−11.7468	−	9.85673i	−1.52930	−	1.28324i	−0.803398	−	0.595443i	$-0.796977\pi$
$59$	−11.7468	−	9.85673i	−1.52930	−	1.28324i	−0.725905	−	0.687795i	$-0.758579\pi$
$60$		0			0
$61$	4.39315	+	1.59898i	0.562485	+	0.204728i	0.607585	−	0.794255i	$-0.292138\pi$
$61$	4.39315	+	1.59898i	0.562485	+	0.204728i	−0.0450999	+	0.998982i	$0.514361\pi$
$62$		0			0
$63$	7.85850	+	5.52434i	0.990078	+	0.696001i
$64$		0			0
$65$	−8.83596	−	10.5303i	−1.09597	−	1.30612i
$66$		0			0
$67$	2.59524	+	0.457612i	0.317060	+	0.0559062i	0.329913	−	0.944011i	$-0.392980\pi$
$67$	2.59524	+	0.457612i	0.317060	+	0.0559062i	−0.0128538	+	0.999917i	$0.504092\pi$
$68$		0			0
$69$	5.74652	−	9.00178i	0.691799	−	1.08369i
$70$		0			0
$71$	−2.55096	+	4.41839i	−0.302743	+	0.524367i	−0.976756	−	0.214353i	$-0.931236\pi$
$71$	−2.55096	+	4.41839i	−0.302743	+	0.524367i	0.674013	+	0.738719i	$0.264569\pi$
$72$		0			0
$73$	−0.592851	−	1.02685i	−0.0693879	−	0.120183i	0.829244	−	0.558887i	$-0.188771\pi$
$73$	−0.592851	−	1.02685i	−0.0693879	−	0.120183i	−0.898632	+	0.438703i	$0.855438\pi$
$74$		0			0
$75$	16.2551	+	14.9228i	1.87698	+	1.72314i
$76$		0			0
$77$	−4.41299	−	12.1246i	−0.502906	−	1.38172i
$78$		0			0
$79$	3.23818	−	0.570978i	0.364324	−	0.0642401i	0.0115101	−	0.999934i	$-0.496336\pi$
$79$	3.23818	−	0.570978i	0.364324	−	0.0642401i	0.352813	+	0.935694i	$0.385225\pi$
$80$		0			0
$81$	−7.77748	−	4.52889i	−0.864164	−	0.503210i
$82$		0			0
$83$	0.925883	+	5.25094i	0.101629	+	0.576366i	0.992513	+	0.122136i	$0.0389744\pi$
$83$	0.925883	+	5.25094i	0.101629	+	0.576366i	−0.890885	+	0.454230i	$0.849914\pi$
$84$		0			0
$85$	−24.9531	+	9.08220i	−2.70655	+	0.985103i
$86$		0			0
$87$	−0.836685	+	0.911382i	−0.0897020	+	0.0977104i
$88$		0			0
$89$	−2.18184	+	1.25968i	−0.231274	+	0.133526i	−0.611160	−	0.791507i	$-0.709297\pi$
$89$	−2.18184	+	1.25968i	−0.231274	+	0.133526i	0.379885	+	0.925034i	$0.375963\pi$
$90$		0			0
$91$	−9.05024	−	5.22516i	−0.948723	−	0.547746i
$92$		0			0
$93$	−3.04610	−	1.94455i	−0.315866	−	0.201641i
$94$		0			0
$95$	−1.18280	+	6.70800i	−0.121353	+	0.688226i
$96$		0			0
$97$	−5.89280	+	4.94464i	−0.598323	+	0.502053i	−0.890906	−	0.454188i	$-0.849930\pi$
$97$	−5.89280	+	4.94464i	−0.598323	+	0.502053i	0.292583	+	0.956240i	$0.405485\pi$
$98$		0			0
$99$	5.08861	+	10.9656i	0.511424	+	1.10209i
$100$		0			0
$101$	−3.39870	+	9.33784i	−0.338183	+	0.929150i	0.647727	+	0.761872i	$0.275720\pi$
$101$	−3.39870	+	9.33784i	−0.338183	+	0.929150i	−0.985910	+	0.167277i	$0.946502\pi$
$102$		0			0
$103$	0.818246	−	0.975148i	0.0806242	−	0.0960841i	−0.724224	−	0.689564i	$-0.757802\pi$
$103$	0.818246	−	0.975148i	0.0806242	−	0.0960841i	0.804849	+	0.593480i	$0.202246\pi$
$104$		0			0
$105$	21.5727	+	8.95916i	2.10528	+	0.874324i
$106$		0			0
$107$	18.8546			1.82275			0.911373	−	0.411581i	$-0.135023\pi$
$107$	18.8546			1.82275			0.911373	+	0.411581i	$0.135023\pi$
$108$		0			0
$109$	−4.11853			−0.394484			−0.197242	−	0.980355i	$-0.563198\pi$
$109$	−4.11853			−0.394484			−0.197242	+	0.980355i	$0.563198\pi$
$110$		0			0
$111$	2.39970	+	18.3591i	0.227769	+	1.74257i
$112$		0			0
$113$	−0.561705	+	0.669414i	−0.0528408	+	0.0629732i	−0.791817	−	0.610758i	$-0.790865\pi$
$113$	−0.561705	+	0.669414i	−0.0528408	+	0.0629732i	0.738977	+	0.673731i	$0.235309\pi$
$114$		0			0
$115$	8.88226	−	24.4038i	0.828275	−	2.27567i
$116$		0			0
$117$	8.86606	+	4.15436i	0.819667	+	0.384070i
$118$		0			0
$119$	−15.4645	+	12.9763i	−1.41763	+	1.18953i
$120$		0			0
$121$	0.909507	−	5.15807i	0.0826824	−	0.468915i
$122$		0			0
$123$	−4.08069	+	2.11946i	−0.367943	+	0.191105i
$124$		0			0
$125$	28.2322	+	16.2999i	2.52516	+	1.45790i
$126$		0			0
$127$	2.50643	−	1.44709i	0.222409	−	0.128408i	−0.384656	−	0.923060i	$-0.625680\pi$
$127$	2.50643	−	1.44709i	0.222409	−	0.128408i	0.607065	+	0.794652i	$0.292347\pi$
$128$		0			0
$129$	−1.84208	−	0.410172i	−0.162186	−	0.0361137i
$130$		0			0
$131$	12.6881	−	4.61810i	1.10857	−	0.403486i	0.278100	−	0.960552i	$-0.410295\pi$
$131$	12.6881	−	4.61810i	1.10857	−	0.403486i	0.830468	+	0.557066i	$0.188073\pi$
$132$		0			0
$133$	0.899197	+	5.09960i	0.0779703	+	0.442191i
$134$		0			0
$135$	−20.8542	−	6.63918i	−1.79485	−	0.571410i
$136$		0			0
$137$	−12.2332	+	2.15705i	−1.04516	+	0.184289i	−0.669762	−	0.742576i	$-0.733604\pi$
$137$	−12.2332	+	2.15705i	−1.04516	+	0.184289i	−0.375394	+	0.926865i	$0.622493\pi$
$138$		0			0
$139$	0.494567	+	1.35881i	0.0419486	+	0.115253i	0.958898	−	0.283750i	$-0.0915786\pi$
$139$	0.494567	+	1.35881i	0.0419486	+	0.115253i	−0.916950	+	0.399003i	$0.869356\pi$
$140$		0			0
$141$	−6.20837	+	1.95116i	−0.522839	+	0.164317i
$142$		0			0
$143$	−6.57570	−	11.3894i	−0.549887	−	0.952433i
$144$		0			0
$145$	−1.50427	+	2.60547i	−0.124923	+	0.216372i
$146$		0			0
$147$	5.62826	+	0.250967i	0.464211	+	0.0206994i
$148$		0			0
$149$	−11.9926	−	2.11461i	−0.982470	−	0.173236i	−0.340732	−	0.940160i	$-0.610675\pi$
$149$	−11.9926	−	2.11461i	−0.982470	−	0.173236i	−0.641737	+	0.766924i	$0.721786\pi$
$150$		0			0
$151$	1.25460	+	1.49518i	0.102098	+	0.121676i	0.814674	−	0.579919i	$-0.196916\pi$
$151$	1.25460	+	1.49518i	0.102098	+	0.121676i	−0.712576	+	0.701595i	$0.752472\pi$
$152$		0			0
$153$	13.3990	−	13.3494i	1.08325	−	1.07924i
$154$		0			0
$155$	−8.25796	−	3.00565i	−0.663295	−	0.241420i
$156$		0			0
$157$	5.48312	+	4.60088i	0.437601	+	0.367191i	0.834811	−	0.550537i	$-0.185577\pi$
$157$	5.48312	+	4.60088i	0.437601	+	0.367191i	−0.397210	+	0.917728i	$0.630022\pi$
$158$		0			0
$159$	−8.37762	−	10.9389i	−0.664389	−	0.867513i
$160$		0			0
$161$		−	19.7431i		−	1.55597i
$162$		0			0
$163$		−	3.09562i		−	0.242468i	−0.992624	−	0.121234i	$-0.961315\pi$
$163$		−	3.09562i		−	0.242468i	0.992624	−	0.121234i	$-0.0386851\pi$
$164$		0			0
$165$	17.8739	+	23.3385i	1.39148	+	1.81690i
$166$		0			0
$167$	11.8813	+	9.96961i	0.919404	+	0.771472i	0.973885	−	0.227043i	$-0.0729058\pi$
$167$	11.8813	+	9.96961i	0.919404	+	0.771472i	−0.0544804	+	0.998515i	$0.517350\pi$
$168$		0			0
$169$	2.20664	+	0.803151i	0.169742	+	0.0617809i
$170$		0			0
$171$	−1.24699	−	4.68862i	−0.0953600	−	0.358548i
$172$		0			0
$173$	4.75485	+	5.66661i	0.361505	+	0.430825i	0.915886	−	0.401438i	$-0.131490\pi$
$173$	4.75485	+	5.66661i	0.361505	+	0.430825i	−0.554381	+	0.832263i	$0.687045\pi$
$174$		0			0
$175$	40.1734	+	7.08365i	3.03682	+	0.535474i
$176$		0			0
$177$	26.5335	+	1.18314i	1.99438	+	0.0889304i
$178$		0			0
$179$	2.12193	−	3.67529i	0.158600	−	0.274704i	−0.775764	−	0.631023i	$-0.782635\pi$
$179$	2.12193	−	3.67529i	0.158600	−	0.274704i	0.934364	+	0.356320i	$0.115969\pi$
$180$		0			0
$181$	−11.3652	−	19.6852i	−0.844771	−	1.46319i	−0.885820	−	0.464029i	$-0.846403\pi$
$181$	−11.3652	−	19.6852i	−0.844771	−	1.46319i	0.0410496	−	0.999157i	$-0.486930\pi$
$182$		0			0
$183$	−7.72498	+	2.42780i	−0.571047	+	0.179468i
$184$		0			0
$185$	15.3992	+	42.3088i	1.13217	+	3.11061i
$186$		0			0
$187$	−25.0194	+	4.41159i	−1.82960	+	0.322607i
$188$		0			0
$189$	−16.6241	+	0.679476i	−1.20923	+	0.0494246i
$190$		0			0
$191$	−2.14394	−	12.1589i	−0.155130	−	0.879785i	−0.958667	−	0.284530i	$-0.908162\pi$
$191$	−2.14394	−	12.1589i	−0.155130	−	0.879785i	0.803537	−	0.595254i	$-0.202949\pi$
$192$		0			0
$193$	−0.124160	+	0.0451907i	−0.00893727	+	0.00325290i	−0.346485	−	0.938056i	$-0.612625\pi$
$193$	−0.124160	+	0.0451907i	−0.00893727	+	0.00325290i	0.337548	+	0.941308i	$0.390403\pi$
$194$		0			0
$195$	23.2402	+	5.17484i	1.66426	+	0.370578i
$196$		0			0
$197$	−17.2738	+	9.97305i	−1.23071	+	0.710551i	−0.967178	−	0.254100i	$-0.918221\pi$
$197$	−17.2738	+	9.97305i	−1.23071	+	0.710551i	−0.263532	+	0.964651i	$0.584887\pi$
$198$		0			0
$199$	7.03614	+	4.06232i	0.498779	+	0.287970i	0.728209	−	0.685355i	$-0.240353\pi$
$199$	7.03614	+	4.06232i	0.498779	+	0.287970i	−0.229430	+	0.973325i	$0.573686\pi$
$200$		0			0
$201$	−4.05066	+	2.10387i	−0.285712	+	0.148395i
$202$		0			0
$203$	−0.397162	+	2.25242i	−0.0278753	+	0.158089i
$204$		0			0
$205$	−8.56573	+	7.18750i	−0.598256	+	0.501997i
$206$		0			0
$207$	1.57799	+	18.4302i	0.109678	+	1.28099i
$208$		0			0
$209$	−2.22884	+	6.12368i	−0.154172	+	0.423584i
$210$		0			0
$211$	−15.9101	+	18.9610i	−1.09530	+	1.30533i	−0.146582	+	0.989199i	$0.546827\pi$
$211$	−15.9101	+	18.9610i	−1.09530	+	1.30533i	−0.948717	+	0.316127i	$0.897617\pi$
$212$		0			0
$213$	−1.14530	−	8.76225i	−0.0784749	−	0.600379i
$214$		0			0
$215$	−4.58915			−0.312977
$216$		0			0
$217$	−6.68083			−0.453524
$218$		0			0
$219$	1.89664	+	0.787675i	0.128163	+	0.0532261i
$220$		0			0
$221$	−13.2264	+	15.7626i	−0.889703	+	1.06031i
$222$		0			0
$223$	6.18444	−	16.9916i	0.414141	−	1.13784i	−0.540828	−	0.841133i	$-0.681889\pi$
$223$	6.18444	−	16.9916i	0.414141	−	1.13784i	0.954968	−	0.296708i	$-0.0958889\pi$
$224$		0			0
$225$	−38.0681	−	3.40171i	−2.53788	−	0.226781i
$226$		0			0
$227$	0.950816	−	0.797830i	0.0631079	−	0.0529538i	−0.610688	−	0.791871i	$-0.709107\pi$
$227$	0.950816	−	0.797830i	0.0631079	−	0.0529538i	0.673796	+	0.738917i	$0.264663\pi$
$228$		0			0
$229$	1.10463	−	6.26465i	0.0729957	−	0.413979i	−0.926311	−	0.376759i	$-0.877039\pi$
$229$	1.10463	−	6.26465i	0.0729957	−	0.413979i	0.999307	−	0.0372205i	$-0.0118504\pi$
$230$		0			0
$231$	18.8371	+	12.0251i	1.23939	+	0.791195i
$232$		0			0
$233$	10.4489	+	6.03265i	0.684527	+	0.395212i	0.801559	−	0.597916i	$-0.204004\pi$
$233$	10.4489	+	6.03265i	0.684527	+	0.395212i	−0.117031	+	0.993128i	$0.537338\pi$
$234$		0			0
$235$	−13.7050	+	7.91256i	−0.894013	+	0.516158i
$236$		0			0
$237$	−3.85152	+	4.19538i	−0.250183	+	0.272519i
$238$		0			0
$239$	−1.95326	+	0.710928i	−0.126346	+	0.0459861i	−0.404419	−	0.914574i	$-0.632526\pi$
$239$	−1.95326	+	0.710928i	−0.126346	+	0.0459861i	0.278073	+	0.960560i	$0.410304\pi$
$240$		0			0
$241$	4.59859	+	26.0799i	0.296221	+	1.67995i	0.662198	+	0.749329i	$0.269624\pi$
$241$	4.59859	+	26.0799i	0.296221	+	1.67995i	−0.365977	+	0.930624i	$0.619265\pi$
$242$		0			0
$243$	15.4644	−	1.96299i	0.992040	−	0.125926i
$244$		0			0
$245$	13.4919	−	2.37898i	0.861965	−	0.151988i
$246$		0			0
$247$	1.80521	+	4.95977i	0.114863	+	0.315582i
$248$		0			0
$249$	−6.80312	−	6.24553i	−0.431130	−	0.395794i
$250$		0			0
$251$	−6.63819	−	11.4977i	−0.418999	−	0.725727i	0.576840	−	0.816857i	$-0.304286\pi$
$251$	−6.63819	−	11.4977i	−0.418999	−	0.725727i	−0.995839	+	0.0911298i	$0.970952\pi$
$252$		0			0
$253$	12.4230	−	21.5173i	0.781029	−	1.35278i
$254$		0			0
$255$	24.7485	−	38.7679i	1.54981	−	2.42774i
$256$		0			0
$257$	−5.54784	−	0.978234i	−0.346065	−	0.0610206i	−0.00208562	−	0.999998i	$-0.500664\pi$
$257$	−5.54784	−	0.978234i	−0.346065	−	0.0610206i	−0.343979	+	0.938977i	$0.611775\pi$
$258$		0			0
$259$	22.0017	+	26.2206i	1.36712	+	1.62927i
$260$		0			0
$261$	0.190726	−	2.13439i	0.0118056	−	0.132115i
$262$		0			0
$263$	−25.9808	−	9.45624i	−1.60204	−	0.583097i	−0.622200	−	0.782858i	$-0.713761\pi$
$263$	−25.9808	−	9.45624i	−1.60204	−	0.583097i	−0.979845	+	0.199761i	$0.935983\pi$
$264$		0			0
$265$	−25.6666	−	21.5369i	−1.57669	−	1.32300i
$266$		0			0
$267$	1.67365	−	4.02996i	0.102425	−	0.246630i
$268$		0			0
$269$		−	21.0294i		−	1.28219i	−0.767463	−	0.641093i	$-0.778481\pi$
$269$		−	21.0294i		−	1.28219i	0.767463	−	0.641093i	$-0.221519\pi$
$270$		0			0
$271$			16.2159i			0.985046i	0.870300	+	0.492523i	$0.163925\pi$
$271$			16.2159i			0.985046i	−0.870300	+	0.492523i	$0.836075\pi$
$272$		0			0
$273$	17.9478	−	2.34594i	1.08625	−	0.141983i
$274$		0			0
$275$	39.3263	+	32.9987i	2.37146	+	1.98989i
$276$		0			0
$277$	1.97917	+	0.720358i	0.118917	+	0.0432821i	0.400793	−	0.916169i	$-0.368735\pi$
$277$	1.97917	+	0.720358i	0.118917	+	0.0432821i	−0.281876	+	0.959451i	$0.590957\pi$
$278$		0			0
$279$	6.23658	−	0.533972i	0.373374	−	0.0319680i
$280$		0			0
$281$	−0.708607	−	0.844485i	−0.0422719	−	0.0503777i	0.744494	−	0.667629i	$-0.232691\pi$
$281$	−0.708607	−	0.844485i	−0.0422719	−	0.0503777i	−0.786766	+	0.617251i	$0.788246\pi$
$282$		0			0
$283$	−8.37338	−	1.47645i	−0.497746	−	0.0877660i	−0.0808609	−	0.996725i	$-0.525767\pi$
$283$	−8.37338	−	1.47645i	−0.497746	−	0.0877660i	−0.416885	+	0.908959i	$0.636878\pi$
$284$		0			0
$285$	−5.43792	−	10.4698i	−0.322115	−	0.620180i
$286$		0			0
$287$	−4.25034	+	7.36180i	−0.250889	+	0.434553i
$288$		0			0
$289$	11.3745	+	19.7012i	0.669089	+	1.15890i
$290$		0			0
$291$	2.89586	−	13.0053i	0.169759	−	0.762384i
$292$		0			0
$293$	−0.809181	−	2.22321i	−0.0472729	−	0.129881i	0.913810	−	0.406143i	$-0.133127\pi$
$293$	−0.809181	−	2.22321i	−0.0472729	−	0.129881i	−0.961082	+	0.276262i	$0.910904\pi$
$294$		0			0
$295$	63.6053	−	11.2153i	3.70324	−	0.652982i
$296$		0			0
$297$	−18.5456	−	9.71993i	−1.07612	−	0.564007i
$298$		0			0
$299$	−3.49443	−	19.8179i	−0.202088	−	1.14610i
$300$		0			0
$301$	−3.27839	+	1.19324i	−0.188963	+	0.0687770i
$302$		0			0
$303$	−5.16040	−	16.4198i	−0.296457	−	0.943292i
$304$		0			0
$305$	−17.0528	+	9.84547i	−0.976443	+	0.563750i
$306$		0			0
$307$	−16.3316	−	9.42906i	−0.932094	−	0.538145i	−0.0446210	−	0.999004i	$-0.514208\pi$
$307$	−16.3316	−	9.42906i	−0.932094	−	0.538145i	−0.887473	+	0.460859i	$0.847541\pi$
$308$		0			0
$309$	−0.0982172	+	2.20265i	−0.00558738	+	0.125304i
$310$		0			0
$311$	−1.94201	+	11.0137i	−0.110121	+	0.624529i	0.878929	+	0.476952i	$0.158258\pi$
$311$	−1.94201	+	11.0137i	−0.110121	+	0.624529i	−0.989051	+	0.147577i	$0.952853\pi$
$312$		0			0
$313$	11.8510	−	9.94415i	0.669857	−	0.562077i	−0.243166	−	0.969985i	$-0.578186\pi$
$313$	11.8510	−	9.94415i	0.669857	−	0.562077i	0.913023	+	0.407908i	$0.133742\pi$
$314$		0			0
$315$	−39.0999	+	10.3991i	−2.20303	+	0.585921i
$316$		0			0
$317$	8.58794	−	23.5952i	0.482347	−	1.32524i	−0.425129	−	0.905133i	$-0.639771\pi$
$317$	8.58794	−	23.5952i	0.482347	−	1.32524i	0.907476	−	0.420104i	$-0.138007\pi$
$318$		0			0
$319$	−1.85015	+	2.20493i	−0.103589	+	0.123452i
$320$		0			0
$321$	−25.9271	+	19.8564i	−1.44711	+	1.10828i
$322$		0			0
$323$	10.1960			0.567319
$324$		0			0
$325$	41.5794			2.30641
$326$		0			0
$327$	5.66341	−	4.33735i	0.313187	−	0.239856i
$328$		0			0
$329$	−7.73317	+	9.21603i	−0.426344	+	0.508096i
$330$		0			0
$331$	8.34790	−	22.9357i	0.458842	−	1.26066i	−0.467506	−	0.883990i	$-0.654847\pi$
$331$	8.34790	−	22.9357i	0.458842	−	1.26066i	0.926348	−	0.376669i	$-0.122930\pi$
$332$		0			0
$333$	−22.6344	−	22.7185i	−1.24036	−	1.24497i
$334$		0			0
$335$	−8.50270	+	7.13461i	−0.464552	+	0.389806i
$336$		0			0
$337$	4.83478	−	27.4194i	0.263367	−	1.49363i	−0.510277	−	0.860010i	$-0.670457\pi$
$337$	4.83478	−	27.4194i	0.263367	−	1.49363i	0.773644	−	0.633620i	$-0.218432\pi$
$338$		0			0
$339$	0.0674236	−	1.51206i	0.00366195	−	0.0821240i
$340$		0			0
$341$	−7.28120	−	4.20380i	−0.394299	−	0.227649i
$342$		0			0
$343$	−10.3912	+	5.99939i	−0.561074	+	0.323936i
$344$		0			0
$345$	13.4863	+	42.9120i	0.726081	+	2.31030i
$346$		0			0
$347$	−20.1820	+	7.34563i	−1.08342	+	0.394334i	−0.821181	−	0.570667i	$-0.806685\pi$
$347$	−20.1820	+	7.34563i	−1.08342	+	0.394334i	−0.262243	+	0.965002i	$0.584462\pi$
$348$		0			0
$349$	1.26072	+	7.14992i	0.0674850	+	0.382726i	0.999779	+	0.0210248i	$0.00669290\pi$
$349$	1.26072	+	7.14992i	0.0674850	+	0.382726i	−0.932294	+	0.361701i	$0.882196\pi$
$350$		0			0
$351$	−16.5668	+	3.62444i	−0.884273	+	0.193458i
$352$		0			0
$353$	15.0136	−	2.64730i	0.799092	−	0.140902i	0.240831	−	0.970567i	$-0.422580\pi$
$353$	15.0136	−	2.64730i	0.799092	−	0.140902i	0.558261	+	0.829665i	$0.311469\pi$
$354$		0			0
$355$	−7.34956	−	20.1928i	−0.390074	−	1.07172i
$356$		0			0
$357$	7.59965	−	34.1299i	0.402216	−	1.80635i
$358$		0			0
$359$	−8.20384	−	14.2095i	−0.432982	−	0.749947i	0.564146	−	0.825675i	$-0.309205\pi$
$359$	−8.20384	−	14.2095i	−0.432982	−	0.749947i	−0.997129	+	0.0757275i	$0.975872\pi$
$360$		0			0
$361$	−8.19232	+	14.1895i	−0.431175	+	0.746817i
$362$		0			0
$363$	4.18145	+	8.05072i	0.219469	+	0.422553i
$364$		0			0
$365$	4.91816	+	0.867205i	0.257428	+	0.0453916i
$366$		0			0
$367$	−18.6520	−	22.2286i	−0.973627	−	1.16032i	−0.987050	−	0.160413i	$-0.948717\pi$
$367$	−18.6520	−	22.2286i	−0.973627	−	1.16032i	0.0134235	−	0.999910i	$-0.495727\pi$
$368$		0			0
$369$	3.37931	−	7.21198i	0.175920	−	0.375441i
$370$		0			0
$371$	−23.9356	−	8.71183i	−1.24267	−	0.452296i
$372$		0			0
$373$	22.5404	+	18.9137i	1.16710	+	0.979312i	0.999978	−	0.00662470i	$-0.00210872\pi$
$373$	22.5404	+	18.9137i	1.16710	+	0.979312i	0.167120	+	0.985937i	$0.446553\pi$
$374$		0			0
$375$	−55.9881	+	7.31814i	−2.89121	+	0.377907i
$376$		0			0
$377$			2.33125i			0.120066i
$378$		0			0
$379$			27.7312i			1.42445i	0.701949	+	0.712227i	$0.252313\pi$
$379$			27.7312i			1.42445i	−0.701949	+	0.712227i	$0.747687\pi$
$380$		0			0
$381$	−1.92263	+	4.62949i	−0.0984994	+	0.237176i
$382$		0			0
$383$	5.96255	+	5.00317i	0.304672	+	0.255650i	0.782286	−	0.622920i	$-0.214054\pi$
$383$	5.96255	+	5.00317i	0.304672	+	0.255650i	−0.477614	+	0.878570i	$0.658498\pi$
$384$		0			0
$385$	51.0673	+	18.5870i	2.60263	+	0.947280i
$386$		0			0
$387$	2.96502	−	1.37592i	0.150720	−	0.0699419i
$388$		0			0
$389$	−13.4849	−	16.0707i	−0.683712	−	0.814816i	0.306868	−	0.951752i	$-0.400719\pi$
$389$	−13.4849	−	16.0707i	−0.683712	−	0.814816i	−0.990580	+	0.136936i	$0.956274\pi$
$390$		0			0
$391$	−38.2834	−	6.75040i	−1.93607	−	0.341382i
$392$		0			0
$393$	−12.5841	+	19.7126i	−0.634782	+	0.994372i
$394$		0			0
$395$	−6.92461	+	11.9938i	−0.348415	+	0.603473i
$396$		0			0
$397$	−12.5762	−	21.7826i	−0.631180	−	1.09324i	−0.987311	−	0.158799i	$-0.949238\pi$
$397$	−12.5762	−	21.7826i	−0.631180	−	1.09324i	0.356131	−	0.934436i	$-0.384096\pi$
$398$		0			0
$399$	−6.60703	−	6.06552i	−0.330765	−	0.303656i
$400$		0			0
$401$	3.72092	+	10.2232i	0.185814	+	0.510520i	0.997266	−	0.0738996i	$-0.0235444\pi$
$401$	3.72092	+	10.2232i	0.185814	+	0.510520i	−0.811452	+	0.584420i	$0.801322\pi$
$402$		0			0
$403$	−6.70614	+	1.18247i	−0.334057	+	0.0589032i
$404$		0			0
$405$	35.6687	−	12.8327i	1.77239	−	0.637660i
$406$		0			0
$407$	7.47999	+	42.4211i	0.370769	+	2.10274i
$408$		0			0
$409$	−17.6809	+	6.43533i	−0.874265	+	0.318207i	−0.739893	−	0.672724i	$-0.765124\pi$
$409$	−17.6809	+	6.43533i	−0.874265	+	0.318207i	−0.134372	+	0.990931i	$0.542902\pi$
$410$		0			0
$411$	14.5503	−	15.8494i	0.717715	−	0.781791i
$412$		0			0
$413$	42.5222	−	24.5502i	2.09238	−	1.20804i
$414$		0			0
$415$	−19.4488	−	11.2288i	−0.954704	−	0.551198i
$416$		0			0
$417$	−2.11109	−	1.34767i	−0.103380	−	0.0659955i
$418$		0			0
$419$	3.94169	−	22.3544i	0.192564	−	1.09208i	−0.723281	−	0.690553i	$-0.757367\pi$
$419$	3.94169	−	22.3544i	0.192564	−	1.09208i	0.915845	−	0.401531i	$-0.131522\pi$
$420$		0			0
$421$	−14.5250	+	12.1879i	−0.707907	+	0.594004i	−0.924011	−	0.382366i	$-0.875109\pi$
$421$	−14.5250	+	12.1879i	−0.707907	+	0.594004i	0.216104	+	0.976370i	$0.430665\pi$
$422$		0			0
$423$	6.48234	−	9.22128i	0.315182	−	0.448354i
$424$		0			0
$425$	27.4715	−	75.4774i	1.33256	−	3.66119i
$426$		0			0
$427$	−9.62226	+	11.4674i	−0.465654	+	0.554944i
$428$		0			0
$429$	21.0368	+	8.73662i	1.01567	+	0.421808i
$430$		0			0
$431$	14.6867			0.707433			0.353716	−	0.935353i	$-0.384918\pi$
$431$	14.6867			0.707433			0.353716	+	0.935353i	$0.384918\pi$
$432$		0			0
$433$	−23.6615			−1.13710			−0.568551	−	0.822648i	$-0.692496\pi$
$433$	−23.6615			−1.13710			−0.568551	+	0.822648i	$0.692496\pi$
$434$		0			0
$435$	−0.675370	−	5.16698i	−0.0323815	−	0.247738i
$436$		0			0
$437$	−6.40956	+	7.63862i	−0.306611	+	0.365405i
$438$		0			0
$439$	−6.89667	+	18.9484i	−0.329160	+	0.904359i	0.659165	+	0.751998i	$0.270910\pi$
$439$	−6.89667	+	18.9484i	−0.329160	+	0.904359i	−0.988325	+	0.152361i	$0.951312\pi$
$440$		0			0
$441$	−8.00376	+	5.58219i	−0.381131	+	0.265819i
$442$		0			0
$443$	16.4201	−	13.7781i	0.780144	−	0.654619i	−0.163141	−	0.986603i	$-0.552162\pi$
$443$	16.4201	−	13.7781i	0.780144	−	0.654619i	0.943285	+	0.331984i	$0.107718\pi$
$444$		0			0
$445$	1.84263	−	10.4501i	0.0873490	−	0.495381i
$446$		0			0
$447$	18.7180	−	9.72193i	0.885332	−	0.459831i
$448$		0			0
$449$	−5.40185	−	3.11876i	−0.254929	−	0.147183i	0.367090	−	0.930185i	$-0.380354\pi$
$449$	−5.40185	−	3.11876i	−0.254929	−	0.147183i	−0.622019	+	0.783002i	$0.713687\pi$
$450$		0			0
$451$	−9.26459	+	5.34891i	−0.436253	+	0.251871i
$452$		0			0
$453$	−3.29983	−	0.734767i	−0.155039	−	0.0345224i
$454$		0			0
$455$	41.3611	−	15.0542i	1.93904	−	0.705751i
$456$		0			0
$457$	1.59101	+	9.02308i	0.0744244	+	0.422082i	0.999142	+	0.0414269i	$0.0131904\pi$
$457$	1.59101	+	9.02308i	0.0744244	+	0.422082i	−0.924717	+	0.380655i	$0.875699\pi$
$458$		0			0
$459$	−4.36643	+	32.4678i	−0.203807	+	1.51547i
$460$		0			0
$461$	−34.9759	+	6.16719i	−1.62899	+	0.287235i	−0.912105	−	0.409957i	$-0.865544\pi$
$461$	−34.9759	+	6.16719i	−1.62899	+	0.287235i	−0.716885	+	0.697192i	$0.754433\pi$
$462$		0			0
$463$	−3.81337	−	10.4771i	−0.177222	−	0.486914i	0.818996	−	0.573799i	$-0.194531\pi$
$463$	−3.81337	−	10.4771i	−0.177222	−	0.486914i	−0.996218	+	0.0868850i	$0.972309\pi$
$464$		0			0
$465$	14.5209	−	4.56362i	0.673391	−	0.211633i
$466$		0			0
$467$	−19.1933	−	33.2438i	−0.888160	−	1.53834i	−0.842048	−	0.539402i	$-0.818650\pi$
$467$	−19.1933	−	33.2438i	−0.888160	−	1.53834i	−0.0461122	−	0.998936i	$-0.514683\pi$
$468$		0			0
$469$	−4.21906	+	7.30763i	−0.194818	+	0.337435i
$470$		0			0
$471$	−12.3852	−	0.552262i	−0.570680	−	0.0254469i
$472$		0			0
$473$	−4.32383	−	0.762408i	−0.198810	−	0.0350556i
$474$		0			0
$475$	−13.2434	−	15.7829i	−0.607650	−	0.724169i
$476$		0			0
$477$	23.0402	+	6.21945i	1.05494	+	0.284769i
$478$		0			0
$479$	14.2277	+	5.17844i	0.650078	+	0.236609i	0.645947	−	0.763382i	$-0.276463\pi$
$479$	14.2277	+	5.17844i	0.650078	+	0.236609i	0.00413131	+	0.999991i	$0.498685\pi$
$480$		0			0
$481$	26.7260	+	22.4258i	1.21860	+	1.02253i
$482$		0			0
$483$	20.7920	+	27.1488i	0.946071	+	1.23531i
$484$		0			0
$485$		−	32.3999i		−	1.47120i
$486$		0			0
$487$			28.0918i			1.27296i	0.771293	+	0.636480i	$0.219610\pi$
$487$			28.0918i			1.27296i	−0.771293	+	0.636480i	$0.780390\pi$
$488$		0			0
$489$	3.26010	+	4.25681i	0.147427	+	0.192500i
$490$		0			0
$491$	6.84927	+	5.74722i	0.309103	+	0.259368i	0.784121	−	0.620608i	$-0.213114\pi$
$491$	6.84927	+	5.74722i	0.309103	+	0.259368i	−0.475018	+	0.879976i	$0.657558\pi$
$492$		0			0
$493$	4.23183	+	1.54026i	0.190592	+	0.0693698i
$494$		0			0
$495$	−49.1571	−	13.2694i	−2.20945	−	0.596415i
$496$		0			0
$497$	−10.5008	−	12.5143i	−0.471023	−	0.561343i
$498$		0			0
$499$	25.2727	+	4.45626i	1.13136	+	0.199489i	0.707823	−	0.706389i	$-0.249677\pi$
$499$	25.2727	+	4.45626i	1.13136	+	0.199489i	0.423537	+	0.905879i	$0.360788\pi$
$500$		0			0
$501$	−26.8374	−	1.19669i	−1.19901	−	0.0534642i
$502$		0			0
$503$	16.7842	−	29.0711i	0.748371	−	1.29622i	−0.200231	−	0.979749i	$-0.564169\pi$
$503$	16.7842	−	29.0711i	0.748371	−	1.29622i	0.948603	−	0.316469i	$-0.102497\pi$
$504$		0			0
$505$	−20.9270	−	36.2466i	−0.931239	−	1.61295i
$506$		0			0
$507$	−3.88019	+	1.21946i	−0.172325	+	0.0541582i
$508$		0			0
$509$	−8.18390	−	22.4851i	−0.362745	−	0.996634i	−0.978055	−	0.208348i	$-0.933191\pi$
$509$	−8.18390	−	22.4851i	−0.362745	−	0.996634i	0.615310	−	0.788285i	$-0.289031\pi$
$510$		0			0
$511$	3.73892	−	0.659272i	0.165400	−	0.0291645i
$512$		0			0
$513$	6.65248	+	5.13411i	0.293714	+	0.226676i
$514$		0			0
$515$	0.931028	+	5.28012i	0.0410260	+	0.232670i
$516$		0			0
$517$	−14.2272	+	5.17826i	−0.625710	+	0.227740i
$518$		0			0
$519$	−12.5061	−	2.78471i	−0.548957	−	0.122235i
$520$		0			0
$521$	−5.63297	+	3.25220i	−0.246785	+	0.142481i	−0.618291	−	0.785949i	$-0.712175\pi$
$521$	−5.63297	+	3.25220i	−0.246785	+	0.142481i	0.371506	+	0.928430i	$0.378841\pi$
$522$		0			0
$523$	−2.95249	−	1.70462i	−0.129103	−	0.0745378i	0.434057	−	0.900885i	$-0.357081\pi$
$523$	−2.95249	−	1.70462i	−0.129103	−	0.0745378i	−0.563161	+	0.826347i	$0.690415\pi$
$524$		0			0
$525$	−62.7026	+	32.5670i	−2.73657	+	1.42134i
$526$		0			0
$527$	−2.28425	+	12.9547i	−0.0995037	+	0.564313i
$528$		0			0
$529$	11.5046	−	9.65351i	0.500200	−	0.419718i
$530$		0			0
$531$	−37.7324	+	26.3163i	−1.63745	+	1.14203i
$532$		0			0
$533$	−2.96344	+	8.14198i	−0.128361	+	0.352668i
$534$		0			0
$535$	−51.0460	+	60.8343i	−2.20691	+	2.63009i
$536$		0			0
$537$	0.952681	+	7.28857i	0.0411112	+	0.314525i
$538$		0			0
$539$	13.1071			0.564563
$540$		0			0
$541$	−34.8518			−1.49840			−0.749198	−	0.662346i	$-0.769561\pi$
$541$	−34.8518			−1.49840			−0.749198	+	0.662346i	$0.769561\pi$
$542$		0			0
$543$	36.3594	+	15.1001i	1.56033	+	0.648007i
$544$		0			0
$545$	11.1503	−	13.2884i	0.477625	−	0.569212i
$546$		0			0
$547$	−8.68866	+	23.8719i	−0.371500	+	1.02069i	0.603281	+	0.797528i	$0.293860\pi$
$547$	−8.68866	+	23.8719i	−0.371500	+	1.02069i	−0.974782	+	0.223160i	$0.928363\pi$
$548$		0			0
$549$	8.06587	−	11.4739i	0.344243	−	0.489694i
$550$		0			0
$551$	0.884907	−	0.742525i	0.0376983	−	0.0316326i
$552$		0			0
$553$	−1.82826	+	10.3686i	−0.0777457	+	0.440918i
$554$		0			0
$555$	−65.7322	−	41.9618i	−2.79018	−	1.78118i
$556$		0			0
$557$	17.5014	+	10.1044i	0.741556	+	0.428138i	0.822635	−	0.568570i	$-0.192503\pi$
$557$	17.5014	+	10.1044i	0.741556	+	0.428138i	−0.0810786	+	0.996708i	$0.525836\pi$
$558$		0			0
$559$	−3.07962	+	1.77802i	−0.130254	+	0.0752021i
$560$		0			0
$561$	29.7583	−	32.4151i	1.25640	−	1.36856i
$562$		0			0
$563$	39.4563	−	14.3609i	1.66289	−	0.605241i	0.672073	−	0.740485i	$-0.265404\pi$
$563$	39.4563	−	14.3609i	1.66289	−	0.605241i	0.990812	+	0.135244i	$0.0431819\pi$
$564$		0			0
$565$	−0.639127	−	3.62467i	−0.0268883	−	0.152491i
$566$		0			0
$567$	22.1444	−	18.4417i	0.929975	−	0.774479i
$568$		0			0
$569$	31.3364	−	5.52546i	1.31369	−	0.231639i	0.527464	−	0.849577i	$-0.323143\pi$
$569$	31.3364	−	5.52546i	1.31369	−	0.231639i	0.786227	+	0.617938i	$0.212032\pi$
$570$		0			0
$571$	3.98836	+	10.9579i	0.166908	+	0.458576i	0.994744	−	0.102395i	$-0.0326504\pi$
$571$	3.98836	+	10.9579i	0.166908	+	0.458576i	−0.827836	+	0.560970i	$0.810428\pi$
$572$		0			0
$573$	15.7530	+	14.4619i	0.658091	+	0.604154i
$574$		0			0
$575$	39.2765	+	68.0290i	1.63794	+	2.83700i
$576$		0			0
$577$	8.45240	−	14.6400i	0.351878	−	0.609470i	−0.634701	−	0.772758i	$-0.718877\pi$
$577$	8.45240	−	14.6400i	0.351878	−	0.609470i	0.986578	+	0.163288i	$0.0522099\pi$
$578$		0			0
$579$	0.123142	−	0.192899i	0.00511761	−	0.00801662i
$580$		0			0
$581$	−16.8134	−	2.96466i	−0.697539	−	0.122995i
$582$		0			0
$583$	−20.6048	−	24.5558i	−0.853362	−	1.01700i
$584$		0			0
$585$	−37.4075	+	17.3590i	−1.54661	+	0.717705i
$586$		0			0
$587$	29.1104	+	10.5953i	1.20151	+	0.437315i	0.863752	−	0.503917i	$-0.168108\pi$
$587$	29.1104	+	10.5953i	1.20151	+	0.437315i	0.337761	+	0.941232i	$0.390330\pi$
$588$		0			0
$589$	2.58482	+	2.16892i	0.106506	+	0.0893688i
$590$		0			0
$591$	13.2504	−	31.9056i	0.545050	−	1.31242i
$592$		0			0
$593$			46.4607i			1.90791i	0.299945	+	0.953956i	$0.403032\pi$
$593$			46.4607i			1.90791i	−0.299945	+	0.953956i	$0.596968\pi$
$594$		0			0
$595$		−	85.0274i		−	3.48578i
$596$		0			0
$597$	−13.9536	+	1.82386i	−0.571082	+	0.0746455i
$598$		0			0
$599$	−17.6443	−	14.8053i	−0.720927	−	0.604930i	0.206714	−	0.978401i	$-0.433723\pi$
$599$	−17.6443	−	14.8053i	−0.720927	−	0.604930i	−0.927642	+	0.373472i	$0.878167\pi$
$600$		0			0
$601$	2.35062	+	0.855554i	0.0958836	+	0.0348988i	0.389517	−	0.921019i	$-0.372642\pi$
$601$	2.35062	+	0.855554i	0.0958836	+	0.0348988i	−0.293633	+	0.955918i	$0.594864\pi$
$602$		0			0
$603$	3.35444	−	7.15891i	0.136603	−	0.291533i
$604$		0			0
$605$	14.1801	+	16.8992i	0.576503	+	0.687050i
$606$		0			0
$607$	32.0538	+	5.65196i	1.30103	+	0.229406i	0.780885	−	0.624675i	$-0.214768\pi$
$607$	32.0538	+	5.65196i	1.30103	+	0.229406i	0.520141	+	0.854081i	$0.325880\pi$
$608$		0			0
$609$	−1.82595	−	3.51558i	−0.0739913	−	0.142458i
$610$		0			0
$611$	−6.13128	+	10.6197i	−0.248045	+	0.429627i
$612$		0			0
$613$	19.3280	+	33.4771i	0.780652	+	1.35213i	0.931562	+	0.363582i	$0.118446\pi$
$613$	19.3280	+	33.4771i	0.780652	+	1.35213i	−0.150910	+	0.988547i	$0.548220\pi$
$614$		0			0
$615$	4.20941	−	18.9044i	0.169740	−	0.762299i
$616$		0			0
$617$	−6.10438	−	16.7716i	−0.245753	−	0.675201i	−0.999830	−	0.0184151i	$-0.994138\pi$
$617$	−6.10438	−	16.7716i	−0.245753	−	0.675201i	0.754078	−	0.656785i	$-0.228084\pi$
$618$		0			0
$619$	27.3963	−	4.83070i	1.10115	−	0.194162i	0.406599	−	0.913607i	$-0.366715\pi$
$619$	27.3963	−	4.83070i	1.10115	−	0.194162i	0.694550	+	0.719445i	$0.255604\pi$
$620$		0			0
$621$	−21.5793	−	23.6817i	−0.865949	−	0.950314i
$622$		0			0
$623$	−1.40082	−	7.94443i	−0.0561225	−	0.318287i
$624$		0			0
$625$	−69.1674	+	25.1749i	−2.76670	+	1.00700i
$626$		0			0
$627$	−3.38415	−	10.7680i	−0.135150	−	0.430031i
$628$		0			0
$629$	58.3664	−	33.6979i	2.32722	−	1.34362i
$630$		0			0
$631$	−18.9743	−	10.9548i	−0.755355	−	0.436105i	0.0722703	−	0.997385i	$-0.476976\pi$
$631$	−18.9743	−	10.9548i	−0.755355	−	0.436105i	−0.827626	+	0.561280i	$0.810309\pi$
$632$		0			0
$633$	1.90975	−	42.8288i	0.0759059	−	1.70229i
$634$		0			0
$635$	−2.11676	+	12.0047i	−0.0840009	+	0.476393i
$636$		0			0
$637$	8.13223	−	6.82375i	0.322210	−	0.270367i
$638$		0			0
$639$	10.8027	+	10.8429i	0.427348	+	0.428937i
$640$		0			0
$641$	3.95530	−	10.8671i	0.156225	−	0.429225i	−0.836745	−	0.547593i	$-0.815544\pi$
$641$	3.95530	−	10.8671i	0.156225	−	0.429225i	0.992970	+	0.118368i	$0.0377664\pi$
$642$		0			0
$643$	−16.7106	+	19.9149i	−0.659000	+	0.785366i	−0.987242	−	0.159228i	$-0.949099\pi$
$643$	−16.7106	+	19.9149i	−0.659000	+	0.785366i	0.328242	+	0.944594i	$0.393544\pi$
$644$		0			0
$645$	6.31056	−	4.83297i	0.248478	−	0.190298i
$646$		0			0
$647$	−24.6429			−0.968813			−0.484407	−	0.874843i	$-0.660964\pi$
$647$	−24.6429			−0.968813			−0.484407	+	0.874843i	$0.660964\pi$
$648$		0			0
$649$	61.7913			2.42552
$650$		0			0
$651$	9.18684	−	7.03578i	0.360061	−	0.275754i
$652$		0			0
$653$	3.48319	−	4.15110i	0.136308	−	0.162445i	−0.693572	−	0.720387i	$-0.743964\pi$
$653$	3.48319	−	4.15110i	0.136308	−	0.162445i	0.829880	+	0.557942i	$0.188409\pi$
$654$		0			0
$655$	−19.4509	+	53.4409i	−0.760010	+	2.08811i
$656$		0			0
$657$	−3.43760	+	0.914270i	−0.134114	+	0.0356691i
$658$		0			0
$659$	−0.944840	+	0.792815i	−0.0368057	+	0.0308837i	−0.661005	−	0.750382i	$-0.729870\pi$
$659$	−0.944840	+	0.792815i	−0.0368057	+	0.0308837i	0.624199	+	0.781265i	$0.285425\pi$
$660$		0			0
$661$	−1.71439	+	9.72282i	−0.0666822	+	0.378174i	0.933143	+	0.359504i	$0.117054\pi$
$661$	−1.71439	+	9.72282i	−0.0666822	+	0.378174i	−0.999826	+	0.0186695i	$0.994057\pi$
$662$		0			0
$663$	1.58761	−	35.6043i	0.0616578	−	1.38276i
$664$		0			0
$665$	−18.8882	−	10.9051i	−0.732454	−	0.422883i
$666$		0			0
$667$	−3.81421	+	2.20214i	−0.147687	+	0.0852671i
$668$		0			0
$669$	9.39012	+	29.8783i	0.363043	+	1.15516i
$670$		0			0
$671$	−17.7026	+	6.44323i	−0.683402	+	0.248738i
$672$		0			0
$673$	8.16340	+	46.2969i	0.314676	+	1.78462i	0.574031	+	0.818833i	$0.305379\pi$
$673$	8.16340	+	46.2969i	0.314676	+	1.78462i	−0.259356	+	0.965782i	$0.583510\pi$
$674$		0			0
$675$	55.9302	−	35.4130i	2.15275	−	1.36305i
$676$		0			0
$677$	−26.9656	+	4.75476i	−1.03637	+	0.182740i	−0.665852	−	0.746084i	$-0.731932\pi$
$677$	−26.9656	+	4.75476i	−1.03637	+	0.182740i	−0.370520	+	0.928825i	$0.620820\pi$
$678$		0			0
$679$	−8.42439	−	23.1458i	−0.323298	−	0.888255i
$680$		0			0
$681$	−0.467254	+	2.09843i	−0.0179052	+	0.0804122i
$682$		0			0
$683$	1.37951	+	2.38938i	0.0527855	+	0.0914271i	0.891211	−	0.453589i	$-0.149857\pi$
$683$	1.37951	+	2.38938i	0.0527855	+	0.0914271i	−0.838425	+	0.545016i	$0.816523\pi$
$684$		0			0
$685$	26.1599	−	45.3103i	0.999518	−	1.73122i
$686$		0			0
$687$	5.07851	+	9.77787i	0.193757	+	0.373049i
$688$		0			0
$689$	−25.5682	−	4.50837i	−0.974071	−	0.171755i
$690$		0			0
$691$	30.4817	+	36.3267i	1.15958	+	1.38193i	0.910531	+	0.413442i	$0.135673\pi$
$691$	30.4817	+	36.3267i	1.15958	+	1.38193i	0.249048	+	0.968491i	$0.419882\pi$
$692$		0			0
$693$	−38.5670	+	3.30208i	−1.46504	+	0.125436i
$694$		0			0
$695$	−5.72315	−	2.08306i	−0.217092	−	0.0790149i
$696$		0			0
$697$	12.8219	+	10.7588i	0.485663	+	0.407520i
$698$		0			0
$699$	−20.7215	+	2.70848i	−0.783757	+	0.102444i
$700$		0			0
$701$			7.18301i			0.271299i	0.990757	+	0.135649i	$0.0433121\pi$
$701$			7.18301i			0.271299i	−0.990757	+	0.135649i	$0.956688\pi$
$702$		0			0
$703$		−	17.2876i		−	0.652014i
$704$		0			0
$705$	10.5128	−	25.3137i	0.395935	−	0.953369i
$706$		0			0
$707$	−24.3744	−	20.4525i	−0.916694	−	0.769197i
$708$		0			0
$709$	−20.3770	−	7.41660i	−0.765272	−	0.278536i	−0.0702548	−	0.997529i	$-0.522381\pi$
$709$	−20.3770	−	7.41660i	−0.765272	−	0.278536i	−0.695018	+	0.718993i	$0.744603\pi$
$710$		0			0
$711$	0.877970	−	9.82525i	0.0329265	−	0.368476i
$712$		0			0
$713$	−8.26940	−	9.85509i	−0.309692	−	0.369076i
$714$		0			0
$715$	54.5506	+	9.61874i	2.04008	+	0.359720i
$716$		0			0
$717$	1.93724	−	3.03464i	0.0723475	−	0.113331i
$718$		0			0
$719$	19.3429	−	33.5029i	0.721368	−	1.24945i	−0.239083	−	0.970999i	$-0.576847\pi$
$719$	19.3429	−	33.5029i	0.721368	−	1.24945i	0.960451	−	0.278448i	$-0.0898199\pi$
$720$		0			0
$721$	2.03801	+	3.52993i	0.0758993	+	0.131462i
$722$		0			0
$723$	−33.7891	−	31.0197i	−1.25663	−	1.15363i
$724$		0			0
$725$	−3.11242	−	8.55130i	−0.115592	−	0.317587i
$726$		0			0
$727$	−7.60267	+	1.34056i	−0.281967	+	0.0497184i	−0.312843	−	0.949805i	$-0.601281\pi$
$727$	−7.60267	+	1.34056i	−0.281967	+	0.0497184i	0.0308759	+	0.999523i	$0.490170\pi$
$728$		0			0
$729$	−19.1979	+	18.9853i	−0.711032	+	0.703160i
$730$		0			0
$731$	1.19286	+	6.76504i	0.0441195	+	0.250214i
$732$		0			0
$733$	24.3734	−	8.87121i	0.900254	−	0.327666i	0.149899	−	0.988701i	$-0.452105\pi$
$733$	24.3734	−	8.87121i	0.900254	−	0.327666i	0.750354	+	0.661036i	$0.229883\pi$
$734$		0			0
$735$	−16.0474	+	17.4801i	−0.591917	+	0.644762i
$736$		0			0
$737$	−9.19642	+	5.30956i	−0.338755	+	0.195580i
$738$		0			0
$739$	8.31837	+	4.80261i	0.305996	+	0.176667i	0.645133	−	0.764070i	$-0.276802\pi$
$739$	8.31837	+	4.80261i	0.305996	+	0.176667i	−0.339137	+	0.940737i	$0.610135\pi$
$740$		0			0
$741$	−7.70564	−	4.91909i	−0.283074	−	0.180707i
$742$		0			0
$743$	1.60612	−	9.10875i	0.0589228	−	0.334168i	−0.941069	−	0.338215i	$-0.890177\pi$
$743$	1.60612	−	9.10875i	0.0589228	−	0.334168i	0.999992	+	0.00404690i	$0.00128817\pi$
$744$		0			0
$745$	39.2908	−	32.9689i	1.43950	−	1.20789i
$746$		0			0
$747$	15.9324	+	1.42369i	0.582935	+	0.0520902i
$748$		0			0
$749$	−20.6485	+	56.7314i	−0.754481	+	2.07292i
$750$		0			0
$751$	13.3365	−	15.8938i	0.486656	−	0.579974i	−0.465708	−	0.884939i	$-0.654200\pi$
$751$	13.3365	−	15.8938i	0.486656	−	0.579974i	0.952364	+	0.304965i	$0.0986447\pi$
$752$		0			0
$753$	21.2368	+	8.81965i	0.773911	+	0.321406i
$754$		0			0
$755$	−8.22082			−0.299186
$756$		0			0
$757$	40.4426			1.46991			0.734956	−	0.678114i	$-0.237203\pi$
$757$	40.4426			1.46991			0.734956	+	0.678114i	$0.237203\pi$
$758$		0			0
$759$	5.57756	+	42.6716i	0.202453	+	1.54888i
$760$		0			0
$761$	3.68535	−	4.39203i	0.133594	−	0.159211i	−0.695100	−	0.718913i	$-0.744640\pi$
$761$	3.68535	−	4.39203i	0.133594	−	0.159211i	0.828694	+	0.559702i	$0.189084\pi$
$762$		0			0
$763$	4.51038	−	12.3922i	0.163287	−	0.448627i
$764$		0			0
$765$	6.79590	+	79.3733i	0.245706	+	2.86975i
$766$		0			0
$767$	38.3380	−	32.1694i	1.38431	−	1.16157i
$768$		0			0
$769$	2.58322	−	14.6502i	0.0931534	−	0.528299i	−0.902144	−	0.431435i	$-0.858008\pi$
$769$	2.58322	−	14.6502i	0.0931534	−	0.528299i	0.995298	−	0.0968646i	$-0.0308814\pi$
$770$		0			0
$771$	8.65908	−	4.49743i	0.311849	−	0.161971i
$772$		0			0
$773$	20.5431	+	11.8606i	0.738885	+	0.426596i	0.821664	−	0.569972i	$-0.193046\pi$
$773$	20.5431	+	11.8606i	0.738885	+	0.426596i	−0.0827785	+	0.996568i	$0.526379\pi$
$774$		0			0
$775$	23.0202	−	13.2907i	0.826910	−	0.477417i
$776$		0			0
$777$	−57.8684	−	12.8854i	−2.07602	−	0.462263i
$778$		0			0
$779$	4.03446	−	1.46842i	0.144549	−	0.0526117i
$780$		0			0
$781$	−3.56998	−	20.2463i	−0.127744	−	0.724471i
$782$		0			0
$783$	1.98552	+	3.13587i	0.0709566	+	0.112067i
$784$		0			0
$785$	−29.6894	+	5.23504i	−1.05966	+	0.186847i
$786$		0			0
$787$	16.3610	+	44.9514i	0.583206	+	1.60235i	0.782667	+	0.622440i	$0.213859\pi$
$787$	16.3610	+	44.9514i	0.583206	+	1.60235i	−0.199461	+	0.979906i	$0.563919\pi$
$788$		0			0
$789$	45.6850	−	14.3578i	1.62643	−	0.511153i
$790$		0			0
$791$	−1.39904	−	2.42321i	−0.0497441	−	0.0861594i
$792$		0			0
$793$	−7.62905	+	13.2139i	−0.270916	+	0.469239i
$794$		0			0
$795$	57.9754	+	2.58515i	2.05618	+	0.0916858i
$796$		0			0
$797$	4.68262	+	0.825673i	0.165867	+	0.0292468i	0.255965	−	0.966686i	$-0.417607\pi$
$797$	4.68262	+	0.825673i	0.165867	+	0.0292468i	−0.0900978	+	0.995933i	$0.528718\pi$
$798$		0			0
$799$	15.2266	+	18.1463i	0.538677	+	0.641970i
$800$		0			0
$801$	1.94263	+	7.30419i	0.0686396	+	0.258081i
$802$		0			0
$803$	4.48975	+	1.63414i	0.158440	+	0.0576674i
$804$		0			0
$805$	63.7008	+	53.4513i	2.24516	+	1.88391i
$806$		0			0
$807$	22.1467	+	28.9177i	0.779601	+	1.01795i
$808$		0			0
$809$			49.5252i			1.74121i	0.491978	+	0.870607i	$0.336274\pi$
$809$			49.5252i			1.74121i	−0.491978	+	0.870607i	$0.663726\pi$
$810$		0			0
$811$			46.4430i			1.63083i	0.578875	+	0.815417i	$0.303492\pi$
$811$			46.4430i			1.63083i	−0.578875	+	0.815417i	$0.696508\pi$
$812$		0			0
$813$	−17.0775	−	22.2986i	−0.598933	−	0.782045i
$814$		0			0
$815$	9.98799	+	8.38092i	0.349864	+	0.293571i
$816$		0			0
$817$	1.65580	+	0.602660i	0.0579290	+	0.0210844i
$818$		0			0
$819$	−22.2096	+	22.1273i	−0.776065	+	0.773191i
$820$		0			0
$821$	−11.9845	−	14.2826i	−0.418262	−	0.498465i	0.515236	−	0.857048i	$-0.327704\pi$
$821$	−11.9845	−	14.2826i	−0.418262	−	0.498465i	−0.933498	+	0.358583i	$0.883260\pi$
$822$		0			0
$823$	32.1502	+	5.66894i	1.12068	+	0.197607i	0.703141	−	0.711050i	$-0.251780\pi$
$823$	32.1502	+	5.66894i	1.12068	+	0.197607i	0.417543	+	0.908657i	$0.362891\pi$
$824$		0			0
$825$	−88.8297	−	3.96096i	−3.09265	−	0.137903i
$826$		0			0
$827$	−1.89085	+	3.27505i	−0.0657512	+	0.113884i	−0.897027	−	0.441976i	$-0.854278\pi$
$827$	−1.89085	+	3.27505i	−0.0657512	+	0.113884i	0.831276	+	0.555860i	$0.187611\pi$
$828$		0			0
$829$	20.9320	+	36.2552i	0.726997	+	1.25920i	0.958147	+	0.286278i	$0.0924180\pi$
$829$	20.9320	+	36.2552i	0.726997	+	1.25920i	−0.231150	+	0.972918i	$0.574249\pi$
$830$		0			0
$831$	−3.48020	+	1.09375i	−0.120727	+	0.0379419i
$832$		0			0
$833$	−7.01391	−	19.2706i	−0.243018	−	0.667685i
$834$		0			0
$835$	−64.3337	+	11.3438i	−2.22636	+	0.392567i
$836$		0			0
$837$	−8.01361	+	7.30219i	−0.276991	+	0.252401i
$838$		0			0
$839$	5.50728	+	31.2333i	0.190132	+	1.07829i	0.919182	+	0.393833i	$0.128851\pi$
$839$	5.50728	+	31.2333i	0.190132	+	1.07829i	−0.729050	+	0.684461i	$0.760038\pi$
$840$		0			0
$841$	−26.7716	+	9.74408i	−0.923160	+	0.336003i
$842$		0			0
$843$	1.86376	+	0.415000i	0.0641914	+	0.0142934i
$844$		0			0
$845$	−8.56550	+	4.94529i	−0.294662	+	0.170123i
$846$		0			0
$847$	14.5240	+	8.38543i	0.499050	+	0.288127i
$848$		0			0
$849$	13.0692	−	6.78798i	0.448533	−	0.232963i
$850$		0			0
$851$	−11.4455	+	64.9107i	−0.392347	+	2.22511i
$852$		0			0
$853$	−4.55869	+	3.82520i	−0.156087	+	0.130972i	−0.717486	−	0.696573i	$-0.754707\pi$
$853$	−4.55869	+	3.82520i	−0.156087	+	0.130972i	0.561400	+	0.827545i	$0.310263\pi$
$854$		0			0
$855$	18.5038	+	8.67031i	0.632818	+	0.296518i
$856$		0			0
$857$	−8.90655	+	24.4706i	−0.304242	+	0.835898i	0.689509	+	0.724277i	$0.257826\pi$
$857$	−8.90655	+	24.4706i	−0.304242	+	0.835898i	−0.993751	+	0.111621i	$0.964396\pi$
$858$		0			0
$859$	4.97726	−	5.93166i	0.169822	−	0.202386i	−0.674420	−	0.738348i	$-0.735606\pi$
$859$	4.97726	−	5.93166i	0.169822	−	0.202386i	0.844242	+	0.535962i	$0.180051\pi$
$860$		0			0
$861$	−1.90827	−	14.5994i	−0.0650338	−	0.497547i
$862$		0			0
$863$	−31.3700			−1.06785			−0.533923	−	0.845533i	$-0.679283\pi$
$863$	−31.3700			−1.06785			−0.533923	+	0.845533i	$0.679283\pi$
$864$		0			0
$865$	−31.1563			−1.05935
$866$		0			0
$867$	−36.3892	−	15.1124i	−1.23584	−	0.513246i
$868$		0			0
$869$	−8.51684	+	10.1500i	−0.288914	+	0.344314i
$870$		0			0
$871$	−2.94164	+	8.08208i	−0.0996735	+	0.273851i
$872$		0			0
$873$	9.71415	+	20.9334i	0.328774	+	0.708488i
$874$		0			0
$875$	−79.9627	+	67.0966i	−2.70323	+	2.26828i
$876$		0			0
$877$	−1.61766	+	9.17421i	−0.0546245	+	0.309791i	−0.999862	−	0.0165912i	$-0.994719\pi$
$877$	−1.61766	+	9.17421i	−0.0546245	+	0.309791i	0.945238	+	0.326382i	$0.105830\pi$
$878$		0			0
$879$	3.45404	+	2.20497i	0.116502	+	0.0743718i
$880$		0			0
$881$	−8.20181	−	4.73532i	−0.276326	−	0.159537i	0.355433	−	0.934702i	$-0.384333\pi$
$881$	−8.20181	−	4.73532i	−0.276326	−	0.159537i	−0.631759	+	0.775165i	$0.717667\pi$
$882$		0			0
$883$	1.68201	−	0.971109i	0.0566041	−	0.0326804i	−0.471431	−	0.881903i	$-0.656262\pi$
$883$	1.68201	−	0.971109i	0.0566041	−	0.0326804i	0.528035	+	0.849223i	$0.322929\pi$
$884$		0			0
$885$	−75.6528	+	82.4069i	−2.54304	+	2.77008i
$886$		0			0
$887$	−19.4340	+	7.07338i	−0.652528	+	0.237501i	−0.647007	−	0.762484i	$-0.723980\pi$
$887$	−19.4340	+	7.07338i	−0.652528	+	0.237501i	−0.00552106	+	0.999985i	$0.501757\pi$
$888$		0			0
$889$	1.60921	+	9.12631i	0.0539713	+	0.306086i
$890$		0			0
$891$	35.7385	−	6.16501i	1.19729	−	0.206536i
$892$		0			0
$893$	5.98394	−	1.05513i	0.200245	−	0.0353086i
$894$		0			0
$895$	6.11348	+	16.7966i	0.204351	+	0.561450i
$896$		0			0
$897$	25.6760	+	23.5716i	0.857298	+	0.787033i
$898$		0			0
$899$	0.745177	+	1.29068i	0.0248531	+	0.0430467i
$900$		0			0
$901$	−25.0768	+	43.4343i	−0.835429	+	1.44701i
$902$		0			0
$903$	3.25150	−	5.09340i	0.108203	−	0.169498i
$904$		0			0
$905$	94.2835	+	16.6247i	3.13409	+	0.552625i
$906$		0			0
$907$	−27.4535	−	32.7178i	−0.911578	−	1.08638i	−0.995947	−	0.0899423i	$-0.971332\pi$
$907$	−27.4535	−	32.7178i	−0.911578	−	1.08638i	0.0843685	−	0.996435i	$-0.473113\pi$
$908$		0			0
$909$	24.3883	+	17.1444i	0.808908	+	0.568643i
$910$		0			0
$911$	−5.35735	−	1.94991i	−0.177497	−	0.0646036i	0.251743	−	0.967794i	$-0.418996\pi$
$911$	−5.35735	−	1.94991i	−0.177497	−	0.0646036i	−0.429240	+	0.903191i	$0.641218\pi$
$912$		0			0
$913$	−16.4589	−	13.8107i	−0.544711	−	0.457067i
$914$		0			0
$915$	13.0809	−	31.4974i	0.432442	−	1.04127i
$916$		0			0
$917$			43.2346i			1.42773i
$918$		0			0
$919$		−	32.6536i		−	1.07714i	−0.842580	−	0.538571i	$-0.818964\pi$
$919$		−	32.6536i		−	1.07714i	0.842580	−	0.538571i	$-0.181036\pi$
$920$		0			0
$921$	32.3877	−	4.23336i	1.06721	−	0.139494i
$922$		0			0
$923$	−12.7555	−	10.7031i	−0.419853	−	0.352298i
$924$		0			0
$925$	−127.974	−	46.5788i	−4.20777	−	1.53150i
$926$		0			0
$927$	−2.18462	−	3.13231i	−0.0717523	−	0.102879i
$928$		0			0
$929$	−16.0223	−	19.0947i	−0.525676	−	0.626476i	0.436237	−	0.899832i	$-0.356311\pi$
$929$	−16.0223	−	19.0947i	−0.525676	−	0.626476i	−0.961913	+	0.273356i	$0.911866\pi$
$930$		0			0
$931$	−5.18038	−	0.913441i	−0.169780	−	0.0299368i
$932$		0			0
$933$	−8.92838	−	17.1902i	−0.292302	−	0.562781i
$934$		0			0
$935$	53.5021	−	92.6684i	1.74971	−	3.03058i
$936$		0			0
$937$	13.6967	+	23.7235i	0.447453	+	0.775012i	0.998219	−	0.0596479i	$-0.0189978\pi$
$937$	13.6967	+	23.7235i	0.447453	+	0.775012i	−0.550766	+	0.834659i	$0.685664\pi$
$938$		0			0
$939$	−5.82386	+	26.1549i	−0.190054	+	0.853532i
$940$		0			0
$941$	7.56327	+	20.7799i	0.246556	+	0.677406i	0.999806	+	0.0196725i	$0.00626235\pi$
$941$	7.56327	+	20.7799i	0.246556	+	0.677406i	−0.753251	+	0.657733i	$0.771515\pi$
$942$		0			0
$943$	−16.1206	+	2.84250i	−0.524959	+	0.0925644i
$944$		0			0
$945$	42.8149	−	55.4771i	1.39277	−	1.80467i
$946$		0			0
$947$	7.39542	+	41.9415i	0.240319	+	1.36292i	0.831117	+	0.556097i	$0.187702\pi$
$947$	7.39542	+	41.9415i	0.240319	+	1.36292i	−0.590798	+	0.806819i	$0.701187\pi$
$948$		0			0
$949$	3.63640	−	1.32354i	0.118042	−	0.0429639i
$950$		0			0
$951$	13.0395	+	41.4901i	0.422834	+	1.34541i
$952$		0			0
$953$	36.6083	−	21.1358i	1.18586	−	0.684656i	0.228497	−	0.973545i	$-0.426619\pi$
$953$	36.6083	−	21.1358i	1.18586	−	0.684656i	0.957363	+	0.288888i	$0.0932857\pi$
$954$		0			0
$955$	45.0348	+	26.0009i	1.45729	+	0.841368i
$956$		0			0
$957$	0.222081	−	4.98046i	0.00717886	−	0.160995i
$958$		0			0
$959$	6.90684	−	39.1706i	0.223033	−	1.26489i
$960$		0			0
$961$	20.4125	−	17.1281i	0.658469	−	0.552521i
$962$		0			0
$963$	14.7412	−	54.6093i	0.475027	−	1.75976i
$964$		0			0
$965$	0.190338	−	0.522949i	0.00612719	−	0.0168343i
$966$		0			0
$967$	−2.27091	+	2.70636i	−0.0730274	+	0.0870307i	−0.801321	−	0.598234i	$-0.795869\pi$
$967$	−2.27091	+	2.70636i	−0.0730274	+	0.0870307i	0.728294	+	0.685265i	$0.240314\pi$
$968$		0			0
$969$	−14.0205	+	10.7377i	−0.450405	+	0.344944i
$970$		0			0
$971$	40.9242			1.31332			0.656661	−	0.754186i	$-0.271968\pi$
$971$	40.9242			1.31332			0.656661	+	0.754186i	$0.271968\pi$
$972$		0			0
$973$	−4.63013			−0.148435
$974$		0			0
$975$	−57.1760	+	43.7885i	−1.83110	+	1.40235i
$976$		0			0
$977$	−13.2569	+	15.7990i	−0.424126	+	0.505454i	−0.935218	−	0.354072i	$-0.884797\pi$
$977$	−13.2569	+	15.7990i	−0.424126	+	0.505454i	0.511092	+	0.859526i	$0.329241\pi$
$978$		0			0
$979$	3.47220	−	9.53980i	0.110972	−	0.304893i
$980$		0			0
$981$	−3.22000	+	11.9286i	−0.102807	+	0.380852i
$982$		0			0
$983$	−15.7237	+	13.1938i	−0.501508	+	0.420816i	−0.858129	−	0.513434i	$-0.828373\pi$
$983$	−15.7237	+	13.1938i	−0.501508	+	0.420816i	0.356621	+	0.934249i	$0.383929\pi$
$984$		0			0
$985$	14.5883	−	82.7343i	0.464822	−	2.63614i
$986$		0			0
$987$	0.928242	−	20.8171i	0.0295463	−	0.662614i
$988$		0			0
$989$	−5.81811	−	3.35909i	−0.185005	−	0.106813i
$990$		0			0
$991$	−4.33802	+	2.50456i	−0.137802	+	0.0795598i	−0.567316	−	0.823500i	$-0.692018\pi$
$991$	−4.33802	+	2.50456i	−0.137802	+	0.0795598i	0.429514	+	0.903060i	$0.358685\pi$
$992$		0			0
$993$	12.6750	+	40.3304i	0.402229	+	1.27985i
$994$		0			0
$995$	−32.1563	+	11.7039i	−1.01942	+	0.371039i
$996$		0			0
$997$	7.18241	+	40.7334i	0.227469	+	1.29004i	0.857908	+	0.513803i	$0.171764\pi$
$997$	7.18241	+	40.7334i	0.227469	+	1.29004i	−0.630439	+	0.776238i	$0.717125\pi$
$998$		0			0
$999$	55.0502	+	7.40342i	1.74171	+	0.234234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bi.a.95.8	✓	216
4.3	odd	2	inner	864.2.bi.a.95.29	yes	216
27.2	odd	18	inner	864.2.bi.a.191.29	yes	216
108.83	even	18	inner	864.2.bi.a.191.8	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bi.a.95.8	✓	216	1.1	even	1	trivial
864.2.bi.a.95.29	yes	216	4.3	odd	2	inner
864.2.bi.a.191.8	yes	216	108.83	even	18	inner
864.2.bi.a.191.29	yes	216	27.2	odd	18	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bi (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37511 + 1.05313i) q^{3} +(-2.70735 + 3.22649i) q^{5} +(-1.09514 + 3.00888i) q^{7} +(0.781832 - 2.89633i) q^{9} +O(q^{10})\)	\(q+(-1.37511 + 1.05313i) q^{3} +(-2.70735 + 3.22649i) q^{5} +(-1.09514 + 3.00888i) q^{7} +(0.781832 - 2.89633i) q^{9} +(-3.08685 + 2.59017i) q^{11} +(-0.566736 + 3.21412i) q^{13} +(0.324973 - 7.28795i) q^{15} +(5.46002 + 3.15234i) q^{17} +(1.40054 - 0.808603i) q^{19} +(-1.66281 - 5.29086i) q^{21} +(-5.79404 + 2.10886i) q^{23} +(-2.21227 - 12.5464i) q^{25} +(1.97511 + 4.80613i) q^{27} +(0.703445 - 0.124036i) q^{29} +(0.713613 + 1.96063i) q^{31} +(1.51695 - 6.81262i) q^{33} +(-6.74319 - 11.6795i) q^{35} +(5.34490 - 9.25763i) q^{37} +(-2.60556 - 5.01660i) q^{39} +(2.61448 + 0.461004i) q^{41} +(0.700363 + 0.834660i) q^{43} +(7.22829 + 10.3639i) q^{45} +(3.53067 + 1.28506i) q^{47} +(-2.49172 - 2.09080i) q^{49} +(-10.8279 + 1.41531i) q^{51} +7.95497i q^{53} -16.9722i q^{55} +(-1.07433 + 2.58687i) q^{57} +(-11.7468 - 9.85673i) q^{59} +(4.39315 + 1.59898i) q^{61} +(7.85850 + 5.52434i) q^{63} +(-8.83596 - 10.5303i) q^{65} +(2.59524 + 0.457612i) q^{67} +(5.74652 - 9.00178i) q^{69} +(-2.55096 + 4.41839i) q^{71} +(-0.592851 - 1.02685i) q^{73} +(16.2551 + 14.9228i) q^{75} +(-4.41299 - 12.1246i) q^{77} +(3.23818 - 0.570978i) q^{79} +(-7.77748 - 4.52889i) q^{81} +(0.925883 + 5.25094i) q^{83} +(-24.9531 + 9.08220i) q^{85} +(-0.836685 + 0.911382i) q^{87} +(-2.18184 + 1.25968i) q^{89} +(-9.05024 - 5.22516i) q^{91} +(-3.04610 - 1.94455i) q^{93} +(-1.18280 + 6.70800i) q^{95} +(-5.89280 + 4.94464i) q^{97} +(5.08861 + 10.9656i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) \) 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more