LMFDB - Embedded newform 1080.2.k.d.541.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1080,2,Mod(541,1080)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1080, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("1080.541");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.k (of order $2$, degree $1$, 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:	$8.62384341830$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} + 5x^{16} + 28x^{12} - 28x^{10} + 112x^{8} + 320x^{4} - 256x^{2} + 1024 $ x^20 - x^18 + 5x^16 + 28x^12 - 28x^10 + 112x^8 + 320x^4 - 256x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			541.15
Root			$1.17425 + 0.788128i$ of defining polynomial
Character	$\chi$	$=$	1080.541
Dual form			1080.2.k.d.541.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17425 - 0.788128i) q^{2} +(0.757708 - 1.85091i) q^{4} +1.00000i q^{5} +2.12726 q^{7} +(-0.569020 - 2.77060i) q^{8} +O(q^{10})$	\(q+(1.17425 - 0.788128i) q^{2} +(0.757708 - 1.85091i) q^{4} +1.00000i q^{5} +2.12726 q^{7} +(-0.569020 - 2.77060i) q^{8} +(0.788128 + 1.17425i) q^{10} -5.48036i q^{11} +4.91228i q^{13} +(2.49792 - 1.67655i) q^{14} +(-2.85176 - 2.80490i) q^{16} -0.235541 q^{17} -5.23139i q^{19} +(1.85091 + 0.757708i) q^{20} +(-4.31922 - 6.43529i) q^{22} +7.42390 q^{23} -1.00000 q^{25} +(3.87150 + 5.76822i) q^{26} +(1.61184 - 3.93737i) q^{28} -4.24894i q^{29} +5.05609 q^{31} +(-5.55929 - 1.04610i) q^{32} +(-0.276583 + 0.185636i) q^{34} +2.12726i q^{35} +2.27608i q^{37} +(-4.12300 - 6.14294i) q^{38} +(2.77060 - 0.569020i) q^{40} +3.26132 q^{41} +9.90812i q^{43} +(-10.1437 - 4.15251i) q^{44} +(8.71749 - 5.85098i) q^{46} -8.17359 q^{47} -2.47478 q^{49} +(-1.17425 + 0.788128i) q^{50} +(9.09220 + 3.72207i) q^{52} -10.6637i q^{53} +5.48036 q^{55} +(-1.21045 - 5.89377i) q^{56} +(-3.34871 - 4.98930i) q^{58} +0.702988i q^{59} -0.319109i q^{61} +(5.93709 - 3.98485i) q^{62} +(-7.35243 + 3.15305i) q^{64} -4.91228 q^{65} +2.70667i q^{67} +(-0.178471 + 0.435965i) q^{68} +(1.67655 + 2.49792i) q^{70} +7.18836 q^{71} +9.66370 q^{73} +(1.79384 + 2.67268i) q^{74} +(-9.68284 - 3.96386i) q^{76} -11.6581i q^{77} -10.8565 q^{79} +(2.80490 - 2.85176i) q^{80} +(3.82959 - 2.57033i) q^{82} +8.53645i q^{83} -0.235541i q^{85} +(7.80887 + 11.6346i) q^{86} +(-15.1839 + 3.11843i) q^{88} -9.90812 q^{89} +10.4497i q^{91} +(5.62515 - 13.7410i) q^{92} +(-9.59781 + 6.44184i) q^{94} +5.23139 q^{95} +14.8895 q^{97} +(-2.90600 + 1.95044i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{4}+O(q^{10}) $ 20 * q + 2 * q^4	$ 20 q + 2 q^{4} - 2 q^{10} - 18 q^{16} + 16 q^{22} - 20 q^{25} + 16 q^{28} + 20 q^{31} - 6 q^{34} - 4 q^{40} + 54 q^{46} + 36 q^{49} + 56 q^{52} - 72 q^{58} - 28 q^{64} - 40 q^{73} + 58 q^{76} - 4 q^{79} - 92 q^{82} - 116 q^{88} + 72 q^{94} + 40 q^{97}+O(q^{100}) $ 20 * q + 2 * q^4 - 2 * q^10 - 18 * q^16 + 16 * q^22 - 20 * q^25 + 16 * q^28 + 20 * q^31 - 6 * q^34 - 4 * q^40 + 54 * q^46 + 36 * q^49 + 56 * q^52 - 72 * q^58 - 28 * q^64 - 40 * q^73 + 58 * q^76 - 4 * q^79 - 92 * q^82 - 116 * q^88 + 72 * q^94 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$541$	$1001$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.17425	−	0.788128i	0.830317	−	0.557291i
$2$	1.17425	−	0.788128i	0.830317	−	0.557291i
$3$		0			0
$3$		0			0
$4$	0.757708	−	1.85091i	0.378854	−	0.925456i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	2.12726			0.804027			0.402014	−	0.915634i	$-0.368310\pi$
$7$	2.12726			0.804027			0.402014	+	0.915634i	$0.368310\pi$
$8$	−0.569020	−	2.77060i	−0.201179	−	0.979554i
$9$		0			0
$10$	0.788128	+	1.17425i	0.249228	+	0.371329i
$11$		−	5.48036i		−	1.65239i	−0.563384	−	0.826195i	$-0.690501\pi$
$11$		−	5.48036i		−	1.65239i	0.563384	−	0.826195i	$-0.309499\pi$
$12$		0			0
$13$			4.91228i			1.36242i	0.732088	+	0.681210i	$0.238546\pi$
$13$			4.91228i			1.36242i	−0.732088	+	0.681210i	$0.761454\pi$
$14$	2.49792	−	1.67655i	0.667598	−	0.448077i
$15$		0			0
$16$	−2.85176	−	2.80490i	−0.712939	−	0.701226i
$17$	−0.235541			−0.0571270			−0.0285635	−	0.999592i	$-0.509093\pi$
$17$	−0.235541			−0.0571270			−0.0285635	+	0.999592i	$0.509093\pi$
$18$		0			0
$19$		−	5.23139i		−	1.20016i	−0.799939	−	0.600081i	$-0.795135\pi$
$19$		−	5.23139i		−	1.20016i	0.799939	−	0.600081i	$-0.204865\pi$
$20$	1.85091	+	0.757708i	0.413877	+	0.169429i
$21$		0			0
$22$	−4.31922	−	6.43529i	−0.920862	−	1.37201i
$23$	7.42390			1.54799			0.773995	−	0.633192i	$-0.218256\pi$
$23$	7.42390			1.54799			0.773995	+	0.633192i	$0.218256\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	3.87150	+	5.76822i	0.759264	+	1.13124i
$27$		0			0
$28$	1.61184	−	3.93737i	0.304609	−	0.744092i
$29$		−	4.24894i		−	0.789008i	−0.918894	−	0.394504i	$-0.870917\pi$
$29$		−	4.24894i		−	0.789008i	0.918894	−	0.394504i	$-0.129083\pi$
$30$		0			0
$31$	5.05609			0.908100			0.454050	−	0.890976i	$-0.349979\pi$
$31$	5.05609			0.908100			0.454050	+	0.890976i	$0.349979\pi$
$32$	−5.55929	−	1.04610i	−0.982752	−	0.184926i
$33$		0			0
$34$	−0.276583	+	0.185636i	−0.0474335	+	0.0318363i
$35$			2.12726i			0.359572i
$36$		0			0
$37$			2.27608i			0.374185i	0.982342	+	0.187093i	$0.0599065\pi$
$37$			2.27608i			0.374185i	−0.982342	+	0.187093i	$0.940094\pi$
$38$	−4.12300	−	6.14294i	−0.668839	−	0.996516i
$39$		0			0
$40$	2.77060	−	0.569020i	0.438070	−	0.0899700i
$41$	3.26132			0.509332			0.254666	−	0.967029i	$-0.418034\pi$
$41$	3.26132			0.509332			0.254666	+	0.967029i	$0.418034\pi$
$42$		0			0
$43$			9.90812i			1.51097i	0.655163	+	0.755487i	$0.272600\pi$
$43$			9.90812i			1.51097i	−0.655163	+	0.755487i	$0.727400\pi$
$44$	−10.1437	−	4.15251i	−1.52921	−	0.626015i
$45$		0			0
$46$	8.71749	−	5.85098i	1.28532	−	0.862680i
$47$	−8.17359			−1.19224			−0.596121	−	0.802895i	$-0.703292\pi$
$47$	−8.17359			−1.19224			−0.596121	+	0.802895i	$0.703292\pi$
$48$		0			0
$49$	−2.47478			−0.353540
$50$	−1.17425	+	0.788128i	−0.166063	+	0.111458i
$51$		0			0
$52$	9.09220	+	3.72207i	1.26086	+	0.516159i
$53$		−	10.6637i		−	1.46477i	−0.680890	−	0.732386i	$-0.738407\pi$
$53$		−	10.6637i		−	1.46477i	0.680890	−	0.732386i	$-0.261593\pi$
$54$		0			0
$55$	5.48036			0.738971
$56$	−1.21045	−	5.89377i	−0.161753	−	0.787589i
$57$		0			0
$58$	−3.34871	−	4.98930i	−0.439707	−	0.655127i
$59$			0.702988i			0.0915212i	0.998952	+	0.0457606i	$0.0145711\pi$
$59$			0.702988i			0.0915212i	−0.998952	+	0.0457606i	$0.985429\pi$
$60$		0			0
$61$		−	0.319109i		−	0.0408577i	−0.999791	−	0.0204288i	$-0.993497\pi$
$61$		−	0.319109i		−	0.0408577i	0.999791	−	0.0204288i	$-0.00650315\pi$
$62$	5.93709	−	3.98485i	0.754012	−	0.506076i
$63$		0			0
$64$	−7.35243	+	3.15305i	−0.919054	+	0.394132i
$65$	−4.91228			−0.609293
$66$		0			0
$67$			2.70667i			0.330672i	0.986237	+	0.165336i	$0.0528708\pi$
$67$			2.70667i			0.330672i	−0.986237	+	0.165336i	$0.947129\pi$
$68$	−0.178471	+	0.435965i	−0.0216428	+	0.0528685i
$69$		0			0
$70$	1.67655	+	2.49792i	0.200386	+	0.298559i
$71$	7.18836			0.853101			0.426551	−	0.904464i	$-0.359729\pi$
$71$	7.18836			0.853101			0.426551	+	0.904464i	$0.359729\pi$
$72$		0			0
$73$	9.66370			1.13105			0.565525	−	0.824731i	$-0.308673\pi$
$73$	9.66370			1.13105			0.565525	+	0.824731i	$0.308673\pi$
$74$	1.79384	+	2.67268i	0.208530	+	0.310693i
$75$		0			0
$76$	−9.68284	−	3.96386i	−1.11070	−	0.454686i
$77$		−	11.6581i		−	1.32857i
$78$		0			0
$79$	−10.8565			−1.22146			−0.610729	−	0.791840i	$-0.709123\pi$
$79$	−10.8565			−1.22146			−0.610729	+	0.791840i	$0.709123\pi$
$80$	2.80490	−	2.85176i	0.313598	−	0.318836i
$81$		0			0
$82$	3.82959	−	2.57033i	0.422907	−	0.283846i
$83$			8.53645i			0.936997i	0.883464	+	0.468498i	$0.155205\pi$
$83$			8.53645i			0.936997i	−0.883464	+	0.468498i	$0.844795\pi$
$84$		0			0
$85$		−	0.235541i		−	0.0255480i
$86$	7.80887	+	11.6346i	0.842052	+	1.25459i
$87$		0			0
$88$	−15.1839	+	3.11843i	−1.61861	+	0.332426i
$89$	−9.90812			−1.05026			−0.525129	−	0.851022i	$-0.675983\pi$
$89$	−9.90812			−1.05026			−0.525129	+	0.851022i	$0.675983\pi$
$90$		0			0
$91$			10.4497i			1.09542i
$92$	5.62515	−	13.7410i	0.586462	−	1.43260i
$93$		0			0
$94$	−9.59781	+	6.44184i	−0.989939	+	0.664425i
$95$	5.23139			0.536729
$96$		0			0
$97$	14.8895			1.51180			0.755902	−	0.654685i	$-0.227199\pi$
$97$	14.8895			1.51180			0.755902	+	0.654685i	$0.227199\pi$
$98$	−2.90600	+	1.95044i	−0.293550	+	0.197025i
$99$		0			0
$100$	−0.757708	+	1.85091i	−0.0757708	+	0.185091i
$101$			6.13283i			0.610240i	0.952314	+	0.305120i	$0.0986965\pi$
$101$			6.13283i			0.610240i	−0.952314	+	0.305120i	$0.901303\pi$
$102$		0			0
$103$	−8.82788			−0.869837			−0.434918	−	0.900470i	$-0.643223\pi$
$103$	−8.82788			−0.869837			−0.434918	+	0.900470i	$0.643223\pi$
$104$	13.6099	−	2.79519i	1.33457	−	0.274090i
$105$		0			0
$106$	−8.40436	−	12.5218i	−0.816304	−	1.21623i
$107$		−	7.48593i		−	0.723693i	−0.932238	−	0.361846i	$-0.882147\pi$
$107$		−	7.48593i		−	0.723693i	0.932238	−	0.361846i	$-0.117853\pi$
$108$		0			0
$109$			17.8462i			1.70935i	0.519160	+	0.854677i	$0.326245\pi$
$109$			17.8462i			1.70935i	−0.519160	+	0.854677i	$0.673755\pi$
$110$	6.43529	−	4.31922i	0.613581	−	0.411822i
$111$		0			0
$112$	−6.06642	−	5.96675i	−0.573223	−	0.563805i
$113$	−14.8609			−1.39800			−0.698998	−	0.715124i	$-0.746370\pi$
$113$	−14.8609			−1.39800			−0.698998	+	0.715124i	$0.746370\pi$
$114$		0			0
$115$			7.42390i			0.692282i
$116$	−7.86441	−	3.21945i	−0.730192	−	0.298919i
$117$		0			0
$118$	0.554045	+	0.825481i	0.0510039	+	0.0759917i
$119$	−0.501055			−0.0459316
$120$		0			0
$121$	−19.0343			−1.73039
$122$	−0.251498	−	0.374712i	−0.0227696	−	0.0339248i
$123$		0			0
$124$	3.83104	−	9.35838i	0.344038	−	0.840407i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	6.82788			0.605876			0.302938	−	0.953010i	$-0.402032\pi$
$127$	6.82788			0.605876			0.302938	+	0.953010i	$0.402032\pi$
$128$	−6.14856	+	9.49712i	−0.543461	+	0.839435i
$129$		0			0
$130$	−5.76822	+	3.87150i	−0.505907	+	0.339553i
$131$			21.3874i			1.86863i	0.356452	+	0.934314i	$0.383986\pi$
$131$			21.3874i			1.86863i	−0.356452	+	0.934314i	$0.616014\pi$
$132$		0			0
$133$		−	11.1285i		−	0.964963i
$134$	2.13320	+	3.17829i	0.184280	+	0.274563i
$135$		0			0
$136$	0.134027	+	0.652588i	0.0114927	+	0.0559590i
$137$	−19.6081			−1.67523			−0.837617	−	0.546259i	$-0.816052\pi$
$137$	−19.6081			−1.67523			−0.837617	+	0.546259i	$0.816052\pi$
$138$		0			0
$139$			0.901666i			0.0764784i	0.999269	+	0.0382392i	$0.0121749\pi$
$139$			0.901666i			0.0764784i	−0.999269	+	0.0382392i	$0.987825\pi$
$140$	3.93737	+	1.61184i	0.332768	+	0.136225i
$141$		0			0
$142$	8.44090	−	5.66535i	0.708345	−	0.475425i
$143$	26.9210			2.25125
$144$		0			0
$145$	4.24894			0.352855
$146$	11.3476	−	7.61624i	0.939131	−	0.630324i
$147$		0			0
$148$	4.21283	+	1.72461i	0.346292	+	0.141762i
$149$			1.75106i			0.143453i	0.997424	+	0.0717264i	$0.0228508\pi$
$149$			1.75106i			0.143453i	−0.997424	+	0.0717264i	$0.977149\pi$
$150$		0			0
$151$	2.90141			0.236114			0.118057	−	0.993007i	$-0.462334\pi$
$151$	2.90141			0.236114			0.118057	+	0.993007i	$0.462334\pi$
$152$	−14.4941	+	2.97676i	−1.17562	+	0.241447i
$153$		0			0
$154$	−9.18810	−	13.6895i	−0.740398	−	1.10313i
$155$			5.05609i			0.406115i
$156$		0			0
$157$			19.7601i			1.57703i	0.615018	+	0.788513i	$0.289149\pi$
$157$			19.7601i			1.57703i	−0.615018	+	0.788513i	$0.710851\pi$
$158$	−12.7483	+	8.55635i	−1.01420	+	0.680707i
$159$		0			0
$160$	1.04610	−	5.55929i	0.0827014	−	0.439500i
$161$	15.7925			1.24463
$162$		0			0
$163$			21.4946i			1.68359i	0.539799	+	0.841794i	$0.318500\pi$
$163$			21.4946i			1.68359i	−0.539799	+	0.841794i	$0.681500\pi$
$164$	2.47113	−	6.03641i	0.192963	−	0.471364i
$165$		0			0
$166$	6.72781	+	10.0239i	0.522180	+	0.778005i
$167$	19.0666			1.47541			0.737707	−	0.675121i	$-0.235909\pi$
$167$	19.0666			1.47541			0.737707	+	0.675121i	$0.235909\pi$
$168$		0			0
$169$	−11.1305			−0.856190
$170$	−0.185636	−	0.276583i	−0.0142376	−	0.0212129i
$171$		0			0
$172$	18.3391	+	7.50747i	1.39834	+	0.572439i
$173$		−	9.31060i		−	0.707872i	−0.935270	−	0.353936i	$-0.884843\pi$
$173$		−	9.31060i		−	0.707872i	0.935270	−	0.353936i	$-0.115157\pi$
$174$		0			0
$175$	−2.12726			−0.160805
$176$	−15.3719	+	15.6286i	−1.15870	+	1.17805i
$177$		0			0
$178$	−11.6346	+	7.80887i	−0.872048	+	0.585300i
$179$			2.70620i			0.202271i	0.994873	+	0.101136i	$0.0322476\pi$
$179$			2.70620i			0.202271i	−0.994873	+	0.101136i	$0.967752\pi$
$180$		0			0
$181$			7.42390i			0.551814i	0.961184	+	0.275907i	$0.0889782\pi$
$181$			7.42390i			0.551814i	−0.961184	+	0.275907i	$0.911022\pi$
$182$	8.23568	+	12.2705i	0.610469	+	0.909549i
$183$		0			0
$184$	−4.22435	−	20.5686i	−0.311423	−	1.51634i
$185$	−2.27608			−0.167341
$186$		0			0
$187$			1.29085i			0.0943960i
$188$	−6.19320	+	15.1286i	−0.451685	+	1.10337i
$189$		0			0
$190$	6.14294	−	4.12300i	0.445655	−	0.299114i
$191$	13.2099			0.955837			0.477919	−	0.878404i	$-0.341391\pi$
$191$	13.2099			0.955837			0.477919	+	0.878404i	$0.341391\pi$
$192$		0			0
$193$	−3.73487			−0.268842			−0.134421	−	0.990924i	$-0.542917\pi$
$193$	−3.73487			−0.268842			−0.134421	+	0.990924i	$0.542917\pi$
$194$	17.4840	−	11.7349i	1.25528	−	0.842515i
$195$		0			0
$196$	−1.87516	+	4.58060i	−0.133940	+	0.327186i
$197$			7.00321i			0.498958i	0.968380	+	0.249479i	$0.0802594\pi$
$197$			7.00321i			0.498958i	−0.968380	+	0.249479i	$0.919741\pi$
$198$		0			0
$199$	21.2769			1.50828			0.754140	−	0.656714i	$-0.228054\pi$
$199$	21.2769			1.50828			0.754140	+	0.656714i	$0.228054\pi$
$200$	0.569020	+	2.77060i	0.0402358	+	0.195911i
$201$		0			0
$202$	4.83346	+	7.20146i	0.340081	+	0.506693i
$203$		−	9.03858i		−	0.634384i
$204$		0			0
$205$			3.26132i			0.227780i
$206$	−10.3661	+	6.95750i	−0.722241	+	0.484752i
$207$		0			0
$208$	13.7785	−	14.0086i	0.955365	−	0.971323i
$209$	−28.6699			−1.98314
$210$		0			0
$211$		−	24.4773i		−	1.68509i	−0.538628	−	0.842544i	$-0.681057\pi$
$211$		−	24.4773i		−	1.68509i	0.538628	−	0.842544i	$-0.318943\pi$
$212$	−19.7376	−	8.07998i	−1.35558	−	0.554935i
$213$		0			0
$214$	−5.89988	−	8.79033i	−0.403307	−	0.600895i
$215$	−9.90812			−0.675728
$216$		0			0
$217$	10.7556			0.730138
$218$	14.0651	+	20.9558i	0.952607	+	1.41931i
$219$		0			0
$220$	4.15251	−	10.1437i	0.279962	−	0.683886i
$221$		−	1.15704i		−	0.0778310i
$222$		0			0
$223$	−16.9862			−1.13748			−0.568741	−	0.822516i	$-0.692569\pi$
$223$	−16.9862			−1.13748			−0.568741	+	0.822516i	$0.692569\pi$
$224$	−11.8260	−	2.22532i	−0.790160	−	0.148685i
$225$		0			0
$226$	−17.4504	+	11.7123i	−1.16078	+	0.779090i
$227$			20.5203i			1.36198i	0.732294	+	0.680988i	$0.238450\pi$
$227$			20.5203i			1.36198i	−0.732294	+	0.680988i	$0.761550\pi$
$228$		0			0
$229$		−	3.01268i		−	0.199083i	−0.995033	−	0.0995416i	$-0.968262\pi$
$229$		−	3.01268i		−	0.199083i	0.995033	−	0.0995416i	$-0.0317376\pi$
$230$	5.85098	+	8.71749i	0.385802	+	0.574814i
$231$		0			0
$232$	−11.7721	+	2.41773i	−0.772876	+	0.158732i
$233$	15.2379			0.998267			0.499134	−	0.866525i	$-0.333652\pi$
$233$	15.2379			0.998267			0.499134	+	0.866525i	$0.333652\pi$
$234$		0			0
$235$		−	8.17359i		−	0.533186i
$236$	1.30117	+	0.532660i	0.0846989	+	0.0346732i
$237$		0			0
$238$	−0.588362	+	0.394896i	−0.0381379	+	0.0255973i
$239$	−15.8761			−1.02694			−0.513470	−	0.858108i	$-0.671640\pi$
$239$	−15.8761			−1.02694			−0.513470	+	0.858108i	$0.671640\pi$
$240$		0			0
$241$	20.9838			1.35169			0.675843	−	0.737046i	$-0.263780\pi$
$241$	20.9838			1.35169			0.675843	+	0.737046i	$0.263780\pi$
$242$	−22.3510	+	15.0015i	−1.43678	+	0.964332i
$243$		0			0
$244$	−0.590642	−	0.241791i	−0.0378120	−	0.0154791i
$245$		−	2.47478i		−	0.158108i
$246$		0			0
$247$	25.6980			1.63513
$248$	−2.87702	−	14.0084i	−0.182691	−	0.889534i
$249$		0			0
$250$	−0.788128	−	1.17425i	−0.0498456	−	0.0742659i
$251$			8.49787i			0.536381i	0.963366	+	0.268190i	$0.0864256\pi$
$251$			8.49787i			0.536381i	−0.963366	+	0.268190i	$0.913574\pi$
$252$		0			0
$253$		−	40.6856i		−	2.55788i
$254$	8.01761	−	5.38124i	0.503070	−	0.337649i
$255$		0			0
$256$	0.265028	+	15.9978i	0.0165642	+	0.999863i
$257$	0.222442			0.0138756			0.00693778	−	0.999976i	$-0.497792\pi$
$257$	0.222442			0.0138756			0.00693778	+	0.999976i	$0.497792\pi$
$258$		0			0
$259$			4.84181i			0.300855i
$260$	−3.72207	+	9.09220i	−0.230833	+	0.563874i
$261$		0			0
$262$	16.8560	+	25.1141i	1.04137	+	1.55155i
$263$	−7.74301			−0.477454			−0.238727	−	0.971087i	$-0.576730\pi$
$263$	−7.74301			−0.477454			−0.238727	+	0.971087i	$0.576730\pi$
$264$		0			0
$265$	10.6637			0.655066
$266$	−8.77068	−	13.0676i	−0.537765	−	0.801226i
$267$		0			0
$268$	5.00980	+	2.05086i	0.306022	+	0.125276i
$269$			2.50903i			0.152978i	0.997070	+	0.0764890i	$0.0243710\pi$
$269$			2.50903i			0.152978i	−0.997070	+	0.0764890i	$0.975629\pi$
$270$		0			0
$271$	−7.00558			−0.425559			−0.212779	−	0.977100i	$-0.568252\pi$
$271$	−7.00558			−0.425559			−0.212779	+	0.977100i	$0.568252\pi$
$272$	0.671704	+	0.660669i	0.0407281	+	0.0400589i
$273$		0			0
$274$	−23.0247	+	15.4537i	−1.39098	+	0.933592i
$275$			5.48036i			0.330478i
$276$		0			0
$277$		−	8.13052i		−	0.488516i	−0.969710	−	0.244258i	$-0.921456\pi$
$277$		−	8.13052i		−	0.488516i	0.969710	−	0.244258i	$-0.0785443\pi$
$278$	0.710629	+	1.05878i	0.0426207	+	0.0635013i
$279$		0			0
$280$	5.89377	−	1.21045i	0.352220	−	0.0723383i
$281$	−20.2038			−1.20526			−0.602628	−	0.798023i	$-0.705880\pi$
$281$	−20.2038			−1.20526			−0.602628	+	0.798023i	$0.705880\pi$
$282$		0			0
$283$		−	27.4626i		−	1.63248i	−0.577712	−	0.816241i	$-0.696054\pi$
$283$		−	27.4626i		−	1.63248i	0.577712	−	0.816241i	$-0.303946\pi$
$284$	5.44668	−	13.3050i	0.323201	−	0.789508i
$285$		0			0
$286$	31.6119	−	21.2172i	1.86925	−	1.25460i
$287$	6.93765			0.409517
$288$		0			0
$289$	−16.9445			−0.996737
$290$	4.98930	−	3.34871i	0.292982	−	0.196643i
$291$		0			0
$292$	7.32227	−	17.8867i	0.428503	−	1.04674i
$293$			5.00321i			0.292291i	0.989263	+	0.146145i	$0.0466867\pi$
$293$			5.00321i			0.292291i	−0.989263	+	0.146145i	$0.953313\pi$
$294$		0			0
$295$	−0.702988			−0.0409295
$296$	6.30611	−	1.29514i	0.366535	−	0.0752783i
$297$		0			0
$298$	1.38006	+	2.05618i	0.0799449	+	0.119111i
$299$			36.4683i			2.10901i
$300$		0			0
$301$			21.0771i			1.21486i
$302$	3.40697	−	2.28668i	0.196049	−	0.131584i
$303$		0			0
$304$	−14.6735	+	14.9186i	−0.841585	+	0.855643i
$305$	0.319109			0.0182721
$306$		0			0
$307$		−	9.18634i		−	0.524292i	−0.965028	−	0.262146i	$-0.915570\pi$
$307$		−	9.18634i		−	0.524292i	0.965028	−	0.262146i	$-0.0844302\pi$
$308$	−21.5782	−	8.83346i	−1.22953	−	0.503333i
$309$		0			0
$310$	3.98485	+	5.93709i	0.226324	+	0.337204i
$311$	1.99798			0.113295			0.0566475	−	0.998394i	$-0.481959\pi$
$311$	1.99798			0.113295			0.0566475	+	0.998394i	$0.481959\pi$
$312$		0			0
$313$	−10.6052			−0.599440			−0.299720	−	0.954027i	$-0.596893\pi$
$313$	−10.6052			−0.599440			−0.299720	+	0.954027i	$0.596893\pi$
$314$	15.5735	+	23.2032i	0.878862	+	1.30943i
$315$		0			0
$316$	−8.22610	+	20.0945i	−0.462754	+	1.13041i
$317$			9.76229i			0.548305i	0.961686	+	0.274152i	$0.0883973\pi$
$317$			9.76229i			0.548305i	−0.961686	+	0.274152i	$0.911603\pi$
$318$		0			0
$319$	−23.2857			−1.30375
$320$	−3.15305	−	7.35243i	−0.176261	−	0.411013i
$321$		0			0
$322$	18.5443	−	12.4465i	1.03343	−	0.693619i
$323$			1.23220i			0.0685616i
$324$		0			0
$325$		−	4.91228i		−	0.272484i
$326$	16.9405	+	25.2400i	0.938248	+	1.39791i
$327$		0			0
$328$	−1.85575	−	9.03580i	−0.102467	−	0.498918i
$329$	−17.3873			−0.958594
$330$		0			0
$331$		−	5.62096i		−	0.308956i	−0.987996	−	0.154478i	$-0.950630\pi$
$331$		−	5.62096i		−	0.308956i	0.987996	−	0.154478i	$-0.0493696\pi$
$332$	15.8002	+	6.46814i	0.867150	+	0.354985i
$333$		0			0
$334$	22.3888	−	15.0269i	1.22506	−	0.822235i
$335$	−2.70667			−0.147881
$336$		0			0
$337$	−0.804011			−0.0437973			−0.0218986	−	0.999760i	$-0.506971\pi$
$337$	−0.804011			−0.0437973			−0.0218986	+	0.999760i	$0.506971\pi$
$338$	−13.0699	+	8.77224i	−0.710910	+	0.477147i
$339$		0			0
$340$	−0.435965	−	0.178471i	−0.0236435	−	0.00967895i
$341$		−	27.7092i		−	1.50054i
$342$		0			0
$343$	−20.1553			−1.08828
$344$	27.4514	−	5.63792i	1.48008	−	0.303976i
$345$		0			0
$346$	−7.33795	−	10.9329i	−0.394490	−	0.587758i
$347$		−	10.7019i		−	0.574507i	−0.957855	−	0.287253i	$-0.907258\pi$
$347$		−	10.7019i		−	0.574507i	0.957855	−	0.287253i	$-0.0927421\pi$
$348$		0			0
$349$		−	24.9915i		−	1.33776i	−0.743369	−	0.668881i	$-0.766774\pi$
$349$		−	24.9915i		−	1.33776i	0.743369	−	0.668881i	$-0.233226\pi$
$350$	−2.49792	+	1.67655i	−0.133520	+	0.0896154i
$351$		0			0
$352$	−5.73299	+	30.4669i	−0.305570	+	1.62389i
$353$	15.4860			0.824237			0.412119	−	0.911130i	$-0.364789\pi$
$353$	15.4860			0.824237			0.412119	+	0.911130i	$0.364789\pi$
$354$		0			0
$355$			7.18836i			0.381518i
$356$	−7.50747	+	18.3391i	−0.397895	+	0.971969i
$357$		0			0
$358$	2.13283	+	3.17775i	0.112724	+	0.167949i
$359$	−11.9335			−0.629826			−0.314913	−	0.949121i	$-0.601975\pi$
$359$	−11.9335			−0.629826			−0.314913	+	0.949121i	$0.601975\pi$
$360$		0			0
$361$	−8.36740			−0.440390
$362$	5.85098	+	8.71749i	0.307521	+	0.458181i
$363$		0			0
$364$	19.3414	+	7.91780i	1.01377	+	0.415006i
$365$			9.66370i			0.505821i
$366$		0			0
$367$	6.95514			0.363055			0.181528	−	0.983386i	$-0.441896\pi$
$367$	6.95514			0.363055			0.181528	+	0.983386i	$0.441896\pi$
$368$	−21.1712	−	20.8233i	−1.10362	−	1.08549i
$369$		0			0
$370$	−2.67268	+	1.79384i	−0.138946	+	0.0932575i
$371$		−	22.6844i		−	1.17772i
$372$		0			0
$373$		−	11.6296i		−	0.602156i	−0.953600	−	0.301078i	$-0.902654\pi$
$373$		−	11.6296i		−	0.602156i	0.953600	−	0.301078i	$-0.0973464\pi$
$374$	1.01735	+	1.51577i	0.0526060	+	0.0783787i
$375$		0			0
$376$	4.65094	+	22.6457i	0.239854	+	1.16787i
$377$	20.8720			1.07496
$378$		0			0
$379$		−	0.235541i		−	0.0120989i	−0.999982	−	0.00604945i	$-0.998074\pi$
$379$		−	0.235541i		−	0.0120989i	0.999982	−	0.00604945i	$-0.00192561\pi$
$380$	3.96386	−	9.68284i	0.203342	−	0.496719i
$381$		0			0
$382$	15.5117	−	10.4111i	0.793648	−	0.532679i
$383$	4.23305			0.216299			0.108149	−	0.994135i	$-0.465507\pi$
$383$	4.23305			0.216299			0.108149	+	0.994135i	$0.465507\pi$
$384$		0			0
$385$	11.6581			0.594153
$386$	−4.38566	+	2.94356i	−0.223224	+	0.149823i
$387$		0			0
$388$	11.2819	−	27.5593i	0.572753	−	1.39911i
$389$			27.0991i			1.37398i	0.726667	+	0.686990i	$0.241068\pi$
$389$			27.0991i			1.37398i	−0.726667	+	0.686990i	$0.758932\pi$
$390$		0			0
$391$	−1.74863			−0.0884320
$392$	1.40820	+	6.85662i	0.0711248	+	0.346312i
$393$		0			0
$394$	5.51943	+	8.22350i	0.278065	+	0.414294i
$395$		−	10.8565i		−	0.546252i
$396$		0			0
$397$		−	21.9552i		−	1.10190i	−0.834539	−	0.550949i	$-0.814266\pi$
$397$		−	21.9552i		−	1.10190i	0.834539	−	0.550949i	$-0.185734\pi$
$398$	24.9843	−	16.7689i	1.25235	−	0.840550i
$399$		0			0
$400$	2.85176	+	2.80490i	0.142588	+	0.140245i
$401$	−8.36813			−0.417884			−0.208942	−	0.977928i	$-0.567002\pi$
$401$	−8.36813			−0.417884			−0.208942	+	0.977928i	$0.567002\pi$
$402$		0			0
$403$			24.8369i			1.23721i
$404$	11.3513	+	4.64690i	0.564750	+	0.231192i
$405$		0			0
$406$	−7.12355	−	10.6135i	−0.353536	−	0.526740i
$407$	12.4737			0.618300
$408$		0			0
$409$	−28.2474			−1.39675			−0.698373	−	0.715734i	$-0.746092\pi$
$409$	−28.2474			−1.39675			−0.698373	+	0.715734i	$0.746092\pi$
$410$	2.57033	+	3.82959i	0.126940	+	0.189130i
$411$		0			0
$412$	−6.68896	+	16.3396i	−0.329541	+	0.804996i
$413$			1.49544i			0.0735856i
$414$		0			0
$415$	−8.53645			−0.419038
$416$	5.13873	−	27.3088i	0.251947	−	1.33892i
$417$		0			0
$418$	−33.6655	+	22.5955i	−1.64663	+	1.10518i
$419$		−	8.68443i		−	0.424262i	−0.977241	−	0.212131i	$-0.931960\pi$
$419$		−	8.68443i		−	0.424262i	0.977241	−	0.212131i	$-0.0680404\pi$
$420$		0			0
$421$			4.73033i			0.230542i	0.993334	+	0.115271i	$0.0367737\pi$
$421$			4.73033i			0.230542i	−0.993334	+	0.115271i	$0.963226\pi$
$422$	−19.2913	−	28.7424i	−0.939084	−	1.39916i
$423$		0			0
$424$	−29.5448	+	6.06786i	−1.43482	+	0.294681i
$425$	0.235541			0.0114254
$426$		0			0
$427$		−	0.678826i		−	0.0328507i
$428$	−13.8558	−	5.67215i	−0.669746	−	0.274174i
$429$		0			0
$430$	−11.6346	+	7.80887i	−0.561069	+	0.376577i
$431$	39.1052			1.88363			0.941817	−	0.336127i	$-0.109117\pi$
$431$	39.1052			1.88363			0.941817	+	0.336127i	$0.109117\pi$
$432$		0			0
$433$	33.8221			1.62538			0.812692	−	0.582693i	$-0.198001\pi$
$433$	33.8221			1.62538			0.812692	+	0.582693i	$0.198001\pi$
$434$	12.6297	−	8.47679i	0.606246	−	0.406899i
$435$		0			0
$436$	33.0317	+	13.5222i	1.58193	+	0.647596i
$437$		−	38.8373i		−	1.85784i
$438$		0			0
$439$	1.59960			0.0763448			0.0381724	−	0.999271i	$-0.487846\pi$
$439$	1.59960			0.0763448			0.0381724	+	0.999271i	$0.487846\pi$
$440$	−3.11843	−	15.1839i	−0.148666	−	0.723863i
$441$		0			0
$442$	−0.911896	−	1.35865i	−0.0433745	−	0.0646244i
$443$		−	8.64862i		−	0.410909i	−0.978667	−	0.205454i	$-0.934133\pi$
$443$		−	8.64862i		−	0.410909i	0.978667	−	0.205454i	$-0.0658672\pi$
$444$		0			0
$445$		−	9.90812i		−	0.469690i
$446$	−19.9460	+	13.3873i	−0.944472	+	0.633909i
$447$		0			0
$448$	−15.6405	+	6.70735i	−0.738945	+	0.316893i
$449$	−15.9597			−0.753184			−0.376592	−	0.926379i	$-0.622904\pi$
$449$	−15.9597			−0.753184			−0.376592	+	0.926379i	$0.622904\pi$
$450$		0			0
$451$		−	17.8732i		−	0.841615i
$452$	−11.2602	+	27.5062i	−0.529636	+	1.29378i
$453$		0			0
$454$	16.1726	+	24.0958i	0.759017	+	1.13087i
$455$	−10.4497			−0.489888
$456$		0			0
$457$	−22.6462			−1.05934			−0.529672	−	0.848203i	$-0.677685\pi$
$457$	−22.6462			−1.05934			−0.529672	+	0.848203i	$0.677685\pi$
$458$	−2.37438	−	3.53762i	−0.110947	−	0.165302i
$459$		0			0
$460$	13.7410	+	5.62515i	0.640677	+	0.262274i
$461$		−	22.4400i		−	1.04513i	−0.852599	−	0.522566i	$-0.824975\pi$
$461$		−	22.4400i		−	1.04513i	0.852599	−	0.522566i	$-0.175025\pi$
$462$		0			0
$463$	30.8710			1.43470			0.717348	−	0.696715i	$-0.245356\pi$
$463$	30.8710			1.43470			0.717348	+	0.696715i	$0.245356\pi$
$464$	−11.9179	+	12.1169i	−0.553273	+	0.562514i
$465$		0			0
$466$	17.8930	−	12.0094i	0.828879	−	0.556325i
$467$			3.05734i			0.141477i	0.997495	+	0.0707383i	$0.0225355\pi$
$467$			3.05734i			0.141477i	−0.997495	+	0.0707383i	$0.977464\pi$
$468$		0			0
$469$			5.75777i			0.265869i
$470$	−6.44184	−	9.59781i	−0.297140	−	0.442714i
$471$		0			0
$472$	1.94770	−	0.400014i	0.0896500	−	0.0184122i
$473$	54.3001			2.49672
$474$		0			0
$475$			5.23139i			0.240032i
$476$	−0.379654	+	0.927409i	−0.0174014	+	0.0425077i
$477$		0			0
$478$	−18.6425	+	12.5124i	−0.852686	+	0.572304i
$479$	−22.4262			−1.02468			−0.512341	−	0.858782i	$-0.671221\pi$
$479$	−22.4262			−1.02468			−0.512341	+	0.858782i	$0.671221\pi$
$480$		0			0
$481$	−11.1807			−0.509798
$482$	24.6402	−	16.5379i	1.12233	−	0.753282i
$483$		0			0
$484$	−14.4225	+	35.2309i	−0.655566	+	1.60140i
$485$			14.8895i			0.676100i
$486$		0			0
$487$	−11.9961			−0.543594			−0.271797	−	0.962355i	$-0.587618\pi$
$487$	−11.9961			−0.543594			−0.271797	+	0.962355i	$0.587618\pi$
$488$	−0.884122	+	0.181579i	−0.0400223	+	0.00821971i
$489$		0			0
$490$	−1.95044	−	2.90600i	−0.0881121	−	0.131280i
$491$		−	0.261916i		−	0.0118201i	−0.999983	−	0.00591005i	$-0.998119\pi$
$491$		−	0.261916i		−	0.0118201i	0.999983	−	0.00591005i	$-0.00188124\pi$
$492$		0			0
$493$			1.00080i			0.0450736i
$494$	30.1758	−	20.2533i	1.35767	−	0.911240i
$495$		0			0
$496$	−14.4187	−	14.1818i	−0.647420	−	0.636784i
$497$	15.2915			0.685917
$498$		0			0
$499$		−	43.0171i		−	1.92571i	−0.270018	−	0.962855i	$-0.587030\pi$
$499$		−	43.0171i		−	1.92571i	0.270018	−	0.962855i	$-0.412970\pi$
$500$	−1.85091	−	0.757708i	−0.0827753	−	0.0338857i
$501$		0			0
$502$	6.69741	+	9.97859i	0.298920	+	0.445366i
$503$	21.3295			0.951037			0.475518	−	0.879706i	$-0.342260\pi$
$503$	21.3295			0.951037			0.475518	+	0.879706i	$0.342260\pi$
$504$		0			0
$505$	−6.13283			−0.272908
$506$	−32.0655	−	47.7749i	−1.42548	−	2.12385i
$507$		0			0
$508$	5.17354	−	12.6378i	0.229539	−	0.560712i
$509$		−	15.0919i		−	0.668936i	−0.942407	−	0.334468i	$-0.891443\pi$
$509$		−	15.0919i		−	0.668936i	0.942407	−	0.334468i	$-0.108557\pi$
$510$		0			0
$511$	20.5572			0.909396
$512$	12.9195	+	18.5765i	0.570968	+	0.820972i
$513$		0			0
$514$	0.261202	−	0.175313i	0.0115211	−	0.00773272i
$515$		−	8.82788i		−	0.389003i
$516$		0			0
$517$			44.7942i			1.97005i
$518$	3.81596	+	5.68547i	0.167664	+	0.249805i
$519$		0			0
$520$	2.79519	+	13.6099i	0.122577	+	0.596836i
$521$	−33.8443			−1.48274			−0.741372	−	0.671094i	$-0.765825\pi$
$521$	−33.8443			−1.48274			−0.741372	+	0.671094i	$0.765825\pi$
$522$		0			0
$523$			10.5034i			0.459281i	0.973276	+	0.229640i	$0.0737550\pi$
$523$			10.5034i			0.459281i	−0.973276	+	0.229640i	$0.926245\pi$
$524$	39.5862	+	16.2054i	1.72933	+	0.707937i
$525$		0			0
$526$	−9.09220	+	6.10248i	−0.396439	+	0.266081i
$527$	−1.19091			−0.0518770
$528$		0			0
$529$	32.1143			1.39627
$530$	12.5218	−	8.40436i	0.543913	−	0.365062i
$531$		0			0
$532$	−20.5979	−	8.43216i	−0.893031	−	0.365580i
$533$			16.0205i			0.693924i
$534$		0			0
$535$	7.48593			0.323645
$536$	7.49909	−	1.54015i	0.323911	−	0.0665243i
$537$		0			0
$538$	1.97743	+	2.94621i	0.0852532	+	0.127020i
$539$			13.5627i			0.584186i
$540$		0			0
$541$			18.2058i			0.782728i	0.920236	+	0.391364i	$0.127997\pi$
$541$			18.2058i			0.782728i	−0.920236	+	0.391364i	$0.872003\pi$
$542$	−8.22627	+	5.52129i	−0.353349	+	0.237160i
$543$		0			0
$544$	1.30944	+	0.246399i	0.0561417	+	0.0105643i
$545$	−17.8462			−0.764446
$546$		0			0
$547$		−	7.81348i		−	0.334080i	−0.985950	−	0.167040i	$-0.946579\pi$
$547$		−	7.81348i		−	0.334080i	0.985950	−	0.167040i	$-0.0534209\pi$
$548$	−14.8572	+	36.2929i	−0.634669	+	1.55036i
$549$		0			0
$550$	4.31922	+	6.43529i	0.184172	+	0.274402i
$551$	−22.2278			−0.946937
$552$		0			0
$553$	−23.0947			−0.982085
$554$	−6.40789	−	9.54723i	−0.272245	−	0.405623i
$555$		0			0
$556$	1.66891	+	0.683200i	0.0707774	+	0.0289741i
$557$		−	14.7679i		−	0.625735i	−0.949797	−	0.312867i	$-0.898710\pi$
$557$		−	14.7679i		−	0.625735i	0.949797	−	0.312867i	$-0.101290\pi$
$558$		0			0
$559$	−48.6715			−2.05858
$560$	5.96675	−	6.06642i	0.252141	−	0.256353i
$561$		0			0
$562$	−23.7242	+	15.9231i	−1.00074	+	0.671678i
$563$		−	29.5041i		−	1.24345i	−0.783236	−	0.621724i	$-0.786433\pi$
$563$		−	29.5041i		−	1.24345i	0.783236	−	0.621724i	$-0.213567\pi$
$564$		0			0
$565$		−	14.8609i		−	0.625203i
$566$	−21.6440	−	32.2478i	−0.909767	−	1.35548i
$567$		0			0
$568$	−4.09032	−	19.9161i	−0.171626	−	0.835659i
$569$	−29.0862			−1.21935			−0.609677	−	0.792650i	$-0.708701\pi$
$569$	−29.0862			−1.21935			−0.609677	+	0.792650i	$0.708701\pi$
$570$		0			0
$571$		−	42.1417i		−	1.76357i	−0.471649	−	0.881787i	$-0.656341\pi$
$571$		−	42.1417i		−	1.76357i	0.471649	−	0.881787i	$-0.343659\pi$
$572$	20.3983	−	49.8285i	0.852895	−	2.08343i
$573$		0			0
$574$	8.14651	−	5.46776i	0.340029	−	0.228220i
$575$	−7.42390			−0.309598
$576$		0			0
$577$	−33.8258			−1.40819			−0.704094	−	0.710107i	$-0.748646\pi$
$577$	−33.8258			−1.40819			−0.704094	+	0.710107i	$0.748646\pi$
$578$	−19.8970	+	13.3545i	−0.827608	+	0.555472i
$579$		0			0
$580$	3.21945	−	7.86441i	0.133681	−	0.326552i
$581$			18.1592i			0.753371i
$582$		0			0
$583$	−58.4409			−2.42037
$584$	−5.49884	−	26.7742i	−0.227544	−	1.10793i
$585$		0			0
$586$	3.94317	+	5.87501i	0.162891	+	0.242694i
$587$			2.36693i			0.0976937i	0.998806	+	0.0488469i	$0.0155546\pi$
$587$			2.36693i			0.0976937i	−0.998806	+	0.0488469i	$0.984445\pi$
$588$		0			0
$589$		−	26.4504i		−	1.08987i
$590$	−0.825481	+	0.554045i	−0.0339845	+	0.0228097i
$591$		0			0
$592$	6.38419	−	6.49083i	0.262389	−	0.266771i
$593$	−14.0133			−0.575459			−0.287729	−	0.957712i	$-0.592900\pi$
$593$	−14.0133			−0.575459			−0.287729	+	0.957712i	$0.592900\pi$
$594$		0			0
$595$		−	0.501055i		−	0.0205413i
$596$	3.24107	+	1.32680i	0.132759	+	0.0543477i
$597$		0			0
$598$	28.7417	+	42.8227i	1.17533	+	1.75115i
$599$	−0.194646			−0.00795304			−0.00397652	−	0.999992i	$-0.501266\pi$
$599$	−0.194646			−0.00795304			−0.00397652	+	0.999992i	$0.501266\pi$
$600$		0			0
$601$	−40.3962			−1.64780			−0.823898	−	0.566738i	$-0.808205\pi$
$601$	−40.3962			−1.64780			−0.823898	+	0.566738i	$0.808205\pi$
$602$	16.6115	+	24.7497i	0.677033	+	1.00872i
$603$		0			0
$604$	2.19842	−	5.37026i	0.0894526	−	0.218513i
$605$		−	19.0343i		−	0.773855i
$606$		0			0
$607$	34.9823			1.41989			0.709944	−	0.704258i	$-0.248720\pi$
$607$	34.9823			1.41989			0.709944	+	0.704258i	$0.248720\pi$
$608$	−5.47255	+	29.0828i	−0.221941	+	1.17946i
$609$		0			0
$610$	0.374712	−	0.251498i	0.0151716	−	0.0101829i
$611$		−	40.1510i		−	1.62433i
$612$		0			0
$613$			6.46784i			0.261233i	0.991433	+	0.130617i	$0.0416957\pi$
$613$			6.46784i			0.261233i	−0.991433	+	0.130617i	$0.958304\pi$
$614$	−7.24001	−	10.7870i	−0.292183	−	0.435329i
$615$		0			0
$616$	−32.3000	+	6.63371i	−1.30140	+	0.267280i
$617$	−20.9261			−0.842451			−0.421226	−	0.906956i	$-0.638400\pi$
$617$	−20.9261			−0.842451			−0.421226	+	0.906956i	$0.638400\pi$
$618$		0			0
$619$		−	11.1568i		−	0.448430i	−0.974540	−	0.224215i	$-0.928018\pi$
$619$		−	11.1568i		−	0.448430i	0.974540	−	0.224215i	$-0.0719818\pi$
$620$	9.35838	+	3.83104i	0.375842	+	0.153858i
$621$		0			0
$622$	2.34612	−	1.57466i	0.0940708	−	0.0631383i
$623$	−21.0771			−0.844437
$624$		0			0
$625$	1.00000			0.0400000
$626$	−12.4531	+	8.35824i	−0.497726	+	0.334062i
$627$		0			0
$628$	36.5742	+	14.9724i	1.45947	+	0.597463i
$629$		−	0.536109i		−	0.0213761i
$630$		0			0
$631$	4.79278			0.190798			0.0953989	−	0.995439i	$-0.469587\pi$
$631$	4.79278			0.190798			0.0953989	+	0.995439i	$0.469587\pi$
$632$	6.17760	+	30.0791i	0.245732	+	1.19648i
$633$		0			0
$634$	7.69394	+	11.4633i	0.305565	+	0.455267i
$635$			6.82788i			0.270956i
$636$		0			0
$637$		−	12.1568i		−	0.481670i
$638$	−27.3431	+	18.3521i	−1.08252	+	0.726567i
$639$		0			0
$640$	−9.49712	−	6.14856i	−0.375407	−	0.243043i
$641$	42.9892			1.69797			0.848986	−	0.528416i	$-0.177214\pi$
$641$	42.9892			1.69797			0.848986	+	0.528416i	$0.177214\pi$
$642$		0			0
$643$			28.0578i			1.10649i	0.833017	+	0.553247i	$0.186611\pi$
$643$			28.0578i			1.10649i	−0.833017	+	0.553247i	$0.813389\pi$
$644$	11.9661	−	29.2306i	0.471532	−	1.15185i
$645$		0			0
$646$	0.971134	+	1.44691i	0.0382088	+	0.0569279i
$647$	5.30186			0.208437			0.104219	−	0.994554i	$-0.466766\pi$
$647$	5.30186			0.208437			0.104219	+	0.994554i	$0.466766\pi$
$648$		0			0
$649$	3.85263			0.151229
$650$	−3.87150	−	5.76822i	−0.151853	−	0.226248i
$651$		0			0
$652$	39.7846	+	16.2866i	1.55809	+	0.637834i
$653$		−	10.6725i		−	0.417647i	−0.977953	−	0.208823i	$-0.933037\pi$
$653$		−	10.6725i		−	0.417647i	0.977953	−	0.208823i	$-0.0669634\pi$
$654$		0			0
$655$	−21.3874			−0.835676
$656$	−9.30048	−	9.14768i	−0.363123	−	0.357157i
$657$		0			0
$658$	−20.4170	+	13.7034i	−0.795938	+	0.534216i
$659$		−	15.6338i		−	0.609008i	−0.952511	−	0.304504i	$-0.901509\pi$
$659$		−	15.6338i		−	0.609008i	0.952511	−	0.304504i	$-0.0984907\pi$
$660$		0			0
$661$			35.2867i			1.37249i	0.727369	+	0.686247i	$0.240743\pi$
$661$			35.2867i			1.37249i	−0.727369	+	0.686247i	$0.759257\pi$
$662$	−4.43004	−	6.60040i	−0.172178	−	0.256532i
$663$		0			0
$664$	23.6511	−	4.85741i	0.917839	−	0.188504i
$665$	11.1285			0.431545
$666$		0			0
$667$		−	31.5437i		−	1.22138i
$668$	14.4469	−	35.2905i	0.558967	−	1.36543i
$669$		0			0
$670$	−3.17829	+	2.13320i	−0.122788	+	0.0824127i
$671$	−1.74883			−0.0675128
$672$		0			0
$673$	43.2233			1.66614			0.833068	−	0.553170i	$-0.186582\pi$
$673$	43.2233			1.66614			0.833068	+	0.553170i	$0.186582\pi$
$674$	−0.944107	+	0.633664i	−0.0363657	+	0.0244078i
$675$		0			0
$676$	−8.43365	+	20.6015i	−0.324371	+	0.792367i
$677$			39.8297i			1.53078i	0.643566	+	0.765391i	$0.277454\pi$
$677$			39.8297i			1.53078i	−0.643566	+	0.765391i	$0.722546\pi$
$678$		0			0
$679$	31.6739			1.21553
$680$	−0.652588	+	0.134027i	−0.0250256	+	0.00513971i
$681$		0			0
$682$	−21.8384	−	32.5374i	−0.836235	−	1.24592i
$683$			14.7286i			0.563574i	0.959477	+	0.281787i	$0.0909271\pi$
$683$			14.7286i			0.563574i	−0.959477	+	0.281787i	$0.909073\pi$
$684$		0			0
$685$		−	19.6081i		−	0.749187i
$686$	−23.6673	+	15.8849i	−0.903621	+	0.606490i
$687$		0			0
$688$	27.7913	−	28.2556i	1.05953	−	1.07723i
$689$	52.3831			1.99564
$690$		0			0
$691$		−	31.2491i		−	1.18877i	−0.804180	−	0.594386i	$-0.797395\pi$
$691$		−	31.2491i		−	1.18877i	0.804180	−	0.594386i	$-0.202605\pi$
$692$	−17.2331	−	7.05472i	−0.655105	−	0.268180i
$693$		0			0
$694$	−8.43445	−	12.5666i	−0.320167	−	0.477023i
$695$	−0.901666			−0.0342022
$696$		0			0
$697$	−0.768172			−0.0290966
$698$	−19.6965	−	29.3461i	−0.745522	−	1.11077i
$699$		0			0
$700$	−1.61184	+	3.93737i	−0.0609218	+	0.148818i
$701$			4.52968i			0.171084i	0.996335	+	0.0855419i	$0.0272621\pi$
$701$			4.52968i			0.171084i	−0.996335	+	0.0855419i	$0.972738\pi$
$702$		0			0
$703$	11.9071			0.449083
$704$	17.2799	+	40.2940i	0.651259	+	1.51864i
$705$		0			0
$706$	18.1844	−	12.2050i	0.684379	−	0.459340i
$707$			13.0461i			0.490649i
$708$		0			0
$709$		−	15.1260i		−	0.568069i	−0.958814	−	0.284035i	$-0.908327\pi$
$709$		−	15.1260i		−	0.568069i	0.958814	−	0.284035i	$-0.0916731\pi$
$710$	5.66535	+	8.44090i	0.212617	+	0.316781i
$711$		0			0
$712$	5.63792	+	27.4514i	0.211290	+	1.02879i
$713$	37.5359			1.40573
$714$		0			0
$715$			26.9210i			1.00679i
$716$	5.00894	+	2.05051i	0.187193	+	0.0766312i
$717$		0			0
$718$	−14.0129	+	9.40513i	−0.522956	+	0.350996i
$719$	−12.8773			−0.480243			−0.240122	−	0.970743i	$-0.577187\pi$
$719$	−12.8773			−0.480243			−0.240122	+	0.970743i	$0.577187\pi$
$720$		0			0
$721$	−18.7792			−0.699373
$722$	−9.82539	+	6.59458i	−0.365663	+	0.245425i
$723$		0			0
$724$	13.7410	+	5.62515i	0.510680	+	0.209057i
$725$			4.24894i			0.157802i
$726$		0			0
$727$	7.50213			0.278239			0.139119	−	0.990276i	$-0.455573\pi$
$727$	7.50213			0.278239			0.139119	+	0.990276i	$0.455573\pi$
$728$	28.9519	−	5.94608i	1.07303	−	0.220376i
$729$		0			0
$730$	7.61624	+	11.3476i	0.281890	+	0.419992i
$731$		−	2.33376i		−	0.0863174i
$732$		0			0
$733$		−	12.4046i		−	0.458174i	−0.973406	−	0.229087i	$-0.926426\pi$
$733$		−	12.4046i		−	0.458174i	0.973406	−	0.229087i	$-0.0735740\pi$
$734$	8.16704	−	5.48154i	0.301451	−	0.202327i
$735$		0			0
$736$	−41.2716	−	7.76613i	−1.52129	−	0.286263i
$737$	14.8335			0.546399
$738$		0			0
$739$			49.6664i			1.82701i	0.406830	+	0.913504i	$0.366634\pi$
$739$			49.6664i			1.82701i	−0.406830	+	0.913504i	$0.633366\pi$
$740$	−1.72461	+	4.21283i	−0.0633978	+	0.154867i
$741$		0			0
$742$	−17.8782	−	26.6371i	−0.656331	−	0.977879i
$743$	26.1312			0.958662			0.479331	−	0.877634i	$-0.340879\pi$
$743$	26.1312			0.958662			0.479331	+	0.877634i	$0.340879\pi$
$744$		0			0
$745$	−1.75106			−0.0641540
$746$	−9.16558	−	13.6560i	−0.335576	−	0.499980i
$747$		0			0
$748$	2.38924	+	0.978085i	0.0873594	+	0.0357623i
$749$		−	15.9245i		−	0.581869i
$750$		0			0
$751$	42.6818			1.55748			0.778741	−	0.627346i	$-0.215859\pi$
$751$	42.6818			1.55748			0.778741	+	0.627346i	$0.215859\pi$
$752$	23.3091	+	22.9261i	0.849995	+	0.836030i
$753$		0			0
$754$	24.5088	−	16.4498i	0.892558	−	0.599065i
$755$			2.90141i			0.105593i
$756$		0			0
$757$		−	37.3850i		−	1.35878i	−0.733777	−	0.679391i	$-0.762244\pi$
$757$		−	37.3850i		−	1.35878i	0.733777	−	0.679391i	$-0.237756\pi$
$758$	−0.185636	−	0.276583i	−0.00674261	−	0.0100459i
$759$		0			0
$760$	−2.97676	−	14.4941i	−0.107979	−	0.525755i
$761$	20.2038			0.732386			0.366193	−	0.930539i	$-0.380661\pi$
$761$	20.2038			0.732386			0.366193	+	0.930539i	$0.380661\pi$
$762$		0			0
$763$			37.9634i			1.37437i
$764$	10.0093	−	24.4504i	0.362123	−	0.884586i
$765$		0			0
$766$	4.97065	−	3.33619i	0.179597	−	0.120541i
$767$	−3.45327			−0.124690
$768$		0			0
$769$	28.9265			1.04312			0.521558	−	0.853216i	$-0.325351\pi$
$769$	28.9265			1.04312			0.521558	+	0.853216i	$0.325351\pi$
$770$	13.6895	−	9.18810i	0.493336	−	0.331116i
$771$		0			0
$772$	−2.82994	+	6.91292i	−0.101852	+	0.248801i
$773$		−	47.0349i		−	1.69173i	−0.533400	−	0.845863i	$-0.679086\pi$
$773$		−	47.0349i		−	1.69173i	0.533400	−	0.845863i	$-0.320914\pi$
$774$		0			0
$775$	−5.05609			−0.181620
$776$	−8.47245	−	41.2530i	−0.304143	−	1.48089i
$777$		0			0
$778$	21.3576	+	31.8210i	0.765706	+	1.14084i
$779$		−	17.0612i		−	0.611281i
$780$		0			0
$781$		−	39.3948i		−	1.40966i
$782$	−2.05332	+	1.37814i	−0.0734266	+	0.0492823i
$783$		0			0
$784$	7.05747	+	6.94152i	0.252052	+	0.247911i
$785$	−19.7601			−0.705267
$786$		0			0
$787$		−	27.5698i		−	0.982756i	−0.870946	−	0.491378i	$-0.836493\pi$
$787$		−	27.5698i		−	0.982756i	0.870946	−	0.491378i	$-0.163507\pi$
$788$	12.9623	+	5.30639i	0.461764	+	0.189032i
$789$		0			0
$790$	−8.55635	−	12.7483i	−0.304421	−	0.453563i
$791$	−31.6129			−1.12403
$792$		0			0
$793$	1.56755			0.0556653
$794$	−17.3035	−	25.7808i	−0.614078	−	0.914925i
$795$		0			0
$796$	16.1217	−	39.3817i	0.571418	−	1.39585i
$797$			46.4890i			1.64672i	0.567516	+	0.823362i	$0.307904\pi$
$797$			46.4890i			1.64672i	−0.567516	+	0.823362i	$0.692096\pi$
$798$		0			0
$799$	1.92521			0.0681091
$800$	5.55929	+	1.04610i	0.196550	+	0.0369852i
$801$		0			0
$802$	−9.82624	+	6.59516i	−0.346977	+	0.232883i
$803$		−	52.9605i		−	1.86894i
$804$		0			0
$805$			15.7925i			0.556614i
$806$	19.5747	+	29.1647i	0.689488	+	1.02728i
$807$		0			0
$808$	16.9916	−	3.48971i	0.597763	−	0.122767i
$809$	47.2189			1.66013			0.830064	−	0.557668i	$-0.188304\pi$
$809$	47.2189			1.66013			0.830064	+	0.557668i	$0.188304\pi$
$810$		0			0
$811$		−	9.83765i		−	0.345447i	−0.984970	−	0.172723i	$-0.944743\pi$
$811$		−	9.83765i		−	0.345447i	0.984970	−	0.172723i	$-0.0552567\pi$
$812$	−16.7296	−	6.84860i	−0.587094	−	0.240339i
$813$		0			0
$814$	14.6472	−	9.83090i	0.513385	−	0.344573i
$815$	−21.4946			−0.752923
$816$		0			0
$817$	51.8332			1.81341
$818$	−33.1695	+	22.2626i	−1.15974	+	0.778394i
$819$		0			0
$820$	6.03641	+	2.47113i	0.210801	+	0.0862955i
$821$		−	35.6781i		−	1.24517i	−0.782551	−	0.622587i	$-0.786082\pi$
$821$		−	35.6781i		−	1.24517i	0.782551	−	0.622587i	$-0.213918\pi$
$822$		0			0
$823$	−23.7092			−0.826450			−0.413225	−	0.910629i	$-0.635598\pi$
$823$	−23.7092			−0.826450			−0.413225	+	0.910629i	$0.635598\pi$
$824$	5.02324	+	24.4585i	0.174993	+	0.852053i
$825$		0			0
$826$	1.17859	+	1.75601i	0.0410086	+	0.0610994i
$827$			9.64454i			0.335373i	0.985840	+	0.167687i	$0.0536297\pi$
$827$			9.64454i			0.335373i	−0.985840	+	0.167687i	$0.946370\pi$
$828$		0			0
$829$			30.3639i			1.05458i	0.849685	+	0.527291i	$0.176792\pi$
$829$			30.3639i			1.05458i	−0.849685	+	0.527291i	$0.823208\pi$
$830$	−10.0239	+	6.72781i	−0.347934	+	0.233526i
$831$		0			0
$832$	−15.4887	−	36.1172i	−0.536973	−	1.25214i
$833$	0.582911			0.0201967
$834$		0			0
$835$			19.0666i			0.659825i
$836$	−21.7234	+	53.0654i	−0.751319	+	1.83531i
$837$		0			0
$838$	−6.84444	−	10.1977i	−0.236437	−	0.352272i
$839$	−5.58047			−0.192659			−0.0963296	−	0.995349i	$-0.530710\pi$
$839$	−5.58047			−0.192659			−0.0963296	+	0.995349i	$0.530710\pi$
$840$		0			0
$841$	10.9465			0.377467
$842$	3.72811	+	5.55457i	0.128479	+	0.191423i
$843$		0			0
$844$	−45.3054	−	18.5467i	−1.55947	−	0.638402i
$845$		−	11.1305i		−	0.382900i
$846$		0			0
$847$	−40.4909			−1.39128
$848$	−29.9107	+	30.4103i	−1.02714	+	1.04429i
$849$		0			0
$850$	0.276583	−	0.185636i	0.00948670	−	0.00636727i
$851$			16.8974i			0.579235i
$852$		0			0
$853$		−	50.6473i		−	1.73413i	−0.498193	−	0.867066i	$-0.666003\pi$
$853$		−	50.6473i		−	1.73413i	0.498193	−	0.867066i	$-0.333997\pi$
$854$	−0.535002	−	0.797109i	−0.0183074	−	0.0272765i
$855$		0			0
$856$	−20.7405	+	4.25965i	−0.708896	+	0.145592i
$857$	19.1906			0.655539			0.327769	−	0.944758i	$-0.393703\pi$
$857$	19.1906			0.655539			0.327769	+	0.944758i	$0.393703\pi$
$858$		0			0
$859$		−	1.31864i		−	0.0449915i	−0.999747	−	0.0224957i	$-0.992839\pi$
$859$		−	1.31864i		−	0.0449915i	0.999747	−	0.0224957i	$-0.00716122\pi$
$860$	−7.50747	+	18.3391i	−0.256003	+	0.625357i
$861$		0			0
$862$	45.9192	−	30.8199i	1.56401	−	1.04973i
$863$	−12.3923			−0.421840			−0.210920	−	0.977503i	$-0.567646\pi$
$863$	−12.3923			−0.421840			−0.210920	+	0.977503i	$0.567646\pi$
$864$		0			0
$865$	9.31060			0.316570
$866$	39.7154	−	26.6561i	1.34959	−	0.905812i
$867$		0			0
$868$	8.14961	−	19.9077i	0.276616	−	0.675710i
$869$			59.4978i			2.01832i
$870$		0			0
$871$	−13.2959			−0.450514
$872$	49.4446	−	10.1548i	1.67440	−	0.343886i
$873$		0			0
$874$	−30.6088	−	45.6045i	−1.03536	−	1.54260i
$875$		−	2.12726i		−	0.0719144i
$876$		0			0
$877$			36.8292i			1.24363i	0.783163	+	0.621816i	$0.213605\pi$
$877$			36.8292i			1.24363i	−0.783163	+	0.621816i	$0.786395\pi$
$878$	1.87833	−	1.26069i	0.0633904	−	0.0425462i
$879$		0			0
$880$	−15.6286	−	15.3719i	−0.526841	−	0.518186i
$881$	21.4110			0.721356			0.360678	−	0.932690i	$-0.382545\pi$
$881$	21.4110			0.721356			0.360678	+	0.932690i	$0.382545\pi$
$882$		0			0
$883$			1.59479i			0.0536690i	0.999640	+	0.0268345i	$0.00854271\pi$
$883$			1.59479i			0.0536690i	−0.999640	+	0.0268345i	$0.991457\pi$
$884$	−2.14158	−	0.876699i	−0.0720292	−	0.0294866i
$885$		0			0
$886$	−6.81622	−	10.1556i	−0.228996	−	0.341185i
$887$	−28.6129			−0.960727			−0.480363	−	0.877070i	$-0.659495\pi$
$887$	−28.6129			−0.960727			−0.480363	+	0.877070i	$0.659495\pi$
$888$		0			0
$889$	14.5247			0.487141
$890$	−7.80887	−	11.6346i	−0.261754	−	0.389992i
$891$		0			0
$892$	−12.8706	+	31.4401i	−0.430940	+	1.05269i
$893$			42.7592i			1.43088i
$894$		0			0
$895$	−2.70620			−0.0904584
$896$	−13.0796	+	20.2028i	−0.436957	+	0.674928i
$897$		0			0
$898$	−18.7406	+	12.5783i	−0.625381	+	0.419742i
$899$		−	21.4830i		−	0.716498i
$900$		0			0
$901$			2.51173i			0.0836780i
$902$	−14.0864	−	20.9875i	−0.469024	−	0.698808i
$903$		0			0
$904$	8.45615	+	41.1736i	0.281247	+	1.36941i
$905$	−7.42390			−0.246779
$906$		0			0
$907$			39.3412i			1.30630i	0.757228	+	0.653151i	$0.226553\pi$
$907$			39.3412i			1.30630i	−0.757228	+	0.653151i	$0.773447\pi$
$908$	37.9812	+	15.5484i	1.26045	+	0.515991i
$909$		0			0
$910$	−12.2705	+	8.23568i	−0.406763	+	0.273010i
$911$	−33.6919			−1.11626			−0.558131	−	0.829753i	$-0.688481\pi$
$911$	−33.6919			−1.11626			−0.558131	+	0.829753i	$0.688481\pi$
$912$		0			0
$913$	46.7828			1.54828
$914$	−26.5922	+	17.8481i	−0.879592	+	0.590363i
$915$		0			0
$916$	−5.57620	−	2.28273i	−0.184243	−	0.0754235i
$917$			45.4965i			1.50243i
$918$		0			0
$919$	39.2196			1.29373			0.646867	−	0.762603i	$-0.276079\pi$
$919$	39.2196			1.29373			0.646867	+	0.762603i	$0.276079\pi$
$920$	20.5686	−	4.22435i	0.678128	−	0.139273i
$921$		0			0
$922$	−17.6856	−	26.3500i	−0.582443	−	0.867792i
$923$			35.3112i			1.16228i
$924$		0			0
$925$		−	2.27608i		−	0.0748371i
$926$	36.2501	−	24.3303i	1.19125	−	0.799543i
$927$		0			0
$928$	−4.44481	+	23.6211i	−0.145908	+	0.775399i
$929$	−45.1242			−1.48048			−0.740239	−	0.672344i	$-0.765288\pi$
$929$	−45.1242			−1.48048			−0.740239	+	0.672344i	$0.765288\pi$
$930$		0			0
$931$			12.9465i			0.424305i
$932$	11.5459	−	28.2040i	0.378198	−	0.923853i
$933$		0			0
$934$	2.40957	+	3.59007i	0.0788436	+	0.117471i
$935$	−1.29085			−0.0422152
$936$		0			0
$937$	−56.9008			−1.85887			−0.929435	−	0.368986i	$-0.879705\pi$
$937$	−56.9008			−1.85887			−0.929435	+	0.368986i	$0.879705\pi$
$938$	4.53786	+	6.76104i	0.148166	+	0.220756i
$939$		0			0
$940$	−15.1286	−	6.19320i	−0.493441	−	0.202000i
$941$			56.6437i			1.84653i	0.384163	+	0.923265i	$0.374490\pi$
$941$			56.6437i			1.84653i	−0.384163	+	0.923265i	$0.625510\pi$
$942$		0			0
$943$	24.2117			0.788441
$944$	1.97181	−	2.00475i	0.0641771	−	0.0652491i
$945$		0			0
$946$	63.7616	−	42.7954i	2.07307	−	1.39140i
$947$		−	19.1789i		−	0.623230i	−0.950208	−	0.311615i	$-0.899130\pi$
$947$		−	19.1789i		−	0.623230i	0.950208	−	0.311615i	$-0.100870\pi$
$948$		0			0
$949$			47.4708i			1.54097i
$950$	4.12300	+	6.14294i	0.133768	+	0.199303i
$951$		0			0
$952$	0.285111	+	1.38822i	0.00924048	+	0.0449926i
$953$	−29.3512			−0.950777			−0.475389	−	0.879776i	$-0.657693\pi$
$953$	−29.3512			−0.950777			−0.475389	+	0.879776i	$0.657693\pi$
$954$		0			0
$955$			13.2099i			0.427463i
$956$	−12.0295	+	29.3853i	−0.389060	+	0.950388i
$957$		0			0
$958$	−26.3339	+	17.6748i	−0.850811	+	0.571045i
$959$	−41.7115			−1.34693
$960$		0			0
$961$	−5.43596			−0.175354
$962$	−13.1289	+	8.81186i	−0.423294	+	0.284106i
$963$		0			0
$964$	15.8996	−	38.8392i	0.512092	−	1.25093i
$965$		−	3.73487i		−	0.120230i
$966$		0			0
$967$	−57.6440			−1.85371			−0.926854	−	0.375423i	$-0.877497\pi$
$967$	−57.6440			−1.85371			−0.926854	+	0.375423i	$0.877497\pi$
$968$	10.8309	+	52.7365i	0.348119	+	1.69501i
$969$		0			0
$970$	11.7349	+	17.4840i	0.376784	+	0.561377i
$971$			6.42670i			0.206243i	0.994669	+	0.103121i	$0.0328830\pi$
$971$			6.42670i			0.206243i	−0.994669	+	0.103121i	$0.967117\pi$
$972$		0			0
$973$			1.91808i			0.0614907i
$974$	−14.0863	+	9.45444i	−0.451356	+	0.302940i
$975$		0			0
$976$	−0.895069	+	0.910020i	−0.0286505	+	0.0291290i
$977$	29.6408			0.948293			0.474147	−	0.880446i	$-0.342757\pi$
$977$	29.6408			0.948293			0.474147	+	0.880446i	$0.342757\pi$
$978$		0			0
$979$			54.3001i			1.73544i
$980$	−4.58060	−	1.87516i	−0.146322	−	0.0598998i
$981$		0			0
$982$	−0.206423	−	0.307554i	−0.00658723	−	0.00981443i
$983$	20.4287			0.651573			0.325787	−	0.945443i	$-0.394371\pi$
$983$	20.4287			0.651573			0.325787	+	0.945443i	$0.394371\pi$
$984$		0			0
$985$	−7.00321			−0.223141
$986$	0.788756	+	1.17518i	0.0251191	+	0.0374254i
$987$		0			0
$988$	19.4716	−	47.5648i	0.619474	−	1.51324i
$989$			73.5569i			2.33897i
$990$		0			0
$991$	43.0135			1.36637			0.683184	−	0.730246i	$-0.260595\pi$
$991$	43.0135			1.36637			0.683184	+	0.730246i	$0.260595\pi$
$992$	−28.1083	−	5.28917i	−0.892438	−	0.167931i
$993$		0			0
$994$	17.9560	−	12.0516i	0.569529	−	0.382255i
$995$			21.2769i			0.674523i
$996$		0			0
$997$			51.4261i			1.62868i	0.580387	+	0.814341i	$0.302901\pi$
$997$			51.4261i			1.62868i	−0.580387	+	0.814341i	$0.697099\pi$
$998$	−33.9030	−	50.5127i	−1.07318	−	1.59895i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.k.d.541.15	yes	20
3.2	odd	2	inner	1080.2.k.d.541.6	yes	20
4.3	odd	2		4320.2.k.d.2161.14		20
8.3	odd	2		4320.2.k.d.2161.3		20
8.5	even	2	inner	1080.2.k.d.541.16	yes	20
12.11	even	2		4320.2.k.d.2161.4		20
24.5	odd	2	inner	1080.2.k.d.541.5	✓	20
24.11	even	2		4320.2.k.d.2161.13		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.k.d.541.5	✓	20	24.5	odd	2	inner
1080.2.k.d.541.6	yes	20	3.2	odd	2	inner
1080.2.k.d.541.15	yes	20	1.1	even	1	trivial
1080.2.k.d.541.16	yes	20	8.5	even	2	inner
4320.2.k.d.2161.3		20	8.3	odd	2
4320.2.k.d.2161.4		20	12.11	even	2
4320.2.k.d.2161.13		20	24.11	even	2
4320.2.k.d.2161.14		20	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17425 - 0.788128i) q^{2} +(0.757708 - 1.85091i) q^{4} +1.00000i q^{5} +2.12726 q^{7} +(-0.569020 - 2.77060i) q^{8} +O(q^{10})\)	\(q+(1.17425 - 0.788128i) q^{2} +(0.757708 - 1.85091i) q^{4} +1.00000i q^{5} +2.12726 q^{7} +(-0.569020 - 2.77060i) q^{8} +(0.788128 + 1.17425i) q^{10} -5.48036i q^{11} +4.91228i q^{13} +(2.49792 - 1.67655i) q^{14} +(-2.85176 - 2.80490i) q^{16} -0.235541 q^{17} -5.23139i q^{19} +(1.85091 + 0.757708i) q^{20} +(-4.31922 - 6.43529i) q^{22} +7.42390 q^{23} -1.00000 q^{25} +(3.87150 + 5.76822i) q^{26} +(1.61184 - 3.93737i) q^{28} -4.24894i q^{29} +5.05609 q^{31} +(-5.55929 - 1.04610i) q^{32} +(-0.276583 + 0.185636i) q^{34} +2.12726i q^{35} +2.27608i q^{37} +(-4.12300 - 6.14294i) q^{38} +(2.77060 - 0.569020i) q^{40} +3.26132 q^{41} +9.90812i q^{43} +(-10.1437 - 4.15251i) q^{44} +(8.71749 - 5.85098i) q^{46} -8.17359 q^{47} -2.47478 q^{49} +(-1.17425 + 0.788128i) q^{50} +(9.09220 + 3.72207i) q^{52} -10.6637i q^{53} +5.48036 q^{55} +(-1.21045 - 5.89377i) q^{56} +(-3.34871 - 4.98930i) q^{58} +0.702988i q^{59} -0.319109i q^{61} +(5.93709 - 3.98485i) q^{62} +(-7.35243 + 3.15305i) q^{64} -4.91228 q^{65} +2.70667i q^{67} +(-0.178471 + 0.435965i) q^{68} +(1.67655 + 2.49792i) q^{70} +7.18836 q^{71} +9.66370 q^{73} +(1.79384 + 2.67268i) q^{74} +(-9.68284 - 3.96386i) q^{76} -11.6581i q^{77} -10.8565 q^{79} +(2.80490 - 2.85176i) q^{80} +(3.82959 - 2.57033i) q^{82} +8.53645i q^{83} -0.235541i q^{85} +(7.80887 + 11.6346i) q^{86} +(-15.1839 + 3.11843i) q^{88} -9.90812 q^{89} +10.4497i q^{91} +(5.62515 - 13.7410i) q^{92} +(-9.59781 + 6.44184i) q^{94} +5.23139 q^{95} +14.8895 q^{97} +(-2.90600 + 1.95044i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{4}+O(q^{10}) \) 20 * q + 2 * q^4	\( 20 q + 2 q^{4} - 2 q^{10} - 18 q^{16} + 16 q^{22} - 20 q^{25} + 16 q^{28} + 20 q^{31} - 6 q^{34} - 4 q^{40} + 54 q^{46} + 36 q^{49} + 56 q^{52} - 72 q^{58} - 28 q^{64} - 40 q^{73} + 58 q^{76} - 4 q^{79} - 92 q^{82} - 116 q^{88} + 72 q^{94} + 40 q^{97}+O(q^{100}) \) 20 * q + 2 * q^4 - 2 * q^10 - 18 * q^16 + 16 * q^22 - 20 * q^25 + 16 * q^28 + 20 * q^31 - 6 * q^34 - 4 * q^40 + 54 * q^46 + 36 * q^49 + 56 * q^52 - 72 * q^58 - 28 * q^64 - 40 * q^73 + 58 * q^76 - 4 * q^79 - 92 * q^82 - 116 * q^88 + 72 * q^94 + 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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