LMFDB - Embedded newform 1080.2.d.g.109.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1080,2,Mod(109,1080)]

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, 1]))

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

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

chi := DirichletCharacter("1080.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.d (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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} - 3 x^{14} + 36 x^{13} - 78 x^{12} - 96 x^{11} + 1194 x^{10} + 1456 x^{9} + \cdots + 45658 $ x^16 - 3x^15 - 3x^14 + 36x^13 - 78x^12 - 96x^11 + 1194x^10 + 1456x^9 + 2243x^8 + 23019x^7 + 49749x^6 + 37798x^5 + 78784x^4 + 244612x^3 + 302532x^2 + 157882*x + 45658
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.16
Root			$1.37578 - 2.65312i$ of defining polynomial
Character	$\chi$	$=$	1080.109
Dual form			1080.2.d.g.109.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05355 + 0.943417i) q^{2} +(0.219928 + 1.98787i) q^{4} +(0.463409 + 2.18752i) q^{5} +3.14971i q^{7} +(-1.64369 + 2.30180i) q^{8} +O(q^{10})$	\(q+(1.05355 + 0.943417i) q^{2} +(0.219928 + 1.98787i) q^{4} +(0.463409 + 2.18752i) q^{5} +3.14971i q^{7} +(-1.64369 + 2.30180i) q^{8} +(-1.57552 + 2.74185i) q^{10} +2.42180i q^{11} +3.12253 q^{13} +(-2.97150 + 3.31838i) q^{14} +(-3.90326 + 0.874375i) q^{16} -7.15192i q^{17} -2.34624i q^{19} +(-4.24660 + 1.40229i) q^{20} +(-2.28477 + 2.55148i) q^{22} +1.28934i q^{23} +(-4.57050 + 2.02743i) q^{25} +(3.28973 + 2.94585i) q^{26} +(-6.26123 + 0.692709i) q^{28} -4.21495i q^{29} +3.05999 q^{31} +(-4.93718 - 2.76121i) q^{32} +(6.74724 - 7.53489i) q^{34} +(-6.89007 + 1.45960i) q^{35} -1.37346 q^{37} +(2.21349 - 2.47188i) q^{38} +(-5.79694 - 2.52893i) q^{40} -11.0754 q^{41} +9.70199 q^{43} +(-4.81422 + 0.532620i) q^{44} +(-1.21639 + 1.35838i) q^{46} +0.627861i q^{47} -2.92070 q^{49} +(-6.72796 - 2.17590i) q^{50} +(0.686730 + 6.20718i) q^{52} +9.54695 q^{53} +(-5.29774 + 1.12228i) q^{55} +(-7.25002 - 5.17715i) q^{56} +(3.97646 - 4.44066i) q^{58} +10.1066i q^{59} +12.7235i q^{61} +(3.22385 + 2.88685i) q^{62} +(-2.59658 - 7.56689i) q^{64} +(1.44701 + 6.83059i) q^{65} +10.5125 q^{67} +(14.2171 - 1.57290i) q^{68} +(-8.63604 - 4.96245i) q^{70} -7.39000 q^{71} +5.73160i q^{73} +(-1.44701 - 1.29575i) q^{74} +(4.66403 - 0.516004i) q^{76} -7.62797 q^{77} +11.2071 q^{79} +(-3.72152 - 8.13328i) q^{80} +(-11.6685 - 10.4488i) q^{82} +3.12640 q^{83} +(15.6450 - 3.31426i) q^{85} +(10.2215 + 9.15303i) q^{86} +(-5.57450 - 3.98068i) q^{88} -15.9470 q^{89} +9.83507i q^{91} +(-2.56305 + 0.283562i) q^{92} +(-0.592335 + 0.661482i) q^{94} +(5.13246 - 1.08727i) q^{95} -14.6589i q^{97} +(-3.07710 - 2.75544i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 6 q^{4} - 6 q^{5} - 2 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 - 6 * q^4 - 6 * q^5 - 2 * q^8	$ 16 q - 2 q^{2} - 6 q^{4} - 6 q^{5} - 2 q^{8} + 5 q^{10} - 30 q^{16} - q^{20} - 22 q^{25} + 18 q^{32} - 4 q^{34} - 2 q^{35} + 56 q^{38} + 19 q^{40} + 40 q^{46} - 44 q^{49} - 27 q^{50} + 96 q^{53} + 34 q^{55} + 2 q^{62} - 6 q^{64} + 72 q^{68} - 7 q^{70} - 12 q^{77} + 4 q^{79} - 9 q^{80} + 64 q^{83} + 20 q^{92} - 20 q^{94} - 36 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 6 * q^4 - 6 * q^5 - 2 * q^8 + 5 * q^10 - 30 * q^16 - q^20 - 22 * q^25 + 18 * q^32 - 4 * q^34 - 2 * q^35 + 56 * q^38 + 19 * q^40 + 40 * q^46 - 44 * q^49 - 27 * q^50 + 96 * q^53 + 34 * q^55 + 2 * q^62 - 6 * q^64 + 72 * q^68 - 7 * q^70 - 12 * q^77 + 4 * q^79 - 9 * q^80 + 64 * q^83 + 20 * q^92 - 20 * q^94 - 36 * q^98

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 $

$2$	1.05355	+	0.943417i	0.744971	+	0.667097i
$2$	1.05355	+	0.943417i	0.744971	+	0.667097i
$3$		0			0
$3$		0			0
$4$	0.219928	+	1.98787i	0.109964	+	0.993936i
$5$	0.463409	+	2.18752i	0.207243	+	0.978290i
$5$	0.463409	+	2.18752i	0.207243	+	0.978290i
$6$		0			0
$7$			3.14971i			1.19048i	0.803548	+	0.595240i	$0.202943\pi$
$7$			3.14971i			1.19048i	−0.803548	+	0.595240i	$0.797057\pi$
$8$	−1.64369	+	2.30180i	−0.581131	+	0.813810i
$9$		0			0
$10$	−1.57552	+	2.74185i	−0.498224	+	0.867048i
$11$			2.42180i			0.730199i	0.930968	+	0.365100i	$0.118965\pi$
$11$			2.42180i			0.730199i	−0.930968	+	0.365100i	$0.881035\pi$
$12$		0			0
$13$	3.12253			0.866033			0.433016	−	0.901386i	$-0.357449\pi$
$13$	3.12253			0.866033			0.433016	+	0.901386i	$0.357449\pi$
$14$	−2.97150	+	3.31838i	−0.794166	+	0.886873i
$15$		0			0
$16$	−3.90326	+	0.874375i	−0.975816	+	0.218594i
$17$		−	7.15192i		−	1.73460i	−0.497790	−	0.867298i	$-0.665855\pi$
$17$		−	7.15192i		−	1.73460i	0.497790	−	0.867298i	$-0.334145\pi$
$18$		0			0
$19$		−	2.34624i		−	0.538265i	−0.963103	−	0.269133i	$-0.913263\pi$
$19$		−	2.34624i		−	0.538265i	0.963103	−	0.269133i	$-0.0867370\pi$
$20$	−4.24660	+	1.40229i	−0.949568	+	0.313562i
$21$		0			0
$22$	−2.28477	+	2.55148i	−0.487114	+	0.543977i
$23$			1.28934i			0.268846i	0.990924	+	0.134423i	$0.0429182\pi$
$23$			1.28934i			0.268846i	−0.990924	+	0.134423i	$0.957082\pi$
$24$		0			0
$25$	−4.57050	+	2.02743i	−0.914101	+	0.405487i
$26$	3.28973	+	2.94585i	0.645169	+	0.577728i
$27$		0			0
$28$	−6.26123	+	0.692709i	−1.18326	+	0.130910i
$29$		−	4.21495i		−	0.782697i	−0.920242	−	0.391349i	$-0.872009\pi$
$29$		−	4.21495i		−	0.782697i	0.920242	−	0.391349i	$-0.127991\pi$
$30$		0			0
$31$	3.05999			0.549590			0.274795	−	0.961503i	$-0.411390\pi$
$31$	3.05999			0.549590			0.274795	+	0.961503i	$0.411390\pi$
$32$	−4.93718	−	2.76121i	−0.872778	−	0.488118i
$33$		0			0
$34$	6.74724	−	7.53489i	1.15714	−	1.29222i
$35$	−6.89007	+	1.45960i	−1.16463	+	0.246718i
$36$		0			0
$37$	−1.37346			−0.225795			−0.112898	−	0.993607i	$-0.536013\pi$
$37$	−1.37346			−0.225795			−0.112898	+	0.993607i	$0.536013\pi$
$38$	2.21349	−	2.47188i	0.359075	−	0.400992i
$39$		0			0
$40$	−5.79694	−	2.52893i	−0.916577	−	0.399859i
$41$	−11.0754			−1.72969			−0.864847	−	0.502035i	$-0.832585\pi$
$41$	−11.0754			−1.72969			−0.864847	+	0.502035i	$0.832585\pi$
$42$		0			0
$43$	9.70199			1.47954			0.739770	−	0.672860i	$-0.234934\pi$
$43$	9.70199			1.47954			0.739770	+	0.672860i	$0.234934\pi$
$44$	−4.81422	+	0.532620i	−0.725771	+	0.0802955i
$45$		0			0
$46$	−1.21639	+	1.35838i	−0.179347	+	0.200283i
$47$			0.627861i			0.0915829i	0.998951	+	0.0457915i	$0.0145810\pi$
$47$			0.627861i			0.0915829i	−0.998951	+	0.0457915i	$0.985419\pi$
$48$		0			0
$49$	−2.92070			−0.417243
$50$	−6.72796	−	2.17590i	−0.951478	−	0.307718i
$51$		0			0
$52$	0.686730	+	6.20718i	0.0952323	+	0.860781i
$53$	9.54695			1.31137			0.655687	−	0.755033i	$-0.272379\pi$
$53$	9.54695			1.31137			0.655687	+	0.755033i	$0.272379\pi$
$54$		0			0
$55$	−5.29774	+	1.12228i	−0.714347	+	0.151328i
$56$	−7.25002	−	5.17715i	−0.968824	−	0.691825i
$57$		0			0
$58$	3.97646	−	4.44066i	0.522135	−	0.583087i
$59$			10.1066i			1.31577i	0.753117	+	0.657887i	$0.228549\pi$
$59$			10.1066i			1.31577i	−0.753117	+	0.657887i	$0.771451\pi$
$60$		0			0
$61$			12.7235i			1.62908i	0.580106	+	0.814541i	$0.303011\pi$
$61$			12.7235i			1.62908i	−0.580106	+	0.814541i	$0.696989\pi$
$62$	3.22385	+	2.88685i	0.409429	+	0.366630i
$63$		0			0
$64$	−2.59658	−	7.56689i	−0.324573	−	0.945861i
$65$	1.44701	+	6.83059i	0.179479	+	0.847231i
$66$		0			0
$67$	10.5125			1.28431			0.642155	−	0.766575i	$-0.278041\pi$
$67$	10.5125			1.28431			0.642155	+	0.766575i	$0.278041\pi$
$68$	14.2171	−	1.57290i	1.72408	−	0.190743i
$69$		0			0
$70$	−8.63604	−	4.96245i	−1.03220	−	0.593126i
$71$	−7.39000			−0.877031			−0.438516	−	0.898724i	$-0.644496\pi$
$71$	−7.39000			−0.877031			−0.438516	+	0.898724i	$0.644496\pi$
$72$		0			0
$73$			5.73160i			0.670833i	0.942070	+	0.335417i	$0.108877\pi$
$73$			5.73160i			0.670833i	−0.942070	+	0.335417i	$0.891123\pi$
$74$	−1.44701	−	1.29575i	−0.168211	−	0.150627i
$75$		0			0
$76$	4.66403	−	0.516004i	0.535001	−	0.0591897i
$77$	−7.62797			−0.869288
$78$		0			0
$79$	11.2071			1.26090			0.630449	−	0.776230i	$-0.282871\pi$
$79$	11.2071			1.26090			0.630449	+	0.776230i	$0.282871\pi$
$80$	−3.72152	−	8.13328i	−0.416079	−	0.909329i
$81$		0			0
$82$	−11.6685	−	10.4488i	−1.28857	−	1.15387i
$83$	3.12640			0.343167			0.171584	−	0.985170i	$-0.445112\pi$
$83$	3.12640			0.343167			0.171584	+	0.985170i	$0.445112\pi$
$84$		0			0
$85$	15.6450	−	3.31426i	1.69694	−	0.359482i
$86$	10.2215	+	9.15303i	1.10221	+	0.986996i
$87$		0			0
$88$	−5.57450	−	3.98068i	−0.594243	−	0.424342i
$89$	−15.9470			−1.69038			−0.845192	−	0.534464i	$-0.820514\pi$
$89$	−15.9470			−1.69038			−0.845192	+	0.534464i	$0.820514\pi$
$90$		0			0
$91$			9.83507i			1.03100i
$92$	−2.56305	+	0.283562i	−0.267216	+	0.0295634i
$93$		0			0
$94$	−0.592335	+	0.661482i	−0.0610947	+	0.0682266i
$95$	5.13246	−	1.08727i	0.526579	−	0.111551i
$96$		0			0
$97$		−	14.6589i		−	1.48839i	−0.667963	−	0.744194i	$-0.732834\pi$
$97$		−	14.6589i		−	1.48839i	0.667963	−	0.744194i	$-0.267166\pi$
$98$	−3.07710	−	2.75544i	−0.310834	−	0.278342i
$99$		0			0
$100$	−5.03546	−	8.63969i	−0.503546	−	0.863969i
$101$		−	6.22901i		−	0.619810i	−0.950768	−	0.309905i	$-0.899703\pi$
$101$		−	6.22901i		−	0.619810i	0.950768	−	0.309905i	$-0.100297\pi$
$102$		0			0
$103$		−	10.6041i		−	1.04485i	−0.852686	−	0.522424i	$-0.825028\pi$
$103$		−	10.6041i		−	1.04485i	0.852686	−	0.522424i	$-0.174972\pi$
$104$	−5.13246	+	7.18744i	−0.503279	+	0.704786i
$105$		0			0
$106$	10.0582	+	9.00676i	0.976936	+	0.874814i
$107$	1.62797			0.157382			0.0786910	−	0.996899i	$-0.474926\pi$
$107$	1.62797			0.157382			0.0786910	+	0.996899i	$0.474926\pi$
$108$		0			0
$109$			1.56551i			0.149949i	0.997185	+	0.0749743i	$0.0238875\pi$
$109$			1.56551i			0.149949i	−0.997185	+	0.0749743i	$0.976113\pi$
$110$	−6.64020	−	3.81560i	−0.633118	−	0.363803i
$111$		0			0
$112$	−2.75403	−	12.2942i	−0.260232	−	1.16169i
$113$			8.57935i			0.807077i	0.914963	+	0.403538i	$0.132220\pi$
$113$			8.57935i			0.807077i	−0.914963	+	0.403538i	$0.867780\pi$
$114$		0			0
$115$	−2.82046	+	0.597492i	−0.263010	+	0.0557164i
$116$	8.37879	−	0.926985i	0.777951	−	0.0860684i
$117$		0			0
$118$	−9.53478	+	10.6478i	−0.877748	+	0.980213i
$119$	22.5265			2.06500
$120$		0			0
$121$	5.13490			0.466809
$122$	−12.0036	+	13.4049i	−1.08676	+	1.21362i
$123$		0			0
$124$	0.672976	+	6.08286i	0.0604350	+	0.546257i
$125$	−6.55307	−	9.05855i	−0.586124	−	0.810221i
$126$		0			0
$127$			10.7524i			0.954124i	0.878870	+	0.477062i	$0.158298\pi$
$127$			10.7524i			0.954124i	−0.878870	+	0.477062i	$0.841702\pi$
$128$	4.40311	−	10.4217i	0.389183	−	0.921160i
$129$		0			0
$130$	−4.91961	+	8.56149i	−0.431478	+	0.750892i
$131$			12.2083i			1.06664i	0.845913	+	0.533321i	$0.179056\pi$
$131$			12.2083i			1.06664i	−0.845913	+	0.533321i	$0.820944\pi$
$132$		0			0
$133$	7.39000			0.640794
$134$	11.0754	+	9.91770i	0.956773	+	0.856758i
$135$		0			0
$136$	16.4623	+	11.7555i	1.41163	+	1.00803i
$137$		−	7.44288i		−	0.635888i	−0.948110	−	0.317944i	$-0.897008\pi$
$137$		−	7.44288i		−	0.635888i	0.948110	−	0.317944i	$-0.102992\pi$
$138$		0			0
$139$		−	10.1260i		−	0.858878i	−0.903096	−	0.429439i	$-0.858711\pi$
$139$		−	10.1260i		−	0.858878i	0.903096	−	0.429439i	$-0.141289\pi$
$140$	−4.41682	−	13.3756i	−0.373290	−	1.13044i
$141$		0			0
$142$	−7.78572	−	6.97185i	−0.653363	−	0.585065i
$143$			7.56213i			0.632377i
$144$		0			0
$145$	9.22031	−	1.95325i	0.765705	−	0.162208i
$146$	−5.40729	+	6.03852i	−0.447511	+	0.499751i
$147$		0			0
$148$	−0.302062	−	2.73026i	−0.0248293	−	0.224426i
$149$		−	11.6233i		−	0.952217i	−0.879386	−	0.476109i	$-0.842047\pi$
$149$		−	11.6233i		−	0.952217i	0.879386	−	0.476109i	$-0.157953\pi$
$150$		0			0
$151$	−10.0529			−0.818094			−0.409047	−	0.912513i	$-0.634139\pi$
$151$	−10.0529			−0.818094			−0.409047	+	0.912513i	$0.634139\pi$
$152$	5.40059	+	3.85649i	0.438045	+	0.312803i
$153$		0			0
$154$	−8.03644	−	7.19636i	−0.647594	−	0.579899i
$155$	1.41803	+	6.69379i	0.113899	+	0.537658i
$156$		0			0
$157$	13.3874			1.06843			0.534217	−	0.845347i	$-0.320606\pi$
$157$	13.3874			1.06843			0.534217	+	0.845347i	$0.320606\pi$
$158$	11.8072	+	10.5730i	0.939333	+	0.841141i
$159$		0			0
$160$	3.75228	−	12.0798i	0.296644	−	0.954988i
$161$	−4.06106			−0.320056
$162$		0			0
$163$	−1.37346			−0.107578			−0.0537888	−	0.998552i	$-0.517130\pi$
$163$	−1.37346			−0.107578			−0.0537888	+	0.998552i	$0.517130\pi$
$164$	−2.43580	−	22.0166i	−0.190204	−	1.71920i
$165$		0			0
$166$	3.29382	+	2.94950i	0.255650	+	0.228926i
$167$		−	14.3227i		−	1.10832i	−0.832410	−	0.554161i	$-0.813039\pi$
$167$		−	14.3227i		−	1.10832i	0.832410	−	0.554161i	$-0.186961\pi$
$168$		0			0
$169$	−3.24983			−0.249987
$170$	19.6095	+	11.2680i	1.50398	+	0.864217i
$171$		0			0
$172$	2.13374	+	19.2863i	0.162696	+	1.47057i
$173$	−3.96953			−0.301798			−0.150899	−	0.988549i	$-0.548217\pi$
$173$	−3.96953			−0.301798			−0.150899	+	0.988549i	$0.548217\pi$
$174$		0			0
$175$	−6.38584	−	14.3958i	−0.482724	−	1.08822i
$176$	−2.11756	−	9.45292i	−0.159617	−	0.712540i
$177$		0			0
$178$	−16.8010	−	15.0447i	−1.25929	−	1.12765i
$179$			11.3491i			0.848273i	0.905598	+	0.424137i	$0.139422\pi$
$179$			11.3491i			0.848273i	−0.905598	+	0.424137i	$0.860578\pi$
$180$		0			0
$181$		−	15.5324i		−	1.15452i	−0.816561	−	0.577259i	$-0.804122\pi$
$181$		−	15.5324i		−	1.15452i	0.816561	−	0.577259i	$-0.195878\pi$
$182$	−9.27857	+	10.3617i	−0.687774	+	0.768062i
$183$		0			0
$184$	−2.96781	−	2.11928i	−0.218790	−	0.156235i
$185$	−0.636473	−	3.00447i	−0.0467944	−	0.220893i
$186$		0			0
$187$	17.3205			1.26660
$188$	−1.24811	+	0.138084i	−0.0910275	+	0.0100708i
$189$		0			0
$190$	6.43304	+	3.69656i	0.466702	+	0.268177i
$191$	27.0225			1.95528			0.977639	−	0.210288i	$-0.0674402\pi$
$191$	27.0225			1.95528			0.977639	+	0.210288i	$0.0674402\pi$
$192$		0			0
$193$			8.40105i			0.604721i	0.953194	+	0.302360i	$0.0977746\pi$
$193$			8.40105i			0.604721i	−0.953194	+	0.302360i	$0.902225\pi$
$194$	13.8295	−	15.4439i	0.992899	−	1.10881i
$195$		0			0
$196$	−0.642343	−	5.80598i	−0.0458817	−	0.414713i
$197$	10.4003			0.740989			0.370494	−	0.928835i	$-0.379188\pi$
$197$	10.4003			0.740989			0.370494	+	0.928835i	$0.379188\pi$
$198$		0			0
$199$	−13.5659			−0.961665			−0.480832	−	0.876813i	$-0.659665\pi$
$199$	−13.5659			−0.961665			−0.480832	+	0.876813i	$0.659665\pi$
$200$	2.84573	−	13.8529i	0.201224	−	0.979545i
$201$		0			0
$202$	5.87656	−	6.56257i	0.413473	−	0.461741i
$203$	13.2759			0.931786
$204$		0			0
$205$	−5.13246	−	24.2278i	−0.358466	−	1.69214i
$206$	10.0041	−	11.1719i	0.697015	−	0.778382i
$207$		0			0
$208$	−12.1880	+	2.73026i	−0.845089	+	0.189309i
$209$	5.68213			0.393041
$210$		0			0
$211$			24.5868i			1.69262i	0.532688	+	0.846312i	$0.321182\pi$
$211$			24.5868i			1.69262i	−0.532688	+	0.846312i	$0.678818\pi$
$212$	2.09964	+	18.9781i	0.144204	+	1.30342i
$213$		0			0
$214$	1.71515	+	1.53586i	0.117245	+	0.104989i
$215$	4.49599	+	21.2233i	0.306624	+	1.44742i
$216$		0			0
$217$			9.63809i			0.654276i
$218$	−1.47693	+	1.64934i	−0.100030	+	0.111707i
$219$		0			0
$220$	−3.39607	−	10.2844i	−0.228963	−	0.693374i
$221$		−	22.3321i		−	1.50222i
$222$		0			0
$223$			10.6041i			0.710100i	0.934847	+	0.355050i	$0.115536\pi$
$223$			10.6041i			0.710100i	−0.934847	+	0.355050i	$0.884464\pi$
$224$	8.69702	−	15.5507i	0.581094	−	1.03902i
$225$		0			0
$226$	−8.09390	+	9.03875i	−0.538398	+	0.601249i
$227$	−12.5958			−0.836011			−0.418006	−	0.908444i	$-0.637271\pi$
$227$	−12.5958			−0.836011			−0.418006	+	0.908444i	$0.637271\pi$
$228$		0			0
$229$			9.75550i			0.644661i	0.946627	+	0.322331i	$0.104466\pi$
$229$			9.75550i			0.644661i	−0.946627	+	0.322331i	$0.895534\pi$
$230$	−3.53518	−	2.03139i	−0.233103	−	0.133946i
$231$		0			0
$232$	9.70199	+	6.92807i	0.636967	+	0.454850i
$233$		−	1.25572i		−	0.0822651i	−0.999154	−	0.0411325i	$-0.986903\pi$
$233$		−	1.25572i		−	0.0822651i	0.999154	−	0.0411325i	$-0.0130966\pi$
$234$		0			0
$235$	−1.37346	+	0.290956i	−0.0895946	+	0.0189799i
$236$	−20.0907	+	2.22273i	−1.30779	+	0.144687i
$237$		0			0
$238$	23.7328	+	21.2519i	1.53837	+	1.37756i
$239$	−2.89401			−0.187198			−0.0935990	−	0.995610i	$-0.529837\pi$
$239$	−2.89401			−0.187198			−0.0935990	+	0.995610i	$0.529837\pi$
$240$		0			0
$241$	22.4166			1.44398			0.721990	−	0.691903i	$-0.243228\pi$
$241$	22.4166			1.44398			0.721990	+	0.691903i	$0.243228\pi$
$242$	5.40986	+	4.84435i	0.347759	+	0.311407i
$243$		0			0
$244$	−25.2928	+	2.79826i	−1.61920	+	0.179140i
$245$	−1.35348	−	6.38910i	−0.0864706	−	0.408185i
$246$		0			0
$247$		−	7.32621i		−	0.466155i
$248$	−5.02967	+	7.04349i	−0.319384	+	0.447262i
$249$		0			0
$250$	1.64202	−	15.7259i	0.103851	−	0.994593i
$251$		−	12.2787i		−	0.775023i	−0.921865	−	0.387512i	$-0.873335\pi$
$251$		−	12.2787i		−	0.775023i	0.921865	−	0.387512i	$-0.126665\pi$
$252$		0			0
$253$	−3.12253			−0.196312
$254$	−10.1440	+	11.3282i	−0.636493	+	0.710795i
$255$		0			0
$256$	14.4709	−	6.82584i	0.904433	−	0.426615i
$257$		−	16.1354i		−	1.00650i	−0.864141	−	0.503250i	$-0.832138\pi$
$257$		−	16.1354i		−	1.00650i	0.864141	−	0.503250i	$-0.167862\pi$
$258$		0			0
$259$		−	4.32600i		−	0.268805i
$260$	−13.2601	+	4.37870i	−0.822357	+	0.271555i
$261$		0			0
$262$	−11.5175	+	12.8620i	−0.711553	+	0.794617i
$263$			5.20982i			0.321251i	0.987015	+	0.160626i	$0.0513512\pi$
$263$			5.20982i			0.321251i	−0.987015	+	0.160626i	$0.948649\pi$
$264$		0			0
$265$	4.42414	+	20.8842i	0.271773	+	1.28290i
$266$	7.78572	+	6.97185i	0.477373	+	0.427472i
$267$		0			0
$268$	2.31199	+	20.8975i	0.141227	+	1.27652i
$269$		−	18.1171i		−	1.10462i	−0.833639	−	0.552310i	$-0.813747\pi$
$269$		−	18.1171i		−	1.10462i	0.833639	−	0.552310i	$-0.186253\pi$
$270$		0			0
$271$	25.1014			1.52480			0.762402	−	0.647104i	$-0.224020\pi$
$271$	25.1014			1.52480			0.762402	+	0.647104i	$0.224020\pi$
$272$	6.25346	+	27.9158i	0.379172	+	1.69265i
$273$		0			0
$274$	7.02174	−	7.84143i	0.424199	−	0.473718i
$275$	−4.91003	−	11.0688i	−0.296086	−	0.667476i
$276$		0			0
$277$	−23.9000			−1.43601			−0.718005	−	0.696038i	$-0.754944\pi$
$277$	−23.9000			−1.43601			−0.718005	+	0.696038i	$0.754944\pi$
$278$	9.55307	−	10.6683i	0.572955	−	0.639839i
$279$		0			0
$280$	7.96540	−	18.2587i	0.476024	−	1.09117i
$281$	18.8411			1.12396			0.561982	−	0.827150i	$-0.310039\pi$
$281$	18.8411			1.12396			0.561982	+	0.827150i	$0.310039\pi$
$282$		0			0
$283$	−30.4794			−1.81181			−0.905907	−	0.423477i	$-0.860810\pi$
$283$	−30.4794			−1.81181			−0.905907	+	0.423477i	$0.860810\pi$
$284$	−1.62526	−	14.6904i	−0.0964417	−	0.871713i
$285$		0			0
$286$	−7.13424	+	7.96706i	−0.421857	+	0.471102i
$287$		−	34.8845i		−	2.05917i
$288$		0			0
$289$	−34.1499			−2.00882
$290$	11.5568	+	6.64076i	0.678637	+	0.389959i
$291$		0			0
$292$	−11.3937	+	1.26054i	−0.666765	+	0.0737674i
$293$	23.6233			1.38009			0.690043	−	0.723768i	$-0.257592\pi$
$293$	23.6233			1.38009			0.690043	+	0.723768i	$0.257592\pi$
$294$		0			0
$295$	−22.1085	+	4.68351i	−1.28721	+	0.272684i
$296$	2.25754	−	3.16143i	0.131217	−	0.183754i
$297$		0			0
$298$	10.9656	−	12.2457i	0.635221	−	0.709374i
$299$			4.02601i			0.232830i
$300$		0			0
$301$			30.5585i			1.76136i
$302$	−10.5912	−	9.48409i	−0.609457	−	0.545748i
$303$		0			0
$304$	2.05150	+	9.15801i	0.117661	+	0.525248i
$305$	−27.8330	+	5.89620i	−1.59371	+	0.337615i
$306$		0			0
$307$	−9.13906			−0.521594			−0.260797	−	0.965394i	$-0.583985\pi$
$307$	−9.13906			−0.521594			−0.260797	+	0.965394i	$0.583985\pi$
$308$	−1.67760	−	15.1634i	−0.0955902	−	0.864016i
$309$		0			0
$310$	−4.82108	+	8.39002i	−0.273819	+	0.476521i
$311$	29.5409			1.67511			0.837555	−	0.546353i	$-0.183984\pi$
$311$	29.5409			1.67511			0.837555	+	0.546353i	$0.183984\pi$
$312$		0			0
$313$		−	11.6116i		−	0.656325i	−0.944621	−	0.328163i	$-0.893571\pi$
$313$		−	11.6116i		−	0.656325i	0.944621	−	0.328163i	$-0.106429\pi$
$314$	14.1043	+	12.6299i	0.795953	+	0.712749i
$315$		0			0
$316$	2.46475	+	22.2783i	0.138653	+	1.25325i
$317$	23.8869			1.34162			0.670812	−	0.741628i	$-0.265946\pi$
$317$	23.8869			1.34162			0.670812	+	0.741628i	$0.265946\pi$
$318$		0			0
$319$	10.2078			0.571525
$320$	15.3495	−	9.18664i	0.858060	−	0.513549i
$321$		0			0
$322$	−4.27852	−	3.83127i	−0.238433	−	0.213509i
$323$	−16.7801			−0.933672
$324$		0			0
$325$	−14.2715	+	6.33071i	−0.791642	+	0.351165i
$326$	−1.44701	−	1.29575i	−0.0801422	−	0.0717647i
$327$		0			0
$328$	18.2046	−	25.4935i	1.00518	−	1.40764i
$329$	−1.97758			−0.109028
$330$		0			0
$331$			10.1260i			0.556577i	0.960498	+	0.278288i	$0.0897671\pi$
$331$			10.1260i			0.556577i	−0.960498	+	0.278288i	$0.910233\pi$
$332$	0.687582	+	6.21489i	0.0377360	+	0.341086i
$333$		0			0
$334$	13.5123	−	15.0896i	0.739358	−	0.825668i
$335$	4.87159	+	22.9964i	0.266164	+	1.25643i
$336$		0			0
$337$		−	1.55511i		−	0.0847123i	−0.999103	−	0.0423561i	$-0.986514\pi$
$337$		−	1.55511i		−	0.0847123i	0.999103	−	0.0423561i	$-0.0134864\pi$
$338$	−3.42385	−	3.06595i	−0.186233	−	0.166765i
$339$		0			0
$340$	10.0291	+	30.3713i	0.543904	+	1.64712i
$341$			7.41068i			0.401311i
$342$		0			0
$343$			12.8486i			0.693760i
$344$	−15.9470	+	22.3321i	−0.859807	+	1.20406i
$345$		0			0
$346$	−4.18210	−	3.74493i	−0.224831	−	0.201329i
$347$	−15.3552			−0.824310			−0.412155	−	0.911114i	$-0.635224\pi$
$347$	−15.3552			−0.824310			−0.412155	+	0.911114i	$0.635224\pi$
$348$		0			0
$349$			3.28995i			0.176107i	0.996116	+	0.0880536i	$0.0280647\pi$
$349$			3.28995i			0.176107i	−0.996116	+	0.0880536i	$0.971935\pi$
$350$	6.85345	−	21.1912i	0.366332	−	1.13272i
$351$		0			0
$352$	6.68709	−	11.9568i	0.356423	−	0.637302i
$353$		−	4.75322i		−	0.252989i	−0.991967	−	0.126494i	$-0.959627\pi$
$353$		−	4.75322i		−	0.252989i	0.991967	−	0.126494i	$-0.0403725\pi$
$354$		0			0
$355$	−3.42459	−	16.1658i	−0.181758	−	0.857990i
$356$	−3.50719	−	31.7007i	−0.185881	−	1.68013i
$357$		0			0
$358$	−10.7070	+	11.9568i	−0.565880	+	0.631939i
$359$	−7.76560			−0.409853			−0.204926	−	0.978777i	$-0.565696\pi$
$359$	−7.76560			−0.409853			−0.204926	+	0.978777i	$0.565696\pi$
$360$		0			0
$361$	13.4951			0.710271
$362$	14.6536	−	16.3642i	0.770175	−	0.860082i
$363$		0			0
$364$	−19.5508	+	2.16300i	−1.02474	+	0.113372i
$365$	−12.5380	+	2.65607i	−0.656269	+	0.139025i
$366$		0			0
$367$			16.8214i			0.878068i	0.898471	+	0.439034i	$0.144679\pi$
$367$			16.8214i			0.878068i	−0.898471	+	0.439034i	$0.855321\pi$
$368$	−1.12737	−	5.03264i	−0.0587682	−	0.262345i
$369$		0			0
$370$	2.16392	−	3.76582i	0.112497	−	0.195775i
$371$			30.0702i			1.56117i
$372$		0			0
$373$	5.99745			0.310536			0.155268	−	0.987872i	$-0.450376\pi$
$373$	5.99745			0.310536			0.155268	+	0.987872i	$0.450376\pi$
$374$	18.2480	+	16.3405i	0.943581	+	0.844945i
$375$		0			0
$376$	−1.44521	−	1.03201i	−0.0745311	−	0.0532217i
$377$		−	13.1613i		−	0.677842i
$378$		0			0
$379$		−	22.3073i		−	1.14585i	−0.819608	−	0.572925i	$-0.805808\pi$
$379$		−	22.3073i		−	1.14585i	0.819608	−	0.572925i	$-0.194192\pi$
$380$	3.29012	+	9.96355i	0.168780	+	0.511119i
$381$		0			0
$382$	28.4695	+	25.4935i	1.45663	+	1.30436i
$383$			38.3484i			1.95951i	0.200198	+	0.979756i	$0.435842\pi$
$383$			38.3484i			1.95951i	−0.200198	+	0.979756i	$0.564158\pi$
$384$		0			0
$385$	−3.53487	−	16.6864i	−0.180154	−	0.850415i
$386$	−7.92570	+	8.85091i	−0.403407	+	0.450499i
$387$		0			0
$388$	29.1401	−	3.22390i	1.47936	−	0.163669i
$389$			17.2044i			0.872298i	0.899874	+	0.436149i	$0.143658\pi$
$389$			17.2044i			0.872298i	−0.899874	+	0.436149i	$0.856342\pi$
$390$		0			0
$391$	9.22127			0.466340
$392$	4.80072	−	6.72288i	0.242473	−	0.339557i
$393$		0			0
$394$	10.9572	+	9.81180i	0.552015	+	0.494311i
$395$	5.19347	+	24.5158i	0.261312	+	1.23352i
$396$		0			0
$397$	−12.0140			−0.602965			−0.301482	−	0.953472i	$-0.597481\pi$
$397$	−12.0140			−0.602965			−0.301482	+	0.953472i	$0.597481\pi$
$398$	−14.2924	−	12.7984i	−0.716412	−	0.641523i
$399$		0			0
$400$	16.0671	−	11.9099i	0.803357	−	0.595497i
$401$	−16.7576			−0.836833			−0.418417	−	0.908255i	$-0.637415\pi$
$401$	−16.7576			−0.836833			−0.418417	+	0.908255i	$0.637415\pi$
$402$		0			0
$403$	9.55490			0.475963
$404$	12.3825	−	1.36993i	0.616051	−	0.0681567i
$405$		0			0
$406$	13.9868	+	12.5247i	0.694154	+	0.621591i
$407$		−	3.32624i		−	0.164876i
$408$		0			0
$409$	−33.7162			−1.66716			−0.833580	−	0.552399i	$-0.813712\pi$
$409$	−33.7162			−1.66716			−0.833580	+	0.552399i	$0.813712\pi$
$410$	17.4496	−	30.3672i	0.861775	−	1.49973i
$411$		0			0
$412$	21.0795	−	2.33212i	1.03851	−	0.114896i
$413$	−31.8331			−1.56640
$414$		0			0
$415$	1.44880	+	6.83908i	0.0711189	+	0.335717i
$416$	−15.4165	−	8.62195i	−0.755854	−	0.422726i
$417$		0			0
$418$	5.98639	+	5.36062i	0.292804	+	0.262196i
$419$		−	25.1125i		−	1.22683i	−0.789762	−	0.613413i	$-0.789796\pi$
$419$		−	25.1125i		−	1.22683i	0.789762	−	0.613413i	$-0.210204\pi$
$420$		0			0
$421$		−	19.7185i		−	0.961023i	−0.876988	−	0.480511i	$-0.840451\pi$
$421$		−	19.7185i		−	0.961023i	0.876988	−	0.480511i	$-0.159549\pi$
$422$	−23.1956	+	25.9034i	−1.12914	+	1.26096i
$423$		0			0
$424$	−15.6922	+	21.9752i	−0.762081	+	1.06721i
$425$	14.5000	+	32.6879i	0.703355	+	1.58560i
$426$		0			0
$427$	−40.0755			−1.93939
$428$	0.358036	+	3.23620i	0.0173063	+	0.156428i
$429$		0			0
$430$	−15.2857	+	26.6014i	−0.737142	+	1.28283i
$431$	−21.2536			−1.02375			−0.511874	−	0.859061i	$-0.671049\pi$
$431$	−21.2536			−1.02375			−0.511874	+	0.859061i	$0.671049\pi$
$432$		0			0
$433$		−	33.7002i		−	1.61953i	−0.586757	−	0.809763i	$-0.699596\pi$
$433$		−	33.7002i		−	1.61953i	0.586757	−	0.809763i	$-0.300404\pi$
$434$	−9.09274	+	10.1542i	−0.436466	+	0.487417i
$435$		0			0
$436$	−3.11203	+	0.344299i	−0.149039	+	0.0164889i
$437$	3.02511			0.144711
$438$		0			0
$439$	25.1313			1.19945			0.599725	−	0.800206i	$-0.295277\pi$
$439$	25.1313			1.19945			0.599725	+	0.800206i	$0.295277\pi$
$440$	6.12455	−	14.0390i	0.291977	−	0.669284i
$441$		0			0
$442$	21.0684	−	23.5279i	1.00212	−	1.11911i
$443$	−20.5894			−0.978230			−0.489115	−	0.872219i	$-0.662680\pi$
$443$	−20.5894			−0.978230			−0.489115	+	0.872219i	$0.662680\pi$
$444$		0			0
$445$	−7.39000	−	34.8845i	−0.350319	−	1.65368i
$446$	−10.0041	+	11.1719i	−0.473706	+	0.529004i
$447$		0			0
$448$	23.8335	−	8.17849i	1.12603	−	0.386397i
$449$	−9.09787			−0.429355			−0.214677	−	0.976685i	$-0.568870\pi$
$449$	−9.09787			−0.429355			−0.214677	+	0.976685i	$0.568870\pi$
$450$		0			0
$451$		−	26.8225i		−	1.26302i
$452$	−17.0546	+	1.88683i	−0.802182	+	0.0887492i
$453$		0			0
$454$	−13.2703	−	11.8831i	−0.622804	−	0.557701i
$455$	−21.5144	+	4.55765i	−1.00861	+	0.213666i
$456$		0			0
$457$			7.10221i			0.332228i	0.986107	+	0.166114i	$0.0531219\pi$
$457$			7.10221i			0.332228i	−0.986107	+	0.166114i	$0.946878\pi$
$458$	−9.20351	+	10.2779i	−0.430052	+	0.480254i
$459$		0			0
$460$	−1.80804	−	5.47532i	−0.0843001	−	0.255288i
$461$		−	2.20090i		−	0.102506i	−0.998686	−	0.0512530i	$-0.983679\pi$
$461$		−	2.20090i		−	0.102506i	0.998686	−	0.0512530i	$-0.0163215\pi$
$462$		0			0
$463$		−	28.7916i		−	1.33806i	−0.743236	−	0.669029i	$-0.766710\pi$
$463$		−	28.7916i		−	1.33806i	0.743236	−	0.669029i	$-0.233290\pi$
$464$	3.68545	+	16.4521i	0.171093	+	0.763769i
$465$		0			0
$466$	1.18467	−	1.32296i	0.0548788	−	0.0612851i
$467$	37.9504			1.75613			0.878067	−	0.478538i	$-0.158833\pi$
$467$	37.9504			1.75613			0.878067	+	0.478538i	$0.158833\pi$
$468$		0			0
$469$			33.1114i			1.52894i
$470$	−1.72150	−	0.989209i	−0.0794068	−	0.0456288i
$471$		0			0
$472$	−23.2635	−	16.6122i	−1.07079	−	0.764637i
$473$			23.4963i			1.08036i
$474$		0			0
$475$	4.75685	+	10.7235i	0.218259	+	0.492029i
$476$	4.95420	+	44.7798i	0.227075	+	2.05248i
$477$		0			0
$478$	−3.04898	−	2.73026i	−0.139457	−	0.124879i
$479$	−4.49599			−0.205427			−0.102713	−	0.994711i	$-0.532752\pi$
$479$	−4.49599			−0.205427			−0.102713	+	0.994711i	$0.532752\pi$
$480$		0			0
$481$	−4.28866			−0.195546
$482$	23.6170	+	21.1482i	1.07572	+	0.963275i
$483$		0			0
$484$	1.12931	+	10.2075i	0.0513321	+	0.463978i
$485$	32.0667	−	6.79307i	1.45607	−	0.308457i
$486$		0			0
$487$		−	38.9154i		−	1.76342i	−0.471789	−	0.881712i	$-0.656391\pi$
$487$		−	38.9154i		−	1.76342i	0.471789	−	0.881712i	$-0.343609\pi$
$488$	−29.2871	−	20.9135i	−1.32576	−	0.946711i
$489$		0			0
$490$	4.60163	−	8.00812i	0.207881	−	0.361770i
$491$			4.19054i			0.189117i	0.995519	+	0.0945583i	$0.0301439\pi$
$491$			4.19054i			0.189117i	−0.995519	+	0.0945583i	$0.969856\pi$
$492$		0			0
$493$	−30.1450			−1.35766
$494$	6.91167	−	7.71851i	0.310971	−	0.347272i
$495$		0			0
$496$	−11.9439	+	2.67558i	−0.536299	+	0.120137i
$497$		−	23.2764i		−	1.04409i
$498$		0			0
$499$		−	37.4693i		−	1.67735i	−0.544629	−	0.838677i	$-0.683330\pi$
$499$		−	37.4693i		−	1.67735i	0.544629	−	0.838677i	$-0.316670\pi$
$500$	16.5660	−	15.0189i	0.740855	−	0.671665i
$501$		0			0
$502$	11.5839	−	12.9362i	0.517016	−	0.577370i
$503$		−	15.8317i		−	0.705900i	−0.935642	−	0.352950i	$-0.885179\pi$
$503$		−	15.8317i		−	0.705900i	0.935642	−	0.352950i	$-0.114821\pi$
$504$		0			0
$505$	13.6261	−	2.88658i	0.606354	−	0.128451i
$506$	−3.28973	−	2.94585i	−0.146246	−	0.130959i
$507$		0			0
$508$	−21.3744	+	2.36476i	−0.948338	+	0.104919i
$509$			15.8382i			0.702018i	0.936372	+	0.351009i	$0.114161\pi$
$509$			15.8382i			0.702018i	−0.936372	+	0.351009i	$0.885839\pi$
$510$		0			0
$511$	−18.0529			−0.798614
$512$	21.6854	+	6.46078i	0.958370	+	0.285529i
$513$		0			0
$514$	15.2224	−	16.9994i	0.671432	−	0.749813i
$515$	23.1966	−	4.91401i	1.02216	−	0.216537i
$516$		0			0
$517$	−1.52055			−0.0668738
$518$	4.08123	−	4.55765i	0.179319	−	0.200252i
$519$		0			0
$520$	−18.1011	−	7.89665i	−0.793786	−	0.346291i
$521$	−2.08348			−0.0912788			−0.0456394	−	0.998958i	$-0.514533\pi$
$521$	−2.08348			−0.0912788			−0.0456394	+	0.998958i	$0.514533\pi$
$522$		0			0
$523$	13.8224			0.604410			0.302205	−	0.953243i	$-0.402277\pi$
$523$	13.8224			0.604410			0.302205	+	0.953243i	$0.402277\pi$
$524$	−24.2685	+	2.68493i	−1.06017	+	0.117292i
$525$		0			0
$526$	−4.91504	+	5.48880i	−0.214306	+	0.239323i
$527$		−	21.8848i		−	0.953317i
$528$		0			0
$529$	21.3376			0.927722
$530$	−15.0414	+	26.1763i	−0.653358	+	1.13703i
$531$		0			0
$532$	1.62526	+	14.6904i	0.0704641	+	0.636908i
$533$	−34.5834			−1.49797
$534$		0			0
$535$	0.754416	+	3.56122i	0.0326163	+	0.153965i
$536$	−17.2793	+	24.1977i	−0.746352	+	1.04518i
$537$		0			0
$538$	17.0920	−	19.0872i	0.736888	−	0.822909i
$539$		−	7.07335i		−	0.304671i
$540$		0			0
$541$		−	6.68097i		−	0.287238i	−0.989633	−	0.143619i	$-0.954126\pi$
$541$		−	6.68097i		−	0.287238i	0.989633	−	0.143619i	$-0.0458739\pi$
$542$	26.4456	+	23.6811i	1.13593	+	1.01719i
$543$		0			0
$544$	−19.7480	+	35.3103i	−0.846686	+	1.51392i
$545$	−3.42459	+	0.725471i	−0.146693	+	0.0310758i
$546$		0			0
$547$	−18.9416			−0.809883			−0.404941	−	0.914343i	$-0.632708\pi$
$547$	−18.9416			−0.809883			−0.404941	+	0.914343i	$0.632708\pi$
$548$	14.7955	−	1.63689i	0.632031	−	0.0699246i
$549$		0			0
$550$	5.26958	−	16.2938i	0.224696	−	0.694768i
$551$	−9.88931			−0.421299
$552$		0			0
$553$			35.2992i			1.50108i
$554$	−25.1798	−	22.5476i	−1.06979	−	0.957957i
$555$		0			0
$556$	20.1292	−	2.22699i	0.853669	−	0.0944455i
$557$	−33.0653			−1.40102			−0.700511	−	0.713642i	$-0.747044\pi$
$557$	−33.0653			−1.40102			−0.700511	+	0.713642i	$0.747044\pi$
$558$		0			0
$559$	30.2947			1.28133
$560$	25.6175	−	11.7217i	1.08254	−	0.495334i
$561$		0			0
$562$	19.8500	+	17.7750i	0.837320	+	0.749792i
$563$	2.95023			0.124337			0.0621686	−	0.998066i	$-0.480198\pi$
$563$	2.95023			0.124337			0.0621686	+	0.998066i	$0.480198\pi$
$564$		0			0
$565$	−18.7675	+	3.97574i	−0.789555	+	0.167261i
$566$	−32.1115	−	28.7548i	−1.34975	−	1.20866i
$567$		0			0
$568$	12.1468	−	17.0103i	0.509670	−	0.713737i
$569$	−2.78811			−0.116884			−0.0584419	−	0.998291i	$-0.518613\pi$
$569$	−2.78811			−0.116884			−0.0584419	+	0.998291i	$0.518613\pi$
$570$		0			0
$571$			15.0427i			0.629516i	0.949172	+	0.314758i	$0.101923\pi$
$571$			15.0427i			0.629516i	−0.949172	+	0.314758i	$0.898077\pi$
$572$	−15.0325	+	1.66312i	−0.628542	+	0.0695385i
$573$		0			0
$574$	32.9106	−	36.7525i	1.37366	−	1.53402i
$575$	−2.61406	−	5.89295i	−0.109014	−	0.245753i
$576$		0			0
$577$		−	23.1614i		−	0.964220i	−0.876111	−	0.482110i	$-0.839871\pi$
$577$		−	23.1614i		−	0.964220i	0.876111	−	0.482110i	$-0.160129\pi$
$578$	−35.9786	−	32.2177i	−1.49651	−	1.34008i
$579$		0			0
$580$	5.91060	+	17.8992i	0.245424	+	0.743224i
$581$			9.84728i			0.408534i
$582$		0			0
$583$			23.1208i			0.957565i
$584$	−13.1930	−	9.42096i	−0.545931	−	0.389842i
$585$		0			0
$586$	24.8883	+	22.2866i	1.02812	+	0.920651i
$587$	14.0705			0.580751			0.290376	−	0.956913i	$-0.406220\pi$
$587$	14.0705			0.580751			0.290376	+	0.956913i	$0.406220\pi$
$588$		0			0
$589$		−	7.17948i		−	0.295825i
$590$	−27.7109	−	15.9233i	−1.14084	−	0.655550i
$591$		0			0
$592$	5.36097	−	1.20092i	0.220335	−	0.0493575i
$593$		−	1.42743i		−	0.0586174i	−0.999570	−	0.0293087i	$-0.990669\pi$
$593$		−	1.42743i		−	0.0586174i	0.999570	−	0.0293087i	$-0.00933058\pi$
$594$		0			0
$595$	10.4390	+	49.2772i	0.427956	+	2.02017i
$596$	23.1056	−	2.55628i	0.946443	−	0.104709i
$597$		0			0
$598$	−3.79820	+	4.24159i	−0.155320	+	0.173452i
$599$	−26.6469			−1.08876			−0.544381	−	0.838838i	$-0.683235\pi$
$599$	−26.6469			−1.08876			−0.544381	+	0.838838i	$0.683235\pi$
$600$		0			0
$601$	−19.8748			−0.810710			−0.405355	−	0.914159i	$-0.632852\pi$
$601$	−19.8748			−0.810710			−0.405355	+	0.914159i	$0.632852\pi$
$602$	−28.8294	+	32.1949i	−1.17500	+	1.31216i
$603$		0			0
$604$	−2.21091	−	19.9839i	−0.0899607	−	0.813133i
$605$	2.37955	+	11.2327i	0.0967427	+	0.456674i
$606$		0			0
$607$		−	20.7546i		−	0.842403i	−0.906967	−	0.421202i	$-0.861609\pi$
$607$		−	20.7546i		−	0.842403i	0.906967	−	0.421202i	$-0.138391\pi$
$608$	−6.47847	+	11.5838i	−0.262737	+	0.469786i
$609$		0			0
$610$	−34.8860	−	20.0462i	−1.41249	−	0.811648i
$611$			1.96051i			0.0793138i
$612$		0			0
$613$	−19.4040			−0.783719			−0.391860	−	0.920025i	$-0.628168\pi$
$613$	−19.4040			−0.783719			−0.391860	+	0.920025i	$0.628168\pi$
$614$	−9.62844	−	8.62195i	−0.388572	−	0.347954i
$615$		0			0
$616$	12.5380	−	17.5581i	0.505171	−	0.707435i
$617$		−	38.5389i		−	1.55152i	−0.631029	−	0.775759i	$-0.717367\pi$
$617$		−	38.5389i		−	1.55152i	0.631029	−	0.775759i	$-0.282633\pi$
$618$		0			0
$619$		−	14.4520i		−	0.580876i	−0.956894	−	0.290438i	$-0.906199\pi$
$619$		−	14.4520i		−	0.580876i	0.956894	−	0.290438i	$-0.0938010\pi$
$620$	−12.9945	+	4.29100i	−0.521873	+	0.172331i
$621$		0			0
$622$	31.1228	+	27.8694i	1.24791	+	1.11746i
$623$		−	50.2286i		−	2.01237i
$624$		0			0
$625$	16.7790	−	18.5328i	0.671161	−	0.741311i
$626$	10.9546	−	12.2334i	0.437832	−	0.488943i
$627$		0			0
$628$	2.94427	+	26.6125i	0.117489	+	1.06195i
$629$			9.82287i			0.391663i
$630$		0			0
$631$	−40.5922			−1.61595			−0.807974	−	0.589218i	$-0.799436\pi$
$631$	−40.5922			−1.61595			−0.807974	+	0.589218i	$0.799436\pi$
$632$	−18.4210	+	25.7966i	−0.732748	+	1.02613i
$633$		0			0
$634$	25.1660	+	22.5353i	0.999471	+	0.894993i
$635$	−23.5212	+	4.98277i	−0.933410	+	0.197735i
$636$		0			0
$637$	−9.11997			−0.361346
$638$	10.7544	+	9.63019i	0.425770	+	0.381263i
$639$		0			0
$640$	24.8382	+	4.80237i	0.981817	+	0.189830i
$641$	−11.8860			−0.469468			−0.234734	−	0.972060i	$-0.575422\pi$
$641$	−11.8860			−0.469468			−0.234734	+	0.972060i	$0.575422\pi$
$642$		0			0
$643$	−29.5630			−1.16585			−0.582925	−	0.812526i	$-0.698092\pi$
$643$	−29.5630			−1.16585			−0.582925	+	0.812526i	$0.698092\pi$
$644$	−0.893139	−	8.07287i	−0.0351946	−	0.318115i
$645$		0			0
$646$	−17.6787	−	15.8307i	−0.695559	−	0.622850i
$647$		−	13.5816i		−	0.533949i	−0.963704	−	0.266974i	$-0.913976\pi$
$647$		−	13.5816i		−	0.533949i	0.963704	−	0.266974i	$-0.0860239\pi$
$648$		0			0
$649$	−24.4763			−0.960777
$650$	−21.0082	−	6.79429i	−0.824011	−	0.266494i
$651$		0			0
$652$	−0.302062	−	2.73026i	−0.0118296	−	0.106925i
$653$	−2.80243			−0.109667			−0.0548337	−	0.998496i	$-0.517463\pi$
$653$	−2.80243			−0.109667			−0.0548337	+	0.998496i	$0.517463\pi$
$654$		0			0
$655$	−26.7058	+	5.65741i	−1.04348	+	0.221053i
$656$	43.2304	−	9.68410i	1.68786	−	0.378101i
$657$		0			0
$658$	−2.08348	−	1.86569i	−0.0812224	−	0.0727320i
$659$			0.0288607i			0.00112425i	1.00000		0.000562127i	$0.000178931\pi$
$659$			0.0288607i			0.00112425i	−1.00000		0.000562127i	$0.999821\pi$
$660$		0			0
$661$			2.35497i			0.0915977i	0.998951	+	0.0457989i	$0.0145833\pi$
$661$			2.35497i			0.0915977i	−0.998951	+	0.0457989i	$0.985417\pi$
$662$	−9.55307	+	10.6683i	−0.371290	+	0.414633i
$663$		0			0
$664$	−5.13883	+	7.19636i	−0.199425	+	0.279273i
$665$	3.42459	+	16.1658i	0.132800	+	0.626882i
$666$		0			0
$667$	5.43452			0.210425
$668$	28.4716	−	3.14995i	1.10160	−	0.121875i
$669$		0			0
$670$	−16.5627	+	28.8237i	−0.639874	+	1.11356i
$671$	−30.8138			−1.18956
$672$		0			0
$673$		−	39.6306i		−	1.52765i	−0.645425	−	0.763823i	$-0.723320\pi$
$673$		−	39.6306i		−	1.52765i	0.645425	−	0.763823i	$-0.276680\pi$
$674$	1.46712	−	1.63838i	0.0565113	−	0.0631082i
$675$		0			0
$676$	−0.714727	−	6.46024i	−0.0274895	−	0.248471i
$677$	−2.57428			−0.0989377			−0.0494688	−	0.998776i	$-0.515753\pi$
$677$	−2.57428			−0.0989377			−0.0494688	+	0.998776i	$0.515753\pi$
$678$		0			0
$679$	46.1714			1.77190
$680$	−18.0867	+	41.4593i	−0.693593	+	1.58989i
$681$		0			0
$682$	−6.99136	+	7.80750i	−0.267713	+	0.298965i
$683$	−4.26099			−0.163042			−0.0815211	−	0.996672i	$-0.525978\pi$
$683$	−4.26099			−0.163042			−0.0815211	+	0.996672i	$0.525978\pi$
$684$		0			0
$685$	16.2815	−	3.44909i	0.622082	−	0.131783i
$686$	−12.1216	+	13.5366i	−0.462805	+	0.516831i
$687$		0			0
$688$	−37.8694	+	8.48318i	−1.44376	+	0.323418i
$689$	29.8106			1.13569
$690$		0			0
$691$			32.7768i			1.24689i	0.781868	+	0.623443i	$0.214267\pi$
$691$			32.7768i			1.24689i	−0.781868	+	0.623443i	$0.785733\pi$
$692$	−0.873010	−	7.89092i	−0.0331869	−	0.299968i
$693$		0			0
$694$	−16.1774	−	14.4864i	−0.614087	−	0.549895i
$695$	22.1509	−	4.69249i	0.840231	−	0.177996i
$696$		0			0
$697$			79.2107i			3.00032i
$698$	−3.10380	+	3.46612i	−0.117481	+	0.131195i
$699$		0			0
$700$	27.2125	−	15.8602i	1.02854	−	0.599461i
$701$			33.0385i			1.24785i	0.781486	+	0.623923i	$0.214462\pi$
$701$			33.0385i			1.24785i	−0.781486	+	0.623923i	$0.785538\pi$
$702$		0			0
$703$			3.22247i			0.121538i
$704$	18.3255	−	6.28839i	0.690667	−	0.237003i
$705$		0			0
$706$	4.48427	−	5.00775i	0.168768	−	0.188469i
$707$	19.6196			0.737872
$708$		0			0
$709$			26.3511i			0.989637i	0.868996	+	0.494818i	$0.164765\pi$
$709$			26.3511i			0.989637i	−0.868996	+	0.494818i	$0.835235\pi$
$710$	11.6431	−	20.2622i	0.436958	−	0.760428i
$711$		0			0
$712$	26.2120	−	36.7069i	0.982335	−	1.37565i
$713$			3.94537i			0.147755i
$714$		0			0
$715$	−16.5423	+	3.50435i	−0.618648	+	0.131055i
$716$	−22.5606	+	2.49598i	−0.843129	+	0.0932793i
$717$		0			0
$718$	−8.18144	−	7.32621i	−0.305329	−	0.273412i
$719$	14.7800			0.551201			0.275600	−	0.961272i	$-0.411123\pi$
$719$	14.7800			0.551201			0.275600	+	0.961272i	$0.411123\pi$
$720$		0			0
$721$	33.3998			1.24387
$722$	14.2178	+	12.7316i	0.529131	+	0.473819i
$723$		0			0
$724$	30.8765	−	3.41601i	1.14752	−	0.126955i
$725$	8.54554	+	19.2645i	0.317373	+	0.715465i
$726$		0			0
$727$			10.7322i			0.398035i	0.979996	+	0.199018i	$0.0637751\pi$
$727$			10.7322i			0.398035i	−0.979996	+	0.199018i	$0.936225\pi$
$728$	−22.6384	−	16.1658i	−0.839034	−	0.599144i
$729$		0			0
$730$	−15.7152	−	9.03027i	−0.581645	−	0.334225i
$731$		−	69.3878i		−	2.56640i
$732$		0			0
$733$	20.7774			0.767432			0.383716	−	0.923451i	$-0.374644\pi$
$733$	20.7774			0.767432			0.383716	+	0.923451i	$0.374644\pi$
$734$	−15.8696	+	17.7221i	−0.585756	+	0.654135i
$735$		0			0
$736$	3.56014	−	6.36571i	0.131229	−	0.234643i
$737$			25.4592i			0.937802i
$738$		0			0
$739$			14.7167i			0.541363i	0.962669	+	0.270682i	$0.0872490\pi$
$739$			14.7167i			0.541363i	−0.962669	+	0.270682i	$0.912751\pi$
$740$	5.83253	−	1.92599i	0.214408	−	0.0708009i
$741$		0			0
$742$	−28.3687	+	31.6804i	−1.04145	+	1.16302i
$743$			10.2244i			0.375098i	0.982255	+	0.187549i	$0.0600543\pi$
$743$			10.2244i			0.375098i	−0.982255	+	0.187549i	$0.939946\pi$
$744$		0			0
$745$	25.4262	−	5.38633i	0.931544	−	0.197340i
$746$	6.31860	+	5.65809i	0.231340	+	0.207158i
$747$		0			0
$748$	3.80926	+	34.4309i	0.139280	+	1.25892i
$749$			5.12765i			0.187360i
$750$		0			0
$751$	−45.7533			−1.66956			−0.834780	−	0.550584i	$-0.814405\pi$
$751$	−45.7533			−1.66956			−0.834780	+	0.550584i	$0.814405\pi$
$752$	−0.548986	−	2.45071i	−0.0200195	−	0.0893681i
$753$		0			0
$754$	12.4166	−	13.8661i	0.452186	−	0.504973i
$755$	−4.65860	−	21.9910i	−0.169544	−	0.800333i
$756$		0			0
$757$	54.8143			1.99226			0.996130	−	0.0878903i	$-0.0280125\pi$
$757$	54.8143			1.99226			0.996130	+	0.0878903i	$0.0280125\pi$
$758$	21.0451	−	23.5019i	0.764393	−	0.853626i
$759$		0			0
$760$	−5.93348	+	13.6010i	−0.215230	+	0.493361i
$761$	23.3179			0.845275			0.422637	−	0.906299i	$-0.361104\pi$
$761$	23.3179			0.845275			0.422637	+	0.906299i	$0.361104\pi$
$762$		0			0
$763$	−4.93091			−0.178511
$764$	5.94299	+	53.7172i	0.215010	+	1.94342i
$765$		0			0
$766$	−36.1785	+	40.4019i	−1.30718	+	1.45978i
$767$			31.5583i			1.13950i
$768$		0			0
$769$	−9.56833			−0.345043			−0.172521	−	0.985006i	$-0.555191\pi$
$769$	−9.56833			−0.345043			−0.172521	+	0.985006i	$0.555191\pi$
$770$	12.0180	−	20.9147i	0.433100	−	0.753715i
$771$		0			0
$772$	−16.7002	+	1.84762i	−0.601053	+	0.0664974i
$773$	22.8294			0.821117			0.410559	−	0.911834i	$-0.365334\pi$
$773$	22.8294			0.821117			0.410559	+	0.911834i	$0.365334\pi$
$774$		0			0
$775$	−13.9857	+	6.20392i	−0.502381	+	0.222852i
$776$	33.7419	+	24.0947i	1.21126	+	0.864949i
$777$		0			0
$778$	−16.2309	+	18.1257i	−0.581907	+	0.649837i
$779$			25.9857i			0.931034i
$780$		0			0
$781$		−	17.8971i		−	0.640408i
$782$	9.71505	+	8.69951i	0.347410	+	0.311094i
$783$		0			0
$784$	11.4003	−	2.55379i	0.407153	−	0.0912068i
$785$	6.20386	+	29.2853i	0.221425	+	1.04524i
$786$		0			0
$787$	−23.6303			−0.842328			−0.421164	−	0.906985i	$-0.638378\pi$
$787$	−23.6303			−0.842328			−0.421164	+	0.906985i	$0.638378\pi$
$788$	2.28731	+	20.6744i	0.0814819	+	0.736495i
$789$		0			0
$790$	−17.6571	+	30.7282i	−0.628210	+	1.09326i
$791$	−27.0225			−0.960809
$792$		0			0
$793$			39.7296i			1.41084i
$794$	−12.6573	−	11.3342i	−0.449191	−	0.402236i
$795$		0			0
$796$	−2.98353	−	26.9674i	−0.105748	−	0.955833i
$797$	15.5592			0.551134			0.275567	−	0.961282i	$-0.411134\pi$
$797$	15.5592			0.551134			0.275567	+	0.961282i	$0.411134\pi$
$798$		0			0
$799$	4.49041			0.158859
$800$	28.1636	+	2.61033i	0.995732	+	0.0922890i
$801$		0			0
$802$	−17.6549	−	15.8094i	−0.623417	−	0.558249i
$803$	−13.8808			−0.489842
$804$		0			0
$805$	−1.88193	−	8.88366i	−0.0663293	−	0.313108i
$806$	10.0665	+	9.01426i	0.354579	+	0.317514i
$807$		0			0
$808$	14.3380	+	10.2386i	0.504407	+	0.360191i
$809$	12.3484			0.434146			0.217073	−	0.976155i	$-0.430349\pi$
$809$	12.3484			0.434146			0.217073	+	0.976155i	$0.430349\pi$
$810$		0			0
$811$		−	36.9485i		−	1.29744i	−0.761028	−	0.648719i	$-0.775305\pi$
$811$		−	36.9485i		−	1.29744i	0.761028	−	0.648719i	$-0.224695\pi$
$812$	2.91974	+	26.3908i	0.102463	+	0.926135i
$813$		0			0
$814$	3.13803	−	3.50435i	0.109988	−	0.122828i
$815$	−0.636473	−	3.00447i	−0.0222947	−	0.105242i
$816$		0			0
$817$		−	22.7632i		−	0.796384i
$818$	−35.5217	−	31.8085i	−1.24199	−	1.11216i
$819$		0			0
$820$	47.0330	−	15.5310i	1.64246	−	0.542367i
$821$			10.1482i			0.354175i	0.984195	+	0.177087i	$0.0566675\pi$
$821$			10.1482i			0.354175i	−0.984195	+	0.177087i	$0.943332\pi$
$822$		0			0
$823$			21.0044i			0.732166i	0.930582	+	0.366083i	$0.119301\pi$
$823$			21.0044i			0.732166i	−0.930582	+	0.366083i	$0.880699\pi$
$824$	24.4084	+	17.4298i	0.850308	+	0.607194i
$825$		0			0
$826$	−33.5377	−	30.0319i	−1.16692	−	1.04494i
$827$	−1.54049			−0.0535682			−0.0267841	−	0.999641i	$-0.508527\pi$
$827$	−1.54049			−0.0535682			−0.0267841	+	0.999641i	$0.508527\pi$
$828$		0			0
$829$			6.68097i			0.232040i	0.993247	+	0.116020i	$0.0370136\pi$
$829$			6.68097i			0.232040i	−0.993247	+	0.116020i	$0.962986\pi$
$830$	−4.92572	+	8.57212i	−0.170974	+	0.297543i
$831$		0			0
$832$	−8.10789	−	23.6278i	−0.281091	−	0.819147i
$833$			20.8886i			0.723748i
$834$		0			0
$835$	31.3312	−	6.63725i	1.08426	−	0.229691i
$836$	1.24966	+	11.2953i	0.0432203	+	0.390657i
$837$		0			0
$838$	23.6916	−	26.4572i	0.818411	−	0.913950i
$839$	−33.1670			−1.14505			−0.572527	−	0.819886i	$-0.694037\pi$
$839$	−33.1670			−1.14505			−0.572527	+	0.819886i	$0.694037\pi$
$840$		0			0
$841$	11.2342			0.387385
$842$	18.6028	−	20.7744i	0.641095	−	0.715934i
$843$		0			0
$844$	−48.8753	+	5.40731i	−1.68236	+	0.186127i
$845$	−1.50600	−	7.10907i	−0.0518079	−	0.244560i
$846$		0			0
$847$			16.1735i			0.555727i
$848$	−37.2643	+	8.34762i	−1.27966	+	0.286658i
$849$		0			0
$850$	−15.5618	+	48.1178i	−0.533766	+	1.65043i
$851$		−	1.77086i		−	0.0607043i
$852$		0			0
$853$	−41.5549			−1.42281			−0.711406	−	0.702781i	$-0.751941\pi$
$853$	−41.5549			−1.42281			−0.711406	+	0.702781i	$0.751941\pi$
$854$	−42.2215	−	37.8079i	−1.44479	−	1.29376i
$855$		0			0
$856$	−2.67588	+	3.74727i	−0.0914596	+	0.128079i
$857$		−	40.4225i		−	1.38081i	−0.723425	−	0.690403i	$-0.757433\pi$
$857$		−	40.4225i		−	1.38081i	0.723425	−	0.690403i	$-0.242567\pi$
$858$		0			0
$859$		−	27.9251i		−	0.952794i	−0.879230	−	0.476397i	$-0.841943\pi$
$859$		−	27.9251i		−	0.952794i	0.879230	−	0.476397i	$-0.158057\pi$
$860$	−41.2004	+	13.6050i	−1.40492	+	0.463928i
$861$		0			0
$862$	−22.3917	−	20.0510i	−0.762663	−	0.682939i
$863$			38.4008i			1.30718i	0.756849	+	0.653590i	$0.226738\pi$
$863$			38.4008i			1.30718i	−0.756849	+	0.653590i	$0.773262\pi$
$864$		0			0
$865$	−1.83952	−	8.68344i	−0.0625454	−	0.295246i
$866$	31.7933	−	35.5047i	1.08038	−	1.20650i
$867$		0			0
$868$	−19.1593	+	2.11968i	−0.650309	+	0.0719467i
$869$			27.1414i			0.920708i
$870$		0			0
$871$	32.8256			1.11225
$872$	−3.60349	−	2.57321i	−0.122030	−	0.0871399i
$873$		0			0
$874$	3.18710	+	2.85394i	0.107805	+	0.0965360i
$875$	28.5318	−	20.6403i	0.964553	−	0.697769i
$876$		0			0
$877$	21.1530			0.714288			0.357144	−	0.934049i	$-0.383751\pi$
$877$	21.1530			0.714288			0.357144	+	0.934049i	$0.383751\pi$
$878$	26.4770	+	23.7093i	0.893555	+	0.800149i
$879$		0			0
$880$	19.6972	−	9.01277i	0.663991	−	0.303820i
$881$	33.9776			1.14473			0.572367	−	0.819998i	$-0.306025\pi$
$881$	33.9776			1.14473			0.572367	+	0.819998i	$0.306025\pi$
$882$		0			0
$883$	14.5736			0.490440			0.245220	−	0.969467i	$-0.421140\pi$
$883$	14.5736			0.490440			0.245220	+	0.969467i	$0.421140\pi$
$884$	44.3932	−	4.91143i	1.49311	−	0.165189i
$885$		0			0
$886$	−21.6919	−	19.4244i	−0.728753	−	0.652574i
$887$		−	24.3962i		−	0.819146i	−0.912277	−	0.409573i	$-0.865678\pi$
$887$		−	24.3962i		−	0.819146i	0.912277	−	0.409573i	$-0.134322\pi$
$888$		0			0
$889$	−33.8671			−1.13587
$890$	25.1249	−	43.7244i	0.842190	−	1.46564i
$891$		0			0
$892$	−21.0795	+	2.33212i	−0.705794	+	0.0780853i
$893$	1.47311			0.0492959
$894$		0			0
$895$	−24.8264	+	5.25928i	−0.829857	+	0.175798i
$896$	32.8255	+	13.8685i	1.09662	+	0.463315i
$897$		0			0
$898$	−9.58504	−	8.58309i	−0.319857	−	0.286421i
$899$		−	12.8977i		−	0.430163i
$900$		0			0
$901$		−	68.2790i		−	2.27470i
$902$	25.3048	−	28.2588i	0.842558	−	0.940915i
$903$		0			0
$904$	−19.7480	−	14.1018i	−0.656807	−	0.469018i
$905$	33.9776	−	7.19787i	1.12945	−	0.239265i
$906$		0			0
$907$	24.7326			0.821233			0.410616	−	0.911808i	$-0.365314\pi$
$907$	24.7326			0.821233			0.410616	+	0.911808i	$0.365314\pi$
$908$	−2.77016	−	25.0388i	−0.0919310	−	0.830942i
$909$		0			0
$910$	−26.9663	−	15.4954i	−0.893923	−	0.513667i
$911$	−29.3757			−0.973260			−0.486630	−	0.873608i	$-0.661774\pi$
$911$	−29.3757			−0.973260			−0.486630	+	0.873608i	$0.661774\pi$
$912$		0			0
$913$			7.57152i			0.250581i
$914$	−6.70035	+	7.48252i	−0.221628	+	0.247500i
$915$		0			0
$916$	−19.3927	+	2.14550i	−0.640752	+	0.0708894i
$917$	−38.4526			−1.26982
$918$		0			0
$919$	18.4626			0.609026			0.304513	−	0.952508i	$-0.401506\pi$
$919$	18.4626			0.609026			0.304513	+	0.952508i	$0.401506\pi$
$920$	3.26065	−	7.47424i	0.107501	−	0.246418i
$921$		0			0
$922$	2.07636	−	2.31875i	0.0683814	−	0.0763640i
$923$	−23.0755			−0.759538
$924$		0			0
$925$	6.27740	−	2.78460i	0.206400	−	0.0915570i
$926$	27.1625	−	30.3333i	0.892614	−	0.996814i
$927$		0			0
$928$	−11.6384	+	20.8100i	−0.382048	+	0.683121i
$929$	45.4688			1.49178			0.745892	−	0.666067i	$-0.232023\pi$
$929$	45.4688			1.49178			0.745892	+	0.666067i	$0.232023\pi$
$930$		0			0
$931$			6.85268i			0.224588i
$932$	2.49621	−	0.276168i	0.0817662	−	0.00904618i
$933$		0			0
$934$	39.9825	+	35.8030i	1.30827	+	1.17151i
$935$	8.02647	+	37.8890i	0.262494	+	1.23910i
$936$		0			0
$937$			5.96656i			0.194919i	0.995239	+	0.0974595i	$0.0310716\pi$
$937$			5.96656i			0.194919i	−0.995239	+	0.0974595i	$0.968928\pi$
$938$	−31.2379	+	34.8845i	−1.01995	+	1.13902i
$939$		0			0
$940$	−0.880445	−	2.66627i	−0.0287169	−	0.0869642i
$941$			11.2275i			0.366006i	0.983112	+	0.183003i	$0.0585818\pi$
$941$			11.2275i			0.366006i	−0.983112	+	0.183003i	$0.941418\pi$
$942$		0			0
$943$		−	14.2800i		−	0.465022i
$944$	−8.83700	−	39.4489i	−0.287620	−	1.28395i
$945$		0			0
$946$	−22.1668	+	24.7544i	−0.720704	+	0.804836i
$947$	−33.1571			−1.07746			−0.538731	−	0.842478i	$-0.681096\pi$
$947$	−33.1571			−1.07746			−0.538731	+	0.842478i	$0.681096\pi$
$948$		0			0
$949$			17.8971i			0.580964i
$950$	−5.10518	+	15.7854i	−0.165634	+	0.512147i
$951$		0			0
$952$	−37.0265	+	51.8515i	−1.20004	+	1.68052i
$953$		−	9.07923i		−	0.294105i	−0.989129	−	0.147053i	$-0.953021\pi$
$953$		−	9.07923i		−	0.294105i	0.989129	−	0.147053i	$-0.0469786\pi$
$954$		0			0
$955$	12.5225	+	59.1123i	0.405217	+	1.91283i
$956$	−0.636473	−	5.75292i	−0.0205850	−	0.186063i
$957$		0			0
$958$	−4.73674	−	4.24159i	−0.153037	−	0.137040i
$959$	23.4429			0.757012
$960$		0			0
$961$	−21.6365			−0.697950
$962$	−4.51831	−	4.04600i	−0.145676	−	0.130448i
$963$		0			0
$964$	4.93003	+	44.5613i	0.158786	+	1.43522i
$965$	−18.3775	+	3.89312i	−0.591592	+	0.125324i
$966$		0			0
$967$		−	41.4918i		−	1.33429i	−0.744929	−	0.667144i	$-0.767517\pi$
$967$		−	41.4918i		−	1.33429i	0.744929	−	0.667144i	$-0.232483\pi$
$968$	−8.44017	+	11.8195i	−0.271277	+	0.379893i
$969$		0			0
$970$	40.1925	+	23.0955i	1.29050	+	0.741551i
$971$		−	50.8245i		−	1.63104i	−0.578731	−	0.815519i	$-0.696452\pi$
$971$		−	50.8245i		−	1.63104i	0.578731	−	0.815519i	$-0.303548\pi$
$972$		0			0
$973$	31.8941			1.02248
$974$	36.7134	−	40.9992i	1.17637	−	1.31370i
$975$		0			0
$976$	−11.1252	−	49.6633i	−0.356107	−	1.58968i
$977$		−	8.25072i		−	0.263964i	−0.991252	−	0.131982i	$-0.957866\pi$
$977$		−	8.25072i		−	0.263964i	0.991252	−	0.131982i	$-0.0421341\pi$
$978$		0			0
$979$		−	38.6205i		−	1.23432i
$980$	12.4030	−	4.09568i	0.396201	−	0.130832i
$981$		0			0
$982$	−3.95343	+	4.41494i	−0.126159	+	0.140886i
$983$			16.5792i			0.528796i	0.964414	+	0.264398i	$0.0851732\pi$
$983$			16.5792i			0.528796i	−0.964414	+	0.264398i	$0.914827\pi$
$984$		0			0
$985$	4.81958	+	22.7508i	0.153564	+	0.724902i
$986$	−31.7592	−	28.4393i	−1.01142	−	0.905693i
$987$		0			0
$988$	14.5636	−	1.61123i	0.463328	−	0.0512602i
$989$			12.5092i			0.397769i
$990$		0			0
$991$	−15.3390			−0.487260			−0.243630	−	0.969868i	$-0.578338\pi$
$991$	−15.3390			−0.487260			−0.243630	+	0.969868i	$0.578338\pi$
$992$	−15.1077	−	8.44927i	−0.479670	−	0.268265i
$993$		0			0
$994$	21.9593	−	24.5228i	0.696508	−	0.777816i
$995$	−6.28658	−	29.6758i	−0.199298	−	0.940786i
$996$		0			0
$997$	40.0534			1.26850			0.634252	−	0.773126i	$-0.281308\pi$
$997$	40.0534			1.26850			0.634252	+	0.773126i	$0.281308\pi$
$998$	35.3491	−	39.4757i	1.11896	−	1.24958i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.d.g.109.16	yes	16
3.2	odd	2		1080.2.d.h.109.1	yes	16
4.3	odd	2		4320.2.d.g.3889.12		16
5.4	even	2		1080.2.d.h.109.2	yes	16
8.3	odd	2		4320.2.d.h.3889.5		16
8.5	even	2		1080.2.d.h.109.3	yes	16
12.11	even	2		4320.2.d.h.3889.6		16
15.14	odd	2	inner	1080.2.d.g.109.15	yes	16
20.19	odd	2		4320.2.d.h.3889.7		16
24.5	odd	2	inner	1080.2.d.g.109.14	yes	16
24.11	even	2		4320.2.d.g.3889.11		16
40.19	odd	2		4320.2.d.g.3889.10		16
40.29	even	2	inner	1080.2.d.g.109.13	✓	16
60.59	even	2		4320.2.d.g.3889.9		16
120.29	odd	2		1080.2.d.h.109.4	yes	16
120.59	even	2		4320.2.d.h.3889.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.d.g.109.13	✓	16	40.29	even	2	inner
1080.2.d.g.109.14	yes	16	24.5	odd	2	inner
1080.2.d.g.109.15	yes	16	15.14	odd	2	inner
1080.2.d.g.109.16	yes	16	1.1	even	1	trivial
1080.2.d.h.109.1	yes	16	3.2	odd	2
1080.2.d.h.109.2	yes	16	5.4	even	2
1080.2.d.h.109.3	yes	16	8.5	even	2
1080.2.d.h.109.4	yes	16	120.29	odd	2
4320.2.d.g.3889.9		16	60.59	even	2
4320.2.d.g.3889.10		16	40.19	odd	2
4320.2.d.g.3889.11		16	24.11	even	2
4320.2.d.g.3889.12		16	4.3	odd	2
4320.2.d.h.3889.5		16	8.3	odd	2
4320.2.d.h.3889.6		16	12.11	even	2
4320.2.d.h.3889.7		16	20.19	odd	2
4320.2.d.h.3889.8		16	120.59	even	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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.05355 + 0.943417i) q^{2} +(0.219928 + 1.98787i) q^{4} +(0.463409 + 2.18752i) q^{5} +3.14971i q^{7} +(-1.64369 + 2.30180i) q^{8} +O(q^{10})\)	\(q+(1.05355 + 0.943417i) q^{2} +(0.219928 + 1.98787i) q^{4} +(0.463409 + 2.18752i) q^{5} +3.14971i q^{7} +(-1.64369 + 2.30180i) q^{8} +(-1.57552 + 2.74185i) q^{10} +2.42180i q^{11} +3.12253 q^{13} +(-2.97150 + 3.31838i) q^{14} +(-3.90326 + 0.874375i) q^{16} -7.15192i q^{17} -2.34624i q^{19} +(-4.24660 + 1.40229i) q^{20} +(-2.28477 + 2.55148i) q^{22} +1.28934i q^{23} +(-4.57050 + 2.02743i) q^{25} +(3.28973 + 2.94585i) q^{26} +(-6.26123 + 0.692709i) q^{28} -4.21495i q^{29} +3.05999 q^{31} +(-4.93718 - 2.76121i) q^{32} +(6.74724 - 7.53489i) q^{34} +(-6.89007 + 1.45960i) q^{35} -1.37346 q^{37} +(2.21349 - 2.47188i) q^{38} +(-5.79694 - 2.52893i) q^{40} -11.0754 q^{41} +9.70199 q^{43} +(-4.81422 + 0.532620i) q^{44} +(-1.21639 + 1.35838i) q^{46} +0.627861i q^{47} -2.92070 q^{49} +(-6.72796 - 2.17590i) q^{50} +(0.686730 + 6.20718i) q^{52} +9.54695 q^{53} +(-5.29774 + 1.12228i) q^{55} +(-7.25002 - 5.17715i) q^{56} +(3.97646 - 4.44066i) q^{58} +10.1066i q^{59} +12.7235i q^{61} +(3.22385 + 2.88685i) q^{62} +(-2.59658 - 7.56689i) q^{64} +(1.44701 + 6.83059i) q^{65} +10.5125 q^{67} +(14.2171 - 1.57290i) q^{68} +(-8.63604 - 4.96245i) q^{70} -7.39000 q^{71} +5.73160i q^{73} +(-1.44701 - 1.29575i) q^{74} +(4.66403 - 0.516004i) q^{76} -7.62797 q^{77} +11.2071 q^{79} +(-3.72152 - 8.13328i) q^{80} +(-11.6685 - 10.4488i) q^{82} +3.12640 q^{83} +(15.6450 - 3.31426i) q^{85} +(10.2215 + 9.15303i) q^{86} +(-5.57450 - 3.98068i) q^{88} -15.9470 q^{89} +9.83507i q^{91} +(-2.56305 + 0.283562i) q^{92} +(-0.592335 + 0.661482i) q^{94} +(5.13246 - 1.08727i) q^{95} -14.6589i q^{97} +(-3.07710 - 2.75544i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 6 q^{4} - 6 q^{5} - 2 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 6 * q^4 - 6 * q^5 - 2 * q^8	\( 16 q - 2 q^{2} - 6 q^{4} - 6 q^{5} - 2 q^{8} + 5 q^{10} - 30 q^{16} - q^{20} - 22 q^{25} + 18 q^{32} - 4 q^{34} - 2 q^{35} + 56 q^{38} + 19 q^{40} + 40 q^{46} - 44 q^{49} - 27 q^{50} + 96 q^{53} + 34 q^{55} + 2 q^{62} - 6 q^{64} + 72 q^{68} - 7 q^{70} - 12 q^{77} + 4 q^{79} - 9 q^{80} + 64 q^{83} + 20 q^{92} - 20 q^{94} - 36 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 6 * q^4 - 6 * q^5 - 2 * q^8 + 5 * q^10 - 30 * q^16 - q^20 - 22 * q^25 + 18 * q^32 - 4 * q^34 - 2 * q^35 + 56 * q^38 + 19 * q^40 + 40 * q^46 - 44 * q^49 - 27 * q^50 + 96 * q^53 + 34 * q^55 + 2 * q^62 - 6 * q^64 + 72 * q^68 - 7 * q^70 - 12 * q^77 + 4 * q^79 - 9 * q^80 + 64 * q^83 + 20 * q^92 - 20 * q^94 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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