LMFDB - Embedded newform 270.2.e.c.91.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(91,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("270.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.e (of order $3$, degree $2$, not 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:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			91.2
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	270.91
Dual form			270.2.e.c.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.18614 + 2.05446i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.18614 + 2.05446i) q^{7} +1.00000 q^{8} +1.00000 q^{10} +(0.686141 + 1.18843i) q^{11} +(-2.37228 + 4.10891i) q^{13} +(1.18614 - 2.05446i) q^{14} +(-0.500000 - 0.866025i) q^{16} +7.37228 q^{17} +3.37228 q^{19} +(-0.500000 - 0.866025i) q^{20} +(0.686141 - 1.18843i) q^{22} +(-2.18614 + 3.78651i) q^{23} +(-0.500000 - 0.866025i) q^{25} +4.74456 q^{26} -2.37228 q^{28} +(-2.18614 - 3.78651i) q^{29} +(3.37228 - 5.84096i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.68614 - 6.38458i) q^{34} -2.37228 q^{35} -4.00000 q^{37} +(-1.68614 - 2.92048i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(5.68614 + 9.84868i) q^{43} -1.37228 q^{44} +4.37228 q^{46} +(-0.813859 - 1.40965i) q^{47} +(0.686141 - 1.18843i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-2.37228 - 4.10891i) q^{52} -11.4891 q^{53} -1.37228 q^{55} +(1.18614 + 2.05446i) q^{56} +(-2.18614 + 3.78651i) q^{58} +(-0.686141 + 1.18843i) q^{59} +(-4.55842 - 7.89542i) q^{61} -6.74456 q^{62} +1.00000 q^{64} +(-2.37228 - 4.10891i) q^{65} +(3.50000 - 6.06218i) q^{67} +(-3.68614 + 6.38458i) q^{68} +(1.18614 + 2.05446i) q^{70} +6.00000 q^{71} -14.1168 q^{73} +(2.00000 + 3.46410i) q^{74} +(-1.68614 + 2.92048i) q^{76} +(-1.62772 + 2.81929i) q^{77} +(-1.00000 - 1.73205i) q^{79} +1.00000 q^{80} +3.00000 q^{82} +(0.813859 + 1.40965i) q^{83} +(-3.68614 + 6.38458i) q^{85} +(5.68614 - 9.84868i) q^{86} +(0.686141 + 1.18843i) q^{88} +1.11684 q^{89} -11.2554 q^{91} +(-2.18614 - 3.78651i) q^{92} +(-0.813859 + 1.40965i) q^{94} +(-1.68614 + 2.92048i) q^{95} +(1.31386 + 2.27567i) q^{97} -1.37228 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 - q^7 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} + 4 q^{8} + 4 q^{10} - 3 q^{11} + 2 q^{13} - q^{14} - 2 q^{16} + 18 q^{17} + 2 q^{19} - 2 q^{20} - 3 q^{22} - 3 q^{23} - 2 q^{25} - 4 q^{26} + 2 q^{28} - 3 q^{29} + 2 q^{31} - 2 q^{32} - 9 q^{34} + 2 q^{35} - 16 q^{37} - q^{38} - 2 q^{40} - 6 q^{41} + 17 q^{43} + 6 q^{44} + 6 q^{46} - 9 q^{47} - 3 q^{49} - 2 q^{50} + 2 q^{52} + 6 q^{55} - q^{56} - 3 q^{58} + 3 q^{59} - q^{61} - 4 q^{62} + 4 q^{64} + 2 q^{65} + 14 q^{67} - 9 q^{68} - q^{70} + 24 q^{71} - 22 q^{73} + 8 q^{74} - q^{76} - 18 q^{77} - 4 q^{79} + 4 q^{80} + 12 q^{82} + 9 q^{83} - 9 q^{85} + 17 q^{86} - 3 q^{88} - 30 q^{89} - 68 q^{91} - 3 q^{92} - 9 q^{94} - q^{95} + 11 q^{97} + 6 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 - q^7 + 4 * q^8 + 4 * q^10 - 3 * q^11 + 2 * q^13 - q^14 - 2 * q^16 + 18 * q^17 + 2 * q^19 - 2 * q^20 - 3 * q^22 - 3 * q^23 - 2 * q^25 - 4 * q^26 + 2 * q^28 - 3 * q^29 + 2 * q^31 - 2 * q^32 - 9 * q^34 + 2 * q^35 - 16 * q^37 - q^38 - 2 * q^40 - 6 * q^41 + 17 * q^43 + 6 * q^44 + 6 * q^46 - 9 * q^47 - 3 * q^49 - 2 * q^50 + 2 * q^52 + 6 * q^55 - q^56 - 3 * q^58 + 3 * q^59 - q^61 - 4 * q^62 + 4 * q^64 + 2 * q^65 + 14 * q^67 - 9 * q^68 - q^70 + 24 * q^71 - 22 * q^73 + 8 * q^74 - q^76 - 18 * q^77 - 4 * q^79 + 4 * q^80 + 12 * q^82 + 9 * q^83 - 9 * q^85 + 17 * q^86 - 3 * q^88 - 30 * q^89 - 68 * q^91 - 3 * q^92 - 9 * q^94 - q^95 + 11 * q^97 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	1.18614	+	2.05446i	0.448319	+	0.776511i	0.998277	−	0.0586811i	$-0.0186895\pi$
$7$	1.18614	+	2.05446i	0.448319	+	0.776511i	−0.549958	+	0.835192i	$0.685356\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	1.00000			0.316228
$11$	0.686141	+	1.18843i	0.206879	+	0.358325i	0.950730	−	0.310021i	$-0.100336\pi$
$11$	0.686141	+	1.18843i	0.206879	+	0.358325i	−0.743851	+	0.668346i	$0.767003\pi$
$12$		0			0
$13$	−2.37228	+	4.10891i	−0.657952	+	1.13961i	0.323192	+	0.946333i	$0.395244\pi$
$13$	−2.37228	+	4.10891i	−0.657952	+	1.13961i	−0.981145	+	0.193274i	$0.938089\pi$
$14$	1.18614	−	2.05446i	0.317009	−	0.549076i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	7.37228			1.78804			0.894020	−	0.448026i	$-0.147873\pi$
$17$	7.37228			1.78804			0.894020	+	0.448026i	$0.147873\pi$
$18$		0			0
$19$	3.37228			0.773654			0.386827	−	0.922152i	$-0.373571\pi$
$19$	3.37228			0.773654			0.386827	+	0.922152i	$0.373571\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		0			0
$22$	0.686141	−	1.18843i	0.146286	−	0.253374i
$23$	−2.18614	+	3.78651i	−0.455842	+	0.789541i	−0.998736	−	0.0502598i	$-0.983995\pi$
$23$	−2.18614	+	3.78651i	−0.455842	+	0.789541i	0.542894	+	0.839801i	$0.317328\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	4.74456			0.930485
$27$		0			0
$28$	−2.37228			−0.448319
$29$	−2.18614	−	3.78651i	−0.405956	−	0.703137i	0.588476	−	0.808515i	$-0.299728\pi$
$29$	−2.18614	−	3.78651i	−0.405956	−	0.703137i	−0.994432	+	0.105378i	$0.966395\pi$
$30$		0			0
$31$	3.37228	−	5.84096i	0.605680	−	1.04907i	−0.386264	−	0.922388i	$-0.626235\pi$
$31$	3.37228	−	5.84096i	0.605680	−	1.04907i	0.991944	−	0.126680i	$-0.0404320\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−3.68614	−	6.38458i	−0.632168	−	1.09495i
$35$	−2.37228			−0.400989
$36$		0			0
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$	−1.68614	−	2.92048i	−0.273528	−	0.473765i
$39$		0			0
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	5.68614	+	9.84868i	0.867128	+	1.50191i	0.864918	+	0.501913i	$0.167370\pi$
$43$	5.68614	+	9.84868i	0.867128	+	1.50191i	0.00221007	+	0.999998i	$0.499297\pi$
$44$	−1.37228			−0.206879
$45$		0			0
$46$	4.37228			0.644658
$47$	−0.813859	−	1.40965i	−0.118714	−	0.205618i	0.800545	−	0.599273i	$-0.204544\pi$
$47$	−0.813859	−	1.40965i	−0.118714	−	0.205618i	−0.919258	+	0.393655i	$0.871210\pi$
$48$		0			0
$49$	0.686141	−	1.18843i	0.0980201	−	0.169776i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$		0			0
$52$	−2.37228	−	4.10891i	−0.328976	−	0.569804i
$53$	−11.4891			−1.57815			−0.789076	−	0.614295i	$-0.789440\pi$
$53$	−11.4891			−1.57815			−0.789076	+	0.614295i	$0.789440\pi$
$54$		0			0
$55$	−1.37228			−0.185038
$56$	1.18614	+	2.05446i	0.158505	+	0.274538i
$57$		0			0
$58$	−2.18614	+	3.78651i	−0.287054	+	0.497193i
$59$	−0.686141	+	1.18843i	−0.0893279	+	0.154720i	−0.907227	−	0.420641i	$-0.861805\pi$
$59$	−0.686141	+	1.18843i	−0.0893279	+	0.154720i	0.817899	+	0.575361i	$0.195139\pi$
$60$		0			0
$61$	−4.55842	−	7.89542i	−0.583646	−	1.01090i	−0.995043	−	0.0994483i	$-0.968292\pi$
$61$	−4.55842	−	7.89542i	−0.583646	−	1.01090i	0.411397	−	0.911456i	$-0.365041\pi$
$62$	−6.74456			−0.856560
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.37228	−	4.10891i	−0.294245	−	0.509648i
$66$		0			0
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	−0.569066	−	0.822292i	$-0.692695\pi$
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	0.996659	+	0.0816792i	$0.0260283\pi$
$68$	−3.68614	+	6.38458i	−0.447010	+	0.774244i
$69$		0			0
$70$	1.18614	+	2.05446i	0.141771	+	0.245554i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	−14.1168			−1.65225			−0.826126	−	0.563486i	$-0.809460\pi$
$73$	−14.1168			−1.65225			−0.826126	+	0.563486i	$0.809460\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$		0			0
$76$	−1.68614	+	2.92048i	−0.193414	+	0.335002i
$77$	−1.62772	+	2.81929i	−0.185496	+	0.321288i
$78$		0			0
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	0.804272	−	0.594261i	$-0.202555\pi$
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	−0.916781	+	0.399390i	$0.869222\pi$
$80$	1.00000			0.111803
$81$		0			0
$82$	3.00000			0.331295
$83$	0.813859	+	1.40965i	0.0893327	+	0.154729i	0.907229	−	0.420637i	$-0.138193\pi$
$83$	0.813859	+	1.40965i	0.0893327	+	0.154729i	−0.817897	+	0.575365i	$0.804860\pi$
$84$		0			0
$85$	−3.68614	+	6.38458i	−0.399818	+	0.692505i
$86$	5.68614	−	9.84868i	0.613152	−	1.06201i
$87$		0			0
$88$	0.686141	+	1.18843i	0.0731428	+	0.126687i
$89$	1.11684			0.118385			0.0591926	−	0.998247i	$-0.481147\pi$
$89$	1.11684			0.118385			0.0591926	+	0.998247i	$0.481147\pi$
$90$		0			0
$91$	−11.2554			−1.17989
$92$	−2.18614	−	3.78651i	−0.227921	−	0.394771i
$93$		0			0
$94$	−0.813859	+	1.40965i	−0.0839432	+	0.145394i
$95$	−1.68614	+	2.92048i	−0.172994	+	0.299635i
$96$		0			0
$97$	1.31386	+	2.27567i	0.133402	+	0.231059i	0.924986	−	0.380001i	$-0.124076\pi$
$97$	1.31386	+	2.27567i	0.133402	+	0.231059i	−0.791584	+	0.611061i	$0.790743\pi$
$98$	−1.37228			−0.138621
$99$		0			0
$100$	1.00000			0.100000
$101$	−4.37228	−	7.57301i	−0.435058	−	0.753543i	0.562242	−	0.826973i	$-0.309939\pi$
$101$	−4.37228	−	7.57301i	−0.435058	−	0.753543i	−0.997300	+	0.0734297i	$0.976606\pi$
$102$		0			0
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	−0.138767	−	0.990325i	$-0.544314\pi$
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	0.927030	−	0.374987i	$-0.122353\pi$
$104$	−2.37228	+	4.10891i	−0.232621	+	0.402912i
$105$		0			0
$106$	5.74456	+	9.94987i	0.557961	+	0.966417i
$107$	14.4891			1.40072			0.700358	−	0.713791i	$-0.253024\pi$
$107$	14.4891			1.40072			0.700358	+	0.713791i	$0.253024\pi$
$108$		0			0
$109$	9.62772			0.922168			0.461084	−	0.887356i	$-0.347461\pi$
$109$	9.62772			0.922168			0.461084	+	0.887356i	$0.347461\pi$
$110$	0.686141	+	1.18843i	0.0654209	+	0.113312i
$111$		0			0
$112$	1.18614	−	2.05446i	0.112080	−	0.194128i
$113$	7.37228	−	12.7692i	0.693526	−	1.20122i	−0.277149	−	0.960827i	$-0.589390\pi$
$113$	7.37228	−	12.7692i	0.693526	−	1.20122i	0.970675	−	0.240395i	$-0.0772770\pi$
$114$		0			0
$115$	−2.18614	−	3.78651i	−0.203859	−	0.353094i
$116$	4.37228			0.405956
$117$		0			0
$118$	1.37228			0.126329
$119$	8.74456	+	15.1460i	0.801613	+	1.38843i
$120$		0			0
$121$	4.55842	−	7.89542i	0.414402	−	0.717765i
$122$	−4.55842	+	7.89542i	−0.412700	+	0.714818i
$123$		0			0
$124$	3.37228	+	5.84096i	0.302840	+	0.524534i
$125$	1.00000			0.0894427
$126$		0			0
$127$	9.11684			0.808989			0.404495	−	0.914540i	$-0.367447\pi$
$127$	9.11684			0.808989			0.404495	+	0.914540i	$0.367447\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−2.37228	+	4.10891i	−0.208063	+	0.360375i
$131$	4.37228	−	7.57301i	0.382008	−	0.661657i	−0.609341	−	0.792908i	$-0.708566\pi$
$131$	4.37228	−	7.57301i	0.382008	−	0.661657i	0.991349	+	0.131251i	$0.0418993\pi$
$132$		0			0
$133$	4.00000	+	6.92820i	0.346844	+	0.600751i
$134$	−7.00000			−0.604708
$135$		0			0
$136$	7.37228			0.632168
$137$	−0.941578	−	1.63086i	−0.0804444	−	0.139334i	0.822996	−	0.568046i	$-0.192301\pi$
$137$	−0.941578	−	1.63086i	−0.0804444	−	0.139334i	−0.903441	+	0.428713i	$0.858967\pi$
$138$		0			0
$139$	−9.05842	+	15.6896i	−0.768325	+	1.33078i	0.170145	+	0.985419i	$0.445576\pi$
$139$	−9.05842	+	15.6896i	−0.768325	+	1.33078i	−0.938470	+	0.345359i	$0.887757\pi$
$140$	1.18614	−	2.05446i	0.100247	−	0.173633i
$141$		0			0
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	−6.51087			−0.544467
$144$		0			0
$145$	4.37228			0.363098
$146$	7.05842	+	12.2255i	0.584159	+	1.01179i
$147$		0			0
$148$	2.00000	−	3.46410i	0.164399	−	0.284747i
$149$	9.55842	−	16.5557i	0.783056	−	1.35629i	−0.147097	−	0.989122i	$-0.546993\pi$
$149$	9.55842	−	16.5557i	0.783056	−	1.35629i	0.930153	−	0.367171i	$-0.119674\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$	3.37228			0.273528
$153$		0			0
$154$	3.25544			0.262331
$155$	3.37228	+	5.84096i	0.270868	+	0.469157i
$156$		0			0
$157$	−2.37228	+	4.10891i	−0.189329	+	0.327927i	−0.945027	−	0.326993i	$-0.893964\pi$
$157$	−2.37228	+	4.10891i	−0.189329	+	0.327927i	0.755698	+	0.654920i	$0.227298\pi$
$158$	−1.00000	+	1.73205i	−0.0795557	+	0.137795i
$159$		0			0
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−10.3723			−0.817450
$162$		0			0
$163$	1.48913			0.116637			0.0583186	−	0.998298i	$-0.481426\pi$
$163$	1.48913			0.116637			0.0583186	+	0.998298i	$0.481426\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$		0			0
$166$	0.813859	−	1.40965i	0.0631677	−	0.109410i
$167$	3.81386	−	6.60580i	0.295125	−	0.511172i	−0.679889	−	0.733315i	$-0.737972\pi$
$167$	3.81386	−	6.60580i	0.295125	−	0.511172i	0.975014	+	0.222143i	$0.0713053\pi$
$168$		0			0
$169$	−4.75544	−	8.23666i	−0.365803	−	0.633589i
$170$	7.37228			0.565428
$171$		0			0
$172$	−11.3723			−0.867128
$173$	4.62772	+	8.01544i	0.351839	+	0.609403i	0.986572	−	0.163329i	$-0.0522231\pi$
$173$	4.62772	+	8.01544i	0.351839	+	0.609403i	−0.634733	+	0.772732i	$0.718890\pi$
$174$		0			0
$175$	1.18614	−	2.05446i	0.0896638	−	0.155302i
$176$	0.686141	−	1.18843i	0.0517198	−	0.0895813i
$177$		0			0
$178$	−0.558422	−	0.967215i	−0.0418555	−	0.0724958i
$179$	3.25544			0.243323			0.121661	−	0.992572i	$-0.461178\pi$
$179$	3.25544			0.243323			0.121661	+	0.992572i	$0.461178\pi$
$180$		0			0
$181$	−7.86141			−0.584334			−0.292167	−	0.956367i	$-0.594376\pi$
$181$	−7.86141			−0.584334			−0.292167	+	0.956367i	$0.594376\pi$
$182$	5.62772	+	9.74749i	0.417154	+	0.722532i
$183$		0			0
$184$	−2.18614	+	3.78651i	−0.161164	+	0.279145i
$185$	2.00000	−	3.46410i	0.147043	−	0.254686i
$186$		0			0
$187$	5.05842	+	8.76144i	0.369908	+	0.640700i
$188$	1.62772			0.118714
$189$		0			0
$190$	3.37228			0.244651
$191$	−2.74456	−	4.75372i	−0.198590	−	0.343967i	0.749482	−	0.662025i	$-0.230303\pi$
$191$	−2.74456	−	4.75372i	−0.198590	−	0.343967i	−0.948071	+	0.318058i	$0.896969\pi$
$192$		0			0
$193$	−1.94158	+	3.36291i	−0.139758	+	0.242068i	−0.927405	−	0.374059i	$-0.877966\pi$
$193$	−1.94158	+	3.36291i	−0.139758	+	0.242068i	0.787647	+	0.616127i	$0.211299\pi$
$194$	1.31386	−	2.27567i	0.0943296	−	0.163384i
$195$		0			0
$196$	0.686141	+	1.18843i	0.0490100	+	0.0848879i
$197$	−17.4891			−1.24605			−0.623024	−	0.782202i	$-0.714096\pi$
$197$	−17.4891			−1.24605			−0.623024	+	0.782202i	$0.714096\pi$
$198$		0			0
$199$	−9.48913			−0.672666			−0.336333	−	0.941743i	$-0.609187\pi$
$199$	−9.48913			−0.672666			−0.336333	+	0.941743i	$0.609187\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$		0			0
$202$	−4.37228	+	7.57301i	−0.307633	+	0.532835i
$203$	5.18614	−	8.98266i	0.363996	−	0.630459i
$204$		0			0
$205$	−1.50000	−	2.59808i	−0.104765	−	0.181458i
$206$	−16.0000			−1.11477
$207$		0			0
$208$	4.74456			0.328976
$209$	2.31386	+	4.00772i	0.160053	+	0.277220i
$210$		0			0
$211$	3.62772	−	6.28339i	0.249742	−	0.432567i	−0.713712	−	0.700439i	$-0.752987\pi$
$211$	3.62772	−	6.28339i	0.249742	−	0.432567i	0.963454	+	0.267873i	$0.0863207\pi$
$212$	5.74456	−	9.94987i	0.394538	−	0.683360i
$213$		0			0
$214$	−7.24456	−	12.5480i	−0.495228	−	0.857760i
$215$	−11.3723			−0.775583
$216$		0			0
$217$	16.0000			1.08615
$218$	−4.81386	−	8.33785i	−0.326036	−	0.564710i
$219$		0			0
$220$	0.686141	−	1.18843i	0.0462596	−	0.0801240i
$221$	−17.4891	+	30.2921i	−1.17645	+	2.03766i
$222$		0			0
$223$	−6.18614	−	10.7147i	−0.414255	−	0.717510i	0.581095	−	0.813836i	$-0.302624\pi$
$223$	−6.18614	−	10.7147i	−0.414255	−	0.717510i	−0.995350	+	0.0963255i	$0.969291\pi$
$224$	−2.37228			−0.158505
$225$		0			0
$226$	−14.7446			−0.980794
$227$	0.941578	+	1.63086i	0.0624947	+	0.108244i	0.895580	−	0.444901i	$-0.146761\pi$
$227$	0.941578	+	1.63086i	0.0624947	+	0.108244i	−0.833085	+	0.553145i	$0.813428\pi$
$228$		0			0
$229$	−9.18614	+	15.9109i	−0.607037	+	1.05142i	0.384689	+	0.923046i	$0.374309\pi$
$229$	−9.18614	+	15.9109i	−0.607037	+	1.05142i	−0.991726	+	0.128373i	$0.959025\pi$
$230$	−2.18614	+	3.78651i	−0.144150	+	0.249675i
$231$		0			0
$232$	−2.18614	−	3.78651i	−0.143527	−	0.248596i
$233$	10.1168			0.662776			0.331388	−	0.943494i	$-0.392483\pi$
$233$	10.1168			0.662776			0.331388	+	0.943494i	$0.392483\pi$
$234$		0			0
$235$	1.62772			0.106181
$236$	−0.686141	−	1.18843i	−0.0446640	−	0.0773602i
$237$		0			0
$238$	8.74456	−	15.1460i	0.566826	−	0.981771i
$239$	−7.37228	+	12.7692i	−0.476873	+	0.825969i	−0.999649	−	0.0265017i	$-0.991563\pi$
$239$	−7.37228	+	12.7692i	−0.476873	+	0.825969i	0.522776	+	0.852470i	$0.324897\pi$
$240$		0			0
$241$	−5.24456	−	9.08385i	−0.337832	−	0.585142i	0.646193	−	0.763174i	$-0.276360\pi$
$241$	−5.24456	−	9.08385i	−0.337832	−	0.585142i	−0.984025	+	0.178032i	$0.943027\pi$
$242$	−9.11684			−0.586053
$243$		0			0
$244$	9.11684			0.583646
$245$	0.686141	+	1.18843i	0.0438359	+	0.0759260i
$246$		0			0
$247$	−8.00000	+	13.8564i	−0.509028	+	0.881662i
$248$	3.37228	−	5.84096i	0.214140	−	0.370901i
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−15.6060			−0.985040			−0.492520	−	0.870301i	$-0.663924\pi$
$251$	−15.6060			−0.985040			−0.492520	+	0.870301i	$0.663924\pi$
$252$		0			0
$253$	−6.00000			−0.377217
$254$	−4.55842	−	7.89542i	−0.286021	−	0.495403i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.686141	+	1.18843i	−0.0428003	+	0.0741323i	−0.886632	−	0.462476i	$-0.846961\pi$
$257$	−0.686141	+	1.18843i	−0.0428003	+	0.0741323i	0.843832	+	0.536608i	$0.180295\pi$
$258$		0			0
$259$	−4.74456	−	8.21782i	−0.294813	−	0.510631i
$260$	4.74456			0.294245
$261$		0			0
$262$	−8.74456			−0.540241
$263$	2.74456	+	4.75372i	0.169237	+	0.293127i	0.938152	−	0.346224i	$-0.112536\pi$
$263$	2.74456	+	4.75372i	0.169237	+	0.293127i	−0.768915	+	0.639351i	$0.779203\pi$
$264$		0			0
$265$	5.74456	−	9.94987i	0.352886	−	0.611216i
$266$	4.00000	−	6.92820i	0.245256	−	0.424795i
$267$		0			0
$268$	3.50000	+	6.06218i	0.213797	+	0.370306i
$269$	−4.37228			−0.266583			−0.133291	−	0.991077i	$-0.542555\pi$
$269$	−4.37228			−0.266583			−0.133291	+	0.991077i	$0.542555\pi$
$270$		0			0
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$	−3.68614	−	6.38458i	−0.223505	−	0.387122i
$273$		0			0
$274$	−0.941578	+	1.63086i	−0.0568828	+	0.0985239i
$275$	0.686141	−	1.18843i	0.0413758	−	0.0716651i
$276$		0			0
$277$	−2.62772	−	4.55134i	−0.157884	−	0.273464i	0.776221	−	0.630461i	$-0.217134\pi$
$277$	−2.62772	−	4.55134i	−0.157884	−	0.273464i	−0.934106	+	0.356997i	$0.883801\pi$
$278$	18.1168			1.08658
$279$		0			0
$280$	−2.37228			−0.141771
$281$	2.18614	+	3.78651i	0.130414	+	0.225884i	0.923836	−	0.382788i	$-0.125036\pi$
$281$	2.18614	+	3.78651i	0.130414	+	0.225884i	−0.793422	+	0.608672i	$0.791703\pi$
$282$		0			0
$283$	15.9307	−	27.5928i	0.946982	−	1.64022i	0.195249	−	0.980754i	$-0.437449\pi$
$283$	15.9307	−	27.5928i	0.946982	−	1.64022i	0.751733	−	0.659467i	$-0.229218\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	3.25544	+	5.63858i	0.192498	+	0.333416i
$287$	−7.11684			−0.420094
$288$		0			0
$289$	37.3505			2.19709
$290$	−2.18614	−	3.78651i	−0.128375	−	0.222351i
$291$		0			0
$292$	7.05842	−	12.2255i	0.413063	−	0.715446i
$293$	−4.11684	+	7.13058i	−0.240509	+	0.416573i	−0.960859	−	0.277037i	$-0.910648\pi$
$293$	−4.11684	+	7.13058i	−0.240509	+	0.416573i	0.720351	+	0.693610i	$0.243981\pi$
$294$		0			0
$295$	−0.686141	−	1.18843i	−0.0399487	−	0.0691931i
$296$	−4.00000			−0.232495
$297$		0			0
$298$	−19.1168			−1.10741
$299$	−10.3723	−	17.9653i	−0.599845	−	1.03896i
$300$		0			0
$301$	−13.4891	+	23.3639i	−0.777500	+	1.34667i
$302$	5.00000	−	8.66025i	0.287718	−	0.498342i
$303$		0			0
$304$	−1.68614	−	2.92048i	−0.0967068	−	0.167501i
$305$	9.11684			0.522029
$306$		0			0
$307$	−33.2337			−1.89675			−0.948373	−	0.317156i	$-0.897272\pi$
$307$	−33.2337			−1.89675			−0.948373	+	0.317156i	$0.897272\pi$
$308$	−1.62772	−	2.81929i	−0.0927479	−	0.160644i
$309$		0			0
$310$	3.37228	−	5.84096i	0.191533	−	0.331744i
$311$	−4.62772	+	8.01544i	−0.262414	+	0.454514i	−0.966883	−	0.255221i	$-0.917852\pi$
$311$	−4.62772	+	8.01544i	−0.262414	+	0.454514i	0.704469	+	0.709735i	$0.251185\pi$
$312$		0			0
$313$	−4.68614	−	8.11663i	−0.264876	−	0.458779i	0.702655	−	0.711531i	$-0.251998\pi$
$313$	−4.68614	−	8.11663i	−0.264876	−	0.458779i	−0.967531	+	0.252752i	$0.918664\pi$
$314$	4.74456			0.267751
$315$		0			0
$316$	2.00000			0.112509
$317$	−4.37228	−	7.57301i	−0.245572	−	0.425343i	0.716720	−	0.697361i	$-0.245642\pi$
$317$	−4.37228	−	7.57301i	−0.245572	−	0.425343i	−0.962292	+	0.272018i	$0.912309\pi$
$318$		0			0
$319$	3.00000	−	5.19615i	0.167968	−	0.290929i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$		0			0
$322$	5.18614	+	8.98266i	0.289012	+	0.500584i
$323$	24.8614			1.38333
$324$		0			0
$325$	4.74456			0.263181
$326$	−0.744563	−	1.28962i	−0.0412375	−	0.0714255i
$327$		0			0
$328$	−1.50000	+	2.59808i	−0.0828236	+	0.143455i
$329$	1.93070	−	3.34408i	0.106443	−	0.184365i
$330$		0			0
$331$	9.11684	+	15.7908i	0.501107	+	0.867943i	0.999999	+	0.00127880i	$0.000407055\pi$
$331$	9.11684	+	15.7908i	0.501107	+	0.867943i	−0.498892	+	0.866664i	$0.666260\pi$
$332$	−1.62772			−0.0893327
$333$		0			0
$334$	−7.62772			−0.417370
$335$	3.50000	+	6.06218i	0.191225	+	0.331212i
$336$		0			0
$337$	−1.68614	+	2.92048i	−0.0918499	+	0.159089i	−0.908290	−	0.418342i	$-0.862611\pi$
$337$	−1.68614	+	2.92048i	−0.0918499	+	0.159089i	0.816440	+	0.577431i	$0.195945\pi$
$338$	−4.75544	+	8.23666i	−0.258662	+	0.448015i
$339$		0			0
$340$	−3.68614	−	6.38458i	−0.199909	−	0.346253i
$341$	9.25544			0.501210
$342$		0			0
$343$	19.8614			1.07242
$344$	5.68614	+	9.84868i	0.306576	+	0.531005i
$345$		0			0
$346$	4.62772	−	8.01544i	0.248788	−	0.430913i
$347$	−11.0584	+	19.1537i	−0.593647	+	1.02823i	0.400089	+	0.916476i	$0.368979\pi$
$347$	−11.0584	+	19.1537i	−0.593647	+	1.02823i	−0.993736	+	0.111751i	$0.964354\pi$
$348$		0			0
$349$	−0.441578	−	0.764836i	−0.0236371	−	0.0409407i	0.853965	−	0.520331i	$-0.174191\pi$
$349$	−0.441578	−	0.764836i	−0.0236371	−	0.0409407i	−0.877602	+	0.479390i	$0.840858\pi$
$350$	−2.37228			−0.126804
$351$		0			0
$352$	−1.37228			−0.0731428
$353$	15.1753	+	26.2843i	0.807698	+	1.39897i	0.914455	+	0.404689i	$0.132620\pi$
$353$	15.1753	+	26.2843i	0.807698	+	1.39897i	−0.106757	+	0.994285i	$0.534047\pi$
$354$		0			0
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$	−0.558422	+	0.967215i	−0.0295963	+	0.0512623i
$357$		0			0
$358$	−1.62772	−	2.81929i	−0.0860276	−	0.149004i
$359$	−5.48913			−0.289705			−0.144852	−	0.989453i	$-0.546271\pi$
$359$	−5.48913			−0.289705			−0.144852	+	0.989453i	$0.546271\pi$
$360$		0			0
$361$	−7.62772			−0.401459
$362$	3.93070	+	6.80818i	0.206593	+	0.357830i
$363$		0			0
$364$	5.62772	−	9.74749i	0.294973	−	0.510908i
$365$	7.05842	−	12.2255i	0.369455	−	0.639914i
$366$		0			0
$367$	8.00000	+	13.8564i	0.417597	+	0.723299i	0.995697	−	0.0926670i	$-0.0295392\pi$
$367$	8.00000	+	13.8564i	0.417597	+	0.723299i	−0.578101	+	0.815966i	$0.696206\pi$
$368$	4.37228			0.227921
$369$		0			0
$370$	−4.00000			−0.207950
$371$	−13.6277	−	23.6039i	−0.707516	−	1.22545i
$372$		0			0
$373$	−3.74456	+	6.48577i	−0.193886	+	0.335821i	−0.946535	−	0.322602i	$-0.895443\pi$
$373$	−3.74456	+	6.48577i	−0.193886	+	0.335821i	0.752649	+	0.658422i	$0.228776\pi$
$374$	5.05842	−	8.76144i	0.261565	−	0.453043i
$375$		0			0
$376$	−0.813859	−	1.40965i	−0.0419716	−	0.0726969i
$377$	20.7446			1.06840
$378$		0			0
$379$	−10.8614			−0.557913			−0.278956	−	0.960304i	$-0.589989\pi$
$379$	−10.8614			−0.557913			−0.278956	+	0.960304i	$0.589989\pi$
$380$	−1.68614	−	2.92048i	−0.0864972	−	0.149818i
$381$		0			0
$382$	−2.74456	+	4.75372i	−0.140424	+	0.243222i
$383$	11.4891	−	19.8997i	0.587067	−	1.01683i	−0.407547	−	0.913184i	$-0.633616\pi$
$383$	11.4891	−	19.8997i	0.587067	−	1.01683i	0.994614	−	0.103646i	$-0.0330508\pi$
$384$		0			0
$385$	−1.62772	−	2.81929i	−0.0829562	−	0.143684i
$386$	3.88316			0.197647
$387$		0			0
$388$	−2.62772			−0.133402
$389$	−5.18614	−	8.98266i	−0.262948	−	0.455439i	0.704076	−	0.710124i	$-0.251361\pi$
$389$	−5.18614	−	8.98266i	−0.262948	−	0.455439i	−0.967024	+	0.254686i	$0.918028\pi$
$390$		0			0
$391$	−16.1168	+	27.9152i	−0.815064	+	1.41173i
$392$	0.686141	−	1.18843i	0.0346553	−	0.0600248i
$393$		0			0
$394$	8.74456	+	15.1460i	0.440545	+	0.763046i
$395$	2.00000			0.100631
$396$		0			0
$397$	11.2554			0.564894			0.282447	−	0.959283i	$-0.408854\pi$
$397$	11.2554			0.564894			0.282447	+	0.959283i	$0.408854\pi$
$398$	4.74456	+	8.21782i	0.237823	+	0.411922i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	8.05842	−	13.9576i	0.402418	−	0.697009i	−0.591599	−	0.806232i	$-0.701503\pi$
$401$	8.05842	−	13.9576i	0.402418	−	0.697009i	0.994017	+	0.109223i	$0.0348364\pi$
$402$		0			0
$403$	16.0000	+	27.7128i	0.797017	+	1.38047i
$404$	8.74456			0.435058
$405$		0			0
$406$	−10.3723			−0.514768
$407$	−2.74456	−	4.75372i	−0.136043	−	0.235633i
$408$		0			0
$409$	5.43070	−	9.40625i	0.268531	−	0.465109i	−0.699952	−	0.714190i	$-0.746795\pi$
$409$	5.43070	−	9.40625i	0.268531	−	0.465109i	0.968483	+	0.249081i	$0.0801285\pi$
$410$	−1.50000	+	2.59808i	−0.0740797	+	0.128310i
$411$		0			0
$412$	8.00000	+	13.8564i	0.394132	+	0.682656i
$413$	−3.25544			−0.160190
$414$		0			0
$415$	−1.62772			−0.0799016
$416$	−2.37228	−	4.10891i	−0.116311	−	0.201456i
$417$		0			0
$418$	2.31386	−	4.00772i	0.113175	−	0.196024i
$419$	−15.8614	+	27.4728i	−0.774880	+	1.34213i	0.159981	+	0.987120i	$0.448857\pi$
$419$	−15.8614	+	27.4728i	−0.774880	+	1.34213i	−0.934862	+	0.355012i	$0.884477\pi$
$420$		0			0
$421$	19.2337	+	33.3137i	0.937393	+	1.62361i	0.770311	+	0.637669i	$0.220101\pi$
$421$	19.2337	+	33.3137i	0.937393	+	1.62361i	0.167082	+	0.985943i	$0.446566\pi$
$422$	−7.25544			−0.353189
$423$		0			0
$424$	−11.4891			−0.557961
$425$	−3.68614	−	6.38458i	−0.178804	−	0.309698i
$426$		0			0
$427$	10.8139	−	18.7302i	0.523319	−	0.906416i
$428$	−7.24456	+	12.5480i	−0.350179	+	0.606528i
$429$		0			0
$430$	5.68614	+	9.84868i	0.274210	+	0.474946i
$431$	26.2337			1.26363			0.631816	−	0.775118i	$-0.282310\pi$
$431$	26.2337			1.26363			0.631816	+	0.775118i	$0.282310\pi$
$432$		0			0
$433$	0.627719			0.0301662			0.0150831	−	0.999886i	$-0.495199\pi$
$433$	0.627719			0.0301662			0.0150831	+	0.999886i	$0.495199\pi$
$434$	−8.00000	−	13.8564i	−0.384012	−	0.665129i
$435$		0			0
$436$	−4.81386	+	8.33785i	−0.230542	+	0.399311i
$437$	−7.37228	+	12.7692i	−0.352664	+	0.610832i
$438$		0			0
$439$	−8.11684	−	14.0588i	−0.387396	−	0.670989i	0.604703	−	0.796451i	$-0.293292\pi$
$439$	−8.11684	−	14.0588i	−0.387396	−	0.670989i	−0.992098	+	0.125462i	$0.959959\pi$
$440$	−1.37228			−0.0654209
$441$		0			0
$442$	34.9783			1.66375
$443$	−13.2446	−	22.9403i	−0.629268	−	1.08992i	−0.987699	−	0.156368i	$-0.950021\pi$
$443$	−13.2446	−	22.9403i	−0.629268	−	1.08992i	0.358431	−	0.933556i	$-0.383312\pi$
$444$		0			0
$445$	−0.558422	+	0.967215i	−0.0264717	+	0.0458504i
$446$	−6.18614	+	10.7147i	−0.292922	+	0.507356i
$447$		0			0
$448$	1.18614	+	2.05446i	0.0560399	+	0.0970639i
$449$	18.8614			0.890125			0.445062	−	0.895500i	$-0.353181\pi$
$449$	18.8614			0.890125			0.445062	+	0.895500i	$0.353181\pi$
$450$		0			0
$451$	−4.11684			−0.193855
$452$	7.37228	+	12.7692i	0.346763	+	0.600611i
$453$		0			0
$454$	0.941578	−	1.63086i	0.0441904	−	0.0765401i
$455$	5.62772	−	9.74749i	0.263832	−	0.456970i
$456$		0			0
$457$	−15.0584	−	26.0820i	−0.704403	−	1.22006i	−0.966906	−	0.255131i	$-0.917881\pi$
$457$	−15.0584	−	26.0820i	−0.704403	−	1.22006i	0.262503	−	0.964931i	$-0.415452\pi$
$458$	18.3723			0.858480
$459$		0			0
$460$	4.37228			0.203859
$461$	9.55842	+	16.5557i	0.445180	+	0.771075i	0.998065	−	0.0621833i	$-0.0198063\pi$
$461$	9.55842	+	16.5557i	0.445180	+	0.771075i	−0.552885	+	0.833258i	$0.686473\pi$
$462$		0			0
$463$	−10.0000	+	17.3205i	−0.464739	+	0.804952i	−0.999190	−	0.0402476i	$-0.987185\pi$
$463$	−10.0000	+	17.3205i	−0.464739	+	0.804952i	0.534450	+	0.845200i	$0.320519\pi$
$464$	−2.18614	+	3.78651i	−0.101489	+	0.175784i
$465$		0			0
$466$	−5.05842	−	8.76144i	−0.234327	−	0.405866i
$467$	−25.8832			−1.19773			−0.598865	−	0.800850i	$-0.704381\pi$
$467$	−25.8832			−1.19773			−0.598865	+	0.800850i	$0.704381\pi$
$468$		0			0
$469$	16.6060			0.766792
$470$	−0.813859	−	1.40965i	−0.0375405	−	0.0650221i
$471$		0			0
$472$	−0.686141	+	1.18843i	−0.0315822	+	0.0547019i
$473$	−7.80298	+	13.5152i	−0.358782	+	0.621428i
$474$		0			0
$475$	−1.68614	−	2.92048i	−0.0773654	−	0.134001i
$476$	−17.4891			−0.801613
$477$		0			0
$478$	14.7446			0.674401
$479$	−11.7446	−	20.3422i	−0.536623	−	0.929458i	−0.999083	−	0.0428178i	$-0.986366\pi$
$479$	−11.7446	−	20.3422i	−0.536623	−	0.929458i	0.462460	−	0.886640i	$-0.346967\pi$
$480$		0			0
$481$	9.48913	−	16.4356i	0.432667	−	0.749401i
$482$	−5.24456	+	9.08385i	−0.238883	+	0.413758i
$483$		0			0
$484$	4.55842	+	7.89542i	0.207201	+	0.358883i
$485$	−2.62772			−0.119319
$486$		0			0
$487$	−1.25544			−0.0568893			−0.0284446	−	0.999595i	$-0.509055\pi$
$487$	−1.25544			−0.0568893			−0.0284446	+	0.999595i	$0.509055\pi$
$488$	−4.55842	−	7.89542i	−0.206350	−	0.357409i
$489$		0			0
$490$	0.686141	−	1.18843i	0.0309967	−	0.0536878i
$491$	1.80298	−	3.12286i	0.0813676	−	0.140933i	−0.822470	−	0.568808i	$-0.807405\pi$
$491$	1.80298	−	3.12286i	0.0813676	−	0.140933i	0.903838	+	0.427876i	$0.140738\pi$
$492$		0			0
$493$	−16.1168	−	27.9152i	−0.725866	−	1.25724i
$494$	16.0000			0.719874
$495$		0			0
$496$	−6.74456			−0.302840
$497$	7.11684	+	12.3267i	0.319234	+	0.552930i
$498$		0			0
$499$	1.05842	−	1.83324i	0.0473815	−	0.0820671i	−0.841362	−	0.540472i	$-0.818246\pi$
$499$	1.05842	−	1.83324i	0.0473815	−	0.0820671i	0.888743	+	0.458405i	$0.151579\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$		0			0
$502$	7.80298	+	13.5152i	0.348264	+	0.603211i
$503$	−21.8614			−0.974752			−0.487376	−	0.873192i	$-0.662046\pi$
$503$	−21.8614			−0.974752			−0.487376	+	0.873192i	$0.662046\pi$
$504$		0			0
$505$	8.74456			0.389128
$506$	3.00000	+	5.19615i	0.133366	+	0.230997i
$507$		0			0
$508$	−4.55842	+	7.89542i	−0.202247	+	0.350303i
$509$	4.67527	−	8.09780i	0.207228	−	0.358929i	−0.743613	−	0.668611i	$-0.766889\pi$
$509$	4.67527	−	8.09780i	0.207228	−	0.358929i	0.950840	+	0.309682i	$0.100223\pi$
$510$		0			0
$511$	−16.7446	−	29.0024i	−0.740736	−	1.28299i
$512$	1.00000			0.0441942
$513$		0			0
$514$	1.37228			0.0605287
$515$	8.00000	+	13.8564i	0.352522	+	0.610586i
$516$		0			0
$517$	1.11684	−	1.93443i	0.0491187	−	0.0850762i
$518$	−4.74456	+	8.21782i	−0.208464	+	0.361070i
$519$		0			0
$520$	−2.37228	−	4.10891i	−0.104031	−	0.180188i
$521$	41.2337			1.80648			0.903240	−	0.429135i	$-0.141182\pi$
$521$	41.2337			1.80648			0.903240	+	0.429135i	$0.141182\pi$
$522$		0			0
$523$	−11.1168			−0.486106			−0.243053	−	0.970013i	$-0.578149\pi$
$523$	−11.1168			−0.486106			−0.243053	+	0.970013i	$0.578149\pi$
$524$	4.37228	+	7.57301i	0.191004	+	0.330829i
$525$		0			0
$526$	2.74456	−	4.75372i	0.119669	−	0.207272i
$527$	24.8614	−	43.0612i	1.08298	−	1.87578i
$528$		0			0
$529$	1.94158	+	3.36291i	0.0844164	+	0.146214i
$530$	−11.4891			−0.499056
$531$		0			0
$532$	−8.00000			−0.346844
$533$	−7.11684	−	12.3267i	−0.308265	−	0.533930i
$534$		0			0
$535$	−7.24456	+	12.5480i	−0.313210	+	0.542495i
$536$	3.50000	−	6.06218i	0.151177	−	0.261846i
$537$		0			0
$538$	2.18614	+	3.78651i	0.0942512	+	0.163248i
$539$	1.88316			0.0811133
$540$		0			0
$541$	21.6277			0.929848			0.464924	−	0.885351i	$-0.346082\pi$
$541$	21.6277			0.929848			0.464924	+	0.885351i	$0.346082\pi$
$542$	−4.00000	−	6.92820i	−0.171815	−	0.297592i
$543$		0			0
$544$	−3.68614	+	6.38458i	−0.158042	+	0.273737i
$545$	−4.81386	+	8.33785i	−0.206203	+	0.357154i
$546$		0			0
$547$	−19.7337	−	34.1798i	−0.843752	−	1.46142i	−0.886701	−	0.462343i	$-0.847009\pi$
$547$	−19.7337	−	34.1798i	−0.843752	−	1.46142i	0.0429494	−	0.999077i	$-0.486325\pi$
$548$	1.88316			0.0804444
$549$		0			0
$550$	−1.37228			−0.0585143
$551$	−7.37228	−	12.7692i	−0.314070	−	0.543985i
$552$		0			0
$553$	2.37228	−	4.10891i	0.100880	−	0.174729i
$554$	−2.62772	+	4.55134i	−0.111641	+	0.193368i
$555$		0			0
$556$	−9.05842	−	15.6896i	−0.384163	−	0.665389i
$557$	9.76631			0.413812			0.206906	−	0.978361i	$-0.433661\pi$
$557$	9.76631			0.413812			0.206906	+	0.978361i	$0.433661\pi$
$558$		0			0
$559$	−53.9565			−2.28212
$560$	1.18614	+	2.05446i	0.0501236	+	0.0868166i
$561$		0			0
$562$	2.18614	−	3.78651i	0.0922168	−	0.159724i
$563$	8.36141	−	14.4824i	0.352391	−	0.610360i	−0.634277	−	0.773106i	$-0.718702\pi$
$563$	8.36141	−	14.4824i	0.352391	−	0.610360i	0.986668	+	0.162747i	$0.0520353\pi$
$564$		0			0
$565$	7.37228	+	12.7692i	0.310154	+	0.537203i
$566$	−31.8614			−1.33923
$567$		0			0
$568$	6.00000			0.251754
$569$	4.80298	+	8.31901i	0.201352	+	0.348751i	0.948964	−	0.315384i	$-0.102133\pi$
$569$	4.80298	+	8.31901i	0.201352	+	0.348751i	−0.747613	+	0.664135i	$0.768800\pi$
$570$		0			0
$571$	15.8030	−	27.3716i	0.661334	−	1.14546i	−0.318931	−	0.947778i	$-0.603324\pi$
$571$	15.8030	−	27.3716i	0.661334	−	1.14546i	0.980265	−	0.197687i	$-0.0633429\pi$
$572$	3.25544	−	5.63858i	0.136117	−	0.235761i
$573$		0			0
$574$	3.55842	+	6.16337i	0.148526	+	0.257254i
$575$	4.37228			0.182337
$576$		0			0
$577$	−23.8832			−0.994269			−0.497134	−	0.867674i	$-0.665614\pi$
$577$	−23.8832			−0.994269			−0.497134	+	0.867674i	$0.665614\pi$
$578$	−18.6753	−	32.3465i	−0.776789	−	1.34544i
$579$		0			0
$580$	−2.18614	+	3.78651i	−0.0907746	+	0.157226i
$581$	−1.93070	+	3.34408i	−0.0800991	+	0.138736i
$582$		0			0
$583$	−7.88316	−	13.6540i	−0.326487	−	0.565492i
$584$	−14.1168			−0.584159
$585$		0			0
$586$	8.23369			0.340131
$587$	13.5000	+	23.3827i	0.557205	+	0.965107i	0.997728	+	0.0673658i	$0.0214594\pi$
$587$	13.5000	+	23.3827i	0.557205	+	0.965107i	−0.440524	+	0.897741i	$0.645207\pi$
$588$		0			0
$589$	11.3723	−	19.6974i	0.468587	−	0.811616i
$590$	−0.686141	+	1.18843i	−0.0282480	+	0.0489269i
$591$		0			0
$592$	2.00000	+	3.46410i	0.0821995	+	0.142374i
$593$	−37.7228			−1.54909			−0.774545	−	0.632519i	$-0.782021\pi$
$593$	−37.7228			−1.54909			−0.774545	+	0.632519i	$0.782021\pi$
$594$		0			0
$595$	−17.4891			−0.716984
$596$	9.55842	+	16.5557i	0.391528	+	0.678147i
$597$		0			0
$598$	−10.3723	+	17.9653i	−0.424154	+	0.734656i
$599$	−19.1168	+	33.1113i	−0.781093	+	1.35289i	0.150212	+	0.988654i	$0.452004\pi$
$599$	−19.1168	+	33.1113i	−0.781093	+	1.35289i	−0.931305	+	0.364239i	$0.881329\pi$
$600$		0			0
$601$	−13.4307	−	23.2627i	−0.547850	−	0.948904i	−0.998422	−	0.0561635i	$-0.982113\pi$
$601$	−13.4307	−	23.2627i	−0.547850	−	0.948904i	0.450572	−	0.892740i	$-0.351220\pi$
$602$	26.9783			1.09955
$603$		0			0
$604$	−10.0000			−0.406894
$605$	4.55842	+	7.89542i	0.185326	+	0.320994i
$606$		0			0
$607$	−0.441578	+	0.764836i	−0.0179231	+	0.0310437i	−0.874848	−	0.484398i	$-0.839039\pi$
$607$	−0.441578	+	0.764836i	−0.0179231	+	0.0310437i	0.856925	+	0.515442i	$0.172372\pi$
$608$	−1.68614	+	2.92048i	−0.0683820	+	0.118441i
$609$		0			0
$610$	−4.55842	−	7.89542i	−0.184565	−	0.319676i
$611$	7.72281			0.312432
$612$		0			0
$613$	−0.233688			−0.00943857			−0.00471928	−	0.999989i	$-0.501502\pi$
$613$	−0.233688			−0.00943857			−0.00471928	+	0.999989i	$0.501502\pi$
$614$	16.6168	+	28.7812i	0.670601	+	1.16152i
$615$		0			0
$616$	−1.62772	+	2.81929i	−0.0655827	+	0.113592i
$617$	−11.0584	+	19.1537i	−0.445195	+	0.771101i	−0.998066	−	0.0621663i	$-0.980199\pi$
$617$	−11.0584	+	19.1537i	−0.445195	+	0.771101i	0.552870	+	0.833267i	$0.313532\pi$
$618$		0			0
$619$	19.0584	+	33.0102i	0.766023	+	1.32679i	0.939704	+	0.341988i	$0.111100\pi$
$619$	19.0584	+	33.0102i	0.766023	+	1.32679i	−0.173682	+	0.984802i	$0.555566\pi$
$620$	−6.74456			−0.270868
$621$		0			0
$622$	9.25544			0.371109
$623$	1.32473	+	2.29451i	0.0530743	+	0.0919275i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−4.68614	+	8.11663i	−0.187296	+	0.324406i
$627$		0			0
$628$	−2.37228	−	4.10891i	−0.0946643	−	0.163963i
$629$	−29.4891			−1.17581
$630$		0			0
$631$	33.7228			1.34248			0.671242	−	0.741238i	$-0.265761\pi$
$631$	33.7228			1.34248			0.671242	+	0.741238i	$0.265761\pi$
$632$	−1.00000	−	1.73205i	−0.0397779	−	0.0688973i
$633$		0			0
$634$	−4.37228	+	7.57301i	−0.173645	+	0.300763i
$635$	−4.55842	+	7.89542i	−0.180895	+	0.313320i
$636$		0			0
$637$	3.25544	+	5.63858i	0.128985	+	0.223409i
$638$	−6.00000			−0.237542
$639$		0			0
$640$	1.00000			0.0395285
$641$	−19.5000	−	33.7750i	−0.770204	−	1.33403i	−0.937451	−	0.348117i	$-0.886821\pi$
$641$	−19.5000	−	33.7750i	−0.770204	−	1.33403i	0.167247	−	0.985915i	$-0.446512\pi$
$642$		0			0
$643$	−5.50000	+	9.52628i	−0.216899	+	0.375680i	−0.953858	−	0.300257i	$-0.902928\pi$
$643$	−5.50000	+	9.52628i	−0.216899	+	0.375680i	0.736959	+	0.675937i	$0.236261\pi$
$644$	5.18614	−	8.98266i	0.204363	−	0.353966i
$645$		0			0
$646$	−12.4307	−	21.5306i	−0.489079	−	0.847111i
$647$	−24.0951			−0.947276			−0.473638	−	0.880720i	$-0.657059\pi$
$647$	−24.0951			−0.947276			−0.473638	+	0.880720i	$0.657059\pi$
$648$		0			0
$649$	−1.88316			−0.0739203
$650$	−2.37228	−	4.10891i	−0.0930485	−	0.161165i
$651$		0			0
$652$	−0.744563	+	1.28962i	−0.0291593	+	0.0505054i
$653$	−18.8614	+	32.6689i	−0.738104	+	1.27843i	0.215244	+	0.976560i	$0.430945\pi$
$653$	−18.8614	+	32.6689i	−0.738104	+	1.27843i	−0.953348	+	0.301873i	$0.902388\pi$
$654$		0			0
$655$	4.37228	+	7.57301i	0.170839	+	0.295902i
$656$	3.00000			0.117130
$657$		0			0
$658$	−3.86141			−0.150533
$659$	−2.74456	−	4.75372i	−0.106913	−	0.185179i	0.807605	−	0.589724i	$-0.200763\pi$
$659$	−2.74456	−	4.75372i	−0.106913	−	0.185179i	−0.914518	+	0.404545i	$0.867430\pi$
$660$		0			0
$661$	−11.1168	+	19.2549i	−0.432395	+	0.748930i	−0.997079	−	0.0763770i	$-0.975665\pi$
$661$	−11.1168	+	19.2549i	−0.432395	+	0.748930i	0.564684	+	0.825307i	$0.308998\pi$
$662$	9.11684	−	15.7908i	0.354336	−	0.613728i
$663$		0			0
$664$	0.813859	+	1.40965i	0.0315839	+	0.0547049i
$665$	−8.00000			−0.310227
$666$		0			0
$667$	19.1168			0.740207
$668$	3.81386	+	6.60580i	0.147563	+	0.255586i
$669$		0			0
$670$	3.50000	−	6.06218i	0.135217	−	0.234202i
$671$	6.25544	−	10.8347i	0.241488	−	0.418270i
$672$		0			0
$673$	5.00000	+	8.66025i	0.192736	+	0.333828i	0.946156	−	0.323711i	$-0.104931\pi$
$673$	5.00000	+	8.66025i	0.192736	+	0.333828i	−0.753420	+	0.657539i	$0.771597\pi$
$674$	3.37228			0.129895
$675$		0			0
$676$	9.51087			0.365803
$677$	−21.8614	−	37.8651i	−0.840202	−	1.45527i	−0.889724	−	0.456500i	$-0.849103\pi$
$677$	−21.8614	−	37.8651i	−0.840202	−	1.45527i	0.0495215	−	0.998773i	$-0.484230\pi$
$678$		0			0
$679$	−3.11684	+	5.39853i	−0.119613	+	0.207177i
$680$	−3.68614	+	6.38458i	−0.141357	+	0.244838i
$681$		0			0
$682$	−4.62772	−	8.01544i	−0.177205	−	0.306927i
$683$	−33.0951			−1.26635			−0.633174	−	0.774009i	$-0.718248\pi$
$683$	−33.0951			−1.26635			−0.633174	+	0.774009i	$0.718248\pi$
$684$		0			0
$685$	1.88316			0.0719517
$686$	−9.93070	−	17.2005i	−0.379156	−	0.656717i
$687$		0			0
$688$	5.68614	−	9.84868i	0.216782	−	0.375478i
$689$	27.2554	−	47.2078i	1.03835	−	1.79847i
$690$		0			0
$691$	0.883156	+	1.52967i	0.0335968	+	0.0581914i	0.882335	−	0.470622i	$-0.155970\pi$
$691$	0.883156	+	1.52967i	0.0335968	+	0.0581914i	−0.848738	+	0.528813i	$0.822637\pi$
$692$	−9.25544			−0.351839
$693$		0			0
$694$	22.1168			0.839544
$695$	−9.05842	−	15.6896i	−0.343606	−	0.595142i
$696$		0			0
$697$	−11.0584	+	19.1537i	−0.418868	+	0.725500i
$698$	−0.441578	+	0.764836i	−0.0167140	+	0.0289495i
$699$		0			0
$700$	1.18614	+	2.05446i	0.0448319	+	0.0776511i
$701$	−14.1386			−0.534007			−0.267004	−	0.963696i	$-0.586034\pi$
$701$	−14.1386			−0.534007			−0.267004	+	0.963696i	$0.586034\pi$
$702$		0			0
$703$	−13.4891			−0.508752
$704$	0.686141	+	1.18843i	0.0258599	+	0.0447907i
$705$		0			0
$706$	15.1753	−	26.2843i	0.571129	−	0.989224i
$707$	10.3723	−	17.9653i	0.390090	−	0.675655i
$708$		0			0
$709$	12.9307	+	22.3966i	0.485623	+	0.841123i	0.999863	−	0.0165226i	$-0.00525955\pi$
$709$	12.9307	+	22.3966i	0.485623	+	0.841123i	−0.514241	+	0.857646i	$0.671926\pi$
$710$	6.00000			0.225176
$711$		0			0
$712$	1.11684			0.0418555
$713$	14.7446	+	25.5383i	0.552188	+	0.956418i
$714$		0			0
$715$	3.25544	−	5.63858i	0.121746	−	0.210871i
$716$	−1.62772	+	2.81929i	−0.0608307	+	0.105362i
$717$		0			0
$718$	2.74456	+	4.75372i	0.102426	+	0.177407i
$719$	38.2337			1.42588			0.712938	−	0.701227i	$-0.247364\pi$
$719$	38.2337			1.42588			0.712938	+	0.701227i	$0.247364\pi$
$720$		0			0
$721$	37.9565			1.41357
$722$	3.81386	+	6.60580i	0.141937	+	0.245842i
$723$		0			0
$724$	3.93070	−	6.80818i	0.146083	−	0.253024i
$725$	−2.18614	+	3.78651i	−0.0811912	+	0.140627i
$726$		0			0
$727$	−0.441578	−	0.764836i	−0.0163772	−	0.0283662i	0.857721	−	0.514116i	$-0.171880\pi$
$727$	−0.441578	−	0.764836i	−0.0163772	−	0.0283662i	−0.874098	+	0.485750i	$0.838547\pi$
$728$	−11.2554			−0.417154
$729$		0			0
$730$	−14.1168			−0.522488
$731$	41.9198	+	72.6073i	1.55046	+	2.68548i
$732$		0			0
$733$	−17.1168	+	29.6472i	−0.632225	+	1.09505i	0.354871	+	0.934915i	$0.384525\pi$
$733$	−17.1168	+	29.6472i	−0.632225	+	1.09505i	−0.987096	+	0.160131i	$0.948808\pi$
$734$	8.00000	−	13.8564i	0.295285	−	0.511449i
$735$		0			0
$736$	−2.18614	−	3.78651i	−0.0805822	−	0.139572i
$737$	9.60597			0.353840
$738$		0			0
$739$	−23.8832			−0.878556			−0.439278	−	0.898351i	$-0.644766\pi$
$739$	−23.8832			−0.878556			−0.439278	+	0.898351i	$0.644766\pi$
$740$	2.00000	+	3.46410i	0.0735215	+	0.127343i
$741$		0			0
$742$	−13.6277	+	23.6039i	−0.500289	+	0.866526i
$743$	12.5584	−	21.7518i	0.460724	−	0.797997i	−0.538273	−	0.842770i	$-0.680923\pi$
$743$	12.5584	−	21.7518i	0.460724	−	0.797997i	0.998997	+	0.0447732i	$0.0142565\pi$
$744$		0			0
$745$	9.55842	+	16.5557i	0.350193	+	0.606553i
$746$	7.48913			0.274196
$747$		0			0
$748$	−10.1168			−0.369908
$749$	17.1861	+	29.7673i	0.627968	+	1.08767i
$750$		0			0
$751$	9.11684	−	15.7908i	0.332678	−	0.576216i	−0.650358	−	0.759628i	$-0.725381\pi$
$751$	9.11684	−	15.7908i	0.332678	−	0.576216i	0.983036	+	0.183412i	$0.0587143\pi$
$752$	−0.813859	+	1.40965i	−0.0296784	+	0.0514045i
$753$		0			0
$754$	−10.3723	−	17.9653i	−0.377736	−	0.654258i
$755$	−10.0000			−0.363937
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$	5.43070	+	9.40625i	0.197252	+	0.341651i
$759$		0			0
$760$	−1.68614	+	2.92048i	−0.0611628	+	0.105937i
$761$	6.04755	−	10.4747i	0.219223	−	0.379706i	−0.735347	−	0.677690i	$-0.762981\pi$
$761$	6.04755	−	10.4747i	0.219223	−	0.379706i	0.954571	+	0.297984i	$0.0963143\pi$
$762$		0			0
$763$	11.4198	+	19.7797i	0.413426	+	0.716074i
$764$	5.48913			0.198590
$765$		0			0
$766$	−22.9783			−0.830238
$767$	−3.25544	−	5.63858i	−0.117547	−	0.203597i
$768$		0			0
$769$	9.06930	−	15.7085i	0.327047	−	0.566462i	−0.654877	−	0.755735i	$-0.727280\pi$
$769$	9.06930	−	15.7085i	0.327047	−	0.566462i	0.981925	+	0.189273i	$0.0606131\pi$
$770$	−1.62772	+	2.81929i	−0.0586589	+	0.101600i
$771$		0			0
$772$	−1.94158	−	3.36291i	−0.0698789	−	0.121034i
$773$	−14.7446			−0.530325			−0.265163	−	0.964204i	$-0.585426\pi$
$773$	−14.7446			−0.530325			−0.265163	+	0.964204i	$0.585426\pi$
$774$		0			0
$775$	−6.74456			−0.242272
$776$	1.31386	+	2.27567i	0.0471648	+	0.0816918i
$777$		0			0
$778$	−5.18614	+	8.98266i	−0.185932	+	0.322044i
$779$	−5.05842	+	8.76144i	−0.181237	+	0.313911i
$780$		0			0
$781$	4.11684	+	7.13058i	0.147312	+	0.255152i
$782$	32.2337			1.15267
$783$		0			0
$784$	−1.37228			−0.0490100
$785$	−2.37228	−	4.10891i	−0.0846704	−	0.146653i
$786$		0			0
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	−0.500953	−	0.865474i	$-0.667017\pi$
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	0.999999	+	0.00110111i	$0.000350496\pi$
$788$	8.74456	−	15.1460i	0.311512	−	0.539555i
$789$		0			0
$790$	−1.00000	−	1.73205i	−0.0355784	−	0.0616236i
$791$	34.9783			1.24368
$792$		0			0
$793$	43.2554			1.53605
$794$	−5.62772	−	9.74749i	−0.199720	−	0.345926i
$795$		0			0
$796$	4.74456	−	8.21782i	0.168167	−	0.291273i
$797$	1.62772	−	2.81929i	0.0576568	−	0.0998644i	−0.835756	−	0.549100i	$-0.814970\pi$
$797$	1.62772	−	2.81929i	0.0576568	−	0.0998644i	0.893413	+	0.449236i	$0.148304\pi$
$798$		0			0
$799$	−6.00000	−	10.3923i	−0.212265	−	0.367653i
$800$	1.00000			0.0353553
$801$		0			0
$802$	−16.1168			−0.569106
$803$	−9.68614	−	16.7769i	−0.341816	−	0.592044i
$804$		0			0
$805$	5.18614	−	8.98266i	0.182787	−	0.316597i
$806$	16.0000	−	27.7128i	0.563576	−	0.976142i
$807$		0			0
$808$	−4.37228	−	7.57301i	−0.153816	−	0.266418i
$809$	12.3505			0.434222			0.217111	−	0.976147i	$-0.430337\pi$
$809$	12.3505			0.434222			0.217111	+	0.976147i	$0.430337\pi$
$810$		0			0
$811$	9.37228			0.329105			0.164553	−	0.986368i	$-0.447382\pi$
$811$	9.37228			0.329105			0.164553	+	0.986368i	$0.447382\pi$
$812$	5.18614	+	8.98266i	0.181998	+	0.315230i
$813$		0			0
$814$	−2.74456	+	4.75372i	−0.0961969	+	0.166618i
$815$	−0.744563	+	1.28962i	−0.0260809	+	0.0451734i
$816$		0			0
$817$	19.1753	+	33.2125i	0.670858	+	1.16196i
$818$	−10.8614			−0.379760
$819$		0			0
$820$	3.00000			0.104765
$821$	25.4198	+	44.0284i	0.887158	+	1.53660i	0.843220	+	0.537569i	$0.180657\pi$
$821$	25.4198	+	44.0284i	0.887158	+	1.53660i	0.0439382	+	0.999034i	$0.486010\pi$
$822$		0			0
$823$	−19.0475	+	32.9913i	−0.663956	+	1.15001i	0.315612	+	0.948888i	$0.397790\pi$
$823$	−19.0475	+	32.9913i	−0.663956	+	1.15001i	−0.979567	+	0.201117i	$0.935543\pi$
$824$	8.00000	−	13.8564i	0.278693	−	0.482711i
$825$		0			0
$826$	1.62772	+	2.81929i	0.0566356	+	0.0980957i
$827$	−8.13859			−0.283007			−0.141503	−	0.989938i	$-0.545194\pi$
$827$	−8.13859			−0.283007			−0.141503	+	0.989938i	$0.545194\pi$
$828$		0			0
$829$	−32.8832			−1.14208			−0.571040	−	0.820923i	$-0.693460\pi$
$829$	−32.8832			−1.14208			−0.571040	+	0.820923i	$0.693460\pi$
$830$	0.813859	+	1.40965i	0.0282495	+	0.0489295i
$831$		0			0
$832$	−2.37228	+	4.10891i	−0.0822441	+	0.142451i
$833$	5.05842	−	8.76144i	0.175264	−	0.303566i
$834$		0			0
$835$	3.81386	+	6.60580i	0.131984	+	0.228603i
$836$	−4.62772			−0.160053
$837$		0			0
$838$	31.7228			1.09585
$839$	22.1168	+	38.3075i	0.763558	+	1.32252i	0.941005	+	0.338391i	$0.109883\pi$
$839$	22.1168	+	38.3075i	0.763558	+	1.32252i	−0.177447	+	0.984130i	$0.556784\pi$
$840$		0			0
$841$	4.94158	−	8.55906i	0.170399	−	0.295140i
$842$	19.2337	−	33.3137i	0.662837	−	1.14807i
$843$		0			0
$844$	3.62772	+	6.28339i	0.124871	+	0.216283i
$845$	9.51087			0.327184
$846$		0			0
$847$	21.6277			0.743137
$848$	5.74456	+	9.94987i	0.197269	+	0.341680i
$849$		0			0
$850$	−3.68614	+	6.38458i	−0.126434	+	0.218989i
$851$	8.74456	−	15.1460i	0.299760	−	0.519199i
$852$		0			0
$853$	0.883156	+	1.52967i	0.0302387	+	0.0523749i	0.880749	−	0.473584i	$-0.157040\pi$
$853$	0.883156	+	1.52967i	0.0302387	+	0.0523749i	−0.850510	+	0.525959i	$0.823707\pi$
$854$	−21.6277			−0.740085
$855$		0			0
$856$	14.4891			0.495228
$857$	11.7446	+	20.3422i	0.401187	+	0.694876i	0.993869	−	0.110560i	$-0.0352646\pi$
$857$	11.7446	+	20.3422i	0.401187	+	0.694876i	−0.592683	+	0.805436i	$0.701931\pi$
$858$		0			0
$859$	−0.0584220	+	0.101190i	−0.00199333	+	0.00345255i	−0.867020	−	0.498273i	$-0.833968\pi$
$859$	−0.0584220	+	0.101190i	−0.00199333	+	0.00345255i	0.865027	+	0.501725i	$0.167301\pi$
$860$	5.68614	−	9.84868i	0.193896	−	0.335837i
$861$		0			0
$862$	−13.1168	−	22.7190i	−0.446761	−	0.773814i
$863$	42.6060			1.45032			0.725162	−	0.688578i	$-0.241765\pi$
$863$	42.6060			1.45032			0.725162	+	0.688578i	$0.241765\pi$
$864$		0			0
$865$	−9.25544			−0.314694
$866$	−0.313859	−	0.543620i	−0.0106654	−	0.0184730i
$867$		0			0
$868$	−8.00000	+	13.8564i	−0.271538	+	0.470317i
$869$	1.37228	−	2.37686i	0.0465515	−	0.0806295i
$870$		0			0
$871$	16.6060	+	28.7624i	0.562672	+	0.974576i
$872$	9.62772			0.326036
$873$		0			0
$874$	14.7446			0.498742
$875$	1.18614	+	2.05446i	0.0400989	+	0.0694533i
$876$		0			0
$877$	27.9783	−	48.4598i	0.944758	−	1.63637i	0.188524	−	0.982069i	$-0.439630\pi$
$877$	27.9783	−	48.4598i	0.944758	−	1.63637i	0.756234	−	0.654301i	$-0.227037\pi$
$878$	−8.11684	+	14.0588i	−0.273930	+	0.474461i
$879$		0			0
$880$	0.686141	+	1.18843i	0.0231298	+	0.0400620i
$881$	−27.3505			−0.921463			−0.460731	−	0.887540i	$-0.652413\pi$
$881$	−27.3505			−0.921463			−0.460731	+	0.887540i	$0.652413\pi$
$882$		0			0
$883$	12.7228			0.428157			0.214078	−	0.976816i	$-0.431325\pi$
$883$	12.7228			0.428157			0.214078	+	0.976816i	$0.431325\pi$
$884$	−17.4891	−	30.2921i	−0.588223	−	1.01883i
$885$		0			0
$886$	−13.2446	+	22.9403i	−0.444960	+	0.770693i
$887$	−18.8614	+	32.6689i	−0.633304	+	1.09691i	0.353568	+	0.935409i	$0.384968\pi$
$887$	−18.8614	+	32.6689i	−0.633304	+	1.09691i	−0.986872	+	0.161506i	$0.948365\pi$
$888$		0			0
$889$	10.8139	+	18.7302i	0.362685	+	0.628189i
$890$	1.11684			0.0374367
$891$		0			0
$892$	12.3723			0.414255
$893$	−2.74456	−	4.75372i	−0.0918433	−	0.159077i
$894$		0			0
$895$	−1.62772	+	2.81929i	−0.0544086	+	0.0942385i
$896$	1.18614	−	2.05446i	0.0396262	−	0.0686346i
$897$		0			0
$898$	−9.43070	−	16.3345i	−0.314707	−	0.545088i
$899$	−29.4891			−0.983517
$900$		0			0
$901$	−84.7011			−2.82180
$902$	2.05842	+	3.56529i	0.0685380	+	0.118711i
$903$		0			0
$904$	7.37228	−	12.7692i	0.245198	−	0.424696i
$905$	3.93070	−	6.80818i	0.130661	−	0.226311i
$906$		0			0
$907$	3.50000	+	6.06218i	0.116216	+	0.201291i	0.918265	−	0.395966i	$-0.129590\pi$
$907$	3.50000	+	6.06218i	0.116216	+	0.201291i	−0.802049	+	0.597258i	$0.796257\pi$
$908$	−1.88316			−0.0624947
$909$		0			0
$910$	−11.2554			−0.373114
$911$	−21.0000	−	36.3731i	−0.695761	−	1.20509i	−0.969923	−	0.243410i	$-0.921734\pi$
$911$	−21.0000	−	36.3731i	−0.695761	−	1.20509i	0.274162	−	0.961683i	$-0.411599\pi$
$912$		0			0
$913$	−1.11684	+	1.93443i	−0.0369621	+	0.0640203i
$914$	−15.0584	+	26.0820i	−0.498088	+	0.862714i
$915$		0			0
$916$	−9.18614	−	15.9109i	−0.303519	−	0.525710i
$917$	20.7446			0.685046
$918$		0			0
$919$	42.4674			1.40087			0.700435	−	0.713716i	$-0.252989\pi$
$919$	42.4674			1.40087			0.700435	+	0.713716i	$0.252989\pi$
$920$	−2.18614	−	3.78651i	−0.0720749	−	0.124837i
$921$		0			0
$922$	9.55842	−	16.5557i	0.314790	−	0.545232i
$923$	−14.2337	+	24.6535i	−0.468508	+	0.811479i
$924$		0			0
$925$	2.00000	+	3.46410i	0.0657596	+	0.113899i
$926$	20.0000			0.657241
$927$		0			0
$928$	4.37228			0.143527
$929$	−19.9783	−	34.6033i	−0.655465	−	1.13530i	−0.981777	−	0.190037i	$-0.939139\pi$
$929$	−19.9783	−	34.6033i	−0.655465	−	1.13530i	0.326312	−	0.945262i	$-0.394194\pi$
$930$		0			0
$931$	2.31386	−	4.00772i	0.0758337	−	0.131348i
$932$	−5.05842	+	8.76144i	−0.165694	+	0.286991i
$933$		0			0
$934$	12.9416	+	22.4155i	0.423461	+	0.733457i
$935$	−10.1168			−0.330856
$936$		0			0
$937$	−17.7228			−0.578979			−0.289490	−	0.957181i	$-0.593486\pi$
$937$	−17.7228			−0.578979			−0.289490	+	0.957181i	$0.593486\pi$
$938$	−8.30298	−	14.3812i	−0.271102	−	0.469563i
$939$		0			0
$940$	−0.813859	+	1.40965i	−0.0265452	+	0.0459776i
$941$	18.8139	−	32.5866i	0.613314	−	1.06229i	−0.377363	−	0.926065i	$-0.623169\pi$
$941$	18.8139	−	32.5866i	0.613314	−	1.06229i	0.990678	−	0.136226i	$-0.0434974\pi$
$942$		0			0
$943$	−6.55842	−	11.3595i	−0.213572	−	0.369917i
$944$	1.37228			0.0446640
$945$		0			0
$946$	15.6060			0.507394
$947$	11.3614	+	19.6785i	0.369196	+	0.639466i	0.989440	−	0.144943i	$-0.0462997\pi$
$947$	11.3614	+	19.6785i	0.369196	+	0.639466i	−0.620244	+	0.784409i	$0.712966\pi$
$948$		0			0
$949$	33.4891	−	58.0049i	1.08710	−	1.88292i
$950$	−1.68614	+	2.92048i	−0.0547056	+	0.0947529i
$951$		0			0
$952$	8.74456	+	15.1460i	0.283413	+	0.490886i
$953$	−30.8614			−0.999699			−0.499850	−	0.866112i	$-0.666611\pi$
$953$	−30.8614			−0.999699			−0.499850	+	0.866112i	$0.666611\pi$
$954$		0			0
$955$	5.48913			0.177624
$956$	−7.37228	−	12.7692i	−0.238437	−	0.412984i
$957$		0			0
$958$	−11.7446	+	20.3422i	−0.379450	+	0.657226i
$959$	2.23369	−	3.86886i	0.0721295	−	0.124932i
$960$		0			0
$961$	−7.24456	−	12.5480i	−0.233696	−	0.404773i
$962$	−18.9783			−0.611883
$963$		0			0
$964$	10.4891			0.337832
$965$	−1.94158	−	3.36291i	−0.0625016	−	0.108256i
$966$		0			0
$967$	−9.44158	+	16.3533i	−0.303621	+	0.525886i	−0.976953	−	0.213453i	$-0.931529\pi$
$967$	−9.44158	+	16.3533i	−0.303621	+	0.525886i	0.673333	+	0.739340i	$0.264862\pi$
$968$	4.55842	−	7.89542i	0.146513	−	0.253768i
$969$		0			0
$970$	1.31386	+	2.27567i	0.0421855	+	0.0730674i
$971$	−22.9783			−0.737407			−0.368704	−	0.929547i	$-0.620198\pi$
$971$	−22.9783			−0.737407			−0.368704	+	0.929547i	$0.620198\pi$
$972$		0			0
$973$	−42.9783			−1.37782
$974$	0.627719	+	1.08724i	0.0201134	+	0.0348374i
$975$		0			0
$976$	−4.55842	+	7.89542i	−0.145912	+	0.252726i
$977$	−20.0584	+	34.7422i	−0.641726	+	1.11150i	0.343322	+	0.939218i	$0.388448\pi$
$977$	−20.0584	+	34.7422i	−0.641726	+	1.11150i	−0.985047	+	0.172284i	$0.944885\pi$
$978$		0			0
$979$	0.766312	+	1.32729i	0.0244914	+	0.0424204i
$980$	−1.37228			−0.0438359
$981$		0			0
$982$	−3.60597			−0.115071
$983$	7.93070	+	13.7364i	0.252950	+	0.438123i	0.964337	−	0.264678i	$-0.0852658\pi$
$983$	7.93070	+	13.7364i	0.252950	+	0.438123i	−0.711387	+	0.702801i	$0.751932\pi$
$984$		0			0
$985$	8.74456	−	15.1460i	0.278625	−	0.482593i
$986$	−16.1168	+	27.9152i	−0.513265	+	0.889001i
$987$		0			0
$988$	−8.00000	−	13.8564i	−0.254514	−	0.440831i
$989$	−49.7228			−1.58109
$990$		0			0
$991$	−18.2337			−0.579212			−0.289606	−	0.957146i	$-0.593524\pi$
$991$	−18.2337			−0.579212			−0.289606	+	0.957146i	$0.593524\pi$
$992$	3.37228	+	5.84096i	0.107070	+	0.185451i
$993$		0			0
$994$	7.11684	−	12.3267i	0.225733	−	0.390980i
$995$	4.74456	−	8.21782i	0.150413	−	0.260523i
$996$		0			0
$997$	−7.00000	−	12.1244i	−0.221692	−	0.383982i	0.733630	−	0.679549i	$-0.237825\pi$
$997$	−7.00000	−	12.1244i	−0.221692	−	0.383982i	−0.955322	+	0.295567i	$0.904491\pi$
$998$	−2.11684			−0.0670075
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.e.c.91.2		4
3.2	odd	2		90.2.e.c.31.1	✓	4
4.3	odd	2		2160.2.q.f.1441.1		4
5.2	odd	4		1350.2.j.f.199.3		8
5.3	odd	4		1350.2.j.f.199.2		8
5.4	even	2		1350.2.e.l.901.1		4
9.2	odd	6		90.2.e.c.61.2	yes	4
9.4	even	3		810.2.a.k.1.1		2
9.5	odd	6		810.2.a.i.1.1		2
9.7	even	3	inner	270.2.e.c.181.2		4
12.11	even	2		720.2.q.f.481.2		4
15.2	even	4		450.2.j.g.49.1		8
15.8	even	4		450.2.j.g.49.4		8
15.14	odd	2		450.2.e.j.301.2		4
36.7	odd	6		2160.2.q.f.721.1		4
36.11	even	6		720.2.q.f.241.1		4
36.23	even	6		6480.2.a.be.1.2		2
36.31	odd	6		6480.2.a.bn.1.2		2
45.2	even	12		450.2.j.g.349.4		8
45.4	even	6		4050.2.a.bo.1.2		2
45.7	odd	12		1350.2.j.f.1099.2		8
45.13	odd	12		4050.2.c.ba.649.2		4
45.14	odd	6		4050.2.a.bw.1.2		2
45.22	odd	12		4050.2.c.ba.649.3		4
45.23	even	12		4050.2.c.v.649.4		4
45.29	odd	6		450.2.e.j.151.1		4
45.32	even	12		4050.2.c.v.649.1		4
45.34	even	6		1350.2.e.l.451.1		4
45.38	even	12		450.2.j.g.349.1		8
45.43	odd	12		1350.2.j.f.1099.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.e.c.31.1	✓	4	3.2	odd	2
90.2.e.c.61.2	yes	4	9.2	odd	6
270.2.e.c.91.2		4	1.1	even	1	trivial
270.2.e.c.181.2		4	9.7	even	3	inner
450.2.e.j.151.1		4	45.29	odd	6
450.2.e.j.301.2		4	15.14	odd	2
450.2.j.g.49.1		8	15.2	even	4
450.2.j.g.49.4		8	15.8	even	4
450.2.j.g.349.1		8	45.38	even	12
450.2.j.g.349.4		8	45.2	even	12
720.2.q.f.241.1		4	36.11	even	6
720.2.q.f.481.2		4	12.11	even	2
810.2.a.i.1.1		2	9.5	odd	6
810.2.a.k.1.1		2	9.4	even	3
1350.2.e.l.451.1		4	45.34	even	6
1350.2.e.l.901.1		4	5.4	even	2
1350.2.j.f.199.2		8	5.3	odd	4
1350.2.j.f.199.3		8	5.2	odd	4
1350.2.j.f.1099.2		8	45.7	odd	12
1350.2.j.f.1099.3		8	45.43	odd	12
2160.2.q.f.721.1		4	36.7	odd	6
2160.2.q.f.1441.1		4	4.3	odd	2
4050.2.a.bo.1.2		2	45.4	even	6
4050.2.a.bw.1.2		2	45.14	odd	6
4050.2.c.v.649.1		4	45.32	even	12
4050.2.c.v.649.4		4	45.23	even	12
4050.2.c.ba.649.2		4	45.13	odd	12
4050.2.c.ba.649.3		4	45.22	odd	12
6480.2.a.be.1.2		2	36.23	even	6
6480.2.a.bn.1.2		2	36.31	odd	6

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.18614 + 2.05446i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.18614 + 2.05446i) q^{7} +1.00000 q^{8} +1.00000 q^{10} +(0.686141 + 1.18843i) q^{11} +(-2.37228 + 4.10891i) q^{13} +(1.18614 - 2.05446i) q^{14} +(-0.500000 - 0.866025i) q^{16} +7.37228 q^{17} +3.37228 q^{19} +(-0.500000 - 0.866025i) q^{20} +(0.686141 - 1.18843i) q^{22} +(-2.18614 + 3.78651i) q^{23} +(-0.500000 - 0.866025i) q^{25} +4.74456 q^{26} -2.37228 q^{28} +(-2.18614 - 3.78651i) q^{29} +(3.37228 - 5.84096i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.68614 - 6.38458i) q^{34} -2.37228 q^{35} -4.00000 q^{37} +(-1.68614 - 2.92048i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(5.68614 + 9.84868i) q^{43} -1.37228 q^{44} +4.37228 q^{46} +(-0.813859 - 1.40965i) q^{47} +(0.686141 - 1.18843i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-2.37228 - 4.10891i) q^{52} -11.4891 q^{53} -1.37228 q^{55} +(1.18614 + 2.05446i) q^{56} +(-2.18614 + 3.78651i) q^{58} +(-0.686141 + 1.18843i) q^{59} +(-4.55842 - 7.89542i) q^{61} -6.74456 q^{62} +1.00000 q^{64} +(-2.37228 - 4.10891i) q^{65} +(3.50000 - 6.06218i) q^{67} +(-3.68614 + 6.38458i) q^{68} +(1.18614 + 2.05446i) q^{70} +6.00000 q^{71} -14.1168 q^{73} +(2.00000 + 3.46410i) q^{74} +(-1.68614 + 2.92048i) q^{76} +(-1.62772 + 2.81929i) q^{77} +(-1.00000 - 1.73205i) q^{79} +1.00000 q^{80} +3.00000 q^{82} +(0.813859 + 1.40965i) q^{83} +(-3.68614 + 6.38458i) q^{85} +(5.68614 - 9.84868i) q^{86} +(0.686141 + 1.18843i) q^{88} +1.11684 q^{89} -11.2554 q^{91} +(-2.18614 - 3.78651i) q^{92} +(-0.813859 + 1.40965i) q^{94} +(-1.68614 + 2.92048i) q^{95} +(1.31386 + 2.27567i) q^{97} -1.37228 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 - q^7 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} + 4 q^{8} + 4 q^{10} - 3 q^{11} + 2 q^{13} - q^{14} - 2 q^{16} + 18 q^{17} + 2 q^{19} - 2 q^{20} - 3 q^{22} - 3 q^{23} - 2 q^{25} - 4 q^{26} + 2 q^{28} - 3 q^{29} + 2 q^{31} - 2 q^{32} - 9 q^{34} + 2 q^{35} - 16 q^{37} - q^{38} - 2 q^{40} - 6 q^{41} + 17 q^{43} + 6 q^{44} + 6 q^{46} - 9 q^{47} - 3 q^{49} - 2 q^{50} + 2 q^{52} + 6 q^{55} - q^{56} - 3 q^{58} + 3 q^{59} - q^{61} - 4 q^{62} + 4 q^{64} + 2 q^{65} + 14 q^{67} - 9 q^{68} - q^{70} + 24 q^{71} - 22 q^{73} + 8 q^{74} - q^{76} - 18 q^{77} - 4 q^{79} + 4 q^{80} + 12 q^{82} + 9 q^{83} - 9 q^{85} + 17 q^{86} - 3 q^{88} - 30 q^{89} - 68 q^{91} - 3 q^{92} - 9 q^{94} - q^{95} + 11 q^{97} + 6 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 - q^7 + 4 * q^8 + 4 * q^10 - 3 * q^11 + 2 * q^13 - q^14 - 2 * q^16 + 18 * q^17 + 2 * q^19 - 2 * q^20 - 3 * q^22 - 3 * q^23 - 2 * q^25 - 4 * q^26 + 2 * q^28 - 3 * q^29 + 2 * q^31 - 2 * q^32 - 9 * q^34 + 2 * q^35 - 16 * q^37 - q^38 - 2 * q^40 - 6 * q^41 + 17 * q^43 + 6 * q^44 + 6 * q^46 - 9 * q^47 - 3 * q^49 - 2 * q^50 + 2 * q^52 + 6 * q^55 - q^56 - 3 * q^58 + 3 * q^59 - q^61 - 4 * q^62 + 4 * q^64 + 2 * q^65 + 14 * q^67 - 9 * q^68 - q^70 + 24 * q^71 - 22 * q^73 + 8 * q^74 - q^76 - 18 * q^77 - 4 * q^79 + 4 * q^80 + 12 * q^82 + 9 * q^83 - 9 * q^85 + 17 * q^86 - 3 * q^88 - 30 * q^89 - 68 * q^91 - 3 * q^92 - 9 * q^94 - q^95 + 11 * q^97 + 6 * q^98

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