LMFDB - Embedded newform 1890.2.l.i.361.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(361,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 4]))

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

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

chi := DirichletCharacter("1890.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.l (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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
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} - x^{15} + 2 x^{14} - 4 x^{13} + 5 x^{12} + 2 x^{11} - 35 x^{10} + 81 x^{9} - 66 x^{8} + \cdots + 6561 $ x^16 - x^15 + 2x^14 - 4x^13 + 5x^12 + 2x^11 - 35x^10 + 81x^9 - 66x^8 + 243x^7 - 315x^6 + 54x^5 + 405x^4 - 972x^3 + 1458x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.4
Root			$-0.579249 - 1.63232i$ of defining polynomial
Character	$\chi$	$=$	1890.361
Dual form			1890.2.l.i.1801.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.445734 + 2.60793i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.445734 + 2.60793i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} -2.29720 q^{11} +(-0.845351 + 1.46419i) q^{13} +(-2.03567 - 1.68998i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.372166 + 0.644610i) q^{17} +(3.89868 + 6.75271i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(1.14860 - 1.98944i) q^{22} -2.15077 q^{23} +1.00000 q^{25} +(-0.845351 - 1.46419i) q^{26} +(2.48140 - 0.917950i) q^{28} +(-2.61618 - 4.53135i) q^{29} +(-2.14860 - 3.72149i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.372166 - 0.644610i) q^{34} +(-0.445734 + 2.60793i) q^{35} +(-5.40503 - 9.36179i) q^{37} -7.79736 q^{38} +1.00000 q^{40} +(2.14946 - 3.72298i) q^{41} +(4.16353 + 7.21144i) q^{43} +(1.14860 + 1.98944i) q^{44} +(1.07539 - 1.86262i) q^{46} +(-4.09118 + 7.08613i) q^{47} +(-6.60264 - 2.32489i) q^{49} +(-0.500000 + 0.866025i) q^{50} +1.69070 q^{52} +(-6.31906 + 10.9449i) q^{53} -2.29720 q^{55} +(-0.445734 + 2.60793i) q^{56} +5.23235 q^{58} +(0.317900 + 0.550619i) q^{59} +(-3.45259 + 5.98007i) q^{61} +4.29720 q^{62} +1.00000 q^{64} +(-0.845351 + 1.46419i) q^{65} +(-4.88563 - 8.46215i) q^{67} +0.744331 q^{68} +(-2.03567 - 1.68998i) q^{70} -2.50553 q^{71} +(-3.42499 + 5.93225i) q^{73} +10.8101 q^{74} +(3.89868 - 6.75271i) q^{76} +(1.02394 - 5.99095i) q^{77} +(4.65402 - 8.06099i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(2.14946 + 3.72298i) q^{82} +(0.645374 + 1.11782i) q^{83} +(-0.372166 + 0.644610i) q^{85} -8.32705 q^{86} -2.29720 q^{88} +(-0.165401 - 0.286482i) q^{89} +(-3.44171 - 2.85726i) q^{91} +(1.07539 + 1.86262i) q^{92} +(-4.09118 - 7.08613i) q^{94} +(3.89868 + 6.75271i) q^{95} +(3.18123 + 5.51006i) q^{97} +(5.31474 - 4.55561i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 8 q^{4} + 16 q^{5} + 4 q^{7} + 16 q^{8}+O(q^{10}) $ 16 * q - 8 * q^2 - 8 * q^4 + 16 * q^5 + 4 * q^7 + 16 * q^8	$ 16 q - 8 q^{2} - 8 q^{4} + 16 q^{5} + 4 q^{7} + 16 q^{8} - 8 q^{10} + 2 q^{11} + 2 q^{13} - 8 q^{14} - 8 q^{16} - 11 q^{17} - 2 q^{19} - 8 q^{20} - q^{22} + 22 q^{23} + 16 q^{25} + 2 q^{26} + 4 q^{28} - 17 q^{29} - 15 q^{31} - 8 q^{32} - 11 q^{34} + 4 q^{35} - 2 q^{37} + 4 q^{38} + 16 q^{40} - 7 q^{41} - 13 q^{43} - q^{44} - 11 q^{46} + 5 q^{47} + 10 q^{49} - 8 q^{50} - 4 q^{52} - 18 q^{53} + 2 q^{55} + 4 q^{56} + 34 q^{58} - q^{59} - 27 q^{61} + 30 q^{62} + 16 q^{64} + 2 q^{65} - 10 q^{67} + 22 q^{68} - 8 q^{70} + 38 q^{71} - 8 q^{73} + 4 q^{74} - 2 q^{76} + 19 q^{77} - 25 q^{79} - 8 q^{80} - 7 q^{82} - 2 q^{83} - 11 q^{85} + 26 q^{86} + 2 q^{88} + 6 q^{89} + 14 q^{91} - 11 q^{92} + 5 q^{94} - 2 q^{95} + 26 q^{97} - 14 q^{98}+O(q^{100}) $ 16 * q - 8 * q^2 - 8 * q^4 + 16 * q^5 + 4 * q^7 + 16 * q^8 - 8 * q^10 + 2 * q^11 + 2 * q^13 - 8 * q^14 - 8 * q^16 - 11 * q^17 - 2 * q^19 - 8 * q^20 - q^22 + 22 * q^23 + 16 * q^25 + 2 * q^26 + 4 * q^28 - 17 * q^29 - 15 * q^31 - 8 * q^32 - 11 * q^34 + 4 * q^35 - 2 * q^37 + 4 * q^38 + 16 * q^40 - 7 * q^41 - 13 * q^43 - q^44 - 11 * q^46 + 5 * q^47 + 10 * q^49 - 8 * q^50 - 4 * q^52 - 18 * q^53 + 2 * q^55 + 4 * q^56 + 34 * q^58 - q^59 - 27 * q^61 + 30 * q^62 + 16 * q^64 + 2 * q^65 - 10 * q^67 + 22 * q^68 - 8 * q^70 + 38 * q^71 - 8 * q^73 + 4 * q^74 - 2 * q^76 + 19 * q^77 - 25 * q^79 - 8 * q^80 - 7 * q^82 - 2 * q^83 - 11 * q^85 + 26 * q^86 + 2 * q^88 + 6 * q^89 + 14 * q^91 - 11 * q^92 + 5 * q^94 - 2 * q^95 + 26 * q^97 - 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	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
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−0.445734	+	2.60793i	−0.168472	+	0.985706i
$7$	−0.445734	+	2.60793i	−0.168472	+	0.985706i
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−2.29720			−0.692633			−0.346316	−	0.938118i	$-0.612568\pi$
$11$	−2.29720			−0.692633			−0.346316	+	0.938118i	$0.612568\pi$
$12$		0			0
$13$	−0.845351	+	1.46419i	−0.234458	+	0.406093i	−0.959115	−	0.283016i	$-0.908665\pi$
$13$	−0.845351	+	1.46419i	−0.234458	+	0.406093i	0.724657	+	0.689110i	$0.241998\pi$
$14$	−2.03567	−	1.68998i	−0.544056	−	0.451667i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.372166	+	0.644610i	−0.0902634	+	0.156341i	−0.907622	−	0.419789i	$-0.862104\pi$
$17$	−0.372166	+	0.644610i	−0.0902634	+	0.156341i	0.817359	+	0.576129i	$0.195438\pi$
$18$		0			0
$19$	3.89868	+	6.75271i	0.894419	+	1.54918i	0.834522	+	0.550974i	$0.185744\pi$
$19$	3.89868	+	6.75271i	0.894419	+	1.54918i	0.0598963	+	0.998205i	$0.480923\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		0			0
$22$	1.14860	−	1.98944i	0.244883	−	0.424149i
$23$	−2.15077			−0.448467			−0.224234	−	0.974535i	$-0.571988\pi$
$23$	−2.15077			−0.448467			−0.224234	+	0.974535i	$0.571988\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−0.845351	−	1.46419i	−0.165787	−	0.287151i
$27$		0			0
$28$	2.48140	−	0.917950i	0.468941	−	0.173476i
$29$	−2.61618	−	4.53135i	−0.485812	−	0.841450i	0.514055	−	0.857757i	$-0.328143\pi$
$29$	−2.61618	−	4.53135i	−0.485812	−	0.841450i	−0.999867	+	0.0163066i	$0.994809\pi$
$30$		0			0
$31$	−2.14860	−	3.72149i	−0.385900	−	0.668399i	0.605993	−	0.795470i	$-0.292776\pi$
$31$	−2.14860	−	3.72149i	−0.385900	−	0.668399i	−0.991894	+	0.127071i	$0.959442\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−0.372166	−	0.644610i	−0.0638259	−	0.110550i
$35$	−0.445734	+	2.60793i	−0.0753428	+	0.440821i
$36$		0			0
$37$	−5.40503	−	9.36179i	−0.888582	−	1.53907i	−0.841553	−	0.540175i	$-0.818358\pi$
$37$	−5.40503	−	9.36179i	−0.888582	−	1.53907i	−0.0470293	−	0.998894i	$-0.514975\pi$
$38$	−7.79736			−1.26490
$39$		0			0
$40$	1.00000			0.158114
$41$	2.14946	−	3.72298i	0.335690	−	0.581431i	−0.647927	−	0.761702i	$-0.724364\pi$
$41$	2.14946	−	3.72298i	0.335690	−	0.581431i	0.983617	+	0.180271i	$0.0576974\pi$
$42$		0			0
$43$	4.16353	+	7.21144i	0.634932	+	1.09973i	0.986530	+	0.163583i	$0.0523051\pi$
$43$	4.16353	+	7.21144i	0.634932	+	1.09973i	−0.351598	+	0.936151i	$0.614362\pi$
$44$	1.14860	+	1.98944i	0.173158	+	0.299919i
$45$		0			0
$46$	1.07539	−	1.86262i	0.158557	−	0.274629i
$47$	−4.09118	+	7.08613i	−0.596760	+	1.03362i	0.396536	+	0.918019i	$0.370212\pi$
$47$	−4.09118	+	7.08613i	−0.596760	+	1.03362i	−0.993296	+	0.115599i	$0.963121\pi$
$48$		0			0
$49$	−6.60264	−	2.32489i	−0.943235	−	0.332127i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$		0			0
$52$	1.69070			0.234458
$53$	−6.31906	+	10.9449i	−0.867990	+	1.50340i	−0.00394299	+	0.999992i	$0.501255\pi$
$53$	−6.31906	+	10.9449i	−0.867990	+	1.50340i	−0.864047	+	0.503411i	$0.832078\pi$
$54$		0			0
$55$	−2.29720			−0.309755
$56$	−0.445734	+	2.60793i	−0.0595638	+	0.348500i
$57$		0			0
$58$	5.23235			0.687041
$59$	0.317900	+	0.550619i	0.0413870	+	0.0716845i	0.885977	−	0.463729i	$-0.153489\pi$
$59$	0.317900	+	0.550619i	0.0413870	+	0.0716845i	−0.844590	+	0.535414i	$0.820156\pi$
$60$		0			0
$61$	−3.45259	+	5.98007i	−0.442059	+	0.765669i	−0.997842	−	0.0656585i	$-0.979085\pi$
$61$	−3.45259	+	5.98007i	−0.442059	+	0.765669i	0.555783	+	0.831327i	$0.312419\pi$
$62$	4.29720			0.545745
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.845351	+	1.46419i	−0.104853	+	0.181610i
$66$		0			0
$67$	−4.88563	−	8.46215i	−0.596874	−	1.03382i	−0.993279	−	0.115741i	$-0.963076\pi$
$67$	−4.88563	−	8.46215i	−0.596874	−	1.03382i	0.396405	−	0.918076i	$-0.370258\pi$
$68$	0.744331			0.0902634
$69$		0			0
$70$	−2.03567	−	1.68998i	−0.243309	−	0.201992i
$71$	−2.50553			−0.297351			−0.148676	−	0.988886i	$-0.547501\pi$
$71$	−2.50553			−0.297351			−0.148676	+	0.988886i	$0.547501\pi$
$72$		0			0
$73$	−3.42499	+	5.93225i	−0.400865	+	0.694318i	−0.993830	−	0.110910i	$-0.964624\pi$
$73$	−3.42499	+	5.93225i	−0.400865	+	0.694318i	0.592966	+	0.805228i	$0.297957\pi$
$74$	10.8101			1.25664
$75$		0			0
$76$	3.89868	−	6.75271i	0.447209	−	0.774589i
$77$	1.02394	−	5.99095i	0.116689	−	0.682732i
$78$		0			0
$79$	4.65402	−	8.06099i	0.523618	−	0.906933i	−0.476004	−	0.879443i	$-0.657915\pi$
$79$	4.65402	−	8.06099i	0.523618	−	0.906933i	0.999622	−	0.0274897i	$-0.00875134\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	2.14946	+	3.72298i	0.237368	+	0.411134i
$83$	0.645374	+	1.11782i	0.0708390	+	0.122697i	0.899269	−	0.437395i	$-0.144099\pi$
$83$	0.645374	+	1.11782i	0.0708390	+	0.122697i	−0.828430	+	0.560092i	$0.810766\pi$
$84$		0			0
$85$	−0.372166	+	0.644610i	−0.0403670	+	0.0699177i
$86$	−8.32705			−0.897929
$87$		0			0
$88$	−2.29720			−0.244883
$89$	−0.165401	−	0.286482i	−0.0175324	−	0.0303671i	0.857126	−	0.515107i	$-0.172248\pi$
$89$	−0.165401	−	0.286482i	−0.0175324	−	0.0303671i	−0.874659	+	0.484740i	$0.838914\pi$
$90$		0			0
$91$	−3.44171	−	2.85726i	−0.360789	−	0.299522i
$92$	1.07539	+	1.86262i	0.112117	+	0.194192i
$93$		0			0
$94$	−4.09118	−	7.08613i	−0.421973	−	0.730878i
$95$	3.89868	+	6.75271i	0.399996	+	0.692814i
$96$		0			0
$97$	3.18123	+	5.51006i	0.323005	+	0.559462i	0.981107	−	0.193468i	$-0.0619735\pi$
$97$	3.18123	+	5.51006i	0.323005	+	0.559462i	−0.658101	+	0.752929i	$0.728640\pi$
$98$	5.31474	−	4.55561i	0.536869	−	0.460186i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−14.8523			−1.47786			−0.738930	−	0.673782i	$-0.764668\pi$
$101$	−14.8523			−1.47786			−0.738930	+	0.673782i	$0.764668\pi$
$102$		0			0
$103$	10.1884			1.00389			0.501947	−	0.864898i	$-0.332617\pi$
$103$	10.1884			1.00389			0.501947	+	0.864898i	$0.332617\pi$
$104$	−0.845351	+	1.46419i	−0.0828934	+	0.143576i
$105$		0			0
$106$	−6.31906	−	10.9449i	−0.613762	−	1.06307i
$107$	6.45353	+	11.1778i	0.623887	+	1.08060i	0.988755	+	0.149544i	$0.0477807\pi$
$107$	6.45353	+	11.1778i	0.623887	+	1.08060i	−0.364868	+	0.931059i	$0.618886\pi$
$108$		0			0
$109$	1.12676	−	1.95161i	0.107924	−	0.186930i	−0.807005	−	0.590545i	$-0.798913\pi$
$109$	1.12676	−	1.95161i	0.107924	−	0.186930i	0.914929	+	0.403614i	$0.132246\pi$
$110$	1.14860	−	1.98944i	0.109515	−	0.189685i
$111$		0			0
$112$	−2.03567	−	1.68998i	−0.192353	−	0.159689i
$113$	−9.72776	+	16.8490i	−0.915111	+	1.58502i	−0.108372	+	0.994110i	$0.534564\pi$
$113$	−9.72776	+	16.8490i	−0.915111	+	1.58502i	−0.806739	+	0.590908i	$0.798770\pi$
$114$		0			0
$115$	−2.15077			−0.200561
$116$	−2.61618	+	4.53135i	−0.242906	+	0.420725i
$117$		0			0
$118$	−0.635800			−0.0585301
$119$	−1.51521	−	1.25791i	−0.138899	−	0.115312i
$120$		0			0
$121$	−5.72286			−0.520260
$122$	−3.45259	−	5.98007i	−0.312583	−	0.541410i
$123$		0			0
$124$	−2.14860	+	3.72149i	−0.192950	+	0.334199i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−12.7583			−1.13212			−0.566058	−	0.824366i	$-0.691532\pi$
$127$	−12.7583			−1.13212			−0.566058	+	0.824366i	$0.691532\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−0.845351	−	1.46419i	−0.0741421	−	0.128418i
$131$	−10.4878			−0.916325			−0.458163	−	0.888868i	$-0.651492\pi$
$131$	−10.4878			−0.916325			−0.458163	+	0.888868i	$0.651492\pi$
$132$		0			0
$133$	−19.3484	+	7.15759i	−1.67772	+	0.620642i
$134$	9.77125			0.844108
$135$		0			0
$136$	−0.372166	+	0.644610i	−0.0319129	+	0.0552748i
$137$	2.19960			0.187924			0.0939621	−	0.995576i	$-0.470047\pi$
$137$	2.19960			0.187924			0.0939621	+	0.995576i	$0.470047\pi$
$138$		0			0
$139$	1.22903	−	2.12875i	0.104245	−	0.180558i	−0.809184	−	0.587555i	$-0.800091\pi$
$139$	1.22903	−	2.12875i	0.104245	−	0.180558i	0.913430	+	0.406997i	$0.133424\pi$
$140$	2.48140	−	0.917950i	0.209717	−	0.0775809i
$141$		0			0
$142$	1.25276	−	2.16985i	0.105130	−	0.182090i
$143$	1.94194	−	3.36354i	0.162393	−	0.281273i
$144$		0			0
$145$	−2.61618	−	4.53135i	−0.217262	−	0.376308i
$146$	−3.42499	−	5.93225i	−0.283454	−	0.490957i
$147$		0			0
$148$	−5.40503	+	9.36179i	−0.444291	+	0.769534i
$149$	−10.2164			−0.836957			−0.418479	−	0.908227i	$-0.637437\pi$
$149$	−10.2164			−0.836957			−0.418479	+	0.908227i	$0.637437\pi$
$150$		0			0
$151$	−2.80320			−0.228121			−0.114061	−	0.993474i	$-0.536386\pi$
$151$	−2.80320			−0.228121			−0.114061	+	0.993474i	$0.536386\pi$
$152$	3.89868	+	6.75271i	0.316225	+	0.547717i
$153$		0			0
$154$	4.67635	+	3.88224i	0.376831	+	0.312840i
$155$	−2.14860	−	3.72149i	−0.172580	−	0.298917i
$156$		0			0
$157$	−3.07725	−	5.32996i	−0.245592	−	0.425377i	0.716706	−	0.697375i	$-0.245649\pi$
$157$	−3.07725	−	5.32996i	−0.245592	−	0.425377i	−0.962298	+	0.271998i	$0.912316\pi$
$158$	4.65402	+	8.06099i	0.370254	+	0.641298i
$159$		0			0
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	0.958673	−	5.60907i	0.0755540	−	0.442057i
$162$		0			0
$163$	2.75802	+	4.77703i	0.216025	+	0.374166i	0.953589	−	0.301111i	$-0.0973574\pi$
$163$	2.75802	+	4.77703i	0.216025	+	0.374166i	−0.737564	+	0.675277i	$0.764024\pi$
$164$	−4.29892			−0.335690
$165$		0			0
$166$	−1.29075			−0.100182
$167$	−5.03727	+	8.72480i	−0.389795	+	0.675145i	−0.992422	−	0.122878i	$-0.960788\pi$
$167$	−5.03727	+	8.72480i	−0.389795	+	0.675145i	0.602626	+	0.798023i	$0.294121\pi$
$168$		0			0
$169$	5.07076	+	8.78282i	0.390059	+	0.675602i
$170$	−0.372166	−	0.644610i	−0.0285438	−	0.0494393i
$171$		0			0
$172$	4.16353	−	7.21144i	0.317466	−	0.549867i
$173$	10.3894	−	17.9951i	0.789895	−	1.36814i	−0.136136	−	0.990690i	$-0.543468\pi$
$173$	10.3894	−	17.9951i	0.789895	−	1.36814i	0.926031	−	0.377448i	$-0.123198\pi$
$174$		0			0
$175$	−0.445734	+	2.60793i	−0.0336943	+	0.197141i
$176$	1.14860	−	1.98944i	0.0865791	−	0.149959i
$177$		0			0
$178$	0.330801			0.0247946
$179$	−1.39534	+	2.41679i	−0.104292	+	0.180640i	−0.913449	−	0.406954i	$-0.866591\pi$
$179$	−1.39534	+	2.41679i	−0.104292	+	0.180640i	0.809157	+	0.587593i	$0.199924\pi$
$180$		0			0
$181$	−22.2958			−1.65723			−0.828616	−	0.559817i	$-0.810871\pi$
$181$	−22.2958			−1.65723			−0.828616	+	0.559817i	$0.810871\pi$
$182$	4.19531	−	1.55198i	0.310977	−	0.115040i
$183$		0			0
$184$	−2.15077			−0.158557
$185$	−5.40503	−	9.36179i	−0.397386	−	0.688292i
$186$		0			0
$187$	0.854940	−	1.48080i	0.0625194	−	0.108287i
$188$	8.18236			0.596760
$189$		0			0
$190$	−7.79736			−0.565680
$191$	7.25620	−	12.5681i	0.525040	−	0.909396i	−0.474535	−	0.880237i	$-0.657384\pi$
$191$	7.25620	−	12.5681i	0.525040	−	0.909396i	0.999575	−	0.0291593i	$-0.00928300\pi$
$192$		0			0
$193$	−3.16439	−	5.48089i	−0.227778	−	0.394523i	0.729371	−	0.684118i	$-0.239813\pi$
$193$	−3.16439	−	5.48089i	−0.227778	−	0.394523i	−0.957149	+	0.289595i	$0.906479\pi$
$194$	−6.36247			−0.456798
$195$		0			0
$196$	1.28791	+	6.88050i	0.0919933	+	0.491464i
$197$	9.15021			0.651925			0.325963	−	0.945383i	$-0.394312\pi$
$197$	9.15021			0.651925			0.325963	+	0.945383i	$0.394312\pi$
$198$		0			0
$199$	2.96846	−	5.14152i	0.210428	−	0.364472i	−0.741420	−	0.671041i	$-0.765847\pi$
$199$	2.96846	−	5.14152i	0.210428	−	0.364472i	0.951849	+	0.306568i	$0.0991808\pi$
$200$	1.00000			0.0707107
$201$		0			0
$202$	7.42615	−	12.8625i	0.522502	−	0.905000i
$203$	12.9836	−	4.80304i	0.911269	−	0.337107i
$204$		0			0
$205$	2.14946	−	3.72298i	0.150125	−	0.260024i
$206$	−5.09421	+	8.82343i	−0.354930	+	0.614757i
$207$		0			0
$208$	−0.845351	−	1.46419i	−0.0586145	−	0.101523i
$209$	−8.95606	−	15.5123i	−0.619504	−	1.07301i
$210$		0			0
$211$	−7.14767	+	12.3801i	−0.492066	+	0.852283i	−0.999958	−	0.00913776i	$-0.997091\pi$
$211$	−7.14767	+	12.3801i	−0.492066	+	0.852283i	0.507893	+	0.861420i	$0.330425\pi$
$212$	12.6381			0.867990
$213$		0			0
$214$	−12.9071			−0.882309
$215$	4.16353	+	7.21144i	0.283950	+	0.491816i
$216$		0			0
$217$	10.6631	−	3.94462i	0.723858	−	0.267778i
$218$	1.12676	+	1.95161i	0.0763139	+	0.132180i
$219$		0			0
$220$	1.14860	+	1.98944i	0.0774387	+	0.134128i
$221$	−0.629221	−	1.08984i	−0.0423260	−	0.0733107i
$222$		0			0
$223$	−8.91331	−	15.4383i	−0.596879	−	1.03383i	−0.993279	−	0.115747i	$-0.963074\pi$
$223$	−8.91331	−	15.4383i	−0.596879	−	1.03383i	0.396399	−	0.918078i	$-0.370260\pi$
$224$	2.48140	−	0.917950i	0.165796	−	0.0613331i
$225$		0			0
$226$	−9.72776	−	16.8490i	−0.647081	−	1.12078i
$227$	20.7505			1.37726			0.688629	−	0.725113i	$-0.258213\pi$
$227$	20.7505			1.37726			0.688629	+	0.725113i	$0.258213\pi$
$228$		0			0
$229$	20.1208			1.32962			0.664811	−	0.747012i	$-0.268512\pi$
$229$	20.1208			1.32962			0.664811	+	0.747012i	$0.268512\pi$
$230$	1.07539	−	1.86262i	0.0709089	−	0.122818i
$231$		0			0
$232$	−2.61618	−	4.53135i	−0.171760	−	0.297498i
$233$	−7.70836	−	13.3513i	−0.504992	−	0.874671i	−0.999983	−	0.00577334i	$-0.998162\pi$
$233$	−7.70836	−	13.3513i	−0.504992	−	0.874671i	0.494992	−	0.868898i	$-0.335171\pi$
$234$		0			0
$235$	−4.09118	+	7.08613i	−0.266879	+	0.462248i
$236$	0.317900	−	0.550619i	0.0206935	−	0.0358422i
$237$		0			0
$238$	1.84699	−	0.683259i	0.119722	−	0.0442891i
$239$	−9.63173	+	16.6826i	−0.623025	+	1.07911i	0.365895	+	0.930656i	$0.380763\pi$
$239$	−9.63173	+	16.6826i	−0.623025	+	1.07911i	−0.988919	+	0.148454i	$0.952570\pi$
$240$		0			0
$241$	26.6335			1.71561			0.857807	−	0.513973i	$-0.171827\pi$
$241$	26.6335			1.71561			0.857807	+	0.513973i	$0.171827\pi$
$242$	2.86143	−	4.95614i	0.183940	−	0.318593i
$243$		0			0
$244$	6.90519			0.442059
$245$	−6.60264	−	2.32489i	−0.421827	−	0.148532i
$246$		0			0
$247$	−13.1830			−0.838815
$248$	−2.14860	−	3.72149i	−0.136436	−	0.236315i
$249$		0			0
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−12.9943			−0.820191			−0.410095	−	0.912043i	$-0.634505\pi$
$251$	−12.9943			−0.820191			−0.410095	+	0.912043i	$0.634505\pi$
$252$		0			0
$253$	4.94076			0.310623
$254$	6.37915	−	11.0490i	0.400263	−	0.693276i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−25.1123			−1.56646			−0.783230	−	0.621732i	$-0.786429\pi$
$257$	−25.1123			−1.56646			−0.783230	+	0.621732i	$0.786429\pi$
$258$		0			0
$259$	26.8241	−	9.92310i	1.66677	−	0.616591i
$260$	1.69070			0.104853
$261$		0			0
$262$	5.24391	−	9.08272i	0.323970	−	0.561132i
$263$	25.8647			1.59489			0.797444	−	0.603393i	$-0.206185\pi$
$263$	25.8647			1.59489			0.797444	+	0.603393i	$0.206185\pi$
$264$		0			0
$265$	−6.31906	+	10.9449i	−0.388177	+	0.672342i
$266$	3.47555	−	20.3350i	0.213100	−	1.24682i
$267$		0			0
$268$	−4.88563	+	8.46215i	−0.298437	+	0.516908i
$269$	−5.30556	+	9.18949i	−0.323485	+	0.560293i	−0.981205	−	0.192970i	$-0.938188\pi$
$269$	−5.30556	+	9.18949i	−0.323485	+	0.560293i	0.657719	+	0.753263i	$0.271521\pi$
$270$		0			0
$271$	6.58607	+	11.4074i	0.400075	+	0.692951i	0.993735	−	0.111766i	$-0.0356506\pi$
$271$	6.58607	+	11.4074i	0.400075	+	0.692951i	−0.593659	+	0.804716i	$0.702317\pi$
$272$	−0.372166	−	0.644610i	−0.0225659	−	0.0390852i
$273$		0			0
$274$	−1.09980	+	1.90491i	−0.0664412	+	0.115080i
$275$	−2.29720			−0.138527
$276$		0			0
$277$	31.7253			1.90619			0.953096	−	0.302669i	$-0.0978776\pi$
$277$	31.7253			1.90619			0.953096	+	0.302669i	$0.0978776\pi$
$278$	1.22903	+	2.12875i	0.0737126	+	0.127674i
$279$		0			0
$280$	−0.445734	+	2.60793i	−0.0266377	+	0.155854i
$281$	−10.3107	−	17.8586i	−0.615084	−	1.06536i	−0.990370	−	0.138448i	$-0.955789\pi$
$281$	−10.3107	−	17.8586i	−0.615084	−	1.06536i	0.375285	−	0.926909i	$-0.377545\pi$
$282$		0			0
$283$	2.17512	+	3.76742i	0.129298	+	0.223950i	0.923405	−	0.383828i	$-0.125394\pi$
$283$	2.17512	+	3.76742i	0.129298	+	0.223950i	−0.794107	+	0.607778i	$0.792061\pi$
$284$	1.25276	+	2.16985i	0.0743379	+	0.128757i
$285$		0			0
$286$	1.94194	+	3.36354i	0.114829	+	0.198890i
$287$	8.75119	+	7.26511i	0.516566	+	0.428846i
$288$		0			0
$289$	8.22299	+	14.2426i	0.483705	+	0.837802i
$290$	5.23235			0.307254
$291$		0			0
$292$	6.84998			0.400865
$293$	0.408724	−	0.707931i	0.0238779	−	0.0413578i	−0.853840	−	0.520536i	$-0.825732\pi$
$293$	0.408724	−	0.707931i	0.0238779	−	0.0413578i	0.877717	+	0.479179i	$0.159065\pi$
$294$		0			0
$295$	0.317900	+	0.550619i	0.0185088	+	0.0320583i
$296$	−5.40503	−	9.36179i	−0.314161	−	0.544143i
$297$		0			0
$298$	5.10818	−	8.84763i	0.295909	−	0.512530i
$299$	1.81816	−	3.14914i	0.105147	−	0.182119i
$300$		0			0
$301$	−20.6628	+	7.64382i	−1.19098	+	0.440582i
$302$	1.40160	−	2.42764i	0.0806530	−	0.139695i
$303$		0			0
$304$	−7.79736			−0.447209
$305$	−3.45259	+	5.98007i	−0.197695	+	0.342418i
$306$		0			0
$307$	10.7190			0.611765			0.305882	−	0.952069i	$-0.401049\pi$
$307$	10.7190			0.611765			0.305882	+	0.952069i	$0.401049\pi$
$308$	−5.70029	+	2.10872i	−0.324804	+	0.120155i
$309$		0			0
$310$	4.29720			0.244065
$311$	−1.63811	−	2.83728i	−0.0928884	−	0.160887i	0.815837	−	0.578282i	$-0.196277\pi$
$311$	−1.63811	−	2.83728i	−0.0928884	−	0.160887i	−0.908725	+	0.417395i	$0.862943\pi$
$312$		0			0
$313$	−11.4284	+	19.7946i	−0.645971	+	1.11885i	0.338106	+	0.941108i	$0.390214\pi$
$313$	−11.4284	+	19.7946i	−0.645971	+	1.11885i	−0.984076	+	0.177746i	$0.943119\pi$
$314$	6.15451			0.347319
$315$		0			0
$316$	−9.30803			−0.523618
$317$	−11.5134	+	19.9418i	−0.646657	+	1.12004i	0.337259	+	0.941412i	$0.390500\pi$
$317$	−11.5134	+	19.9418i	−0.646657	+	1.12004i	−0.983916	+	0.178631i	$0.942833\pi$
$318$		0			0
$319$	6.00988	+	10.4094i	0.336489	+	0.582816i
$320$	1.00000			0.0559017
$321$		0			0
$322$	4.37826	+	3.63477i	0.243991	+	0.202558i
$323$	−5.80382			−0.322933
$324$		0			0
$325$	−0.845351	+	1.46419i	−0.0468916	+	0.0812187i
$326$	−5.51604			−0.305505
$327$		0			0
$328$	2.14946	−	3.72298i	0.118684	−	0.205567i
$329$	−16.6566	−	13.8281i	−0.918307	−	0.762365i
$330$		0			0
$331$	12.0210	−	20.8209i	0.660732	−	1.14442i	−0.319691	−	0.947522i	$-0.603579\pi$
$331$	12.0210	−	20.8209i	0.660732	−	1.14442i	0.980424	−	0.196900i	$-0.0630874\pi$
$332$	0.645374	−	1.11782i	0.0354195	−	0.0613484i
$333$		0			0
$334$	−5.03727	−	8.72480i	−0.275627	−	0.477400i
$335$	−4.88563	−	8.46215i	−0.266930	−	0.462337i
$336$		0			0
$337$	2.92411	−	5.06471i	0.159287	−	0.275892i	−0.775325	−	0.631562i	$-0.782414\pi$
$337$	2.92411	−	5.06471i	0.159287	−	0.275892i	0.934612	+	0.355670i	$0.115747\pi$
$338$	−10.1415			−0.551626
$339$		0			0
$340$	0.744331			0.0403670
$341$	4.93577	+	8.54901i	0.267287	+	0.462955i
$342$		0			0
$343$	9.00619	−	16.1830i	0.486288	−	0.873798i
$344$	4.16353	+	7.21144i	0.224482	+	0.388815i
$345$		0			0
$346$	10.3894	+	17.9951i	0.558540	+	0.967420i
$347$	16.2261	+	28.1045i	0.871065	+	1.50873i	0.860896	+	0.508780i	$0.169903\pi$
$347$	16.2261	+	28.1045i	0.871065	+	1.50873i	0.0101686	+	0.999948i	$0.496763\pi$
$348$		0			0
$349$	−1.58495	−	2.74522i	−0.0848405	−	0.146948i	0.820483	−	0.571671i	$-0.193705\pi$
$349$	−1.58495	−	2.74522i	−0.0848405	−	0.146948i	−0.905323	+	0.424723i	$0.860371\pi$
$350$	−2.03567	−	1.68998i	−0.108811	−	0.0903335i
$351$		0			0
$352$	1.14860	+	1.98944i	0.0612207	+	0.106037i
$353$	13.0300			0.693518			0.346759	−	0.937954i	$-0.387282\pi$
$353$	13.0300			0.693518			0.346759	+	0.937954i	$0.387282\pi$
$354$		0			0
$355$	−2.50553			−0.132980
$356$	−0.165401	+	0.286482i	−0.00876622	+	0.0151835i
$357$		0			0
$358$	−1.39534	−	2.41679i	−0.0737458	−	0.127732i
$359$	−3.51577	−	6.08949i	−0.185555	−	0.321391i	0.758208	−	0.652012i	$-0.226075\pi$
$359$	−3.51577	−	6.08949i	−0.185555	−	0.321391i	−0.943763	+	0.330621i	$0.892742\pi$
$360$		0			0
$361$	−20.8994	+	36.1989i	−1.09997	+	1.90520i
$362$	11.1479	−	19.3087i	0.585920	−	1.01484i
$363$		0			0
$364$	−0.753603	+	4.40924i	−0.0394996	+	0.231107i
$365$	−3.42499	+	5.93225i	−0.179272	+	0.310508i
$366$		0			0
$367$	9.43352			0.492426			0.246213	−	0.969216i	$-0.420814\pi$
$367$	9.43352			0.492426			0.246213	+	0.969216i	$0.420814\pi$
$368$	1.07539	−	1.86262i	0.0560584	−	0.0970960i
$369$		0			0
$370$	10.8101			0.561988
$371$	−25.7271	−	21.3582i	−1.33568	−	1.10886i
$372$		0			0
$373$	37.7256			1.95336			0.976678	−	0.214707i	$-0.0688797\pi$
$373$	37.7256			1.95336			0.976678	+	0.214707i	$0.0688797\pi$
$374$	0.854940	+	1.48080i	0.0442079	+	0.0765703i
$375$		0			0
$376$	−4.09118	+	7.08613i	−0.210986	+	0.365439i
$377$	8.84634			0.455610
$378$		0			0
$379$	6.94296			0.356636			0.178318	−	0.983973i	$-0.442934\pi$
$379$	6.94296			0.356636			0.178318	+	0.983973i	$0.442934\pi$
$380$	3.89868	−	6.75271i	0.199998	−	0.346407i
$381$		0			0
$382$	7.25620	+	12.5681i	0.371259	+	0.643040i
$383$	27.1762			1.38864			0.694320	−	0.719667i	$-0.255705\pi$
$383$	27.1762			1.38864			0.694320	+	0.719667i	$0.255705\pi$
$384$		0			0
$385$	1.02394	−	5.99095i	0.0521849	−	0.305327i
$386$	6.32879			0.322127
$387$		0			0
$388$	3.18123	−	5.51006i	0.161503	−	0.279731i
$389$	27.0881			1.37342			0.686710	−	0.726931i	$-0.259054\pi$
$389$	27.0881			1.37342			0.686710	+	0.726931i	$0.259054\pi$
$390$		0			0
$391$	0.800444	−	1.38641i	0.0404802	−	0.0701137i
$392$	−6.60264	−	2.32489i	−0.333484	−	0.117425i
$393$		0			0
$394$	−4.57510	+	7.92431i	−0.230490	+	0.399221i
$395$	4.65402	−	8.06099i	0.234169	−	0.405593i
$396$		0			0
$397$	18.7475	+	32.4716i	0.940908	+	1.62970i	0.763744	+	0.645519i	$0.223359\pi$
$397$	18.7475	+	32.4716i	0.940908	+	1.62970i	0.177164	+	0.984181i	$0.443308\pi$
$398$	2.96846	+	5.14152i	0.148795	+	0.257721i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	12.6852			0.633469			0.316735	−	0.948514i	$-0.397414\pi$
$401$	12.6852			0.633469			0.316735	+	0.948514i	$0.397414\pi$
$402$		0			0
$403$	7.26528			0.361910
$404$	7.42615	+	12.8625i	0.369465	+	0.639932i
$405$		0			0
$406$	−2.33224	+	13.6456i	−0.115747	+	0.677221i
$407$	12.4165	+	21.5059i	0.615461	+	1.06601i
$408$		0			0
$409$	−6.01056	−	10.4106i	−0.297203	−	0.514771i	0.678292	−	0.734793i	$-0.262721\pi$
$409$	−6.01056	−	10.4106i	−0.297203	−	0.514771i	−0.975495	+	0.220022i	$0.929387\pi$
$410$	2.14946	+	3.72298i	0.106154	+	0.183865i
$411$		0			0
$412$	−5.09421	−	8.82343i	−0.250974	−	0.434699i
$413$	−1.57768	+	0.583632i	−0.0776324	+	0.0287187i
$414$		0			0
$415$	0.645374	+	1.11782i	0.0316802	+	0.0548717i
$416$	1.69070			0.0828934
$417$		0			0
$418$	17.9121			0.876110
$419$	0.923993	−	1.60040i	0.0451400	−	0.0781848i	−0.842573	−	0.538583i	$-0.818960\pi$
$419$	0.923993	−	1.60040i	0.0451400	−	0.0781848i	0.887713	+	0.460398i	$0.152293\pi$
$420$		0			0
$421$	−3.88451	−	6.72817i	−0.189320	−	0.327911i	0.755704	−	0.654913i	$-0.227295\pi$
$421$	−3.88451	−	6.72817i	−0.189320	−	0.327911i	−0.945024	+	0.327002i	$0.893962\pi$
$422$	−7.14767	−	12.3801i	−0.347943	−	0.602655i
$423$		0			0
$424$	−6.31906	+	10.9449i	−0.306881	+	0.531533i
$425$	−0.372166	+	0.644610i	−0.0180527	+	0.0312682i
$426$		0			0
$427$	−14.0567	−	11.6697i	−0.680250	−	0.564734i
$428$	6.45353	−	11.1778i	0.311943	−	0.540302i
$429$		0			0
$430$	−8.32705			−0.401566
$431$	−6.54581	+	11.3377i	−0.315301	+	0.546117i	−0.979501	−	0.201437i	$-0.935439\pi$
$431$	−6.54581	+	11.3377i	−0.315301	+	0.546117i	0.664201	+	0.747554i	$0.268772\pi$
$432$		0			0
$433$	−29.2502			−1.40567			−0.702836	−	0.711352i	$-0.748083\pi$
$433$	−29.2502			−1.40567			−0.702836	+	0.711352i	$0.748083\pi$
$434$	−1.91541	+	11.2068i	−0.0919426	+	0.537945i
$435$		0			0
$436$	−2.25352			−0.107924
$437$	−8.38518	−	14.5236i	−0.401117	−	0.694756i
$438$		0			0
$439$	7.47257	−	12.9429i	0.356646	−	0.617730i	−0.630752	−	0.775985i	$-0.717253\pi$
$439$	7.47257	−	12.9429i	0.356646	−	0.617730i	0.987398	+	0.158255i	$0.0505868\pi$
$440$	−2.29720			−0.109515
$441$		0			0
$442$	1.25844			0.0598580
$443$	−11.6420	+	20.1645i	−0.553127	+	0.958045i	0.444919	+	0.895571i	$0.353232\pi$
$443$	−11.6420	+	20.1645i	−0.553127	+	0.958045i	−0.998047	+	0.0624740i	$0.980101\pi$
$444$		0			0
$445$	−0.165401	−	0.286482i	−0.00784074	−	0.0135806i
$446$	17.8266			0.844115
$447$		0			0
$448$	−0.445734	+	2.60793i	−0.0210590	+	0.123213i
$449$	13.2825			0.626839			0.313419	−	0.949615i	$-0.398525\pi$
$449$	13.2825			0.626839			0.313419	+	0.949615i	$0.398525\pi$
$450$		0			0
$451$	−4.93775	+	8.55243i	−0.232510	+	0.402718i
$452$	19.4555			0.915111
$453$		0			0
$454$	−10.3752	+	17.9705i	−0.486935	+	0.843395i
$455$	−3.44171	−	2.85726i	−0.161350	−	0.133950i
$456$		0			0
$457$	−17.5492	+	30.3961i	−0.820916	+	1.42187i	0.0840843	+	0.996459i	$0.473203\pi$
$457$	−17.5492	+	30.3961i	−0.820916	+	1.42187i	−0.905001	+	0.425410i	$0.860130\pi$
$458$	−10.0604	+	17.4251i	−0.470092	+	0.814223i
$459$		0			0
$460$	1.07539	+	1.86262i	0.0501401	+	0.0868453i
$461$	4.53012	+	7.84640i	0.210989	+	0.365443i	0.952024	−	0.306023i	$-0.0989983\pi$
$461$	4.53012	+	7.84640i	0.210989	+	0.365443i	−0.741036	+	0.671466i	$0.765665\pi$
$462$		0			0
$463$	−21.1130	+	36.5688i	−0.981204	+	1.69950i	−0.323484	+	0.946234i	$0.604854\pi$
$463$	−21.1130	+	36.5688i	−0.981204	+	1.69950i	−0.657721	+	0.753262i	$0.728479\pi$
$464$	5.23235			0.242906
$465$		0			0
$466$	15.4167			0.714166
$467$	−5.26870	−	9.12565i	−0.243806	−	0.422285i	0.717989	−	0.696054i	$-0.245063\pi$
$467$	−5.26870	−	9.12565i	−0.243806	−	0.422285i	−0.961795	+	0.273770i	$0.911729\pi$
$468$		0			0
$469$	24.2464	−	8.96952i	1.11960	−	0.414174i
$470$	−4.09118	−	7.08613i	−0.188712	−	0.326859i
$471$		0			0
$472$	0.317900	+	0.550619i	0.0146325	+	0.0253443i
$473$	−9.56446	−	16.5661i	−0.439774	−	0.761712i
$474$		0			0
$475$	3.89868	+	6.75271i	0.178884	+	0.309836i
$476$	−0.331774	+	1.94117i	−0.0152068	+	0.0889732i
$477$		0			0
$478$	−9.63173	−	16.6826i	−0.440545	−	0.763046i
$479$	37.4257			1.71002			0.855011	−	0.518610i	$-0.173550\pi$
$479$	37.4257			1.71002			0.855011	+	0.518610i	$0.173550\pi$
$480$		0			0
$481$	18.2766			0.833341
$482$	−13.3167	+	23.0653i	−0.606561	+	1.05059i
$483$		0			0
$484$	2.86143	+	4.95614i	0.130065	+	0.225279i
$485$	3.18123	+	5.51006i	0.144452	+	0.250199i
$486$		0			0
$487$	7.69208	−	13.3231i	0.348561	−	0.603726i	−0.637433	−	0.770506i	$-0.720004\pi$
$487$	7.69208	−	13.3231i	0.348561	−	0.603726i	0.985994	+	0.166780i	$0.0533370\pi$
$488$	−3.45259	+	5.98007i	−0.156292	+	0.270705i
$489$		0			0
$490$	5.31474	−	4.55561i	0.240095	−	0.205801i
$491$	−11.7768	+	20.3981i	−0.531481	+	0.920551i	0.467844	+	0.883811i	$0.345031\pi$
$491$	−11.7768	+	20.3981i	−0.531481	+	0.920551i	−0.999325	+	0.0367405i	$0.988303\pi$
$492$		0			0
$493$	3.89460			0.175404
$494$	6.59150	−	11.4168i	0.296566	−	0.513667i
$495$		0			0
$496$	4.29720			0.192950
$497$	1.11680	−	6.53425i	0.0500953	−	0.293101i
$498$		0			0
$499$	−6.86763			−0.307437			−0.153719	−	0.988115i	$-0.549125\pi$
$499$	−6.86763			−0.307437			−0.153719	+	0.988115i	$0.549125\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$		0			0
$502$	6.49713	−	11.2534i	0.289981	−	0.502262i
$503$	19.9980			0.891665			0.445833	−	0.895116i	$-0.352908\pi$
$503$	19.9980			0.891665			0.445833	+	0.895116i	$0.352908\pi$
$504$		0			0
$505$	−14.8523			−0.660919
$506$	−2.47038	+	4.27882i	−0.109822	+	0.190217i
$507$		0			0
$508$	6.37915	+	11.0490i	0.283029	+	0.490220i
$509$	4.31010			0.191042			0.0955210	−	0.995427i	$-0.469548\pi$
$509$	4.31010			0.191042			0.0955210	+	0.995427i	$0.469548\pi$
$510$		0			0
$511$	−13.9443	−	11.5764i	−0.616859	−	0.512108i
$512$	1.00000			0.0441942
$513$		0			0
$514$	12.5561	−	21.7479i	0.553827	−	0.959257i
$515$	10.1884			0.448955
$516$		0			0
$517$	9.39826	−	16.2783i	0.413335	−	0.715918i
$518$	−4.81842	+	28.1919i	−0.211709	+	1.23868i
$519$		0			0
$520$	−0.845351	+	1.46419i	−0.0370711	+	0.0642090i
$521$	9.77625	−	16.9330i	0.428305	−	0.741847i	−0.568417	−	0.822740i	$-0.692444\pi$
$521$	9.77625	−	16.9330i	0.428305	−	0.741847i	0.996723	+	0.0808936i	$0.0257774\pi$
$522$		0			0
$523$	13.2331	+	22.9204i	0.578643	+	1.00224i	0.995635	+	0.0933291i	$0.0297509\pi$
$523$	13.2331	+	22.9204i	0.578643	+	1.00224i	−0.416992	+	0.908910i	$0.636916\pi$
$524$	5.24391	+	9.08272i	0.229081	+	0.396780i
$525$		0			0
$526$	−12.9324	+	22.3995i	−0.563878	+	0.976666i
$527$	3.19854			0.139331
$528$		0			0
$529$	−18.3742			−0.798877
$530$	−6.31906	−	10.9449i	−0.274483	−	0.475418i
$531$		0			0
$532$	15.8729	+	13.1774i	0.688176	+	0.571314i
$533$	3.63410	+	6.29444i	0.157410	+	0.272643i
$534$		0			0
$535$	6.45353	+	11.1778i	0.279011	+	0.483261i
$536$	−4.88563	−	8.46215i	−0.211027	−	0.365509i
$537$		0			0
$538$	−5.30556	−	9.18949i	−0.228739	−	0.396187i
$539$	15.1676	+	5.34075i	0.653315	+	0.230042i
$540$		0			0
$541$	−9.96183	−	17.2544i	−0.428292	−	0.741824i	0.568429	−	0.822732i	$-0.307551\pi$
$541$	−9.96183	−	17.2544i	−0.428292	−	0.741824i	−0.996722	+	0.0809080i	$0.974218\pi$
$542$	−13.1721			−0.565792
$543$		0			0
$544$	0.744331			0.0319129
$545$	1.12676	−	1.95161i	0.0482652	−	0.0835977i
$546$		0			0
$547$	−2.95824	−	5.12382i	−0.126485	−	0.219079i	0.795827	−	0.605524i	$-0.207036\pi$
$547$	−2.95824	−	5.12382i	−0.126485	−	0.219079i	−0.922313	+	0.386445i	$0.873703\pi$
$548$	−1.09980	−	1.90491i	−0.0469811	−	0.0813736i
$549$		0			0
$550$	1.14860	−	1.98944i	0.0489765	−	0.0848298i
$551$	20.3993	−	35.3326i	0.869038	−	1.50522i
$552$		0			0
$553$	18.9481	+	15.7304i	0.805755	+	0.668926i
$554$	−15.8627	+	27.4750i	−0.673940	+	1.16730i
$555$		0			0
$556$	−2.45807			−0.104245
$557$	2.53724	−	4.39463i	0.107506	−	0.186206i	−0.807253	−	0.590205i	$-0.799047\pi$
$557$	2.53724	−	4.39463i	0.107506	−	0.186206i	0.914759	+	0.403999i	$0.132380\pi$
$558$		0			0
$559$	−14.0786			−0.595459
$560$	−2.03567	−	1.68998i	−0.0860228	−	0.0714149i
$561$		0			0
$562$	20.6214			0.869860
$563$	−10.0496	−	17.4064i	−0.423540	−	0.733593i	0.572743	−	0.819735i	$-0.305879\pi$
$563$	−10.0496	−	17.4064i	−0.423540	−	0.733593i	−0.996283	+	0.0861424i	$0.972546\pi$
$564$		0			0
$565$	−9.72776	+	16.8490i	−0.409250	+	0.708842i
$566$	−4.35025			−0.182854
$567$		0			0
$568$	−2.50553			−0.105130
$569$	−1.71073	+	2.96307i	−0.0717176	+	0.124218i	−0.899654	−	0.436603i	$-0.856181\pi$
$569$	−1.71073	+	2.96307i	−0.0717176	+	0.124218i	0.827937	+	0.560822i	$0.189515\pi$
$570$		0			0
$571$	3.93869	+	6.82200i	0.164829	+	0.285492i	0.936594	−	0.350415i	$-0.113959\pi$
$571$	3.93869	+	6.82200i	0.164829	+	0.285492i	−0.771766	+	0.635907i	$0.780626\pi$
$572$	−3.88388			−0.162393
$573$		0			0
$574$	−10.6674	+	3.94620i	−0.445247	+	0.164711i
$575$	−2.15077			−0.0896934
$576$		0			0
$577$	−4.38883	+	7.60168i	−0.182709	+	0.316462i	−0.942802	−	0.333353i	$-0.891820\pi$
$577$	−4.38883	+	7.60168i	−0.182709	+	0.316462i	0.760093	+	0.649814i	$0.225153\pi$
$578$	−16.4460			−0.684062
$579$		0			0
$580$	−2.61618	+	4.53135i	−0.108631	+	0.188154i
$581$	−3.20287	+	1.18484i	−0.132877	+	0.0491555i
$582$		0			0
$583$	14.5162	−	25.1427i	0.601198	−	1.04131i
$584$	−3.42499	+	5.93225i	−0.141727	+	0.245478i
$585$		0			0
$586$	0.408724	+	0.707931i	0.0168842	+	0.0292444i
$587$	13.3521	+	23.1266i	0.551102	+	0.954536i	0.998195	+	0.0600488i	$0.0191256\pi$
$587$	13.3521	+	23.1266i	0.551102	+	0.954536i	−0.447094	+	0.894487i	$0.647541\pi$
$588$		0			0
$589$	16.7534	−	29.0178i	0.690313	−	1.19566i
$590$	−0.635800			−0.0261755
$591$		0			0
$592$	10.8101			0.444291
$593$	−2.36570	−	4.09751i	−0.0971477	−	0.168265i	0.813355	−	0.581767i	$-0.197639\pi$
$593$	−2.36570	−	4.09751i	−0.0971477	−	0.168265i	−0.910503	+	0.413503i	$0.864305\pi$
$594$		0			0
$595$	−1.51521	−	1.25791i	−0.0621177	−	0.0515692i
$596$	5.10818	+	8.84763i	0.209239	+	0.362413i
$597$		0			0
$598$	1.81816	+	3.14914i	0.0743500	+	0.128778i
$599$	2.00235	+	3.46817i	0.0818138	+	0.141706i	0.904029	−	0.427471i	$-0.140595\pi$
$599$	2.00235	+	3.46817i	0.0818138	+	0.141706i	−0.822215	+	0.569177i	$0.807262\pi$
$600$		0			0
$601$	−7.44908	−	12.9022i	−0.303854	−	0.526291i	0.673151	−	0.739505i	$-0.264940\pi$
$601$	−7.44908	−	12.9022i	−0.303854	−	0.526291i	−0.977006	+	0.213214i	$0.931607\pi$
$602$	3.71165	−	21.7164i	0.151276	−	0.885095i
$603$		0			0
$604$	1.40160	+	2.42764i	0.0570303	+	0.0987793i
$605$	−5.72286			−0.232667
$606$		0			0
$607$	2.44410			0.0992028			0.0496014	−	0.998769i	$-0.484205\pi$
$607$	2.44410			0.0992028			0.0496014	+	0.998769i	$0.484205\pi$
$608$	3.89868	−	6.75271i	0.158112	−	0.273859i
$609$		0			0
$610$	−3.45259	−	5.98007i	−0.139791	−	0.242126i
$611$	−6.91696	−	11.9805i	−0.279830	−	0.484680i
$612$		0			0
$613$	−4.65652	+	8.06533i	−0.188075	+	0.325755i	−0.944608	−	0.328200i	$-0.893558\pi$
$613$	−4.65652	+	8.06533i	−0.188075	+	0.325755i	0.756533	+	0.653955i	$0.226891\pi$
$614$	−5.35949	+	9.28292i	−0.216292	+	0.374628i
$615$		0			0
$616$	1.02394	−	5.99095i	0.0412558	−	0.241382i
$617$	−17.1834	+	29.7625i	−0.691777	+	1.19819i	0.279479	+	0.960152i	$0.409838\pi$
$617$	−17.1834	+	29.7625i	−0.691777	+	1.19819i	−0.971255	+	0.238040i	$0.923495\pi$
$618$		0			0
$619$	15.8298			0.636251			0.318126	−	0.948049i	$-0.396947\pi$
$619$	15.8298			0.636251			0.318126	+	0.948049i	$0.396947\pi$
$620$	−2.14860	+	3.72149i	−0.0862899	+	0.149458i
$621$		0			0
$622$	3.27621			0.131364
$623$	0.820852	−	0.303659i	0.0328867	−	0.0121658i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−11.4284	−	19.7946i	−0.456770	−	0.791149i
$627$		0			0
$628$	−3.07725	+	5.32996i	−0.122796	+	0.212689i
$629$	8.04627			0.320826
$630$		0			0
$631$	−1.08144			−0.0430515			−0.0215257	−	0.999768i	$-0.506852\pi$
$631$	−1.08144			−0.0430515			−0.0215257	+	0.999768i	$0.506852\pi$
$632$	4.65402	−	8.06099i	0.185127	−	0.320649i
$633$		0			0
$634$	−11.5134	−	19.9418i	−0.457256	−	0.791990i
$635$	−12.7583			−0.506297
$636$		0			0
$637$	8.98563	−	7.70217i	0.356024	−	0.305171i
$638$	−12.0198			−0.475867
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−29.5343			−1.16653			−0.583267	−	0.812280i	$-0.698226\pi$
$641$	−29.5343			−1.16653			−0.583267	+	0.812280i	$0.698226\pi$
$642$		0			0
$643$	13.0513	−	22.6055i	0.514693	−	0.891474i	−0.485162	−	0.874424i	$-0.661239\pi$
$643$	13.0513	−	22.6055i	0.514693	−	0.891474i	0.999855	−	0.0170499i	$-0.00542741\pi$
$644$	−5.33694	+	1.97430i	−0.210305	+	0.0777984i
$645$		0			0
$646$	2.90191	−	5.02626i	0.114174	−	0.197755i
$647$	13.1677	−	22.8071i	0.517675	−	0.896639i	−0.482115	−	0.876108i	$-0.660131\pi$
$647$	13.1677	−	22.8071i	0.517675	−	0.896639i	0.999789	−	0.0205305i	$-0.00653551\pi$
$648$		0			0
$649$	−0.730281	−	1.26488i	−0.0286660	−	0.0496510i
$650$	−0.845351	−	1.46419i	−0.0331574	−	0.0574303i
$651$		0			0
$652$	2.75802	−	4.77703i	0.108012	−	0.187083i
$653$	42.2438			1.65313			0.826565	−	0.562842i	$-0.190292\pi$
$653$	42.2438			1.65313			0.826565	+	0.562842i	$0.190292\pi$
$654$		0			0
$655$	−10.4878			−0.409793
$656$	2.14946	+	3.72298i	0.0839224	+	0.145358i
$657$		0			0
$658$	20.3037	−	7.51099i	0.791522	−	0.292809i
$659$	4.06632	+	7.04308i	0.158401	+	0.274359i	0.934292	−	0.356508i	$-0.116033\pi$
$659$	4.06632	+	7.04308i	0.158401	+	0.274359i	−0.775891	+	0.630867i	$0.782699\pi$
$660$		0			0
$661$	−22.6120	−	39.1651i	−0.879504	−	1.52335i	−0.851886	−	0.523727i	$-0.824541\pi$
$661$	−22.6120	−	39.1651i	−0.879504	−	1.52335i	−0.0276182	−	0.999619i	$-0.508792\pi$
$662$	12.0210	+	20.8209i	0.467208	+	0.809228i
$663$		0			0
$664$	0.645374	+	1.11782i	0.0250454	+	0.0433799i
$665$	−19.3484	+	7.15759i	−0.750299	+	0.277559i
$666$		0			0
$667$	5.62680	+	9.74590i	0.217871	+	0.377363i
$668$	10.0745			0.389795
$669$		0			0
$670$	9.77125			0.377496
$671$	7.93130	−	13.7374i	0.306185	−	0.530327i
$672$		0			0
$673$	−15.9941	−	27.7025i	−0.616526	−	1.06785i	−0.990115	−	0.140260i	$-0.955206\pi$
$673$	−15.9941	−	27.7025i	−0.616526	−	1.06785i	0.373589	−	0.927594i	$-0.378127\pi$
$674$	2.92411	+	5.06471i	0.112633	+	0.195085i
$675$		0			0
$676$	5.07076	−	8.78282i	0.195029	−	0.337801i
$677$	0.574149	−	0.994454i	0.0220663	−	0.0382200i	−0.854781	−	0.518988i	$-0.826309\pi$
$677$	0.574149	−	0.994454i	0.0220663	−	0.0382200i	0.876848	+	0.480768i	$0.159642\pi$
$678$		0			0
$679$	−15.7879	+	5.84042i	−0.605882	+	0.224135i
$680$	−0.372166	+	0.644610i	−0.0142719	+	0.0247197i
$681$		0			0
$682$	−9.87154			−0.378001
$683$	−8.62552	+	14.9398i	−0.330046	+	0.571657i	−0.982521	−	0.186154i	$-0.940398\pi$
$683$	−8.62552	+	14.9398i	−0.330046	+	0.571657i	0.652474	+	0.757811i	$0.273731\pi$
$684$		0			0
$685$	2.19960			0.0840423
$686$	9.51177	+	15.8911i	0.363161	+	0.606724i
$687$		0			0
$688$	−8.32705			−0.317466
$689$	−10.6836	−	18.5046i	−0.407015	−	0.704970i
$690$		0			0
$691$	7.94759	−	13.7656i	0.302340	−	0.523669i	−0.674325	−	0.738435i	$-0.735565\pi$
$691$	7.94759	−	13.7656i	0.302340	−	0.523669i	0.976666	+	0.214766i	$0.0688987\pi$
$692$	−20.7789			−0.789895
$693$		0			0
$694$	−32.4523			−1.23187
$695$	1.22903	−	2.12875i	0.0466199	−	0.0807481i
$696$		0			0
$697$	1.59991	+	2.77113i	0.0606010	+	0.104964i
$698$	3.16990			0.119983
$699$		0			0
$700$	2.48140	−	0.917950i	0.0937883	−	0.0346952i
$701$	8.85839			0.334577			0.167288	−	0.985908i	$-0.446499\pi$
$701$	8.85839			0.334577			0.167288	+	0.985908i	$0.446499\pi$
$702$		0			0
$703$	42.1450	−	72.9973i	1.58953	−	2.75314i
$704$	−2.29720			−0.0865791
$705$		0			0
$706$	−6.51501	+	11.2843i	−0.245196	+	0.424691i
$707$	6.62018	−	38.7338i	0.248978	−	1.45674i
$708$		0			0
$709$	−13.8720	+	24.0270i	−0.520973	+	0.902352i	0.478729	+	0.877963i	$0.341098\pi$
$709$	−13.8720	+	24.0270i	−0.520973	+	0.902352i	−0.999703	+	0.0243897i	$0.992236\pi$
$710$	1.25276	−	2.16985i	0.0470154	−	0.0814331i
$711$		0			0
$712$	−0.165401	−	0.286482i	−0.00619865	−	0.0107364i
$713$	4.62115	+	8.00407i	0.173064	+	0.299755i
$714$		0			0
$715$	1.94194	−	3.36354i	0.0726245	−	0.125789i
$716$	2.79067			0.104292
$717$		0			0
$718$	7.03154			0.262415
$719$	23.7618	+	41.1566i	0.886166	+	1.53488i	0.844372	+	0.535758i	$0.179974\pi$
$719$	23.7618	+	41.1566i	0.886166	+	1.53488i	0.0417937	+	0.999126i	$0.486693\pi$
$720$		0			0
$721$	−4.54133	+	26.5707i	−0.169128	+	0.989545i
$722$	−20.8994	−	36.1989i	−0.777796	−	1.34718i
$723$		0			0
$724$	11.1479	+	19.3087i	0.414308	+	0.717603i
$725$	−2.61618	−	4.53135i	−0.0971623	−	0.168290i
$726$		0			0
$727$	4.61919	+	8.00066i	0.171316	+	0.296728i	0.938880	−	0.344244i	$-0.111865\pi$
$727$	4.61919	+	8.00066i	0.171316	+	0.296728i	−0.767564	+	0.640972i	$0.778531\pi$
$728$	−3.44171	−	2.85726i	−0.127558	−	0.105897i
$729$		0			0
$730$	−3.42499	−	5.93225i	−0.126765	−	0.219563i
$731$	−6.19809			−0.229244
$732$		0			0
$733$	−47.2195			−1.74409			−0.872047	−	0.489422i	$-0.837208\pi$
$733$	−47.2195			−1.74409			−0.872047	+	0.489422i	$0.837208\pi$
$734$	−4.71676	+	8.16967i	−0.174099	+	0.301548i
$735$		0			0
$736$	1.07539	+	1.86262i	0.0396393	+	0.0686572i
$737$	11.2233	+	19.4393i	0.413415	+	0.716055i
$738$		0			0
$739$	−11.3561	+	19.6693i	−0.417740	+	0.723546i	−0.995712	−	0.0925102i	$-0.970511\pi$
$739$	−11.3561	+	19.6693i	−0.417740	+	0.723546i	0.577972	+	0.816057i	$0.303844\pi$
$740$	−5.40503	+	9.36179i	−0.198693	+	0.344146i
$741$		0			0
$742$	31.3603	−	11.6012i	1.15127	−	0.425892i
$743$	−7.29685	+	12.6385i	−0.267696	+	0.463662i	−0.968266	−	0.249921i	$-0.919595\pi$
$743$	−7.29685	+	12.6385i	−0.267696	+	0.463662i	0.700571	+	0.713583i	$0.252929\pi$
$744$		0			0
$745$	−10.2164			−0.374299
$746$	−18.8628	+	32.6713i	−0.690616	+	1.19618i
$747$		0			0
$748$	−1.70988			−0.0625194
$749$	−32.0277	+	11.8480i	−1.17027	+	0.432918i
$750$		0			0
$751$	−23.3456			−0.851893			−0.425946	−	0.904748i	$-0.640059\pi$
$751$	−23.3456			−0.851893			−0.425946	+	0.904748i	$0.640059\pi$
$752$	−4.09118	−	7.08613i	−0.149190	−	0.258405i
$753$		0			0
$754$	−4.42317	+	7.66116i	−0.161082	+	0.279003i
$755$	−2.80320			−0.102019
$756$		0			0
$757$	8.35341			0.303610			0.151805	−	0.988410i	$-0.451491\pi$
$757$	8.35341			0.303610			0.151805	+	0.988410i	$0.451491\pi$
$758$	−3.47148	+	6.01278i	−0.126090	+	0.218394i
$759$		0			0
$760$	3.89868	+	6.75271i	0.141420	+	0.244947i
$761$	37.1827			1.34787			0.673936	−	0.738790i	$-0.264602\pi$
$761$	37.1827			1.34787			0.673936	+	0.738790i	$0.264602\pi$
$762$		0			0
$763$	4.58743	+	3.80842i	0.166076	+	0.137874i
$764$	−14.5124			−0.525040
$765$		0			0
$766$	−13.5881	+	23.5353i	−0.490958	+	0.850365i
$767$	−1.07495			−0.0388141
$768$		0			0
$769$	−8.53353	+	14.7805i	−0.307727	+	0.532998i	−0.977865	−	0.209238i	$-0.932902\pi$
$769$	−8.53353	+	14.7805i	−0.307727	+	0.532998i	0.670138	+	0.742237i	$0.266235\pi$
$770$	4.67635	+	3.88224i	0.168524	+	0.139906i
$771$		0			0
$772$	−3.16439	+	5.48089i	−0.113889	+	0.197262i
$773$	14.2643	−	24.7066i	0.513052	−	0.888633i	−0.486833	−	0.873495i	$-0.661848\pi$
$773$	14.2643	−	24.7066i	0.513052	−	0.888633i	0.999885	−	0.0151379i	$-0.00481872\pi$
$774$		0			0
$775$	−2.14860	−	3.72149i	−0.0771800	−	0.133680i
$776$	3.18123	+	5.51006i	0.114200	+	0.197800i
$777$		0			0
$778$	−13.5440	+	23.4590i	−0.485577	+	0.841045i
$779$	33.5203			1.20099
$780$		0			0
$781$	5.75571			0.205955
$782$	0.800444	+	1.38641i	0.0286238	+	0.0495779i
$783$		0			0
$784$	5.31474	−	4.55561i	0.189812	−	0.162700i
$785$	−3.07725	−	5.32996i	−0.109832	−	0.190234i
$786$		0			0
$787$	−18.3712	−	31.8198i	−0.654861	−	1.13425i	−0.981929	−	0.189252i	$-0.939394\pi$
$787$	−18.3712	−	31.8198i	−0.654861	−	1.13425i	0.327068	−	0.945001i	$-0.393940\pi$
$788$	−4.57510	−	7.92431i	−0.162981	−	0.282292i
$789$		0			0
$790$	4.65402	+	8.06099i	0.165582	+	0.286797i
$791$	−39.6050	−	32.8795i	−1.40819	−	1.16906i
$792$		0			0
$793$	−5.83730	−	10.1105i	−0.207289	−	0.359035i
$794$	−37.4949			−1.33064
$795$		0			0
$796$	−5.93691			−0.210428
$797$	1.29107	−	2.23620i	0.0457320	−	0.0792102i	−0.842253	−	0.539082i	$-0.818771\pi$
$797$	1.29107	−	2.23620i	0.0457320	−	0.0792102i	0.887985	+	0.459872i	$0.152105\pi$
$798$		0			0
$799$	−3.04519	−	5.27443i	−0.107731	−	0.186596i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	−6.34260	+	10.9857i	−0.223965	+	0.387919i
$803$	7.86789	−	13.6276i	0.277652	−	0.480907i
$804$		0			0
$805$	0.958673	−	5.60907i	0.0337888	−	0.197694i
$806$	−3.63264	+	6.29192i	−0.127954	+	0.221623i
$807$		0			0
$808$	−14.8523			−0.522502
$809$	16.3871	−	28.3832i	0.576139	−	0.997901i	−0.419778	−	0.907627i	$-0.637892\pi$
$809$	16.3871	−	28.3832i	0.576139	−	0.997901i	0.995917	−	0.0902748i	$-0.0287745\pi$
$810$		0			0
$811$	−15.6307			−0.548868			−0.274434	−	0.961606i	$-0.588490\pi$
$811$	−15.6307			−0.548868			−0.274434	+	0.961606i	$0.588490\pi$
$812$	−10.6513	−	8.84259i	−0.373789	−	0.310314i
$813$		0			0
$814$	−24.8329			−0.870393
$815$	2.75802	+	4.77703i	0.0966093	+	0.167332i
$816$		0			0
$817$	−32.4645	+	56.2302i	−1.13579	+	1.96725i
$818$	12.0211			0.420309
$819$		0			0
$820$	−4.29892			−0.150125
$821$	−21.5706	+	37.3614i	−0.752820	+	1.30392i	0.193631	+	0.981074i	$0.437974\pi$
$821$	−21.5706	+	37.3614i	−0.752820	+	1.30392i	−0.946451	+	0.322848i	$0.895360\pi$
$822$		0			0
$823$	2.49529	+	4.32196i	0.0869803	+	0.150654i	0.906233	−	0.422778i	$-0.138945\pi$
$823$	2.49529	+	4.32196i	0.0869803	+	0.150654i	−0.819253	+	0.573432i	$0.805612\pi$
$824$	10.1884			0.354930
$825$		0			0
$826$	0.283398	−	1.65812i	0.00986067	−	0.0576935i
$827$	34.1979			1.18918			0.594589	−	0.804030i	$-0.297315\pi$
$827$	34.1979			1.18918			0.594589	+	0.804030i	$0.297315\pi$
$828$		0			0
$829$	13.9941	−	24.2385i	0.486036	−	0.841839i	−0.513835	−	0.857889i	$-0.671776\pi$
$829$	13.9941	−	24.2385i	0.486036	−	0.841839i	0.999871	+	0.0160499i	$0.00510906\pi$
$830$	−1.29075			−0.0448025
$831$		0			0
$832$	−0.845351	+	1.46419i	−0.0293073	+	0.0507617i
$833$	3.95592	−	3.39088i	0.137065	−	0.117487i
$834$		0			0
$835$	−5.03727	+	8.72480i	−0.174322	+	0.301934i
$836$	−8.95606	+	15.5123i	−0.309752	+	0.536506i
$837$		0			0
$838$	0.923993	+	1.60040i	0.0319188	+	0.0552850i
$839$	−20.9174	−	36.2300i	−0.722149	−	1.25080i	−0.960137	−	0.279531i	$-0.909821\pi$
$839$	−20.9174	−	36.2300i	−0.722149	−	1.25080i	0.237988	−	0.971268i	$-0.423512\pi$
$840$		0			0
$841$	0.811251	−	1.40513i	0.0279742	−	0.0484527i
$842$	7.76902			0.267738
$843$		0			0
$844$	14.2953			0.492066
$845$	5.07076	+	8.78282i	0.174440	+	0.302138i
$846$		0			0
$847$	2.55088	−	14.9248i	0.0876491	−	0.512824i
$848$	−6.31906	−	10.9449i	−0.216998	−	0.375851i
$849$		0			0
$850$	−0.372166	−	0.644610i	−0.0127652	−	0.0221099i
$851$	11.6250	+	20.1351i	0.398500	+	0.690222i
$852$		0			0
$853$	−6.54489	−	11.3361i	−0.224093	−	0.388140i	0.731954	−	0.681354i	$-0.238609\pi$
$853$	−6.54489	−	11.3361i	−0.224093	−	0.388140i	−0.956047	+	0.293214i	$0.905275\pi$
$854$	17.1346	−	6.33861i	0.586332	−	0.216903i
$855$		0			0
$856$	6.45353	+	11.1778i	0.220577	+	0.382051i
$857$	11.3137			0.386470			0.193235	−	0.981153i	$-0.438102\pi$
$857$	11.3137			0.386470			0.193235	+	0.981153i	$0.438102\pi$
$858$		0			0
$859$	39.0361			1.33190			0.665948	−	0.745998i	$-0.268027\pi$
$859$	39.0361			1.33190			0.665948	+	0.745998i	$0.268027\pi$
$860$	4.16353	−	7.21144i	0.141975	−	0.245908i
$861$		0			0
$862$	−6.54581	−	11.3377i	−0.222951	−	0.386163i
$863$	3.61316	+	6.25818i	0.122993	+	0.213031i	0.920947	−	0.389688i	$-0.127417\pi$
$863$	3.61316	+	6.25818i	0.122993	+	0.213031i	−0.797953	+	0.602719i	$0.794084\pi$
$864$		0			0
$865$	10.3894	−	17.9951i	0.353252	−	0.611850i
$866$	14.6251	−	25.3314i	0.496980	−	0.860795i
$867$		0			0
$868$	−8.74769	−	7.26220i	−0.296916	−	0.246495i
$869$	−10.6912	+	18.5177i	−0.362675	+	0.628171i
$870$		0			0
$871$	16.5203			0.559768
$872$	1.12676	−	1.95161i	0.0381570	−	0.0660898i
$873$		0			0
$874$	16.7704			0.567266
$875$	−0.445734	+	2.60793i	−0.0150686	+	0.0881643i
$876$		0			0
$877$	−22.1514			−0.748001			−0.374000	−	0.927429i	$-0.622014\pi$
$877$	−22.1514			−0.748001			−0.374000	+	0.927429i	$0.622014\pi$
$878$	7.47257	+	12.9429i	0.252187	+	0.436801i
$879$		0			0
$880$	1.14860	−	1.98944i	0.0387193	−	0.0670639i
$881$	18.1808			0.612526			0.306263	−	0.951947i	$-0.400921\pi$
$881$	18.1808			0.612526			0.306263	+	0.951947i	$0.400921\pi$
$882$		0			0
$883$	28.6224			0.963219			0.481610	−	0.876386i	$-0.340052\pi$
$883$	28.6224			0.963219			0.481610	+	0.876386i	$0.340052\pi$
$884$	−0.629221	+	1.08984i	−0.0211630	+	0.0366554i
$885$		0			0
$886$	−11.6420	−	20.1645i	−0.391120	−	0.677440i
$887$	44.0404			1.47873			0.739366	−	0.673303i	$-0.235125\pi$
$887$	44.0404			1.47873			0.739366	+	0.673303i	$0.235125\pi$
$888$		0			0
$889$	5.68681	−	33.2728i	0.190729	−	1.11593i
$890$	0.330801			0.0110885
$891$		0			0
$892$	−8.91331	+	15.4383i	−0.298440	+	0.516913i
$893$	−63.8008			−2.13501
$894$		0			0
$895$	−1.39534	+	2.41679i	−0.0466410	+	0.0807845i
$896$	−2.03567	−	1.68998i	−0.0680070	−	0.0564584i
$897$		0			0
$898$	−6.64124	+	11.5030i	−0.221621	+	0.383859i
$899$	−11.2422	+	19.4721i	−0.374950	+	0.649432i
$900$		0			0
$901$	−4.70348	−	8.14666i	−0.156696	−	0.271405i
$902$	−4.93775	−	8.55243i	−0.164409	−	0.284765i
$903$		0			0
$904$	−9.72776	+	16.8490i	−0.323540	+	0.560389i
$905$	−22.2958			−0.741137
$906$		0			0
$907$	55.0760			1.82877			0.914383	−	0.404849i	$-0.132676\pi$
$907$	55.0760			1.82877			0.914383	+	0.404849i	$0.132676\pi$
$908$	−10.3752	−	17.9705i	−0.344315	−	0.596371i
$909$		0			0
$910$	4.19531	−	1.55198i	0.139073	−	0.0514476i
$911$	−7.85937	−	13.6128i	−0.260393	−	0.451013i	0.705954	−	0.708258i	$-0.250519\pi$
$911$	−7.85937	−	13.6128i	−0.260393	−	0.451013i	−0.966346	+	0.257245i	$0.917185\pi$
$912$		0			0
$913$	−1.48256	−	2.56786i	−0.0490654	−	0.0849838i
$914$	−17.5492	−	30.3961i	−0.580476	−	1.00541i
$915$		0			0
$916$	−10.0604	−	17.4251i	−0.332405	−	0.575743i
$917$	4.67478	−	27.3516i	0.154375	−	0.903228i
$918$		0			0
$919$	−2.47726	−	4.29074i	−0.0817172	−	0.141538i	0.822270	−	0.569097i	$-0.192707\pi$
$919$	−2.47726	−	4.29074i	−0.0817172	−	0.141538i	−0.903988	+	0.427559i	$0.859374\pi$
$920$	−2.15077			−0.0709089
$921$		0			0
$922$	−9.06024			−0.298383
$923$	2.11805	−	3.66857i	0.0697165	−	0.120752i
$924$		0			0
$925$	−5.40503	−	9.36179i	−0.177716	−	0.307814i
$926$	−21.1130	−	36.5688i	−0.693816	−	1.20172i
$927$		0			0
$928$	−2.61618	+	4.53135i	−0.0858802	+	0.148749i
$929$	24.8037	−	42.9613i	0.813784	−	1.40951i	−0.0964143	−	0.995341i	$-0.530737\pi$
$929$	24.8037	−	42.9613i	0.813784	−	1.40951i	0.910198	−	0.414173i	$-0.135929\pi$
$930$		0			0
$931$	−10.0423	−	53.6498i	−0.329122	−	1.75830i
$932$	−7.70836	+	13.3513i	−0.252496	+	0.437335i
$933$		0			0
$934$	10.5374			0.344794
$935$	0.854940	−	1.48080i	0.0279595	−	0.0484273i
$936$		0			0
$937$	−8.05753			−0.263228			−0.131614	−	0.991301i	$-0.542016\pi$
$937$	−8.05753			−0.263228			−0.131614	+	0.991301i	$0.542016\pi$
$938$	−4.35538	+	25.4828i	−0.142208	+	0.832042i
$939$		0			0
$940$	8.18236			0.266879
$941$	9.26721	+	16.0513i	0.302102	+	0.523256i	0.976612	−	0.215010i	$-0.0689783\pi$
$941$	9.26721	+	16.0513i	0.302102	+	0.523256i	−0.674510	+	0.738266i	$0.735645\pi$
$942$		0			0
$943$	−4.62300	+	8.00728i	−0.150546	+	0.260753i
$944$	−0.635800			−0.0206935
$945$		0			0
$946$	19.1289			0.621935
$947$	−28.2044	+	48.8515i	−0.916521	+	1.58746i	−0.111861	+	0.993724i	$0.535681\pi$
$947$	−28.2044	+	48.8515i	−0.916521	+	1.58746i	−0.804659	+	0.593737i	$0.797652\pi$
$948$		0			0
$949$	−5.79063	−	10.0297i	−0.187972	−	0.325577i
$950$	−7.79736			−0.252980
$951$		0			0
$952$	−1.51521	−	1.25791i	−0.0491083	−	0.0407690i
$953$	−44.4290			−1.43920			−0.719599	−	0.694390i	$-0.755674\pi$
$953$	−44.4290			−1.43920			−0.719599	+	0.694390i	$0.755674\pi$
$954$		0			0
$955$	7.25620	−	12.5681i	0.234805	−	0.406694i
$956$	19.2635			0.623025
$957$		0			0
$958$	−18.7128	+	32.4116i	−0.604584	+	1.04717i
$959$	−0.980436	+	5.73640i	−0.0316599	+	0.185238i
$960$		0			0
$961$	6.26703	−	10.8548i	0.202162	−	0.350155i
$962$	−9.13829	+	15.8280i	−0.294630	+	0.510315i
$963$		0			0
$964$	−13.3167	−	23.0653i	−0.428903	−	0.742882i
$965$	−3.16439	−	5.48089i	−0.101865	−	0.176436i
$966$		0			0
$967$	−10.3142	+	17.8647i	−0.331681	+	0.574489i	−0.982842	−	0.184451i	$-0.940949\pi$
$967$	−10.3142	+	17.8647i	−0.331681	+	0.574489i	0.651160	+	0.758940i	$0.274282\pi$
$968$	−5.72286			−0.183940
$969$		0			0
$970$	−6.36247			−0.204286
$971$	23.0979	+	40.0067i	0.741247	+	1.28388i	0.951928	+	0.306322i	$0.0990985\pi$
$971$	23.0979	+	40.0067i	0.741247	+	1.28388i	−0.210681	+	0.977555i	$0.567568\pi$
$972$		0			0
$973$	5.00382	+	4.15410i	0.160415	+	0.133174i
$974$	7.69208	+	13.3231i	0.246470	+	0.426899i
$975$		0			0
$976$	−3.45259	−	5.98007i	−0.110515	−	0.191417i
$977$	−15.6943	−	27.1834i	−0.502106	−	0.869673i	−0.999997	−	0.00243376i	$-0.999225\pi$
$977$	−15.6943	−	27.1834i	−0.502106	−	0.869673i	0.497891	−	0.867240i	$-0.334108\pi$
$978$		0			0
$979$	0.379959	+	0.658108i	0.0121435	+	0.0210332i
$980$	1.28791	+	6.88050i	0.0411406	+	0.219790i
$981$		0			0
$982$	−11.7768	−	20.3981i	−0.375814	−	0.650928i
$983$	−24.3633			−0.777070			−0.388535	−	0.921434i	$-0.627019\pi$
$983$	−24.3633			−0.777070			−0.388535	+	0.921434i	$0.627019\pi$
$984$		0			0
$985$	9.15021			0.291550
$986$	−1.94730	+	3.37282i	−0.0620147	+	0.107413i
$987$		0			0
$988$	6.59150	+	11.4168i	0.209704	+	0.363217i
$989$	−8.95480	−	15.5102i	−0.284746	−	0.493195i
$990$		0			0
$991$	−29.1185	+	50.4348i	−0.924981	+	1.60211i	−0.133388	+	0.991064i	$0.542586\pi$
$991$	−29.1185	+	50.4348i	−0.924981	+	1.60211i	−0.791592	+	0.611050i	$0.790748\pi$
$992$	−2.14860	+	3.72149i	−0.0682182	+	0.118157i
$993$		0			0
$994$	5.10043	+	4.23430i	0.161776	+	0.134304i
$995$	2.96846	−	5.14152i	0.0941064	−	0.162997i
$996$		0			0
$997$	−37.9556			−1.20206			−0.601032	−	0.799225i	$-0.705244\pi$
$997$	−37.9556			−1.20206			−0.601032	+	0.799225i	$0.705244\pi$
$998$	3.43382	−	5.94754i	0.108696	−	0.188266i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.l.i.361.4		16
3.2	odd	2		630.2.l.i.571.6	yes	16
7.2	even	3		1890.2.i.i.1171.7		16
9.2	odd	6		630.2.i.i.151.1	yes	16
9.7	even	3		1890.2.i.i.991.7		16
21.2	odd	6		630.2.i.i.121.1	✓	16
63.2	odd	6		630.2.l.i.331.6	yes	16
63.16	even	3	inner	1890.2.l.i.1801.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.i.121.1	✓	16	21.2	odd	6
630.2.i.i.151.1	yes	16	9.2	odd	6
630.2.l.i.331.6	yes	16	63.2	odd	6
630.2.l.i.571.6	yes	16	3.2	odd	2
1890.2.i.i.991.7		16	9.7	even	3
1890.2.i.i.1171.7		16	7.2	even	3
1890.2.l.i.361.4		16	1.1	even	1	trivial
1890.2.l.i.1801.4		16	63.16	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.445734 + 2.60793i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.445734 + 2.60793i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} -2.29720 q^{11} +(-0.845351 + 1.46419i) q^{13} +(-2.03567 - 1.68998i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.372166 + 0.644610i) q^{17} +(3.89868 + 6.75271i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(1.14860 - 1.98944i) q^{22} -2.15077 q^{23} +1.00000 q^{25} +(-0.845351 - 1.46419i) q^{26} +(2.48140 - 0.917950i) q^{28} +(-2.61618 - 4.53135i) q^{29} +(-2.14860 - 3.72149i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.372166 - 0.644610i) q^{34} +(-0.445734 + 2.60793i) q^{35} +(-5.40503 - 9.36179i) q^{37} -7.79736 q^{38} +1.00000 q^{40} +(2.14946 - 3.72298i) q^{41} +(4.16353 + 7.21144i) q^{43} +(1.14860 + 1.98944i) q^{44} +(1.07539 - 1.86262i) q^{46} +(-4.09118 + 7.08613i) q^{47} +(-6.60264 - 2.32489i) q^{49} +(-0.500000 + 0.866025i) q^{50} +1.69070 q^{52} +(-6.31906 + 10.9449i) q^{53} -2.29720 q^{55} +(-0.445734 + 2.60793i) q^{56} +5.23235 q^{58} +(0.317900 + 0.550619i) q^{59} +(-3.45259 + 5.98007i) q^{61} +4.29720 q^{62} +1.00000 q^{64} +(-0.845351 + 1.46419i) q^{65} +(-4.88563 - 8.46215i) q^{67} +0.744331 q^{68} +(-2.03567 - 1.68998i) q^{70} -2.50553 q^{71} +(-3.42499 + 5.93225i) q^{73} +10.8101 q^{74} +(3.89868 - 6.75271i) q^{76} +(1.02394 - 5.99095i) q^{77} +(4.65402 - 8.06099i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(2.14946 + 3.72298i) q^{82} +(0.645374 + 1.11782i) q^{83} +(-0.372166 + 0.644610i) q^{85} -8.32705 q^{86} -2.29720 q^{88} +(-0.165401 - 0.286482i) q^{89} +(-3.44171 - 2.85726i) q^{91} +(1.07539 + 1.86262i) q^{92} +(-4.09118 - 7.08613i) q^{94} +(3.89868 + 6.75271i) q^{95} +(3.18123 + 5.51006i) q^{97} +(5.31474 - 4.55561i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 8 q^{4} + 16 q^{5} + 4 q^{7} + 16 q^{8}+O(q^{10}) \) 16 * q - 8 * q^2 - 8 * q^4 + 16 * q^5 + 4 * q^7 + 16 * q^8	\( 16 q - 8 q^{2} - 8 q^{4} + 16 q^{5} + 4 q^{7} + 16 q^{8} - 8 q^{10} + 2 q^{11} + 2 q^{13} - 8 q^{14} - 8 q^{16} - 11 q^{17} - 2 q^{19} - 8 q^{20} - q^{22} + 22 q^{23} + 16 q^{25} + 2 q^{26} + 4 q^{28} - 17 q^{29} - 15 q^{31} - 8 q^{32} - 11 q^{34} + 4 q^{35} - 2 q^{37} + 4 q^{38} + 16 q^{40} - 7 q^{41} - 13 q^{43} - q^{44} - 11 q^{46} + 5 q^{47} + 10 q^{49} - 8 q^{50} - 4 q^{52} - 18 q^{53} + 2 q^{55} + 4 q^{56} + 34 q^{58} - q^{59} - 27 q^{61} + 30 q^{62} + 16 q^{64} + 2 q^{65} - 10 q^{67} + 22 q^{68} - 8 q^{70} + 38 q^{71} - 8 q^{73} + 4 q^{74} - 2 q^{76} + 19 q^{77} - 25 q^{79} - 8 q^{80} - 7 q^{82} - 2 q^{83} - 11 q^{85} + 26 q^{86} + 2 q^{88} + 6 q^{89} + 14 q^{91} - 11 q^{92} + 5 q^{94} - 2 q^{95} + 26 q^{97} - 14 q^{98}+O(q^{100}) \) 16 * q - 8 * q^2 - 8 * q^4 + 16 * q^5 + 4 * q^7 + 16 * q^8 - 8 * q^10 + 2 * q^11 + 2 * q^13 - 8 * q^14 - 8 * q^16 - 11 * q^17 - 2 * q^19 - 8 * q^20 - q^22 + 22 * q^23 + 16 * q^25 + 2 * q^26 + 4 * q^28 - 17 * q^29 - 15 * q^31 - 8 * q^32 - 11 * q^34 + 4 * q^35 - 2 * q^37 + 4 * q^38 + 16 * q^40 - 7 * q^41 - 13 * q^43 - q^44 - 11 * q^46 + 5 * q^47 + 10 * q^49 - 8 * q^50 - 4 * q^52 - 18 * q^53 + 2 * q^55 + 4 * q^56 + 34 * q^58 - q^59 - 27 * q^61 + 30 * q^62 + 16 * q^64 + 2 * q^65 - 10 * q^67 + 22 * q^68 - 8 * q^70 + 38 * q^71 - 8 * q^73 + 4 * q^74 - 2 * q^76 + 19 * q^77 - 25 * q^79 - 8 * q^80 - 7 * q^82 - 2 * q^83 - 11 * q^85 + 26 * q^86 + 2 * q^88 + 6 * q^89 + 14 * q^91 - 11 * q^92 + 5 * q^94 - 2 * q^95 + 26 * q^97 - 14 * q^98

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