LMFDB - Embedded newform 1386.2.k.t.991.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(793,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("1386.793");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.k (of order $3$, degree $2$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1386.991
Dual form			1386.2.k.t.793.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.70711 - 2.95680i) q^{5} +(-2.62132 + 0.358719i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.70711 - 2.95680i) q^{5} +(-2.62132 + 0.358719i) q^{7} -1.00000 q^{8} +(1.70711 - 2.95680i) q^{10} +(0.500000 - 0.866025i) q^{11} +1.82843 q^{13} +(-1.62132 - 2.09077i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.82843 + 6.63103i) q^{17} +(1.70711 + 2.95680i) q^{19} +3.41421 q^{20} +1.00000 q^{22} +(1.12132 + 1.94218i) q^{23} +(-3.32843 + 5.76500i) q^{25} +(0.914214 + 1.58346i) q^{26} +(1.00000 - 2.44949i) q^{28} +8.65685 q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} -7.65685 q^{34} +(5.53553 + 7.13834i) q^{35} +(3.29289 + 5.70346i) q^{37} +(-1.70711 + 2.95680i) q^{38} +(1.70711 + 2.95680i) q^{40} +2.58579 q^{41} +5.65685 q^{43} +(0.500000 + 0.866025i) q^{44} +(-1.12132 + 1.94218i) q^{46} +(3.24264 + 5.61642i) q^{47} +(6.74264 - 1.88064i) q^{49} -6.65685 q^{50} +(-0.914214 + 1.58346i) q^{52} +(-5.94975 + 10.3053i) q^{53} -3.41421 q^{55} +(2.62132 - 0.358719i) q^{56} +(4.32843 + 7.49706i) q^{58} +(-4.20711 + 7.28692i) q^{59} +(-3.08579 - 5.34474i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-3.12132 - 5.40629i) q^{65} +(-5.62132 + 9.73641i) q^{67} +(-3.82843 - 6.63103i) q^{68} +(-3.41421 + 8.36308i) q^{70} -3.07107 q^{71} +(3.29289 - 5.70346i) q^{73} +(-3.29289 + 5.70346i) q^{74} -3.41421 q^{76} +(-1.00000 + 2.44949i) q^{77} +(2.37868 + 4.11999i) q^{79} +(-1.70711 + 2.95680i) q^{80} +(1.29289 + 2.23936i) q^{82} -16.1421 q^{83} +26.1421 q^{85} +(2.82843 + 4.89898i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(-2.24264 - 3.88437i) q^{89} +(-4.79289 + 0.655892i) q^{91} -2.24264 q^{92} +(-3.24264 + 5.61642i) q^{94} +(5.82843 - 10.0951i) q^{95} +1.82843 q^{97} +(5.00000 + 4.89898i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} - 2 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 - 2 * q^7 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} - 2 q^{7} - 4 q^{8} + 4 q^{10} + 2 q^{11} - 4 q^{13} + 2 q^{14} - 2 q^{16} - 4 q^{17} + 4 q^{19} + 8 q^{20} + 4 q^{22} - 4 q^{23} - 2 q^{25} - 2 q^{26} + 4 q^{28} + 12 q^{29} + 8 q^{31} + 2 q^{32} - 8 q^{34} + 8 q^{35} + 16 q^{37} - 4 q^{38} + 4 q^{40} + 16 q^{41} + 2 q^{44} + 4 q^{46} - 4 q^{47} + 10 q^{49} - 4 q^{50} + 2 q^{52} - 4 q^{53} - 8 q^{55} + 2 q^{56} + 6 q^{58} - 14 q^{59} - 18 q^{61} + 16 q^{62} + 4 q^{64} - 4 q^{65} - 14 q^{67} - 4 q^{68} - 8 q^{70} + 16 q^{71} + 16 q^{73} - 16 q^{74} - 8 q^{76} - 4 q^{77} + 18 q^{79} - 4 q^{80} + 8 q^{82} - 8 q^{83} + 48 q^{85} - 2 q^{88} + 8 q^{89} - 22 q^{91} + 8 q^{92} + 4 q^{94} + 12 q^{95} - 4 q^{97} + 20 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 - 2 * q^7 - 4 * q^8 + 4 * q^10 + 2 * q^11 - 4 * q^13 + 2 * q^14 - 2 * q^16 - 4 * q^17 + 4 * q^19 + 8 * q^20 + 4 * q^22 - 4 * q^23 - 2 * q^25 - 2 * q^26 + 4 * q^28 + 12 * q^29 + 8 * q^31 + 2 * q^32 - 8 * q^34 + 8 * q^35 + 16 * q^37 - 4 * q^38 + 4 * q^40 + 16 * q^41 + 2 * q^44 + 4 * q^46 - 4 * q^47 + 10 * q^49 - 4 * q^50 + 2 * q^52 - 4 * q^53 - 8 * q^55 + 2 * q^56 + 6 * q^58 - 14 * q^59 - 18 * q^61 + 16 * q^62 + 4 * q^64 - 4 * q^65 - 14 * q^67 - 4 * q^68 - 8 * q^70 + 16 * q^71 + 16 * q^73 - 16 * q^74 - 8 * q^76 - 4 * q^77 + 18 * q^79 - 4 * q^80 + 8 * q^82 - 8 * q^83 + 48 * q^85 - 2 * q^88 + 8 * q^89 - 22 * q^91 + 8 * q^92 + 4 * q^94 + 12 * q^95 - 4 * q^97 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	−1.70711	−	2.95680i	−0.763441	−	1.32232i	−0.941067	−	0.338221i	$-0.890175\pi$
$5$	−1.70711	−	2.95680i	−0.763441	−	1.32232i	0.177625	−	0.984098i	$-0.443158\pi$
$6$		0			0
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.70711	−	2.95680i	0.539835	−	0.935021i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	1.82843			0.507114			0.253557	−	0.967320i	$-0.418399\pi$
$13$	1.82843			0.507114			0.253557	+	0.967320i	$0.418399\pi$
$14$	−1.62132	−	2.09077i	−0.433316	−	0.558782i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.82843	+	6.63103i	−0.928530	+	1.60826i	−0.142747	+	0.989759i	$0.545593\pi$
$17$	−3.82843	+	6.63103i	−0.928530	+	1.60826i	−0.785783	+	0.618502i	$0.787740\pi$
$18$		0			0
$19$	1.70711	+	2.95680i	0.391637	+	0.678335i	0.992666	−	0.120892i	$-0.0385755\pi$
$19$	1.70711	+	2.95680i	0.391637	+	0.678335i	−0.601028	+	0.799228i	$0.705242\pi$
$20$	3.41421			0.763441
$21$		0			0
$22$	1.00000			0.213201
$23$	1.12132	+	1.94218i	0.233811	+	0.404973i	0.958927	−	0.283654i	$-0.0915468\pi$
$23$	1.12132	+	1.94218i	0.233811	+	0.404973i	−0.725115	+	0.688628i	$0.758213\pi$
$24$		0			0
$25$	−3.32843	+	5.76500i	−0.665685	+	1.15300i
$26$	0.914214	+	1.58346i	0.179292	+	0.310543i
$27$		0			0
$28$	1.00000	−	2.44949i	0.188982	−	0.462910i
$29$	8.65685			1.60754			0.803769	−	0.594942i	$-0.202825\pi$
$29$	8.65685			1.60754			0.803769	+	0.594942i	$0.202825\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−7.65685			−1.31314
$35$	5.53553	+	7.13834i	0.935676	+	1.20660i
$36$		0			0
$37$	3.29289	+	5.70346i	0.541348	+	0.937643i	0.998827	+	0.0484222i	$0.0154193\pi$
$37$	3.29289	+	5.70346i	0.541348	+	0.937643i	−0.457479	+	0.889221i	$0.651247\pi$
$38$	−1.70711	+	2.95680i	−0.276929	+	0.479656i
$39$		0			0
$40$	1.70711	+	2.95680i	0.269917	+	0.467510i
$41$	2.58579			0.403832			0.201916	−	0.979403i	$-0.435283\pi$
$41$	2.58579			0.403832			0.201916	+	0.979403i	$0.435283\pi$
$42$		0			0
$43$	5.65685			0.862662			0.431331	−	0.902194i	$-0.358044\pi$
$43$	5.65685			0.862662			0.431331	+	0.902194i	$0.358044\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$		0			0
$46$	−1.12132	+	1.94218i	−0.165330	+	0.286359i
$47$	3.24264	+	5.61642i	0.472988	+	0.819239i	0.999522	−	0.0309151i	$-0.00984215\pi$
$47$	3.24264	+	5.61642i	0.472988	+	0.819239i	−0.526534	+	0.850154i	$0.676509\pi$
$48$		0			0
$49$	6.74264	−	1.88064i	0.963234	−	0.268662i
$50$	−6.65685			−0.941421
$51$		0			0
$52$	−0.914214	+	1.58346i	−0.126779	+	0.219587i
$53$	−5.94975	+	10.3053i	−0.817261	+	1.41554i	0.0904325	+	0.995903i	$0.471175\pi$
$53$	−5.94975	+	10.3053i	−0.817261	+	1.41554i	−0.907693	+	0.419634i	$0.862158\pi$
$54$		0			0
$55$	−3.41421			−0.460372
$56$	2.62132	−	0.358719i	0.350289	−	0.0479359i
$57$		0			0
$58$	4.32843	+	7.49706i	0.568350	+	0.984412i
$59$	−4.20711	+	7.28692i	−0.547719	+	0.948677i	0.450712	+	0.892670i	$0.351170\pi$
$59$	−4.20711	+	7.28692i	−0.547719	+	0.948677i	−0.998430	+	0.0560070i	$0.982163\pi$
$60$		0			0
$61$	−3.08579	−	5.34474i	−0.395094	−	0.684324i	0.598019	−	0.801482i	$-0.295955\pi$
$61$	−3.08579	−	5.34474i	−0.395094	−	0.684324i	−0.993113	+	0.117158i	$0.962621\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.12132	−	5.40629i	−0.387152	−	0.670567i
$66$		0			0
$67$	−5.62132	+	9.73641i	−0.686754	+	1.18949i	0.286129	+	0.958191i	$0.407632\pi$
$67$	−5.62132	+	9.73641i	−0.686754	+	1.18949i	−0.972882	+	0.231301i	$0.925702\pi$
$68$	−3.82843	−	6.63103i	−0.464265	−	0.804131i
$69$		0			0
$70$	−3.41421	+	8.36308i	−0.408077	+	0.999579i
$71$	−3.07107			−0.364469			−0.182234	−	0.983255i	$-0.558333\pi$
$71$	−3.07107			−0.364469			−0.182234	+	0.983255i	$0.558333\pi$
$72$		0			0
$73$	3.29289	−	5.70346i	0.385404	−	0.667539i	−0.606421	−	0.795144i	$-0.707395\pi$
$73$	3.29289	−	5.70346i	0.385404	−	0.667539i	0.991825	+	0.127604i	$0.0407288\pi$
$74$	−3.29289	+	5.70346i	−0.382791	+	0.663014i
$75$		0			0
$76$	−3.41421			−0.391637
$77$	−1.00000	+	2.44949i	−0.113961	+	0.279145i
$78$		0			0
$79$	2.37868	+	4.11999i	0.267622	+	0.463536i	0.968247	−	0.249994i	$-0.0804287\pi$
$79$	2.37868	+	4.11999i	0.267622	+	0.463536i	−0.700625	+	0.713530i	$0.747095\pi$
$80$	−1.70711	+	2.95680i	−0.190860	+	0.330580i
$81$		0			0
$82$	1.29289	+	2.23936i	0.142776	+	0.247296i
$83$	−16.1421			−1.77183			−0.885915	−	0.463848i	$-0.846468\pi$
$83$	−16.1421			−1.77183			−0.885915	+	0.463848i	$0.846468\pi$
$84$		0			0
$85$	26.1421			2.83551
$86$	2.82843	+	4.89898i	0.304997	+	0.528271i
$87$		0			0
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	−2.24264	−	3.88437i	−0.237719	−	0.411742i	0.722340	−	0.691538i	$-0.243067\pi$
$89$	−2.24264	−	3.88437i	−0.237719	−	0.411742i	−0.960060	+	0.279796i	$0.909733\pi$
$90$		0			0
$91$	−4.79289	+	0.655892i	−0.502432	+	0.0687562i
$92$	−2.24264			−0.233811
$93$		0			0
$94$	−3.24264	+	5.61642i	−0.334453	+	0.579289i
$95$	5.82843	−	10.0951i	0.597984	−	1.03574i
$96$		0			0
$97$	1.82843			0.185649			0.0928243	−	0.995683i	$-0.470411\pi$
$97$	1.82843			0.185649			0.0928243	+	0.995683i	$0.470411\pi$
$98$	5.00000	+	4.89898i	0.505076	+	0.494872i
$99$		0			0
$100$	−3.32843	−	5.76500i	−0.332843	−	0.576500i
$101$	5.91421	−	10.2437i	0.588486	−	1.01929i	−0.405945	−	0.913898i	$-0.633057\pi$
$101$	5.91421	−	10.2437i	0.588486	−	1.01929i	0.994431	−	0.105390i	$-0.0336092\pi$
$102$		0			0
$103$	−5.29289	−	9.16756i	−0.521524	−	0.903307i	−0.999687	−	0.0250350i	$-0.992030\pi$
$103$	−5.29289	−	9.16756i	−0.521524	−	0.903307i	0.478162	−	0.878271i	$-0.341303\pi$
$104$	−1.82843			−0.179292
$105$		0			0
$106$	−11.8995			−1.15578
$107$	5.53553	+	9.58783i	0.535140	+	0.926890i	0.999157	+	0.0410635i	$0.0130746\pi$
$107$	5.53553	+	9.58783i	0.535140	+	0.926890i	−0.464016	+	0.885827i	$0.653592\pi$
$108$		0			0
$109$	0.242641	−	0.420266i	0.0232408	−	0.0402542i	−0.854171	−	0.519992i	$-0.825935\pi$
$109$	0.242641	−	0.420266i	0.0232408	−	0.0402542i	0.877412	+	0.479738i	$0.159268\pi$
$110$	−1.70711	−	2.95680i	−0.162766	−	0.281919i
$111$		0			0
$112$	1.62132	+	2.09077i	0.153200	+	0.197559i
$113$	13.8284			1.30087			0.650434	−	0.759562i	$-0.274587\pi$
$113$	13.8284			1.30087			0.650434	+	0.759562i	$0.274587\pi$
$114$		0			0
$115$	3.82843	−	6.63103i	0.357003	−	0.618347i
$116$	−4.32843	+	7.49706i	−0.401884	+	0.696084i
$117$		0			0
$118$	−8.41421			−0.774591
$119$	7.65685	−	18.7554i	0.701903	−	1.71930i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	3.08579	−	5.34474i	0.279374	−	0.483890i
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	5.65685			0.505964
$126$		0			0
$127$	−9.72792			−0.863213			−0.431607	−	0.902062i	$-0.642053\pi$
$127$	−9.72792			−0.863213			−0.431607	+	0.902062i	$0.642053\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	3.12132	−	5.40629i	0.273758	−	0.474163i
$131$	−1.70711	−	2.95680i	−0.149151	−	0.258336i	0.781763	−	0.623575i	$-0.214321\pi$
$131$	−1.70711	−	2.95680i	−0.149151	−	0.258336i	−0.930914	+	0.365239i	$0.880987\pi$
$132$		0			0
$133$	−5.53553	−	7.13834i	−0.479992	−	0.618972i
$134$	−11.2426			−0.971216
$135$		0			0
$136$	3.82843	−	6.63103i	0.328285	−	0.568606i
$137$	−2.67157	+	4.62730i	−0.228248	+	0.395337i	−0.957289	−	0.289133i	$-0.906633\pi$
$137$	−2.67157	+	4.62730i	−0.228248	+	0.395337i	0.729041	+	0.684470i	$0.239966\pi$
$138$		0			0
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$	−8.94975	+	1.22474i	−0.756392	+	0.103510i
$141$		0			0
$142$	−1.53553	−	2.65962i	−0.128859	−	0.223191i
$143$	0.914214	−	1.58346i	0.0764504	−	0.132416i
$144$		0			0
$145$	−14.7782	−	25.5965i	−1.22726	−	2.12568i
$146$	6.58579			0.545044
$147$		0			0
$148$	−6.58579			−0.541348
$149$	3.17157	+	5.49333i	0.259825	+	0.450031i	0.966195	−	0.257812i	$-0.0830017\pi$
$149$	3.17157	+	5.49333i	0.259825	+	0.450031i	−0.706370	+	0.707843i	$0.749668\pi$
$150$		0			0
$151$	−4.86396	+	8.42463i	−0.395824	+	0.685586i	−0.993206	−	0.116370i	$-0.962874\pi$
$151$	−4.86396	+	8.42463i	−0.395824	+	0.685586i	0.597382	+	0.801957i	$0.296207\pi$
$152$	−1.70711	−	2.95680i	−0.138465	−	0.239828i
$153$		0			0
$154$	−2.62132	+	0.358719i	−0.211232	+	0.0289064i
$155$	−13.6569			−1.09694
$156$		0			0
$157$	−3.17157	+	5.49333i	−0.253119	+	0.438415i	−0.964383	−	0.264510i	$-0.914790\pi$
$157$	−3.17157	+	5.49333i	−0.253119	+	0.438415i	0.711264	+	0.702925i	$0.248123\pi$
$158$	−2.37868	+	4.11999i	−0.189238	+	0.327769i
$159$		0			0
$160$	−3.41421			−0.269917
$161$	−3.63604	−	4.68885i	−0.286560	−	0.369533i
$162$		0			0
$163$	7.86396	+	13.6208i	0.615953	+	1.06686i	0.990217	+	0.139539i	$0.0445622\pi$
$163$	7.86396	+	13.6208i	0.615953	+	1.06686i	−0.374264	+	0.927322i	$0.622104\pi$
$164$	−1.29289	+	2.23936i	−0.100958	+	0.174864i
$165$		0			0
$166$	−8.07107	−	13.9795i	−0.626436	−	1.08502i
$167$	11.7279			0.907534			0.453767	−	0.891120i	$-0.350080\pi$
$167$	11.7279			0.907534			0.453767	+	0.891120i	$0.350080\pi$
$168$		0			0
$169$	−9.65685			−0.742835
$170$	13.0711	+	22.6398i	1.00251	+	1.73639i
$171$		0			0
$172$	−2.82843	+	4.89898i	−0.215666	+	0.373544i
$173$	−2.08579	−	3.61269i	−0.158579	−	0.274668i	0.775777	−	0.631007i	$-0.217358\pi$
$173$	−2.08579	−	3.61269i	−0.158579	−	0.274668i	−0.934357	+	0.356339i	$0.884025\pi$
$174$		0			0
$175$	6.65685	−	16.3059i	0.503211	−	1.23261i
$176$	−1.00000			−0.0753778
$177$		0			0
$178$	2.24264	−	3.88437i	0.168093	−	0.291146i
$179$	−9.44975	+	16.3674i	−0.706307	+	1.22336i	0.259910	+	0.965633i	$0.416307\pi$
$179$	−9.44975	+	16.3674i	−0.706307	+	1.22336i	−0.966218	+	0.257727i	$0.917026\pi$
$180$		0			0
$181$	3.65685			0.271812			0.135906	−	0.990722i	$-0.456606\pi$
$181$	3.65685			0.271812			0.135906	+	0.990722i	$0.456606\pi$
$182$	−2.96447	−	3.82282i	−0.219741	−	0.283366i
$183$		0			0
$184$	−1.12132	−	1.94218i	−0.0826648	−	0.143180i
$185$	11.2426	−	19.4728i	0.826575	−	1.43167i
$186$		0			0
$187$	3.82843	+	6.63103i	0.279962	+	0.484909i
$188$	−6.48528			−0.472988
$189$		0			0
$190$	11.6569			0.845677
$191$	−6.41421	−	11.1097i	−0.464116	−	0.803873i	0.535045	−	0.844824i	$-0.320295\pi$
$191$	−6.41421	−	11.1097i	−0.464116	−	0.803873i	−0.999161	+	0.0409507i	$0.986961\pi$
$192$		0			0
$193$	−1.05025	+	1.81909i	−0.0755988	+	0.130941i	−0.901347	−	0.433099i	$-0.857420\pi$
$193$	−1.05025	+	1.81909i	−0.0755988	+	0.130941i	0.825748	+	0.564040i	$0.190754\pi$
$194$	0.914214	+	1.58346i	0.0656367	+	0.113686i
$195$		0			0
$196$	−1.74264	+	6.77962i	−0.124474	+	0.484258i
$197$	17.4853			1.24577			0.622887	−	0.782312i	$-0.285959\pi$
$197$	17.4853			1.24577			0.622887	+	0.782312i	$0.285959\pi$
$198$		0			0
$199$	−9.94975	+	17.2335i	−0.705319	+	1.22165i	0.261257	+	0.965269i	$0.415863\pi$
$199$	−9.94975	+	17.2335i	−0.705319	+	1.22165i	−0.966576	+	0.256379i	$0.917470\pi$
$200$	3.32843	−	5.76500i	0.235355	−	0.407647i
$201$		0			0
$202$	11.8284			0.832245
$203$	−22.6924	+	3.10538i	−1.59269	+	0.217955i
$204$		0			0
$205$	−4.41421	−	7.64564i	−0.308302	−	0.533995i
$206$	5.29289	−	9.16756i	0.368773	−	0.638734i
$207$		0			0
$208$	−0.914214	−	1.58346i	−0.0633893	−	0.109793i
$209$	3.41421			0.236166
$210$		0			0
$211$	4.58579			0.315699			0.157849	−	0.987463i	$-0.449544\pi$
$211$	4.58579			0.315699			0.157849	+	0.987463i	$0.449544\pi$
$212$	−5.94975	−	10.3053i	−0.408630	−	0.707768i
$213$		0			0
$214$	−5.53553	+	9.58783i	−0.378401	+	0.655410i
$215$	−9.65685	−	16.7262i	−0.658592	−	1.14071i
$216$		0			0
$217$	−4.00000	+	9.79796i	−0.271538	+	0.665129i
$218$	0.485281			0.0328674
$219$		0			0
$220$	1.70711	−	2.95680i	0.115093	−	0.199347i
$221$	−7.00000	+	12.1244i	−0.470871	+	0.815572i
$222$		0			0
$223$	11.4142			0.764352			0.382176	−	0.924089i	$-0.375175\pi$
$223$	11.4142			0.764352			0.382176	+	0.924089i	$0.375175\pi$
$224$	−1.00000	+	2.44949i	−0.0668153	+	0.163663i
$225$		0			0
$226$	6.91421	+	11.9758i	0.459927	+	0.796616i
$227$	−11.5858	+	20.0672i	−0.768976	+	1.33190i	0.169143	+	0.985591i	$0.445900\pi$
$227$	−11.5858	+	20.0672i	−0.768976	+	1.33190i	−0.938119	+	0.346313i	$0.887433\pi$
$228$		0			0
$229$	−0.343146	−	0.594346i	−0.0226757	−	0.0392755i	0.854465	−	0.519509i	$-0.173885\pi$
$229$	−0.343146	−	0.594346i	−0.0226757	−	0.0392755i	−0.877141	+	0.480234i	$0.840552\pi$
$230$	7.65685			0.504878
$231$		0			0
$232$	−8.65685			−0.568350
$233$	−0.707107	−	1.22474i	−0.0463241	−	0.0802357i	0.841934	−	0.539581i	$-0.181417\pi$
$233$	−0.707107	−	1.22474i	−0.0463241	−	0.0802357i	−0.888258	+	0.459345i	$0.848084\pi$
$234$		0			0
$235$	11.0711	−	19.1757i	0.722197	−	1.25088i
$236$	−4.20711	−	7.28692i	−0.273859	−	0.474338i
$237$		0			0
$238$	20.0711	−	2.74666i	1.30101	−	0.178040i
$239$	22.2132			1.43685			0.718426	−	0.695603i	$-0.244863\pi$
$239$	22.2132			1.43685			0.718426	+	0.695603i	$0.244863\pi$
$240$		0			0
$241$	−1.87868	+	3.25397i	−0.121016	+	0.209607i	−0.920169	−	0.391522i	$-0.871949\pi$
$241$	−1.87868	+	3.25397i	−0.121016	+	0.209607i	0.799152	+	0.601129i	$0.205282\pi$
$242$	0.500000	−	0.866025i	0.0321412	−	0.0556702i
$243$		0			0
$244$	6.17157			0.395094
$245$	−17.0711	−	16.7262i	−1.09063	−	1.06860i
$246$		0			0
$247$	3.12132	+	5.40629i	0.198605	+	0.343994i
$248$	−2.00000	+	3.46410i	−0.127000	+	0.219971i
$249$		0			0
$250$	2.82843	+	4.89898i	0.178885	+	0.309839i
$251$	−2.14214			−0.135210			−0.0676052	−	0.997712i	$-0.521536\pi$
$251$	−2.14214			−0.135210			−0.0676052	+	0.997712i	$0.521536\pi$
$252$		0			0
$253$	2.24264			0.140994
$254$	−4.86396	−	8.42463i	−0.305192	−	0.528608i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.57107	+	2.72117i	0.0980005	+	0.169742i	0.910857	−	0.412722i	$-0.135422\pi$
$257$	1.57107	+	2.72117i	0.0980005	+	0.169742i	−0.812856	+	0.582464i	$0.802089\pi$
$258$		0			0
$259$	−10.6777	−	13.7694i	−0.663478	−	0.855587i
$260$	6.24264			0.387152
$261$		0			0
$262$	1.70711	−	2.95680i	0.105465	−	0.182671i
$263$	15.5208	−	26.8828i	0.957054	−	1.65767i	0.227459	−	0.973788i	$-0.426958\pi$
$263$	15.5208	−	26.8828i	0.957054	−	1.65767i	0.729595	−	0.683879i	$-0.239709\pi$
$264$		0			0
$265$	40.6274			2.49572
$266$	3.41421	−	8.36308i	0.209339	−	0.512773i
$267$		0			0
$268$	−5.62132	−	9.73641i	−0.343377	−	0.594746i
$269$	6.82843	−	11.8272i	0.416337	−	0.721116i	−0.579231	−	0.815163i	$-0.696647\pi$
$269$	6.82843	−	11.8272i	0.416337	−	0.721116i	0.995568	+	0.0940473i	$0.0299805\pi$
$270$		0			0
$271$	13.2782	+	22.9985i	0.806592	+	1.39706i	0.915211	+	0.402974i	$0.132024\pi$
$271$	13.2782	+	22.9985i	0.806592	+	1.39706i	−0.108620	+	0.994083i	$0.534643\pi$
$272$	7.65685			0.464265
$273$		0			0
$274$	−5.34315			−0.322791
$275$	3.32843	+	5.76500i	0.200712	+	0.347643i
$276$		0			0
$277$	1.91421	−	3.31552i	0.115014	−	0.199210i	−0.802771	−	0.596287i	$-0.796642\pi$
$277$	1.91421	−	3.31552i	0.115014	−	0.199210i	0.917785	+	0.397077i	$0.129975\pi$
$278$		0			0
$279$		0			0
$280$	−5.53553	−	7.13834i	−0.330811	−	0.426597i
$281$	16.7279			0.997904			0.498952	−	0.866630i	$-0.333718\pi$
$281$	16.7279			0.997904			0.498952	+	0.866630i	$0.333718\pi$
$282$		0			0
$283$	10.2929	−	17.8278i	0.611849	−	1.05975i	−0.379080	−	0.925364i	$-0.623759\pi$
$283$	10.2929	−	17.8278i	0.611849	−	1.05975i	0.990929	−	0.134389i	$-0.0429073\pi$
$284$	1.53553	−	2.65962i	0.0911172	−	0.157820i
$285$		0			0
$286$	1.82843			0.108117
$287$	−6.77817	+	0.927572i	−0.400103	+	0.0547528i
$288$		0			0
$289$	−20.8137	−	36.0504i	−1.22434	−	2.12061i
$290$	14.7782	−	25.5965i	0.867804	−	1.50308i
$291$		0			0
$292$	3.29289	+	5.70346i	0.192702	+	0.333770i
$293$	5.17157			0.302127			0.151063	−	0.988524i	$-0.451730\pi$
$293$	5.17157			0.302127			0.151063	+	0.988524i	$0.451730\pi$
$294$		0			0
$295$	28.7279			1.67260
$296$	−3.29289	−	5.70346i	−0.191396	−	0.331507i
$297$		0			0
$298$	−3.17157	+	5.49333i	−0.183724	+	0.318220i
$299$	2.05025	+	3.55114i	0.118569	+	0.205368i
$300$		0			0
$301$	−14.8284	+	2.02922i	−0.854696	+	0.116963i
$302$	−9.72792			−0.559779
$303$		0			0
$304$	1.70711	−	2.95680i	0.0979093	−	0.169584i
$305$	−10.5355	+	18.2481i	−0.603263	+	1.04488i
$306$		0			0
$307$	−9.89949			−0.564994			−0.282497	−	0.959268i	$-0.591163\pi$
$307$	−9.89949			−0.564994			−0.282497	+	0.959268i	$0.591163\pi$
$308$	−1.62132	−	2.09077i	−0.0923833	−	0.119133i
$309$		0			0
$310$	−6.82843	−	11.8272i	−0.387829	−	0.671739i
$311$	−4.36396	+	7.55860i	−0.247458	+	0.428609i	−0.962820	−	0.270145i	$-0.912928\pi$
$311$	−4.36396	+	7.55860i	−0.247458	+	0.428609i	0.715362	+	0.698754i	$0.246262\pi$
$312$		0			0
$313$	4.67157	+	8.09140i	0.264053	+	0.457353i	0.967315	−	0.253578i	$-0.0816073\pi$
$313$	4.67157	+	8.09140i	0.264053	+	0.457353i	−0.703262	+	0.710931i	$0.748274\pi$
$314$	−6.34315			−0.357964
$315$		0			0
$316$	−4.75736			−0.267622
$317$	15.6569	+	27.1185i	0.879377	+	1.52312i	0.852026	+	0.523499i	$0.175374\pi$
$317$	15.6569	+	27.1185i	0.879377	+	1.52312i	0.0273502	+	0.999626i	$0.491293\pi$
$318$		0			0
$319$	4.32843	−	7.49706i	0.242345	−	0.419755i
$320$	−1.70711	−	2.95680i	−0.0954302	−	0.165290i
$321$		0			0
$322$	2.24264	−	5.49333i	0.124977	−	0.306131i
$323$	−26.1421			−1.45459
$324$		0			0
$325$	−6.08579	+	10.5409i	−0.337579	+	0.584703i
$326$	−7.86396	+	13.6208i	−0.435545	+	0.754385i
$327$		0			0
$328$	−2.58579			−0.142776
$329$	−10.5147	−	13.5592i	−0.579695	−	0.747545i
$330$		0			0
$331$	4.96447	+	8.59871i	0.272872	+	0.472628i	0.969596	−	0.244711i	$-0.0786932\pi$
$331$	4.96447	+	8.59871i	0.272872	+	0.472628i	−0.696724	+	0.717339i	$0.745360\pi$
$332$	8.07107	−	13.9795i	0.442957	−	0.767225i
$333$		0			0
$334$	5.86396	+	10.1567i	0.320862	+	0.555749i
$335$	38.3848			2.09718
$336$		0			0
$337$	−19.7574			−1.07625			−0.538126	−	0.842864i	$-0.680868\pi$
$337$	−19.7574			−1.07625			−0.538126	+	0.842864i	$0.680868\pi$
$338$	−4.82843	−	8.36308i	−0.262632	−	0.454892i
$339$		0			0
$340$	−13.0711	+	22.6398i	−0.708878	+	1.22781i
$341$	−2.00000	−	3.46410i	−0.108306	−	0.187592i
$342$		0			0
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$	−5.65685			−0.304997
$345$		0			0
$346$	2.08579	−	3.61269i	0.112133	−	0.194219i
$347$	7.29289	−	12.6317i	0.391503	−	0.678103i	−0.601145	−	0.799140i	$-0.705289\pi$
$347$	7.29289	−	12.6317i	0.391503	−	0.678103i	0.992648	+	0.121037i	$0.0386219\pi$
$348$		0			0
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$	17.4497	−	2.38794i	0.932728	−	0.127641i
$351$		0			0
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	−12.6569	+	21.9223i	−0.673656	+	1.16681i	0.303203	+	0.952926i	$0.401944\pi$
$353$	−12.6569	+	21.9223i	−0.673656	+	1.16681i	−0.976860	+	0.213881i	$0.931389\pi$
$354$		0			0
$355$	5.24264	+	9.08052i	0.278250	+	0.481944i
$356$	4.48528			0.237719
$357$		0			0
$358$	−18.8995			−0.998869
$359$	5.37868	+	9.31615i	0.283876	+	0.491687i	0.972336	−	0.233587i	$-0.0750463\pi$
$359$	5.37868	+	9.31615i	0.283876	+	0.491687i	−0.688460	+	0.725274i	$0.741713\pi$
$360$		0			0
$361$	3.67157	−	6.35935i	0.193241	−	0.334703i
$362$	1.82843	+	3.16693i	0.0961000	+	0.166450i
$363$		0			0
$364$	1.82843	−	4.47871i	0.0958356	−	0.234748i
$365$	−22.4853			−1.17693
$366$		0			0
$367$	−7.36396	+	12.7548i	−0.384396	+	0.665793i	−0.991685	−	0.128688i	$-0.958923\pi$
$367$	−7.36396	+	12.7548i	−0.384396	+	0.665793i	0.607290	+	0.794481i	$0.292257\pi$
$368$	1.12132	−	1.94218i	0.0584529	−	0.101243i
$369$		0			0
$370$	22.4853			1.16895
$371$	11.8995	−	29.1477i	0.617791	−	1.51327i
$372$		0			0
$373$	−6.98528	−	12.0989i	−0.361684	−	0.626455i	0.626554	−	0.779378i	$-0.284465\pi$
$373$	−6.98528	−	12.0989i	−0.361684	−	0.626455i	−0.988238	+	0.152923i	$0.951131\pi$
$374$	−3.82843	+	6.63103i	−0.197963	+	0.342882i
$375$		0			0
$376$	−3.24264	−	5.61642i	−0.167226	−	0.289645i
$377$	15.8284			0.815205
$378$		0			0
$379$	−25.8701			−1.32886			−0.664428	−	0.747352i	$-0.731325\pi$
$379$	−25.8701			−1.32886			−0.664428	+	0.747352i	$0.731325\pi$
$380$	5.82843	+	10.0951i	0.298992	+	0.517869i
$381$		0			0
$382$	6.41421	−	11.1097i	0.328180	−	0.568424i
$383$	15.1924	+	26.3140i	0.776295	+	1.34458i	0.934064	+	0.357106i	$0.116236\pi$
$383$	15.1924	+	26.3140i	0.776295	+	1.34458i	−0.157769	+	0.987476i	$0.550430\pi$
$384$		0			0
$385$	8.94975	−	1.22474i	0.456121	−	0.0624188i
$386$	−2.10051			−0.106913
$387$		0			0
$388$	−0.914214	+	1.58346i	−0.0464122	+	0.0803882i
$389$	1.36396	−	2.36245i	0.0691556	−	0.119781i	−0.829374	−	0.558693i	$-0.811303\pi$
$389$	1.36396	−	2.36245i	0.0691556	−	0.119781i	0.898530	+	0.438912i	$0.144636\pi$
$390$		0			0
$391$	−17.1716			−0.868404
$392$	−6.74264	+	1.88064i	−0.340555	+	0.0949865i
$393$		0			0
$394$	8.74264	+	15.1427i	0.440448	+	0.762878i
$395$	8.12132	−	14.0665i	0.408628	−	0.707764i
$396$		0			0
$397$	−11.0000	−	19.0526i	−0.552074	−	0.956221i	−0.998125	−	0.0612128i	$-0.980503\pi$
$397$	−11.0000	−	19.0526i	−0.552074	−	0.956221i	0.446051	−	0.895008i	$-0.352830\pi$
$398$	−19.8995			−0.997472
$399$		0			0
$400$	6.65685			0.332843
$401$	−2.15685	−	3.73578i	−0.107708	−	0.186556i	0.807133	−	0.590369i	$-0.201018\pi$
$401$	−2.15685	−	3.73578i	−0.107708	−	0.186556i	−0.914841	+	0.403813i	$0.867685\pi$
$402$		0			0
$403$	3.65685	−	6.33386i	0.182161	−	0.315512i
$404$	5.91421	+	10.2437i	0.294243	+	0.509644i
$405$		0			0
$406$	−14.0355	−	18.0995i	−0.696572	−	0.898263i
$407$	6.58579			0.326445
$408$		0			0
$409$	11.3640	−	19.6830i	0.561912	−	0.973260i	−0.435418	−	0.900228i	$-0.643399\pi$
$409$	11.3640	−	19.6830i	0.561912	−	0.973260i	0.997330	−	0.0730312i	$-0.0232673\pi$
$410$	4.41421	−	7.64564i	0.218002	−	0.377591i
$411$		0			0
$412$	10.5858			0.521524
$413$	8.41421	−	20.6105i	0.414036	−	1.01418i
$414$		0			0
$415$	27.5563	+	47.7290i	1.35269	+	2.34292i
$416$	0.914214	−	1.58346i	0.0448230	−	0.0776357i
$417$		0			0
$418$	1.70711	+	2.95680i	0.0834973	+	0.144622i
$419$	−2.14214			−0.104650			−0.0523251	−	0.998630i	$-0.516663\pi$
$419$	−2.14214			−0.104650			−0.0523251	+	0.998630i	$0.516663\pi$
$420$		0			0
$421$	23.3137			1.13624			0.568120	−	0.822946i	$-0.307671\pi$
$421$	23.3137			1.13624			0.568120	+	0.822946i	$0.307671\pi$
$422$	2.29289	+	3.97141i	0.111616	+	0.193325i
$423$		0			0
$424$	5.94975	−	10.3053i	0.288945	−	0.500468i
$425$	−25.4853	−	44.1418i	−1.23622	−	2.14119i
$426$		0			0
$427$	10.0061	+	12.9033i	0.484229	+	0.624436i
$428$	−11.0711			−0.535140
$429$		0			0
$430$	9.65685	−	16.7262i	0.465695	−	0.806607i
$431$	−10.2071	+	17.6792i	−0.491659	+	0.851578i	−0.999954	−	0.00960469i	$-0.996943\pi$
$431$	−10.2071	+	17.6792i	−0.491659	+	0.851578i	0.508295	+	0.861183i	$0.330276\pi$
$432$		0			0
$433$	−2.14214			−0.102944			−0.0514722	−	0.998674i	$-0.516391\pi$
$433$	−2.14214			−0.102944			−0.0514722	+	0.998674i	$0.516391\pi$
$434$	−10.4853	+	1.43488i	−0.503310	+	0.0688763i
$435$		0			0
$436$	0.242641	+	0.420266i	0.0116204	+	0.0201271i
$437$	−3.82843	+	6.63103i	−0.183139	+	0.317205i
$438$		0			0
$439$	−4.69239	−	8.12745i	−0.223955	−	0.387902i	0.732050	−	0.681251i	$-0.238564\pi$
$439$	−4.69239	−	8.12745i	−0.223955	−	0.387902i	−0.956006	+	0.293349i	$0.905230\pi$
$440$	3.41421			0.162766
$441$		0			0
$442$	−14.0000			−0.665912
$443$	−16.3137	−	28.2562i	−0.775088	−	1.34249i	−0.934745	−	0.355319i	$-0.884372\pi$
$443$	−16.3137	−	28.2562i	−0.775088	−	1.34249i	0.159658	−	0.987172i	$-0.448961\pi$
$444$		0			0
$445$	−7.65685	+	13.2621i	−0.362970	+	0.628682i
$446$	5.70711	+	9.88500i	0.270239	+	0.468068i
$447$		0			0
$448$	−2.62132	+	0.358719i	−0.123846	+	0.0169479i
$449$	−33.6569			−1.58837			−0.794183	−	0.607679i	$-0.792101\pi$
$449$	−33.6569			−1.58837			−0.794183	+	0.607679i	$0.792101\pi$
$450$		0			0
$451$	1.29289	−	2.23936i	0.0608800	−	0.105447i
$452$	−6.91421	+	11.9758i	−0.325217	+	0.563293i
$453$		0			0
$454$	−23.1716			−1.08750
$455$	10.1213	+	13.0519i	0.474495	+	0.611884i
$456$		0			0
$457$	0.171573	+	0.297173i	0.00802584	+	0.0139012i	0.870010	−	0.493033i	$-0.164112\pi$
$457$	0.171573	+	0.297173i	0.00802584	+	0.0139012i	−0.861985	+	0.506934i	$0.830779\pi$
$458$	0.343146	−	0.594346i	0.0160341	−	0.0277720i
$459$		0			0
$460$	3.82843	+	6.63103i	0.178501	+	0.309173i
$461$	−14.3137			−0.666656			−0.333328	−	0.942811i	$-0.608172\pi$
$461$	−14.3137			−0.666656			−0.333328	+	0.942811i	$0.608172\pi$
$462$		0			0
$463$	7.17157			0.333291			0.166646	−	0.986017i	$-0.446706\pi$
$463$	7.17157			0.333291			0.166646	+	0.986017i	$0.446706\pi$
$464$	−4.32843	−	7.49706i	−0.200942	−	0.348042i
$465$		0			0
$466$	0.707107	−	1.22474i	0.0327561	−	0.0567352i
$467$	−17.0000	−	29.4449i	−0.786666	−	1.36255i	−0.927999	−	0.372584i	$-0.878472\pi$
$467$	−17.0000	−	29.4449i	−0.786666	−	1.36255i	0.141332	−	0.989962i	$-0.454861\pi$
$468$		0			0
$469$	11.2426	−	27.5387i	0.519137	−	1.27162i
$470$	22.1421			1.02134
$471$		0			0
$472$	4.20711	−	7.28692i	0.193648	−	0.335408i
$473$	2.82843	−	4.89898i	0.130051	−	0.225255i
$474$		0			0
$475$	−22.7279			−1.04283
$476$	12.4142	+	16.0087i	0.569005	+	0.733759i
$477$		0			0
$478$	11.1066	+	19.2372i	0.508004	+	0.879889i
$479$	−13.0355	+	22.5782i	−0.595609	+	1.03162i	0.397852	+	0.917450i	$0.369756\pi$
$479$	−13.0355	+	22.5782i	−0.595609	+	1.03162i	−0.993461	+	0.114175i	$0.963578\pi$
$480$		0			0
$481$	6.02082	+	10.4284i	0.274526	+	0.475492i
$482$	−3.75736			−0.171143
$483$		0			0
$484$	1.00000			0.0454545
$485$	−3.12132	−	5.40629i	−0.141732	−	0.245487i
$486$		0			0
$487$	−0.828427	+	1.43488i	−0.0375396	+	0.0650205i	−0.884185	−	0.467137i	$-0.845285\pi$
$487$	−0.828427	+	1.43488i	−0.0375396	+	0.0650205i	0.846645	+	0.532158i	$0.178619\pi$
$488$	3.08579	+	5.34474i	0.139687	+	0.241945i
$489$		0			0
$490$	5.94975	−	23.1471i	0.268782	−	1.04568i
$491$	−24.8284			−1.12049			−0.560246	−	0.828327i	$-0.689293\pi$
$491$	−24.8284			−1.12049			−0.560246	+	0.828327i	$0.689293\pi$
$492$		0			0
$493$	−33.1421	+	57.4039i	−1.49265	+	2.58534i
$494$	−3.12132	+	5.40629i	−0.140435	+	0.243240i
$495$		0			0
$496$	−4.00000			−0.179605
$497$	8.05025	−	1.10165i	0.361103	−	0.0494158i
$498$		0			0
$499$	3.07107	+	5.31925i	0.137480	+	0.238122i	0.926542	−	0.376191i	$-0.122766\pi$
$499$	3.07107	+	5.31925i	0.137480	+	0.238122i	−0.789062	+	0.614313i	$0.789433\pi$
$500$	−2.82843	+	4.89898i	−0.126491	+	0.219089i
$501$		0			0
$502$	−1.07107	−	1.85514i	−0.0478041	−	0.0827991i
$503$	38.2132			1.70384			0.851921	−	0.523670i	$-0.175437\pi$
$503$	38.2132			1.70384			0.851921	+	0.523670i	$0.175437\pi$
$504$		0			0
$505$	−40.3848			−1.79710
$506$	1.12132	+	1.94218i	0.0498488	+	0.0863406i
$507$		0			0
$508$	4.86396	−	8.42463i	0.215803	−	0.373782i
$509$	−6.65685	−	11.5300i	−0.295060	−	0.511059i	0.679939	−	0.733269i	$-0.262006\pi$
$509$	−6.65685	−	11.5300i	−0.295060	−	0.511059i	−0.974999	+	0.222210i	$0.928673\pi$
$510$		0			0
$511$	−6.58579	+	16.1318i	−0.291338	+	0.713630i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−1.57107	+	2.72117i	−0.0692968	+	0.120026i
$515$	−18.0711	+	31.3000i	−0.796306	+	1.37924i
$516$		0			0
$517$	6.48528			0.285222
$518$	6.58579	−	16.1318i	0.289363	−	0.708791i
$519$		0			0
$520$	3.12132	+	5.40629i	0.136879	+	0.237081i
$521$	14.1421	−	24.4949i	0.619578	−	1.07314i	−0.369984	−	0.929038i	$-0.620637\pi$
$521$	14.1421	−	24.4949i	0.619578	−	1.07314i	0.989563	−	0.144103i	$-0.0460297\pi$
$522$		0			0
$523$	−6.36396	−	11.0227i	−0.278277	−	0.481989i	0.692680	−	0.721245i	$-0.256430\pi$
$523$	−6.36396	−	11.0227i	−0.278277	−	0.481989i	−0.970957	+	0.239256i	$0.923097\pi$
$524$	3.41421			0.149151
$525$		0			0
$526$	31.0416			1.35348
$527$	15.3137	+	26.5241i	0.667076	+	1.15541i
$528$		0			0
$529$	8.98528	−	15.5630i	0.390664	−	0.676651i
$530$	20.3137	+	35.1844i	0.882371	+	1.52831i
$531$		0			0
$532$	8.94975	−	1.22474i	0.388021	−	0.0530994i
$533$	4.72792			0.204789
$534$		0			0
$535$	18.8995	−	32.7349i	0.817096	−	1.41525i
$536$	5.62132	−	9.73641i	0.242804	−	0.420549i
$537$		0			0
$538$	13.6569			0.588789
$539$	1.74264	−	6.77962i	0.0750608	−	0.292019i
$540$		0			0
$541$	20.5711	+	35.6301i	0.884419	+	1.53186i	0.846378	+	0.532583i	$0.178779\pi$
$541$	20.5711	+	35.6301i	0.884419	+	1.53186i	0.0380415	+	0.999276i	$0.487888\pi$
$542$	−13.2782	+	22.9985i	−0.570346	+	0.987869i
$543$		0			0
$544$	3.82843	+	6.63103i	0.164142	+	0.284303i
$545$	−1.65685			−0.0709718
$546$		0			0
$547$	−18.8701			−0.806825			−0.403413	−	0.915018i	$-0.632176\pi$
$547$	−18.8701			−0.806825			−0.403413	+	0.915018i	$0.632176\pi$
$548$	−2.67157	−	4.62730i	−0.114124	−	0.197668i
$549$		0			0
$550$	−3.32843	+	5.76500i	−0.141925	+	0.245821i
$551$	14.7782	+	25.5965i	0.629571	+	1.09045i
$552$		0			0
$553$	−7.71320	−	9.94655i	−0.327999	−	0.422970i
$554$	3.82843			0.162654
$555$		0			0
$556$		0			0
$557$	12.2426	−	21.2049i	0.518737	−	0.898479i	−0.481026	−	0.876707i	$-0.659736\pi$
$557$	12.2426	−	21.2049i	0.518737	−	0.898479i	0.999763	−	0.0217729i	$-0.00693107\pi$
$558$		0			0
$559$	10.3431			0.437468
$560$	3.41421	−	8.36308i	0.144277	−	0.353405i
$561$		0			0
$562$	8.36396	+	14.4868i	0.352812	+	0.611089i
$563$	−2.53553	+	4.39167i	−0.106860	+	0.185087i	−0.914497	−	0.404594i	$-0.867413\pi$
$563$	−2.53553	+	4.39167i	−0.106860	+	0.185087i	0.807637	+	0.589681i	$0.200746\pi$
$564$		0			0
$565$	−23.6066	−	40.8878i	−0.993137	−	1.72016i
$566$	20.5858			0.865285
$567$		0			0
$568$	3.07107			0.128859
$569$	−2.00000	−	3.46410i	−0.0838444	−	0.145223i	0.821054	−	0.570851i	$-0.193387\pi$
$569$	−2.00000	−	3.46410i	−0.0838444	−	0.145223i	−0.904898	+	0.425628i	$0.860053\pi$
$570$		0			0
$571$	5.19239	−	8.99348i	0.217295	−	0.376365i	−0.736685	−	0.676236i	$-0.763610\pi$
$571$	5.19239	−	8.99348i	0.217295	−	0.376365i	0.953980	+	0.299870i	$0.0969434\pi$
$572$	0.914214	+	1.58346i	0.0382252	+	0.0662080i
$573$		0			0
$574$	−4.19239	−	5.40629i	−0.174987	−	0.225654i
$575$	−14.9289			−0.622580
$576$		0			0
$577$	16.1569	−	27.9845i	0.672619	−	1.16501i	−0.304540	−	0.952499i	$-0.598503\pi$
$577$	16.1569	−	27.9845i	0.672619	−	1.16501i	0.977159	−	0.212510i	$-0.0681639\pi$
$578$	20.8137	−	36.0504i	0.865736	−	1.49950i
$579$		0			0
$580$	29.5563			1.22726
$581$	42.3137	−	5.79050i	1.75547	−	0.240230i
$582$		0			0
$583$	5.94975	+	10.3053i	0.246413	+	0.426800i
$584$	−3.29289	+	5.70346i	−0.136261	+	0.236011i
$585$		0			0
$586$	2.58579	+	4.47871i	0.106818	+	0.185014i
$587$	44.8995			1.85320			0.926600	−	0.376048i	$-0.122717\pi$
$587$	44.8995			1.85320			0.926600	+	0.376048i	$0.122717\pi$
$588$		0			0
$589$	13.6569			0.562721
$590$	14.3640	+	24.8791i	0.591355	+	1.02426i
$591$		0			0
$592$	3.29289	−	5.70346i	0.135337	−	0.234411i
$593$	−17.8492	−	30.9158i	−0.732981	−	1.26956i	−0.955604	−	0.294655i	$-0.904795\pi$
$593$	−17.8492	−	30.9158i	−0.732981	−	1.26956i	0.222623	−	0.974905i	$-0.428538\pi$
$594$		0			0
$595$	−68.5269	+	9.37769i	−2.80933	+	0.384448i
$596$	−6.34315			−0.259825
$597$		0			0
$598$	−2.05025	+	3.55114i	−0.0838411	+	0.145217i
$599$	−1.31371	+	2.27541i	−0.0536767	+	0.0929707i	−0.891615	−	0.452794i	$-0.850427\pi$
$599$	−1.31371	+	2.27541i	−0.0536767	+	0.0929707i	0.837939	+	0.545765i	$0.183761\pi$
$600$		0			0
$601$	−35.9411			−1.46607			−0.733035	−	0.680191i	$-0.761897\pi$
$601$	−35.9411			−1.46607			−0.733035	+	0.680191i	$0.761897\pi$
$602$	−9.17157	−	11.8272i	−0.373805	−	0.482040i
$603$		0			0
$604$	−4.86396	−	8.42463i	−0.197912	−	0.342793i
$605$	−1.70711	+	2.95680i	−0.0694038	+	0.120211i
$606$		0			0
$607$	4.51472	+	7.81972i	0.183247	+	0.317393i	0.942984	−	0.332837i	$-0.108006\pi$
$607$	4.51472	+	7.81972i	0.183247	+	0.317393i	−0.759738	+	0.650230i	$0.774673\pi$
$608$	3.41421			0.138465
$609$		0			0
$610$	−21.0711			−0.853143
$611$	5.92893	+	10.2692i	0.239859	+	0.415448i
$612$		0			0
$613$	8.31371	−	14.3998i	0.335788	−	0.581601i	−0.647848	−	0.761769i	$-0.724331\pi$
$613$	8.31371	−	14.3998i	0.335788	−	0.581601i	0.983636	+	0.180168i	$0.0576643\pi$
$614$	−4.94975	−	8.57321i	−0.199756	−	0.345987i
$615$		0			0
$616$	1.00000	−	2.44949i	0.0402911	−	0.0986928i
$617$	8.02944			0.323253			0.161626	−	0.986852i	$-0.448326\pi$
$617$	8.02944			0.323253			0.161626	+	0.986852i	$0.448326\pi$
$618$		0			0
$619$	−22.9706	+	39.7862i	−0.923265	+	1.59914i	−0.128937	+	0.991653i	$0.541156\pi$
$619$	−22.9706	+	39.7862i	−0.923265	+	1.59914i	−0.794328	+	0.607489i	$0.792177\pi$
$620$	6.82843	−	11.8272i	0.274236	−	0.474991i
$621$		0			0
$622$	−8.72792			−0.349958
$623$	7.27208	+	9.37769i	0.291350	+	0.375709i
$624$		0			0
$625$	6.98528	+	12.0989i	0.279411	+	0.483954i
$626$	−4.67157	+	8.09140i	−0.186714	+	0.323397i
$627$		0			0
$628$	−3.17157	−	5.49333i	−0.126560	−	0.219208i
$629$	−50.4264			−2.01063
$630$		0			0
$631$	48.7279			1.93983			0.969914	−	0.243448i	$-0.0782785\pi$
$631$	48.7279			1.93983			0.969914	+	0.243448i	$0.0782785\pi$
$632$	−2.37868	−	4.11999i	−0.0946188	−	0.163885i
$633$		0			0
$634$	−15.6569	+	27.1185i	−0.621813	+	1.07701i
$635$	16.6066	+	28.7635i	0.659013	+	1.14144i
$636$		0			0
$637$	12.3284	−	3.43861i	0.488470	−	0.136243i
$638$	8.65685			0.342728
$639$		0			0
$640$	1.70711	−	2.95680i	0.0674793	−	0.116878i
$641$	−20.6421	+	35.7532i	−0.815315	+	1.41217i	0.0937859	+	0.995592i	$0.470103\pi$
$641$	−20.6421	+	35.7532i	−0.815315	+	1.41217i	−0.909101	+	0.416575i	$0.863230\pi$
$642$		0			0
$643$	4.41421			0.174080			0.0870398	−	0.996205i	$-0.472259\pi$
$643$	4.41421			0.174080			0.0870398	+	0.996205i	$0.472259\pi$
$644$	5.87868	−	0.804479i	0.231652	−	0.0317009i
$645$		0			0
$646$	−13.0711	−	22.6398i	−0.514274	−	0.890749i
$647$	−23.0919	+	39.9963i	−0.907836	+	1.57242i	−0.0907706	+	0.995872i	$0.528933\pi$
$647$	−23.0919	+	39.9963i	−0.907836	+	1.57242i	−0.817065	+	0.576546i	$0.804400\pi$
$648$		0			0
$649$	4.20711	+	7.28692i	0.165143	+	0.286037i
$650$	−12.1716			−0.477408
$651$		0			0
$652$	−15.7279			−0.615953
$653$	9.19239	+	15.9217i	0.359726	+	0.623064i	0.987915	−	0.154997i	$-0.0495369\pi$
$653$	9.19239	+	15.9217i	0.359726	+	0.623064i	−0.628189	+	0.778061i	$0.716204\pi$
$654$		0			0
$655$	−5.82843	+	10.0951i	−0.227735	+	0.394449i
$656$	−1.29289	−	2.23936i	−0.0504790	−	0.0874322i
$657$		0			0
$658$	6.48528	−	15.8856i	0.252823	−	0.619286i
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$	7.48528	−	12.9649i	0.291144	−	0.504276i	−0.682937	−	0.730478i	$-0.739298\pi$
$661$	7.48528	−	12.9649i	0.291144	−	0.504276i	0.974080	+	0.226202i	$0.0726309\pi$
$662$	−4.96447	+	8.59871i	−0.192949	+	0.334198i
$663$		0			0
$664$	16.1421			0.626436
$665$	−11.6569	+	28.5533i	−0.452033	+	1.10725i
$666$		0			0
$667$	9.70711	+	16.8132i	0.375861	+	0.651010i
$668$	−5.86396	+	10.1567i	−0.226883	+	0.392974i
$669$		0			0
$670$	19.1924	+	33.2422i	0.741467	+	1.28426i
$671$	−6.17157			−0.238251
$672$		0			0
$673$	−25.5563			−0.985125			−0.492562	−	0.870277i	$-0.663940\pi$
$673$	−25.5563			−0.985125			−0.492562	+	0.870277i	$0.663940\pi$
$674$	−9.87868	−	17.1104i	−0.380513	−	0.659067i
$675$		0			0
$676$	4.82843	−	8.36308i	0.185709	−	0.321657i
$677$	−6.34315	−	10.9867i	−0.243787	−	0.422251i	0.718003	−	0.696040i	$-0.245056\pi$
$677$	−6.34315	−	10.9867i	−0.243787	−	0.422251i	−0.961790	+	0.273789i	$0.911723\pi$
$678$		0			0
$679$	−4.79289	+	0.655892i	−0.183934	+	0.0251708i
$680$	−26.1421			−1.00251
$681$		0			0
$682$	2.00000	−	3.46410i	0.0765840	−	0.132647i
$683$	8.20711	−	14.2151i	0.314036	−	0.543927i	−0.665196	−	0.746669i	$-0.731652\pi$
$683$	8.20711	−	14.2151i	0.314036	−	0.543927i	0.979232	+	0.202742i	$0.0649853\pi$
$684$		0			0
$685$	18.2426			0.697015
$686$	−14.8640	−	11.0482i	−0.567509	−	0.421822i
$687$		0			0
$688$	−2.82843	−	4.89898i	−0.107833	−	0.186772i
$689$	−10.8787	+	18.8424i	−0.414445	+	0.717839i
$690$		0			0
$691$	−6.96447	−	12.0628i	−0.264941	−	0.458891i	0.702607	−	0.711578i	$-0.252019\pi$
$691$	−6.96447	−	12.0628i	−0.264941	−	0.458891i	−0.967548	+	0.252687i	$0.918686\pi$
$692$	4.17157			0.158579
$693$		0			0
$694$	14.5858			0.553669
$695$		0			0
$696$		0			0
$697$	−9.89949	+	17.1464i	−0.374970	+	0.649467i
$698$		0			0
$699$		0			0
$700$	10.7929	+	13.9180i	0.407933	+	0.526049i
$701$	−36.1127			−1.36396			−0.681979	−	0.731372i	$-0.738880\pi$
$701$	−36.1127			−1.36396			−0.681979	+	0.731372i	$0.738880\pi$
$702$		0			0
$703$	−11.2426	+	19.4728i	−0.424024	+	0.734432i
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$		0			0
$706$	−25.3137			−0.952694
$707$	−11.8284	+	28.9736i	−0.444854	+	1.08966i
$708$		0			0
$709$	−18.0208	−	31.2130i	−0.676786	−	1.17223i	−0.975943	−	0.218024i	$-0.930039\pi$
$709$	−18.0208	−	31.2130i	−0.676786	−	1.17223i	0.299158	−	0.954204i	$-0.403294\pi$
$710$	−5.24264	+	9.08052i	−0.196753	+	0.340786i
$711$		0			0
$712$	2.24264	+	3.88437i	0.0840465	+	0.145573i
$713$	8.97056			0.335950
$714$		0			0
$715$	−6.24264			−0.233462
$716$	−9.44975	−	16.3674i	−0.353154	−	0.611680i
$717$		0			0
$718$	−5.37868	+	9.31615i	−0.200731	+	0.347675i
$719$	−9.24264	−	16.0087i	−0.344692	−	0.597025i	0.640605	−	0.767870i	$-0.278683\pi$
$719$	−9.24264	−	16.0087i	−0.344692	−	0.597025i	−0.985298	+	0.170846i	$0.945350\pi$
$720$		0			0
$721$	17.1630	+	22.1324i	0.639182	+	0.824255i
$722$	7.34315			0.273284
$723$		0			0
$724$	−1.82843	+	3.16693i	−0.0679530	+	0.117698i
$725$	−28.8137	+	49.9068i	−1.07011	+	1.85349i
$726$		0			0
$727$	−48.4264			−1.79604			−0.898018	−	0.439959i	$-0.854993\pi$
$727$	−48.4264			−1.79604			−0.898018	+	0.439959i	$0.854993\pi$
$728$	4.79289	−	0.655892i	0.177636	−	0.0243090i
$729$		0			0
$730$	−11.2426	−	19.4728i	−0.416109	−	0.720722i
$731$	−21.6569	+	37.5108i	−0.801008	+	1.38739i
$732$		0			0
$733$	6.50000	+	11.2583i	0.240083	+	0.415836i	0.960738	−	0.277458i	$-0.0894920\pi$
$733$	6.50000	+	11.2583i	0.240083	+	0.415836i	−0.720655	+	0.693294i	$0.756159\pi$
$734$	−14.7279			−0.543618
$735$		0			0
$736$	2.24264			0.0826648
$737$	5.62132	+	9.73641i	0.207064	+	0.358645i
$738$		0			0
$739$	−16.2132	+	28.0821i	−0.596412	+	1.03302i	0.396934	+	0.917847i	$0.370074\pi$
$739$	−16.2132	+	28.0821i	−0.596412	+	1.03302i	−0.993346	+	0.115169i	$0.963259\pi$
$740$	11.2426	+	19.4728i	0.413288	+	0.715835i
$741$		0			0
$742$	31.1924	−	4.26858i	1.14511	−	0.156705i
$743$	−9.31371			−0.341687			−0.170843	−	0.985298i	$-0.554649\pi$
$743$	−9.31371			−0.341687			−0.170843	+	0.985298i	$0.554649\pi$
$744$		0			0
$745$	10.8284	−	18.7554i	0.396723	−	0.687144i
$746$	6.98528	−	12.0989i	0.255749	−	0.442971i
$747$		0			0
$748$	−7.65685			−0.279962
$749$	−17.9497	−	23.1471i	−0.655869	−	0.845775i
$750$		0			0
$751$	−17.1716	−	29.7420i	−0.626600	−	1.08530i	−0.988229	−	0.152980i	$-0.951113\pi$
$751$	−17.1716	−	29.7420i	−0.626600	−	1.08530i	0.361630	−	0.932322i	$-0.382220\pi$
$752$	3.24264	−	5.61642i	0.118247	−	0.204810i
$753$		0			0
$754$	7.91421	+	13.7078i	0.288219	+	0.499209i
$755$	33.2132			1.20875
$756$		0			0
$757$	19.6569			0.714441			0.357220	−	0.934020i	$-0.383725\pi$
$757$	19.6569			0.714441			0.357220	+	0.934020i	$0.383725\pi$
$758$	−12.9350	−	22.4041i	−0.469821	−	0.813755i
$759$		0			0
$760$	−5.82843	+	10.0951i	−0.211419	+	0.366189i
$761$	−1.48528	−	2.57258i	−0.0538414	−	0.0932561i	0.837849	−	0.545903i	$-0.183813\pi$
$761$	−1.48528	−	2.57258i	−0.0538414	−	0.0932561i	−0.891690	+	0.452647i	$0.850480\pi$
$762$		0			0
$763$	−0.485281	+	1.18869i	−0.0175684	+	0.0430335i
$764$	12.8284			0.464116
$765$		0			0
$766$	−15.1924	+	26.3140i	−0.548923	+	0.950763i
$767$	−7.69239	+	13.3236i	−0.277756	+	0.481088i
$768$		0			0
$769$	−10.9706			−0.395609			−0.197804	−	0.980242i	$-0.563381\pi$
$769$	−10.9706			−0.395609			−0.197804	+	0.980242i	$0.563381\pi$
$770$	5.53553	+	7.13834i	0.199487	+	0.257248i
$771$		0			0
$772$	−1.05025	−	1.81909i	−0.0377994	−	0.0654705i
$773$	22.9706	−	39.7862i	0.826194	−	1.43101i	−0.0748099	−	0.997198i	$-0.523835\pi$
$773$	22.9706	−	39.7862i	0.826194	−	1.43101i	0.901004	−	0.433812i	$-0.142832\pi$
$774$		0			0
$775$	13.3137	+	23.0600i	0.478243	+	0.828340i
$776$	−1.82843			−0.0656367
$777$		0			0
$778$	2.72792			0.0978007
$779$	4.41421	+	7.64564i	0.158156	+	0.273934i
$780$		0			0
$781$	−1.53553	+	2.65962i	−0.0549457	+	0.0951688i
$782$	−8.58579	−	14.8710i	−0.307027	−	0.531787i
$783$		0			0
$784$	−5.00000	−	4.89898i	−0.178571	−	0.174964i
$785$	21.6569			0.772966
$786$		0			0
$787$	8.77817	−	15.2042i	0.312908	−	0.541973i	−0.666082	−	0.745878i	$-0.732030\pi$
$787$	8.77817	−	15.2042i	0.312908	−	0.541973i	0.978991	+	0.203905i	$0.0653635\pi$
$788$	−8.74264	+	15.1427i	−0.311444	+	0.539436i
$789$		0			0
$790$	16.2426			0.577887
$791$	−36.2487	+	4.96053i	−1.28886	+	0.176376i
$792$		0			0
$793$	−5.64214	−	9.77247i	−0.200358	−	0.347030i
$794$	11.0000	−	19.0526i	0.390375	−	0.676150i
$795$		0			0
$796$	−9.94975	−	17.2335i	−0.352659	−	0.610824i
$797$	−3.65685			−0.129532			−0.0647662	−	0.997900i	$-0.520630\pi$
$797$	−3.65685			−0.129532			−0.0647662	+	0.997900i	$0.520630\pi$
$798$		0			0
$799$	−49.6569			−1.75673
$800$	3.32843	+	5.76500i	0.117678	+	0.203824i
$801$		0			0
$802$	2.15685	−	3.73578i	0.0761612	−	0.131915i
$803$	−3.29289	−	5.70346i	−0.116204	−	0.201271i
$804$		0			0
$805$	−7.65685	+	18.7554i	−0.269869	+	0.661040i
$806$	7.31371			0.257614
$807$		0			0
$808$	−5.91421	+	10.2437i	−0.208061	+	0.360373i
$809$	−0.686292	+	1.18869i	−0.0241287	+	0.0417922i	−0.877838	−	0.478958i	$-0.841014\pi$
$809$	−0.686292	+	1.18869i	−0.0241287	+	0.0417922i	0.853709	+	0.520751i	$0.174348\pi$
$810$		0			0
$811$	32.2843			1.13365			0.566827	−	0.823837i	$-0.308171\pi$
$811$	32.2843			1.13365			0.566827	+	0.823837i	$0.308171\pi$
$812$	8.65685	−	21.2049i	0.303796	−	0.744145i
$813$		0			0
$814$	3.29289	+	5.70346i	0.115416	+	0.199906i
$815$	26.8492	−	46.5043i	0.940488	−	1.62897i
$816$		0			0
$817$	9.65685	+	16.7262i	0.337851	+	0.585174i
$818$	22.7279			0.794663
$819$		0			0
$820$	8.82843			0.308302
$821$	−6.25736	−	10.8381i	−0.218383	−	0.378251i	0.735931	−	0.677057i	$-0.236745\pi$
$821$	−6.25736	−	10.8381i	−0.218383	−	0.378251i	−0.954314	+	0.298806i	$0.903412\pi$
$822$		0			0
$823$	−3.72792	+	6.45695i	−0.129947	+	0.225075i	−0.923656	−	0.383223i	$-0.874814\pi$
$823$	−3.72792	+	6.45695i	−0.129947	+	0.225075i	0.793709	+	0.608298i	$0.208147\pi$
$824$	5.29289	+	9.16756i	0.184387	+	0.319367i
$825$		0			0
$826$	22.0563	−	3.01834i	0.767439	−	0.105022i
$827$	−49.3553			−1.71625			−0.858127	−	0.513438i	$-0.828372\pi$
$827$	−49.3553			−1.71625			−0.858127	+	0.513438i	$0.828372\pi$
$828$		0			0
$829$	−15.1213	+	26.1909i	−0.525185	+	0.909647i	0.474385	+	0.880318i	$0.342671\pi$
$829$	−15.1213	+	26.1909i	−0.525185	+	0.909647i	−0.999570	+	0.0293297i	$0.990663\pi$
$830$	−27.5563	+	47.7290i	−0.956495	+	1.65670i
$831$		0			0
$832$	1.82843			0.0633893
$833$	−13.3431	+	51.9105i	−0.462313	+	1.79859i
$834$		0			0
$835$	−20.0208	−	34.6771i	−0.692849	−	1.20005i
$836$	−1.70711	+	2.95680i	−0.0590415	+	0.102263i
$837$		0			0
$838$	−1.07107	−	1.85514i	−0.0369994	−	0.0640849i
$839$	1.51472			0.0522939			0.0261469	−	0.999658i	$-0.491676\pi$
$839$	1.51472			0.0522939			0.0261469	+	0.999658i	$0.491676\pi$
$840$		0			0
$841$	45.9411			1.58418
$842$	11.6569	+	20.1903i	0.401722	+	0.695802i
$843$		0			0
$844$	−2.29289	+	3.97141i	−0.0789246	+	0.136701i
$845$	16.4853	+	28.5533i	0.567111	+	0.982265i
$846$		0			0
$847$	1.62132	+	2.09077i	0.0557092	+	0.0718397i
$848$	11.8995			0.408630
$849$		0			0
$850$	25.4853	−	44.1418i	0.874138	−	1.51405i
$851$	−7.38478	+	12.7908i	−0.253147	+	0.438463i
$852$		0			0
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$	−6.17157	+	15.1172i	−0.211187	+	0.517300i
$855$		0			0
$856$	−5.53553	−	9.58783i	−0.189201	−	0.327705i
$857$	5.31371	−	9.20361i	0.181513	−	0.314389i	−0.760883	−	0.648889i	$-0.775234\pi$
$857$	5.31371	−	9.20361i	0.181513	−	0.314389i	0.942396	+	0.334500i	$0.108567\pi$
$858$		0			0
$859$	−9.86396	−	17.0849i	−0.336554	−	0.582929i	0.647228	−	0.762296i	$-0.275928\pi$
$859$	−9.86396	−	17.0849i	−0.336554	−	0.582929i	−0.983782	+	0.179368i	$0.942595\pi$
$860$	19.3137			0.658592
$861$		0			0
$862$	−20.4142			−0.695311
$863$	−3.60660	−	6.24682i	−0.122770	−	0.212644i	0.798089	−	0.602540i	$-0.205844\pi$
$863$	−3.60660	−	6.24682i	−0.122770	−	0.212644i	−0.920859	+	0.389895i	$0.872511\pi$
$864$		0			0
$865$	−7.12132	+	12.3345i	−0.242132	+	0.419385i
$866$	−1.07107	−	1.85514i	−0.0363964	−	0.0630404i
$867$		0			0
$868$	−6.48528	−	8.36308i	−0.220125	−	0.283861i
$869$	4.75736			0.161382
$870$		0			0
$871$	−10.2782	+	17.8023i	−0.348263	+	0.603209i
$872$	−0.242641	+	0.420266i	−0.00821685	+	0.0142320i
$873$		0			0
$874$	−7.65685			−0.258997
$875$	−14.8284	+	2.02922i	−0.501292	+	0.0686003i
$876$		0			0
$877$	12.8137	+	22.1940i	0.432688	+	0.749438i	0.997104	−	0.0760529i	$-0.0242318\pi$
$877$	12.8137	+	22.1940i	0.432688	+	0.749438i	−0.564416	+	0.825491i	$0.690898\pi$
$878$	4.69239	−	8.12745i	0.158360	−	0.274288i
$879$		0			0
$880$	1.70711	+	2.95680i	0.0575466	+	0.0996736i
$881$	44.4558			1.49776			0.748878	−	0.662708i	$-0.230593\pi$
$881$	44.4558			1.49776			0.748878	+	0.662708i	$0.230593\pi$
$882$		0			0
$883$	−9.72792			−0.327371			−0.163685	−	0.986513i	$-0.552338\pi$
$883$	−9.72792			−0.327371			−0.163685	+	0.986513i	$0.552338\pi$
$884$	−7.00000	−	12.1244i	−0.235435	−	0.407786i
$885$		0			0
$886$	16.3137	−	28.2562i	0.548070	−	0.949285i
$887$	−11.4497	−	19.8315i	−0.384445	−	0.665878i	0.607247	−	0.794513i	$-0.292274\pi$
$887$	−11.4497	−	19.8315i	−0.384445	−	0.665878i	−0.991692	+	0.128635i	$0.958940\pi$
$888$		0			0
$889$	25.5000	−	3.48960i	0.855243	−	0.117037i
$890$	−15.3137			−0.513317
$891$		0			0
$892$	−5.70711	+	9.88500i	−0.191088	+	0.330974i
$893$	−11.0711	+	19.1757i	−0.370479	+	0.641689i
$894$		0			0
$895$	64.5269			2.15690
$896$	−1.62132	−	2.09077i	−0.0541645	−	0.0698477i
$897$		0			0
$898$	−16.8284	−	29.1477i	−0.561572	−	0.972671i
$899$	17.3137	−	29.9882i	0.577445	−	1.00016i
$900$		0			0
$901$	−45.5563	−	78.9059i	−1.51770	−	2.62874i
$902$	2.58579			0.0860973
$903$		0			0
$904$	−13.8284			−0.459927
$905$	−6.24264	−	10.8126i	−0.207512	−	0.359422i
$906$		0			0
$907$	−16.6569	+	28.8505i	−0.553082	+	0.957966i	0.444968	+	0.895546i	$0.353215\pi$
$907$	−16.6569	+	28.8505i	−0.553082	+	0.957966i	−0.998050	+	0.0624194i	$0.980118\pi$
$908$	−11.5858	−	20.0672i	−0.384488	−	0.665952i
$909$		0			0
$910$	−6.24264	+	15.2913i	−0.206942	+	0.506901i
$911$	13.5147			0.447763			0.223881	−	0.974616i	$-0.428127\pi$
$911$	13.5147			0.447763			0.223881	+	0.974616i	$0.428127\pi$
$912$		0			0
$913$	−8.07107	+	13.9795i	−0.267113	+	0.462654i
$914$	−0.171573	+	0.297173i	−0.00567513	+	0.00982961i
$915$		0			0
$916$	0.686292			0.0226757
$917$	5.53553	+	7.13834i	0.182799	+	0.235729i
$918$		0			0
$919$	3.07107	+	5.31925i	0.101305	+	0.175466i	0.912223	−	0.409695i	$-0.134365\pi$
$919$	3.07107	+	5.31925i	0.101305	+	0.175466i	−0.810917	+	0.585161i	$0.801031\pi$
$920$	−3.82843	+	6.63103i	−0.126220	+	0.218619i
$921$		0			0
$922$	−7.15685	−	12.3960i	−0.235698	−	0.408242i
$923$	−5.61522			−0.184827
$924$		0			0
$925$	−43.8406			−1.44147
$926$	3.58579	+	6.21076i	0.117836	+	0.204098i
$927$		0			0
$928$	4.32843	−	7.49706i	0.142088	−	0.246103i
$929$	5.22792	+	9.05503i	0.171523	+	0.297086i	0.938952	−	0.344047i	$-0.111798\pi$
$929$	5.22792	+	9.05503i	0.171523	+	0.297086i	−0.767430	+	0.641133i	$0.778465\pi$
$930$		0			0
$931$	17.0711	+	16.7262i	0.559482	+	0.548178i
$932$	1.41421			0.0463241
$933$		0			0
$934$	17.0000	−	29.4449i	0.556257	−	0.963465i
$935$	13.0711	−	22.6398i	0.427470	−	0.740399i
$936$		0			0
$937$	−16.5858			−0.541834			−0.270917	−	0.962603i	$-0.587327\pi$
$937$	−16.5858			−0.541834			−0.270917	+	0.962603i	$0.587327\pi$
$938$	29.4706	−	4.03295i	0.962248	−	0.131681i
$939$		0			0
$940$	11.0711	+	19.1757i	0.361098	+	0.625441i
$941$	6.67157	−	11.5555i	0.217487	−	0.376699i	−0.736552	−	0.676381i	$-0.763547\pi$
$941$	6.67157	−	11.5555i	0.217487	−	0.376699i	0.954039	+	0.299682i	$0.0968807\pi$
$942$		0			0
$943$	2.89949	+	5.02207i	0.0944205	+	0.163541i
$944$	8.41421			0.273859
$945$		0			0
$946$	5.65685			0.183920
$947$	14.5858	+	25.2633i	0.473974	+	0.820948i	0.999556	−	0.0297955i	$-0.00948560\pi$
$947$	14.5858	+	25.2633i	0.473974	+	0.820948i	−0.525582	+	0.850743i	$0.676152\pi$
$948$		0			0
$949$	6.02082	−	10.4284i	0.195444	−	0.338519i
$950$	−11.3640	−	19.6830i	−0.368696	−	0.638599i
$951$		0			0
$952$	−7.65685	+	18.7554i	−0.248160	+	0.607866i
$953$	25.5563			0.827851			0.413926	−	0.910311i	$-0.364157\pi$
$953$	25.5563			0.827851			0.413926	+	0.910311i	$0.364157\pi$
$954$		0			0
$955$	−21.8995	+	37.9310i	−0.708651	+	1.22742i
$956$	−11.1066	+	19.2372i	−0.359213	+	0.622175i
$957$		0			0
$958$	−26.0711			−0.842318
$959$	5.34315	−	13.0880i	0.172539	−	0.422633i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	−6.02082	+	10.4284i	−0.194119	+	0.336224i
$963$		0			0
$964$	−1.87868	−	3.25397i	−0.0605082	−	0.104803i
$965$	7.17157			0.230861
$966$		0			0
$967$	20.2843			0.652298			0.326149	−	0.945318i	$-0.394249\pi$
$967$	20.2843			0.652298			0.326149	+	0.945318i	$0.394249\pi$
$968$	0.500000	+	0.866025i	0.0160706	+	0.0278351i
$969$		0			0
$970$	3.12132	−	5.40629i	0.100220	−	0.173585i
$971$	23.8640	+	41.3336i	0.765831	+	1.32646i	0.939806	+	0.341708i	$0.111005\pi$
$971$	23.8640	+	41.3336i	0.765831	+	1.32646i	−0.173975	+	0.984750i	$0.555661\pi$
$972$		0			0
$973$		0			0
$974$	−1.65685			−0.0530890
$975$		0			0
$976$	−3.08579	+	5.34474i	−0.0987736	+	0.171081i
$977$	20.0000	−	34.6410i	0.639857	−	1.10826i	−0.345607	−	0.938379i	$-0.612327\pi$
$977$	20.0000	−	34.6410i	0.639857	−	1.10826i	0.985464	−	0.169885i	$-0.0543396\pi$
$978$		0			0
$979$	−4.48528			−0.143350
$980$	23.0208	−	6.42090i	0.735373	−	0.205108i
$981$		0			0
$982$	−12.4142	−	21.5020i	−0.396153	−	0.686158i
$983$	−26.2132	+	45.4026i	−0.836071	+	1.44812i	0.0570838	+	0.998369i	$0.481820\pi$
$983$	−26.2132	+	45.4026i	−0.836071	+	1.44812i	−0.893155	+	0.449749i	$0.851514\pi$
$984$		0			0
$985$	−29.8492	−	51.7004i	−0.951076	−	1.64731i
$986$	−66.2843			−2.11092
$987$		0			0
$988$	−6.24264			−0.198605
$989$	6.34315	+	10.9867i	0.201700	+	0.349355i
$990$		0			0
$991$	19.1924	−	33.2422i	0.609666	−	1.05597i	−0.381629	−	0.924316i	$-0.624637\pi$
$991$	19.1924	−	33.2422i	0.609666	−	1.05597i	0.991295	−	0.131657i	$-0.0420299\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$		0			0
$994$	4.97918	+	6.42090i	0.157930	+	0.203658i
$995$	67.9411			2.15388
$996$		0			0
$997$	−9.41421	+	16.3059i	−0.298151	+	0.516413i	−0.975713	−	0.219053i	$-0.929703\pi$
$997$	−9.41421	+	16.3059i	−0.298151	+	0.516413i	0.677562	+	0.735466i	$0.263037\pi$
$998$	−3.07107	+	5.31925i	−0.0972130	+	0.168378i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.k.t.991.1		4
3.2	odd	2		154.2.e.e.67.1	yes	4
7.2	even	3	inner	1386.2.k.t.793.1		4
7.3	odd	6		9702.2.a.ch.1.1		2
7.4	even	3		9702.2.a.cx.1.2		2
12.11	even	2		1232.2.q.f.529.2		4
21.2	odd	6		154.2.e.e.23.1	✓	4
21.5	even	6		1078.2.e.m.177.2		4
21.11	odd	6		1078.2.a.t.1.2		2
21.17	even	6		1078.2.a.x.1.1		2
21.20	even	2		1078.2.e.m.67.2		4
84.11	even	6		8624.2.a.cc.1.1		2
84.23	even	6		1232.2.q.f.177.2		4
84.59	odd	6		8624.2.a.bh.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.e.e.23.1	✓	4	21.2	odd	6
154.2.e.e.67.1	yes	4	3.2	odd	2
1078.2.a.t.1.2		2	21.11	odd	6
1078.2.a.x.1.1		2	21.17	even	6
1078.2.e.m.67.2		4	21.20	even	2
1078.2.e.m.177.2		4	21.5	even	6
1232.2.q.f.177.2		4	84.23	even	6
1232.2.q.f.529.2		4	12.11	even	2
1386.2.k.t.793.1		4	7.2	even	3	inner
1386.2.k.t.991.1		4	1.1	even	1	trivial
8624.2.a.bh.1.2		2	84.59	odd	6
8624.2.a.cc.1.1		2	84.11	even	6
9702.2.a.ch.1.1		2	7.3	odd	6
9702.2.a.cx.1.2		2	7.4	even	3

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.70711 - 2.95680i) q^{5} +(-2.62132 + 0.358719i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.70711 - 2.95680i) q^{5} +(-2.62132 + 0.358719i) q^{7} -1.00000 q^{8} +(1.70711 - 2.95680i) q^{10} +(0.500000 - 0.866025i) q^{11} +1.82843 q^{13} +(-1.62132 - 2.09077i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.82843 + 6.63103i) q^{17} +(1.70711 + 2.95680i) q^{19} +3.41421 q^{20} +1.00000 q^{22} +(1.12132 + 1.94218i) q^{23} +(-3.32843 + 5.76500i) q^{25} +(0.914214 + 1.58346i) q^{26} +(1.00000 - 2.44949i) q^{28} +8.65685 q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} -7.65685 q^{34} +(5.53553 + 7.13834i) q^{35} +(3.29289 + 5.70346i) q^{37} +(-1.70711 + 2.95680i) q^{38} +(1.70711 + 2.95680i) q^{40} +2.58579 q^{41} +5.65685 q^{43} +(0.500000 + 0.866025i) q^{44} +(-1.12132 + 1.94218i) q^{46} +(3.24264 + 5.61642i) q^{47} +(6.74264 - 1.88064i) q^{49} -6.65685 q^{50} +(-0.914214 + 1.58346i) q^{52} +(-5.94975 + 10.3053i) q^{53} -3.41421 q^{55} +(2.62132 - 0.358719i) q^{56} +(4.32843 + 7.49706i) q^{58} +(-4.20711 + 7.28692i) q^{59} +(-3.08579 - 5.34474i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-3.12132 - 5.40629i) q^{65} +(-5.62132 + 9.73641i) q^{67} +(-3.82843 - 6.63103i) q^{68} +(-3.41421 + 8.36308i) q^{70} -3.07107 q^{71} +(3.29289 - 5.70346i) q^{73} +(-3.29289 + 5.70346i) q^{74} -3.41421 q^{76} +(-1.00000 + 2.44949i) q^{77} +(2.37868 + 4.11999i) q^{79} +(-1.70711 + 2.95680i) q^{80} +(1.29289 + 2.23936i) q^{82} -16.1421 q^{83} +26.1421 q^{85} +(2.82843 + 4.89898i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(-2.24264 - 3.88437i) q^{89} +(-4.79289 + 0.655892i) q^{91} -2.24264 q^{92} +(-3.24264 + 5.61642i) q^{94} +(5.82843 - 10.0951i) q^{95} +1.82843 q^{97} +(5.00000 + 4.89898i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} - 2 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 - 2 * q^7 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} - 2 q^{7} - 4 q^{8} + 4 q^{10} + 2 q^{11} - 4 q^{13} + 2 q^{14} - 2 q^{16} - 4 q^{17} + 4 q^{19} + 8 q^{20} + 4 q^{22} - 4 q^{23} - 2 q^{25} - 2 q^{26} + 4 q^{28} + 12 q^{29} + 8 q^{31} + 2 q^{32} - 8 q^{34} + 8 q^{35} + 16 q^{37} - 4 q^{38} + 4 q^{40} + 16 q^{41} + 2 q^{44} + 4 q^{46} - 4 q^{47} + 10 q^{49} - 4 q^{50} + 2 q^{52} - 4 q^{53} - 8 q^{55} + 2 q^{56} + 6 q^{58} - 14 q^{59} - 18 q^{61} + 16 q^{62} + 4 q^{64} - 4 q^{65} - 14 q^{67} - 4 q^{68} - 8 q^{70} + 16 q^{71} + 16 q^{73} - 16 q^{74} - 8 q^{76} - 4 q^{77} + 18 q^{79} - 4 q^{80} + 8 q^{82} - 8 q^{83} + 48 q^{85} - 2 q^{88} + 8 q^{89} - 22 q^{91} + 8 q^{92} + 4 q^{94} + 12 q^{95} - 4 q^{97} + 20 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 - 2 * q^7 - 4 * q^8 + 4 * q^10 + 2 * q^11 - 4 * q^13 + 2 * q^14 - 2 * q^16 - 4 * q^17 + 4 * q^19 + 8 * q^20 + 4 * q^22 - 4 * q^23 - 2 * q^25 - 2 * q^26 + 4 * q^28 + 12 * q^29 + 8 * q^31 + 2 * q^32 - 8 * q^34 + 8 * q^35 + 16 * q^37 - 4 * q^38 + 4 * q^40 + 16 * q^41 + 2 * q^44 + 4 * q^46 - 4 * q^47 + 10 * q^49 - 4 * q^50 + 2 * q^52 - 4 * q^53 - 8 * q^55 + 2 * q^56 + 6 * q^58 - 14 * q^59 - 18 * q^61 + 16 * q^62 + 4 * q^64 - 4 * q^65 - 14 * q^67 - 4 * q^68 - 8 * q^70 + 16 * q^71 + 16 * q^73 - 16 * q^74 - 8 * q^76 - 4 * q^77 + 18 * q^79 - 4 * q^80 + 8 * q^82 - 8 * q^83 + 48 * q^85 - 2 * q^88 + 8 * q^89 - 22 * q^91 + 8 * q^92 + 4 * q^94 + 12 * q^95 - 4 * q^97 + 20 * q^98

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