LMFDB - Embedded newform 847.2.f.v.323.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([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("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			323.3
Root			$-0.206962 - 0.636964i$ of defining polynomial
Character	$\chi$	$=$	847.323
Dual form			847.2.f.v.729.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.541834 + 0.393666i) q^{2} +(0.970243 - 2.98610i) q^{3} +(-0.479422 - 1.47551i) q^{4} +(-1.73435 + 1.26008i) q^{5} +(1.70124 - 1.23602i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.735015 - 2.26214i) q^{8} +(-5.54838 - 4.03113i) q^{9} +O(q^{10})$	\(q+(0.541834 + 0.393666i) q^{2} +(0.970243 - 2.98610i) q^{3} +(-0.479422 - 1.47551i) q^{4} +(-1.73435 + 1.26008i) q^{5} +(1.70124 - 1.23602i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.735015 - 2.26214i) q^{8} +(-5.54838 - 4.03113i) q^{9} -1.43578 q^{10} -4.87118 q^{12} +(2.04541 + 1.48608i) q^{13} +(0.206962 - 0.636964i) q^{14} +(2.07999 + 6.40154i) q^{15} +(-1.22150 + 0.887475i) q^{16} +(-1.44888 + 1.05268i) q^{17} +(-1.41938 - 4.36841i) q^{18} +(2.07888 - 6.39814i) q^{19} +(2.69075 + 1.95494i) q^{20} -3.13977 q^{21} -3.16429 q^{23} +(-6.04184 - 4.38966i) q^{24} +(-0.124909 + 0.384430i) q^{25} +(0.523255 + 1.61041i) q^{26} +(-9.80027 + 7.12031i) q^{27} +(-1.25514 + 0.911915i) q^{28} +(0.285584 + 0.878938i) q^{29} +(-1.39306 + 4.28739i) q^{30} +(-2.42849 - 1.76440i) q^{31} -5.76834 q^{32} -1.19946 q^{34} +(1.73435 + 1.26008i) q^{35} +(-3.28796 + 10.1193i) q^{36} +(-0.465744 - 1.43341i) q^{37} +(3.64514 - 2.64835i) q^{38} +(6.42211 - 4.66594i) q^{39} +(1.57571 + 4.84953i) q^{40} +(-1.71846 + 5.28886i) q^{41} +(-1.70124 - 1.23602i) q^{42} +8.42985 q^{43} +14.7024 q^{45} +(-1.71452 - 1.24567i) q^{46} +(1.35897 - 4.18247i) q^{47} +(1.46493 + 4.50860i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-0.219017 + 0.159125i) q^{50} +(1.73763 + 5.34787i) q^{51} +(1.21211 - 3.73048i) q^{52} +(-0.539955 - 0.392300i) q^{53} -8.11314 q^{54} -2.37856 q^{56} +(-17.0885 - 12.4155i) q^{57} +(-0.191268 + 0.588663i) q^{58} +(-0.113830 - 0.350331i) q^{59} +(8.44835 - 6.13808i) q^{60} +(4.05438 - 2.94568i) q^{61} +(-0.621256 - 1.91203i) q^{62} +(-2.11929 + 6.52251i) q^{63} +(-0.682474 - 0.495846i) q^{64} -5.42003 q^{65} -0.902129 q^{67} +(2.24786 + 1.63317i) q^{68} +(-3.07013 + 9.44888i) q^{69} +(0.443681 + 1.36551i) q^{70} +(12.0296 - 8.74000i) q^{71} +(-13.1971 + 9.58828i) q^{72} +(-2.48393 - 7.64474i) q^{73} +(0.311929 - 0.960019i) q^{74} +(1.02676 + 0.745981i) q^{75} -10.4372 q^{76} +5.31654 q^{78} +(3.28192 + 2.38446i) q^{79} +(1.00023 - 3.07839i) q^{80} +(5.39545 + 16.6055i) q^{81} +(-3.01316 + 2.18919i) q^{82} +(-3.27760 + 2.38132i) q^{83} +(1.50528 + 4.63277i) q^{84} +(1.18642 - 3.65142i) q^{85} +(4.56758 + 3.31854i) q^{86} +2.90168 q^{87} -8.30727 q^{89} +(7.96627 + 5.78783i) q^{90} +(0.781276 - 2.40452i) q^{91} +(1.51703 + 4.66894i) q^{92} +(-7.62492 + 5.53983i) q^{93} +(2.38283 - 1.73123i) q^{94} +(4.45666 + 13.7162i) q^{95} +(-5.59669 + 17.2248i) q^{96} +(-6.88945 - 5.00548i) q^{97} -0.669744 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 4 q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 + 2 * q^6 + 4 * q^7 - 5 * q^8 - 2 * q^9	\( 16 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 4 q^{7} - 5 q^{8} - 2 q^{9} - 12 q^{10} + 18 q^{12} - 13 q^{13} - 3 q^{14} + 7 q^{15} - 18 q^{16} - 10 q^{17} + 19 q^{18} + 6 q^{19} - 24 q^{20} - 8 q^{21} + 32 q^{23} - 45 q^{24} - 23 q^{25} + 33 q^{26} - 20 q^{27} + 11 q^{28} + 12 q^{29} - 38 q^{30} - 2 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} - 38 q^{36} - 11 q^{37} + 15 q^{38} + 24 q^{39} - 5 q^{40} - 20 q^{41} - 2 q^{42} + 8 q^{43} + 70 q^{45} - 38 q^{46} + 7 q^{47} + 39 q^{48} - 4 q^{49} + 58 q^{50} - 16 q^{51} - 8 q^{52} - 41 q^{53} - 60 q^{54} - 9 q^{57} - 5 q^{58} - 18 q^{59} + 25 q^{60} + 12 q^{61} + 61 q^{62} + 12 q^{63} - 3 q^{64} + 8 q^{65} - 38 q^{67} + 7 q^{68} - 30 q^{69} + 12 q^{70} + q^{71} - 35 q^{72} - 60 q^{73} + 4 q^{74} + 4 q^{75} - 52 q^{76} - 58 q^{78} + 15 q^{79} + 83 q^{80} + 6 q^{81} - 6 q^{82} - 20 q^{83} + 17 q^{84} + 9 q^{85} + 48 q^{86} + 72 q^{87} + 74 q^{89} - 16 q^{90} - 7 q^{91} + 20 q^{92} - 53 q^{93} - 66 q^{94} + 53 q^{95} - 48 q^{96} - 35 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 + 2 * q^6 + 4 * q^7 - 5 * q^8 - 2 * q^9 - 12 * q^10 + 18 * q^12 - 13 * q^13 - 3 * q^14 + 7 * q^15 - 18 * q^16 - 10 * q^17 + 19 * q^18 + 6 * q^19 - 24 * q^20 - 8 * q^21 + 32 * q^23 - 45 * q^24 - 23 * q^25 + 33 * q^26 - 20 * q^27 + 11 * q^28 + 12 * q^29 - 38 * q^30 - 2 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 - 38 * q^36 - 11 * q^37 + 15 * q^38 + 24 * q^39 - 5 * q^40 - 20 * q^41 - 2 * q^42 + 8 * q^43 + 70 * q^45 - 38 * q^46 + 7 * q^47 + 39 * q^48 - 4 * q^49 + 58 * q^50 - 16 * q^51 - 8 * q^52 - 41 * q^53 - 60 * q^54 - 9 * q^57 - 5 * q^58 - 18 * q^59 + 25 * q^60 + 12 * q^61 + 61 * q^62 + 12 * q^63 - 3 * q^64 + 8 * q^65 - 38 * q^67 + 7 * q^68 - 30 * q^69 + 12 * q^70 + q^71 - 35 * q^72 - 60 * q^73 + 4 * q^74 + 4 * q^75 - 52 * q^76 - 58 * q^78 + 15 * q^79 + 83 * q^80 + 6 * q^81 - 6 * q^82 - 20 * q^83 + 17 * q^84 + 9 * q^85 + 48 * q^86 + 72 * q^87 + 74 * q^89 - 16 * q^90 - 7 * q^91 + 20 * q^92 - 53 * q^93 - 66 * q^94 + 53 * q^95 - 48 * q^96 - 35 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.541834	+	0.393666i	0.383135	+	0.278364i	0.762636	−	0.646827i	$-0.223905\pi$
$2$	0.541834	+	0.393666i	0.383135	+	0.278364i	−0.379502	+	0.925191i	$0.623905\pi$
$3$	0.970243	−	2.98610i	0.560170	−	1.72403i	−0.121713	−	0.992565i	$-0.538839\pi$
$3$	0.970243	−	2.98610i	0.560170	−	1.72403i	0.681883	−	0.731461i	$-0.261161\pi$
$4$	−0.479422	−	1.47551i	−0.239711	−	0.737755i
$5$	−1.73435	+	1.26008i	−0.775626	+	0.563526i	−0.903663	−	0.428244i	$-0.859132\pi$
$5$	−1.73435	+	1.26008i	−0.775626	+	0.563526i	0.128037	+	0.991769i	$0.459132\pi$
$6$	1.70124	−	1.23602i	0.694527	−	0.504603i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	0.735015	−	2.26214i	0.259867	−	0.799788i
$9$	−5.54838	−	4.03113i	−1.84946	−	1.34371i
$10$	−1.43578			−0.454034
$11$		0			0
$11$		0			0
$12$	−4.87118			−1.40619
$13$	2.04541	+	1.48608i	0.567294	+	0.412163i	0.834121	−	0.551581i	$-0.185975\pi$
$13$	2.04541	+	1.48608i	0.567294	+	0.412163i	−0.266827	+	0.963744i	$0.585975\pi$
$14$	0.206962	−	0.636964i	0.0553130	−	0.170236i
$15$	2.07999	+	6.40154i	0.537050	+	1.65287i
$16$	−1.22150	+	0.887475i	−0.305376	+	0.221869i
$17$	−1.44888	+	1.05268i	−0.351406	+	0.255311i	−0.749459	−	0.662051i	$-0.769686\pi$
$17$	−1.44888	+	1.05268i	−0.351406	+	0.255311i	0.398053	+	0.917363i	$0.369686\pi$
$18$	−1.41938	−	4.36841i	−0.334552	−	1.02964i
$19$	2.07888	−	6.39814i	0.476928	−	1.46783i	−0.366412	−	0.930453i	$-0.619414\pi$
$19$	2.07888	−	6.39814i	0.476928	−	1.46783i	0.843340	−	0.537381i	$-0.180586\pi$
$20$	2.69075	+	1.95494i	0.601670	+	0.437139i
$21$	−3.13977			−0.685155
$22$		0			0
$23$	−3.16429			−0.659799			−0.329900	−	0.944016i	$-0.607015\pi$
$23$	−3.16429			−0.659799			−0.329900	+	0.944016i	$0.607015\pi$
$24$	−6.04184	−	4.38966i	−1.23329	−	0.896035i
$25$	−0.124909	+	0.384430i	−0.0249818	+	0.0768860i
$26$	0.523255	+	1.61041i	0.102619	+	0.315828i
$27$	−9.80027	+	7.12031i	−1.88606	+	1.37030i
$28$	−1.25514	+	0.911915i	−0.237200	+	0.172336i
$29$	0.285584	+	0.878938i	0.0530317	+	0.163215i	0.974065	−	0.226270i	$-0.0726531\pi$
$29$	0.285584	+	0.878938i	0.0530317	+	0.163215i	−0.921033	+	0.389485i	$0.872653\pi$
$30$	−1.39306	+	4.28739i	−0.254337	+	0.782767i
$31$	−2.42849	−	1.76440i	−0.436170	−	0.316896i	0.347941	−	0.937516i	$-0.386881\pi$
$31$	−2.42849	−	1.76440i	−0.436170	−	0.316896i	−0.784111	+	0.620620i	$0.786881\pi$
$32$	−5.76834			−1.01971
$33$		0			0
$34$	−1.19946			−0.205705
$35$	1.73435	+	1.26008i	0.293159	+	0.212993i
$36$	−3.28796	+	10.1193i	−0.547994	+	1.68655i
$37$	−0.465744	−	1.43341i	−0.0765678	−	0.235652i	0.905446	−	0.424462i	$-0.139537\pi$
$37$	−0.465744	−	1.43341i	−0.0765678	−	0.235652i	−0.982014	+	0.188811i	$0.939537\pi$
$38$	3.64514	−	2.64835i	0.591319	−	0.429618i
$39$	6.42211	−	4.66594i	1.02836	−	0.747148i
$40$	1.57571	+	4.84953i	0.249141	+	0.766778i
$41$	−1.71846	+	5.28886i	−0.268378	+	0.825981i	0.722518	+	0.691352i	$0.242984\pi$
$41$	−1.71846	+	5.28886i	−0.268378	+	0.825981i	−0.990896	+	0.134630i	$0.957016\pi$
$42$	−1.70124	−	1.23602i	−0.262506	−	0.190722i
$43$	8.42985			1.28554			0.642770	−	0.766059i	$-0.277785\pi$
$43$	8.42985			1.28554			0.642770	+	0.766059i	$0.277785\pi$
$44$		0			0
$45$	14.7024			2.19171
$46$	−1.71452	−	1.24567i	−0.252792	−	0.183664i
$47$	1.35897	−	4.18247i	0.198226	−	0.610076i	−0.801698	−	0.597729i	$-0.796070\pi$
$47$	1.35897	−	4.18247i	0.198226	−	0.610076i	0.999924	−	0.0123466i	$-0.00393014\pi$
$48$	1.46493	+	4.50860i	0.211445	+	0.650761i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−0.219017	+	0.159125i	−0.0309737	+	0.0225037i
$51$	1.73763	+	5.34787i	0.243317	+	0.748851i
$52$	1.21211	−	3.73048i	0.168089	−	0.517324i
$53$	−0.539955	−	0.392300i	−0.0741685	−	0.0538866i	0.550083	−	0.835110i	$-0.314596\pi$
$53$	−0.539955	−	0.392300i	−0.0741685	−	0.0538866i	−0.624252	+	0.781223i	$0.714596\pi$
$54$	−8.11314			−1.10406
$55$		0			0
$56$	−2.37856			−0.317848
$57$	−17.0885	−	12.4155i	−2.26342	−	1.64447i
$58$	−0.191268	+	0.588663i	−0.0251148	+	0.0772953i
$59$	−0.113830	−	0.350331i	−0.0148193	−	0.0456093i	0.943373	−	0.331733i	$-0.107633\pi$
$59$	−0.113830	−	0.350331i	−0.0148193	−	0.0456093i	−0.958193	+	0.286124i	$0.907633\pi$
$60$	8.44835	−	6.13808i	1.09068	−	0.792423i
$61$	4.05438	−	2.94568i	0.519110	−	0.377155i	−0.297159	−	0.954828i	$-0.596039\pi$
$61$	4.05438	−	2.94568i	0.519110	−	0.377155i	0.816268	+	0.577673i	$0.196039\pi$
$62$	−0.621256	−	1.91203i	−0.0788996	−	0.242828i
$63$	−2.11929	+	6.52251i	−0.267006	+	0.821759i
$64$	−0.682474	−	0.495846i	−0.0853092	−	0.0619808i
$65$	−5.42003			−0.672273
$66$		0			0
$67$	−0.902129			−0.110213			−0.0551063	−	0.998480i	$-0.517550\pi$
$67$	−0.902129			−0.110213			−0.0551063	+	0.998480i	$0.517550\pi$
$68$	2.24786	+	1.63317i	0.272593	+	0.198051i
$69$	−3.07013	+	9.44888i	−0.369600	+	1.13751i
$70$	0.443681	+	1.36551i	0.0530300	+	0.163210i
$71$	12.0296	−	8.74000i	1.42765	−	1.03725i	0.437199	−	0.899365i	$-0.355971\pi$
$71$	12.0296	−	8.74000i	1.42765	−	1.03725i	0.990449	−	0.137882i	$-0.0440294\pi$
$72$	−13.1971	+	9.58828i	−1.55530	+	1.12999i
$73$	−2.48393	−	7.64474i	−0.290722	−	0.894750i	−0.984625	−	0.174681i	$-0.944110\pi$
$73$	−2.48393	−	7.64474i	−0.290722	−	0.894750i	0.693903	−	0.720068i	$-0.255890\pi$
$74$	0.311929	−	0.960019i	0.0362610	−	0.111600i
$75$	1.02676	+	0.745981i	0.118559	+	0.0861385i
$76$	−10.4372			−1.19723
$77$		0			0
$78$	5.31654			0.601980
$79$	3.28192	+	2.38446i	0.369245	+	0.268272i	0.756898	−	0.653533i	$-0.226714\pi$
$79$	3.28192	+	2.38446i	0.369245	+	0.268272i	−0.387653	+	0.921805i	$0.626714\pi$
$80$	1.00023	−	3.07839i	0.111829	−	0.344174i
$81$	5.39545	+	16.6055i	0.599495	+	1.84505i
$82$	−3.01316	+	2.18919i	−0.332748	+	0.241756i
$83$	−3.27760	+	2.38132i	−0.359764	+	0.261384i	−0.752954	−	0.658074i	$-0.771372\pi$
$83$	−3.27760	+	2.38132i	−0.359764	+	0.261384i	0.393190	+	0.919457i	$0.371372\pi$
$84$	1.50528	+	4.63277i	0.164239	+	0.505476i
$85$	1.18642	−	3.65142i	0.128685	−	0.396053i
$86$	4.56758	+	3.31854i	0.492535	+	0.357847i
$87$	2.90168			0.311093
$88$		0			0
$89$	−8.30727			−0.880569			−0.440284	−	0.897858i	$-0.645122\pi$
$89$	−8.30727			−0.880569			−0.440284	+	0.897858i	$0.645122\pi$
$90$	7.96627	+	5.78783i	0.839718	+	0.610091i
$91$	0.781276	−	2.40452i	0.0819000	−	0.252062i
$92$	1.51703	+	4.66894i	0.158161	+	0.486770i
$93$	−7.62492	+	5.53983i	−0.790667	+	0.574453i
$94$	2.38283	−	1.73123i	0.245770	−	0.178562i
$95$	4.45666	+	13.7162i	0.457244	+	1.40725i
$96$	−5.59669	+	17.2248i	−0.571210	+	1.75800i
$97$	−6.88945	−	5.00548i	−0.699518	−	0.508230i	0.180257	−	0.983620i	$-0.442307\pi$
$97$	−6.88945	−	5.00548i	−0.699518	−	0.508230i	−0.879775	+	0.475390i	$0.842307\pi$
$98$	−0.669744			−0.0676544
$99$		0			0
$100$	0.627115			0.0627115
$101$	−3.25797	−	2.36705i	−0.324180	−	0.235530i	0.413777	−	0.910378i	$-0.364209\pi$
$101$	−3.25797	−	2.36705i	−0.324180	−	0.235530i	−0.737957	+	0.674848i	$0.764209\pi$
$102$	−1.16377	+	3.58170i	−0.115230	+	0.354641i
$103$	−5.44668	−	16.7632i	−0.536678	−	1.65172i	−0.739996	−	0.672611i	$-0.765173\pi$
$103$	−5.44668	−	16.7632i	−0.536678	−	1.65172i	0.203319	−	0.979113i	$-0.434827\pi$
$104$	4.86512	−	3.53472i	0.477064	−	0.346607i
$105$	5.44548	−	3.95637i	0.531424	−	0.386102i
$106$	−0.138131	−	0.425123i	−0.0134165	−	0.0412916i
$107$	4.76001	−	14.6498i	0.460168	−	1.41625i	−0.404792	−	0.914409i	$-0.632656\pi$
$107$	4.76001	−	14.6498i	0.460168	−	1.41625i	0.864959	−	0.501842i	$-0.167344\pi$
$108$	15.2046	+	11.0468i	1.46306	+	1.06297i
$109$	18.9265			1.81283			0.906416	−	0.422386i	$-0.138807\pi$
$109$	18.9265			1.81283			0.906416	+	0.422386i	$0.138807\pi$
$110$		0			0
$111$	−4.73220			−0.449161
$112$	1.22150	+	0.887475i	0.115421	+	0.0838585i
$113$	0.519340	−	1.59837i	0.0488554	−	0.150362i	−0.923653	−	0.383231i	$-0.874811\pi$
$113$	0.519340	−	1.59837i	0.0488554	−	0.150362i	0.972508	+	0.232869i	$0.0748114\pi$
$114$	−4.37156	−	13.4543i	−0.409434	−	1.26011i
$115$	5.48799	−	3.98726i	0.511758	−	0.371814i
$116$	1.15997	−	0.842765i	0.107700	−	0.0782487i
$117$	−5.35813	−	16.4906i	−0.495359	−	1.52456i
$118$	0.0762367	−	0.234632i	0.00701815	−	0.0215997i
$119$	1.44888	+	1.05268i	0.132819	+	0.0964987i
$120$	16.0100			1.46151
$121$		0			0
$122$	3.35641			0.303875
$123$	14.1258	+	10.2630i	1.27368	+	0.925380i
$124$	−1.43912	+	4.42916i	−0.129237	+	0.397750i
$125$	−3.58010	−	11.0184i	−0.320214	−	0.985516i
$126$	−3.71599	+	2.69983i	−0.331047	+	0.240520i
$127$	14.2119	−	10.3256i	1.26111	−	0.916247i	0.262294	−	0.964988i	$-0.415521\pi$
$127$	14.2119	−	10.3256i	1.26111	−	0.916247i	0.998811	+	0.0487414i	$0.0155210\pi$
$128$	3.39044	+	10.4347i	0.299675	+	0.922305i
$129$	8.17900	−	25.1724i	0.720121	−	2.21630i
$130$	−2.93676	−	2.13368i	−0.257571	−	0.187136i
$131$	−6.72557			−0.587616			−0.293808	−	0.955865i	$-0.594923\pi$
$131$	−6.72557			−0.587616			−0.293808	+	0.955865i	$0.594923\pi$
$132$		0			0
$133$	−6.72740			−0.583340
$134$	−0.488804	−	0.355137i	−0.0422263	−	0.0306792i
$135$	8.02495	−	24.6983i	0.690678	−	2.12569i
$136$	1.31635	+	4.05132i	0.112876	+	0.347397i
$137$	−11.2191	+	8.15119i	−0.958516	+	0.696403i	−0.952806	−	0.303581i	$-0.901818\pi$
$137$	−11.2191	+	8.15119i	−0.958516	+	0.696403i	−0.00571070	+	0.999984i	$0.501818\pi$
$138$	−5.38320	+	3.91112i	−0.458248	+	0.332937i
$139$	−4.40990	−	13.5723i	−0.374043	−	1.15118i	−0.944122	−	0.329595i	$-0.893088\pi$
$139$	−4.40990	−	13.5723i	−0.374043	−	1.15118i	0.570080	−	0.821589i	$-0.306912\pi$
$140$	1.02778	−	3.16317i	0.0868629	−	0.267336i
$141$	−11.1707	−	8.11602i	−0.940747	−	0.683492i
$142$	9.95867			0.835713
$143$		0			0
$144$	10.3549			0.862908
$145$	−1.60284	−	1.16453i	−0.133108	−	0.0967089i
$146$	1.66360	−	5.12002i	0.137680	−	0.423736i
$147$	0.970243	+	2.98610i	0.0800243	+	0.246290i
$148$	−1.89173	+	1.37442i	−0.155499	+	0.112977i
$149$	2.12199	−	1.54171i	0.173840	−	0.126302i	−0.497463	−	0.867485i	$-0.665735\pi$
$149$	2.12199	−	1.54171i	0.173840	−	0.126302i	0.671303	+	0.741183i	$0.265735\pi$
$150$	0.262664	+	0.808396i	0.0214464	+	0.0660053i
$151$	0.923837	−	2.84328i	0.0751808	−	0.231383i	−0.906403	−	0.422413i	$-0.861183\pi$
$151$	0.923837	−	2.84328i	0.0751808	−	0.231383i	0.981584	+	0.191031i	$0.0611830\pi$
$152$	−12.9455	−	9.40545i	−1.05002	−	0.762883i
$153$	12.2824			0.992977
$154$		0			0
$155$	6.43516			0.516884
$156$	−9.96355	−	7.23894i	−0.797722	−	0.579579i
$157$	3.47789	−	10.7038i	0.277566	−	0.854260i	−0.710963	−	0.703229i	$-0.751741\pi$
$157$	3.47789	−	10.7038i	0.277566	−	0.854260i	0.988529	−	0.151031i	$-0.0482593\pi$
$158$	0.839579	+	2.58396i	0.0667934	+	0.205569i
$159$	−1.69534	+	1.23173i	−0.134449	+	0.0976828i
$160$	10.0043	−	7.26857i	0.790912	−	0.574631i
$161$	0.977818	+	3.00941i	0.0770629	+	0.237175i
$162$	−3.61357	+	11.1214i	−0.283909	+	0.873782i
$163$	14.7265	+	10.6994i	1.15347	+	0.838044i	0.988938	−	0.148328i	$-0.0473892\pi$
$163$	14.7265	+	10.6994i	1.15347	+	0.838044i	0.164530	+	0.986372i	$0.447389\pi$
$164$	8.62763			0.673705
$165$		0			0
$166$	−2.71336			−0.210598
$167$	16.1247	+	11.7153i	1.24777	+	0.906556i	0.998090	−	0.0617729i	$-0.0196754\pi$
$167$	16.1247	+	11.7153i	1.24777	+	0.906556i	0.249677	+	0.968329i	$0.419675\pi$
$168$	−2.30778	+	7.10261i	−0.178049	+	0.547979i
$169$	−2.04195	−	6.28448i	−0.157073	−	0.483421i
$170$	2.08028	−	1.51141i	0.159550	−	0.115920i
$171$	−37.3262	+	27.1191i	−2.85440	+	2.07385i
$172$	−4.04146	−	12.4383i	−0.308158	−	0.948413i
$173$	−1.85104	+	5.69690i	−0.140732	+	0.433127i	−0.996437	−	0.0843352i	$-0.973123\pi$
$173$	−1.85104	+	5.69690i	−0.140732	+	0.433127i	0.855706	+	0.517463i	$0.173123\pi$
$174$	1.57223	+	1.14229i	0.119191	+	0.0865970i
$175$	0.404214			0.0305557
$176$		0			0
$177$	−1.15657			−0.0869329
$178$	−4.50116	−	3.27029i	−0.337376	−	0.245118i
$179$	−0.500280	+	1.53970i	−0.0373927	+	0.115083i	−0.968011	−	0.250910i	$-0.919270\pi$
$179$	−0.500280	+	1.53970i	−0.0373927	+	0.115083i	0.930618	+	0.365992i	$0.119270\pi$
$180$	−7.04866	−	21.6936i	−0.525376	−	1.61694i
$181$	−1.96334	+	1.42645i	−0.145934	+	0.106027i	−0.658357	−	0.752706i	$-0.728748\pi$
$181$	−1.96334	+	1.42645i	−0.145934	+	0.106027i	0.512423	+	0.858733i	$0.328748\pi$
$182$	1.36990	−	0.995290i	0.101544	−	0.0737758i
$183$	−4.86236	−	14.9648i	−0.359436	−	1.10623i
$184$	−2.32580	+	7.15806i	−0.171460	+	0.527700i
$185$	2.61398	+	1.89917i	0.192184	+	0.139630i
$186$	−6.31228			−0.462839
$187$		0			0
$188$	−6.82279			−0.497603
$189$	9.80027	+	7.12031i	0.712865	+	0.517926i
$190$	−2.98482	+	9.18634i	−0.216542	+	0.666447i
$191$	3.92480	+	12.0793i	0.283989	+	0.874027i	0.986700	+	0.162552i	$0.0519725\pi$
$191$	3.92480	+	12.0793i	0.283989	+	0.874027i	−0.702711	+	0.711475i	$0.748027\pi$
$192$	−2.14281	+	1.55684i	−0.154644	+	0.112356i
$193$	−1.42331	+	1.03410i	−0.102452	+	0.0744359i	−0.637832	−	0.770176i	$-0.720169\pi$
$193$	−1.42331	+	1.03410i	−0.102452	+	0.0744359i	0.535380	+	0.844612i	$0.320169\pi$
$194$	−1.76246	−	5.42428i	−0.126537	−	0.389441i
$195$	−5.25875	+	16.1848i	−0.376587	+	1.15902i
$196$	1.25514	+	0.911915i	0.0896531	+	0.0651368i
$197$	0.903053			0.0643399			0.0321699	−	0.999482i	$-0.489758\pi$
$197$	0.903053			0.0643399			0.0321699	+	0.999482i	$0.489758\pi$
$198$		0			0
$199$	−15.6296			−1.10795			−0.553976	−	0.832533i	$-0.686890\pi$
$199$	−15.6296			−1.10795			−0.553976	+	0.832533i	$0.686890\pi$
$200$	0.777826	+	0.565123i	0.0550006	+	0.0399603i
$201$	−0.875285	+	2.69385i	−0.0617378	+	0.190009i
$202$	−0.833451	−	2.56510i	−0.0586414	−	0.180480i
$203$	0.747669	−	0.543213i	0.0524761	−	0.0381261i
$204$	7.05778	−	5.12777i	0.494143	−	0.359016i
$205$	−3.68399	−	11.3381i	−0.257301	−	0.791891i
$206$	3.64788	−	11.2270i	0.254160	−	0.782224i
$207$	17.5567	+	12.7557i	1.22027	+	0.886580i
$208$	−3.81733			−0.264684
$209$		0			0
$210$	4.50803			0.311084
$211$	11.9481	+	8.68083i	0.822544	+	0.597613i	0.917440	−	0.397874i	$-0.130252\pi$
$211$	11.9481	+	8.68083i	0.822544	+	0.597613i	−0.0948964	+	0.995487i	$0.530252\pi$
$212$	−0.319976	+	0.984786i	−0.0219761	+	0.0676354i
$213$	−14.4269	−	44.4014i	−0.988515	−	3.04234i
$214$	8.34626	−	6.06392i	0.570539	−	0.414521i
$215$	−14.6203	+	10.6223i	−0.997099	+	0.724434i
$216$	8.90382	+	27.4031i	0.605828	+	1.86455i
$217$	−0.927602	+	2.85487i	−0.0629697	+	0.193801i
$218$	10.2550	+	7.45072i	0.694559	+	0.504626i
$219$	−25.2380			−1.70543
$220$		0			0
$221$	−4.52791			−0.304581
$222$	−2.56407	−	1.86290i	−0.172089	−	0.125030i
$223$	−0.570250	+	1.75505i	−0.0381868	+	0.117527i	−0.968333	−	0.249663i	$-0.919680\pi$
$223$	−0.570250	+	1.75505i	−0.0381868	+	0.117527i	0.930146	+	0.367190i	$0.119680\pi$
$224$	1.78251	+	5.48601i	0.119099	+	0.366550i
$225$	2.24273	−	1.62944i	0.149515	−	0.108629i
$226$	0.910618	−	0.661603i	0.0605734	−	0.0440092i
$227$	6.77981	+	20.8661i	0.449992	+	1.38493i	0.876915	+	0.480645i	$0.159597\pi$
$227$	6.77981	+	20.8661i	0.449992	+	1.38493i	−0.426923	+	0.904288i	$0.640403\pi$
$228$	−10.1266	+	31.1665i	−0.670651	+	2.06405i
$229$	16.3840	+	11.9037i	1.08269	+	0.786619i	0.978150	−	0.207902i	$-0.0666634\pi$
$229$	16.3840	+	11.9037i	1.08269	+	0.786619i	0.104539	+	0.994521i	$0.466663\pi$
$230$	4.54323			0.299571
$231$		0			0
$232$	2.19819			0.144318
$233$	17.0400	+	12.3803i	1.11633	+	0.811059i	0.983648	−	0.180100i	$-0.0576422\pi$
$233$	17.0400	+	12.3803i	1.11633	+	0.811059i	0.132678	+	0.991159i	$0.457642\pi$
$234$	3.58857	−	11.0445i	0.234592	−	0.722001i
$235$	2.91332	+	8.96628i	0.190044	+	0.584896i
$236$	−0.462345	+	0.335913i	−0.0300961	+	0.0218661i
$237$	10.3045	−	7.48665i	0.669349	−	0.486310i
$238$	0.370653	+	1.14075i	0.0240259	+	0.0739440i
$239$	−4.78869	+	14.7381i	−0.309755	+	0.953327i	0.668105	+	0.744067i	$0.267106\pi$
$239$	−4.78869	+	14.7381i	−0.309755	+	0.953327i	−0.977860	+	0.209260i	$0.932894\pi$
$240$	−8.22192	−	5.97357i	−0.530722	−	0.385592i
$241$	−14.0848			−0.907283			−0.453641	−	0.891184i	$-0.649875\pi$
$241$	−14.0848			−0.907283			−0.453641	+	0.891184i	$0.649875\pi$
$242$		0			0
$243$	18.4792			1.18544
$244$	−6.29014	−	4.57005i	−0.402685	−	0.292568i
$245$	0.662464	−	2.03885i	0.0423233	−	0.130258i
$246$	3.61364	+	11.1217i	0.230397	+	0.709091i
$247$	13.7603	−	9.99742i	0.875545	−	0.636121i
$248$	−5.77631	+	4.19674i	−0.366796	+	0.266493i
$249$	3.93079	+	12.0977i	0.249103	+	0.766662i
$250$	2.39775	−	7.37951i	0.151647	−	0.466721i
$251$	0.871529	+	0.633203i	0.0550104	+	0.0399674i	0.614951	−	0.788566i	$-0.289176\pi$
$251$	0.871529	+	0.633203i	0.0550104	+	0.0399674i	−0.559940	+	0.828533i	$0.689176\pi$
$252$	10.6401			0.670261
$253$		0			0
$254$	11.7653			0.738223
$255$	−9.75241	−	7.08554i	−0.610720	−	0.443714i
$256$	−2.79209	+	8.59316i	−0.174506	+	0.537073i
$257$	4.04226	+	12.4408i	0.252149	+	0.776035i	0.994378	+	0.105889i	$0.0337687\pi$
$257$	4.04226	+	12.4408i	0.252149	+	0.776035i	−0.742229	+	0.670146i	$0.766231\pi$
$258$	14.3412	−	10.4195i	0.892842	−	0.648688i
$259$	−1.21933	+	0.885898i	−0.0757657	+	0.0550470i
$260$	2.59849	+	7.99732i	0.161151	+	0.495972i
$261$	1.95859	−	6.02791i	0.121233	−	0.373118i
$262$	−3.64414	−	2.64763i	−0.225136	−	0.163571i
$263$	9.57216			0.590245			0.295122	−	0.955459i	$-0.404640\pi$
$263$	9.57216			0.590245			0.295122	+	0.955459i	$0.404640\pi$
$264$		0			0
$265$	1.43080			0.0878935
$266$	−3.64514	−	2.64835i	−0.223498	−	0.162381i
$267$	−8.06007	+	24.8064i	−0.493268	+	1.51812i
$268$	0.432501	+	1.33110i	0.0264192	+	0.0813099i
$269$	3.85782	−	2.80287i	0.235216	−	0.170894i	−0.463933	−	0.885870i	$-0.653562\pi$
$269$	3.85782	−	2.80287i	0.235216	−	0.170894i	0.699149	+	0.714976i	$0.253562\pi$
$270$	14.0711	−	10.2232i	0.856337	−	0.622165i
$271$	6.19650	+	19.0709i	0.376410	+	1.15847i	0.942522	+	0.334144i	$0.108447\pi$
$271$	6.19650	+	19.0709i	0.376410	+	1.15847i	−0.566112	+	0.824328i	$0.691553\pi$
$272$	0.835595	−	2.57170i	0.0506654	−	0.155932i
$273$	−6.42211	−	4.66594i	−0.388684	−	0.282395i
$274$	−9.28776			−0.561094
$275$		0			0
$276$	15.4138			0.927802
$277$	−9.38658	−	6.81975i	−0.563985	−	0.409759i	0.268930	−	0.963160i	$-0.413330\pi$
$277$	−9.38658	−	6.81975i	−0.563985	−	0.409759i	−0.832915	+	0.553401i	$0.813330\pi$
$278$	2.95350	−	9.08994i	0.177139	−	0.545179i
$279$	6.36166	+	19.5792i	0.380862	+	1.17217i
$280$	4.12526	−	2.99718i	0.246531	−	0.179116i
$281$	9.77197	−	7.09975i	0.582947	−	0.423536i	−0.256838	−	0.966454i	$-0.582681\pi$
$281$	9.77197	−	7.09975i	0.582947	−	0.423536i	0.839785	+	0.542919i	$0.182681\pi$
$282$	−2.85769	−	8.79508i	−0.170173	−	0.523739i
$283$	−6.79628	+	20.9168i	−0.403997	+	1.24337i	0.517733	+	0.855542i	$0.326776\pi$
$283$	−6.79628	+	20.9168i	−0.403997	+	1.24337i	−0.921730	+	0.387832i	$0.873224\pi$
$284$	−18.6632	−	13.5596i	−1.10746	−	0.804615i
$285$	45.2820			2.68227
$286$		0			0
$287$	5.56104			0.328258
$288$	32.0049	+	23.2529i	1.88591	+	1.37019i
$289$	−4.26215	+	13.1175i	−0.250715	+	0.771620i
$290$	−0.410037	−	1.26196i	−0.0240782	−	0.0741051i
$291$	−21.6313	+	15.7161i	−1.26805	+	0.921293i
$292$	−10.0890	+	7.33012i	−0.590417	+	0.428963i
$293$	−0.437941	−	1.34784i	−0.0255848	−	0.0787419i	0.937449	−	0.348123i	$-0.113181\pi$
$293$	−0.437941	−	1.34784i	−0.0255848	−	0.0787419i	−0.963034	+	0.269381i	$0.913181\pi$
$294$	−0.649815	+	1.99992i	−0.0378980	+	0.116638i
$295$	0.638867	+	0.464164i	0.0371963	+	0.0270247i
$296$	−3.58491			−0.208369
$297$		0			0
$298$	1.75669			0.101762
$299$	−6.47225	−	4.70237i	−0.374300	−	0.271945i
$300$	0.608454	−	1.87263i	0.0351291	−	0.108116i
$301$	−2.60497	−	8.01726i	−0.150148	−	0.462107i
$302$	1.61987	−	1.17690i	0.0932129	−	0.0677231i
$303$	−10.2293	+	7.43200i	−0.587657	+	0.426957i
$304$	3.13882	+	9.66031i	0.180024	+	0.554057i
$305$	−3.31993	+	10.2177i	−0.190099	+	0.585063i
$306$	6.65505	+	4.83517i	0.380444	+	0.276409i
$307$	−29.4646			−1.68163			−0.840817	−	0.541319i	$-0.817925\pi$
$307$	−29.4646			−1.68163			−0.840817	+	0.541319i	$0.817925\pi$
$308$		0			0
$309$	−55.3411			−3.14825
$310$	3.48679	+	2.53330i	0.198036	+	0.143882i
$311$	8.30597	−	25.5631i	0.470988	−	1.44955i	−0.380304	−	0.924862i	$-0.624181\pi$
$311$	8.30597	−	25.5631i	0.470988	−	1.44955i	0.851292	−	0.524692i	$-0.175819\pi$
$312$	−5.83467	−	17.9573i	−0.330323	−	1.01663i
$313$	3.63467	−	2.64074i	0.205444	−	0.149264i	−0.480306	−	0.877101i	$-0.659474\pi$
$313$	3.63467	−	2.64074i	0.205444	−	0.149264i	0.685750	+	0.727837i	$0.259474\pi$
$314$	6.09818	−	4.43059i	0.344140	−	0.250032i
$315$	−4.54329	−	13.9828i	−0.255986	−	0.787843i
$316$	1.94486	−	5.98567i	0.109407	−	0.336720i
$317$	8.85879	+	6.43628i	0.497559	+	0.361498i	0.808084	−	0.589068i	$-0.200505\pi$
$317$	8.85879	+	6.43628i	0.497559	+	0.361498i	−0.310525	+	0.950565i	$0.600505\pi$
$318$	−1.40348			−0.0787034
$319$		0			0
$320$	1.80846			0.101096
$321$	−39.1275	−	28.4278i	−2.18388	−	1.58668i
$322$	−0.654888	+	2.01554i	−0.0364955	+	0.112321i
$323$	3.72311	+	11.4586i	0.207159	+	0.637571i
$324$	21.9149	−	15.9221i	1.21749	−	0.884560i
$325$	−0.826781	+	0.600692i	−0.0458616	+	0.0333204i
$326$	3.76732	+	11.5946i	0.208653	+	0.642167i
$327$	18.3633	−	56.5165i	1.01549	−	3.12537i
$328$	10.7011	+	7.77478i	0.590868	+	0.429290i
$329$	−4.39771			−0.242453
$330$		0			0
$331$	16.5226			0.908166			0.454083	−	0.890959i	$-0.349967\pi$
$331$	16.5226			0.908166			0.454083	+	0.890959i	$0.349967\pi$
$332$	5.08502	+	3.69448i	0.279077	+	0.202761i
$333$	−3.19415	+	9.83060i	−0.175039	+	0.538713i
$334$	4.12501	+	12.6955i	0.225711	+	0.694666i
$335$	1.56461	−	1.13676i	0.0854838	−	0.0621076i
$336$	3.83525	−	2.78647i	0.209230	−	0.152014i
$337$	3.74551	+	11.5275i	0.204031	+	0.627943i	0.999752	+	0.0222794i	$0.00709233\pi$
$337$	3.74551	+	11.5275i	0.204031	+	0.627943i	−0.795721	+	0.605664i	$0.792908\pi$
$338$	1.36758	−	4.20899i	0.0743868	−	0.228939i
$339$	−4.26900	−	3.10161i	−0.231860	−	0.168456i
$340$	−5.95651			−0.323037
$341$		0			0
$342$	−30.9004			−1.67090
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	6.19606	−	19.0695i	0.334069	−	1.02816i
$345$	−6.58167	−	20.2563i	−0.354345	−	1.09056i
$346$	−3.24563	+	2.35809i	−0.174486	+	0.126772i
$347$	−19.6471	+	14.2744i	−1.05471	+	0.766292i	−0.973103	−	0.230372i	$-0.926006\pi$
$347$	−19.6471	+	14.2744i	−1.05471	+	0.766292i	−0.0816081	+	0.996664i	$0.526006\pi$
$348$	−1.39113	−	4.28146i	−0.0745725	−	0.229511i
$349$	1.02557	−	3.15637i	0.0548973	−	0.168957i	−0.919849	−	0.392274i	$-0.871689\pi$
$349$	1.02557	−	3.15637i	0.0548973	−	0.168957i	0.974746	+	0.223317i	$0.0716886\pi$
$350$	0.219017	+	0.159125i	0.0117069	+	0.00850559i
$351$	−30.6269			−1.63474
$352$		0			0
$353$	20.3272			1.08191			0.540955	−	0.841051i	$-0.318063\pi$
$353$	20.3272			1.08191			0.540955	+	0.841051i	$0.318063\pi$
$354$	−0.626668	−	0.455301i	−0.0333070	−	0.0241990i
$355$	−9.85042	+	30.3165i	−0.522806	+	1.60903i
$356$	3.98269	+	12.2575i	0.211082	+	0.649644i
$357$	4.54917	−	3.30516i	0.240768	−	0.174928i
$358$	−0.877196	+	0.637321i	−0.0463613	+	0.0336834i
$359$	−8.97423	−	27.6199i	−0.473642	−	1.45772i	−0.847780	−	0.530347i	$-0.822062\pi$
$359$	−8.97423	−	27.6199i	−0.473642	−	1.45772i	0.374139	−	0.927373i	$-0.377938\pi$
$360$	10.8065	−	33.2589i	0.569552	−	1.75290i
$361$	−21.2431	−	15.4340i	−1.11806	−	0.812317i
$362$	−1.62535			−0.0854264
$363$		0			0
$364$	−3.92246			−0.205593
$365$	13.9410	+	10.1287i	0.729706	+	0.530162i
$366$	3.25654	−	10.0226i	0.170222	−	0.523889i
$367$	−7.03285	−	21.6449i	−0.367112	−	1.12985i	−0.948648	−	0.316333i	$-0.897548\pi$
$367$	−7.03285	−	21.6449i	−0.367112	−	1.12985i	0.581536	−	0.813520i	$-0.302452\pi$
$368$	3.86519	−	2.80822i	0.201487	−	0.146389i
$369$	30.8548	−	22.4173i	1.60623	−	1.16700i
$370$	0.668707	+	2.05807i	0.0347644	+	0.106994i
$371$	−0.206244	+	0.634755i	−0.0107077	+	0.0329548i
$372$	11.8296	+	8.59473i	0.613338	+	0.445616i
$373$	22.2412			1.15160			0.575802	−	0.817589i	$-0.304690\pi$
$373$	22.2412			1.15160			0.575802	+	0.817589i	$0.304690\pi$
$374$		0			0
$375$	−36.3756			−1.87843
$376$	−8.46248	−	6.14835i	−0.436419	−	0.317077i
$377$	−0.722032	+	2.22219i	−0.0371865	+	0.114448i
$378$	2.50710	+	7.71606i	0.128951	+	0.396871i
$379$	−27.0784	+	19.6736i	−1.39092	+	1.01056i	−0.395158	+	0.918613i	$0.629310\pi$
$379$	−27.0784	+	19.6736i	−1.39092	+	1.01056i	−0.995764	+	0.0919503i	$0.970690\pi$
$380$	18.1018	−	13.1517i	0.928601	−	0.674668i
$381$	−17.0442	−	52.4566i	−0.873200	−	2.68743i
$382$	−2.62861	+	8.09003i	−0.134491	+	0.413922i
$383$	4.97216	+	3.61248i	0.254065	+	0.184589i	0.707527	−	0.706687i	$-0.249811\pi$
$383$	4.97216	+	3.61248i	0.254065	+	0.184589i	−0.453461	+	0.891276i	$0.649811\pi$
$384$	34.4486			1.75795
$385$		0			0
$386$	−1.17829			−0.0599733
$387$	−46.7720	−	33.9819i	−2.37755	−	1.72739i
$388$	−4.08268	+	12.5652i	−0.207267	+	0.637901i
$389$	2.28785	+	7.04128i	0.115999	+	0.357007i	0.992154	−	0.125022i	$-0.0399000\pi$
$389$	2.28785	+	7.04128i	0.115999	+	0.357007i	−0.876155	+	0.482029i	$0.839900\pi$
$390$	−9.22076	+	6.69927i	−0.466911	+	0.339231i
$391$	4.58468	−	3.33097i	0.231857	−	0.168454i
$392$	0.735015	+	2.26214i	0.0371238	+	0.114255i
$393$	−6.52544	+	20.0832i	−0.329165	+	1.01307i
$394$	0.489305	+	0.355501i	0.0246508	+	0.0179099i
$395$	−8.69662			−0.437575
$396$		0			0
$397$	17.8079			0.893752			0.446876	−	0.894596i	$-0.352537\pi$
$397$	17.8079			0.893752			0.446876	+	0.894596i	$0.352537\pi$
$398$	−8.46865	−	6.15283i	−0.424495	−	0.308414i
$399$	−6.52722	+	20.0887i	−0.326769	+	1.00569i
$400$	−0.188595	−	0.580436i	−0.00942976	−	0.0290218i
$401$	−20.7746	+	15.0937i	−1.03744	+	0.753741i	−0.969783	−	0.243968i	$-0.921551\pi$
$401$	−20.7746	+	15.0937i	−1.03744	+	0.753741i	−0.0676523	+	0.997709i	$0.521551\pi$
$402$	−1.53474	+	1.11505i	−0.0765456	+	0.0556137i
$403$	−2.34522	−	7.21785i	−0.116824	−	0.359547i
$404$	−1.93067	+	5.94198i	−0.0960542	+	0.295625i
$405$	−30.2819	−	22.0011i	−1.50472	−	1.09324i
$406$	0.618957			0.0307183
$407$		0			0
$408$	13.3748			0.662152
$409$	1.08210	+	0.786189i	0.0535062	+	0.0388746i	0.614217	−	0.789137i	$-0.289472\pi$
$409$	1.08210	+	0.786189i	0.0535062	+	0.0388746i	−0.560711	+	0.828012i	$0.689472\pi$
$410$	2.46733	−	7.59366i	0.121853	−	0.375024i
$411$	13.4550	+	41.4101i	0.663685	+	2.04261i
$412$	−22.1230	+	16.0733i	−1.08992	+	0.791873i
$413$	−0.298010	+	0.216517i	−0.0146641	+	0.0106541i
$414$	4.49133	+	13.8229i	0.220737	+	0.679359i
$415$	2.68387	−	8.26010i	0.131746	−	0.405472i
$416$	−11.7986	−	8.57218i	−0.578474	−	0.420286i
$417$	−44.8068			−2.19420
$418$		0			0
$419$	37.4618			1.83013			0.915064	−	0.403310i	$-0.132140\pi$
$419$	37.4618			1.83013			0.915064	+	0.403310i	$0.132140\pi$
$420$	−8.44835	−	6.13808i	−0.412237	−	0.299508i
$421$	2.55296	−	7.85721i	0.124424	−	0.382937i	−0.869372	−	0.494158i	$-0.835476\pi$
$421$	2.55296	−	7.85721i	0.124424	−	0.382937i	0.993796	+	0.111221i	$0.0354763\pi$
$422$	3.05656	+	9.40714i	0.148791	+	0.457932i
$423$	−24.4002	+	17.7277i	−1.18638	+	0.861953i
$424$	−1.28431	+	0.933108i	−0.0623718	+	0.0453158i
$425$	−0.223702	−	0.688483i	−0.0108511	−	0.0333963i
$426$	9.66233	−	29.7376i	0.468141	−	1.44079i
$427$	−4.05438	−	2.94568i	−0.196205	−	0.142551i
$428$	−23.8980			−1.15515
$429$		0			0
$430$	−12.1034			−0.583679
$431$	26.4196	+	19.1950i	1.27259	+	0.924590i	0.999302	−	0.0373433i	$-0.0118895\pi$
$431$	26.4196	+	19.1950i	1.27259	+	0.924590i	0.273286	+	0.961933i	$0.411890\pi$
$432$	5.65197	−	17.3950i	0.271931	−	0.836916i
$433$	4.88100	+	15.0222i	0.234566	+	0.721920i	0.997179	+	0.0750647i	$0.0239163\pi$
$433$	4.88100	+	15.0222i	0.234566	+	0.721920i	−0.762613	+	0.646856i	$0.776084\pi$
$434$	−1.62647	+	1.18170i	−0.0780730	+	0.0567234i
$435$	−5.03254	+	3.65636i	−0.241292	+	0.175309i
$436$	−9.07380	−	27.9263i	−0.434556	−	1.33743i
$437$	−6.57817	+	20.2455i	−0.314677	+	0.968475i
$438$	−13.6748	−	9.93533i	−0.653408	−	0.474728i
$439$	20.6942			0.987678			0.493839	−	0.869553i	$-0.335593\pi$
$439$	20.6942			0.987678			0.493839	+	0.869553i	$0.335593\pi$
$440$		0			0
$441$	6.85818			0.326580
$442$	−2.45338	−	1.78248i	−0.116695	−	0.0847841i
$443$	9.30001	−	28.6225i	0.441857	−	1.35990i	−0.444037	−	0.896008i	$-0.646454\pi$
$443$	9.30001	−	28.6225i	0.441857	−	1.35990i	0.885894	−	0.463887i	$-0.153546\pi$
$444$	2.26872	+	6.98241i	0.107669	+	0.331371i
$445$	14.4077	−	10.4678i	0.682992	−	0.496223i
$446$	−0.999883	+	0.726458i	−0.0473459	+	0.0343988i
$447$	−2.54487	−	7.83231i	−0.120368	−	0.370456i
$448$	−0.260682	+	0.802296i	−0.0123161	+	0.0379049i
$449$	−29.4437	−	21.3921i	−1.38953	−	1.00956i	−0.995916	−	0.0902818i	$-0.971223\pi$
$449$	−29.4437	−	21.3921i	−1.38953	−	1.00956i	−0.393618	−	0.919274i	$-0.628777\pi$
$450$	1.85664			0.0875230
$451$		0			0
$452$	−2.60739			−0.122641
$453$	−7.59397	−	5.51734i	−0.356796	−	0.259227i
$454$	−4.54074	+	13.9750i	−0.213107	+	0.655877i
$455$	1.67488	+	5.15476i	0.0785197	+	0.241659i
$456$	−40.6459	+	29.5310i	−1.90342	+	1.38291i
$457$	−7.92352	+	5.75678i	−0.370647	+	0.269291i	−0.757479	−	0.652859i	$-0.773569\pi$
$457$	−7.92352	+	5.75678i	−0.370647	+	0.269291i	0.386832	+	0.922150i	$0.373569\pi$
$458$	4.19136	+	12.8997i	0.195849	+	0.602762i
$459$	6.70407	−	20.6330i	0.312919	−	0.963067i
$460$	−8.51430	−	6.18600i	−0.396981	−	0.288424i
$461$	21.8596			1.01810			0.509052	−	0.860736i	$-0.329996\pi$
$461$	21.8596			1.01810			0.509052	+	0.860736i	$0.329996\pi$
$462$		0			0
$463$	6.75889			0.314112			0.157056	−	0.987590i	$-0.449800\pi$
$463$	6.75889			0.314112			0.157056	+	0.987590i	$0.449800\pi$
$464$	−1.12888	−	0.820177i	−0.0524068	−	0.0380758i
$465$	6.24367	−	19.2160i	0.289543	−	0.891122i
$466$	4.35916	+	13.4161i	0.201934	+	0.621489i
$467$	24.2893	−	17.6472i	1.12397	−	0.816615i	0.139167	−	0.990269i	$-0.455558\pi$
$467$	24.2893	−	17.6472i	1.12397	−	0.816615i	0.984807	+	0.173654i	$0.0555575\pi$
$468$	−21.7633	+	15.8119i	−1.00601	+	0.730907i
$469$	0.278773	+	0.857976i	0.0128726	+	0.0396176i
$470$	−1.95118	+	6.00511i	−0.0900012	+	0.276995i
$471$	−28.5884	−	20.7707i	−1.31728	−	0.957062i
$472$	−0.876166			−0.0403288
$473$		0			0
$474$	8.53056			0.391822
$475$	2.19997	+	1.59837i	0.100941	+	0.0733382i
$476$	0.858607	−	2.64252i	0.0393542	−	0.121120i
$477$	1.41446	+	4.35326i	0.0647637	+	0.199322i
$478$	−8.39655	+	6.10045i	−0.384049	+	0.279028i
$479$	−4.85696	+	3.52879i	−0.221920	+	0.161234i	−0.693191	−	0.720754i	$-0.743796\pi$
$479$	−4.85696	+	3.52879i	−0.221920	+	0.161234i	0.471270	+	0.881989i	$0.343796\pi$
$480$	−11.9981	−	36.9262i	−0.547634	−	1.68544i
$481$	1.17752	−	3.62404i	0.0536904	−	0.165242i
$482$	−7.63164	−	5.54471i	−0.347612	−	0.252555i
$483$	9.93514			0.452064
$484$		0			0
$485$	18.2561			0.828965
$486$	10.0127	+	7.27462i	0.454184	+	0.329984i
$487$	1.96758	−	6.05559i	0.0891596	−	0.274405i	−0.896528	−	0.442987i	$-0.853919\pi$
$487$	1.96758	−	6.05559i	0.0891596	−	0.274405i	0.985688	+	0.168582i	$0.0539188\pi$
$488$	−3.68352	−	11.3367i	−0.166745	−	0.513188i
$489$	46.2379	−	33.5938i	2.09095	−	1.51916i
$490$	1.16157	−	0.843932i	0.0524745	−	0.0381250i
$491$	−3.82467	−	11.7711i	−0.172605	−	0.531223i	0.826911	−	0.562333i	$-0.190096\pi$
$491$	−3.82467	−	11.7711i	−0.172605	−	0.531223i	−0.999516	+	0.0311093i	$0.990096\pi$
$492$	8.37090	−	25.7630i	0.377390	−	1.16149i
$493$	−1.33902	−	0.972852i	−0.0603062	−	0.0438150i
$494$	11.3914			0.512525
$495$		0			0
$496$	4.53228			0.203505
$497$	−12.0296	−	8.74000i	−0.539600	−	0.392042i
$498$	−2.63262	+	8.10237i	−0.117971	+	0.363076i
$499$	−4.41266	−	13.5808i	−0.197538	−	0.607958i	−0.999938	−	0.0111716i	$-0.996444\pi$
$499$	−4.41266	−	13.5808i	−0.197538	−	0.607958i	0.802400	−	0.596787i	$-0.203556\pi$
$500$	−14.5414	+	10.5649i	−0.650311	+	0.472478i
$501$	50.6279	−	36.7833i	2.26189	−	1.64336i
$502$	0.222954	+	0.686182i	0.00995092	+	0.0306258i
$503$	−1.83115	+	5.63571i	−0.0816470	+	0.251284i	−0.983544	−	0.180667i	$-0.942174\pi$
$503$	−1.83115	+	5.63571i	−0.0816470	+	0.251284i	0.901897	+	0.431950i	$0.142174\pi$
$504$	13.1971	+	9.58828i	0.587847	+	0.427096i
$505$	8.63314			0.384170
$506$		0			0
$507$	−20.7473			−0.921419
$508$	−22.0490	−	16.0195i	−0.978267	−	0.710752i
$509$	9.54043	−	29.3624i	0.422872	−	1.30147i	−0.482145	−	0.876092i	$-0.660142\pi$
$509$	9.54043	−	29.3624i	0.422872	−	1.30147i	0.905017	−	0.425376i	$-0.139858\pi$
$510$	−2.49486	−	7.67838i	−0.110474	−	0.340004i
$511$	−6.50301	+	4.72471i	−0.287676	+	0.209009i
$512$	12.8569	−	9.34107i	0.568199	−	0.412821i
$513$	25.1831	+	77.5057i	1.11186	+	3.42196i
$514$	−2.70728	+	8.33214i	−0.119413	+	0.367515i
$515$	30.5694	+	22.2100i	1.34705	+	0.978689i
$516$	−41.0633			−1.80771
$517$		0			0
$518$	−1.00942			−0.0443516
$519$	15.2156	+	11.0548i	0.667890	+	0.485250i
$520$	−3.98380	+	12.2609i	−0.174701	+	0.537676i
$521$	5.83639	+	17.9626i	0.255697	+	0.786954i	0.993692	+	0.112148i	$0.0357730\pi$
$521$	5.83639	+	17.9626i	0.255697	+	0.786954i	−0.737995	+	0.674807i	$0.764227\pi$
$522$	3.43421	−	2.49510i	0.150311	−	0.109208i
$523$	−6.42528	+	4.66824i	−0.280958	+	0.204128i	−0.719335	−	0.694663i	$-0.755553\pi$
$523$	−6.42528	+	4.66824i	−0.280958	+	0.204128i	0.438377	+	0.898791i	$0.355553\pi$
$524$	3.22439	+	9.92365i	0.140858	+	0.433516i
$525$	0.392186	−	1.20702i	0.0171164	−	0.0526788i
$526$	5.18652	+	3.76823i	0.226143	+	0.164303i
$527$	5.37595			0.234180
$528$		0			0
$529$	−12.9873			−0.564665
$530$	0.775258	+	0.563258i	0.0336750	+	0.0244664i
$531$	−0.780663	+	2.40263i	−0.0338779	+	0.104265i
$532$	3.22527	+	9.92635i	0.139833	+	0.430362i
$533$	−11.3746	+	8.26412i	−0.492688	+	0.357959i
$534$	−14.1326	+	10.2680i	−0.611579	+	0.444338i
$535$	10.2044	+	31.4060i	0.441175	+	1.35780i
$536$	−0.663078	+	2.04074i	−0.0286406	+	0.0881467i
$537$	4.11231	+	2.98777i	0.177459	+	0.128932i
$538$	3.19370			0.137690
$539$		0			0
$540$	−40.2899			−1.73380
$541$	6.14986	+	4.46814i	0.264403	+	0.192100i	0.712086	−	0.702092i	$-0.247751\pi$
$541$	6.14986	+	4.46814i	0.264403	+	0.192100i	−0.447683	+	0.894192i	$0.647751\pi$
$542$	−4.15007	+	12.7726i	−0.178261	+	0.548630i
$543$	2.35461	+	7.24673i	0.101046	+	0.310987i
$544$	8.35765	−	6.07219i	0.358331	−	0.260343i
$545$	−32.8253	+	23.8490i	−1.40608	+	1.02158i
$546$	−1.64290	−	5.05633i	−0.0703097	−	0.216391i
$547$	−6.70534	+	20.6369i	−0.286700	+	0.882371i	0.699184	+	0.714942i	$0.253547\pi$
$547$	−6.70534	+	20.6369i	−0.286700	+	0.882371i	−0.985884	+	0.167430i	$0.946453\pi$
$548$	17.4059	+	12.6461i	0.743542	+	0.540215i
$549$	−34.3697			−1.46686
$550$		0			0
$551$	6.21726			0.264864
$552$	19.1181	+	13.8901i	0.813721	+	0.591203i
$553$	1.25358	−	3.85813i	0.0533078	−	0.164064i
$554$	−2.40127	−	7.39035i	−0.102020	−	0.313986i
$555$	8.20731	−	5.96296i	0.348381	−	0.253114i
$556$	−17.9118	+	13.0137i	−0.759630	+	0.551904i
$557$	12.5502	+	38.6256i	0.531770	+	1.63662i	0.750527	+	0.660840i	$0.229800\pi$
$557$	12.5502	+	38.6256i	0.531770	+	1.63662i	−0.218757	+	0.975779i	$0.570200\pi$
$558$	−4.26068	+	13.1130i	−0.180369	+	0.555119i
$559$	17.2425	+	12.5274i	0.729279	+	0.529852i
$560$	−3.23681			−0.136780
$561$		0			0
$562$	8.08972			0.341244
$563$	−18.9547	−	13.7714i	−0.798844	−	0.580394i	0.111731	−	0.993739i	$-0.464361\pi$
$563$	−18.9547	−	13.7714i	−0.798844	−	0.580394i	−0.910575	+	0.413344i	$0.864361\pi$
$564$	−6.61977	+	20.3736i	−0.278743	+	0.857881i
$565$	1.11335	+	3.42654i	0.0468390	+	0.144156i
$566$	−11.9167	+	8.65797i	−0.500895	+	0.363922i
$567$	14.1255	−	10.2628i	0.593214	−	0.430995i
$568$	−10.9292	−	33.6366i	−0.458579	−	1.41136i
$569$	3.44410	−	10.5999i	0.144384	−	0.444369i	−0.852547	−	0.522650i	$-0.824943\pi$
$569$	3.44410	−	10.5999i	0.144384	−	0.444369i	0.996931	+	0.0782814i	$0.0249433\pi$
$570$	24.5353	+	17.8260i	1.02767	+	0.746647i
$571$	6.15846			0.257724			0.128862	−	0.991663i	$-0.458868\pi$
$571$	6.15846			0.257724			0.128862	+	0.991663i	$0.458868\pi$
$572$		0			0
$573$	39.8780			1.66593
$574$	3.01316	+	2.18919i	0.125767	+	0.0913750i
$575$	0.395247	−	1.21645i	0.0164830	−	0.0507293i
$576$	1.78780	+	5.50229i	0.0744917	+	0.229262i
$577$	11.7179	−	8.51357i	0.487824	−	0.354425i	−0.316523	−	0.948585i	$-0.602515\pi$
$577$	11.7179	−	8.51357i	0.487824	−	0.354425i	0.804347	+	0.594160i	$0.202515\pi$
$578$	−7.47331	+	5.42967i	−0.310849	+	0.225845i
$579$	1.70696	+	5.25348i	0.0709388	+	0.218327i
$580$	−0.949839	+	2.92330i	−0.0394399	+	0.121384i
$581$	3.27760	+	2.38132i	0.135978	+	0.0987937i
$582$	−17.9075			−0.742288
$583$		0			0
$584$	−19.1192			−0.791159
$585$	30.0724	+	21.8489i	1.24334	+	0.903340i
$586$	0.293308	−	0.902710i	0.0121165	−	0.0372906i
$587$	4.90007	+	15.0809i	0.202247	+	0.622454i	0.999815	+	0.0192243i	$0.00611967\pi$
$587$	4.90007	+	15.0809i	0.202247	+	0.622454i	−0.797568	+	0.603229i	$0.793880\pi$
$588$	3.94087	−	2.86321i	0.162519	−	0.118077i
$589$	−16.3374	+	11.8699i	−0.673173	+	0.489089i
$590$	0.163435	+	0.503000i	0.00672849	+	0.0207082i
$591$	0.876181	−	2.69661i	0.0360413	−	0.110924i
$592$	1.84103	+	1.33758i	0.0756657	+	0.0549743i
$593$	−22.9285			−0.941560			−0.470780	−	0.882251i	$-0.656027\pi$
$593$	−22.9285			−0.941560			−0.470780	+	0.882251i	$0.656027\pi$
$594$		0			0
$595$	−3.83934			−0.157397
$596$	−3.29214	−	2.39188i	−0.134851	−	0.0979753i
$597$	−15.1645	+	46.6715i	−0.620642	+	1.91014i
$598$	−1.65573	−	5.09581i	−0.0677077	−	0.208383i
$599$	−10.6395	+	7.73008i	−0.434720	+	0.315843i	−0.783533	−	0.621350i	$-0.786585\pi$
$599$	−10.6395	+	7.73008i	−0.434720	+	0.315843i	0.348813	+	0.937192i	$0.386585\pi$
$600$	2.44220	−	1.77436i	0.0997022	−	0.0724379i
$601$	−8.45237	−	26.0137i	−0.344780	−	1.06112i	−0.961702	−	0.274098i	$-0.911621\pi$
$601$	−8.45237	−	26.0137i	−0.344780	−	1.06112i	0.616922	−	0.787024i	$-0.288379\pi$
$602$	1.74466	−	5.36951i	0.0711070	−	0.218845i
$603$	5.00536	+	3.63660i	0.203834	+	0.148094i
$604$	−4.63819			−0.188725
$605$		0			0
$606$	−8.46830			−0.344001
$607$	−37.9221	−	27.5520i	−1.53921	−	1.11830i	−0.950827	−	0.309721i	$-0.899764\pi$
$607$	−37.9221	−	27.5520i	−1.53921	−	1.11830i	−0.588384	−	0.808582i	$-0.700236\pi$
$608$	−11.9917	+	36.9066i	−0.486327	+	1.49676i
$609$	−0.896670	−	2.75967i	−0.0363349	−	0.111827i
$610$	−5.82120	+	4.22935i	−0.235694	+	0.171241i
$611$	8.99510	−	6.53532i	0.363903	−	0.264391i
$612$	−5.88848	−	18.1229i	−0.238028	−	0.732573i
$613$	6.32540	−	19.4676i	0.255481	−	0.786288i	−0.738254	−	0.674523i	$-0.764349\pi$
$613$	6.32540	−	19.4676i	0.255481	−	0.786288i	0.993735	−	0.111765i	$-0.0356505\pi$
$614$	−15.9649	−	11.5992i	−0.644292	−	0.468106i
$615$	−37.4312			−1.50937
$616$		0			0
$617$	44.1691			1.77818			0.889090	−	0.457733i	$-0.151338\pi$
$617$	44.1691			1.77818			0.889090	+	0.457733i	$0.151338\pi$
$618$	−29.9857	−	21.7859i	−1.20620	−	0.876357i
$619$	0.210621	−	0.648225i	0.00846557	−	0.0260544i	−0.946735	−	0.322015i	$-0.895640\pi$
$619$	0.210621	−	0.648225i	0.00846557	−	0.0260544i	0.955200	+	0.295961i	$0.0956398\pi$
$620$	−3.08516	−	9.49514i	−0.123903	−	0.381334i
$621$	31.0108	−	22.5307i	1.24442	−	0.904126i
$622$	14.5638	−	10.5812i	0.583955	−	0.424268i
$623$	2.56709	+	7.90068i	0.102848	+	0.316534i
$624$	−3.70374	+	11.3989i	−0.148268	+	0.456322i
$625$	18.4582	+	13.4106i	0.738326	+	0.536426i
$626$	3.00896			0.120262
$627$		0			0
$628$	−17.4610			−0.696770
$629$	2.18373	+	1.58657i	0.0870710	+	0.0632608i
$630$	3.04284	−	9.36491i	0.121230	−	0.373107i
$631$	−11.3940	−	35.0672i	−0.453588	−	1.39600i	−0.872784	−	0.488106i	$-0.837688\pi$
$631$	−11.3940	−	35.0672i	−0.453588	−	1.39600i	0.419196	−	0.907896i	$-0.362312\pi$
$632$	7.80624	−	5.67157i	0.310516	−	0.225603i
$633$	37.5144	−	27.2558i	1.49106	−	1.08332i
$634$	2.26625	+	6.97480i	0.0900043	+	0.277005i
$635$	−11.6375	+	35.8164i	−0.461818	+	1.42133i
$636$	2.63022	+	1.91096i	0.104295	+	0.0757747i
$637$	−2.52826			−0.100173
$638$		0			0
$639$	−101.977			−4.03414
$640$	−19.0288	−	13.8252i	−0.752179	−	0.546490i
$641$	−6.33875	+	19.5087i	−0.250366	+	0.770546i	0.744342	+	0.667799i	$0.232763\pi$
$641$	−6.33875	+	19.5087i	−0.250366	+	0.770546i	−0.994707	+	0.102748i	$0.967237\pi$
$642$	−10.0096	−	30.8063i	−0.395046	−	1.21583i
$643$	6.17814	−	4.48868i	0.243642	−	0.177016i	−0.459262	−	0.888301i	$-0.651886\pi$
$643$	6.17814	−	4.48868i	0.243642	−	0.177016i	0.702904	+	0.711284i	$0.251886\pi$
$644$	3.97163	−	2.88556i	0.156504	−	0.113707i
$645$	17.5340	+	53.9640i	0.690399	+	2.12483i
$646$	−2.49353	+	7.67430i	−0.0981066	+	0.301941i
$647$	−11.8787	−	8.63035i	−0.466998	−	0.339294i	0.329272	−	0.944235i	$-0.393197\pi$
$647$	−11.8787	−	8.63035i	−0.466998	−	0.339294i	−0.796270	+	0.604941i	$0.793197\pi$
$648$	41.5297			1.63144
$649$		0			0
$650$	−0.684450			−0.0268463
$651$	7.62492	+	5.53983i	0.298844	+	0.217123i
$652$	8.72690	−	26.8586i	0.341772	−	1.05187i
$653$	0.348273	+	1.07187i	0.0136290	+	0.0419457i	0.957640	−	0.287969i	$-0.0929800\pi$
$653$	0.348273	+	1.07187i	0.0136290	+	0.0419457i	−0.944011	+	0.329915i	$0.892980\pi$
$654$	32.1985	−	23.3936i	1.25906	−	0.914761i
$655$	11.6645	−	8.47476i	0.455770	−	0.331136i
$656$	−2.59463	−	7.98545i	−0.101303	−	0.311779i
$657$	−17.0352	+	52.4290i	−0.664607	+	2.04545i
$658$	−2.38283	−	1.73123i	−0.0928923	−	0.0674902i
$659$	−10.0215			−0.390384			−0.195192	−	0.980765i	$-0.562533\pi$
$659$	−10.0215			−0.390384			−0.195192	+	0.980765i	$0.562533\pi$
$660$		0			0
$661$	15.7371			0.612101			0.306050	−	0.952015i	$-0.400992\pi$
$661$	15.7371			0.612101			0.306050	+	0.952015i	$0.400992\pi$
$662$	8.95253	+	6.50439i	0.347950	+	0.252800i
$663$	−4.39318	+	13.5208i	−0.170617	+	0.525105i
$664$	2.97780	+	9.16471i	0.115561	+	0.355660i
$665$	11.6677	−	8.47707i	0.452454	−	0.328727i
$666$	−5.60067	+	4.06912i	−0.217022	+	0.157675i
$667$	−0.903670	−	2.78121i	−0.0349902	−	0.107689i
$668$	9.55548	−	29.4087i	0.369713	−	1.13786i
$669$	4.68747	+	3.40565i	0.181228	+	0.131670i
$670$	1.29526			0.0500403
$671$		0			0
$672$	18.1113			0.698657
$673$	25.8983	+	18.8162i	0.998305	+	0.725311i	0.961724	−	0.274020i	$-0.0883533\pi$
$673$	25.8983	+	18.8162i	0.998305	+	0.725311i	0.0365810	+	0.999331i	$0.488353\pi$
$674$	−2.50853	+	7.72048i	−0.0966251	+	0.297382i
$675$	−1.51312	−	4.65691i	−0.0582401	−	0.179244i
$676$	−8.29385	+	6.02584i	−0.318994	+	0.231763i
$677$	−12.4104	+	9.01665i	−0.476969	+	0.346538i	−0.800151	−	0.599799i	$-0.795247\pi$
$677$	−12.4104	+	9.01665i	−0.476969	+	0.346538i	0.323182	+	0.946337i	$0.395247\pi$
$678$	−1.09209	−	3.36111i	−0.0419415	−	0.129083i
$679$	−2.63154	+	8.09904i	−0.100989	+	0.310813i
$680$	−7.38801	−	5.36770i	−0.283317	−	0.205842i
$681$	68.8864			2.63973
$682$		0			0
$683$	1.04764			0.0400868			0.0200434	−	0.999799i	$-0.493620\pi$
$683$	1.04764			0.0400868			0.0200434	+	0.999799i	$0.493620\pi$
$684$	57.9094	+	42.0737i	2.21422	+	1.60873i
$685$	9.18680	−	28.2741i	0.351010	−	1.08030i
$686$	0.206962	+	0.636964i	0.00790186	+	0.0243194i
$687$	51.4422	−	37.3749i	1.96264	−	1.42594i
$688$	−10.2971	+	7.48128i	−0.392573	+	0.285221i
$689$	−0.521440	−	1.60483i	−0.0198653	−	0.0611390i
$690$	4.40803	−	13.5665i	0.167811	−	0.516469i
$691$	−23.6138	−	17.1565i	−0.898313	−	0.652663i	0.0397191	−	0.999211i	$-0.487354\pi$
$691$	−23.6138	−	17.1565i	−0.898313	−	0.652663i	−0.938032	+	0.346548i	$0.887354\pi$
$692$	9.29326			0.353277
$693$		0			0
$694$	−16.2648			−0.617404
$695$	24.7505	+	17.9823i	0.938839	+	0.682107i
$696$	2.13278	−	6.56402i	0.0808428	−	0.248809i
$697$	−3.07762	−	9.47193i	−0.116573	−	0.358775i
$698$	1.79824	−	1.30650i	0.0680644	−	0.0494517i
$699$	53.5017	−	38.8713i	2.02362	−	1.47025i
$700$	−0.193789	−	0.596421i	−0.00732454	−	0.0225426i
$701$	−3.94877	+	12.1531i	−0.149143	+	0.459015i	−0.997520	−	0.0703770i	$-0.977580\pi$
$701$	−3.94877	+	12.1531i	−0.149143	+	0.459015i	0.848378	+	0.529392i	$0.177580\pi$
$702$	−16.5947	−	12.0567i	−0.626326	−	0.455052i
$703$	−10.1394			−0.382415
$704$		0			0
$705$	29.6009			1.11483
$706$	11.0140	+	8.00214i	0.414517	+	0.301164i
$707$	−1.24443	+	3.82997i	−0.0468017	+	0.144041i
$708$	0.554484	+	1.70653i	0.0208388	+	0.0641352i
$709$	−30.8001	+	22.3775i	−1.15672	+	0.840406i	−0.989360	−	0.145489i	$-0.953524\pi$
$709$	−30.8001	+	22.3775i	−1.15672	+	0.840406i	−0.167360	+	0.985896i	$0.553524\pi$
$710$	−17.2718	+	12.5487i	−0.648201	+	0.470946i
$711$	−8.59729	−	26.4597i	−0.322424	−	0.992318i
$712$	−6.10596	+	18.7922i	−0.228831	+	0.704269i
$713$	7.68445	+	5.58308i	0.287785	+	0.209088i
$714$	3.76602			0.140940
$715$		0			0
$716$	2.51169			0.0938663
$717$	39.3632	+	28.5990i	1.47005	+	1.06805i
$718$	6.01044	−	18.4982i	0.224308	−	0.690348i
$719$	−12.1349	−	37.3474i	−0.452555	−	1.39282i	−0.873981	−	0.485959i	$-0.838470\pi$
$719$	−12.1349	−	37.3474i	−0.452555	−	1.39282i	0.421426	−	0.906863i	$-0.361530\pi$
$720$	−17.9591	+	13.0480i	−0.669294	+	0.486271i
$721$	−14.2596	+	10.3602i	−0.531055	+	0.385834i
$722$	−5.43440	−	16.7254i	−0.202247	−	0.622453i
$723$	−13.6657	+	42.0587i	−0.508233	+	1.56418i
$724$	3.04601	+	2.21305i	0.113204	+	0.0822475i
$725$	−0.373562			−0.0138737
$726$		0			0
$727$	−28.4699			−1.05589			−0.527946	−	0.849278i	$-0.677037\pi$
$727$	−28.4699			−1.05589			−0.527946	+	0.849278i	$0.677037\pi$
$728$	−4.86512	−	3.53472i	−0.180313	−	0.131005i
$729$	1.74296	−	5.36429i	0.0645542	−	0.198677i
$730$	3.56638	+	10.9762i	0.131998	+	0.406247i
$731$	−12.2139	+	8.87390i	−0.451747	+	0.328213i
$732$	−19.7496	+	14.3489i	−0.729966	+	0.530352i
$733$	0.925001	+	2.84686i	0.0341657	+	0.105151i	0.966685	−	0.255969i	$-0.0823945\pi$
$733$	0.925001	+	2.84686i	0.0341657	+	0.105151i	−0.932519	+	0.361120i	$0.882394\pi$
$734$	4.71021	−	14.4965i	0.173857	−	0.535077i
$735$	−5.44548	−	3.95637i	−0.200859	−	0.145933i
$736$	18.2527			0.672802
$737$		0			0
$738$	25.5431			0.940254
$739$	−41.0438	−	29.8200i	−1.50982	−	1.09695i	−0.966257	−	0.257579i	$-0.917075\pi$
$739$	−41.0438	−	29.8200i	−1.50982	−	1.09695i	−0.543562	−	0.839369i	$-0.682925\pi$
$740$	1.54904	−	4.76746i	0.0569439	−	0.175255i
$741$	−16.5025	−	50.7895i	−0.606235	−	1.86580i
$742$	−0.361631	+	0.262741i	−0.0132759	+	0.00964551i
$743$	−0.310563	+	0.225637i	−0.0113935	+	0.00827783i	−0.593467	−	0.804858i	$-0.702241\pi$
$743$	−0.310563	+	0.225637i	−0.0113935	+	0.00827783i	0.582074	+	0.813136i	$0.302241\pi$
$744$	6.92745	+	21.3205i	0.253973	+	0.781648i
$745$	−1.73759	+	5.34776i	−0.0636604	+	0.195927i
$746$	12.0510	+	8.75559i	0.441220	+	0.320565i
$747$	27.7848			1.01659
$748$		0			0
$749$	−15.4037			−0.562840
$750$	−19.7096	−	14.3198i	−0.719692	−	0.522887i
$751$	−12.1620	+	37.4307i	−0.443797	+	1.36587i	0.440002	+	0.897997i	$0.354978\pi$
$751$	−12.1620	+	37.4307i	−0.443797	+	1.36587i	−0.883798	+	0.467868i	$0.845022\pi$
$752$	2.05185	+	6.31495i	0.0748233	+	0.230282i
$753$	2.73640	−	1.98811i	0.0997200	−	0.0724509i
$754$	−1.26602	+	0.919817i	−0.0461057	+	0.0334978i
$755$	1.98050	+	6.09536i	0.0720778	+	0.221833i
$756$	5.80762	−	17.8740i	0.211221	−	0.650072i
$757$	−9.21202	−	6.69292i	−0.334817	−	0.243258i	0.407655	−	0.913136i	$-0.366347\pi$
$757$	−9.21202	−	6.69292i	−0.334817	−	0.243258i	−0.742472	+	0.669878i	$0.766347\pi$
$758$	−22.4168			−0.814214
$759$		0			0
$760$	34.3037			1.24433
$761$	−6.05278	−	4.39760i	−0.219413	−	0.159413i	0.472649	−	0.881251i	$-0.343298\pi$
$761$	−6.05278	−	4.39760i	−0.219413	−	0.159413i	−0.692062	+	0.721838i	$0.743298\pi$
$762$	11.4152	−	35.1325i	0.413530	−	1.27272i
$763$	−5.84862	−	18.0002i	−0.211734	−	0.651651i
$764$	15.9415	−	11.5822i	0.576743	−	0.419028i
$765$	−21.3021	+	15.4769i	−0.770179	+	0.559568i
$766$	1.27197	+	3.91473i	0.0459583	+	0.141445i
$767$	0.287791	−	0.885730i	0.0103915	−	0.0319818i
$768$	22.9511	+	16.6749i	0.828175	+	0.601704i
$769$	26.8378			0.967798			0.483899	−	0.875124i	$-0.339220\pi$
$769$	26.8378			0.967798			0.483899	+	0.875124i	$0.339220\pi$
$770$		0			0
$771$	41.0714			1.47915
$772$	2.20819	+	1.60434i	0.0794745	+	0.0577416i
$773$	1.38063	−	4.24914i	0.0496577	−	0.152831i	−0.923153	−	0.384433i	$-0.874397\pi$
$773$	1.38063	−	4.24914i	0.0496577	−	0.152831i	0.972811	+	0.231602i	$0.0743969\pi$
$774$	−11.9652	−	36.8251i	−0.430080	−	1.32365i
$775$	0.981630	−	0.713196i	0.0352612	−	0.0256188i
$776$	−16.3870	+	11.9058i	−0.588258	+	0.427394i
$777$	1.46233	+	4.50059i	0.0524608	+	0.161458i
$778$	−1.53227	+	4.71586i	−0.0549347	+	0.169072i
$779$	30.2664	+	21.9898i	1.08441	+	0.787867i
$780$	26.4020			0.945342
$781$		0			0
$782$	3.79543			0.135724
$783$	−9.05711	−	6.58038i	−0.323675	−	0.235163i
$784$	0.466573	−	1.43596i	0.0166633	−	0.0512844i
$785$	7.45583	+	22.9467i	0.266110	+	0.819002i
$786$	−11.4418	+	8.31294i	−0.408115	+	0.296513i
$787$	−10.9103	+	7.92683i	−0.388912	+	0.282561i	−0.765009	−	0.644019i	$-0.777266\pi$
$787$	−10.9103	+	7.92683i	−0.388912	+	0.282561i	0.376098	+	0.926580i	$0.377266\pi$
$788$	−0.432944	−	1.33246i	−0.0154230	−	0.0474671i
$789$	9.28732	−	28.5834i	0.330638	−	1.01760i
$790$	−4.71213	−	3.42356i	−0.167650	−	0.121805i
$791$	−1.68062			−0.0597560
$792$		0			0
$793$	12.6704			0.449937
$794$	9.64892	+	7.01035i	0.342427	+	0.248788i
$795$	1.38823	−	4.27252i	0.0492353	−	0.151531i
$796$	7.49317	+	23.0616i	0.265588	+	0.817397i
$797$	−42.4776	+	30.8618i	−1.50463	+	1.09318i	−0.536144	+	0.844127i	$0.680120\pi$
$797$	−42.4776	+	30.8618i	−1.50463	+	1.09318i	−0.968490	+	0.249054i	$0.919880\pi$
$798$	−11.4449	+	8.31521i	−0.405145	+	0.294355i
$799$	2.43380	+	7.49046i	0.0861016	+	0.264994i
$800$	0.720516	−	2.21752i	0.0254741	−	0.0784012i
$801$	46.0919	+	33.4877i	1.62858	+	1.18323i
$802$	−17.1983			−0.607292
$803$		0			0
$804$	4.39443			0.154980
$805$	−5.48799	−	3.98726i	−0.193426	−	0.140532i
$806$	1.57070	−	4.83411i	0.0553255	−	0.170274i
$807$	−4.62664	−	14.2393i	−0.162865	−	0.501248i
$808$	−7.74926	+	5.63017i	−0.272618	+	0.198069i
$809$	−1.04350	+	0.758150i	−0.0366877	+	0.0266551i	−0.605978	−	0.795481i	$-0.707218\pi$
$809$	−1.04350	+	0.758150i	−0.0366877	+	0.0266551i	0.569290	+	0.822137i	$0.307218\pi$
$810$	−7.74669	−	23.8419i	−0.272191	−	0.837718i
$811$	10.5646	−	32.5145i	0.370973	−	1.14174i	−0.575182	−	0.818025i	$-0.695069\pi$
$811$	10.5646	−	32.5145i	0.370973	−	1.14174i	0.946155	−	0.323713i	$-0.104931\pi$
$812$	−1.15997	−	0.842765i	−0.0407068	−	0.0295752i
$813$	62.9596			2.20809
$814$		0			0
$815$	−39.0231			−1.36692
$816$	−6.86862	−	4.99034i	−0.240450	−	0.174697i
$817$	17.5247	−	53.9353i	0.613110	−	1.88696i
$818$	0.276821	+	0.851968i	0.00967883	+	0.0297884i
$819$	−14.0278	+	10.1918i	−0.490170	+	0.356129i
$820$	−14.9634	+	10.8715i	−0.522543	+	0.379650i
$821$	−12.2556	−	37.7188i	−0.427723	−	1.31640i	−0.900363	−	0.435141i	$-0.856699\pi$
$821$	−12.2556	−	37.7188i	−0.427723	−	1.31640i	0.472639	−	0.881256i	$-0.343301\pi$
$822$	−9.01139	+	27.7342i	−0.314308	+	0.967341i
$823$	7.46492	+	5.42358i	0.260211	+	0.189054i	0.710240	−	0.703960i	$-0.248586\pi$
$823$	7.46492	+	5.42358i	0.260211	+	0.189054i	−0.450029	+	0.893014i	$0.648586\pi$
$824$	−41.9241			−1.46049
$825$		0			0
$826$	−0.246707			−0.00858403
$827$	−20.7883	−	15.1036i	−0.722881	−	0.525204i	0.164423	−	0.986390i	$-0.447424\pi$
$827$	−20.7883	−	15.1036i	−0.722881	−	0.525204i	−0.887303	+	0.461186i	$0.847424\pi$
$828$	10.4041	−	32.0204i	0.361566	−	1.11279i
$829$	3.38019	+	10.4032i	0.117399	+	0.361316i	0.992440	−	0.122732i	$-0.0391657\pi$
$829$	3.38019	+	10.4032i	0.117399	+	0.361316i	−0.875041	+	0.484049i	$0.839166\pi$
$830$	4.70593	−	3.41906i	0.163345	−	0.118677i
$831$	−29.4717	+	21.4125i	−1.02236	+	0.742790i
$832$	−0.659072	−	2.02841i	−0.0228492	−	0.0703226i
$833$	0.553425	−	1.70327i	0.0191750	−	0.0590147i
$834$	−24.2779	−	17.6389i	−0.840674	−	0.610786i
$835$	−42.7282			−1.47867
$836$		0			0
$837$	36.3630			1.25689
$838$	20.2981	+	14.7474i	0.701185	+	0.509441i
$839$	−10.7344	+	33.0372i	−0.370594	+	1.14057i	0.575809	+	0.817584i	$0.304687\pi$
$839$	−10.7344	+	33.0372i	−0.370594	+	1.14057i	−0.946403	+	0.322987i	$0.895313\pi$
$840$	−4.94737	−	15.2264i	−0.170700	−	0.525362i
$841$	22.7705	−	16.5438i	0.785190	−	0.570474i
$842$	4.47640	−	3.25229i	0.154267	−	0.112081i
$843$	−11.7194	−	36.0686i	−0.403637	−	1.24227i
$844$	7.08045	−	21.7914i	0.243719	−	0.750090i
$845$	11.4604	+	8.32648i	0.394250	+	0.286440i
$846$	−20.1996			−0.694478
$847$		0			0
$848$	1.00771			0.0346050
$849$	55.8656	+	40.5888i	1.91730	+	1.39300i
$850$	0.149823	−	0.461108i	0.00513888	−	0.0158159i
$851$	1.47375	+	4.53573i	0.0505194	+	0.155483i
$852$	−58.5982	+	42.5741i	−2.00754	+	1.45856i
$853$	−16.6999	+	12.1332i	−0.571795	+	0.415433i	−0.835757	−	0.549100i	$-0.814971\pi$
$853$	−16.6999	+	12.1332i	−0.571795	+	0.415433i	0.263962	+	0.964533i	$0.414971\pi$
$854$	−1.03719	−	3.19214i	−0.0354919	−	0.109233i
$855$	30.5646	−	94.0681i	1.04529	−	3.21706i
$856$	−29.6413	−	21.5357i	−1.01312	−	0.736073i
$857$	34.1512			1.16658			0.583291	−	0.812263i	$-0.301765\pi$
$857$	34.1512			1.16658			0.583291	+	0.812263i	$0.301765\pi$
$858$		0			0
$859$	−33.4493			−1.14127			−0.570637	−	0.821202i	$-0.693304\pi$
$859$	−33.4493			−1.14127			−0.570637	+	0.821202i	$0.693304\pi$
$860$	22.6826	+	16.4799i	0.773471	+	0.561959i
$861$	5.39556	−	16.6058i	0.183880	−	0.565925i
$862$	6.75865	+	20.8010i	0.230201	+	0.708485i
$863$	27.5341	−	20.0047i	0.937271	−	0.680967i	−0.0104912	−	0.999945i	$-0.503340\pi$
$863$	27.5341	−	20.0047i	0.937271	−	0.680967i	0.947762	+	0.318978i	$0.103340\pi$
$864$	56.5312	−	41.0723i	1.92323	−	1.39731i
$865$	−3.96821	−	12.2129i	−0.134923	−	0.415251i
$866$	−3.26902	+	10.0610i	−0.111086	+	0.341887i
$867$	35.0350	+	25.4544i	1.18985	+	0.864478i
$868$	4.65710			0.158072
$869$		0			0
$870$	−4.16619			−0.141247
$871$	−1.84522	−	1.34063i	−0.0625229	−	0.0454256i
$872$	13.9113	−	42.8145i	0.471095	−	1.44988i
$873$	18.0475	+	55.5446i	0.610817	+	1.87990i
$874$	−11.5343	+	8.38012i	−0.390152	+	0.283462i
$875$	−9.37282	+	6.80975i	−0.316859	+	0.230212i
$876$	12.0997	+	37.2389i	0.408810	+	1.25819i
$877$	−2.43106	+	7.48202i	−0.0820909	+	0.252650i	−0.983675	−	0.179954i	$-0.942405\pi$
$877$	−2.43106	+	7.48202i	−0.0820909	+	0.252650i	0.901584	+	0.432604i	$0.142405\pi$
$878$	11.2128	+	8.14658i	0.378414	+	0.274934i
$879$	−4.44971			−0.150085
$880$		0			0
$881$	13.3289			0.449063			0.224531	−	0.974467i	$-0.427915\pi$
$881$	13.3289			0.449063			0.224531	+	0.974467i	$0.427915\pi$
$882$	3.71599	+	2.69983i	0.125124	+	0.0909079i
$883$	−5.28413	+	16.2629i	−0.177825	+	0.547289i	−0.999751	−	0.0223048i	$-0.992900\pi$
$883$	−5.28413	+	16.2629i	−0.177825	+	0.547289i	0.821926	+	0.569594i	$0.192900\pi$
$884$	2.17078	+	6.68098i	0.0730113	+	0.224706i
$885$	2.00590	−	1.45737i	0.0674275	−	0.0489889i
$886$	16.3068	−	11.8475i	0.547836	−	0.398026i
$887$	8.19466	+	25.2206i	0.275150	+	0.846823i	0.989180	+	0.146709i	$0.0468679\pi$
$887$	8.19466	+	25.2206i	0.275150	+	0.846823i	−0.714030	+	0.700115i	$0.753132\pi$
$888$	−3.47824	+	10.7049i	−0.116722	+	0.359233i
$889$	−14.2119	−	10.3256i	−0.476653	−	0.346309i
$890$	11.9274			0.399808
$891$		0			0
$892$	2.86298			0.0958598
$893$	−23.9349	−	17.3897i	−0.800950	−	0.581924i
$894$	1.70441	−	5.24564i	0.0570041	−	0.175441i
$895$	−1.07249	−	3.30078i	−0.0358493	−	0.110333i
$896$	8.87628	−	6.44900i	0.296536	−	0.215446i
$897$	−20.3214	+	14.7644i	−0.678512	+	0.492968i
$898$	−7.53227	−	23.1819i	−0.251355	−	0.773592i
$899$	0.857262	−	2.63838i	0.0285913	−	0.0879949i
$900$	−3.47947	−	2.52798i	−0.115982	−	0.0842661i
$901$	1.19530			0.0398211
$902$		0			0
$903$	−26.4678			−0.880794
$904$	−3.23401	−	2.34964i	−0.107561	−	0.0781480i
$905$	1.60768	−	4.94793i	0.0534411	−	0.164475i
$906$	−1.94268	−	5.97897i	−0.0645414	−	0.198638i
$907$	−7.16187	+	5.20340i	−0.237806	+	0.172776i	−0.700305	−	0.713844i	$-0.746953\pi$
$907$	−7.16187	+	5.20340i	−0.237806	+	0.172776i	0.462499	+	0.886620i	$0.346953\pi$
$908$	27.5378	−	20.0074i	0.913873	−	0.663968i
$909$	8.53454	+	26.2666i	0.283073	+	0.871208i
$910$	−1.12174	+	3.45237i	−0.0371854	+	0.114445i
$911$	45.2239	+	32.8571i	1.49834	+	1.08860i	0.971039	+	0.238923i	$0.0767944\pi$
$911$	45.2239	+	32.8571i	1.49834	+	1.08860i	0.527297	+	0.849681i	$0.323206\pi$
$912$	31.8921			1.05605
$913$		0			0
$914$	−6.55948			−0.216968
$915$	27.2899	+	19.8273i	0.902177	+	0.655470i
$916$	9.70916	−	29.8817i	0.320800	−	0.987320i
$917$	2.07832	+	6.39640i	0.0686320	+	0.211228i
$918$	11.7550	−	8.54051i	0.387973	−	0.281879i
$919$	39.1383	−	28.4356i	1.29105	−	0.938005i	0.291227	−	0.956654i	$-0.405936\pi$
$919$	39.1383	−	28.4356i	1.29105	−	0.938005i	0.999826	+	0.0186486i	$0.00593637\pi$
$920$	−4.98599	−	15.3453i	−0.164383	−	0.505920i
$921$	−28.5878	+	87.9843i	−0.942001	+	2.89918i
$922$	11.8443	+	8.60539i	0.390071	+	0.283403i
$923$	37.5937			1.23741
$924$		0			0
$925$	0.609223			0.0200311
$926$	3.66220	+	2.66074i	0.120347	+	0.0874374i
$927$	−37.3543	+	114.965i	−1.22688	+	3.77594i
$928$	−1.64735	−	5.07001i	−0.0540768	−	0.166431i
$929$	−0.699229	+	0.508020i	−0.0229410	+	0.0166676i	−0.599197	−	0.800602i	$-0.704513\pi$
$929$	−0.699229	+	0.508020i	−0.0229410	+	0.0166676i	0.576256	+	0.817269i	$0.304513\pi$
$930$	10.9477	−	7.95399i	0.358990	−	0.260822i
$931$	2.07888	+	6.39814i	0.0681326	+	0.209691i
$932$	10.0979	−	31.0781i	0.330767	−	1.01800i
$933$	−68.2753	−	49.6049i	−2.23523	−	1.62399i
$934$	20.1079			0.657949
$935$		0			0
$936$	−41.2424			−1.34805
$937$	43.2485	+	31.4218i	1.41287	+	1.02651i	0.992898	+	0.118967i	$0.0379584\pi$
$937$	43.2485	+	31.4218i	1.41287	+	1.02651i	0.419967	+	0.907539i	$0.362042\pi$
$938$	−0.186707	+	0.574624i	−0.00609619	+	0.0187621i
$939$	−4.35901	−	13.4157i	−0.142251	−	0.437804i
$940$	11.8331	−	8.59727i	0.385954	−	0.280412i
$941$	11.0835	−	8.05265i	0.361313	−	0.262509i	−0.392287	−	0.919843i	$-0.628316\pi$
$941$	11.0835	−	8.05265i	0.361313	−	0.262509i	0.753599	+	0.657334i	$0.228316\pi$
$942$	−7.31346	−	22.5085i	−0.238286	−	0.733367i
$943$	5.43768	−	16.7355i	0.177075	−	0.544982i
$944$	0.449953	+	0.326910i	0.0146447	+	0.0106400i
$945$	−25.9693			−0.844781
$946$		0			0
$947$	31.6444			1.02830			0.514152	−	0.857699i	$-0.328107\pi$
$947$	31.6444			1.02830			0.514152	+	0.857699i	$0.328107\pi$
$948$	−15.9868	−	11.6151i	−0.519228	−	0.377241i
$949$	6.28002	−	19.3279i	0.203858	−	0.627411i
$950$	0.562794	+	1.73210i	0.0182594	+	0.0561968i
$951$	27.8146	−	20.2085i	0.901949	−	0.655305i
$952$	3.44625	−	2.50385i	0.111694	−	0.0811503i
$953$	−10.1166	−	31.1356i	−0.327708	−	1.00858i	−0.970203	−	0.242292i	$-0.922101\pi$
$953$	−10.1166	−	31.1356i	−0.327708	−	1.00858i	0.642495	−	0.766290i	$-0.277899\pi$
$954$	−0.947326	+	2.91557i	−0.0306708	+	0.0943951i
$955$	−22.0279	−	16.0042i	−0.712806	−	0.517884i
$956$	24.0420			0.777573
$957$		0			0
$958$	−4.02083			−0.129907
$959$	11.2191	+	8.15119i	0.362285	+	0.263216i
$960$	1.75464	−	5.40024i	0.0566309	−	0.174292i
$961$	−6.79507	−	20.9131i	−0.219196	−	0.674615i
$962$	2.06468	−	1.50008i	0.0665681	−	0.0483645i
$963$	−85.4657	+	62.0945i	−2.75409	+	2.00097i
$964$	6.75258	+	20.7823i	0.217486	+	0.669353i
$965$	1.16548	−	3.58698i	0.0375181	−	0.115469i
$966$	5.38320	+	3.91112i	0.173202	+	0.125838i
$967$	32.3487			1.04026			0.520132	−	0.854086i	$-0.325883\pi$
$967$	32.3487			1.04026			0.520132	+	0.854086i	$0.325883\pi$
$968$		0			0
$969$	37.8287			1.21523
$970$	9.89176	+	7.18678i	0.317605	+	0.230754i
$971$	−9.09344	+	27.9867i	−0.291823	+	0.898137i	0.692448	+	0.721468i	$0.256532\pi$
$971$	−9.09344	+	27.9867i	−0.291823	+	0.898137i	−0.984270	+	0.176669i	$0.943468\pi$
$972$	−8.85934	−	27.2662i	−0.284163	−	0.874565i
$973$	−11.5453	+	8.38812i	−0.370124	+	0.268911i
$974$	3.44998	−	2.50656i	0.110545	−	0.0803153i
$975$	0.991548	+	3.05167i	0.0317550	+	0.0977317i
$976$	−2.33822	+	7.19631i	−0.0748447	+	0.230348i
$977$	−11.0790	−	8.04939i	−0.354450	−	0.257523i	0.396284	−	0.918128i	$-0.370300\pi$
$977$	−11.0790	−	8.04939i	−0.354450	−	0.257523i	−0.750733	+	0.660605i	$0.770300\pi$
$978$	38.2780			1.22399
$979$		0			0
$980$	−3.32595			−0.106244
$981$	−105.012	−	76.2954i	−3.35276	−	2.43592i
$982$	2.56155	−	7.88364i	0.0817423	−	0.251577i
$983$	5.26316	+	16.1983i	0.167869	+	0.516647i	0.999236	−	0.0390763i	$-0.0124415\pi$
$983$	5.26316	+	16.1983i	0.167869	+	0.516647i	−0.831368	+	0.555723i	$0.812442\pi$
$984$	33.5989	−	24.4111i	1.07109	−	0.778196i
$985$	−1.56621	+	1.13792i	−0.0499037	+	0.0362572i
$986$	−0.342546	−	1.05425i	−0.0109089	−	0.0335741i
$987$	−4.26685	+	13.1320i	−0.135815	+	0.417996i
$988$	−21.3483	−	15.5104i	−0.679179	−	0.493453i
$989$	−26.6744			−0.848198
$990$		0			0
$991$	23.2202			0.737614			0.368807	−	0.929506i	$-0.379766\pi$
$991$	23.2202			0.737614			0.368807	+	0.929506i	$0.379766\pi$
$992$	14.0084	+	10.1777i	0.444766	+	0.323141i
$993$	16.0310	−	49.3383i	0.508728	−	1.56570i
$994$	−3.07740	−	9.47126i	−0.0976091	−	0.300410i
$995$	27.1072	−	19.6946i	0.859357	−	0.624359i
$996$	15.9658	−	11.5998i	0.505896	−	0.367555i
$997$	5.67899	+	17.4781i	0.179855	+	0.553538i	0.999822	−	0.0188734i	$-0.00600795\pi$
$997$	5.67899	+	17.4781i	0.179855	+	0.553538i	−0.819966	+	0.572412i	$0.806008\pi$
$998$	2.95535	−	9.09563i	0.0935499	−	0.287917i
$999$	14.7708	+	10.7316i	0.467326	+	0.339532i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.v.323.3		16
11.2	odd	10		77.2.f.b.71.3	yes	16
11.3	even	5	inner	847.2.f.v.729.3		16
11.4	even	5		847.2.f.x.372.2		16
11.5	even	5		847.2.a.o.1.4		8
11.6	odd	10		847.2.a.p.1.5		8
11.7	odd	10		77.2.f.b.64.3	✓	16
11.8	odd	10		847.2.f.w.729.2		16
11.9	even	5		847.2.f.x.148.2		16
11.10	odd	2		847.2.f.w.323.2		16
33.2	even	10		693.2.m.i.379.2		16
33.5	odd	10		7623.2.a.cw.1.5		8
33.17	even	10		7623.2.a.ct.1.4		8
33.29	even	10		693.2.m.i.64.2		16
77.2	odd	30		539.2.q.g.214.3		32
77.6	even	10		5929.2.a.bt.1.5		8
77.13	even	10		539.2.f.e.148.3		16
77.18	odd	30		539.2.q.g.471.3		32
77.24	even	30		539.2.q.f.324.2		32
77.27	odd	10		5929.2.a.bs.1.4		8
77.40	even	30		539.2.q.f.361.2		32
77.46	odd	30		539.2.q.g.324.2		32
77.51	odd	30		539.2.q.g.361.2		32
77.62	even	10		539.2.f.e.295.3		16
77.68	even	30		539.2.q.f.214.3		32
77.73	even	30		539.2.q.f.471.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.3	✓	16	11.7	odd	10
77.2.f.b.71.3	yes	16	11.2	odd	10
539.2.f.e.148.3		16	77.13	even	10
539.2.f.e.295.3		16	77.62	even	10
539.2.q.f.214.3		32	77.68	even	30
539.2.q.f.324.2		32	77.24	even	30
539.2.q.f.361.2		32	77.40	even	30
539.2.q.f.471.3		32	77.73	even	30
539.2.q.g.214.3		32	77.2	odd	30
539.2.q.g.324.2		32	77.46	odd	30
539.2.q.g.361.2		32	77.51	odd	30
539.2.q.g.471.3		32	77.18	odd	30
693.2.m.i.64.2		16	33.29	even	10
693.2.m.i.379.2		16	33.2	even	10
847.2.a.o.1.4		8	11.5	even	5
847.2.a.p.1.5		8	11.6	odd	10
847.2.f.v.323.3		16	1.1	even	1	trivial
847.2.f.v.729.3		16	11.3	even	5	inner
847.2.f.w.323.2		16	11.10	odd	2
847.2.f.w.729.2		16	11.8	odd	10
847.2.f.x.148.2		16	11.9	even	5
847.2.f.x.372.2		16	11.4	even	5
5929.2.a.bs.1.4		8	77.27	odd	10
5929.2.a.bt.1.5		8	77.6	even	10
7623.2.a.ct.1.4		8	33.17	even	10
7623.2.a.cw.1.5		8	33.5	odd	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.541834 + 0.393666i) q^{2} +(0.970243 - 2.98610i) q^{3} +(-0.479422 - 1.47551i) q^{4} +(-1.73435 + 1.26008i) q^{5} +(1.70124 - 1.23602i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.735015 - 2.26214i) q^{8} +(-5.54838 - 4.03113i) q^{9} +O(q^{10})\)	\(q+(0.541834 + 0.393666i) q^{2} +(0.970243 - 2.98610i) q^{3} +(-0.479422 - 1.47551i) q^{4} +(-1.73435 + 1.26008i) q^{5} +(1.70124 - 1.23602i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.735015 - 2.26214i) q^{8} +(-5.54838 - 4.03113i) q^{9} -1.43578 q^{10} -4.87118 q^{12} +(2.04541 + 1.48608i) q^{13} +(0.206962 - 0.636964i) q^{14} +(2.07999 + 6.40154i) q^{15} +(-1.22150 + 0.887475i) q^{16} +(-1.44888 + 1.05268i) q^{17} +(-1.41938 - 4.36841i) q^{18} +(2.07888 - 6.39814i) q^{19} +(2.69075 + 1.95494i) q^{20} -3.13977 q^{21} -3.16429 q^{23} +(-6.04184 - 4.38966i) q^{24} +(-0.124909 + 0.384430i) q^{25} +(0.523255 + 1.61041i) q^{26} +(-9.80027 + 7.12031i) q^{27} +(-1.25514 + 0.911915i) q^{28} +(0.285584 + 0.878938i) q^{29} +(-1.39306 + 4.28739i) q^{30} +(-2.42849 - 1.76440i) q^{31} -5.76834 q^{32} -1.19946 q^{34} +(1.73435 + 1.26008i) q^{35} +(-3.28796 + 10.1193i) q^{36} +(-0.465744 - 1.43341i) q^{37} +(3.64514 - 2.64835i) q^{38} +(6.42211 - 4.66594i) q^{39} +(1.57571 + 4.84953i) q^{40} +(-1.71846 + 5.28886i) q^{41} +(-1.70124 - 1.23602i) q^{42} +8.42985 q^{43} +14.7024 q^{45} +(-1.71452 - 1.24567i) q^{46} +(1.35897 - 4.18247i) q^{47} +(1.46493 + 4.50860i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-0.219017 + 0.159125i) q^{50} +(1.73763 + 5.34787i) q^{51} +(1.21211 - 3.73048i) q^{52} +(-0.539955 - 0.392300i) q^{53} -8.11314 q^{54} -2.37856 q^{56} +(-17.0885 - 12.4155i) q^{57} +(-0.191268 + 0.588663i) q^{58} +(-0.113830 - 0.350331i) q^{59} +(8.44835 - 6.13808i) q^{60} +(4.05438 - 2.94568i) q^{61} +(-0.621256 - 1.91203i) q^{62} +(-2.11929 + 6.52251i) q^{63} +(-0.682474 - 0.495846i) q^{64} -5.42003 q^{65} -0.902129 q^{67} +(2.24786 + 1.63317i) q^{68} +(-3.07013 + 9.44888i) q^{69} +(0.443681 + 1.36551i) q^{70} +(12.0296 - 8.74000i) q^{71} +(-13.1971 + 9.58828i) q^{72} +(-2.48393 - 7.64474i) q^{73} +(0.311929 - 0.960019i) q^{74} +(1.02676 + 0.745981i) q^{75} -10.4372 q^{76} +5.31654 q^{78} +(3.28192 + 2.38446i) q^{79} +(1.00023 - 3.07839i) q^{80} +(5.39545 + 16.6055i) q^{81} +(-3.01316 + 2.18919i) q^{82} +(-3.27760 + 2.38132i) q^{83} +(1.50528 + 4.63277i) q^{84} +(1.18642 - 3.65142i) q^{85} +(4.56758 + 3.31854i) q^{86} +2.90168 q^{87} -8.30727 q^{89} +(7.96627 + 5.78783i) q^{90} +(0.781276 - 2.40452i) q^{91} +(1.51703 + 4.66894i) q^{92} +(-7.62492 + 5.53983i) q^{93} +(2.38283 - 1.73123i) q^{94} +(4.45666 + 13.7162i) q^{95} +(-5.59669 + 17.2248i) q^{96} +(-6.88945 - 5.00548i) q^{97} -0.669744 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 4 q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 + 2 * q^6 + 4 * q^7 - 5 * q^8 - 2 * q^9	\( 16 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 4 q^{7} - 5 q^{8} - 2 q^{9} - 12 q^{10} + 18 q^{12} - 13 q^{13} - 3 q^{14} + 7 q^{15} - 18 q^{16} - 10 q^{17} + 19 q^{18} + 6 q^{19} - 24 q^{20} - 8 q^{21} + 32 q^{23} - 45 q^{24} - 23 q^{25} + 33 q^{26} - 20 q^{27} + 11 q^{28} + 12 q^{29} - 38 q^{30} - 2 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} - 38 q^{36} - 11 q^{37} + 15 q^{38} + 24 q^{39} - 5 q^{40} - 20 q^{41} - 2 q^{42} + 8 q^{43} + 70 q^{45} - 38 q^{46} + 7 q^{47} + 39 q^{48} - 4 q^{49} + 58 q^{50} - 16 q^{51} - 8 q^{52} - 41 q^{53} - 60 q^{54} - 9 q^{57} - 5 q^{58} - 18 q^{59} + 25 q^{60} + 12 q^{61} + 61 q^{62} + 12 q^{63} - 3 q^{64} + 8 q^{65} - 38 q^{67} + 7 q^{68} - 30 q^{69} + 12 q^{70} + q^{71} - 35 q^{72} - 60 q^{73} + 4 q^{74} + 4 q^{75} - 52 q^{76} - 58 q^{78} + 15 q^{79} + 83 q^{80} + 6 q^{81} - 6 q^{82} - 20 q^{83} + 17 q^{84} + 9 q^{85} + 48 q^{86} + 72 q^{87} + 74 q^{89} - 16 q^{90} - 7 q^{91} + 20 q^{92} - 53 q^{93} - 66 q^{94} + 53 q^{95} - 48 q^{96} - 35 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 + 2 * q^6 + 4 * q^7 - 5 * q^8 - 2 * q^9 - 12 * q^10 + 18 * q^12 - 13 * q^13 - 3 * q^14 + 7 * q^15 - 18 * q^16 - 10 * q^17 + 19 * q^18 + 6 * q^19 - 24 * q^20 - 8 * q^21 + 32 * q^23 - 45 * q^24 - 23 * q^25 + 33 * q^26 - 20 * q^27 + 11 * q^28 + 12 * q^29 - 38 * q^30 - 2 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 - 38 * q^36 - 11 * q^37 + 15 * q^38 + 24 * q^39 - 5 * q^40 - 20 * q^41 - 2 * q^42 + 8 * q^43 + 70 * q^45 - 38 * q^46 + 7 * q^47 + 39 * q^48 - 4 * q^49 + 58 * q^50 - 16 * q^51 - 8 * q^52 - 41 * q^53 - 60 * q^54 - 9 * q^57 - 5 * q^58 - 18 * q^59 + 25 * q^60 + 12 * q^61 + 61 * q^62 + 12 * q^63 - 3 * q^64 + 8 * q^65 - 38 * q^67 + 7 * q^68 - 30 * q^69 + 12 * q^70 + q^71 - 35 * q^72 - 60 * q^73 + 4 * q^74 + 4 * q^75 - 52 * q^76 - 58 * q^78 + 15 * q^79 + 83 * q^80 + 6 * q^81 - 6 * q^82 - 20 * q^83 + 17 * q^84 + 9 * q^85 + 48 * q^86 + 72 * q^87 + 74 * q^89 - 16 * q^90 - 7 * q^91 + 20 * q^92 - 53 * q^93 - 66 * q^94 + 53 * q^95 - 48 * q^96 - 35 * q^97 - 2 * q^98

Introduction

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