LMFDB - Embedded newform 847.2.f.o.729.2

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.446265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 4x^{6} - 7x^{5} + 19x^{4} + 21x^{3} + 36x^{2} + 27x + 81 $ x^8 - x^7 + 4x^6 - 7x^5 + 19x^4 + 21x^3 + 36x^2 + 27x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			729.2
Root			$0.402580 - 1.23901i$ of defining polynomial
Character	$\chi$	$=$	847.729
Dual form			847.2.f.o.323.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05397 - 0.765752i) q^{2} +(0.402580 + 1.23901i) q^{3} +(-0.0935628 + 0.287957i) q^{4} +(2.91695 + 2.11929i) q^{5} +(1.37308 + 0.997603i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.927051 + 2.85317i) q^{8} +(1.05397 - 0.765752i) q^{9} +O(q^{10})$	\(q+(1.05397 - 0.765752i) q^{2} +(0.402580 + 1.23901i) q^{3} +(-0.0935628 + 0.287957i) q^{4} +(2.91695 + 2.11929i) q^{5} +(1.37308 + 0.997603i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.927051 + 2.85317i) q^{8} +(1.05397 - 0.765752i) q^{9} +4.69722 q^{10} -0.394449 q^{12} +(0.489901 - 0.355934i) q^{13} +(0.402580 + 1.23901i) q^{14} +(-1.45152 + 4.46733i) q^{15} +(2.67200 + 1.94132i) q^{16} +(-5.09905 - 3.70468i) q^{17} +(0.524471 - 1.61416i) q^{18} +(-0.927051 - 2.85317i) q^{19} +(-0.883182 + 0.641669i) q^{20} -1.30278 q^{21} -6.30278 q^{23} +(-3.16190 + 2.29726i) q^{24} +(2.47214 + 7.60845i) q^{25} +(0.243783 - 0.750286i) q^{26} +(4.53499 + 3.29486i) q^{27} +(-0.244951 - 0.177967i) q^{28} +(2.56570 - 7.89641i) q^{29} +(1.89101 + 5.81992i) q^{30} +(-0.809017 + 0.587785i) q^{31} -1.69722 q^{32} -8.21110 q^{34} +(-2.91695 + 2.11929i) q^{35} +(0.121891 + 0.375143i) q^{36} +(2.84639 - 8.76028i) q^{37} +(-3.16190 - 2.29726i) q^{38} +(0.638231 + 0.463702i) q^{39} +(-3.34253 + 10.2872i) q^{40} +(2.16312 + 6.65740i) q^{41} +(-1.37308 + 0.997603i) q^{42} +5.30278 q^{43} +4.69722 q^{45} +(-6.64292 + 4.82636i) q^{46} +(2.75282 + 8.47232i) q^{47} +(-1.32963 + 4.09218i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(8.43174 + 6.12602i) q^{50} +(2.53737 - 7.80922i) q^{51} +(0.0566571 + 0.174373i) q^{52} +(1.69220 - 1.22945i) q^{53} +7.30278 q^{54} -3.00000 q^{56} +(3.16190 - 2.29726i) q^{57} +(-3.34253 - 10.2872i) q^{58} +(3.18373 - 9.79852i) q^{59} +(-1.15059 - 0.835951i) q^{60} +(0.564066 + 0.409818i) q^{61} +(-0.402580 + 1.23901i) q^{62} +(0.402580 + 1.23901i) q^{63} +(-7.13282 + 5.18230i) q^{64} +2.18335 q^{65} -9.51388 q^{67} +(1.54387 - 1.12169i) q^{68} +(-2.53737 - 7.80922i) q^{69} +(-1.45152 + 4.46733i) q^{70} +(0.564066 + 0.409818i) q^{71} +(3.16190 + 2.29726i) q^{72} +(-1.54508 + 4.75528i) q^{73} +(-3.70820 - 11.4127i) q^{74} +(-8.43174 + 6.12602i) q^{75} +0.908327 q^{76} +1.02776 q^{78} +(3.80013 - 2.76096i) q^{79} +(3.67988 + 11.3255i) q^{80} +(-1.04894 + 3.22831i) q^{81} +(7.37777 + 5.36027i) q^{82} +(-2.42705 - 1.76336i) q^{83} +(0.121891 - 0.375143i) q^{84} +(-7.02241 - 21.6127i) q^{85} +(5.58895 - 4.06061i) q^{86} +10.8167 q^{87} +17.7250 q^{89} +(4.95072 - 3.59691i) q^{90} +(0.187126 + 0.575913i) q^{91} +(0.589705 - 1.81493i) q^{92} +(-1.05397 - 0.765752i) q^{93} +(9.38909 + 6.82157i) q^{94} +(3.34253 - 10.2872i) q^{95} +(-0.683268 - 2.10288i) q^{96} +(-2.91695 + 2.11929i) q^{97} -1.30278 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + q^{3} - 3 q^{4} + 7 q^{6} + 2 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) $ 8 * q - q^2 + q^3 - 3 * q^4 + 7 * q^6 + 2 * q^7 - 6 * q^8 - q^9	$ 8 q - q^{2} + q^{3} - 3 q^{4} + 7 q^{6} + 2 q^{7} - 6 q^{8} - q^{9} + 52 q^{10} - 32 q^{12} - 6 q^{13} + q^{14} + 13 q^{15} + 3 q^{16} - 9 q^{17} - 7 q^{18} + 6 q^{19} - 13 q^{20} + 4 q^{21} - 36 q^{23} + 3 q^{24} - 16 q^{25} - 16 q^{26} + 4 q^{27} + 3 q^{28} - 13 q^{29} + 13 q^{30} - 2 q^{31} - 28 q^{32} - 8 q^{34} - 8 q^{36} - 4 q^{37} + 3 q^{38} + 16 q^{39} - 14 q^{41} - 7 q^{42} + 28 q^{43} + 52 q^{45} - 2 q^{46} - 7 q^{47} + 5 q^{48} - 2 q^{49} - 8 q^{50} - 2 q^{51} - 22 q^{52} + 15 q^{53} + 44 q^{54} - 24 q^{56} - 3 q^{57} - 17 q^{59} + 26 q^{60} + 5 q^{61} - q^{62} + q^{63} + 4 q^{64} + 104 q^{65} - 4 q^{67} - 7 q^{68} + 2 q^{69} + 13 q^{70} + 5 q^{71} - 3 q^{72} + 10 q^{73} + 24 q^{74} + 8 q^{75} - 36 q^{76} - 136 q^{78} + 13 q^{79} - 13 q^{80} + 14 q^{81} - 7 q^{82} - 6 q^{83} - 8 q^{84} + 13 q^{85} + 3 q^{86} + 12 q^{89} - 13 q^{90} + 6 q^{91} + 7 q^{92} + q^{93} + 16 q^{94} - 10 q^{96} + 4 q^{98}+O(q^{100}) $ 8 * q - q^2 + q^3 - 3 * q^4 + 7 * q^6 + 2 * q^7 - 6 * q^8 - q^9 + 52 * q^10 - 32 * q^12 - 6 * q^13 + q^14 + 13 * q^15 + 3 * q^16 - 9 * q^17 - 7 * q^18 + 6 * q^19 - 13 * q^20 + 4 * q^21 - 36 * q^23 + 3 * q^24 - 16 * q^25 - 16 * q^26 + 4 * q^27 + 3 * q^28 - 13 * q^29 + 13 * q^30 - 2 * q^31 - 28 * q^32 - 8 * q^34 - 8 * q^36 - 4 * q^37 + 3 * q^38 + 16 * q^39 - 14 * q^41 - 7 * q^42 + 28 * q^43 + 52 * q^45 - 2 * q^46 - 7 * q^47 + 5 * q^48 - 2 * q^49 - 8 * q^50 - 2 * q^51 - 22 * q^52 + 15 * q^53 + 44 * q^54 - 24 * q^56 - 3 * q^57 - 17 * q^59 + 26 * q^60 + 5 * q^61 - q^62 + q^63 + 4 * q^64 + 104 * q^65 - 4 * q^67 - 7 * q^68 + 2 * q^69 + 13 * q^70 + 5 * q^71 - 3 * q^72 + 10 * q^73 + 24 * q^74 + 8 * q^75 - 36 * q^76 - 136 * q^78 + 13 * q^79 - 13 * q^80 + 14 * q^81 - 7 * q^82 - 6 * q^83 - 8 * q^84 + 13 * q^85 + 3 * q^86 + 12 * q^89 - 13 * q^90 + 6 * q^91 + 7 * q^92 + q^93 + 16 * q^94 - 10 * q^96 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	1.05397	−	0.765752i	0.745268	−	0.541469i	−0.149089	−	0.988824i	$-0.547634\pi$
$2$	1.05397	−	0.765752i	0.745268	−	0.541469i	0.894356	+	0.447355i	$0.147634\pi$
$3$	0.402580	+	1.23901i	0.232430	+	0.715345i	0.997452	+	0.0713410i	$0.0227279\pi$
$3$	0.402580	+	1.23901i	0.232430	+	0.715345i	−0.765022	+	0.644004i	$0.777272\pi$
$4$	−0.0935628	+	0.287957i	−0.0467814	+	0.143978i
$5$	2.91695	+	2.11929i	1.30450	+	0.947775i	0.999989	−	0.00473329i	$-0.00150666\pi$
$5$	2.91695	+	2.11929i	1.30450	+	0.947775i	0.304512	+	0.952509i	$0.401507\pi$
$6$	1.37308	+	0.997603i	0.560559	+	0.407270i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	0.927051	+	2.85317i	0.327762	+	1.00875i
$9$	1.05397	−	0.765752i	0.351323	−	0.255251i
$10$	4.69722			1.48539
$11$		0			0
$11$		0			0
$12$	−0.394449			−0.113868
$13$	0.489901	−	0.355934i	0.135874	−	0.0987184i	−0.517772	−	0.855519i	$-0.673238\pi$
$13$	0.489901	−	0.355934i	0.135874	−	0.0987184i	0.653646	+	0.756800i	$0.273238\pi$
$14$	0.402580	+	1.23901i	0.107594	+	0.331140i
$15$	−1.45152	+	4.46733i	−0.374781	+	1.15346i
$16$	2.67200	+	1.94132i	0.668000	+	0.485331i
$17$	−5.09905	−	3.70468i	−1.23670	−	0.898517i	−0.239328	−	0.970939i	$-0.576927\pi$
$17$	−5.09905	−	3.70468i	−1.23670	−	0.898517i	−0.997374	+	0.0724223i	$0.976927\pi$
$18$	0.524471	−	1.61416i	0.123619	−	0.380460i
$19$	−0.927051	−	2.85317i	−0.212680	−	0.654562i	−0.999310	−	0.0371374i	$-0.988176\pi$
$19$	−0.927051	−	2.85317i	−0.212680	−	0.654562i	0.786630	−	0.617425i	$-0.211824\pi$
$20$	−0.883182	+	0.641669i	−0.197486	+	0.143482i
$21$	−1.30278			−0.284289
$22$		0			0
$23$	−6.30278			−1.31422			−0.657110	−	0.753795i	$-0.728221\pi$
$23$	−6.30278			−1.31422			−0.657110	+	0.753795i	$0.728221\pi$
$24$	−3.16190	+	2.29726i	−0.645421	+	0.468926i
$25$	2.47214	+	7.60845i	0.494427	+	1.52169i
$26$	0.243783	−	0.750286i	0.0478097	−	0.147143i
$27$	4.53499	+	3.29486i	0.872759	+	0.634096i
$28$	−0.244951	−	0.177967i	−0.0462913	−	0.0336326i
$29$	2.56570	−	7.89641i	0.476438	−	1.46633i	−0.367570	−	0.929996i	$-0.619810\pi$
$29$	2.56570	−	7.89641i	0.476438	−	1.46633i	0.844008	−	0.536330i	$-0.180190\pi$
$30$	1.89101	+	5.81992i	0.345249	+	1.06257i
$31$	−0.809017	+	0.587785i	−0.145304	+	0.105569i	−0.658062	−	0.752964i	$-0.728624\pi$
$31$	−0.809017	+	0.587785i	−0.145304	+	0.105569i	0.512758	+	0.858533i	$0.328624\pi$
$32$	−1.69722			−0.300030
$33$		0			0
$34$	−8.21110			−1.40819
$35$	−2.91695	+	2.11929i	−0.493055	+	0.358225i
$36$	0.121891	+	0.375143i	0.0203152	+	0.0625238i
$37$	2.84639	−	8.76028i	0.467943	−	1.44018i	−0.387300	−	0.921954i	$-0.626592\pi$
$37$	2.84639	−	8.76028i	0.467943	−	1.44018i	0.855243	−	0.518227i	$-0.173408\pi$
$38$	−3.16190	−	2.29726i	−0.512928	−	0.372664i
$39$	0.638231	+	0.463702i	0.102199	+	0.0742518i
$40$	−3.34253	+	10.2872i	−0.528500	+	1.62656i
$41$	2.16312	+	6.65740i	0.337822	+	1.03971i	0.965315	+	0.261088i	$0.0840813\pi$
$41$	2.16312	+	6.65740i	0.337822	+	1.03971i	−0.627493	+	0.778623i	$0.715919\pi$
$42$	−1.37308	+	0.997603i	−0.211871	+	0.153934i
$43$	5.30278			0.808666			0.404333	−	0.914612i	$-0.367504\pi$
$43$	5.30278			0.808666			0.404333	+	0.914612i	$0.367504\pi$
$44$		0			0
$45$	4.69722			0.700221
$46$	−6.64292	+	4.82636i	−0.979445	+	0.711609i
$47$	2.75282	+	8.47232i	0.401541	+	1.23582i	0.923749	+	0.382997i	$0.125108\pi$
$47$	2.75282	+	8.47232i	0.401541	+	1.23582i	−0.522209	+	0.852818i	$0.674892\pi$
$48$	−1.32963	+	4.09218i	−0.191916	+	0.590656i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	8.43174	+	6.12602i	1.19243	+	0.866350i
$51$	2.53737	−	7.80922i	0.355303	−	1.09351i
$52$	0.0566571	+	0.174373i	0.00785692	+	0.0241811i
$53$	1.69220	−	1.22945i	0.232441	−	0.168879i	−0.465468	−	0.885065i	$-0.654114\pi$
$53$	1.69220	−	1.22945i	0.232441	−	0.168879i	0.697909	+	0.716186i	$0.254114\pi$
$54$	7.30278			0.993782
$55$		0			0
$56$	−3.00000			−0.400892
$57$	3.16190	−	2.29726i	0.418804	−	0.304279i
$58$	−3.34253	−	10.2872i	−0.438896	−	1.35078i
$59$	3.18373	−	9.79852i	0.414487	−	1.27566i	−0.498223	−	0.867049i	$-0.666014\pi$
$59$	3.18373	−	9.79852i	0.414487	−	1.27566i	0.912709	−	0.408610i	$-0.133986\pi$
$60$	−1.15059	−	0.835951i	−0.148540	−	0.107921i
$61$	0.564066	+	0.409818i	0.0722213	+	0.0524718i	0.623310	−	0.781975i	$-0.285787\pi$
$61$	0.564066	+	0.409818i	0.0722213	+	0.0524718i	−0.551089	+	0.834447i	$0.685787\pi$
$62$	−0.402580	+	1.23901i	−0.0511277	+	0.157355i
$63$	0.402580	+	1.23901i	0.0507203	+	0.156101i
$64$	−7.13282	+	5.18230i	−0.891603	+	0.647787i
$65$	2.18335			0.270811
$66$		0			0
$67$	−9.51388			−1.16231			−0.581153	−	0.813795i	$-0.697398\pi$
$67$	−9.51388			−1.16231			−0.581153	+	0.813795i	$0.697398\pi$
$68$	1.54387	−	1.12169i	0.187222	−	0.136024i
$69$	−2.53737	−	7.80922i	−0.305463	−	0.940120i
$70$	−1.45152	+	4.46733i	−0.173490	+	0.533948i
$71$	0.564066	+	0.409818i	0.0669424	+	0.0486365i	0.620753	−	0.784006i	$-0.286827\pi$
$71$	0.564066	+	0.409818i	0.0669424	+	0.0486365i	−0.553811	+	0.832643i	$0.686827\pi$
$72$	3.16190	+	2.29726i	0.372634	+	0.270734i
$73$	−1.54508	+	4.75528i	−0.180839	+	0.556564i	−0.999852	−	0.0172107i	$-0.994521\pi$
$73$	−1.54508	+	4.75528i	−0.180839	+	0.556564i	0.819013	+	0.573774i	$0.194521\pi$
$74$	−3.70820	−	11.4127i	−0.431070	−	1.32670i
$75$	−8.43174	+	6.12602i	−0.973614	+	0.707372i
$76$	0.908327			0.104192
$77$		0			0
$78$	1.02776			0.116370
$79$	3.80013	−	2.76096i	0.427549	−	0.310632i	−0.353119	−	0.935578i	$-0.614879\pi$
$79$	3.80013	−	2.76096i	0.427549	−	0.310632i	0.780668	+	0.624946i	$0.214879\pi$
$80$	3.67988	+	11.3255i	0.411423	+	1.26623i
$81$	−1.04894	+	3.22831i	−0.116549	+	0.358701i
$82$	7.37777	+	5.36027i	0.814739	+	0.591942i
$83$	−2.42705	−	1.76336i	−0.266403	−	0.193553i	0.446562	−	0.894753i	$-0.352648\pi$
$83$	−2.42705	−	1.76336i	−0.266403	−	0.193553i	−0.712965	+	0.701199i	$0.752648\pi$
$84$	0.121891	−	0.375143i	0.0132994	−	0.0409315i
$85$	−7.02241	−	21.6127i	−0.761687	−	2.34423i
$86$	5.58895	−	4.06061i	0.602672	−	0.437867i
$87$	10.8167			1.15967
$88$		0			0
$89$	17.7250			1.87884			0.939422	−	0.342762i	$-0.111363\pi$
$89$	17.7250			1.87884			0.939422	+	0.342762i	$0.111363\pi$
$90$	4.95072	−	3.59691i	0.521852	−	0.379148i
$91$	0.187126	+	0.575913i	0.0196161	+	0.0603721i
$92$	0.589705	−	1.81493i	0.0614810	−	0.189219i
$93$	−1.05397	−	0.765752i	−0.109291	−	0.0794048i
$94$	9.38909	+	6.82157i	0.968411	+	0.703591i
$95$	3.34253	−	10.2872i	0.342936	−	1.05545i
$96$	−0.683268	−	2.10288i	−0.0697358	−	0.214625i
$97$	−2.91695	+	2.11929i	−0.296172	+	0.215181i	−0.725940	−	0.687758i	$-0.758595\pi$
$97$	−2.91695	+	2.11929i	−0.296172	+	0.215181i	0.429769	+	0.902939i	$0.358595\pi$
$98$	−1.30278			−0.131600
$99$		0			0
$100$	−2.42221			−0.242221
$101$	1.37308	−	0.997603i	0.136627	−	0.0992653i	−0.517373	−	0.855760i	$-0.673090\pi$
$101$	1.37308	−	0.997603i	0.136627	−	0.0992653i	0.653999	+	0.756495i	$0.273090\pi$
$102$	−3.30562	−	10.1737i	−0.327306	−	1.00734i
$103$	−3.30562	+	10.1737i	−0.325713	+	1.00244i	0.645405	+	0.763841i	$0.276689\pi$
$103$	−3.30562	+	10.1737i	−0.325713	+	1.00244i	−0.971118	+	0.238600i	$0.923311\pi$
$104$	1.46970	+	1.06780i	0.144116	+	0.104707i
$105$	−3.80013	−	2.76096i	−0.370855	−	0.269442i
$106$	0.842065	−	2.59161i	0.0817886	−	0.251719i
$107$	6.05845	+	18.6460i	0.585692	+	1.80258i	0.596472	+	0.802634i	$0.296569\pi$
$107$	6.05845	+	18.6460i	0.585692	+	1.80258i	−0.0107799	+	0.999942i	$0.503431\pi$
$108$	−1.37308	+	0.997603i	−0.132125	+	0.0959944i
$109$	−8.00000			−0.766261			−0.383131	−	0.923694i	$-0.625154\pi$
$109$	−8.00000			−0.766261			−0.383131	+	0.923694i	$0.625154\pi$
$110$		0			0
$111$	12.0000			1.13899
$112$	−2.67200	+	1.94132i	−0.252480	+	0.183438i
$113$	−4.41980	−	13.6027i	−0.415780	−	1.27964i	−0.911551	−	0.411186i	$-0.865115\pi$
$113$	−4.41980	−	13.6027i	−0.415780	−	1.27964i	0.495772	−	0.868453i	$-0.334885\pi$
$114$	1.57341	−	4.84247i	0.147364	−	0.453539i
$115$	−18.3849	−	13.3574i	−1.71440	−	1.24558i
$116$	2.03377	+	1.47762i	0.188831	+	0.137194i
$117$	0.243783	−	0.750286i	0.0225377	−	0.0693640i
$118$	−4.14769	−	12.7653i	−0.381826	−	1.17514i
$119$	5.09905	−	3.70468i	0.467429	−	0.339607i
$120$	−14.0917			−1.28639
$121$		0			0
$122$	0.908327			0.0822361
$123$	−7.37777	+	5.36027i	−0.665231	+	0.483319i
$124$	−0.0935628	−	0.287957i	−0.00840219	−	0.0258593i
$125$	−3.34253	+	10.2872i	−0.298965	+	0.920120i
$126$	1.37308	+	0.997603i	0.122324	+	0.0888736i
$127$	−1.61803	−	1.17557i	−0.143577	−	0.104315i	0.513678	−	0.857983i	$-0.328283\pi$
$127$	−1.61803	−	1.17557i	−0.143577	−	0.104315i	−0.657255	+	0.753668i	$0.728283\pi$
$128$	−2.50046	+	7.69564i	−0.221012	+	0.680205i
$129$	2.13479	+	6.57021i	0.187958	+	0.578475i
$130$	2.30118	−	1.67190i	0.201827	−	0.146636i
$131$	−6.00000			−0.524222			−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000			−0.524222			−0.262111	+	0.965038i	$0.584419\pi$
$132$		0			0
$133$	3.00000			0.260133
$134$	−10.0273	+	7.28527i	−0.866228	+	0.629352i
$135$	6.24557	+	19.2219i	0.537533	+	1.65436i
$136$	5.84299	−	17.9829i	0.501033	−	1.54202i
$137$	−12.2319	−	8.88698i	−1.04504	−	0.759266i	−0.0737767	−	0.997275i	$-0.523505\pi$
$137$	−12.2319	−	8.88698i	−1.04504	−	0.759266i	−0.971263	+	0.238009i	$0.923505\pi$
$138$	−8.65424	−	6.28767i	−0.736698	−	0.535242i
$139$	4.44813	−	13.6899i	0.377285	−	1.16117i	−0.564638	−	0.825338i	$-0.690984\pi$
$139$	4.44813	−	13.6899i	0.377285	−	1.16117i	0.941924	−	0.335827i	$-0.109016\pi$
$140$	−0.337346	−	1.03824i	−0.0285109	−	0.0877475i
$141$	−9.38909	+	6.82157i	−0.790704	+	0.574480i
$142$	0.908327			0.0762251
$143$		0			0
$144$	4.30278			0.358565
$145$	24.2188	−	17.5960i	2.01126	−	1.46127i
$146$	2.01290	+	6.19507i	0.166589	+	0.512707i
$147$	0.402580	−	1.23901i	0.0332042	−	0.102192i
$148$	2.25627	+	1.63927i	0.185464	+	0.134747i
$149$	−4.77994	−	3.47283i	−0.391588	−	0.284505i	0.374518	−	0.927220i	$-0.377808\pi$
$149$	−4.77994	−	3.47283i	−0.391588	−	0.284505i	−0.766106	+	0.642714i	$0.777808\pi$
$150$	−4.19577	+	12.9133i	−0.342583	+	1.05436i
$151$	4.39147	+	13.5156i	0.357373	+	1.09988i	0.954621	+	0.297824i	$0.0962609\pi$
$151$	4.39147	+	13.5156i	0.357373	+	1.09988i	−0.597248	+	0.802057i	$0.703739\pi$
$152$	7.28115	−	5.29007i	0.590579	−	0.429081i
$153$	−8.21110			−0.663828
$154$		0			0
$155$	−3.60555			−0.289605
$156$	−0.193241	+	0.140398i	−0.0154717	+	0.0112408i
$157$	−2.22835	−	6.85817i	−0.177842	−	0.547341i	0.821910	−	0.569618i	$-0.192909\pi$
$157$	−2.22835	−	6.85817i	−0.177842	−	0.547341i	−0.999752	+	0.0222763i	$0.992909\pi$
$158$	1.89101	−	5.81992i	0.150440	−	0.463008i
$159$	2.20456	+	1.60170i	0.174833	+	0.127023i
$160$	−4.95072	−	3.59691i	−0.391389	−	0.284361i
$161$	1.94766	−	5.99430i	0.153497	−	0.472417i
$162$	1.36654	+	4.20577i	0.107365	+	0.330436i
$163$	15.2230	−	11.0602i	1.19236	−	0.866298i	0.198845	−	0.980031i	$-0.436281\pi$
$163$	15.2230	−	11.0602i	1.19236	−	0.866298i	0.993511	+	0.113733i	$0.0362808\pi$
$164$	−2.11943			−0.165500
$165$		0			0
$166$	−3.90833			−0.303345
$167$	−7.45194	+	5.41415i	−0.576648	+	0.418960i	−0.837514	−	0.546416i	$-0.815992\pi$
$167$	−7.45194	+	5.41415i	−0.576648	+	0.418960i	0.260866	+	0.965375i	$0.415992\pi$
$168$	−1.20774	−	3.71704i	−0.0931791	−	0.286776i
$169$	−3.90391	+	12.0150i	−0.300301	+	0.924230i
$170$	−23.9514	−	17.4017i	−1.83699	−	1.33465i
$171$	−3.16190	−	2.29726i	−0.241797	−	0.175676i
$172$	−0.496143	+	1.52697i	−0.0378305	+	0.116430i
$173$	0.711597	+	2.19007i	0.0541017	+	0.166508i	0.974456	−	0.224577i	$-0.0721000\pi$
$173$	0.711597	+	2.19007i	0.0541017	+	0.166508i	−0.920355	+	0.391085i	$0.872100\pi$
$174$	11.4004	−	8.28288i	0.864262	−	0.627923i
$175$	−8.00000			−0.604743
$176$		0			0
$177$	13.4222			1.00887
$178$	18.6816	−	13.5729i	1.40024	−	1.01734i
$179$	−4.20435	−	12.9396i	−0.314248	−	0.967155i	−0.976063	−	0.217488i	$-0.930214\pi$
$179$	−4.20435	−	12.9396i	−0.314248	−	0.967155i	0.661815	−	0.749667i	$-0.269786\pi$
$180$	−0.439486	+	1.35260i	−0.0327573	+	0.100817i
$181$	8.72840	+	6.34155i	0.648777	+	0.471364i	0.862854	−	0.505453i	$-0.168674\pi$
$181$	8.72840	+	6.34155i	0.648777	+	0.471364i	−0.214077	+	0.976817i	$0.568674\pi$
$182$	0.638231	+	0.463702i	0.0473089	+	0.0343719i
$183$	−0.280688	+	0.863870i	−0.0207491	+	0.0638591i
$184$	−5.84299	−	17.9829i	−0.430751	−	1.32572i
$185$	26.8683	−	19.5210i	1.97540	−	1.43521i
$186$	−1.69722			−0.124447
$187$		0			0
$188$	−2.69722			−0.196715
$189$	−4.53499	+	3.29486i	−0.329872	+	0.239666i
$190$	−4.35457	−	13.4020i	−0.315913	−	0.972282i
$191$	−1.60174	+	4.92966i	−0.115898	+	0.356697i	−0.992133	−	0.125186i	$-0.960047\pi$
$191$	−1.60174	+	4.92966i	−0.115898	+	0.356697i	0.876235	+	0.481884i	$0.160047\pi$
$192$	−9.29247	−	6.75137i	−0.670626	−	0.487238i
$193$	−18.7040	−	13.5893i	−1.34634	−	0.978176i	−0.999185	−	0.0403702i	$-0.987146\pi$
$193$	−18.7040	−	13.5893i	−1.34634	−	0.978176i	−0.347159	−	0.937806i	$-0.612854\pi$
$194$	−1.45152	+	4.46733i	−0.104213	+	0.320735i
$195$	0.878971	+	2.70519i	0.0629444	+	0.193723i
$196$	0.244951	−	0.177967i	0.0174965	−	0.0127119i
$197$	−3.39445			−0.241844			−0.120922	−	0.992662i	$-0.538585\pi$
$197$	−3.39445			−0.241844			−0.120922	+	0.992662i	$0.538585\pi$
$198$		0			0
$199$	−9.42221			−0.667922			−0.333961	−	0.942587i	$-0.608385\pi$
$199$	−9.42221			−0.667922			−0.333961	+	0.942587i	$0.608385\pi$
$200$	−19.4164	+	14.1068i	−1.37295	+	0.997505i
$201$	−3.83010	−	11.7878i	−0.270154	−	0.831449i
$202$	0.683268	−	2.10288i	0.0480746	−	0.147958i
$203$	6.71709	+	4.88025i	0.471447	+	0.342526i
$204$	2.01131	+	1.46131i	0.140820	+	0.102312i
$205$	−7.79924	+	24.0036i	−0.544722	+	1.67648i
$206$	4.30649	+	13.2540i	0.300047	+	0.923450i
$207$	−6.64292	+	4.82636i	−0.461715	+	0.335456i
$208$	2.00000			0.138675
$209$		0			0
$210$	−6.11943			−0.422281
$211$	2.03377	−	1.47762i	0.140011	−	0.101724i	−0.515575	−	0.856844i	$-0.672422\pi$
$211$	2.03377	−	1.47762i	0.140011	−	0.101724i	0.655586	+	0.755121i	$0.272422\pi$
$212$	0.195703	+	0.602311i	0.0134409	+	0.0413669i
$213$	−0.280688	+	0.863870i	−0.0192325	+	0.0591914i
$214$	20.6636	+	15.0130i	1.41254	+	1.02627i
$215$	15.4679	+	11.2381i	1.05490	+	0.766433i
$216$	−5.19663	+	15.9936i	−0.353586	+	1.08823i
$217$	−0.309017	−	0.951057i	−0.0209774	−	0.0645619i
$218$	−8.43174	+	6.12602i	−0.571070	+	0.414906i
$219$	−6.51388			−0.440167
$220$		0			0
$221$	−3.81665			−0.256736
$222$	12.6476	−	9.18903i	0.848852	−	0.616727i
$223$	0.955380	+	2.94036i	0.0639769	+	0.196901i	0.977936	−	0.208906i	$-0.0669904\pi$
$223$	0.955380	+	2.94036i	0.0639769	+	0.196901i	−0.913959	+	0.405807i	$0.866990\pi$
$224$	0.524471	−	1.61416i	0.0350427	−	0.107850i
$225$	8.43174	+	6.12602i	0.562116	+	0.408401i
$226$	−15.0747	−	10.9524i	−1.00275	−	0.728542i
$227$	−3.55798	+	10.9503i	−0.236152	+	0.726800i	0.760815	+	0.648969i	$0.224800\pi$
$227$	−3.55798	+	10.9503i	−0.236152	+	0.726800i	−0.996967	+	0.0778312i	$0.975200\pi$
$228$	0.365674	+	1.12543i	0.0242174	+	0.0745334i
$229$	−3.72597	+	2.70708i	−0.246219	+	0.178889i	−0.704049	−	0.710151i	$-0.748627\pi$
$229$	−3.72597	+	2.70708i	−0.246219	+	0.178889i	0.457830	+	0.889040i	$0.348627\pi$
$230$	−29.6056			−1.95213
$231$		0			0
$232$	24.9083			1.63531
$233$	−14.5623	+	10.5801i	−0.954008	+	0.693128i	−0.951752	−	0.306870i	$-0.900718\pi$
$233$	−14.5623	+	10.5801i	−0.954008	+	0.693128i	−0.00225687	+	0.999997i	$0.500718\pi$
$234$	−0.317594	−	0.977454i	−0.0207618	−	0.0638982i
$235$	−9.92545	+	30.5474i	−0.647465	+	1.99269i
$236$	2.52367	+	1.83355i	0.164277	+	0.119354i
$237$	4.95072	+	3.59691i	0.321584	+	0.233644i
$238$	2.53737	−	7.80922i	0.164473	−	0.506197i
$239$	−4.11936	−	12.6781i	−0.266459	−	0.820077i	−0.991354	−	0.131217i	$-0.958111\pi$
$239$	−4.11936	−	12.6781i	−0.266459	−	0.820077i	0.724894	−	0.688860i	$-0.241889\pi$
$240$	−12.5510	+	9.11883i	−0.810163	+	0.588618i
$241$	18.5139			1.19258			0.596292	−	0.802768i	$-0.296640\pi$
$241$	18.5139			1.19258			0.596292	+	0.802768i	$0.296640\pi$
$242$		0			0
$243$	12.3944			0.795104
$244$	−0.170786	+	0.124083i	−0.0109334	+	0.00794360i
$245$	−1.11418	−	3.42908i	−0.0711821	−	0.219076i
$246$	−3.67130	+	11.2991i	−0.234073	+	0.720404i
$247$	−1.46970	−	1.06780i	−0.0935150	−	0.0679426i
$248$	−2.42705	−	1.76336i	−0.154118	−	0.111973i
$249$	1.20774	−	3.71704i	0.0765374	−	0.235558i
$250$	4.35457	+	13.4020i	0.275407	+	0.847615i
$251$	−9.38909	+	6.82157i	−0.592634	+	0.430574i	−0.843257	−	0.537511i	$-0.819365\pi$
$251$	−9.38909	+	6.82157i	−0.592634	+	0.430574i	0.250623	+	0.968085i	$0.419365\pi$
$252$	−0.394449			−0.0248479
$253$		0			0
$254$	−2.60555			−0.163487
$255$	23.9514	−	17.4017i	1.49989	−	1.08974i
$256$	−2.19145	−	6.74458i	−0.136965	−	0.421536i
$257$	7.57520	−	23.3141i	0.472528	−	1.45429i	−0.376734	−	0.926321i	$-0.622953\pi$
$257$	7.57520	−	23.3141i	0.472528	−	1.45429i	0.849262	−	0.527971i	$-0.177047\pi$
$258$	7.28115	+	5.29007i	0.453305	+	0.329345i
$259$	7.45194	+	5.41415i	0.463041	+	0.336419i
$260$	−0.204280	+	0.628709i	−0.0126689	+	0.0389909i
$261$	−3.34253	−	10.2872i	−0.206897	−	0.636765i
$262$	−6.32381	+	4.59451i	−0.390686	+	0.283850i
$263$	−30.2389			−1.86461			−0.932304	−	0.361676i	$-0.882205\pi$
$263$	−30.2389			−1.86461			−0.932304	+	0.361676i	$0.882205\pi$
$264$		0			0
$265$	7.54163			0.463279
$266$	3.16190	−	2.29726i	0.193869	−	0.140854i
$267$	7.13572	+	21.9615i	0.436699	+	1.34402i
$268$	0.890145	−	2.73959i	0.0543743	−	0.167347i
$269$	7.37777	+	5.36027i	0.449831	+	0.326821i	0.789529	−	0.613713i	$-0.210325\pi$
$269$	7.37777	+	5.36027i	0.449831	+	0.326821i	−0.339698	+	0.940535i	$0.610325\pi$
$270$	21.3018	+	15.4767i	1.29639	+	0.941882i
$271$	−3.24039	+	9.97289i	−0.196840	+	0.605810i	0.803111	+	0.595830i	$0.203177\pi$
$271$	−3.24039	+	9.97289i	−0.196840	+	0.605810i	−0.999950	+	0.00998013i	$0.996823\pi$
$272$	−6.43270	−	19.7978i	−0.390040	−	1.20042i
$273$	−0.638231	+	0.463702i	−0.0386275	+	0.0280645i
$274$	−19.6972			−1.18995
$275$		0			0
$276$	2.48612			0.149647
$277$	13.7016	−	9.95478i	0.823248	−	0.598125i	−0.0943929	−	0.995535i	$-0.530091\pi$
$277$	13.7016	−	9.95478i	0.823248	−	0.598125i	0.917641	+	0.397410i	$0.130091\pi$
$278$	−5.79491	−	17.8349i	−0.347556	−	1.06967i
$279$	−0.402580	+	1.23901i	−0.0241018	+	0.0741778i
$280$	−8.75086	−	6.35787i	−0.522964	−	0.379955i
$281$	−11.0071	−	7.99714i	−0.656630	−	0.477070i	0.208893	−	0.977938i	$-0.433014\pi$
$281$	−11.0071	−	7.99714i	−0.656630	−	0.477070i	−0.865523	+	0.500869i	$0.833014\pi$
$282$	−4.67216	+	14.3794i	−0.278223	+	0.856283i
$283$	3.58631	+	11.0375i	0.213184	+	0.656113i	0.999278	+	0.0380056i	$0.0121005\pi$
$283$	3.58631	+	11.0375i	0.213184	+	0.656113i	−0.786093	+	0.618108i	$0.787900\pi$
$284$	−0.170786	+	0.124083i	−0.0101343	+	0.00736297i
$285$	14.0917			0.834719
$286$		0			0
$287$	−7.00000			−0.413197
$288$	−1.78882	+	1.29965i	−0.105407	+	0.0765828i
$289$	7.02241	+	21.6127i	0.413083	+	1.27134i
$290$	12.0517	−	37.0912i	0.707698	−	2.17807i
$291$	−3.80013	−	2.76096i	−0.222768	−	0.161850i
$292$	−1.22475	−	0.889835i	−0.0716733	−	0.0520737i
$293$	−5.19663	+	15.9936i	−0.303590	+	0.934355i	0.676609	+	0.736343i	$0.263449\pi$
$293$	−5.19663	+	15.9936i	−0.303590	+	0.934355i	−0.980199	+	0.198013i	$0.936551\pi$
$294$	−0.524471	−	1.61416i	−0.0305878	−	0.0941395i
$295$	30.0527	−	21.8346i	1.74974	−	1.27126i
$296$	27.6333			1.60615
$297$		0			0
$298$	−7.69722			−0.445888
$299$	−3.08774	+	2.24337i	−0.178568	+	0.129738i
$300$	−0.975131	−	3.00114i	−0.0562992	−	0.173271i
$301$	−1.63865	+	5.04324i	−0.0944501	+	0.290687i
$302$	14.9780	+	10.8822i	0.861889	+	0.626199i
$303$	1.78882	+	1.29965i	0.102765	+	0.0746631i
$304$	3.06184	−	9.42338i	0.175609	−	0.540468i
$305$	0.776831	+	2.39084i	0.0444812	+	0.136899i
$306$	−8.65424	+	6.28767i	−0.494730	+	0.359442i
$307$	26.6333			1.52004			0.760022	−	0.649898i	$-0.225188\pi$
$307$	26.6333			1.52004			0.760022	+	0.649898i	$0.225188\pi$
$308$		0			0
$309$	−13.9361			−0.792796
$310$	−3.80013	+	2.76096i	−0.215833	+	0.156812i
$311$	4.20435	+	12.9396i	0.238407	+	0.733740i	0.996651	+	0.0817700i	$0.0260573\pi$
$311$	4.20435	+	12.9396i	0.238407	+	0.733740i	−0.758245	+	0.651970i	$0.773943\pi$
$312$	−0.731348	+	2.25086i	−0.0414044	+	0.127430i
$313$	−9.46325	−	6.87546i	−0.534895	−	0.388624i	0.287291	−	0.957843i	$-0.407245\pi$
$313$	−9.46325	−	6.87546i	−0.534895	−	0.388624i	−0.822185	+	0.569220i	$0.807245\pi$
$314$	−7.60027	−	5.52192i	−0.428908	−	0.311620i
$315$	−1.45152	+	4.46733i	−0.0817840	+	0.251705i
$316$	0.439486	+	1.35260i	0.0247230	+	0.0760896i
$317$	−11.0813	+	8.05103i	−0.622387	+	0.452191i	−0.853755	−	0.520676i	$-0.825680\pi$
$317$	−11.0813	+	8.05103i	−0.622387	+	0.452191i	0.231367	+	0.972866i	$0.425680\pi$
$318$	3.55004			0.199076
$319$		0			0
$320$	−31.7889			−1.77705
$321$	−20.6636	+	15.0130i	−1.15333	+	0.837944i
$322$	−2.53737	−	7.80922i	−0.141402	−	0.435191i
$323$	−5.84299	+	17.9829i	−0.325113	+	1.00059i
$324$	−0.831472	−	0.604100i	−0.0461929	−	0.0335611i
$325$	3.91921	+	2.84747i	0.217399	+	0.157949i
$326$	7.57520	−	23.3141i	0.419552	−	1.29125i
$327$	−3.22064	−	9.91211i	−0.178102	−	0.548141i
$328$	−16.9894	+	12.3435i	−0.938080	+	0.681555i
$329$	−8.90833			−0.491132
$330$		0			0
$331$	2.18335			0.120008			0.0600038	−	0.998198i	$-0.480889\pi$
$331$	2.18335			0.120008			0.0600038	+	0.998198i	$0.480889\pi$
$332$	0.734852	−	0.533901i	0.0403302	−	0.0293016i
$333$	−3.70820	−	11.4127i	−0.203208	−	0.625411i
$334$	−3.70820	+	11.4127i	−0.202904	+	0.624474i
$335$	−27.7515	−	20.1627i	−1.51623	−	1.10160i
$336$	−3.48102	−	2.52911i	−0.189905	−	0.137974i
$337$	8.09968	−	24.9282i	0.441217	−	1.35793i	−0.445362	−	0.895351i	$-0.646925\pi$
$337$	8.09968	−	24.9282i	0.441217	−	1.35793i	0.886579	−	0.462577i	$-0.153075\pi$
$338$	5.08591	+	15.6528i	0.276637	+	0.851402i
$339$	15.0747	−	10.9524i	0.818743	−	0.594852i
$340$	6.88057			0.373151
$341$		0			0
$342$	−5.09167			−0.275326
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	4.91594	+	15.1297i	0.265050	+	0.815740i
$345$	9.14862	−	28.1566i	0.492545	−	1.51590i
$346$	2.42705	+	1.76336i	0.130479	+	0.0947986i
$347$	−1.93715	−	1.40742i	−0.103992	−	0.0755544i	0.534574	−	0.845122i	$-0.320472\pi$
$347$	−1.93715	−	1.40742i	−0.103992	−	0.0755544i	−0.638566	+	0.769567i	$0.720472\pi$
$348$	−1.01204	+	3.11473i	−0.0542509	+	0.166967i
$349$	−2.56570	−	7.89641i	−0.137339	−	0.422685i	0.858608	−	0.512633i	$-0.171330\pi$
$349$	−2.56570	−	7.89641i	−0.137339	−	0.422685i	−0.995946	+	0.0899481i	$0.971330\pi$
$350$	−8.43174	+	6.12602i	−0.450696	+	0.327449i
$351$	3.39445			0.181182
$352$		0			0
$353$	15.9083			0.846715			0.423357	−	0.905963i	$-0.360851\pi$
$353$	15.9083			0.846715			0.423357	+	0.905963i	$0.360851\pi$
$354$	14.1466	−	10.2781i	0.751882	−	0.546274i
$355$	0.776831	+	2.39084i	0.0412299	+	0.126893i
$356$	−1.65840	+	5.10403i	−0.0878950	+	0.270513i
$357$	6.64292	+	4.82636i	0.351581	+	0.255438i
$358$	−14.3398	−	10.4185i	−0.757883	−	0.550634i
$359$	3.99747	−	12.3029i	0.210978	−	0.649325i	−0.788436	−	0.615116i	$-0.789109\pi$
$359$	3.99747	−	12.3029i	0.210978	−	0.649325i	0.999415	−	0.0342083i	$-0.0108910\pi$
$360$	4.35457	+	13.4020i	0.229506	+	0.706346i
$361$	8.09017	−	5.87785i	0.425798	−	0.309361i
$362$	14.0555			0.738741
$363$		0			0
$364$	−0.183346			−0.00960995
$365$	−14.5848	+	10.5964i	−0.763401	+	0.554644i
$366$	0.365674	+	1.12543i	0.0191141	+	0.0588271i
$367$	7.92113	−	24.3787i	0.413479	−	1.27256i	−0.500124	−	0.865954i	$-0.666712\pi$
$367$	7.92113	−	24.3787i	0.413479	−	1.27256i	0.913604	−	0.406605i	$-0.133288\pi$
$368$	−16.8410	−	12.2357i	−0.877899	−	0.637831i
$369$	7.37777	+	5.36027i	0.384072	+	0.279044i
$370$	13.3701	−	41.1490i	0.695079	−	2.13923i
$371$	0.646363	+	1.98930i	0.0335575	+	0.103279i
$372$	0.319116	−	0.231851i	0.0165454	−	0.0120209i
$373$	5.11943			0.265074			0.132537	−	0.991178i	$-0.457688\pi$
$373$	5.11943			0.265074			0.132537	+	0.991178i	$0.457688\pi$
$374$		0			0
$375$	−14.0917			−0.727691
$376$	−21.6210	+	15.7085i	−1.11502	+	0.810107i
$377$	−1.55366	−	4.78168i	−0.0800177	−	0.246269i
$378$	−2.25668	+	6.94535i	−0.116071	+	0.357230i
$379$	−4.70577	−	3.41894i	−0.241719	−	0.175619i	0.460330	−	0.887748i	$-0.347731\pi$
$379$	−4.70577	−	3.41894i	−0.241719	−	0.175619i	−0.702049	+	0.712129i	$0.747731\pi$
$380$	2.64955	+	1.92501i	0.135919	+	0.0987508i
$381$	0.805160	−	2.47803i	0.0412496	−	0.126953i
$382$	2.08671	+	6.42223i	0.106765	+	0.328590i
$383$	3.74842	−	2.72339i	0.191536	−	0.139159i	−0.487885	−	0.872908i	$-0.662231\pi$
$383$	3.74842	−	2.72339i	0.191536	−	0.139159i	0.679420	+	0.733749i	$0.262231\pi$
$384$	−10.5416			−0.537951
$385$		0			0
$386$	−30.1194			−1.53304
$387$	5.58895	−	4.06061i	0.284102	−	0.206413i
$388$	−0.337346	−	1.03824i	−0.0171261	−	0.0527088i
$389$	4.26958	−	13.1404i	0.216476	−	0.666246i	−0.782569	−	0.622564i	$-0.786091\pi$
$389$	4.26958	−	13.1404i	0.216476	−	0.666246i	0.999045	−	0.0436820i	$-0.0139088\pi$
$390$	2.99792	+	2.17811i	0.151805	+	0.110293i
$391$	32.1382	+	23.3498i	1.62530	+	1.18085i
$392$	0.927051	−	2.85317i	0.0468231	−	0.144107i
$393$	−2.41548	−	7.43408i	−0.121845	−	0.375000i
$394$	−3.57764	+	2.59931i	−0.180239	+	0.130951i
$395$	16.9361			0.852147
$396$		0			0
$397$	15.7889			0.792422			0.396211	−	0.918159i	$-0.370325\pi$
$397$	15.7889			0.792422			0.396211	+	0.918159i	$0.370325\pi$
$398$	−9.93070	+	7.21508i	−0.497781	+	0.361659i
$399$	1.20774	+	3.71704i	0.0604626	+	0.186085i
$400$	−8.16491	+	25.1290i	−0.408246	+	1.25645i
$401$	5.49233	+	3.99041i	0.274274	+	0.199272i	0.716416	−	0.697673i	$-0.245781\pi$
$401$	5.49233	+	3.99041i	0.274274	+	0.199272i	−0.442142	+	0.896945i	$0.645781\pi$
$402$	−13.0633	−	9.49108i	−0.651541	−	0.473372i
$403$	−0.187126	+	0.575913i	−0.00932139	+	0.0286883i
$404$	0.158797	+	0.488727i	0.00790045	+	0.0243151i
$405$	−9.90144	+	7.19382i	−0.492007	+	0.357464i
$406$	10.8167			0.536822
$407$		0			0
$408$	24.6333			1.21953
$409$	−10.8363	+	7.87306i	−0.535822	+	0.389298i	−0.822531	−	0.568720i	$-0.807439\pi$
$409$	−10.8363	+	7.87306i	−0.535822	+	0.389298i	0.286709	+	0.958018i	$0.407439\pi$
$410$	10.1607	+	31.2713i	0.501799	+	1.54438i
$411$	6.08678	−	18.7332i	0.300239	−	0.924039i
$412$	−2.62029	−	1.90375i	−0.129093	−	0.0937912i
$413$	8.33512	+	6.05582i	0.410144	+	0.297987i
$414$	−3.30562	+	10.1737i	−0.162463	+	0.500008i
$415$	−3.34253	−	10.2872i	−0.164078	−	0.504981i
$416$	−0.831472	+	0.604100i	−0.0407663	+	0.0296184i
$417$	18.7527			0.918325
$418$		0			0
$419$	−9.57779			−0.467906			−0.233953	−	0.972248i	$-0.575166\pi$
$419$	−9.57779			−0.467906			−0.233953	+	0.972248i	$0.575166\pi$
$420$	1.15059	−	0.835951i	0.0561430	−	0.0407902i
$421$	−0.0566571	−	0.174373i	−0.00276130	−	0.00849840i	0.949666	−	0.313263i	$-0.101422\pi$
$421$	−0.0566571	−	0.174373i	−0.00276130	−	0.00849840i	−0.952428	+	0.304765i	$0.901422\pi$
$422$	1.01204	−	3.11473i	0.0492652	−	0.151623i
$423$	9.38909	+	6.82157i	0.456513	+	0.331676i
$424$	5.07660	+	3.68836i	0.246541	+	0.179123i
$425$	15.5813	−	47.9544i	0.755805	−	2.32613i
$426$	0.365674	+	1.12543i	0.0177170	+	0.0545272i
$427$	−0.564066	+	0.409818i	−0.0272971	+	0.0198325i
$428$	−5.93608			−0.286931
$429$		0			0
$430$	24.9083			1.20119
$431$	−17.8950	+	13.0015i	−0.861972	+	0.626259i	−0.928421	−	0.371531i	$-0.878833\pi$
$431$	−17.8950	+	13.0015i	−0.861972	+	0.626259i	0.0664491	+	0.997790i	$0.478833\pi$
$432$	5.72110	+	17.6077i	0.275257	+	0.847153i
$433$	−9.93403	+	30.5738i	−0.477399	+	1.46928i	0.365296	+	0.930891i	$0.380968\pi$
$433$	−9.93403	+	30.5738i	−0.477399	+	1.46928i	−0.842695	+	0.538391i	$0.819032\pi$
$434$	−1.05397	−	0.765752i	−0.0505921	−	0.0367573i
$435$	31.5517	+	22.9236i	1.51279	+	1.09910i
$436$	0.748503	−	2.30365i	0.0358468	−	0.110325i
$437$	5.84299	+	17.9829i	0.279508	+	0.860238i
$438$	−6.86542	+	4.98802i	−0.328042	+	0.238337i
$439$	−4.72498			−0.225511			−0.112756	−	0.993623i	$-0.535968\pi$
$439$	−4.72498			−0.225511			−0.112756	+	0.993623i	$0.535968\pi$
$440$		0			0
$441$	−1.30278			−0.0620369
$442$	−4.02263	+	2.92261i	−0.191337	+	0.139014i
$443$	−6.16059	−	18.9603i	−0.292698	−	0.900833i	−0.983985	−	0.178252i	$-0.942956\pi$
$443$	−6.16059	−	18.9603i	−0.292698	−	0.900833i	0.691286	−	0.722581i	$-0.257044\pi$
$444$	−1.12275	+	3.45548i	−0.0532835	+	0.163990i
$445$	51.7029	+	37.5644i	2.45095	+	1.78072i
$446$	3.25852	+	2.36746i	0.154296	+	0.112102i
$447$	2.37857	−	7.32050i	0.112503	−	0.346248i
$448$	−2.72450	−	8.38514i	−0.128720	−	0.396160i
$449$	−0.541611	+	0.393503i	−0.0255602	+	0.0185706i	−0.600492	−	0.799631i	$-0.705029\pi$
$449$	−0.541611	+	0.393503i	−0.0255602	+	0.0185706i	0.574932	+	0.818201i	$0.305029\pi$
$450$	13.5778			0.640063
$451$		0			0
$452$	4.33053			0.203691
$453$	−14.9780	+	10.8822i	−0.703730	+	0.511290i
$454$	4.63525	+	14.2658i	0.217543	+	0.669529i
$455$	−0.674691	+	2.07649i	−0.0316300	+	0.0973471i
$456$	9.48571	+	6.89177i	0.444209	+	0.322737i
$457$	3.33269	+	2.42134i	0.155897	+	0.113266i	0.662999	−	0.748620i	$-0.269283\pi$
$457$	3.33269	+	2.42134i	0.155897	+	0.113266i	−0.507102	+	0.861886i	$0.669283\pi$
$458$	−1.85410	+	5.70634i	−0.0866365	+	0.266640i
$459$	−10.9177	−	33.6013i	−0.509596	−	1.56838i
$460$	5.56650	−	4.04430i	0.259539	−	0.188566i
$461$	18.9083			0.880649			0.440324	−	0.897839i	$-0.354863\pi$
$461$	18.9083			0.880649			0.440324	+	0.897839i	$0.354863\pi$
$462$		0			0
$463$	−9.18335			−0.426786			−0.213393	−	0.976966i	$-0.568452\pi$
$463$	−9.18335			−0.426786			−0.213393	+	0.976966i	$0.568452\pi$
$464$	22.1850	−	16.1184i	1.02991	−	0.748276i
$465$	−1.45152	−	4.46733i	−0.0673127	−	0.207167i
$466$	−7.24644	+	22.3022i	−0.335685	+	1.03313i
$467$	−32.7989	−	23.8298i	−1.51775	−	1.10271i	−0.962588	−	0.270969i	$-0.912656\pi$
$467$	−32.7989	−	23.8298i	−1.51775	−	1.10271i	−0.555163	−	0.831742i	$-0.687344\pi$
$468$	0.193241	+	0.140398i	0.00893257	+	0.00648989i
$469$	2.93995	−	9.04824i	0.135754	−	0.417809i
$470$	12.9306	+	39.7964i	0.596446	+	1.83567i
$471$	7.60027	−	5.52192i	0.350202	−	0.254437i
$472$	30.9083			1.42267
$473$		0			0
$474$	7.97224			0.366177
$475$	19.4164	−	14.1068i	0.890886	−	0.647266i
$476$	0.589705	+	1.81493i	0.0270291	+	0.0831870i
$477$	0.842065	−	2.59161i	0.0385555	−	0.118662i
$478$	−14.0499	−	10.2079i	−0.642630	−	0.466898i
$479$	−11.8386	−	8.60124i	−0.540919	−	0.393001i	0.283507	−	0.958970i	$-0.408502\pi$
$479$	−11.8386	−	8.60124i	−0.540919	−	0.393001i	−0.824426	+	0.565969i	$0.808502\pi$
$480$	2.46356	−	7.58205i	0.112446	−	0.346072i
$481$	−1.72363	−	5.30480i	−0.0785909	−	0.241878i
$482$	19.5130	−	14.1770i	0.888794	−	0.645747i
$483$	8.21110			0.373618
$484$		0			0
$485$	−13.0000			−0.590300
$486$	13.0633	−	9.49108i	0.592565	−	0.430524i
$487$	5.81467	+	17.8957i	0.263488	+	0.810932i	0.992038	+	0.125939i	$0.0401945\pi$
$487$	5.81467	+	17.8957i	0.263488	+	0.810932i	−0.728550	+	0.684992i	$0.759806\pi$
$488$	−0.646363	+	1.98930i	−0.0292595	+	0.0900513i
$489$	19.8321	+	14.4089i	0.896841	+	0.651593i
$490$	−3.80013	−	2.76096i	−0.171673	−	0.124727i
$491$	−5.03783	+	15.5049i	−0.227354	+	0.699725i	0.770690	+	0.637211i	$0.219912\pi$
$491$	−5.03783	+	15.5049i	−0.227354	+	0.699725i	−0.998044	+	0.0625141i	$0.980088\pi$
$492$	−0.853240	−	2.62600i	−0.0384670	−	0.118389i
$493$	−42.3363	+	30.7591i	−1.90673	+	1.38532i
$494$	−2.36669			−0.106483
$495$		0			0
$496$	−3.30278			−0.148299
$497$	−0.564066	+	0.409818i	−0.0253018	+	0.0183829i
$498$	−1.57341	−	4.84247i	−0.0705063	−	0.216996i
$499$	−2.44381	+	7.52127i	−0.109400	+	0.336698i	−0.990738	−	0.135788i	$-0.956643\pi$
$499$	−2.44381	+	7.52127i	−0.109400	+	0.336698i	0.881338	+	0.472486i	$0.156643\pi$
$500$	−2.64955	−	1.92501i	−0.118491	−	0.0860890i
$501$	−9.70820	−	7.05342i	−0.433731	−	0.315124i
$502$	−4.67216	+	14.3794i	−0.208529	+	0.641785i
$503$	10.6370	+	32.7375i	0.474282	+	1.45969i	0.846923	+	0.531716i	$0.178452\pi$
$503$	10.6370	+	32.7375i	0.474282	+	1.45969i	−0.372641	+	0.927976i	$0.621548\pi$
$504$	−3.16190	+	2.29726i	−0.140842	+	0.102328i
$505$	6.11943			0.272311
$506$		0			0
$507$	−16.4584			−0.730942
$508$	0.489901	−	0.355934i	0.0217359	−	0.0157920i
$509$	5.77776	+	17.7821i	0.256095	+	0.788178i	0.993612	+	0.112850i	$0.0359980\pi$
$509$	5.77776	+	17.7821i	0.256095	+	0.788178i	−0.737517	+	0.675328i	$0.764002\pi$
$510$	11.9186	−	36.6817i	0.527764	−	1.62429i
$511$	−4.04508	−	2.93893i	−0.178944	−	0.130010i
$512$	−20.5670	−	14.9428i	−0.908941	−	0.660385i
$513$	5.19663	−	15.9936i	0.229437	−	0.706134i
$514$	−9.86879	−	30.3730i	−0.435294	−	1.33970i
$515$	−31.2033	+	22.6705i	−1.37498	+	0.998982i
$516$	−2.09167			−0.0920808
$517$		0			0
$518$	12.0000			0.527250
$519$	−2.42705	+	1.76336i	−0.106536	+	0.0774027i
$520$	2.02407	+	6.22946i	0.0887615	+	0.273180i
$521$	−6.61983	+	20.3737i	−0.290020	+	0.892589i	0.694829	+	0.719175i	$0.255480\pi$
$521$	−6.61983	+	20.3737i	−0.290020	+	0.892589i	−0.984849	+	0.173414i	$0.944520\pi$
$522$	−11.4004	−	8.28288i	−0.498982	−	0.362532i
$523$	−7.71934	−	5.60843i	−0.337543	−	0.245240i	0.406081	−	0.913837i	$-0.366895\pi$
$523$	−7.71934	−	5.60843i	−0.337543	−	0.245240i	−0.743625	+	0.668597i	$0.766895\pi$
$524$	0.561377	−	1.72774i	0.0245239	−	0.0754767i
$525$	−3.22064	−	9.91211i	−0.140560	−	0.432600i
$526$	−31.8708	+	23.1555i	−1.38963	+	1.00963i
$527$	6.30278			0.274553
$528$		0			0
$529$	16.7250			0.727173
$530$	7.94864	−	5.77502i	0.345267	−	0.250851i
$531$	−4.14769	−	12.7653i	−0.179994	−	0.553966i
$532$	−0.280688	+	0.863870i	−0.0121694	+	0.0374535i
$533$	3.42931	+	2.49154i	0.148540	+	0.107921i
$534$	24.3379	+	17.6825i	1.05320	+	0.765197i
$535$	−21.8440	+	67.2291i	−0.944400	+	2.90657i
$536$	−8.81985	−	27.1447i	−0.380960	−	1.17247i
$537$	14.3398	−	10.4185i	0.618809	−	0.449591i
$538$	11.8806			0.512208
$539$		0			0
$540$	−6.11943			−0.263338
$541$	32.0416	−	23.2796i	1.37757	−	1.00087i	0.380472	−	0.924792i	$-0.375761\pi$
$541$	32.0416	−	23.2796i	1.37757	−	1.00087i	0.997102	−	0.0760741i	$-0.0242386\pi$
$542$	4.22150	+	12.9924i	0.181329	+	0.558073i
$543$	−4.34339	+	13.3676i	−0.186393	+	0.573658i
$544$	8.65424	+	6.28767i	0.371047	+	0.269582i
$545$	−23.3356	−	16.9543i	−0.999588	−	0.726243i
$546$	−0.317594	+	0.977454i	−0.0135918	+	0.0418312i
$547$	5.23354	+	16.1072i	0.223770	+	0.688693i	0.998414	+	0.0562957i	$0.0179290\pi$
$547$	5.23354	+	16.1072i	0.223770	+	0.688693i	−0.774644	+	0.632397i	$0.782071\pi$
$548$	3.70351	−	2.69076i	0.158206	−	0.114944i
$549$	0.908327			0.0387664
$550$		0			0
$551$	−24.9083			−1.06113
$552$	19.9288	−	14.4791i	0.848225	−	0.616271i
$553$	1.45152	+	4.46733i	0.0617250	+	0.189970i
$554$	6.81813	−	20.9840i	0.289674	−	0.891526i
$555$	35.0034	+	25.4315i	1.48581	+	1.07951i
$556$	3.52593	+	2.56174i	0.149533	+	0.108642i
$557$	−13.3615	+	41.1226i	−0.566147	+	1.74242i	0.0983729	+	0.995150i	$0.468636\pi$
$557$	−13.3615	+	41.1226i	−0.566147	+	1.74242i	−0.664520	+	0.747271i	$0.731364\pi$
$558$	0.524471	+	1.61416i	0.0222026	+	0.0683327i
$559$	2.59784	−	1.88744i	0.109877	−	0.0798302i
$560$	−11.9083			−0.503219
$561$		0			0
$562$	−17.7250			−0.747683
$563$	−2.67200	+	1.94132i	−0.112611	+	0.0818170i	−0.642666	−	0.766147i	$-0.722172\pi$
$563$	−2.67200	+	1.94132i	−0.112611	+	0.0818170i	0.530054	+	0.847964i	$0.322172\pi$
$564$	−1.08585	−	3.34190i	−0.0457225	−	0.140719i
$565$	15.9358	−	49.0454i	0.670425	−	2.06336i
$566$	12.2319	+	8.88698i	0.514144	+	0.373548i
$567$	−2.74617	−	1.99521i	−0.115328	−	0.0837908i
$568$	−0.646363	+	1.98930i	−0.0271208	+	0.0834691i
$569$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$569$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$570$	14.8522	−	10.7907i	0.622089	−	0.451974i
$571$	−31.8444			−1.33265			−0.666324	−	0.745663i	$-0.732133\pi$
$571$	−31.8444			−1.33265			−0.666324	+	0.745663i	$0.732133\pi$
$572$		0			0
$573$	−6.75274			−0.282100
$574$	−7.37777	+	5.36027i	−0.307942	+	0.223733i
$575$	−15.5813	−	47.9544i	−0.649786	−	1.99984i
$576$	−3.54941	+	10.9240i	−0.147892	+	0.455165i
$577$	9.87899	+	7.17751i	0.411268	+	0.298803i	0.774115	−	0.633045i	$-0.218195\pi$
$577$	9.87899	+	7.17751i	0.411268	+	0.298803i	−0.362847	+	0.931849i	$0.618195\pi$
$578$	23.9514	+	17.4017i	0.996247	+	0.723816i
$579$	9.30742	−	28.6453i	0.386803	−	1.19046i
$580$	2.80090	+	8.62030i	0.116301	+	0.357938i
$581$	2.42705	−	1.76336i	0.100691	−	0.0731563i
$582$	−6.11943			−0.253659
$583$		0			0
$584$	−15.0000			−0.620704
$585$	2.30118	−	1.67190i	0.0951419	−	0.0691247i
$586$	6.77005	+	20.8361i	0.279668	+	0.860730i
$587$	−1.97599	+	6.08148i	−0.0815580	+	0.251010i	−0.983518	−	0.180810i	$-0.942128\pi$
$587$	−1.97599	+	6.08148i	−0.0815580	+	0.251010i	0.901960	+	0.431819i	$0.142128\pi$
$588$	0.319116	+	0.231851i	0.0131601	+	0.00956138i
$589$	2.42705	+	1.76336i	0.100005	+	0.0726578i
$590$	14.9547	−	46.0259i	0.615676	−	1.89485i
$591$	−1.36654	−	4.20577i	−0.0562118	−	0.173002i
$592$	24.6121	−	17.8817i	1.01155	−	0.734934i
$593$	15.3944			0.632174			0.316087	−	0.948730i	$-0.397631\pi$
$593$	15.3944			0.632174			0.316087	+	0.948730i	$0.397631\pi$
$594$		0			0
$595$	22.7250			0.931633
$596$	1.44725	−	1.05149i	0.0592816	−	0.0430706i
$597$	−3.79319	−	11.6742i	−0.155245	−	0.477795i
$598$	−1.53651	+	4.72888i	−0.0628325	+	0.193378i
$599$	23.6323	+	17.1699i	0.965589	+	0.701541i	0.954442	−	0.298397i	$-0.0964518\pi$
$599$	23.6323	+	17.1699i	0.965589	+	0.701541i	0.0111468	+	0.999938i	$0.496452\pi$
$600$	−25.2952	−	18.3781i	−1.03267	−	0.750281i
$601$	4.88761	−	15.0425i	0.199370	−	0.613598i	−0.800528	−	0.599296i	$-0.795447\pi$
$601$	4.88761	−	15.0425i	0.199370	−	0.613598i	0.999898	−	0.0143020i	$-0.00455262\pi$
$602$	2.13479	+	6.57021i	0.0870076	+	0.267782i
$603$	−10.0273	+	7.28527i	−0.408344	+	0.296679i
$604$	−4.30278			−0.175077
$605$		0			0
$606$	2.88057			0.117015
$607$	−27.1358	+	19.7153i	−1.10141	+	0.800218i	−0.981289	−	0.192541i	$-0.938327\pi$
$607$	−27.1358	+	19.7153i	−1.10141	+	0.800218i	−0.120117	+	0.992760i	$0.538327\pi$
$608$	1.57341	+	4.84247i	0.0638103	+	0.196388i
$609$	−3.34253	+	10.2872i	−0.135446	+	0.416860i
$610$	2.64955	+	1.92501i	0.107277	+	0.0779413i
$611$	4.36420	+	3.17078i	0.176557	+	0.128276i
$612$	0.768254	−	2.36444i	0.0310548	−	0.0955769i
$613$	12.0688	+	37.1440i	0.487455	+	1.50023i	0.828394	+	0.560146i	$0.189255\pi$
$613$	12.0688	+	37.1440i	0.487455	+	1.50023i	−0.340939	+	0.940086i	$0.610745\pi$
$614$	28.0706	−	20.3945i	1.13284	−	0.823056i
$615$	−32.8806			−1.32587
$616$		0			0
$617$	−21.6333			−0.870924			−0.435462	−	0.900207i	$-0.643415\pi$
$617$	−21.6333			−0.870924			−0.435462	+	0.900207i	$0.643415\pi$
$618$	−14.6882	+	10.6716i	−0.590845	+	0.429274i
$619$	5.61896	+	17.2934i	0.225845	+	0.695080i	0.998205	+	0.0598944i	$0.0190764\pi$
$619$	5.61896	+	17.2934i	0.225845	+	0.695080i	−0.772360	+	0.635186i	$0.780924\pi$
$620$	0.337346	−	1.03824i	0.0135481	−	0.0416968i
$621$	−28.5830	−	20.7668i	−1.14700	−	0.833342i
$622$	14.3398	+	10.4185i	0.574974	+	0.417743i
$623$	−5.47732	+	16.8575i	−0.219444	+	0.675380i
$624$	0.805160	+	2.47803i	0.0322322	+	0.0992005i
$625$	0.809017	−	0.587785i	0.0323607	−	0.0235114i
$626$	−15.2389			−0.609067
$627$		0			0
$628$	2.18335			0.0871250
$629$	−46.9679	+	34.1242i	−1.87273	+	1.36062i
$630$	1.89101	+	5.81992i	0.0753396	+	0.231871i
$631$	12.6869	−	39.0461i	0.505056	−	1.55440i	−0.295622	−	0.955305i	$-0.595527\pi$
$631$	12.6869	−	39.0461i	0.505056	−	1.55440i	0.800677	−	0.599096i	$-0.204473\pi$
$632$	11.4004	+	8.28288i	0.453484	+	0.329475i
$633$	2.64955	+	1.92501i	0.105310	+	0.0765122i
$634$	−5.51423	+	16.9710i	−0.218998	+	0.674006i
$635$	−2.22835	−	6.85817i	−0.0884295	−	0.272158i
$636$	−0.667486	+	0.484957i	−0.0264675	+	0.0192298i
$637$	−0.605551			−0.0239928
$638$		0			0
$639$	0.908327			0.0359329
$640$	−23.6030	+	17.1486i	−0.932991	+	0.677858i
$641$	−2.21978	−	6.83177i	−0.0876759	−	0.269839i	0.897600	−	0.440811i	$-0.145309\pi$
$641$	−2.21978	−	6.83177i	−0.0876759	−	0.269839i	−0.985276	+	0.170972i	$0.945309\pi$
$642$	−10.2825	+	31.6464i	−0.405820	+	1.24898i
$643$	−39.8351	−	28.9419i	−1.57094	−	1.14136i	−0.926248	−	0.376916i	$-0.876985\pi$
$643$	−39.8351	−	28.9419i	−1.57094	−	1.14136i	−0.644694	−	0.764440i	$-0.723015\pi$
$644$	1.54387	+	1.12169i	0.0608370	+	0.0442006i
$645$	−7.69710	+	23.6892i	−0.303073	+	0.932762i
$646$	7.61211	+	23.4277i	0.299494	+	0.921749i
$647$	−2.74617	+	1.99521i	−0.107963	+	0.0784397i	−0.640457	−	0.767994i	$-0.721255\pi$
$647$	−2.74617	+	1.99521i	−0.107963	+	0.0784397i	0.532494	+	0.846434i	$0.321255\pi$
$648$	−10.1833			−0.400040
$649$		0			0
$650$	6.31118			0.247545
$651$	1.05397	−	0.765752i	0.0413082	−	0.0300122i
$652$	1.76054	+	5.41838i	0.0689480	+	0.212200i
$653$	4.57860	−	14.0915i	0.179174	−	0.551442i	−0.820625	−	0.571467i	$-0.806375\pi$
$653$	4.57860	−	14.0915i	0.179174	−	0.551442i	0.999799	+	0.0200249i	$0.00637454\pi$
$654$	−10.9847	−	7.98083i	−0.429534	−	0.312075i
$655$	−17.5017	−	12.7157i	−0.683849	−	0.496845i
$656$	−7.14430	+	21.9879i	−0.278938	+	0.858483i
$657$	2.01290	+	6.19507i	0.0785307	+	0.241693i
$658$	−9.38909	+	6.82157i	−0.366025	+	0.265933i
$659$	−38.6333			−1.50494			−0.752470	−	0.658627i	$-0.771138\pi$
$659$	−38.6333			−1.50494			−0.752470	+	0.658627i	$0.771138\pi$
$660$		0			0
$661$	−14.6972			−0.571656			−0.285828	−	0.958281i	$-0.592269\pi$
$661$	−14.6972			−0.571656			−0.285828	+	0.958281i	$0.592269\pi$
$662$	2.30118	−	1.67190i	0.0894378	−	0.0649803i
$663$	−1.53651	−	4.72888i	−0.0596730	−	0.183655i
$664$	2.78115	−	8.55951i	0.107930	−	0.332173i
$665$	8.75086	+	6.35787i	0.339344	+	0.246548i
$666$	−12.6476	−	9.18903i	−0.490085	−	0.356068i
$667$	−16.1710	+	49.7693i	−0.626145	+	1.92707i
$668$	−0.861817	−	2.65240i	−0.0333447	−	0.102624i
$669$	−3.25852	+	2.36746i	−0.125982	+	0.0915311i
$670$	−44.6888			−1.72648
$671$		0			0
$672$	2.21110			0.0852951
$673$	−16.5219	+	12.0039i	−0.636873	+	0.462715i	−0.858774	−	0.512354i	$-0.828774\pi$
$673$	−16.5219	+	12.0039i	−0.636873	+	0.462715i	0.221902	+	0.975069i	$0.428774\pi$
$674$	−10.5521	−	32.4759i	−0.406450	−	1.25093i
$675$	−13.8577	+	42.6496i	−0.533383	+	1.64158i
$676$	−3.09454	−	2.24831i	−0.119021	−	0.0864736i
$677$	−5.41817	−	3.93653i	−0.208237	−	0.151293i	0.478779	−	0.877936i	$-0.341080\pi$
$677$	−5.41817	−	3.93653i	−0.208237	−	0.151293i	−0.687016	+	0.726643i	$0.741080\pi$
$678$	7.50139	−	23.0869i	0.288089	−	0.886648i
$679$	−1.11418	−	3.42908i	−0.0427582	−	0.131596i
$680$	55.1547	−	40.0722i	2.11509	−	1.53670i
$681$	−15.0000			−0.574801
$682$		0			0
$683$	19.3028			0.738600			0.369300	−	0.929310i	$-0.379597\pi$
$683$	19.3028			0.738600			0.369300	+	0.929310i	$0.379597\pi$
$684$	0.957347	−	0.695553i	0.0366051	−	0.0265952i
$685$	−16.8457	−	51.8458i	−0.643642	−	1.98093i
$686$	0.402580	−	1.23901i	0.0153706	−	0.0473057i
$687$	−4.85410	−	3.52671i	−0.185196	−	0.134552i
$688$	14.1690	+	10.2944i	0.540189	+	0.392470i
$689$	0.391406	−	1.20462i	0.0149114	−	0.0458925i
$690$	−11.9186	−	36.6817i	−0.453733	−	1.39645i
$691$	−15.3938	+	11.1842i	−0.585607	+	0.425468i	−0.840741	−	0.541437i	$-0.817880\pi$
$691$	−15.3938	+	11.1842i	−0.585607	+	0.425468i	0.255134	+	0.966906i	$0.417880\pi$
$692$	−0.697224			−0.0265045
$693$		0			0
$694$	−3.11943			−0.118412
$695$	41.9879	−	30.5060i	1.59269	−	1.15716i
$696$	10.0276	+	30.8617i	0.380095	+	1.16981i
$697$	13.6337	−	41.9601i	0.516411	−	1.58935i
$698$	−8.75086	−	6.35787i	−0.331225	−	0.240649i
$699$	−18.9714	−	13.7835i	−0.717565	−	0.521341i
$700$	0.748503	−	2.30365i	0.0282907	−	0.0870699i
$701$	−1.81720	−	5.59275i	−0.0686346	−	0.211235i	0.910856	−	0.412723i	$-0.135422\pi$
$701$	−1.81720	−	5.59275i	−0.0686346	−	0.211235i	−0.979491	+	0.201488i	$0.935422\pi$
$702$	3.57764	−	2.59931i	0.135029	−	0.0981045i
$703$	−27.6333			−1.04221
$704$		0			0
$705$	−41.8444			−1.57595
$706$	16.7669	−	12.1818i	0.631029	−	0.458470i
$707$	0.524471	+	1.61416i	0.0197248	+	0.0607066i
$708$	−1.25582	+	3.86501i	−0.0471966	+	0.145256i
$709$	11.5936	+	8.42328i	0.435408	+	0.316343i	0.783808	−	0.621003i	$-0.213275\pi$
$709$	11.5936	+	8.42328i	0.435408	+	0.316343i	−0.348399	+	0.937346i	$0.613275\pi$
$710$	2.64955	+	1.92501i	0.0994357	+	0.0722443i
$711$	1.89101	−	5.81992i	0.0709183	−	0.218264i
$712$	16.4320	+	50.5724i	0.615814	+	1.89528i
$713$	5.09905	−	3.70468i	0.190961	−	0.138741i
$714$	10.6972			0.400334
$715$		0			0
$716$	4.11943			0.153950
$717$	14.0499	−	10.2079i	0.524705	−	0.381220i
$718$	−5.20781	−	16.0280i	−0.194354	−	0.598159i
$719$	−9.03530	+	27.8078i	−0.336960	+	1.03706i	0.628789	+	0.777576i	$0.283551\pi$
$719$	−9.03530	+	27.8078i	−0.336960	+	1.03706i	−0.965749	+	0.259480i	$0.916449\pi$
$720$	12.5510	+	9.11883i	0.467748	+	0.339839i
$721$	−8.65424	−	6.28767i	−0.322301	−	0.234165i
$722$	4.02580	−	12.3901i	0.149825	−	0.461113i
$723$	7.45331	+	22.9389i	0.277192	+	0.853108i
$724$	−2.64275	+	1.92007i	−0.0982169	+	0.0713588i
$725$	66.4222			2.46686
$726$		0			0
$727$	−1.11943			−0.0415173			−0.0207587	−	0.999785i	$-0.506608\pi$
$727$	−1.11943			−0.0415173			−0.0207587	+	0.999785i	$0.506608\pi$
$728$	−1.46970	+	1.06780i	−0.0544708	+	0.0395754i
$729$	8.13658	+	25.0418i	0.301355	+	0.927475i
$730$	−7.25761	+	22.3366i	−0.268616	+	0.826716i
$731$	−27.0391	−	19.6451i	−1.00008	−	0.726600i
$732$	−0.222495	−	0.161652i	−0.00822366	−	0.00597484i
$733$	−6.55459	+	20.1730i	−0.242099	+	0.745105i	0.754001	+	0.656874i	$0.228122\pi$
$733$	−6.55459	+	20.1730i	−0.242099	+	0.745105i	−0.996100	+	0.0882315i	$0.971878\pi$
$734$	−10.3195	−	31.7600i	−0.380898	−	1.17228i
$735$	3.80013	−	2.76096i	0.140170	−	0.101840i
$736$	10.6972			0.394305
$737$		0			0
$738$	11.8806			0.437330
$739$	14.4657	−	10.5099i	0.532129	−	0.386614i	−0.289025	−	0.957322i	$-0.593331\pi$
$739$	14.4657	−	10.5099i	0.532129	−	0.386614i	0.821153	+	0.570707i	$0.193331\pi$
$740$	3.10732	+	9.56336i	0.114228	+	0.351556i
$741$	0.731348	−	2.25086i	0.0268667	−	0.0826873i
$742$	2.20456	+	1.60170i	0.0809318	+	0.0588004i
$743$	1.56632	+	1.13800i	0.0574629	+	0.0417492i	0.616146	−	0.787632i	$-0.288693\pi$
$743$	1.56632	+	1.13800i	0.0574629	+	0.0417492i	−0.558683	+	0.829381i	$0.688693\pi$
$744$	1.20774	−	3.71704i	0.0442779	−	0.136273i
$745$	−6.58292	−	20.2601i	−0.241180	−	0.742274i
$746$	5.39571	−	3.92021i	0.197551	−	0.143529i
$747$	−3.90833			−0.142998
$748$		0			0
$749$	−19.6056			−0.716371
$750$	−14.8522	+	10.7907i	−0.542324	+	0.394022i
$751$	−11.0113	−	33.8893i	−0.401808	−	1.23664i	−0.923531	−	0.383523i	$-0.874711\pi$
$751$	−11.0113	−	33.8893i	−0.401808	−	1.23664i	0.521723	−	0.853115i	$-0.325289\pi$
$752$	−9.09196	+	27.9822i	−0.331550	+	1.02041i
$753$	−12.2319	−	8.88698i	−0.445754	−	0.323859i
$754$	−5.29909	−	3.85002i	−0.192982	−	0.140209i
$755$	−15.8337	+	48.7311i	−0.576247	+	1.77350i
$756$	−0.524471	−	1.61416i	−0.0190748	−	0.0587063i
$757$	1.76636	−	1.28334i	0.0641996	−	0.0466437i	−0.555223	−	0.831702i	$-0.687367\pi$
$757$	1.76636	−	1.28334i	0.0641996	−	0.0466437i	0.619422	+	0.785058i	$0.287367\pi$
$758$	−7.57779			−0.275238
$759$		0			0
$760$	32.4500			1.17708
$761$	−33.9787	+	24.6870i	−1.23173	+	0.894902i	−0.997018	−	0.0771633i	$-0.975414\pi$
$761$	−33.9787	+	24.6870i	−1.23173	+	0.894902i	−0.234709	+	0.972066i	$0.575414\pi$
$762$	−1.04894	−	3.22831i	−0.0379992	−	0.116949i
$763$	2.47214	−	7.60845i	0.0894973	−	0.275444i
$764$	−1.26966	−	0.922465i	−0.0459348	−	0.0333736i
$765$	−23.9514	−	17.4017i	−0.865964	−	0.629160i
$766$	1.86528	−	5.74073i	0.0673952	−	0.207421i
$767$	−1.92791	−	5.93351i	−0.0696129	−	0.214247i
$768$	7.47439	−	5.43047i	0.269709	−	0.195955i
$769$	0.330532			0.0119193			0.00595964	−	0.999982i	$-0.498103\pi$
$769$	0.330532			0.0119193			0.00595964	+	0.999982i	$0.498103\pi$
$770$		0			0
$771$	31.9361			1.15015
$772$	5.66312	−	4.11450i	0.203820	−	0.148084i
$773$	−3.90391	−	12.0150i	−0.140414	−	0.432149i	0.855979	−	0.517011i	$-0.172955\pi$
$773$	−3.90391	−	12.0150i	−0.140414	−	0.432149i	−0.996393	+	0.0848615i	$0.972955\pi$
$774$	2.78115	−	8.55951i	0.0999665	−	0.307665i
$775$	−6.47214	−	4.70228i	−0.232486	−	0.168911i
$776$	−8.75086	−	6.35787i	−0.314137	−	0.228234i
$777$	−3.70820	+	11.4127i	−0.133031	+	0.409428i
$778$	−5.56231	−	17.1190i	−0.199418	−	0.613747i
$779$	16.9894	−	12.3435i	0.608707	−	0.442251i
$780$	−0.861218			−0.0308366
$781$		0			0
$782$	51.7527			1.85067
$783$	37.6530	−	27.3565i	1.34561	−	0.977641i
$784$	−1.02061	−	3.14113i	−0.0364505	−	0.112183i
$785$	8.03444	−	24.7275i	0.286762	−	0.882561i
$786$	−8.23850	−	5.98562i	−0.293858	−	0.213500i
$787$	32.7764	+	23.8135i	1.16835	+	0.848858i	0.990811	−	0.135255i	$-0.0431854\pi$
$787$	32.7764	+	23.8135i	1.16835	+	0.848858i	0.177542	+	0.984113i	$0.443185\pi$
$788$	0.317594	−	0.977454i	0.0113138	−	0.0348204i
$789$	−12.1736	−	37.4663i	−0.433390	−	1.33384i
$790$	17.8501	−	12.9688i	0.635077	−	0.461411i
$791$	14.3028			0.508548
$792$		0			0
$793$	0.422205			0.0149929
$794$	16.6410	−	12.0904i	0.590567	−	0.429072i
$795$	3.03611	+	9.34419i	0.107680	+	0.331404i
$796$	0.881568	−	2.71319i	0.0312464	−	0.0961664i
$797$	−11.8386	−	8.60124i	−0.419345	−	0.304672i	0.358030	−	0.933710i	$-0.383449\pi$
$797$	−11.8386	−	8.60124i	−0.419345	−	0.304672i	−0.777374	+	0.629039i	$0.783449\pi$
$798$	4.11925	+	2.99281i	0.145820	+	0.105944i
$799$	17.3504	−	53.3991i	0.613814	−	1.88913i
$800$	−4.19577	−	12.9133i	−0.148343	−	0.456552i
$801$	18.6816	−	13.5729i	0.660080	−	0.479576i
$802$	8.84441			0.312307
$803$		0			0
$804$	3.75274			0.132349
$805$	18.3849	−	13.3574i	0.647982	−	0.470787i
$806$	0.243783	+	0.750286i	0.00858688	+	0.0264277i
$807$	−3.67130	+	11.2991i	−0.129236	+	0.397747i
$808$	4.11925	+	2.99281i	0.144915	+	0.105287i
$809$	−15.2972	−	11.1140i	−0.537819	−	0.390749i	0.285455	−	0.958392i	$-0.407855\pi$
$809$	−15.2972	−	11.1140i	−0.537819	−	0.390749i	−0.823275	+	0.567643i	$0.807855\pi$
$810$	−4.92712	+	15.1641i	−0.173121	+	0.532812i
$811$	5.20521	+	16.0200i	0.182780	+	0.562538i	0.999903	−	0.0139249i	$-0.00443259\pi$
$811$	5.20521	+	16.0200i	0.182780	+	0.562538i	−0.817123	+	0.576463i	$0.804433\pi$
$812$	−2.03377	+	1.47762i	−0.0713713	+	0.0518543i
$813$	−13.6611			−0.479114
$814$		0			0
$815$	67.8444			2.37649
$816$	21.9401	−	15.9404i	0.768056	−	0.558026i
$817$	−4.91594	−	15.1297i	−0.171987	−	0.529322i
$818$	−5.39233	+	16.5959i	−0.188539	+	0.580262i
$819$	0.638231	+	0.463702i	0.0223016	+	0.0162031i
$820$	−6.18227	−	4.49169i	−0.215894	−	0.156856i
$821$	0.439486	−	1.35260i	0.0153382	−	0.0472060i	−0.943095	−	0.332525i	$-0.892099\pi$
$821$	0.439486	−	1.35260i	0.0153382	−	0.0472060i	0.958433	+	0.285319i	$0.0920995\pi$
$822$	−7.92970	−	24.4051i	−0.276580	−	0.851226i
$823$	−16.8186	+	12.2194i	−0.586259	+	0.425942i	−0.840975	−	0.541074i	$-0.818018\pi$
$823$	−16.8186	+	12.2194i	−0.586259	+	0.425942i	0.254716	+	0.967016i	$0.418018\pi$
$824$	−32.0917			−1.11797
$825$		0			0
$826$	13.4222			0.467018
$827$	28.9763	−	21.0525i	1.00760	−	0.732067i	0.0438989	−	0.999036i	$-0.486022\pi$
$827$	28.9763	−	21.0525i	1.00760	−	0.732067i	0.963705	+	0.266969i	$0.0860221\pi$
$828$	−0.768254	−	2.36444i	−0.0266987	−	0.0821701i
$829$	14.1298	−	43.4870i	0.490748	−	1.51037i	−0.332732	−	0.943022i	$-0.607970\pi$
$829$	14.1298	−	43.4870i	0.490748	−	1.51037i	0.823480	−	0.567346i	$-0.192030\pi$
$830$	−11.4004	−	8.28288i	−0.395714	−	0.287503i
$831$	17.8501	+	12.9688i	0.619213	+	0.449884i
$832$	−1.64982	+	5.07763i	−0.0571973	+	0.176035i
$833$	1.94766	+	5.99430i	0.0674826	+	0.207690i
$834$	19.7648	−	14.3600i	0.684398	−	0.497244i
$835$	−33.2111			−1.14932
$836$		0			0
$837$	−5.60555			−0.193756
$838$	−10.0947	+	7.33422i	−0.348715	+	0.253356i
$839$	8.58724	+	26.4288i	0.296465	+	0.912424i	0.982726	+	0.185069i	$0.0592507\pi$
$839$	8.58724	+	26.4288i	0.296465	+	0.912424i	−0.686261	+	0.727355i	$0.740749\pi$
$840$	4.35457	−	13.4020i	0.150247	−	0.462412i
$841$	−32.3090	−	23.4738i	−1.11410	−	0.809443i
$842$	−0.193241	−	0.140398i	−0.00665952	−	0.00483843i
$843$	5.47732	−	16.8575i	0.188649	−	0.580602i
$844$	0.235206	+	0.723888i	0.00809611	+	0.0249173i
$845$	−36.8508	+	26.7736i	−1.26770	+	0.921041i
$846$	15.1194			0.519817
$847$		0			0
$848$	6.90833			0.237233
$849$	−12.2319	+	8.88698i	−0.419797	+	0.305000i
$850$	−20.2990	−	62.4738i	−0.696249	−	2.14283i
$851$	−17.9401	+	55.2141i	−0.614980	+	1.89271i
$852$	−0.222495	−	0.161652i	−0.00762256	−	0.00553812i
$853$	10.7397	+	7.80286i	0.367721	+	0.267165i	0.756265	−	0.654265i	$-0.227022\pi$
$853$	10.7397	+	7.80286i	0.367721	+	0.267165i	−0.388544	+	0.921430i	$0.627022\pi$
$854$	−0.280688	+	0.863870i	−0.00960496	+	0.0295610i
$855$	−4.35457	−	13.4020i	−0.148923	−	0.458338i
$856$	−47.5837	+	34.5716i	−1.62638	+	1.18163i
$857$	−40.3583			−1.37861			−0.689306	−	0.724470i	$-0.742085\pi$
$857$	−40.3583			−1.37861			−0.689306	+	0.724470i	$0.742085\pi$
$858$		0			0
$859$	−21.6972			−0.740300			−0.370150	−	0.928972i	$-0.620694\pi$
$859$	−21.6972			−0.740300			−0.370150	+	0.928972i	$0.620694\pi$
$860$	−4.68332	+	3.40263i	−0.159700	+	0.116029i
$861$	−2.81806	−	8.67309i	−0.0960392	−	0.295578i
$862$	−8.90484	+	27.4063i	−0.303300	+	0.933461i
$863$	−2.08548	−	1.51519i	−0.0709906	−	0.0515777i	0.551724	−	0.834027i	$-0.313970\pi$
$863$	−2.08548	−	1.51519i	−0.0709906	−	0.0515777i	−0.622715	+	0.782449i	$0.713970\pi$
$864$	−7.69689	−	5.59212i	−0.261853	−	0.190248i
$865$	−2.56570	+	7.89641i	−0.0872364	+	0.268486i
$866$	12.9418	+	39.8308i	0.439781	+	1.35351i
$867$	−23.9514	+	17.4017i	−0.813432	+	0.590993i
$868$	0.302776			0.0102769
$869$		0			0
$870$	50.8082			1.72256
$871$	−4.66086	+	3.38631i	−0.157927	+	0.114741i
$872$	−7.41641	−	22.8254i	−0.251151	−	0.772964i
$873$	−1.45152	+	4.46733i	−0.0491266	+	0.151196i
$874$	19.9288	+	14.4791i	0.674101	+	0.489763i
$875$	−8.75086	−	6.35787i	−0.295833	−	0.214935i
$876$	0.609457	−	1.87572i	0.0205916	−	0.0633745i
$877$	−7.74258	−	23.8292i	−0.261448	−	0.804655i	−0.992490	−	0.122323i	$-0.960966\pi$
$877$	−7.74258	−	23.8292i	−0.261448	−	0.804655i	0.731042	−	0.682332i	$-0.239034\pi$
$878$	−4.97998	+	3.61816i	−0.168066	+	0.122107i
$879$	−21.9083			−0.738950
$880$		0			0
$881$	−5.33053			−0.179590			−0.0897951	−	0.995960i	$-0.528621\pi$
$881$	−5.33053			−0.179590			−0.0897951	+	0.995960i	$0.528621\pi$
$882$	−1.37308	+	0.997603i	−0.0462341	+	0.0335911i
$883$	7.64044	+	23.5149i	0.257121	+	0.791338i	0.993404	+	0.114664i	$0.0365792\pi$
$883$	7.64044	+	23.5149i	0.257121	+	0.791338i	−0.736283	+	0.676674i	$0.763421\pi$
$884$	0.357097	−	1.09903i	0.0120105	−	0.0369644i
$885$	39.1519	+	28.4455i	1.31608	+	0.956186i
$886$	−21.0120	−	15.2661i	−0.705911	−	0.512875i
$887$	5.83442	−	17.9565i	0.195901	−	0.602920i	−0.804064	−	0.594542i	$-0.797333\pi$
$887$	5.83442	−	17.9565i	0.195901	−	0.602920i	0.999965	−	0.00837764i	$-0.00266672\pi$
$888$	11.1246	+	34.2380i	0.373318	+	1.14895i
$889$	1.61803	−	1.17557i	0.0542671	−	0.0394274i
$890$	83.2582			2.79082
$891$		0			0
$892$	−0.936083			−0.0313424
$893$	21.6210	−	15.7085i	0.723518	−	0.525667i
$894$	−3.09875	−	9.53696i	−0.103638	−	0.318964i
$895$	15.1590	−	46.6546i	0.506709	−	1.55949i
$896$	−6.54630	−	4.75617i	−0.218697	−	0.158892i
$897$	−4.02263	−	2.92261i	−0.134312	−	0.0975832i
$898$	−0.269514	+	0.829480i	−0.00899381	+	0.0276801i
$899$	2.56570	+	7.89641i	0.0855708	+	0.263360i
$900$	−2.55293	+	1.85481i	−0.0850975	+	0.0618270i
$901$	−13.1833			−0.439201
$902$		0			0
$903$	−6.90833			−0.229895
$904$	34.7136	−	25.2209i	1.15456	−	0.838834i
$905$	12.0207	+	36.9960i	0.399583	+	1.22979i
$906$	−7.45331	+	22.9389i	−0.247620	+	0.762095i
$907$	−6.15302	−	4.47043i	−0.204308	−	0.148438i	0.480927	−	0.876761i	$-0.340300\pi$
$907$	−6.15302	−	4.47043i	−0.204308	−	0.148438i	−0.685234	+	0.728323i	$0.740300\pi$
$908$	−2.82033	−	2.04909i	−0.0935960	−	0.0680015i
$909$	0.683268	−	2.10288i	0.0226626	−	0.0697482i
$910$	0.878971	+	2.70519i	0.0291376	+	0.0896763i
$911$	−11.6903	+	8.49347i	−0.387316	+	0.281401i	−0.764355	−	0.644796i	$-0.776942\pi$
$911$	−11.6903	+	8.49347i	−0.387316	+	0.281401i	0.377039	+	0.926197i	$0.376942\pi$
$912$	12.9083			0.427437
$913$		0			0
$914$	5.36669			0.177514
$915$	−2.64955	+	1.92501i	−0.0875913	+	0.0636388i
$916$	−0.430908	−	1.32620i	−0.0142376	−	0.0438189i
$917$	1.85410	−	5.70634i	0.0612278	−	0.188440i
$918$	−37.2372	−	27.0544i	−1.22901	−	0.892929i
$919$	36.7922	+	26.7311i	1.21366	+	0.881779i	0.995558	−	0.0941464i	$-0.0300122\pi$
$919$	36.7922	+	26.7311i	1.21366	+	0.881779i	0.218106	+	0.975925i	$0.430012\pi$
$920$	21.0672	−	64.8382i	0.694566	−	2.13765i
$921$	10.7220	+	32.9990i	0.353303	+	1.08735i
$922$	19.9288	−	14.4791i	0.656319	−	0.476844i
$923$	0.422205			0.0138971
$924$		0			0
$925$	73.6888			2.42287
$926$	−9.67895	+	7.03217i	−0.318070	+	0.231091i
$927$	4.30649	+	13.2540i	0.141444	+	0.435319i
$928$	−4.35457	+	13.4020i	−0.142946	+	0.439941i
$929$	−12.6476	−	9.18903i	−0.414955	−	0.301482i	0.360650	−	0.932701i	$-0.382555\pi$
$929$	−12.6476	−	9.18903i	−0.414955	−	0.301482i	−0.775605	+	0.631219i	$0.782555\pi$
$930$	−4.95072	−	3.59691i	−0.162341	−	0.117947i
$931$	−0.927051	+	2.85317i	−0.0303829	+	0.0935089i
$932$	−1.68413	−	5.18322i	−0.0551655	−	0.169782i
$933$	−14.3398	+	10.4185i	−0.469464	+	0.341086i
$934$	−52.8167			−1.72821
$935$		0			0
$936$	2.36669			0.0773578
$937$	−19.7355	+	14.3387i	−0.644731	+	0.468425i	−0.861472	−	0.507804i	$-0.830457\pi$
$937$	−19.7355	+	14.3387i	−0.644731	+	0.468425i	0.216741	+	0.976229i	$0.430457\pi$
$938$	−3.83010	−	11.7878i	−0.125057	−	0.384886i
$939$	4.70907	−	14.4930i	0.153675	−	0.472962i
$940$	−7.86767	−	5.71620i	−0.256615	−	0.186442i
$941$	−6.93958	−	5.04190i	−0.226224	−	0.164361i	0.468900	−	0.883251i	$-0.344650\pi$
$941$	−6.93958	−	5.04190i	−0.226224	−	0.164361i	−0.695124	+	0.718890i	$0.744650\pi$
$942$	3.78202	−	11.6398i	0.123225	−	0.379247i
$943$	−13.6337	−	41.9601i	−0.443973	−	1.36641i
$944$	27.5290	−	20.0010i	0.895994	−	0.650978i
$945$	−20.2111			−0.657467
$946$		0			0
$947$	−32.6611			−1.06134			−0.530671	−	0.847578i	$-0.678060\pi$
$947$	−32.6611			−1.06134			−0.530671	+	0.847578i	$0.678060\pi$
$948$	−1.49896	+	1.08906i	−0.0486839	+	0.0353709i
$949$	0.935628	+	2.87957i	0.0303718	+	0.0934747i
$950$	9.66192	−	29.7363i	0.313474	−	0.964774i
$951$	−14.4364	−	10.4887i	−0.468133	−	0.340119i
$952$	15.2972	+	11.1140i	0.495784	+	0.360208i
$953$	9.27909	−	28.5581i	0.300579	−	0.925087i	−0.680711	−	0.732552i	$-0.738329\pi$
$953$	9.27909	−	28.5581i	0.300579	−	0.925087i	0.981290	−	0.192535i	$-0.0616710\pi$
$954$	−1.09702	−	3.37629i	−0.0355174	−	0.109311i
$955$	−15.1196	+	10.9850i	−0.489258	+	0.355467i
$956$	4.03616			0.130539
$957$		0			0
$958$	−19.0639			−0.615927
$959$	12.2319	−	8.88698i	0.394988	−	0.286975i
$960$	−12.7976	−	39.3869i	−0.413040	−	1.27121i
$961$	−9.27051	+	28.5317i	−0.299049	+	0.920377i
$962$	−5.87882	−	4.27121i	−0.189541	−	0.137709i
$963$	20.6636	+	15.0130i	0.665876	+	0.483787i
$964$	−1.73221	+	5.33120i	−0.0557907	+	0.171706i
$965$	−25.7591	−	79.2784i	−0.829216	−	2.55206i
$966$	8.65424	−	6.28767i	0.278445	−	0.202302i
$967$	22.4861			0.723105			0.361552	−	0.932352i	$-0.382247\pi$
$967$	22.4861			0.723105			0.361552	+	0.932352i	$0.382247\pi$
$968$		0			0
$969$	−24.6333			−0.791336
$970$	−13.7016	+	9.95478i	−0.439931	+	0.319629i
$971$	−15.3375	−	47.2041i	−0.492205	−	1.51485i	−0.821268	−	0.570543i	$-0.806733\pi$
$971$	−15.3375	−	47.2041i	−0.492205	−	1.51485i	0.329063	−	0.944308i	$-0.393267\pi$
$972$	−1.15966	+	3.56907i	−0.0371961	+	0.114478i
$973$	11.6454	+	8.46084i	0.373333	+	0.271242i
$974$	19.8321	+	14.4089i	0.635463	+	0.461691i
$975$	−1.95026	+	6.00229i	−0.0624584	+	0.192227i
$976$	0.711597	+	2.19007i	0.0227777	+	0.0701024i
$977$	−3.21361	+	2.33483i	−0.102813	+	0.0746977i	−0.638004	−	0.770033i	$-0.720240\pi$
$977$	−3.21361	+	2.33483i	−0.102813	+	0.0746977i	0.535191	+	0.844731i	$0.320240\pi$
$978$	31.9361			1.02120
$979$		0			0
$980$	1.09167			0.0348722
$981$	−8.43174	+	6.12602i	−0.269205	+	0.195589i
$982$	6.56317	+	20.1994i	0.209439	+	0.644587i
$983$	−12.8937	+	39.6828i	−0.411246	+	1.26569i	0.504320	+	0.863517i	$0.331743\pi$
$983$	−12.8937	+	39.6828i	−0.411246	+	1.26569i	−0.915566	+	0.402168i	$0.868257\pi$
$984$	−22.1333	−	16.0808i	−0.705584	−	0.512637i
$985$	−9.90144	−	7.19382i	−0.315486	−	0.229214i
$986$	−21.0672	+	64.8382i	−0.670917	+	2.06487i
$987$	−3.58631	−	11.0375i	−0.114154	−	0.351329i
$988$	0.444991	−	0.323305i	0.0141570	−	0.0102857i
$989$	−33.4222			−1.06276
$990$		0			0
$991$	−11.2750			−0.358163			−0.179081	−	0.983834i	$-0.557313\pi$
$991$	−11.2750			−0.358163			−0.179081	+	0.983834i	$0.557313\pi$
$992$	1.37308	−	0.997603i	0.0435954	−	0.0316739i
$993$	0.878971	+	2.70519i	0.0278933	+	0.0858468i
$994$	−0.280688	+	0.863870i	−0.00890290	+	0.0274003i
$995$	−27.4841	−	19.9684i	−0.871305	−	0.633040i
$996$	0.957347	+	0.695553i	0.0303347	+	0.0220395i
$997$	15.2354	−	46.8897i	0.482510	−	1.48501i	−0.353045	−	0.935606i	$-0.614854\pi$
$997$	15.2354	−	46.8897i	0.482510	−	1.48501i	0.835555	−	0.549406i	$-0.185146\pi$
$998$	3.18373	+	9.79852i	0.100779	+	0.310167i
$999$	41.7722	−	30.3493i	1.32161	−	0.960209i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.o.729.2		8
11.2	odd	10		847.2.a.e.1.2	✓	2
11.3	even	5	inner	847.2.f.o.148.1		8
11.4	even	5	inner	847.2.f.o.323.2		8
11.5	even	5	inner	847.2.f.o.372.1		8
11.6	odd	10		847.2.f.r.372.2		8
11.7	odd	10		847.2.f.r.323.1		8
11.8	odd	10		847.2.f.r.148.2		8
11.9	even	5		847.2.a.g.1.1	yes	2
11.10	odd	2		847.2.f.r.729.1		8
33.2	even	10		7623.2.a.bs.1.1		2
33.20	odd	10		7623.2.a.bc.1.2		2
77.13	even	10		5929.2.a.k.1.2		2
77.20	odd	10		5929.2.a.p.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.e.1.2	✓	2	11.2	odd	10
847.2.a.g.1.1	yes	2	11.9	even	5
847.2.f.o.148.1		8	11.3	even	5	inner
847.2.f.o.323.2		8	11.4	even	5	inner
847.2.f.o.372.1		8	11.5	even	5	inner
847.2.f.o.729.2		8	1.1	even	1	trivial
847.2.f.r.148.2		8	11.8	odd	10
847.2.f.r.323.1		8	11.7	odd	10
847.2.f.r.372.2		8	11.6	odd	10
847.2.f.r.729.1		8	11.10	odd	2
5929.2.a.k.1.2		2	77.13	even	10
5929.2.a.p.1.1		2	77.20	odd	10
7623.2.a.bc.1.2		2	33.20	odd	10
7623.2.a.bs.1.1		2	33.2	even	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)

\(f(q)\)	\(=\)	\(q+(1.05397 - 0.765752i) q^{2} +(0.402580 + 1.23901i) q^{3} +(-0.0935628 + 0.287957i) q^{4} +(2.91695 + 2.11929i) q^{5} +(1.37308 + 0.997603i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.927051 + 2.85317i) q^{8} +(1.05397 - 0.765752i) q^{9} +O(q^{10})\)	\(q+(1.05397 - 0.765752i) q^{2} +(0.402580 + 1.23901i) q^{3} +(-0.0935628 + 0.287957i) q^{4} +(2.91695 + 2.11929i) q^{5} +(1.37308 + 0.997603i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.927051 + 2.85317i) q^{8} +(1.05397 - 0.765752i) q^{9} +4.69722 q^{10} -0.394449 q^{12} +(0.489901 - 0.355934i) q^{13} +(0.402580 + 1.23901i) q^{14} +(-1.45152 + 4.46733i) q^{15} +(2.67200 + 1.94132i) q^{16} +(-5.09905 - 3.70468i) q^{17} +(0.524471 - 1.61416i) q^{18} +(-0.927051 - 2.85317i) q^{19} +(-0.883182 + 0.641669i) q^{20} -1.30278 q^{21} -6.30278 q^{23} +(-3.16190 + 2.29726i) q^{24} +(2.47214 + 7.60845i) q^{25} +(0.243783 - 0.750286i) q^{26} +(4.53499 + 3.29486i) q^{27} +(-0.244951 - 0.177967i) q^{28} +(2.56570 - 7.89641i) q^{29} +(1.89101 + 5.81992i) q^{30} +(-0.809017 + 0.587785i) q^{31} -1.69722 q^{32} -8.21110 q^{34} +(-2.91695 + 2.11929i) q^{35} +(0.121891 + 0.375143i) q^{36} +(2.84639 - 8.76028i) q^{37} +(-3.16190 - 2.29726i) q^{38} +(0.638231 + 0.463702i) q^{39} +(-3.34253 + 10.2872i) q^{40} +(2.16312 + 6.65740i) q^{41} +(-1.37308 + 0.997603i) q^{42} +5.30278 q^{43} +4.69722 q^{45} +(-6.64292 + 4.82636i) q^{46} +(2.75282 + 8.47232i) q^{47} +(-1.32963 + 4.09218i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(8.43174 + 6.12602i) q^{50} +(2.53737 - 7.80922i) q^{51} +(0.0566571 + 0.174373i) q^{52} +(1.69220 - 1.22945i) q^{53} +7.30278 q^{54} -3.00000 q^{56} +(3.16190 - 2.29726i) q^{57} +(-3.34253 - 10.2872i) q^{58} +(3.18373 - 9.79852i) q^{59} +(-1.15059 - 0.835951i) q^{60} +(0.564066 + 0.409818i) q^{61} +(-0.402580 + 1.23901i) q^{62} +(0.402580 + 1.23901i) q^{63} +(-7.13282 + 5.18230i) q^{64} +2.18335 q^{65} -9.51388 q^{67} +(1.54387 - 1.12169i) q^{68} +(-2.53737 - 7.80922i) q^{69} +(-1.45152 + 4.46733i) q^{70} +(0.564066 + 0.409818i) q^{71} +(3.16190 + 2.29726i) q^{72} +(-1.54508 + 4.75528i) q^{73} +(-3.70820 - 11.4127i) q^{74} +(-8.43174 + 6.12602i) q^{75} +0.908327 q^{76} +1.02776 q^{78} +(3.80013 - 2.76096i) q^{79} +(3.67988 + 11.3255i) q^{80} +(-1.04894 + 3.22831i) q^{81} +(7.37777 + 5.36027i) q^{82} +(-2.42705 - 1.76336i) q^{83} +(0.121891 - 0.375143i) q^{84} +(-7.02241 - 21.6127i) q^{85} +(5.58895 - 4.06061i) q^{86} +10.8167 q^{87} +17.7250 q^{89} +(4.95072 - 3.59691i) q^{90} +(0.187126 + 0.575913i) q^{91} +(0.589705 - 1.81493i) q^{92} +(-1.05397 - 0.765752i) q^{93} +(9.38909 + 6.82157i) q^{94} +(3.34253 - 10.2872i) q^{95} +(-0.683268 - 2.10288i) q^{96} +(-2.91695 + 2.11929i) q^{97} -1.30278 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + q^{3} - 3 q^{4} + 7 q^{6} + 2 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) \) 8 * q - q^2 + q^3 - 3 * q^4 + 7 * q^6 + 2 * q^7 - 6 * q^8 - q^9	\( 8 q - q^{2} + q^{3} - 3 q^{4} + 7 q^{6} + 2 q^{7} - 6 q^{8} - q^{9} + 52 q^{10} - 32 q^{12} - 6 q^{13} + q^{14} + 13 q^{15} + 3 q^{16} - 9 q^{17} - 7 q^{18} + 6 q^{19} - 13 q^{20} + 4 q^{21} - 36 q^{23} + 3 q^{24} - 16 q^{25} - 16 q^{26} + 4 q^{27} + 3 q^{28} - 13 q^{29} + 13 q^{30} - 2 q^{31} - 28 q^{32} - 8 q^{34} - 8 q^{36} - 4 q^{37} + 3 q^{38} + 16 q^{39} - 14 q^{41} - 7 q^{42} + 28 q^{43} + 52 q^{45} - 2 q^{46} - 7 q^{47} + 5 q^{48} - 2 q^{49} - 8 q^{50} - 2 q^{51} - 22 q^{52} + 15 q^{53} + 44 q^{54} - 24 q^{56} - 3 q^{57} - 17 q^{59} + 26 q^{60} + 5 q^{61} - q^{62} + q^{63} + 4 q^{64} + 104 q^{65} - 4 q^{67} - 7 q^{68} + 2 q^{69} + 13 q^{70} + 5 q^{71} - 3 q^{72} + 10 q^{73} + 24 q^{74} + 8 q^{75} - 36 q^{76} - 136 q^{78} + 13 q^{79} - 13 q^{80} + 14 q^{81} - 7 q^{82} - 6 q^{83} - 8 q^{84} + 13 q^{85} + 3 q^{86} + 12 q^{89} - 13 q^{90} + 6 q^{91} + 7 q^{92} + q^{93} + 16 q^{94} - 10 q^{96} + 4 q^{98}+O(q^{100}) \) 8 * q - q^2 + q^3 - 3 * q^4 + 7 * q^6 + 2 * q^7 - 6 * q^8 - q^9 + 52 * q^10 - 32 * q^12 - 6 * q^13 + q^14 + 13 * q^15 + 3 * q^16 - 9 * q^17 - 7 * q^18 + 6 * q^19 - 13 * q^20 + 4 * q^21 - 36 * q^23 + 3 * q^24 - 16 * q^25 - 16 * q^26 + 4 * q^27 + 3 * q^28 - 13 * q^29 + 13 * q^30 - 2 * q^31 - 28 * q^32 - 8 * q^34 - 8 * q^36 - 4 * q^37 + 3 * q^38 + 16 * q^39 - 14 * q^41 - 7 * q^42 + 28 * q^43 + 52 * q^45 - 2 * q^46 - 7 * q^47 + 5 * q^48 - 2 * q^49 - 8 * q^50 - 2 * q^51 - 22 * q^52 + 15 * q^53 + 44 * q^54 - 24 * q^56 - 3 * q^57 - 17 * q^59 + 26 * q^60 + 5 * q^61 - q^62 + q^63 + 4 * q^64 + 104 * q^65 - 4 * q^67 - 7 * q^68 + 2 * q^69 + 13 * q^70 + 5 * q^71 - 3 * q^72 + 10 * q^73 + 24 * q^74 + 8 * q^75 - 36 * q^76 - 136 * q^78 + 13 * q^79 - 13 * q^80 + 14 * q^81 - 7 * q^82 - 6 * q^83 - 8 * q^84 + 13 * q^85 + 3 * q^86 + 12 * q^89 - 13 * q^90 + 6 * q^91 + 7 * q^92 + q^93 + 16 * q^94 - 10 * q^96 + 4 * q^98

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