LMFDB - Embedded newform 686.2.g.b.459.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [686,2,Mod(67,686)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(686, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("686.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 686 = 2 \cdot 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	686.g (of order $21$, degree $12$, 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:	$5.47773757866$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 98)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			459.2
Character	$\chi$	$=$	686.459
Dual form			686.2.g.b.275.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0747301 - 0.997204i) q^{2} +(1.08331 + 0.334156i) q^{3} +(-0.988831 + 0.149042i) q^{4} +(-2.80532 + 2.60296i) q^{5} +(0.252266 - 1.10525i) q^{6} +(0.222521 + 0.974928i) q^{8} +(-1.41682 - 0.965972i) q^{9} +O(q^{10})$	\(q+(-0.0747301 - 0.997204i) q^{2} +(1.08331 + 0.334156i) q^{3} +(-0.988831 + 0.149042i) q^{4} +(-2.80532 + 2.60296i) q^{5} +(0.252266 - 1.10525i) q^{6} +(0.222521 + 0.974928i) q^{8} +(-1.41682 - 0.965972i) q^{9} +(2.80532 + 2.60296i) q^{10} +(2.00403 - 1.36632i) q^{11} +(-1.12101 - 0.168965i) q^{12} +(-3.52337 - 1.69676i) q^{13} +(-3.90882 + 1.88239i) q^{15} +(0.955573 - 0.294755i) q^{16} +(-1.90797 - 4.86142i) q^{17} +(-0.857392 + 1.48505i) q^{18} +(-1.60059 - 2.77231i) q^{19} +(2.38604 - 2.99200i) q^{20} +(-1.51226 - 1.89632i) q^{22} +(-1.50100 + 3.82450i) q^{23} +(-0.0847196 + 1.13050i) q^{24} +(0.720789 - 9.61826i) q^{25} +(-1.42872 + 3.64031i) q^{26} +(-3.33257 - 4.17891i) q^{27} +(-0.332203 + 0.416569i) q^{29} +(2.16923 + 3.75722i) q^{30} +(-3.70735 + 6.42133i) q^{31} +(-0.365341 - 0.930874i) q^{32} +(2.62755 - 0.810490i) q^{33} +(-4.70525 + 2.26593i) q^{34} +(1.54497 + 0.744017i) q^{36} +(-11.5026 - 1.73374i) q^{37} +(-2.64494 + 1.80329i) q^{38} +(-3.24991 - 3.01547i) q^{39} +(-3.16194 - 2.15577i) q^{40} +(-0.288200 - 1.26269i) q^{41} +(0.0321723 - 0.140956i) q^{43} +(-1.77801 + 1.64975i) q^{44} +(6.48902 - 0.978063i) q^{45} +(3.92597 + 1.21100i) q^{46} +(-0.221635 - 2.95751i) q^{47} +1.13367 q^{48} -9.64523 q^{50} +(-0.442442 - 5.90398i) q^{51} +(3.73690 + 1.15268i) q^{52} +(5.40760 - 0.815064i) q^{53} +(-3.91818 + 3.63554i) q^{54} +(-2.06546 + 9.04938i) q^{55} +(-0.807551 - 3.53811i) q^{57} +(0.440230 + 0.300143i) q^{58} +(6.24369 + 5.79330i) q^{59} +(3.58461 - 2.44395i) q^{60} +(2.28706 + 0.344718i) q^{61} +(6.68042 + 3.21712i) q^{62} +(-0.900969 + 0.433884i) q^{64} +(14.3008 - 4.41121i) q^{65} +(-1.00458 - 2.55963i) q^{66} +(-3.95589 + 6.85180i) q^{67} +(2.61122 + 4.52276i) q^{68} +(-2.90403 + 3.64154i) q^{69} +(5.76742 + 7.23212i) q^{71} +(0.626481 - 1.59625i) q^{72} +(0.296625 - 3.95819i) q^{73} +(-0.869300 + 11.6000i) q^{74} +(3.99484 - 10.1787i) q^{75} +(1.99591 + 2.50279i) q^{76} +(-2.76417 + 3.46616i) q^{78} +(-6.52866 - 11.3080i) q^{79} +(-1.91345 + 3.31420i) q^{80} +(-0.334348 - 0.851905i) q^{81} +(-1.23762 + 0.381755i) q^{82} +(0.622177 - 0.299625i) q^{83} +(18.0066 + 8.67150i) q^{85} +(-0.142966 - 0.0215487i) q^{86} +(-0.499077 + 0.340265i) q^{87} +(1.77801 + 1.64975i) q^{88} +(2.01773 + 1.37567i) q^{89} +(-1.46025 - 6.39779i) q^{90} +(0.914228 - 4.00549i) q^{92} +(-6.16193 + 5.71744i) q^{93} +(-2.93268 + 0.442030i) q^{94} +(11.7064 + 3.61094i) q^{95} +(-0.0847196 - 1.13050i) q^{96} +9.70001 q^{97} -4.15918 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} - 7 q^{3} + 2 q^{4} + 7 q^{6} + 4 q^{8} - 33 q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 - 7 * q^3 + 2 * q^4 + 7 * q^6 + 4 * q^8 - 33 * q^9	$ 24 q - 2 q^{2} - 7 q^{3} + 2 q^{4} + 7 q^{6} + 4 q^{8} - 33 q^{9} - 7 q^{11} - 14 q^{13} - 7 q^{15} + 2 q^{16} + 7 q^{17} + 5 q^{18} + 7 q^{20} - 7 q^{22} - 21 q^{23} + 4 q^{25} + 7 q^{26} + 35 q^{27} - 11 q^{29} - 28 q^{31} - 2 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{36} - 24 q^{37} + 7 q^{38} - 40 q^{39} - 14 q^{40} - 28 q^{41} + 10 q^{43} + 21 q^{44} - 7 q^{45} + 42 q^{46} + 70 q^{47} + 14 q^{48} + 8 q^{50} + 60 q^{51} + 7 q^{52} + 26 q^{53} - 63 q^{54} - 56 q^{55} - 33 q^{57} - 30 q^{58} + 7 q^{59} + 14 q^{60} - 14 q^{61} - 28 q^{62} - 4 q^{64} + 21 q^{66} - 36 q^{67} + 14 q^{68} + 35 q^{69} - 2 q^{72} + 7 q^{73} - 11 q^{74} + 28 q^{75} - 24 q^{78} - 26 q^{79} + 55 q^{81} - 14 q^{82} + 7 q^{83} + 49 q^{85} - 16 q^{86} - 35 q^{87} - 21 q^{88} + 56 q^{89} + 21 q^{90} + 21 q^{92} + 72 q^{93} + 35 q^{94} - 14 q^{95} + 126 q^{97} - 14 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 - 7 * q^3 + 2 * q^4 + 7 * q^6 + 4 * q^8 - 33 * q^9 - 7 * q^11 - 14 * q^13 - 7 * q^15 + 2 * q^16 + 7 * q^17 + 5 * q^18 + 7 * q^20 - 7 * q^22 - 21 * q^23 + 4 * q^25 + 7 * q^26 + 35 * q^27 - 11 * q^29 - 28 * q^31 - 2 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^36 - 24 * q^37 + 7 * q^38 - 40 * q^39 - 14 * q^40 - 28 * q^41 + 10 * q^43 + 21 * q^44 - 7 * q^45 + 42 * q^46 + 70 * q^47 + 14 * q^48 + 8 * q^50 + 60 * q^51 + 7 * q^52 + 26 * q^53 - 63 * q^54 - 56 * q^55 - 33 * q^57 - 30 * q^58 + 7 * q^59 + 14 * q^60 - 14 * q^61 - 28 * q^62 - 4 * q^64 + 21 * q^66 - 36 * q^67 + 14 * q^68 + 35 * q^69 - 2 * q^72 + 7 * q^73 - 11 * q^74 + 28 * q^75 - 24 * q^78 - 26 * q^79 + 55 * q^81 - 14 * q^82 + 7 * q^83 + 49 * q^85 - 16 * q^86 - 35 * q^87 - 21 * q^88 + 56 * q^89 + 21 * q^90 + 21 * q^92 + 72 * q^93 + 35 * q^94 - 14 * q^95 + 126 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/686\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{21}\right)$

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 $

$2$	−0.0747301	−	0.997204i	−0.0528422	−	0.705130i
$2$	−0.0747301	−	0.997204i	−0.0528422	−	0.705130i
$3$	1.08331	+	0.334156i	0.625448	+	0.192925i	0.591248	−	0.806490i	$-0.298635\pi$
$3$	1.08331	+	0.334156i	0.625448	+	0.192925i	0.0342001	+	0.999415i	$0.489112\pi$
$4$	−0.988831	+	0.149042i	−0.494415	+	0.0745211i
$5$	−2.80532	+	2.60296i	−1.25458	+	1.16408i	−0.275344	+	0.961346i	$0.588792\pi$
$5$	−2.80532	+	2.60296i	−1.25458	+	1.16408i	−0.979234	+	0.202733i	$0.935018\pi$
$6$	0.252266	−	1.10525i	0.102987	−	0.451217i
$7$		0			0
$7$		0			0
$8$	0.222521	+	0.974928i	0.0786730	+	0.344689i
$9$	−1.41682	−	0.965972i	−0.472274	−	0.321991i
$10$	2.80532	+	2.60296i	0.887121	+	0.823128i
$11$	2.00403	−	1.36632i	0.604237	−	0.411962i	−0.222192	−	0.975003i	$-0.571321\pi$
$11$	2.00403	−	1.36632i	0.604237	−	0.411962i	0.826429	+	0.563041i	$0.190369\pi$
$12$	−1.12101	−	0.168965i	−0.323608	−	0.0487761i
$13$	−3.52337	−	1.69676i	−0.977206	−	0.470597i	−0.124063	−	0.992274i	$-0.539592\pi$
$13$	−3.52337	−	1.69676i	−0.977206	−	0.470597i	−0.853143	+	0.521677i	$0.825307\pi$
$14$		0			0
$15$	−3.90882	+	1.88239i	−1.00925	+	0.486031i
$16$	0.955573	−	0.294755i	0.238893	−	0.0736888i
$17$	−1.90797	−	4.86142i	−0.462750	−	1.17907i	−0.951775	−	0.306798i	$-0.900742\pi$
$17$	−1.90797	−	4.86142i	−0.462750	−	1.17907i	0.489024	−	0.872270i	$-0.337353\pi$
$18$	−0.857392	+	1.48505i	−0.202089	+	0.350029i
$19$	−1.60059	−	2.77231i	−0.367201	−	0.636011i	0.621926	−	0.783076i	$-0.286351\pi$
$19$	−1.60059	−	2.77231i	−0.367201	−	0.636011i	−0.989127	+	0.147065i	$0.953017\pi$
$20$	2.38604	−	2.99200i	0.533534	−	0.669031i
$21$		0			0
$22$	−1.51226	−	1.89632i	−0.322416	−	0.404297i
$23$	−1.50100	+	3.82450i	−0.312981	+	0.797463i	0.684663	+	0.728860i	$0.259949\pi$
$23$	−1.50100	+	3.82450i	−0.312981	+	0.797463i	−0.997644	+	0.0686030i	$0.978146\pi$
$24$	−0.0847196	+	1.13050i	−0.0172933	+	0.230763i
$25$	0.720789	−	9.61826i	0.144158	−	1.92365i
$26$	−1.42872	+	3.64031i	−0.280195	+	0.713924i
$27$	−3.33257	−	4.17891i	−0.641353	−	0.804232i
$28$		0			0
$29$	−0.332203	+	0.416569i	−0.0616885	+	0.0773549i	−0.811718	−	0.584049i	$-0.801468\pi$
$29$	−0.332203	+	0.416569i	−0.0616885	+	0.0773549i	0.750030	+	0.661404i	$0.230039\pi$
$30$	2.16923	+	3.75722i	0.396046	+	0.685972i
$31$	−3.70735	+	6.42133i	−0.665861	+	1.15330i	0.313191	+	0.949690i	$0.398602\pi$
$31$	−3.70735	+	6.42133i	−0.665861	+	1.15330i	−0.979051	+	0.203614i	$0.934731\pi$
$32$	−0.365341	−	0.930874i	−0.0645838	−	0.164557i
$33$	2.62755	−	0.810490i	0.457397	−	0.141088i
$34$	−4.70525	+	2.26593i	−0.806943	+	0.388604i
$35$		0			0
$36$	1.54497	+	0.744017i	0.257494	+	0.124003i
$37$	−11.5026	−	1.73374i	−1.89102	−	0.285025i	−0.901876	−	0.431995i	$-0.857810\pi$
$37$	−11.5026	−	1.73374i	−1.89102	−	0.285025i	−0.989141	+	0.146970i	$0.953048\pi$
$38$	−2.64494	+	1.80329i	−0.429066	+	0.292532i
$39$	−3.24991	−	3.01547i	−0.520401	−	0.482862i
$40$	−3.16194	−	2.15577i	−0.499947	−	0.340858i
$41$	−0.288200	−	1.26269i	−0.0450093	−	0.197199i	0.947425	−	0.319979i	$-0.103676\pi$
$41$	−0.288200	−	1.26269i	−0.0450093	−	0.197199i	−0.992434	+	0.122781i	$0.960819\pi$
$42$		0			0
$43$	0.0321723	−	0.140956i	0.00490624	−	0.0214956i	−0.972416	−	0.233255i	$-0.925062\pi$
$43$	0.0321723	−	0.140956i	0.00490624	−	0.0214956i	0.977322	+	0.211760i	$0.0679194\pi$
$44$	−1.77801	+	1.64975i	−0.268044	+	0.248709i
$45$	6.48902	−	0.978063i	0.967327	−	0.145801i
$46$	3.92597	+	1.21100i	0.578853	+	0.178553i
$47$	−0.221635	−	2.95751i	−0.0323288	−	0.431397i	−0.989761	−	0.142738i	$-0.954409\pi$
$47$	−0.221635	−	2.95751i	−0.0323288	−	0.431397i	0.957432	−	0.288660i	$-0.0932096\pi$
$48$	1.13367			0.163632
$49$		0			0
$50$	−9.64523			−1.36404
$51$	−0.442442	−	5.90398i	−0.0619543	−	0.826723i
$52$	3.73690	+	1.15268i	0.518215	+	0.159848i
$53$	5.40760	−	0.815064i	0.742791	−	0.111958i	0.233265	−	0.972413i	$-0.425059\pi$
$53$	5.40760	−	0.815064i	0.742791	−	0.111958i	0.509526	+	0.860456i	$0.329821\pi$
$54$	−3.91818	+	3.63554i	−0.533197	+	0.494735i
$55$	−2.06546	+	9.04938i	−0.278507	+	1.22022i
$56$		0			0
$57$	−0.807551	−	3.53811i	−0.106963	−	0.468634i
$58$	0.440230	+	0.300143i	0.0578050	+	0.0394108i
$59$	6.24369	+	5.79330i	0.812860	+	0.754224i	0.972488	−	0.232954i	$-0.0748390\pi$
$59$	6.24369	+	5.79330i	0.812860	+	0.754224i	−0.159628	+	0.987177i	$0.551030\pi$
$60$	3.58461	−	2.44395i	0.462771	−	0.315512i
$61$	2.28706	+	0.344718i	0.292827	+	0.0441366i	0.293813	−	0.955863i	$-0.405076\pi$
$61$	2.28706	+	0.344718i	0.292827	+	0.0441366i	−0.000985677		1.00000i	$0.500314\pi$
$62$	6.68042	+	3.21712i	0.848414	+	0.408575i
$63$		0			0
$64$	−0.900969	+	0.433884i	−0.112621	+	0.0542355i
$65$	14.3008	−	4.41121i	1.77379	−	0.547143i
$66$	−1.00458	−	2.55963i	−0.123655	−	0.315069i
$67$	−3.95589	+	6.85180i	−0.483288	+	0.837080i	−0.999816	−	0.0191906i	$-0.993891\pi$
$67$	−3.95589	+	6.85180i	−0.483288	+	0.837080i	0.516527	+	0.856271i	$0.327224\pi$
$68$	2.61122	+	4.52276i	0.316656	+	0.548465i
$69$	−2.90403	+	3.64154i	−0.349604	+	0.438390i
$70$		0			0
$71$	5.76742	+	7.23212i	0.684467	+	0.858295i	0.995757	−	0.0920204i	$-0.0293325\pi$
$71$	5.76742	+	7.23212i	0.684467	+	0.858295i	−0.311290	+	0.950315i	$0.600761\pi$
$72$	0.626481	−	1.59625i	0.0738315	−	0.188120i
$73$	0.296625	−	3.95819i	0.0347173	−	0.463271i	−0.952569	−	0.304321i	$-0.901570\pi$
$73$	0.296625	−	3.95819i	0.0347173	−	0.463271i	0.987287	−	0.158949i	$-0.0508106\pi$
$74$	−0.869300	+	11.6000i	−0.101054	+	1.34847i
$75$	3.99484	−	10.1787i	0.461284	−	1.17533i
$76$	1.99591	+	2.50279i	0.228946	+	0.287089i
$77$		0			0
$78$	−2.76417	+	3.46616i	−0.312981	+	0.392466i
$79$	−6.52866	−	11.3080i	−0.734532	−	1.27225i	−0.954928	−	0.296836i	$-0.904068\pi$
$79$	−6.52866	−	11.3080i	−0.734532	−	1.27225i	0.220396	−	0.975410i	$-0.429265\pi$
$80$	−1.91345	+	3.31420i	−0.213931	+	0.370539i
$81$	−0.334348	−	0.851905i	−0.0371498	−	0.0946561i
$82$	−1.23762	+	0.381755i	−0.136672	+	0.0421578i
$83$	0.622177	−	0.299625i	0.0682928	−	0.0328881i	−0.399426	−	0.916766i	$-0.630790\pi$
$83$	0.622177	−	0.299625i	0.0682928	−	0.0328881i	0.467718	+	0.883878i	$0.345076\pi$
$84$		0			0
$85$	18.0066	+	8.67150i	1.95309	+	0.940556i
$86$	−0.142966	−	0.0215487i	−0.0154165	−	0.00232366i
$87$	−0.499077	+	0.340265i	−0.0535067	+	0.0364802i
$88$	1.77801	+	1.64975i	0.189536	+	0.175864i
$89$	2.01773	+	1.37567i	0.213879	+	0.145820i	0.665521	−	0.746379i	$-0.268209\pi$
$89$	2.01773	+	1.37567i	0.213879	+	0.145820i	−0.451642	+	0.892199i	$0.649162\pi$
$90$	−1.46025	−	6.39779i	−0.153924	−	0.674386i
$91$		0			0
$92$	0.914228	−	4.00549i	0.0953148	−	0.417602i
$93$	−6.16193	+	5.71744i	−0.638963	+	0.592871i
$94$	−2.93268	+	0.442030i	−0.302483	+	0.0455919i
$95$	11.7064	+	3.61094i	1.20105	+	0.370475i
$96$	−0.0847196	−	1.13050i	−0.00864665	−	0.115382i
$97$	9.70001			0.984887			0.492443	−	0.870344i	$-0.336104\pi$
$97$	9.70001			0.984887			0.492443	+	0.870344i	$0.336104\pi$
$98$		0			0
$99$	−4.15918			−0.418013
$100$	0.720789	+	9.61826i	0.0720789	+	0.961826i
$101$	−14.0905	−	4.34636i	−1.40206	−	0.432479i	−0.500728	−	0.865605i	$-0.666934\pi$
$101$	−14.0905	−	4.34636i	−1.40206	−	0.432479i	−0.901333	+	0.433126i	$0.857410\pi$
$102$	−5.85441	+	0.882410i	−0.579673	+	0.0873716i
$103$	−5.00856	+	4.64726i	−0.493508	+	0.457908i	−0.887234	−	0.461319i	$-0.847376\pi$
$103$	−5.00856	+	4.64726i	−0.493508	+	0.457908i	0.393726	+	0.919228i	$0.371186\pi$
$104$	0.870199	−	3.81259i	0.0853301	−	0.373855i
$105$		0			0
$106$	−1.21690	−	5.33157i	−0.118195	−	0.517847i
$107$	3.92182	+	2.67385i	0.379137	+	0.258491i	0.737861	−	0.674952i	$-0.235836\pi$
$107$	3.92182	+	2.67385i	0.379137	+	0.258491i	−0.358724	+	0.933444i	$0.616788\pi$
$108$	3.91818	+	3.63554i	0.377027	+	0.349830i
$109$	−11.6645	+	7.95271i	−1.11725	+	0.761731i	−0.973683	−	0.227909i	$-0.926811\pi$
$109$	−11.6645	+	7.95271i	−1.11725	+	0.761731i	−0.143572	+	0.989640i	$0.545859\pi$
$110$	9.17843	+	1.38343i	0.875129	+	0.131904i
$111$	−11.8815	−	5.72184i	−1.12774	−	0.543093i
$112$		0			0
$113$	−10.3752	+	4.99643i	−0.976017	+	0.470025i	−0.852733	−	0.522347i	$-0.825057\pi$
$113$	−10.3752	+	4.99643i	−0.976017	+	0.470025i	−0.123284	+	0.992371i	$0.539342\pi$
$114$	−3.46787	+	1.06970i	−0.324796	+	0.100186i
$115$	−5.74421	−	14.6360i	−0.535650	−	1.36481i
$116$	0.266406	−	0.461428i	0.0247352	−	0.0428426i
$117$	3.35295	+	5.80748i	0.309980	+	0.536902i
$118$	5.31051	−	6.65917i	0.488872	−	0.613026i
$119$		0			0
$120$	−2.70499	−	3.39195i	−0.246931	−	0.309641i
$121$	−1.86946	+	4.76331i	−0.169951	+	0.433028i
$122$	0.172842	−	2.30642i	0.0156484	−	0.208814i
$123$	0.109725	−	1.46418i	0.00989360	−	0.132021i
$124$	2.70890	−	6.90216i	0.243266	−	0.619832i
$125$	11.0837	+	13.8985i	0.991357	+	1.24312i
$126$		0			0
$127$	7.39823	−	9.27709i	0.656487	−	0.823209i	−0.336469	−	0.941695i	$-0.609233\pi$
$127$	7.39823	−	9.27709i	0.656487	−	0.823209i	0.992956	+	0.118486i	$0.0378040\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	0.0819539	−	0.141948i	0.00721564	−	0.0124979i
$130$	−5.46757	−	13.9311i	−0.479538	−	1.22184i
$131$	5.02761	−	1.55081i	0.439265	−	0.135495i	−0.0672316	−	0.997737i	$-0.521417\pi$
$131$	5.02761	−	1.55081i	0.439265	−	0.135495i	0.506496	+	0.862242i	$0.330940\pi$
$132$	−2.47740	+	1.19305i	−0.215630	+	0.103842i
$133$		0			0
$134$	7.12826	+	3.43279i	0.615788	+	0.296548i
$135$	20.2265	+	3.04865i	1.74082	+	0.262386i
$136$	4.31498	−	2.94190i	0.370006	−	0.252266i
$137$	−6.20104	−	5.75373i	−0.529791	−	0.491574i	0.369316	−	0.929304i	$-0.379592\pi$
$137$	−6.20104	−	5.75373i	−0.529791	−	0.491574i	−0.899107	+	0.437730i	$0.855783\pi$
$138$	3.84837	+	2.62378i	0.327595	+	0.223351i
$139$	0.0297204	+	0.130214i	0.00252086	+	0.0110446i	0.976173	−	0.216995i	$-0.0696256\pi$
$139$	0.0297204	+	0.130214i	0.00252086	+	0.0110446i	−0.973652	+	0.228040i	$0.926768\pi$
$140$		0			0
$141$	0.748172	−	3.27796i	0.0630075	−	0.276054i
$142$	6.78090	−	6.29175i	0.569040	−	0.527992i
$143$	−9.37925	+	1.41369i	−0.784332	+	0.118219i
$144$	−1.63860	−	0.505441i	−0.136550	−	0.0421201i
$145$	−0.152376	−	2.03332i	−0.0126542	−	0.168858i
$146$	−3.96928			−0.328500
$147$		0			0
$148$	11.6325			0.956188
$149$	0.361990	+	4.83042i	0.0296554	+	0.395723i	0.992205	+	0.124617i	$0.0397703\pi$
$149$	0.361990	+	4.83042i	0.0296554	+	0.395723i	−0.962550	+	0.271106i	$0.912611\pi$
$150$	−10.4488	−	3.22301i	−0.853137	−	0.263158i
$151$	7.99425	−	1.20494i	0.650563	−	0.0980565i	0.184534	−	0.982826i	$-0.440922\pi$
$151$	7.99425	−	1.20494i	0.650563	−	0.0980565i	0.466029	+	0.884770i	$0.345684\pi$
$152$	2.34663	−	2.17736i	0.190337	−	0.176607i
$153$	−1.99275	+	8.73081i	−0.161104	+	0.705844i
$154$		0			0
$155$	−6.31412	−	27.6640i	−0.507163	−	2.22202i
$156$	3.66304	+	2.49742i	0.293278	+	0.199953i
$157$	0.867135	+	0.804584i	0.0692049	+	0.0642128i	0.714017	−	0.700128i	$-0.246874\pi$
$157$	0.867135	+	0.804584i	0.0692049	+	0.0642128i	−0.644812	+	0.764341i	$0.723064\pi$
$158$	−10.7885	+	7.35545i	−0.858284	+	0.585168i
$159$	6.13045	+	0.924017i	0.486176	+	0.0732793i
$160$	3.44793	+	1.66043i	0.272582	+	0.131269i
$161$		0			0
$162$	−0.824537	+	0.397076i	−0.0647818	+	0.0311973i
$163$	−14.1088	+	4.35197i	−1.10508	+	0.340873i	−0.793024	−	0.609190i	$-0.791495\pi$
$163$	−14.1088	+	4.35197i	−1.10508	+	0.340873i	−0.312058	+	0.950063i	$0.601018\pi$
$164$	0.473175	+	1.20563i	0.0369488	+	0.0941439i
$165$	−5.26144	+	9.11308i	−0.409603	+	0.709452i
$166$	−0.345282	−	0.598046i	−0.0267991	−	0.0464174i
$167$	10.4691	−	13.1278i	0.810120	−	1.01586i	−0.189304	−	0.981919i	$-0.560623\pi$
$167$	10.4691	−	13.1278i	0.810120	−	1.01586i	0.999424	−	0.0339399i	$-0.0108055\pi$
$168$		0			0
$169$	1.42973	+	1.79282i	0.109979	+	0.137910i
$170$	7.30162	−	18.6042i	0.560009	−	1.42688i
$171$	−0.410219	+	5.47399i	−0.0313702	+	0.418606i
$172$	−0.0108046	+	0.144177i	−0.000823840	+	0.0109934i
$173$	−0.0774547	+	0.197351i	−0.00588877	+	0.0150043i	−0.933788	−	0.357827i	$-0.883518\pi$
$173$	−0.0774547	+	0.197351i	−0.00588877	+	0.0150043i	0.927899	+	0.372831i	$0.121613\pi$
$174$	0.376609	+	0.472253i	0.0285507	+	0.0358014i
$175$		0			0
$176$	1.51226	−	1.89632i	0.113991	−	0.142940i
$177$	4.82798	+	8.36230i	0.362893	+	0.628549i
$178$	1.22103	−	2.11489i	0.0915204	−	0.158518i
$179$	2.94496	+	7.50363i	0.220116	+	0.560848i	0.997689	−	0.0679456i	$-0.0216444\pi$
$179$	2.94496	+	7.50363i	0.220116	+	0.560848i	−0.777573	+	0.628793i	$0.783549\pi$
$180$	−6.27077	+	1.93428i	−0.467396	+	0.144173i
$181$	−5.29904	+	2.55189i	−0.393875	+	0.189680i	−0.620329	−	0.784342i	$-0.713001\pi$
$181$	−5.29904	+	2.55189i	−0.393875	+	0.189680i	0.226454	+	0.974022i	$0.427287\pi$
$182$		0			0
$183$	2.36240	+	1.13767i	0.174633	+	0.0840990i
$184$	−4.06261	−	0.612341i	−0.299500	−	0.0451423i
$185$	36.7814	−	25.0771i	2.70422	−	1.84371i
$186$	6.16193	+	5.71744i	0.451815	+	0.419223i
$187$	−10.4659	−	7.13553i	−0.765343	−	0.521802i
$188$	0.659953	+	2.89145i	0.0481321	+	0.210880i
$189$		0			0
$190$	2.72602	−	11.9435i	0.197767	−	0.866472i
$191$	11.2005	−	10.3926i	0.810442	−	0.751981i	−0.161582	−	0.986859i	$-0.551660\pi$
$191$	11.2005	−	10.3926i	0.810442	−	0.751981i	0.972025	+	0.234879i	$0.0754692\pi$
$192$	−1.12101	+	0.168965i	−0.0809021	+	0.0121940i
$193$	−20.2879	−	6.25797i	−1.46035	−	0.450459i	−0.540038	−	0.841641i	$-0.681590\pi$
$193$	−20.2879	−	6.25797i	−1.46035	−	0.450459i	−0.920313	+	0.391182i	$0.872066\pi$
$194$	−0.724883	−	9.67289i	−0.0520435	−	0.694473i
$195$	16.9662			1.21497
$196$		0			0
$197$	17.2861			1.23159			0.615793	−	0.787908i	$-0.288836\pi$
$197$	17.2861			1.23159			0.615793	+	0.787908i	$0.288836\pi$
$198$	0.310816	+	4.14755i	0.0220887	+	0.294753i
$199$	−19.7265	−	6.08482i	−1.39837	−	0.431341i	−0.498272	−	0.867021i	$-0.666032\pi$
$199$	−19.7265	−	6.08482i	−1.39837	−	0.431341i	−0.900102	+	0.435679i	$0.856508\pi$
$200$	9.53750	−	1.43755i	0.674403	−	0.101650i
$201$	−6.57501	+	6.10072i	−0.463766	+	0.430312i
$202$	−3.28122	+	14.3759i	−0.230866	+	1.01149i
$203$		0			0
$204$	1.31744	+	5.77209i	0.0922395	+	0.404127i
$205$	4.09522	+	2.79207i	0.286022	+	0.195007i
$206$	5.00856	+	4.64726i	0.348963	+	0.323790i
$207$	5.82101	−	3.96870i	0.404588	−	0.275844i
$208$	−3.86696	−	0.582851i	−0.268126	−	0.0404134i
$209$	−6.99550	−	3.36886i	−0.483889	−	0.233029i
$210$		0			0
$211$	−9.56828	+	4.60784i	−0.658707	+	0.317217i	−0.733208	−	0.680004i	$-0.761978\pi$
$211$	−9.56828	+	4.60784i	−0.658707	+	0.317217i	0.0745009	+	0.997221i	$0.476264\pi$
$212$	−5.22572	+	1.61192i	−0.358904	+	0.110707i
$213$	3.83124	+	9.76183i	0.262512	+	0.668870i
$214$	2.37330	−	4.11067i	0.162235	−	0.281000i
$215$	0.276649	+	0.479171i	0.0188673	+	0.0326792i
$216$	3.33257	−	4.17891i	0.226753	−	0.284339i
$217$		0			0
$218$	8.80216	+	11.0376i	0.596157	+	0.747558i
$219$	1.64399	−	4.18881i	0.111090	−	0.283054i
$220$	0.693653	−	9.25615i	0.0467660	−	0.624050i
$221$	−1.52622	+	20.3659i	−0.102664	+	1.36996i
$222$	−4.81793	+	12.2759i	−0.323359	+	0.823904i
$223$	12.0879	+	15.1578i	0.809467	+	1.01504i	0.999447	+	0.0332512i	$0.0105861\pi$
$223$	12.0879	+	15.1578i	0.809467	+	1.01504i	−0.189980	+	0.981788i	$0.560842\pi$
$224$		0			0
$225$	−10.3122	+	12.9311i	−0.687480	+	0.862073i
$226$	5.75780	+	9.97281i	0.383003	+	0.663381i
$227$	0.00482040	−	0.00834917i	0.000319941	−	0.000554154i	−0.865865	−	0.500277i	$-0.833231\pi$
$227$	0.00482040	−	0.00834917i	0.000319941	−	0.000554154i	0.866185	+	0.499723i	$0.166565\pi$
$228$	1.32586	+	3.37823i	0.0878071	+	0.223729i
$229$	20.3224	−	6.26861i	1.34294	−	0.414242i	0.461752	−	0.887009i	$-0.347221\pi$
$229$	20.3224	−	6.26861i	1.34294	−	0.414242i	0.881187	+	0.472768i	$0.156745\pi$
$230$	−14.1658	+	6.82190i	−0.934066	+	0.449822i
$231$		0			0
$232$	−0.480047	−	0.231178i	−0.0315166	−	0.0151776i
$233$	20.1508	+	3.03725i	1.32012	+	0.198977i	0.771038	−	0.636789i	$-0.219738\pi$
$233$	20.1508	+	3.03725i	1.32012	+	0.198977i	0.549086	+	0.835766i	$0.314976\pi$
$234$	5.54068	−	3.77757i	0.362205	−	0.246947i
$235$	8.32004	+	7.71987i	0.542739	+	0.503589i
$236$	−7.03740	−	4.79802i	−0.458096	−	0.312325i
$237$	−3.29392	−	14.4316i	−0.213963	−	0.937434i
$238$		0			0
$239$	5.29316	−	23.1909i	0.342386	−	1.50009i	−0.451636	−	0.892203i	$-0.649159\pi$
$239$	5.29316	−	23.1909i	0.342386	−	1.50009i	0.794022	−	0.607889i	$-0.207984\pi$
$240$	−3.18032	+	2.95091i	−0.205289	+	0.190480i
$241$	7.50339	−	1.13095i	0.483336	−	0.0728512i	0.0971454	−	0.995270i	$-0.469029\pi$
$241$	7.50339	−	1.13095i	0.483336	−	0.0728512i	0.386191	+	0.922419i	$0.373791\pi$
$242$	4.88969	+	1.50827i	0.314321	+	0.0969553i
$243$	1.12077	+	14.9556i	0.0718975	+	0.959405i
$244$	−2.31289			−0.148068
$245$		0			0
$246$	−1.46829			−0.0936147
$247$	0.935522	+	12.4837i	0.0595259	+	0.794317i
$248$	−7.08529	−	2.18552i	−0.449917	−	0.138781i
$249$	0.774131	−	0.116681i	0.0490585	−	0.00739438i
$250$	13.0314	−	12.0914i	0.824177	−	0.764724i
$251$	6.57630	−	28.8127i	0.415093	−	1.81864i	−0.144054	−	0.989570i	$-0.546014\pi$
$251$	6.57630	−	28.8127i	0.415093	−	1.81864i	0.559146	−	0.829069i	$-0.311129\pi$
$252$		0			0
$253$	2.21744	+	9.71526i	0.139410	+	0.610793i
$254$	−9.80402	−	6.68427i	−0.615159	−	0.419408i
$255$	16.6090	+	15.4109i	1.04010	+	0.965069i
$256$	0.826239	−	0.563320i	0.0516399	−	0.0352075i
$257$	−15.0040	−	2.26149i	−0.935923	−	0.141068i	−0.336666	−	0.941624i	$-0.609299\pi$
$257$	−15.0040	−	2.26149i	−0.935923	−	0.141068i	−0.599257	+	0.800557i	$0.704537\pi$
$258$	−0.147676	−	0.0711170i	−0.00919390	−	0.00442755i
$259$		0			0
$260$	−13.4836	+	6.49336i	−0.836217	+	0.402701i
$261$	0.873065	−	0.269305i	0.0540414	−	0.0166696i
$262$	−1.92219	−	4.89766i	−0.118753	−	0.302579i
$263$	10.7984	−	18.7034i	0.665859	−	1.15330i	−0.313193	−	0.949690i	$-0.601399\pi$
$263$	10.7984	−	18.7034i	0.665859	−	1.15330i	0.979052	−	0.203612i	$-0.0652680\pi$
$264$	1.37485	+	2.38132i	0.0846164	+	0.146560i
$265$	−13.0485	+	16.3623i	−0.801562	+	1.00513i
$266$		0			0
$267$	1.72614	+	2.16451i	0.105638	+	0.132466i
$268$	2.89049	−	7.36486i	0.176565	−	0.449880i
$269$	−1.99786	+	26.6596i	−0.121812	+	1.62547i	0.516918	+	0.856035i	$0.327079\pi$
$269$	−1.99786	+	26.6596i	−0.121812	+	1.62547i	−0.638730	+	0.769431i	$0.720540\pi$
$270$	1.52860	−	20.3977i	0.0930276	−	1.24137i
$271$	−2.35631	+	6.00377i	−0.143135	+	0.364703i	−0.984406	−	0.175911i	$-0.943713\pi$
$271$	−2.35631	+	6.00377i	−0.143135	+	0.364703i	0.841271	+	0.540614i	$0.181808\pi$
$272$	−3.25613	−	4.08306i	−0.197432	−	0.247572i
$273$		0			0
$274$	−5.27424	+	6.61368i	−0.318628	+	0.399547i
$275$	−11.6972	−	20.2601i	−0.705366	−	1.22173i
$276$	2.32885	−	4.03369i	0.140180	−	0.242800i
$277$	−9.60388	−	24.4703i	−0.577042	−	1.47028i	−0.859570	−	0.511019i	$-0.829268\pi$
$277$	−9.60388	−	24.4703i	−0.577042	−	1.47028i	0.282528	−	0.959259i	$-0.408827\pi$
$278$	0.127629	−	0.0393682i	0.00765466	−	0.00236115i
$279$	11.4555	−	5.51667i	0.685822	−	0.330274i
$280$		0			0
$281$	−11.7565	−	5.66163i	−0.701333	−	0.337744i	0.0490049	−	0.998799i	$-0.484395\pi$
$281$	−11.7565	−	5.66163i	−0.701333	−	0.337744i	−0.750338	+	0.661054i	$0.770109\pi$
$282$	−3.32470	−	0.501118i	−0.197983	−	0.0298411i
$283$	−13.7538	+	9.37717i	−0.817577	+	0.557415i	−0.898331	−	0.439319i	$-0.855220\pi$
$283$	−13.7538	+	9.37717i	−0.817577	+	0.557415i	0.0807538	+	0.996734i	$0.474267\pi$
$284$	−6.78090	−	6.29175i	−0.402372	−	0.373347i
$285$	11.4750	+	7.82352i	0.679720	+	0.463425i
$286$	2.11065	+	9.24738i	0.124806	+	0.546809i
$287$		0			0
$288$	−0.381575	+	1.67179i	−0.0224845	+	0.0985112i
$289$	−7.53123	+	6.98796i	−0.443013	+	0.411056i
$290$	−2.01625	+	0.303900i	−0.118398	+	0.0178456i
$291$	10.5081	+	3.24132i	0.615996	+	0.190009i
$292$	0.296625	+	3.95819i	0.0173587	+	0.231635i
$293$	−14.4623			−0.844896			−0.422448	−	0.906387i	$-0.638829\pi$
$293$	−14.4623			−0.844896			−0.422448	+	0.906387i	$0.638829\pi$
$294$		0			0
$295$	−32.5953			−1.89777
$296$	−0.869300	−	11.6000i	−0.0505271	−	0.674237i
$297$	−12.3883	−	3.82129i	−0.718843	−	0.221734i
$298$	4.78986	−	0.721955i	0.277469	−	0.0418217i
$299$	11.7779	−	10.9283i	0.681131	−	0.631997i
$300$	−2.43317	+	10.6604i	−0.140479	+	0.615478i
$301$		0			0
$302$	−1.79898	−	7.88185i	−0.103520	−	0.453549i
$303$	−13.8120	−	9.41688i	−0.793481	−	0.540986i
$304$	−2.34663	−	2.17736i	−0.134589	−	0.124880i
$305$	−7.31322	+	4.98607i	−0.418754	+	0.285501i
$306$	8.85532	+	1.33472i	0.506225	+	0.0763011i
$307$	−17.4231	−	8.39050i	−0.994387	−	0.478871i	−0.135357	−	0.990797i	$-0.543218\pi$
$307$	−17.4231	−	8.39050i	−0.994387	−	0.478871i	−0.859030	+	0.511926i	$0.828932\pi$
$308$		0			0
$309$	−6.97872	+	3.36077i	−0.397005	+	0.191188i
$310$	−27.1148	+	8.36380i	−1.54002	+	0.475032i
$311$	0.599012	+	1.52626i	0.0339669	+	0.0865462i	0.946851	−	0.321673i	$-0.104245\pi$
$311$	0.599012	+	1.52626i	0.0339669	+	0.0865462i	−0.912884	+	0.408219i	$0.866150\pi$
$312$	2.21670	−	3.83943i	0.125496	−	0.217365i
$313$	−3.06925	−	5.31609i	−0.173484	−	0.300483i	0.766152	−	0.642660i	$-0.222169\pi$
$313$	−3.06925	−	5.31609i	−0.173484	−	0.300483i	−0.939636	+	0.342177i	$0.888836\pi$
$314$	0.737533	−	0.924837i	0.0416214	−	0.0521916i
$315$		0			0
$316$	8.14111	+	10.2086i	0.457973	+	0.574280i
$317$	−10.3153	+	26.2829i	−0.579364	+	1.47620i	0.277537	+	0.960715i	$0.410482\pi$
$317$	−10.3153	+	26.2829i	−0.579364	+	1.47620i	−0.856901	+	0.515481i	$0.827613\pi$
$318$	0.463304	−	6.18236i	0.0259808	−	0.346690i
$319$	−0.0965756	+	1.28871i	−0.00540720	+	0.0721540i
$320$	1.39813	−	3.56237i	0.0781577	−	0.199142i
$321$	3.35506	+	4.20711i	0.187261	+	0.234818i
$322$		0			0
$323$	−10.4235	+	13.0706i	−0.579978	+	0.727269i
$324$	0.457584	+	0.792558i	0.0254213	+	0.0440310i
$325$	−18.8595	+	32.6656i	−1.04614	+	1.81196i
$326$	5.39415	+	13.7441i	0.298754	+	0.761214i
$327$	−15.2937	+	4.71747i	−0.845742	+	0.260877i
$328$	1.16690	−	0.561949i	0.0644312	−	0.0310284i
$329$		0			0
$330$	9.48079	+	4.56571i	0.521900	+	0.251334i
$331$	−11.2309	−	1.69278i	−0.617305	−	0.0930438i	−0.167057	−	0.985947i	$-0.553426\pi$
$331$	−11.2309	−	1.69278i	−0.617305	−	0.0930438i	−0.450248	+	0.892903i	$0.648665\pi$
$332$	−0.570571	+	0.389009i	−0.0313141	+	0.0213496i
$333$	14.6224	+	13.5676i	0.801302	+	0.743500i
$334$	−13.8734	−	9.45874i	−0.759120	−	0.517559i
$335$	−6.73741	−	29.5185i	−0.368104	−	1.61277i
$336$		0			0
$337$	4.07096	−	17.8361i	0.221760	−	0.971592i	−0.734393	−	0.678724i	$-0.762533\pi$
$337$	4.07096	−	17.8361i	0.221760	−	0.971592i	0.956153	−	0.292868i	$-0.0946097\pi$
$338$	1.68097	−	1.55971i	0.0914326	−	0.0848371i
$339$	−12.9091	+	1.94574i	−0.701128	+	0.105678i
$340$	−19.0979	−	5.89091i	−1.03573	−	0.319479i
$341$	1.34397	+	17.9340i	0.0727798	+	0.971179i
$342$	5.48934			0.296829
$343$		0			0
$344$	0.144581			0.00779529
$345$	−1.33203	−	17.7748i	−0.0717143	−	0.956961i
$346$	0.202588	+	0.0624900i	0.0108912	+	0.00335949i
$347$	−28.5861	+	4.30866i	−1.53458	+	0.231301i	−0.861304	−	0.508090i	$-0.830352\pi$
$347$	−28.5861	+	4.30866i	−1.53458	+	0.231301i	−0.673277	+	0.739390i	$0.735114\pi$
$348$	0.442789	−	0.410848i	0.0237360	−	0.0220238i
$349$	−1.43370	+	6.28145i	−0.0767442	+	0.336238i	−0.998695	−	0.0510684i	$-0.983737\pi$
$349$	−1.43370	+	6.28145i	−0.0767442	+	0.336238i	0.921951	+	0.387307i	$0.126594\pi$
$350$		0			0
$351$	4.65124	+	20.3784i	0.248265	+	1.08772i
$352$	−2.00403	−	1.36632i	−0.106815	−	0.0728253i
$353$	9.70953	+	9.00912i	0.516786	+	0.479507i	0.894909	−	0.446248i	$-0.147240\pi$
$353$	9.70953	+	9.00912i	0.516786	+	0.479507i	−0.378123	+	0.925755i	$0.623431\pi$
$354$	7.97812	−	5.43939i	0.424032	−	0.289100i
$355$	−35.0044	−	5.27606i	−1.85784	−	0.280024i
$356$	−2.20023	−	1.05957i	−0.116612	−	0.0561573i
$357$		0			0
$358$	7.26257	−	3.49747i	0.383839	−	0.184847i
$359$	−10.7944	+	3.32964i	−0.569708	+	0.175731i	−0.566208	−	0.824262i	$-0.691590\pi$
$359$	−10.7944	+	3.32964i	−0.569708	+	0.175731i	−0.00349950	+	0.999994i	$0.501114\pi$
$360$	2.39748	+	6.10869i	0.126359	+	0.321956i
$361$	4.37621	−	7.57982i	0.230327	−	0.398938i
$362$	2.94075	+	5.09352i	0.154562	+	0.267710i
$363$	−3.61689	+	4.53544i	−0.189838	+	0.238049i
$364$		0			0
$365$	9.47087	+	11.8761i	0.495728	+	0.621623i
$366$	0.957947	−	2.44081i	0.0500727	−	0.127583i
$367$	1.21310	−	16.1877i	0.0633233	−	0.844991i	−0.871617	−	0.490187i	$-0.836929\pi$
$367$	1.21310	−	16.1877i	0.0633233	−	0.844991i	0.934941	−	0.354804i	$-0.115452\pi$
$368$	−0.307029	+	4.09701i	−0.0160050	+	0.213572i
$369$	−0.811393	+	2.06739i	−0.0422394	+	0.107624i
$370$	−27.7557	−	34.8045i	−1.44295	−	1.80940i
$371$		0			0
$372$	5.24097	−	6.57197i	0.271732	−	0.340741i
$373$	0.230517	+	0.399267i	0.0119357	+	0.0206732i	0.871932	−	0.489628i	$-0.162867\pi$
$373$	0.230517	+	0.399267i	0.0119357	+	0.0206732i	−0.859996	+	0.510301i	$0.829534\pi$
$374$	−6.33346	+	10.9699i	−0.327495	+	0.567239i
$375$	7.36279	+	18.7601i	0.380213	+	0.968766i
$376$	2.83404	−	0.874186i	0.146155	−	0.0450827i
$377$	1.87729	−	0.904055i	0.0966854	−	0.0465612i
$378$		0			0
$379$	14.1662	+	6.82210i	0.727671	+	0.350428i	0.760768	−	0.649024i	$-0.224823\pi$
$379$	14.1662	+	6.82210i	0.727671	+	0.350428i	−0.0330968	+	0.999452i	$0.510537\pi$
$380$	−12.1138	−	1.82586i	−0.621425	−	0.0936648i
$381$	11.1146	−	7.57778i	0.569416	−	0.388222i
$382$	−11.2005	−	10.3926i	−0.573069	−	0.531731i
$383$	−0.631170	−	0.430325i	−0.0322513	−	0.0219886i	0.547087	−	0.837076i	$-0.315737\pi$
$383$	−0.631170	−	0.430325i	−0.0322513	−	0.0219886i	−0.579338	+	0.815087i	$0.696689\pi$
$384$	0.252266	+	1.10525i	0.0128734	+	0.0564021i
$385$		0			0
$386$	−4.72436	+	20.6988i	−0.240464	+	1.05354i
$387$	−0.181742	+	0.168632i	−0.00923847	+	0.00857205i
$388$	−9.59167	+	1.44571i	−0.486943	+	0.0733949i
$389$	18.6863	+	5.76395i	0.947432	+	0.292244i	0.729702	−	0.683765i	$-0.239659\pi$
$389$	18.6863	+	5.76395i	0.947432	+	0.292244i	0.217730	+	0.976009i	$0.430135\pi$
$390$	−1.26788	−	16.9187i	−0.0642018	−	0.856714i
$391$	21.4564			1.08510
$392$		0			0
$393$	5.96467			0.300878
$394$	−1.29179	−	17.2378i	−0.0650796	−	0.868428i
$395$	47.7492	+	14.7287i	2.40252	+	0.741080i
$396$	4.11272	−	0.619893i	0.206672	−	0.0311508i
$397$	−12.8143	+	11.8899i	−0.643129	+	0.596737i	−0.932802	−	0.360389i	$-0.882644\pi$
$397$	−12.8143	+	11.8899i	−0.643129	+	0.596737i	0.289673	+	0.957126i	$0.406453\pi$
$398$	−4.59364	+	20.1261i	−0.230258	+	1.00883i
$399$		0			0
$400$	−2.14627	−	9.40341i	−0.107313	−	0.470170i
$401$	6.34604	+	4.32666i	0.316906	+	0.216063i	0.711317	−	0.702871i	$-0.248099\pi$
$401$	6.34604	+	4.32666i	0.316906	+	0.216063i	−0.394411	+	0.918934i	$0.629051\pi$
$402$	6.57501	+	6.10072i	0.327932	+	0.304276i
$403$	23.9578	−	16.3342i	1.19342	−	0.813663i
$404$	14.5810	+	2.19772i	0.725429	+	0.109341i
$405$	3.15543	+	1.51957i	0.156795	+	0.0755083i
$406$		0			0
$407$	−25.4204	+	12.2418i	−1.26004	+	0.606805i
$408$	5.65750	−	1.74511i	0.280088	−	0.0863957i
$409$	−3.14004	−	8.00069i	−0.155265	−	0.395609i	0.831982	−	0.554802i	$-0.187206\pi$
$409$	−3.14004	−	8.00069i	−0.155265	−	0.395609i	−0.987247	+	0.159193i	$0.949111\pi$
$410$	2.47823	−	4.29242i	0.122391	−	0.211987i
$411$	−4.79500	−	8.30518i	−0.236520	−	0.409664i
$412$	4.25998	−	5.34184i	0.209874	−	0.263174i
$413$		0			0
$414$	−4.39261	−	5.50815i	−0.215885	−	0.270711i
$415$	−0.965496	+	2.46004i	−0.0473944	+	0.120759i
$416$	−0.292243	+	3.89971i	−0.0143284	+	0.191199i
$417$	−0.0113154	+	0.150993i	−0.000554115	+	0.00739415i
$418$	−2.83666	+	7.22769i	−0.138746	+	0.353518i
$419$	19.6163	+	24.5981i	0.958320	+	1.20170i	0.979402	+	0.201918i	$0.0647174\pi$
$419$	19.6163	+	24.5981i	0.958320	+	1.20170i	−0.0210822	+	0.999778i	$0.506711\pi$
$420$		0			0
$421$	−15.0649	+	18.8907i	−0.734216	+	0.920678i	−0.999048	−	0.0436164i	$-0.986112\pi$
$421$	−15.0649	+	18.8907i	−0.734216	+	0.920678i	0.264832	+	0.964295i	$0.414683\pi$
$422$	5.30999	+	9.19718i	0.258486	+	0.447712i
$423$	−2.54286	+	4.40436i	−0.123638	+	0.214147i
$424$	1.99793	+	5.09065i	0.0970282	+	0.247224i
$425$	−48.1337	+	14.8473i	−2.33483	+	0.720199i
$426$	9.44823	−	4.55003i	0.457768	−	0.220449i
$427$		0			0
$428$	−4.27654	−	2.05947i	−0.206714	−	0.0995483i
$429$	−10.6330	−	1.60267i	−0.513367	−	0.0773776i
$430$	0.457157	−	0.311684i	0.0220461	−	0.0150308i
$431$	−13.9835	−	12.9748i	−0.673563	−	0.624975i	0.267360	−	0.963597i	$-0.413849\pi$
$431$	−13.9835	−	12.9748i	−0.673563	−	0.624975i	−0.940923	+	0.338622i	$0.890039\pi$
$432$	−4.41627	−	3.01096i	−0.212478	−	0.144865i
$433$	2.17592	+	9.53333i	0.104568	+	0.458143i	0.999918	+	0.0127800i	$0.00406811\pi$
$433$	2.17592	+	9.53333i	0.104568	+	0.458143i	−0.895350	+	0.445363i	$0.853075\pi$
$434$		0			0
$435$	0.514376	−	2.25363i	0.0246625	−	0.108053i
$436$	10.3489	−	9.60238i	0.495623	−	0.459871i
$437$	13.0052	−	1.96021i	0.622122	−	0.0937698i
$438$	−4.29996	−	1.32636i	−0.205460	−	0.0633760i
$439$	−0.773190	−	10.3175i	−0.0369023	−	0.492427i	−0.984781	−	0.173797i	$-0.944396\pi$
$439$	−0.773190	−	10.3175i	−0.0369023	−	0.492427i	0.947879	−	0.318630i	$-0.103223\pi$
$440$	−9.28210			−0.442507
$441$		0			0
$442$	20.4231			0.971426
$443$	−0.414354	−	5.52917i	−0.0196865	−	0.262699i	−0.998359	−	0.0572703i	$-0.981760\pi$
$443$	−0.414354	−	5.52917i	−0.0196865	−	0.262699i	0.978672	−	0.205428i	$-0.0658587\pi$
$444$	12.6016	+	3.88708i	0.598046	+	0.184473i
$445$	−9.24119	+	1.39289i	−0.438074	+	0.0660291i
$446$	14.2120	−	13.1869i	0.672960	−	0.624416i
$447$	−1.22197	+	5.35379i	−0.0577971	+	0.253226i
$448$		0			0
$449$	−1.60805	−	7.04534i	−0.0758888	−	0.332490i	0.922705	−	0.385507i	$-0.125973\pi$
$449$	−1.60805	−	7.04534i	−0.0758888	−	0.332490i	−0.998594	+	0.0530167i	$0.983116\pi$
$450$	13.6656	+	9.31702i	0.644201	+	0.439209i
$451$	−2.30280	−	2.13669i	−0.108435	−	0.100613i
$452$	9.51464	−	6.48697i	0.447531	−	0.305121i
$453$	9.06287	+	1.36601i	0.425811	+	0.0641806i
$454$	−0.00868606	−	0.00418298i	−0.000407657	−	0.000196317i
$455$		0			0
$456$	3.26971	−	1.57461i	0.153118	−	0.0737377i
$457$	38.2025	−	11.7839i	1.78704	−	0.551228i	0.789031	−	0.614354i	$-0.210583\pi$
$457$	38.2025	−	11.7839i	1.78704	−	0.551228i	0.998006	+	0.0631260i	$0.0201070\pi$
$458$	−7.76978	−	19.7971i	−0.363058	−	0.925056i
$459$	−13.9570	+	24.1743i	−0.651458	+	1.12836i
$460$	7.86143	+	13.6164i	0.366541	+	0.634868i
$461$	0.619234	−	0.776495i	0.0288406	−	0.0361650i	−0.767202	−	0.641405i	$-0.778352\pi$
$461$	0.619234	−	0.776495i	0.0288406	−	0.0361650i	0.796043	+	0.605241i	$0.206923\pi$
$462$		0			0
$463$	−15.7874	−	19.7968i	−0.733705	−	0.920036i	0.265322	−	0.964160i	$-0.414522\pi$
$463$	−15.7874	−	19.7968i	−0.733705	−	0.920036i	−0.999026	+	0.0441236i	$0.985950\pi$
$464$	−0.194658	+	0.495980i	−0.00903677	+	0.0230253i
$465$	2.40395	−	32.0785i	0.111481	−	1.48761i
$466$	1.52288	−	20.3215i	0.0705462	−	0.941373i
$467$	0.0293086	−	0.0746770i	0.00135624	−	0.00345564i	−0.930194	−	0.367068i	$-0.880362\pi$
$467$	0.0293086	−	0.0746770i	0.00135624	−	0.00345564i	0.931550	+	0.363613i	$0.118457\pi$
$468$	−4.18106	−	5.24289i	−0.193270	−	0.242352i
$469$		0			0
$470$	7.07652	−	8.87368i	0.326416	−	0.409312i
$471$	0.670518	+	1.16137i	0.0308958	+	0.0535132i
$472$	−4.25870	+	7.37628i	−0.196022	+	0.339521i
$473$	−0.128118	−	0.326438i	−0.00589085	−	0.0150096i
$474$	−14.1451	+	4.36319i	−0.649706	+	0.200408i
$475$	−27.8185	+	13.3967i	−1.27640	+	0.614681i
$476$		0			0
$477$	−8.44892	−	4.06879i	−0.386850	−	0.186297i
$478$	−23.5216	−	3.54531i	−1.07585	−	0.162159i
$479$	−15.0116	+	10.2347i	−0.685896	+	0.467636i	−0.855450	−	0.517885i	$-0.826720\pi$
$479$	−15.0116	+	10.2347i	−0.685896	+	0.467636i	0.169554	+	0.985521i	$0.445767\pi$
$480$	3.18032	+	2.95091i	0.145161	+	0.134690i
$481$	37.5861	+	25.6258i	1.71378	+	1.16844i
$482$	−1.68852	−	7.39789i	−0.0769100	−	0.336965i
$483$		0			0
$484$	1.13865	−	4.98874i	0.0517566	−	0.226761i
$485$	−27.2117	+	25.2487i	−1.23562	+	1.14649i
$486$	14.8301	−	2.23527i	0.672706	−	0.101394i
$487$	−10.3649	−	3.19715i	−0.469678	−	0.144877i	0.0508762	−	0.998705i	$-0.483799\pi$
$487$	−10.3649	−	3.19715i	−0.469678	−	0.144877i	−0.520555	+	0.853828i	$0.674275\pi$
$488$	0.172842	+	2.30642i	0.00782421	+	0.104407i
$489$	−16.7384			−0.756935
$490$		0			0
$491$	−11.7931			−0.532213			−0.266107	−	0.963944i	$-0.585737\pi$
$491$	−11.7931			−0.532213			−0.266107	+	0.963944i	$0.585737\pi$
$492$	0.109725	+	1.46418i	0.00494680	+	0.0660105i
$493$	2.65895	+	0.820178i	0.119753	+	0.0369389i
$494$	12.3789	−	1.86581i	0.556951	−	0.0839469i
$495$	11.6678	−	10.8262i	0.524430	−	0.486600i
$496$	−1.64993	+	7.22881i	−0.0740840	+	0.324583i
$497$		0			0
$498$	−0.174206	−	0.763246i	−0.00780636	−	0.0342019i
$499$	−3.37872	−	2.30357i	−0.151252	−	0.103122i	0.485329	−	0.874331i	$-0.338700\pi$
$499$	−3.37872	−	2.30357i	−0.151252	−	0.103122i	−0.636582	+	0.771209i	$0.719652\pi$
$500$	−13.0314	−	12.0914i	−0.582781	−	0.540742i
$501$	15.7279	−	10.7231i	0.702673	−	0.479074i
$502$	−29.2235	−	4.40474i	−1.30431	−	0.196593i
$503$	−1.93681	−	0.932719i	−0.0863581	−	0.0415879i	0.390206	−	0.920728i	$-0.372404\pi$
$503$	−1.93681	−	0.932719i	−0.0863581	−	0.0415879i	−0.476564	+	0.879140i	$0.658118\pi$
$504$		0			0
$505$	50.8419	−	24.4842i	2.26244	−	1.08953i
$506$	9.52238	−	2.93727i	0.423322	−	0.130577i
$507$	0.949754	+	2.41993i	0.0421801	+	0.107473i
$508$	−5.93292	+	10.2761i	−0.263231	+	0.455929i
$509$	−0.530046	−	0.918067i	−0.0234939	−	0.0406926i	0.854039	−	0.520208i	$-0.174146\pi$
$509$	−0.530046	−	0.918067i	−0.0234939	−	0.0406926i	−0.877533	+	0.479516i	$0.840812\pi$
$510$	14.1266	−	17.7142i	0.625538	−	0.784399i
$511$		0			0
$512$	−0.623490	−	0.781831i	−0.0275546	−	0.0345524i
$513$	−6.25114	+	15.9276i	−0.275994	+	0.703222i
$514$	−1.13391	+	15.1310i	−0.0500148	+	0.667401i
$515$	1.95399	−	26.0741i	0.0861029	−	1.14896i
$516$	−0.0598823	+	0.152578i	−0.00263617	+	0.00671685i
$517$	−4.48508	−	5.62411i	−0.197254	−	0.247348i
$518$		0			0
$519$	−0.149854	+	0.187910i	−0.00657784	+	0.00824835i
$520$	7.48283	+	12.9606i	0.328144	+	0.568362i
$521$	−7.97937	+	13.8207i	−0.349583	+	0.605495i	−0.986175	−	0.165705i	$-0.947010\pi$
$521$	−7.97937	+	13.8207i	−0.349583	+	0.605495i	0.636593	+	0.771200i	$0.280343\pi$
$522$	−0.333796	−	0.850499i	−0.0146099	−	0.0372253i
$523$	33.4890	−	10.3300i	1.46437	−	0.451700i	0.542787	−	0.839871i	$-0.317369\pi$
$523$	33.4890	−	10.3300i	1.46437	−	0.451700i	0.921587	+	0.388171i	$0.126893\pi$
$524$	−4.74032	+	2.28282i	−0.207082	+	0.0997254i
$525$		0			0
$526$	−19.4581	−	9.37051i	−0.848412	−	0.408574i
$527$	38.2903	+	5.77134i	1.66795	+	0.251403i
$528$	2.27191	−	1.54897i	0.0988724	−	0.0674101i
$529$	4.48643	+	4.16280i	0.195062	+	0.180991i
$530$	17.2916	+	11.7892i	0.751101	+	0.512092i
$531$	−3.25003	−	14.2393i	−0.141039	−	0.617933i
$532$		0			0
$533$	−1.12705	+	4.93792i	−0.0488178	+	0.213885i
$534$	2.02946	−	1.88306i	0.0878233	−	0.0814881i
$535$	−17.9619	+	2.70732i	−0.776561	+	0.117048i
$536$	−7.56027	−	2.33204i	−0.326554	−	0.100729i
$537$	0.682911	+	9.11282i	0.0294698	+	0.393247i
$538$	26.7344			1.15260
$539$		0			0
$540$	−20.4549			−0.880240
$541$	−0.881599	−	11.7641i	−0.0379029	−	0.505779i	−0.983556	−	0.180603i	$-0.942195\pi$
$541$	−0.881599	−	11.7641i	−0.0379029	−	0.505779i	0.945653	−	0.325177i	$-0.105424\pi$
$542$	6.16307	+	1.90105i	0.264726	+	0.0816573i
$543$	−6.59323	+	0.993769i	−0.282942	+	0.0426467i
$544$	−3.82831	+	3.55216i	−0.164138	+	0.152297i
$545$	12.0221	−	52.6721i	0.514968	−	2.25622i
$546$		0			0
$547$	−5.48351	−	24.0248i	−0.234458	−	1.02723i	−0.945894	−	0.324477i	$-0.894812\pi$
$547$	−5.48351	−	24.0248i	−0.234458	−	1.02723i	0.711436	−	0.702751i	$-0.248045\pi$
$548$	6.98933	+	4.76525i	0.298570	+	0.203561i
$549$	−2.90736	−	2.69764i	−0.124083	−	0.115132i
$550$	−19.3293	+	13.1785i	−0.824205	+	0.561933i
$551$	1.68658	+	0.254211i	0.0718506	+	0.0108297i
$552$	−4.19644	−	2.02090i	−0.178613	−	0.0860153i
$553$		0			0
$554$	−23.6842	+	11.4057i	−1.00624	+	0.484582i
$555$	48.2252	−	14.8755i	2.04705	−	0.631430i
$556$	−0.0487959	−	0.124330i	−0.00206941	−	0.00527276i
$557$	15.4047	−	26.6817i	0.652718	−	1.13054i	−0.329743	−	0.944071i	$-0.606962\pi$
$557$	15.4047	−	26.6817i	0.652718	−	1.13054i	0.982461	−	0.186470i	$-0.0597046\pi$
$558$	−6.35731	−	11.0112i	−0.269126	−	0.466141i
$559$	−0.352524	+	0.442051i	−0.0149102	+	0.0186968i
$560$		0			0
$561$	−8.95341	−	11.2272i	−0.378013	−	0.474014i
$562$	−4.76723	+	12.1467i	−0.201093	+	0.512378i
$563$	2.00254	−	26.7220i	0.0843968	−	1.12620i	−0.780805	−	0.624774i	$-0.785191\pi$
$563$	2.00254	−	26.7220i	0.0843968	−	1.12620i	0.865202	−	0.501423i	$-0.167190\pi$
$564$	−0.251262	+	3.35285i	−0.0105800	+	0.141181i
$565$	16.1003	−	41.0228i	0.677344	−	1.72584i
$566$	10.3788	+	13.0146i	0.436252	+	0.547043i
$567$		0			0
$568$	−5.76742	+	7.23212i	−0.241996	+	0.303453i
$569$	3.90343	+	6.76094i	0.163640	+	0.283433i	0.936172	−	0.351543i	$-0.114343\pi$
$569$	3.90343	+	6.76094i	0.163640	+	0.283433i	−0.772531	+	0.634977i	$0.781010\pi$
$570$	6.94412	−	12.0276i	0.290857	−	0.503779i
$571$	3.65070	+	9.30184i	0.152777	+	0.389270i	0.986687	−	0.162631i	$-0.0519979\pi$
$571$	3.65070	+	9.30184i	0.152777	+	0.389270i	−0.833910	+	0.551901i	$0.813903\pi$
$572$	9.06379	−	2.79581i	0.378976	−	0.116899i
$573$	15.6064	−	7.51564i	0.651966	−	0.313970i
$574$		0			0
$575$	35.7031	+	17.1937i	1.48892	+	0.717027i
$576$	1.69563	+	0.255575i	0.0706513	+	0.0106490i
$577$	11.7895	−	8.03792i	0.490802	−	0.334623i	−0.292499	−	0.956266i	$-0.594487\pi$
$577$	11.7895	−	8.03792i	0.490802	−	0.334623i	0.783301	+	0.621643i	$0.213534\pi$
$578$	7.53123	+	6.98796i	0.313258	+	0.290661i
$579$	−19.8869	−	13.5586i	−0.826469	−	0.563477i
$580$	0.453725	+	1.98790i	0.0188399	+	0.0825430i
$581$		0			0
$582$	2.44698	−	10.7209i	0.101431	−	0.444397i
$583$	9.72334	−	9.02194i	0.402699	−	0.373651i
$584$	3.92495	−	0.591591i	0.162416	−	0.0244802i
$585$	−24.5227	−	7.56427i	−1.01389	−	0.312744i
$586$	1.08077	+	14.4219i	0.0446461	+	0.595761i
$587$	−21.5201			−0.888230			−0.444115	−	0.895970i	$-0.646482\pi$
$587$	−21.5201			−0.888230			−0.444115	+	0.895970i	$0.646482\pi$
$588$		0			0
$589$	23.7359			0.978019
$590$	2.43585	+	32.5042i	0.100282	+	1.33818i
$591$	18.7262	+	5.77627i	0.770293	+	0.237604i
$592$	−11.5026	+	1.73374i	−0.472754	+	0.0712562i
$593$	12.9273	−	11.9948i	0.530861	−	0.492567i	−0.368588	−	0.929593i	$-0.620159\pi$
$593$	12.9273	−	11.9948i	0.530861	−	0.492567i	0.899449	+	0.437026i	$0.143968\pi$
$594$	−2.88482	+	12.6392i	−0.118366	+	0.518594i
$595$		0			0
$596$	−1.07788	−	4.72251i	−0.0441518	−	0.193442i
$597$	−19.3366	−	13.1835i	−0.791394	−	0.539563i
$598$	−11.7779	−	10.9283i	−0.481632	−	0.446889i
$599$	−4.18826	+	2.85551i	−0.171128	+	0.116673i	−0.645855	−	0.763460i	$-0.723499\pi$
$599$	−4.18826	+	2.85551i	−0.171128	+	0.116673i	0.474727	+	0.880133i	$0.342547\pi$
$600$	10.8124	+	1.62971i	0.441415	+	0.0665326i
$601$	0.951205	+	0.458076i	0.0388005	+	0.0186853i	0.453183	−	0.891417i	$-0.350288\pi$
$601$	0.951205	+	0.458076i	0.0388005	+	0.0186853i	−0.414383	+	0.910103i	$0.636003\pi$
$602$		0			0
$603$	12.2234	−	5.88649i	0.497776	−	0.239716i
$604$	−7.72537	+	2.38296i	−0.314341	+	0.0969613i
$605$	−7.15426	−	18.2287i	−0.290862	−	0.741104i
$606$	−8.35838	+	14.4771i	−0.339536	+	0.588093i
$607$	−22.8953	−	39.6558i	−0.929290	−	1.60958i	−0.784512	−	0.620114i	$-0.787086\pi$
$607$	−22.8953	−	39.6558i	−0.929290	−	1.60958i	−0.144778	−	0.989464i	$-0.546247\pi$
$608$	−1.99591	+	2.50279i	−0.0809447	+	0.101501i
$609$		0			0
$610$	5.51864	+	6.92016i	0.223443	+	0.280189i
$611$	−4.23730	+	10.7965i	−0.171423	+	0.436778i
$612$	0.669233	−	8.93030i	0.0270522	−	0.360986i
$613$	−1.55127	+	20.7003i	−0.0626553	+	0.836077i	0.874023	+	0.485885i	$0.161503\pi$
$613$	−1.55127	+	20.7003i	−0.0626553	+	0.836077i	−0.936678	+	0.350192i	$0.886116\pi$
$614$	−7.06502	+	18.0014i	−0.285121	+	0.726476i
$615$	3.50339	+	4.39312i	0.141270	+	0.177148i
$616$		0			0
$617$	20.1516	−	25.2693i	0.811273	−	1.01730i	−0.188108	−	0.982148i	$-0.560236\pi$
$617$	20.1516	−	25.2693i	0.811273	−	1.01730i	0.999382	−	0.0351565i	$-0.0111930\pi$
$618$	3.87290	+	6.70805i	0.155791	+	0.269838i
$619$	14.8645	−	25.7461i	0.597455	−	1.03482i	−0.395741	−	0.918362i	$-0.629512\pi$
$619$	14.8645	−	25.7461i	0.597455	−	1.03482i	0.993195	−	0.116460i	$-0.0371546\pi$
$620$	10.3667	+	26.4139i	0.416337	+	1.06081i
$621$	20.9844	−	6.47284i	0.842076	−	0.259746i
$622$	1.47723	−	0.711395i	0.0592314	−	0.0285243i
$623$		0			0
$624$	−3.99435	−	1.92358i	−0.159902	−	0.0770047i
$625$	−19.5832	−	2.95169i	−0.783326	−	0.118067i
$626$	−5.07186	+	3.45794i	−0.202712	+	0.138207i
$627$	−6.45256	−	5.98710i	−0.257690	−	0.239102i
$628$	−0.977367	−	0.666358i	−0.0390012	−	0.0265906i
$629$	13.5182	+	59.2270i	0.539005	+	2.36153i
$630$		0			0
$631$	−2.21544	+	9.70648i	−0.0881953	+	0.386409i	−0.999690	−	0.0249032i	$-0.992072\pi$
$631$	−2.21544	+	9.70648i	−0.0881953	+	0.386409i	0.911495	+	0.411312i	$0.134929\pi$
$632$	9.57170	−	8.88124i	0.380742	−	0.353277i
$633$	−11.9051	+	1.79441i	−0.473186	+	0.0713214i
$634$	26.9803	+	8.32232i	1.07152	+	0.330522i
$635$	3.39346	+	45.2825i	0.134665	+	1.79698i
$636$	−6.19970			−0.245834
$637$		0			0
$638$	1.29233			0.0511637
$639$	−1.18538	−	15.8178i	−0.0468929	−	0.625742i
$640$	−3.65689	−	1.12800i	−0.144551	−	0.0445882i
$641$	−20.8195	+	3.13803i	−0.822320	+	0.123945i	−0.546707	−	0.837324i	$-0.684119\pi$
$641$	−20.8195	+	3.13803i	−0.822320	+	0.123945i	−0.275613	+	0.961269i	$0.588881\pi$
$642$	3.94462	−	3.66007i	0.155682	−	0.144452i
$643$	−2.67820	+	11.7340i	−0.105618	+	0.462742i	0.894266	+	0.447535i	$0.147698\pi$
$643$	−2.67820	+	11.7340i	−0.105618	+	0.462742i	−0.999884	+	0.0152073i	$0.995159\pi$
$644$		0			0
$645$	0.139579	+	0.611534i	0.00549590	+	0.0240791i
$646$	13.8130	+	9.41757i	0.543467	+	0.370529i
$647$	−34.1458	−	31.6827i	−1.34241	−	1.24558i	−0.944647	−	0.328087i	$-0.893596\pi$
$647$	−34.1458	−	31.6827i	−1.34241	−	1.24558i	−0.397764	−	0.917488i	$-0.630214\pi$
$648$	0.756147	−	0.515532i	0.0297042	−	0.0202520i
$649$	20.4281	+	3.07904i	0.801872	+	0.120863i
$650$	33.9837	+	16.3657i	1.33295	+	0.641915i
$651$		0			0
$652$	13.3025	−	6.40617i	0.520968	−	0.250885i
$653$	−7.72417	+	2.38259i	−0.302270	+	0.0932380i	−0.442180	−	0.896926i	$-0.645795\pi$
$653$	−7.72417	+	2.38259i	−0.302270	+	0.0932380i	0.139910	+	0.990164i	$0.455319\pi$
$654$	5.84718	+	14.8984i	0.228643	+	0.582572i
$655$	−10.0674	+	17.4372i	−0.393365	+	0.681328i
$656$	−0.647580	−	1.12164i	−0.0252837	−	0.0437927i
$657$	−4.24376	+	5.32151i	−0.165565	+	0.207612i
$658$		0			0
$659$	29.0518	+	36.4298i	1.13170	+	1.41910i	0.894173	+	0.447722i	$0.147765\pi$
$659$	29.0518	+	36.4298i	1.13170	+	1.41910i	0.237524	+	0.971382i	$0.423664\pi$
$660$	3.84444	−	9.79547i	0.149645	−	0.381288i
$661$	0.799779	−	10.6723i	0.0311078	−	0.415105i	−0.959811	−	0.280646i	$-0.909451\pi$
$661$	0.799779	−	10.6723i	0.0311078	−	0.415105i	0.990919	−	0.134459i	$-0.0429296\pi$
$662$	−0.848765	+	11.3260i	−0.0329882	+	0.440197i
$663$	−8.45877	+	21.5526i	−0.328511	+	0.837034i
$664$	0.430560	+	0.539905i	0.0167090	+	0.0209524i
$665$		0			0
$666$	12.4369	−	15.5954i	0.481921	−	0.604310i
$667$	−1.09453	−	1.89578i	−0.0423803	−	0.0734049i
$668$	−8.39553	+	14.5415i	−0.324833	+	0.562627i
$669$	8.02987	+	20.4598i	0.310453	+	0.791021i
$670$	−28.9325	+	8.92449i	−1.11776	+	0.344783i
$671$	5.05432	−	2.43403i	0.195120	−	0.0939648i
$672$		0			0
$673$	−16.1016	−	7.75413i	−0.620671	−	0.298900i	0.0969969	−	0.995285i	$-0.469076\pi$
$673$	−16.1016	−	7.75413i	−0.620671	−	0.298900i	−0.717668	+	0.696385i	$0.754791\pi$
$674$	−18.0904	−	2.72669i	−0.696817	−	0.105028i
$675$	−42.5959	+	29.0414i	−1.63952	+	1.11780i
$676$	−1.68097	−	1.55971i	−0.0646526	−	0.0599889i
$677$	−5.41303	−	3.69054i	−0.208040	−	0.141839i	0.454818	−	0.890584i	$-0.349704\pi$
$677$	−5.41303	−	3.69054i	−0.208040	−	0.141839i	−0.662858	+	0.748745i	$0.730657\pi$
$678$	2.90500	+	12.7276i	0.111566	+	0.488802i
$679$		0			0
$680$	−4.44725	+	19.4847i	−0.170544	+	0.747204i
$681$	0.00801190	−	0.00743396i	0.000307017	−	0.000284870i
$682$	17.7834	−	2.68041i	0.680961	−	0.102638i
$683$	−4.51200	−	1.39177i	−0.172647	−	0.0532545i	0.207227	−	0.978293i	$-0.433556\pi$
$683$	−4.51200	−	1.39177i	−0.172647	−	0.0532545i	−0.379873	+	0.925038i	$0.624032\pi$
$684$	−0.410219	−	5.47399i	−0.0156851	−	0.209303i
$685$	32.3727			1.23690
$686$		0			0
$687$	24.1101			0.919856
$688$	−0.0108046	−	0.144177i	−0.000411920	−	0.00549669i
$689$	−20.4359	−	6.30364i	−0.778546	−	0.240150i
$690$	−17.6255	+	2.65662i	−0.670992	+	0.101136i
$691$	−3.47553	+	3.22482i	−0.132215	+	0.122678i	−0.743509	−	0.668726i	$-0.766840\pi$
$691$	−3.47553	+	3.22482i	−0.132215	+	0.122678i	0.611294	+	0.791404i	$0.290649\pi$
$692$	0.0471759	−	0.206691i	0.00179336	−	0.00785722i
$693$		0			0
$694$	6.43285	+	28.1842i	0.244188	+	1.06986i
$695$	−0.422317	−	0.287931i	−0.0160194	−	0.0109218i
$696$	−0.442789	−	0.410848i	−0.0167839	−	0.0155731i
$697$	−5.58858	+	3.81023i	−0.211683	+	0.144323i
$698$	6.37102	+	0.960277i	0.241147	+	0.0363470i
$699$	20.8146	+	10.0238i	0.787282	+	0.379135i
$700$		0			0
$701$	−6.84704	+	3.29736i	−0.258609	+	0.124540i	−0.558697	−	0.829372i	$-0.688698\pi$
$701$	−6.84704	+	3.29736i	−0.258609	+	0.124540i	0.300088	+	0.953912i	$0.402984\pi$
$702$	19.9738	−	6.16111i	0.753864	−	0.232536i
$703$	13.6045	+	34.6638i	0.513104	+	1.30737i
$704$	−1.21274	+	2.10053i	−0.0457069	+	0.0791667i
$705$	6.43352	+	11.1432i	0.242300	+	0.419677i
$706$	8.25834	−	10.3556i	0.310807	−	0.389739i
$707$		0			0
$708$	−6.02039	−	7.54933i	−0.226260	−	0.283721i
$709$	15.5419	−	39.6002i	0.583689	−	1.48722i	−0.268131	−	0.963382i	$-0.586406\pi$
$709$	15.5419	−	39.6002i	0.583689	−	1.48722i	0.851821	−	0.523834i	$-0.175499\pi$
$710$	−2.64543	+	35.3008i	−0.0992812	+	1.32482i
$711$	−1.67324	+	22.3279i	−0.0627515	+	0.837361i
$712$	−0.892187	+	2.27326i	−0.0334361	+	0.0851939i
$713$	−18.9936	−	23.8172i	−0.711316	−	0.891961i
$714$		0			0
$715$	22.6320	−	28.3797i	0.846390	−	1.06134i
$716$	−4.03042	−	6.98090i	−0.150624	−	0.260888i
$717$	13.4835	−	23.3541i	0.503550	−	0.872175i
$718$	4.12699	+	10.5154i	0.154018	+	0.392432i
$719$	38.8786	−	11.9925i	1.44993	−	0.447243i	0.532937	−	0.846155i	$-0.321088\pi$
$719$	38.8786	−	11.9925i	1.44993	−	0.447243i	0.916989	+	0.398912i	$0.130612\pi$
$720$	5.91245	−	2.84728i	0.220344	−	0.106112i
$721$		0			0
$722$	−7.88566	−	3.79753i	−0.293474	−	0.141330i
$723$	8.50640	+	1.28213i	0.316356	+	0.0476831i
$724$	4.85952	−	3.31316i	0.180603	−	0.123133i
$725$	3.76722	+	3.49547i	0.139911	+	0.129819i
$726$	4.79305	+	3.26784i	0.177887	+	0.121281i
$727$	5.71242	+	25.0277i	0.211862	+	0.928228i	0.963301	+	0.268425i	$0.0865031\pi$
$727$	5.71242	+	25.0277i	0.211862	+	0.928228i	−0.751439	+	0.659803i	$0.770640\pi$
$728$		0			0
$729$	−4.39431	+	19.2527i	−0.162752	+	0.713065i
$730$	11.1351	−	10.3319i	0.412129	−	0.382400i
$731$	−0.746632	+	0.112537i	−0.0276152	+	0.00416232i
$732$	−2.50557	−	0.772866i	−0.0926086	−	0.0285660i
$733$	−3.87736	−	51.7398i	−0.143214	−	1.91105i	−0.356887	−	0.934148i	$-0.616162\pi$
$733$	−3.87736	−	51.7398i	−0.143214	−	1.91105i	0.213673	−	0.976905i	$-0.431457\pi$
$734$	−16.2331			−0.599174
$735$		0			0
$736$	4.10850			0.151441
$737$	1.43406	+	19.1362i	0.0528243	+	0.704891i
$738$	2.12225	+	0.654627i	0.0781211	+	0.0240972i
$739$	11.3618	−	1.71251i	0.417950	−	0.0629958i	0.0632991	−	0.997995i	$-0.479838\pi$
$739$	11.3618	−	1.71251i	0.417950	−	0.0629958i	0.354651	+	0.934999i	$0.384600\pi$
$740$	−32.6330	+	30.2790i	−1.19961	+	1.11308i
$741$	−3.15804	+	13.8363i	−0.116013	+	0.508288i
$742$		0			0
$743$	8.97471	+	39.3208i	0.329250	+	1.44254i	0.820563	+	0.571556i	$0.193660\pi$
$743$	8.97471	+	39.3208i	0.329250	+	1.44254i	−0.491313	+	0.870983i	$0.663483\pi$
$744$	−6.94525	−	4.73519i	−0.254625	−	0.173601i
$745$	−13.5889	−	12.6086i	−0.497858	−	0.461945i
$746$	0.380924	−	0.259709i	0.0139466	−	0.00950863i
$747$	−1.17094	−	0.176491i	−0.0428425	−	0.00645747i
$748$	11.4125	+	5.49597i	0.417282	+	0.200953i
$749$		0			0
$750$	18.1574	−	8.74414i	0.663014	−	0.319291i
$751$	−48.7278	+	15.0305i	−1.77810	+	0.548472i	−0.997103	−	0.0760600i	$-0.975766\pi$
$751$	−48.7278	+	15.0305i	−1.77810	+	0.548472i	−0.780999	+	0.624532i	$0.785290\pi$
$752$	−1.08353	−	2.76079i	−0.0395123	−	0.100676i
$753$	16.7521	−	29.0155i	0.610480	−	1.05738i
$754$	−1.04182	−	1.80448i	−0.0379408	−	0.0657153i
$755$	−19.2900	+	24.1889i	−0.702036	+	0.880326i
$756$		0			0
$757$	−19.3200	−	24.2265i	−0.702198	−	0.880528i	0.294988	−	0.955501i	$-0.404684\pi$
$757$	−19.3200	−	24.2265i	−0.702198	−	0.880528i	−0.997186	+	0.0749728i	$0.976113\pi$
$758$	5.74438	−	14.6364i	0.208645	−	0.531620i
$759$	−0.844239	+	11.2656i	−0.0306439	+	0.408915i
$760$	−0.915492	+	12.2164i	−0.0332084	+	0.443135i
$761$	−8.34731	+	21.2686i	−0.302590	+	0.770986i	0.696008	+	0.718035i	$0.254958\pi$
$761$	−8.34731	+	21.2686i	−0.302590	+	0.770986i	−0.998597	+	0.0529512i	$0.983137\pi$
$762$	−8.38718	−	10.5172i	−0.303836	−	0.380998i
$763$		0			0
$764$	−9.52650	+	11.9459i	−0.344657	+	0.432186i
$765$	−17.1356	−	29.6798i	−0.619540	−	1.07308i
$766$	−0.381954	+	0.661564i	−0.0138006	+	0.0239033i
$767$	−12.1690	−	31.0060i	−0.439395	−	1.11956i
$768$	1.08331	−	0.334156i	0.0390905	−	0.0120578i
$769$	5.01401	−	2.41462i	0.180810	−	0.0870734i	−0.341289	−	0.939958i	$-0.610863\pi$
$769$	5.01401	−	2.41462i	0.180810	−	0.0870734i	0.522099	+	0.852885i	$0.325149\pi$
$770$		0			0
$771$	−15.4982	−	7.46356i	−0.558156	−	0.268794i
$772$	20.9940	+	3.16433i	0.755589	+	0.113887i
$773$	−9.40015	+	6.40891i	−0.338100	+	0.230513i	−0.720453	−	0.693504i	$-0.756066\pi$
$773$	−9.40015	+	6.40891i	−0.338100	+	0.230513i	0.382353	+	0.924016i	$0.375114\pi$
$774$	0.181742	+	0.168632i	0.00653259	+	0.00606136i
$775$	59.0898	+	40.2867i	2.12257	+	1.44714i
$776$	2.15846	+	9.45681i	0.0774840	+	0.339480i
$777$		0			0
$778$	4.35141	−	19.0648i	0.156006	−	0.683505i
$779$	−3.03927	+	2.82003i	−0.108893	+	0.101038i
$780$	−16.7767	+	2.52868i	−0.600702	+	0.0905412i
$781$	21.4395	+	6.61321i	0.767165	+	0.236639i
$782$	−1.60344	−	21.3964i	−0.0573388	−	0.765133i
$783$	2.84789			0.101775
$784$		0			0
$785$	−4.52689			−0.161572
$786$	−0.445740	−	5.94799i	−0.0158990	−	0.212158i
$787$	−4.01650	−	1.23893i	−0.143173	−	0.0441630i	0.222340	−	0.974969i	$-0.428630\pi$
$787$	−4.01650	−	1.23893i	−0.143173	−	0.0441630i	−0.365513	+	0.930806i	$0.619107\pi$
$788$	−17.0931	+	2.57636i	−0.608915	+	0.0917792i
$789$	17.9479	−	16.6532i	0.638961	−	0.592869i
$790$	11.1192	−	48.7164i	0.395603	−	1.73325i
$791$		0			0
$792$	−0.925504	−	4.05490i	−0.0328864	−	0.144085i
$793$	−7.47323	−	5.09516i	−0.265382	−	0.180934i
$794$	12.8143	+	11.8899i	0.454761	+	0.421957i
$795$	−19.6031	+	13.3651i	−0.695249	+	0.474013i
$796$	20.4131	+	3.07677i	0.723522	+	0.109053i
$797$	7.34703	+	3.53814i	0.260245	+	0.125328i	0.559457	−	0.828859i	$-0.311010\pi$
$797$	7.34703	+	3.53814i	0.260245	+	0.125328i	−0.299212	+	0.954187i	$0.596724\pi$
$798$		0			0
$799$	−13.9548	+	6.72030i	−0.493687	+	0.237747i
$800$	−9.21672	+	2.84298i	−0.325860	+	0.100515i
$801$	−1.52991	−	3.89814i	−0.0540567	−	0.137734i
$802$	3.84032	−	6.65163i	0.135606	−	0.234877i
$803$	−4.81372	−	8.33760i	−0.169872	−	0.294228i
$804$	5.59231	−	7.01254i	0.197226	−	0.247313i
$805$		0			0
$806$	−18.0789	−	22.6702i	−0.636801	−	0.798523i
$807$	−11.0728	+	28.2130i	−0.389780	+	0.993144i
$808$	1.10194	−	14.7044i	0.0387662	−	0.517300i
$809$	−0.268571	+	3.58384i	−0.00944247	+	0.126001i	−0.999933	−	0.0115803i	$-0.996314\pi$
$809$	−0.268571	+	3.58384i	−0.00944247	+	0.126001i	0.990490	+	0.137581i	$0.0439328\pi$
$810$	1.27952	−	3.26016i	0.0449578	−	0.114550i
$811$	−9.26165	−	11.6137i	−0.325220	−	0.407814i	0.592163	−	0.805818i	$-0.298274\pi$
$811$	−9.26165	−	11.6137i	−0.325220	−	0.407814i	−0.917383	+	0.398005i	$0.869703\pi$
$812$		0			0
$813$	−4.55880	+	5.71656i	−0.159884	+	0.200488i
$814$	14.1073	+	24.4345i	0.494459	+	0.856428i
$815$	28.2516	−	48.9332i	0.989610	−	1.71406i
$816$	−2.16301	−	5.51127i	−0.0757206	−	0.192933i
$817$	−0.442269	+	0.136422i	−0.0154730	+	0.00477280i
$818$	−7.74366	+	3.72915i	−0.270751	+	0.130387i
$819$		0			0
$820$	−4.46561	−	2.15053i	−0.155946	−	0.0750996i
$821$	25.9629	+	3.91327i	0.906110	+	0.136574i	0.585533	−	0.810648i	$-0.300885\pi$
$821$	25.9629	+	3.91327i	0.906110	+	0.136574i	0.320577	+	0.947223i	$0.396123\pi$
$822$	−7.92362	+	5.40224i	−0.276368	+	0.188425i
$823$	17.1331	+	15.8972i	0.597223	+	0.554142i	0.919793	−	0.392404i	$-0.128356\pi$
$823$	17.1331	+	15.8972i	0.597223	+	0.554142i	−0.322570	+	0.946546i	$0.604547\pi$
$824$	−5.64525	−	3.84887i	−0.196662	−	0.134082i
$825$	−5.90160	−	25.8566i	−0.205467	−	0.900212i
$826$		0			0
$827$	0.632079	−	2.76932i	0.0219796	−	0.0962987i	−0.962748	−	0.270399i	$-0.912844\pi$
$827$	0.632079	−	2.76932i	0.0219796	−	0.0962987i	0.984728	+	0.174100i	$0.0557016\pi$
$828$	−5.16449	+	4.79195i	−0.179478	+	0.166532i
$829$	9.78817	−	1.47533i	0.339957	−	0.0512403i	0.0231550	−	0.999732i	$-0.492629\pi$
$829$	9.78817	−	1.47533i	0.339957	−	0.0512403i	0.316802	+	0.948492i	$0.397391\pi$
$830$	2.52532	+	0.778957i	0.0876551	+	0.0270380i
$831$	−2.22706	−	29.7181i	−0.0772559	−	1.03091i
$832$	3.91064			0.135577
$833$		0			0
$834$	0.151416			0.00524312
$835$	4.80200	+	64.0782i	0.166180	+	2.21752i
$836$	7.41947	+	2.28860i	0.256608	+	0.0791530i
$837$	39.1892	−	5.90682i	1.35458	−	0.204169i
$838$	23.0634	−	21.3997i	0.796711	−	0.739240i
$839$	−5.51627	+	24.1683i	−0.190443	+	0.834384i	0.785934	+	0.618310i	$0.212182\pi$
$839$	−5.51627	+	24.1683i	−0.190443	+	0.834384i	−0.976377	+	0.216074i	$0.930675\pi$
$840$		0			0
$841$	6.38994	+	27.9961i	0.220343	+	0.965384i
$842$	19.9637	+	13.6110i	0.687995	+	0.469067i
$843$	−10.8440	−	10.0618i	−0.373488	−	0.346546i
$844$	8.77464	−	5.98245i	0.302036	−	0.205924i
$845$	−8.67750	−	1.30792i	−0.298515	−	0.0449939i
$846$	4.58207	+	2.20661i	0.157535	+	0.0758647i
$847$		0			0
$848$	4.92711	−	2.37277i	0.169198	−	0.0814813i
$849$	−18.0330	+	5.56245i	−0.618891	+	0.190903i
$850$	18.4028	+	46.8896i	0.631211	+	1.60830i
$851$	23.8961	−	41.3893i	0.819149	−	1.41881i
$852$	−5.24337	−	9.08178i	−0.179635	−	0.311137i
$853$	−10.4098	+	13.0534i	−0.356424	+	0.446941i	−0.927426	−	0.374008i	$-0.877983\pi$
$853$	−10.4098	+	13.0534i	−0.356424	+	0.446941i	0.571002	+	0.820949i	$0.306555\pi$
$854$		0			0
$855$	−13.0978	−	16.4241i	−0.447934	−	0.561692i
$856$	−1.73413	+	4.41848i	−0.0592712	+	0.151021i
$857$	−1.60662	+	21.4389i	−0.0548812	+	0.732339i	0.900102	+	0.435679i	$0.143492\pi$
$857$	−1.60662	+	21.4389i	−0.0548812	+	0.732339i	−0.954983	+	0.296660i	$0.904127\pi$
$858$	−0.803581	+	10.7230i	−0.0274338	+	0.366079i
$859$	2.77933	−	7.08163i	0.0948296	−	0.241622i	−0.875586	−	0.483062i	$-0.839525\pi$
$859$	2.77933	−	7.08163i	0.0948296	−	0.241622i	0.970416	+	0.241440i	$0.0776198\pi$
$860$	−0.344976	−	0.432587i	−0.0117636	−	0.0147511i
$861$		0			0
$862$	−11.8935	+	14.9140i	−0.405096	+	0.507974i
$863$	−15.4433	−	26.7487i	−0.525698	−	0.910535i	−0.999552	−	0.0299318i	$-0.990471\pi$
$863$	−15.4433	−	26.7487i	−0.525698	−	0.910535i	0.473854	−	0.880603i	$-0.342862\pi$
$864$	−2.67251	+	4.62893i	−0.0909208	+	0.157479i
$865$	−0.296412	−	0.755246i	−0.0100783	−	0.0256791i
$866$	9.34407	−	2.88226i	0.317524	−	0.0979433i
$867$	−10.4937	+	5.05350i	−0.356385	+	0.171626i
$868$		0			0
$869$	−28.5340	−	13.7412i	−0.967949	−	0.466140i
$870$	−2.28577	−	0.344524i	−0.0774948	−	0.0116805i
$871$	25.5639	−	17.4292i	0.866200	−	0.590565i
$872$	−10.3489	−	9.60238i	−0.350458	−	0.325178i
$873$	−13.7432	−	9.36994i	−0.465136	−	0.317124i
$874$	−2.92661	−	12.8223i	−0.0989941	−	0.433722i
$875$		0			0
$876$	−1.00132	+	4.38705i	−0.0338313	+	0.148225i
$877$	19.2555	−	17.8665i	0.650213	−	0.603310i	−0.284516	−	0.958671i	$-0.591833\pi$
$877$	19.2555	−	17.8665i	0.650213	−	0.603310i	0.934729	+	0.355362i	$0.115642\pi$
$878$	−10.2309	+	1.54206i	−0.345275	+	0.0520418i
$879$	−15.6671	−	4.83267i	−0.528439	−	0.163002i
$880$	0.693653	+	9.25615i	0.0233830	+	0.312025i
$881$	−51.1262			−1.72248			−0.861242	−	0.508195i	$-0.830313\pi$
$881$	−51.1262			−1.72248			−0.861242	+	0.508195i	$0.830313\pi$
$882$		0			0
$883$	−35.1649			−1.18339			−0.591696	−	0.806161i	$-0.701541\pi$
$883$	−35.1649			−1.18339			−0.591696	+	0.806161i	$0.701541\pi$
$884$	−1.52622	−	20.3659i	−0.0513322	−	0.684981i
$885$	−35.3108	−	10.8919i	−1.18696	−	0.366128i
$886$	−5.48274	+	0.826390i	−0.184196	+	0.0277631i
$887$	−33.0898	+	30.7029i	−1.11105	+	1.03090i	−0.111739	+	0.993738i	$0.535642\pi$
$887$	−33.0898	+	30.7029i	−1.11105	+	1.03090i	−0.999309	+	0.0371645i	$0.988167\pi$
$888$	2.93449	−	12.8569i	0.0984752	−	0.431448i
$889$		0			0
$890$	2.07959	+	9.11126i	0.0697079	+	0.305410i
$891$	−1.83402	−	1.25041i	−0.0614420	−	0.0418905i
$892$	−14.2120	−	13.1869i	−0.475855	−	0.441529i
$893$	−7.84438	+	5.34821i	−0.262502	+	0.178971i
$894$	5.43014	+	0.818462i	0.181611	+	0.0273735i
$895$	−27.7932	−	13.3845i	−0.929024	−	0.447395i
$896$		0			0
$897$	16.4108	−	7.90302i	0.547940	−	0.263874i
$898$	−6.90547	+	2.13006i	−0.230439	+	0.0710809i
$899$	−1.44333	−	3.67755i	−0.0481378	−	0.122653i
$900$	8.26974	−	14.3236i	0.275658	−	0.477454i
$901$	−14.2799	−	24.7335i	−0.475732	−	0.823993i
$902$	−1.95862	+	2.45604i	−0.0652150	+	0.0817771i
$903$		0			0
$904$	−7.17986	−	9.00326i	−0.238799	−	0.299444i
$905$	8.22308	−	20.9521i	0.273344	−	0.696470i
$906$	0.684919	−	9.13961i	0.0227549	−	0.303643i
$907$	0.954864	−	12.7418i	0.0317057	−	0.423084i	−0.958655	−	0.284571i	$-0.908149\pi$
$907$	0.954864	−	12.7418i	0.0317057	−	0.423084i	0.990361	−	0.138513i	$-0.0442321\pi$
$908$	−0.00352218	+	0.00897436i	−0.000116888	+	0.000297825i
$909$	15.7653	+	19.7691i	0.522902	+	0.655699i
$910$		0			0
$911$	26.8953	−	33.7256i	0.891080	−	1.11738i	−0.101384	−	0.994847i	$-0.532327\pi$
$911$	26.8953	−	33.7256i	0.891080	−	1.11738i	0.992465	−	0.122532i	$-0.0391014\pi$
$912$	−1.81455	−	3.14289i	−0.0600857	−	0.104072i
$913$	0.837476	−	1.45055i	0.0277164	−	0.0480062i
$914$	−14.6058	−	37.2150i	−0.483118	−	1.23096i
$915$	−9.58859	+	2.95769i	−0.316989	+	0.0977782i
$916$	−19.1611	+	9.22749i	−0.633100	+	0.304885i
$917$		0			0
$918$	25.1497	+	12.1114i	0.830063	+	0.399737i
$919$	18.8615	+	2.84291i	0.622183	+	0.0937789i	0.452566	−	0.891731i	$-0.350509\pi$
$919$	18.8615	+	2.84291i	0.622183	+	0.0937789i	0.169617	+	0.985510i	$0.445747\pi$
$920$	12.9908	−	8.85701i	0.428295	−	0.292007i
$921$	−16.0708	−	14.9115i	−0.529551	−	0.491351i
$922$	−0.820599	−	0.559475i	−0.0270250	−	0.0184253i
$923$	−8.04954	−	35.2673i	−0.264954	−	1.16084i
$924$		0			0
$925$	−24.9665	+	109.385i	−0.820894	+	3.59657i
$926$	−18.5617	+	17.2227i	−0.609974	+	0.565973i
$927$	11.5853	−	1.74621i	0.380513	−	0.0573531i
$928$	0.509140	+	0.157049i	0.0167133	+	0.00515539i
$929$	−0.971743	−	12.9670i	−0.0318818	−	0.425434i	−0.990193	−	0.139707i	$-0.955384\pi$
$929$	−0.971743	−	12.9670i	−0.0318818	−	0.425434i	0.958311	−	0.285727i	$-0.0922350\pi$
$930$	−32.1685			−1.05485
$931$		0			0
$932$	−20.3784			−0.667518
$933$	0.138906	+	1.85357i	0.00454758	+	0.0606832i
$934$	−0.0766584	−	0.0236460i	−0.00250834	−	0.000773720i
$935$	47.9337	−	7.22485i	1.56760	−	0.236278i
$936$	−4.91577	+	4.56117i	−0.160677	+	0.149087i
$937$	11.6840	−	51.1909i	0.381699	−	1.67233i	−0.310459	−	0.950587i	$-0.600483\pi$
$937$	11.6840	−	51.1909i	0.381699	−	1.67233i	0.692158	−	0.721746i	$-0.256660\pi$
$938$		0			0
$939$	−1.54853	−	6.78457i	−0.0505345	−	0.221406i
$940$	−9.37770	−	6.39361i	−0.305867	−	0.208536i
$941$	30.9356	+	28.7041i	1.00847	+	0.935726i	0.997936	−	0.0642182i	$-0.0204554\pi$
$941$	30.9356	+	28.7041i	1.00847	+	0.935726i	0.0105372	+	0.999944i	$0.496646\pi$
$942$	1.10802	−	0.755432i	0.0361011	−	0.0246133i
$943$	5.26173	+	0.793079i	0.171346	+	0.0258262i
$944$	7.67391	+	3.69556i	0.249764	+	0.120280i
$945$		0			0
$946$	−0.315951	+	0.152154i	−0.0102725	+	0.00494695i
$947$	−0.356152	+	0.109858i	−0.0115734	+	0.00356992i	−0.300536	−	0.953770i	$-0.597166\pi$
$947$	−0.356152	+	0.109858i	−0.0115734	+	0.00356992i	0.288963	+	0.957340i	$0.406690\pi$
$948$	5.40805	+	13.7795i	0.175645	+	0.447537i
$949$	−7.76122	+	13.4428i	−0.251940	+	0.436373i
$950$	15.4381	+	26.7395i	0.500878	+	0.867545i
$951$	−19.9572	+	25.0256i	−0.647158	+	0.811510i
$952$		0			0
$953$	−25.6111	−	32.1153i	−0.829625	−	1.04032i	−0.998504	−	0.0546804i	$-0.982586\pi$
$953$	−25.6111	−	32.1153i	−0.829625	−	1.04032i	0.168879	−	0.985637i	$-0.445985\pi$
$954$	−3.42602	+	8.72936i	−0.110922	+	0.282623i
$955$	−4.36966	+	58.3091i	−0.141399	+	1.88684i
$956$	−1.77762	+	23.7207i	−0.0574925	+	0.767184i
$957$	−0.535252	+	1.36380i	−0.0173023	+	0.0440854i
$958$	11.3279	+	14.2048i	0.365988	+	0.458935i
$959$		0			0
$960$	2.70499	−	3.39195i	0.0873032	−	0.109475i
$961$	−11.9890	−	20.7655i	−0.386741	−	0.669854i
$962$	22.7453	−	39.3961i	0.733339	−	1.27018i
$963$	−2.97365	−	7.57674i	−0.0958246	−	0.244157i
$964$	−7.25102	+	2.23664i	−0.233540	+	0.0720375i
$965$	73.2032	−	35.2528i	2.35650	−	1.13483i
$966$		0			0
$967$	−5.41633	−	2.60837i	−0.174178	−	0.0838795i	0.344763	−	0.938690i	$-0.387959\pi$
$967$	−5.41633	−	2.60837i	−0.174178	−	0.0838795i	−0.518941	+	0.854810i	$0.673673\pi$
$968$	−5.05988	−	0.762654i	−0.162631	−	0.0245126i
$969$	−15.6595	+	10.6764i	−0.503055	+	0.342977i
$970$	27.2117	+	25.2487i	0.873714	+	0.810688i
$971$	−36.0163	−	24.5555i	−1.15582	−	0.788023i	−0.175312	−	0.984513i	$-0.556093\pi$
$971$	−36.0163	−	24.5555i	−1.15582	−	0.788023i	−0.980506	+	0.196490i	$0.937046\pi$
$972$	−3.33728	−	14.6216i	−0.107043	−	0.468987i
$973$		0			0
$974$	−2.41364	+	10.5748i	−0.0773380	+	0.338840i
$975$	−31.3461	+	29.0849i	−1.00388	+	0.931463i
$976$	2.28706	−	0.344718i	0.0732069	−	0.0110342i
$977$	−47.1051	−	14.5300i	−1.50703	−	0.464856i	−0.572245	−	0.820083i	$-0.693927\pi$
$977$	−47.1051	−	14.5300i	−1.50703	−	0.464856i	−0.934780	+	0.355227i	$0.884404\pi$
$978$	1.25086	+	16.6916i	0.0399981	+	0.533737i
$979$	5.92319			0.189306
$980$		0			0
$981$	24.2086			0.772920
$982$	0.881297	+	11.7601i	0.0281233	+	0.375279i
$983$	57.7031	+	17.7991i	1.84044	+	0.567702i	0.999653	+	0.0263424i	$0.00838602\pi$
$983$	57.7031	+	17.7991i	1.84044	+	0.567702i	0.840791	+	0.541359i	$0.182090\pi$
$984$	1.45189	−	0.218837i	0.0462845	−	0.00697627i
$985$	−48.4932	+	44.9951i	−1.54512	+	1.43366i
$986$	0.619181	−	2.71281i	0.0197187	−	0.0863934i
$987$		0			0
$988$	−2.78567	−	12.2048i	−0.0886239	−	0.388287i
$989$	0.490796	+	0.334619i	0.0156064	+	0.0106403i
$990$	−11.6678	−	10.8262i	−0.370828	−	0.344078i
$991$	−20.2394	+	13.7990i	−0.642926	+	0.438340i	−0.840399	−	0.541969i	$-0.817679\pi$
$991$	−20.2394	+	13.7990i	−0.642926	+	0.438340i	0.197472	+	0.980308i	$0.436727\pi$
$992$	7.33189	+	1.10511i	0.232788	+	0.0350871i
$993$	−11.6009	−	5.58668i	−0.368142	−	0.177288i
$994$		0			0
$995$	71.1777	−	34.2774i	2.25649	−	1.08667i
$996$	−0.748094	+	0.230756i	−0.0237043	+	0.00731179i
$997$	22.7012	+	57.8416i	0.718953	+	1.83186i	0.525599	+	0.850733i	$0.323841\pi$
$997$	22.7012	+	57.8416i	0.718953	+	1.83186i	0.193354	+	0.981129i	$0.438063\pi$
$998$	−2.04464	+	3.54142i	−0.0647219	+	0.112102i
$999$	31.0881	+	53.8462i	0.983584	+	1.70362i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	686.2.g.b.459.2		24
7.2	even	3		686.2.g.c.373.1		24
7.3	odd	6		686.2.e.f.197.3		24
7.4	even	3		686.2.e.e.197.2		24
7.5	odd	6		686.2.g.a.373.2		24
7.6	odd	2		98.2.g.a.81.1	yes	24
21.20	even	2		882.2.z.d.865.1		24
28.27	even	2		784.2.bg.a.81.2		24
49.4	even	21		686.2.e.e.491.2		24
49.11	even	21		4802.2.a.k.1.7		12
49.22	even	7		686.2.g.c.263.1		24
49.23	even	21	inner	686.2.g.b.275.2		24
49.26	odd	42		98.2.g.a.23.1	✓	24
49.27	odd	14		686.2.g.a.263.2		24
49.38	odd	42		4802.2.a.i.1.6		12
49.45	odd	42		686.2.e.f.491.3		24
147.26	even	42		882.2.z.d.415.1		24
196.75	even	42		784.2.bg.a.513.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.a.23.1	✓	24	49.26	odd	42
98.2.g.a.81.1	yes	24	7.6	odd	2
686.2.e.e.197.2		24	7.4	even	3
686.2.e.e.491.2		24	49.4	even	21
686.2.e.f.197.3		24	7.3	odd	6
686.2.e.f.491.3		24	49.45	odd	42
686.2.g.a.263.2		24	49.27	odd	14
686.2.g.a.373.2		24	7.5	odd	6
686.2.g.b.275.2		24	49.23	even	21	inner
686.2.g.b.459.2		24	1.1	even	1	trivial
686.2.g.c.263.1		24	49.22	even	7
686.2.g.c.373.1		24	7.2	even	3
784.2.bg.a.81.2		24	28.27	even	2
784.2.bg.a.513.2		24	196.75	even	42
882.2.z.d.415.1		24	147.26	even	42
882.2.z.d.865.1		24	21.20	even	2
4802.2.a.i.1.6		12	49.38	odd	42
4802.2.a.k.1.7		12	49.11	even	21

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:	\( N \)	\(=\)	\( 686 = 2 \cdot 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	686.g (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0747301 - 0.997204i) q^{2} +(1.08331 + 0.334156i) q^{3} +(-0.988831 + 0.149042i) q^{4} +(-2.80532 + 2.60296i) q^{5} +(0.252266 - 1.10525i) q^{6} +(0.222521 + 0.974928i) q^{8} +(-1.41682 - 0.965972i) q^{9} +O(q^{10})\)	\(q+(-0.0747301 - 0.997204i) q^{2} +(1.08331 + 0.334156i) q^{3} +(-0.988831 + 0.149042i) q^{4} +(-2.80532 + 2.60296i) q^{5} +(0.252266 - 1.10525i) q^{6} +(0.222521 + 0.974928i) q^{8} +(-1.41682 - 0.965972i) q^{9} +(2.80532 + 2.60296i) q^{10} +(2.00403 - 1.36632i) q^{11} +(-1.12101 - 0.168965i) q^{12} +(-3.52337 - 1.69676i) q^{13} +(-3.90882 + 1.88239i) q^{15} +(0.955573 - 0.294755i) q^{16} +(-1.90797 - 4.86142i) q^{17} +(-0.857392 + 1.48505i) q^{18} +(-1.60059 - 2.77231i) q^{19} +(2.38604 - 2.99200i) q^{20} +(-1.51226 - 1.89632i) q^{22} +(-1.50100 + 3.82450i) q^{23} +(-0.0847196 + 1.13050i) q^{24} +(0.720789 - 9.61826i) q^{25} +(-1.42872 + 3.64031i) q^{26} +(-3.33257 - 4.17891i) q^{27} +(-0.332203 + 0.416569i) q^{29} +(2.16923 + 3.75722i) q^{30} +(-3.70735 + 6.42133i) q^{31} +(-0.365341 - 0.930874i) q^{32} +(2.62755 - 0.810490i) q^{33} +(-4.70525 + 2.26593i) q^{34} +(1.54497 + 0.744017i) q^{36} +(-11.5026 - 1.73374i) q^{37} +(-2.64494 + 1.80329i) q^{38} +(-3.24991 - 3.01547i) q^{39} +(-3.16194 - 2.15577i) q^{40} +(-0.288200 - 1.26269i) q^{41} +(0.0321723 - 0.140956i) q^{43} +(-1.77801 + 1.64975i) q^{44} +(6.48902 - 0.978063i) q^{45} +(3.92597 + 1.21100i) q^{46} +(-0.221635 - 2.95751i) q^{47} +1.13367 q^{48} -9.64523 q^{50} +(-0.442442 - 5.90398i) q^{51} +(3.73690 + 1.15268i) q^{52} +(5.40760 - 0.815064i) q^{53} +(-3.91818 + 3.63554i) q^{54} +(-2.06546 + 9.04938i) q^{55} +(-0.807551 - 3.53811i) q^{57} +(0.440230 + 0.300143i) q^{58} +(6.24369 + 5.79330i) q^{59} +(3.58461 - 2.44395i) q^{60} +(2.28706 + 0.344718i) q^{61} +(6.68042 + 3.21712i) q^{62} +(-0.900969 + 0.433884i) q^{64} +(14.3008 - 4.41121i) q^{65} +(-1.00458 - 2.55963i) q^{66} +(-3.95589 + 6.85180i) q^{67} +(2.61122 + 4.52276i) q^{68} +(-2.90403 + 3.64154i) q^{69} +(5.76742 + 7.23212i) q^{71} +(0.626481 - 1.59625i) q^{72} +(0.296625 - 3.95819i) q^{73} +(-0.869300 + 11.6000i) q^{74} +(3.99484 - 10.1787i) q^{75} +(1.99591 + 2.50279i) q^{76} +(-2.76417 + 3.46616i) q^{78} +(-6.52866 - 11.3080i) q^{79} +(-1.91345 + 3.31420i) q^{80} +(-0.334348 - 0.851905i) q^{81} +(-1.23762 + 0.381755i) q^{82} +(0.622177 - 0.299625i) q^{83} +(18.0066 + 8.67150i) q^{85} +(-0.142966 - 0.0215487i) q^{86} +(-0.499077 + 0.340265i) q^{87} +(1.77801 + 1.64975i) q^{88} +(2.01773 + 1.37567i) q^{89} +(-1.46025 - 6.39779i) q^{90} +(0.914228 - 4.00549i) q^{92} +(-6.16193 + 5.71744i) q^{93} +(-2.93268 + 0.442030i) q^{94} +(11.7064 + 3.61094i) q^{95} +(-0.0847196 - 1.13050i) q^{96} +9.70001 q^{97} -4.15918 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} - 7 q^{3} + 2 q^{4} + 7 q^{6} + 4 q^{8} - 33 q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 - 7 * q^3 + 2 * q^4 + 7 * q^6 + 4 * q^8 - 33 * q^9	\( 24 q - 2 q^{2} - 7 q^{3} + 2 q^{4} + 7 q^{6} + 4 q^{8} - 33 q^{9} - 7 q^{11} - 14 q^{13} - 7 q^{15} + 2 q^{16} + 7 q^{17} + 5 q^{18} + 7 q^{20} - 7 q^{22} - 21 q^{23} + 4 q^{25} + 7 q^{26} + 35 q^{27} - 11 q^{29} - 28 q^{31} - 2 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{36} - 24 q^{37} + 7 q^{38} - 40 q^{39} - 14 q^{40} - 28 q^{41} + 10 q^{43} + 21 q^{44} - 7 q^{45} + 42 q^{46} + 70 q^{47} + 14 q^{48} + 8 q^{50} + 60 q^{51} + 7 q^{52} + 26 q^{53} - 63 q^{54} - 56 q^{55} - 33 q^{57} - 30 q^{58} + 7 q^{59} + 14 q^{60} - 14 q^{61} - 28 q^{62} - 4 q^{64} + 21 q^{66} - 36 q^{67} + 14 q^{68} + 35 q^{69} - 2 q^{72} + 7 q^{73} - 11 q^{74} + 28 q^{75} - 24 q^{78} - 26 q^{79} + 55 q^{81} - 14 q^{82} + 7 q^{83} + 49 q^{85} - 16 q^{86} - 35 q^{87} - 21 q^{88} + 56 q^{89} + 21 q^{90} + 21 q^{92} + 72 q^{93} + 35 q^{94} - 14 q^{95} + 126 q^{97} - 14 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 - 7 * q^3 + 2 * q^4 + 7 * q^6 + 4 * q^8 - 33 * q^9 - 7 * q^11 - 14 * q^13 - 7 * q^15 + 2 * q^16 + 7 * q^17 + 5 * q^18 + 7 * q^20 - 7 * q^22 - 21 * q^23 + 4 * q^25 + 7 * q^26 + 35 * q^27 - 11 * q^29 - 28 * q^31 - 2 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^36 - 24 * q^37 + 7 * q^38 - 40 * q^39 - 14 * q^40 - 28 * q^41 + 10 * q^43 + 21 * q^44 - 7 * q^45 + 42 * q^46 + 70 * q^47 + 14 * q^48 + 8 * q^50 + 60 * q^51 + 7 * q^52 + 26 * q^53 - 63 * q^54 - 56 * q^55 - 33 * q^57 - 30 * q^58 + 7 * q^59 + 14 * q^60 - 14 * q^61 - 28 * q^62 - 4 * q^64 + 21 * q^66 - 36 * q^67 + 14 * q^68 + 35 * q^69 - 2 * q^72 + 7 * q^73 - 11 * q^74 + 28 * q^75 - 24 * q^78 - 26 * q^79 + 55 * q^81 - 14 * q^82 + 7 * q^83 + 49 * q^85 - 16 * q^86 - 35 * q^87 - 21 * q^88 + 56 * q^89 + 21 * q^90 + 21 * q^92 + 72 * q^93 + 35 * q^94 - 14 * q^95 + 126 * q^97 - 14 * q^99

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