LMFDB - Embedded newform 775.2.bl.a.51.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [775,2,Mod(51,775)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("775.51"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(775, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.bl (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,6,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			51.1
Root			$0.333129i$ of defining polynomial
Character	$\chi$	$=$	775.51
Dual form			775.2.bl.a.76.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.640321 - 1.97070i) q^{2} +(1.43153 + 1.58988i) q^{3} +(-1.85563 + 1.34820i) q^{4} +(2.21654 - 3.83916i) q^{6} +(-0.384094 - 3.65441i) q^{7} +(0.492333 + 0.357701i) q^{8} +(-0.164841 + 1.56836i) q^{9} +(-3.91056 - 1.74109i) q^{11} +(-4.79986 - 1.02024i) q^{12} +(-2.04159 + 0.433953i) q^{13} +(-6.95582 + 3.09693i) q^{14} +(-1.02791 + 3.16357i) q^{16} +(-1.94411 + 0.865573i) q^{17} +(3.19632 - 0.679399i) q^{18} +(0.606466 + 0.128908i) q^{19} +(5.26022 - 5.84207i) q^{21} +(-0.927168 + 8.82142i) q^{22} +(-2.71334 - 1.97136i) q^{23} +(0.136090 + 1.29481i) q^{24} +(2.16247 + 3.74550i) q^{26} +(2.46294 - 1.78943i) q^{27} +(5.63960 + 6.26341i) q^{28} +(-0.425645 - 1.31000i) q^{29} +(-1.44334 - 5.37743i) q^{31} +8.10976 q^{32} +(-2.82997 - 8.70975i) q^{33} +(2.95064 + 3.27702i) q^{34} +(-1.80857 - 3.13253i) q^{36} +(0.137239 - 0.237704i) q^{37} +(-0.134293 - 1.27771i) q^{38} +(-3.61253 - 2.62466i) q^{39} +(-2.86248 + 3.17911i) q^{41} +(-14.8812 - 6.62555i) q^{42} +(0.263799 + 0.0560722i) q^{43} +(9.60390 - 2.04137i) q^{44} +(-2.14756 + 6.60950i) q^{46} +(-1.66225 + 5.11589i) q^{47} +(-6.50117 + 2.89451i) q^{48} +(-6.36016 + 1.35189i) q^{49} +(-4.15921 - 1.85180i) q^{51} +(3.20338 - 3.55772i) q^{52} +(0.993928 - 9.45659i) q^{53} +(-5.10351 - 3.70792i) q^{54} +(1.11808 - 1.93658i) q^{56} +(0.663228 + 1.14874i) q^{57} +(-2.30908 + 1.67764i) q^{58} +(-3.89932 - 4.33063i) q^{59} +2.22719 q^{61} +(-9.67313 + 6.28768i) q^{62} +5.79474 q^{63} +(-3.13704 - 9.65481i) q^{64} +(-15.3522 + 11.1541i) q^{66} +(-6.80719 - 11.7904i) q^{67} +(2.44059 - 4.22722i) q^{68} +(-0.750018 - 7.13595i) q^{69} +(0.139642 - 1.32861i) q^{71} +(-0.642159 + 0.713189i) q^{72} +(12.9413 + 5.76184i) q^{73} +(-0.556321 - 0.118250i) q^{74} +(-1.29917 + 0.578429i) q^{76} +(-4.86065 + 14.9595i) q^{77} +(-2.85925 + 8.79986i) q^{78} +(7.92648 - 3.52910i) q^{79} +(10.9984 + 2.33777i) q^{81} +(8.09799 + 3.60546i) q^{82} +(3.46976 - 3.85356i) q^{83} +(-1.88479 + 17.9325i) q^{84} +(-0.0584142 - 0.555774i) q^{86} +(1.47342 - 2.55203i) q^{87} +(-1.30251 - 2.25601i) q^{88} +(-4.05526 + 2.94632i) q^{89} +(2.37001 + 7.29413i) q^{91} +7.69274 q^{92} +(6.48327 - 9.99270i) q^{93} +11.1463 q^{94} +(11.6094 + 12.8935i) q^{96} +(5.43173 - 3.94638i) q^{97} +(6.73673 + 11.6684i) q^{98} +(3.37528 - 5.84615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} + 12 q^{3} - 14 q^{4} + 11 q^{6} - 2 q^{7} - 17 q^{8} - 10 q^{9} - 7 q^{11} - 5 q^{12} + 7 q^{13} - 6 q^{14} - 2 q^{16} + 6 q^{17} + 3 q^{18} + 16 q^{19} + 9 q^{21} - 9 q^{22} - q^{23} - 20 q^{24}+ \cdots + 6 q^{99}+O(q^{100}) $ 16 * q + 6 * q^2 + 12 * q^3 - 14 * q^4 + 11 * q^6 - 2 * q^7 - 17 * q^8 - 10 * q^9 - 7 * q^11 - 5 * q^12 + 7 * q^13 - 6 * q^14 - 2 * q^16 + 6 * q^17 + 3 * q^18 + 16 * q^19 + 9 * q^21 - 9 * q^22 - q^23 - 20 * q^24 + 9 * q^26 - 9 * q^27 + 30 * q^28 - 14 * q^29 + 15 * q^31 + 42 * q^32 + 13 * q^33 - 32 * q^34 + q^36 + 8 * q^37 - 8 * q^38 - 3 * q^39 - 8 * q^41 - 69 * q^42 - 23 * q^43 + 39 * q^44 + 34 * q^46 - 14 * q^47 - 34 * q^48 + 2 * q^49 - 42 * q^51 - 29 * q^52 - 6 * q^53 - 46 * q^54 - 30 * q^56 + 17 * q^57 + 15 * q^58 + 4 * q^59 - 60 * q^61 + 25 * q^62 + 46 * q^63 + 23 * q^64 - 30 * q^66 - 13 * q^67 - 30 * q^68 + 38 * q^69 - 14 * q^71 - 37 * q^72 - 2 * q^73 + 13 * q^74 - 12 * q^76 - 18 * q^77 + 15 * q^78 + 18 * q^79 + 23 * q^81 - 14 * q^82 + 16 * q^83 + 8 * q^84 - 26 * q^86 - 15 * q^87 + 17 * q^88 + q^89 + 8 * q^91 + 64 * q^92 - 17 * q^93 + 44 * q^94 + 8 * q^96 - 3 * q^97 + 10 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{4}{15}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.640321	−	1.97070i	−0.452775	−	1.39350i	−0.873727	−	0.486416i	$-0.838304\pi$
$2$	−0.640321	−	1.97070i	−0.452775	−	1.39350i	0.420952	−	0.907083i	$-0.361696\pi$
$3$	1.43153	+	1.58988i	0.826496	+	0.917916i	0.997732	−	0.0673137i	$-0.0214428\pi$
$3$	1.43153	+	1.58988i	0.826496	+	0.917916i	−0.171236	+	0.985230i	$0.554776\pi$
$4$	−1.85563	+	1.34820i	−0.927816	+	0.674098i
$5$		0			0
$5$		0			0
$6$	2.21654	−	3.83916i	0.904898	−	1.56733i
$7$	−0.384094	−	3.65441i	−0.145174	−	1.38124i	−0.788212	−	0.615404i	$-0.788993\pi$
$7$	−0.384094	−	3.65441i	−0.145174	−	1.38124i	0.643038	−	0.765834i	$-0.277674\pi$
$8$	0.492333	+	0.357701i	0.174066	+	0.126466i
$9$	−0.164841	+	1.56836i	−0.0549470	+	0.522786i
$10$		0			0
$11$	−3.91056	−	1.74109i	−1.17908	−	0.524960i	−0.278832	−	0.960340i	$-0.589947\pi$
$11$	−3.91056	−	1.74109i	−1.17908	−	0.524960i	−0.900247	+	0.435380i	$0.856614\pi$
$12$	−4.79986	−	1.02024i	−1.38560	−	0.294519i
$13$	−2.04159	+	0.433953i	−0.566235	+	0.120357i	−0.482130	−	0.876100i	$-0.660137\pi$
$13$	−2.04159	+	0.433953i	−0.566235	+	0.120357i	−0.0841053	+	0.996457i	$0.526803\pi$
$14$	−6.95582	+	3.09693i	−1.85902	+	0.827690i
$15$		0			0
$16$	−1.02791	+	3.16357i	−0.256976	+	0.790892i
$17$	−1.94411	+	0.865573i	−0.471516	+	0.209932i	−0.628717	−	0.777634i	$-0.716420\pi$
$17$	−1.94411	+	0.865573i	−0.471516	+	0.209932i	0.157201	+	0.987567i	$0.449753\pi$
$18$	3.19632	−	0.679399i	0.753380	−	0.160136i
$19$	0.606466	+	0.128908i	0.139133	+	0.0295736i	0.276952	−	0.960884i	$-0.410676\pi$
$19$	0.606466	+	0.128908i	0.139133	+	0.0295736i	−0.137819	+	0.990457i	$0.544009\pi$
$20$		0			0
$21$	5.26022	−	5.84207i	1.14788	−	1.27484i
$22$	−0.927168	+	8.82142i	−0.197673	+	1.88073i
$23$	−2.71334	−	1.97136i	−0.565771	−	0.411057i	0.267796	−	0.963476i	$-0.413705\pi$
$23$	−2.71334	−	1.97136i	−0.565771	−	0.411057i	−0.833567	+	0.552419i	$0.813705\pi$
$24$	0.136090	+	1.29481i	0.0277792	+	0.264302i
$25$		0			0
$26$	2.16247	+	3.74550i	0.424094	+	0.734553i
$27$	2.46294	−	1.78943i	0.473993	−	0.344376i
$28$	5.63960	+	6.26341i	1.06578	+	1.18367i
$29$	−0.425645	−	1.31000i	−0.0790403	−	0.243261i	0.903727	−	0.428110i	$-0.140820\pi$
$29$	−0.425645	−	1.31000i	−0.0790403	−	0.243261i	−0.982767	+	0.184849i	$0.940820\pi$
$30$		0			0
$31$	−1.44334	−	5.37743i	−0.259231	−	0.965815i
$31$	−1.44334	−	5.37743i	−0.259231	−	0.965815i
$32$	8.10976			1.43362
$33$	−2.82997	−	8.70975i	−0.492634	−	1.51617i
$34$	2.95064	+	3.27702i	0.506031	+	0.562004i
$35$		0			0
$36$	−1.80857	−	3.13253i	−0.301428	−	0.522089i
$37$	0.137239	−	0.237704i	0.0225619	−	0.0390783i	−0.854524	−	0.519412i	$-0.826151\pi$
$37$	0.137239	−	0.237704i	0.0225619	−	0.0390783i	0.877086	+	0.480334i	$0.159484\pi$
$38$	−0.134293	−	1.27771i	−0.0217851	−	0.207272i
$39$	−3.61253	−	2.62466i	−0.578468	−	0.420282i
$40$		0			0
$41$	−2.86248	+	3.17911i	−0.447045	+	0.496494i	−0.923978	−	0.382446i	$-0.875082\pi$
$41$	−2.86248	+	3.17911i	−0.447045	+	0.496494i	0.476933	+	0.878940i	$0.341748\pi$
$42$	−14.8812	−	6.62555i	−2.29622	−	1.02234i
$43$	0.263799	+	0.0560722i	0.0402290	+	0.00855093i	0.227982	−	0.973665i	$-0.426787\pi$
$43$	0.263799	+	0.0560722i	0.0402290	+	0.00855093i	−0.187753	+	0.982216i	$0.560121\pi$
$44$	9.60390	−	2.04137i	1.44784	−	0.307748i
$45$		0			0
$46$	−2.14756	+	6.60950i	−0.316640	+	0.974517i
$47$	−1.66225	+	5.11589i	−0.242464	+	0.746229i	0.753579	+	0.657358i	$0.228326\pi$
$47$	−1.66225	+	5.11589i	−0.242464	+	0.746229i	−0.996043	+	0.0888711i	$0.971674\pi$
$48$	−6.50117	+	2.89451i	−0.938363	+	0.417786i
$49$	−6.36016	+	1.35189i	−0.908595	+	0.193128i
$50$		0			0
$51$	−4.15921	−	1.85180i	−0.582406	−	0.259304i
$52$	3.20338	−	3.55772i	0.444229	−	0.493367i
$53$	0.993928	−	9.45659i	0.136527	−	1.29896i	−0.684895	−	0.728642i	$-0.740152\pi$
$53$	0.993928	−	9.45659i	0.136527	−	1.29896i	0.821422	−	0.570321i	$-0.193181\pi$
$54$	−5.10351	−	3.70792i	−0.694500	−	0.504584i
$55$		0			0
$56$	1.11808	−	1.93658i	0.149410	−	0.258786i
$57$	0.663228	+	1.14874i	0.0878467	+	0.152155i
$58$	−2.30908	+	1.67764i	−0.303196	+	0.220285i
$59$	−3.89932	−	4.33063i	−0.507648	−	0.563800i	0.433778	−	0.901020i	$-0.357180\pi$
$59$	−3.89932	−	4.33063i	−0.507648	−	0.563800i	−0.941426	+	0.337220i	$0.890513\pi$
$60$		0			0
$61$	2.22719			0.285162			0.142581	−	0.989783i	$-0.454460\pi$
$61$	2.22719			0.285162			0.142581	+	0.989783i	$0.454460\pi$
$62$	−9.67313	+	6.28768i	−1.22849	+	0.798536i
$63$	5.79474			0.730068
$64$	−3.13704	−	9.65481i	−0.392130	−	1.20685i
$65$		0			0
$66$	−15.3522	+	11.1541i	−1.88973	+	1.37297i
$67$	−6.80719	−	11.7904i	−0.831631	−	1.44043i	−0.896744	−	0.442550i	$-0.854074\pi$
$67$	−6.80719	−	11.7904i	−0.831631	−	1.44043i	0.0651129	−	0.997878i	$-0.479259\pi$
$68$	2.44059	−	4.22722i	0.295965	−	0.512626i
$69$	−0.750018	−	7.13595i	−0.0902916	−	0.859067i
$70$		0			0
$71$	0.139642	−	1.32861i	0.0165725	−	0.157676i	−0.983106	−	0.183038i	$-0.941407\pi$
$71$	0.139642	−	1.32861i	0.0165725	−	0.157676i	0.999678	+	0.0253613i	$0.00807361\pi$
$72$	−0.642159	+	0.713189i	−0.0756791	+	0.0840502i
$73$	12.9413	+	5.76184i	1.51466	+	0.674372i	0.984797	−	0.173708i	$-0.0555749\pi$
$73$	12.9413	+	5.76184i	1.51466	+	0.674372i	0.529868	+	0.848080i	$0.322242\pi$
$74$	−0.556321	−	0.118250i	−0.0646710	−	0.0137463i
$75$		0			0
$76$	−1.29917	+	0.578429i	−0.149025	+	0.0663503i
$77$	−4.86065	+	14.9595i	−0.553922	+	1.70480i
$78$	−2.85925	+	8.79986i	−0.323746	+	0.996388i
$79$	7.92648	−	3.52910i	0.891799	−	0.397054i	0.0909042	−	0.995860i	$-0.471024\pi$
$79$	7.92648	−	3.52910i	0.891799	−	0.397054i	0.800895	+	0.598805i	$0.204358\pi$
$80$		0			0
$81$	10.9984	+	2.33777i	1.22204	+	0.259753i
$82$	8.09799	+	3.60546i	0.894274	+	0.398156i
$83$	3.46976	−	3.85356i	0.380856	−	0.422983i	−0.521987	−	0.852953i	$-0.674809\pi$
$83$	3.46976	−	3.85356i	0.380856	−	0.422983i	0.902843	+	0.429970i	$0.141476\pi$
$84$	−1.88479	+	17.9325i	−0.205647	+	1.95660i
$85$		0			0
$86$	−0.0584142	−	0.555774i	−0.00629897	−	0.0599307i
$87$	1.47342	−	2.55203i	0.157967	−	0.273607i
$88$	−1.30251	−	2.25601i	−0.138848	−	0.240491i
$89$	−4.05526	+	2.94632i	−0.429857	+	0.312309i	−0.781592	−	0.623790i	$-0.785592\pi$
$89$	−4.05526	+	2.94632i	−0.429857	+	0.312309i	0.351735	+	0.936100i	$0.385592\pi$
$90$		0			0
$91$	2.37001	+	7.29413i	0.248444	+	0.764632i
$92$	7.69274			0.802024
$93$	6.48327	−	9.99270i	0.672284	−	1.03619i
$94$	11.1463			1.14965
$95$		0			0
$96$	11.6094	+	12.8935i	1.18488	+	1.31594i
$97$	5.43173	−	3.94638i	0.551508	−	0.400694i	−0.276833	−	0.960918i	$-0.589285\pi$
$97$	5.43173	−	3.94638i	0.551508	−	0.400694i	0.828341	+	0.560224i	$0.189285\pi$
$98$	6.73673	+	11.6684i	0.680512	+	1.17868i
$99$	3.37528	−	5.84615i	0.339228	−	0.587560i
$100$		0			0
$101$	14.6130	+	10.6169i	1.45404	+	1.05642i	0.984866	+	0.173320i	$0.0554495\pi$
$101$	14.6130	+	10.6169i	1.45404	+	1.05642i	0.469177	+	0.883104i	$0.344550\pi$
$102$	−0.986121	+	9.38232i	−0.0976406	+	0.928988i
$103$	−2.61986	+	2.90965i	−0.258142	+	0.286696i	−0.858260	−	0.513216i	$-0.828454\pi$
$103$	−2.61986	+	2.90965i	−0.258142	+	0.286696i	0.600117	+	0.799912i	$0.295121\pi$
$104$	−1.16037	−	0.516628i	−0.113783	−	0.0506596i
$105$		0			0
$106$	−19.2726	+	4.09652i	−1.87192	+	0.397889i
$107$	−10.1546	+	4.52113i	−0.981685	+	0.437074i	−0.833882	−	0.551943i	$-0.813887\pi$
$107$	−10.1546	+	4.52113i	−0.981685	+	0.437074i	−0.147803	+	0.989017i	$0.547220\pi$
$108$	−2.15781	+	6.64105i	−0.207635	+	0.639036i
$109$	5.59116	−	17.2078i	0.535536	−	1.64821i	−0.206951	−	0.978351i	$-0.566354\pi$
$109$	5.59116	−	17.2078i	0.535536	−	1.64821i	0.742488	−	0.669860i	$-0.233646\pi$
$110$		0			0
$111$	0.574382	−	0.122089i	0.0545179	−	0.0115881i
$112$	11.9558	+	2.54128i	1.12972	+	0.240129i
$113$	−16.0224	−	7.13365i	−1.50727	−	0.671078i	−0.523745	−	0.851875i	$-0.675465\pi$
$113$	−16.0224	−	7.13365i	−1.50727	−	0.671078i	−0.983520	+	0.180798i	$0.942132\pi$
$114$	1.83916	−	2.04259i	0.172253	−	0.191306i
$115$		0			0
$116$	2.55598	+	1.85703i	0.237317	+	0.172421i
$117$	−0.344056	−	3.27347i	−0.0318080	−	0.302633i
$118$	−6.03758	+	10.4574i	−0.555804	+	0.962681i
$119$	3.90988	+	6.77211i	0.358418	+	0.620798i
$120$		0			0
$121$	4.90064	+	5.44271i	0.445513	+	0.494792i
$122$	−1.42611	−	4.38913i	−0.129114	−	0.397373i
$123$	−9.15213			−0.825220
$124$	9.92814	+	8.03263i	0.891573	+	0.721352i
$125$		0			0
$126$	−3.71049	−	11.4197i	−0.330557	−	1.01735i
$127$	9.50050	+	10.5514i	0.843033	+	0.936283i	0.998671	−	0.0515308i	$-0.0164100\pi$
$127$	9.50050	+	10.5514i	0.843033	+	0.936283i	−0.155638	+	0.987814i	$0.549743\pi$
$128$	−3.89620	+	2.83075i	−0.344378	+	0.250205i
$129$	0.288489	+	0.499677i	0.0254000	+	0.0439941i
$130$		0			0
$131$	−0.751404	−	7.14913i	−0.0656505	−	0.624623i	−0.977037	−	0.213071i	$-0.931654\pi$
$131$	−0.751404	−	7.14913i	−0.0656505	−	0.624623i	0.911386	−	0.411552i	$-0.135013\pi$
$132$	16.9938	+	12.3467i	1.47912	+	1.07465i
$133$	0.238144	−	2.26579i	0.0206497	−	0.196469i
$134$	−18.8766	+	20.9646i	−1.63069	+	1.81107i
$135$		0			0
$136$	−1.26676	−	0.269259i	−0.108624	−	0.0230888i
$137$	7.41206	−	1.57548i	0.633255	−	0.134603i	0.119910	−	0.992785i	$-0.461739\pi$
$137$	7.41206	−	1.57548i	0.633255	−	0.134603i	0.513345	+	0.858182i	$0.328406\pi$
$138$	−13.5826	+	6.04736i	−1.15623	+	0.514785i
$139$	−6.21069	+	19.1145i	−0.526784	+	1.62127i	0.233977	+	0.972242i	$0.424826\pi$
$139$	−6.21069	+	19.1145i	−0.526784	+	1.62127i	−0.760761	+	0.649032i	$0.775174\pi$
$140$		0			0
$141$	−10.5132	+	4.68078i	−0.885371	+	0.394193i
$142$	−2.70771	+	0.575541i	−0.227226	+	0.0482983i
$143$	8.73931	+	1.85760i	0.730818	+	0.155340i
$144$	−4.79216	−	2.13361i	−0.399347	−	0.177801i
$145$		0			0
$146$	3.06830	−	29.1929i	0.253934	−	2.41602i
$147$	−11.2541	−	8.17660i	−0.928225	−	0.674395i
$148$	0.0658074	+	0.626116i	0.00540934	+	0.0514664i
$149$	−6.15749	+	10.6651i	−0.504441	+	0.873717i	0.495546	+	0.868582i	$0.334968\pi$
$149$	−6.15749	+	10.6651i	−0.504441	+	0.873717i	−0.999987	+	0.00513554i	$0.998365\pi$
$150$		0			0
$151$	16.0808	−	11.6834i	1.30864	−	0.950781i	0.308637	−	0.951180i	$-0.400127\pi$
$151$	16.0808	−	11.6834i	1.30864	−	0.950781i	1.00000		0.000399262i	$0.000127089\pi$
$152$	0.252473	+	0.280399i	0.0204782	+	0.0227434i
$153$	−1.03706	−	3.19174i	−0.0838412	−	0.258037i
$154$	32.5932			2.62644
$155$		0			0
$156$	10.2421			0.820023
$157$	1.79373	+	5.52052i	0.143155	+	0.440585i	0.996769	−	0.0803203i	$-0.0255943\pi$
$157$	1.79373	+	5.52052i	0.143155	+	0.440585i	−0.853614	+	0.520906i	$0.825594\pi$
$158$	−12.0303	−	13.3610i	−0.957079	−	1.06294i
$159$	16.4577	−	11.9572i	1.30518	−	0.948267i
$160$		0			0
$161$	−6.16198	+	10.6729i	−0.485632	+	0.841139i
$162$	−2.43542	−	23.1714i	−0.191344	−	1.82052i
$163$	14.3870	+	10.4528i	1.12688	+	0.818725i	0.985237	−	0.171194i	$-0.0547624\pi$
$163$	14.3870	+	10.4528i	1.12688	+	0.818725i	0.141640	+	0.989918i	$0.454762\pi$
$164$	1.02565	−	9.75845i	0.0800901	−	0.762007i
$165$		0			0
$166$	−9.81599	−	4.37036i	−0.761869	−	0.339206i
$167$	2.13435	+	0.453670i	0.165161	+	0.0351060i	0.289750	−	0.957102i	$-0.406428\pi$
$167$	2.13435	+	0.453670i	0.165161	+	0.0351060i	−0.124589	+	0.992208i	$0.539761\pi$
$168$	4.67949	−	0.994657i	0.361031	−	0.0767394i
$169$	−7.89632	+	3.51567i	−0.607409	+	0.270436i
$170$		0			0
$171$	−0.302145	+	0.929907i	−0.0231056	+	0.0711117i
$172$	−0.565110	+	0.251603i	−0.0430892	+	0.0191846i
$173$	−5.38757	+	1.14516i	−0.409609	+	0.0870651i	−0.408108	−	0.912934i	$-0.633811\pi$
$173$	−5.38757	+	1.14516i	−0.409609	+	0.0870651i	−0.00150131	+	0.999999i	$0.500478\pi$
$174$	−5.97276	−	1.26955i	−0.452794	−	0.0962443i
$175$		0			0
$176$	9.52776	−	10.5816i	0.718182	−	0.797621i
$177$	1.30317	−	12.3989i	0.0979526	−	0.931956i
$178$	8.40300	+	6.10514i	0.629831	+	0.457599i
$179$	−1.26834	−	12.0674i	−0.0947999	−	0.901961i	−0.933792	−	0.357817i	$-0.883521\pi$
$179$	−1.26834	−	12.0674i	−0.0947999	−	0.901961i	0.838992	−	0.544144i	$-0.183146\pi$
$180$		0			0
$181$	−4.82344	−	8.35444i	−0.358523	−	0.620980i	0.629191	−	0.777251i	$-0.283386\pi$
$181$	−4.82344	−	8.35444i	−0.358523	−	0.620980i	−0.987714	+	0.156270i	$0.950053\pi$
$182$	12.8570	−	9.34116i	0.953025	−	0.692413i
$183$	3.18829	+	3.54096i	0.235685	+	0.261755i
$184$	−0.630711	−	1.94113i	−0.0464966	−	0.143102i
$185$		0			0
$186$	−23.8440	−	6.37808i	−1.74833	−	0.467663i
$187$	9.10960			0.666160
$188$	−3.81269	−	11.7342i	−0.278069	−	0.855808i
$189$	−7.48532	−	8.31329i	−0.544477	−	0.604703i
$190$		0			0
$191$	−5.23270	−	9.06331i	−0.378625	−	0.655798i	0.612237	−	0.790674i	$-0.290270\pi$
$191$	−5.23270	−	9.06331i	−0.378625	−	0.655798i	−0.990862	+	0.134876i	$0.956936\pi$
$192$	10.8592	−	18.8087i	0.783695	−	1.35740i
$193$	−0.187174	−	1.78084i	−0.0134731	−	0.128188i	0.985718	−	0.168405i	$-0.0538616\pi$
$193$	−0.187174	−	1.78084i	−0.0134731	−	0.128188i	−0.999191	+	0.0402173i	$0.987195\pi$
$194$	−11.2552	−	8.17738i	−0.808076	−	0.587102i
$195$		0			0
$196$	9.97950	−	11.0834i	0.712822	−	0.791669i
$197$	−5.84391	−	2.60188i	−0.416361	−	0.185376i	0.187854	−	0.982197i	$-0.439847\pi$
$197$	−5.84391	−	2.60188i	−0.416361	−	0.185376i	−0.604216	+	0.796821i	$0.706513\pi$
$198$	−13.6823	−	2.90826i	−0.972359	−	0.206681i
$199$	−0.906896	+	0.192767i	−0.0642881	+	0.0136649i	−0.239943	−	0.970787i	$-0.577129\pi$
$199$	−0.906896	+	0.192767i	−0.0642881	+	0.0136649i	0.175655	+	0.984452i	$0.443796\pi$
$200$		0			0
$201$	9.00059	−	27.7010i	0.634852	−	1.95387i
$202$	11.5659	−	35.5961i	0.813771	−	2.50453i
$203$	−4.62379	+	2.05865i	−0.324527	+	0.144489i
$204$	10.2146	−	2.17117i	0.715162	−	0.152012i
$205$		0			0
$206$	7.41161	+	3.29986i	0.516391	+	0.229912i
$207$	3.53906	−	3.93053i	0.245982	−	0.273191i
$208$	0.725720	−	6.90477i	0.0503197	−	0.478759i
$209$	−2.14718	−	1.56002i	−0.148524	−	0.107909i
$210$		0			0
$211$	3.09072	−	5.35328i	0.212774	−	0.368535i	−0.739808	−	0.672818i	$-0.765084\pi$
$211$	3.09072	−	5.35328i	0.212774	−	0.368535i	0.952582	+	0.304283i	$0.0984169\pi$
$212$	10.9050	+	18.8880i	0.748957	+	1.29723i
$213$	2.31222	−	1.67993i	0.158431	−	0.115107i
$214$	15.4120	+	17.1168i	1.05354	+	1.17008i
$215$		0			0
$216$	1.85267			0.126058
$217$	−19.0970	+	7.34000i	−1.29639	+	0.498272i
$218$	−37.4917			−2.53926
$219$	9.36527	+	28.8233i	0.632846	+	1.94770i
$220$		0			0
$221$	3.59345	−	2.61080i	0.241722	−	0.175621i
$222$	−0.608389	−	1.05376i	−0.0408324	−	0.0707238i
$223$	7.94891	−	13.7679i	0.532298	−	0.921968i	−0.466991	−	0.884262i	$-0.654662\pi$
$223$	7.94891	−	13.7679i	0.532298	−	0.921968i	0.999289	−	0.0377054i	$-0.0120048\pi$
$224$	−3.11491	−	29.6364i	−0.208124	−	1.98017i
$225$		0			0
$226$	−3.79882	+	36.1433i	−0.252694	+	2.40422i
$227$	3.10808	−	3.45188i	0.206291	−	0.229109i	−0.631117	−	0.775688i	$-0.717403\pi$
$227$	3.10808	−	3.45188i	0.206291	−	0.229109i	0.837408	+	0.546578i	$0.184070\pi$
$228$	−2.77944	−	1.23749i	−0.184073	−	0.0819545i
$229$	18.9940	+	4.03731i	1.25516	+	0.266793i	0.787057	−	0.616881i	$-0.211604\pi$
$229$	18.9940	+	4.03731i	1.25516	+	0.266793i	0.468104	+	0.883673i	$0.344937\pi$
$230$		0			0
$231$	−30.7420	+	13.6872i	−2.02268	+	0.900554i
$232$	0.259029	−	0.797210i	0.0170061	−	0.0523394i
$233$	4.40302	−	13.5511i	0.288452	−	0.887763i	−0.696891	−	0.717177i	$-0.745434\pi$
$233$	4.40302	−	13.5511i	0.288452	−	0.887763i	0.985343	−	0.170586i	$-0.0545660\pi$
$234$	−6.23074	+	2.77411i	−0.407316	+	0.181349i
$235$		0			0
$236$	13.0742	+	2.77901i	0.851060	+	0.180898i
$237$	16.9578	+	7.55012i	1.10153	+	0.490433i
$238$	10.8423	−	12.0415i	0.702799	−	0.780537i
$239$	0.710952	−	6.76426i	0.0459877	−	0.437544i	−0.947167	−	0.320740i	$-0.896068\pi$
$239$	0.710952	−	6.76426i	0.0459877	−	0.437544i	0.993155	−	0.116804i	$-0.0372648\pi$
$240$		0			0
$241$	1.20261	+	11.4421i	0.0774671	+	0.737050i	0.962456	+	0.271438i	$0.0874992\pi$
$241$	1.20261	+	11.4421i	0.0774671	+	0.737050i	−0.884989	+	0.465612i	$0.845834\pi$
$242$	7.58800	−	13.1428i	0.487775	−	0.844851i
$243$	7.46119	+	12.9232i	0.478636	+	0.829021i
$244$	−4.13284	+	3.00269i	−0.264578	+	0.192227i
$245$		0			0
$246$	5.86030	+	18.0362i	0.373639	+	1.14994i
$247$	−1.29410			−0.0823413
$248$	1.21291	−	3.16377i	0.0770197	−	0.200899i
$249$	11.0938			0.703039
$250$		0			0
$251$	−4.88091	−	5.42080i	−0.308080	−	0.342158i	0.569145	−	0.822237i	$-0.307274\pi$
$251$	−4.88091	−	5.42080i	−0.308080	−	0.342158i	−0.877225	+	0.480080i	$0.840608\pi$
$252$	−10.7529	+	7.81244i	−0.677369	+	0.492137i
$253$	7.17837	+	12.4333i	0.451300	+	0.781675i
$254$	14.7103	−	25.4790i	0.923005	−	1.59869i
$255$		0			0
$256$	−8.35235	−	6.06834i	−0.522022	−	0.379271i
$257$	−2.57722	+	24.5206i	−0.160763	+	1.52955i	0.555378	+	0.831598i	$0.312574\pi$
$257$	−2.57722	+	24.5206i	−0.160763	+	1.52955i	−0.716140	+	0.697956i	$0.754093\pi$
$258$	0.799991	−	0.888480i	0.0498053	−	0.0553143i
$259$	−0.921381	−	0.410225i	−0.0572518	−	0.0254902i
$260$		0			0
$261$	2.12471	−	0.451622i	0.131516	−	0.0279547i
$262$	−13.6077	+	6.05853i	−0.840686	+	0.374297i
$263$	8.12313	−	25.0004i	0.500894	−	1.54159i	−0.306672	−	0.951815i	$-0.599215\pi$
$263$	8.12313	−	25.0004i	0.500894	−	1.54159i	0.807566	−	0.589777i	$-0.200785\pi$
$264$	1.72220	−	5.30037i	0.105994	−	0.326215i
$265$		0			0
$266$	−4.61769	+	0.981521i	−0.283129	+	0.0601809i
$267$	−10.4895	−	2.22962i	−0.641949	−	0.136450i
$268$	28.5274	+	12.7012i	1.74259	+	0.775851i
$269$	−13.9713	+	15.5167i	−0.851846	+	0.946071i	−0.999074	−	0.0430321i	$-0.986298\pi$
$269$	−13.9713	+	15.5167i	−0.851846	+	0.946071i	0.147228	+	0.989103i	$0.452965\pi$
$270$		0			0
$271$	16.9981	+	12.3499i	1.03256	+	0.750201i	0.968820	−	0.247765i	$-0.0796962\pi$
$271$	16.9981	+	12.3499i	1.03256	+	0.750201i	0.0637431	+	0.997966i	$0.479696\pi$
$272$	−0.739939	−	7.04005i	−0.0448654	−	0.426866i
$273$	−8.20403	+	14.2098i	−0.496530	+	0.860016i
$274$	−7.85091	−	13.5982i	−0.474291	−	0.821496i
$275$		0			0
$276$	11.0124	+	12.2305i	0.662869	+	0.736191i
$277$	1.47070	+	4.52635i	0.0883657	+	0.271962i	0.985468	−	0.169861i	$-0.0543319\pi$
$277$	1.47070	+	4.52635i	0.0883657	+	0.271962i	−0.897102	+	0.441823i	$0.854332\pi$
$278$	41.6459			2.49776
$279$	8.67165	−	1.37725i	0.519158	−	0.0824539i
$280$		0			0
$281$	−2.05645	−	6.32910i	−0.122678	−	0.377563i	0.870793	−	0.491649i	$-0.163606\pi$
$281$	−2.05645	−	6.32910i	−0.122678	−	0.377563i	−0.993471	+	0.114087i	$0.963606\pi$
$282$	15.9563	+	17.7212i	0.950181	+	1.05528i
$283$	−5.86234	+	4.25924i	−0.348480	+	0.253185i	−0.748231	−	0.663438i	$-0.769096\pi$
$283$	−5.86234	+	4.25924i	−0.348480	+	0.253185i	0.399751	+	0.916624i	$0.369096\pi$
$284$	1.53210	+	2.65367i	0.0909132	+	0.157466i
$285$		0			0
$286$	−1.93519	−	18.4121i	−0.114430	−	1.08873i
$287$	12.7172	+	9.23961i	0.750675	+	0.545397i
$288$	−1.33682	+	12.7190i	−0.0787729	+	0.749474i
$289$	−8.34488	+	9.26793i	−0.490875	+	0.545172i
$290$		0			0
$291$	14.0500	+	2.98641i	0.823623	+	0.175066i
$292$	−31.7824	+	6.75555i	−1.85992	+	0.395339i
$293$	−12.3434	+	5.49563i	−0.721108	+	0.321058i	−0.734272	−	0.678855i	$-0.762476\pi$
$293$	−12.3434	+	5.49563i	−0.721108	+	0.321058i	0.0131637	+	0.999913i	$0.495810\pi$
$294$	−8.90741	+	27.4142i	−0.519491	+	1.59883i
$295$		0			0
$296$	0.152594	−	0.0679392i	0.00886934	−	0.00394888i
$297$	−12.7471	+	2.70947i	−0.739659	+	0.157219i
$298$	24.9605	+	5.30552i	1.44592	+	0.307340i
$299$	6.39501	+	2.84724i	0.369833	+	0.164660i
$300$		0			0
$301$	0.103587	−	0.985567i	0.00597067	−	0.0568071i
$302$	−33.3214	−	24.2094i	−1.91743	−	1.39309i
$303$	4.03929	+	38.4313i	0.232051	+	2.20782i
$304$	−1.03120	+	1.78609i	−0.0591434	+	0.102439i
$305$		0			0
$306$	−5.62592	+	4.08747i	−0.321613	+	0.233665i
$307$	15.2065	+	16.8886i	0.867883	+	0.963882i	0.999624	−	0.0274020i	$-0.00872341\pi$
$307$	15.2065	+	16.8886i	0.867883	+	0.963882i	−0.131741	+	0.991284i	$0.542057\pi$
$308$	−11.1488	−	34.3125i	−0.635263	−	1.95514i
$309$	−8.37640			−0.476517
$310$		0			0
$311$	9.49330			0.538315			0.269158	−	0.963096i	$-0.413255\pi$
$311$	9.49330			0.538315			0.269158	+	0.963096i	$0.413255\pi$
$312$	−0.839726	−	2.58441i	−0.0475401	−	0.146313i
$313$	−18.8006	−	20.8802i	−1.06267	−	1.18022i	−0.983040	−	0.183393i	$-0.941292\pi$
$313$	−18.8006	−	20.8802i	−1.06267	−	1.18022i	−0.0796330	−	0.996824i	$-0.525375\pi$
$314$	9.73075	−	7.06981i	0.549138	−	0.398972i
$315$		0			0
$316$	−9.95072	+	17.2352i	−0.559772	+	0.969553i
$317$	−1.65331	−	15.7302i	−0.0928591	−	0.883495i	−0.937459	−	0.348096i	$-0.886828\pi$
$317$	−1.65331	−	15.7302i	−0.0928591	−	0.883495i	0.844600	−	0.535398i	$-0.179839\pi$
$318$	−34.1023	−	24.7768i	−1.91236	−	1.38941i
$319$	−0.616323	+	5.86393i	−0.0345075	+	0.328317i
$320$		0			0
$321$	−21.7247	−	9.67247i	−1.21256	−	0.539865i
$322$	24.9787	+	5.30938i	1.39201	+	0.295880i
$323$	−1.29062	+	0.274329i	−0.0718118	+	0.0152641i
$324$	−23.5607	+	10.4899i	−1.30893	+	0.582772i
$325$		0			0
$326$	11.3870	−	35.0457i	0.630669	−	1.94100i
$327$	35.3623	−	15.7443i	1.95554	−	0.870662i
$328$	−2.54646	+	0.541267i	−0.140605	+	0.0298865i
$329$	19.3340	+	4.10957i	1.06592	+	0.226568i
$330$		0			0
$331$	8.66131	−	9.61936i	0.476069	−	0.528728i	−0.456499	−	0.889724i	$-0.650897\pi$
$331$	8.66131	−	9.61936i	0.476069	−	0.528728i	0.932567	+	0.360996i	$0.117563\pi$
$332$	−1.24325	+	11.8287i	−0.0682321	+	0.649185i
$333$	0.350182	+	0.254422i	0.0191899	+	0.0139423i
$334$	−0.472618	−	4.49666i	−0.0258605	−	0.246046i
$335$		0			0
$336$	13.0748	+	22.6462i	0.713287	+	1.23545i
$337$	−22.5443	+	16.3794i	−1.22807	+	0.892243i	−0.996744	−	0.0806338i	$-0.974306\pi$
$337$	−22.5443	+	16.3794i	−1.22807	+	0.892243i	−0.231323	+	0.972877i	$0.574306\pi$
$338$	11.9845	+	13.3102i	0.651872	+	0.723977i
$339$	−11.5950	−	35.6858i	−0.629755	−	1.93819i
$340$		0			0
$341$	−3.71834	+	23.5418i	−0.201360	+	1.27486i
$342$	2.02604			0.109556
$343$	−0.565190	−	1.73948i	−0.0305174	−	0.0939229i
$344$	0.109820	+	0.121967i	0.00592108	+	0.00657603i
$345$		0			0
$346$	5.70655	+	9.88403i	0.306786	+	0.531369i
$347$	2.66175	−	4.61029i	0.142890	−	0.247493i	−0.785693	−	0.618616i	$-0.787694\pi$
$347$	2.66175	−	4.61029i	0.142890	−	0.247493i	0.928584	+	0.371123i	$0.121027\pi$
$348$	0.706520	+	6.72209i	0.0378734	+	0.360342i
$349$	3.31528	+	2.40869i	0.177463	+	0.128934i	0.672971	−	0.739669i	$-0.265018\pi$
$349$	3.31528	+	2.40869i	0.177463	+	0.128934i	−0.495508	+	0.868603i	$0.665018\pi$
$350$		0			0
$351$	−4.25178	+	4.72208i	−0.226943	+	0.252046i
$352$	−31.7137	−	14.1199i	−1.69035	−	0.752591i
$353$	21.3132	+	4.53026i	1.13439	+	0.241122i	0.736582	−	0.676348i	$-0.236438\pi$
$353$	21.3132	+	4.53026i	1.13439	+	0.241122i	0.397806	+	0.917470i	$0.369772\pi$
$354$	−25.2690	+	5.37109i	−1.34303	+	0.285470i
$355$		0			0
$356$	3.55286	−	10.9346i	0.188301	−	0.579531i
$357$	−5.16971	+	15.9107i	−0.273610	+	0.842085i
$358$	−22.9692	+	10.2265i	−1.21396	+	0.540489i
$359$	6.92668	−	1.47231i	0.365576	−	0.0777057i	−0.0214610	−	0.999770i	$-0.506832\pi$
$359$	6.92668	−	1.47231i	0.365576	−	0.0777057i	0.387037	+	0.922064i	$0.373498\pi$
$360$		0			0
$361$	−17.0062	−	7.57164i	−0.895062	−	0.398507i
$362$	−13.3756	+	14.8551i	−0.703005	+	0.780766i
$363$	−1.63782	+	15.5828i	−0.0859634	+	0.817887i
$364$	−14.2318	−	10.3400i	−0.745947	−	0.541963i
$365$		0			0
$366$	4.93665	−	8.55053i	0.258043	−	0.446943i
$367$	−8.05884	−	13.9583i	−0.420668	−	0.728619i	0.575337	−	0.817917i	$-0.304871\pi$
$367$	−8.05884	−	13.9583i	−0.420668	−	0.728619i	−0.996005	+	0.0892980i	$0.971538\pi$
$368$	9.02559	−	6.55747i	0.470491	−	0.341832i
$369$	−4.51412	−	5.01344i	−0.234996	−	0.260989i
$370$		0			0
$371$	−34.9401			−1.81400
$372$	1.44155	+	27.2835i	0.0747409	+	1.41458i
$373$	9.81895			0.508406			0.254203	−	0.967151i	$-0.418187\pi$
$373$	9.81895			0.508406			0.254203	+	0.967151i	$0.418187\pi$
$374$	−5.83306	−	17.9523i	−0.301621	−	0.928293i
$375$		0			0
$376$	−2.64834	+	1.92413i	−0.136578	+	0.0992294i
$377$	1.43747	+	2.48977i	0.0740335	+	0.128230i
$378$	−11.5900	+	20.0745i	−0.596127	+	1.03252i
$379$	1.44413	+	13.7399i	0.0741798	+	0.705773i	0.966899	+	0.255160i	$0.0821281\pi$
$379$	1.44413	+	13.7399i	0.0741798	+	0.705773i	−0.892719	+	0.450614i	$0.851205\pi$
$380$		0			0
$381$	−3.17512	+	30.2093i	−0.162666	+	1.54767i
$382$	−14.5105	+	16.1155i	−0.742421	+	0.824542i
$383$	−9.41502	−	4.19184i	−0.481085	−	0.214193i	0.151841	−	0.988405i	$-0.451480\pi$
$383$	−9.41502	−	4.19184i	−0.481085	−	0.214193i	−0.632926	+	0.774212i	$0.718146\pi$
$384$	−10.0781	−	2.14216i	−0.514295	−	0.109317i
$385$		0			0
$386$	−3.38966	+	1.50917i	−0.172529	+	0.0768149i
$387$	−0.131426	+	0.404488i	−0.00668076	+	0.0205613i
$388$	−4.75879	+	14.6461i	−0.241591	+	0.743541i
$389$	−23.1725	+	10.3170i	−1.17489	+	0.523095i	−0.898938	−	0.438077i	$-0.855660\pi$
$389$	−23.1725	+	10.3170i	−1.17489	+	0.523095i	−0.275952	+	0.961171i	$0.588993\pi$
$390$		0			0
$391$	6.98139	+	1.48394i	0.353064	+	0.0750460i
$392$	−3.61489	−	1.60945i	−0.182579	−	0.0812896i
$393$	10.2906	−	11.4289i	0.519091	−	0.576509i
$394$	−1.38555	+	13.1827i	−0.0698032	+	0.664133i
$395$		0			0
$396$	1.61848	+	15.3988i	0.0813319	+	0.773821i
$397$	8.37941	−	14.5136i	0.420550	−	0.728415i	−0.575443	−	0.817842i	$-0.695170\pi$
$397$	8.37941	−	14.5136i	0.420550	−	0.728415i	0.995993	+	0.0894272i	$0.0285036\pi$
$398$	0.960590	+	1.66379i	0.0481500	+	0.0833983i
$399$	3.94324	−	2.86493i	0.197409	−	0.143426i
$400$		0			0
$401$	−8.53615	−	26.2716i	−0.426275	−	1.31194i	−0.901768	−	0.432220i	$-0.857730\pi$
$401$	−8.53615	−	26.2716i	−0.426275	−	1.31194i	0.475493	−	0.879720i	$-0.342270\pi$
$402$	−60.3537			−3.01017
$403$	5.28026	+	10.3522i	0.263028	+	0.515678i
$404$	−41.4300			−2.06122
$405$		0			0
$406$	7.01769	+	7.79394i	0.348282	+	0.386807i
$407$	−0.950545	+	0.690611i	−0.0471168	+	0.0342323i
$408$	−1.38532	−	2.39945i	−0.0685838	−	0.118791i
$409$	11.3053	−	19.5814i	0.559013	−	0.968239i	−0.438566	−	0.898699i	$-0.644514\pi$
$409$	11.3053	−	19.5814i	0.559013	−	0.968239i	0.997579	−	0.0695399i	$-0.0221531\pi$
$410$		0			0
$411$	13.1154	+	9.52892i	0.646936	+	0.470027i
$412$	0.938720	−	8.93132i	0.0462474	−	0.440015i
$413$	−14.3282	+	15.9131i	−0.705045	+	0.783031i
$414$	−10.0120	−	4.45765i	−0.492065	−	0.219082i
$415$		0			0
$416$	−16.5568	+	3.51926i	−0.811764	+	0.172546i
$417$	−39.2806	+	17.4888i	−1.92358	+	0.856432i
$418$	−1.69945	+	5.23038i	−0.0831229	+	0.255826i
$419$	−1.91312	+	5.88796i	−0.0934618	+	0.287646i	−0.986850	−	0.161640i	$-0.948322\pi$
$419$	−1.91312	+	5.88796i	−0.0934618	+	0.287646i	0.893388	+	0.449286i	$0.148322\pi$
$420$		0			0
$421$	−6.41600	+	1.36376i	−0.312697	+	0.0664657i	−0.361587	−	0.932338i	$-0.617765\pi$
$421$	−6.41600	+	1.36376i	−0.312697	+	0.0664657i	0.0488901	+	0.998804i	$0.484432\pi$
$422$	−12.5288	−	2.66308i	−0.609892	−	0.129637i
$423$	−7.74953	−	3.45031i	−0.376795	−	0.167760i
$424$	3.87197	−	4.30026i	0.188040	−	0.208839i
$425$		0			0
$426$	−4.79121	−	3.48102i	−0.232135	−	0.168656i
$427$	−0.855450	−	8.13906i	−0.0413981	−	0.393877i
$428$	12.7479	−	22.0800i	0.616192	−	1.06728i
$429$	9.55725	+	16.5536i	0.461428	+	0.799217i
$430$		0			0
$431$	15.7030	+	17.4399i	0.756385	+	0.840051i	0.991253	−	0.131977i	$-0.0421324\pi$
$431$	15.7030	+	17.4399i	0.756385	+	0.840051i	−0.234868	+	0.972027i	$0.575466\pi$
$432$	3.12932	+	9.63105i	0.150559	+	0.463374i
$433$	−24.3130			−1.16841			−0.584203	−	0.811607i	$-0.698593\pi$
$433$	−24.3130			−1.16841			−0.584203	+	0.811607i	$0.698593\pi$
$434$	26.6932	+	32.9345i	1.28131	+	1.58091i
$435$		0			0
$436$	12.8244	+	39.4694i	0.614176	+	1.89024i
$437$	−1.39143	−	1.54534i	−0.0665610	−	0.0739234i
$438$	50.8055	−	36.9124i	2.42758	−	1.76374i
$439$	−7.25318	−	12.5629i	−0.346175	−	0.599593i	0.639391	−	0.768881i	$-0.279186\pi$
$439$	−7.25318	−	12.5629i	−0.346175	−	0.599593i	−0.985567	+	0.169288i	$0.945853\pi$
$440$		0			0
$441$	−1.07184	−	10.1979i	−0.0510399	−	0.485612i
$442$	−7.44607	−	5.40989i	−0.354173	−	0.257322i
$443$	−1.73162	+	16.4752i	−0.0822716	+	0.782762i	0.873137	+	0.487475i	$0.162082\pi$
$443$	−1.73162	+	16.4752i	−0.0822716	+	0.782762i	−0.955409	+	0.295287i	$0.904585\pi$
$444$	−0.901242	+	1.00093i	−0.0427711	+	0.0475021i
$445$		0			0
$446$	−32.2223	−	6.84907i	−1.52577	−	0.324313i
$447$	−25.7708	+	5.47775i	−1.21892	+	0.259089i
$448$	−34.0777	+	15.1724i	−1.61002	+	0.716828i
$449$	2.10667	−	6.48365i	0.0994197	−	0.305982i	−0.888961	−	0.457984i	$-0.848572\pi$
$449$	2.10667	−	6.48365i	0.0994197	−	0.305982i	0.988380	+	0.152001i	$0.0485718\pi$
$450$		0			0
$451$	16.7290	−	7.44825i	0.787740	−	0.350724i
$452$	39.3493	−	8.36396i	1.85084	−	0.393408i
$453$	41.5953	+	8.84136i	1.95432	+	0.415403i
$454$	−8.79280	−	3.91481i	−0.412667	−	0.183731i
$455$		0			0
$456$	−0.0843778	+	0.802801i	−0.00395135	+	0.0375946i
$457$	17.3354	+	12.5949i	0.810916	+	0.589165i	0.914096	−	0.405497i	$-0.132902\pi$
$457$	17.3354	+	12.5949i	0.810916	+	0.589165i	−0.103180	+	0.994663i	$0.532902\pi$
$458$	−4.20594	−	40.0168i	−0.196530	−	1.86986i
$459$	−3.23934	+	5.61070i	−0.151200	+	0.261885i
$460$		0			0
$461$	7.01782	−	5.09875i	0.326853	−	0.237472i	−0.412241	−	0.911075i	$-0.635254\pi$
$461$	7.01782	−	5.09875i	0.326853	−	0.237472i	0.739094	+	0.673602i	$0.235254\pi$
$462$	46.6582	+	51.8192i	2.17074	+	2.41085i
$463$	−1.12787	−	3.47124i	−0.0524167	−	0.161322i	0.921421	−	0.388565i	$-0.127029\pi$
$463$	−1.12787	−	3.47124i	−0.0524167	−	0.161322i	−0.973838	+	0.227243i	$0.927029\pi$
$464$	4.58180			0.212705
$465$		0			0
$466$	−29.5246			−1.36770
$467$	0.952115	+	2.93031i	0.0440586	+	0.135599i	0.970666	−	0.240431i	$-0.0772889\pi$
$467$	0.952115	+	2.93031i	0.0440586	+	0.135599i	−0.926607	+	0.376030i	$0.877289\pi$
$468$	5.05172	+	5.61051i	0.233516	+	0.259346i
$469$	−40.4724	+	29.4049i	−1.86884	+	1.35779i
$470$		0			0
$471$	−6.20917	+	10.7546i	−0.286104	+	0.495546i
$472$	−0.370692	−	3.52690i	−0.0170625	−	0.162339i
$473$	−0.933975	−	0.678572i	−0.0429442	−	0.0312008i
$474$	4.02060	−	38.2534i	0.184672	−	1.75704i
$475$		0			0
$476$	−16.3854	−	7.29526i	−0.751025	−	0.334378i
$477$	14.6675	+	3.11767i	0.671578	+	0.142748i
$478$	−13.7856	+	2.93022i	−0.630538	+	0.134025i
$479$	−15.9050	+	7.08138i	−0.726720	+	0.323556i	−0.736539	−	0.676395i	$-0.763541\pi$
$479$	−15.9050	+	7.08138i	−0.726720	+	0.323556i	0.00981912	+	0.999952i	$0.496874\pi$
$480$		0			0
$481$	−0.177032	+	0.544849i	−0.00807197	+	0.0248430i
$482$	21.7789	−	9.69661i	0.992003	−	0.441668i
$483$	−25.7896	+	5.48175i	−1.17347	+	0.249428i
$484$	−16.4316	−	3.49265i	−0.746892	−	0.158757i
$485$		0			0
$486$	20.6902	−	22.9788i	0.938526	−	1.04234i
$487$	3.00766	−	28.6160i	0.136290	−	1.29671i	−0.685981	−	0.727619i	$-0.740627\pi$
$487$	3.00766	−	28.6160i	0.136290	−	1.29671i	0.822272	−	0.569095i	$-0.192706\pi$
$488$	1.09652	+	0.796666i	0.0496370	+	0.0360634i
$489$	3.97684	+	37.8371i	0.179839	+	1.71105i
$490$		0			0
$491$	4.91284	+	8.50929i	0.221713	+	0.384019i	0.955328	−	0.295546i	$-0.0955017\pi$
$491$	4.91284	+	8.50929i	0.221713	+	0.384019i	−0.733615	+	0.679565i	$0.762168\pi$
$492$	16.9830	−	12.3389i	0.765652	−	0.556279i
$493$	1.96140	+	2.17836i	0.0883371	+	0.0981083i
$494$	0.828636	+	2.55028i	0.0372821	+	0.114743i
$495$		0			0
$496$	18.4955	+	0.961388i	0.830472	+	0.0431676i
$497$	−4.90891			−0.220195
$498$	−7.10357	−	21.8625i	−0.318319	−	0.979684i
$499$	−7.25874	−	8.06164i	−0.324946	−	0.360889i	0.558432	−	0.829550i	$-0.311403\pi$
$499$	−7.25874	−	8.06164i	−0.324946	−	0.360889i	−0.883378	+	0.468661i	$0.844736\pi$
$500$		0			0
$501$	2.33411	+	4.04280i	0.104280	+	0.180619i
$502$	−7.55745	+	13.0899i	−0.337305	+	0.584230i
$503$	0.894863	+	8.51405i	0.0399000	+	0.379623i	0.996190	+	0.0872044i	$0.0277933\pi$
$503$	0.894863	+	8.51405i	0.0399000	+	0.379623i	−0.956290	+	0.292418i	$0.905540\pi$
$504$	2.85294	+	2.07278i	0.127080	+	0.0923290i
$505$		0			0
$506$	19.9059	−	22.1077i	0.884925	−	0.982809i
$507$	−16.8933	−	7.52139i	−0.750259	−	0.334037i
$508$	−31.8548	−	6.77094i	−1.41333	−	0.300412i
$509$	38.7174	−	8.22963i	1.71612	−	0.364772i	0.758245	−	0.651969i	$-0.226057\pi$
$509$	38.7174	−	8.22963i	1.71612	−	0.364772i	0.957871	+	0.287197i	$0.0927236\pi$
$510$		0			0
$511$	16.0855	−	49.5059i	0.711579	−	2.19001i
$512$	−9.58715	+	29.5062i	−0.423696	+	1.30400i
$513$	1.72436	−	0.767736i	0.0761325	−	0.0338964i
$514$	49.9732	−	10.6221i	2.20422	−	0.468522i
$515$		0			0
$516$	−1.20899	−	0.538278i	−0.0532229	−	0.0236964i
$517$	15.4076	−	17.1119i	0.677625	−	0.752578i
$518$	−0.218453	+	2.07845i	−0.00959830	+	0.0913217i
$519$	−9.53314	−	6.92623i	−0.418458	−	0.304028i
$520$		0			0
$521$	0.674660	−	1.16855i	0.0295574	−	0.0511949i	−0.850868	−	0.525379i	$-0.823924\pi$
$521$	0.674660	−	1.16855i	0.0295574	−	0.0511949i	0.880426	+	0.474184i	$0.157257\pi$
$522$	−2.25051	−	3.89800i	−0.0985022	−	0.170611i
$523$	23.0351	−	16.7360i	1.00725	−	0.731812i	0.0436219	−	0.999048i	$-0.486110\pi$
$523$	23.0351	−	16.7360i	1.00725	−	0.731812i	0.963631	+	0.267236i	$0.0861103\pi$
$524$	11.0328	+	12.2531i	0.481968	+	0.535280i
$525$		0			0
$526$	−54.4699			−2.37500
$527$	7.46057	+	9.20499i	0.324987	+	0.400976i
$528$	30.4628			1.32572
$529$	−3.63142	−	11.1764i	−0.157888	−	0.485929i
$530$		0			0
$531$	7.43474	−	5.40166i	0.322640	−	0.234412i
$532$	2.61282	+	4.52554i	0.113280	+	0.196207i
$533$	4.46443	−	7.73262i	0.193376	−	0.334937i
$534$	2.32274	+	22.0994i	0.100515	+	0.956336i
$535$		0			0
$536$	0.866031	−	8.23974i	0.0374069	−	0.355902i
$537$	17.3701	−	19.2914i	0.749573	−	0.832485i
$538$	39.5250	+	17.5977i	1.70404	+	0.758689i
$539$	27.2256	+	5.78697i	1.17269	+	0.249263i
$540$		0			0
$541$	−13.0725	+	5.82024i	−0.562029	+	0.250232i	−0.668030	−	0.744134i	$-0.732862\pi$
$541$	−13.0725	+	5.82024i	−0.562029	+	0.250232i	0.106000	+	0.994366i	$0.466196\pi$
$542$	13.4537	−	41.4062i	0.577885	−	1.77855i
$543$	6.37763	−	19.6283i	0.273690	−	0.842332i
$544$	−15.7663	+	7.01959i	−0.675973	+	0.300962i
$545$		0			0
$546$	33.2565	+	7.06889i	1.42325	+	0.302521i
$547$	−38.7041	−	17.2322i	−1.65487	−	0.736795i	−0.655044	−	0.755590i	$-0.727350\pi$
$547$	−38.7041	−	17.2322i	−1.65487	−	0.736795i	−0.999823	+	0.0187957i	$0.994017\pi$
$548$	−11.6300	+	12.9164i	−0.496809	+	0.551762i
$549$	−0.367132	+	3.49303i	−0.0156688	+	0.149079i
$550$		0			0
$551$	−0.0892693	−	0.849341i	−0.00380300	−	0.0361831i
$552$	2.18327	−	3.78154i	0.0929263	−	0.160953i
$553$	−15.9413	−	27.6111i	−0.677893	−	1.17414i
$554$	7.97837	−	5.79663i	0.338969	−	0.246275i
$555$		0			0
$556$	−14.2454	−	43.8428i	−0.604139	−	1.85935i
$557$	−27.3019			−1.15682			−0.578409	−	0.815747i	$-0.696326\pi$
$557$	−27.3019			−1.15682			−0.578409	+	0.815747i	$0.696326\pi$
$558$	−8.26679	−	16.2074i	−0.349961	−	0.686113i
$559$	−0.562902			−0.0238082
$560$		0			0
$561$	13.0407	+	14.4831i	0.550578	+	0.611479i
$562$	−11.1560	+	8.10531i	−0.470588	+	0.341902i
$563$	2.59399	+	4.49293i	0.109324	+	0.189354i	0.915497	−	0.402326i	$-0.131798\pi$
$563$	2.59399	+	4.49293i	0.109324	+	0.189354i	−0.806173	+	0.591680i	$0.798465\pi$
$564$	13.1980	−	22.8597i	0.555737	−	0.962565i
$565$		0			0
$566$	12.1475	+	8.82566i	0.510596	+	0.370970i
$567$	4.31878	−	41.0905i	0.181372	−	1.72564i
$568$	0.543993	−	0.604166i	0.0228255	−	0.0253502i
$569$	2.16312	+	0.963083i	0.0906827	+	0.0403746i	0.451577	−	0.892232i	$-0.350862\pi$
$569$	2.16312	+	0.963083i	0.0906827	+	0.0403746i	−0.360894	+	0.932607i	$0.617528\pi$
$570$		0			0
$571$	−19.9170	+	4.23348i	−0.833500	+	0.177166i	−0.604846	−	0.796342i	$-0.706765\pi$
$571$	−19.9170	+	4.23348i	−0.833500	+	0.177166i	−0.228653	+	0.973508i	$0.573432\pi$
$572$	−18.7214	+	8.33528i	−0.782779	+	0.348516i
$573$	6.91877	−	21.2938i	0.289036	−	0.889560i
$574$	10.0654	−	30.9782i	0.420123	−	1.29301i
$575$		0			0
$576$	15.6593	−	3.32849i	0.652471	−	0.138687i
$577$	25.0227	+	5.31874i	1.04171	+	0.221422i	0.696839	−	0.717228i	$-0.254589\pi$
$577$	25.0227	+	5.31874i	1.04171	+	0.221422i	0.344871	+	0.938650i	$0.387923\pi$
$578$	23.6077	+	10.5108i	0.981953	+	0.437194i
$579$	2.56337	−	2.84691i	0.106530	−	0.118314i
$580$		0			0
$581$	−15.4152	−	11.1998i	−0.639531	−	0.464646i
$582$	−3.11115	−	29.6006i	−0.128961	−	1.22698i
$583$	−20.3516	+	35.2501i	−0.842879	+	1.45991i
$584$	4.31041	+	7.46585i	0.178366	+	0.308939i
$585$		0			0
$586$	18.7340	+	20.8062i	0.773894	+	0.859497i
$587$	−12.3489	−	38.0060i	−0.509694	−	1.56868i	−0.792733	−	0.609568i	$-0.791343\pi$
$587$	−12.3489	−	38.0060i	−0.509694	−	1.56868i	0.283040	−	0.959108i	$-0.408657\pi$
$588$	31.9072			1.31583
$589$	−0.182141	−	3.44729i	−0.00750499	−	0.142043i
$590$		0			0
$591$	−4.22908	−	13.0158i	−0.173961	−	0.535397i
$592$	0.610925	+	0.678501i	0.0251089	+	0.0278862i
$593$	−16.9709	+	12.3301i	−0.696911	+	0.506335i	−0.878925	−	0.476961i	$-0.841738\pi$
$593$	−16.9709	+	12.3301i	−0.696911	+	0.506335i	0.182014	+	0.983296i	$0.441738\pi$
$594$	13.5018	+	23.3857i	0.553984	+	0.959529i
$595$		0			0
$596$	−2.95258	−	28.0920i	−0.120943	−	1.15069i
$597$	−1.60473	−	1.16590i	−0.0656771	−	0.0477172i
$598$	1.51621	−	14.4258i	0.0620026	−	0.589915i
$599$	14.0125	−	15.5625i	0.572535	−	0.635865i	−0.385434	−	0.922735i	$-0.625948\pi$
$599$	14.0125	−	15.5625i	0.572535	−	0.635865i	0.957969	+	0.286870i	$0.0926149\pi$
$600$		0			0
$601$	16.2555	+	3.45522i	0.663076	+	0.140941i	0.527143	−	0.849777i	$-0.323263\pi$
$601$	16.2555	+	3.45522i	0.663076	+	0.140941i	0.135933	+	0.990718i	$0.456597\pi$
$602$	−2.00859	+	0.426939i	−0.0818640	+	0.0174007i
$603$	19.6137	−	8.73257i	0.798730	−	0.355618i
$604$	−14.0886	+	43.3601i	−0.573256	+	1.76430i
$605$		0			0
$606$	73.1503	−	32.5686i	2.97153	−	1.32301i
$607$	28.9056	−	6.14407i	1.17324	−	0.249380i	0.420249	−	0.907409i	$-0.361943\pi$
$607$	28.9056	−	6.14407i	1.17324	−	0.249380i	0.752993	+	0.658029i	$0.228610\pi$
$608$	4.91830	+	1.04542i	0.199463	+	0.0423972i
$609$	−9.89211	−	4.40425i	−0.400848	−	0.178469i
$610$		0			0
$611$	1.17358	−	11.1659i	0.0474780	−	0.451723i
$612$	6.22749	+	4.52453i	0.251731	+	0.182893i
$613$	3.87799	+	36.8966i	0.156631	+	1.49024i	0.737003	+	0.675889i	$0.236240\pi$
$613$	3.87799	+	36.8966i	0.156631	+	1.49024i	−0.580373	+	0.814351i	$0.697093\pi$
$614$	23.5453	−	40.7817i	0.950212	−	1.64582i
$615$		0			0
$616$	−7.74409	+	5.62641i	−0.312018	+	0.226695i
$617$	17.6270	+	19.5768i	0.709636	+	0.788131i	0.984879	−	0.173244i	$-0.0554249\pi$
$617$	17.6270	+	19.5768i	0.709636	+	0.788131i	−0.275243	+	0.961375i	$0.588758\pi$
$618$	5.36358	+	16.5074i	0.215755	+	0.664026i
$619$	−26.3796			−1.06029			−0.530144	−	0.847908i	$-0.677862\pi$
$619$	−26.3796			−1.06029			−0.530144	+	0.847908i	$0.677862\pi$
$620$		0			0
$621$	−10.2104			−0.409730
$622$	−6.07875	−	18.7085i	−0.243736	−	0.750142i
$623$	12.3247	+	13.6879i	0.493778	+	0.548396i
$624$	12.0166	−	8.73059i	0.481050	−	0.349503i
$625$		0			0
$626$	−29.1103	+	50.4204i	−1.16348	+	2.01521i
$627$	−0.593521	−	5.64698i	−0.0237029	−	0.225518i
$628$	−10.7712	−	7.82576i	−0.429819	−	0.312282i
$629$	−0.0610564	+	0.580913i	−0.00243448	+	0.0231625i
$630$		0			0
$631$	18.2446	+	8.12304i	0.726308	+	0.323373i	0.736372	−	0.676576i	$-0.236537\pi$
$631$	18.2446	+	8.12304i	0.726308	+	0.323373i	−0.0100649	+	0.999949i	$0.503204\pi$
$632$	5.16483	+	1.09782i	0.205446	+	0.0436688i
$633$	12.9355	−	2.74953i	0.514141	−	0.109284i
$634$	−29.9409	+	13.3305i	−1.18910	+	0.529423i
$635$		0			0
$636$	−14.4187	+	44.3763i	−0.571740	+	1.75964i
$637$	12.3982	−	5.52002i	0.491234	−	0.218711i
$638$	11.9507	−	2.54020i	0.473133	−	0.100568i
$639$	2.06071	+	0.438017i	0.0815204	+	0.0173277i
$640$		0			0
$641$	15.5874	−	17.3115i	0.615664	−	0.683764i	−0.352002	−	0.935999i	$-0.614499\pi$
$641$	15.5874	−	17.3115i	0.615664	−	0.683764i	0.967666	+	0.252235i	$0.0811657\pi$
$642$	−5.15079	+	49.0065i	−0.203285	+	1.93413i
$643$	−31.4658	−	22.8612i	−1.24089	−	0.901559i	−0.243232	−	0.969968i	$-0.578208\pi$
$643$	−31.4658	−	22.8612i	−1.24089	−	0.901559i	−0.997657	+	0.0684089i	$0.978208\pi$
$644$	−2.95474	−	28.1124i	−0.116433	−	1.10779i
$645$		0			0
$646$	1.36703	+	2.36777i	0.0537851	+	0.0931585i
$647$	−1.80444	+	1.31100i	−0.0709399	+	0.0515408i	−0.622690	−	0.782469i	$-0.713960\pi$
$647$	−1.80444	+	1.31100i	−0.0709399	+	0.0515408i	0.551750	+	0.834009i	$0.313960\pi$
$648$	4.57863	+	5.08508i	0.179866	+	0.199761i
$649$	7.70848	+	23.7243i	0.302584	+	0.931259i
$650$		0			0
$651$	−39.0076	−	19.8544i	−1.52883	−	0.778155i
$652$	−40.7894			−1.59744
$653$	8.82960	+	27.1747i	0.345529	+	1.06343i	0.961300	+	0.275504i	$0.0888446\pi$
$653$	8.82960	+	27.1747i	0.345529	+	1.06343i	−0.615771	+	0.787925i	$0.711155\pi$
$654$	−53.6706	−	59.6072i	−2.09869	−	2.33083i
$655$		0			0
$656$	−7.11497	−	12.3235i	−0.277793	−	0.481151i
$657$	−11.1699	+	19.3468i	−0.435778	+	0.754790i
$658$	−4.28122	−	40.7331i	−0.166899	−	1.58794i
$659$	−4.15656	−	3.01991i	−0.161916	−	0.117639i	0.503877	−	0.863776i	$-0.331907\pi$
$659$	−4.15656	−	3.01991i	−0.161916	−	0.117639i	−0.665793	+	0.746136i	$0.731907\pi$
$660$		0			0
$661$	−3.94482	+	4.38117i	−0.153436	+	0.170408i	−0.814962	−	0.579514i	$-0.803242\pi$
$661$	−3.94482	+	4.38117i	−0.153436	+	0.170408i	0.661526	+	0.749922i	$0.269909\pi$
$662$	−24.5029	−	10.9094i	−0.952333	−	0.424006i
$663$	9.29499	+	1.97571i	0.360987	+	0.0767302i
$664$	3.08670	−	0.656098i	0.119787	−	0.0254615i
$665$		0			0
$666$	0.277162	−	0.853018i	0.0107398	−	0.0330538i
$667$	−1.42756	+	4.39358i	−0.0552754	+	0.170120i
$668$	−4.57220	+	2.03567i	−0.176904	+	0.0787626i
$669$	33.2684	−	7.07142i	1.28623	−	0.273397i
$670$		0			0
$671$	−8.70955	−	3.87774i	−0.336229	−	0.149699i
$672$	42.6592	−	47.3778i	1.64561	−	1.82764i
$673$	2.84979	−	27.1140i	0.109851	−	1.04517i	−0.791231	−	0.611518i	$-0.790559\pi$
$673$	2.84979	−	27.1140i	0.109851	−	1.04517i	0.901082	−	0.433649i	$-0.142774\pi$
$674$	46.7146	+	33.9401i	1.79938	+	1.30732i
$675$		0			0
$676$	9.91286	−	17.1696i	0.381264	−	0.660368i
$677$	−1.31511	−	2.27784i	−0.0505438	−	0.0875444i	0.839647	−	0.543133i	$-0.182762\pi$
$677$	−1.31511	−	2.27784i	−0.0505438	−	0.0875444i	−0.890190	+	0.455589i	$0.849429\pi$
$678$	−62.9016	+	45.7007i	−2.41572	+	1.75512i
$679$	−16.5080	−	18.3340i	−0.633519	−	0.703594i
$680$		0			0
$681$	9.93738			0.380801
$682$	48.7748	−	7.74652i	1.86768	−	0.296630i
$683$	−29.5859			−1.13207			−0.566037	−	0.824380i	$-0.691524\pi$
$683$	−29.5859			−1.13207			−0.566037	+	0.824380i	$0.691524\pi$
$684$	−0.693026	−	2.13292i	−0.0264985	−	0.0815540i
$685$		0			0
$686$	−3.06609	+	2.22765i	−0.117064	+	0.0850519i
$687$	20.7717	+	35.9777i	0.792492	+	1.37264i
$688$	−0.448549	+	0.776909i	−0.0171008	+	0.0296194i
$689$	2.07453	+	19.7378i	0.0790331	+	0.751950i
$690$		0			0
$691$	−1.76087	+	16.7535i	−0.0669866	+	0.637334i	0.908592	+	0.417684i	$0.137158\pi$
$691$	−1.76087	+	16.7535i	−0.0669866	+	0.637334i	−0.975579	+	0.219650i	$0.929508\pi$
$692$	8.45344	−	9.38849i	0.321351	−	0.356897i
$693$	−22.6607	−	10.0892i	−0.860808	−	0.383256i
$694$	−10.7899	−	2.29346i	−0.409579	−	0.0870587i
$695$		0			0
$696$	1.63827	−	0.729407i	0.0620986	−	0.0276481i
$697$	2.81323	−	8.65822i	0.106559	−	0.327954i
$698$	2.62397	−	8.07576i	0.0993189	−	0.305672i
$699$	27.8477	−	12.3986i	1.05330	−	0.468957i
$700$		0			0
$701$	−20.7605	−	4.41279i	−0.784114	−	0.166669i	−0.201577	−	0.979473i	$-0.564607\pi$
$701$	−20.7605	−	4.41279i	−0.784114	−	0.166669i	−0.582537	+	0.812804i	$0.697940\pi$
$702$	12.0283	+	5.35536i	0.453980	+	0.202125i
$703$	0.113873	−	0.126468i	0.00429479	−	0.00476985i
$704$	−4.54235	+	43.2176i	−0.171196	+	1.62882i
$705$		0			0
$706$	−4.71948	−	44.9029i	−0.177620	−	1.68994i
$707$	33.1859	−	57.4796i	1.24808	−	2.16174i
$708$	14.2979	+	24.7647i	0.537348	+	0.930714i
$709$	−41.5383	+	30.1794i	−1.56001	+	1.13341i	−0.624000	+	0.781424i	$0.714494\pi$
$709$	−41.5383	+	30.1794i	−1.56001	+	1.13341i	−0.936005	+	0.351986i	$0.885506\pi$
$710$		0			0
$711$	4.22828	+	13.0133i	0.158573	+	0.488037i
$712$	−3.05044			−0.114320
$713$	−6.68457	+	17.4362i	−0.250339	+	0.652989i
$714$	34.6656			1.29733
$715$		0			0
$716$	18.6228	+	20.6827i	0.695967	+	0.772950i
$717$	11.7721	−	8.55293i	0.439637	−	0.319415i
$718$	−7.33679	−	12.7077i	−0.273807	−	0.474247i
$719$	20.0999	−	34.8141i	0.749601	−	1.29835i	−0.198413	−	0.980119i	$-0.563579\pi$
$719$	20.0999	−	34.8141i	0.749601	−	1.29835i	0.948014	−	0.318229i	$-0.103088\pi$
$720$		0			0
$721$	11.6393	+	8.45647i	0.433471	+	0.314935i
$722$	−4.03205	+	38.3624i	−0.150058	+	1.42770i
$723$	−16.4700	+	18.2917i	−0.612524	+	0.680277i
$724$	20.2139	+	8.99983i	0.751245	+	0.334476i
$725$		0			0
$726$	31.7579	−	6.75035i	1.17865	−	0.250529i
$727$	19.6265	−	8.73827i	0.727906	−	0.324084i	−0.00911160	−	0.999958i	$-0.502900\pi$
$727$	19.6265	−	8.73827i	0.727906	−	0.324084i	0.737017	+	0.675874i	$0.236234\pi$
$728$	−1.44228	+	4.43889i	−0.0534545	+	0.164516i
$729$	0.558517	−	1.71894i	0.0206858	−	0.0636644i
$730$		0			0
$731$	−0.561388	+	0.119327i	−0.0207637	+	0.00441346i
$732$	−10.6902	−	2.27227i	−0.395121	−	0.0839856i
$733$	−20.5286	−	9.13991i	−0.758241	−	0.337590i	−0.00906234	−	0.999959i	$-0.502885\pi$
$733$	−20.5286	−	9.13991i	−0.758241	−	0.337590i	−0.749178	+	0.662368i	$0.769551\pi$
$734$	−22.3475	+	24.8194i	−0.824861	+	0.916101i
$735$		0			0
$736$	−22.0046	−	15.9872i	−0.811099	−	0.589298i
$737$	6.09174	+	57.9591i	0.224392	+	2.13495i
$738$	−6.98953	+	12.1062i	−0.257288	+	0.445636i
$739$	−26.2750	−	45.5097i	−0.966542	−	1.67410i	−0.705413	−	0.708797i	$-0.749238\pi$
$739$	−26.2750	−	45.5097i	−0.966542	−	1.67410i	−0.261129	−	0.965304i	$-0.584095\pi$
$740$		0			0
$741$	−1.85254	−	2.05745i	−0.0680547	−	0.0755824i
$742$	22.3728	+	68.8565i	0.821333	+	2.52780i
$743$	17.4032			0.638460			0.319230	−	0.947677i	$-0.396576\pi$
$743$	17.4032			0.638460			0.319230	+	0.947677i	$0.396576\pi$
$744$	6.76632	−	2.60066i	0.248065	−	0.0953449i
$745$		0			0
$746$	−6.28728	−	19.3503i	−0.230194	−	0.708463i
$747$	5.47180	+	6.07705i	0.200203	+	0.222348i
$748$	−16.9041	+	12.2815i	−0.618074	+	0.449057i
$749$	20.4224	+	35.3727i	0.746219	+	1.29249i
$750$		0			0
$751$	2.34603	+	22.3210i	0.0856080	+	0.814505i	0.950118	+	0.311890i	$0.100962\pi$
$751$	2.34603	+	22.3210i	0.0856080	+	0.814505i	−0.864510	+	0.502615i	$0.832371\pi$
$752$	−14.4758	−	10.5173i	−0.527879	−	0.383526i
$753$	1.63123	−	15.5201i	0.0594453	−	0.565584i
$754$	3.98616	−	4.42708i	0.145168	−	0.161225i
$755$		0			0
$756$	25.0979	+	5.33473i	0.912804	+	0.194022i
$757$	−14.4696	+	3.07560i	−0.525906	+	0.111785i	−0.463211	−	0.886248i	$-0.653303\pi$
$757$	−14.4696	+	3.07560i	−0.525906	+	0.111785i	−0.0626946	+	0.998033i	$0.519969\pi$
$758$	26.1527	−	11.6439i	0.949907	−	0.422926i
$759$	−9.49136	+	29.2114i	−0.344515	+	1.06031i
$760$		0			0
$761$	−18.1807	+	8.09457i	−0.659050	+	0.293428i	−0.708879	−	0.705330i	$-0.750799\pi$
$761$	−18.1807	+	8.09457i	−0.659050	+	0.293428i	0.0498293	+	0.998758i	$0.484132\pi$
$762$	61.5667	−	13.0864i	2.23032	−	0.474070i
$763$	−65.0320	−	13.8230i	−2.35432	−	0.500426i
$764$	21.9291	+	9.76346i	0.793366	+	0.353229i
$765$		0			0
$766$	−2.23224	+	21.2383i	−0.0806541	+	0.767373i
$767$	9.84009	+	7.14925i	0.355305	+	0.258144i
$768$	−2.30874	−	21.9662i	−0.0833096	−	0.792638i
$769$	−2.09853	+	3.63477i	−0.0756751	+	0.131073i	−0.901380	−	0.433030i	$-0.857445\pi$
$769$	−2.09853	+	3.63477i	−0.0756751	+	0.131073i	0.825705	+	0.564103i	$0.190778\pi$
$770$		0			0
$771$	−42.6742	+	31.0046i	−1.53687	+	1.11660i
$772$	2.74825	+	3.05224i	0.0989116	+	0.109852i
$773$	−3.67070	−	11.2973i	−0.132026	−	0.406334i	0.863090	−	0.505051i	$-0.168526\pi$
$773$	−3.67070	−	11.2973i	−0.132026	−	0.406334i	−0.995116	+	0.0987167i	$0.968526\pi$
$774$	0.881281			0.0316770
$775$		0			0
$776$	4.08584			0.146673
$777$	−0.666779	−	2.05213i	−0.0239206	−	0.0736199i
$778$	35.1696	+	39.0598i	1.26089	+	1.40036i
$779$	−2.14581	+	1.55903i	−0.0768818	+	0.0558579i
$780$		0			0
$781$	−2.85931	+	4.95246i	−0.102314	+	0.177213i
$782$	−1.54592	−	14.7084i	−0.0552820	−	0.525973i
$783$	−3.39250	−	2.46479i	−0.121238	−	0.0880845i
$784$	2.26084	−	21.5104i	0.0807442	−	0.768230i
$785$		0			0
$786$	−29.1122	−	12.9616i	−1.03840	−	0.462324i
$787$	1.94067	+	0.412503i	0.0691776	+	0.0147042i	0.242370	−	0.970184i	$-0.422075\pi$
$787$	1.94067	+	0.412503i	0.0691776	+	0.0147042i	−0.173193	+	0.984888i	$0.555408\pi$
$788$	14.3520	−	3.05061i	0.511269	−	0.108673i
$789$	51.3762	−	22.8741i	1.82904	−	0.814341i
$790$		0			0
$791$	−19.9152	+	61.2926i	−0.708102	+	2.17931i
$792$	3.75293	−	1.67091i	0.133355	−	0.0593733i
$793$	−4.54700	+	0.966495i	−0.161469	+	0.0343212i
$794$	−33.9675	−	7.22001i	−1.20546	−	0.256228i
$795$		0			0
$796$	1.42298	−	1.58038i	0.0504361	−	0.0560150i
$797$	−5.26681	+	50.1103i	−0.186560	+	1.77500i	0.355517	+	0.934670i	$0.384305\pi$
$797$	−5.26681	+	50.1103i	−0.186560	+	1.77500i	−0.542077	+	0.840329i	$0.682362\pi$
$798$	−8.17088	−	5.93649i	−0.289246	−	0.210149i
$799$	−1.19657	−	11.3846i	−0.0423317	−	0.402760i
$800$		0			0
$801$	−3.95241	−	6.84577i	−0.139652	−	0.241884i
$802$	−46.3076	+	33.6445i	−1.63518	+	1.18803i
$803$	−40.5758	−	45.0640i	−1.43189	−	1.59028i
$804$	20.6445	+	63.5373i	0.728077	+	2.24079i
$805$		0			0
$806$	17.0200	−	17.0345i	0.599504	−	0.600016i
$807$	−44.6701			−1.57246
$808$	3.39675	+	10.4541i	0.119497	+	0.367775i
$809$	−10.4200	−	11.5726i	−0.366347	−	0.406870i	0.531584	−	0.847005i	$-0.321597\pi$
$809$	−10.4200	−	11.5726i	−0.366347	−	0.406870i	−0.897931	+	0.440136i	$0.854930\pi$
$810$		0			0
$811$	−10.3694	−	17.9604i	−0.364119	−	0.630673i	0.624515	−	0.781013i	$-0.285297\pi$
$811$	−10.3694	−	17.9604i	−0.364119	−	0.630673i	−0.988634	+	0.150340i	$0.951963\pi$
$812$	5.80460	−	10.0539i	0.203702	−	0.352822i
$813$	4.69860	+	44.7042i	0.164787	+	1.56784i
$814$	1.96964	+	1.43103i	0.0690360	+	0.0501576i
$815$		0			0
$816$	10.1336	−	11.2545i	0.354746	−	0.393985i
$817$	0.152757	+	0.0680118i	0.00534429	+	0.00237943i
$818$	−45.8282	−	9.74109i	−1.60235	−	0.340589i
$819$	−11.8305	+	2.51464i	−0.413390	+	0.0878688i
$820$		0			0
$821$	6.05511	−	18.6357i	0.211325	−	0.650391i	−0.788069	−	0.615587i	$-0.788919\pi$
$821$	6.05511	−	18.6357i	0.211325	−	0.650391i	0.999394	−	0.0348044i	$-0.0110808\pi$
$822$	10.3806	−	31.9482i	0.362065	−	1.11432i
$823$	−1.91901	+	0.854399i	−0.0668925	+	0.0297825i	−0.439910	−	0.898042i	$-0.644990\pi$
$823$	−1.91901	+	0.854399i	−0.0668925	+	0.0297825i	0.373018	+	0.927824i	$0.378323\pi$
$824$	−2.33063	+	0.495390i	−0.0811912	+	0.0172577i
$825$		0			0
$826$	40.5346	+	18.0472i	1.41038	+	0.627942i
$827$	2.34540	−	2.60483i	0.0815575	−	0.0905787i	−0.700985	−	0.713176i	$-0.747256\pi$
$827$	2.34540	−	2.60483i	0.0815575	−	0.0905787i	0.782542	+	0.622597i	$0.213923\pi$
$828$	−1.26808	+	12.0650i	−0.0440688	+	0.419287i
$829$	1.68971	+	1.22765i	0.0586860	+	0.0426379i	0.616742	−	0.787166i	$-0.288452\pi$
$829$	1.68971	+	1.22765i	0.0586860	+	0.0426379i	−0.558056	+	0.829804i	$0.688452\pi$
$830$		0			0
$831$	−5.09098	+	8.81784i	−0.176604	+	0.305888i
$832$	10.5943	+	18.3498i	0.367290	+	0.636166i
$833$	11.1947	−	8.13341i	0.387873	−	0.281806i
$834$	59.6175	+	66.2120i	2.06439	+	2.29273i
$835$		0			0
$836$	6.08759			0.210544
$837$	−13.1774	−	10.6615i	−0.455478	−	0.368517i
$838$	12.8284			0.443151
$839$	−3.32915	−	10.2461i	−0.114935	−	0.353734i	0.876998	−	0.480493i	$-0.159542\pi$
$839$	−3.32915	−	10.2461i	−0.114935	−	0.353734i	−0.991933	+	0.126759i	$0.959542\pi$
$840$		0			0
$841$	21.9266	−	15.9306i	0.756088	−	0.549330i
$842$	6.79587	+	11.7708i	0.234201	+	0.405648i
$843$	7.11863	−	12.3298i	0.245178	−	0.424662i
$844$	1.48203	+	14.1006i	0.0510137	+	0.485363i
$845$		0			0
$846$	−1.83736	+	17.4813i	−0.0631698	+	0.601021i
$847$	18.0076	−	19.9995i	0.618749	−	0.687190i
$848$	28.8949	+	12.8648i	0.992256	+	0.441781i
$849$	−15.1638	−	3.22316i	−0.520420	−	0.110619i
$850$		0			0
$851$	−0.840975	+	0.374426i	−0.0288283	+	0.0128352i
$852$	−2.02576	+	6.23466i	−0.0694015	+	0.213596i
$853$	−10.0895	+	31.0524i	−0.345459	+	1.06321i	0.615879	+	0.787841i	$0.288801\pi$
$853$	−10.0895	+	31.0524i	−0.345459	+	1.06321i	−0.961338	+	0.275372i	$0.911199\pi$
$854$	−15.4919	+	6.89745i	−0.530123	+	0.236026i
$855$		0			0
$856$	−6.61667	−	1.40642i	−0.226153	−	0.0480703i
$857$	39.9528	+	17.7881i	1.36476	+	0.607631i	0.952808	−	0.303573i	$-0.0981798\pi$
$857$	39.9528	+	17.7881i	1.36476	+	0.607631i	0.411954	+	0.911205i	$0.364846\pi$
$858$	26.5026	−	29.4342i	0.904785	−	1.00487i
$859$	2.54697	−	24.2328i	0.0869016	−	0.826813i	−0.861076	−	0.508476i	$-0.830209\pi$
$859$	2.54697	−	24.2328i	0.0869016	−	0.826813i	0.947978	−	0.318337i	$-0.103124\pi$
$860$		0			0
$861$	3.51528	+	33.4457i	0.119800	+	1.13983i
$862$	24.3140	−	42.1130i	0.828137	−	1.43438i
$863$	−21.7570	−	37.6842i	−0.740616	−	1.28279i	−0.952215	−	0.305429i	$-0.901200\pi$
$863$	−21.7570	−	37.6842i	−0.740616	−	1.28279i	0.211599	−	0.977357i	$-0.432133\pi$
$864$	19.9739	−	14.5119i	0.679525	−	0.493704i
$865$		0			0
$866$	15.5681	+	47.9137i	0.529025	+	1.62817i
$867$	−26.6808			−0.906129
$868$	25.5412	−	39.3668i	0.866925	−	1.33620i
$869$	−37.1415			−1.25994
$870$		0			0
$871$	19.0140	+	21.1172i	0.644264	+	0.715528i
$872$	8.90796	−	6.47201i	0.301662	−	0.219170i
$873$	5.29396	+	9.16941i	0.179173	+	0.310338i
$874$	−2.15444	+	3.73160i	−0.0728751	+	0.126223i
$875$		0			0
$876$	−56.2380	−	40.8593i	−1.90011	−	1.38051i
$877$	−3.99757	+	38.0343i	−0.134988	+	1.28433i	0.691913	+	0.721981i	$0.256768\pi$
$877$	−3.99757	+	38.0343i	−0.134988	+	1.28433i	−0.826901	+	0.562347i	$0.809899\pi$
$878$	−20.1133	+	22.3381i	−0.678793	+	0.753876i
$879$	−26.4073	−	11.7573i	−0.890697	−	0.396564i
$880$		0			0
$881$	−39.8511	+	8.47062i	−1.34262	+	0.285382i	−0.822526	−	0.568728i	$-0.807436\pi$
$881$	−39.8511	+	8.47062i	−1.34262	+	0.285382i	−0.520092	+	0.854110i	$0.674102\pi$
$882$	−19.4106	+	8.64217i	−0.653590	+	0.290997i
$883$	−10.2334	+	31.4952i	−0.344382	+	1.05990i	0.617532	+	0.786546i	$0.288133\pi$
$883$	−10.2334	+	31.4952i	−0.344382	+	1.05990i	−0.961914	+	0.273353i	$0.911867\pi$
$884$	−3.14826	+	9.68935i	−0.105888	+	0.325888i
$885$		0			0
$886$	33.5766	−	7.13693i	1.12803	−	0.239770i
$887$	12.1951	+	2.59214i	0.409470	+	0.0870356i	0.408042	−	0.912963i	$-0.366212\pi$
$887$	12.1951	+	2.59214i	0.409470	+	0.0870356i	0.00142883	+	0.999999i	$0.499545\pi$
$888$	0.326458	+	0.145349i	0.0109552	+	0.00487758i
$889$	34.9100	−	38.7715i	1.17084	−	1.30035i
$890$		0			0
$891$	−38.9395	−	28.2912i	−1.30452	−	0.947790i
$892$	3.81159	+	36.2649i	0.127622	+	1.21424i
$893$	−1.66758	+	2.88834i	−0.0558035	+	0.0966545i
$894$	27.2966	+	47.2791i	0.912936	+	1.58125i
$895$		0			0
$896$	11.8412	+	13.1510i	0.395588	+	0.439345i
$897$	4.62789	+	14.2432i	0.154521	+	0.475566i
$898$	−14.1263			−0.471401
$899$	−6.43009	+	4.17965i	−0.214455	+	0.139399i
$900$		0			0
$901$	6.25307	+	19.2450i	0.208320	+	0.641143i
$902$	−25.3903	−	28.1987i	−0.845403	−	0.938915i
$903$	1.71522	−	1.24618i	0.0570789	−	0.0414703i
$904$	−5.33666	−	9.24337i	−0.177495	−	0.307430i
$905$		0			0
$906$	−9.21065	−	87.6335i	−0.306003	−	2.91143i
$907$	13.6734	+	9.93431i	0.454018	+	0.329863i	0.791180	−	0.611583i	$-0.209467\pi$
$907$	13.6734	+	9.93431i	0.454018	+	0.329863i	−0.337162	+	0.941447i	$0.609467\pi$
$908$	−1.11365	+	10.5957i	−0.0369579	+	0.351631i
$909$	−19.0599	+	21.1682i	−0.632179	+	0.702105i
$910$		0			0
$911$	53.2794	+	11.3249i	1.76522	+	0.375210i	0.972231	−	0.234022i	$-0.0751887\pi$
$911$	53.2794	+	11.3249i	1.76522	+	0.375210i	0.792992	+	0.609232i	$0.208522\pi$
$912$	−4.31587	+	0.917366i	−0.142913	+	0.0303770i
$913$	−20.2781	+	9.02841i	−0.671108	+	0.298797i
$914$	13.7206	−	42.2278i	0.453838	−	1.39677i
$915$		0			0
$916$	−40.6890	+	18.1159i	−1.34440	+	0.598567i
$917$	−25.8373	+	5.49188i	−0.853222	+	0.181358i
$918$	13.1313	+	2.79114i	0.433396	+	0.0921212i
$919$	−8.00934	−	3.56599i	−0.264204	−	0.117631i	0.270360	−	0.962759i	$-0.412857\pi$
$919$	−8.00934	−	3.56599i	−0.264204	−	0.117631i	−0.534564	+	0.845128i	$0.679524\pi$
$920$		0			0
$921$	−5.08212	+	48.3531i	−0.167461	+	1.59329i
$922$	−14.5418	−	10.5652i	−0.478908	−	0.347947i
$923$	0.291461	+	2.77306i	0.00959355	+	0.0912765i
$924$	38.5928	−	66.8447i	1.26961	−	2.19903i
$925$		0			0
$926$	−6.11858	+	4.44541i	−0.201069	+	0.146085i
$927$	−4.13151	−	4.58851i	−0.135697	−	0.150706i
$928$	−3.45188	−	10.6238i	−0.113313	−	0.348743i
$929$	−44.2868			−1.45300			−0.726501	−	0.687165i	$-0.758855\pi$
$929$	−44.2868			−1.45300			−0.726501	+	0.687165i	$0.758855\pi$
$930$		0			0
$931$	−4.03150			−0.132127
$932$	10.0992	+	31.0820i	0.330809	+	1.01813i
$933$	13.5900	+	15.0932i	0.444915	+	0.494129i
$934$	5.16512	−	3.75268i	0.169008	−	0.122791i
$935$		0			0
$936$	1.00153	−	1.73471i	0.0327361	−	0.0567006i
$937$	−5.38495	−	51.2343i	−0.175919	−	1.67375i	−0.625278	−	0.780402i	$-0.715014\pi$
$937$	−5.38495	−	51.2343i	−0.175919	−	1.67375i	0.449359	−	0.893351i	$-0.351652\pi$
$938$	83.8637	+	60.9306i	2.73825	+	1.98945i
$939$	6.28327	−	59.7813i	0.205047	−	1.95089i
$940$		0			0
$941$	35.8083	+	15.9429i	1.16732	+	0.519722i	0.896559	−	0.442925i	$-0.146059\pi$
$941$	35.8083	+	15.9429i	1.16732	+	0.519722i	0.270757	+	0.962648i	$0.412726\pi$
$942$	25.1700	+	5.35005i	0.820083	+	0.174314i
$943$	14.0341	−	2.98303i	0.457012	−	0.0971409i
$944$	17.7084	−	7.88428i	0.576358	−	0.256611i
$945$		0			0
$946$	−0.739222	+	2.27509i	−0.0240342	+	0.0739696i
$947$	−51.9956	+	23.1500i	−1.68963	+	0.752272i	−0.690038	+	0.723773i	$0.742406\pi$
$947$	−51.9956	+	23.1500i	−1.68963	+	0.752272i	−0.999594	+	0.0284989i	$0.990927\pi$
$948$	−41.6466	+	8.85225i	−1.35262	+	0.287508i
$949$	−28.9212	−	6.14739i	−0.938821	−	0.199553i
$950$		0			0
$951$	22.6423	−	25.1468i	0.734227	−	0.815441i
$952$	−0.497427	+	4.73270i	−0.0161217	+	0.153388i
$953$	−12.3568	−	8.97773i	−0.400275	−	0.290817i	0.369378	−	0.929279i	$-0.379571\pi$
$953$	−12.3568	−	8.97773i	−0.400275	−	0.290817i	−0.769653	+	0.638462i	$0.779571\pi$
$954$	−3.24789	−	30.9016i	−0.105154	−	1.00048i
$955$		0			0
$956$	7.80028	+	13.5105i	0.252279	+	0.436960i
$957$	−10.2052	+	7.41452i	−0.329888	+	0.239677i
$958$	24.1396	+	26.8098i	0.779916	+	0.866184i
$959$	−8.60439	−	26.4816i	−0.277850	−	0.855135i
$960$		0			0
$961$	−26.8335	+	15.5229i	−0.865598	+	0.500739i
$962$	1.18709			0.0382735
$963$	−5.41685	−	16.6713i	−0.174556	−	0.537227i
$964$	−17.6578	−	19.6110i	−0.568719	−	0.631627i
$965$		0			0
$966$	27.3165	+	47.3136i	0.878895	+	1.52229i
$967$	5.64979	−	9.78573i	0.181685	−	0.314688i	−0.760769	−	0.649022i	$-0.775178\pi$
$967$	5.64979	−	9.78573i	0.181685	−	0.314688i	0.942455	+	0.334334i	$0.108511\pi$
$968$	0.465884	+	4.43259i	0.0149741	+	0.142469i
$969$	−2.28371	−	1.65921i	−0.0733633	−	0.0533015i
$970$		0			0
$971$	−10.6179	+	11.7924i	−0.340745	+	0.378436i	−0.889025	−	0.457859i	$-0.848616\pi$
$971$	−10.6179	+	11.7924i	−0.340745	+	0.378436i	0.548280	+	0.836295i	$0.315283\pi$
$972$	−31.2682	−	13.9215i	−1.00293	−	0.446532i
$973$	72.2379	+	15.3546i	2.31584	+	0.492247i
$974$	−58.3195	+	12.3962i	−1.86868	+	0.397200i
$975$		0			0
$976$	−2.28934	+	7.04586i	−0.0732800	+	0.225533i
$977$	5.11731	−	15.7495i	0.163717	−	0.503870i	−0.835222	−	0.549913i	$-0.814661\pi$
$977$	5.11731	−	15.7495i	0.163717	−	0.503870i	0.998939	+	0.0460426i	$0.0146610\pi$
$978$	72.0193	−	32.0650i	2.30292	−	1.02533i
$979$	20.9882	−	4.46117i	0.670785	−	0.142580i
$980$		0			0
$981$	26.0664	+	11.6055i	0.832235	+	0.370535i
$982$	13.6235	−	15.1304i	0.434743	−	0.482832i
$983$	2.26302	−	21.5312i	0.0721792	−	0.686739i	−0.897276	−	0.441470i	$-0.854457\pi$
$983$	2.26302	−	21.5312i	0.0721792	−	0.686739i	0.969455	−	0.245269i	$-0.0788763\pi$
$984$	−4.50589	−	3.27372i	−0.143643	−	0.104362i
$985$		0			0
$986$	3.03697	−	5.26019i	0.0967169	−	0.167519i
$987$	21.1436	+	36.6217i	0.673007	+	1.16568i
$988$	2.40137	−	1.74469i	0.0763976	−	0.0555061i
$989$	−0.605238	−	0.672185i	−0.0192455	−	0.0213743i
$990$		0			0
$991$	32.3028			1.02613			0.513066	−	0.858349i	$-0.328510\pi$
$991$	32.3028			1.02613			0.513066	+	0.858349i	$0.328510\pi$
$992$	−11.7051	−	43.6097i	−0.371639	−	1.38461i
$993$	27.6925			0.878796
$994$	3.14328	+	9.67401i	0.0996987	+	0.306841i
$995$		0			0
$996$	−20.5860	+	14.9566i	−0.652291	+	0.473917i
$997$	−5.74360	−	9.94821i	−0.181902	−	0.315063i	0.760626	−	0.649190i	$-0.224892\pi$
$997$	−5.74360	−	9.94821i	−0.181902	−	0.315063i	−0.942528	+	0.334127i	$0.891559\pi$
$998$	−11.2392	+	19.4669i	−0.355771	+	0.616213i
$999$	−0.0873448	−	0.831030i	−0.00276347	−	0.0262926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.bl.a.51.1		16
5.2	odd	4		775.2.ck.a.299.3		32
5.3	odd	4		775.2.ck.a.299.2		32
5.4	even	2		31.2.g.a.20.2	yes	16
15.14	odd	2		279.2.y.c.82.1		16
20.19	odd	2		496.2.bg.c.113.2		16
31.14	even	15	inner	775.2.bl.a.76.1		16
155.4	even	10		961.2.g.t.816.1		16
155.9	even	30		961.2.d.o.628.4		16
155.14	even	30		31.2.g.a.14.2	✓	16
155.19	even	30		961.2.g.t.338.1		16
155.24	odd	30		961.2.g.m.732.1		16
155.29	odd	10		961.2.g.m.235.1		16
155.34	odd	30		961.2.c.i.521.7		16
155.39	even	10		961.2.g.k.846.2		16
155.44	odd	30		961.2.a.j.1.7		8
155.49	even	30		961.2.a.i.1.7		8
155.54	odd	10		961.2.g.j.846.2		16
155.59	even	30		961.2.c.j.521.7		16
155.64	even	10		961.2.g.s.235.1		16
155.69	even	30		961.2.g.s.732.1		16
155.74	odd	30		961.2.g.n.338.1		16
155.79	odd	30		961.2.g.l.448.2		16
155.84	odd	30		961.2.d.n.628.4		16
155.89	odd	10		961.2.g.n.816.1		16
155.99	odd	6		961.2.g.j.844.2		16
155.104	odd	30		961.2.d.q.374.1		16
155.107	odd	60		775.2.ck.a.324.2		32
155.109	even	10		961.2.c.j.439.7		16
155.114	odd	30		961.2.d.q.388.1		16
155.119	odd	6		961.2.d.n.531.4		16
155.129	even	6		961.2.d.o.531.4		16
155.134	even	30		961.2.d.p.388.1		16
155.138	odd	60		775.2.ck.a.324.3		32
155.139	odd	10		961.2.c.i.439.7		16
155.144	even	30		961.2.d.p.374.1		16
155.149	even	6		961.2.g.k.844.2		16
155.154	odd	2		961.2.g.l.547.2		16
465.14	odd	30		279.2.y.c.262.1		16
465.44	even	30		8649.2.a.be.1.2		8
465.359	odd	30		8649.2.a.bf.1.2		8
620.479	odd	30		496.2.bg.c.417.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.14.2	✓	16	155.14	even	30
31.2.g.a.20.2	yes	16	5.4	even	2
279.2.y.c.82.1		16	15.14	odd	2
279.2.y.c.262.1		16	465.14	odd	30
496.2.bg.c.113.2		16	20.19	odd	2
496.2.bg.c.417.2		16	620.479	odd	30
775.2.bl.a.51.1		16	1.1	even	1	trivial
775.2.bl.a.76.1		16	31.14	even	15	inner
775.2.ck.a.299.2		32	5.3	odd	4
775.2.ck.a.299.3		32	5.2	odd	4
775.2.ck.a.324.2		32	155.107	odd	60
775.2.ck.a.324.3		32	155.138	odd	60
961.2.a.i.1.7		8	155.49	even	30
961.2.a.j.1.7		8	155.44	odd	30
961.2.c.i.439.7		16	155.139	odd	10
961.2.c.i.521.7		16	155.34	odd	30
961.2.c.j.439.7		16	155.109	even	10
961.2.c.j.521.7		16	155.59	even	30
961.2.d.n.531.4		16	155.119	odd	6
961.2.d.n.628.4		16	155.84	odd	30
961.2.d.o.531.4		16	155.129	even	6
961.2.d.o.628.4		16	155.9	even	30
961.2.d.p.374.1		16	155.144	even	30
961.2.d.p.388.1		16	155.134	even	30
961.2.d.q.374.1		16	155.104	odd	30
961.2.d.q.388.1		16	155.114	odd	30
961.2.g.j.844.2		16	155.99	odd	6
961.2.g.j.846.2		16	155.54	odd	10
961.2.g.k.844.2		16	155.149	even	6
961.2.g.k.846.2		16	155.39	even	10
961.2.g.l.448.2		16	155.79	odd	30
961.2.g.l.547.2		16	155.154	odd	2
961.2.g.m.235.1		16	155.29	odd	10
961.2.g.m.732.1		16	155.24	odd	30
961.2.g.n.338.1		16	155.74	odd	30
961.2.g.n.816.1		16	155.89	odd	10
961.2.g.s.235.1		16	155.64	even	10
961.2.g.s.732.1		16	155.69	even	30
961.2.g.t.338.1		16	155.19	even	30
961.2.g.t.816.1		16	155.4	even	10
8649.2.a.be.1.2		8	465.44	even	30
8649.2.a.bf.1.2		8	465.359	odd	30

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.bl (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.640321 - 1.97070i) q^{2} +(1.43153 + 1.58988i) q^{3} +(-1.85563 + 1.34820i) q^{4} +(2.21654 - 3.83916i) q^{6} +(-0.384094 - 3.65441i) q^{7} +(0.492333 + 0.357701i) q^{8} +(-0.164841 + 1.56836i) q^{9} +(-3.91056 - 1.74109i) q^{11} +(-4.79986 - 1.02024i) q^{12} +(-2.04159 + 0.433953i) q^{13} +(-6.95582 + 3.09693i) q^{14} +(-1.02791 + 3.16357i) q^{16} +(-1.94411 + 0.865573i) q^{17} +(3.19632 - 0.679399i) q^{18} +(0.606466 + 0.128908i) q^{19} +(5.26022 - 5.84207i) q^{21} +(-0.927168 + 8.82142i) q^{22} +(-2.71334 - 1.97136i) q^{23} +(0.136090 + 1.29481i) q^{24} +(2.16247 + 3.74550i) q^{26} +(2.46294 - 1.78943i) q^{27} +(5.63960 + 6.26341i) q^{28} +(-0.425645 - 1.31000i) q^{29} +(-1.44334 - 5.37743i) q^{31} +8.10976 q^{32} +(-2.82997 - 8.70975i) q^{33} +(2.95064 + 3.27702i) q^{34} +(-1.80857 - 3.13253i) q^{36} +(0.137239 - 0.237704i) q^{37} +(-0.134293 - 1.27771i) q^{38} +(-3.61253 - 2.62466i) q^{39} +(-2.86248 + 3.17911i) q^{41} +(-14.8812 - 6.62555i) q^{42} +(0.263799 + 0.0560722i) q^{43} +(9.60390 - 2.04137i) q^{44} +(-2.14756 + 6.60950i) q^{46} +(-1.66225 + 5.11589i) q^{47} +(-6.50117 + 2.89451i) q^{48} +(-6.36016 + 1.35189i) q^{49} +(-4.15921 - 1.85180i) q^{51} +(3.20338 - 3.55772i) q^{52} +(0.993928 - 9.45659i) q^{53} +(-5.10351 - 3.70792i) q^{54} +(1.11808 - 1.93658i) q^{56} +(0.663228 + 1.14874i) q^{57} +(-2.30908 + 1.67764i) q^{58} +(-3.89932 - 4.33063i) q^{59} +2.22719 q^{61} +(-9.67313 + 6.28768i) q^{62} +5.79474 q^{63} +(-3.13704 - 9.65481i) q^{64} +(-15.3522 + 11.1541i) q^{66} +(-6.80719 - 11.7904i) q^{67} +(2.44059 - 4.22722i) q^{68} +(-0.750018 - 7.13595i) q^{69} +(0.139642 - 1.32861i) q^{71} +(-0.642159 + 0.713189i) q^{72} +(12.9413 + 5.76184i) q^{73} +(-0.556321 - 0.118250i) q^{74} +(-1.29917 + 0.578429i) q^{76} +(-4.86065 + 14.9595i) q^{77} +(-2.85925 + 8.79986i) q^{78} +(7.92648 - 3.52910i) q^{79} +(10.9984 + 2.33777i) q^{81} +(8.09799 + 3.60546i) q^{82} +(3.46976 - 3.85356i) q^{83} +(-1.88479 + 17.9325i) q^{84} +(-0.0584142 - 0.555774i) q^{86} +(1.47342 - 2.55203i) q^{87} +(-1.30251 - 2.25601i) q^{88} +(-4.05526 + 2.94632i) q^{89} +(2.37001 + 7.29413i) q^{91} +7.69274 q^{92} +(6.48327 - 9.99270i) q^{93} +11.1463 q^{94} +(11.6094 + 12.8935i) q^{96} +(5.43173 - 3.94638i) q^{97} +(6.73673 + 11.6684i) q^{98} +(3.37528 - 5.84615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 12 q^{3} - 14 q^{4} + 11 q^{6} - 2 q^{7} - 17 q^{8} - 10 q^{9} - 7 q^{11} - 5 q^{12} + 7 q^{13} - 6 q^{14} - 2 q^{16} + 6 q^{17} + 3 q^{18} + 16 q^{19} + 9 q^{21} - 9 q^{22} - q^{23} - 20 q^{24}+ \cdots + 6 q^{99}+O(q^{100}) \) 16 * q + 6 * q^2 + 12 * q^3 - 14 * q^4 + 11 * q^6 - 2 * q^7 - 17 * q^8 - 10 * q^9 - 7 * q^11 - 5 * q^12 + 7 * q^13 - 6 * q^14 - 2 * q^16 + 6 * q^17 + 3 * q^18 + 16 * q^19 + 9 * q^21 - 9 * q^22 - q^23 - 20 * q^24 + 9 * q^26 - 9 * q^27 + 30 * q^28 - 14 * q^29 + 15 * q^31 + 42 * q^32 + 13 * q^33 - 32 * q^34 + q^36 + 8 * q^37 - 8 * q^38 - 3 * q^39 - 8 * q^41 - 69 * q^42 - 23 * q^43 + 39 * q^44 + 34 * q^46 - 14 * q^47 - 34 * q^48 + 2 * q^49 - 42 * q^51 - 29 * q^52 - 6 * q^53 - 46 * q^54 - 30 * q^56 + 17 * q^57 + 15 * q^58 + 4 * q^59 - 60 * q^61 + 25 * q^62 + 46 * q^63 + 23 * q^64 - 30 * q^66 - 13 * q^67 - 30 * q^68 + 38 * q^69 - 14 * q^71 - 37 * q^72 - 2 * q^73 + 13 * q^74 - 12 * q^76 - 18 * q^77 + 15 * q^78 + 18 * q^79 + 23 * q^81 - 14 * q^82 + 16 * q^83 + 8 * q^84 - 26 * q^86 - 15 * q^87 + 17 * q^88 + q^89 + 8 * q^91 + 64 * q^92 - 17 * q^93 + 44 * q^94 + 8 * q^96 - 3 * q^97 + 10 * q^98 + 6 * q^99

Introduction

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