LMFDB - Embedded newform 961.2.g.l.448.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(235,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([26])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.235"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-6,12,-14,-3,-11,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
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			448.1
Root			$-1.14660i$ of defining polynomial
Character	$\chi$	$=$	961.448
Dual form			961.2.g.l.547.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.831304 + 2.55849i) q^{2} +(-0.949606 + 1.05464i) q^{3} +(-4.23677 - 3.07819i) q^{4} +(-0.304192 + 0.526876i) q^{5} +(-1.90889 - 3.30629i) q^{6} +(0.180508 - 1.71742i) q^{7} +(7.04481 - 5.11835i) q^{8} +(0.103062 + 0.980572i) q^{9} +(-1.09513 - 1.21627i) q^{10} +(1.22177 - 0.543967i) q^{11} +(7.26966 - 1.54521i) q^{12} +(3.59045 + 0.763174i) q^{13} +(4.24394 + 1.88952i) q^{14} +(-0.266804 - 0.821139i) q^{15} +(4.00227 + 12.3177i) q^{16} +(2.52396 + 1.12374i) q^{17} +(-2.59446 - 0.551469i) q^{18} +(2.51157 - 0.533850i) q^{19} +(2.91062 - 1.29589i) q^{20} +(1.63986 + 1.82124i) q^{21} +(0.376072 + 3.57808i) q^{22} +(-0.436271 + 0.316969i) q^{23} +(-1.29175 + 12.2902i) q^{24} +(2.31493 + 4.00958i) q^{25} +(-4.93733 + 8.55171i) q^{26} +(-4.57641 - 3.32495i) q^{27} +(-6.05132 + 6.72067i) q^{28} +(2.51258 - 7.73291i) q^{29} +2.32267 q^{30} -17.4262 q^{32} +(-0.586508 + 1.80509i) q^{33} +(-4.97326 + 5.52336i) q^{34} +(0.849957 + 0.617530i) q^{35} +(2.58174 - 4.47170i) q^{36} +(3.87249 + 6.70735i) q^{37} +(-0.722025 + 6.86961i) q^{38} +(-4.21439 + 3.06194i) q^{39} +(0.553763 + 5.26870i) q^{40} +(-0.0696243 - 0.0773256i) q^{41} +(-6.02285 + 2.68155i) q^{42} +(-2.93904 + 0.624713i) q^{43} +(-6.85079 - 1.45618i) q^{44} +(-0.547990 - 0.243981i) q^{45} +(-0.448289 - 1.37969i) q^{46} +(-2.07813 - 6.39584i) q^{47} +(-16.7914 - 7.47602i) q^{48} +(3.93009 + 0.835366i) q^{49} +(-12.1829 + 2.58955i) q^{50} +(-3.58192 + 1.59477i) q^{51} +(-12.8627 - 14.2855i) q^{52} +(0.292549 + 2.78341i) q^{53} +(12.3112 - 8.94464i) q^{54} +(-0.0850494 + 0.809191i) q^{55} +(-7.51871 - 13.0228i) q^{56} +(-1.82198 + 3.15576i) q^{57} +(17.6959 + 12.8568i) q^{58} +(0.311970 - 0.346478i) q^{59} +(-1.39724 + 4.30025i) q^{60} +5.11468 q^{61} +1.70266 q^{63} +(6.48190 - 19.9492i) q^{64} +(-1.49428 + 1.65957i) q^{65} +(-4.13073 - 3.00115i) q^{66} +(-4.14923 + 7.18668i) q^{67} +(-7.23436 - 12.5303i) q^{68} +(0.0799956 - 0.761107i) q^{69} +(-2.28652 + 1.66125i) q^{70} +(-0.497420 - 4.73264i) q^{71} +(5.74497 + 6.38043i) q^{72} +(-6.85725 + 3.05304i) q^{73} +(-20.3799 + 4.33188i) q^{74} +(-6.42696 - 1.36609i) q^{75} +(-12.2842 - 5.46929i) q^{76} +(-0.713679 - 2.19648i) q^{77} +(-4.33049 - 13.3279i) q^{78} +(8.86044 + 3.94492i) q^{79} +(-7.70738 - 1.63825i) q^{80} +(4.95915 - 1.05410i) q^{81} +(0.255716 - 0.113852i) q^{82} +(11.1642 + 12.3991i) q^{83} +(-1.34155 - 12.7640i) q^{84} +(-1.35984 + 0.987981i) q^{85} +(0.844916 - 8.03884i) q^{86} +(5.76952 + 9.99310i) q^{87} +(5.82292 - 10.0856i) q^{88} +(-12.3911 - 9.00268i) q^{89} +(1.07977 - 1.19920i) q^{90} +(1.95880 - 6.02855i) q^{91} +2.82407 q^{92} +18.0912 q^{94} +(-0.482726 + 1.48568i) q^{95} +(16.5480 - 18.3784i) q^{96} +(1.03488 + 0.751881i) q^{97} +(-5.40437 + 9.36065i) q^{98} +(0.659316 + 1.14197i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 12 q^{3} - 14 q^{4} - 3 q^{5} - 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9} - 2 q^{10} + 7 q^{11} - 5 q^{12} + 7 q^{13} - 6 q^{14} - 14 q^{15} - 2 q^{16} + 6 q^{17} - 3 q^{18} + 16 q^{19}+ \cdots - 6 q^{99}+O(q^{100}) $ 16 * q - 6 * q^2 + 12 * q^3 - 14 * q^4 - 3 * q^5 - 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9 - 2 * q^10 + 7 * q^11 - 5 * q^12 + 7 * q^13 - 6 * q^14 - 14 * q^15 - 2 * q^16 + 6 * q^17 - 3 * q^18 + 16 * q^19 + 37 * q^20 - 9 * q^21 - 9 * q^22 - q^23 + 20 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 - 30 * q^28 + 14 * q^29 + 22 * q^30 - 42 * q^32 - 13 * q^33 + 32 * q^34 - 9 * q^35 + q^36 + 8 * q^37 + 8 * q^38 - 3 * q^39 - q^40 - 8 * q^41 - 69 * q^42 - 23 * q^43 - 39 * q^44 + 65 * q^45 - 34 * q^46 + 14 * q^47 - 34 * q^48 + 2 * q^49 + 3 * q^50 - 42 * q^51 - 29 * q^52 - 6 * q^53 + 46 * q^54 + 7 * q^55 - 30 * q^56 + 17 * q^57 + 15 * q^58 + 4 * q^59 + 75 * q^60 + 60 * q^61 - 46 * q^63 + 23 * q^64 + 12 * q^65 - 30 * q^66 + 13 * q^67 - 30 * q^68 + 38 * q^69 + 12 * q^70 - 14 * q^71 + 37 * q^72 - 2 * q^73 - 13 * q^74 - 13 * q^75 - 12 * q^76 - 18 * q^77 - 15 * q^78 - 18 * q^79 + 36 * q^80 + 23 * q^81 + 14 * q^82 + 16 * q^83 - 8 * q^84 - 37 * q^85 + 26 * q^86 + 15 * q^87 + 17 * q^88 - q^89 - 23 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 - 22 * q^95 - 8 * q^96 + 3 * q^97 - 10 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{15}\right)$

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 $

$2$	−0.831304	+	2.55849i	−0.587821	+	1.80913i	−0.000184800		1.00000i	$0.500059\pi$
$2$	−0.831304	+	2.55849i	−0.587821	+	1.80913i	−0.587636	+	0.809126i	$0.699941\pi$
$3$	−0.949606	+	1.05464i	−0.548255	+	0.608899i	−0.952047	−	0.305952i	$-0.901025\pi$
$3$	−0.949606	+	1.05464i	−0.548255	+	0.608899i	0.403792	+	0.914851i	$0.367692\pi$
$4$	−4.23677	−	3.07819i	−2.11839	−	1.53910i
$5$	−0.304192	+	0.526876i	−0.136039	+	0.235626i	−0.925994	−	0.377539i	$-0.876770\pi$
$5$	−0.304192	+	0.526876i	−0.136039	+	0.235626i	0.789955	+	0.613165i	$0.210104\pi$
$6$	−1.90889	−	3.30629i	−0.779300	−	1.34979i
$7$	0.180508	−	1.71742i	0.0682256	−	0.649123i	−0.905958	−	0.423367i	$-0.860848\pi$
$7$	0.180508	−	1.71742i	0.0682256	−	0.649123i	0.974184	−	0.225756i	$-0.0724853\pi$
$8$	7.04481	−	5.11835i	2.49072	−	1.80961i
$9$	0.103062	+	0.980572i	0.0343541	+	0.326857i
$10$	−1.09513	−	1.21627i	−0.346311	−	0.384617i
$11$	1.22177	−	0.543967i	0.368377	−	0.164012i	−0.214195	−	0.976791i	$-0.568713\pi$
$11$	1.22177	−	0.543967i	0.368377	−	0.164012i	0.582572	+	0.812779i	$0.302046\pi$
$12$	7.26966	−	1.54521i	2.09857	−	0.446065i
$13$	3.59045	+	0.763174i	0.995812	+	0.211666i	0.676866	−	0.736106i	$-0.263338\pi$
$13$	3.59045	+	0.763174i	0.995812	+	0.211666i	0.318946	+	0.947773i	$0.396671\pi$
$14$	4.24394	+	1.88952i	1.13424	+	0.504997i
$15$	−0.266804	−	0.821139i	−0.0688885	−	0.212017i
$16$	4.00227	+	12.3177i	1.00057	+	3.07943i
$17$	2.52396	+	1.12374i	0.612150	+	0.272547i	0.689304	−	0.724472i	$-0.257916\pi$
$17$	2.52396	+	1.12374i	0.612150	+	0.272547i	−0.0771534	+	0.997019i	$0.524583\pi$
$18$	−2.59446	−	0.551469i	−0.611520	−	0.129983i
$19$	2.51157	−	0.533850i	0.576193	−	0.122474i	0.0894075	−	0.995995i	$-0.471503\pi$
$19$	2.51157	−	0.533850i	0.576193	−	0.122474i	0.486786	+	0.873522i	$0.338169\pi$
$20$	2.91062	−	1.29589i	0.650834	−	0.289770i
$21$	1.63986	+	1.82124i	0.357846	+	0.397428i
$22$	0.376072	+	3.57808i	0.0801788	+	0.762850i
$23$	−0.436271	+	0.316969i	−0.0909688	+	0.0660927i	−0.632340	−	0.774691i	$-0.717905\pi$
$23$	−0.436271	+	0.316969i	−0.0909688	+	0.0660927i	0.541371	+	0.840784i	$0.317905\pi$
$24$	−1.29175	+	12.2902i	−0.263678	+	2.50872i
$25$	2.31493	+	4.00958i	0.462987	+	0.801917i
$26$	−4.93733	+	8.55171i	−0.968290	+	1.67713i
$27$	−4.57641	−	3.32495i	−0.880730	−	0.639888i
$28$	−6.05132	+	6.72067i	−1.14359	+	1.27009i
$29$	2.51258	−	7.73291i	0.466574	−	1.43597i	−0.390419	−	0.920637i	$-0.627670\pi$
$29$	2.51258	−	7.73291i	0.466574	−	1.43597i	0.856993	−	0.515329i	$-0.172330\pi$
$30$	2.32267			0.424060
$31$		0			0
$31$		0			0
$32$	−17.4262			−3.08054
$33$	−0.586508	+	1.80509i	−0.102098	+	0.314225i
$34$	−4.97326	+	5.52336i	−0.852906	+	0.947248i
$35$	0.849957	+	0.617530i	0.143669	+	0.104382i
$36$	2.58174	−	4.47170i	0.430290	−	0.745284i
$37$	3.87249	+	6.70735i	0.636633	+	1.10268i	0.986167	+	0.165757i	$0.0530068\pi$
$37$	3.87249	+	6.70735i	0.636633	+	1.10268i	−0.349533	+	0.936924i	$0.613660\pi$
$38$	−0.722025	+	6.86961i	−0.117128	+	1.11440i
$39$	−4.21439	+	3.06194i	−0.674843	+	0.490302i
$40$	0.553763	+	5.26870i	0.0875576	+	0.833055i
$41$	−0.0696243	−	0.0773256i	−0.0108735	−	0.0120762i	0.737684	−	0.675147i	$-0.235920\pi$
$41$	−0.0696243	−	0.0773256i	−0.0108735	−	0.0120762i	−0.748557	+	0.663070i	$0.769253\pi$
$42$	−6.02285	+	2.68155i	−0.929346	+	0.413772i
$43$	−2.93904	+	0.624713i	−0.448200	+	0.0952678i	−0.426481	−	0.904496i	$-0.640247\pi$
$43$	−2.93904	+	0.624713i	−0.448200	+	0.0952678i	−0.0217184	+	0.999764i	$0.506914\pi$
$44$	−6.85079	−	1.45618i	−1.03280	−	0.219527i
$45$	−0.547990	−	0.243981i	−0.0816895	−	0.0363705i
$46$	−0.448289	−	1.37969i	−0.0660967	−	0.203425i
$47$	−2.07813	−	6.39584i	−0.303127	−	0.932929i	−0.980370	−	0.197169i	$-0.936825\pi$
$47$	−2.07813	−	6.39584i	−0.303127	−	0.932929i	0.677243	−	0.735760i	$-0.263175\pi$
$48$	−16.7914	−	7.47602i	−2.42363	−	1.07907i
$49$	3.93009	+	0.835366i	0.561441	+	0.119338i
$50$	−12.1829	+	2.58955i	−1.72292	+	0.366218i
$51$	−3.58192	+	1.59477i	−0.501568	+	0.223313i
$52$	−12.8627	−	14.2855i	−1.78374	−	1.98104i
$53$	0.292549	+	2.78341i	0.0401846	+	0.382331i	0.996068	+	0.0885864i	$0.0282349\pi$
$53$	0.292549	+	2.78341i	0.0401846	+	0.382331i	−0.955884	+	0.293745i	$0.905098\pi$
$54$	12.3112	−	8.94464i	1.67535	−	1.21721i
$55$	−0.0850494	+	0.809191i	−0.0114681	+	0.109111i
$56$	−7.51871	−	13.0228i	−1.00473	−	1.74024i
$57$	−1.82198	+	3.15576i	−0.241327	+	0.417990i
$58$	17.6959	+	12.8568i	2.32358	+	1.68818i
$59$	0.311970	−	0.346478i	0.0406151	−	0.0451076i	−0.722495	−	0.691376i	$-0.757005\pi$
$59$	0.311970	−	0.346478i	0.0406151	−	0.0451076i	0.763110	+	0.646269i	$0.223671\pi$
$60$	−1.39724	+	4.30025i	−0.180382	+	0.555160i
$61$	5.11468			0.654867			0.327434	−	0.944874i	$-0.393816\pi$
$61$	5.11468			0.654867			0.327434	+	0.944874i	$0.393816\pi$
$62$		0			0
$63$	1.70266			0.214514
$64$	6.48190	−	19.9492i	0.810238	−	2.49365i
$65$	−1.49428	+	1.65957i	−0.185343	+	0.205844i
$66$	−4.13073	−	3.00115i	−0.508457	−	0.369416i
$67$	−4.14923	+	7.18668i	−0.506910	+	0.877993i	0.493058	+	0.869996i	$0.335879\pi$
$67$	−4.14923	+	7.18668i	−0.506910	+	0.877993i	−0.999968	+	0.00799701i	$0.997454\pi$
$68$	−7.23436	−	12.5303i	−0.877294	−	1.51952i
$69$	0.0799956	−	0.761107i	0.00963034	−	0.0916265i
$70$	−2.28652	+	1.66125i	−0.273291	+	0.198558i
$71$	−0.497420	−	4.73264i	−0.0590329	−	0.561661i	−0.983565	−	0.180556i	$-0.942210\pi$
$71$	−0.497420	−	4.73264i	−0.0590329	−	0.561661i	0.924532	−	0.381105i	$-0.124456\pi$
$72$	5.74497	+	6.38043i	0.677051	+	0.751941i
$73$	−6.85725	+	3.05304i	−0.802580	+	0.357332i	−0.766685	−	0.642024i	$-0.778095\pi$
$73$	−6.85725	+	3.05304i	−0.802580	+	0.357332i	−0.0358953	+	0.999356i	$0.511428\pi$
$74$	−20.3799	+	4.33188i	−2.36911	+	0.503571i
$75$	−6.42696	−	1.36609i	−0.742122	−	0.157743i
$76$	−12.2842	−	5.46929i	−1.40910	−	0.627371i
$77$	−0.713679	−	2.19648i	−0.0813313	−	0.250312i
$78$	−4.33049	−	13.3279i	−0.490332	−	1.50909i
$79$	8.86044	+	3.94492i	0.996877	+	0.443838i	0.839300	−	0.543668i	$-0.182965\pi$
$79$	8.86044	+	3.94492i	0.996877	+	0.443838i	0.157577	+	0.987507i	$0.449632\pi$
$80$	−7.70738	−	1.63825i	−0.861711	−	0.183162i
$81$	4.95915	−	1.05410i	0.551017	−	0.117122i
$82$	0.255716	−	0.113852i	0.0282391	−	0.0125728i
$83$	11.1642	+	12.3991i	1.22543	+	1.36097i	0.911380	+	0.411567i	$0.135018\pi$
$83$	11.1642	+	12.3991i	1.22543	+	1.36097i	0.314047	+	0.949407i	$0.398315\pi$
$84$	−1.34155	−	12.7640i	−0.146375	−	1.39266i
$85$	−1.35984	+	0.987981i	−0.147495	+	0.107162i
$86$	0.844916	−	8.03884i	0.0911096	−	0.866850i
$87$	5.76952	+	9.99310i	0.618557	+	1.07137i
$88$	5.82292	−	10.0856i	0.620725	−	1.07513i
$89$	−12.3911	−	9.00268i	−1.31346	−	0.954282i	−0.999989	−	0.00468333i	$-0.998509\pi$
$89$	−12.3911	−	9.00268i	−1.31346	−	0.954282i	−0.313468	−	0.949599i	$-0.601491\pi$
$90$	1.07977	−	1.19920i	0.113818	−	0.126407i
$91$	1.95880	−	6.02855i	0.205338	−	0.631964i
$92$	2.82407			0.294430
$93$		0			0
$94$	18.0912			1.86597
$95$	−0.482726	+	1.48568i	−0.0495266	+	0.152427i
$96$	16.5480	−	18.3784i	1.68892	−	1.87574i
$97$	1.03488	+	0.751881i	0.105076	+	0.0763420i	0.639082	−	0.769138i	$-0.279314\pi$
$97$	1.03488	+	0.751881i	0.105076	+	0.0763420i	−0.534007	+	0.845480i	$0.679314\pi$
$98$	−5.40437	+	9.36065i	−0.545924	+	0.945568i
$99$	0.659316	+	1.14197i	0.0662638	+	0.114772i
$100$	2.53443	−	24.1135i	0.253443	−	2.41135i
$101$	−6.56941	+	4.77296i	−0.653681	+	0.474927i	−0.864523	−	0.502593i	$-0.832379\pi$
$101$	−6.56941	+	4.77296i	−0.653681	+	0.474927i	0.210842	+	0.977520i	$0.432379\pi$
$102$	−1.10255	−	10.4900i	−0.109168	−	1.03867i
$103$	10.1390	+	11.2605i	0.999026	+	1.10953i	0.993982	+	0.109544i	$0.0349389\pi$
$103$	10.1390	+	11.2605i	0.999026	+	1.10953i	0.00504416	+	0.999987i	$0.498394\pi$
$104$	29.2002	−	13.0008i	2.86332	−	1.27483i
$105$	−1.45840	+	0.309992i	−0.142325	+	0.0302522i
$106$	−7.36453	−	1.56538i	−0.715307	−	0.152043i
$107$	−11.3057	−	5.03362i	−1.09296	−	0.486618i	−0.220543	−	0.975377i	$-0.570783\pi$
$107$	−11.3057	−	5.03362i	−1.09296	−	0.486618i	−0.872419	+	0.488759i	$0.837450\pi$
$108$	9.15433	+	28.1741i	0.880876	+	2.71106i
$109$	2.22788	+	6.85672i	0.213392	+	0.656755i	0.999264	+	0.0383645i	$0.0122148\pi$
$109$	2.22788	+	6.85672i	0.213392	+	0.656755i	−0.785871	+	0.618390i	$0.787785\pi$
$110$	−1.99960	−	0.890281i	−0.190655	−	0.0848850i
$111$	−10.7512	−	2.28524i	−1.02046	−	0.216905i
$112$	21.8772	−	4.65013i	2.06720	−	0.439396i
$113$	15.2304	−	6.78103i	1.43276	−	0.637906i	0.463984	−	0.885844i	$-0.346420\pi$
$113$	15.2304	−	6.78103i	1.43276	−	0.637906i	0.968776	+	0.247938i	$0.0797528\pi$
$114$	−6.55936	−	7.28491i	−0.614340	−	0.682294i
$115$	−0.0342934	−	0.326280i	−0.00319788	−	0.0304258i
$116$	−34.4486	+	25.0284i	−3.19847	+	2.32383i
$117$	−0.378307	+	3.59935i	−0.0349745	+	0.332760i
$118$	0.627119	+	1.08620i	0.0577310	+	0.0999930i
$119$	2.38553	−	4.13185i	0.218681	−	0.378767i
$120$	−6.08246	−	4.41917i	−0.555250	−	0.403413i
$121$	−6.16362	+	6.84539i	−0.560329	+	0.622308i
$122$	−4.25185	+	13.0859i	−0.384944	+	1.18474i
$123$	0.147667			0.0133147
$124$		0			0
$125$	−5.85866			−0.524014
$126$	−1.41542	+	4.35623i	−0.126096	+	0.388084i
$127$	8.63810	−	9.59358i	0.766507	−	0.851293i	−0.225918	−	0.974146i	$-0.572538\pi$
$127$	8.63810	−	9.59358i	0.766507	−	0.851293i	0.992425	+	0.122854i	$0.0392046\pi$
$128$	17.4553	+	12.6820i	1.54285	+	1.12095i
$129$	2.13208	−	3.69288i	0.187720	−	0.325140i
$130$	−3.00379	−	5.20272i	−0.263450	−	0.456309i
$131$	0.254818	−	2.42443i	0.0222635	−	0.211823i	−0.977735	−	0.209846i	$-0.932704\pi$
$131$	0.254818	−	2.42443i	0.0222635	−	0.211823i	0.999998	−	0.00197767i	$-0.000629511\pi$
$132$	8.04130	−	5.84235i	0.699906	−	0.508511i
$133$	−0.463486	−	4.40978i	−0.0401894	−	0.382376i
$134$	−14.9378	−	16.5901i	−1.29043	−	1.43317i
$135$	3.14394	−	1.39977i	0.270588	−	0.120473i
$136$	23.5325	−	5.00199i	2.01790	−	0.428917i
$137$	7.96586	+	1.69320i	0.680570	+	0.144660i	0.535210	−	0.844719i	$-0.320233\pi$
$137$	7.96586	+	1.69320i	0.680570	+	0.144660i	0.145360	+	0.989379i	$0.453566\pi$
$138$	1.88078	+	0.837379i	0.160103	+	0.0712824i
$139$	0.418212	+	1.28712i	0.0354723	+	0.109172i	0.967225	−	0.253921i	$-0.0817204\pi$
$139$	0.418212	+	1.28712i	0.0354723	+	0.109172i	−0.931753	+	0.363094i	$0.881720\pi$
$140$	−1.70020	−	5.23267i	−0.143693	−	0.442241i
$141$	8.71874	+	3.88183i	0.734251	+	0.326909i
$142$	12.5219	+	2.66162i	1.05082	+	0.223358i
$143$	4.80184	−	1.02066i	0.401550	−	0.0853522i
$144$	−11.6659	+	5.19401i	−0.972161	+	0.432834i
$145$	3.30998	+	3.67611i	0.274879	+	0.305284i
$146$	−2.11072	−	20.0822i	−0.174685	−	1.66201i
$147$	−4.61305	+	3.35158i	−0.380478	+	0.276433i
$148$	4.23967	−	40.3378i	0.348499	−	3.31574i
$149$	4.50192	+	7.79756i	0.368812	+	0.638801i	0.989380	−	0.145351i	$-0.0464313\pi$
$149$	4.50192	+	7.79756i	0.368812	+	0.638801i	−0.620568	+	0.784153i	$0.713098\pi$
$150$	8.83789	−	15.3077i	0.721611	−	1.24987i
$151$	−2.59566	−	1.88585i	−0.211232	−	0.153469i	0.477139	−	0.878828i	$-0.341674\pi$
$151$	−2.59566	−	1.88585i	−0.211232	−	0.153469i	−0.688371	+	0.725359i	$0.741674\pi$
$152$	14.9611	−	16.6160i	1.21350	−	1.34773i
$153$	−0.841782	+	2.59074i	−0.0680541	+	0.209449i
$154$	6.21295			0.500654
$155$		0			0
$156$	27.2807			2.18420
$157$	−1.02803	+	3.16395i	−0.0820456	+	0.252510i	−0.983662	−	0.180027i	$-0.942382\pi$
$157$	−1.02803	+	3.16395i	−0.0820456	+	0.252510i	0.901616	+	0.432537i	$0.142382\pi$
$158$	−17.4588	+	19.3899i	−1.38894	+	1.54258i
$159$	−3.21332	−	2.33461i	−0.254833	−	0.185147i
$160$	5.30090	−	9.18143i	0.419073	−	0.725856i
$161$	0.465619	+	0.806476i	0.0366959	+	0.0635592i
$162$	−1.42566	+	13.5642i	−0.112010	+	1.06570i
$163$	−1.40797	+	1.02295i	−0.110281	+	0.0801236i	−0.641559	−	0.767074i	$-0.721712\pi$
$163$	−1.40797	+	1.02295i	−0.110281	+	0.0801236i	0.531278	+	0.847198i	$0.321712\pi$
$164$	0.0569589	+	0.541928i	0.00444774	+	0.0423175i
$165$	−0.772645	−	0.858109i	−0.0601503	−	0.0668037i
$166$	−41.0037	+	18.2560i	−3.18250	+	1.41694i
$167$	−13.7102	+	2.91419i	−1.06093	+	0.225507i	−0.705145	−	0.709063i	$-0.749118\pi$
$167$	−13.7102	+	2.91419i	−1.06093	+	0.225507i	−0.355780	+	0.934570i	$0.615785\pi$
$168$	20.8742	+	4.43696i	1.61048	+	0.342319i
$169$	0.432821	+	0.192704i	0.0332939	+	0.0148234i
$170$	−1.39730	−	4.30045i	−0.107168	−	0.329829i
$171$	0.782326	+	2.40775i	0.0598260	+	0.184125i
$172$	14.3750	+	6.40018i	1.09609	+	0.488009i
$173$	0.0117191	+	0.00249097i	0.000890985	+	0.000189385i	0.208357	−	0.978053i	$-0.433188\pi$
$173$	0.0117191	+	0.00249097i	0.000890985	+	0.000189385i	−0.207466	+	0.978242i	$0.566522\pi$
$174$	−30.3635	+	6.45395i	−2.30185	+	0.489273i
$175$	7.30400	−	3.25195i	0.552131	−	0.245824i
$176$	11.5903	+	12.8723i	0.873651	+	0.970288i
$177$	0.0691624	+	0.658036i	0.00519856	+	0.0494610i
$178$	33.3341	−	24.2186i	2.49849	−	1.81526i
$179$	−1.04299	+	9.92334i	−0.0779564	+	0.741706i	0.883812	+	0.467842i	$0.154968\pi$
$179$	−1.04299	+	9.92334i	−0.0779564	+	0.741706i	−0.961769	+	0.273864i	$0.911698\pi$
$180$	1.57069	+	2.72051i	0.117072	+	0.202775i
$181$	−9.30158	+	16.1108i	−0.691381	+	1.19751i	0.280004	+	0.959999i	$0.409664\pi$
$181$	−9.30158	+	16.1108i	−0.691381	+	1.19751i	−0.971385	+	0.237509i	$0.923669\pi$
$182$	13.7956	+	10.0231i	1.02260	+	0.742963i
$183$	−4.85693	+	5.39417i	−0.359035	+	0.398748i
$184$	−1.45108	+	4.46598i	−0.106975	+	0.329236i
$185$	−4.71192			−0.346427
$186$		0			0
$187$	3.69497			0.270203
$188$	−10.8831	+	33.4946i	−0.793728	+	2.44284i
$189$	−6.53642	+	7.25943i	−0.475454	+	0.528046i
$190$	−3.39980	−	2.47010i	−0.246647	−	0.179200i
$191$	−0.599059	+	1.03760i	−0.0433464	+	0.0750782i	−0.886885	−	0.461991i	$-0.847135\pi$
$191$	−0.599059	+	1.03760i	−0.0433464	+	0.0750782i	0.843538	+	0.537069i	$0.180469\pi$
$192$	14.8841	+	25.7800i	1.07417	+	1.86051i
$193$	−1.33029	+	12.6568i	−0.0957562	+	0.911059i	0.836184	+	0.548448i	$0.184781\pi$
$193$	−1.33029	+	12.6568i	−0.0957562	+	0.911059i	−0.931941	+	0.362611i	$0.881885\pi$
$194$	−2.78398	+	2.02268i	−0.199878	+	0.145220i
$195$	−0.331276	−	3.15188i	−0.0237231	−	0.225711i
$196$	−14.0795	−	15.6368i	−1.00568	−	1.11692i
$197$	2.71195	−	1.20744i	0.193218	−	0.0860263i	−0.307847	−	0.951436i	$-0.599608\pi$
$197$	2.71195	−	1.20744i	0.193218	−	0.0860263i	0.501065	+	0.865410i	$0.332942\pi$
$198$	−3.46981	+	0.737531i	−0.246589	+	0.0524140i
$199$	−12.8960	−	2.74112i	−0.914170	−	0.194313i	−0.273270	−	0.961937i	$-0.588105\pi$
$199$	−12.8960	−	2.74112i	−0.914170	−	0.194313i	−0.640900	+	0.767625i	$0.721439\pi$
$200$	36.8307	+	16.3981i	2.60433	+	1.15952i
$201$	−3.63926	−	11.2005i	−0.256694	−	0.790021i
$202$	−6.75039	−	20.7755i	−0.474955	−	1.46176i
$203$	−12.8271	−	5.71100i	−0.900287	−	0.400834i
$204$	20.0848	+	4.26915i	1.40622	+	0.298900i
$205$	0.0619201	−	0.0131615i	0.00432469	−	0.000919241i
$206$	−37.2385	+	16.5796i	−2.59453	+	1.15516i
$207$	−0.355774	−	0.395127i	−0.0247280	−	0.0274633i
$208$	4.96940	+	47.2807i	0.344566	+	3.27832i
$209$	2.77816	−	2.01845i	0.192169	−	0.139619i
$210$	0.419261	−	3.98900i	0.0289317	−	0.275267i
$211$	−9.16614	−	15.8762i	−0.631023	−	1.09296i	−0.987343	−	0.158600i	$-0.949302\pi$
$211$	−9.16614	−	15.8762i	−0.631023	−	1.09296i	0.356320	−	0.934364i	$-0.384031\pi$
$212$	7.32843	−	12.6932i	0.503318	−	0.871773i
$213$	5.46361	+	3.96954i	0.374360	+	0.271989i
$214$	22.2769	−	24.7410i	1.52282	−	1.69126i
$215$	0.564887	−	1.73854i	0.0385250	−	0.118568i
$216$	−49.2582			−3.35160
$217$		0			0
$218$	−19.3949			−1.31359
$219$	3.29181	−	10.1311i	0.222440	−	0.684599i
$220$	2.85118	−	3.16656i	0.192227	−	0.213489i
$221$	8.20455	+	5.96096i	0.551898	+	0.400977i
$222$	14.7843	−	25.6071i	0.992256	−	1.71864i
$223$	4.69801	+	8.13718i	0.314602	+	0.544906i	0.979353	−	0.202159i	$-0.0647957\pi$
$223$	4.69801	+	8.13718i	0.314602	+	0.544906i	−0.664751	+	0.747065i	$0.731462\pi$
$224$	−3.14557	+	29.9281i	−0.210172	+	1.99965i
$225$	−3.69310	+	2.68320i	−0.246207	+	0.178880i
$226$	4.68807	+	44.6040i	0.311846	+	2.96702i
$227$	5.66046	+	6.28658i	0.375698	+	0.417255i	0.901108	−	0.433594i	$-0.142755\pi$
$227$	5.66046	+	6.28658i	0.375698	+	0.417255i	−0.525410	+	0.850849i	$0.676088\pi$
$228$	17.4333	−	7.76182i	1.15455	−	0.514039i
$229$	22.3443	−	4.74942i	1.47655	−	0.313850i	0.601887	−	0.798582i	$-0.294416\pi$
$229$	22.3443	−	4.74942i	1.47655	−	0.313850i	0.874663	+	0.484731i	$0.161083\pi$
$230$	0.863293	+	0.183499i	0.0569238	+	0.0120995i
$231$	2.99422	+	1.33311i	0.197005	+	0.0877123i
$232$	−21.8792	−	67.3372i	−1.43644	−	4.42090i
$233$	5.02260	+	15.4580i	0.329042	+	1.01269i	0.969583	+	0.244762i	$0.0787099\pi$
$233$	5.02260	+	15.4580i	0.329042	+	1.01269i	−0.640542	+	0.767923i	$0.721290\pi$
$234$	−8.89441	−	3.96005i	−0.581446	−	0.258876i
$235$	4.00196	+	0.850643i	0.261059	+	0.0554899i
$236$	−2.38828	+	0.507644i	−0.155463	+	0.0330448i
$237$	−12.5744	+	5.59849i	−0.816796	+	0.363661i
$238$	8.58821	+	9.53817i	0.556691	+	0.618268i
$239$	1.91005	+	18.1729i	0.123551	+	1.17551i	0.864035	+	0.503433i	$0.167930\pi$
$239$	1.91005	+	18.1729i	0.123551	+	1.17551i	−0.740484	+	0.672074i	$0.765404\pi$
$240$	9.04675	−	6.57285i	0.583965	−	0.424275i
$241$	−1.89944	+	18.0720i	−0.122354	+	1.16412i	0.745222	+	0.666816i	$0.232343\pi$
$241$	−1.89944	+	18.0720i	−0.122354	+	1.16412i	−0.867576	+	0.497304i	$0.834323\pi$
$242$	−12.3900	−	21.4602i	−0.796461	−	1.37951i
$243$	4.88759	−	8.46555i	0.313539	−	0.543065i
$244$	−21.6697	−	15.7440i	−1.38726	−	1.00790i
$245$	−1.63564	+	1.81656i	−0.104497	+	0.116056i
$246$	−0.122756	+	0.377804i	−0.00782663	+	0.0240879i
$247$	9.42508			0.599704
$248$		0			0
$249$	−23.6782			−1.50054
$250$	4.87032	−	14.9893i	0.308026	−	0.948007i
$251$	15.3433	−	17.0405i	0.968461	−	1.07558i	−0.0286471	−	0.999590i	$-0.509120\pi$
$251$	15.3433	−	17.0405i	0.968461	−	1.07558i	0.997108	−	0.0759953i	$-0.0242134\pi$
$252$	−7.21376	−	5.24111i	−0.454424	−	0.330159i
$253$	−0.360602	+	0.624580i	−0.0226708	+	0.0392670i
$254$	17.3642	+	30.0757i	1.08953	+	1.88712i
$255$	0.249343	−	2.37234i	0.0156145	−	0.148562i
$256$	−13.0179	+	9.45807i	−0.813620	+	0.591129i
$257$	−0.0111002	−	0.105611i	−0.000692411	−	0.00658785i	0.994170	−	0.107822i	$-0.0343876\pi$
$257$	−0.0111002	−	0.105611i	−0.000692411	−	0.00658785i	−0.994863	+	0.101234i	$0.967721\pi$
$258$	7.67578	+	8.52482i	0.477873	+	0.530732i
$259$	12.2183	−	5.43996i	0.759211	−	0.338022i
$260$	11.4394	−	2.43152i	0.709443	−	0.150797i
$261$	7.84163	+	1.66679i	0.485385	+	0.103172i
$262$	5.99105	+	2.66739i	0.370128	+	0.164792i
$263$	2.25499	+	6.94015i	0.139049	+	0.427948i	0.996198	−	0.0871204i	$-0.0277665\pi$
$263$	2.25499	+	6.94015i	0.139049	+	0.427948i	−0.857149	+	0.515068i	$0.827766\pi$
$264$	5.10723	+	15.7184i	0.314328	+	0.967403i
$265$	−1.55550	−	0.692555i	−0.0955539	−	0.0425433i
$266$	11.6677	+	2.48004i	0.715391	+	0.152061i
$267$	21.2613	−	4.51923i	1.30117	−	0.276573i
$268$	39.7014	−	17.6762i	2.42515	−	1.07974i
$269$	−10.8529	−	12.0533i	−0.661711	−	0.734905i	0.315088	−	0.949063i	$-0.397966\pi$
$269$	−10.8529	−	12.0533i	−0.661711	−	0.734905i	−0.976799	+	0.214158i	$0.931299\pi$
$270$	0.967735	+	9.20739i	0.0588945	+	0.560344i
$271$	−4.16291	+	3.02453i	−0.252879	+	0.183727i	−0.707002	−	0.707212i	$-0.749953\pi$
$271$	−4.16291	+	3.02453i	−0.252879	+	0.183727i	0.454123	+	0.890939i	$0.349953\pi$
$272$	−3.74034	+	35.5870i	−0.226792	+	2.15778i
$273$	4.49790	+	7.79058i	0.272225	+	0.471508i
$274$	−10.9541	+	18.9730i	−0.661760	+	1.14620i
$275$	5.00939	+	3.63954i	0.302078	+	0.219472i
$276$	−2.68176	+	2.97839i	−0.161423	+	0.179278i
$277$	5.22944	−	16.0946i	0.314207	−	0.967029i	−0.661873	−	0.749616i	$-0.730238\pi$
$277$	5.22944	−	16.0946i	0.314207	−	0.967029i	0.976080	−	0.217413i	$-0.0697618\pi$
$278$	−3.64076			−0.218358
$279$		0			0
$280$	9.14853			0.546729
$281$	0.589193	−	1.81335i	0.0351483	−	0.108175i	−0.931943	−	0.362605i	$-0.881888\pi$
$281$	0.589193	−	1.81335i	0.0351483	−	0.108175i	0.967091	+	0.254429i	$0.0818876\pi$
$282$	−17.1796	+	19.0798i	−1.02303	+	1.13619i
$283$	12.3859	+	8.99888i	0.736265	+	0.534928i	0.891539	−	0.452944i	$-0.149626\pi$
$283$	12.3859	+	8.99888i	0.736265	+	0.534928i	−0.155274	+	0.987871i	$0.549626\pi$
$284$	−12.4605	+	21.5823i	−0.739396	+	1.28067i
$285$	−1.10846	−	1.91991i	−0.0656596	−	0.113726i
$286$	−1.38043	+	13.1339i	−0.0816268	+	0.776627i
$287$	−0.145368	+	0.105616i	−0.00858081	+	0.00623433i
$288$	−1.79598	−	17.0876i	−0.105829	−	1.00690i
$289$	−6.26763	−	6.96091i	−0.368684	−	0.409465i
$290$	−12.1569	+	5.41259i	−0.713876	+	0.317838i
$291$	−1.77569	+	0.377435i	−0.104093	+	0.0221256i
$292$	38.4504	+	8.17289i	2.25014	+	0.478282i
$293$	24.4772	+	10.8980i	1.42998	+	0.636666i	0.968165	−	0.250313i	$-0.0805334\pi$
$293$	24.4772	+	10.8980i	1.42998	+	0.636666i	0.461810	+	0.886979i	$0.347200\pi$
$294$	−4.74013	−	14.5886i	−0.276450	−	0.850826i
$295$	0.0876522	+	0.269766i	0.00510331	+	0.0157064i
$296$	61.6115	+	27.4312i	3.58110	+	1.59441i
$297$	−7.39998	−	1.57291i	−0.429390	−	0.0912697i
$298$	−23.6924	+	5.03599i	−1.37247	+	0.291727i
$299$	−1.80831	+	0.805113i	−0.104577	+	0.0465609i
$300$	23.0245	+	25.5713i	1.32932	+	1.47636i
$301$	0.542373	+	5.16033i	0.0312619	+	0.297437i
$302$	6.98272	−	5.07324i	0.401810	−	0.291932i
$303$	1.20458	−	11.4608i	0.0692014	−	0.658407i
$304$	16.6278	+	28.8002i	0.953670	+	1.65181i
$305$	−1.55584	+	2.69480i	−0.0890873	+	0.154304i
$306$	−5.92860	−	4.30738i	−0.338916	−	0.246237i
$307$	5.98956	−	6.65208i	0.341842	−	0.379654i	−0.547570	−	0.836760i	$-0.684447\pi$
$307$	5.98956	−	6.65208i	0.341842	−	0.379654i	0.889413	+	0.457105i	$0.151114\pi$
$308$	−3.73749	+	11.5028i	−0.212963	+	0.655434i
$309$	−21.5039			−1.22331
$310$		0			0
$311$	20.6556			1.17127			0.585637	−	0.810574i	$-0.300844\pi$
$311$	20.6556			1.17127			0.585637	+	0.810574i	$0.300844\pi$
$312$	−14.0175	+	43.1415i	−0.793586	+	2.44241i
$313$	−0.301993	+	0.335397i	−0.0170696	+	0.0189577i	−0.751619	−	0.659597i	$-0.770727\pi$
$313$	−0.301993	+	0.335397i	−0.0170696	+	0.0189577i	0.734550	+	0.678555i	$0.237394\pi$
$314$	−7.24032	−	5.26040i	−0.408595	−	0.296862i
$315$	−0.517934	+	0.897088i	−0.0291823	+	0.0505452i
$316$	−25.3964	−	43.9879i	−1.42866	−	2.47451i
$317$	0.583357	−	5.55027i	0.0327646	−	0.311734i	−0.965849	−	0.259104i	$-0.916573\pi$
$317$	0.583357	−	5.55027i	0.0327646	−	0.311734i	0.998614	−	0.0526304i	$-0.0167605\pi$
$318$	8.64432	−	6.28047i	0.484750	−	0.352191i
$319$	−1.13666	−	10.8146i	−0.0636407	−	0.605501i
$320$	8.53903	+	9.48355i	0.477346	+	0.530147i
$321$	16.0446	−	7.14353i	0.895524	−	0.398713i
$322$	−2.45043	+	0.520855i	−0.136557	+	0.0290261i
$323$	6.93901	+	1.47493i	0.386097	+	0.0820674i
$324$	−24.2555	−	10.7992i	−1.34753	−	0.599958i
$325$	5.25165	+	16.1629i	0.291309	+	0.896557i
$326$	−1.44676	−	4.45266i	−0.0801284	−	0.246610i
$327$	−9.34701	−	4.16156i	−0.516891	−	0.230135i
$328$	−0.886270	−	0.188382i	−0.0489360	−	0.0104017i
$329$	−11.3595	+	2.41453i	−0.626267	+	0.133117i
$330$	2.83777	−	1.26346i	0.156214	−	0.0695509i
$331$	−16.1966	−	17.9882i	−0.890246	−	0.988719i	0.109740	−	0.993960i	$-0.464998\pi$
$331$	−16.1966	−	17.9882i	−0.890246	−	0.988719i	−0.999986	+	0.00524168i	$0.998332\pi$
$332$	−9.13329	−	86.8975i	−0.501255	−	4.76912i
$333$	−6.17793	+	4.48853i	−0.338548	+	0.245970i
$334$	3.94140	−	37.4999i	0.215664	−	2.05191i
$335$	−2.52433	−	4.37226i	−0.137919	−	0.238882i
$336$	−15.8704	+	27.4884i	−0.865804	+	1.49962i
$337$	8.92830	+	6.48679i	0.486355	+	0.353358i	0.803781	−	0.594925i	$-0.202818\pi$
$337$	8.92830	+	6.48679i	0.486355	+	0.353358i	−0.317426	+	0.948283i	$0.602818\pi$
$338$	−0.852838	+	0.947173i	−0.0463883	+	0.0515194i
$339$	−7.31135	+	22.5020i	−0.397098	+	1.22214i
$340$	8.80253			0.477384
$341$		0			0
$342$	−6.81056			−0.368273
$343$	5.87953	−	18.0953i	0.317465	−	0.977056i
$344$	−17.5075	+	19.4440i	−0.943941	+	1.04835i
$345$	0.376675	+	0.273670i	0.0202795	+	0.0147339i
$346$	−0.0161152	+	0.0279124i	−0.000866360	+	0.00150058i
$347$	−9.28369	−	16.0798i	−0.498375	−	0.863210i	0.501624	−	0.865086i	$-0.332736\pi$
$347$	−9.28369	−	16.0798i	−0.498375	−	0.863210i	−0.999998	+	0.00187589i	$0.999403\pi$
$348$	6.31657	−	60.0982i	0.338604	−	3.22160i
$349$	26.0298	−	18.9118i	1.39334	−	1.01232i	0.397855	−	0.917448i	$-0.369755\pi$
$349$	26.0298	−	18.9118i	1.39334	−	1.01232i	0.995489	−	0.0948756i	$-0.0302453\pi$
$350$	2.24824	+	21.3906i	0.120173	+	1.14337i
$351$	−13.8939	−	15.4307i	−0.741599	−	0.823629i
$352$	−21.2908	+	9.47926i	−1.13480	+	0.505246i
$353$	31.5094	−	6.69754i	1.67708	−	0.356474i	0.731493	−	0.681849i	$-0.238824\pi$
$353$	31.5094	−	6.69754i	1.67708	−	0.356474i	0.945585	+	0.325375i	$0.105490\pi$
$354$	−1.74107	−	0.370077i	−0.0925370	−	0.0196693i
$355$	2.64482	+	1.17755i	0.140373	+	0.0624980i
$356$	24.7864	+	76.2846i	1.31367	+	4.04307i
$357$	2.09233	+	6.43952i	0.110738	+	0.340815i
$358$	−24.5217	−	10.9178i	−1.29601	−	0.577023i
$359$	−20.6998	−	4.39988i	−1.09249	−	0.232217i	−0.373777	−	0.927519i	$-0.621937\pi$
$359$	−20.6998	−	4.39988i	−1.09249	−	0.232217i	−0.718718	+	0.695302i	$0.755271\pi$
$360$	−5.10927	+	1.08601i	−0.269282	+	0.0572377i
$361$	−11.3344	+	5.04639i	−0.596547	+	0.265600i
$362$	−33.4869	−	37.1910i	−1.76003	−	1.95472i
$363$	−1.36644	−	13.0009i	−0.0717197	−	0.682368i
$364$	−26.8560	+	19.5120i	−1.40764	+	1.02271i
$365$	0.477344	−	4.54163i	0.0249853	−	0.237720i
$366$	−9.76334	−	16.9106i	−0.510338	−	0.883931i
$367$	6.49822	−	11.2552i	0.339204	−	0.587519i	−0.645079	−	0.764116i	$-0.723176\pi$
$367$	6.49822	−	11.2552i	0.339204	−	0.587519i	0.984283	+	0.176597i	$0.0565089\pi$
$368$	−5.65042	−	4.10527i	−0.294549	−	0.214002i
$369$	0.0686477	−	0.0762409i	0.00357365	−	0.00396894i
$370$	3.91704	−	12.0554i	0.203637	−	0.626730i
$371$	4.83309			0.250922
$372$		0			0
$373$	−4.42592			−0.229166			−0.114583	−	0.993414i	$-0.536553\pi$
$373$	−4.42592			−0.229166			−0.114583	+	0.993414i	$0.536553\pi$
$374$	−3.07165	+	9.45355i	−0.158831	+	0.488832i
$375$	5.56342	−	6.17880i	0.287294	−	0.319072i
$376$	−47.3762	−	34.4208i	−2.44324	−	1.77512i
$377$	14.9228	−	25.8471i	0.768566	−	1.33119i
$378$	−13.1394	−	22.7581i	−0.675819	−	1.17055i
$379$	1.56330	−	14.8738i	0.0803013	−	0.764016i	−0.878078	−	0.478518i	$-0.841174\pi$
$379$	1.56330	−	14.8738i	0.0803013	−	0.764016i	0.958379	−	0.285498i	$-0.0921591\pi$
$380$	6.61840	−	4.80855i	0.339517	−	0.246673i
$381$	1.91503	+	18.2202i	0.0981097	+	0.933452i
$382$	−2.15669	−	2.39525i	−0.110346	−	0.122552i
$383$	10.6431	−	4.73862i	0.543838	−	0.242132i	−0.116382	−	0.993205i	$-0.537130\pi$
$383$	10.6431	−	4.73862i	0.543838	−	0.242132i	0.660220	+	0.751072i	$0.270463\pi$
$384$	−29.9508	+	6.36623i	−1.52842	+	0.324875i
$385$	1.37437	+	0.292131i	0.0700442	+	0.0148884i
$386$	−31.2765	−	13.9252i	−1.59193	−	0.708774i
$387$	−0.915480	−	2.81756i	−0.0465365	−	0.143225i
$388$	−2.07009	−	6.37110i	−0.105093	−	0.323443i
$389$	−13.1568	−	5.85779i	−0.667077	−	0.297002i	0.0451198	−	0.998982i	$-0.485633\pi$
$389$	−13.1568	−	5.85779i	−0.667077	−	0.297002i	−0.712197	+	0.701980i	$0.752300\pi$
$390$	8.33944	+	1.77260i	0.422284	+	0.0897592i
$391$	−1.45732	+	0.309763i	−0.0737000	+	0.0156654i
$392$	31.9624	−	14.2306i	1.61435	−	0.718753i
$393$	2.31493	+	2.57100i	0.116773	+	0.129690i
$394$	0.834763	+	7.94224i	0.0420547	+	0.400124i
$395$	−4.77376	+	3.46834i	−0.240194	+	0.174511i
$396$	0.721831	−	6.86777i	0.0362734	−	0.345118i
$397$	−7.89506	−	13.6746i	−0.396242	−	0.686311i	0.597017	−	0.802229i	$-0.296352\pi$
$397$	−7.89506	−	13.6746i	−0.396242	−	0.686311i	−0.993259	+	0.115918i	$0.963019\pi$
$398$	17.7336	−	30.7155i	0.888904	−	1.53963i
$399$	5.09088	+	3.69874i	0.254863	+	0.185169i
$400$	−40.1240	+	44.5622i	−2.00620	+	2.22811i
$401$	−9.58670	+	29.5048i	−0.478737	+	1.47340i	0.362114	+	0.932134i	$0.382055\pi$
$401$	−9.58670	+	29.5048i	−0.478737	+	1.47340i	−0.840851	+	0.541267i	$0.817945\pi$
$402$	31.6817			1.58014
$403$		0			0
$404$	42.5252			2.11571
$405$	−0.953153	+	2.93350i	−0.0473626	+	0.145767i
$406$	25.2748	−	28.0705i	1.25437	−	1.39311i
$407$	8.37986	+	6.08832i	0.415374	+	0.301787i
$408$	−17.0713	+	29.5684i	−0.845156	+	1.46385i
$409$	3.29291	+	5.70349i	0.162824	+	0.282019i	0.935880	−	0.352318i	$-0.114606\pi$
$409$	3.29291	+	5.70349i	0.162824	+	0.282019i	−0.773056	+	0.634337i	$0.781273\pi$
$410$	−0.0178008	+	0.169363i	−0.000879119	+	0.00836425i
$411$	−9.35015	+	6.79328i	−0.461209	+	0.335088i
$412$	−8.29462	−	78.9180i	−0.408647	−	3.88801i
$413$	−0.538735	−	0.598326i	−0.0265094	−	0.0294417i
$414$	1.30669	−	0.581774i	0.0642201	−	0.0285926i
$415$	−9.92882	+	2.11043i	−0.487386	+	0.103597i
$416$	−62.5679	−	13.2992i	−3.06764	−	0.652047i
$417$	−1.75460	−	0.781196i	−0.0859229	−	0.0382554i
$418$	2.85469	+	8.78583i	0.139627	+	0.429729i
$419$	−4.53389	−	13.9539i	−0.221495	−	0.681692i	−0.998628	−	0.0523559i	$-0.983327\pi$
$419$	−4.53389	−	13.9539i	−0.221495	−	0.681692i	0.777133	−	0.629336i	$-0.216673\pi$
$420$	7.13312	+	3.17587i	0.348061	+	0.154967i
$421$	26.1321	+	5.55454i	1.27360	+	0.270712i	0.794616	−	0.607112i	$-0.207672\pi$
$421$	26.1321	+	5.55454i	1.27360	+	0.270712i	0.478983	+	0.877824i	$0.341006\pi$
$422$	48.2390	−	10.2535i	2.34824	−	0.499133i
$423$	6.05740	−	2.69693i	0.294521	−	0.131129i
$424$	16.3074	+	18.1113i	0.791959	+	0.879560i
$425$	1.33708	+	12.7214i	0.0648577	+	0.617079i
$426$	−14.6980	+	10.6787i	−0.712118	+	0.517384i
$427$	0.923240	−	8.78404i	0.0446787	−	0.425090i
$428$	32.4052	+	56.1274i	1.56636	+	2.71302i
$429$	−3.48342	+	6.03347i	−0.168181	+	0.291299i
$430$	3.97845	+	2.89052i	0.191858	+	0.139393i
$431$	2.66850	−	2.96367i	0.128537	−	0.142755i	−0.675441	−	0.737414i	$-0.736046\pi$
$431$	2.66850	−	2.96367i	0.128537	−	0.142755i	0.803978	+	0.594660i	$0.202713\pi$
$432$	22.6399	−	69.6783i	1.08926	−	3.35240i
$433$	−18.0766			−0.868704			−0.434352	−	0.900743i	$-0.643023\pi$
$433$	−18.0766			−0.868704			−0.434352	+	0.900743i	$0.643023\pi$
$434$		0			0
$435$	−7.02016			−0.336591
$436$	11.6673	−	35.9082i	0.558762	−	1.71969i
$437$	−0.926510	+	1.02899i	−0.0443210	+	0.0492234i
$438$	23.1839	+	16.8441i	1.10777	+	0.804843i
$439$	−11.4543	+	19.8394i	−0.546684	+	0.946884i	0.451815	+	0.892112i	$0.350777\pi$
$439$	−11.4543	+	19.8394i	−0.546684	+	0.946884i	−0.998499	+	0.0547723i	$0.982557\pi$
$440$	3.54257	+	6.13591i	0.168885	+	0.292518i
$441$	−0.414093	+	3.93983i	−0.0197187	+	0.187611i
$442$	−22.0715	+	16.0359i	−1.04984	+	0.762750i
$443$	2.24645	+	21.3736i	0.106732	+	1.01549i	0.908509	+	0.417866i	$0.137222\pi$
$443$	2.24645	+	21.3736i	0.106732	+	1.01549i	−0.801777	+	0.597624i	$0.796112\pi$
$444$	38.5160	+	42.7763i	1.82789	+	2.03008i
$445$	8.51257	−	3.79004i	0.403535	−	0.179665i
$446$	−24.7244	+	5.25533i	−1.17073	+	0.248847i
$447$	−12.4987	−	2.65668i	−0.591169	−	0.125657i
$448$	−33.0912	−	14.7331i	−1.56341	−	0.696075i
$449$	−5.80940	−	17.8795i	−0.274163	−	0.843786i	−0.989440	−	0.144945i	$-0.953700\pi$
$449$	−5.80940	−	17.8795i	−0.274163	−	0.843786i	0.715277	−	0.698841i	$-0.246300\pi$
$450$	−3.79484	−	11.6793i	−0.178890	−	0.550568i
$451$	−0.127127	−	0.0566007i	−0.00598619	−	0.00266522i
$452$	−85.4012	−	18.1526i	−4.01694	−	0.853826i
$453$	4.45376	−	0.946676i	0.209256	−	0.0444787i
$454$	−20.7897	+	9.25617i	−0.975709	+	0.434414i
$455$	2.58045	+	2.86588i	0.120973	+	0.134354i
$456$	3.31680	+	31.5572i	0.155323	+	1.47780i
$457$	3.32182	−	2.41344i	0.155388	−	0.112896i	−0.507374	−	0.861726i	$-0.669384\pi$
$457$	3.32182	−	2.41344i	0.155388	−	0.112896i	0.662763	+	0.748830i	$0.269384\pi$
$458$	−6.42352	+	61.1158i	−0.300152	+	2.85575i
$459$	−7.81429	−	13.5347i	−0.364740	−	0.631748i
$460$	−0.859060	+	1.48794i	−0.0400539	+	0.0693754i
$461$	−18.5063	−	13.4456i	−0.861924	−	0.626225i	0.0664836	−	0.997788i	$-0.478822\pi$
$461$	−18.5063	−	13.4456i	−0.861924	−	0.626225i	−0.928408	+	0.371563i	$0.878822\pi$
$462$	−5.89986	+	6.55246i	−0.274486	+	0.304848i
$463$	5.11947	−	15.7561i	0.237922	−	0.732249i	−0.758798	−	0.651326i	$-0.774213\pi$
$463$	5.11947	−	15.7561i	0.237922	−	0.732249i	0.996720	−	0.0809233i	$-0.0257869\pi$
$464$	105.308			4.88880
$465$		0			0
$466$	−43.7244			−2.02549
$467$	11.7878	−	36.2792i	0.545476	−	1.67880i	−0.174379	−	0.984679i	$-0.555792\pi$
$467$	11.7878	−	36.2792i	0.545476	−	1.67880i	0.719855	−	0.694124i	$-0.244208\pi$
$468$	12.6823	−	14.0851i	0.586239	−	0.651085i
$469$	11.5936	+	8.42323i	0.535342	+	0.388949i
$470$	−5.50321	+	9.53184i	−0.253844	+	0.439671i
$471$	−2.36062	−	4.08871i	−0.108771	−	0.188398i
$472$	0.424374	−	4.03765i	0.0195334	−	0.185848i
$473$	−3.25101	+	2.36200i	−0.149482	+	0.108605i
$474$	−3.87052	−	36.8256i	−0.177779	−	1.69145i
$475$	7.95463	+	8.83451i	0.364984	+	0.405355i
$476$	−22.8256	+	10.1626i	−1.04621	+	0.465802i
$477$	−2.69919	+	0.573730i	−0.123587	+	0.0262693i
$478$	−48.0830	−	10.2204i	−2.19926	−	0.467468i
$479$	−30.7726	−	13.7008i	−1.40603	−	0.626007i	−0.443279	−	0.896383i	$-0.646185\pi$
$479$	−30.7726	−	13.7008i	−1.40603	−	0.626007i	−0.962755	+	0.270377i	$0.912852\pi$
$480$	4.64938	+	14.3093i	0.212214	+	0.653128i
$481$	8.78511	+	27.0378i	0.400567	+	1.23282i
$482$	−44.6580	−	19.8830i	−2.03412	−	0.905647i
$483$	−1.29270	−	0.274772i	−0.0588199	−	0.0125026i
$484$	47.1853	−	10.0295i	2.14479	−	0.455888i
$485$	−0.710949	+	0.316535i	−0.0322825	+	0.0143731i
$486$	17.5960	+	19.5423i	0.798169	+	0.886456i
$487$	−2.16130	−	20.5634i	−0.0979379	−	0.931817i	−0.927606	−	0.373560i	$-0.878137\pi$
$487$	−2.16130	−	20.5634i	−0.0979379	−	0.931817i	0.829668	−	0.558257i	$-0.188530\pi$
$488$	36.0319	−	26.1787i	1.63109	−	1.18506i
$489$	0.258168	−	2.45631i	0.0116748	−	0.111078i
$490$	−3.28793	−	5.69487i	−0.148534	−	0.257268i
$491$	12.3664	−	21.4192i	0.558087	−	0.966634i	−0.439570	−	0.898209i	$-0.644869\pi$
$491$	12.3664	−	21.4192i	0.558087	−	0.966634i	0.997656	−	0.0684258i	$-0.0217976\pi$
$492$	−0.625630	−	0.454547i	−0.0282056	−	0.0204925i
$493$	15.0314	−	16.6941i	0.676982	−	0.751864i
$494$	−7.83511	+	24.1140i	−0.352518	+	1.08494i
$495$	−0.802235			−0.0360578
$496$		0			0
$497$	−8.21771			−0.368615
$498$	19.6838	−	60.5804i	0.882050	−	2.71467i
$499$	16.4340	−	18.2518i	0.735685	−	0.817061i	−0.252937	−	0.967483i	$-0.581396\pi$
$499$	16.4340	−	18.2518i	0.735685	−	0.817061i	0.988622	+	0.150422i	$0.0480631\pi$
$500$	24.8218	+	18.0341i	1.11006	+	0.806509i
$501$	9.94584	−	17.2267i	0.444347	−	0.769632i
$502$	30.8429	+	53.4215i	1.37659	+	2.38432i
$503$	−1.54066	+	14.6584i	−0.0686946	+	0.653585i	0.904951	+	0.425517i	$0.139908\pi$
$503$	−1.54066	+	14.6584i	−0.0686946	+	0.653585i	−0.973645	+	0.228068i	$0.926759\pi$
$504$	11.9949	−	8.71479i	0.534295	−	0.388188i
$505$	−0.516394	−	4.91316i	−0.0229792	−	0.218633i
$506$	−1.29821	−	1.44181i	−0.0577126	−	0.0640963i
$507$	−0.614244	+	0.273479i	−0.0272795	+	0.0121456i
$508$	−66.1285	+	14.0561i	−2.93398	+	0.623637i
$509$	15.1674	+	3.22394i	0.672285	+	0.142899i	0.531392	−	0.847126i	$-0.321669\pi$
$509$	15.1674	+	3.22394i	0.672285	+	0.142899i	0.140893	+	0.990025i	$0.455003\pi$
$510$	5.86233	+	2.61008i	0.259588	+	0.115576i
$511$	4.00557	+	12.3279i	0.177196	+	0.545353i
$512$	−0.0418393	−	0.128768i	−0.00184905	−	0.00569080i
$513$	−13.2690	−	5.90773i	−0.585840	−	0.260833i
$514$	0.279433	+	0.0593953i	0.0123253	+	0.00261982i
$515$	−9.01709	+	1.91664i	−0.397341	+	0.0844574i
$516$	−20.4005	+	9.08291i	−0.898084	+	0.399853i
$517$	−6.01812	−	6.68380i	−0.264677	−	0.293953i
$518$	3.76092	+	35.7828i	0.165245	+	1.57220i
$519$	−0.0137556	+	0.00999402i	−0.000603803	+	0.000438689i
$520$	−2.03268	+	19.3396i	−0.0891388	+	0.848099i
$521$	−14.7073	−	25.4738i	−0.644337	−	1.11603i	−0.984454	−	0.175642i	$-0.943800\pi$
$521$	−14.7073	−	25.4738i	−0.644337	−	1.11603i	0.340117	−	0.940383i	$-0.389533\pi$
$522$	−10.7832	+	18.6771i	−0.471970	+	0.817475i
$523$	36.4268	+	26.4656i	1.59283	+	1.15726i	0.899754	+	0.436397i	$0.143746\pi$
$523$	36.4268	+	26.4656i	1.59283	+	1.15726i	0.693078	+	0.720863i	$0.256254\pi$
$524$	−8.54247	+	9.48737i	−0.373180	+	0.414458i
$525$	−3.50627	+	10.7912i	−0.153026	+	0.470966i
$526$	−19.6309			−0.855947
$527$		0			0
$528$	−24.5819			−1.06979
$529$	−7.01753	+	21.5977i	−0.305110	+	0.939032i
$530$	3.06499	−	3.40402i	0.133135	−	0.147861i
$531$	0.371899	+	0.270201i	0.0161391	+	0.0117257i
$532$	−11.6105	+	20.1099i	−0.503378	+	0.871876i
$533$	−0.190970	−	0.330769i	−0.00827182	−	0.0143272i
$534$	−6.11220	+	58.1537i	−0.264501	+	2.51656i
$535$	6.09119	−	4.42551i	0.263345	−	0.191331i
$536$	7.55343	+	71.8661i	0.326258	+	3.10414i
$537$	−9.47518	−	10.5232i	−0.408884	−	0.454112i
$538$	39.8604	−	17.7470i	1.71850	−	0.765127i
$539$	5.25607	−	1.11721i	0.226395	−	0.0481217i
$540$	−17.6289	−	3.74715i	−0.758629	−	0.161252i
$541$	34.5126	+	15.3660i	1.48381	+	0.660635i	0.979234	−	0.202731i	$-0.0649818\pi$
$541$	34.5126	+	15.3660i	1.48381	+	0.660635i	0.504577	+	0.863367i	$0.331648\pi$
$542$	−4.27759	−	13.1651i	−0.183738	−	0.565488i
$543$	−8.15834	−	25.1088i	−0.350108	−	1.07752i
$544$	−43.9830	−	19.5825i	−1.88576	−	0.839593i
$545$	−4.29034	−	0.911941i	−0.183778	−	0.0390632i
$546$	−23.6712	+	5.03148i	−1.01304	+	0.215327i
$547$	−16.6345	+	7.40617i	−0.711241	+	0.316665i	−0.730274	−	0.683154i	$-0.760608\pi$
$547$	−16.6345	+	7.40617i	−0.711241	+	0.316665i	0.0190333	+	0.999819i	$0.493941\pi$
$548$	−28.5375	−	31.6942i	−1.21906	−	1.35391i
$549$	0.527130	+	5.01531i	0.0224974	+	0.214048i
$550$	−13.4761	+	9.79092i	−0.574621	+	0.417486i
$551$	2.18229	−	20.7631i	0.0929686	−	0.884537i
$552$	−3.33206	−	5.77130i	−0.141822	−	0.245643i
$553$	8.37446	−	14.5050i	0.356118	−	0.616815i
$554$	36.8305	+	26.7590i	1.56478	+	1.13688i
$555$	4.47447	−	4.96940i	0.189931	−	0.210939i
$556$	2.19015	−	6.74059i	0.0928831	−	0.285865i
$557$	9.19760			0.389715			0.194857	−	0.980832i	$-0.437576\pi$
$557$	9.19760			0.389715			0.194857	+	0.980832i	$0.437576\pi$
$558$		0			0
$559$	−11.0293			−0.466488
$560$	−4.20481	+	12.9411i	−0.177686	+	0.546860i
$561$	−3.50877	+	3.89688i	−0.148140	+	0.164527i
$562$	4.14964	+	3.01489i	0.175042	+	0.127175i
$563$	18.0809	−	31.3170i	0.762019	−	1.31986i	−0.179790	−	0.983705i	$-0.557542\pi$
$563$	18.0809	−	31.3170i	0.762019	−	1.31986i	0.941808	−	0.336150i	$-0.109125\pi$
$564$	−24.9903	−	43.2844i	−1.05228	−	1.82260i
$565$	−1.06022	+	10.0873i	−0.0446037	+	0.424375i
$566$	−33.3200	+	24.2084i	−1.40054	+	1.01755i
$567$	−0.915165	−	8.70721i	−0.0384333	−	0.365668i
$568$	−27.7276	−	30.7946i	−1.16342	−	1.29211i
$569$	−37.9119	+	16.8795i	−1.58935	+	0.707624i	−0.995303	−	0.0968056i	$-0.969137\pi$
$569$	−37.9119	+	16.8795i	−1.58935	+	0.707624i	−0.594047	+	0.804430i	$0.702471\pi$
$570$	5.83354	−	1.23996i	0.244340	−	0.0519361i
$571$	−31.6853	−	6.73491i	−1.32599	−	0.281847i	−0.510128	−	0.860099i	$-0.670402\pi$
$571$	−31.6853	−	6.73491i	−1.32599	−	0.281847i	−0.815859	+	0.578251i	$0.803735\pi$
$572$	−23.4861	−	10.4567i	−0.982004	−	0.437216i
$573$	−0.525430	−	1.61711i	−0.0219501	−	0.0675556i
$574$	−0.149373	−	0.459722i	−0.00623470	−	0.0191884i
$575$	−2.28085	−	1.01550i	−0.0951182	−	0.0423494i
$576$	20.2297	+	4.29995i	0.842904	+	0.179165i
$577$	−40.0870	+	8.52075i	−1.66884	+	0.354723i	−0.942911	−	0.333044i	$-0.891924\pi$
$577$	−40.0870	+	8.52075i	−1.66884	+	0.354723i	−0.725931	+	0.687768i	$0.758591\pi$
$578$	23.0197	−	10.2490i	0.957494	−	0.426304i
$579$	−12.0852	−	13.4220i	−0.502245	−	0.557799i
$580$	−2.70786	−	25.7636i	−0.112438	−	1.06977i
$581$	23.3096	−	16.9354i	0.967046	−	0.702600i
$582$	0.510476	−	4.85685i	0.0211599	−	0.201323i
$583$	1.87151	+	3.24155i	0.0775100	+	0.134251i
$584$	−32.6814	+	56.6059i	−1.35237	+	2.34237i
$585$	−1.78133	−	1.29421i	−0.0736490	−	0.0535092i
$586$	−48.2304	+	53.5652i	−1.99238	+	2.21276i
$587$	−7.88963	+	24.2818i	−0.325640	+	1.00222i	0.645511	+	0.763751i	$0.276644\pi$
$587$	−7.88963	+	24.2818i	−0.325640	+	1.00222i	−0.971151	+	0.238466i	$0.923356\pi$
$588$	29.8612			1.23146
$589$		0			0
$590$	−0.763058			−0.0314146
$591$	−1.30187	+	4.00673i	−0.0535516	+	0.164815i
$592$	−67.1206	+	74.5449i	−2.75864	+	3.06378i
$593$	−36.0269	−	26.1751i	−1.47945	−	1.07488i	−0.977734	−	0.209850i	$-0.932702\pi$
$593$	−36.0269	−	26.1751i	−1.47945	−	1.07488i	−0.501716	−	0.865033i	$-0.667298\pi$
$594$	10.1759	−	17.6252i	0.417523	−	0.723170i
$595$	1.45132	+	2.51375i	0.0594982	+	0.103054i
$596$	4.92879	−	46.8943i	0.201891	−	1.92086i
$597$	15.1370	−	10.9977i	0.619515	−	0.450104i
$598$	−0.556616	−	5.29584i	−0.0227617	−	0.216563i
$599$	12.7001	+	14.1049i	0.518911	+	0.576309i	0.944460	−	0.328627i	$-0.106586\pi$
$599$	12.7001	+	14.1049i	0.518911	+	0.576309i	−0.425549	+	0.904935i	$0.639919\pi$
$600$	−52.2689	+	23.2716i	−2.13387	+	0.950059i
$601$	−12.5592	+	2.66955i	−0.512301	+	0.108893i	−0.456807	−	0.889566i	$-0.651007\pi$
$601$	−12.5592	+	2.66955i	−0.512301	+	0.108893i	−0.0554947	+	0.998459i	$0.517674\pi$
$602$	−13.6535	−	2.90215i	−0.556477	−	0.118283i
$603$	−7.47469	−	3.32795i	−0.304393	−	0.135524i
$604$	5.19217	+	15.9799i	0.211267	+	0.650212i
$605$	−1.73175	−	5.32977i	−0.0704056	−	0.216686i
$606$	28.3210	+	12.6093i	1.15046	+	0.512219i
$607$	37.3059	+	7.92960i	1.51420	+	0.321853i	0.888742	−	0.458407i	$-0.151580\pi$
$607$	37.3059	+	7.92960i	1.51420	+	0.321853i	0.625456	+	0.780260i	$0.284913\pi$
$608$	−43.7670	+	9.30297i	−1.77499	+	0.377285i
$609$	18.2038	−	8.10485i	0.737654	−	0.328425i
$610$	−5.60124	−	6.22081i	−0.226788	−	0.251873i
$611$	−2.58030	−	24.5499i	−0.104388	−	0.993184i
$612$	11.5412	−	8.38520i	0.466527	−	0.338952i
$613$	−1.93821	+	18.4408i	−0.0782834	+	0.744817i	0.883022	+	0.469332i	$0.155505\pi$
$613$	−1.93821	+	18.4408i	−0.0782834	+	0.744817i	−0.961305	+	0.275485i	$0.911162\pi$
$614$	12.0401	+	20.8541i	0.485901	+	0.841605i
$615$	−0.0449190	+	0.0778020i	−0.00181131	+	0.00313728i
$616$	−16.2701	−	11.8209i	−0.655541	−	0.476278i
$617$	5.44374	−	6.04589i	0.219157	−	0.243398i	−0.623534	−	0.781796i	$-0.714304\pi$
$617$	5.44374	−	6.04589i	0.219157	−	0.243398i	0.842691	+	0.538398i	$0.180970\pi$
$618$	17.8763	−	55.0175i	0.719089	−	2.21313i
$619$	5.36063			0.215462			0.107731	−	0.994180i	$-0.465641\pi$
$619$	5.36063			0.215462			0.107731	+	0.994180i	$0.465641\pi$
$620$		0			0
$621$	3.05046			0.122411
$622$	−17.1711	+	52.8472i	−0.688499	+	2.11898i
$623$	−17.6981	+	19.6557i	−0.709058	+	0.787489i
$624$	−54.5833	−	39.6571i	−2.18508	−	1.58755i
$625$	−9.79252	+	16.9611i	−0.391701	+	0.678446i
$626$	−0.607062	−	1.05146i	−0.0242631	−	0.0420249i
$627$	−0.509409	+	4.84670i	−0.0203438	+	0.193559i
$628$	14.0948	−	10.2404i	0.562442	−	0.408638i
$629$	2.23670	+	21.2808i	0.0891830	+	0.848519i
$630$	−1.86463	−	2.07088i	−0.0742887	−	0.0825059i
$631$	−26.5358	+	11.8145i	−1.05637	+	0.470327i	−0.860049	−	0.510212i	$-0.829567\pi$
$631$	−26.5358	+	11.8145i	−1.05637	+	0.470327i	−0.196324	+	0.980539i	$0.562900\pi$
$632$	82.6116	−	17.5596i	3.28611	−	0.698485i
$633$	25.4480	+	5.40914i	1.01147	+	0.214994i
$634$	13.7154	+	6.10647i	0.544707	+	0.242519i
$635$	2.42699	+	7.46949i	0.0963120	+	0.296418i
$636$	6.42770	+	19.7824i	0.254875	+	0.784424i
$637$	13.4733	+	5.99868i	0.533830	+	0.237677i
$638$	28.6139	+	6.08208i	1.13284	+	0.240792i
$639$	4.58943	−	0.975513i	0.181555	−	0.0385907i
$640$	−11.9916	+	5.33902i	−0.474011	+	0.211043i
$641$	18.4717	+	20.5149i	0.729589	+	0.810290i	0.987788	−	0.155801i	$-0.0497959\pi$
$641$	18.4717	+	20.5149i	0.729589	+	0.810290i	−0.258200	+	0.966092i	$0.583129\pi$
$642$	4.93868	+	46.9884i	0.194914	+	1.85449i
$643$	−3.42136	+	2.48577i	−0.134925	+	0.0980291i	−0.653201	−	0.757185i	$-0.726574\pi$
$643$	−3.42136	+	2.48577i	−0.134925	+	0.0980291i	0.518275	+	0.855214i	$0.326574\pi$
$644$	0.509768	−	4.85012i	0.0200877	−	0.191121i
$645$	1.29713	+	2.24669i	0.0510742	+	0.0884632i
$646$	−9.54202	+	16.5273i	−0.375426	+	0.650257i
$647$	−21.2617	−	15.4475i	−0.835883	−	0.607304i	0.0853349	−	0.996352i	$-0.472804\pi$
$647$	−21.2617	−	15.4475i	−0.835883	−	0.607304i	−0.921217	+	0.389048i	$0.872804\pi$
$648$	29.5410	−	32.8086i	1.16048	−	1.28884i
$649$	0.192683	−	0.593018i	0.00756348	−	0.0232780i
$650$	−45.7184			−1.79322
$651$		0			0
$652$	9.11408			0.356935
$653$	−4.12592	+	12.6983i	−0.161460	+	0.496922i	−0.998758	−	0.0498246i	$-0.984134\pi$
$653$	−4.12592	+	12.6983i	−0.161460	+	0.496922i	0.837298	+	0.546746i	$0.184134\pi$
$654$	18.4175	−	20.4547i	0.720182	−	0.799843i
$655$	1.19986	+	0.871749i	0.0468824	+	0.0340621i
$656$	0.673821	−	1.16709i	0.0263083	−	0.0455673i
$657$	−3.70045	−	6.40937i	−0.144368	−	0.250053i
$658$	3.26561	−	31.0702i	0.127307	−	1.21124i
$659$	12.4717	−	9.06119i	0.485827	−	0.352974i	−0.317750	−	0.948174i	$-0.602927\pi$
$659$	12.4717	−	9.06119i	0.485827	−	0.352974i	0.803577	+	0.595200i	$0.202927\pi$
$660$	0.632093	+	6.01396i	0.0246042	+	0.234093i
$661$	−3.16035	−	3.50992i	−0.122923	−	0.136520i	0.678542	−	0.734562i	$-0.262612\pi$
$661$	−3.16035	−	3.50992i	−0.122923	−	0.136520i	−0.801465	+	0.598042i	$0.795946\pi$
$662$	59.4868	−	26.4852i	2.31202	−	1.02938i
$663$	−14.0778	+	2.99233i	−0.546736	+	0.116212i
$664$	142.112	+	30.2069i	5.51502	+	1.17225i
$665$	2.46439	+	1.09722i	0.0955651	+	0.0425483i
$666$	−6.34812	−	19.5375i	−0.245984	−	0.757062i
$667$	1.35493	+	4.17006i	0.0524632	+	0.161465i
$668$	67.0573	+	29.8558i	2.59453	+	1.15516i
$669$	−13.0431	−	2.77239i	−0.504275	−	0.107187i
$670$	13.2849	−	2.82379i	0.513239	−	0.109092i
$671$	6.24895	−	2.78221i	0.241238	−	0.107406i
$672$	−28.5764	−	31.7373i	−1.10236	−	1.22429i
$673$	−3.24801	−	30.9028i	−0.125202	−	1.19121i	−0.859046	−	0.511898i	$-0.828943\pi$
$673$	−3.24801	−	30.9028i	−0.125202	−	1.19121i	0.733845	−	0.679317i	$-0.237724\pi$
$674$	−24.0185	+	17.4505i	−0.925158	+	0.672167i
$675$	2.73760	−	26.0465i	0.105370	−	1.00253i
$676$	−1.24058	−	2.14875i	−0.0477147	−	0.0826443i
$677$	−4.51998	+	7.82883i	−0.173717	+	0.300886i	−0.939716	−	0.341955i	$-0.888911\pi$
$677$	−4.51998	+	7.82883i	−0.173717	+	0.300886i	0.766000	+	0.642841i	$0.222244\pi$
$678$	−51.4932	−	37.4120i	−1.97759	−	1.43680i
$679$	1.47810	−	1.64159i	0.0567242	−	0.0629986i
$680$	−4.52297	+	13.9203i	−0.173448	+	0.533818i
$681$	−12.0053			−0.460044
$682$		0			0
$683$	7.13535			0.273027			0.136513	−	0.990638i	$-0.456410\pi$
$683$	7.13535			0.273027			0.136513	+	0.990638i	$0.456410\pi$
$684$	4.09699	−	12.6092i	0.156652	−	0.482127i
$685$	−3.31525	+	3.68196i	−0.126669	+	0.140681i
$686$	41.4091	+	30.0854i	1.58101	+	1.14867i
$687$	−16.2093	+	28.0753i	−0.618423	+	1.07114i
$688$	−19.4579	−	33.7021i	−0.741826	−	1.28488i
$689$	−1.07385	+	10.2170i	−0.0409103	+	0.389236i
$690$	−1.01331	+	0.736216i	−0.0385762	+	0.0280273i
$691$	−3.81272	−	36.2756i	−0.145043	−	1.37999i	−0.788749	−	0.614716i	$-0.789271\pi$
$691$	−3.81272	−	36.2756i	−0.145043	−	1.37999i	0.643706	−	0.765273i	$-0.277396\pi$
$692$	−0.0419833	−	0.0466272i	−0.00159597	−	0.00177250i
$693$	2.08025	−	0.926188i	0.0790222	−	0.0351830i
$694$	48.8576	−	10.3850i	1.85461	−	0.394210i
$695$	−0.805371	−	0.171187i	−0.0305495	−	0.00649349i
$696$	91.7934	+	40.8690i	3.47942	+	1.54914i
$697$	−0.0888351	−	0.273406i	−0.00336487	−	0.0103560i
$698$	26.7469	+	82.3185i	1.01238	+	3.11580i
$699$	−21.0722	−	9.38193i	−0.797022	−	0.354857i
$700$	−40.9555	−	8.70536i	−1.54797	−	0.329032i
$701$	1.57916	−	0.335661i	0.0596441	−	0.0126777i	−0.177993	−	0.984032i	$-0.556960\pi$
$701$	1.57916	−	0.335661i	0.0596441	−	0.0126777i	0.237637	+	0.971354i	$0.423627\pi$
$702$	51.0293	−	22.7197i	1.92598	−	0.857500i
$703$	13.3067	+	14.7786i	0.501873	+	0.557386i
$704$	−2.93233	−	27.8993i	−0.110516	−	1.05149i
$705$	−4.69742	+	3.41287i	−0.176915	+	0.128536i
$706$	−9.05833	+	86.1843i	−0.340915	+	3.24359i
$707$	7.01134	+	12.1440i	0.263688	+	0.456722i
$708$	1.73254	−	3.00084i	0.0651127	−	0.112779i
$709$	9.29395	+	6.75245i	0.349042	+	0.253594i	0.748467	−	0.663172i	$-0.230790\pi$
$709$	9.29395	+	6.75245i	0.349042	+	0.253594i	−0.399425	+	0.916766i	$0.630790\pi$
$710$	−5.21141	+	5.78785i	−0.195581	+	0.217214i
$711$	−2.95510	+	9.09487i	−0.110825	+	0.341084i
$712$	−133.372			−4.99833
$713$		0			0
$714$	−18.2148			−0.681672
$715$	−0.922919	+	2.84045i	−0.0345152	+	0.106227i
$716$	34.9649	−	38.8324i	1.30670	−	1.45124i
$717$	−20.9797	−	15.2427i	−0.783503	−	0.569248i
$718$	28.4649	−	49.3026i	1.06230	−	1.83996i
$719$	−7.08549	−	12.2724i	−0.264244	−	0.457685i	0.703121	−	0.711070i	$-0.251789\pi$
$719$	−7.08549	−	12.2724i	−0.264244	−	0.457685i	−0.967365	+	0.253386i	$0.918456\pi$
$720$	0.812085	−	7.72648i	0.0302646	−	0.287949i
$721$	21.1692	−	15.3803i	0.788382	−	0.572793i
$722$	−3.48883	−	33.1940i	−0.129841	−	1.23535i
$723$	−17.2558	−	19.1645i	−0.641751	−	0.712736i
$724$	89.0009	−	39.6258i	3.30769	−	1.47268i
$725$	36.8222	−	7.82681i	1.36754	−	0.290680i
$726$	34.3985	+	7.31162i	1.27665	+	0.271360i
$727$	−24.6180	−	10.9606i	−0.913030	−	0.406507i	−0.104205	−	0.994556i	$-0.533230\pi$
$727$	−24.6180	−	10.9606i	−0.913030	−	0.406507i	−0.808826	+	0.588049i	$0.799896\pi$
$728$	−17.0569	−	52.4958i	−0.632172	−	1.94562i
$729$	8.98695	+	27.6590i	0.332850	+	1.02441i
$730$	11.2229	+	4.99675i	0.415378	+	0.184938i
$731$	−8.12005	−	1.72597i	−0.300331	−	0.0638373i
$732$	37.1820	−	7.90328i	1.37429	−	0.292113i
$733$	−25.9662	+	11.5609i	−0.959083	+	0.427011i	−0.825735	−	0.564058i	$-0.809239\pi$
$733$	−25.9662	+	11.5609i	−0.959083	+	0.427011i	−0.133348	+	0.991069i	$0.542573\pi$
$734$	23.3944	+	25.9822i	0.863504	+	0.959019i
$735$	−0.362612	−	3.45003i	−0.0133752	−	0.127256i
$736$	7.60254	−	5.52357i	0.280233	−	0.203601i
$737$	−1.16009	+	11.0375i	−0.0427324	+	0.406572i
$738$	0.137995	+	0.239014i	0.00507965	+	0.00879822i
$739$	−0.348653	+	0.603885i	−0.0128254	+	0.0222143i	−0.872367	−	0.488852i	$-0.837416\pi$
$739$	−0.348653	+	0.603885i	−0.0128254	+	0.0222143i	0.859541	+	0.511066i	$0.170749\pi$
$740$	19.9633	+	14.5042i	0.733866	+	0.533185i
$741$	−8.95012	+	9.94011i	−0.328791	+	0.365159i
$742$	−4.01777	+	12.3654i	−0.147497	+	0.453949i
$743$	18.1815			0.667015			0.333508	−	0.942747i	$-0.391768\pi$
$743$	18.1815			0.667015			0.333508	+	0.942747i	$0.391768\pi$
$744$		0			0
$745$	−5.47779			−0.200691
$746$	3.67929	−	11.3237i	0.134708	−	0.414589i
$747$	−11.0076	+	12.2251i	−0.402746	+	0.447295i
$748$	−15.6548	−	11.3738i	−0.572395	−	0.415869i
$749$	−10.6856	+	18.5080i	−0.390443	+	0.676267i
$750$	11.1835	+	19.3704i	0.408364	+	0.707307i
$751$	3.87445	−	36.8629i	0.141381	−	1.34515i	−0.661920	−	0.749574i	$-0.730258\pi$
$751$	3.87445	−	36.8629i	0.141381	−	1.34515i	0.803301	−	0.595573i	$-0.203075\pi$
$752$	70.4650	−	51.1958i	2.56959	−	1.86692i
$753$	3.40154	+	32.3635i	0.123959	+	1.17939i
$754$	53.7242	+	59.6668i	1.95652	+	2.17294i
$755$	1.78319	−	0.793927i	0.0648969	−	0.0288940i
$756$	50.0392	−	10.6362i	1.81991	−	0.386834i
$757$	6.26211	+	1.33105i	0.227600	+	0.0483779i	0.320300	−	0.947316i	$-0.396216\pi$
$757$	6.26211	+	1.33105i	0.227600	+	0.0483779i	−0.0926997	+	0.995694i	$0.529550\pi$
$758$	36.7549	+	16.3643i	1.33500	+	0.594380i
$759$	−0.316281	−	0.973412i	−0.0114803	−	0.0353326i
$760$	4.20351	+	12.9371i	0.152477	+	0.469277i
$761$	19.4940	+	8.67928i	0.706657	+	0.314624i	0.728412	−	0.685140i	$-0.240259\pi$
$761$	19.4940	+	8.67928i	0.706657	+	0.314624i	−0.0217552	+	0.999763i	$0.506925\pi$
$762$	−48.2083	−	10.2470i	−1.74640	−	0.371209i
$763$	12.1780	−	2.58852i	0.440874	−	0.0937106i
$764$	5.73201	−	2.55206i	0.207377	−	0.0923302i
$765$	−1.10893	−	1.23160i	−0.0400936	−	0.0445285i
$766$	3.27605	+	31.1696i	0.118369	+	1.12620i
$767$	1.38454	−	1.00593i	0.0499928	−	0.0363219i
$768$	2.38699	−	22.7107i	0.0861332	−	0.819502i
$769$	6.12828	+	10.6145i	0.220991	+	0.382768i	0.955109	−	0.296254i	$-0.0957374\pi$
$769$	6.12828	+	10.6145i	0.220991	+	0.382768i	−0.734118	+	0.679022i	$0.762404\pi$
$770$	−1.88993	+	3.27346i	−0.0681084	+	0.117967i
$771$	0.121923	+	0.0885824i	0.00439096	+	0.00319022i
$772$	44.5963	−	49.5292i	1.60506	−	1.78260i
$773$	10.7240	−	33.0050i	0.385714	−	1.18711i	−0.550247	−	0.835002i	$-0.685466\pi$
$773$	10.7240	−	33.0050i	0.385714	−	1.18711i	0.935961	−	0.352104i	$-0.114534\pi$
$774$	7.96974			0.286466
$775$		0			0
$776$	11.1389			0.399863
$777$	−5.86539	+	18.0518i	−0.210420	+	0.647605i
$778$	25.9244	−	28.7920i	0.929435	−	1.03224i
$779$	−0.216146	−	0.157040i	−0.00774425	−	0.00562652i
$780$	−8.29855	+	14.3735i	−0.297136	+	0.514654i
$781$	−3.18213	−	5.51161i	−0.113866	−	0.197221i
$782$	0.418951	−	3.98605i	0.0149817	−	0.142541i
$783$	−37.2102	+	27.0348i	−1.32978	+	0.966144i
$784$	5.43948	+	51.7532i	0.194267	+	1.84833i
$785$	−1.35429	−	1.50409i	−0.0483366	−	0.0536833i
$786$	−8.50228	+	3.78546i	−0.303266	+	0.135023i
$787$	−19.6786	+	4.18281i	−0.701465	+	0.149101i	−0.544819	−	0.838554i	$-0.683402\pi$
$787$	−19.6786	+	4.18281i	−0.701465	+	0.149101i	−0.156646	+	0.987655i	$0.550068\pi$
$788$	−15.2066	−	3.23227i	−0.541714	−	0.115145i
$789$	−9.46075	−	4.21220i	−0.336812	−	0.149958i
$790$	−4.90526	−	15.0968i	−0.174521	−	0.537122i
$791$	−8.89666	−	27.3811i	−0.316329	−	0.973559i
$792$	10.4898	+	4.67034i	0.372737	+	0.165953i
$793$	18.3640	+	3.90339i	0.652125	+	0.138613i
$794$	41.5496	−	8.83165i	1.47454	−	0.313423i
$795$	2.20752	−	0.982849i	0.0782925	−	0.0348581i
$796$	46.1995	+	51.3097i	1.63750	+	1.81863i
$797$	2.73885	+	26.0584i	0.0970150	+	0.923036i	0.929459	+	0.368926i	$0.120275\pi$
$797$	2.73885	+	26.0584i	0.0970150	+	0.923036i	−0.832444	+	0.554110i	$0.813059\pi$
$798$	−13.6953	+	9.95018i	−0.484807	+	0.352233i
$799$	1.94213	−	18.4781i	0.0687076	−	0.653709i
$800$	−40.3405	−	69.8717i	−1.42625	−	2.47034i
$801$	7.55072	−	13.0782i	0.266791	−	0.462096i
$802$	−67.5183	−	49.0549i	−2.38416	−	1.73219i
$803$	−6.71722	+	7.46022i	−0.237045	+	0.263266i
$804$	−19.0586	+	58.6562i	−0.672144	+	2.06865i
$805$	−0.566550			−0.0199683
$806$		0			0
$807$	23.0179			0.810270
$808$	−21.8506	+	67.2491i	−0.768700	+	2.36582i
$809$	−24.3899	+	27.0877i	−0.857504	+	0.952354i	−0.999295	−	0.0375423i	$-0.988047\pi$
$809$	−24.3899	+	27.0877i	−0.857504	+	0.952354i	0.141791	+	0.989897i	$0.454714\pi$
$810$	−6.71298	−	4.87727i	−0.235870	−	0.171370i
$811$	9.55322	−	16.5467i	0.335459	−	0.581032i	−0.648114	−	0.761543i	$-0.724442\pi$
$811$	9.55322	−	16.5467i	0.335459	−	0.581032i	0.983573	+	0.180511i	$0.0577753\pi$
$812$	36.7660	+	63.6805i	1.29023	+	2.23475i
$813$	0.763320	−	7.26250i	0.0267708	−	0.254707i
$814$	−22.5431	+	16.3785i	−0.790136	+	0.574067i
$815$	−0.110675	−	1.05300i	−0.00387676	−	0.0368849i
$816$	−33.9798	−	37.7384i	−1.18953	−	1.32111i
$817$	−7.04810	+	3.13802i	−0.246582	+	0.109785i
$818$	−17.3297	+	3.68355i	−0.605920	+	0.128792i
$819$	6.11330	+	1.29942i	0.213616	+	0.0454055i
$820$	−0.302855	−	0.134840i	−0.0105762	−	0.00470881i
$821$	−12.1937	−	37.5285i	−0.425565	−	1.30975i	−0.902453	−	0.430789i	$-0.858235\pi$
$821$	−12.1937	−	37.5285i	−0.425565	−	1.30975i	0.476888	−	0.878964i	$-0.341765\pi$
$822$	−9.60773	−	29.5696i	−0.335108	−	1.03136i
$823$	28.8571	+	12.8480i	1.00589	+	0.447853i	0.842493	−	0.538707i	$-0.181087\pi$
$823$	28.8571	+	12.8480i	1.00589	+	0.447853i	0.163401	+	0.986560i	$0.447754\pi$
$824$	129.063	+	27.4331i	4.49611	+	0.955678i
$825$	−8.59537	+	1.82700i	−0.299252	+	0.0636081i
$826$	1.97866	−	0.880958i	0.0688465	−	0.0306525i
$827$	−13.2688	−	14.7364i	−0.461400	−	0.512436i	0.466879	−	0.884321i	$-0.345378\pi$
$827$	−13.2688	−	14.7364i	−0.461400	−	0.512436i	−0.928279	+	0.371885i	$0.878712\pi$
$828$	0.291055	+	2.76921i	0.0101149	+	0.0962366i
$829$	7.28104	−	5.28999i	0.252881	−	0.183729i	−0.454122	−	0.890940i	$-0.650047\pi$
$829$	7.28104	−	5.28999i	0.252881	−	0.183729i	0.707003	+	0.707211i	$0.250047\pi$
$830$	2.85434	−	27.1572i	0.0990754	−	0.942640i
$831$	12.0081	+	20.7987i	0.416558	+	0.721499i
$832$	38.4977	−	66.6800i	1.33467	−	2.31171i
$833$	8.98066	+	6.52483i	0.311161	+	0.226072i
$834$	3.45729	−	3.83970i	0.119716	−	0.132958i
$835$	2.63511	−	8.11003i	0.0911917	−	0.280659i
$836$	−17.9836			−0.621976
$837$		0			0
$838$	39.4699			1.36347
$839$	−9.84070	+	30.2866i	−0.339739	+	1.04561i	0.624602	+	0.780944i	$0.285261\pi$
$839$	−9.84070	+	30.2866i	−0.339739	+	1.04561i	−0.964340	+	0.264665i	$0.914739\pi$
$840$	−8.68750	+	9.64844i	−0.299747	+	0.332903i
$841$	−30.0234	−	21.8133i	−1.03529	−	0.752183i
$842$	−35.9349	+	62.2411i	−1.23840	+	2.14497i
$843$	1.35294	+	2.34336i	0.0465976	+	0.0807095i
$844$	−10.0353	+	95.4791i	−0.345428	+	3.28652i
$845$	−0.233192	+	0.169424i	−0.00802205	+	0.00582836i
$846$	1.86452	+	17.7398i	0.0641037	+	0.609906i
$847$	10.6438	+	11.8212i	0.365726	+	0.406180i
$848$	−33.1145	+	14.7435i	−1.13716	+	0.506295i
$849$	−21.2523	+	4.51733i	−0.729379	+	0.155034i
$850$	−33.6591	−	7.15447i	−1.15450	−	0.245396i
$851$	−3.81548	−	1.69876i	−0.130793	−	0.0582328i
$852$	−10.9290	−	33.6361i	−0.374422	−	1.15235i
$853$	−15.1702	−	46.6890i	−0.519417	−	1.59860i	−0.775099	−	0.631839i	$-0.782300\pi$
$853$	−15.1702	−	46.6890i	−0.519417	−	1.59860i	0.255683	−	0.966761i	$-0.417700\pi$
$854$	21.7064	+	9.66431i	0.742778	+	0.330706i
$855$	−1.50656	−	0.320230i	−0.0515234	−	0.0109516i
$856$	−105.410	+	22.4056i	−3.60285	+	0.765809i
$857$	17.5770	−	7.82580i	0.600420	−	0.267324i	−0.0839371	−	0.996471i	$-0.526749\pi$
$857$	17.5770	−	7.82580i	0.600420	−	0.267324i	0.684357	+	0.729147i	$0.260083\pi$
$858$	−12.5408	−	13.9279i	−0.428135	−	0.475492i
$859$	0.485236	+	4.61672i	0.0165561	+	0.157520i	0.999676	−	0.0254400i	$-0.00809867\pi$
$859$	0.485236	+	4.61672i	0.0165561	+	0.157520i	−0.983120	+	0.182960i	$0.941432\pi$
$860$	−7.74487	+	5.62698i	−0.264098	+	0.191878i
$861$	0.0266550	−	0.253606i	0.000908401	−	0.00864285i
$862$	5.36418	+	9.29104i	0.182705	+	0.316454i
$863$	−19.2652	+	33.3683i	−0.655795	+	1.13587i	0.325899	+	0.945405i	$0.394333\pi$
$863$	−19.2652	+	33.3683i	−0.655795	+	1.13587i	−0.981694	+	0.190466i	$0.939000\pi$
$864$	79.7493	+	57.9413i	2.71313	+	1.97120i
$865$	−0.00487728	+	0.00541676i	−0.000165832	+	0.000184175i
$866$	15.0271	−	46.2487i	0.510642	−	1.57159i
$867$	13.2931			0.451456
$868$		0			0
$869$	12.9713			0.440022
$870$	5.83589	−	17.9610i	0.197855	−	0.608935i
$871$	−20.3823	+	22.6369i	−0.690629	+	0.767021i
$872$	50.7901	+	36.9012i	1.71997	+	1.24963i
$873$	−0.630617	+	1.09226i	−0.0213431	+	0.0369674i
$874$	−1.86246	−	3.22587i	−0.0629986	−	0.109117i
$875$	−1.05753	+	10.0618i	−0.0357512	+	0.340150i
$876$	−45.1323	+	32.7905i	−1.52488	+	1.10789i
$877$	0.967760	+	9.20763i	0.0326789	+	0.310919i	0.998636	+	0.0522162i	$0.0166285\pi$
$877$	0.967760	+	9.20763i	0.0326789	+	0.310919i	−0.965957	+	0.258703i	$0.916705\pi$
$878$	−41.2370	−	45.7983i	−1.39168	−	1.54562i
$879$	−34.7372	+	15.4660i	−1.17166	+	0.521655i
$880$	−10.3078	+	2.19099i	−0.347475	+	0.0738582i
$881$	−17.4884	−	3.71727i	−0.589198	−	0.125238i	−0.0963414	−	0.995348i	$-0.530714\pi$
$881$	−17.4884	−	3.71727i	−0.589198	−	0.125238i	−0.492857	+	0.870110i	$0.664047\pi$
$882$	−9.73577	−	4.33465i	−0.327821	−	0.145955i
$883$	14.9303	+	45.9509i	0.502446	+	1.54637i	0.805022	+	0.593244i	$0.202153\pi$
$883$	14.9303	+	45.9509i	0.502446	+	1.54637i	−0.302577	+	0.953125i	$0.597847\pi$
$884$	−16.4118	−	50.5104i	−0.551990	−	1.69885i
$885$	−0.367742	−	0.163729i	−0.0123615	−	0.00550370i
$886$	−56.5516	−	12.0204i	−1.89989	−	0.403834i
$887$	−22.9984	+	4.88847i	−0.772211	+	0.164139i	−0.577134	−	0.816649i	$-0.695829\pi$
$887$	−22.9984	+	4.88847i	−0.772211	+	0.164139i	−0.195077	+	0.980788i	$0.562496\pi$
$888$	−87.4369	+	38.9294i	−2.93419	+	1.30639i
$889$	−14.9170	−	16.5670i	−0.500298	−	0.555638i
$890$	2.62025	+	24.9300i	0.0878310	+	0.835656i
$891$	5.48554	−	3.98548i	0.183772	−	0.133518i
$892$	5.14346	−	48.9368i	0.172216	−	1.63852i
$893$	−8.63379	−	14.9542i	−0.288919	−	0.500422i
$894$	17.1873	−	29.7693i	0.574830	−	0.995635i
$895$	−4.91110	−	3.56812i	−0.164160	−	0.119269i
$896$	24.9312	−	27.6889i	0.832894	−	0.925022i
$897$	0.868078	−	2.67167i	0.0289843	−	0.0892044i
$898$	50.5739			1.68767
$899$		0			0
$900$	23.9062			0.796874
$901$	−2.38945	+	7.35398i	−0.0796042	+	0.244996i
$902$	0.250494	−	0.278202i	0.00834053	−	0.00926310i
$903$	−5.95736	−	4.32827i	−0.198249	−	0.144036i
$904$	72.5879	−	125.726i	2.41424	−	4.18158i
$905$	−5.65893	−	9.80156i	−0.188109	−	0.325815i
$906$	−1.28037	+	12.1819i	−0.0425373	+	0.404716i
$907$	10.1792	−	7.39560i	0.337994	−	0.245567i	−0.405821	−	0.913952i	$-0.633014\pi$
$907$	10.1792	−	7.39560i	0.337994	−	0.245567i	0.743815	+	0.668386i	$0.233014\pi$
$908$	−4.63076	−	44.0588i	−0.153677	−	1.46214i
$909$	−5.35728	−	5.94987i	−0.177690	−	0.197345i
$910$	−9.47746	+	4.21964i	−0.314175	+	0.139880i
$911$	−46.2512	+	9.83100i	−1.53237	+	0.325715i	−0.895432	−	0.445199i	$-0.853133\pi$
$911$	−46.2512	+	9.83100i	−1.53237	+	0.325715i	−0.636939	+	0.770914i	$0.719800\pi$
$912$	−46.1639	−	9.81243i	−1.52864	−	0.324922i
$913$	20.3847	+	9.07586i	0.674635	+	0.300367i
$914$	3.41333	+	10.5051i	0.112903	+	0.347479i
$915$	−1.36462	−	4.19986i	−0.0451129	−	0.138843i
$916$	−109.287	−	48.6578i	−3.61095	−	1.60770i
$917$	−4.11776	−	0.875258i	−0.135981	−	0.0289036i
$918$	41.1246	−	8.74130i	1.35731	−	0.288506i
$919$	−21.1320	+	9.40858i	−0.697081	+	0.310360i	−0.724511	−	0.689263i	$-0.757934\pi$
$919$	−21.1320	+	9.40858i	−0.697081	+	0.310360i	0.0274300	+	0.999624i	$0.491268\pi$
$920$	−1.91161	−	2.12306i	−0.0630238	−	0.0699951i
$921$	1.32786	+	12.6337i	0.0437544	+	0.416295i
$922$	49.7848	−	36.1708i	1.63958	−	1.19122i
$923$	1.82586	−	17.3719i	0.0600990	−	0.571804i
$924$	−8.58224	−	14.8649i	−0.282335	−	0.489019i
$925$	−17.9291	+	31.0541i	−0.589506	+	1.02105i
$926$	36.0560	+	26.1962i	1.18488	+	0.860862i
$927$	−9.99679	+	11.1026i	−0.328338	+	0.364656i
$928$	−43.7846	+	134.755i	−1.43730	+	4.42355i
$929$	−1.68694			−0.0553468			−0.0276734	−	0.999617i	$-0.508810\pi$
$929$	−1.68694			−0.0553468			−0.0276734	+	0.999617i	$0.508810\pi$
$930$		0			0
$931$	10.3166			0.338114
$932$	26.3030	−	80.9524i	0.861585	−	2.65169i
$933$	−19.6147	+	21.7844i	−0.642157	+	0.713188i
$934$	83.0208	+	60.3181i	2.71652	+	1.97367i
$935$	−1.12398	+	1.94679i	−0.0367581	+	0.0636669i
$936$	15.7576	+	27.2930i	0.515055	+	0.892101i
$937$	−2.06200	+	19.6186i	−0.0673625	+	0.640911i	0.907797	+	0.419409i	$0.137763\pi$
$937$	−2.06200	+	19.6186i	−0.0673625	+	0.640911i	−0.975160	+	0.221502i	$0.928904\pi$
$938$	−31.1885	+	22.6598i	−1.01834	+	0.739868i
$939$	−0.0669503	−	0.636990i	−0.00218484	−	0.0207874i
$940$	−14.3370	−	15.9228i	−0.467620	−	0.519344i
$941$	8.06045	−	3.58874i	0.262763	−	0.116990i	−0.271127	−	0.962544i	$-0.587396\pi$
$941$	8.06045	−	3.58874i	0.262763	−	0.116990i	0.533890	+	0.845554i	$0.320730\pi$
$942$	12.4233	−	2.64066i	0.404773	−	0.0860372i
$943$	0.0548849	+	0.0116661i	0.00178730	+	0.000379902i
$944$	5.51642	+	2.45607i	0.179544	+	0.0799382i
$945$	−1.83649	−	5.65214i	−0.0597411	−	0.183864i
$946$	−3.34057	−	10.2812i	−0.108611	−	0.334271i
$947$	−14.2158	−	6.32930i	−0.461953	−	0.205675i	0.162545	−	0.986701i	$-0.448030\pi$
$947$	−14.2158	−	6.32930i	−0.461953	−	0.205675i	−0.624498	+	0.781026i	$0.714696\pi$
$948$	70.5082	+	14.9870i	2.29000	+	0.486754i
$949$	−26.9506	+	5.72853i	−0.874854	+	0.185956i
$950$	−29.2157	+	13.0077i	−0.947883	+	0.422025i
$951$	5.29960	+	5.88581i	0.171851	+	0.190860i
$952$	−4.34271	−	41.3181i	−0.140748	−	1.33913i
$953$	7.80840	−	5.67314i	0.252939	−	0.183771i	−0.454089	−	0.890956i	$-0.650035\pi$
$953$	7.80840	−	5.67314i	0.252939	−	0.183771i	0.707028	+	0.707185i	$0.250035\pi$
$954$	0.775962	−	7.38278i	0.0251227	−	0.239026i
$955$	−0.364458	−	0.631260i	−0.0117936	−	0.0204271i
$956$	47.8473	−	82.8739i	1.54749	−	2.68033i
$957$	12.4849	+	9.07083i	0.403580	+	0.293218i
$958$	60.6348	−	67.3417i	1.95902	−	2.17571i
$959$	4.34583	−	13.3751i	0.140334	−	0.431904i
$960$	−18.1105			−0.584514
$961$		0			0
$962$	−76.4790			−2.46578
$963$	3.77063	−	11.6048i	0.121507	−	0.373960i
$964$	63.6766	−	70.7201i	2.05089	−	2.27774i
$965$	−6.26392	−	4.55100i	−0.201643	−	0.146502i
$966$	1.77763	−	3.07894i	0.0571942	−	0.0990633i
$967$	14.1988	+	24.5930i	0.456602	+	0.790858i	0.998779	−	0.0494066i	$-0.0157330\pi$
$967$	14.1988	+	24.5930i	0.456602	+	0.790858i	−0.542177	+	0.840264i	$0.682400\pi$
$968$	−8.38438	+	79.7720i	−0.269484	+	2.56397i
$969$	−8.14485	+	5.91758i	−0.261650	+	0.190100i
$970$	−0.218837	−	2.08209i	−0.00702642	−	0.0668519i
$971$	−14.8059	−	16.4436i	−0.475144	−	0.527701i	0.457156	−	0.889386i	$-0.348868\pi$
$971$	−14.8059	−	16.4436i	−0.475144	−	0.527701i	−0.932300	+	0.361686i	$0.882201\pi$
$972$	−46.7662	+	20.8217i	−1.50003	+	0.667855i
$973$	2.28602	−	0.485909i	0.0732865	−	0.0155775i
$974$	54.4080	+	11.5648i	1.74334	+	0.370559i
$975$	−22.0331	−	9.80978i	−0.705625	−	0.314165i
$976$	20.4703	+	63.0012i	0.655240	+	2.01662i
$977$	−6.15324	−	18.9377i	−0.196859	−	0.605871i	−0.999950	−	0.0100140i	$-0.996812\pi$
$977$	−6.15324	−	18.9377i	−0.196859	−	0.605871i	0.803090	−	0.595857i	$-0.203188\pi$
$978$	6.06982	+	2.70246i	0.194091	+	0.0864151i
$979$	−20.0362	−	4.25884i	−0.640361	−	0.136113i
$980$	12.5215	−	2.66153i	0.399985	−	0.0850195i
$981$	−6.49389	+	2.89127i	−0.207334	+	0.0923111i
$982$	44.5206	+	49.4451i	1.42071	+	1.57786i
$983$	−2.60593	−	24.7938i	−0.0831164	−	0.790800i	−0.954100	−	0.299488i	$-0.903184\pi$
$983$	−2.60593	−	24.7938i	−0.0831164	−	0.790800i	0.870984	−	0.491312i	$-0.163482\pi$
$984$	1.04028	−	0.755810i	0.0331630	−	0.0240944i
$985$	−0.188783	+	1.79615i	−0.00601513	+	0.0572302i
$986$	30.2160	+	52.3356i	0.962273	+	1.66671i
$987$	8.24054	−	14.2730i	0.262299	−	0.454316i
$988$	−39.9319	−	29.0122i	−1.27040	−	0.923002i
$989$	1.08420	−	1.20413i	0.0344757	−	0.0382891i
$990$	0.666901	−	2.05251i	0.0211955	−	0.0652330i
$991$	42.0512			1.33580			0.667900	−	0.744251i	$-0.267193\pi$
$991$	42.0512			1.33580			0.667900	+	0.744251i	$0.267193\pi$
$992$		0			0
$993$	34.3515			1.09011
$994$	6.83142	−	21.0249i	0.216679	−	0.666871i
$995$	5.36707	−	5.96074i	0.170148	−	0.188968i
$996$	100.319	+	72.8860i	3.17873	+	2.30948i
$997$	−7.23233	+	12.5268i	−0.229050	+	0.396727i	−0.957527	−	0.288344i	$-0.906895\pi$
$997$	−7.23233	+	12.5268i	−0.229050	+	0.396727i	0.728477	+	0.685071i	$0.240229\pi$
$998$	33.0353	+	57.2189i	1.04572	+	1.81123i
$999$	4.57954	−	43.5714i	0.144890	−	1.37854i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.l.448.1		16
31.2	even	5		961.2.c.i.521.1		16
31.3	odd	30		961.2.d.p.374.4		16
31.4	even	5		961.2.g.j.844.1		16
31.5	even	3		961.2.g.j.846.1		16
31.6	odd	6		961.2.d.o.628.1		16
31.7	even	15		961.2.d.n.531.1		16
31.8	even	5		961.2.g.n.338.2		16
31.9	even	15		961.2.g.m.235.2		16
31.10	even	15		961.2.c.i.439.1		16
31.11	odd	30		31.2.g.a.20.1	yes	16
31.12	odd	30		961.2.a.i.1.1		8
31.13	odd	30		961.2.g.t.816.2		16
31.14	even	15		961.2.d.q.388.4		16
31.15	odd	10		961.2.g.s.732.2		16
31.16	even	5		961.2.g.m.732.2		16
31.17	odd	30		961.2.d.p.388.4		16
31.18	even	15		961.2.g.n.816.2		16
31.19	even	15		961.2.a.j.1.1		8
31.20	even	15	inner	961.2.g.l.547.1		16
31.21	odd	30		961.2.c.j.439.1		16
31.22	odd	30		961.2.g.s.235.2		16
31.23	odd	10		961.2.g.t.338.2		16
31.24	odd	30		961.2.d.o.531.1		16
31.25	even	3		961.2.d.n.628.1		16
31.26	odd	6		961.2.g.k.846.1		16
31.27	odd	10		961.2.g.k.844.1		16
31.28	even	15		961.2.d.q.374.4		16
31.29	odd	10		961.2.c.j.521.1		16
31.30	odd	2		31.2.g.a.14.1	✓	16
93.11	even	30		279.2.y.c.82.2		16
93.50	odd	30		8649.2.a.be.1.8		8
93.74	even	30		8649.2.a.bf.1.8		8
93.92	even	2		279.2.y.c.262.2		16
124.11	even	30		496.2.bg.c.113.1		16
124.123	even	2		496.2.bg.c.417.1		16
155.42	even	60		775.2.ck.a.299.4		32
155.73	even	60		775.2.ck.a.299.1		32
155.92	even	4		775.2.ck.a.324.1		32
155.104	odd	30		775.2.bl.a.51.2		16
155.123	even	4		775.2.ck.a.324.4		32
155.154	odd	2		775.2.bl.a.76.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.14.1	✓	16	31.30	odd	2
31.2.g.a.20.1	yes	16	31.11	odd	30
279.2.y.c.82.2		16	93.11	even	30
279.2.y.c.262.2		16	93.92	even	2
496.2.bg.c.113.1		16	124.11	even	30
496.2.bg.c.417.1		16	124.123	even	2
775.2.bl.a.51.2		16	155.104	odd	30
775.2.bl.a.76.2		16	155.154	odd	2
775.2.ck.a.299.1		32	155.73	even	60
775.2.ck.a.299.4		32	155.42	even	60
775.2.ck.a.324.1		32	155.92	even	4
775.2.ck.a.324.4		32	155.123	even	4
961.2.a.i.1.1		8	31.12	odd	30
961.2.a.j.1.1		8	31.19	even	15
961.2.c.i.439.1		16	31.10	even	15
961.2.c.i.521.1		16	31.2	even	5
961.2.c.j.439.1		16	31.21	odd	30
961.2.c.j.521.1		16	31.29	odd	10
961.2.d.n.531.1		16	31.7	even	15
961.2.d.n.628.1		16	31.25	even	3
961.2.d.o.531.1		16	31.24	odd	30
961.2.d.o.628.1		16	31.6	odd	6
961.2.d.p.374.4		16	31.3	odd	30
961.2.d.p.388.4		16	31.17	odd	30
961.2.d.q.374.4		16	31.28	even	15
961.2.d.q.388.4		16	31.14	even	15
961.2.g.j.844.1		16	31.4	even	5
961.2.g.j.846.1		16	31.5	even	3
961.2.g.k.844.1		16	31.27	odd	10
961.2.g.k.846.1		16	31.26	odd	6
961.2.g.l.448.1		16	1.1	even	1	trivial
961.2.g.l.547.1		16	31.20	even	15	inner
961.2.g.m.235.2		16	31.9	even	15
961.2.g.m.732.2		16	31.16	even	5
961.2.g.n.338.2		16	31.8	even	5
961.2.g.n.816.2		16	31.18	even	15
961.2.g.s.235.2		16	31.22	odd	30
961.2.g.s.732.2		16	31.15	odd	10
961.2.g.t.338.2		16	31.23	odd	10
961.2.g.t.816.2		16	31.13	odd	30
8649.2.a.be.1.8		8	93.50	odd	30
8649.2.a.bf.1.8		8	93.74	even	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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.831304 + 2.55849i) q^{2} +(-0.949606 + 1.05464i) q^{3} +(-4.23677 - 3.07819i) q^{4} +(-0.304192 + 0.526876i) q^{5} +(-1.90889 - 3.30629i) q^{6} +(0.180508 - 1.71742i) q^{7} +(7.04481 - 5.11835i) q^{8} +(0.103062 + 0.980572i) q^{9} +(-1.09513 - 1.21627i) q^{10} +(1.22177 - 0.543967i) q^{11} +(7.26966 - 1.54521i) q^{12} +(3.59045 + 0.763174i) q^{13} +(4.24394 + 1.88952i) q^{14} +(-0.266804 - 0.821139i) q^{15} +(4.00227 + 12.3177i) q^{16} +(2.52396 + 1.12374i) q^{17} +(-2.59446 - 0.551469i) q^{18} +(2.51157 - 0.533850i) q^{19} +(2.91062 - 1.29589i) q^{20} +(1.63986 + 1.82124i) q^{21} +(0.376072 + 3.57808i) q^{22} +(-0.436271 + 0.316969i) q^{23} +(-1.29175 + 12.2902i) q^{24} +(2.31493 + 4.00958i) q^{25} +(-4.93733 + 8.55171i) q^{26} +(-4.57641 - 3.32495i) q^{27} +(-6.05132 + 6.72067i) q^{28} +(2.51258 - 7.73291i) q^{29} +2.32267 q^{30} -17.4262 q^{32} +(-0.586508 + 1.80509i) q^{33} +(-4.97326 + 5.52336i) q^{34} +(0.849957 + 0.617530i) q^{35} +(2.58174 - 4.47170i) q^{36} +(3.87249 + 6.70735i) q^{37} +(-0.722025 + 6.86961i) q^{38} +(-4.21439 + 3.06194i) q^{39} +(0.553763 + 5.26870i) q^{40} +(-0.0696243 - 0.0773256i) q^{41} +(-6.02285 + 2.68155i) q^{42} +(-2.93904 + 0.624713i) q^{43} +(-6.85079 - 1.45618i) q^{44} +(-0.547990 - 0.243981i) q^{45} +(-0.448289 - 1.37969i) q^{46} +(-2.07813 - 6.39584i) q^{47} +(-16.7914 - 7.47602i) q^{48} +(3.93009 + 0.835366i) q^{49} +(-12.1829 + 2.58955i) q^{50} +(-3.58192 + 1.59477i) q^{51} +(-12.8627 - 14.2855i) q^{52} +(0.292549 + 2.78341i) q^{53} +(12.3112 - 8.94464i) q^{54} +(-0.0850494 + 0.809191i) q^{55} +(-7.51871 - 13.0228i) q^{56} +(-1.82198 + 3.15576i) q^{57} +(17.6959 + 12.8568i) q^{58} +(0.311970 - 0.346478i) q^{59} +(-1.39724 + 4.30025i) q^{60} +5.11468 q^{61} +1.70266 q^{63} +(6.48190 - 19.9492i) q^{64} +(-1.49428 + 1.65957i) q^{65} +(-4.13073 - 3.00115i) q^{66} +(-4.14923 + 7.18668i) q^{67} +(-7.23436 - 12.5303i) q^{68} +(0.0799956 - 0.761107i) q^{69} +(-2.28652 + 1.66125i) q^{70} +(-0.497420 - 4.73264i) q^{71} +(5.74497 + 6.38043i) q^{72} +(-6.85725 + 3.05304i) q^{73} +(-20.3799 + 4.33188i) q^{74} +(-6.42696 - 1.36609i) q^{75} +(-12.2842 - 5.46929i) q^{76} +(-0.713679 - 2.19648i) q^{77} +(-4.33049 - 13.3279i) q^{78} +(8.86044 + 3.94492i) q^{79} +(-7.70738 - 1.63825i) q^{80} +(4.95915 - 1.05410i) q^{81} +(0.255716 - 0.113852i) q^{82} +(11.1642 + 12.3991i) q^{83} +(-1.34155 - 12.7640i) q^{84} +(-1.35984 + 0.987981i) q^{85} +(0.844916 - 8.03884i) q^{86} +(5.76952 + 9.99310i) q^{87} +(5.82292 - 10.0856i) q^{88} +(-12.3911 - 9.00268i) q^{89} +(1.07977 - 1.19920i) q^{90} +(1.95880 - 6.02855i) q^{91} +2.82407 q^{92} +18.0912 q^{94} +(-0.482726 + 1.48568i) q^{95} +(16.5480 - 18.3784i) q^{96} +(1.03488 + 0.751881i) q^{97} +(-5.40437 + 9.36065i) q^{98} +(0.659316 + 1.14197i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 12 q^{3} - 14 q^{4} - 3 q^{5} - 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9} - 2 q^{10} + 7 q^{11} - 5 q^{12} + 7 q^{13} - 6 q^{14} - 14 q^{15} - 2 q^{16} + 6 q^{17} - 3 q^{18} + 16 q^{19}+ \cdots - 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 + 12 * q^3 - 14 * q^4 - 3 * q^5 - 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9 - 2 * q^10 + 7 * q^11 - 5 * q^12 + 7 * q^13 - 6 * q^14 - 14 * q^15 - 2 * q^16 + 6 * q^17 - 3 * q^18 + 16 * q^19 + 37 * q^20 - 9 * q^21 - 9 * q^22 - q^23 + 20 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 - 30 * q^28 + 14 * q^29 + 22 * q^30 - 42 * q^32 - 13 * q^33 + 32 * q^34 - 9 * q^35 + q^36 + 8 * q^37 + 8 * q^38 - 3 * q^39 - q^40 - 8 * q^41 - 69 * q^42 - 23 * q^43 - 39 * q^44 + 65 * q^45 - 34 * q^46 + 14 * q^47 - 34 * q^48 + 2 * q^49 + 3 * q^50 - 42 * q^51 - 29 * q^52 - 6 * q^53 + 46 * q^54 + 7 * q^55 - 30 * q^56 + 17 * q^57 + 15 * q^58 + 4 * q^59 + 75 * q^60 + 60 * q^61 - 46 * q^63 + 23 * q^64 + 12 * q^65 - 30 * q^66 + 13 * q^67 - 30 * q^68 + 38 * q^69 + 12 * q^70 - 14 * q^71 + 37 * q^72 - 2 * q^73 - 13 * q^74 - 13 * q^75 - 12 * q^76 - 18 * q^77 - 15 * q^78 - 18 * q^79 + 36 * q^80 + 23 * q^81 + 14 * q^82 + 16 * q^83 - 8 * q^84 - 37 * q^85 + 26 * q^86 + 15 * q^87 + 17 * q^88 - q^89 - 23 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 - 22 * q^95 - 8 * q^96 + 3 * q^97 - 10 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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