LMFDB - Embedded newform 961.2.g.k.844.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			844.1
Root			$1.14660i$ of defining polynomial
Character	$\chi$	$=$	961.844
Dual form			961.2.g.k.846.1

$q$ -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} +(-1.38815 + 0.295061i) q^{3} +(-4.23677 + 3.07819i) q^{4} +(-0.304192 + 0.526876i) q^{5} +(1.90889 + 3.30629i) q^{6} +(-1.57758 - 0.702385i) q^{7} +(7.04481 + 5.11835i) q^{8} +(-0.900731 + 0.401031i) q^{9} +(1.60088 + 0.340278i) q^{10} +(0.139796 + 1.33007i) q^{11} +(4.97303 - 5.52311i) q^{12} +(2.45615 + 2.72784i) q^{13} +(-0.485595 + 4.62012i) q^{14} +(0.266804 - 0.821139i) q^{15} +(4.00227 - 12.3177i) q^{16} +(0.288793 - 2.74768i) q^{17} +(1.77482 + 1.97113i) q^{18} +(-1.71811 + 1.90816i) q^{19} +(-0.333035 - 3.16861i) q^{20} +(2.39717 + 0.509534i) q^{21} +(3.28675 - 1.46335i) q^{22} +(0.436271 + 0.316969i) q^{23} +(-11.2895 - 5.02641i) q^{24} +(2.31493 + 4.00958i) q^{25} +(4.93733 - 8.55171i) q^{26} +(4.57641 - 3.32495i) q^{27} +(8.84593 - 1.88026i) q^{28} +(-2.51258 - 7.73291i) q^{29} -2.32267 q^{30} -17.4262 q^{32} +(-0.586508 - 1.80509i) q^{33} +(-7.27000 + 1.54529i) q^{34} +(0.849957 - 0.617530i) q^{35} +(2.58174 - 4.47170i) q^{36} +(-3.87249 - 6.70735i) q^{37} +(6.31027 + 2.80951i) q^{38} +(-4.21439 - 3.06194i) q^{39} +(-4.83971 + 2.15478i) q^{40} +(0.101778 + 0.0216336i) q^{41} +(-0.689139 - 6.55671i) q^{42} +(-2.01054 + 2.23293i) q^{43} +(-4.68648 - 5.20487i) q^{44} +(0.0627014 - 0.596564i) q^{45} +(0.448289 - 1.37969i) q^{46} +(-2.07813 + 6.39584i) q^{47} +(-1.92128 + 18.2798i) q^{48} +(-2.68849 - 2.98587i) q^{49} +(8.33407 - 9.25592i) q^{50} +(0.409845 + 3.89942i) q^{51} +(-18.8030 - 3.99669i) q^{52} +(2.55678 - 1.13835i) q^{53} +(-12.3112 - 8.94464i) q^{54} +(-0.743304 - 0.330940i) q^{55} +(-7.51871 - 13.0228i) q^{56} +(1.82198 - 3.15576i) q^{57} +(-17.6959 + 12.8568i) q^{58} +(-0.456044 + 0.0969352i) q^{59} +(1.39724 + 4.30025i) q^{60} -5.11468 q^{61} +1.70266 q^{63} +(6.48190 + 19.9492i) q^{64} +(-2.18437 + 0.464303i) q^{65} +(-4.13073 + 3.00115i) q^{66} +(-4.14923 + 7.18668i) q^{67} +(7.23436 + 12.5303i) q^{68} +(-0.699136 - 0.311275i) q^{69} +(-2.28652 - 1.66125i) q^{70} +(4.34730 - 1.93554i) q^{71} +(-8.39810 - 1.78507i) q^{72} +(-0.784611 - 7.46507i) q^{73} +(-13.9415 + 15.4836i) q^{74} +(-4.39655 - 4.88287i) q^{75} +(1.40557 - 13.3731i) q^{76} +(0.713679 - 2.19648i) q^{77} +(-4.33049 + 13.3279i) q^{78} +(1.01382 - 9.64582i) q^{79} +(5.27246 + 5.85566i) q^{80} +(-3.39245 + 3.76770i) q^{81} +(-0.0292592 - 0.278382i) q^{82} +(16.3200 + 3.46892i) q^{83} +(-11.7247 + 5.22018i) q^{84} +(1.35984 + 0.987981i) q^{85} +(7.38430 + 3.28770i) q^{86} +(5.76952 + 9.99310i) q^{87} +(-5.82292 + 10.0856i) q^{88} +(12.3911 - 9.00268i) q^{89} +(-1.57843 + 0.335505i) q^{90} +(-1.95880 - 6.02855i) q^{91} -2.82407 q^{92} +18.0912 q^{94} +(-0.482726 - 1.48568i) q^{95} +(24.1902 - 5.14178i) q^{96} +(1.03488 - 0.751881i) q^{97} +(-5.40437 + 9.36065i) q^{98} +(-0.659316 - 1.14197i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q - 6 q^{2} + 3 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9} - 17 q^{10} - 7 q^{11} - 10 q^{12} + 8 q^{13} - 21 q^{14} + 14 q^{15} - 2 q^{16} + 9 q^{17} + 12 q^{18} - 29 q^{19}+ \cdots + 6 q^{99}+O(q^{100})$ 16 * q - 6 * q^2 + 3 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9 - 17 * q^10 - 7 * q^11 - 10 * q^12 + 8 * q^13 - 21 * q^14 + 14 * q^15 - 2 * q^16 + 9 * q^17 + 12 * q^18 - 29 * q^19 - 8 * q^20 - 6 * q^21 - 21 * q^22 + q^23 - 5 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 + 45 * q^28 - 14 * q^29 - 22 * q^30 - 42 * q^32 - 13 * q^33 - 17 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 23 * q^38 - 3 * q^39 - q^40 - 8 * q^41 - 51 * q^42 - 37 * q^43 - 6 * q^44 - 70 * q^45 + 34 * q^46 + 14 * q^47 + 4 * q^48 - 43 * q^49 + 3 * q^50 + 33 * q^51 - 46 * q^52 - 9 * q^53 - 46 * q^54 + 8 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 - 11 * q^59 - 75 * q^60 - 60 * q^61 - 46 * q^63 + 23 * q^64 + 18 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 - 37 * q^69 + 12 * q^70 + 31 * q^71 - 38 * q^72 - 13 * q^73 + 43 * q^74 - 17 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 - 12 * q^79 + 6 * q^80 - 22 * q^81 - q^82 + 44 * q^83 + 23 * q^84 + 37 * q^85 + 19 * q^86 + 15 * q^87 - 17 * q^88 + q^89 + 7 * 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 $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$ .

$n$	$3$
$\chi(n)$	$e\left(\frac{14}{15}\right)$

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	−0.587636	−	0.809126i	$-0.699941\pi$
$2$	−0.831304	−	2.55849i	−0.587821	−	1.80913i	−0.000184800	−	1.00000i	$-0.500059\pi$
$3$	−1.38815	+	0.295061i	−0.801450	+	0.170353i	−0.590388	−	0.807119i	$-0.701025\pi$
$3$	−1.38815	+	0.295061i	−0.801450	+	0.170353i	−0.211062	+	0.977473i	$0.567692\pi$
$4$	−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
$7$	−1.57758	−	0.702385i	−0.596270	−	0.265477i	0.0863324	−	0.996266i	$-0.472485\pi$
$7$	−1.57758	−	0.702385i	−0.596270	−	0.265477i	−0.682603	+	0.730790i	$0.739152\pi$
$8$	7.04481	+	5.11835i	2.49072	+	1.80961i
$9$	−0.900731	+	0.401031i	−0.300244	+	0.133677i
$10$	1.60088	+	0.340278i	0.506243	+	0.107605i
$11$	0.139796	+	1.33007i	0.0421500	+	0.401030i	0.995173	+	0.0981331i	$0.0312871\pi$
$11$	0.139796	+	1.33007i	0.0421500	+	0.401030i	−0.953023	+	0.302897i	$0.902046\pi$
$12$	4.97303	−	5.52311i	1.43559	−	1.59438i
$13$	2.45615	+	2.72784i	0.681215	+	0.756566i	0.980268	−	0.197671i	$-0.0633377\pi$
$13$	2.45615	+	2.72784i	0.681215	+	0.756566i	−0.299054	+	0.954236i	$0.596671\pi$
$14$	−0.485595	+	4.62012i	−0.129781	+	1.23478i
$15$	0.266804	−	0.821139i	0.0688885	−	0.212017i
$16$	4.00227	−	12.3177i	1.00057	−	3.07943i
$17$	0.288793	−	2.74768i	0.0700427	−	0.666411i	−0.902021	−	0.431693i	$-0.857916\pi$
$17$	0.288793	−	2.74768i	0.0700427	−	0.666411i	0.972063	−	0.234719i	$-0.0754169\pi$
$18$	1.77482	+	1.97113i	0.418328	+	0.464600i
$19$	−1.71811	+	1.90816i	−0.394162	+	0.437761i	−0.907261	−	0.420568i	$-0.861831\pi$
$19$	−1.71811	+	1.90816i	−0.394162	+	0.437761i	0.513099	+	0.858329i	$0.328497\pi$
$20$	−0.333035	−	3.16861i	−0.0744688	−	0.708524i
$21$	2.39717	+	0.509534i	0.523106	+	0.111190i
$22$	3.28675	−	1.46335i	0.700737	−	0.311988i
$23$	0.436271	+	0.316969i	0.0909688	+	0.0660927i	0.632340	−	0.774691i	$-0.282095\pi$
$23$	0.436271	+	0.316969i	0.0909688	+	0.0660927i	−0.541371	+	0.840784i	$0.682095\pi$
$24$	−11.2895	−	5.02641i	−2.30446	−	1.02601i
$25$	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
$28$	8.84593	−	1.88026i	1.67172	−	0.355336i
$29$	−2.51258	−	7.73291i	−0.466574	−	1.43597i	−0.856993	−	0.515329i	$-0.827670\pi$
$29$	−2.51258	−	7.73291i	−0.466574	−	1.43597i	0.390419	−	0.920637i	$-0.372330\pi$
$30$	−2.32267			−0.424060
$31$		0			0
$31$		0			0
$32$	−17.4262			−3.08054
$33$	−0.586508	−	1.80509i	−0.102098	−	0.314225i
$34$	−7.27000	+	1.54529i	−1.24679	+	0.265014i
$35$	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	$-0.946993\pi$
$37$	−3.87249	−	6.70735i	−0.636633	−	1.10268i	0.349533	−	0.936924i	$-0.386340\pi$
$38$	6.31027	+	2.80951i	1.02366	+	0.455763i
$39$	−4.21439	−	3.06194i	−0.674843	−	0.490302i
$40$	−4.83971	+	2.15478i	−0.765225	+	0.340700i
$41$	0.101778	+	0.0216336i	0.0158951	+	0.00337860i	0.215852	−	0.976426i	$-0.430747\pi$
$41$	0.101778	+	0.0216336i	0.0158951	+	0.00337860i	−0.199957	+	0.979805i	$0.564080\pi$
$42$	−0.689139	−	6.55671i	−0.106336	−	1.01172i
$43$	−2.01054	+	2.23293i	−0.306604	+	0.340519i	−0.876680	−	0.481073i	$-0.840247\pi$
$43$	−2.01054	+	2.23293i	−0.306604	+	0.340519i	0.570076	+	0.821592i	$0.306914\pi$
$44$	−4.68648	−	5.20487i	−0.706514	−	0.784663i
$45$	0.0627014	−	0.596564i	0.00934697	−	0.0889305i
$46$	0.448289	−	1.37969i	0.0660967	−	0.203425i
$47$	−2.07813	+	6.39584i	−0.303127	+	0.932929i	0.677243	+	0.735760i	$0.263175\pi$
$47$	−2.07813	+	6.39584i	−0.303127	+	0.932929i	−0.980370	+	0.197169i	$0.936825\pi$
$48$	−1.92128	+	18.2798i	−0.277314	+	2.63846i
$49$	−2.68849	−	2.98587i	−0.384070	−	0.426553i
$50$	8.33407	−	9.25592i	1.17862	−	1.30898i
$51$	0.409845	+	3.89942i	0.0573898	+	0.546027i
$52$	−18.8030	−	3.99669i	−2.60750	−	0.554242i
$53$	2.55678	−	1.13835i	0.351201	−	0.156365i	−0.223551	−	0.974692i	$-0.571765\pi$
$53$	2.55678	−	1.13835i	0.351201	−	0.156365i	0.574752	+	0.818327i	$0.305098\pi$
$54$	−12.3112	−	8.94464i	−1.67535	−	1.21721i
$55$	−0.743304	−	0.330940i	−0.100227	−	0.0446240i
$56$	−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
$59$	−0.456044	+	0.0969352i	−0.0593719	+	0.0126199i	−0.237502	−	0.971387i	$-0.576329\pi$
$59$	−0.456044	+	0.0969352i	−0.0593719	+	0.0126199i	0.178130	+	0.984007i	$0.442995\pi$
$60$	1.39724	+	4.30025i	0.180382	+	0.555160i
$61$	−5.11468			−0.654867			−0.327434	−	0.944874i	$-0.606184\pi$
$61$	−5.11468			−0.654867			−0.327434	+	0.944874i	$0.606184\pi$
$62$		0			0
$63$	1.70266			0.214514
$64$	6.48190	+	19.9492i	0.810238	+	2.49365i
$65$	−2.18437	+	0.464303i	−0.270938	+	0.0575897i
$66$	−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
$69$	−0.699136	−	0.311275i	−0.0841661	−	0.0374731i
$70$	−2.28652	−	1.66125i	−0.273291	−	0.198558i
$71$	4.34730	−	1.93554i	0.515929	−	0.229706i	−0.132219	−	0.991220i	$-0.542210\pi$
$71$	4.34730	−	1.93554i	0.515929	−	0.229706i	0.648148	+	0.761514i	$0.275544\pi$
$72$	−8.39810	−	1.78507i	−0.989725	−	0.210373i
$73$	−0.784611	−	7.46507i	−0.0918317	−	0.873720i	−0.939351	−	0.342956i	$-0.888572\pi$
$73$	−0.784611	−	7.46507i	−0.0918317	−	0.873720i	0.847520	−	0.530764i	$-0.178095\pi$
$74$	−13.9415	+	15.4836i	−1.62066	+	1.79993i
$75$	−4.39655	−	4.88287i	−0.507670	−	0.563825i
$76$	1.40557	−	13.3731i	0.161230	−	1.53400i
$77$	0.713679	−	2.19648i	0.0813313	−	0.250312i
$78$	−4.33049	+	13.3279i	−0.490332	+	1.50909i
$79$	1.01382	−	9.64582i	0.114063	−	1.08524i	−0.776417	−	0.630219i	$-0.782965\pi$
$79$	1.01382	−	9.64582i	0.114063	−	1.08524i	0.890481	−	0.455021i	$-0.150368\pi$
$80$	5.27246	+	5.85566i	0.589479	+	0.654682i
$81$	−3.39245	+	3.76770i	−0.376939	+	0.418633i
$82$	−0.0292592	−	0.278382i	−0.00323113	−	0.0307422i
$83$	16.3200	+	3.46892i	1.79135	+	0.380764i	0.979234	−	0.202731i	$-0.0649817\pi$
$83$	16.3200	+	3.46892i	1.79135	+	0.380764i	0.812117	+	0.583495i	$0.198315\pi$
$84$	−11.7247	+	5.22018i	−1.27927	+	0.569568i
$85$	1.35984	+	0.987981i	0.147495	+	0.107162i
$86$	7.38430	+	3.28770i	0.796269	+	0.354522i
$87$	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	0.313468	−	0.949599i	$-0.398509\pi$
$89$	12.3911	−	9.00268i	1.31346	−	0.954282i	0.999989	−	0.00468333i	$-0.00149075\pi$
$90$	−1.57843	+	0.335505i	−0.166381	+	0.0353653i
$91$	−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
$96$	24.1902	−	5.14178i	2.46890	−	0.524781i
$97$	1.03488	−	0.751881i	0.105076	−	0.0763420i	−0.534007	−	0.845480i	$-0.679314\pi$
$97$	1.03488	−	0.751881i	0.105076	−	0.0763420i	0.639082	+	0.769138i	$0.279314\pi$
$98$	−5.40437	+	9.36065i	−0.545924	+	0.945568i
$99$	−0.659316	−	1.14197i	−0.0662638	−	0.114772i
$100$	−22.1501	−	9.86187i	−2.21501	−	0.986187i
$101$	−6.56941	−	4.77296i	−0.653681	−	0.474927i	0.210842	−	0.977520i	$-0.432379\pi$
$101$	−6.56941	−	4.77296i	−0.653681	−	0.474927i	−0.864523	+	0.502593i	$0.832379\pi$
$102$	9.63591	−	4.29018i	0.954097	−	0.424791i
$103$	−14.8214	−	3.15038i	−1.46040	−	0.310417i	−0.591859	−	0.806042i	$-0.701606\pi$
$103$	−14.8214	−	3.15038i	−1.46040	−	0.310417i	−0.868536	+	0.495625i	$0.834939\pi$
$104$	3.34111	+	31.7885i	0.327623	+	3.11712i
$105$	−0.997661	+	1.10801i	−0.0973618	+	0.108131i
$106$	−5.03792	−	5.59518i	−0.489327	−	0.543452i
$107$	1.29360	−	12.3078i	0.125057	−	1.18984i	−0.734430	−	0.678685i	$-0.762550\pi$
$107$	1.29360	−	12.3078i	0.125057	−	1.18984i	0.859487	−	0.511157i	$-0.170783\pi$
$108$	−9.15433	+	28.1741i	−0.880876	+	2.71106i
$109$	2.22788	−	6.85672i	0.213392	−	0.656755i	−0.785871	−	0.618390i	$-0.787785\pi$
$109$	2.22788	−	6.85672i	0.213392	−	0.656755i	0.999264	−	0.0383645i	$-0.0122148\pi$
$110$	−0.228796	+	2.17685i	−0.0218148	+	0.207554i
$111$	7.35468	+	8.16820i	0.698075	+	0.775291i
$112$	−14.9657	+	16.6211i	−1.41413	+	1.57055i
$113$	−1.74268	−	16.5805i	−0.163937	−	1.55976i	−0.699108	−	0.715016i	$-0.746420\pi$
$113$	−1.74268	−	16.5805i	−0.163937	−	1.55976i	0.535171	−	0.844744i	$-0.320247\pi$
$114$	−9.58859	−	2.03812i	−0.898054	−	0.190887i
$115$	−0.299714	+	0.133441i	−0.0279484	+	0.0124434i
$116$	34.4486	+	25.0284i	3.19847	+	2.32383i
$117$	−3.30628	−	1.47205i	−0.305666	−	0.136091i
$118$	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
$121$	9.01009	−	1.91515i	0.819099	−	0.174105i
$122$	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
$127$	12.6273	−	2.68402i	1.12049	−	0.238168i	0.389818	−	0.920892i	$-0.372538\pi$
$127$	12.6273	−	2.68402i	1.12049	−	0.238168i	0.730677	+	0.682724i	$0.239205\pi$
$128$	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
$131$	−2.22703	−	0.991536i	−0.194576	−	0.0866309i	0.307136	−	0.951666i	$-0.400630\pi$
$131$	−2.22703	−	0.991536i	−0.194576	−	0.0866309i	−0.501712	+	0.865035i	$0.667296\pi$
$132$	8.04130	+	5.84235i	0.699906	+	0.508511i
$133$	4.05072	−	1.80350i	0.351242	−	0.156383i
$134$	21.8363	+	4.64146i	1.88637	+	0.400961i
$135$	0.359732	+	3.42262i	0.0309608	+	0.294572i
$136$	16.0981	−	17.8788i	1.38040	−	1.53309i
$137$	5.44928	+	6.05204i	0.465564	+	0.517061i	0.929507	−	0.368804i	$-0.120233\pi$
$137$	5.44928	+	6.05204i	0.465564	+	0.517061i	−0.463944	+	0.885865i	$0.653566\pi$
$138$	−0.215201	+	2.04750i	−0.0183191	+	0.174294i
$139$	−0.418212	+	1.28712i	−0.0354723	+	0.109172i	−0.967225	−	0.253921i	$-0.918280\pi$
$139$	−0.418212	+	1.28712i	−0.0354723	+	0.109172i	0.931753	+	0.363094i	$0.118280\pi$
$140$	−1.70020	+	5.23267i	−0.143693	+	0.442241i
$141$	0.997604	−	9.49157i	0.0840134	−	0.799334i
$142$	−8.56599	−	9.51349i	−0.718842	−	0.798354i
$143$	−3.28484	+	3.64819i	−0.274692	+	0.305077i
$144$	1.33482	+	12.7000i	0.111235	+	1.05833i
$145$	4.83859	+	1.02847i	0.401823	+	0.0854101i
$146$	−18.4471	+	8.21316i	−1.52669	+	0.679726i
$147$	4.61305	+	3.35158i	0.380478	+	0.276433i
$148$	37.0534	+	16.4972i	3.04577	+	1.35606i
$149$	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	$-0.658326\pi$
$151$	2.59566	−	1.88585i	0.211232	−	0.153469i	0.688371	+	0.725359i	$0.258326\pi$
$152$	−21.8704	+	4.64869i	−1.77392	+	0.377059i
$153$	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	0.901616	−	0.432537i	$-0.142382\pi$
$157$	−1.02803	−	3.16395i	−0.0820456	−	0.252510i	−0.983662	+	0.180027i	$0.942382\pi$
$158$	−25.5215	+	5.42477i	−2.03038	+	0.431571i
$159$	−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
$162$	12.4598	+	5.54745i	0.978933	+	0.435849i
$163$	−1.40797	−	1.02295i	−0.110281	−	0.0801236i	0.531278	−	0.847198i	$-0.321712\pi$
$163$	−1.40797	−	1.02295i	−0.110281	−	0.0801236i	−0.641559	+	0.767074i	$0.721712\pi$
$164$	−0.497803	+	0.221636i	−0.0388719	+	0.0173069i
$165$	1.12947	+	0.240076i	0.0879289	+	0.0186899i
$166$	−4.69167	−	44.6383i	−0.364144	−	3.46460i
$167$	−9.37885	+	10.4163i	−0.725757	+	0.806035i	−0.987251	−	0.159170i	$-0.949118\pi$
$167$	−9.37885	+	10.4163i	−0.725757	+	0.806035i	0.261494	+	0.965205i	$0.415785\pi$
$168$	14.2796	+	15.8591i	1.10170	+	1.22356i
$169$	−0.0495237	+	0.471186i	−0.00380951	+	0.0362451i
$170$	1.39730	−	4.30045i	0.107168	−	0.329829i
$171$	0.782326	−	2.40775i	0.0598260	−	0.184125i
$172$	1.64480	−	15.6492i	0.125415	−	1.19324i
$173$	−0.00801678	−	0.00890353i	−0.000609504	−	0.000676923i	0.742840	−	0.669469i	$-0.233478\pi$
$173$	−0.00801678	−	0.00890353i	−0.000609504	−	0.000676923i	−0.743450	+	0.668792i	$0.766812\pi$
$174$	20.7710	−	23.0686i	1.57465	−	1.74882i
$175$	−0.835728	−	7.95143i	−0.0631751	−	0.601071i
$176$	16.9429	+	3.60132i	1.27712	+	0.271460i
$177$	0.604457	−	0.269122i	0.0454338	−	0.0202284i
$178$	−33.3341	−	24.2186i	−2.49849	−	1.81526i
$179$	−9.11536	−	4.05842i	−0.681314	−	0.303341i	0.0367430	−	0.999325i	$-0.488302\pi$
$179$	−9.11536	−	4.05842i	−0.681314	−	0.303341i	−0.718057	+	0.695984i	$0.754968\pi$
$180$	1.57069	+	2.72051i	0.117072	+	0.202775i
$181$	9.30158	−	16.1108i	0.691381	−	1.19751i	−0.280004	−	0.959999i	$-0.590336\pi$
$181$	9.30158	−	16.1108i	0.691381	−	1.19751i	0.971385	−	0.237509i	$-0.0763308\pi$
$182$	−13.7956	+	10.0231i	−1.02260	+	0.742963i
$183$	7.09995	−	1.50914i	0.524843	−	0.111559i
$184$	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
$189$	−9.55506	+	2.03099i	−0.695028	+	0.147733i
$190$	−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
$193$	11.6263	+	5.17636i	0.836879	+	0.372602i	0.780001	−	0.625779i	$-0.215219\pi$
$193$	11.6263	+	5.17636i	0.836879	+	0.372602i	0.0568780	+	0.998381i	$0.481885\pi$
$194$	−2.78398	−	2.02268i	−0.199878	−	0.145220i
$195$	2.89524	−	1.28905i	0.207333	−	0.0923105i
$196$	20.5816	+	4.37476i	1.47012	+	0.312483i
$197$	0.310303	+	2.95233i	0.0221082	+	0.210345i	0.999999	+	0.00123020i	$0.000391585\pi$
$197$	0.310303	+	2.95233i	0.0221082	+	0.210345i	−0.977891	+	0.209115i	$0.932942\pi$
$198$	−2.37363	+	2.63618i	−0.168686	+	0.187345i
$199$	−8.82185	−	9.79766i	−0.625365	−	0.694538i	0.344333	−	0.938848i	$-0.388105\pi$
$199$	−8.82185	−	9.79766i	−0.625365	−	0.694538i	−0.969697	+	0.244310i	$0.921439\pi$
$200$	−4.21420	+	40.0954i	−0.297989	+	2.83517i
$201$	3.63926	−	11.2005i	0.256694	−	0.790021i
$202$	−6.75039	+	20.7755i	−0.474955	+	1.46176i
$203$	−1.46769	+	13.9641i	−0.103011	+	0.980088i
$204$	−13.7396	−	15.2593i	−0.961963	−	1.06837i
$205$	−0.0423583	+	0.0470436i	−0.00295843	+	0.00328567i
$206$	4.26085	+	40.5393i	0.296868	+	2.82451i
$207$	−0.520078	−	0.110546i	−0.0361479	−	0.00768347i
$208$	43.4310	−	19.3367i	3.01140	−	1.34076i
$209$	−2.77816	−	2.01845i	−0.192169	−	0.139619i
$210$	3.66420	+	1.63141i	0.252854	+	0.112578i
$211$	−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
$214$	−32.5648	+	6.92186i	−2.22608	+	0.473169i
$215$	−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
$220$	4.16791	−	0.885916i	0.281000	−	0.0597285i
$221$	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	0.664751	−	0.747065i	$-0.268538\pi$
$223$	−4.69801	−	8.13718i	−0.314602	−	0.544906i	−0.979353	+	0.202159i	$0.935204\pi$
$224$	27.4912	+	12.2399i	1.83684	+	0.817812i
$225$	−3.69310	−	2.68320i	−0.246207	−	0.178880i
$226$	−40.9723	+	18.2420i	−2.72543	+	1.21344i
$227$	−8.27456	−	1.75881i	−0.549202	−	0.116737i	−0.0750505	−	0.997180i	$-0.523912\pi$
$227$	−8.27456	−	1.75881i	−0.549202	−	0.116737i	−0.474152	+	0.880443i	$0.657245\pi$
$228$	1.99473	+	18.9786i	0.132104	+	1.25689i
$229$	15.2852	−	16.9760i	1.01008	−	1.12180i	0.0175421	−	0.999846i	$-0.494416\pi$
$229$	15.2852	−	16.9760i	1.01008	−	1.12180i	0.992535	−	0.121958i	$-0.0389174\pi$
$230$	0.590561	+	0.655884i	0.0389404	+	0.0432477i
$231$	−0.342601	+	3.25963i	−0.0225415	+	0.214468i
$232$	21.8792	−	67.3372i	1.43644	−	4.42090i
$233$	5.02260	−	15.4580i	0.329042	−	1.01269i	−0.640542	−	0.767923i	$-0.721290\pi$
$233$	5.02260	−	15.4580i	0.329042	−	1.01269i	0.969583	−	0.244762i	$-0.0787099\pi$
$234$	−1.01770	+	9.68281i	−0.0665294	+	0.632985i
$235$	−2.73766	−	3.04048i	−0.178585	−	0.198339i
$236$	1.63377	−	1.81449i	0.106349	−	0.118113i
$237$	1.43877	+	13.6890i	0.0934583	+	0.889197i
$238$	12.5544	+	2.66852i	0.813781	+	0.172975i
$239$	16.6932	−	7.43230i	1.07979	−	0.480755i	0.211791	−	0.977315i	$-0.432070\pi$
$239$	16.6932	−	7.43230i	1.07979	−	0.480755i	0.868003	+	0.496560i	$0.165404\pi$
$240$	−9.04675	−	6.57285i	−0.583965	−	0.424275i
$241$	−16.6005	−	7.39103i	−1.06933	−	0.476098i	−0.204868	−	0.978790i	$-0.565677\pi$
$241$	−16.6005	−	7.39103i	−1.06933	−	0.476098i	−0.864466	+	0.502691i	$0.832343\pi$
$242$	−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
$245$	2.39100	−	0.508223i	0.152756	−	0.0324692i
$246$	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
$251$	22.4291	−	4.76746i	1.41571	−	0.300919i	0.564368	−	0.825523i	$-0.309120\pi$
$251$	22.4291	−	4.76746i	1.41571	−	0.300919i	0.851346	+	0.524604i	$0.175787\pi$
$252$	−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
$255$	−2.17918	−	0.970233i	−0.136465	−	0.0607583i
$256$	−13.0179	−	9.45807i	−0.813620	−	0.591129i
$257$	0.0970122	−	0.0431926i	0.00605145	−	0.00269428i	−0.403709	−	0.914888i	$-0.632279\pi$
$257$	0.0970122	−	0.0431926i	0.00605145	−	0.00269428i	0.409760	+	0.912193i	$0.365612\pi$
$258$	−11.2206	−	2.38501i	−0.698564	−	0.148484i
$259$	1.39803	+	13.3014i	0.0868694	+	0.826507i
$260$	7.82547	−	8.69107i	0.485315	−	0.538997i
$261$	5.36430	+	5.95765i	0.332042	+	0.368770i
$262$	−0.685500	+	6.52209i	−0.0423503	+	0.402936i
$263$	−2.25499	+	6.94015i	−0.139049	+	0.427948i	−0.996198	−	0.0871204i	$-0.972234\pi$
$263$	−2.25499	+	6.94015i	−0.139049	+	0.427948i	0.857149	+	0.515068i	$0.172234\pi$
$264$	5.10723	−	15.7184i	0.314328	−	0.967403i
$265$	−0.177982	+	1.69338i	−0.0109333	+	0.104024i
$266$	−7.98161	−	8.86448i	−0.489384	−	0.543516i
$267$	−14.5444	+	16.1532i	−0.890105	+	0.988561i
$268$	−4.54266	−	43.2205i	−0.277487	−	2.64011i
$269$	−15.8649	−	3.37219i	−0.967302	−	0.205606i	−0.302934	−	0.953012i	$-0.597966\pi$
$269$	−15.8649	−	3.37219i	−0.967302	−	0.205606i	−0.664368	+	0.747405i	$0.731299\pi$
$270$	8.45770	−	3.76561i	0.514719	−	0.229168i
$271$	4.16291	+	3.02453i	0.252879	+	0.183727i	0.707002	−	0.707212i	$-0.250047\pi$
$271$	4.16291	+	3.02453i	0.252879	+	0.183727i	−0.454123	+	0.890939i	$0.650047\pi$
$272$	−32.6894	−	14.5543i	−1.98209	−	0.882482i
$273$	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
$276$	3.92024	−	0.833274i	0.235971	−	0.0501572i
$277$	−5.22944	−	16.0946i	−0.314207	−	0.967029i	−0.976080	−	0.217413i	$-0.930238\pi$
$277$	−5.22944	−	16.0946i	−0.314207	−	0.967029i	0.661873	−	0.749616i	$-0.269762\pi$
$278$	3.64076			0.218358
$279$		0			0
$280$	9.14853			0.546729
$281$	0.589193	+	1.81335i	0.0351483	+	0.108175i	0.967091	−	0.254429i	$-0.0818876\pi$
$281$	0.589193	+	1.81335i	0.0351483	+	0.108175i	−0.931943	+	0.362605i	$0.881888\pi$
$282$	−25.1134	+	5.33802i	−1.49548	+	0.317874i
$283$	12.3859	−	8.99888i	0.736265	−	0.534928i	−0.155274	−	0.987871i	$-0.549626\pi$
$283$	12.3859	−	8.99888i	0.736265	−	0.534928i	0.891539	+	0.452944i	$0.149626\pi$
$284$	−12.4605	+	21.5823i	−0.739396	+	1.28067i
$285$	1.10846	+	1.91991i	0.0656596	+	0.113726i
$286$	12.0646	+	5.37148i	0.713392	+	0.317623i
$287$	−0.145368	−	0.105616i	−0.00858081	−	0.00623433i
$288$	15.6963	−	6.98844i	0.924913	−	0.411798i
$289$	9.16214	+	1.94747i	0.538949	+	0.114557i
$290$	−1.39100	−	13.2345i	−0.0816822	−	0.777154i
$291$	−1.21471	+	1.34908i	−0.0712078	+	0.0790843i
$292$	26.3032	+	29.2126i	1.53928	+	1.70954i
$293$	−2.80070	+	26.6469i	−0.163619	+	1.55673i	0.537241	+	0.843429i	$0.319467\pi$
$293$	−2.80070	+	26.6469i	−0.163619	+	1.55673i	−0.700860	+	0.713299i	$0.747200\pi$
$294$	4.74013	−	14.5886i	0.276450	−	0.850826i
$295$	0.0876522	−	0.269766i	0.00510331	−	0.0157064i
$296$	7.04963	−	67.0727i	0.409751	−	3.89852i
$297$	5.06217	+	5.62211i	0.293737	+	0.326228i
$298$	16.2075	−	18.0003i	0.938876	−	1.04273i
$299$	0.206908	+	1.96860i	0.0119658	+	0.113847i
$300$	33.6576	+	7.15414i	1.94322	+	0.413045i
$301$	4.74017	−	2.11046i	0.273219	−	0.121645i
$302$	−6.98272	−	5.07324i	−0.401810	−	0.291932i
$303$	10.5277	+	4.68721i	0.604798	+	0.269273i
$304$	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
$307$	−8.75565	+	1.86107i	−0.499712	+	0.106217i	−0.450870	−	0.892590i	$-0.648886\pi$
$307$	−8.75565	+	1.86107i	−0.499712	+	0.106217i	−0.0488415	+	0.998807i	$0.515553\pi$
$308$	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
$313$	−0.441458	+	0.0938349i	−0.0249527	+	0.00530386i	−0.220371	−	0.975416i	$-0.570727\pi$
$313$	−0.441458	+	0.0938349i	−0.0249527	+	0.00530386i	0.195418	+	0.980720i	$0.437394\pi$
$314$	−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
$317$	−5.09835	−	2.26993i	−0.286352	−	0.127492i	0.258534	−	0.966002i	$-0.416761\pi$
$317$	−5.09835	−	2.26993i	−0.286352	−	0.127492i	−0.544886	+	0.838510i	$0.683427\pi$
$318$	8.64432	+	6.28047i	0.484750	+	0.352191i
$319$	9.93404	−	4.42292i	0.556199	−	0.247636i
$320$	−12.4825	−	2.65324i	−0.697794	−	0.148321i
$321$	1.83584	+	17.4668i	0.102466	+	0.974903i
$322$	−1.67629	+	1.86171i	−0.0934159	+	0.103749i
$323$	4.74683	+	5.27189i	0.264121	+	0.293336i
$324$	2.77533	−	26.4055i	0.154185	−	1.46697i
$325$	−5.25165	+	16.1629i	−0.291309	+	0.896557i
$326$	−1.44676	+	4.45266i	−0.0801284	+	0.246610i
$327$	−1.06949	+	10.1755i	−0.0591430	+	0.562708i
$328$	0.606279	+	0.673341i	0.0334761	+	0.0371790i
$329$	7.77077	−	8.63031i	0.428416	−	0.475804i
$330$	−0.324699	−	3.08931i	−0.0178741	−	0.170061i
$331$	−23.6765	−	5.03260i	−1.30138	−	0.276617i	−0.495454	−	0.868634i	$-0.664998\pi$
$331$	−23.6765	−	5.03260i	−1.30138	−	0.276617i	−0.805925	+	0.592018i	$0.798332\pi$
$332$	−79.8221	+	35.5391i	−4.38080	+	1.95046i
$333$	6.17793	+	4.48853i	0.338548	+	0.245970i
$334$	34.4466	+	15.3366i	1.88483	+	0.839182i
$335$	−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	$-0.797182\pi$
$337$	−8.92830	+	6.48679i	−0.486355	+	0.353358i	0.317426	+	0.948283i	$0.397182\pi$
$338$	1.24669	−	0.264993i	0.0678112	−	0.0144137i
$339$	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
$344$	−25.5928	+	5.43991i	−1.37987	+	0.293301i
$345$	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	0.999998	−	0.00187589i	$-0.000597114\pi$
$347$	9.28369	+	16.0798i	0.498375	+	0.863210i	−0.501624	+	0.865086i	$0.667264\pi$
$348$	−55.2048	−	24.5788i	−2.95929	−	1.31756i
$349$	26.0298	+	18.9118i	1.39334	+	1.01232i	0.995489	+	0.0948756i	$0.0302453\pi$
$349$	26.0298	+	18.9118i	1.39334	+	1.01232i	0.397855	+	0.917448i	$0.369755\pi$
$350$	−19.6489	+	8.74825i	−1.05028	+	0.467614i
$351$	20.3103	+	4.31709i	1.08408	+	0.230429i
$352$	−2.43610	−	23.1780i	−0.129845	−	1.23539i
$353$	21.5550	−	23.9392i	1.14725	−	1.27416i	0.191010	−	0.981588i	$-0.438824\pi$
$353$	21.5550	−	23.9392i	1.14725	−	1.27416i	0.956245	−	0.292567i	$-0.0945096\pi$
$354$	−1.19103	−	1.32278i	−0.0633027	−	0.0703047i
$355$	−0.302623	+	2.87926i	−0.0160615	+	0.152815i
$356$	−24.7864	+	76.2846i	−1.31367	+	4.04307i
$357$	2.09233	−	6.43952i	0.110738	−	0.340815i
$358$	−2.80579	+	26.6953i	−0.148291	+	1.41089i
$359$	14.1603	+	15.7266i	0.747353	+	0.830019i	0.990143	−	0.140059i	$-0.0447293\pi$
$359$	14.1603	+	15.7266i	0.747353	+	0.830019i	−0.242790	+	0.970079i	$0.578063\pi$
$360$	3.49514	−	3.88175i	0.184210	−	0.204586i
$361$	1.29689	+	12.3391i	0.0682573	+	0.649425i
$362$	−48.9518	−	10.4050i	−2.57285	−	0.546876i
$363$	−11.9423	+	5.31705i	−0.626808	+	0.279073i
$364$	26.8560	+	19.5120i	1.40764	+	1.02271i
$365$	4.17184	+	1.85742i	0.218364	+	0.0972219i
$366$	−9.76334	−	16.9106i	−0.510338	−	0.883931i
$367$	−6.49822	+	11.2552i	−0.339204	+	0.587519i	−0.984283	−	0.176597i	$-0.943491\pi$
$367$	−6.49822	+	11.2552i	−0.339204	+	0.587519i	0.645079	+	0.764116i	$0.276824\pi$
$368$	5.65042	−	4.10527i	0.294549	−	0.214002i
$369$	−0.100350	+	0.0213301i	−0.00522403	+	0.00111040i
$370$	−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
$375$	8.13271	−	1.72866i	0.419971	−	0.0892676i
$376$	−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
$379$	−13.6627	−	6.08305i	−0.701808	−	0.312465i	0.0246303	−	0.999697i	$-0.492159\pi$
$379$	−13.6627	−	6.08305i	−0.701808	−	0.312465i	−0.726438	+	0.687231i	$0.758826\pi$
$380$	6.61840	+	4.80855i	0.339517	+	0.246673i
$381$	−16.7367	+	7.45166i	−0.857448	+	0.381760i
$382$	3.15269	+	0.670125i	0.161306	+	0.0342866i
$383$	1.21779	+	11.5865i	0.0622263	+	0.592044i	0.980558	+	0.196231i	$0.0628703\pi$
$383$	1.21779	+	11.5865i	0.0622263	+	0.592044i	−0.918331	+	0.395812i	$0.870463\pi$
$384$	−20.4887	+	22.7550i	−1.04556	+	1.16121i
$385$	0.940176	+	1.04417i	0.0479158	+	0.0532159i
$386$	3.57868	−	34.0489i	0.182150	−	1.73304i
$387$	0.915480	−	2.81756i	0.0465365	−	0.143225i
$388$	−2.07009	+	6.37110i	−0.105093	+	0.323443i
$389$	−1.50541	+	14.3230i	−0.0763274	+	0.726207i	0.887703	+	0.460416i	$0.152300\pi$
$389$	−1.50541	+	14.3230i	−0.0763274	+	0.726207i	−0.964031	+	0.265791i	$0.914367\pi$
$390$	−5.70484	−	6.33586i	−0.288876	−	0.320829i
$391$	0.996924	−	1.10720i	0.0504166	−	0.0559933i
$392$	−3.65716	−	34.7956i	−0.184715	−	1.75744i
$393$	3.38402	+	0.719295i	0.170701	+	0.0362836i
$394$	7.29556	−	3.24819i	0.367545	−	0.163642i
$395$	4.77376	+	3.46834i	0.240194	+	0.174511i
$396$	6.30858	+	2.80876i	0.317018	+	0.141145i
$397$	−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
$400$	58.6540	−	12.4673i	2.93270	−	0.623365i
$401$	9.58670	+	29.5048i	0.478737	+	1.47340i	0.840851	+	0.541267i	$0.182055\pi$
$401$	9.58670	+	29.5048i	0.478737	+	1.47340i	−0.362114	+	0.932134i	$0.617945\pi$
$402$	−31.6817			−1.58014
$403$		0			0
$404$	42.5252			2.11571
$405$	−0.953153	−	2.93350i	−0.0473626	−	0.145767i
$406$	36.9471	−	7.85335i	1.83365	−	0.389755i
$407$	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	0.773056	−	0.634337i	$-0.218727\pi$
$409$	−3.29291	−	5.70349i	−0.162824	−	0.282019i	−0.935880	+	0.352318i	$0.885394\pi$
$410$	0.155573	+	0.0692657i	0.00768322	+	0.00342079i
$411$	−9.35015	−	6.79328i	−0.461209	−	0.335088i
$412$	72.4923	−	32.2757i	3.57144	−	1.59011i
$413$	0.787533	+	0.167395i	0.0387520	+	0.00823699i
$414$	0.149512	+	1.42251i	0.00734811	+	0.0699126i
$415$	−6.79210	+	7.54339i	−0.333411	+	0.370290i
$416$	−42.8014	−	47.5358i	−2.09851	−	2.33063i
$417$	0.200762	−	1.91012i	0.00983136	−	0.0935391i
$418$	−2.85469	+	8.78583i	−0.139627	+	0.429729i
$419$	−4.53389	+	13.9539i	−0.221495	+	0.681692i	0.777133	+	0.629336i	$0.216673\pi$
$419$	−4.53389	+	13.9539i	−0.221495	+	0.681692i	−0.998628	+	0.0523559i	$0.983327\pi$
$420$	0.816176	−	7.76540i	0.0398253	−	0.378913i
$421$	−17.8764	−	19.8538i	−0.871243	−	0.967613i	0.128467	−	0.991714i	$-0.458994\pi$
$421$	−17.8764	−	19.8538i	−0.871243	−	0.967613i	−0.999710	+	0.0241008i	$0.992328\pi$
$422$	−32.9993	+	36.6494i	−1.60638	+	1.78407i
$423$	−0.693091	−	6.59432i	−0.0336993	−	0.320627i
$424$	23.8385	+	5.06703i	1.15770	+	0.246077i
$425$	11.6856	−	5.20277i	0.566835	−	0.252371i
$426$	14.6980	+	10.6787i	0.712118	+	0.517384i
$427$	8.06883	+	3.59247i	0.390478	+	0.173852i
$428$	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
$431$	−3.90086	+	0.829154i	−0.187898	+	0.0399389i	−0.300899	−	0.953656i	$-0.597287\pi$
$431$	−3.90086	+	0.829154i	−0.187898	+	0.0399389i	0.113002	+	0.993595i	$0.463954\pi$
$432$	−22.6399	−	69.6783i	−1.08926	−	3.35240i
$433$	18.0766			0.868704			0.434352	−	0.900743i	$-0.356977\pi$
$433$	18.0766			0.868704			0.434352	+	0.900743i	$0.356977\pi$
$434$		0			0
$435$	−7.02016			−0.336591
$436$	11.6673	+	35.9082i	0.558762	+	1.71969i
$437$	−1.35439	+	0.287884i	−0.0647892	+	0.0137714i
$438$	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
$441$	3.61904	+	1.61130i	0.172335	+	0.0767285i
$442$	−22.0715	−	16.0359i	−1.04984	−	0.762750i
$443$	−19.6333	+	8.74131i	−0.932806	+	0.415312i	−0.816137	−	0.577859i	$-0.803888\pi$
$443$	−19.6333	+	8.74131i	−0.932806	+	0.415312i	−0.116669	+	0.993171i	$0.537222\pi$
$444$	−56.3034	−	11.9677i	−2.67204	−	0.567960i
$445$	0.974014	+	9.26713i	0.0461727	+	0.439304i
$446$	−16.9134	+	18.7843i	−0.800874	+	0.889461i
$447$	−8.55011	−	9.49586i	−0.404406	−	0.449139i
$448$	3.78631	−	36.0244i	0.178886	−	1.70199i
$449$	5.80940	−	17.8795i	0.274163	−	0.843786i	−0.715277	−	0.698841i	$-0.753700\pi$
$449$	5.80940	−	17.8795i	0.274163	−	0.843786i	0.989440	−	0.144945i	$-0.0463005\pi$
$450$	−3.79484	+	11.6793i	−0.178890	+	0.550568i
$451$	−0.0145460	+	0.138396i	−0.000684944	+	0.00651681i
$452$	58.4212	+	64.8834i	2.74790	+	3.05186i
$453$	−3.04672	+	3.38373i	−0.143148	+	0.158982i
$454$	2.37877	+	22.6325i	0.111641	+	1.06220i
$455$	3.77215	+	0.801795i	0.176841	+	0.0375887i
$456$	28.9878	−	12.9062i	1.35748	−	0.604388i
$457$	−3.32182	−	2.41344i	−0.155388	−	0.112896i	0.507374	−	0.861726i	$-0.330616\pi$
$457$	−3.32182	−	2.41344i	−0.155388	−	0.112896i	−0.662763	+	0.748830i	$0.730616\pi$
$458$	−56.1396	−	24.9949i	−2.62323	−	1.16794i
$459$	−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	$-0.521178\pi$
$461$	18.5063	−	13.4456i	0.861924	−	0.626225i	0.928408	+	0.371563i	$0.121178\pi$
$462$	8.62453	−	1.83320i	0.401249	−	0.0852882i
$463$	−5.11947	−	15.7561i	−0.237922	−	0.732249i	−0.996720	−	0.0809233i	$-0.974213\pi$
$463$	−5.11947	−	15.7561i	−0.237922	−	0.732249i	0.758798	−	0.651326i	$-0.225787\pi$
$464$	−105.308			−4.88880
$465$		0			0
$466$	−43.7244			−2.02549
$467$	11.7878	+	36.2792i	0.545476	+	1.67880i	0.719855	+	0.694124i	$0.244208\pi$
$467$	11.7878	+	36.2792i	0.545476	+	1.67880i	−0.174379	+	0.984679i	$0.555792\pi$
$468$	18.5392	−	3.94063i	0.856976	−	0.182156i
$469$	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
$472$	−3.70889	−	1.65131i	−0.170716	−	0.0760075i
$473$	−3.25101	−	2.36200i	−0.149482	−	0.108605i
$474$	33.8271	−	15.0608i	1.55373	−	0.691766i
$475$	−11.6282	−	2.47166i	−0.533540	−	0.113407i
$476$	−2.61172	−	24.8488i	−0.119708	−	1.13894i
$477$	−1.84646	+	2.05070i	−0.0845435	+	0.0938950i
$478$	−32.8926	−	36.5309i	−1.50447	−	1.67089i
$479$	3.52102	−	33.5002i	0.160879	−	1.53066i	−0.554651	−	0.832083i	$-0.687148\pi$
$479$	3.52102	−	33.5002i	0.160879	−	1.53066i	0.715530	−	0.698582i	$-0.246185\pi$
$480$	−4.64938	+	14.3093i	−0.212214	+	0.653128i
$481$	8.78511	−	27.0378i	0.400567	−	1.23282i
$482$	−5.10980	+	48.6165i	−0.232745	+	2.21442i
$483$	0.884309	+	0.982125i	0.0402375	+	0.0446882i
$484$	−32.2785	+	35.8489i	−1.46720	+	1.62949i
$485$	0.0813472	+	0.773967i	0.00369379	+	0.0351440i
$486$	25.7221	+	5.46740i	1.16678	+	0.248006i
$487$	−18.8891	+	8.40996i	−0.855946	+	0.381092i	−0.787315	−	0.616550i	$-0.788530\pi$
$487$	−18.8891	+	8.40996i	−0.855946	+	0.381092i	−0.0686306	+	0.997642i	$0.521863\pi$
$488$	−36.0319	−	26.1787i	−1.63109	−	1.18506i
$489$	2.25631	+	1.00457i	0.102034	+	0.0454284i
$490$	−3.28793	−	5.69487i	−0.148534	−	0.257268i
$491$	−12.3664	+	21.4192i	−0.558087	+	0.966634i	0.439570	+	0.898209i	$0.355131\pi$
$491$	−12.3664	+	21.4192i	−0.558087	+	0.966634i	−0.997656	+	0.0684258i	$0.978202\pi$
$492$	0.625630	−	0.454547i	0.0282056	−	0.0204925i
$493$	−21.9732	+	4.67055i	−0.989624	+	0.210351i
$494$	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
$499$	24.0235	−	5.10635i	1.07544	−	0.228591i	0.364042	−	0.931383i	$-0.381396\pi$
$499$	24.0235	−	5.10635i	1.07544	−	0.228591i	0.711396	+	0.702791i	$0.248063\pi$
$500$	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
$503$	13.4649	+	5.99494i	0.600369	+	0.267301i	0.684336	−	0.729167i	$-0.260092\pi$
$503$	13.4649	+	5.99494i	0.600369	+	0.267301i	−0.0839669	+	0.996469i	$0.526759\pi$
$504$	11.9949	+	8.71479i	0.534295	+	0.388188i
$505$	4.51312	−	2.00937i	0.200831	−	0.0894157i
$506$	1.89775	+	0.403380i	0.0843654	+	0.0179324i
$507$	−0.0702822	−	0.668691i	−0.00312134	−	0.0296976i
$508$	−45.2372	+	50.2410i	−2.00708	+	2.22908i
$509$	10.3757	+	11.5234i	0.459896	+	0.510767i	0.927833	−	0.372995i	$-0.121669\pi$
$509$	10.3757	+	11.5234i	0.459896	+	0.510767i	−0.467937	+	0.883762i	$0.655003\pi$
$510$	−0.670772	+	6.38197i	−0.0297023	+	0.282598i
$511$	−4.00557	+	12.3279i	−0.177196	+	0.545353i
$512$	−0.0418393	+	0.128768i	−0.00184905	+	0.00569080i
$513$	−1.51825	+	14.4451i	−0.0670322	+	0.637769i
$514$	−0.191154	−	0.212298i	−0.00843146	−	0.00936409i
$515$	6.16841	−	6.85071i	0.271813	−	0.301878i
$516$	2.33424	+	22.2088i	0.102759	+	0.977690i
$517$	−8.79740	−	1.86994i	−0.386909	−	0.0822401i
$518$	32.8692	−	14.6343i	1.44419	−	0.642995i
$519$	0.0137556	+	0.00999402i	0.000603803	+	0.000438689i
$520$	−17.7650	−	7.90947i	−0.779045	−	0.346853i
$521$	−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	−0.693078	+	0.720863i	$0.743746\pi$
$523$	−36.4268	+	26.4656i	−1.59283	+	1.15726i	−0.899754	+	0.436397i	$0.856254\pi$
$524$	12.4875	−	2.65431i	0.545521	−	0.115954i
$525$	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
$530$	4.48046	−	0.952352i	0.194619	−	0.0413675i
$531$	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
$534$	53.4187	+	23.7835i	2.31165	+	1.02921i
$535$	6.09119	+	4.42551i	0.263345	+	0.191331i
$536$	−66.0146	+	29.3916i	−2.85139	+	1.26952i
$537$	13.8510	+	2.94412i	0.597714	+	0.127048i
$538$	4.56085	+	43.3936i	0.196632	+	1.87083i
$539$	3.59557	−	3.99328i	0.154872	−	0.172003i
$540$	−12.0596	−	13.3935i	−0.518962	−	0.576366i
$541$	−3.94895	+	37.5718i	−0.169779	+	1.61534i	0.495409	+	0.868660i	$0.335018\pi$
$541$	−3.94895	+	37.5718i	−0.169779	+	1.61534i	−0.665188	+	0.746676i	$0.731648\pi$
$542$	4.27759	−	13.1651i	0.183738	−	0.565488i
$543$	−8.15834	+	25.1088i	−0.350108	+	1.07752i
$544$	−5.03256	+	47.8816i	−0.215769	+	2.05291i
$545$	2.93494	+	3.25958i	0.125719	+	0.139625i
$546$	16.1930	−	17.9842i	0.692997	−	0.769651i
$547$	1.90333	+	18.1090i	0.0813807	+	0.774285i	0.956766	+	0.290859i	$0.0939412\pi$
$547$	1.90333	+	18.1090i	0.0813807	+	0.774285i	−0.875385	+	0.483426i	$0.839392\pi$
$548$	−41.7167	−	8.86716i	−1.78205	−	0.378786i
$549$	4.60695	−	2.05115i	0.196620	−	0.0875408i
$550$	13.4761	+	9.79092i	0.574621	+	0.417486i
$551$	19.0725	+	8.49162i	0.812516	+	0.361755i
$552$	−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
$555$	−6.54086	+	1.39030i	−0.277644	+	0.0590151i
$556$	−2.19015	−	6.74059i	−0.0928831	−	0.285865i
$557$	−9.19760			−0.389715			−0.194857	−	0.980832i	$-0.562424\pi$
$557$	−9.19760			−0.389715			−0.194857	+	0.980832i	$0.562424\pi$
$558$		0			0
$559$	−11.0293			−0.466488
$560$	−4.20481	−	12.9411i	−0.177686	−	0.546860i
$561$	−5.12919	+	1.09024i	−0.216554	+	0.0460301i
$562$	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
$565$	9.26596	+	4.12547i	0.389822	+	0.173560i
$566$	−33.3200	−	24.2084i	−1.40054	−	1.01755i
$567$	7.99825	−	3.56105i	0.335895	−	0.149550i
$568$	40.5327	+	8.61548i	1.70071	+	0.361498i
$569$	−4.33791	−	41.2724i	−0.181855	−	1.73023i	−0.581488	−	0.813555i	$-0.697529\pi$
$569$	−4.33791	−	41.2724i	−0.181855	−	1.73023i	0.399633	−	0.916675i	$-0.369137\pi$
$570$	3.99061	−	4.43202i	0.167148	−	0.185637i
$571$	−21.6752	−	24.0728i	−0.907080	−	1.00741i	−0.999931	−	0.0117345i	$-0.996265\pi$
$571$	−21.6752	−	24.0728i	−0.907080	−	1.00741i	0.0928510	−	0.995680i	$-0.470402\pi$
$572$	2.68730	−	25.5679i	0.112361	−	1.06905i
$573$	0.525430	−	1.61711i	0.0219501	−	0.0675556i
$574$	−0.149373	+	0.459722i	−0.00623470	+	0.0191884i
$575$	−0.260977	+	2.48303i	−0.0108835	+	0.103549i
$576$	−13.8387	−	15.3695i	−0.576613	−	0.640394i
$577$	27.4227	−	30.4560i	1.14162	−	1.26790i	0.183031	−	0.983107i	$-0.441409\pi$
$577$	27.4227	−	30.4560i	1.14162	−	1.26790i	0.958590	−	0.284791i	$-0.0919241\pi$
$578$	−2.63393	−	25.0602i	−0.109557	−	1.04237i
$579$	−17.6664	−	3.75511i	−0.734190	−	0.156057i
$580$	−23.6658	+	10.5367i	−0.982671	+	0.437513i
$581$	−23.3096	−	16.9354i	−0.967046	−	0.702600i
$582$	4.46140	+	1.98634i	0.184931	+	0.0823365i
$583$	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
$586$	70.5040	−	14.9861i	2.91249	−	0.619070i
$587$	7.88963	+	24.2818i	0.325640	+	1.00222i	0.971151	+	0.238466i	$0.0766445\pi$
$587$	7.88963	+	24.2818i	0.325640	+	1.00222i	−0.645511	+	0.763751i	$0.723356\pi$
$588$	−29.8612			−1.23146
$589$		0			0
$590$	−0.763058			−0.0314146
$591$	−1.30187	−	4.00673i	−0.0535516	−	0.164815i
$592$	−98.1181	+	20.8556i	−4.03263	+	0.857162i
$593$	−36.0269	+	26.1751i	−1.47945	+	1.07488i	−0.501716	+	0.865033i	$0.667298\pi$
$593$	−36.0269	+	26.1751i	−1.47945	+	1.07488i	−0.977734	+	0.209850i	$0.932702\pi$
$594$	10.1759	−	17.6252i	0.417523	−	0.723170i
$595$	−1.45132	−	2.51375i	−0.0594982	−	0.103054i
$596$	−43.0760	−	19.1787i	−1.76446	−	0.785589i
$597$	15.1370	+	10.9977i	0.619515	+	0.450104i
$598$	4.86464	−	2.16588i	0.198930	−	0.0885694i
$599$	−18.5652	−	3.94615i	−0.758553	−	0.161235i	−0.187631	−	0.982240i	$-0.560081\pi$
$599$	−18.5652	−	3.94615i	−0.758553	−	0.161235i	−0.570922	+	0.821004i	$0.693414\pi$
$600$	−5.98064	−	56.9020i	−0.244159	−	2.32301i
$601$	−8.59151	+	9.54184i	−0.350455	+	0.389220i	−0.892438	−	0.451170i	$-0.851007\pi$
$601$	−8.59151	+	9.54184i	−0.350455	+	0.389220i	0.541983	+	0.840389i	$0.317674\pi$
$602$	−9.34011	−	10.3732i	−0.380674	−	0.422782i
$603$	0.855259	−	8.13724i	0.0348288	−	0.331374i
$604$	−5.19217	+	15.9799i	−0.211267	+	0.650212i
$605$	−1.73175	+	5.32977i	−0.0704056	+	0.216686i
$606$	3.24051	−	30.8314i	0.131637	−	1.25244i
$607$	−25.5202	−	28.3430i	−1.03583	−	1.15041i	−0.988453	−	0.151531i	$-0.951580\pi$
$607$	−25.5202	−	28.3430i	−1.03583	−	1.15041i	−0.0473790	−	0.998877i	$-0.515087\pi$
$608$	29.9401	−	33.2519i	1.21423	−	1.34854i
$609$	−2.08289	−	19.8174i	−0.0844029	−	0.803040i
$610$	−8.18800	−	1.74041i	−0.331522	−	0.0704672i
$611$	−22.5510	+	10.0404i	−0.912316	+	0.406189i
$612$	−11.5412	−	8.38520i	−0.466527	−	0.338952i
$613$	−16.9393	−	7.54186i	−0.684172	−	0.304613i	0.0350577	−	0.999385i	$-0.488838\pi$
$613$	−16.9393	−	7.54186i	−0.684172	−	0.304613i	−0.719230	+	0.694772i	$0.755505\pi$
$614$	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
$617$	−7.95777	+	1.69148i	−0.320368	+	0.0680962i	−0.365289	−	0.930894i	$-0.619030\pi$
$617$	−7.95777	+	1.69148i	−0.320368	+	0.0680962i	0.0449211	+	0.998991i	$0.485696\pi$
$618$	−17.8763	−	55.0175i	−0.719089	−	2.21313i
$619$	−5.36063			−0.215462			−0.107731	−	0.994180i	$-0.534359\pi$
$619$	−5.36063			−0.215462			−0.107731	+	0.994180i	$0.534359\pi$
$620$		0			0
$621$	3.05046			0.122411
$622$	−17.1711	−	52.8472i	−0.688499	−	2.11898i
$623$	−25.8714	+	5.49913i	−1.03651	+	0.220318i
$624$	−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
$627$	4.45207	+	1.98219i	0.177799	+	0.0791610i
$628$	14.0948	+	10.2404i	0.562442	+	0.408638i
$629$	−19.5480	+	8.70334i	−0.779431	+	0.347025i
$630$	2.72575	+	0.579376i	0.108597	+	0.0230829i
$631$	−3.03624	−	28.8879i	−0.120871	−	1.15001i	−0.871881	−	0.489718i	$-0.837100\pi$
$631$	−3.03624	−	28.8879i	−0.120871	−	1.15001i	0.751010	−	0.660291i	$-0.229567\pi$
$632$	56.5129	−	62.7639i	2.24796	−	2.49661i
$633$	17.4084	+	19.3340i	0.691924	+	0.768459i
$634$	−1.56932	+	14.9311i	−0.0623257	+	0.592989i
$635$	−2.42699	+	7.46949i	−0.0963120	+	0.296418i
$636$	6.42770	−	19.7824i	0.254875	−	0.784424i
$637$	1.54162	−	14.6675i	0.0610812	−	0.581149i
$638$	−19.5742	−	21.7394i	−0.774950	−	0.860669i
$639$	−3.13953	+	3.48680i	−0.124198	+	0.137936i
$640$	1.37209	+	13.0546i	0.0542367	+	0.516027i
$641$	27.0023	+	5.73951i	1.06653	+	0.226697i	0.707560	−	0.706653i	$-0.249796\pi$
$641$	27.0023	+	5.73951i	1.06653	+	0.226697i	0.358966	+	0.933350i	$0.383129\pi$
$642$	43.1625	−	19.2172i	1.70349	−	0.758442i
$643$	3.42136	+	2.48577i	0.134925	+	0.0980291i	0.653201	−	0.757185i	$-0.273426\pi$
$643$	3.42136	+	2.48577i	0.134925	+	0.0980291i	−0.518275	+	0.855214i	$0.673426\pi$
$644$	4.45521	+	1.98359i	0.175560	+	0.0781643i
$645$	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	$-0.527196\pi$
$647$	21.2617	−	15.4475i	0.835883	−	0.607304i	0.921217	+	0.389048i	$0.127196\pi$
$648$	−43.1836	+	9.17895i	−1.69641	+	0.360583i
$649$	−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	0.837298	−	0.546746i	$-0.184134\pi$
$653$	−4.12592	−	12.6983i	−0.161460	−	0.496922i	−0.998758	+	0.0498246i	$0.984134\pi$
$654$	26.9231	−	5.72267i	1.05278	−	0.223774i
$655$	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
$658$	−28.5404	−	12.7070i	−1.11262	−	0.495371i
$659$	12.4717	+	9.06119i	0.485827	+	0.352974i	0.803577	−	0.595200i	$-0.202927\pi$
$659$	12.4717	+	9.06119i	0.485827	+	0.352974i	−0.317750	+	0.948174i	$0.602927\pi$
$660$	−5.52429	+	2.45957i	−0.215033	+	0.0957388i
$661$	4.61985	+	0.981980i	0.179691	+	0.0381946i	0.296879	−	0.954915i	$-0.404054\pi$
$661$	4.61985	+	0.981980i	0.179691	+	0.0381946i	−0.117187	+	0.993110i	$0.537388\pi$
$662$	6.80652	+	64.7597i	0.264543	+	2.51696i
$663$	−9.63032	+	10.6956i	−0.374011	+	0.415381i
$664$	97.2160	+	107.969i	3.77271	+	4.19002i
$665$	−0.281978	+	2.68284i	−0.0109346	+	0.104036i
$666$	6.34812	−	19.5375i	0.245984	−	0.757062i
$667$	1.35493	−	4.17006i	0.0524632	−	0.161465i
$668$	7.67274	−	73.0013i	0.296867	−	2.82450i
$669$	8.92251	+	9.90945i	0.344964	+	0.383122i
$670$	−9.08791	+	10.0931i	−0.351096	+	0.389932i
$671$	−0.715009	−	6.80286i	−0.0276026	−	0.262621i
$672$	−41.7735	−	8.87924i	−1.61145	−	0.342524i
$673$	−28.3866	+	12.6385i	−1.09422	+	0.487180i	−0.872840	−	0.488007i	$-0.837724\pi$
$673$	−28.3866	+	12.6385i	−1.09422	+	0.487180i	−0.221384	+	0.975187i	$0.571057\pi$
$674$	24.0185	+	17.4505i	0.925158	+	0.672167i
$675$	23.9258	+	10.6524i	0.920903	+	0.410013i
$676$	−1.24058	−	2.14875i	−0.0477147	−	0.0826443i
$677$	4.51998	−	7.82883i	0.173717	−	0.300886i	−0.766000	−	0.642841i	$-0.777756\pi$
$677$	4.51998	−	7.82883i	0.173717	−	0.300886i	0.939716	+	0.341955i	$0.111089\pi$
$678$	51.4932	−	37.4120i	1.97759	−	1.43680i
$679$	−2.16071	+	0.459273i	−0.0829205	+	0.0176253i
$680$	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
$685$	−4.84630	+	1.03011i	−0.185168	+	0.0393586i
$686$	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
$689$	9.38509	+	4.17851i	0.357543	+	0.159189i
$690$	−1.01331	−	0.736216i	−0.0385762	−	0.0280273i
$691$	33.3220	−	14.8359i	1.26763	−	0.564384i	0.340893	−	0.940102i	$-0.389271\pi$
$691$	33.3220	−	14.8359i	1.26763	−	0.564384i	0.926734	+	0.375718i	$0.122604\pi$
$692$	0.0613720	+	0.0130450i	0.00233301	+	0.000495898i
$693$	0.238024	+	2.26464i	0.00904177	+	0.0860267i
$694$	33.4225	−	37.1194i	1.26870	−	1.40903i
$695$	−0.550938	−	0.611879i	−0.0208983	−	0.0232099i
$696$	−10.5031	+	99.9299i	−0.398117	+	3.78783i
$697$	0.0888351	−	0.273406i	0.00336487	−	0.0103560i
$698$	26.7469	−	82.3185i	1.01238	−	3.11580i
$699$	−2.41109	+	22.9400i	−0.0911958	+	0.867670i
$700$	28.0168	+	31.1158i	1.05894	+	1.17607i
$701$	−1.08027	+	1.19976i	−0.0408013	+	0.0453144i	−0.763200	−	0.646162i	$-0.776373\pi$
$701$	−1.08027	+	1.19976i	−0.0408013	+	0.0453144i	0.722399	+	0.691477i	$0.243040\pi$
$702$	−5.83880	−	55.5525i	−0.220371	−	2.09669i
$703$	19.4520	+	4.13466i	0.733647	+	0.155942i
$704$	−25.6277	+	11.4102i	−0.965879	+	0.430037i
$705$	4.69742	+	3.41287i	0.176915	+	0.128536i
$706$	−79.1669	−	35.2474i	−2.97949	−	1.32655i
$707$	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	$-0.769210\pi$
$709$	−9.29395	+	6.75245i	−0.349042	+	0.253594i	0.399425	+	0.916766i	$0.369210\pi$
$710$	7.61813	−	1.61928i	0.285903	−	0.0607706i
$711$	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
$716$	51.1123	−	10.8643i	1.91016	−	0.406016i
$717$	−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	0.967365	−	0.253386i	$-0.0815441\pi$
$719$	7.08549	+	12.2724i	0.264244	+	0.457685i	−0.703121	+	0.711070i	$0.748211\pi$
$720$	−7.09737	−	3.15995i	−0.264503	−	0.117764i
$721$	21.1692	+	15.3803i	0.788382	+	0.572793i
$722$	30.4913	−	13.5756i	1.13477	−	0.505231i
$723$	25.2249	+	5.36171i	0.938123	+	0.199404i
$724$	10.1835	+	96.8899i	0.378468	+	3.60089i
$725$	25.1893	−	27.9756i	0.935508	−	1.03899i
$726$	23.5313	+	26.1341i	0.873328	+	0.969929i
$727$	2.81680	−	26.8001i	0.104470	−	0.993961i	−0.809208	−	0.587522i	$-0.800104\pi$
$727$	2.81680	−	26.8001i	0.104470	−	0.993961i	0.913678	−	0.406439i	$-0.133230\pi$
$728$	17.0569	−	52.4958i	0.632172	−	1.94562i
$729$	8.98695	−	27.6590i	0.332850	−	1.02441i
$730$	1.28413	−	12.2177i	0.0475278	−	0.452197i
$731$	5.55476	+	6.16918i	0.205450	+	0.228175i
$732$	−25.4354	+	28.2489i	−0.940121	+	1.04411i
$733$	2.97107	+	28.2678i	0.109739	+	1.04410i	0.901356	+	0.433079i	$0.142573\pi$
$733$	2.97107	+	28.2678i	0.109739	+	1.04410i	−0.791617	+	0.611017i	$0.790761\pi$
$734$	34.1984	+	7.26910i	1.26229	+	0.268307i
$735$	−3.16912	+	1.41098i	−0.116895	+	0.0520449i
$736$	−7.60254	−	5.52357i	−0.280233	−	0.203601i
$737$	−10.1388	−	4.51409i	−0.373468	−	0.166279i
$738$	0.137995	+	0.239014i	0.00507965	+	0.00879822i
$739$	0.348653	−	0.603885i	0.0128254	−	0.0222143i	−0.859541	−	0.511066i	$-0.829251\pi$
$739$	0.348653	−	0.603885i	0.0128254	−	0.0222143i	0.872367	+	0.488852i	$0.162584\pi$
$740$	−19.9633	+	14.5042i	−0.733866	+	0.533185i
$741$	13.0834	−	2.78097i	0.480633	−	0.102162i
$742$	4.01777	+	12.3654i	0.147497	+	0.453949i
$743$	−18.1815			−0.667015			−0.333508	−	0.942747i	$-0.608232\pi$
$743$	−18.1815			−0.667015			−0.333508	+	0.942747i	$0.608232\pi$
$744$		0			0
$745$	−5.47779			−0.200691
$746$	3.67929	+	11.3237i	0.134708	+	0.414589i
$747$	−16.0911	+	3.42026i	−0.588741	+	0.125141i
$748$	−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
$751$	−33.8615	−	15.0761i	−1.23562	−	0.550135i	−0.318190	−	0.948027i	$-0.603075\pi$
$751$	−33.8615	−	15.0761i	−1.23562	−	0.550135i	−0.917432	+	0.397892i	$0.869742\pi$
$752$	70.4650	+	51.1958i	2.56959	+	1.86692i
$753$	−29.7284	+	13.2359i	−1.08336	+	0.482344i
$754$	−78.5350	−	16.6931i	−2.86008	−	0.607928i
$755$	0.204034	+	1.94125i	0.00742554	+	0.0706493i
$756$	34.2308	−	38.0172i	1.24496	−	1.38267i
$757$	4.28378	+	4.75762i	0.155697	+	0.172919i	0.815947	−	0.578127i	$-0.196216\pi$
$757$	4.28378	+	4.75762i	0.155697	+	0.172919i	−0.660250	+	0.751046i	$0.729550\pi$
$758$	−4.20552	+	40.0129i	−0.152751	+	1.45333i
$759$	0.316281	−	0.973412i	0.0114803	−	0.0353326i
$760$	4.20351	−	12.9371i	0.152477	−	0.469277i
$761$	2.23052	−	21.2219i	0.0808561	−	0.769294i	−0.876698	−	0.481041i	$-0.840259\pi$
$761$	2.23052	−	21.2219i	0.0808561	−	0.769294i	0.957554	−	0.288253i	$-0.0930745\pi$
$762$	32.9783	+	36.6261i	1.19468	+	1.32682i
$763$	−8.33073	+	9.25221i	−0.301593	+	0.334952i
$764$	−0.655861	−	6.24010i	−0.0237282	−	0.225759i
$765$	−1.62106	−	0.344567i	−0.0586096	−	0.0124579i
$766$	28.6316	−	12.7476i	1.03450	−	0.460591i
$767$	−1.38454	−	1.00593i	−0.0499928	−	0.0363219i
$768$	20.8616	+	9.28816i	0.752777	+	0.335158i
$769$	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
$772$	−65.1918	+	13.8569i	−2.34630	+	0.498722i
$773$	−10.7240	−	33.0050i	−0.385714	−	1.18711i	−0.935961	−	0.352104i	$-0.885466\pi$
$773$	−10.7240	−	33.0050i	−0.385714	−	1.18711i	0.550247	−	0.835002i	$-0.314534\pi$
$774$	−7.96974			−0.286466
$775$		0			0
$776$	11.1389			0.399863
$777$	−5.86539	−	18.0518i	−0.210420	−	0.647605i
$778$	37.8968	−	8.05521i	1.35867	−	0.288793i
$779$	−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
$782$	−3.66150	−	1.63020i	−0.130935	−	0.0582960i
$783$	−37.2102	−	27.0348i	−1.32978	−	0.966144i
$784$	−47.5393	+	21.1659i	−1.69783	+	0.755923i
$785$	1.97972	+	0.420804i	0.0706594	+	0.0150191i
$786$	−0.972836	−	9.25592i	−0.0346999	−	0.330148i
$787$	−13.4617	+	14.9507i	−0.479858	+	0.532936i	−0.933657	−	0.358168i	$-0.883402\pi$
$787$	−13.4617	+	14.9507i	−0.479858	+	0.532936i	0.453799	+	0.891104i	$0.350068\pi$
$788$	−10.4025	−	11.5532i	−0.370575	−	0.411565i
$789$	1.08250	−	10.2993i	0.0385382	−	0.366666i
$790$	4.90526	−	15.0968i	0.174521	−	0.537122i
$791$	−8.89666	+	27.3811i	−0.316329	+	0.973559i
$792$	1.20025	−	11.4196i	0.0426489	−	0.405777i
$793$	−12.5624	−	13.9520i	−0.446105	−	0.495450i
$794$	−28.4233	+	31.5672i	−1.00870	+	1.12028i
$795$	−0.252585	−	2.40319i	−0.00895828	−	0.0852323i
$796$	67.5353	+	14.3551i	2.39372	+	0.508802i
$797$	23.9367	−	10.6573i	0.847880	−	0.377501i	0.0636514	−	0.997972i	$-0.479725\pi$
$797$	23.9367	−	10.6573i	0.847880	−	0.377501i	0.784229	+	0.620472i	$0.213059\pi$
$798$	13.6953	+	9.95018i	0.484807	+	0.352233i
$799$	16.9736	+	7.55713i	0.600482	+	0.267352i
$800$	−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
$803$	9.81935	−	2.08717i	0.346517	−	0.0736545i
$804$	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
$809$	−35.6536	+	7.57841i	−1.25351	+	0.266443i	−0.786380	−	0.617743i	$-0.788047\pi$
$809$	−35.6536	+	7.57841i	−1.25351	+	0.266443i	−0.467135	+	0.884186i	$0.654714\pi$
$810$	−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
$813$	−6.67117	−	2.97020i	−0.233968	−	0.104169i
$814$	−22.5431	−	16.3785i	−0.790136	−	0.574067i
$815$	0.967260	−	0.430652i	0.0338816	−	0.0150851i
$816$	49.6723	+	10.5582i	1.73888	+	0.369610i
$817$	−0.806448	−	7.67284i	−0.0282141	−	0.268439i
$818$	−11.8549	+	13.1662i	−0.414497	+	0.460346i
$819$	4.18199	+	4.64457i	0.146130	+	0.162294i
$820$	0.0346529	−	0.329700i	0.00121013	−	0.0115136i
$821$	12.1937	−	37.5285i	0.425565	−	1.30975i	−0.476888	−	0.878964i	$-0.658235\pi$
$821$	12.1937	−	37.5285i	0.425565	−	1.30975i	0.902453	−	0.430789i	$-0.141765\pi$
$822$	−9.60773	+	29.5696i	−0.335108	+	1.03136i
$823$	3.30184	−	31.4149i	0.115095	−	1.09506i	−0.772686	−	0.634789i	$-0.781087\pi$
$823$	3.30184	−	31.4149i	0.115095	−	1.09506i	0.887781	−	0.460267i	$-0.152246\pi$
$824$	−88.2891	−	98.0550i	−3.07570	−	3.41591i
$825$	5.87992	−	6.53031i	0.204712	−	0.227356i
$826$	−0.226400	−	2.15405i	−0.00787746	−	0.0749491i
$827$	−19.3965	−	4.12286i	−0.674483	−	0.143366i	−0.142078	−	0.989855i	$-0.545378\pi$
$827$	−19.3965	−	4.12286i	−0.674483	−	0.143366i	−0.532405	+	0.846490i	$0.678712\pi$
$828$	2.54373	−	1.13254i	0.0884008	−	0.0393586i
$829$	−7.28104	−	5.28999i	−0.252881	−	0.183729i	0.454122	−	0.890940i	$-0.349953\pi$
$829$	−7.28104	−	5.28999i	−0.252881	−	0.183729i	−0.707003	+	0.707211i	$0.749953\pi$
$830$	24.9460	+	11.1067i	0.865888	+	0.385518i
$831$	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
$834$	−5.05392	+	1.07424i	−0.175003	+	0.0371981i
$835$	−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	−0.964340	−	0.264665i	$-0.914739\pi$
$839$	−9.84070	−	30.2866i	−0.339739	−	1.04561i	0.624602	−	0.780944i	$-0.285261\pi$
$840$	−12.6995	+	2.69937i	−0.438176	+	0.0931372i
$841$	−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
$844$	87.7049	+	39.0487i	3.01893	+	1.34411i
$845$	−0.233192	−	0.169424i	−0.00802205	−	0.00582836i
$846$	−16.2953	+	7.25515i	−0.560245	+	0.249437i
$847$	−15.5593	−	3.30724i	−0.534625	−	0.113638i
$848$	−3.78898	−	36.0498i	−0.130114	−	1.23795i
$849$	−14.5383	+	16.1464i	−0.498953	+	0.554143i
$850$	−23.0255	−	25.5724i	−0.789769	−	0.877127i
$851$	0.436570	−	4.15368i	0.0149654	−	0.142386i
$852$	10.9290	−	33.6361i	0.374422	−	1.15235i
$853$	−15.1702	+	46.6890i	−0.519417	+	1.59860i	0.255683	+	0.966761i	$0.417700\pi$
$853$	−15.1702	+	46.6890i	−0.519417	+	1.59860i	−0.775099	+	0.631839i	$0.782300\pi$
$854$	2.48366	−	23.6304i	0.0849891	−	0.808617i
$855$	1.03061	+	1.14461i	0.0352461	+	0.0391447i
$856$	72.1090	−	80.0851i	2.46463	−	2.73725i
$857$	−2.01118	−	19.1351i	−0.0687005	−	0.653641i	−0.973638	−	0.228098i	$-0.926749\pi$
$857$	−2.01118	−	19.1351i	−0.0687005	−	0.653641i	0.904938	−	0.425544i	$-0.139917\pi$
$858$	−18.3323	−	3.89666i	−0.625856	−	0.133030i
$859$	4.24081	−	1.88813i	0.144695	−	0.0644222i	−0.333112	−	0.942887i	$-0.608099\pi$
$859$	4.24081	−	1.88813i	0.144695	−	0.0644222i	0.477806	+	0.878465i	$0.341432\pi$
$860$	7.74487	+	5.62698i	0.264098	+	0.191878i
$861$	0.232956	+	0.103719i	0.00793913	+	0.00353473i
$862$	5.36418	+	9.29104i	0.182705	+	0.316454i
$863$	19.2652	−	33.3683i	0.655795	−	1.13587i	−0.325899	−	0.945405i	$-0.605667\pi$
$863$	19.2652	−	33.3683i	0.655795	−	1.13587i	0.981694	−	0.190466i	$-0.0609999\pi$
$864$	−79.7493	+	57.9413i	−2.71313	+	1.97120i
$865$	0.00712969	−	0.00151546i	0.000242417	−	5.15273e-5i
$866$	−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
$871$	−29.7953	+	6.33318i	−1.00957	+	0.214592i
$872$	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
$875$	9.24251	+	4.11503i	0.312454	+	0.139113i
$876$	−45.1323	−	32.7905i	−1.52488	−	1.10789i
$877$	−8.45792	+	3.76571i	−0.285604	+	0.127159i	−0.544538	−	0.838736i	$-0.683295\pi$
$877$	−8.45792	+	3.76571i	−0.285604	+	0.127159i	0.258935	+	0.965895i	$0.416628\pi$
$878$	60.2810	+	12.8131i	2.03438	+	0.432422i
$879$	−3.97465	−	37.8163i	−0.134062	−	1.27551i
$880$	−7.05134	+	7.83131i	−0.237701	+	0.263993i
$881$	−11.9634	−	13.2867i	−0.403058	−	0.447642i	0.507109	−	0.861882i	$-0.330714\pi$
$881$	−11.9634	−	13.2867i	−0.403058	−	0.447642i	−0.910168	+	0.414240i	$0.864047\pi$
$882$	1.11397	−	10.5987i	0.0375094	−	0.356878i
$883$	−14.9303	+	45.9509i	−0.502446	+	1.54637i	0.302577	+	0.953125i	$0.402153\pi$
$883$	−14.9303	+	45.9509i	−0.502446	+	1.54637i	−0.805022	+	0.593244i	$0.797847\pi$
$884$	−16.4118	+	50.5104i	−0.551990	+	1.69885i
$885$	−0.0420773	+	0.400338i	−0.00141441	+	0.0134572i
$886$	38.6858	+	42.9649i	1.29967	+	1.44343i
$887$	15.7327	−	17.4730i	0.528254	−	0.586685i	−0.418672	−	0.908138i	$-0.637504\pi$
$887$	15.7327	−	17.4730i	0.528254	−	0.586685i	0.946926	+	0.321452i	$0.104171\pi$
$888$	10.0046	+	95.1872i	0.335732	+	3.19427i
$889$	−21.8059	−	4.63498i	−0.731346	−	0.155452i
$890$	22.9001	−	10.1958i	0.767615	−	0.341764i
$891$	−5.48554	−	3.98548i	−0.183772	−	0.133518i
$892$	44.9522	+	20.0140i	1.50511	+	0.670119i
$893$	−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
$896$	−36.4449	+	7.74661i	−1.21754	+	0.258796i
$897$	−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
$902$	0.366177	−	0.0778332i	0.0121923	−	0.00259156i
$903$	−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
$906$	11.1900	+	4.98211i	0.371763	+	0.165519i
$907$	10.1792	+	7.39560i	0.337994	+	0.245567i	0.743815	−	0.668386i	$-0.233014\pi$
$907$	10.1792	+	7.39560i	0.337994	+	0.245567i	−0.405821	+	0.913952i	$0.633014\pi$
$908$	40.4714	−	18.0190i	1.34309	−	0.597982i
$909$	7.83138	+	1.66461i	0.259750	+	0.0552117i
$910$	−1.08442	−	10.3175i	−0.0359481	−	0.342023i
$911$	−31.6395	+	35.1392i	−1.04826	+	1.16421i	−0.0621624	+	0.998066i	$0.519800\pi$
$911$	−31.6395	+	35.1392i	−1.04826	+	1.16421i	−0.986101	+	0.166148i	$0.946867\pi$
$912$	−31.5797	−	35.0729i	−1.04571	−	1.16138i
$913$	−2.33243	+	22.1916i	−0.0771922	+	0.734435i
$914$	−3.41333	+	10.5051i	−0.112903	+	0.347479i
$915$	−1.36462	+	4.19986i	−0.0451129	+	0.138843i
$916$	−12.5047	+	118.974i	−0.413167	+	3.93102i
$917$	2.81688	+	3.12846i	0.0930215	+	0.103311i
$918$	−28.1325	+	31.2443i	−0.928510	+	1.03121i
$919$	2.41794	+	23.0052i	0.0797605	+	0.758870i	0.959175	+	0.282813i	$0.0912677\pi$
$919$	2.41794	+	23.0052i	0.0797605	+	0.758870i	−0.879415	+	0.476057i	$0.842066\pi$
$920$	−2.79442	−	0.593973i	−0.0921294	−	0.0195827i
$921$	11.6051	−	5.16690i	0.382399	−	0.170255i
$922$	−49.7848	−	36.1708i	−1.63958	−	1.19122i
$923$	15.9575	+	7.10472i	0.525246	+	0.233855i
$924$	−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
$927$	14.6135	−	3.10619i	0.479970	−	0.102021i
$928$	43.7846	+	134.755i	1.43730	+	4.42355i
$929$	1.68694			0.0553468			0.0276734	−	0.999617i	$-0.491190\pi$
$929$	1.68694			0.0553468			0.0276734	+	0.999617i	$0.491190\pi$
$930$		0			0
$931$	10.3166			0.338114
$932$	26.3030	+	80.9524i	0.861585	+	2.65169i
$933$	−28.6732	+	6.09467i	−0.938717	+	0.199531i
$934$	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
$937$	18.0212	+	8.02355i	0.588727	+	0.262118i	0.679407	−	0.733762i	$-0.262237\pi$
$937$	18.0212	+	8.02355i	0.588727	+	0.262118i	−0.0906798	+	0.995880i	$0.528904\pi$
$938$	−31.1885	−	22.6598i	−1.01834	−	0.739868i
$939$	0.585124	−	0.260514i	0.0190948	−	0.00850156i
$940$	20.9580	+	4.45477i	0.683575	+	0.145298i
$941$	0.922282	+	8.77493i	0.0300655	+	0.286054i	0.999216	+	0.0395854i	$0.0126037\pi$
$941$	0.922282	+	8.77493i	0.0300655	+	0.286054i	−0.969151	+	0.246469i	$0.920730\pi$
$942$	8.49853	−	9.43857i	0.276897	−	0.307525i
$943$	0.0375456	+	0.0416987i	0.00122265	+	0.00135789i
$944$	−0.631192	+	6.00539i	−0.0205436	+	0.195459i
$945$	1.83649	−	5.65214i	0.0597411	−	0.183864i
$946$	−3.34057	+	10.2812i	−0.108611	+	0.334271i
$947$	−1.62659	+	15.4759i	−0.0528569	+	0.502900i	0.935781	+	0.352582i	$0.114696\pi$
$947$	−1.62659	+	15.4759i	−0.0528569	+	0.502900i	−0.988638	+	0.150318i	$0.951970\pi$
$948$	−48.2332	−	53.5684i	−1.56654	−	1.73982i
$949$	18.4364	−	20.4757i	0.598470	−	0.664668i
$950$	3.34288	+	31.8054i	0.108457	+	1.03190i
$951$	7.74706	+	1.64669i	0.251216	+	0.0533975i
$952$	−37.9539	+	16.8982i	−1.23009	+	0.547672i
$953$	−7.80840	−	5.67314i	−0.252939	−	0.183771i	0.454089	−	0.890956i	$-0.349965\pi$
$953$	−7.80840	−	5.67314i	−0.252939	−	0.183771i	−0.707028	+	0.707185i	$0.749965\pi$
$954$	6.78166	+	3.01939i	0.219564	+	0.0977563i
$955$	−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
$958$	−88.6370	+	18.8404i	−2.86373	+	0.608705i
$959$	−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
$964$	93.0837	−	19.7856i	2.99802	−	0.637250i
$965$	−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	0.542177	−	0.840264i	$-0.317600\pi$
$967$	−14.1988	−	24.5930i	−0.456602	−	0.790858i	−0.998779	+	0.0494066i	$0.984267\pi$
$968$	73.2768	+	32.6249i	2.35521	+	1.04861i
$969$	−8.14485	−	5.91758i	−0.261650	−	0.190100i
$970$	1.91256	−	0.851528i	0.0614087	−	0.0273409i
$971$	21.6435	+	4.60048i	0.694574	+	0.147636i	0.541653	−	0.840602i	$-0.317799\pi$
$971$	21.6435	+	4.60048i	0.694574	+	0.147636i	0.152921	+	0.988238i	$0.451132\pi$
$972$	−5.35102	−	50.9115i	−0.171634	−	1.63299i
$973$	1.56382	−	1.73680i	0.0501338	−	0.0556792i
$974$	37.2194	+	41.3363i	1.19259	+	1.32450i
$975$	2.52105	−	23.9861i	0.0807381	−	0.768171i
$976$	−20.4703	+	63.0012i	−0.655240	+	2.01662i
$977$	−6.15324	+	18.9377i	−0.196859	+	0.605871i	0.803090	+	0.595857i	$0.203188\pi$
$977$	−6.15324	+	18.9377i	−0.196859	+	0.605871i	−0.999950	+	0.0100140i	$0.996812\pi$
$978$	0.694513	−	6.60785i	0.0222081	−	0.211296i
$979$	13.7064	+	15.2225i	0.438058	+	0.486513i
$980$	−8.56572	+	9.51319i	−0.273622	+	0.303888i
$981$	0.743036	+	7.06951i	0.0237233	+	0.225712i
$982$	65.0810	+	13.8334i	2.07682	+	0.441441i
$983$	−22.7750	+	10.1401i	−0.726411	+	0.323419i	−0.736414	−	0.676531i	$-0.763482\pi$
$983$	−22.7750	+	10.1401i	−0.726411	+	0.323419i	0.0100033	+	0.999950i	$0.496816\pi$
$984$	−1.04028	−	0.755810i	−0.0331630	−	0.0240944i
$985$	−1.64990	−	0.734585i	−0.0525703	−	0.0234058i
$986$	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
$989$	−1.58491	+	0.336883i	−0.0503972	+	0.0107123i
$990$	−0.666901	−	2.05251i	−0.0211955	−	0.0652330i
$991$	−42.0512			−1.33580			−0.667900	−	0.744251i	$-0.732807\pi$
$991$	−42.0512			−1.33580			−0.667900	+	0.744251i	$0.732807\pi$
$992$		0			0
$993$	34.3515			1.09011
$994$	6.83142	+	21.0249i	0.216679	+	0.666871i
$995$	7.84569	−	1.66765i	0.248725	−	0.0528681i
$996$	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
$999$	−40.0237	−	17.8197i	−1.26629	−	0.563790i

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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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.k.844.1		16
31.2	even	5		961.2.g.t.338.2		16
31.3	odd	30		961.2.a.j.1.1		8
31.4	even	5		961.2.g.s.732.2		16
31.5	even	3		31.2.g.a.20.1	yes	16
31.6	odd	6		961.2.d.n.531.1		16
31.7	even	15		961.2.d.p.374.4		16
31.8	even	5		31.2.g.a.14.1	✓	16
31.9	even	15	inner	961.2.g.k.846.1		16
31.10	even	15		961.2.g.s.235.2		16
31.11	odd	30		961.2.g.n.816.2		16
31.12	odd	30		961.2.d.q.388.4		16
31.13	odd	30		961.2.c.i.439.1		16
31.14	even	15		961.2.d.o.628.1		16
31.15	odd	10		961.2.c.i.521.1		16
31.16	even	5		961.2.c.j.521.1		16
31.17	odd	30		961.2.d.n.628.1		16
31.18	even	15		961.2.c.j.439.1		16
31.19	even	15		961.2.d.p.388.4		16
31.20	even	15		961.2.g.t.816.2		16
31.21	odd	30		961.2.g.m.235.2		16
31.22	odd	30		961.2.g.j.846.1		16
31.23	odd	10		961.2.g.l.448.1		16
31.24	odd	30		961.2.d.q.374.4		16
31.25	even	3		961.2.d.o.531.1		16
31.26	odd	6		961.2.g.l.547.1		16
31.27	odd	10		961.2.g.m.732.2		16
31.28	even	15		961.2.a.i.1.1		8
31.29	odd	10		961.2.g.n.338.2		16
31.30	odd	2		961.2.g.j.844.1		16
93.5	odd	6		279.2.y.c.82.2		16
93.8	odd	10		279.2.y.c.262.2		16
93.59	odd	30		8649.2.a.bf.1.8		8
93.65	even	30		8649.2.a.be.1.8		8
124.39	odd	10		496.2.bg.c.417.1		16
124.67	odd	6		496.2.bg.c.113.1		16
155.8	odd	20		775.2.ck.a.324.4		32
155.39	even	10		775.2.bl.a.76.2		16
155.67	odd	12		775.2.ck.a.299.4		32
155.98	odd	12		775.2.ck.a.299.1		32
155.129	even	6		775.2.bl.a.51.2		16
155.132	odd	20		775.2.ck.a.324.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.14.1	✓	16	31.8	even	5
31.2.g.a.20.1	yes	16	31.5	even	3
279.2.y.c.82.2		16	93.5	odd	6
279.2.y.c.262.2		16	93.8	odd	10
496.2.bg.c.113.1		16	124.67	odd	6
496.2.bg.c.417.1		16	124.39	odd	10
775.2.bl.a.51.2		16	155.129	even	6
775.2.bl.a.76.2		16	155.39	even	10
775.2.ck.a.299.1		32	155.98	odd	12
775.2.ck.a.299.4		32	155.67	odd	12
775.2.ck.a.324.1		32	155.132	odd	20
775.2.ck.a.324.4		32	155.8	odd	20
961.2.a.i.1.1		8	31.28	even	15
961.2.a.j.1.1		8	31.3	odd	30
961.2.c.i.439.1		16	31.13	odd	30
961.2.c.i.521.1		16	31.15	odd	10
961.2.c.j.439.1		16	31.18	even	15
961.2.c.j.521.1		16	31.16	even	5
961.2.d.n.531.1		16	31.6	odd	6
961.2.d.n.628.1		16	31.17	odd	30
961.2.d.o.531.1		16	31.25	even	3
961.2.d.o.628.1		16	31.14	even	15
961.2.d.p.374.4		16	31.7	even	15
961.2.d.p.388.4		16	31.19	even	15
961.2.d.q.374.4		16	31.24	odd	30
961.2.d.q.388.4		16	31.12	odd	30
961.2.g.j.844.1		16	31.30	odd	2
961.2.g.j.846.1		16	31.22	odd	30
961.2.g.k.844.1		16	1.1	even	1	trivial
961.2.g.k.846.1		16	31.9	even	15	inner
961.2.g.l.448.1		16	31.23	odd	10
961.2.g.l.547.1		16	31.26	odd	6
961.2.g.m.235.2		16	31.21	odd	30
961.2.g.m.732.2		16	31.27	odd	10
961.2.g.n.338.2		16	31.29	odd	10
961.2.g.n.816.2		16	31.11	odd	30
961.2.g.s.235.2		16	31.10	even	15
961.2.g.s.732.2		16	31.4	even	5
961.2.g.t.338.2		16	31.2	even	5
961.2.g.t.816.2		16	31.20	even	15
8649.2.a.be.1.8		8	93.65	even	30
8649.2.a.bf.1.8		8	93.59	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 $\F_{q}$

Introduction

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	961.2.g.k.844.1

Level	$961$
Weight	$2$
Character	961.844
Analytic conductor	$7.674$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$