LMFDB - Embedded newform 950.2.l.h.701.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 12x^{10} + 105x^{8} + 394x^{6} + 1077x^{4} + 1443x^{2} + 1369 $ x^12 + 12x^10 + 105x^8 + 394x^6 + 1077x^4 + 1443*x^2 + 1369
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			701.1
Root			$-0.838929 + 1.45307i$ of defining polynomial
Character	$\chi$	$=$	950.701
Dual form			950.2.l.h.351.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(-1.28531 - 1.07851i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-1.28531 + 1.07851i) q^{6} +(-1.23774 - 2.14383i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.0320889 - 0.181985i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{2} +(-1.28531 - 1.07851i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-1.28531 + 1.07851i) q^{6} +(-1.23774 - 2.14383i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.0320889 - 0.181985i) q^{9} +(-1.45059 + 2.51250i) q^{11} +(0.838929 + 1.45307i) q^{12} +(-0.993308 + 0.833484i) q^{13} +(-2.32619 + 0.846665i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-0.215843 + 1.22411i) q^{17} -0.184793 q^{18} +(-4.22186 - 1.08440i) q^{19} +(-0.721249 + 4.09041i) q^{21} +(2.22244 + 1.86485i) q^{22} +(2.06330 + 0.750979i) q^{23} +(1.57667 - 0.573861i) q^{24} +(0.648336 + 1.12295i) q^{26} +(-2.67181 + 4.62772i) q^{27} +(0.429863 + 2.43788i) q^{28} +(-1.12586 - 6.38509i) q^{29} +(3.04442 + 5.27310i) q^{31} +(0.766044 - 0.642788i) q^{32} +(4.57422 - 1.66488i) q^{33} +(1.16803 + 0.425128i) q^{34} +(-0.0320889 + 0.181985i) q^{36} -1.44520 q^{37} +(-1.80104 + 3.96942i) q^{38} +2.17563 q^{39} +(1.82601 + 1.53221i) q^{41} +(3.90302 + 1.42058i) q^{42} +(-8.64591 + 3.14685i) q^{43} +(2.22244 - 1.86485i) q^{44} +(1.09786 - 1.90155i) q^{46} +(1.93233 + 10.9588i) q^{47} +(-0.291357 - 1.65237i) q^{48} +(0.435991 - 0.755158i) q^{49} +(1.59763 - 1.34057i) q^{51} +(1.21847 - 0.443488i) q^{52} +(11.3107 + 4.11677i) q^{53} +(4.09346 + 3.43482i) q^{54} +2.47548 q^{56} +(4.25688 + 5.94709i) q^{57} -6.48359 q^{58} +(-0.351292 + 1.99228i) q^{59} +(1.25853 + 0.458067i) q^{61} +(5.72164 - 2.08251i) q^{62} +(-0.350428 + 0.294044i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.845282 - 4.79383i) q^{66} +(-0.584560 - 3.31520i) q^{67} +(0.621495 - 1.07646i) q^{68} +(-1.84205 - 3.19052i) q^{69} +(-14.2805 + 5.19768i) q^{71} +(0.173648 + 0.0632028i) q^{72} +(-0.429457 - 0.360357i) q^{73} +(-0.250956 + 1.42324i) q^{74} +(3.59636 + 2.46296i) q^{76} +7.18185 q^{77} +(0.377794 - 2.14258i) q^{78} +(4.96611 + 4.16706i) q^{79} +(7.90420 - 2.87689i) q^{81} +(1.82601 - 1.53221i) q^{82} +(-4.22735 - 7.32198i) q^{83} +(2.07675 - 3.59705i) q^{84} +(1.59770 + 9.06100i) q^{86} +(-5.43927 + 9.42109i) q^{87} +(-1.45059 - 2.51250i) q^{88} +(-9.11595 + 7.64919i) q^{89} +(3.01631 + 1.09785i) q^{91} +(-1.68202 - 1.41138i) q^{92} +(1.77403 - 10.0610i) q^{93} +11.1279 q^{94} -1.67786 q^{96} +(0.469830 - 2.66454i) q^{97} +(-0.667976 - 0.560499i) q^{98} +(0.503786 + 0.183363i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9}+O(q^{10}) $ 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9	$ 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9} + 6 q^{11} - 6 q^{13} + 18 q^{17} + 12 q^{18} + 12 q^{21} + 6 q^{22} + 30 q^{23} - 6 q^{29} + 6 q^{31} + 24 q^{33} + 18 q^{36} - 36 q^{37} - 18 q^{38} - 36 q^{39} - 6 q^{41} + 30 q^{42} + 6 q^{44} - 12 q^{46} + 6 q^{47} - 18 q^{49} + 12 q^{52} + 12 q^{53} + 12 q^{56} + 18 q^{57} + 36 q^{58} - 24 q^{59} - 30 q^{61} + 6 q^{62} - 18 q^{63} - 6 q^{64} + 24 q^{66} - 12 q^{67} - 12 q^{68} + 6 q^{69} - 42 q^{71} - 6 q^{73} + 6 q^{74} + 18 q^{76} + 24 q^{77} - 48 q^{78} + 60 q^{79} + 18 q^{81} - 6 q^{82} - 24 q^{83} - 24 q^{84} - 36 q^{86} - 54 q^{87} + 6 q^{88} - 12 q^{89} + 24 q^{91} - 24 q^{92} - 6 q^{93} + 60 q^{94} - 30 q^{97} - 36 q^{98} - 12 q^{99}+O(q^{100}) $ 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9 + 6 * q^11 - 6 * q^13 + 18 * q^17 + 12 * q^18 + 12 * q^21 + 6 * q^22 + 30 * q^23 - 6 * q^29 + 6 * q^31 + 24 * q^33 + 18 * q^36 - 36 * q^37 - 18 * q^38 - 36 * q^39 - 6 * q^41 + 30 * q^42 + 6 * q^44 - 12 * q^46 + 6 * q^47 - 18 * q^49 + 12 * q^52 + 12 * q^53 + 12 * q^56 + 18 * q^57 + 36 * q^58 - 24 * q^59 - 30 * q^61 + 6 * q^62 - 18 * q^63 - 6 * q^64 + 24 * q^66 - 12 * q^67 - 12 * q^68 + 6 * q^69 - 42 * q^71 - 6 * q^73 + 6 * q^74 + 18 * q^76 + 24 * q^77 - 48 * q^78 + 60 * q^79 + 18 * q^81 - 6 * q^82 - 24 * q^83 - 24 * q^84 - 36 * q^86 - 54 * q^87 + 6 * q^88 - 12 * q^89 + 24 * q^91 - 24 * q^92 - 6 * q^93 + 60 * q^94 - 30 * q^97 - 36 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	−1.28531	−	1.07851i	−0.742076	−	0.622676i	0.191318	−	0.981528i	$-0.438724\pi$
$3$	−1.28531	−	1.07851i	−0.742076	−	0.622676i	−0.933394	+	0.358852i	$0.883168\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$		0			0
$5$		0			0
$6$	−1.28531	+	1.07851i	−0.524727	+	0.440298i
$7$	−1.23774	−	2.14383i	−0.467822	−	0.810292i	0.531502	−	0.847057i	$-0.321628\pi$
$7$	−1.23774	−	2.14383i	−0.467822	−	0.810292i	−0.999324	+	0.0367651i	$0.988295\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−0.0320889	−	0.181985i	−0.0106963	−	0.0606617i
$10$		0			0
$11$	−1.45059	+	2.51250i	−0.437371	+	0.757548i	−0.997486	−	0.0708665i	$-0.977424\pi$
$11$	−1.45059	+	2.51250i	−0.437371	+	0.757548i	0.560115	+	0.828415i	$0.310757\pi$
$12$	0.838929	+	1.45307i	0.242178	+	0.419465i
$13$	−0.993308	+	0.833484i	−0.275494	+	0.231167i	−0.770057	−	0.637975i	$-0.779772\pi$
$13$	−0.993308	+	0.833484i	−0.275494	+	0.231167i	0.494563	+	0.869142i	$0.335328\pi$
$14$	−2.32619	+	0.846665i	−0.621701	+	0.226281i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−0.215843	+	1.22411i	−0.0523496	+	0.296889i	−0.999730	−	0.0232194i	$-0.992608\pi$
$17$	−0.215843	+	1.22411i	−0.0523496	+	0.296889i	0.947381	+	0.320109i	$0.103719\pi$
$18$	−0.184793			−0.0435560
$19$	−4.22186	−	1.08440i	−0.968561	−	0.248777i
$19$	−4.22186	−	1.08440i	−0.968561	−	0.248777i
$20$		0			0
$21$	−0.721249	+	4.09041i	−0.157390	+	0.892600i
$22$	2.22244	+	1.86485i	0.473826	+	0.397587i
$23$	2.06330	+	0.750979i	0.430227	+	0.156590i	0.548052	−	0.836445i	$-0.315370\pi$
$23$	2.06330	+	0.750979i	0.430227	+	0.156590i	−0.117824	+	0.993034i	$0.537592\pi$
$24$	1.57667	−	0.573861i	0.321837	−	0.117139i
$25$		0			0
$26$	0.648336	+	1.12295i	0.127149	+	0.220229i
$27$	−2.67181	+	4.62772i	−0.514191	+	0.890605i
$28$	0.429863	+	2.43788i	0.0812365	+	0.460715i
$29$	−1.12586	−	6.38509i	−0.209068	−	1.18568i	−0.890909	−	0.454181i	$-0.849932\pi$
$29$	−1.12586	−	6.38509i	−0.209068	−	1.18568i	0.681842	−	0.731500i	$-0.261179\pi$
$30$		0			0
$31$	3.04442	+	5.27310i	0.546795	+	0.947076i	0.998492	+	0.0549047i	$0.0174855\pi$
$31$	3.04442	+	5.27310i	0.546795	+	0.947076i	−0.451697	+	0.892171i	$0.649181\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	4.57422	−	1.66488i	0.796270	−	0.289818i
$34$	1.16803	+	0.425128i	0.200315	+	0.0729088i
$35$		0			0
$36$	−0.0320889	+	0.181985i	−0.00534815	+	0.0303309i
$37$	−1.44520			−0.237589			−0.118794	−	0.992919i	$-0.537903\pi$
$37$	−1.44520			−0.237589			−0.118794	+	0.992919i	$0.537903\pi$
$38$	−1.80104	+	3.96942i	−0.292167	+	0.643924i
$39$	2.17563			0.348380
$40$		0			0
$41$	1.82601	+	1.53221i	0.285175	+	0.239290i	0.774142	−	0.633012i	$-0.218182\pi$
$41$	1.82601	+	1.53221i	0.285175	+	0.239290i	−0.488967	+	0.872302i	$0.662626\pi$
$42$	3.90302	+	1.42058i	0.602249	+	0.219201i
$43$	−8.64591	+	3.14685i	−1.31849	+	0.479891i	−0.902974	−	0.429696i	$-0.858621\pi$
$43$	−8.64591	+	3.14685i	−1.31849	+	0.479891i	−0.415515	+	0.909586i	$0.636399\pi$
$44$	2.22244	−	1.86485i	0.335045	−	0.281136i
$45$		0			0
$46$	1.09786	−	1.90155i	0.161870	−	0.280368i
$47$	1.93233	+	10.9588i	0.281860	+	1.59851i	0.716291	+	0.697802i	$0.245838\pi$
$47$	1.93233	+	10.9588i	0.281860	+	1.59851i	−0.434431	+	0.900705i	$0.643050\pi$
$48$	−0.291357	−	1.65237i	−0.0420538	−	0.238499i
$49$	0.435991	−	0.755158i	0.0622844	−	0.107880i
$50$		0			0
$51$	1.59763	−	1.34057i	0.223713	−	0.187718i
$52$	1.21847	−	0.443488i	0.168972	−	0.0615007i
$53$	11.3107	+	4.11677i	1.55365	+	0.565482i	0.969270	−	0.245999i	$-0.0791160\pi$
$53$	11.3107	+	4.11677i	1.55365	+	0.565482i	0.584379	+	0.811481i	$0.301338\pi$
$54$	4.09346	+	3.43482i	0.557049	+	0.467420i
$55$		0			0
$56$	2.47548			0.330800
$57$	4.25688	+	5.94709i	0.563838	+	0.787711i
$58$	−6.48359			−0.851337
$59$	−0.351292	+	1.99228i	−0.0457343	+	0.259372i	−0.999099	−	0.0424499i	$-0.986484\pi$
$59$	−0.351292	+	1.99228i	−0.0457343	+	0.259372i	0.953364	+	0.301822i	$0.0975948\pi$
$60$		0			0
$61$	1.25853	+	0.458067i	0.161138	+	0.0586494i	0.421330	−	0.906908i	$-0.361564\pi$
$61$	1.25853	+	0.458067i	0.161138	+	0.0586494i	−0.260192	+	0.965557i	$0.583786\pi$
$62$	5.72164	−	2.08251i	0.726650	−	0.264479i
$63$	−0.350428	+	0.294044i	−0.0441497	+	0.0370460i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	−0.845282	−	4.79383i	−0.104047	−	0.590080i
$67$	−0.584560	−	3.31520i	−0.0714153	−	0.405016i	−0.999469	−	0.0325710i	$-0.989630\pi$
$67$	−0.584560	−	3.31520i	−0.0714153	−	0.405016i	0.928054	−	0.372445i	$-0.121481\pi$
$68$	0.621495	−	1.07646i	0.0753673	−	0.130540i
$69$	−1.84205	−	3.19052i	−0.221757	−	0.384094i
$70$		0			0
$71$	−14.2805	+	5.19768i	−1.69478	+	0.616851i	−0.995215	−	0.0977142i	$-0.968847\pi$
$71$	−14.2805	+	5.19768i	−1.69478	+	0.616851i	−0.699569	+	0.714565i	$0.746625\pi$
$72$	0.173648	+	0.0632028i	0.0204646	+	0.00744852i
$73$	−0.429457	−	0.360357i	−0.0502641	−	0.0421766i	0.617310	−	0.786720i	$-0.288223\pi$
$73$	−0.429457	−	0.360357i	−0.0502641	−	0.0421766i	−0.667574	+	0.744544i	$0.732667\pi$
$74$	−0.250956	+	1.42324i	−0.0291730	+	0.165448i
$75$		0			0
$76$	3.59636	+	2.46296i	0.412531	+	0.282521i
$77$	7.18185			0.818447
$78$	0.377794	−	2.14258i	0.0427768	−	0.242599i
$79$	4.96611	+	4.16706i	0.558731	+	0.468831i	0.877885	−	0.478872i	$-0.158954\pi$
$79$	4.96611	+	4.16706i	0.558731	+	0.468831i	−0.319154	+	0.947703i	$0.603399\pi$
$80$		0			0
$81$	7.90420	−	2.87689i	0.878244	−	0.319655i
$82$	1.82601	−	1.53221i	0.201649	−	0.169204i
$83$	−4.22735	−	7.32198i	−0.464012	−	0.803692i	0.535145	−	0.844760i	$-0.320257\pi$
$83$	−4.22735	−	7.32198i	−0.464012	−	0.803692i	−0.999156	+	0.0410686i	$0.986924\pi$
$84$	2.07675	−	3.59705i	0.226593	−	0.392470i
$85$		0			0
$86$	1.59770	+	9.06100i	0.172284	+	0.977073i
$87$	−5.43927	+	9.42109i	−0.583151	+	1.01005i
$88$	−1.45059	−	2.51250i	−0.154634	−	0.267834i
$89$	−9.11595	+	7.64919i	−0.966289	+	0.810812i	−0.981965	−	0.189065i	$-0.939454\pi$
$89$	−9.11595	+	7.64919i	−0.966289	+	0.810812i	0.0156760	+	0.999877i	$0.495010\pi$
$90$		0			0
$91$	3.01631	+	1.09785i	0.316195	+	0.115086i
$92$	−1.68202	−	1.41138i	−0.175362	−	0.147146i
$93$	1.77403	−	10.0610i	0.183958	−	1.04328i
$94$	11.1279			1.14775
$95$		0			0
$96$	−1.67786			−0.171246
$97$	0.469830	−	2.66454i	0.0477040	−	0.270543i	−0.951621	−	0.307274i	$-0.900583\pi$
$97$	0.469830	−	2.66454i	0.0477040	−	0.270543i	0.999325	+	0.0367308i	$0.0116944\pi$
$98$	−0.667976	−	0.560499i	−0.0674758	−	0.0566189i
$99$	0.503786	+	0.183363i	0.0506324	+	0.0184287i
$100$		0			0
$101$	0.0902852	−	0.0757583i	0.00898372	−	0.00753823i	−0.638285	−	0.769800i	$-0.720356\pi$
$101$	0.0902852	−	0.0757583i	0.00898372	−	0.00753823i	0.647268	+	0.762262i	$0.275911\pi$
$102$	−1.04278	−	1.80615i	−0.103251	−	0.178835i
$103$	0.870691	−	1.50808i	0.0857918	−	0.148596i	−0.819937	−	0.572454i	$-0.805991\pi$
$103$	0.870691	−	1.50808i	0.0857918	−	0.148596i	0.905728	+	0.423859i	$0.139325\pi$
$104$	−0.225165	−	1.27697i	−0.0220792	−	0.125217i
$105$		0			0
$106$	6.01832	−	10.4240i	0.584551	−	1.01247i
$107$	−8.35318	−	14.4681i	−0.807533	−	1.39869i	−0.914568	−	0.404432i	$-0.867469\pi$
$107$	−8.35318	−	14.4681i	−0.807533	−	1.39869i	0.107035	−	0.994255i	$-0.465864\pi$
$108$	4.09346	−	3.43482i	0.393893	−	0.330516i
$109$	−19.0267	+	6.92515i	−1.82243	+	0.663309i	−0.827649	+	0.561246i	$0.810322\pi$
$109$	−19.0267	+	6.92515i	−1.82243	+	0.663309i	−0.994778	+	0.102063i	$0.967456\pi$
$110$		0			0
$111$	1.85753	+	1.55865i	0.176309	+	0.147941i
$112$	0.429863	−	2.43788i	0.0406183	−	0.230358i
$113$	16.5448			1.55641			0.778204	−	0.628012i	$-0.216131\pi$
$113$	16.5448			1.55641			0.778204	+	0.628012i	$0.216131\pi$
$114$	6.59594	−	3.15951i	0.617766	−	0.295915i
$115$		0			0
$116$	−1.12586	+	6.38509i	−0.104534	+	0.592840i
$117$	0.183556	+	0.154022i	0.0169697	+	0.0142393i
$118$	1.90101	+	0.691910i	0.175002	+	0.0636955i
$119$	2.89144	−	1.05240i	0.265057	−	0.0964730i
$120$		0			0
$121$	1.29155	+	2.23703i	0.117414	+	0.203366i
$122$	0.669649	−	1.15987i	0.0606272	−	0.105009i
$123$	−0.694505	−	3.93873i	−0.0626214	−	0.355143i
$124$	−1.05732	−	5.99634i	−0.0949499	−	0.538488i
$125$		0			0
$126$	0.228725	+	0.396164i	0.0203765	+	0.0352931i
$127$	−0.100392	+	0.0842392i	−0.00890838	+	0.00747502i	−0.647231	−	0.762294i	$-0.724073\pi$
$127$	−0.100392	+	0.0842392i	−0.00890838	+	0.00747502i	0.638323	+	0.769769i	$0.279629\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	14.5066	+	5.27997i	1.27724	+	0.464876i
$130$		0			0
$131$	2.22302	−	12.6074i	0.194226	−	1.10151i	−0.719290	−	0.694710i	$-0.755533\pi$
$131$	2.22302	−	12.6074i	0.194226	−	1.10151i	0.913516	−	0.406802i	$-0.133356\pi$
$132$	−4.86778			−0.423686
$133$	2.90081	+	10.3932i	0.251532	+	0.901201i
$134$	−3.36634			−0.290808
$135$		0			0
$136$	−0.952186	−	0.798979i	−0.0816492	−	0.0685119i
$137$	−14.6862	−	5.34535i	−1.25473	−	0.456684i	−0.372732	−	0.927939i	$-0.621579\pi$
$137$	−14.6862	−	5.34535i	−1.25473	−	0.456684i	−0.881997	+	0.471255i	$0.843801\pi$
$138$	−3.46192	+	1.26004i	−0.294698	+	0.107261i
$139$	−8.79431	+	7.37930i	−0.745924	+	0.625904i	−0.934421	−	0.356169i	$-0.884083\pi$
$139$	−8.79431	+	7.37930i	−0.745924	+	0.625904i	0.188498	+	0.982074i	$0.439638\pi$
$140$		0			0
$141$	9.33549	−	16.1695i	0.786190	−	1.36172i
$142$	2.63893	+	14.9661i	0.221454	+	1.25593i
$143$	−0.653245	−	3.70474i	−0.0546271	−	0.309806i
$144$	0.0923963	−	0.160035i	0.00769969	−	0.0133363i
$145$		0			0
$146$	−0.429457	+	0.360357i	−0.0355421	+	0.0298233i
$147$	−1.37483	+	0.500396i	−0.113394	+	0.0412720i
$148$	1.35804	+	0.494286i	0.111630	+	0.0406301i
$149$	−11.6068	−	9.73926i	−0.950866	−	0.797871i	0.0285771	−	0.999592i	$-0.490902\pi$
$149$	−11.6068	−	9.73926i	−0.950866	−	0.797871i	−0.979443	+	0.201720i	$0.935347\pi$
$150$		0			0
$151$	−5.78759			−0.470988			−0.235494	−	0.971876i	$-0.575671\pi$
$151$	−5.78759			−0.470988			−0.235494	+	0.971876i	$0.575671\pi$
$152$	3.05004	−	3.11404i	0.247391	−	0.252582i
$153$	0.229695			0.0185698
$154$	1.24711	−	7.07274i	0.100495	−	0.569937i
$155$		0			0
$156$	−2.04442	−	0.744109i	−0.163685	−	0.0595764i
$157$	−10.3544	+	3.76870i	−0.826372	+	0.300775i	−0.720369	−	0.693591i	$-0.756028\pi$
$157$	−10.3544	+	3.76870i	−0.826372	+	0.300775i	−0.106003	+	0.994366i	$0.533805\pi$
$158$	4.96611	−	4.16706i	0.395082	−	0.331514i
$159$	−10.0979	−	17.4900i	−0.800814	−	1.38705i
$160$		0			0
$161$	−0.943857	−	5.35288i	−0.0743864	−	0.421866i
$162$	−1.46064	−	8.28368i	−0.114758	−	0.650828i
$163$	−11.0896	+	19.2078i	−0.868605	+	1.50447i	−0.00518168	+	0.999987i	$0.501649\pi$
$163$	−11.0896	+	19.2078i	−0.868605	+	1.50447i	−0.863423	+	0.504481i	$0.831684\pi$
$164$	−1.19184	−	2.06434i	−0.0930675	−	0.161198i
$165$		0			0
$166$	−7.94481	+	2.89168i	−0.616637	+	0.224438i
$167$	−16.3396	−	5.94713i	−1.26440	−	0.460203i	−0.379155	−	0.925333i	$-0.623785\pi$
$167$	−16.3396	−	5.94713i	−1.26440	−	0.460203i	−0.885242	+	0.465130i	$0.846007\pi$
$168$	−3.18177	−	2.66982i	−0.245479	−	0.205981i
$169$	−1.96546	+	11.1467i	−0.151189	+	0.857438i
$170$		0			0
$171$	−0.0618692	+	0.803112i	−0.00473125	+	0.0614155i
$172$	9.20078			0.701553
$173$	−0.373025	+	2.11553i	−0.0283606	+	0.160841i	−0.995699	−	0.0926478i	$-0.970467\pi$
$173$	−0.373025	+	2.11553i	−0.0283606	+	0.160841i	0.967338	+	0.253489i	$0.0815781\pi$
$174$	8.33344	+	6.99259i	0.631757	+	0.530107i
$175$		0			0
$176$	−2.72623	+	0.992265i	−0.205497	+	0.0747948i
$177$	2.60020	−	2.18183i	0.195443	−	0.163996i
$178$	5.95001	+	10.3057i	0.445972	+	0.772447i
$179$	5.19089	−	8.99089i	0.387985	−	0.672011i	−0.604193	−	0.796838i	$-0.706504\pi$
$179$	5.19089	−	8.99089i	0.387985	−	0.672011i	0.992178	+	0.124827i	$0.0398377\pi$
$180$		0			0
$181$	−2.89049	−	16.3928i	−0.214848	−	1.21846i	−0.881170	−	0.472800i	$-0.843243\pi$
$181$	−2.89049	−	16.3928i	−0.214848	−	1.21846i	0.666322	−	0.745664i	$-0.267868\pi$
$182$	1.60494	−	2.77984i	0.118966	−	0.206056i
$183$	−1.12358	−	1.94609i	−0.0830571	−	0.143859i
$184$	−1.68202	+	1.41138i	−0.124000	+	0.104048i
$185$		0			0
$186$	−9.60011	−	3.49415i	−0.703914	−	0.256204i
$187$	−2.76247	−	2.31799i	−0.202012	−	0.169508i
$188$	1.93233	−	10.9588i	0.140930	−	0.799254i
$189$	13.2281			0.962200
$190$		0			0
$191$	−21.7916			−1.57679			−0.788393	−	0.615172i	$-0.789086\pi$
$191$	−21.7916			−1.57679			−0.788393	+	0.615172i	$0.789086\pi$
$192$	−0.291357	+	1.65237i	−0.0210269	+	0.119249i
$193$	−17.5503	−	14.7264i	−1.26330	−	1.06003i	−0.995323	−	0.0966060i	$-0.969201\pi$
$193$	−17.5503	−	14.7264i	−1.26330	−	1.06003i	−0.267974	−	0.963426i	$-0.586354\pi$
$194$	−2.54247	−	0.925384i	−0.182539	−	0.0664387i
$195$		0			0
$196$	−0.667976	+	0.560499i	−0.0477126	+	0.0400356i
$197$	−2.47777	−	4.29163i	−0.176534	−	0.305766i	0.764157	−	0.645030i	$-0.223155\pi$
$197$	−2.47777	−	4.29163i	−0.176534	−	0.305766i	−0.940691	+	0.339264i	$0.889822\pi$
$198$	0.268059	−	0.464292i	0.0190501	−	0.0329958i
$199$	4.27197	+	24.2276i	0.302832	+	1.71745i	0.633537	+	0.773713i	$0.281603\pi$
$199$	4.27197	+	24.2276i	0.302832	+	1.71745i	−0.330704	+	0.943734i	$0.607286\pi$
$200$		0			0
$201$	−2.82412	+	4.89153i	−0.199198	+	0.345022i
$202$	−0.0589295	−	0.102069i	−0.00414626	−	0.00718154i
$203$	−12.2950	+	10.3167i	−0.862941	+	0.724094i
$204$	−1.95979	+	0.713304i	−0.137212	+	0.0499413i
$205$		0			0
$206$	−1.33398	−	1.11934i	−0.0929426	−	0.0779881i
$207$	0.0704581	−	0.399588i	0.00489717	−	0.0277733i
$208$	−1.29667			−0.0899080
$209$	8.84875	−	9.03442i	0.612081	−	0.624924i
$210$		0			0
$211$	−0.638032	+	3.61846i	−0.0439239	+	0.249105i	−0.998862	−	0.0477014i	$-0.984810\pi$
$211$	−0.638032	+	3.61846i	−0.0439239	+	0.249105i	0.954938	+	0.296806i	$0.0959215\pi$
$212$	−9.22060	−	7.73700i	−0.633273	−	0.531379i
$213$	23.9607	+	8.72096i	1.64176	+	0.597551i
$214$	−15.6988	+	5.71391i	−1.07315	+	0.390595i
$215$		0			0
$216$	−2.67181	−	4.62772i	−0.181794	−	0.314876i
$217$	7.53642	−	13.0535i	0.511606	−	0.886127i
$218$	3.51599	+	19.9402i	0.238133	+	1.35052i
$219$	0.163339	+	0.926343i	0.0110374	+	0.0625965i
$220$		0			0
$221$	−0.805875	−	1.39582i	−0.0542090	−	0.0938927i
$222$	1.85753	−	1.55865i	0.124669	−	0.104610i
$223$	7.00387	−	2.54920i	0.469014	−	0.170707i	−0.0966918	−	0.995314i	$-0.530826\pi$
$223$	7.00387	−	2.54920i	0.469014	−	0.170707i	0.565706	+	0.824607i	$0.308604\pi$
$224$	−2.32619	−	0.846665i	−0.155425	−	0.0565702i
$225$		0			0
$226$	2.87298	−	16.2935i	0.191108	−	1.08383i
$227$	11.4167			0.757750			0.378875	−	0.925448i	$-0.376311\pi$
$227$	11.4167			0.757750			0.378875	+	0.925448i	$0.376311\pi$
$228$	−1.96614	−	7.04438i	−0.130211	−	0.466525i
$229$	−3.19332			−0.211021			−0.105510	−	0.994418i	$-0.533648\pi$
$229$	−3.19332			−0.211021			−0.105510	+	0.994418i	$0.533648\pi$
$230$		0			0
$231$	−9.23093	−	7.74567i	−0.607350	−	0.509627i
$232$	6.09258	+	2.21752i	0.399997	+	0.145587i
$233$	−21.8940	+	7.96876i	−1.43432	+	0.522051i	−0.938167	−	0.346183i	$-0.887478\pi$
$233$	−21.8940	+	7.96876i	−1.43432	+	0.522051i	−0.496156	+	0.868234i	$0.665255\pi$
$234$	0.183556	−	0.154022i	0.0119994	−	0.0100687i
$235$		0			0
$236$	1.01150	−	1.75198i	0.0658433	−	0.114044i
$237$	−1.88881	−	10.7120i	−0.122691	−	0.695817i
$238$	−0.534316	−	3.03025i	−0.0346345	−	0.196422i
$239$	4.11104	−	7.12053i	0.265921	−	0.460589i	−0.701883	−	0.712292i	$-0.747657\pi$
$239$	4.11104	−	7.12053i	0.265921	−	0.460589i	0.967805	+	0.251703i	$0.0809906\pi$
$240$		0			0
$241$	15.9574	−	13.3899i	1.02791	−	0.862518i	0.0373080	−	0.999304i	$-0.488122\pi$
$241$	15.9574	−	13.3899i	1.02791	−	0.862518i	0.990601	+	0.136786i	$0.0436773\pi$
$242$	2.42732	−	0.883473i	0.156034	−	0.0567918i
$243$	1.80198	+	0.655868i	0.115597	+	0.0420740i
$244$	−1.02596	−	0.860884i	−0.0656805	−	0.0551124i
$245$		0			0
$246$	−3.99949			−0.254998
$247$	5.09743	−	2.44171i	0.324342	−	0.155363i
$248$	−6.08885			−0.386642
$249$	−2.46333	+	13.9703i	−0.156107	+	0.885330i
$250$		0			0
$251$	−10.7939	−	3.92864i	−0.681302	−	0.247974i	−0.0218955	−	0.999760i	$-0.506970\pi$
$251$	−10.7939	−	3.92864i	−0.681302	−	0.247974i	−0.659406	+	0.751787i	$0.729192\pi$
$252$	0.429863	−	0.156457i	0.0270788	−	0.00985589i
$253$	−4.87985	+	4.09468i	−0.306793	+	0.257430i
$254$	0.0655264	+	0.113495i	0.00411149	+	0.00712132i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−0.322408	−	1.82847i	−0.0201112	−	0.114057i	0.973100	−	0.230385i	$-0.0739986\pi$
$257$	−0.322408	−	1.82847i	−0.0201112	−	0.114057i	−0.993211	+	0.116329i	$0.962887\pi$
$258$	7.71881	−	13.3694i	0.480552	−	0.832340i
$259$	1.78878	+	3.09826i	0.111149	+	0.192516i
$260$		0			0
$261$	−1.12586	+	0.409781i	−0.0696892	+	0.0253648i
$262$	−12.0298	−	4.37850i	−0.743205	−	0.270505i
$263$	−7.85464	−	6.59082i	−0.484338	−	0.406407i	0.367654	−	0.929963i	$-0.380161\pi$
$263$	−7.85464	−	6.59082i	−0.484338	−	0.406407i	−0.851992	+	0.523555i	$0.824605\pi$
$264$	−0.845282	+	4.79383i	−0.0520235	+	0.295040i
$265$		0			0
$266$	10.7390	−	1.05199i	0.658449	−	0.0645014i
$267$	19.9666			1.22193
$268$	−0.584560	+	3.31520i	−0.0357077	+	0.202508i
$269$	20.2958	+	17.0302i	1.23746	+	1.03835i	0.997719	+	0.0675114i	$0.0215059\pi$
$269$	20.2958	+	17.0302i	1.23746	+	1.03835i	0.239738	+	0.970838i	$0.422939\pi$
$270$		0			0
$271$	−23.4094	+	8.52031i	−1.42202	+	0.517572i	−0.934633	−	0.355615i	$-0.884272\pi$
$271$	−23.4094	+	8.52031i	−1.42202	+	0.517572i	−0.487385	+	0.873187i	$0.662049\pi$
$272$	−0.952186	+	0.798979i	−0.0577347	+	0.0484452i
$273$	−2.69287	−	4.66419i	−0.162980	−	0.282289i
$274$	−7.81438	+	13.5349i	−0.472084	+	0.817673i
$275$		0			0
$276$	0.639737	+	3.62813i	0.0385076	+	0.218388i
$277$	−7.18265	+	12.4407i	−0.431564	+	0.747490i	−0.997008	−	0.0772960i	$-0.975371\pi$
$277$	−7.18265	+	12.4407i	−0.431564	+	0.747490i	0.565444	+	0.824786i	$0.308705\pi$
$278$	5.74008	+	9.94211i	0.344267	+	0.596288i
$279$	0.861933	−	0.723248i	0.0516026	−	0.0432997i
$280$		0			0
$281$	25.2726	+	9.19849i	1.50764	+	0.548736i	0.958025	−	0.286683i	$-0.0925527\pi$
$281$	25.2726	+	9.19849i	1.50764	+	0.548736i	0.549614	+	0.835419i	$0.314775\pi$
$282$	−14.3028	−	12.0015i	−0.851720	−	0.714678i
$283$	3.50163	−	19.8587i	0.208150	−	1.18048i	−0.684255	−	0.729243i	$-0.739873\pi$
$283$	3.50163	−	19.8587i	0.208150	−	1.18048i	0.892405	−	0.451235i	$-0.149016\pi$
$284$	15.1970			0.901776
$285$		0			0
$286$	−3.76189			−0.222445
$287$	1.02466	−	5.81114i	0.0604838	−	0.343021i
$288$	−0.141559	−	0.118782i	−0.00834146	−	0.00699932i
$289$	14.5229	+	5.28591i	0.854290	+	0.310936i
$290$		0			0
$291$	−3.47760	+	2.91805i	−0.203860	+	0.171059i
$292$	0.280308	+	0.485507i	0.0164038	+	0.0284122i
$293$	9.99952	−	17.3197i	0.584178	−	1.01183i	−0.410799	−	0.911726i	$-0.634750\pi$
$293$	9.99952	−	17.3197i	0.584178	−	1.01183i	0.994977	−	0.100100i	$-0.0319163\pi$
$294$	0.254058	+	1.44083i	0.0148170	+	0.0840311i
$295$		0			0
$296$	0.722598	−	1.25158i	0.0420002	−	0.0727464i
$297$	−7.75144	−	13.4259i	−0.449784	−	0.779049i
$298$	−11.6068	+	9.73926i	−0.672364	+	0.564180i
$299$	−2.67542	+	0.973773i	−0.154723	+	0.0563147i
$300$		0			0
$301$	17.4477	+	14.6404i	1.00567	+	0.843858i
$302$	−1.00500	+	5.69967i	−0.0578315	+	0.327979i
$303$	−0.197751			−0.0113605
$304$	−2.53709	−	3.54445i	−0.145512	−	0.203288i
$305$		0			0
$306$	0.0398862	−	0.226206i	0.00228014	−	0.0129313i
$307$	14.8627	+	12.4713i	0.848257	+	0.711772i	0.959405	−	0.282032i	$-0.0910084\pi$
$307$	14.8627	+	12.4713i	0.848257	+	0.711772i	−0.111148	+	0.993804i	$0.535453\pi$
$308$	−6.74873	−	2.45634i	−0.384544	−	0.139963i
$309$	−2.74559	+	0.999312i	−0.156191	+	0.0568489i
$310$		0			0
$311$	−2.69949	−	4.67566i	−0.153074	−	0.265132i	0.779282	−	0.626673i	$-0.215584\pi$
$311$	−2.69949	−	4.67566i	−0.153074	−	0.265132i	−0.932356	+	0.361541i	$0.882251\pi$
$312$	−1.08782	+	1.88415i	−0.0615854	+	0.106669i
$313$	2.81021	+	15.9375i	0.158843	+	0.900841i	0.955188	+	0.295999i	$0.0956527\pi$
$313$	2.81021	+	15.9375i	0.158843	+	0.900841i	−0.796345	+	0.604842i	$0.793236\pi$
$314$	1.91342	+	10.8515i	0.107980	+	0.612388i
$315$		0			0
$316$	−3.24140	−	5.61427i	−0.182343	−	0.315827i
$317$	1.87753	−	1.57543i	0.105453	−	0.0884852i	−0.588537	−	0.808470i	$-0.700296\pi$
$317$	1.87753	−	1.57543i	0.105453	−	0.0884852i	0.693989	+	0.719985i	$0.255851\pi$
$318$	−18.9778	+	6.90736i	−1.06422	+	0.387345i
$319$	17.6757	+	6.43344i	0.989651	+	0.360203i
$320$		0			0
$321$	−4.86752	+	27.6051i	−0.271678	+	1.54076i
$322$	−5.43546			−0.302906
$323$	2.23867	−	4.93394i	0.124563	−	0.274532i
$324$	−8.41147			−0.467304
$325$		0			0
$326$	16.9903	+	14.2565i	0.941003	+	0.789595i
$327$	31.9241	+	11.6194i	1.76541	+	0.642555i
$328$	−2.23994	+	0.815270i	−0.123680	+	0.0450158i
$329$	21.1021	−	17.7068i	1.16340	−	0.976206i
$330$		0			0
$331$	−1.51812	+	2.62947i	−0.0834436	+	0.144529i	−0.904727	−	0.425992i	$-0.859925\pi$
$331$	−1.51812	+	2.62947i	−0.0834436	+	0.144529i	0.821283	+	0.570521i	$0.193259\pi$
$332$	1.46814	+	8.32625i	0.0805748	+	0.456962i
$333$	0.0463747	+	0.263004i	0.00254132	+	0.0144125i
$334$	−8.69412	+	15.0587i	−0.475721	+	0.823973i
$335$		0			0
$336$	−3.18177	+	2.66982i	−0.173580	+	0.145651i
$337$	−5.69742	+	2.07369i	−0.310358	+	0.112961i	−0.492504	−	0.870310i	$-0.663918\pi$
$337$	−5.69742	+	2.07369i	−0.310358	+	0.112961i	0.182145	+	0.983272i	$0.441696\pi$
$338$	10.6360	+	3.87120i	0.578525	+	0.210566i
$339$	−21.2653	−	17.8437i	−1.15497	−	0.969138i
$340$		0			0
$341$	−17.6649			−0.956608
$342$	0.780168	+	0.200388i	0.0421866	+	0.0108358i
$343$	−19.4870			−1.05220
$344$	1.59770	−	9.06100i	0.0861422	−	0.488537i
$345$		0			0
$346$	2.01862	+	0.734716i	0.108522	+	0.0394986i
$347$	2.70335	−	0.983940i	0.145124	−	0.0528207i	−0.268437	−	0.963297i	$-0.586507\pi$
$347$	2.70335	−	0.983940i	0.145124	−	0.0528207i	0.413561	+	0.910477i	$0.364285\pi$
$348$	8.33344	−	6.99259i	0.446719	−	0.374842i
$349$	−16.3979	−	28.4020i	−0.877761	−	1.52033i	−0.853793	−	0.520613i	$-0.825703\pi$
$349$	−16.3979	−	28.4020i	−0.877761	−	1.52033i	−0.0239680	−	0.999713i	$-0.507630\pi$
$350$		0			0
$351$	−1.20320	−	6.82367i	−0.0642219	−	0.364220i
$352$	0.503786	+	2.85711i	0.0268519	+	0.152285i
$353$	10.6004	−	18.3605i	0.564204	−	0.977231i	−0.432919	−	0.901433i	$-0.642516\pi$
$353$	10.6004	−	18.3605i	0.564204	−	0.977231i	0.997123	−	0.0757977i	$-0.0241503\pi$
$354$	−1.69716	−	2.93957i	−0.0902031	−	0.156236i
$355$		0			0
$356$	11.1824	−	4.07005i	0.592664	−	0.215712i
$357$	−4.85142	−	1.76577i	−0.256764	−	0.0934546i
$358$	−7.95291	−	6.67328i	−0.420324	−	0.352694i
$359$	3.22806	−	18.3072i	0.170370	−	0.966218i	−0.772983	−	0.634427i	$-0.781236\pi$
$359$	3.22806	−	18.3072i	0.170370	−	0.966218i	0.943353	−	0.331791i	$-0.107653\pi$
$360$		0			0
$361$	16.6482	+	9.15633i	0.876220	+	0.481912i
$362$	−16.6456			−0.874876
$363$	0.752605	−	4.26823i	0.0395015	−	0.224024i
$364$	−2.45892	−	2.06328i	−0.128882	−	0.108145i
$365$		0			0
$366$	−2.11163	+	0.768571i	−0.110377	+	0.0401739i
$367$	16.6403	−	13.9628i	0.868615	−	0.728855i	−0.0951910	−	0.995459i	$-0.530346\pi$
$367$	16.6403	−	13.9628i	0.868615	−	0.728855i	0.963806	+	0.266605i	$0.0859017\pi$
$368$	1.09786	+	1.90155i	0.0572298	+	0.0991249i
$369$	0.220244	−	0.381474i	0.0114654	−	0.0198587i
$370$		0			0
$371$	−5.17411	−	29.3438i	−0.268626	−	1.52345i
$372$	−5.10811	+	8.84751i	−0.264843	+	0.458722i
$373$	11.2077	+	19.4123i	0.580312	+	1.00513i	0.995442	+	0.0953679i	$0.0304027\pi$
$373$	11.2077	+	19.4123i	0.580312	+	1.00513i	−0.415130	+	0.909762i	$0.636264\pi$
$374$	−2.76247	+	2.31799i	−0.142844	+	0.119860i
$375$		0			0
$376$	−10.4568	−	3.80596i	−0.539267	−	0.196277i
$377$	6.44020	+	5.40397i	0.331687	+	0.278318i
$378$	2.29703	−	13.0271i	0.118146	−	0.670042i
$379$	−8.45251			−0.434176			−0.217088	−	0.976152i	$-0.569656\pi$
$379$	−8.45251			−0.434176			−0.217088	+	0.976152i	$0.569656\pi$
$380$		0			0
$381$	0.219888			0.0112652
$382$	−3.78407	+	21.4605i	−0.193610	+	1.09802i
$383$	7.54187	+	6.32838i	0.385372	+	0.323365i	0.814807	−	0.579732i	$-0.196843\pi$
$383$	7.54187	+	6.32838i	0.385372	+	0.323365i	−0.429435	+	0.903098i	$0.641287\pi$
$384$	1.57667	+	0.573861i	0.0804591	+	0.0292847i
$385$		0			0
$386$	−17.5503	+	14.7264i	−0.893286	+	0.749556i
$387$	0.850118	+	1.47245i	0.0432139	+	0.0748487i
$388$	−1.35282	+	2.34315i	−0.0686791	+	0.118956i
$389$	−1.47850	−	8.38497i	−0.0749627	−	0.425135i	−0.999075	−	0.0430125i	$-0.986304\pi$
$389$	−1.47850	−	8.38497i	−0.0749627	−	0.425135i	0.924112	−	0.382122i	$-0.124807\pi$
$390$		0			0
$391$	−1.36463	+	2.36360i	−0.0690121	+	0.119532i
$392$	0.435991	+	0.755158i	0.0220208	+	0.0381412i
$393$	−16.4544	+	13.8069i	−0.830016	+	0.696466i
$394$	−4.65669	+	1.69490i	−0.234601	+	0.0853877i
$395$		0			0
$396$	−0.410690	−	0.344610i	−0.0206380	−	0.0173173i
$397$	−4.25698	+	24.1425i	−0.213651	+	1.21168i	0.669580	+	0.742740i	$0.266474\pi$
$397$	−4.25698	+	24.1425i	−0.213651	+	1.21168i	−0.883231	+	0.468938i	$0.844637\pi$
$398$	24.6013			1.23315
$399$	7.48063	−	16.4870i	0.374500	−	0.825383i
$400$		0			0
$401$	−0.863801	+	4.89886i	−0.0431362	+	0.244637i	−0.998750	−	0.0499849i	$-0.984083\pi$
$401$	−0.863801	+	4.89886i	−0.0431362	+	0.244637i	0.955614	+	0.294622i	$0.0951938\pi$
$402$	4.32681	+	3.63062i	0.215802	+	0.181079i
$403$	−7.41909	−	2.70033i	−0.369571	−	0.134513i
$404$	−0.110751	+	0.0403101i	−0.00551008	+	0.00200550i
$405$		0			0
$406$	8.02501	+	13.8997i	0.398274	+	0.689831i
$407$	2.09639	−	3.63106i	0.103914	−	0.179985i
$408$	0.362154	+	2.05388i	0.0179293	+	0.101682i
$409$	3.14232	+	17.8210i	0.155377	+	0.881189i	0.958440	+	0.285295i	$0.0920914\pi$
$409$	3.14232	+	17.8210i	0.155377	+	0.881189i	−0.803062	+	0.595895i	$0.796797\pi$
$410$		0			0
$411$	13.1114	+	22.7096i	0.646739	+	1.12018i
$412$	−1.33398	+	1.11934i	−0.0657203	+	0.0551459i
$413$	4.70591	−	1.71281i	0.231563	−	0.0842819i
$414$	−0.381282	−	0.138775i	−0.0187390	−	0.00682043i
$415$		0			0
$416$	−0.225165	+	1.27697i	−0.0110396	+	0.0626087i
$417$	19.2621			0.943268
$418$	−7.36059	−	10.2831i	−0.360018	−	0.502964i
$419$	−10.5816			−0.516945			−0.258472	−	0.966019i	$-0.583219\pi$
$419$	−10.5816			−0.516945			−0.258472	+	0.966019i	$0.583219\pi$
$420$		0			0
$421$	−18.5815	−	15.5917i	−0.905605	−	0.759893i	0.0656729	−	0.997841i	$-0.479081\pi$
$421$	−18.5815	−	15.5917i	−0.905605	−	0.759893i	−0.971278	+	0.237949i	$0.923525\pi$
$422$	3.45269	+	1.25668i	0.168074	+	0.0611741i
$423$	1.93233	−	0.703312i	0.0939533	−	0.0341962i
$424$	−9.22060	+	7.73700i	−0.447792	+	0.375742i
$425$		0			0
$426$	12.7492	−	22.0823i	0.617701	−	1.06989i
$427$	−0.575715	−	3.26504i	−0.0278608	−	0.158006i
$428$	2.90103	+	16.4526i	0.140227	+	0.795264i
$429$	−3.15596	+	5.46628i	−0.152371	+	0.263914i
$430$		0			0
$431$	27.3497	−	22.9491i	1.31739	−	1.10542i	0.330536	−	0.943794i	$-0.392771\pi$
$431$	27.3497	−	22.9491i	1.31739	−	1.10542i	0.986852	−	0.161626i	$-0.0516738\pi$
$432$	−5.02137	+	1.82763i	−0.241591	+	0.0879318i
$433$	31.0738	+	11.3099i	1.49331	+	0.543521i	0.954319	−	0.298790i	$-0.0965830\pi$
$433$	31.0738	+	11.3099i	1.49331	+	0.543521i	0.538992	+	0.842311i	$0.318805\pi$
$434$	−11.5465	−	9.68864i	−0.554248	−	0.465069i
$435$		0			0
$436$	20.2478			0.969693
$437$	−7.89659	−	5.40796i	−0.377745	−	0.258698i
$438$	0.940634			0.0449452
$439$	1.02662	−	5.82227i	0.0489981	−	0.277882i	−0.950458	−	0.310852i	$-0.899386\pi$
$439$	1.02662	−	5.82227i	0.0489981	−	0.277882i	0.999456	+	0.0329703i	$0.0104967\pi$
$440$		0			0
$441$	−0.151418	−	0.0551116i	−0.00721038	−	0.00262436i
$442$	−1.51455	+	0.551251i	−0.0720398	+	0.0262203i
$443$	−9.06436	+	7.60590i	−0.430661	+	0.361367i	−0.832201	−	0.554474i	$-0.812919\pi$
$443$	−9.06436	+	7.60590i	−0.430661	+	0.361367i	0.401540	+	0.915841i	$0.368475\pi$
$444$	−1.21242	−	2.09997i	−0.0575388	−	0.0996601i
$445$		0			0
$446$	−1.29426	−	7.34013i	−0.0612851	−	0.347565i
$447$	4.41452	+	25.0360i	0.208800	+	1.18416i
$448$	−1.23774	+	2.14383i	−0.0584778	+	0.101287i
$449$	3.79197	+	6.56789i	0.178954	+	0.309958i	0.941523	−	0.336950i	$-0.109395\pi$
$449$	3.79197	+	6.56789i	0.178954	+	0.309958i	−0.762568	+	0.646908i	$0.776062\pi$
$450$		0			0
$451$	−6.49848	+	2.36525i	−0.306001	+	0.111375i
$452$	−15.5471	−	5.65867i	−0.731273	−	0.266161i
$453$	7.43887	+	6.24195i	0.349509	+	0.293273i
$454$	1.98248	−	11.2432i	0.0930424	−	0.527670i
$455$		0			0
$456$	−7.27877	+	0.713026i	−0.340860	+	0.0333905i
$457$	−13.0616			−0.610995			−0.305497	−	0.952193i	$-0.598823\pi$
$457$	−13.0616			−0.610995			−0.305497	+	0.952193i	$0.598823\pi$
$458$	−0.554515	+	3.14481i	−0.0259108	+	0.146947i
$459$	−5.08813	−	4.26945i	−0.237493	−	0.199281i
$460$		0			0
$461$	29.3589	−	10.6858i	1.36738	−	0.497685i	0.449051	−	0.893506i	$-0.351762\pi$
$461$	29.3589	−	10.6858i	1.36738	−	0.497685i	0.918328	+	0.395821i	$0.129540\pi$
$462$	−9.23093	+	7.74567i	−0.429462	+	0.360361i
$463$	−6.98180	−	12.0928i	−0.324472	−	0.562002i	0.656933	−	0.753949i	$-0.271853\pi$
$463$	−6.98180	−	12.0928i	−0.324472	−	0.562002i	−0.981405	+	0.191947i	$0.938520\pi$
$464$	3.24179	−	5.61495i	0.150496	−	0.260668i
$465$		0			0
$466$	4.04585	+	22.9451i	0.187420	+	1.06291i
$467$	−5.90352	+	10.2252i	−0.273182	+	0.473165i	−0.969675	−	0.244399i	$-0.921409\pi$
$467$	−5.90352	+	10.2252i	−0.273182	+	0.473165i	0.696493	+	0.717564i	$0.254743\pi$
$468$	−0.119808	−	0.207513i	−0.00553811	−	0.00959228i
$469$	−6.38370	+	5.35656i	−0.294772	+	0.247343i
$470$		0			0
$471$	17.3732	+	6.32334i	0.800517	+	0.291364i
$472$	−1.54971	−	1.30037i	−0.0713314	−	0.0598542i
$473$	4.63523	−	26.2877i	0.213128	−	1.20871i
$474$	−10.8772			−0.499607
$475$		0			0
$476$	−3.07700			−0.141034
$477$	0.386242	−	2.19049i	0.0176848	−	0.100296i
$478$	−6.29848	−	5.28505i	−0.288086	−	0.241733i
$479$	30.1189	+	10.9624i	1.37617	+	0.500884i	0.921014	−	0.389529i	$-0.127362\pi$
$479$	30.1189	+	10.9624i	1.37617	+	0.500884i	0.455153	+	0.890413i	$0.349585\pi$
$480$		0			0
$481$	1.43552	−	1.20455i	0.0654543	−	0.0549227i
$482$	−10.4155	−	18.0401i	−0.474412	−	0.821705i
$483$	−4.55996	+	7.89809i	−0.207485	+	0.359375i
$484$	−0.448551	−	2.54386i	−0.0203887	−	0.115630i
$485$		0			0
$486$	0.958815	−	1.66072i	0.0434927	−	0.0753316i
$487$	−8.73726	−	15.1334i	−0.395923	−	0.685759i	0.597296	−	0.802021i	$-0.296242\pi$
$487$	−8.73726	−	15.1334i	−0.395923	−	0.685759i	−0.993219	+	0.116263i	$0.962909\pi$
$488$	−1.02596	+	0.860884i	−0.0464431	+	0.0389704i
$489$	34.9693	−	12.7278i	1.58137	−	0.575570i
$490$		0			0
$491$	−1.62811	−	1.36614i	−0.0734754	−	0.0616531i	0.605310	−	0.795990i	$-0.293049\pi$
$491$	−1.62811	−	1.36614i	−0.0734754	−	0.0616531i	−0.678786	+	0.734336i	$0.737493\pi$
$492$	−0.694505	+	3.93873i	−0.0313107	+	0.177572i
$493$	8.05903			0.362961
$494$	−1.51946	−	5.44399i	−0.0683637	−	0.244937i
$495$		0			0
$496$	−1.05732	+	5.99634i	−0.0474749	+	0.269244i
$497$	28.8185	+	24.1816i	1.29269	+	1.08469i
$498$	13.3303	+	4.85182i	0.597344	+	0.217415i
$499$	−34.1891	+	12.4438i	−1.53051	+	0.557062i	−0.963747	−	0.266817i	$-0.914028\pi$
$499$	−34.1891	+	12.4438i	−1.53051	+	0.557062i	−0.566767	+	0.823878i	$0.691806\pi$
$500$		0			0
$501$	14.5875	+	25.2663i	0.651722	+	1.12882i
$502$	−5.74329	+	9.94767i	−0.256336	+	0.443986i
$503$	−1.60048	−	9.07677i	−0.0713619	−	0.404713i	−0.999475	−	0.0324139i	$-0.989681\pi$
$503$	−1.60048	−	9.07677i	−0.0713619	−	0.404713i	0.928113	−	0.372299i	$-0.121431\pi$
$504$	−0.0794355	−	0.450501i	−0.00353834	−	0.0200669i
$505$		0			0
$506$	3.18509	+	5.51674i	0.141595	+	0.245249i
$507$	14.5480	−	12.2072i	0.646100	−	0.542142i
$508$	0.123149	−	0.0448227i	0.00546387	−	0.00198869i
$509$	−16.3916	−	5.96606i	−0.726546	−	0.264441i	−0.0478437	−	0.998855i	$-0.515235\pi$
$509$	−16.3916	−	5.96606i	−0.726546	−	0.264441i	−0.678702	+	0.734414i	$0.737457\pi$
$510$		0			0
$511$	−0.240988	+	1.36671i	−0.0106607	+	0.0604597i
$512$	1.00000			0.0441942
$513$	16.2983	−	16.6403i	0.719588	−	0.734686i
$514$	−1.85667			−0.0818943
$515$		0			0
$516$	−11.8259	−	9.92310i	−0.520606	−	0.436840i
$517$	−30.3371	−	11.0418i	−1.33422	−	0.485618i
$518$	3.36181	−	1.22360i	0.147709	−	0.0537618i
$519$	2.76107	−	2.31681i	0.121197	−	0.101697i
$520$		0			0
$521$	−10.5137	+	18.2102i	−0.460611	+	0.797802i	−0.998992	−	0.0448997i	$-0.985703\pi$
$521$	−10.5137	+	18.2102i	−0.460611	+	0.797802i	0.538380	+	0.842702i	$0.319037\pi$
$522$	0.208051	+	1.17992i	0.00910615	+	0.0516435i
$523$	1.48848	+	8.44161i	0.0650868	+	0.369126i	0.999902	+	0.0139914i	$0.00445376\pi$
$523$	1.48848	+	8.44161i	0.0650868	+	0.369126i	−0.934815	+	0.355134i	$0.884435\pi$
$524$	−6.40094	+	11.0867i	−0.279626	+	0.484327i
$525$		0			0
$526$	−7.85464	+	6.59082i	−0.342478	+	0.287373i
$527$	−7.11195	+	2.58854i	−0.309801	+	0.112758i
$528$	4.57422	+	1.66488i	0.199067	+	0.0724546i
$529$	−13.9258	−	11.6851i	−0.605469	−	0.508049i
$530$		0			0
$531$	0.373837			0.0162231
$532$	0.828800	−	10.7585i	0.0359330	−	0.466440i
$533$	−3.09086			−0.133880
$534$	3.46716	−	19.6632i	0.150038	−	0.850911i
$535$		0			0
$536$	3.16333	+	1.15136i	0.136635	+	0.0497311i
$537$	−16.3687	+	5.95770i	−0.706360	+	0.257094i
$538$	20.2958	−	17.0302i	0.875014	−	0.734224i
$539$	1.26489	+	2.19086i	0.0544827	+	0.0943668i
$540$		0			0
$541$	3.75653	+	21.3044i	0.161506	+	0.915946i	0.952594	+	0.304244i	$0.0984038\pi$
$541$	3.75653	+	21.3044i	0.161506	+	0.915946i	−0.791088	+	0.611702i	$0.790485\pi$
$542$	4.32588	+	24.5333i	0.185812	+	1.05379i
$543$	−13.9645	+	24.1872i	−0.599275	+	1.03797i
$544$	0.621495	+	1.07646i	0.0266464	+	0.0461529i
$545$		0			0
$546$	−5.06094	+	1.84203i	−0.216588	+	0.0788316i
$547$	29.4938	+	10.7349i	1.26106	+	0.458989i	0.884126	−	0.467249i	$-0.154755\pi$
$547$	29.4938	+	10.7349i	1.26106	+	0.458989i	0.376937	+	0.926239i	$0.376977\pi$
$548$	11.9723	+	10.0460i	0.511432	+	0.429143i
$549$	0.0429766	−	0.243732i	0.00183420	−	0.0104022i
$550$		0			0
$551$	−2.17073	+	28.1778i	−0.0924761	+	1.20042i
$552$	3.68410			0.156806
$553$	2.78672	−	15.8042i	0.118503	−	0.672065i
$554$	11.0045	+	9.23384i	0.467535	+	0.392308i
$555$		0			0
$556$	10.7878	−	3.92644i	0.457505	−	0.166518i
$557$	−4.36296	+	3.66096i	−0.184864	+	0.155120i	−0.730523	−	0.682888i	$-0.760724\pi$
$557$	−4.36296	+	3.66096i	−0.184864	+	0.155120i	0.545659	+	0.838007i	$0.316279\pi$
$558$	−0.562587	−	0.974429i	−0.0238162	−	0.0412509i
$559$	5.96520	−	10.3320i	0.252301	−	0.436998i
$560$		0			0
$561$	1.05068	+	5.95868i	0.0443596	+	0.251576i
$562$	13.4473	−	23.2914i	0.567240	−	0.982488i
$563$	4.02935	+	6.97904i	0.169817	+	0.294132i	0.938355	−	0.345672i	$-0.112349\pi$
$563$	4.02935	+	6.97904i	0.169817	+	0.294132i	−0.768538	+	0.639804i	$0.779016\pi$
$564$	−14.3028	+	12.0015i	−0.602257	+	0.505353i
$565$		0			0
$566$	−18.9490	−	6.89686i	−0.796484	−	0.289896i
$567$	−15.9509	−	13.3844i	−0.669876	−	0.562093i
$568$	2.63893	−	14.9661i	0.110727	−	0.627964i
$569$	22.1220			0.927404			0.463702	−	0.885991i	$-0.346521\pi$
$569$	22.1220			0.927404			0.463702	+	0.885991i	$0.346521\pi$
$570$		0			0
$571$	45.8413			1.91840			0.959200	−	0.282729i	$-0.0912396\pi$
$571$	45.8413			1.91840			0.959200	+	0.282729i	$0.0912396\pi$
$572$	−0.653245	+	3.70474i	−0.0273136	+	0.154903i
$573$	28.0091	+	23.5024i	1.17009	+	0.981826i
$574$	−5.54492	−	2.01819i	−0.231441	−	0.0842375i
$575$		0			0
$576$	−0.141559	+	0.118782i	−0.00589830	+	0.00494926i
$577$	15.8503	+	27.4535i	0.659857	+	1.14291i	0.980652	+	0.195757i	$0.0627164\pi$
$577$	15.8503	+	27.4535i	0.659857	+	1.14291i	−0.320796	+	0.947148i	$0.603950\pi$
$578$	7.72749	−	13.3844i	0.321421	−	0.556718i
$579$	6.67507	+	37.8562i	0.277406	+	1.57325i
$580$		0			0
$581$	−10.4647	+	18.1254i	−0.434150	+	0.751970i
$582$	2.26984	+	3.93148i	0.0940880	+	0.162965i
$583$	−26.7507	+	22.4465i	−1.10790	+	0.929639i
$584$	0.526806	−	0.191742i	0.0217994	−	0.00793434i
$585$		0			0
$586$	−15.3201	−	12.8551i	−0.632869	−	0.531041i
$587$	−2.22328	+	12.6088i	−0.0917644	+	0.520422i	0.903926	+	0.427688i	$0.140672\pi$
$587$	−2.22328	+	12.6088i	−0.0917644	+	0.520422i	−0.995691	+	0.0927341i	$0.970439\pi$
$588$	1.46306			0.0603356
$589$	−7.13500	−	25.5636i	−0.293993	−	1.05333i
$590$		0			0
$591$	−1.44383	+	8.18839i	−0.0593914	+	0.336825i
$592$	−1.10708	−	0.928954i	−0.0455009	−	0.0381798i
$593$	−34.8002	−	12.6662i	−1.42907	−	0.520140i	−0.492407	−	0.870365i	$-0.663883\pi$
$593$	−34.8002	−	12.6662i	−1.42907	−	0.520140i	−0.936665	+	0.350225i	$0.886105\pi$
$594$	−14.5679	+	5.30230i	−0.597730	+	0.217556i
$595$		0			0
$596$	7.57580	+	13.1217i	0.310317	+	0.537485i
$597$	20.6388	−	35.7474i	0.844688	−	1.46304i
$598$	0.494397	+	2.80387i	0.0202174	+	0.114659i
$599$	1.00225	+	5.68403i	0.0409507	+	0.232243i	0.998413	−	0.0563153i	$-0.0179352\pi$
$599$	1.00225	+	5.68403i	0.0409507	+	0.232243i	−0.957462	+	0.288558i	$0.906824\pi$
$600$		0			0
$601$	−8.26350	−	14.3128i	−0.337075	−	0.583831i	0.646806	−	0.762655i	$-0.276104\pi$
$601$	−8.26350	−	14.3128i	−0.337075	−	0.583831i	−0.983881	+	0.178823i	$0.942771\pi$
$602$	17.4477	−	14.6404i	0.711116	−	0.596697i
$603$	−0.584560	+	0.212762i	−0.0238051	+	0.00866435i
$604$	5.43856	+	1.97947i	0.221292	+	0.0805436i
$605$		0			0
$606$	−0.0343390	+	0.194746i	−0.00139493	+	0.00791103i
$607$	2.34282			0.0950920			0.0475460	−	0.998869i	$-0.484860\pi$
$607$	2.34282			0.0950920			0.0475460	+	0.998869i	$0.484860\pi$
$608$	−3.93117	+	1.88306i	−0.159430	+	0.0763683i
$609$	26.9296			1.09124
$610$		0			0
$611$	−11.0534	−	9.27490i	−0.447173	−	0.375222i
$612$	−0.215843	−	0.0785604i	−0.00872493	−	0.00317562i
$613$	−28.2173	+	10.2703i	−1.13969	+	0.414812i	−0.841800	−	0.539789i	$-0.818504\pi$
$613$	−28.2173	+	10.2703i	−1.13969	+	0.414812i	−0.297886	+	0.954601i	$0.596282\pi$
$614$	14.8627	−	12.4713i	0.599808	−	0.503299i
$615$		0			0
$616$	−3.59092	+	6.21966i	−0.144682	+	0.250597i
$617$	2.81756	+	15.9792i	0.113431	+	0.643298i	0.987515	+	0.157524i	$0.0503512\pi$
$617$	2.81756	+	15.9792i	0.113431	+	0.643298i	−0.874084	+	0.485774i	$0.838538\pi$
$618$	0.507364	+	2.87740i	0.0204092	+	0.115746i
$619$	−23.8503	+	41.3099i	−0.958624	+	1.66039i	−0.232776	+	0.972530i	$0.574781\pi$
$619$	−23.8503	+	41.3099i	−0.958624	+	1.66039i	−0.725848	+	0.687855i	$0.758552\pi$
$620$		0			0
$621$	−8.98807	+	7.54188i	−0.360679	+	0.302645i
$622$	−5.07338	+	1.84656i	−0.203424	+	0.0740403i
$623$	27.6818	+	10.0753i	1.10905	+	0.403660i
$624$	1.66663	+	1.39847i	0.0667186	+	0.0559835i
$625$		0			0
$626$	16.1834			0.646818
$627$	−21.1171	+	2.06862i	−0.843336	+	0.0826128i
$628$	11.0189			0.439704
$629$	0.311935	−	1.76907i	0.0124377	−	0.0705376i
$630$		0			0
$631$	11.5071	+	4.18824i	0.458090	+	0.166731i	0.560750	−	0.827985i	$-0.310513\pi$
$631$	11.5071	+	4.18824i	0.458090	+	0.166731i	−0.102660	+	0.994717i	$0.532735\pi$
$632$	−6.09184	+	2.21725i	−0.242320	+	0.0881973i
$633$	4.72260	−	3.96273i	0.187706	−	0.157504i
$634$	−1.22547	−	2.12258i	−0.0486696	−	0.0842983i
$635$		0			0
$636$	3.50696	+	19.8889i	0.139060	+	0.788648i
$637$	0.196339	+	1.11350i	0.00777925	+	0.0441183i
$638$	9.40506	−	16.2900i	0.372350	−	0.644929i
$639$	1.40415	+	2.43205i	0.0555471	+	0.0962104i
$640$		0			0
$641$	27.9385	−	10.1688i	1.10350	−	0.401643i	0.274897	−	0.961474i	$-0.411356\pi$
$641$	27.9385	−	10.1688i	1.10350	−	0.401643i	0.828607	+	0.559831i	$0.189134\pi$
$642$	26.3404	+	9.58714i	1.03957	+	0.378374i
$643$	−16.1016	−	13.5109i	−0.634987	−	0.532817i	0.267487	−	0.963561i	$-0.413807\pi$
$643$	−16.1016	−	13.5109i	−0.634987	−	0.532817i	−0.902474	+	0.430744i	$0.858251\pi$
$644$	−0.943857	+	5.35288i	−0.0371932	+	0.210933i
$645$		0			0
$646$	−4.47024	−	3.06143i	−0.175879	−	0.120451i
$647$	10.8225			0.425476			0.212738	−	0.977109i	$-0.431762\pi$
$647$	10.8225			0.425476			0.212738	+	0.977109i	$0.431762\pi$
$648$	−1.46064	+	8.28368i	−0.0573792	+	0.325414i
$649$	−4.49602	−	3.77261i	−0.176484	−	0.148088i
$650$		0			0
$651$	−23.7649	+	8.64972i	−0.931420	+	0.339009i
$652$	16.9903	−	14.2565i	0.665390	−	0.558328i
$653$	−21.4738	−	37.1937i	−0.840334	−	1.45550i	−0.889613	−	0.456716i	$-0.849026\pi$
$653$	−21.4738	−	37.1937i	−0.840334	−	1.45550i	0.0492789	−	0.998785i	$-0.484308\pi$
$654$	16.9865	−	29.4214i	0.664223	−	1.15047i
$655$		0			0
$656$	0.413923	+	2.34748i	0.0161610	+	0.0916536i
$657$	−0.0517988	+	0.0897182i	−0.00202086	+	0.00350024i
$658$	−13.7734	−	23.8563i	−0.536944	−	0.930015i
$659$	−4.59278	+	3.85380i	−0.178909	+	0.150123i	−0.727845	−	0.685742i	$-0.759478\pi$
$659$	−4.59278	+	3.85380i	−0.178909	+	0.150123i	0.548935	+	0.835865i	$0.315033\pi$
$660$		0			0
$661$	−16.9338	−	6.16342i	−0.658650	−	0.239729i	−0.00899680	−	0.999960i	$-0.502864\pi$
$661$	−16.9338	−	6.16342i	−0.658650	−	0.239729i	−0.649654	+	0.760230i	$0.725086\pi$
$662$	2.32590	+	1.95166i	0.0903986	+	0.0758535i
$663$	−0.469594	+	2.66320i	−0.0182375	+	0.103430i
$664$	8.45470			0.328106
$665$		0			0
$666$	0.267061			0.0103484
$667$	2.47207	−	14.0198i	0.0957191	−	0.542850i
$668$	13.3202	+	11.1770i	0.515373	+	0.432449i
$669$	−11.7515	−	4.27719i	−0.454339	−	0.165366i
$670$		0			0
$671$	−2.97651	+	2.49759i	−0.114907	+	0.0964183i
$672$	2.07675	+	3.59705i	0.0801126	+	0.138759i
$673$	−13.6781	+	23.6912i	−0.527254	+	0.913231i	0.472242	+	0.881469i	$0.343445\pi$
$673$	−13.6781	+	23.6912i	−0.527254	+	0.913231i	−0.999495	+	0.0317614i	$0.989888\pi$
$674$	1.05284	+	5.97096i	0.0405539	+	0.229993i
$675$		0			0
$676$	5.65932	−	9.80223i	0.217666	−	0.377009i
$677$	15.1015	+	26.1566i	0.580398	+	1.00528i	0.995432	+	0.0954734i	$0.0304365\pi$
$677$	15.1015	+	26.1566i	0.580398	+	1.00528i	−0.415034	+	0.909806i	$0.636230\pi$
$678$	−21.2653	+	17.8437i	−0.816689	+	0.685284i
$679$	−6.29385	+	2.29077i	−0.241536	+	0.0879118i
$680$		0			0
$681$	−14.6740	−	12.3129i	−0.562308	−	0.471833i
$682$	−3.06748	+	17.3965i	−0.117460	+	0.666148i
$683$	−42.2829			−1.61791			−0.808955	−	0.587871i	$-0.799966\pi$
$683$	−42.2829			−1.61791			−0.808955	+	0.587871i	$0.799966\pi$
$684$	0.332819	−	0.733518i	0.0127256	−	0.0280468i
$685$		0			0
$686$	−3.38388	+	19.1909i	−0.129197	+	0.732712i
$687$	4.10442	+	3.44402i	0.156594	+	0.131398i
$688$	−8.64591	−	3.14685i	−0.329622	−	0.119973i
$689$	−14.6663	+	5.33810i	−0.558742	+	0.203365i
$690$		0			0
$691$	−7.96853	−	13.8019i	−0.303137	−	0.525049i	0.673708	−	0.738998i	$-0.264701\pi$
$691$	−7.96853	−	13.8019i	−0.303137	−	0.525049i	−0.976845	+	0.213949i	$0.931367\pi$
$692$	1.07408	−	1.86037i	0.0408305	−	0.0707205i
$693$	−0.230457	−	1.30699i	−0.00875435	−	0.0496484i
$694$	−0.499559	−	2.83314i	−0.0189630	−	0.107545i
$695$		0			0
$696$	−5.43927	−	9.42109i	−0.206175	−	0.357106i
$697$	−2.26972	+	1.90452i	−0.0859716	+	0.0721387i
$698$	−30.8180	+	11.2168i	−1.16648	+	0.424564i
$699$	36.7350	+	13.3704i	1.38945	+	0.505717i
$700$		0			0
$701$	−1.03691	+	5.88059i	−0.0391634	+	0.222107i	−0.998108	−	0.0614872i	$-0.980416\pi$
$701$	−1.03691	+	5.88059i	−0.0391634	+	0.222107i	0.958944	+	0.283594i	$0.0915268\pi$
$702$	−6.92893			−0.261516
$703$	6.10141	+	1.56716i	0.230119	+	0.0591067i
$704$	2.90119			0.109343
$705$		0			0
$706$	−16.2408	−	13.6277i	−0.611231	−	0.512884i
$707$	−0.274163	−	0.0997871i	−0.0103110	−	0.00375288i
$708$	−3.18962	+	1.16093i	−0.119873	+	0.0436303i
$709$	35.7131	−	29.9669i	1.34123	−	1.12543i	0.359928	−	0.932980i	$-0.382801\pi$
$709$	35.7131	−	29.9669i	1.34123	−	1.12543i	0.981307	−	0.192450i	$-0.0616432\pi$
$710$		0			0
$711$	0.598986	−	1.03747i	0.0224637	−	0.0389083i
$712$	−2.06642	−	11.7192i	−0.0774423	−	0.439197i
$713$	2.32157	+	13.1663i	0.0869434	+	0.493080i
$714$	−2.58139	+	4.47109i	−0.0966059	+	0.167326i
$715$		0			0
$716$	−7.95291	+	6.67328i	−0.297214	+	0.249392i
$717$	−12.9635	+	4.71833i	−0.484131	+	0.176209i
$718$	−17.4685	−	6.35803i	−0.651920	−	0.237280i
$719$	−31.8698	−	26.7420i	−1.18854	−	0.997307i	−0.999883	−	0.0152650i	$-0.995141\pi$
$719$	−31.8698	−	26.7420i	−1.18854	−	0.997307i	−0.188661	−	0.982042i	$-0.560415\pi$
$720$		0			0
$721$	−4.31076			−0.160541
$722$	11.9081	−	14.8053i	0.443175	−	0.550995i
$723$	−34.9514			−1.29986
$724$	−2.89049	+	16.3928i	−0.107424	+	0.609232i
$725$		0			0
$726$	−4.07270	−	1.48234i	−0.151152	−	0.0550149i
$727$	19.5154	−	7.10304i	0.723787	−	0.263437i	0.0462546	−	0.998930i	$-0.485271\pi$
$727$	19.5154	−	7.10304i	0.723787	−	0.263437i	0.677533	+	0.735493i	$0.263049\pi$
$728$	−2.45892	+	2.06328i	−0.0911335	+	0.0764701i
$729$	−14.2260	−	24.6401i	−0.526888	−	0.912596i
$730$		0			0
$731$	−1.98592	−	11.2627i	−0.0734521	−	0.416567i
$732$	0.390214	+	2.21301i	0.0144227	+	0.0817953i
$733$	−14.7331	+	25.5184i	−0.544179	+	0.942545i	0.454480	+	0.890757i	$0.349825\pi$
$733$	−14.7331	+	25.5184i	−0.544179	+	0.942545i	−0.998658	+	0.0517877i	$0.983508\pi$
$734$	−10.8612	−	18.8121i	−0.400893	−	0.694367i
$735$		0			0
$736$	2.06330	−	0.750979i	0.0760542	−	0.0276814i
$737$	9.17742	+	3.34031i	0.338054	+	0.123042i
$738$	−0.337433	−	0.283140i	−0.0124211	−	0.0104225i
$739$	4.63253	−	26.2724i	0.170410	−	0.966446i	−0.772898	−	0.634530i	$-0.781194\pi$
$739$	4.63253	−	26.2724i	0.170410	−	0.966446i	0.943309	−	0.331916i	$-0.107695\pi$
$740$		0			0
$741$	−9.18520	−	2.35924i	−0.337427	−	0.0866690i
$742$	−29.7965			−1.09386
$743$	7.85099	−	44.5252i	0.288025	−	1.63347i	−0.406252	−	0.913761i	$-0.633164\pi$
$743$	7.85099	−	44.5252i	0.288025	−	1.63347i	0.694276	−	0.719708i	$-0.255725\pi$
$744$	7.82608	+	6.56686i	0.286918	+	0.240753i
$745$		0			0
$746$	21.0636	−	7.66651i	0.771192	−	0.280691i
$747$	−1.19684	+	1.00427i	−0.0437901	+	0.0367443i
$748$	1.80307	+	3.12302i	0.0659269	+	0.114189i
$749$	−20.6782	+	35.8156i	−0.755564	+	1.30867i
$750$		0			0
$751$	−0.599478	−	3.39981i	−0.0218753	−	0.124061i	0.971915	−	0.235334i	$-0.0756183\pi$
$751$	−0.599478	−	3.39981i	−0.0218753	−	0.124061i	−0.993790	+	0.111273i	$0.964507\pi$
$752$	−5.56394	+	9.63702i	−0.202896	+	0.351426i
$753$	9.63642	+	16.6908i	0.351171	+	0.608246i
$754$	6.44020	−	5.40397i	0.234538	−	0.196801i
$755$		0			0
$756$	−12.4303	−	4.52427i	−0.452086	−	0.164546i
$757$	−30.9109	−	25.9373i	−1.12348	−	0.942708i	−0.124701	−	0.992194i	$-0.539797\pi$
$757$	−30.9109	−	25.9373i	−1.12348	−	0.942708i	−0.998775	+	0.0494862i	$0.984242\pi$
$758$	−1.46776	+	8.32410i	−0.0533116	+	0.302345i
$759$	10.6883			0.387960
$760$		0			0
$761$	−12.4450			−0.451132			−0.225566	−	0.974228i	$-0.572423\pi$
$761$	−12.4450			−0.451132			−0.225566	+	0.974228i	$0.572423\pi$
$762$	0.0381832	−	0.216547i	0.00138323	−	0.00784469i
$763$	38.3965	+	32.2185i	1.39005	+	1.16639i
$764$	20.4774	+	7.45317i	0.740847	+	0.269646i
$765$		0			0
$766$	7.54187	−	6.32838i	0.272499	−	0.228654i
$767$	−1.31159	−	2.27174i	−0.0473587	−	0.0820277i
$768$	0.838929	−	1.45307i	0.0302722	−	0.0524331i
$769$	5.55178	+	31.4857i	0.200202	+	1.13540i	0.904813	+	0.425810i	$0.140011\pi$
$769$	5.55178	+	31.4857i	0.200202	+	1.13540i	−0.704610	+	0.709594i	$0.748878\pi$
$770$		0			0
$771$	−1.55762	+	2.69787i	−0.0560962	+	0.0971615i
$772$	11.4551	+	19.8409i	0.412279	+	0.714089i
$773$	27.0224	−	22.6745i	0.971929	−	0.815545i	−0.0109230	−	0.999940i	$-0.503477\pi$
$773$	27.0224	−	22.6745i	0.971929	−	0.815545i	0.982852	+	0.184395i	$0.0590325\pi$
$774$	1.59770	−	0.581515i	0.0574281	−	0.0209021i
$775$		0			0
$776$	2.07264	+	1.73915i	0.0744035	+	0.0624320i
$777$	1.04235	−	5.91144i	0.0373940	−	0.212072i
$778$	−8.51432			−0.305253
$779$	−6.04765	−	8.44888i	−0.216679	−	0.302712i
$780$		0			0
$781$	7.65603	−	43.4195i	0.273954	−	1.55367i
$782$	2.09073	+	1.75433i	0.0747643	+	0.0627347i
$783$	32.5565	+	11.8496i	1.16347	+	0.423470i
$784$	0.819394	−	0.298235i	0.0292641	−	0.0106513i
$785$		0			0
$786$	10.7399	+	18.6020i	0.383078	+	0.663511i
$787$	−19.7471	+	34.2030i	−0.703909	+	1.21921i	0.263175	+	0.964748i	$0.415230\pi$
$787$	−19.7471	+	34.2030i	−0.703909	+	1.21921i	−0.967084	+	0.254458i	$0.918103\pi$
$788$	0.860522	+	4.88026i	0.0306548	+	0.173852i
$789$	2.98743	+	16.9425i	0.106355	+	0.603171i
$790$		0			0
$791$	−20.4782	−	35.4694i	−0.728123	−	1.26115i
$792$	−0.410690	+	0.344610i	−0.0145932	+	0.0122452i
$793$	−1.63190	+	0.593962i	−0.0579504	+	0.0210922i
$794$	23.0365	+	8.38460i	0.817535	+	0.297558i
$795$		0			0
$796$	4.27197	−	24.2276i	0.151416	−	0.858724i
$797$	18.0151			0.638128			0.319064	−	0.947733i	$-0.396631\pi$
$797$	18.0151			0.638128			0.319064	+	0.947733i	$0.396631\pi$
$798$	−14.9375	−	10.2299i	−0.528783	−	0.362135i
$799$	−13.8318			−0.489335
$800$		0			0
$801$	1.68456	+	1.41351i	0.0595210	+	0.0499440i
$802$	4.67444	+	1.70136i	0.165060	+	0.0600770i
$803$	1.52837	−	0.556279i	0.0539348	−	0.0196307i
$804$	4.32681	−	3.63062i	0.152595	−	0.128042i
$805$		0			0
$806$	−3.94762	+	6.83747i	−0.139049	+	0.240840i
$807$	−7.71929	−	43.7783i	−0.271732	−	1.54107i
$808$	0.0204660	+	0.116068i	0.000719991	+	0.00408327i
$809$	−14.5518	+	25.2045i	−0.511615	+	0.886144i	0.488294	+	0.872679i	$0.337619\pi$
$809$	−14.5518	+	25.2045i	−0.511615	+	0.886144i	−0.999909	+	0.0134647i	$0.995714\pi$
$810$		0			0
$811$	12.3496	−	10.3626i	0.433654	−	0.363879i	−0.399675	−	0.916657i	$-0.630877\pi$
$811$	12.3496	−	10.3626i	0.433654	−	0.363879i	0.833328	+	0.552779i	$0.186432\pi$
$812$	15.0821	−	5.48943i	0.529277	−	0.192641i
$813$	39.2776	+	14.2959i	1.37753	+	0.501378i
$814$	−3.21186	−	2.69507i	−0.112576	−	0.0944622i
$815$		0			0
$816$	2.08556			0.0730092
$817$	39.9142	−	3.90998i	1.39642	−	0.136793i
$818$	18.0959			0.632707
$819$	0.103002	−	0.584152i	0.00359917	−	0.0204119i
$820$		0			0
$821$	−27.8660	−	10.1424i	−0.972530	−	0.353972i	−0.193598	−	0.981081i	$-0.562016\pi$
$821$	−27.8660	−	10.1424i	−0.972530	−	0.353972i	−0.778932	+	0.627109i	$0.784238\pi$
$822$	24.6414	−	8.96874i	0.859468	−	0.312821i
$823$	18.1522	−	15.2315i	0.632746	−	0.530937i	−0.269035	−	0.963130i	$-0.586705\pi$
$823$	18.1522	−	15.2315i	0.632746	−	0.530937i	0.901781	+	0.432194i	$0.142260\pi$
$824$	0.870691	+	1.50808i	0.0303320	+	0.0525365i
$825$		0			0
$826$	−0.869617	−	4.93184i	−0.0302579	−	0.171601i
$827$	−6.60682	−	37.4692i	−0.229742	−	1.30293i	−0.853410	−	0.521241i	$-0.825469\pi$
$827$	−6.60682	−	37.4692i	−0.229742	−	1.30293i	0.623668	−	0.781689i	$-0.285642\pi$
$828$	−0.202876	+	0.351391i	−0.00705042	+	0.0122117i
$829$	−11.9638	−	20.7219i	−0.415520	−	0.719701i	0.579963	−	0.814643i	$-0.303067\pi$
$829$	−11.9638	−	20.7219i	−0.415520	−	0.719701i	−0.995483	+	0.0949413i	$0.969734\pi$
$830$		0			0
$831$	22.6494	−	8.24369i	0.785698	−	0.285971i
$832$	1.21847	+	0.443488i	0.0422429	+	0.0153752i
$833$	0.830288	+	0.696694i	0.0287678	+	0.0241390i
$834$	3.34482	−	18.9694i	0.115822	−	0.656858i
$835$		0			0
$836$	−11.4051	+	5.46312i	−0.394452	+	0.188946i
$837$	−32.5365			−1.12463
$838$	−1.83747	+	10.4208i	−0.0634745	+	0.359982i
$839$	13.6980	+	11.4940i	0.472908	+	0.396817i	0.847854	−	0.530230i	$-0.177894\pi$
$839$	13.6980	+	11.4940i	0.472908	+	0.396817i	−0.374946	+	0.927047i	$0.622339\pi$
$840$		0			0
$841$	−12.2507	+	4.45888i	−0.422437	+	0.153755i
$842$	−18.5815	+	15.5917i	−0.640359	+	0.537325i
$843$	−22.5626	−	39.0796i	−0.777099	−	1.34597i
$844$	1.83714	−	3.18202i	0.0632369	−	0.109530i
$845$		0			0
$846$	−0.357081	−	2.02511i	−0.0122767	−	0.0696246i
$847$	3.19721	−	5.53773i	0.109858	−	0.190279i
$848$	6.01832	+	10.4240i	0.206670	+	0.357963i
$849$	−25.9184	+	21.7481i	−0.889518	+	0.746394i
$850$		0			0
$851$	−2.98187	−	1.08531i	−0.102217	−	0.0372040i
$852$	−19.5329	−	16.3901i	−0.669186	−	0.561514i
$853$	−6.24081	+	35.3934i	−0.213681	+	1.21185i	0.669499	+	0.742813i	$0.266509\pi$
$853$	−6.24081	+	35.3934i	−0.213681	+	1.21185i	−0.883181	+	0.469033i	$0.844602\pi$
$854$	−3.31541			−0.113451
$855$		0			0
$856$	16.7064			0.571012
$857$	−0.925930	+	5.25121i	−0.0316292	+	0.179378i	−0.996530	−	0.0832376i	$-0.973474\pi$
$857$	−0.925930	+	5.25121i	−0.0316292	+	0.179378i	0.964901	+	0.262615i	$0.0845851\pi$
$858$	4.83521	+	4.05722i	0.165071	+	0.138511i
$859$	8.81020	+	3.20665i	0.300600	+	0.109410i	0.487917	−	0.872890i	$-0.337757\pi$
$859$	8.81020	+	3.20665i	0.300600	+	0.109410i	−0.187317	+	0.982300i	$0.559979\pi$
$860$		0			0
$861$	−7.58436	+	6.36403i	−0.258474	+	0.216886i
$862$	−17.8512	−	30.9192i	−0.608015	−	1.05311i
$863$	−2.64200	+	4.57608i	−0.0899348	+	0.155772i	−0.907483	−	0.420088i	$-0.861999\pi$
$863$	−2.64200	+	4.57608i	−0.0899348	+	0.155772i	0.817549	+	0.575860i	$0.195333\pi$
$864$	0.927912	+	5.26245i	0.0315682	+	0.179032i
$865$		0			0
$866$	16.5340	−	28.6378i	0.561849	−	0.973151i
$867$	−12.9656	−	22.4571i	−0.440336	−	0.762684i
$868$	−11.5465	+	9.68864i	−0.391913	+	0.328854i
$869$	−17.6736	+	6.43265i	−0.599535	+	0.218213i
$870$		0			0
$871$	3.34382	+	2.80580i	0.113301	+	0.0950707i
$872$	3.51599	−	19.9402i	0.119066	−	0.675260i
$873$	−0.499982			−0.0169218
$874$	−6.69703	+	6.83754i	−0.226530	+	0.231283i
$875$		0			0
$876$	0.163339	−	0.926343i	0.00551872	−	0.0312982i
$877$	−38.6673	−	32.4457i	−1.30570	−	1.09561i	−0.989130	−	0.147045i	$-0.953024\pi$
$877$	−38.6673	−	32.4457i	−1.30570	−	1.09561i	−0.316572	−	0.948569i	$-0.602532\pi$
$878$	−5.55555	−	2.02205i	−0.187491	−	0.0682410i
$879$	−31.5319	+	11.4767i	−1.06354	+	0.387098i
$880$		0			0
$881$	−10.2170	−	17.6964i	−0.344221	−	0.596208i	0.640991	−	0.767549i	$-0.278524\pi$
$881$	−10.2170	−	17.6964i	−0.344221	−	0.596208i	−0.985212	+	0.171340i	$0.945190\pi$
$882$	−0.0805678	+	0.139548i	−0.00271286	+	0.00469881i
$883$	−0.0219697	−	0.124596i	−0.000739339	−	0.00419300i	0.984436	−	0.175744i	$-0.0562332\pi$
$883$	−0.0219697	−	0.124596i	−0.000739339	−	0.00419300i	−0.985175	+	0.171551i	$0.945122\pi$
$884$	0.279877	+	1.58726i	0.00941329	+	0.0533854i
$885$		0			0
$886$	5.91634	+	10.2474i	0.198763	+	0.344268i
$887$	19.8231	−	16.6336i	0.665594	−	0.558500i	−0.246163	−	0.969228i	$-0.579170\pi$
$887$	19.8231	−	16.6336i	0.665594	−	0.558500i	0.911758	+	0.410728i	$0.134726\pi$
$888$	−2.27860	+	0.829342i	−0.0764648	+	0.0278309i
$889$	0.304854	+	0.110958i	0.0102245	+	0.00372141i
$890$		0			0
$891$	−4.23758	+	24.0325i	−0.141964	+	0.805120i
$892$	−7.45336			−0.249557
$893$	3.72565	−	48.3620i	0.124674	−	1.61837i
$894$	25.4222			0.850247
$895$		0			0
$896$	1.89633	+	1.59121i	0.0633520	+	0.0531586i
$897$	4.48897	+	1.63385i	0.149882	+	0.0545527i
$898$	7.12658	−	2.59386i	0.237817	−	0.0865583i
$899$	30.2416	−	25.3757i	1.00861	−	0.846327i
$900$		0			0
$901$	−7.48071	+	12.9570i	−0.249218	+	0.431659i
$902$	1.20087	+	6.81047i	0.0399846	+	0.226764i
$903$	−6.63606	−	37.6350i	−0.220834	−	1.25241i
$904$	−8.27242	+	14.3283i	−0.275137	+	0.476551i
$905$		0			0
$906$	7.43887	−	6.24195i	0.247140	−	0.207375i
$907$	−50.6020	+	18.4176i	−1.68021	+	0.611547i	−0.993339	−	0.115229i	$-0.963240\pi$
$907$	−50.6020	+	18.4176i	−1.68021	+	0.611547i	−0.686874	+	0.726777i	$0.741018\pi$
$908$	−10.7281	−	3.90473i	−0.356026	−	0.129583i
$909$	−0.0166840	−	0.0139996i	−0.000553374	−	0.000464336i
$910$		0			0
$911$	2.63989			0.0874634			0.0437317	−	0.999043i	$-0.486075\pi$
$911$	2.63989			0.0874634			0.0437317	+	0.999043i	$0.486075\pi$
$912$	−0.561752	+	7.29201i	−0.0186015	+	0.241463i
$913$	24.5287			0.811781
$914$	−2.26812	+	12.8631i	−0.0750227	+	0.425475i
$915$		0			0
$916$	3.00074	+	1.09218i	0.0991474	+	0.0360867i
$917$	−29.7796	+	10.8389i	−0.983410	+	0.357932i
$918$	−5.08813	+	4.26945i	−0.167933	+	0.140913i
$919$	15.6083	+	27.0343i	0.514869	+	0.891779i	0.999851	+	0.0172553i	$0.00549282\pi$
$919$	15.6083	+	27.0343i	0.514869	+	0.891779i	−0.484982	+	0.874524i	$0.661174\pi$
$920$		0			0
$921$	−5.65286	−	32.0589i	−0.186268	−	1.05638i
$922$	−5.42530	−	30.7684i	−0.178673	−	1.01330i
$923$	9.85275	−	17.0655i	0.324307	−	0.561717i
$924$	6.02506	+	10.4357i	0.198210	+	0.343310i
$925$		0			0
$926$	−13.1215	+	4.77583i	−0.431199	+	0.156944i
$927$	−0.302388	−	0.110060i	−0.00993172	−	0.00361485i
$928$	−4.96672	−	4.16757i	−0.163040	−	0.136807i
$929$	0.849031	−	4.81509i	0.0278558	−	0.157978i	−0.967707	−	0.252078i	$-0.918886\pi$
$929$	0.849031	−	4.81509i	0.0278558	−	0.157978i	0.995563	+	0.0940997i	$0.0299972\pi$
$930$		0			0
$931$	−2.65958	+	2.71538i	−0.0871642	+	0.0889931i
$932$	23.2991			0.763187
$933$	−1.57303	+	8.92110i	−0.0514987	+	0.292064i
$934$	9.04471	+	7.58941i	0.295952	+	0.248333i
$935$		0			0
$936$	−0.225165	+	0.0819532i	−0.00735974	+	0.00267872i
$937$	−6.09056	+	5.11059i	−0.198970	+	0.166956i	−0.736829	−	0.676079i	$-0.763678\pi$
$937$	−6.09056	+	5.11059i	−0.198970	+	0.166956i	0.537859	+	0.843035i	$0.319233\pi$
$938$	4.16667	+	7.21688i	0.136046	+	0.235639i
$939$	13.5767	−	23.5155i	0.443059	−	0.767401i
$940$		0			0
$941$	−4.40739	−	24.9956i	−0.143677	−	0.814832i	−0.968420	−	0.249325i	$-0.919791\pi$
$941$	−4.40739	−	24.9956i	−0.143677	−	0.814832i	0.824743	−	0.565508i	$-0.191320\pi$
$942$	9.24411	−	16.0113i	0.301189	−	0.521675i
$943$	2.61695	+	4.53269i	0.0852197	+	0.147605i
$944$	−1.54971	+	1.30037i	−0.0504389	+	0.0423233i
$945$		0			0
$946$	−25.0834	−	9.12962i	−0.815532	−	0.296829i
$947$	22.6940	+	19.0425i	0.737456	+	0.618799i	0.932153	−	0.362064i	$-0.117928\pi$
$947$	22.6940	+	19.0425i	0.737456	+	0.618799i	−0.194697	+	0.980863i	$0.562372\pi$
$948$	−1.88881	+	10.7120i	−0.0613456	+	0.347908i
$949$	0.726934			0.0235973
$950$		0			0
$951$	−4.11233			−0.133351
$952$	−0.534316	+	3.03025i	−0.0173173	+	0.0982111i
$953$	−11.4866	−	9.63837i	−0.372086	−	0.312217i	0.437500	−	0.899218i	$-0.355864\pi$
$953$	−11.4866	−	9.63837i	−0.372086	−	0.312217i	−0.809586	+	0.587001i	$0.800308\pi$
$954$	−2.09014	−	0.760748i	−0.0676708	−	0.0246301i
$955$		0			0
$956$	−6.29848	+	5.28505i	−0.203707	+	0.170931i
$957$	−15.7803	−	27.3324i	−0.510106	−	0.883530i
$958$	16.0259	−	27.7577i	0.517774	−	0.896811i
$959$	6.71823	+	38.1010i	0.216943	+	1.23034i
$960$		0			0
$961$	−3.03703	+	5.26029i	−0.0979688	+	0.169687i
$962$	−0.936972	−	1.62288i	−0.0302092	−	0.0523239i
$963$	−2.36494	+	1.98442i	−0.0762092	+	0.0639471i
$964$	−19.5747	+	7.12460i	−0.630458	+	0.229468i
$965$		0			0
$966$	6.98627	+	5.86218i	0.224779	+	0.188612i
$967$	−2.41259	+	13.6825i	−0.0775835	+	0.439998i	0.921128	+	0.389259i	$0.127269\pi$
$967$	−2.41259	+	13.6825i	−0.0775835	+	0.439998i	−0.998712	+	0.0507392i	$0.983842\pi$
$968$	−2.58310			−0.0830240
$969$	−8.19869	+	3.92724i	−0.263380	+	0.126161i
$970$		0			0
$971$	−2.47187	+	14.0186i	−0.0793260	+	0.449880i	0.919111	+	0.393998i	$0.128908\pi$
$971$	−2.47187	+	14.0186i	−0.0793260	+	0.449880i	−0.998437	+	0.0558821i	$0.982203\pi$
$972$	−1.46899	−	1.23263i	−0.0471179	−	0.0395366i
$973$	26.7051	+	9.71985i	0.856125	+	0.311604i
$974$	−16.4207	+	5.97664i	−0.526152	+	0.191504i
$975$		0			0
$976$	0.669649	+	1.15987i	0.0214349	+	0.0371264i
$977$	4.12547	−	7.14552i	0.131985	−	0.228606i	−0.792456	−	0.609929i	$-0.791198\pi$
$977$	4.12547	−	7.14552i	0.131985	−	0.228606i	0.924442	+	0.381323i	$0.124531\pi$
$978$	−6.46207	−	36.6482i	−0.206634	−	1.17188i
$979$	−5.99507	−	33.9997i	−0.191603	−	1.08664i
$980$		0			0
$981$	1.87082	+	3.24035i	0.0597307	+	0.103457i
$982$	−1.62811	+	1.36614i	−0.0519549	+	0.0435954i
$983$	12.3437	−	4.49274i	0.393703	−	0.143296i	−0.137580	−	0.990491i	$-0.543932\pi$
$983$	12.3437	−	4.49274i	0.393703	−	0.143296i	0.531283	+	0.847194i	$0.321710\pi$
$984$	3.75829	+	1.36791i	0.119810	+	0.0436073i
$985$		0			0
$986$	1.39944	−	7.93660i	0.0445671	−	0.252753i
$987$	−46.2197			−1.47119
$988$	−5.62513	+	0.551036i	−0.178959	+	0.0175308i
$989$	−20.2023			−0.642396
$990$		0			0
$991$	−19.4973	−	16.3602i	−0.619352	−	0.519698i	0.278248	−	0.960509i	$-0.410246\pi$
$991$	−19.4973	−	16.3602i	−0.619352	−	0.519698i	−0.897600	+	0.440811i	$0.854691\pi$
$992$	5.72164	+	2.08251i	0.181662	+	0.0661197i
$993$	4.78716	−	1.74238i	0.151916	−	0.0552929i
$994$	28.8185	−	24.1816i	0.914068	−	0.766994i
$995$		0			0
$996$	7.09289	−	12.2852i	0.224747	−	0.389273i
$997$	−3.90784	−	22.1625i	−0.123763	−	0.701892i	−0.982035	−	0.188698i	$-0.939573\pi$
$997$	−3.90784	−	22.1625i	−0.123763	−	0.701892i	0.858273	−	0.513194i	$-0.171538\pi$
$998$	6.31789	+	35.8305i	0.199989	+	1.13420i
$999$	3.86130	−	6.68796i	0.122166	−	0.211598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.h.701.1		12
5.2	odd	4		950.2.u.e.549.3		24
5.3	odd	4		950.2.u.e.549.2		24
5.4	even	2		190.2.k.b.131.2	✓	12
19.9	even	9	inner	950.2.l.h.351.1		12
95.9	even	18		190.2.k.b.161.2	yes	12
95.28	odd	36		950.2.u.e.199.3		24
95.47	odd	36		950.2.u.e.199.2		24
95.54	even	18		3610.2.a.bc.1.5		6
95.79	odd	18		3610.2.a.be.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.b.131.2	✓	12	5.4	even	2
190.2.k.b.161.2	yes	12	95.9	even	18
950.2.l.h.351.1		12	19.9	even	9	inner
950.2.l.h.701.1		12	1.1	even	1	trivial
950.2.u.e.199.2		24	95.47	odd	36
950.2.u.e.199.3		24	95.28	odd	36
950.2.u.e.549.2		24	5.3	odd	4
950.2.u.e.549.3		24	5.2	odd	4
3610.2.a.bc.1.5		6	95.54	even	18
3610.2.a.be.1.2		6	95.79	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(-1.28531 - 1.07851i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-1.28531 + 1.07851i) q^{6} +(-1.23774 - 2.14383i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.0320889 - 0.181985i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{2} +(-1.28531 - 1.07851i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-1.28531 + 1.07851i) q^{6} +(-1.23774 - 2.14383i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.0320889 - 0.181985i) q^{9} +(-1.45059 + 2.51250i) q^{11} +(0.838929 + 1.45307i) q^{12} +(-0.993308 + 0.833484i) q^{13} +(-2.32619 + 0.846665i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-0.215843 + 1.22411i) q^{17} -0.184793 q^{18} +(-4.22186 - 1.08440i) q^{19} +(-0.721249 + 4.09041i) q^{21} +(2.22244 + 1.86485i) q^{22} +(2.06330 + 0.750979i) q^{23} +(1.57667 - 0.573861i) q^{24} +(0.648336 + 1.12295i) q^{26} +(-2.67181 + 4.62772i) q^{27} +(0.429863 + 2.43788i) q^{28} +(-1.12586 - 6.38509i) q^{29} +(3.04442 + 5.27310i) q^{31} +(0.766044 - 0.642788i) q^{32} +(4.57422 - 1.66488i) q^{33} +(1.16803 + 0.425128i) q^{34} +(-0.0320889 + 0.181985i) q^{36} -1.44520 q^{37} +(-1.80104 + 3.96942i) q^{38} +2.17563 q^{39} +(1.82601 + 1.53221i) q^{41} +(3.90302 + 1.42058i) q^{42} +(-8.64591 + 3.14685i) q^{43} +(2.22244 - 1.86485i) q^{44} +(1.09786 - 1.90155i) q^{46} +(1.93233 + 10.9588i) q^{47} +(-0.291357 - 1.65237i) q^{48} +(0.435991 - 0.755158i) q^{49} +(1.59763 - 1.34057i) q^{51} +(1.21847 - 0.443488i) q^{52} +(11.3107 + 4.11677i) q^{53} +(4.09346 + 3.43482i) q^{54} +2.47548 q^{56} +(4.25688 + 5.94709i) q^{57} -6.48359 q^{58} +(-0.351292 + 1.99228i) q^{59} +(1.25853 + 0.458067i) q^{61} +(5.72164 - 2.08251i) q^{62} +(-0.350428 + 0.294044i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.845282 - 4.79383i) q^{66} +(-0.584560 - 3.31520i) q^{67} +(0.621495 - 1.07646i) q^{68} +(-1.84205 - 3.19052i) q^{69} +(-14.2805 + 5.19768i) q^{71} +(0.173648 + 0.0632028i) q^{72} +(-0.429457 - 0.360357i) q^{73} +(-0.250956 + 1.42324i) q^{74} +(3.59636 + 2.46296i) q^{76} +7.18185 q^{77} +(0.377794 - 2.14258i) q^{78} +(4.96611 + 4.16706i) q^{79} +(7.90420 - 2.87689i) q^{81} +(1.82601 - 1.53221i) q^{82} +(-4.22735 - 7.32198i) q^{83} +(2.07675 - 3.59705i) q^{84} +(1.59770 + 9.06100i) q^{86} +(-5.43927 + 9.42109i) q^{87} +(-1.45059 - 2.51250i) q^{88} +(-9.11595 + 7.64919i) q^{89} +(3.01631 + 1.09785i) q^{91} +(-1.68202 - 1.41138i) q^{92} +(1.77403 - 10.0610i) q^{93} +11.1279 q^{94} -1.67786 q^{96} +(0.469830 - 2.66454i) q^{97} +(-0.667976 - 0.560499i) q^{98} +(0.503786 + 0.183363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9}+O(q^{10}) \) 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9	\( 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9} + 6 q^{11} - 6 q^{13} + 18 q^{17} + 12 q^{18} + 12 q^{21} + 6 q^{22} + 30 q^{23} - 6 q^{29} + 6 q^{31} + 24 q^{33} + 18 q^{36} - 36 q^{37} - 18 q^{38} - 36 q^{39} - 6 q^{41} + 30 q^{42} + 6 q^{44} - 12 q^{46} + 6 q^{47} - 18 q^{49} + 12 q^{52} + 12 q^{53} + 12 q^{56} + 18 q^{57} + 36 q^{58} - 24 q^{59} - 30 q^{61} + 6 q^{62} - 18 q^{63} - 6 q^{64} + 24 q^{66} - 12 q^{67} - 12 q^{68} + 6 q^{69} - 42 q^{71} - 6 q^{73} + 6 q^{74} + 18 q^{76} + 24 q^{77} - 48 q^{78} + 60 q^{79} + 18 q^{81} - 6 q^{82} - 24 q^{83} - 24 q^{84} - 36 q^{86} - 54 q^{87} + 6 q^{88} - 12 q^{89} + 24 q^{91} - 24 q^{92} - 6 q^{93} + 60 q^{94} - 30 q^{97} - 36 q^{98} - 12 q^{99}+O(q^{100}) \) 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9 + 6 * q^11 - 6 * q^13 + 18 * q^17 + 12 * q^18 + 12 * q^21 + 6 * q^22 + 30 * q^23 - 6 * q^29 + 6 * q^31 + 24 * q^33 + 18 * q^36 - 36 * q^37 - 18 * q^38 - 36 * q^39 - 6 * q^41 + 30 * q^42 + 6 * q^44 - 12 * q^46 + 6 * q^47 - 18 * q^49 + 12 * q^52 + 12 * q^53 + 12 * q^56 + 18 * q^57 + 36 * q^58 - 24 * q^59 - 30 * q^61 + 6 * q^62 - 18 * q^63 - 6 * q^64 + 24 * q^66 - 12 * q^67 - 12 * q^68 + 6 * q^69 - 42 * q^71 - 6 * q^73 + 6 * q^74 + 18 * q^76 + 24 * q^77 - 48 * q^78 + 60 * q^79 + 18 * q^81 - 6 * q^82 - 24 * q^83 - 24 * q^84 - 36 * q^86 - 54 * q^87 + 6 * q^88 - 12 * q^89 + 24 * q^91 - 24 * q^92 - 6 * q^93 + 60 * q^94 - 30 * q^97 - 36 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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