LMFDB - Embedded newform 950.2.l.g.301.2

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} - 24x^{10} + 264x^{8} - 1511x^{6} + 4812x^{4} - 7788x^{2} + 5329 $ x^12 - 24x^10 + 264x^8 - 1511x^6 + 4812x^4 - 7788*x^2 + 5329
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			301.2
Root			$-1.97287 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	950.301
Dual form			950.2.l.g.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(1.13405 - 0.412760i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.13405 - 0.412760i) q^{6} +(-1.09813 - 1.90202i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.18244 + 0.992183i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(1.13405 - 0.412760i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.13405 - 0.412760i) q^{6} +(-1.09813 - 1.90202i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.18244 + 0.992183i) q^{9} +(0.158441 - 0.274427i) q^{11} +(0.603415 + 1.04514i) q^{12} +(0.0644966 + 0.0234748i) q^{13} +(-0.381378 + 2.16290i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-5.12494 - 4.30034i) q^{17} +1.54356 q^{18} +(-0.761855 - 4.29180i) q^{19} +(-2.03042 - 1.70372i) q^{21} +(-0.297771 + 0.108380i) q^{22} +(0.0905620 + 0.513603i) q^{23} +(0.209564 - 1.18849i) q^{24} +(-0.0343179 - 0.0594403i) q^{26} +(-2.74165 + 4.74868i) q^{27} +(1.68244 - 1.41173i) q^{28} +(5.22668 - 4.38571i) q^{29} +(-2.96958 - 5.14347i) q^{31} +(0.939693 + 0.342020i) q^{32} +(0.0664068 - 0.376612i) q^{33} +(1.16173 + 6.58850i) q^{34} +(-1.18244 - 0.992183i) q^{36} -10.8376 q^{37} +(-2.17510 + 3.77742i) q^{38} +0.0828317 q^{39} +(-2.78749 + 1.01456i) q^{41} +(0.460258 + 2.61025i) q^{42} +(-1.01617 + 5.76298i) q^{43} +(0.297771 + 0.108380i) q^{44} +(0.260763 - 0.451655i) q^{46} +(6.66521 - 5.59278i) q^{47} +(-0.924485 + 0.775735i) q^{48} +(1.08821 - 1.88483i) q^{49} +(-7.58694 - 2.76142i) q^{51} +(-0.0119185 + 0.0675931i) q^{52} +(-1.58055 - 8.96377i) q^{53} +(5.15262 - 1.87540i) q^{54} -2.19627 q^{56} +(-2.63547 - 4.55265i) q^{57} -6.82295 q^{58} +(1.57825 + 1.32431i) q^{59} +(0.313061 + 1.77546i) q^{61} +(-1.03133 + 5.84894i) q^{62} +(3.18563 + 1.15947i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.292952 + 0.245816i) q^{66} +(0.179873 - 0.150932i) q^{67} +(3.34507 - 5.79383i) q^{68} +(0.314696 + 0.545070i) q^{69} +(-0.314696 + 1.78473i) q^{71} +(0.268037 + 1.52011i) q^{72} +(7.05084 - 2.56629i) q^{73} +(8.30210 + 6.96629i) q^{74} +(4.09431 - 1.49554i) q^{76} -0.695955 q^{77} +(-0.0634528 - 0.0532432i) q^{78} +(-3.32526 + 1.21030i) q^{79} +(-0.344991 + 1.95654i) q^{81} +(2.78749 + 1.01456i) q^{82} +(0.0487683 + 0.0844691i) q^{83} +(1.32526 - 2.29542i) q^{84} +(4.48280 - 3.76152i) q^{86} +(4.11707 - 7.13097i) q^{87} +(-0.158441 - 0.274427i) q^{88} +(-6.00343 - 2.18507i) q^{89} +(-0.0261762 - 0.148452i) q^{91} +(-0.490074 + 0.178372i) q^{92} +(-5.49067 - 4.60722i) q^{93} -8.70082 q^{94} +1.20683 q^{96} +(5.64307 + 4.73510i) q^{97} +(-2.04516 + 0.744377i) q^{98} +(0.0849358 + 0.481695i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9	$ 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9} - 6 q^{11} + 18 q^{13} - 6 q^{14} - 12 q^{17} - 24 q^{18} + 6 q^{19} - 36 q^{21} + 9 q^{22} - 3 q^{23} + 3 q^{24} - 3 q^{26} - 15 q^{27} - 3 q^{28} + 36 q^{29} - 24 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{36} - 24 q^{37} - 15 q^{38} - 12 q^{39} - 12 q^{41} - 18 q^{42} + 12 q^{43} - 9 q^{44} - 18 q^{46} + 6 q^{48} - 27 q^{51} - 18 q^{52} + 36 q^{53} + 9 q^{54} + 12 q^{56} + 42 q^{57} - 27 q^{59} + 54 q^{61} + 24 q^{62} + 3 q^{63} - 6 q^{64} - 39 q^{66} - 39 q^{67} + 15 q^{68} - 24 q^{69} + 24 q^{71} + 18 q^{72} + 15 q^{74} + 9 q^{76} - 78 q^{77} + 6 q^{78} - 36 q^{79} - 9 q^{81} + 12 q^{82} + 12 q^{84} + 24 q^{86} - 18 q^{87} + 6 q^{88} + 18 q^{89} + 12 q^{91} - 12 q^{92} - 54 q^{93} + 18 q^{94} + 27 q^{97} + 18 q^{98} + 18 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9 - 6 * q^11 + 18 * q^13 - 6 * q^14 - 12 * q^17 - 24 * q^18 + 6 * q^19 - 36 * q^21 + 9 * q^22 - 3 * q^23 + 3 * q^24 - 3 * q^26 - 15 * q^27 - 3 * q^28 + 36 * q^29 - 24 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^36 - 24 * q^37 - 15 * q^38 - 12 * q^39 - 12 * q^41 - 18 * q^42 + 12 * q^43 - 9 * q^44 - 18 * q^46 + 6 * q^48 - 27 * q^51 - 18 * q^52 + 36 * q^53 + 9 * q^54 + 12 * q^56 + 42 * q^57 - 27 * q^59 + 54 * q^61 + 24 * q^62 + 3 * q^63 - 6 * q^64 - 39 * q^66 - 39 * q^67 + 15 * q^68 - 24 * q^69 + 24 * q^71 + 18 * q^72 + 15 * q^74 + 9 * q^76 - 78 * q^77 + 6 * q^78 - 36 * q^79 - 9 * q^81 + 12 * q^82 + 12 * q^84 + 24 * q^86 - 18 * q^87 + 6 * q^88 + 18 * q^89 + 12 * q^91 - 12 * q^92 - 54 * q^93 + 18 * q^94 + 27 * q^97 + 18 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	1.13405	−	0.412760i	0.654743	−	0.238307i	0.00677814	−	0.999977i	$-0.497842\pi$
$3$	1.13405	−	0.412760i	0.654743	−	0.238307i	0.647965	+	0.761670i	$0.275620\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$		0			0
$5$		0			0
$6$	−1.13405	−	0.412760i	−0.462973	−	0.168509i
$7$	−1.09813	−	1.90202i	−0.415055	−	0.718897i	0.580379	−	0.814347i	$-0.302904\pi$
$7$	−1.09813	−	1.90202i	−0.415055	−	0.718897i	−0.995434	+	0.0954496i	$0.969571\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−1.18244	+	0.992183i	−0.394146	+	0.330728i
$10$		0			0
$11$	0.158441	−	0.274427i	0.0477716	−	0.0827429i	−0.841151	−	0.540801i	$-0.818121\pi$
$11$	0.158441	−	0.274427i	0.0477716	−	0.0827429i	0.888922	+	0.458058i	$0.151455\pi$
$12$	0.603415	+	1.04514i	0.174191	+	0.301707i
$13$	0.0644966	+	0.0234748i	0.0178881	+	0.00651075i	0.350949	−	0.936395i	$-0.385859\pi$
$13$	0.0644966	+	0.0234748i	0.0178881	+	0.00651075i	−0.333061	+	0.942905i	$0.608081\pi$
$14$	−0.381378	+	2.16290i	−0.101927	+	0.578059i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−5.12494	−	4.30034i	−1.24298	−	1.04298i	−0.997285	−	0.0736376i	$-0.976539\pi$
$17$	−5.12494	−	4.30034i	−1.24298	−	1.04298i	−0.245696	−	0.969347i	$-0.579016\pi$
$18$	1.54356			0.363821
$19$	−0.761855	−	4.29180i	−0.174782	−	0.984607i
$19$	−0.761855	−	4.29180i	−0.174782	−	0.984607i
$20$		0			0
$21$	−2.03042	−	1.70372i	−0.443073	−	0.371782i
$22$	−0.297771	+	0.108380i	−0.0634850	+	0.0231066i
$23$	0.0905620	+	0.513603i	0.0188835	+	0.107094i	0.992793	−	0.119845i	$-0.0382396\pi$
$23$	0.0905620	+	0.513603i	0.0188835	+	0.107094i	−0.973909	+	0.226938i	$0.927128\pi$
$24$	0.209564	−	1.18849i	0.0427770	−	0.242601i
$25$		0			0
$26$	−0.0343179	−	0.0594403i	−0.00673029	−	0.0116572i
$27$	−2.74165	+	4.74868i	−0.527631	+	0.913884i
$28$	1.68244	−	1.41173i	0.317951	−	0.266792i
$29$	5.22668	−	4.38571i	0.970570	−	0.814405i	−0.0120697	−	0.999927i	$-0.503842\pi$
$29$	5.22668	−	4.38571i	0.970570	−	0.814405i	0.982640	+	0.185522i	$0.0593976\pi$
$30$		0			0
$31$	−2.96958	−	5.14347i	−0.533353	−	0.923795i	−0.999241	−	0.0389511i	$-0.987598\pi$
$31$	−2.96958	−	5.14347i	−0.533353	−	0.923795i	0.465888	−	0.884844i	$-0.345735\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	0.0664068	−	0.376612i	0.0115599	−	0.0655597i
$34$	1.16173	+	6.58850i	0.199235	+	1.12992i
$35$		0			0
$36$	−1.18244	−	0.992183i	−0.197073	−	0.165364i
$37$	−10.8376			−1.78169			−0.890847	−	0.454304i	$-0.849888\pi$
$37$	−10.8376			−1.78169			−0.890847	+	0.454304i	$0.849888\pi$
$38$	−2.17510	+	3.77742i	−0.352848	+	0.612779i
$39$	0.0828317			0.0132637
$40$		0			0
$41$	−2.78749	+	1.01456i	−0.435333	+	0.158448i	−0.550385	−	0.834911i	$-0.685519\pi$
$41$	−2.78749	+	1.01456i	−0.435333	+	0.158448i	0.115051	+	0.993360i	$0.463297\pi$
$42$	0.460258	+	2.61025i	0.0710193	+	0.402771i
$43$	−1.01617	+	5.76298i	−0.154964	+	0.878846i	0.803854	+	0.594826i	$0.202779\pi$
$43$	−1.01617	+	5.76298i	−0.154964	+	0.878846i	−0.958819	+	0.284019i	$0.908332\pi$
$44$	0.297771	+	0.108380i	0.0448906	+	0.0163389i
$45$		0			0
$46$	0.260763	−	0.451655i	0.0384474	−	0.0665928i
$47$	6.66521	−	5.59278i	0.972221	−	0.815791i	−0.0106763	−	0.999943i	$-0.503398\pi$
$47$	6.66521	−	5.59278i	0.972221	−	0.815791i	0.982898	+	0.184152i	$0.0589540\pi$
$48$	−0.924485	+	0.775735i	−0.133438	+	0.111968i
$49$	1.08821	−	1.88483i	0.155458	−	0.269261i
$50$		0			0
$51$	−7.58694	−	2.76142i	−1.06238	−	0.386676i
$52$	−0.0119185	+	0.0675931i	−0.00165280	+	0.00937347i
$53$	−1.58055	−	8.96377i	−0.217106	−	1.23127i	−0.877215	−	0.480098i	$-0.840601\pi$
$53$	−1.58055	−	8.96377i	−0.217106	−	1.23127i	0.660109	−	0.751170i	$-0.270510\pi$
$54$	5.15262	−	1.87540i	0.701183	−	0.255210i
$55$		0			0
$56$	−2.19627			−0.293488
$57$	−2.63547	−	4.55265i	−0.349076	−	0.603013i
$58$	−6.82295			−0.895897
$59$	1.57825	+	1.32431i	0.205470	+	0.172410i	0.739716	−	0.672919i	$-0.234960\pi$
$59$	1.57825	+	1.32431i	0.205470	+	0.172410i	−0.534246	+	0.845329i	$0.679404\pi$
$60$		0			0
$61$	0.313061	+	1.77546i	0.0400833	+	0.227324i	0.998268	−	0.0588259i	$-0.0187357\pi$
$61$	0.313061	+	1.77546i	0.0400833	+	0.227324i	−0.958185	+	0.286150i	$0.907625\pi$
$62$	−1.03133	+	5.84894i	−0.130979	+	0.742816i
$63$	3.18563	+	1.15947i	0.401351	+	0.146080i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	−0.292952	+	0.245816i	−0.0360599	+	0.0302578i
$67$	0.179873	−	0.150932i	0.0219750	−	0.0184393i	−0.631734	−	0.775185i	$-0.717656\pi$
$67$	0.179873	−	0.150932i	0.0219750	−	0.0184393i	0.653709	+	0.756746i	$0.273212\pi$
$68$	3.34507	−	5.79383i	0.405649	−	0.702605i
$69$	0.314696	+	0.545070i	0.0378850	+	0.0656187i
$70$		0			0
$71$	−0.314696	+	1.78473i	−0.0373476	+	0.211809i	−0.997771	−	0.0667369i	$-0.978741\pi$
$71$	−0.314696	+	1.78473i	−0.0373476	+	0.211809i	0.960423	+	0.278546i	$0.0898523\pi$
$72$	0.268037	+	1.52011i	0.0315884	+	0.179147i
$73$	7.05084	−	2.56629i	0.825238	−	0.300362i	0.105335	−	0.994437i	$-0.466409\pi$
$73$	7.05084	−	2.56629i	0.825238	−	0.300362i	0.719903	+	0.694075i	$0.244186\pi$
$74$	8.30210	+	6.96629i	0.965099	+	0.809814i
$75$		0			0
$76$	4.09431	−	1.49554i	0.469649	−	0.171551i
$77$	−0.695955			−0.0793115
$78$	−0.0634528	−	0.0532432i	−0.00718461	−	0.00602860i
$79$	−3.32526	+	1.21030i	−0.374121	+	0.136169i	−0.522235	−	0.852801i	$-0.674902\pi$
$79$	−3.32526	+	1.21030i	−0.374121	+	0.136169i	0.148115	+	0.988970i	$0.452680\pi$
$80$		0			0
$81$	−0.344991	+	1.95654i	−0.0383324	+	0.217394i
$82$	2.78749	+	1.01456i	0.307827	+	0.112040i
$83$	0.0487683	+	0.0844691i	0.00535301	+	0.00927169i	0.868690	−	0.495357i	$-0.164963\pi$
$83$	0.0487683	+	0.0844691i	0.00535301	+	0.00927169i	−0.863336	+	0.504629i	$0.831629\pi$
$84$	1.32526	−	2.29542i	0.144598	−	0.250450i
$85$		0			0
$86$	4.48280	−	3.76152i	0.483393	−	0.405615i
$87$	4.11707	−	7.13097i	0.441396	−	0.764520i
$88$	−0.158441	−	0.274427i	−0.0168898	−	0.0292540i
$89$	−6.00343	−	2.18507i	−0.636362	−	0.231617i	0.00363610	−	0.999993i	$-0.498843\pi$
$89$	−6.00343	−	2.18507i	−0.636362	−	0.231617i	−0.639998	+	0.768377i	$0.721065\pi$
$90$		0			0
$91$	−0.0261762	−	0.148452i	−0.00274401	−	0.0155620i
$92$	−0.490074	+	0.178372i	−0.0510937	+	0.0185966i
$93$	−5.49067	−	4.60722i	−0.569356	−	0.477747i
$94$	−8.70082			−0.897421
$95$		0			0
$96$	1.20683			0.123172
$97$	5.64307	+	4.73510i	0.572967	+	0.480777i	0.882629	−	0.470070i	$-0.155771\pi$
$97$	5.64307	+	4.73510i	0.572967	+	0.480777i	−0.309662	+	0.950847i	$0.600216\pi$
$98$	−2.04516	+	0.744377i	−0.206592	+	0.0751935i
$99$	0.0849358	+	0.481695i	0.00853637	+	0.0484122i
$100$		0			0
$101$	−9.05592	−	3.29609i	−0.901098	−	0.327973i	−0.150405	−	0.988624i	$-0.548058\pi$
$101$	−9.05592	−	3.29609i	−0.901098	−	0.327973i	−0.750693	+	0.660652i	$0.770280\pi$
$102$	4.03693	+	6.99216i	0.399715	+	0.692327i
$103$	−9.21811	+	15.9662i	−0.908287	+	1.57320i	−0.0918448	+	0.995773i	$0.529276\pi$
$103$	−9.21811	+	15.9662i	−0.908287	+	1.57320i	−0.816443	+	0.577427i	$0.804057\pi$
$104$	0.0525781	−	0.0441182i	0.00515570	−	0.00432615i
$105$		0			0
$106$	−4.55102	+	7.88260i	−0.442034	+	0.765626i
$107$	−5.92148	−	10.2563i	−0.572451	−	0.991515i	−0.996313	−	0.0857880i	$-0.972659\pi$
$107$	−5.92148	−	10.2563i	−0.572451	−	0.991515i	0.423862	−	0.905727i	$-0.360674\pi$
$108$	−5.15262	−	1.87540i	−0.495811	−	0.180461i
$109$	−0.136009	+	0.771345i	−0.0130273	+	0.0738814i	−0.990628	−	0.136585i	$-0.956387\pi$
$109$	−0.136009	+	0.771345i	−0.0130273	+	0.0738814i	0.977601	+	0.210467i	$0.0674983\pi$
$110$		0			0
$111$	−12.2904	+	4.47333i	−1.16655	+	0.424590i
$112$	1.68244	+	1.41173i	0.158975	+	0.133396i
$113$	−1.07256			−0.100898			−0.0504488	−	0.998727i	$-0.516065\pi$
$113$	−1.07256			−0.100898			−0.0504488	+	0.998727i	$0.516065\pi$
$114$	−0.907504	+	5.18158i	−0.0849955	+	0.485299i
$115$		0			0
$116$	5.22668	+	4.38571i	0.485285	+	0.407203i
$117$	−0.0995545	+	0.0362349i	−0.00920381	+	0.00334991i
$118$	−0.357760	−	2.02896i	−0.0329345	−	0.186781i
$119$	−2.55147	+	14.4701i	−0.233893	+	1.32647i
$120$		0			0
$121$	5.44979	+	9.43932i	0.495436	+	0.858120i
$122$	0.901422	−	1.56131i	0.0816109	−	0.141354i
$123$	−2.74238	+	2.30113i	−0.247272	+	0.207486i
$124$	4.54967	−	3.81762i	0.408572	−	0.342833i
$125$		0			0
$126$	−1.69504	−	2.93589i	−0.151006	−	0.261550i
$127$	8.32450	+	3.02987i	0.738680	+	0.268857i	0.683834	−	0.729637i	$-0.260311\pi$
$127$	8.32450	+	3.02987i	0.738680	+	0.268857i	0.0548454	+	0.998495i	$0.482533\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	1.22634	+	6.95493i	0.107973	+	0.612347i
$130$		0			0
$131$	5.91581	+	4.96395i	0.516866	+	0.433702i	0.863538	−	0.504284i	$-0.168244\pi$
$131$	5.91581	+	4.96395i	0.516866	+	0.433702i	−0.346671	+	0.937987i	$0.612688\pi$
$132$	0.382421			0.0332855
$133$	−7.32649	+	6.16204i	−0.635287	+	0.534316i
$134$	−0.234808			−0.0202843
$135$		0			0
$136$	−6.28667	+	2.28816i	−0.539078	+	0.196208i
$137$	−2.93106	−	16.6228i	−0.250417	−	1.42019i	−0.807568	−	0.589774i	$-0.799217\pi$
$137$	−2.93106	−	16.6228i	−0.250417	−	1.42019i	0.557151	−	0.830411i	$-0.311894\pi$
$138$	0.109293	−	0.619831i	0.00930363	−	0.0527635i
$139$	−18.7585	−	6.82755i	−1.59108	−	0.579105i	−0.613504	−	0.789692i	$-0.710240\pi$
$139$	−18.7585	−	6.82755i	−1.59108	−	0.579105i	−0.977575	+	0.210586i	$0.932463\pi$
$140$		0			0
$141$	5.25020	−	9.09362i	0.442147	−	0.765821i
$142$	1.38827	−	1.16490i	0.116501	−	0.0977563i
$143$	0.0166610	−	0.0139802i	0.00139326	−	0.00116909i
$144$	0.771781	−	1.33676i	0.0643151	−	0.111397i
$145$		0			0
$146$	−7.05084	−	2.56629i	−0.583531	−	0.212388i
$147$	0.456097	−	2.58666i	0.0376183	−	0.213344i
$148$	−1.88193	−	10.6730i	−0.154694	−	0.877313i
$149$	14.7196	−	5.35751i	1.20588	−	0.438904i	0.340606	−	0.940206i	$-0.389368\pi$
$149$	14.7196	−	5.35751i	1.20588	−	0.438904i	0.865272	+	0.501302i	$0.167145\pi$
$150$		0			0
$151$	13.6401			1.11001			0.555007	−	0.831846i	$-0.312716\pi$
$151$	13.6401			1.11001			0.555007	+	0.831846i	$0.312716\pi$
$152$	−4.09774	−	1.48612i	−0.332370	−	0.120540i
$153$	10.3266			0.834860
$154$	0.533133	+	0.447351i	0.0429611	+	0.0360486i
$155$		0			0
$156$	0.0143836	+	0.0815733i	0.00115161	+	0.00653109i
$157$	−2.68020	+	15.2002i	−0.213903	+	1.21310i	0.668897	+	0.743355i	$0.266767\pi$
$157$	−2.68020	+	15.2002i	−0.213903	+	1.21310i	−0.882800	+	0.469749i	$0.844344\pi$
$158$	3.32526	+	1.21030i	0.264543	+	0.0962859i
$159$	−5.49231	−	9.51296i	−0.435568	−	0.754427i
$160$		0			0
$161$	0.877435	−	0.736255i	0.0691515	−	0.0580250i
$162$	1.52192	−	1.27704i	0.119573	−	0.100334i
$163$	−0.355607	+	0.615929i	−0.0278533	+	0.0482433i	−0.879616	−	0.475684i	$-0.842200\pi$
$163$	−0.355607	+	0.615929i	−0.0278533	+	0.0482433i	0.851763	+	0.523928i	$0.175534\pi$
$164$	−1.48319	−	2.56897i	−0.115818	−	0.200603i
$165$		0			0
$166$	0.0169370	−	0.0960548i	0.00131457	−	0.00745529i
$167$	1.87678	+	10.6438i	0.145230	+	0.823639i	0.967182	+	0.254083i	$0.0817737\pi$
$167$	1.87678	+	10.6438i	0.145230	+	0.823639i	−0.821953	+	0.569556i	$0.807115\pi$
$168$	−2.49067	+	0.906531i	−0.192160	+	0.0699404i
$169$	−9.95497	−	8.35321i	−0.765767	−	0.642555i
$170$		0			0
$171$	5.15910	+	4.31889i	0.394526	+	0.330274i
$172$	−5.85188			−0.446202
$173$	16.3757	+	13.7408i	1.24502	+	1.04470i	0.997115	+	0.0759108i	$0.0241864\pi$
$173$	16.3757	+	13.7408i	1.24502	+	1.04470i	0.247905	+	0.968784i	$0.420258\pi$
$174$	−7.73756	+	2.81624i	−0.586583	+	0.213499i
$175$		0			0
$176$	−0.0550258	+	0.312067i	−0.00414773	+	0.0235229i
$177$	2.33643	+	0.850392i	0.175617	+	0.0639194i
$178$	3.19436	+	5.53279i	0.239427	+	0.414700i
$179$	9.05582	−	15.6851i	0.676864	−	1.17236i	−0.299057	−	0.954235i	$-0.596672\pi$
$179$	9.05582	−	15.6851i	0.676864	−	1.17236i	0.975920	−	0.218127i	$-0.0699946\pi$
$180$		0			0
$181$	20.0377	−	16.8136i	1.48939	−	1.24975i	0.594001	−	0.804464i	$-0.297548\pi$
$181$	20.0377	−	16.8136i	1.48939	−	1.24975i	0.895390	−	0.445283i	$-0.146897\pi$
$182$	−0.0753712	+	0.130547i	−0.00558689	+	0.00967677i
$183$	1.08786	+	1.88423i	0.0804171	+	0.139287i
$184$	0.490074	+	0.178372i	0.0361287	+	0.0131498i
$185$		0			0
$186$	1.24463	+	7.05867i	0.0912610	+	0.517567i
$187$	−1.99213	+	0.725075i	−0.145679	+	0.0530227i
$188$	6.66521	+	5.59278i	0.486111	+	0.407895i
$189$	12.0428			0.875985
$190$		0			0
$191$	15.6106			1.12954			0.564770	−	0.825248i	$-0.308965\pi$
$191$	15.6106			1.12954			0.564770	+	0.825248i	$0.308965\pi$
$192$	−0.924485	−	0.775735i	−0.0667190	−	0.0559839i
$193$	10.0505	−	3.65810i	0.723453	−	0.263315i	0.0460623	−	0.998939i	$-0.485333\pi$
$193$	10.0505	−	3.65810i	0.723453	−	0.263315i	0.677391	+	0.735623i	$0.263111\pi$
$194$	−1.27918	−	7.25460i	−0.0918399	−	0.520850i
$195$		0			0
$196$	2.04516	+	0.744377i	0.146083	+	0.0531698i
$197$	3.80477	+	6.59006i	0.271079	+	0.469522i	0.969138	−	0.246518i	$-0.0792863\pi$
$197$	3.80477	+	6.59006i	0.271079	+	0.469522i	−0.698060	+	0.716040i	$0.745953\pi$
$198$	0.244563	−	0.423595i	0.0173803	−	0.0301036i
$199$	−15.0459	+	12.6250i	−1.06658	+	0.894963i	−0.994738	−	0.102453i	$-0.967331\pi$
$199$	−15.0459	+	12.6250i	−1.06658	+	0.894963i	−0.0718375	+	0.997416i	$0.522886\pi$
$200$		0			0
$201$	0.141687	−	0.245409i	0.00999381	−	0.0173098i
$202$	4.81855	+	8.34598i	0.339032	+	0.587221i
$203$	−14.0813	−	5.12518i	−0.988314	−	0.359717i
$204$	1.40201	−	7.95119i	0.0981603	−	0.556695i
$205$		0			0
$206$	17.3244	−	6.30556i	1.20705	−	0.439329i
$207$	−0.616672	−	0.517449i	−0.0428616	−	0.0359652i
$208$	−0.0686358			−0.00475904
$209$	−1.29850	−	0.470922i	−0.0898188	−	0.0325744i
$210$		0			0
$211$	−14.5809	−	12.2348i	−1.00379	−	0.842278i	−0.0162836	−	0.999867i	$-0.505183\pi$
$211$	−14.5809	−	12.2348i	−1.00379	−	0.842278i	−0.987505	+	0.157589i	$0.949628\pi$
$212$	8.55313	−	3.11308i	0.587431	−	0.213807i
$213$	0.379785	+	2.15387i	0.0260224	+	0.147581i
$214$	−2.05651	+	11.6630i	−0.140580	+	0.797269i
$215$		0			0
$216$	2.74165	+	4.74868i	0.186546	+	0.323107i
$217$	−6.52200	+	11.2964i	−0.442742	+	0.766852i
$218$	0.600000	−	0.503460i	0.0406371	−	0.0340986i
$219$	6.93673	−	5.82061i	0.468741	−	0.393320i
$220$		0			0
$221$	−0.229591	−	0.397664i	−0.0154440	−	0.0267498i
$222$	12.2904	+	4.47333i	0.824877	+	0.300231i
$223$	−0.267505	+	1.51709i	−0.0179134	+	0.101592i	−0.992454	−	0.122621i	$-0.960870\pi$
$223$	−0.267505	+	1.51709i	−0.0179134	+	0.101592i	0.974540	+	0.224213i	$0.0719812\pi$
$224$	−0.381378	−	2.16290i	−0.0254819	−	0.144515i
$225$		0			0
$226$	0.821626	+	0.689426i	0.0546537	+	0.0458599i
$227$	21.9238			1.45514			0.727568	−	0.686036i	$-0.240651\pi$
$227$	21.9238			1.45514			0.727568	+	0.686036i	$0.240651\pi$
$228$	4.02584	−	3.38599i	0.266618	−	0.224242i
$229$	−22.5988			−1.49337			−0.746687	−	0.665176i	$-0.768357\pi$
$229$	−22.5988			−1.49337			−0.746687	+	0.665176i	$0.768357\pi$
$230$		0			0
$231$	−0.789247	+	0.287262i	−0.0519287	+	0.0189005i
$232$	−1.18479	−	6.71929i	−0.0777854	−	0.441143i
$233$	1.56986	−	8.90312i	0.102845	−	0.583263i	−0.889214	−	0.457491i	$-0.848748\pi$
$233$	1.56986	−	8.90312i	0.102845	−	0.583263i	0.992059	−	0.125772i	$-0.0401407\pi$
$234$	0.0995545	+	0.0362349i	0.00650808	+	0.00236875i
$235$		0			0
$236$	−1.03013	+	1.78424i	−0.0670557	+	0.116144i
$237$	−3.27144	+	2.74507i	−0.212503	+	0.178311i
$238$	11.2557	−	9.44468i	0.729601	−	0.612208i
$239$	11.7361	−	20.3275i	0.759145	−	1.31488i	−0.184142	−	0.982900i	$-0.558951\pi$
$239$	11.7361	−	20.3275i	0.759145	−	1.31488i	0.943287	−	0.331978i	$-0.107716\pi$
$240$		0			0
$241$	25.8548	+	9.41039i	1.66546	+	0.606177i	0.991206	−	0.132326i	$-0.0422447\pi$
$241$	25.8548	+	9.41039i	1.66546	+	0.606177i	0.674250	+	0.738503i	$0.264467\pi$
$242$	1.89269	−	10.7340i	0.121667	−	0.690007i
$243$	−2.44015	−	13.8388i	−0.156536	−	0.887759i
$244$	−1.69412	+	0.616609i	−0.108455	+	0.0394744i
$245$		0			0
$246$	3.57993			0.228248
$247$	0.0516123	−	0.294691i	0.00328401	−	0.0187507i
$248$	−5.93917			−0.377138
$249$	0.0901711	+	0.0756625i	0.00571436	+	0.00479492i
$250$		0			0
$251$	4.58954	+	26.0286i	0.289689	+	1.64291i	0.688037	+	0.725675i	$0.258473\pi$
$251$	4.58954	+	26.0286i	0.289689	+	1.64291i	−0.398348	+	0.917234i	$0.630416\pi$
$252$	−0.588680	+	3.33857i	−0.0370834	+	0.210310i
$253$	0.155295	+	0.0565228i	0.00976332	+	0.00355356i
$254$	−4.42937	−	7.67190i	−0.277924	−	0.481378i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	8.50084	−	7.13305i	0.530268	−	0.444947i	−0.337926	−	0.941173i	$-0.609725\pi$
$257$	8.50084	−	7.13305i	0.530268	−	0.444947i	0.868194	+	0.496225i	$0.165281\pi$
$258$	3.53111	−	6.11606i	0.219837	−	0.380769i
$259$	11.9011	+	20.6134i	0.739501	+	1.28085i
$260$		0			0
$261$	−1.82880	+	10.3716i	−0.113200	+	0.641989i
$262$	−1.34100	−	7.60521i	−0.0828475	−	0.469852i
$263$	26.2306	−	9.54717i	1.61745	−	0.588704i	0.634557	−	0.772876i	$-0.281183\pi$
$263$	26.2306	−	9.54717i	1.61745	−	0.588704i	0.982894	+	0.184173i	$0.0589605\pi$
$264$	−0.292952	−	0.245816i	−0.0180299	−	0.0151289i
$265$		0			0
$266$	9.57330	−	0.0110190i	0.586976	−	0.000675616i
$267$	−7.71009			−0.471850
$268$	0.179873	+	0.150932i	0.0109875	+	0.00921963i
$269$	7.91172	−	2.87963i	0.482386	−	0.175574i	−0.0893689	−	0.995999i	$-0.528485\pi$
$269$	7.91172	−	2.87963i	0.482386	−	0.175574i	0.571755	+	0.820424i	$0.306263\pi$
$270$		0			0
$271$	−2.07262	+	11.7544i	−0.125903	+	0.714030i	0.854865	+	0.518851i	$0.173640\pi$
$271$	−2.07262	+	11.7544i	−0.125903	+	0.714030i	−0.980768	+	0.195179i	$0.937471\pi$
$272$	6.28667	+	2.28816i	0.381185	+	0.138740i
$273$	−0.0909602	−	0.157548i	−0.00550516	−	0.00953522i
$274$	−8.43964	+	14.6179i	−0.509857	+	0.883098i
$275$		0			0
$276$	−0.482143	+	0.404566i	−0.0290216	+	0.0243520i
$277$	−1.57008	+	2.71945i	−0.0943367	+	0.163396i	−0.909332	−	0.416072i	$-0.863406\pi$
$277$	−1.57008	+	2.71945i	−0.0943367	+	0.163396i	0.814995	+	0.579468i	$0.196740\pi$
$278$	9.98121	+	17.2880i	0.598633	+	1.03686i
$279$	8.61461	+	3.13546i	0.515743	+	0.187715i
$280$		0			0
$281$	−2.67896	−	15.1931i	−0.159813	−	0.906345i	−0.954253	−	0.299002i	$-0.903346\pi$
$281$	−2.67896	−	15.1931i	−0.159813	−	0.906345i	0.794439	−	0.607343i	$-0.207765\pi$
$282$	−9.86715	+	3.59135i	−0.587580	+	0.213862i
$283$	−12.0165	−	10.0831i	−0.714309	−	0.599376i	0.211496	−	0.977379i	$-0.432166\pi$
$283$	−12.0165	−	10.0831i	−0.714309	−	0.599376i	−0.925804	+	0.378003i	$0.876611\pi$
$284$	−1.81226			−0.107538
$285$		0			0
$286$	−0.0217494			−0.00128607
$287$	4.99077	+	4.18775i	0.294596	+	0.247195i
$288$	−1.45047	+	0.527930i	−0.0854700	+	0.0311085i
$289$	4.82011	+	27.3362i	0.283536	+	1.60801i
$290$		0			0
$291$	8.35398	+	3.04060i	0.489719	+	0.178243i
$292$	3.75167	+	6.49809i	0.219550	+	0.380272i
$293$	5.17925	−	8.97073i	0.302575	−	0.524076i	−0.674143	−	0.738601i	$-0.735487\pi$
$293$	5.17925	−	8.97073i	0.302575	−	0.524076i	0.976719	+	0.214525i	$0.0688203\pi$
$294$	−2.01206	+	1.68832i	−0.117346	+	0.0984649i
$295$		0			0
$296$	−5.41881	+	9.38565i	−0.314962	+	0.545530i
$297$	0.868778	+	1.50477i	0.0504116	+	0.0873155i
$298$	−14.7196	−	5.35751i	−0.852685	−	0.310352i
$299$	−0.00621580	+	0.0352515i	−0.000359469	+	0.00203865i
$300$		0			0
$301$	12.0772	−	4.39574i	0.696118	−	0.253366i
$302$	−10.4489	−	8.76767i	−0.601267	−	0.504523i
$303$	−11.6303			−0.668146
$304$	2.18379	+	3.77241i	0.125249	+	0.216362i
$305$		0			0
$306$	−7.91067	−	6.63784i	−0.452223	−	0.379460i
$307$	8.06402	−	2.93506i	0.460238	−	0.167513i	−0.101487	−	0.994837i	$-0.532360\pi$
$307$	8.06402	−	2.93506i	0.460238	−	0.167513i	0.561725	+	0.827324i	$0.310138\pi$
$308$	−0.120851	−	0.685382i	−0.00688615	−	0.0390533i
$309$	−3.86356	+	21.9114i	−0.219790	+	1.24649i
$310$		0			0
$311$	−2.12890	−	3.68737i	−0.120719	−	0.209092i	0.799332	−	0.600889i	$-0.205187\pi$
$311$	−2.12890	−	3.68737i	−0.120719	−	0.209092i	−0.920051	+	0.391798i	$0.871853\pi$
$312$	0.0414159	−	0.0717344i	0.00234471	−	0.00406116i
$313$	1.44113	−	1.20925i	0.0814576	−	0.0683511i	−0.601150	−	0.799136i	$-0.705290\pi$
$313$	1.44113	−	1.20925i	0.0814576	−	0.0683511i	0.682607	+	0.730785i	$0.260846\pi$
$314$	11.8236	−	9.92120i	0.667246	−	0.559886i
$315$		0			0
$316$	−1.76933	−	3.06458i	−0.0995328	−	0.172396i
$317$	22.6622	+	8.24838i	1.27284	+	0.463275i	0.888057	−	0.459733i	$-0.152055\pi$
$317$	22.6622	+	8.24838i	1.27284	+	0.463275i	0.384780	+	0.923008i	$0.374277\pi$
$318$	−1.90746	+	10.8177i	−0.106965	+	0.606629i
$319$	−0.375438	−	2.12922i	−0.0210205	−	0.119213i
$320$		0			0
$321$	−10.9486	−	9.18700i	−0.611094	−	0.512768i
$322$	−1.14541			−0.0638312
$323$	−14.5517	+	25.2715i	−0.809680	+	1.40614i
$324$	−1.98673			−0.110374
$325$		0			0
$326$	0.668322	−	0.243249i	0.0370150	−	0.0134723i
$327$	0.164140	+	0.930882i	0.00907694	+	0.0514779i
$328$	−0.515108	+	2.92132i	−0.0284421	+	0.161303i
$329$	−17.9569	−	6.53577i	−0.989995	−	0.360329i
$330$		0			0
$331$	−10.3508	+	17.9282i	−0.568934	+	0.985422i	0.427738	+	0.903903i	$0.359311\pi$
$331$	−10.3508	+	17.9282i	−0.568934	+	0.985422i	−0.996672	+	0.0815193i	$0.974023\pi$
$332$	−0.0747173	+	0.0626953i	−0.00410065	+	0.00344085i
$333$	12.8148	−	10.7529i	0.702247	−	0.589255i
$334$	5.40398	−	9.35997i	0.295693	−	0.512155i
$335$		0			0
$336$	2.49067	+	0.906531i	0.135877	+	0.0494553i
$337$	0.849268	−	4.81644i	0.0462626	−	0.262368i	−0.952900	−	0.303285i	$-0.901917\pi$
$337$	0.849268	−	4.81644i	0.0462626	−	0.262368i	0.999163	+	0.0409166i	$0.0130278\pi$
$338$	2.25661	+	12.7979i	0.122743	+	0.696112i
$339$	−1.21633	+	0.442708i	−0.0660620	+	0.0240446i
$340$		0			0
$341$	−1.88201			−0.101917
$342$	−1.17597	−	6.62467i	−0.0635892	−	0.358221i
$343$	−20.1538			−1.08821
$344$	4.48280	+	3.76152i	0.241696	+	0.202807i
$345$		0			0
$346$	−3.71206	−	21.0522i	−0.199562	−	1.13177i
$347$	−0.622405	+	3.52984i	−0.0334125	+	0.189492i	−0.996946	−	0.0780969i	$-0.975116\pi$
$347$	−0.622405	+	3.52984i	−0.0334125	+	0.189492i	0.963533	+	0.267588i	$0.0862268\pi$
$348$	7.73756	+	2.81624i	0.414777	+	0.150966i
$349$	−4.16579	−	7.21535i	−0.222989	−	0.386229i	0.732725	−	0.680525i	$-0.238248\pi$
$349$	−4.16579	−	7.21535i	−0.222989	−	0.386229i	−0.955714	+	0.294296i	$0.904915\pi$
$350$		0			0
$351$	−0.288302	+	0.241914i	−0.0153884	+	0.0129124i
$352$	0.242745	−	0.203687i	0.0129384	−	0.0108566i
$353$	7.12593	−	12.3425i	0.379275	−	0.656924i	−0.611682	−	0.791104i	$-0.709507\pi$
$353$	7.12593	−	12.3425i	0.379275	−	0.656924i	0.990957	+	0.134180i	$0.0428400\pi$
$354$	−1.24319	−	2.15327i	−0.0660748	−	0.114445i
$355$		0			0
$356$	1.10939	−	6.29165i	0.0587975	−	0.333457i
$357$	3.07919	+	17.4629i	0.162968	+	0.924236i
$358$	−17.0194	+	6.19454i	−0.899502	+	0.327392i
$359$	16.7438	+	14.0497i	0.883706	+	0.741517i	0.966938	−	0.255013i	$-0.0820797\pi$
$359$	16.7438	+	14.0497i	0.883706	+	0.741517i	−0.0832317	+	0.996530i	$0.526524\pi$
$360$		0			0
$361$	−17.8392	+	6.53947i	−0.938903	+	0.344182i
$362$	−26.1574			−1.37480
$363$	10.0765	+	8.45519i	0.528879	+	0.443782i
$364$	0.141652	−	0.0515570i	0.00742456	−	0.00270232i
$365$		0			0
$366$	0.377811	−	2.14267i	0.0197485	−	0.111999i
$367$	−17.5942	−	6.40378i	−0.918412	−	0.334275i	−0.160805	−	0.986986i	$-0.551409\pi$
$367$	−17.5942	−	6.40378i	−0.918412	−	0.334275i	−0.757606	+	0.652712i	$0.773631\pi$
$368$	−0.260763	−	0.451655i	−0.0135932	−	0.0235441i
$369$	2.28940	−	3.96536i	0.119182	−	0.206429i
$370$		0			0
$371$	−15.3136	+	12.8497i	−0.795044	+	0.667121i
$372$	3.58378	−	6.20729i	0.185810	−	0.321833i
$373$	0.261678	+	0.453240i	0.0135492	+	0.0234679i	0.872721	−	0.488220i	$-0.162354\pi$
$373$	0.261678	+	0.453240i	0.0135492	+	0.0234679i	−0.859171	+	0.511688i	$0.829020\pi$
$374$	1.99213	+	0.725075i	0.103010	+	0.0374927i
$375$		0			0
$376$	−1.51088	−	8.56863i	−0.0779178	−	0.441894i
$377$	0.440057	−	0.160168i	0.0226641	−	0.00824905i
$378$	−9.22532	−	7.74096i	−0.474499	−	0.398152i
$379$	−17.7944			−0.914037			−0.457018	−	0.889457i	$-0.651083\pi$
$379$	−17.7944			−0.914037			−0.457018	+	0.889457i	$0.651083\pi$
$380$		0			0
$381$	10.6910			0.547716
$382$	−11.9584	−	10.0343i	−0.611844	−	0.513398i
$383$	−12.7545	+	4.64225i	−0.651723	+	0.237208i	−0.646659	−	0.762780i	$-0.723834\pi$
$383$	−12.7545	+	4.64225i	−0.651723	+	0.237208i	−0.00506405	+	0.999987i	$0.501612\pi$
$384$	0.209564	+	1.18849i	0.0106943	+	0.0606501i
$385$		0			0
$386$	−10.0505	−	3.65810i	−0.511559	−	0.186192i
$387$	−4.51637	−	7.82259i	−0.229580	−	0.397644i
$388$	−3.68326	+	6.37959i	−0.186989	+	0.323874i
$389$	18.7194	−	15.7075i	0.949113	−	0.796400i	−0.0300352	−	0.999549i	$-0.509562\pi$
$389$	18.7194	−	15.7075i	0.949113	−	0.796400i	0.979148	+	0.203149i	$0.0651175\pi$
$390$		0			0
$391$	1.74454	−	3.02163i	0.0882251	−	0.152810i
$392$	−1.08821	−	1.88483i	−0.0549628	−	0.0951983i
$393$	8.75773	+	3.18755i	0.441769	+	0.160791i
$394$	1.32138	−	7.49393i	0.0665703	−	0.377539i
$395$		0			0
$396$	−0.459628	+	0.167291i	−0.0230972	+	0.00840668i
$397$	21.7972	+	18.2900i	1.09397	+	0.917951i	0.997005	−	0.0773367i	$-0.0246417\pi$
$397$	21.7972	+	18.2900i	1.09397	+	0.917951i	0.0969663	+	0.995288i	$0.469086\pi$
$398$	19.6410			0.984516
$399$	−5.76515	+	10.0121i	−0.288619	+	0.501234i
$400$		0			0
$401$	−27.2549	−	22.8696i	−1.36104	−	1.14205i	−0.975658	−	0.219297i	$-0.929624\pi$
$401$	−27.2549	−	22.8696i	−1.36104	−	1.14205i	−0.385387	−	0.922755i	$-0.625932\pi$
$402$	−0.266284	+	0.0969194i	−0.0132810	+	0.00483390i
$403$	−0.0707859	−	0.401447i	−0.00352610	−	0.0199975i
$404$	1.67347	−	9.49070i	0.0832581	−	0.472180i
$405$		0			0
$406$	7.49251	+	12.9774i	0.371847	+	0.644058i
$407$	−1.71712	+	2.97414i	−0.0851144	+	0.147422i
$408$	−6.18493	+	5.18977i	−0.306200	+	0.256932i
$409$	12.1081	−	10.1599i	0.598708	−	0.502376i	−0.292322	−	0.956320i	$-0.594428\pi$
$409$	12.1081	−	10.1599i	0.598708	−	0.502376i	0.891030	+	0.453944i	$0.149984\pi$
$410$		0			0
$411$	−10.1852	−	17.6413i	−0.502399	−	0.870181i
$412$	−17.3244	−	6.30556i	−0.853511	−	0.310653i
$413$	0.785736	−	4.45613i	0.0386635	−	0.219272i
$414$	0.139788	+	0.792778i	0.00687021	+	0.0389629i
$415$		0			0
$416$	0.0525781	+	0.0441182i	0.00257785	+	0.00216307i
$417$	−24.0912			−1.17975
$418$	0.692003	+	1.19540i	0.0338470	+	0.0584691i
$419$	−37.3327			−1.82382			−0.911910	−	0.410390i	$-0.865393\pi$
$419$	−37.3327			−1.82382			−0.911910	+	0.410390i	$0.865393\pi$
$420$		0			0
$421$	18.6383	−	6.78380i	0.908377	−	0.330622i	0.154772	−	0.987950i	$-0.450536\pi$
$421$	18.6383	−	6.78380i	0.908377	−	0.330622i	0.753605	+	0.657328i	$0.228313\pi$
$422$	3.30521	+	18.7448i	0.160895	+	0.912483i
$423$	−2.33214	+	13.2262i	−0.113393	+	0.643081i
$424$	−8.55313	−	3.11308i	−0.415377	−	0.151185i
$425$		0			0
$426$	1.09355	−	1.89408i	0.0529825	−	0.0917684i
$427$	3.03317	−	2.54513i	0.146786	−	0.123168i
$428$	9.07224	−	7.61251i	0.438523	−	0.367965i
$429$	0.0131239	−	0.0227313i	0.000633628	−	0.00109748i
$430$		0			0
$431$	−18.7166	−	6.81227i	−0.901545	−	0.328135i	−0.150673	−	0.988584i	$-0.548144\pi$
$431$	−18.7166	−	6.81227i	−0.901545	−	0.328135i	−0.750872	+	0.660448i	$0.770366\pi$
$432$	0.952166	−	5.40000i	0.0458111	−	0.259808i
$433$	−3.22780	−	18.3058i	−0.155118	−	0.879719i	−0.958678	−	0.284494i	$-0.908174\pi$
$433$	−3.22780	−	18.3058i	−0.155118	−	0.879719i	0.803560	−	0.595224i	$-0.202937\pi$
$434$	12.2573	−	4.46131i	0.588372	−	0.214150i
$435$		0			0
$436$	−0.783244			−0.0375106
$437$	2.13529	−	0.779965i	0.102145	−	0.0373108i
$438$	−9.05526			−0.432677
$439$	16.2135	+	13.6048i	0.773830	+	0.649320i	0.941687	−	0.336491i	$-0.109240\pi$
$439$	16.2135	+	13.6048i	0.773830	+	0.649320i	−0.167857	+	0.985811i	$0.553685\pi$
$440$		0			0
$441$	0.583359	+	3.30839i	0.0277790	+	0.157543i
$442$	−0.0797362	+	0.452207i	−0.00379267	+	0.0215093i
$443$	−30.5947	−	11.1356i	−1.45360	−	0.529066i	−0.510004	−	0.860172i	$-0.670356\pi$
$443$	−30.5947	−	11.1356i	−1.45360	−	0.529066i	−0.943593	+	0.331106i	$0.892578\pi$
$444$	−6.53958	−	11.3269i	−0.310355	−	0.537550i
$445$		0			0
$446$	1.18009	−	0.990213i	0.0558789	−	0.0468879i
$447$	14.4814	−	12.1513i	0.684947	−	0.574739i
$448$	−1.09813	+	1.90202i	−0.0518819	+	0.0898621i
$449$	−1.96092	−	3.39641i	−0.0925413	−	0.160286i	0.816038	−	0.577998i	$-0.196166\pi$
$449$	−1.96092	−	3.39641i	−0.0925413	−	0.160286i	−0.908580	+	0.417711i	$0.862832\pi$
$450$		0			0
$451$	−0.163228	+	0.925712i	−0.00768611	+	0.0435901i
$452$	−0.186247	−	1.05626i	−0.00876034	−	0.0496824i
$453$	15.4685	−	5.63008i	0.726774	−	0.264524i
$454$	−16.7946	−	14.0924i	−0.788211	−	0.661388i
$455$		0			0
$456$	−5.26044	+	0.00605483i	−0.246343	+	0.000283543i
$457$	−32.6101			−1.52543			−0.762717	−	0.646732i	$-0.776135\pi$
$457$	−32.6101			−1.52543			−0.762717	+	0.646732i	$0.776135\pi$
$458$	17.3117	+	14.5263i	0.808924	+	0.678767i
$459$	34.4717	−	12.5467i	1.60900	−	0.585629i
$460$		0			0
$461$	5.45172	−	30.9182i	0.253912	−	1.44000i	−0.544939	−	0.838476i	$-0.683447\pi$
$461$	5.45172	−	30.9182i	0.253912	−	1.44000i	0.798851	−	0.601529i	$-0.205442\pi$
$462$	0.789247	+	0.287262i	0.0367191	+	0.0133647i
$463$	4.50489	+	7.80271i	0.209360	+	0.362623i	0.951513	−	0.307608i	$-0.0995285\pi$
$463$	4.50489	+	7.80271i	0.209360	+	0.362623i	−0.742153	+	0.670231i	$0.766195\pi$
$464$	−3.41147	+	5.90885i	−0.158374	+	0.274311i
$465$		0			0
$466$	−6.92540	+	5.81110i	−0.320813	+	0.269194i
$467$	−8.14522	+	14.1079i	−0.376916	+	0.652838i	−0.990612	−	0.136705i	$-0.956349\pi$
$467$	−8.14522	+	14.1079i	−0.376916	+	0.652838i	0.613696	+	0.789543i	$0.289682\pi$
$468$	−0.0529718	−	0.0917499i	−0.00244862	−	0.00424114i
$469$	−0.484601	−	0.176380i	−0.0223768	−	0.00814448i
$470$		0			0
$471$	3.23454	+	18.3440i	0.149040	+	0.845247i
$472$	1.93601	−	0.704650i	0.0891120	−	0.0324341i
$473$	1.42051	+	1.19195i	0.0653153	+	0.0548061i
$474$	4.27057			0.196154
$475$		0			0
$476$	−14.6933			−0.673467
$477$	10.7626	+	9.03090i	0.492786	+	0.413496i
$478$	−22.0566	+	8.02796i	−1.00885	+	0.367190i
$479$	4.31953	+	24.4973i	0.197364	+	1.11931i	0.909011	+	0.416771i	$0.136838\pi$
$479$	4.31953	+	24.4973i	0.197364	+	1.11931i	−0.711647	+	0.702537i	$0.752051\pi$
$480$		0			0
$481$	−0.698989	−	0.254411i	−0.0318712	−	0.0116002i
$482$	−13.7571	−	23.8279i	−0.626617	−	1.08533i
$483$	0.691157	−	1.19712i	0.0314487	−	0.0544708i
$484$	−8.34957	+	7.00612i	−0.379526	+	0.318460i
$485$		0			0
$486$	−7.02614	+	12.1696i	−0.318712	+	0.552026i
$487$	−17.2199	−	29.8258i	−0.780310	−	1.35154i	−0.931761	−	0.363071i	$-0.881728\pi$
$487$	−17.2199	−	29.8258i	−0.780310	−	1.35154i	0.151452	−	0.988465i	$-0.451605\pi$
$488$	1.69412	+	0.616609i	0.0766892	+	0.0279126i
$489$	−0.149045	+	0.845274i	−0.00674003	+	0.0382246i
$490$		0			0
$491$	−32.1757	+	11.7110i	−1.45207	+	0.528510i	−0.943168	−	0.332315i	$-0.892170\pi$
$491$	−32.1757	+	11.7110i	−1.45207	+	0.528510i	−0.508901	+	0.860825i	$0.669948\pi$
$492$	−2.74238	−	2.30113i	−0.123636	−	0.103743i
$493$	−45.6464			−2.05581
$494$	−0.228961	+	0.192571i	−0.0103014	+	0.00866416i
$495$		0			0
$496$	4.54967	+	3.81762i	0.204286	+	0.171416i
$497$	3.74018	−	1.36131i	0.167770	−	0.0610633i
$498$	−0.0204401	−	0.115922i	−0.000915944	−	0.00519458i
$499$	−3.85653	+	21.8715i	−0.172642	+	0.979102i	0.768188	+	0.640224i	$0.221158\pi$
$499$	−3.85653	+	21.8715i	−0.172642	+	0.979102i	−0.940830	+	0.338878i	$0.889953\pi$
$500$		0			0
$501$	6.52168	+	11.2959i	0.291367	+	0.504663i
$502$	13.2151	−	22.8892i	0.589817	−	1.02159i
$503$	−25.8806	+	21.7164i	−1.15396	+	0.968286i	−0.999805	−	0.0197614i	$-0.993709\pi$
$503$	−25.8806	+	21.7164i	−1.15396	+	0.968286i	−0.154153	+	0.988047i	$0.549265\pi$
$504$	2.59695	−	2.17910i	0.115677	−	0.0970647i
$505$		0			0
$506$	−0.0826308	−	0.143121i	−0.00367339	−	0.00636250i
$507$	−14.7373	−	5.36394i	−0.654506	−	0.238221i
$508$	−1.53830	+	8.72416i	−0.0682512	+	0.387072i
$509$	−2.04246	−	11.5834i	−0.0905303	−	0.513423i	−0.996026	−	0.0890668i	$-0.971612\pi$
$509$	−2.04246	−	11.5834i	−0.0905303	−	0.513423i	0.905495	−	0.424356i	$-0.139500\pi$
$510$		0			0
$511$	−12.6239	−	10.5927i	−0.558449	−	0.468594i
$512$	−1.00000			−0.0441942
$513$	22.4692	+	8.14883i	0.992037	+	0.359779i
$514$	−11.0971			−0.489470
$515$		0			0
$516$	−6.63632	+	2.41542i	−0.292148	+	0.106333i
$517$	−0.478770	−	2.71524i	−0.0210563	−	0.119416i
$518$	4.13323	−	23.4407i	0.181603	−	1.02992i
$519$	24.2425	+	8.82354i	1.06413	+	0.387310i
$520$		0			0
$521$	−10.3001	+	17.8403i	−0.451257	+	0.781600i	−0.998464	−	0.0553972i	$-0.982357\pi$
$521$	−10.3001	+	17.8403i	−0.451257	+	0.781600i	0.547208	+	0.836997i	$0.315691\pi$
$522$	8.06771	−	6.76961i	0.353114	−	0.296298i
$523$	1.65498	−	1.38869i	0.0723671	−	0.0607232i	−0.605887	−	0.795551i	$-0.707181\pi$
$523$	1.65498	−	1.38869i	0.0723671	−	0.0607232i	0.678254	+	0.734828i	$0.262737\pi$
$524$	−3.86127	+	6.68791i	−0.168680	+	0.292163i
$525$		0			0
$526$	−26.2306	−	9.54717i	−1.14371	−	0.416276i
$527$	−6.89971	+	39.1302i	−0.300556	+	1.70454i
$528$	0.0664068	+	0.376612i	0.00288998	+	0.0163899i
$529$	21.3573	−	7.77344i	0.928580	−	0.337976i
$530$		0			0
$531$	−3.18014			−0.138006
$532$	−7.34065	−	6.14516i	−0.318258	−	0.266426i
$533$	−0.203601			−0.00881892
$534$	5.90627	+	4.95595i	0.255589	+	0.214465i
$535$		0			0
$536$	−0.0407740	−	0.231241i	−0.00176117	−	0.00998809i
$537$	3.79554	−	21.5256i	0.163790	−	0.928898i
$538$	−7.91172	−	2.87963i	−0.341099	−	0.124150i
$539$	−0.344832	−	0.597267i	−0.0148530	−	0.0257261i
$540$		0			0
$541$	−2.61563	+	2.19477i	−0.112455	+	0.0943606i	−0.697281	−	0.716798i	$-0.745607\pi$
$541$	−2.61563	+	2.19477i	−0.112455	+	0.0943606i	0.584826	+	0.811158i	$0.301163\pi$
$542$	9.14331	−	7.67215i	0.392739	−	0.329547i
$543$	15.7837	−	27.3382i	0.677345	−	1.17320i
$544$	−3.34507	−	5.79383i	−0.143419	−	0.248408i
$545$		0			0
$546$	−0.0315902	+	0.179157i	−0.00135193	+	0.00766720i
$547$	1.74690	+	9.90714i	0.0746919	+	0.423599i	0.999109	+	0.0422146i	$0.0134413\pi$
$547$	1.74690	+	9.90714i	0.0746919	+	0.423599i	−0.924417	+	0.381384i	$0.875448\pi$
$548$	15.8613	−	5.77305i	0.677562	−	0.246613i
$549$	−2.13175	−	1.78875i	−0.0909809	−	0.0763421i
$550$		0			0
$551$	−22.8046	−	19.0906i	−0.971507	−	0.813288i
$552$	0.629393			0.0267887
$553$	5.95359	+	4.99565i	0.253172	+	0.212437i
$554$	2.95078	−	1.07399i	0.125366	−	0.0456297i
$555$		0			0
$556$	3.46644	−	19.6592i	0.147010	−	0.833734i
$557$	−3.05407	−	1.11159i	−0.129405	−	0.0470997i	0.276506	−	0.961012i	$-0.410824\pi$
$557$	−3.05407	−	1.11159i	−0.129405	−	0.0470997i	−0.405911	+	0.913913i	$0.633046\pi$
$558$	−4.58374	−	7.93927i	−0.194045	−	0.336096i
$559$	−0.200824	+	0.347838i	−0.00849396	+	0.0147120i
$560$		0			0
$561$	−1.95989	+	1.64454i	−0.0827465	+	0.0694326i
$562$	−7.71375	+	13.3606i	−0.325385	+	0.563583i
$563$	0.296917	+	0.514275i	0.0125136	+	0.0216741i	0.872214	−	0.489124i	$-0.162683\pi$
$563$	0.296917	+	0.514275i	0.0125136	+	0.0216741i	−0.859701	+	0.510798i	$0.829350\pi$
$564$	9.86715	+	3.59135i	0.415482	+	0.151223i
$565$		0			0
$566$	2.72393	+	15.4482i	0.114495	+	0.649334i
$567$	4.10024	−	1.49236i	0.172194	−	0.0626734i
$568$	1.38827	+	1.16490i	0.0582507	+	0.0488782i
$569$	−39.0985			−1.63910			−0.819548	−	0.573011i	$-0.805775\pi$
$569$	−39.0985			−1.63910			−0.819548	+	0.573011i	$0.805775\pi$
$570$		0			0
$571$	−1.29501			−0.0541946			−0.0270973	−	0.999633i	$-0.508626\pi$
$571$	−1.29501			−0.0541946			−0.0270973	+	0.999633i	$0.508626\pi$
$572$	0.0166610	+	0.0139802i	0.000696631	+	0.000584543i
$573$	17.7031	−	6.44342i	0.739559	−	0.269178i
$574$	−1.13131	−	6.41600i	−0.0472202	−	0.267799i
$575$		0			0
$576$	1.45047	+	0.527930i	0.0604364	+	0.0219971i
$577$	−23.9536	−	41.4888i	−0.997201	−	1.72720i	−0.563350	−	0.826218i	$-0.690488\pi$
$577$	−23.9536	−	41.4888i	−0.997201	−	1.72720i	−0.433851	−	0.900985i	$-0.642845\pi$
$578$	13.8790	−	24.0390i	0.577288	−	0.999893i
$579$	9.88788	−	8.29692i	0.410926	−	0.344808i
$580$		0			0
$581$	0.107108	−	0.185517i	0.00444359	−	0.00769653i
$582$	−4.44506	−	7.69907i	−0.184254	−	0.319137i
$583$	−2.71032	−	0.986477i	−0.112250	−	0.0408557i
$584$	1.30294	−	7.38935i	0.0539161	−	0.305773i
$585$		0			0
$586$	−9.73381	+	3.54282i	−0.402100	+	0.146352i
$587$	−6.30973	−	5.29449i	−0.260431	−	0.218527i	0.503218	−	0.864160i	$-0.332149\pi$
$587$	−6.30973	−	5.29449i	−0.260431	−	0.218527i	−0.763648	+	0.645632i	$0.776594\pi$
$588$	2.62656			0.108318
$589$	−19.8124	+	16.6635i	−0.816355	+	0.686606i
$590$		0			0
$591$	7.03491	+	5.90299i	0.289377	+	0.242816i
$592$	10.1840	−	3.70668i	0.418561	−	0.152344i
$593$	2.44840	+	13.8856i	0.100544	+	0.570213i	0.992907	+	0.118894i	$0.0379350\pi$
$593$	2.44840	+	13.8856i	0.100544	+	0.570213i	−0.892363	+	0.451318i	$0.850954\pi$
$594$	0.301723	−	1.71116i	0.0123799	−	0.0702097i
$595$		0			0
$596$	7.83215	+	13.5657i	0.320817	+	0.555672i
$597$	−11.8517	+	20.5277i	−0.485057	+	0.840144i
$598$	0.0274208	−	0.0230088i	0.00112132	−	0.000940900i
$599$	20.4865	−	17.1902i	0.837055	−	0.702373i	−0.119844	−	0.992793i	$-0.538239\pi$
$599$	20.4865	−	17.1902i	0.837055	−	0.702373i	0.956899	+	0.290420i	$0.0937950\pi$
$600$		0			0
$601$	1.94626	+	3.37103i	0.0793898	+	0.137507i	0.902987	−	0.429668i	$-0.141369\pi$
$601$	1.94626	+	3.37103i	0.0793898	+	0.137507i	−0.823597	+	0.567175i	$0.808036\pi$
$602$	−12.0772	−	4.39574i	−0.492230	−	0.179157i
$603$	−0.0629372	+	0.356935i	−0.00256300	+	0.0145355i
$604$	2.36857	+	13.4329i	0.0963759	+	0.546575i
$605$		0			0
$606$	8.90936	+	7.47584i	0.361918	+	0.303685i
$607$	37.1711			1.50873			0.754364	−	0.656456i	$-0.227945\pi$
$607$	37.1711			1.50873			0.754364	+	0.656456i	$0.227945\pi$
$608$	0.751973	−	4.29355i	0.0304966	−	0.174126i
$609$	−18.0844			−0.732815
$610$		0			0
$611$	0.561173	−	0.204250i	0.0227026	−	0.00826308i
$612$	1.79320	+	10.1698i	0.0724859	+	0.411088i
$613$	−6.57252	+	37.2746i	−0.265461	+	1.50551i	0.502257	+	0.864719i	$0.332503\pi$
$613$	−6.57252	+	37.2746i	−0.265461	+	1.50551i	−0.767718	+	0.640788i	$0.778608\pi$
$614$	−8.06402	−	2.93506i	−0.325437	−	0.118450i
$615$		0			0
$616$	−0.347978	+	0.602715i	−0.0140204	+	0.0242841i
$617$	−5.49191	+	4.60826i	−0.221096	+	0.185521i	−0.746607	−	0.665265i	$-0.768319\pi$
$617$	−5.49191	+	4.60826i	−0.221096	+	0.185521i	0.525511	+	0.850787i	$0.323874\pi$
$618$	17.0440	−	14.3016i	0.685611	−	0.575296i
$619$	−3.61107	+	6.25456i	−0.145141	+	0.251392i	−0.929426	−	0.369009i	$-0.879697\pi$
$619$	−3.61107	+	6.25456i	−0.145141	+	0.251392i	0.784284	+	0.620402i	$0.213030\pi$
$620$		0			0
$621$	−2.68722	−	0.978070i	−0.107835	−	0.0392486i
$622$	−0.739361	+	4.19312i	−0.0296457	+	0.168129i
$623$	2.43651	+	13.8181i	0.0976168	+	0.553612i
$624$	−0.0778363	+	0.0283301i	−0.00311595	+	0.00113411i
$625$		0			0
$626$	−1.88127			−0.0751905
$627$	−1.66694	+	0.00191866i	−0.0665710	+	7.66239e-5i
$628$	−15.4346			−0.615909
$629$	55.5421	+	46.6054i	2.21461	+	1.85828i
$630$		0			0
$631$	−2.02752	−	11.4987i	−0.0807144	−	0.457754i	−0.998199	−	0.0599838i	$-0.980895\pi$
$631$	−2.02752	−	11.4987i	−0.0807144	−	0.457754i	0.917485	−	0.397771i	$-0.130216\pi$
$632$	−0.614483	+	3.48491i	−0.0244428	+	0.138622i
$633$	−21.5855	−	7.85646i	−0.857945	−	0.312266i
$634$	−12.0583	−	20.8856i	−0.478897	−	0.829474i
$635$		0			0
$636$	8.41471	−	7.06078i	0.333665	−	0.279978i
$637$	0.114432	−	0.0960196i	0.00453395	−	0.00380443i
$638$	−1.08103	+	1.87240i	−0.0427985	+	0.0741291i
$639$	−1.39867	−	2.42257i	−0.0553306	−	0.0958354i
$640$		0			0
$641$	2.14712	−	12.1769i	0.0848062	−	0.480960i	−0.912592	−	0.408871i	$-0.865922\pi$
$641$	2.14712	−	12.1769i	0.0848062	−	0.480960i	0.997398	−	0.0720885i	$-0.0229664\pi$
$642$	2.48186	+	14.0753i	0.0979510	+	0.555508i
$643$	11.0389	−	4.01782i	0.435331	−	0.158447i	−0.115053	−	0.993359i	$-0.536704\pi$
$643$	11.0389	−	4.01782i	0.435331	−	0.158447i	0.550384	+	0.834912i	$0.314481\pi$
$644$	0.877435	+	0.736255i	0.0345758	+	0.0290125i
$645$		0			0
$646$	27.3915	−	10.0054i	1.07770	−	0.393657i
$647$	−4.96567			−0.195221			−0.0976103	−	0.995225i	$-0.531120\pi$
$647$	−4.96567			−0.195221			−0.0976103	+	0.995225i	$0.531120\pi$
$648$	1.52192	+	1.27704i	0.0597867	+	0.0501670i
$649$	0.613485	−	0.223290i	0.0240814	−	0.00876490i
$650$		0			0
$651$	−2.73355	+	15.5027i	−0.107136	+	0.607600i
$652$	−0.668322	−	0.243249i	−0.0261735	−	0.00952638i
$653$	−23.4277	−	40.5780i	−0.916797	−	1.58794i	−0.804249	−	0.594293i	$-0.797432\pi$
$653$	−23.4277	−	40.5780i	−0.916797	−	1.58794i	−0.112548	−	0.993646i	$-0.535901\pi$
$654$	0.472621	−	0.818603i	0.0184809	−	0.0320099i
$655$		0			0
$656$	2.27239	−	1.90676i	0.0887218	−	0.0744464i
$657$	−5.79094	+	10.0302i	−0.225926	+	0.391315i
$658$	9.55466	+	16.5492i	0.372479	+	0.645153i
$659$	13.9640	+	5.08247i	0.543959	+	0.197985i	0.599360	−	0.800479i	$-0.295422\pi$
$659$	13.9640	+	5.08247i	0.543959	+	0.197985i	−0.0554016	+	0.998464i	$0.517644\pi$
$660$		0			0
$661$	−3.68654	−	20.9074i	−0.143390	−	0.813203i	−0.968646	−	0.248445i	$-0.920081\pi$
$661$	−3.68654	−	20.9074i	−0.143390	−	0.813203i	0.825256	−	0.564758i	$-0.191031\pi$
$662$	19.4532	−	7.08039i	0.756071	−	0.275187i
$663$	−0.424508	−	0.356204i	−0.0164865	−	0.0138338i
$664$	0.0975366			0.00378515
$665$		0			0
$666$	−16.7285			−0.648218
$667$	2.72585	+	2.28726i	0.105545	+	0.0885630i
$668$	−10.1562	+	3.69654i	−0.392954	+	0.143023i
$669$	0.322833	+	1.83087i	0.0124814	+	0.0707857i
$670$		0			0
$671$	0.536834	+	0.195392i	0.0207243	+	0.00754302i
$672$	−1.32526	−	2.29542i	−0.0511230	−	0.0885476i
$673$	15.8227	−	27.4058i	0.609922	−	1.05642i	−0.381331	−	0.924439i	$-0.624534\pi$
$673$	15.8227	−	27.4058i	0.609922	−	1.05642i	0.991253	−	0.131977i	$-0.0421325\pi$
$674$	−3.74652	+	3.14371i	−0.144311	+	0.121091i
$675$		0			0
$676$	6.49764	−	11.2543i	0.249909	−	0.432856i
$677$	2.62655	+	4.54932i	0.100946	+	0.174844i	0.912075	−	0.410024i	$-0.134480\pi$
$677$	2.62655	+	4.54932i	0.100946	+	0.174844i	−0.811128	+	0.584868i	$0.801146\pi$
$678$	1.21633	+	0.442708i	0.0467129	+	0.0170021i
$679$	2.80942	−	15.9330i	0.107816	−	0.611453i
$680$		0			0
$681$	24.8627	−	9.04928i	0.952740	−	0.346769i
$682$	1.44170	+	1.20973i	0.0552057	+	0.0463231i
$683$	3.28296			0.125619			0.0628095	−	0.998026i	$-0.479994\pi$
$683$	3.28296			0.125619			0.0628095	+	0.998026i	$0.479994\pi$
$684$	−3.35741	+	5.83069i	−0.128374	+	0.222942i
$685$		0			0
$686$	15.4387	+	12.9546i	0.589454	+	0.494611i
$687$	−25.6282	+	9.32790i	−0.977777	+	0.355882i
$688$	−1.01617	−	5.76298i	−0.0387411	−	0.219711i
$689$	0.108483	−	0.615235i	0.00413286	−	0.0234386i
$690$		0			0
$691$	−6.31652	−	10.9405i	−0.240292	−	0.416197i	0.720506	−	0.693449i	$-0.243910\pi$
$691$	−6.31652	−	10.9405i	−0.240292	−	0.416197i	−0.960797	+	0.277252i	$0.910576\pi$
$692$	−10.6885	+	18.5130i	−0.406314	+	0.703757i
$693$	0.822924	−	0.690515i	0.0312603	−	0.0262305i
$694$	2.74572	−	2.30394i	0.104226	−	0.0874562i
$695$		0			0
$696$	−4.11707	−	7.13097i	−0.156057	−	0.270299i
$697$	18.6487	+	6.78758i	0.706370	+	0.257098i
$698$	−1.44676	+	8.20500i	−0.0547608	+	0.310564i
$699$	−1.89455	−	10.7445i	−0.0716586	−	0.406396i
$700$		0			0
$701$	21.6536	+	18.1696i	0.817847	+	0.686255i	0.952467	−	0.304642i	$-0.0985370\pi$
$701$	21.6536	+	18.1696i	0.817847	+	0.686255i	−0.134620	+	0.990897i	$0.542981\pi$
$702$	0.376351			0.0142045
$703$	8.25670	+	46.5129i	0.311407	+	1.75427i
$704$	−0.316881			−0.0119429
$705$		0			0
$706$	−13.3924	+	4.87443i	−0.504029	+	0.183451i
$707$	3.67538	+	20.8441i	0.138227	+	0.783923i
$708$	−0.431755	+	2.44861i	−0.0162264	+	0.0920242i
$709$	32.4404	+	11.8074i	1.21833	+	0.443435i	0.869585	−	0.493784i	$-0.164387\pi$
$709$	32.4404	+	11.8074i	1.21833	+	0.443435i	0.348742	+	0.937219i	$0.386609\pi$
$710$		0			0
$711$	2.73108	−	4.73036i	0.102423	−	0.177403i
$712$	−4.89404	+	4.10659i	−0.183412	+	0.153901i
$713$	2.37277	−	1.99099i	0.0888609	−	0.0745631i
$714$	8.86616	−	15.3566i	0.331808	−	0.574708i
$715$		0			0
$716$	17.0194	+	6.19454i	0.636044	+	0.231501i
$717$	4.91892	−	27.8966i	0.183700	−	1.04182i
$718$	−3.79552	−	21.5255i	−0.141648	−	0.803323i
$719$	−23.2373	+	8.45770i	−0.866606	+	0.315419i	−0.736792	−	0.676119i	$-0.763660\pi$
$719$	−23.2373	+	8.45770i	−0.866606	+	0.315419i	−0.129814	+	0.991538i	$0.541438\pi$
$720$		0			0
$721$	40.4909			1.50796
$722$	17.8691	+	6.45726i	0.665018	+	0.240315i
$723$	33.2049			1.23490
$724$	20.0377	+	16.8136i	0.744695	+	0.624874i
$725$		0			0
$726$	−2.28416	−	12.9541i	−0.0847731	−	0.480772i
$727$	−5.43786	+	30.8396i	−0.201679	+	1.14378i	0.700901	+	0.713258i	$0.252781\pi$
$727$	−5.43786	+	30.8396i	−0.201679	+	1.14378i	−0.902581	+	0.430521i	$0.858330\pi$
$728$	−0.141652	−	0.0515570i	−0.00524996	−	0.00191083i
$729$	−11.4594	−	19.8483i	−0.424424	−	0.735123i
$730$		0			0
$731$	29.9905	−	25.1650i	1.10924	−	0.930763i
$732$	−1.66670	+	1.39853i	−0.0616031	+	0.0516911i
$733$	14.3578	−	24.8684i	0.530317	−	0.918536i	−0.469057	−	0.883168i	$-0.655406\pi$
$733$	14.3578	−	24.8684i	0.530317	−	0.918536i	0.999374	−	0.0353683i	$-0.0112604\pi$
$734$	9.36170	+	16.2149i	0.345547	+	0.598504i
$735$		0			0
$736$	−0.0905620	+	0.513603i	−0.00333816	+	0.0189316i
$737$	−0.0129205	−	0.0732759i	−0.000475933	−	0.00269915i
$738$	−4.30267	+	1.56604i	−0.158384	+	0.0576469i
$739$	−34.1487	−	28.6541i	−1.25618	−	1.05406i	−0.996078	−	0.0884783i	$-0.971800\pi$
$739$	−34.1487	−	28.6541i	−1.25618	−	1.05406i	−0.260101	−	0.965581i	$-0.583756\pi$
$740$		0			0
$741$	−0.0631058	−	0.355497i	−0.00231825	−	0.0130595i
$742$	19.9905			0.733875
$743$	−23.5202	−	19.7358i	−0.862871	−	0.724035i	0.0997136	−	0.995016i	$-0.468207\pi$
$743$	−23.5202	−	19.7358i	−0.862871	−	0.724035i	−0.962585	+	0.270981i	$0.912652\pi$
$744$	−6.73531	+	2.45145i	−0.246928	+	0.0898746i
$745$		0			0
$746$	0.0908799	−	0.515406i	0.00332735	−	0.0188703i
$747$	−0.141474	−	0.0514924i	−0.00517627	−	0.00188401i
$748$	−1.05999	−	1.83595i	−0.0387570	−	0.0671291i
$749$	−13.0052	+	22.5256i	−0.475198	+	0.823067i
$750$		0			0
$751$	−33.3471	+	27.9816i	−1.21685	+	1.02106i	−0.217870	+	0.975978i	$0.569911\pi$
$751$	−33.3471	+	27.9816i	−1.21685	+	1.02106i	−0.998983	+	0.0450837i	$0.985645\pi$
$752$	−4.35041	+	7.53513i	−0.158643	+	0.274778i
$753$	15.9483	+	27.6233i	0.581189	+	1.00665i
$754$	−0.440057	−	0.160168i	−0.0160259	−	0.00583296i
$755$		0			0
$756$	2.09121	+	11.8598i	0.0760566	+	0.431338i
$757$	−3.89923	+	1.41920i	−0.141720	+	0.0515818i	−0.411906	−	0.911226i	$-0.635137\pi$
$757$	−3.89923	+	1.41920i	−0.141720	+	0.0515818i	0.270186	+	0.962808i	$0.412915\pi$
$758$	13.6313	+	11.4380i	0.495111	+	0.415448i
$759$	0.199443			0.00723931
$760$		0			0
$761$	19.2254			0.696920			0.348460	−	0.937324i	$-0.386705\pi$
$761$	19.2254			0.696920			0.348460	+	0.937324i	$0.386705\pi$
$762$	−8.18978	−	6.87204i	−0.296684	−	0.248948i
$763$	1.61647	−	0.588347i	0.0585202	−	0.0212996i
$764$	2.71075	+	15.3734i	0.0980713	+	0.556190i
$765$		0			0
$766$	12.7545	+	4.64225i	0.460838	+	0.167731i
$767$	0.0707037	+	0.122462i	0.00255296	+	0.00442186i
$768$	0.603415	−	1.04514i	0.0217739	−	0.0377134i
$769$	−18.8160	+	15.7885i	−0.678522	+	0.569347i	−0.915574	−	0.402150i	$-0.868263\pi$
$769$	−18.8160	+	15.7885i	−0.678522	+	0.569347i	0.237052	+	0.971497i	$0.423819\pi$
$770$		0			0
$771$	6.69612	−	11.5980i	0.241155	−	0.417693i
$772$	5.34778	+	9.26262i	0.192471	+	0.333369i
$773$	12.3648	+	4.50041i	0.444730	+	0.161869i	0.554671	−	0.832070i	$-0.312844\pi$
$773$	12.3648	+	4.50041i	0.444730	+	0.161869i	−0.109941	+	0.993938i	$0.535066\pi$
$774$	−1.56852	+	8.89552i	−0.0563793	+	0.319743i
$775$		0			0
$776$	6.92226	−	2.51950i	0.248495	−	0.0904446i
$777$	22.0049	+	18.4643i	0.789420	+	0.662402i
$778$	−24.4365			−0.876090
$779$	6.47798	+	11.1904i	0.232098	+	0.400939i
$780$		0			0
$781$	0.439918	+	0.369135i	0.0157415	+	0.0132087i
$782$	−3.27866	+	1.19333i	−0.117245	+	0.0426736i
$783$	6.49658	+	36.8439i	0.232169	+	1.31669i
$784$	−0.377930	+	2.14335i	−0.0134975	+	0.0765482i
$785$		0			0
$786$	−4.65989	−	8.07117i	−0.166213	−	0.287889i
$787$	15.5110	−	26.8659i	0.552909	−	0.957667i	−0.445154	−	0.895454i	$-0.646851\pi$
$787$	15.5110	−	26.8659i	0.552909	−	0.957667i	0.998063	−	0.0622126i	$-0.0198157\pi$
$788$	−5.82925	+	4.89132i	−0.207658	+	0.174246i
$789$	25.8061	−	21.6539i	0.918723	−	0.770900i
$790$		0			0
$791$	1.17781	+	2.04003i	0.0418781	+	0.0725350i
$792$	0.459628	+	0.167291i	0.0163322	+	0.00594442i
$793$	−0.0214872	+	0.121860i	−0.000763032	+	0.00432737i
$794$	−4.94103	−	28.0220i	−0.175351	−	0.994463i
$795$		0			0
$796$	−15.0459	−	12.6250i	−0.533288	−	0.447481i
$797$	3.22825			0.114350			0.0571752	−	0.998364i	$-0.481791\pi$
$797$	3.22825			0.114350			0.0571752	+	0.998364i	$0.481791\pi$
$798$	10.8520	−	3.96397i	0.384158	−	0.140323i
$799$	−58.2097			−2.05931
$800$		0			0
$801$	9.26666	−	3.37279i	0.327421	−	0.119172i
$802$	6.17819	+	35.0382i	0.218159	+	1.23724i
$803$	0.412878	−	2.34155i	0.0145701	−	0.0826313i
$804$	0.266284	+	0.0969194i	0.00939111	+	0.00341808i
$805$		0			0
$806$	−0.203820	+	0.353026i	−0.00717925	+	0.0124348i
$807$	7.78368	−	6.53128i	0.273999	−	0.229912i
$808$	−7.38245	+	6.19461i	−0.259714	+	0.217926i
$809$	17.3364	−	30.0275i	0.609515	−	1.05571i	−0.381806	−	0.924243i	$-0.624698\pi$
$809$	17.3364	−	30.0275i	0.609515	−	1.05571i	0.991320	−	0.131468i	$-0.0419690\pi$
$810$		0			0
$811$	53.2716	+	19.3893i	1.87062	+	0.680850i	0.968304	+	0.249773i	$0.0803562\pi$
$811$	53.2716	+	19.3893i	1.87062	+	0.680850i	0.902315	+	0.431076i	$0.141866\pi$
$812$	2.60212	−	14.7574i	0.0913165	−	0.517882i
$813$	2.50130	+	14.1856i	0.0877244	+	0.497510i
$814$	3.22713	−	1.17458i	0.113111	−	0.0411689i
$815$		0			0
$816$	8.07385			0.282641
$817$	25.5077	−	0.0293597i	0.892403	−	0.00102716i
$818$	−15.8060			−0.552645
$819$	0.178244	+	0.149564i	0.00622834	+	0.00522619i
$820$		0			0
$821$	4.12052	+	23.3686i	0.143807	+	0.815571i	0.968317	+	0.249723i	$0.0803397\pi$
$821$	4.12052	+	23.3686i	0.143807	+	0.815571i	−0.824510	+	0.565847i	$0.808549\pi$
$822$	−3.53728	+	20.0609i	−0.123377	+	0.699705i
$823$	34.6806	+	12.6227i	1.20889	+	0.439999i	0.866318	−	0.499493i	$-0.166480\pi$
$823$	34.6806	+	12.6227i	1.20889	+	0.439999i	0.342570	+	0.939492i	$0.388702\pi$
$824$	9.21811	+	15.9662i	0.321128	+	0.556210i
$825$		0			0
$826$	−3.46625	+	2.90853i	−0.120606	+	0.101201i
$827$	10.4774	−	8.79156i	0.364334	−	0.305713i	−0.442181	−	0.896926i	$-0.645795\pi$
$827$	10.4774	−	8.79156i	0.364334	−	0.305713i	0.806515	+	0.591213i	$0.201351\pi$
$828$	0.402504	−	0.697157i	0.0139880	−	0.0242279i
$829$	5.92228	+	10.2577i	0.205689	+	0.356265i	0.950352	−	0.311176i	$-0.100723\pi$
$829$	5.92228	+	10.2577i	0.205689	+	0.356265i	−0.744663	+	0.667441i	$0.767390\pi$
$830$		0			0
$831$	−0.658062	+	3.73205i	−0.0228279	+	0.129463i
$832$	−0.0119185	−	0.0675931i	−0.000413199	−	0.00234337i
$833$	−13.6824	+	4.97999i	−0.474067	+	0.172546i
$834$	18.4550	+	15.4856i	0.639043	+	0.536221i
$835$		0			0
$836$	0.238286	−	1.36054i	0.00824130	−	0.0470554i
$837$	32.5663			1.12566
$838$	28.5985	+	23.9970i	0.987918	+	0.828962i
$839$	−9.87612	+	3.59461i	−0.340962	+	0.124100i	−0.506825	−	0.862049i	$-0.669181\pi$
$839$	−9.87612	+	3.59461i	−0.340962	+	0.124100i	0.165864	+	0.986149i	$0.446959\pi$
$840$		0			0
$841$	3.04798	−	17.2860i	0.105103	−	0.596068i
$842$	−18.6383	−	6.78380i	−0.642320	−	0.233785i
$843$	−9.30918	−	16.1240i	−0.320625	−	0.555339i
$844$	9.51699	−	16.4839i	0.327588	−	0.567399i
$845$		0			0
$846$	10.2882	−	8.63280i	0.353715	−	0.296802i
$847$	11.9692	−	20.7313i	0.411266	−	0.712334i
$848$	4.55102	+	7.88260i	0.156283	+	0.270690i
$849$	−17.7892	−	6.47475i	−0.610524	−	0.222213i
$850$		0			0
$851$	−0.981476	−	5.56623i	−0.0336446	−	0.190808i
$852$	−2.05520	+	0.748030i	−0.0704098	+	0.0256271i
$853$	−23.6265	−	19.8250i	−0.808957	−	0.678795i	0.141402	−	0.989952i	$-0.454839\pi$
$853$	−23.6265	−	19.8250i	−0.808957	−	0.678795i	−0.950359	+	0.311157i	$0.899283\pi$
$854$	−3.95953			−0.135492
$855$		0			0
$856$	−11.8430			−0.404784
$857$	−23.4119	−	19.6449i	−0.799734	−	0.671056i	0.148400	−	0.988927i	$-0.452588\pi$
$857$	−23.4119	−	19.6449i	−0.799734	−	0.671056i	−0.948134	+	0.317871i	$0.897032\pi$
$858$	−0.0246649	+	0.00897728i	−0.000842045	+	0.000306479i
$859$	−7.71242	−	43.7393i	−0.263144	−	1.49237i	−0.774268	−	0.632858i	$-0.781882\pi$
$859$	−7.71242	−	43.7393i	−0.263144	−	1.49237i	0.511123	−	0.859507i	$-0.329230\pi$
$860$		0			0
$861$	7.38831	+	2.68912i	0.251793	+	0.0916451i
$862$	9.95887	+	17.2493i	0.339200	+	0.587512i
$863$	9.65731	−	16.7269i	0.328739	−	0.569392i	−0.653523	−	0.756906i	$-0.726710\pi$
$863$	9.65731	−	16.7269i	0.328739	−	0.569392i	0.982262	+	0.187514i	$0.0600432\pi$
$864$	−4.20046	+	3.52460i	−0.142902	+	0.119909i
$865$		0			0
$866$	−9.29408	+	16.0978i	−0.315826	+	0.547026i
$867$	16.7495	+	29.0110i	0.568844	+	0.985266i
$868$	−12.2573	−	4.46131i	−0.416042	−	0.151427i
$869$	−0.194718	+	1.10430i	−0.00660536	+	0.0374608i
$870$		0			0
$871$	0.0151443	−	0.00551208i	0.000513146	−	0.000186770i
$872$	0.600000	+	0.503460i	0.0203186	+	0.0170493i
$873$	−11.3707			−0.384839
$874$	−2.13708	−	0.775048i	−0.0722877	−	0.0262164i
$875$		0			0
$876$	6.93673	+	5.82061i	0.234370	+	0.196660i
$877$	12.7345	−	4.63497i	0.430013	−	0.156512i	−0.117941	−	0.993021i	$-0.537629\pi$
$877$	12.7345	−	4.63497i	0.430013	−	0.156512i	0.547953	+	0.836509i	$0.315407\pi$
$878$	−3.67531	−	20.8437i	−0.124036	−	0.703441i
$879$	2.17077	−	12.3110i	0.0732182	−	0.415241i
$880$		0			0
$881$	10.2941	+	17.8298i	0.346816	+	0.600703i	0.985682	−	0.168615i	$-0.0539295\pi$
$881$	10.2941	+	17.8298i	0.346816	+	0.600703i	−0.638866	+	0.769318i	$0.720596\pi$
$882$	1.67972	−	2.90935i	0.0565590	−	0.0979630i
$883$	−3.05346	+	2.56215i	−0.102757	+	0.0862233i	−0.692719	−	0.721208i	$-0.743587\pi$
$883$	−3.05346	+	2.56215i	−0.102757	+	0.0862233i	0.589962	+	0.807431i	$0.299143\pi$
$884$	0.351754	−	0.295157i	0.0118308	−	0.00992720i
$885$		0			0
$886$	16.2791	+	28.1962i	0.546907	+	0.947270i
$887$	−14.5804	−	5.30684i	−0.489563	−	0.178186i	0.0854309	−	0.996344i	$-0.472773\pi$
$887$	−14.5804	−	5.30684i	−0.489563	−	0.178186i	−0.574994	+	0.818158i	$0.694996\pi$
$888$	−2.27117	+	12.8805i	−0.0762155	+	0.432240i
$889$	−3.37853	−	19.1606i	−0.113312	−	0.642625i
$890$		0			0
$891$	0.482268	+	0.404671i	0.0161566	+	0.0135570i
$892$	−1.54050			−0.0515797
$893$	−29.0810	−	24.3449i	−0.973160	−	0.814671i
$894$	−18.9041			−0.632249
$895$		0			0
$896$	2.06382	−	0.751167i	0.0689472	−	0.0250947i
$897$	0.00750140	+	0.0425426i	0.000250465	+	0.00142046i
$898$	−0.681019	+	3.86225i	−0.0227259	+	0.128885i
$899$	−38.0788	−	13.8596i	−1.27000	−	0.462242i
$900$		0			0
$901$	−30.4470	+	52.7357i	−1.01434	+	1.75688i
$902$	0.720076	−	0.604216i	0.0239759	−	0.0201182i
$903$	11.8817	−	9.96997i	0.395400	−	0.331780i
$904$	−0.536278	+	0.928861i	−0.0178363	+	0.0308935i
$905$		0			0
$906$	−15.4685	−	5.63008i	−0.513907	−	0.187047i
$907$	5.35875	−	30.3910i	0.177934	−	1.00912i	−0.756768	−	0.653684i	$-0.773223\pi$
$907$	5.35875	−	30.3910i	0.177934	−	1.00912i	0.934702	−	0.355432i	$-0.115666\pi$
$908$	3.80703	+	21.5908i	0.126341	+	0.716515i
$909$	13.9784	−	5.08771i	0.463634	−	0.168749i
$910$		0			0
$911$	−34.4064			−1.13994			−0.569968	−	0.821667i	$-0.693044\pi$
$911$	−34.4064			−1.13994			−0.569968	+	0.821667i	$0.693044\pi$
$912$	4.03363	+	3.37671i	0.133567	+	0.111814i
$913$	0.0309075			0.00102289
$914$	24.9808	+	20.9613i	0.826290	+	0.693340i
$915$		0			0
$916$	−3.92425	−	22.2555i	−0.129661	−	0.735343i
$917$	2.94520	−	16.7031i	0.0972592	−	0.551584i
$918$	−34.4717	−	12.5467i	−1.13774	−	0.414102i
$919$	−9.26696	−	16.0508i	−0.305689	−	0.529468i	0.671726	−	0.740800i	$-0.265553\pi$
$919$	−9.26696	−	16.0508i	−0.305689	−	0.529468i	−0.977414	+	0.211332i	$0.932220\pi$
$920$		0			0
$921$	7.93352	−	6.65701i	0.261418	−	0.219356i
$922$	−24.0501	+	20.1804i	−0.792048	+	0.664607i
$923$	−0.0621931	+	0.107722i	−0.00204711	+	0.00354570i
$924$	−0.419950	−	0.727374i	−0.0138153	−	0.0239289i
$925$		0			0
$926$	1.56453	−	8.87291i	0.0514138	−	0.291582i
$927$	−4.94159	−	28.0251i	−0.162303	−	0.920466i
$928$	6.41147	−	2.33359i	0.210467	−	0.0766037i
$929$	−18.2652	−	15.3263i	−0.599262	−	0.502840i	0.291946	−	0.956435i	$-0.405697\pi$
$929$	−18.2652	−	15.3263i	−0.599262	−	0.502840i	−0.891208	+	0.453594i	$0.850142\pi$
$930$		0			0
$931$	−8.91838	−	3.23440i	−0.292288	−	0.106003i
$932$	9.04046			0.296130
$933$	−3.93628	−	3.30293i	−0.128868	−	0.108133i
$934$	15.3080	−	5.57166i	0.500894	−	0.182310i
$935$		0			0
$936$	−0.0183969	+	0.104334i	−0.000601322	+	0.00341027i
$937$	−56.4418	−	20.5431i	−1.84387	−	0.671115i	−0.988111	−	0.153744i	$-0.950867\pi$
$937$	−56.4418	−	20.5431i	−1.84387	−	0.671115i	−0.855762	−	0.517370i	$-0.826911\pi$
$938$	0.257851	+	0.446610i	0.00841912	+	0.0145823i
$939$	1.13518	−	1.96619i	0.0370453	−	0.0641643i
$940$		0			0
$941$	−30.6397	+	25.7097i	−0.998825	+	0.838113i	−0.986821	−	0.161814i	$-0.948265\pi$
$941$	−30.6397	+	25.7097i	−0.998825	+	0.838113i	−0.0120035	+	0.999928i	$0.503821\pi$
$942$	9.31349	−	16.1314i	0.303450	−	0.525591i
$943$	−0.773524	−	1.33978i	−0.0251894	−	0.0436293i
$944$	−1.93601	−	0.704650i	−0.0630117	−	0.0229344i
$945$		0			0
$946$	−0.322005	−	1.82618i	−0.0104693	−	0.0593742i
$947$	27.8284	−	10.1287i	0.904301	−	0.329139i	0.152326	−	0.988330i	$-0.451324\pi$
$947$	27.8284	−	10.1287i	0.904301	−	0.329139i	0.751975	+	0.659192i	$0.229101\pi$
$948$	−3.27144	−	2.74507i	−0.106252	−	0.0891557i
$949$	0.514998			0.0167175
$950$		0			0
$951$	29.1047			0.943784
$952$	11.2557	+	9.44468i	0.364800	+	0.306104i
$953$	33.2440	−	12.0998i	1.07688	−	0.391952i	0.258134	−	0.966109i	$-0.416893\pi$
$953$	33.2440	−	12.0998i	1.07688	−	0.391952i	0.818745	+	0.574158i	$0.194670\pi$
$954$	−2.43968	−	13.8361i	−0.0789877	−	0.447961i
$955$		0			0
$956$	22.0566	+	8.02796i	0.713363	+	0.259643i
$957$	−1.30462	−	2.25967i	−0.0421724	−	0.0730447i
$958$	12.4376	−	21.5425i	0.401840	−	0.696007i
$959$	−28.3983	+	23.8290i	−0.917030	+	0.769479i
$960$		0			0
$961$	−2.13687	+	3.70116i	−0.0689312	+	0.119392i
$962$	0.371924	+	0.644192i	0.0119913	+	0.0207696i
$963$	17.1779	+	6.25225i	0.553551	+	0.201476i
$964$	−4.77778	+	27.0961i	−0.153882	+	0.872708i
$965$		0			0
$966$	−1.29895	+	0.472779i	−0.0417930	+	0.0152114i
$967$	13.6001	+	11.4118i	0.437349	+	0.366979i	0.834716	−	0.550680i	$-0.185632\pi$
$967$	13.6001	+	11.4118i	0.437349	+	0.366979i	−0.397367	+	0.917660i	$0.630076\pi$
$968$	10.8996			0.350326
$969$	−6.07132	+	34.6655i	−0.195039	+	1.11361i
$970$		0			0
$971$	17.7532	+	14.8967i	0.569729	+	0.478059i	0.881556	−	0.472080i	$-0.156497\pi$
$971$	17.7532	+	14.8967i	0.569729	+	0.478059i	−0.311827	+	0.950139i	$0.600941\pi$
$972$	13.2048	−	4.80616i	0.423545	−	0.154158i
$973$	7.61322	+	43.1767i	0.244069	+	1.38418i
$974$	−5.98042	+	33.9166i	−0.191625	+	1.08676i
$975$		0			0
$976$	−0.901422	−	1.56131i	−0.0288538	−	0.0499763i
$977$	8.03404	−	13.9154i	0.257032	−	0.445192i	−0.708414	−	0.705797i	$-0.750589\pi$
$977$	8.03404	−	13.9154i	0.257032	−	0.445192i	0.965445	+	0.260605i	$0.0839222\pi$
$978$	0.657506	−	0.551713i	0.0210247	−	0.0176419i
$979$	−1.55083	+	1.30130i	−0.0495647	+	0.0415897i
$980$		0			0
$981$	−0.604493	−	1.04701i	−0.0193000	−	0.0334285i
$982$	32.1757	+	11.7110i	1.02677	+	0.373713i
$983$	7.72449	−	43.8078i	0.246373	−	1.39725i	−0.570910	−	0.821013i	$-0.693409\pi$
$983$	7.72449	−	43.8078i	0.246373	−	1.39725i	0.817282	−	0.576237i	$-0.195480\pi$
$984$	0.621648	+	3.52554i	0.0198174	+	0.112390i
$985$		0			0
$986$	34.9672	+	29.3410i	1.11358	+	0.934407i
$987$	−23.0617			−0.734062
$988$	0.299176		0.000344355i	0.00951807		1.09554e-5i
$989$	−3.05191			−0.0970450
$990$		0			0
$991$	8.83050	−	3.21404i	0.280510	−	0.102097i	−0.197934	−	0.980215i	$-0.563423\pi$
$991$	8.83050	−	3.21404i	0.280510	−	0.102097i	0.478444	+	0.878118i	$0.341201\pi$
$992$	−1.03133	−	5.84894i	−0.0327446	−	0.185704i
$993$	−4.33832	+	24.6038i	−0.137672	+	0.780779i
$994$	−3.74018	−	1.36131i	−0.118631	−	0.0431782i
$995$		0			0
$996$	−0.0588550	+	0.101940i	−0.00186489	+	0.00323009i
$997$	−12.6250	+	10.5936i	−0.399837	+	0.335503i	−0.820431	−	0.571746i	$-0.806266\pi$
$997$	−12.6250	+	10.5936i	−0.399837	+	0.335503i	0.420593	+	0.907249i	$0.361822\pi$
$998$	17.0130	−	14.2756i	0.538537	−	0.451886i
$999$	29.7130	−	51.4644i	0.940077	−	1.62826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.g.301.2		12
5.2	odd	4		950.2.u.f.149.3		24
5.3	odd	4		950.2.u.f.149.2		24
5.4	even	2		190.2.k.c.111.1	yes	12
19.6	even	9	inner	950.2.l.g.101.2		12
95.14	odd	18		3610.2.a.bd.1.3		6
95.24	even	18		3610.2.a.bf.1.4		6
95.44	even	18		190.2.k.c.101.1	✓	12
95.63	odd	36		950.2.u.f.899.3		24
95.82	odd	36		950.2.u.f.899.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.c.101.1	✓	12	95.44	even	18
190.2.k.c.111.1	yes	12	5.4	even	2
950.2.l.g.101.2		12	19.6	even	9	inner
950.2.l.g.301.2		12	1.1	even	1	trivial
950.2.u.f.149.2		24	5.3	odd	4
950.2.u.f.149.3		24	5.2	odd	4
950.2.u.f.899.2		24	95.82	odd	36
950.2.u.f.899.3		24	95.63	odd	36
3610.2.a.bd.1.3		6	95.14	odd	18
3610.2.a.bf.1.4		6	95.24	even	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)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(1.13405 - 0.412760i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.13405 - 0.412760i) q^{6} +(-1.09813 - 1.90202i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.18244 + 0.992183i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(1.13405 - 0.412760i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.13405 - 0.412760i) q^{6} +(-1.09813 - 1.90202i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.18244 + 0.992183i) q^{9} +(0.158441 - 0.274427i) q^{11} +(0.603415 + 1.04514i) q^{12} +(0.0644966 + 0.0234748i) q^{13} +(-0.381378 + 2.16290i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-5.12494 - 4.30034i) q^{17} +1.54356 q^{18} +(-0.761855 - 4.29180i) q^{19} +(-2.03042 - 1.70372i) q^{21} +(-0.297771 + 0.108380i) q^{22} +(0.0905620 + 0.513603i) q^{23} +(0.209564 - 1.18849i) q^{24} +(-0.0343179 - 0.0594403i) q^{26} +(-2.74165 + 4.74868i) q^{27} +(1.68244 - 1.41173i) q^{28} +(5.22668 - 4.38571i) q^{29} +(-2.96958 - 5.14347i) q^{31} +(0.939693 + 0.342020i) q^{32} +(0.0664068 - 0.376612i) q^{33} +(1.16173 + 6.58850i) q^{34} +(-1.18244 - 0.992183i) q^{36} -10.8376 q^{37} +(-2.17510 + 3.77742i) q^{38} +0.0828317 q^{39} +(-2.78749 + 1.01456i) q^{41} +(0.460258 + 2.61025i) q^{42} +(-1.01617 + 5.76298i) q^{43} +(0.297771 + 0.108380i) q^{44} +(0.260763 - 0.451655i) q^{46} +(6.66521 - 5.59278i) q^{47} +(-0.924485 + 0.775735i) q^{48} +(1.08821 - 1.88483i) q^{49} +(-7.58694 - 2.76142i) q^{51} +(-0.0119185 + 0.0675931i) q^{52} +(-1.58055 - 8.96377i) q^{53} +(5.15262 - 1.87540i) q^{54} -2.19627 q^{56} +(-2.63547 - 4.55265i) q^{57} -6.82295 q^{58} +(1.57825 + 1.32431i) q^{59} +(0.313061 + 1.77546i) q^{61} +(-1.03133 + 5.84894i) q^{62} +(3.18563 + 1.15947i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.292952 + 0.245816i) q^{66} +(0.179873 - 0.150932i) q^{67} +(3.34507 - 5.79383i) q^{68} +(0.314696 + 0.545070i) q^{69} +(-0.314696 + 1.78473i) q^{71} +(0.268037 + 1.52011i) q^{72} +(7.05084 - 2.56629i) q^{73} +(8.30210 + 6.96629i) q^{74} +(4.09431 - 1.49554i) q^{76} -0.695955 q^{77} +(-0.0634528 - 0.0532432i) q^{78} +(-3.32526 + 1.21030i) q^{79} +(-0.344991 + 1.95654i) q^{81} +(2.78749 + 1.01456i) q^{82} +(0.0487683 + 0.0844691i) q^{83} +(1.32526 - 2.29542i) q^{84} +(4.48280 - 3.76152i) q^{86} +(4.11707 - 7.13097i) q^{87} +(-0.158441 - 0.274427i) q^{88} +(-6.00343 - 2.18507i) q^{89} +(-0.0261762 - 0.148452i) q^{91} +(-0.490074 + 0.178372i) q^{92} +(-5.49067 - 4.60722i) q^{93} -8.70082 q^{94} +1.20683 q^{96} +(5.64307 + 4.73510i) q^{97} +(-2.04516 + 0.744377i) q^{98} +(0.0849358 + 0.481695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9	\( 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9} - 6 q^{11} + 18 q^{13} - 6 q^{14} - 12 q^{17} - 24 q^{18} + 6 q^{19} - 36 q^{21} + 9 q^{22} - 3 q^{23} + 3 q^{24} - 3 q^{26} - 15 q^{27} - 3 q^{28} + 36 q^{29} - 24 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{36} - 24 q^{37} - 15 q^{38} - 12 q^{39} - 12 q^{41} - 18 q^{42} + 12 q^{43} - 9 q^{44} - 18 q^{46} + 6 q^{48} - 27 q^{51} - 18 q^{52} + 36 q^{53} + 9 q^{54} + 12 q^{56} + 42 q^{57} - 27 q^{59} + 54 q^{61} + 24 q^{62} + 3 q^{63} - 6 q^{64} - 39 q^{66} - 39 q^{67} + 15 q^{68} - 24 q^{69} + 24 q^{71} + 18 q^{72} + 15 q^{74} + 9 q^{76} - 78 q^{77} + 6 q^{78} - 36 q^{79} - 9 q^{81} + 12 q^{82} + 12 q^{84} + 24 q^{86} - 18 q^{87} + 6 q^{88} + 18 q^{89} + 12 q^{91} - 12 q^{92} - 54 q^{93} + 18 q^{94} + 27 q^{97} + 18 q^{98} + 18 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9 - 6 * q^11 + 18 * q^13 - 6 * q^14 - 12 * q^17 - 24 * q^18 + 6 * q^19 - 36 * q^21 + 9 * q^22 - 3 * q^23 + 3 * q^24 - 3 * q^26 - 15 * q^27 - 3 * q^28 + 36 * q^29 - 24 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^36 - 24 * q^37 - 15 * q^38 - 12 * q^39 - 12 * q^41 - 18 * q^42 + 12 * q^43 - 9 * q^44 - 18 * q^46 + 6 * q^48 - 27 * q^51 - 18 * q^52 + 36 * q^53 + 9 * q^54 + 12 * q^56 + 42 * q^57 - 27 * q^59 + 54 * q^61 + 24 * q^62 + 3 * q^63 - 6 * q^64 - 39 * q^66 - 39 * q^67 + 15 * q^68 - 24 * q^69 + 24 * q^71 + 18 * q^72 + 15 * q^74 + 9 * q^76 - 78 * q^77 + 6 * q^78 - 36 * q^79 - 9 * q^81 + 12 * q^82 + 12 * q^84 + 24 * q^86 - 18 * q^87 + 6 * q^88 + 18 * q^89 + 12 * q^91 - 12 * q^92 - 54 * q^93 + 18 * q^94 + 27 * q^97 + 18 * q^98 + 18 * q^99

Introduction

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