LMFDB - Embedded newform 950.2.l.a.651.1

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:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			651.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	950.651
Dual form			950.2.l.a.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(-0.0603074 + 0.342020i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.0603074 - 0.342020i) q^{6} +(-0.766044 - 1.32683i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.70574 + 0.984808i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.0603074 + 0.342020i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.0603074 - 0.342020i) q^{6} +(-0.766044 - 1.32683i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.70574 + 0.984808i) q^{9} +(-1.55303 + 2.68993i) q^{11} +(0.173648 + 0.300767i) q^{12} +(-0.794263 - 4.50449i) q^{13} +(1.17365 + 0.984808i) q^{14} +(0.173648 - 0.984808i) q^{16} +(1.99273 - 0.725293i) q^{17} -2.87939 q^{18} +(4.34002 + 0.405223i) q^{19} +(0.500000 - 0.181985i) q^{21} +(0.539363 - 3.05888i) q^{22} +(-2.25490 + 1.89209i) q^{23} +(-0.266044 - 0.223238i) q^{24} +(2.28699 + 3.96118i) q^{26} +(-1.02094 + 1.76833i) q^{27} +(-1.43969 - 0.524005i) q^{28} +(6.12449 + 2.22913i) q^{29} +(-3.29813 - 5.71253i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-0.826352 - 0.693392i) q^{33} +(-1.62449 + 1.36310i) q^{34} +(2.70574 - 0.984808i) q^{36} +9.45336 q^{37} +(-4.21688 + 1.10359i) q^{38} +1.58853 q^{39} +(0.773318 - 4.38571i) q^{41} +(-0.407604 + 0.342020i) q^{42} +(2.20574 + 1.85083i) q^{43} +(0.539363 + 3.05888i) q^{44} +(1.47178 - 2.54920i) q^{46} +(-3.25877 - 1.18610i) q^{47} +(0.326352 + 0.118782i) q^{48} +(2.32635 - 4.02936i) q^{49} +(0.127889 + 0.725293i) q^{51} +(-3.50387 - 2.94010i) q^{52} +(0.124485 - 0.104455i) q^{53} +(0.354570 - 2.01087i) q^{54} +1.53209 q^{56} +(-0.400330 + 1.45994i) q^{57} -6.51754 q^{58} +(13.3157 - 4.84651i) q^{59} +(-6.14543 + 5.15663i) q^{61} +(5.05303 + 4.24000i) q^{62} +(-0.766044 - 4.34445i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.01367 + 0.368946i) q^{66} +(8.07785 + 2.94010i) q^{67} +(1.06031 - 1.83651i) q^{68} +(-0.511144 - 0.885328i) q^{69} +(7.37211 + 6.18594i) q^{71} +(-2.20574 + 1.85083i) q^{72} +(0.538019 - 3.05126i) q^{73} +(-8.88326 + 3.23324i) q^{74} +(3.58512 - 2.47929i) q^{76} +4.75877 q^{77} +(-1.49273 + 0.543308i) q^{78} +(-0.173648 + 0.984808i) q^{79} +(6.07398 + 5.09667i) q^{81} +(0.773318 + 4.38571i) q^{82} +(2.66637 + 4.61830i) q^{83} +(0.266044 - 0.460802i) q^{84} +(-2.70574 - 0.984808i) q^{86} +(-1.13176 + 1.96026i) q^{87} +(-1.55303 - 2.68993i) q^{88} +(1.21941 + 6.91560i) q^{89} +(-5.36824 + 4.50449i) q^{91} +(-0.511144 + 2.89884i) q^{92} +(2.15270 - 0.783520i) q^{93} +3.46791 q^{94} -0.347296 q^{96} +(5.77972 - 2.10364i) q^{97} +(-0.807934 + 4.58202i) q^{98} +(-6.85117 + 5.74881i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{3} - 6 q^{6} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^3 - 6 * q^6 - 3 * q^8 + 6 * q^9	$ 6 q - 6 q^{3} - 6 q^{6} - 3 q^{8} + 6 q^{9} + 3 q^{11} - 15 q^{13} + 6 q^{14} - 6 q^{17} - 6 q^{18} + 6 q^{19} + 3 q^{21} + 12 q^{22} - 15 q^{23} + 3 q^{24} + 6 q^{26} - 3 q^{27} - 3 q^{28} + 24 q^{29} - 6 q^{31} - 6 q^{33} + 3 q^{34} + 6 q^{36} + 30 q^{37} - 9 q^{38} + 30 q^{39} + 18 q^{41} - 6 q^{42} + 3 q^{43} + 12 q^{44} - 6 q^{46} + 3 q^{47} + 3 q^{48} + 15 q^{49} + 30 q^{51} + 3 q^{52} - 12 q^{53} + 18 q^{54} + 12 q^{57} + 6 q^{58} + 21 q^{59} - 21 q^{61} + 18 q^{62} - 3 q^{64} - 15 q^{66} + 9 q^{67} + 12 q^{68} + 3 q^{69} + 15 q^{71} - 3 q^{72} + 21 q^{73} - 18 q^{74} + 6 q^{77} + 9 q^{78} + 21 q^{81} + 18 q^{82} - 3 q^{83} - 3 q^{84} - 6 q^{86} - 12 q^{87} + 3 q^{88} - 24 q^{89} - 27 q^{91} + 3 q^{92} + 15 q^{93} + 30 q^{94} + 9 q^{97} + 6 q^{98} - 15 q^{99}+O(q^{100}) $ 6 * q - 6 * q^3 - 6 * q^6 - 3 * q^8 + 6 * q^9 + 3 * q^11 - 15 * q^13 + 6 * q^14 - 6 * q^17 - 6 * q^18 + 6 * q^19 + 3 * q^21 + 12 * q^22 - 15 * q^23 + 3 * q^24 + 6 * q^26 - 3 * q^27 - 3 * q^28 + 24 * q^29 - 6 * q^31 - 6 * q^33 + 3 * q^34 + 6 * q^36 + 30 * q^37 - 9 * q^38 + 30 * q^39 + 18 * q^41 - 6 * q^42 + 3 * q^43 + 12 * q^44 - 6 * q^46 + 3 * q^47 + 3 * q^48 + 15 * q^49 + 30 * q^51 + 3 * q^52 - 12 * q^53 + 18 * q^54 + 12 * q^57 + 6 * q^58 + 21 * q^59 - 21 * q^61 + 18 * q^62 - 3 * q^64 - 15 * q^66 + 9 * q^67 + 12 * q^68 + 3 * q^69 + 15 * q^71 - 3 * q^72 + 21 * q^73 - 18 * q^74 + 6 * q^77 + 9 * q^78 + 21 * q^81 + 18 * q^82 - 3 * q^83 - 3 * q^84 - 6 * q^86 - 12 * q^87 + 3 * q^88 - 24 * q^89 - 27 * q^91 + 3 * q^92 + 15 * q^93 + 30 * q^94 + 9 * q^97 + 6 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	−0.0603074	+	0.342020i	−0.0348185	+	0.197465i	−0.997255	−	0.0740406i	$-0.976411\pi$
$3$	−0.0603074	+	0.342020i	−0.0348185	+	0.197465i	0.962437	+	0.271506i	$0.0875217\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$		0			0
$5$		0			0
$6$	−0.0603074	−	0.342020i	−0.0246204	−	0.139629i
$7$	−0.766044	−	1.32683i	−0.289538	−	0.501494i	0.684162	−	0.729330i	$-0.260168\pi$
$7$	−0.766044	−	1.32683i	−0.289538	−	0.501494i	−0.973699	+	0.227836i	$0.926835\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	2.70574	+	0.984808i	0.901912	+	0.328269i
$10$		0			0
$11$	−1.55303	+	2.68993i	−0.468257	+	0.811045i	−0.999342	−	0.0362735i	$-0.988451\pi$
$11$	−1.55303	+	2.68993i	−0.468257	+	0.811045i	0.531085	+	0.847319i	$0.321785\pi$
$12$	0.173648	+	0.300767i	0.0501279	+	0.0868241i
$13$	−0.794263	−	4.50449i	−0.220289	−	1.24932i	−0.871489	−	0.490415i	$-0.836845\pi$
$13$	−0.794263	−	4.50449i	−0.220289	−	1.24932i	0.651200	−	0.758906i	$-0.274266\pi$
$14$	1.17365	+	0.984808i	0.313671	+	0.263201i
$15$		0			0
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	1.99273	−	0.725293i	0.483307	−	0.175909i	−0.0888639	−	0.996044i	$-0.528324\pi$
$17$	1.99273	−	0.725293i	0.483307	−	0.175909i	0.572171	+	0.820134i	$0.306101\pi$
$18$	−2.87939			−0.678678
$19$	4.34002	+	0.405223i	0.995669	+	0.0929645i
$19$	4.34002	+	0.405223i	0.995669	+	0.0929645i
$20$		0			0
$21$	0.500000	−	0.181985i	0.109109	−	0.0397124i
$22$	0.539363	−	3.05888i	0.114993	−	0.652155i
$23$	−2.25490	+	1.89209i	−0.470179	+	0.394527i	−0.846860	−	0.531816i	$-0.821510\pi$
$23$	−2.25490	+	1.89209i	−0.470179	+	0.394527i	0.376681	+	0.926343i	$0.377065\pi$
$24$	−0.266044	−	0.223238i	−0.0543061	−	0.0455682i
$25$		0			0
$26$	2.28699	+	3.96118i	0.448515	+	0.776852i
$27$	−1.02094	+	1.76833i	−0.196481	+	0.340315i
$28$	−1.43969	−	0.524005i	−0.272076	−	0.0990277i
$29$	6.12449	+	2.22913i	1.13729	+	0.413939i	0.840933	−	0.541139i	$-0.182007\pi$
$29$	6.12449	+	2.22913i	1.13729	+	0.413939i	0.296355	+	0.955078i	$0.404229\pi$
$30$		0			0
$31$	−3.29813	−	5.71253i	−0.592362	−	1.02600i	−0.993913	−	0.110165i	$-0.964862\pi$
$31$	−3.29813	−	5.71253i	−0.592362	−	1.02600i	0.401551	−	0.915837i	$-0.368471\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−0.826352	−	0.693392i	−0.143849	−	0.120704i
$34$	−1.62449	+	1.36310i	−0.278597	+	0.233771i
$35$		0			0
$36$	2.70574	−	0.984808i	0.450956	−	0.164135i
$37$	9.45336			1.55412			0.777062	−	0.629424i	$-0.216709\pi$
$37$	9.45336			1.55412			0.777062	+	0.629424i	$0.216709\pi$
$38$	−4.21688	+	1.10359i	−0.684068	+	0.179026i
$39$	1.58853			0.254368
$40$		0			0
$41$	0.773318	−	4.38571i	0.120772	−	0.684932i	−0.862957	−	0.505277i	$-0.831390\pi$
$41$	0.773318	−	4.38571i	0.120772	−	0.684932i	0.983730	−	0.179656i	$-0.0574984\pi$
$42$	−0.407604	+	0.342020i	−0.0628946	+	0.0527749i
$43$	2.20574	+	1.85083i	0.336372	+	0.282249i	0.795290	−	0.606229i	$-0.207319\pi$
$43$	2.20574	+	1.85083i	0.336372	+	0.282249i	−0.458918	+	0.888478i	$0.651763\pi$
$44$	0.539363	+	3.05888i	0.0813120	+	0.461143i
$45$		0			0
$46$	1.47178	−	2.54920i	0.217002	−	0.375859i
$47$	−3.25877	−	1.18610i	−0.475341	−	0.173010i	0.0932295	−	0.995645i	$-0.470281\pi$
$47$	−3.25877	−	1.18610i	−0.475341	−	0.173010i	−0.568570	+	0.822635i	$0.692503\pi$
$48$	0.326352	+	0.118782i	0.0471048	+	0.0171448i
$49$	2.32635	−	4.02936i	0.332336	−	0.575623i
$50$		0			0
$51$	0.127889	+	0.725293i	0.0179080	+	0.101561i
$52$	−3.50387	−	2.94010i	−0.485899	−	0.407718i
$53$	0.124485	−	0.104455i	0.0170994	−	0.0143481i	−0.634198	−	0.773171i	$-0.718670\pi$
$53$	0.124485	−	0.104455i	0.0170994	−	0.0143481i	0.651297	+	0.758823i	$0.274225\pi$
$54$	0.354570	−	2.01087i	0.0482509	−	0.273644i
$55$		0			0
$56$	1.53209			0.204734
$57$	−0.400330	+	1.45994i	−0.0530250	+	0.193373i
$58$	−6.51754			−0.855795
$59$	13.3157	−	4.84651i	1.73355	−	0.630962i	0.734680	−	0.678414i	$-0.237332\pi$
$59$	13.3157	−	4.84651i	1.73355	−	0.630962i	0.998873	+	0.0474525i	$0.0151103\pi$
$60$		0			0
$61$	−6.14543	+	5.15663i	−0.786842	+	0.660239i	−0.944962	−	0.327181i	$-0.893901\pi$
$61$	−6.14543	+	5.15663i	−0.786842	+	0.660239i	0.158120	+	0.987420i	$0.449457\pi$
$62$	5.05303	+	4.24000i	0.641736	+	0.538480i
$63$	−0.766044	−	4.34445i	−0.0965125	−	0.547350i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	1.01367	+	0.368946i	0.124774	+	0.0454141i
$67$	8.07785	+	2.94010i	0.986866	+	0.359190i	0.784506	−	0.620121i	$-0.212917\pi$
$67$	8.07785	+	2.94010i	0.986866	+	0.359190i	0.202360	+	0.979311i	$0.435139\pi$
$68$	1.06031	−	1.83651i	0.128581	−	0.222709i
$69$	−0.511144	−	0.885328i	−0.0615345	−	0.106581i
$70$		0			0
$71$	7.37211	+	6.18594i	0.874909	+	0.734136i	0.965126	−	0.261787i	$-0.0843117\pi$
$71$	7.37211	+	6.18594i	0.874909	+	0.734136i	−0.0902171	+	0.995922i	$0.528756\pi$
$72$	−2.20574	+	1.85083i	−0.259949	+	0.218123i
$73$	0.538019	−	3.05126i	0.0629703	−	0.357122i	−0.936999	−	0.349331i	$-0.886409\pi$
$73$	0.538019	−	3.05126i	0.0629703	−	0.357122i	0.999970	−	0.00779128i	$-0.00248007\pi$
$74$	−8.88326	+	3.23324i	−1.03266	+	0.375857i
$75$		0			0
$76$	3.58512	−	2.47929i	0.411242	−	0.284395i
$77$	4.75877			0.542312
$78$	−1.49273	+	0.543308i	−0.169018	+	0.0615175i
$79$	−0.173648	+	0.984808i	−0.0195369	+	0.110800i	−0.993017	−	0.117973i	$-0.962360\pi$
$79$	−0.173648	+	0.984808i	−0.0195369	+	0.110800i	0.973480	+	0.228773i	$0.0734713\pi$
$80$		0			0
$81$	6.07398	+	5.09667i	0.674886	+	0.566297i
$82$	0.773318	+	4.38571i	0.0853987	+	0.484320i
$83$	2.66637	+	4.61830i	0.292673	+	0.506924i	0.974441	−	0.224644i	$-0.0721221\pi$
$83$	2.66637	+	4.61830i	0.292673	+	0.506924i	−0.681768	+	0.731568i	$0.738789\pi$
$84$	0.266044	−	0.460802i	0.0290278	−	0.0502777i
$85$		0			0
$86$	−2.70574	−	0.984808i	−0.291767	−	0.106195i
$87$	−1.13176	+	1.96026i	−0.121337	+	0.210162i
$88$	−1.55303	−	2.68993i	−0.165554	−	0.286748i
$89$	1.21941	+	6.91560i	0.129257	+	0.733053i	0.978688	+	0.205353i	$0.0658342\pi$
$89$	1.21941	+	6.91560i	0.129257	+	0.733053i	−0.849431	+	0.527700i	$0.823055\pi$
$90$		0			0
$91$	−5.36824	+	4.50449i	−0.562745	+	0.472199i
$92$	−0.511144	+	2.89884i	−0.0532905	+	0.302225i
$93$	2.15270	−	0.783520i	0.223225	−	0.0812472i
$94$	3.46791			0.357688
$95$		0			0
$96$	−0.347296			−0.0354458
$97$	5.77972	−	2.10364i	0.586841	−	0.213593i	−0.0314984	−	0.999504i	$-0.510028\pi$
$97$	5.77972	−	2.10364i	0.586841	−	0.213593i	0.618340	+	0.785911i	$0.287806\pi$
$98$	−0.807934	+	4.58202i	−0.0816136	+	0.462854i
$99$	−6.85117	+	5.74881i	−0.688568	+	0.577777i
$100$		0			0
$101$	−2.36959	−	13.4386i	−0.235783	−	1.33719i	−0.840959	−	0.541098i	$-0.818009\pi$
$101$	−2.36959	−	13.4386i	−0.235783	−	1.33719i	0.605177	−	0.796091i	$-0.293102\pi$
$102$	−0.368241	−	0.637812i	−0.0364613	−	0.0631528i
$103$	−3.46064	+	5.99400i	−0.340987	+	0.590606i	−0.984616	−	0.174731i	$-0.944094\pi$
$103$	−3.46064	+	5.99400i	−0.340987	+	0.590606i	0.643630	+	0.765337i	$0.277428\pi$
$104$	4.29813	+	1.56439i	0.421467	+	0.153401i
$105$		0			0
$106$	−0.0812519	+	0.140732i	−0.00789188	+	0.0136691i
$107$	1.13176	+	1.96026i	0.109411	+	0.189506i	0.915532	−	0.402245i	$-0.131770\pi$
$107$	1.13176	+	1.96026i	0.109411	+	0.189506i	−0.806121	+	0.591751i	$0.798437\pi$
$108$	0.354570	+	2.01087i	0.0341185	+	0.193496i
$109$	−8.08512	−	6.78422i	−0.774414	−	0.649811i	0.167421	−	0.985885i	$-0.446456\pi$
$109$	−8.08512	−	6.78422i	−0.774414	−	0.649811i	−0.941835	+	0.336075i	$0.890901\pi$
$110$		0			0
$111$	−0.570108	+	3.23324i	−0.0541122	+	0.306886i
$112$	−1.43969	+	0.524005i	−0.136038	+	0.0495138i
$113$	19.6955			1.85280			0.926400	−	0.376542i	$-0.122887\pi$
$113$	19.6955			1.85280			0.926400	+	0.376542i	$0.122887\pi$
$114$	−0.123141	−	1.50881i	−0.0115332	−	0.141313i
$115$		0			0
$116$	6.12449	−	2.22913i	0.568644	−	0.206970i
$117$	2.28699	−	12.9702i	0.211432	−	1.19909i
$118$	−10.8550	+	9.10846i	−0.999287	+	0.838501i
$119$	−2.48886	−	2.08840i	−0.228153	−	0.191443i
$120$		0			0
$121$	0.676174	+	1.17117i	0.0614704	+	0.106470i
$122$	4.01114	−	6.94751i	0.363152	−	0.628998i
$123$	1.45336	+	0.528981i	0.131045	+	0.0476966i
$124$	−6.19846	−	2.25606i	−0.556638	−	0.202600i
$125$		0			0
$126$	2.20574	+	3.82045i	0.196503	+	0.340353i
$127$	1.61216	+	9.14301i	0.143056	+	0.811311i	0.968908	+	0.247423i	$0.0795838\pi$
$127$	1.61216	+	9.14301i	0.143056	+	0.811311i	−0.825852	+	0.563888i	$0.809305\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	−0.766044	+	0.642788i	−0.0674465	+	0.0565943i
$130$		0			0
$131$	−2.64796	+	0.963777i	−0.231353	+	0.0842056i	−0.455095	−	0.890443i	$-0.650395\pi$
$131$	−2.64796	+	0.963777i	−0.231353	+	0.0842056i	0.223742	+	0.974648i	$0.428173\pi$
$132$	−1.07873			−0.0938910
$133$	−2.78699	−	6.06888i	−0.241663	−	0.526239i
$134$	−8.59627			−0.742604
$135$		0			0
$136$	−0.368241	+	2.08840i	−0.0315764	+	0.179079i
$137$	−0.511144	+	0.428901i	−0.0436700	+	0.0366435i	−0.664361	−	0.747411i	$-0.731296\pi$
$137$	−0.511144	+	0.428901i	−0.0436700	+	0.0366435i	0.620691	+	0.784055i	$0.286852\pi$
$138$	0.783119	+	0.657115i	0.0666635	+	0.0559373i
$139$	−1.81134	−	10.2726i	−0.153636	−	0.871311i	−0.960023	−	0.279923i	$-0.909691\pi$
$139$	−1.81134	−	10.2726i	−0.153636	−	0.871311i	0.806387	−	0.591388i	$-0.201420\pi$
$140$		0			0
$141$	0.602196	−	1.04303i	0.0507141	−	0.0878394i
$142$	−9.04323	−	3.29147i	−0.758891	−	0.276214i
$143$	13.3503	+	4.85911i	1.11641	+	0.406339i
$144$	1.43969	−	2.49362i	0.119974	−	0.207802i
$145$		0			0
$146$	0.538019	+	3.05126i	0.0445267	+	0.252524i
$147$	1.23783	+	1.03866i	0.102094	+	0.0856672i
$148$	7.24170	−	6.07650i	0.595264	−	0.499486i
$149$	−1.26945	+	7.19940i	−0.103997	+	0.589798i	0.887619	+	0.460579i	$0.152358\pi$
$149$	−1.26945	+	7.19940i	−0.103997	+	0.589798i	−0.991616	+	0.129219i	$0.958753\pi$
$150$		0			0
$151$	1.00774			0.0820088			0.0410044	−	0.999159i	$-0.486944\pi$
$151$	1.00774			0.0820088			0.0410044	+	0.999159i	$0.486944\pi$
$152$	−2.52094	+	3.55596i	−0.204476	+	0.288426i
$153$	6.10607			0.493646
$154$	−4.47178	+	1.62760i	−0.360346	+	0.131155i
$155$		0			0
$156$	1.21688	−	1.02108i	0.0974285	−	0.0817522i
$157$	−15.0326	−	12.6138i	−1.19973	−	1.00669i	−0.999638	−	0.0269144i	$-0.991432\pi$
$157$	−15.0326	−	12.6138i	−1.19973	−	1.00669i	−0.200091	−	0.979777i	$-0.564124\pi$
$158$	−0.173648	−	0.984808i	−0.0138147	−	0.0783471i
$159$	0.0282185	+	0.0488759i	0.00223787	+	0.00387611i
$160$		0			0
$161$	4.23783	+	1.54244i	0.333987	+	0.121561i
$162$	−7.45084	−	2.71188i	−0.585393	−	0.213066i
$163$	10.3414	−	17.9118i	0.809998	−	1.40296i	−0.102866	−	0.994695i	$-0.532801\pi$
$163$	10.3414	−	17.9118i	0.809998	−	1.40296i	0.912864	−	0.408263i	$-0.133865\pi$
$164$	−2.22668	−	3.85673i	−0.173875	−	0.301160i
$165$		0			0
$166$	−4.08512	−	3.42782i	−0.317067	−	0.266051i
$167$	−6.53074	+	5.47995i	−0.505364	+	0.424051i	−0.859494	−	0.511145i	$-0.829221\pi$
$167$	−6.53074	+	5.47995i	−0.505364	+	0.424051i	0.354130	+	0.935196i	$0.384777\pi$
$168$	−0.0923963	+	0.524005i	−0.00712853	+	0.0404279i
$169$	−7.44356	+	2.70924i	−0.572582	+	0.208403i
$170$		0			0
$171$	11.3439	+	5.37051i	0.867489	+	0.410693i
$172$	2.87939			0.219551
$173$	−4.31908	+	1.57202i	−0.328373	+	0.119518i	−0.500946	−	0.865479i	$-0.667014\pi$
$173$	−4.31908	+	1.57202i	−0.328373	+	0.119518i	0.172572	+	0.984997i	$0.444792\pi$
$174$	0.393056	−	2.22913i	0.0297975	−	0.168990i
$175$		0			0
$176$	2.37939	+	1.99654i	0.179353	+	0.150495i
$177$	0.854570	+	4.84651i	0.0642334	+	0.364286i
$178$	−3.51114	−	6.08148i	−0.263171	−	0.455826i
$179$	3.23055	−	5.59548i	0.241463	−	0.418226i	−0.719668	−	0.694318i	$-0.755706\pi$
$179$	3.23055	−	5.59548i	0.241463	−	0.418226i	0.961131	+	0.276092i	$0.0890395\pi$
$180$		0			0
$181$	−7.85756	−	2.85992i	−0.584048	−	0.212576i	0.0330615	−	0.999453i	$-0.489474\pi$
$181$	−7.85756	−	2.85992i	−0.584048	−	0.212576i	−0.617110	+	0.786877i	$0.711696\pi$
$182$	3.50387	−	6.06888i	0.259724	−	0.449855i
$183$	−1.39306	−	2.41284i	−0.102978	−	0.178363i
$184$	−0.511144	−	2.89884i	−0.0376821	−	0.213706i
$185$		0			0
$186$	−1.75490	+	1.47254i	−0.128676	+	0.107972i
$187$	−1.14378	+	6.48670i	−0.0836415	+	0.474355i
$188$	−3.25877	+	1.18610i	−0.237670	+	0.0865049i
$189$	3.12836			0.227554
$190$		0			0
$191$	−26.6486			−1.92822			−0.964112	−	0.265496i	$-0.914464\pi$
$191$	−26.6486			−1.92822			−0.964112	+	0.265496i	$0.914464\pi$
$192$	0.326352	−	0.118782i	0.0235524	−	0.00857238i
$193$	−4.14930	+	23.5319i	−0.298673	+	1.69386i	0.353213	+	0.935543i	$0.385089\pi$
$193$	−4.14930	+	23.5319i	−0.298673	+	1.69386i	−0.651886	+	0.758317i	$0.726022\pi$
$194$	−4.71167	+	3.95356i	−0.338278	+	0.283849i
$195$		0			0
$196$	−0.807934	−	4.58202i	−0.0577095	−	0.327287i
$197$	−6.09967	−	10.5649i	−0.434584	−	0.752721i	0.562678	−	0.826676i	$-0.309771\pi$
$197$	−6.09967	−	10.5649i	−0.434584	−	0.752721i	−0.997262	+	0.0739554i	$0.976438\pi$
$198$	4.47178	−	7.74535i	0.317796	−	0.550438i
$199$	−12.9089	−	4.69847i	−0.915091	−	0.333066i	−0.158807	−	0.987310i	$-0.550765\pi$
$199$	−12.9089	−	4.69847i	−0.915091	−	0.333066i	−0.756284	+	0.654244i	$0.772987\pi$
$200$		0			0
$201$	−1.49273	+	2.58548i	−0.105289	+	0.182366i
$202$	6.82295	+	11.8177i	0.480061	+	0.831490i
$203$	−1.73396	−	9.83375i	−0.121700	−	0.690194i
$204$	0.564178	+	0.473401i	0.0395003	+	0.0331447i
$205$		0			0
$206$	1.20187	−	6.81612i	0.0837380	−	0.474902i
$207$	−7.96451	+	2.89884i	−0.553572	+	0.201484i
$208$	−4.57398			−0.317148
$209$	−7.83022	+	11.0450i	−0.541628	+	0.764002i
$210$		0			0
$211$	−14.2442	+	5.18447i	−0.980613	+	0.356914i	−0.782078	−	0.623180i	$-0.785840\pi$
$211$	−14.2442	+	5.18447i	−0.980613	+	0.356914i	−0.198534	+	0.980094i	$0.563618\pi$
$212$	0.0282185	−	0.160035i	0.00193805	−	0.0109913i
$213$	−2.56031	+	2.14835i	−0.175429	+	0.147203i
$214$	−1.73396	−	1.45496i	−0.118531	−	0.0994591i
$215$		0			0
$216$	−1.02094	−	1.76833i	−0.0694665	−	0.120319i
$217$	−5.05303	+	8.75211i	−0.343022	+	0.594132i
$218$	9.91787	+	3.60981i	0.671723	+	0.244487i
$219$	1.01114	+	0.368026i	0.0683268	+	0.0248689i
$220$		0			0
$221$	−4.84982	−	8.40014i	−0.326234	−	0.565055i
$222$	−0.570108	−	3.23324i	−0.0382631	−	0.217001i
$223$	0.0452926	+	0.0380050i	0.00303302	+	0.00254501i	0.644303	−	0.764770i	$-0.277148\pi$
$223$	0.0452926	+	0.0380050i	0.00303302	+	0.00254501i	−0.641270	+	0.767315i	$0.721592\pi$
$224$	1.17365	−	0.984808i	0.0784177	−	0.0658002i
$225$		0			0
$226$	−18.5077	+	6.73627i	−1.23112	+	0.448090i
$227$	−29.5449			−1.96096			−0.980481	−	0.196612i	$-0.937006\pi$
$227$	−29.5449			−1.96096			−0.980481	+	0.196612i	$0.937006\pi$
$228$	0.631759	+	1.37570i	0.0418393	+	0.0911082i
$229$	−12.6578			−0.836448			−0.418224	−	0.908344i	$-0.637347\pi$
$229$	−12.6578			−0.836448			−0.418224	+	0.908344i	$0.637347\pi$
$230$		0			0
$231$	−0.286989	+	1.62760i	−0.0188825	+	0.107088i
$232$	−4.99273	+	4.18939i	−0.327789	+	0.275047i
$233$	3.90239	+	3.27449i	0.255654	+	0.214519i	0.761602	−	0.648045i	$-0.224413\pi$
$233$	3.90239	+	3.27449i	0.255654	+	0.214519i	−0.505948	+	0.862564i	$0.668857\pi$
$234$	2.28699	+	12.9702i	0.149505	+	0.847886i
$235$		0			0
$236$	7.08512	−	12.2718i	0.461202	−	0.798826i
$237$	−0.326352	−	0.118782i	−0.0211988	−	0.00771574i
$238$	3.05303	+	1.11121i	0.197899	+	0.0720293i
$239$	3.91740	−	6.78514i	0.253396	−	0.438894i	−0.711063	−	0.703129i	$-0.751786\pi$
$239$	3.91740	−	6.78514i	0.253396	−	0.438894i	0.964459	+	0.264234i	$0.0851192\pi$
$240$		0			0
$241$	−3.07280	−	17.4267i	−0.197936	−	1.12255i	−0.908175	−	0.418591i	$-0.862524\pi$
$241$	−3.07280	−	17.4267i	−0.197936	−	1.12255i	0.710239	−	0.703961i	$-0.248587\pi$
$242$	−1.03596	−	0.869273i	−0.0665940	−	0.0558790i
$243$	−6.80200	+	5.70756i	−0.436349	+	0.366140i
$244$	−1.39306	+	7.90041i	−0.0891813	+	0.505772i
$245$		0			0
$246$	−1.54664			−0.0986100
$247$	−1.62180	−	19.8714i	−0.103192	−	1.26439i
$248$	6.59627			0.418863
$249$	−1.74035	+	0.633436i	−0.110290	+	0.0401424i
$250$		0			0
$251$	−4.15136	+	3.48340i	−0.262031	+	0.219871i	−0.764333	−	0.644822i	$-0.776931\pi$
$251$	−4.15136	+	3.48340i	−0.262031	+	0.219871i	0.502301	+	0.864693i	$0.332487\pi$
$252$	−3.37939	−	2.83564i	−0.212881	−	0.178629i
$253$	−1.58765	−	9.00400i	−0.0998146	−	0.566077i
$254$	−4.64203	−	8.04023i	−0.291267	−	0.504489i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	6.48070	+	2.35878i	0.404255	+	0.147137i	0.536142	−	0.844128i	$-0.319881\pi$
$257$	6.48070	+	2.35878i	0.404255	+	0.147137i	−0.131887	+	0.991265i	$0.542103\pi$
$258$	0.500000	−	0.866025i	0.0311286	−	0.0539164i
$259$	−7.24170	−	12.5430i	−0.449977	−	0.779383i
$260$		0			0
$261$	14.3760	+	12.0629i	0.889851	+	0.746674i
$262$	2.15863	−	1.81131i	0.133361	−	0.111903i
$263$	−2.12361	+	12.0436i	−0.130947	+	0.742639i	0.846649	+	0.532151i	$0.178616\pi$
$263$	−2.12361	+	12.0436i	−0.130947	+	0.742639i	−0.977597	+	0.210488i	$0.932495\pi$
$264$	1.01367	−	0.368946i	0.0623871	−	0.0227071i
$265$		0			0
$266$	4.69459	+	4.74968i	0.287844	+	0.291221i
$267$	−2.43882			−0.149253
$268$	8.07785	−	2.94010i	0.493433	−	0.179595i
$269$	−1.94087	+	11.0072i	−0.118337	+	0.671124i	0.866706	+	0.498819i	$0.166233\pi$
$269$	−1.94087	+	11.0072i	−0.118337	+	0.671124i	−0.985044	+	0.172305i	$0.944879\pi$
$270$		0			0
$271$	−14.9795	−	12.5693i	−0.909941	−	0.763531i	0.0621666	−	0.998066i	$-0.480199\pi$
$271$	−14.9795	−	12.5693i	−0.909941	−	0.763531i	−0.972108	+	0.234534i	$0.924643\pi$
$272$	−0.368241	−	2.08840i	−0.0223279	−	0.126628i
$273$	−1.21688	−	2.10770i	−0.0736490	−	0.127564i
$274$	0.333626	−	0.577857i	0.0201551	−	0.0349096i
$275$		0			0
$276$	−0.960637	−	0.349643i	−0.0578236	−	0.0210461i
$277$	12.7057	−	22.0070i	0.763414	−	1.32227i	−0.177667	−	0.984091i	$-0.556855\pi$
$277$	12.7057	−	22.0070i	0.763414	−	1.32227i	0.941081	−	0.338181i	$-0.109812\pi$
$278$	5.21554	+	9.03358i	0.312807	+	0.541798i
$279$	−3.29813	−	18.7046i	−0.197454	−	1.11982i
$280$		0			0
$281$	14.6302	−	12.2762i	0.872763	−	0.732335i	−0.0919154	−	0.995767i	$-0.529299\pi$
$281$	14.6302	−	12.2762i	0.872763	−	0.732335i	0.964678	+	0.263432i	$0.0848545\pi$
$282$	−0.209141	+	1.18610i	−0.0124541	+	0.0706310i
$283$	−17.0471	+	6.20464i	−1.01335	+	0.368827i	−0.794717	−	0.606981i	$-0.792381\pi$
$283$	−17.0471	+	6.20464i	−1.01335	+	0.368827i	−0.218629	+	0.975808i	$0.570158\pi$
$284$	9.62361			0.571056
$285$		0			0
$286$	−14.2071			−0.840082
$287$	−6.41147	+	2.33359i	−0.378457	+	0.137747i
$288$	−0.500000	+	2.83564i	−0.0294628	+	0.167092i
$289$	−9.57785	+	8.03677i	−0.563403	+	0.472751i
$290$		0			0
$291$	0.370929	+	2.10364i	0.0217443	+	0.123318i
$292$	−1.54916	−	2.68323i	−0.0906579	−	0.157024i
$293$	14.4508	−	25.0296i	0.844227	−	1.46224i	−0.0420640	−	0.999115i	$-0.513393\pi$
$293$	14.4508	−	25.0296i	0.844227	−	1.46224i	0.886291	−	0.463129i	$-0.153273\pi$
$294$	−1.51842	−	0.552659i	−0.0885560	−	0.0322317i
$295$		0			0
$296$	−4.72668	+	8.18685i	−0.274733	+	0.475851i
$297$	−3.17112	−	5.49254i	−0.184007	−	0.318710i
$298$	−1.26945	−	7.19940i	−0.0735371	−	0.417050i
$299$	10.3139	+	8.65436i	0.596466	+	0.500494i
$300$		0			0
$301$	0.766044	−	4.34445i	0.0441541	−	0.250410i
$302$	−0.946967	+	0.344668i	−0.0544918	+	0.0198334i
$303$	4.73917			0.272258
$304$	1.15270	−	4.20372i	0.0661121	−	0.241100i
$305$		0			0
$306$	−5.73783	+	2.08840i	−0.328010	+	0.119386i
$307$	−3.61856	+	20.5218i	−0.206522	+	1.17124i	0.688505	+	0.725232i	$0.258267\pi$
$307$	−3.61856	+	20.5218i	−0.206522	+	1.17124i	−0.895027	+	0.446012i	$0.852844\pi$
$308$	3.64543	−	3.05888i	0.207718	−	0.174296i
$309$	−1.84137	−	1.54509i	−0.104752	−	0.0878971i
$310$		0			0
$311$	7.06670	+	12.2399i	0.400716	+	0.694061i	0.993812	−	0.111071i	$-0.0354281\pi$
$311$	7.06670	+	12.2399i	0.400716	+	0.694061i	−0.593096	+	0.805131i	$0.702095\pi$
$312$	−0.794263	+	1.37570i	−0.0449663	+	0.0778839i
$313$	−15.9500	−	5.80531i	−0.901545	−	0.328136i	−0.150673	−	0.988584i	$-0.548144\pi$
$313$	−15.9500	−	5.80531i	−0.901545	−	0.328136i	−0.750872	+	0.660448i	$0.770366\pi$
$314$	18.4402	+	6.71167i	1.04064	+	0.378761i
$315$		0			0
$316$	0.500000	+	0.866025i	0.0281272	+	0.0487177i
$317$	1.50521	+	8.53650i	0.0845413	+	0.479457i	0.997455	+	0.0713040i	$0.0227160\pi$
$317$	1.50521	+	8.53650i	0.0845413	+	0.479457i	−0.912913	+	0.408153i	$0.866173\pi$
$318$	−0.0432332	−	0.0362770i	−0.00242440	−	0.00203431i
$319$	−15.5077	+	13.0125i	−0.868267	+	0.728562i
$320$		0			0
$321$	−0.738703	+	0.268866i	−0.0412304	+	0.0150066i
$322$	−4.50980			−0.251321
$323$	8.94238	−	2.34029i	0.497567	−	0.130217i
$324$	7.92902			0.440501
$325$		0			0
$326$	−3.59152	+	20.3685i	−0.198916	+	1.12811i
$327$	2.80793	−	2.35614i	0.155279	−	0.130295i
$328$	3.41147	+	2.86257i	0.188367	+	0.158059i
$329$	0.922618	+	5.23243i	0.0508656	+	0.288473i
$330$		0			0
$331$	14.5412	−	25.1861i	0.799255	−	1.38435i	−0.120847	−	0.992671i	$-0.538561\pi$
$331$	14.5412	−	25.1861i	0.799255	−	1.38435i	0.920102	−	0.391679i	$-0.128106\pi$
$332$	5.01114	+	1.82391i	0.275022	+	0.100100i
$333$	25.5783	+	9.30975i	1.40168	+	0.510171i
$334$	4.26264	−	7.38311i	0.233241	−	0.403986i
$335$		0			0
$336$	−0.0923963	−	0.524005i	−0.00504063	−	0.0285868i
$337$	6.62907	+	5.56245i	0.361108	+	0.303006i	0.805232	−	0.592959i	$-0.202041\pi$
$337$	6.62907	+	5.56245i	0.361108	+	0.303006i	−0.444124	+	0.895965i	$0.646485\pi$
$338$	6.06805	−	5.09170i	0.330058	−	0.276952i
$339$	−1.18779	+	6.73627i	−0.0645117	+	0.365864i
$340$		0			0
$341$	20.4884			1.10951
$342$	−12.4966	−	1.16679i	−0.675739	−	0.0630929i
$343$	−17.8530			−0.963970
$344$	−2.70574	+	0.984808i	−0.145884	+	0.0530973i
$345$		0			0
$346$	3.52094	−	2.95442i	0.189287	−	0.158831i
$347$	−12.9572	−	10.8724i	−0.695581	−	0.583662i	0.224932	−	0.974375i	$-0.427784\pi$
$347$	−12.9572	−	10.8724i	−0.695581	−	0.583662i	−0.920513	+	0.390713i	$0.872229\pi$
$348$	0.393056	+	2.22913i	0.0210700	+	0.119494i
$349$	6.70574	+	11.6147i	0.358950	+	0.621719i	0.987786	−	0.155819i	$-0.0498016\pi$
$349$	6.70574	+	11.6147i	0.358950	+	0.621719i	−0.628836	+	0.777538i	$0.716468\pi$
$350$		0			0
$351$	8.77631	+	3.19432i	0.468445	+	0.170500i
$352$	−2.91875	−	1.06234i	−0.155570	−	0.0566228i
$353$	−14.3097	+	24.7852i	−0.761631	+	1.31918i	0.180379	+	0.983597i	$0.442268\pi$
$353$	−14.3097	+	24.7852i	−0.761631	+	1.31918i	−0.942010	+	0.335586i	$0.891066\pi$
$354$	−2.46064	−	4.26195i	−0.130781	−	0.226520i
$355$		0			0
$356$	5.37939	+	4.51384i	0.285107	+	0.239233i
$357$	0.864370	−	0.725293i	0.0457473	−	0.0383866i
$358$	−1.12196	+	6.36295i	−0.0592974	+	0.336292i
$359$	16.3503	−	5.95102i	0.862935	−	0.314083i	0.127633	−	0.991822i	$-0.459262\pi$
$359$	16.3503	−	5.95102i	0.862935	−	0.314083i	0.735303	+	0.677739i	$0.237040\pi$
$360$		0			0
$361$	18.6716	+	3.51735i	0.982715	+	0.185124i
$362$	8.36184			0.439489
$363$	−0.441341	+	0.160635i	−0.0231644	+	0.00843116i
$364$	−1.21688	+	6.90128i	−0.0637819	+	0.361725i
$365$		0			0
$366$	2.13429	+	1.79088i	0.111561	+	0.0936107i
$367$	5.27420	+	29.9115i	0.275311	+	1.56137i	0.737973	+	0.674830i	$0.235783\pi$
$367$	5.27420	+	29.9115i	0.275311	+	1.56137i	−0.462662	+	0.886535i	$0.653106\pi$
$368$	1.47178	+	2.54920i	0.0767219	+	0.132886i
$369$	6.41147	−	11.1050i	0.333768	−	0.578103i
$370$		0			0
$371$	−0.233956	−	0.0851529i	−0.0121464	−	0.00442092i
$372$	1.14543	−	1.98394i	0.0593878	−	0.102863i
$373$	−16.5239	−	28.6203i	−0.855577	−	1.48190i	−0.876109	−	0.482114i	$-0.839869\pi$
$373$	−16.5239	−	28.6203i	−0.855577	−	1.48190i	0.0205316	−	0.999789i	$-0.493464\pi$
$374$	−1.14378	−	6.48670i	−0.0591435	−	0.335419i
$375$		0			0
$376$	2.65657	−	2.22913i	0.137002	−	0.114959i
$377$	5.17664	−	29.3582i	0.266611	−	1.51202i
$378$	−2.93969	+	1.06996i	−0.151201	+	0.0550328i
$379$	18.2344			0.936639			0.468320	−	0.883559i	$-0.344860\pi$
$379$	18.2344			0.936639			0.468320	+	0.883559i	$0.344860\pi$
$380$		0			0
$381$	−3.22432			−0.165187
$382$	25.0415	−	9.11435i	1.28123	−	0.466331i
$383$	−5.77285	+	32.7395i	−0.294979	+	1.67291i	0.372309	+	0.928109i	$0.378566\pi$
$383$	−5.77285	+	32.7395i	−0.294979	+	1.67291i	−0.667288	+	0.744800i	$0.732545\pi$
$384$	−0.266044	+	0.223238i	−0.0135765	+	0.0113921i
$385$		0			0
$386$	−4.14930	−	23.5319i	−0.211194	−	1.19774i
$387$	4.14543	+	7.18009i	0.210724	+	0.364985i
$388$	3.07532	−	5.32661i	0.156126	−	0.270418i
$389$	−6.70486	−	2.44037i	−0.339950	−	0.123732i	0.166403	−	0.986058i	$-0.446785\pi$
$389$	−6.70486	−	2.44037i	−0.339950	−	0.123732i	−0.506353	+	0.862326i	$0.669007\pi$
$390$		0			0
$391$	−3.12108	+	5.40587i	−0.157840	+	0.273387i
$392$	2.32635	+	4.02936i	0.117499	+	0.203513i
$393$	−0.169940	−	0.963777i	−0.00857233	−	0.0486161i
$394$	9.34524	+	7.84158i	0.470806	+	0.395053i
$395$		0			0
$396$	−1.55303	+	8.80769i	−0.0780429	+	0.442603i
$397$	19.9522	−	7.26200i	1.00137	−	0.364469i	0.211258	−	0.977430i	$-0.432244\pi$
$397$	19.9522	−	7.26200i	1.00137	−	0.364469i	0.790113	+	0.612961i	$0.210022\pi$
$398$	13.7374			0.688594
$399$	2.24376	−	0.587208i	0.112328	−	0.0293972i
$400$		0			0
$401$	−30.7327	+	11.1858i	−1.53472	+	0.558591i	−0.964771	−	0.263092i	$-0.915258\pi$
$401$	−30.7327	+	11.1858i	−1.53472	+	0.558591i	−0.569945	+	0.821683i	$0.693036\pi$
$402$	0.518418	−	2.94010i	0.0258564	−	0.146639i
$403$	−23.1125	+	19.3937i	−1.15131	+	0.966067i
$404$	−10.4534	−	8.77141i	−0.520074	−	0.436394i
$405$		0			0
$406$	4.99273	+	8.64766i	0.247785	+	0.429176i
$407$	−14.6814	+	25.4289i	−0.727729	+	1.26046i
$408$	−0.692066	−	0.251892i	−0.0342624	−	0.0124705i
$409$	−10.7947	−	3.92896i	−0.533765	−	0.194275i	0.0610536	−	0.998134i	$-0.480554\pi$
$409$	−10.7947	−	3.92896i	−0.533765	−	0.194275i	−0.594819	+	0.803860i	$0.702776\pi$
$410$		0			0
$411$	−0.115867	−	0.200688i	−0.00571530	−	0.00989919i
$412$	1.20187	+	6.81612i	0.0592117	+	0.335806i
$413$	−16.6309	−	13.9550i	−0.818352	−	0.686679i
$414$	6.49273	−	5.44804i	0.319100	−	0.267757i
$415$		0			0
$416$	4.29813	−	1.56439i	0.210733	−	0.0767007i
$417$	3.62267			0.177403
$418$	3.58037	−	13.0570i	0.175122	−	0.638641i
$419$	−17.0401			−0.832465			−0.416233	−	0.909258i	$-0.636650\pi$
$419$	−17.0401			−0.832465			−0.416233	+	0.909258i	$0.636650\pi$
$420$		0			0
$421$	−2.92989	+	16.6162i	−0.142794	+	0.809826i	0.826318	+	0.563204i	$0.190432\pi$
$421$	−2.92989	+	16.6162i	−0.142794	+	0.809826i	−0.969112	+	0.246622i	$0.920679\pi$
$422$	11.6120	−	9.74362i	0.565263	−	0.474312i
$423$	−7.64930	−	6.41852i	−0.371922	−	0.312079i
$424$	0.0282185	+	0.160035i	0.00137041	+	0.00777199i
$425$		0			0
$426$	1.67112	−	2.89447i	0.0809661	−	0.140237i
$427$	11.5496	+	4.20372i	0.558926	+	0.203432i
$428$	2.12701	+	0.774169i	0.102813	+	0.0374209i
$429$	−2.46703	+	4.27303i	−0.119110	+	0.206304i
$430$		0			0
$431$	3.69547	+	20.9581i	0.178005	+	1.00951i	0.934618	+	0.355652i	$0.115741\pi$
$431$	3.69547	+	20.9581i	0.178005	+	1.00951i	−0.756614	+	0.653862i	$0.773148\pi$
$432$	1.56418	+	1.31250i	0.0752565	+	0.0631477i
$433$	11.9192	−	10.0014i	0.572801	−	0.480637i	−0.309773	−	0.950811i	$-0.600253\pi$
$433$	11.9192	−	10.0014i	0.572801	−	0.480637i	0.882574	+	0.470173i	$0.155809\pi$
$434$	1.75490	−	9.95253i	0.0842379	−	0.477737i
$435$		0			0
$436$	−10.5544			−0.505463
$437$	−10.5530	+	7.29796i	−0.504820	+	0.349109i
$438$	−1.07604			−0.0514151
$439$	7.84389	−	2.85494i	0.374369	−	0.136259i	−0.147982	−	0.988990i	$-0.547278\pi$
$439$	7.84389	−	2.85494i	0.374369	−	0.136259i	0.522350	+	0.852731i	$0.325055\pi$
$440$		0			0
$441$	10.2626	−	8.61138i	0.488697	−	0.410066i
$442$	7.43036	+	6.23481i	0.353426	+	0.296560i
$443$	3.78194	+	21.4484i	0.179685	+	1.01905i	0.932596	+	0.360923i	$0.117538\pi$
$443$	3.78194	+	21.4484i	0.179685	+	1.01905i	−0.752911	+	0.658123i	$0.771351\pi$
$444$	1.64156	+	2.84326i	0.0779050	+	0.134935i
$445$		0			0
$446$	−0.0555596	−	0.0202221i	−0.00263083	−	0.000957542i
$447$	−2.38578	−	0.868354i	−0.112844	−	0.0410717i
$448$	−0.766044	+	1.32683i	−0.0361922	+	0.0626867i
$449$	2.48886	+	4.31082i	0.117456	+	0.203440i	0.918759	−	0.394819i	$-0.129193\pi$
$449$	2.48886	+	4.31082i	0.117456	+	0.203440i	−0.801303	+	0.598259i	$0.795859\pi$
$450$		0			0
$451$	10.5963	+	8.89132i	0.498959	+	0.418676i
$452$	15.0876	−	12.6600i	0.709663	−	0.595478i
$453$	−0.0607742	+	0.344668i	−0.00285542	+	0.0161939i
$454$	27.7631	−	10.1049i	1.30299	−	0.474249i
$455$		0			0
$456$	−1.06418	−	1.07666i	−0.0498347	−	0.0504194i
$457$	38.4047			1.79649			0.898247	−	0.439490i	$-0.144841\pi$
$457$	38.4047			1.79649			0.898247	+	0.439490i	$0.144841\pi$
$458$	11.8944	−	4.32921i	0.555789	−	0.202291i
$459$	−0.751907	+	4.26428i	−0.0350960	+	0.199039i
$460$		0			0
$461$	30.5187	+	25.6082i	1.42140	+	1.19270i	0.950586	+	0.310462i	$0.100484\pi$
$461$	30.5187	+	25.6082i	1.42140	+	1.19270i	0.470813	+	0.882233i	$0.343961\pi$
$462$	−0.286989	−	1.62760i	−0.0133519	−	0.0757226i
$463$	−13.7135	−	23.7524i	−0.637319	−	1.10387i	−0.986019	−	0.166635i	$-0.946710\pi$
$463$	−13.7135	−	23.7524i	−0.637319	−	1.10387i	0.348699	−	0.937235i	$-0.386623\pi$
$464$	3.25877	−	5.64436i	0.151285	−	0.262033i
$465$		0			0
$466$	−4.78699	−	1.74232i	−0.221753	−	0.0807115i
$467$	0.393056	−	0.680793i	0.0181885	−	0.0315033i	−0.856788	−	0.515669i	$-0.827543\pi$
$467$	0.393056	−	0.680793i	0.0181885	−	0.0315033i	0.874976	+	0.484166i	$0.160877\pi$
$468$	−6.58512	−	11.4058i	−0.304397	−	0.527232i
$469$	−2.28699	−	12.9702i	−0.105603	−	0.598906i
$470$		0			0
$471$	5.22075	−	4.38073i	0.240560	−	0.201853i
$472$	−2.46064	+	13.9550i	−0.113260	+	0.642329i
$473$	−8.40420	+	3.05888i	−0.386426	+	0.140647i
$474$	0.347296			0.0159518
$475$		0			0
$476$	−3.24897			−0.148916
$477$	0.439693	−	0.160035i	0.0201321	−	0.00732750i
$478$	−1.36050	+	7.71578i	−0.0622278	+	0.352912i
$479$	5.37417	−	4.50946i	0.245552	−	0.206043i	−0.511702	−	0.859163i	$-0.670985\pi$
$479$	5.37417	−	4.50946i	0.245552	−	0.206043i	0.757254	+	0.653120i	$0.226540\pi$
$480$		0			0
$481$	−7.50846	−	42.5826i	−0.342356	−	1.94160i
$482$	8.84776	+	15.3248i	0.403005	+	0.698024i
$483$	−0.783119	+	1.35640i	−0.0356331	+	0.0617184i
$484$	1.27079	+	0.462531i	0.0577633	+	0.0210241i
$485$		0			0
$486$	4.43969	−	7.68977i	0.201389	−	0.348815i
$487$	11.4611	+	19.8512i	0.519352	+	0.899544i	0.999747	+	0.0224920i	$0.00716004\pi$
$487$	11.4611	+	19.8512i	0.519352	+	0.899544i	−0.480395	+	0.877052i	$0.659507\pi$
$488$	−1.39306	−	7.90041i	−0.0630607	−	0.357635i
$489$	5.50253	+	4.61717i	0.248833	+	0.208796i
$490$		0			0
$491$	2.21167	−	12.5430i	0.0998111	−	0.566057i	−0.893355	−	0.449351i	$-0.851655\pi$
$491$	2.21167	−	12.5430i	0.0998111	−	0.566057i	0.993166	−	0.116706i	$-0.0372336\pi$
$492$	1.45336	−	0.528981i	0.0655227	−	0.0238483i
$493$	13.8212			0.622475
$494$	8.32042	+	18.1184i	0.374353	+	0.815183i
$495$		0			0
$496$	−6.19846	+	2.25606i	−0.278319	+	0.101300i
$497$	2.56031	−	14.5202i	0.114845	−	0.651321i
$498$	1.41875	−	1.19047i	0.0635756	−	0.0533463i
$499$	24.4782	+	20.5396i	1.09579	+	0.919480i	0.997135	−	0.0756412i	$-0.0241004\pi$
$499$	24.4782	+	20.5396i	1.09579	+	0.919480i	0.0986586	+	0.995121i	$0.468545\pi$
$500$		0			0
$501$	−1.48040	−	2.56413i	−0.0661394	−	0.114557i
$502$	2.70961	−	4.69318i	0.120936	−	0.209467i
$503$	−12.4765	−	4.54109i	−0.556301	−	0.202477i	0.0485429	−	0.998821i	$-0.484542\pi$
$503$	−12.4765	−	4.54109i	−0.556301	−	0.202477i	−0.604844	+	0.796344i	$0.706764\pi$
$504$	4.14543	+	1.50881i	0.184652	+	0.0672079i
$505$		0			0
$506$	4.57145	+	7.91799i	0.203226	+	0.351997i
$507$	−0.477711	−	2.70924i	−0.0212159	−	0.120321i
$508$	7.11200	+	5.96767i	0.315544	+	0.264773i
$509$	26.0522	−	21.8604i	1.15474	−	0.968943i	0.154922	−	0.987927i	$-0.450487\pi$
$509$	26.0522	−	21.8604i	1.15474	−	0.968943i	0.999820	+	0.0189836i	$0.00604302\pi$
$510$		0			0
$511$	−4.46064	+	1.62354i	−0.197327	+	0.0718211i
$512$	1.00000			0.0441942
$513$	−5.14749	+	7.26087i	−0.227267	+	0.320575i
$514$	−6.89662			−0.304197
$515$		0			0
$516$	−0.173648	+	0.984808i	−0.00764443	+	0.0433537i
$517$	8.25150	−	6.92383i	0.362900	−	0.304510i
$518$	11.0949	+	9.30975i	0.487483	+	0.409047i
$519$	−0.277189	−	1.57202i	−0.0121672	−	0.0690038i
$520$		0			0
$521$	6.03802	−	10.4582i	0.264530	−	0.458180i	−0.702910	−	0.711279i	$-0.748116\pi$
$521$	6.03802	−	10.4582i	0.264530	−	0.458180i	0.967440	+	0.253099i	$0.0814497\pi$
$522$	−17.6348	−	6.41852i	−0.771852	−	0.280931i
$523$	−13.3960	−	4.87576i	−0.585768	−	0.213202i	0.0320989	−	0.999485i	$-0.489781\pi$
$523$	−13.3960	−	4.87576i	−0.585768	−	0.213202i	−0.617867	+	0.786282i	$0.712003\pi$
$524$	−1.40895	+	2.44037i	−0.0615502	+	0.106608i
$525$		0			0
$526$	−2.12361	−	12.0436i	−0.0925937	−	0.525125i
$527$	−10.7155	−	8.99140i	−0.466776	−	0.391672i
$528$	−0.826352	+	0.693392i	−0.0359623	+	0.0301760i
$529$	−2.48932	+	14.1176i	−0.108231	+	0.613811i
$530$		0			0
$531$	40.8016			1.77064
$532$	−6.03596	−	2.85759i	−0.261692	−	0.123892i
$533$	−20.3696			−0.882305
$534$	2.29174	−	0.834124i	0.0991731	−	0.0360961i
$535$		0			0
$536$	−6.58512	+	5.52557i	−0.284434	+	0.238668i
$537$	1.71894	+	1.44236i	0.0741778	+	0.0622425i
$538$	−1.94087	−	11.0072i	−0.0836770	−	0.474556i
$539$	7.22580	+	12.5155i	0.311237	+	0.539079i
$540$		0			0
$541$	29.9948	+	10.9172i	1.28958	+	0.469368i	0.893589	−	0.448886i	$-0.148179\pi$
$541$	29.9948	+	10.9172i	1.28958	+	0.469368i	0.395990	+	0.918255i	$0.370401\pi$
$542$	18.3751	+	6.68799i	0.789278	+	0.287274i
$543$	1.45202	−	2.51497i	0.0623121	−	0.107928i
$544$	1.06031	+	1.83651i	0.0454603	+	0.0787396i
$545$		0			0
$546$	1.86437	+	1.56439i	0.0797877	+	0.0669498i
$547$	−0.913534	+	0.766546i	−0.0390599	+	0.0327751i	−0.662109	−	0.749408i	$-0.730338\pi$
$547$	−0.913534	+	0.766546i	−0.0390599	+	0.0327751i	0.623049	+	0.782183i	$0.285894\pi$
$548$	−0.115867	+	0.657115i	−0.00494959	+	0.0280705i
$549$	−21.7062	+	7.90041i	−0.926398	+	0.337181i
$550$		0			0
$551$	25.6771	+	12.1563i	1.09388	+	0.517874i
$552$	1.02229			0.0435115
$553$	1.43969	−	0.524005i	0.0612220	−	0.0222830i
$554$	−4.41266	+	25.0254i	−0.187476	+	1.06323i
$555$		0			0
$556$	−7.99067	−	6.70497i	−0.338880	−	0.284354i
$557$	6.37922	+	36.1784i	0.270296	+	1.53293i	0.753517	+	0.657428i	$0.228356\pi$
$557$	6.37922	+	36.1784i	0.270296	+	1.53293i	−0.483221	+	0.875499i	$0.660533\pi$
$558$	9.49660	+	16.4486i	0.402023	+	0.696324i
$559$	6.58512	−	11.4058i	0.278521	−	0.482413i
$560$		0			0
$561$	−2.14960	−	0.782392i	−0.0907564	−	0.0330326i
$562$	−9.54916	+	16.5396i	−0.402807	+	0.697682i
$563$	−18.5239	−	32.0844i	−0.780691	−	1.35220i	−0.931540	−	0.363639i	$-0.881534\pi$
$563$	−18.5239	−	32.0844i	−0.780691	−	1.35220i	0.150849	−	0.988557i	$-0.451799\pi$
$564$	−0.209141	−	1.18610i	−0.00880641	−	0.0499436i
$565$		0			0
$566$	13.8969	−	11.6609i	0.584131	−	0.490144i
$567$	2.10947	−	11.9634i	0.0885894	−	0.502416i
$568$	−9.04323	+	3.29147i	−0.379446	+	0.138107i
$569$	−6.61081			−0.277140			−0.138570	−	0.990353i	$-0.544251\pi$
$569$	−6.61081			−0.277140			−0.138570	+	0.990353i	$0.544251\pi$
$570$		0			0
$571$	−44.6263			−1.86755			−0.933776	−	0.357858i	$-0.883507\pi$
$571$	−44.6263			−1.86755			−0.933776	+	0.357858i	$0.883507\pi$
$572$	13.3503	−	4.85911i	0.558204	−	0.203170i
$573$	1.60711	−	9.11435i	0.0671378	−	0.380758i
$574$	5.22668	−	4.38571i	0.218157	−	0.183056i
$575$		0			0
$576$	−0.500000	−	2.83564i	−0.0208333	−	0.118152i
$577$	5.25237	+	9.09738i	0.218659	+	0.378729i	0.954398	−	0.298536i	$-0.0964984\pi$
$577$	5.25237	+	9.09738i	0.218659	+	0.378729i	−0.735739	+	0.677265i	$0.763165\pi$
$578$	6.25150	−	10.8279i	0.260028	−	0.450382i
$579$	−7.79813	−	2.83829i	−0.324079	−	0.117955i
$580$		0			0
$581$	4.08512	−	7.07564i	0.169479	−	0.293547i
$582$	−1.06805	−	1.84991i	−0.0442720	−	0.0766814i
$583$	0.0876485	+	0.497079i	0.00363003	+	0.0205869i
$584$	2.37346	+	1.99157i	0.0982143	+	0.0824116i
$585$		0			0
$586$	−5.01872	+	28.4626i	−0.207322	+	1.17578i
$587$	21.1677	−	7.70442i	0.873685	−	0.317995i	0.134027	−	0.990978i	$-0.457209\pi$
$587$	21.1677	−	7.70442i	0.873685	−	0.317995i	0.739659	+	0.672982i	$0.234987\pi$
$588$	1.61587			0.0666372
$589$	−11.9991	−	26.1290i	−0.494415	−	1.07663i
$590$		0			0
$591$	3.98128	−	1.44907i	0.163768	−	0.0596066i
$592$	1.64156	−	9.30975i	0.0674677	−	0.382628i
$593$	−28.3141	+	23.7583i	−1.16272	+	0.975638i	−0.999939	−	0.0110244i	$-0.996491\pi$
$593$	−28.3141	+	23.7583i	−1.16272	+	0.975638i	−0.162781	+	0.986662i	$0.552046\pi$
$594$	4.85844	+	4.07672i	0.199344	+	0.167270i
$595$		0			0
$596$	3.65523	+	6.33104i	0.149724	+	0.259330i
$597$	2.38548	−	4.13177i	0.0976311	−	0.169102i
$598$	−12.6518	−	4.60489i	−0.517372	−	0.188308i
$599$	20.5125	+	7.46594i	0.838118	+	0.305050i	0.725186	−	0.688553i	$-0.241754\pi$
$599$	20.5125	+	7.46594i	0.838118	+	0.305050i	0.112931	+	0.993603i	$0.463976\pi$
$600$		0			0
$601$	−19.6074	−	33.9610i	−0.799803	−	1.38530i	−0.919744	−	0.392518i	$-0.871604\pi$
$601$	−19.6074	−	33.9610i	−0.799803	−	1.38530i	0.119941	−	0.992781i	$-0.461729\pi$
$602$	0.766044	+	4.34445i	0.0312216	+	0.177067i
$603$	18.9611	+	15.9103i	0.772156	+	0.647916i
$604$	0.771974	−	0.647763i	0.0314112	−	0.0263571i
$605$		0			0
$606$	−4.45336	+	1.62089i	−0.180906	+	0.0658442i
$607$	10.9135			0.442967			0.221483	−	0.975164i	$-0.428910\pi$
$607$	10.9135			0.442967			0.221483	+	0.975164i	$0.428910\pi$
$608$	0.354570	+	4.34445i	0.0143797	+	0.176191i
$609$	3.46791			0.140527
$610$		0			0
$611$	−2.75443	+	15.6212i	−0.111432	+	0.631965i
$612$	4.67752	−	3.92490i	0.189077	−	0.158655i
$613$	1.77126	+	1.48626i	0.0715405	+	0.0600296i	0.677857	−	0.735194i	$-0.262909\pi$
$613$	1.77126	+	1.48626i	0.0715405	+	0.0600296i	−0.606316	+	0.795224i	$0.707353\pi$
$614$	−3.61856	−	20.5218i	−0.146033	−	0.828194i
$615$		0			0
$616$	−2.37939	+	4.12122i	−0.0958682	+	0.166049i
$617$	−41.4004	−	15.0685i	−1.66672	−	0.606635i	−0.675320	−	0.737525i	$-0.735994\pi$
$617$	−41.4004	−	15.0685i	−1.66672	−	0.606635i	−0.991397	+	0.130890i	$0.958217\pi$
$618$	2.25877	+	0.822125i	0.0908611	+	0.0330707i
$619$	13.2883	−	23.0161i	0.534103	−	0.925094i	−0.465103	−	0.885257i	$-0.653983\pi$
$619$	13.2883	−	23.0161i	0.534103	−	0.925094i	0.999206	−	0.0398373i	$-0.0126840\pi$
$620$		0			0
$621$	−1.04370	−	5.91912i	−0.0418822	−	0.237526i
$622$	−10.8268	−	9.08478i	−0.434116	−	0.364266i
$623$	8.24170	−	6.91560i	0.330197	−	0.277068i
$624$	0.275845	−	1.56439i	0.0110426	−	0.0626258i
$625$		0			0
$626$	16.9736			0.678401
$627$	−3.30541	−	3.34419i	−0.132005	−	0.133554i
$628$	−19.6236			−0.783067
$629$	18.8380	−	6.85646i	0.751119	−	0.273385i
$630$		0			0
$631$	−33.0822	+	27.7592i	−1.31698	+	1.10508i	−0.330045	+	0.943965i	$0.607064\pi$
$631$	−33.0822	+	27.7592i	−1.31698	+	1.10508i	−0.986936	+	0.161113i	$0.948492\pi$
$632$	−0.766044	−	0.642788i	−0.0304716	−	0.0255687i
$633$	−0.914162	−	5.18447i	−0.0363347	−	0.206064i
$634$	−4.33409	−	7.50687i	−0.172129	−	0.298136i
$635$		0			0
$636$	0.0530334	+	0.0193026i	0.00210291	+	0.000765397i
$637$	−19.9979	−	7.27866i	−0.792347	−	0.288391i
$638$	10.1220	−	17.5317i	0.400732	−	0.694089i
$639$	13.8550	+	23.9976i	0.548097	+	0.949332i
$640$		0			0
$641$	−16.7536	−	14.0579i	−0.661726	−	0.555254i	0.248878	−	0.968535i	$-0.419938\pi$
$641$	−16.7536	−	14.0579i	−0.661726	−	0.555254i	−0.910603	+	0.413281i	$0.864383\pi$
$642$	0.602196	−	0.505303i	0.0237668	−	0.0199427i
$643$	−3.09121	+	17.5311i	−0.121906	+	0.691361i	0.861192	+	0.508280i	$0.169718\pi$
$643$	−3.09121	+	17.5311i	−0.121906	+	0.691361i	−0.983098	+	0.183081i	$0.941393\pi$
$644$	4.23783	−	1.54244i	0.166994	−	0.0607807i
$645$		0			0
$646$	−7.60266	+	5.25763i	−0.299123	+	0.206859i
$647$	36.6641			1.44141			0.720707	−	0.693240i	$-0.243818\pi$
$647$	36.6641			1.44141			0.720707	+	0.693240i	$0.243818\pi$
$648$	−7.45084	+	2.71188i	−0.292697	+	0.106533i
$649$	−7.64290	+	43.3451i	−0.300010	+	1.70144i
$650$		0			0
$651$	−2.68866	−	2.25606i	−0.105377	−	0.0884218i
$652$	−3.59152	−	20.3685i	−0.140655	−	0.797693i
$653$	5.70439	+	9.88030i	0.223230	+	0.386646i	0.955787	−	0.294060i	$-0.0950065\pi$
$653$	5.70439	+	9.88030i	0.223230	+	0.386646i	−0.732557	+	0.680706i	$0.761673\pi$
$654$	−1.83275	+	3.17441i	−0.0716661	+	0.124129i
$655$		0			0
$656$	−4.18479	−	1.52314i	−0.163389	−	0.0594686i
$657$	4.46064	−	7.72605i	0.174026	−	0.301422i
$658$	−2.65657	−	4.60132i	−0.103564	−	0.179378i
$659$	−4.58606	−	26.0088i	−0.178647	−	1.01316i	−0.933849	−	0.357667i	$-0.883572\pi$
$659$	−4.58606	−	26.0088i	−0.178647	−	1.01316i	0.755202	−	0.655492i	$-0.227539\pi$
$660$		0			0
$661$	−14.5858	+	12.2390i	−0.567323	+	0.476041i	−0.880756	−	0.473569i	$-0.842965\pi$
$661$	−14.5858	+	12.2390i	−0.567323	+	0.476041i	0.313433	+	0.949610i	$0.398521\pi$
$662$	−5.05010	+	28.6405i	−0.196278	+	1.11315i
$663$	3.16550	−	1.15215i	0.122938	−	0.0447457i
$664$	−5.33275			−0.206951
$665$		0			0
$666$	−27.2199			−1.05475
$667$	−18.0278	+	6.56159i	−0.698040	+	0.254066i
$668$	−1.48040	+	8.39576i	−0.0572784	+	0.324842i
$669$	−0.0157300	+	0.0131990i	−0.000608156	+	0.000510303i
$670$		0			0
$671$	−4.32692	−	24.5392i	−0.167039	−	0.947326i
$672$	0.266044	+	0.460802i	0.0102629	+	0.0177758i
$673$	−3.75402	+	6.50216i	−0.144707	+	0.250640i	−0.929264	−	0.369417i	$-0.879557\pi$
$673$	−3.75402	+	6.50216i	−0.144707	+	0.250640i	0.784557	+	0.620057i	$0.212891\pi$
$674$	−8.13176	−	2.95972i	−0.313224	−	0.114004i
$675$		0			0
$676$	−3.96064	+	6.86002i	−0.152332	+	0.263847i
$677$	−19.6707	−	34.0707i	−0.756007	−	1.30944i	−0.944872	−	0.327439i	$-0.893814\pi$
$677$	−19.6707	−	34.0707i	−0.756007	−	1.30944i	0.188865	−	0.982003i	$-0.439519\pi$
$678$	−1.18779	−	6.73627i	−0.0456166	−	0.258705i
$679$	−7.21869	−	6.05720i	−0.277028	−	0.232454i
$680$		0			0
$681$	1.78177	−	10.1049i	0.0682777	−	0.387222i
$682$	−19.2528	+	7.00746i	−0.737229	+	0.268330i
$683$	−8.36278			−0.319993			−0.159996	−	0.987118i	$-0.551148\pi$
$683$	−8.36278			−0.319993			−0.159996	+	0.987118i	$0.551148\pi$
$684$	12.1420	−	3.17766i	0.464262	−	0.121501i
$685$		0			0
$686$	16.7763	−	6.10608i	0.640523	−	0.233131i
$687$	0.763356	−	4.32921i	0.0291239	−	0.165170i
$688$	2.20574	−	1.85083i	0.0840929	−	0.0705624i
$689$	−0.569392	−	0.477777i	−0.0216921	−	0.0182019i
$690$		0			0
$691$	23.8143	+	41.2476i	0.905940	+	1.56913i	0.819651	+	0.572864i	$0.194168\pi$
$691$	23.8143	+	41.2476i	0.905940	+	1.56913i	0.0862891	+	0.996270i	$0.472499\pi$
$692$	−2.29813	+	3.98048i	−0.0873619	+	0.151315i
$693$	12.8760	+	4.68647i	0.489118	+	0.178024i
$694$	15.8944	+	5.78509i	0.603343	+	0.219599i
$695$		0			0
$696$	−1.13176	−	1.96026i	−0.0428992	−	0.0743036i
$697$	−1.63991	−	9.30039i	−0.0621160	−	0.352278i
$698$	−10.2738	−	8.62073i	−0.388869	−	0.326299i
$699$	−1.35529	+	1.13722i	−0.0512616	+	0.0430136i
$700$		0			0
$701$	7.66550	−	2.79001i	0.289522	−	0.105377i	−0.193176	−	0.981164i	$-0.561879\pi$
$701$	7.66550	−	2.79001i	0.289522	−	0.105377i	0.482698	+	0.875787i	$0.339657\pi$
$702$	−9.33956			−0.352499
$703$	41.0278	+	3.83072i	1.54739	+	0.144478i
$704$	3.10607			0.117064
$705$		0			0
$706$	4.96972	−	28.1847i	0.187038	−	1.06074i
$707$	−16.0155	+	13.4386i	−0.602324	+	0.505410i
$708$	3.76991	+	3.16333i	0.141682	+	0.118885i
$709$	−0.574693	−	3.25925i	−0.0215831	−	0.122404i	0.972113	−	0.234514i	$-0.0753500\pi$
$709$	−0.574693	−	3.25925i	−0.0215831	−	0.122404i	−0.993696	+	0.112111i	$0.964239\pi$
$710$		0			0
$711$	−1.43969	+	2.49362i	−0.0539927	+	0.0935181i
$712$	−6.59879	−	2.40176i	−0.247300	−	0.0900099i
$713$	18.2456	+	6.64084i	0.683302	+	0.248702i
$714$	−0.564178	+	0.977185i	−0.0211138	+	0.0365702i
$715$		0			0
$716$	−1.12196	−	6.36295i	−0.0419296	−	0.237794i
$717$	2.08441	+	1.74903i	0.0778436	+	0.0653185i
$718$	−13.3289	+	11.1843i	−0.497429	+	0.417393i
$719$	−3.32723	+	18.8697i	−0.124085	+	0.703719i	0.857763	+	0.514046i	$0.171854\pi$
$719$	−3.32723	+	18.8697i	−0.124085	+	0.703719i	−0.981847	+	0.189673i	$0.939257\pi$
$720$		0			0
$721$	10.6040			0.394914
$722$	−18.7486	+	3.08083i	−0.697749	+	0.114657i
$723$	6.14559			0.228557
$724$	−7.85756	+	2.85992i	−0.292024	+	0.106288i
$725$		0			0
$726$	0.359785	−	0.301895i	0.0133529	−	0.0112044i
$727$	−3.77063	−	3.16393i	−0.139845	−	0.117344i	0.570182	−	0.821519i	$-0.306873\pi$
$727$	−3.77063	−	3.16393i	−0.139845	−	0.117344i	−0.710027	+	0.704175i	$0.751317\pi$
$728$	−1.21688	−	6.90128i	−0.0451006	−	0.255778i
$729$	10.3516	+	17.9296i	0.383394	+	0.664058i
$730$		0			0
$731$	5.73783	+	2.08840i	0.212221	+	0.0772422i
$732$	−2.61809	−	0.952906i	−0.0967673	−	0.0352204i
$733$	7.02956	−	12.1756i	0.259643	−	0.449715i	−0.706503	−	0.707710i	$-0.749729\pi$
$733$	7.02956	−	12.1756i	0.259643	−	0.449715i	0.966146	+	0.257995i	$0.0830618\pi$
$734$	−15.1864	−	26.3037i	−0.560542	−	0.970887i
$735$		0			0
$736$	−2.25490	−	1.89209i	−0.0831167	−	0.0697432i
$737$	−20.4538	+	17.1628i	−0.753427	+	0.632200i
$738$	−2.22668	+	12.6281i	−0.0819653	+	0.464848i
$739$	−29.9923	+	10.9163i	−1.10329	+	0.401563i	−0.828526	−	0.559950i	$-0.810820\pi$
$739$	−29.9923	+	10.9163i	−1.10329	+	0.401563i	−0.274759	+	0.961513i	$0.588598\pi$
$740$		0			0
$741$	6.89424	+	0.643707i	0.253266	+	0.0236472i
$742$	0.248970			0.00913999
$743$	−3.32800	+	1.21129i	−0.122093	+	0.0444380i	−0.402344	−	0.915489i	$-0.631804\pi$
$743$	−3.32800	+	1.21129i	−0.122093	+	0.0444380i	0.280251	+	0.959927i	$0.409582\pi$
$744$	−0.397804	+	2.25606i	−0.0145842	+	0.0827110i
$745$		0			0
$746$	25.3161	+	21.2428i	0.926890	+	0.777753i
$747$	2.66637	+	15.1218i	0.0975575	+	0.553276i
$748$	3.29339	+	5.70431i	0.120418	+	0.208570i
$749$	1.73396	−	3.00330i	0.0633574	−	0.109738i
$750$		0			0
$751$	6.10354	+	2.22151i	0.222721	+	0.0810639i	0.450971	−	0.892539i	$-0.351078\pi$
$751$	6.10354	+	2.22151i	0.222721	+	0.0810639i	−0.228249	+	0.973603i	$0.573300\pi$
$752$	−1.73396	+	3.00330i	−0.0632309	+	0.109519i
$753$	−0.941037	−	1.62992i	−0.0342933	−	0.0593977i
$754$	5.17664	+	29.3582i	0.188522	+	1.06916i
$755$		0			0
$756$	2.39646	−	2.01087i	0.0871584	−	0.0731346i
$757$	−4.07486	+	23.1097i	−0.148103	+	0.839935i	0.816720	+	0.577034i	$0.195790\pi$
$757$	−4.07486	+	23.1097i	−0.148103	+	0.839935i	−0.964823	+	0.262900i	$0.915321\pi$
$758$	−17.1348	+	6.23654i	−0.622362	+	0.226521i
$759$	3.17530			0.115256
$760$		0			0
$761$	−20.8399			−0.755444			−0.377722	−	0.925919i	$-0.623293\pi$
$761$	−20.8399			−0.755444			−0.377722	+	0.925919i	$0.623293\pi$
$762$	3.02987	−	1.10278i	0.109761	−	0.0399496i
$763$	−2.80793	+	15.9246i	−0.101654	+	0.576509i
$764$	−20.4140	+	17.1294i	−0.738553	+	0.619719i
$765$		0			0
$766$	−5.77285	−	32.7395i	−0.208582	−	1.18293i
$767$	−32.4072	−	56.1309i	−1.17016	−	2.02677i
$768$	0.173648	−	0.300767i	0.00626599	−	0.0108530i
$769$	35.9632	+	13.0895i	1.29687	+	0.472021i	0.895975	−	0.444104i	$-0.146478\pi$
$769$	35.9632	+	13.0895i	1.29687	+	0.472021i	0.400892	+	0.916125i	$0.368700\pi$
$770$		0			0
$771$	−1.19759	+	2.07428i	−0.0431300	+	0.0747033i
$772$	11.9474	+	20.6936i	0.429998	+	0.744778i
$773$	−5.56330	−	31.5510i	−0.200098	−	1.13481i	−0.904969	−	0.425477i	$-0.860106\pi$
$773$	−5.56330	−	31.5510i	−0.200098	−	1.13481i	0.704871	−	0.709335i	$-0.251005\pi$
$774$	−6.35117	−	5.32926i	−0.228288	−	0.191556i
$775$		0			0
$776$	−1.06805	+	6.05720i	−0.0383407	+	0.217441i
$777$	4.72668	−	1.72037i	0.169569	−	0.0617180i
$778$	7.13516			0.255808
$779$	5.13341	−	18.7207i	0.183923	−	0.670739i
$780$		0			0
$781$	−28.0889	+	10.2235i	−1.00510	+	0.365826i
$782$	1.08394	−	6.14733i	0.0387616	−	0.219828i
$783$	−10.1946	+	8.55428i	−0.364325	+	0.305705i
$784$	−3.56418	−	2.99070i	−0.127292	−	0.106811i
$785$		0			0
$786$	0.489322	+	0.847531i	0.0174536	+	0.0302304i
$787$	−14.0805	+	24.3882i	−0.501917	+	0.869346i	0.498081	+	0.867131i	$0.334038\pi$
$787$	−14.0805	+	24.3882i	−0.501917	+	0.869346i	−0.999998	+	0.00221489i	$0.999295\pi$
$788$	−11.4636	−	4.17242i	−0.408375	−	0.148636i
$789$	−3.99108	−	1.45263i	−0.142086	−	0.0517151i
$790$		0			0
$791$	−15.0876	−	26.1326i	−0.536455	−	0.929167i
$792$	−1.55303	−	8.80769i	−0.0551846	−	0.312968i
$793$	28.1091	+	23.5863i	0.998182	+	0.837574i
$794$	−16.2652	+	13.6481i	−0.577229	+	0.484353i
$795$		0			0
$796$	−12.9089	+	4.69847i	−0.457546	+	0.166533i
$797$	−5.97596			−0.211679			−0.105840	−	0.994383i	$-0.533753\pi$
$797$	−5.97596			−0.211679			−0.105840	+	0.994383i	$0.533753\pi$
$798$	−1.90760	+	1.31920i	−0.0675284	+	0.0466993i
$799$	−7.35410			−0.260169
$800$		0			0
$801$	−3.51114	+	19.9127i	−0.124060	+	0.703580i
$802$	25.0535	−	21.0224i	0.884670	−	0.742326i
$803$	7.37211	+	6.18594i	0.260156	+	0.218297i
$804$	0.518418	+	2.94010i	0.0182832	+	0.103689i
$805$		0			0
$806$	15.0856	−	26.1290i	0.531367	−	0.920355i
$807$	−3.64765	−	1.32764i	−0.128403	−	0.0467350i
$808$	12.8229	+	4.66717i	0.451110	+	0.164191i
$809$	−22.2875	+	38.6030i	−0.783585	+	1.35721i	0.146255	+	0.989247i	$0.453278\pi$
$809$	−22.2875	+	38.6030i	−0.783585	+	1.35721i	−0.929841	+	0.367963i	$0.880055\pi$
$810$		0			0
$811$	−7.99588	−	45.3469i	−0.280773	−	1.59234i	−0.720004	−	0.693970i	$-0.755860\pi$
$811$	−7.99588	−	45.3469i	−0.280773	−	1.59234i	0.439230	−	0.898375i	$-0.355251\pi$
$812$	−7.64930	−	6.41852i	−0.268438	−	0.225246i
$813$	5.20233	−	4.36528i	0.182454	−	0.153097i
$814$	5.09879	−	28.9167i	0.178713	−	1.01353i
$815$		0			0
$816$	0.736482			0.0257820
$817$	8.82295	+	8.92647i	0.308676	+	0.312298i
$818$	11.4875			0.401651
$819$	−18.9611	+	6.90128i	−0.662555	+	0.241150i
$820$		0			0
$821$	−25.9957	+	21.8130i	−0.907257	+	0.761279i	−0.971595	−	0.236649i	$-0.923951\pi$
$821$	−25.9957	+	21.8130i	−0.907257	+	0.761279i	0.0643383	+	0.997928i	$0.479506\pi$
$822$	0.177519	+	0.148956i	0.00619167	+	0.00519543i
$823$	−4.36865	−	24.7759i	−0.152282	−	0.863632i	−0.961229	−	0.275751i	$-0.911073\pi$
$823$	−4.36865	−	24.7759i	−0.152282	−	0.863632i	0.808947	−	0.587881i	$-0.200038\pi$
$824$	−3.46064	−	5.99400i	−0.120557	−	0.208811i
$825$		0			0
$826$	20.4008	+	7.42528i	0.709834	+	0.258359i
$827$	2.05556	+	0.748163i	0.0714788	+	0.0260162i	0.377512	−	0.926005i	$-0.376780\pi$
$827$	2.05556	+	0.748163i	0.0714788	+	0.0260162i	−0.306033	+	0.952021i	$0.599002\pi$
$828$	−4.23783	+	7.34013i	−0.147275	+	0.255087i
$829$	−21.7160	−	37.6132i	−0.754228	−	1.30636i	−0.945757	−	0.324874i	$-0.894678\pi$
$829$	−21.7160	−	37.6132i	−0.754228	−	1.30636i	0.191529	−	0.981487i	$-0.438655\pi$
$830$		0			0
$831$	6.76058	+	5.67280i	0.234522	+	0.196787i
$832$	−3.50387	+	2.94010i	−0.121475	+	0.101930i
$833$	1.71332	−	9.71670i	0.0593629	−	0.336664i
$834$	−3.40420	+	1.23903i	−0.117878	+	0.0429040i
$835$		0			0
$836$	1.10132	+	13.4942i	0.0380899	+	0.466705i
$837$	13.4688			0.465551
$838$	16.0125	−	5.82807i	0.553142	−	0.201327i
$839$	2.54411	−	14.4284i	0.0878325	−	0.498123i	−0.908877	−	0.417064i	$-0.863059\pi$
$839$	2.54411	−	14.4284i	0.0878325	−	0.498123i	0.996709	−	0.0810582i	$-0.0258300\pi$
$840$		0			0
$841$	10.3250	+	8.66371i	0.356035	+	0.298749i
$842$	−2.92989	−	16.6162i	−0.100971	−	0.572634i
$843$	3.31639	+	5.74416i	0.114223	+	0.197839i
$844$	−7.57919	+	13.1275i	−0.260887	+	0.451869i
$845$		0			0
$846$	9.38326	+	3.41523i	0.322603	+	0.117418i
$847$	1.03596	−	1.79433i	0.0355960	−	0.0616540i
$848$	−0.0812519	−	0.140732i	−0.00279020	−	0.00483277i
$849$	−1.09405	−	6.20464i	−0.0375475	−	0.212943i
$850$		0			0
$851$	−21.3164	+	17.8866i	−0.730716	+	0.613144i
$852$	−0.580375	+	3.29147i	−0.0198833	+	0.112764i
$853$	26.6570	−	9.70237i	0.912720	−	0.332203i	0.157381	−	0.987538i	$-0.449695\pi$
$853$	26.6570	−	9.70237i	0.912720	−	0.332203i	0.755338	+	0.655335i	$0.227473\pi$
$854$	−12.2909			−0.420585
$855$		0			0
$856$	−2.26352			−0.0773655
$857$	−19.2344	+	7.00076i	−0.657035	+	0.239141i	−0.648956	−	0.760826i	$-0.724794\pi$
$857$	−19.2344	+	7.00076i	−0.657035	+	0.239141i	−0.00807948	+	0.999967i	$0.502572\pi$
$858$	0.856792	−	4.85911i	0.0292504	−	0.165887i
$859$	−23.4368	+	19.6658i	−0.799652	+	0.670988i	−0.948114	−	0.317931i	$-0.897012\pi$
$859$	−23.4368	+	19.6658i	−0.799652	+	0.670988i	0.148462	+	0.988918i	$0.452568\pi$
$860$		0			0
$861$	−0.411474	−	2.33359i	−0.0140230	−	0.0795284i
$862$	−10.6407	−	18.4302i	−0.362423	−	0.627735i
$863$	29.2015	−	50.5784i	0.994029	−	1.72171i	0.402518	−	0.915412i	$-0.368135\pi$
$863$	29.2015	−	50.5784i	0.994029	−	1.72171i	0.591511	−	0.806297i	$-0.298532\pi$
$864$	−1.91875	−	0.698367i	−0.0652771	−	0.0237589i
$865$		0			0
$866$	−7.77972	+	13.4749i	−0.264365	+	0.457894i
$867$	−2.17112	−	3.76049i	−0.0737352	−	0.127713i
$868$	1.75490	+	9.95253i	0.0595652	+	0.337811i
$869$	−2.37939	−	1.99654i	−0.0807151	−	0.0677280i
$870$		0			0
$871$	6.82770	−	38.7218i	0.231348	−	1.31204i
$872$	9.91787	−	3.60981i	0.335861	−	0.122244i
$873$	17.7101			0.599395
$874$	7.42056	−	10.4672i	0.251004	−	0.354058i
$875$		0			0
$876$	1.01114	−	0.368026i	0.0341634	−	0.0124345i
$877$	8.22715	−	46.6585i	0.277811	−	1.57554i	−0.452077	−	0.891979i	$-0.649317\pi$
$877$	8.22715	−	46.6585i	0.277811	−	1.57554i	0.729889	−	0.683566i	$-0.239572\pi$
$878$	−6.39440	+	5.36554i	−0.215801	+	0.181078i
$879$	7.68913	+	6.45195i	0.259348	+	0.217619i
$880$		0			0
$881$	2.89171	+	5.00859i	0.0974242	+	0.168744i	0.910618	−	0.413250i	$-0.135606\pi$
$881$	2.89171	+	5.00859i	0.0974242	+	0.168744i	−0.813194	+	0.581993i	$0.802273\pi$
$882$	−6.69846	+	11.6021i	−0.225549	+	0.390662i
$883$	13.7690	+	5.01152i	0.463365	+	0.168651i	0.563144	−	0.826359i	$-0.309591\pi$
$883$	13.7690	+	5.01152i	0.463365	+	0.168651i	−0.0997794	+	0.995010i	$0.531814\pi$
$884$	−9.11468	−	3.31747i	−0.306560	−	0.111579i
$885$		0			0
$886$	−10.8897	−	18.8614i	−0.365845	−	0.633662i
$887$	4.04788	+	22.9566i	0.135914	+	0.770809i	0.974219	+	0.225606i	$0.0724362\pi$
$887$	4.04788	+	22.9566i	0.135914	+	0.770809i	−0.838304	+	0.545203i	$0.816453\pi$
$888$	−2.51501	−	2.11035i	−0.0843984	−	0.0708186i
$889$	10.8962	−	9.14301i	0.365447	−	0.306647i
$890$		0			0
$891$	−23.1428	+	8.42329i	−0.775313	+	0.282191i
$892$	0.0591253			0.00197966
$893$	−13.6625	−	6.46821i	−0.457198	−	0.216450i
$894$	2.53890			0.0849134
$895$		0			0
$896$	0.266044	−	1.50881i	0.00888792	−	0.0504059i
$897$	−3.58197	+	3.00563i	−0.119598	+	0.100355i
$898$	−3.81315	−	3.19961i	−0.127246	−	0.106772i
$899$	−7.46538	−	42.3383i	−0.248985	−	1.41206i
$900$		0			0
$901$	0.172304	−	0.298439i	0.00574028	−	0.00994245i
$902$	−12.9982	−	4.73097i	−0.432794	−	0.157524i
$903$	1.43969	+	0.524005i	0.0479100	+	0.0174378i
$904$	−9.84776	+	17.0568i	−0.327532	+	0.567302i
$905$		0			0
$906$	−0.0607742	−	0.344668i	−0.00201909	−	0.0114508i
$907$	−8.29086	−	6.95686i	−0.275293	−	0.230999i	0.494679	−	0.869076i	$-0.335286\pi$
$907$	−8.29086	−	6.95686i	−0.275293	−	0.230999i	−0.769972	+	0.638077i	$0.779730\pi$
$908$	−22.6327	+	18.9911i	−0.751092	+	0.630241i
$909$	6.82295	−	38.6949i	0.226303	−	1.28343i
$910$		0			0
$911$	−37.2508			−1.23418			−0.617088	−	0.786894i	$-0.711688\pi$
$911$	−37.2508			−1.23418			−0.617088	+	0.786894i	$0.711688\pi$
$912$	1.36824	+	0.647763i	0.0453070	+	0.0214496i
$913$	−16.5639			−0.548184
$914$	−36.0886	+	13.1352i	−1.19370	+	0.434473i
$915$		0			0
$916$	−9.69640	+	8.13625i	−0.320378	+	0.268829i
$917$	3.30722	+	2.77509i	0.109214	+	0.0916414i
$918$	−0.751907	−	4.26428i	−0.0248166	−	0.140742i
$919$	−22.4115	−	38.8178i	−0.739286	−	1.28048i	−0.952817	−	0.303545i	$-0.901830\pi$
$919$	−22.4115	−	38.8178i	−0.739286	−	1.28048i	0.213531	−	0.976936i	$-0.431504\pi$
$920$		0			0
$921$	−6.80066	−	2.47524i	−0.224089	−	0.0815619i
$922$	−37.4368	−	13.6259i	−1.23291	−	0.448744i
$923$	22.0091	−	38.1209i	0.724438	−	1.25476i
$924$	0.826352	+	1.43128i	0.0271850	+	0.0470858i
$925$		0			0
$926$	21.0103	+	17.6297i	0.690440	+	0.579348i
$927$	−15.2665	+	12.8101i	−0.501418	+	0.420740i
$928$	−1.13176	+	6.41852i	−0.0371518	+	0.210698i
$929$	−33.5269	+	12.2028i	−1.09998	+	0.400361i	−0.827310	−	0.561746i	$-0.810130\pi$
$929$	−33.5269	+	12.2028i	−1.09998	+	0.400361i	−0.272673	+	0.962107i	$0.587908\pi$
$930$		0			0
$931$	11.7292	−	16.5448i	0.384409	−	0.542235i
$932$	5.09421			0.166866
$933$	−4.61246	+	1.67880i	−0.151005	+	0.0549614i
$934$	−0.136507	+	0.774169i	−0.00446664	+	0.0253316i
$935$		0			0
$936$	10.0890	+	8.46567i	0.329769	+	0.276709i
$937$	7.16802	+	40.6519i	0.234169	+	1.32804i	0.844356	+	0.535782i	$0.179983\pi$
$937$	7.16802	+	40.6519i	0.234169	+	1.32804i	−0.610187	+	0.792257i	$0.708906\pi$
$938$	6.58512	+	11.4058i	0.215012	+	0.372411i
$939$	2.94743	−	5.10510i	0.0961859	−	0.166599i
$940$		0			0
$941$	14.6836	+	5.34440i	0.478672	+	0.174222i	0.570077	−	0.821591i	$-0.306913\pi$
$941$	14.6836	+	5.34440i	0.478672	+	0.174222i	−0.0914047	+	0.995814i	$0.529136\pi$
$942$	−3.40760	+	5.90214i	−0.111026	+	0.192302i
$943$	6.55438	+	11.3525i	0.213440	+	0.369689i
$944$	−2.46064	−	13.9550i	−0.0800869	−	0.454195i
$945$		0			0
$946$	6.85117	−	5.74881i	0.222751	−	0.186910i
$947$	9.50656	−	53.9144i	0.308922	−	1.75198i	−0.295524	−	0.955335i	$-0.595494\pi$
$947$	9.50656	−	53.9144i	0.308922	−	1.75198i	0.604446	−	0.796646i	$-0.293395\pi$
$948$	−0.326352	+	0.118782i	−0.0105994	+	0.00385787i
$949$	−14.1717			−0.460032
$950$		0			0
$951$	−3.01043			−0.0976199
$952$	3.05303	−	1.11121i	0.0989494	−	0.0360146i
$953$	−1.01811	+	5.77401i	−0.0329799	+	0.187039i	−0.996847	−	0.0793442i	$-0.974717\pi$
$953$	−1.01811	+	5.77401i	−0.0329799	+	0.187039i	0.963867	+	0.266383i	$0.0858285\pi$
$954$	−0.358441	+	0.300767i	−0.0116049	+	0.00973771i
$955$		0			0
$956$	−1.36050	−	7.71578i	−0.0440017	−	0.249546i
$957$	−3.51532	−	6.08871i	−0.113634	−	0.196820i
$958$	−3.50774	+	6.07559i	−0.113330	+	0.196293i
$959$	0.960637	+	0.349643i	0.0310206	+	0.0112906i
$960$		0			0
$961$	−6.25537	+	10.8346i	−0.201786	+	0.349504i
$962$	21.6197	+	37.4465i	0.697048	+	1.20732i
$963$	1.13176	+	6.41852i	0.0364704	+	0.206834i
$964$	−13.5556	−	11.3745i	−0.436595	−	0.366347i
$965$		0			0
$966$	0.271974	−	1.54244i	0.00875063	−	0.0496273i
$967$	23.9820	−	8.72875i	0.771211	−	0.280698i	0.0737080	−	0.997280i	$-0.476517\pi$
$967$	23.9820	−	8.72875i	0.771211	−	0.280698i	0.697503	+	0.716582i	$0.254295\pi$
$968$	−1.35235			−0.0434661
$969$	0.261135	+	3.19961i	0.00838885	+	0.102786i
$970$		0			0
$971$	−21.2900	+	7.74892i	−0.683228	+	0.248675i	−0.660233	−	0.751061i	$-0.729542\pi$
$971$	−21.2900	+	7.74892i	−0.683228	+	0.248675i	−0.0229951	+	0.999736i	$0.507320\pi$
$972$	−1.54189	+	8.74449i	−0.0494561	+	0.280480i
$973$	−12.2424	+	10.2726i	−0.392474	+	0.329325i
$974$	−17.5594	−	14.7341i	−0.562640	−	0.472111i
$975$		0			0
$976$	4.01114	+	6.94751i	0.128394	+	0.222384i
$977$	−16.2765	+	28.1917i	−0.520731	+	0.901932i	0.478979	+	0.877826i	$0.341007\pi$
$977$	−16.2765	+	28.1917i	−0.520731	+	0.901932i	−0.999709	+	0.0241053i	$0.992326\pi$
$978$	−6.74985	−	2.45674i	−0.215836	−	0.0785580i
$979$	−20.4963	−	7.46004i	−0.655064	−	0.238424i
$980$		0			0
$981$	−15.1951	−	26.3186i	−0.485141	−	0.840289i
$982$	2.21167	+	12.5430i	0.0705771	+	0.400263i
$983$	28.7139	+	24.0939i	0.915833	+	0.768475i	0.973220	−	0.229877i	$-0.0738325\pi$
$983$	28.7139	+	24.0939i	0.915833	+	0.768475i	−0.0573870	+	0.998352i	$0.518277\pi$
$984$	−1.18479	+	0.994159i	−0.0377698	+	0.0316926i
$985$		0			0
$986$	−12.9877	+	4.72713i	−0.413612	+	0.150542i
$987$	−1.84524			−0.0587345
$988$	−14.0155	−	14.1799i	−0.445892	−	0.451124i
$989$	−8.47565			−0.269510
$990$		0			0
$991$	−4.03580	+	22.8881i	−0.128201	+	0.727066i	0.851153	+	0.524917i	$0.175904\pi$
$991$	−4.03580	+	22.8881i	−0.128201	+	0.727066i	−0.979355	+	0.202149i	$0.935208\pi$
$992$	5.05303	−	4.24000i	0.160434	−	0.134620i
$993$	7.73720	+	6.49228i	0.245533	+	0.206026i
$994$	2.56031	+	14.5202i	0.0812080	+	0.460554i
$995$		0			0
$996$	−0.926022	+	1.60392i	−0.0293421	+	0.0508221i
$997$	33.4530	+	12.1759i	1.05947	+	0.385614i	0.812228	−	0.583341i	$-0.198255\pi$
$997$	33.4530	+	12.1759i	1.05947	+	0.385614i	0.247238	+	0.968955i	$0.420477\pi$
$998$	−30.0269	−	10.9289i	−0.950486	−	0.345949i
$999$	−9.65136	+	16.7166i	−0.305356	+	0.528891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.a.651.1	yes	6
5.2	odd	4		950.2.u.a.499.1		12
5.3	odd	4		950.2.u.a.499.2		12
5.4	even	2		950.2.l.f.651.1	yes	6
19.4	even	9	inner	950.2.l.a.251.1	✓	6
95.4	even	18		950.2.l.f.251.1	yes	6
95.23	odd	36		950.2.u.a.99.1		12
95.42	odd	36		950.2.u.a.99.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.a.251.1	✓	6	19.4	even	9	inner
950.2.l.a.651.1	yes	6	1.1	even	1	trivial
950.2.l.f.251.1	yes	6	95.4	even	18
950.2.l.f.651.1	yes	6	5.4	even	2
950.2.u.a.99.1		12	95.23	odd	36
950.2.u.a.99.2		12	95.42	odd	36
950.2.u.a.499.1		12	5.2	odd	4
950.2.u.a.499.2		12	5.3	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.0603074 + 0.342020i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.0603074 - 0.342020i) q^{6} +(-0.766044 - 1.32683i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.70574 + 0.984808i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.0603074 + 0.342020i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.0603074 - 0.342020i) q^{6} +(-0.766044 - 1.32683i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.70574 + 0.984808i) q^{9} +(-1.55303 + 2.68993i) q^{11} +(0.173648 + 0.300767i) q^{12} +(-0.794263 - 4.50449i) q^{13} +(1.17365 + 0.984808i) q^{14} +(0.173648 - 0.984808i) q^{16} +(1.99273 - 0.725293i) q^{17} -2.87939 q^{18} +(4.34002 + 0.405223i) q^{19} +(0.500000 - 0.181985i) q^{21} +(0.539363 - 3.05888i) q^{22} +(-2.25490 + 1.89209i) q^{23} +(-0.266044 - 0.223238i) q^{24} +(2.28699 + 3.96118i) q^{26} +(-1.02094 + 1.76833i) q^{27} +(-1.43969 - 0.524005i) q^{28} +(6.12449 + 2.22913i) q^{29} +(-3.29813 - 5.71253i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-0.826352 - 0.693392i) q^{33} +(-1.62449 + 1.36310i) q^{34} +(2.70574 - 0.984808i) q^{36} +9.45336 q^{37} +(-4.21688 + 1.10359i) q^{38} +1.58853 q^{39} +(0.773318 - 4.38571i) q^{41} +(-0.407604 + 0.342020i) q^{42} +(2.20574 + 1.85083i) q^{43} +(0.539363 + 3.05888i) q^{44} +(1.47178 - 2.54920i) q^{46} +(-3.25877 - 1.18610i) q^{47} +(0.326352 + 0.118782i) q^{48} +(2.32635 - 4.02936i) q^{49} +(0.127889 + 0.725293i) q^{51} +(-3.50387 - 2.94010i) q^{52} +(0.124485 - 0.104455i) q^{53} +(0.354570 - 2.01087i) q^{54} +1.53209 q^{56} +(-0.400330 + 1.45994i) q^{57} -6.51754 q^{58} +(13.3157 - 4.84651i) q^{59} +(-6.14543 + 5.15663i) q^{61} +(5.05303 + 4.24000i) q^{62} +(-0.766044 - 4.34445i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.01367 + 0.368946i) q^{66} +(8.07785 + 2.94010i) q^{67} +(1.06031 - 1.83651i) q^{68} +(-0.511144 - 0.885328i) q^{69} +(7.37211 + 6.18594i) q^{71} +(-2.20574 + 1.85083i) q^{72} +(0.538019 - 3.05126i) q^{73} +(-8.88326 + 3.23324i) q^{74} +(3.58512 - 2.47929i) q^{76} +4.75877 q^{77} +(-1.49273 + 0.543308i) q^{78} +(-0.173648 + 0.984808i) q^{79} +(6.07398 + 5.09667i) q^{81} +(0.773318 + 4.38571i) q^{82} +(2.66637 + 4.61830i) q^{83} +(0.266044 - 0.460802i) q^{84} +(-2.70574 - 0.984808i) q^{86} +(-1.13176 + 1.96026i) q^{87} +(-1.55303 - 2.68993i) q^{88} +(1.21941 + 6.91560i) q^{89} +(-5.36824 + 4.50449i) q^{91} +(-0.511144 + 2.89884i) q^{92} +(2.15270 - 0.783520i) q^{93} +3.46791 q^{94} -0.347296 q^{96} +(5.77972 - 2.10364i) q^{97} +(-0.807934 + 4.58202i) q^{98} +(-6.85117 + 5.74881i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{3} - 6 q^{6} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^3 - 6 * q^6 - 3 * q^8 + 6 * q^9	\( 6 q - 6 q^{3} - 6 q^{6} - 3 q^{8} + 6 q^{9} + 3 q^{11} - 15 q^{13} + 6 q^{14} - 6 q^{17} - 6 q^{18} + 6 q^{19} + 3 q^{21} + 12 q^{22} - 15 q^{23} + 3 q^{24} + 6 q^{26} - 3 q^{27} - 3 q^{28} + 24 q^{29} - 6 q^{31} - 6 q^{33} + 3 q^{34} + 6 q^{36} + 30 q^{37} - 9 q^{38} + 30 q^{39} + 18 q^{41} - 6 q^{42} + 3 q^{43} + 12 q^{44} - 6 q^{46} + 3 q^{47} + 3 q^{48} + 15 q^{49} + 30 q^{51} + 3 q^{52} - 12 q^{53} + 18 q^{54} + 12 q^{57} + 6 q^{58} + 21 q^{59} - 21 q^{61} + 18 q^{62} - 3 q^{64} - 15 q^{66} + 9 q^{67} + 12 q^{68} + 3 q^{69} + 15 q^{71} - 3 q^{72} + 21 q^{73} - 18 q^{74} + 6 q^{77} + 9 q^{78} + 21 q^{81} + 18 q^{82} - 3 q^{83} - 3 q^{84} - 6 q^{86} - 12 q^{87} + 3 q^{88} - 24 q^{89} - 27 q^{91} + 3 q^{92} + 15 q^{93} + 30 q^{94} + 9 q^{97} + 6 q^{98} - 15 q^{99}+O(q^{100}) \) 6 * q - 6 * q^3 - 6 * q^6 - 3 * q^8 + 6 * q^9 + 3 * q^11 - 15 * q^13 + 6 * q^14 - 6 * q^17 - 6 * q^18 + 6 * q^19 + 3 * q^21 + 12 * q^22 - 15 * q^23 + 3 * q^24 + 6 * q^26 - 3 * q^27 - 3 * q^28 + 24 * q^29 - 6 * q^31 - 6 * q^33 + 3 * q^34 + 6 * q^36 + 30 * q^37 - 9 * q^38 + 30 * q^39 + 18 * q^41 - 6 * q^42 + 3 * q^43 + 12 * q^44 - 6 * q^46 + 3 * q^47 + 3 * q^48 + 15 * q^49 + 30 * q^51 + 3 * q^52 - 12 * q^53 + 18 * q^54 + 12 * q^57 + 6 * q^58 + 21 * q^59 - 21 * q^61 + 18 * q^62 - 3 * q^64 - 15 * q^66 + 9 * q^67 + 12 * q^68 + 3 * q^69 + 15 * q^71 - 3 * q^72 + 21 * q^73 - 18 * q^74 + 6 * q^77 + 9 * q^78 + 21 * q^81 + 18 * q^82 - 3 * q^83 - 3 * q^84 - 6 * q^86 - 12 * q^87 + 3 * q^88 - 24 * q^89 - 27 * q^91 + 3 * q^92 + 15 * q^93 + 30 * q^94 + 9 * q^97 + 6 * q^98 - 15 * q^99

Introduction

L-functions

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