LMFDB - Embedded newform 950.2.u.a.499.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			499.2
Root			$-0.642788 + 0.766044i$ of defining polynomial
Character	$\chi$	$=$	950.499
Dual form			950.2.u.a.99.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.342020 + 0.939693i) q^{2} +(-0.342020 - 0.0603074i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.0603074 - 0.342020i) q^{6} +(-1.32683 + 0.766044i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.70574 - 0.984808i) q^{9} +O(q^{10})$	\(q+(0.342020 + 0.939693i) q^{2} +(-0.342020 - 0.0603074i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.0603074 - 0.342020i) q^{6} +(-1.32683 + 0.766044i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.70574 - 0.984808i) q^{9} +(-1.55303 + 2.68993i) q^{11} +(0.300767 - 0.173648i) q^{12} +(4.50449 - 0.794263i) q^{13} +(-1.17365 - 0.984808i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-0.725293 - 1.99273i) q^{17} -2.87939i q^{18} +(-4.34002 - 0.405223i) q^{19} +(0.500000 - 0.181985i) q^{21} +(-3.05888 - 0.539363i) q^{22} +(-1.89209 - 2.25490i) q^{23} +(0.266044 + 0.223238i) q^{24} +(2.28699 + 3.96118i) q^{26} +(1.76833 + 1.02094i) q^{27} +(0.524005 - 1.43969i) q^{28} +(-6.12449 - 2.22913i) q^{29} +(-3.29813 - 5.71253i) q^{31} +(0.984808 - 0.173648i) q^{32} +(0.693392 - 0.826352i) q^{33} +(1.62449 - 1.36310i) q^{34} +(2.70574 - 0.984808i) q^{36} -9.45336i q^{37} +(-1.10359 - 4.21688i) q^{38} -1.58853 q^{39} +(0.773318 - 4.38571i) q^{41} +(0.342020 + 0.407604i) q^{42} +(-1.85083 + 2.20574i) q^{43} +(-0.539363 - 3.05888i) q^{44} +(1.47178 - 2.54920i) q^{46} +(-1.18610 + 3.25877i) q^{47} +(-0.118782 + 0.326352i) q^{48} +(-2.32635 + 4.02936i) q^{49} +(0.127889 + 0.725293i) q^{51} +(-2.94010 + 3.50387i) q^{52} +(0.104455 + 0.124485i) q^{53} +(-0.354570 + 2.01087i) q^{54} +1.53209 q^{56} +(1.45994 + 0.400330i) q^{57} -6.51754i q^{58} +(-13.3157 + 4.84651i) q^{59} +(-6.14543 + 5.15663i) q^{61} +(4.24000 - 5.05303i) q^{62} +(4.34445 - 0.766044i) q^{63} +(0.500000 + 0.866025i) q^{64} +(1.01367 + 0.368946i) q^{66} +(2.94010 - 8.07785i) q^{67} +(1.83651 + 1.06031i) q^{68} +(0.511144 + 0.885328i) q^{69} +(7.37211 + 6.18594i) q^{71} +(1.85083 + 2.20574i) q^{72} +(3.05126 + 0.538019i) q^{73} +(8.88326 - 3.23324i) q^{74} +(3.58512 - 2.47929i) q^{76} -4.75877i q^{77} +(-0.543308 - 1.49273i) q^{78} +(0.173648 - 0.984808i) q^{79} +(6.07398 + 5.09667i) q^{81} +(4.38571 - 0.773318i) q^{82} +(-4.61830 + 2.66637i) q^{83} +(-0.266044 + 0.460802i) q^{84} +(-2.70574 - 0.984808i) q^{86} +(1.96026 + 1.13176i) q^{87} +(2.68993 - 1.55303i) q^{88} +(-1.21941 - 6.91560i) q^{89} +(-5.36824 + 4.50449i) q^{91} +(2.89884 + 0.511144i) q^{92} +(0.783520 + 2.15270i) q^{93} -3.46791 q^{94} -0.347296 q^{96} +(-2.10364 - 5.77972i) q^{97} +(-4.58202 - 0.807934i) q^{98} +(6.85117 - 5.74881i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{6} - 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^6 - 12 * q^9	$ 12 q - 12 q^{6} - 12 q^{9} + 6 q^{11} - 12 q^{14} - 12 q^{19} + 6 q^{21} - 6 q^{24} + 12 q^{26} - 48 q^{29} - 12 q^{31} - 6 q^{34} + 12 q^{36} - 60 q^{39} + 36 q^{41} - 24 q^{44} - 12 q^{46} - 30 q^{49} + 60 q^{51} - 36 q^{54} - 42 q^{59} - 42 q^{61} + 6 q^{64} - 30 q^{66} - 6 q^{69} + 30 q^{71} + 36 q^{74} + 42 q^{81} + 6 q^{84} - 12 q^{86} + 48 q^{89} - 54 q^{91} - 60 q^{94} + 30 q^{99}+O(q^{100}) $ 12 * q - 12 * q^6 - 12 * q^9 + 6 * q^11 - 12 * q^14 - 12 * q^19 + 6 * q^21 - 6 * q^24 + 12 * q^26 - 48 * q^29 - 12 * q^31 - 6 * q^34 + 12 * q^36 - 60 * q^39 + 36 * q^41 - 24 * q^44 - 12 * q^46 - 30 * q^49 + 60 * q^51 - 36 * q^54 - 42 * q^59 - 42 * q^61 + 6 * q^64 - 30 * q^66 - 6 * q^69 + 30 * q^71 + 36 * q^74 + 42 * q^81 + 6 * q^84 - 12 * q^86 + 48 * q^89 - 54 * q^91 - 60 * q^94 + 30 * 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 $

$2$	0.342020	+	0.939693i	0.241845	+	0.664463i
$2$	0.342020	+	0.939693i	0.241845	+	0.664463i
$3$	−0.342020	−	0.0603074i	−0.197465	−	0.0348185i	0.0740406	−	0.997255i	$-0.476411\pi$
$3$	−0.342020	−	0.0603074i	−0.197465	−	0.0348185i	−0.271506	+	0.962437i	$0.587522\pi$
$4$	−0.766044	+	0.642788i	−0.383022	+	0.321394i
$5$		0			0
$5$		0			0
$6$	−0.0603074	−	0.342020i	−0.0246204	−	0.139629i
$7$	−1.32683	+	0.766044i	−0.501494	+	0.289538i	−0.729330	−	0.684162i	$-0.760168\pi$
$7$	−1.32683	+	0.766044i	−0.501494	+	0.289538i	0.227836	+	0.973699i	$0.426835\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	−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	$0.321785\pi$
$12$	0.300767	−	0.173648i	0.0868241	−	0.0501279i
$13$	4.50449	−	0.794263i	1.24932	−	0.220289i	0.490415	−	0.871489i	$-0.336845\pi$
$13$	4.50449	−	0.794263i	1.24932	−	0.220289i	0.758906	+	0.651200i	$0.225734\pi$
$14$	−1.17365	−	0.984808i	−0.313671	−	0.263201i
$15$		0			0
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−0.725293	−	1.99273i	−0.175909	−	0.483307i	0.820134	−	0.572171i	$-0.193899\pi$
$17$	−0.725293	−	1.99273i	−0.175909	−	0.483307i	−0.996044	+	0.0888639i	$0.971676\pi$
$18$		−	2.87939i		−	0.678678i
$19$	−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
$22$	−3.05888	−	0.539363i	−0.652155	−	0.114993i
$23$	−1.89209	−	2.25490i	−0.394527	−	0.470179i	0.531816	−	0.846860i	$-0.321510\pi$
$23$	−1.89209	−	2.25490i	−0.394527	−	0.470179i	−0.926343	+	0.376681i	$0.877065\pi$
$24$	0.266044	+	0.223238i	0.0543061	+	0.0455682i
$25$		0			0
$26$	2.28699	+	3.96118i	0.448515	+	0.776852i
$27$	1.76833	+	1.02094i	0.340315	+	0.196481i
$28$	0.524005	−	1.43969i	0.0990277	−	0.272076i
$29$	−6.12449	−	2.22913i	−1.13729	−	0.413939i	−0.296355	−	0.955078i	$-0.595771\pi$
$29$	−6.12449	−	2.22913i	−1.13729	−	0.413939i	−0.840933	+	0.541139i	$0.817993\pi$
$30$		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	$-0.368471\pi$
$32$	0.984808	−	0.173648i	0.174091	−	0.0306970i
$33$	0.693392	−	0.826352i	0.120704	−	0.143849i
$34$	1.62449	−	1.36310i	0.278597	−	0.233771i
$35$		0			0
$36$	2.70574	−	0.984808i	0.450956	−	0.164135i
$37$		−	9.45336i		−	1.55412i	−0.629424	−	0.777062i	$-0.716709\pi$
$37$		−	9.45336i		−	1.55412i	0.629424	−	0.777062i	$-0.283291\pi$
$38$	−1.10359	−	4.21688i	−0.179026	−	0.684068i
$39$	−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	$-0.0574984\pi$
$42$	0.342020	+	0.407604i	0.0527749	+	0.0628946i
$43$	−1.85083	+	2.20574i	−0.282249	+	0.336372i	−0.888478	−	0.458918i	$-0.848237\pi$
$43$	−1.85083	+	2.20574i	−0.282249	+	0.336372i	0.606229	+	0.795290i	$0.292681\pi$
$44$	−0.539363	−	3.05888i	−0.0813120	−	0.461143i
$45$		0			0
$46$	1.47178	−	2.54920i	0.217002	−	0.375859i
$47$	−1.18610	+	3.25877i	−0.173010	+	0.475341i	−0.995645	−	0.0932295i	$-0.970281\pi$
$47$	−1.18610	+	3.25877i	−0.173010	+	0.475341i	0.822635	+	0.568570i	$0.192503\pi$
$48$	−0.118782	+	0.326352i	−0.0171448	+	0.0471048i
$49$	−2.32635	+	4.02936i	−0.332336	+	0.575623i
$50$		0			0
$51$	0.127889	+	0.725293i	0.0179080	+	0.101561i
$52$	−2.94010	+	3.50387i	−0.407718	+	0.485899i
$53$	0.104455	+	0.124485i	0.0143481	+	0.0170994i	0.773171	−	0.634198i	$-0.218670\pi$
$53$	0.104455	+	0.124485i	0.0143481	+	0.0170994i	−0.758823	+	0.651297i	$0.774225\pi$
$54$	−0.354570	+	2.01087i	−0.0482509	+	0.273644i
$55$		0			0
$56$	1.53209			0.204734
$57$	1.45994	+	0.400330i	0.193373	+	0.0530250i
$58$		−	6.51754i		−	0.855795i
$59$	−13.3157	+	4.84651i	−1.73355	+	0.630962i	−0.998873	−	0.0474525i	$-0.984890\pi$
$59$	−13.3157	+	4.84651i	−1.73355	+	0.630962i	−0.734680	+	0.678414i	$0.762668\pi$
$60$		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	$0.449457\pi$
$62$	4.24000	−	5.05303i	0.538480	−	0.641736i
$63$	4.34445	−	0.766044i	0.547350	−	0.0965125i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	1.01367	+	0.368946i	0.124774	+	0.0454141i
$67$	2.94010	−	8.07785i	0.359190	−	0.986866i	−0.620121	−	0.784506i	$-0.712917\pi$
$67$	2.94010	−	8.07785i	0.359190	−	0.986866i	0.979311	−	0.202360i	$-0.0648612\pi$
$68$	1.83651	+	1.06031i	0.222709	+	0.128581i
$69$	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	$0.528756\pi$
$72$	1.85083	+	2.20574i	0.218123	+	0.259949i
$73$	3.05126	+	0.538019i	0.357122	+	0.0629703i	0.349331	−	0.936999i	$-0.386409\pi$
$73$	3.05126	+	0.538019i	0.357122	+	0.0629703i	0.00779128	+	0.999970i	$0.497520\pi$
$74$	8.88326	−	3.23324i	1.03266	−	0.375857i
$75$		0			0
$76$	3.58512	−	2.47929i	0.411242	−	0.284395i
$77$		−	4.75877i		−	0.542312i
$78$	−0.543308	−	1.49273i	−0.0615175	−	0.169018i
$79$	0.173648	−	0.984808i	0.0195369	−	0.110800i	−0.973480	−	0.228773i	$-0.926529\pi$
$79$	0.173648	−	0.984808i	0.0195369	−	0.110800i	0.993017	+	0.117973i	$0.0376398\pi$
$80$		0			0
$81$	6.07398	+	5.09667i	0.674886	+	0.566297i
$82$	4.38571	−	0.773318i	0.484320	−	0.0853987i
$83$	−4.61830	+	2.66637i	−0.506924	+	0.292673i	−0.731568	−	0.681768i	$-0.761211\pi$
$83$	−4.61830	+	2.66637i	−0.506924	+	0.292673i	0.224644	+	0.974441i	$0.427878\pi$
$84$	−0.266044	+	0.460802i	−0.0290278	+	0.0502777i
$85$		0			0
$86$	−2.70574	−	0.984808i	−0.291767	−	0.106195i
$87$	1.96026	+	1.13176i	0.210162	+	0.121337i
$88$	2.68993	−	1.55303i	0.286748	−	0.165554i
$89$	−1.21941	−	6.91560i	−0.129257	−	0.733053i	−0.978688	−	0.205353i	$-0.934166\pi$
$89$	−1.21941	−	6.91560i	−0.129257	−	0.733053i	0.849431	−	0.527700i	$-0.176945\pi$
$90$		0			0
$91$	−5.36824	+	4.50449i	−0.562745	+	0.472199i
$92$	2.89884	+	0.511144i	0.302225	+	0.0532905i
$93$	0.783520	+	2.15270i	0.0812472	+	0.223225i
$94$	−3.46791			−0.357688
$95$		0			0
$96$	−0.347296			−0.0354458
$97$	−2.10364	−	5.77972i	−0.213593	−	0.586841i	0.785911	−	0.618340i	$-0.212194\pi$
$97$	−2.10364	−	5.77972i	−0.213593	−	0.586841i	−0.999504	+	0.0314984i	$0.989972\pi$
$98$	−4.58202	−	0.807934i	−0.462854	−	0.0816136i
$99$	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	$-0.293102\pi$
$102$	−0.637812	+	0.368241i	−0.0631528	+	0.0364613i
$103$	−5.99400	−	3.46064i	−0.590606	−	0.340987i	0.174731	−	0.984616i	$-0.444094\pi$
$103$	−5.99400	−	3.46064i	−0.590606	−	0.340987i	−0.765337	+	0.643630i	$0.777428\pi$
$104$	−4.29813	−	1.56439i	−0.421467	−	0.153401i
$105$		0			0
$106$	−0.0812519	+	0.140732i	−0.00789188	+	0.0136691i
$107$	1.96026	−	1.13176i	0.189506	−	0.109411i	−0.402245	−	0.915532i	$-0.631770\pi$
$107$	1.96026	−	1.13176i	0.189506	−	0.109411i	0.591751	+	0.806121i	$0.298437\pi$
$108$	−2.01087	+	0.354570i	−0.193496	+	0.0341185i
$109$	8.08512	+	6.78422i	0.774414	+	0.649811i	0.941835	−	0.336075i	$-0.109099\pi$
$109$	8.08512	+	6.78422i	0.774414	+	0.649811i	−0.167421	+	0.985885i	$0.553544\pi$
$110$		0			0
$111$	−0.570108	+	3.23324i	−0.0541122	+	0.306886i
$112$	0.524005	+	1.43969i	0.0495138	+	0.136038i
$113$			19.6955i			1.85280i	0.376542	+	0.926400i	$0.377113\pi$
$113$			19.6955i			1.85280i	−0.376542	+	0.926400i	$0.622887\pi$
$114$	0.123141	+	1.50881i	0.0115332	+	0.141313i
$115$		0			0
$116$	6.12449	−	2.22913i	0.568644	−	0.206970i
$117$	−12.9702	−	2.28699i	−1.19909	−	0.211432i
$118$	−9.10846	−	10.8550i	−0.838501	−	0.999287i
$119$	2.48886	+	2.08840i	0.228153	+	0.191443i
$120$		0			0
$121$	0.676174	+	1.17117i	0.0614704	+	0.106470i
$122$	−6.94751	−	4.01114i	−0.628998	−	0.363152i
$123$	−0.528981	+	1.45336i	−0.0476966	+	0.131045i
$124$	6.19846	+	2.25606i	0.556638	+	0.202600i
$125$		0			0
$126$	2.20574	+	3.82045i	0.196503	+	0.340353i
$127$	9.14301	−	1.61216i	0.811311	−	0.143056i	0.247423	−	0.968908i	$-0.420416\pi$
$127$	9.14301	−	1.61216i	0.811311	−	0.143056i	0.563888	+	0.825852i	$0.309305\pi$
$128$	−0.642788	+	0.766044i	−0.0568149	+	0.0677094i
$129$	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	$0.428173\pi$
$132$			1.07873i			0.0938910i
$133$	6.06888	−	2.78699i	0.526239	−	0.241663i
$134$	8.59627			0.742604
$135$		0			0
$136$	−0.368241	+	2.08840i	−0.0315764	+	0.179079i
$137$	0.428901	+	0.511144i	0.0366435	+	0.0436700i	0.784055	−	0.620691i	$-0.213148\pi$
$137$	0.428901	+	0.511144i	0.0366435	+	0.0436700i	−0.747411	+	0.664361i	$0.768704\pi$
$138$	−0.657115	+	0.783119i	−0.0559373	+	0.0666635i
$139$	1.81134	+	10.2726i	0.153636	+	0.871311i	0.960023	+	0.279923i	$0.0903088\pi$
$139$	1.81134	+	10.2726i	0.153636	+	0.871311i	−0.806387	+	0.591388i	$0.798580\pi$
$140$		0			0
$141$	0.602196	−	1.04303i	0.0507141	−	0.0878394i
$142$	−3.29147	+	9.04323i	−0.276214	+	0.758891i
$143$	−4.85911	+	13.3503i	−0.406339	+	1.11641i
$144$	−1.43969	+	2.49362i	−0.119974	+	0.207802i
$145$		0			0
$146$	0.538019	+	3.05126i	0.0445267	+	0.252524i
$147$	1.03866	−	1.23783i	0.0856672	−	0.102094i
$148$	6.07650	+	7.24170i	0.499486	+	0.595264i
$149$	1.26945	−	7.19940i	0.103997	−	0.589798i	−0.887619	−	0.460579i	$-0.847642\pi$
$149$	1.26945	−	7.19940i	0.103997	−	0.589798i	0.991616	−	0.129219i	$-0.0412470\pi$
$150$		0			0
$151$	1.00774			0.0820088			0.0410044	−	0.999159i	$-0.486944\pi$
$151$	1.00774			0.0820088			0.0410044	+	0.999159i	$0.486944\pi$
$152$	3.55596	+	2.52094i	0.288426	+	0.204476i
$153$			6.10607i			0.493646i
$154$	4.47178	−	1.62760i	0.360346	−	0.131155i
$155$		0			0
$156$	1.21688	−	1.02108i	0.0974285	−	0.0817522i
$157$	−12.6138	+	15.0326i	−1.00669	+	1.19973i	−0.0269144	+	0.999638i	$0.508568\pi$
$157$	−12.6138	+	15.0326i	−1.00669	+	1.19973i	−0.979777	+	0.200091i	$0.935876\pi$
$158$	0.984808	−	0.173648i	0.0783471	−	0.0138147i
$159$	−0.0282185	−	0.0488759i	−0.00223787	−	0.00387611i
$160$		0			0
$161$	4.23783	+	1.54244i	0.333987	+	0.121561i
$162$	−2.71188	+	7.45084i	−0.213066	+	0.585393i
$163$	17.9118	+	10.3414i	1.40296	+	0.809998i	0.994695	−	0.102866i	$-0.0328013\pi$
$163$	17.9118	+	10.3414i	1.40296	+	0.809998i	0.408263	+	0.912864i	$0.366135\pi$
$164$	2.22668	+	3.85673i	0.173875	+	0.301160i
$165$		0			0
$166$	−4.08512	−	3.42782i	−0.317067	−	0.266051i
$167$	5.47995	+	6.53074i	0.424051	+	0.505364i	0.935196	−	0.354130i	$-0.115223\pi$
$167$	5.47995	+	6.53074i	0.424051	+	0.505364i	−0.511145	+	0.859494i	$0.670779\pi$
$168$	−0.524005	−	0.0923963i	−0.0404279	−	0.00712853i
$169$	7.44356	−	2.70924i	0.572582	−	0.208403i
$170$		0			0
$171$	11.3439	+	5.37051i	0.867489	+	0.410693i
$172$		−	2.87939i		−	0.219551i
$173$	−1.57202	−	4.31908i	−0.119518	−	0.328373i	0.865479	−	0.500946i	$-0.167014\pi$
$173$	−1.57202	−	4.31908i	−0.119518	−	0.328373i	−0.984997	+	0.172572i	$0.944792\pi$
$174$	−0.393056	+	2.22913i	−0.0297975	+	0.168990i
$175$		0			0
$176$	2.37939	+	1.99654i	0.179353	+	0.150495i
$177$	4.84651	−	0.854570i	0.364286	−	0.0642334i
$178$	6.08148	−	3.51114i	0.455826	−	0.263171i
$179$	−3.23055	+	5.59548i	−0.241463	+	0.418226i	−0.961131	−	0.276092i	$-0.910961\pi$
$179$	−3.23055	+	5.59548i	−0.241463	+	0.418226i	0.719668	+	0.694318i	$0.244294\pi$
$180$		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	$0.711696\pi$
$182$	−6.06888	−	3.50387i	−0.449855	−	0.259724i
$183$	2.41284	−	1.39306i	0.178363	−	0.102978i
$184$	0.511144	+	2.89884i	0.0376821	+	0.213706i
$185$		0			0
$186$	−1.75490	+	1.47254i	−0.128676	+	0.107972i
$187$	6.48670	+	1.14378i	0.474355	+	0.0836415i
$188$	−1.18610	−	3.25877i	−0.0865049	−	0.237670i
$189$	−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	$0.914464\pi$
$192$	−0.118782	−	0.326352i	−0.00857238	−	0.0235524i
$193$	−23.5319	−	4.14930i	−1.69386	−	0.298673i	−0.758317	−	0.651886i	$-0.773978\pi$
$193$	−23.5319	−	4.14930i	−1.69386	−	0.298673i	−0.935543	+	0.353213i	$0.885089\pi$
$194$	4.71167	−	3.95356i	0.338278	−	0.283849i
$195$		0			0
$196$	−0.807934	−	4.58202i	−0.0577095	−	0.327287i
$197$	−10.5649	+	6.09967i	−0.752721	+	0.434584i	−0.826676	−	0.562678i	$-0.809771\pi$
$197$	−10.5649	+	6.09967i	−0.752721	+	0.434584i	0.0739554	+	0.997262i	$0.476438\pi$
$198$	7.74535	+	4.47178i	0.550438	+	0.317796i
$199$	12.9089	+	4.69847i	0.915091	+	0.333066i	0.756284	−	0.654244i	$-0.227013\pi$
$199$	12.9089	+	4.69847i	0.915091	+	0.333066i	0.158807	+	0.987310i	$0.449235\pi$
$200$		0			0
$201$	−1.49273	+	2.58548i	−0.105289	+	0.182366i
$202$	11.8177	−	6.82295i	0.831490	−	0.480061i
$203$	9.83375	−	1.73396i	0.690194	−	0.121700i
$204$	−0.564178	−	0.473401i	−0.0395003	−	0.0331447i
$205$		0			0
$206$	1.20187	−	6.81612i	0.0837380	−	0.474902i
$207$	2.89884	+	7.96451i	0.201484	+	0.553572i
$208$		−	4.57398i		−	0.317148i
$209$	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	$0.563618\pi$
$212$	−0.160035	−	0.0282185i	−0.0109913	−	0.00193805i
$213$	−2.14835	−	2.56031i	−0.147203	−	0.175429i
$214$	1.73396	+	1.45496i	0.118531	+	0.0994591i
$215$		0			0
$216$	−1.02094	−	1.76833i	−0.0694665	−	0.120319i
$217$	8.75211	+	5.05303i	0.594132	+	0.343022i
$218$	−3.60981	+	9.91787i	−0.244487	+	0.671723i
$219$	−1.01114	−	0.368026i	−0.0683268	−	0.0248689i
$220$		0			0
$221$	−4.84982	−	8.40014i	−0.326234	−	0.565055i
$222$	−3.23324	+	0.570108i	−0.217001	+	0.0382631i
$223$	−0.0380050	+	0.0452926i	−0.00254501	+	0.00303302i	−0.767315	−	0.641270i	$-0.778408\pi$
$223$	−0.0380050	+	0.0452926i	−0.00254501	+	0.00303302i	0.764770	+	0.644303i	$0.222852\pi$
$224$	−1.17365	+	0.984808i	−0.0784177	+	0.0658002i
$225$		0			0
$226$	−18.5077	+	6.73627i	−1.23112	+	0.448090i
$227$			29.5449i			1.96096i	0.196612	+	0.980481i	$0.437006\pi$
$227$			29.5449i			1.96096i	−0.196612	+	0.980481i	$0.562994\pi$
$228$	−1.37570	+	0.631759i	−0.0911082	+	0.0418393i
$229$	12.6578			0.836448			0.418224	−	0.908344i	$-0.362653\pi$
$229$	12.6578			0.836448			0.418224	+	0.908344i	$0.362653\pi$
$230$		0			0
$231$	−0.286989	+	1.62760i	−0.0188825	+	0.107088i
$232$	4.18939	+	4.99273i	0.275047	+	0.327789i
$233$	−3.27449	+	3.90239i	−0.214519	+	0.255654i	−0.862564	−	0.505948i	$-0.831143\pi$
$233$	−3.27449	+	3.90239i	−0.214519	+	0.255654i	0.648045	+	0.761602i	$0.275587\pi$
$234$	−2.28699	−	12.9702i	−0.149505	−	0.847886i
$235$		0			0
$236$	7.08512	−	12.2718i	0.461202	−	0.798826i
$237$	−0.118782	+	0.326352i	−0.00771574	+	0.0211988i
$238$	−1.11121	+	3.05303i	−0.0720293	+	0.197899i
$239$	−3.91740	+	6.78514i	−0.253396	+	0.438894i	−0.964459	−	0.264234i	$-0.914881\pi$
$239$	−3.91740	+	6.78514i	−0.253396	+	0.438894i	0.711063	+	0.703129i	$0.248214\pi$
$240$		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	$-0.248587\pi$
$242$	−0.869273	+	1.03596i	−0.0558790	+	0.0665940i
$243$	−5.70756	−	6.80200i	−0.366140	−	0.436349i
$244$	1.39306	−	7.90041i	0.0891813	−	0.505772i
$245$		0			0
$246$	−1.54664			−0.0986100
$247$	−19.8714	+	1.62180i	−1.26439	+	0.103192i
$248$			6.59627i			0.418863i
$249$	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	$0.332487\pi$
$252$	−2.83564	+	3.37939i	−0.178629	+	0.212881i
$253$	9.00400	−	1.58765i	0.566077	−	0.0998146i
$254$	4.64203	+	8.04023i	0.291267	+	0.504489i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	2.35878	−	6.48070i	0.147137	−	0.404255i	−0.844128	−	0.536142i	$-0.819881\pi$
$257$	2.35878	−	6.48070i	0.147137	−	0.404255i	0.991265	+	0.131887i	$0.0421035\pi$
$258$	0.866025	+	0.500000i	0.0539164	+	0.0311286i
$259$	7.24170	+	12.5430i	0.449977	+	0.779383i
$260$		0			0
$261$	14.3760	+	12.0629i	0.889851	+	0.746674i
$262$	−1.81131	−	2.15863i	−0.111903	−	0.133361i
$263$	−12.0436	−	2.12361i	−0.742639	−	0.130947i	−0.210488	−	0.977597i	$-0.567505\pi$
$263$	−12.0436	−	2.12361i	−0.742639	−	0.130947i	−0.532151	+	0.846649i	$0.678616\pi$
$264$	−1.01367	+	0.368946i	−0.0623871	+	0.0227071i
$265$		0			0
$266$	4.69459	+	4.74968i	0.287844	+	0.291221i
$267$			2.43882i			0.149253i
$268$	2.94010	+	8.07785i	0.179595	+	0.493433i
$269$	1.94087	−	11.0072i	0.118337	−	0.671124i	−0.866706	−	0.498819i	$-0.833767\pi$
$269$	1.94087	−	11.0072i	0.118337	−	0.671124i	0.985044	−	0.172305i	$-0.0551215\pi$
$270$		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	$0.924643\pi$
$272$	−2.08840	+	0.368241i	−0.126628	+	0.0223279i
$273$	2.10770	−	1.21688i	0.127564	−	0.0736490i
$274$	−0.333626	+	0.577857i	−0.0201551	+	0.0349096i
$275$		0			0
$276$	−0.960637	−	0.349643i	−0.0578236	−	0.0210461i
$277$	−22.0070	−	12.7057i	−1.32227	−	0.763414i	−0.338181	−	0.941081i	$-0.609812\pi$
$277$	−22.0070	−	12.7057i	−1.32227	−	0.763414i	−0.984091	+	0.177667i	$0.943145\pi$
$278$	−9.03358	+	5.21554i	−0.541798	+	0.312807i
$279$	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	$0.0848545\pi$
$282$	1.18610	+	0.209141i	0.0706310	+	0.0124541i
$283$	−6.20464	−	17.0471i	−0.368827	−	1.01335i	−0.975808	−	0.218629i	$-0.929842\pi$
$283$	−6.20464	−	17.0471i	−0.368827	−	1.01335i	0.606981	−	0.794717i	$-0.292381\pi$
$284$	−9.62361			−0.571056
$285$		0			0
$286$	−14.2071			−0.840082
$287$	2.33359	+	6.41147i	0.137747	+	0.378457i
$288$	−2.83564	−	0.500000i	−0.167092	−	0.0294628i
$289$	9.57785	−	8.03677i	0.563403	−	0.472751i
$290$		0			0
$291$	0.370929	+	2.10364i	0.0217443	+	0.123318i
$292$	−2.68323	+	1.54916i	−0.157024	+	0.0906579i
$293$	25.0296	+	14.4508i	1.46224	+	0.844227i	0.999115	−	0.0420640i	$-0.0133933\pi$
$293$	25.0296	+	14.4508i	1.46224	+	0.844227i	0.463129	+	0.886291i	$0.346727\pi$
$294$	1.51842	+	0.552659i	0.0885560	+	0.0322317i
$295$		0			0
$296$	−4.72668	+	8.18685i	−0.274733	+	0.475851i
$297$	−5.49254	+	3.17112i	−0.318710	+	0.184007i
$298$	7.19940	−	1.26945i	0.417050	−	0.0735371i
$299$	−10.3139	−	8.65436i	−0.596466	−	0.500494i
$300$		0			0
$301$	0.766044	−	4.34445i	0.0441541	−	0.250410i
$302$	0.344668	+	0.946967i	0.0198334	+	0.0544918i
$303$			4.73917i			0.272258i
$304$	−1.15270	+	4.20372i	−0.0661121	+	0.241100i
$305$		0			0
$306$	−5.73783	+	2.08840i	−0.328010	+	0.119386i
$307$	20.5218	+	3.61856i	1.17124	+	0.206522i	0.725232	−	0.688505i	$-0.241733\pi$
$307$	20.5218	+	3.61856i	1.17124	+	0.206522i	0.446012	+	0.895027i	$0.352844\pi$
$308$	3.05888	+	3.64543i	0.174296	+	0.207718i
$309$	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	$0.702095\pi$
$312$	1.37570	+	0.794263i	0.0778839	+	0.0449663i
$313$	5.80531	−	15.9500i	0.328136	−	0.901545i	−0.660448	−	0.750872i	$-0.729634\pi$
$313$	5.80531	−	15.9500i	0.328136	−	0.901545i	0.988584	−	0.150673i	$-0.0481441\pi$
$314$	−18.4402	−	6.71167i	−1.04064	−	0.378761i
$315$		0			0
$316$	0.500000	+	0.866025i	0.0281272	+	0.0487177i
$317$	8.53650	−	1.50521i	0.479457	−	0.0845413i	0.0713040	−	0.997455i	$-0.477284\pi$
$317$	8.53650	−	1.50521i	0.479457	−	0.0845413i	0.408153	+	0.912913i	$0.366173\pi$
$318$	0.0362770	−	0.0432332i	0.00203431	−	0.00242440i
$319$	15.5077	−	13.0125i	0.868267	−	0.728562i
$320$		0			0
$321$	−0.738703	+	0.268866i	−0.0412304	+	0.0150066i
$322$			4.50980i			0.251321i
$323$	2.34029	+	8.94238i	0.130217	+	0.497567i
$324$	−7.92902			−0.440501
$325$		0			0
$326$	−3.59152	+	20.3685i	−0.198916	+	1.12811i
$327$	−2.35614	−	2.80793i	−0.130295	−	0.155279i
$328$	−2.86257	+	3.41147i	−0.158059	+	0.188367i
$329$	−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	$-0.128106\pi$
$332$	1.82391	−	5.01114i	0.100100	−	0.275022i
$333$	−9.30975	+	25.5783i	−0.510171	+	1.40168i
$334$	−4.26264	+	7.38311i	−0.233241	+	0.403986i
$335$		0			0
$336$	−0.0923963	−	0.524005i	−0.00504063	−	0.0285868i
$337$	5.56245	−	6.62907i	0.303006	−	0.361108i	−0.592959	−	0.805232i	$-0.702041\pi$
$337$	5.56245	−	6.62907i	0.303006	−	0.361108i	0.895965	+	0.444124i	$0.146485\pi$
$338$	5.09170	+	6.06805i	0.276952	+	0.330058i
$339$	1.18779	−	6.73627i	0.0645117	−	0.365864i
$340$		0			0
$341$	20.4884			1.10951
$342$	−1.16679	+	12.4966i	−0.0630929	+	0.675739i
$343$		−	17.8530i		−	0.963970i
$344$	2.70574	−	0.984808i	0.145884	−	0.0530973i
$345$		0			0
$346$	3.52094	−	2.95442i	0.189287	−	0.158831i
$347$	−10.8724	+	12.9572i	−0.583662	+	0.695581i	−0.974375	−	0.224932i	$-0.927784\pi$
$347$	−10.8724	+	12.9572i	−0.583662	+	0.695581i	0.390713	+	0.920513i	$0.372229\pi$
$348$	−2.22913	+	0.393056i	−0.119494	+	0.0210700i
$349$	−6.70574	−	11.6147i	−0.358950	−	0.621719i	0.628836	−	0.777538i	$-0.283532\pi$
$349$	−6.70574	−	11.6147i	−0.358950	−	0.621719i	−0.987786	+	0.155819i	$0.950198\pi$
$350$		0			0
$351$	8.77631	+	3.19432i	0.468445	+	0.170500i
$352$	−1.06234	+	2.91875i	−0.0566228	+	0.155570i
$353$	−24.7852	−	14.3097i	−1.31918	−	0.761631i	−0.335586	−	0.942010i	$-0.608934\pi$
$353$	−24.7852	−	14.3097i	−1.31918	−	0.761631i	−0.983597	+	0.180379i	$0.942268\pi$
$354$	2.46064	+	4.26195i	0.130781	+	0.226520i
$355$		0			0
$356$	5.37939	+	4.51384i	0.285107	+	0.239233i
$357$	−0.725293	−	0.864370i	−0.0383866	−	0.0457473i
$358$	−6.36295	−	1.12196i	−0.336292	−	0.0592974i
$359$	−16.3503	+	5.95102i	−0.862935	+	0.314083i	−0.735303	−	0.677739i	$-0.762960\pi$
$359$	−16.3503	+	5.95102i	−0.862935	+	0.314083i	−0.127633	+	0.991822i	$0.540738\pi$
$360$		0			0
$361$	18.6716	+	3.51735i	0.982715	+	0.185124i
$362$		−	8.36184i		−	0.439489i
$363$	−0.160635	−	0.441341i	−0.00843116	−	0.0231644i
$364$	1.21688	−	6.90128i	0.0637819	−	0.361725i
$365$		0			0
$366$	2.13429	+	1.79088i	0.111561	+	0.0936107i
$367$	29.9115	−	5.27420i	1.56137	−	0.275311i	0.674830	−	0.737973i	$-0.264217\pi$
$367$	29.9115	−	5.27420i	1.56137	−	0.275311i	0.886535	+	0.462662i	$0.153106\pi$
$368$	−2.54920	+	1.47178i	−0.132886	+	0.0767219i
$369$	−6.41147	+	11.1050i	−0.333768	+	0.578103i
$370$		0			0
$371$	−0.233956	−	0.0851529i	−0.0121464	−	0.00442092i
$372$	−1.98394	−	1.14543i	−0.102863	−	0.0593878i
$373$	28.6203	−	16.5239i	1.48190	−	0.855577i	0.482114	−	0.876109i	$-0.339869\pi$
$373$	28.6203	−	16.5239i	1.48190	−	0.855577i	0.999789	+	0.0205316i	$0.00653587\pi$
$374$	1.14378	+	6.48670i	0.0591435	+	0.335419i
$375$		0			0
$376$	2.65657	−	2.22913i	0.137002	−	0.114959i
$377$	−29.3582	−	5.17664i	−1.51202	−	0.266611i
$378$	−1.06996	−	2.93969i	−0.0550328	−	0.151201i
$379$	−18.2344			−0.936639			−0.468320	−	0.883559i	$-0.655140\pi$
$379$	−18.2344			−0.936639			−0.468320	+	0.883559i	$0.655140\pi$
$380$		0			0
$381$	−3.22432			−0.165187
$382$	−9.11435	−	25.0415i	−0.466331	−	1.28123i
$383$	−32.7395	−	5.77285i	−1.67291	−	0.294979i	−0.744800	−	0.667288i	$-0.767455\pi$
$383$	−32.7395	−	5.77285i	−1.67291	−	0.294979i	−0.928109	+	0.372309i	$0.878566\pi$
$384$	0.266044	−	0.223238i	0.0135765	−	0.0113921i
$385$		0			0
$386$	−4.14930	−	23.5319i	−0.211194	−	1.19774i
$387$	7.18009	−	4.14543i	0.364985	−	0.210724i
$388$	5.32661	+	3.07532i	0.270418	+	0.156126i
$389$	6.70486	+	2.44037i	0.339950	+	0.123732i	0.506353	−	0.862326i	$-0.330993\pi$
$389$	6.70486	+	2.44037i	0.339950	+	0.123732i	−0.166403	+	0.986058i	$0.553215\pi$
$390$		0			0
$391$	−3.12108	+	5.40587i	−0.157840	+	0.273387i
$392$	4.02936	−	2.32635i	0.203513	−	0.117499i
$393$	0.963777	−	0.169940i	0.0486161	−	0.00857233i
$394$	−9.34524	−	7.84158i	−0.470806	−	0.395053i
$395$		0			0
$396$	−1.55303	+	8.80769i	−0.0780429	+	0.442603i
$397$	−7.26200	−	19.9522i	−0.364469	−	1.00137i	−0.977430	−	0.211258i	$-0.932244\pi$
$397$	−7.26200	−	19.9522i	−0.364469	−	1.00137i	0.612961	−	0.790113i	$-0.289978\pi$
$398$			13.7374i			0.688594i
$399$	−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	$0.693036\pi$
$402$	−2.94010	−	0.518418i	−0.146639	−	0.0258564i
$403$	−19.3937	−	23.1125i	−0.966067	−	1.15131i
$404$	10.4534	+	8.77141i	0.520074	+	0.436394i
$405$		0			0
$406$	4.99273	+	8.64766i	0.247785	+	0.429176i
$407$	25.4289	+	14.6814i	1.26046	+	0.727729i
$408$	0.251892	−	0.692066i	0.0124705	−	0.0342624i
$409$	10.7947	+	3.92896i	0.533765	+	0.194275i	0.594819	−	0.803860i	$-0.297224\pi$
$409$	10.7947	+	3.92896i	0.533765	+	0.194275i	−0.0610536	+	0.998134i	$0.519446\pi$
$410$		0			0
$411$	−0.115867	−	0.200688i	−0.00571530	−	0.00989919i
$412$	6.81612	−	1.20187i	0.335806	−	0.0592117i
$413$	13.9550	−	16.6309i	0.686679	−	0.818352i
$414$	−6.49273	+	5.44804i	−0.319100	+	0.267757i
$415$		0			0
$416$	4.29813	−	1.56439i	0.210733	−	0.0767007i
$417$		−	3.62267i		−	0.177403i
$418$	13.0570	+	3.58037i	0.638641	+	0.175122i
$419$	17.0401			0.832465			0.416233	−	0.909258i	$-0.363350\pi$
$419$	17.0401			0.832465			0.416233	+	0.909258i	$0.363350\pi$
$420$		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	$0.920679\pi$
$422$	−9.74362	−	11.6120i	−0.474312	−	0.565263i
$423$	6.41852	−	7.64930i	0.312079	−	0.371922i
$424$	−0.0282185	−	0.160035i	−0.00137041	−	0.00777199i
$425$		0			0
$426$	1.67112	−	2.89447i	0.0809661	−	0.140237i
$427$	4.20372	−	11.5496i	0.203432	−	0.558926i
$428$	−0.774169	+	2.12701i	−0.0374209	+	0.102813i
$429$	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	$0.773148\pi$
$432$	1.31250	−	1.56418i	0.0631477	−	0.0752565i
$433$	10.0014	+	11.9192i	0.480637	+	0.572801i	0.950811	−	0.309773i	$-0.100253\pi$
$433$	10.0014	+	11.9192i	0.480637	+	0.572801i	−0.470173	+	0.882574i	$0.655809\pi$
$434$	−1.75490	+	9.95253i	−0.0842379	+	0.477737i
$435$		0			0
$436$	−10.5544			−0.505463
$437$	7.29796	+	10.5530i	0.349109	+	0.504820i
$438$		−	1.07604i		−	0.0514151i
$439$	−7.84389	+	2.85494i	−0.374369	+	0.136259i	−0.522350	−	0.852731i	$-0.674945\pi$
$439$	−7.84389	+	2.85494i	−0.374369	+	0.136259i	0.147982	+	0.988990i	$0.452722\pi$
$440$		0			0
$441$	10.2626	−	8.61138i	0.488697	−	0.410066i
$442$	6.23481	−	7.43036i	0.296560	−	0.353426i
$443$	−21.4484	+	3.78194i	−1.01905	+	0.179685i	−0.658123	−	0.752911i	$-0.728649\pi$
$443$	−21.4484	+	3.78194i	−1.01905	+	0.179685i	−0.360923	+	0.932596i	$0.617538\pi$
$444$	−1.64156	−	2.84326i	−0.0779050	−	0.134935i
$445$		0			0
$446$	−0.0555596	−	0.0202221i	−0.00263083	−	0.000957542i
$447$	−0.868354	+	2.38578i	−0.0410717	+	0.112844i
$448$	−1.32683	−	0.766044i	−0.0626867	−	0.0361922i
$449$	−2.48886	−	4.31082i	−0.117456	−	0.203440i	0.801303	−	0.598259i	$-0.204141\pi$
$449$	−2.48886	−	4.31082i	−0.117456	−	0.203440i	−0.918759	+	0.394819i	$0.870807\pi$
$450$		0			0
$451$	10.5963	+	8.89132i	0.498959	+	0.418676i
$452$	−12.6600	−	15.0876i	−0.595478	−	0.709663i
$453$	−0.344668	−	0.0607742i	−0.0161939	−	0.00285542i
$454$	−27.7631	+	10.1049i	−1.30299	+	0.474249i
$455$		0			0
$456$	−1.06418	−	1.07666i	−0.0498347	−	0.0504194i
$457$		−	38.4047i		−	1.79649i	−0.439490	−	0.898247i	$-0.644841\pi$
$457$		−	38.4047i		−	1.79649i	0.439490	−	0.898247i	$-0.355159\pi$
$458$	4.32921	+	11.8944i	0.202291	+	0.555789i
$459$	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	$0.343961\pi$
$462$	−1.62760	+	0.286989i	−0.0757226	+	0.0133519i
$463$	23.7524	−	13.7135i	1.10387	−	0.637319i	0.166635	−	0.986019i	$-0.446710\pi$
$463$	23.7524	−	13.7135i	1.10387	−	0.637319i	0.937235	+	0.348699i	$0.113377\pi$
$464$	−3.25877	+	5.64436i	−0.151285	+	0.262033i
$465$		0			0
$466$	−4.78699	−	1.74232i	−0.221753	−	0.0807115i
$467$	−0.680793	−	0.393056i	−0.0315033	−	0.0181885i	0.484166	−	0.874976i	$-0.339123\pi$
$467$	−0.680793	−	0.393056i	−0.0315033	−	0.0181885i	−0.515669	+	0.856788i	$0.672457\pi$
$468$	11.4058	−	6.58512i	0.527232	−	0.304397i
$469$	2.28699	+	12.9702i	0.105603	+	0.598906i
$470$		0			0
$471$	5.22075	−	4.38073i	0.240560	−	0.201853i
$472$	13.9550	+	2.46064i	0.642329	+	0.113260i
$473$	−3.05888	−	8.40420i	−0.140647	−	0.386426i
$474$	−0.347296			−0.0159518
$475$		0			0
$476$	−3.24897			−0.148916
$477$	−0.160035	−	0.439693i	−0.00732750	−	0.0201321i
$478$	−7.71578	−	1.36050i	−0.352912	−	0.0622278i
$479$	−5.37417	+	4.50946i	−0.245552	+	0.206043i	−0.757254	−	0.653120i	$-0.773460\pi$
$479$	−5.37417	+	4.50946i	−0.245552	+	0.206043i	0.511702	+	0.859163i	$0.329015\pi$
$480$		0			0
$481$	−7.50846	−	42.5826i	−0.342356	−	1.94160i
$482$	15.3248	−	8.84776i	0.698024	−	0.403005i
$483$	−1.35640	−	0.783119i	−0.0617184	−	0.0356331i
$484$	−1.27079	−	0.462531i	−0.0577633	−	0.0210241i
$485$		0			0
$486$	4.43969	−	7.68977i	0.201389	−	0.348815i
$487$	19.8512	−	11.4611i	0.899544	−	0.519352i	0.0224920	−	0.999747i	$-0.492840\pi$
$487$	19.8512	−	11.4611i	0.899544	−	0.519352i	0.877052	+	0.480395i	$0.159507\pi$
$488$	7.90041	−	1.39306i	0.357635	−	0.0630607i
$489$	−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	$-0.0372336\pi$
$492$	−0.528981	−	1.45336i	−0.0238483	−	0.0655227i
$493$			13.8212i			0.622475i
$494$	−8.32042	−	18.1184i	−0.374353	−	0.815183i
$495$		0			0
$496$	−6.19846	+	2.25606i	−0.278319	+	0.101300i
$497$	−14.5202	−	2.56031i	−0.651321	−	0.114845i
$498$	1.19047	+	1.41875i	0.0533463	+	0.0635756i
$499$	−24.4782	−	20.5396i	−1.09579	−	0.919480i	−0.0986586	−	0.995121i	$-0.531455\pi$
$499$	−24.4782	−	20.5396i	−1.09579	−	0.919480i	−0.997135	+	0.0756412i	$0.975900\pi$
$500$		0			0
$501$	−1.48040	−	2.56413i	−0.0661394	−	0.114557i
$502$	−4.69318	−	2.70961i	−0.209467	−	0.120936i
$503$	4.54109	−	12.4765i	0.202477	−	0.556301i	−0.796344	−	0.604844i	$-0.793236\pi$
$503$	4.54109	−	12.4765i	0.202477	−	0.556301i	0.998821	+	0.0485429i	$0.0154578\pi$
$504$	−4.14543	−	1.50881i	−0.184652	−	0.0672079i
$505$		0			0
$506$	4.57145	+	7.91799i	0.203226	+	0.351997i
$507$	−2.70924	+	0.477711i	−0.120321	+	0.0212159i
$508$	−5.96767	+	7.11200i	−0.264773	+	0.315544i
$509$	−26.0522	+	21.8604i	−1.15474	+	0.968943i	−0.999820	−	0.0189836i	$-0.993957\pi$
$509$	−26.0522	+	21.8604i	−1.15474	+	0.968943i	−0.154922	+	0.987927i	$0.549513\pi$
$510$		0			0
$511$	−4.46064	+	1.62354i	−0.197327	+	0.0718211i
$512$		−	1.00000i		−	0.0441942i
$513$	−7.26087	−	5.14749i	−0.320575	−	0.227267i
$514$	6.89662			0.304197
$515$		0			0
$516$	−0.173648	+	0.984808i	−0.00764443	+	0.0433537i
$517$	−6.92383	−	8.25150i	−0.304510	−	0.362900i
$518$	−9.30975	+	11.0949i	−0.409047	+	0.487483i
$519$	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	$0.0814497\pi$
$522$	−6.41852	+	17.6348i	−0.280931	+	0.771852i
$523$	4.87576	−	13.3960i	0.213202	−	0.585768i	−0.786282	−	0.617867i	$-0.787997\pi$
$523$	4.87576	−	13.3960i	0.213202	−	0.585768i	0.999485	+	0.0320989i	$0.0102191\pi$
$524$	1.40895	−	2.44037i	0.0615502	−	0.106608i
$525$		0			0
$526$	−2.12361	−	12.0436i	−0.0925937	−	0.525125i
$527$	−8.99140	+	10.7155i	−0.391672	+	0.466776i
$528$	−0.693392	−	0.826352i	−0.0301760	−	0.0359623i
$529$	2.48932	−	14.1176i	0.108231	−	0.613811i
$530$		0			0
$531$	40.8016			1.77064
$532$	−2.85759	+	6.03596i	−0.123892	+	0.261692i
$533$		−	20.3696i		−	0.882305i
$534$	−2.29174	+	0.834124i	−0.0991731	+	0.0360961i
$535$		0			0
$536$	−6.58512	+	5.52557i	−0.284434	+	0.238668i
$537$	1.44236	−	1.71894i	0.0622425	−	0.0741778i
$538$	11.0072	−	1.94087i	0.474556	−	0.0836770i
$539$	−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	$0.370401\pi$
$542$	6.68799	−	18.3751i	0.287274	−	0.789278i
$543$	2.51497	+	1.45202i	0.107928	+	0.0623121i
$544$	−1.06031	−	1.83651i	−0.0454603	−	0.0787396i
$545$		0			0
$546$	1.86437	+	1.56439i	0.0797877	+	0.0669498i
$547$	0.766546	+	0.913534i	0.0327751	+	0.0390599i	0.782183	−	0.623049i	$-0.214106\pi$
$547$	0.766546	+	0.913534i	0.0327751	+	0.0390599i	−0.749408	+	0.662109i	$0.769662\pi$
$548$	−0.657115	−	0.115867i	−0.0280705	−	0.00494959i
$549$	21.7062	−	7.90041i	0.926398	−	0.337181i
$550$		0			0
$551$	25.6771	+	12.1563i	1.09388	+	0.517874i
$552$		−	1.02229i		−	0.0435115i
$553$	0.524005	+	1.43969i	0.0222830	+	0.0612220i
$554$	4.41266	−	25.0254i	0.187476	−	1.06323i
$555$		0			0
$556$	−7.99067	−	6.70497i	−0.338880	−	0.284354i
$557$	36.1784	−	6.37922i	1.53293	−	0.270296i	0.657428	−	0.753517i	$-0.271644\pi$
$557$	36.1784	−	6.37922i	1.53293	−	0.270296i	0.875499	+	0.483221i	$0.160533\pi$
$558$	−16.4486	+	9.49660i	−0.696324	+	0.402023i
$559$	−6.58512	+	11.4058i	−0.278521	+	0.482413i
$560$		0			0
$561$	−2.14960	−	0.782392i	−0.0907564	−	0.0330326i
$562$	16.5396	+	9.54916i	0.697682	+	0.402807i
$563$	32.0844	−	18.5239i	1.35220	−	0.780691i	0.363639	−	0.931540i	$-0.381534\pi$
$563$	32.0844	−	18.5239i	1.35220	−	0.780691i	0.988557	+	0.150849i	$0.0482007\pi$
$564$	0.209141	+	1.18610i	0.00880641	+	0.0499436i
$565$		0			0
$566$	13.8969	−	11.6609i	0.584131	−	0.490144i
$567$	−11.9634	−	2.10947i	−0.502416	−	0.0885894i
$568$	−3.29147	−	9.04323i	−0.138107	−	0.379446i
$569$	6.61081			0.277140			0.138570	−	0.990353i	$-0.455749\pi$
$569$	6.61081			0.277140			0.138570	+	0.990353i	$0.455749\pi$
$570$		0			0
$571$	−44.6263			−1.86755			−0.933776	−	0.357858i	$-0.883507\pi$
$571$	−44.6263			−1.86755			−0.933776	+	0.357858i	$0.883507\pi$
$572$	−4.85911	−	13.3503i	−0.203170	−	0.558204i
$573$	9.11435	+	1.60711i	0.380758	+	0.0671378i
$574$	−5.22668	+	4.38571i	−0.218157	+	0.183056i
$575$		0			0
$576$	−0.500000	−	2.83564i	−0.0208333	−	0.118152i
$577$	9.09738	−	5.25237i	0.378729	−	0.218659i	−0.298536	−	0.954398i	$-0.596498\pi$
$577$	9.09738	−	5.25237i	0.378729	−	0.218659i	0.677265	+	0.735739i	$0.263165\pi$
$578$	10.8279	+	6.25150i	0.450382	+	0.260028i
$579$	7.79813	+	2.83829i	0.324079	+	0.117955i
$580$		0			0
$581$	4.08512	−	7.07564i	0.169479	−	0.293547i
$582$	−1.84991	+	1.06805i	−0.0766814	+	0.0442720i
$583$	−0.497079	+	0.0876485i	−0.0205869	+	0.00363003i
$584$	−2.37346	−	1.99157i	−0.0982143	−	0.0824116i
$585$		0			0
$586$	−5.01872	+	28.4626i	−0.207322	+	1.17578i
$587$	−7.70442	−	21.1677i	−0.317995	−	0.873685i	−0.990978	−	0.134027i	$-0.957209\pi$
$587$	−7.70442	−	21.1677i	−0.317995	−	0.873685i	0.672982	−	0.739659i	$-0.265013\pi$
$588$			1.61587i			0.0666372i
$589$	11.9991	+	26.1290i	0.494415	+	1.07663i
$590$		0			0
$591$	3.98128	−	1.44907i	0.163768	−	0.0596066i
$592$	−9.30975	−	1.64156i	−0.382628	−	0.0674677i
$593$	−23.7583	−	28.3141i	−0.975638	−	1.16272i	−0.986662	−	0.162781i	$-0.947954\pi$
$593$	−23.7583	−	28.3141i	−0.975638	−	1.16272i	0.0110244	−	0.999939i	$-0.496491\pi$
$594$	−4.85844	−	4.07672i	−0.199344	−	0.167270i
$595$		0			0
$596$	3.65523	+	6.33104i	0.149724	+	0.259330i
$597$	−4.13177	−	2.38548i	−0.169102	−	0.0976311i
$598$	4.60489	−	12.6518i	0.188308	−	0.517372i
$599$	−20.5125	−	7.46594i	−0.838118	−	0.305050i	−0.112931	−	0.993603i	$-0.536024\pi$
$599$	−20.5125	−	7.46594i	−0.838118	−	0.305050i	−0.725186	+	0.688553i	$0.758246\pi$
$600$		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	$-0.461729\pi$
$602$	4.34445	−	0.766044i	0.177067	−	0.0312216i
$603$	−15.9103	+	18.9611i	−0.647916	+	0.772156i
$604$	−0.771974	+	0.647763i	−0.0314112	+	0.0263571i
$605$		0			0
$606$	−4.45336	+	1.62089i	−0.180906	+	0.0658442i
$607$		−	10.9135i		−	0.442967i	−0.975164	−	0.221483i	$-0.928910\pi$
$607$		−	10.9135i		−	0.442967i	0.975164	−	0.221483i	$-0.0710898\pi$
$608$	−4.34445	+	0.354570i	−0.176191	+	0.0143797i
$609$	−3.46791			−0.140527
$610$		0			0
$611$	−2.75443	+	15.6212i	−0.111432	+	0.631965i
$612$	−3.92490	−	4.67752i	−0.158655	−	0.189077i
$613$	−1.48626	+	1.77126i	−0.0600296	+	0.0715405i	−0.795224	−	0.606316i	$-0.792647\pi$
$613$	−1.48626	+	1.77126i	−0.0600296	+	0.0715405i	0.735194	+	0.677857i	$0.237091\pi$
$614$	3.61856	+	20.5218i	0.146033	+	0.828194i
$615$		0			0
$616$	−2.37939	+	4.12122i	−0.0958682	+	0.166049i
$617$	−15.0685	+	41.4004i	−0.606635	+	1.66672i	0.130890	+	0.991397i	$0.458217\pi$
$617$	−15.0685	+	41.4004i	−0.606635	+	1.66672i	−0.737525	+	0.675320i	$0.764006\pi$
$618$	−0.822125	+	2.25877i	−0.0330707	+	0.0908611i
$619$	−13.2883	+	23.0161i	−0.534103	+	0.925094i	0.465103	+	0.885257i	$0.346017\pi$
$619$	−13.2883	+	23.0161i	−0.534103	+	0.925094i	−0.999206	+	0.0398373i	$0.987316\pi$
$620$		0			0
$621$	−1.04370	−	5.91912i	−0.0418822	−	0.237526i
$622$	−9.08478	+	10.8268i	−0.364266	+	0.434116i
$623$	6.91560	+	8.24170i	0.277068	+	0.330197i
$624$	−0.275845	+	1.56439i	−0.0110426	+	0.0626258i
$625$		0			0
$626$	16.9736			0.678401
$627$	−3.34419	+	3.30541i	−0.133554	+	0.132005i
$628$		−	19.6236i		−	0.783067i
$629$	−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	$0.948492\pi$
$632$	−0.642788	+	0.766044i	−0.0255687	+	0.0304716i
$633$	5.18447	−	0.914162i	0.206064	−	0.0363347i
$634$	4.33409	+	7.50687i	0.172129	+	0.298136i
$635$		0			0
$636$	0.0530334	+	0.0193026i	0.00210291	+	0.000765397i
$637$	−7.27866	+	19.9979i	−0.288391	+	0.792347i
$638$	17.5317	+	10.1220i	0.694089	+	0.400732i
$639$	−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	$0.864383\pi$
$642$	−0.505303	−	0.602196i	−0.0199427	−	0.0237668i
$643$	−17.5311	−	3.09121i	−0.691361	−	0.121906i	−0.183081	−	0.983098i	$-0.558607\pi$
$643$	−17.5311	−	3.09121i	−0.691361	−	0.121906i	−0.508280	+	0.861192i	$0.669718\pi$
$644$	−4.23783	+	1.54244i	−0.166994	+	0.0607807i
$645$		0			0
$646$	−7.60266	+	5.25763i	−0.299123	+	0.206859i
$647$		−	36.6641i		−	1.44141i	−0.693240	−	0.720707i	$-0.743818\pi$
$647$		−	36.6641i		−	1.44141i	0.693240	−	0.720707i	$-0.256182\pi$
$648$	−2.71188	−	7.45084i	−0.106533	−	0.292697i
$649$	7.64290	−	43.3451i	0.300010	−	1.70144i
$650$		0			0
$651$	−2.68866	−	2.25606i	−0.105377	−	0.0884218i
$652$	−20.3685	+	3.59152i	−0.797693	+	0.140655i
$653$	−9.88030	+	5.70439i	−0.386646	+	0.223230i	−0.680706	−	0.732557i	$-0.738327\pi$
$653$	−9.88030	+	5.70439i	−0.386646	+	0.223230i	0.294060	+	0.955787i	$0.404993\pi$
$654$	1.83275	−	3.17441i	0.0716661	−	0.124129i
$655$		0			0
$656$	−4.18479	−	1.52314i	−0.163389	−	0.0594686i
$657$	−7.72605	−	4.46064i	−0.301422	−	0.174026i
$658$	4.60132	−	2.65657i	0.179378	−	0.103564i
$659$	4.58606	+	26.0088i	0.178647	+	1.01316i	0.933849	+	0.357667i	$0.116428\pi$
$659$	4.58606	+	26.0088i	0.178647	+	1.01316i	−0.755202	+	0.655492i	$0.772461\pi$
$660$		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	$0.398521\pi$
$662$	28.6405	+	5.05010i	1.11315	+	0.196278i
$663$	1.15215	+	3.16550i	0.0447457	+	0.122938i
$664$	5.33275			0.206951
$665$		0			0
$666$	−27.2199			−1.05475
$667$	6.56159	+	18.0278i	0.254066	+	0.698040i
$668$	−8.39576	−	1.48040i	−0.324842	−	0.0572784i
$669$	0.0157300	−	0.0131990i	0.000608156	−	0.000510303i
$670$		0			0
$671$	−4.32692	−	24.5392i	−0.167039	−	0.947326i
$672$	0.460802	−	0.266044i	0.0177758	−	0.0102629i
$673$	−6.50216	−	3.75402i	−0.250640	−	0.144707i	0.369417	−	0.929264i	$-0.379557\pi$
$673$	−6.50216	−	3.75402i	−0.250640	−	0.144707i	−0.620057	+	0.784557i	$0.712891\pi$
$674$	8.13176	+	2.95972i	0.313224	+	0.114004i
$675$		0			0
$676$	−3.96064	+	6.86002i	−0.152332	+	0.263847i
$677$	−34.0707	+	19.6707i	−1.30944	+	0.756007i	−0.982003	−	0.188865i	$-0.939519\pi$
$677$	−34.0707	+	19.6707i	−1.30944	+	0.756007i	−0.327439	+	0.944872i	$0.606186\pi$
$678$	6.73627	−	1.18779i	0.258705	−	0.0456166i
$679$	7.21869	+	6.05720i	0.277028	+	0.232454i
$680$		0			0
$681$	1.78177	−	10.1049i	0.0682777	−	0.387222i
$682$	7.00746	+	19.2528i	0.268330	+	0.737229i
$683$		−	8.36278i		−	0.319993i	−0.987118	−	0.159996i	$-0.948852\pi$
$683$		−	8.36278i		−	0.319993i	0.987118	−	0.159996i	$-0.0511483\pi$
$684$	−12.1420	+	3.17766i	−0.464262	+	0.121501i
$685$		0			0
$686$	16.7763	−	6.10608i	0.640523	−	0.233131i
$687$	−4.32921	−	0.763356i	−0.165170	−	0.0291239i
$688$	1.85083	+	2.20574i	0.0705624	+	0.0840929i
$689$	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	$0.472499\pi$
$692$	3.98048	+	2.29813i	0.151315	+	0.0873619i
$693$	−4.68647	+	12.8760i	−0.178024	+	0.489118i
$694$	−15.8944	−	5.78509i	−0.603343	−	0.219599i
$695$		0			0
$696$	−1.13176	−	1.96026i	−0.0428992	−	0.0743036i
$697$	−9.30039	+	1.63991i	−0.352278	+	0.0621160i
$698$	8.62073	−	10.2738i	0.326299	−	0.388869i
$699$	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	$0.339657\pi$
$702$			9.33956i			0.352499i
$703$	−3.83072	+	41.0278i	−0.144478	+	1.54739i
$704$	−3.10607			−0.117064
$705$		0			0
$706$	4.96972	−	28.1847i	0.187038	−	1.06074i
$707$	13.4386	+	16.0155i	0.505410	+	0.602324i
$708$	−3.16333	+	3.76991i	−0.118885	+	0.141682i
$709$	0.574693	+	3.25925i	0.0215831	+	0.122404i	0.993696	−	0.112111i	$-0.0357611\pi$
$709$	0.574693	+	3.25925i	0.0215831	+	0.122404i	−0.972113	+	0.234514i	$0.924650\pi$
$710$		0			0
$711$	−1.43969	+	2.49362i	−0.0539927	+	0.0935181i
$712$	−2.40176	+	6.59879i	−0.0900099	+	0.247300i
$713$	−6.64084	+	18.2456i	−0.248702	+	0.683302i
$714$	0.564178	−	0.977185i	0.0211138	−	0.0365702i
$715$		0			0
$716$	−1.12196	−	6.36295i	−0.0419296	−	0.237794i
$717$	1.74903	−	2.08441i	0.0653185	−	0.0778436i
$718$	−11.1843	−	13.3289i	−0.417393	−	0.497429i
$719$	3.32723	−	18.8697i	0.124085	−	0.703719i	−0.857763	−	0.514046i	$-0.828146\pi$
$719$	3.32723	−	18.8697i	0.124085	−	0.703719i	0.981847	−	0.189673i	$-0.0607429\pi$
$720$		0			0
$721$	10.6040			0.394914
$722$	3.08083	+	18.7486i	0.114657	+	0.697749i
$723$			6.14559i			0.228557i
$724$	7.85756	−	2.85992i	0.292024	−	0.106288i
$725$		0			0
$726$	0.359785	−	0.301895i	0.0133529	−	0.0112044i
$727$	−3.16393	+	3.77063i	−0.117344	+	0.139845i	−0.821519	−	0.570182i	$-0.806873\pi$
$727$	−3.16393	+	3.77063i	−0.117344	+	0.139845i	0.704175	+	0.710027i	$0.251317\pi$
$728$	6.90128	−	1.21688i	0.255778	−	0.0451006i
$729$	−10.3516	−	17.9296i	−0.383394	−	0.664058i
$730$		0			0
$731$	5.73783	+	2.08840i	0.212221	+	0.0772422i
$732$	−0.952906	+	2.61809i	−0.0352204	+	0.0967673i
$733$	12.1756	+	7.02956i	0.449715	+	0.259643i	0.707710	−	0.706503i	$-0.249729\pi$
$733$	12.1756	+	7.02956i	0.449715	+	0.259643i	−0.257995	+	0.966146i	$0.583062\pi$
$734$	15.1864	+	26.3037i	0.560542	+	0.970887i
$735$		0			0
$736$	−2.25490	−	1.89209i	−0.0831167	−	0.0697432i
$737$	17.1628	+	20.4538i	0.632200	+	0.753427i
$738$	−12.6281	−	2.22668i	−0.464848	−	0.0819653i
$739$	29.9923	−	10.9163i	1.10329	−	0.401563i	0.274759	−	0.961513i	$-0.411402\pi$
$739$	29.9923	−	10.9163i	1.10329	−	0.401563i	0.828526	+	0.559950i	$0.189180\pi$
$740$		0			0
$741$	6.89424	+	0.643707i	0.253266	+	0.0236472i
$742$		−	0.248970i		−	0.00913999i
$743$	−1.21129	−	3.32800i	−0.0444380	−	0.122093i	0.915489	−	0.402344i	$-0.131804\pi$
$743$	−1.21129	−	3.32800i	−0.0444380	−	0.122093i	−0.959927	+	0.280251i	$0.909582\pi$
$744$	0.397804	−	2.25606i	0.0145842	−	0.0827110i
$745$		0			0
$746$	25.3161	+	21.2428i	0.926890	+	0.777753i
$747$	15.1218	−	2.66637i	0.553276	−	0.0975575i
$748$	−5.70431	+	3.29339i	−0.208570	+	0.120418i
$749$	−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	$0.573300\pi$
$752$	3.00330	+	1.73396i	0.109519	+	0.0632309i
$753$	1.62992	−	0.941037i	0.0593977	−	0.0342933i
$754$	−5.17664	−	29.3582i	−0.188522	−	1.06916i
$755$		0			0
$756$	2.39646	−	2.01087i	0.0871584	−	0.0731346i
$757$	23.1097	+	4.07486i	0.839935	+	0.148103i	0.577034	−	0.816720i	$-0.304210\pi$
$757$	23.1097	+	4.07486i	0.839935	+	0.148103i	0.262900	+	0.964823i	$0.415321\pi$
$758$	−6.23654	−	17.1348i	−0.226521	−	0.622362i
$759$	−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	$0.623293\pi$
$762$	−1.10278	−	3.02987i	−0.0399496	−	0.109761i
$763$	−15.9246	−	2.80793i	−0.576509	−	0.101654i
$764$	20.4140	−	17.1294i	0.738553	−	0.619719i
$765$		0			0
$766$	−5.77285	−	32.7395i	−0.208582	−	1.18293i
$767$	−56.1309	+	32.4072i	−2.02677	+	1.17016i
$768$	0.300767	+	0.173648i	0.0108530	+	0.00626599i
$769$	−35.9632	−	13.0895i	−1.29687	−	0.472021i	−0.400892	−	0.916125i	$-0.631300\pi$
$769$	−35.9632	−	13.0895i	−1.29687	−	0.472021i	−0.895975	+	0.444104i	$0.853522\pi$
$770$		0			0
$771$	−1.19759	+	2.07428i	−0.0431300	+	0.0747033i
$772$	20.6936	−	11.9474i	0.744778	−	0.429998i
$773$	31.5510	−	5.56330i	1.13481	−	0.200098i	0.425477	−	0.904969i	$-0.360106\pi$
$773$	31.5510	−	5.56330i	1.13481	−	0.200098i	0.709335	+	0.704871i	$0.248995\pi$
$774$	6.35117	+	5.32926i	0.228288	+	0.191556i
$775$		0			0
$776$	−1.06805	+	6.05720i	−0.0383407	+	0.217441i
$777$	−1.72037	−	4.72668i	−0.0617180	−	0.169569i
$778$			7.13516i			0.255808i
$779$	−5.13341	+	18.7207i	−0.183923	+	0.670739i
$780$		0			0
$781$	−28.0889	+	10.2235i	−1.00510	+	0.365826i
$782$	−6.14733	−	1.08394i	−0.219828	−	0.0387616i
$783$	−8.55428	−	10.1946i	−0.305705	−	0.364325i
$784$	3.56418	+	2.99070i	0.127292	+	0.106811i
$785$		0			0
$786$	0.489322	+	0.847531i	0.0174536	+	0.0302304i
$787$	24.3882	+	14.0805i	0.869346	+	0.501917i	0.867131	−	0.498081i	$-0.165962\pi$
$787$	24.3882	+	14.0805i	0.869346	+	0.501917i	0.00221489	+	0.999998i	$0.499295\pi$
$788$	4.17242	−	11.4636i	0.148636	−	0.408375i
$789$	3.99108	+	1.45263i	0.142086	+	0.0517151i
$790$		0			0
$791$	−15.0876	−	26.1326i	−0.536455	−	0.929167i
$792$	−8.80769	+	1.55303i	−0.312968	+	0.0551846i
$793$	−23.5863	+	28.1091i	−0.837574	+	0.998182i
$794$	16.2652	−	13.6481i	0.577229	−	0.484353i
$795$		0			0
$796$	−12.9089	+	4.69847i	−0.457546	+	0.166533i
$797$			5.97596i			0.211679i	0.994383	+	0.105840i	$0.0337530\pi$
$797$			5.97596i			0.211679i	−0.994383	+	0.105840i	$0.966247\pi$
$798$	−1.31920	−	1.90760i	−0.0466993	−	0.0675284i
$799$	7.35410			0.260169
$800$		0			0
$801$	−3.51114	+	19.9127i	−0.124060	+	0.703580i
$802$	−21.0224	−	25.0535i	−0.742326	−	0.884670i
$803$	−6.18594	+	7.37211i	−0.218297	+	0.260156i
$804$	−0.518418	−	2.94010i	−0.0182832	−	0.103689i
$805$		0			0
$806$	15.0856	−	26.1290i	0.531367	−	0.920355i
$807$	−1.32764	+	3.64765i	−0.0467350	+	0.128403i
$808$	−4.66717	+	12.8229i	−0.164191	+	0.451110i
$809$	22.2875	−	38.6030i	0.783585	−	1.35721i	−0.146255	−	0.989247i	$-0.546722\pi$
$809$	22.2875	−	38.6030i	0.783585	−	1.35721i	0.929841	−	0.367963i	$-0.119945\pi$
$810$		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	$-0.355251\pi$
$812$	−6.41852	+	7.64930i	−0.225246	+	0.268438i
$813$	4.36528	+	5.20233i	0.153097	+	0.182454i
$814$	−5.09879	+	28.9167i	−0.178713	+	1.01353i
$815$		0			0
$816$	0.736482			0.0257820
$817$	8.92647	−	8.82295i	0.312298	−	0.308676i
$818$			11.4875i			0.401651i
$819$	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	$0.479506\pi$
$822$	0.148956	−	0.177519i	0.00519543	−	0.00619167i
$823$	24.7759	−	4.36865i	0.863632	−	0.152282i	0.275751	−	0.961229i	$-0.411073\pi$
$823$	24.7759	−	4.36865i	0.863632	−	0.152282i	0.587881	+	0.808947i	$0.299962\pi$
$824$	3.46064	+	5.99400i	0.120557	+	0.208811i
$825$		0			0
$826$	20.4008	+	7.42528i	0.709834	+	0.258359i
$827$	0.748163	−	2.05556i	0.0260162	−	0.0714788i	−0.926005	−	0.377512i	$-0.876780\pi$
$827$	0.748163	−	2.05556i	0.0260162	−	0.0714788i	0.952021	+	0.306033i	$0.0990019\pi$
$828$	−7.34013	−	4.23783i	−0.255087	−	0.147275i
$829$	21.7160	+	37.6132i	0.754228	+	1.30636i	0.945757	+	0.324874i	$0.105322\pi$
$829$	21.7160	+	37.6132i	0.754228	+	1.30636i	−0.191529	+	0.981487i	$0.561345\pi$
$830$		0			0
$831$	6.76058	+	5.67280i	0.234522	+	0.196787i
$832$	2.94010	+	3.50387i	0.101930	+	0.121475i
$833$	9.71670	+	1.71332i	0.336664	+	0.0593629i
$834$	3.40420	−	1.23903i	0.117878	−	0.0429040i
$835$		0			0
$836$	1.10132	+	13.4942i	0.0380899	+	0.466705i
$837$		−	13.4688i		−	0.465551i
$838$	5.82807	+	16.0125i	0.201327	+	0.553142i
$839$	−2.54411	+	14.4284i	−0.0878325	+	0.498123i	0.908877	+	0.417064i	$0.136941\pi$
$839$	−2.54411	+	14.4284i	−0.0878325	+	0.498123i	−0.996709	+	0.0810582i	$0.974170\pi$
$840$		0			0
$841$	10.3250	+	8.66371i	0.356035	+	0.298749i
$842$	−16.6162	+	2.92989i	−0.572634	+	0.100971i
$843$	−5.74416	+	3.31639i	−0.197839	+	0.114223i
$844$	7.57919	−	13.1275i	0.260887	−	0.451869i
$845$		0			0
$846$	9.38326	+	3.41523i	0.322603	+	0.117418i
$847$	−1.79433	−	1.03596i	−0.0616540	−	0.0355960i
$848$	0.140732	−	0.0812519i	0.00483277	−	0.00279020i
$849$	1.09405	+	6.20464i	0.0375475	+	0.212943i
$850$		0			0
$851$	−21.3164	+	17.8866i	−0.730716	+	0.613144i
$852$	3.29147	+	0.580375i	0.112764	+	0.0198833i
$853$	9.70237	+	26.6570i	0.332203	+	0.912720i	0.987538	+	0.157381i	$0.0503052\pi$
$853$	9.70237	+	26.6570i	0.332203	+	0.912720i	−0.655335	+	0.755338i	$0.727473\pi$
$854$	12.2909			0.420585
$855$		0			0
$856$	−2.26352			−0.0773655
$857$	7.00076	+	19.2344i	0.239141	+	0.657035i	0.999967	+	0.00807948i	$0.00257181\pi$
$857$	7.00076	+	19.2344i	0.239141	+	0.657035i	−0.760826	+	0.648956i	$0.775206\pi$
$858$	4.85911	+	0.856792i	0.165887	+	0.0292504i
$859$	23.4368	−	19.6658i	0.799652	−	0.670988i	−0.148462	−	0.988918i	$-0.547432\pi$
$859$	23.4368	−	19.6658i	0.799652	−	0.670988i	0.948114	+	0.317931i	$0.102988\pi$
$860$		0			0
$861$	−0.411474	−	2.33359i	−0.0140230	−	0.0795284i
$862$	−18.4302	+	10.6407i	−0.627735	+	0.362423i
$863$	50.5784	+	29.2015i	1.72171	+	0.994029i	0.915412	+	0.402518i	$0.131865\pi$
$863$	50.5784	+	29.2015i	1.72171	+	0.994029i	0.806297	+	0.591511i	$0.201468\pi$
$864$	1.91875	+	0.698367i	0.0652771	+	0.0237589i
$865$		0			0
$866$	−7.77972	+	13.4749i	−0.264365	+	0.457894i
$867$	−3.76049	+	2.17112i	−0.127713	+	0.0737352i
$868$	−9.95253	+	1.75490i	−0.337811	+	0.0595652i
$869$	2.37939	+	1.99654i	0.0807151	+	0.0677280i
$870$		0			0
$871$	6.82770	−	38.7218i	0.231348	−	1.31204i
$872$	−3.60981	−	9.91787i	−0.122244	−	0.335861i
$873$			17.7101i			0.599395i
$874$	−7.42056	+	10.4672i	−0.251004	+	0.354058i
$875$		0			0
$876$	1.01114	−	0.368026i	0.0341634	−	0.0124345i
$877$	−46.6585	−	8.22715i	−1.57554	−	0.277811i	−0.683566	−	0.729889i	$-0.739572\pi$
$877$	−46.6585	−	8.22715i	−1.57554	−	0.277811i	−0.891979	+	0.452077i	$0.850683\pi$
$878$	−5.36554	−	6.39440i	−0.181078	−	0.215801i
$879$	−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	$0.802273\pi$
$882$	11.6021	+	6.69846i	0.390662	+	0.225549i
$883$	−5.01152	+	13.7690i	−0.168651	+	0.463365i	−0.995010	−	0.0997794i	$-0.968186\pi$
$883$	−5.01152	+	13.7690i	−0.168651	+	0.463365i	0.826359	+	0.563144i	$0.190409\pi$
$884$	9.11468	+	3.31747i	0.306560	+	0.111579i
$885$		0			0
$886$	−10.8897	−	18.8614i	−0.365845	−	0.633662i
$887$	22.9566	−	4.04788i	0.770809	−	0.135914i	0.225606	−	0.974219i	$-0.427564\pi$
$887$	22.9566	−	4.04788i	0.770809	−	0.135914i	0.545203	+	0.838304i	$0.316453\pi$
$888$	2.11035	−	2.51501i	0.0708186	−	0.0843984i
$889$	−10.8962	+	9.14301i	−0.365447	+	0.306647i
$890$		0			0
$891$	−23.1428	+	8.42329i	−0.775313	+	0.282191i
$892$		−	0.0591253i		−	0.00197966i
$893$	6.46821	−	13.6625i	0.216450	−	0.457198i
$894$	−2.53890			−0.0849134
$895$		0			0
$896$	0.266044	−	1.50881i	0.00888792	−	0.0504059i
$897$	3.00563	+	3.58197i	0.100355	+	0.119598i
$898$	3.19961	−	3.81315i	0.106772	−	0.127246i
$899$	7.46538	+	42.3383i	0.248985	+	1.41206i
$900$		0			0
$901$	0.172304	−	0.298439i	0.00574028	−	0.00994245i
$902$	−4.73097	+	12.9982i	−0.157524	+	0.432794i
$903$	−0.524005	+	1.43969i	−0.0174378	+	0.0479100i
$904$	9.84776	−	17.0568i	0.327532	−	0.567302i
$905$		0			0
$906$	−0.0607742	−	0.344668i	−0.00201909	−	0.0114508i
$907$	−6.95686	+	8.29086i	−0.230999	+	0.275293i	−0.869076	−	0.494679i	$-0.835286\pi$
$907$	−6.95686	+	8.29086i	−0.230999	+	0.275293i	0.638077	+	0.769972i	$0.279730\pi$
$908$	−18.9911	−	22.6327i	−0.630241	−	0.751092i
$909$	−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	$0.711688\pi$
$912$	0.647763	−	1.36824i	0.0214496	−	0.0453070i
$913$		−	16.5639i		−	0.548184i
$914$	36.0886	−	13.1352i	1.19370	−	0.434473i
$915$		0			0
$916$	−9.69640	+	8.13625i	−0.320378	+	0.268829i
$917$	2.77509	−	3.30722i	0.0916414	−	0.109214i
$918$	4.26428	−	0.751907i	0.140742	−	0.0248166i
$919$	22.4115	+	38.8178i	0.739286	+	1.28048i	0.952817	+	0.303545i	$0.0981703\pi$
$919$	22.4115	+	38.8178i	0.739286	+	1.28048i	−0.213531	+	0.976936i	$0.568496\pi$
$920$		0			0
$921$	−6.80066	−	2.47524i	−0.224089	−	0.0815619i
$922$	−13.6259	+	37.4368i	−0.448744	+	1.23291i
$923$	38.1209	+	22.0091i	1.25476	+	0.724438i
$924$	−0.826352	−	1.43128i	−0.0271850	−	0.0470858i
$925$		0			0
$926$	21.0103	+	17.6297i	0.690440	+	0.579348i
$927$	12.8101	+	15.2665i	0.420740	+	0.501418i
$928$	−6.41852	−	1.13176i	−0.210698	−	0.0371518i
$929$	33.5269	−	12.2028i	1.09998	−	0.400361i	0.272673	−	0.962107i	$-0.412092\pi$
$929$	33.5269	−	12.2028i	1.09998	−	0.400361i	0.827310	+	0.561746i	$0.189870\pi$
$930$		0			0
$931$	11.7292	−	16.5448i	0.384409	−	0.542235i
$932$		−	5.09421i		−	0.166866i
$933$	−1.67880	−	4.61246i	−0.0549614	−	0.151005i
$934$	0.136507	−	0.774169i	0.00446664	−	0.0253316i
$935$		0			0
$936$	10.0890	+	8.46567i	0.329769	+	0.276709i
$937$	40.6519	−	7.16802i	1.32804	−	0.234169i	0.535782	−	0.844356i	$-0.320017\pi$
$937$	40.6519	−	7.16802i	1.32804	−	0.234169i	0.792257	+	0.610187i	$0.208906\pi$
$938$	−11.4058	+	6.58512i	−0.372411	+	0.215012i
$939$	−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	$0.529136\pi$
$942$	5.90214	+	3.40760i	0.192302	+	0.111026i
$943$	−11.3525	+	6.55438i	−0.369689	+	0.213440i
$944$	2.46064	+	13.9550i	0.0800869	+	0.454195i
$945$		0			0
$946$	6.85117	−	5.74881i	0.222751	−	0.186910i
$947$	−53.9144	−	9.50656i	−1.75198	−	0.308922i	−0.796646	−	0.604446i	$-0.793395\pi$
$947$	−53.9144	−	9.50656i	−1.75198	−	0.308922i	−0.955335	+	0.295524i	$0.904506\pi$
$948$	−0.118782	−	0.326352i	−0.00385787	−	0.0105994i
$949$	14.1717			0.460032
$950$		0			0
$951$	−3.01043			−0.0976199
$952$	−1.11121	−	3.05303i	−0.0360146	−	0.0989494i
$953$	−5.77401	−	1.01811i	−0.187039	−	0.0329799i	0.0793442	−	0.996847i	$-0.474717\pi$
$953$	−5.77401	−	1.01811i	−0.187039	−	0.0329799i	−0.266383	+	0.963867i	$0.585828\pi$
$954$	0.358441	−	0.300767i	0.0116049	−	0.00973771i
$955$		0			0
$956$	−1.36050	−	7.71578i	−0.0440017	−	0.249546i
$957$	−6.08871	+	3.51532i	−0.196820	+	0.113634i
$958$	−6.07559	−	3.50774i	−0.196293	−	0.113330i
$959$	−0.960637	−	0.349643i	−0.0310206	−	0.0112906i
$960$		0			0
$961$	−6.25537	+	10.8346i	−0.201786	+	0.349504i
$962$	37.4465	−	21.6197i	1.20732	−	0.697048i
$963$	−6.41852	+	1.13176i	−0.206834	+	0.0364704i
$964$	13.5556	+	11.3745i	0.436595	+	0.366347i
$965$		0			0
$966$	0.271974	−	1.54244i	0.00875063	−	0.0496273i
$967$	−8.72875	−	23.9820i	−0.280698	−	0.771211i	−0.997280	−	0.0737080i	$-0.976517\pi$
$967$	−8.72875	−	23.9820i	−0.280698	−	0.771211i	0.716582	−	0.697503i	$-0.245705\pi$
$968$		−	1.35235i		−	0.0434661i
$969$	−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	$0.507320\pi$
$972$	8.74449	+	1.54189i	0.280480	+	0.0494561i
$973$	−10.2726	−	12.2424i	−0.329325	−	0.392474i
$974$	17.5594	+	14.7341i	0.562640	+	0.472111i
$975$		0			0
$976$	4.01114	+	6.94751i	0.128394	+	0.222384i
$977$	28.1917	+	16.2765i	0.901932	+	0.520731i	0.877826	−	0.478979i	$-0.158993\pi$
$977$	28.1917	+	16.2765i	0.901932	+	0.520731i	0.0241053	+	0.999709i	$0.492326\pi$
$978$	2.45674	−	6.74985i	0.0785580	−	0.215836i
$979$	20.4963	+	7.46004i	0.655064	+	0.238424i
$980$		0			0
$981$	−15.1951	−	26.3186i	−0.485141	−	0.840289i
$982$	12.5430	−	2.21167i	0.400263	−	0.0705771i
$983$	−24.0939	+	28.7139i	−0.768475	+	0.915833i	−0.998352	−	0.0573870i	$-0.981723\pi$
$983$	−24.0939	+	28.7139i	−0.768475	+	0.915833i	0.229877	+	0.973220i	$0.426168\pi$
$984$	1.18479	−	0.994159i	0.0377698	−	0.0316926i
$985$		0			0
$986$	−12.9877	+	4.72713i	−0.413612	+	0.150542i
$987$			1.84524i			0.0587345i
$988$	14.1799	−	14.0155i	0.451124	−	0.445892i
$989$	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	$0.935208\pi$
$992$	−4.24000	−	5.05303i	−0.134620	−	0.160434i
$993$	−6.49228	+	7.73720i	−0.206026	+	0.245533i
$994$	−2.56031	−	14.5202i	−0.0812080	−	0.460554i
$995$		0			0
$996$	−0.926022	+	1.60392i	−0.0293421	+	0.0508221i
$997$	12.1759	−	33.4530i	0.385614	−	1.05947i	−0.583341	−	0.812228i	$-0.698255\pi$
$997$	12.1759	−	33.4530i	0.385614	−	1.05947i	0.968955	−	0.247238i	$-0.0795230\pi$
$998$	10.9289	−	30.0269i	0.345949	−	0.950486i
$999$	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.u.a.499.2		12
5.2	odd	4		950.2.l.a.651.1	yes	6
5.3	odd	4		950.2.l.f.651.1	yes	6
5.4	even	2	inner	950.2.u.a.499.1		12
19.4	even	9	inner	950.2.u.a.99.1		12
95.4	even	18	inner	950.2.u.a.99.2		12
95.23	odd	36		950.2.l.f.251.1	yes	6
95.42	odd	36		950.2.l.a.251.1	✓	6

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

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.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.342020 + 0.939693i) q^{2} +(-0.342020 - 0.0603074i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.0603074 - 0.342020i) q^{6} +(-1.32683 + 0.766044i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.70574 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.342020 + 0.939693i) q^{2} +(-0.342020 - 0.0603074i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.0603074 - 0.342020i) q^{6} +(-1.32683 + 0.766044i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.70574 - 0.984808i) q^{9} +(-1.55303 + 2.68993i) q^{11} +(0.300767 - 0.173648i) q^{12} +(4.50449 - 0.794263i) q^{13} +(-1.17365 - 0.984808i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-0.725293 - 1.99273i) q^{17} -2.87939i q^{18} +(-4.34002 - 0.405223i) q^{19} +(0.500000 - 0.181985i) q^{21} +(-3.05888 - 0.539363i) q^{22} +(-1.89209 - 2.25490i) q^{23} +(0.266044 + 0.223238i) q^{24} +(2.28699 + 3.96118i) q^{26} +(1.76833 + 1.02094i) q^{27} +(0.524005 - 1.43969i) q^{28} +(-6.12449 - 2.22913i) q^{29} +(-3.29813 - 5.71253i) q^{31} +(0.984808 - 0.173648i) q^{32} +(0.693392 - 0.826352i) q^{33} +(1.62449 - 1.36310i) q^{34} +(2.70574 - 0.984808i) q^{36} -9.45336i q^{37} +(-1.10359 - 4.21688i) q^{38} -1.58853 q^{39} +(0.773318 - 4.38571i) q^{41} +(0.342020 + 0.407604i) q^{42} +(-1.85083 + 2.20574i) q^{43} +(-0.539363 - 3.05888i) q^{44} +(1.47178 - 2.54920i) q^{46} +(-1.18610 + 3.25877i) q^{47} +(-0.118782 + 0.326352i) q^{48} +(-2.32635 + 4.02936i) q^{49} +(0.127889 + 0.725293i) q^{51} +(-2.94010 + 3.50387i) q^{52} +(0.104455 + 0.124485i) q^{53} +(-0.354570 + 2.01087i) q^{54} +1.53209 q^{56} +(1.45994 + 0.400330i) q^{57} -6.51754i q^{58} +(-13.3157 + 4.84651i) q^{59} +(-6.14543 + 5.15663i) q^{61} +(4.24000 - 5.05303i) q^{62} +(4.34445 - 0.766044i) q^{63} +(0.500000 + 0.866025i) q^{64} +(1.01367 + 0.368946i) q^{66} +(2.94010 - 8.07785i) q^{67} +(1.83651 + 1.06031i) q^{68} +(0.511144 + 0.885328i) q^{69} +(7.37211 + 6.18594i) q^{71} +(1.85083 + 2.20574i) q^{72} +(3.05126 + 0.538019i) q^{73} +(8.88326 - 3.23324i) q^{74} +(3.58512 - 2.47929i) q^{76} -4.75877i q^{77} +(-0.543308 - 1.49273i) q^{78} +(0.173648 - 0.984808i) q^{79} +(6.07398 + 5.09667i) q^{81} +(4.38571 - 0.773318i) q^{82} +(-4.61830 + 2.66637i) q^{83} +(-0.266044 + 0.460802i) q^{84} +(-2.70574 - 0.984808i) q^{86} +(1.96026 + 1.13176i) q^{87} +(2.68993 - 1.55303i) q^{88} +(-1.21941 - 6.91560i) q^{89} +(-5.36824 + 4.50449i) q^{91} +(2.89884 + 0.511144i) q^{92} +(0.783520 + 2.15270i) q^{93} -3.46791 q^{94} -0.347296 q^{96} +(-2.10364 - 5.77972i) q^{97} +(-4.58202 - 0.807934i) q^{98} +(6.85117 - 5.74881i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{6} - 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^6 - 12 * q^9	\( 12 q - 12 q^{6} - 12 q^{9} + 6 q^{11} - 12 q^{14} - 12 q^{19} + 6 q^{21} - 6 q^{24} + 12 q^{26} - 48 q^{29} - 12 q^{31} - 6 q^{34} + 12 q^{36} - 60 q^{39} + 36 q^{41} - 24 q^{44} - 12 q^{46} - 30 q^{49} + 60 q^{51} - 36 q^{54} - 42 q^{59} - 42 q^{61} + 6 q^{64} - 30 q^{66} - 6 q^{69} + 30 q^{71} + 36 q^{74} + 42 q^{81} + 6 q^{84} - 12 q^{86} + 48 q^{89} - 54 q^{91} - 60 q^{94} + 30 q^{99}+O(q^{100}) \) 12 * q - 12 * q^6 - 12 * q^9 + 6 * q^11 - 12 * q^14 - 12 * q^19 + 6 * q^21 - 6 * q^24 + 12 * q^26 - 48 * q^29 - 12 * q^31 - 6 * q^34 + 12 * q^36 - 60 * q^39 + 36 * q^41 - 24 * q^44 - 12 * q^46 - 30 * q^49 + 60 * q^51 - 36 * q^54 - 42 * q^59 - 42 * q^61 + 6 * q^64 - 30 * q^66 - 6 * q^69 + 30 * q^71 + 36 * q^74 + 42 * q^81 + 6 * q^84 - 12 * q^86 + 48 * q^89 - 54 * q^91 - 60 * q^94 + 30 * q^99

Introduction

L-functions

Modular forms

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Database

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